[
  {
    "path": ".gitignore",
    "content": "# Created by .ignore support plugin (hsz.mobi)\n### JetBrains template\n# Covers JetBrains IDEs: IntelliJ, RubyMine, PhpStorm, AppCode, PyCharm, CLion, Android Studio and WebStorm\n# Reference: https://intellij-support.jetbrains.com/hc/en-us/articles/206544839\n\n# User-specific stuff\n.idea/**/workspace.xml\n.idea/**/tasks.xml\n.idea/**/usage.statistics.xml\n.idea/**/dictionaries\n.idea/**/shelf\n\n# Sensitive or high-churn files\n.idea/**/dataSources/\n.idea/**/dataSources.ids\n.idea/**/dataSources.local.xml\n.idea/**/sqlDataSources.xml\n.idea/**/dynamic.xml\n.idea/**/uiDesigner.xml\n.idea/**/dbnavigator.xml\n\n# Gradle\n.idea/**/gradle.xml\n.idea/**/libraries\n\n# Gradle and Maven with auto-import\n# When using Gradle or Maven with auto-import, you should exclude module files,\n# since they will be recreated, and may cause churn.  Uncomment if using\n# auto-import.\n# .idea/modules.xml\n# .idea/*.iml\n# .idea/modules\n\n# CMake\ncmake-build-*/\n\n# Mongo Explorer plugin\n.idea/**/mongoSettings.xml\n\n# File-based project format\n*.iws\n\n# IntelliJ\nout/\n\n# mpeltonen/sbt-idea plugin\n.idea_modules/\n\n# JIRA plugin\natlassian-ide-plugin.xml\n\n# Cursive Clojure plugin\n.idea/replstate.xml\n\n# Crashlytics plugin (for Android Studio and IntelliJ)\ncom_crashlytics_export_strings.xml\ncrashlytics.properties\ncrashlytics-build.properties\nfabric.properties\n\n# Editor-based Rest Client\n.idea/httpRequests\n.idea"
  },
  {
    "path": ".travis.yml",
    "content": "language: cpp\n\ncompiler:\n  - gcc\n\nscript:\n  - mkdir build\n  - cd build\n  - cmake .. && make\n  - ./Location"
  },
  {
    "path": "CMakeLists.txt",
    "content": "cmake_minimum_required(VERSION 3.9)\nproject(Location)\nset(CMAKE_CXX_STANDARD 11)\n\nset(INC_DIR ./include/eigen3/)\ninclude_directories(${INC_DIR})\n\ninclude_directories(${PROJECT_SOURCE_DIR}/math)\nadd_subdirectory(math)\n\ninclude_directories(${PROJECT_SOURCE_DIR}/models)\nadd_subdirectory(models)\n\ninclude_directories(${PROJECT_SOURCE_DIR}/location)\nadd_subdirectory(location)\n\ninclude_directories(${PROJECT_SOURCE_DIR}/sensor)\nadd_subdirectory(sensor)\n\ninclude_directories(${PROJECT_SOURCE_DIR}/system)\nadd_subdirectory(system)\n\ninclude_directories(${PROJECT_SOURCE_DIR}/utils)\nadd_subdirectory(utils)\n\ninclude_directories(${PROJECT_SOURCE_DIR}/test)\nadd_subdirectory(test)\n\n#add_library(lib ./math/KalmanFilter.h ./math/KalmanFilter.cpp ./models/AHRS.cpp ./sensor/Accelerometer.cpp ./sensor/Gyroscope.cpp ./sensor/GPS.cpp ./sensor/Magnetometer.cpp ./math/Quaternions.cpp math/Optimizer.cpp sensor/Sensor.cpp sensor/Sensor.h location/Location.cpp system/Status.cpp ./include/googletest/ test/utils/DataFormat.cpp test/utils/DataFormat.h test/TestLocation.cpp test/TestCalibration.cpp test/TestCalibration.h math/LPF.cpp math/LPF.h models/StrapdownAHRS.cpp config/Config.cpp config/Config.h sensor/Gravity.cpp sensor/Gravity.h sensor/Compass.cpp sensor/Compass.h)\n#link_libraries(lib)\n#add_executable(Location main.cpp ${lib})\nadd_executable(Location main.cpp)\n\ntarget_link_libraries(Location Location_math)\ntarget_link_libraries(Location Location_models)\ntarget_link_libraries(Location Location_location)\ntarget_link_libraries(Location Location_sensor)\ntarget_link_libraries(Location Location_system)\ntarget_link_libraries(Location Location_utils)\ntarget_link_libraries(Location Location_test)"
  },
  {
    "path": "README.md",
    "content": "# LOCATION\n\n[![Build Status](https://travis-ci.org/yyccR/Location.svg?branch=master)](https://travis-ci.org/yyccR/Location)\n\n> Positioning is the most basic and crucial step in the driving navigation. An accurate positioning can effectively improve the accuracy of the road-binding, and can also sense the change of the driving pattern more accurately. Since the project is mainly based on mobile phones for navigation and positioning, Currently used is the built-in sensor data (gyroscope, accelerometer, geomagnetic meter, direction sensor, gravity sensor) and GPS data fusion positioning.\n\n## Sensor data required.\n\n- [X] gyroscope(x, y, z).\n- [X] accelerometer(x, y, z).\n- [X] geomagnetic meter(x, y, z).\n- [X] gravity sensor(x, y, z).\n- [X] direction sensor(roll, pitch, yaw).\n- [X] compass(degree).\n- [X] road info(distance to next cross, bearing, road type).\n- [X] GPS(lng, lat, alt, accuracy, speed, bearing, t).\n\n\n## Some implement details\n\n- sensor data filter.\n\n<img src=\"https://raw.githubusercontent.com/yyccR/Pictures/master/INS/ornt_filter.png\" width=\"1000\" height=\"800\" />\n\n- GPS fusion INS under uncoupling system.\n\n<img src=\"https://raw.githubusercontent.com/yyccR/Pictures/master/INS/origin location.png\" width=\"390\" height=\"310\" /> <img src=\"https://raw.githubusercontent.com/yyccR/Pictures/master/INS/final location.png\" width=\"390\" height=\"310\" />\n\n## Quick start\nFirst make sure gcc and cmake was installed, and include this library into your project.\n\n```\ngit clone https://github.com/yyccR/Location.git\n```\n\nSecond open your `CMakeLists.txt` and add these:\n\n```\ninclude_directories(${PROJECT_SOURCE_DIR}/Location/include/eigen3)\n\ninclude_directories(${PROJECT_SOURCE_DIR}/Location/math)\nadd_subdirectory(Location/math)\n\ninclude_directories(${PROJECT_SOURCE_DIR}/Location/models)\nadd_subdirectory(Location/models)\n\ninclude_directories(${PROJECT_SOURCE_DIR}/Location/location)\nadd_subdirectory(Location/location)\n\ninclude_directories(${PROJECT_SOURCE_DIR}/Location/sensor)\nadd_subdirectory(Location/sensor)\n\ninclude_directories(${PROJECT_SOURCE_DIR}/Location/system)\nadd_subdirectory(Location/system)\n\ntarget_link_libraries(${PROJECT_NAME} Location_math)\ntarget_link_libraries(${PROJECT_NAME} Location_models)\ntarget_link_libraries(${PROJECT_NAME} Location_location)\ntarget_link_libraries(${PROJECT_NAME} Location_sensor)\ntarget_link_libraries(${PROJECT_NAME} Location_system)\ntarget_link_libraries(${PROJECT_NAME} Location_test)\n```\n\nfinal open your main file, and add the test code.\n\n```\n#include <iomanip>\n#include <Eigen/Dense>\n#include \"sensor/GPS.h\"\n#include \"location/Location.h\"\n\nusing namespace Eigen;\nusing namespace std;\n\nint main() {\n\n    Location location;\n    Vector3d gyro_data_v(0.004263,0.019169,-0.001014);\n    Vector3d mag_data_v(-2.313675,-82.446960,-366.183838);\n    Vector3d acc_data_v(0.105081,0.108075,9.774973);\n    VectorXd gps_data_v(7);\n    gps_data_v << 114.174118,22.283789,0.0,0.0,24.0,0.0,1554348968704.665039;\n    Vector3d g_data_v(0.094139, 0.107857,9.808955);\n    Vector3d ornt_data_v(-0.549866,0.629957,-0.069398);\n    Vector3d road_data(1000.0, 0.0, 0);\n    location.PredictCurrentPosition(gyro_data_v,acc_data_v,mag_data_v,gps_data_v,g_data_v,ornt_data_v, road_data);\n    cout << location.GetGNSSINS().lng << \" \" << location.GetGNSSINS().lat << endl;\n    return 0;\n}\n```\n\nif you see the output `114.174 22.2838` that means this library was embedded to your project successfully.\n\n## Input data format.\n\n- gyroscope(x, y, z), origin gyroscope data, unit rad/s\n\n- accelerometer(x, y, z), origin accelerometer data, unit m/s²\n\n- geomagnetic meter(x, y, z), origin geomagnetic data, unit μt\n\n- gravity sensor(x, y, z), origin gravity data, unit m/s²\n\n- direction sensor(roll, pitch, yaw), origin sensor data, unit degree\n\nNote that direction sensor doesn't exit actually , the 'sensor data' is computation result from system underlying algorithm.\n\n- compass(degree), origin sensor data, unit degree\n\n- road info(distance to next cross, bearing, road type)\n\nThis data is from map data, and if you couldn't search map server data, just fill in all zero `(0.0, 0.0, 0.0)`\n\n- GPS(lng, lat, alt, accuracy, speed, bearing, t)\n  - lng, longitude, double\n  - lat, latitude, double\n  - alt, altitude, double\n  - accuracy, double\n  - speed, double\n  - bearing, double, unit degree\n  - t, timestampe, unit millisecond\n\n## More detail tutorial.\n\n- [Api calls details](docs/apiCallDetails.md)\n- [Sensor data checking](docs/SensorDataChecking.md)\n- [Impelement details](docs/implementDetails.md)\n- [Sensor calibration](docs/SensorCalibration.md)\n- [Training Stop detection model](docs/trainingStopDetectModel.md)\n\n## TODO\n\n- [X] improve CMake.\n- [X] Clean the garbage code.\n- [ ] Template processing.\n- [X] Using smart pointer instead.\n- [X] Complete all kinds of documents.\n- [X] Add quick start.\n- [ ] Add more test case.\n- [ ] Design a suitable pattern.\n\n## reference:\n\n1. 《惯性导航》秦永元\n2. 《捷联惯性导航技术(第2版 译本)》译者:张天光/王秀萍/王丽霞 作者:DavidH.Titte\n3. [An efficient orientation filter for inertial and\n    inertial/magnetic sensor arrays](http://x-io.co.uk/res/doc/madgwick_internal_report.pdf)\n4. [Estimation of IMU and MARG orientation using a gradient descent algorithm](http://vigir.missouri.edu/~gdesouza/Research/Conference_CDs/RehabWeekZ%C3%BCrich/icorr/papers/Madgwick_Estimation%20of%20IMU%20and%20MARG%20orientation%20using%20a%20gradient%20descent%20algorithm_ICORR2011.pdf)\n5. [Direction Cosine Matrix IMU Theory](https://www.researchgate.net/publication/265755808_Direction_Cosine_Matrix_IMU_Theory)\n6. [METHODS FOR NON-LINEAR LEAST SQUARES PROBLEMS](http://www2.imm.dtu.dk/pubdb/views/edoc_download.php/3215/pdf/imm3215.pdf)\n7. [A Calibration Algorithm for Microelectromechanical Systems Accelerometers in Inertial Navigation Sensors](https://arxiv.org/pdf/1309.5075.pdf)\n8. [A Calibration Method of Three-axis Magnetic Sensor Based on Ellipsoid Fitting](https://www.researchgate.net/publication/273845104_A_Calibration_Method_of_Three-axis_Magnetic_Sensor_Based_on_Ellipsoid_Fitting)\n9. [Accuracy Improvement of Low Cost INS/GPS for Land Applications](https://prism.ucalgary.ca/bitstream/handle/1880/41142/2001_Shin.pdf?sequence=1)\n10. [Trajectory preprocessing: Computing with Spatial Trajectories](https://books.google.com.hk/books?hl=zh-CN&lr=&id=JShQJF23xBgC&oi=fnd&pg=PR3&dq=Trajectory+preprocessing.+Computing+with+Spatial+Trajectories&ots=6NUeew5i9_&sig=o7XM_QcuUnmOv5KNeezTN4H8PMw&redir_esc=y&hl=zh-CN&sourceid=cndr#v=onepage&q=Trajectory%20preprocessing.%20Computing%20with%20Spatial%20Trajectories&f=false)"
  },
  {
    "path": "README_CN.md",
    "content": "# Location\n\n> 定位是驾驶导航过程中是最基础的一步，也是十分关键的一步，一个准确的定位可以有效提高绑路的精度，也能更加精准感知驾驶形态的变化，由于本项目主要基于手机做导航定位，目前采用的是手机内置的传感器数据（陀螺仪，加速计，地磁计）以及GPS数据融合定位。\n\n## 项目所需的传感器.\n\n- [X] 陀螺仪(x, y, z).\n- [X] 加速计(x, y, z).\n- [X] 地磁计(x, y, z).\n- [X] 重力感应器(x, y, z).\n- [X] 方向传感器(roll, pitch, yaw).\n- [X] 指南针(degree).\n- [X] 道路信息(距下个路口的距离, 道路方向, 道路类型).\n- [X] GPS(经度, 纬度, 海拔, 精度, 速度, 方向, 时间戳).\n\n\n## 一些实现细节\n\n- 传感器噪声过滤与修正.\n\n<img src=\"https://raw.githubusercontent.com/yyccR/Pictures/master/INS/ornt_filter.png\" width=\"1000\" height=\"800\" />\n\n- 基于非耦合的GPS融合INS.\n\n<img src=\"https://raw.githubusercontent.com/yyccR/Pictures/master/INS/origin location.png\" width=\"350\" height=\"290\" /> <img src=\"https://raw.githubusercontent.com/yyccR/Pictures/master/INS/final location.png\" width=\"350\" height=\"290\" />\n\n## 快速开始\n确保安装了gcc和cmake, 下载本项目到你的项目下\n\n```\ngit clone https://github.com/yyccR/Location.git\n```\n\n在项目根目录下新建`CMakeLists.txt`, 同时添加如下:\n\n```\ninclude_directories(${PROJECT_SOURCE_DIR}/Location/include/eigen3)\n\ninclude_directories(${PROJECT_SOURCE_DIR}/Location/math)\nadd_subdirectory(Location/math)\n\ninclude_directories(${PROJECT_SOURCE_DIR}/Location/models)\nadd_subdirectory(Location/models)\n\ninclude_directories(${PROJECT_SOURCE_DIR}/Location/location)\nadd_subdirectory(Location/location)\n\ninclude_directories(${PROJECT_SOURCE_DIR}/Location/sensor)\nadd_subdirectory(Location/sensor)\n\ninclude_directories(${PROJECT_SOURCE_DIR}/Location/system)\nadd_subdirectory(Location/system)\n\ntarget_link_libraries(${PROJECT_NAME} Location_math)\ntarget_link_libraries(${PROJECT_NAME} Location_models)\ntarget_link_libraries(${PROJECT_NAME} Location_location)\ntarget_link_libraries(${PROJECT_NAME} Location_sensor)\ntarget_link_libraries(${PROJECT_NAME} Location_system)\ntarget_link_libraries(${PROJECT_NAME} Location_test)\n```\n\n在main文件里添加如下测试代码.\n\n```\n#include <iomanip>\n#include <Eigen/Dense>\n#include \"sensor/GPS.h\"\n#include \"location/Location.h\"\n\nusing namespace Eigen;\nusing namespace std;\n\nint main() {\n\n    Location location;\n    Vector3d gyro_data_v(0.004263,0.019169,-0.001014);\n    Vector3d mag_data_v(-2.313675,-82.446960,-366.183838);\n    Vector3d acc_data_v(0.105081,0.108075,9.774973);\n    VectorXd gps_data_v(7);\n    gps_data_v << 114.174118,22.283789,0.0,0.0,24.0,0.0,1554348968704.665039;\n    Vector3d g_data_v(0.094139, 0.107857,9.808955);\n    Vector3d ornt_data_v(-0.549866,0.629957,-0.069398);\n    Vector3d road_data(1000.0, 0.0, 0);\n    location.PredictCurrentPosition(gyro_data_v,acc_data_v,mag_data_v,gps_data_v,g_data_v,ornt_data_v, road_data);\n    cout << location.GetGNSSINS().lng << \" \" << location.GetGNSSINS().lat << endl;\n    return 0;\n}\n```\n\n如果输出 `114.174 22.2838` 表示已经成功内嵌了本项目.\n\n## 数据格式.\n\n- 陀螺仪(x, y, z), 单位 rad/s\n\n- 加速计(x, y, z), 单位 m/s²\n\n- 地磁计(x, y, z), 单位 μt\n\n- 重力感应器(x, y, z), 单位 m/s²\n\n- 方向传感器(roll, pitch, yaw), 单位 角度(degree)\n\n手机并没有方向传感器, 这个所谓的传感器数据是手机底层算法计算得到的。\n\n- 指南针(degree), 单位 角度(degree)\n\n- 道路信息(距离下个路口距离, 当前位置道路方向, 道路类型编码)\n\n如果拿不到道路数据, 则全部填0即可, `(0.0, 0.0, 0.0)`\n\n- GPS(lng, lat, alt, accuracy, speed, bearing, t)\n  - lng, 经度, double\n  - lat, 纬度, double\n  - alt, 海拔, double\n  - accuracy, 精度, double\n  - speed, 速度, double\n  - bearing, 方向, double, 单位 角度(degree)\n  - t, 时间戳, 单位 毫秒(millisecond)\n\n## 更加详细的调用细节\n\n详见 docs/apiCallDetails.md\n\n## TODO\n\n- [X] CMakeLists 优化.\n- [ ] 清理垃圾代码.\n- [ ] 模板化.\n- [ ] 替换普通指针为智能指针.\n- [ ] 完善文档.\n- [x] 添加快速开始.\n- [ ] 增加更多测试案例.\n- [ ] 使用合适的设计模式.\n\n\n## 参考:\n\n1. 《惯性导航》秦永元\n2. 《捷联惯性导航技术(第2版 译本)》译者:张天光/王秀萍/王丽霞 作者:DavidH.Titte\n3. [An efficient orientation filter for inertial and\n    inertial/magnetic sensor arrays](http://x-io.co.uk/res/doc/madgwick_internal_report.pdf)\n4. [Estimation of IMU and MARG orientation using a gradient descent algorithm](http://vigir.missouri.edu/~gdesouza/Research/Conference_CDs/RehabWeekZ%C3%BCrich/icorr/papers/Madgwick_Estimation%20of%20IMU%20and%20MARG%20orientation%20using%20a%20gradient%20descent%20algorithm_ICORR2011.pdf)\n5. [Direction Cosine Matrix IMU Theory](https://www.researchgate.net/publication/265755808_Direction_Cosine_Matrix_IMU_Theory)\n6. [METHODS FOR NON-LINEAR LEAST SQUARES PROBLEMS](http://www2.imm.dtu.dk/pubdb/views/edoc_download.php/3215/pdf/imm3215.pdf)\n7. [A Calibration Algorithm for Microelectromechanical Systems Accelerometers in Inertial Navigation Sensors](https://arxiv.org/pdf/1309.5075.pdf)\n8. [A Calibration Method of Three-axis Magnetic Sensor Based on Ellipsoid Fitting](https://www.researchgate.net/publication/273845104_A_Calibration_Method_of_Three-axis_Magnetic_Sensor_Based_on_Ellipsoid_Fitting)\n9. [Accuracy Improvement of Low Cost INS/GPS for Land Applications](https://prism.ucalgary.ca/bitstream/handle/1880/41142/2001_Shin.pdf?sequence=1)\n10. [Trajectory preprocessing: Computing with Spatial Trajectories](https://books.google.com.hk/books?hl=zh-CN&lr=&id=JShQJF23xBgC&oi=fnd&pg=PR3&dq=Trajectory+preprocessing.+Computing+with+Spatial+Trajectories&ots=6NUeew5i9_&sig=o7XM_QcuUnmOv5KNeezTN4H8PMw&redir_esc=y&hl=zh-CN&sourceid=cndr#v=onepage&q=Trajectory%20preprocessing.%20Computing%20with%20Spatial%20Trajectories&f=false)"
  },
  {
    "path": "config/CMakeLists.txt",
    "content": "aux_source_directory(. config_src_lists)\nadd_library(Location_config ${config_src_lists})"
  },
  {
    "path": "config/Config.cpp",
    "content": "//\n// Created by yangcheng on 2019/3/22.\n//\n\n#include <fstream>\n#include \"Config.h\"\n#include <string>\n#include \"iostream\"\n#include <exception>\n\nusing namespace std;\n\nclass FileNotFoundException : public  exception {\n    virtual const char* what() const throw()\n    {\n        return \"file not found!\";\n    }\n};\n\nConfig::Config(string file_name, string delimiter, string comment) : delimiter(delimiter), comment(comment) {\n    std::ifstream in_file(file_name);\n    cout << file_name << endl;\n    if (!in_file) throw FileNotFoundException();\n    in_file >> (*this);\n    in_file.close();\n}\n\n\nistream &operator>>(istream &is, Config &cfg) {\n\n    string line;\n    while (getline(is, line)) {\n\n        // 忽略开头注释和空行\n        string::size_type pos = line.find(cfg.comment);\n        if (line.length() == 0 || pos == 0) continue;\n\n        // 忽略末尾注释\n        string param = line;\n        if (pos < string::npos) param = line.substr(0, pos + cfg.comment.length());\n\n        // key value截取\n        string::size_type pos2 = param.find(cfg.delimiter);\n        if (pos2 < string::npos) {\n            string key = param.substr(0, pos2);\n            string value = param.replace(0, pos2 + 1, \"\");\n            // 删除前后空白和一些特殊字符\n            cfg.Trim(key);\n            cfg.Trim(value);\n            cfg.cfg_settings[key] = value;\n        }\n    }\n    return is;\n}\n\nostream &operator<<(std::ostream &os, const Config &cfg) {\n    map<string, string>::const_iterator key_value;\n    for (key_value = cfg.cfg_settings.begin(); key_value != cfg.cfg_settings.end(); ++key_value) {\n        os << key_value->first << \" : \" << key_value->second << endl;\n    }\n    return os;\n}\n\nvoid Config::Trim(std::string &s) {\n    // 删掉头尾的特殊符号\n    const char whitespace[] = \" \\n\\t\\v\\r\\f\";\n    s.erase(0, s.find_first_not_of(whitespace));\n    s.erase(s.find_last_not_of(whitespace) + 1);\n}\n\nvoid Config::SetDelimiter(std::string &d) {\n    this->delimiter = d;\n}\n\nvoid Config::SetComment(std::string &c) {\n    this->comment = c;\n}\n\nstd::string Config::Read(const std::string &key) const {\n    auto value = this->cfg_settings.find(key);\n    if (value != this->cfg_settings.end()) {\n        return value->second;\n    } else {\n        return \"\";\n    }\n}\n\nbool Config::FileExist(const std::string file_name) {\n    bool exist = false;\n    ifstream in(file_name);\n    if (in) {\n        exist = true;\n    }\n    in.close();\n    return exist;\n}\n\nvoid Config::ReadFile(const std::string file_name, const std::string delimiter, const std::string comment) {\n    this->delimiter = delimiter;\n    this->comment = comment;\n    ifstream in(file_name);\n    if (!in) {\n        throw \"file not found\";\n    } else {\n        in >> (*this);\n    }\n}\n\n"
  },
  {
    "path": "config/Config.h",
    "content": "//\n// Created by yangcheng on 2019/3/22.\n//\n\n#ifndef LOCATION_CONFIG_H\n#define LOCATION_CONFIG_H\n\n\n#include <string>\n#include <map>\n#include <exception>\n\nclass Config {\nprivate:\n    std::string delimiter;\n    std::string comment;\n    std::map<std::string, std::string> cfg_settings;\n\npublic:\n\n    Config(std::string file_name, std::string delimiter = \"=\", std::string comment = \"#\");\n\n    std::string Read(const std::string &key) const;\n\n    bool FileExist(const std::string file_name);\n    void ReadFile(const std::string file_name, const std::string delimiter, const std::string comment);\n\n    friend std::istream &operator>>(std::istream &is, Config &cfg);\n    friend std::ostream &operator<<(std::ostream &os, const Config &cfg);\n\n    void Trim(std::string &s);\n    void SetDelimiter(std::string &d);\n    void SetComment(std::string &c);\n\n};\n\n\n#endif //LOCATION_CONFIG_H\n"
  },
  {
    "path": "config/config_files/Android.config",
    "content": "gnssins.lng = 0.0\ngnssins.lat = 0.0\ngnssins.altitude = 0.0\ngnssins.accuracy = 0.0\ngnssins.speed = 0.0\ngnssins.bearing = 0.0\n\nvelocity.v_x = 0.0\nvelocity.v_y = 0.0\nvelocity.v_z = 0.0\n\nposition.x = 0.0\nposition.y = 0.0\nposition.z = 0.0\nposition.lng = 0.0\nposition.lat = 0.0\nposition.altitude = 0.0\n\nattitude.roll = 0.0\nattitude.pitch = 0.0\nattitude.yaw = 0.0\n\n\nVector3d gyro_coef(0.0,0.0,0.0)\nparameters.gyro_coef = gyro_coef\nVectorXd acc_coef(6)\nacc_coef << 0.0,0.0,0.0,1.0,1.0,1.0\nparameters.acc_coef = acc_coef\nVectorXd mag_coef(6)\nmag_coef << 0.0,0.0,0.0,1.0,1.0,1.0\nparameters.mag_coef = mag_coef\n\nparameters.weak_gps = 100\nparameters.gamma = 1.0\nparameters.epsilon = 0.000001\nparameters.max_step = 200\n\nparameters.acc_a1 = 0.0\nparameters.acc_a2 = 0.0\nparameters.acc_b0 = 0.0\nparameters.acc_hz = 5.0\nVector3d acc(0.0,0.0,0.0)\nparameters.last_acc_data = acc\nparameters.sec_last_acc_data = acc\nparameters.acc_thres = 0.1\n\nVector3d err(0.0,0.0,0.0)\nparameters.err = err\nparameters.ki = 0.05\nparameters.kp = 10.0\nparameters.Hz = 10.0\nparameters.halfT = 0.05\nparameters.static_t_factor = 0.35\nparameters.move_t_factor = 0.27\nparameters.t = 0.285714\n\nparameters.move_distance_threshod = 500000.0\nparameters.ins_count = 0\n\nparameters.gps_static_speed_threshold = 0.02\nparameters.gps_count = 0\nparameters.gps_init_threshold = 1\nparameters.gps_pre_lng = 0.0\nparameters.gps_pre_lat = 0.0\nparameters.gps_pre_t = 0.0\nparameters.gps_pre_speed = 0.0\nparameters.gps_pre_accuracy = 0.0\nparameters.gps_pre_bearing = 0.0\nparameters.gps_pre_altitude = 0.0\n\nparameters.g = 9.805567\nparameters.mag = 157.44\nparameters.we = 0.000072921158\nparameters.R = 6378137.0\n\n"
  },
  {
    "path": "config/config_files/IOS.config",
    "content": ""
  },
  {
    "path": "docs/SensorCalibration.md",
    "content": ""
  },
  {
    "path": "docs/SensorDataChecking.md",
    "content": "# Sensor data checking\n\n- [X] checking orientation sensor data\n\nThe orientation sensor contains roll, pitch and yaw three values. Actually it is not a hardware output, it is\ncalculated by accelerometer and magnetometer. Some smartphone systems may contain the method\n`getRotationMatrix` and `getOrientation` to calculate the orientation, so if we have got the orientation data,\nwe need to make sure it's available, below show the steps how to do these:\n\nSuppose we have got the orientation `(57.221,-0.543, 143.2)` and the corresponding gravity\n`(0.041, 8.248, 5.311)`, then using the follow code:\n\n```\n#include <iostream>\n#include <Eigen/Dense>\n#include <math/Quaternions.cpp>\nusing namespace std;\n\nEigen::Vector3d e(57.221,-0.543, 143.2);\nQuaternions quaternions;\nEigen::Vector4d q = quaternions.GetQFromEuler(e);\nEigen::MatrixXd dcm = quaternions.GetDCMFromQ(q);\nEigen::Vector3d gb(0.041, 8.248, 5.311);\nEigen::Vector3d gn = dcm * gb;\ncout << gn.transpose() << endl;\n```\n  The code above doing three things:\n  1. convert the orientation into quaternion.\n  2. convert the quaternion into direction cosine matrix(DCM).\n  3. using the DCM to rotate the gravity.\n\n  We can see the output vector is `(0.0415164,-0.0312637,9.80995)`, that means we succeed in\nrotating the gravity from body frame to navigation frame using the orientation data.\n\n  Because the gravity in navigation frame should always similar to  `(0,0,g)`, so we can say that the\norientation data is available if it can rotate the origin gravity data into `(0,0,g)`.\n\n\n- [ ] checking magnetometer sensor data\n\n- [ ] checking accelerometer sensor data\n\n- [ ] checking gyroscope sensor data\n"
  },
  {
    "path": "docs/SomeTestCaseResults.md",
    "content": "# Some test case results.\n\n- left is origin GPS trajectory, right is INS trajectory.\n\n|      |                    origin GPS trajectory                     |                        INS trajectory                        |\n| :--: | :----------------------------------------------------------: | :----------------------------------------------------------: |\n|  1   | <img src=\"https://raw.githubusercontent.com/yyccR/Pictures/master/INS/origin location.png\" width=\"430\" height=\"350\" /> | <img src=\"https://raw.githubusercontent.com/yyccR/Pictures/master/INS/final location.png\" width=\"430\" height=\"350\" /> |\n|  2   |                                                              |                                                              |\n|  3   |                                                              |                                                              |\n|  4   |                                                              |                                                              |\n"
  },
  {
    "path": "docs/apiCallDetails.md",
    "content": "# Api call details\n\n## Input data format\n\n- gyroscope(x, y, z), origin gyroscope data, unit rad/s\n\n- accelerometer(x, y, z), origin accelerometer data, unit m/s²\n\n- geomagnetic meter(x, y, z), origin geomagnetic data, unit μt\n\n- gravity sensor(x, y, z), origin gravity data, unit m/s²\n\n- direction sensor(roll, pitch, yaw), origin sensor data, unit degree\n\nNote that direction sensor doesn't exit actually , the 'sensor data' is computation result from system underlying algorithm.\n\n- compass(degree), origin sensor data, unit degree\n\n- road info(distance to next cross, bearing, road type)\n\nThis data is from map data, and if you couldn't search map server data, just fill in all zero `(0.0, 0.0, 0.0)`, road type now have two value, 0 represent common road, and 1 represent tunnel.\n\n- GPS(lng, lat, alt, accuracy, speed, bearing, t)\n  - lng, longitude, double\n  - lat, latitude, double\n  - alt, altitude, double\n  - accuracy, double\n  - speed, double\n  - bearing, double, unit degree\n  - t, timestampe, unit millisecond\n\n## Api call details\n\nThere only one entry class needed consider, `location/Location.h`.\n\nFirst need to initial the Location class.\n\n```\n#include <Eigen/Dense>\n#include \"location/Location.h\"\nusing namespace routing;\n\nLocation location;\n```\n\nSecond set the data frequency you provided, default is 20.\n\n```\nlocation.SetHz(20.0);\n```\n\nThird call the `PredictCurrentPosition` method to compute the current position according to the input sensor data.\n\n```\nlocation.PredictCurrentPosition(gyro_data_v, acc_data_v, mag_data_v, gps_data_v, g_data_v, ornt_data_v, road_data_v);\n```\n\nNote that all the data here using Eigen::Vector structure, for example:\n\n```\nVector3d gyro_data_v(0.004263,0.019169,-0.001014);\nVector3d mag_data_v(-2.313675,-82.446960,-366.183838);\nVector3d acc_data_v(0.105081,0.108075,9.774973);\nVectorXd gps_data_v(7);\ngps_data_v << 114.174118,22.283789,0.0,0.0,24.0,0.0,1554348968704.665039;\nVector3d g_data_v(0.094139, 0.107857,9.808955);\nVector3d ornt_data_v(-0.549866,0.629957,-0.069398);\nVector3d road_data(1000.0, 0.0, 0);\n```\n\nThe method `PredictCurrentPosition` will not return any values, all the process result was store in Status structure.\n\nFinal if you want to get the positioning result, just type:\n\n```\nGNSSINS gnssins = location.GetGNSSINS();\n```\n\nBelow is the `GNSSINS` structure which defined in `system/Status.h`\n\n```\nstruct GNSSINS {\n    double lng;\n    double lat;\n    double altitude;\n    double accuracy;\n    double speed;\n    double bearing;\n};\n```\n\n## Input data frequency\n\n- The frequency of `PredictCurrentPosition` calls should be the same or not very different from the frequency set by the `location.SetHz()` method.\n\n- When GPS is in gap period, all data of GPS should be sent 0, v(0, 0, 0, 0, 0, 0, 0)\n\n- When `road info` in gap period, the data should be the same as before, and should be set to zero during rerouting or no such server.\n\n\n## Data examples\n\n| acc_x      | acc_y     | acc_z     | g_x       | g_y       | g_z       | gyro_x       | gyro_y      | gyro_z      | mag_x   | mag_y    | mag_z    | ornt_z    | ornt_x    | ornt_y    | latitude    | longitude   | altitude | altitude-google | gps-speed   | gps-accuracy | gps-bearing | gps-Satellites | time-using | time-format | timestamp     | road-dist to next cross | road-heading | road-type |\n| ---------- | --------- | --------- | --------- | --------- | --------- | ------------ | ----------- | ----------- | ------- | -------- | -------- | --------- | --------- | --------- | ----------- | ----------- | -------- | --------------- | ----------- | ------------ | ----------- | -------------- | ---------- | ----------- | ------------- | ----------------------- | ------------ | --------- |\n| 1.3190615  | 7.3327217 | 6.973821  | 0.9129    | 7.2721996 | 6.5154    | 0.15892968   | 0.026389379 | 0.043231804 | 59.3125 | -25.5625 | -30.75   | 269.3907  | 47.864853 | 7.976027  | 23.14972849 | 113.3213488 | 87.41    | 0               | 0.75        | 55           | 334.0499878 | 0              | 0          | 0           | 1558586596582 | 64.29145398             | 257.9223308  | 0         |\n| 0.52454084 | 7.3596897 | 5.2365403 | 0.8429    | 7.5298996 | 6.2257    | 0.29626963   | 0.07393215  | 0.06407104  | 59.75   | -24.9375 | -28.25   | 269.42166 | 50.160385 | 7.7104144 | 0           | 0           | 0        | 0               | 0           | 0            | 0           | 0              | 0          | 0           | 0             | 64.29145398             | 257.9223308  | 0         |\n| 1.1784357  | 7.0913377 | 4.977162  | 0.8384    | 7.5929    | 6.1492996 | 0.162176     | 0.15879005  | 0.031991884 | 59.9375 | -24.875  | -28.25   | 269.6926  | 50.73855  | 7.763878  | 0           | 0           | 0        | 0               | 0           | 0            | 0           | 0              | 0          | 0           | 0             | 64.29145398             | 257.9223308  | 0         |\n| 0.2054225  | 6.91365   | 5.1467767 | 0.7237    | 7.6397996 | 6.1056    | -0.014154621 | 0.6226113   | 0.15730652  | 60.25   | -25      | -26.6875 | 269.49725 | 51.173664 | 6.75976   | 0           | 0           | 0        | 0               | 0           | 0            | 0           | 0              | 0          | 0           | 0             | 64.29145398             | 257.9223308  | 0         |\n| 0.6924606  | 7.58598   | 6.012683  | 0.6529    | 7.634     | 6.1208    | -0.11070623  | 0.2043955   | 0.10725048  | 60.3125 | -25.4375 | -26.0625 | 269.29425 | 51.119728 | 6.0886636 | 0           | 0           | 0        | 0               | 0           | 0            | 0           | 0              | 0          | 0           | 0             | 64.29145398             | 257.9223308  | 0         |\n| 1.6083577  | 7.45473   | 7.067147  | 0.6153    | 7.5783997 | 6.1934    | -0.19556414  | 0.43769366  | 0.14540339  | 60.9375 | -26.5    | -24.75   | 267.7838  | 50.604874 | 5.6735864 | 0           | 0           | 0        | 0               | 0           | 0            | 0           | 0              | 0          | 0           | 0             | 64.29145398             | 257.9223308  | 0         |\n| 0.23061907 | 6.588575  | 6.834823  | 0.5119    | 7.5508    | 6.2363997 | 0.22787018   | 0.29204595  | 0.06716027  | 61      | -27.3125 | -23.5    | 267.04623 | 50.351337 | 4.6924677 | 0           | 0           | 0        | 0               | 0           | 0            | 0           | 0              | 0          | 0           | 0             | 64.29145398             | 257.9223308  | 0         |\n| 1.0430675  | 7.6366796 | 5.488736  | 0.4615    | 7.6019998 | 6.1777997 | 0.16502088   | 0.5134933   | 0.259513    | 61.125  | -27.9375 | -22.4375 | 266.4972  | 50.822758 | 4.2722297 | 0           | 0           | 0        | 0               | 0           | 0            | 0           | 0              | 0          | 0           | 0             | 64.29145398             | 257.9223308  | 0         |\n| 2.6479583  | 6.8948793 | 6.831893  | 1.9764999 | 6.5432    | 7.0319996 | 0.081279986  | 0.031311207 | -0.07298967 | 53.9375 | -53.375  | -18      | 236.26198 | 41.853275 | 15.6992   | 23.14982671 | 113.3206776 | 131.78   | 0               | 2.700000048 | 47           | 258.3500061 | 0              | 0          | 0           | 1558586640000 | 47.3517091              | 257.9223308  | 0         |\n| 1.9768157  | 6.7945433 | 6.9858017 | 1.9095    | 6.5825    | 7.0137997 | 0.059236474  | 0.13137093  | -0.16161749 | 54.375  | -53.125  | -17.6875 | 236.70316 | 42.16233  | 15.22961  | 0           | 0           | 0        | 0               | 0           | 0            | 0           | 0              | 0          | 0           | 0             | 47.3517091              | 257.9223308  | 0         |\n\n\n- Note that in gps gap time, all the gps data should be fill zero, and the road info should be the same as before."
  },
  {
    "path": "docs/implementDetails.md",
    "content": ""
  },
  {
    "path": "docs/sensors.md",
    "content": "- Smartphone sensor data：\n\n<img src=\"https://raw.githubusercontent.com/yyccR/Pictures/master/Location/sensordata1.png\" width=\"300\" height=\"600\" />\n\n- Because the posture of the smartphone could be arbitrary, so we need the gps bearing and road heading to correct the compass, below show some difference between compass and gps bearing.\n\n<img src=\"https://raw.githubusercontent.com/yyccR/Pictures/master/INS/gps_compass.png\" width=\"1000\" height=\"300\" />"
  },
  {
    "path": "docs/trainingStopDetectModel.md",
    "content": "# Training stop detection model.\n\n## Xgboost model\n\n- **data input**\n\n  - orientation diff between previous record and current.\n  ```\n  Vector3d pre_ornt = ornt_data.row(i-1);\n  Vector3d current_ornt = ornt_data.row(i);\n  Vector3d ornt_diff = current_ornt - pre_ornt;\n  ```\n\n  - normalized accelerometer in b frame and n frame.\n  ```\n  Vector4d q = quaternions.GetQFromEuler(current_ornt);\n  Matrix3d dcm = quaternions.GetDCMFromQ(q);\n\n  Vector3d acc_v = acc_data;\n  Vector3d acc_n = dcm * acc_v;\n  Vector3d acc_v_norm = Normalise(acc_v);\n  Vector3d acc_n_norm = Normalise(acc_n);\n  ```\n\n  - normalized gravity in b frame and n frame.\n  ```\n  Vector3d g_v = g_data;\n  Vector3d g_n = dcm * g_v;\n  Vector3d g_v_norm = Normalise(g_v);\n  Vector3d g_n_norm = Normalise(g_n);\n  ```\n\n  - diff between accelerometer and gravity in n frame.\n  ```\n  Vector3d a_diff = acc_n - g_n;\n  ```\n\n  - normalized gyroscope.\n  ```\n  Vector3d gyro_v = gyro_data;\n  Vector3d gyro_v_norm = Normalise(gyro_v);\n  ```\n\n  - normalized magnetic diff between previous record and current in n frame.\n  ```\n  Vector3d pre_mag_v = mag_data.row(i-1);\n  Vector3d current_mag_v = mag_data.row(i);\n  Vector3d mag_v_diff = (dcm * current_mag_v) - (dcm * pre_mag_v);\n  Vector3d mag_v_norm = accelerometer.Normalise(mag_v_diff);\n  ```\n\n  - examples:\n\n| acc_b_norm_x | acc_b_norm_y | acc_b_norm_z | acc_n_norm_x | acc_n_norm_y | acc_n_norm_z | g_b_norm_x   | g_b_norm_y   | g_b_norm_z  | g_n_norm_x   | g_n_norm_y  | g_n_norm_z  | gyro_norm_x  | gyro_norm_y  | gyro_norm_z  | mag_n_norm_x | mag_n_norm_y | mag_n_norm_z | mag_n_diff_norm_x | mag_n_diff_norm_y | mag_n_diff_norm_z | acc_g_n_diff_x | acc_g_n_diff_y | acc_g_n_diff_z | ornt_diff_x | ornt_diff_y | ornt_diff_z | label |\n| ------------ | ------------ | ------------ | ------------ | ------------ | ------------ | ------------ | ------------ | ----------- | ------------ | ----------- | ----------- | ------------ | ------------ | ------------ | ------------ | ------------ | ------------ | ----------------- | ----------------- | ----------------- | -------------- | -------------- | -------------- | ----------- | ----------- | ----------- | ----- |\n| 0.129066189  | 0.489784426  | 0.862237285  | -0.504075138 | 0.568416979  | 0.65023872   | 0.161449964  | 0.394004726  | 0.904817211 | -0.406554964 | 0.597145075 | 0.691470043 | 0.457245866  | -0.07097188  | -0.886503925 | 0.482868564  | 0.285974018  | 0.827681588  | 3.382281287       | 2.003121847       | 5.797544418       | -1.374394617   | 0.189218618    | 0.134366798    | -2.456686   | 2.903637    | -2.6312     | 1     |\n| 0.098092756  | 0.441567958  | 0.891849511  | -0.417273415 | 0.538611451  | 0.731970356  | 0.115516734  | 0.376209022  | 0.919305529 | -0.350114553 | 0.550039758 | 0.758205819 | -0.52091589  | 0.693465674  | -0.497746918 | 0.485898133  | -0.436930527 | -0.756964146 | 1.580799524       | -1.421490477      | -2.462673718      | -0.715750162   | -0.038637689   | -0.157519063   | 2.954984    | -1.104863   | -1.016671   | 1     |\n| 0.128268463  | 0.385579444  | 0.913715324  | -0.340256272 | 0.575695299  | 0.74350561   | 0.11413304   | 0.384831439  | 0.915903058 | -0.34341474  | 0.563926869 | 0.751034489 | 0.785250568  | -0.150309687 | -0.60065676  | 0.722509897  | 0.322986569  | 0.611276635  | 0.872183616       | 0.389895827       | 0.737907491       | 0.210543669    | -0.188356055   | -0.466219017   | 0.05889     | 0.534217    | -1.278368   | 1     |\n| 0.090377072  | 0.506492751  | 0.857494652  | -0.430280858 | 0.540274825  | 0.723160768  | 0.0714945    | 0.373371378  | 0.924922889 | -0.305098583 | 0.513380471 | 0.80209435  | -0.40415878  | 0.907416845  | -0.115110168 | -0.018786556 | -0.478580999 | -0.877842408 | -0.056784486      | -1.446565096      | -2.653377777      | -1.56801271    | 0.690716987    | -0.202952674   | 2.683109    | -0.709583   | 0.002222    | 1     |\n| 0.003769136  | 0.413187081  | 0.910638364  | -0.273759419 | 0.441200565  | 0.854633162  | -0.006953619 | 0.349818259  | 0.936791777 | -0.214272881 | 0.418783958 | 0.882443839 | -0.299333594 | 0.767442181  | -0.566949644 | 0.452037207  | -0.074923127 | -0.888846943 | 1.474141036       | -0.244332222      | -2.898623682      | -0.583401164   | 0.219646233    | -0.273327666   | 4.845336    | -1.44749    | -2.451917   | 1     |\n| -0.012789521 | 0.414001052  | 0.910186551  | -0.238513744 | 0.437943501  | 0.866785258  | -0.033002042 | 0.360327767  | 0.932241796 | -0.192046192 | 0.40733654  | 0.892857885 | 0.761586392  | 0.040498834  | -0.646796732 | 0.696550054  | -0.020242884 | -0.717222593 | 1.845812816       | -0.053642339      | -1.900593713      | -0.3771996     | 0.155847649    | -0.54158446    | 1.602177    | 0.644123    | -1.650386   | 1     |\n| -0.08225435  | -0.306475501 | 0.948317979  | -0.278243257 | 0.417762745  | 0.864901716  | -0.059733105 | -0.286562656 | 0.956197574 | -0.263618426 | 0.394924855 | 0.880079363 | -0.425352445 | -0.817550551 | -0.388183453 | 0.75555205   | -0.627310411 | -0.188739898 | 0.464302059       | -0.385494971      | -0.115984495      | -0.155815903   | 0.242576808    | -0.110514225   | -0.023439   | 0.017182    | -0.004636   | 0     |\n| -0.072043    | -0.295740867 | 0.952547713  | -0.269786878 | 0.407713857  | 0.872344227  | -0.05961394  | -0.287154194 | 0.956027535 | -0.264061745 | 0.395357894 | 0.879751971 | -0.463747259 | -0.805428147 | -0.369085328 | -0.402699867 | 0.40874646   | -0.81899887  | -0.229401034      | 0.232845521       | -0.466548918      | -0.066589347   | 0.136967852    | -0.038958311   | -0.006482   | -0.035383   | 0.009744    | 0     |\n| -0.06279196  | -0.294665    | 0.953535373  | -0.270584795 | 0.399787014  | 0.87575922   | -0.059551967 | -0.287931685 | 0.955797525 | -0.264696252 | 0.396037988 | 0.879255256 | -0.259987511 | -0.746441091 | -0.61256199  | 0.52469785   | -0.850812152 | 0.028475391  | 0.171805847       | -0.278587957      | 0.009323916       | -0.044139517   | 0.016644083    | -0.078400482   | -0.002848   | -0.046509   | 0.009805    | 0     |\n| -0.060826806 | -0.287624644 | 0.95580969   | -0.26442447  | 0.397496032  | 0.878678897  | -0.059906299 | -0.288264403 | 0.955675086 | -0.265247511 | 0.396729437 | 0.878777282 | 0.260738265  | -0.506384611 | -0.821942932 | 0.162231636  | -0.868545219 | 0.468305562  | 0.066946532       | -0.358414006      | 0.193251046       | 0.034322951    | -0.031938411   | -0.088189996   | 0.02162     | -0.019908   | 0.002586    | 0     |\n| -0.069062529 | -0.288161093 | 0.955088243  | -0.263882463 | 0.405076711  | 0.87537358   | -0.060623123 | -0.288152188 | 0.955663724 | -0.265685523 | 0.397368956 | 0.878355916 | 0.06959041   | -0.568321684 | -0.819858304 | 0.812688923  | -0.011961465 | 0.582575006  | 0.219561499       | -0.00323159       | 0.157392377       | 0.059482981    | 0.011454942    | -0.16790262    | 0.042848    | 0.006716    | -0.002917   | 0     |\n\n\n- **training**\n```\nimport xgboost as xgb\ntrain_x, train_y, test_x, test_y = LoadData()\nx, y = LoadVaildData()\n\nD_train = xgb.DMatrix(train_x, label=train_y)\nD_test = xgb.DMatrix(test_x, label=test_y)\nD_validation = xgb.DMatrix(x, label=y)\n\nparam = {\n    'objective':'multi:softprob',\n    'eta': 0.3,\n    'max_depth': 10,\n    'num_class': 2\n}\n\nstart_time = time.time()\nmodel = xgb.train(param, D_train, 100)\nend_time = time.time()\n\ntest_preds = model.predict(D_test)\ntest_best_preds = np.asarray([np.argmax(line) for line in test_preds])\nvali_preds = model.predict(D_validation)\nvali_best_preds = np.asarray([np.argmax(line) for line in vali_preds])\n\n# dump model\n model.dump_model('./raw_model.txt', dump_format='txt')\nprint(\"Cost time: \" + str(int(end_time - start_time)))\nprint(classification_report(test_y, test_best_preds, target_names=[\"停车\", \"运动\"]))\nprint(classification_report(y, vali_best_preds, target_names=[\"停车\", \"运动\"]))\n```\n\n- **rewrite the prediction in c++**\n```\n#include \"utils/Tools.h\"\n#include \"models/XgboostDetector.h\"\nstd::string model_path = \"raw_model.txt\";\nXgboostDetector xgboostDetector = XgboostDetector(model_path);\nStopDetection &stopDetection = xgboostDetector;\nbool is_stop = stopDetection.IsStopping(input_data);\n```\n"
  },
  {
    "path": "docs/workflow.md",
    "content": "## Workflow:\n\n<img src=\"https://raw.githubusercontent.com/yyccR/Pictures/master/INS/framework.png\" width=\"1100\" height=\"800\" />"
  },
  {
    "path": "include/eigen3/.hg_archival.txt",
    "content": "repo: 8a21fd850624c931e448cbcfb38168cb2717c790\nnode: b3f3d4950030e3fa2e8fde6b68405106ae5685e1\nbranch: 3.3\ntag: 3.3.5\n"
  },
  {
    "path": "include/eigen3/.hgeol",
    "content": "[patterns]\n*.sh = LF\n*.MINPACK = CRLF\nscripts/*.in = LF\ndebug/msvc/*.dat = CRLF\ndebug/msvc/*.natvis = CRLF\nunsupported/test/mpreal/*.* = CRLF\n** = native\n\n[repository]\nnative = LF\n"
  },
  {
    "path": "include/eigen3/.hgignore",
    "content": "syntax: glob\nqrc_*cxx\n*.orig\n*.pyc\n*.diff\ndiff\n*.save\nsave\n*.old\n*.gmo\n*.qm\ncore\ncore.*\n*.bak\n*~\n*build*\n*.moc.*\n*.moc\nui_*\nCMakeCache.txt\ntags\n.*.swp\nactivity.png\n*.out\n*.php*\n*.log\n*.orig\n*.rej\nlog\npatch\na\na.*\nlapack/testing\nlapack/reference\n"
  },
  {
    "path": "include/eigen3/.hgtags",
    "content": "2db9468678c6480c9633b6272ff0e3599d1e11a3 2.0-beta3\n375224817dce669b6fa31d920d4c895a63fabf32 2.0-beta1\n3b8120f077865e2a072e10f5be33e1d942b83a06 2.0-rc1\n19dfc0e7666bcee26f7a49eb42f39a0280a3485e 2.0-beta5\n7a7d8a9526f003ffa2430dfb0c2c535b5add3023 2.0-beta4\n7d14ad088ac23769c349518762704f0257f6a39b 2.0.1\nb9d48561579fd7d4c05b2aa42235dc9de6484bf2 2.0-beta6\ne17630a40408243cb1a51ad0fe3a99beb75b7450 before-hg-migration\neda654d4cda2210ce80719addcf854773e6dec5a 2.0.0\nee9a7c468a9e73fab12f38f02bac24b07f29ed71 2.0-beta2\nd49097c25d8049e730c254a2fed725a240ce4858 after-hg-migration\n655348878731bcb5d9bbe0854077b052e75e5237 actual-start-from-scratch\n12a658962d4e6dfdc9a1c350fe7b69e36e70675c 3.0-beta1\n5c4180ad827b3f869b13b1d82f5a6ce617d6fcee 3.0-beta2\n7ae24ca6f3891d5ac58ddc7db60ad413c8d6ec35 3.0-beta3\nc40708b9088d622567fecc9208ad4a426621d364 3.0-beta4\nb6456624eae74f49ae8683d8e7b2882a2ca0342a 3.0-rc1\na810d5dbab47acfe65b3350236efdd98f67d4d8a 3.1.0-alpha1\n304c88ca3affc16dd0b008b1104873986edd77af 3.1.0-alpha2\n920fc730b5930daae0a6dbe296d60ce2e3808215 3.1.0-beta1\n8383e883ebcc6f14695ff0b5e20bb631abab43fb 3.1.0-rc1\nbf4cb8c934fa3a79f45f1e629610f0225e93e493 3.1.0-rc2\nda195914abcc1d739027cbee7c52077aab30b336 3.2-beta1\na8e0d153fc5e239ef8b06e3665f1f9e8cb8d49c8 before-evaluators\n09a8e21866106b49c5dec1d6d543e5794e82efa0 3.3-alpha1\nce5a455b34c0a0ac3545a1497cb4a16c38ed90e8 3.3-beta1\n69d418c0699907bcd0bf9e0b3ba0a112ed091d85 3.3-beta2\nbef509908b9da05d0d07ffc0da105e2c8c6d3996 3.3-rc1\n04ab5fa4b241754afcf631117572276444c67239 3.3-rc2\n26667be4f70baf4f0d39e96f330714c87b399090 3.3.0\nf562a193118d4f40514e2f4a0ace6e974926ef06 3.3.1\nda9b4e14c2550e0d11078a3c39e6d56eba9905df 3.3.2\n67e894c6cd8f5f1f604b27d37ed47fdf012674ff 3.3.3\n5a0156e40feb7c4136680b493c6e433d91a6f355 3.3.4\n"
  },
  {
    "path": "include/eigen3/CMakeLists.txt",
    "content": "project(Eigen3)\n\ncmake_minimum_required(VERSION 2.8.5)\n\n# guard against in-source builds\n\nif(${CMAKE_SOURCE_DIR} STREQUAL ${CMAKE_BINARY_DIR})\n  message(FATAL_ERROR \"In-source builds not allowed. Please make a new directory (called a build directory) and run CMake from there. You may need to remove CMakeCache.txt. \")\nendif()\n\n# Alias Eigen_*_DIR to Eigen3_*_DIR:\n\nset(Eigen_SOURCE_DIR ${Eigen3_SOURCE_DIR})\nset(Eigen_BINARY_DIR ${Eigen3_BINARY_DIR})\n\n# guard against bad build-type strings\n\nif (NOT CMAKE_BUILD_TYPE)\n  set(CMAKE_BUILD_TYPE \"Release\")\nendif()\n\nstring(TOLOWER \"${CMAKE_BUILD_TYPE}\" cmake_build_type_tolower)\nif(    NOT cmake_build_type_tolower STREQUAL \"debug\"\n   AND NOT cmake_build_type_tolower STREQUAL \"release\"\n   AND NOT cmake_build_type_tolower STREQUAL \"relwithdebinfo\")\n  message(FATAL_ERROR \"Unknown build type \\\"${CMAKE_BUILD_TYPE}\\\". Allowed values are Debug, Release, RelWithDebInfo (case-insensitive).\")\nendif()\n\n\n#############################################################################\n# retrieve version infomation                                               #\n#############################################################################\n\n# automatically parse the version number\nfile(READ \"${PROJECT_SOURCE_DIR}/Eigen/src/Core/util/Macros.h\" _eigen_version_header)\nstring(REGEX MATCH \"define[ \\t]+EIGEN_WORLD_VERSION[ \\t]+([0-9]+)\" _eigen_world_version_match \"${_eigen_version_header}\")\nset(EIGEN_WORLD_VERSION \"${CMAKE_MATCH_1}\")\nstring(REGEX MATCH \"define[ \\t]+EIGEN_MAJOR_VERSION[ \\t]+([0-9]+)\" _eigen_major_version_match \"${_eigen_version_header}\")\nset(EIGEN_MAJOR_VERSION \"${CMAKE_MATCH_1}\")\nstring(REGEX MATCH \"define[ \\t]+EIGEN_MINOR_VERSION[ \\t]+([0-9]+)\" _eigen_minor_version_match \"${_eigen_version_header}\")\nset(EIGEN_MINOR_VERSION \"${CMAKE_MATCH_1}\")\nset(EIGEN_VERSION_NUMBER ${EIGEN_WORLD_VERSION}.${EIGEN_MAJOR_VERSION}.${EIGEN_MINOR_VERSION})\n\n# if we are not in a mercurial clone\nif(IS_DIRECTORY ${CMAKE_SOURCE_DIR}/.hg)\n  # if the mercurial program is absent or this will leave the EIGEN_HG_CHANGESET string empty,\n  # but won't stop CMake.\n  execute_process(COMMAND hg tip -R ${CMAKE_SOURCE_DIR} OUTPUT_VARIABLE EIGEN_HGTIP_OUTPUT)\n  execute_process(COMMAND hg branch -R ${CMAKE_SOURCE_DIR} OUTPUT_VARIABLE EIGEN_BRANCH_OUTPUT)\nendif()\n\n# if this is the default (aka development) branch, extract the mercurial changeset number from the hg tip output...\nif(EIGEN_BRANCH_OUTPUT MATCHES \"default\")\nstring(REGEX MATCH \"^changeset: *[0-9]*:([0-9;a-f]+).*\" EIGEN_HG_CHANGESET_MATCH \"${EIGEN_HGTIP_OUTPUT}\")\nset(EIGEN_HG_CHANGESET \"${CMAKE_MATCH_1}\")\nendif(EIGEN_BRANCH_OUTPUT MATCHES \"default\")\n#...and show it next to the version number\nif(EIGEN_HG_CHANGESET)\n  set(EIGEN_VERSION \"${EIGEN_VERSION_NUMBER} (mercurial changeset ${EIGEN_HG_CHANGESET})\")\nelse(EIGEN_HG_CHANGESET)\n  set(EIGEN_VERSION \"${EIGEN_VERSION_NUMBER}\")\nendif(EIGEN_HG_CHANGESET)\n\n\ninclude(CheckCXXCompilerFlag)\ninclude(GNUInstallDirs)\n\nset(CMAKE_MODULE_PATH ${PROJECT_SOURCE_DIR}/cmake)\n\n#############################################################################\n# find how to link to the standard libraries                                #\n#############################################################################\n\nfind_package(StandardMathLibrary)\n\n\nset(EIGEN_TEST_CUSTOM_LINKER_FLAGS  \"\" CACHE STRING \"Additional linker flags when linking unit tests.\")\nset(EIGEN_TEST_CUSTOM_CXX_FLAGS     \"\" CACHE STRING \"Additional compiler flags when compiling unit tests.\")\n\nset(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO \"\")\n\nif(NOT STANDARD_MATH_LIBRARY_FOUND)\n\n  message(FATAL_ERROR\n    \"Can't link to the standard math library. Please report to the Eigen developers, telling them about your platform.\")\n\nelse()\n\n  if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO)\n    set(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO \"${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO} ${STANDARD_MATH_LIBRARY}\")\n  else()\n    set(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO \"${STANDARD_MATH_LIBRARY}\")\n  endif()\n\nendif()\n\nif(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO)\n  message(STATUS \"Standard libraries to link to explicitly: ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO}\")\nelse()\n  message(STATUS \"Standard libraries to link to explicitly: none\")\nendif()\n\noption(EIGEN_BUILD_BTL \"Build benchmark suite\" OFF)\n\n# Disable pkgconfig only for native Windows builds\nif(NOT WIN32 OR NOT CMAKE_HOST_SYSTEM_NAME MATCHES Windows)\n  option(EIGEN_BUILD_PKGCONFIG \"Build pkg-config .pc file for Eigen\" ON)\nendif()\n\nset(CMAKE_INCLUDE_CURRENT_DIR ON)\n\noption(EIGEN_SPLIT_LARGE_TESTS \"Split large tests into smaller executables\" ON)\n\noption(EIGEN_DEFAULT_TO_ROW_MAJOR \"Use row-major as default matrix storage order\" OFF)\nif(EIGEN_DEFAULT_TO_ROW_MAJOR)\n  add_definitions(\"-DEIGEN_DEFAULT_TO_ROW_MAJOR\")\nendif()\n\nset(EIGEN_TEST_MAX_SIZE \"320\" CACHE STRING \"Maximal matrix/vector size, default is 320\")\n\nmacro(ei_add_cxx_compiler_flag FLAG)\n  string(REGEX REPLACE \"-\" \"\" SFLAG1 ${FLAG})\n  string(REGEX REPLACE \"\\\\+\" \"p\" SFLAG ${SFLAG1})\n  check_cxx_compiler_flag(${FLAG} COMPILER_SUPPORT_${SFLAG})\n  if(COMPILER_SUPPORT_${SFLAG})\n    set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} ${FLAG}\")\n  endif()\nendmacro(ei_add_cxx_compiler_flag)\n\nif(NOT MSVC)\n  # We assume that other compilers are partly compatible with GNUCC\n\n  # clang outputs some warnings for unknown flags that are not caught by check_cxx_compiler_flag\n  # adding -Werror turns such warnings into errors\n  check_cxx_compiler_flag(\"-Werror\" COMPILER_SUPPORT_WERROR)\n  if(COMPILER_SUPPORT_WERROR)\n    set(CMAKE_REQUIRED_FLAGS \"-Werror\")\n  endif()\n  ei_add_cxx_compiler_flag(\"-pedantic\")\n  ei_add_cxx_compiler_flag(\"-Wall\")\n  ei_add_cxx_compiler_flag(\"-Wextra\")\n  #ei_add_cxx_compiler_flag(\"-Weverything\")              # clang\n  \n  ei_add_cxx_compiler_flag(\"-Wundef\")\n  ei_add_cxx_compiler_flag(\"-Wcast-align\")\n  ei_add_cxx_compiler_flag(\"-Wchar-subscripts\")\n  ei_add_cxx_compiler_flag(\"-Wnon-virtual-dtor\")\n  ei_add_cxx_compiler_flag(\"-Wunused-local-typedefs\")\n  ei_add_cxx_compiler_flag(\"-Wpointer-arith\")\n  ei_add_cxx_compiler_flag(\"-Wwrite-strings\")\n  ei_add_cxx_compiler_flag(\"-Wformat-security\")\n  ei_add_cxx_compiler_flag(\"-Wshorten-64-to-32\")\n  ei_add_cxx_compiler_flag(\"-Wlogical-op\")\n  ei_add_cxx_compiler_flag(\"-Wenum-conversion\")\n  ei_add_cxx_compiler_flag(\"-Wc++11-extensions\")\n  ei_add_cxx_compiler_flag(\"-Wdouble-promotion\")\n#  ei_add_cxx_compiler_flag(\"-Wconversion\")\n  \n  # -Wshadow is insanely too strict with gcc, hopefully it will become usable with gcc 6\n  # if(NOT CMAKE_COMPILER_IS_GNUCXX OR (CMAKE_CXX_COMPILER_VERSION VERSION_GREATER \"5.0.0\"))\n  if(NOT CMAKE_COMPILER_IS_GNUCXX)\n    ei_add_cxx_compiler_flag(\"-Wshadow\")\n  endif()\n  \n  ei_add_cxx_compiler_flag(\"-Wno-psabi\")\n  ei_add_cxx_compiler_flag(\"-Wno-variadic-macros\")\n  ei_add_cxx_compiler_flag(\"-Wno-long-long\")\n  \n  ei_add_cxx_compiler_flag(\"-fno-check-new\")\n  ei_add_cxx_compiler_flag(\"-fno-common\")\n  ei_add_cxx_compiler_flag(\"-fstrict-aliasing\")\n  ei_add_cxx_compiler_flag(\"-wd981\")                    # disable ICC's \"operands are evaluated in unspecified order\" remark\n  ei_add_cxx_compiler_flag(\"-wd2304\")                   # disable ICC's \"warning #2304: non-explicit constructor with single argument may cause implicit type conversion\" produced by -Wnon-virtual-dtor\n  \n  \n  # The -ansi flag must be added last, otherwise it is also used as a linker flag by check_cxx_compiler_flag making it fails\n  # Moreover we should not set both -strict-ansi and -ansi\n  check_cxx_compiler_flag(\"-strict-ansi\" COMPILER_SUPPORT_STRICTANSI)\n  ei_add_cxx_compiler_flag(\"-Qunused-arguments\")        # disable clang warning: argument unused during compilation: '-ansi'\n  \n  if(COMPILER_SUPPORT_STRICTANSI)\n    set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} -strict-ansi\")\n  else()\n    ei_add_cxx_compiler_flag(\"-ansi\")\n  endif()\n\n  if(ANDROID_NDK)\n    ei_add_cxx_compiler_flag(\"-pie\")\n    ei_add_cxx_compiler_flag(\"-fPIE\")\n  endif()\n  \n  set(CMAKE_REQUIRED_FLAGS \"\")\n\n  option(EIGEN_TEST_SSE2 \"Enable/Disable SSE2 in tests/examples\" OFF)\n  if(EIGEN_TEST_SSE2)\n    set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} -msse2\")\n    message(STATUS \"Enabling SSE2 in tests/examples\")\n  endif()\n\n  option(EIGEN_TEST_SSE3 \"Enable/Disable SSE3 in tests/examples\" OFF)\n  if(EIGEN_TEST_SSE3)\n    set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} -msse3\")\n    message(STATUS \"Enabling SSE3 in tests/examples\")\n  endif()\n\n  option(EIGEN_TEST_SSSE3 \"Enable/Disable SSSE3 in tests/examples\" OFF)\n  if(EIGEN_TEST_SSSE3)\n    set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} -mssse3\")\n    message(STATUS \"Enabling SSSE3 in tests/examples\")\n  endif()\n\n  option(EIGEN_TEST_SSE4_1 \"Enable/Disable SSE4.1 in tests/examples\" OFF)\n  if(EIGEN_TEST_SSE4_1)\n    set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} -msse4.1\")\n    message(STATUS \"Enabling SSE4.1 in tests/examples\")\n  endif()\n\n  option(EIGEN_TEST_SSE4_2 \"Enable/Disable SSE4.2 in tests/examples\" OFF)\n  if(EIGEN_TEST_SSE4_2)\n    set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} -msse4.2\")\n    message(STATUS \"Enabling SSE4.2 in tests/examples\")\n  endif()\n\n  option(EIGEN_TEST_AVX \"Enable/Disable AVX in tests/examples\" OFF)\n  if(EIGEN_TEST_AVX)\n    set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} -mavx\")\n    message(STATUS \"Enabling AVX in tests/examples\")\n  endif()\n\n  option(EIGEN_TEST_FMA \"Enable/Disable FMA in tests/examples\" OFF)\n  if(EIGEN_TEST_FMA AND NOT EIGEN_TEST_NEON)\n    set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} -mfma\")\n    message(STATUS \"Enabling FMA in tests/examples\")\n  endif()\n\n  option(EIGEN_TEST_AVX512 \"Enable/Disable AVX512 in tests/examples\" OFF)\n  if(EIGEN_TEST_AVX512)\n    set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} -mavx512f -fabi-version=6 -DEIGEN_ENABLE_AVX512\")\n    message(STATUS \"Enabling AVX512 in tests/examples\")\n  endif()\n\n  option(EIGEN_TEST_F16C \"Enable/Disable F16C in tests/examples\" OFF)\n  if(EIGEN_TEST_F16C)\n    set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} -mf16c\")\n    message(STATUS \"Enabling F16C in tests/examples\")\n  endif()\n\n  option(EIGEN_TEST_ALTIVEC \"Enable/Disable AltiVec in tests/examples\" OFF)\n  if(EIGEN_TEST_ALTIVEC)\n    set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} -maltivec -mabi=altivec\")\n    message(STATUS \"Enabling AltiVec in tests/examples\")\n  endif()\n\n  option(EIGEN_TEST_VSX \"Enable/Disable VSX in tests/examples\" OFF)\n  if(EIGEN_TEST_VSX)\n    set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} -m64 -mvsx\")\n    message(STATUS \"Enabling VSX in tests/examples\")\n  endif()\n\n  option(EIGEN_TEST_NEON \"Enable/Disable Neon in tests/examples\" OFF)\n  if(EIGEN_TEST_NEON)\n    if(EIGEN_TEST_FMA)\n      set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} -mfpu=neon-vfpv4\")\n    else()\n      set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} -mfpu=neon\")\n    endif()\n    set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} -mfloat-abi=hard\")\n    message(STATUS \"Enabling NEON in tests/examples\")\n  endif()\n\n  option(EIGEN_TEST_NEON64 \"Enable/Disable Neon in tests/examples\" OFF)\n  if(EIGEN_TEST_NEON64)\n    set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS}\")\n    message(STATUS \"Enabling NEON in tests/examples\")\n  endif()\n\n  option(EIGEN_TEST_ZVECTOR \"Enable/Disable S390X(zEC13) ZVECTOR in tests/examples\" OFF)\n  if(EIGEN_TEST_ZVECTOR)\n    set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} -march=z13 -mzvector\")\n    message(STATUS \"Enabling S390X(zEC13) ZVECTOR in tests/examples\")\n  endif()\n\n  check_cxx_compiler_flag(\"-fopenmp\" COMPILER_SUPPORT_OPENMP)\n  if(COMPILER_SUPPORT_OPENMP)\n    option(EIGEN_TEST_OPENMP \"Enable/Disable OpenMP in tests/examples\" OFF)\n    if(EIGEN_TEST_OPENMP)\n      set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} -fopenmp\")\n      message(STATUS \"Enabling OpenMP in tests/examples\")\n    endif()\n  endif()\n\nelse(NOT MSVC)\n\n  # C4127 - conditional expression is constant\n  # C4714 - marked as __forceinline not inlined (I failed to deactivate it selectively)\n  #         We can disable this warning in the unit tests since it is clear that it occurs\n  #         because we are oftentimes returning objects that have a destructor or may\n  #         throw exceptions - in particular in the unit tests we are throwing extra many\n  #         exceptions to cover indexing errors.\n  # C4505 - unreferenced local function has been removed (impossible to deactive selectively)\n  set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} /EHsc /wd4127 /wd4505 /wd4714\")\n\n  # replace all /Wx by /W4\n  string(REGEX REPLACE \"/W[0-9]\" \"/W4\" CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS}\")\n\n  check_cxx_compiler_flag(\"/openmp\" COMPILER_SUPPORT_OPENMP)\n  if(COMPILER_SUPPORT_OPENMP)\n    option(EIGEN_TEST_OPENMP \"Enable/Disable OpenMP in tests/examples\" OFF)\n    if(EIGEN_TEST_OPENMP)\n      set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} /openmp\")\n      message(STATUS \"Enabling OpenMP in tests/examples\")\n    endif()\n  endif()\n\n  option(EIGEN_TEST_SSE2 \"Enable/Disable SSE2 in tests/examples\" OFF)\n  if(EIGEN_TEST_SSE2)\n    if(NOT CMAKE_CL_64)\n      # arch is not supported on 64 bit systems, SSE is enabled automatically.\n      set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} /arch:SSE2\")\n    endif(NOT CMAKE_CL_64)\n    message(STATUS \"Enabling SSE2 in tests/examples\")\n  endif(EIGEN_TEST_SSE2)\nendif(NOT MSVC)\n\noption(EIGEN_TEST_NO_EXPLICIT_VECTORIZATION \"Disable explicit vectorization in tests/examples\" OFF)\noption(EIGEN_TEST_X87 \"Force using X87 instructions. Implies no vectorization.\" OFF)\noption(EIGEN_TEST_32BIT \"Force generating 32bit code.\" OFF)\n\nif(EIGEN_TEST_X87)\n  set(EIGEN_TEST_NO_EXPLICIT_VECTORIZATION ON)\n  if(CMAKE_COMPILER_IS_GNUCXX)\n    set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} -mfpmath=387\")\n    message(STATUS \"Forcing use of x87 instructions in tests/examples\")\n  else()\n    message(STATUS \"EIGEN_TEST_X87 ignored on your compiler\")\n  endif()\nendif()\n\nif(EIGEN_TEST_32BIT)\n  if(CMAKE_COMPILER_IS_GNUCXX)\n    set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} -m32\")\n    message(STATUS \"Forcing generation of 32-bit code in tests/examples\")\n  else()\n    message(STATUS \"EIGEN_TEST_32BIT ignored on your compiler\")\n  endif()\nendif()\n\nif(EIGEN_TEST_NO_EXPLICIT_VECTORIZATION)\n  add_definitions(-DEIGEN_DONT_VECTORIZE=1)\n  message(STATUS \"Disabling vectorization in tests/examples\")\nendif()\n\noption(EIGEN_TEST_NO_EXPLICIT_ALIGNMENT \"Disable explicit alignment (hence vectorization) in tests/examples\" OFF)\nif(EIGEN_TEST_NO_EXPLICIT_ALIGNMENT)\n  add_definitions(-DEIGEN_DONT_ALIGN=1)\n  message(STATUS \"Disabling alignment in tests/examples\")\nendif()\n\noption(EIGEN_TEST_NO_EXCEPTIONS \"Disables C++ exceptions\" OFF)\nif(EIGEN_TEST_NO_EXCEPTIONS)\n  ei_add_cxx_compiler_flag(\"-fno-exceptions\")\n  message(STATUS \"Disabling exceptions in tests/examples\")\nendif()\n\noption(EIGEN_TEST_CXX11 \"Enable testing with C++11 and C++11 features (e.g. Tensor module).\" OFF)\n\nset(EIGEN_CUDA_COMPUTE_ARCH 30 CACHE STRING \"The CUDA compute architecture level to target when compiling CUDA code\")\n\ninclude_directories(${CMAKE_CURRENT_SOURCE_DIR} ${CMAKE_CURRENT_BINARY_DIR})\n\n# Backward compatibility support for EIGEN_INCLUDE_INSTALL_DIR\nif(EIGEN_INCLUDE_INSTALL_DIR)\n  message(WARNING \"EIGEN_INCLUDE_INSTALL_DIR is deprecated. Use INCLUDE_INSTALL_DIR instead.\")\nendif()\n\nif(EIGEN_INCLUDE_INSTALL_DIR AND NOT INCLUDE_INSTALL_DIR)\n  set(INCLUDE_INSTALL_DIR ${EIGEN_INCLUDE_INSTALL_DIR}\n      CACHE PATH \"The directory relative to CMAKE_PREFIX_PATH where Eigen header files are installed\")\nelse()\n  set(INCLUDE_INSTALL_DIR\n      \"${CMAKE_INSTALL_INCLUDEDIR}/eigen3\"\n      CACHE PATH \"The directory relative to CMAKE_PREFIX_PATH where Eigen header files are installed\"\n      )\nendif()\nset(CMAKEPACKAGE_INSTALL_DIR\n    \"${CMAKE_INSTALL_DATADIR}/eigen3/cmake\"\n    CACHE PATH \"The directory relative to CMAKE_PREFIX_PATH where Eigen3Config.cmake is installed\"\n    )\nset(PKGCONFIG_INSTALL_DIR\n    \"${CMAKE_INSTALL_DATADIR}/pkgconfig\"\n    CACHE PATH \"The directory relative to CMAKE_PREFIX_PATH where eigen3.pc is installed\"\n    )\n\n\n# similar to set_target_properties but append the property instead of overwriting it\nmacro(ei_add_target_property target prop value)\n\n  get_target_property(previous ${target} ${prop})\n  # if the property wasn't previously set, ${previous} is now \"previous-NOTFOUND\" which cmake allows catching with plain if()\n  if(NOT previous)\n    set(previous \"\")\n  endif(NOT previous)\n  set_target_properties(${target} PROPERTIES ${prop} \"${previous} ${value}\")\nendmacro(ei_add_target_property)\n\ninstall(FILES\n  signature_of_eigen3_matrix_library\n  DESTINATION ${INCLUDE_INSTALL_DIR} COMPONENT Devel\n  )\n\nif(EIGEN_BUILD_PKGCONFIG)\n    configure_file(eigen3.pc.in eigen3.pc @ONLY)\n    install(FILES ${CMAKE_CURRENT_BINARY_DIR}/eigen3.pc\n        DESTINATION ${PKGCONFIG_INSTALL_DIR}\n        )\nendif()\n\nadd_subdirectory(Eigen)\n\nadd_subdirectory(doc EXCLUDE_FROM_ALL)\n\noption(BUILD_TESTING \"Enable creation of Eigen tests.\" ON)\nif(BUILD_TESTING)\n  include(EigenConfigureTesting)\n\n  if(EIGEN_LEAVE_TEST_IN_ALL_TARGET)\n    add_subdirectory(test) # can't do EXCLUDE_FROM_ALL here, breaks CTest\n  else()\n    add_subdirectory(test EXCLUDE_FROM_ALL)\n  endif()\nendif()\n\nif(EIGEN_LEAVE_TEST_IN_ALL_TARGET)\n  add_subdirectory(blas)\n  add_subdirectory(lapack)\nelse()\n  add_subdirectory(blas EXCLUDE_FROM_ALL)\n  add_subdirectory(lapack EXCLUDE_FROM_ALL)\nendif()\n\n# add SYCL\noption(EIGEN_TEST_SYCL \"Add Sycl support.\" OFF)\nif(EIGEN_TEST_SYCL)\n  set (CMAKE_MODULE_PATH \"${CMAKE_ROOT}/Modules\" \"cmake/Modules/\" \"${CMAKE_MODULE_PATH}\")\n  include(FindComputeCpp)\nendif()\n\nadd_subdirectory(unsupported)\n\nadd_subdirectory(demos EXCLUDE_FROM_ALL)\n\n# must be after test and unsupported, for configuring buildtests.in\nadd_subdirectory(scripts EXCLUDE_FROM_ALL)\n\n# TODO: consider also replacing EIGEN_BUILD_BTL by a custom target \"make btl\"?\nif(EIGEN_BUILD_BTL)\n  add_subdirectory(bench/btl EXCLUDE_FROM_ALL)\nendif(EIGEN_BUILD_BTL)\n\nif(NOT WIN32)\n  add_subdirectory(bench/spbench EXCLUDE_FROM_ALL)\nendif(NOT WIN32)\n\nconfigure_file(scripts/cdashtesting.cmake.in cdashtesting.cmake @ONLY)\n\nif(BUILD_TESTING)\n  ei_testing_print_summary()\nendif()\n\nmessage(STATUS \"\")\nmessage(STATUS \"Configured Eigen ${EIGEN_VERSION_NUMBER}\")\nmessage(STATUS \"\")\n\noption(EIGEN_FAILTEST \"Enable failtests.\" OFF)\nif(EIGEN_FAILTEST)\n  add_subdirectory(failtest)\nendif()\n\nstring(TOLOWER \"${CMAKE_GENERATOR}\" cmake_generator_tolower)\nif(cmake_generator_tolower MATCHES \"makefile\")\n  message(STATUS \"Some things you can do now:\")\n  message(STATUS \"--------------+--------------------------------------------------------------\")\n  message(STATUS \"Command       |   Description\")\n  message(STATUS \"--------------+--------------------------------------------------------------\")\n  message(STATUS \"make install  | Install Eigen. Headers will be installed to:\")\n  message(STATUS \"              |     <CMAKE_INSTALL_PREFIX>/<INCLUDE_INSTALL_DIR>\")\n  message(STATUS \"              |   Using the following values:\")\n  message(STATUS \"              |     CMAKE_INSTALL_PREFIX: ${CMAKE_INSTALL_PREFIX}\")\n  message(STATUS \"              |     INCLUDE_INSTALL_DIR:  ${INCLUDE_INSTALL_DIR}\")\n  message(STATUS \"              |   Change the install location of Eigen headers using:\")\n  message(STATUS \"              |     cmake . -DCMAKE_INSTALL_PREFIX=yourprefix\")\n  message(STATUS \"              |   Or:\")\n  message(STATUS \"              |     cmake . -DINCLUDE_INSTALL_DIR=yourdir\")\n  message(STATUS \"make doc      | Generate the API documentation, requires Doxygen & LaTeX\")\n  message(STATUS \"make check    | Build and run the unit-tests. Read this page:\")\n  message(STATUS \"              |   http://eigen.tuxfamily.org/index.php?title=Tests\")\n  message(STATUS \"make blas     | Build BLAS library (not the same thing as Eigen)\")\n  message(STATUS \"make uninstall| Removes files installed by make install\")\n  message(STATUS \"--------------+--------------------------------------------------------------\")\nelse()\n  message(STATUS \"To build/run the unit tests, read this page:\")\n  message(STATUS \"  http://eigen.tuxfamily.org/index.php?title=Tests\")\nendif()\n\nmessage(STATUS \"\")\n\n\nset ( EIGEN_VERSION_STRING ${EIGEN_VERSION_NUMBER} )\nset ( EIGEN_VERSION_MAJOR  ${EIGEN_WORLD_VERSION} )\nset ( EIGEN_VERSION_MINOR  ${EIGEN_MAJOR_VERSION} )\nset ( EIGEN_VERSION_PATCH  ${EIGEN_MINOR_VERSION} )\nset ( EIGEN_DEFINITIONS \"\")\nset ( EIGEN_INCLUDE_DIR \"${CMAKE_INSTALL_PREFIX}/${INCLUDE_INSTALL_DIR}\" )\nset ( EIGEN_ROOT_DIR ${CMAKE_INSTALL_PREFIX} )\n\n# Interface libraries require at least CMake 3.0\nif (NOT CMAKE_VERSION VERSION_LESS 3.0)\n  include (CMakePackageConfigHelpers)\n\n  # Imported target support\n  add_library (eigen INTERFACE)\n\n  target_compile_definitions (eigen INTERFACE ${EIGEN_DEFINITIONS})\n  target_include_directories (eigen INTERFACE\n    $<BUILD_INTERFACE:${CMAKE_CURRENT_SOURCE_DIR}>\n    $<INSTALL_INTERFACE:${INCLUDE_INSTALL_DIR}>\n  )\n\n  # Export as title case Eigen\n  set_target_properties (eigen PROPERTIES EXPORT_NAME Eigen)\n\n  install (TARGETS eigen EXPORT Eigen3Targets)\n\n  configure_package_config_file (\n    ${CMAKE_CURRENT_SOURCE_DIR}/cmake/Eigen3Config.cmake.in\n    ${CMAKE_CURRENT_BINARY_DIR}/Eigen3Config.cmake\n    PATH_VARS EIGEN_INCLUDE_DIR EIGEN_ROOT_DIR\n    INSTALL_DESTINATION ${CMAKEPACKAGE_INSTALL_DIR}\n    NO_CHECK_REQUIRED_COMPONENTS_MACRO # Eigen does not provide components\n  )\n  # Remove CMAKE_SIZEOF_VOID_P from Eigen3ConfigVersion.cmake since Eigen does\n  # not depend on architecture specific settings or libraries. More\n  # specifically, an Eigen3Config.cmake generated from a 64 bit target can be\n  # used for 32 bit targets as well (and vice versa).\n  set (_Eigen3_CMAKE_SIZEOF_VOID_P ${CMAKE_SIZEOF_VOID_P})\n  unset (CMAKE_SIZEOF_VOID_P)\n  write_basic_package_version_file (Eigen3ConfigVersion.cmake\n                                    VERSION ${EIGEN_VERSION_NUMBER}\n                                    COMPATIBILITY SameMajorVersion)\n  set (CMAKE_SIZEOF_VOID_P ${_Eigen3_CMAKE_SIZEOF_VOID_P})\n\n  # The Eigen target will be located in the Eigen3 namespace. Other CMake\n  # targets can refer to it using Eigen3::Eigen.\n  export (TARGETS eigen NAMESPACE Eigen3:: FILE Eigen3Targets.cmake)\n  # Export Eigen3 package to CMake registry such that it can be easily found by\n  # CMake even if it has not been installed to a standard directory.\n  export (PACKAGE Eigen3)\n\n  install (EXPORT Eigen3Targets NAMESPACE Eigen3:: DESTINATION ${CMAKEPACKAGE_INSTALL_DIR})\n\nelse (NOT CMAKE_VERSION VERSION_LESS 3.0)\n  # Fallback to legacy Eigen3Config.cmake without the imported target\n  \n  # If CMakePackageConfigHelpers module is available (CMake >= 2.8.8)\n  # create a relocatable Config file, otherwise leave the hardcoded paths       \n  include(CMakePackageConfigHelpers OPTIONAL RESULT_VARIABLE CPCH_PATH)\n  \n  if(CPCH_PATH)\n    configure_package_config_file (\n      ${CMAKE_CURRENT_SOURCE_DIR}/cmake/Eigen3ConfigLegacy.cmake.in\n      ${CMAKE_CURRENT_BINARY_DIR}/Eigen3Config.cmake\n      PATH_VARS EIGEN_INCLUDE_DIR EIGEN_ROOT_DIR\n      INSTALL_DESTINATION ${CMAKEPACKAGE_INSTALL_DIR}\n      NO_CHECK_REQUIRED_COMPONENTS_MACRO # Eigen does not provide components\n    )\n  else() \n    # The PACKAGE_* variables are defined by the configure_package_config_file\n    # but without it we define them manually to the hardcoded paths\n    set(PACKAGE_INIT \"\")\n    set(PACKAGE_EIGEN_INCLUDE_DIR ${EIGEN_INCLUDE_DIR})\n    set(PACKAGE_EIGEN_ROOT_DIR ${EIGEN_ROOT_DIR})\n    configure_file ( ${CMAKE_CURRENT_SOURCE_DIR}/cmake/Eigen3ConfigLegacy.cmake.in\n                     ${CMAKE_CURRENT_BINARY_DIR}/Eigen3Config.cmake\n                     @ONLY ESCAPE_QUOTES )\n  endif()\n\n  write_basic_package_version_file( Eigen3ConfigVersion.cmake\n                                    VERSION ${EIGEN_VERSION_NUMBER}\n                                    COMPATIBILITY SameMajorVersion )\n\nendif (NOT CMAKE_VERSION VERSION_LESS 3.0)\n\ninstall ( FILES ${CMAKE_CURRENT_SOURCE_DIR}/cmake/UseEigen3.cmake\n                ${CMAKE_CURRENT_BINARY_DIR}/Eigen3Config.cmake\n                ${CMAKE_CURRENT_BINARY_DIR}/Eigen3ConfigVersion.cmake\n          DESTINATION ${CMAKEPACKAGE_INSTALL_DIR} )\n\n# Add uninstall target\nadd_custom_target ( uninstall\n    COMMAND ${CMAKE_COMMAND} -P ${CMAKE_CURRENT_SOURCE_DIR}/cmake/EigenUninstall.cmake)\n"
  },
  {
    "path": "include/eigen3/COPYING.BSD",
    "content": "/*\n Copyright (c) 2011, Intel Corporation. All rights reserved.\n\n Redistribution and use in source and binary forms, with or without modification,\n are permitted provided that the following conditions are met:\n\n * Redistributions of source code must retain the above copyright notice, this\n   list of conditions and the following disclaimer.\n * Redistributions in binary form must reproduce the above copyright notice,\n   this list of conditions and the following disclaimer in the documentation\n   and/or other materials provided with the distribution.\n * Neither the name of Intel Corporation nor the names of its contributors may\n   be used to endorse or promote products derived from this software without\n   specific prior written permission.\n\n THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\" AND\n ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED\n WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\n DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR\n ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES\n (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;\n LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON\n ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT\n (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS\n SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n*/"
  },
  {
    "path": "include/eigen3/COPYING.GPL",
    "content": "                    GNU GENERAL PUBLIC LICENSE\n                       Version 3, 29 June 2007\n\n Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>\n Everyone is permitted to copy and distribute verbatim copies\n of this license document, but changing it is not allowed.\n\n                            Preamble\n\n  The GNU General Public License is a free, copyleft license for\nsoftware and other kinds of works.\n\n  The licenses for most software and other practical works are designed\nto take away your freedom to share and change the works.  By contrast,\nthe GNU General Public License is intended to guarantee your freedom to\nshare and change all versions of a program--to make sure it remains free\nsoftware for all its users.  We, the Free Software Foundation, use the\nGNU General Public License for most of our software; it applies also to\nany other work released this way by its authors.  You can apply it to\nyour programs, too.\n\n  When we speak of free software, we are referring to freedom, not\nprice.  Our General Public Licenses are designed to make sure that you\nhave the freedom to distribute copies of free software (and charge for\nthem if you wish), that you receive source code or can get it if you\nwant it, that you can change the software or use pieces of it in new\nfree programs, and that you know you can do these things.\n\n  To protect your rights, we need to prevent others from denying you\nthese rights or asking you to surrender the rights.  Therefore, you have\ncertain responsibilities if you distribute copies of the software, or if\nyou modify it: responsibilities to respect the freedom of others.\n\n  For example, if you distribute copies of such a program, whether\ngratis or for a fee, you must pass on to the recipients the same\nfreedoms that you received.  You must make sure that they, too, receive\nor can get the source code.  And you must show them these terms so they\nknow their rights.\n\n  Developers that use the GNU GPL protect your rights with two steps:\n(1) assert copyright on the software, and (2) offer you this License\ngiving you legal permission to copy, distribute and/or modify it.\n\n  For the developers' and authors' protection, the GPL clearly explains\nthat there is no warranty for this free software.  For both users' and\nauthors' sake, the GPL requires that modified versions be marked as\nchanged, so that their problems will not be attributed erroneously to\nauthors of previous versions.\n\n  Some devices are designed to deny users access to install or run\nmodified versions of the software inside them, although the manufacturer\ncan do so.  This is fundamentally incompatible with the aim of\nprotecting users' freedom to change the software.  The systematic\npattern of such abuse occurs in the area of products for individuals to\nuse, which is precisely where it is most unacceptable.  Therefore, we\nhave designed this version of the GPL to prohibit the practice for those\nproducts.  If such problems arise substantially in other domains, we\nstand ready to extend this provision to those domains in future versions\nof the GPL, as needed to protect the freedom of users.\n\n  Finally, every program is threatened constantly by software patents.\nStates should not allow patents to restrict development and use of\nsoftware on general-purpose computers, but in those that do, we wish to\navoid the special danger that patents applied to a free program could\nmake it effectively proprietary.  To prevent this, the GPL assures that\npatents cannot be used to render the program non-free.\n\n  The precise terms and conditions for copying, distribution and\nmodification follow.\n\n                       TERMS AND CONDITIONS\n\n  0. Definitions.\n\n  \"This License\" refers to version 3 of the GNU General Public License.\n\n  \"Copyright\" also means copyright-like laws that apply to other kinds of\nworks, such as semiconductor masks.\n\n  \"The Program\" refers to any copyrightable work licensed under this\nLicense.  Each licensee is addressed as \"you\".  \"Licensees\" and\n\"recipients\" may be individuals or organizations.\n\n  To \"modify\" a work means to copy from or adapt all or part of the work\nin a fashion requiring copyright permission, other than the making of an\nexact copy.  The resulting work is called a \"modified version\" of the\nearlier work or a work \"based on\" the earlier work.\n\n  A \"covered work\" means either the unmodified Program or a work based\non the Program.\n\n  To \"propagate\" a work means to do anything with it that, without\npermission, would make you directly or secondarily liable for\ninfringement under applicable copyright law, except executing it on a\ncomputer or modifying a private copy.  Propagation includes copying,\ndistribution (with or without modification), making available to the\npublic, and in some countries other activities as well.\n\n  To \"convey\" a work means any kind of propagation that enables other\nparties to make or receive copies.  Mere interaction with a user through\na computer network, with no transfer of a copy, is not conveying.\n\n  An interactive user interface displays \"Appropriate Legal Notices\"\nto the extent that it includes a convenient and prominently visible\nfeature that (1) displays an appropriate copyright notice, and (2)\ntells the user that there is no warranty for the work (except to the\nextent that warranties are provided), that licensees may convey the\nwork under this License, and how to view a copy of this License.  If\nthe interface presents a list of user commands or options, such as a\nmenu, a prominent item in the list meets this criterion.\n\n  1. 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A\n\"Major Component\", in this context, means a major essential component\n(kernel, window system, and so on) of the specific operating system\n(if any) on which the executable work runs, or a compiler used to\nproduce the work, or an object code interpreter used to run it.\n\n  The \"Corresponding Source\" for a work in object code form means all\nthe source code needed to generate, install, and (for an executable\nwork) run the object code and to modify the work, including scripts to\ncontrol those activities.  However, it does not include the work's\nSystem Libraries, or general-purpose tools or generally available free\nprograms which are used unmodified in performing those activities but\nwhich are not part of the work.  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No Surrender of Others' Freedom.\n\n  If conditions are imposed on you (whether by court order, agreement or\notherwise) that contradict the conditions of this License, they do not\nexcuse you from the conditions of this License.  If you cannot convey a\ncovered work so as to satisfy simultaneously your obligations under this\nLicense and any other pertinent obligations, then as a consequence you may\nnot convey it at all.  For example, if you agree to terms that obligate you\nto collect a royalty for further conveying from those to whom you convey\nthe Program, the only way you could satisfy both those terms and this\nLicense would be to refrain entirely from conveying the Program.\n\n  13. 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Interpretation of Sections 15 and 16.\n\n  If the disclaimer of warranty and limitation of liability provided\nabove cannot be given local legal effect according to their terms,\nreviewing courts shall apply local law that most closely approximates\nan absolute waiver of all civil liability in connection with the\nProgram, unless a warranty or assumption of liability accompanies a\ncopy of the Program in return for a fee.\n\n                     END OF TERMS AND CONDITIONS\n\n            How to Apply These Terms to Your New Programs\n\n  If you develop a new program, and you want it to be of the greatest\npossible use to the public, the best way to achieve this is to make it\nfree software which everyone can redistribute and change under these terms.\n\n  To do so, attach the following notices to the program.  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Of course, your program's commands\nmight be different; for a GUI interface, you would use an \"about box\".\n\n  You should also get your employer (if you work as a programmer) or school,\nif any, to sign a \"copyright disclaimer\" for the program, if necessary.\nFor more information on this, and how to apply and follow the GNU GPL, see\n<http://www.gnu.org/licenses/>.\n\n  The GNU General Public License does not permit incorporating your program\ninto proprietary programs.  If your program is a subroutine library, you\nmay consider it more useful to permit linking proprietary applications with\nthe library.  If this is what you want to do, use the GNU Lesser General\nPublic License instead of this License.  But first, please read\n<http://www.gnu.org/philosophy/why-not-lgpl.html>.\n"
  },
  {
    "path": "include/eigen3/COPYING.LGPL",
    "content": "                  GNU LESSER GENERAL PUBLIC LICENSE\n                       Version 2.1, February 1999\n\n Copyright (C) 1991, 1999 Free Software Foundation, Inc.\n 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA\n Everyone is permitted to copy and distribute verbatim copies\n of this license document, but changing it is not allowed.\n\n[This is the first released version of the Lesser GPL.  It also counts\n as the successor of the GNU Library Public License, version 2, hence\n the version number 2.1.]\n\n                            Preamble\n\n  The licenses for most software are designed to take away your\nfreedom to share and change it.  By contrast, the GNU General Public\nLicenses are intended to guarantee your freedom to share and change\nfree software--to make sure the software is free for all its users.\n\n  This license, the Lesser General Public License, applies to some\nspecially designated software packages--typically libraries--of the\nFree Software Foundation and other authors who decide to use it.  You\ncan use it too, but we suggest you first think carefully about whether\nthis license or the ordinary General Public License is the better\nstrategy to use in any particular case, based on the explanations below.\n\n  When we speak of free software, we are referring to freedom of use,\nnot price.  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  },
  {
    "path": "include/eigen3/COPYING.MINPACK",
    "content": "Minpack Copyright Notice (1999) University of Chicago.  All rights reserved\n\nRedistribution and use in source and binary forms, with or\nwithout modification, are permitted provided that the\nfollowing conditions are met:\n\n1. Redistributions of source code must retain the above\ncopyright notice, this list of conditions and the following\ndisclaimer.\n\n2. Redistributions in binary form must reproduce the above\ncopyright notice, this list of conditions and the following\ndisclaimer in the documentation and/or other materials\nprovided with the distribution.\n\n3. The end-user documentation included with the\nredistribution, if any, must include the following\nacknowledgment:\n\n   \"This product includes software developed by the\n   University of Chicago, as Operator of Argonne National\n   Laboratory.\n\nAlternately, this acknowledgment may appear in the software\nitself, if and wherever such third-party acknowledgments\nnormally appear.\n\n4. WARRANTY DISCLAIMER. THE SOFTWARE IS SUPPLIED \"AS IS\"\nWITHOUT WARRANTY OF ANY KIND. THE COPYRIGHT HOLDER, THE\nUNITED STATES, THE UNITED STATES DEPARTMENT OF ENERGY, AND\nTHEIR EMPLOYEES: (1) DISCLAIM ANY WARRANTIES, EXPRESS OR\nIMPLIED, INCLUDING BUT NOT LIMITED TO ANY IMPLIED WARRANTIES\nOF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE\nOR NON-INFRINGEMENT, (2) DO NOT ASSUME ANY LEGAL LIABILITY\nOR RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS, OR\nUSEFULNESS OF THE SOFTWARE, (3) DO NOT REPRESENT THAT USE OF\nTHE SOFTWARE WOULD NOT INFRINGE PRIVATELY OWNED RIGHTS, (4)\nDO NOT WARRANT THAT THE SOFTWARE WILL FUNCTION\nUNINTERRUPTED, THAT IT IS ERROR-FREE OR THAT ANY ERRORS WILL\nBE CORRECTED.\n\n5. LIMITATION OF LIABILITY. IN NO EVENT WILL THE COPYRIGHT\nHOLDER, THE UNITED STATES, THE UNITED STATES DEPARTMENT OF\nENERGY, OR THEIR EMPLOYEES: BE LIABLE FOR ANY INDIRECT,\nINCIDENTAL, CONSEQUENTIAL, SPECIAL OR PUNITIVE DAMAGES OF\nANY KIND OR NATURE, INCLUDING BUT NOT LIMITED TO LOSS OF\nPROFITS OR LOSS OF DATA, FOR ANY REASON WHATSOEVER, WHETHER\nSUCH LIABILITY IS ASSERTED ON THE BASIS OF CONTRACT, TORT\n(INCLUDING NEGLIGENCE OR STRICT LIABILITY), OR OTHERWISE,\nEVEN IF ANY OF SAID PARTIES HAS BEEN WARNED OF THE\nPOSSIBILITY OF SUCH LOSS OR DAMAGES.\n\n"
  },
  {
    "path": "include/eigen3/COPYING.MPL2",
    "content": "Mozilla Public License Version 2.0\n==================================\n\n1. Definitions\n--------------\n\n1.1. \"Contributor\"\n    means each individual or legal entity that creates, contributes to\n    the creation of, or owns Covered Software.\n\n1.2. \"Contributor Version\"\n    means the combination of the Contributions of others (if any) used\n    by a Contributor and that particular Contributor's Contribution.\n\n1.3. \"Contribution\"\n    means Covered Software of a particular Contributor.\n\n1.4. \"Covered Software\"\n    means Source Code Form to which the initial Contributor has attached\n    the notice in Exhibit A, the Executable Form of such Source Code\n    Form, and Modifications of such Source Code Form, in each case\n    including portions thereof.\n\n1.5. \"Incompatible With Secondary Licenses\"\n    means\n\n    (a) that the initial Contributor has attached the notice described\n        in Exhibit B to the Covered Software; or\n\n    (b) that the Covered Software was made available under the terms of\n        version 1.1 or earlier of the License, but not also under the\n        terms of a Secondary License.\n\n1.6. \"Executable Form\"\n    means any form of the work other than Source Code Form.\n\n1.7. \"Larger Work\"\n    means a work that combines Covered Software with other material, in \n    a separate file or files, that is not Covered Software.\n\n1.8. \"License\"\n    means this document.\n\n1.9. \"Licensable\"\n    means having the right to grant, to the maximum extent possible,\n    whether at the time of the initial grant or subsequently, any and\n    all of the rights conveyed by this License.\n\n1.10. \"Modifications\"\n    means any of the following:\n\n    (a) any file in Source Code Form that results from an addition to,\n        deletion from, or modification of the contents of Covered\n        Software; or\n\n    (b) any new file in Source Code Form that contains any Covered\n        Software.\n\n1.11. \"Patent Claims\" of a Contributor\n    means any patent claim(s), including without limitation, method,\n    process, and apparatus claims, in any patent Licensable by such\n    Contributor that would be infringed, but for the grant of the\n    License, by the making, using, selling, offering for sale, having\n    made, import, or transfer of either its Contributions or its\n    Contributor Version.\n\n1.12. \"Secondary License\"\n    means either the GNU General Public License, Version 2.0, the GNU\n    Lesser General Public License, Version 2.1, the GNU Affero General\n    Public License, Version 3.0, or any later versions of those\n    licenses.\n\n1.13. \"Source Code Form\"\n    means the form of the work preferred for making modifications.\n\n1.14. \"You\" (or \"Your\")\n    means an individual or a legal entity exercising rights under this\n    License. For legal entities, \"You\" includes any entity that\n    controls, is controlled by, or is under common control with You. For\n    purposes of this definition, \"control\" means (a) the power, direct\n    or indirect, to cause the direction or management of such entity,\n    whether by contract or otherwise, or (b) ownership of more than\n    fifty percent (50%) of the outstanding shares or beneficial\n    ownership of such entity.\n\n2. License Grants and Conditions\n--------------------------------\n\n2.1. Grants\n\nEach Contributor hereby grants You a world-wide, royalty-free,\nnon-exclusive license:\n\n(a) under intellectual property rights (other than patent or trademark)\n    Licensable by such Contributor to use, reproduce, make available,\n    modify, display, perform, distribute, and otherwise exploit its\n    Contributions, either on an unmodified basis, with Modifications, or\n    as part of a Larger Work; and\n\n(b) under Patent Claims of such Contributor to make, use, sell, offer\n    for sale, have made, import, and otherwise transfer either its\n    Contributions or its Contributor Version.\n\n2.2. Effective Date\n\nThe licenses granted in Section 2.1 with respect to any Contribution\nbecome effective for each Contribution on the date the Contributor first\ndistributes such Contribution.\n\n2.3. Limitations on Grant Scope\n\nThe licenses granted in this Section 2 are the only rights granted under\nthis License. No additional rights or licenses will be implied from the\ndistribution or licensing of Covered Software under this License.\nNotwithstanding Section 2.1(b) above, no patent license is granted by a\nContributor:\n\n(a) for any code that a Contributor has removed from Covered Software;\n    or\n\n(b) for infringements caused by: (i) Your and any other third party's\n    modifications of Covered Software, or (ii) the combination of its\n    Contributions with other software (except as part of its Contributor\n    Version); or\n\n(c) under Patent Claims infringed by Covered Software in the absence of\n    its Contributions.\n\nThis License does not grant any rights in the trademarks, service marks,\nor logos of any Contributor (except as may be necessary to comply with\nthe notice requirements in Section 3.4).\n\n2.4. Subsequent Licenses\n\nNo Contributor makes additional grants as a result of Your choice to\ndistribute the Covered Software under a subsequent version of this\nLicense (see Section 10.2) or under the terms of a Secondary License (if\npermitted under the terms of Section 3.3).\n\n2.5. Representation\n\nEach Contributor represents that the Contributor believes its\nContributions are its original creation(s) or it has sufficient rights\nto grant the rights to its Contributions conveyed by this License.\n\n2.6. Fair Use\n\nThis License is not intended to limit any rights You have under\napplicable copyright doctrines of fair use, fair dealing, or other\nequivalents.\n\n2.7. Conditions\n\nSections 3.1, 3.2, 3.3, and 3.4 are conditions of the licenses granted\nin Section 2.1.\n\n3. Responsibilities\n-------------------\n\n3.1. Distribution of Source Form\n\nAll distribution of Covered Software in Source Code Form, including any\nModifications that You create or to which You contribute, must be under\nthe terms of this License. You must inform recipients that the Source\nCode Form of the Covered Software is governed by the terms of this\nLicense, and how they can obtain a copy of this License. You may not\nattempt to alter or restrict the recipients' rights in the Source Code\nForm.\n\n3.2. Distribution of Executable Form\n\nIf You distribute Covered Software in Executable Form then:\n\n(a) such Covered Software must also be made available in Source Code\n    Form, as described in Section 3.1, and You must inform recipients of\n    the Executable Form how they can obtain a copy of such Source Code\n    Form by reasonable means in a timely manner, at a charge no more\n    than the cost of distribution to the recipient; and\n\n(b) You may distribute such Executable Form under the terms of this\n    License, or sublicense it under different terms, provided that the\n    license for the Executable Form does not attempt to limit or alter\n    the recipients' rights in the Source Code Form under this License.\n\n3.3. Distribution of a Larger Work\n\nYou may create and distribute a Larger Work under terms of Your choice,\nprovided that You also comply with the requirements of this License for\nthe Covered Software. If the Larger Work is a combination of Covered\nSoftware with a work governed by one or more Secondary Licenses, and the\nCovered Software is not Incompatible With Secondary Licenses, this\nLicense permits You to additionally distribute such Covered Software\nunder the terms of such Secondary License(s), so that the recipient of\nthe Larger Work may, at their option, further distribute the Covered\nSoftware under the terms of either this License or such Secondary\nLicense(s).\n\n3.4. Notices\n\nYou may not remove or alter the substance of any license notices\n(including copyright notices, patent notices, disclaimers of warranty,\nor limitations of liability) contained within the Source Code Form of\nthe Covered Software, except that You may alter any license notices to\nthe extent required to remedy known factual inaccuracies.\n\n3.5. Application of Additional Terms\n\nYou may choose to offer, and to charge a fee for, warranty, support,\nindemnity or liability obligations to one or more recipients of Covered\nSoftware. However, You may do so only on Your own behalf, and not on\nbehalf of any Contributor. You must make it absolutely clear that any\nsuch warranty, support, indemnity, or liability obligation is offered by\nYou alone, and You hereby agree to indemnify every Contributor for any\nliability incurred by such Contributor as a result of warranty, support,\nindemnity or liability terms You offer. You may include additional\ndisclaimers of warranty and limitations of liability specific to any\njurisdiction.\n\n4. Inability to Comply Due to Statute or Regulation\n---------------------------------------------------\n\nIf it is impossible for You to comply with any of the terms of this\nLicense with respect to some or all of the Covered Software due to\nstatute, judicial order, or regulation then You must: (a) comply with\nthe terms of this License to the maximum extent possible; and (b)\ndescribe the limitations and the code they affect. Such description must\nbe placed in a text file included with all distributions of the Covered\nSoftware under this License. Except to the extent prohibited by statute\nor regulation, such description must be sufficiently detailed for a\nrecipient of ordinary skill to be able to understand it.\n\n5. Termination\n--------------\n\n5.1. The rights granted under this License will terminate automatically\nif You fail to comply with any of its terms. However, if You become\ncompliant, then the rights granted under this License from a particular\nContributor are reinstated (a) provisionally, unless and until such\nContributor explicitly and finally terminates Your grants, and (b) on an\nongoing basis, if such Contributor fails to notify You of the\nnon-compliance by some reasonable means prior to 60 days after You have\ncome back into compliance. Moreover, Your grants from a particular\nContributor are reinstated on an ongoing basis if such Contributor\nnotifies You of the non-compliance by some reasonable means, this is the\nfirst time You have received notice of non-compliance with this License\nfrom such Contributor, and You become compliant prior to 30 days after\nYour receipt of the notice.\n\n5.2. If You initiate litigation against any entity by asserting a patent\ninfringement claim (excluding declaratory judgment actions,\ncounter-claims, and cross-claims) alleging that a Contributor Version\ndirectly or indirectly infringes any patent, then the rights granted to\nYou by any and all Contributors for the Covered Software under Section\n2.1 of this License shall terminate.\n\n5.3. In the event of termination under Sections 5.1 or 5.2 above, all\nend user license agreements (excluding distributors and resellers) which\nhave been validly granted by You or Your distributors under this License\nprior to termination shall survive termination.\n\n************************************************************************\n*                                                                      *\n*  6. Disclaimer of Warranty                                           *\n*  -------------------------                                           *\n*                                                                      *\n*  Covered Software is provided under this License on an \"as is\"       *\n*  basis, without warranty of any kind, either expressed, implied, or  *\n*  statutory, including, without limitation, warranties that the       *\n*  Covered Software is free of defects, merchantable, fit for a        *\n*  particular purpose or non-infringing. The entire risk as to the     *\n*  quality and performance of the Covered Software is with You.        *\n*  Should any Covered Software prove defective in any respect, You     *\n*  (not any Contributor) assume the cost of any necessary servicing,   *\n*  repair, or correction. This disclaimer of warranty constitutes an   *\n*  essential part of this License. No use of any Covered Software is   *\n*  authorized under this License except under this disclaimer.         *\n*                                                                      *\n************************************************************************\n\n************************************************************************\n*                                                                      *\n*  7. Limitation of Liability                                          *\n*  --------------------------                                          *\n*                                                                      *\n*  Under no circumstances and under no legal theory, whether tort      *\n*  (including negligence), contract, or otherwise, shall any           *\n*  Contributor, or anyone who distributes Covered Software as          *\n*  permitted above, be liable to You for any direct, indirect,         *\n*  special, incidental, or consequential damages of any character      *\n*  including, without limitation, damages for lost profits, loss of    *\n*  goodwill, work stoppage, computer failure or malfunction, or any    *\n*  and all other commercial damages or losses, even if such party      *\n*  shall have been informed of the possibility of such damages. This   *\n*  limitation of liability shall not apply to liability for death or   *\n*  personal injury resulting from such party's negligence to the       *\n*  extent applicable law prohibits such limitation. Some               *\n*  jurisdictions do not allow the exclusion or limitation of           *\n*  incidental or consequential damages, so this exclusion and          *\n*  limitation may not apply to You.                                    *\n*                                                                      *\n************************************************************************\n\n8. Litigation\n-------------\n\nAny litigation relating to this License may be brought only in the\ncourts of a jurisdiction where the defendant maintains its principal\nplace of business and such litigation shall be governed by laws of that\njurisdiction, without reference to its conflict-of-law provisions.\nNothing in this Section shall prevent a party's ability to bring\ncross-claims or counter-claims.\n\n9. Miscellaneous\n----------------\n\nThis License represents the complete agreement concerning the subject\nmatter hereof. If any provision of this License is held to be\nunenforceable, such provision shall be reformed only to the extent\nnecessary to make it enforceable. Any law or regulation which provides\nthat the language of a contract shall be construed against the drafter\nshall not be used to construe this License against a Contributor.\n\n10. Versions of the License\n---------------------------\n\n10.1. New Versions\n\nMozilla Foundation is the license steward. Except as provided in Section\n10.3, no one other than the license steward has the right to modify or\npublish new versions of this License. Each version will be given a\ndistinguishing version number.\n\n10.2. Effect of New Versions\n\nYou may distribute the Covered Software under the terms of the version\nof the License under which You originally received the Covered Software,\nor under the terms of any subsequent version published by the license\nsteward.\n\n10.3. Modified Versions\n\nIf you create software not governed by this License, and you want to\ncreate a new license for such software, you may create and use a\nmodified version of this License if you rename the license and remove\nany references to the name of the license steward (except to note that\nsuch modified license differs from this License).\n\n10.4. Distributing Source Code Form that is Incompatible With Secondary\nLicenses\n\nIf You choose to distribute Source Code Form that is Incompatible With\nSecondary Licenses under the terms of this version of the License, the\nnotice described in Exhibit B of this License must be attached.\n\nExhibit A - Source Code Form License Notice\n-------------------------------------------\n\n  This Source Code Form is subject to the terms of the Mozilla Public\n  License, v. 2.0. If a copy of the MPL was not distributed with this\n  file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\nIf it is not possible or desirable to put the notice in a particular\nfile, then You may include the notice in a location (such as a LICENSE\nfile in a relevant directory) where a recipient would be likely to look\nfor such a notice.\n\nYou may add additional accurate notices of copyright ownership.\n\nExhibit B - \"Incompatible With Secondary Licenses\" Notice\n---------------------------------------------------------\n\n  This Source Code Form is \"Incompatible With Secondary Licenses\", as\n  defined by the Mozilla Public License, v. 2.0.\n"
  },
  {
    "path": "include/eigen3/COPYING.README",
    "content": "Eigen is primarily MPL2 licensed. See COPYING.MPL2 and these links:\n  http://www.mozilla.org/MPL/2.0/\n  http://www.mozilla.org/MPL/2.0/FAQ.html\n\nSome files contain third-party code under BSD or LGPL licenses, whence the other\nCOPYING.* files here.\n\nAll the LGPL code is either LGPL 2.1-only, or LGPL 2.1-or-later.\nFor this reason, the COPYING.LGPL file contains the LGPL 2.1 text.\n\nIf you want to guarantee that the Eigen code that you are #including is licensed\nunder the MPL2 and possibly more permissive licenses (like BSD), #define this\npreprocessor symbol:\n  EIGEN_MPL2_ONLY\nFor example, with most compilers, you could add this to your project CXXFLAGS:\n  -DEIGEN_MPL2_ONLY\nThis will cause a compilation error to be generated if you #include any code that is\nLGPL licensed.\n"
  },
  {
    "path": "include/eigen3/CTestConfig.cmake",
    "content": "## This file should be placed in the root directory of your project.\n## Then modify the CMakeLists.txt file in the root directory of your\n## project to incorporate the testing dashboard.\n## # The following are required to uses Dart and the Cdash dashboard\n##   ENABLE_TESTING()\n##   INCLUDE(CTest)\nset(CTEST_PROJECT_NAME \"Eigen 3.3\")\nset(CTEST_NIGHTLY_START_TIME \"00:00:00 UTC\")\n\nset(CTEST_DROP_METHOD \"http\")\nset(CTEST_DROP_SITE \"manao.inria.fr\")\nset(CTEST_DROP_LOCATION \"/CDash/submit.php?project=Eigen+3.3\")\nset(CTEST_DROP_SITE_CDASH TRUE)\n"
  },
  {
    "path": "include/eigen3/CTestCustom.cmake.in",
    "content": "\nset(CTEST_CUSTOM_MAXIMUM_NUMBER_OF_WARNINGS \"2000\")\nset(CTEST_CUSTOM_MAXIMUM_NUMBER_OF_ERRORS   \"2000\")\n"
  },
  {
    "path": "include/eigen3/Eigen/CMakeLists.txt",
    "content": "include(RegexUtils)\ntest_escape_string_as_regex()\n\nfile(GLOB Eigen_directory_files \"*\")\n\nescape_string_as_regex(ESCAPED_CMAKE_CURRENT_SOURCE_DIR \"${CMAKE_CURRENT_SOURCE_DIR}\")\n\nforeach(f ${Eigen_directory_files})\n  if(NOT f MATCHES \"\\\\.txt\" AND NOT f MATCHES \"${ESCAPED_CMAKE_CURRENT_SOURCE_DIR}/[.].+\" AND NOT f MATCHES \"${ESCAPED_CMAKE_CURRENT_SOURCE_DIR}/src\")\n    list(APPEND Eigen_directory_files_to_install ${f})\n  endif()\nendforeach(f ${Eigen_directory_files})\n\ninstall(FILES\n  ${Eigen_directory_files_to_install}\n  DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen COMPONENT Devel\n  )\n\ninstall(DIRECTORY src DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen COMPONENT Devel FILES_MATCHING PATTERN \"*.h\")\n"
  },
  {
    "path": "include/eigen3/Eigen/Cholesky",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CHOLESKY_MODULE_H\n#define EIGEN_CHOLESKY_MODULE_H\n\n#include \"Core\"\n#include \"Jacobi\"\n\n#include \"src/Core/util/DisableStupidWarnings.h\"\n\n/** \\defgroup Cholesky_Module Cholesky module\n  *\n  *\n  *\n  * This module provides two variants of the Cholesky decomposition for selfadjoint (hermitian) matrices.\n  * Those decompositions are also accessible via the following methods:\n  *  - MatrixBase::llt()\n  *  - MatrixBase::ldlt()\n  *  - SelfAdjointView::llt()\n  *  - SelfAdjointView::ldlt()\n  *\n  * \\code\n  * #include <Eigen/Cholesky>\n  * \\endcode\n  */\n\n#include \"src/Cholesky/LLT.h\"\n#include \"src/Cholesky/LDLT.h\"\n#ifdef EIGEN_USE_LAPACKE\n#ifdef EIGEN_USE_MKL\n#include \"mkl_lapacke.h\"\n#else\n#include \"src/misc/lapacke.h\"\n#endif\n#include \"src/Cholesky/LLT_LAPACKE.h\"\n#endif\n\n#include \"src/Core/util/ReenableStupidWarnings.h\"\n\n#endif // EIGEN_CHOLESKY_MODULE_H\n/* vim: set filetype=cpp et sw=2 ts=2 ai: */\n"
  },
  {
    "path": "include/eigen3/Eigen/CholmodSupport",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CHOLMODSUPPORT_MODULE_H\n#define EIGEN_CHOLMODSUPPORT_MODULE_H\n\n#include \"SparseCore\"\n\n#include \"src/Core/util/DisableStupidWarnings.h\"\n\nextern \"C\" {\n  #include <cholmod.h>\n}\n\n/** \\ingroup Support_modules\n  * \\defgroup CholmodSupport_Module CholmodSupport module\n  *\n  * This module provides an interface to the Cholmod library which is part of the <a href=\"http://www.suitesparse.com\">suitesparse</a> package.\n  * It provides the two following main factorization classes:\n  * - class CholmodSupernodalLLT: a supernodal LLT Cholesky factorization.\n  * - class CholmodDecomposiiton: a general L(D)LT Cholesky factorization with automatic or explicit runtime selection of the underlying factorization method (supernodal or simplicial).\n  *\n  * For the sake of completeness, this module also propose the two following classes:\n  * - class CholmodSimplicialLLT\n  * - class CholmodSimplicialLDLT\n  * Note that these classes does not bring any particular advantage compared to the built-in\n  * SimplicialLLT and SimplicialLDLT factorization classes.\n  *\n  * \\code\n  * #include <Eigen/CholmodSupport>\n  * \\endcode\n  *\n  * In order to use this module, the cholmod headers must be accessible from the include paths, and your binary must be linked to the cholmod library and its dependencies.\n  * The dependencies depend on how cholmod has been compiled.\n  * For a cmake based project, you can use our FindCholmod.cmake module to help you in this task.\n  *\n  */\n\n#include \"src/CholmodSupport/CholmodSupport.h\"\n\n#include \"src/Core/util/ReenableStupidWarnings.h\"\n\n#endif // EIGEN_CHOLMODSUPPORT_MODULE_H\n\n"
  },
  {
    "path": "include/eigen3/Eigen/Core",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2007-2011 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CORE_H\n#define EIGEN_CORE_H\n\n// first thing Eigen does: stop the compiler from committing suicide\n#include \"src/Core/util/DisableStupidWarnings.h\"\n\n#if defined(__CUDACC__) && !defined(EIGEN_NO_CUDA)\n  #define EIGEN_CUDACC __CUDACC__\n#endif\n\n#if defined(__CUDA_ARCH__) && !defined(EIGEN_NO_CUDA)\n  #define EIGEN_CUDA_ARCH __CUDA_ARCH__\n#endif\n\n#if defined(__CUDACC_VER_MAJOR__) && (__CUDACC_VER_MAJOR__ >= 9)\n#define EIGEN_CUDACC_VER  ((__CUDACC_VER_MAJOR__ * 10000) + (__CUDACC_VER_MINOR__ * 100))\n#elif defined(__CUDACC_VER__)\n#define EIGEN_CUDACC_VER __CUDACC_VER__\n#else\n#define EIGEN_CUDACC_VER 0\n#endif\n\n// Handle NVCC/CUDA/SYCL\n#if defined(__CUDACC__) || defined(__SYCL_DEVICE_ONLY__)\n  // Do not try asserts on CUDA and SYCL!\n  #ifndef EIGEN_NO_DEBUG\n  #define EIGEN_NO_DEBUG\n  #endif\n\n  #ifdef EIGEN_INTERNAL_DEBUGGING\n  #undef EIGEN_INTERNAL_DEBUGGING\n  #endif\n\n  #ifdef EIGEN_EXCEPTIONS\n  #undef EIGEN_EXCEPTIONS\n  #endif\n\n  // All functions callable from CUDA code must be qualified with __device__\n  #ifdef __CUDACC__\n    // Do not try to vectorize on CUDA and SYCL!\n    #ifndef EIGEN_DONT_VECTORIZE\n    #define EIGEN_DONT_VECTORIZE\n    #endif\n\n    #define EIGEN_DEVICE_FUNC __host__ __device__\n    // We need math_functions.hpp to ensure that that EIGEN_USING_STD_MATH macro\n    // works properly on the device side\n    #include <math_functions.hpp>\n  #else\n    #define EIGEN_DEVICE_FUNC\n  #endif\n\n#else\n  #define EIGEN_DEVICE_FUNC\n\n#endif\n\n// When compiling CUDA device code with NVCC, pull in math functions from the\n// global namespace.  In host mode, and when device doee with clang, use the\n// std versions.\n#if defined(__CUDA_ARCH__) && defined(__NVCC__)\n  #define EIGEN_USING_STD_MATH(FUNC) using ::FUNC;\n#else\n  #define EIGEN_USING_STD_MATH(FUNC) using std::FUNC;\n#endif\n\n#if (defined(_CPPUNWIND) || defined(__EXCEPTIONS)) && !defined(__CUDA_ARCH__) && !defined(EIGEN_EXCEPTIONS) && !defined(EIGEN_USE_SYCL)\n  #define EIGEN_EXCEPTIONS\n#endif\n\n#ifdef EIGEN_EXCEPTIONS\n  #include <new>\n#endif\n\n// then include this file where all our macros are defined. It's really important to do it first because\n// it's where we do all the alignment settings (platform detection and honoring the user's will if he\n// defined e.g. EIGEN_DONT_ALIGN) so it needs to be done before we do anything with vectorization.\n#include \"src/Core/util/Macros.h\"\n\n// Disable the ipa-cp-clone optimization flag with MinGW 6.x or newer (enabled by default with -O3)\n// See http://eigen.tuxfamily.org/bz/show_bug.cgi?id=556 for details.\n#if EIGEN_COMP_MINGW && EIGEN_GNUC_AT_LEAST(4,6)\n  #pragma GCC optimize (\"-fno-ipa-cp-clone\")\n#endif\n\n#include <complex>\n\n// this include file manages BLAS and MKL related macros\n// and inclusion of their respective header files\n#include \"src/Core/util/MKL_support.h\"\n\n// if alignment is disabled, then disable vectorization. Note: EIGEN_MAX_ALIGN_BYTES is the proper check, it takes into\n// account both the user's will (EIGEN_MAX_ALIGN_BYTES,EIGEN_DONT_ALIGN) and our own platform checks\n#if EIGEN_MAX_ALIGN_BYTES==0\n  #ifndef EIGEN_DONT_VECTORIZE\n    #define EIGEN_DONT_VECTORIZE\n  #endif\n#endif\n\n#if EIGEN_COMP_MSVC\n  #include <malloc.h> // for _aligned_malloc -- need it regardless of whether vectorization is enabled\n  #if (EIGEN_COMP_MSVC >= 1500) // 2008 or later\n    // Remember that usage of defined() in a #define is undefined by the standard.\n    // a user reported that in 64-bit mode, MSVC doesn't care to define _M_IX86_FP.\n    #if (defined(_M_IX86_FP) && (_M_IX86_FP >= 2)) || EIGEN_ARCH_x86_64\n      #define EIGEN_SSE2_ON_MSVC_2008_OR_LATER\n    #endif\n  #endif\n#else\n  // Remember that usage of defined() in a #define is undefined by the standard\n  #if (defined __SSE2__) && ( (!EIGEN_COMP_GNUC) || EIGEN_COMP_ICC || EIGEN_GNUC_AT_LEAST(4,2) )\n    #define EIGEN_SSE2_ON_NON_MSVC_BUT_NOT_OLD_GCC\n  #endif\n#endif\n\n#ifndef EIGEN_DONT_VECTORIZE\n\n  #if defined (EIGEN_SSE2_ON_NON_MSVC_BUT_NOT_OLD_GCC) || defined(EIGEN_SSE2_ON_MSVC_2008_OR_LATER)\n\n    // Defines symbols for compile-time detection of which instructions are\n    // used.\n    // EIGEN_VECTORIZE_YY is defined if and only if the instruction set YY is used\n    #define EIGEN_VECTORIZE\n    #define EIGEN_VECTORIZE_SSE\n    #define EIGEN_VECTORIZE_SSE2\n\n    // Detect sse3/ssse3/sse4:\n    // gcc and icc defines __SSE3__, ...\n    // there is no way to know about this on msvc. You can define EIGEN_VECTORIZE_SSE* if you\n    // want to force the use of those instructions with msvc.\n    #ifdef __SSE3__\n      #define EIGEN_VECTORIZE_SSE3\n    #endif\n    #ifdef __SSSE3__\n      #define EIGEN_VECTORIZE_SSSE3\n    #endif\n    #ifdef __SSE4_1__\n      #define EIGEN_VECTORIZE_SSE4_1\n    #endif\n    #ifdef __SSE4_2__\n      #define EIGEN_VECTORIZE_SSE4_2\n    #endif\n    #ifdef __AVX__\n      #define EIGEN_VECTORIZE_AVX\n      #define EIGEN_VECTORIZE_SSE3\n      #define EIGEN_VECTORIZE_SSSE3\n      #define EIGEN_VECTORIZE_SSE4_1\n      #define EIGEN_VECTORIZE_SSE4_2\n    #endif\n    #ifdef __AVX2__\n      #define EIGEN_VECTORIZE_AVX2\n    #endif\n    #ifdef __FMA__\n      #define EIGEN_VECTORIZE_FMA\n    #endif\n    #if defined(__AVX512F__) && defined(EIGEN_ENABLE_AVX512)\n      #define EIGEN_VECTORIZE_AVX512\n      #define EIGEN_VECTORIZE_AVX2\n      #define EIGEN_VECTORIZE_AVX\n      #define EIGEN_VECTORIZE_FMA\n      #ifdef __AVX512DQ__\n        #define EIGEN_VECTORIZE_AVX512DQ\n      #endif\n      #ifdef __AVX512ER__\n        #define EIGEN_VECTORIZE_AVX512ER\n      #endif\n    #endif\n\n    // include files\n\n    // This extern \"C\" works around a MINGW-w64 compilation issue\n    // https://sourceforge.net/tracker/index.php?func=detail&aid=3018394&group_id=202880&atid=983354\n    // In essence, intrin.h is included by windows.h and also declares intrinsics (just as emmintrin.h etc. below do).\n    // However, intrin.h uses an extern \"C\" declaration, and g++ thus complains of duplicate declarations\n    // with conflicting linkage.  The linkage for intrinsics doesn't matter, but at that stage the compiler doesn't know;\n    // so, to avoid compile errors when windows.h is included after Eigen/Core, ensure intrinsics are extern \"C\" here too.\n    // notice that since these are C headers, the extern \"C\" is theoretically needed anyways.\n    extern \"C\" {\n      // In theory we should only include immintrin.h and not the other *mmintrin.h header files directly.\n      // Doing so triggers some issues with ICC. However old gcc versions seems to not have this file, thus:\n      #if EIGEN_COMP_ICC >= 1110\n        #include <immintrin.h>\n      #else\n        #include <mmintrin.h>\n        #include <emmintrin.h>\n        #include <xmmintrin.h>\n        #ifdef  EIGEN_VECTORIZE_SSE3\n        #include <pmmintrin.h>\n        #endif\n        #ifdef EIGEN_VECTORIZE_SSSE3\n        #include <tmmintrin.h>\n        #endif\n        #ifdef EIGEN_VECTORIZE_SSE4_1\n        #include <smmintrin.h>\n        #endif\n        #ifdef EIGEN_VECTORIZE_SSE4_2\n        #include <nmmintrin.h>\n        #endif\n        #if defined(EIGEN_VECTORIZE_AVX) || defined(EIGEN_VECTORIZE_AVX512)\n        #include <immintrin.h>\n        #endif\n      #endif\n    } // end extern \"C\"\n  #elif defined __VSX__\n    #define EIGEN_VECTORIZE\n    #define EIGEN_VECTORIZE_VSX\n    #include <altivec.h>\n    // We need to #undef all these ugly tokens defined in <altivec.h>\n    // => use __vector instead of vector\n    #undef bool\n    #undef vector\n    #undef pixel\n  #elif defined __ALTIVEC__\n    #define EIGEN_VECTORIZE\n    #define EIGEN_VECTORIZE_ALTIVEC\n    #include <altivec.h>\n    // We need to #undef all these ugly tokens defined in <altivec.h>\n    // => use __vector instead of vector\n    #undef bool\n    #undef vector\n    #undef pixel\n  #elif (defined  __ARM_NEON) || (defined __ARM_NEON__)\n    #define EIGEN_VECTORIZE\n    #define EIGEN_VECTORIZE_NEON\n    #include <arm_neon.h>\n  #elif (defined __s390x__ && defined __VEC__)\n    #define EIGEN_VECTORIZE\n    #define EIGEN_VECTORIZE_ZVECTOR\n    #include <vecintrin.h>\n  #endif\n#endif\n\n#if defined(__F16C__) && !defined(EIGEN_COMP_CLANG)\n  // We can use the optimized fp16 to float and float to fp16 conversion routines\n  #define EIGEN_HAS_FP16_C\n#endif\n\n#if defined __CUDACC__\n  #define EIGEN_VECTORIZE_CUDA\n  #include <vector_types.h>\n  #if EIGEN_CUDACC_VER >= 70500\n    #define EIGEN_HAS_CUDA_FP16\n  #endif\n#endif\n\n#if defined EIGEN_HAS_CUDA_FP16\n  #include <host_defines.h>\n  #include <cuda_fp16.h>\n#endif\n\n#if (defined _OPENMP) && (!defined EIGEN_DONT_PARALLELIZE)\n  #define EIGEN_HAS_OPENMP\n#endif\n\n#ifdef EIGEN_HAS_OPENMP\n#include <omp.h>\n#endif\n\n// MSVC for windows mobile does not have the errno.h file\n#if !(EIGEN_COMP_MSVC && EIGEN_OS_WINCE) && !EIGEN_COMP_ARM\n#define EIGEN_HAS_ERRNO\n#endif\n\n#ifdef EIGEN_HAS_ERRNO\n#include <cerrno>\n#endif\n#include <cstddef>\n#include <cstdlib>\n#include <cmath>\n#include <cassert>\n#include <functional>\n#include <iosfwd>\n#include <cstring>\n#include <string>\n#include <limits>\n#include <climits> // for CHAR_BIT\n// for min/max:\n#include <algorithm>\n\n// for std::is_nothrow_move_assignable\n#ifdef EIGEN_INCLUDE_TYPE_TRAITS\n#include <type_traits>\n#endif\n\n// for outputting debug info\n#ifdef EIGEN_DEBUG_ASSIGN\n#include <iostream>\n#endif\n\n// required for __cpuid, needs to be included after cmath\n#if EIGEN_COMP_MSVC && EIGEN_ARCH_i386_OR_x86_64 && !EIGEN_OS_WINCE\n  #include <intrin.h>\n#endif\n\n/** \\brief Namespace containing all symbols from the %Eigen library. */\nnamespace Eigen {\n\ninline static const char *SimdInstructionSetsInUse(void) {\n#if defined(EIGEN_VECTORIZE_AVX512)\n  return \"AVX512, FMA, AVX2, AVX, SSE, SSE2, SSE3, SSSE3, SSE4.1, SSE4.2\";\n#elif defined(EIGEN_VECTORIZE_AVX)\n  return \"AVX SSE, SSE2, SSE3, SSSE3, SSE4.1, SSE4.2\";\n#elif defined(EIGEN_VECTORIZE_SSE4_2)\n  return \"SSE, SSE2, SSE3, SSSE3, SSE4.1, SSE4.2\";\n#elif defined(EIGEN_VECTORIZE_SSE4_1)\n  return \"SSE, SSE2, SSE3, SSSE3, SSE4.1\";\n#elif defined(EIGEN_VECTORIZE_SSSE3)\n  return \"SSE, SSE2, SSE3, SSSE3\";\n#elif defined(EIGEN_VECTORIZE_SSE3)\n  return \"SSE, SSE2, SSE3\";\n#elif defined(EIGEN_VECTORIZE_SSE2)\n  return \"SSE, SSE2\";\n#elif defined(EIGEN_VECTORIZE_ALTIVEC)\n  return \"AltiVec\";\n#elif defined(EIGEN_VECTORIZE_VSX)\n  return \"VSX\";\n#elif defined(EIGEN_VECTORIZE_NEON)\n  return \"ARM NEON\";\n#elif defined(EIGEN_VECTORIZE_ZVECTOR)\n  return \"S390X ZVECTOR\";\n#else\n  return \"None\";\n#endif\n}\n\n} // end namespace Eigen\n\n#if defined EIGEN2_SUPPORT_STAGE40_FULL_EIGEN3_STRICTNESS || defined EIGEN2_SUPPORT_STAGE30_FULL_EIGEN3_API || defined EIGEN2_SUPPORT_STAGE20_RESOLVE_API_CONFLICTS || defined EIGEN2_SUPPORT_STAGE10_FULL_EIGEN2_API || defined EIGEN2_SUPPORT\n// This will generate an error message:\n#error Eigen2-support is only available up to version 3.2. Please go to \"http://eigen.tuxfamily.org/index.php?title=Eigen2\" for further information\n#endif\n\nnamespace Eigen {\n\n// we use size_t frequently and we'll never remember to prepend it with std:: everytime just to\n// ensure QNX/QCC support\nusing std::size_t;\n// gcc 4.6.0 wants std:: for ptrdiff_t\nusing std::ptrdiff_t;\n\n}\n\n/** \\defgroup Core_Module Core module\n  * This is the main module of Eigen providing dense matrix and vector support\n  * (both fixed and dynamic size) with all the features corresponding to a BLAS library\n  * and much more...\n  *\n  * \\code\n  * #include <Eigen/Core>\n  * \\endcode\n  */\n\n#include \"src/Core/util/Constants.h\"\n#include \"src/Core/util/Meta.h\"\n#include \"src/Core/util/ForwardDeclarations.h\"\n#include \"src/Core/util/StaticAssert.h\"\n#include \"src/Core/util/XprHelper.h\"\n#include \"src/Core/util/Memory.h\"\n\n#include \"src/Core/NumTraits.h\"\n#include \"src/Core/MathFunctions.h\"\n#include \"src/Core/GenericPacketMath.h\"\n#include \"src/Core/MathFunctionsImpl.h\"\n#include \"src/Core/arch/Default/ConjHelper.h\"\n\n#if defined EIGEN_VECTORIZE_AVX512\n  #include \"src/Core/arch/SSE/PacketMath.h\"\n  #include \"src/Core/arch/AVX/PacketMath.h\"\n  #include \"src/Core/arch/AVX512/PacketMath.h\"\n  #include \"src/Core/arch/AVX512/MathFunctions.h\"\n#elif defined EIGEN_VECTORIZE_AVX\n  // Use AVX for floats and doubles, SSE for integers\n  #include \"src/Core/arch/SSE/PacketMath.h\"\n  #include \"src/Core/arch/SSE/Complex.h\"\n  #include \"src/Core/arch/SSE/MathFunctions.h\"\n  #include \"src/Core/arch/AVX/PacketMath.h\"\n  #include \"src/Core/arch/AVX/MathFunctions.h\"\n  #include \"src/Core/arch/AVX/Complex.h\"\n  #include \"src/Core/arch/AVX/TypeCasting.h\"\n  #include \"src/Core/arch/SSE/TypeCasting.h\"\n#elif defined EIGEN_VECTORIZE_SSE\n  #include \"src/Core/arch/SSE/PacketMath.h\"\n  #include \"src/Core/arch/SSE/MathFunctions.h\"\n  #include \"src/Core/arch/SSE/Complex.h\"\n  #include \"src/Core/arch/SSE/TypeCasting.h\"\n#elif defined(EIGEN_VECTORIZE_ALTIVEC) || defined(EIGEN_VECTORIZE_VSX)\n  #include \"src/Core/arch/AltiVec/PacketMath.h\"\n  #include \"src/Core/arch/AltiVec/MathFunctions.h\"\n  #include \"src/Core/arch/AltiVec/Complex.h\"\n#elif defined EIGEN_VECTORIZE_NEON\n  #include \"src/Core/arch/NEON/PacketMath.h\"\n  #include \"src/Core/arch/NEON/MathFunctions.h\"\n  #include \"src/Core/arch/NEON/Complex.h\"\n#elif defined EIGEN_VECTORIZE_ZVECTOR\n  #include \"src/Core/arch/ZVector/PacketMath.h\"\n  #include \"src/Core/arch/ZVector/MathFunctions.h\"\n  #include \"src/Core/arch/ZVector/Complex.h\"\n#endif\n\n// Half float support\n#include \"src/Core/arch/CUDA/Half.h\"\n#include \"src/Core/arch/CUDA/PacketMathHalf.h\"\n#include \"src/Core/arch/CUDA/TypeCasting.h\"\n\n#if defined EIGEN_VECTORIZE_CUDA\n  #include \"src/Core/arch/CUDA/PacketMath.h\"\n  #include \"src/Core/arch/CUDA/MathFunctions.h\"\n#endif\n\n#include \"src/Core/arch/Default/Settings.h\"\n\n#include \"src/Core/functors/TernaryFunctors.h\"\n#include \"src/Core/functors/BinaryFunctors.h\"\n#include \"src/Core/functors/UnaryFunctors.h\"\n#include \"src/Core/functors/NullaryFunctors.h\"\n#include \"src/Core/functors/StlFunctors.h\"\n#include \"src/Core/functors/AssignmentFunctors.h\"\n\n// Specialized functors to enable the processing of complex numbers\n// on CUDA devices\n#include \"src/Core/arch/CUDA/Complex.h\"\n\n#include \"src/Core/IO.h\"\n#include \"src/Core/DenseCoeffsBase.h\"\n#include \"src/Core/DenseBase.h\"\n#include \"src/Core/MatrixBase.h\"\n#include \"src/Core/EigenBase.h\"\n\n#include \"src/Core/Product.h\"\n#include \"src/Core/CoreEvaluators.h\"\n#include \"src/Core/AssignEvaluator.h\"\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN // work around Doxygen bug triggered by Assign.h r814874\n                                // at least confirmed with Doxygen 1.5.5 and 1.5.6\n  #include \"src/Core/Assign.h\"\n#endif\n\n#include \"src/Core/ArrayBase.h\"\n#include \"src/Core/util/BlasUtil.h\"\n#include \"src/Core/DenseStorage.h\"\n#include \"src/Core/NestByValue.h\"\n\n// #include \"src/Core/ForceAlignedAccess.h\"\n\n#include \"src/Core/ReturnByValue.h\"\n#include \"src/Core/NoAlias.h\"\n#include \"src/Core/PlainObjectBase.h\"\n#include \"src/Core/Matrix.h\"\n#include \"src/Core/Array.h\"\n#include \"src/Core/CwiseTernaryOp.h\"\n#include \"src/Core/CwiseBinaryOp.h\"\n#include \"src/Core/CwiseUnaryOp.h\"\n#include \"src/Core/CwiseNullaryOp.h\"\n#include \"src/Core/CwiseUnaryView.h\"\n#include \"src/Core/SelfCwiseBinaryOp.h\"\n#include \"src/Core/Dot.h\"\n#include \"src/Core/StableNorm.h\"\n#include \"src/Core/Stride.h\"\n#include \"src/Core/MapBase.h\"\n#include \"src/Core/Map.h\"\n#include \"src/Core/Ref.h\"\n#include \"src/Core/Block.h\"\n#include \"src/Core/VectorBlock.h\"\n#include \"src/Core/Transpose.h\"\n#include \"src/Core/DiagonalMatrix.h\"\n#include \"src/Core/Diagonal.h\"\n#include \"src/Core/DiagonalProduct.h\"\n#include \"src/Core/Redux.h\"\n#include \"src/Core/Visitor.h\"\n#include \"src/Core/Fuzzy.h\"\n#include \"src/Core/Swap.h\"\n#include \"src/Core/CommaInitializer.h\"\n#include \"src/Core/GeneralProduct.h\"\n#include \"src/Core/Solve.h\"\n#include \"src/Core/Inverse.h\"\n#include \"src/Core/SolverBase.h\"\n#include \"src/Core/PermutationMatrix.h\"\n#include \"src/Core/Transpositions.h\"\n#include \"src/Core/TriangularMatrix.h\"\n#include \"src/Core/SelfAdjointView.h\"\n#include \"src/Core/products/GeneralBlockPanelKernel.h\"\n#include \"src/Core/products/Parallelizer.h\"\n#include \"src/Core/ProductEvaluators.h\"\n#include \"src/Core/products/GeneralMatrixVector.h\"\n#include \"src/Core/products/GeneralMatrixMatrix.h\"\n#include \"src/Core/SolveTriangular.h\"\n#include \"src/Core/products/GeneralMatrixMatrixTriangular.h\"\n#include \"src/Core/products/SelfadjointMatrixVector.h\"\n#include \"src/Core/products/SelfadjointMatrixMatrix.h\"\n#include \"src/Core/products/SelfadjointProduct.h\"\n#include \"src/Core/products/SelfadjointRank2Update.h\"\n#include \"src/Core/products/TriangularMatrixVector.h\"\n#include \"src/Core/products/TriangularMatrixMatrix.h\"\n#include \"src/Core/products/TriangularSolverMatrix.h\"\n#include \"src/Core/products/TriangularSolverVector.h\"\n#include \"src/Core/BandMatrix.h\"\n#include \"src/Core/CoreIterators.h\"\n#include \"src/Core/ConditionEstimator.h\"\n\n#include \"src/Core/BooleanRedux.h\"\n#include \"src/Core/Select.h\"\n#include \"src/Core/VectorwiseOp.h\"\n#include \"src/Core/Random.h\"\n#include \"src/Core/Replicate.h\"\n#include \"src/Core/Reverse.h\"\n#include \"src/Core/ArrayWrapper.h\"\n\n#ifdef EIGEN_USE_BLAS\n#include \"src/Core/products/GeneralMatrixMatrix_BLAS.h\"\n#include \"src/Core/products/GeneralMatrixVector_BLAS.h\"\n#include \"src/Core/products/GeneralMatrixMatrixTriangular_BLAS.h\"\n#include \"src/Core/products/SelfadjointMatrixMatrix_BLAS.h\"\n#include \"src/Core/products/SelfadjointMatrixVector_BLAS.h\"\n#include \"src/Core/products/TriangularMatrixMatrix_BLAS.h\"\n#include \"src/Core/products/TriangularMatrixVector_BLAS.h\"\n#include \"src/Core/products/TriangularSolverMatrix_BLAS.h\"\n#endif // EIGEN_USE_BLAS\n\n#ifdef EIGEN_USE_MKL_VML\n#include \"src/Core/Assign_MKL.h\"\n#endif\n\n#include \"src/Core/GlobalFunctions.h\"\n\n#include \"src/Core/util/ReenableStupidWarnings.h\"\n\n#endif // EIGEN_CORE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/Dense",
    "content": "#include \"Core\"\n#include \"LU\"\n#include \"Cholesky\"\n#include \"QR\"\n#include \"SVD\"\n#include \"Geometry\"\n#include \"Eigenvalues\"\n"
  },
  {
    "path": "include/eigen3/Eigen/Eigen",
    "content": "#include \"Dense\"\n#include \"Sparse\"\n"
  },
  {
    "path": "include/eigen3/Eigen/Eigenvalues",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_EIGENVALUES_MODULE_H\n#define EIGEN_EIGENVALUES_MODULE_H\n\n#include \"Core\"\n\n#include \"src/Core/util/DisableStupidWarnings.h\"\n\n#include \"Cholesky\"\n#include \"Jacobi\"\n#include \"Householder\"\n#include \"LU\"\n#include \"Geometry\"\n\n/** \\defgroup Eigenvalues_Module Eigenvalues module\n  *\n  *\n  *\n  * This module mainly provides various eigenvalue solvers.\n  * This module also provides some MatrixBase methods, including:\n  *  - MatrixBase::eigenvalues(),\n  *  - MatrixBase::operatorNorm()\n  *\n  * \\code\n  * #include <Eigen/Eigenvalues>\n  * \\endcode\n  */\n\n#include \"src/misc/RealSvd2x2.h\"\n#include \"src/Eigenvalues/Tridiagonalization.h\"\n#include \"src/Eigenvalues/RealSchur.h\"\n#include \"src/Eigenvalues/EigenSolver.h\"\n#include \"src/Eigenvalues/SelfAdjointEigenSolver.h\"\n#include \"src/Eigenvalues/GeneralizedSelfAdjointEigenSolver.h\"\n#include \"src/Eigenvalues/HessenbergDecomposition.h\"\n#include \"src/Eigenvalues/ComplexSchur.h\"\n#include \"src/Eigenvalues/ComplexEigenSolver.h\"\n#include \"src/Eigenvalues/RealQZ.h\"\n#include \"src/Eigenvalues/GeneralizedEigenSolver.h\"\n#include \"src/Eigenvalues/MatrixBaseEigenvalues.h\"\n#ifdef EIGEN_USE_LAPACKE\n#ifdef EIGEN_USE_MKL\n#include \"mkl_lapacke.h\"\n#else\n#include \"src/misc/lapacke.h\"\n#endif\n#include \"src/Eigenvalues/RealSchur_LAPACKE.h\"\n#include \"src/Eigenvalues/ComplexSchur_LAPACKE.h\"\n#include \"src/Eigenvalues/SelfAdjointEigenSolver_LAPACKE.h\"\n#endif\n\n#include \"src/Core/util/ReenableStupidWarnings.h\"\n\n#endif // EIGEN_EIGENVALUES_MODULE_H\n/* vim: set filetype=cpp et sw=2 ts=2 ai: */\n"
  },
  {
    "path": "include/eigen3/Eigen/Geometry",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_GEOMETRY_MODULE_H\n#define EIGEN_GEOMETRY_MODULE_H\n\n#include \"Core\"\n\n#include \"src/Core/util/DisableStupidWarnings.h\"\n\n#include \"SVD\"\n#include \"LU\"\n#include <limits>\n\n/** \\defgroup Geometry_Module Geometry module\n  *\n  * This module provides support for:\n  *  - fixed-size homogeneous transformations\n  *  - translation, scaling, 2D and 3D rotations\n  *  - \\link Quaternion quaternions \\endlink\n  *  - cross products (\\ref MatrixBase::cross, \\ref MatrixBase::cross3)\n  *  - orthognal vector generation (\\ref MatrixBase::unitOrthogonal)\n  *  - some linear components: \\link ParametrizedLine parametrized-lines \\endlink and \\link Hyperplane hyperplanes \\endlink\n  *  - \\link AlignedBox axis aligned bounding boxes \\endlink\n  *  - \\link umeyama least-square transformation fitting \\endlink\n  *\n  * \\code\n  * #include <Eigen/Geometry>\n  * \\endcode\n  */\n\n#include \"src/Geometry/OrthoMethods.h\"\n#include \"src/Geometry/EulerAngles.h\"\n\n#include \"src/Geometry/Homogeneous.h\"\n#include \"src/Geometry/RotationBase.h\"\n#include \"src/Geometry/Rotation2D.h\"\n#include \"src/Geometry/Quaternion.h\"\n#include \"src/Geometry/AngleAxis.h\"\n#include \"src/Geometry/Transform.h\"\n#include \"src/Geometry/Translation.h\"\n#include \"src/Geometry/Scaling.h\"\n#include \"src/Geometry/Hyperplane.h\"\n#include \"src/Geometry/ParametrizedLine.h\"\n#include \"src/Geometry/AlignedBox.h\"\n#include \"src/Geometry/Umeyama.h\"\n\n// Use the SSE optimized version whenever possible. At the moment the\n// SSE version doesn't compile when AVX is enabled\n#if defined EIGEN_VECTORIZE_SSE && !defined EIGEN_VECTORIZE_AVX\n#include \"src/Geometry/arch/Geometry_SSE.h\"\n#endif\n\n#include \"src/Core/util/ReenableStupidWarnings.h\"\n\n#endif // EIGEN_GEOMETRY_MODULE_H\n/* vim: set filetype=cpp et sw=2 ts=2 ai: */\n\n"
  },
  {
    "path": "include/eigen3/Eigen/Householder",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_HOUSEHOLDER_MODULE_H\n#define EIGEN_HOUSEHOLDER_MODULE_H\n\n#include \"Core\"\n\n#include \"src/Core/util/DisableStupidWarnings.h\"\n\n/** \\defgroup Householder_Module Householder module\n  * This module provides Householder transformations.\n  *\n  * \\code\n  * #include <Eigen/Householder>\n  * \\endcode\n  */\n\n#include \"src/Householder/Householder.h\"\n#include \"src/Householder/HouseholderSequence.h\"\n#include \"src/Householder/BlockHouseholder.h\"\n\n#include \"src/Core/util/ReenableStupidWarnings.h\"\n\n#endif // EIGEN_HOUSEHOLDER_MODULE_H\n/* vim: set filetype=cpp et sw=2 ts=2 ai: */\n"
  },
  {
    "path": "include/eigen3/Eigen/IterativeLinearSolvers",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_ITERATIVELINEARSOLVERS_MODULE_H\n#define EIGEN_ITERATIVELINEARSOLVERS_MODULE_H\n\n#include \"SparseCore\"\n#include \"OrderingMethods\"\n\n#include \"src/Core/util/DisableStupidWarnings.h\"\n\n/** \n  * \\defgroup IterativeLinearSolvers_Module IterativeLinearSolvers module\n  *\n  * This module currently provides iterative methods to solve problems of the form \\c A \\c x = \\c b, where \\c A is a squared matrix, usually very large and sparse.\n  * Those solvers are accessible via the following classes:\n  *  - ConjugateGradient for selfadjoint (hermitian) matrices,\n  *  - LeastSquaresConjugateGradient for rectangular least-square problems,\n  *  - BiCGSTAB for general square matrices.\n  *\n  * These iterative solvers are associated with some preconditioners:\n  *  - IdentityPreconditioner - not really useful\n  *  - DiagonalPreconditioner - also called Jacobi preconditioner, work very well on diagonal dominant matrices.\n  *  - IncompleteLUT - incomplete LU factorization with dual thresholding\n  *\n  * Such problems can also be solved using the direct sparse decomposition modules: SparseCholesky, CholmodSupport, UmfPackSupport, SuperLUSupport.\n  *\n    \\code\n    #include <Eigen/IterativeLinearSolvers>\n    \\endcode\n  */\n\n#include \"src/IterativeLinearSolvers/SolveWithGuess.h\"\n#include \"src/IterativeLinearSolvers/IterativeSolverBase.h\"\n#include \"src/IterativeLinearSolvers/BasicPreconditioners.h\"\n#include \"src/IterativeLinearSolvers/ConjugateGradient.h\"\n#include \"src/IterativeLinearSolvers/LeastSquareConjugateGradient.h\"\n#include \"src/IterativeLinearSolvers/BiCGSTAB.h\"\n#include \"src/IterativeLinearSolvers/IncompleteLUT.h\"\n#include \"src/IterativeLinearSolvers/IncompleteCholesky.h\"\n\n#include \"src/Core/util/ReenableStupidWarnings.h\"\n\n#endif // EIGEN_ITERATIVELINEARSOLVERS_MODULE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/Jacobi",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_JACOBI_MODULE_H\n#define EIGEN_JACOBI_MODULE_H\n\n#include \"Core\"\n\n#include \"src/Core/util/DisableStupidWarnings.h\"\n\n/** \\defgroup Jacobi_Module Jacobi module\n  * This module provides Jacobi and Givens rotations.\n  *\n  * \\code\n  * #include <Eigen/Jacobi>\n  * \\endcode\n  *\n  * In addition to listed classes, it defines the two following MatrixBase methods to apply a Jacobi or Givens rotation:\n  *  - MatrixBase::applyOnTheLeft()\n  *  - MatrixBase::applyOnTheRight().\n  */\n\n#include \"src/Jacobi/Jacobi.h\"\n\n#include \"src/Core/util/ReenableStupidWarnings.h\"\n\n#endif // EIGEN_JACOBI_MODULE_H\n/* vim: set filetype=cpp et sw=2 ts=2 ai: */\n\n"
  },
  {
    "path": "include/eigen3/Eigen/LU",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_LU_MODULE_H\n#define EIGEN_LU_MODULE_H\n\n#include \"Core\"\n\n#include \"src/Core/util/DisableStupidWarnings.h\"\n\n/** \\defgroup LU_Module LU module\n  * This module includes %LU decomposition and related notions such as matrix inversion and determinant.\n  * This module defines the following MatrixBase methods:\n  *  - MatrixBase::inverse()\n  *  - MatrixBase::determinant()\n  *\n  * \\code\n  * #include <Eigen/LU>\n  * \\endcode\n  */\n\n#include \"src/misc/Kernel.h\"\n#include \"src/misc/Image.h\"\n#include \"src/LU/FullPivLU.h\"\n#include \"src/LU/PartialPivLU.h\"\n#ifdef EIGEN_USE_LAPACKE\n#ifdef EIGEN_USE_MKL\n#include \"mkl_lapacke.h\"\n#else\n#include \"src/misc/lapacke.h\"\n#endif\n#include \"src/LU/PartialPivLU_LAPACKE.h\"\n#endif\n#include \"src/LU/Determinant.h\"\n#include \"src/LU/InverseImpl.h\"\n\n// Use the SSE optimized version whenever possible. At the moment the\n// SSE version doesn't compile when AVX is enabled\n#if defined EIGEN_VECTORIZE_SSE && !defined EIGEN_VECTORIZE_AVX\n  #include \"src/LU/arch/Inverse_SSE.h\"\n#endif\n\n#include \"src/Core/util/ReenableStupidWarnings.h\"\n\n#endif // EIGEN_LU_MODULE_H\n/* vim: set filetype=cpp et sw=2 ts=2 ai: */\n"
  },
  {
    "path": "include/eigen3/Eigen/MetisSupport",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_METISSUPPORT_MODULE_H\n#define EIGEN_METISSUPPORT_MODULE_H\n\n#include \"SparseCore\"\n\n#include \"src/Core/util/DisableStupidWarnings.h\"\n\nextern \"C\" {\n#include <metis.h>\n}\n\n\n/** \\ingroup Support_modules\n  * \\defgroup MetisSupport_Module MetisSupport module\n  *\n  * \\code\n  * #include <Eigen/MetisSupport>\n  * \\endcode\n  * This module defines an interface to the METIS reordering package (http://glaros.dtc.umn.edu/gkhome/views/metis). \n  * It can be used just as any other built-in method as explained in \\link OrderingMethods_Module here. \\endlink\n  */\n\n\n#include \"src/MetisSupport/MetisSupport.h\"\n\n#include \"src/Core/util/ReenableStupidWarnings.h\"\n\n#endif // EIGEN_METISSUPPORT_MODULE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/OrderingMethods",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_ORDERINGMETHODS_MODULE_H\n#define EIGEN_ORDERINGMETHODS_MODULE_H\n\n#include \"SparseCore\"\n\n#include \"src/Core/util/DisableStupidWarnings.h\"\n\n/** \n  * \\defgroup OrderingMethods_Module OrderingMethods module\n  *\n  * This module is currently for internal use only\n  * \n  * It defines various built-in and external ordering methods for sparse matrices. \n  * They are typically used to reduce the number of elements during \n  * the sparse matrix decomposition (LLT, LU, QR).\n  * Precisely, in a preprocessing step, a permutation matrix P is computed using \n  * those ordering methods and applied to the columns of the matrix. \n  * Using for instance the sparse Cholesky decomposition, it is expected that \n  * the nonzeros elements in LLT(A*P) will be much smaller than that in LLT(A).\n  * \n  * \n  * Usage : \n  * \\code\n  * #include <Eigen/OrderingMethods>\n  * \\endcode\n  * \n  * A simple usage is as a template parameter in the sparse decomposition classes : \n  * \n  * \\code \n  * SparseLU<MatrixType, COLAMDOrdering<int> > solver;\n  * \\endcode \n  * \n  * \\code \n  * SparseQR<MatrixType, COLAMDOrdering<int> > solver;\n  * \\endcode\n  * \n  * It is possible as well to call directly a particular ordering method for your own purpose, \n  * \\code \n  * AMDOrdering<int> ordering;\n  * PermutationMatrix<Dynamic, Dynamic, int> perm;\n  * SparseMatrix<double> A; \n  * //Fill the matrix ...\n  * \n  * ordering(A, perm); // Call AMD\n  * \\endcode\n  * \n  * \\note Some of these methods (like AMD or METIS), need the sparsity pattern \n  * of the input matrix to be symmetric. When the matrix is structurally unsymmetric, \n  * Eigen computes internally the pattern of \\f$A^T*A\\f$ before calling the method.\n  * If your matrix is already symmetric (at leat in structure), you can avoid that\n  * by calling the method with a SelfAdjointView type.\n  * \n  * \\code\n  *  // Call the ordering on the pattern of the lower triangular matrix A\n  * ordering(A.selfadjointView<Lower>(), perm);\n  * \\endcode\n  */\n\n#ifndef EIGEN_MPL2_ONLY\n#include \"src/OrderingMethods/Amd.h\"\n#endif\n\n#include \"src/OrderingMethods/Ordering.h\"\n#include \"src/Core/util/ReenableStupidWarnings.h\"\n\n#endif // EIGEN_ORDERINGMETHODS_MODULE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/PaStiXSupport",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_PASTIXSUPPORT_MODULE_H\n#define EIGEN_PASTIXSUPPORT_MODULE_H\n\n#include \"SparseCore\"\n\n#include \"src/Core/util/DisableStupidWarnings.h\"\n\nextern \"C\" {\n#include <pastix_nompi.h>\n#include <pastix.h>\n}\n\n#ifdef complex\n#undef complex\n#endif\n\n/** \\ingroup Support_modules\n  * \\defgroup PaStiXSupport_Module PaStiXSupport module\n  * \n  * This module provides an interface to the <a href=\"http://pastix.gforge.inria.fr/\">PaSTiX</a> library.\n  * PaSTiX is a general \\b supernodal, \\b parallel and \\b opensource sparse solver.\n  * It provides the two following main factorization classes:\n  * - class PastixLLT : a supernodal, parallel LLt Cholesky factorization.\n  * - class PastixLDLT: a supernodal, parallel LDLt Cholesky factorization.\n  * - class PastixLU : a supernodal, parallel LU factorization (optimized for a symmetric pattern).\n  * \n  * \\code\n  * #include <Eigen/PaStiXSupport>\n  * \\endcode\n  *\n  * In order to use this module, the PaSTiX headers must be accessible from the include paths, and your binary must be linked to the PaSTiX library and its dependencies.\n  * The dependencies depend on how PaSTiX has been compiled.\n  * For a cmake based project, you can use our FindPaSTiX.cmake module to help you in this task.\n  *\n  */\n\n#include \"src/PaStiXSupport/PaStiXSupport.h\"\n\n#include \"src/Core/util/ReenableStupidWarnings.h\"\n\n#endif // EIGEN_PASTIXSUPPORT_MODULE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/PardisoSupport",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_PARDISOSUPPORT_MODULE_H\n#define EIGEN_PARDISOSUPPORT_MODULE_H\n\n#include \"SparseCore\"\n\n#include \"src/Core/util/DisableStupidWarnings.h\"\n\n#include <mkl_pardiso.h>\n\n/** \\ingroup Support_modules\n  * \\defgroup PardisoSupport_Module PardisoSupport module\n  *\n  * This module brings support for the Intel(R) MKL PARDISO direct sparse solvers.\n  *\n  * \\code\n  * #include <Eigen/PardisoSupport>\n  * \\endcode\n  *\n  * In order to use this module, the MKL headers must be accessible from the include paths, and your binary must be linked to the MKL library and its dependencies.\n  * See this \\ref TopicUsingIntelMKL \"page\" for more information on MKL-Eigen integration.\n  * \n  */\n\n#include \"src/PardisoSupport/PardisoSupport.h\"\n\n#include \"src/Core/util/ReenableStupidWarnings.h\"\n\n#endif // EIGEN_PARDISOSUPPORT_MODULE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/QR",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_QR_MODULE_H\n#define EIGEN_QR_MODULE_H\n\n#include \"Core\"\n\n#include \"src/Core/util/DisableStupidWarnings.h\"\n\n#include \"Cholesky\"\n#include \"Jacobi\"\n#include \"Householder\"\n\n/** \\defgroup QR_Module QR module\n  *\n  *\n  *\n  * This module provides various QR decompositions\n  * This module also provides some MatrixBase methods, including:\n  *  - MatrixBase::householderQr()\n  *  - MatrixBase::colPivHouseholderQr()\n  *  - MatrixBase::fullPivHouseholderQr()\n  *\n  * \\code\n  * #include <Eigen/QR>\n  * \\endcode\n  */\n\n#include \"src/QR/HouseholderQR.h\"\n#include \"src/QR/FullPivHouseholderQR.h\"\n#include \"src/QR/ColPivHouseholderQR.h\"\n#include \"src/QR/CompleteOrthogonalDecomposition.h\"\n#ifdef EIGEN_USE_LAPACKE\n#ifdef EIGEN_USE_MKL\n#include \"mkl_lapacke.h\"\n#else\n#include \"src/misc/lapacke.h\"\n#endif\n#include \"src/QR/HouseholderQR_LAPACKE.h\"\n#include \"src/QR/ColPivHouseholderQR_LAPACKE.h\"\n#endif\n\n#include \"src/Core/util/ReenableStupidWarnings.h\"\n\n#endif // EIGEN_QR_MODULE_H\n/* vim: set filetype=cpp et sw=2 ts=2 ai: */\n"
  },
  {
    "path": "include/eigen3/Eigen/QtAlignedMalloc",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_QTMALLOC_MODULE_H\n#define EIGEN_QTMALLOC_MODULE_H\n\n#include \"Core\"\n\n#if (!EIGEN_MALLOC_ALREADY_ALIGNED)\n\n#include \"src/Core/util/DisableStupidWarnings.h\"\n\nvoid *qMalloc(std::size_t size)\n{\n  return Eigen::internal::aligned_malloc(size);\n}\n\nvoid qFree(void *ptr)\n{\n  Eigen::internal::aligned_free(ptr);\n}\n\nvoid *qRealloc(void *ptr, std::size_t size)\n{\n  void* newPtr = Eigen::internal::aligned_malloc(size);\n  std::memcpy(newPtr, ptr, size);\n  Eigen::internal::aligned_free(ptr);\n  return newPtr;\n}\n\n#include \"src/Core/util/ReenableStupidWarnings.h\"\n\n#endif\n\n#endif // EIGEN_QTMALLOC_MODULE_H\n/* vim: set filetype=cpp et sw=2 ts=2 ai: */\n"
  },
  {
    "path": "include/eigen3/Eigen/SPQRSupport",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPQRSUPPORT_MODULE_H\n#define EIGEN_SPQRSUPPORT_MODULE_H\n\n#include \"SparseCore\"\n\n#include \"src/Core/util/DisableStupidWarnings.h\"\n\n#include \"SuiteSparseQR.hpp\"\n\n/** \\ingroup Support_modules\n  * \\defgroup SPQRSupport_Module SuiteSparseQR module\n  * \n  * This module provides an interface to the SPQR library, which is part of the <a href=\"http://www.suitesparse.com\">suitesparse</a> package.\n  *\n  * \\code\n  * #include <Eigen/SPQRSupport>\n  * \\endcode\n  *\n  * In order to use this module, the SPQR headers must be accessible from the include paths, and your binary must be linked to the SPQR library and its dependencies (Cholmod, AMD, COLAMD,...).\n  * For a cmake based project, you can use our FindSPQR.cmake and FindCholmod.Cmake modules\n  *\n  */\n\n#include \"src/CholmodSupport/CholmodSupport.h\"\n#include \"src/SPQRSupport/SuiteSparseQRSupport.h\"\n\n#endif\n"
  },
  {
    "path": "include/eigen3/Eigen/SVD",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SVD_MODULE_H\n#define EIGEN_SVD_MODULE_H\n\n#include \"QR\"\n#include \"Householder\"\n#include \"Jacobi\"\n\n#include \"src/Core/util/DisableStupidWarnings.h\"\n\n/** \\defgroup SVD_Module SVD module\n  *\n  *\n  *\n  * This module provides SVD decomposition for matrices (both real and complex).\n  * Two decomposition algorithms are provided:\n  *  - JacobiSVD implementing two-sided Jacobi iterations is numerically very accurate, fast for small matrices, but very slow for larger ones.\n  *  - BDCSVD implementing a recursive divide & conquer strategy on top of an upper-bidiagonalization which remains fast for large problems.\n  * These decompositions are accessible via the respective classes and following MatrixBase methods:\n  *  - MatrixBase::jacobiSvd()\n  *  - MatrixBase::bdcSvd()\n  *\n  * \\code\n  * #include <Eigen/SVD>\n  * \\endcode\n  */\n\n#include \"src/misc/RealSvd2x2.h\"\n#include \"src/SVD/UpperBidiagonalization.h\"\n#include \"src/SVD/SVDBase.h\"\n#include \"src/SVD/JacobiSVD.h\"\n#include \"src/SVD/BDCSVD.h\"\n#if defined(EIGEN_USE_LAPACKE) && !defined(EIGEN_USE_LAPACKE_STRICT)\n#ifdef EIGEN_USE_MKL\n#include \"mkl_lapacke.h\"\n#else\n#include \"src/misc/lapacke.h\"\n#endif\n#include \"src/SVD/JacobiSVD_LAPACKE.h\"\n#endif\n\n#include \"src/Core/util/ReenableStupidWarnings.h\"\n\n#endif // EIGEN_SVD_MODULE_H\n/* vim: set filetype=cpp et sw=2 ts=2 ai: */\n"
  },
  {
    "path": "include/eigen3/Eigen/Sparse",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSE_MODULE_H\n#define EIGEN_SPARSE_MODULE_H\n\n/** \\defgroup Sparse_Module Sparse meta-module\n  *\n  * Meta-module including all related modules:\n  * - \\ref SparseCore_Module\n  * - \\ref OrderingMethods_Module\n  * - \\ref SparseCholesky_Module\n  * - \\ref SparseLU_Module\n  * - \\ref SparseQR_Module\n  * - \\ref IterativeLinearSolvers_Module\n  *\n    \\code\n    #include <Eigen/Sparse>\n    \\endcode\n  */\n\n#include \"SparseCore\"\n#include \"OrderingMethods\"\n#ifndef EIGEN_MPL2_ONLY\n#include \"SparseCholesky\"\n#endif\n#include \"SparseLU\"\n#include \"SparseQR\"\n#include \"IterativeLinearSolvers\"\n\n#endif // EIGEN_SPARSE_MODULE_H\n\n"
  },
  {
    "path": "include/eigen3/Eigen/SparseCholesky",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2013 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSECHOLESKY_MODULE_H\n#define EIGEN_SPARSECHOLESKY_MODULE_H\n\n#include \"SparseCore\"\n#include \"OrderingMethods\"\n\n#include \"src/Core/util/DisableStupidWarnings.h\"\n\n/** \n  * \\defgroup SparseCholesky_Module SparseCholesky module\n  *\n  * This module currently provides two variants of the direct sparse Cholesky decomposition for selfadjoint (hermitian) matrices.\n  * Those decompositions are accessible via the following classes:\n  *  - SimplicialLLt,\n  *  - SimplicialLDLt\n  *\n  * Such problems can also be solved using the ConjugateGradient solver from the IterativeLinearSolvers module.\n  *\n  * \\code\n  * #include <Eigen/SparseCholesky>\n  * \\endcode\n  */\n\n#ifdef EIGEN_MPL2_ONLY\n#error The SparseCholesky module has nothing to offer in MPL2 only mode\n#endif\n\n#include \"src/SparseCholesky/SimplicialCholesky.h\"\n\n#ifndef EIGEN_MPL2_ONLY\n#include \"src/SparseCholesky/SimplicialCholesky_impl.h\"\n#endif\n\n#include \"src/Core/util/ReenableStupidWarnings.h\"\n\n#endif // EIGEN_SPARSECHOLESKY_MODULE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/SparseCore",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSECORE_MODULE_H\n#define EIGEN_SPARSECORE_MODULE_H\n\n#include \"Core\"\n\n#include \"src/Core/util/DisableStupidWarnings.h\"\n\n#include <vector>\n#include <map>\n#include <cstdlib>\n#include <cstring>\n#include <algorithm>\n\n/** \n  * \\defgroup SparseCore_Module SparseCore module\n  *\n  * This module provides a sparse matrix representation, and basic associated matrix manipulations\n  * and operations.\n  *\n  * See the \\ref TutorialSparse \"Sparse tutorial\"\n  *\n  * \\code\n  * #include <Eigen/SparseCore>\n  * \\endcode\n  *\n  * This module depends on: Core.\n  */\n\n#include \"src/SparseCore/SparseUtil.h\"\n#include \"src/SparseCore/SparseMatrixBase.h\"\n#include \"src/SparseCore/SparseAssign.h\"\n#include \"src/SparseCore/CompressedStorage.h\"\n#include \"src/SparseCore/AmbiVector.h\"\n#include \"src/SparseCore/SparseCompressedBase.h\"\n#include \"src/SparseCore/SparseMatrix.h\"\n#include \"src/SparseCore/SparseMap.h\"\n#include \"src/SparseCore/MappedSparseMatrix.h\"\n#include \"src/SparseCore/SparseVector.h\"\n#include \"src/SparseCore/SparseRef.h\"\n#include \"src/SparseCore/SparseCwiseUnaryOp.h\"\n#include \"src/SparseCore/SparseCwiseBinaryOp.h\"\n#include \"src/SparseCore/SparseTranspose.h\"\n#include \"src/SparseCore/SparseBlock.h\"\n#include \"src/SparseCore/SparseDot.h\"\n#include \"src/SparseCore/SparseRedux.h\"\n#include \"src/SparseCore/SparseView.h\"\n#include \"src/SparseCore/SparseDiagonalProduct.h\"\n#include \"src/SparseCore/ConservativeSparseSparseProduct.h\"\n#include \"src/SparseCore/SparseSparseProductWithPruning.h\"\n#include \"src/SparseCore/SparseProduct.h\"\n#include \"src/SparseCore/SparseDenseProduct.h\"\n#include \"src/SparseCore/SparseSelfAdjointView.h\"\n#include \"src/SparseCore/SparseTriangularView.h\"\n#include \"src/SparseCore/TriangularSolver.h\"\n#include \"src/SparseCore/SparsePermutation.h\"\n#include \"src/SparseCore/SparseFuzzy.h\"\n#include \"src/SparseCore/SparseSolverBase.h\"\n\n#include \"src/Core/util/ReenableStupidWarnings.h\"\n\n#endif // EIGEN_SPARSECORE_MODULE_H\n\n"
  },
  {
    "path": "include/eigen3/Eigen/SparseLU",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>\n// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSELU_MODULE_H\n#define EIGEN_SPARSELU_MODULE_H\n\n#include \"SparseCore\"\n\n/** \n  * \\defgroup SparseLU_Module SparseLU module\n  * This module defines a supernodal factorization of general sparse matrices.\n  * The code is fully optimized for supernode-panel updates with specialized kernels.\n  * Please, see the documentation of the SparseLU class for more details.\n  */\n\n// Ordering interface\n#include \"OrderingMethods\"\n\n#include \"src/SparseLU/SparseLU_gemm_kernel.h\"\n\n#include \"src/SparseLU/SparseLU_Structs.h\"\n#include \"src/SparseLU/SparseLU_SupernodalMatrix.h\"\n#include \"src/SparseLU/SparseLUImpl.h\"\n#include \"src/SparseCore/SparseColEtree.h\"\n#include \"src/SparseLU/SparseLU_Memory.h\"\n#include \"src/SparseLU/SparseLU_heap_relax_snode.h\"\n#include \"src/SparseLU/SparseLU_relax_snode.h\"\n#include \"src/SparseLU/SparseLU_pivotL.h\"\n#include \"src/SparseLU/SparseLU_panel_dfs.h\"\n#include \"src/SparseLU/SparseLU_kernel_bmod.h\"\n#include \"src/SparseLU/SparseLU_panel_bmod.h\"\n#include \"src/SparseLU/SparseLU_column_dfs.h\"\n#include \"src/SparseLU/SparseLU_column_bmod.h\"\n#include \"src/SparseLU/SparseLU_copy_to_ucol.h\"\n#include \"src/SparseLU/SparseLU_pruneL.h\"\n#include \"src/SparseLU/SparseLU_Utils.h\"\n#include \"src/SparseLU/SparseLU.h\"\n\n#endif // EIGEN_SPARSELU_MODULE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/SparseQR",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSEQR_MODULE_H\n#define EIGEN_SPARSEQR_MODULE_H\n\n#include \"SparseCore\"\n#include \"OrderingMethods\"\n#include \"src/Core/util/DisableStupidWarnings.h\"\n\n/** \\defgroup SparseQR_Module SparseQR module\n  * \\brief Provides QR decomposition for sparse matrices\n  * \n  * This module provides a simplicial version of the left-looking Sparse QR decomposition. \n  * The columns of the input matrix should be reordered to limit the fill-in during the \n  * decomposition. Built-in methods (COLAMD, AMD) or external  methods (METIS) can be used to this end.\n  * See the \\link OrderingMethods_Module OrderingMethods\\endlink module for the list \n  * of built-in and external ordering methods.\n  * \n  * \\code\n  * #include <Eigen/SparseQR>\n  * \\endcode\n  * \n  * \n  */\n\n#include \"OrderingMethods\"\n#include \"src/SparseCore/SparseColEtree.h\"\n#include \"src/SparseQR/SparseQR.h\"\n\n#include \"src/Core/util/ReenableStupidWarnings.h\"\n\n#endif\n"
  },
  {
    "path": "include/eigen3/Eigen/StdDeque",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2009 Hauke Heibel <hauke.heibel@googlemail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_STDDEQUE_MODULE_H\n#define EIGEN_STDDEQUE_MODULE_H\n\n#include \"Core\"\n#include <deque>\n\n#if EIGEN_COMP_MSVC && EIGEN_OS_WIN64 && (EIGEN_MAX_STATIC_ALIGN_BYTES<=16) /* MSVC auto aligns up to 16 bytes in 64 bit builds */\n\n#define EIGEN_DEFINE_STL_DEQUE_SPECIALIZATION(...)\n\n#else\n\n#include \"src/StlSupport/StdDeque.h\"\n\n#endif\n\n#endif // EIGEN_STDDEQUE_MODULE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/StdList",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Hauke Heibel <hauke.heibel@googlemail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_STDLIST_MODULE_H\n#define EIGEN_STDLIST_MODULE_H\n\n#include \"Core\"\n#include <list>\n\n#if EIGEN_COMP_MSVC && EIGEN_OS_WIN64 && (EIGEN_MAX_STATIC_ALIGN_BYTES<=16) /* MSVC auto aligns up to 16 bytes in 64 bit builds */\n\n#define EIGEN_DEFINE_STL_LIST_SPECIALIZATION(...)\n\n#else\n\n#include \"src/StlSupport/StdList.h\"\n\n#endif\n\n#endif // EIGEN_STDLIST_MODULE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/StdVector",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2009 Hauke Heibel <hauke.heibel@googlemail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_STDVECTOR_MODULE_H\n#define EIGEN_STDVECTOR_MODULE_H\n\n#include \"Core\"\n#include <vector>\n\n#if EIGEN_COMP_MSVC && EIGEN_OS_WIN64 && (EIGEN_MAX_STATIC_ALIGN_BYTES<=16) /* MSVC auto aligns up to 16 bytes in 64 bit builds */\n\n#define EIGEN_DEFINE_STL_VECTOR_SPECIALIZATION(...)\n\n#else\n\n#include \"src/StlSupport/StdVector.h\"\n\n#endif\n\n#endif // EIGEN_STDVECTOR_MODULE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/SuperLUSupport",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SUPERLUSUPPORT_MODULE_H\n#define EIGEN_SUPERLUSUPPORT_MODULE_H\n\n#include \"SparseCore\"\n\n#include \"src/Core/util/DisableStupidWarnings.h\"\n\n#ifdef EMPTY\n#define EIGEN_EMPTY_WAS_ALREADY_DEFINED\n#endif\n\ntypedef int int_t;\n#include <slu_Cnames.h>\n#include <supermatrix.h>\n#include <slu_util.h>\n\n// slu_util.h defines a preprocessor token named EMPTY which is really polluting,\n// so we remove it in favor of a SUPERLU_EMPTY token.\n// If EMPTY was already defined then we don't undef it.\n\n#if defined(EIGEN_EMPTY_WAS_ALREADY_DEFINED)\n# undef EIGEN_EMPTY_WAS_ALREADY_DEFINED\n#elif defined(EMPTY)\n# undef EMPTY\n#endif\n\n#define SUPERLU_EMPTY (-1)\n\nnamespace Eigen { struct SluMatrix; }\n\n/** \\ingroup Support_modules\n  * \\defgroup SuperLUSupport_Module SuperLUSupport module\n  *\n  * This module provides an interface to the <a href=\"http://crd-legacy.lbl.gov/~xiaoye/SuperLU/\">SuperLU</a> library.\n  * It provides the following factorization class:\n  * - class SuperLU: a supernodal sequential LU factorization.\n  * - class SuperILU: a supernodal sequential incomplete LU factorization (to be used as a preconditioner for iterative methods).\n  *\n  * \\warning This wrapper requires at least versions 4.0 of SuperLU. The 3.x versions are not supported.\n  *\n  * \\warning When including this module, you have to use SUPERLU_EMPTY instead of EMPTY which is no longer defined because it is too polluting.\n  *\n  * \\code\n  * #include <Eigen/SuperLUSupport>\n  * \\endcode\n  *\n  * In order to use this module, the superlu headers must be accessible from the include paths, and your binary must be linked to the superlu library and its dependencies.\n  * The dependencies depend on how superlu has been compiled.\n  * For a cmake based project, you can use our FindSuperLU.cmake module to help you in this task.\n  *\n  */\n\n#include \"src/SuperLUSupport/SuperLUSupport.h\"\n\n#include \"src/Core/util/ReenableStupidWarnings.h\"\n\n#endif // EIGEN_SUPERLUSUPPORT_MODULE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/UmfPackSupport",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_UMFPACKSUPPORT_MODULE_H\n#define EIGEN_UMFPACKSUPPORT_MODULE_H\n\n#include \"SparseCore\"\n\n#include \"src/Core/util/DisableStupidWarnings.h\"\n\nextern \"C\" {\n#include <umfpack.h>\n}\n\n/** \\ingroup Support_modules\n  * \\defgroup UmfPackSupport_Module UmfPackSupport module\n  *\n  * This module provides an interface to the UmfPack library which is part of the <a href=\"http://www.suitesparse.com\">suitesparse</a> package.\n  * It provides the following factorization class:\n  * - class UmfPackLU: a multifrontal sequential LU factorization.\n  *\n  * \\code\n  * #include <Eigen/UmfPackSupport>\n  * \\endcode\n  *\n  * In order to use this module, the umfpack headers must be accessible from the include paths, and your binary must be linked to the umfpack library and its dependencies.\n  * The dependencies depend on how umfpack has been compiled.\n  * For a cmake based project, you can use our FindUmfPack.cmake module to help you in this task.\n  *\n  */\n\n#include \"src/UmfPackSupport/UmfPackSupport.h\"\n\n#include \"src/Core/util/ReenableStupidWarnings.h\"\n\n#endif // EIGEN_UMFPACKSUPPORT_MODULE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Cholesky/LDLT.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2009 Keir Mierle <mierle@gmail.com>\n// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2011 Timothy E. Holy <tim.holy@gmail.com >\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_LDLT_H\n#define EIGEN_LDLT_H\n\nnamespace Eigen {\n\nnamespace internal {\n  template<typename MatrixType, int UpLo> struct LDLT_Traits;\n\n  // PositiveSemiDef means positive semi-definite and non-zero; same for NegativeSemiDef\n  enum SignMatrix { PositiveSemiDef, NegativeSemiDef, ZeroSign, Indefinite };\n}\n\n/** \\ingroup Cholesky_Module\n  *\n  * \\class LDLT\n  *\n  * \\brief Robust Cholesky decomposition of a matrix with pivoting\n  *\n  * \\tparam _MatrixType the type of the matrix of which to compute the LDL^T Cholesky decomposition\n  * \\tparam _UpLo the triangular part that will be used for the decompositon: Lower (default) or Upper.\n  *             The other triangular part won't be read.\n  *\n  * Perform a robust Cholesky decomposition of a positive semidefinite or negative semidefinite\n  * matrix \\f$ A \\f$ such that \\f$ A =  P^TLDL^*P \\f$, where P is a permutation matrix, L\n  * is lower triangular with a unit diagonal and D is a diagonal matrix.\n  *\n  * The decomposition uses pivoting to ensure stability, so that L will have\n  * zeros in the bottom right rank(A) - n submatrix. Avoiding the square root\n  * on D also stabilizes the computation.\n  *\n  * Remember that Cholesky decompositions are not rank-revealing. Also, do not use a Cholesky\n  * decomposition to determine whether a system of equations has a solution.\n  *\n  * This class supports the \\link InplaceDecomposition inplace decomposition \\endlink mechanism.\n  * \n  * \\sa MatrixBase::ldlt(), SelfAdjointView::ldlt(), class LLT\n  */\ntemplate<typename _MatrixType, int _UpLo> class LDLT\n{\n  public:\n    typedef _MatrixType MatrixType;\n    enum {\n      RowsAtCompileTime = MatrixType::RowsAtCompileTime,\n      ColsAtCompileTime = MatrixType::ColsAtCompileTime,\n      MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,\n      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,\n      UpLo = _UpLo\n    };\n    typedef typename MatrixType::Scalar Scalar;\n    typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;\n    typedef Eigen::Index Index; ///< \\deprecated since Eigen 3.3\n    typedef typename MatrixType::StorageIndex StorageIndex;\n    typedef Matrix<Scalar, RowsAtCompileTime, 1, 0, MaxRowsAtCompileTime, 1> TmpMatrixType;\n\n    typedef Transpositions<RowsAtCompileTime, MaxRowsAtCompileTime> TranspositionType;\n    typedef PermutationMatrix<RowsAtCompileTime, MaxRowsAtCompileTime> PermutationType;\n\n    typedef internal::LDLT_Traits<MatrixType,UpLo> Traits;\n\n    /** \\brief Default Constructor.\n      *\n      * The default constructor is useful in cases in which the user intends to\n      * perform decompositions via LDLT::compute(const MatrixType&).\n      */\n    LDLT()\n      : m_matrix(),\n        m_transpositions(),\n        m_sign(internal::ZeroSign),\n        m_isInitialized(false)\n    {}\n\n    /** \\brief Default Constructor with memory preallocation\n      *\n      * Like the default constructor but with preallocation of the internal data\n      * according to the specified problem \\a size.\n      * \\sa LDLT()\n      */\n    explicit LDLT(Index size)\n      : m_matrix(size, size),\n        m_transpositions(size),\n        m_temporary(size),\n        m_sign(internal::ZeroSign),\n        m_isInitialized(false)\n    {}\n\n    /** \\brief Constructor with decomposition\n      *\n      * This calculates the decomposition for the input \\a matrix.\n      *\n      * \\sa LDLT(Index size)\n      */\n    template<typename InputType>\n    explicit LDLT(const EigenBase<InputType>& matrix)\n      : m_matrix(matrix.rows(), matrix.cols()),\n        m_transpositions(matrix.rows()),\n        m_temporary(matrix.rows()),\n        m_sign(internal::ZeroSign),\n        m_isInitialized(false)\n    {\n      compute(matrix.derived());\n    }\n\n    /** \\brief Constructs a LDLT factorization from a given matrix\n      *\n      * This overloaded constructor is provided for \\link InplaceDecomposition inplace decomposition \\endlink when \\c MatrixType is a Eigen::Ref.\n      *\n      * \\sa LDLT(const EigenBase&)\n      */\n    template<typename InputType>\n    explicit LDLT(EigenBase<InputType>& matrix)\n      : m_matrix(matrix.derived()),\n        m_transpositions(matrix.rows()),\n        m_temporary(matrix.rows()),\n        m_sign(internal::ZeroSign),\n        m_isInitialized(false)\n    {\n      compute(matrix.derived());\n    }\n\n    /** Clear any existing decomposition\n     * \\sa rankUpdate(w,sigma)\n     */\n    void setZero()\n    {\n      m_isInitialized = false;\n    }\n\n    /** \\returns a view of the upper triangular matrix U */\n    inline typename Traits::MatrixU matrixU() const\n    {\n      eigen_assert(m_isInitialized && \"LDLT is not initialized.\");\n      return Traits::getU(m_matrix);\n    }\n\n    /** \\returns a view of the lower triangular matrix L */\n    inline typename Traits::MatrixL matrixL() const\n    {\n      eigen_assert(m_isInitialized && \"LDLT is not initialized.\");\n      return Traits::getL(m_matrix);\n    }\n\n    /** \\returns the permutation matrix P as a transposition sequence.\n      */\n    inline const TranspositionType& transpositionsP() const\n    {\n      eigen_assert(m_isInitialized && \"LDLT is not initialized.\");\n      return m_transpositions;\n    }\n\n    /** \\returns the coefficients of the diagonal matrix D */\n    inline Diagonal<const MatrixType> vectorD() const\n    {\n      eigen_assert(m_isInitialized && \"LDLT is not initialized.\");\n      return m_matrix.diagonal();\n    }\n\n    /** \\returns true if the matrix is positive (semidefinite) */\n    inline bool isPositive() const\n    {\n      eigen_assert(m_isInitialized && \"LDLT is not initialized.\");\n      return m_sign == internal::PositiveSemiDef || m_sign == internal::ZeroSign;\n    }\n\n    /** \\returns true if the matrix is negative (semidefinite) */\n    inline bool isNegative(void) const\n    {\n      eigen_assert(m_isInitialized && \"LDLT is not initialized.\");\n      return m_sign == internal::NegativeSemiDef || m_sign == internal::ZeroSign;\n    }\n\n    /** \\returns a solution x of \\f$ A x = b \\f$ using the current decomposition of A.\n      *\n      * This function also supports in-place solves using the syntax <tt>x = decompositionObject.solve(x)</tt> .\n      *\n      * \\note_about_checking_solutions\n      *\n      * More precisely, this method solves \\f$ A x = b \\f$ using the decomposition \\f$ A = P^T L D L^* P \\f$\n      * by solving the systems \\f$ P^T y_1 = b \\f$, \\f$ L y_2 = y_1 \\f$, \\f$ D y_3 = y_2 \\f$,\n      * \\f$ L^* y_4 = y_3 \\f$ and \\f$ P x = y_4 \\f$ in succession. If the matrix \\f$ A \\f$ is singular, then\n      * \\f$ D \\f$ will also be singular (all the other matrices are invertible). In that case, the\n      * least-square solution of \\f$ D y_3 = y_2 \\f$ is computed. This does not mean that this function\n      * computes the least-square solution of \\f$ A x = b \\f$ is \\f$ A \\f$ is singular.\n      *\n      * \\sa MatrixBase::ldlt(), SelfAdjointView::ldlt()\n      */\n    template<typename Rhs>\n    inline const Solve<LDLT, Rhs>\n    solve(const MatrixBase<Rhs>& b) const\n    {\n      eigen_assert(m_isInitialized && \"LDLT is not initialized.\");\n      eigen_assert(m_matrix.rows()==b.rows()\n                && \"LDLT::solve(): invalid number of rows of the right hand side matrix b\");\n      return Solve<LDLT, Rhs>(*this, b.derived());\n    }\n\n    template<typename Derived>\n    bool solveInPlace(MatrixBase<Derived> &bAndX) const;\n\n    template<typename InputType>\n    LDLT& compute(const EigenBase<InputType>& matrix);\n\n    /** \\returns an estimate of the reciprocal condition number of the matrix of\n     *  which \\c *this is the LDLT decomposition.\n     */\n    RealScalar rcond() const\n    {\n      eigen_assert(m_isInitialized && \"LDLT is not initialized.\");\n      return internal::rcond_estimate_helper(m_l1_norm, *this);\n    }\n\n    template <typename Derived>\n    LDLT& rankUpdate(const MatrixBase<Derived>& w, const RealScalar& alpha=1);\n\n    /** \\returns the internal LDLT decomposition matrix\n      *\n      * TODO: document the storage layout\n      */\n    inline const MatrixType& matrixLDLT() const\n    {\n      eigen_assert(m_isInitialized && \"LDLT is not initialized.\");\n      return m_matrix;\n    }\n\n    MatrixType reconstructedMatrix() const;\n\n    /** \\returns the adjoint of \\c *this, that is, a const reference to the decomposition itself as the underlying matrix is self-adjoint.\n      *\n      * This method is provided for compatibility with other matrix decompositions, thus enabling generic code such as:\n      * \\code x = decomposition.adjoint().solve(b) \\endcode\n      */\n    const LDLT& adjoint() const { return *this; };\n\n    inline Index rows() const { return m_matrix.rows(); }\n    inline Index cols() const { return m_matrix.cols(); }\n\n    /** \\brief Reports whether previous computation was successful.\n      *\n      * \\returns \\c Success if computation was succesful,\n      *          \\c NumericalIssue if the factorization failed because of a zero pivot.\n      */\n    ComputationInfo info() const\n    {\n      eigen_assert(m_isInitialized && \"LDLT is not initialized.\");\n      return m_info;\n    }\n\n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    template<typename RhsType, typename DstType>\n    EIGEN_DEVICE_FUNC\n    void _solve_impl(const RhsType &rhs, DstType &dst) const;\n    #endif\n\n  protected:\n\n    static void check_template_parameters()\n    {\n      EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);\n    }\n\n    /** \\internal\n      * Used to compute and store the Cholesky decomposition A = L D L^* = U^* D U.\n      * The strict upper part is used during the decomposition, the strict lower\n      * part correspond to the coefficients of L (its diagonal is equal to 1 and\n      * is not stored), and the diagonal entries correspond to D.\n      */\n    MatrixType m_matrix;\n    RealScalar m_l1_norm;\n    TranspositionType m_transpositions;\n    TmpMatrixType m_temporary;\n    internal::SignMatrix m_sign;\n    bool m_isInitialized;\n    ComputationInfo m_info;\n};\n\nnamespace internal {\n\ntemplate<int UpLo> struct ldlt_inplace;\n\ntemplate<> struct ldlt_inplace<Lower>\n{\n  template<typename MatrixType, typename TranspositionType, typename Workspace>\n  static bool unblocked(MatrixType& mat, TranspositionType& transpositions, Workspace& temp, SignMatrix& sign)\n  {\n    using std::abs;\n    typedef typename MatrixType::Scalar Scalar;\n    typedef typename MatrixType::RealScalar RealScalar;\n    typedef typename TranspositionType::StorageIndex IndexType;\n    eigen_assert(mat.rows()==mat.cols());\n    const Index size = mat.rows();\n    bool found_zero_pivot = false;\n    bool ret = true;\n\n    if (size <= 1)\n    {\n      transpositions.setIdentity();\n      if (numext::real(mat.coeff(0,0)) > static_cast<RealScalar>(0) ) sign = PositiveSemiDef;\n      else if (numext::real(mat.coeff(0,0)) < static_cast<RealScalar>(0)) sign = NegativeSemiDef;\n      else sign = ZeroSign;\n      return true;\n    }\n\n    for (Index k = 0; k < size; ++k)\n    {\n      // Find largest diagonal element\n      Index index_of_biggest_in_corner;\n      mat.diagonal().tail(size-k).cwiseAbs().maxCoeff(&index_of_biggest_in_corner);\n      index_of_biggest_in_corner += k;\n\n      transpositions.coeffRef(k) = IndexType(index_of_biggest_in_corner);\n      if(k != index_of_biggest_in_corner)\n      {\n        // apply the transposition while taking care to consider only\n        // the lower triangular part\n        Index s = size-index_of_biggest_in_corner-1; // trailing size after the biggest element\n        mat.row(k).head(k).swap(mat.row(index_of_biggest_in_corner).head(k));\n        mat.col(k).tail(s).swap(mat.col(index_of_biggest_in_corner).tail(s));\n        std::swap(mat.coeffRef(k,k),mat.coeffRef(index_of_biggest_in_corner,index_of_biggest_in_corner));\n        for(Index i=k+1;i<index_of_biggest_in_corner;++i)\n        {\n          Scalar tmp = mat.coeffRef(i,k);\n          mat.coeffRef(i,k) = numext::conj(mat.coeffRef(index_of_biggest_in_corner,i));\n          mat.coeffRef(index_of_biggest_in_corner,i) = numext::conj(tmp);\n        }\n        if(NumTraits<Scalar>::IsComplex)\n          mat.coeffRef(index_of_biggest_in_corner,k) = numext::conj(mat.coeff(index_of_biggest_in_corner,k));\n      }\n\n      // partition the matrix:\n      //       A00 |  -  |  -\n      // lu  = A10 | A11 |  -\n      //       A20 | A21 | A22\n      Index rs = size - k - 1;\n      Block<MatrixType,Dynamic,1> A21(mat,k+1,k,rs,1);\n      Block<MatrixType,1,Dynamic> A10(mat,k,0,1,k);\n      Block<MatrixType,Dynamic,Dynamic> A20(mat,k+1,0,rs,k);\n\n      if(k>0)\n      {\n        temp.head(k) = mat.diagonal().real().head(k).asDiagonal() * A10.adjoint();\n        mat.coeffRef(k,k) -= (A10 * temp.head(k)).value();\n        if(rs>0)\n          A21.noalias() -= A20 * temp.head(k);\n      }\n\n      // In some previous versions of Eigen (e.g., 3.2.1), the scaling was omitted if the pivot\n      // was smaller than the cutoff value. However, since LDLT is not rank-revealing\n      // we should only make sure that we do not introduce INF or NaN values.\n      // Remark that LAPACK also uses 0 as the cutoff value.\n      RealScalar realAkk = numext::real(mat.coeffRef(k,k));\n      bool pivot_is_valid = (abs(realAkk) > RealScalar(0));\n\n      if(k==0 && !pivot_is_valid)\n      {\n        // The entire diagonal is zero, there is nothing more to do\n        // except filling the transpositions, and checking whether the matrix is zero.\n        sign = ZeroSign;\n        for(Index j = 0; j<size; ++j)\n        {\n          transpositions.coeffRef(j) = IndexType(j);\n          ret = ret && (mat.col(j).tail(size-j-1).array()==Scalar(0)).all();\n        }\n        return ret;\n      }\n\n      if((rs>0) && pivot_is_valid)\n        A21 /= realAkk;\n      else if(rs>0)\n        ret = ret && (A21.array()==Scalar(0)).all();\n\n      if(found_zero_pivot && pivot_is_valid) ret = false; // factorization failed\n      else if(!pivot_is_valid) found_zero_pivot = true;\n\n      if (sign == PositiveSemiDef) {\n        if (realAkk < static_cast<RealScalar>(0)) sign = Indefinite;\n      } else if (sign == NegativeSemiDef) {\n        if (realAkk > static_cast<RealScalar>(0)) sign = Indefinite;\n      } else if (sign == ZeroSign) {\n        if (realAkk > static_cast<RealScalar>(0)) sign = PositiveSemiDef;\n        else if (realAkk < static_cast<RealScalar>(0)) sign = NegativeSemiDef;\n      }\n    }\n\n    return ret;\n  }\n\n  // Reference for the algorithm: Davis and Hager, \"Multiple Rank\n  // Modifications of a Sparse Cholesky Factorization\" (Algorithm 1)\n  // Trivial rearrangements of their computations (Timothy E. Holy)\n  // allow their algorithm to work for rank-1 updates even if the\n  // original matrix is not of full rank.\n  // Here only rank-1 updates are implemented, to reduce the\n  // requirement for intermediate storage and improve accuracy\n  template<typename MatrixType, typename WDerived>\n  static bool updateInPlace(MatrixType& mat, MatrixBase<WDerived>& w, const typename MatrixType::RealScalar& sigma=1)\n  {\n    using numext::isfinite;\n    typedef typename MatrixType::Scalar Scalar;\n    typedef typename MatrixType::RealScalar RealScalar;\n\n    const Index size = mat.rows();\n    eigen_assert(mat.cols() == size && w.size()==size);\n\n    RealScalar alpha = 1;\n\n    // Apply the update\n    for (Index j = 0; j < size; j++)\n    {\n      // Check for termination due to an original decomposition of low-rank\n      if (!(isfinite)(alpha))\n        break;\n\n      // Update the diagonal terms\n      RealScalar dj = numext::real(mat.coeff(j,j));\n      Scalar wj = w.coeff(j);\n      RealScalar swj2 = sigma*numext::abs2(wj);\n      RealScalar gamma = dj*alpha + swj2;\n\n      mat.coeffRef(j,j) += swj2/alpha;\n      alpha += swj2/dj;\n\n\n      // Update the terms of L\n      Index rs = size-j-1;\n      w.tail(rs) -= wj * mat.col(j).tail(rs);\n      if(gamma != 0)\n        mat.col(j).tail(rs) += (sigma*numext::conj(wj)/gamma)*w.tail(rs);\n    }\n    return true;\n  }\n\n  template<typename MatrixType, typename TranspositionType, typename Workspace, typename WType>\n  static bool update(MatrixType& mat, const TranspositionType& transpositions, Workspace& tmp, const WType& w, const typename MatrixType::RealScalar& sigma=1)\n  {\n    // Apply the permutation to the input w\n    tmp = transpositions * w;\n\n    return ldlt_inplace<Lower>::updateInPlace(mat,tmp,sigma);\n  }\n};\n\ntemplate<> struct ldlt_inplace<Upper>\n{\n  template<typename MatrixType, typename TranspositionType, typename Workspace>\n  static EIGEN_STRONG_INLINE bool unblocked(MatrixType& mat, TranspositionType& transpositions, Workspace& temp, SignMatrix& sign)\n  {\n    Transpose<MatrixType> matt(mat);\n    return ldlt_inplace<Lower>::unblocked(matt, transpositions, temp, sign);\n  }\n\n  template<typename MatrixType, typename TranspositionType, typename Workspace, typename WType>\n  static EIGEN_STRONG_INLINE bool update(MatrixType& mat, TranspositionType& transpositions, Workspace& tmp, WType& w, const typename MatrixType::RealScalar& sigma=1)\n  {\n    Transpose<MatrixType> matt(mat);\n    return ldlt_inplace<Lower>::update(matt, transpositions, tmp, w.conjugate(), sigma);\n  }\n};\n\ntemplate<typename MatrixType> struct LDLT_Traits<MatrixType,Lower>\n{\n  typedef const TriangularView<const MatrixType, UnitLower> MatrixL;\n  typedef const TriangularView<const typename MatrixType::AdjointReturnType, UnitUpper> MatrixU;\n  static inline MatrixL getL(const MatrixType& m) { return MatrixL(m); }\n  static inline MatrixU getU(const MatrixType& m) { return MatrixU(m.adjoint()); }\n};\n\ntemplate<typename MatrixType> struct LDLT_Traits<MatrixType,Upper>\n{\n  typedef const TriangularView<const typename MatrixType::AdjointReturnType, UnitLower> MatrixL;\n  typedef const TriangularView<const MatrixType, UnitUpper> MatrixU;\n  static inline MatrixL getL(const MatrixType& m) { return MatrixL(m.adjoint()); }\n  static inline MatrixU getU(const MatrixType& m) { return MatrixU(m); }\n};\n\n} // end namespace internal\n\n/** Compute / recompute the LDLT decomposition A = L D L^* = U^* D U of \\a matrix\n  */\ntemplate<typename MatrixType, int _UpLo>\ntemplate<typename InputType>\nLDLT<MatrixType,_UpLo>& LDLT<MatrixType,_UpLo>::compute(const EigenBase<InputType>& a)\n{\n  check_template_parameters();\n\n  eigen_assert(a.rows()==a.cols());\n  const Index size = a.rows();\n\n  m_matrix = a.derived();\n\n  // Compute matrix L1 norm = max abs column sum.\n  m_l1_norm = RealScalar(0);\n  // TODO move this code to SelfAdjointView\n  for (Index col = 0; col < size; ++col) {\n    RealScalar abs_col_sum;\n    if (_UpLo == Lower)\n      abs_col_sum = m_matrix.col(col).tail(size - col).template lpNorm<1>() + m_matrix.row(col).head(col).template lpNorm<1>();\n    else\n      abs_col_sum = m_matrix.col(col).head(col).template lpNorm<1>() + m_matrix.row(col).tail(size - col).template lpNorm<1>();\n    if (abs_col_sum > m_l1_norm)\n      m_l1_norm = abs_col_sum;\n  }\n\n  m_transpositions.resize(size);\n  m_isInitialized = false;\n  m_temporary.resize(size);\n  m_sign = internal::ZeroSign;\n\n  m_info = internal::ldlt_inplace<UpLo>::unblocked(m_matrix, m_transpositions, m_temporary, m_sign) ? Success : NumericalIssue;\n\n  m_isInitialized = true;\n  return *this;\n}\n\n/** Update the LDLT decomposition:  given A = L D L^T, efficiently compute the decomposition of A + sigma w w^T.\n * \\param w a vector to be incorporated into the decomposition.\n * \\param sigma a scalar, +1 for updates and -1 for \"downdates,\" which correspond to removing previously-added column vectors. Optional; default value is +1.\n * \\sa setZero()\n  */\ntemplate<typename MatrixType, int _UpLo>\ntemplate<typename Derived>\nLDLT<MatrixType,_UpLo>& LDLT<MatrixType,_UpLo>::rankUpdate(const MatrixBase<Derived>& w, const typename LDLT<MatrixType,_UpLo>::RealScalar& sigma)\n{\n  typedef typename TranspositionType::StorageIndex IndexType;\n  const Index size = w.rows();\n  if (m_isInitialized)\n  {\n    eigen_assert(m_matrix.rows()==size);\n  }\n  else\n  {\n    m_matrix.resize(size,size);\n    m_matrix.setZero();\n    m_transpositions.resize(size);\n    for (Index i = 0; i < size; i++)\n      m_transpositions.coeffRef(i) = IndexType(i);\n    m_temporary.resize(size);\n    m_sign = sigma>=0 ? internal::PositiveSemiDef : internal::NegativeSemiDef;\n    m_isInitialized = true;\n  }\n\n  internal::ldlt_inplace<UpLo>::update(m_matrix, m_transpositions, m_temporary, w, sigma);\n\n  return *this;\n}\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\ntemplate<typename _MatrixType, int _UpLo>\ntemplate<typename RhsType, typename DstType>\nvoid LDLT<_MatrixType,_UpLo>::_solve_impl(const RhsType &rhs, DstType &dst) const\n{\n  eigen_assert(rhs.rows() == rows());\n  // dst = P b\n  dst = m_transpositions * rhs;\n\n  // dst = L^-1 (P b)\n  matrixL().solveInPlace(dst);\n\n  // dst = D^-1 (L^-1 P b)\n  // more precisely, use pseudo-inverse of D (see bug 241)\n  using std::abs;\n  const typename Diagonal<const MatrixType>::RealReturnType vecD(vectorD());\n  // In some previous versions, tolerance was set to the max of 1/highest (or rather numeric_limits::min())\n  // and the maximal diagonal entry * epsilon as motivated by LAPACK's xGELSS:\n  // RealScalar tolerance = numext::maxi(vecD.array().abs().maxCoeff() * NumTraits<RealScalar>::epsilon(),RealScalar(1) / NumTraits<RealScalar>::highest());\n  // However, LDLT is not rank revealing, and so adjusting the tolerance wrt to the highest\n  // diagonal element is not well justified and leads to numerical issues in some cases.\n  // Moreover, Lapack's xSYTRS routines use 0 for the tolerance.\n  // Using numeric_limits::min() gives us more robustness to denormals.\n  RealScalar tolerance = (std::numeric_limits<RealScalar>::min)();\n\n  for (Index i = 0; i < vecD.size(); ++i)\n  {\n    if(abs(vecD(i)) > tolerance)\n      dst.row(i) /= vecD(i);\n    else\n      dst.row(i).setZero();\n  }\n\n  // dst = L^-T (D^-1 L^-1 P b)\n  matrixU().solveInPlace(dst);\n\n  // dst = P^-1 (L^-T D^-1 L^-1 P b) = A^-1 b\n  dst = m_transpositions.transpose() * dst;\n}\n#endif\n\n/** \\internal use x = ldlt_object.solve(x);\n  *\n  * This is the \\em in-place version of solve().\n  *\n  * \\param bAndX represents both the right-hand side matrix b and result x.\n  *\n  * \\returns true always! If you need to check for existence of solutions, use another decomposition like LU, QR, or SVD.\n  *\n  * This version avoids a copy when the right hand side matrix b is not\n  * needed anymore.\n  *\n  * \\sa LDLT::solve(), MatrixBase::ldlt()\n  */\ntemplate<typename MatrixType,int _UpLo>\ntemplate<typename Derived>\nbool LDLT<MatrixType,_UpLo>::solveInPlace(MatrixBase<Derived> &bAndX) const\n{\n  eigen_assert(m_isInitialized && \"LDLT is not initialized.\");\n  eigen_assert(m_matrix.rows() == bAndX.rows());\n\n  bAndX = this->solve(bAndX);\n\n  return true;\n}\n\n/** \\returns the matrix represented by the decomposition,\n * i.e., it returns the product: P^T L D L^* P.\n * This function is provided for debug purpose. */\ntemplate<typename MatrixType, int _UpLo>\nMatrixType LDLT<MatrixType,_UpLo>::reconstructedMatrix() const\n{\n  eigen_assert(m_isInitialized && \"LDLT is not initialized.\");\n  const Index size = m_matrix.rows();\n  MatrixType res(size,size);\n\n  // P\n  res.setIdentity();\n  res = transpositionsP() * res;\n  // L^* P\n  res = matrixU() * res;\n  // D(L^*P)\n  res = vectorD().real().asDiagonal() * res;\n  // L(DL^*P)\n  res = matrixL() * res;\n  // P^T (LDL^*P)\n  res = transpositionsP().transpose() * res;\n\n  return res;\n}\n\n/** \\cholesky_module\n  * \\returns the Cholesky decomposition with full pivoting without square root of \\c *this\n  * \\sa MatrixBase::ldlt()\n  */\ntemplate<typename MatrixType, unsigned int UpLo>\ninline const LDLT<typename SelfAdjointView<MatrixType, UpLo>::PlainObject, UpLo>\nSelfAdjointView<MatrixType, UpLo>::ldlt() const\n{\n  return LDLT<PlainObject,UpLo>(m_matrix);\n}\n\n/** \\cholesky_module\n  * \\returns the Cholesky decomposition with full pivoting without square root of \\c *this\n  * \\sa SelfAdjointView::ldlt()\n  */\ntemplate<typename Derived>\ninline const LDLT<typename MatrixBase<Derived>::PlainObject>\nMatrixBase<Derived>::ldlt() const\n{\n  return LDLT<PlainObject>(derived());\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_LDLT_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Cholesky/LLT.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_LLT_H\n#define EIGEN_LLT_H\n\nnamespace Eigen {\n\nnamespace internal{\ntemplate<typename MatrixType, int UpLo> struct LLT_Traits;\n}\n\n/** \\ingroup Cholesky_Module\n  *\n  * \\class LLT\n  *\n  * \\brief Standard Cholesky decomposition (LL^T) of a matrix and associated features\n  *\n  * \\tparam _MatrixType the type of the matrix of which we are computing the LL^T Cholesky decomposition\n  * \\tparam _UpLo the triangular part that will be used for the decompositon: Lower (default) or Upper.\n  *               The other triangular part won't be read.\n  *\n  * This class performs a LL^T Cholesky decomposition of a symmetric, positive definite\n  * matrix A such that A = LL^* = U^*U, where L is lower triangular.\n  *\n  * While the Cholesky decomposition is particularly useful to solve selfadjoint problems like  D^*D x = b,\n  * for that purpose, we recommend the Cholesky decomposition without square root which is more stable\n  * and even faster. Nevertheless, this standard Cholesky decomposition remains useful in many other\n  * situations like generalised eigen problems with hermitian matrices.\n  *\n  * Remember that Cholesky decompositions are not rank-revealing. This LLT decomposition is only stable on positive definite matrices,\n  * use LDLT instead for the semidefinite case. Also, do not use a Cholesky decomposition to determine whether a system of equations\n  * has a solution.\n  *\n  * Example: \\include LLT_example.cpp\n  * Output: \\verbinclude LLT_example.out\n  *\n  * \\b Performance: for best performance, it is recommended to use a column-major storage format\n  * with the Lower triangular part (the default), or, equivalently, a row-major storage format\n  * with the Upper triangular part. Otherwise, you might get a 20% slowdown for the full factorization\n  * step, and rank-updates can be up to 3 times slower.\n  *\n  * This class supports the \\link InplaceDecomposition inplace decomposition \\endlink mechanism.\n  *\n  * Note that during the decomposition, only the lower (or upper, as defined by _UpLo) triangular part of A is considered.\n  * Therefore, the strict lower part does not have to store correct values.\n  *\n  * \\sa MatrixBase::llt(), SelfAdjointView::llt(), class LDLT\n  */\ntemplate<typename _MatrixType, int _UpLo> class LLT\n{\n  public:\n    typedef _MatrixType MatrixType;\n    enum {\n      RowsAtCompileTime = MatrixType::RowsAtCompileTime,\n      ColsAtCompileTime = MatrixType::ColsAtCompileTime,\n      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime\n    };\n    typedef typename MatrixType::Scalar Scalar;\n    typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;\n    typedef Eigen::Index Index; ///< \\deprecated since Eigen 3.3\n    typedef typename MatrixType::StorageIndex StorageIndex;\n\n    enum {\n      PacketSize = internal::packet_traits<Scalar>::size,\n      AlignmentMask = int(PacketSize)-1,\n      UpLo = _UpLo\n    };\n\n    typedef internal::LLT_Traits<MatrixType,UpLo> Traits;\n\n    /**\n      * \\brief Default Constructor.\n      *\n      * The default constructor is useful in cases in which the user intends to\n      * perform decompositions via LLT::compute(const MatrixType&).\n      */\n    LLT() : m_matrix(), m_isInitialized(false) {}\n\n    /** \\brief Default Constructor with memory preallocation\n      *\n      * Like the default constructor but with preallocation of the internal data\n      * according to the specified problem \\a size.\n      * \\sa LLT()\n      */\n    explicit LLT(Index size) : m_matrix(size, size),\n                    m_isInitialized(false) {}\n\n    template<typename InputType>\n    explicit LLT(const EigenBase<InputType>& matrix)\n      : m_matrix(matrix.rows(), matrix.cols()),\n        m_isInitialized(false)\n    {\n      compute(matrix.derived());\n    }\n\n    /** \\brief Constructs a LDLT factorization from a given matrix\n      *\n      * This overloaded constructor is provided for \\link InplaceDecomposition inplace decomposition \\endlink when\n      * \\c MatrixType is a Eigen::Ref.\n      *\n      * \\sa LLT(const EigenBase&)\n      */\n    template<typename InputType>\n    explicit LLT(EigenBase<InputType>& matrix)\n      : m_matrix(matrix.derived()),\n        m_isInitialized(false)\n    {\n      compute(matrix.derived());\n    }\n\n    /** \\returns a view of the upper triangular matrix U */\n    inline typename Traits::MatrixU matrixU() const\n    {\n      eigen_assert(m_isInitialized && \"LLT is not initialized.\");\n      return Traits::getU(m_matrix);\n    }\n\n    /** \\returns a view of the lower triangular matrix L */\n    inline typename Traits::MatrixL matrixL() const\n    {\n      eigen_assert(m_isInitialized && \"LLT is not initialized.\");\n      return Traits::getL(m_matrix);\n    }\n\n    /** \\returns the solution x of \\f$ A x = b \\f$ using the current decomposition of A.\n      *\n      * Since this LLT class assumes anyway that the matrix A is invertible, the solution\n      * theoretically exists and is unique regardless of b.\n      *\n      * Example: \\include LLT_solve.cpp\n      * Output: \\verbinclude LLT_solve.out\n      *\n      * \\sa solveInPlace(), MatrixBase::llt(), SelfAdjointView::llt()\n      */\n    template<typename Rhs>\n    inline const Solve<LLT, Rhs>\n    solve(const MatrixBase<Rhs>& b) const\n    {\n      eigen_assert(m_isInitialized && \"LLT is not initialized.\");\n      eigen_assert(m_matrix.rows()==b.rows()\n                && \"LLT::solve(): invalid number of rows of the right hand side matrix b\");\n      return Solve<LLT, Rhs>(*this, b.derived());\n    }\n\n    template<typename Derived>\n    void solveInPlace(const MatrixBase<Derived> &bAndX) const;\n\n    template<typename InputType>\n    LLT& compute(const EigenBase<InputType>& matrix);\n\n    /** \\returns an estimate of the reciprocal condition number of the matrix of\n      *  which \\c *this is the Cholesky decomposition.\n      */\n    RealScalar rcond() const\n    {\n      eigen_assert(m_isInitialized && \"LLT is not initialized.\");\n      eigen_assert(m_info == Success && \"LLT failed because matrix appears to be negative\");\n      return internal::rcond_estimate_helper(m_l1_norm, *this);\n    }\n\n    /** \\returns the LLT decomposition matrix\n      *\n      * TODO: document the storage layout\n      */\n    inline const MatrixType& matrixLLT() const\n    {\n      eigen_assert(m_isInitialized && \"LLT is not initialized.\");\n      return m_matrix;\n    }\n\n    MatrixType reconstructedMatrix() const;\n\n\n    /** \\brief Reports whether previous computation was successful.\n      *\n      * \\returns \\c Success if computation was succesful,\n      *          \\c NumericalIssue if the matrix.appears not to be positive definite.\n      */\n    ComputationInfo info() const\n    {\n      eigen_assert(m_isInitialized && \"LLT is not initialized.\");\n      return m_info;\n    }\n\n    /** \\returns the adjoint of \\c *this, that is, a const reference to the decomposition itself as the underlying matrix is self-adjoint.\n      *\n      * This method is provided for compatibility with other matrix decompositions, thus enabling generic code such as:\n      * \\code x = decomposition.adjoint().solve(b) \\endcode\n      */\n    const LLT& adjoint() const { return *this; };\n\n    inline Index rows() const { return m_matrix.rows(); }\n    inline Index cols() const { return m_matrix.cols(); }\n\n    template<typename VectorType>\n    LLT rankUpdate(const VectorType& vec, const RealScalar& sigma = 1);\n\n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    template<typename RhsType, typename DstType>\n    EIGEN_DEVICE_FUNC\n    void _solve_impl(const RhsType &rhs, DstType &dst) const;\n    #endif\n\n  protected:\n\n    static void check_template_parameters()\n    {\n      EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);\n    }\n\n    /** \\internal\n      * Used to compute and store L\n      * The strict upper part is not used and even not initialized.\n      */\n    MatrixType m_matrix;\n    RealScalar m_l1_norm;\n    bool m_isInitialized;\n    ComputationInfo m_info;\n};\n\nnamespace internal {\n\ntemplate<typename Scalar, int UpLo> struct llt_inplace;\n\ntemplate<typename MatrixType, typename VectorType>\nstatic Index llt_rank_update_lower(MatrixType& mat, const VectorType& vec, const typename MatrixType::RealScalar& sigma)\n{\n  using std::sqrt;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename MatrixType::RealScalar RealScalar;\n  typedef typename MatrixType::ColXpr ColXpr;\n  typedef typename internal::remove_all<ColXpr>::type ColXprCleaned;\n  typedef typename ColXprCleaned::SegmentReturnType ColXprSegment;\n  typedef Matrix<Scalar,Dynamic,1> TempVectorType;\n  typedef typename TempVectorType::SegmentReturnType TempVecSegment;\n\n  Index n = mat.cols();\n  eigen_assert(mat.rows()==n && vec.size()==n);\n\n  TempVectorType temp;\n\n  if(sigma>0)\n  {\n    // This version is based on Givens rotations.\n    // It is faster than the other one below, but only works for updates,\n    // i.e., for sigma > 0\n    temp = sqrt(sigma) * vec;\n\n    for(Index i=0; i<n; ++i)\n    {\n      JacobiRotation<Scalar> g;\n      g.makeGivens(mat(i,i), -temp(i), &mat(i,i));\n\n      Index rs = n-i-1;\n      if(rs>0)\n      {\n        ColXprSegment x(mat.col(i).tail(rs));\n        TempVecSegment y(temp.tail(rs));\n        apply_rotation_in_the_plane(x, y, g);\n      }\n    }\n  }\n  else\n  {\n    temp = vec;\n    RealScalar beta = 1;\n    for(Index j=0; j<n; ++j)\n    {\n      RealScalar Ljj = numext::real(mat.coeff(j,j));\n      RealScalar dj = numext::abs2(Ljj);\n      Scalar wj = temp.coeff(j);\n      RealScalar swj2 = sigma*numext::abs2(wj);\n      RealScalar gamma = dj*beta + swj2;\n\n      RealScalar x = dj + swj2/beta;\n      if (x<=RealScalar(0))\n        return j;\n      RealScalar nLjj = sqrt(x);\n      mat.coeffRef(j,j) = nLjj;\n      beta += swj2/dj;\n\n      // Update the terms of L\n      Index rs = n-j-1;\n      if(rs)\n      {\n        temp.tail(rs) -= (wj/Ljj) * mat.col(j).tail(rs);\n        if(gamma != 0)\n          mat.col(j).tail(rs) = (nLjj/Ljj) * mat.col(j).tail(rs) + (nLjj * sigma*numext::conj(wj)/gamma)*temp.tail(rs);\n      }\n    }\n  }\n  return -1;\n}\n\ntemplate<typename Scalar> struct llt_inplace<Scalar, Lower>\n{\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  template<typename MatrixType>\n  static Index unblocked(MatrixType& mat)\n  {\n    using std::sqrt;\n\n    eigen_assert(mat.rows()==mat.cols());\n    const Index size = mat.rows();\n    for(Index k = 0; k < size; ++k)\n    {\n      Index rs = size-k-1; // remaining size\n\n      Block<MatrixType,Dynamic,1> A21(mat,k+1,k,rs,1);\n      Block<MatrixType,1,Dynamic> A10(mat,k,0,1,k);\n      Block<MatrixType,Dynamic,Dynamic> A20(mat,k+1,0,rs,k);\n\n      RealScalar x = numext::real(mat.coeff(k,k));\n      if (k>0) x -= A10.squaredNorm();\n      if (x<=RealScalar(0))\n        return k;\n      mat.coeffRef(k,k) = x = sqrt(x);\n      if (k>0 && rs>0) A21.noalias() -= A20 * A10.adjoint();\n      if (rs>0) A21 /= x;\n    }\n    return -1;\n  }\n\n  template<typename MatrixType>\n  static Index blocked(MatrixType& m)\n  {\n    eigen_assert(m.rows()==m.cols());\n    Index size = m.rows();\n    if(size<32)\n      return unblocked(m);\n\n    Index blockSize = size/8;\n    blockSize = (blockSize/16)*16;\n    blockSize = (std::min)((std::max)(blockSize,Index(8)), Index(128));\n\n    for (Index k=0; k<size; k+=blockSize)\n    {\n      // partition the matrix:\n      //       A00 |  -  |  -\n      // lu  = A10 | A11 |  -\n      //       A20 | A21 | A22\n      Index bs = (std::min)(blockSize, size-k);\n      Index rs = size - k - bs;\n      Block<MatrixType,Dynamic,Dynamic> A11(m,k,   k,   bs,bs);\n      Block<MatrixType,Dynamic,Dynamic> A21(m,k+bs,k,   rs,bs);\n      Block<MatrixType,Dynamic,Dynamic> A22(m,k+bs,k+bs,rs,rs);\n\n      Index ret;\n      if((ret=unblocked(A11))>=0) return k+ret;\n      if(rs>0) A11.adjoint().template triangularView<Upper>().template solveInPlace<OnTheRight>(A21);\n      if(rs>0) A22.template selfadjointView<Lower>().rankUpdate(A21,typename NumTraits<RealScalar>::Literal(-1)); // bottleneck\n    }\n    return -1;\n  }\n\n  template<typename MatrixType, typename VectorType>\n  static Index rankUpdate(MatrixType& mat, const VectorType& vec, const RealScalar& sigma)\n  {\n    return Eigen::internal::llt_rank_update_lower(mat, vec, sigma);\n  }\n};\n\ntemplate<typename Scalar> struct llt_inplace<Scalar, Upper>\n{\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n\n  template<typename MatrixType>\n  static EIGEN_STRONG_INLINE Index unblocked(MatrixType& mat)\n  {\n    Transpose<MatrixType> matt(mat);\n    return llt_inplace<Scalar, Lower>::unblocked(matt);\n  }\n  template<typename MatrixType>\n  static EIGEN_STRONG_INLINE Index blocked(MatrixType& mat)\n  {\n    Transpose<MatrixType> matt(mat);\n    return llt_inplace<Scalar, Lower>::blocked(matt);\n  }\n  template<typename MatrixType, typename VectorType>\n  static Index rankUpdate(MatrixType& mat, const VectorType& vec, const RealScalar& sigma)\n  {\n    Transpose<MatrixType> matt(mat);\n    return llt_inplace<Scalar, Lower>::rankUpdate(matt, vec.conjugate(), sigma);\n  }\n};\n\ntemplate<typename MatrixType> struct LLT_Traits<MatrixType,Lower>\n{\n  typedef const TriangularView<const MatrixType, Lower> MatrixL;\n  typedef const TriangularView<const typename MatrixType::AdjointReturnType, Upper> MatrixU;\n  static inline MatrixL getL(const MatrixType& m) { return MatrixL(m); }\n  static inline MatrixU getU(const MatrixType& m) { return MatrixU(m.adjoint()); }\n  static bool inplace_decomposition(MatrixType& m)\n  { return llt_inplace<typename MatrixType::Scalar, Lower>::blocked(m)==-1; }\n};\n\ntemplate<typename MatrixType> struct LLT_Traits<MatrixType,Upper>\n{\n  typedef const TriangularView<const typename MatrixType::AdjointReturnType, Lower> MatrixL;\n  typedef const TriangularView<const MatrixType, Upper> MatrixU;\n  static inline MatrixL getL(const MatrixType& m) { return MatrixL(m.adjoint()); }\n  static inline MatrixU getU(const MatrixType& m) { return MatrixU(m); }\n  static bool inplace_decomposition(MatrixType& m)\n  { return llt_inplace<typename MatrixType::Scalar, Upper>::blocked(m)==-1; }\n};\n\n} // end namespace internal\n\n/** Computes / recomputes the Cholesky decomposition A = LL^* = U^*U of \\a matrix\n  *\n  * \\returns a reference to *this\n  *\n  * Example: \\include TutorialLinAlgComputeTwice.cpp\n  * Output: \\verbinclude TutorialLinAlgComputeTwice.out\n  */\ntemplate<typename MatrixType, int _UpLo>\ntemplate<typename InputType>\nLLT<MatrixType,_UpLo>& LLT<MatrixType,_UpLo>::compute(const EigenBase<InputType>& a)\n{\n  check_template_parameters();\n\n  eigen_assert(a.rows()==a.cols());\n  const Index size = a.rows();\n  m_matrix.resize(size, size);\n  if (!internal::is_same_dense(m_matrix, a.derived()))\n    m_matrix = a.derived();\n\n  // Compute matrix L1 norm = max abs column sum.\n  m_l1_norm = RealScalar(0);\n  // TODO move this code to SelfAdjointView\n  for (Index col = 0; col < size; ++col) {\n    RealScalar abs_col_sum;\n    if (_UpLo == Lower)\n      abs_col_sum = m_matrix.col(col).tail(size - col).template lpNorm<1>() + m_matrix.row(col).head(col).template lpNorm<1>();\n    else\n      abs_col_sum = m_matrix.col(col).head(col).template lpNorm<1>() + m_matrix.row(col).tail(size - col).template lpNorm<1>();\n    if (abs_col_sum > m_l1_norm)\n      m_l1_norm = abs_col_sum;\n  }\n\n  m_isInitialized = true;\n  bool ok = Traits::inplace_decomposition(m_matrix);\n  m_info = ok ? Success : NumericalIssue;\n\n  return *this;\n}\n\n/** Performs a rank one update (or dowdate) of the current decomposition.\n  * If A = LL^* before the rank one update,\n  * then after it we have LL^* = A + sigma * v v^* where \\a v must be a vector\n  * of same dimension.\n  */\ntemplate<typename _MatrixType, int _UpLo>\ntemplate<typename VectorType>\nLLT<_MatrixType,_UpLo> LLT<_MatrixType,_UpLo>::rankUpdate(const VectorType& v, const RealScalar& sigma)\n{\n  EIGEN_STATIC_ASSERT_VECTOR_ONLY(VectorType);\n  eigen_assert(v.size()==m_matrix.cols());\n  eigen_assert(m_isInitialized);\n  if(internal::llt_inplace<typename MatrixType::Scalar, UpLo>::rankUpdate(m_matrix,v,sigma)>=0)\n    m_info = NumericalIssue;\n  else\n    m_info = Success;\n\n  return *this;\n}\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\ntemplate<typename _MatrixType,int _UpLo>\ntemplate<typename RhsType, typename DstType>\nvoid LLT<_MatrixType,_UpLo>::_solve_impl(const RhsType &rhs, DstType &dst) const\n{\n  dst = rhs;\n  solveInPlace(dst);\n}\n#endif\n\n/** \\internal use x = llt_object.solve(x);\n  *\n  * This is the \\em in-place version of solve().\n  *\n  * \\param bAndX represents both the right-hand side matrix b and result x.\n  *\n  * This version avoids a copy when the right hand side matrix b is not needed anymore.\n  *\n  * \\warning The parameter is only marked 'const' to make the C++ compiler accept a temporary expression here.\n  * This function will const_cast it, so constness isn't honored here.\n  *\n  * \\sa LLT::solve(), MatrixBase::llt()\n  */\ntemplate<typename MatrixType, int _UpLo>\ntemplate<typename Derived>\nvoid LLT<MatrixType,_UpLo>::solveInPlace(const MatrixBase<Derived> &bAndX) const\n{\n  eigen_assert(m_isInitialized && \"LLT is not initialized.\");\n  eigen_assert(m_matrix.rows()==bAndX.rows());\n  matrixL().solveInPlace(bAndX);\n  matrixU().solveInPlace(bAndX);\n}\n\n/** \\returns the matrix represented by the decomposition,\n * i.e., it returns the product: L L^*.\n * This function is provided for debug purpose. */\ntemplate<typename MatrixType, int _UpLo>\nMatrixType LLT<MatrixType,_UpLo>::reconstructedMatrix() const\n{\n  eigen_assert(m_isInitialized && \"LLT is not initialized.\");\n  return matrixL() * matrixL().adjoint().toDenseMatrix();\n}\n\n/** \\cholesky_module\n  * \\returns the LLT decomposition of \\c *this\n  * \\sa SelfAdjointView::llt()\n  */\ntemplate<typename Derived>\ninline const LLT<typename MatrixBase<Derived>::PlainObject>\nMatrixBase<Derived>::llt() const\n{\n  return LLT<PlainObject>(derived());\n}\n\n/** \\cholesky_module\n  * \\returns the LLT decomposition of \\c *this\n  * \\sa SelfAdjointView::llt()\n  */\ntemplate<typename MatrixType, unsigned int UpLo>\ninline const LLT<typename SelfAdjointView<MatrixType, UpLo>::PlainObject, UpLo>\nSelfAdjointView<MatrixType, UpLo>::llt() const\n{\n  return LLT<PlainObject,UpLo>(m_matrix);\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_LLT_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Cholesky/LLT_LAPACKE.h",
    "content": "/*\n Copyright (c) 2011, Intel Corporation. All rights reserved.\n\n Redistribution and use in source and binary forms, with or without modification,\n are permitted provided that the following conditions are met:\n\n * Redistributions of source code must retain the above copyright notice, this\n   list of conditions and the following disclaimer.\n * Redistributions in binary form must reproduce the above copyright notice,\n   this list of conditions and the following disclaimer in the documentation\n   and/or other materials provided with the distribution.\n * Neither the name of Intel Corporation nor the names of its contributors may\n   be used to endorse or promote products derived from this software without\n   specific prior written permission.\n\n THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\" AND\n ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED\n WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\n DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR\n ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES\n (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;\n LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON\n ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT\n (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS\n SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n\n ********************************************************************************\n *   Content : Eigen bindings to LAPACKe\n *     LLt decomposition based on LAPACKE_?potrf function.\n ********************************************************************************\n*/\n\n#ifndef EIGEN_LLT_LAPACKE_H\n#define EIGEN_LLT_LAPACKE_H\n\nnamespace Eigen { \n\nnamespace internal {\n\ntemplate<typename Scalar> struct lapacke_llt;\n\n#define EIGEN_LAPACKE_LLT(EIGTYPE, BLASTYPE, LAPACKE_PREFIX) \\\ntemplate<> struct lapacke_llt<EIGTYPE> \\\n{ \\\n  template<typename MatrixType> \\\n  static inline Index potrf(MatrixType& m, char uplo) \\\n  { \\\n    lapack_int matrix_order; \\\n    lapack_int size, lda, info, StorageOrder; \\\n    EIGTYPE* a; \\\n    eigen_assert(m.rows()==m.cols()); \\\n    /* Set up parameters for ?potrf */ \\\n    size = convert_index<lapack_int>(m.rows()); \\\n    StorageOrder = MatrixType::Flags&RowMajorBit?RowMajor:ColMajor; \\\n    matrix_order = StorageOrder==RowMajor ? LAPACK_ROW_MAJOR : LAPACK_COL_MAJOR; \\\n    a = &(m.coeffRef(0,0)); \\\n    lda = convert_index<lapack_int>(m.outerStride()); \\\n\\\n    info = LAPACKE_##LAPACKE_PREFIX##potrf( matrix_order, uplo, size, (BLASTYPE*)a, lda ); \\\n    info = (info==0) ? -1 : info>0 ? info-1 : size; \\\n    return info; \\\n  } \\\n}; \\\ntemplate<> struct llt_inplace<EIGTYPE, Lower> \\\n{ \\\n  template<typename MatrixType> \\\n  static Index blocked(MatrixType& m) \\\n  { \\\n    return lapacke_llt<EIGTYPE>::potrf(m, 'L'); \\\n  } \\\n  template<typename MatrixType, typename VectorType> \\\n  static Index rankUpdate(MatrixType& mat, const VectorType& vec, const typename MatrixType::RealScalar& sigma) \\\n  { return Eigen::internal::llt_rank_update_lower(mat, vec, sigma); } \\\n}; \\\ntemplate<> struct llt_inplace<EIGTYPE, Upper> \\\n{ \\\n  template<typename MatrixType> \\\n  static Index blocked(MatrixType& m) \\\n  { \\\n    return lapacke_llt<EIGTYPE>::potrf(m, 'U'); \\\n  } \\\n  template<typename MatrixType, typename VectorType> \\\n  static Index rankUpdate(MatrixType& mat, const VectorType& vec, const typename MatrixType::RealScalar& sigma) \\\n  { \\\n    Transpose<MatrixType> matt(mat); \\\n    return llt_inplace<EIGTYPE, Lower>::rankUpdate(matt, vec.conjugate(), sigma); \\\n  } \\\n};\n\nEIGEN_LAPACKE_LLT(double, double, d)\nEIGEN_LAPACKE_LLT(float, float, s)\nEIGEN_LAPACKE_LLT(dcomplex, lapack_complex_double, z)\nEIGEN_LAPACKE_LLT(scomplex, lapack_complex_float, c)\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_LLT_LAPACKE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/CholmodSupport/CholmodSupport.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CHOLMODSUPPORT_H\n#define EIGEN_CHOLMODSUPPORT_H\n\nnamespace Eigen { \n\nnamespace internal {\n\ntemplate<typename Scalar> struct cholmod_configure_matrix;\n\ntemplate<> struct cholmod_configure_matrix<double> {\n  template<typename CholmodType>\n  static void run(CholmodType& mat) {\n    mat.xtype = CHOLMOD_REAL;\n    mat.dtype = CHOLMOD_DOUBLE;\n  }\n};\n\ntemplate<> struct cholmod_configure_matrix<std::complex<double> > {\n  template<typename CholmodType>\n  static void run(CholmodType& mat) {\n    mat.xtype = CHOLMOD_COMPLEX;\n    mat.dtype = CHOLMOD_DOUBLE;\n  }\n};\n\n// Other scalar types are not yet suppotred by Cholmod\n// template<> struct cholmod_configure_matrix<float> {\n//   template<typename CholmodType>\n//   static void run(CholmodType& mat) {\n//     mat.xtype = CHOLMOD_REAL;\n//     mat.dtype = CHOLMOD_SINGLE;\n//   }\n// };\n//\n// template<> struct cholmod_configure_matrix<std::complex<float> > {\n//   template<typename CholmodType>\n//   static void run(CholmodType& mat) {\n//     mat.xtype = CHOLMOD_COMPLEX;\n//     mat.dtype = CHOLMOD_SINGLE;\n//   }\n// };\n\n} // namespace internal\n\n/** Wraps the Eigen sparse matrix \\a mat into a Cholmod sparse matrix object.\n  * Note that the data are shared.\n  */\ntemplate<typename _Scalar, int _Options, typename _StorageIndex>\ncholmod_sparse viewAsCholmod(Ref<SparseMatrix<_Scalar,_Options,_StorageIndex> > mat)\n{\n  cholmod_sparse res;\n  res.nzmax   = mat.nonZeros();\n  res.nrow    = mat.rows();\n  res.ncol    = mat.cols();\n  res.p       = mat.outerIndexPtr();\n  res.i       = mat.innerIndexPtr();\n  res.x       = mat.valuePtr();\n  res.z       = 0;\n  res.sorted  = 1;\n  if(mat.isCompressed())\n  {\n    res.packed  = 1;\n    res.nz = 0;\n  }\n  else\n  {\n    res.packed  = 0;\n    res.nz = mat.innerNonZeroPtr();\n  }\n\n  res.dtype   = 0;\n  res.stype   = -1;\n  \n  if (internal::is_same<_StorageIndex,int>::value)\n  {\n    res.itype = CHOLMOD_INT;\n  }\n  else if (internal::is_same<_StorageIndex,long>::value)\n  {\n    res.itype = CHOLMOD_LONG;\n  }\n  else\n  {\n    eigen_assert(false && \"Index type not supported yet\");\n  }\n\n  // setup res.xtype\n  internal::cholmod_configure_matrix<_Scalar>::run(res);\n  \n  res.stype = 0;\n  \n  return res;\n}\n\ntemplate<typename _Scalar, int _Options, typename _Index>\nconst cholmod_sparse viewAsCholmod(const SparseMatrix<_Scalar,_Options,_Index>& mat)\n{\n  cholmod_sparse res = viewAsCholmod(Ref<SparseMatrix<_Scalar,_Options,_Index> >(mat.const_cast_derived()));\n  return res;\n}\n\ntemplate<typename _Scalar, int _Options, typename _Index>\nconst cholmod_sparse viewAsCholmod(const SparseVector<_Scalar,_Options,_Index>& mat)\n{\n  cholmod_sparse res = viewAsCholmod(Ref<SparseMatrix<_Scalar,_Options,_Index> >(mat.const_cast_derived()));\n  return res;\n}\n\n/** Returns a view of the Eigen sparse matrix \\a mat as Cholmod sparse matrix.\n  * The data are not copied but shared. */\ntemplate<typename _Scalar, int _Options, typename _Index, unsigned int UpLo>\ncholmod_sparse viewAsCholmod(const SparseSelfAdjointView<const SparseMatrix<_Scalar,_Options,_Index>, UpLo>& mat)\n{\n  cholmod_sparse res = viewAsCholmod(Ref<SparseMatrix<_Scalar,_Options,_Index> >(mat.matrix().const_cast_derived()));\n  \n  if(UpLo==Upper) res.stype =  1;\n  if(UpLo==Lower) res.stype = -1;\n\n  return res;\n}\n\n/** Returns a view of the Eigen \\b dense matrix \\a mat as Cholmod dense matrix.\n  * The data are not copied but shared. */\ntemplate<typename Derived>\ncholmod_dense viewAsCholmod(MatrixBase<Derived>& mat)\n{\n  EIGEN_STATIC_ASSERT((internal::traits<Derived>::Flags&RowMajorBit)==0,THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);\n  typedef typename Derived::Scalar Scalar;\n\n  cholmod_dense res;\n  res.nrow   = mat.rows();\n  res.ncol   = mat.cols();\n  res.nzmax  = res.nrow * res.ncol;\n  res.d      = Derived::IsVectorAtCompileTime ? mat.derived().size() : mat.derived().outerStride();\n  res.x      = (void*)(mat.derived().data());\n  res.z      = 0;\n\n  internal::cholmod_configure_matrix<Scalar>::run(res);\n\n  return res;\n}\n\n/** Returns a view of the Cholmod sparse matrix \\a cm as an Eigen sparse matrix.\n  * The data are not copied but shared. */\ntemplate<typename Scalar, int Flags, typename StorageIndex>\nMappedSparseMatrix<Scalar,Flags,StorageIndex> viewAsEigen(cholmod_sparse& cm)\n{\n  return MappedSparseMatrix<Scalar,Flags,StorageIndex>\n         (cm.nrow, cm.ncol, static_cast<StorageIndex*>(cm.p)[cm.ncol],\n          static_cast<StorageIndex*>(cm.p), static_cast<StorageIndex*>(cm.i),static_cast<Scalar*>(cm.x) );\n}\n\nenum CholmodMode {\n  CholmodAuto, CholmodSimplicialLLt, CholmodSupernodalLLt, CholmodLDLt\n};\n\n\n/** \\ingroup CholmodSupport_Module\n  * \\class CholmodBase\n  * \\brief The base class for the direct Cholesky factorization of Cholmod\n  * \\sa class CholmodSupernodalLLT, class CholmodSimplicialLDLT, class CholmodSimplicialLLT\n  */\ntemplate<typename _MatrixType, int _UpLo, typename Derived>\nclass CholmodBase : public SparseSolverBase<Derived>\n{\n  protected:\n    typedef SparseSolverBase<Derived> Base;\n    using Base::derived;\n    using Base::m_isInitialized;\n  public:\n    typedef _MatrixType MatrixType;\n    enum { UpLo = _UpLo };\n    typedef typename MatrixType::Scalar Scalar;\n    typedef typename MatrixType::RealScalar RealScalar;\n    typedef MatrixType CholMatrixType;\n    typedef typename MatrixType::StorageIndex StorageIndex;\n    enum {\n      ColsAtCompileTime = MatrixType::ColsAtCompileTime,\n      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime\n    };\n\n  public:\n\n    CholmodBase()\n      : m_cholmodFactor(0), m_info(Success), m_factorizationIsOk(false), m_analysisIsOk(false)\n    {\n      EIGEN_STATIC_ASSERT((internal::is_same<double,RealScalar>::value), CHOLMOD_SUPPORTS_DOUBLE_PRECISION_ONLY);\n      m_shiftOffset[0] = m_shiftOffset[1] = 0.0;\n      cholmod_start(&m_cholmod);\n    }\n\n    explicit CholmodBase(const MatrixType& matrix)\n      : m_cholmodFactor(0), m_info(Success), m_factorizationIsOk(false), m_analysisIsOk(false)\n    {\n      EIGEN_STATIC_ASSERT((internal::is_same<double,RealScalar>::value), CHOLMOD_SUPPORTS_DOUBLE_PRECISION_ONLY);\n      m_shiftOffset[0] = m_shiftOffset[1] = 0.0;\n      cholmod_start(&m_cholmod);\n      compute(matrix);\n    }\n\n    ~CholmodBase()\n    {\n      if(m_cholmodFactor)\n        cholmod_free_factor(&m_cholmodFactor, &m_cholmod);\n      cholmod_finish(&m_cholmod);\n    }\n    \n    inline StorageIndex cols() const { return internal::convert_index<StorageIndex, Index>(m_cholmodFactor->n); }\n    inline StorageIndex rows() const { return internal::convert_index<StorageIndex, Index>(m_cholmodFactor->n); }\n    \n    /** \\brief Reports whether previous computation was successful.\n      *\n      * \\returns \\c Success if computation was succesful,\n      *          \\c NumericalIssue if the matrix.appears to be negative.\n      */\n    ComputationInfo info() const\n    {\n      eigen_assert(m_isInitialized && \"Decomposition is not initialized.\");\n      return m_info;\n    }\n\n    /** Computes the sparse Cholesky decomposition of \\a matrix */\n    Derived& compute(const MatrixType& matrix)\n    {\n      analyzePattern(matrix);\n      factorize(matrix);\n      return derived();\n    }\n    \n    /** Performs a symbolic decomposition on the sparsity pattern of \\a matrix.\n      *\n      * This function is particularly useful when solving for several problems having the same structure.\n      * \n      * \\sa factorize()\n      */\n    void analyzePattern(const MatrixType& matrix)\n    {\n      if(m_cholmodFactor)\n      {\n        cholmod_free_factor(&m_cholmodFactor, &m_cholmod);\n        m_cholmodFactor = 0;\n      }\n      cholmod_sparse A = viewAsCholmod(matrix.template selfadjointView<UpLo>());\n      m_cholmodFactor = cholmod_analyze(&A, &m_cholmod);\n      \n      this->m_isInitialized = true;\n      this->m_info = Success;\n      m_analysisIsOk = true;\n      m_factorizationIsOk = false;\n    }\n    \n    /** Performs a numeric decomposition of \\a matrix\n      *\n      * The given matrix must have the same sparsity pattern as the matrix on which the symbolic decomposition has been performed.\n      *\n      * \\sa analyzePattern()\n      */\n    void factorize(const MatrixType& matrix)\n    {\n      eigen_assert(m_analysisIsOk && \"You must first call analyzePattern()\");\n      cholmod_sparse A = viewAsCholmod(matrix.template selfadjointView<UpLo>());\n      cholmod_factorize_p(&A, m_shiftOffset, 0, 0, m_cholmodFactor, &m_cholmod);\n\n      // If the factorization failed, minor is the column at which it did. On success minor == n.\n      this->m_info = (m_cholmodFactor->minor == m_cholmodFactor->n ? Success : NumericalIssue);\n      m_factorizationIsOk = true;\n    }\n    \n    /** Returns a reference to the Cholmod's configuration structure to get a full control over the performed operations.\n     *  See the Cholmod user guide for details. */\n    cholmod_common& cholmod() { return m_cholmod; }\n    \n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    /** \\internal */\n    template<typename Rhs,typename Dest>\n    void _solve_impl(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const\n    {\n      eigen_assert(m_factorizationIsOk && \"The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()\");\n      const Index size = m_cholmodFactor->n;\n      EIGEN_UNUSED_VARIABLE(size);\n      eigen_assert(size==b.rows());\n      \n      // Cholmod needs column-major stoarge without inner-stride, which corresponds to the default behavior of Ref.\n      Ref<const Matrix<typename Rhs::Scalar,Dynamic,Dynamic,ColMajor> > b_ref(b.derived());\n\n      cholmod_dense b_cd = viewAsCholmod(b_ref);\n      cholmod_dense* x_cd = cholmod_solve(CHOLMOD_A, m_cholmodFactor, &b_cd, &m_cholmod);\n      if(!x_cd)\n      {\n        this->m_info = NumericalIssue;\n        return;\n      }\n      // TODO optimize this copy by swapping when possible (be careful with alignment, etc.)\n      dest = Matrix<Scalar,Dest::RowsAtCompileTime,Dest::ColsAtCompileTime>::Map(reinterpret_cast<Scalar*>(x_cd->x),b.rows(),b.cols());\n      cholmod_free_dense(&x_cd, &m_cholmod);\n    }\n    \n    /** \\internal */\n    template<typename RhsDerived, typename DestDerived>\n    void _solve_impl(const SparseMatrixBase<RhsDerived> &b, SparseMatrixBase<DestDerived> &dest) const\n    {\n      eigen_assert(m_factorizationIsOk && \"The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()\");\n      const Index size = m_cholmodFactor->n;\n      EIGEN_UNUSED_VARIABLE(size);\n      eigen_assert(size==b.rows());\n\n      // note: cs stands for Cholmod Sparse\n      Ref<SparseMatrix<typename RhsDerived::Scalar,ColMajor,typename RhsDerived::StorageIndex> > b_ref(b.const_cast_derived());\n      cholmod_sparse b_cs = viewAsCholmod(b_ref);\n      cholmod_sparse* x_cs = cholmod_spsolve(CHOLMOD_A, m_cholmodFactor, &b_cs, &m_cholmod);\n      if(!x_cs)\n      {\n        this->m_info = NumericalIssue;\n        return;\n      }\n      // TODO optimize this copy by swapping when possible (be careful with alignment, etc.)\n      dest.derived() = viewAsEigen<typename DestDerived::Scalar,ColMajor,typename DestDerived::StorageIndex>(*x_cs);\n      cholmod_free_sparse(&x_cs, &m_cholmod);\n    }\n    #endif // EIGEN_PARSED_BY_DOXYGEN\n    \n    \n    /** Sets the shift parameter that will be used to adjust the diagonal coefficients during the numerical factorization.\n      *\n      * During the numerical factorization, an offset term is added to the diagonal coefficients:\\n\n      * \\c d_ii = \\a offset + \\c d_ii\n      *\n      * The default is \\a offset=0.\n      *\n      * \\returns a reference to \\c *this.\n      */\n    Derived& setShift(const RealScalar& offset)\n    {\n      m_shiftOffset[0] = double(offset);\n      return derived();\n    }\n    \n    /** \\returns the determinant of the underlying matrix from the current factorization */\n    Scalar determinant() const\n    {\n      using std::exp;\n      return exp(logDeterminant());\n    }\n\n    /** \\returns the log determinant of the underlying matrix from the current factorization */\n    Scalar logDeterminant() const\n    {\n      using std::log;\n      using numext::real;\n      eigen_assert(m_factorizationIsOk && \"The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()\");\n\n      RealScalar logDet = 0;\n      Scalar *x = static_cast<Scalar*>(m_cholmodFactor->x);\n      if (m_cholmodFactor->is_super)\n      {\n        // Supernodal factorization stored as a packed list of dense column-major blocs,\n        // as described by the following structure:\n\n        // super[k] == index of the first column of the j-th super node\n        StorageIndex *super = static_cast<StorageIndex*>(m_cholmodFactor->super);\n        // pi[k] == offset to the description of row indices\n        StorageIndex *pi = static_cast<StorageIndex*>(m_cholmodFactor->pi);\n        // px[k] == offset to the respective dense block\n        StorageIndex *px = static_cast<StorageIndex*>(m_cholmodFactor->px);\n\n        Index nb_super_nodes = m_cholmodFactor->nsuper;\n        for (Index k=0; k < nb_super_nodes; ++k)\n        {\n          StorageIndex ncols = super[k + 1] - super[k];\n          StorageIndex nrows = pi[k + 1] - pi[k];\n\n          Map<const Array<Scalar,1,Dynamic>, 0, InnerStride<> > sk(x + px[k], ncols, InnerStride<>(nrows+1));\n          logDet += sk.real().log().sum();\n        }\n      }\n      else\n      {\n        // Simplicial factorization stored as standard CSC matrix.\n        StorageIndex *p = static_cast<StorageIndex*>(m_cholmodFactor->p);\n        Index size = m_cholmodFactor->n;\n        for (Index k=0; k<size; ++k)\n          logDet += log(real( x[p[k]] ));\n      }\n      if (m_cholmodFactor->is_ll)\n        logDet *= 2.0;\n      return logDet;\n    };\n\n    template<typename Stream>\n    void dumpMemory(Stream& /*s*/)\n    {}\n    \n  protected:\n    mutable cholmod_common m_cholmod;\n    cholmod_factor* m_cholmodFactor;\n    double m_shiftOffset[2];\n    mutable ComputationInfo m_info;\n    int m_factorizationIsOk;\n    int m_analysisIsOk;\n};\n\n/** \\ingroup CholmodSupport_Module\n  * \\class CholmodSimplicialLLT\n  * \\brief A simplicial direct Cholesky (LLT) factorization and solver based on Cholmod\n  *\n  * This class allows to solve for A.X = B sparse linear problems via a simplicial LL^T Cholesky factorization\n  * using the Cholmod library.\n  * This simplicial variant is equivalent to Eigen's built-in SimplicialLLT class. Therefore, it has little practical interest.\n  * The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices\n  * X and B can be either dense or sparse.\n  *\n  * \\tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>\n  * \\tparam _UpLo the triangular part that will be used for the computations. It can be Lower\n  *               or Upper. Default is Lower.\n  *\n  * \\implsparsesolverconcept\n  *\n  * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.\n  *\n  * \\warning Only double precision real and complex scalar types are supported by Cholmod.\n  *\n  * \\sa \\ref TutorialSparseSolverConcept, class CholmodSupernodalLLT, class SimplicialLLT\n  */\ntemplate<typename _MatrixType, int _UpLo = Lower>\nclass CholmodSimplicialLLT : public CholmodBase<_MatrixType, _UpLo, CholmodSimplicialLLT<_MatrixType, _UpLo> >\n{\n    typedef CholmodBase<_MatrixType, _UpLo, CholmodSimplicialLLT> Base;\n    using Base::m_cholmod;\n    \n  public:\n    \n    typedef _MatrixType MatrixType;\n    \n    CholmodSimplicialLLT() : Base() { init(); }\n\n    CholmodSimplicialLLT(const MatrixType& matrix) : Base()\n    {\n      init();\n      this->compute(matrix);\n    }\n\n    ~CholmodSimplicialLLT() {}\n  protected:\n    void init()\n    {\n      m_cholmod.final_asis = 0;\n      m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;\n      m_cholmod.final_ll = 1;\n    }\n};\n\n\n/** \\ingroup CholmodSupport_Module\n  * \\class CholmodSimplicialLDLT\n  * \\brief A simplicial direct Cholesky (LDLT) factorization and solver based on Cholmod\n  *\n  * This class allows to solve for A.X = B sparse linear problems via a simplicial LDL^T Cholesky factorization\n  * using the Cholmod library.\n  * This simplicial variant is equivalent to Eigen's built-in SimplicialLDLT class. Therefore, it has little practical interest.\n  * The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices\n  * X and B can be either dense or sparse.\n  *\n  * \\tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>\n  * \\tparam _UpLo the triangular part that will be used for the computations. It can be Lower\n  *               or Upper. Default is Lower.\n  *\n  * \\implsparsesolverconcept\n  *\n  * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.\n  *\n  * \\warning Only double precision real and complex scalar types are supported by Cholmod.\n  *\n  * \\sa \\ref TutorialSparseSolverConcept, class CholmodSupernodalLLT, class SimplicialLDLT\n  */\ntemplate<typename _MatrixType, int _UpLo = Lower>\nclass CholmodSimplicialLDLT : public CholmodBase<_MatrixType, _UpLo, CholmodSimplicialLDLT<_MatrixType, _UpLo> >\n{\n    typedef CholmodBase<_MatrixType, _UpLo, CholmodSimplicialLDLT> Base;\n    using Base::m_cholmod;\n    \n  public:\n    \n    typedef _MatrixType MatrixType;\n    \n    CholmodSimplicialLDLT() : Base() { init(); }\n\n    CholmodSimplicialLDLT(const MatrixType& matrix) : Base()\n    {\n      init();\n      this->compute(matrix);\n    }\n\n    ~CholmodSimplicialLDLT() {}\n  protected:\n    void init()\n    {\n      m_cholmod.final_asis = 1;\n      m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;\n    }\n};\n\n/** \\ingroup CholmodSupport_Module\n  * \\class CholmodSupernodalLLT\n  * \\brief A supernodal Cholesky (LLT) factorization and solver based on Cholmod\n  *\n  * This class allows to solve for A.X = B sparse linear problems via a supernodal LL^T Cholesky factorization\n  * using the Cholmod library.\n  * This supernodal variant performs best on dense enough problems, e.g., 3D FEM, or very high order 2D FEM.\n  * The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices\n  * X and B can be either dense or sparse.\n  *\n  * \\tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>\n  * \\tparam _UpLo the triangular part that will be used for the computations. It can be Lower\n  *               or Upper. Default is Lower.\n  *\n  * \\implsparsesolverconcept\n  *\n  * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.\n  *\n  * \\warning Only double precision real and complex scalar types are supported by Cholmod.\n  *\n  * \\sa \\ref TutorialSparseSolverConcept\n  */\ntemplate<typename _MatrixType, int _UpLo = Lower>\nclass CholmodSupernodalLLT : public CholmodBase<_MatrixType, _UpLo, CholmodSupernodalLLT<_MatrixType, _UpLo> >\n{\n    typedef CholmodBase<_MatrixType, _UpLo, CholmodSupernodalLLT> Base;\n    using Base::m_cholmod;\n    \n  public:\n    \n    typedef _MatrixType MatrixType;\n    \n    CholmodSupernodalLLT() : Base() { init(); }\n\n    CholmodSupernodalLLT(const MatrixType& matrix) : Base()\n    {\n      init();\n      this->compute(matrix);\n    }\n\n    ~CholmodSupernodalLLT() {}\n  protected:\n    void init()\n    {\n      m_cholmod.final_asis = 1;\n      m_cholmod.supernodal = CHOLMOD_SUPERNODAL;\n    }\n};\n\n/** \\ingroup CholmodSupport_Module\n  * \\class CholmodDecomposition\n  * \\brief A general Cholesky factorization and solver based on Cholmod\n  *\n  * This class allows to solve for A.X = B sparse linear problems via a LL^T or LDL^T Cholesky factorization\n  * using the Cholmod library. The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices\n  * X and B can be either dense or sparse.\n  *\n  * This variant permits to change the underlying Cholesky method at runtime.\n  * On the other hand, it does not provide access to the result of the factorization.\n  * The default is to let Cholmod automatically choose between a simplicial and supernodal factorization.\n  *\n  * \\tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>\n  * \\tparam _UpLo the triangular part that will be used for the computations. It can be Lower\n  *               or Upper. Default is Lower.\n  *\n  * \\implsparsesolverconcept\n  *\n  * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.\n  *\n  * \\warning Only double precision real and complex scalar types are supported by Cholmod.\n  *\n  * \\sa \\ref TutorialSparseSolverConcept\n  */\ntemplate<typename _MatrixType, int _UpLo = Lower>\nclass CholmodDecomposition : public CholmodBase<_MatrixType, _UpLo, CholmodDecomposition<_MatrixType, _UpLo> >\n{\n    typedef CholmodBase<_MatrixType, _UpLo, CholmodDecomposition> Base;\n    using Base::m_cholmod;\n    \n  public:\n    \n    typedef _MatrixType MatrixType;\n    \n    CholmodDecomposition() : Base() { init(); }\n\n    CholmodDecomposition(const MatrixType& matrix) : Base()\n    {\n      init();\n      this->compute(matrix);\n    }\n\n    ~CholmodDecomposition() {}\n    \n    void setMode(CholmodMode mode)\n    {\n      switch(mode)\n      {\n        case CholmodAuto:\n          m_cholmod.final_asis = 1;\n          m_cholmod.supernodal = CHOLMOD_AUTO;\n          break;\n        case CholmodSimplicialLLt:\n          m_cholmod.final_asis = 0;\n          m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;\n          m_cholmod.final_ll = 1;\n          break;\n        case CholmodSupernodalLLt:\n          m_cholmod.final_asis = 1;\n          m_cholmod.supernodal = CHOLMOD_SUPERNODAL;\n          break;\n        case CholmodLDLt:\n          m_cholmod.final_asis = 1;\n          m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;\n          break;\n        default:\n          break;\n      }\n    }\n  protected:\n    void init()\n    {\n      m_cholmod.final_asis = 1;\n      m_cholmod.supernodal = CHOLMOD_AUTO;\n    }\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_CHOLMODSUPPORT_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/Array.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_ARRAY_H\n#define EIGEN_ARRAY_H\n\nnamespace Eigen {\n\nnamespace internal {\ntemplate<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>\nstruct traits<Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> > : traits<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >\n{\n  typedef ArrayXpr XprKind;\n  typedef ArrayBase<Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> > XprBase;\n};\n}\n\n/** \\class Array\n  * \\ingroup Core_Module\n  *\n  * \\brief General-purpose arrays with easy API for coefficient-wise operations\n  *\n  * The %Array class is very similar to the Matrix class. It provides\n  * general-purpose one- and two-dimensional arrays. The difference between the\n  * %Array and the %Matrix class is primarily in the API: the API for the\n  * %Array class provides easy access to coefficient-wise operations, while the\n  * API for the %Matrix class provides easy access to linear-algebra\n  * operations.\n  *\n  * See documentation of class Matrix for detailed information on the template parameters\n  * storage layout.\n  *\n  * This class can be extended with the help of the plugin mechanism described on the page\n  * \\ref TopicCustomizing_Plugins by defining the preprocessor symbol \\c EIGEN_ARRAY_PLUGIN.\n  *\n  * \\sa \\blank \\ref TutorialArrayClass, \\ref TopicClassHierarchy\n  */\ntemplate<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>\nclass Array\n  : public PlainObjectBase<Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >\n{\n  public:\n\n    typedef PlainObjectBase<Array> Base;\n    EIGEN_DENSE_PUBLIC_INTERFACE(Array)\n\n    enum { Options = _Options };\n    typedef typename Base::PlainObject PlainObject;\n\n  protected:\n    template <typename Derived, typename OtherDerived, bool IsVector>\n    friend struct internal::conservative_resize_like_impl;\n\n    using Base::m_storage;\n\n  public:\n\n    using Base::base;\n    using Base::coeff;\n    using Base::coeffRef;\n\n    /**\n      * The usage of\n      *   using Base::operator=;\n      * fails on MSVC. Since the code below is working with GCC and MSVC, we skipped\n      * the usage of 'using'. This should be done only for operator=.\n      */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Array& operator=(const EigenBase<OtherDerived> &other)\n    {\n      return Base::operator=(other);\n    }\n\n    /** Set all the entries to \\a value.\n      * \\sa DenseBase::setConstant(), DenseBase::fill()\n      */\n    /* This overload is needed because the usage of\n      *   using Base::operator=;\n      * fails on MSVC. Since the code below is working with GCC and MSVC, we skipped\n      * the usage of 'using'. This should be done only for operator=.\n      */\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Array& operator=(const Scalar &value)\n    {\n      Base::setConstant(value);\n      return *this;\n    }\n\n    /** Copies the value of the expression \\a other into \\c *this with automatic resizing.\n      *\n      * *this might be resized to match the dimensions of \\a other. If *this was a null matrix (not already initialized),\n      * it will be initialized.\n      *\n      * Note that copying a row-vector into a vector (and conversely) is allowed.\n      * The resizing, if any, is then done in the appropriate way so that row-vectors\n      * remain row-vectors and vectors remain vectors.\n      */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Array& operator=(const DenseBase<OtherDerived>& other)\n    {\n      return Base::_set(other);\n    }\n\n    /** This is a special case of the templated operator=. Its purpose is to\n      * prevent a default operator= from hiding the templated operator=.\n      */\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Array& operator=(const Array& other)\n    {\n      return Base::_set(other);\n    }\n    \n    /** Default constructor.\n      *\n      * For fixed-size matrices, does nothing.\n      *\n      * For dynamic-size matrices, creates an empty matrix of size 0. Does not allocate any array. Such a matrix\n      * is called a null matrix. This constructor is the unique way to create null matrices: resizing\n      * a matrix to 0 is not supported.\n      *\n      * \\sa resize(Index,Index)\n      */\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Array() : Base()\n    {\n      Base::_check_template_params();\n      EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED\n    }\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\n    // FIXME is it still needed ??\n    /** \\internal */\n    EIGEN_DEVICE_FUNC\n    Array(internal::constructor_without_unaligned_array_assert)\n      : Base(internal::constructor_without_unaligned_array_assert())\n    {\n      Base::_check_template_params();\n      EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED\n    }\n#endif\n\n#if EIGEN_HAS_RVALUE_REFERENCES\n    EIGEN_DEVICE_FUNC\n    Array(Array&& other) EIGEN_NOEXCEPT_IF(std::is_nothrow_move_constructible<Scalar>::value)\n      : Base(std::move(other))\n    {\n      Base::_check_template_params();\n      if (RowsAtCompileTime!=Dynamic && ColsAtCompileTime!=Dynamic)\n        Base::_set_noalias(other);\n    }\n    EIGEN_DEVICE_FUNC\n    Array& operator=(Array&& other) EIGEN_NOEXCEPT_IF(std::is_nothrow_move_assignable<Scalar>::value)\n    {\n      other.swap(*this);\n      return *this;\n    }\n#endif\n\n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    template<typename T>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE explicit Array(const T& x)\n    {\n      Base::_check_template_params();\n      Base::template _init1<T>(x);\n    }\n\n    template<typename T0, typename T1>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Array(const T0& val0, const T1& val1)\n    {\n      Base::_check_template_params();\n      this->template _init2<T0,T1>(val0, val1);\n    }\n    #else\n    /** \\brief Constructs a fixed-sized array initialized with coefficients starting at \\a data */\n    EIGEN_DEVICE_FUNC explicit Array(const Scalar *data);\n    /** Constructs a vector or row-vector with given dimension. \\only_for_vectors\n      *\n      * Note that this is only useful for dynamic-size vectors. For fixed-size vectors,\n      * it is redundant to pass the dimension here, so it makes more sense to use the default\n      * constructor Array() instead.\n      */\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE explicit Array(Index dim);\n    /** constructs an initialized 1x1 Array with the given coefficient */\n    Array(const Scalar& value);\n    /** constructs an uninitialized array with \\a rows rows and \\a cols columns.\n      *\n      * This is useful for dynamic-size arrays. For fixed-size arrays,\n      * it is redundant to pass these parameters, so one should use the default constructor\n      * Array() instead. */\n    Array(Index rows, Index cols);\n    /** constructs an initialized 2D vector with given coefficients */\n    Array(const Scalar& val0, const Scalar& val1);\n    #endif\n\n    /** constructs an initialized 3D vector with given coefficients */\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Array(const Scalar& val0, const Scalar& val1, const Scalar& val2)\n    {\n      Base::_check_template_params();\n      EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Array, 3)\n      m_storage.data()[0] = val0;\n      m_storage.data()[1] = val1;\n      m_storage.data()[2] = val2;\n    }\n    /** constructs an initialized 4D vector with given coefficients */\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Array(const Scalar& val0, const Scalar& val1, const Scalar& val2, const Scalar& val3)\n    {\n      Base::_check_template_params();\n      EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Array, 4)\n      m_storage.data()[0] = val0;\n      m_storage.data()[1] = val1;\n      m_storage.data()[2] = val2;\n      m_storage.data()[3] = val3;\n    }\n\n    /** Copy constructor */\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Array(const Array& other)\n            : Base(other)\n    { }\n\n  private:\n    struct PrivateType {};\n  public:\n\n    /** \\sa MatrixBase::operator=(const EigenBase<OtherDerived>&) */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Array(const EigenBase<OtherDerived> &other,\n                              typename internal::enable_if<internal::is_convertible<typename OtherDerived::Scalar,Scalar>::value,\n                                                           PrivateType>::type = PrivateType())\n      : Base(other.derived())\n    { }\n\n    EIGEN_DEVICE_FUNC inline Index innerStride() const { return 1; }\n    EIGEN_DEVICE_FUNC inline Index outerStride() const { return this->innerSize(); }\n\n    #ifdef EIGEN_ARRAY_PLUGIN\n    #include EIGEN_ARRAY_PLUGIN\n    #endif\n\n  private:\n\n    template<typename MatrixType, typename OtherDerived, bool SwapPointers>\n    friend struct internal::matrix_swap_impl;\n};\n\n/** \\defgroup arraytypedefs Global array typedefs\n  * \\ingroup Core_Module\n  *\n  * Eigen defines several typedef shortcuts for most common 1D and 2D array types.\n  *\n  * The general patterns are the following:\n  *\n  * \\c ArrayRowsColsType where \\c Rows and \\c Cols can be \\c 2,\\c 3,\\c 4 for fixed size square matrices or \\c X for dynamic size,\n  * and where \\c Type can be \\c i for integer, \\c f for float, \\c d for double, \\c cf for complex float, \\c cd\n  * for complex double.\n  *\n  * For example, \\c Array33d is a fixed-size 3x3 array type of doubles, and \\c ArrayXXf is a dynamic-size matrix of floats.\n  *\n  * There are also \\c ArraySizeType which are self-explanatory. For example, \\c Array4cf is\n  * a fixed-size 1D array of 4 complex floats.\n  *\n  * \\sa class Array\n  */\n\n#define EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix)   \\\n/** \\ingroup arraytypedefs */                                    \\\ntypedef Array<Type, Size, Size> Array##SizeSuffix##SizeSuffix##TypeSuffix;  \\\n/** \\ingroup arraytypedefs */                                    \\\ntypedef Array<Type, Size, 1>    Array##SizeSuffix##TypeSuffix;\n\n#define EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, Size)         \\\n/** \\ingroup arraytypedefs */                                    \\\ntypedef Array<Type, Size, Dynamic> Array##Size##X##TypeSuffix;  \\\n/** \\ingroup arraytypedefs */                                    \\\ntypedef Array<Type, Dynamic, Size> Array##X##Size##TypeSuffix;\n\n#define EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \\\nEIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, 2, 2) \\\nEIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, 3, 3) \\\nEIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, 4, 4) \\\nEIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, Dynamic, X) \\\nEIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, 2) \\\nEIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, 3) \\\nEIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, 4)\n\nEIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(int,                  i)\nEIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(float,                f)\nEIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(double,               d)\nEIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(std::complex<float>,  cf)\nEIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(std::complex<double>, cd)\n\n#undef EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES\n#undef EIGEN_MAKE_ARRAY_TYPEDEFS\n\n#undef EIGEN_MAKE_ARRAY_TYPEDEFS_LARGE\n\n#define EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, SizeSuffix) \\\nusing Eigen::Matrix##SizeSuffix##TypeSuffix; \\\nusing Eigen::Vector##SizeSuffix##TypeSuffix; \\\nusing Eigen::RowVector##SizeSuffix##TypeSuffix;\n\n#define EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(TypeSuffix) \\\nEIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 2) \\\nEIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 3) \\\nEIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 4) \\\nEIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, X) \\\n\n#define EIGEN_USING_ARRAY_TYPEDEFS \\\nEIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(i) \\\nEIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(f) \\\nEIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(d) \\\nEIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(cf) \\\nEIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(cd)\n\n} // end namespace Eigen\n\n#endif // EIGEN_ARRAY_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/ArrayBase.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_ARRAYBASE_H\n#define EIGEN_ARRAYBASE_H\n\nnamespace Eigen { \n\ntemplate<typename ExpressionType> class MatrixWrapper;\n\n/** \\class ArrayBase\n  * \\ingroup Core_Module\n  *\n  * \\brief Base class for all 1D and 2D array, and related expressions\n  *\n  * An array is similar to a dense vector or matrix. While matrices are mathematical\n  * objects with well defined linear algebra operators, an array is just a collection\n  * of scalar values arranged in a one or two dimensionnal fashion. As the main consequence,\n  * all operations applied to an array are performed coefficient wise. Furthermore,\n  * arrays support scalar math functions of the c++ standard library (e.g., std::sin(x)), and convenient\n  * constructors allowing to easily write generic code working for both scalar values\n  * and arrays.\n  *\n  * This class is the base that is inherited by all array expression types.\n  *\n  * \\tparam Derived is the derived type, e.g., an array or an expression type.\n  *\n  * This class can be extended with the help of the plugin mechanism described on the page\n  * \\ref TopicCustomizing_Plugins by defining the preprocessor symbol \\c EIGEN_ARRAYBASE_PLUGIN.\n  *\n  * \\sa class MatrixBase, \\ref TopicClassHierarchy\n  */\ntemplate<typename Derived> class ArrayBase\n  : public DenseBase<Derived>\n{\n  public:\n#ifndef EIGEN_PARSED_BY_DOXYGEN\n    /** The base class for a given storage type. */\n    typedef ArrayBase StorageBaseType;\n\n    typedef ArrayBase Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl;\n\n    typedef typename internal::traits<Derived>::StorageKind StorageKind;\n    typedef typename internal::traits<Derived>::Scalar Scalar;\n    typedef typename internal::packet_traits<Scalar>::type PacketScalar;\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n\n    typedef DenseBase<Derived> Base;\n    using Base::RowsAtCompileTime;\n    using Base::ColsAtCompileTime;\n    using Base::SizeAtCompileTime;\n    using Base::MaxRowsAtCompileTime;\n    using Base::MaxColsAtCompileTime;\n    using Base::MaxSizeAtCompileTime;\n    using Base::IsVectorAtCompileTime;\n    using Base::Flags;\n    \n    using Base::derived;\n    using Base::const_cast_derived;\n    using Base::rows;\n    using Base::cols;\n    using Base::size;\n    using Base::coeff;\n    using Base::coeffRef;\n    using Base::lazyAssign;\n    using Base::operator=;\n    using Base::operator+=;\n    using Base::operator-=;\n    using Base::operator*=;\n    using Base::operator/=;\n\n    typedef typename Base::CoeffReturnType CoeffReturnType;\n\n#endif // not EIGEN_PARSED_BY_DOXYGEN\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\n    typedef typename Base::PlainObject PlainObject;\n\n    /** \\internal Represents a matrix with all coefficients equal to one another*/\n    typedef CwiseNullaryOp<internal::scalar_constant_op<Scalar>,PlainObject> ConstantReturnType;\n#endif // not EIGEN_PARSED_BY_DOXYGEN\n\n#define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::ArrayBase\n#define EIGEN_DOC_UNARY_ADDONS(X,Y)\n#   include \"../plugins/CommonCwiseUnaryOps.h\"\n#   include \"../plugins/MatrixCwiseUnaryOps.h\"\n#   include \"../plugins/ArrayCwiseUnaryOps.h\"\n#   include \"../plugins/CommonCwiseBinaryOps.h\"\n#   include \"../plugins/MatrixCwiseBinaryOps.h\"\n#   include \"../plugins/ArrayCwiseBinaryOps.h\"\n#   ifdef EIGEN_ARRAYBASE_PLUGIN\n#     include EIGEN_ARRAYBASE_PLUGIN\n#   endif\n#undef EIGEN_CURRENT_STORAGE_BASE_CLASS\n#undef EIGEN_DOC_UNARY_ADDONS\n\n    /** Special case of the template operator=, in order to prevent the compiler\n      * from generating a default operator= (issue hit with g++ 4.1)\n      */\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    Derived& operator=(const ArrayBase& other)\n    {\n      internal::call_assignment(derived(), other.derived());\n      return derived();\n    }\n    \n    /** Set all the entries to \\a value.\n      * \\sa DenseBase::setConstant(), DenseBase::fill() */\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    Derived& operator=(const Scalar &value)\n    { Base::setConstant(value); return derived(); }\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    Derived& operator+=(const Scalar& scalar);\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    Derived& operator-=(const Scalar& scalar);\n\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    Derived& operator+=(const ArrayBase<OtherDerived>& other);\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    Derived& operator-=(const ArrayBase<OtherDerived>& other);\n\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    Derived& operator*=(const ArrayBase<OtherDerived>& other);\n\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    Derived& operator/=(const ArrayBase<OtherDerived>& other);\n\n  public:\n    EIGEN_DEVICE_FUNC\n    ArrayBase<Derived>& array() { return *this; }\n    EIGEN_DEVICE_FUNC\n    const ArrayBase<Derived>& array() const { return *this; }\n\n    /** \\returns an \\link Eigen::MatrixBase Matrix \\endlink expression of this array\n      * \\sa MatrixBase::array() */\n    EIGEN_DEVICE_FUNC\n    MatrixWrapper<Derived> matrix() { return MatrixWrapper<Derived>(derived()); }\n    EIGEN_DEVICE_FUNC\n    const MatrixWrapper<const Derived> matrix() const { return MatrixWrapper<const Derived>(derived()); }\n\n//     template<typename Dest>\n//     inline void evalTo(Dest& dst) const { dst = matrix(); }\n\n  protected:\n    EIGEN_DEVICE_FUNC\n    ArrayBase() : Base() {}\n\n  private:\n    explicit ArrayBase(Index);\n    ArrayBase(Index,Index);\n    template<typename OtherDerived> explicit ArrayBase(const ArrayBase<OtherDerived>&);\n  protected:\n    // mixing arrays and matrices is not legal\n    template<typename OtherDerived> Derived& operator+=(const MatrixBase<OtherDerived>& )\n    {EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}\n    // mixing arrays and matrices is not legal\n    template<typename OtherDerived> Derived& operator-=(const MatrixBase<OtherDerived>& )\n    {EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}\n};\n\n/** replaces \\c *this by \\c *this - \\a other.\n  *\n  * \\returns a reference to \\c *this\n  */\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &\nArrayBase<Derived>::operator-=(const ArrayBase<OtherDerived> &other)\n{\n  call_assignment(derived(), other.derived(), internal::sub_assign_op<Scalar,typename OtherDerived::Scalar>());\n  return derived();\n}\n\n/** replaces \\c *this by \\c *this + \\a other.\n  *\n  * \\returns a reference to \\c *this\n  */\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &\nArrayBase<Derived>::operator+=(const ArrayBase<OtherDerived>& other)\n{\n  call_assignment(derived(), other.derived(), internal::add_assign_op<Scalar,typename OtherDerived::Scalar>());\n  return derived();\n}\n\n/** replaces \\c *this by \\c *this * \\a other coefficient wise.\n  *\n  * \\returns a reference to \\c *this\n  */\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &\nArrayBase<Derived>::operator*=(const ArrayBase<OtherDerived>& other)\n{\n  call_assignment(derived(), other.derived(), internal::mul_assign_op<Scalar,typename OtherDerived::Scalar>());\n  return derived();\n}\n\n/** replaces \\c *this by \\c *this / \\a other coefficient wise.\n  *\n  * \\returns a reference to \\c *this\n  */\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &\nArrayBase<Derived>::operator/=(const ArrayBase<OtherDerived>& other)\n{\n  call_assignment(derived(), other.derived(), internal::div_assign_op<Scalar,typename OtherDerived::Scalar>());\n  return derived();\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_ARRAYBASE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/ArrayWrapper.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_ARRAYWRAPPER_H\n#define EIGEN_ARRAYWRAPPER_H\n\nnamespace Eigen { \n\n/** \\class ArrayWrapper\n  * \\ingroup Core_Module\n  *\n  * \\brief Expression of a mathematical vector or matrix as an array object\n  *\n  * This class is the return type of MatrixBase::array(), and most of the time\n  * this is the only way it is use.\n  *\n  * \\sa MatrixBase::array(), class MatrixWrapper\n  */\n\nnamespace internal {\ntemplate<typename ExpressionType>\nstruct traits<ArrayWrapper<ExpressionType> >\n  : public traits<typename remove_all<typename ExpressionType::Nested>::type >\n{\n  typedef ArrayXpr XprKind;\n  // Let's remove NestByRefBit\n  enum {\n    Flags0 = traits<typename remove_all<typename ExpressionType::Nested>::type >::Flags,\n    LvalueBitFlag = is_lvalue<ExpressionType>::value ? LvalueBit : 0,\n    Flags = (Flags0 & ~(NestByRefBit | LvalueBit)) | LvalueBitFlag\n  };\n};\n}\n\ntemplate<typename ExpressionType>\nclass ArrayWrapper : public ArrayBase<ArrayWrapper<ExpressionType> >\n{\n  public:\n    typedef ArrayBase<ArrayWrapper> Base;\n    EIGEN_DENSE_PUBLIC_INTERFACE(ArrayWrapper)\n    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(ArrayWrapper)\n    typedef typename internal::remove_all<ExpressionType>::type NestedExpression;\n\n    typedef typename internal::conditional<\n                       internal::is_lvalue<ExpressionType>::value,\n                       Scalar,\n                       const Scalar\n                     >::type ScalarWithConstIfNotLvalue;\n\n    typedef typename internal::ref_selector<ExpressionType>::non_const_type NestedExpressionType;\n\n    using Base::coeffRef;\n\n    EIGEN_DEVICE_FUNC\n    explicit EIGEN_STRONG_INLINE ArrayWrapper(ExpressionType& matrix) : m_expression(matrix) {}\n\n    EIGEN_DEVICE_FUNC\n    inline Index rows() const { return m_expression.rows(); }\n    EIGEN_DEVICE_FUNC\n    inline Index cols() const { return m_expression.cols(); }\n    EIGEN_DEVICE_FUNC\n    inline Index outerStride() const { return m_expression.outerStride(); }\n    EIGEN_DEVICE_FUNC\n    inline Index innerStride() const { return m_expression.innerStride(); }\n\n    EIGEN_DEVICE_FUNC\n    inline ScalarWithConstIfNotLvalue* data() { return m_expression.data(); }\n    EIGEN_DEVICE_FUNC\n    inline const Scalar* data() const { return m_expression.data(); }\n\n    EIGEN_DEVICE_FUNC\n    inline const Scalar& coeffRef(Index rowId, Index colId) const\n    {\n      return m_expression.coeffRef(rowId, colId);\n    }\n\n    EIGEN_DEVICE_FUNC\n    inline const Scalar& coeffRef(Index index) const\n    {\n      return m_expression.coeffRef(index);\n    }\n\n    template<typename Dest>\n    EIGEN_DEVICE_FUNC\n    inline void evalTo(Dest& dst) const { dst = m_expression; }\n\n    const typename internal::remove_all<NestedExpressionType>::type& \n    EIGEN_DEVICE_FUNC\n    nestedExpression() const \n    {\n      return m_expression;\n    }\n\n    /** Forwards the resizing request to the nested expression\n      * \\sa DenseBase::resize(Index)  */\n    EIGEN_DEVICE_FUNC\n    void resize(Index newSize) { m_expression.resize(newSize); }\n    /** Forwards the resizing request to the nested expression\n      * \\sa DenseBase::resize(Index,Index)*/\n    EIGEN_DEVICE_FUNC\n    void resize(Index rows, Index cols) { m_expression.resize(rows,cols); }\n\n  protected:\n    NestedExpressionType m_expression;\n};\n\n/** \\class MatrixWrapper\n  * \\ingroup Core_Module\n  *\n  * \\brief Expression of an array as a mathematical vector or matrix\n  *\n  * This class is the return type of ArrayBase::matrix(), and most of the time\n  * this is the only way it is use.\n  *\n  * \\sa MatrixBase::matrix(), class ArrayWrapper\n  */\n\nnamespace internal {\ntemplate<typename ExpressionType>\nstruct traits<MatrixWrapper<ExpressionType> >\n : public traits<typename remove_all<typename ExpressionType::Nested>::type >\n{\n  typedef MatrixXpr XprKind;\n  // Let's remove NestByRefBit\n  enum {\n    Flags0 = traits<typename remove_all<typename ExpressionType::Nested>::type >::Flags,\n    LvalueBitFlag = is_lvalue<ExpressionType>::value ? LvalueBit : 0,\n    Flags = (Flags0 & ~(NestByRefBit | LvalueBit)) | LvalueBitFlag\n  };\n};\n}\n\ntemplate<typename ExpressionType>\nclass MatrixWrapper : public MatrixBase<MatrixWrapper<ExpressionType> >\n{\n  public:\n    typedef MatrixBase<MatrixWrapper<ExpressionType> > Base;\n    EIGEN_DENSE_PUBLIC_INTERFACE(MatrixWrapper)\n    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(MatrixWrapper)\n    typedef typename internal::remove_all<ExpressionType>::type NestedExpression;\n\n    typedef typename internal::conditional<\n                       internal::is_lvalue<ExpressionType>::value,\n                       Scalar,\n                       const Scalar\n                     >::type ScalarWithConstIfNotLvalue;\n\n    typedef typename internal::ref_selector<ExpressionType>::non_const_type NestedExpressionType;\n\n    using Base::coeffRef;\n\n    EIGEN_DEVICE_FUNC\n    explicit inline MatrixWrapper(ExpressionType& matrix) : m_expression(matrix) {}\n\n    EIGEN_DEVICE_FUNC\n    inline Index rows() const { return m_expression.rows(); }\n    EIGEN_DEVICE_FUNC\n    inline Index cols() const { return m_expression.cols(); }\n    EIGEN_DEVICE_FUNC\n    inline Index outerStride() const { return m_expression.outerStride(); }\n    EIGEN_DEVICE_FUNC\n    inline Index innerStride() const { return m_expression.innerStride(); }\n\n    EIGEN_DEVICE_FUNC\n    inline ScalarWithConstIfNotLvalue* data() { return m_expression.data(); }\n    EIGEN_DEVICE_FUNC\n    inline const Scalar* data() const { return m_expression.data(); }\n\n    EIGEN_DEVICE_FUNC\n    inline const Scalar& coeffRef(Index rowId, Index colId) const\n    {\n      return m_expression.derived().coeffRef(rowId, colId);\n    }\n\n    EIGEN_DEVICE_FUNC\n    inline const Scalar& coeffRef(Index index) const\n    {\n      return m_expression.coeffRef(index);\n    }\n\n    EIGEN_DEVICE_FUNC\n    const typename internal::remove_all<NestedExpressionType>::type& \n    nestedExpression() const \n    {\n      return m_expression;\n    }\n\n    /** Forwards the resizing request to the nested expression\n      * \\sa DenseBase::resize(Index)  */\n    EIGEN_DEVICE_FUNC\n    void resize(Index newSize) { m_expression.resize(newSize); }\n    /** Forwards the resizing request to the nested expression\n      * \\sa DenseBase::resize(Index,Index)*/\n    EIGEN_DEVICE_FUNC\n    void resize(Index rows, Index cols) { m_expression.resize(rows,cols); }\n\n  protected:\n    NestedExpressionType m_expression;\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_ARRAYWRAPPER_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/Assign.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2007 Michael Olbrich <michael.olbrich@gmx.net>\n// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_ASSIGN_H\n#define EIGEN_ASSIGN_H\n\nnamespace Eigen {\n\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\nEIGEN_STRONG_INLINE Derived& DenseBase<Derived>\n  ::lazyAssign(const DenseBase<OtherDerived>& other)\n{\n  enum{\n    SameType = internal::is_same<typename Derived::Scalar,typename OtherDerived::Scalar>::value\n  };\n\n  EIGEN_STATIC_ASSERT_LVALUE(Derived)\n  EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Derived,OtherDerived)\n  EIGEN_STATIC_ASSERT(SameType,YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)\n\n  eigen_assert(rows() == other.rows() && cols() == other.cols());\n  internal::call_assignment_no_alias(derived(),other.derived());\n  \n  return derived();\n}\n\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\nEIGEN_DEVICE_FUNC\nEIGEN_STRONG_INLINE Derived& DenseBase<Derived>::operator=(const DenseBase<OtherDerived>& other)\n{\n  internal::call_assignment(derived(), other.derived());\n  return derived();\n}\n\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC\nEIGEN_STRONG_INLINE Derived& DenseBase<Derived>::operator=(const DenseBase& other)\n{\n  internal::call_assignment(derived(), other.derived());\n  return derived();\n}\n\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC\nEIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const MatrixBase& other)\n{\n  internal::call_assignment(derived(), other.derived());\n  return derived();\n}\n\ntemplate<typename Derived>\ntemplate <typename OtherDerived>\nEIGEN_DEVICE_FUNC\nEIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const DenseBase<OtherDerived>& other)\n{\n  internal::call_assignment(derived(), other.derived());\n  return derived();\n}\n\ntemplate<typename Derived>\ntemplate <typename OtherDerived>\nEIGEN_DEVICE_FUNC\nEIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const EigenBase<OtherDerived>& other)\n{\n  internal::call_assignment(derived(), other.derived());\n  return derived();\n}\n\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\nEIGEN_DEVICE_FUNC\nEIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const ReturnByValue<OtherDerived>& other)\n{\n  other.derived().evalTo(derived());\n  return derived();\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_ASSIGN_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/AssignEvaluator.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2011 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2011-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2011-2012 Jitse Niesen <jitse@maths.leeds.ac.uk>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_ASSIGN_EVALUATOR_H\n#define EIGEN_ASSIGN_EVALUATOR_H\n\nnamespace Eigen {\n\n// This implementation is based on Assign.h\n\nnamespace internal {\n  \n/***************************************************************************\n* Part 1 : the logic deciding a strategy for traversal and unrolling       *\n***************************************************************************/\n\n// copy_using_evaluator_traits is based on assign_traits\n\ntemplate <typename DstEvaluator, typename SrcEvaluator, typename AssignFunc>\nstruct copy_using_evaluator_traits\n{\n  typedef typename DstEvaluator::XprType Dst;\n  typedef typename Dst::Scalar DstScalar;\n  \n  enum {\n    DstFlags = DstEvaluator::Flags,\n    SrcFlags = SrcEvaluator::Flags\n  };\n  \npublic:\n  enum {\n    DstAlignment = DstEvaluator::Alignment,\n    SrcAlignment = SrcEvaluator::Alignment,\n    DstHasDirectAccess = (DstFlags & DirectAccessBit) == DirectAccessBit,\n    JointAlignment = EIGEN_PLAIN_ENUM_MIN(DstAlignment,SrcAlignment)\n  };\n\nprivate:\n  enum {\n    InnerSize = int(Dst::IsVectorAtCompileTime) ? int(Dst::SizeAtCompileTime)\n              : int(DstFlags)&RowMajorBit ? int(Dst::ColsAtCompileTime)\n              : int(Dst::RowsAtCompileTime),\n    InnerMaxSize = int(Dst::IsVectorAtCompileTime) ? int(Dst::MaxSizeAtCompileTime)\n              : int(DstFlags)&RowMajorBit ? int(Dst::MaxColsAtCompileTime)\n              : int(Dst::MaxRowsAtCompileTime),\n    OuterStride = int(outer_stride_at_compile_time<Dst>::ret),\n    MaxSizeAtCompileTime = Dst::SizeAtCompileTime\n  };\n\n  // TODO distinguish between linear traversal and inner-traversals\n  typedef typename find_best_packet<DstScalar,Dst::SizeAtCompileTime>::type LinearPacketType;\n  typedef typename find_best_packet<DstScalar,InnerSize>::type InnerPacketType;\n\n  enum {\n    LinearPacketSize = unpacket_traits<LinearPacketType>::size,\n    InnerPacketSize = unpacket_traits<InnerPacketType>::size\n  };\n\npublic:\n  enum {\n    LinearRequiredAlignment = unpacket_traits<LinearPacketType>::alignment,\n    InnerRequiredAlignment = unpacket_traits<InnerPacketType>::alignment\n  };\n\nprivate:\n  enum {\n    DstIsRowMajor = DstFlags&RowMajorBit,\n    SrcIsRowMajor = SrcFlags&RowMajorBit,\n    StorageOrdersAgree = (int(DstIsRowMajor) == int(SrcIsRowMajor)),\n    MightVectorize = bool(StorageOrdersAgree)\n                  && (int(DstFlags) & int(SrcFlags) & ActualPacketAccessBit)\n                  && bool(functor_traits<AssignFunc>::PacketAccess),\n    MayInnerVectorize  = MightVectorize\n                       && int(InnerSize)!=Dynamic && int(InnerSize)%int(InnerPacketSize)==0\n                       && int(OuterStride)!=Dynamic && int(OuterStride)%int(InnerPacketSize)==0\n                       && (EIGEN_UNALIGNED_VECTORIZE  || int(JointAlignment)>=int(InnerRequiredAlignment)),\n    MayLinearize = bool(StorageOrdersAgree) && (int(DstFlags) & int(SrcFlags) & LinearAccessBit),\n    MayLinearVectorize = bool(MightVectorize) && bool(MayLinearize) && bool(DstHasDirectAccess)\n                       && (EIGEN_UNALIGNED_VECTORIZE || (int(DstAlignment)>=int(LinearRequiredAlignment)) || MaxSizeAtCompileTime == Dynamic),\n      /* If the destination isn't aligned, we have to do runtime checks and we don't unroll,\n         so it's only good for large enough sizes. */\n    MaySliceVectorize  = bool(MightVectorize) && bool(DstHasDirectAccess)\n                       && (int(InnerMaxSize)==Dynamic || int(InnerMaxSize)>=(EIGEN_UNALIGNED_VECTORIZE?InnerPacketSize:(3*InnerPacketSize)))\n      /* slice vectorization can be slow, so we only want it if the slices are big, which is\n         indicated by InnerMaxSize rather than InnerSize, think of the case of a dynamic block\n         in a fixed-size matrix\n         However, with EIGEN_UNALIGNED_VECTORIZE and unrolling, slice vectorization is still worth it */\n  };\n\npublic:\n  enum {\n    Traversal = int(MayLinearVectorize) && (LinearPacketSize>InnerPacketSize) ? int(LinearVectorizedTraversal)\n              : int(MayInnerVectorize)   ? int(InnerVectorizedTraversal)\n              : int(MayLinearVectorize)  ? int(LinearVectorizedTraversal)\n              : int(MaySliceVectorize)   ? int(SliceVectorizedTraversal)\n              : int(MayLinearize)        ? int(LinearTraversal)\n                                         : int(DefaultTraversal),\n    Vectorized = int(Traversal) == InnerVectorizedTraversal\n              || int(Traversal) == LinearVectorizedTraversal\n              || int(Traversal) == SliceVectorizedTraversal\n  };\n\n  typedef typename conditional<int(Traversal)==LinearVectorizedTraversal, LinearPacketType, InnerPacketType>::type PacketType;\n\nprivate:\n  enum {\n    ActualPacketSize    = int(Traversal)==LinearVectorizedTraversal ? LinearPacketSize\n                        : Vectorized ? InnerPacketSize\n                        : 1,\n    UnrollingLimit      = EIGEN_UNROLLING_LIMIT * ActualPacketSize,\n    MayUnrollCompletely = int(Dst::SizeAtCompileTime) != Dynamic\n                       && int(Dst::SizeAtCompileTime) * (int(DstEvaluator::CoeffReadCost)+int(SrcEvaluator::CoeffReadCost)) <= int(UnrollingLimit),\n    MayUnrollInner      = int(InnerSize) != Dynamic\n                       && int(InnerSize) * (int(DstEvaluator::CoeffReadCost)+int(SrcEvaluator::CoeffReadCost)) <= int(UnrollingLimit)\n  };\n\npublic:\n  enum {\n    Unrolling = (int(Traversal) == int(InnerVectorizedTraversal) || int(Traversal) == int(DefaultTraversal))\n                ? (\n                    int(MayUnrollCompletely) ? int(CompleteUnrolling)\n                  : int(MayUnrollInner)      ? int(InnerUnrolling)\n                                             : int(NoUnrolling)\n                  )\n              : int(Traversal) == int(LinearVectorizedTraversal)\n                ? ( bool(MayUnrollCompletely) && ( EIGEN_UNALIGNED_VECTORIZE || (int(DstAlignment)>=int(LinearRequiredAlignment)))\n                          ? int(CompleteUnrolling)\n                          : int(NoUnrolling) )\n              : int(Traversal) == int(LinearTraversal)\n                ? ( bool(MayUnrollCompletely) ? int(CompleteUnrolling) \n                                              : int(NoUnrolling) )\n#if EIGEN_UNALIGNED_VECTORIZE\n              : int(Traversal) == int(SliceVectorizedTraversal)\n                ? ( bool(MayUnrollInner) ? int(InnerUnrolling)\n                                         : int(NoUnrolling) )\n#endif\n              : int(NoUnrolling)\n  };\n\n#ifdef EIGEN_DEBUG_ASSIGN\n  static void debug()\n  {\n    std::cerr << \"DstXpr: \" << typeid(typename DstEvaluator::XprType).name() << std::endl;\n    std::cerr << \"SrcXpr: \" << typeid(typename SrcEvaluator::XprType).name() << std::endl;\n    std::cerr.setf(std::ios::hex, std::ios::basefield);\n    std::cerr << \"DstFlags\" << \" = \" << DstFlags << \" (\" << demangle_flags(DstFlags) << \" )\" << std::endl;\n    std::cerr << \"SrcFlags\" << \" = \" << SrcFlags << \" (\" << demangle_flags(SrcFlags) << \" )\" << std::endl;\n    std::cerr.unsetf(std::ios::hex);\n    EIGEN_DEBUG_VAR(DstAlignment)\n    EIGEN_DEBUG_VAR(SrcAlignment)\n    EIGEN_DEBUG_VAR(LinearRequiredAlignment)\n    EIGEN_DEBUG_VAR(InnerRequiredAlignment)\n    EIGEN_DEBUG_VAR(JointAlignment)\n    EIGEN_DEBUG_VAR(InnerSize)\n    EIGEN_DEBUG_VAR(InnerMaxSize)\n    EIGEN_DEBUG_VAR(LinearPacketSize)\n    EIGEN_DEBUG_VAR(InnerPacketSize)\n    EIGEN_DEBUG_VAR(ActualPacketSize)\n    EIGEN_DEBUG_VAR(StorageOrdersAgree)\n    EIGEN_DEBUG_VAR(MightVectorize)\n    EIGEN_DEBUG_VAR(MayLinearize)\n    EIGEN_DEBUG_VAR(MayInnerVectorize)\n    EIGEN_DEBUG_VAR(MayLinearVectorize)\n    EIGEN_DEBUG_VAR(MaySliceVectorize)\n    std::cerr << \"Traversal\" << \" = \" << Traversal << \" (\" << demangle_traversal(Traversal) << \")\" << std::endl;\n    EIGEN_DEBUG_VAR(SrcEvaluator::CoeffReadCost)\n    EIGEN_DEBUG_VAR(UnrollingLimit)\n    EIGEN_DEBUG_VAR(MayUnrollCompletely)\n    EIGEN_DEBUG_VAR(MayUnrollInner)\n    std::cerr << \"Unrolling\" << \" = \" << Unrolling << \" (\" << demangle_unrolling(Unrolling) << \")\" << std::endl;\n    std::cerr << std::endl;\n  }\n#endif\n};\n\n/***************************************************************************\n* Part 2 : meta-unrollers\n***************************************************************************/\n\n/************************\n*** Default traversal ***\n************************/\n\ntemplate<typename Kernel, int Index, int Stop>\nstruct copy_using_evaluator_DefaultTraversal_CompleteUnrolling\n{\n  // FIXME: this is not very clean, perhaps this information should be provided by the kernel?\n  typedef typename Kernel::DstEvaluatorType DstEvaluatorType;\n  typedef typename DstEvaluatorType::XprType DstXprType;\n  \n  enum {\n    outer = Index / DstXprType::InnerSizeAtCompileTime,\n    inner = Index % DstXprType::InnerSizeAtCompileTime\n  };\n\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel)\n  {\n    kernel.assignCoeffByOuterInner(outer, inner);\n    copy_using_evaluator_DefaultTraversal_CompleteUnrolling<Kernel, Index+1, Stop>::run(kernel);\n  }\n};\n\ntemplate<typename Kernel, int Stop>\nstruct copy_using_evaluator_DefaultTraversal_CompleteUnrolling<Kernel, Stop, Stop>\n{\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel&) { }\n};\n\ntemplate<typename Kernel, int Index_, int Stop>\nstruct copy_using_evaluator_DefaultTraversal_InnerUnrolling\n{\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel, Index outer)\n  {\n    kernel.assignCoeffByOuterInner(outer, Index_);\n    copy_using_evaluator_DefaultTraversal_InnerUnrolling<Kernel, Index_+1, Stop>::run(kernel, outer);\n  }\n};\n\ntemplate<typename Kernel, int Stop>\nstruct copy_using_evaluator_DefaultTraversal_InnerUnrolling<Kernel, Stop, Stop>\n{\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel&, Index) { }\n};\n\n/***********************\n*** Linear traversal ***\n***********************/\n\ntemplate<typename Kernel, int Index, int Stop>\nstruct copy_using_evaluator_LinearTraversal_CompleteUnrolling\n{\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel& kernel)\n  {\n    kernel.assignCoeff(Index);\n    copy_using_evaluator_LinearTraversal_CompleteUnrolling<Kernel, Index+1, Stop>::run(kernel);\n  }\n};\n\ntemplate<typename Kernel, int Stop>\nstruct copy_using_evaluator_LinearTraversal_CompleteUnrolling<Kernel, Stop, Stop>\n{\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel&) { }\n};\n\n/**************************\n*** Inner vectorization ***\n**************************/\n\ntemplate<typename Kernel, int Index, int Stop>\nstruct copy_using_evaluator_innervec_CompleteUnrolling\n{\n  // FIXME: this is not very clean, perhaps this information should be provided by the kernel?\n  typedef typename Kernel::DstEvaluatorType DstEvaluatorType;\n  typedef typename DstEvaluatorType::XprType DstXprType;\n  typedef typename Kernel::PacketType PacketType;\n  \n  enum {\n    outer = Index / DstXprType::InnerSizeAtCompileTime,\n    inner = Index % DstXprType::InnerSizeAtCompileTime,\n    SrcAlignment = Kernel::AssignmentTraits::SrcAlignment,\n    DstAlignment = Kernel::AssignmentTraits::DstAlignment\n  };\n\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel)\n  {\n    kernel.template assignPacketByOuterInner<DstAlignment, SrcAlignment, PacketType>(outer, inner);\n    enum { NextIndex = Index + unpacket_traits<PacketType>::size };\n    copy_using_evaluator_innervec_CompleteUnrolling<Kernel, NextIndex, Stop>::run(kernel);\n  }\n};\n\ntemplate<typename Kernel, int Stop>\nstruct copy_using_evaluator_innervec_CompleteUnrolling<Kernel, Stop, Stop>\n{\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel&) { }\n};\n\ntemplate<typename Kernel, int Index_, int Stop, int SrcAlignment, int DstAlignment>\nstruct copy_using_evaluator_innervec_InnerUnrolling\n{\n  typedef typename Kernel::PacketType PacketType;\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel, Index outer)\n  {\n    kernel.template assignPacketByOuterInner<DstAlignment, SrcAlignment, PacketType>(outer, Index_);\n    enum { NextIndex = Index_ + unpacket_traits<PacketType>::size };\n    copy_using_evaluator_innervec_InnerUnrolling<Kernel, NextIndex, Stop, SrcAlignment, DstAlignment>::run(kernel, outer);\n  }\n};\n\ntemplate<typename Kernel, int Stop, int SrcAlignment, int DstAlignment>\nstruct copy_using_evaluator_innervec_InnerUnrolling<Kernel, Stop, Stop, SrcAlignment, DstAlignment>\n{\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &, Index) { }\n};\n\n/***************************************************************************\n* Part 3 : implementation of all cases\n***************************************************************************/\n\n// dense_assignment_loop is based on assign_impl\n\ntemplate<typename Kernel,\n         int Traversal = Kernel::AssignmentTraits::Traversal,\n         int Unrolling = Kernel::AssignmentTraits::Unrolling>\nstruct dense_assignment_loop;\n\n/************************\n*** Default traversal ***\n************************/\n\ntemplate<typename Kernel>\nstruct dense_assignment_loop<Kernel, DefaultTraversal, NoUnrolling>\n{\n  EIGEN_DEVICE_FUNC static void EIGEN_STRONG_INLINE run(Kernel &kernel)\n  {\n    for(Index outer = 0; outer < kernel.outerSize(); ++outer) {\n      for(Index inner = 0; inner < kernel.innerSize(); ++inner) {\n        kernel.assignCoeffByOuterInner(outer, inner);\n      }\n    }\n  }\n};\n\ntemplate<typename Kernel>\nstruct dense_assignment_loop<Kernel, DefaultTraversal, CompleteUnrolling>\n{\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel)\n  {\n    typedef typename Kernel::DstEvaluatorType::XprType DstXprType;\n    copy_using_evaluator_DefaultTraversal_CompleteUnrolling<Kernel, 0, DstXprType::SizeAtCompileTime>::run(kernel);\n  }\n};\n\ntemplate<typename Kernel>\nstruct dense_assignment_loop<Kernel, DefaultTraversal, InnerUnrolling>\n{\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel)\n  {\n    typedef typename Kernel::DstEvaluatorType::XprType DstXprType;\n\n    const Index outerSize = kernel.outerSize();\n    for(Index outer = 0; outer < outerSize; ++outer)\n      copy_using_evaluator_DefaultTraversal_InnerUnrolling<Kernel, 0, DstXprType::InnerSizeAtCompileTime>::run(kernel, outer);\n  }\n};\n\n/***************************\n*** Linear vectorization ***\n***************************/\n\n\n// The goal of unaligned_dense_assignment_loop is simply to factorize the handling\n// of the non vectorizable beginning and ending parts\n\ntemplate <bool IsAligned = false>\nstruct unaligned_dense_assignment_loop\n{\n  // if IsAligned = true, then do nothing\n  template <typename Kernel>\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel&, Index, Index) {}\n};\n\ntemplate <>\nstruct unaligned_dense_assignment_loop<false>\n{\n  // MSVC must not inline this functions. If it does, it fails to optimize the\n  // packet access path.\n  // FIXME check which version exhibits this issue\n#if EIGEN_COMP_MSVC\n  template <typename Kernel>\n  static EIGEN_DONT_INLINE void run(Kernel &kernel,\n                                    Index start,\n                                    Index end)\n#else\n  template <typename Kernel>\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel,\n                                      Index start,\n                                      Index end)\n#endif\n  {\n    for (Index index = start; index < end; ++index)\n      kernel.assignCoeff(index);\n  }\n};\n\ntemplate<typename Kernel>\nstruct dense_assignment_loop<Kernel, LinearVectorizedTraversal, NoUnrolling>\n{\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel)\n  {\n    const Index size = kernel.size();\n    typedef typename Kernel::Scalar Scalar;\n    typedef typename Kernel::PacketType PacketType;\n    enum {\n      requestedAlignment = Kernel::AssignmentTraits::LinearRequiredAlignment,\n      packetSize = unpacket_traits<PacketType>::size,\n      dstIsAligned = int(Kernel::AssignmentTraits::DstAlignment)>=int(requestedAlignment),\n      dstAlignment = packet_traits<Scalar>::AlignedOnScalar ? int(requestedAlignment)\n                                                            : int(Kernel::AssignmentTraits::DstAlignment),\n      srcAlignment = Kernel::AssignmentTraits::JointAlignment\n    };\n    const Index alignedStart = dstIsAligned ? 0 : internal::first_aligned<requestedAlignment>(kernel.dstDataPtr(), size);\n    const Index alignedEnd = alignedStart + ((size-alignedStart)/packetSize)*packetSize;\n\n    unaligned_dense_assignment_loop<dstIsAligned!=0>::run(kernel, 0, alignedStart);\n\n    for(Index index = alignedStart; index < alignedEnd; index += packetSize)\n      kernel.template assignPacket<dstAlignment, srcAlignment, PacketType>(index);\n\n    unaligned_dense_assignment_loop<>::run(kernel, alignedEnd, size);\n  }\n};\n\ntemplate<typename Kernel>\nstruct dense_assignment_loop<Kernel, LinearVectorizedTraversal, CompleteUnrolling>\n{\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel)\n  {\n    typedef typename Kernel::DstEvaluatorType::XprType DstXprType;\n    typedef typename Kernel::PacketType PacketType;\n    \n    enum { size = DstXprType::SizeAtCompileTime,\n           packetSize =unpacket_traits<PacketType>::size,\n           alignedSize = (size/packetSize)*packetSize };\n\n    copy_using_evaluator_innervec_CompleteUnrolling<Kernel, 0, alignedSize>::run(kernel);\n    copy_using_evaluator_DefaultTraversal_CompleteUnrolling<Kernel, alignedSize, size>::run(kernel);\n  }\n};\n\n/**************************\n*** Inner vectorization ***\n**************************/\n\ntemplate<typename Kernel>\nstruct dense_assignment_loop<Kernel, InnerVectorizedTraversal, NoUnrolling>\n{\n  typedef typename Kernel::PacketType PacketType;\n  enum {\n    SrcAlignment = Kernel::AssignmentTraits::SrcAlignment,\n    DstAlignment = Kernel::AssignmentTraits::DstAlignment\n  };\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel)\n  {\n    const Index innerSize = kernel.innerSize();\n    const Index outerSize = kernel.outerSize();\n    const Index packetSize = unpacket_traits<PacketType>::size;\n    for(Index outer = 0; outer < outerSize; ++outer)\n      for(Index inner = 0; inner < innerSize; inner+=packetSize)\n        kernel.template assignPacketByOuterInner<DstAlignment, SrcAlignment, PacketType>(outer, inner);\n  }\n};\n\ntemplate<typename Kernel>\nstruct dense_assignment_loop<Kernel, InnerVectorizedTraversal, CompleteUnrolling>\n{\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel)\n  {\n    typedef typename Kernel::DstEvaluatorType::XprType DstXprType;\n    copy_using_evaluator_innervec_CompleteUnrolling<Kernel, 0, DstXprType::SizeAtCompileTime>::run(kernel);\n  }\n};\n\ntemplate<typename Kernel>\nstruct dense_assignment_loop<Kernel, InnerVectorizedTraversal, InnerUnrolling>\n{\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel)\n  {\n    typedef typename Kernel::DstEvaluatorType::XprType DstXprType;\n    typedef typename Kernel::AssignmentTraits Traits;\n    const Index outerSize = kernel.outerSize();\n    for(Index outer = 0; outer < outerSize; ++outer)\n      copy_using_evaluator_innervec_InnerUnrolling<Kernel, 0, DstXprType::InnerSizeAtCompileTime,\n                                                   Traits::SrcAlignment, Traits::DstAlignment>::run(kernel, outer);\n  }\n};\n\n/***********************\n*** Linear traversal ***\n***********************/\n\ntemplate<typename Kernel>\nstruct dense_assignment_loop<Kernel, LinearTraversal, NoUnrolling>\n{\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel)\n  {\n    const Index size = kernel.size();\n    for(Index i = 0; i < size; ++i)\n      kernel.assignCoeff(i);\n  }\n};\n\ntemplate<typename Kernel>\nstruct dense_assignment_loop<Kernel, LinearTraversal, CompleteUnrolling>\n{\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel)\n  {\n    typedef typename Kernel::DstEvaluatorType::XprType DstXprType;\n    copy_using_evaluator_LinearTraversal_CompleteUnrolling<Kernel, 0, DstXprType::SizeAtCompileTime>::run(kernel);\n  }\n};\n\n/**************************\n*** Slice vectorization ***\n***************************/\n\ntemplate<typename Kernel>\nstruct dense_assignment_loop<Kernel, SliceVectorizedTraversal, NoUnrolling>\n{\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel)\n  {\n    typedef typename Kernel::Scalar Scalar;\n    typedef typename Kernel::PacketType PacketType;\n    enum {\n      packetSize = unpacket_traits<PacketType>::size,\n      requestedAlignment = int(Kernel::AssignmentTraits::InnerRequiredAlignment),\n      alignable = packet_traits<Scalar>::AlignedOnScalar || int(Kernel::AssignmentTraits::DstAlignment)>=sizeof(Scalar),\n      dstIsAligned = int(Kernel::AssignmentTraits::DstAlignment)>=int(requestedAlignment),\n      dstAlignment = alignable ? int(requestedAlignment)\n                               : int(Kernel::AssignmentTraits::DstAlignment)\n    };\n    const Scalar *dst_ptr = kernel.dstDataPtr();\n    if((!bool(dstIsAligned)) && (UIntPtr(dst_ptr) % sizeof(Scalar))>0)\n    {\n      // the pointer is not aligend-on scalar, so alignment is not possible\n      return dense_assignment_loop<Kernel,DefaultTraversal,NoUnrolling>::run(kernel);\n    }\n    const Index packetAlignedMask = packetSize - 1;\n    const Index innerSize = kernel.innerSize();\n    const Index outerSize = kernel.outerSize();\n    const Index alignedStep = alignable ? (packetSize - kernel.outerStride() % packetSize) & packetAlignedMask : 0;\n    Index alignedStart = ((!alignable) || bool(dstIsAligned)) ? 0 : internal::first_aligned<requestedAlignment>(dst_ptr, innerSize);\n\n    for(Index outer = 0; outer < outerSize; ++outer)\n    {\n      const Index alignedEnd = alignedStart + ((innerSize-alignedStart) & ~packetAlignedMask);\n      // do the non-vectorizable part of the assignment\n      for(Index inner = 0; inner<alignedStart ; ++inner)\n        kernel.assignCoeffByOuterInner(outer, inner);\n\n      // do the vectorizable part of the assignment\n      for(Index inner = alignedStart; inner<alignedEnd; inner+=packetSize)\n        kernel.template assignPacketByOuterInner<dstAlignment, Unaligned, PacketType>(outer, inner);\n\n      // do the non-vectorizable part of the assignment\n      for(Index inner = alignedEnd; inner<innerSize ; ++inner)\n        kernel.assignCoeffByOuterInner(outer, inner);\n\n      alignedStart = numext::mini((alignedStart+alignedStep)%packetSize, innerSize);\n    }\n  }\n};\n\n#if EIGEN_UNALIGNED_VECTORIZE\ntemplate<typename Kernel>\nstruct dense_assignment_loop<Kernel, SliceVectorizedTraversal, InnerUnrolling>\n{\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel)\n  {\n    typedef typename Kernel::DstEvaluatorType::XprType DstXprType;\n    typedef typename Kernel::PacketType PacketType;\n\n    enum { size = DstXprType::InnerSizeAtCompileTime,\n           packetSize =unpacket_traits<PacketType>::size,\n           vectorizableSize = (size/packetSize)*packetSize };\n\n    for(Index outer = 0; outer < kernel.outerSize(); ++outer)\n    {\n      copy_using_evaluator_innervec_InnerUnrolling<Kernel, 0, vectorizableSize, 0, 0>::run(kernel, outer);\n      copy_using_evaluator_DefaultTraversal_InnerUnrolling<Kernel, vectorizableSize, size>::run(kernel, outer);\n    }\n  }\n};\n#endif\n\n\n/***************************************************************************\n* Part 4 : Generic dense assignment kernel\n***************************************************************************/\n\n// This class generalize the assignment of a coefficient (or packet) from one dense evaluator\n// to another dense writable evaluator.\n// It is parametrized by the two evaluators, and the actual assignment functor.\n// This abstraction level permits to keep the evaluation loops as simple and as generic as possible.\n// One can customize the assignment using this generic dense_assignment_kernel with different\n// functors, or by completely overloading it, by-passing a functor.\ntemplate<typename DstEvaluatorTypeT, typename SrcEvaluatorTypeT, typename Functor, int Version = Specialized>\nclass generic_dense_assignment_kernel\n{\nprotected:\n  typedef typename DstEvaluatorTypeT::XprType DstXprType;\n  typedef typename SrcEvaluatorTypeT::XprType SrcXprType;\npublic:\n  \n  typedef DstEvaluatorTypeT DstEvaluatorType;\n  typedef SrcEvaluatorTypeT SrcEvaluatorType;\n  typedef typename DstEvaluatorType::Scalar Scalar;\n  typedef copy_using_evaluator_traits<DstEvaluatorTypeT, SrcEvaluatorTypeT, Functor> AssignmentTraits;\n  typedef typename AssignmentTraits::PacketType PacketType;\n  \n  \n  EIGEN_DEVICE_FUNC generic_dense_assignment_kernel(DstEvaluatorType &dst, const SrcEvaluatorType &src, const Functor &func, DstXprType& dstExpr)\n    : m_dst(dst), m_src(src), m_functor(func), m_dstExpr(dstExpr)\n  {\n    #ifdef EIGEN_DEBUG_ASSIGN\n    AssignmentTraits::debug();\n    #endif\n  }\n  \n  EIGEN_DEVICE_FUNC Index size() const        { return m_dstExpr.size(); }\n  EIGEN_DEVICE_FUNC Index innerSize() const   { return m_dstExpr.innerSize(); }\n  EIGEN_DEVICE_FUNC Index outerSize() const   { return m_dstExpr.outerSize(); }\n  EIGEN_DEVICE_FUNC Index rows() const        { return m_dstExpr.rows(); }\n  EIGEN_DEVICE_FUNC Index cols() const        { return m_dstExpr.cols(); }\n  EIGEN_DEVICE_FUNC Index outerStride() const { return m_dstExpr.outerStride(); }\n  \n  EIGEN_DEVICE_FUNC DstEvaluatorType& dstEvaluator() { return m_dst; }\n  EIGEN_DEVICE_FUNC const SrcEvaluatorType& srcEvaluator() const { return m_src; }\n  \n  /// Assign src(row,col) to dst(row,col) through the assignment functor.\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignCoeff(Index row, Index col)\n  {\n    m_functor.assignCoeff(m_dst.coeffRef(row,col), m_src.coeff(row,col));\n  }\n  \n  /// \\sa assignCoeff(Index,Index)\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignCoeff(Index index)\n  {\n    m_functor.assignCoeff(m_dst.coeffRef(index), m_src.coeff(index));\n  }\n  \n  /// \\sa assignCoeff(Index,Index)\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignCoeffByOuterInner(Index outer, Index inner)\n  {\n    Index row = rowIndexByOuterInner(outer, inner); \n    Index col = colIndexByOuterInner(outer, inner); \n    assignCoeff(row, col);\n  }\n  \n  \n  template<int StoreMode, int LoadMode, typename PacketType>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignPacket(Index row, Index col)\n  {\n    m_functor.template assignPacket<StoreMode>(&m_dst.coeffRef(row,col), m_src.template packet<LoadMode,PacketType>(row,col));\n  }\n  \n  template<int StoreMode, int LoadMode, typename PacketType>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignPacket(Index index)\n  {\n    m_functor.template assignPacket<StoreMode>(&m_dst.coeffRef(index), m_src.template packet<LoadMode,PacketType>(index));\n  }\n  \n  template<int StoreMode, int LoadMode, typename PacketType>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignPacketByOuterInner(Index outer, Index inner)\n  {\n    Index row = rowIndexByOuterInner(outer, inner); \n    Index col = colIndexByOuterInner(outer, inner);\n    assignPacket<StoreMode,LoadMode,PacketType>(row, col);\n  }\n  \n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Index rowIndexByOuterInner(Index outer, Index inner)\n  {\n    typedef typename DstEvaluatorType::ExpressionTraits Traits;\n    return int(Traits::RowsAtCompileTime) == 1 ? 0\n      : int(Traits::ColsAtCompileTime) == 1 ? inner\n      : int(DstEvaluatorType::Flags)&RowMajorBit ? outer\n      : inner;\n  }\n\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Index colIndexByOuterInner(Index outer, Index inner)\n  {\n    typedef typename DstEvaluatorType::ExpressionTraits Traits;\n    return int(Traits::ColsAtCompileTime) == 1 ? 0\n      : int(Traits::RowsAtCompileTime) == 1 ? inner\n      : int(DstEvaluatorType::Flags)&RowMajorBit ? inner\n      : outer;\n  }\n\n  EIGEN_DEVICE_FUNC const Scalar* dstDataPtr() const\n  {\n    return m_dstExpr.data();\n  }\n  \nprotected:\n  DstEvaluatorType& m_dst;\n  const SrcEvaluatorType& m_src;\n  const Functor &m_functor;\n  // TODO find a way to avoid the needs of the original expression\n  DstXprType& m_dstExpr;\n};\n\n/***************************************************************************\n* Part 5 : Entry point for dense rectangular assignment\n***************************************************************************/\n\ntemplate<typename DstXprType,typename SrcXprType, typename Functor>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nvoid resize_if_allowed(DstXprType &dst, const SrcXprType& src, const Functor &/*func*/)\n{\n  EIGEN_ONLY_USED_FOR_DEBUG(dst);\n  EIGEN_ONLY_USED_FOR_DEBUG(src);\n  eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols());\n}\n\ntemplate<typename DstXprType,typename SrcXprType, typename T1, typename T2>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nvoid resize_if_allowed(DstXprType &dst, const SrcXprType& src, const internal::assign_op<T1,T2> &/*func*/)\n{\n  Index dstRows = src.rows();\n  Index dstCols = src.cols();\n  if(((dst.rows()!=dstRows) || (dst.cols()!=dstCols)))\n    dst.resize(dstRows, dstCols);\n  eigen_assert(dst.rows() == dstRows && dst.cols() == dstCols);\n}\n\ntemplate<typename DstXprType, typename SrcXprType, typename Functor>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void call_dense_assignment_loop(DstXprType& dst, const SrcXprType& src, const Functor &func)\n{\n  typedef evaluator<DstXprType> DstEvaluatorType;\n  typedef evaluator<SrcXprType> SrcEvaluatorType;\n\n  SrcEvaluatorType srcEvaluator(src);\n\n  // NOTE To properly handle A = (A*A.transpose())/s with A rectangular,\n  // we need to resize the destination after the source evaluator has been created.\n  resize_if_allowed(dst, src, func);\n\n  DstEvaluatorType dstEvaluator(dst);\n    \n  typedef generic_dense_assignment_kernel<DstEvaluatorType,SrcEvaluatorType,Functor> Kernel;\n  Kernel kernel(dstEvaluator, srcEvaluator, func, dst.const_cast_derived());\n\n  dense_assignment_loop<Kernel>::run(kernel);\n}\n\ntemplate<typename DstXprType, typename SrcXprType>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void call_dense_assignment_loop(DstXprType& dst, const SrcXprType& src)\n{\n  call_dense_assignment_loop(dst, src, internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar>());\n}\n\n/***************************************************************************\n* Part 6 : Generic assignment\n***************************************************************************/\n\n// Based on the respective shapes of the destination and source,\n// the class AssignmentKind determine the kind of assignment mechanism.\n// AssignmentKind must define a Kind typedef.\ntemplate<typename DstShape, typename SrcShape> struct AssignmentKind;\n\n// Assignement kind defined in this file:\nstruct Dense2Dense {};\nstruct EigenBase2EigenBase {};\n\ntemplate<typename,typename> struct AssignmentKind { typedef EigenBase2EigenBase Kind; };\ntemplate<> struct AssignmentKind<DenseShape,DenseShape> { typedef Dense2Dense Kind; };\n    \n// This is the main assignment class\ntemplate< typename DstXprType, typename SrcXprType, typename Functor,\n          typename Kind = typename AssignmentKind< typename evaluator_traits<DstXprType>::Shape , typename evaluator_traits<SrcXprType>::Shape >::Kind,\n          typename EnableIf = void>\nstruct Assignment;\n\n\n// The only purpose of this call_assignment() function is to deal with noalias() / \"assume-aliasing\" and automatic transposition.\n// Indeed, I (Gael) think that this concept of \"assume-aliasing\" was a mistake, and it makes thing quite complicated.\n// So this intermediate function removes everything related to \"assume-aliasing\" such that Assignment\n// does not has to bother about these annoying details.\n\ntemplate<typename Dst, typename Src>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nvoid call_assignment(Dst& dst, const Src& src)\n{\n  call_assignment(dst, src, internal::assign_op<typename Dst::Scalar,typename Src::Scalar>());\n}\ntemplate<typename Dst, typename Src>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nvoid call_assignment(const Dst& dst, const Src& src)\n{\n  call_assignment(dst, src, internal::assign_op<typename Dst::Scalar,typename Src::Scalar>());\n}\n                     \n// Deal with \"assume-aliasing\"\ntemplate<typename Dst, typename Src, typename Func>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nvoid call_assignment(Dst& dst, const Src& src, const Func& func, typename enable_if< evaluator_assume_aliasing<Src>::value, void*>::type = 0)\n{\n  typename plain_matrix_type<Src>::type tmp(src);\n  call_assignment_no_alias(dst, tmp, func);\n}\n\ntemplate<typename Dst, typename Src, typename Func>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nvoid call_assignment(Dst& dst, const Src& src, const Func& func, typename enable_if<!evaluator_assume_aliasing<Src>::value, void*>::type = 0)\n{\n  call_assignment_no_alias(dst, src, func);\n}\n\n// by-pass \"assume-aliasing\"\n// When there is no aliasing, we require that 'dst' has been properly resized\ntemplate<typename Dst, template <typename> class StorageBase, typename Src, typename Func>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nvoid call_assignment(NoAlias<Dst,StorageBase>& dst, const Src& src, const Func& func)\n{\n  call_assignment_no_alias(dst.expression(), src, func);\n}\n\n\ntemplate<typename Dst, typename Src, typename Func>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nvoid call_assignment_no_alias(Dst& dst, const Src& src, const Func& func)\n{\n  enum {\n    NeedToTranspose = (    (int(Dst::RowsAtCompileTime) == 1 && int(Src::ColsAtCompileTime) == 1)\n                        || (int(Dst::ColsAtCompileTime) == 1 && int(Src::RowsAtCompileTime) == 1)\n                      ) && int(Dst::SizeAtCompileTime) != 1\n  };\n\n  typedef typename internal::conditional<NeedToTranspose, Transpose<Dst>, Dst>::type ActualDstTypeCleaned;\n  typedef typename internal::conditional<NeedToTranspose, Transpose<Dst>, Dst&>::type ActualDstType;\n  ActualDstType actualDst(dst);\n  \n  // TODO check whether this is the right place to perform these checks:\n  EIGEN_STATIC_ASSERT_LVALUE(Dst)\n  EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(ActualDstTypeCleaned,Src)\n  EIGEN_CHECK_BINARY_COMPATIBILIY(Func,typename ActualDstTypeCleaned::Scalar,typename Src::Scalar);\n  \n  Assignment<ActualDstTypeCleaned,Src,Func>::run(actualDst, src, func);\n}\ntemplate<typename Dst, typename Src>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nvoid call_assignment_no_alias(Dst& dst, const Src& src)\n{\n  call_assignment_no_alias(dst, src, internal::assign_op<typename Dst::Scalar,typename Src::Scalar>());\n}\n\ntemplate<typename Dst, typename Src, typename Func>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nvoid call_assignment_no_alias_no_transpose(Dst& dst, const Src& src, const Func& func)\n{\n  // TODO check whether this is the right place to perform these checks:\n  EIGEN_STATIC_ASSERT_LVALUE(Dst)\n  EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Dst,Src)\n  EIGEN_CHECK_BINARY_COMPATIBILIY(Func,typename Dst::Scalar,typename Src::Scalar);\n\n  Assignment<Dst,Src,Func>::run(dst, src, func);\n}\ntemplate<typename Dst, typename Src>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nvoid call_assignment_no_alias_no_transpose(Dst& dst, const Src& src)\n{\n  call_assignment_no_alias_no_transpose(dst, src, internal::assign_op<typename Dst::Scalar,typename Src::Scalar>());\n}\n\n// forward declaration\ntemplate<typename Dst, typename Src> void check_for_aliasing(const Dst &dst, const Src &src);\n\n// Generic Dense to Dense assignment\n// Note that the last template argument \"Weak\" is needed to make it possible to perform\n// both partial specialization+SFINAE without ambiguous specialization\ntemplate< typename DstXprType, typename SrcXprType, typename Functor, typename Weak>\nstruct Assignment<DstXprType, SrcXprType, Functor, Dense2Dense, Weak>\n{\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE void run(DstXprType &dst, const SrcXprType &src, const Functor &func)\n  {\n#ifndef EIGEN_NO_DEBUG\n    internal::check_for_aliasing(dst, src);\n#endif\n    \n    call_dense_assignment_loop(dst, src, func);\n  }\n};\n\n// Generic assignment through evalTo.\n// TODO: not sure we have to keep that one, but it helps porting current code to new evaluator mechanism.\n// Note that the last template argument \"Weak\" is needed to make it possible to perform\n// both partial specialization+SFINAE without ambiguous specialization\ntemplate< typename DstXprType, typename SrcXprType, typename Functor, typename Weak>\nstruct Assignment<DstXprType, SrcXprType, Functor, EigenBase2EigenBase, Weak>\n{\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)\n  {\n    Index dstRows = src.rows();\n    Index dstCols = src.cols();\n    if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))\n      dst.resize(dstRows, dstCols);\n\n    eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols());\n    src.evalTo(dst);\n  }\n\n  // NOTE The following two functions are templated to avoid their instanciation if not needed\n  //      This is needed because some expressions supports evalTo only and/or have 'void' as scalar type.\n  template<typename SrcScalarType>\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op<typename DstXprType::Scalar,SrcScalarType> &/*func*/)\n  {\n    Index dstRows = src.rows();\n    Index dstCols = src.cols();\n    if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))\n      dst.resize(dstRows, dstCols);\n\n    eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols());\n    src.addTo(dst);\n  }\n\n  template<typename SrcScalarType>\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op<typename DstXprType::Scalar,SrcScalarType> &/*func*/)\n  {\n    Index dstRows = src.rows();\n    Index dstCols = src.cols();\n    if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))\n      dst.resize(dstRows, dstCols);\n\n    eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols());\n    src.subTo(dst);\n  }\n};\n\n} // namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_ASSIGN_EVALUATOR_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/Assign_MKL.h",
    "content": "/*\n Copyright (c) 2011, Intel Corporation. All rights reserved.\n Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>\n \n Redistribution and use in source and binary forms, with or without modification,\n are permitted provided that the following conditions are met:\n\n * Redistributions of source code must retain the above copyright notice, this\n   list of conditions and the following disclaimer.\n * Redistributions in binary form must reproduce the above copyright notice,\n   this list of conditions and the following disclaimer in the documentation\n   and/or other materials provided with the distribution.\n * Neither the name of Intel Corporation nor the names of its contributors may\n   be used to endorse or promote products derived from this software without\n   specific prior written permission.\n\n THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\" AND\n ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED\n WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\n DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR\n ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES\n (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;\n LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON\n ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT\n (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS\n SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n\n ********************************************************************************\n *   Content : Eigen bindings to Intel(R) MKL\n *   MKL VML support for coefficient-wise unary Eigen expressions like a=b.sin()\n ********************************************************************************\n*/\n\n#ifndef EIGEN_ASSIGN_VML_H\n#define EIGEN_ASSIGN_VML_H\n\nnamespace Eigen { \n\nnamespace internal {\n\ntemplate<typename Dst, typename Src>\nclass vml_assign_traits\n{\n  private:\n    enum {\n      DstHasDirectAccess = Dst::Flags & DirectAccessBit,\n      SrcHasDirectAccess = Src::Flags & DirectAccessBit,\n      StorageOrdersAgree = (int(Dst::IsRowMajor) == int(Src::IsRowMajor)),\n      InnerSize = int(Dst::IsVectorAtCompileTime) ? int(Dst::SizeAtCompileTime)\n                : int(Dst::Flags)&RowMajorBit ? int(Dst::ColsAtCompileTime)\n                : int(Dst::RowsAtCompileTime),\n      InnerMaxSize  = int(Dst::IsVectorAtCompileTime) ? int(Dst::MaxSizeAtCompileTime)\n                    : int(Dst::Flags)&RowMajorBit ? int(Dst::MaxColsAtCompileTime)\n                    : int(Dst::MaxRowsAtCompileTime),\n      MaxSizeAtCompileTime = Dst::SizeAtCompileTime,\n\n      MightEnableVml = StorageOrdersAgree && DstHasDirectAccess && SrcHasDirectAccess && Src::InnerStrideAtCompileTime==1 && Dst::InnerStrideAtCompileTime==1,\n      MightLinearize = MightEnableVml && (int(Dst::Flags) & int(Src::Flags) & LinearAccessBit),\n      VmlSize = MightLinearize ? MaxSizeAtCompileTime : InnerMaxSize,\n      LargeEnough = VmlSize==Dynamic || VmlSize>=EIGEN_MKL_VML_THRESHOLD\n    };\n  public:\n    enum {\n      EnableVml = MightEnableVml && LargeEnough,\n      Traversal = MightLinearize ? LinearTraversal : DefaultTraversal\n    };\n};\n\n#define EIGEN_PP_EXPAND(ARG) ARG\n#if !defined (EIGEN_FAST_MATH) || (EIGEN_FAST_MATH != 1)\n#define EIGEN_VMLMODE_EXPAND_LA , VML_HA\n#else\n#define EIGEN_VMLMODE_EXPAND_LA , VML_LA\n#endif\n\n#define EIGEN_VMLMODE_EXPAND__ \n\n#define EIGEN_VMLMODE_PREFIX_LA vm\n#define EIGEN_VMLMODE_PREFIX__  v\n#define EIGEN_VMLMODE_PREFIX(VMLMODE) EIGEN_CAT(EIGEN_VMLMODE_PREFIX_,VMLMODE)\n\n#define EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, VMLOP, EIGENTYPE, VMLTYPE, VMLMODE)                                           \\\n  template< typename DstXprType, typename SrcXprNested>                                                                         \\\n  struct Assignment<DstXprType, CwiseUnaryOp<scalar_##EIGENOP##_op<EIGENTYPE>, SrcXprNested>, assign_op<EIGENTYPE,EIGENTYPE>,   \\\n                   Dense2Dense, typename enable_if<vml_assign_traits<DstXprType,SrcXprNested>::EnableVml>::type> {              \\\n    typedef CwiseUnaryOp<scalar_##EIGENOP##_op<EIGENTYPE>, SrcXprNested> SrcXprType;                                            \\\n    static void run(DstXprType &dst, const SrcXprType &src, const assign_op<EIGENTYPE,EIGENTYPE> &func) {                       \\\n      resize_if_allowed(dst, src, func);                                                                                        \\\n      eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols());                                                       \\\n      if(vml_assign_traits<DstXprType,SrcXprNested>::Traversal==LinearTraversal) {                                              \\\n        VMLOP(dst.size(), (const VMLTYPE*)src.nestedExpression().data(),                                                        \\\n              (VMLTYPE*)dst.data() EIGEN_PP_EXPAND(EIGEN_VMLMODE_EXPAND_##VMLMODE) );                                           \\\n      } else {                                                                                                                  \\\n        const Index outerSize = dst.outerSize();                                                                                \\\n        for(Index outer = 0; outer < outerSize; ++outer) {                                                                      \\\n          const EIGENTYPE *src_ptr = src.IsRowMajor ? &(src.nestedExpression().coeffRef(outer,0)) :                             \\\n                                                      &(src.nestedExpression().coeffRef(0, outer));                             \\\n          EIGENTYPE *dst_ptr = dst.IsRowMajor ? &(dst.coeffRef(outer,0)) : &(dst.coeffRef(0, outer));                           \\\n          VMLOP( dst.innerSize(), (const VMLTYPE*)src_ptr,                                                                      \\\n                (VMLTYPE*)dst_ptr EIGEN_PP_EXPAND(EIGEN_VMLMODE_EXPAND_##VMLMODE));                                             \\\n        }                                                                                                                       \\\n      }                                                                                                                         \\\n    }                                                                                                                           \\\n  };                                                                                                                            \\\n\n\n#define EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(EIGENOP, VMLOP, VMLMODE)                                                         \\\n  EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, EIGEN_CAT(EIGEN_VMLMODE_PREFIX(VMLMODE),s##VMLOP), float, float, VMLMODE)           \\\n  EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, EIGEN_CAT(EIGEN_VMLMODE_PREFIX(VMLMODE),d##VMLOP), double, double, VMLMODE)\n\n#define EIGEN_MKL_VML_DECLARE_UNARY_CALLS_CPLX(EIGENOP, VMLOP, VMLMODE)                                                         \\\n  EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, EIGEN_CAT(EIGEN_VMLMODE_PREFIX(VMLMODE),c##VMLOP), scomplex, MKL_Complex8, VMLMODE) \\\n  EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, EIGEN_CAT(EIGEN_VMLMODE_PREFIX(VMLMODE),z##VMLOP), dcomplex, MKL_Complex16, VMLMODE)\n  \n#define EIGEN_MKL_VML_DECLARE_UNARY_CALLS(EIGENOP, VMLOP, VMLMODE)                                                              \\\n  EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(EIGENOP, VMLOP, VMLMODE)                                                               \\\n  EIGEN_MKL_VML_DECLARE_UNARY_CALLS_CPLX(EIGENOP, VMLOP, VMLMODE)\n\n  \nEIGEN_MKL_VML_DECLARE_UNARY_CALLS(sin,   Sin,   LA)\nEIGEN_MKL_VML_DECLARE_UNARY_CALLS(asin,  Asin,  LA)\nEIGEN_MKL_VML_DECLARE_UNARY_CALLS(sinh,  Sinh,  LA)\nEIGEN_MKL_VML_DECLARE_UNARY_CALLS(cos,   Cos,   LA)\nEIGEN_MKL_VML_DECLARE_UNARY_CALLS(acos,  Acos,  LA)\nEIGEN_MKL_VML_DECLARE_UNARY_CALLS(cosh,  Cosh,  LA)\nEIGEN_MKL_VML_DECLARE_UNARY_CALLS(tan,   Tan,   LA)\nEIGEN_MKL_VML_DECLARE_UNARY_CALLS(atan,  Atan,  LA)\nEIGEN_MKL_VML_DECLARE_UNARY_CALLS(tanh,  Tanh,  LA)\n// EIGEN_MKL_VML_DECLARE_UNARY_CALLS(abs,   Abs,    _)\nEIGEN_MKL_VML_DECLARE_UNARY_CALLS(exp,   Exp,   LA)\nEIGEN_MKL_VML_DECLARE_UNARY_CALLS(log,   Ln,    LA)\nEIGEN_MKL_VML_DECLARE_UNARY_CALLS(log10, Log10, LA)\nEIGEN_MKL_VML_DECLARE_UNARY_CALLS(sqrt,  Sqrt,  _)\n\nEIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(square, Sqr,   _)\nEIGEN_MKL_VML_DECLARE_UNARY_CALLS_CPLX(arg, Arg,      _)\nEIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(round, Round,  _)\nEIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(floor, Floor,  _)\nEIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(ceil,  Ceil,   _)\n\n#define EIGEN_MKL_VML_DECLARE_POW_CALL(EIGENOP, VMLOP, EIGENTYPE, VMLTYPE, VMLMODE)                                           \\\n  template< typename DstXprType, typename SrcXprNested, typename Plain>                                                       \\\n  struct Assignment<DstXprType, CwiseBinaryOp<scalar_##EIGENOP##_op<EIGENTYPE,EIGENTYPE>, SrcXprNested,                       \\\n                    const CwiseNullaryOp<internal::scalar_constant_op<EIGENTYPE>,Plain> >, assign_op<EIGENTYPE,EIGENTYPE>,    \\\n                   Dense2Dense, typename enable_if<vml_assign_traits<DstXprType,SrcXprNested>::EnableVml>::type> {            \\\n    typedef CwiseBinaryOp<scalar_##EIGENOP##_op<EIGENTYPE,EIGENTYPE>, SrcXprNested,                                           \\\n                    const CwiseNullaryOp<internal::scalar_constant_op<EIGENTYPE>,Plain> > SrcXprType;                         \\\n    static void run(DstXprType &dst, const SrcXprType &src, const assign_op<EIGENTYPE,EIGENTYPE> &func) {                     \\\n      resize_if_allowed(dst, src, func);                                                                                      \\\n      eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols());                                                     \\\n      VMLTYPE exponent = reinterpret_cast<const VMLTYPE&>(src.rhs().functor().m_other);                                       \\\n      if(vml_assign_traits<DstXprType,SrcXprNested>::Traversal==LinearTraversal)                                              \\\n      {                                                                                                                       \\\n        VMLOP( dst.size(), (const VMLTYPE*)src.lhs().data(), exponent,                                                        \\\n              (VMLTYPE*)dst.data() EIGEN_PP_EXPAND(EIGEN_VMLMODE_EXPAND_##VMLMODE) );                                         \\\n      } else {                                                                                                                \\\n        const Index outerSize = dst.outerSize();                                                                              \\\n        for(Index outer = 0; outer < outerSize; ++outer) {                                                                    \\\n          const EIGENTYPE *src_ptr = src.IsRowMajor ? &(src.lhs().coeffRef(outer,0)) :                                        \\\n                                                      &(src.lhs().coeffRef(0, outer));                                        \\\n          EIGENTYPE *dst_ptr = dst.IsRowMajor ? &(dst.coeffRef(outer,0)) : &(dst.coeffRef(0, outer));                         \\\n          VMLOP( dst.innerSize(), (const VMLTYPE*)src_ptr, exponent,                                                          \\\n                 (VMLTYPE*)dst_ptr EIGEN_PP_EXPAND(EIGEN_VMLMODE_EXPAND_##VMLMODE));                                          \\\n        }                                                                                                                     \\\n      }                                                                                                                       \\\n    }                                                                                                                         \\\n  };\n  \nEIGEN_MKL_VML_DECLARE_POW_CALL(pow, vmsPowx, float,    float,         LA)\nEIGEN_MKL_VML_DECLARE_POW_CALL(pow, vmdPowx, double,   double,        LA)\nEIGEN_MKL_VML_DECLARE_POW_CALL(pow, vmcPowx, scomplex, MKL_Complex8,  LA)\nEIGEN_MKL_VML_DECLARE_POW_CALL(pow, vmzPowx, dcomplex, MKL_Complex16, LA)\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_ASSIGN_VML_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/BandMatrix.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_BANDMATRIX_H\n#define EIGEN_BANDMATRIX_H\n\nnamespace Eigen { \n\nnamespace internal {\n\ntemplate<typename Derived>\nclass BandMatrixBase : public EigenBase<Derived>\n{\n  public:\n\n    enum {\n      Flags = internal::traits<Derived>::Flags,\n      CoeffReadCost = internal::traits<Derived>::CoeffReadCost,\n      RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,\n      ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,\n      MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime,\n      MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime,\n      Supers = internal::traits<Derived>::Supers,\n      Subs   = internal::traits<Derived>::Subs,\n      Options = internal::traits<Derived>::Options\n    };\n    typedef typename internal::traits<Derived>::Scalar Scalar;\n    typedef Matrix<Scalar,RowsAtCompileTime,ColsAtCompileTime> DenseMatrixType;\n    typedef typename DenseMatrixType::StorageIndex StorageIndex;\n    typedef typename internal::traits<Derived>::CoefficientsType CoefficientsType;\n    typedef EigenBase<Derived> Base;\n\n  protected:\n    enum {\n      DataRowsAtCompileTime = ((Supers!=Dynamic) && (Subs!=Dynamic))\n                            ? 1 + Supers + Subs\n                            : Dynamic,\n      SizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime,ColsAtCompileTime)\n    };\n\n  public:\n    \n    using Base::derived;\n    using Base::rows;\n    using Base::cols;\n\n    /** \\returns the number of super diagonals */\n    inline Index supers() const { return derived().supers(); }\n\n    /** \\returns the number of sub diagonals */\n    inline Index subs() const { return derived().subs(); }\n    \n    /** \\returns an expression of the underlying coefficient matrix */\n    inline const CoefficientsType& coeffs() const { return derived().coeffs(); }\n    \n    /** \\returns an expression of the underlying coefficient matrix */\n    inline CoefficientsType& coeffs() { return derived().coeffs(); }\n\n    /** \\returns a vector expression of the \\a i -th column,\n      * only the meaningful part is returned.\n      * \\warning the internal storage must be column major. */\n    inline Block<CoefficientsType,Dynamic,1> col(Index i)\n    {\n      EIGEN_STATIC_ASSERT((Options&RowMajor)==0,THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);\n      Index start = 0;\n      Index len = coeffs().rows();\n      if (i<=supers())\n      {\n        start = supers()-i;\n        len = (std::min)(rows(),std::max<Index>(0,coeffs().rows() - (supers()-i)));\n      }\n      else if (i>=rows()-subs())\n        len = std::max<Index>(0,coeffs().rows() - (i + 1 - rows() + subs()));\n      return Block<CoefficientsType,Dynamic,1>(coeffs(), start, i, len, 1);\n    }\n\n    /** \\returns a vector expression of the main diagonal */\n    inline Block<CoefficientsType,1,SizeAtCompileTime> diagonal()\n    { return Block<CoefficientsType,1,SizeAtCompileTime>(coeffs(),supers(),0,1,(std::min)(rows(),cols())); }\n\n    /** \\returns a vector expression of the main diagonal (const version) */\n    inline const Block<const CoefficientsType,1,SizeAtCompileTime> diagonal() const\n    { return Block<const CoefficientsType,1,SizeAtCompileTime>(coeffs(),supers(),0,1,(std::min)(rows(),cols())); }\n\n    template<int Index> struct DiagonalIntReturnType {\n      enum {\n        ReturnOpposite = (Options&SelfAdjoint) && (((Index)>0 && Supers==0) || ((Index)<0 && Subs==0)),\n        Conjugate = ReturnOpposite && NumTraits<Scalar>::IsComplex,\n        ActualIndex = ReturnOpposite ? -Index : Index,\n        DiagonalSize = (RowsAtCompileTime==Dynamic || ColsAtCompileTime==Dynamic)\n                     ? Dynamic\n                     : (ActualIndex<0\n                     ? EIGEN_SIZE_MIN_PREFER_DYNAMIC(ColsAtCompileTime, RowsAtCompileTime + ActualIndex)\n                     : EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime, ColsAtCompileTime - ActualIndex))\n      };\n      typedef Block<CoefficientsType,1, DiagonalSize> BuildType;\n      typedef typename internal::conditional<Conjugate,\n                 CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>,BuildType >,\n                 BuildType>::type Type;\n    };\n\n    /** \\returns a vector expression of the \\a N -th sub or super diagonal */\n    template<int N> inline typename DiagonalIntReturnType<N>::Type diagonal()\n    {\n      return typename DiagonalIntReturnType<N>::BuildType(coeffs(), supers()-N, (std::max)(0,N), 1, diagonalLength(N));\n    }\n\n    /** \\returns a vector expression of the \\a N -th sub or super diagonal */\n    template<int N> inline const typename DiagonalIntReturnType<N>::Type diagonal() const\n    {\n      return typename DiagonalIntReturnType<N>::BuildType(coeffs(), supers()-N, (std::max)(0,N), 1, diagonalLength(N));\n    }\n\n    /** \\returns a vector expression of the \\a i -th sub or super diagonal */\n    inline Block<CoefficientsType,1,Dynamic> diagonal(Index i)\n    {\n      eigen_assert((i<0 && -i<=subs()) || (i>=0 && i<=supers()));\n      return Block<CoefficientsType,1,Dynamic>(coeffs(), supers()-i, std::max<Index>(0,i), 1, diagonalLength(i));\n    }\n\n    /** \\returns a vector expression of the \\a i -th sub or super diagonal */\n    inline const Block<const CoefficientsType,1,Dynamic> diagonal(Index i) const\n    {\n      eigen_assert((i<0 && -i<=subs()) || (i>=0 && i<=supers()));\n      return Block<const CoefficientsType,1,Dynamic>(coeffs(), supers()-i, std::max<Index>(0,i), 1, diagonalLength(i));\n    }\n    \n    template<typename Dest> inline void evalTo(Dest& dst) const\n    {\n      dst.resize(rows(),cols());\n      dst.setZero();\n      dst.diagonal() = diagonal();\n      for (Index i=1; i<=supers();++i)\n        dst.diagonal(i) = diagonal(i);\n      for (Index i=1; i<=subs();++i)\n        dst.diagonal(-i) = diagonal(-i);\n    }\n\n    DenseMatrixType toDenseMatrix() const\n    {\n      DenseMatrixType res(rows(),cols());\n      evalTo(res);\n      return res;\n    }\n\n  protected:\n\n    inline Index diagonalLength(Index i) const\n    { return i<0 ? (std::min)(cols(),rows()+i) : (std::min)(rows(),cols()-i); }\n};\n\n/**\n  * \\class BandMatrix\n  * \\ingroup Core_Module\n  *\n  * \\brief Represents a rectangular matrix with a banded storage\n  *\n  * \\tparam _Scalar Numeric type, i.e. float, double, int\n  * \\tparam _Rows Number of rows, or \\b Dynamic\n  * \\tparam _Cols Number of columns, or \\b Dynamic\n  * \\tparam _Supers Number of super diagonal\n  * \\tparam _Subs Number of sub diagonal\n  * \\tparam _Options A combination of either \\b #RowMajor or \\b #ColMajor, and of \\b #SelfAdjoint\n  *                  The former controls \\ref TopicStorageOrders \"storage order\", and defaults to\n  *                  column-major. The latter controls whether the matrix represents a selfadjoint\n  *                  matrix in which case either Supers of Subs have to be null.\n  *\n  * \\sa class TridiagonalMatrix\n  */\n\ntemplate<typename _Scalar, int _Rows, int _Cols, int _Supers, int _Subs, int _Options>\nstruct traits<BandMatrix<_Scalar,_Rows,_Cols,_Supers,_Subs,_Options> >\n{\n  typedef _Scalar Scalar;\n  typedef Dense StorageKind;\n  typedef Eigen::Index StorageIndex;\n  enum {\n    CoeffReadCost = NumTraits<Scalar>::ReadCost,\n    RowsAtCompileTime = _Rows,\n    ColsAtCompileTime = _Cols,\n    MaxRowsAtCompileTime = _Rows,\n    MaxColsAtCompileTime = _Cols,\n    Flags = LvalueBit,\n    Supers = _Supers,\n    Subs = _Subs,\n    Options = _Options,\n    DataRowsAtCompileTime = ((Supers!=Dynamic) && (Subs!=Dynamic)) ? 1 + Supers + Subs : Dynamic\n  };\n  typedef Matrix<Scalar,DataRowsAtCompileTime,ColsAtCompileTime,Options&RowMajor?RowMajor:ColMajor> CoefficientsType;\n};\n\ntemplate<typename _Scalar, int Rows, int Cols, int Supers, int Subs, int Options>\nclass BandMatrix : public BandMatrixBase<BandMatrix<_Scalar,Rows,Cols,Supers,Subs,Options> >\n{\n  public:\n\n    typedef typename internal::traits<BandMatrix>::Scalar Scalar;\n    typedef typename internal::traits<BandMatrix>::StorageIndex StorageIndex;\n    typedef typename internal::traits<BandMatrix>::CoefficientsType CoefficientsType;\n\n    explicit inline BandMatrix(Index rows=Rows, Index cols=Cols, Index supers=Supers, Index subs=Subs)\n      : m_coeffs(1+supers+subs,cols),\n        m_rows(rows), m_supers(supers), m_subs(subs)\n    {\n    }\n\n    /** \\returns the number of columns */\n    inline Index rows() const { return m_rows.value(); }\n\n    /** \\returns the number of rows */\n    inline Index cols() const { return m_coeffs.cols(); }\n\n    /** \\returns the number of super diagonals */\n    inline Index supers() const { return m_supers.value(); }\n\n    /** \\returns the number of sub diagonals */\n    inline Index subs() const { return m_subs.value(); }\n\n    inline const CoefficientsType& coeffs() const { return m_coeffs; }\n    inline CoefficientsType& coeffs() { return m_coeffs; }\n\n  protected:\n\n    CoefficientsType m_coeffs;\n    internal::variable_if_dynamic<Index, Rows>   m_rows;\n    internal::variable_if_dynamic<Index, Supers> m_supers;\n    internal::variable_if_dynamic<Index, Subs>   m_subs;\n};\n\ntemplate<typename _CoefficientsType,int _Rows, int _Cols, int _Supers, int _Subs,int _Options>\nclass BandMatrixWrapper;\n\ntemplate<typename _CoefficientsType,int _Rows, int _Cols, int _Supers, int _Subs,int _Options>\nstruct traits<BandMatrixWrapper<_CoefficientsType,_Rows,_Cols,_Supers,_Subs,_Options> >\n{\n  typedef typename _CoefficientsType::Scalar Scalar;\n  typedef typename _CoefficientsType::StorageKind StorageKind;\n  typedef typename _CoefficientsType::StorageIndex StorageIndex;\n  enum {\n    CoeffReadCost = internal::traits<_CoefficientsType>::CoeffReadCost,\n    RowsAtCompileTime = _Rows,\n    ColsAtCompileTime = _Cols,\n    MaxRowsAtCompileTime = _Rows,\n    MaxColsAtCompileTime = _Cols,\n    Flags = LvalueBit,\n    Supers = _Supers,\n    Subs = _Subs,\n    Options = _Options,\n    DataRowsAtCompileTime = ((Supers!=Dynamic) && (Subs!=Dynamic)) ? 1 + Supers + Subs : Dynamic\n  };\n  typedef _CoefficientsType CoefficientsType;\n};\n\ntemplate<typename _CoefficientsType,int _Rows, int _Cols, int _Supers, int _Subs,int _Options>\nclass BandMatrixWrapper : public BandMatrixBase<BandMatrixWrapper<_CoefficientsType,_Rows,_Cols,_Supers,_Subs,_Options> >\n{\n  public:\n\n    typedef typename internal::traits<BandMatrixWrapper>::Scalar Scalar;\n    typedef typename internal::traits<BandMatrixWrapper>::CoefficientsType CoefficientsType;\n    typedef typename internal::traits<BandMatrixWrapper>::StorageIndex StorageIndex;\n\n    explicit inline BandMatrixWrapper(const CoefficientsType& coeffs, Index rows=_Rows, Index cols=_Cols, Index supers=_Supers, Index subs=_Subs)\n      : m_coeffs(coeffs),\n        m_rows(rows), m_supers(supers), m_subs(subs)\n    {\n      EIGEN_UNUSED_VARIABLE(cols);\n      //internal::assert(coeffs.cols()==cols() && (supers()+subs()+1)==coeffs.rows());\n    }\n\n    /** \\returns the number of columns */\n    inline Index rows() const { return m_rows.value(); }\n\n    /** \\returns the number of rows */\n    inline Index cols() const { return m_coeffs.cols(); }\n\n    /** \\returns the number of super diagonals */\n    inline Index supers() const { return m_supers.value(); }\n\n    /** \\returns the number of sub diagonals */\n    inline Index subs() const { return m_subs.value(); }\n\n    inline const CoefficientsType& coeffs() const { return m_coeffs; }\n\n  protected:\n\n    const CoefficientsType& m_coeffs;\n    internal::variable_if_dynamic<Index, _Rows>   m_rows;\n    internal::variable_if_dynamic<Index, _Supers> m_supers;\n    internal::variable_if_dynamic<Index, _Subs>   m_subs;\n};\n\n/**\n  * \\class TridiagonalMatrix\n  * \\ingroup Core_Module\n  *\n  * \\brief Represents a tridiagonal matrix with a compact banded storage\n  *\n  * \\tparam Scalar Numeric type, i.e. float, double, int\n  * \\tparam Size Number of rows and cols, or \\b Dynamic\n  * \\tparam Options Can be 0 or \\b SelfAdjoint\n  *\n  * \\sa class BandMatrix\n  */\ntemplate<typename Scalar, int Size, int Options>\nclass TridiagonalMatrix : public BandMatrix<Scalar,Size,Size,Options&SelfAdjoint?0:1,1,Options|RowMajor>\n{\n    typedef BandMatrix<Scalar,Size,Size,Options&SelfAdjoint?0:1,1,Options|RowMajor> Base;\n    typedef typename Base::StorageIndex StorageIndex;\n  public:\n    explicit TridiagonalMatrix(Index size = Size) : Base(size,size,Options&SelfAdjoint?0:1,1) {}\n\n    inline typename Base::template DiagonalIntReturnType<1>::Type super()\n    { return Base::template diagonal<1>(); }\n    inline const typename Base::template DiagonalIntReturnType<1>::Type super() const\n    { return Base::template diagonal<1>(); }\n    inline typename Base::template DiagonalIntReturnType<-1>::Type sub()\n    { return Base::template diagonal<-1>(); }\n    inline const typename Base::template DiagonalIntReturnType<-1>::Type sub() const\n    { return Base::template diagonal<-1>(); }\n  protected:\n};\n\n\nstruct BandShape {};\n\ntemplate<typename _Scalar, int _Rows, int _Cols, int _Supers, int _Subs, int _Options>\nstruct evaluator_traits<BandMatrix<_Scalar,_Rows,_Cols,_Supers,_Subs,_Options> >\n  : public evaluator_traits_base<BandMatrix<_Scalar,_Rows,_Cols,_Supers,_Subs,_Options> >\n{\n  typedef BandShape Shape;\n};\n\ntemplate<typename _CoefficientsType,int _Rows, int _Cols, int _Supers, int _Subs,int _Options>\nstruct evaluator_traits<BandMatrixWrapper<_CoefficientsType,_Rows,_Cols,_Supers,_Subs,_Options> >\n  : public evaluator_traits_base<BandMatrixWrapper<_CoefficientsType,_Rows,_Cols,_Supers,_Subs,_Options> >\n{\n  typedef BandShape Shape;\n};\n\ntemplate<> struct AssignmentKind<DenseShape,BandShape> { typedef EigenBase2EigenBase Kind; };\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_BANDMATRIX_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/Block.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_BLOCK_H\n#define EIGEN_BLOCK_H\n\nnamespace Eigen { \n\nnamespace internal {\ntemplate<typename XprType, int BlockRows, int BlockCols, bool InnerPanel>\nstruct traits<Block<XprType, BlockRows, BlockCols, InnerPanel> > : traits<XprType>\n{\n  typedef typename traits<XprType>::Scalar Scalar;\n  typedef typename traits<XprType>::StorageKind StorageKind;\n  typedef typename traits<XprType>::XprKind XprKind;\n  typedef typename ref_selector<XprType>::type XprTypeNested;\n  typedef typename remove_reference<XprTypeNested>::type _XprTypeNested;\n  enum{\n    MatrixRows = traits<XprType>::RowsAtCompileTime,\n    MatrixCols = traits<XprType>::ColsAtCompileTime,\n    RowsAtCompileTime = MatrixRows == 0 ? 0 : BlockRows,\n    ColsAtCompileTime = MatrixCols == 0 ? 0 : BlockCols,\n    MaxRowsAtCompileTime = BlockRows==0 ? 0\n                         : RowsAtCompileTime != Dynamic ? int(RowsAtCompileTime)\n                         : int(traits<XprType>::MaxRowsAtCompileTime),\n    MaxColsAtCompileTime = BlockCols==0 ? 0\n                         : ColsAtCompileTime != Dynamic ? int(ColsAtCompileTime)\n                         : int(traits<XprType>::MaxColsAtCompileTime),\n\n    XprTypeIsRowMajor = (int(traits<XprType>::Flags)&RowMajorBit) != 0,\n    IsRowMajor = (MaxRowsAtCompileTime==1&&MaxColsAtCompileTime!=1) ? 1\n               : (MaxColsAtCompileTime==1&&MaxRowsAtCompileTime!=1) ? 0\n               : XprTypeIsRowMajor,\n    HasSameStorageOrderAsXprType = (IsRowMajor == XprTypeIsRowMajor),\n    InnerSize = IsRowMajor ? int(ColsAtCompileTime) : int(RowsAtCompileTime),\n    InnerStrideAtCompileTime = HasSameStorageOrderAsXprType\n                             ? int(inner_stride_at_compile_time<XprType>::ret)\n                             : int(outer_stride_at_compile_time<XprType>::ret),\n    OuterStrideAtCompileTime = HasSameStorageOrderAsXprType\n                             ? int(outer_stride_at_compile_time<XprType>::ret)\n                             : int(inner_stride_at_compile_time<XprType>::ret),\n\n    // FIXME, this traits is rather specialized for dense object and it needs to be cleaned further\n    FlagsLvalueBit = is_lvalue<XprType>::value ? LvalueBit : 0,\n    FlagsRowMajorBit = IsRowMajor ? RowMajorBit : 0,\n    Flags = (traits<XprType>::Flags & (DirectAccessBit | (InnerPanel?CompressedAccessBit:0))) | FlagsLvalueBit | FlagsRowMajorBit,\n    // FIXME DirectAccessBit should not be handled by expressions\n    // \n    // Alignment is needed by MapBase's assertions\n    // We can sefely set it to false here. Internal alignment errors will be detected by an eigen_internal_assert in the respective evaluator\n    Alignment = 0\n  };\n};\n\ntemplate<typename XprType, int BlockRows=Dynamic, int BlockCols=Dynamic, bool InnerPanel = false,\n         bool HasDirectAccess = internal::has_direct_access<XprType>::ret> class BlockImpl_dense;\n         \n} // end namespace internal\n\ntemplate<typename XprType, int BlockRows, int BlockCols, bool InnerPanel, typename StorageKind> class BlockImpl;\n\n/** \\class Block\n  * \\ingroup Core_Module\n  *\n  * \\brief Expression of a fixed-size or dynamic-size block\n  *\n  * \\tparam XprType the type of the expression in which we are taking a block\n  * \\tparam BlockRows the number of rows of the block we are taking at compile time (optional)\n  * \\tparam BlockCols the number of columns of the block we are taking at compile time (optional)\n  * \\tparam InnerPanel is true, if the block maps to a set of rows of a row major matrix or\n  *         to set of columns of a column major matrix (optional). The parameter allows to determine\n  *         at compile time whether aligned access is possible on the block expression.\n  *\n  * This class represents an expression of either a fixed-size or dynamic-size block. It is the return\n  * type of DenseBase::block(Index,Index,Index,Index) and DenseBase::block<int,int>(Index,Index) and\n  * most of the time this is the only way it is used.\n  *\n  * However, if you want to directly maniputate block expressions,\n  * for instance if you want to write a function returning such an expression, you\n  * will need to use this class.\n  *\n  * Here is an example illustrating the dynamic case:\n  * \\include class_Block.cpp\n  * Output: \\verbinclude class_Block.out\n  *\n  * \\note Even though this expression has dynamic size, in the case where \\a XprType\n  * has fixed size, this expression inherits a fixed maximal size which means that evaluating\n  * it does not cause a dynamic memory allocation.\n  *\n  * Here is an example illustrating the fixed-size case:\n  * \\include class_FixedBlock.cpp\n  * Output: \\verbinclude class_FixedBlock.out\n  *\n  * \\sa DenseBase::block(Index,Index,Index,Index), DenseBase::block(Index,Index), class VectorBlock\n  */\ntemplate<typename XprType, int BlockRows, int BlockCols, bool InnerPanel> class Block\n  : public BlockImpl<XprType, BlockRows, BlockCols, InnerPanel, typename internal::traits<XprType>::StorageKind>\n{\n    typedef BlockImpl<XprType, BlockRows, BlockCols, InnerPanel, typename internal::traits<XprType>::StorageKind> Impl;\n  public:\n    //typedef typename Impl::Base Base;\n    typedef Impl Base;\n    EIGEN_GENERIC_PUBLIC_INTERFACE(Block)\n    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Block)\n    \n    typedef typename internal::remove_all<XprType>::type NestedExpression;\n  \n    /** Column or Row constructor\n      */\n    EIGEN_DEVICE_FUNC\n    inline Block(XprType& xpr, Index i) : Impl(xpr,i)\n    {\n      eigen_assert( (i>=0) && (\n          ((BlockRows==1) && (BlockCols==XprType::ColsAtCompileTime) && i<xpr.rows())\n        ||((BlockRows==XprType::RowsAtCompileTime) && (BlockCols==1) && i<xpr.cols())));\n    }\n\n    /** Fixed-size constructor\n      */\n    EIGEN_DEVICE_FUNC\n    inline Block(XprType& xpr, Index startRow, Index startCol)\n      : Impl(xpr, startRow, startCol)\n    {\n      EIGEN_STATIC_ASSERT(RowsAtCompileTime!=Dynamic && ColsAtCompileTime!=Dynamic,THIS_METHOD_IS_ONLY_FOR_FIXED_SIZE)\n      eigen_assert(startRow >= 0 && BlockRows >= 0 && startRow + BlockRows <= xpr.rows()\n             && startCol >= 0 && BlockCols >= 0 && startCol + BlockCols <= xpr.cols());\n    }\n\n    /** Dynamic-size constructor\n      */\n    EIGEN_DEVICE_FUNC\n    inline Block(XprType& xpr,\n          Index startRow, Index startCol,\n          Index blockRows, Index blockCols)\n      : Impl(xpr, startRow, startCol, blockRows, blockCols)\n    {\n      eigen_assert((RowsAtCompileTime==Dynamic || RowsAtCompileTime==blockRows)\n          && (ColsAtCompileTime==Dynamic || ColsAtCompileTime==blockCols));\n      eigen_assert(startRow >= 0 && blockRows >= 0 && startRow  <= xpr.rows() - blockRows\n          && startCol >= 0 && blockCols >= 0 && startCol <= xpr.cols() - blockCols);\n    }\n};\n         \n// The generic default implementation for dense block simplu forward to the internal::BlockImpl_dense\n// that must be specialized for direct and non-direct access...\ntemplate<typename XprType, int BlockRows, int BlockCols, bool InnerPanel>\nclass BlockImpl<XprType, BlockRows, BlockCols, InnerPanel, Dense>\n  : public internal::BlockImpl_dense<XprType, BlockRows, BlockCols, InnerPanel>\n{\n    typedef internal::BlockImpl_dense<XprType, BlockRows, BlockCols, InnerPanel> Impl;\n    typedef typename XprType::StorageIndex StorageIndex;\n  public:\n    typedef Impl Base;\n    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(BlockImpl)\n    EIGEN_DEVICE_FUNC inline BlockImpl(XprType& xpr, Index i) : Impl(xpr,i) {}\n    EIGEN_DEVICE_FUNC inline BlockImpl(XprType& xpr, Index startRow, Index startCol) : Impl(xpr, startRow, startCol) {}\n    EIGEN_DEVICE_FUNC\n    inline BlockImpl(XprType& xpr, Index startRow, Index startCol, Index blockRows, Index blockCols)\n      : Impl(xpr, startRow, startCol, blockRows, blockCols) {}\n};\n\nnamespace internal {\n\n/** \\internal Internal implementation of dense Blocks in the general case. */\ntemplate<typename XprType, int BlockRows, int BlockCols, bool InnerPanel, bool HasDirectAccess> class BlockImpl_dense\n  : public internal::dense_xpr_base<Block<XprType, BlockRows, BlockCols, InnerPanel> >::type\n{\n    typedef Block<XprType, BlockRows, BlockCols, InnerPanel> BlockType;\n    typedef typename internal::ref_selector<XprType>::non_const_type XprTypeNested;\n  public:\n\n    typedef typename internal::dense_xpr_base<BlockType>::type Base;\n    EIGEN_DENSE_PUBLIC_INTERFACE(BlockType)\n    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(BlockImpl_dense)\n\n    // class InnerIterator; // FIXME apparently never used\n\n    /** Column or Row constructor\n      */\n    EIGEN_DEVICE_FUNC\n    inline BlockImpl_dense(XprType& xpr, Index i)\n      : m_xpr(xpr),\n        // It is a row if and only if BlockRows==1 and BlockCols==XprType::ColsAtCompileTime,\n        // and it is a column if and only if BlockRows==XprType::RowsAtCompileTime and BlockCols==1,\n        // all other cases are invalid.\n        // The case a 1x1 matrix seems ambiguous, but the result is the same anyway.\n        m_startRow( (BlockRows==1) && (BlockCols==XprType::ColsAtCompileTime) ? i : 0),\n        m_startCol( (BlockRows==XprType::RowsAtCompileTime) && (BlockCols==1) ? i : 0),\n        m_blockRows(BlockRows==1 ? 1 : xpr.rows()),\n        m_blockCols(BlockCols==1 ? 1 : xpr.cols())\n    {}\n\n    /** Fixed-size constructor\n      */\n    EIGEN_DEVICE_FUNC\n    inline BlockImpl_dense(XprType& xpr, Index startRow, Index startCol)\n      : m_xpr(xpr), m_startRow(startRow), m_startCol(startCol),\n                    m_blockRows(BlockRows), m_blockCols(BlockCols)\n    {}\n\n    /** Dynamic-size constructor\n      */\n    EIGEN_DEVICE_FUNC\n    inline BlockImpl_dense(XprType& xpr,\n          Index startRow, Index startCol,\n          Index blockRows, Index blockCols)\n      : m_xpr(xpr), m_startRow(startRow), m_startCol(startCol),\n                    m_blockRows(blockRows), m_blockCols(blockCols)\n    {}\n\n    EIGEN_DEVICE_FUNC inline Index rows() const { return m_blockRows.value(); }\n    EIGEN_DEVICE_FUNC inline Index cols() const { return m_blockCols.value(); }\n\n    EIGEN_DEVICE_FUNC\n    inline Scalar& coeffRef(Index rowId, Index colId)\n    {\n      EIGEN_STATIC_ASSERT_LVALUE(XprType)\n      return m_xpr.coeffRef(rowId + m_startRow.value(), colId + m_startCol.value());\n    }\n\n    EIGEN_DEVICE_FUNC\n    inline const Scalar& coeffRef(Index rowId, Index colId) const\n    {\n      return m_xpr.derived().coeffRef(rowId + m_startRow.value(), colId + m_startCol.value());\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const CoeffReturnType coeff(Index rowId, Index colId) const\n    {\n      return m_xpr.coeff(rowId + m_startRow.value(), colId + m_startCol.value());\n    }\n\n    EIGEN_DEVICE_FUNC\n    inline Scalar& coeffRef(Index index)\n    {\n      EIGEN_STATIC_ASSERT_LVALUE(XprType)\n      return m_xpr.coeffRef(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),\n                            m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));\n    }\n\n    EIGEN_DEVICE_FUNC\n    inline const Scalar& coeffRef(Index index) const\n    {\n      return m_xpr.coeffRef(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),\n                            m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));\n    }\n\n    EIGEN_DEVICE_FUNC\n    inline const CoeffReturnType coeff(Index index) const\n    {\n      return m_xpr.coeff(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),\n                         m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));\n    }\n\n    template<int LoadMode>\n    inline PacketScalar packet(Index rowId, Index colId) const\n    {\n      return m_xpr.template packet<Unaligned>(rowId + m_startRow.value(), colId + m_startCol.value());\n    }\n\n    template<int LoadMode>\n    inline void writePacket(Index rowId, Index colId, const PacketScalar& val)\n    {\n      m_xpr.template writePacket<Unaligned>(rowId + m_startRow.value(), colId + m_startCol.value(), val);\n    }\n\n    template<int LoadMode>\n    inline PacketScalar packet(Index index) const\n    {\n      return m_xpr.template packet<Unaligned>\n              (m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),\n               m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));\n    }\n\n    template<int LoadMode>\n    inline void writePacket(Index index, const PacketScalar& val)\n    {\n      m_xpr.template writePacket<Unaligned>\n         (m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),\n          m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0), val);\n    }\n\n    #ifdef EIGEN_PARSED_BY_DOXYGEN\n    /** \\sa MapBase::data() */\n    EIGEN_DEVICE_FUNC inline const Scalar* data() const;\n    EIGEN_DEVICE_FUNC inline Index innerStride() const;\n    EIGEN_DEVICE_FUNC inline Index outerStride() const;\n    #endif\n\n    EIGEN_DEVICE_FUNC\n    const typename internal::remove_all<XprTypeNested>::type& nestedExpression() const\n    { \n      return m_xpr; \n    }\n\n    EIGEN_DEVICE_FUNC\n    XprType& nestedExpression() { return m_xpr; }\n      \n    EIGEN_DEVICE_FUNC\n    StorageIndex startRow() const\n    { \n      return m_startRow.value(); \n    }\n      \n    EIGEN_DEVICE_FUNC\n    StorageIndex startCol() const\n    { \n      return m_startCol.value(); \n    }\n\n  protected:\n\n    XprTypeNested m_xpr;\n    const internal::variable_if_dynamic<StorageIndex, (XprType::RowsAtCompileTime == 1 && BlockRows==1) ? 0 : Dynamic> m_startRow;\n    const internal::variable_if_dynamic<StorageIndex, (XprType::ColsAtCompileTime == 1 && BlockCols==1) ? 0 : Dynamic> m_startCol;\n    const internal::variable_if_dynamic<StorageIndex, RowsAtCompileTime> m_blockRows;\n    const internal::variable_if_dynamic<StorageIndex, ColsAtCompileTime> m_blockCols;\n};\n\n/** \\internal Internal implementation of dense Blocks in the direct access case.*/\ntemplate<typename XprType, int BlockRows, int BlockCols, bool InnerPanel>\nclass BlockImpl_dense<XprType,BlockRows,BlockCols, InnerPanel,true>\n  : public MapBase<Block<XprType, BlockRows, BlockCols, InnerPanel> >\n{\n    typedef Block<XprType, BlockRows, BlockCols, InnerPanel> BlockType;\n    typedef typename internal::ref_selector<XprType>::non_const_type XprTypeNested;\n    enum {\n      XprTypeIsRowMajor = (int(traits<XprType>::Flags)&RowMajorBit) != 0\n    };\n  public:\n\n    typedef MapBase<BlockType> Base;\n    EIGEN_DENSE_PUBLIC_INTERFACE(BlockType)\n    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(BlockImpl_dense)\n\n    /** Column or Row constructor\n      */\n    EIGEN_DEVICE_FUNC\n    inline BlockImpl_dense(XprType& xpr, Index i)\n      : Base(xpr.data() + i * (    ((BlockRows==1) && (BlockCols==XprType::ColsAtCompileTime) && (!XprTypeIsRowMajor)) \n                                || ((BlockRows==XprType::RowsAtCompileTime) && (BlockCols==1) && ( XprTypeIsRowMajor)) ? xpr.innerStride() : xpr.outerStride()),\n             BlockRows==1 ? 1 : xpr.rows(),\n             BlockCols==1 ? 1 : xpr.cols()),\n        m_xpr(xpr),\n        m_startRow( (BlockRows==1) && (BlockCols==XprType::ColsAtCompileTime) ? i : 0),\n        m_startCol( (BlockRows==XprType::RowsAtCompileTime) && (BlockCols==1) ? i : 0)\n    {\n      init();\n    }\n\n    /** Fixed-size constructor\n      */\n    EIGEN_DEVICE_FUNC\n    inline BlockImpl_dense(XprType& xpr, Index startRow, Index startCol)\n      : Base(xpr.data()+xpr.innerStride()*(XprTypeIsRowMajor?startCol:startRow) + xpr.outerStride()*(XprTypeIsRowMajor?startRow:startCol)),\n        m_xpr(xpr), m_startRow(startRow), m_startCol(startCol)\n    {\n      init();\n    }\n\n    /** Dynamic-size constructor\n      */\n    EIGEN_DEVICE_FUNC\n    inline BlockImpl_dense(XprType& xpr,\n          Index startRow, Index startCol,\n          Index blockRows, Index blockCols)\n      : Base(xpr.data()+xpr.innerStride()*(XprTypeIsRowMajor?startCol:startRow) + xpr.outerStride()*(XprTypeIsRowMajor?startRow:startCol), blockRows, blockCols),\n        m_xpr(xpr), m_startRow(startRow), m_startCol(startCol)\n    {\n      init();\n    }\n\n    EIGEN_DEVICE_FUNC\n    const typename internal::remove_all<XprTypeNested>::type& nestedExpression() const\n    { \n      return m_xpr; \n    }\n\n    EIGEN_DEVICE_FUNC\n    XprType& nestedExpression() { return m_xpr; }\n      \n    /** \\sa MapBase::innerStride() */\n    EIGEN_DEVICE_FUNC\n    inline Index innerStride() const\n    {\n      return internal::traits<BlockType>::HasSameStorageOrderAsXprType\n             ? m_xpr.innerStride()\n             : m_xpr.outerStride();\n    }\n\n    /** \\sa MapBase::outerStride() */\n    EIGEN_DEVICE_FUNC\n    inline Index outerStride() const\n    {\n      return m_outerStride;\n    }\n\n    EIGEN_DEVICE_FUNC\n    StorageIndex startRow() const\n    {\n      return m_startRow.value();\n    }\n\n    EIGEN_DEVICE_FUNC\n    StorageIndex startCol() const\n    {\n      return m_startCol.value();\n    }\n\n  #ifndef __SUNPRO_CC\n  // FIXME sunstudio is not friendly with the above friend...\n  // META-FIXME there is no 'friend' keyword around here. Is this obsolete?\n  protected:\n  #endif\n\n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    /** \\internal used by allowAligned() */\n    EIGEN_DEVICE_FUNC\n    inline BlockImpl_dense(XprType& xpr, const Scalar* data, Index blockRows, Index blockCols)\n      : Base(data, blockRows, blockCols), m_xpr(xpr)\n    {\n      init();\n    }\n    #endif\n\n  protected:\n    EIGEN_DEVICE_FUNC\n    void init()\n    {\n      m_outerStride = internal::traits<BlockType>::HasSameStorageOrderAsXprType\n                    ? m_xpr.outerStride()\n                    : m_xpr.innerStride();\n    }\n\n    XprTypeNested m_xpr;\n    const internal::variable_if_dynamic<StorageIndex, (XprType::RowsAtCompileTime == 1 && BlockRows==1) ? 0 : Dynamic> m_startRow;\n    const internal::variable_if_dynamic<StorageIndex, (XprType::ColsAtCompileTime == 1 && BlockCols==1) ? 0 : Dynamic> m_startCol;\n    Index m_outerStride;\n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_BLOCK_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/BooleanRedux.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_ALLANDANY_H\n#define EIGEN_ALLANDANY_H\n\nnamespace Eigen { \n\nnamespace internal {\n\ntemplate<typename Derived, int UnrollCount>\nstruct all_unroller\n{\n  typedef typename Derived::ExpressionTraits Traits;\n  enum {\n    col = (UnrollCount-1) / Traits::RowsAtCompileTime,\n    row = (UnrollCount-1) % Traits::RowsAtCompileTime\n  };\n\n  static inline bool run(const Derived &mat)\n  {\n    return all_unroller<Derived, UnrollCount-1>::run(mat) && mat.coeff(row, col);\n  }\n};\n\ntemplate<typename Derived>\nstruct all_unroller<Derived, 0>\n{\n  static inline bool run(const Derived &/*mat*/) { return true; }\n};\n\ntemplate<typename Derived>\nstruct all_unroller<Derived, Dynamic>\n{\n  static inline bool run(const Derived &) { return false; }\n};\n\ntemplate<typename Derived, int UnrollCount>\nstruct any_unroller\n{\n  typedef typename Derived::ExpressionTraits Traits;\n  enum {\n    col = (UnrollCount-1) / Traits::RowsAtCompileTime,\n    row = (UnrollCount-1) % Traits::RowsAtCompileTime\n  };\n  \n  static inline bool run(const Derived &mat)\n  {\n    return any_unroller<Derived, UnrollCount-1>::run(mat) || mat.coeff(row, col);\n  }\n};\n\ntemplate<typename Derived>\nstruct any_unroller<Derived, 0>\n{\n  static inline bool run(const Derived & /*mat*/) { return false; }\n};\n\ntemplate<typename Derived>\nstruct any_unroller<Derived, Dynamic>\n{\n  static inline bool run(const Derived &) { return false; }\n};\n\n} // end namespace internal\n\n/** \\returns true if all coefficients are true\n  *\n  * Example: \\include MatrixBase_all.cpp\n  * Output: \\verbinclude MatrixBase_all.out\n  *\n  * \\sa any(), Cwise::operator<()\n  */\ntemplate<typename Derived>\ninline bool DenseBase<Derived>::all() const\n{\n  typedef internal::evaluator<Derived> Evaluator;\n  enum {\n    unroll = SizeAtCompileTime != Dynamic\n          && SizeAtCompileTime * (Evaluator::CoeffReadCost + NumTraits<Scalar>::AddCost) <= EIGEN_UNROLLING_LIMIT\n  };\n  Evaluator evaluator(derived());\n  if(unroll)\n    return internal::all_unroller<Evaluator, unroll ? int(SizeAtCompileTime) : Dynamic>::run(evaluator);\n  else\n  {\n    for(Index j = 0; j < cols(); ++j)\n      for(Index i = 0; i < rows(); ++i)\n        if (!evaluator.coeff(i, j)) return false;\n    return true;\n  }\n}\n\n/** \\returns true if at least one coefficient is true\n  *\n  * \\sa all()\n  */\ntemplate<typename Derived>\ninline bool DenseBase<Derived>::any() const\n{\n  typedef internal::evaluator<Derived> Evaluator;\n  enum {\n    unroll = SizeAtCompileTime != Dynamic\n          && SizeAtCompileTime * (Evaluator::CoeffReadCost + NumTraits<Scalar>::AddCost) <= EIGEN_UNROLLING_LIMIT\n  };\n  Evaluator evaluator(derived());\n  if(unroll)\n    return internal::any_unroller<Evaluator, unroll ? int(SizeAtCompileTime) : Dynamic>::run(evaluator);\n  else\n  {\n    for(Index j = 0; j < cols(); ++j)\n      for(Index i = 0; i < rows(); ++i)\n        if (evaluator.coeff(i, j)) return true;\n    return false;\n  }\n}\n\n/** \\returns the number of coefficients which evaluate to true\n  *\n  * \\sa all(), any()\n  */\ntemplate<typename Derived>\ninline Eigen::Index DenseBase<Derived>::count() const\n{\n  return derived().template cast<bool>().template cast<Index>().sum();\n}\n\n/** \\returns true is \\c *this contains at least one Not A Number (NaN).\n  *\n  * \\sa allFinite()\n  */\ntemplate<typename Derived>\ninline bool DenseBase<Derived>::hasNaN() const\n{\n#if EIGEN_COMP_MSVC || (defined __FAST_MATH__)\n  return derived().array().isNaN().any();\n#else\n  return !((derived().array()==derived().array()).all());\n#endif\n}\n\n/** \\returns true if \\c *this contains only finite numbers, i.e., no NaN and no +/-INF values.\n  *\n  * \\sa hasNaN()\n  */\ntemplate<typename Derived>\ninline bool DenseBase<Derived>::allFinite() const\n{\n#if EIGEN_COMP_MSVC || (defined __FAST_MATH__)\n  return derived().array().isFinite().all();\n#else\n  return !((derived()-derived()).hasNaN());\n#endif\n}\n    \n} // end namespace Eigen\n\n#endif // EIGEN_ALLANDANY_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/CommaInitializer.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_COMMAINITIALIZER_H\n#define EIGEN_COMMAINITIALIZER_H\n\nnamespace Eigen { \n\n/** \\class CommaInitializer\n  * \\ingroup Core_Module\n  *\n  * \\brief Helper class used by the comma initializer operator\n  *\n  * This class is internally used to implement the comma initializer feature. It is\n  * the return type of MatrixBase::operator<<, and most of the time this is the only\n  * way it is used.\n  *\n  * \\sa \\blank \\ref MatrixBaseCommaInitRef \"MatrixBase::operator<<\", CommaInitializer::finished()\n  */\ntemplate<typename XprType>\nstruct CommaInitializer\n{\n  typedef typename XprType::Scalar Scalar;\n\n  EIGEN_DEVICE_FUNC\n  inline CommaInitializer(XprType& xpr, const Scalar& s)\n    : m_xpr(xpr), m_row(0), m_col(1), m_currentBlockRows(1)\n  {\n    m_xpr.coeffRef(0,0) = s;\n  }\n\n  template<typename OtherDerived>\n  EIGEN_DEVICE_FUNC\n  inline CommaInitializer(XprType& xpr, const DenseBase<OtherDerived>& other)\n    : m_xpr(xpr), m_row(0), m_col(other.cols()), m_currentBlockRows(other.rows())\n  {\n    m_xpr.block(0, 0, other.rows(), other.cols()) = other;\n  }\n\n  /* Copy/Move constructor which transfers ownership. This is crucial in \n   * absence of return value optimization to avoid assertions during destruction. */\n  // FIXME in C++11 mode this could be replaced by a proper RValue constructor\n  EIGEN_DEVICE_FUNC\n  inline CommaInitializer(const CommaInitializer& o)\n  : m_xpr(o.m_xpr), m_row(o.m_row), m_col(o.m_col), m_currentBlockRows(o.m_currentBlockRows) {\n    // Mark original object as finished. In absence of R-value references we need to const_cast:\n    const_cast<CommaInitializer&>(o).m_row = m_xpr.rows();\n    const_cast<CommaInitializer&>(o).m_col = m_xpr.cols();\n    const_cast<CommaInitializer&>(o).m_currentBlockRows = 0;\n  }\n\n  /* inserts a scalar value in the target matrix */\n  EIGEN_DEVICE_FUNC\n  CommaInitializer& operator,(const Scalar& s)\n  {\n    if (m_col==m_xpr.cols())\n    {\n      m_row+=m_currentBlockRows;\n      m_col = 0;\n      m_currentBlockRows = 1;\n      eigen_assert(m_row<m_xpr.rows()\n        && \"Too many rows passed to comma initializer (operator<<)\");\n    }\n    eigen_assert(m_col<m_xpr.cols()\n      && \"Too many coefficients passed to comma initializer (operator<<)\");\n    eigen_assert(m_currentBlockRows==1);\n    m_xpr.coeffRef(m_row, m_col++) = s;\n    return *this;\n  }\n\n  /* inserts a matrix expression in the target matrix */\n  template<typename OtherDerived>\n  EIGEN_DEVICE_FUNC\n  CommaInitializer& operator,(const DenseBase<OtherDerived>& other)\n  {\n    if (m_col==m_xpr.cols() && (other.cols()!=0 || other.rows()!=m_currentBlockRows))\n    {\n      m_row+=m_currentBlockRows;\n      m_col = 0;\n      m_currentBlockRows = other.rows();\n      eigen_assert(m_row+m_currentBlockRows<=m_xpr.rows()\n        && \"Too many rows passed to comma initializer (operator<<)\");\n    }\n    eigen_assert((m_col + other.cols() <= m_xpr.cols())\n      && \"Too many coefficients passed to comma initializer (operator<<)\");\n    eigen_assert(m_currentBlockRows==other.rows());\n    m_xpr.template block<OtherDerived::RowsAtCompileTime, OtherDerived::ColsAtCompileTime>\n                    (m_row, m_col, other.rows(), other.cols()) = other;\n    m_col += other.cols();\n    return *this;\n  }\n\n  EIGEN_DEVICE_FUNC\n  inline ~CommaInitializer()\n#if defined VERIFY_RAISES_ASSERT && (!defined EIGEN_NO_ASSERTION_CHECKING) && defined EIGEN_EXCEPTIONS\n  EIGEN_EXCEPTION_SPEC(Eigen::eigen_assert_exception)\n#endif\n  {\n      finished();\n  }\n\n  /** \\returns the built matrix once all its coefficients have been set.\n    * Calling finished is 100% optional. Its purpose is to write expressions\n    * like this:\n    * \\code\n    * quaternion.fromRotationMatrix((Matrix3f() << axis0, axis1, axis2).finished());\n    * \\endcode\n    */\n  EIGEN_DEVICE_FUNC\n  inline XprType& finished() {\n      eigen_assert(((m_row+m_currentBlockRows) == m_xpr.rows() || m_xpr.cols() == 0)\n           && m_col == m_xpr.cols()\n           && \"Too few coefficients passed to comma initializer (operator<<)\");\n      return m_xpr;\n  }\n\n  XprType& m_xpr;           // target expression\n  Index m_row;              // current row id\n  Index m_col;              // current col id\n  Index m_currentBlockRows; // current block height\n};\n\n/** \\anchor MatrixBaseCommaInitRef\n  * Convenient operator to set the coefficients of a matrix.\n  *\n  * The coefficients must be provided in a row major order and exactly match\n  * the size of the matrix. Otherwise an assertion is raised.\n  *\n  * Example: \\include MatrixBase_set.cpp\n  * Output: \\verbinclude MatrixBase_set.out\n  * \n  * \\note According the c++ standard, the argument expressions of this comma initializer are evaluated in arbitrary order.\n  *\n  * \\sa CommaInitializer::finished(), class CommaInitializer\n  */\ntemplate<typename Derived>\ninline CommaInitializer<Derived> DenseBase<Derived>::operator<< (const Scalar& s)\n{\n  return CommaInitializer<Derived>(*static_cast<Derived*>(this), s);\n}\n\n/** \\sa operator<<(const Scalar&) */\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\ninline CommaInitializer<Derived>\nDenseBase<Derived>::operator<<(const DenseBase<OtherDerived>& other)\n{\n  return CommaInitializer<Derived>(*static_cast<Derived *>(this), other);\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_COMMAINITIALIZER_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/ConditionEstimator.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Rasmus Munk Larsen (rmlarsen@google.com)\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CONDITIONESTIMATOR_H\n#define EIGEN_CONDITIONESTIMATOR_H\n\nnamespace Eigen {\n\nnamespace internal {\n\ntemplate <typename Vector, typename RealVector, bool IsComplex>\nstruct rcond_compute_sign {\n  static inline Vector run(const Vector& v) {\n    const RealVector v_abs = v.cwiseAbs();\n    return (v_abs.array() == static_cast<typename Vector::RealScalar>(0))\n            .select(Vector::Ones(v.size()), v.cwiseQuotient(v_abs));\n  }\n};\n\n// Partial specialization to avoid elementwise division for real vectors.\ntemplate <typename Vector>\nstruct rcond_compute_sign<Vector, Vector, false> {\n  static inline Vector run(const Vector& v) {\n    return (v.array() < static_cast<typename Vector::RealScalar>(0))\n           .select(-Vector::Ones(v.size()), Vector::Ones(v.size()));\n  }\n};\n\n/**\n  * \\returns an estimate of ||inv(matrix)||_1 given a decomposition of\n  * \\a matrix that implements .solve() and .adjoint().solve() methods.\n  *\n  * This function implements Algorithms 4.1 and 5.1 from\n  *   http://www.maths.manchester.ac.uk/~higham/narep/narep135.pdf\n  * which also forms the basis for the condition number estimators in\n  * LAPACK. Since at most 10 calls to the solve method of dec are\n  * performed, the total cost is O(dims^2), as opposed to O(dims^3)\n  * needed to compute the inverse matrix explicitly.\n  *\n  * The most common usage is in estimating the condition number\n  * ||matrix||_1 * ||inv(matrix)||_1. The first term ||matrix||_1 can be\n  * computed directly in O(n^2) operations.\n  *\n  * Supports the following decompositions: FullPivLU, PartialPivLU, LDLT, and\n  * LLT.\n  *\n  * \\sa FullPivLU, PartialPivLU, LDLT, LLT.\n  */\ntemplate <typename Decomposition>\ntypename Decomposition::RealScalar rcond_invmatrix_L1_norm_estimate(const Decomposition& dec)\n{\n  typedef typename Decomposition::MatrixType MatrixType;\n  typedef typename Decomposition::Scalar Scalar;\n  typedef typename Decomposition::RealScalar RealScalar;\n  typedef typename internal::plain_col_type<MatrixType>::type Vector;\n  typedef typename internal::plain_col_type<MatrixType, RealScalar>::type RealVector;\n  const bool is_complex = (NumTraits<Scalar>::IsComplex != 0);\n\n  eigen_assert(dec.rows() == dec.cols());\n  const Index n = dec.rows();\n  if (n == 0)\n    return 0;\n\n  // Disable Index to float conversion warning\n#ifdef __INTEL_COMPILER\n  #pragma warning push\n  #pragma warning ( disable : 2259 )\n#endif\n  Vector v = dec.solve(Vector::Ones(n) / Scalar(n));\n#ifdef __INTEL_COMPILER\n  #pragma warning pop\n#endif\n\n  // lower_bound is a lower bound on\n  //   ||inv(matrix)||_1  = sup_v ||inv(matrix) v||_1 / ||v||_1\n  // and is the objective maximized by the (\"super-\") gradient ascent\n  // algorithm below.\n  RealScalar lower_bound = v.template lpNorm<1>();\n  if (n == 1)\n    return lower_bound;\n\n  // Gradient ascent algorithm follows: We know that the optimum is achieved at\n  // one of the simplices v = e_i, so in each iteration we follow a\n  // super-gradient to move towards the optimal one.\n  RealScalar old_lower_bound = lower_bound;\n  Vector sign_vector(n);\n  Vector old_sign_vector;\n  Index v_max_abs_index = -1;\n  Index old_v_max_abs_index = v_max_abs_index;\n  for (int k = 0; k < 4; ++k)\n  {\n    sign_vector = internal::rcond_compute_sign<Vector, RealVector, is_complex>::run(v);\n    if (k > 0 && !is_complex && sign_vector == old_sign_vector) {\n      // Break if the solution stagnated.\n      break;\n    }\n    // v_max_abs_index = argmax |real( inv(matrix)^T * sign_vector )|\n    v = dec.adjoint().solve(sign_vector);\n    v.real().cwiseAbs().maxCoeff(&v_max_abs_index);\n    if (v_max_abs_index == old_v_max_abs_index) {\n      // Break if the solution stagnated.\n      break;\n    }\n    // Move to the new simplex e_j, where j = v_max_abs_index.\n    v = dec.solve(Vector::Unit(n, v_max_abs_index));  // v = inv(matrix) * e_j.\n    lower_bound = v.template lpNorm<1>();\n    if (lower_bound <= old_lower_bound) {\n      // Break if the gradient step did not increase the lower_bound.\n      break;\n    }\n    if (!is_complex) {\n      old_sign_vector = sign_vector;\n    }\n    old_v_max_abs_index = v_max_abs_index;\n    old_lower_bound = lower_bound;\n  }\n  // The following calculates an independent estimate of ||matrix||_1 by\n  // multiplying matrix by a vector with entries of slowly increasing\n  // magnitude and alternating sign:\n  //   v_i = (-1)^{i} (1 + (i / (dim-1))), i = 0,...,dim-1.\n  // This improvement to Hager's algorithm above is due to Higham. It was\n  // added to make the algorithm more robust in certain corner cases where\n  // large elements in the matrix might otherwise escape detection due to\n  // exact cancellation (especially when op and op_adjoint correspond to a\n  // sequence of backsubstitutions and permutations), which could cause\n  // Hager's algorithm to vastly underestimate ||matrix||_1.\n  Scalar alternating_sign(RealScalar(1));\n  for (Index i = 0; i < n; ++i) {\n    // The static_cast is needed when Scalar is a complex and RealScalar implements expression templates\n    v[i] = alternating_sign * static_cast<RealScalar>(RealScalar(1) + (RealScalar(i) / (RealScalar(n - 1))));\n    alternating_sign = -alternating_sign;\n  }\n  v = dec.solve(v);\n  const RealScalar alternate_lower_bound = (2 * v.template lpNorm<1>()) / (3 * RealScalar(n));\n  return numext::maxi(lower_bound, alternate_lower_bound);\n}\n\n/** \\brief Reciprocal condition number estimator.\n  *\n  * Computing a decomposition of a dense matrix takes O(n^3) operations, while\n  * this method estimates the condition number quickly and reliably in O(n^2)\n  * operations.\n  *\n  * \\returns an estimate of the reciprocal condition number\n  * (1 / (||matrix||_1 * ||inv(matrix)||_1)) of matrix, given ||matrix||_1 and\n  * its decomposition. Supports the following decompositions: FullPivLU,\n  * PartialPivLU, LDLT, and LLT.\n  *\n  * \\sa FullPivLU, PartialPivLU, LDLT, LLT.\n  */\ntemplate <typename Decomposition>\ntypename Decomposition::RealScalar\nrcond_estimate_helper(typename Decomposition::RealScalar matrix_norm, const Decomposition& dec)\n{\n  typedef typename Decomposition::RealScalar RealScalar;\n  eigen_assert(dec.rows() == dec.cols());\n  if (dec.rows() == 0)              return RealScalar(1);\n  if (matrix_norm == RealScalar(0)) return RealScalar(0);\n  if (dec.rows() == 1)              return RealScalar(1);\n  const RealScalar inverse_matrix_norm = rcond_invmatrix_L1_norm_estimate(dec);\n  return (inverse_matrix_norm == RealScalar(0) ? RealScalar(0)\n                                               : (RealScalar(1) / inverse_matrix_norm) / matrix_norm);\n}\n\n}  // namespace internal\n\n}  // namespace Eigen\n\n#endif\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/CoreEvaluators.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2011 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2011-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2011-2012 Jitse Niesen <jitse@maths.leeds.ac.uk>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n\n#ifndef EIGEN_COREEVALUATORS_H\n#define EIGEN_COREEVALUATORS_H\n\nnamespace Eigen {\n  \nnamespace internal {\n\n// This class returns the evaluator kind from the expression storage kind.\n// Default assumes index based accessors\ntemplate<typename StorageKind>\nstruct storage_kind_to_evaluator_kind {\n  typedef IndexBased Kind;\n};\n\n// This class returns the evaluator shape from the expression storage kind.\n// It can be Dense, Sparse, Triangular, Diagonal, SelfAdjoint, Band, etc.\ntemplate<typename StorageKind> struct storage_kind_to_shape;\n\ntemplate<> struct storage_kind_to_shape<Dense>                  { typedef DenseShape Shape;           };\ntemplate<> struct storage_kind_to_shape<SolverStorage>          { typedef SolverShape Shape;           };\ntemplate<> struct storage_kind_to_shape<PermutationStorage>     { typedef PermutationShape Shape;     };\ntemplate<> struct storage_kind_to_shape<TranspositionsStorage>  { typedef TranspositionsShape Shape;  };\n\n// Evaluators have to be specialized with respect to various criteria such as:\n//  - storage/structure/shape\n//  - scalar type\n//  - etc.\n// Therefore, we need specialization of evaluator providing additional template arguments for each kind of evaluators.\n// We currently distinguish the following kind of evaluators:\n// - unary_evaluator    for expressions taking only one arguments (CwiseUnaryOp, CwiseUnaryView, Transpose, MatrixWrapper, ArrayWrapper, Reverse, Replicate)\n// - binary_evaluator   for expression taking two arguments (CwiseBinaryOp)\n// - ternary_evaluator   for expression taking three arguments (CwiseTernaryOp)\n// - product_evaluator  for linear algebra products (Product); special case of binary_evaluator because it requires additional tags for dispatching.\n// - mapbase_evaluator  for Map, Block, Ref\n// - block_evaluator    for Block (special dispatching to a mapbase_evaluator or unary_evaluator)\n\ntemplate< typename T,\n          typename Arg1Kind   = typename evaluator_traits<typename T::Arg1>::Kind,\n          typename Arg2Kind   = typename evaluator_traits<typename T::Arg2>::Kind,\n          typename Arg3Kind   = typename evaluator_traits<typename T::Arg3>::Kind,\n          typename Arg1Scalar = typename traits<typename T::Arg1>::Scalar,\n          typename Arg2Scalar = typename traits<typename T::Arg2>::Scalar,\n          typename Arg3Scalar = typename traits<typename T::Arg3>::Scalar> struct ternary_evaluator;\n\ntemplate< typename T,\n          typename LhsKind   = typename evaluator_traits<typename T::Lhs>::Kind,\n          typename RhsKind   = typename evaluator_traits<typename T::Rhs>::Kind,\n          typename LhsScalar = typename traits<typename T::Lhs>::Scalar,\n          typename RhsScalar = typename traits<typename T::Rhs>::Scalar> struct binary_evaluator;\n\ntemplate< typename T,\n          typename Kind   = typename evaluator_traits<typename T::NestedExpression>::Kind,\n          typename Scalar = typename T::Scalar> struct unary_evaluator;\n          \n// evaluator_traits<T> contains traits for evaluator<T> \n\ntemplate<typename T>\nstruct evaluator_traits_base\n{\n  // by default, get evaluator kind and shape from storage\n  typedef typename storage_kind_to_evaluator_kind<typename traits<T>::StorageKind>::Kind Kind;\n  typedef typename storage_kind_to_shape<typename traits<T>::StorageKind>::Shape Shape;\n};\n\n// Default evaluator traits\ntemplate<typename T>\nstruct evaluator_traits : public evaluator_traits_base<T>\n{\n};\n\ntemplate<typename T, typename Shape = typename evaluator_traits<T>::Shape >\nstruct evaluator_assume_aliasing {\n  static const bool value = false;\n};\n\n// By default, we assume a unary expression:\ntemplate<typename T>\nstruct evaluator : public unary_evaluator<T>\n{\n  typedef unary_evaluator<T> Base;\n  EIGEN_DEVICE_FUNC explicit evaluator(const T& xpr) : Base(xpr) {}\n};\n\n\n// TODO: Think about const-correctness\ntemplate<typename T>\nstruct evaluator<const T>\n  : evaluator<T>\n{\n  EIGEN_DEVICE_FUNC\n  explicit evaluator(const T& xpr) : evaluator<T>(xpr) {}\n};\n\n// ---------- base class for all evaluators ----------\n\ntemplate<typename ExpressionType>\nstruct evaluator_base : public noncopyable\n{\n  // TODO that's not very nice to have to propagate all these traits. They are currently only needed to handle outer,inner indices.\n  typedef traits<ExpressionType> ExpressionTraits;\n  \n  enum {\n    Alignment = 0\n  };\n};\n\n// -------------------- Matrix and Array --------------------\n//\n// evaluator<PlainObjectBase> is a common base class for the\n// Matrix and Array evaluators.\n// Here we directly specialize evaluator. This is not really a unary expression, and it is, by definition, dense,\n// so no need for more sophisticated dispatching.\n\ntemplate<typename Derived>\nstruct evaluator<PlainObjectBase<Derived> >\n  : evaluator_base<Derived>\n{\n  typedef PlainObjectBase<Derived> PlainObjectType;\n  typedef typename PlainObjectType::Scalar Scalar;\n  typedef typename PlainObjectType::CoeffReturnType CoeffReturnType;\n\n  enum {\n    IsRowMajor = PlainObjectType::IsRowMajor,\n    IsVectorAtCompileTime = PlainObjectType::IsVectorAtCompileTime,\n    RowsAtCompileTime = PlainObjectType::RowsAtCompileTime,\n    ColsAtCompileTime = PlainObjectType::ColsAtCompileTime,\n    \n    CoeffReadCost = NumTraits<Scalar>::ReadCost,\n    Flags = traits<Derived>::EvaluatorFlags,\n    Alignment = traits<Derived>::Alignment\n  };\n  \n  EIGEN_DEVICE_FUNC evaluator()\n    : m_data(0),\n      m_outerStride(IsVectorAtCompileTime  ? 0 \n                                           : int(IsRowMajor) ? ColsAtCompileTime \n                                           : RowsAtCompileTime)\n  {\n    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);\n  }\n  \n  EIGEN_DEVICE_FUNC explicit evaluator(const PlainObjectType& m)\n    : m_data(m.data()), m_outerStride(IsVectorAtCompileTime ? 0 : m.outerStride()) \n  {\n    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  CoeffReturnType coeff(Index row, Index col) const\n  {\n    if (IsRowMajor)\n      return m_data[row * m_outerStride.value() + col];\n    else\n      return m_data[row + col * m_outerStride.value()];\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  CoeffReturnType coeff(Index index) const\n  {\n    return m_data[index];\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  Scalar& coeffRef(Index row, Index col)\n  {\n    if (IsRowMajor)\n      return const_cast<Scalar*>(m_data)[row * m_outerStride.value() + col];\n    else\n      return const_cast<Scalar*>(m_data)[row + col * m_outerStride.value()];\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  Scalar& coeffRef(Index index)\n  {\n    return const_cast<Scalar*>(m_data)[index];\n  }\n\n  template<int LoadMode, typename PacketType>\n  EIGEN_STRONG_INLINE\n  PacketType packet(Index row, Index col) const\n  {\n    if (IsRowMajor)\n      return ploadt<PacketType, LoadMode>(m_data + row * m_outerStride.value() + col);\n    else\n      return ploadt<PacketType, LoadMode>(m_data + row + col * m_outerStride.value());\n  }\n\n  template<int LoadMode, typename PacketType>\n  EIGEN_STRONG_INLINE\n  PacketType packet(Index index) const\n  {\n    return ploadt<PacketType, LoadMode>(m_data + index);\n  }\n\n  template<int StoreMode,typename PacketType>\n  EIGEN_STRONG_INLINE\n  void writePacket(Index row, Index col, const PacketType& x)\n  {\n    if (IsRowMajor)\n      return pstoret<Scalar, PacketType, StoreMode>\n\t            (const_cast<Scalar*>(m_data) + row * m_outerStride.value() + col, x);\n    else\n      return pstoret<Scalar, PacketType, StoreMode>\n                    (const_cast<Scalar*>(m_data) + row + col * m_outerStride.value(), x);\n  }\n\n  template<int StoreMode, typename PacketType>\n  EIGEN_STRONG_INLINE\n  void writePacket(Index index, const PacketType& x)\n  {\n    return pstoret<Scalar, PacketType, StoreMode>(const_cast<Scalar*>(m_data) + index, x);\n  }\n\nprotected:\n  const Scalar *m_data;\n\n  // We do not need to know the outer stride for vectors\n  variable_if_dynamic<Index, IsVectorAtCompileTime  ? 0 \n                                                    : int(IsRowMajor) ? ColsAtCompileTime \n                                                    : RowsAtCompileTime> m_outerStride;\n};\n\ntemplate<typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>\nstruct evaluator<Matrix<Scalar, Rows, Cols, Options, MaxRows, MaxCols> >\n  : evaluator<PlainObjectBase<Matrix<Scalar, Rows, Cols, Options, MaxRows, MaxCols> > >\n{\n  typedef Matrix<Scalar, Rows, Cols, Options, MaxRows, MaxCols> XprType;\n  \n  EIGEN_DEVICE_FUNC evaluator() {}\n\n  EIGEN_DEVICE_FUNC explicit evaluator(const XprType& m)\n    : evaluator<PlainObjectBase<XprType> >(m) \n  { }\n};\n\ntemplate<typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>\nstruct evaluator<Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> >\n  : evaluator<PlainObjectBase<Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> > >\n{\n  typedef Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> XprType;\n\n  EIGEN_DEVICE_FUNC evaluator() {}\n  \n  EIGEN_DEVICE_FUNC explicit evaluator(const XprType& m)\n    : evaluator<PlainObjectBase<XprType> >(m) \n  { }\n};\n\n// -------------------- Transpose --------------------\n\ntemplate<typename ArgType>\nstruct unary_evaluator<Transpose<ArgType>, IndexBased>\n  : evaluator_base<Transpose<ArgType> >\n{\n  typedef Transpose<ArgType> XprType;\n  \n  enum {\n    CoeffReadCost = evaluator<ArgType>::CoeffReadCost,    \n    Flags = evaluator<ArgType>::Flags ^ RowMajorBit,\n    Alignment = evaluator<ArgType>::Alignment\n  };\n\n  EIGEN_DEVICE_FUNC explicit unary_evaluator(const XprType& t) : m_argImpl(t.nestedExpression()) {}\n\n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  CoeffReturnType coeff(Index row, Index col) const\n  {\n    return m_argImpl.coeff(col, row);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  CoeffReturnType coeff(Index index) const\n  {\n    return m_argImpl.coeff(index);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  Scalar& coeffRef(Index row, Index col)\n  {\n    return m_argImpl.coeffRef(col, row);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  typename XprType::Scalar& coeffRef(Index index)\n  {\n    return m_argImpl.coeffRef(index);\n  }\n\n  template<int LoadMode, typename PacketType>\n  EIGEN_STRONG_INLINE\n  PacketType packet(Index row, Index col) const\n  {\n    return m_argImpl.template packet<LoadMode,PacketType>(col, row);\n  }\n\n  template<int LoadMode, typename PacketType>\n  EIGEN_STRONG_INLINE\n  PacketType packet(Index index) const\n  {\n    return m_argImpl.template packet<LoadMode,PacketType>(index);\n  }\n\n  template<int StoreMode, typename PacketType>\n  EIGEN_STRONG_INLINE\n  void writePacket(Index row, Index col, const PacketType& x)\n  {\n    m_argImpl.template writePacket<StoreMode,PacketType>(col, row, x);\n  }\n\n  template<int StoreMode, typename PacketType>\n  EIGEN_STRONG_INLINE\n  void writePacket(Index index, const PacketType& x)\n  {\n    m_argImpl.template writePacket<StoreMode,PacketType>(index, x);\n  }\n\nprotected:\n  evaluator<ArgType> m_argImpl;\n};\n\n// -------------------- CwiseNullaryOp --------------------\n// Like Matrix and Array, this is not really a unary expression, so we directly specialize evaluator.\n// Likewise, there is not need to more sophisticated dispatching here.\n\ntemplate<typename Scalar,typename NullaryOp,\n         bool has_nullary = has_nullary_operator<NullaryOp>::value,\n         bool has_unary   = has_unary_operator<NullaryOp>::value,\n         bool has_binary  = has_binary_operator<NullaryOp>::value>\nstruct nullary_wrapper\n{\n  template <typename IndexType>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const NullaryOp& op, IndexType i, IndexType j) const { return op(i,j); }\n  template <typename IndexType>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const NullaryOp& op, IndexType i) const { return op(i); }\n\n  template <typename T, typename IndexType> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T packetOp(const NullaryOp& op, IndexType i, IndexType j) const { return op.template packetOp<T>(i,j); }\n  template <typename T, typename IndexType> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T packetOp(const NullaryOp& op, IndexType i) const { return op.template packetOp<T>(i); }\n};\n\ntemplate<typename Scalar,typename NullaryOp>\nstruct nullary_wrapper<Scalar,NullaryOp,true,false,false>\n{\n  template <typename IndexType>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const NullaryOp& op, IndexType=0, IndexType=0) const { return op(); }\n  template <typename T, typename IndexType> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T packetOp(const NullaryOp& op, IndexType=0, IndexType=0) const { return op.template packetOp<T>(); }\n};\n\ntemplate<typename Scalar,typename NullaryOp>\nstruct nullary_wrapper<Scalar,NullaryOp,false,false,true>\n{\n  template <typename IndexType>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const NullaryOp& op, IndexType i, IndexType j=0) const { return op(i,j); }\n  template <typename T, typename IndexType> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T packetOp(const NullaryOp& op, IndexType i, IndexType j=0) const { return op.template packetOp<T>(i,j); }\n};\n\n// We need the following specialization for vector-only functors assigned to a runtime vector,\n// for instance, using linspace and assigning a RowVectorXd to a MatrixXd or even a row of a MatrixXd.\n// In this case, i==0 and j is used for the actual iteration.\ntemplate<typename Scalar,typename NullaryOp>\nstruct nullary_wrapper<Scalar,NullaryOp,false,true,false>\n{\n  template <typename IndexType>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const NullaryOp& op, IndexType i, IndexType j) const {\n    eigen_assert(i==0 || j==0);\n    return op(i+j);\n  }\n  template <typename T, typename IndexType> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T packetOp(const NullaryOp& op, IndexType i, IndexType j) const {\n    eigen_assert(i==0 || j==0);\n    return op.template packetOp<T>(i+j);\n  }\n\n  template <typename IndexType>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const NullaryOp& op, IndexType i) const { return op(i); }\n  template <typename T, typename IndexType>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T packetOp(const NullaryOp& op, IndexType i) const { return op.template packetOp<T>(i); }\n};\n\ntemplate<typename Scalar,typename NullaryOp>\nstruct nullary_wrapper<Scalar,NullaryOp,false,false,false> {};\n\n#if 0 && EIGEN_COMP_MSVC>0\n// Disable this ugly workaround. This is now handled in traits<Ref>::match,\n// but this piece of code might still become handly if some other weird compilation\n// erros pop up again.\n\n// MSVC exhibits a weird compilation error when\n// compiling:\n//    Eigen::MatrixXf A = MatrixXf::Random(3,3);\n//    Ref<const MatrixXf> R = 2.f*A;\n// and that has_*ary_operator<scalar_constant_op<float>> have not been instantiated yet.\n// The \"problem\" is that evaluator<2.f*A> is instantiated by traits<Ref>::match<2.f*A>\n// and at that time has_*ary_operator<T> returns true regardless of T.\n// Then nullary_wrapper is badly instantiated as nullary_wrapper<.,.,true,true,true>.\n// The trick is thus to defer the proper instantiation of nullary_wrapper when coeff(),\n// and packet() are really instantiated as implemented below:\n\n// This is a simple wrapper around Index to enforce the re-instantiation of\n// has_*ary_operator when needed.\ntemplate<typename T> struct nullary_wrapper_workaround_msvc {\n  nullary_wrapper_workaround_msvc(const T&);\n  operator T()const;\n};\n\ntemplate<typename Scalar,typename NullaryOp>\nstruct nullary_wrapper<Scalar,NullaryOp,true,true,true>\n{\n  template <typename IndexType>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const NullaryOp& op, IndexType i, IndexType j) const {\n    return nullary_wrapper<Scalar,NullaryOp,\n    has_nullary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value,\n    has_unary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value,\n    has_binary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value>().operator()(op,i,j);\n  }\n  template <typename IndexType>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const NullaryOp& op, IndexType i) const {\n    return nullary_wrapper<Scalar,NullaryOp,\n    has_nullary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value,\n    has_unary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value,\n    has_binary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value>().operator()(op,i);\n  }\n\n  template <typename T, typename IndexType>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T packetOp(const NullaryOp& op, IndexType i, IndexType j) const {\n    return nullary_wrapper<Scalar,NullaryOp,\n    has_nullary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value,\n    has_unary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value,\n    has_binary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value>().template packetOp<T>(op,i,j);\n  }\n  template <typename T, typename IndexType>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T packetOp(const NullaryOp& op, IndexType i) const {\n    return nullary_wrapper<Scalar,NullaryOp,\n    has_nullary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value,\n    has_unary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value,\n    has_binary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value>().template packetOp<T>(op,i);\n  }\n};\n#endif // MSVC workaround\n\ntemplate<typename NullaryOp, typename PlainObjectType>\nstruct evaluator<CwiseNullaryOp<NullaryOp,PlainObjectType> >\n  : evaluator_base<CwiseNullaryOp<NullaryOp,PlainObjectType> >\n{\n  typedef CwiseNullaryOp<NullaryOp,PlainObjectType> XprType;\n  typedef typename internal::remove_all<PlainObjectType>::type PlainObjectTypeCleaned;\n  \n  enum {\n    CoeffReadCost = internal::functor_traits<NullaryOp>::Cost,\n    \n    Flags = (evaluator<PlainObjectTypeCleaned>::Flags\n          &  (  HereditaryBits\n              | (functor_has_linear_access<NullaryOp>::ret  ? LinearAccessBit : 0)\n              | (functor_traits<NullaryOp>::PacketAccess    ? PacketAccessBit : 0)))\n          | (functor_traits<NullaryOp>::IsRepeatable ? 0 : EvalBeforeNestingBit),\n    Alignment = AlignedMax\n  };\n\n  EIGEN_DEVICE_FUNC explicit evaluator(const XprType& n)\n    : m_functor(n.functor()), m_wrapper()\n  {\n    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);\n  }\n\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n\n  template <typename IndexType>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  CoeffReturnType coeff(IndexType row, IndexType col) const\n  {\n    return m_wrapper(m_functor, row, col);\n  }\n\n  template <typename IndexType>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  CoeffReturnType coeff(IndexType index) const\n  {\n    return m_wrapper(m_functor,index);\n  }\n\n  template<int LoadMode, typename PacketType, typename IndexType>\n  EIGEN_STRONG_INLINE\n  PacketType packet(IndexType row, IndexType col) const\n  {\n    return m_wrapper.template packetOp<PacketType>(m_functor, row, col);\n  }\n\n  template<int LoadMode, typename PacketType, typename IndexType>\n  EIGEN_STRONG_INLINE\n  PacketType packet(IndexType index) const\n  {\n    return m_wrapper.template packetOp<PacketType>(m_functor, index);\n  }\n\nprotected:\n  const NullaryOp m_functor;\n  const internal::nullary_wrapper<CoeffReturnType,NullaryOp> m_wrapper;\n};\n\n// -------------------- CwiseUnaryOp --------------------\n\ntemplate<typename UnaryOp, typename ArgType>\nstruct unary_evaluator<CwiseUnaryOp<UnaryOp, ArgType>, IndexBased >\n  : evaluator_base<CwiseUnaryOp<UnaryOp, ArgType> >\n{\n  typedef CwiseUnaryOp<UnaryOp, ArgType> XprType;\n  \n  enum {\n    CoeffReadCost = evaluator<ArgType>::CoeffReadCost + functor_traits<UnaryOp>::Cost,\n    \n    Flags = evaluator<ArgType>::Flags\n          & (HereditaryBits | LinearAccessBit | (functor_traits<UnaryOp>::PacketAccess ? PacketAccessBit : 0)),\n    Alignment = evaluator<ArgType>::Alignment\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  explicit unary_evaluator(const XprType& op)\n    : m_functor(op.functor()), \n      m_argImpl(op.nestedExpression()) \n  {\n    EIGEN_INTERNAL_CHECK_COST_VALUE(functor_traits<UnaryOp>::Cost);\n    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);\n  }\n\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  CoeffReturnType coeff(Index row, Index col) const\n  {\n    return m_functor(m_argImpl.coeff(row, col));\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  CoeffReturnType coeff(Index index) const\n  {\n    return m_functor(m_argImpl.coeff(index));\n  }\n\n  template<int LoadMode, typename PacketType>\n  EIGEN_STRONG_INLINE\n  PacketType packet(Index row, Index col) const\n  {\n    return m_functor.packetOp(m_argImpl.template packet<LoadMode, PacketType>(row, col));\n  }\n\n  template<int LoadMode, typename PacketType>\n  EIGEN_STRONG_INLINE\n  PacketType packet(Index index) const\n  {\n    return m_functor.packetOp(m_argImpl.template packet<LoadMode, PacketType>(index));\n  }\n\nprotected:\n  const UnaryOp m_functor;\n  evaluator<ArgType> m_argImpl;\n};\n\n// -------------------- CwiseTernaryOp --------------------\n\n// this is a ternary expression\ntemplate<typename TernaryOp, typename Arg1, typename Arg2, typename Arg3>\nstruct evaluator<CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3> >\n  : public ternary_evaluator<CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3> >\n{\n  typedef CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3> XprType;\n  typedef ternary_evaluator<CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3> > Base;\n  \n  EIGEN_DEVICE_FUNC explicit evaluator(const XprType& xpr) : Base(xpr) {}\n};\n\ntemplate<typename TernaryOp, typename Arg1, typename Arg2, typename Arg3>\nstruct ternary_evaluator<CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3>, IndexBased, IndexBased>\n  : evaluator_base<CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3> >\n{\n  typedef CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3> XprType;\n  \n  enum {\n    CoeffReadCost = evaluator<Arg1>::CoeffReadCost + evaluator<Arg2>::CoeffReadCost + evaluator<Arg3>::CoeffReadCost + functor_traits<TernaryOp>::Cost,\n    \n    Arg1Flags = evaluator<Arg1>::Flags,\n    Arg2Flags = evaluator<Arg2>::Flags,\n    Arg3Flags = evaluator<Arg3>::Flags,\n    SameType = is_same<typename Arg1::Scalar,typename Arg2::Scalar>::value && is_same<typename Arg1::Scalar,typename Arg3::Scalar>::value,\n    StorageOrdersAgree = (int(Arg1Flags)&RowMajorBit)==(int(Arg2Flags)&RowMajorBit) && (int(Arg1Flags)&RowMajorBit)==(int(Arg3Flags)&RowMajorBit),\n    Flags0 = (int(Arg1Flags) | int(Arg2Flags) | int(Arg3Flags)) & (\n        HereditaryBits\n        | (int(Arg1Flags) & int(Arg2Flags) & int(Arg3Flags) &\n           ( (StorageOrdersAgree ? LinearAccessBit : 0)\n           | (functor_traits<TernaryOp>::PacketAccess && StorageOrdersAgree && SameType ? PacketAccessBit : 0)\n           )\n        )\n     ),\n    Flags = (Flags0 & ~RowMajorBit) | (Arg1Flags & RowMajorBit),\n    Alignment = EIGEN_PLAIN_ENUM_MIN(\n        EIGEN_PLAIN_ENUM_MIN(evaluator<Arg1>::Alignment, evaluator<Arg2>::Alignment),\n        evaluator<Arg3>::Alignment)\n  };\n\n  EIGEN_DEVICE_FUNC explicit ternary_evaluator(const XprType& xpr)\n    : m_functor(xpr.functor()),\n      m_arg1Impl(xpr.arg1()), \n      m_arg2Impl(xpr.arg2()), \n      m_arg3Impl(xpr.arg3())  \n  {\n    EIGEN_INTERNAL_CHECK_COST_VALUE(functor_traits<TernaryOp>::Cost);\n    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);\n  }\n\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  CoeffReturnType coeff(Index row, Index col) const\n  {\n    return m_functor(m_arg1Impl.coeff(row, col), m_arg2Impl.coeff(row, col), m_arg3Impl.coeff(row, col));\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  CoeffReturnType coeff(Index index) const\n  {\n    return m_functor(m_arg1Impl.coeff(index), m_arg2Impl.coeff(index), m_arg3Impl.coeff(index));\n  }\n\n  template<int LoadMode, typename PacketType>\n  EIGEN_STRONG_INLINE\n  PacketType packet(Index row, Index col) const\n  {\n    return m_functor.packetOp(m_arg1Impl.template packet<LoadMode,PacketType>(row, col),\n                              m_arg2Impl.template packet<LoadMode,PacketType>(row, col),\n                              m_arg3Impl.template packet<LoadMode,PacketType>(row, col));\n  }\n\n  template<int LoadMode, typename PacketType>\n  EIGEN_STRONG_INLINE\n  PacketType packet(Index index) const\n  {\n    return m_functor.packetOp(m_arg1Impl.template packet<LoadMode,PacketType>(index),\n                              m_arg2Impl.template packet<LoadMode,PacketType>(index),\n                              m_arg3Impl.template packet<LoadMode,PacketType>(index));\n  }\n\nprotected:\n  const TernaryOp m_functor;\n  evaluator<Arg1> m_arg1Impl;\n  evaluator<Arg2> m_arg2Impl;\n  evaluator<Arg3> m_arg3Impl;\n};\n\n// -------------------- CwiseBinaryOp --------------------\n\n// this is a binary expression\ntemplate<typename BinaryOp, typename Lhs, typename Rhs>\nstruct evaluator<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >\n  : public binary_evaluator<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >\n{\n  typedef CwiseBinaryOp<BinaryOp, Lhs, Rhs> XprType;\n  typedef binary_evaluator<CwiseBinaryOp<BinaryOp, Lhs, Rhs> > Base;\n  \n  EIGEN_DEVICE_FUNC explicit evaluator(const XprType& xpr) : Base(xpr) {}\n};\n\ntemplate<typename BinaryOp, typename Lhs, typename Rhs>\nstruct binary_evaluator<CwiseBinaryOp<BinaryOp, Lhs, Rhs>, IndexBased, IndexBased>\n  : evaluator_base<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >\n{\n  typedef CwiseBinaryOp<BinaryOp, Lhs, Rhs> XprType;\n  \n  enum {\n    CoeffReadCost = evaluator<Lhs>::CoeffReadCost + evaluator<Rhs>::CoeffReadCost + functor_traits<BinaryOp>::Cost,\n    \n    LhsFlags = evaluator<Lhs>::Flags,\n    RhsFlags = evaluator<Rhs>::Flags,\n    SameType = is_same<typename Lhs::Scalar,typename Rhs::Scalar>::value,\n    StorageOrdersAgree = (int(LhsFlags)&RowMajorBit)==(int(RhsFlags)&RowMajorBit),\n    Flags0 = (int(LhsFlags) | int(RhsFlags)) & (\n        HereditaryBits\n      | (int(LhsFlags) & int(RhsFlags) &\n           ( (StorageOrdersAgree ? LinearAccessBit : 0)\n           | (functor_traits<BinaryOp>::PacketAccess && StorageOrdersAgree && SameType ? PacketAccessBit : 0)\n           )\n        )\n     ),\n    Flags = (Flags0 & ~RowMajorBit) | (LhsFlags & RowMajorBit),\n    Alignment = EIGEN_PLAIN_ENUM_MIN(evaluator<Lhs>::Alignment,evaluator<Rhs>::Alignment)\n  };\n\n  EIGEN_DEVICE_FUNC explicit binary_evaluator(const XprType& xpr)\n    : m_functor(xpr.functor()),\n      m_lhsImpl(xpr.lhs()), \n      m_rhsImpl(xpr.rhs())  \n  {\n    EIGEN_INTERNAL_CHECK_COST_VALUE(functor_traits<BinaryOp>::Cost);\n    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);\n  }\n\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  CoeffReturnType coeff(Index row, Index col) const\n  {\n    return m_functor(m_lhsImpl.coeff(row, col), m_rhsImpl.coeff(row, col));\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  CoeffReturnType coeff(Index index) const\n  {\n    return m_functor(m_lhsImpl.coeff(index), m_rhsImpl.coeff(index));\n  }\n\n  template<int LoadMode, typename PacketType>\n  EIGEN_STRONG_INLINE\n  PacketType packet(Index row, Index col) const\n  {\n    return m_functor.packetOp(m_lhsImpl.template packet<LoadMode,PacketType>(row, col),\n                              m_rhsImpl.template packet<LoadMode,PacketType>(row, col));\n  }\n\n  template<int LoadMode, typename PacketType>\n  EIGEN_STRONG_INLINE\n  PacketType packet(Index index) const\n  {\n    return m_functor.packetOp(m_lhsImpl.template packet<LoadMode,PacketType>(index),\n                              m_rhsImpl.template packet<LoadMode,PacketType>(index));\n  }\n\nprotected:\n  const BinaryOp m_functor;\n  evaluator<Lhs> m_lhsImpl;\n  evaluator<Rhs> m_rhsImpl;\n};\n\n// -------------------- CwiseUnaryView --------------------\n\ntemplate<typename UnaryOp, typename ArgType>\nstruct unary_evaluator<CwiseUnaryView<UnaryOp, ArgType>, IndexBased>\n  : evaluator_base<CwiseUnaryView<UnaryOp, ArgType> >\n{\n  typedef CwiseUnaryView<UnaryOp, ArgType> XprType;\n  \n  enum {\n    CoeffReadCost = evaluator<ArgType>::CoeffReadCost + functor_traits<UnaryOp>::Cost,\n    \n    Flags = (evaluator<ArgType>::Flags & (HereditaryBits | LinearAccessBit | DirectAccessBit)),\n    \n    Alignment = 0 // FIXME it is not very clear why alignment is necessarily lost...\n  };\n\n  EIGEN_DEVICE_FUNC explicit unary_evaluator(const XprType& op)\n    : m_unaryOp(op.functor()), \n      m_argImpl(op.nestedExpression()) \n  {\n    EIGEN_INTERNAL_CHECK_COST_VALUE(functor_traits<UnaryOp>::Cost);\n    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);\n  }\n\n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  CoeffReturnType coeff(Index row, Index col) const\n  {\n    return m_unaryOp(m_argImpl.coeff(row, col));\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  CoeffReturnType coeff(Index index) const\n  {\n    return m_unaryOp(m_argImpl.coeff(index));\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  Scalar& coeffRef(Index row, Index col)\n  {\n    return m_unaryOp(m_argImpl.coeffRef(row, col));\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  Scalar& coeffRef(Index index)\n  {\n    return m_unaryOp(m_argImpl.coeffRef(index));\n  }\n\nprotected:\n  const UnaryOp m_unaryOp;\n  evaluator<ArgType> m_argImpl;\n};\n\n// -------------------- Map --------------------\n\n// FIXME perhaps the PlainObjectType could be provided by Derived::PlainObject ?\n// but that might complicate template specialization\ntemplate<typename Derived, typename PlainObjectType>\nstruct mapbase_evaluator;\n\ntemplate<typename Derived, typename PlainObjectType>\nstruct mapbase_evaluator : evaluator_base<Derived>\n{\n  typedef Derived  XprType;\n  typedef typename XprType::PointerType PointerType;\n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  \n  enum {\n    IsRowMajor = XprType::RowsAtCompileTime,\n    ColsAtCompileTime = XprType::ColsAtCompileTime,\n    CoeffReadCost = NumTraits<Scalar>::ReadCost\n  };\n\n  EIGEN_DEVICE_FUNC explicit mapbase_evaluator(const XprType& map)\n    : m_data(const_cast<PointerType>(map.data())),\n      m_innerStride(map.innerStride()),\n      m_outerStride(map.outerStride())\n  {\n    EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(evaluator<Derived>::Flags&PacketAccessBit, internal::inner_stride_at_compile_time<Derived>::ret==1),\n                        PACKET_ACCESS_REQUIRES_TO_HAVE_INNER_STRIDE_FIXED_TO_1);\n    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  CoeffReturnType coeff(Index row, Index col) const\n  {\n    return m_data[col * colStride() + row * rowStride()];\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  CoeffReturnType coeff(Index index) const\n  {\n    return m_data[index * m_innerStride.value()];\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  Scalar& coeffRef(Index row, Index col)\n  {\n    return m_data[col * colStride() + row * rowStride()];\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  Scalar& coeffRef(Index index)\n  {\n    return m_data[index * m_innerStride.value()];\n  }\n\n  template<int LoadMode, typename PacketType>\n  EIGEN_STRONG_INLINE\n  PacketType packet(Index row, Index col) const\n  {\n    PointerType ptr = m_data + row * rowStride() + col * colStride();\n    return internal::ploadt<PacketType, LoadMode>(ptr);\n  }\n\n  template<int LoadMode, typename PacketType>\n  EIGEN_STRONG_INLINE\n  PacketType packet(Index index) const\n  {\n    return internal::ploadt<PacketType, LoadMode>(m_data + index * m_innerStride.value());\n  }\n\n  template<int StoreMode, typename PacketType>\n  EIGEN_STRONG_INLINE\n  void writePacket(Index row, Index col, const PacketType& x)\n  {\n    PointerType ptr = m_data + row * rowStride() + col * colStride();\n    return internal::pstoret<Scalar, PacketType, StoreMode>(ptr, x);\n  }\n\n  template<int StoreMode, typename PacketType>\n  EIGEN_STRONG_INLINE\n  void writePacket(Index index, const PacketType& x)\n  {\n    internal::pstoret<Scalar, PacketType, StoreMode>(m_data + index * m_innerStride.value(), x);\n  }\nprotected:\n  EIGEN_DEVICE_FUNC\n  inline Index rowStride() const { return XprType::IsRowMajor ? m_outerStride.value() : m_innerStride.value(); }\n  EIGEN_DEVICE_FUNC\n  inline Index colStride() const { return XprType::IsRowMajor ? m_innerStride.value() : m_outerStride.value(); }\n\n  PointerType m_data;\n  const internal::variable_if_dynamic<Index, XprType::InnerStrideAtCompileTime> m_innerStride;\n  const internal::variable_if_dynamic<Index, XprType::OuterStrideAtCompileTime> m_outerStride;\n};\n\ntemplate<typename PlainObjectType, int MapOptions, typename StrideType> \nstruct evaluator<Map<PlainObjectType, MapOptions, StrideType> >\n  : public mapbase_evaluator<Map<PlainObjectType, MapOptions, StrideType>, PlainObjectType>\n{\n  typedef Map<PlainObjectType, MapOptions, StrideType> XprType;\n  typedef typename XprType::Scalar Scalar;\n  // TODO: should check for smaller packet types once we can handle multi-sized packet types\n  typedef typename packet_traits<Scalar>::type PacketScalar;\n  \n  enum {\n    InnerStrideAtCompileTime = StrideType::InnerStrideAtCompileTime == 0\n                             ? int(PlainObjectType::InnerStrideAtCompileTime)\n                             : int(StrideType::InnerStrideAtCompileTime),\n    OuterStrideAtCompileTime = StrideType::OuterStrideAtCompileTime == 0\n                             ? int(PlainObjectType::OuterStrideAtCompileTime)\n                             : int(StrideType::OuterStrideAtCompileTime),\n    HasNoInnerStride = InnerStrideAtCompileTime == 1,\n    HasNoOuterStride = StrideType::OuterStrideAtCompileTime == 0,\n    HasNoStride = HasNoInnerStride && HasNoOuterStride,\n    IsDynamicSize = PlainObjectType::SizeAtCompileTime==Dynamic,\n    \n    PacketAccessMask = bool(HasNoInnerStride) ? ~int(0) : ~int(PacketAccessBit),\n    LinearAccessMask = bool(HasNoStride) || bool(PlainObjectType::IsVectorAtCompileTime) ? ~int(0) : ~int(LinearAccessBit),\n    Flags = int( evaluator<PlainObjectType>::Flags) & (LinearAccessMask&PacketAccessMask),\n    \n    Alignment = int(MapOptions)&int(AlignedMask)\n  };\n\n  EIGEN_DEVICE_FUNC explicit evaluator(const XprType& map)\n    : mapbase_evaluator<XprType, PlainObjectType>(map) \n  { }\n};\n\n// -------------------- Ref --------------------\n\ntemplate<typename PlainObjectType, int RefOptions, typename StrideType> \nstruct evaluator<Ref<PlainObjectType, RefOptions, StrideType> >\n  : public mapbase_evaluator<Ref<PlainObjectType, RefOptions, StrideType>, PlainObjectType>\n{\n  typedef Ref<PlainObjectType, RefOptions, StrideType> XprType;\n  \n  enum {\n    Flags = evaluator<Map<PlainObjectType, RefOptions, StrideType> >::Flags,\n    Alignment = evaluator<Map<PlainObjectType, RefOptions, StrideType> >::Alignment\n  };\n\n  EIGEN_DEVICE_FUNC explicit evaluator(const XprType& ref)\n    : mapbase_evaluator<XprType, PlainObjectType>(ref) \n  { }\n};\n\n// -------------------- Block --------------------\n\ntemplate<typename ArgType, int BlockRows, int BlockCols, bool InnerPanel,\n         bool HasDirectAccess = internal::has_direct_access<ArgType>::ret> struct block_evaluator;\n         \ntemplate<typename ArgType, int BlockRows, int BlockCols, bool InnerPanel> \nstruct evaluator<Block<ArgType, BlockRows, BlockCols, InnerPanel> >\n  : block_evaluator<ArgType, BlockRows, BlockCols, InnerPanel>\n{\n  typedef Block<ArgType, BlockRows, BlockCols, InnerPanel> XprType;\n  typedef typename XprType::Scalar Scalar;\n  // TODO: should check for smaller packet types once we can handle multi-sized packet types\n  typedef typename packet_traits<Scalar>::type PacketScalar;\n  \n  enum {\n    CoeffReadCost = evaluator<ArgType>::CoeffReadCost,\n    \n    RowsAtCompileTime = traits<XprType>::RowsAtCompileTime,\n    ColsAtCompileTime = traits<XprType>::ColsAtCompileTime,\n    MaxRowsAtCompileTime = traits<XprType>::MaxRowsAtCompileTime,\n    MaxColsAtCompileTime = traits<XprType>::MaxColsAtCompileTime,\n    \n    ArgTypeIsRowMajor = (int(evaluator<ArgType>::Flags)&RowMajorBit) != 0,\n    IsRowMajor = (MaxRowsAtCompileTime==1 && MaxColsAtCompileTime!=1) ? 1\n               : (MaxColsAtCompileTime==1 && MaxRowsAtCompileTime!=1) ? 0\n               : ArgTypeIsRowMajor,\n    HasSameStorageOrderAsArgType = (IsRowMajor == ArgTypeIsRowMajor),\n    InnerSize = IsRowMajor ? int(ColsAtCompileTime) : int(RowsAtCompileTime),\n    InnerStrideAtCompileTime = HasSameStorageOrderAsArgType\n                             ? int(inner_stride_at_compile_time<ArgType>::ret)\n                             : int(outer_stride_at_compile_time<ArgType>::ret),\n    OuterStrideAtCompileTime = HasSameStorageOrderAsArgType\n                             ? int(outer_stride_at_compile_time<ArgType>::ret)\n                             : int(inner_stride_at_compile_time<ArgType>::ret),\n    MaskPacketAccessBit = (InnerStrideAtCompileTime == 1 || HasSameStorageOrderAsArgType) ? PacketAccessBit : 0,\n    \n    FlagsLinearAccessBit = (RowsAtCompileTime == 1 || ColsAtCompileTime == 1 || (InnerPanel && (evaluator<ArgType>::Flags&LinearAccessBit))) ? LinearAccessBit : 0,    \n    FlagsRowMajorBit = XprType::Flags&RowMajorBit,\n    Flags0 = evaluator<ArgType>::Flags & ( (HereditaryBits & ~RowMajorBit) |\n                                           DirectAccessBit |\n                                           MaskPacketAccessBit),\n    Flags = Flags0 | FlagsLinearAccessBit | FlagsRowMajorBit,\n    \n    PacketAlignment = unpacket_traits<PacketScalar>::alignment,\n    Alignment0 = (InnerPanel && (OuterStrideAtCompileTime!=Dynamic)\n                             && (OuterStrideAtCompileTime!=0)\n                             && (((OuterStrideAtCompileTime * int(sizeof(Scalar))) % int(PacketAlignment)) == 0)) ? int(PacketAlignment) : 0,\n    Alignment = EIGEN_PLAIN_ENUM_MIN(evaluator<ArgType>::Alignment, Alignment0)\n  };\n  typedef block_evaluator<ArgType, BlockRows, BlockCols, InnerPanel> block_evaluator_type;\n  EIGEN_DEVICE_FUNC explicit evaluator(const XprType& block) : block_evaluator_type(block)\n  {\n    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);\n  }\n};\n\n// no direct-access => dispatch to a unary evaluator\ntemplate<typename ArgType, int BlockRows, int BlockCols, bool InnerPanel>\nstruct block_evaluator<ArgType, BlockRows, BlockCols, InnerPanel, /*HasDirectAccess*/ false>\n  : unary_evaluator<Block<ArgType, BlockRows, BlockCols, InnerPanel> >\n{\n  typedef Block<ArgType, BlockRows, BlockCols, InnerPanel> XprType;\n\n  EIGEN_DEVICE_FUNC explicit block_evaluator(const XprType& block)\n    : unary_evaluator<XprType>(block) \n  {}\n};\n\ntemplate<typename ArgType, int BlockRows, int BlockCols, bool InnerPanel>\nstruct unary_evaluator<Block<ArgType, BlockRows, BlockCols, InnerPanel>, IndexBased>\n  : evaluator_base<Block<ArgType, BlockRows, BlockCols, InnerPanel> >\n{\n  typedef Block<ArgType, BlockRows, BlockCols, InnerPanel> XprType;\n\n  EIGEN_DEVICE_FUNC explicit unary_evaluator(const XprType& block)\n    : m_argImpl(block.nestedExpression()), \n      m_startRow(block.startRow()), \n      m_startCol(block.startCol()),\n      m_linear_offset(InnerPanel?(XprType::IsRowMajor ? block.startRow()*block.cols() : block.startCol()*block.rows()):0)\n  { }\n \n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n\n  enum {\n    RowsAtCompileTime = XprType::RowsAtCompileTime,\n    ForwardLinearAccess = InnerPanel && bool(evaluator<ArgType>::Flags&LinearAccessBit)\n  };\n \n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  CoeffReturnType coeff(Index row, Index col) const\n  { \n    return m_argImpl.coeff(m_startRow.value() + row, m_startCol.value() + col); \n  }\n  \n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  CoeffReturnType coeff(Index index) const\n  { \n    if (ForwardLinearAccess)\n      return m_argImpl.coeff(m_linear_offset.value() + index); \n    else\n      return coeff(RowsAtCompileTime == 1 ? 0 : index, RowsAtCompileTime == 1 ? index : 0);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  Scalar& coeffRef(Index row, Index col)\n  { \n    return m_argImpl.coeffRef(m_startRow.value() + row, m_startCol.value() + col); \n  }\n  \n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  Scalar& coeffRef(Index index)\n  { \n    if (ForwardLinearAccess)\n      return m_argImpl.coeffRef(m_linear_offset.value() + index); \n    else\n      return coeffRef(RowsAtCompileTime == 1 ? 0 : index, RowsAtCompileTime == 1 ? index : 0);\n  }\n \n  template<int LoadMode, typename PacketType>\n  EIGEN_STRONG_INLINE\n  PacketType packet(Index row, Index col) const \n  { \n    return m_argImpl.template packet<LoadMode,PacketType>(m_startRow.value() + row, m_startCol.value() + col); \n  }\n\n  template<int LoadMode, typename PacketType>\n  EIGEN_STRONG_INLINE\n  PacketType packet(Index index) const \n  { \n    if (ForwardLinearAccess)\n      return m_argImpl.template packet<LoadMode,PacketType>(m_linear_offset.value() + index);\n    else\n      return packet<LoadMode,PacketType>(RowsAtCompileTime == 1 ? 0 : index,\n                                         RowsAtCompileTime == 1 ? index : 0);\n  }\n  \n  template<int StoreMode, typename PacketType>\n  EIGEN_STRONG_INLINE\n  void writePacket(Index row, Index col, const PacketType& x) \n  {\n    return m_argImpl.template writePacket<StoreMode,PacketType>(m_startRow.value() + row, m_startCol.value() + col, x); \n  }\n  \n  template<int StoreMode, typename PacketType>\n  EIGEN_STRONG_INLINE\n  void writePacket(Index index, const PacketType& x) \n  {\n    if (ForwardLinearAccess)\n      return m_argImpl.template writePacket<StoreMode,PacketType>(m_linear_offset.value() + index, x);\n    else\n      return writePacket<StoreMode,PacketType>(RowsAtCompileTime == 1 ? 0 : index,\n                                              RowsAtCompileTime == 1 ? index : 0,\n                                              x);\n  }\n \nprotected:\n  evaluator<ArgType> m_argImpl;\n  const variable_if_dynamic<Index, (ArgType::RowsAtCompileTime == 1 && BlockRows==1) ? 0 : Dynamic> m_startRow;\n  const variable_if_dynamic<Index, (ArgType::ColsAtCompileTime == 1 && BlockCols==1) ? 0 : Dynamic> m_startCol;\n  const variable_if_dynamic<Index, InnerPanel ? Dynamic : 0> m_linear_offset;\n};\n\n// TODO: This evaluator does not actually use the child evaluator; \n// all action is via the data() as returned by the Block expression.\n\ntemplate<typename ArgType, int BlockRows, int BlockCols, bool InnerPanel> \nstruct block_evaluator<ArgType, BlockRows, BlockCols, InnerPanel, /* HasDirectAccess */ true>\n  : mapbase_evaluator<Block<ArgType, BlockRows, BlockCols, InnerPanel>,\n                      typename Block<ArgType, BlockRows, BlockCols, InnerPanel>::PlainObject>\n{\n  typedef Block<ArgType, BlockRows, BlockCols, InnerPanel> XprType;\n  typedef typename XprType::Scalar Scalar;\n\n  EIGEN_DEVICE_FUNC explicit block_evaluator(const XprType& block)\n    : mapbase_evaluator<XprType, typename XprType::PlainObject>(block) \n  {\n    // TODO: for the 3.3 release, this should be turned to an internal assertion, but let's keep it as is for the beta lifetime\n    eigen_assert(((internal::UIntPtr(block.data()) % EIGEN_PLAIN_ENUM_MAX(1,evaluator<XprType>::Alignment)) == 0) && \"data is not aligned\");\n  }\n};\n\n\n// -------------------- Select --------------------\n// NOTE shall we introduce a ternary_evaluator?\n\n// TODO enable vectorization for Select\ntemplate<typename ConditionMatrixType, typename ThenMatrixType, typename ElseMatrixType>\nstruct evaluator<Select<ConditionMatrixType, ThenMatrixType, ElseMatrixType> >\n  : evaluator_base<Select<ConditionMatrixType, ThenMatrixType, ElseMatrixType> >\n{\n  typedef Select<ConditionMatrixType, ThenMatrixType, ElseMatrixType> XprType;\n  enum {\n    CoeffReadCost = evaluator<ConditionMatrixType>::CoeffReadCost\n                  + EIGEN_PLAIN_ENUM_MAX(evaluator<ThenMatrixType>::CoeffReadCost,\n                                         evaluator<ElseMatrixType>::CoeffReadCost),\n\n    Flags = (unsigned int)evaluator<ThenMatrixType>::Flags & evaluator<ElseMatrixType>::Flags & HereditaryBits,\n    \n    Alignment = EIGEN_PLAIN_ENUM_MIN(evaluator<ThenMatrixType>::Alignment, evaluator<ElseMatrixType>::Alignment)\n  };\n\n  EIGEN_DEVICE_FUNC explicit evaluator(const XprType& select)\n    : m_conditionImpl(select.conditionMatrix()),\n      m_thenImpl(select.thenMatrix()),\n      m_elseImpl(select.elseMatrix())\n  {\n    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);\n  }\n \n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  CoeffReturnType coeff(Index row, Index col) const\n  {\n    if (m_conditionImpl.coeff(row, col))\n      return m_thenImpl.coeff(row, col);\n    else\n      return m_elseImpl.coeff(row, col);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  CoeffReturnType coeff(Index index) const\n  {\n    if (m_conditionImpl.coeff(index))\n      return m_thenImpl.coeff(index);\n    else\n      return m_elseImpl.coeff(index);\n  }\n \nprotected:\n  evaluator<ConditionMatrixType> m_conditionImpl;\n  evaluator<ThenMatrixType> m_thenImpl;\n  evaluator<ElseMatrixType> m_elseImpl;\n};\n\n\n// -------------------- Replicate --------------------\n\ntemplate<typename ArgType, int RowFactor, int ColFactor> \nstruct unary_evaluator<Replicate<ArgType, RowFactor, ColFactor> >\n  : evaluator_base<Replicate<ArgType, RowFactor, ColFactor> >\n{\n  typedef Replicate<ArgType, RowFactor, ColFactor> XprType;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  enum {\n    Factor = (RowFactor==Dynamic || ColFactor==Dynamic) ? Dynamic : RowFactor*ColFactor\n  };\n  typedef typename internal::nested_eval<ArgType,Factor>::type ArgTypeNested;\n  typedef typename internal::remove_all<ArgTypeNested>::type ArgTypeNestedCleaned;\n  \n  enum {\n    CoeffReadCost = evaluator<ArgTypeNestedCleaned>::CoeffReadCost,\n    LinearAccessMask = XprType::IsVectorAtCompileTime ? LinearAccessBit : 0,\n    Flags = (evaluator<ArgTypeNestedCleaned>::Flags & (HereditaryBits|LinearAccessMask) & ~RowMajorBit) | (traits<XprType>::Flags & RowMajorBit),\n    \n    Alignment = evaluator<ArgTypeNestedCleaned>::Alignment\n  };\n\n  EIGEN_DEVICE_FUNC explicit unary_evaluator(const XprType& replicate)\n    : m_arg(replicate.nestedExpression()),\n      m_argImpl(m_arg),\n      m_rows(replicate.nestedExpression().rows()),\n      m_cols(replicate.nestedExpression().cols())\n  {}\n \n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  CoeffReturnType coeff(Index row, Index col) const\n  {\n    // try to avoid using modulo; this is a pure optimization strategy\n    const Index actual_row = internal::traits<XprType>::RowsAtCompileTime==1 ? 0\n                           : RowFactor==1 ? row\n                           : row % m_rows.value();\n    const Index actual_col = internal::traits<XprType>::ColsAtCompileTime==1 ? 0\n                           : ColFactor==1 ? col\n                           : col % m_cols.value();\n    \n    return m_argImpl.coeff(actual_row, actual_col);\n  }\n  \n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  CoeffReturnType coeff(Index index) const\n  {\n    // try to avoid using modulo; this is a pure optimization strategy\n    const Index actual_index = internal::traits<XprType>::RowsAtCompileTime==1\n                                  ? (ColFactor==1 ?  index : index%m_cols.value())\n                                  : (RowFactor==1 ?  index : index%m_rows.value());\n    \n    return m_argImpl.coeff(actual_index);\n  }\n\n  template<int LoadMode, typename PacketType>\n  EIGEN_STRONG_INLINE\n  PacketType packet(Index row, Index col) const\n  {\n    const Index actual_row = internal::traits<XprType>::RowsAtCompileTime==1 ? 0\n                           : RowFactor==1 ? row\n                           : row % m_rows.value();\n    const Index actual_col = internal::traits<XprType>::ColsAtCompileTime==1 ? 0\n                           : ColFactor==1 ? col\n                           : col % m_cols.value();\n\n    return m_argImpl.template packet<LoadMode,PacketType>(actual_row, actual_col);\n  }\n  \n  template<int LoadMode, typename PacketType>\n  EIGEN_STRONG_INLINE\n  PacketType packet(Index index) const\n  {\n    const Index actual_index = internal::traits<XprType>::RowsAtCompileTime==1\n                                  ? (ColFactor==1 ?  index : index%m_cols.value())\n                                  : (RowFactor==1 ?  index : index%m_rows.value());\n\n    return m_argImpl.template packet<LoadMode,PacketType>(actual_index);\n  }\n \nprotected:\n  const ArgTypeNested m_arg;\n  evaluator<ArgTypeNestedCleaned> m_argImpl;\n  const variable_if_dynamic<Index, ArgType::RowsAtCompileTime> m_rows;\n  const variable_if_dynamic<Index, ArgType::ColsAtCompileTime> m_cols;\n};\n\n\n// -------------------- PartialReduxExpr --------------------\n\ntemplate< typename ArgType, typename MemberOp, int Direction>\nstruct evaluator<PartialReduxExpr<ArgType, MemberOp, Direction> >\n  : evaluator_base<PartialReduxExpr<ArgType, MemberOp, Direction> >\n{\n  typedef PartialReduxExpr<ArgType, MemberOp, Direction> XprType;\n  typedef typename internal::nested_eval<ArgType,1>::type ArgTypeNested;\n  typedef typename internal::remove_all<ArgTypeNested>::type ArgTypeNestedCleaned;\n  typedef typename ArgType::Scalar InputScalar;\n  typedef typename XprType::Scalar Scalar;\n  enum {\n    TraversalSize = Direction==int(Vertical) ? int(ArgType::RowsAtCompileTime) :  int(ArgType::ColsAtCompileTime)\n  };\n  typedef typename MemberOp::template Cost<InputScalar,int(TraversalSize)> CostOpType;\n  enum {\n    CoeffReadCost = TraversalSize==Dynamic ? HugeCost\n                  : TraversalSize * evaluator<ArgType>::CoeffReadCost + int(CostOpType::value),\n    \n    Flags = (traits<XprType>::Flags&RowMajorBit) | (evaluator<ArgType>::Flags&(HereditaryBits&(~RowMajorBit))) | LinearAccessBit,\n    \n    Alignment = 0 // FIXME this will need to be improved once PartialReduxExpr is vectorized\n  };\n\n  EIGEN_DEVICE_FUNC explicit evaluator(const XprType xpr)\n    : m_arg(xpr.nestedExpression()), m_functor(xpr.functor())\n  {\n    EIGEN_INTERNAL_CHECK_COST_VALUE(TraversalSize==Dynamic ? HugeCost : int(CostOpType::value));\n    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);\n  }\n\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  const Scalar coeff(Index i, Index j) const\n  {\n    if (Direction==Vertical)\n      return m_functor(m_arg.col(j));\n    else\n      return m_functor(m_arg.row(i));\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  const Scalar coeff(Index index) const\n  {\n    if (Direction==Vertical)\n      return m_functor(m_arg.col(index));\n    else\n      return m_functor(m_arg.row(index));\n  }\n\nprotected:\n  typename internal::add_const_on_value_type<ArgTypeNested>::type m_arg;\n  const MemberOp m_functor;\n};\n\n\n// -------------------- MatrixWrapper and ArrayWrapper --------------------\n//\n// evaluator_wrapper_base<T> is a common base class for the\n// MatrixWrapper and ArrayWrapper evaluators.\n\ntemplate<typename XprType>\nstruct evaluator_wrapper_base\n  : evaluator_base<XprType>\n{\n  typedef typename remove_all<typename XprType::NestedExpressionType>::type ArgType;\n  enum {\n    CoeffReadCost = evaluator<ArgType>::CoeffReadCost,\n    Flags = evaluator<ArgType>::Flags,\n    Alignment = evaluator<ArgType>::Alignment\n  };\n\n  EIGEN_DEVICE_FUNC explicit evaluator_wrapper_base(const ArgType& arg) : m_argImpl(arg) {}\n\n  typedef typename ArgType::Scalar Scalar;\n  typedef typename ArgType::CoeffReturnType CoeffReturnType;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  CoeffReturnType coeff(Index row, Index col) const\n  {\n    return m_argImpl.coeff(row, col);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  CoeffReturnType coeff(Index index) const\n  {\n    return m_argImpl.coeff(index);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  Scalar& coeffRef(Index row, Index col)\n  {\n    return m_argImpl.coeffRef(row, col);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  Scalar& coeffRef(Index index)\n  {\n    return m_argImpl.coeffRef(index);\n  }\n\n  template<int LoadMode, typename PacketType>\n  EIGEN_STRONG_INLINE\n  PacketType packet(Index row, Index col) const\n  {\n    return m_argImpl.template packet<LoadMode,PacketType>(row, col);\n  }\n\n  template<int LoadMode, typename PacketType>\n  EIGEN_STRONG_INLINE\n  PacketType packet(Index index) const\n  {\n    return m_argImpl.template packet<LoadMode,PacketType>(index);\n  }\n\n  template<int StoreMode, typename PacketType>\n  EIGEN_STRONG_INLINE\n  void writePacket(Index row, Index col, const PacketType& x)\n  {\n    m_argImpl.template writePacket<StoreMode>(row, col, x);\n  }\n\n  template<int StoreMode, typename PacketType>\n  EIGEN_STRONG_INLINE\n  void writePacket(Index index, const PacketType& x)\n  {\n    m_argImpl.template writePacket<StoreMode>(index, x);\n  }\n\nprotected:\n  evaluator<ArgType> m_argImpl;\n};\n\ntemplate<typename TArgType>\nstruct unary_evaluator<MatrixWrapper<TArgType> >\n  : evaluator_wrapper_base<MatrixWrapper<TArgType> >\n{\n  typedef MatrixWrapper<TArgType> XprType;\n\n  EIGEN_DEVICE_FUNC explicit unary_evaluator(const XprType& wrapper)\n    : evaluator_wrapper_base<MatrixWrapper<TArgType> >(wrapper.nestedExpression())\n  { }\n};\n\ntemplate<typename TArgType>\nstruct unary_evaluator<ArrayWrapper<TArgType> >\n  : evaluator_wrapper_base<ArrayWrapper<TArgType> >\n{\n  typedef ArrayWrapper<TArgType> XprType;\n\n  EIGEN_DEVICE_FUNC explicit unary_evaluator(const XprType& wrapper)\n    : evaluator_wrapper_base<ArrayWrapper<TArgType> >(wrapper.nestedExpression())\n  { }\n};\n\n\n// -------------------- Reverse --------------------\n\n// defined in Reverse.h:\ntemplate<typename PacketType, bool ReversePacket> struct reverse_packet_cond;\n\ntemplate<typename ArgType, int Direction>\nstruct unary_evaluator<Reverse<ArgType, Direction> >\n  : evaluator_base<Reverse<ArgType, Direction> >\n{\n  typedef Reverse<ArgType, Direction> XprType;\n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n\n  enum {\n    IsRowMajor = XprType::IsRowMajor,\n    IsColMajor = !IsRowMajor,\n    ReverseRow = (Direction == Vertical)   || (Direction == BothDirections),\n    ReverseCol = (Direction == Horizontal) || (Direction == BothDirections),\n    ReversePacket = (Direction == BothDirections)\n                    || ((Direction == Vertical)   && IsColMajor)\n                    || ((Direction == Horizontal) && IsRowMajor),\n                    \n    CoeffReadCost = evaluator<ArgType>::CoeffReadCost,\n    \n    // let's enable LinearAccess only with vectorization because of the product overhead\n    // FIXME enable DirectAccess with negative strides?\n    Flags0 = evaluator<ArgType>::Flags,\n    LinearAccess = ( (Direction==BothDirections) && (int(Flags0)&PacketAccessBit) )\n                  || ((ReverseRow && XprType::ColsAtCompileTime==1) || (ReverseCol && XprType::RowsAtCompileTime==1))\n                 ? LinearAccessBit : 0,\n\n    Flags = int(Flags0) & (HereditaryBits | PacketAccessBit | LinearAccess),\n    \n    Alignment = 0 // FIXME in some rare cases, Alignment could be preserved, like a Vector4f.\n  };\n\n  EIGEN_DEVICE_FUNC explicit unary_evaluator(const XprType& reverse)\n    : m_argImpl(reverse.nestedExpression()),\n      m_rows(ReverseRow ? reverse.nestedExpression().rows() : 1),\n      m_cols(ReverseCol ? reverse.nestedExpression().cols() : 1)\n  { }\n \n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  CoeffReturnType coeff(Index row, Index col) const\n  {\n    return m_argImpl.coeff(ReverseRow ? m_rows.value() - row - 1 : row,\n                           ReverseCol ? m_cols.value() - col - 1 : col);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  CoeffReturnType coeff(Index index) const\n  {\n    return m_argImpl.coeff(m_rows.value() * m_cols.value() - index - 1);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  Scalar& coeffRef(Index row, Index col)\n  {\n    return m_argImpl.coeffRef(ReverseRow ? m_rows.value() - row - 1 : row,\n                              ReverseCol ? m_cols.value() - col - 1 : col);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  Scalar& coeffRef(Index index)\n  {\n    return m_argImpl.coeffRef(m_rows.value() * m_cols.value() - index - 1);\n  }\n\n  template<int LoadMode, typename PacketType>\n  EIGEN_STRONG_INLINE\n  PacketType packet(Index row, Index col) const\n  {\n    enum {\n      PacketSize = unpacket_traits<PacketType>::size,\n      OffsetRow  = ReverseRow && IsColMajor ? PacketSize : 1,\n      OffsetCol  = ReverseCol && IsRowMajor ? PacketSize : 1\n    };\n    typedef internal::reverse_packet_cond<PacketType,ReversePacket> reverse_packet;\n    return reverse_packet::run(m_argImpl.template packet<LoadMode,PacketType>(\n                                  ReverseRow ? m_rows.value() - row - OffsetRow : row,\n                                  ReverseCol ? m_cols.value() - col - OffsetCol : col));\n  }\n\n  template<int LoadMode, typename PacketType>\n  EIGEN_STRONG_INLINE\n  PacketType packet(Index index) const\n  {\n    enum { PacketSize = unpacket_traits<PacketType>::size };\n    return preverse(m_argImpl.template packet<LoadMode,PacketType>(m_rows.value() * m_cols.value() - index - PacketSize));\n  }\n\n  template<int LoadMode, typename PacketType>\n  EIGEN_STRONG_INLINE\n  void writePacket(Index row, Index col, const PacketType& x)\n  {\n    // FIXME we could factorize some code with packet(i,j)\n    enum {\n      PacketSize = unpacket_traits<PacketType>::size,\n      OffsetRow  = ReverseRow && IsColMajor ? PacketSize : 1,\n      OffsetCol  = ReverseCol && IsRowMajor ? PacketSize : 1\n    };\n    typedef internal::reverse_packet_cond<PacketType,ReversePacket> reverse_packet;\n    m_argImpl.template writePacket<LoadMode>(\n                                  ReverseRow ? m_rows.value() - row - OffsetRow : row,\n                                  ReverseCol ? m_cols.value() - col - OffsetCol : col,\n                                  reverse_packet::run(x));\n  }\n\n  template<int LoadMode, typename PacketType>\n  EIGEN_STRONG_INLINE\n  void writePacket(Index index, const PacketType& x)\n  {\n    enum { PacketSize = unpacket_traits<PacketType>::size };\n    m_argImpl.template writePacket<LoadMode>\n      (m_rows.value() * m_cols.value() - index - PacketSize, preverse(x));\n  }\n \nprotected:\n  evaluator<ArgType> m_argImpl;\n\n  // If we do not reverse rows, then we do not need to know the number of rows; same for columns\n  // Nonetheless, in this case it is important to set to 1 such that the coeff(index) method works fine for vectors.\n  const variable_if_dynamic<Index, ReverseRow ? ArgType::RowsAtCompileTime : 1> m_rows;\n  const variable_if_dynamic<Index, ReverseCol ? ArgType::ColsAtCompileTime : 1> m_cols;\n};\n\n\n// -------------------- Diagonal --------------------\n\ntemplate<typename ArgType, int DiagIndex>\nstruct evaluator<Diagonal<ArgType, DiagIndex> >\n  : evaluator_base<Diagonal<ArgType, DiagIndex> >\n{\n  typedef Diagonal<ArgType, DiagIndex> XprType;\n  \n  enum {\n    CoeffReadCost = evaluator<ArgType>::CoeffReadCost,\n    \n    Flags = (unsigned int)(evaluator<ArgType>::Flags & (HereditaryBits | DirectAccessBit) & ~RowMajorBit) | LinearAccessBit,\n    \n    Alignment = 0\n  };\n\n  EIGEN_DEVICE_FUNC explicit evaluator(const XprType& diagonal)\n    : m_argImpl(diagonal.nestedExpression()),\n      m_index(diagonal.index())\n  { }\n \n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  CoeffReturnType coeff(Index row, Index) const\n  {\n    return m_argImpl.coeff(row + rowOffset(), row + colOffset());\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  CoeffReturnType coeff(Index index) const\n  {\n    return m_argImpl.coeff(index + rowOffset(), index + colOffset());\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  Scalar& coeffRef(Index row, Index)\n  {\n    return m_argImpl.coeffRef(row + rowOffset(), row + colOffset());\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  Scalar& coeffRef(Index index)\n  {\n    return m_argImpl.coeffRef(index + rowOffset(), index + colOffset());\n  }\n\nprotected:\n  evaluator<ArgType> m_argImpl;\n  const internal::variable_if_dynamicindex<Index, XprType::DiagIndex> m_index;\n\nprivate:\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index rowOffset() const { return m_index.value() > 0 ? 0 : -m_index.value(); }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index colOffset() const { return m_index.value() > 0 ? m_index.value() : 0; }\n};\n\n\n//----------------------------------------------------------------------\n// deprecated code\n//----------------------------------------------------------------------\n\n// -------------------- EvalToTemp --------------------\n\n// expression class for evaluating nested expression to a temporary\n\ntemplate<typename ArgType> class EvalToTemp;\n\ntemplate<typename ArgType>\nstruct traits<EvalToTemp<ArgType> >\n  : public traits<ArgType>\n{ };\n\ntemplate<typename ArgType>\nclass EvalToTemp\n  : public dense_xpr_base<EvalToTemp<ArgType> >::type\n{\n public:\n \n  typedef typename dense_xpr_base<EvalToTemp>::type Base;\n  EIGEN_GENERIC_PUBLIC_INTERFACE(EvalToTemp)\n \n  explicit EvalToTemp(const ArgType& arg)\n    : m_arg(arg)\n  { }\n \n  const ArgType& arg() const\n  {\n    return m_arg;\n  }\n\n  Index rows() const \n  {\n    return m_arg.rows();\n  }\n\n  Index cols() const \n  {\n    return m_arg.cols();\n  }\n\n private:\n  const ArgType& m_arg;\n};\n \ntemplate<typename ArgType>\nstruct evaluator<EvalToTemp<ArgType> >\n  : public evaluator<typename ArgType::PlainObject>\n{\n  typedef EvalToTemp<ArgType>                   XprType;\n  typedef typename ArgType::PlainObject         PlainObject;\n  typedef evaluator<PlainObject> Base;\n  \n  EIGEN_DEVICE_FUNC explicit evaluator(const XprType& xpr)\n    : m_result(xpr.arg())\n  {\n    ::new (static_cast<Base*>(this)) Base(m_result);\n  }\n\n  // This constructor is used when nesting an EvalTo evaluator in another evaluator\n  EIGEN_DEVICE_FUNC evaluator(const ArgType& arg)\n    : m_result(arg)\n  {\n    ::new (static_cast<Base*>(this)) Base(m_result);\n  }\n\nprotected:\n  PlainObject m_result;\n};\n\n} // namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_COREEVALUATORS_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/CoreIterators.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_COREITERATORS_H\n#define EIGEN_COREITERATORS_H\n\nnamespace Eigen { \n\n/* This file contains the respective InnerIterator definition of the expressions defined in Eigen/Core\n */\n\nnamespace internal {\n\ntemplate<typename XprType, typename EvaluatorKind>\nclass inner_iterator_selector;\n\n}\n\n/** \\class InnerIterator\n  * \\brief An InnerIterator allows to loop over the element of any matrix expression.\n  * \n  * \\warning To be used with care because an evaluator is constructed every time an InnerIterator iterator is constructed.\n  * \n  * TODO: add a usage example\n  */\ntemplate<typename XprType>\nclass InnerIterator\n{\nprotected:\n  typedef internal::inner_iterator_selector<XprType, typename internal::evaluator_traits<XprType>::Kind> IteratorType;\n  typedef internal::evaluator<XprType> EvaluatorType;\n  typedef typename internal::traits<XprType>::Scalar Scalar;\npublic:\n  /** Construct an iterator over the \\a outerId -th row or column of \\a xpr */\n  InnerIterator(const XprType &xpr, const Index &outerId)\n    : m_eval(xpr), m_iter(m_eval, outerId, xpr.innerSize())\n  {}\n  \n  /// \\returns the value of the current coefficient.\n  EIGEN_STRONG_INLINE Scalar value() const          { return m_iter.value(); }\n  /** Increment the iterator \\c *this to the next non-zero coefficient.\n    * Explicit zeros are not skipped over. To skip explicit zeros, see class SparseView\n    */\n  EIGEN_STRONG_INLINE InnerIterator& operator++()   { m_iter.operator++(); return *this; }\n  /// \\returns the column or row index of the current coefficient.\n  EIGEN_STRONG_INLINE Index index() const           { return m_iter.index(); }\n  /// \\returns the row index of the current coefficient.\n  EIGEN_STRONG_INLINE Index row() const             { return m_iter.row(); }\n  /// \\returns the column index of the current coefficient.\n  EIGEN_STRONG_INLINE Index col() const             { return m_iter.col(); }\n  /// \\returns \\c true if the iterator \\c *this still references a valid coefficient.\n  EIGEN_STRONG_INLINE operator bool() const         { return m_iter; }\n  \nprotected:\n  EvaluatorType m_eval;\n  IteratorType m_iter;\nprivate:\n  // If you get here, then you're not using the right InnerIterator type, e.g.:\n  //   SparseMatrix<double,RowMajor> A;\n  //   SparseMatrix<double>::InnerIterator it(A,0);\n  template<typename T> InnerIterator(const EigenBase<T>&,Index outer);\n};\n\nnamespace internal {\n\n// Generic inner iterator implementation for dense objects\ntemplate<typename XprType>\nclass inner_iterator_selector<XprType, IndexBased>\n{\nprotected:\n  typedef evaluator<XprType> EvaluatorType;\n  typedef typename traits<XprType>::Scalar Scalar;\n  enum { IsRowMajor = (XprType::Flags&RowMajorBit)==RowMajorBit };\n  \npublic:\n  EIGEN_STRONG_INLINE inner_iterator_selector(const EvaluatorType &eval, const Index &outerId, const Index &innerSize)\n    : m_eval(eval), m_inner(0), m_outer(outerId), m_end(innerSize)\n  {}\n\n  EIGEN_STRONG_INLINE Scalar value() const\n  {\n    return (IsRowMajor) ? m_eval.coeff(m_outer, m_inner)\n                        : m_eval.coeff(m_inner, m_outer);\n  }\n\n  EIGEN_STRONG_INLINE inner_iterator_selector& operator++() { m_inner++; return *this; }\n\n  EIGEN_STRONG_INLINE Index index() const { return m_inner; }\n  inline Index row() const { return IsRowMajor ? m_outer : index(); }\n  inline Index col() const { return IsRowMajor ? index() : m_outer; }\n\n  EIGEN_STRONG_INLINE operator bool() const { return m_inner < m_end && m_inner>=0; }\n\nprotected:\n  const EvaluatorType& m_eval;\n  Index m_inner;\n  const Index m_outer;\n  const Index m_end;\n};\n\n// For iterator-based evaluator, inner-iterator is already implemented as\n// evaluator<>::InnerIterator\ntemplate<typename XprType>\nclass inner_iterator_selector<XprType, IteratorBased>\n : public evaluator<XprType>::InnerIterator\n{\nprotected:\n  typedef typename evaluator<XprType>::InnerIterator Base;\n  typedef evaluator<XprType> EvaluatorType;\n  \npublic:\n  EIGEN_STRONG_INLINE inner_iterator_selector(const EvaluatorType &eval, const Index &outerId, const Index &/*innerSize*/)\n    : Base(eval, outerId)\n  {}  \n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_COREITERATORS_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/CwiseBinaryOp.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CWISE_BINARY_OP_H\n#define EIGEN_CWISE_BINARY_OP_H\n\nnamespace Eigen {\n\nnamespace internal {\ntemplate<typename BinaryOp, typename Lhs, typename Rhs>\nstruct traits<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >\n{\n  // we must not inherit from traits<Lhs> since it has\n  // the potential to cause problems with MSVC\n  typedef typename remove_all<Lhs>::type Ancestor;\n  typedef typename traits<Ancestor>::XprKind XprKind;\n  enum {\n    RowsAtCompileTime = traits<Ancestor>::RowsAtCompileTime,\n    ColsAtCompileTime = traits<Ancestor>::ColsAtCompileTime,\n    MaxRowsAtCompileTime = traits<Ancestor>::MaxRowsAtCompileTime,\n    MaxColsAtCompileTime = traits<Ancestor>::MaxColsAtCompileTime\n  };\n\n  // even though we require Lhs and Rhs to have the same scalar type (see CwiseBinaryOp constructor),\n  // we still want to handle the case when the result type is different.\n  typedef typename result_of<\n                     BinaryOp(\n                       const typename Lhs::Scalar&,\n                       const typename Rhs::Scalar&\n                     )\n                   >::type Scalar;\n  typedef typename cwise_promote_storage_type<typename traits<Lhs>::StorageKind,\n                                              typename traits<Rhs>::StorageKind,\n                                              BinaryOp>::ret StorageKind;\n  typedef typename promote_index_type<typename traits<Lhs>::StorageIndex,\n                                      typename traits<Rhs>::StorageIndex>::type StorageIndex;\n  typedef typename Lhs::Nested LhsNested;\n  typedef typename Rhs::Nested RhsNested;\n  typedef typename remove_reference<LhsNested>::type _LhsNested;\n  typedef typename remove_reference<RhsNested>::type _RhsNested;\n  enum {\n    Flags = cwise_promote_storage_order<typename traits<Lhs>::StorageKind,typename traits<Rhs>::StorageKind,_LhsNested::Flags & RowMajorBit,_RhsNested::Flags & RowMajorBit>::value\n  };\n};\n} // end namespace internal\n\ntemplate<typename BinaryOp, typename Lhs, typename Rhs, typename StorageKind>\nclass CwiseBinaryOpImpl;\n\n/** \\class CwiseBinaryOp\n  * \\ingroup Core_Module\n  *\n  * \\brief Generic expression where a coefficient-wise binary operator is applied to two expressions\n  *\n  * \\tparam BinaryOp template functor implementing the operator\n  * \\tparam LhsType the type of the left-hand side\n  * \\tparam RhsType the type of the right-hand side\n  *\n  * This class represents an expression  where a coefficient-wise binary operator is applied to two expressions.\n  * It is the return type of binary operators, by which we mean only those binary operators where\n  * both the left-hand side and the right-hand side are Eigen expressions.\n  * For example, the return type of matrix1+matrix2 is a CwiseBinaryOp.\n  *\n  * Most of the time, this is the only way that it is used, so you typically don't have to name\n  * CwiseBinaryOp types explicitly.\n  *\n  * \\sa MatrixBase::binaryExpr(const MatrixBase<OtherDerived> &,const CustomBinaryOp &) const, class CwiseUnaryOp, class CwiseNullaryOp\n  */\ntemplate<typename BinaryOp, typename LhsType, typename RhsType>\nclass CwiseBinaryOp : \n  public CwiseBinaryOpImpl<\n          BinaryOp, LhsType, RhsType,\n          typename internal::cwise_promote_storage_type<typename internal::traits<LhsType>::StorageKind,\n                                                        typename internal::traits<RhsType>::StorageKind,\n                                                        BinaryOp>::ret>,\n  internal::no_assignment_operator\n{\n  public:\n    \n    typedef typename internal::remove_all<BinaryOp>::type Functor;\n    typedef typename internal::remove_all<LhsType>::type Lhs;\n    typedef typename internal::remove_all<RhsType>::type Rhs;\n\n    typedef typename CwiseBinaryOpImpl<\n        BinaryOp, LhsType, RhsType,\n        typename internal::cwise_promote_storage_type<typename internal::traits<LhsType>::StorageKind,\n                                                      typename internal::traits<Rhs>::StorageKind,\n                                                      BinaryOp>::ret>::Base Base;\n    EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseBinaryOp)\n\n    typedef typename internal::ref_selector<LhsType>::type LhsNested;\n    typedef typename internal::ref_selector<RhsType>::type RhsNested;\n    typedef typename internal::remove_reference<LhsNested>::type _LhsNested;\n    typedef typename internal::remove_reference<RhsNested>::type _RhsNested;\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE CwiseBinaryOp(const Lhs& aLhs, const Rhs& aRhs, const BinaryOp& func = BinaryOp())\n      : m_lhs(aLhs), m_rhs(aRhs), m_functor(func)\n    {\n      EIGEN_CHECK_BINARY_COMPATIBILIY(BinaryOp,typename Lhs::Scalar,typename Rhs::Scalar);\n      // require the sizes to match\n      EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Lhs, Rhs)\n      eigen_assert(aLhs.rows() == aRhs.rows() && aLhs.cols() == aRhs.cols());\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Index rows() const {\n      // return the fixed size type if available to enable compile time optimizations\n      if (internal::traits<typename internal::remove_all<LhsNested>::type>::RowsAtCompileTime==Dynamic)\n        return m_rhs.rows();\n      else\n        return m_lhs.rows();\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Index cols() const {\n      // return the fixed size type if available to enable compile time optimizations\n      if (internal::traits<typename internal::remove_all<LhsNested>::type>::ColsAtCompileTime==Dynamic)\n        return m_rhs.cols();\n      else\n        return m_lhs.cols();\n    }\n\n    /** \\returns the left hand side nested expression */\n    EIGEN_DEVICE_FUNC\n    const _LhsNested& lhs() const { return m_lhs; }\n    /** \\returns the right hand side nested expression */\n    EIGEN_DEVICE_FUNC\n    const _RhsNested& rhs() const { return m_rhs; }\n    /** \\returns the functor representing the binary operation */\n    EIGEN_DEVICE_FUNC\n    const BinaryOp& functor() const { return m_functor; }\n\n  protected:\n    LhsNested m_lhs;\n    RhsNested m_rhs;\n    const BinaryOp m_functor;\n};\n\n// Generic API dispatcher\ntemplate<typename BinaryOp, typename Lhs, typename Rhs, typename StorageKind>\nclass CwiseBinaryOpImpl\n  : public internal::generic_xpr_base<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >::type\n{\npublic:\n  typedef typename internal::generic_xpr_base<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >::type Base;\n};\n\n/** replaces \\c *this by \\c *this - \\a other.\n  *\n  * \\returns a reference to \\c *this\n  */\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\nEIGEN_STRONG_INLINE Derived &\nMatrixBase<Derived>::operator-=(const MatrixBase<OtherDerived> &other)\n{\n  call_assignment(derived(), other.derived(), internal::sub_assign_op<Scalar,typename OtherDerived::Scalar>());\n  return derived();\n}\n\n/** replaces \\c *this by \\c *this + \\a other.\n  *\n  * \\returns a reference to \\c *this\n  */\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\nEIGEN_STRONG_INLINE Derived &\nMatrixBase<Derived>::operator+=(const MatrixBase<OtherDerived>& other)\n{\n  call_assignment(derived(), other.derived(), internal::add_assign_op<Scalar,typename OtherDerived::Scalar>());\n  return derived();\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_CWISE_BINARY_OP_H\n\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/CwiseNullaryOp.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CWISE_NULLARY_OP_H\n#define EIGEN_CWISE_NULLARY_OP_H\n\nnamespace Eigen {\n\nnamespace internal {\ntemplate<typename NullaryOp, typename PlainObjectType>\nstruct traits<CwiseNullaryOp<NullaryOp, PlainObjectType> > : traits<PlainObjectType>\n{\n  enum {\n    Flags = traits<PlainObjectType>::Flags & RowMajorBit\n  };\n};\n\n} // namespace internal\n\n/** \\class CwiseNullaryOp\n  * \\ingroup Core_Module\n  *\n  * \\brief Generic expression of a matrix where all coefficients are defined by a functor\n  *\n  * \\tparam NullaryOp template functor implementing the operator\n  * \\tparam PlainObjectType the underlying plain matrix/array type\n  *\n  * This class represents an expression of a generic nullary operator.\n  * It is the return type of the Ones(), Zero(), Constant(), Identity() and Random() methods,\n  * and most of the time this is the only way it is used.\n  *\n  * However, if you want to write a function returning such an expression, you\n  * will need to use this class.\n  *\n  * The functor NullaryOp must expose one of the following method:\n    <table class=\"manual\">\n    <tr            ><td>\\c operator()() </td><td>if the procedural generation does not depend on the coefficient entries (e.g., random numbers)</td></tr>\n    <tr class=\"alt\"><td>\\c operator()(Index i)</td><td>if the procedural generation makes sense for vectors only and that it depends on the coefficient index \\c i (e.g., linspace) </td></tr>\n    <tr            ><td>\\c operator()(Index i,Index j)</td><td>if the procedural generation depends on the matrix coordinates \\c i, \\c j (e.g., to generate a checkerboard with 0 and 1)</td></tr>\n    </table>\n  * It is also possible to expose the last two operators if the generation makes sense for matrices but can be optimized for vectors.\n  *\n  * See DenseBase::NullaryExpr(Index,const CustomNullaryOp&) for an example binding\n  * C++11 random number generators.\n  *\n  * A nullary expression can also be used to implement custom sophisticated matrix manipulations\n  * that cannot be covered by the existing set of natively supported matrix manipulations.\n  * See this \\ref TopicCustomizing_NullaryExpr \"page\" for some examples and additional explanations\n  * on the behavior of CwiseNullaryOp.\n  *\n  * \\sa class CwiseUnaryOp, class CwiseBinaryOp, DenseBase::NullaryExpr\n  */\ntemplate<typename NullaryOp, typename PlainObjectType>\nclass CwiseNullaryOp : public internal::dense_xpr_base< CwiseNullaryOp<NullaryOp, PlainObjectType> >::type, internal::no_assignment_operator\n{\n  public:\n\n    typedef typename internal::dense_xpr_base<CwiseNullaryOp>::type Base;\n    EIGEN_DENSE_PUBLIC_INTERFACE(CwiseNullaryOp)\n\n    EIGEN_DEVICE_FUNC\n    CwiseNullaryOp(Index rows, Index cols, const NullaryOp& func = NullaryOp())\n      : m_rows(rows), m_cols(cols), m_functor(func)\n    {\n      eigen_assert(rows >= 0\n            && (RowsAtCompileTime == Dynamic || RowsAtCompileTime == rows)\n            &&  cols >= 0\n            && (ColsAtCompileTime == Dynamic || ColsAtCompileTime == cols));\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Index rows() const { return m_rows.value(); }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Index cols() const { return m_cols.value(); }\n\n    /** \\returns the functor representing the nullary operation */\n    EIGEN_DEVICE_FUNC\n    const NullaryOp& functor() const { return m_functor; }\n\n  protected:\n    const internal::variable_if_dynamic<Index, RowsAtCompileTime> m_rows;\n    const internal::variable_if_dynamic<Index, ColsAtCompileTime> m_cols;\n    const NullaryOp m_functor;\n};\n\n\n/** \\returns an expression of a matrix defined by a custom functor \\a func\n  *\n  * The parameters \\a rows and \\a cols are the number of rows and of columns of\n  * the returned matrix. Must be compatible with this MatrixBase type.\n  *\n  * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,\n  * it is redundant to pass \\a rows and \\a cols as arguments, so Zero() should be used\n  * instead.\n  *\n  * The template parameter \\a CustomNullaryOp is the type of the functor.\n  *\n  * \\sa class CwiseNullaryOp\n  */\ntemplate<typename Derived>\ntemplate<typename CustomNullaryOp>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseNullaryOp<CustomNullaryOp, typename DenseBase<Derived>::PlainObject>\nDenseBase<Derived>::NullaryExpr(Index rows, Index cols, const CustomNullaryOp& func)\n{\n  return CwiseNullaryOp<CustomNullaryOp, PlainObject>(rows, cols, func);\n}\n\n/** \\returns an expression of a matrix defined by a custom functor \\a func\n  *\n  * The parameter \\a size is the size of the returned vector.\n  * Must be compatible with this MatrixBase type.\n  *\n  * \\only_for_vectors\n  *\n  * This variant is meant to be used for dynamic-size vector types. For fixed-size types,\n  * it is redundant to pass \\a size as argument, so Zero() should be used\n  * instead.\n  *\n  * The template parameter \\a CustomNullaryOp is the type of the functor.\n  *\n  * Here is an example with C++11 random generators: \\include random_cpp11.cpp\n  * Output: \\verbinclude random_cpp11.out\n  * \n  * \\sa class CwiseNullaryOp\n  */\ntemplate<typename Derived>\ntemplate<typename CustomNullaryOp>\nEIGEN_STRONG_INLINE const CwiseNullaryOp<CustomNullaryOp, typename DenseBase<Derived>::PlainObject>\nDenseBase<Derived>::NullaryExpr(Index size, const CustomNullaryOp& func)\n{\n  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)\n  if(RowsAtCompileTime == 1) return CwiseNullaryOp<CustomNullaryOp, PlainObject>(1, size, func);\n  else return CwiseNullaryOp<CustomNullaryOp, PlainObject>(size, 1, func);\n}\n\n/** \\returns an expression of a matrix defined by a custom functor \\a func\n  *\n  * This variant is only for fixed-size DenseBase types. For dynamic-size types, you\n  * need to use the variants taking size arguments.\n  *\n  * The template parameter \\a CustomNullaryOp is the type of the functor.\n  *\n  * \\sa class CwiseNullaryOp\n  */\ntemplate<typename Derived>\ntemplate<typename CustomNullaryOp>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseNullaryOp<CustomNullaryOp, typename DenseBase<Derived>::PlainObject>\nDenseBase<Derived>::NullaryExpr(const CustomNullaryOp& func)\n{\n  return CwiseNullaryOp<CustomNullaryOp, PlainObject>(RowsAtCompileTime, ColsAtCompileTime, func);\n}\n\n/** \\returns an expression of a constant matrix of value \\a value\n  *\n  * The parameters \\a rows and \\a cols are the number of rows and of columns of\n  * the returned matrix. Must be compatible with this DenseBase type.\n  *\n  * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,\n  * it is redundant to pass \\a rows and \\a cols as arguments, so Zero() should be used\n  * instead.\n  *\n  * The template parameter \\a CustomNullaryOp is the type of the functor.\n  *\n  * \\sa class CwiseNullaryOp\n  */\ntemplate<typename Derived>\nEIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType\nDenseBase<Derived>::Constant(Index rows, Index cols, const Scalar& value)\n{\n  return DenseBase<Derived>::NullaryExpr(rows, cols, internal::scalar_constant_op<Scalar>(value));\n}\n\n/** \\returns an expression of a constant matrix of value \\a value\n  *\n  * The parameter \\a size is the size of the returned vector.\n  * Must be compatible with this DenseBase type.\n  *\n  * \\only_for_vectors\n  *\n  * This variant is meant to be used for dynamic-size vector types. For fixed-size types,\n  * it is redundant to pass \\a size as argument, so Zero() should be used\n  * instead.\n  *\n  * The template parameter \\a CustomNullaryOp is the type of the functor.\n  *\n  * \\sa class CwiseNullaryOp\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType\nDenseBase<Derived>::Constant(Index size, const Scalar& value)\n{\n  return DenseBase<Derived>::NullaryExpr(size, internal::scalar_constant_op<Scalar>(value));\n}\n\n/** \\returns an expression of a constant matrix of value \\a value\n  *\n  * This variant is only for fixed-size DenseBase types. For dynamic-size types, you\n  * need to use the variants taking size arguments.\n  *\n  * The template parameter \\a CustomNullaryOp is the type of the functor.\n  *\n  * \\sa class CwiseNullaryOp\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType\nDenseBase<Derived>::Constant(const Scalar& value)\n{\n  EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)\n  return DenseBase<Derived>::NullaryExpr(RowsAtCompileTime, ColsAtCompileTime, internal::scalar_constant_op<Scalar>(value));\n}\n\n/** \\deprecated because of accuracy loss. In Eigen 3.3, it is an alias for LinSpaced(Index,const Scalar&,const Scalar&)\n  *\n  * \\sa LinSpaced(Index,Scalar,Scalar), setLinSpaced(Index,const Scalar&,const Scalar&)\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType\nDenseBase<Derived>::LinSpaced(Sequential_t, Index size, const Scalar& low, const Scalar& high)\n{\n  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)\n  return DenseBase<Derived>::NullaryExpr(size, internal::linspaced_op<Scalar,PacketScalar>(low,high,size));\n}\n\n/** \\deprecated because of accuracy loss. In Eigen 3.3, it is an alias for LinSpaced(const Scalar&,const Scalar&)\n  *\n  * \\sa LinSpaced(Scalar,Scalar)\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType\nDenseBase<Derived>::LinSpaced(Sequential_t, const Scalar& low, const Scalar& high)\n{\n  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)\n  EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)\n  return DenseBase<Derived>::NullaryExpr(Derived::SizeAtCompileTime, internal::linspaced_op<Scalar,PacketScalar>(low,high,Derived::SizeAtCompileTime));\n}\n\n/**\n  * \\brief Sets a linearly spaced vector.\n  *\n  * The function generates 'size' equally spaced values in the closed interval [low,high].\n  * When size is set to 1, a vector of length 1 containing 'high' is returned.\n  *\n  * \\only_for_vectors\n  *\n  * Example: \\include DenseBase_LinSpaced.cpp\n  * Output: \\verbinclude DenseBase_LinSpaced.out\n  *\n  * For integer scalar types, an even spacing is possible if and only if the length of the range,\n  * i.e., \\c high-low is a scalar multiple of \\c size-1, or if \\c size is a scalar multiple of the\n  * number of values \\c high-low+1 (meaning each value can be repeated the same number of time).\n  * If one of these two considions is not satisfied, then \\c high is lowered to the largest value\n  * satisfying one of this constraint.\n  * Here are some examples:\n  *\n  * Example: \\include DenseBase_LinSpacedInt.cpp\n  * Output: \\verbinclude DenseBase_LinSpacedInt.out\n  *\n  * \\sa setLinSpaced(Index,const Scalar&,const Scalar&), CwiseNullaryOp\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType\nDenseBase<Derived>::LinSpaced(Index size, const Scalar& low, const Scalar& high)\n{\n  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)\n  return DenseBase<Derived>::NullaryExpr(size, internal::linspaced_op<Scalar,PacketScalar>(low,high,size));\n}\n\n/**\n  * \\copydoc DenseBase::LinSpaced(Index, const Scalar&, const Scalar&)\n  * Special version for fixed size types which does not require the size parameter.\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType\nDenseBase<Derived>::LinSpaced(const Scalar& low, const Scalar& high)\n{\n  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)\n  EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)\n  return DenseBase<Derived>::NullaryExpr(Derived::SizeAtCompileTime, internal::linspaced_op<Scalar,PacketScalar>(low,high,Derived::SizeAtCompileTime));\n}\n\n/** \\returns true if all coefficients in this matrix are approximately equal to \\a val, to within precision \\a prec */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC bool DenseBase<Derived>::isApproxToConstant\n(const Scalar& val, const RealScalar& prec) const\n{\n  typename internal::nested_eval<Derived,1>::type self(derived());\n  for(Index j = 0; j < cols(); ++j)\n    for(Index i = 0; i < rows(); ++i)\n      if(!internal::isApprox(self.coeff(i, j), val, prec))\n        return false;\n  return true;\n}\n\n/** This is just an alias for isApproxToConstant().\n  *\n  * \\returns true if all coefficients in this matrix are approximately equal to \\a value, to within precision \\a prec */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC bool DenseBase<Derived>::isConstant\n(const Scalar& val, const RealScalar& prec) const\n{\n  return isApproxToConstant(val, prec);\n}\n\n/** Alias for setConstant(): sets all coefficients in this expression to \\a val.\n  *\n  * \\sa setConstant(), Constant(), class CwiseNullaryOp\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void DenseBase<Derived>::fill(const Scalar& val)\n{\n  setConstant(val);\n}\n\n/** Sets all coefficients in this expression to value \\a val.\n  *\n  * \\sa fill(), setConstant(Index,const Scalar&), setConstant(Index,Index,const Scalar&), setZero(), setOnes(), Constant(), class CwiseNullaryOp, setZero(), setOnes()\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setConstant(const Scalar& val)\n{\n  return derived() = Constant(rows(), cols(), val);\n}\n\n/** Resizes to the given \\a size, and sets all coefficients in this expression to the given value \\a val.\n  *\n  * \\only_for_vectors\n  *\n  * Example: \\include Matrix_setConstant_int.cpp\n  * Output: \\verbinclude Matrix_setConstant_int.out\n  *\n  * \\sa MatrixBase::setConstant(const Scalar&), setConstant(Index,Index,const Scalar&), class CwiseNullaryOp, MatrixBase::Constant(const Scalar&)\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived&\nPlainObjectBase<Derived>::setConstant(Index size, const Scalar& val)\n{\n  resize(size);\n  return setConstant(val);\n}\n\n/** Resizes to the given size, and sets all coefficients in this expression to the given value \\a val.\n  *\n  * \\param rows the new number of rows\n  * \\param cols the new number of columns\n  * \\param val the value to which all coefficients are set\n  *\n  * Example: \\include Matrix_setConstant_int_int.cpp\n  * Output: \\verbinclude Matrix_setConstant_int_int.out\n  *\n  * \\sa MatrixBase::setConstant(const Scalar&), setConstant(Index,const Scalar&), class CwiseNullaryOp, MatrixBase::Constant(const Scalar&)\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived&\nPlainObjectBase<Derived>::setConstant(Index rows, Index cols, const Scalar& val)\n{\n  resize(rows, cols);\n  return setConstant(val);\n}\n\n/**\n  * \\brief Sets a linearly spaced vector.\n  *\n  * The function generates 'size' equally spaced values in the closed interval [low,high].\n  * When size is set to 1, a vector of length 1 containing 'high' is returned.\n  *\n  * \\only_for_vectors\n  *\n  * Example: \\include DenseBase_setLinSpaced.cpp\n  * Output: \\verbinclude DenseBase_setLinSpaced.out\n  *\n  * For integer scalar types, do not miss the explanations on the definition\n  * of \\link LinSpaced(Index,const Scalar&,const Scalar&) even spacing \\endlink.\n  *\n  * \\sa LinSpaced(Index,const Scalar&,const Scalar&), CwiseNullaryOp\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setLinSpaced(Index newSize, const Scalar& low, const Scalar& high)\n{\n  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)\n  return derived() = Derived::NullaryExpr(newSize, internal::linspaced_op<Scalar,PacketScalar>(low,high,newSize));\n}\n\n/**\n  * \\brief Sets a linearly spaced vector.\n  *\n  * The function fills \\c *this with equally spaced values in the closed interval [low,high].\n  * When size is set to 1, a vector of length 1 containing 'high' is returned.\n  *\n  * \\only_for_vectors\n  *\n  * For integer scalar types, do not miss the explanations on the definition\n  * of \\link LinSpaced(Index,const Scalar&,const Scalar&) even spacing \\endlink.\n  *\n  * \\sa LinSpaced(Index,const Scalar&,const Scalar&), setLinSpaced(Index, const Scalar&, const Scalar&), CwiseNullaryOp\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setLinSpaced(const Scalar& low, const Scalar& high)\n{\n  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)\n  return setLinSpaced(size(), low, high);\n}\n\n// zero:\n\n/** \\returns an expression of a zero matrix.\n  *\n  * The parameters \\a rows and \\a cols are the number of rows and of columns of\n  * the returned matrix. Must be compatible with this MatrixBase type.\n  *\n  * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,\n  * it is redundant to pass \\a rows and \\a cols as arguments, so Zero() should be used\n  * instead.\n  *\n  * Example: \\include MatrixBase_zero_int_int.cpp\n  * Output: \\verbinclude MatrixBase_zero_int_int.out\n  *\n  * \\sa Zero(), Zero(Index)\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType\nDenseBase<Derived>::Zero(Index rows, Index cols)\n{\n  return Constant(rows, cols, Scalar(0));\n}\n\n/** \\returns an expression of a zero vector.\n  *\n  * The parameter \\a size is the size of the returned vector.\n  * Must be compatible with this MatrixBase type.\n  *\n  * \\only_for_vectors\n  *\n  * This variant is meant to be used for dynamic-size vector types. For fixed-size types,\n  * it is redundant to pass \\a size as argument, so Zero() should be used\n  * instead.\n  *\n  * Example: \\include MatrixBase_zero_int.cpp\n  * Output: \\verbinclude MatrixBase_zero_int.out\n  *\n  * \\sa Zero(), Zero(Index,Index)\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType\nDenseBase<Derived>::Zero(Index size)\n{\n  return Constant(size, Scalar(0));\n}\n\n/** \\returns an expression of a fixed-size zero matrix or vector.\n  *\n  * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you\n  * need to use the variants taking size arguments.\n  *\n  * Example: \\include MatrixBase_zero.cpp\n  * Output: \\verbinclude MatrixBase_zero.out\n  *\n  * \\sa Zero(Index), Zero(Index,Index)\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType\nDenseBase<Derived>::Zero()\n{\n  return Constant(Scalar(0));\n}\n\n/** \\returns true if *this is approximately equal to the zero matrix,\n  *          within the precision given by \\a prec.\n  *\n  * Example: \\include MatrixBase_isZero.cpp\n  * Output: \\verbinclude MatrixBase_isZero.out\n  *\n  * \\sa class CwiseNullaryOp, Zero()\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC bool DenseBase<Derived>::isZero(const RealScalar& prec) const\n{\n  typename internal::nested_eval<Derived,1>::type self(derived());\n  for(Index j = 0; j < cols(); ++j)\n    for(Index i = 0; i < rows(); ++i)\n      if(!internal::isMuchSmallerThan(self.coeff(i, j), static_cast<Scalar>(1), prec))\n        return false;\n  return true;\n}\n\n/** Sets all coefficients in this expression to zero.\n  *\n  * Example: \\include MatrixBase_setZero.cpp\n  * Output: \\verbinclude MatrixBase_setZero.out\n  *\n  * \\sa class CwiseNullaryOp, Zero()\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setZero()\n{\n  return setConstant(Scalar(0));\n}\n\n/** Resizes to the given \\a size, and sets all coefficients in this expression to zero.\n  *\n  * \\only_for_vectors\n  *\n  * Example: \\include Matrix_setZero_int.cpp\n  * Output: \\verbinclude Matrix_setZero_int.out\n  *\n  * \\sa DenseBase::setZero(), setZero(Index,Index), class CwiseNullaryOp, DenseBase::Zero()\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived&\nPlainObjectBase<Derived>::setZero(Index newSize)\n{\n  resize(newSize);\n  return setConstant(Scalar(0));\n}\n\n/** Resizes to the given size, and sets all coefficients in this expression to zero.\n  *\n  * \\param rows the new number of rows\n  * \\param cols the new number of columns\n  *\n  * Example: \\include Matrix_setZero_int_int.cpp\n  * Output: \\verbinclude Matrix_setZero_int_int.out\n  *\n  * \\sa DenseBase::setZero(), setZero(Index), class CwiseNullaryOp, DenseBase::Zero()\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived&\nPlainObjectBase<Derived>::setZero(Index rows, Index cols)\n{\n  resize(rows, cols);\n  return setConstant(Scalar(0));\n}\n\n// ones:\n\n/** \\returns an expression of a matrix where all coefficients equal one.\n  *\n  * The parameters \\a rows and \\a cols are the number of rows and of columns of\n  * the returned matrix. Must be compatible with this MatrixBase type.\n  *\n  * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,\n  * it is redundant to pass \\a rows and \\a cols as arguments, so Ones() should be used\n  * instead.\n  *\n  * Example: \\include MatrixBase_ones_int_int.cpp\n  * Output: \\verbinclude MatrixBase_ones_int_int.out\n  *\n  * \\sa Ones(), Ones(Index), isOnes(), class Ones\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType\nDenseBase<Derived>::Ones(Index rows, Index cols)\n{\n  return Constant(rows, cols, Scalar(1));\n}\n\n/** \\returns an expression of a vector where all coefficients equal one.\n  *\n  * The parameter \\a newSize is the size of the returned vector.\n  * Must be compatible with this MatrixBase type.\n  *\n  * \\only_for_vectors\n  *\n  * This variant is meant to be used for dynamic-size vector types. For fixed-size types,\n  * it is redundant to pass \\a size as argument, so Ones() should be used\n  * instead.\n  *\n  * Example: \\include MatrixBase_ones_int.cpp\n  * Output: \\verbinclude MatrixBase_ones_int.out\n  *\n  * \\sa Ones(), Ones(Index,Index), isOnes(), class Ones\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType\nDenseBase<Derived>::Ones(Index newSize)\n{\n  return Constant(newSize, Scalar(1));\n}\n\n/** \\returns an expression of a fixed-size matrix or vector where all coefficients equal one.\n  *\n  * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you\n  * need to use the variants taking size arguments.\n  *\n  * Example: \\include MatrixBase_ones.cpp\n  * Output: \\verbinclude MatrixBase_ones.out\n  *\n  * \\sa Ones(Index), Ones(Index,Index), isOnes(), class Ones\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType\nDenseBase<Derived>::Ones()\n{\n  return Constant(Scalar(1));\n}\n\n/** \\returns true if *this is approximately equal to the matrix where all coefficients\n  *          are equal to 1, within the precision given by \\a prec.\n  *\n  * Example: \\include MatrixBase_isOnes.cpp\n  * Output: \\verbinclude MatrixBase_isOnes.out\n  *\n  * \\sa class CwiseNullaryOp, Ones()\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC bool DenseBase<Derived>::isOnes\n(const RealScalar& prec) const\n{\n  return isApproxToConstant(Scalar(1), prec);\n}\n\n/** Sets all coefficients in this expression to one.\n  *\n  * Example: \\include MatrixBase_setOnes.cpp\n  * Output: \\verbinclude MatrixBase_setOnes.out\n  *\n  * \\sa class CwiseNullaryOp, Ones()\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setOnes()\n{\n  return setConstant(Scalar(1));\n}\n\n/** Resizes to the given \\a newSize, and sets all coefficients in this expression to one.\n  *\n  * \\only_for_vectors\n  *\n  * Example: \\include Matrix_setOnes_int.cpp\n  * Output: \\verbinclude Matrix_setOnes_int.out\n  *\n  * \\sa MatrixBase::setOnes(), setOnes(Index,Index), class CwiseNullaryOp, MatrixBase::Ones()\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived&\nPlainObjectBase<Derived>::setOnes(Index newSize)\n{\n  resize(newSize);\n  return setConstant(Scalar(1));\n}\n\n/** Resizes to the given size, and sets all coefficients in this expression to one.\n  *\n  * \\param rows the new number of rows\n  * \\param cols the new number of columns\n  *\n  * Example: \\include Matrix_setOnes_int_int.cpp\n  * Output: \\verbinclude Matrix_setOnes_int_int.out\n  *\n  * \\sa MatrixBase::setOnes(), setOnes(Index), class CwiseNullaryOp, MatrixBase::Ones()\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived&\nPlainObjectBase<Derived>::setOnes(Index rows, Index cols)\n{\n  resize(rows, cols);\n  return setConstant(Scalar(1));\n}\n\n// Identity:\n\n/** \\returns an expression of the identity matrix (not necessarily square).\n  *\n  * The parameters \\a rows and \\a cols are the number of rows and of columns of\n  * the returned matrix. Must be compatible with this MatrixBase type.\n  *\n  * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,\n  * it is redundant to pass \\a rows and \\a cols as arguments, so Identity() should be used\n  * instead.\n  *\n  * Example: \\include MatrixBase_identity_int_int.cpp\n  * Output: \\verbinclude MatrixBase_identity_int_int.out\n  *\n  * \\sa Identity(), setIdentity(), isIdentity()\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::IdentityReturnType\nMatrixBase<Derived>::Identity(Index rows, Index cols)\n{\n  return DenseBase<Derived>::NullaryExpr(rows, cols, internal::scalar_identity_op<Scalar>());\n}\n\n/** \\returns an expression of the identity matrix (not necessarily square).\n  *\n  * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you\n  * need to use the variant taking size arguments.\n  *\n  * Example: \\include MatrixBase_identity.cpp\n  * Output: \\verbinclude MatrixBase_identity.out\n  *\n  * \\sa Identity(Index,Index), setIdentity(), isIdentity()\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::IdentityReturnType\nMatrixBase<Derived>::Identity()\n{\n  EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)\n  return MatrixBase<Derived>::NullaryExpr(RowsAtCompileTime, ColsAtCompileTime, internal::scalar_identity_op<Scalar>());\n}\n\n/** \\returns true if *this is approximately equal to the identity matrix\n  *          (not necessarily square),\n  *          within the precision given by \\a prec.\n  *\n  * Example: \\include MatrixBase_isIdentity.cpp\n  * Output: \\verbinclude MatrixBase_isIdentity.out\n  *\n  * \\sa class CwiseNullaryOp, Identity(), Identity(Index,Index), setIdentity()\n  */\ntemplate<typename Derived>\nbool MatrixBase<Derived>::isIdentity\n(const RealScalar& prec) const\n{\n  typename internal::nested_eval<Derived,1>::type self(derived());\n  for(Index j = 0; j < cols(); ++j)\n  {\n    for(Index i = 0; i < rows(); ++i)\n    {\n      if(i == j)\n      {\n        if(!internal::isApprox(self.coeff(i, j), static_cast<Scalar>(1), prec))\n          return false;\n      }\n      else\n      {\n        if(!internal::isMuchSmallerThan(self.coeff(i, j), static_cast<RealScalar>(1), prec))\n          return false;\n      }\n    }\n  }\n  return true;\n}\n\nnamespace internal {\n\ntemplate<typename Derived, bool Big = (Derived::SizeAtCompileTime>=16)>\nstruct setIdentity_impl\n{\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE Derived& run(Derived& m)\n  {\n    return m = Derived::Identity(m.rows(), m.cols());\n  }\n};\n\ntemplate<typename Derived>\nstruct setIdentity_impl<Derived, true>\n{\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE Derived& run(Derived& m)\n  {\n    m.setZero();\n    const Index size = numext::mini(m.rows(), m.cols());\n    for(Index i = 0; i < size; ++i) m.coeffRef(i,i) = typename Derived::Scalar(1);\n    return m;\n  }\n};\n\n} // end namespace internal\n\n/** Writes the identity expression (not necessarily square) into *this.\n  *\n  * Example: \\include MatrixBase_setIdentity.cpp\n  * Output: \\verbinclude MatrixBase_setIdentity.out\n  *\n  * \\sa class CwiseNullaryOp, Identity(), Identity(Index,Index), isIdentity()\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setIdentity()\n{\n  return internal::setIdentity_impl<Derived>::run(derived());\n}\n\n/** \\brief Resizes to the given size, and writes the identity expression (not necessarily square) into *this.\n  *\n  * \\param rows the new number of rows\n  * \\param cols the new number of columns\n  *\n  * Example: \\include Matrix_setIdentity_int_int.cpp\n  * Output: \\verbinclude Matrix_setIdentity_int_int.out\n  *\n  * \\sa MatrixBase::setIdentity(), class CwiseNullaryOp, MatrixBase::Identity()\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setIdentity(Index rows, Index cols)\n{\n  derived().resize(rows, cols);\n  return setIdentity();\n}\n\n/** \\returns an expression of the i-th unit (basis) vector.\n  *\n  * \\only_for_vectors\n  *\n  * \\sa MatrixBase::Unit(Index), MatrixBase::UnitX(), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::Unit(Index newSize, Index i)\n{\n  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)\n  return BasisReturnType(SquareMatrixType::Identity(newSize,newSize), i);\n}\n\n/** \\returns an expression of the i-th unit (basis) vector.\n  *\n  * \\only_for_vectors\n  *\n  * This variant is for fixed-size vector only.\n  *\n  * \\sa MatrixBase::Unit(Index,Index), MatrixBase::UnitX(), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::Unit(Index i)\n{\n  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)\n  return BasisReturnType(SquareMatrixType::Identity(),i);\n}\n\n/** \\returns an expression of the X axis unit vector (1{,0}^*)\n  *\n  * \\only_for_vectors\n  *\n  * \\sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitX()\n{ return Derived::Unit(0); }\n\n/** \\returns an expression of the Y axis unit vector (0,1{,0}^*)\n  *\n  * \\only_for_vectors\n  *\n  * \\sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitY()\n{ return Derived::Unit(1); }\n\n/** \\returns an expression of the Z axis unit vector (0,0,1{,0}^*)\n  *\n  * \\only_for_vectors\n  *\n  * \\sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitZ()\n{ return Derived::Unit(2); }\n\n/** \\returns an expression of the W axis unit vector (0,0,0,1)\n  *\n  * \\only_for_vectors\n  *\n  * \\sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitW()\n{ return Derived::Unit(3); }\n\n} // end namespace Eigen\n\n#endif // EIGEN_CWISE_NULLARY_OP_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/CwiseTernaryOp.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2016 Eugene Brevdo <ebrevdo@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CWISE_TERNARY_OP_H\n#define EIGEN_CWISE_TERNARY_OP_H\n\nnamespace Eigen {\n\nnamespace internal {\ntemplate <typename TernaryOp, typename Arg1, typename Arg2, typename Arg3>\nstruct traits<CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3> > {\n  // we must not inherit from traits<Arg1> since it has\n  // the potential to cause problems with MSVC\n  typedef typename remove_all<Arg1>::type Ancestor;\n  typedef typename traits<Ancestor>::XprKind XprKind;\n  enum {\n    RowsAtCompileTime = traits<Ancestor>::RowsAtCompileTime,\n    ColsAtCompileTime = traits<Ancestor>::ColsAtCompileTime,\n    MaxRowsAtCompileTime = traits<Ancestor>::MaxRowsAtCompileTime,\n    MaxColsAtCompileTime = traits<Ancestor>::MaxColsAtCompileTime\n  };\n\n  // even though we require Arg1, Arg2, and Arg3 to have the same scalar type\n  // (see CwiseTernaryOp constructor),\n  // we still want to handle the case when the result type is different.\n  typedef typename result_of<TernaryOp(\n      const typename Arg1::Scalar&, const typename Arg2::Scalar&,\n      const typename Arg3::Scalar&)>::type Scalar;\n\n  typedef typename internal::traits<Arg1>::StorageKind StorageKind;\n  typedef typename internal::traits<Arg1>::StorageIndex StorageIndex;\n\n  typedef typename Arg1::Nested Arg1Nested;\n  typedef typename Arg2::Nested Arg2Nested;\n  typedef typename Arg3::Nested Arg3Nested;\n  typedef typename remove_reference<Arg1Nested>::type _Arg1Nested;\n  typedef typename remove_reference<Arg2Nested>::type _Arg2Nested;\n  typedef typename remove_reference<Arg3Nested>::type _Arg3Nested;\n  enum { Flags = _Arg1Nested::Flags & RowMajorBit };\n};\n}  // end namespace internal\n\ntemplate <typename TernaryOp, typename Arg1, typename Arg2, typename Arg3,\n          typename StorageKind>\nclass CwiseTernaryOpImpl;\n\n/** \\class CwiseTernaryOp\n  * \\ingroup Core_Module\n  *\n  * \\brief Generic expression where a coefficient-wise ternary operator is\n * applied to two expressions\n  *\n  * \\tparam TernaryOp template functor implementing the operator\n  * \\tparam Arg1Type the type of the first argument\n  * \\tparam Arg2Type the type of the second argument\n  * \\tparam Arg3Type the type of the third argument\n  *\n  * This class represents an expression where a coefficient-wise ternary\n * operator is applied to three expressions.\n  * It is the return type of ternary operators, by which we mean only those\n * ternary operators where\n  * all three arguments are Eigen expressions.\n  * For example, the return type of betainc(matrix1, matrix2, matrix3) is a\n * CwiseTernaryOp.\n  *\n  * Most of the time, this is the only way that it is used, so you typically\n * don't have to name\n  * CwiseTernaryOp types explicitly.\n  *\n  * \\sa MatrixBase::ternaryExpr(const MatrixBase<Argument2> &, const\n * MatrixBase<Argument3> &, const CustomTernaryOp &) const, class CwiseBinaryOp,\n * class CwiseUnaryOp, class CwiseNullaryOp\n  */\ntemplate <typename TernaryOp, typename Arg1Type, typename Arg2Type,\n          typename Arg3Type>\nclass CwiseTernaryOp : public CwiseTernaryOpImpl<\n                           TernaryOp, Arg1Type, Arg2Type, Arg3Type,\n                           typename internal::traits<Arg1Type>::StorageKind>,\n                       internal::no_assignment_operator\n{\n public:\n  typedef typename internal::remove_all<Arg1Type>::type Arg1;\n  typedef typename internal::remove_all<Arg2Type>::type Arg2;\n  typedef typename internal::remove_all<Arg3Type>::type Arg3;\n\n  typedef typename CwiseTernaryOpImpl<\n      TernaryOp, Arg1Type, Arg2Type, Arg3Type,\n      typename internal::traits<Arg1Type>::StorageKind>::Base Base;\n  EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseTernaryOp)\n\n  typedef typename internal::ref_selector<Arg1Type>::type Arg1Nested;\n  typedef typename internal::ref_selector<Arg2Type>::type Arg2Nested;\n  typedef typename internal::ref_selector<Arg3Type>::type Arg3Nested;\n  typedef typename internal::remove_reference<Arg1Nested>::type _Arg1Nested;\n  typedef typename internal::remove_reference<Arg2Nested>::type _Arg2Nested;\n  typedef typename internal::remove_reference<Arg3Nested>::type _Arg3Nested;\n\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE CwiseTernaryOp(const Arg1& a1, const Arg2& a2,\n                                     const Arg3& a3,\n                                     const TernaryOp& func = TernaryOp())\n      : m_arg1(a1), m_arg2(a2), m_arg3(a3), m_functor(func) {\n    // require the sizes to match\n    EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Arg1, Arg2)\n    EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Arg1, Arg3)\n\n    // The index types should match\n    EIGEN_STATIC_ASSERT((internal::is_same<\n                         typename internal::traits<Arg1Type>::StorageKind,\n                         typename internal::traits<Arg2Type>::StorageKind>::value),\n                        STORAGE_KIND_MUST_MATCH)\n    EIGEN_STATIC_ASSERT((internal::is_same<\n                         typename internal::traits<Arg1Type>::StorageKind,\n                         typename internal::traits<Arg3Type>::StorageKind>::value),\n                        STORAGE_KIND_MUST_MATCH)\n\n    eigen_assert(a1.rows() == a2.rows() && a1.cols() == a2.cols() &&\n                 a1.rows() == a3.rows() && a1.cols() == a3.cols());\n  }\n\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE Index rows() const {\n    // return the fixed size type if available to enable compile time\n    // optimizations\n    if (internal::traits<typename internal::remove_all<Arg1Nested>::type>::\n                RowsAtCompileTime == Dynamic &&\n        internal::traits<typename internal::remove_all<Arg2Nested>::type>::\n                RowsAtCompileTime == Dynamic)\n      return m_arg3.rows();\n    else if (internal::traits<typename internal::remove_all<Arg1Nested>::type>::\n                     RowsAtCompileTime == Dynamic &&\n             internal::traits<typename internal::remove_all<Arg3Nested>::type>::\n                     RowsAtCompileTime == Dynamic)\n      return m_arg2.rows();\n    else\n      return m_arg1.rows();\n  }\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE Index cols() const {\n    // return the fixed size type if available to enable compile time\n    // optimizations\n    if (internal::traits<typename internal::remove_all<Arg1Nested>::type>::\n                ColsAtCompileTime == Dynamic &&\n        internal::traits<typename internal::remove_all<Arg2Nested>::type>::\n                ColsAtCompileTime == Dynamic)\n      return m_arg3.cols();\n    else if (internal::traits<typename internal::remove_all<Arg1Nested>::type>::\n                     ColsAtCompileTime == Dynamic &&\n             internal::traits<typename internal::remove_all<Arg3Nested>::type>::\n                     ColsAtCompileTime == Dynamic)\n      return m_arg2.cols();\n    else\n      return m_arg1.cols();\n  }\n\n  /** \\returns the first argument nested expression */\n  EIGEN_DEVICE_FUNC\n  const _Arg1Nested& arg1() const { return m_arg1; }\n  /** \\returns the first argument nested expression */\n  EIGEN_DEVICE_FUNC\n  const _Arg2Nested& arg2() const { return m_arg2; }\n  /** \\returns the third argument nested expression */\n  EIGEN_DEVICE_FUNC\n  const _Arg3Nested& arg3() const { return m_arg3; }\n  /** \\returns the functor representing the ternary operation */\n  EIGEN_DEVICE_FUNC\n  const TernaryOp& functor() const { return m_functor; }\n\n protected:\n  Arg1Nested m_arg1;\n  Arg2Nested m_arg2;\n  Arg3Nested m_arg3;\n  const TernaryOp m_functor;\n};\n\n// Generic API dispatcher\ntemplate <typename TernaryOp, typename Arg1, typename Arg2, typename Arg3,\n          typename StorageKind>\nclass CwiseTernaryOpImpl\n    : public internal::generic_xpr_base<\n          CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3> >::type {\n public:\n  typedef typename internal::generic_xpr_base<\n      CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3> >::type Base;\n};\n\n}  // end namespace Eigen\n\n#endif  // EIGEN_CWISE_TERNARY_OP_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/CwiseUnaryOp.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CWISE_UNARY_OP_H\n#define EIGEN_CWISE_UNARY_OP_H\n\nnamespace Eigen { \n\nnamespace internal {\ntemplate<typename UnaryOp, typename XprType>\nstruct traits<CwiseUnaryOp<UnaryOp, XprType> >\n : traits<XprType>\n{\n  typedef typename result_of<\n                     UnaryOp(const typename XprType::Scalar&)\n                   >::type Scalar;\n  typedef typename XprType::Nested XprTypeNested;\n  typedef typename remove_reference<XprTypeNested>::type _XprTypeNested;\n  enum {\n    Flags = _XprTypeNested::Flags & RowMajorBit \n  };\n};\n}\n\ntemplate<typename UnaryOp, typename XprType, typename StorageKind>\nclass CwiseUnaryOpImpl;\n\n/** \\class CwiseUnaryOp\n  * \\ingroup Core_Module\n  *\n  * \\brief Generic expression where a coefficient-wise unary operator is applied to an expression\n  *\n  * \\tparam UnaryOp template functor implementing the operator\n  * \\tparam XprType the type of the expression to which we are applying the unary operator\n  *\n  * This class represents an expression where a unary operator is applied to an expression.\n  * It is the return type of all operations taking exactly 1 input expression, regardless of the\n  * presence of other inputs such as scalars. For example, the operator* in the expression 3*matrix\n  * is considered unary, because only the right-hand side is an expression, and its\n  * return type is a specialization of CwiseUnaryOp.\n  *\n  * Most of the time, this is the only way that it is used, so you typically don't have to name\n  * CwiseUnaryOp types explicitly.\n  *\n  * \\sa MatrixBase::unaryExpr(const CustomUnaryOp &) const, class CwiseBinaryOp, class CwiseNullaryOp\n  */\ntemplate<typename UnaryOp, typename XprType>\nclass CwiseUnaryOp : public CwiseUnaryOpImpl<UnaryOp, XprType, typename internal::traits<XprType>::StorageKind>, internal::no_assignment_operator\n{\n  public:\n\n    typedef typename CwiseUnaryOpImpl<UnaryOp, XprType,typename internal::traits<XprType>::StorageKind>::Base Base;\n    EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseUnaryOp)\n    typedef typename internal::ref_selector<XprType>::type XprTypeNested;\n    typedef typename internal::remove_all<XprType>::type NestedExpression;\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    explicit CwiseUnaryOp(const XprType& xpr, const UnaryOp& func = UnaryOp())\n      : m_xpr(xpr), m_functor(func) {}\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    Index rows() const { return m_xpr.rows(); }\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    Index cols() const { return m_xpr.cols(); }\n\n    /** \\returns the functor representing the unary operation */\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const UnaryOp& functor() const { return m_functor; }\n\n    /** \\returns the nested expression */\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const typename internal::remove_all<XprTypeNested>::type&\n    nestedExpression() const { return m_xpr; }\n\n    /** \\returns the nested expression */\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    typename internal::remove_all<XprTypeNested>::type&\n    nestedExpression() { return m_xpr; }\n\n  protected:\n    XprTypeNested m_xpr;\n    const UnaryOp m_functor;\n};\n\n// Generic API dispatcher\ntemplate<typename UnaryOp, typename XprType, typename StorageKind>\nclass CwiseUnaryOpImpl\n  : public internal::generic_xpr_base<CwiseUnaryOp<UnaryOp, XprType> >::type\n{\npublic:\n  typedef typename internal::generic_xpr_base<CwiseUnaryOp<UnaryOp, XprType> >::type Base;\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_CWISE_UNARY_OP_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/CwiseUnaryView.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CWISE_UNARY_VIEW_H\n#define EIGEN_CWISE_UNARY_VIEW_H\n\nnamespace Eigen {\n\nnamespace internal {\ntemplate<typename ViewOp, typename MatrixType>\nstruct traits<CwiseUnaryView<ViewOp, MatrixType> >\n : traits<MatrixType>\n{\n  typedef typename result_of<\n                     ViewOp(const typename traits<MatrixType>::Scalar&)\n                   >::type Scalar;\n  typedef typename MatrixType::Nested MatrixTypeNested;\n  typedef typename remove_all<MatrixTypeNested>::type _MatrixTypeNested;\n  enum {\n    FlagsLvalueBit = is_lvalue<MatrixType>::value ? LvalueBit : 0,\n    Flags = traits<_MatrixTypeNested>::Flags & (RowMajorBit | FlagsLvalueBit | DirectAccessBit), // FIXME DirectAccessBit should not be handled by expressions\n    MatrixTypeInnerStride =  inner_stride_at_compile_time<MatrixType>::ret,\n    // need to cast the sizeof's from size_t to int explicitly, otherwise:\n    // \"error: no integral type can represent all of the enumerator values\n    InnerStrideAtCompileTime = MatrixTypeInnerStride == Dynamic\n                             ? int(Dynamic)\n                             : int(MatrixTypeInnerStride) * int(sizeof(typename traits<MatrixType>::Scalar) / sizeof(Scalar)),\n    OuterStrideAtCompileTime = outer_stride_at_compile_time<MatrixType>::ret == Dynamic\n                             ? int(Dynamic)\n                             : outer_stride_at_compile_time<MatrixType>::ret * int(sizeof(typename traits<MatrixType>::Scalar) / sizeof(Scalar))\n  };\n};\n}\n\ntemplate<typename ViewOp, typename MatrixType, typename StorageKind>\nclass CwiseUnaryViewImpl;\n\n/** \\class CwiseUnaryView\n  * \\ingroup Core_Module\n  *\n  * \\brief Generic lvalue expression of a coefficient-wise unary operator of a matrix or a vector\n  *\n  * \\tparam ViewOp template functor implementing the view\n  * \\tparam MatrixType the type of the matrix we are applying the unary operator\n  *\n  * This class represents a lvalue expression of a generic unary view operator of a matrix or a vector.\n  * It is the return type of real() and imag(), and most of the time this is the only way it is used.\n  *\n  * \\sa MatrixBase::unaryViewExpr(const CustomUnaryOp &) const, class CwiseUnaryOp\n  */\ntemplate<typename ViewOp, typename MatrixType>\nclass CwiseUnaryView : public CwiseUnaryViewImpl<ViewOp, MatrixType, typename internal::traits<MatrixType>::StorageKind>\n{\n  public:\n\n    typedef typename CwiseUnaryViewImpl<ViewOp, MatrixType,typename internal::traits<MatrixType>::StorageKind>::Base Base;\n    EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseUnaryView)\n    typedef typename internal::ref_selector<MatrixType>::non_const_type MatrixTypeNested;\n    typedef typename internal::remove_all<MatrixType>::type NestedExpression;\n\n    explicit inline CwiseUnaryView(MatrixType& mat, const ViewOp& func = ViewOp())\n      : m_matrix(mat), m_functor(func) {}\n\n    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(CwiseUnaryView)\n\n    EIGEN_STRONG_INLINE Index rows() const { return m_matrix.rows(); }\n    EIGEN_STRONG_INLINE Index cols() const { return m_matrix.cols(); }\n\n    /** \\returns the functor representing unary operation */\n    const ViewOp& functor() const { return m_functor; }\n\n    /** \\returns the nested expression */\n    const typename internal::remove_all<MatrixTypeNested>::type&\n    nestedExpression() const { return m_matrix; }\n\n    /** \\returns the nested expression */\n    typename internal::remove_reference<MatrixTypeNested>::type&\n    nestedExpression() { return m_matrix.const_cast_derived(); }\n\n  protected:\n    MatrixTypeNested m_matrix;\n    ViewOp m_functor;\n};\n\n// Generic API dispatcher\ntemplate<typename ViewOp, typename XprType, typename StorageKind>\nclass CwiseUnaryViewImpl\n  : public internal::generic_xpr_base<CwiseUnaryView<ViewOp, XprType> >::type\n{\npublic:\n  typedef typename internal::generic_xpr_base<CwiseUnaryView<ViewOp, XprType> >::type Base;\n};\n\ntemplate<typename ViewOp, typename MatrixType>\nclass CwiseUnaryViewImpl<ViewOp,MatrixType,Dense>\n  : public internal::dense_xpr_base< CwiseUnaryView<ViewOp, MatrixType> >::type\n{\n  public:\n\n    typedef CwiseUnaryView<ViewOp, MatrixType> Derived;\n    typedef typename internal::dense_xpr_base< CwiseUnaryView<ViewOp, MatrixType> >::type Base;\n\n    EIGEN_DENSE_PUBLIC_INTERFACE(Derived)\n    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(CwiseUnaryViewImpl)\n    \n    EIGEN_DEVICE_FUNC inline Scalar* data() { return &(this->coeffRef(0)); }\n    EIGEN_DEVICE_FUNC inline const Scalar* data() const { return &(this->coeff(0)); }\n\n    EIGEN_DEVICE_FUNC inline Index innerStride() const\n    {\n      return derived().nestedExpression().innerStride() * sizeof(typename internal::traits<MatrixType>::Scalar) / sizeof(Scalar);\n    }\n\n    EIGEN_DEVICE_FUNC inline Index outerStride() const\n    {\n      return derived().nestedExpression().outerStride() * sizeof(typename internal::traits<MatrixType>::Scalar) / sizeof(Scalar);\n    }\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_CWISE_UNARY_VIEW_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/DenseBase.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2007-2010 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_DENSEBASE_H\n#define EIGEN_DENSEBASE_H\n\nnamespace Eigen {\n\nnamespace internal {\n  \n// The index type defined by EIGEN_DEFAULT_DENSE_INDEX_TYPE must be a signed type.\n// This dummy function simply aims at checking that at compile time.\nstatic inline void check_DenseIndex_is_signed() {\n  EIGEN_STATIC_ASSERT(NumTraits<DenseIndex>::IsSigned,THE_INDEX_TYPE_MUST_BE_A_SIGNED_TYPE); \n}\n\n} // end namespace internal\n  \n/** \\class DenseBase\n  * \\ingroup Core_Module\n  *\n  * \\brief Base class for all dense matrices, vectors, and arrays\n  *\n  * This class is the base that is inherited by all dense objects (matrix, vector, arrays,\n  * and related expression types). The common Eigen API for dense objects is contained in this class.\n  *\n  * \\tparam Derived is the derived type, e.g., a matrix type or an expression.\n  *\n  * This class can be extended with the help of the plugin mechanism described on the page\n  * \\ref TopicCustomizing_Plugins by defining the preprocessor symbol \\c EIGEN_DENSEBASE_PLUGIN.\n  *\n  * \\sa \\blank \\ref TopicClassHierarchy\n  */\ntemplate<typename Derived> class DenseBase\n#ifndef EIGEN_PARSED_BY_DOXYGEN\n  : public DenseCoeffsBase<Derived>\n#else\n  : public DenseCoeffsBase<Derived,DirectWriteAccessors>\n#endif // not EIGEN_PARSED_BY_DOXYGEN\n{\n  public:\n\n    /** Inner iterator type to iterate over the coefficients of a row or column.\n      * \\sa class InnerIterator\n      */\n    typedef Eigen::InnerIterator<Derived> InnerIterator;\n\n    typedef typename internal::traits<Derived>::StorageKind StorageKind;\n\n    /**\n      * \\brief The type used to store indices\n      * \\details This typedef is relevant for types that store multiple indices such as\n      *          PermutationMatrix or Transpositions, otherwise it defaults to Eigen::Index\n      * \\sa \\blank \\ref TopicPreprocessorDirectives, Eigen::Index, SparseMatrixBase.\n     */\n    typedef typename internal::traits<Derived>::StorageIndex StorageIndex;\n\n    /** The numeric type of the expression' coefficients, e.g. float, double, int or std::complex<float>, etc. */\n    typedef typename internal::traits<Derived>::Scalar Scalar;\n    \n    /** The numeric type of the expression' coefficients, e.g. float, double, int or std::complex<float>, etc.\n      *\n      * It is an alias for the Scalar type */\n    typedef Scalar value_type;\n    \n    typedef typename NumTraits<Scalar>::Real RealScalar;\n    typedef DenseCoeffsBase<Derived> Base;\n\n    using Base::derived;\n    using Base::const_cast_derived;\n    using Base::rows;\n    using Base::cols;\n    using Base::size;\n    using Base::rowIndexByOuterInner;\n    using Base::colIndexByOuterInner;\n    using Base::coeff;\n    using Base::coeffByOuterInner;\n    using Base::operator();\n    using Base::operator[];\n    using Base::x;\n    using Base::y;\n    using Base::z;\n    using Base::w;\n    using Base::stride;\n    using Base::innerStride;\n    using Base::outerStride;\n    using Base::rowStride;\n    using Base::colStride;\n    typedef typename Base::CoeffReturnType CoeffReturnType;\n\n    enum {\n\n      RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,\n        /**< The number of rows at compile-time. This is just a copy of the value provided\n          * by the \\a Derived type. If a value is not known at compile-time,\n          * it is set to the \\a Dynamic constant.\n          * \\sa MatrixBase::rows(), MatrixBase::cols(), ColsAtCompileTime, SizeAtCompileTime */\n\n      ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,\n        /**< The number of columns at compile-time. This is just a copy of the value provided\n          * by the \\a Derived type. If a value is not known at compile-time,\n          * it is set to the \\a Dynamic constant.\n          * \\sa MatrixBase::rows(), MatrixBase::cols(), RowsAtCompileTime, SizeAtCompileTime */\n\n\n      SizeAtCompileTime = (internal::size_at_compile_time<internal::traits<Derived>::RowsAtCompileTime,\n                                                   internal::traits<Derived>::ColsAtCompileTime>::ret),\n        /**< This is equal to the number of coefficients, i.e. the number of\n          * rows times the number of columns, or to \\a Dynamic if this is not\n          * known at compile-time. \\sa RowsAtCompileTime, ColsAtCompileTime */\n\n      MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime,\n        /**< This value is equal to the maximum possible number of rows that this expression\n          * might have. If this expression might have an arbitrarily high number of rows,\n          * this value is set to \\a Dynamic.\n          *\n          * This value is useful to know when evaluating an expression, in order to determine\n          * whether it is possible to avoid doing a dynamic memory allocation.\n          *\n          * \\sa RowsAtCompileTime, MaxColsAtCompileTime, MaxSizeAtCompileTime\n          */\n\n      MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime,\n        /**< This value is equal to the maximum possible number of columns that this expression\n          * might have. If this expression might have an arbitrarily high number of columns,\n          * this value is set to \\a Dynamic.\n          *\n          * This value is useful to know when evaluating an expression, in order to determine\n          * whether it is possible to avoid doing a dynamic memory allocation.\n          *\n          * \\sa ColsAtCompileTime, MaxRowsAtCompileTime, MaxSizeAtCompileTime\n          */\n\n      MaxSizeAtCompileTime = (internal::size_at_compile_time<internal::traits<Derived>::MaxRowsAtCompileTime,\n                                                      internal::traits<Derived>::MaxColsAtCompileTime>::ret),\n        /**< This value is equal to the maximum possible number of coefficients that this expression\n          * might have. If this expression might have an arbitrarily high number of coefficients,\n          * this value is set to \\a Dynamic.\n          *\n          * This value is useful to know when evaluating an expression, in order to determine\n          * whether it is possible to avoid doing a dynamic memory allocation.\n          *\n          * \\sa SizeAtCompileTime, MaxRowsAtCompileTime, MaxColsAtCompileTime\n          */\n\n      IsVectorAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime == 1\n                           || internal::traits<Derived>::MaxColsAtCompileTime == 1,\n        /**< This is set to true if either the number of rows or the number of\n          * columns is known at compile-time to be equal to 1. Indeed, in that case,\n          * we are dealing with a column-vector (if there is only one column) or with\n          * a row-vector (if there is only one row). */\n\n      Flags = internal::traits<Derived>::Flags,\n        /**< This stores expression \\ref flags flags which may or may not be inherited by new expressions\n          * constructed from this one. See the \\ref flags \"list of flags\".\n          */\n\n      IsRowMajor = int(Flags) & RowMajorBit, /**< True if this expression has row-major storage order. */\n\n      InnerSizeAtCompileTime = int(IsVectorAtCompileTime) ? int(SizeAtCompileTime)\n                             : int(IsRowMajor) ? int(ColsAtCompileTime) : int(RowsAtCompileTime),\n\n      InnerStrideAtCompileTime = internal::inner_stride_at_compile_time<Derived>::ret,\n      OuterStrideAtCompileTime = internal::outer_stride_at_compile_time<Derived>::ret\n    };\n    \n    typedef typename internal::find_best_packet<Scalar,SizeAtCompileTime>::type PacketScalar;\n\n    enum { IsPlainObjectBase = 0 };\n    \n    /** The plain matrix type corresponding to this expression.\n      * \\sa PlainObject */\n    typedef Matrix<typename internal::traits<Derived>::Scalar,\n                internal::traits<Derived>::RowsAtCompileTime,\n                internal::traits<Derived>::ColsAtCompileTime,\n                AutoAlign | (internal::traits<Derived>::Flags&RowMajorBit ? RowMajor : ColMajor),\n                internal::traits<Derived>::MaxRowsAtCompileTime,\n                internal::traits<Derived>::MaxColsAtCompileTime\n          > PlainMatrix;\n    \n    /** The plain array type corresponding to this expression.\n      * \\sa PlainObject */\n    typedef Array<typename internal::traits<Derived>::Scalar,\n                internal::traits<Derived>::RowsAtCompileTime,\n                internal::traits<Derived>::ColsAtCompileTime,\n                AutoAlign | (internal::traits<Derived>::Flags&RowMajorBit ? RowMajor : ColMajor),\n                internal::traits<Derived>::MaxRowsAtCompileTime,\n                internal::traits<Derived>::MaxColsAtCompileTime\n          > PlainArray;\n\n    /** \\brief The plain matrix or array type corresponding to this expression.\n      *\n      * This is not necessarily exactly the return type of eval(). In the case of plain matrices,\n      * the return type of eval() is a const reference to a matrix, not a matrix! It is however guaranteed\n      * that the return type of eval() is either PlainObject or const PlainObject&.\n      */\n    typedef typename internal::conditional<internal::is_same<typename internal::traits<Derived>::XprKind,MatrixXpr >::value,\n                                 PlainMatrix, PlainArray>::type PlainObject;\n\n    /** \\returns the number of nonzero coefficients which is in practice the number\n      * of stored coefficients. */\n    EIGEN_DEVICE_FUNC\n    inline Index nonZeros() const { return size(); }\n\n    /** \\returns the outer size.\n      *\n      * \\note For a vector, this returns just 1. For a matrix (non-vector), this is the major dimension\n      * with respect to the \\ref TopicStorageOrders \"storage order\", i.e., the number of columns for a\n      * column-major matrix, and the number of rows for a row-major matrix. */\n    EIGEN_DEVICE_FUNC\n    Index outerSize() const\n    {\n      return IsVectorAtCompileTime ? 1\n           : int(IsRowMajor) ? this->rows() : this->cols();\n    }\n\n    /** \\returns the inner size.\n      *\n      * \\note For a vector, this is just the size. For a matrix (non-vector), this is the minor dimension\n      * with respect to the \\ref TopicStorageOrders \"storage order\", i.e., the number of rows for a \n      * column-major matrix, and the number of columns for a row-major matrix. */\n    EIGEN_DEVICE_FUNC\n    Index innerSize() const\n    {\n      return IsVectorAtCompileTime ? this->size()\n           : int(IsRowMajor) ? this->cols() : this->rows();\n    }\n\n    /** Only plain matrices/arrays, not expressions, may be resized; therefore the only useful resize methods are\n      * Matrix::resize() and Array::resize(). The present method only asserts that the new size equals the old size, and does\n      * nothing else.\n      */\n    EIGEN_DEVICE_FUNC\n    void resize(Index newSize)\n    {\n      EIGEN_ONLY_USED_FOR_DEBUG(newSize);\n      eigen_assert(newSize == this->size()\n                && \"DenseBase::resize() does not actually allow to resize.\");\n    }\n    /** Only plain matrices/arrays, not expressions, may be resized; therefore the only useful resize methods are\n      * Matrix::resize() and Array::resize(). The present method only asserts that the new size equals the old size, and does\n      * nothing else.\n      */\n    EIGEN_DEVICE_FUNC\n    void resize(Index rows, Index cols)\n    {\n      EIGEN_ONLY_USED_FOR_DEBUG(rows);\n      EIGEN_ONLY_USED_FOR_DEBUG(cols);\n      eigen_assert(rows == this->rows() && cols == this->cols()\n                && \"DenseBase::resize() does not actually allow to resize.\");\n    }\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\n    /** \\internal Represents a matrix with all coefficients equal to one another*/\n    typedef CwiseNullaryOp<internal::scalar_constant_op<Scalar>,PlainObject> ConstantReturnType;\n    /** \\internal \\deprecated Represents a vector with linearly spaced coefficients that allows sequential access only. */\n    typedef CwiseNullaryOp<internal::linspaced_op<Scalar,PacketScalar>,PlainObject> SequentialLinSpacedReturnType;\n    /** \\internal Represents a vector with linearly spaced coefficients that allows random access. */\n    typedef CwiseNullaryOp<internal::linspaced_op<Scalar,PacketScalar>,PlainObject> RandomAccessLinSpacedReturnType;\n    /** \\internal the return type of MatrixBase::eigenvalues() */\n    typedef Matrix<typename NumTraits<typename internal::traits<Derived>::Scalar>::Real, internal::traits<Derived>::ColsAtCompileTime, 1> EigenvaluesReturnType;\n\n#endif // not EIGEN_PARSED_BY_DOXYGEN\n\n    /** Copies \\a other into *this. \\returns a reference to *this. */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    Derived& operator=(const DenseBase<OtherDerived>& other);\n\n    /** Special case of the template operator=, in order to prevent the compiler\n      * from generating a default operator= (issue hit with g++ 4.1)\n      */\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    Derived& operator=(const DenseBase& other);\n\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    Derived& operator=(const EigenBase<OtherDerived> &other);\n\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    Derived& operator+=(const EigenBase<OtherDerived> &other);\n\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    Derived& operator-=(const EigenBase<OtherDerived> &other);\n\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    Derived& operator=(const ReturnByValue<OtherDerived>& func);\n\n    /** \\internal\n      * Copies \\a other into *this without evaluating other. \\returns a reference to *this.\n      * \\deprecated */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    Derived& lazyAssign(const DenseBase<OtherDerived>& other);\n\n    EIGEN_DEVICE_FUNC\n    CommaInitializer<Derived> operator<< (const Scalar& s);\n\n    /** \\deprecated it now returns \\c *this */\n    template<unsigned int Added,unsigned int Removed>\n    EIGEN_DEPRECATED\n    const Derived& flagged() const\n    { return derived(); }\n\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    CommaInitializer<Derived> operator<< (const DenseBase<OtherDerived>& other);\n\n    typedef Transpose<Derived> TransposeReturnType;\n    EIGEN_DEVICE_FUNC\n    TransposeReturnType transpose();\n    typedef typename internal::add_const<Transpose<const Derived> >::type ConstTransposeReturnType;\n    EIGEN_DEVICE_FUNC\n    ConstTransposeReturnType transpose() const;\n    EIGEN_DEVICE_FUNC\n    void transposeInPlace();\n\n    EIGEN_DEVICE_FUNC static const ConstantReturnType\n    Constant(Index rows, Index cols, const Scalar& value);\n    EIGEN_DEVICE_FUNC static const ConstantReturnType\n    Constant(Index size, const Scalar& value);\n    EIGEN_DEVICE_FUNC static const ConstantReturnType\n    Constant(const Scalar& value);\n\n    EIGEN_DEVICE_FUNC static const SequentialLinSpacedReturnType\n    LinSpaced(Sequential_t, Index size, const Scalar& low, const Scalar& high);\n    EIGEN_DEVICE_FUNC static const RandomAccessLinSpacedReturnType\n    LinSpaced(Index size, const Scalar& low, const Scalar& high);\n    EIGEN_DEVICE_FUNC static const SequentialLinSpacedReturnType\n    LinSpaced(Sequential_t, const Scalar& low, const Scalar& high);\n    EIGEN_DEVICE_FUNC static const RandomAccessLinSpacedReturnType\n    LinSpaced(const Scalar& low, const Scalar& high);\n\n    template<typename CustomNullaryOp> EIGEN_DEVICE_FUNC\n    static const CwiseNullaryOp<CustomNullaryOp, PlainObject>\n    NullaryExpr(Index rows, Index cols, const CustomNullaryOp& func);\n    template<typename CustomNullaryOp> EIGEN_DEVICE_FUNC\n    static const CwiseNullaryOp<CustomNullaryOp, PlainObject>\n    NullaryExpr(Index size, const CustomNullaryOp& func);\n    template<typename CustomNullaryOp> EIGEN_DEVICE_FUNC\n    static const CwiseNullaryOp<CustomNullaryOp, PlainObject>\n    NullaryExpr(const CustomNullaryOp& func);\n\n    EIGEN_DEVICE_FUNC static const ConstantReturnType Zero(Index rows, Index cols);\n    EIGEN_DEVICE_FUNC static const ConstantReturnType Zero(Index size);\n    EIGEN_DEVICE_FUNC static const ConstantReturnType Zero();\n    EIGEN_DEVICE_FUNC static const ConstantReturnType Ones(Index rows, Index cols);\n    EIGEN_DEVICE_FUNC static const ConstantReturnType Ones(Index size);\n    EIGEN_DEVICE_FUNC static const ConstantReturnType Ones();\n\n    EIGEN_DEVICE_FUNC void fill(const Scalar& value);\n    EIGEN_DEVICE_FUNC Derived& setConstant(const Scalar& value);\n    EIGEN_DEVICE_FUNC Derived& setLinSpaced(Index size, const Scalar& low, const Scalar& high);\n    EIGEN_DEVICE_FUNC Derived& setLinSpaced(const Scalar& low, const Scalar& high);\n    EIGEN_DEVICE_FUNC Derived& setZero();\n    EIGEN_DEVICE_FUNC Derived& setOnes();\n    EIGEN_DEVICE_FUNC Derived& setRandom();\n\n    template<typename OtherDerived> EIGEN_DEVICE_FUNC\n    bool isApprox(const DenseBase<OtherDerived>& other,\n                  const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;\n    EIGEN_DEVICE_FUNC \n    bool isMuchSmallerThan(const RealScalar& other,\n                           const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;\n    template<typename OtherDerived> EIGEN_DEVICE_FUNC\n    bool isMuchSmallerThan(const DenseBase<OtherDerived>& other,\n                           const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;\n\n    EIGEN_DEVICE_FUNC bool isApproxToConstant(const Scalar& value, const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;\n    EIGEN_DEVICE_FUNC bool isConstant(const Scalar& value, const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;\n    EIGEN_DEVICE_FUNC bool isZero(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;\n    EIGEN_DEVICE_FUNC bool isOnes(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;\n    \n    inline bool hasNaN() const;\n    inline bool allFinite() const;\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    Derived& operator*=(const Scalar& other);\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    Derived& operator/=(const Scalar& other);\n\n    typedef typename internal::add_const_on_value_type<typename internal::eval<Derived>::type>::type EvalReturnType;\n    /** \\returns the matrix or vector obtained by evaluating this expression.\n      *\n      * Notice that in the case of a plain matrix or vector (not an expression) this function just returns\n      * a const reference, in order to avoid a useless copy.\n      * \n      * \\warning Be carefull with eval() and the auto C++ keyword, as detailed in this \\link TopicPitfalls_auto_keyword page \\endlink.\n      */\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE EvalReturnType eval() const\n    {\n      // Even though MSVC does not honor strong inlining when the return type\n      // is a dynamic matrix, we desperately need strong inlining for fixed\n      // size types on MSVC.\n      return typename internal::eval<Derived>::type(derived());\n    }\n    \n    /** swaps *this with the expression \\a other.\n      *\n      */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    void swap(const DenseBase<OtherDerived>& other)\n    {\n      EIGEN_STATIC_ASSERT(!OtherDerived::IsPlainObjectBase,THIS_EXPRESSION_IS_NOT_A_LVALUE__IT_IS_READ_ONLY);\n      eigen_assert(rows()==other.rows() && cols()==other.cols());\n      call_assignment(derived(), other.const_cast_derived(), internal::swap_assign_op<Scalar>());\n    }\n\n    /** swaps *this with the matrix or array \\a other.\n      *\n      */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    void swap(PlainObjectBase<OtherDerived>& other)\n    {\n      eigen_assert(rows()==other.rows() && cols()==other.cols());\n      call_assignment(derived(), other.derived(), internal::swap_assign_op<Scalar>());\n    }\n\n    EIGEN_DEVICE_FUNC inline const NestByValue<Derived> nestByValue() const;\n    EIGEN_DEVICE_FUNC inline const ForceAlignedAccess<Derived> forceAlignedAccess() const;\n    EIGEN_DEVICE_FUNC inline ForceAlignedAccess<Derived> forceAlignedAccess();\n    template<bool Enable> EIGEN_DEVICE_FUNC\n    inline const typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type forceAlignedAccessIf() const;\n    template<bool Enable> EIGEN_DEVICE_FUNC\n    inline typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type forceAlignedAccessIf();\n\n    EIGEN_DEVICE_FUNC Scalar sum() const;\n    EIGEN_DEVICE_FUNC Scalar mean() const;\n    EIGEN_DEVICE_FUNC Scalar trace() const;\n\n    EIGEN_DEVICE_FUNC Scalar prod() const;\n\n    EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar minCoeff() const;\n    EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar maxCoeff() const;\n\n    template<typename IndexType> EIGEN_DEVICE_FUNC\n    typename internal::traits<Derived>::Scalar minCoeff(IndexType* row, IndexType* col) const;\n    template<typename IndexType> EIGEN_DEVICE_FUNC\n    typename internal::traits<Derived>::Scalar maxCoeff(IndexType* row, IndexType* col) const;\n    template<typename IndexType> EIGEN_DEVICE_FUNC\n    typename internal::traits<Derived>::Scalar minCoeff(IndexType* index) const;\n    template<typename IndexType> EIGEN_DEVICE_FUNC\n    typename internal::traits<Derived>::Scalar maxCoeff(IndexType* index) const;\n\n    template<typename BinaryOp>\n    EIGEN_DEVICE_FUNC\n    Scalar redux(const BinaryOp& func) const;\n\n    template<typename Visitor>\n    EIGEN_DEVICE_FUNC\n    void visit(Visitor& func) const;\n\n    /** \\returns a WithFormat proxy object allowing to print a matrix the with given\n      * format \\a fmt.\n      *\n      * See class IOFormat for some examples.\n      *\n      * \\sa class IOFormat, class WithFormat\n      */\n    inline const WithFormat<Derived> format(const IOFormat& fmt) const\n    {\n      return WithFormat<Derived>(derived(), fmt);\n    }\n\n    /** \\returns the unique coefficient of a 1x1 expression */\n    EIGEN_DEVICE_FUNC\n    CoeffReturnType value() const\n    {\n      EIGEN_STATIC_ASSERT_SIZE_1x1(Derived)\n      eigen_assert(this->rows() == 1 && this->cols() == 1);\n      return derived().coeff(0,0);\n    }\n\n    EIGEN_DEVICE_FUNC bool all() const;\n    EIGEN_DEVICE_FUNC bool any() const;\n    EIGEN_DEVICE_FUNC Index count() const;\n\n    typedef VectorwiseOp<Derived, Horizontal> RowwiseReturnType;\n    typedef const VectorwiseOp<const Derived, Horizontal> ConstRowwiseReturnType;\n    typedef VectorwiseOp<Derived, Vertical> ColwiseReturnType;\n    typedef const VectorwiseOp<const Derived, Vertical> ConstColwiseReturnType;\n\n    /** \\returns a VectorwiseOp wrapper of *this providing additional partial reduction operations\n    *\n    * Example: \\include MatrixBase_rowwise.cpp\n    * Output: \\verbinclude MatrixBase_rowwise.out\n    *\n    * \\sa colwise(), class VectorwiseOp, \\ref TutorialReductionsVisitorsBroadcasting\n    */\n    //Code moved here due to a CUDA compiler bug\n    EIGEN_DEVICE_FUNC inline ConstRowwiseReturnType rowwise() const {\n      return ConstRowwiseReturnType(derived());\n    }\n    EIGEN_DEVICE_FUNC RowwiseReturnType rowwise();\n\n    /** \\returns a VectorwiseOp wrapper of *this providing additional partial reduction operations\n    *\n    * Example: \\include MatrixBase_colwise.cpp\n    * Output: \\verbinclude MatrixBase_colwise.out\n    *\n    * \\sa rowwise(), class VectorwiseOp, \\ref TutorialReductionsVisitorsBroadcasting\n    */\n    EIGEN_DEVICE_FUNC inline ConstColwiseReturnType colwise() const {\n      return ConstColwiseReturnType(derived());\n    }\n    EIGEN_DEVICE_FUNC ColwiseReturnType colwise();\n\n    typedef CwiseNullaryOp<internal::scalar_random_op<Scalar>,PlainObject> RandomReturnType;\n    static const RandomReturnType Random(Index rows, Index cols);\n    static const RandomReturnType Random(Index size);\n    static const RandomReturnType Random();\n\n    template<typename ThenDerived,typename ElseDerived>\n    const Select<Derived,ThenDerived,ElseDerived>\n    select(const DenseBase<ThenDerived>& thenMatrix,\n           const DenseBase<ElseDerived>& elseMatrix) const;\n\n    template<typename ThenDerived>\n    inline const Select<Derived,ThenDerived, typename ThenDerived::ConstantReturnType>\n    select(const DenseBase<ThenDerived>& thenMatrix, const typename ThenDerived::Scalar& elseScalar) const;\n\n    template<typename ElseDerived>\n    inline const Select<Derived, typename ElseDerived::ConstantReturnType, ElseDerived >\n    select(const typename ElseDerived::Scalar& thenScalar, const DenseBase<ElseDerived>& elseMatrix) const;\n\n    template<int p> RealScalar lpNorm() const;\n\n    template<int RowFactor, int ColFactor>\n    EIGEN_DEVICE_FUNC\n    const Replicate<Derived,RowFactor,ColFactor> replicate() const;\n    /**\n    * \\return an expression of the replication of \\c *this\n    *\n    * Example: \\include MatrixBase_replicate_int_int.cpp\n    * Output: \\verbinclude MatrixBase_replicate_int_int.out\n    *\n    * \\sa VectorwiseOp::replicate(), DenseBase::replicate<int,int>(), class Replicate\n    */\n    //Code moved here due to a CUDA compiler bug\n    EIGEN_DEVICE_FUNC\n    const Replicate<Derived, Dynamic, Dynamic> replicate(Index rowFactor, Index colFactor) const\n    {\n      return Replicate<Derived, Dynamic, Dynamic>(derived(), rowFactor, colFactor);\n    }\n\n    typedef Reverse<Derived, BothDirections> ReverseReturnType;\n    typedef const Reverse<const Derived, BothDirections> ConstReverseReturnType;\n    EIGEN_DEVICE_FUNC ReverseReturnType reverse();\n    /** This is the const version of reverse(). */\n    //Code moved here due to a CUDA compiler bug\n    EIGEN_DEVICE_FUNC ConstReverseReturnType reverse() const\n    {\n      return ConstReverseReturnType(derived());\n    }\n    EIGEN_DEVICE_FUNC void reverseInPlace();\n\n#define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::DenseBase\n#define EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL\n#define EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(COND)\n#   include \"../plugins/BlockMethods.h\"\n#   ifdef EIGEN_DENSEBASE_PLUGIN\n#     include EIGEN_DENSEBASE_PLUGIN\n#   endif\n#undef EIGEN_CURRENT_STORAGE_BASE_CLASS\n#undef EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL\n#undef EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF\n\n    // disable the use of evalTo for dense objects with a nice compilation error\n    template<typename Dest>\n    EIGEN_DEVICE_FUNC\n    inline void evalTo(Dest& ) const\n    {\n      EIGEN_STATIC_ASSERT((internal::is_same<Dest,void>::value),THE_EVAL_EVALTO_FUNCTION_SHOULD_NEVER_BE_CALLED_FOR_DENSE_OBJECTS);\n    }\n\n  protected:\n    /** Default constructor. Do nothing. */\n    EIGEN_DEVICE_FUNC DenseBase()\n    {\n      /* Just checks for self-consistency of the flags.\n       * Only do it when debugging Eigen, as this borders on paranoiac and could slow compilation down\n       */\n#ifdef EIGEN_INTERNAL_DEBUGGING\n      EIGEN_STATIC_ASSERT((EIGEN_IMPLIES(MaxRowsAtCompileTime==1 && MaxColsAtCompileTime!=1, int(IsRowMajor))\n                        && EIGEN_IMPLIES(MaxColsAtCompileTime==1 && MaxRowsAtCompileTime!=1, int(!IsRowMajor))),\n                          INVALID_STORAGE_ORDER_FOR_THIS_VECTOR_EXPRESSION)\n#endif\n    }\n\n  private:\n    EIGEN_DEVICE_FUNC explicit DenseBase(int);\n    EIGEN_DEVICE_FUNC DenseBase(int,int);\n    template<typename OtherDerived> EIGEN_DEVICE_FUNC explicit DenseBase(const DenseBase<OtherDerived>&);\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_DENSEBASE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/DenseCoeffsBase.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_DENSECOEFFSBASE_H\n#define EIGEN_DENSECOEFFSBASE_H\n\nnamespace Eigen {\n\nnamespace internal {\ntemplate<typename T> struct add_const_on_value_type_if_arithmetic\n{\n  typedef typename conditional<is_arithmetic<T>::value, T, typename add_const_on_value_type<T>::type>::type type;\n};\n}\n\n/** \\brief Base class providing read-only coefficient access to matrices and arrays.\n  * \\ingroup Core_Module\n  * \\tparam Derived Type of the derived class\n  * \\tparam #ReadOnlyAccessors Constant indicating read-only access\n  *\n  * This class defines the \\c operator() \\c const function and friends, which can be used to read specific\n  * entries of a matrix or array.\n  * \n  * \\sa DenseCoeffsBase<Derived, WriteAccessors>, DenseCoeffsBase<Derived, DirectAccessors>,\n  *     \\ref TopicClassHierarchy\n  */\ntemplate<typename Derived>\nclass DenseCoeffsBase<Derived,ReadOnlyAccessors> : public EigenBase<Derived>\n{\n  public:\n    typedef typename internal::traits<Derived>::StorageKind StorageKind;\n    typedef typename internal::traits<Derived>::Scalar Scalar;\n    typedef typename internal::packet_traits<Scalar>::type PacketScalar;\n\n    // Explanation for this CoeffReturnType typedef.\n    // - This is the return type of the coeff() method.\n    // - The LvalueBit means exactly that we can offer a coeffRef() method, which means exactly that we can get references\n    // to coeffs, which means exactly that we can have coeff() return a const reference (as opposed to returning a value).\n    // - The is_artihmetic check is required since \"const int\", \"const double\", etc. will cause warnings on some systems\n    // while the declaration of \"const T\", where T is a non arithmetic type does not. Always returning \"const Scalar&\" is\n    // not possible, since the underlying expressions might not offer a valid address the reference could be referring to.\n    typedef typename internal::conditional<bool(internal::traits<Derived>::Flags&LvalueBit),\n                         const Scalar&,\n                         typename internal::conditional<internal::is_arithmetic<Scalar>::value, Scalar, const Scalar>::type\n                     >::type CoeffReturnType;\n\n    typedef typename internal::add_const_on_value_type_if_arithmetic<\n                         typename internal::packet_traits<Scalar>::type\n                     >::type PacketReturnType;\n\n    typedef EigenBase<Derived> Base;\n    using Base::rows;\n    using Base::cols;\n    using Base::size;\n    using Base::derived;\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Index rowIndexByOuterInner(Index outer, Index inner) const\n    {\n      return int(Derived::RowsAtCompileTime) == 1 ? 0\n          : int(Derived::ColsAtCompileTime) == 1 ? inner\n          : int(Derived::Flags)&RowMajorBit ? outer\n          : inner;\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Index colIndexByOuterInner(Index outer, Index inner) const\n    {\n      return int(Derived::ColsAtCompileTime) == 1 ? 0\n          : int(Derived::RowsAtCompileTime) == 1 ? inner\n          : int(Derived::Flags)&RowMajorBit ? inner\n          : outer;\n    }\n\n    /** Short version: don't use this function, use\n      * \\link operator()(Index,Index) const \\endlink instead.\n      *\n      * Long version: this function is similar to\n      * \\link operator()(Index,Index) const \\endlink, but without the assertion.\n      * Use this for limiting the performance cost of debugging code when doing\n      * repeated coefficient access. Only use this when it is guaranteed that the\n      * parameters \\a row and \\a col are in range.\n      *\n      * If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this\n      * function equivalent to \\link operator()(Index,Index) const \\endlink.\n      *\n      * \\sa operator()(Index,Index) const, coeffRef(Index,Index), coeff(Index) const\n      */\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE CoeffReturnType coeff(Index row, Index col) const\n    {\n      eigen_internal_assert(row >= 0 && row < rows()\n                         && col >= 0 && col < cols());\n      return internal::evaluator<Derived>(derived()).coeff(row,col);\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE CoeffReturnType coeffByOuterInner(Index outer, Index inner) const\n    {\n      return coeff(rowIndexByOuterInner(outer, inner),\n                   colIndexByOuterInner(outer, inner));\n    }\n\n    /** \\returns the coefficient at given the given row and column.\n      *\n      * \\sa operator()(Index,Index), operator[](Index)\n      */\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE CoeffReturnType operator()(Index row, Index col) const\n    {\n      eigen_assert(row >= 0 && row < rows()\n          && col >= 0 && col < cols());\n      return coeff(row, col);\n    }\n\n    /** Short version: don't use this function, use\n      * \\link operator[](Index) const \\endlink instead.\n      *\n      * Long version: this function is similar to\n      * \\link operator[](Index) const \\endlink, but without the assertion.\n      * Use this for limiting the performance cost of debugging code when doing\n      * repeated coefficient access. Only use this when it is guaranteed that the\n      * parameter \\a index is in range.\n      *\n      * If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this\n      * function equivalent to \\link operator[](Index) const \\endlink.\n      *\n      * \\sa operator[](Index) const, coeffRef(Index), coeff(Index,Index) const\n      */\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE CoeffReturnType\n    coeff(Index index) const\n    {\n      EIGEN_STATIC_ASSERT(internal::evaluator<Derived>::Flags & LinearAccessBit,\n                          THIS_COEFFICIENT_ACCESSOR_TAKING_ONE_ACCESS_IS_ONLY_FOR_EXPRESSIONS_ALLOWING_LINEAR_ACCESS)\n      eigen_internal_assert(index >= 0 && index < size());\n      return internal::evaluator<Derived>(derived()).coeff(index);\n    }\n\n\n    /** \\returns the coefficient at given index.\n      *\n      * This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.\n      *\n      * \\sa operator[](Index), operator()(Index,Index) const, x() const, y() const,\n      * z() const, w() const\n      */\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE CoeffReturnType\n    operator[](Index index) const\n    {\n      EIGEN_STATIC_ASSERT(Derived::IsVectorAtCompileTime,\n                          THE_BRACKET_OPERATOR_IS_ONLY_FOR_VECTORS__USE_THE_PARENTHESIS_OPERATOR_INSTEAD)\n      eigen_assert(index >= 0 && index < size());\n      return coeff(index);\n    }\n\n    /** \\returns the coefficient at given index.\n      *\n      * This is synonymous to operator[](Index) const.\n      *\n      * This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.\n      *\n      * \\sa operator[](Index), operator()(Index,Index) const, x() const, y() const,\n      * z() const, w() const\n      */\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE CoeffReturnType\n    operator()(Index index) const\n    {\n      eigen_assert(index >= 0 && index < size());\n      return coeff(index);\n    }\n\n    /** equivalent to operator[](0).  */\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE CoeffReturnType\n    x() const { return (*this)[0]; }\n\n    /** equivalent to operator[](1).  */\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE CoeffReturnType\n    y() const\n    {\n      EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=2, OUT_OF_RANGE_ACCESS);\n      return (*this)[1];\n    }\n\n    /** equivalent to operator[](2).  */\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE CoeffReturnType\n    z() const\n    {\n      EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=3, OUT_OF_RANGE_ACCESS);\n      return (*this)[2];\n    }\n\n    /** equivalent to operator[](3).  */\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE CoeffReturnType\n    w() const\n    {\n      EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=4, OUT_OF_RANGE_ACCESS);\n      return (*this)[3];\n    }\n\n    /** \\internal\n      * \\returns the packet of coefficients starting at the given row and column. It is your responsibility\n      * to ensure that a packet really starts there. This method is only available on expressions having the\n      * PacketAccessBit.\n      *\n      * The \\a LoadMode parameter may have the value \\a #Aligned or \\a #Unaligned. Its effect is to select\n      * the appropriate vectorization instruction. Aligned access is faster, but is only possible for packets\n      * starting at an address which is a multiple of the packet size.\n      */\n\n    template<int LoadMode>\n    EIGEN_STRONG_INLINE PacketReturnType packet(Index row, Index col) const\n    {\n      typedef typename internal::packet_traits<Scalar>::type DefaultPacketType;\n      eigen_internal_assert(row >= 0 && row < rows() && col >= 0 && col < cols());\n      return internal::evaluator<Derived>(derived()).template packet<LoadMode,DefaultPacketType>(row,col);\n    }\n\n\n    /** \\internal */\n    template<int LoadMode>\n    EIGEN_STRONG_INLINE PacketReturnType packetByOuterInner(Index outer, Index inner) const\n    {\n      return packet<LoadMode>(rowIndexByOuterInner(outer, inner),\n                              colIndexByOuterInner(outer, inner));\n    }\n\n    /** \\internal\n      * \\returns the packet of coefficients starting at the given index. It is your responsibility\n      * to ensure that a packet really starts there. This method is only available on expressions having the\n      * PacketAccessBit and the LinearAccessBit.\n      *\n      * The \\a LoadMode parameter may have the value \\a #Aligned or \\a #Unaligned. Its effect is to select\n      * the appropriate vectorization instruction. Aligned access is faster, but is only possible for packets\n      * starting at an address which is a multiple of the packet size.\n      */\n\n    template<int LoadMode>\n    EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const\n    {\n      EIGEN_STATIC_ASSERT(internal::evaluator<Derived>::Flags & LinearAccessBit,\n                          THIS_COEFFICIENT_ACCESSOR_TAKING_ONE_ACCESS_IS_ONLY_FOR_EXPRESSIONS_ALLOWING_LINEAR_ACCESS)\n      typedef typename internal::packet_traits<Scalar>::type DefaultPacketType;\n      eigen_internal_assert(index >= 0 && index < size());\n      return internal::evaluator<Derived>(derived()).template packet<LoadMode,DefaultPacketType>(index);\n    }\n\n  protected:\n    // explanation: DenseBase is doing \"using ...\" on the methods from DenseCoeffsBase.\n    // But some methods are only available in the DirectAccess case.\n    // So we add dummy methods here with these names, so that \"using... \" doesn't fail.\n    // It's not private so that the child class DenseBase can access them, and it's not public\n    // either since it's an implementation detail, so has to be protected.\n    void coeffRef();\n    void coeffRefByOuterInner();\n    void writePacket();\n    void writePacketByOuterInner();\n    void copyCoeff();\n    void copyCoeffByOuterInner();\n    void copyPacket();\n    void copyPacketByOuterInner();\n    void stride();\n    void innerStride();\n    void outerStride();\n    void rowStride();\n    void colStride();\n};\n\n/** \\brief Base class providing read/write coefficient access to matrices and arrays.\n  * \\ingroup Core_Module\n  * \\tparam Derived Type of the derived class\n  * \\tparam #WriteAccessors Constant indicating read/write access\n  *\n  * This class defines the non-const \\c operator() function and friends, which can be used to write specific\n  * entries of a matrix or array. This class inherits DenseCoeffsBase<Derived, ReadOnlyAccessors> which\n  * defines the const variant for reading specific entries.\n  * \n  * \\sa DenseCoeffsBase<Derived, DirectAccessors>, \\ref TopicClassHierarchy\n  */\ntemplate<typename Derived>\nclass DenseCoeffsBase<Derived, WriteAccessors> : public DenseCoeffsBase<Derived, ReadOnlyAccessors>\n{\n  public:\n\n    typedef DenseCoeffsBase<Derived, ReadOnlyAccessors> Base;\n\n    typedef typename internal::traits<Derived>::StorageKind StorageKind;\n    typedef typename internal::traits<Derived>::Scalar Scalar;\n    typedef typename internal::packet_traits<Scalar>::type PacketScalar;\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n\n    using Base::coeff;\n    using Base::rows;\n    using Base::cols;\n    using Base::size;\n    using Base::derived;\n    using Base::rowIndexByOuterInner;\n    using Base::colIndexByOuterInner;\n    using Base::operator[];\n    using Base::operator();\n    using Base::x;\n    using Base::y;\n    using Base::z;\n    using Base::w;\n\n    /** Short version: don't use this function, use\n      * \\link operator()(Index,Index) \\endlink instead.\n      *\n      * Long version: this function is similar to\n      * \\link operator()(Index,Index) \\endlink, but without the assertion.\n      * Use this for limiting the performance cost of debugging code when doing\n      * repeated coefficient access. Only use this when it is guaranteed that the\n      * parameters \\a row and \\a col are in range.\n      *\n      * If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this\n      * function equivalent to \\link operator()(Index,Index) \\endlink.\n      *\n      * \\sa operator()(Index,Index), coeff(Index, Index) const, coeffRef(Index)\n      */\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar& coeffRef(Index row, Index col)\n    {\n      eigen_internal_assert(row >= 0 && row < rows()\n                         && col >= 0 && col < cols());\n      return internal::evaluator<Derived>(derived()).coeffRef(row,col);\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar&\n    coeffRefByOuterInner(Index outer, Index inner)\n    {\n      return coeffRef(rowIndexByOuterInner(outer, inner),\n                      colIndexByOuterInner(outer, inner));\n    }\n\n    /** \\returns a reference to the coefficient at given the given row and column.\n      *\n      * \\sa operator[](Index)\n      */\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar&\n    operator()(Index row, Index col)\n    {\n      eigen_assert(row >= 0 && row < rows()\n          && col >= 0 && col < cols());\n      return coeffRef(row, col);\n    }\n\n\n    /** Short version: don't use this function, use\n      * \\link operator[](Index) \\endlink instead.\n      *\n      * Long version: this function is similar to\n      * \\link operator[](Index) \\endlink, but without the assertion.\n      * Use this for limiting the performance cost of debugging code when doing\n      * repeated coefficient access. Only use this when it is guaranteed that the\n      * parameters \\a row and \\a col are in range.\n      *\n      * If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this\n      * function equivalent to \\link operator[](Index) \\endlink.\n      *\n      * \\sa operator[](Index), coeff(Index) const, coeffRef(Index,Index)\n      */\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar&\n    coeffRef(Index index)\n    {\n      EIGEN_STATIC_ASSERT(internal::evaluator<Derived>::Flags & LinearAccessBit,\n                          THIS_COEFFICIENT_ACCESSOR_TAKING_ONE_ACCESS_IS_ONLY_FOR_EXPRESSIONS_ALLOWING_LINEAR_ACCESS)\n      eigen_internal_assert(index >= 0 && index < size());\n      return internal::evaluator<Derived>(derived()).coeffRef(index);\n    }\n\n    /** \\returns a reference to the coefficient at given index.\n      *\n      * This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.\n      *\n      * \\sa operator[](Index) const, operator()(Index,Index), x(), y(), z(), w()\n      */\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar&\n    operator[](Index index)\n    {\n      EIGEN_STATIC_ASSERT(Derived::IsVectorAtCompileTime,\n                          THE_BRACKET_OPERATOR_IS_ONLY_FOR_VECTORS__USE_THE_PARENTHESIS_OPERATOR_INSTEAD)\n      eigen_assert(index >= 0 && index < size());\n      return coeffRef(index);\n    }\n\n    /** \\returns a reference to the coefficient at given index.\n      *\n      * This is synonymous to operator[](Index).\n      *\n      * This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.\n      *\n      * \\sa operator[](Index) const, operator()(Index,Index), x(), y(), z(), w()\n      */\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar&\n    operator()(Index index)\n    {\n      eigen_assert(index >= 0 && index < size());\n      return coeffRef(index);\n    }\n\n    /** equivalent to operator[](0).  */\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar&\n    x() { return (*this)[0]; }\n\n    /** equivalent to operator[](1).  */\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar&\n    y()\n    {\n      EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=2, OUT_OF_RANGE_ACCESS);\n      return (*this)[1];\n    }\n\n    /** equivalent to operator[](2).  */\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar&\n    z()\n    {\n      EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=3, OUT_OF_RANGE_ACCESS);\n      return (*this)[2];\n    }\n\n    /** equivalent to operator[](3).  */\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar&\n    w()\n    {\n      EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=4, OUT_OF_RANGE_ACCESS);\n      return (*this)[3];\n    }\n};\n\n/** \\brief Base class providing direct read-only coefficient access to matrices and arrays.\n  * \\ingroup Core_Module\n  * \\tparam Derived Type of the derived class\n  * \\tparam #DirectAccessors Constant indicating direct access\n  *\n  * This class defines functions to work with strides which can be used to access entries directly. This class\n  * inherits DenseCoeffsBase<Derived, ReadOnlyAccessors> which defines functions to access entries read-only using\n  * \\c operator() .\n  *\n  * \\sa \\blank \\ref TopicClassHierarchy\n  */\ntemplate<typename Derived>\nclass DenseCoeffsBase<Derived, DirectAccessors> : public DenseCoeffsBase<Derived, ReadOnlyAccessors>\n{\n  public:\n\n    typedef DenseCoeffsBase<Derived, ReadOnlyAccessors> Base;\n    typedef typename internal::traits<Derived>::Scalar Scalar;\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n\n    using Base::rows;\n    using Base::cols;\n    using Base::size;\n    using Base::derived;\n\n    /** \\returns the pointer increment between two consecutive elements within a slice in the inner direction.\n      *\n      * \\sa outerStride(), rowStride(), colStride()\n      */\n    EIGEN_DEVICE_FUNC\n    inline Index innerStride() const\n    {\n      return derived().innerStride();\n    }\n\n    /** \\returns the pointer increment between two consecutive inner slices (for example, between two consecutive columns\n      *          in a column-major matrix).\n      *\n      * \\sa innerStride(), rowStride(), colStride()\n      */\n    EIGEN_DEVICE_FUNC\n    inline Index outerStride() const\n    {\n      return derived().outerStride();\n    }\n\n    // FIXME shall we remove it ?\n    inline Index stride() const\n    {\n      return Derived::IsVectorAtCompileTime ? innerStride() : outerStride();\n    }\n\n    /** \\returns the pointer increment between two consecutive rows.\n      *\n      * \\sa innerStride(), outerStride(), colStride()\n      */\n    EIGEN_DEVICE_FUNC\n    inline Index rowStride() const\n    {\n      return Derived::IsRowMajor ? outerStride() : innerStride();\n    }\n\n    /** \\returns the pointer increment between two consecutive columns.\n      *\n      * \\sa innerStride(), outerStride(), rowStride()\n      */\n    EIGEN_DEVICE_FUNC\n    inline Index colStride() const\n    {\n      return Derived::IsRowMajor ? innerStride() : outerStride();\n    }\n};\n\n/** \\brief Base class providing direct read/write coefficient access to matrices and arrays.\n  * \\ingroup Core_Module\n  * \\tparam Derived Type of the derived class\n  * \\tparam #DirectWriteAccessors Constant indicating direct access\n  *\n  * This class defines functions to work with strides which can be used to access entries directly. This class\n  * inherits DenseCoeffsBase<Derived, WriteAccessors> which defines functions to access entries read/write using\n  * \\c operator().\n  *\n  * \\sa \\blank \\ref TopicClassHierarchy\n  */\ntemplate<typename Derived>\nclass DenseCoeffsBase<Derived, DirectWriteAccessors>\n  : public DenseCoeffsBase<Derived, WriteAccessors>\n{\n  public:\n\n    typedef DenseCoeffsBase<Derived, WriteAccessors> Base;\n    typedef typename internal::traits<Derived>::Scalar Scalar;\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n\n    using Base::rows;\n    using Base::cols;\n    using Base::size;\n    using Base::derived;\n\n    /** \\returns the pointer increment between two consecutive elements within a slice in the inner direction.\n      *\n      * \\sa outerStride(), rowStride(), colStride()\n      */\n    EIGEN_DEVICE_FUNC\n    inline Index innerStride() const\n    {\n      return derived().innerStride();\n    }\n\n    /** \\returns the pointer increment between two consecutive inner slices (for example, between two consecutive columns\n      *          in a column-major matrix).\n      *\n      * \\sa innerStride(), rowStride(), colStride()\n      */\n    EIGEN_DEVICE_FUNC\n    inline Index outerStride() const\n    {\n      return derived().outerStride();\n    }\n\n    // FIXME shall we remove it ?\n    inline Index stride() const\n    {\n      return Derived::IsVectorAtCompileTime ? innerStride() : outerStride();\n    }\n\n    /** \\returns the pointer increment between two consecutive rows.\n      *\n      * \\sa innerStride(), outerStride(), colStride()\n      */\n    EIGEN_DEVICE_FUNC\n    inline Index rowStride() const\n    {\n      return Derived::IsRowMajor ? outerStride() : innerStride();\n    }\n\n    /** \\returns the pointer increment between two consecutive columns.\n      *\n      * \\sa innerStride(), outerStride(), rowStride()\n      */\n    EIGEN_DEVICE_FUNC\n    inline Index colStride() const\n    {\n      return Derived::IsRowMajor ? innerStride() : outerStride();\n    }\n};\n\nnamespace internal {\n\ntemplate<int Alignment, typename Derived, bool JustReturnZero>\nstruct first_aligned_impl\n{\n  static inline Index run(const Derived&)\n  { return 0; }\n};\n\ntemplate<int Alignment, typename Derived>\nstruct first_aligned_impl<Alignment, Derived, false>\n{\n  static inline Index run(const Derived& m)\n  {\n    return internal::first_aligned<Alignment>(m.data(), m.size());\n  }\n};\n\n/** \\internal \\returns the index of the first element of the array stored by \\a m that is properly aligned with respect to \\a Alignment for vectorization.\n  *\n  * \\tparam Alignment requested alignment in Bytes.\n  *\n  * There is also the variant first_aligned(const Scalar*, Integer) defined in Memory.h. See it for more\n  * documentation.\n  */\ntemplate<int Alignment, typename Derived>\nstatic inline Index first_aligned(const DenseBase<Derived>& m)\n{\n  enum { ReturnZero = (int(evaluator<Derived>::Alignment) >= Alignment) || !(Derived::Flags & DirectAccessBit) };\n  return first_aligned_impl<Alignment, Derived, ReturnZero>::run(m.derived());\n}\n\ntemplate<typename Derived>\nstatic inline Index first_default_aligned(const DenseBase<Derived>& m)\n{\n  typedef typename Derived::Scalar Scalar;\n  typedef typename packet_traits<Scalar>::type DefaultPacketType;\n  return internal::first_aligned<int(unpacket_traits<DefaultPacketType>::alignment),Derived>(m);\n}\n\ntemplate<typename Derived, bool HasDirectAccess = has_direct_access<Derived>::ret>\nstruct inner_stride_at_compile_time\n{\n  enum { ret = traits<Derived>::InnerStrideAtCompileTime };\n};\n\ntemplate<typename Derived>\nstruct inner_stride_at_compile_time<Derived, false>\n{\n  enum { ret = 0 };\n};\n\ntemplate<typename Derived, bool HasDirectAccess = has_direct_access<Derived>::ret>\nstruct outer_stride_at_compile_time\n{\n  enum { ret = traits<Derived>::OuterStrideAtCompileTime };\n};\n\ntemplate<typename Derived>\nstruct outer_stride_at_compile_time<Derived, false>\n{\n  enum { ret = 0 };\n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_DENSECOEFFSBASE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/DenseStorage.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2006-2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2010-2013 Hauke Heibel <hauke.heibel@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_MATRIXSTORAGE_H\n#define EIGEN_MATRIXSTORAGE_H\n\n#ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN\n  #define EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(X) X; EIGEN_DENSE_STORAGE_CTOR_PLUGIN;\n#else\n  #define EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(X)\n#endif\n\nnamespace Eigen {\n\nnamespace internal {\n\nstruct constructor_without_unaligned_array_assert {};\n\ntemplate<typename T, int Size>\nEIGEN_DEVICE_FUNC\nvoid check_static_allocation_size()\n{\n  // if EIGEN_STACK_ALLOCATION_LIMIT is defined to 0, then no limit\n  #if EIGEN_STACK_ALLOCATION_LIMIT\n  EIGEN_STATIC_ASSERT(Size * sizeof(T) <= EIGEN_STACK_ALLOCATION_LIMIT, OBJECT_ALLOCATED_ON_STACK_IS_TOO_BIG);\n  #endif\n}\n\n/** \\internal\n  * Static array. If the MatrixOrArrayOptions require auto-alignment, the array will be automatically aligned:\n  * to 16 bytes boundary if the total size is a multiple of 16 bytes.\n  */\ntemplate <typename T, int Size, int MatrixOrArrayOptions,\n          int Alignment = (MatrixOrArrayOptions&DontAlign) ? 0\n                        : compute_default_alignment<T,Size>::value >\nstruct plain_array\n{\n  T array[Size];\n\n  EIGEN_DEVICE_FUNC\n  plain_array()\n  { \n    check_static_allocation_size<T,Size>();\n  }\n\n  EIGEN_DEVICE_FUNC\n  plain_array(constructor_without_unaligned_array_assert)\n  { \n    check_static_allocation_size<T,Size>();\n  }\n};\n\n#if defined(EIGEN_DISABLE_UNALIGNED_ARRAY_ASSERT)\n  #define EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(sizemask)\n#elif EIGEN_GNUC_AT_LEAST(4,7) \n  // GCC 4.7 is too aggressive in its optimizations and remove the alignement test based on the fact the array is declared to be aligned.\n  // See this bug report: http://gcc.gnu.org/bugzilla/show_bug.cgi?id=53900\n  // Hiding the origin of the array pointer behind a function argument seems to do the trick even if the function is inlined:\n  template<typename PtrType>\n  EIGEN_ALWAYS_INLINE PtrType eigen_unaligned_array_assert_workaround_gcc47(PtrType array) { return array; }\n  #define EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(sizemask) \\\n    eigen_assert((internal::UIntPtr(eigen_unaligned_array_assert_workaround_gcc47(array)) & (sizemask)) == 0 \\\n              && \"this assertion is explained here: \" \\\n              \"http://eigen.tuxfamily.org/dox-devel/group__TopicUnalignedArrayAssert.html\" \\\n              \" **** READ THIS WEB PAGE !!! ****\");\n#else\n  #define EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(sizemask) \\\n    eigen_assert((internal::UIntPtr(array) & (sizemask)) == 0 \\\n              && \"this assertion is explained here: \" \\\n              \"http://eigen.tuxfamily.org/dox-devel/group__TopicUnalignedArrayAssert.html\" \\\n              \" **** READ THIS WEB PAGE !!! ****\");\n#endif\n\ntemplate <typename T, int Size, int MatrixOrArrayOptions>\nstruct plain_array<T, Size, MatrixOrArrayOptions, 8>\n{\n  EIGEN_ALIGN_TO_BOUNDARY(8) T array[Size];\n\n  EIGEN_DEVICE_FUNC\n  plain_array() \n  {\n    EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(7);\n    check_static_allocation_size<T,Size>();\n  }\n\n  EIGEN_DEVICE_FUNC\n  plain_array(constructor_without_unaligned_array_assert) \n  { \n    check_static_allocation_size<T,Size>();\n  }\n};\n\ntemplate <typename T, int Size, int MatrixOrArrayOptions>\nstruct plain_array<T, Size, MatrixOrArrayOptions, 16>\n{\n  EIGEN_ALIGN_TO_BOUNDARY(16) T array[Size];\n\n  EIGEN_DEVICE_FUNC\n  plain_array() \n  { \n    EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(15);\n    check_static_allocation_size<T,Size>();\n  }\n\n  EIGEN_DEVICE_FUNC\n  plain_array(constructor_without_unaligned_array_assert) \n  { \n    check_static_allocation_size<T,Size>();\n  }\n};\n\ntemplate <typename T, int Size, int MatrixOrArrayOptions>\nstruct plain_array<T, Size, MatrixOrArrayOptions, 32>\n{\n  EIGEN_ALIGN_TO_BOUNDARY(32) T array[Size];\n\n  EIGEN_DEVICE_FUNC\n  plain_array() \n  {\n    EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(31);\n    check_static_allocation_size<T,Size>();\n  }\n\n  EIGEN_DEVICE_FUNC\n  plain_array(constructor_without_unaligned_array_assert) \n  { \n    check_static_allocation_size<T,Size>();\n  }\n};\n\ntemplate <typename T, int Size, int MatrixOrArrayOptions>\nstruct plain_array<T, Size, MatrixOrArrayOptions, 64>\n{\n  EIGEN_ALIGN_TO_BOUNDARY(64) T array[Size];\n\n  EIGEN_DEVICE_FUNC\n  plain_array() \n  { \n    EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(63);\n    check_static_allocation_size<T,Size>();\n  }\n\n  EIGEN_DEVICE_FUNC\n  plain_array(constructor_without_unaligned_array_assert) \n  { \n    check_static_allocation_size<T,Size>();\n  }\n};\n\ntemplate <typename T, int MatrixOrArrayOptions, int Alignment>\nstruct plain_array<T, 0, MatrixOrArrayOptions, Alignment>\n{\n  T array[1];\n  EIGEN_DEVICE_FUNC plain_array() {}\n  EIGEN_DEVICE_FUNC plain_array(constructor_without_unaligned_array_assert) {}\n};\n\n} // end namespace internal\n\n/** \\internal\n  *\n  * \\class DenseStorage\n  * \\ingroup Core_Module\n  *\n  * \\brief Stores the data of a matrix\n  *\n  * This class stores the data of fixed-size, dynamic-size or mixed matrices\n  * in a way as compact as possible.\n  *\n  * \\sa Matrix\n  */\ntemplate<typename T, int Size, int _Rows, int _Cols, int _Options> class DenseStorage;\n\n// purely fixed-size matrix\ntemplate<typename T, int Size, int _Rows, int _Cols, int _Options> class DenseStorage\n{\n    internal::plain_array<T,Size,_Options> m_data;\n  public:\n    EIGEN_DEVICE_FUNC DenseStorage() {\n      EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(Index size = Size)\n    }\n    EIGEN_DEVICE_FUNC\n    explicit DenseStorage(internal::constructor_without_unaligned_array_assert)\n      : m_data(internal::constructor_without_unaligned_array_assert()) {}\n    EIGEN_DEVICE_FUNC \n    DenseStorage(const DenseStorage& other) : m_data(other.m_data) {\n      EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(Index size = Size)\n    }\n    EIGEN_DEVICE_FUNC \n    DenseStorage& operator=(const DenseStorage& other)\n    { \n      if (this != &other) m_data = other.m_data;\n      return *this; \n    }\n    EIGEN_DEVICE_FUNC DenseStorage(Index size, Index rows, Index cols) {\n      EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({})\n      eigen_internal_assert(size==rows*cols && rows==_Rows && cols==_Cols);\n      EIGEN_UNUSED_VARIABLE(size);\n      EIGEN_UNUSED_VARIABLE(rows);\n      EIGEN_UNUSED_VARIABLE(cols);\n    }\n    EIGEN_DEVICE_FUNC void swap(DenseStorage& other) { std::swap(m_data,other.m_data); }\n    EIGEN_DEVICE_FUNC static Index rows(void) {return _Rows;}\n    EIGEN_DEVICE_FUNC static Index cols(void) {return _Cols;}\n    EIGEN_DEVICE_FUNC void conservativeResize(Index,Index,Index) {}\n    EIGEN_DEVICE_FUNC void resize(Index,Index,Index) {}\n    EIGEN_DEVICE_FUNC const T *data() const { return m_data.array; }\n    EIGEN_DEVICE_FUNC T *data() { return m_data.array; }\n};\n\n// null matrix\ntemplate<typename T, int _Rows, int _Cols, int _Options> class DenseStorage<T, 0, _Rows, _Cols, _Options>\n{\n  public:\n    EIGEN_DEVICE_FUNC DenseStorage() {}\n    EIGEN_DEVICE_FUNC explicit DenseStorage(internal::constructor_without_unaligned_array_assert) {}\n    EIGEN_DEVICE_FUNC DenseStorage(const DenseStorage&) {}\n    EIGEN_DEVICE_FUNC DenseStorage& operator=(const DenseStorage&) { return *this; }\n    EIGEN_DEVICE_FUNC DenseStorage(Index,Index,Index) {}\n    EIGEN_DEVICE_FUNC void swap(DenseStorage& ) {}\n    EIGEN_DEVICE_FUNC static Index rows(void) {return _Rows;}\n    EIGEN_DEVICE_FUNC static Index cols(void) {return _Cols;}\n    EIGEN_DEVICE_FUNC void conservativeResize(Index,Index,Index) {}\n    EIGEN_DEVICE_FUNC void resize(Index,Index,Index) {}\n    EIGEN_DEVICE_FUNC const T *data() const { return 0; }\n    EIGEN_DEVICE_FUNC T *data() { return 0; }\n};\n\n// more specializations for null matrices; these are necessary to resolve ambiguities\ntemplate<typename T, int _Options> class DenseStorage<T, 0, Dynamic, Dynamic, _Options>\n: public DenseStorage<T, 0, 0, 0, _Options> { };\n\ntemplate<typename T, int _Rows, int _Options> class DenseStorage<T, 0, _Rows, Dynamic, _Options>\n: public DenseStorage<T, 0, 0, 0, _Options> { };\n\ntemplate<typename T, int _Cols, int _Options> class DenseStorage<T, 0, Dynamic, _Cols, _Options>\n: public DenseStorage<T, 0, 0, 0, _Options> { };\n\n// dynamic-size matrix with fixed-size storage\ntemplate<typename T, int Size, int _Options> class DenseStorage<T, Size, Dynamic, Dynamic, _Options>\n{\n    internal::plain_array<T,Size,_Options> m_data;\n    Index m_rows;\n    Index m_cols;\n  public:\n    EIGEN_DEVICE_FUNC DenseStorage() : m_rows(0), m_cols(0) {}\n    EIGEN_DEVICE_FUNC explicit DenseStorage(internal::constructor_without_unaligned_array_assert)\n      : m_data(internal::constructor_without_unaligned_array_assert()), m_rows(0), m_cols(0) {}\n    EIGEN_DEVICE_FUNC DenseStorage(const DenseStorage& other) : m_data(other.m_data), m_rows(other.m_rows), m_cols(other.m_cols) {}\n    EIGEN_DEVICE_FUNC DenseStorage& operator=(const DenseStorage& other) \n    { \n      if (this != &other)\n      {\n        m_data = other.m_data;\n        m_rows = other.m_rows;\n        m_cols = other.m_cols;\n      }\n      return *this; \n    }\n    EIGEN_DEVICE_FUNC DenseStorage(Index, Index rows, Index cols) : m_rows(rows), m_cols(cols) {}\n    EIGEN_DEVICE_FUNC void swap(DenseStorage& other)\n    { std::swap(m_data,other.m_data); std::swap(m_rows,other.m_rows); std::swap(m_cols,other.m_cols); }\n    EIGEN_DEVICE_FUNC Index rows() const {return m_rows;}\n    EIGEN_DEVICE_FUNC Index cols() const {return m_cols;}\n    EIGEN_DEVICE_FUNC void conservativeResize(Index, Index rows, Index cols) { m_rows = rows; m_cols = cols; }\n    EIGEN_DEVICE_FUNC void resize(Index, Index rows, Index cols) { m_rows = rows; m_cols = cols; }\n    EIGEN_DEVICE_FUNC const T *data() const { return m_data.array; }\n    EIGEN_DEVICE_FUNC T *data() { return m_data.array; }\n};\n\n// dynamic-size matrix with fixed-size storage and fixed width\ntemplate<typename T, int Size, int _Cols, int _Options> class DenseStorage<T, Size, Dynamic, _Cols, _Options>\n{\n    internal::plain_array<T,Size,_Options> m_data;\n    Index m_rows;\n  public:\n    EIGEN_DEVICE_FUNC DenseStorage() : m_rows(0) {}\n    EIGEN_DEVICE_FUNC explicit DenseStorage(internal::constructor_without_unaligned_array_assert)\n      : m_data(internal::constructor_without_unaligned_array_assert()), m_rows(0) {}\n    EIGEN_DEVICE_FUNC DenseStorage(const DenseStorage& other) : m_data(other.m_data), m_rows(other.m_rows) {}\n    EIGEN_DEVICE_FUNC DenseStorage& operator=(const DenseStorage& other) \n    {\n      if (this != &other)\n      {\n        m_data = other.m_data;\n        m_rows = other.m_rows;\n      }\n      return *this; \n    }\n    EIGEN_DEVICE_FUNC DenseStorage(Index, Index rows, Index) : m_rows(rows) {}\n    EIGEN_DEVICE_FUNC void swap(DenseStorage& other) { std::swap(m_data,other.m_data); std::swap(m_rows,other.m_rows); }\n    EIGEN_DEVICE_FUNC Index rows(void) const {return m_rows;}\n    EIGEN_DEVICE_FUNC Index cols(void) const {return _Cols;}\n    EIGEN_DEVICE_FUNC void conservativeResize(Index, Index rows, Index) { m_rows = rows; }\n    EIGEN_DEVICE_FUNC void resize(Index, Index rows, Index) { m_rows = rows; }\n    EIGEN_DEVICE_FUNC const T *data() const { return m_data.array; }\n    EIGEN_DEVICE_FUNC T *data() { return m_data.array; }\n};\n\n// dynamic-size matrix with fixed-size storage and fixed height\ntemplate<typename T, int Size, int _Rows, int _Options> class DenseStorage<T, Size, _Rows, Dynamic, _Options>\n{\n    internal::plain_array<T,Size,_Options> m_data;\n    Index m_cols;\n  public:\n    EIGEN_DEVICE_FUNC DenseStorage() : m_cols(0) {}\n    EIGEN_DEVICE_FUNC explicit DenseStorage(internal::constructor_without_unaligned_array_assert)\n      : m_data(internal::constructor_without_unaligned_array_assert()), m_cols(0) {}\n    EIGEN_DEVICE_FUNC DenseStorage(const DenseStorage& other) : m_data(other.m_data), m_cols(other.m_cols) {}\n    EIGEN_DEVICE_FUNC DenseStorage& operator=(const DenseStorage& other)\n    {\n      if (this != &other)\n      {\n        m_data = other.m_data;\n        m_cols = other.m_cols;\n      }\n      return *this;\n    }\n    EIGEN_DEVICE_FUNC DenseStorage(Index, Index, Index cols) : m_cols(cols) {}\n    EIGEN_DEVICE_FUNC void swap(DenseStorage& other) { std::swap(m_data,other.m_data); std::swap(m_cols,other.m_cols); }\n    EIGEN_DEVICE_FUNC Index rows(void) const {return _Rows;}\n    EIGEN_DEVICE_FUNC Index cols(void) const {return m_cols;}\n    void conservativeResize(Index, Index, Index cols) { m_cols = cols; }\n    void resize(Index, Index, Index cols) { m_cols = cols; }\n    EIGEN_DEVICE_FUNC const T *data() const { return m_data.array; }\n    EIGEN_DEVICE_FUNC T *data() { return m_data.array; }\n};\n\n// purely dynamic matrix.\ntemplate<typename T, int _Options> class DenseStorage<T, Dynamic, Dynamic, Dynamic, _Options>\n{\n    T *m_data;\n    Index m_rows;\n    Index m_cols;\n  public:\n    EIGEN_DEVICE_FUNC DenseStorage() : m_data(0), m_rows(0), m_cols(0) {}\n    EIGEN_DEVICE_FUNC explicit DenseStorage(internal::constructor_without_unaligned_array_assert)\n       : m_data(0), m_rows(0), m_cols(0) {}\n    EIGEN_DEVICE_FUNC DenseStorage(Index size, Index rows, Index cols)\n      : m_data(internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size)), m_rows(rows), m_cols(cols)\n    {\n      EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({})\n      eigen_internal_assert(size==rows*cols && rows>=0 && cols >=0);\n    }\n    EIGEN_DEVICE_FUNC DenseStorage(const DenseStorage& other)\n      : m_data(internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(other.m_rows*other.m_cols))\n      , m_rows(other.m_rows)\n      , m_cols(other.m_cols)\n    {\n      EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(Index size = m_rows*m_cols)\n      internal::smart_copy(other.m_data, other.m_data+other.m_rows*other.m_cols, m_data);\n    }\n    EIGEN_DEVICE_FUNC DenseStorage& operator=(const DenseStorage& other)\n    {\n      if (this != &other)\n      {\n        DenseStorage tmp(other);\n        this->swap(tmp);\n      }\n      return *this;\n    }\n#if EIGEN_HAS_RVALUE_REFERENCES\n    EIGEN_DEVICE_FUNC\n    DenseStorage(DenseStorage&& other) EIGEN_NOEXCEPT\n      : m_data(std::move(other.m_data))\n      , m_rows(std::move(other.m_rows))\n      , m_cols(std::move(other.m_cols))\n    {\n      other.m_data = nullptr;\n      other.m_rows = 0;\n      other.m_cols = 0;\n    }\n    EIGEN_DEVICE_FUNC\n    DenseStorage& operator=(DenseStorage&& other) EIGEN_NOEXCEPT\n    {\n      using std::swap;\n      swap(m_data, other.m_data);\n      swap(m_rows, other.m_rows);\n      swap(m_cols, other.m_cols);\n      return *this;\n    }\n#endif\n    EIGEN_DEVICE_FUNC ~DenseStorage() { internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, m_rows*m_cols); }\n    EIGEN_DEVICE_FUNC void swap(DenseStorage& other)\n    { std::swap(m_data,other.m_data); std::swap(m_rows,other.m_rows); std::swap(m_cols,other.m_cols); }\n    EIGEN_DEVICE_FUNC Index rows(void) const {return m_rows;}\n    EIGEN_DEVICE_FUNC Index cols(void) const {return m_cols;}\n    void conservativeResize(Index size, Index rows, Index cols)\n    {\n      m_data = internal::conditional_aligned_realloc_new_auto<T,(_Options&DontAlign)==0>(m_data, size, m_rows*m_cols);\n      m_rows = rows;\n      m_cols = cols;\n    }\n    EIGEN_DEVICE_FUNC void resize(Index size, Index rows, Index cols)\n    {\n      if(size != m_rows*m_cols)\n      {\n        internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, m_rows*m_cols);\n        if (size)\n          m_data = internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size);\n        else\n          m_data = 0;\n        EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({})\n      }\n      m_rows = rows;\n      m_cols = cols;\n    }\n    EIGEN_DEVICE_FUNC const T *data() const { return m_data; }\n    EIGEN_DEVICE_FUNC T *data() { return m_data; }\n};\n\n// matrix with dynamic width and fixed height (so that matrix has dynamic size).\ntemplate<typename T, int _Rows, int _Options> class DenseStorage<T, Dynamic, _Rows, Dynamic, _Options>\n{\n    T *m_data;\n    Index m_cols;\n  public:\n    EIGEN_DEVICE_FUNC DenseStorage() : m_data(0), m_cols(0) {}\n    explicit DenseStorage(internal::constructor_without_unaligned_array_assert) : m_data(0), m_cols(0) {}\n    EIGEN_DEVICE_FUNC DenseStorage(Index size, Index rows, Index cols) : m_data(internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size)), m_cols(cols)\n    {\n      EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({})\n      eigen_internal_assert(size==rows*cols && rows==_Rows && cols >=0);\n      EIGEN_UNUSED_VARIABLE(rows);\n    }\n    EIGEN_DEVICE_FUNC DenseStorage(const DenseStorage& other)\n      : m_data(internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(_Rows*other.m_cols))\n      , m_cols(other.m_cols)\n    {\n      EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(Index size = m_cols*_Rows)\n      internal::smart_copy(other.m_data, other.m_data+_Rows*m_cols, m_data);\n    }\n    EIGEN_DEVICE_FUNC DenseStorage& operator=(const DenseStorage& other)\n    {\n      if (this != &other)\n      {\n        DenseStorage tmp(other);\n        this->swap(tmp);\n      }\n      return *this;\n    }    \n#if EIGEN_HAS_RVALUE_REFERENCES\n    EIGEN_DEVICE_FUNC\n    DenseStorage(DenseStorage&& other) EIGEN_NOEXCEPT\n      : m_data(std::move(other.m_data))\n      , m_cols(std::move(other.m_cols))\n    {\n      other.m_data = nullptr;\n      other.m_cols = 0;\n    }\n    EIGEN_DEVICE_FUNC\n    DenseStorage& operator=(DenseStorage&& other) EIGEN_NOEXCEPT\n    {\n      using std::swap;\n      swap(m_data, other.m_data);\n      swap(m_cols, other.m_cols);\n      return *this;\n    }\n#endif\n    EIGEN_DEVICE_FUNC ~DenseStorage() { internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, _Rows*m_cols); }\n    EIGEN_DEVICE_FUNC void swap(DenseStorage& other) { std::swap(m_data,other.m_data); std::swap(m_cols,other.m_cols); }\n    EIGEN_DEVICE_FUNC static Index rows(void) {return _Rows;}\n    EIGEN_DEVICE_FUNC Index cols(void) const {return m_cols;}\n    EIGEN_DEVICE_FUNC void conservativeResize(Index size, Index, Index cols)\n    {\n      m_data = internal::conditional_aligned_realloc_new_auto<T,(_Options&DontAlign)==0>(m_data, size, _Rows*m_cols);\n      m_cols = cols;\n    }\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void resize(Index size, Index, Index cols)\n    {\n      if(size != _Rows*m_cols)\n      {\n        internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, _Rows*m_cols);\n        if (size)\n          m_data = internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size);\n        else\n          m_data = 0;\n        EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({})\n      }\n      m_cols = cols;\n    }\n    EIGEN_DEVICE_FUNC const T *data() const { return m_data; }\n    EIGEN_DEVICE_FUNC T *data() { return m_data; }\n};\n\n// matrix with dynamic height and fixed width (so that matrix has dynamic size).\ntemplate<typename T, int _Cols, int _Options> class DenseStorage<T, Dynamic, Dynamic, _Cols, _Options>\n{\n    T *m_data;\n    Index m_rows;\n  public:\n    EIGEN_DEVICE_FUNC DenseStorage() : m_data(0), m_rows(0) {}\n    explicit DenseStorage(internal::constructor_without_unaligned_array_assert) : m_data(0), m_rows(0) {}\n    EIGEN_DEVICE_FUNC DenseStorage(Index size, Index rows, Index cols) : m_data(internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size)), m_rows(rows)\n    {\n      EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({})\n      eigen_internal_assert(size==rows*cols && rows>=0 && cols == _Cols);\n      EIGEN_UNUSED_VARIABLE(cols);\n    }\n    EIGEN_DEVICE_FUNC DenseStorage(const DenseStorage& other)\n      : m_data(internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(other.m_rows*_Cols))\n      , m_rows(other.m_rows)\n    {\n      EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(Index size = m_rows*_Cols)\n      internal::smart_copy(other.m_data, other.m_data+other.m_rows*_Cols, m_data);\n    }\n    EIGEN_DEVICE_FUNC DenseStorage& operator=(const DenseStorage& other)\n    {\n      if (this != &other)\n      {\n        DenseStorage tmp(other);\n        this->swap(tmp);\n      }\n      return *this;\n    }    \n#if EIGEN_HAS_RVALUE_REFERENCES\n    EIGEN_DEVICE_FUNC\n    DenseStorage(DenseStorage&& other) EIGEN_NOEXCEPT\n      : m_data(std::move(other.m_data))\n      , m_rows(std::move(other.m_rows))\n    {\n      other.m_data = nullptr;\n      other.m_rows = 0;\n    }\n    EIGEN_DEVICE_FUNC\n    DenseStorage& operator=(DenseStorage&& other) EIGEN_NOEXCEPT\n    {\n      using std::swap;\n      swap(m_data, other.m_data);\n      swap(m_rows, other.m_rows);\n      return *this;\n    }\n#endif\n    EIGEN_DEVICE_FUNC ~DenseStorage() { internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, _Cols*m_rows); }\n    EIGEN_DEVICE_FUNC void swap(DenseStorage& other) { std::swap(m_data,other.m_data); std::swap(m_rows,other.m_rows); }\n    EIGEN_DEVICE_FUNC Index rows(void) const {return m_rows;}\n    EIGEN_DEVICE_FUNC static Index cols(void) {return _Cols;}\n    void conservativeResize(Index size, Index rows, Index)\n    {\n      m_data = internal::conditional_aligned_realloc_new_auto<T,(_Options&DontAlign)==0>(m_data, size, m_rows*_Cols);\n      m_rows = rows;\n    }\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void resize(Index size, Index rows, Index)\n    {\n      if(size != m_rows*_Cols)\n      {\n        internal::conditional_aligned_delete_auto<T,(_Options&DontAlign)==0>(m_data, _Cols*m_rows);\n        if (size)\n          m_data = internal::conditional_aligned_new_auto<T,(_Options&DontAlign)==0>(size);\n        else\n          m_data = 0;\n        EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({})\n      }\n      m_rows = rows;\n    }\n    EIGEN_DEVICE_FUNC const T *data() const { return m_data; }\n    EIGEN_DEVICE_FUNC T *data() { return m_data; }\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_MATRIX_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/Diagonal.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_DIAGONAL_H\n#define EIGEN_DIAGONAL_H\n\nnamespace Eigen { \n\n/** \\class Diagonal\n  * \\ingroup Core_Module\n  *\n  * \\brief Expression of a diagonal/subdiagonal/superdiagonal in a matrix\n  *\n  * \\param MatrixType the type of the object in which we are taking a sub/main/super diagonal\n  * \\param DiagIndex the index of the sub/super diagonal. The default is 0 and it means the main diagonal.\n  *              A positive value means a superdiagonal, a negative value means a subdiagonal.\n  *              You can also use DynamicIndex so the index can be set at runtime.\n  *\n  * The matrix is not required to be square.\n  *\n  * This class represents an expression of the main diagonal, or any sub/super diagonal\n  * of a square matrix. It is the return type of MatrixBase::diagonal() and MatrixBase::diagonal(Index) and most of the\n  * time this is the only way it is used.\n  *\n  * \\sa MatrixBase::diagonal(), MatrixBase::diagonal(Index)\n  */\n\nnamespace internal {\ntemplate<typename MatrixType, int DiagIndex>\nstruct traits<Diagonal<MatrixType,DiagIndex> >\n : traits<MatrixType>\n{\n  typedef typename ref_selector<MatrixType>::type MatrixTypeNested;\n  typedef typename remove_reference<MatrixTypeNested>::type _MatrixTypeNested;\n  typedef typename MatrixType::StorageKind StorageKind;\n  enum {\n    RowsAtCompileTime = (int(DiagIndex) == DynamicIndex || int(MatrixType::SizeAtCompileTime) == Dynamic) ? Dynamic\n                      : (EIGEN_PLAIN_ENUM_MIN(MatrixType::RowsAtCompileTime - EIGEN_PLAIN_ENUM_MAX(-DiagIndex, 0),\n                                              MatrixType::ColsAtCompileTime - EIGEN_PLAIN_ENUM_MAX( DiagIndex, 0))),\n    ColsAtCompileTime = 1,\n    MaxRowsAtCompileTime = int(MatrixType::MaxSizeAtCompileTime) == Dynamic ? Dynamic\n                         : DiagIndex == DynamicIndex ? EIGEN_SIZE_MIN_PREFER_FIXED(MatrixType::MaxRowsAtCompileTime,\n                                                                              MatrixType::MaxColsAtCompileTime)\n                         : (EIGEN_PLAIN_ENUM_MIN(MatrixType::MaxRowsAtCompileTime - EIGEN_PLAIN_ENUM_MAX(-DiagIndex, 0),\n                                                 MatrixType::MaxColsAtCompileTime - EIGEN_PLAIN_ENUM_MAX( DiagIndex, 0))),\n    MaxColsAtCompileTime = 1,\n    MaskLvalueBit = is_lvalue<MatrixType>::value ? LvalueBit : 0,\n    Flags = (unsigned int)_MatrixTypeNested::Flags & (RowMajorBit | MaskLvalueBit | DirectAccessBit) & ~RowMajorBit, // FIXME DirectAccessBit should not be handled by expressions\n    MatrixTypeOuterStride = outer_stride_at_compile_time<MatrixType>::ret,\n    InnerStrideAtCompileTime = MatrixTypeOuterStride == Dynamic ? Dynamic : MatrixTypeOuterStride+1,\n    OuterStrideAtCompileTime = 0\n  };\n};\n}\n\ntemplate<typename MatrixType, int _DiagIndex> class Diagonal\n   : public internal::dense_xpr_base< Diagonal<MatrixType,_DiagIndex> >::type\n{\n  public:\n\n    enum { DiagIndex = _DiagIndex };\n    typedef typename internal::dense_xpr_base<Diagonal>::type Base;\n    EIGEN_DENSE_PUBLIC_INTERFACE(Diagonal)\n\n    EIGEN_DEVICE_FUNC\n    explicit inline Diagonal(MatrixType& matrix, Index a_index = DiagIndex) : m_matrix(matrix), m_index(a_index)\n    {\n      eigen_assert( a_index <= m_matrix.cols() && -a_index <= m_matrix.rows() );\n    }\n\n    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Diagonal)\n\n    EIGEN_DEVICE_FUNC\n    inline Index rows() const\n    {\n      return m_index.value()<0 ? numext::mini<Index>(m_matrix.cols(),m_matrix.rows()+m_index.value())\n                               : numext::mini<Index>(m_matrix.rows(),m_matrix.cols()-m_index.value());\n    }\n\n    EIGEN_DEVICE_FUNC\n    inline Index cols() const { return 1; }\n\n    EIGEN_DEVICE_FUNC\n    inline Index innerStride() const\n    {\n      return m_matrix.outerStride() + 1;\n    }\n\n    EIGEN_DEVICE_FUNC\n    inline Index outerStride() const\n    {\n      return 0;\n    }\n\n    typedef typename internal::conditional<\n                       internal::is_lvalue<MatrixType>::value,\n                       Scalar,\n                       const Scalar\n                     >::type ScalarWithConstIfNotLvalue;\n\n    EIGEN_DEVICE_FUNC\n    inline ScalarWithConstIfNotLvalue* data() { return &(m_matrix.coeffRef(rowOffset(), colOffset())); }\n    EIGEN_DEVICE_FUNC\n    inline const Scalar* data() const { return &(m_matrix.coeffRef(rowOffset(), colOffset())); }\n\n    EIGEN_DEVICE_FUNC\n    inline Scalar& coeffRef(Index row, Index)\n    {\n      EIGEN_STATIC_ASSERT_LVALUE(MatrixType)\n      return m_matrix.coeffRef(row+rowOffset(), row+colOffset());\n    }\n\n    EIGEN_DEVICE_FUNC\n    inline const Scalar& coeffRef(Index row, Index) const\n    {\n      return m_matrix.coeffRef(row+rowOffset(), row+colOffset());\n    }\n\n    EIGEN_DEVICE_FUNC\n    inline CoeffReturnType coeff(Index row, Index) const\n    {\n      return m_matrix.coeff(row+rowOffset(), row+colOffset());\n    }\n\n    EIGEN_DEVICE_FUNC\n    inline Scalar& coeffRef(Index idx)\n    {\n      EIGEN_STATIC_ASSERT_LVALUE(MatrixType)\n      return m_matrix.coeffRef(idx+rowOffset(), idx+colOffset());\n    }\n\n    EIGEN_DEVICE_FUNC\n    inline const Scalar& coeffRef(Index idx) const\n    {\n      return m_matrix.coeffRef(idx+rowOffset(), idx+colOffset());\n    }\n\n    EIGEN_DEVICE_FUNC\n    inline CoeffReturnType coeff(Index idx) const\n    {\n      return m_matrix.coeff(idx+rowOffset(), idx+colOffset());\n    }\n\n    EIGEN_DEVICE_FUNC\n    inline const typename internal::remove_all<typename MatrixType::Nested>::type& \n    nestedExpression() const \n    {\n      return m_matrix;\n    }\n\n    EIGEN_DEVICE_FUNC\n    inline Index index() const\n    {\n      return m_index.value();\n    }\n\n  protected:\n    typename internal::ref_selector<MatrixType>::non_const_type m_matrix;\n    const internal::variable_if_dynamicindex<Index, DiagIndex> m_index;\n\n  private:\n    // some compilers may fail to optimize std::max etc in case of compile-time constants...\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Index absDiagIndex() const { return m_index.value()>0 ? m_index.value() : -m_index.value(); }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Index rowOffset() const { return m_index.value()>0 ? 0 : -m_index.value(); }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Index colOffset() const { return m_index.value()>0 ? m_index.value() : 0; }\n    // trigger a compile-time error if someone try to call packet\n    template<int LoadMode> typename MatrixType::PacketReturnType packet(Index) const;\n    template<int LoadMode> typename MatrixType::PacketReturnType packet(Index,Index) const;\n};\n\n/** \\returns an expression of the main diagonal of the matrix \\c *this\n  *\n  * \\c *this is not required to be square.\n  *\n  * Example: \\include MatrixBase_diagonal.cpp\n  * Output: \\verbinclude MatrixBase_diagonal.out\n  *\n  * \\sa class Diagonal */\ntemplate<typename Derived>\ninline typename MatrixBase<Derived>::DiagonalReturnType\nMatrixBase<Derived>::diagonal()\n{\n  return DiagonalReturnType(derived());\n}\n\n/** This is the const version of diagonal(). */\ntemplate<typename Derived>\ninline typename MatrixBase<Derived>::ConstDiagonalReturnType\nMatrixBase<Derived>::diagonal() const\n{\n  return ConstDiagonalReturnType(derived());\n}\n\n/** \\returns an expression of the \\a DiagIndex-th sub or super diagonal of the matrix \\c *this\n  *\n  * \\c *this is not required to be square.\n  *\n  * The template parameter \\a DiagIndex represent a super diagonal if \\a DiagIndex > 0\n  * and a sub diagonal otherwise. \\a DiagIndex == 0 is equivalent to the main diagonal.\n  *\n  * Example: \\include MatrixBase_diagonal_int.cpp\n  * Output: \\verbinclude MatrixBase_diagonal_int.out\n  *\n  * \\sa MatrixBase::diagonal(), class Diagonal */\ntemplate<typename Derived>\ninline typename MatrixBase<Derived>::DiagonalDynamicIndexReturnType\nMatrixBase<Derived>::diagonal(Index index)\n{\n  return DiagonalDynamicIndexReturnType(derived(), index);\n}\n\n/** This is the const version of diagonal(Index). */\ntemplate<typename Derived>\ninline typename MatrixBase<Derived>::ConstDiagonalDynamicIndexReturnType\nMatrixBase<Derived>::diagonal(Index index) const\n{\n  return ConstDiagonalDynamicIndexReturnType(derived(), index);\n}\n\n/** \\returns an expression of the \\a DiagIndex-th sub or super diagonal of the matrix \\c *this\n  *\n  * \\c *this is not required to be square.\n  *\n  * The template parameter \\a DiagIndex represent a super diagonal if \\a DiagIndex > 0\n  * and a sub diagonal otherwise. \\a DiagIndex == 0 is equivalent to the main diagonal.\n  *\n  * Example: \\include MatrixBase_diagonal_template_int.cpp\n  * Output: \\verbinclude MatrixBase_diagonal_template_int.out\n  *\n  * \\sa MatrixBase::diagonal(), class Diagonal */\ntemplate<typename Derived>\ntemplate<int Index_>\ninline typename MatrixBase<Derived>::template DiagonalIndexReturnType<Index_>::Type\nMatrixBase<Derived>::diagonal()\n{\n  return typename DiagonalIndexReturnType<Index_>::Type(derived());\n}\n\n/** This is the const version of diagonal<int>(). */\ntemplate<typename Derived>\ntemplate<int Index_>\ninline typename MatrixBase<Derived>::template ConstDiagonalIndexReturnType<Index_>::Type\nMatrixBase<Derived>::diagonal() const\n{\n  return typename ConstDiagonalIndexReturnType<Index_>::Type(derived());\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_DIAGONAL_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/DiagonalMatrix.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_DIAGONALMATRIX_H\n#define EIGEN_DIAGONALMATRIX_H\n\nnamespace Eigen { \n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\ntemplate<typename Derived>\nclass DiagonalBase : public EigenBase<Derived>\n{\n  public:\n    typedef typename internal::traits<Derived>::DiagonalVectorType DiagonalVectorType;\n    typedef typename DiagonalVectorType::Scalar Scalar;\n    typedef typename DiagonalVectorType::RealScalar RealScalar;\n    typedef typename internal::traits<Derived>::StorageKind StorageKind;\n    typedef typename internal::traits<Derived>::StorageIndex StorageIndex;\n\n    enum {\n      RowsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,\n      ColsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,\n      MaxRowsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,\n      MaxColsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,\n      IsVectorAtCompileTime = 0,\n      Flags = NoPreferredStorageOrderBit\n    };\n\n    typedef Matrix<Scalar, RowsAtCompileTime, ColsAtCompileTime, 0, MaxRowsAtCompileTime, MaxColsAtCompileTime> DenseMatrixType;\n    typedef DenseMatrixType DenseType;\n    typedef DiagonalMatrix<Scalar,DiagonalVectorType::SizeAtCompileTime,DiagonalVectorType::MaxSizeAtCompileTime> PlainObject;\n\n    EIGEN_DEVICE_FUNC\n    inline const Derived& derived() const { return *static_cast<const Derived*>(this); }\n    EIGEN_DEVICE_FUNC\n    inline Derived& derived() { return *static_cast<Derived*>(this); }\n\n    EIGEN_DEVICE_FUNC\n    DenseMatrixType toDenseMatrix() const { return derived(); }\n    \n    EIGEN_DEVICE_FUNC\n    inline const DiagonalVectorType& diagonal() const { return derived().diagonal(); }\n    EIGEN_DEVICE_FUNC\n    inline DiagonalVectorType& diagonal() { return derived().diagonal(); }\n\n    EIGEN_DEVICE_FUNC\n    inline Index rows() const { return diagonal().size(); }\n    EIGEN_DEVICE_FUNC\n    inline Index cols() const { return diagonal().size(); }\n\n    template<typename MatrixDerived>\n    EIGEN_DEVICE_FUNC\n    const Product<Derived,MatrixDerived,LazyProduct>\n    operator*(const MatrixBase<MatrixDerived> &matrix) const\n    {\n      return Product<Derived, MatrixDerived, LazyProduct>(derived(),matrix.derived());\n    }\n\n    typedef DiagonalWrapper<const CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const DiagonalVectorType> > InverseReturnType;\n    EIGEN_DEVICE_FUNC\n    inline const InverseReturnType\n    inverse() const\n    {\n      return InverseReturnType(diagonal().cwiseInverse());\n    }\n    \n    EIGEN_DEVICE_FUNC\n    inline const DiagonalWrapper<const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DiagonalVectorType,Scalar,product) >\n    operator*(const Scalar& scalar) const\n    {\n      return DiagonalWrapper<const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DiagonalVectorType,Scalar,product) >(diagonal() * scalar);\n    }\n    EIGEN_DEVICE_FUNC\n    friend inline const DiagonalWrapper<const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,DiagonalVectorType,product) >\n    operator*(const Scalar& scalar, const DiagonalBase& other)\n    {\n      return DiagonalWrapper<const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,DiagonalVectorType,product) >(scalar * other.diagonal());\n    }\n};\n\n#endif\n\n/** \\class DiagonalMatrix\n  * \\ingroup Core_Module\n  *\n  * \\brief Represents a diagonal matrix with its storage\n  *\n  * \\param _Scalar the type of coefficients\n  * \\param SizeAtCompileTime the dimension of the matrix, or Dynamic\n  * \\param MaxSizeAtCompileTime the dimension of the matrix, or Dynamic. This parameter is optional and defaults\n  *        to SizeAtCompileTime. Most of the time, you do not need to specify it.\n  *\n  * \\sa class DiagonalWrapper\n  */\n\nnamespace internal {\ntemplate<typename _Scalar, int SizeAtCompileTime, int MaxSizeAtCompileTime>\nstruct traits<DiagonalMatrix<_Scalar,SizeAtCompileTime,MaxSizeAtCompileTime> >\n : traits<Matrix<_Scalar,SizeAtCompileTime,SizeAtCompileTime,0,MaxSizeAtCompileTime,MaxSizeAtCompileTime> >\n{\n  typedef Matrix<_Scalar,SizeAtCompileTime,1,0,MaxSizeAtCompileTime,1> DiagonalVectorType;\n  typedef DiagonalShape StorageKind;\n  enum {\n    Flags = LvalueBit | NoPreferredStorageOrderBit\n  };\n};\n}\ntemplate<typename _Scalar, int SizeAtCompileTime, int MaxSizeAtCompileTime>\nclass DiagonalMatrix\n  : public DiagonalBase<DiagonalMatrix<_Scalar,SizeAtCompileTime,MaxSizeAtCompileTime> >\n{\n  public:\n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    typedef typename internal::traits<DiagonalMatrix>::DiagonalVectorType DiagonalVectorType;\n    typedef const DiagonalMatrix& Nested;\n    typedef _Scalar Scalar;\n    typedef typename internal::traits<DiagonalMatrix>::StorageKind StorageKind;\n    typedef typename internal::traits<DiagonalMatrix>::StorageIndex StorageIndex;\n    #endif\n\n  protected:\n\n    DiagonalVectorType m_diagonal;\n\n  public:\n\n    /** const version of diagonal(). */\n    EIGEN_DEVICE_FUNC\n    inline const DiagonalVectorType& diagonal() const { return m_diagonal; }\n    /** \\returns a reference to the stored vector of diagonal coefficients. */\n    EIGEN_DEVICE_FUNC\n    inline DiagonalVectorType& diagonal() { return m_diagonal; }\n\n    /** Default constructor without initialization */\n    EIGEN_DEVICE_FUNC\n    inline DiagonalMatrix() {}\n\n    /** Constructs a diagonal matrix with given dimension  */\n    EIGEN_DEVICE_FUNC\n    explicit inline DiagonalMatrix(Index dim) : m_diagonal(dim) {}\n\n    /** 2D constructor. */\n    EIGEN_DEVICE_FUNC\n    inline DiagonalMatrix(const Scalar& x, const Scalar& y) : m_diagonal(x,y) {}\n\n    /** 3D constructor. */\n    EIGEN_DEVICE_FUNC\n    inline DiagonalMatrix(const Scalar& x, const Scalar& y, const Scalar& z) : m_diagonal(x,y,z) {}\n\n    /** Copy constructor. */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    inline DiagonalMatrix(const DiagonalBase<OtherDerived>& other) : m_diagonal(other.diagonal()) {}\n\n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    /** copy constructor. prevent a default copy constructor from hiding the other templated constructor */\n    inline DiagonalMatrix(const DiagonalMatrix& other) : m_diagonal(other.diagonal()) {}\n    #endif\n\n    /** generic constructor from expression of the diagonal coefficients */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    explicit inline DiagonalMatrix(const MatrixBase<OtherDerived>& other) : m_diagonal(other)\n    {}\n\n    /** Copy operator. */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    DiagonalMatrix& operator=(const DiagonalBase<OtherDerived>& other)\n    {\n      m_diagonal = other.diagonal();\n      return *this;\n    }\n\n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    /** This is a special case of the templated operator=. Its purpose is to\n      * prevent a default operator= from hiding the templated operator=.\n      */\n    EIGEN_DEVICE_FUNC\n    DiagonalMatrix& operator=(const DiagonalMatrix& other)\n    {\n      m_diagonal = other.diagonal();\n      return *this;\n    }\n    #endif\n\n    /** Resizes to given size. */\n    EIGEN_DEVICE_FUNC\n    inline void resize(Index size) { m_diagonal.resize(size); }\n    /** Sets all coefficients to zero. */\n    EIGEN_DEVICE_FUNC\n    inline void setZero() { m_diagonal.setZero(); }\n    /** Resizes and sets all coefficients to zero. */\n    EIGEN_DEVICE_FUNC\n    inline void setZero(Index size) { m_diagonal.setZero(size); }\n    /** Sets this matrix to be the identity matrix of the current size. */\n    EIGEN_DEVICE_FUNC\n    inline void setIdentity() { m_diagonal.setOnes(); }\n    /** Sets this matrix to be the identity matrix of the given size. */\n    EIGEN_DEVICE_FUNC\n    inline void setIdentity(Index size) { m_diagonal.setOnes(size); }\n};\n\n/** \\class DiagonalWrapper\n  * \\ingroup Core_Module\n  *\n  * \\brief Expression of a diagonal matrix\n  *\n  * \\param _DiagonalVectorType the type of the vector of diagonal coefficients\n  *\n  * This class is an expression of a diagonal matrix, but not storing its own vector of diagonal coefficients,\n  * instead wrapping an existing vector expression. It is the return type of MatrixBase::asDiagonal()\n  * and most of the time this is the only way that it is used.\n  *\n  * \\sa class DiagonalMatrix, class DiagonalBase, MatrixBase::asDiagonal()\n  */\n\nnamespace internal {\ntemplate<typename _DiagonalVectorType>\nstruct traits<DiagonalWrapper<_DiagonalVectorType> >\n{\n  typedef _DiagonalVectorType DiagonalVectorType;\n  typedef typename DiagonalVectorType::Scalar Scalar;\n  typedef typename DiagonalVectorType::StorageIndex StorageIndex;\n  typedef DiagonalShape StorageKind;\n  typedef typename traits<DiagonalVectorType>::XprKind XprKind;\n  enum {\n    RowsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,\n    ColsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,\n    MaxRowsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,\n    MaxColsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,\n    Flags =  (traits<DiagonalVectorType>::Flags & LvalueBit) | NoPreferredStorageOrderBit\n  };\n};\n}\n\ntemplate<typename _DiagonalVectorType>\nclass DiagonalWrapper\n  : public DiagonalBase<DiagonalWrapper<_DiagonalVectorType> >, internal::no_assignment_operator\n{\n  public:\n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    typedef _DiagonalVectorType DiagonalVectorType;\n    typedef DiagonalWrapper Nested;\n    #endif\n\n    /** Constructor from expression of diagonal coefficients to wrap. */\n    EIGEN_DEVICE_FUNC\n    explicit inline DiagonalWrapper(DiagonalVectorType& a_diagonal) : m_diagonal(a_diagonal) {}\n\n    /** \\returns a const reference to the wrapped expression of diagonal coefficients. */\n    EIGEN_DEVICE_FUNC\n    const DiagonalVectorType& diagonal() const { return m_diagonal; }\n\n  protected:\n    typename DiagonalVectorType::Nested m_diagonal;\n};\n\n/** \\returns a pseudo-expression of a diagonal matrix with *this as vector of diagonal coefficients\n  *\n  * \\only_for_vectors\n  *\n  * Example: \\include MatrixBase_asDiagonal.cpp\n  * Output: \\verbinclude MatrixBase_asDiagonal.out\n  *\n  * \\sa class DiagonalWrapper, class DiagonalMatrix, diagonal(), isDiagonal()\n  **/\ntemplate<typename Derived>\ninline const DiagonalWrapper<const Derived>\nMatrixBase<Derived>::asDiagonal() const\n{\n  return DiagonalWrapper<const Derived>(derived());\n}\n\n/** \\returns true if *this is approximately equal to a diagonal matrix,\n  *          within the precision given by \\a prec.\n  *\n  * Example: \\include MatrixBase_isDiagonal.cpp\n  * Output: \\verbinclude MatrixBase_isDiagonal.out\n  *\n  * \\sa asDiagonal()\n  */\ntemplate<typename Derived>\nbool MatrixBase<Derived>::isDiagonal(const RealScalar& prec) const\n{\n  if(cols() != rows()) return false;\n  RealScalar maxAbsOnDiagonal = static_cast<RealScalar>(-1);\n  for(Index j = 0; j < cols(); ++j)\n  {\n    RealScalar absOnDiagonal = numext::abs(coeff(j,j));\n    if(absOnDiagonal > maxAbsOnDiagonal) maxAbsOnDiagonal = absOnDiagonal;\n  }\n  for(Index j = 0; j < cols(); ++j)\n    for(Index i = 0; i < j; ++i)\n    {\n      if(!internal::isMuchSmallerThan(coeff(i, j), maxAbsOnDiagonal, prec)) return false;\n      if(!internal::isMuchSmallerThan(coeff(j, i), maxAbsOnDiagonal, prec)) return false;\n    }\n  return true;\n}\n\nnamespace internal {\n\ntemplate<> struct storage_kind_to_shape<DiagonalShape> { typedef DiagonalShape Shape; };\n\nstruct Diagonal2Dense {};\n\ntemplate<> struct AssignmentKind<DenseShape,DiagonalShape> { typedef Diagonal2Dense Kind; };\n\n// Diagonal matrix to Dense assignment\ntemplate< typename DstXprType, typename SrcXprType, typename Functor>\nstruct Assignment<DstXprType, SrcXprType, Functor, Diagonal2Dense>\n{\n  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)\n  {\n    Index dstRows = src.rows();\n    Index dstCols = src.cols();\n    if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))\n      dst.resize(dstRows, dstCols);\n    \n    dst.setZero();\n    dst.diagonal() = src.diagonal();\n  }\n  \n  static void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)\n  { dst.diagonal() += src.diagonal(); }\n  \n  static void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)\n  { dst.diagonal() -= src.diagonal(); }\n};\n\n} // namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_DIAGONALMATRIX_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/DiagonalProduct.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_DIAGONALPRODUCT_H\n#define EIGEN_DIAGONALPRODUCT_H\n\nnamespace Eigen { \n\n/** \\returns the diagonal matrix product of \\c *this by the diagonal matrix \\a diagonal.\n  */\ntemplate<typename Derived>\ntemplate<typename DiagonalDerived>\ninline const Product<Derived, DiagonalDerived, LazyProduct>\nMatrixBase<Derived>::operator*(const DiagonalBase<DiagonalDerived> &a_diagonal) const\n{\n  return Product<Derived, DiagonalDerived, LazyProduct>(derived(),a_diagonal.derived());\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_DIAGONALPRODUCT_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/Dot.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2006-2008, 2010 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_DOT_H\n#define EIGEN_DOT_H\n\nnamespace Eigen { \n\nnamespace internal {\n\n// helper function for dot(). The problem is that if we put that in the body of dot(), then upon calling dot\n// with mismatched types, the compiler emits errors about failing to instantiate cwiseProduct BEFORE\n// looking at the static assertions. Thus this is a trick to get better compile errors.\ntemplate<typename T, typename U,\n// the NeedToTranspose condition here is taken straight from Assign.h\n         bool NeedToTranspose = T::IsVectorAtCompileTime\n                && U::IsVectorAtCompileTime\n                && ((int(T::RowsAtCompileTime) == 1 && int(U::ColsAtCompileTime) == 1)\n                      |  // FIXME | instead of || to please GCC 4.4.0 stupid warning \"suggest parentheses around &&\".\n                         // revert to || as soon as not needed anymore.\n                    (int(T::ColsAtCompileTime) == 1 && int(U::RowsAtCompileTime) == 1))\n>\nstruct dot_nocheck\n{\n  typedef scalar_conj_product_op<typename traits<T>::Scalar,typename traits<U>::Scalar> conj_prod;\n  typedef typename conj_prod::result_type ResScalar;\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE\n  static ResScalar run(const MatrixBase<T>& a, const MatrixBase<U>& b)\n  {\n    return a.template binaryExpr<conj_prod>(b).sum();\n  }\n};\n\ntemplate<typename T, typename U>\nstruct dot_nocheck<T, U, true>\n{\n  typedef scalar_conj_product_op<typename traits<T>::Scalar,typename traits<U>::Scalar> conj_prod;\n  typedef typename conj_prod::result_type ResScalar;\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE\n  static ResScalar run(const MatrixBase<T>& a, const MatrixBase<U>& b)\n  {\n    return a.transpose().template binaryExpr<conj_prod>(b).sum();\n  }\n};\n\n} // end namespace internal\n\n/** \\fn MatrixBase::dot\n  * \\returns the dot product of *this with other.\n  *\n  * \\only_for_vectors\n  *\n  * \\note If the scalar type is complex numbers, then this function returns the hermitian\n  * (sesquilinear) dot product, conjugate-linear in the first variable and linear in the\n  * second variable.\n  *\n  * \\sa squaredNorm(), norm()\n  */\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\nEIGEN_DEVICE_FUNC\nEIGEN_STRONG_INLINE\ntypename ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType\nMatrixBase<Derived>::dot(const MatrixBase<OtherDerived>& other) const\n{\n  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)\n  EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)\n  EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)\n#if !(defined(EIGEN_NO_STATIC_ASSERT) && defined(EIGEN_NO_DEBUG))\n  typedef internal::scalar_conj_product_op<Scalar,typename OtherDerived::Scalar> func;\n  EIGEN_CHECK_BINARY_COMPATIBILIY(func,Scalar,typename OtherDerived::Scalar);\n#endif\n  \n  eigen_assert(size() == other.size());\n\n  return internal::dot_nocheck<Derived,OtherDerived>::run(*this, other);\n}\n\n//---------- implementation of L2 norm and related functions ----------\n\n/** \\returns, for vectors, the squared \\em l2 norm of \\c *this, and for matrices the Frobenius norm.\n  * In both cases, it consists in the sum of the square of all the matrix entries.\n  * For vectors, this is also equals to the dot product of \\c *this with itself.\n  *\n  * \\sa dot(), norm(), lpNorm()\n  */\ntemplate<typename Derived>\nEIGEN_STRONG_INLINE typename NumTraits<typename internal::traits<Derived>::Scalar>::Real MatrixBase<Derived>::squaredNorm() const\n{\n  return numext::real((*this).cwiseAbs2().sum());\n}\n\n/** \\returns, for vectors, the \\em l2 norm of \\c *this, and for matrices the Frobenius norm.\n  * In both cases, it consists in the square root of the sum of the square of all the matrix entries.\n  * For vectors, this is also equals to the square root of the dot product of \\c *this with itself.\n  *\n  * \\sa lpNorm(), dot(), squaredNorm()\n  */\ntemplate<typename Derived>\nEIGEN_STRONG_INLINE typename NumTraits<typename internal::traits<Derived>::Scalar>::Real MatrixBase<Derived>::norm() const\n{\n  return numext::sqrt(squaredNorm());\n}\n\n/** \\returns an expression of the quotient of \\c *this by its own norm.\n  *\n  * \\warning If the input vector is too small (i.e., this->norm()==0),\n  *          then this function returns a copy of the input.\n  *\n  * \\only_for_vectors\n  *\n  * \\sa norm(), normalize()\n  */\ntemplate<typename Derived>\nEIGEN_STRONG_INLINE const typename MatrixBase<Derived>::PlainObject\nMatrixBase<Derived>::normalized() const\n{\n  typedef typename internal::nested_eval<Derived,2>::type _Nested;\n  _Nested n(derived());\n  RealScalar z = n.squaredNorm();\n  // NOTE: after extensive benchmarking, this conditional does not impact performance, at least on recent x86 CPU\n  if(z>RealScalar(0))\n    return n / numext::sqrt(z);\n  else\n    return n;\n}\n\n/** Normalizes the vector, i.e. divides it by its own norm.\n  *\n  * \\only_for_vectors\n  *\n  * \\warning If the input vector is too small (i.e., this->norm()==0), then \\c *this is left unchanged.\n  *\n  * \\sa norm(), normalized()\n  */\ntemplate<typename Derived>\nEIGEN_STRONG_INLINE void MatrixBase<Derived>::normalize()\n{\n  RealScalar z = squaredNorm();\n  // NOTE: after extensive benchmarking, this conditional does not impact performance, at least on recent x86 CPU\n  if(z>RealScalar(0))\n    derived() /= numext::sqrt(z);\n}\n\n/** \\returns an expression of the quotient of \\c *this by its own norm while avoiding underflow and overflow.\n  *\n  * \\only_for_vectors\n  *\n  * This method is analogue to the normalized() method, but it reduces the risk of\n  * underflow and overflow when computing the norm.\n  *\n  * \\warning If the input vector is too small (i.e., this->norm()==0),\n  *          then this function returns a copy of the input.\n  *\n  * \\sa stableNorm(), stableNormalize(), normalized()\n  */\ntemplate<typename Derived>\nEIGEN_STRONG_INLINE const typename MatrixBase<Derived>::PlainObject\nMatrixBase<Derived>::stableNormalized() const\n{\n  typedef typename internal::nested_eval<Derived,3>::type _Nested;\n  _Nested n(derived());\n  RealScalar w = n.cwiseAbs().maxCoeff();\n  RealScalar z = (n/w).squaredNorm();\n  if(z>RealScalar(0))\n    return n / (numext::sqrt(z)*w);\n  else\n    return n;\n}\n\n/** Normalizes the vector while avoid underflow and overflow\n  *\n  * \\only_for_vectors\n  *\n  * This method is analogue to the normalize() method, but it reduces the risk of\n  * underflow and overflow when computing the norm.\n  *\n  * \\warning If the input vector is too small (i.e., this->norm()==0), then \\c *this is left unchanged.\n  *\n  * \\sa stableNorm(), stableNormalized(), normalize()\n  */\ntemplate<typename Derived>\nEIGEN_STRONG_INLINE void MatrixBase<Derived>::stableNormalize()\n{\n  RealScalar w = cwiseAbs().maxCoeff();\n  RealScalar z = (derived()/w).squaredNorm();\n  if(z>RealScalar(0))\n    derived() /= numext::sqrt(z)*w;\n}\n\n//---------- implementation of other norms ----------\n\nnamespace internal {\n\ntemplate<typename Derived, int p>\nstruct lpNorm_selector\n{\n  typedef typename NumTraits<typename traits<Derived>::Scalar>::Real RealScalar;\n  EIGEN_DEVICE_FUNC\n  static inline RealScalar run(const MatrixBase<Derived>& m)\n  {\n    EIGEN_USING_STD_MATH(pow)\n    return pow(m.cwiseAbs().array().pow(p).sum(), RealScalar(1)/p);\n  }\n};\n\ntemplate<typename Derived>\nstruct lpNorm_selector<Derived, 1>\n{\n  EIGEN_DEVICE_FUNC\n  static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m)\n  {\n    return m.cwiseAbs().sum();\n  }\n};\n\ntemplate<typename Derived>\nstruct lpNorm_selector<Derived, 2>\n{\n  EIGEN_DEVICE_FUNC\n  static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m)\n  {\n    return m.norm();\n  }\n};\n\ntemplate<typename Derived>\nstruct lpNorm_selector<Derived, Infinity>\n{\n  typedef typename NumTraits<typename traits<Derived>::Scalar>::Real RealScalar;\n  EIGEN_DEVICE_FUNC\n  static inline RealScalar run(const MatrixBase<Derived>& m)\n  {\n    if(Derived::SizeAtCompileTime==0 || (Derived::SizeAtCompileTime==Dynamic && m.size()==0))\n      return RealScalar(0);\n    return m.cwiseAbs().maxCoeff();\n  }\n};\n\n} // end namespace internal\n\n/** \\returns the \\b coefficient-wise \\f$ \\ell^p \\f$ norm of \\c *this, that is, returns the p-th root of the sum of the p-th powers of the absolute values\n  *          of the coefficients of \\c *this. If \\a p is the special value \\a Eigen::Infinity, this function returns the \\f$ \\ell^\\infty \\f$\n  *          norm, that is the maximum of the absolute values of the coefficients of \\c *this.\n  *\n  * In all cases, if \\c *this is empty, then the value 0 is returned.\n  *\n  * \\note For matrices, this function does not compute the <a href=\"https://en.wikipedia.org/wiki/Operator_norm\">operator-norm</a>. That is, if \\c *this is a matrix, then its coefficients are interpreted as a 1D vector. Nonetheless, you can easily compute the 1-norm and \\f$\\infty\\f$-norm matrix operator norms using \\link TutorialReductionsVisitorsBroadcastingReductionsNorm partial reductions \\endlink.\n  *\n  * \\sa norm()\n  */\ntemplate<typename Derived>\ntemplate<int p>\n#ifndef EIGEN_PARSED_BY_DOXYGEN\ninline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real\n#else\nMatrixBase<Derived>::RealScalar\n#endif\nMatrixBase<Derived>::lpNorm() const\n{\n  return internal::lpNorm_selector<Derived, p>::run(*this);\n}\n\n//---------- implementation of isOrthogonal / isUnitary ----------\n\n/** \\returns true if *this is approximately orthogonal to \\a other,\n  *          within the precision given by \\a prec.\n  *\n  * Example: \\include MatrixBase_isOrthogonal.cpp\n  * Output: \\verbinclude MatrixBase_isOrthogonal.out\n  */\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\nbool MatrixBase<Derived>::isOrthogonal\n(const MatrixBase<OtherDerived>& other, const RealScalar& prec) const\n{\n  typename internal::nested_eval<Derived,2>::type nested(derived());\n  typename internal::nested_eval<OtherDerived,2>::type otherNested(other.derived());\n  return numext::abs2(nested.dot(otherNested)) <= prec * prec * nested.squaredNorm() * otherNested.squaredNorm();\n}\n\n/** \\returns true if *this is approximately an unitary matrix,\n  *          within the precision given by \\a prec. In the case where the \\a Scalar\n  *          type is real numbers, a unitary matrix is an orthogonal matrix, whence the name.\n  *\n  * \\note This can be used to check whether a family of vectors forms an orthonormal basis.\n  *       Indeed, \\c m.isUnitary() returns true if and only if the columns (equivalently, the rows) of m form an\n  *       orthonormal basis.\n  *\n  * Example: \\include MatrixBase_isUnitary.cpp\n  * Output: \\verbinclude MatrixBase_isUnitary.out\n  */\ntemplate<typename Derived>\nbool MatrixBase<Derived>::isUnitary(const RealScalar& prec) const\n{\n  typename internal::nested_eval<Derived,1>::type self(derived());\n  for(Index i = 0; i < cols(); ++i)\n  {\n    if(!internal::isApprox(self.col(i).squaredNorm(), static_cast<RealScalar>(1), prec))\n      return false;\n    for(Index j = 0; j < i; ++j)\n      if(!internal::isMuchSmallerThan(self.col(i).dot(self.col(j)), static_cast<Scalar>(1), prec))\n        return false;\n  }\n  return true;\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_DOT_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/EigenBase.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_EIGENBASE_H\n#define EIGEN_EIGENBASE_H\n\nnamespace Eigen {\n\n/** \\class EigenBase\n  * \\ingroup Core_Module\n  * \n  * Common base class for all classes T such that MatrixBase has an operator=(T) and a constructor MatrixBase(T).\n  *\n  * In other words, an EigenBase object is an object that can be copied into a MatrixBase.\n  *\n  * Besides MatrixBase-derived classes, this also includes special matrix classes such as diagonal matrices, etc.\n  *\n  * Notice that this class is trivial, it is only used to disambiguate overloaded functions.\n  *\n  * \\sa \\blank \\ref TopicClassHierarchy\n  */\ntemplate<typename Derived> struct EigenBase\n{\n//   typedef typename internal::plain_matrix_type<Derived>::type PlainObject;\n  \n  /** \\brief The interface type of indices\n    * \\details To change this, \\c \\#define the preprocessor symbol \\c EIGEN_DEFAULT_DENSE_INDEX_TYPE.\n    * \\deprecated Since Eigen 3.3, its usage is deprecated. Use Eigen::Index instead.\n    * \\sa StorageIndex, \\ref TopicPreprocessorDirectives.\n    */\n  typedef Eigen::Index Index;\n\n  // FIXME is it needed?\n  typedef typename internal::traits<Derived>::StorageKind StorageKind;\n\n  /** \\returns a reference to the derived object */\n  EIGEN_DEVICE_FUNC\n  Derived& derived() { return *static_cast<Derived*>(this); }\n  /** \\returns a const reference to the derived object */\n  EIGEN_DEVICE_FUNC\n  const Derived& derived() const { return *static_cast<const Derived*>(this); }\n\n  EIGEN_DEVICE_FUNC\n  inline Derived& const_cast_derived() const\n  { return *static_cast<Derived*>(const_cast<EigenBase*>(this)); }\n  EIGEN_DEVICE_FUNC\n  inline const Derived& const_derived() const\n  { return *static_cast<const Derived*>(this); }\n\n  /** \\returns the number of rows. \\sa cols(), RowsAtCompileTime */\n  EIGEN_DEVICE_FUNC\n  inline Index rows() const { return derived().rows(); }\n  /** \\returns the number of columns. \\sa rows(), ColsAtCompileTime*/\n  EIGEN_DEVICE_FUNC\n  inline Index cols() const { return derived().cols(); }\n  /** \\returns the number of coefficients, which is rows()*cols().\n    * \\sa rows(), cols(), SizeAtCompileTime. */\n  EIGEN_DEVICE_FUNC\n  inline Index size() const { return rows() * cols(); }\n\n  /** \\internal Don't use it, but do the equivalent: \\code dst = *this; \\endcode */\n  template<typename Dest>\n  EIGEN_DEVICE_FUNC\n  inline void evalTo(Dest& dst) const\n  { derived().evalTo(dst); }\n\n  /** \\internal Don't use it, but do the equivalent: \\code dst += *this; \\endcode */\n  template<typename Dest>\n  EIGEN_DEVICE_FUNC\n  inline void addTo(Dest& dst) const\n  {\n    // This is the default implementation,\n    // derived class can reimplement it in a more optimized way.\n    typename Dest::PlainObject res(rows(),cols());\n    evalTo(res);\n    dst += res;\n  }\n\n  /** \\internal Don't use it, but do the equivalent: \\code dst -= *this; \\endcode */\n  template<typename Dest>\n  EIGEN_DEVICE_FUNC\n  inline void subTo(Dest& dst) const\n  {\n    // This is the default implementation,\n    // derived class can reimplement it in a more optimized way.\n    typename Dest::PlainObject res(rows(),cols());\n    evalTo(res);\n    dst -= res;\n  }\n\n  /** \\internal Don't use it, but do the equivalent: \\code dst.applyOnTheRight(*this); \\endcode */\n  template<typename Dest>\n  EIGEN_DEVICE_FUNC inline void applyThisOnTheRight(Dest& dst) const\n  {\n    // This is the default implementation,\n    // derived class can reimplement it in a more optimized way.\n    dst = dst * this->derived();\n  }\n\n  /** \\internal Don't use it, but do the equivalent: \\code dst.applyOnTheLeft(*this); \\endcode */\n  template<typename Dest>\n  EIGEN_DEVICE_FUNC inline void applyThisOnTheLeft(Dest& dst) const\n  {\n    // This is the default implementation,\n    // derived class can reimplement it in a more optimized way.\n    dst = this->derived() * dst;\n  }\n\n};\n\n/***************************************************************************\n* Implementation of matrix base methods\n***************************************************************************/\n\n/** \\brief Copies the generic expression \\a other into *this.\n  *\n  * \\details The expression must provide a (templated) evalTo(Derived& dst) const\n  * function which does the actual job. In practice, this allows any user to write\n  * its own special matrix without having to modify MatrixBase\n  *\n  * \\returns a reference to *this.\n  */\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\nEIGEN_DEVICE_FUNC\nDerived& DenseBase<Derived>::operator=(const EigenBase<OtherDerived> &other)\n{\n  call_assignment(derived(), other.derived());\n  return derived();\n}\n\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\nEIGEN_DEVICE_FUNC\nDerived& DenseBase<Derived>::operator+=(const EigenBase<OtherDerived> &other)\n{\n  call_assignment(derived(), other.derived(), internal::add_assign_op<Scalar,typename OtherDerived::Scalar>());\n  return derived();\n}\n\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\nEIGEN_DEVICE_FUNC\nDerived& DenseBase<Derived>::operator-=(const EigenBase<OtherDerived> &other)\n{\n  call_assignment(derived(), other.derived(), internal::sub_assign_op<Scalar,typename OtherDerived::Scalar>());\n  return derived();\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_EIGENBASE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/ForceAlignedAccess.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_FORCEALIGNEDACCESS_H\n#define EIGEN_FORCEALIGNEDACCESS_H\n\nnamespace Eigen {\n\n/** \\class ForceAlignedAccess\n  * \\ingroup Core_Module\n  *\n  * \\brief Enforce aligned packet loads and stores regardless of what is requested\n  *\n  * \\param ExpressionType the type of the object of which we are forcing aligned packet access\n  *\n  * This class is the return type of MatrixBase::forceAlignedAccess()\n  * and most of the time this is the only way it is used.\n  *\n  * \\sa MatrixBase::forceAlignedAccess()\n  */\n\nnamespace internal {\ntemplate<typename ExpressionType>\nstruct traits<ForceAlignedAccess<ExpressionType> > : public traits<ExpressionType>\n{};\n}\n\ntemplate<typename ExpressionType> class ForceAlignedAccess\n  : public internal::dense_xpr_base< ForceAlignedAccess<ExpressionType> >::type\n{\n  public:\n\n    typedef typename internal::dense_xpr_base<ForceAlignedAccess>::type Base;\n    EIGEN_DENSE_PUBLIC_INTERFACE(ForceAlignedAccess)\n\n    EIGEN_DEVICE_FUNC explicit inline ForceAlignedAccess(const ExpressionType& matrix) : m_expression(matrix) {}\n\n    EIGEN_DEVICE_FUNC inline Index rows() const { return m_expression.rows(); }\n    EIGEN_DEVICE_FUNC inline Index cols() const { return m_expression.cols(); }\n    EIGEN_DEVICE_FUNC inline Index outerStride() const { return m_expression.outerStride(); }\n    EIGEN_DEVICE_FUNC inline Index innerStride() const { return m_expression.innerStride(); }\n\n    EIGEN_DEVICE_FUNC inline const CoeffReturnType coeff(Index row, Index col) const\n    {\n      return m_expression.coeff(row, col);\n    }\n\n    EIGEN_DEVICE_FUNC inline Scalar& coeffRef(Index row, Index col)\n    {\n      return m_expression.const_cast_derived().coeffRef(row, col);\n    }\n\n    EIGEN_DEVICE_FUNC inline const CoeffReturnType coeff(Index index) const\n    {\n      return m_expression.coeff(index);\n    }\n\n    EIGEN_DEVICE_FUNC inline Scalar& coeffRef(Index index)\n    {\n      return m_expression.const_cast_derived().coeffRef(index);\n    }\n\n    template<int LoadMode>\n    inline const PacketScalar packet(Index row, Index col) const\n    {\n      return m_expression.template packet<Aligned>(row, col);\n    }\n\n    template<int LoadMode>\n    inline void writePacket(Index row, Index col, const PacketScalar& x)\n    {\n      m_expression.const_cast_derived().template writePacket<Aligned>(row, col, x);\n    }\n\n    template<int LoadMode>\n    inline const PacketScalar packet(Index index) const\n    {\n      return m_expression.template packet<Aligned>(index);\n    }\n\n    template<int LoadMode>\n    inline void writePacket(Index index, const PacketScalar& x)\n    {\n      m_expression.const_cast_derived().template writePacket<Aligned>(index, x);\n    }\n\n    EIGEN_DEVICE_FUNC operator const ExpressionType&() const { return m_expression; }\n\n  protected:\n    const ExpressionType& m_expression;\n\n  private:\n    ForceAlignedAccess& operator=(const ForceAlignedAccess&);\n};\n\n/** \\returns an expression of *this with forced aligned access\n  * \\sa forceAlignedAccessIf(),class ForceAlignedAccess\n  */\ntemplate<typename Derived>\ninline const ForceAlignedAccess<Derived>\nMatrixBase<Derived>::forceAlignedAccess() const\n{\n  return ForceAlignedAccess<Derived>(derived());\n}\n\n/** \\returns an expression of *this with forced aligned access\n  * \\sa forceAlignedAccessIf(), class ForceAlignedAccess\n  */\ntemplate<typename Derived>\ninline ForceAlignedAccess<Derived>\nMatrixBase<Derived>::forceAlignedAccess()\n{\n  return ForceAlignedAccess<Derived>(derived());\n}\n\n/** \\returns an expression of *this with forced aligned access if \\a Enable is true.\n  * \\sa forceAlignedAccess(), class ForceAlignedAccess\n  */\ntemplate<typename Derived>\ntemplate<bool Enable>\ninline typename internal::add_const_on_value_type<typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type>::type\nMatrixBase<Derived>::forceAlignedAccessIf() const\n{\n  return derived();  // FIXME This should not work but apparently is never used\n}\n\n/** \\returns an expression of *this with forced aligned access if \\a Enable is true.\n  * \\sa forceAlignedAccess(), class ForceAlignedAccess\n  */\ntemplate<typename Derived>\ntemplate<bool Enable>\ninline typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type\nMatrixBase<Derived>::forceAlignedAccessIf()\n{\n  return derived();  // FIXME This should not work but apparently is never used\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_FORCEALIGNEDACCESS_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/Fuzzy.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_FUZZY_H\n#define EIGEN_FUZZY_H\n\nnamespace Eigen { \n\nnamespace internal\n{\n\ntemplate<typename Derived, typename OtherDerived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger>\nstruct isApprox_selector\n{\n  EIGEN_DEVICE_FUNC\n  static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar& prec)\n  {\n    typename internal::nested_eval<Derived,2>::type nested(x);\n    typename internal::nested_eval<OtherDerived,2>::type otherNested(y);\n    return (nested - otherNested).cwiseAbs2().sum() <= prec * prec * numext::mini(nested.cwiseAbs2().sum(), otherNested.cwiseAbs2().sum());\n  }\n};\n\ntemplate<typename Derived, typename OtherDerived>\nstruct isApprox_selector<Derived, OtherDerived, true>\n{\n  EIGEN_DEVICE_FUNC\n  static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar&)\n  {\n    return x.matrix() == y.matrix();\n  }\n};\n\ntemplate<typename Derived, typename OtherDerived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger>\nstruct isMuchSmallerThan_object_selector\n{\n  EIGEN_DEVICE_FUNC\n  static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar& prec)\n  {\n    return x.cwiseAbs2().sum() <= numext::abs2(prec) * y.cwiseAbs2().sum();\n  }\n};\n\ntemplate<typename Derived, typename OtherDerived>\nstruct isMuchSmallerThan_object_selector<Derived, OtherDerived, true>\n{\n  EIGEN_DEVICE_FUNC\n  static bool run(const Derived& x, const OtherDerived&, const typename Derived::RealScalar&)\n  {\n    return x.matrix() == Derived::Zero(x.rows(), x.cols()).matrix();\n  }\n};\n\ntemplate<typename Derived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger>\nstruct isMuchSmallerThan_scalar_selector\n{\n  EIGEN_DEVICE_FUNC\n  static bool run(const Derived& x, const typename Derived::RealScalar& y, const typename Derived::RealScalar& prec)\n  {\n    return x.cwiseAbs2().sum() <= numext::abs2(prec * y);\n  }\n};\n\ntemplate<typename Derived>\nstruct isMuchSmallerThan_scalar_selector<Derived, true>\n{\n  EIGEN_DEVICE_FUNC\n  static bool run(const Derived& x, const typename Derived::RealScalar&, const typename Derived::RealScalar&)\n  {\n    return x.matrix() == Derived::Zero(x.rows(), x.cols()).matrix();\n  }\n};\n\n} // end namespace internal\n\n\n/** \\returns \\c true if \\c *this is approximately equal to \\a other, within the precision\n  * determined by \\a prec.\n  *\n  * \\note The fuzzy compares are done multiplicatively. Two vectors \\f$ v \\f$ and \\f$ w \\f$\n  * are considered to be approximately equal within precision \\f$ p \\f$ if\n  * \\f[ \\Vert v - w \\Vert \\leqslant p\\,\\min(\\Vert v\\Vert, \\Vert w\\Vert). \\f]\n  * For matrices, the comparison is done using the Hilbert-Schmidt norm (aka Frobenius norm\n  * L2 norm).\n  *\n  * \\note Because of the multiplicativeness of this comparison, one can't use this function\n  * to check whether \\c *this is approximately equal to the zero matrix or vector.\n  * Indeed, \\c isApprox(zero) returns false unless \\c *this itself is exactly the zero matrix\n  * or vector. If you want to test whether \\c *this is zero, use internal::isMuchSmallerThan(const\n  * RealScalar&, RealScalar) instead.\n  *\n  * \\sa internal::isMuchSmallerThan(const RealScalar&, RealScalar) const\n  */\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\nbool DenseBase<Derived>::isApprox(\n  const DenseBase<OtherDerived>& other,\n  const RealScalar& prec\n) const\n{\n  return internal::isApprox_selector<Derived, OtherDerived>::run(derived(), other.derived(), prec);\n}\n\n/** \\returns \\c true if the norm of \\c *this is much smaller than \\a other,\n  * within the precision determined by \\a prec.\n  *\n  * \\note The fuzzy compares are done multiplicatively. A vector \\f$ v \\f$ is\n  * considered to be much smaller than \\f$ x \\f$ within precision \\f$ p \\f$ if\n  * \\f[ \\Vert v \\Vert \\leqslant p\\,\\vert x\\vert. \\f]\n  *\n  * For matrices, the comparison is done using the Hilbert-Schmidt norm. For this reason,\n  * the value of the reference scalar \\a other should come from the Hilbert-Schmidt norm\n  * of a reference matrix of same dimensions.\n  *\n  * \\sa isApprox(), isMuchSmallerThan(const DenseBase<OtherDerived>&, RealScalar) const\n  */\ntemplate<typename Derived>\nbool DenseBase<Derived>::isMuchSmallerThan(\n  const typename NumTraits<Scalar>::Real& other,\n  const RealScalar& prec\n) const\n{\n  return internal::isMuchSmallerThan_scalar_selector<Derived>::run(derived(), other, prec);\n}\n\n/** \\returns \\c true if the norm of \\c *this is much smaller than the norm of \\a other,\n  * within the precision determined by \\a prec.\n  *\n  * \\note The fuzzy compares are done multiplicatively. A vector \\f$ v \\f$ is\n  * considered to be much smaller than a vector \\f$ w \\f$ within precision \\f$ p \\f$ if\n  * \\f[ \\Vert v \\Vert \\leqslant p\\,\\Vert w\\Vert. \\f]\n  * For matrices, the comparison is done using the Hilbert-Schmidt norm.\n  *\n  * \\sa isApprox(), isMuchSmallerThan(const RealScalar&, RealScalar) const\n  */\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\nbool DenseBase<Derived>::isMuchSmallerThan(\n  const DenseBase<OtherDerived>& other,\n  const RealScalar& prec\n) const\n{\n  return internal::isMuchSmallerThan_object_selector<Derived, OtherDerived>::run(derived(), other.derived(), prec);\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_FUZZY_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/GeneralProduct.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_GENERAL_PRODUCT_H\n#define EIGEN_GENERAL_PRODUCT_H\n\nnamespace Eigen {\n\nenum {\n  Large = 2,\n  Small = 3\n};\n\nnamespace internal {\n\ntemplate<int Rows, int Cols, int Depth> struct product_type_selector;\n\ntemplate<int Size, int MaxSize> struct product_size_category\n{\n  enum {\n    #ifndef EIGEN_CUDA_ARCH\n    is_large = MaxSize == Dynamic ||\n               Size >= EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD ||\n               (Size==Dynamic && MaxSize>=EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD),\n    #else\n    is_large = 0,\n    #endif\n    value = is_large  ? Large\n          : Size == 1 ? 1\n                      : Small\n  };\n};\n\ntemplate<typename Lhs, typename Rhs> struct product_type\n{\n  typedef typename remove_all<Lhs>::type _Lhs;\n  typedef typename remove_all<Rhs>::type _Rhs;\n  enum {\n    MaxRows = traits<_Lhs>::MaxRowsAtCompileTime,\n    Rows    = traits<_Lhs>::RowsAtCompileTime,\n    MaxCols = traits<_Rhs>::MaxColsAtCompileTime,\n    Cols    = traits<_Rhs>::ColsAtCompileTime,\n    MaxDepth = EIGEN_SIZE_MIN_PREFER_FIXED(traits<_Lhs>::MaxColsAtCompileTime,\n                                           traits<_Rhs>::MaxRowsAtCompileTime),\n    Depth = EIGEN_SIZE_MIN_PREFER_FIXED(traits<_Lhs>::ColsAtCompileTime,\n                                        traits<_Rhs>::RowsAtCompileTime)\n  };\n\n  // the splitting into different lines of code here, introducing the _select enums and the typedef below,\n  // is to work around an internal compiler error with gcc 4.1 and 4.2.\nprivate:\n  enum {\n    rows_select = product_size_category<Rows,MaxRows>::value,\n    cols_select = product_size_category<Cols,MaxCols>::value,\n    depth_select = product_size_category<Depth,MaxDepth>::value\n  };\n  typedef product_type_selector<rows_select, cols_select, depth_select> selector;\n\npublic:\n  enum {\n    value = selector::ret,\n    ret = selector::ret\n  };\n#ifdef EIGEN_DEBUG_PRODUCT\n  static void debug()\n  {\n      EIGEN_DEBUG_VAR(Rows);\n      EIGEN_DEBUG_VAR(Cols);\n      EIGEN_DEBUG_VAR(Depth);\n      EIGEN_DEBUG_VAR(rows_select);\n      EIGEN_DEBUG_VAR(cols_select);\n      EIGEN_DEBUG_VAR(depth_select);\n      EIGEN_DEBUG_VAR(value);\n  }\n#endif\n};\n\n/* The following allows to select the kind of product at compile time\n * based on the three dimensions of the product.\n * This is a compile time mapping from {1,Small,Large}^3 -> {product types} */\n// FIXME I'm not sure the current mapping is the ideal one.\ntemplate<int M, int N>  struct product_type_selector<M,N,1>              { enum { ret = OuterProduct }; };\ntemplate<int M>         struct product_type_selector<M, 1, 1>            { enum { ret = LazyCoeffBasedProductMode }; };\ntemplate<int N>         struct product_type_selector<1, N, 1>            { enum { ret = LazyCoeffBasedProductMode }; };\ntemplate<int Depth>     struct product_type_selector<1,    1,    Depth>  { enum { ret = InnerProduct }; };\ntemplate<>              struct product_type_selector<1,    1,    1>      { enum { ret = InnerProduct }; };\ntemplate<>              struct product_type_selector<Small,1,    Small>  { enum { ret = CoeffBasedProductMode }; };\ntemplate<>              struct product_type_selector<1,    Small,Small>  { enum { ret = CoeffBasedProductMode }; };\ntemplate<>              struct product_type_selector<Small,Small,Small>  { enum { ret = CoeffBasedProductMode }; };\ntemplate<>              struct product_type_selector<Small, Small, 1>    { enum { ret = LazyCoeffBasedProductMode }; };\ntemplate<>              struct product_type_selector<Small, Large, 1>    { enum { ret = LazyCoeffBasedProductMode }; };\ntemplate<>              struct product_type_selector<Large, Small, 1>    { enum { ret = LazyCoeffBasedProductMode }; };\ntemplate<>              struct product_type_selector<1,    Large,Small>  { enum { ret = CoeffBasedProductMode }; };\ntemplate<>              struct product_type_selector<1,    Large,Large>  { enum { ret = GemvProduct }; };\ntemplate<>              struct product_type_selector<1,    Small,Large>  { enum { ret = CoeffBasedProductMode }; };\ntemplate<>              struct product_type_selector<Large,1,    Small>  { enum { ret = CoeffBasedProductMode }; };\ntemplate<>              struct product_type_selector<Large,1,    Large>  { enum { ret = GemvProduct }; };\ntemplate<>              struct product_type_selector<Small,1,    Large>  { enum { ret = CoeffBasedProductMode }; };\ntemplate<>              struct product_type_selector<Small,Small,Large>  { enum { ret = GemmProduct }; };\ntemplate<>              struct product_type_selector<Large,Small,Large>  { enum { ret = GemmProduct }; };\ntemplate<>              struct product_type_selector<Small,Large,Large>  { enum { ret = GemmProduct }; };\ntemplate<>              struct product_type_selector<Large,Large,Large>  { enum { ret = GemmProduct }; };\ntemplate<>              struct product_type_selector<Large,Small,Small>  { enum { ret = CoeffBasedProductMode }; };\ntemplate<>              struct product_type_selector<Small,Large,Small>  { enum { ret = CoeffBasedProductMode }; };\ntemplate<>              struct product_type_selector<Large,Large,Small>  { enum { ret = GemmProduct }; };\n\n} // end namespace internal\n\n/***********************************************************************\n*  Implementation of Inner Vector Vector Product\n***********************************************************************/\n\n// FIXME : maybe the \"inner product\" could return a Scalar\n// instead of a 1x1 matrix ??\n// Pro: more natural for the user\n// Cons: this could be a problem if in a meta unrolled algorithm a matrix-matrix\n// product ends up to a row-vector times col-vector product... To tackle this use\n// case, we could have a specialization for Block<MatrixType,1,1> with: operator=(Scalar x);\n\n/***********************************************************************\n*  Implementation of Outer Vector Vector Product\n***********************************************************************/\n\n/***********************************************************************\n*  Implementation of General Matrix Vector Product\n***********************************************************************/\n\n/*  According to the shape/flags of the matrix we have to distinghish 3 different cases:\n *   1 - the matrix is col-major, BLAS compatible and M is large => call fast BLAS-like colmajor routine\n *   2 - the matrix is row-major, BLAS compatible and N is large => call fast BLAS-like rowmajor routine\n *   3 - all other cases are handled using a simple loop along the outer-storage direction.\n *  Therefore we need a lower level meta selector.\n *  Furthermore, if the matrix is the rhs, then the product has to be transposed.\n */\nnamespace internal {\n\ntemplate<int Side, int StorageOrder, bool BlasCompatible>\nstruct gemv_dense_selector;\n\n} // end namespace internal\n\nnamespace internal {\n\ntemplate<typename Scalar,int Size,int MaxSize,bool Cond> struct gemv_static_vector_if;\n\ntemplate<typename Scalar,int Size,int MaxSize>\nstruct gemv_static_vector_if<Scalar,Size,MaxSize,false>\n{\n  EIGEN_STRONG_INLINE  Scalar* data() { eigen_internal_assert(false && \"should never be called\"); return 0; }\n};\n\ntemplate<typename Scalar,int Size>\nstruct gemv_static_vector_if<Scalar,Size,Dynamic,true>\n{\n  EIGEN_STRONG_INLINE Scalar* data() { return 0; }\n};\n\ntemplate<typename Scalar,int Size,int MaxSize>\nstruct gemv_static_vector_if<Scalar,Size,MaxSize,true>\n{\n  enum {\n    ForceAlignment  = internal::packet_traits<Scalar>::Vectorizable,\n    PacketSize      = internal::packet_traits<Scalar>::size\n  };\n  #if EIGEN_MAX_STATIC_ALIGN_BYTES!=0\n  internal::plain_array<Scalar,EIGEN_SIZE_MIN_PREFER_FIXED(Size,MaxSize),0,EIGEN_PLAIN_ENUM_MIN(AlignedMax,PacketSize)> m_data;\n  EIGEN_STRONG_INLINE Scalar* data() { return m_data.array; }\n  #else\n  // Some architectures cannot align on the stack,\n  // => let's manually enforce alignment by allocating more data and return the address of the first aligned element.\n  internal::plain_array<Scalar,EIGEN_SIZE_MIN_PREFER_FIXED(Size,MaxSize)+(ForceAlignment?EIGEN_MAX_ALIGN_BYTES:0),0> m_data;\n  EIGEN_STRONG_INLINE Scalar* data() {\n    return ForceAlignment\n            ? reinterpret_cast<Scalar*>((internal::UIntPtr(m_data.array) & ~(std::size_t(EIGEN_MAX_ALIGN_BYTES-1))) + EIGEN_MAX_ALIGN_BYTES)\n            : m_data.array;\n  }\n  #endif\n};\n\n// The vector is on the left => transposition\ntemplate<int StorageOrder, bool BlasCompatible>\nstruct gemv_dense_selector<OnTheLeft,StorageOrder,BlasCompatible>\n{\n  template<typename Lhs, typename Rhs, typename Dest>\n  static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)\n  {\n    Transpose<Dest> destT(dest);\n    enum { OtherStorageOrder = StorageOrder == RowMajor ? ColMajor : RowMajor };\n    gemv_dense_selector<OnTheRight,OtherStorageOrder,BlasCompatible>\n      ::run(rhs.transpose(), lhs.transpose(), destT, alpha);\n  }\n};\n\ntemplate<> struct gemv_dense_selector<OnTheRight,ColMajor,true>\n{\n  template<typename Lhs, typename Rhs, typename Dest>\n  static inline void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)\n  {\n    typedef typename Lhs::Scalar   LhsScalar;\n    typedef typename Rhs::Scalar   RhsScalar;\n    typedef typename Dest::Scalar  ResScalar;\n    typedef typename Dest::RealScalar  RealScalar;\n    \n    typedef internal::blas_traits<Lhs> LhsBlasTraits;\n    typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;\n    typedef internal::blas_traits<Rhs> RhsBlasTraits;\n    typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;\n  \n    typedef Map<Matrix<ResScalar,Dynamic,1>, EIGEN_PLAIN_ENUM_MIN(AlignedMax,internal::packet_traits<ResScalar>::size)> MappedDest;\n\n    ActualLhsType actualLhs = LhsBlasTraits::extract(lhs);\n    ActualRhsType actualRhs = RhsBlasTraits::extract(rhs);\n\n    ResScalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(lhs)\n                                  * RhsBlasTraits::extractScalarFactor(rhs);\n\n    // make sure Dest is a compile-time vector type (bug 1166)\n    typedef typename conditional<Dest::IsVectorAtCompileTime, Dest, typename Dest::ColXpr>::type ActualDest;\n\n    enum {\n      // FIXME find a way to allow an inner stride on the result if packet_traits<Scalar>::size==1\n      // on, the other hand it is good for the cache to pack the vector anyways...\n      EvalToDestAtCompileTime = (ActualDest::InnerStrideAtCompileTime==1),\n      ComplexByReal = (NumTraits<LhsScalar>::IsComplex) && (!NumTraits<RhsScalar>::IsComplex),\n      MightCannotUseDest = (!EvalToDestAtCompileTime) || ComplexByReal\n    };\n\n    typedef const_blas_data_mapper<LhsScalar,Index,ColMajor> LhsMapper;\n    typedef const_blas_data_mapper<RhsScalar,Index,RowMajor> RhsMapper;\n    RhsScalar compatibleAlpha = get_factor<ResScalar,RhsScalar>::run(actualAlpha);\n\n    if(!MightCannotUseDest)\n    {\n      // shortcut if we are sure to be able to use dest directly,\n      // this ease the compiler to generate cleaner and more optimzized code for most common cases\n      general_matrix_vector_product\n          <Index,LhsScalar,LhsMapper,ColMajor,LhsBlasTraits::NeedToConjugate,RhsScalar,RhsMapper,RhsBlasTraits::NeedToConjugate>::run(\n          actualLhs.rows(), actualLhs.cols(),\n          LhsMapper(actualLhs.data(), actualLhs.outerStride()),\n          RhsMapper(actualRhs.data(), actualRhs.innerStride()),\n          dest.data(), 1,\n          compatibleAlpha);\n    }\n    else\n    {\n      gemv_static_vector_if<ResScalar,ActualDest::SizeAtCompileTime,ActualDest::MaxSizeAtCompileTime,MightCannotUseDest> static_dest;\n\n      const bool alphaIsCompatible = (!ComplexByReal) || (numext::imag(actualAlpha)==RealScalar(0));\n      const bool evalToDest = EvalToDestAtCompileTime && alphaIsCompatible;\n\n      ei_declare_aligned_stack_constructed_variable(ResScalar,actualDestPtr,dest.size(),\n                                                    evalToDest ? dest.data() : static_dest.data());\n\n      if(!evalToDest)\n      {\n        #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN\n        Index size = dest.size();\n        EIGEN_DENSE_STORAGE_CTOR_PLUGIN\n        #endif\n        if(!alphaIsCompatible)\n        {\n          MappedDest(actualDestPtr, dest.size()).setZero();\n          compatibleAlpha = RhsScalar(1);\n        }\n        else\n          MappedDest(actualDestPtr, dest.size()) = dest;\n      }\n\n      general_matrix_vector_product\n          <Index,LhsScalar,LhsMapper,ColMajor,LhsBlasTraits::NeedToConjugate,RhsScalar,RhsMapper,RhsBlasTraits::NeedToConjugate>::run(\n          actualLhs.rows(), actualLhs.cols(),\n          LhsMapper(actualLhs.data(), actualLhs.outerStride()),\n          RhsMapper(actualRhs.data(), actualRhs.innerStride()),\n          actualDestPtr, 1,\n          compatibleAlpha);\n\n      if (!evalToDest)\n      {\n        if(!alphaIsCompatible)\n          dest.matrix() += actualAlpha * MappedDest(actualDestPtr, dest.size());\n        else\n          dest = MappedDest(actualDestPtr, dest.size());\n      }\n    }\n  }\n};\n\ntemplate<> struct gemv_dense_selector<OnTheRight,RowMajor,true>\n{\n  template<typename Lhs, typename Rhs, typename Dest>\n  static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)\n  {\n    typedef typename Lhs::Scalar   LhsScalar;\n    typedef typename Rhs::Scalar   RhsScalar;\n    typedef typename Dest::Scalar  ResScalar;\n    \n    typedef internal::blas_traits<Lhs> LhsBlasTraits;\n    typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;\n    typedef internal::blas_traits<Rhs> RhsBlasTraits;\n    typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;\n    typedef typename internal::remove_all<ActualRhsType>::type ActualRhsTypeCleaned;\n\n    typename add_const<ActualLhsType>::type actualLhs = LhsBlasTraits::extract(lhs);\n    typename add_const<ActualRhsType>::type actualRhs = RhsBlasTraits::extract(rhs);\n\n    ResScalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(lhs)\n                                  * RhsBlasTraits::extractScalarFactor(rhs);\n\n    enum {\n      // FIXME find a way to allow an inner stride on the result if packet_traits<Scalar>::size==1\n      // on, the other hand it is good for the cache to pack the vector anyways...\n      DirectlyUseRhs = ActualRhsTypeCleaned::InnerStrideAtCompileTime==1\n    };\n\n    gemv_static_vector_if<RhsScalar,ActualRhsTypeCleaned::SizeAtCompileTime,ActualRhsTypeCleaned::MaxSizeAtCompileTime,!DirectlyUseRhs> static_rhs;\n\n    ei_declare_aligned_stack_constructed_variable(RhsScalar,actualRhsPtr,actualRhs.size(),\n        DirectlyUseRhs ? const_cast<RhsScalar*>(actualRhs.data()) : static_rhs.data());\n\n    if(!DirectlyUseRhs)\n    {\n      #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN\n      Index size = actualRhs.size();\n      EIGEN_DENSE_STORAGE_CTOR_PLUGIN\n      #endif\n      Map<typename ActualRhsTypeCleaned::PlainObject>(actualRhsPtr, actualRhs.size()) = actualRhs;\n    }\n\n    typedef const_blas_data_mapper<LhsScalar,Index,RowMajor> LhsMapper;\n    typedef const_blas_data_mapper<RhsScalar,Index,ColMajor> RhsMapper;\n    general_matrix_vector_product\n        <Index,LhsScalar,LhsMapper,RowMajor,LhsBlasTraits::NeedToConjugate,RhsScalar,RhsMapper,RhsBlasTraits::NeedToConjugate>::run(\n        actualLhs.rows(), actualLhs.cols(),\n        LhsMapper(actualLhs.data(), actualLhs.outerStride()),\n        RhsMapper(actualRhsPtr, 1),\n        dest.data(), dest.col(0).innerStride(), //NOTE  if dest is not a vector at compile-time, then dest.innerStride() might be wrong. (bug 1166)\n        actualAlpha);\n  }\n};\n\ntemplate<> struct gemv_dense_selector<OnTheRight,ColMajor,false>\n{\n  template<typename Lhs, typename Rhs, typename Dest>\n  static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)\n  {\n    EIGEN_STATIC_ASSERT((!nested_eval<Lhs,1>::Evaluate),EIGEN_INTERNAL_COMPILATION_ERROR_OR_YOU_MADE_A_PROGRAMMING_MISTAKE);\n    // TODO if rhs is large enough it might be beneficial to make sure that dest is sequentially stored in memory, otherwise use a temp\n    typename nested_eval<Rhs,1>::type actual_rhs(rhs);\n    const Index size = rhs.rows();\n    for(Index k=0; k<size; ++k)\n      dest += (alpha*actual_rhs.coeff(k)) * lhs.col(k);\n  }\n};\n\ntemplate<> struct gemv_dense_selector<OnTheRight,RowMajor,false>\n{\n  template<typename Lhs, typename Rhs, typename Dest>\n  static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)\n  {\n    EIGEN_STATIC_ASSERT((!nested_eval<Lhs,1>::Evaluate),EIGEN_INTERNAL_COMPILATION_ERROR_OR_YOU_MADE_A_PROGRAMMING_MISTAKE);\n    typename nested_eval<Rhs,Lhs::RowsAtCompileTime>::type actual_rhs(rhs);\n    const Index rows = dest.rows();\n    for(Index i=0; i<rows; ++i)\n      dest.coeffRef(i) += alpha * (lhs.row(i).cwiseProduct(actual_rhs.transpose())).sum();\n  }\n};\n\n} // end namespace internal\n\n/***************************************************************************\n* Implementation of matrix base methods\n***************************************************************************/\n\n/** \\returns the matrix product of \\c *this and \\a other.\n  *\n  * \\note If instead of the matrix product you want the coefficient-wise product, see Cwise::operator*().\n  *\n  * \\sa lazyProduct(), operator*=(const MatrixBase&), Cwise::operator*()\n  */\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\ninline const Product<Derived, OtherDerived>\nMatrixBase<Derived>::operator*(const MatrixBase<OtherDerived> &other) const\n{\n  // A note regarding the function declaration: In MSVC, this function will sometimes\n  // not be inlined since DenseStorage is an unwindable object for dynamic\n  // matrices and product types are holding a member to store the result.\n  // Thus it does not help tagging this function with EIGEN_STRONG_INLINE.\n  enum {\n    ProductIsValid =  Derived::ColsAtCompileTime==Dynamic\n                   || OtherDerived::RowsAtCompileTime==Dynamic\n                   || int(Derived::ColsAtCompileTime)==int(OtherDerived::RowsAtCompileTime),\n    AreVectors = Derived::IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime,\n    SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(Derived,OtherDerived)\n  };\n  // note to the lost user:\n  //    * for a dot product use: v1.dot(v2)\n  //    * for a coeff-wise product use: v1.cwiseProduct(v2)\n  EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes),\n    INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)\n  EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),\n    INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)\n  EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)\n#ifdef EIGEN_DEBUG_PRODUCT\n  internal::product_type<Derived,OtherDerived>::debug();\n#endif\n\n  return Product<Derived, OtherDerived>(derived(), other.derived());\n}\n\n/** \\returns an expression of the matrix product of \\c *this and \\a other without implicit evaluation.\n  *\n  * The returned product will behave like any other expressions: the coefficients of the product will be\n  * computed once at a time as requested. This might be useful in some extremely rare cases when only\n  * a small and no coherent fraction of the result's coefficients have to be computed.\n  *\n  * \\warning This version of the matrix product can be much much slower. So use it only if you know\n  * what you are doing and that you measured a true speed improvement.\n  *\n  * \\sa operator*(const MatrixBase&)\n  */\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\nconst Product<Derived,OtherDerived,LazyProduct>\nMatrixBase<Derived>::lazyProduct(const MatrixBase<OtherDerived> &other) const\n{\n  enum {\n    ProductIsValid =  Derived::ColsAtCompileTime==Dynamic\n                   || OtherDerived::RowsAtCompileTime==Dynamic\n                   || int(Derived::ColsAtCompileTime)==int(OtherDerived::RowsAtCompileTime),\n    AreVectors = Derived::IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime,\n    SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(Derived,OtherDerived)\n  };\n  // note to the lost user:\n  //    * for a dot product use: v1.dot(v2)\n  //    * for a coeff-wise product use: v1.cwiseProduct(v2)\n  EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes),\n    INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)\n  EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),\n    INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)\n  EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)\n\n  return Product<Derived,OtherDerived,LazyProduct>(derived(), other.derived());\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_PRODUCT_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/GenericPacketMath.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_GENERIC_PACKET_MATH_H\n#define EIGEN_GENERIC_PACKET_MATH_H\n\nnamespace Eigen {\n\nnamespace internal {\n\n/** \\internal\n  * \\file GenericPacketMath.h\n  *\n  * Default implementation for types not supported by the vectorization.\n  * In practice these functions are provided to make easier the writing\n  * of generic vectorized code.\n  */\n\n#ifndef EIGEN_DEBUG_ALIGNED_LOAD\n#define EIGEN_DEBUG_ALIGNED_LOAD\n#endif\n\n#ifndef EIGEN_DEBUG_UNALIGNED_LOAD\n#define EIGEN_DEBUG_UNALIGNED_LOAD\n#endif\n\n#ifndef EIGEN_DEBUG_ALIGNED_STORE\n#define EIGEN_DEBUG_ALIGNED_STORE\n#endif\n\n#ifndef EIGEN_DEBUG_UNALIGNED_STORE\n#define EIGEN_DEBUG_UNALIGNED_STORE\n#endif\n\nstruct default_packet_traits\n{\n  enum {\n    HasHalfPacket = 0,\n\n    HasAdd    = 1,\n    HasSub    = 1,\n    HasMul    = 1,\n    HasNegate = 1,\n    HasAbs    = 1,\n    HasArg    = 0,\n    HasAbs2   = 1,\n    HasMin    = 1,\n    HasMax    = 1,\n    HasConj   = 1,\n    HasSetLinear = 1,\n    HasBlend  = 0,\n\n    HasDiv    = 0,\n    HasSqrt   = 0,\n    HasRsqrt  = 0,\n    HasExp    = 0,\n    HasLog    = 0,\n    HasLog1p  = 0,\n    HasLog10  = 0,\n    HasPow    = 0,\n\n    HasSin    = 0,\n    HasCos    = 0,\n    HasTan    = 0,\n    HasASin   = 0,\n    HasACos   = 0,\n    HasATan   = 0,\n    HasSinh   = 0,\n    HasCosh   = 0,\n    HasTanh   = 0,\n    HasLGamma = 0,\n    HasDiGamma = 0,\n    HasZeta = 0,\n    HasPolygamma = 0,\n    HasErf = 0,\n    HasErfc = 0,\n    HasIGamma = 0,\n    HasIGammac = 0,\n    HasBetaInc = 0,\n\n    HasRound  = 0,\n    HasFloor  = 0,\n    HasCeil   = 0,\n\n    HasSign   = 0\n  };\n};\n\ntemplate<typename T> struct packet_traits : default_packet_traits\n{\n  typedef T type;\n  typedef T half;\n  enum {\n    Vectorizable = 0,\n    size = 1,\n    AlignedOnScalar = 0,\n    HasHalfPacket = 0\n  };\n  enum {\n    HasAdd    = 0,\n    HasSub    = 0,\n    HasMul    = 0,\n    HasNegate = 0,\n    HasAbs    = 0,\n    HasAbs2   = 0,\n    HasMin    = 0,\n    HasMax    = 0,\n    HasConj   = 0,\n    HasSetLinear = 0\n  };\n};\n\ntemplate<typename T> struct packet_traits<const T> : packet_traits<T> { };\n\ntemplate <typename Src, typename Tgt> struct type_casting_traits {\n  enum {\n    VectorizedCast = 0,\n    SrcCoeffRatio = 1,\n    TgtCoeffRatio = 1\n  };\n};\n\n\n/** \\internal \\returns static_cast<TgtType>(a) (coeff-wise) */\ntemplate <typename SrcPacket, typename TgtPacket>\nEIGEN_DEVICE_FUNC inline TgtPacket\npcast(const SrcPacket& a) {\n  return static_cast<TgtPacket>(a);\n}\ntemplate <typename SrcPacket, typename TgtPacket>\nEIGEN_DEVICE_FUNC inline TgtPacket\npcast(const SrcPacket& a, const SrcPacket& /*b*/) {\n  return static_cast<TgtPacket>(a);\n}\n\ntemplate <typename SrcPacket, typename TgtPacket>\nEIGEN_DEVICE_FUNC inline TgtPacket\npcast(const SrcPacket& a, const SrcPacket& /*b*/, const SrcPacket& /*c*/, const SrcPacket& /*d*/) {\n  return static_cast<TgtPacket>(a);\n}\n\n/** \\internal \\returns a + b (coeff-wise) */\ntemplate<typename Packet> EIGEN_DEVICE_FUNC inline Packet\npadd(const Packet& a,\n        const Packet& b) { return a+b; }\n\n/** \\internal \\returns a - b (coeff-wise) */\ntemplate<typename Packet> EIGEN_DEVICE_FUNC inline Packet\npsub(const Packet& a,\n        const Packet& b) { return a-b; }\n\n/** \\internal \\returns -a (coeff-wise) */\ntemplate<typename Packet> EIGEN_DEVICE_FUNC inline Packet\npnegate(const Packet& a) { return -a; }\n\n/** \\internal \\returns conj(a) (coeff-wise) */\n\ntemplate<typename Packet> EIGEN_DEVICE_FUNC inline Packet\npconj(const Packet& a) { return numext::conj(a); }\n\n/** \\internal \\returns a * b (coeff-wise) */\ntemplate<typename Packet> EIGEN_DEVICE_FUNC inline Packet\npmul(const Packet& a,\n        const Packet& b) { return a*b; }\n\n/** \\internal \\returns a / b (coeff-wise) */\ntemplate<typename Packet> EIGEN_DEVICE_FUNC inline Packet\npdiv(const Packet& a,\n        const Packet& b) { return a/b; }\n\n/** \\internal \\returns the min of \\a a and \\a b  (coeff-wise) */\ntemplate<typename Packet> EIGEN_DEVICE_FUNC inline Packet\npmin(const Packet& a,\n        const Packet& b) { return numext::mini(a, b); }\n\n/** \\internal \\returns the max of \\a a and \\a b  (coeff-wise) */\ntemplate<typename Packet> EIGEN_DEVICE_FUNC inline Packet\npmax(const Packet& a,\n        const Packet& b) { return numext::maxi(a, b); }\n\n/** \\internal \\returns the absolute value of \\a a */\ntemplate<typename Packet> EIGEN_DEVICE_FUNC inline Packet\npabs(const Packet& a) { using std::abs; return abs(a); }\n\n/** \\internal \\returns the phase angle of \\a a */\ntemplate<typename Packet> EIGEN_DEVICE_FUNC inline Packet\nparg(const Packet& a) { using numext::arg; return arg(a); }\n\n/** \\internal \\returns the bitwise and of \\a a and \\a b */\ntemplate<typename Packet> EIGEN_DEVICE_FUNC inline Packet\npand(const Packet& a, const Packet& b) { return a & b; }\n\n/** \\internal \\returns the bitwise or of \\a a and \\a b */\ntemplate<typename Packet> EIGEN_DEVICE_FUNC inline Packet\npor(const Packet& a, const Packet& b) { return a | b; }\n\n/** \\internal \\returns the bitwise xor of \\a a and \\a b */\ntemplate<typename Packet> EIGEN_DEVICE_FUNC inline Packet\npxor(const Packet& a, const Packet& b) { return a ^ b; }\n\n/** \\internal \\returns the bitwise andnot of \\a a and \\a b */\ntemplate<typename Packet> EIGEN_DEVICE_FUNC inline Packet\npandnot(const Packet& a, const Packet& b) { return a & (!b); }\n\n/** \\internal \\returns a packet version of \\a *from, from must be 16 bytes aligned */\ntemplate<typename Packet> EIGEN_DEVICE_FUNC inline Packet\npload(const typename unpacket_traits<Packet>::type* from) { return *from; }\n\n/** \\internal \\returns a packet version of \\a *from, (un-aligned load) */\ntemplate<typename Packet> EIGEN_DEVICE_FUNC inline Packet\nploadu(const typename unpacket_traits<Packet>::type* from) { return *from; }\n\n/** \\internal \\returns a packet with constant coefficients \\a a, e.g.: (a,a,a,a) */\ntemplate<typename Packet> EIGEN_DEVICE_FUNC inline Packet\npset1(const typename unpacket_traits<Packet>::type& a) { return a; }\n\n/** \\internal \\returns a packet with constant coefficients \\a a[0], e.g.: (a[0],a[0],a[0],a[0]) */\ntemplate<typename Packet> EIGEN_DEVICE_FUNC inline Packet\npload1(const typename unpacket_traits<Packet>::type  *a) { return pset1<Packet>(*a); }\n\n/** \\internal \\returns a packet with elements of \\a *from duplicated.\n  * For instance, for a packet of 8 elements, 4 scalars will be read from \\a *from and\n  * duplicated to form: {from[0],from[0],from[1],from[1],from[2],from[2],from[3],from[3]}\n  * Currently, this function is only used for scalar * complex products.\n  */\ntemplate<typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet\nploaddup(const typename unpacket_traits<Packet>::type* from) { return *from; }\n\n/** \\internal \\returns a packet with elements of \\a *from quadrupled.\n  * For instance, for a packet of 8 elements, 2 scalars will be read from \\a *from and\n  * replicated to form: {from[0],from[0],from[0],from[0],from[1],from[1],from[1],from[1]}\n  * Currently, this function is only used in matrix products.\n  * For packet-size smaller or equal to 4, this function is equivalent to pload1 \n  */\ntemplate<typename Packet> EIGEN_DEVICE_FUNC inline Packet\nploadquad(const typename unpacket_traits<Packet>::type* from)\n{ return pload1<Packet>(from); }\n\n/** \\internal equivalent to\n  * \\code\n  * a0 = pload1(a+0);\n  * a1 = pload1(a+1);\n  * a2 = pload1(a+2);\n  * a3 = pload1(a+3);\n  * \\endcode\n  * \\sa pset1, pload1, ploaddup, pbroadcast2\n  */\ntemplate<typename Packet> EIGEN_DEVICE_FUNC\ninline void pbroadcast4(const typename unpacket_traits<Packet>::type *a,\n                        Packet& a0, Packet& a1, Packet& a2, Packet& a3)\n{\n  a0 = pload1<Packet>(a+0);\n  a1 = pload1<Packet>(a+1);\n  a2 = pload1<Packet>(a+2);\n  a3 = pload1<Packet>(a+3);\n}\n\n/** \\internal equivalent to\n  * \\code\n  * a0 = pload1(a+0);\n  * a1 = pload1(a+1);\n  * \\endcode\n  * \\sa pset1, pload1, ploaddup, pbroadcast4\n  */\ntemplate<typename Packet> EIGEN_DEVICE_FUNC\ninline void pbroadcast2(const typename unpacket_traits<Packet>::type *a,\n                        Packet& a0, Packet& a1)\n{\n  a0 = pload1<Packet>(a+0);\n  a1 = pload1<Packet>(a+1);\n}\n\n/** \\internal \\brief Returns a packet with coefficients (a,a+1,...,a+packet_size-1). */\ntemplate<typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet\nplset(const typename unpacket_traits<Packet>::type& a) { return a; }\n\n/** \\internal copy the packet \\a from to \\a *to, \\a to must be 16 bytes aligned */\ntemplate<typename Scalar, typename Packet> EIGEN_DEVICE_FUNC inline void pstore(Scalar* to, const Packet& from)\n{ (*to) = from; }\n\n/** \\internal copy the packet \\a from to \\a *to, (un-aligned store) */\ntemplate<typename Scalar, typename Packet> EIGEN_DEVICE_FUNC inline void pstoreu(Scalar* to, const Packet& from)\n{  (*to) = from; }\n\n template<typename Scalar, typename Packet> EIGEN_DEVICE_FUNC inline Packet pgather(const Scalar* from, Index /*stride*/)\n { return ploadu<Packet>(from); }\n\n template<typename Scalar, typename Packet> EIGEN_DEVICE_FUNC inline void pscatter(Scalar* to, const Packet& from, Index /*stride*/)\n { pstore(to, from); }\n\n/** \\internal tries to do cache prefetching of \\a addr */\ntemplate<typename Scalar> EIGEN_DEVICE_FUNC inline void prefetch(const Scalar* addr)\n{\n#ifdef __CUDA_ARCH__\n#if defined(__LP64__)\n  // 64-bit pointer operand constraint for inlined asm\n  asm(\" prefetch.L1 [ %1 ];\" : \"=l\"(addr) : \"l\"(addr));\n#else\n  // 32-bit pointer operand constraint for inlined asm\n  asm(\" prefetch.L1 [ %1 ];\" : \"=r\"(addr) : \"r\"(addr));\n#endif\n#elif (!EIGEN_COMP_MSVC) && (EIGEN_COMP_GNUC || EIGEN_COMP_CLANG || EIGEN_COMP_ICC)\n  __builtin_prefetch(addr);\n#endif\n}\n\n/** \\internal \\returns the first element of a packet */\ntemplate<typename Packet> EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type pfirst(const Packet& a)\n{ return a; }\n\n/** \\internal \\returns a packet where the element i contains the sum of the packet of \\a vec[i] */\ntemplate<typename Packet> EIGEN_DEVICE_FUNC inline Packet\npreduxp(const Packet* vecs) { return vecs[0]; }\n\n/** \\internal \\returns the sum of the elements of \\a a*/\ntemplate<typename Packet> EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type predux(const Packet& a)\n{ return a; }\n\n/** \\internal \\returns the sum of the elements of \\a a by block of 4 elements.\n  * For a packet {a0, a1, a2, a3, a4, a5, a6, a7}, it returns a half packet {a0+a4, a1+a5, a2+a6, a3+a7}\n  * For packet-size smaller or equal to 4, this boils down to a noop.\n  */\ntemplate<typename Packet> EIGEN_DEVICE_FUNC inline\ntypename conditional<(unpacket_traits<Packet>::size%8)==0,typename unpacket_traits<Packet>::half,Packet>::type\npredux_downto4(const Packet& a)\n{ return a; }\n\n/** \\internal \\returns the product of the elements of \\a a*/\ntemplate<typename Packet> EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type predux_mul(const Packet& a)\n{ return a; }\n\n/** \\internal \\returns the min of the elements of \\a a*/\ntemplate<typename Packet> EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type predux_min(const Packet& a)\n{ return a; }\n\n/** \\internal \\returns the max of the elements of \\a a*/\ntemplate<typename Packet> EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type predux_max(const Packet& a)\n{ return a; }\n\n/** \\internal \\returns the reversed elements of \\a a*/\ntemplate<typename Packet> EIGEN_DEVICE_FUNC inline Packet preverse(const Packet& a)\n{ return a; }\n\n/** \\internal \\returns \\a a with real and imaginary part flipped (for complex type only) */\ntemplate<typename Packet> EIGEN_DEVICE_FUNC inline Packet pcplxflip(const Packet& a)\n{\n  // FIXME: uncomment the following in case we drop the internal imag and real functions.\n//   using std::imag;\n//   using std::real;\n  return Packet(imag(a),real(a));\n}\n\n/**************************\n* Special math functions\n***************************/\n\n/** \\internal \\returns the sine of \\a a (coeff-wise) */\ntemplate<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS\nPacket psin(const Packet& a) { using std::sin; return sin(a); }\n\n/** \\internal \\returns the cosine of \\a a (coeff-wise) */\ntemplate<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS\nPacket pcos(const Packet& a) { using std::cos; return cos(a); }\n\n/** \\internal \\returns the tan of \\a a (coeff-wise) */\ntemplate<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS\nPacket ptan(const Packet& a) { using std::tan; return tan(a); }\n\n/** \\internal \\returns the arc sine of \\a a (coeff-wise) */\ntemplate<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS\nPacket pasin(const Packet& a) { using std::asin; return asin(a); }\n\n/** \\internal \\returns the arc cosine of \\a a (coeff-wise) */\ntemplate<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS\nPacket pacos(const Packet& a) { using std::acos; return acos(a); }\n\n/** \\internal \\returns the arc tangent of \\a a (coeff-wise) */\ntemplate<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS\nPacket patan(const Packet& a) { using std::atan; return atan(a); }\n\n/** \\internal \\returns the hyperbolic sine of \\a a (coeff-wise) */\ntemplate<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS\nPacket psinh(const Packet& a) { using std::sinh; return sinh(a); }\n\n/** \\internal \\returns the hyperbolic cosine of \\a a (coeff-wise) */\ntemplate<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS\nPacket pcosh(const Packet& a) { using std::cosh; return cosh(a); }\n\n/** \\internal \\returns the hyperbolic tan of \\a a (coeff-wise) */\ntemplate<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS\nPacket ptanh(const Packet& a) { using std::tanh; return tanh(a); }\n\n/** \\internal \\returns the exp of \\a a (coeff-wise) */\ntemplate<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS\nPacket pexp(const Packet& a) { using std::exp; return exp(a); }\n\n/** \\internal \\returns the log of \\a a (coeff-wise) */\ntemplate<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS\nPacket plog(const Packet& a) { using std::log; return log(a); }\n\n/** \\internal \\returns the log1p of \\a a (coeff-wise) */\ntemplate<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS\nPacket plog1p(const Packet& a) { return numext::log1p(a); }\n\n/** \\internal \\returns the log10 of \\a a (coeff-wise) */\ntemplate<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS\nPacket plog10(const Packet& a) { using std::log10; return log10(a); }\n\n/** \\internal \\returns the square-root of \\a a (coeff-wise) */\ntemplate<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS\nPacket psqrt(const Packet& a) { using std::sqrt; return sqrt(a); }\n\n/** \\internal \\returns the reciprocal square-root of \\a a (coeff-wise) */\ntemplate<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS\nPacket prsqrt(const Packet& a) {\n  return pdiv(pset1<Packet>(1), psqrt(a));\n}\n\n/** \\internal \\returns the rounded value of \\a a (coeff-wise) */\ntemplate<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS\nPacket pround(const Packet& a) { using numext::round; return round(a); }\n\n/** \\internal \\returns the floor of \\a a (coeff-wise) */\ntemplate<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS\nPacket pfloor(const Packet& a) { using numext::floor; return floor(a); }\n\n/** \\internal \\returns the ceil of \\a a (coeff-wise) */\ntemplate<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS\nPacket pceil(const Packet& a) { using numext::ceil; return ceil(a); }\n\n/***************************************************************************\n* The following functions might not have to be overwritten for vectorized types\n***************************************************************************/\n\n/** \\internal copy a packet with constant coeficient \\a a (e.g., [a,a,a,a]) to \\a *to. \\a to must be 16 bytes aligned */\n// NOTE: this function must really be templated on the packet type (think about different packet types for the same scalar type)\ntemplate<typename Packet>\ninline void pstore1(typename unpacket_traits<Packet>::type* to, const typename unpacket_traits<Packet>::type& a)\n{\n  pstore(to, pset1<Packet>(a));\n}\n\n/** \\internal \\returns a * b + c (coeff-wise) */\ntemplate<typename Packet> EIGEN_DEVICE_FUNC inline Packet\npmadd(const Packet&  a,\n         const Packet&  b,\n         const Packet&  c)\n{ return padd(pmul(a, b),c); }\n\n/** \\internal \\returns a packet version of \\a *from.\n  * The pointer \\a from must be aligned on a \\a Alignment bytes boundary. */\ntemplate<typename Packet, int Alignment>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet ploadt(const typename unpacket_traits<Packet>::type* from)\n{\n  if(Alignment >= unpacket_traits<Packet>::alignment)\n    return pload<Packet>(from);\n  else\n    return ploadu<Packet>(from);\n}\n\n/** \\internal copy the packet \\a from to \\a *to.\n  * The pointer \\a from must be aligned on a \\a Alignment bytes boundary. */\ntemplate<typename Scalar, typename Packet, int Alignment>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pstoret(Scalar* to, const Packet& from)\n{\n  if(Alignment >= unpacket_traits<Packet>::alignment)\n    pstore(to, from);\n  else\n    pstoreu(to, from);\n}\n\n/** \\internal \\returns a packet version of \\a *from.\n  * Unlike ploadt, ploadt_ro takes advantage of the read-only memory path on the\n  * hardware if available to speedup the loading of data that won't be modified\n  * by the current computation.\n  */\ntemplate<typename Packet, int LoadMode>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet ploadt_ro(const typename unpacket_traits<Packet>::type* from)\n{\n  return ploadt<Packet, LoadMode>(from);\n}\n\n/** \\internal default implementation of palign() allowing partial specialization */\ntemplate<int Offset,typename PacketType>\nstruct palign_impl\n{\n  // by default data are aligned, so there is nothing to be done :)\n  static inline void run(PacketType&, const PacketType&) {}\n};\n\n/** \\internal update \\a first using the concatenation of the packet_size minus \\a Offset last elements\n  * of \\a first and \\a Offset first elements of \\a second.\n  * \n  * This function is currently only used to optimize matrix-vector products on unligned matrices.\n  * It takes 2 packets that represent a contiguous memory array, and returns a packet starting\n  * at the position \\a Offset. For instance, for packets of 4 elements, we have:\n  *  Input:\n  *  - first = {f0,f1,f2,f3}\n  *  - second = {s0,s1,s2,s3}\n  * Output: \n  *   - if Offset==0 then {f0,f1,f2,f3}\n  *   - if Offset==1 then {f1,f2,f3,s0}\n  *   - if Offset==2 then {f2,f3,s0,s1}\n  *   - if Offset==3 then {f3,s0,s1,s3}\n  */\ntemplate<int Offset,typename PacketType>\ninline void palign(PacketType& first, const PacketType& second)\n{\n  palign_impl<Offset,PacketType>::run(first,second);\n}\n\n/***************************************************************************\n* Fast complex products (GCC generates a function call which is very slow)\n***************************************************************************/\n\n// Eigen+CUDA does not support complexes.\n#ifndef __CUDACC__\n\ntemplate<> inline std::complex<float> pmul(const std::complex<float>& a, const std::complex<float>& b)\n{ return std::complex<float>(real(a)*real(b) - imag(a)*imag(b), imag(a)*real(b) + real(a)*imag(b)); }\n\ntemplate<> inline std::complex<double> pmul(const std::complex<double>& a, const std::complex<double>& b)\n{ return std::complex<double>(real(a)*real(b) - imag(a)*imag(b), imag(a)*real(b) + real(a)*imag(b)); }\n\n#endif\n\n\n/***************************************************************************\n * PacketBlock, that is a collection of N packets where the number of words\n * in the packet is a multiple of N.\n***************************************************************************/\ntemplate <typename Packet,int N=unpacket_traits<Packet>::size> struct PacketBlock {\n  Packet packet[N];\n};\n\ntemplate<typename Packet> EIGEN_DEVICE_FUNC inline void\nptranspose(PacketBlock<Packet,1>& /*kernel*/) {\n  // Nothing to do in the scalar case, i.e. a 1x1 matrix.\n}\n\n/***************************************************************************\n * Selector, i.e. vector of N boolean values used to select (i.e. blend)\n * words from 2 packets.\n***************************************************************************/\ntemplate <size_t N> struct Selector {\n  bool select[N];\n};\n\ntemplate<typename Packet> EIGEN_DEVICE_FUNC inline Packet\npblend(const Selector<unpacket_traits<Packet>::size>& ifPacket, const Packet& thenPacket, const Packet& elsePacket) {\n  return ifPacket.select[0] ? thenPacket : elsePacket;\n}\n\n/** \\internal \\returns \\a a with the first coefficient replaced by the scalar b */\ntemplate<typename Packet> EIGEN_DEVICE_FUNC inline Packet\npinsertfirst(const Packet& a, typename unpacket_traits<Packet>::type b)\n{\n  // Default implementation based on pblend.\n  // It must be specialized for higher performance.\n  Selector<unpacket_traits<Packet>::size> mask;\n  mask.select[0] = true;\n  // This for loop should be optimized away by the compiler.\n  for(Index i=1; i<unpacket_traits<Packet>::size; ++i)\n    mask.select[i] = false;\n  return pblend(mask, pset1<Packet>(b), a);\n}\n\n/** \\internal \\returns \\a a with the last coefficient replaced by the scalar b */\ntemplate<typename Packet> EIGEN_DEVICE_FUNC inline Packet\npinsertlast(const Packet& a, typename unpacket_traits<Packet>::type b)\n{\n  // Default implementation based on pblend.\n  // It must be specialized for higher performance.\n  Selector<unpacket_traits<Packet>::size> mask;\n  // This for loop should be optimized away by the compiler.\n  for(Index i=0; i<unpacket_traits<Packet>::size-1; ++i)\n    mask.select[i] = false;\n  mask.select[unpacket_traits<Packet>::size-1] = true;\n  return pblend(mask, pset1<Packet>(b), a);\n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_GENERIC_PACKET_MATH_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/GlobalFunctions.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2010-2016 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_GLOBAL_FUNCTIONS_H\n#define EIGEN_GLOBAL_FUNCTIONS_H\n\n#ifdef EIGEN_PARSED_BY_DOXYGEN\n\n#define EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(NAME,FUNCTOR,DOC_OP,DOC_DETAILS) \\\n  /** \\returns an expression of the coefficient-wise DOC_OP of \\a x\n\n    DOC_DETAILS\n\n    \\sa <a href=\"group__CoeffwiseMathFunctions.html#cwisetable_##NAME\">Math functions</a>, class CwiseUnaryOp\n    */ \\\n  template<typename Derived> \\\n  inline const Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived> \\\n  NAME(const Eigen::ArrayBase<Derived>& x);\n\n#else\n\n#define EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(NAME,FUNCTOR,DOC_OP,DOC_DETAILS) \\\n  template<typename Derived> \\\n  inline const Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived> \\\n  (NAME)(const Eigen::ArrayBase<Derived>& x) { \\\n    return Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived>(x.derived()); \\\n  }\n\n#endif // EIGEN_PARSED_BY_DOXYGEN\n\n#define EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(NAME,FUNCTOR) \\\n  \\\n  template<typename Derived> \\\n  struct NAME##_retval<ArrayBase<Derived> > \\\n  { \\\n    typedef const Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived> type; \\\n  }; \\\n  template<typename Derived> \\\n  struct NAME##_impl<ArrayBase<Derived> > \\\n  { \\\n    static inline typename NAME##_retval<ArrayBase<Derived> >::type run(const Eigen::ArrayBase<Derived>& x) \\\n    { \\\n      return typename NAME##_retval<ArrayBase<Derived> >::type(x.derived()); \\\n    } \\\n  };\n\nnamespace Eigen\n{\n  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(real,scalar_real_op,real part,\\sa ArrayBase::real)\n  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(imag,scalar_imag_op,imaginary part,\\sa ArrayBase::imag)\n  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(conj,scalar_conjugate_op,complex conjugate,\\sa ArrayBase::conjugate)\n  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(inverse,scalar_inverse_op,inverse,\\sa ArrayBase::inverse)\n  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sin,scalar_sin_op,sine,\\sa ArrayBase::sin)\n  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(cos,scalar_cos_op,cosine,\\sa ArrayBase::cos)\n  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(tan,scalar_tan_op,tangent,\\sa ArrayBase::tan)\n  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(atan,scalar_atan_op,arc-tangent,\\sa ArrayBase::atan)\n  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(asin,scalar_asin_op,arc-sine,\\sa ArrayBase::asin)\n  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(acos,scalar_acos_op,arc-consine,\\sa ArrayBase::acos)\n  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sinh,scalar_sinh_op,hyperbolic sine,\\sa ArrayBase::sinh)\n  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(cosh,scalar_cosh_op,hyperbolic cosine,\\sa ArrayBase::cosh)\n  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(tanh,scalar_tanh_op,hyperbolic tangent,\\sa ArrayBase::tanh)\n  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(lgamma,scalar_lgamma_op,natural logarithm of the gamma function,\\sa ArrayBase::lgamma)\n  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(digamma,scalar_digamma_op,derivative of lgamma,\\sa ArrayBase::digamma)\n  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(erf,scalar_erf_op,error function,\\sa ArrayBase::erf)\n  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(erfc,scalar_erfc_op,complement error function,\\sa ArrayBase::erfc)\n  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(exp,scalar_exp_op,exponential,\\sa ArrayBase::exp)\n  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log,scalar_log_op,natural logarithm,\\sa Eigen::log10 DOXCOMMA ArrayBase::log)\n  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log1p,scalar_log1p_op,natural logarithm of 1 plus the value,\\sa ArrayBase::log1p)\n  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log10,scalar_log10_op,base 10 logarithm,\\sa Eigen::log DOXCOMMA ArrayBase::log)\n  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(abs,scalar_abs_op,absolute value,\\sa ArrayBase::abs DOXCOMMA MatrixBase::cwiseAbs)\n  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(abs2,scalar_abs2_op,squared absolute value,\\sa ArrayBase::abs2 DOXCOMMA MatrixBase::cwiseAbs2)\n  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(arg,scalar_arg_op,complex argument,\\sa ArrayBase::arg)\n  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sqrt,scalar_sqrt_op,square root,\\sa ArrayBase::sqrt DOXCOMMA MatrixBase::cwiseSqrt)\n  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(rsqrt,scalar_rsqrt_op,reciprocal square root,\\sa ArrayBase::rsqrt)\n  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(square,scalar_square_op,square (power 2),\\sa Eigen::abs2 DOXCOMMA Eigen::pow DOXCOMMA ArrayBase::square)\n  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(cube,scalar_cube_op,cube (power 3),\\sa Eigen::pow DOXCOMMA ArrayBase::cube)\n  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(round,scalar_round_op,nearest integer,\\sa Eigen::floor DOXCOMMA Eigen::ceil DOXCOMMA ArrayBase::round)\n  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(floor,scalar_floor_op,nearest integer not greater than the giben value,\\sa Eigen::ceil DOXCOMMA ArrayBase::floor)\n  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(ceil,scalar_ceil_op,nearest integer not less than the giben value,\\sa Eigen::floor DOXCOMMA ArrayBase::ceil)\n  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(isnan,scalar_isnan_op,not-a-number test,\\sa Eigen::isinf DOXCOMMA Eigen::isfinite DOXCOMMA ArrayBase::isnan)\n  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(isinf,scalar_isinf_op,infinite value test,\\sa Eigen::isnan DOXCOMMA Eigen::isfinite DOXCOMMA ArrayBase::isinf)\n  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(isfinite,scalar_isfinite_op,finite value test,\\sa Eigen::isinf DOXCOMMA Eigen::isnan DOXCOMMA ArrayBase::isfinite)\n  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sign,scalar_sign_op,sign (or 0),\\sa ArrayBase::sign)\n  \n  /** \\returns an expression of the coefficient-wise power of \\a x to the given constant \\a exponent.\n    *\n    * \\tparam ScalarExponent is the scalar type of \\a exponent. It must be compatible with the scalar type of the given expression (\\c Derived::Scalar).\n    *\n    * \\sa ArrayBase::pow()\n    *\n    * \\relates ArrayBase\n    */\n#ifdef EIGEN_PARSED_BY_DOXYGEN\n  template<typename Derived,typename ScalarExponent>\n  inline const CwiseBinaryOp<internal::scalar_pow_op<Derived::Scalar,ScalarExponent>,Derived,Constant<ScalarExponent> >\n  pow(const Eigen::ArrayBase<Derived>& x, const ScalarExponent& exponent);\n#else\n  template<typename Derived,typename ScalarExponent>\n  inline typename internal::enable_if<   !(internal::is_same<typename Derived::Scalar,ScalarExponent>::value) && EIGEN_SCALAR_BINARY_SUPPORTED(pow,typename Derived::Scalar,ScalarExponent),\n          const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,ScalarExponent,pow) >::type\n  pow(const Eigen::ArrayBase<Derived>& x, const ScalarExponent& exponent) {\n    return x.derived().pow(exponent);\n  }\n\n  template<typename Derived>\n  inline const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,typename Derived::Scalar,pow)\n  pow(const Eigen::ArrayBase<Derived>& x, const typename Derived::Scalar& exponent) {\n    return x.derived().pow(exponent);\n  }\n#endif\n\n  /** \\returns an expression of the coefficient-wise power of \\a x to the given array of \\a exponents.\n    *\n    * This function computes the coefficient-wise power.\n    *\n    * Example: \\include Cwise_array_power_array.cpp\n    * Output: \\verbinclude Cwise_array_power_array.out\n    * \n    * \\sa ArrayBase::pow()\n    *\n    * \\relates ArrayBase\n    */\n  template<typename Derived,typename ExponentDerived>\n  inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_pow_op<typename Derived::Scalar, typename ExponentDerived::Scalar>, const Derived, const ExponentDerived>\n  pow(const Eigen::ArrayBase<Derived>& x, const Eigen::ArrayBase<ExponentDerived>& exponents) \n  {\n    return Eigen::CwiseBinaryOp<Eigen::internal::scalar_pow_op<typename Derived::Scalar, typename ExponentDerived::Scalar>, const Derived, const ExponentDerived>(\n      x.derived(),\n      exponents.derived()\n    );\n  }\n  \n  /** \\returns an expression of the coefficient-wise power of the scalar \\a x to the given array of \\a exponents.\n    *\n    * This function computes the coefficient-wise power between a scalar and an array of exponents.\n    *\n    * \\tparam Scalar is the scalar type of \\a x. It must be compatible with the scalar type of the given array expression (\\c Derived::Scalar).\n    *\n    * Example: \\include Cwise_scalar_power_array.cpp\n    * Output: \\verbinclude Cwise_scalar_power_array.out\n    * \n    * \\sa ArrayBase::pow()\n    *\n    * \\relates ArrayBase\n    */\n#ifdef EIGEN_PARSED_BY_DOXYGEN\n  template<typename Scalar,typename Derived>\n  inline const CwiseBinaryOp<internal::scalar_pow_op<Scalar,Derived::Scalar>,Constant<Scalar>,Derived>\n  pow(const Scalar& x,const Eigen::ArrayBase<Derived>& x);\n#else\n  template<typename Scalar, typename Derived>\n  inline typename internal::enable_if<   !(internal::is_same<typename Derived::Scalar,Scalar>::value) && EIGEN_SCALAR_BINARY_SUPPORTED(pow,Scalar,typename Derived::Scalar),\n          const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,Derived,pow) >::type\n  pow(const Scalar& x, const Eigen::ArrayBase<Derived>& exponents)\n  {\n    return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,Derived,pow)(\n            typename internal::plain_constant_type<Derived,Scalar>::type(exponents.rows(), exponents.cols(), x), exponents.derived() );\n  }\n\n  template<typename Derived>\n  inline const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(typename Derived::Scalar,Derived,pow)\n  pow(const typename Derived::Scalar& x, const Eigen::ArrayBase<Derived>& exponents)\n  {\n    return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(typename Derived::Scalar,Derived,pow)(\n      typename internal::plain_constant_type<Derived,typename Derived::Scalar>::type(exponents.rows(), exponents.cols(), x), exponents.derived() );\n  }\n#endif\n\n\n  namespace internal\n  {\n    EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(real,scalar_real_op)\n    EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(imag,scalar_imag_op)\n    EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(abs2,scalar_abs2_op)\n  }\n}\n\n// TODO: cleanly disable those functions that are not supported on Array (numext::real_ref, internal::random, internal::isApprox...)\n\n#endif // EIGEN_GLOBAL_FUNCTIONS_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/IO.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_IO_H\n#define EIGEN_IO_H\n\nnamespace Eigen { \n\nenum { DontAlignCols = 1 };\nenum { StreamPrecision = -1,\n       FullPrecision = -2 };\n\nnamespace internal {\ntemplate<typename Derived>\nstd::ostream & print_matrix(std::ostream & s, const Derived& _m, const IOFormat& fmt);\n}\n\n/** \\class IOFormat\n  * \\ingroup Core_Module\n  *\n  * \\brief Stores a set of parameters controlling the way matrices are printed\n  *\n  * List of available parameters:\n  *  - \\b precision number of digits for floating point values, or one of the special constants \\c StreamPrecision and \\c FullPrecision.\n  *                 The default is the special value \\c StreamPrecision which means to use the\n  *                 stream's own precision setting, as set for instance using \\c cout.precision(3). The other special value\n  *                 \\c FullPrecision means that the number of digits will be computed to match the full precision of each floating-point\n  *                 type.\n  *  - \\b flags an OR-ed combination of flags, the default value is 0, the only currently available flag is \\c DontAlignCols which\n  *             allows to disable the alignment of columns, resulting in faster code.\n  *  - \\b coeffSeparator string printed between two coefficients of the same row\n  *  - \\b rowSeparator string printed between two rows\n  *  - \\b rowPrefix string printed at the beginning of each row\n  *  - \\b rowSuffix string printed at the end of each row\n  *  - \\b matPrefix string printed at the beginning of the matrix\n  *  - \\b matSuffix string printed at the end of the matrix\n  *\n  * Example: \\include IOFormat.cpp\n  * Output: \\verbinclude IOFormat.out\n  *\n  * \\sa DenseBase::format(), class WithFormat\n  */\nstruct IOFormat\n{\n  /** Default constructor, see class IOFormat for the meaning of the parameters */\n  IOFormat(int _precision = StreamPrecision, int _flags = 0,\n    const std::string& _coeffSeparator = \" \",\n    const std::string& _rowSeparator = \"\\n\", const std::string& _rowPrefix=\"\", const std::string& _rowSuffix=\"\",\n    const std::string& _matPrefix=\"\", const std::string& _matSuffix=\"\")\n  : matPrefix(_matPrefix), matSuffix(_matSuffix), rowPrefix(_rowPrefix), rowSuffix(_rowSuffix), rowSeparator(_rowSeparator),\n    rowSpacer(\"\"), coeffSeparator(_coeffSeparator), precision(_precision), flags(_flags)\n  {\n    // TODO check if rowPrefix, rowSuffix or rowSeparator contains a newline\n    // don't add rowSpacer if columns are not to be aligned\n    if((flags & DontAlignCols))\n      return;\n    int i = int(matSuffix.length())-1;\n    while (i>=0 && matSuffix[i]!='\\n')\n    {\n      rowSpacer += ' ';\n      i--;\n    }\n  }\n  std::string matPrefix, matSuffix;\n  std::string rowPrefix, rowSuffix, rowSeparator, rowSpacer;\n  std::string coeffSeparator;\n  int precision;\n  int flags;\n};\n\n/** \\class WithFormat\n  * \\ingroup Core_Module\n  *\n  * \\brief Pseudo expression providing matrix output with given format\n  *\n  * \\tparam ExpressionType the type of the object on which IO stream operations are performed\n  *\n  * This class represents an expression with stream operators controlled by a given IOFormat.\n  * It is the return type of DenseBase::format()\n  * and most of the time this is the only way it is used.\n  *\n  * See class IOFormat for some examples.\n  *\n  * \\sa DenseBase::format(), class IOFormat\n  */\ntemplate<typename ExpressionType>\nclass WithFormat\n{\n  public:\n\n    WithFormat(const ExpressionType& matrix, const IOFormat& format)\n      : m_matrix(matrix), m_format(format)\n    {}\n\n    friend std::ostream & operator << (std::ostream & s, const WithFormat& wf)\n    {\n      return internal::print_matrix(s, wf.m_matrix.eval(), wf.m_format);\n    }\n\n  protected:\n    typename ExpressionType::Nested m_matrix;\n    IOFormat m_format;\n};\n\nnamespace internal {\n\n// NOTE: This helper is kept for backward compatibility with previous code specializing\n//       this internal::significant_decimals_impl structure. In the future we should directly\n//       call digits10() which has been introduced in July 2016 in 3.3.\ntemplate<typename Scalar>\nstruct significant_decimals_impl\n{\n  static inline int run()\n  {\n    return NumTraits<Scalar>::digits10();\n  }\n};\n\n/** \\internal\n  * print the matrix \\a _m to the output stream \\a s using the output format \\a fmt */\ntemplate<typename Derived>\nstd::ostream & print_matrix(std::ostream & s, const Derived& _m, const IOFormat& fmt)\n{\n  if(_m.size() == 0)\n  {\n    s << fmt.matPrefix << fmt.matSuffix;\n    return s;\n  }\n  \n  typename Derived::Nested m = _m;\n  typedef typename Derived::Scalar Scalar;\n\n  Index width = 0;\n\n  std::streamsize explicit_precision;\n  if(fmt.precision == StreamPrecision)\n  {\n    explicit_precision = 0;\n  }\n  else if(fmt.precision == FullPrecision)\n  {\n    if (NumTraits<Scalar>::IsInteger)\n    {\n      explicit_precision = 0;\n    }\n    else\n    {\n      explicit_precision = significant_decimals_impl<Scalar>::run();\n    }\n  }\n  else\n  {\n    explicit_precision = fmt.precision;\n  }\n\n  std::streamsize old_precision = 0;\n  if(explicit_precision) old_precision = s.precision(explicit_precision);\n\n  bool align_cols = !(fmt.flags & DontAlignCols);\n  if(align_cols)\n  {\n    // compute the largest width\n    for(Index j = 0; j < m.cols(); ++j)\n      for(Index i = 0; i < m.rows(); ++i)\n      {\n        std::stringstream sstr;\n        sstr.copyfmt(s);\n        sstr << m.coeff(i,j);\n        width = std::max<Index>(width, Index(sstr.str().length()));\n      }\n  }\n  s << fmt.matPrefix;\n  for(Index i = 0; i < m.rows(); ++i)\n  {\n    if (i)\n      s << fmt.rowSpacer;\n    s << fmt.rowPrefix;\n    if(width) s.width(width);\n    s << m.coeff(i, 0);\n    for(Index j = 1; j < m.cols(); ++j)\n    {\n      s << fmt.coeffSeparator;\n      if (width) s.width(width);\n      s << m.coeff(i, j);\n    }\n    s << fmt.rowSuffix;\n    if( i < m.rows() - 1)\n      s << fmt.rowSeparator;\n  }\n  s << fmt.matSuffix;\n  if(explicit_precision) s.precision(old_precision);\n  return s;\n}\n\n} // end namespace internal\n\n/** \\relates DenseBase\n  *\n  * Outputs the matrix, to the given stream.\n  *\n  * If you wish to print the matrix with a format different than the default, use DenseBase::format().\n  *\n  * It is also possible to change the default format by defining EIGEN_DEFAULT_IO_FORMAT before including Eigen headers.\n  * If not defined, this will automatically be defined to Eigen::IOFormat(), that is the Eigen::IOFormat with default parameters.\n  *\n  * \\sa DenseBase::format()\n  */\ntemplate<typename Derived>\nstd::ostream & operator <<\n(std::ostream & s,\n const DenseBase<Derived> & m)\n{\n  return internal::print_matrix(s, m.eval(), EIGEN_DEFAULT_IO_FORMAT);\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_IO_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/Inverse.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_INVERSE_H\n#define EIGEN_INVERSE_H\n\nnamespace Eigen { \n\ntemplate<typename XprType,typename StorageKind> class InverseImpl;\n\nnamespace internal {\n\ntemplate<typename XprType>\nstruct traits<Inverse<XprType> >\n  : traits<typename XprType::PlainObject>\n{\n  typedef typename XprType::PlainObject PlainObject;\n  typedef traits<PlainObject> BaseTraits;\n  enum {\n    Flags = BaseTraits::Flags & RowMajorBit\n  };\n};\n\n} // end namespace internal\n\n/** \\class Inverse\n  *\n  * \\brief Expression of the inverse of another expression\n  *\n  * \\tparam XprType the type of the expression we are taking the inverse\n  *\n  * This class represents an abstract expression of A.inverse()\n  * and most of the time this is the only way it is used.\n  *\n  */\ntemplate<typename XprType>\nclass Inverse : public InverseImpl<XprType,typename internal::traits<XprType>::StorageKind>\n{\npublic:\n  typedef typename XprType::StorageIndex StorageIndex;\n  typedef typename XprType::PlainObject                       PlainObject;\n  typedef typename XprType::Scalar                            Scalar;\n  typedef typename internal::ref_selector<XprType>::type      XprTypeNested;\n  typedef typename internal::remove_all<XprTypeNested>::type  XprTypeNestedCleaned;\n  typedef typename internal::ref_selector<Inverse>::type Nested;\n  typedef typename internal::remove_all<XprType>::type NestedExpression;\n  \n  explicit EIGEN_DEVICE_FUNC Inverse(const XprType &xpr)\n    : m_xpr(xpr)\n  {}\n\n  EIGEN_DEVICE_FUNC Index rows() const { return m_xpr.rows(); }\n  EIGEN_DEVICE_FUNC Index cols() const { return m_xpr.cols(); }\n\n  EIGEN_DEVICE_FUNC const XprTypeNestedCleaned& nestedExpression() const { return m_xpr; }\n\nprotected:\n  XprTypeNested m_xpr;\n};\n\n// Generic API dispatcher\ntemplate<typename XprType, typename StorageKind>\nclass InverseImpl\n  : public internal::generic_xpr_base<Inverse<XprType> >::type\n{\npublic:\n  typedef typename internal::generic_xpr_base<Inverse<XprType> >::type Base;\n  typedef typename XprType::Scalar Scalar;\nprivate:\n\n  Scalar coeff(Index row, Index col) const;\n  Scalar coeff(Index i) const;\n};\n\nnamespace internal {\n\n/** \\internal\n  * \\brief Default evaluator for Inverse expression.\n  * \n  * This default evaluator for Inverse expression simply evaluate the inverse into a temporary\n  * by a call to internal::call_assignment_no_alias.\n  * Therefore, inverse implementers only have to specialize Assignment<Dst,Inverse<...>, ...> for\n  * there own nested expression.\n  *\n  * \\sa class Inverse\n  */\ntemplate<typename ArgType>\nstruct unary_evaluator<Inverse<ArgType> >\n  : public evaluator<typename Inverse<ArgType>::PlainObject>\n{\n  typedef Inverse<ArgType> InverseType;\n  typedef typename InverseType::PlainObject PlainObject;\n  typedef evaluator<PlainObject> Base;\n  \n  enum { Flags = Base::Flags | EvalBeforeNestingBit };\n\n  unary_evaluator(const InverseType& inv_xpr)\n    : m_result(inv_xpr.rows(), inv_xpr.cols())\n  {\n    ::new (static_cast<Base*>(this)) Base(m_result);\n    internal::call_assignment_no_alias(m_result, inv_xpr);\n  }\n  \nprotected:\n  PlainObject m_result;\n};\n  \n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_INVERSE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/Map.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2007-2010 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_MAP_H\n#define EIGEN_MAP_H\n\nnamespace Eigen { \n\nnamespace internal {\ntemplate<typename PlainObjectType, int MapOptions, typename StrideType>\nstruct traits<Map<PlainObjectType, MapOptions, StrideType> >\n  : public traits<PlainObjectType>\n{\n  typedef traits<PlainObjectType> TraitsBase;\n  enum {\n    PlainObjectTypeInnerSize = ((traits<PlainObjectType>::Flags&RowMajorBit)==RowMajorBit)\n                             ? PlainObjectType::ColsAtCompileTime\n                             : PlainObjectType::RowsAtCompileTime,\n\n    InnerStrideAtCompileTime = StrideType::InnerStrideAtCompileTime == 0\n                             ? int(PlainObjectType::InnerStrideAtCompileTime)\n                             : int(StrideType::InnerStrideAtCompileTime),\n    OuterStrideAtCompileTime = StrideType::OuterStrideAtCompileTime == 0\n                             ? (InnerStrideAtCompileTime==Dynamic || PlainObjectTypeInnerSize==Dynamic\n                                ? Dynamic\n                                : int(InnerStrideAtCompileTime) * int(PlainObjectTypeInnerSize))\n                             : int(StrideType::OuterStrideAtCompileTime),\n    Alignment = int(MapOptions)&int(AlignedMask),\n    Flags0 = TraitsBase::Flags & (~NestByRefBit),\n    Flags = is_lvalue<PlainObjectType>::value ? int(Flags0) : (int(Flags0) & ~LvalueBit)\n  };\nprivate:\n  enum { Options }; // Expressions don't have Options\n};\n}\n\n/** \\class Map\n  * \\ingroup Core_Module\n  *\n  * \\brief A matrix or vector expression mapping an existing array of data.\n  *\n  * \\tparam PlainObjectType the equivalent matrix type of the mapped data\n  * \\tparam MapOptions specifies the pointer alignment in bytes. It can be: \\c #Aligned128, , \\c #Aligned64, \\c #Aligned32, \\c #Aligned16, \\c #Aligned8 or \\c #Unaligned.\n  *                The default is \\c #Unaligned.\n  * \\tparam StrideType optionally specifies strides. By default, Map assumes the memory layout\n  *                   of an ordinary, contiguous array. This can be overridden by specifying strides.\n  *                   The type passed here must be a specialization of the Stride template, see examples below.\n  *\n  * This class represents a matrix or vector expression mapping an existing array of data.\n  * It can be used to let Eigen interface without any overhead with non-Eigen data structures,\n  * such as plain C arrays or structures from other libraries. By default, it assumes that the\n  * data is laid out contiguously in memory. You can however override this by explicitly specifying\n  * inner and outer strides.\n  *\n  * Here's an example of simply mapping a contiguous array as a \\ref TopicStorageOrders \"column-major\" matrix:\n  * \\include Map_simple.cpp\n  * Output: \\verbinclude Map_simple.out\n  *\n  * If you need to map non-contiguous arrays, you can do so by specifying strides:\n  *\n  * Here's an example of mapping an array as a vector, specifying an inner stride, that is, the pointer\n  * increment between two consecutive coefficients. Here, we're specifying the inner stride as a compile-time\n  * fixed value.\n  * \\include Map_inner_stride.cpp\n  * Output: \\verbinclude Map_inner_stride.out\n  *\n  * Here's an example of mapping an array while specifying an outer stride. Here, since we're mapping\n  * as a column-major matrix, 'outer stride' means the pointer increment between two consecutive columns.\n  * Here, we're specifying the outer stride as a runtime parameter. Note that here \\c OuterStride<> is\n  * a short version of \\c OuterStride<Dynamic> because the default template parameter of OuterStride\n  * is  \\c Dynamic\n  * \\include Map_outer_stride.cpp\n  * Output: \\verbinclude Map_outer_stride.out\n  *\n  * For more details and for an example of specifying both an inner and an outer stride, see class Stride.\n  *\n  * \\b Tip: to change the array of data mapped by a Map object, you can use the C++\n  * placement new syntax:\n  *\n  * Example: \\include Map_placement_new.cpp\n  * Output: \\verbinclude Map_placement_new.out\n  *\n  * This class is the return type of PlainObjectBase::Map() but can also be used directly.\n  *\n  * \\sa PlainObjectBase::Map(), \\ref TopicStorageOrders\n  */\ntemplate<typename PlainObjectType, int MapOptions, typename StrideType> class Map\n  : public MapBase<Map<PlainObjectType, MapOptions, StrideType> >\n{\n  public:\n\n    typedef MapBase<Map> Base;\n    EIGEN_DENSE_PUBLIC_INTERFACE(Map)\n\n    typedef typename Base::PointerType PointerType;\n    typedef PointerType PointerArgType;\n    EIGEN_DEVICE_FUNC\n    inline PointerType cast_to_pointer_type(PointerArgType ptr) { return ptr; }\n\n    EIGEN_DEVICE_FUNC\n    inline Index innerStride() const\n    {\n      return StrideType::InnerStrideAtCompileTime != 0 ? m_stride.inner() : 1;\n    }\n\n    EIGEN_DEVICE_FUNC\n    inline Index outerStride() const\n    {\n      return int(StrideType::OuterStrideAtCompileTime) != 0 ? m_stride.outer()\n           : int(internal::traits<Map>::OuterStrideAtCompileTime) != Dynamic ? Index(internal::traits<Map>::OuterStrideAtCompileTime)\n           : IsVectorAtCompileTime ? (this->size() * innerStride())\n           : (int(Flags)&RowMajorBit) ? (this->cols() * innerStride())\n           : (this->rows() * innerStride());\n    }\n\n    /** Constructor in the fixed-size case.\n      *\n      * \\param dataPtr pointer to the array to map\n      * \\param stride optional Stride object, passing the strides.\n      */\n    EIGEN_DEVICE_FUNC\n    explicit inline Map(PointerArgType dataPtr, const StrideType& stride = StrideType())\n      : Base(cast_to_pointer_type(dataPtr)), m_stride(stride)\n    {\n      PlainObjectType::Base::_check_template_params();\n    }\n\n    /** Constructor in the dynamic-size vector case.\n      *\n      * \\param dataPtr pointer to the array to map\n      * \\param size the size of the vector expression\n      * \\param stride optional Stride object, passing the strides.\n      */\n    EIGEN_DEVICE_FUNC\n    inline Map(PointerArgType dataPtr, Index size, const StrideType& stride = StrideType())\n      : Base(cast_to_pointer_type(dataPtr), size), m_stride(stride)\n    {\n      PlainObjectType::Base::_check_template_params();\n    }\n\n    /** Constructor in the dynamic-size matrix case.\n      *\n      * \\param dataPtr pointer to the array to map\n      * \\param rows the number of rows of the matrix expression\n      * \\param cols the number of columns of the matrix expression\n      * \\param stride optional Stride object, passing the strides.\n      */\n    EIGEN_DEVICE_FUNC\n    inline Map(PointerArgType dataPtr, Index rows, Index cols, const StrideType& stride = StrideType())\n      : Base(cast_to_pointer_type(dataPtr), rows, cols), m_stride(stride)\n    {\n      PlainObjectType::Base::_check_template_params();\n    }\n\n    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Map)\n\n  protected:\n    StrideType m_stride;\n};\n\n\n} // end namespace Eigen\n\n#endif // EIGEN_MAP_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/MapBase.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2007-2010 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_MAPBASE_H\n#define EIGEN_MAPBASE_H\n\n#define EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived) \\\n      EIGEN_STATIC_ASSERT((int(internal::evaluator<Derived>::Flags) & LinearAccessBit) || Derived::IsVectorAtCompileTime, \\\n                          YOU_ARE_TRYING_TO_USE_AN_INDEX_BASED_ACCESSOR_ON_AN_EXPRESSION_THAT_DOES_NOT_SUPPORT_THAT)\n\nnamespace Eigen { \n\n/** \\ingroup Core_Module\n  *\n  * \\brief Base class for dense Map and Block expression with direct access\n  *\n  * This base class provides the const low-level accessors (e.g. coeff, coeffRef) of dense\n  * Map and Block objects with direct access.\n  * Typical users do not have to directly deal with this class.\n  *\n  * This class can be extended by through the macro plugin \\c EIGEN_MAPBASE_PLUGIN.\n  * See \\link TopicCustomizing_Plugins customizing Eigen \\endlink for details.\n  *\n  * The \\c Derived class has to provide the following two methods describing the memory layout:\n  *  \\code Index innerStride() const; \\endcode\n  *  \\code Index outerStride() const; \\endcode\n  *\n  * \\sa class Map, class Block\n  */\ntemplate<typename Derived> class MapBase<Derived, ReadOnlyAccessors>\n  : public internal::dense_xpr_base<Derived>::type\n{\n  public:\n\n    typedef typename internal::dense_xpr_base<Derived>::type Base;\n    enum {\n      RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,\n      ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,\n      SizeAtCompileTime = Base::SizeAtCompileTime\n    };\n\n    typedef typename internal::traits<Derived>::StorageKind StorageKind;\n    typedef typename internal::traits<Derived>::Scalar Scalar;\n    typedef typename internal::packet_traits<Scalar>::type PacketScalar;\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n    typedef typename internal::conditional<\n                         bool(internal::is_lvalue<Derived>::value),\n                         Scalar *,\n                         const Scalar *>::type\n                     PointerType;\n\n    using Base::derived;\n//    using Base::RowsAtCompileTime;\n//    using Base::ColsAtCompileTime;\n//    using Base::SizeAtCompileTime;\n    using Base::MaxRowsAtCompileTime;\n    using Base::MaxColsAtCompileTime;\n    using Base::MaxSizeAtCompileTime;\n    using Base::IsVectorAtCompileTime;\n    using Base::Flags;\n    using Base::IsRowMajor;\n\n    using Base::rows;\n    using Base::cols;\n    using Base::size;\n    using Base::coeff;\n    using Base::coeffRef;\n    using Base::lazyAssign;\n    using Base::eval;\n\n    using Base::innerStride;\n    using Base::outerStride;\n    using Base::rowStride;\n    using Base::colStride;\n\n    // bug 217 - compile error on ICC 11.1\n    using Base::operator=;\n\n    typedef typename Base::CoeffReturnType CoeffReturnType;\n\n    /** \\copydoc DenseBase::rows() */\n    EIGEN_DEVICE_FUNC inline Index rows() const { return m_rows.value(); }\n    /** \\copydoc DenseBase::cols() */\n    EIGEN_DEVICE_FUNC inline Index cols() const { return m_cols.value(); }\n\n    /** Returns a pointer to the first coefficient of the matrix or vector.\n      *\n      * \\note When addressing this data, make sure to honor the strides returned by innerStride() and outerStride().\n      *\n      * \\sa innerStride(), outerStride()\n      */\n    EIGEN_DEVICE_FUNC inline const Scalar* data() const { return m_data; }\n\n    /** \\copydoc PlainObjectBase::coeff(Index,Index) const */\n    EIGEN_DEVICE_FUNC\n    inline const Scalar& coeff(Index rowId, Index colId) const\n    {\n      return m_data[colId * colStride() + rowId * rowStride()];\n    }\n\n    /** \\copydoc PlainObjectBase::coeff(Index) const */\n    EIGEN_DEVICE_FUNC\n    inline const Scalar& coeff(Index index) const\n    {\n      EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)\n      return m_data[index * innerStride()];\n    }\n\n    /** \\copydoc PlainObjectBase::coeffRef(Index,Index) const */\n    EIGEN_DEVICE_FUNC\n    inline const Scalar& coeffRef(Index rowId, Index colId) const\n    {\n      return this->m_data[colId * colStride() + rowId * rowStride()];\n    }\n\n    /** \\copydoc PlainObjectBase::coeffRef(Index) const */\n    EIGEN_DEVICE_FUNC\n    inline const Scalar& coeffRef(Index index) const\n    {\n      EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)\n      return this->m_data[index * innerStride()];\n    }\n\n    /** \\internal */\n    template<int LoadMode>\n    inline PacketScalar packet(Index rowId, Index colId) const\n    {\n      return internal::ploadt<PacketScalar, LoadMode>\n               (m_data + (colId * colStride() + rowId * rowStride()));\n    }\n\n    /** \\internal */\n    template<int LoadMode>\n    inline PacketScalar packet(Index index) const\n    {\n      EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)\n      return internal::ploadt<PacketScalar, LoadMode>(m_data + index * innerStride());\n    }\n\n    /** \\internal Constructor for fixed size matrices or vectors */\n    EIGEN_DEVICE_FUNC\n    explicit inline MapBase(PointerType dataPtr) : m_data(dataPtr), m_rows(RowsAtCompileTime), m_cols(ColsAtCompileTime)\n    {\n      EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)\n      checkSanity<Derived>();\n    }\n\n    /** \\internal Constructor for dynamically sized vectors */\n    EIGEN_DEVICE_FUNC\n    inline MapBase(PointerType dataPtr, Index vecSize)\n            : m_data(dataPtr),\n              m_rows(RowsAtCompileTime == Dynamic ? vecSize : Index(RowsAtCompileTime)),\n              m_cols(ColsAtCompileTime == Dynamic ? vecSize : Index(ColsAtCompileTime))\n    {\n      EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)\n      eigen_assert(vecSize >= 0);\n      eigen_assert(dataPtr == 0 || SizeAtCompileTime == Dynamic || SizeAtCompileTime == vecSize);\n      checkSanity<Derived>();\n    }\n\n    /** \\internal Constructor for dynamically sized matrices */\n    EIGEN_DEVICE_FUNC\n    inline MapBase(PointerType dataPtr, Index rows, Index cols)\n            : m_data(dataPtr), m_rows(rows), m_cols(cols)\n    {\n      eigen_assert( (dataPtr == 0)\n              || (   rows >= 0 && (RowsAtCompileTime == Dynamic || RowsAtCompileTime == rows)\n                  && cols >= 0 && (ColsAtCompileTime == Dynamic || ColsAtCompileTime == cols)));\n      checkSanity<Derived>();\n    }\n\n    #ifdef EIGEN_MAPBASE_PLUGIN\n    #include EIGEN_MAPBASE_PLUGIN\n    #endif\n\n  protected:\n\n    template<typename T>\n    EIGEN_DEVICE_FUNC\n    void checkSanity(typename internal::enable_if<(internal::traits<T>::Alignment>0),void*>::type = 0) const\n    {\n#if EIGEN_MAX_ALIGN_BYTES>0\n      eigen_assert((   ((internal::UIntPtr(m_data) % internal::traits<Derived>::Alignment) == 0)\n                    || (cols() * rows() * innerStride() * sizeof(Scalar)) < internal::traits<Derived>::Alignment ) && \"data is not aligned\");\n#endif\n    }\n\n    template<typename T>\n    EIGEN_DEVICE_FUNC\n    void checkSanity(typename internal::enable_if<internal::traits<T>::Alignment==0,void*>::type = 0) const\n    {}\n\n    PointerType m_data;\n    const internal::variable_if_dynamic<Index, RowsAtCompileTime> m_rows;\n    const internal::variable_if_dynamic<Index, ColsAtCompileTime> m_cols;\n};\n\n/** \\ingroup Core_Module\n  *\n  * \\brief Base class for non-const dense Map and Block expression with direct access\n  *\n  * This base class provides the non-const low-level accessors (e.g. coeff and coeffRef) of\n  * dense Map and Block objects with direct access.\n  * It inherits MapBase<Derived, ReadOnlyAccessors> which defines the const variant for reading specific entries.\n  *\n  * \\sa class Map, class Block\n  */\ntemplate<typename Derived> class MapBase<Derived, WriteAccessors>\n  : public MapBase<Derived, ReadOnlyAccessors>\n{\n    typedef MapBase<Derived, ReadOnlyAccessors> ReadOnlyMapBase;\n  public:\n\n    typedef MapBase<Derived, ReadOnlyAccessors> Base;\n\n    typedef typename Base::Scalar Scalar;\n    typedef typename Base::PacketScalar PacketScalar;\n    typedef typename Base::StorageIndex StorageIndex;\n    typedef typename Base::PointerType PointerType;\n\n    using Base::derived;\n    using Base::rows;\n    using Base::cols;\n    using Base::size;\n    using Base::coeff;\n    using Base::coeffRef;\n\n    using Base::innerStride;\n    using Base::outerStride;\n    using Base::rowStride;\n    using Base::colStride;\n\n    typedef typename internal::conditional<\n                    internal::is_lvalue<Derived>::value,\n                    Scalar,\n                    const Scalar\n                  >::type ScalarWithConstIfNotLvalue;\n\n    EIGEN_DEVICE_FUNC\n    inline const Scalar* data() const { return this->m_data; }\n    EIGEN_DEVICE_FUNC\n    inline ScalarWithConstIfNotLvalue* data() { return this->m_data; } // no const-cast here so non-const-correct code will give a compile error\n\n    EIGEN_DEVICE_FUNC\n    inline ScalarWithConstIfNotLvalue& coeffRef(Index row, Index col)\n    {\n      return this->m_data[col * colStride() + row * rowStride()];\n    }\n\n    EIGEN_DEVICE_FUNC\n    inline ScalarWithConstIfNotLvalue& coeffRef(Index index)\n    {\n      EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)\n      return this->m_data[index * innerStride()];\n    }\n\n    template<int StoreMode>\n    inline void writePacket(Index row, Index col, const PacketScalar& val)\n    {\n      internal::pstoret<Scalar, PacketScalar, StoreMode>\n               (this->m_data + (col * colStride() + row * rowStride()), val);\n    }\n\n    template<int StoreMode>\n    inline void writePacket(Index index, const PacketScalar& val)\n    {\n      EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)\n      internal::pstoret<Scalar, PacketScalar, StoreMode>\n                (this->m_data + index * innerStride(), val);\n    }\n\n    EIGEN_DEVICE_FUNC explicit inline MapBase(PointerType dataPtr) : Base(dataPtr) {}\n    EIGEN_DEVICE_FUNC inline MapBase(PointerType dataPtr, Index vecSize) : Base(dataPtr, vecSize) {}\n    EIGEN_DEVICE_FUNC inline MapBase(PointerType dataPtr, Index rows, Index cols) : Base(dataPtr, rows, cols) {}\n\n    EIGEN_DEVICE_FUNC\n    Derived& operator=(const MapBase& other)\n    {\n      ReadOnlyMapBase::Base::operator=(other);\n      return derived();\n    }\n\n    // In theory we could simply refer to Base:Base::operator=, but MSVC does not like Base::Base,\n    // see bugs 821 and 920.\n    using ReadOnlyMapBase::Base::operator=;\n};\n\n#undef EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS\n\n} // end namespace Eigen\n\n#endif // EIGEN_MAPBASE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/MathFunctions.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_MATHFUNCTIONS_H\n#define EIGEN_MATHFUNCTIONS_H\n\n// source: http://www.geom.uiuc.edu/~huberty/math5337/groupe/digits.html\n// TODO this should better be moved to NumTraits\n#define EIGEN_PI 3.141592653589793238462643383279502884197169399375105820974944592307816406L\n\n\nnamespace Eigen {\n\n// On WINCE, std::abs is defined for int only, so let's defined our own overloads:\n// This issue has been confirmed with MSVC 2008 only, but the issue might exist for more recent versions too.\n#if EIGEN_OS_WINCE && EIGEN_COMP_MSVC && EIGEN_COMP_MSVC<=1500\nlong        abs(long        x) { return (labs(x));  }\ndouble      abs(double      x) { return (fabs(x));  }\nfloat       abs(float       x) { return (fabsf(x)); }\nlong double abs(long double x) { return (fabsl(x)); }\n#endif\n\nnamespace internal {\n\n/** \\internal \\class global_math_functions_filtering_base\n  *\n  * What it does:\n  * Defines a typedef 'type' as follows:\n  * - if type T has a member typedef Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl, then\n  *   global_math_functions_filtering_base<T>::type is a typedef for it.\n  * - otherwise, global_math_functions_filtering_base<T>::type is a typedef for T.\n  *\n  * How it's used:\n  * To allow to defined the global math functions (like sin...) in certain cases, like the Array expressions.\n  * When you do sin(array1+array2), the object array1+array2 has a complicated expression type, all what you want to know\n  * is that it inherits ArrayBase. So we implement a partial specialization of sin_impl for ArrayBase<Derived>.\n  * So we must make sure to use sin_impl<ArrayBase<Derived> > and not sin_impl<Derived>, otherwise our partial specialization\n  * won't be used. How does sin know that? That's exactly what global_math_functions_filtering_base tells it.\n  *\n  * How it's implemented:\n  * SFINAE in the style of enable_if. Highly susceptible of breaking compilers. With GCC, it sure does work, but if you replace\n  * the typename dummy by an integer template parameter, it doesn't work anymore!\n  */\n\ntemplate<typename T, typename dummy = void>\nstruct global_math_functions_filtering_base\n{\n  typedef T type;\n};\n\ntemplate<typename T> struct always_void { typedef void type; };\n\ntemplate<typename T>\nstruct global_math_functions_filtering_base\n  <T,\n   typename always_void<typename T::Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl>::type\n  >\n{\n  typedef typename T::Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl type;\n};\n\n#define EIGEN_MATHFUNC_IMPL(func, scalar) Eigen::internal::func##_impl<typename Eigen::internal::global_math_functions_filtering_base<scalar>::type>\n#define EIGEN_MATHFUNC_RETVAL(func, scalar) typename Eigen::internal::func##_retval<typename Eigen::internal::global_math_functions_filtering_base<scalar>::type>::type\n\n/****************************************************************************\n* Implementation of real                                                 *\n****************************************************************************/\n\ntemplate<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>\nstruct real_default_impl\n{\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  EIGEN_DEVICE_FUNC\n  static inline RealScalar run(const Scalar& x)\n  {\n    return x;\n  }\n};\n\ntemplate<typename Scalar>\nstruct real_default_impl<Scalar,true>\n{\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  EIGEN_DEVICE_FUNC\n  static inline RealScalar run(const Scalar& x)\n  {\n    using std::real;\n    return real(x);\n  }\n};\n\ntemplate<typename Scalar> struct real_impl : real_default_impl<Scalar> {};\n\n#ifdef __CUDA_ARCH__\ntemplate<typename T>\nstruct real_impl<std::complex<T> >\n{\n  typedef T RealScalar;\n  EIGEN_DEVICE_FUNC\n  static inline T run(const std::complex<T>& x)\n  {\n    return x.real();\n  }\n};\n#endif\n\ntemplate<typename Scalar>\nstruct real_retval\n{\n  typedef typename NumTraits<Scalar>::Real type;\n};\n\n/****************************************************************************\n* Implementation of imag                                                 *\n****************************************************************************/\n\ntemplate<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>\nstruct imag_default_impl\n{\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  EIGEN_DEVICE_FUNC\n  static inline RealScalar run(const Scalar&)\n  {\n    return RealScalar(0);\n  }\n};\n\ntemplate<typename Scalar>\nstruct imag_default_impl<Scalar,true>\n{\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  EIGEN_DEVICE_FUNC\n  static inline RealScalar run(const Scalar& x)\n  {\n    using std::imag;\n    return imag(x);\n  }\n};\n\ntemplate<typename Scalar> struct imag_impl : imag_default_impl<Scalar> {};\n\n#ifdef __CUDA_ARCH__\ntemplate<typename T>\nstruct imag_impl<std::complex<T> >\n{\n  typedef T RealScalar;\n  EIGEN_DEVICE_FUNC\n  static inline T run(const std::complex<T>& x)\n  {\n    return x.imag();\n  }\n};\n#endif\n\ntemplate<typename Scalar>\nstruct imag_retval\n{\n  typedef typename NumTraits<Scalar>::Real type;\n};\n\n/****************************************************************************\n* Implementation of real_ref                                             *\n****************************************************************************/\n\ntemplate<typename Scalar>\nstruct real_ref_impl\n{\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  EIGEN_DEVICE_FUNC\n  static inline RealScalar& run(Scalar& x)\n  {\n    return reinterpret_cast<RealScalar*>(&x)[0];\n  }\n  EIGEN_DEVICE_FUNC\n  static inline const RealScalar& run(const Scalar& x)\n  {\n    return reinterpret_cast<const RealScalar*>(&x)[0];\n  }\n};\n\ntemplate<typename Scalar>\nstruct real_ref_retval\n{\n  typedef typename NumTraits<Scalar>::Real & type;\n};\n\n/****************************************************************************\n* Implementation of imag_ref                                             *\n****************************************************************************/\n\ntemplate<typename Scalar, bool IsComplex>\nstruct imag_ref_default_impl\n{\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  EIGEN_DEVICE_FUNC\n  static inline RealScalar& run(Scalar& x)\n  {\n    return reinterpret_cast<RealScalar*>(&x)[1];\n  }\n  EIGEN_DEVICE_FUNC\n  static inline const RealScalar& run(const Scalar& x)\n  {\n    return reinterpret_cast<RealScalar*>(&x)[1];\n  }\n};\n\ntemplate<typename Scalar>\nstruct imag_ref_default_impl<Scalar, false>\n{\n  EIGEN_DEVICE_FUNC\n  static inline Scalar run(Scalar&)\n  {\n    return Scalar(0);\n  }\n  EIGEN_DEVICE_FUNC\n  static inline const Scalar run(const Scalar&)\n  {\n    return Scalar(0);\n  }\n};\n\ntemplate<typename Scalar>\nstruct imag_ref_impl : imag_ref_default_impl<Scalar, NumTraits<Scalar>::IsComplex> {};\n\ntemplate<typename Scalar>\nstruct imag_ref_retval\n{\n  typedef typename NumTraits<Scalar>::Real & type;\n};\n\n/****************************************************************************\n* Implementation of conj                                                 *\n****************************************************************************/\n\ntemplate<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>\nstruct conj_impl\n{\n  EIGEN_DEVICE_FUNC\n  static inline Scalar run(const Scalar& x)\n  {\n    return x;\n  }\n};\n\ntemplate<typename Scalar>\nstruct conj_impl<Scalar,true>\n{\n  EIGEN_DEVICE_FUNC\n  static inline Scalar run(const Scalar& x)\n  {\n    using std::conj;\n    return conj(x);\n  }\n};\n\ntemplate<typename Scalar>\nstruct conj_retval\n{\n  typedef Scalar type;\n};\n\n/****************************************************************************\n* Implementation of abs2                                                 *\n****************************************************************************/\n\ntemplate<typename Scalar,bool IsComplex>\nstruct abs2_impl_default\n{\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  EIGEN_DEVICE_FUNC\n  static inline RealScalar run(const Scalar& x)\n  {\n    return x*x;\n  }\n};\n\ntemplate<typename Scalar>\nstruct abs2_impl_default<Scalar, true> // IsComplex\n{\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  EIGEN_DEVICE_FUNC\n  static inline RealScalar run(const Scalar& x)\n  {\n    return real(x)*real(x) + imag(x)*imag(x);\n  }\n};\n\ntemplate<typename Scalar>\nstruct abs2_impl\n{\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  EIGEN_DEVICE_FUNC\n  static inline RealScalar run(const Scalar& x)\n  {\n    return abs2_impl_default<Scalar,NumTraits<Scalar>::IsComplex>::run(x);\n  }\n};\n\ntemplate<typename Scalar>\nstruct abs2_retval\n{\n  typedef typename NumTraits<Scalar>::Real type;\n};\n\n/****************************************************************************\n* Implementation of norm1                                                *\n****************************************************************************/\n\ntemplate<typename Scalar, bool IsComplex>\nstruct norm1_default_impl\n{\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  EIGEN_DEVICE_FUNC\n  static inline RealScalar run(const Scalar& x)\n  {\n    EIGEN_USING_STD_MATH(abs);\n    return abs(real(x)) + abs(imag(x));\n  }\n};\n\ntemplate<typename Scalar>\nstruct norm1_default_impl<Scalar, false>\n{\n  EIGEN_DEVICE_FUNC\n  static inline Scalar run(const Scalar& x)\n  {\n    EIGEN_USING_STD_MATH(abs);\n    return abs(x);\n  }\n};\n\ntemplate<typename Scalar>\nstruct norm1_impl : norm1_default_impl<Scalar, NumTraits<Scalar>::IsComplex> {};\n\ntemplate<typename Scalar>\nstruct norm1_retval\n{\n  typedef typename NumTraits<Scalar>::Real type;\n};\n\n/****************************************************************************\n* Implementation of hypot                                                *\n****************************************************************************/\n\ntemplate<typename Scalar> struct hypot_impl;\n\ntemplate<typename Scalar>\nstruct hypot_retval\n{\n  typedef typename NumTraits<Scalar>::Real type;\n};\n\n/****************************************************************************\n* Implementation of cast                                                 *\n****************************************************************************/\n\ntemplate<typename OldType, typename NewType>\nstruct cast_impl\n{\n  EIGEN_DEVICE_FUNC\n  static inline NewType run(const OldType& x)\n  {\n    return static_cast<NewType>(x);\n  }\n};\n\n// here, for once, we're plainly returning NewType: we don't want cast to do weird things.\n\ntemplate<typename OldType, typename NewType>\nEIGEN_DEVICE_FUNC\ninline NewType cast(const OldType& x)\n{\n  return cast_impl<OldType, NewType>::run(x);\n}\n\n/****************************************************************************\n* Implementation of round                                                   *\n****************************************************************************/\n\n#if EIGEN_HAS_CXX11_MATH\n  template<typename Scalar>\n  struct round_impl {\n    static inline Scalar run(const Scalar& x)\n    {\n      EIGEN_STATIC_ASSERT((!NumTraits<Scalar>::IsComplex), NUMERIC_TYPE_MUST_BE_REAL)\n      using std::round;\n      return round(x);\n    }\n  };\n#else\n  template<typename Scalar>\n  struct round_impl\n  {\n    static inline Scalar run(const Scalar& x)\n    {\n      EIGEN_STATIC_ASSERT((!NumTraits<Scalar>::IsComplex), NUMERIC_TYPE_MUST_BE_REAL)\n      EIGEN_USING_STD_MATH(floor);\n      EIGEN_USING_STD_MATH(ceil);\n      return (x > Scalar(0)) ? floor(x + Scalar(0.5)) : ceil(x - Scalar(0.5));\n    }\n  };\n#endif\n\ntemplate<typename Scalar>\nstruct round_retval\n{\n  typedef Scalar type;\n};\n\n/****************************************************************************\n* Implementation of arg                                                     *\n****************************************************************************/\n\n#if EIGEN_HAS_CXX11_MATH\n  template<typename Scalar>\n  struct arg_impl {\n    static inline Scalar run(const Scalar& x)\n    {\n      EIGEN_USING_STD_MATH(arg);\n      return arg(x);\n    }\n  };\n#else\n  template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>\n  struct arg_default_impl\n  {\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n    EIGEN_DEVICE_FUNC\n    static inline RealScalar run(const Scalar& x)\n    {\n      return (x < Scalar(0)) ? Scalar(EIGEN_PI) : Scalar(0); }\n  };\n\n  template<typename Scalar>\n  struct arg_default_impl<Scalar,true>\n  {\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n    EIGEN_DEVICE_FUNC\n    static inline RealScalar run(const Scalar& x)\n    {\n      EIGEN_USING_STD_MATH(arg);\n      return arg(x);\n    }\n  };\n\n  template<typename Scalar> struct arg_impl : arg_default_impl<Scalar> {};\n#endif\n\ntemplate<typename Scalar>\nstruct arg_retval\n{\n  typedef typename NumTraits<Scalar>::Real type;\n};\n\n/****************************************************************************\n* Implementation of log1p                                                   *\n****************************************************************************/\n\nnamespace std_fallback {\n  // fallback log1p implementation in case there is no log1p(Scalar) function in namespace of Scalar,\n  // or that there is no suitable std::log1p function available\n  template<typename Scalar>\n  EIGEN_DEVICE_FUNC inline Scalar log1p(const Scalar& x) {\n    EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n    EIGEN_USING_STD_MATH(log);\n    Scalar x1p = RealScalar(1) + x;\n    return numext::equal_strict(x1p, Scalar(1)) ? x : x * ( log(x1p) / (x1p - RealScalar(1)) );\n  }\n}\n\ntemplate<typename Scalar>\nstruct log1p_impl {\n  static inline Scalar run(const Scalar& x)\n  {\n    EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)\n    #if EIGEN_HAS_CXX11_MATH\n    using std::log1p;\n    #endif\n    using std_fallback::log1p;\n    return log1p(x);\n  }\n};\n\n\ntemplate<typename Scalar>\nstruct log1p_retval\n{\n  typedef Scalar type;\n};\n\n/****************************************************************************\n* Implementation of pow                                                  *\n****************************************************************************/\n\ntemplate<typename ScalarX,typename ScalarY, bool IsInteger = NumTraits<ScalarX>::IsInteger&&NumTraits<ScalarY>::IsInteger>\nstruct pow_impl\n{\n  //typedef Scalar retval;\n  typedef typename ScalarBinaryOpTraits<ScalarX,ScalarY,internal::scalar_pow_op<ScalarX,ScalarY> >::ReturnType result_type;\n  static EIGEN_DEVICE_FUNC inline result_type run(const ScalarX& x, const ScalarY& y)\n  {\n    EIGEN_USING_STD_MATH(pow);\n    return pow(x, y);\n  }\n};\n\ntemplate<typename ScalarX,typename ScalarY>\nstruct pow_impl<ScalarX,ScalarY, true>\n{\n  typedef ScalarX result_type;\n  static EIGEN_DEVICE_FUNC inline ScalarX run(ScalarX x, ScalarY y)\n  {\n    ScalarX res(1);\n    eigen_assert(!NumTraits<ScalarY>::IsSigned || y >= 0);\n    if(y & 1) res *= x;\n    y >>= 1;\n    while(y)\n    {\n      x *= x;\n      if(y&1) res *= x;\n      y >>= 1;\n    }\n    return res;\n  }\n};\n\n/****************************************************************************\n* Implementation of random                                               *\n****************************************************************************/\n\ntemplate<typename Scalar,\n         bool IsComplex,\n         bool IsInteger>\nstruct random_default_impl {};\n\ntemplate<typename Scalar>\nstruct random_impl : random_default_impl<Scalar, NumTraits<Scalar>::IsComplex, NumTraits<Scalar>::IsInteger> {};\n\ntemplate<typename Scalar>\nstruct random_retval\n{\n  typedef Scalar type;\n};\n\ntemplate<typename Scalar> inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random(const Scalar& x, const Scalar& y);\ntemplate<typename Scalar> inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random();\n\ntemplate<typename Scalar>\nstruct random_default_impl<Scalar, false, false>\n{\n  static inline Scalar run(const Scalar& x, const Scalar& y)\n  {\n    return x + (y-x) * Scalar(std::rand()) / Scalar(RAND_MAX);\n  }\n  static inline Scalar run()\n  {\n    return run(Scalar(NumTraits<Scalar>::IsSigned ? -1 : 0), Scalar(1));\n  }\n};\n\nenum {\n  meta_floor_log2_terminate,\n  meta_floor_log2_move_up,\n  meta_floor_log2_move_down,\n  meta_floor_log2_bogus\n};\n\ntemplate<unsigned int n, int lower, int upper> struct meta_floor_log2_selector\n{\n  enum { middle = (lower + upper) / 2,\n         value = (upper <= lower + 1) ? int(meta_floor_log2_terminate)\n               : (n < (1 << middle)) ? int(meta_floor_log2_move_down)\n               : (n==0) ? int(meta_floor_log2_bogus)\n               : int(meta_floor_log2_move_up)\n  };\n};\n\ntemplate<unsigned int n,\n         int lower = 0,\n         int upper = sizeof(unsigned int) * CHAR_BIT - 1,\n         int selector = meta_floor_log2_selector<n, lower, upper>::value>\nstruct meta_floor_log2 {};\n\ntemplate<unsigned int n, int lower, int upper>\nstruct meta_floor_log2<n, lower, upper, meta_floor_log2_move_down>\n{\n  enum { value = meta_floor_log2<n, lower, meta_floor_log2_selector<n, lower, upper>::middle>::value };\n};\n\ntemplate<unsigned int n, int lower, int upper>\nstruct meta_floor_log2<n, lower, upper, meta_floor_log2_move_up>\n{\n  enum { value = meta_floor_log2<n, meta_floor_log2_selector<n, lower, upper>::middle, upper>::value };\n};\n\ntemplate<unsigned int n, int lower, int upper>\nstruct meta_floor_log2<n, lower, upper, meta_floor_log2_terminate>\n{\n  enum { value = (n >= ((unsigned int)(1) << (lower+1))) ? lower+1 : lower };\n};\n\ntemplate<unsigned int n, int lower, int upper>\nstruct meta_floor_log2<n, lower, upper, meta_floor_log2_bogus>\n{\n  // no value, error at compile time\n};\n\ntemplate<typename Scalar>\nstruct random_default_impl<Scalar, false, true>\n{\n  static inline Scalar run(const Scalar& x, const Scalar& y)\n  { \n    typedef typename conditional<NumTraits<Scalar>::IsSigned,std::ptrdiff_t,std::size_t>::type ScalarX;\n    if(y<x)\n      return x;\n    // the following difference might overflow on a 32 bits system,\n    // but since y>=x the result converted to an unsigned long is still correct.\n    std::size_t range = ScalarX(y)-ScalarX(x);\n    std::size_t offset = 0;\n    // rejection sampling\n    std::size_t divisor = 1;\n    std::size_t multiplier = 1;\n    if(range<RAND_MAX) divisor = (std::size_t(RAND_MAX)+1)/(range+1);\n    else               multiplier = 1 + range/(std::size_t(RAND_MAX)+1);\n    do {\n      offset = (std::size_t(std::rand()) * multiplier) / divisor;\n    } while (offset > range);\n    return Scalar(ScalarX(x) + offset);\n  }\n\n  static inline Scalar run()\n  {\n#ifdef EIGEN_MAKING_DOCS\n    return run(Scalar(NumTraits<Scalar>::IsSigned ? -10 : 0), Scalar(10));\n#else\n    enum { rand_bits = meta_floor_log2<(unsigned int)(RAND_MAX)+1>::value,\n           scalar_bits = sizeof(Scalar) * CHAR_BIT,\n           shift = EIGEN_PLAIN_ENUM_MAX(0, int(rand_bits) - int(scalar_bits)),\n           offset = NumTraits<Scalar>::IsSigned ? (1 << (EIGEN_PLAIN_ENUM_MIN(rand_bits,scalar_bits)-1)) : 0\n    };\n    return Scalar((std::rand() >> shift) - offset);\n#endif\n  }\n};\n\ntemplate<typename Scalar>\nstruct random_default_impl<Scalar, true, false>\n{\n  static inline Scalar run(const Scalar& x, const Scalar& y)\n  {\n    return Scalar(random(real(x), real(y)),\n                  random(imag(x), imag(y)));\n  }\n  static inline Scalar run()\n  {\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n    return Scalar(random<RealScalar>(), random<RealScalar>());\n  }\n};\n\ntemplate<typename Scalar>\ninline EIGEN_MATHFUNC_RETVAL(random, Scalar) random(const Scalar& x, const Scalar& y)\n{\n  return EIGEN_MATHFUNC_IMPL(random, Scalar)::run(x, y);\n}\n\ntemplate<typename Scalar>\ninline EIGEN_MATHFUNC_RETVAL(random, Scalar) random()\n{\n  return EIGEN_MATHFUNC_IMPL(random, Scalar)::run();\n}\n\n// Implementatin of is* functions\n\n// std::is* do not work with fast-math and gcc, std::is* are available on MSVC 2013 and newer, as well as in clang.\n#if (EIGEN_HAS_CXX11_MATH && !(EIGEN_COMP_GNUC_STRICT && __FINITE_MATH_ONLY__)) || (EIGEN_COMP_MSVC>=1800) || (EIGEN_COMP_CLANG)\n#define EIGEN_USE_STD_FPCLASSIFY 1\n#else\n#define EIGEN_USE_STD_FPCLASSIFY 0\n#endif\n\ntemplate<typename T>\nEIGEN_DEVICE_FUNC\ntypename internal::enable_if<internal::is_integral<T>::value,bool>::type\nisnan_impl(const T&) { return false; }\n\ntemplate<typename T>\nEIGEN_DEVICE_FUNC\ntypename internal::enable_if<internal::is_integral<T>::value,bool>::type\nisinf_impl(const T&) { return false; }\n\ntemplate<typename T>\nEIGEN_DEVICE_FUNC\ntypename internal::enable_if<internal::is_integral<T>::value,bool>::type\nisfinite_impl(const T&) { return true; }\n\ntemplate<typename T>\nEIGEN_DEVICE_FUNC\ntypename internal::enable_if<(!internal::is_integral<T>::value)&&(!NumTraits<T>::IsComplex),bool>::type\nisfinite_impl(const T& x)\n{\n  #ifdef __CUDA_ARCH__\n    return (::isfinite)(x);\n  #elif EIGEN_USE_STD_FPCLASSIFY\n    using std::isfinite;\n    return isfinite EIGEN_NOT_A_MACRO (x);\n  #else\n    return x<=NumTraits<T>::highest() && x>=NumTraits<T>::lowest();\n  #endif\n}\n\ntemplate<typename T>\nEIGEN_DEVICE_FUNC\ntypename internal::enable_if<(!internal::is_integral<T>::value)&&(!NumTraits<T>::IsComplex),bool>::type\nisinf_impl(const T& x)\n{\n  #ifdef __CUDA_ARCH__\n    return (::isinf)(x);\n  #elif EIGEN_USE_STD_FPCLASSIFY\n    using std::isinf;\n    return isinf EIGEN_NOT_A_MACRO (x);\n  #else\n    return x>NumTraits<T>::highest() || x<NumTraits<T>::lowest();\n  #endif\n}\n\ntemplate<typename T>\nEIGEN_DEVICE_FUNC\ntypename internal::enable_if<(!internal::is_integral<T>::value)&&(!NumTraits<T>::IsComplex),bool>::type\nisnan_impl(const T& x)\n{\n  #ifdef __CUDA_ARCH__\n    return (::isnan)(x);\n  #elif EIGEN_USE_STD_FPCLASSIFY\n    using std::isnan;\n    return isnan EIGEN_NOT_A_MACRO (x);\n  #else\n    return x != x;\n  #endif\n}\n\n#if (!EIGEN_USE_STD_FPCLASSIFY)\n\n#if EIGEN_COMP_MSVC\n\ntemplate<typename T> EIGEN_DEVICE_FUNC bool isinf_msvc_helper(T x)\n{\n  return _fpclass(x)==_FPCLASS_NINF || _fpclass(x)==_FPCLASS_PINF;\n}\n\n//MSVC defines a _isnan builtin function, but for double only\nEIGEN_DEVICE_FUNC inline bool isnan_impl(const long double& x) { return _isnan(x)!=0; }\nEIGEN_DEVICE_FUNC inline bool isnan_impl(const double& x)      { return _isnan(x)!=0; }\nEIGEN_DEVICE_FUNC inline bool isnan_impl(const float& x)       { return _isnan(x)!=0; }\n\nEIGEN_DEVICE_FUNC inline bool isinf_impl(const long double& x) { return isinf_msvc_helper(x); }\nEIGEN_DEVICE_FUNC inline bool isinf_impl(const double& x)      { return isinf_msvc_helper(x); }\nEIGEN_DEVICE_FUNC inline bool isinf_impl(const float& x)       { return isinf_msvc_helper(x); }\n\n#elif (defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ && EIGEN_COMP_GNUC)\n\n#if EIGEN_GNUC_AT_LEAST(5,0)\n  #define EIGEN_TMP_NOOPT_ATTRIB EIGEN_DEVICE_FUNC inline __attribute__((optimize(\"no-finite-math-only\")))\n#else\n  // NOTE the inline qualifier and noinline attribute are both needed: the former is to avoid linking issue (duplicate symbol),\n  //      while the second prevent too aggressive optimizations in fast-math mode:\n  #define EIGEN_TMP_NOOPT_ATTRIB EIGEN_DEVICE_FUNC inline __attribute__((noinline,optimize(\"no-finite-math-only\")))\n#endif\n\ntemplate<> EIGEN_TMP_NOOPT_ATTRIB bool isnan_impl(const long double& x) { return __builtin_isnan(x); }\ntemplate<> EIGEN_TMP_NOOPT_ATTRIB bool isnan_impl(const double& x)      { return __builtin_isnan(x); }\ntemplate<> EIGEN_TMP_NOOPT_ATTRIB bool isnan_impl(const float& x)       { return __builtin_isnan(x); }\ntemplate<> EIGEN_TMP_NOOPT_ATTRIB bool isinf_impl(const double& x)      { return __builtin_isinf(x); }\ntemplate<> EIGEN_TMP_NOOPT_ATTRIB bool isinf_impl(const float& x)       { return __builtin_isinf(x); }\ntemplate<> EIGEN_TMP_NOOPT_ATTRIB bool isinf_impl(const long double& x) { return __builtin_isinf(x); }\n\n#undef EIGEN_TMP_NOOPT_ATTRIB\n\n#endif\n\n#endif\n\n// The following overload are defined at the end of this file\ntemplate<typename T> EIGEN_DEVICE_FUNC bool isfinite_impl(const std::complex<T>& x);\ntemplate<typename T> EIGEN_DEVICE_FUNC bool isnan_impl(const std::complex<T>& x);\ntemplate<typename T> EIGEN_DEVICE_FUNC bool isinf_impl(const std::complex<T>& x);\n\ntemplate<typename T> T generic_fast_tanh_float(const T& a_x);\n\n} // end namespace internal\n\n/****************************************************************************\n* Generic math functions                                                    *\n****************************************************************************/\n\nnamespace numext {\n\n#ifndef __CUDA_ARCH__\ntemplate<typename T>\nEIGEN_DEVICE_FUNC\nEIGEN_ALWAYS_INLINE T mini(const T& x, const T& y)\n{\n  EIGEN_USING_STD_MATH(min);\n  return min EIGEN_NOT_A_MACRO (x,y);\n}\n\ntemplate<typename T>\nEIGEN_DEVICE_FUNC\nEIGEN_ALWAYS_INLINE T maxi(const T& x, const T& y)\n{\n  EIGEN_USING_STD_MATH(max);\n  return max EIGEN_NOT_A_MACRO (x,y);\n}\n#else\ntemplate<typename T>\nEIGEN_DEVICE_FUNC\nEIGEN_ALWAYS_INLINE T mini(const T& x, const T& y)\n{\n  return y < x ? y : x;\n}\ntemplate<>\nEIGEN_DEVICE_FUNC\nEIGEN_ALWAYS_INLINE float mini(const float& x, const float& y)\n{\n  return fminf(x, y);\n}\ntemplate<typename T>\nEIGEN_DEVICE_FUNC\nEIGEN_ALWAYS_INLINE T maxi(const T& x, const T& y)\n{\n  return x < y ? y : x;\n}\ntemplate<>\nEIGEN_DEVICE_FUNC\nEIGEN_ALWAYS_INLINE float maxi(const float& x, const float& y)\n{\n  return fmaxf(x, y);\n}\n#endif\n\n\ntemplate<typename Scalar>\nEIGEN_DEVICE_FUNC\ninline EIGEN_MATHFUNC_RETVAL(real, Scalar) real(const Scalar& x)\n{\n  return EIGEN_MATHFUNC_IMPL(real, Scalar)::run(x);\n}\n\ntemplate<typename Scalar>\nEIGEN_DEVICE_FUNC\ninline typename internal::add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) >::type real_ref(const Scalar& x)\n{\n  return internal::real_ref_impl<Scalar>::run(x);\n}\n\ntemplate<typename Scalar>\nEIGEN_DEVICE_FUNC\ninline EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) real_ref(Scalar& x)\n{\n  return EIGEN_MATHFUNC_IMPL(real_ref, Scalar)::run(x);\n}\n\ntemplate<typename Scalar>\nEIGEN_DEVICE_FUNC\ninline EIGEN_MATHFUNC_RETVAL(imag, Scalar) imag(const Scalar& x)\n{\n  return EIGEN_MATHFUNC_IMPL(imag, Scalar)::run(x);\n}\n\ntemplate<typename Scalar>\nEIGEN_DEVICE_FUNC\ninline EIGEN_MATHFUNC_RETVAL(arg, Scalar) arg(const Scalar& x)\n{\n  return EIGEN_MATHFUNC_IMPL(arg, Scalar)::run(x);\n}\n\ntemplate<typename Scalar>\nEIGEN_DEVICE_FUNC\ninline typename internal::add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) >::type imag_ref(const Scalar& x)\n{\n  return internal::imag_ref_impl<Scalar>::run(x);\n}\n\ntemplate<typename Scalar>\nEIGEN_DEVICE_FUNC\ninline EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) imag_ref(Scalar& x)\n{\n  return EIGEN_MATHFUNC_IMPL(imag_ref, Scalar)::run(x);\n}\n\ntemplate<typename Scalar>\nEIGEN_DEVICE_FUNC\ninline EIGEN_MATHFUNC_RETVAL(conj, Scalar) conj(const Scalar& x)\n{\n  return EIGEN_MATHFUNC_IMPL(conj, Scalar)::run(x);\n}\n\ntemplate<typename Scalar>\nEIGEN_DEVICE_FUNC\ninline EIGEN_MATHFUNC_RETVAL(abs2, Scalar) abs2(const Scalar& x)\n{\n  return EIGEN_MATHFUNC_IMPL(abs2, Scalar)::run(x);\n}\n\ntemplate<typename Scalar>\nEIGEN_DEVICE_FUNC\ninline EIGEN_MATHFUNC_RETVAL(norm1, Scalar) norm1(const Scalar& x)\n{\n  return EIGEN_MATHFUNC_IMPL(norm1, Scalar)::run(x);\n}\n\ntemplate<typename Scalar>\nEIGEN_DEVICE_FUNC\ninline EIGEN_MATHFUNC_RETVAL(hypot, Scalar) hypot(const Scalar& x, const Scalar& y)\n{\n  return EIGEN_MATHFUNC_IMPL(hypot, Scalar)::run(x, y);\n}\n\ntemplate<typename Scalar>\nEIGEN_DEVICE_FUNC\ninline EIGEN_MATHFUNC_RETVAL(log1p, Scalar) log1p(const Scalar& x)\n{\n  return EIGEN_MATHFUNC_IMPL(log1p, Scalar)::run(x);\n}\n\n#ifdef __CUDACC__\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nfloat log1p(const float &x) { return ::log1pf(x); }\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\ndouble log1p(const double &x) { return ::log1p(x); }\n#endif\n\ntemplate<typename ScalarX,typename ScalarY>\nEIGEN_DEVICE_FUNC\ninline typename internal::pow_impl<ScalarX,ScalarY>::result_type pow(const ScalarX& x, const ScalarY& y)\n{\n  return internal::pow_impl<ScalarX,ScalarY>::run(x, y);\n}\n\ntemplate<typename T> EIGEN_DEVICE_FUNC bool (isnan)   (const T &x) { return internal::isnan_impl(x); }\ntemplate<typename T> EIGEN_DEVICE_FUNC bool (isinf)   (const T &x) { return internal::isinf_impl(x); }\ntemplate<typename T> EIGEN_DEVICE_FUNC bool (isfinite)(const T &x) { return internal::isfinite_impl(x); }\n\ntemplate<typename Scalar>\nEIGEN_DEVICE_FUNC\ninline EIGEN_MATHFUNC_RETVAL(round, Scalar) round(const Scalar& x)\n{\n  return EIGEN_MATHFUNC_IMPL(round, Scalar)::run(x);\n}\n\ntemplate<typename T>\nEIGEN_DEVICE_FUNC\nT (floor)(const T& x)\n{\n  EIGEN_USING_STD_MATH(floor);\n  return floor(x);\n}\n\n#ifdef __CUDACC__\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nfloat floor(const float &x) { return ::floorf(x); }\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\ndouble floor(const double &x) { return ::floor(x); }\n#endif\n\ntemplate<typename T>\nEIGEN_DEVICE_FUNC\nT (ceil)(const T& x)\n{\n  EIGEN_USING_STD_MATH(ceil);\n  return ceil(x);\n}\n\n#ifdef __CUDACC__\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nfloat ceil(const float &x) { return ::ceilf(x); }\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\ndouble ceil(const double &x) { return ::ceil(x); }\n#endif\n\n\n/** Log base 2 for 32 bits positive integers.\n  * Conveniently returns 0 for x==0. */\ninline int log2(int x)\n{\n  eigen_assert(x>=0);\n  unsigned int v(x);\n  static const int table[32] = { 0, 9, 1, 10, 13, 21, 2, 29, 11, 14, 16, 18, 22, 25, 3, 30, 8, 12, 20, 28, 15, 17, 24, 7, 19, 27, 23, 6, 26, 5, 4, 31 };\n  v |= v >> 1;\n  v |= v >> 2;\n  v |= v >> 4;\n  v |= v >> 8;\n  v |= v >> 16;\n  return table[(v * 0x07C4ACDDU) >> 27];\n}\n\n/** \\returns the square root of \\a x.\n  *\n  * It is essentially equivalent to \\code using std::sqrt; return sqrt(x); \\endcode,\n  * but slightly faster for float/double and some compilers (e.g., gcc), thanks to\n  * specializations when SSE is enabled.\n  *\n  * It's usage is justified in performance critical functions, like norm/normalize.\n  */\ntemplate<typename T>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nT sqrt(const T &x)\n{\n  EIGEN_USING_STD_MATH(sqrt);\n  return sqrt(x);\n}\n\ntemplate<typename T>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nT log(const T &x) {\n  EIGEN_USING_STD_MATH(log);\n  return log(x);\n}\n\n#ifdef __CUDACC__\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nfloat log(const float &x) { return ::logf(x); }\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\ndouble log(const double &x) { return ::log(x); }\n#endif\n\ntemplate<typename T>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\ntypename internal::enable_if<NumTraits<T>::IsSigned || NumTraits<T>::IsComplex,typename NumTraits<T>::Real>::type\nabs(const T &x) {\n  EIGEN_USING_STD_MATH(abs);\n  return abs(x);\n}\n\ntemplate<typename T>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\ntypename internal::enable_if<!(NumTraits<T>::IsSigned || NumTraits<T>::IsComplex),typename NumTraits<T>::Real>::type\nabs(const T &x) {\n  return x;\n}\n\n#if defined(__SYCL_DEVICE_ONLY__)\nEIGEN_ALWAYS_INLINE float   abs(float x) { return cl::sycl::fabs(x); }\nEIGEN_ALWAYS_INLINE double  abs(double x) { return cl::sycl::fabs(x); }\n#endif // defined(__SYCL_DEVICE_ONLY__)\n\n#ifdef __CUDACC__\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nfloat abs(const float &x) { return ::fabsf(x); }\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\ndouble abs(const double &x) { return ::fabs(x); }\n\ntemplate <> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nfloat abs(const std::complex<float>& x) {\n  return ::hypotf(x.real(), x.imag());\n}\n\ntemplate <> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\ndouble abs(const std::complex<double>& x) {\n  return ::hypot(x.real(), x.imag());\n}\n#endif\n\ntemplate<typename T>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nT exp(const T &x) {\n  EIGEN_USING_STD_MATH(exp);\n  return exp(x);\n}\n\n#ifdef __CUDACC__\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nfloat exp(const float &x) { return ::expf(x); }\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\ndouble exp(const double &x) { return ::exp(x); }\n#endif\n\ntemplate<typename T>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nT cos(const T &x) {\n  EIGEN_USING_STD_MATH(cos);\n  return cos(x);\n}\n\n#ifdef __CUDACC__\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nfloat cos(const float &x) { return ::cosf(x); }\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\ndouble cos(const double &x) { return ::cos(x); }\n#endif\n\ntemplate<typename T>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nT sin(const T &x) {\n  EIGEN_USING_STD_MATH(sin);\n  return sin(x);\n}\n\n#ifdef __CUDACC__\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nfloat sin(const float &x) { return ::sinf(x); }\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\ndouble sin(const double &x) { return ::sin(x); }\n#endif\n\ntemplate<typename T>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nT tan(const T &x) {\n  EIGEN_USING_STD_MATH(tan);\n  return tan(x);\n}\n\n#ifdef __CUDACC__\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nfloat tan(const float &x) { return ::tanf(x); }\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\ndouble tan(const double &x) { return ::tan(x); }\n#endif\n\ntemplate<typename T>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nT acos(const T &x) {\n  EIGEN_USING_STD_MATH(acos);\n  return acos(x);\n}\n\n#ifdef __CUDACC__\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nfloat acos(const float &x) { return ::acosf(x); }\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\ndouble acos(const double &x) { return ::acos(x); }\n#endif\n\ntemplate<typename T>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nT asin(const T &x) {\n  EIGEN_USING_STD_MATH(asin);\n  return asin(x);\n}\n\n#ifdef __CUDACC__\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nfloat asin(const float &x) { return ::asinf(x); }\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\ndouble asin(const double &x) { return ::asin(x); }\n#endif\n\ntemplate<typename T>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nT atan(const T &x) {\n  EIGEN_USING_STD_MATH(atan);\n  return atan(x);\n}\n\n#ifdef __CUDACC__\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nfloat atan(const float &x) { return ::atanf(x); }\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\ndouble atan(const double &x) { return ::atan(x); }\n#endif\n\n\ntemplate<typename T>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nT cosh(const T &x) {\n  EIGEN_USING_STD_MATH(cosh);\n  return cosh(x);\n}\n\n#ifdef __CUDACC__\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nfloat cosh(const float &x) { return ::coshf(x); }\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\ndouble cosh(const double &x) { return ::cosh(x); }\n#endif\n\ntemplate<typename T>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nT sinh(const T &x) {\n  EIGEN_USING_STD_MATH(sinh);\n  return sinh(x);\n}\n\n#ifdef __CUDACC__\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nfloat sinh(const float &x) { return ::sinhf(x); }\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\ndouble sinh(const double &x) { return ::sinh(x); }\n#endif\n\ntemplate<typename T>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nT tanh(const T &x) {\n  EIGEN_USING_STD_MATH(tanh);\n  return tanh(x);\n}\n\n#if (!defined(__CUDACC__)) && EIGEN_FAST_MATH\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nfloat tanh(float x) { return internal::generic_fast_tanh_float(x); }\n#endif\n\n#ifdef __CUDACC__\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nfloat tanh(const float &x) { return ::tanhf(x); }\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\ndouble tanh(const double &x) { return ::tanh(x); }\n#endif\n\ntemplate <typename T>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nT fmod(const T& a, const T& b) {\n  EIGEN_USING_STD_MATH(fmod);\n  return fmod(a, b);\n}\n\n#ifdef __CUDACC__\ntemplate <>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nfloat fmod(const float& a, const float& b) {\n  return ::fmodf(a, b);\n}\n\ntemplate <>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\ndouble fmod(const double& a, const double& b) {\n  return ::fmod(a, b);\n}\n#endif\n\n} // end namespace numext\n\nnamespace internal {\n\ntemplate<typename T>\nEIGEN_DEVICE_FUNC bool isfinite_impl(const std::complex<T>& x)\n{\n  return (numext::isfinite)(numext::real(x)) && (numext::isfinite)(numext::imag(x));\n}\n\ntemplate<typename T>\nEIGEN_DEVICE_FUNC bool isnan_impl(const std::complex<T>& x)\n{\n  return (numext::isnan)(numext::real(x)) || (numext::isnan)(numext::imag(x));\n}\n\ntemplate<typename T>\nEIGEN_DEVICE_FUNC bool isinf_impl(const std::complex<T>& x)\n{\n  return ((numext::isinf)(numext::real(x)) || (numext::isinf)(numext::imag(x))) && (!(numext::isnan)(x));\n}\n\n/****************************************************************************\n* Implementation of fuzzy comparisons                                       *\n****************************************************************************/\n\ntemplate<typename Scalar,\n         bool IsComplex,\n         bool IsInteger>\nstruct scalar_fuzzy_default_impl {};\n\ntemplate<typename Scalar>\nstruct scalar_fuzzy_default_impl<Scalar, false, false>\n{\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  template<typename OtherScalar> EIGEN_DEVICE_FUNC\n  static inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y, const RealScalar& prec)\n  {\n    return numext::abs(x) <= numext::abs(y) * prec;\n  }\n  EIGEN_DEVICE_FUNC\n  static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar& prec)\n  {\n    return numext::abs(x - y) <= numext::mini(numext::abs(x), numext::abs(y)) * prec;\n  }\n  EIGEN_DEVICE_FUNC\n  static inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y, const RealScalar& prec)\n  {\n    return x <= y || isApprox(x, y, prec);\n  }\n};\n\ntemplate<typename Scalar>\nstruct scalar_fuzzy_default_impl<Scalar, false, true>\n{\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  template<typename OtherScalar> EIGEN_DEVICE_FUNC\n  static inline bool isMuchSmallerThan(const Scalar& x, const Scalar&, const RealScalar&)\n  {\n    return x == Scalar(0);\n  }\n  EIGEN_DEVICE_FUNC\n  static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar&)\n  {\n    return x == y;\n  }\n  EIGEN_DEVICE_FUNC\n  static inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y, const RealScalar&)\n  {\n    return x <= y;\n  }\n};\n\ntemplate<typename Scalar>\nstruct scalar_fuzzy_default_impl<Scalar, true, false>\n{\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  template<typename OtherScalar> EIGEN_DEVICE_FUNC\n  static inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y, const RealScalar& prec)\n  {\n    return numext::abs2(x) <= numext::abs2(y) * prec * prec;\n  }\n  EIGEN_DEVICE_FUNC\n  static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar& prec)\n  {\n    return numext::abs2(x - y) <= numext::mini(numext::abs2(x), numext::abs2(y)) * prec * prec;\n  }\n};\n\ntemplate<typename Scalar>\nstruct scalar_fuzzy_impl : scalar_fuzzy_default_impl<Scalar, NumTraits<Scalar>::IsComplex, NumTraits<Scalar>::IsInteger> {};\n\ntemplate<typename Scalar, typename OtherScalar> EIGEN_DEVICE_FUNC\ninline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y,\n                              const typename NumTraits<Scalar>::Real &precision = NumTraits<Scalar>::dummy_precision())\n{\n  return scalar_fuzzy_impl<Scalar>::template isMuchSmallerThan<OtherScalar>(x, y, precision);\n}\n\ntemplate<typename Scalar> EIGEN_DEVICE_FUNC\ninline bool isApprox(const Scalar& x, const Scalar& y,\n                     const typename NumTraits<Scalar>::Real &precision = NumTraits<Scalar>::dummy_precision())\n{\n  return scalar_fuzzy_impl<Scalar>::isApprox(x, y, precision);\n}\n\ntemplate<typename Scalar> EIGEN_DEVICE_FUNC\ninline bool isApproxOrLessThan(const Scalar& x, const Scalar& y,\n                               const typename NumTraits<Scalar>::Real &precision = NumTraits<Scalar>::dummy_precision())\n{\n  return scalar_fuzzy_impl<Scalar>::isApproxOrLessThan(x, y, precision);\n}\n\n/******************************************\n***  The special case of the  bool type ***\n******************************************/\n\ntemplate<> struct random_impl<bool>\n{\n  static inline bool run()\n  {\n    return random<int>(0,1)==0 ? false : true;\n  }\n};\n\ntemplate<> struct scalar_fuzzy_impl<bool>\n{\n  typedef bool RealScalar;\n  \n  template<typename OtherScalar> EIGEN_DEVICE_FUNC\n  static inline bool isMuchSmallerThan(const bool& x, const bool&, const bool&)\n  {\n    return !x;\n  }\n  \n  EIGEN_DEVICE_FUNC\n  static inline bool isApprox(bool x, bool y, bool)\n  {\n    return x == y;\n  }\n\n  EIGEN_DEVICE_FUNC\n  static inline bool isApproxOrLessThan(const bool& x, const bool& y, const bool&)\n  {\n    return (!x) || y;\n  }\n  \n};\n\n  \n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_MATHFUNCTIONS_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/MathFunctionsImpl.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Pedro Gonnet (pedro.gonnet@gmail.com)\n// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_MATHFUNCTIONSIMPL_H\n#define EIGEN_MATHFUNCTIONSIMPL_H\n\nnamespace Eigen {\n\nnamespace internal {\n\n/** \\internal \\returns the hyperbolic tan of \\a a (coeff-wise)\n    Doesn't do anything fancy, just a 13/6-degree rational interpolant which\n    is accurate up to a couple of ulp in the range [-9, 9], outside of which\n    the tanh(x) = +/-1.\n\n    This implementation works on both scalars and packets.\n*/\ntemplate<typename T>\nT generic_fast_tanh_float(const T& a_x)\n{\n  // Clamp the inputs to the range [-9, 9] since anything outside\n  // this range is +/-1.0f in single-precision.\n  const T plus_9 = pset1<T>(9.f);\n  const T minus_9 = pset1<T>(-9.f);\n  // NOTE GCC prior to 6.3 might improperly optimize this max/min\n  //      step such that if a_x is nan, x will be either 9 or -9,\n  //      and tanh will return 1 or -1 instead of nan.\n  //      This is supposed to be fixed in gcc6.3,\n  //      see: https://gcc.gnu.org/bugzilla/show_bug.cgi?id=72867\n  const T x = pmax(minus_9,pmin(plus_9,a_x));\n  // The monomial coefficients of the numerator polynomial (odd).\n  const T alpha_1 = pset1<T>(4.89352455891786e-03f);\n  const T alpha_3 = pset1<T>(6.37261928875436e-04f);\n  const T alpha_5 = pset1<T>(1.48572235717979e-05f);\n  const T alpha_7 = pset1<T>(5.12229709037114e-08f);\n  const T alpha_9 = pset1<T>(-8.60467152213735e-11f);\n  const T alpha_11 = pset1<T>(2.00018790482477e-13f);\n  const T alpha_13 = pset1<T>(-2.76076847742355e-16f);\n\n  // The monomial coefficients of the denominator polynomial (even).\n  const T beta_0 = pset1<T>(4.89352518554385e-03f);\n  const T beta_2 = pset1<T>(2.26843463243900e-03f);\n  const T beta_4 = pset1<T>(1.18534705686654e-04f);\n  const T beta_6 = pset1<T>(1.19825839466702e-06f);\n\n  // Since the polynomials are odd/even, we need x^2.\n  const T x2 = pmul(x, x);\n\n  // Evaluate the numerator polynomial p.\n  T p = pmadd(x2, alpha_13, alpha_11);\n  p = pmadd(x2, p, alpha_9);\n  p = pmadd(x2, p, alpha_7);\n  p = pmadd(x2, p, alpha_5);\n  p = pmadd(x2, p, alpha_3);\n  p = pmadd(x2, p, alpha_1);\n  p = pmul(x, p);\n\n  // Evaluate the denominator polynomial p.\n  T q = pmadd(x2, beta_6, beta_4);\n  q = pmadd(x2, q, beta_2);\n  q = pmadd(x2, q, beta_0);\n\n  // Divide the numerator by the denominator.\n  return pdiv(p, q);\n}\n\ntemplate<typename RealScalar>\nEIGEN_STRONG_INLINE\nRealScalar positive_real_hypot(const RealScalar& x, const RealScalar& y)\n{\n  EIGEN_USING_STD_MATH(sqrt);\n  RealScalar p, qp;\n  p = numext::maxi(x,y);\n  if(p==RealScalar(0)) return RealScalar(0);\n  qp = numext::mini(y,x) / p;    \n  return p * sqrt(RealScalar(1) + qp*qp);\n}\n\ntemplate<typename Scalar>\nstruct hypot_impl\n{\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  static inline RealScalar run(const Scalar& x, const Scalar& y)\n  {\n    EIGEN_USING_STD_MATH(abs);\n    return positive_real_hypot<RealScalar>(abs(x), abs(y));\n  }\n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_MATHFUNCTIONSIMPL_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/Matrix.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_MATRIX_H\n#define EIGEN_MATRIX_H\n\nnamespace Eigen {\n\nnamespace internal {\ntemplate<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>\nstruct traits<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >\n{\nprivate:\n  enum { size = internal::size_at_compile_time<_Rows,_Cols>::ret };\n  typedef typename find_best_packet<_Scalar,size>::type PacketScalar;\n  enum {\n      row_major_bit = _Options&RowMajor ? RowMajorBit : 0,\n      is_dynamic_size_storage = _MaxRows==Dynamic || _MaxCols==Dynamic,\n      max_size = is_dynamic_size_storage ? Dynamic : _MaxRows*_MaxCols,\n      default_alignment = compute_default_alignment<_Scalar,max_size>::value,\n      actual_alignment = ((_Options&DontAlign)==0) ? default_alignment : 0,\n      required_alignment = unpacket_traits<PacketScalar>::alignment,\n      packet_access_bit = (packet_traits<_Scalar>::Vectorizable && (EIGEN_UNALIGNED_VECTORIZE || (actual_alignment>=required_alignment))) ? PacketAccessBit : 0\n    };\n    \npublic:\n  typedef _Scalar Scalar;\n  typedef Dense StorageKind;\n  typedef Eigen::Index StorageIndex;\n  typedef MatrixXpr XprKind;\n  enum {\n    RowsAtCompileTime = _Rows,\n    ColsAtCompileTime = _Cols,\n    MaxRowsAtCompileTime = _MaxRows,\n    MaxColsAtCompileTime = _MaxCols,\n    Flags = compute_matrix_flags<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>::ret,\n    Options = _Options,\n    InnerStrideAtCompileTime = 1,\n    OuterStrideAtCompileTime = (Options&RowMajor) ? ColsAtCompileTime : RowsAtCompileTime,\n    \n    // FIXME, the following flag in only used to define NeedsToAlign in PlainObjectBase\n    EvaluatorFlags = LinearAccessBit | DirectAccessBit | packet_access_bit | row_major_bit,\n    Alignment = actual_alignment\n  };\n};\n}\n\n/** \\class Matrix\n  * \\ingroup Core_Module\n  *\n  * \\brief The matrix class, also used for vectors and row-vectors\n  *\n  * The %Matrix class is the work-horse for all \\em dense (\\ref dense \"note\") matrices and vectors within Eigen.\n  * Vectors are matrices with one column, and row-vectors are matrices with one row.\n  *\n  * The %Matrix class encompasses \\em both fixed-size and dynamic-size objects (\\ref fixedsize \"note\").\n  *\n  * The first three template parameters are required:\n  * \\tparam _Scalar Numeric type, e.g. float, double, int or std::complex<float>.\n  *                 User defined scalar types are supported as well (see \\ref user_defined_scalars \"here\").\n  * \\tparam _Rows Number of rows, or \\b Dynamic\n  * \\tparam _Cols Number of columns, or \\b Dynamic\n  *\n  * The remaining template parameters are optional -- in most cases you don't have to worry about them.\n  * \\tparam _Options A combination of either \\b #RowMajor or \\b #ColMajor, and of either\n  *                 \\b #AutoAlign or \\b #DontAlign.\n  *                 The former controls \\ref TopicStorageOrders \"storage order\", and defaults to column-major. The latter controls alignment, which is required\n  *                 for vectorization. It defaults to aligning matrices except for fixed sizes that aren't a multiple of the packet size.\n  * \\tparam _MaxRows Maximum number of rows. Defaults to \\a _Rows (\\ref maxrows \"note\").\n  * \\tparam _MaxCols Maximum number of columns. Defaults to \\a _Cols (\\ref maxrows \"note\").\n  *\n  * Eigen provides a number of typedefs covering the usual cases. Here are some examples:\n  *\n  * \\li \\c Matrix2d is a 2x2 square matrix of doubles (\\c Matrix<double, 2, 2>)\n  * \\li \\c Vector4f is a vector of 4 floats (\\c Matrix<float, 4, 1>)\n  * \\li \\c RowVector3i is a row-vector of 3 ints (\\c Matrix<int, 1, 3>)\n  *\n  * \\li \\c MatrixXf is a dynamic-size matrix of floats (\\c Matrix<float, Dynamic, Dynamic>)\n  * \\li \\c VectorXf is a dynamic-size vector of floats (\\c Matrix<float, Dynamic, 1>)\n  *\n  * \\li \\c Matrix2Xf is a partially fixed-size (dynamic-size) matrix of floats (\\c Matrix<float, 2, Dynamic>)\n  * \\li \\c MatrixX3d is a partially dynamic-size (fixed-size) matrix of double (\\c Matrix<double, Dynamic, 3>)\n  *\n  * See \\link matrixtypedefs this page \\endlink for a complete list of predefined \\em %Matrix and \\em Vector typedefs.\n  *\n  * You can access elements of vectors and matrices using normal subscripting:\n  *\n  * \\code\n  * Eigen::VectorXd v(10);\n  * v[0] = 0.1;\n  * v[1] = 0.2;\n  * v(0) = 0.3;\n  * v(1) = 0.4;\n  *\n  * Eigen::MatrixXi m(10, 10);\n  * m(0, 1) = 1;\n  * m(0, 2) = 2;\n  * m(0, 3) = 3;\n  * \\endcode\n  *\n  * This class can be extended with the help of the plugin mechanism described on the page\n  * \\ref TopicCustomizing_Plugins by defining the preprocessor symbol \\c EIGEN_MATRIX_PLUGIN.\n  *\n  * <i><b>Some notes:</b></i>\n  *\n  * <dl>\n  * <dt><b>\\anchor dense Dense versus sparse:</b></dt>\n  * <dd>This %Matrix class handles dense, not sparse matrices and vectors. For sparse matrices and vectors, see the Sparse module.\n  *\n  * Dense matrices and vectors are plain usual arrays of coefficients. All the coefficients are stored, in an ordinary contiguous array.\n  * This is unlike Sparse matrices and vectors where the coefficients are stored as a list of nonzero coefficients.</dd>\n  *\n  * <dt><b>\\anchor fixedsize Fixed-size versus dynamic-size:</b></dt>\n  * <dd>Fixed-size means that the numbers of rows and columns are known are compile-time. In this case, Eigen allocates the array\n  * of coefficients as a fixed-size array, as a class member. This makes sense for very small matrices, typically up to 4x4, sometimes up\n  * to 16x16. Larger matrices should be declared as dynamic-size even if one happens to know their size at compile-time.\n  *\n  * Dynamic-size means that the numbers of rows or columns are not necessarily known at compile-time. In this case they are runtime\n  * variables, and the array of coefficients is allocated dynamically on the heap.\n  *\n  * Note that \\em dense matrices, be they Fixed-size or Dynamic-size, <em>do not</em> expand dynamically in the sense of a std::map.\n  * If you want this behavior, see the Sparse module.</dd>\n  *\n  * <dt><b>\\anchor maxrows _MaxRows and _MaxCols:</b></dt>\n  * <dd>In most cases, one just leaves these parameters to the default values.\n  * These parameters mean the maximum size of rows and columns that the matrix may have. They are useful in cases\n  * when the exact numbers of rows and columns are not known are compile-time, but it is known at compile-time that they cannot\n  * exceed a certain value. This happens when taking dynamic-size blocks inside fixed-size matrices: in this case _MaxRows and _MaxCols\n  * are the dimensions of the original matrix, while _Rows and _Cols are Dynamic.</dd>\n  * </dl>\n  *\n  * <i><b>ABI and storage layout</b></i>\n  *\n  * The table below summarizes the ABI of some possible Matrix instances which is fixed thorough the lifetime of Eigen 3.\n  * <table  class=\"manual\">\n  * <tr><th>Matrix type</th><th>Equivalent C structure</th></tr>\n  * <tr><td>\\code Matrix<T,Dynamic,Dynamic> \\endcode</td><td>\\code\n  * struct {\n  *   T *data;                  // with (size_t(data)%EIGEN_MAX_ALIGN_BYTES)==0\n  *   Eigen::Index rows, cols;\n  *  };\n  * \\endcode</td></tr>\n  * <tr class=\"alt\"><td>\\code\n  * Matrix<T,Dynamic,1>\n  * Matrix<T,1,Dynamic> \\endcode</td><td>\\code\n  * struct {\n  *   T *data;                  // with (size_t(data)%EIGEN_MAX_ALIGN_BYTES)==0\n  *   Eigen::Index size;\n  *  };\n  * \\endcode</td></tr>\n  * <tr><td>\\code Matrix<T,Rows,Cols> \\endcode</td><td>\\code\n  * struct {\n  *   T data[Rows*Cols];        // with (size_t(data)%A(Rows*Cols*sizeof(T)))==0\n  *  };\n  * \\endcode</td></tr>\n  * <tr class=\"alt\"><td>\\code Matrix<T,Dynamic,Dynamic,0,MaxRows,MaxCols> \\endcode</td><td>\\code\n  * struct {\n  *   T data[MaxRows*MaxCols];  // with (size_t(data)%A(MaxRows*MaxCols*sizeof(T)))==0\n  *   Eigen::Index rows, cols;\n  *  };\n  * \\endcode</td></tr>\n  * </table>\n  * Note that in this table Rows, Cols, MaxRows and MaxCols are all positive integers. A(S) is defined to the largest possible power-of-two\n  * smaller to EIGEN_MAX_STATIC_ALIGN_BYTES.\n  *\n  * \\see MatrixBase for the majority of the API methods for matrices, \\ref TopicClassHierarchy,\n  * \\ref TopicStorageOrders\n  */\n\ntemplate<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>\nclass Matrix\n  : public PlainObjectBase<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >\n{\n  public:\n\n    /** \\brief Base class typedef.\n      * \\sa PlainObjectBase\n      */\n    typedef PlainObjectBase<Matrix> Base;\n\n    enum { Options = _Options };\n\n    EIGEN_DENSE_PUBLIC_INTERFACE(Matrix)\n\n    typedef typename Base::PlainObject PlainObject;\n\n    using Base::base;\n    using Base::coeffRef;\n\n    /**\n      * \\brief Assigns matrices to each other.\n      *\n      * \\note This is a special case of the templated operator=. Its purpose is\n      * to prevent a default operator= from hiding the templated operator=.\n      *\n      * \\callgraph\n      */\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Matrix& operator=(const Matrix& other)\n    {\n      return Base::_set(other);\n    }\n\n    /** \\internal\n      * \\brief Copies the value of the expression \\a other into \\c *this with automatic resizing.\n      *\n      * *this might be resized to match the dimensions of \\a other. If *this was a null matrix (not already initialized),\n      * it will be initialized.\n      *\n      * Note that copying a row-vector into a vector (and conversely) is allowed.\n      * The resizing, if any, is then done in the appropriate way so that row-vectors\n      * remain row-vectors and vectors remain vectors.\n      */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Matrix& operator=(const DenseBase<OtherDerived>& other)\n    {\n      return Base::_set(other);\n    }\n\n    /* Here, doxygen failed to copy the brief information when using \\copydoc */\n\n    /**\n      * \\brief Copies the generic expression \\a other into *this.\n      * \\copydetails DenseBase::operator=(const EigenBase<OtherDerived> &other)\n      */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Matrix& operator=(const EigenBase<OtherDerived> &other)\n    {\n      return Base::operator=(other);\n    }\n\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Matrix& operator=(const ReturnByValue<OtherDerived>& func)\n    {\n      return Base::operator=(func);\n    }\n\n    /** \\brief Default constructor.\n      *\n      * For fixed-size matrices, does nothing.\n      *\n      * For dynamic-size matrices, creates an empty matrix of size 0. Does not allocate any array. Such a matrix\n      * is called a null matrix. This constructor is the unique way to create null matrices: resizing\n      * a matrix to 0 is not supported.\n      *\n      * \\sa resize(Index,Index)\n      */\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Matrix() : Base()\n    {\n      Base::_check_template_params();\n      EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED\n    }\n\n    // FIXME is it still needed\n    EIGEN_DEVICE_FUNC\n    explicit Matrix(internal::constructor_without_unaligned_array_assert)\n      : Base(internal::constructor_without_unaligned_array_assert())\n    { Base::_check_template_params(); EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED }\n\n#if EIGEN_HAS_RVALUE_REFERENCES\n    EIGEN_DEVICE_FUNC\n    Matrix(Matrix&& other) EIGEN_NOEXCEPT_IF(std::is_nothrow_move_constructible<Scalar>::value)\n      : Base(std::move(other))\n    {\n      Base::_check_template_params();\n      if (RowsAtCompileTime!=Dynamic && ColsAtCompileTime!=Dynamic)\n        Base::_set_noalias(other);\n    }\n    EIGEN_DEVICE_FUNC\n    Matrix& operator=(Matrix&& other) EIGEN_NOEXCEPT_IF(std::is_nothrow_move_assignable<Scalar>::value)\n    {\n      other.swap(*this);\n      return *this;\n    }\n#endif\n\n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n\n    // This constructor is for both 1x1 matrices and dynamic vectors\n    template<typename T>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE explicit Matrix(const T& x)\n    {\n      Base::_check_template_params();\n      Base::template _init1<T>(x);\n    }\n\n    template<typename T0, typename T1>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Matrix(const T0& x, const T1& y)\n    {\n      Base::_check_template_params();\n      Base::template _init2<T0,T1>(x, y);\n    }\n    #else\n    /** \\brief Constructs a fixed-sized matrix initialized with coefficients starting at \\a data */\n    EIGEN_DEVICE_FUNC\n    explicit Matrix(const Scalar *data);\n\n    /** \\brief Constructs a vector or row-vector with given dimension. \\only_for_vectors\n      *\n      * This is useful for dynamic-size vectors. For fixed-size vectors,\n      * it is redundant to pass these parameters, so one should use the default constructor\n      * Matrix() instead.\n      * \n      * \\warning This constructor is disabled for fixed-size \\c 1x1 matrices. For instance,\n      * calling Matrix<double,1,1>(1) will call the initialization constructor: Matrix(const Scalar&).\n      * For fixed-size \\c 1x1 matrices it is therefore recommended to use the default\n      * constructor Matrix() instead, especially when using one of the non standard\n      * \\c EIGEN_INITIALIZE_MATRICES_BY_{ZERO,\\c NAN} macros (see \\ref TopicPreprocessorDirectives).\n      */\n    EIGEN_STRONG_INLINE explicit Matrix(Index dim);\n    /** \\brief Constructs an initialized 1x1 matrix with the given coefficient */\n    Matrix(const Scalar& x);\n    /** \\brief Constructs an uninitialized matrix with \\a rows rows and \\a cols columns.\n      *\n      * This is useful for dynamic-size matrices. For fixed-size matrices,\n      * it is redundant to pass these parameters, so one should use the default constructor\n      * Matrix() instead.\n      * \n      * \\warning This constructor is disabled for fixed-size \\c 1x2 and \\c 2x1 vectors. For instance,\n      * calling Matrix2f(2,1) will call the initialization constructor: Matrix(const Scalar& x, const Scalar& y).\n      * For fixed-size \\c 1x2 or \\c 2x1 vectors it is therefore recommended to use the default\n      * constructor Matrix() instead, especially when using one of the non standard\n      * \\c EIGEN_INITIALIZE_MATRICES_BY_{ZERO,\\c NAN} macros (see \\ref TopicPreprocessorDirectives).\n      */\n    EIGEN_DEVICE_FUNC\n    Matrix(Index rows, Index cols);\n    \n    /** \\brief Constructs an initialized 2D vector with given coefficients */\n    Matrix(const Scalar& x, const Scalar& y);\n    #endif\n\n    /** \\brief Constructs an initialized 3D vector with given coefficients */\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Matrix(const Scalar& x, const Scalar& y, const Scalar& z)\n    {\n      Base::_check_template_params();\n      EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Matrix, 3)\n      m_storage.data()[0] = x;\n      m_storage.data()[1] = y;\n      m_storage.data()[2] = z;\n    }\n    /** \\brief Constructs an initialized 4D vector with given coefficients */\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Matrix(const Scalar& x, const Scalar& y, const Scalar& z, const Scalar& w)\n    {\n      Base::_check_template_params();\n      EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Matrix, 4)\n      m_storage.data()[0] = x;\n      m_storage.data()[1] = y;\n      m_storage.data()[2] = z;\n      m_storage.data()[3] = w;\n    }\n\n\n    /** \\brief Copy constructor */\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Matrix(const Matrix& other) : Base(other)\n    { }\n\n    /** \\brief Copy constructor for generic expressions.\n      * \\sa MatrixBase::operator=(const EigenBase<OtherDerived>&)\n      */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Matrix(const EigenBase<OtherDerived> &other)\n      : Base(other.derived())\n    { }\n\n    EIGEN_DEVICE_FUNC inline Index innerStride() const { return 1; }\n    EIGEN_DEVICE_FUNC inline Index outerStride() const { return this->innerSize(); }\n\n    /////////// Geometry module ///////////\n\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    explicit Matrix(const RotationBase<OtherDerived,ColsAtCompileTime>& r);\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    Matrix& operator=(const RotationBase<OtherDerived,ColsAtCompileTime>& r);\n\n    // allow to extend Matrix outside Eigen\n    #ifdef EIGEN_MATRIX_PLUGIN\n    #include EIGEN_MATRIX_PLUGIN\n    #endif\n\n  protected:\n    template <typename Derived, typename OtherDerived, bool IsVector>\n    friend struct internal::conservative_resize_like_impl;\n\n    using Base::m_storage;\n};\n\n/** \\defgroup matrixtypedefs Global matrix typedefs\n  *\n  * \\ingroup Core_Module\n  *\n  * Eigen defines several typedef shortcuts for most common matrix and vector types.\n  *\n  * The general patterns are the following:\n  *\n  * \\c MatrixSizeType where \\c Size can be \\c 2,\\c 3,\\c 4 for fixed size square matrices or \\c X for dynamic size,\n  * and where \\c Type can be \\c i for integer, \\c f for float, \\c d for double, \\c cf for complex float, \\c cd\n  * for complex double.\n  *\n  * For example, \\c Matrix3d is a fixed-size 3x3 matrix type of doubles, and \\c MatrixXf is a dynamic-size matrix of floats.\n  *\n  * There are also \\c VectorSizeType and \\c RowVectorSizeType which are self-explanatory. For example, \\c Vector4cf is\n  * a fixed-size vector of 4 complex floats.\n  *\n  * \\sa class Matrix\n  */\n\n#define EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix)   \\\n/** \\ingroup matrixtypedefs */                                    \\\ntypedef Matrix<Type, Size, Size> Matrix##SizeSuffix##TypeSuffix;  \\\n/** \\ingroup matrixtypedefs */                                    \\\ntypedef Matrix<Type, Size, 1>    Vector##SizeSuffix##TypeSuffix;  \\\n/** \\ingroup matrixtypedefs */                                    \\\ntypedef Matrix<Type, 1, Size>    RowVector##SizeSuffix##TypeSuffix;\n\n#define EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, Size)         \\\n/** \\ingroup matrixtypedefs */                                    \\\ntypedef Matrix<Type, Size, Dynamic> Matrix##Size##X##TypeSuffix;  \\\n/** \\ingroup matrixtypedefs */                                    \\\ntypedef Matrix<Type, Dynamic, Size> Matrix##X##Size##TypeSuffix;\n\n#define EIGEN_MAKE_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \\\nEIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 2, 2) \\\nEIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 3, 3) \\\nEIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 4, 4) \\\nEIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Dynamic, X) \\\nEIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 2) \\\nEIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 3) \\\nEIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 4)\n\nEIGEN_MAKE_TYPEDEFS_ALL_SIZES(int,                  i)\nEIGEN_MAKE_TYPEDEFS_ALL_SIZES(float,                f)\nEIGEN_MAKE_TYPEDEFS_ALL_SIZES(double,               d)\nEIGEN_MAKE_TYPEDEFS_ALL_SIZES(std::complex<float>,  cf)\nEIGEN_MAKE_TYPEDEFS_ALL_SIZES(std::complex<double>, cd)\n\n#undef EIGEN_MAKE_TYPEDEFS_ALL_SIZES\n#undef EIGEN_MAKE_TYPEDEFS\n#undef EIGEN_MAKE_FIXED_TYPEDEFS\n\n} // end namespace Eigen\n\n#endif // EIGEN_MATRIX_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/MatrixBase.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2006-2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_MATRIXBASE_H\n#define EIGEN_MATRIXBASE_H\n\nnamespace Eigen {\n\n/** \\class MatrixBase\n  * \\ingroup Core_Module\n  *\n  * \\brief Base class for all dense matrices, vectors, and expressions\n  *\n  * This class is the base that is inherited by all matrix, vector, and related expression\n  * types. Most of the Eigen API is contained in this class, and its base classes. Other important\n  * classes for the Eigen API are Matrix, and VectorwiseOp.\n  *\n  * Note that some methods are defined in other modules such as the \\ref LU_Module LU module\n  * for all functions related to matrix inversions.\n  *\n  * \\tparam Derived is the derived type, e.g. a matrix type, or an expression, etc.\n  *\n  * When writing a function taking Eigen objects as argument, if you want your function\n  * to take as argument any matrix, vector, or expression, just let it take a\n  * MatrixBase argument. As an example, here is a function printFirstRow which, given\n  * a matrix, vector, or expression \\a x, prints the first row of \\a x.\n  *\n  * \\code\n    template<typename Derived>\n    void printFirstRow(const Eigen::MatrixBase<Derived>& x)\n    {\n      cout << x.row(0) << endl;\n    }\n  * \\endcode\n  *\n  * This class can be extended with the help of the plugin mechanism described on the page\n  * \\ref TopicCustomizing_Plugins by defining the preprocessor symbol \\c EIGEN_MATRIXBASE_PLUGIN.\n  *\n  * \\sa \\blank \\ref TopicClassHierarchy\n  */\ntemplate<typename Derived> class MatrixBase\n  : public DenseBase<Derived>\n{\n  public:\n#ifndef EIGEN_PARSED_BY_DOXYGEN\n    typedef MatrixBase StorageBaseType;\n    typedef typename internal::traits<Derived>::StorageKind StorageKind;\n    typedef typename internal::traits<Derived>::StorageIndex StorageIndex;\n    typedef typename internal::traits<Derived>::Scalar Scalar;\n    typedef typename internal::packet_traits<Scalar>::type PacketScalar;\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n\n    typedef DenseBase<Derived> Base;\n    using Base::RowsAtCompileTime;\n    using Base::ColsAtCompileTime;\n    using Base::SizeAtCompileTime;\n    using Base::MaxRowsAtCompileTime;\n    using Base::MaxColsAtCompileTime;\n    using Base::MaxSizeAtCompileTime;\n    using Base::IsVectorAtCompileTime;\n    using Base::Flags;\n\n    using Base::derived;\n    using Base::const_cast_derived;\n    using Base::rows;\n    using Base::cols;\n    using Base::size;\n    using Base::coeff;\n    using Base::coeffRef;\n    using Base::lazyAssign;\n    using Base::eval;\n    using Base::operator+=;\n    using Base::operator-=;\n    using Base::operator*=;\n    using Base::operator/=;\n\n    typedef typename Base::CoeffReturnType CoeffReturnType;\n    typedef typename Base::ConstTransposeReturnType ConstTransposeReturnType;\n    typedef typename Base::RowXpr RowXpr;\n    typedef typename Base::ColXpr ColXpr;\n#endif // not EIGEN_PARSED_BY_DOXYGEN\n\n\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\n    /** type of the equivalent square matrix */\n    typedef Matrix<Scalar,EIGEN_SIZE_MAX(RowsAtCompileTime,ColsAtCompileTime),\n                          EIGEN_SIZE_MAX(RowsAtCompileTime,ColsAtCompileTime)> SquareMatrixType;\n#endif // not EIGEN_PARSED_BY_DOXYGEN\n\n    /** \\returns the size of the main diagonal, which is min(rows(),cols()).\n      * \\sa rows(), cols(), SizeAtCompileTime. */\n    EIGEN_DEVICE_FUNC\n    inline Index diagonalSize() const { return (numext::mini)(rows(),cols()); }\n\n    typedef typename Base::PlainObject PlainObject;\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\n    /** \\internal Represents a matrix with all coefficients equal to one another*/\n    typedef CwiseNullaryOp<internal::scalar_constant_op<Scalar>,PlainObject> ConstantReturnType;\n    /** \\internal the return type of MatrixBase::adjoint() */\n    typedef typename internal::conditional<NumTraits<Scalar>::IsComplex,\n                        CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>, ConstTransposeReturnType>,\n                        ConstTransposeReturnType\n                     >::type AdjointReturnType;\n    /** \\internal Return type of eigenvalues() */\n    typedef Matrix<std::complex<RealScalar>, internal::traits<Derived>::ColsAtCompileTime, 1, ColMajor> EigenvaluesReturnType;\n    /** \\internal the return type of identity */\n    typedef CwiseNullaryOp<internal::scalar_identity_op<Scalar>,PlainObject> IdentityReturnType;\n    /** \\internal the return type of unit vectors */\n    typedef Block<const CwiseNullaryOp<internal::scalar_identity_op<Scalar>, SquareMatrixType>,\n                  internal::traits<Derived>::RowsAtCompileTime,\n                  internal::traits<Derived>::ColsAtCompileTime> BasisReturnType;\n#endif // not EIGEN_PARSED_BY_DOXYGEN\n\n#define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::MatrixBase\n#define EIGEN_DOC_UNARY_ADDONS(X,Y)\n#   include \"../plugins/CommonCwiseUnaryOps.h\"\n#   include \"../plugins/CommonCwiseBinaryOps.h\"\n#   include \"../plugins/MatrixCwiseUnaryOps.h\"\n#   include \"../plugins/MatrixCwiseBinaryOps.h\"\n#   ifdef EIGEN_MATRIXBASE_PLUGIN\n#     include EIGEN_MATRIXBASE_PLUGIN\n#   endif\n#undef EIGEN_CURRENT_STORAGE_BASE_CLASS\n#undef EIGEN_DOC_UNARY_ADDONS\n\n    /** Special case of the template operator=, in order to prevent the compiler\n      * from generating a default operator= (issue hit with g++ 4.1)\n      */\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    Derived& operator=(const MatrixBase& other);\n\n    // We cannot inherit here via Base::operator= since it is causing\n    // trouble with MSVC.\n\n    template <typename OtherDerived>\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    Derived& operator=(const DenseBase<OtherDerived>& other);\n\n    template <typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    Derived& operator=(const EigenBase<OtherDerived>& other);\n\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    Derived& operator=(const ReturnByValue<OtherDerived>& other);\n\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    Derived& operator+=(const MatrixBase<OtherDerived>& other);\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    Derived& operator-=(const MatrixBase<OtherDerived>& other);\n\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    const Product<Derived,OtherDerived>\n    operator*(const MatrixBase<OtherDerived> &other) const;\n\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    const Product<Derived,OtherDerived,LazyProduct>\n    lazyProduct(const MatrixBase<OtherDerived> &other) const;\n\n    template<typename OtherDerived>\n    Derived& operator*=(const EigenBase<OtherDerived>& other);\n\n    template<typename OtherDerived>\n    void applyOnTheLeft(const EigenBase<OtherDerived>& other);\n\n    template<typename OtherDerived>\n    void applyOnTheRight(const EigenBase<OtherDerived>& other);\n\n    template<typename DiagonalDerived>\n    EIGEN_DEVICE_FUNC\n    const Product<Derived, DiagonalDerived, LazyProduct>\n    operator*(const DiagonalBase<DiagonalDerived> &diagonal) const;\n\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    typename ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType\n    dot(const MatrixBase<OtherDerived>& other) const;\n\n    EIGEN_DEVICE_FUNC RealScalar squaredNorm() const;\n    EIGEN_DEVICE_FUNC RealScalar norm() const;\n    RealScalar stableNorm() const;\n    RealScalar blueNorm() const;\n    RealScalar hypotNorm() const;\n    EIGEN_DEVICE_FUNC const PlainObject normalized() const;\n    EIGEN_DEVICE_FUNC const PlainObject stableNormalized() const;\n    EIGEN_DEVICE_FUNC void normalize();\n    EIGEN_DEVICE_FUNC void stableNormalize();\n\n    EIGEN_DEVICE_FUNC const AdjointReturnType adjoint() const;\n    EIGEN_DEVICE_FUNC void adjointInPlace();\n\n    typedef Diagonal<Derived> DiagonalReturnType;\n    EIGEN_DEVICE_FUNC\n    DiagonalReturnType diagonal();\n\n    typedef typename internal::add_const<Diagonal<const Derived> >::type ConstDiagonalReturnType;\n    EIGEN_DEVICE_FUNC\n    ConstDiagonalReturnType diagonal() const;\n\n    template<int Index> struct DiagonalIndexReturnType { typedef Diagonal<Derived,Index> Type; };\n    template<int Index> struct ConstDiagonalIndexReturnType { typedef const Diagonal<const Derived,Index> Type; };\n\n    template<int Index>\n    EIGEN_DEVICE_FUNC\n    typename DiagonalIndexReturnType<Index>::Type diagonal();\n\n    template<int Index>\n    EIGEN_DEVICE_FUNC\n    typename ConstDiagonalIndexReturnType<Index>::Type diagonal() const;\n\n    typedef Diagonal<Derived,DynamicIndex> DiagonalDynamicIndexReturnType;\n    typedef typename internal::add_const<Diagonal<const Derived,DynamicIndex> >::type ConstDiagonalDynamicIndexReturnType;\n\n    EIGEN_DEVICE_FUNC\n    DiagonalDynamicIndexReturnType diagonal(Index index);\n    EIGEN_DEVICE_FUNC\n    ConstDiagonalDynamicIndexReturnType diagonal(Index index) const;\n\n    template<unsigned int Mode> struct TriangularViewReturnType { typedef TriangularView<Derived, Mode> Type; };\n    template<unsigned int Mode> struct ConstTriangularViewReturnType { typedef const TriangularView<const Derived, Mode> Type; };\n\n    template<unsigned int Mode>\n    EIGEN_DEVICE_FUNC\n    typename TriangularViewReturnType<Mode>::Type triangularView();\n    template<unsigned int Mode>\n    EIGEN_DEVICE_FUNC\n    typename ConstTriangularViewReturnType<Mode>::Type triangularView() const;\n\n    template<unsigned int UpLo> struct SelfAdjointViewReturnType { typedef SelfAdjointView<Derived, UpLo> Type; };\n    template<unsigned int UpLo> struct ConstSelfAdjointViewReturnType { typedef const SelfAdjointView<const Derived, UpLo> Type; };\n\n    template<unsigned int UpLo>\n    EIGEN_DEVICE_FUNC\n    typename SelfAdjointViewReturnType<UpLo>::Type selfadjointView();\n    template<unsigned int UpLo>\n    EIGEN_DEVICE_FUNC\n    typename ConstSelfAdjointViewReturnType<UpLo>::Type selfadjointView() const;\n\n    const SparseView<Derived> sparseView(const Scalar& m_reference = Scalar(0),\n                                         const typename NumTraits<Scalar>::Real& m_epsilon = NumTraits<Scalar>::dummy_precision()) const;\n    EIGEN_DEVICE_FUNC static const IdentityReturnType Identity();\n    EIGEN_DEVICE_FUNC static const IdentityReturnType Identity(Index rows, Index cols);\n    EIGEN_DEVICE_FUNC static const BasisReturnType Unit(Index size, Index i);\n    EIGEN_DEVICE_FUNC static const BasisReturnType Unit(Index i);\n    EIGEN_DEVICE_FUNC static const BasisReturnType UnitX();\n    EIGEN_DEVICE_FUNC static const BasisReturnType UnitY();\n    EIGEN_DEVICE_FUNC static const BasisReturnType UnitZ();\n    EIGEN_DEVICE_FUNC static const BasisReturnType UnitW();\n\n    EIGEN_DEVICE_FUNC\n    const DiagonalWrapper<const Derived> asDiagonal() const;\n    const PermutationWrapper<const Derived> asPermutation() const;\n\n    EIGEN_DEVICE_FUNC\n    Derived& setIdentity();\n    EIGEN_DEVICE_FUNC\n    Derived& setIdentity(Index rows, Index cols);\n\n    bool isIdentity(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;\n    bool isDiagonal(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;\n\n    bool isUpperTriangular(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;\n    bool isLowerTriangular(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;\n\n    template<typename OtherDerived>\n    bool isOrthogonal(const MatrixBase<OtherDerived>& other,\n                      const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;\n    bool isUnitary(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;\n\n    /** \\returns true if each coefficients of \\c *this and \\a other are all exactly equal.\n      * \\warning When using floating point scalar values you probably should rather use a\n      *          fuzzy comparison such as isApprox()\n      * \\sa isApprox(), operator!= */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC inline bool operator==(const MatrixBase<OtherDerived>& other) const\n    { return cwiseEqual(other).all(); }\n\n    /** \\returns true if at least one pair of coefficients of \\c *this and \\a other are not exactly equal to each other.\n      * \\warning When using floating point scalar values you probably should rather use a\n      *          fuzzy comparison such as isApprox()\n      * \\sa isApprox(), operator== */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC inline bool operator!=(const MatrixBase<OtherDerived>& other) const\n    { return cwiseNotEqual(other).any(); }\n\n    NoAlias<Derived,Eigen::MatrixBase > noalias();\n\n    // TODO forceAlignedAccess is temporarily disabled\n    // Need to find a nicer workaround.\n    inline const Derived& forceAlignedAccess() const { return derived(); }\n    inline Derived& forceAlignedAccess() { return derived(); }\n    template<bool Enable> inline const Derived& forceAlignedAccessIf() const { return derived(); }\n    template<bool Enable> inline Derived& forceAlignedAccessIf() { return derived(); }\n\n    EIGEN_DEVICE_FUNC Scalar trace() const;\n\n    template<int p> EIGEN_DEVICE_FUNC RealScalar lpNorm() const;\n\n    EIGEN_DEVICE_FUNC MatrixBase<Derived>& matrix() { return *this; }\n    EIGEN_DEVICE_FUNC const MatrixBase<Derived>& matrix() const { return *this; }\n\n    /** \\returns an \\link Eigen::ArrayBase Array \\endlink expression of this matrix\n      * \\sa ArrayBase::matrix() */\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ArrayWrapper<Derived> array() { return ArrayWrapper<Derived>(derived()); }\n    /** \\returns a const \\link Eigen::ArrayBase Array \\endlink expression of this matrix\n      * \\sa ArrayBase::matrix() */\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const ArrayWrapper<const Derived> array() const { return ArrayWrapper<const Derived>(derived()); }\n\n/////////// LU module ///////////\n\n    inline const FullPivLU<PlainObject> fullPivLu() const;\n    inline const PartialPivLU<PlainObject> partialPivLu() const;\n\n    inline const PartialPivLU<PlainObject> lu() const;\n\n    inline const Inverse<Derived> inverse() const;\n\n    template<typename ResultType>\n    inline void computeInverseAndDetWithCheck(\n      ResultType& inverse,\n      typename ResultType::Scalar& determinant,\n      bool& invertible,\n      const RealScalar& absDeterminantThreshold = NumTraits<Scalar>::dummy_precision()\n    ) const;\n    template<typename ResultType>\n    inline void computeInverseWithCheck(\n      ResultType& inverse,\n      bool& invertible,\n      const RealScalar& absDeterminantThreshold = NumTraits<Scalar>::dummy_precision()\n    ) const;\n    Scalar determinant() const;\n\n/////////// Cholesky module ///////////\n\n    inline const LLT<PlainObject>  llt() const;\n    inline const LDLT<PlainObject> ldlt() const;\n\n/////////// QR module ///////////\n\n    inline const HouseholderQR<PlainObject> householderQr() const;\n    inline const ColPivHouseholderQR<PlainObject> colPivHouseholderQr() const;\n    inline const FullPivHouseholderQR<PlainObject> fullPivHouseholderQr() const;\n    inline const CompleteOrthogonalDecomposition<PlainObject> completeOrthogonalDecomposition() const;\n\n/////////// Eigenvalues module ///////////\n\n    inline EigenvaluesReturnType eigenvalues() const;\n    inline RealScalar operatorNorm() const;\n\n/////////// SVD module ///////////\n\n    inline JacobiSVD<PlainObject> jacobiSvd(unsigned int computationOptions = 0) const;\n    inline BDCSVD<PlainObject>    bdcSvd(unsigned int computationOptions = 0) const;\n\n/////////// Geometry module ///////////\n\n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    /// \\internal helper struct to form the return type of the cross product\n    template<typename OtherDerived> struct cross_product_return_type {\n      typedef typename ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType Scalar;\n      typedef Matrix<Scalar,MatrixBase::RowsAtCompileTime,MatrixBase::ColsAtCompileTime> type;\n    };\n    #endif // EIGEN_PARSED_BY_DOXYGEN\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n#ifndef EIGEN_PARSED_BY_DOXYGEN\n    inline typename cross_product_return_type<OtherDerived>::type\n#else\n    inline PlainObject\n#endif\n    cross(const MatrixBase<OtherDerived>& other) const;\n\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    inline PlainObject cross3(const MatrixBase<OtherDerived>& other) const;\n\n    EIGEN_DEVICE_FUNC\n    inline PlainObject unitOrthogonal(void) const;\n\n    EIGEN_DEVICE_FUNC\n    inline Matrix<Scalar,3,1> eulerAngles(Index a0, Index a1, Index a2) const;\n\n    // put this as separate enum value to work around possible GCC 4.3 bug (?)\n    enum { HomogeneousReturnTypeDirection = ColsAtCompileTime==1&&RowsAtCompileTime==1 ? ((internal::traits<Derived>::Flags&RowMajorBit)==RowMajorBit ? Horizontal : Vertical)\n                                          : ColsAtCompileTime==1 ? Vertical : Horizontal };\n    typedef Homogeneous<Derived, HomogeneousReturnTypeDirection> HomogeneousReturnType;\n    EIGEN_DEVICE_FUNC\n    inline HomogeneousReturnType homogeneous() const;\n\n    enum {\n      SizeMinusOne = SizeAtCompileTime==Dynamic ? Dynamic : SizeAtCompileTime-1\n    };\n    typedef Block<const Derived,\n                  internal::traits<Derived>::ColsAtCompileTime==1 ? SizeMinusOne : 1,\n                  internal::traits<Derived>::ColsAtCompileTime==1 ? 1 : SizeMinusOne> ConstStartMinusOne;\n    typedef EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(ConstStartMinusOne,Scalar,quotient) HNormalizedReturnType;\n    EIGEN_DEVICE_FUNC\n    inline const HNormalizedReturnType hnormalized() const;\n\n////////// Householder module ///////////\n\n    void makeHouseholderInPlace(Scalar& tau, RealScalar& beta);\n    template<typename EssentialPart>\n    void makeHouseholder(EssentialPart& essential,\n                         Scalar& tau, RealScalar& beta) const;\n    template<typename EssentialPart>\n    void applyHouseholderOnTheLeft(const EssentialPart& essential,\n                                   const Scalar& tau,\n                                   Scalar* workspace);\n    template<typename EssentialPart>\n    void applyHouseholderOnTheRight(const EssentialPart& essential,\n                                    const Scalar& tau,\n                                    Scalar* workspace);\n\n///////// Jacobi module /////////\n\n    template<typename OtherScalar>\n    void applyOnTheLeft(Index p, Index q, const JacobiRotation<OtherScalar>& j);\n    template<typename OtherScalar>\n    void applyOnTheRight(Index p, Index q, const JacobiRotation<OtherScalar>& j);\n\n///////// SparseCore module /////////\n\n    template<typename OtherDerived>\n    EIGEN_STRONG_INLINE const typename SparseMatrixBase<OtherDerived>::template CwiseProductDenseReturnType<Derived>::Type\n    cwiseProduct(const SparseMatrixBase<OtherDerived> &other) const\n    {\n      return other.cwiseProduct(derived());\n    }\n\n///////// MatrixFunctions module /////////\n\n    typedef typename internal::stem_function<Scalar>::type StemFunction;\n    const MatrixExponentialReturnValue<Derived> exp() const;\n    const MatrixFunctionReturnValue<Derived> matrixFunction(StemFunction f) const;\n    const MatrixFunctionReturnValue<Derived> cosh() const;\n    const MatrixFunctionReturnValue<Derived> sinh() const;\n    const MatrixFunctionReturnValue<Derived> cos() const;\n    const MatrixFunctionReturnValue<Derived> sin() const;\n    const MatrixSquareRootReturnValue<Derived> sqrt() const;\n    const MatrixLogarithmReturnValue<Derived> log() const;\n    const MatrixPowerReturnValue<Derived> pow(const RealScalar& p) const;\n    const MatrixComplexPowerReturnValue<Derived> pow(const std::complex<RealScalar>& p) const;\n\n  protected:\n    EIGEN_DEVICE_FUNC MatrixBase() : Base() {}\n\n  private:\n    EIGEN_DEVICE_FUNC explicit MatrixBase(int);\n    EIGEN_DEVICE_FUNC MatrixBase(int,int);\n    template<typename OtherDerived> EIGEN_DEVICE_FUNC explicit MatrixBase(const MatrixBase<OtherDerived>&);\n  protected:\n    // mixing arrays and matrices is not legal\n    template<typename OtherDerived> Derived& operator+=(const ArrayBase<OtherDerived>& )\n    {EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}\n    // mixing arrays and matrices is not legal\n    template<typename OtherDerived> Derived& operator-=(const ArrayBase<OtherDerived>& )\n    {EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}\n};\n\n\n/***************************************************************************\n* Implementation of matrix base methods\n***************************************************************************/\n\n/** replaces \\c *this by \\c *this * \\a other.\n  *\n  * \\returns a reference to \\c *this\n  *\n  * Example: \\include MatrixBase_applyOnTheRight.cpp\n  * Output: \\verbinclude MatrixBase_applyOnTheRight.out\n  */\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\ninline Derived&\nMatrixBase<Derived>::operator*=(const EigenBase<OtherDerived> &other)\n{\n  other.derived().applyThisOnTheRight(derived());\n  return derived();\n}\n\n/** replaces \\c *this by \\c *this * \\a other. It is equivalent to MatrixBase::operator*=().\n  *\n  * Example: \\include MatrixBase_applyOnTheRight.cpp\n  * Output: \\verbinclude MatrixBase_applyOnTheRight.out\n  */\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\ninline void MatrixBase<Derived>::applyOnTheRight(const EigenBase<OtherDerived> &other)\n{\n  other.derived().applyThisOnTheRight(derived());\n}\n\n/** replaces \\c *this by \\a other * \\c *this.\n  *\n  * Example: \\include MatrixBase_applyOnTheLeft.cpp\n  * Output: \\verbinclude MatrixBase_applyOnTheLeft.out\n  */\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\ninline void MatrixBase<Derived>::applyOnTheLeft(const EigenBase<OtherDerived> &other)\n{\n  other.derived().applyThisOnTheLeft(derived());\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_MATRIXBASE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/NestByValue.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_NESTBYVALUE_H\n#define EIGEN_NESTBYVALUE_H\n\nnamespace Eigen {\n\nnamespace internal {\ntemplate<typename ExpressionType>\nstruct traits<NestByValue<ExpressionType> > : public traits<ExpressionType>\n{};\n}\n\n/** \\class NestByValue\n  * \\ingroup Core_Module\n  *\n  * \\brief Expression which must be nested by value\n  *\n  * \\tparam ExpressionType the type of the object of which we are requiring nesting-by-value\n  *\n  * This class is the return type of MatrixBase::nestByValue()\n  * and most of the time this is the only way it is used.\n  *\n  * \\sa MatrixBase::nestByValue()\n  */\ntemplate<typename ExpressionType> class NestByValue\n  : public internal::dense_xpr_base< NestByValue<ExpressionType> >::type\n{\n  public:\n\n    typedef typename internal::dense_xpr_base<NestByValue>::type Base;\n    EIGEN_DENSE_PUBLIC_INTERFACE(NestByValue)\n\n    EIGEN_DEVICE_FUNC explicit inline NestByValue(const ExpressionType& matrix) : m_expression(matrix) {}\n\n    EIGEN_DEVICE_FUNC inline Index rows() const { return m_expression.rows(); }\n    EIGEN_DEVICE_FUNC inline Index cols() const { return m_expression.cols(); }\n    EIGEN_DEVICE_FUNC inline Index outerStride() const { return m_expression.outerStride(); }\n    EIGEN_DEVICE_FUNC inline Index innerStride() const { return m_expression.innerStride(); }\n\n    EIGEN_DEVICE_FUNC inline const CoeffReturnType coeff(Index row, Index col) const\n    {\n      return m_expression.coeff(row, col);\n    }\n\n    EIGEN_DEVICE_FUNC inline Scalar& coeffRef(Index row, Index col)\n    {\n      return m_expression.const_cast_derived().coeffRef(row, col);\n    }\n\n    EIGEN_DEVICE_FUNC inline const CoeffReturnType coeff(Index index) const\n    {\n      return m_expression.coeff(index);\n    }\n\n    EIGEN_DEVICE_FUNC inline Scalar& coeffRef(Index index)\n    {\n      return m_expression.const_cast_derived().coeffRef(index);\n    }\n\n    template<int LoadMode>\n    inline const PacketScalar packet(Index row, Index col) const\n    {\n      return m_expression.template packet<LoadMode>(row, col);\n    }\n\n    template<int LoadMode>\n    inline void writePacket(Index row, Index col, const PacketScalar& x)\n    {\n      m_expression.const_cast_derived().template writePacket<LoadMode>(row, col, x);\n    }\n\n    template<int LoadMode>\n    inline const PacketScalar packet(Index index) const\n    {\n      return m_expression.template packet<LoadMode>(index);\n    }\n\n    template<int LoadMode>\n    inline void writePacket(Index index, const PacketScalar& x)\n    {\n      m_expression.const_cast_derived().template writePacket<LoadMode>(index, x);\n    }\n\n    EIGEN_DEVICE_FUNC operator const ExpressionType&() const { return m_expression; }\n\n  protected:\n    const ExpressionType m_expression;\n};\n\n/** \\returns an expression of the temporary version of *this.\n  */\ntemplate<typename Derived>\ninline const NestByValue<Derived>\nDenseBase<Derived>::nestByValue() const\n{\n  return NestByValue<Derived>(derived());\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_NESTBYVALUE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/NoAlias.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_NOALIAS_H\n#define EIGEN_NOALIAS_H\n\nnamespace Eigen {\n\n/** \\class NoAlias\n  * \\ingroup Core_Module\n  *\n  * \\brief Pseudo expression providing an operator = assuming no aliasing\n  *\n  * \\tparam ExpressionType the type of the object on which to do the lazy assignment\n  *\n  * This class represents an expression with special assignment operators\n  * assuming no aliasing between the target expression and the source expression.\n  * More precisely it alloas to bypass the EvalBeforeAssignBit flag of the source expression.\n  * It is the return type of MatrixBase::noalias()\n  * and most of the time this is the only way it is used.\n  *\n  * \\sa MatrixBase::noalias()\n  */\ntemplate<typename ExpressionType, template <typename> class StorageBase>\nclass NoAlias\n{\n  public:\n    typedef typename ExpressionType::Scalar Scalar;\n    \n    explicit NoAlias(ExpressionType& expression) : m_expression(expression) {}\n    \n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE ExpressionType& operator=(const StorageBase<OtherDerived>& other)\n    {\n      call_assignment_no_alias(m_expression, other.derived(), internal::assign_op<Scalar,typename OtherDerived::Scalar>());\n      return m_expression;\n    }\n    \n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE ExpressionType& operator+=(const StorageBase<OtherDerived>& other)\n    {\n      call_assignment_no_alias(m_expression, other.derived(), internal::add_assign_op<Scalar,typename OtherDerived::Scalar>());\n      return m_expression;\n    }\n    \n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE ExpressionType& operator-=(const StorageBase<OtherDerived>& other)\n    {\n      call_assignment_no_alias(m_expression, other.derived(), internal::sub_assign_op<Scalar,typename OtherDerived::Scalar>());\n      return m_expression;\n    }\n\n    EIGEN_DEVICE_FUNC\n    ExpressionType& expression() const\n    {\n      return m_expression;\n    }\n\n  protected:\n    ExpressionType& m_expression;\n};\n\n/** \\returns a pseudo expression of \\c *this with an operator= assuming\n  * no aliasing between \\c *this and the source expression.\n  *\n  * More precisely, noalias() allows to bypass the EvalBeforeAssignBit flag.\n  * Currently, even though several expressions may alias, only product\n  * expressions have this flag. Therefore, noalias() is only usefull when\n  * the source expression contains a matrix product.\n  *\n  * Here are some examples where noalias is usefull:\n  * \\code\n  * D.noalias()  = A * B;\n  * D.noalias() += A.transpose() * B;\n  * D.noalias() -= 2 * A * B.adjoint();\n  * \\endcode\n  *\n  * On the other hand the following example will lead to a \\b wrong result:\n  * \\code\n  * A.noalias() = A * B;\n  * \\endcode\n  * because the result matrix A is also an operand of the matrix product. Therefore,\n  * there is no alternative than evaluating A * B in a temporary, that is the default\n  * behavior when you write:\n  * \\code\n  * A = A * B;\n  * \\endcode\n  *\n  * \\sa class NoAlias\n  */\ntemplate<typename Derived>\nNoAlias<Derived,MatrixBase> MatrixBase<Derived>::noalias()\n{\n  return NoAlias<Derived, Eigen::MatrixBase >(derived());\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_NOALIAS_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/NumTraits.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_NUMTRAITS_H\n#define EIGEN_NUMTRAITS_H\n\nnamespace Eigen {\n\nnamespace internal {\n\n// default implementation of digits10(), based on numeric_limits if specialized,\n// 0 for integer types, and log10(epsilon()) otherwise.\ntemplate< typename T,\n          bool use_numeric_limits = std::numeric_limits<T>::is_specialized,\n          bool is_integer = NumTraits<T>::IsInteger>\nstruct default_digits10_impl\n{\n  static int run() { return std::numeric_limits<T>::digits10; }\n};\n\ntemplate<typename T>\nstruct default_digits10_impl<T,false,false> // Floating point\n{\n  static int run() {\n    using std::log10;\n    using std::ceil;\n    typedef typename NumTraits<T>::Real Real;\n    return int(ceil(-log10(NumTraits<Real>::epsilon())));\n  }\n};\n\ntemplate<typename T>\nstruct default_digits10_impl<T,false,true> // Integer\n{\n  static int run() { return 0; }\n};\n\n} // end namespace internal\n\n/** \\class NumTraits\n  * \\ingroup Core_Module\n  *\n  * \\brief Holds information about the various numeric (i.e. scalar) types allowed by Eigen.\n  *\n  * \\tparam T the numeric type at hand\n  *\n  * This class stores enums, typedefs and static methods giving information about a numeric type.\n  *\n  * The provided data consists of:\n  * \\li A typedef \\c Real, giving the \"real part\" type of \\a T. If \\a T is already real,\n  *     then \\c Real is just a typedef to \\a T. If \\a T is \\c std::complex<U> then \\c Real\n  *     is a typedef to \\a U.\n  * \\li A typedef \\c NonInteger, giving the type that should be used for operations producing non-integral values,\n  *     such as quotients, square roots, etc. If \\a T is a floating-point type, then this typedef just gives\n  *     \\a T again. Note however that many Eigen functions such as internal::sqrt simply refuse to\n  *     take integers. Outside of a few cases, Eigen doesn't do automatic type promotion. Thus, this typedef is\n  *     only intended as a helper for code that needs to explicitly promote types.\n  * \\li A typedef \\c Literal giving the type to use for numeric literals such as \"2\" or \"0.5\". For instance, for \\c std::complex<U>, Literal is defined as \\c U.\n  *     Of course, this type must be fully compatible with \\a T. In doubt, just use \\a T here.\n  * \\li A typedef \\a Nested giving the type to use to nest a value inside of the expression tree. If you don't know what\n  *     this means, just use \\a T here.\n  * \\li An enum value \\a IsComplex. It is equal to 1 if \\a T is a \\c std::complex\n  *     type, and to 0 otherwise.\n  * \\li An enum value \\a IsInteger. It is equal to \\c 1 if \\a T is an integer type such as \\c int,\n  *     and to \\c 0 otherwise.\n  * \\li Enum values ReadCost, AddCost and MulCost representing a rough estimate of the number of CPU cycles needed\n  *     to by move / add / mul instructions respectively, assuming the data is already stored in CPU registers.\n  *     Stay vague here. No need to do architecture-specific stuff.\n  * \\li An enum value \\a IsSigned. It is equal to \\c 1 if \\a T is a signed type and to 0 if \\a T is unsigned.\n  * \\li An enum value \\a RequireInitialization. It is equal to \\c 1 if the constructor of the numeric type \\a T must\n  *     be called, and to 0 if it is safe not to call it. Default is 0 if \\a T is an arithmetic type, and 1 otherwise.\n  * \\li An epsilon() function which, unlike <a href=\"http://en.cppreference.com/w/cpp/types/numeric_limits/epsilon\">std::numeric_limits::epsilon()</a>,\n  *     it returns a \\a Real instead of a \\a T.\n  * \\li A dummy_precision() function returning a weak epsilon value. It is mainly used as a default\n  *     value by the fuzzy comparison operators.\n  * \\li highest() and lowest() functions returning the highest and lowest possible values respectively.\n  * \\li digits10() function returning the number of decimal digits that can be represented without change. This is\n  *     the analogue of <a href=\"http://en.cppreference.com/w/cpp/types/numeric_limits/digits10\">std::numeric_limits<T>::digits10</a>\n  *     which is used as the default implementation if specialized.\n  */\n\ntemplate<typename T> struct GenericNumTraits\n{\n  enum {\n    IsInteger = std::numeric_limits<T>::is_integer,\n    IsSigned = std::numeric_limits<T>::is_signed,\n    IsComplex = 0,\n    RequireInitialization = internal::is_arithmetic<T>::value ? 0 : 1,\n    ReadCost = 1,\n    AddCost = 1,\n    MulCost = 1\n  };\n\n  typedef T Real;\n  typedef typename internal::conditional<\n                     IsInteger,\n                     typename internal::conditional<sizeof(T)<=2, float, double>::type,\n                     T\n                   >::type NonInteger;\n  typedef T Nested;\n  typedef T Literal;\n\n  EIGEN_DEVICE_FUNC\n  static inline Real epsilon()\n  {\n    return numext::numeric_limits<T>::epsilon();\n  }\n\n  EIGEN_DEVICE_FUNC\n  static inline int digits10()\n  {\n    return internal::default_digits10_impl<T>::run();\n  }\n\n  EIGEN_DEVICE_FUNC\n  static inline Real dummy_precision()\n  {\n    // make sure to override this for floating-point types\n    return Real(0);\n  }\n\n\n  EIGEN_DEVICE_FUNC\n  static inline T highest() {\n    return (numext::numeric_limits<T>::max)();\n  }\n\n  EIGEN_DEVICE_FUNC\n  static inline T lowest()  {\n    return IsInteger ? (numext::numeric_limits<T>::min)() : (-(numext::numeric_limits<T>::max)());\n  }\n\n  EIGEN_DEVICE_FUNC\n  static inline T infinity() {\n    return numext::numeric_limits<T>::infinity();\n  }\n\n  EIGEN_DEVICE_FUNC\n  static inline T quiet_NaN() {\n    return numext::numeric_limits<T>::quiet_NaN();\n  }\n};\n\ntemplate<typename T> struct NumTraits : GenericNumTraits<T>\n{};\n\ntemplate<> struct NumTraits<float>\n  : GenericNumTraits<float>\n{\n  EIGEN_DEVICE_FUNC\n  static inline float dummy_precision() { return 1e-5f; }\n};\n\ntemplate<> struct NumTraits<double> : GenericNumTraits<double>\n{\n  EIGEN_DEVICE_FUNC\n  static inline double dummy_precision() { return 1e-12; }\n};\n\ntemplate<> struct NumTraits<long double>\n  : GenericNumTraits<long double>\n{\n  static inline long double dummy_precision() { return 1e-15l; }\n};\n\ntemplate<typename _Real> struct NumTraits<std::complex<_Real> >\n  : GenericNumTraits<std::complex<_Real> >\n{\n  typedef _Real Real;\n  typedef typename NumTraits<_Real>::Literal Literal;\n  enum {\n    IsComplex = 1,\n    RequireInitialization = NumTraits<_Real>::RequireInitialization,\n    ReadCost = 2 * NumTraits<_Real>::ReadCost,\n    AddCost = 2 * NumTraits<Real>::AddCost,\n    MulCost = 4 * NumTraits<Real>::MulCost + 2 * NumTraits<Real>::AddCost\n  };\n\n  EIGEN_DEVICE_FUNC\n  static inline Real epsilon() { return NumTraits<Real>::epsilon(); }\n  EIGEN_DEVICE_FUNC\n  static inline Real dummy_precision() { return NumTraits<Real>::dummy_precision(); }\n  EIGEN_DEVICE_FUNC\n  static inline int digits10() { return NumTraits<Real>::digits10(); }\n};\n\ntemplate<typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>\nstruct NumTraits<Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> >\n{\n  typedef Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> ArrayType;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  typedef Array<RealScalar, Rows, Cols, Options, MaxRows, MaxCols> Real;\n  typedef typename NumTraits<Scalar>::NonInteger NonIntegerScalar;\n  typedef Array<NonIntegerScalar, Rows, Cols, Options, MaxRows, MaxCols> NonInteger;\n  typedef ArrayType & Nested;\n  typedef typename NumTraits<Scalar>::Literal Literal;\n\n  enum {\n    IsComplex = NumTraits<Scalar>::IsComplex,\n    IsInteger = NumTraits<Scalar>::IsInteger,\n    IsSigned  = NumTraits<Scalar>::IsSigned,\n    RequireInitialization = 1,\n    ReadCost = ArrayType::SizeAtCompileTime==Dynamic ? HugeCost : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::ReadCost,\n    AddCost  = ArrayType::SizeAtCompileTime==Dynamic ? HugeCost : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::AddCost,\n    MulCost  = ArrayType::SizeAtCompileTime==Dynamic ? HugeCost : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::MulCost\n  };\n\n  EIGEN_DEVICE_FUNC\n  static inline RealScalar epsilon() { return NumTraits<RealScalar>::epsilon(); }\n  EIGEN_DEVICE_FUNC\n  static inline RealScalar dummy_precision() { return NumTraits<RealScalar>::dummy_precision(); }\n\n  static inline int digits10() { return NumTraits<Scalar>::digits10(); }\n};\n\ntemplate<> struct NumTraits<std::string>\n  : GenericNumTraits<std::string>\n{\n  enum {\n    RequireInitialization = 1,\n    ReadCost = HugeCost,\n    AddCost  = HugeCost,\n    MulCost  = HugeCost\n  };\n\n  static inline int digits10() { return 0; }\n\nprivate:\n  static inline std::string epsilon();\n  static inline std::string dummy_precision();\n  static inline std::string lowest();\n  static inline std::string highest();\n  static inline std::string infinity();\n  static inline std::string quiet_NaN();\n};\n\n// Empty specialization for void to allow template specialization based on NumTraits<T>::Real with T==void and SFINAE.\ntemplate<> struct NumTraits<void> {};\n\n} // end namespace Eigen\n\n#endif // EIGEN_NUMTRAITS_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/PermutationMatrix.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2009-2015 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_PERMUTATIONMATRIX_H\n#define EIGEN_PERMUTATIONMATRIX_H\n\nnamespace Eigen { \n\nnamespace internal {\n\nenum PermPermProduct_t {PermPermProduct};\n\n} // end namespace internal\n\n/** \\class PermutationBase\n  * \\ingroup Core_Module\n  *\n  * \\brief Base class for permutations\n  *\n  * \\tparam Derived the derived class\n  *\n  * This class is the base class for all expressions representing a permutation matrix,\n  * internally stored as a vector of integers.\n  * The convention followed here is that if \\f$ \\sigma \\f$ is a permutation, the corresponding permutation matrix\n  * \\f$ P_\\sigma \\f$ is such that if \\f$ (e_1,\\ldots,e_p) \\f$ is the canonical basis, we have:\n  *  \\f[ P_\\sigma(e_i) = e_{\\sigma(i)}. \\f]\n  * This convention ensures that for any two permutations \\f$ \\sigma, \\tau \\f$, we have:\n  *  \\f[ P_{\\sigma\\circ\\tau} = P_\\sigma P_\\tau. \\f]\n  *\n  * Permutation matrices are square and invertible.\n  *\n  * Notice that in addition to the member functions and operators listed here, there also are non-member\n  * operator* to multiply any kind of permutation object with any kind of matrix expression (MatrixBase)\n  * on either side.\n  *\n  * \\sa class PermutationMatrix, class PermutationWrapper\n  */\ntemplate<typename Derived>\nclass PermutationBase : public EigenBase<Derived>\n{\n    typedef internal::traits<Derived> Traits;\n    typedef EigenBase<Derived> Base;\n  public:\n\n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    typedef typename Traits::IndicesType IndicesType;\n    enum {\n      Flags = Traits::Flags,\n      RowsAtCompileTime = Traits::RowsAtCompileTime,\n      ColsAtCompileTime = Traits::ColsAtCompileTime,\n      MaxRowsAtCompileTime = Traits::MaxRowsAtCompileTime,\n      MaxColsAtCompileTime = Traits::MaxColsAtCompileTime\n    };\n    typedef typename Traits::StorageIndex StorageIndex;\n    typedef Matrix<StorageIndex,RowsAtCompileTime,ColsAtCompileTime,0,MaxRowsAtCompileTime,MaxColsAtCompileTime>\n            DenseMatrixType;\n    typedef PermutationMatrix<IndicesType::SizeAtCompileTime,IndicesType::MaxSizeAtCompileTime,StorageIndex>\n            PlainPermutationType;\n    typedef PlainPermutationType PlainObject;\n    using Base::derived;\n    typedef Inverse<Derived> InverseReturnType;\n    typedef void Scalar;\n    #endif\n\n    /** Copies the other permutation into *this */\n    template<typename OtherDerived>\n    Derived& operator=(const PermutationBase<OtherDerived>& other)\n    {\n      indices() = other.indices();\n      return derived();\n    }\n\n    /** Assignment from the Transpositions \\a tr */\n    template<typename OtherDerived>\n    Derived& operator=(const TranspositionsBase<OtherDerived>& tr)\n    {\n      setIdentity(tr.size());\n      for(Index k=size()-1; k>=0; --k)\n        applyTranspositionOnTheRight(k,tr.coeff(k));\n      return derived();\n    }\n\n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    /** This is a special case of the templated operator=. Its purpose is to\n      * prevent a default operator= from hiding the templated operator=.\n      */\n    Derived& operator=(const PermutationBase& other)\n    {\n      indices() = other.indices();\n      return derived();\n    }\n    #endif\n\n    /** \\returns the number of rows */\n    inline Index rows() const { return Index(indices().size()); }\n\n    /** \\returns the number of columns */\n    inline Index cols() const { return Index(indices().size()); }\n\n    /** \\returns the size of a side of the respective square matrix, i.e., the number of indices */\n    inline Index size() const { return Index(indices().size()); }\n\n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    template<typename DenseDerived>\n    void evalTo(MatrixBase<DenseDerived>& other) const\n    {\n      other.setZero();\n      for (Index i=0; i<rows(); ++i)\n        other.coeffRef(indices().coeff(i),i) = typename DenseDerived::Scalar(1);\n    }\n    #endif\n\n    /** \\returns a Matrix object initialized from this permutation matrix. Notice that it\n      * is inefficient to return this Matrix object by value. For efficiency, favor using\n      * the Matrix constructor taking EigenBase objects.\n      */\n    DenseMatrixType toDenseMatrix() const\n    {\n      return derived();\n    }\n\n    /** const version of indices(). */\n    const IndicesType& indices() const { return derived().indices(); }\n    /** \\returns a reference to the stored array representing the permutation. */\n    IndicesType& indices() { return derived().indices(); }\n\n    /** Resizes to given size.\n      */\n    inline void resize(Index newSize)\n    {\n      indices().resize(newSize);\n    }\n\n    /** Sets *this to be the identity permutation matrix */\n    void setIdentity()\n    {\n      StorageIndex n = StorageIndex(size());\n      for(StorageIndex i = 0; i < n; ++i)\n        indices().coeffRef(i) = i;\n    }\n\n    /** Sets *this to be the identity permutation matrix of given size.\n      */\n    void setIdentity(Index newSize)\n    {\n      resize(newSize);\n      setIdentity();\n    }\n\n    /** Multiplies *this by the transposition \\f$(ij)\\f$ on the left.\n      *\n      * \\returns a reference to *this.\n      *\n      * \\warning This is much slower than applyTranspositionOnTheRight(Index,Index):\n      * this has linear complexity and requires a lot of branching.\n      *\n      * \\sa applyTranspositionOnTheRight(Index,Index)\n      */\n    Derived& applyTranspositionOnTheLeft(Index i, Index j)\n    {\n      eigen_assert(i>=0 && j>=0 && i<size() && j<size());\n      for(Index k = 0; k < size(); ++k)\n      {\n        if(indices().coeff(k) == i) indices().coeffRef(k) = StorageIndex(j);\n        else if(indices().coeff(k) == j) indices().coeffRef(k) = StorageIndex(i);\n      }\n      return derived();\n    }\n\n    /** Multiplies *this by the transposition \\f$(ij)\\f$ on the right.\n      *\n      * \\returns a reference to *this.\n      *\n      * This is a fast operation, it only consists in swapping two indices.\n      *\n      * \\sa applyTranspositionOnTheLeft(Index,Index)\n      */\n    Derived& applyTranspositionOnTheRight(Index i, Index j)\n    {\n      eigen_assert(i>=0 && j>=0 && i<size() && j<size());\n      std::swap(indices().coeffRef(i), indices().coeffRef(j));\n      return derived();\n    }\n\n    /** \\returns the inverse permutation matrix.\n      *\n      * \\note \\blank \\note_try_to_help_rvo\n      */\n    inline InverseReturnType inverse() const\n    { return InverseReturnType(derived()); }\n    /** \\returns the tranpose permutation matrix.\n      *\n      * \\note \\blank \\note_try_to_help_rvo\n      */\n    inline InverseReturnType transpose() const\n    { return InverseReturnType(derived()); }\n\n    /**** multiplication helpers to hopefully get RVO ****/\n\n  \n#ifndef EIGEN_PARSED_BY_DOXYGEN\n  protected:\n    template<typename OtherDerived>\n    void assignTranspose(const PermutationBase<OtherDerived>& other)\n    {\n      for (Index i=0; i<rows();++i) indices().coeffRef(other.indices().coeff(i)) = i;\n    }\n    template<typename Lhs,typename Rhs>\n    void assignProduct(const Lhs& lhs, const Rhs& rhs)\n    {\n      eigen_assert(lhs.cols() == rhs.rows());\n      for (Index i=0; i<rows();++i) indices().coeffRef(i) = lhs.indices().coeff(rhs.indices().coeff(i));\n    }\n#endif\n\n  public:\n\n    /** \\returns the product permutation matrix.\n      *\n      * \\note \\blank \\note_try_to_help_rvo\n      */\n    template<typename Other>\n    inline PlainPermutationType operator*(const PermutationBase<Other>& other) const\n    { return PlainPermutationType(internal::PermPermProduct, derived(), other.derived()); }\n\n    /** \\returns the product of a permutation with another inverse permutation.\n      *\n      * \\note \\blank \\note_try_to_help_rvo\n      */\n    template<typename Other>\n    inline PlainPermutationType operator*(const InverseImpl<Other,PermutationStorage>& other) const\n    { return PlainPermutationType(internal::PermPermProduct, *this, other.eval()); }\n\n    /** \\returns the product of an inverse permutation with another permutation.\n      *\n      * \\note \\blank \\note_try_to_help_rvo\n      */\n    template<typename Other> friend\n    inline PlainPermutationType operator*(const InverseImpl<Other, PermutationStorage>& other, const PermutationBase& perm)\n    { return PlainPermutationType(internal::PermPermProduct, other.eval(), perm); }\n    \n    /** \\returns the determinant of the permutation matrix, which is either 1 or -1 depending on the parity of the permutation.\n      *\n      * This function is O(\\c n) procedure allocating a buffer of \\c n booleans.\n      */\n    Index determinant() const\n    {\n      Index res = 1;\n      Index n = size();\n      Matrix<bool,RowsAtCompileTime,1,0,MaxRowsAtCompileTime> mask(n);\n      mask.fill(false);\n      Index r = 0;\n      while(r < n)\n      {\n        // search for the next seed\n        while(r<n && mask[r]) r++;\n        if(r>=n)\n          break;\n        // we got one, let's follow it until we are back to the seed\n        Index k0 = r++;\n        mask.coeffRef(k0) = true;\n        for(Index k=indices().coeff(k0); k!=k0; k=indices().coeff(k))\n        {\n          mask.coeffRef(k) = true;\n          res = -res;\n        }\n      }\n      return res;\n    }\n\n  protected:\n\n};\n\nnamespace internal {\ntemplate<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename _StorageIndex>\nstruct traits<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, _StorageIndex> >\n : traits<Matrix<_StorageIndex,SizeAtCompileTime,SizeAtCompileTime,0,MaxSizeAtCompileTime,MaxSizeAtCompileTime> >\n{\n  typedef PermutationStorage StorageKind;\n  typedef Matrix<_StorageIndex, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1> IndicesType;\n  typedef _StorageIndex StorageIndex;\n  typedef void Scalar;\n};\n}\n\n/** \\class PermutationMatrix\n  * \\ingroup Core_Module\n  *\n  * \\brief Permutation matrix\n  *\n  * \\tparam SizeAtCompileTime the number of rows/cols, or Dynamic\n  * \\tparam MaxSizeAtCompileTime the maximum number of rows/cols, or Dynamic. This optional parameter defaults to SizeAtCompileTime. Most of the time, you should not have to specify it.\n  * \\tparam _StorageIndex the integer type of the indices\n  *\n  * This class represents a permutation matrix, internally stored as a vector of integers.\n  *\n  * \\sa class PermutationBase, class PermutationWrapper, class DiagonalMatrix\n  */\ntemplate<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename _StorageIndex>\nclass PermutationMatrix : public PermutationBase<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, _StorageIndex> >\n{\n    typedef PermutationBase<PermutationMatrix> Base;\n    typedef internal::traits<PermutationMatrix> Traits;\n  public:\n\n    typedef const PermutationMatrix& Nested;\n\n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    typedef typename Traits::IndicesType IndicesType;\n    typedef typename Traits::StorageIndex StorageIndex;\n    #endif\n\n    inline PermutationMatrix()\n    {}\n\n    /** Constructs an uninitialized permutation matrix of given size.\n      */\n    explicit inline PermutationMatrix(Index size) : m_indices(size)\n    {\n      eigen_internal_assert(size <= NumTraits<StorageIndex>::highest());\n    }\n\n    /** Copy constructor. */\n    template<typename OtherDerived>\n    inline PermutationMatrix(const PermutationBase<OtherDerived>& other)\n      : m_indices(other.indices()) {}\n\n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    /** Standard copy constructor. Defined only to prevent a default copy constructor\n      * from hiding the other templated constructor */\n    inline PermutationMatrix(const PermutationMatrix& other) : m_indices(other.indices()) {}\n    #endif\n\n    /** Generic constructor from expression of the indices. The indices\n      * array has the meaning that the permutations sends each integer i to indices[i].\n      *\n      * \\warning It is your responsibility to check that the indices array that you passes actually\n      * describes a permutation, i.e., each value between 0 and n-1 occurs exactly once, where n is the\n      * array's size.\n      */\n    template<typename Other>\n    explicit inline PermutationMatrix(const MatrixBase<Other>& indices) : m_indices(indices)\n    {}\n\n    /** Convert the Transpositions \\a tr to a permutation matrix */\n    template<typename Other>\n    explicit PermutationMatrix(const TranspositionsBase<Other>& tr)\n      : m_indices(tr.size())\n    {\n      *this = tr;\n    }\n\n    /** Copies the other permutation into *this */\n    template<typename Other>\n    PermutationMatrix& operator=(const PermutationBase<Other>& other)\n    {\n      m_indices = other.indices();\n      return *this;\n    }\n\n    /** Assignment from the Transpositions \\a tr */\n    template<typename Other>\n    PermutationMatrix& operator=(const TranspositionsBase<Other>& tr)\n    {\n      return Base::operator=(tr.derived());\n    }\n\n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    /** This is a special case of the templated operator=. Its purpose is to\n      * prevent a default operator= from hiding the templated operator=.\n      */\n    PermutationMatrix& operator=(const PermutationMatrix& other)\n    {\n      m_indices = other.m_indices;\n      return *this;\n    }\n    #endif\n\n    /** const version of indices(). */\n    const IndicesType& indices() const { return m_indices; }\n    /** \\returns a reference to the stored array representing the permutation. */\n    IndicesType& indices() { return m_indices; }\n\n\n    /**** multiplication helpers to hopefully get RVO ****/\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\n    template<typename Other>\n    PermutationMatrix(const InverseImpl<Other,PermutationStorage>& other)\n      : m_indices(other.derived().nestedExpression().size())\n    {\n      eigen_internal_assert(m_indices.size() <= NumTraits<StorageIndex>::highest());\n      StorageIndex end = StorageIndex(m_indices.size());\n      for (StorageIndex i=0; i<end;++i)\n        m_indices.coeffRef(other.derived().nestedExpression().indices().coeff(i)) = i;\n    }\n    template<typename Lhs,typename Rhs>\n    PermutationMatrix(internal::PermPermProduct_t, const Lhs& lhs, const Rhs& rhs)\n      : m_indices(lhs.indices().size())\n    {\n      Base::assignProduct(lhs,rhs);\n    }\n#endif\n\n  protected:\n\n    IndicesType m_indices;\n};\n\n\nnamespace internal {\ntemplate<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename _StorageIndex, int _PacketAccess>\nstruct traits<Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, _StorageIndex>,_PacketAccess> >\n : traits<Matrix<_StorageIndex,SizeAtCompileTime,SizeAtCompileTime,0,MaxSizeAtCompileTime,MaxSizeAtCompileTime> >\n{\n  typedef PermutationStorage StorageKind;\n  typedef Map<const Matrix<_StorageIndex, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1>, _PacketAccess> IndicesType;\n  typedef _StorageIndex StorageIndex;\n  typedef void Scalar;\n};\n}\n\ntemplate<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename _StorageIndex, int _PacketAccess>\nclass Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, _StorageIndex>,_PacketAccess>\n  : public PermutationBase<Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, _StorageIndex>,_PacketAccess> >\n{\n    typedef PermutationBase<Map> Base;\n    typedef internal::traits<Map> Traits;\n  public:\n\n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    typedef typename Traits::IndicesType IndicesType;\n    typedef typename IndicesType::Scalar StorageIndex;\n    #endif\n\n    inline Map(const StorageIndex* indicesPtr)\n      : m_indices(indicesPtr)\n    {}\n\n    inline Map(const StorageIndex* indicesPtr, Index size)\n      : m_indices(indicesPtr,size)\n    {}\n\n    /** Copies the other permutation into *this */\n    template<typename Other>\n    Map& operator=(const PermutationBase<Other>& other)\n    { return Base::operator=(other.derived()); }\n\n    /** Assignment from the Transpositions \\a tr */\n    template<typename Other>\n    Map& operator=(const TranspositionsBase<Other>& tr)\n    { return Base::operator=(tr.derived()); }\n\n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    /** This is a special case of the templated operator=. Its purpose is to\n      * prevent a default operator= from hiding the templated operator=.\n      */\n    Map& operator=(const Map& other)\n    {\n      m_indices = other.m_indices;\n      return *this;\n    }\n    #endif\n\n    /** const version of indices(). */\n    const IndicesType& indices() const { return m_indices; }\n    /** \\returns a reference to the stored array representing the permutation. */\n    IndicesType& indices() { return m_indices; }\n\n  protected:\n\n    IndicesType m_indices;\n};\n\ntemplate<typename _IndicesType> class TranspositionsWrapper;\nnamespace internal {\ntemplate<typename _IndicesType>\nstruct traits<PermutationWrapper<_IndicesType> >\n{\n  typedef PermutationStorage StorageKind;\n  typedef void Scalar;\n  typedef typename _IndicesType::Scalar StorageIndex;\n  typedef _IndicesType IndicesType;\n  enum {\n    RowsAtCompileTime = _IndicesType::SizeAtCompileTime,\n    ColsAtCompileTime = _IndicesType::SizeAtCompileTime,\n    MaxRowsAtCompileTime = IndicesType::MaxSizeAtCompileTime,\n    MaxColsAtCompileTime = IndicesType::MaxSizeAtCompileTime,\n    Flags = 0\n  };\n};\n}\n\n/** \\class PermutationWrapper\n  * \\ingroup Core_Module\n  *\n  * \\brief Class to view a vector of integers as a permutation matrix\n  *\n  * \\tparam _IndicesType the type of the vector of integer (can be any compatible expression)\n  *\n  * This class allows to view any vector expression of integers as a permutation matrix.\n  *\n  * \\sa class PermutationBase, class PermutationMatrix\n  */\ntemplate<typename _IndicesType>\nclass PermutationWrapper : public PermutationBase<PermutationWrapper<_IndicesType> >\n{\n    typedef PermutationBase<PermutationWrapper> Base;\n    typedef internal::traits<PermutationWrapper> Traits;\n  public:\n\n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    typedef typename Traits::IndicesType IndicesType;\n    #endif\n\n    inline PermutationWrapper(const IndicesType& indices)\n      : m_indices(indices)\n    {}\n\n    /** const version of indices(). */\n    const typename internal::remove_all<typename IndicesType::Nested>::type&\n    indices() const { return m_indices; }\n\n  protected:\n\n    typename IndicesType::Nested m_indices;\n};\n\n\n/** \\returns the matrix with the permutation applied to the columns.\n  */\ntemplate<typename MatrixDerived, typename PermutationDerived>\nEIGEN_DEVICE_FUNC\nconst Product<MatrixDerived, PermutationDerived, AliasFreeProduct>\noperator*(const MatrixBase<MatrixDerived> &matrix,\n          const PermutationBase<PermutationDerived>& permutation)\n{\n  return Product<MatrixDerived, PermutationDerived, AliasFreeProduct>\n            (matrix.derived(), permutation.derived());\n}\n\n/** \\returns the matrix with the permutation applied to the rows.\n  */\ntemplate<typename PermutationDerived, typename MatrixDerived>\nEIGEN_DEVICE_FUNC\nconst Product<PermutationDerived, MatrixDerived, AliasFreeProduct>\noperator*(const PermutationBase<PermutationDerived> &permutation,\n          const MatrixBase<MatrixDerived>& matrix)\n{\n  return Product<PermutationDerived, MatrixDerived, AliasFreeProduct>\n            (permutation.derived(), matrix.derived());\n}\n\n\ntemplate<typename PermutationType>\nclass InverseImpl<PermutationType, PermutationStorage>\n  : public EigenBase<Inverse<PermutationType> >\n{\n    typedef typename PermutationType::PlainPermutationType PlainPermutationType;\n    typedef internal::traits<PermutationType> PermTraits;\n  protected:\n    InverseImpl() {}\n  public:\n    typedef Inverse<PermutationType> InverseType;\n    using EigenBase<Inverse<PermutationType> >::derived;\n\n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    typedef typename PermutationType::DenseMatrixType DenseMatrixType;\n    enum {\n      RowsAtCompileTime = PermTraits::RowsAtCompileTime,\n      ColsAtCompileTime = PermTraits::ColsAtCompileTime,\n      MaxRowsAtCompileTime = PermTraits::MaxRowsAtCompileTime,\n      MaxColsAtCompileTime = PermTraits::MaxColsAtCompileTime\n    };\n    #endif\n\n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    template<typename DenseDerived>\n    void evalTo(MatrixBase<DenseDerived>& other) const\n    {\n      other.setZero();\n      for (Index i=0; i<derived().rows();++i)\n        other.coeffRef(i, derived().nestedExpression().indices().coeff(i)) = typename DenseDerived::Scalar(1);\n    }\n    #endif\n\n    /** \\return the equivalent permutation matrix */\n    PlainPermutationType eval() const { return derived(); }\n\n    DenseMatrixType toDenseMatrix() const { return derived(); }\n\n    /** \\returns the matrix with the inverse permutation applied to the columns.\n      */\n    template<typename OtherDerived> friend\n    const Product<OtherDerived, InverseType, AliasFreeProduct>\n    operator*(const MatrixBase<OtherDerived>& matrix, const InverseType& trPerm)\n    {\n      return Product<OtherDerived, InverseType, AliasFreeProduct>(matrix.derived(), trPerm.derived());\n    }\n\n    /** \\returns the matrix with the inverse permutation applied to the rows.\n      */\n    template<typename OtherDerived>\n    const Product<InverseType, OtherDerived, AliasFreeProduct>\n    operator*(const MatrixBase<OtherDerived>& matrix) const\n    {\n      return Product<InverseType, OtherDerived, AliasFreeProduct>(derived(), matrix.derived());\n    }\n};\n\ntemplate<typename Derived>\nconst PermutationWrapper<const Derived> MatrixBase<Derived>::asPermutation() const\n{\n  return derived();\n}\n\nnamespace internal {\n\ntemplate<> struct AssignmentKind<DenseShape,PermutationShape> { typedef EigenBase2EigenBase Kind; };\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_PERMUTATIONMATRIX_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/PlainObjectBase.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_DENSESTORAGEBASE_H\n#define EIGEN_DENSESTORAGEBASE_H\n\n#if defined(EIGEN_INITIALIZE_MATRICES_BY_ZERO)\n# define EIGEN_INITIALIZE_COEFFS\n# define EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED for(int i=0;i<base().size();++i) coeffRef(i)=Scalar(0);\n#elif defined(EIGEN_INITIALIZE_MATRICES_BY_NAN)\n# define EIGEN_INITIALIZE_COEFFS\n# define EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED for(int i=0;i<base().size();++i) coeffRef(i)=std::numeric_limits<Scalar>::quiet_NaN();\n#else\n# undef EIGEN_INITIALIZE_COEFFS\n# define EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED\n#endif\n\nnamespace Eigen {\n\nnamespace internal {\n\ntemplate<int MaxSizeAtCompileTime> struct check_rows_cols_for_overflow {\n  template<typename Index>\n  EIGEN_DEVICE_FUNC\n  static EIGEN_ALWAYS_INLINE void run(Index, Index)\n  {\n  }\n};\n\ntemplate<> struct check_rows_cols_for_overflow<Dynamic> {\n  template<typename Index>\n  EIGEN_DEVICE_FUNC\n  static EIGEN_ALWAYS_INLINE void run(Index rows, Index cols)\n  {\n    // http://hg.mozilla.org/mozilla-central/file/6c8a909977d3/xpcom/ds/CheckedInt.h#l242\n    // we assume Index is signed\n    Index max_index = (std::size_t(1) << (8 * sizeof(Index) - 1)) - 1; // assume Index is signed\n    bool error = (rows == 0 || cols == 0) ? false\n               : (rows > max_index / cols);\n    if (error)\n      throw_std_bad_alloc();\n  }\n};\n\ntemplate <typename Derived,\n          typename OtherDerived = Derived,\n          bool IsVector = bool(Derived::IsVectorAtCompileTime) && bool(OtherDerived::IsVectorAtCompileTime)>\nstruct conservative_resize_like_impl;\n\ntemplate<typename MatrixTypeA, typename MatrixTypeB, bool SwapPointers> struct matrix_swap_impl;\n\n} // end namespace internal\n\n#ifdef EIGEN_PARSED_BY_DOXYGEN\nnamespace doxygen {\n\n// This is a workaround to doxygen not being able to understand the inheritance logic\n// when it is hidden by the dense_xpr_base helper struct.\n// Moreover, doxygen fails to include members that are not documented in the declaration body of\n// MatrixBase if we inherits MatrixBase<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >,\n// this is why we simply inherits MatrixBase, though this does not make sense.\n\n/** This class is just a workaround for Doxygen and it does not not actually exist. */\ntemplate<typename Derived> struct dense_xpr_base_dispatcher;\n/** This class is just a workaround for Doxygen and it does not not actually exist. */\ntemplate<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>\nstruct dense_xpr_base_dispatcher<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >\n    : public MatrixBase {};\n/** This class is just a workaround for Doxygen and it does not not actually exist. */\ntemplate<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>\nstruct dense_xpr_base_dispatcher<Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >\n    : public ArrayBase {};\n\n} // namespace doxygen\n\n/** \\class PlainObjectBase\n  * \\ingroup Core_Module\n  * \\brief %Dense storage base class for matrices and arrays.\n  *\n  * This class can be extended with the help of the plugin mechanism described on the page\n  * \\ref TopicCustomizing_Plugins by defining the preprocessor symbol \\c EIGEN_PLAINOBJECTBASE_PLUGIN.\n  *\n  * \\tparam Derived is the derived type, e.g., a Matrix or Array\n  *\n  * \\sa \\ref TopicClassHierarchy\n  */\ntemplate<typename Derived>\nclass PlainObjectBase : public doxygen::dense_xpr_base_dispatcher<Derived>\n#else\ntemplate<typename Derived>\nclass PlainObjectBase : public internal::dense_xpr_base<Derived>::type\n#endif\n{\n  public:\n    enum { Options = internal::traits<Derived>::Options };\n    typedef typename internal::dense_xpr_base<Derived>::type Base;\n\n    typedef typename internal::traits<Derived>::StorageKind StorageKind;\n    typedef typename internal::traits<Derived>::Scalar Scalar;\n    \n    typedef typename internal::packet_traits<Scalar>::type PacketScalar;\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n    typedef Derived DenseType;\n\n    using Base::RowsAtCompileTime;\n    using Base::ColsAtCompileTime;\n    using Base::SizeAtCompileTime;\n    using Base::MaxRowsAtCompileTime;\n    using Base::MaxColsAtCompileTime;\n    using Base::MaxSizeAtCompileTime;\n    using Base::IsVectorAtCompileTime;\n    using Base::Flags;\n\n    template<typename PlainObjectType, int MapOptions, typename StrideType> friend class Eigen::Map;\n    friend  class Eigen::Map<Derived, Unaligned>;\n    typedef Eigen::Map<Derived, Unaligned>  MapType;\n    friend  class Eigen::Map<const Derived, Unaligned>;\n    typedef const Eigen::Map<const Derived, Unaligned> ConstMapType;\n#if EIGEN_MAX_ALIGN_BYTES>0\n    // for EIGEN_MAX_ALIGN_BYTES==0, AlignedMax==Unaligned, and many compilers generate warnings for friend-ing a class twice.\n    friend  class Eigen::Map<Derived, AlignedMax>;\n    friend  class Eigen::Map<const Derived, AlignedMax>;\n#endif\n    typedef Eigen::Map<Derived, AlignedMax> AlignedMapType;\n    typedef const Eigen::Map<const Derived, AlignedMax> ConstAlignedMapType;\n    template<typename StrideType> struct StridedMapType { typedef Eigen::Map<Derived, Unaligned, StrideType> type; };\n    template<typename StrideType> struct StridedConstMapType { typedef Eigen::Map<const Derived, Unaligned, StrideType> type; };\n    template<typename StrideType> struct StridedAlignedMapType { typedef Eigen::Map<Derived, AlignedMax, StrideType> type; };\n    template<typename StrideType> struct StridedConstAlignedMapType { typedef Eigen::Map<const Derived, AlignedMax, StrideType> type; };\n\n  protected:\n    DenseStorage<Scalar, Base::MaxSizeAtCompileTime, Base::RowsAtCompileTime, Base::ColsAtCompileTime, Options> m_storage;\n\n  public:\n    enum { NeedsToAlign = (SizeAtCompileTime != Dynamic) && (internal::traits<Derived>::Alignment>0) };\n    EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(NeedsToAlign)\n\n    EIGEN_DEVICE_FUNC\n    Base& base() { return *static_cast<Base*>(this); }\n    EIGEN_DEVICE_FUNC\n    const Base& base() const { return *static_cast<const Base*>(this); }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Index rows() const { return m_storage.rows(); }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Index cols() const { return m_storage.cols(); }\n\n    /** This is an overloaded version of DenseCoeffsBase<Derived,ReadOnlyAccessors>::coeff(Index,Index) const\n      * provided to by-pass the creation of an evaluator of the expression, thus saving compilation efforts.\n      *\n      * See DenseCoeffsBase<Derived,ReadOnlyAccessors>::coeff(Index) const for details. */\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar& coeff(Index rowId, Index colId) const\n    {\n      if(Flags & RowMajorBit)\n        return m_storage.data()[colId + rowId * m_storage.cols()];\n      else // column-major\n        return m_storage.data()[rowId + colId * m_storage.rows()];\n    }\n\n    /** This is an overloaded version of DenseCoeffsBase<Derived,ReadOnlyAccessors>::coeff(Index) const\n      * provided to by-pass the creation of an evaluator of the expression, thus saving compilation efforts.\n      *\n      * See DenseCoeffsBase<Derived,ReadOnlyAccessors>::coeff(Index) const for details. */\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar& coeff(Index index) const\n    {\n      return m_storage.data()[index];\n    }\n\n    /** This is an overloaded version of DenseCoeffsBase<Derived,WriteAccessors>::coeffRef(Index,Index) const\n      * provided to by-pass the creation of an evaluator of the expression, thus saving compilation efforts.\n      *\n      * See DenseCoeffsBase<Derived,WriteAccessors>::coeffRef(Index,Index) const for details. */\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar& coeffRef(Index rowId, Index colId)\n    {\n      if(Flags & RowMajorBit)\n        return m_storage.data()[colId + rowId * m_storage.cols()];\n      else // column-major\n        return m_storage.data()[rowId + colId * m_storage.rows()];\n    }\n\n    /** This is an overloaded version of DenseCoeffsBase<Derived,WriteAccessors>::coeffRef(Index) const\n      * provided to by-pass the creation of an evaluator of the expression, thus saving compilation efforts.\n      *\n      * See DenseCoeffsBase<Derived,WriteAccessors>::coeffRef(Index) const for details. */\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar& coeffRef(Index index)\n    {\n      return m_storage.data()[index];\n    }\n\n    /** This is the const version of coeffRef(Index,Index) which is thus synonym of coeff(Index,Index).\n      * It is provided for convenience. */\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar& coeffRef(Index rowId, Index colId) const\n    {\n      if(Flags & RowMajorBit)\n        return m_storage.data()[colId + rowId * m_storage.cols()];\n      else // column-major\n        return m_storage.data()[rowId + colId * m_storage.rows()];\n    }\n\n    /** This is the const version of coeffRef(Index) which is thus synonym of coeff(Index).\n      * It is provided for convenience. */\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar& coeffRef(Index index) const\n    {\n      return m_storage.data()[index];\n    }\n\n    /** \\internal */\n    template<int LoadMode>\n    EIGEN_STRONG_INLINE PacketScalar packet(Index rowId, Index colId) const\n    {\n      return internal::ploadt<PacketScalar, LoadMode>\n               (m_storage.data() + (Flags & RowMajorBit\n                                   ? colId + rowId * m_storage.cols()\n                                   : rowId + colId * m_storage.rows()));\n    }\n\n    /** \\internal */\n    template<int LoadMode>\n    EIGEN_STRONG_INLINE PacketScalar packet(Index index) const\n    {\n      return internal::ploadt<PacketScalar, LoadMode>(m_storage.data() + index);\n    }\n\n    /** \\internal */\n    template<int StoreMode>\n    EIGEN_STRONG_INLINE void writePacket(Index rowId, Index colId, const PacketScalar& val)\n    {\n      internal::pstoret<Scalar, PacketScalar, StoreMode>\n              (m_storage.data() + (Flags & RowMajorBit\n                                   ? colId + rowId * m_storage.cols()\n                                   : rowId + colId * m_storage.rows()), val);\n    }\n\n    /** \\internal */\n    template<int StoreMode>\n    EIGEN_STRONG_INLINE void writePacket(Index index, const PacketScalar& val)\n    {\n      internal::pstoret<Scalar, PacketScalar, StoreMode>(m_storage.data() + index, val);\n    }\n\n    /** \\returns a const pointer to the data array of this matrix */\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar *data() const\n    { return m_storage.data(); }\n\n    /** \\returns a pointer to the data array of this matrix */\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar *data()\n    { return m_storage.data(); }\n\n    /** Resizes \\c *this to a \\a rows x \\a cols matrix.\n      *\n      * This method is intended for dynamic-size matrices, although it is legal to call it on any\n      * matrix as long as fixed dimensions are left unchanged. If you only want to change the number\n      * of rows and/or of columns, you can use resize(NoChange_t, Index), resize(Index, NoChange_t).\n      *\n      * If the current number of coefficients of \\c *this exactly matches the\n      * product \\a rows * \\a cols, then no memory allocation is performed and\n      * the current values are left unchanged. In all other cases, including\n      * shrinking, the data is reallocated and all previous values are lost.\n      *\n      * Example: \\include Matrix_resize_int_int.cpp\n      * Output: \\verbinclude Matrix_resize_int_int.out\n      *\n      * \\sa resize(Index) for vectors, resize(NoChange_t, Index), resize(Index, NoChange_t)\n      */\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE void resize(Index rows, Index cols)\n    {\n      eigen_assert(   EIGEN_IMPLIES(RowsAtCompileTime!=Dynamic,rows==RowsAtCompileTime)\n                   && EIGEN_IMPLIES(ColsAtCompileTime!=Dynamic,cols==ColsAtCompileTime)\n                   && EIGEN_IMPLIES(RowsAtCompileTime==Dynamic && MaxRowsAtCompileTime!=Dynamic,rows<=MaxRowsAtCompileTime)\n                   && EIGEN_IMPLIES(ColsAtCompileTime==Dynamic && MaxColsAtCompileTime!=Dynamic,cols<=MaxColsAtCompileTime)\n                   && rows>=0 && cols>=0 && \"Invalid sizes when resizing a matrix or array.\");\n      internal::check_rows_cols_for_overflow<MaxSizeAtCompileTime>::run(rows, cols);\n      #ifdef EIGEN_INITIALIZE_COEFFS\n        Index size = rows*cols;\n        bool size_changed = size != this->size();\n        m_storage.resize(size, rows, cols);\n        if(size_changed) EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED\n      #else\n        m_storage.resize(rows*cols, rows, cols);\n      #endif\n    }\n\n    /** Resizes \\c *this to a vector of length \\a size\n      *\n      * \\only_for_vectors. This method does not work for\n      * partially dynamic matrices when the static dimension is anything other\n      * than 1. For example it will not work with Matrix<double, 2, Dynamic>.\n      *\n      * Example: \\include Matrix_resize_int.cpp\n      * Output: \\verbinclude Matrix_resize_int.out\n      *\n      * \\sa resize(Index,Index), resize(NoChange_t, Index), resize(Index, NoChange_t)\n      */\n    EIGEN_DEVICE_FUNC\n    inline void resize(Index size)\n    {\n      EIGEN_STATIC_ASSERT_VECTOR_ONLY(PlainObjectBase)\n      eigen_assert(((SizeAtCompileTime == Dynamic && (MaxSizeAtCompileTime==Dynamic || size<=MaxSizeAtCompileTime)) || SizeAtCompileTime == size) && size>=0);\n      #ifdef EIGEN_INITIALIZE_COEFFS\n        bool size_changed = size != this->size();\n      #endif\n      if(RowsAtCompileTime == 1)\n        m_storage.resize(size, 1, size);\n      else\n        m_storage.resize(size, size, 1);\n      #ifdef EIGEN_INITIALIZE_COEFFS\n        if(size_changed) EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED\n      #endif\n    }\n\n    /** Resizes the matrix, changing only the number of columns. For the parameter of type NoChange_t, just pass the special value \\c NoChange\n      * as in the example below.\n      *\n      * Example: \\include Matrix_resize_NoChange_int.cpp\n      * Output: \\verbinclude Matrix_resize_NoChange_int.out\n      *\n      * \\sa resize(Index,Index)\n      */\n    EIGEN_DEVICE_FUNC\n    inline void resize(NoChange_t, Index cols)\n    {\n      resize(rows(), cols);\n    }\n\n    /** Resizes the matrix, changing only the number of rows. For the parameter of type NoChange_t, just pass the special value \\c NoChange\n      * as in the example below.\n      *\n      * Example: \\include Matrix_resize_int_NoChange.cpp\n      * Output: \\verbinclude Matrix_resize_int_NoChange.out\n      *\n      * \\sa resize(Index,Index)\n      */\n    EIGEN_DEVICE_FUNC\n    inline void resize(Index rows, NoChange_t)\n    {\n      resize(rows, cols());\n    }\n\n    /** Resizes \\c *this to have the same dimensions as \\a other.\n      * Takes care of doing all the checking that's needed.\n      *\n      * Note that copying a row-vector into a vector (and conversely) is allowed.\n      * The resizing, if any, is then done in the appropriate way so that row-vectors\n      * remain row-vectors and vectors remain vectors.\n      */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC \n    EIGEN_STRONG_INLINE void resizeLike(const EigenBase<OtherDerived>& _other)\n    {\n      const OtherDerived& other = _other.derived();\n      internal::check_rows_cols_for_overflow<MaxSizeAtCompileTime>::run(other.rows(), other.cols());\n      const Index othersize = other.rows()*other.cols();\n      if(RowsAtCompileTime == 1)\n      {\n        eigen_assert(other.rows() == 1 || other.cols() == 1);\n        resize(1, othersize);\n      }\n      else if(ColsAtCompileTime == 1)\n      {\n        eigen_assert(other.rows() == 1 || other.cols() == 1);\n        resize(othersize, 1);\n      }\n      else resize(other.rows(), other.cols());\n    }\n\n    /** Resizes the matrix to \\a rows x \\a cols while leaving old values untouched.\n      *\n      * The method is intended for matrices of dynamic size. If you only want to change the number\n      * of rows and/or of columns, you can use conservativeResize(NoChange_t, Index) or\n      * conservativeResize(Index, NoChange_t).\n      *\n      * Matrices are resized relative to the top-left element. In case values need to be \n      * appended to the matrix they will be uninitialized.\n      */\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE void conservativeResize(Index rows, Index cols)\n    {\n      internal::conservative_resize_like_impl<Derived>::run(*this, rows, cols);\n    }\n\n    /** Resizes the matrix to \\a rows x \\a cols while leaving old values untouched.\n      *\n      * As opposed to conservativeResize(Index rows, Index cols), this version leaves\n      * the number of columns unchanged.\n      *\n      * In case the matrix is growing, new rows will be uninitialized.\n      */\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE void conservativeResize(Index rows, NoChange_t)\n    {\n      // Note: see the comment in conservativeResize(Index,Index)\n      conservativeResize(rows, cols());\n    }\n\n    /** Resizes the matrix to \\a rows x \\a cols while leaving old values untouched.\n      *\n      * As opposed to conservativeResize(Index rows, Index cols), this version leaves\n      * the number of rows unchanged.\n      *\n      * In case the matrix is growing, new columns will be uninitialized.\n      */\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE void conservativeResize(NoChange_t, Index cols)\n    {\n      // Note: see the comment in conservativeResize(Index,Index)\n      conservativeResize(rows(), cols);\n    }\n\n    /** Resizes the vector to \\a size while retaining old values.\n      *\n      * \\only_for_vectors. This method does not work for\n      * partially dynamic matrices when the static dimension is anything other\n      * than 1. For example it will not work with Matrix<double, 2, Dynamic>.\n      *\n      * When values are appended, they will be uninitialized.\n      */\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE void conservativeResize(Index size)\n    {\n      internal::conservative_resize_like_impl<Derived>::run(*this, size);\n    }\n\n    /** Resizes the matrix to \\a rows x \\a cols of \\c other, while leaving old values untouched.\n      *\n      * The method is intended for matrices of dynamic size. If you only want to change the number\n      * of rows and/or of columns, you can use conservativeResize(NoChange_t, Index) or\n      * conservativeResize(Index, NoChange_t).\n      *\n      * Matrices are resized relative to the top-left element. In case values need to be \n      * appended to the matrix they will copied from \\c other.\n      */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE void conservativeResizeLike(const DenseBase<OtherDerived>& other)\n    {\n      internal::conservative_resize_like_impl<Derived,OtherDerived>::run(*this, other);\n    }\n\n    /** This is a special case of the templated operator=. Its purpose is to\n      * prevent a default operator= from hiding the templated operator=.\n      */\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Derived& operator=(const PlainObjectBase& other)\n    {\n      return _set(other);\n    }\n\n    /** \\sa MatrixBase::lazyAssign() */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Derived& lazyAssign(const DenseBase<OtherDerived>& other)\n    {\n      _resize_to_match(other);\n      return Base::lazyAssign(other.derived());\n    }\n\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Derived& operator=(const ReturnByValue<OtherDerived>& func)\n    {\n      resize(func.rows(), func.cols());\n      return Base::operator=(func);\n    }\n\n    // Prevent user from trying to instantiate PlainObjectBase objects\n    // by making all its constructor protected. See bug 1074.\n  protected:\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE PlainObjectBase() : m_storage()\n    {\n//       _check_template_params();\n//       EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED\n    }\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\n    // FIXME is it still needed ?\n    /** \\internal */\n    EIGEN_DEVICE_FUNC\n    explicit PlainObjectBase(internal::constructor_without_unaligned_array_assert)\n      : m_storage(internal::constructor_without_unaligned_array_assert())\n    {\n//       _check_template_params(); EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED\n    }\n#endif\n\n#if EIGEN_HAS_RVALUE_REFERENCES\n    EIGEN_DEVICE_FUNC\n    PlainObjectBase(PlainObjectBase&& other) EIGEN_NOEXCEPT\n      : m_storage( std::move(other.m_storage) )\n    {\n    }\n\n    EIGEN_DEVICE_FUNC\n    PlainObjectBase& operator=(PlainObjectBase&& other) EIGEN_NOEXCEPT\n    {\n      using std::swap;\n      swap(m_storage, other.m_storage);\n      return *this;\n    }\n#endif\n\n    /** Copy constructor */\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE PlainObjectBase(const PlainObjectBase& other)\n      : Base(), m_storage(other.m_storage) { }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE PlainObjectBase(Index size, Index rows, Index cols)\n      : m_storage(size, rows, cols)\n    {\n//       _check_template_params();\n//       EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED\n    }\n\n    /** \\sa PlainObjectBase::operator=(const EigenBase<OtherDerived>&) */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE PlainObjectBase(const DenseBase<OtherDerived> &other)\n      : m_storage()\n    {\n      _check_template_params();\n      resizeLike(other);\n      _set_noalias(other);\n    }\n\n    /** \\sa PlainObjectBase::operator=(const EigenBase<OtherDerived>&) */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE PlainObjectBase(const EigenBase<OtherDerived> &other)\n      : m_storage()\n    {\n      _check_template_params();\n      resizeLike(other);\n      *this = other.derived();\n    }\n    /** \\brief Copy constructor with in-place evaluation */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE PlainObjectBase(const ReturnByValue<OtherDerived>& other)\n    {\n      _check_template_params();\n      // FIXME this does not automatically transpose vectors if necessary\n      resize(other.rows(), other.cols());\n      other.evalTo(this->derived());\n    }\n\n  public:\n\n    /** \\brief Copies the generic expression \\a other into *this.\n      * \\copydetails DenseBase::operator=(const EigenBase<OtherDerived> &other)\n      */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC \n    EIGEN_STRONG_INLINE Derived& operator=(const EigenBase<OtherDerived> &other)\n    {\n      _resize_to_match(other);\n      Base::operator=(other.derived());\n      return this->derived();\n    }\n\n    /** \\name Map\n      * These are convenience functions returning Map objects. The Map() static functions return unaligned Map objects,\n      * while the AlignedMap() functions return aligned Map objects and thus should be called only with 16-byte-aligned\n      * \\a data pointers.\n      *\n      * Here is an example using strides:\n      * \\include Matrix_Map_stride.cpp\n      * Output: \\verbinclude Matrix_Map_stride.out\n      *\n      * \\see class Map\n      */\n    //@{\n    static inline ConstMapType Map(const Scalar* data)\n    { return ConstMapType(data); }\n    static inline MapType Map(Scalar* data)\n    { return MapType(data); }\n    static inline ConstMapType Map(const Scalar* data, Index size)\n    { return ConstMapType(data, size); }\n    static inline MapType Map(Scalar* data, Index size)\n    { return MapType(data, size); }\n    static inline ConstMapType Map(const Scalar* data, Index rows, Index cols)\n    { return ConstMapType(data, rows, cols); }\n    static inline MapType Map(Scalar* data, Index rows, Index cols)\n    { return MapType(data, rows, cols); }\n\n    static inline ConstAlignedMapType MapAligned(const Scalar* data)\n    { return ConstAlignedMapType(data); }\n    static inline AlignedMapType MapAligned(Scalar* data)\n    { return AlignedMapType(data); }\n    static inline ConstAlignedMapType MapAligned(const Scalar* data, Index size)\n    { return ConstAlignedMapType(data, size); }\n    static inline AlignedMapType MapAligned(Scalar* data, Index size)\n    { return AlignedMapType(data, size); }\n    static inline ConstAlignedMapType MapAligned(const Scalar* data, Index rows, Index cols)\n    { return ConstAlignedMapType(data, rows, cols); }\n    static inline AlignedMapType MapAligned(Scalar* data, Index rows, Index cols)\n    { return AlignedMapType(data, rows, cols); }\n\n    template<int Outer, int Inner>\n    static inline typename StridedConstMapType<Stride<Outer, Inner> >::type Map(const Scalar* data, const Stride<Outer, Inner>& stride)\n    { return typename StridedConstMapType<Stride<Outer, Inner> >::type(data, stride); }\n    template<int Outer, int Inner>\n    static inline typename StridedMapType<Stride<Outer, Inner> >::type Map(Scalar* data, const Stride<Outer, Inner>& stride)\n    { return typename StridedMapType<Stride<Outer, Inner> >::type(data, stride); }\n    template<int Outer, int Inner>\n    static inline typename StridedConstMapType<Stride<Outer, Inner> >::type Map(const Scalar* data, Index size, const Stride<Outer, Inner>& stride)\n    { return typename StridedConstMapType<Stride<Outer, Inner> >::type(data, size, stride); }\n    template<int Outer, int Inner>\n    static inline typename StridedMapType<Stride<Outer, Inner> >::type Map(Scalar* data, Index size, const Stride<Outer, Inner>& stride)\n    { return typename StridedMapType<Stride<Outer, Inner> >::type(data, size, stride); }\n    template<int Outer, int Inner>\n    static inline typename StridedConstMapType<Stride<Outer, Inner> >::type Map(const Scalar* data, Index rows, Index cols, const Stride<Outer, Inner>& stride)\n    { return typename StridedConstMapType<Stride<Outer, Inner> >::type(data, rows, cols, stride); }\n    template<int Outer, int Inner>\n    static inline typename StridedMapType<Stride<Outer, Inner> >::type Map(Scalar* data, Index rows, Index cols, const Stride<Outer, Inner>& stride)\n    { return typename StridedMapType<Stride<Outer, Inner> >::type(data, rows, cols, stride); }\n\n    template<int Outer, int Inner>\n    static inline typename StridedConstAlignedMapType<Stride<Outer, Inner> >::type MapAligned(const Scalar* data, const Stride<Outer, Inner>& stride)\n    { return typename StridedConstAlignedMapType<Stride<Outer, Inner> >::type(data, stride); }\n    template<int Outer, int Inner>\n    static inline typename StridedAlignedMapType<Stride<Outer, Inner> >::type MapAligned(Scalar* data, const Stride<Outer, Inner>& stride)\n    { return typename StridedAlignedMapType<Stride<Outer, Inner> >::type(data, stride); }\n    template<int Outer, int Inner>\n    static inline typename StridedConstAlignedMapType<Stride<Outer, Inner> >::type MapAligned(const Scalar* data, Index size, const Stride<Outer, Inner>& stride)\n    { return typename StridedConstAlignedMapType<Stride<Outer, Inner> >::type(data, size, stride); }\n    template<int Outer, int Inner>\n    static inline typename StridedAlignedMapType<Stride<Outer, Inner> >::type MapAligned(Scalar* data, Index size, const Stride<Outer, Inner>& stride)\n    { return typename StridedAlignedMapType<Stride<Outer, Inner> >::type(data, size, stride); }\n    template<int Outer, int Inner>\n    static inline typename StridedConstAlignedMapType<Stride<Outer, Inner> >::type MapAligned(const Scalar* data, Index rows, Index cols, const Stride<Outer, Inner>& stride)\n    { return typename StridedConstAlignedMapType<Stride<Outer, Inner> >::type(data, rows, cols, stride); }\n    template<int Outer, int Inner>\n    static inline typename StridedAlignedMapType<Stride<Outer, Inner> >::type MapAligned(Scalar* data, Index rows, Index cols, const Stride<Outer, Inner>& stride)\n    { return typename StridedAlignedMapType<Stride<Outer, Inner> >::type(data, rows, cols, stride); }\n    //@}\n\n    using Base::setConstant;\n    EIGEN_DEVICE_FUNC Derived& setConstant(Index size, const Scalar& val);\n    EIGEN_DEVICE_FUNC Derived& setConstant(Index rows, Index cols, const Scalar& val);\n\n    using Base::setZero;\n    EIGEN_DEVICE_FUNC Derived& setZero(Index size);\n    EIGEN_DEVICE_FUNC Derived& setZero(Index rows, Index cols);\n\n    using Base::setOnes;\n    EIGEN_DEVICE_FUNC Derived& setOnes(Index size);\n    EIGEN_DEVICE_FUNC Derived& setOnes(Index rows, Index cols);\n\n    using Base::setRandom;\n    Derived& setRandom(Index size);\n    Derived& setRandom(Index rows, Index cols);\n\n    #ifdef EIGEN_PLAINOBJECTBASE_PLUGIN\n    #include EIGEN_PLAINOBJECTBASE_PLUGIN\n    #endif\n\n  protected:\n    /** \\internal Resizes *this in preparation for assigning \\a other to it.\n      * Takes care of doing all the checking that's needed.\n      *\n      * Note that copying a row-vector into a vector (and conversely) is allowed.\n      * The resizing, if any, is then done in the appropriate way so that row-vectors\n      * remain row-vectors and vectors remain vectors.\n      */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC \n    EIGEN_STRONG_INLINE void _resize_to_match(const EigenBase<OtherDerived>& other)\n    {\n      #ifdef EIGEN_NO_AUTOMATIC_RESIZING\n      eigen_assert((this->size()==0 || (IsVectorAtCompileTime ? (this->size() == other.size())\n                 : (rows() == other.rows() && cols() == other.cols())))\n        && \"Size mismatch. Automatic resizing is disabled because EIGEN_NO_AUTOMATIC_RESIZING is defined\");\n      EIGEN_ONLY_USED_FOR_DEBUG(other);\n      #else\n      resizeLike(other);\n      #endif\n    }\n\n    /**\n      * \\brief Copies the value of the expression \\a other into \\c *this with automatic resizing.\n      *\n      * *this might be resized to match the dimensions of \\a other. If *this was a null matrix (not already initialized),\n      * it will be initialized.\n      *\n      * Note that copying a row-vector into a vector (and conversely) is allowed.\n      * The resizing, if any, is then done in the appropriate way so that row-vectors\n      * remain row-vectors and vectors remain vectors.\n      *\n      * \\sa operator=(const MatrixBase<OtherDerived>&), _set_noalias()\n      *\n      * \\internal\n      */\n    // aliasing is dealt once in internall::call_assignment\n    // so at this stage we have to assume aliasing... and resising has to be done later.\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC \n    EIGEN_STRONG_INLINE Derived& _set(const DenseBase<OtherDerived>& other)\n    {\n      internal::call_assignment(this->derived(), other.derived());\n      return this->derived();\n    }\n\n    /** \\internal Like _set() but additionally makes the assumption that no aliasing effect can happen (which\n      * is the case when creating a new matrix) so one can enforce lazy evaluation.\n      *\n      * \\sa operator=(const MatrixBase<OtherDerived>&), _set()\n      */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC \n    EIGEN_STRONG_INLINE Derived& _set_noalias(const DenseBase<OtherDerived>& other)\n    {\n      // I don't think we need this resize call since the lazyAssign will anyways resize\n      // and lazyAssign will be called by the assign selector.\n      //_resize_to_match(other);\n      // the 'false' below means to enforce lazy evaluation. We don't use lazyAssign() because\n      // it wouldn't allow to copy a row-vector into a column-vector.\n      internal::call_assignment_no_alias(this->derived(), other.derived(), internal::assign_op<Scalar,typename OtherDerived::Scalar>());\n      return this->derived();\n    }\n\n    template<typename T0, typename T1>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE void _init2(Index rows, Index cols, typename internal::enable_if<Base::SizeAtCompileTime!=2,T0>::type* = 0)\n    {\n      EIGEN_STATIC_ASSERT(bool(NumTraits<T0>::IsInteger) &&\n                          bool(NumTraits<T1>::IsInteger),\n                          FLOATING_POINT_ARGUMENT_PASSED__INTEGER_WAS_EXPECTED)\n      resize(rows,cols);\n    }\n    \n    template<typename T0, typename T1>\n    EIGEN_DEVICE_FUNC \n    EIGEN_STRONG_INLINE void _init2(const T0& val0, const T1& val1, typename internal::enable_if<Base::SizeAtCompileTime==2,T0>::type* = 0)\n    {\n      EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(PlainObjectBase, 2)\n      m_storage.data()[0] = Scalar(val0);\n      m_storage.data()[1] = Scalar(val1);\n    }\n    \n    template<typename T0, typename T1>\n    EIGEN_DEVICE_FUNC \n    EIGEN_STRONG_INLINE void _init2(const Index& val0, const Index& val1,\n                                    typename internal::enable_if<    (!internal::is_same<Index,Scalar>::value)\n                                                                  && (internal::is_same<T0,Index>::value)\n                                                                  && (internal::is_same<T1,Index>::value)\n                                                                  && Base::SizeAtCompileTime==2,T1>::type* = 0)\n    {\n      EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(PlainObjectBase, 2)\n      m_storage.data()[0] = Scalar(val0);\n      m_storage.data()[1] = Scalar(val1);\n    }\n\n    // The argument is convertible to the Index type and we either have a non 1x1 Matrix, or a dynamic-sized Array,\n    // then the argument is meant to be the size of the object.\n    template<typename T>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE void _init1(Index size, typename internal::enable_if<    (Base::SizeAtCompileTime!=1 || !internal::is_convertible<T, Scalar>::value)\n                                                                              && ((!internal::is_same<typename internal::traits<Derived>::XprKind,ArrayXpr>::value || Base::SizeAtCompileTime==Dynamic)),T>::type* = 0)\n    {\n      // NOTE MSVC 2008 complains if we directly put bool(NumTraits<T>::IsInteger) as the EIGEN_STATIC_ASSERT argument.\n      const bool is_integer = NumTraits<T>::IsInteger;\n      EIGEN_UNUSED_VARIABLE(is_integer);\n      EIGEN_STATIC_ASSERT(is_integer,\n                          FLOATING_POINT_ARGUMENT_PASSED__INTEGER_WAS_EXPECTED)\n      resize(size);\n    }\n    \n    // We have a 1x1 matrix/array => the argument is interpreted as the value of the unique coefficient (case where scalar type can be implicitely converted)\n    template<typename T>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE void _init1(const Scalar& val0, typename internal::enable_if<Base::SizeAtCompileTime==1 && internal::is_convertible<T, Scalar>::value,T>::type* = 0)\n    {\n      EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(PlainObjectBase, 1)\n      m_storage.data()[0] = val0;\n    }\n    \n    // We have a 1x1 matrix/array => the argument is interpreted as the value of the unique coefficient (case where scalar type match the index type)\n    template<typename T>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE void _init1(const Index& val0,\n                                    typename internal::enable_if<    (!internal::is_same<Index,Scalar>::value)\n                                                                  && (internal::is_same<Index,T>::value)\n                                                                  && Base::SizeAtCompileTime==1\n                                                                  && internal::is_convertible<T, Scalar>::value,T*>::type* = 0)\n    {\n      EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(PlainObjectBase, 1)\n      m_storage.data()[0] = Scalar(val0);\n    }\n\n    // Initialize a fixed size matrix from a pointer to raw data\n    template<typename T>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE void _init1(const Scalar* data){\n      this->_set_noalias(ConstMapType(data));\n    }\n\n    // Initialize an arbitrary matrix from a dense expression\n    template<typename T, typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE void _init1(const DenseBase<OtherDerived>& other){\n      this->_set_noalias(other);\n    }\n\n    // Initialize an arbitrary matrix from an object convertible to the Derived type.\n    template<typename T>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE void _init1(const Derived& other){\n      this->_set_noalias(other);\n    }\n\n    // Initialize an arbitrary matrix from a generic Eigen expression\n    template<typename T, typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE void _init1(const EigenBase<OtherDerived>& other){\n      this->derived() = other;\n    }\n\n    template<typename T, typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE void _init1(const ReturnByValue<OtherDerived>& other)\n    {\n      resize(other.rows(), other.cols());\n      other.evalTo(this->derived());\n    }\n\n    template<typename T, typename OtherDerived, int ColsAtCompileTime>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE void _init1(const RotationBase<OtherDerived,ColsAtCompileTime>& r)\n    {\n      this->derived() = r;\n    }\n    \n    // For fixed-size Array<Scalar,...>\n    template<typename T>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE void _init1(const Scalar& val0,\n                                    typename internal::enable_if<    Base::SizeAtCompileTime!=Dynamic\n                                                                  && Base::SizeAtCompileTime!=1\n                                                                  && internal::is_convertible<T, Scalar>::value\n                                                                  && internal::is_same<typename internal::traits<Derived>::XprKind,ArrayXpr>::value,T>::type* = 0)\n    {\n      Base::setConstant(val0);\n    }\n    \n    // For fixed-size Array<Index,...>\n    template<typename T>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE void _init1(const Index& val0,\n                                    typename internal::enable_if<    (!internal::is_same<Index,Scalar>::value)\n                                                                  && (internal::is_same<Index,T>::value)\n                                                                  && Base::SizeAtCompileTime!=Dynamic\n                                                                  && Base::SizeAtCompileTime!=1\n                                                                  && internal::is_convertible<T, Scalar>::value\n                                                                  && internal::is_same<typename internal::traits<Derived>::XprKind,ArrayXpr>::value,T*>::type* = 0)\n    {\n      Base::setConstant(val0);\n    }\n    \n    template<typename MatrixTypeA, typename MatrixTypeB, bool SwapPointers>\n    friend struct internal::matrix_swap_impl;\n\n  public:\n    \n#ifndef EIGEN_PARSED_BY_DOXYGEN\n    /** \\internal\n      * \\brief Override DenseBase::swap() since for dynamic-sized matrices\n      * of same type it is enough to swap the data pointers.\n      */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    void swap(DenseBase<OtherDerived> & other)\n    {\n      enum { SwapPointers = internal::is_same<Derived, OtherDerived>::value && Base::SizeAtCompileTime==Dynamic };\n      internal::matrix_swap_impl<Derived, OtherDerived, bool(SwapPointers)>::run(this->derived(), other.derived());\n    }\n    \n    /** \\internal\n      * \\brief const version forwarded to DenseBase::swap\n      */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    void swap(DenseBase<OtherDerived> const & other)\n    { Base::swap(other.derived()); }\n    \n    EIGEN_DEVICE_FUNC \n    static EIGEN_STRONG_INLINE void _check_template_params()\n    {\n      EIGEN_STATIC_ASSERT((EIGEN_IMPLIES(MaxRowsAtCompileTime==1 && MaxColsAtCompileTime!=1, (Options&RowMajor)==RowMajor)\n                        && EIGEN_IMPLIES(MaxColsAtCompileTime==1 && MaxRowsAtCompileTime!=1, (Options&RowMajor)==0)\n                        && ((RowsAtCompileTime == Dynamic) || (RowsAtCompileTime >= 0))\n                        && ((ColsAtCompileTime == Dynamic) || (ColsAtCompileTime >= 0))\n                        && ((MaxRowsAtCompileTime == Dynamic) || (MaxRowsAtCompileTime >= 0))\n                        && ((MaxColsAtCompileTime == Dynamic) || (MaxColsAtCompileTime >= 0))\n                        && (MaxRowsAtCompileTime == RowsAtCompileTime || RowsAtCompileTime==Dynamic)\n                        && (MaxColsAtCompileTime == ColsAtCompileTime || ColsAtCompileTime==Dynamic)\n                        && (Options & (DontAlign|RowMajor)) == Options),\n        INVALID_MATRIX_TEMPLATE_PARAMETERS)\n    }\n\n    enum { IsPlainObjectBase = 1 };\n#endif\n};\n\nnamespace internal {\n\ntemplate <typename Derived, typename OtherDerived, bool IsVector>\nstruct conservative_resize_like_impl\n{\n  static void run(DenseBase<Derived>& _this, Index rows, Index cols)\n  {\n    if (_this.rows() == rows && _this.cols() == cols) return;\n    EIGEN_STATIC_ASSERT_DYNAMIC_SIZE(Derived)\n\n    if ( ( Derived::IsRowMajor && _this.cols() == cols) || // row-major and we change only the number of rows\n         (!Derived::IsRowMajor && _this.rows() == rows) )  // column-major and we change only the number of columns\n    {\n      internal::check_rows_cols_for_overflow<Derived::MaxSizeAtCompileTime>::run(rows, cols);\n      _this.derived().m_storage.conservativeResize(rows*cols,rows,cols);\n    }\n    else\n    {\n      // The storage order does not allow us to use reallocation.\n      typename Derived::PlainObject tmp(rows,cols);\n      const Index common_rows = numext::mini(rows, _this.rows());\n      const Index common_cols = numext::mini(cols, _this.cols());\n      tmp.block(0,0,common_rows,common_cols) = _this.block(0,0,common_rows,common_cols);\n      _this.derived().swap(tmp);\n    }\n  }\n\n  static void run(DenseBase<Derived>& _this, const DenseBase<OtherDerived>& other)\n  {\n    if (_this.rows() == other.rows() && _this.cols() == other.cols()) return;\n\n    // Note: Here is space for improvement. Basically, for conservativeResize(Index,Index),\n    // neither RowsAtCompileTime or ColsAtCompileTime must be Dynamic. If only one of the\n    // dimensions is dynamic, one could use either conservativeResize(Index rows, NoChange_t) or\n    // conservativeResize(NoChange_t, Index cols). For these methods new static asserts like\n    // EIGEN_STATIC_ASSERT_DYNAMIC_ROWS and EIGEN_STATIC_ASSERT_DYNAMIC_COLS would be good.\n    EIGEN_STATIC_ASSERT_DYNAMIC_SIZE(Derived)\n    EIGEN_STATIC_ASSERT_DYNAMIC_SIZE(OtherDerived)\n\n    if ( ( Derived::IsRowMajor && _this.cols() == other.cols()) || // row-major and we change only the number of rows\n         (!Derived::IsRowMajor && _this.rows() == other.rows()) )  // column-major and we change only the number of columns\n    {\n      const Index new_rows = other.rows() - _this.rows();\n      const Index new_cols = other.cols() - _this.cols();\n      _this.derived().m_storage.conservativeResize(other.size(),other.rows(),other.cols());\n      if (new_rows>0)\n        _this.bottomRightCorner(new_rows, other.cols()) = other.bottomRows(new_rows);\n      else if (new_cols>0)\n        _this.bottomRightCorner(other.rows(), new_cols) = other.rightCols(new_cols);\n    }\n    else\n    {\n      // The storage order does not allow us to use reallocation.\n      typename Derived::PlainObject tmp(other);\n      const Index common_rows = numext::mini(tmp.rows(), _this.rows());\n      const Index common_cols = numext::mini(tmp.cols(), _this.cols());\n      tmp.block(0,0,common_rows,common_cols) = _this.block(0,0,common_rows,common_cols);\n      _this.derived().swap(tmp);\n    }\n  }\n};\n\n// Here, the specialization for vectors inherits from the general matrix case\n// to allow calling .conservativeResize(rows,cols) on vectors.\ntemplate <typename Derived, typename OtherDerived>\nstruct conservative_resize_like_impl<Derived,OtherDerived,true>\n  : conservative_resize_like_impl<Derived,OtherDerived,false>\n{\n  using conservative_resize_like_impl<Derived,OtherDerived,false>::run;\n  \n  static void run(DenseBase<Derived>& _this, Index size)\n  {\n    const Index new_rows = Derived::RowsAtCompileTime==1 ? 1 : size;\n    const Index new_cols = Derived::RowsAtCompileTime==1 ? size : 1;\n    _this.derived().m_storage.conservativeResize(size,new_rows,new_cols);\n  }\n\n  static void run(DenseBase<Derived>& _this, const DenseBase<OtherDerived>& other)\n  {\n    if (_this.rows() == other.rows() && _this.cols() == other.cols()) return;\n\n    const Index num_new_elements = other.size() - _this.size();\n\n    const Index new_rows = Derived::RowsAtCompileTime==1 ? 1 : other.rows();\n    const Index new_cols = Derived::RowsAtCompileTime==1 ? other.cols() : 1;\n    _this.derived().m_storage.conservativeResize(other.size(),new_rows,new_cols);\n\n    if (num_new_elements > 0)\n      _this.tail(num_new_elements) = other.tail(num_new_elements);\n  }\n};\n\ntemplate<typename MatrixTypeA, typename MatrixTypeB, bool SwapPointers>\nstruct matrix_swap_impl\n{\n  EIGEN_DEVICE_FUNC\n  static inline void run(MatrixTypeA& a, MatrixTypeB& b)\n  {\n    a.base().swap(b);\n  }\n};\n\ntemplate<typename MatrixTypeA, typename MatrixTypeB>\nstruct matrix_swap_impl<MatrixTypeA, MatrixTypeB, true>\n{\n  EIGEN_DEVICE_FUNC\n  static inline void run(MatrixTypeA& a, MatrixTypeB& b)\n  {\n    static_cast<typename MatrixTypeA::Base&>(a).m_storage.swap(static_cast<typename MatrixTypeB::Base&>(b).m_storage);\n  }\n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_DENSESTORAGEBASE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/Product.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_PRODUCT_H\n#define EIGEN_PRODUCT_H\n\nnamespace Eigen {\n\ntemplate<typename Lhs, typename Rhs, int Option, typename StorageKind> class ProductImpl;\n\nnamespace internal {\n\ntemplate<typename Lhs, typename Rhs, int Option>\nstruct traits<Product<Lhs, Rhs, Option> >\n{\n  typedef typename remove_all<Lhs>::type LhsCleaned;\n  typedef typename remove_all<Rhs>::type RhsCleaned;\n  typedef traits<LhsCleaned> LhsTraits;\n  typedef traits<RhsCleaned> RhsTraits;\n  \n  typedef MatrixXpr XprKind;\n  \n  typedef typename ScalarBinaryOpTraits<typename traits<LhsCleaned>::Scalar, typename traits<RhsCleaned>::Scalar>::ReturnType Scalar;\n  typedef typename product_promote_storage_type<typename LhsTraits::StorageKind,\n                                                typename RhsTraits::StorageKind,\n                                                internal::product_type<Lhs,Rhs>::ret>::ret StorageKind;\n  typedef typename promote_index_type<typename LhsTraits::StorageIndex,\n                                      typename RhsTraits::StorageIndex>::type StorageIndex;\n  \n  enum {\n    RowsAtCompileTime    = LhsTraits::RowsAtCompileTime,\n    ColsAtCompileTime    = RhsTraits::ColsAtCompileTime,\n    MaxRowsAtCompileTime = LhsTraits::MaxRowsAtCompileTime,\n    MaxColsAtCompileTime = RhsTraits::MaxColsAtCompileTime,\n    \n    // FIXME: only needed by GeneralMatrixMatrixTriangular\n    InnerSize = EIGEN_SIZE_MIN_PREFER_FIXED(LhsTraits::ColsAtCompileTime, RhsTraits::RowsAtCompileTime),\n    \n    // The storage order is somewhat arbitrary here. The correct one will be determined through the evaluator.\n    Flags = (MaxRowsAtCompileTime==1 && MaxColsAtCompileTime!=1) ? RowMajorBit\n          : (MaxColsAtCompileTime==1 && MaxRowsAtCompileTime!=1) ? 0\n          : (   ((LhsTraits::Flags&NoPreferredStorageOrderBit) && (RhsTraits::Flags&RowMajorBit))\n             || ((RhsTraits::Flags&NoPreferredStorageOrderBit) && (LhsTraits::Flags&RowMajorBit)) ) ? RowMajorBit\n          : NoPreferredStorageOrderBit\n  };\n};\n\n} // end namespace internal\n\n/** \\class Product\n  * \\ingroup Core_Module\n  *\n  * \\brief Expression of the product of two arbitrary matrices or vectors\n  *\n  * \\tparam _Lhs the type of the left-hand side expression\n  * \\tparam _Rhs the type of the right-hand side expression\n  *\n  * This class represents an expression of the product of two arbitrary matrices.\n  *\n  * The other template parameters are:\n  * \\tparam Option     can be DefaultProduct, AliasFreeProduct, or LazyProduct\n  *\n  */\ntemplate<typename _Lhs, typename _Rhs, int Option>\nclass Product : public ProductImpl<_Lhs,_Rhs,Option,\n                                   typename internal::product_promote_storage_type<typename internal::traits<_Lhs>::StorageKind,\n                                                                                   typename internal::traits<_Rhs>::StorageKind,\n                                                                                   internal::product_type<_Lhs,_Rhs>::ret>::ret>\n{\n  public:\n    \n    typedef _Lhs Lhs;\n    typedef _Rhs Rhs;\n    \n    typedef typename ProductImpl<\n        Lhs, Rhs, Option,\n        typename internal::product_promote_storage_type<typename internal::traits<Lhs>::StorageKind,\n                                                        typename internal::traits<Rhs>::StorageKind,\n                                                        internal::product_type<Lhs,Rhs>::ret>::ret>::Base Base;\n    EIGEN_GENERIC_PUBLIC_INTERFACE(Product)\n\n    typedef typename internal::ref_selector<Lhs>::type LhsNested;\n    typedef typename internal::ref_selector<Rhs>::type RhsNested;\n    typedef typename internal::remove_all<LhsNested>::type LhsNestedCleaned;\n    typedef typename internal::remove_all<RhsNested>::type RhsNestedCleaned;\n\n    EIGEN_DEVICE_FUNC Product(const Lhs& lhs, const Rhs& rhs) : m_lhs(lhs), m_rhs(rhs)\n    {\n      eigen_assert(lhs.cols() == rhs.rows()\n        && \"invalid matrix product\"\n        && \"if you wanted a coeff-wise or a dot product use the respective explicit functions\");\n    }\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index rows() const { return m_lhs.rows(); }\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index cols() const { return m_rhs.cols(); }\n\n    EIGEN_DEVICE_FUNC const LhsNestedCleaned& lhs() const { return m_lhs; }\n    EIGEN_DEVICE_FUNC const RhsNestedCleaned& rhs() const { return m_rhs; }\n\n  protected:\n\n    LhsNested m_lhs;\n    RhsNested m_rhs;\n};\n\nnamespace internal {\n  \ntemplate<typename Lhs, typename Rhs, int Option, int ProductTag = internal::product_type<Lhs,Rhs>::ret>\nclass dense_product_base\n : public internal::dense_xpr_base<Product<Lhs,Rhs,Option> >::type\n{};\n\n/** Convertion to scalar for inner-products */\ntemplate<typename Lhs, typename Rhs, int Option>\nclass dense_product_base<Lhs, Rhs, Option, InnerProduct>\n : public internal::dense_xpr_base<Product<Lhs,Rhs,Option> >::type\n{\n  typedef Product<Lhs,Rhs,Option> ProductXpr;\n  typedef typename internal::dense_xpr_base<ProductXpr>::type Base;\npublic:\n  using Base::derived;\n  typedef typename Base::Scalar Scalar;\n  \n  EIGEN_STRONG_INLINE operator const Scalar() const\n  {\n    return internal::evaluator<ProductXpr>(derived()).coeff(0,0);\n  }\n};\n\n} // namespace internal\n\n// Generic API dispatcher\ntemplate<typename Lhs, typename Rhs, int Option, typename StorageKind>\nclass ProductImpl : public internal::generic_xpr_base<Product<Lhs,Rhs,Option>, MatrixXpr, StorageKind>::type\n{\n  public:\n    typedef typename internal::generic_xpr_base<Product<Lhs,Rhs,Option>, MatrixXpr, StorageKind>::type Base;\n};\n\ntemplate<typename Lhs, typename Rhs, int Option>\nclass ProductImpl<Lhs,Rhs,Option,Dense>\n  : public internal::dense_product_base<Lhs,Rhs,Option>\n{\n    typedef Product<Lhs, Rhs, Option> Derived;\n    \n  public:\n    \n    typedef typename internal::dense_product_base<Lhs, Rhs, Option> Base;\n    EIGEN_DENSE_PUBLIC_INTERFACE(Derived)\n  protected:\n    enum {\n      IsOneByOne = (RowsAtCompileTime == 1 || RowsAtCompileTime == Dynamic) && \n                   (ColsAtCompileTime == 1 || ColsAtCompileTime == Dynamic),\n      EnableCoeff = IsOneByOne || Option==LazyProduct\n    };\n    \n  public:\n  \n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(Index row, Index col) const\n    {\n      EIGEN_STATIC_ASSERT(EnableCoeff, THIS_METHOD_IS_ONLY_FOR_INNER_OR_LAZY_PRODUCTS);\n      eigen_assert( (Option==LazyProduct) || (this->rows() == 1 && this->cols() == 1) );\n      \n      return internal::evaluator<Derived>(derived()).coeff(row,col);\n    }\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(Index i) const\n    {\n      EIGEN_STATIC_ASSERT(EnableCoeff, THIS_METHOD_IS_ONLY_FOR_INNER_OR_LAZY_PRODUCTS);\n      eigen_assert( (Option==LazyProduct) || (this->rows() == 1 && this->cols() == 1) );\n      \n      return internal::evaluator<Derived>(derived()).coeff(i);\n    }\n    \n  \n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_PRODUCT_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/ProductEvaluators.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2011 Jitse Niesen <jitse@maths.leeds.ac.uk>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n\n#ifndef EIGEN_PRODUCTEVALUATORS_H\n#define EIGEN_PRODUCTEVALUATORS_H\n\nnamespace Eigen {\n  \nnamespace internal {\n\n/** \\internal\n  * Evaluator of a product expression.\n  * Since products require special treatments to handle all possible cases,\n  * we simply deffer the evaluation logic to a product_evaluator class\n  * which offers more partial specialization possibilities.\n  * \n  * \\sa class product_evaluator\n  */\ntemplate<typename Lhs, typename Rhs, int Options>\nstruct evaluator<Product<Lhs, Rhs, Options> > \n : public product_evaluator<Product<Lhs, Rhs, Options> >\n{\n  typedef Product<Lhs, Rhs, Options> XprType;\n  typedef product_evaluator<XprType> Base;\n  \n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit evaluator(const XprType& xpr) : Base(xpr) {}\n};\n \n// Catch \"scalar * ( A * B )\" and transform it to \"(A*scalar) * B\"\n// TODO we should apply that rule only if that's really helpful\ntemplate<typename Lhs, typename Rhs, typename Scalar1, typename Scalar2, typename Plain1>\nstruct evaluator_assume_aliasing<CwiseBinaryOp<internal::scalar_product_op<Scalar1,Scalar2>,\n                                               const CwiseNullaryOp<internal::scalar_constant_op<Scalar1>, Plain1>,\n                                               const Product<Lhs, Rhs, DefaultProduct> > >\n{\n  static const bool value = true;\n};\ntemplate<typename Lhs, typename Rhs, typename Scalar1, typename Scalar2, typename Plain1>\nstruct evaluator<CwiseBinaryOp<internal::scalar_product_op<Scalar1,Scalar2>,\n                               const CwiseNullaryOp<internal::scalar_constant_op<Scalar1>, Plain1>,\n                               const Product<Lhs, Rhs, DefaultProduct> > >\n : public evaluator<Product<EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar1,Lhs,product), Rhs, DefaultProduct> >\n{\n  typedef CwiseBinaryOp<internal::scalar_product_op<Scalar1,Scalar2>,\n                               const CwiseNullaryOp<internal::scalar_constant_op<Scalar1>, Plain1>,\n                               const Product<Lhs, Rhs, DefaultProduct> > XprType;\n  typedef evaluator<Product<EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar1,Lhs,product), Rhs, DefaultProduct> > Base;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit evaluator(const XprType& xpr)\n    : Base(xpr.lhs().functor().m_other * xpr.rhs().lhs() * xpr.rhs().rhs())\n  {}\n};\n\n\ntemplate<typename Lhs, typename Rhs, int DiagIndex>\nstruct evaluator<Diagonal<const Product<Lhs, Rhs, DefaultProduct>, DiagIndex> > \n : public evaluator<Diagonal<const Product<Lhs, Rhs, LazyProduct>, DiagIndex> >\n{\n  typedef Diagonal<const Product<Lhs, Rhs, DefaultProduct>, DiagIndex> XprType;\n  typedef evaluator<Diagonal<const Product<Lhs, Rhs, LazyProduct>, DiagIndex> > Base;\n  \n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit evaluator(const XprType& xpr)\n    : Base(Diagonal<const Product<Lhs, Rhs, LazyProduct>, DiagIndex>(\n        Product<Lhs, Rhs, LazyProduct>(xpr.nestedExpression().lhs(), xpr.nestedExpression().rhs()),\n        xpr.index() ))\n  {}\n};\n\n\n// Helper class to perform a matrix product with the destination at hand.\n// Depending on the sizes of the factors, there are different evaluation strategies\n// as controlled by internal::product_type.\ntemplate< typename Lhs, typename Rhs,\n          typename LhsShape = typename evaluator_traits<Lhs>::Shape,\n          typename RhsShape = typename evaluator_traits<Rhs>::Shape,\n          int ProductType = internal::product_type<Lhs,Rhs>::value>\nstruct generic_product_impl;\n\ntemplate<typename Lhs, typename Rhs>\nstruct evaluator_assume_aliasing<Product<Lhs, Rhs, DefaultProduct> > {\n  static const bool value = true;\n};\n\n// This is the default evaluator implementation for products:\n// It creates a temporary and call generic_product_impl\ntemplate<typename Lhs, typename Rhs, int Options, int ProductTag, typename LhsShape, typename RhsShape>\nstruct product_evaluator<Product<Lhs, Rhs, Options>, ProductTag, LhsShape, RhsShape>\n  : public evaluator<typename Product<Lhs, Rhs, Options>::PlainObject>\n{\n  typedef Product<Lhs, Rhs, Options> XprType;\n  typedef typename XprType::PlainObject PlainObject;\n  typedef evaluator<PlainObject> Base;\n  enum {\n    Flags = Base::Flags | EvalBeforeNestingBit\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  explicit product_evaluator(const XprType& xpr)\n    : m_result(xpr.rows(), xpr.cols())\n  {\n    ::new (static_cast<Base*>(this)) Base(m_result);\n    \n// FIXME shall we handle nested_eval here?,\n// if so, then we must take care at removing the call to nested_eval in the specializations (e.g., in permutation_matrix_product, transposition_matrix_product, etc.)\n//     typedef typename internal::nested_eval<Lhs,Rhs::ColsAtCompileTime>::type LhsNested;\n//     typedef typename internal::nested_eval<Rhs,Lhs::RowsAtCompileTime>::type RhsNested;\n//     typedef typename internal::remove_all<LhsNested>::type LhsNestedCleaned;\n//     typedef typename internal::remove_all<RhsNested>::type RhsNestedCleaned;\n//     \n//     const LhsNested lhs(xpr.lhs());\n//     const RhsNested rhs(xpr.rhs());\n//   \n//     generic_product_impl<LhsNestedCleaned, RhsNestedCleaned>::evalTo(m_result, lhs, rhs);\n\n    generic_product_impl<Lhs, Rhs, LhsShape, RhsShape, ProductTag>::evalTo(m_result, xpr.lhs(), xpr.rhs());\n  }\n  \nprotected:  \n  PlainObject m_result;\n};\n\n// The following three shortcuts are enabled only if the scalar types match excatly.\n// TODO: we could enable them for different scalar types when the product is not vectorized.\n\n// Dense = Product\ntemplate< typename DstXprType, typename Lhs, typename Rhs, int Options, typename Scalar>\nstruct Assignment<DstXprType, Product<Lhs,Rhs,Options>, internal::assign_op<Scalar,Scalar>, Dense2Dense,\n  typename enable_if<(Options==DefaultProduct || Options==AliasFreeProduct)>::type>\n{\n  typedef Product<Lhs,Rhs,Options> SrcXprType;\n  static EIGEN_STRONG_INLINE\n  void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &)\n  {\n    Index dstRows = src.rows();\n    Index dstCols = src.cols();\n    if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))\n      dst.resize(dstRows, dstCols);\n    // FIXME shall we handle nested_eval here?\n    generic_product_impl<Lhs, Rhs>::evalTo(dst, src.lhs(), src.rhs());\n  }\n};\n\n// Dense += Product\ntemplate< typename DstXprType, typename Lhs, typename Rhs, int Options, typename Scalar>\nstruct Assignment<DstXprType, Product<Lhs,Rhs,Options>, internal::add_assign_op<Scalar,Scalar>, Dense2Dense,\n  typename enable_if<(Options==DefaultProduct || Options==AliasFreeProduct)>::type>\n{\n  typedef Product<Lhs,Rhs,Options> SrcXprType;\n  static EIGEN_STRONG_INLINE\n  void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op<Scalar,Scalar> &)\n  {\n    eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols());\n    // FIXME shall we handle nested_eval here?\n    generic_product_impl<Lhs, Rhs>::addTo(dst, src.lhs(), src.rhs());\n  }\n};\n\n// Dense -= Product\ntemplate< typename DstXprType, typename Lhs, typename Rhs, int Options, typename Scalar>\nstruct Assignment<DstXprType, Product<Lhs,Rhs,Options>, internal::sub_assign_op<Scalar,Scalar>, Dense2Dense,\n  typename enable_if<(Options==DefaultProduct || Options==AliasFreeProduct)>::type>\n{\n  typedef Product<Lhs,Rhs,Options> SrcXprType;\n  static EIGEN_STRONG_INLINE\n  void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op<Scalar,Scalar> &)\n  {\n    eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols());\n    // FIXME shall we handle nested_eval here?\n    generic_product_impl<Lhs, Rhs>::subTo(dst, src.lhs(), src.rhs());\n  }\n};\n\n\n// Dense ?= scalar * Product\n// TODO we should apply that rule if that's really helpful\n// for instance, this is not good for inner products\ntemplate< typename DstXprType, typename Lhs, typename Rhs, typename AssignFunc, typename Scalar, typename ScalarBis, typename Plain>\nstruct Assignment<DstXprType, CwiseBinaryOp<internal::scalar_product_op<ScalarBis,Scalar>, const CwiseNullaryOp<internal::scalar_constant_op<ScalarBis>,Plain>,\n                                           const Product<Lhs,Rhs,DefaultProduct> >, AssignFunc, Dense2Dense>\n{\n  typedef CwiseBinaryOp<internal::scalar_product_op<ScalarBis,Scalar>,\n                        const CwiseNullaryOp<internal::scalar_constant_op<ScalarBis>,Plain>,\n                        const Product<Lhs,Rhs,DefaultProduct> > SrcXprType;\n  static EIGEN_STRONG_INLINE\n  void run(DstXprType &dst, const SrcXprType &src, const AssignFunc& func)\n  {\n    call_assignment_no_alias(dst, (src.lhs().functor().m_other * src.rhs().lhs())*src.rhs().rhs(), func);\n  }\n};\n\n//----------------------------------------\n// Catch \"Dense ?= xpr + Product<>\" expression to save one temporary\n// FIXME we could probably enable these rules for any product, i.e., not only Dense and DefaultProduct\n\ntemplate<typename OtherXpr, typename Lhs, typename Rhs>\nstruct evaluator_assume_aliasing<CwiseBinaryOp<internal::scalar_sum_op<typename OtherXpr::Scalar,typename Product<Lhs,Rhs,DefaultProduct>::Scalar>, const OtherXpr,\n                                               const Product<Lhs,Rhs,DefaultProduct> >, DenseShape > {\n  static const bool value = true;\n};\n\ntemplate<typename OtherXpr, typename Lhs, typename Rhs>\nstruct evaluator_assume_aliasing<CwiseBinaryOp<internal::scalar_difference_op<typename OtherXpr::Scalar,typename Product<Lhs,Rhs,DefaultProduct>::Scalar>, const OtherXpr,\n                                               const Product<Lhs,Rhs,DefaultProduct> >, DenseShape > {\n  static const bool value = true;\n};\n\ntemplate<typename DstXprType, typename OtherXpr, typename ProductType, typename Func1, typename Func2>\nstruct assignment_from_xpr_op_product\n{\n  template<typename SrcXprType, typename InitialFunc>\n  static EIGEN_STRONG_INLINE\n  void run(DstXprType &dst, const SrcXprType &src, const InitialFunc& /*func*/)\n  {\n    call_assignment_no_alias(dst, src.lhs(), Func1());\n    call_assignment_no_alias(dst, src.rhs(), Func2());\n  }\n};\n\n#define EIGEN_CATCH_ASSIGN_XPR_OP_PRODUCT(ASSIGN_OP,BINOP,ASSIGN_OP2) \\\n  template< typename DstXprType, typename OtherXpr, typename Lhs, typename Rhs, typename DstScalar, typename SrcScalar, typename OtherScalar,typename ProdScalar> \\\n  struct Assignment<DstXprType, CwiseBinaryOp<internal::BINOP<OtherScalar,ProdScalar>, const OtherXpr, \\\n                                            const Product<Lhs,Rhs,DefaultProduct> >, internal::ASSIGN_OP<DstScalar,SrcScalar>, Dense2Dense> \\\n    : assignment_from_xpr_op_product<DstXprType, OtherXpr, Product<Lhs,Rhs,DefaultProduct>, internal::ASSIGN_OP<DstScalar,OtherScalar>, internal::ASSIGN_OP2<DstScalar,ProdScalar> > \\\n  {}\n\nEIGEN_CATCH_ASSIGN_XPR_OP_PRODUCT(assign_op,    scalar_sum_op,add_assign_op);\nEIGEN_CATCH_ASSIGN_XPR_OP_PRODUCT(add_assign_op,scalar_sum_op,add_assign_op);\nEIGEN_CATCH_ASSIGN_XPR_OP_PRODUCT(sub_assign_op,scalar_sum_op,sub_assign_op);\n\nEIGEN_CATCH_ASSIGN_XPR_OP_PRODUCT(assign_op,    scalar_difference_op,sub_assign_op);\nEIGEN_CATCH_ASSIGN_XPR_OP_PRODUCT(add_assign_op,scalar_difference_op,sub_assign_op);\nEIGEN_CATCH_ASSIGN_XPR_OP_PRODUCT(sub_assign_op,scalar_difference_op,add_assign_op);\n\n//----------------------------------------\n\ntemplate<typename Lhs, typename Rhs>\nstruct generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,InnerProduct>\n{\n  template<typename Dst>\n  static EIGEN_STRONG_INLINE void evalTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)\n  {\n    dst.coeffRef(0,0) = (lhs.transpose().cwiseProduct(rhs)).sum();\n  }\n  \n  template<typename Dst>\n  static EIGEN_STRONG_INLINE void addTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)\n  {\n    dst.coeffRef(0,0) += (lhs.transpose().cwiseProduct(rhs)).sum();\n  }\n  \n  template<typename Dst>\n  static EIGEN_STRONG_INLINE void subTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)\n  { dst.coeffRef(0,0) -= (lhs.transpose().cwiseProduct(rhs)).sum(); }\n};\n\n\n/***********************************************************************\n*  Implementation of outer dense * dense vector product\n***********************************************************************/\n\n// Column major result\ntemplate<typename Dst, typename Lhs, typename Rhs, typename Func>\nvoid outer_product_selector_run(Dst& dst, const Lhs &lhs, const Rhs &rhs, const Func& func, const false_type&)\n{\n  evaluator<Rhs> rhsEval(rhs);\n  typename nested_eval<Lhs,Rhs::SizeAtCompileTime>::type actual_lhs(lhs);\n  // FIXME if cols is large enough, then it might be useful to make sure that lhs is sequentially stored\n  // FIXME not very good if rhs is real and lhs complex while alpha is real too\n  const Index cols = dst.cols();\n  for (Index j=0; j<cols; ++j)\n    func(dst.col(j), rhsEval.coeff(Index(0),j) * actual_lhs);\n}\n\n// Row major result\ntemplate<typename Dst, typename Lhs, typename Rhs, typename Func>\nvoid outer_product_selector_run(Dst& dst, const Lhs &lhs, const Rhs &rhs, const Func& func, const true_type&)\n{\n  evaluator<Lhs> lhsEval(lhs);\n  typename nested_eval<Rhs,Lhs::SizeAtCompileTime>::type actual_rhs(rhs);\n  // FIXME if rows is large enough, then it might be useful to make sure that rhs is sequentially stored\n  // FIXME not very good if lhs is real and rhs complex while alpha is real too\n  const Index rows = dst.rows();\n  for (Index i=0; i<rows; ++i)\n    func(dst.row(i), lhsEval.coeff(i,Index(0)) * actual_rhs);\n}\n\ntemplate<typename Lhs, typename Rhs>\nstruct generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,OuterProduct>\n{\n  template<typename T> struct is_row_major : internal::conditional<(int(T::Flags)&RowMajorBit), internal::true_type, internal::false_type>::type {};\n  typedef typename Product<Lhs,Rhs>::Scalar Scalar;\n  \n  // TODO it would be nice to be able to exploit our *_assign_op functors for that purpose\n  struct set  { template<typename Dst, typename Src> void operator()(const Dst& dst, const Src& src) const { dst.const_cast_derived()  = src; } };\n  struct add  { template<typename Dst, typename Src> void operator()(const Dst& dst, const Src& src) const { dst.const_cast_derived() += src; } };\n  struct sub  { template<typename Dst, typename Src> void operator()(const Dst& dst, const Src& src) const { dst.const_cast_derived() -= src; } };\n  struct adds {\n    Scalar m_scale;\n    explicit adds(const Scalar& s) : m_scale(s) {}\n    template<typename Dst, typename Src> void operator()(const Dst& dst, const Src& src) const {\n      dst.const_cast_derived() += m_scale * src;\n    }\n  };\n  \n  template<typename Dst>\n  static EIGEN_STRONG_INLINE void evalTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)\n  {\n    internal::outer_product_selector_run(dst, lhs, rhs, set(), is_row_major<Dst>());\n  }\n  \n  template<typename Dst>\n  static EIGEN_STRONG_INLINE void addTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)\n  {\n    internal::outer_product_selector_run(dst, lhs, rhs, add(), is_row_major<Dst>());\n  }\n  \n  template<typename Dst>\n  static EIGEN_STRONG_INLINE void subTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)\n  {\n    internal::outer_product_selector_run(dst, lhs, rhs, sub(), is_row_major<Dst>());\n  }\n  \n  template<typename Dst>\n  static EIGEN_STRONG_INLINE void scaleAndAddTo(Dst& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)\n  {\n    internal::outer_product_selector_run(dst, lhs, rhs, adds(alpha), is_row_major<Dst>());\n  }\n  \n};\n\n\n// This base class provides default implementations for evalTo, addTo, subTo, in terms of scaleAndAddTo\ntemplate<typename Lhs, typename Rhs, typename Derived>\nstruct generic_product_impl_base\n{\n  typedef typename Product<Lhs,Rhs>::Scalar Scalar;\n  \n  template<typename Dst>\n  static EIGEN_STRONG_INLINE void evalTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)\n  { dst.setZero(); scaleAndAddTo(dst, lhs, rhs, Scalar(1)); }\n\n  template<typename Dst>\n  static EIGEN_STRONG_INLINE void addTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)\n  { scaleAndAddTo(dst,lhs, rhs, Scalar(1)); }\n\n  template<typename Dst>\n  static EIGEN_STRONG_INLINE void subTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)\n  { scaleAndAddTo(dst, lhs, rhs, Scalar(-1)); }\n  \n  template<typename Dst>\n  static EIGEN_STRONG_INLINE void scaleAndAddTo(Dst& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)\n  { Derived::scaleAndAddTo(dst,lhs,rhs,alpha); }\n\n};\n\ntemplate<typename Lhs, typename Rhs>\nstruct generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,GemvProduct>\n  : generic_product_impl_base<Lhs,Rhs,generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,GemvProduct> >\n{\n  typedef typename nested_eval<Lhs,1>::type LhsNested;\n  typedef typename nested_eval<Rhs,1>::type RhsNested;\n  typedef typename Product<Lhs,Rhs>::Scalar Scalar;\n  enum { Side = Lhs::IsVectorAtCompileTime ? OnTheLeft : OnTheRight };\n  typedef typename internal::remove_all<typename internal::conditional<int(Side)==OnTheRight,LhsNested,RhsNested>::type>::type MatrixType;\n\n  template<typename Dest>\n  static EIGEN_STRONG_INLINE void scaleAndAddTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)\n  {\n    LhsNested actual_lhs(lhs);\n    RhsNested actual_rhs(rhs);\n    internal::gemv_dense_selector<Side,\n                            (int(MatrixType::Flags)&RowMajorBit) ? RowMajor : ColMajor,\n                            bool(internal::blas_traits<MatrixType>::HasUsableDirectAccess)\n                           >::run(actual_lhs, actual_rhs, dst, alpha);\n  }\n};\n\ntemplate<typename Lhs, typename Rhs>\nstruct generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,CoeffBasedProductMode> \n{\n  typedef typename Product<Lhs,Rhs>::Scalar Scalar;\n  \n  template<typename Dst>\n  static EIGEN_STRONG_INLINE void evalTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)\n  {\n    // Same as: dst.noalias() = lhs.lazyProduct(rhs);\n    // but easier on the compiler side\n    call_assignment_no_alias(dst, lhs.lazyProduct(rhs), internal::assign_op<typename Dst::Scalar,Scalar>());\n  }\n  \n  template<typename Dst>\n  static EIGEN_STRONG_INLINE void addTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)\n  {\n    // dst.noalias() += lhs.lazyProduct(rhs);\n    call_assignment_no_alias(dst, lhs.lazyProduct(rhs), internal::add_assign_op<typename Dst::Scalar,Scalar>());\n  }\n  \n  template<typename Dst>\n  static EIGEN_STRONG_INLINE void subTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)\n  {\n    // dst.noalias() -= lhs.lazyProduct(rhs);\n    call_assignment_no_alias(dst, lhs.lazyProduct(rhs), internal::sub_assign_op<typename Dst::Scalar,Scalar>());\n  }\n  \n//   template<typename Dst>\n//   static inline void scaleAndAddTo(Dst& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)\n//   { dst.noalias() += alpha * lhs.lazyProduct(rhs); }\n};\n\n// This specialization enforces the use of a coefficient-based evaluation strategy\ntemplate<typename Lhs, typename Rhs>\nstruct generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,LazyCoeffBasedProductMode>\n  : generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,CoeffBasedProductMode> {};\n\n// Case 2: Evaluate coeff by coeff\n//\n// This is mostly taken from CoeffBasedProduct.h\n// The main difference is that we add an extra argument to the etor_product_*_impl::run() function\n// for the inner dimension of the product, because evaluator object do not know their size.\n\ntemplate<int Traversal, int UnrollingIndex, typename Lhs, typename Rhs, typename RetScalar>\nstruct etor_product_coeff_impl;\n\ntemplate<int StorageOrder, int UnrollingIndex, typename Lhs, typename Rhs, typename Packet, int LoadMode>\nstruct etor_product_packet_impl;\n\ntemplate<typename Lhs, typename Rhs, int ProductTag>\nstruct product_evaluator<Product<Lhs, Rhs, LazyProduct>, ProductTag, DenseShape, DenseShape>\n    : evaluator_base<Product<Lhs, Rhs, LazyProduct> >\n{\n  typedef Product<Lhs, Rhs, LazyProduct> XprType;\n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  explicit product_evaluator(const XprType& xpr)\n    : m_lhs(xpr.lhs()),\n      m_rhs(xpr.rhs()),\n      m_lhsImpl(m_lhs),     // FIXME the creation of the evaluator objects should result in a no-op, but check that!\n      m_rhsImpl(m_rhs),     //       Moreover, they are only useful for the packet path, so we could completely disable them when not needed,\n                            //       or perhaps declare them on the fly on the packet method... We have experiment to check what's best.\n      m_innerDim(xpr.lhs().cols())\n  {\n    EIGEN_INTERNAL_CHECK_COST_VALUE(NumTraits<Scalar>::MulCost);\n    EIGEN_INTERNAL_CHECK_COST_VALUE(NumTraits<Scalar>::AddCost);\n    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);\n#if 0\n    std::cerr << \"LhsOuterStrideBytes=  \" << LhsOuterStrideBytes << \"\\n\";\n    std::cerr << \"RhsOuterStrideBytes=  \" << RhsOuterStrideBytes << \"\\n\";\n    std::cerr << \"LhsAlignment=         \" << LhsAlignment << \"\\n\";\n    std::cerr << \"RhsAlignment=         \" << RhsAlignment << \"\\n\";\n    std::cerr << \"CanVectorizeLhs=      \" << CanVectorizeLhs << \"\\n\";\n    std::cerr << \"CanVectorizeRhs=      \" << CanVectorizeRhs << \"\\n\";\n    std::cerr << \"CanVectorizeInner=    \" << CanVectorizeInner << \"\\n\";\n    std::cerr << \"EvalToRowMajor=       \" << EvalToRowMajor << \"\\n\";\n    std::cerr << \"Alignment=            \" << Alignment << \"\\n\";\n    std::cerr << \"Flags=                \" << Flags << \"\\n\";\n#endif\n  }\n\n  // Everything below here is taken from CoeffBasedProduct.h\n\n  typedef typename internal::nested_eval<Lhs,Rhs::ColsAtCompileTime>::type LhsNested;\n  typedef typename internal::nested_eval<Rhs,Lhs::RowsAtCompileTime>::type RhsNested;\n  \n  typedef typename internal::remove_all<LhsNested>::type LhsNestedCleaned;\n  typedef typename internal::remove_all<RhsNested>::type RhsNestedCleaned;\n\n  typedef evaluator<LhsNestedCleaned> LhsEtorType;\n  typedef evaluator<RhsNestedCleaned> RhsEtorType;\n\n  enum {\n    RowsAtCompileTime = LhsNestedCleaned::RowsAtCompileTime,\n    ColsAtCompileTime = RhsNestedCleaned::ColsAtCompileTime,\n    InnerSize = EIGEN_SIZE_MIN_PREFER_FIXED(LhsNestedCleaned::ColsAtCompileTime, RhsNestedCleaned::RowsAtCompileTime),\n    MaxRowsAtCompileTime = LhsNestedCleaned::MaxRowsAtCompileTime,\n    MaxColsAtCompileTime = RhsNestedCleaned::MaxColsAtCompileTime\n  };\n\n  typedef typename find_best_packet<Scalar,RowsAtCompileTime>::type LhsVecPacketType;\n  typedef typename find_best_packet<Scalar,ColsAtCompileTime>::type RhsVecPacketType;\n\n  enum {\n      \n    LhsCoeffReadCost = LhsEtorType::CoeffReadCost,\n    RhsCoeffReadCost = RhsEtorType::CoeffReadCost,\n    CoeffReadCost = InnerSize==0 ? NumTraits<Scalar>::ReadCost\n                  : InnerSize == Dynamic ? HugeCost\n                  : InnerSize * (NumTraits<Scalar>::MulCost + LhsCoeffReadCost + RhsCoeffReadCost)\n                    + (InnerSize - 1) * NumTraits<Scalar>::AddCost,\n\n    Unroll = CoeffReadCost <= EIGEN_UNROLLING_LIMIT,\n    \n    LhsFlags = LhsEtorType::Flags,\n    RhsFlags = RhsEtorType::Flags,\n    \n    LhsRowMajor = LhsFlags & RowMajorBit,\n    RhsRowMajor = RhsFlags & RowMajorBit,\n\n    LhsVecPacketSize = unpacket_traits<LhsVecPacketType>::size,\n    RhsVecPacketSize = unpacket_traits<RhsVecPacketType>::size,\n\n    // Here, we don't care about alignment larger than the usable packet size.\n    LhsAlignment = EIGEN_PLAIN_ENUM_MIN(LhsEtorType::Alignment,LhsVecPacketSize*int(sizeof(typename LhsNestedCleaned::Scalar))),\n    RhsAlignment = EIGEN_PLAIN_ENUM_MIN(RhsEtorType::Alignment,RhsVecPacketSize*int(sizeof(typename RhsNestedCleaned::Scalar))),\n      \n    SameType = is_same<typename LhsNestedCleaned::Scalar,typename RhsNestedCleaned::Scalar>::value,\n\n    CanVectorizeRhs = bool(RhsRowMajor) && (RhsFlags & PacketAccessBit) && (ColsAtCompileTime!=1),\n    CanVectorizeLhs = (!LhsRowMajor) && (LhsFlags & PacketAccessBit) && (RowsAtCompileTime!=1),\n\n    EvalToRowMajor = (MaxRowsAtCompileTime==1&&MaxColsAtCompileTime!=1) ? 1\n                    : (MaxColsAtCompileTime==1&&MaxRowsAtCompileTime!=1) ? 0\n                    : (bool(RhsRowMajor) && !CanVectorizeLhs),\n\n    Flags = ((unsigned int)(LhsFlags | RhsFlags) & HereditaryBits & ~RowMajorBit)\n          | (EvalToRowMajor ? RowMajorBit : 0)\n          // TODO enable vectorization for mixed types\n          | (SameType && (CanVectorizeLhs || CanVectorizeRhs) ? PacketAccessBit : 0)\n          | (XprType::IsVectorAtCompileTime ? LinearAccessBit : 0),\n          \n    LhsOuterStrideBytes = int(LhsNestedCleaned::OuterStrideAtCompileTime) * int(sizeof(typename LhsNestedCleaned::Scalar)),\n    RhsOuterStrideBytes = int(RhsNestedCleaned::OuterStrideAtCompileTime) * int(sizeof(typename RhsNestedCleaned::Scalar)),\n\n    Alignment = bool(CanVectorizeLhs) ? (LhsOuterStrideBytes<=0 || (int(LhsOuterStrideBytes) % EIGEN_PLAIN_ENUM_MAX(1,LhsAlignment))!=0 ? 0 : LhsAlignment)\n              : bool(CanVectorizeRhs) ? (RhsOuterStrideBytes<=0 || (int(RhsOuterStrideBytes) % EIGEN_PLAIN_ENUM_MAX(1,RhsAlignment))!=0 ? 0 : RhsAlignment)\n              : 0,\n\n    /* CanVectorizeInner deserves special explanation. It does not affect the product flags. It is not used outside\n     * of Product. If the Product itself is not a packet-access expression, there is still a chance that the inner\n     * loop of the product might be vectorized. This is the meaning of CanVectorizeInner. Since it doesn't affect\n     * the Flags, it is safe to make this value depend on ActualPacketAccessBit, that doesn't affect the ABI.\n     */\n    CanVectorizeInner =    SameType\n                        && LhsRowMajor\n                        && (!RhsRowMajor)\n                        && (LhsFlags & RhsFlags & ActualPacketAccessBit)\n                        && (InnerSize % packet_traits<Scalar>::size == 0)\n  };\n  \n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CoeffReturnType coeff(Index row, Index col) const\n  {\n    return (m_lhs.row(row).transpose().cwiseProduct( m_rhs.col(col) )).sum();\n  }\n\n  /* Allow index-based non-packet access. It is impossible though to allow index-based packed access,\n   * which is why we don't set the LinearAccessBit.\n   * TODO: this seems possible when the result is a vector\n   */\n  EIGEN_DEVICE_FUNC const CoeffReturnType coeff(Index index) const\n  {\n    const Index row = (RowsAtCompileTime == 1 || MaxRowsAtCompileTime==1) ? 0 : index;\n    const Index col = (RowsAtCompileTime == 1 || MaxRowsAtCompileTime==1) ? index : 0;\n    return (m_lhs.row(row).transpose().cwiseProduct( m_rhs.col(col) )).sum();\n  }\n\n  template<int LoadMode, typename PacketType>\n  const PacketType packet(Index row, Index col) const\n  {\n    PacketType res;\n    typedef etor_product_packet_impl<bool(int(Flags)&RowMajorBit) ? RowMajor : ColMajor,\n                                     Unroll ? int(InnerSize) : Dynamic,\n                                     LhsEtorType, RhsEtorType, PacketType, LoadMode> PacketImpl;\n    PacketImpl::run(row, col, m_lhsImpl, m_rhsImpl, m_innerDim, res);\n    return res;\n  }\n\n  template<int LoadMode, typename PacketType>\n  const PacketType packet(Index index) const\n  {\n    const Index row = (RowsAtCompileTime == 1 || MaxRowsAtCompileTime==1) ? 0 : index;\n    const Index col = (RowsAtCompileTime == 1 || MaxRowsAtCompileTime==1) ? index : 0;\n    return packet<LoadMode,PacketType>(row,col);\n  }\n\nprotected:\n  typename internal::add_const_on_value_type<LhsNested>::type m_lhs;\n  typename internal::add_const_on_value_type<RhsNested>::type m_rhs;\n  \n  LhsEtorType m_lhsImpl;\n  RhsEtorType m_rhsImpl;\n\n  // TODO: Get rid of m_innerDim if known at compile time\n  Index m_innerDim;\n};\n\ntemplate<typename Lhs, typename Rhs>\nstruct product_evaluator<Product<Lhs, Rhs, DefaultProduct>, LazyCoeffBasedProductMode, DenseShape, DenseShape>\n  : product_evaluator<Product<Lhs, Rhs, LazyProduct>, CoeffBasedProductMode, DenseShape, DenseShape>\n{\n  typedef Product<Lhs, Rhs, DefaultProduct> XprType;\n  typedef Product<Lhs, Rhs, LazyProduct> BaseProduct;\n  typedef product_evaluator<BaseProduct, CoeffBasedProductMode, DenseShape, DenseShape> Base;\n  enum {\n    Flags = Base::Flags | EvalBeforeNestingBit\n  };\n  EIGEN_DEVICE_FUNC explicit product_evaluator(const XprType& xpr)\n    : Base(BaseProduct(xpr.lhs(),xpr.rhs()))\n  {}\n};\n\n/****************************************\n*** Coeff based product, Packet path  ***\n****************************************/\n\ntemplate<int UnrollingIndex, typename Lhs, typename Rhs, typename Packet, int LoadMode>\nstruct etor_product_packet_impl<RowMajor, UnrollingIndex, Lhs, Rhs, Packet, LoadMode>\n{\n  static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index innerDim, Packet &res)\n  {\n    etor_product_packet_impl<RowMajor, UnrollingIndex-1, Lhs, Rhs, Packet, LoadMode>::run(row, col, lhs, rhs, innerDim, res);\n    res =  pmadd(pset1<Packet>(lhs.coeff(row, Index(UnrollingIndex-1))), rhs.template packet<LoadMode,Packet>(Index(UnrollingIndex-1), col), res);\n  }\n};\n\ntemplate<int UnrollingIndex, typename Lhs, typename Rhs, typename Packet, int LoadMode>\nstruct etor_product_packet_impl<ColMajor, UnrollingIndex, Lhs, Rhs, Packet, LoadMode>\n{\n  static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index innerDim, Packet &res)\n  {\n    etor_product_packet_impl<ColMajor, UnrollingIndex-1, Lhs, Rhs, Packet, LoadMode>::run(row, col, lhs, rhs, innerDim, res);\n    res =  pmadd(lhs.template packet<LoadMode,Packet>(row, Index(UnrollingIndex-1)), pset1<Packet>(rhs.coeff(Index(UnrollingIndex-1), col)), res);\n  }\n};\n\ntemplate<typename Lhs, typename Rhs, typename Packet, int LoadMode>\nstruct etor_product_packet_impl<RowMajor, 1, Lhs, Rhs, Packet, LoadMode>\n{\n  static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index /*innerDim*/, Packet &res)\n  {\n    res = pmul(pset1<Packet>(lhs.coeff(row, Index(0))),rhs.template packet<LoadMode,Packet>(Index(0), col));\n  }\n};\n\ntemplate<typename Lhs, typename Rhs, typename Packet, int LoadMode>\nstruct etor_product_packet_impl<ColMajor, 1, Lhs, Rhs, Packet, LoadMode>\n{\n  static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index /*innerDim*/, Packet &res)\n  {\n    res = pmul(lhs.template packet<LoadMode,Packet>(row, Index(0)), pset1<Packet>(rhs.coeff(Index(0), col)));\n  }\n};\n\ntemplate<typename Lhs, typename Rhs, typename Packet, int LoadMode>\nstruct etor_product_packet_impl<RowMajor, 0, Lhs, Rhs, Packet, LoadMode>\n{\n  static EIGEN_STRONG_INLINE void run(Index /*row*/, Index /*col*/, const Lhs& /*lhs*/, const Rhs& /*rhs*/, Index /*innerDim*/, Packet &res)\n  {\n    res = pset1<Packet>(typename unpacket_traits<Packet>::type(0));\n  }\n};\n\ntemplate<typename Lhs, typename Rhs, typename Packet, int LoadMode>\nstruct etor_product_packet_impl<ColMajor, 0, Lhs, Rhs, Packet, LoadMode>\n{\n  static EIGEN_STRONG_INLINE void run(Index /*row*/, Index /*col*/, const Lhs& /*lhs*/, const Rhs& /*rhs*/, Index /*innerDim*/, Packet &res)\n  {\n    res = pset1<Packet>(typename unpacket_traits<Packet>::type(0));\n  }\n};\n\ntemplate<typename Lhs, typename Rhs, typename Packet, int LoadMode>\nstruct etor_product_packet_impl<RowMajor, Dynamic, Lhs, Rhs, Packet, LoadMode>\n{\n  static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index innerDim, Packet& res)\n  {\n    res = pset1<Packet>(typename unpacket_traits<Packet>::type(0));\n    for(Index i = 0; i < innerDim; ++i)\n      res =  pmadd(pset1<Packet>(lhs.coeff(row, i)), rhs.template packet<LoadMode,Packet>(i, col), res);\n  }\n};\n\ntemplate<typename Lhs, typename Rhs, typename Packet, int LoadMode>\nstruct etor_product_packet_impl<ColMajor, Dynamic, Lhs, Rhs, Packet, LoadMode>\n{\n  static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index innerDim, Packet& res)\n  {\n    res = pset1<Packet>(typename unpacket_traits<Packet>::type(0));\n    for(Index i = 0; i < innerDim; ++i)\n      res =  pmadd(lhs.template packet<LoadMode,Packet>(row, i), pset1<Packet>(rhs.coeff(i, col)), res);\n  }\n};\n\n\n/***************************************************************************\n* Triangular products\n***************************************************************************/\ntemplate<int Mode, bool LhsIsTriangular,\n         typename Lhs, bool LhsIsVector,\n         typename Rhs, bool RhsIsVector>\nstruct triangular_product_impl;\n\ntemplate<typename Lhs, typename Rhs, int ProductTag>\nstruct generic_product_impl<Lhs,Rhs,TriangularShape,DenseShape,ProductTag>\n  : generic_product_impl_base<Lhs,Rhs,generic_product_impl<Lhs,Rhs,TriangularShape,DenseShape,ProductTag> >\n{\n  typedef typename Product<Lhs,Rhs>::Scalar Scalar;\n  \n  template<typename Dest>\n  static void scaleAndAddTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)\n  {\n    triangular_product_impl<Lhs::Mode,true,typename Lhs::MatrixType,false,Rhs, Rhs::ColsAtCompileTime==1>\n        ::run(dst, lhs.nestedExpression(), rhs, alpha);\n  }\n};\n\ntemplate<typename Lhs, typename Rhs, int ProductTag>\nstruct generic_product_impl<Lhs,Rhs,DenseShape,TriangularShape,ProductTag>\n: generic_product_impl_base<Lhs,Rhs,generic_product_impl<Lhs,Rhs,DenseShape,TriangularShape,ProductTag> >\n{\n  typedef typename Product<Lhs,Rhs>::Scalar Scalar;\n  \n  template<typename Dest>\n  static void scaleAndAddTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)\n  {\n    triangular_product_impl<Rhs::Mode,false,Lhs,Lhs::RowsAtCompileTime==1, typename Rhs::MatrixType, false>::run(dst, lhs, rhs.nestedExpression(), alpha);\n  }\n};\n\n\n/***************************************************************************\n* SelfAdjoint products\n***************************************************************************/\ntemplate <typename Lhs, int LhsMode, bool LhsIsVector,\n          typename Rhs, int RhsMode, bool RhsIsVector>\nstruct selfadjoint_product_impl;\n\ntemplate<typename Lhs, typename Rhs, int ProductTag>\nstruct generic_product_impl<Lhs,Rhs,SelfAdjointShape,DenseShape,ProductTag>\n  : generic_product_impl_base<Lhs,Rhs,generic_product_impl<Lhs,Rhs,SelfAdjointShape,DenseShape,ProductTag> >\n{\n  typedef typename Product<Lhs,Rhs>::Scalar Scalar;\n  \n  template<typename Dest>\n  static void scaleAndAddTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)\n  {\n    selfadjoint_product_impl<typename Lhs::MatrixType,Lhs::Mode,false,Rhs,0,Rhs::IsVectorAtCompileTime>::run(dst, lhs.nestedExpression(), rhs, alpha);\n  }\n};\n\ntemplate<typename Lhs, typename Rhs, int ProductTag>\nstruct generic_product_impl<Lhs,Rhs,DenseShape,SelfAdjointShape,ProductTag>\n: generic_product_impl_base<Lhs,Rhs,generic_product_impl<Lhs,Rhs,DenseShape,SelfAdjointShape,ProductTag> >\n{\n  typedef typename Product<Lhs,Rhs>::Scalar Scalar;\n  \n  template<typename Dest>\n  static void scaleAndAddTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)\n  {\n    selfadjoint_product_impl<Lhs,0,Lhs::IsVectorAtCompileTime,typename Rhs::MatrixType,Rhs::Mode,false>::run(dst, lhs, rhs.nestedExpression(), alpha);\n  }\n};\n\n\n/***************************************************************************\n* Diagonal products\n***************************************************************************/\n  \ntemplate<typename MatrixType, typename DiagonalType, typename Derived, int ProductOrder>\nstruct diagonal_product_evaluator_base\n  : evaluator_base<Derived>\n{\n   typedef typename ScalarBinaryOpTraits<typename MatrixType::Scalar, typename DiagonalType::Scalar>::ReturnType Scalar;\npublic:\n  enum {\n    CoeffReadCost = NumTraits<Scalar>::MulCost + evaluator<MatrixType>::CoeffReadCost + evaluator<DiagonalType>::CoeffReadCost,\n    \n    MatrixFlags = evaluator<MatrixType>::Flags,\n    DiagFlags = evaluator<DiagonalType>::Flags,\n    _StorageOrder = MatrixFlags & RowMajorBit ? RowMajor : ColMajor,\n    _ScalarAccessOnDiag =  !((int(_StorageOrder) == ColMajor && int(ProductOrder) == OnTheLeft)\n                           ||(int(_StorageOrder) == RowMajor && int(ProductOrder) == OnTheRight)),\n    _SameTypes = is_same<typename MatrixType::Scalar, typename DiagonalType::Scalar>::value,\n    // FIXME currently we need same types, but in the future the next rule should be the one\n    //_Vectorizable = bool(int(MatrixFlags)&PacketAccessBit) && ((!_PacketOnDiag) || (_SameTypes && bool(int(DiagFlags)&PacketAccessBit))),\n    _Vectorizable = bool(int(MatrixFlags)&PacketAccessBit) && _SameTypes && (_ScalarAccessOnDiag || (bool(int(DiagFlags)&PacketAccessBit))),\n    _LinearAccessMask = (MatrixType::RowsAtCompileTime==1 || MatrixType::ColsAtCompileTime==1) ? LinearAccessBit : 0,\n    Flags = ((HereditaryBits|_LinearAccessMask) & (unsigned int)(MatrixFlags)) | (_Vectorizable ? PacketAccessBit : 0),\n    Alignment = evaluator<MatrixType>::Alignment,\n\n    AsScalarProduct =     (DiagonalType::SizeAtCompileTime==1)\n                      ||  (DiagonalType::SizeAtCompileTime==Dynamic && MatrixType::RowsAtCompileTime==1 && ProductOrder==OnTheLeft)\n                      ||  (DiagonalType::SizeAtCompileTime==Dynamic && MatrixType::ColsAtCompileTime==1 && ProductOrder==OnTheRight)\n  };\n  \n  diagonal_product_evaluator_base(const MatrixType &mat, const DiagonalType &diag)\n    : m_diagImpl(diag), m_matImpl(mat)\n  {\n    EIGEN_INTERNAL_CHECK_COST_VALUE(NumTraits<Scalar>::MulCost);\n    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);\n  }\n  \n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar coeff(Index idx) const\n  {\n    if(AsScalarProduct)\n      return m_diagImpl.coeff(0) * m_matImpl.coeff(idx);\n    else\n      return m_diagImpl.coeff(idx) * m_matImpl.coeff(idx);\n  }\n  \nprotected:\n  template<int LoadMode,typename PacketType>\n  EIGEN_STRONG_INLINE PacketType packet_impl(Index row, Index col, Index id, internal::true_type) const\n  {\n    return internal::pmul(m_matImpl.template packet<LoadMode,PacketType>(row, col),\n                          internal::pset1<PacketType>(m_diagImpl.coeff(id)));\n  }\n  \n  template<int LoadMode,typename PacketType>\n  EIGEN_STRONG_INLINE PacketType packet_impl(Index row, Index col, Index id, internal::false_type) const\n  {\n    enum {\n      InnerSize = (MatrixType::Flags & RowMajorBit) ? MatrixType::ColsAtCompileTime : MatrixType::RowsAtCompileTime,\n      DiagonalPacketLoadMode = EIGEN_PLAIN_ENUM_MIN(LoadMode,((InnerSize%16) == 0) ? int(Aligned16) : int(evaluator<DiagonalType>::Alignment)) // FIXME hardcoded 16!!\n    };\n    return internal::pmul(m_matImpl.template packet<LoadMode,PacketType>(row, col),\n                          m_diagImpl.template packet<DiagonalPacketLoadMode,PacketType>(id));\n  }\n  \n  evaluator<DiagonalType> m_diagImpl;\n  evaluator<MatrixType>   m_matImpl;\n};\n\n// diagonal * dense\ntemplate<typename Lhs, typename Rhs, int ProductKind, int ProductTag>\nstruct product_evaluator<Product<Lhs, Rhs, ProductKind>, ProductTag, DiagonalShape, DenseShape>\n  : diagonal_product_evaluator_base<Rhs, typename Lhs::DiagonalVectorType, Product<Lhs, Rhs, LazyProduct>, OnTheLeft>\n{\n  typedef diagonal_product_evaluator_base<Rhs, typename Lhs::DiagonalVectorType, Product<Lhs, Rhs, LazyProduct>, OnTheLeft> Base;\n  using Base::m_diagImpl;\n  using Base::m_matImpl;\n  using Base::coeff;\n  typedef typename Base::Scalar Scalar;\n  \n  typedef Product<Lhs, Rhs, ProductKind> XprType;\n  typedef typename XprType::PlainObject PlainObject;\n  \n  enum {\n    StorageOrder = int(Rhs::Flags) & RowMajorBit ? RowMajor : ColMajor\n  };\n\n  EIGEN_DEVICE_FUNC explicit product_evaluator(const XprType& xpr)\n    : Base(xpr.rhs(), xpr.lhs().diagonal())\n  {\n  }\n  \n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar coeff(Index row, Index col) const\n  {\n    return m_diagImpl.coeff(row) * m_matImpl.coeff(row, col);\n  }\n  \n#ifndef __CUDACC__\n  template<int LoadMode,typename PacketType>\n  EIGEN_STRONG_INLINE PacketType packet(Index row, Index col) const\n  {\n    // FIXME: NVCC used to complain about the template keyword, but we have to check whether this is still the case.\n    // See also similar calls below.\n    return this->template packet_impl<LoadMode,PacketType>(row,col, row,\n                                 typename internal::conditional<int(StorageOrder)==RowMajor, internal::true_type, internal::false_type>::type());\n  }\n  \n  template<int LoadMode,typename PacketType>\n  EIGEN_STRONG_INLINE PacketType packet(Index idx) const\n  {\n    return packet<LoadMode,PacketType>(int(StorageOrder)==ColMajor?idx:0,int(StorageOrder)==ColMajor?0:idx);\n  }\n#endif\n};\n\n// dense * diagonal\ntemplate<typename Lhs, typename Rhs, int ProductKind, int ProductTag>\nstruct product_evaluator<Product<Lhs, Rhs, ProductKind>, ProductTag, DenseShape, DiagonalShape>\n  : diagonal_product_evaluator_base<Lhs, typename Rhs::DiagonalVectorType, Product<Lhs, Rhs, LazyProduct>, OnTheRight>\n{\n  typedef diagonal_product_evaluator_base<Lhs, typename Rhs::DiagonalVectorType, Product<Lhs, Rhs, LazyProduct>, OnTheRight> Base;\n  using Base::m_diagImpl;\n  using Base::m_matImpl;\n  using Base::coeff;\n  typedef typename Base::Scalar Scalar;\n  \n  typedef Product<Lhs, Rhs, ProductKind> XprType;\n  typedef typename XprType::PlainObject PlainObject;\n  \n  enum { StorageOrder = int(Lhs::Flags) & RowMajorBit ? RowMajor : ColMajor };\n\n  EIGEN_DEVICE_FUNC explicit product_evaluator(const XprType& xpr)\n    : Base(xpr.lhs(), xpr.rhs().diagonal())\n  {\n  }\n  \n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar coeff(Index row, Index col) const\n  {\n    return m_matImpl.coeff(row, col) * m_diagImpl.coeff(col);\n  }\n  \n#ifndef __CUDACC__\n  template<int LoadMode,typename PacketType>\n  EIGEN_STRONG_INLINE PacketType packet(Index row, Index col) const\n  {\n    return this->template packet_impl<LoadMode,PacketType>(row,col, col,\n                                 typename internal::conditional<int(StorageOrder)==ColMajor, internal::true_type, internal::false_type>::type());\n  }\n  \n  template<int LoadMode,typename PacketType>\n  EIGEN_STRONG_INLINE PacketType packet(Index idx) const\n  {\n    return packet<LoadMode,PacketType>(int(StorageOrder)==ColMajor?idx:0,int(StorageOrder)==ColMajor?0:idx);\n  }\n#endif\n};\n\n/***************************************************************************\n* Products with permutation matrices\n***************************************************************************/\n\n/** \\internal\n  * \\class permutation_matrix_product\n  * Internal helper class implementing the product between a permutation matrix and a matrix.\n  * This class is specialized for DenseShape below and for SparseShape in SparseCore/SparsePermutation.h\n  */\ntemplate<typename ExpressionType, int Side, bool Transposed, typename ExpressionShape>\nstruct permutation_matrix_product;\n\ntemplate<typename ExpressionType, int Side, bool Transposed>\nstruct permutation_matrix_product<ExpressionType, Side, Transposed, DenseShape>\n{\n    typedef typename nested_eval<ExpressionType, 1>::type MatrixType;\n    typedef typename remove_all<MatrixType>::type MatrixTypeCleaned;\n\n    template<typename Dest, typename PermutationType>\n    static inline void run(Dest& dst, const PermutationType& perm, const ExpressionType& xpr)\n    {\n      MatrixType mat(xpr);\n      const Index n = Side==OnTheLeft ? mat.rows() : mat.cols();\n      // FIXME we need an is_same for expression that is not sensitive to constness. For instance\n      // is_same_xpr<Block<const Matrix>, Block<Matrix> >::value should be true.\n      //if(is_same<MatrixTypeCleaned,Dest>::value && extract_data(dst) == extract_data(mat))\n      if(is_same_dense(dst, mat))\n      {\n        // apply the permutation inplace\n        Matrix<bool,PermutationType::RowsAtCompileTime,1,0,PermutationType::MaxRowsAtCompileTime> mask(perm.size());\n        mask.fill(false);\n        Index r = 0;\n        while(r < perm.size())\n        {\n          // search for the next seed\n          while(r<perm.size() && mask[r]) r++;\n          if(r>=perm.size())\n            break;\n          // we got one, let's follow it until we are back to the seed\n          Index k0 = r++;\n          Index kPrev = k0;\n          mask.coeffRef(k0) = true;\n          for(Index k=perm.indices().coeff(k0); k!=k0; k=perm.indices().coeff(k))\n          {\n                  Block<Dest, Side==OnTheLeft ? 1 : Dest::RowsAtCompileTime, Side==OnTheRight ? 1 : Dest::ColsAtCompileTime>(dst, k)\n            .swap(Block<Dest, Side==OnTheLeft ? 1 : Dest::RowsAtCompileTime, Side==OnTheRight ? 1 : Dest::ColsAtCompileTime>\n                       (dst,((Side==OnTheLeft) ^ Transposed) ? k0 : kPrev));\n\n            mask.coeffRef(k) = true;\n            kPrev = k;\n          }\n        }\n      }\n      else\n      {\n        for(Index i = 0; i < n; ++i)\n        {\n          Block<Dest, Side==OnTheLeft ? 1 : Dest::RowsAtCompileTime, Side==OnTheRight ? 1 : Dest::ColsAtCompileTime>\n               (dst, ((Side==OnTheLeft) ^ Transposed) ? perm.indices().coeff(i) : i)\n\n          =\n\n          Block<const MatrixTypeCleaned,Side==OnTheLeft ? 1 : MatrixTypeCleaned::RowsAtCompileTime,Side==OnTheRight ? 1 : MatrixTypeCleaned::ColsAtCompileTime>\n               (mat, ((Side==OnTheRight) ^ Transposed) ? perm.indices().coeff(i) : i);\n        }\n      }\n    }\n};\n\ntemplate<typename Lhs, typename Rhs, int ProductTag, typename MatrixShape>\nstruct generic_product_impl<Lhs, Rhs, PermutationShape, MatrixShape, ProductTag>\n{\n  template<typename Dest>\n  static void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs)\n  {\n    permutation_matrix_product<Rhs, OnTheLeft, false, MatrixShape>::run(dst, lhs, rhs);\n  }\n};\n\ntemplate<typename Lhs, typename Rhs, int ProductTag, typename MatrixShape>\nstruct generic_product_impl<Lhs, Rhs, MatrixShape, PermutationShape, ProductTag>\n{\n  template<typename Dest>\n  static void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs)\n  {\n    permutation_matrix_product<Lhs, OnTheRight, false, MatrixShape>::run(dst, rhs, lhs);\n  }\n};\n\ntemplate<typename Lhs, typename Rhs, int ProductTag, typename MatrixShape>\nstruct generic_product_impl<Inverse<Lhs>, Rhs, PermutationShape, MatrixShape, ProductTag>\n{\n  template<typename Dest>\n  static void evalTo(Dest& dst, const Inverse<Lhs>& lhs, const Rhs& rhs)\n  {\n    permutation_matrix_product<Rhs, OnTheLeft, true, MatrixShape>::run(dst, lhs.nestedExpression(), rhs);\n  }\n};\n\ntemplate<typename Lhs, typename Rhs, int ProductTag, typename MatrixShape>\nstruct generic_product_impl<Lhs, Inverse<Rhs>, MatrixShape, PermutationShape, ProductTag>\n{\n  template<typename Dest>\n  static void evalTo(Dest& dst, const Lhs& lhs, const Inverse<Rhs>& rhs)\n  {\n    permutation_matrix_product<Lhs, OnTheRight, true, MatrixShape>::run(dst, rhs.nestedExpression(), lhs);\n  }\n};\n\n\n/***************************************************************************\n* Products with transpositions matrices\n***************************************************************************/\n\n// FIXME could we unify Transpositions and Permutation into a single \"shape\"??\n\n/** \\internal\n  * \\class transposition_matrix_product\n  * Internal helper class implementing the product between a permutation matrix and a matrix.\n  */\ntemplate<typename ExpressionType, int Side, bool Transposed, typename ExpressionShape>\nstruct transposition_matrix_product\n{\n  typedef typename nested_eval<ExpressionType, 1>::type MatrixType;\n  typedef typename remove_all<MatrixType>::type MatrixTypeCleaned;\n  \n  template<typename Dest, typename TranspositionType>\n  static inline void run(Dest& dst, const TranspositionType& tr, const ExpressionType& xpr)\n  {\n    MatrixType mat(xpr);\n    typedef typename TranspositionType::StorageIndex StorageIndex;\n    const Index size = tr.size();\n    StorageIndex j = 0;\n\n    if(!is_same_dense(dst,mat))\n      dst = mat;\n\n    for(Index k=(Transposed?size-1:0) ; Transposed?k>=0:k<size ; Transposed?--k:++k)\n      if(Index(j=tr.coeff(k))!=k)\n      {\n        if(Side==OnTheLeft)        dst.row(k).swap(dst.row(j));\n        else if(Side==OnTheRight)  dst.col(k).swap(dst.col(j));\n      }\n  }\n};\n\ntemplate<typename Lhs, typename Rhs, int ProductTag, typename MatrixShape>\nstruct generic_product_impl<Lhs, Rhs, TranspositionsShape, MatrixShape, ProductTag>\n{\n  template<typename Dest>\n  static void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs)\n  {\n    transposition_matrix_product<Rhs, OnTheLeft, false, MatrixShape>::run(dst, lhs, rhs);\n  }\n};\n\ntemplate<typename Lhs, typename Rhs, int ProductTag, typename MatrixShape>\nstruct generic_product_impl<Lhs, Rhs, MatrixShape, TranspositionsShape, ProductTag>\n{\n  template<typename Dest>\n  static void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs)\n  {\n    transposition_matrix_product<Lhs, OnTheRight, false, MatrixShape>::run(dst, rhs, lhs);\n  }\n};\n\n\ntemplate<typename Lhs, typename Rhs, int ProductTag, typename MatrixShape>\nstruct generic_product_impl<Transpose<Lhs>, Rhs, TranspositionsShape, MatrixShape, ProductTag>\n{\n  template<typename Dest>\n  static void evalTo(Dest& dst, const Transpose<Lhs>& lhs, const Rhs& rhs)\n  {\n    transposition_matrix_product<Rhs, OnTheLeft, true, MatrixShape>::run(dst, lhs.nestedExpression(), rhs);\n  }\n};\n\ntemplate<typename Lhs, typename Rhs, int ProductTag, typename MatrixShape>\nstruct generic_product_impl<Lhs, Transpose<Rhs>, MatrixShape, TranspositionsShape, ProductTag>\n{\n  template<typename Dest>\n  static void evalTo(Dest& dst, const Lhs& lhs, const Transpose<Rhs>& rhs)\n  {\n    transposition_matrix_product<Lhs, OnTheRight, true, MatrixShape>::run(dst, rhs.nestedExpression(), lhs);\n  }\n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_PRODUCT_EVALUATORS_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/Random.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_RANDOM_H\n#define EIGEN_RANDOM_H\n\nnamespace Eigen { \n\nnamespace internal {\n\ntemplate<typename Scalar> struct scalar_random_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_random_op)\n  inline const Scalar operator() () const { return random<Scalar>(); }\n};\n\ntemplate<typename Scalar>\nstruct functor_traits<scalar_random_op<Scalar> >\n{ enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = false, IsRepeatable = false }; };\n\n} // end namespace internal\n\n/** \\returns a random matrix expression\n  *\n  * Numbers are uniformly spread through their whole definition range for integer types,\n  * and in the [-1:1] range for floating point scalar types.\n  * \n  * The parameters \\a rows and \\a cols are the number of rows and of columns of\n  * the returned matrix. Must be compatible with this MatrixBase type.\n  *\n  * \\not_reentrant\n  * \n  * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,\n  * it is redundant to pass \\a rows and \\a cols as arguments, so Random() should be used\n  * instead.\n  * \n  *\n  * Example: \\include MatrixBase_random_int_int.cpp\n  * Output: \\verbinclude MatrixBase_random_int_int.out\n  *\n  * This expression has the \"evaluate before nesting\" flag so that it will be evaluated into\n  * a temporary matrix whenever it is nested in a larger expression. This prevents unexpected\n  * behavior with expressions involving random matrices.\n  * \n  * See DenseBase::NullaryExpr(Index, const CustomNullaryOp&) for an example using C++11 random generators.\n  *\n  * \\sa DenseBase::setRandom(), DenseBase::Random(Index), DenseBase::Random()\n  */\ntemplate<typename Derived>\ninline const typename DenseBase<Derived>::RandomReturnType\nDenseBase<Derived>::Random(Index rows, Index cols)\n{\n  return NullaryExpr(rows, cols, internal::scalar_random_op<Scalar>());\n}\n\n/** \\returns a random vector expression\n  *\n  * Numbers are uniformly spread through their whole definition range for integer types,\n  * and in the [-1:1] range for floating point scalar types.\n  *\n  * The parameter \\a size is the size of the returned vector.\n  * Must be compatible with this MatrixBase type.\n  *\n  * \\only_for_vectors\n  * \\not_reentrant\n  *\n  * This variant is meant to be used for dynamic-size vector types. For fixed-size types,\n  * it is redundant to pass \\a size as argument, so Random() should be used\n  * instead.\n  *\n  * Example: \\include MatrixBase_random_int.cpp\n  * Output: \\verbinclude MatrixBase_random_int.out\n  *\n  * This expression has the \"evaluate before nesting\" flag so that it will be evaluated into\n  * a temporary vector whenever it is nested in a larger expression. This prevents unexpected\n  * behavior with expressions involving random matrices.\n  *\n  * \\sa DenseBase::setRandom(), DenseBase::Random(Index,Index), DenseBase::Random()\n  */\ntemplate<typename Derived>\ninline const typename DenseBase<Derived>::RandomReturnType\nDenseBase<Derived>::Random(Index size)\n{\n  return NullaryExpr(size, internal::scalar_random_op<Scalar>());\n}\n\n/** \\returns a fixed-size random matrix or vector expression\n  *\n  * Numbers are uniformly spread through their whole definition range for integer types,\n  * and in the [-1:1] range for floating point scalar types.\n  * \n  * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you\n  * need to use the variants taking size arguments.\n  *\n  * Example: \\include MatrixBase_random.cpp\n  * Output: \\verbinclude MatrixBase_random.out\n  *\n  * This expression has the \"evaluate before nesting\" flag so that it will be evaluated into\n  * a temporary matrix whenever it is nested in a larger expression. This prevents unexpected\n  * behavior with expressions involving random matrices.\n  * \n  * \\not_reentrant\n  *\n  * \\sa DenseBase::setRandom(), DenseBase::Random(Index,Index), DenseBase::Random(Index)\n  */\ntemplate<typename Derived>\ninline const typename DenseBase<Derived>::RandomReturnType\nDenseBase<Derived>::Random()\n{\n  return NullaryExpr(RowsAtCompileTime, ColsAtCompileTime, internal::scalar_random_op<Scalar>());\n}\n\n/** Sets all coefficients in this expression to random values.\n  *\n  * Numbers are uniformly spread through their whole definition range for integer types,\n  * and in the [-1:1] range for floating point scalar types.\n  * \n  * \\not_reentrant\n  * \n  * Example: \\include MatrixBase_setRandom.cpp\n  * Output: \\verbinclude MatrixBase_setRandom.out\n  *\n  * \\sa class CwiseNullaryOp, setRandom(Index), setRandom(Index,Index)\n  */\ntemplate<typename Derived>\ninline Derived& DenseBase<Derived>::setRandom()\n{\n  return *this = Random(rows(), cols());\n}\n\n/** Resizes to the given \\a newSize, and sets all coefficients in this expression to random values.\n  *\n  * Numbers are uniformly spread through their whole definition range for integer types,\n  * and in the [-1:1] range for floating point scalar types.\n  * \n  * \\only_for_vectors\n  * \\not_reentrant\n  *\n  * Example: \\include Matrix_setRandom_int.cpp\n  * Output: \\verbinclude Matrix_setRandom_int.out\n  *\n  * \\sa DenseBase::setRandom(), setRandom(Index,Index), class CwiseNullaryOp, DenseBase::Random()\n  */\ntemplate<typename Derived>\nEIGEN_STRONG_INLINE Derived&\nPlainObjectBase<Derived>::setRandom(Index newSize)\n{\n  resize(newSize);\n  return setRandom();\n}\n\n/** Resizes to the given size, and sets all coefficients in this expression to random values.\n  *\n  * Numbers are uniformly spread through their whole definition range for integer types,\n  * and in the [-1:1] range for floating point scalar types.\n  *\n  * \\not_reentrant\n  * \n  * \\param rows the new number of rows\n  * \\param cols the new number of columns\n  *\n  * Example: \\include Matrix_setRandom_int_int.cpp\n  * Output: \\verbinclude Matrix_setRandom_int_int.out\n  *\n  * \\sa DenseBase::setRandom(), setRandom(Index), class CwiseNullaryOp, DenseBase::Random()\n  */\ntemplate<typename Derived>\nEIGEN_STRONG_INLINE Derived&\nPlainObjectBase<Derived>::setRandom(Index rows, Index cols)\n{\n  resize(rows, cols);\n  return setRandom();\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_RANDOM_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/Redux.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_REDUX_H\n#define EIGEN_REDUX_H\n\nnamespace Eigen { \n\nnamespace internal {\n\n// TODO\n//  * implement other kind of vectorization\n//  * factorize code\n\n/***************************************************************************\n* Part 1 : the logic deciding a strategy for vectorization and unrolling\n***************************************************************************/\n\ntemplate<typename Func, typename Derived>\nstruct redux_traits\n{\npublic:\n    typedef typename find_best_packet<typename Derived::Scalar,Derived::SizeAtCompileTime>::type PacketType;\n  enum {\n    PacketSize = unpacket_traits<PacketType>::size,\n    InnerMaxSize = int(Derived::IsRowMajor)\n                 ? Derived::MaxColsAtCompileTime\n                 : Derived::MaxRowsAtCompileTime\n  };\n\n  enum {\n    MightVectorize = (int(Derived::Flags)&ActualPacketAccessBit)\n                  && (functor_traits<Func>::PacketAccess),\n    MayLinearVectorize = bool(MightVectorize) && (int(Derived::Flags)&LinearAccessBit),\n    MaySliceVectorize  = bool(MightVectorize) && int(InnerMaxSize)>=3*PacketSize\n  };\n\npublic:\n  enum {\n    Traversal = int(MayLinearVectorize) ? int(LinearVectorizedTraversal)\n              : int(MaySliceVectorize)  ? int(SliceVectorizedTraversal)\n                                        : int(DefaultTraversal)\n  };\n\npublic:\n  enum {\n    Cost = Derived::SizeAtCompileTime == Dynamic ? HugeCost\n         : Derived::SizeAtCompileTime * Derived::CoeffReadCost + (Derived::SizeAtCompileTime-1) * functor_traits<Func>::Cost,\n    UnrollingLimit = EIGEN_UNROLLING_LIMIT * (int(Traversal) == int(DefaultTraversal) ? 1 : int(PacketSize))\n  };\n\npublic:\n  enum {\n    Unrolling = Cost <= UnrollingLimit ? CompleteUnrolling : NoUnrolling\n  };\n  \n#ifdef EIGEN_DEBUG_ASSIGN\n  static void debug()\n  {\n    std::cerr << \"Xpr: \" << typeid(typename Derived::XprType).name() << std::endl;\n    std::cerr.setf(std::ios::hex, std::ios::basefield);\n    EIGEN_DEBUG_VAR(Derived::Flags)\n    std::cerr.unsetf(std::ios::hex);\n    EIGEN_DEBUG_VAR(InnerMaxSize)\n    EIGEN_DEBUG_VAR(PacketSize)\n    EIGEN_DEBUG_VAR(MightVectorize)\n    EIGEN_DEBUG_VAR(MayLinearVectorize)\n    EIGEN_DEBUG_VAR(MaySliceVectorize)\n    EIGEN_DEBUG_VAR(Traversal)\n    EIGEN_DEBUG_VAR(UnrollingLimit)\n    EIGEN_DEBUG_VAR(Unrolling)\n    std::cerr << std::endl;\n  }\n#endif\n};\n\n/***************************************************************************\n* Part 2 : unrollers\n***************************************************************************/\n\n/*** no vectorization ***/\n\ntemplate<typename Func, typename Derived, int Start, int Length>\nstruct redux_novec_unroller\n{\n  enum {\n    HalfLength = Length/2\n  };\n\n  typedef typename Derived::Scalar Scalar;\n\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE Scalar run(const Derived &mat, const Func& func)\n  {\n    return func(redux_novec_unroller<Func, Derived, Start, HalfLength>::run(mat,func),\n                redux_novec_unroller<Func, Derived, Start+HalfLength, Length-HalfLength>::run(mat,func));\n  }\n};\n\ntemplate<typename Func, typename Derived, int Start>\nstruct redux_novec_unroller<Func, Derived, Start, 1>\n{\n  enum {\n    outer = Start / Derived::InnerSizeAtCompileTime,\n    inner = Start % Derived::InnerSizeAtCompileTime\n  };\n\n  typedef typename Derived::Scalar Scalar;\n\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE Scalar run(const Derived &mat, const Func&)\n  {\n    return mat.coeffByOuterInner(outer, inner);\n  }\n};\n\n// This is actually dead code and will never be called. It is required\n// to prevent false warnings regarding failed inlining though\n// for 0 length run() will never be called at all.\ntemplate<typename Func, typename Derived, int Start>\nstruct redux_novec_unroller<Func, Derived, Start, 0>\n{\n  typedef typename Derived::Scalar Scalar;\n  EIGEN_DEVICE_FUNC \n  static EIGEN_STRONG_INLINE Scalar run(const Derived&, const Func&) { return Scalar(); }\n};\n\n/*** vectorization ***/\n\ntemplate<typename Func, typename Derived, int Start, int Length>\nstruct redux_vec_unroller\n{\n  enum {\n    PacketSize = redux_traits<Func, Derived>::PacketSize,\n    HalfLength = Length/2\n  };\n\n  typedef typename Derived::Scalar Scalar;\n  typedef typename redux_traits<Func, Derived>::PacketType PacketScalar;\n\n  static EIGEN_STRONG_INLINE PacketScalar run(const Derived &mat, const Func& func)\n  {\n    return func.packetOp(\n            redux_vec_unroller<Func, Derived, Start, HalfLength>::run(mat,func),\n            redux_vec_unroller<Func, Derived, Start+HalfLength, Length-HalfLength>::run(mat,func) );\n  }\n};\n\ntemplate<typename Func, typename Derived, int Start>\nstruct redux_vec_unroller<Func, Derived, Start, 1>\n{\n  enum {\n    index = Start * redux_traits<Func, Derived>::PacketSize,\n    outer = index / int(Derived::InnerSizeAtCompileTime),\n    inner = index % int(Derived::InnerSizeAtCompileTime),\n    alignment = Derived::Alignment\n  };\n\n  typedef typename Derived::Scalar Scalar;\n  typedef typename redux_traits<Func, Derived>::PacketType PacketScalar;\n\n  static EIGEN_STRONG_INLINE PacketScalar run(const Derived &mat, const Func&)\n  {\n    return mat.template packetByOuterInner<alignment,PacketScalar>(outer, inner);\n  }\n};\n\n/***************************************************************************\n* Part 3 : implementation of all cases\n***************************************************************************/\n\ntemplate<typename Func, typename Derived,\n         int Traversal = redux_traits<Func, Derived>::Traversal,\n         int Unrolling = redux_traits<Func, Derived>::Unrolling\n>\nstruct redux_impl;\n\ntemplate<typename Func, typename Derived>\nstruct redux_impl<Func, Derived, DefaultTraversal, NoUnrolling>\n{\n  typedef typename Derived::Scalar Scalar;\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE Scalar run(const Derived &mat, const Func& func)\n  {\n    eigen_assert(mat.rows()>0 && mat.cols()>0 && \"you are using an empty matrix\");\n    Scalar res;\n    res = mat.coeffByOuterInner(0, 0);\n    for(Index i = 1; i < mat.innerSize(); ++i)\n      res = func(res, mat.coeffByOuterInner(0, i));\n    for(Index i = 1; i < mat.outerSize(); ++i)\n      for(Index j = 0; j < mat.innerSize(); ++j)\n        res = func(res, mat.coeffByOuterInner(i, j));\n    return res;\n  }\n};\n\ntemplate<typename Func, typename Derived>\nstruct redux_impl<Func,Derived, DefaultTraversal, CompleteUnrolling>\n  : public redux_novec_unroller<Func,Derived, 0, Derived::SizeAtCompileTime>\n{};\n\ntemplate<typename Func, typename Derived>\nstruct redux_impl<Func, Derived, LinearVectorizedTraversal, NoUnrolling>\n{\n  typedef typename Derived::Scalar Scalar;\n  typedef typename redux_traits<Func, Derived>::PacketType PacketScalar;\n\n  static Scalar run(const Derived &mat, const Func& func)\n  {\n    const Index size = mat.size();\n    \n    const Index packetSize = redux_traits<Func, Derived>::PacketSize;\n    const int packetAlignment = unpacket_traits<PacketScalar>::alignment;\n    enum {\n      alignment0 = (bool(Derived::Flags & DirectAccessBit) && bool(packet_traits<Scalar>::AlignedOnScalar)) ? int(packetAlignment) : int(Unaligned),\n      alignment = EIGEN_PLAIN_ENUM_MAX(alignment0, Derived::Alignment)\n    };\n    const Index alignedStart = internal::first_default_aligned(mat.nestedExpression());\n    const Index alignedSize2 = ((size-alignedStart)/(2*packetSize))*(2*packetSize);\n    const Index alignedSize = ((size-alignedStart)/(packetSize))*(packetSize);\n    const Index alignedEnd2 = alignedStart + alignedSize2;\n    const Index alignedEnd  = alignedStart + alignedSize;\n    Scalar res;\n    if(alignedSize)\n    {\n      PacketScalar packet_res0 = mat.template packet<alignment,PacketScalar>(alignedStart);\n      if(alignedSize>packetSize) // we have at least two packets to partly unroll the loop\n      {\n        PacketScalar packet_res1 = mat.template packet<alignment,PacketScalar>(alignedStart+packetSize);\n        for(Index index = alignedStart + 2*packetSize; index < alignedEnd2; index += 2*packetSize)\n        {\n          packet_res0 = func.packetOp(packet_res0, mat.template packet<alignment,PacketScalar>(index));\n          packet_res1 = func.packetOp(packet_res1, mat.template packet<alignment,PacketScalar>(index+packetSize));\n        }\n\n        packet_res0 = func.packetOp(packet_res0,packet_res1);\n        if(alignedEnd>alignedEnd2)\n          packet_res0 = func.packetOp(packet_res0, mat.template packet<alignment,PacketScalar>(alignedEnd2));\n      }\n      res = func.predux(packet_res0);\n\n      for(Index index = 0; index < alignedStart; ++index)\n        res = func(res,mat.coeff(index));\n\n      for(Index index = alignedEnd; index < size; ++index)\n        res = func(res,mat.coeff(index));\n    }\n    else // too small to vectorize anything.\n         // since this is dynamic-size hence inefficient anyway for such small sizes, don't try to optimize.\n    {\n      res = mat.coeff(0);\n      for(Index index = 1; index < size; ++index)\n        res = func(res,mat.coeff(index));\n    }\n\n    return res;\n  }\n};\n\n// NOTE: for SliceVectorizedTraversal we simply bypass unrolling\ntemplate<typename Func, typename Derived, int Unrolling>\nstruct redux_impl<Func, Derived, SliceVectorizedTraversal, Unrolling>\n{\n  typedef typename Derived::Scalar Scalar;\n  typedef typename redux_traits<Func, Derived>::PacketType PacketType;\n\n  EIGEN_DEVICE_FUNC static Scalar run(const Derived &mat, const Func& func)\n  {\n    eigen_assert(mat.rows()>0 && mat.cols()>0 && \"you are using an empty matrix\");\n    const Index innerSize = mat.innerSize();\n    const Index outerSize = mat.outerSize();\n    enum {\n      packetSize = redux_traits<Func, Derived>::PacketSize\n    };\n    const Index packetedInnerSize = ((innerSize)/packetSize)*packetSize;\n    Scalar res;\n    if(packetedInnerSize)\n    {\n      PacketType packet_res = mat.template packet<Unaligned,PacketType>(0,0);\n      for(Index j=0; j<outerSize; ++j)\n        for(Index i=(j==0?packetSize:0); i<packetedInnerSize; i+=Index(packetSize))\n          packet_res = func.packetOp(packet_res, mat.template packetByOuterInner<Unaligned,PacketType>(j,i));\n\n      res = func.predux(packet_res);\n      for(Index j=0; j<outerSize; ++j)\n        for(Index i=packetedInnerSize; i<innerSize; ++i)\n          res = func(res, mat.coeffByOuterInner(j,i));\n    }\n    else // too small to vectorize anything.\n         // since this is dynamic-size hence inefficient anyway for such small sizes, don't try to optimize.\n    {\n      res = redux_impl<Func, Derived, DefaultTraversal, NoUnrolling>::run(mat, func);\n    }\n\n    return res;\n  }\n};\n\ntemplate<typename Func, typename Derived>\nstruct redux_impl<Func, Derived, LinearVectorizedTraversal, CompleteUnrolling>\n{\n  typedef typename Derived::Scalar Scalar;\n\n  typedef typename redux_traits<Func, Derived>::PacketType PacketScalar;\n  enum {\n    PacketSize = redux_traits<Func, Derived>::PacketSize,\n    Size = Derived::SizeAtCompileTime,\n    VectorizedSize = (Size / PacketSize) * PacketSize\n  };\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Scalar run(const Derived &mat, const Func& func)\n  {\n    eigen_assert(mat.rows()>0 && mat.cols()>0 && \"you are using an empty matrix\");\n    if (VectorizedSize > 0) {\n      Scalar res = func.predux(redux_vec_unroller<Func, Derived, 0, Size / PacketSize>::run(mat,func));\n      if (VectorizedSize != Size)\n        res = func(res,redux_novec_unroller<Func, Derived, VectorizedSize, Size-VectorizedSize>::run(mat,func));\n      return res;\n    }\n    else {\n      return redux_novec_unroller<Func, Derived, 0, Size>::run(mat,func);\n    }\n  }\n};\n\n// evaluator adaptor\ntemplate<typename _XprType>\nclass redux_evaluator\n{\npublic:\n  typedef _XprType XprType;\n  EIGEN_DEVICE_FUNC explicit redux_evaluator(const XprType &xpr) : m_evaluator(xpr), m_xpr(xpr) {}\n  \n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename XprType::PacketScalar PacketScalar;\n  typedef typename XprType::PacketReturnType PacketReturnType;\n  \n  enum {\n    MaxRowsAtCompileTime = XprType::MaxRowsAtCompileTime,\n    MaxColsAtCompileTime = XprType::MaxColsAtCompileTime,\n    // TODO we should not remove DirectAccessBit and rather find an elegant way to query the alignment offset at runtime from the evaluator\n    Flags = evaluator<XprType>::Flags & ~DirectAccessBit,\n    IsRowMajor = XprType::IsRowMajor,\n    SizeAtCompileTime = XprType::SizeAtCompileTime,\n    InnerSizeAtCompileTime = XprType::InnerSizeAtCompileTime,\n    CoeffReadCost = evaluator<XprType>::CoeffReadCost,\n    Alignment = evaluator<XprType>::Alignment\n  };\n  \n  EIGEN_DEVICE_FUNC Index rows() const { return m_xpr.rows(); }\n  EIGEN_DEVICE_FUNC Index cols() const { return m_xpr.cols(); }\n  EIGEN_DEVICE_FUNC Index size() const { return m_xpr.size(); }\n  EIGEN_DEVICE_FUNC Index innerSize() const { return m_xpr.innerSize(); }\n  EIGEN_DEVICE_FUNC Index outerSize() const { return m_xpr.outerSize(); }\n\n  EIGEN_DEVICE_FUNC\n  CoeffReturnType coeff(Index row, Index col) const\n  { return m_evaluator.coeff(row, col); }\n\n  EIGEN_DEVICE_FUNC\n  CoeffReturnType coeff(Index index) const\n  { return m_evaluator.coeff(index); }\n\n  template<int LoadMode, typename PacketType>\n  PacketType packet(Index row, Index col) const\n  { return m_evaluator.template packet<LoadMode,PacketType>(row, col); }\n\n  template<int LoadMode, typename PacketType>\n  PacketType packet(Index index) const\n  { return m_evaluator.template packet<LoadMode,PacketType>(index); }\n  \n  EIGEN_DEVICE_FUNC\n  CoeffReturnType coeffByOuterInner(Index outer, Index inner) const\n  { return m_evaluator.coeff(IsRowMajor ? outer : inner, IsRowMajor ? inner : outer); }\n  \n  template<int LoadMode, typename PacketType>\n  PacketType packetByOuterInner(Index outer, Index inner) const\n  { return m_evaluator.template packet<LoadMode,PacketType>(IsRowMajor ? outer : inner, IsRowMajor ? inner : outer); }\n  \n  const XprType & nestedExpression() const { return m_xpr; }\n  \nprotected:\n  internal::evaluator<XprType> m_evaluator;\n  const XprType &m_xpr;\n};\n\n} // end namespace internal\n\n/***************************************************************************\n* Part 4 : public API\n***************************************************************************/\n\n\n/** \\returns the result of a full redux operation on the whole matrix or vector using \\a func\n  *\n  * The template parameter \\a BinaryOp is the type of the functor \\a func which must be\n  * an associative operator. Both current C++98 and C++11 functor styles are handled.\n  *\n  * \\sa DenseBase::sum(), DenseBase::minCoeff(), DenseBase::maxCoeff(), MatrixBase::colwise(), MatrixBase::rowwise()\n  */\ntemplate<typename Derived>\ntemplate<typename Func>\nEIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar\nDenseBase<Derived>::redux(const Func& func) const\n{\n  eigen_assert(this->rows()>0 && this->cols()>0 && \"you are using an empty matrix\");\n\n  typedef typename internal::redux_evaluator<Derived> ThisEvaluator;\n  ThisEvaluator thisEval(derived());\n  \n  return internal::redux_impl<Func, ThisEvaluator>::run(thisEval, func);\n}\n\n/** \\returns the minimum of all coefficients of \\c *this.\n  * \\warning the result is undefined if \\c *this contains NaN.\n  */\ntemplate<typename Derived>\nEIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar\nDenseBase<Derived>::minCoeff() const\n{\n  return derived().redux(Eigen::internal::scalar_min_op<Scalar,Scalar>());\n}\n\n/** \\returns the maximum of all coefficients of \\c *this.\n  * \\warning the result is undefined if \\c *this contains NaN.\n  */\ntemplate<typename Derived>\nEIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar\nDenseBase<Derived>::maxCoeff() const\n{\n  return derived().redux(Eigen::internal::scalar_max_op<Scalar,Scalar>());\n}\n\n/** \\returns the sum of all coefficients of \\c *this\n  *\n  * If \\c *this is empty, then the value 0 is returned.\n  *\n  * \\sa trace(), prod(), mean()\n  */\ntemplate<typename Derived>\nEIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar\nDenseBase<Derived>::sum() const\n{\n  if(SizeAtCompileTime==0 || (SizeAtCompileTime==Dynamic && size()==0))\n    return Scalar(0);\n  return derived().redux(Eigen::internal::scalar_sum_op<Scalar,Scalar>());\n}\n\n/** \\returns the mean of all coefficients of *this\n*\n* \\sa trace(), prod(), sum()\n*/\ntemplate<typename Derived>\nEIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar\nDenseBase<Derived>::mean() const\n{\n#ifdef __INTEL_COMPILER\n  #pragma warning push\n  #pragma warning ( disable : 2259 )\n#endif\n  return Scalar(derived().redux(Eigen::internal::scalar_sum_op<Scalar,Scalar>())) / Scalar(this->size());\n#ifdef __INTEL_COMPILER\n  #pragma warning pop\n#endif\n}\n\n/** \\returns the product of all coefficients of *this\n  *\n  * Example: \\include MatrixBase_prod.cpp\n  * Output: \\verbinclude MatrixBase_prod.out\n  *\n  * \\sa sum(), mean(), trace()\n  */\ntemplate<typename Derived>\nEIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar\nDenseBase<Derived>::prod() const\n{\n  if(SizeAtCompileTime==0 || (SizeAtCompileTime==Dynamic && size()==0))\n    return Scalar(1);\n  return derived().redux(Eigen::internal::scalar_product_op<Scalar>());\n}\n\n/** \\returns the trace of \\c *this, i.e. the sum of the coefficients on the main diagonal.\n  *\n  * \\c *this can be any matrix, not necessarily square.\n  *\n  * \\sa diagonal(), sum()\n  */\ntemplate<typename Derived>\nEIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar\nMatrixBase<Derived>::trace() const\n{\n  return derived().diagonal().sum();\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_REDUX_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/Ref.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_REF_H\n#define EIGEN_REF_H\n\nnamespace Eigen { \n\nnamespace internal {\n\ntemplate<typename _PlainObjectType, int _Options, typename _StrideType>\nstruct traits<Ref<_PlainObjectType, _Options, _StrideType> >\n  : public traits<Map<_PlainObjectType, _Options, _StrideType> >\n{\n  typedef _PlainObjectType PlainObjectType;\n  typedef _StrideType StrideType;\n  enum {\n    Options = _Options,\n    Flags = traits<Map<_PlainObjectType, _Options, _StrideType> >::Flags | NestByRefBit,\n    Alignment = traits<Map<_PlainObjectType, _Options, _StrideType> >::Alignment\n  };\n\n  template<typename Derived> struct match {\n    enum {\n      HasDirectAccess = internal::has_direct_access<Derived>::ret,\n      StorageOrderMatch = PlainObjectType::IsVectorAtCompileTime || Derived::IsVectorAtCompileTime || ((PlainObjectType::Flags&RowMajorBit)==(Derived::Flags&RowMajorBit)),\n      InnerStrideMatch = int(StrideType::InnerStrideAtCompileTime)==int(Dynamic)\n                      || int(StrideType::InnerStrideAtCompileTime)==int(Derived::InnerStrideAtCompileTime)\n                      || (int(StrideType::InnerStrideAtCompileTime)==0 && int(Derived::InnerStrideAtCompileTime)==1),\n      OuterStrideMatch = Derived::IsVectorAtCompileTime\n                      || int(StrideType::OuterStrideAtCompileTime)==int(Dynamic) || int(StrideType::OuterStrideAtCompileTime)==int(Derived::OuterStrideAtCompileTime),\n      // NOTE, this indirection of evaluator<Derived>::Alignment is needed\n      // to workaround a very strange bug in MSVC related to the instantiation\n      // of has_*ary_operator in evaluator<CwiseNullaryOp>.\n      // This line is surprisingly very sensitive. For instance, simply adding parenthesis\n      // as \"DerivedAlignment = (int(evaluator<Derived>::Alignment)),\" will make MSVC fail...\n      DerivedAlignment = int(evaluator<Derived>::Alignment),\n      AlignmentMatch = (int(traits<PlainObjectType>::Alignment)==int(Unaligned)) || (DerivedAlignment >= int(Alignment)), // FIXME the first condition is not very clear, it should be replaced by the required alignment\n      ScalarTypeMatch = internal::is_same<typename PlainObjectType::Scalar, typename Derived::Scalar>::value,\n      MatchAtCompileTime = HasDirectAccess && StorageOrderMatch && InnerStrideMatch && OuterStrideMatch && AlignmentMatch && ScalarTypeMatch\n    };\n    typedef typename internal::conditional<MatchAtCompileTime,internal::true_type,internal::false_type>::type type;\n  };\n  \n};\n\ntemplate<typename Derived>\nstruct traits<RefBase<Derived> > : public traits<Derived> {};\n\n}\n\ntemplate<typename Derived> class RefBase\n : public MapBase<Derived>\n{\n  typedef typename internal::traits<Derived>::PlainObjectType PlainObjectType;\n  typedef typename internal::traits<Derived>::StrideType StrideType;\n\npublic:\n\n  typedef MapBase<Derived> Base;\n  EIGEN_DENSE_PUBLIC_INTERFACE(RefBase)\n\n  EIGEN_DEVICE_FUNC inline Index innerStride() const\n  {\n    return StrideType::InnerStrideAtCompileTime != 0 ? m_stride.inner() : 1;\n  }\n\n  EIGEN_DEVICE_FUNC inline Index outerStride() const\n  {\n    return StrideType::OuterStrideAtCompileTime != 0 ? m_stride.outer()\n         : IsVectorAtCompileTime ? this->size()\n         : int(Flags)&RowMajorBit ? this->cols()\n         : this->rows();\n  }\n\n  EIGEN_DEVICE_FUNC RefBase()\n    : Base(0,RowsAtCompileTime==Dynamic?0:RowsAtCompileTime,ColsAtCompileTime==Dynamic?0:ColsAtCompileTime),\n      // Stride<> does not allow default ctor for Dynamic strides, so let' initialize it with dummy values:\n      m_stride(StrideType::OuterStrideAtCompileTime==Dynamic?0:StrideType::OuterStrideAtCompileTime,\n               StrideType::InnerStrideAtCompileTime==Dynamic?0:StrideType::InnerStrideAtCompileTime)\n  {}\n  \n  EIGEN_INHERIT_ASSIGNMENT_OPERATORS(RefBase)\n\nprotected:\n\n  typedef Stride<StrideType::OuterStrideAtCompileTime,StrideType::InnerStrideAtCompileTime> StrideBase;\n\n  template<typename Expression>\n  EIGEN_DEVICE_FUNC void construct(Expression& expr)\n  {\n    EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(PlainObjectType,Expression);\n\n    if(PlainObjectType::RowsAtCompileTime==1)\n    {\n      eigen_assert(expr.rows()==1 || expr.cols()==1);\n      ::new (static_cast<Base*>(this)) Base(expr.data(), 1, expr.size());\n    }\n    else if(PlainObjectType::ColsAtCompileTime==1)\n    {\n      eigen_assert(expr.rows()==1 || expr.cols()==1);\n      ::new (static_cast<Base*>(this)) Base(expr.data(), expr.size(), 1);\n    }\n    else\n      ::new (static_cast<Base*>(this)) Base(expr.data(), expr.rows(), expr.cols());\n    \n    if(Expression::IsVectorAtCompileTime && (!PlainObjectType::IsVectorAtCompileTime) && ((Expression::Flags&RowMajorBit)!=(PlainObjectType::Flags&RowMajorBit)))\n      ::new (&m_stride) StrideBase(expr.innerStride(), StrideType::InnerStrideAtCompileTime==0?0:1);\n    else\n      ::new (&m_stride) StrideBase(StrideType::OuterStrideAtCompileTime==0?0:expr.outerStride(),\n                                   StrideType::InnerStrideAtCompileTime==0?0:expr.innerStride());    \n  }\n\n  StrideBase m_stride;\n};\n\n/** \\class Ref\n  * \\ingroup Core_Module\n  *\n  * \\brief A matrix or vector expression mapping an existing expression\n  *\n  * \\tparam PlainObjectType the equivalent matrix type of the mapped data\n  * \\tparam Options specifies the pointer alignment in bytes. It can be: \\c #Aligned128, , \\c #Aligned64, \\c #Aligned32, \\c #Aligned16, \\c #Aligned8 or \\c #Unaligned.\n  *                 The default is \\c #Unaligned.\n  * \\tparam StrideType optionally specifies strides. By default, Ref implies a contiguous storage along the inner dimension (inner stride==1),\n  *                   but accepts a variable outer stride (leading dimension).\n  *                   This can be overridden by specifying strides.\n  *                   The type passed here must be a specialization of the Stride template, see examples below.\n  *\n  * This class provides a way to write non-template functions taking Eigen objects as parameters while limiting the number of copies.\n  * A Ref<> object can represent either a const expression or a l-value:\n  * \\code\n  * // in-out argument:\n  * void foo1(Ref<VectorXf> x);\n  *\n  * // read-only const argument:\n  * void foo2(const Ref<const VectorXf>& x);\n  * \\endcode\n  *\n  * In the in-out case, the input argument must satisfy the constraints of the actual Ref<> type, otherwise a compilation issue will be triggered.\n  * By default, a Ref<VectorXf> can reference any dense vector expression of float having a contiguous memory layout.\n  * Likewise, a Ref<MatrixXf> can reference any column-major dense matrix expression of float whose column's elements are contiguously stored with\n  * the possibility to have a constant space in-between each column, i.e. the inner stride must be equal to 1, but the outer stride (or leading dimension)\n  * can be greater than the number of rows.\n  *\n  * In the const case, if the input expression does not match the above requirement, then it is evaluated into a temporary before being passed to the function.\n  * Here are some examples:\n  * \\code\n  * MatrixXf A;\n  * VectorXf a;\n  * foo1(a.head());             // OK\n  * foo1(A.col());              // OK\n  * foo1(A.row());              // Compilation error because here innerstride!=1\n  * foo2(A.row());              // Compilation error because A.row() is a 1xN object while foo2 is expecting a Nx1 object\n  * foo2(A.row().transpose());  // The row is copied into a contiguous temporary\n  * foo2(2*a);                  // The expression is evaluated into a temporary\n  * foo2(A.col().segment(2,4)); // No temporary\n  * \\endcode\n  *\n  * The range of inputs that can be referenced without temporary can be enlarged using the last two template parameters.\n  * Here is an example accepting an innerstride!=1:\n  * \\code\n  * // in-out argument:\n  * void foo3(Ref<VectorXf,0,InnerStride<> > x);\n  * foo3(A.row());              // OK\n  * \\endcode\n  * The downside here is that the function foo3 might be significantly slower than foo1 because it won't be able to exploit vectorization, and will involve more\n  * expensive address computations even if the input is contiguously stored in memory. To overcome this issue, one might propose to overload internally calling a\n  * template function, e.g.:\n  * \\code\n  * // in the .h:\n  * void foo(const Ref<MatrixXf>& A);\n  * void foo(const Ref<MatrixXf,0,Stride<> >& A);\n  *\n  * // in the .cpp:\n  * template<typename TypeOfA> void foo_impl(const TypeOfA& A) {\n  *     ... // crazy code goes here\n  * }\n  * void foo(const Ref<MatrixXf>& A) { foo_impl(A); }\n  * void foo(const Ref<MatrixXf,0,Stride<> >& A) { foo_impl(A); }\n  * \\endcode\n  *\n  *\n  * \\sa PlainObjectBase::Map(), \\ref TopicStorageOrders\n  */\ntemplate<typename PlainObjectType, int Options, typename StrideType> class Ref\n  : public RefBase<Ref<PlainObjectType, Options, StrideType> >\n{\n  private:\n    typedef internal::traits<Ref> Traits;\n    template<typename Derived>\n    EIGEN_DEVICE_FUNC inline Ref(const PlainObjectBase<Derived>& expr,\n                                 typename internal::enable_if<bool(Traits::template match<Derived>::MatchAtCompileTime),Derived>::type* = 0);\n  public:\n\n    typedef RefBase<Ref> Base;\n    EIGEN_DENSE_PUBLIC_INTERFACE(Ref)\n\n\n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    template<typename Derived>\n    EIGEN_DEVICE_FUNC inline Ref(PlainObjectBase<Derived>& expr,\n                                 typename internal::enable_if<bool(Traits::template match<Derived>::MatchAtCompileTime),Derived>::type* = 0)\n    {\n      EIGEN_STATIC_ASSERT(bool(Traits::template match<Derived>::MatchAtCompileTime), STORAGE_LAYOUT_DOES_NOT_MATCH);\n      Base::construct(expr.derived());\n    }\n    template<typename Derived>\n    EIGEN_DEVICE_FUNC inline Ref(const DenseBase<Derived>& expr,\n                                 typename internal::enable_if<bool(Traits::template match<Derived>::MatchAtCompileTime),Derived>::type* = 0)\n    #else\n    /** Implicit constructor from any dense expression */\n    template<typename Derived>\n    inline Ref(DenseBase<Derived>& expr)\n    #endif\n    {\n      EIGEN_STATIC_ASSERT(bool(internal::is_lvalue<Derived>::value), THIS_EXPRESSION_IS_NOT_A_LVALUE__IT_IS_READ_ONLY);\n      EIGEN_STATIC_ASSERT(bool(Traits::template match<Derived>::MatchAtCompileTime), STORAGE_LAYOUT_DOES_NOT_MATCH);\n      EIGEN_STATIC_ASSERT(!Derived::IsPlainObjectBase,THIS_EXPRESSION_IS_NOT_A_LVALUE__IT_IS_READ_ONLY);\n      Base::construct(expr.const_cast_derived());\n    }\n\n    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Ref)\n\n};\n\n// this is the const ref version\ntemplate<typename TPlainObjectType, int Options, typename StrideType> class Ref<const TPlainObjectType, Options, StrideType>\n  : public RefBase<Ref<const TPlainObjectType, Options, StrideType> >\n{\n    typedef internal::traits<Ref> Traits;\n  public:\n\n    typedef RefBase<Ref> Base;\n    EIGEN_DENSE_PUBLIC_INTERFACE(Ref)\n\n    template<typename Derived>\n    EIGEN_DEVICE_FUNC inline Ref(const DenseBase<Derived>& expr,\n                                 typename internal::enable_if<bool(Traits::template match<Derived>::ScalarTypeMatch),Derived>::type* = 0)\n    {\n//      std::cout << match_helper<Derived>::HasDirectAccess << \",\" << match_helper<Derived>::OuterStrideMatch << \",\" << match_helper<Derived>::InnerStrideMatch << \"\\n\";\n//      std::cout << int(StrideType::OuterStrideAtCompileTime) << \" - \" << int(Derived::OuterStrideAtCompileTime) << \"\\n\";\n//      std::cout << int(StrideType::InnerStrideAtCompileTime) << \" - \" << int(Derived::InnerStrideAtCompileTime) << \"\\n\";\n      construct(expr.derived(), typename Traits::template match<Derived>::type());\n    }\n\n    EIGEN_DEVICE_FUNC inline Ref(const Ref& other) : Base(other) {\n      // copy constructor shall not copy the m_object, to avoid unnecessary malloc and copy\n    }\n\n    template<typename OtherRef>\n    EIGEN_DEVICE_FUNC inline Ref(const RefBase<OtherRef>& other) {\n      construct(other.derived(), typename Traits::template match<OtherRef>::type());\n    }\n\n  protected:\n\n    template<typename Expression>\n    EIGEN_DEVICE_FUNC void construct(const Expression& expr,internal::true_type)\n    {\n      Base::construct(expr);\n    }\n\n    template<typename Expression>\n    EIGEN_DEVICE_FUNC void construct(const Expression& expr, internal::false_type)\n    {\n      internal::call_assignment_no_alias(m_object,expr,internal::assign_op<Scalar,Scalar>());\n      Base::construct(m_object);\n    }\n\n  protected:\n    TPlainObjectType m_object;\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_REF_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/Replicate.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_REPLICATE_H\n#define EIGEN_REPLICATE_H\n\nnamespace Eigen { \n\nnamespace internal {\ntemplate<typename MatrixType,int RowFactor,int ColFactor>\nstruct traits<Replicate<MatrixType,RowFactor,ColFactor> >\n : traits<MatrixType>\n{\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename traits<MatrixType>::StorageKind StorageKind;\n  typedef typename traits<MatrixType>::XprKind XprKind;\n  typedef typename ref_selector<MatrixType>::type MatrixTypeNested;\n  typedef typename remove_reference<MatrixTypeNested>::type _MatrixTypeNested;\n  enum {\n    RowsAtCompileTime = RowFactor==Dynamic || int(MatrixType::RowsAtCompileTime)==Dynamic\n                      ? Dynamic\n                      : RowFactor * MatrixType::RowsAtCompileTime,\n    ColsAtCompileTime = ColFactor==Dynamic || int(MatrixType::ColsAtCompileTime)==Dynamic\n                      ? Dynamic\n                      : ColFactor * MatrixType::ColsAtCompileTime,\n   //FIXME we don't propagate the max sizes !!!\n    MaxRowsAtCompileTime = RowsAtCompileTime,\n    MaxColsAtCompileTime = ColsAtCompileTime,\n    IsRowMajor = MaxRowsAtCompileTime==1 && MaxColsAtCompileTime!=1 ? 1\n               : MaxColsAtCompileTime==1 && MaxRowsAtCompileTime!=1 ? 0\n               : (MatrixType::Flags & RowMajorBit) ? 1 : 0,\n    \n    // FIXME enable DirectAccess with negative strides?\n    Flags = IsRowMajor ? RowMajorBit : 0\n  };\n};\n}\n\n/**\n  * \\class Replicate\n  * \\ingroup Core_Module\n  *\n  * \\brief Expression of the multiple replication of a matrix or vector\n  *\n  * \\tparam MatrixType the type of the object we are replicating\n  * \\tparam RowFactor number of repetitions at compile time along the vertical direction, can be Dynamic.\n  * \\tparam ColFactor number of repetitions at compile time along the horizontal direction, can be Dynamic.\n  *\n  * This class represents an expression of the multiple replication of a matrix or vector.\n  * It is the return type of DenseBase::replicate() and most of the time\n  * this is the only way it is used.\n  *\n  * \\sa DenseBase::replicate()\n  */\ntemplate<typename MatrixType,int RowFactor,int ColFactor> class Replicate\n  : public internal::dense_xpr_base< Replicate<MatrixType,RowFactor,ColFactor> >::type\n{\n    typedef typename internal::traits<Replicate>::MatrixTypeNested MatrixTypeNested;\n    typedef typename internal::traits<Replicate>::_MatrixTypeNested _MatrixTypeNested;\n  public:\n\n    typedef typename internal::dense_xpr_base<Replicate>::type Base;\n    EIGEN_DENSE_PUBLIC_INTERFACE(Replicate)\n    typedef typename internal::remove_all<MatrixType>::type NestedExpression;\n\n    template<typename OriginalMatrixType>\n    EIGEN_DEVICE_FUNC\n    inline explicit Replicate(const OriginalMatrixType& matrix)\n      : m_matrix(matrix), m_rowFactor(RowFactor), m_colFactor(ColFactor)\n    {\n      EIGEN_STATIC_ASSERT((internal::is_same<typename internal::remove_const<MatrixType>::type,OriginalMatrixType>::value),\n                          THE_MATRIX_OR_EXPRESSION_THAT_YOU_PASSED_DOES_NOT_HAVE_THE_EXPECTED_TYPE)\n      eigen_assert(RowFactor!=Dynamic && ColFactor!=Dynamic);\n    }\n\n    template<typename OriginalMatrixType>\n    EIGEN_DEVICE_FUNC\n    inline Replicate(const OriginalMatrixType& matrix, Index rowFactor, Index colFactor)\n      : m_matrix(matrix), m_rowFactor(rowFactor), m_colFactor(colFactor)\n    {\n      EIGEN_STATIC_ASSERT((internal::is_same<typename internal::remove_const<MatrixType>::type,OriginalMatrixType>::value),\n                          THE_MATRIX_OR_EXPRESSION_THAT_YOU_PASSED_DOES_NOT_HAVE_THE_EXPECTED_TYPE)\n    }\n\n    EIGEN_DEVICE_FUNC\n    inline Index rows() const { return m_matrix.rows() * m_rowFactor.value(); }\n    EIGEN_DEVICE_FUNC\n    inline Index cols() const { return m_matrix.cols() * m_colFactor.value(); }\n\n    EIGEN_DEVICE_FUNC\n    const _MatrixTypeNested& nestedExpression() const\n    { \n      return m_matrix; \n    }\n\n  protected:\n    MatrixTypeNested m_matrix;\n    const internal::variable_if_dynamic<Index, RowFactor> m_rowFactor;\n    const internal::variable_if_dynamic<Index, ColFactor> m_colFactor;\n};\n\n/**\n  * \\return an expression of the replication of \\c *this\n  *\n  * Example: \\include MatrixBase_replicate.cpp\n  * Output: \\verbinclude MatrixBase_replicate.out\n  *\n  * \\sa VectorwiseOp::replicate(), DenseBase::replicate(Index,Index), class Replicate\n  */\ntemplate<typename Derived>\ntemplate<int RowFactor, int ColFactor>\nconst Replicate<Derived,RowFactor,ColFactor>\nDenseBase<Derived>::replicate() const\n{\n  return Replicate<Derived,RowFactor,ColFactor>(derived());\n}\n\n/**\n  * \\return an expression of the replication of each column (or row) of \\c *this\n  *\n  * Example: \\include DirectionWise_replicate_int.cpp\n  * Output: \\verbinclude DirectionWise_replicate_int.out\n  *\n  * \\sa VectorwiseOp::replicate(), DenseBase::replicate(), class Replicate\n  */\ntemplate<typename ExpressionType, int Direction>\nconst typename VectorwiseOp<ExpressionType,Direction>::ReplicateReturnType\nVectorwiseOp<ExpressionType,Direction>::replicate(Index factor) const\n{\n  return typename VectorwiseOp<ExpressionType,Direction>::ReplicateReturnType\n          (_expression(),Direction==Vertical?factor:1,Direction==Horizontal?factor:1);\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_REPLICATE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/ReturnByValue.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_RETURNBYVALUE_H\n#define EIGEN_RETURNBYVALUE_H\n\nnamespace Eigen {\n\nnamespace internal {\n\ntemplate<typename Derived>\nstruct traits<ReturnByValue<Derived> >\n  : public traits<typename traits<Derived>::ReturnType>\n{\n  enum {\n    // We're disabling the DirectAccess because e.g. the constructor of\n    // the Block-with-DirectAccess expression requires to have a coeffRef method.\n    // Also, we don't want to have to implement the stride stuff.\n    Flags = (traits<typename traits<Derived>::ReturnType>::Flags\n             | EvalBeforeNestingBit) & ~DirectAccessBit\n  };\n};\n\n/* The ReturnByValue object doesn't even have a coeff() method.\n * So the only way that nesting it in an expression can work, is by evaluating it into a plain matrix.\n * So internal::nested always gives the plain return matrix type.\n *\n * FIXME: I don't understand why we need this specialization: isn't this taken care of by the EvalBeforeNestingBit ??\n * Answer: EvalBeforeNestingBit should be deprecated since we have the evaluators\n */\ntemplate<typename Derived,int n,typename PlainObject>\nstruct nested_eval<ReturnByValue<Derived>, n, PlainObject>\n{\n  typedef typename traits<Derived>::ReturnType type;\n};\n\n} // end namespace internal\n\n/** \\class ReturnByValue\n  * \\ingroup Core_Module\n  *\n  */\ntemplate<typename Derived> class ReturnByValue\n  : public internal::dense_xpr_base< ReturnByValue<Derived> >::type, internal::no_assignment_operator\n{\n  public:\n    typedef typename internal::traits<Derived>::ReturnType ReturnType;\n\n    typedef typename internal::dense_xpr_base<ReturnByValue>::type Base;\n    EIGEN_DENSE_PUBLIC_INTERFACE(ReturnByValue)\n\n    template<typename Dest>\n    EIGEN_DEVICE_FUNC\n    inline void evalTo(Dest& dst) const\n    { static_cast<const Derived*>(this)->evalTo(dst); }\n    EIGEN_DEVICE_FUNC inline Index rows() const { return static_cast<const Derived*>(this)->rows(); }\n    EIGEN_DEVICE_FUNC inline Index cols() const { return static_cast<const Derived*>(this)->cols(); }\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\n#define Unusable YOU_ARE_TRYING_TO_ACCESS_A_SINGLE_COEFFICIENT_IN_A_SPECIAL_EXPRESSION_WHERE_THAT_IS_NOT_ALLOWED_BECAUSE_THAT_WOULD_BE_INEFFICIENT\n    class Unusable{\n      Unusable(const Unusable&) {}\n      Unusable& operator=(const Unusable&) {return *this;}\n    };\n    const Unusable& coeff(Index) const { return *reinterpret_cast<const Unusable*>(this); }\n    const Unusable& coeff(Index,Index) const { return *reinterpret_cast<const Unusable*>(this); }\n    Unusable& coeffRef(Index) { return *reinterpret_cast<Unusable*>(this); }\n    Unusable& coeffRef(Index,Index) { return *reinterpret_cast<Unusable*>(this); }\n#undef Unusable\n#endif\n};\n\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\nDerived& DenseBase<Derived>::operator=(const ReturnByValue<OtherDerived>& other)\n{\n  other.evalTo(derived());\n  return derived();\n}\n\nnamespace internal {\n\n// Expression is evaluated in a temporary; default implementation of Assignment is bypassed so that\n// when a ReturnByValue expression is assigned, the evaluator is not constructed.\n// TODO: Finalize port to new regime; ReturnByValue should not exist in the expression world\n  \ntemplate<typename Derived>\nstruct evaluator<ReturnByValue<Derived> >\n  : public evaluator<typename internal::traits<Derived>::ReturnType>\n{\n  typedef ReturnByValue<Derived> XprType;\n  typedef typename internal::traits<Derived>::ReturnType PlainObject;\n  typedef evaluator<PlainObject> Base;\n  \n  EIGEN_DEVICE_FUNC explicit evaluator(const XprType& xpr)\n    : m_result(xpr.rows(), xpr.cols())\n  {\n    ::new (static_cast<Base*>(this)) Base(m_result);\n    xpr.evalTo(m_result);\n  }\n\nprotected:\n  PlainObject m_result;\n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_RETURNBYVALUE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/Reverse.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2009 Ricard Marxer <email@ricardmarxer.com>\n// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_REVERSE_H\n#define EIGEN_REVERSE_H\n\nnamespace Eigen { \n\nnamespace internal {\n\ntemplate<typename MatrixType, int Direction>\nstruct traits<Reverse<MatrixType, Direction> >\n : traits<MatrixType>\n{\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename traits<MatrixType>::StorageKind StorageKind;\n  typedef typename traits<MatrixType>::XprKind XprKind;\n  typedef typename ref_selector<MatrixType>::type MatrixTypeNested;\n  typedef typename remove_reference<MatrixTypeNested>::type _MatrixTypeNested;\n  enum {\n    RowsAtCompileTime = MatrixType::RowsAtCompileTime,\n    ColsAtCompileTime = MatrixType::ColsAtCompileTime,\n    MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,\n    MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,\n    Flags = _MatrixTypeNested::Flags & (RowMajorBit | LvalueBit)\n  };\n};\n\ntemplate<typename PacketType, bool ReversePacket> struct reverse_packet_cond\n{\n  static inline PacketType run(const PacketType& x) { return preverse(x); }\n};\n\ntemplate<typename PacketType> struct reverse_packet_cond<PacketType,false>\n{\n  static inline PacketType run(const PacketType& x) { return x; }\n};\n\n} // end namespace internal \n\n/** \\class Reverse\n  * \\ingroup Core_Module\n  *\n  * \\brief Expression of the reverse of a vector or matrix\n  *\n  * \\tparam MatrixType the type of the object of which we are taking the reverse\n  * \\tparam Direction defines the direction of the reverse operation, can be Vertical, Horizontal, or BothDirections\n  *\n  * This class represents an expression of the reverse of a vector.\n  * It is the return type of MatrixBase::reverse() and VectorwiseOp::reverse()\n  * and most of the time this is the only way it is used.\n  *\n  * \\sa MatrixBase::reverse(), VectorwiseOp::reverse()\n  */\ntemplate<typename MatrixType, int Direction> class Reverse\n  : public internal::dense_xpr_base< Reverse<MatrixType, Direction> >::type\n{\n  public:\n\n    typedef typename internal::dense_xpr_base<Reverse>::type Base;\n    EIGEN_DENSE_PUBLIC_INTERFACE(Reverse)\n    typedef typename internal::remove_all<MatrixType>::type NestedExpression;\n    using Base::IsRowMajor;\n\n  protected:\n    enum {\n      PacketSize = internal::packet_traits<Scalar>::size,\n      IsColMajor = !IsRowMajor,\n      ReverseRow = (Direction == Vertical)   || (Direction == BothDirections),\n      ReverseCol = (Direction == Horizontal) || (Direction == BothDirections),\n      OffsetRow  = ReverseRow && IsColMajor ? PacketSize : 1,\n      OffsetCol  = ReverseCol && IsRowMajor ? PacketSize : 1,\n      ReversePacket = (Direction == BothDirections)\n                    || ((Direction == Vertical)   && IsColMajor)\n                    || ((Direction == Horizontal) && IsRowMajor)\n    };\n    typedef internal::reverse_packet_cond<PacketScalar,ReversePacket> reverse_packet;\n  public:\n\n    EIGEN_DEVICE_FUNC explicit inline Reverse(const MatrixType& matrix) : m_matrix(matrix) { }\n\n    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Reverse)\n\n    EIGEN_DEVICE_FUNC inline Index rows() const { return m_matrix.rows(); }\n    EIGEN_DEVICE_FUNC inline Index cols() const { return m_matrix.cols(); }\n\n    EIGEN_DEVICE_FUNC inline Index innerStride() const\n    {\n      return -m_matrix.innerStride();\n    }\n\n    EIGEN_DEVICE_FUNC const typename internal::remove_all<typename MatrixType::Nested>::type&\n    nestedExpression() const \n    {\n      return m_matrix;\n    }\n\n  protected:\n    typename MatrixType::Nested m_matrix;\n};\n\n/** \\returns an expression of the reverse of *this.\n  *\n  * Example: \\include MatrixBase_reverse.cpp\n  * Output: \\verbinclude MatrixBase_reverse.out\n  *\n  */\ntemplate<typename Derived>\ninline typename DenseBase<Derived>::ReverseReturnType\nDenseBase<Derived>::reverse()\n{\n  return ReverseReturnType(derived());\n}\n\n\n//reverse const overload moved DenseBase.h due to a CUDA compiler bug\n\n/** This is the \"in place\" version of reverse: it reverses \\c *this.\n  *\n  * In most cases it is probably better to simply use the reversed expression\n  * of a matrix. However, when reversing the matrix data itself is really needed,\n  * then this \"in-place\" version is probably the right choice because it provides\n  * the following additional benefits:\n  *  - less error prone: doing the same operation with .reverse() requires special care:\n  *    \\code m = m.reverse().eval(); \\endcode\n  *  - this API enables reverse operations without the need for a temporary\n  *  - it allows future optimizations (cache friendliness, etc.)\n  *\n  * \\sa VectorwiseOp::reverseInPlace(), reverse() */\ntemplate<typename Derived>\ninline void DenseBase<Derived>::reverseInPlace()\n{\n  if(cols()>rows())\n  {\n    Index half = cols()/2;\n    leftCols(half).swap(rightCols(half).reverse());\n    if((cols()%2)==1)\n    {\n      Index half2 = rows()/2;\n      col(half).head(half2).swap(col(half).tail(half2).reverse());\n    }\n  }\n  else\n  {\n    Index half = rows()/2;\n    topRows(half).swap(bottomRows(half).reverse());\n    if((rows()%2)==1)\n    {\n      Index half2 = cols()/2;\n      row(half).head(half2).swap(row(half).tail(half2).reverse());\n    }\n  }\n}\n\nnamespace internal {\n  \ntemplate<int Direction>\nstruct vectorwise_reverse_inplace_impl;\n\ntemplate<>\nstruct vectorwise_reverse_inplace_impl<Vertical>\n{\n  template<typename ExpressionType>\n  static void run(ExpressionType &xpr)\n  {\n    Index half = xpr.rows()/2;\n    xpr.topRows(half).swap(xpr.bottomRows(half).colwise().reverse());\n  }\n};\n\ntemplate<>\nstruct vectorwise_reverse_inplace_impl<Horizontal>\n{\n  template<typename ExpressionType>\n  static void run(ExpressionType &xpr)\n  {\n    Index half = xpr.cols()/2;\n    xpr.leftCols(half).swap(xpr.rightCols(half).rowwise().reverse());\n  }\n};\n\n} // end namespace internal\n\n/** This is the \"in place\" version of VectorwiseOp::reverse: it reverses each column or row of \\c *this.\n  *\n  * In most cases it is probably better to simply use the reversed expression\n  * of a matrix. However, when reversing the matrix data itself is really needed,\n  * then this \"in-place\" version is probably the right choice because it provides\n  * the following additional benefits:\n  *  - less error prone: doing the same operation with .reverse() requires special care:\n  *    \\code m = m.reverse().eval(); \\endcode\n  *  - this API enables reverse operations without the need for a temporary\n  *\n  * \\sa DenseBase::reverseInPlace(), reverse() */\ntemplate<typename ExpressionType, int Direction>\nvoid VectorwiseOp<ExpressionType,Direction>::reverseInPlace()\n{\n  internal::vectorwise_reverse_inplace_impl<Direction>::run(_expression().const_cast_derived());\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_REVERSE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/Select.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SELECT_H\n#define EIGEN_SELECT_H\n\nnamespace Eigen { \n\n/** \\class Select\n  * \\ingroup Core_Module\n  *\n  * \\brief Expression of a coefficient wise version of the C++ ternary operator ?:\n  *\n  * \\param ConditionMatrixType the type of the \\em condition expression which must be a boolean matrix\n  * \\param ThenMatrixType the type of the \\em then expression\n  * \\param ElseMatrixType the type of the \\em else expression\n  *\n  * This class represents an expression of a coefficient wise version of the C++ ternary operator ?:.\n  * It is the return type of DenseBase::select() and most of the time this is the only way it is used.\n  *\n  * \\sa DenseBase::select(const DenseBase<ThenDerived>&, const DenseBase<ElseDerived>&) const\n  */\n\nnamespace internal {\ntemplate<typename ConditionMatrixType, typename ThenMatrixType, typename ElseMatrixType>\nstruct traits<Select<ConditionMatrixType, ThenMatrixType, ElseMatrixType> >\n : traits<ThenMatrixType>\n{\n  typedef typename traits<ThenMatrixType>::Scalar Scalar;\n  typedef Dense StorageKind;\n  typedef typename traits<ThenMatrixType>::XprKind XprKind;\n  typedef typename ConditionMatrixType::Nested ConditionMatrixNested;\n  typedef typename ThenMatrixType::Nested ThenMatrixNested;\n  typedef typename ElseMatrixType::Nested ElseMatrixNested;\n  enum {\n    RowsAtCompileTime = ConditionMatrixType::RowsAtCompileTime,\n    ColsAtCompileTime = ConditionMatrixType::ColsAtCompileTime,\n    MaxRowsAtCompileTime = ConditionMatrixType::MaxRowsAtCompileTime,\n    MaxColsAtCompileTime = ConditionMatrixType::MaxColsAtCompileTime,\n    Flags = (unsigned int)ThenMatrixType::Flags & ElseMatrixType::Flags & RowMajorBit\n  };\n};\n}\n\ntemplate<typename ConditionMatrixType, typename ThenMatrixType, typename ElseMatrixType>\nclass Select : public internal::dense_xpr_base< Select<ConditionMatrixType, ThenMatrixType, ElseMatrixType> >::type,\n               internal::no_assignment_operator\n{\n  public:\n\n    typedef typename internal::dense_xpr_base<Select>::type Base;\n    EIGEN_DENSE_PUBLIC_INTERFACE(Select)\n\n    inline EIGEN_DEVICE_FUNC\n    Select(const ConditionMatrixType& a_conditionMatrix,\n           const ThenMatrixType& a_thenMatrix,\n           const ElseMatrixType& a_elseMatrix)\n      : m_condition(a_conditionMatrix), m_then(a_thenMatrix), m_else(a_elseMatrix)\n    {\n      eigen_assert(m_condition.rows() == m_then.rows() && m_condition.rows() == m_else.rows());\n      eigen_assert(m_condition.cols() == m_then.cols() && m_condition.cols() == m_else.cols());\n    }\n\n    inline EIGEN_DEVICE_FUNC Index rows() const { return m_condition.rows(); }\n    inline EIGEN_DEVICE_FUNC Index cols() const { return m_condition.cols(); }\n\n    inline EIGEN_DEVICE_FUNC\n    const Scalar coeff(Index i, Index j) const\n    {\n      if (m_condition.coeff(i,j))\n        return m_then.coeff(i,j);\n      else\n        return m_else.coeff(i,j);\n    }\n\n    inline EIGEN_DEVICE_FUNC\n    const Scalar coeff(Index i) const\n    {\n      if (m_condition.coeff(i))\n        return m_then.coeff(i);\n      else\n        return m_else.coeff(i);\n    }\n\n    inline EIGEN_DEVICE_FUNC const ConditionMatrixType& conditionMatrix() const\n    {\n      return m_condition;\n    }\n\n    inline EIGEN_DEVICE_FUNC const ThenMatrixType& thenMatrix() const\n    {\n      return m_then;\n    }\n\n    inline EIGEN_DEVICE_FUNC const ElseMatrixType& elseMatrix() const\n    {\n      return m_else;\n    }\n\n  protected:\n    typename ConditionMatrixType::Nested m_condition;\n    typename ThenMatrixType::Nested m_then;\n    typename ElseMatrixType::Nested m_else;\n};\n\n\n/** \\returns a matrix where each coefficient (i,j) is equal to \\a thenMatrix(i,j)\n  * if \\c *this(i,j), and \\a elseMatrix(i,j) otherwise.\n  *\n  * Example: \\include MatrixBase_select.cpp\n  * Output: \\verbinclude MatrixBase_select.out\n  *\n  * \\sa class Select\n  */\ntemplate<typename Derived>\ntemplate<typename ThenDerived,typename ElseDerived>\ninline const Select<Derived,ThenDerived,ElseDerived>\nDenseBase<Derived>::select(const DenseBase<ThenDerived>& thenMatrix,\n                            const DenseBase<ElseDerived>& elseMatrix) const\n{\n  return Select<Derived,ThenDerived,ElseDerived>(derived(), thenMatrix.derived(), elseMatrix.derived());\n}\n\n/** Version of DenseBase::select(const DenseBase&, const DenseBase&) with\n  * the \\em else expression being a scalar value.\n  *\n  * \\sa DenseBase::select(const DenseBase<ThenDerived>&, const DenseBase<ElseDerived>&) const, class Select\n  */\ntemplate<typename Derived>\ntemplate<typename ThenDerived>\ninline const Select<Derived,ThenDerived, typename ThenDerived::ConstantReturnType>\nDenseBase<Derived>::select(const DenseBase<ThenDerived>& thenMatrix,\n                           const typename ThenDerived::Scalar& elseScalar) const\n{\n  return Select<Derived,ThenDerived,typename ThenDerived::ConstantReturnType>(\n    derived(), thenMatrix.derived(), ThenDerived::Constant(rows(),cols(),elseScalar));\n}\n\n/** Version of DenseBase::select(const DenseBase&, const DenseBase&) with\n  * the \\em then expression being a scalar value.\n  *\n  * \\sa DenseBase::select(const DenseBase<ThenDerived>&, const DenseBase<ElseDerived>&) const, class Select\n  */\ntemplate<typename Derived>\ntemplate<typename ElseDerived>\ninline const Select<Derived, typename ElseDerived::ConstantReturnType, ElseDerived >\nDenseBase<Derived>::select(const typename ElseDerived::Scalar& thenScalar,\n                           const DenseBase<ElseDerived>& elseMatrix) const\n{\n  return Select<Derived,typename ElseDerived::ConstantReturnType,ElseDerived>(\n    derived(), ElseDerived::Constant(rows(),cols(),thenScalar), elseMatrix.derived());\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_SELECT_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/SelfAdjointView.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SELFADJOINTMATRIX_H\n#define EIGEN_SELFADJOINTMATRIX_H\n\nnamespace Eigen { \n\n/** \\class SelfAdjointView\n  * \\ingroup Core_Module\n  *\n  *\n  * \\brief Expression of a selfadjoint matrix from a triangular part of a dense matrix\n  *\n  * \\param MatrixType the type of the dense matrix storing the coefficients\n  * \\param TriangularPart can be either \\c #Lower or \\c #Upper\n  *\n  * This class is an expression of a sefladjoint matrix from a triangular part of a matrix\n  * with given dense storage of the coefficients. It is the return type of MatrixBase::selfadjointView()\n  * and most of the time this is the only way that it is used.\n  *\n  * \\sa class TriangularBase, MatrixBase::selfadjointView()\n  */\n\nnamespace internal {\ntemplate<typename MatrixType, unsigned int UpLo>\nstruct traits<SelfAdjointView<MatrixType, UpLo> > : traits<MatrixType>\n{\n  typedef typename ref_selector<MatrixType>::non_const_type MatrixTypeNested;\n  typedef typename remove_all<MatrixTypeNested>::type MatrixTypeNestedCleaned;\n  typedef MatrixType ExpressionType;\n  typedef typename MatrixType::PlainObject FullMatrixType;\n  enum {\n    Mode = UpLo | SelfAdjoint,\n    FlagsLvalueBit = is_lvalue<MatrixType>::value ? LvalueBit : 0,\n    Flags =  MatrixTypeNestedCleaned::Flags & (HereditaryBits|FlagsLvalueBit)\n           & (~(PacketAccessBit | DirectAccessBit | LinearAccessBit)) // FIXME these flags should be preserved\n  };\n};\n}\n\n\ntemplate<typename _MatrixType, unsigned int UpLo> class SelfAdjointView\n  : public TriangularBase<SelfAdjointView<_MatrixType, UpLo> >\n{\n  public:\n\n    typedef _MatrixType MatrixType;\n    typedef TriangularBase<SelfAdjointView> Base;\n    typedef typename internal::traits<SelfAdjointView>::MatrixTypeNested MatrixTypeNested;\n    typedef typename internal::traits<SelfAdjointView>::MatrixTypeNestedCleaned MatrixTypeNestedCleaned;\n    typedef MatrixTypeNestedCleaned NestedExpression;\n\n    /** \\brief The type of coefficients in this matrix */\n    typedef typename internal::traits<SelfAdjointView>::Scalar Scalar; \n    typedef typename MatrixType::StorageIndex StorageIndex;\n    typedef typename internal::remove_all<typename MatrixType::ConjugateReturnType>::type MatrixConjugateReturnType;\n\n    enum {\n      Mode = internal::traits<SelfAdjointView>::Mode,\n      Flags = internal::traits<SelfAdjointView>::Flags,\n      TransposeMode = ((Mode & Upper) ? Lower : 0) | ((Mode & Lower) ? Upper : 0)\n    };\n    typedef typename MatrixType::PlainObject PlainObject;\n\n    EIGEN_DEVICE_FUNC\n    explicit inline SelfAdjointView(MatrixType& matrix) : m_matrix(matrix)\n    {\n      EIGEN_STATIC_ASSERT(UpLo==Lower || UpLo==Upper,SELFADJOINTVIEW_ACCEPTS_UPPER_AND_LOWER_MODE_ONLY);\n    }\n\n    EIGEN_DEVICE_FUNC\n    inline Index rows() const { return m_matrix.rows(); }\n    EIGEN_DEVICE_FUNC\n    inline Index cols() const { return m_matrix.cols(); }\n    EIGEN_DEVICE_FUNC\n    inline Index outerStride() const { return m_matrix.outerStride(); }\n    EIGEN_DEVICE_FUNC\n    inline Index innerStride() const { return m_matrix.innerStride(); }\n\n    /** \\sa MatrixBase::coeff()\n      * \\warning the coordinates must fit into the referenced triangular part\n      */\n    EIGEN_DEVICE_FUNC\n    inline Scalar coeff(Index row, Index col) const\n    {\n      Base::check_coordinates_internal(row, col);\n      return m_matrix.coeff(row, col);\n    }\n\n    /** \\sa MatrixBase::coeffRef()\n      * \\warning the coordinates must fit into the referenced triangular part\n      */\n    EIGEN_DEVICE_FUNC\n    inline Scalar& coeffRef(Index row, Index col)\n    {\n      EIGEN_STATIC_ASSERT_LVALUE(SelfAdjointView);\n      Base::check_coordinates_internal(row, col);\n      return m_matrix.coeffRef(row, col);\n    }\n\n    /** \\internal */\n    EIGEN_DEVICE_FUNC\n    const MatrixTypeNestedCleaned& _expression() const { return m_matrix; }\n\n    EIGEN_DEVICE_FUNC\n    const MatrixTypeNestedCleaned& nestedExpression() const { return m_matrix; }\n    EIGEN_DEVICE_FUNC\n    MatrixTypeNestedCleaned& nestedExpression() { return m_matrix; }\n\n    /** Efficient triangular matrix times vector/matrix product */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    const Product<SelfAdjointView,OtherDerived>\n    operator*(const MatrixBase<OtherDerived>& rhs) const\n    {\n      return Product<SelfAdjointView,OtherDerived>(*this, rhs.derived());\n    }\n\n    /** Efficient vector/matrix times triangular matrix product */\n    template<typename OtherDerived> friend\n    EIGEN_DEVICE_FUNC\n    const Product<OtherDerived,SelfAdjointView>\n    operator*(const MatrixBase<OtherDerived>& lhs, const SelfAdjointView& rhs)\n    {\n      return Product<OtherDerived,SelfAdjointView>(lhs.derived(),rhs);\n    }\n    \n    friend EIGEN_DEVICE_FUNC\n    const SelfAdjointView<const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,MatrixType,product),UpLo>\n    operator*(const Scalar& s, const SelfAdjointView& mat)\n    {\n      return (s*mat.nestedExpression()).template selfadjointView<UpLo>();\n    }\n\n    /** Perform a symmetric rank 2 update of the selfadjoint matrix \\c *this:\n      * \\f$ this = this + \\alpha u v^* + conj(\\alpha) v u^* \\f$\n      * \\returns a reference to \\c *this\n      *\n      * The vectors \\a u and \\c v \\b must be column vectors, however they can be\n      * a adjoint expression without any overhead. Only the meaningful triangular\n      * part of the matrix is updated, the rest is left unchanged.\n      *\n      * \\sa rankUpdate(const MatrixBase<DerivedU>&, Scalar)\n      */\n    template<typename DerivedU, typename DerivedV>\n    EIGEN_DEVICE_FUNC\n    SelfAdjointView& rankUpdate(const MatrixBase<DerivedU>& u, const MatrixBase<DerivedV>& v, const Scalar& alpha = Scalar(1));\n\n    /** Perform a symmetric rank K update of the selfadjoint matrix \\c *this:\n      * \\f$ this = this + \\alpha ( u u^* ) \\f$ where \\a u is a vector or matrix.\n      *\n      * \\returns a reference to \\c *this\n      *\n      * Note that to perform \\f$ this = this + \\alpha ( u^* u ) \\f$ you can simply\n      * call this function with u.adjoint().\n      *\n      * \\sa rankUpdate(const MatrixBase<DerivedU>&, const MatrixBase<DerivedV>&, Scalar)\n      */\n    template<typename DerivedU>\n    EIGEN_DEVICE_FUNC\n    SelfAdjointView& rankUpdate(const MatrixBase<DerivedU>& u, const Scalar& alpha = Scalar(1));\n\n    /** \\returns an expression of a triangular view extracted from the current selfadjoint view of a given triangular part\n      *\n      * The parameter \\a TriMode can have the following values: \\c #Upper, \\c #StrictlyUpper, \\c #UnitUpper,\n      * \\c #Lower, \\c #StrictlyLower, \\c #UnitLower.\n      *\n      * If \\c TriMode references the same triangular part than \\c *this, then this method simply return a \\c TriangularView of the nested expression,\n      * otherwise, the nested expression is first transposed, thus returning a \\c TriangularView<Transpose<MatrixType>> object.\n      *\n      * \\sa MatrixBase::triangularView(), class TriangularView\n      */\n    template<unsigned int TriMode>\n    EIGEN_DEVICE_FUNC\n    typename internal::conditional<(TriMode&(Upper|Lower))==(UpLo&(Upper|Lower)),\n                                   TriangularView<MatrixType,TriMode>,\n                                   TriangularView<typename MatrixType::AdjointReturnType,TriMode> >::type\n    triangularView() const\n    {\n      typename internal::conditional<(TriMode&(Upper|Lower))==(UpLo&(Upper|Lower)), MatrixType&, typename MatrixType::ConstTransposeReturnType>::type tmp1(m_matrix);\n      typename internal::conditional<(TriMode&(Upper|Lower))==(UpLo&(Upper|Lower)), MatrixType&, typename MatrixType::AdjointReturnType>::type tmp2(tmp1);\n      return typename internal::conditional<(TriMode&(Upper|Lower))==(UpLo&(Upper|Lower)),\n                                   TriangularView<MatrixType,TriMode>,\n                                   TriangularView<typename MatrixType::AdjointReturnType,TriMode> >::type(tmp2);\n    }\n\n    typedef SelfAdjointView<const MatrixConjugateReturnType,UpLo> ConjugateReturnType;\n    /** \\sa MatrixBase::conjugate() const */\n    EIGEN_DEVICE_FUNC\n    inline const ConjugateReturnType conjugate() const\n    { return ConjugateReturnType(m_matrix.conjugate()); }\n\n    typedef SelfAdjointView<const typename MatrixType::AdjointReturnType,TransposeMode> AdjointReturnType;\n    /** \\sa MatrixBase::adjoint() const */\n    EIGEN_DEVICE_FUNC\n    inline const AdjointReturnType adjoint() const\n    { return AdjointReturnType(m_matrix.adjoint()); }\n\n    typedef SelfAdjointView<typename MatrixType::TransposeReturnType,TransposeMode> TransposeReturnType;\n     /** \\sa MatrixBase::transpose() */\n    EIGEN_DEVICE_FUNC\n    inline TransposeReturnType transpose()\n    {\n      EIGEN_STATIC_ASSERT_LVALUE(MatrixType)\n      typename MatrixType::TransposeReturnType tmp(m_matrix);\n      return TransposeReturnType(tmp);\n    }\n\n    typedef SelfAdjointView<const typename MatrixType::ConstTransposeReturnType,TransposeMode> ConstTransposeReturnType;\n    /** \\sa MatrixBase::transpose() const */\n    EIGEN_DEVICE_FUNC\n    inline const ConstTransposeReturnType transpose() const\n    {\n      return ConstTransposeReturnType(m_matrix.transpose());\n    }\n\n    /** \\returns a const expression of the main diagonal of the matrix \\c *this\n      *\n      * This method simply returns the diagonal of the nested expression, thus by-passing the SelfAdjointView decorator.\n      *\n      * \\sa MatrixBase::diagonal(), class Diagonal */\n    EIGEN_DEVICE_FUNC\n    typename MatrixType::ConstDiagonalReturnType diagonal() const\n    {\n      return typename MatrixType::ConstDiagonalReturnType(m_matrix);\n    }\n\n/////////// Cholesky module ///////////\n\n    const LLT<PlainObject, UpLo> llt() const;\n    const LDLT<PlainObject, UpLo> ldlt() const;\n\n/////////// Eigenvalue module ///////////\n\n    /** Real part of #Scalar */\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n    /** Return type of eigenvalues() */\n    typedef Matrix<RealScalar, internal::traits<MatrixType>::ColsAtCompileTime, 1> EigenvaluesReturnType;\n\n    EIGEN_DEVICE_FUNC\n    EigenvaluesReturnType eigenvalues() const;\n    EIGEN_DEVICE_FUNC\n    RealScalar operatorNorm() const;\n\n  protected:\n    MatrixTypeNested m_matrix;\n};\n\n\n// template<typename OtherDerived, typename MatrixType, unsigned int UpLo>\n// internal::selfadjoint_matrix_product_returntype<OtherDerived,SelfAdjointView<MatrixType,UpLo> >\n// operator*(const MatrixBase<OtherDerived>& lhs, const SelfAdjointView<MatrixType,UpLo>& rhs)\n// {\n//   return internal::matrix_selfadjoint_product_returntype<OtherDerived,SelfAdjointView<MatrixType,UpLo> >(lhs.derived(),rhs);\n// }\n\n// selfadjoint to dense matrix\n\nnamespace internal {\n\n// TODO currently a selfadjoint expression has the form SelfAdjointView<.,.>\n//      in the future selfadjoint-ness should be defined by the expression traits\n//      such that Transpose<SelfAdjointView<.,.> > is valid. (currently TriangularBase::transpose() is overloaded to make it work)\ntemplate<typename MatrixType, unsigned int Mode>\nstruct evaluator_traits<SelfAdjointView<MatrixType,Mode> >\n{\n  typedef typename storage_kind_to_evaluator_kind<typename MatrixType::StorageKind>::Kind Kind;\n  typedef SelfAdjointShape Shape;\n};\n\ntemplate<int UpLo, int SetOpposite, typename DstEvaluatorTypeT, typename SrcEvaluatorTypeT, typename Functor, int Version>\nclass triangular_dense_assignment_kernel<UpLo,SelfAdjoint,SetOpposite,DstEvaluatorTypeT,SrcEvaluatorTypeT,Functor,Version>\n  : public generic_dense_assignment_kernel<DstEvaluatorTypeT, SrcEvaluatorTypeT, Functor, Version>\n{\nprotected:\n  typedef generic_dense_assignment_kernel<DstEvaluatorTypeT, SrcEvaluatorTypeT, Functor, Version> Base;\n  typedef typename Base::DstXprType DstXprType;\n  typedef typename Base::SrcXprType SrcXprType;\n  using Base::m_dst;\n  using Base::m_src;\n  using Base::m_functor;\npublic:\n  \n  typedef typename Base::DstEvaluatorType DstEvaluatorType;\n  typedef typename Base::SrcEvaluatorType SrcEvaluatorType;\n  typedef typename Base::Scalar Scalar;\n  typedef typename Base::AssignmentTraits AssignmentTraits;\n  \n  \n  EIGEN_DEVICE_FUNC triangular_dense_assignment_kernel(DstEvaluatorType &dst, const SrcEvaluatorType &src, const Functor &func, DstXprType& dstExpr)\n    : Base(dst, src, func, dstExpr)\n  {}\n  \n  EIGEN_DEVICE_FUNC void assignCoeff(Index row, Index col)\n  {\n    eigen_internal_assert(row!=col);\n    Scalar tmp = m_src.coeff(row,col);\n    m_functor.assignCoeff(m_dst.coeffRef(row,col), tmp);\n    m_functor.assignCoeff(m_dst.coeffRef(col,row), numext::conj(tmp));\n  }\n  \n  EIGEN_DEVICE_FUNC void assignDiagonalCoeff(Index id)\n  {\n    Base::assignCoeff(id,id);\n  }\n  \n  EIGEN_DEVICE_FUNC void assignOppositeCoeff(Index, Index)\n  { eigen_internal_assert(false && \"should never be called\"); }\n};\n\n} // end namespace internal\n\n/***************************************************************************\n* Implementation of MatrixBase methods\n***************************************************************************/\n\n/** This is the const version of MatrixBase::selfadjointView() */\ntemplate<typename Derived>\ntemplate<unsigned int UpLo>\ntypename MatrixBase<Derived>::template ConstSelfAdjointViewReturnType<UpLo>::Type\nMatrixBase<Derived>::selfadjointView() const\n{\n  return typename ConstSelfAdjointViewReturnType<UpLo>::Type(derived());\n}\n\n/** \\returns an expression of a symmetric/self-adjoint view extracted from the upper or lower triangular part of the current matrix\n  *\n  * The parameter \\a UpLo can be either \\c #Upper or \\c #Lower\n  *\n  * Example: \\include MatrixBase_selfadjointView.cpp\n  * Output: \\verbinclude MatrixBase_selfadjointView.out\n  *\n  * \\sa class SelfAdjointView\n  */\ntemplate<typename Derived>\ntemplate<unsigned int UpLo>\ntypename MatrixBase<Derived>::template SelfAdjointViewReturnType<UpLo>::Type\nMatrixBase<Derived>::selfadjointView()\n{\n  return typename SelfAdjointViewReturnType<UpLo>::Type(derived());\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_SELFADJOINTMATRIX_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/SelfCwiseBinaryOp.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SELFCWISEBINARYOP_H\n#define EIGEN_SELFCWISEBINARYOP_H\n\nnamespace Eigen { \n\n// TODO generalize the scalar type of 'other'\n\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::operator*=(const Scalar& other)\n{\n  internal::call_assignment(this->derived(), PlainObject::Constant(rows(),cols(),other), internal::mul_assign_op<Scalar,Scalar>());\n  return derived();\n}\n\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& ArrayBase<Derived>::operator+=(const Scalar& other)\n{\n  internal::call_assignment(this->derived(), PlainObject::Constant(rows(),cols(),other), internal::add_assign_op<Scalar,Scalar>());\n  return derived();\n}\n\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& ArrayBase<Derived>::operator-=(const Scalar& other)\n{\n  internal::call_assignment(this->derived(), PlainObject::Constant(rows(),cols(),other), internal::sub_assign_op<Scalar,Scalar>());\n  return derived();\n}\n\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::operator/=(const Scalar& other)\n{\n  internal::call_assignment(this->derived(), PlainObject::Constant(rows(),cols(),other), internal::div_assign_op<Scalar,Scalar>());\n  return derived();\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_SELFCWISEBINARYOP_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/Solve.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SOLVE_H\n#define EIGEN_SOLVE_H\n\nnamespace Eigen {\n\ntemplate<typename Decomposition, typename RhsType, typename StorageKind> class SolveImpl;\n  \n/** \\class Solve\n  * \\ingroup Core_Module\n  *\n  * \\brief Pseudo expression representing a solving operation\n  *\n  * \\tparam Decomposition the type of the matrix or decomposion object\n  * \\tparam Rhstype the type of the right-hand side\n  *\n  * This class represents an expression of A.solve(B)\n  * and most of the time this is the only way it is used.\n  *\n  */\nnamespace internal {\n\n// this solve_traits class permits to determine the evaluation type with respect to storage kind (Dense vs Sparse)\ntemplate<typename Decomposition, typename RhsType,typename StorageKind> struct solve_traits;\n\ntemplate<typename Decomposition, typename RhsType>\nstruct solve_traits<Decomposition,RhsType,Dense>\n{\n  typedef typename make_proper_matrix_type<typename RhsType::Scalar,\n                 Decomposition::ColsAtCompileTime,\n                 RhsType::ColsAtCompileTime,\n                 RhsType::PlainObject::Options,\n                 Decomposition::MaxColsAtCompileTime,\n                 RhsType::MaxColsAtCompileTime>::type PlainObject;\n};\n\ntemplate<typename Decomposition, typename RhsType>\nstruct traits<Solve<Decomposition, RhsType> >\n  : traits<typename solve_traits<Decomposition,RhsType,typename internal::traits<RhsType>::StorageKind>::PlainObject>\n{\n  typedef typename solve_traits<Decomposition,RhsType,typename internal::traits<RhsType>::StorageKind>::PlainObject PlainObject;\n  typedef typename promote_index_type<typename Decomposition::StorageIndex, typename RhsType::StorageIndex>::type StorageIndex;\n  typedef traits<PlainObject> BaseTraits;\n  enum {\n    Flags = BaseTraits::Flags & RowMajorBit,\n    CoeffReadCost = HugeCost\n  };\n};\n\n}\n\n\ntemplate<typename Decomposition, typename RhsType>\nclass Solve : public SolveImpl<Decomposition,RhsType,typename internal::traits<RhsType>::StorageKind>\n{\npublic:\n  typedef typename internal::traits<Solve>::PlainObject PlainObject;\n  typedef typename internal::traits<Solve>::StorageIndex StorageIndex;\n  \n  Solve(const Decomposition &dec, const RhsType &rhs)\n    : m_dec(dec), m_rhs(rhs)\n  {}\n  \n  EIGEN_DEVICE_FUNC Index rows() const { return m_dec.cols(); }\n  EIGEN_DEVICE_FUNC Index cols() const { return m_rhs.cols(); }\n\n  EIGEN_DEVICE_FUNC const Decomposition& dec() const { return m_dec; }\n  EIGEN_DEVICE_FUNC const RhsType&       rhs() const { return m_rhs; }\n\nprotected:\n  const Decomposition &m_dec;\n  const RhsType       &m_rhs;\n};\n\n\n// Specialization of the Solve expression for dense results\ntemplate<typename Decomposition, typename RhsType>\nclass SolveImpl<Decomposition,RhsType,Dense>\n  : public MatrixBase<Solve<Decomposition,RhsType> >\n{\n  typedef Solve<Decomposition,RhsType> Derived;\n  \npublic:\n  \n  typedef MatrixBase<Solve<Decomposition,RhsType> > Base;\n  EIGEN_DENSE_PUBLIC_INTERFACE(Derived)\n\nprivate:\n  \n  Scalar coeff(Index row, Index col) const;\n  Scalar coeff(Index i) const;\n};\n\n// Generic API dispatcher\ntemplate<typename Decomposition, typename RhsType, typename StorageKind>\nclass SolveImpl : public internal::generic_xpr_base<Solve<Decomposition,RhsType>, MatrixXpr, StorageKind>::type\n{\n  public:\n    typedef typename internal::generic_xpr_base<Solve<Decomposition,RhsType>, MatrixXpr, StorageKind>::type Base;\n};\n\nnamespace internal {\n\n// Evaluator of Solve -> eval into a temporary\ntemplate<typename Decomposition, typename RhsType>\nstruct evaluator<Solve<Decomposition,RhsType> >\n  : public evaluator<typename Solve<Decomposition,RhsType>::PlainObject>\n{\n  typedef Solve<Decomposition,RhsType> SolveType;\n  typedef typename SolveType::PlainObject PlainObject;\n  typedef evaluator<PlainObject> Base;\n\n  enum { Flags = Base::Flags | EvalBeforeNestingBit };\n  \n  EIGEN_DEVICE_FUNC explicit evaluator(const SolveType& solve)\n    : m_result(solve.rows(), solve.cols())\n  {\n    ::new (static_cast<Base*>(this)) Base(m_result);\n    solve.dec()._solve_impl(solve.rhs(), m_result);\n  }\n  \nprotected:  \n  PlainObject m_result;\n};\n\n// Specialization for \"dst = dec.solve(rhs)\"\n// NOTE we need to specialize it for Dense2Dense to avoid ambiguous specialization error and a Sparse2Sparse specialization must exist somewhere\ntemplate<typename DstXprType, typename DecType, typename RhsType, typename Scalar>\nstruct Assignment<DstXprType, Solve<DecType,RhsType>, internal::assign_op<Scalar,Scalar>, Dense2Dense>\n{\n  typedef Solve<DecType,RhsType> SrcXprType;\n  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &)\n  {\n    Index dstRows = src.rows();\n    Index dstCols = src.cols();\n    if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))\n      dst.resize(dstRows, dstCols);\n\n    src.dec()._solve_impl(src.rhs(), dst);\n  }\n};\n\n// Specialization for \"dst = dec.transpose().solve(rhs)\"\ntemplate<typename DstXprType, typename DecType, typename RhsType, typename Scalar>\nstruct Assignment<DstXprType, Solve<Transpose<const DecType>,RhsType>, internal::assign_op<Scalar,Scalar>, Dense2Dense>\n{\n  typedef Solve<Transpose<const DecType>,RhsType> SrcXprType;\n  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &)\n  {\n    Index dstRows = src.rows();\n    Index dstCols = src.cols();\n    if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))\n      dst.resize(dstRows, dstCols);\n\n    src.dec().nestedExpression().template _solve_impl_transposed<false>(src.rhs(), dst);\n  }\n};\n\n// Specialization for \"dst = dec.adjoint().solve(rhs)\"\ntemplate<typename DstXprType, typename DecType, typename RhsType, typename Scalar>\nstruct Assignment<DstXprType, Solve<CwiseUnaryOp<internal::scalar_conjugate_op<typename DecType::Scalar>, const Transpose<const DecType> >,RhsType>,\n                  internal::assign_op<Scalar,Scalar>, Dense2Dense>\n{\n  typedef Solve<CwiseUnaryOp<internal::scalar_conjugate_op<typename DecType::Scalar>, const Transpose<const DecType> >,RhsType> SrcXprType;\n  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &)\n  {\n    Index dstRows = src.rows();\n    Index dstCols = src.cols();\n    if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))\n      dst.resize(dstRows, dstCols);\n    \n    src.dec().nestedExpression().nestedExpression().template _solve_impl_transposed<true>(src.rhs(), dst);\n  }\n};\n\n} // end namepsace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_SOLVE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/SolveTriangular.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SOLVETRIANGULAR_H\n#define EIGEN_SOLVETRIANGULAR_H\n\nnamespace Eigen { \n\nnamespace internal {\n\n// Forward declarations:\n// The following two routines are implemented in the products/TriangularSolver*.h files\ntemplate<typename LhsScalar, typename RhsScalar, typename Index, int Side, int Mode, bool Conjugate, int StorageOrder>\nstruct triangular_solve_vector;\n\ntemplate <typename Scalar, typename Index, int Side, int Mode, bool Conjugate, int TriStorageOrder, int OtherStorageOrder>\nstruct triangular_solve_matrix;\n\n// small helper struct extracting some traits on the underlying solver operation\ntemplate<typename Lhs, typename Rhs, int Side>\nclass trsolve_traits\n{\n  private:\n    enum {\n      RhsIsVectorAtCompileTime = (Side==OnTheLeft ? Rhs::ColsAtCompileTime : Rhs::RowsAtCompileTime)==1\n    };\n  public:\n    enum {\n      Unrolling   = (RhsIsVectorAtCompileTime && Rhs::SizeAtCompileTime != Dynamic && Rhs::SizeAtCompileTime <= 8)\n                  ? CompleteUnrolling : NoUnrolling,\n      RhsVectors  = RhsIsVectorAtCompileTime ? 1 : Dynamic\n    };\n};\n\ntemplate<typename Lhs, typename Rhs,\n  int Side, // can be OnTheLeft/OnTheRight\n  int Mode, // can be Upper/Lower | UnitDiag\n  int Unrolling = trsolve_traits<Lhs,Rhs,Side>::Unrolling,\n  int RhsVectors = trsolve_traits<Lhs,Rhs,Side>::RhsVectors\n  >\nstruct triangular_solver_selector;\n\ntemplate<typename Lhs, typename Rhs, int Side, int Mode>\nstruct triangular_solver_selector<Lhs,Rhs,Side,Mode,NoUnrolling,1>\n{\n  typedef typename Lhs::Scalar LhsScalar;\n  typedef typename Rhs::Scalar RhsScalar;\n  typedef blas_traits<Lhs> LhsProductTraits;\n  typedef typename LhsProductTraits::ExtractType ActualLhsType;\n  typedef Map<Matrix<RhsScalar,Dynamic,1>, Aligned> MappedRhs;\n  static void run(const Lhs& lhs, Rhs& rhs)\n  {\n    ActualLhsType actualLhs = LhsProductTraits::extract(lhs);\n\n    // FIXME find a way to allow an inner stride if packet_traits<Scalar>::size==1\n\n    bool useRhsDirectly = Rhs::InnerStrideAtCompileTime==1 || rhs.innerStride()==1;\n\n    ei_declare_aligned_stack_constructed_variable(RhsScalar,actualRhs,rhs.size(),\n                                                  (useRhsDirectly ? rhs.data() : 0));\n                                                  \n    if(!useRhsDirectly)\n      MappedRhs(actualRhs,rhs.size()) = rhs;\n\n    triangular_solve_vector<LhsScalar, RhsScalar, Index, Side, Mode, LhsProductTraits::NeedToConjugate,\n                            (int(Lhs::Flags) & RowMajorBit) ? RowMajor : ColMajor>\n      ::run(actualLhs.cols(), actualLhs.data(), actualLhs.outerStride(), actualRhs);\n\n    if(!useRhsDirectly)\n      rhs = MappedRhs(actualRhs, rhs.size());\n  }\n};\n\n// the rhs is a matrix\ntemplate<typename Lhs, typename Rhs, int Side, int Mode>\nstruct triangular_solver_selector<Lhs,Rhs,Side,Mode,NoUnrolling,Dynamic>\n{\n  typedef typename Rhs::Scalar Scalar;\n  typedef blas_traits<Lhs> LhsProductTraits;\n  typedef typename LhsProductTraits::DirectLinearAccessType ActualLhsType;\n\n  static void run(const Lhs& lhs, Rhs& rhs)\n  {\n    typename internal::add_const_on_value_type<ActualLhsType>::type actualLhs = LhsProductTraits::extract(lhs);\n\n    const Index size = lhs.rows();\n    const Index othersize = Side==OnTheLeft? rhs.cols() : rhs.rows();\n\n    typedef internal::gemm_blocking_space<(Rhs::Flags&RowMajorBit) ? RowMajor : ColMajor,Scalar,Scalar,\n              Rhs::MaxRowsAtCompileTime, Rhs::MaxColsAtCompileTime, Lhs::MaxRowsAtCompileTime,4> BlockingType;\n\n    BlockingType blocking(rhs.rows(), rhs.cols(), size, 1, false);\n\n    triangular_solve_matrix<Scalar,Index,Side,Mode,LhsProductTraits::NeedToConjugate,(int(Lhs::Flags) & RowMajorBit) ? RowMajor : ColMajor,\n                               (Rhs::Flags&RowMajorBit) ? RowMajor : ColMajor>\n      ::run(size, othersize, &actualLhs.coeffRef(0,0), actualLhs.outerStride(), &rhs.coeffRef(0,0), rhs.outerStride(), blocking);\n  }\n};\n\n/***************************************************************************\n* meta-unrolling implementation\n***************************************************************************/\n\ntemplate<typename Lhs, typename Rhs, int Mode, int LoopIndex, int Size,\n         bool Stop = LoopIndex==Size>\nstruct triangular_solver_unroller;\n\ntemplate<typename Lhs, typename Rhs, int Mode, int LoopIndex, int Size>\nstruct triangular_solver_unroller<Lhs,Rhs,Mode,LoopIndex,Size,false> {\n  enum {\n    IsLower = ((Mode&Lower)==Lower),\n    DiagIndex  = IsLower ? LoopIndex : Size - LoopIndex - 1,\n    StartIndex = IsLower ? 0         : DiagIndex+1\n  };\n  static void run(const Lhs& lhs, Rhs& rhs)\n  {\n    if (LoopIndex>0)\n      rhs.coeffRef(DiagIndex) -= lhs.row(DiagIndex).template segment<LoopIndex>(StartIndex).transpose()\n                                .cwiseProduct(rhs.template segment<LoopIndex>(StartIndex)).sum();\n\n    if(!(Mode & UnitDiag))\n      rhs.coeffRef(DiagIndex) /= lhs.coeff(DiagIndex,DiagIndex);\n\n    triangular_solver_unroller<Lhs,Rhs,Mode,LoopIndex+1,Size>::run(lhs,rhs);\n  }\n};\n\ntemplate<typename Lhs, typename Rhs, int Mode, int LoopIndex, int Size>\nstruct triangular_solver_unroller<Lhs,Rhs,Mode,LoopIndex,Size,true> {\n  static void run(const Lhs&, Rhs&) {}\n};\n\ntemplate<typename Lhs, typename Rhs, int Mode>\nstruct triangular_solver_selector<Lhs,Rhs,OnTheLeft,Mode,CompleteUnrolling,1> {\n  static void run(const Lhs& lhs, Rhs& rhs)\n  { triangular_solver_unroller<Lhs,Rhs,Mode,0,Rhs::SizeAtCompileTime>::run(lhs,rhs); }\n};\n\ntemplate<typename Lhs, typename Rhs, int Mode>\nstruct triangular_solver_selector<Lhs,Rhs,OnTheRight,Mode,CompleteUnrolling,1> {\n  static void run(const Lhs& lhs, Rhs& rhs)\n  {\n    Transpose<const Lhs> trLhs(lhs);\n    Transpose<Rhs> trRhs(rhs);\n    \n    triangular_solver_unroller<Transpose<const Lhs>,Transpose<Rhs>,\n                              ((Mode&Upper)==Upper ? Lower : Upper) | (Mode&UnitDiag),\n                              0,Rhs::SizeAtCompileTime>::run(trLhs,trRhs);\n  }\n};\n\n} // end namespace internal\n\n/***************************************************************************\n* TriangularView methods\n***************************************************************************/\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\ntemplate<typename MatrixType, unsigned int Mode>\ntemplate<int Side, typename OtherDerived>\nvoid TriangularViewImpl<MatrixType,Mode,Dense>::solveInPlace(const MatrixBase<OtherDerived>& _other) const\n{\n  OtherDerived& other = _other.const_cast_derived();\n  eigen_assert( derived().cols() == derived().rows() && ((Side==OnTheLeft && derived().cols() == other.rows()) || (Side==OnTheRight && derived().cols() == other.cols())) );\n  eigen_assert((!(Mode & ZeroDiag)) && bool(Mode & (Upper|Lower)));\n\n  enum { copy = (internal::traits<OtherDerived>::Flags & RowMajorBit)  && OtherDerived::IsVectorAtCompileTime && OtherDerived::SizeAtCompileTime!=1};\n  typedef typename internal::conditional<copy,\n    typename internal::plain_matrix_type_column_major<OtherDerived>::type, OtherDerived&>::type OtherCopy;\n  OtherCopy otherCopy(other);\n\n  internal::triangular_solver_selector<MatrixType, typename internal::remove_reference<OtherCopy>::type,\n    Side, Mode>::run(derived().nestedExpression(), otherCopy);\n\n  if (copy)\n    other = otherCopy;\n}\n\ntemplate<typename Derived, unsigned int Mode>\ntemplate<int Side, typename Other>\nconst internal::triangular_solve_retval<Side,TriangularView<Derived,Mode>,Other>\nTriangularViewImpl<Derived,Mode,Dense>::solve(const MatrixBase<Other>& other) const\n{\n  return internal::triangular_solve_retval<Side,TriangularViewType,Other>(derived(), other.derived());\n}\n#endif\n\nnamespace internal {\n\n\ntemplate<int Side, typename TriangularType, typename Rhs>\nstruct traits<triangular_solve_retval<Side, TriangularType, Rhs> >\n{\n  typedef typename internal::plain_matrix_type_column_major<Rhs>::type ReturnType;\n};\n\ntemplate<int Side, typename TriangularType, typename Rhs> struct triangular_solve_retval\n : public ReturnByValue<triangular_solve_retval<Side, TriangularType, Rhs> >\n{\n  typedef typename remove_all<typename Rhs::Nested>::type RhsNestedCleaned;\n  typedef ReturnByValue<triangular_solve_retval> Base;\n\n  triangular_solve_retval(const TriangularType& tri, const Rhs& rhs)\n    : m_triangularMatrix(tri), m_rhs(rhs)\n  {}\n\n  inline Index rows() const { return m_rhs.rows(); }\n  inline Index cols() const { return m_rhs.cols(); }\n\n  template<typename Dest> inline void evalTo(Dest& dst) const\n  {\n    if(!is_same_dense(dst,m_rhs))\n      dst = m_rhs;\n    m_triangularMatrix.template solveInPlace<Side>(dst);\n  }\n\n  protected:\n    const TriangularType& m_triangularMatrix;\n    typename Rhs::Nested m_rhs;\n};\n\n} // namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_SOLVETRIANGULAR_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/SolverBase.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SOLVERBASE_H\n#define EIGEN_SOLVERBASE_H\n\nnamespace Eigen {\n\nnamespace internal {\n\n\n\n} // end namespace internal\n\n/** \\class SolverBase\n  * \\brief A base class for matrix decomposition and solvers\n  *\n  * \\tparam Derived the actual type of the decomposition/solver.\n  *\n  * Any matrix decomposition inheriting this base class provide the following API:\n  *\n  * \\code\n  * MatrixType A, b, x;\n  * DecompositionType dec(A);\n  * x = dec.solve(b);             // solve A   * x = b\n  * x = dec.transpose().solve(b); // solve A^T * x = b\n  * x = dec.adjoint().solve(b);   // solve A'  * x = b\n  * \\endcode\n  *\n  * \\warning Currently, any other usage of transpose() and adjoint() are not supported and will produce compilation errors.\n  *\n  * \\sa class PartialPivLU, class FullPivLU\n  */\ntemplate<typename Derived>\nclass SolverBase : public EigenBase<Derived>\n{\n  public:\n\n    typedef EigenBase<Derived> Base;\n    typedef typename internal::traits<Derived>::Scalar Scalar;\n    typedef Scalar CoeffReturnType;\n\n    enum {\n      RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,\n      ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,\n      SizeAtCompileTime = (internal::size_at_compile_time<internal::traits<Derived>::RowsAtCompileTime,\n                                                          internal::traits<Derived>::ColsAtCompileTime>::ret),\n      MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime,\n      MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime,\n      MaxSizeAtCompileTime = (internal::size_at_compile_time<internal::traits<Derived>::MaxRowsAtCompileTime,\n                                                             internal::traits<Derived>::MaxColsAtCompileTime>::ret),\n      IsVectorAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime == 1\n                           || internal::traits<Derived>::MaxColsAtCompileTime == 1\n    };\n\n    /** Default constructor */\n    SolverBase()\n    {}\n\n    ~SolverBase()\n    {}\n\n    using Base::derived;\n\n    /** \\returns an expression of the solution x of \\f$ A x = b \\f$ using the current decomposition of A.\n      */\n    template<typename Rhs>\n    inline const Solve<Derived, Rhs>\n    solve(const MatrixBase<Rhs>& b) const\n    {\n      eigen_assert(derived().rows()==b.rows() && \"solve(): invalid number of rows of the right hand side matrix b\");\n      return Solve<Derived, Rhs>(derived(), b.derived());\n    }\n\n    /** \\internal the return type of transpose() */\n    typedef typename internal::add_const<Transpose<const Derived> >::type ConstTransposeReturnType;\n    /** \\returns an expression of the transposed of the factored matrix.\n      *\n      * A typical usage is to solve for the transposed problem A^T x = b:\n      * \\code x = dec.transpose().solve(b); \\endcode\n      *\n      * \\sa adjoint(), solve()\n      */\n    inline ConstTransposeReturnType transpose() const\n    {\n      return ConstTransposeReturnType(derived());\n    }\n\n    /** \\internal the return type of adjoint() */\n    typedef typename internal::conditional<NumTraits<Scalar>::IsComplex,\n                        CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>, ConstTransposeReturnType>,\n                        ConstTransposeReturnType\n                     >::type AdjointReturnType;\n    /** \\returns an expression of the adjoint of the factored matrix\n      *\n      * A typical usage is to solve for the adjoint problem A' x = b:\n      * \\code x = dec.adjoint().solve(b); \\endcode\n      *\n      * For real scalar types, this function is equivalent to transpose().\n      *\n      * \\sa transpose(), solve()\n      */\n    inline AdjointReturnType adjoint() const\n    {\n      return AdjointReturnType(derived().transpose());\n    }\n\n  protected:\n};\n\nnamespace internal {\n\ntemplate<typename Derived>\nstruct generic_xpr_base<Derived, MatrixXpr, SolverStorage>\n{\n  typedef SolverBase<Derived> type;\n\n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_SOLVERBASE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/StableNorm.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_STABLENORM_H\n#define EIGEN_STABLENORM_H\n\nnamespace Eigen { \n\nnamespace internal {\n\ntemplate<typename ExpressionType, typename Scalar>\ninline void stable_norm_kernel(const ExpressionType& bl, Scalar& ssq, Scalar& scale, Scalar& invScale)\n{\n  Scalar maxCoeff = bl.cwiseAbs().maxCoeff();\n  \n  if(maxCoeff>scale)\n  {\n    ssq = ssq * numext::abs2(scale/maxCoeff);\n    Scalar tmp = Scalar(1)/maxCoeff;\n    if(tmp > NumTraits<Scalar>::highest())\n    {\n      invScale = NumTraits<Scalar>::highest();\n      scale = Scalar(1)/invScale;\n    }\n    else if(maxCoeff>NumTraits<Scalar>::highest()) // we got a INF\n    {\n      invScale = Scalar(1);\n      scale = maxCoeff;\n    }\n    else\n    {\n      scale = maxCoeff;\n      invScale = tmp;\n    }\n  }\n  else if(maxCoeff!=maxCoeff) // we got a NaN\n  {\n    scale = maxCoeff;\n  }\n  \n  // TODO if the maxCoeff is much much smaller than the current scale,\n  // then we can neglect this sub vector\n  if(scale>Scalar(0)) // if scale==0, then bl is 0 \n    ssq += (bl*invScale).squaredNorm();\n}\n\ntemplate<typename Derived>\ninline typename NumTraits<typename traits<Derived>::Scalar>::Real\nblueNorm_impl(const EigenBase<Derived>& _vec)\n{\n  typedef typename Derived::RealScalar RealScalar;  \n  using std::pow;\n  using std::sqrt;\n  using std::abs;\n  const Derived& vec(_vec.derived());\n  static bool initialized = false;\n  static RealScalar b1, b2, s1m, s2m, rbig, relerr;\n  if(!initialized)\n  {\n    int ibeta, it, iemin, iemax, iexp;\n    RealScalar eps;\n    // This program calculates the machine-dependent constants\n    // bl, b2, slm, s2m, relerr overfl\n    // from the \"basic\" machine-dependent numbers\n    // nbig, ibeta, it, iemin, iemax, rbig.\n    // The following define the basic machine-dependent constants.\n    // For portability, the PORT subprograms \"ilmaeh\" and \"rlmach\"\n    // are used. For any specific computer, each of the assignment\n    // statements can be replaced\n    ibeta = std::numeric_limits<RealScalar>::radix;                 // base for floating-point numbers\n    it    = std::numeric_limits<RealScalar>::digits;                // number of base-beta digits in mantissa\n    iemin = std::numeric_limits<RealScalar>::min_exponent;          // minimum exponent\n    iemax = std::numeric_limits<RealScalar>::max_exponent;          // maximum exponent\n    rbig  = (std::numeric_limits<RealScalar>::max)();               // largest floating-point number\n\n    iexp  = -((1-iemin)/2);\n    b1    = RealScalar(pow(RealScalar(ibeta),RealScalar(iexp)));    // lower boundary of midrange\n    iexp  = (iemax + 1 - it)/2;\n    b2    = RealScalar(pow(RealScalar(ibeta),RealScalar(iexp)));    // upper boundary of midrange\n\n    iexp  = (2-iemin)/2;\n    s1m   = RealScalar(pow(RealScalar(ibeta),RealScalar(iexp)));    // scaling factor for lower range\n    iexp  = - ((iemax+it)/2);\n    s2m   = RealScalar(pow(RealScalar(ibeta),RealScalar(iexp)));    // scaling factor for upper range\n\n    eps     = RealScalar(pow(double(ibeta), 1-it));\n    relerr  = sqrt(eps);                                            // tolerance for neglecting asml\n    initialized = true;\n  }\n  Index n = vec.size();\n  RealScalar ab2 = b2 / RealScalar(n);\n  RealScalar asml = RealScalar(0);\n  RealScalar amed = RealScalar(0);\n  RealScalar abig = RealScalar(0);\n  for(typename Derived::InnerIterator it(vec, 0); it; ++it)\n  {\n    RealScalar ax = abs(it.value());\n    if(ax > ab2)     abig += numext::abs2(ax*s2m);\n    else if(ax < b1) asml += numext::abs2(ax*s1m);\n    else             amed += numext::abs2(ax);\n  }\n  if(amed!=amed)\n    return amed;  // we got a NaN\n  if(abig > RealScalar(0))\n  {\n    abig = sqrt(abig);\n    if(abig > rbig) // overflow, or *this contains INF values\n      return abig;  // return INF\n    if(amed > RealScalar(0))\n    {\n      abig = abig/s2m;\n      amed = sqrt(amed);\n    }\n    else\n      return abig/s2m;\n  }\n  else if(asml > RealScalar(0))\n  {\n    if (amed > RealScalar(0))\n    {\n      abig = sqrt(amed);\n      amed = sqrt(asml) / s1m;\n    }\n    else\n      return sqrt(asml)/s1m;\n  }\n  else\n    return sqrt(amed);\n  asml = numext::mini(abig, amed);\n  abig = numext::maxi(abig, amed);\n  if(asml <= abig*relerr)\n    return abig;\n  else\n    return abig * sqrt(RealScalar(1) + numext::abs2(asml/abig));\n}\n\n} // end namespace internal\n\n/** \\returns the \\em l2 norm of \\c *this avoiding underflow and overflow.\n  * This version use a blockwise two passes algorithm:\n  *  1 - find the absolute largest coefficient \\c s\n  *  2 - compute \\f$ s \\Vert \\frac{*this}{s} \\Vert \\f$ in a standard way\n  *\n  * For architecture/scalar types supporting vectorization, this version\n  * is faster than blueNorm(). Otherwise the blueNorm() is much faster.\n  *\n  * \\sa norm(), blueNorm(), hypotNorm()\n  */\ntemplate<typename Derived>\ninline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real\nMatrixBase<Derived>::stableNorm() const\n{\n  using std::sqrt;\n  using std::abs;\n  const Index blockSize = 4096;\n  RealScalar scale(0);\n  RealScalar invScale(1);\n  RealScalar ssq(0); // sum of square\n  \n  typedef typename internal::nested_eval<Derived,2>::type DerivedCopy;\n  typedef typename internal::remove_all<DerivedCopy>::type DerivedCopyClean;\n  const DerivedCopy copy(derived());\n  \n  enum {\n    CanAlign = (   (int(DerivedCopyClean::Flags)&DirectAccessBit)\n                || (int(internal::evaluator<DerivedCopyClean>::Alignment)>0) // FIXME Alignment)>0 might not be enough\n               ) && (blockSize*sizeof(Scalar)*2<EIGEN_STACK_ALLOCATION_LIMIT)\n                 && (EIGEN_MAX_STATIC_ALIGN_BYTES>0) // if we cannot allocate on the stack, then let's not bother about this optimization\n  };\n  typedef typename internal::conditional<CanAlign, Ref<const Matrix<Scalar,Dynamic,1,0,blockSize,1>, internal::evaluator<DerivedCopyClean>::Alignment>,\n                                                   typename DerivedCopyClean::ConstSegmentReturnType>::type SegmentWrapper;\n  Index n = size();\n  \n  if(n==1)\n    return abs(this->coeff(0));\n  \n  Index bi = internal::first_default_aligned(copy);\n  if (bi>0)\n    internal::stable_norm_kernel(copy.head(bi), ssq, scale, invScale);\n  for (; bi<n; bi+=blockSize)\n    internal::stable_norm_kernel(SegmentWrapper(copy.segment(bi,numext::mini(blockSize, n - bi))), ssq, scale, invScale);\n  return scale * sqrt(ssq);\n}\n\n/** \\returns the \\em l2 norm of \\c *this using the Blue's algorithm.\n  * A Portable Fortran Program to Find the Euclidean Norm of a Vector,\n  * ACM TOMS, Vol 4, Issue 1, 1978.\n  *\n  * For architecture/scalar types without vectorization, this version\n  * is much faster than stableNorm(). Otherwise the stableNorm() is faster.\n  *\n  * \\sa norm(), stableNorm(), hypotNorm()\n  */\ntemplate<typename Derived>\ninline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real\nMatrixBase<Derived>::blueNorm() const\n{\n  return internal::blueNorm_impl(*this);\n}\n\n/** \\returns the \\em l2 norm of \\c *this avoiding undeflow and overflow.\n  * This version use a concatenation of hypot() calls, and it is very slow.\n  *\n  * \\sa norm(), stableNorm()\n  */\ntemplate<typename Derived>\ninline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real\nMatrixBase<Derived>::hypotNorm() const\n{\n  return this->cwiseAbs().redux(internal::scalar_hypot_op<RealScalar>());\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_STABLENORM_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/Stride.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_STRIDE_H\n#define EIGEN_STRIDE_H\n\nnamespace Eigen { \n\n/** \\class Stride\n  * \\ingroup Core_Module\n  *\n  * \\brief Holds strides information for Map\n  *\n  * This class holds the strides information for mapping arrays with strides with class Map.\n  *\n  * It holds two values: the inner stride and the outer stride.\n  *\n  * The inner stride is the pointer increment between two consecutive entries within a given row of a\n  * row-major matrix or within a given column of a column-major matrix.\n  *\n  * The outer stride is the pointer increment between two consecutive rows of a row-major matrix or\n  * between two consecutive columns of a column-major matrix.\n  *\n  * These two values can be passed either at compile-time as template parameters, or at runtime as\n  * arguments to the constructor.\n  *\n  * Indeed, this class takes two template parameters:\n  *  \\tparam _OuterStrideAtCompileTime the outer stride, or Dynamic if you want to specify it at runtime.\n  *  \\tparam _InnerStrideAtCompileTime the inner stride, or Dynamic if you want to specify it at runtime.\n  *\n  * Here is an example:\n  * \\include Map_general_stride.cpp\n  * Output: \\verbinclude Map_general_stride.out\n  *\n  * \\sa class InnerStride, class OuterStride, \\ref TopicStorageOrders\n  */\ntemplate<int _OuterStrideAtCompileTime, int _InnerStrideAtCompileTime>\nclass Stride\n{\n  public:\n    typedef Eigen::Index Index; ///< \\deprecated since Eigen 3.3\n    enum {\n      InnerStrideAtCompileTime = _InnerStrideAtCompileTime,\n      OuterStrideAtCompileTime = _OuterStrideAtCompileTime\n    };\n\n    /** Default constructor, for use when strides are fixed at compile time */\n    EIGEN_DEVICE_FUNC\n    Stride()\n      : m_outer(OuterStrideAtCompileTime), m_inner(InnerStrideAtCompileTime)\n    {\n      eigen_assert(InnerStrideAtCompileTime != Dynamic && OuterStrideAtCompileTime != Dynamic);\n    }\n\n    /** Constructor allowing to pass the strides at runtime */\n    EIGEN_DEVICE_FUNC\n    Stride(Index outerStride, Index innerStride)\n      : m_outer(outerStride), m_inner(innerStride)\n    {\n      eigen_assert(innerStride>=0 && outerStride>=0);\n    }\n\n    /** Copy constructor */\n    EIGEN_DEVICE_FUNC\n    Stride(const Stride& other)\n      : m_outer(other.outer()), m_inner(other.inner())\n    {}\n\n    /** \\returns the outer stride */\n    EIGEN_DEVICE_FUNC\n    inline Index outer() const { return m_outer.value(); }\n    /** \\returns the inner stride */\n    EIGEN_DEVICE_FUNC\n    inline Index inner() const { return m_inner.value(); }\n\n  protected:\n    internal::variable_if_dynamic<Index, OuterStrideAtCompileTime> m_outer;\n    internal::variable_if_dynamic<Index, InnerStrideAtCompileTime> m_inner;\n};\n\n/** \\brief Convenience specialization of Stride to specify only an inner stride\n  * See class Map for some examples */\ntemplate<int Value>\nclass InnerStride : public Stride<0, Value>\n{\n    typedef Stride<0, Value> Base;\n  public:\n    EIGEN_DEVICE_FUNC InnerStride() : Base() {}\n    EIGEN_DEVICE_FUNC InnerStride(Index v) : Base(0, v) {} // FIXME making this explicit could break valid code\n};\n\n/** \\brief Convenience specialization of Stride to specify only an outer stride\n  * See class Map for some examples */\ntemplate<int Value>\nclass OuterStride : public Stride<Value, 0>\n{\n    typedef Stride<Value, 0> Base;\n  public:\n    EIGEN_DEVICE_FUNC OuterStride() : Base() {}\n    EIGEN_DEVICE_FUNC OuterStride(Index v) : Base(v,0) {} // FIXME making this explicit could break valid code\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_STRIDE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/Swap.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SWAP_H\n#define EIGEN_SWAP_H\n\nnamespace Eigen { \n\nnamespace internal {\n\n// Overload default assignPacket behavior for swapping them\ntemplate<typename DstEvaluatorTypeT, typename SrcEvaluatorTypeT>\nclass generic_dense_assignment_kernel<DstEvaluatorTypeT, SrcEvaluatorTypeT, swap_assign_op<typename DstEvaluatorTypeT::Scalar>, Specialized>\n : public generic_dense_assignment_kernel<DstEvaluatorTypeT, SrcEvaluatorTypeT, swap_assign_op<typename DstEvaluatorTypeT::Scalar>, BuiltIn>\n{\nprotected:\n  typedef generic_dense_assignment_kernel<DstEvaluatorTypeT, SrcEvaluatorTypeT, swap_assign_op<typename DstEvaluatorTypeT::Scalar>, BuiltIn> Base;\n  using Base::m_dst;\n  using Base::m_src;\n  using Base::m_functor;\n  \npublic:\n  typedef typename Base::Scalar Scalar;\n  typedef typename Base::DstXprType DstXprType;\n  typedef swap_assign_op<Scalar> Functor;\n  \n  EIGEN_DEVICE_FUNC generic_dense_assignment_kernel(DstEvaluatorTypeT &dst, const SrcEvaluatorTypeT &src, const Functor &func, DstXprType& dstExpr)\n    : Base(dst, src, func, dstExpr)\n  {}\n  \n  template<int StoreMode, int LoadMode, typename PacketType>\n  void assignPacket(Index row, Index col)\n  {\n    PacketType tmp = m_src.template packet<LoadMode,PacketType>(row,col);\n    const_cast<SrcEvaluatorTypeT&>(m_src).template writePacket<LoadMode>(row,col, m_dst.template packet<StoreMode,PacketType>(row,col));\n    m_dst.template writePacket<StoreMode>(row,col,tmp);\n  }\n  \n  template<int StoreMode, int LoadMode, typename PacketType>\n  void assignPacket(Index index)\n  {\n    PacketType tmp = m_src.template packet<LoadMode,PacketType>(index);\n    const_cast<SrcEvaluatorTypeT&>(m_src).template writePacket<LoadMode>(index, m_dst.template packet<StoreMode,PacketType>(index));\n    m_dst.template writePacket<StoreMode>(index,tmp);\n  }\n  \n  // TODO find a simple way not to have to copy/paste this function from generic_dense_assignment_kernel, by simple I mean no CRTP (Gael)\n  template<int StoreMode, int LoadMode, typename PacketType>\n  void assignPacketByOuterInner(Index outer, Index inner)\n  {\n    Index row = Base::rowIndexByOuterInner(outer, inner); \n    Index col = Base::colIndexByOuterInner(outer, inner);\n    assignPacket<StoreMode,LoadMode,PacketType>(row, col);\n  }\n};\n\n} // namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_SWAP_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/Transpose.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2009-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_TRANSPOSE_H\n#define EIGEN_TRANSPOSE_H\n\nnamespace Eigen { \n\nnamespace internal {\ntemplate<typename MatrixType>\nstruct traits<Transpose<MatrixType> > : public traits<MatrixType>\n{\n  typedef typename ref_selector<MatrixType>::type MatrixTypeNested;\n  typedef typename remove_reference<MatrixTypeNested>::type MatrixTypeNestedPlain;\n  enum {\n    RowsAtCompileTime = MatrixType::ColsAtCompileTime,\n    ColsAtCompileTime = MatrixType::RowsAtCompileTime,\n    MaxRowsAtCompileTime = MatrixType::MaxColsAtCompileTime,\n    MaxColsAtCompileTime = MatrixType::MaxRowsAtCompileTime,\n    FlagsLvalueBit = is_lvalue<MatrixType>::value ? LvalueBit : 0,\n    Flags0 = traits<MatrixTypeNestedPlain>::Flags & ~(LvalueBit | NestByRefBit),\n    Flags1 = Flags0 | FlagsLvalueBit,\n    Flags = Flags1 ^ RowMajorBit,\n    InnerStrideAtCompileTime = inner_stride_at_compile_time<MatrixType>::ret,\n    OuterStrideAtCompileTime = outer_stride_at_compile_time<MatrixType>::ret\n  };\n};\n}\n\ntemplate<typename MatrixType, typename StorageKind> class TransposeImpl;\n\n/** \\class Transpose\n  * \\ingroup Core_Module\n  *\n  * \\brief Expression of the transpose of a matrix\n  *\n  * \\tparam MatrixType the type of the object of which we are taking the transpose\n  *\n  * This class represents an expression of the transpose of a matrix.\n  * It is the return type of MatrixBase::transpose() and MatrixBase::adjoint()\n  * and most of the time this is the only way it is used.\n  *\n  * \\sa MatrixBase::transpose(), MatrixBase::adjoint()\n  */\ntemplate<typename MatrixType> class Transpose\n  : public TransposeImpl<MatrixType,typename internal::traits<MatrixType>::StorageKind>\n{\n  public:\n\n    typedef typename internal::ref_selector<MatrixType>::non_const_type MatrixTypeNested;\n\n    typedef typename TransposeImpl<MatrixType,typename internal::traits<MatrixType>::StorageKind>::Base Base;\n    EIGEN_GENERIC_PUBLIC_INTERFACE(Transpose)\n    typedef typename internal::remove_all<MatrixType>::type NestedExpression;\n\n    EIGEN_DEVICE_FUNC\n    explicit inline Transpose(MatrixType& matrix) : m_matrix(matrix) {}\n\n    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Transpose)\n\n    EIGEN_DEVICE_FUNC inline Index rows() const { return m_matrix.cols(); }\n    EIGEN_DEVICE_FUNC inline Index cols() const { return m_matrix.rows(); }\n\n    /** \\returns the nested expression */\n    EIGEN_DEVICE_FUNC\n    const typename internal::remove_all<MatrixTypeNested>::type&\n    nestedExpression() const { return m_matrix; }\n\n    /** \\returns the nested expression */\n    EIGEN_DEVICE_FUNC\n    typename internal::remove_reference<MatrixTypeNested>::type&\n    nestedExpression() { return m_matrix; }\n\n    /** \\internal */\n    void resize(Index nrows, Index ncols) {\n      m_matrix.resize(ncols,nrows);\n    }\n\n  protected:\n    typename internal::ref_selector<MatrixType>::non_const_type m_matrix;\n};\n\nnamespace internal {\n\ntemplate<typename MatrixType, bool HasDirectAccess = has_direct_access<MatrixType>::ret>\nstruct TransposeImpl_base\n{\n  typedef typename dense_xpr_base<Transpose<MatrixType> >::type type;\n};\n\ntemplate<typename MatrixType>\nstruct TransposeImpl_base<MatrixType, false>\n{\n  typedef typename dense_xpr_base<Transpose<MatrixType> >::type type;\n};\n\n} // end namespace internal\n\n// Generic API dispatcher\ntemplate<typename XprType, typename StorageKind>\nclass TransposeImpl\n  : public internal::generic_xpr_base<Transpose<XprType> >::type\n{\npublic:\n  typedef typename internal::generic_xpr_base<Transpose<XprType> >::type Base;\n};\n\ntemplate<typename MatrixType> class TransposeImpl<MatrixType,Dense>\n  : public internal::TransposeImpl_base<MatrixType>::type\n{\n  public:\n\n    typedef typename internal::TransposeImpl_base<MatrixType>::type Base;\n    using Base::coeffRef;\n    EIGEN_DENSE_PUBLIC_INTERFACE(Transpose<MatrixType>)\n    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(TransposeImpl)\n\n    EIGEN_DEVICE_FUNC inline Index innerStride() const { return derived().nestedExpression().innerStride(); }\n    EIGEN_DEVICE_FUNC inline Index outerStride() const { return derived().nestedExpression().outerStride(); }\n\n    typedef typename internal::conditional<\n                       internal::is_lvalue<MatrixType>::value,\n                       Scalar,\n                       const Scalar\n                     >::type ScalarWithConstIfNotLvalue;\n\n    EIGEN_DEVICE_FUNC inline ScalarWithConstIfNotLvalue* data() { return derived().nestedExpression().data(); }\n    EIGEN_DEVICE_FUNC inline const Scalar* data() const { return derived().nestedExpression().data(); }\n\n    // FIXME: shall we keep the const version of coeffRef?\n    EIGEN_DEVICE_FUNC\n    inline const Scalar& coeffRef(Index rowId, Index colId) const\n    {\n      return derived().nestedExpression().coeffRef(colId, rowId);\n    }\n\n    EIGEN_DEVICE_FUNC\n    inline const Scalar& coeffRef(Index index) const\n    {\n      return derived().nestedExpression().coeffRef(index);\n    }\n};\n\n/** \\returns an expression of the transpose of *this.\n  *\n  * Example: \\include MatrixBase_transpose.cpp\n  * Output: \\verbinclude MatrixBase_transpose.out\n  *\n  * \\warning If you want to replace a matrix by its own transpose, do \\b NOT do this:\n  * \\code\n  * m = m.transpose(); // bug!!! caused by aliasing effect\n  * \\endcode\n  * Instead, use the transposeInPlace() method:\n  * \\code\n  * m.transposeInPlace();\n  * \\endcode\n  * which gives Eigen good opportunities for optimization, or alternatively you can also do:\n  * \\code\n  * m = m.transpose().eval();\n  * \\endcode\n  *\n  * \\sa transposeInPlace(), adjoint() */\ntemplate<typename Derived>\ninline Transpose<Derived>\nDenseBase<Derived>::transpose()\n{\n  return TransposeReturnType(derived());\n}\n\n/** This is the const version of transpose().\n  *\n  * Make sure you read the warning for transpose() !\n  *\n  * \\sa transposeInPlace(), adjoint() */\ntemplate<typename Derived>\ninline typename DenseBase<Derived>::ConstTransposeReturnType\nDenseBase<Derived>::transpose() const\n{\n  return ConstTransposeReturnType(derived());\n}\n\n/** \\returns an expression of the adjoint (i.e. conjugate transpose) of *this.\n  *\n  * Example: \\include MatrixBase_adjoint.cpp\n  * Output: \\verbinclude MatrixBase_adjoint.out\n  *\n  * \\warning If you want to replace a matrix by its own adjoint, do \\b NOT do this:\n  * \\code\n  * m = m.adjoint(); // bug!!! caused by aliasing effect\n  * \\endcode\n  * Instead, use the adjointInPlace() method:\n  * \\code\n  * m.adjointInPlace();\n  * \\endcode\n  * which gives Eigen good opportunities for optimization, or alternatively you can also do:\n  * \\code\n  * m = m.adjoint().eval();\n  * \\endcode\n  *\n  * \\sa adjointInPlace(), transpose(), conjugate(), class Transpose, class internal::scalar_conjugate_op */\ntemplate<typename Derived>\ninline const typename MatrixBase<Derived>::AdjointReturnType\nMatrixBase<Derived>::adjoint() const\n{\n  return AdjointReturnType(this->transpose());\n}\n\n/***************************************************************************\n* \"in place\" transpose implementation\n***************************************************************************/\n\nnamespace internal {\n\ntemplate<typename MatrixType,\n  bool IsSquare = (MatrixType::RowsAtCompileTime == MatrixType::ColsAtCompileTime) && MatrixType::RowsAtCompileTime!=Dynamic,\n  bool MatchPacketSize =\n        (int(MatrixType::RowsAtCompileTime) == int(internal::packet_traits<typename MatrixType::Scalar>::size))\n    &&  (internal::evaluator<MatrixType>::Flags&PacketAccessBit) >\nstruct inplace_transpose_selector;\n\ntemplate<typename MatrixType>\nstruct inplace_transpose_selector<MatrixType,true,false> { // square matrix\n  static void run(MatrixType& m) {\n    m.matrix().template triangularView<StrictlyUpper>().swap(m.matrix().transpose());\n  }\n};\n\n// TODO: vectorized path is currently limited to LargestPacketSize x LargestPacketSize cases only.\ntemplate<typename MatrixType>\nstruct inplace_transpose_selector<MatrixType,true,true> { // PacketSize x PacketSize\n  static void run(MatrixType& m) {\n    typedef typename MatrixType::Scalar Scalar;\n    typedef typename internal::packet_traits<typename MatrixType::Scalar>::type Packet;\n    const Index PacketSize = internal::packet_traits<Scalar>::size;\n    const Index Alignment = internal::evaluator<MatrixType>::Alignment;\n    PacketBlock<Packet> A;\n    for (Index i=0; i<PacketSize; ++i)\n      A.packet[i] = m.template packetByOuterInner<Alignment>(i,0);\n    internal::ptranspose(A);\n    for (Index i=0; i<PacketSize; ++i)\n      m.template writePacket<Alignment>(m.rowIndexByOuterInner(i,0), m.colIndexByOuterInner(i,0), A.packet[i]);\n  }\n};\n\ntemplate<typename MatrixType,bool MatchPacketSize>\nstruct inplace_transpose_selector<MatrixType,false,MatchPacketSize> { // non square matrix\n  static void run(MatrixType& m) {\n    if (m.rows()==m.cols())\n      m.matrix().template triangularView<StrictlyUpper>().swap(m.matrix().transpose());\n    else\n      m = m.transpose().eval();\n  }\n};\n\n} // end namespace internal\n\n/** This is the \"in place\" version of transpose(): it replaces \\c *this by its own transpose.\n  * Thus, doing\n  * \\code\n  * m.transposeInPlace();\n  * \\endcode\n  * has the same effect on m as doing\n  * \\code\n  * m = m.transpose().eval();\n  * \\endcode\n  * and is faster and also safer because in the latter line of code, forgetting the eval() results\n  * in a bug caused by \\ref TopicAliasing \"aliasing\".\n  *\n  * Notice however that this method is only useful if you want to replace a matrix by its own transpose.\n  * If you just need the transpose of a matrix, use transpose().\n  *\n  * \\note if the matrix is not square, then \\c *this must be a resizable matrix. \n  * This excludes (non-square) fixed-size matrices, block-expressions and maps.\n  *\n  * \\sa transpose(), adjoint(), adjointInPlace() */\ntemplate<typename Derived>\ninline void DenseBase<Derived>::transposeInPlace()\n{\n  eigen_assert((rows() == cols() || (RowsAtCompileTime == Dynamic && ColsAtCompileTime == Dynamic))\n               && \"transposeInPlace() called on a non-square non-resizable matrix\");\n  internal::inplace_transpose_selector<Derived>::run(derived());\n}\n\n/***************************************************************************\n* \"in place\" adjoint implementation\n***************************************************************************/\n\n/** This is the \"in place\" version of adjoint(): it replaces \\c *this by its own transpose.\n  * Thus, doing\n  * \\code\n  * m.adjointInPlace();\n  * \\endcode\n  * has the same effect on m as doing\n  * \\code\n  * m = m.adjoint().eval();\n  * \\endcode\n  * and is faster and also safer because in the latter line of code, forgetting the eval() results\n  * in a bug caused by aliasing.\n  *\n  * Notice however that this method is only useful if you want to replace a matrix by its own adjoint.\n  * If you just need the adjoint of a matrix, use adjoint().\n  *\n  * \\note if the matrix is not square, then \\c *this must be a resizable matrix.\n  * This excludes (non-square) fixed-size matrices, block-expressions and maps.\n  *\n  * \\sa transpose(), adjoint(), transposeInPlace() */\ntemplate<typename Derived>\ninline void MatrixBase<Derived>::adjointInPlace()\n{\n  derived() = adjoint().eval();\n}\n\n#ifndef EIGEN_NO_DEBUG\n\n// The following is to detect aliasing problems in most common cases.\n\nnamespace internal {\n\ntemplate<bool DestIsTransposed, typename OtherDerived>\nstruct check_transpose_aliasing_compile_time_selector\n{\n  enum { ret = bool(blas_traits<OtherDerived>::IsTransposed) != DestIsTransposed };\n};\n\ntemplate<bool DestIsTransposed, typename BinOp, typename DerivedA, typename DerivedB>\nstruct check_transpose_aliasing_compile_time_selector<DestIsTransposed,CwiseBinaryOp<BinOp,DerivedA,DerivedB> >\n{\n  enum { ret =    bool(blas_traits<DerivedA>::IsTransposed) != DestIsTransposed\n               || bool(blas_traits<DerivedB>::IsTransposed) != DestIsTransposed\n  };\n};\n\ntemplate<typename Scalar, bool DestIsTransposed, typename OtherDerived>\nstruct check_transpose_aliasing_run_time_selector\n{\n  static bool run(const Scalar* dest, const OtherDerived& src)\n  {\n    return (bool(blas_traits<OtherDerived>::IsTransposed) != DestIsTransposed) && (dest!=0 && dest==(const Scalar*)extract_data(src));\n  }\n};\n\ntemplate<typename Scalar, bool DestIsTransposed, typename BinOp, typename DerivedA, typename DerivedB>\nstruct check_transpose_aliasing_run_time_selector<Scalar,DestIsTransposed,CwiseBinaryOp<BinOp,DerivedA,DerivedB> >\n{\n  static bool run(const Scalar* dest, const CwiseBinaryOp<BinOp,DerivedA,DerivedB>& src)\n  {\n    return ((blas_traits<DerivedA>::IsTransposed != DestIsTransposed) && (dest!=0 && dest==(const Scalar*)extract_data(src.lhs())))\n        || ((blas_traits<DerivedB>::IsTransposed != DestIsTransposed) && (dest!=0 && dest==(const Scalar*)extract_data(src.rhs())));\n  }\n};\n\n// the following selector, checkTransposeAliasing_impl, based on MightHaveTransposeAliasing,\n// is because when the condition controlling the assert is known at compile time, ICC emits a warning.\n// This is actually a good warning: in expressions that don't have any transposing, the condition is\n// known at compile time to be false, and using that, we can avoid generating the code of the assert again\n// and again for all these expressions that don't need it.\n\ntemplate<typename Derived, typename OtherDerived,\n         bool MightHaveTransposeAliasing\n                 = check_transpose_aliasing_compile_time_selector\n                     <blas_traits<Derived>::IsTransposed,OtherDerived>::ret\n        >\nstruct checkTransposeAliasing_impl\n{\n    static void run(const Derived& dst, const OtherDerived& other)\n    {\n        eigen_assert((!check_transpose_aliasing_run_time_selector\n                      <typename Derived::Scalar,blas_traits<Derived>::IsTransposed,OtherDerived>\n                      ::run(extract_data(dst), other))\n          && \"aliasing detected during transposition, use transposeInPlace() \"\n             \"or evaluate the rhs into a temporary using .eval()\");\n\n    }\n};\n\ntemplate<typename Derived, typename OtherDerived>\nstruct checkTransposeAliasing_impl<Derived, OtherDerived, false>\n{\n    static void run(const Derived&, const OtherDerived&)\n    {\n    }\n};\n\ntemplate<typename Dst, typename Src>\nvoid check_for_aliasing(const Dst &dst, const Src &src)\n{\n  internal::checkTransposeAliasing_impl<Dst, Src>::run(dst, src);\n}\n\n} // end namespace internal\n\n#endif // EIGEN_NO_DEBUG\n\n} // end namespace Eigen\n\n#endif // EIGEN_TRANSPOSE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/Transpositions.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2010-2011 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_TRANSPOSITIONS_H\n#define EIGEN_TRANSPOSITIONS_H\n\nnamespace Eigen { \n\ntemplate<typename Derived>\nclass TranspositionsBase\n{\n    typedef internal::traits<Derived> Traits;\n    \n  public:\n\n    typedef typename Traits::IndicesType IndicesType;\n    typedef typename IndicesType::Scalar StorageIndex;\n    typedef Eigen::Index Index; ///< \\deprecated since Eigen 3.3\n\n    Derived& derived() { return *static_cast<Derived*>(this); }\n    const Derived& derived() const { return *static_cast<const Derived*>(this); }\n\n    /** Copies the \\a other transpositions into \\c *this */\n    template<typename OtherDerived>\n    Derived& operator=(const TranspositionsBase<OtherDerived>& other)\n    {\n      indices() = other.indices();\n      return derived();\n    }\n    \n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    /** This is a special case of the templated operator=. Its purpose is to\n      * prevent a default operator= from hiding the templated operator=.\n      */\n    Derived& operator=(const TranspositionsBase& other)\n    {\n      indices() = other.indices();\n      return derived();\n    }\n    #endif\n\n    /** \\returns the number of transpositions */\n    Index size() const { return indices().size(); }\n    /** \\returns the number of rows of the equivalent permutation matrix */\n    Index rows() const { return indices().size(); }\n    /** \\returns the number of columns of the equivalent permutation matrix */\n    Index cols() const { return indices().size(); }\n\n    /** Direct access to the underlying index vector */\n    inline const StorageIndex& coeff(Index i) const { return indices().coeff(i); }\n    /** Direct access to the underlying index vector */\n    inline StorageIndex& coeffRef(Index i) { return indices().coeffRef(i); }\n    /** Direct access to the underlying index vector */\n    inline const StorageIndex& operator()(Index i) const { return indices()(i); }\n    /** Direct access to the underlying index vector */\n    inline StorageIndex& operator()(Index i) { return indices()(i); }\n    /** Direct access to the underlying index vector */\n    inline const StorageIndex& operator[](Index i) const { return indices()(i); }\n    /** Direct access to the underlying index vector */\n    inline StorageIndex& operator[](Index i) { return indices()(i); }\n\n    /** const version of indices(). */\n    const IndicesType& indices() const { return derived().indices(); }\n    /** \\returns a reference to the stored array representing the transpositions. */\n    IndicesType& indices() { return derived().indices(); }\n\n    /** Resizes to given size. */\n    inline void resize(Index newSize)\n    {\n      indices().resize(newSize);\n    }\n\n    /** Sets \\c *this to represents an identity transformation */\n    void setIdentity()\n    {\n      for(StorageIndex i = 0; i < indices().size(); ++i)\n        coeffRef(i) = i;\n    }\n\n    // FIXME: do we want such methods ?\n    // might be usefull when the target matrix expression is complex, e.g.:\n    // object.matrix().block(..,..,..,..) = trans * object.matrix().block(..,..,..,..);\n    /*\n    template<typename MatrixType>\n    void applyForwardToRows(MatrixType& mat) const\n    {\n      for(Index k=0 ; k<size() ; ++k)\n        if(m_indices(k)!=k)\n          mat.row(k).swap(mat.row(m_indices(k)));\n    }\n\n    template<typename MatrixType>\n    void applyBackwardToRows(MatrixType& mat) const\n    {\n      for(Index k=size()-1 ; k>=0 ; --k)\n        if(m_indices(k)!=k)\n          mat.row(k).swap(mat.row(m_indices(k)));\n    }\n    */\n\n    /** \\returns the inverse transformation */\n    inline Transpose<TranspositionsBase> inverse() const\n    { return Transpose<TranspositionsBase>(derived()); }\n\n    /** \\returns the tranpose transformation */\n    inline Transpose<TranspositionsBase> transpose() const\n    { return Transpose<TranspositionsBase>(derived()); }\n\n  protected:\n};\n\nnamespace internal {\ntemplate<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename _StorageIndex>\nstruct traits<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,_StorageIndex> >\n : traits<PermutationMatrix<SizeAtCompileTime,MaxSizeAtCompileTime,_StorageIndex> >\n{\n  typedef Matrix<_StorageIndex, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1> IndicesType;\n  typedef TranspositionsStorage StorageKind;\n};\n}\n\n/** \\class Transpositions\n  * \\ingroup Core_Module\n  *\n  * \\brief Represents a sequence of transpositions (row/column interchange)\n  *\n  * \\tparam SizeAtCompileTime the number of transpositions, or Dynamic\n  * \\tparam MaxSizeAtCompileTime the maximum number of transpositions, or Dynamic. This optional parameter defaults to SizeAtCompileTime. Most of the time, you should not have to specify it.\n  *\n  * This class represents a permutation transformation as a sequence of \\em n transpositions\n  * \\f$[T_{n-1} \\ldots T_{i} \\ldots T_{0}]\\f$. It is internally stored as a vector of integers \\c indices.\n  * Each transposition \\f$ T_{i} \\f$ applied on the left of a matrix (\\f$ T_{i} M\\f$) interchanges\n  * the rows \\c i and \\c indices[i] of the matrix \\c M.\n  * A transposition applied on the right (e.g., \\f$ M T_{i}\\f$) yields a column interchange.\n  *\n  * Compared to the class PermutationMatrix, such a sequence of transpositions is what is\n  * computed during a decomposition with pivoting, and it is faster when applying the permutation in-place.\n  *\n  * To apply a sequence of transpositions to a matrix, simply use the operator * as in the following example:\n  * \\code\n  * Transpositions tr;\n  * MatrixXf mat;\n  * mat = tr * mat;\n  * \\endcode\n  * In this example, we detect that the matrix appears on both side, and so the transpositions\n  * are applied in-place without any temporary or extra copy.\n  *\n  * \\sa class PermutationMatrix\n  */\n\ntemplate<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename _StorageIndex>\nclass Transpositions : public TranspositionsBase<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,_StorageIndex> >\n{\n    typedef internal::traits<Transpositions> Traits;\n  public:\n\n    typedef TranspositionsBase<Transpositions> Base;\n    typedef typename Traits::IndicesType IndicesType;\n    typedef typename IndicesType::Scalar StorageIndex;\n\n    inline Transpositions() {}\n\n    /** Copy constructor. */\n    template<typename OtherDerived>\n    inline Transpositions(const TranspositionsBase<OtherDerived>& other)\n      : m_indices(other.indices()) {}\n\n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    /** Standard copy constructor. Defined only to prevent a default copy constructor\n      * from hiding the other templated constructor */\n    inline Transpositions(const Transpositions& other) : m_indices(other.indices()) {}\n    #endif\n\n    /** Generic constructor from expression of the transposition indices. */\n    template<typename Other>\n    explicit inline Transpositions(const MatrixBase<Other>& indices) : m_indices(indices)\n    {}\n\n    /** Copies the \\a other transpositions into \\c *this */\n    template<typename OtherDerived>\n    Transpositions& operator=(const TranspositionsBase<OtherDerived>& other)\n    {\n      return Base::operator=(other);\n    }\n\n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    /** This is a special case of the templated operator=. Its purpose is to\n      * prevent a default operator= from hiding the templated operator=.\n      */\n    Transpositions& operator=(const Transpositions& other)\n    {\n      m_indices = other.m_indices;\n      return *this;\n    }\n    #endif\n\n    /** Constructs an uninitialized permutation matrix of given size.\n      */\n    inline Transpositions(Index size) : m_indices(size)\n    {}\n\n    /** const version of indices(). */\n    const IndicesType& indices() const { return m_indices; }\n    /** \\returns a reference to the stored array representing the transpositions. */\n    IndicesType& indices() { return m_indices; }\n\n  protected:\n\n    IndicesType m_indices;\n};\n\n\nnamespace internal {\ntemplate<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename _StorageIndex, int _PacketAccess>\nstruct traits<Map<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,_StorageIndex>,_PacketAccess> >\n : traits<PermutationMatrix<SizeAtCompileTime,MaxSizeAtCompileTime,_StorageIndex> >\n{\n  typedef Map<const Matrix<_StorageIndex,SizeAtCompileTime,1,0,MaxSizeAtCompileTime,1>, _PacketAccess> IndicesType;\n  typedef _StorageIndex StorageIndex;\n  typedef TranspositionsStorage StorageKind;\n};\n}\n\ntemplate<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename _StorageIndex, int PacketAccess>\nclass Map<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,_StorageIndex>,PacketAccess>\n : public TranspositionsBase<Map<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,_StorageIndex>,PacketAccess> >\n{\n    typedef internal::traits<Map> Traits;\n  public:\n\n    typedef TranspositionsBase<Map> Base;\n    typedef typename Traits::IndicesType IndicesType;\n    typedef typename IndicesType::Scalar StorageIndex;\n\n    explicit inline Map(const StorageIndex* indicesPtr)\n      : m_indices(indicesPtr)\n    {}\n\n    inline Map(const StorageIndex* indicesPtr, Index size)\n      : m_indices(indicesPtr,size)\n    {}\n\n    /** Copies the \\a other transpositions into \\c *this */\n    template<typename OtherDerived>\n    Map& operator=(const TranspositionsBase<OtherDerived>& other)\n    {\n      return Base::operator=(other);\n    }\n\n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    /** This is a special case of the templated operator=. Its purpose is to\n      * prevent a default operator= from hiding the templated operator=.\n      */\n    Map& operator=(const Map& other)\n    {\n      m_indices = other.m_indices;\n      return *this;\n    }\n    #endif\n\n    /** const version of indices(). */\n    const IndicesType& indices() const { return m_indices; }\n    \n    /** \\returns a reference to the stored array representing the transpositions. */\n    IndicesType& indices() { return m_indices; }\n\n  protected:\n\n    IndicesType m_indices;\n};\n\nnamespace internal {\ntemplate<typename _IndicesType>\nstruct traits<TranspositionsWrapper<_IndicesType> >\n : traits<PermutationWrapper<_IndicesType> >\n{\n  typedef TranspositionsStorage StorageKind;\n};\n}\n\ntemplate<typename _IndicesType>\nclass TranspositionsWrapper\n : public TranspositionsBase<TranspositionsWrapper<_IndicesType> >\n{\n    typedef internal::traits<TranspositionsWrapper> Traits;\n  public:\n\n    typedef TranspositionsBase<TranspositionsWrapper> Base;\n    typedef typename Traits::IndicesType IndicesType;\n    typedef typename IndicesType::Scalar StorageIndex;\n\n    explicit inline TranspositionsWrapper(IndicesType& indices)\n      : m_indices(indices)\n    {}\n\n    /** Copies the \\a other transpositions into \\c *this */\n    template<typename OtherDerived>\n    TranspositionsWrapper& operator=(const TranspositionsBase<OtherDerived>& other)\n    {\n      return Base::operator=(other);\n    }\n\n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    /** This is a special case of the templated operator=. Its purpose is to\n      * prevent a default operator= from hiding the templated operator=.\n      */\n    TranspositionsWrapper& operator=(const TranspositionsWrapper& other)\n    {\n      m_indices = other.m_indices;\n      return *this;\n    }\n    #endif\n\n    /** const version of indices(). */\n    const IndicesType& indices() const { return m_indices; }\n\n    /** \\returns a reference to the stored array representing the transpositions. */\n    IndicesType& indices() { return m_indices; }\n\n  protected:\n\n    typename IndicesType::Nested m_indices;\n};\n\n\n\n/** \\returns the \\a matrix with the \\a transpositions applied to the columns.\n  */\ntemplate<typename MatrixDerived, typename TranspositionsDerived>\nEIGEN_DEVICE_FUNC\nconst Product<MatrixDerived, TranspositionsDerived, AliasFreeProduct>\noperator*(const MatrixBase<MatrixDerived> &matrix,\n          const TranspositionsBase<TranspositionsDerived>& transpositions)\n{\n  return Product<MatrixDerived, TranspositionsDerived, AliasFreeProduct>\n            (matrix.derived(), transpositions.derived());\n}\n\n/** \\returns the \\a matrix with the \\a transpositions applied to the rows.\n  */\ntemplate<typename TranspositionsDerived, typename MatrixDerived>\nEIGEN_DEVICE_FUNC\nconst Product<TranspositionsDerived, MatrixDerived, AliasFreeProduct>\noperator*(const TranspositionsBase<TranspositionsDerived> &transpositions,\n          const MatrixBase<MatrixDerived>& matrix)\n{\n  return Product<TranspositionsDerived, MatrixDerived, AliasFreeProduct>\n            (transpositions.derived(), matrix.derived());\n}\n\n// Template partial specialization for transposed/inverse transpositions\n\nnamespace internal {\n\ntemplate<typename Derived>\nstruct traits<Transpose<TranspositionsBase<Derived> > >\n : traits<Derived>\n{};\n\n} // end namespace internal\n\ntemplate<typename TranspositionsDerived>\nclass Transpose<TranspositionsBase<TranspositionsDerived> >\n{\n    typedef TranspositionsDerived TranspositionType;\n    typedef typename TranspositionType::IndicesType IndicesType;\n  public:\n\n    explicit Transpose(const TranspositionType& t) : m_transpositions(t) {}\n\n    Index size() const { return m_transpositions.size(); }\n    Index rows() const { return m_transpositions.size(); }\n    Index cols() const { return m_transpositions.size(); }\n\n    /** \\returns the \\a matrix with the inverse transpositions applied to the columns.\n      */\n    template<typename OtherDerived> friend\n    const Product<OtherDerived, Transpose, AliasFreeProduct>\n    operator*(const MatrixBase<OtherDerived>& matrix, const Transpose& trt)\n    {\n      return Product<OtherDerived, Transpose, AliasFreeProduct>(matrix.derived(), trt);\n    }\n\n    /** \\returns the \\a matrix with the inverse transpositions applied to the rows.\n      */\n    template<typename OtherDerived>\n    const Product<Transpose, OtherDerived, AliasFreeProduct>\n    operator*(const MatrixBase<OtherDerived>& matrix) const\n    {\n      return Product<Transpose, OtherDerived, AliasFreeProduct>(*this, matrix.derived());\n    }\n    \n    const TranspositionType& nestedExpression() const { return m_transpositions; }\n\n  protected:\n    const TranspositionType& m_transpositions;\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_TRANSPOSITIONS_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/TriangularMatrix.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_TRIANGULARMATRIX_H\n#define EIGEN_TRIANGULARMATRIX_H\n\nnamespace Eigen { \n\nnamespace internal {\n  \ntemplate<int Side, typename TriangularType, typename Rhs> struct triangular_solve_retval;\n  \n}\n\n/** \\class TriangularBase\n  * \\ingroup Core_Module\n  *\n  * \\brief Base class for triangular part in a matrix\n  */\ntemplate<typename Derived> class TriangularBase : public EigenBase<Derived>\n{\n  public:\n\n    enum {\n      Mode = internal::traits<Derived>::Mode,\n      RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,\n      ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,\n      MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime,\n      MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime,\n      \n      SizeAtCompileTime = (internal::size_at_compile_time<internal::traits<Derived>::RowsAtCompileTime,\n                                                   internal::traits<Derived>::ColsAtCompileTime>::ret),\n      /**< This is equal to the number of coefficients, i.e. the number of\n          * rows times the number of columns, or to \\a Dynamic if this is not\n          * known at compile-time. \\sa RowsAtCompileTime, ColsAtCompileTime */\n      \n      MaxSizeAtCompileTime = (internal::size_at_compile_time<internal::traits<Derived>::MaxRowsAtCompileTime,\n                                                   internal::traits<Derived>::MaxColsAtCompileTime>::ret)\n        \n    };\n    typedef typename internal::traits<Derived>::Scalar Scalar;\n    typedef typename internal::traits<Derived>::StorageKind StorageKind;\n    typedef typename internal::traits<Derived>::StorageIndex StorageIndex;\n    typedef typename internal::traits<Derived>::FullMatrixType DenseMatrixType;\n    typedef DenseMatrixType DenseType;\n    typedef Derived const& Nested;\n\n    EIGEN_DEVICE_FUNC\n    inline TriangularBase() { eigen_assert(!((Mode&UnitDiag) && (Mode&ZeroDiag))); }\n\n    EIGEN_DEVICE_FUNC\n    inline Index rows() const { return derived().rows(); }\n    EIGEN_DEVICE_FUNC\n    inline Index cols() const { return derived().cols(); }\n    EIGEN_DEVICE_FUNC\n    inline Index outerStride() const { return derived().outerStride(); }\n    EIGEN_DEVICE_FUNC\n    inline Index innerStride() const { return derived().innerStride(); }\n    \n    // dummy resize function\n    void resize(Index rows, Index cols)\n    {\n      EIGEN_UNUSED_VARIABLE(rows);\n      EIGEN_UNUSED_VARIABLE(cols);\n      eigen_assert(rows==this->rows() && cols==this->cols());\n    }\n\n    EIGEN_DEVICE_FUNC\n    inline Scalar coeff(Index row, Index col) const  { return derived().coeff(row,col); }\n    EIGEN_DEVICE_FUNC\n    inline Scalar& coeffRef(Index row, Index col) { return derived().coeffRef(row,col); }\n\n    /** \\see MatrixBase::copyCoeff(row,col)\n      */\n    template<typename Other>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE void copyCoeff(Index row, Index col, Other& other)\n    {\n      derived().coeffRef(row, col) = other.coeff(row, col);\n    }\n\n    EIGEN_DEVICE_FUNC\n    inline Scalar operator()(Index row, Index col) const\n    {\n      check_coordinates(row, col);\n      return coeff(row,col);\n    }\n    EIGEN_DEVICE_FUNC\n    inline Scalar& operator()(Index row, Index col)\n    {\n      check_coordinates(row, col);\n      return coeffRef(row,col);\n    }\n\n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    EIGEN_DEVICE_FUNC\n    inline const Derived& derived() const { return *static_cast<const Derived*>(this); }\n    EIGEN_DEVICE_FUNC\n    inline Derived& derived() { return *static_cast<Derived*>(this); }\n    #endif // not EIGEN_PARSED_BY_DOXYGEN\n\n    template<typename DenseDerived>\n    EIGEN_DEVICE_FUNC\n    void evalTo(MatrixBase<DenseDerived> &other) const;\n    template<typename DenseDerived>\n    EIGEN_DEVICE_FUNC\n    void evalToLazy(MatrixBase<DenseDerived> &other) const;\n\n    EIGEN_DEVICE_FUNC\n    DenseMatrixType toDenseMatrix() const\n    {\n      DenseMatrixType res(rows(), cols());\n      evalToLazy(res);\n      return res;\n    }\n\n  protected:\n\n    void check_coordinates(Index row, Index col) const\n    {\n      EIGEN_ONLY_USED_FOR_DEBUG(row);\n      EIGEN_ONLY_USED_FOR_DEBUG(col);\n      eigen_assert(col>=0 && col<cols() && row>=0 && row<rows());\n      const int mode = int(Mode) & ~SelfAdjoint;\n      EIGEN_ONLY_USED_FOR_DEBUG(mode);\n      eigen_assert((mode==Upper && col>=row)\n                || (mode==Lower && col<=row)\n                || ((mode==StrictlyUpper || mode==UnitUpper) && col>row)\n                || ((mode==StrictlyLower || mode==UnitLower) && col<row));\n    }\n\n    #ifdef EIGEN_INTERNAL_DEBUGGING\n    void check_coordinates_internal(Index row, Index col) const\n    {\n      check_coordinates(row, col);\n    }\n    #else\n    void check_coordinates_internal(Index , Index ) const {}\n    #endif\n\n};\n\n/** \\class TriangularView\n  * \\ingroup Core_Module\n  *\n  * \\brief Expression of a triangular part in a matrix\n  *\n  * \\param MatrixType the type of the object in which we are taking the triangular part\n  * \\param Mode the kind of triangular matrix expression to construct. Can be #Upper,\n  *             #Lower, #UnitUpper, #UnitLower, #StrictlyUpper, or #StrictlyLower.\n  *             This is in fact a bit field; it must have either #Upper or #Lower, \n  *             and additionally it may have #UnitDiag or #ZeroDiag or neither.\n  *\n  * This class represents a triangular part of a matrix, not necessarily square. Strictly speaking, for rectangular\n  * matrices one should speak of \"trapezoid\" parts. This class is the return type\n  * of MatrixBase::triangularView() and SparseMatrixBase::triangularView(), and most of the time this is the only way it is used.\n  *\n  * \\sa MatrixBase::triangularView()\n  */\nnamespace internal {\ntemplate<typename MatrixType, unsigned int _Mode>\nstruct traits<TriangularView<MatrixType, _Mode> > : traits<MatrixType>\n{\n  typedef typename ref_selector<MatrixType>::non_const_type MatrixTypeNested;\n  typedef typename remove_reference<MatrixTypeNested>::type MatrixTypeNestedNonRef;\n  typedef typename remove_all<MatrixTypeNested>::type MatrixTypeNestedCleaned;\n  typedef typename MatrixType::PlainObject FullMatrixType;\n  typedef MatrixType ExpressionType;\n  enum {\n    Mode = _Mode,\n    FlagsLvalueBit = is_lvalue<MatrixType>::value ? LvalueBit : 0,\n    Flags = (MatrixTypeNestedCleaned::Flags & (HereditaryBits | FlagsLvalueBit) & (~(PacketAccessBit | DirectAccessBit | LinearAccessBit)))\n  };\n};\n}\n\ntemplate<typename _MatrixType, unsigned int _Mode, typename StorageKind> class TriangularViewImpl;\n\ntemplate<typename _MatrixType, unsigned int _Mode> class TriangularView\n  : public TriangularViewImpl<_MatrixType, _Mode, typename internal::traits<_MatrixType>::StorageKind >\n{\n  public:\n\n    typedef TriangularViewImpl<_MatrixType, _Mode, typename internal::traits<_MatrixType>::StorageKind > Base;\n    typedef typename internal::traits<TriangularView>::Scalar Scalar;\n    typedef _MatrixType MatrixType;\n\n  protected:\n    typedef typename internal::traits<TriangularView>::MatrixTypeNested MatrixTypeNested;\n    typedef typename internal::traits<TriangularView>::MatrixTypeNestedNonRef MatrixTypeNestedNonRef;\n\n    typedef typename internal::remove_all<typename MatrixType::ConjugateReturnType>::type MatrixConjugateReturnType;\n    \n  public:\n\n    typedef typename internal::traits<TriangularView>::StorageKind StorageKind;\n    typedef typename internal::traits<TriangularView>::MatrixTypeNestedCleaned NestedExpression;\n\n    enum {\n      Mode = _Mode,\n      Flags = internal::traits<TriangularView>::Flags,\n      TransposeMode = (Mode & Upper ? Lower : 0)\n                    | (Mode & Lower ? Upper : 0)\n                    | (Mode & (UnitDiag))\n                    | (Mode & (ZeroDiag)),\n      IsVectorAtCompileTime = false\n    };\n\n    EIGEN_DEVICE_FUNC\n    explicit inline TriangularView(MatrixType& matrix) : m_matrix(matrix)\n    {}\n    \n    using Base::operator=;\n    TriangularView& operator=(const TriangularView &other)\n    { return Base::operator=(other); }\n\n    /** \\copydoc EigenBase::rows() */\n    EIGEN_DEVICE_FUNC\n    inline Index rows() const { return m_matrix.rows(); }\n    /** \\copydoc EigenBase::cols() */\n    EIGEN_DEVICE_FUNC\n    inline Index cols() const { return m_matrix.cols(); }\n\n    /** \\returns a const reference to the nested expression */\n    EIGEN_DEVICE_FUNC\n    const NestedExpression& nestedExpression() const { return m_matrix; }\n\n    /** \\returns a reference to the nested expression */\n    EIGEN_DEVICE_FUNC\n    NestedExpression& nestedExpression() { return m_matrix; }\n    \n    typedef TriangularView<const MatrixConjugateReturnType,Mode> ConjugateReturnType;\n    /** \\sa MatrixBase::conjugate() const */\n    EIGEN_DEVICE_FUNC\n    inline const ConjugateReturnType conjugate() const\n    { return ConjugateReturnType(m_matrix.conjugate()); }\n\n    typedef TriangularView<const typename MatrixType::AdjointReturnType,TransposeMode> AdjointReturnType;\n    /** \\sa MatrixBase::adjoint() const */\n    EIGEN_DEVICE_FUNC\n    inline const AdjointReturnType adjoint() const\n    { return AdjointReturnType(m_matrix.adjoint()); }\n\n    typedef TriangularView<typename MatrixType::TransposeReturnType,TransposeMode> TransposeReturnType;\n     /** \\sa MatrixBase::transpose() */\n    EIGEN_DEVICE_FUNC\n    inline TransposeReturnType transpose()\n    {\n      EIGEN_STATIC_ASSERT_LVALUE(MatrixType)\n      typename MatrixType::TransposeReturnType tmp(m_matrix);\n      return TransposeReturnType(tmp);\n    }\n    \n    typedef TriangularView<const typename MatrixType::ConstTransposeReturnType,TransposeMode> ConstTransposeReturnType;\n    /** \\sa MatrixBase::transpose() const */\n    EIGEN_DEVICE_FUNC\n    inline const ConstTransposeReturnType transpose() const\n    {\n      return ConstTransposeReturnType(m_matrix.transpose());\n    }\n\n    template<typename Other>\n    EIGEN_DEVICE_FUNC\n    inline const Solve<TriangularView, Other> \n    solve(const MatrixBase<Other>& other) const\n    { return Solve<TriangularView, Other>(*this, other.derived()); }\n    \n  // workaround MSVC ICE\n  #if EIGEN_COMP_MSVC\n    template<int Side, typename Other>\n    EIGEN_DEVICE_FUNC\n    inline const internal::triangular_solve_retval<Side,TriangularView, Other>\n    solve(const MatrixBase<Other>& other) const\n    { return Base::template solve<Side>(other); }\n  #else\n    using Base::solve;\n  #endif\n\n    /** \\returns a selfadjoint view of the referenced triangular part which must be either \\c #Upper or \\c #Lower.\n      *\n      * This is a shortcut for \\code this->nestedExpression().selfadjointView<(*this)::Mode>() \\endcode\n      * \\sa MatrixBase::selfadjointView() */\n    EIGEN_DEVICE_FUNC\n    SelfAdjointView<MatrixTypeNestedNonRef,Mode> selfadjointView()\n    {\n      EIGEN_STATIC_ASSERT((Mode&(UnitDiag|ZeroDiag))==0,PROGRAMMING_ERROR);\n      return SelfAdjointView<MatrixTypeNestedNonRef,Mode>(m_matrix);\n    }\n\n    /** This is the const version of selfadjointView() */\n    EIGEN_DEVICE_FUNC\n    const SelfAdjointView<MatrixTypeNestedNonRef,Mode> selfadjointView() const\n    {\n      EIGEN_STATIC_ASSERT((Mode&(UnitDiag|ZeroDiag))==0,PROGRAMMING_ERROR);\n      return SelfAdjointView<MatrixTypeNestedNonRef,Mode>(m_matrix);\n    }\n\n\n    /** \\returns the determinant of the triangular matrix\n      * \\sa MatrixBase::determinant() */\n    EIGEN_DEVICE_FUNC\n    Scalar determinant() const\n    {\n      if (Mode & UnitDiag)\n        return 1;\n      else if (Mode & ZeroDiag)\n        return 0;\n      else\n        return m_matrix.diagonal().prod();\n    }\n      \n  protected:\n\n    MatrixTypeNested m_matrix;\n};\n\n/** \\ingroup Core_Module\n  *\n  * \\brief Base class for a triangular part in a \\b dense matrix\n  *\n  * This class is an abstract base class of class TriangularView, and objects of type TriangularViewImpl cannot be instantiated.\n  * It extends class TriangularView with additional methods which available for dense expressions only.\n  *\n  * \\sa class TriangularView, MatrixBase::triangularView()\n  */\ntemplate<typename _MatrixType, unsigned int _Mode> class TriangularViewImpl<_MatrixType,_Mode,Dense>\n  : public TriangularBase<TriangularView<_MatrixType, _Mode> >\n{\n  public:\n\n    typedef TriangularView<_MatrixType, _Mode> TriangularViewType;\n    typedef TriangularBase<TriangularViewType> Base;\n    typedef typename internal::traits<TriangularViewType>::Scalar Scalar;\n\n    typedef _MatrixType MatrixType;\n    typedef typename MatrixType::PlainObject DenseMatrixType;\n    typedef DenseMatrixType PlainObject;\n\n  public:\n    using Base::evalToLazy;\n    using Base::derived;\n\n    typedef typename internal::traits<TriangularViewType>::StorageKind StorageKind;\n\n    enum {\n      Mode = _Mode,\n      Flags = internal::traits<TriangularViewType>::Flags\n    };\n\n    /** \\returns the outer-stride of the underlying dense matrix\n      * \\sa DenseCoeffsBase::outerStride() */\n    EIGEN_DEVICE_FUNC\n    inline Index outerStride() const { return derived().nestedExpression().outerStride(); }\n    /** \\returns the inner-stride of the underlying dense matrix\n      * \\sa DenseCoeffsBase::innerStride() */\n    EIGEN_DEVICE_FUNC\n    inline Index innerStride() const { return derived().nestedExpression().innerStride(); }\n\n    /** \\sa MatrixBase::operator+=() */\n    template<typename Other>\n    EIGEN_DEVICE_FUNC\n    TriangularViewType&  operator+=(const DenseBase<Other>& other) {\n      internal::call_assignment_no_alias(derived(), other.derived(), internal::add_assign_op<Scalar,typename Other::Scalar>());\n      return derived();\n    }\n    /** \\sa MatrixBase::operator-=() */\n    template<typename Other>\n    EIGEN_DEVICE_FUNC\n    TriangularViewType&  operator-=(const DenseBase<Other>& other) {\n      internal::call_assignment_no_alias(derived(), other.derived(), internal::sub_assign_op<Scalar,typename Other::Scalar>());\n      return derived();\n    }\n    \n    /** \\sa MatrixBase::operator*=() */\n    EIGEN_DEVICE_FUNC\n    TriangularViewType&  operator*=(const typename internal::traits<MatrixType>::Scalar& other) { return *this = derived().nestedExpression() * other; }\n    /** \\sa DenseBase::operator/=() */\n    EIGEN_DEVICE_FUNC\n    TriangularViewType&  operator/=(const typename internal::traits<MatrixType>::Scalar& other) { return *this = derived().nestedExpression() / other; }\n\n    /** \\sa MatrixBase::fill() */\n    EIGEN_DEVICE_FUNC\n    void fill(const Scalar& value) { setConstant(value); }\n    /** \\sa MatrixBase::setConstant() */\n    EIGEN_DEVICE_FUNC\n    TriangularViewType& setConstant(const Scalar& value)\n    { return *this = MatrixType::Constant(derived().rows(), derived().cols(), value); }\n    /** \\sa MatrixBase::setZero() */\n    EIGEN_DEVICE_FUNC\n    TriangularViewType& setZero() { return setConstant(Scalar(0)); }\n    /** \\sa MatrixBase::setOnes() */\n    EIGEN_DEVICE_FUNC\n    TriangularViewType& setOnes() { return setConstant(Scalar(1)); }\n\n    /** \\sa MatrixBase::coeff()\n      * \\warning the coordinates must fit into the referenced triangular part\n      */\n    EIGEN_DEVICE_FUNC\n    inline Scalar coeff(Index row, Index col) const\n    {\n      Base::check_coordinates_internal(row, col);\n      return derived().nestedExpression().coeff(row, col);\n    }\n\n    /** \\sa MatrixBase::coeffRef()\n      * \\warning the coordinates must fit into the referenced triangular part\n      */\n    EIGEN_DEVICE_FUNC\n    inline Scalar& coeffRef(Index row, Index col)\n    {\n      EIGEN_STATIC_ASSERT_LVALUE(TriangularViewType);\n      Base::check_coordinates_internal(row, col);\n      return derived().nestedExpression().coeffRef(row, col);\n    }\n\n    /** Assigns a triangular matrix to a triangular part of a dense matrix */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    TriangularViewType& operator=(const TriangularBase<OtherDerived>& other);\n\n    /** Shortcut for\\code *this = other.other.triangularView<(*this)::Mode>() \\endcode */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    TriangularViewType& operator=(const MatrixBase<OtherDerived>& other);\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\n    EIGEN_DEVICE_FUNC\n    TriangularViewType& operator=(const TriangularViewImpl& other)\n    { return *this = other.derived().nestedExpression(); }\n\n    /** \\deprecated */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    void lazyAssign(const TriangularBase<OtherDerived>& other);\n\n    /** \\deprecated */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    void lazyAssign(const MatrixBase<OtherDerived>& other);\n#endif\n\n    /** Efficient triangular matrix times vector/matrix product */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    const Product<TriangularViewType,OtherDerived>\n    operator*(const MatrixBase<OtherDerived>& rhs) const\n    {\n      return Product<TriangularViewType,OtherDerived>(derived(), rhs.derived());\n    }\n\n    /** Efficient vector/matrix times triangular matrix product */\n    template<typename OtherDerived> friend\n    EIGEN_DEVICE_FUNC\n    const Product<OtherDerived,TriangularViewType>\n    operator*(const MatrixBase<OtherDerived>& lhs, const TriangularViewImpl& rhs)\n    {\n      return Product<OtherDerived,TriangularViewType>(lhs.derived(),rhs.derived());\n    }\n\n    /** \\returns the product of the inverse of \\c *this with \\a other, \\a *this being triangular.\n      *\n      * This function computes the inverse-matrix matrix product inverse(\\c *this) * \\a other if\n      * \\a Side==OnTheLeft (the default), or the right-inverse-multiply  \\a other * inverse(\\c *this) if\n      * \\a Side==OnTheRight.\n      *\n      * Note that the template parameter \\c Side can be ommitted, in which case \\c Side==OnTheLeft\n      *\n      * The matrix \\c *this must be triangular and invertible (i.e., all the coefficients of the\n      * diagonal must be non zero). It works as a forward (resp. backward) substitution if \\c *this\n      * is an upper (resp. lower) triangular matrix.\n      *\n      * Example: \\include Triangular_solve.cpp\n      * Output: \\verbinclude Triangular_solve.out\n      *\n      * This function returns an expression of the inverse-multiply and can works in-place if it is assigned\n      * to the same matrix or vector \\a other.\n      *\n      * For users coming from BLAS, this function (and more specifically solveInPlace()) offer\n      * all the operations supported by the \\c *TRSV and \\c *TRSM BLAS routines.\n      *\n      * \\sa TriangularView::solveInPlace()\n      */\n    template<int Side, typename Other>\n    EIGEN_DEVICE_FUNC\n    inline const internal::triangular_solve_retval<Side,TriangularViewType, Other>\n    solve(const MatrixBase<Other>& other) const;\n\n    /** \"in-place\" version of TriangularView::solve() where the result is written in \\a other\n      *\n      * \\warning The parameter is only marked 'const' to make the C++ compiler accept a temporary expression here.\n      * This function will const_cast it, so constness isn't honored here.\n      *\n      * Note that the template parameter \\c Side can be ommitted, in which case \\c Side==OnTheLeft\n      *\n      * See TriangularView:solve() for the details.\n      */\n    template<int Side, typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    void solveInPlace(const MatrixBase<OtherDerived>& other) const;\n\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    void solveInPlace(const MatrixBase<OtherDerived>& other) const\n    { return solveInPlace<OnTheLeft>(other); }\n\n    /** Swaps the coefficients of the common triangular parts of two matrices */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n#ifdef EIGEN_PARSED_BY_DOXYGEN\n    void swap(TriangularBase<OtherDerived> &other)\n#else\n    void swap(TriangularBase<OtherDerived> const & other)\n#endif\n    {\n      EIGEN_STATIC_ASSERT_LVALUE(OtherDerived);\n      call_assignment(derived(), other.const_cast_derived(), internal::swap_assign_op<Scalar>());\n    }\n\n    /** \\deprecated\n      * Shortcut for \\code (*this).swap(other.triangularView<(*this)::Mode>()) \\endcode */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    void swap(MatrixBase<OtherDerived> const & other)\n    {\n      EIGEN_STATIC_ASSERT_LVALUE(OtherDerived);\n      call_assignment(derived(), other.const_cast_derived(), internal::swap_assign_op<Scalar>());\n    }\n\n    template<typename RhsType, typename DstType>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE void _solve_impl(const RhsType &rhs, DstType &dst) const {\n      if(!internal::is_same_dense(dst,rhs))\n        dst = rhs;\n      this->solveInPlace(dst);\n    }\n\n    template<typename ProductType>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE TriangularViewType& _assignProduct(const ProductType& prod, const Scalar& alpha, bool beta);\n};\n\n/***************************************************************************\n* Implementation of triangular evaluation/assignment\n***************************************************************************/\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\n// FIXME should we keep that possibility\ntemplate<typename MatrixType, unsigned int Mode>\ntemplate<typename OtherDerived>\ninline TriangularView<MatrixType, Mode>&\nTriangularViewImpl<MatrixType, Mode, Dense>::operator=(const MatrixBase<OtherDerived>& other)\n{\n  internal::call_assignment_no_alias(derived(), other.derived(), internal::assign_op<Scalar,typename OtherDerived::Scalar>());\n  return derived();\n}\n\n// FIXME should we keep that possibility\ntemplate<typename MatrixType, unsigned int Mode>\ntemplate<typename OtherDerived>\nvoid TriangularViewImpl<MatrixType, Mode, Dense>::lazyAssign(const MatrixBase<OtherDerived>& other)\n{\n  internal::call_assignment_no_alias(derived(), other.template triangularView<Mode>());\n}\n\n\n\ntemplate<typename MatrixType, unsigned int Mode>\ntemplate<typename OtherDerived>\ninline TriangularView<MatrixType, Mode>&\nTriangularViewImpl<MatrixType, Mode, Dense>::operator=(const TriangularBase<OtherDerived>& other)\n{\n  eigen_assert(Mode == int(OtherDerived::Mode));\n  internal::call_assignment(derived(), other.derived());\n  return derived();\n}\n\ntemplate<typename MatrixType, unsigned int Mode>\ntemplate<typename OtherDerived>\nvoid TriangularViewImpl<MatrixType, Mode, Dense>::lazyAssign(const TriangularBase<OtherDerived>& other)\n{\n  eigen_assert(Mode == int(OtherDerived::Mode));\n  internal::call_assignment_no_alias(derived(), other.derived());\n}\n#endif\n\n/***************************************************************************\n* Implementation of TriangularBase methods\n***************************************************************************/\n\n/** Assigns a triangular or selfadjoint matrix to a dense matrix.\n  * If the matrix is triangular, the opposite part is set to zero. */\ntemplate<typename Derived>\ntemplate<typename DenseDerived>\nvoid TriangularBase<Derived>::evalTo(MatrixBase<DenseDerived> &other) const\n{\n  evalToLazy(other.derived());\n}\n\n/***************************************************************************\n* Implementation of TriangularView methods\n***************************************************************************/\n\n/***************************************************************************\n* Implementation of MatrixBase methods\n***************************************************************************/\n\n/**\n  * \\returns an expression of a triangular view extracted from the current matrix\n  *\n  * The parameter \\a Mode can have the following values: \\c #Upper, \\c #StrictlyUpper, \\c #UnitUpper,\n  * \\c #Lower, \\c #StrictlyLower, \\c #UnitLower.\n  *\n  * Example: \\include MatrixBase_triangularView.cpp\n  * Output: \\verbinclude MatrixBase_triangularView.out\n  *\n  * \\sa class TriangularView\n  */\ntemplate<typename Derived>\ntemplate<unsigned int Mode>\ntypename MatrixBase<Derived>::template TriangularViewReturnType<Mode>::Type\nMatrixBase<Derived>::triangularView()\n{\n  return typename TriangularViewReturnType<Mode>::Type(derived());\n}\n\n/** This is the const version of MatrixBase::triangularView() */\ntemplate<typename Derived>\ntemplate<unsigned int Mode>\ntypename MatrixBase<Derived>::template ConstTriangularViewReturnType<Mode>::Type\nMatrixBase<Derived>::triangularView() const\n{\n  return typename ConstTriangularViewReturnType<Mode>::Type(derived());\n}\n\n/** \\returns true if *this is approximately equal to an upper triangular matrix,\n  *          within the precision given by \\a prec.\n  *\n  * \\sa isLowerTriangular()\n  */\ntemplate<typename Derived>\nbool MatrixBase<Derived>::isUpperTriangular(const RealScalar& prec) const\n{\n  RealScalar maxAbsOnUpperPart = static_cast<RealScalar>(-1);\n  for(Index j = 0; j < cols(); ++j)\n  {\n    Index maxi = numext::mini(j, rows()-1);\n    for(Index i = 0; i <= maxi; ++i)\n    {\n      RealScalar absValue = numext::abs(coeff(i,j));\n      if(absValue > maxAbsOnUpperPart) maxAbsOnUpperPart = absValue;\n    }\n  }\n  RealScalar threshold = maxAbsOnUpperPart * prec;\n  for(Index j = 0; j < cols(); ++j)\n    for(Index i = j+1; i < rows(); ++i)\n      if(numext::abs(coeff(i, j)) > threshold) return false;\n  return true;\n}\n\n/** \\returns true if *this is approximately equal to a lower triangular matrix,\n  *          within the precision given by \\a prec.\n  *\n  * \\sa isUpperTriangular()\n  */\ntemplate<typename Derived>\nbool MatrixBase<Derived>::isLowerTriangular(const RealScalar& prec) const\n{\n  RealScalar maxAbsOnLowerPart = static_cast<RealScalar>(-1);\n  for(Index j = 0; j < cols(); ++j)\n    for(Index i = j; i < rows(); ++i)\n    {\n      RealScalar absValue = numext::abs(coeff(i,j));\n      if(absValue > maxAbsOnLowerPart) maxAbsOnLowerPart = absValue;\n    }\n  RealScalar threshold = maxAbsOnLowerPart * prec;\n  for(Index j = 1; j < cols(); ++j)\n  {\n    Index maxi = numext::mini(j, rows()-1);\n    for(Index i = 0; i < maxi; ++i)\n      if(numext::abs(coeff(i, j)) > threshold) return false;\n  }\n  return true;\n}\n\n\n/***************************************************************************\n****************************************************************************\n* Evaluators and Assignment of triangular expressions\n***************************************************************************\n***************************************************************************/\n\nnamespace internal {\n\n  \n// TODO currently a triangular expression has the form TriangularView<.,.>\n//      in the future triangular-ness should be defined by the expression traits\n//      such that Transpose<TriangularView<.,.> > is valid. (currently TriangularBase::transpose() is overloaded to make it work)\ntemplate<typename MatrixType, unsigned int Mode>\nstruct evaluator_traits<TriangularView<MatrixType,Mode> >\n{\n  typedef typename storage_kind_to_evaluator_kind<typename MatrixType::StorageKind>::Kind Kind;\n  typedef typename glue_shapes<typename evaluator_traits<MatrixType>::Shape, TriangularShape>::type Shape;\n};\n\ntemplate<typename MatrixType, unsigned int Mode>\nstruct unary_evaluator<TriangularView<MatrixType,Mode>, IndexBased>\n : evaluator<typename internal::remove_all<MatrixType>::type>\n{\n  typedef TriangularView<MatrixType,Mode> XprType;\n  typedef evaluator<typename internal::remove_all<MatrixType>::type> Base;\n  unary_evaluator(const XprType &xpr) : Base(xpr.nestedExpression()) {}\n};\n\n// Additional assignment kinds:\nstruct Triangular2Triangular    {};\nstruct Triangular2Dense         {};\nstruct Dense2Triangular         {};\n\n\ntemplate<typename Kernel, unsigned int Mode, int UnrollCount, bool ClearOpposite> struct triangular_assignment_loop;\n\n \n/** \\internal Specialization of the dense assignment kernel for triangular matrices.\n  * The main difference is that the triangular, diagonal, and opposite parts are processed through three different functions.\n  * \\tparam UpLo must be either Lower or Upper\n  * \\tparam Mode must be either 0, UnitDiag, ZeroDiag, or SelfAdjoint\n  */\ntemplate<int UpLo, int Mode, int SetOpposite, typename DstEvaluatorTypeT, typename SrcEvaluatorTypeT, typename Functor, int Version = Specialized>\nclass triangular_dense_assignment_kernel : public generic_dense_assignment_kernel<DstEvaluatorTypeT, SrcEvaluatorTypeT, Functor, Version>\n{\nprotected:\n  typedef generic_dense_assignment_kernel<DstEvaluatorTypeT, SrcEvaluatorTypeT, Functor, Version> Base;\n  typedef typename Base::DstXprType DstXprType;\n  typedef typename Base::SrcXprType SrcXprType;\n  using Base::m_dst;\n  using Base::m_src;\n  using Base::m_functor;\npublic:\n  \n  typedef typename Base::DstEvaluatorType DstEvaluatorType;\n  typedef typename Base::SrcEvaluatorType SrcEvaluatorType;\n  typedef typename Base::Scalar Scalar;\n  typedef typename Base::AssignmentTraits AssignmentTraits;\n  \n  \n  EIGEN_DEVICE_FUNC triangular_dense_assignment_kernel(DstEvaluatorType &dst, const SrcEvaluatorType &src, const Functor &func, DstXprType& dstExpr)\n    : Base(dst, src, func, dstExpr)\n  {}\n  \n#ifdef EIGEN_INTERNAL_DEBUGGING\n  EIGEN_DEVICE_FUNC void assignCoeff(Index row, Index col)\n  {\n    eigen_internal_assert(row!=col);\n    Base::assignCoeff(row,col);\n  }\n#else\n  using Base::assignCoeff;\n#endif\n  \n  EIGEN_DEVICE_FUNC void assignDiagonalCoeff(Index id)\n  {\n         if(Mode==UnitDiag && SetOpposite) m_functor.assignCoeff(m_dst.coeffRef(id,id), Scalar(1));\n    else if(Mode==ZeroDiag && SetOpposite) m_functor.assignCoeff(m_dst.coeffRef(id,id), Scalar(0));\n    else if(Mode==0)                       Base::assignCoeff(id,id);\n  }\n  \n  EIGEN_DEVICE_FUNC void assignOppositeCoeff(Index row, Index col)\n  { \n    eigen_internal_assert(row!=col);\n    if(SetOpposite)\n      m_functor.assignCoeff(m_dst.coeffRef(row,col), Scalar(0));\n  }\n};\n\ntemplate<int Mode, bool SetOpposite, typename DstXprType, typename SrcXprType, typename Functor>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nvoid call_triangular_assignment_loop(DstXprType& dst, const SrcXprType& src, const Functor &func)\n{\n  typedef evaluator<DstXprType> DstEvaluatorType;\n  typedef evaluator<SrcXprType> SrcEvaluatorType;\n\n  SrcEvaluatorType srcEvaluator(src);\n\n  Index dstRows = src.rows();\n  Index dstCols = src.cols();\n  if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))\n    dst.resize(dstRows, dstCols);\n  DstEvaluatorType dstEvaluator(dst);\n    \n  typedef triangular_dense_assignment_kernel< Mode&(Lower|Upper),Mode&(UnitDiag|ZeroDiag|SelfAdjoint),SetOpposite,\n                                              DstEvaluatorType,SrcEvaluatorType,Functor> Kernel;\n  Kernel kernel(dstEvaluator, srcEvaluator, func, dst.const_cast_derived());\n  \n  enum {\n      unroll = DstXprType::SizeAtCompileTime != Dynamic\n            && SrcEvaluatorType::CoeffReadCost < HugeCost\n            && DstXprType::SizeAtCompileTime * (DstEvaluatorType::CoeffReadCost+SrcEvaluatorType::CoeffReadCost) / 2 <= EIGEN_UNROLLING_LIMIT\n    };\n  \n  triangular_assignment_loop<Kernel, Mode, unroll ? int(DstXprType::SizeAtCompileTime) : Dynamic, SetOpposite>::run(kernel);\n}\n\ntemplate<int Mode, bool SetOpposite, typename DstXprType, typename SrcXprType>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nvoid call_triangular_assignment_loop(DstXprType& dst, const SrcXprType& src)\n{\n  call_triangular_assignment_loop<Mode,SetOpposite>(dst, src, internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar>());\n}\n\ntemplate<> struct AssignmentKind<TriangularShape,TriangularShape> { typedef Triangular2Triangular Kind; };\ntemplate<> struct AssignmentKind<DenseShape,TriangularShape>      { typedef Triangular2Dense      Kind; };\ntemplate<> struct AssignmentKind<TriangularShape,DenseShape>      { typedef Dense2Triangular      Kind; };\n\n\ntemplate< typename DstXprType, typename SrcXprType, typename Functor>\nstruct Assignment<DstXprType, SrcXprType, Functor, Triangular2Triangular>\n{\n  EIGEN_DEVICE_FUNC static void run(DstXprType &dst, const SrcXprType &src, const Functor &func)\n  {\n    eigen_assert(int(DstXprType::Mode) == int(SrcXprType::Mode));\n    \n    call_triangular_assignment_loop<DstXprType::Mode, false>(dst, src, func);  \n  }\n};\n\ntemplate< typename DstXprType, typename SrcXprType, typename Functor>\nstruct Assignment<DstXprType, SrcXprType, Functor, Triangular2Dense>\n{\n  EIGEN_DEVICE_FUNC static void run(DstXprType &dst, const SrcXprType &src, const Functor &func)\n  {\n    call_triangular_assignment_loop<SrcXprType::Mode, (SrcXprType::Mode&SelfAdjoint)==0>(dst, src, func);  \n  }\n};\n\ntemplate< typename DstXprType, typename SrcXprType, typename Functor>\nstruct Assignment<DstXprType, SrcXprType, Functor, Dense2Triangular>\n{\n  EIGEN_DEVICE_FUNC static void run(DstXprType &dst, const SrcXprType &src, const Functor &func)\n  {\n    call_triangular_assignment_loop<DstXprType::Mode, false>(dst, src, func);  \n  }\n};\n\n\ntemplate<typename Kernel, unsigned int Mode, int UnrollCount, bool SetOpposite>\nstruct triangular_assignment_loop\n{\n  // FIXME: this is not very clean, perhaps this information should be provided by the kernel?\n  typedef typename Kernel::DstEvaluatorType DstEvaluatorType;\n  typedef typename DstEvaluatorType::XprType DstXprType;\n  \n  enum {\n    col = (UnrollCount-1) / DstXprType::RowsAtCompileTime,\n    row = (UnrollCount-1) % DstXprType::RowsAtCompileTime\n  };\n  \n  typedef typename Kernel::Scalar Scalar;\n\n  EIGEN_DEVICE_FUNC\n  static inline void run(Kernel &kernel)\n  {\n    triangular_assignment_loop<Kernel, Mode, UnrollCount-1, SetOpposite>::run(kernel);\n    \n    if(row==col)\n      kernel.assignDiagonalCoeff(row);\n    else if( ((Mode&Lower) && row>col) || ((Mode&Upper) && row<col) )\n      kernel.assignCoeff(row,col);\n    else if(SetOpposite)\n      kernel.assignOppositeCoeff(row,col);\n  }\n};\n\n// prevent buggy user code from causing an infinite recursion\ntemplate<typename Kernel, unsigned int Mode, bool SetOpposite>\nstruct triangular_assignment_loop<Kernel, Mode, 0, SetOpposite>\n{\n  EIGEN_DEVICE_FUNC\n  static inline void run(Kernel &) {}\n};\n\n\n\n// TODO: experiment with a recursive assignment procedure splitting the current\n//       triangular part into one rectangular and two triangular parts.\n\n\ntemplate<typename Kernel, unsigned int Mode, bool SetOpposite>\nstruct triangular_assignment_loop<Kernel, Mode, Dynamic, SetOpposite>\n{\n  typedef typename Kernel::Scalar Scalar;\n  EIGEN_DEVICE_FUNC\n  static inline void run(Kernel &kernel)\n  {\n    for(Index j = 0; j < kernel.cols(); ++j)\n    {\n      Index maxi = numext::mini(j, kernel.rows());\n      Index i = 0;\n      if (((Mode&Lower) && SetOpposite) || (Mode&Upper))\n      {\n        for(; i < maxi; ++i)\n          if(Mode&Upper) kernel.assignCoeff(i, j);\n          else           kernel.assignOppositeCoeff(i, j);\n      }\n      else\n        i = maxi;\n      \n      if(i<kernel.rows()) // then i==j\n        kernel.assignDiagonalCoeff(i++);\n      \n      if (((Mode&Upper) && SetOpposite) || (Mode&Lower))\n      {\n        for(; i < kernel.rows(); ++i)\n          if(Mode&Lower) kernel.assignCoeff(i, j);\n          else           kernel.assignOppositeCoeff(i, j);\n      }\n    }\n  }\n};\n\n} // end namespace internal\n\n/** Assigns a triangular or selfadjoint matrix to a dense matrix.\n  * If the matrix is triangular, the opposite part is set to zero. */\ntemplate<typename Derived>\ntemplate<typename DenseDerived>\nvoid TriangularBase<Derived>::evalToLazy(MatrixBase<DenseDerived> &other) const\n{\n  other.derived().resize(this->rows(), this->cols());\n  internal::call_triangular_assignment_loop<Derived::Mode,(Derived::Mode&SelfAdjoint)==0 /* SetOpposite */>(other.derived(), derived().nestedExpression());\n}\n\nnamespace internal {\n  \n// Triangular = Product\ntemplate< typename DstXprType, typename Lhs, typename Rhs, typename Scalar>\nstruct Assignment<DstXprType, Product<Lhs,Rhs,DefaultProduct>, internal::assign_op<Scalar,typename Product<Lhs,Rhs,DefaultProduct>::Scalar>, Dense2Triangular>\n{\n  typedef Product<Lhs,Rhs,DefaultProduct> SrcXprType;\n  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,typename SrcXprType::Scalar> &)\n  {\n    Index dstRows = src.rows();\n    Index dstCols = src.cols();\n    if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))\n      dst.resize(dstRows, dstCols);\n\n    dst._assignProduct(src, 1, 0);\n  }\n};\n\n// Triangular += Product\ntemplate< typename DstXprType, typename Lhs, typename Rhs, typename Scalar>\nstruct Assignment<DstXprType, Product<Lhs,Rhs,DefaultProduct>, internal::add_assign_op<Scalar,typename Product<Lhs,Rhs,DefaultProduct>::Scalar>, Dense2Triangular>\n{\n  typedef Product<Lhs,Rhs,DefaultProduct> SrcXprType;\n  static void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op<Scalar,typename SrcXprType::Scalar> &)\n  {\n    dst._assignProduct(src, 1, 1);\n  }\n};\n\n// Triangular -= Product\ntemplate< typename DstXprType, typename Lhs, typename Rhs, typename Scalar>\nstruct Assignment<DstXprType, Product<Lhs,Rhs,DefaultProduct>, internal::sub_assign_op<Scalar,typename Product<Lhs,Rhs,DefaultProduct>::Scalar>, Dense2Triangular>\n{\n  typedef Product<Lhs,Rhs,DefaultProduct> SrcXprType;\n  static void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op<Scalar,typename SrcXprType::Scalar> &)\n  {\n    dst._assignProduct(src, -1, 1);\n  }\n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_TRIANGULARMATRIX_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/VectorBlock.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_VECTORBLOCK_H\n#define EIGEN_VECTORBLOCK_H\n\nnamespace Eigen { \n\nnamespace internal {\ntemplate<typename VectorType, int Size>\nstruct traits<VectorBlock<VectorType, Size> >\n  : public traits<Block<VectorType,\n                     traits<VectorType>::Flags & RowMajorBit ? 1 : Size,\n                     traits<VectorType>::Flags & RowMajorBit ? Size : 1> >\n{\n};\n}\n\n/** \\class VectorBlock\n  * \\ingroup Core_Module\n  *\n  * \\brief Expression of a fixed-size or dynamic-size sub-vector\n  *\n  * \\tparam VectorType the type of the object in which we are taking a sub-vector\n  * \\tparam Size size of the sub-vector we are taking at compile time (optional)\n  *\n  * This class represents an expression of either a fixed-size or dynamic-size sub-vector.\n  * It is the return type of DenseBase::segment(Index,Index) and DenseBase::segment<int>(Index) and\n  * most of the time this is the only way it is used.\n  *\n  * However, if you want to directly maniputate sub-vector expressions,\n  * for instance if you want to write a function returning such an expression, you\n  * will need to use this class.\n  *\n  * Here is an example illustrating the dynamic case:\n  * \\include class_VectorBlock.cpp\n  * Output: \\verbinclude class_VectorBlock.out\n  *\n  * \\note Even though this expression has dynamic size, in the case where \\a VectorType\n  * has fixed size, this expression inherits a fixed maximal size which means that evaluating\n  * it does not cause a dynamic memory allocation.\n  *\n  * Here is an example illustrating the fixed-size case:\n  * \\include class_FixedVectorBlock.cpp\n  * Output: \\verbinclude class_FixedVectorBlock.out\n  *\n  * \\sa class Block, DenseBase::segment(Index,Index,Index,Index), DenseBase::segment(Index,Index)\n  */\ntemplate<typename VectorType, int Size> class VectorBlock\n  : public Block<VectorType,\n                     internal::traits<VectorType>::Flags & RowMajorBit ? 1 : Size,\n                     internal::traits<VectorType>::Flags & RowMajorBit ? Size : 1>\n{\n    typedef Block<VectorType,\n                     internal::traits<VectorType>::Flags & RowMajorBit ? 1 : Size,\n                     internal::traits<VectorType>::Flags & RowMajorBit ? Size : 1> Base;\n    enum {\n      IsColVector = !(internal::traits<VectorType>::Flags & RowMajorBit)\n    };\n  public:\n    EIGEN_DENSE_PUBLIC_INTERFACE(VectorBlock)\n\n    using Base::operator=;\n\n    /** Dynamic-size constructor\n      */\n    EIGEN_DEVICE_FUNC\n    inline VectorBlock(VectorType& vector, Index start, Index size)\n      : Base(vector,\n             IsColVector ? start : 0, IsColVector ? 0 : start,\n             IsColVector ? size  : 1, IsColVector ? 1 : size)\n    {\n      EIGEN_STATIC_ASSERT_VECTOR_ONLY(VectorBlock);\n    }\n\n    /** Fixed-size constructor\n      */\n    EIGEN_DEVICE_FUNC\n    inline VectorBlock(VectorType& vector, Index start)\n      : Base(vector, IsColVector ? start : 0, IsColVector ? 0 : start)\n    {\n      EIGEN_STATIC_ASSERT_VECTOR_ONLY(VectorBlock);\n    }\n};\n\n\n} // end namespace Eigen\n\n#endif // EIGEN_VECTORBLOCK_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/VectorwiseOp.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_PARTIAL_REDUX_H\n#define EIGEN_PARTIAL_REDUX_H\n\nnamespace Eigen {\n\n/** \\class PartialReduxExpr\n  * \\ingroup Core_Module\n  *\n  * \\brief Generic expression of a partially reduxed matrix\n  *\n  * \\tparam MatrixType the type of the matrix we are applying the redux operation\n  * \\tparam MemberOp type of the member functor\n  * \\tparam Direction indicates the direction of the redux (#Vertical or #Horizontal)\n  *\n  * This class represents an expression of a partial redux operator of a matrix.\n  * It is the return type of some VectorwiseOp functions,\n  * and most of the time this is the only way it is used.\n  *\n  * \\sa class VectorwiseOp\n  */\n\ntemplate< typename MatrixType, typename MemberOp, int Direction>\nclass PartialReduxExpr;\n\nnamespace internal {\ntemplate<typename MatrixType, typename MemberOp, int Direction>\nstruct traits<PartialReduxExpr<MatrixType, MemberOp, Direction> >\n : traits<MatrixType>\n{\n  typedef typename MemberOp::result_type Scalar;\n  typedef typename traits<MatrixType>::StorageKind StorageKind;\n  typedef typename traits<MatrixType>::XprKind XprKind;\n  typedef typename MatrixType::Scalar InputScalar;\n  enum {\n    RowsAtCompileTime = Direction==Vertical   ? 1 : MatrixType::RowsAtCompileTime,\n    ColsAtCompileTime = Direction==Horizontal ? 1 : MatrixType::ColsAtCompileTime,\n    MaxRowsAtCompileTime = Direction==Vertical   ? 1 : MatrixType::MaxRowsAtCompileTime,\n    MaxColsAtCompileTime = Direction==Horizontal ? 1 : MatrixType::MaxColsAtCompileTime,\n    Flags = RowsAtCompileTime == 1 ? RowMajorBit : 0,\n    TraversalSize = Direction==Vertical ? MatrixType::RowsAtCompileTime :  MatrixType::ColsAtCompileTime\n  };\n};\n}\n\ntemplate< typename MatrixType, typename MemberOp, int Direction>\nclass PartialReduxExpr : public internal::dense_xpr_base< PartialReduxExpr<MatrixType, MemberOp, Direction> >::type,\n                         internal::no_assignment_operator\n{\n  public:\n\n    typedef typename internal::dense_xpr_base<PartialReduxExpr>::type Base;\n    EIGEN_DENSE_PUBLIC_INTERFACE(PartialReduxExpr)\n\n    EIGEN_DEVICE_FUNC\n    explicit PartialReduxExpr(const MatrixType& mat, const MemberOp& func = MemberOp())\n      : m_matrix(mat), m_functor(func) {}\n\n    EIGEN_DEVICE_FUNC\n    Index rows() const { return (Direction==Vertical   ? 1 : m_matrix.rows()); }\n    EIGEN_DEVICE_FUNC\n    Index cols() const { return (Direction==Horizontal ? 1 : m_matrix.cols()); }\n\n    EIGEN_DEVICE_FUNC\n    typename MatrixType::Nested nestedExpression() const { return m_matrix; }\n\n    EIGEN_DEVICE_FUNC\n    const MemberOp& functor() const { return m_functor; }\n\n  protected:\n    typename MatrixType::Nested m_matrix;\n    const MemberOp m_functor;\n};\n\n#define EIGEN_MEMBER_FUNCTOR(MEMBER,COST)                               \\\n  template <typename ResultType>                                        \\\n  struct member_##MEMBER {                                              \\\n    EIGEN_EMPTY_STRUCT_CTOR(member_##MEMBER)                            \\\n    typedef ResultType result_type;                                     \\\n    template<typename Scalar, int Size> struct Cost                     \\\n    { enum { value = COST }; };                                         \\\n    template<typename XprType>                                          \\\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE                               \\\n    ResultType operator()(const XprType& mat) const                     \\\n    { return mat.MEMBER(); } \\\n  }\n\nnamespace internal {\n\nEIGEN_MEMBER_FUNCTOR(squaredNorm, Size * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);\nEIGEN_MEMBER_FUNCTOR(norm, (Size+5) * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);\nEIGEN_MEMBER_FUNCTOR(stableNorm, (Size+5) * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);\nEIGEN_MEMBER_FUNCTOR(blueNorm, (Size+5) * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);\nEIGEN_MEMBER_FUNCTOR(hypotNorm, (Size-1) * functor_traits<scalar_hypot_op<Scalar> >::Cost );\nEIGEN_MEMBER_FUNCTOR(sum, (Size-1)*NumTraits<Scalar>::AddCost);\nEIGEN_MEMBER_FUNCTOR(mean, (Size-1)*NumTraits<Scalar>::AddCost + NumTraits<Scalar>::MulCost);\nEIGEN_MEMBER_FUNCTOR(minCoeff, (Size-1)*NumTraits<Scalar>::AddCost);\nEIGEN_MEMBER_FUNCTOR(maxCoeff, (Size-1)*NumTraits<Scalar>::AddCost);\nEIGEN_MEMBER_FUNCTOR(all, (Size-1)*NumTraits<Scalar>::AddCost);\nEIGEN_MEMBER_FUNCTOR(any, (Size-1)*NumTraits<Scalar>::AddCost);\nEIGEN_MEMBER_FUNCTOR(count, (Size-1)*NumTraits<Scalar>::AddCost);\nEIGEN_MEMBER_FUNCTOR(prod, (Size-1)*NumTraits<Scalar>::MulCost);\n\ntemplate <int p, typename ResultType>\nstruct member_lpnorm {\n  typedef ResultType result_type;\n  template<typename Scalar, int Size> struct Cost\n  { enum { value = (Size+5) * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost }; };\n  EIGEN_DEVICE_FUNC member_lpnorm() {}\n  template<typename XprType>\n  EIGEN_DEVICE_FUNC inline ResultType operator()(const XprType& mat) const\n  { return mat.template lpNorm<p>(); }\n};\n\ntemplate <typename BinaryOp, typename Scalar>\nstruct member_redux {\n  typedef typename result_of<\n                     BinaryOp(const Scalar&,const Scalar&)\n                   >::type  result_type;\n  template<typename _Scalar, int Size> struct Cost\n  { enum { value = (Size-1) * functor_traits<BinaryOp>::Cost }; };\n  EIGEN_DEVICE_FUNC explicit member_redux(const BinaryOp func) : m_functor(func) {}\n  template<typename Derived>\n  EIGEN_DEVICE_FUNC inline result_type operator()(const DenseBase<Derived>& mat) const\n  { return mat.redux(m_functor); }\n  const BinaryOp m_functor;\n};\n}\n\n/** \\class VectorwiseOp\n  * \\ingroup Core_Module\n  *\n  * \\brief Pseudo expression providing partial reduction operations\n  *\n  * \\tparam ExpressionType the type of the object on which to do partial reductions\n  * \\tparam Direction indicates the direction of the redux (#Vertical or #Horizontal)\n  *\n  * This class represents a pseudo expression with partial reduction features.\n  * It is the return type of DenseBase::colwise() and DenseBase::rowwise()\n  * and most of the time this is the only way it is used.\n  *\n  * Example: \\include MatrixBase_colwise.cpp\n  * Output: \\verbinclude MatrixBase_colwise.out\n  *\n  * \\sa DenseBase::colwise(), DenseBase::rowwise(), class PartialReduxExpr\n  */\ntemplate<typename ExpressionType, int Direction> class VectorwiseOp\n{\n  public:\n\n    typedef typename ExpressionType::Scalar Scalar;\n    typedef typename ExpressionType::RealScalar RealScalar;\n    typedef Eigen::Index Index; ///< \\deprecated since Eigen 3.3\n    typedef typename internal::ref_selector<ExpressionType>::non_const_type ExpressionTypeNested;\n    typedef typename internal::remove_all<ExpressionTypeNested>::type ExpressionTypeNestedCleaned;\n\n    template<template<typename _Scalar> class Functor,\n                      typename Scalar_=Scalar> struct ReturnType\n    {\n      typedef PartialReduxExpr<ExpressionType,\n                               Functor<Scalar_>,\n                               Direction\n                              > Type;\n    };\n\n    template<typename BinaryOp> struct ReduxReturnType\n    {\n      typedef PartialReduxExpr<ExpressionType,\n                               internal::member_redux<BinaryOp,Scalar>,\n                               Direction\n                              > Type;\n    };\n\n    enum {\n      isVertical   = (Direction==Vertical) ? 1 : 0,\n      isHorizontal = (Direction==Horizontal) ? 1 : 0\n    };\n\n  protected:\n\n    typedef typename internal::conditional<isVertical,\n                               typename ExpressionType::ColXpr,\n                               typename ExpressionType::RowXpr>::type SubVector;\n    /** \\internal\n      * \\returns the i-th subvector according to the \\c Direction */\n    EIGEN_DEVICE_FUNC\n    SubVector subVector(Index i)\n    {\n      return SubVector(m_matrix.derived(),i);\n    }\n\n    /** \\internal\n      * \\returns the number of subvectors in the direction \\c Direction */\n    EIGEN_DEVICE_FUNC\n    Index subVectors() const\n    { return isVertical?m_matrix.cols():m_matrix.rows(); }\n\n    template<typename OtherDerived> struct ExtendedType {\n      typedef Replicate<OtherDerived,\n                        isVertical   ? 1 : ExpressionType::RowsAtCompileTime,\n                        isHorizontal ? 1 : ExpressionType::ColsAtCompileTime> Type;\n    };\n\n    /** \\internal\n      * Replicates a vector to match the size of \\c *this */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    typename ExtendedType<OtherDerived>::Type\n    extendedTo(const DenseBase<OtherDerived>& other) const\n    {\n      EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(isVertical, OtherDerived::MaxColsAtCompileTime==1),\n                          YOU_PASSED_A_ROW_VECTOR_BUT_A_COLUMN_VECTOR_WAS_EXPECTED)\n      EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(isHorizontal, OtherDerived::MaxRowsAtCompileTime==1),\n                          YOU_PASSED_A_COLUMN_VECTOR_BUT_A_ROW_VECTOR_WAS_EXPECTED)\n      return typename ExtendedType<OtherDerived>::Type\n                      (other.derived(),\n                       isVertical   ? 1 : m_matrix.rows(),\n                       isHorizontal ? 1 : m_matrix.cols());\n    }\n\n    template<typename OtherDerived> struct OppositeExtendedType {\n      typedef Replicate<OtherDerived,\n                        isHorizontal ? 1 : ExpressionType::RowsAtCompileTime,\n                        isVertical   ? 1 : ExpressionType::ColsAtCompileTime> Type;\n    };\n\n    /** \\internal\n      * Replicates a vector in the opposite direction to match the size of \\c *this */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    typename OppositeExtendedType<OtherDerived>::Type\n    extendedToOpposite(const DenseBase<OtherDerived>& other) const\n    {\n      EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(isHorizontal, OtherDerived::MaxColsAtCompileTime==1),\n                          YOU_PASSED_A_ROW_VECTOR_BUT_A_COLUMN_VECTOR_WAS_EXPECTED)\n      EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(isVertical, OtherDerived::MaxRowsAtCompileTime==1),\n                          YOU_PASSED_A_COLUMN_VECTOR_BUT_A_ROW_VECTOR_WAS_EXPECTED)\n      return typename OppositeExtendedType<OtherDerived>::Type\n                      (other.derived(),\n                       isHorizontal  ? 1 : m_matrix.rows(),\n                       isVertical    ? 1 : m_matrix.cols());\n    }\n\n  public:\n    EIGEN_DEVICE_FUNC\n    explicit inline VectorwiseOp(ExpressionType& matrix) : m_matrix(matrix) {}\n\n    /** \\internal */\n    EIGEN_DEVICE_FUNC\n    inline const ExpressionType& _expression() const { return m_matrix; }\n\n    /** \\returns a row or column vector expression of \\c *this reduxed by \\a func\n      *\n      * The template parameter \\a BinaryOp is the type of the functor\n      * of the custom redux operator. Note that func must be an associative operator.\n      *\n      * \\sa class VectorwiseOp, DenseBase::colwise(), DenseBase::rowwise()\n      */\n    template<typename BinaryOp>\n    EIGEN_DEVICE_FUNC\n    const typename ReduxReturnType<BinaryOp>::Type\n    redux(const BinaryOp& func = BinaryOp()) const\n    { return typename ReduxReturnType<BinaryOp>::Type(_expression(), internal::member_redux<BinaryOp,Scalar>(func)); }\n\n    typedef typename ReturnType<internal::member_minCoeff>::Type MinCoeffReturnType;\n    typedef typename ReturnType<internal::member_maxCoeff>::Type MaxCoeffReturnType;\n    typedef typename ReturnType<internal::member_squaredNorm,RealScalar>::Type SquaredNormReturnType;\n    typedef typename ReturnType<internal::member_norm,RealScalar>::Type NormReturnType;\n    typedef typename ReturnType<internal::member_blueNorm,RealScalar>::Type BlueNormReturnType;\n    typedef typename ReturnType<internal::member_stableNorm,RealScalar>::Type StableNormReturnType;\n    typedef typename ReturnType<internal::member_hypotNorm,RealScalar>::Type HypotNormReturnType;\n    typedef typename ReturnType<internal::member_sum>::Type SumReturnType;\n    typedef typename ReturnType<internal::member_mean>::Type MeanReturnType;\n    typedef typename ReturnType<internal::member_all>::Type AllReturnType;\n    typedef typename ReturnType<internal::member_any>::Type AnyReturnType;\n    typedef PartialReduxExpr<ExpressionType, internal::member_count<Index>, Direction> CountReturnType;\n    typedef typename ReturnType<internal::member_prod>::Type ProdReturnType;\n    typedef Reverse<const ExpressionType, Direction> ConstReverseReturnType;\n    typedef Reverse<ExpressionType, Direction> ReverseReturnType;\n\n    template<int p> struct LpNormReturnType {\n      typedef PartialReduxExpr<ExpressionType, internal::member_lpnorm<p,RealScalar>,Direction> Type;\n    };\n\n    /** \\returns a row (or column) vector expression of the smallest coefficient\n      * of each column (or row) of the referenced expression.\n      *\n      * \\warning the result is undefined if \\c *this contains NaN.\n      *\n      * Example: \\include PartialRedux_minCoeff.cpp\n      * Output: \\verbinclude PartialRedux_minCoeff.out\n      *\n      * \\sa DenseBase::minCoeff() */\n    EIGEN_DEVICE_FUNC\n    const MinCoeffReturnType minCoeff() const\n    { return MinCoeffReturnType(_expression()); }\n\n    /** \\returns a row (or column) vector expression of the largest coefficient\n      * of each column (or row) of the referenced expression.\n      *\n      * \\warning the result is undefined if \\c *this contains NaN.\n      *\n      * Example: \\include PartialRedux_maxCoeff.cpp\n      * Output: \\verbinclude PartialRedux_maxCoeff.out\n      *\n      * \\sa DenseBase::maxCoeff() */\n    EIGEN_DEVICE_FUNC\n    const MaxCoeffReturnType maxCoeff() const\n    { return MaxCoeffReturnType(_expression()); }\n\n    /** \\returns a row (or column) vector expression of the squared norm\n      * of each column (or row) of the referenced expression.\n      * This is a vector with real entries, even if the original matrix has complex entries.\n      *\n      * Example: \\include PartialRedux_squaredNorm.cpp\n      * Output: \\verbinclude PartialRedux_squaredNorm.out\n      *\n      * \\sa DenseBase::squaredNorm() */\n    EIGEN_DEVICE_FUNC\n    const SquaredNormReturnType squaredNorm() const\n    { return SquaredNormReturnType(_expression()); }\n\n    /** \\returns a row (or column) vector expression of the norm\n      * of each column (or row) of the referenced expression.\n      * This is a vector with real entries, even if the original matrix has complex entries.\n      *\n      * Example: \\include PartialRedux_norm.cpp\n      * Output: \\verbinclude PartialRedux_norm.out\n      *\n      * \\sa DenseBase::norm() */\n    EIGEN_DEVICE_FUNC\n    const NormReturnType norm() const\n    { return NormReturnType(_expression()); }\n\n    /** \\returns a row (or column) vector expression of the norm\n      * of each column (or row) of the referenced expression.\n      * This is a vector with real entries, even if the original matrix has complex entries.\n      *\n      * Example: \\include PartialRedux_norm.cpp\n      * Output: \\verbinclude PartialRedux_norm.out\n      *\n      * \\sa DenseBase::norm() */\n    template<int p>\n    EIGEN_DEVICE_FUNC\n    const typename LpNormReturnType<p>::Type lpNorm() const\n    { return typename LpNormReturnType<p>::Type(_expression()); }\n\n\n    /** \\returns a row (or column) vector expression of the norm\n      * of each column (or row) of the referenced expression, using\n      * Blue's algorithm.\n      * This is a vector with real entries, even if the original matrix has complex entries.\n      *\n      * \\sa DenseBase::blueNorm() */\n    EIGEN_DEVICE_FUNC\n    const BlueNormReturnType blueNorm() const\n    { return BlueNormReturnType(_expression()); }\n\n\n    /** \\returns a row (or column) vector expression of the norm\n      * of each column (or row) of the referenced expression, avoiding\n      * underflow and overflow.\n      * This is a vector with real entries, even if the original matrix has complex entries.\n      *\n      * \\sa DenseBase::stableNorm() */\n    EIGEN_DEVICE_FUNC\n    const StableNormReturnType stableNorm() const\n    { return StableNormReturnType(_expression()); }\n\n\n    /** \\returns a row (or column) vector expression of the norm\n      * of each column (or row) of the referenced expression, avoiding\n      * underflow and overflow using a concatenation of hypot() calls.\n      * This is a vector with real entries, even if the original matrix has complex entries.\n      *\n      * \\sa DenseBase::hypotNorm() */\n    EIGEN_DEVICE_FUNC\n    const HypotNormReturnType hypotNorm() const\n    { return HypotNormReturnType(_expression()); }\n\n    /** \\returns a row (or column) vector expression of the sum\n      * of each column (or row) of the referenced expression.\n      *\n      * Example: \\include PartialRedux_sum.cpp\n      * Output: \\verbinclude PartialRedux_sum.out\n      *\n      * \\sa DenseBase::sum() */\n    EIGEN_DEVICE_FUNC\n    const SumReturnType sum() const\n    { return SumReturnType(_expression()); }\n\n    /** \\returns a row (or column) vector expression of the mean\n    * of each column (or row) of the referenced expression.\n    *\n    * \\sa DenseBase::mean() */\n    EIGEN_DEVICE_FUNC\n    const MeanReturnType mean() const\n    { return MeanReturnType(_expression()); }\n\n    /** \\returns a row (or column) vector expression representing\n      * whether \\b all coefficients of each respective column (or row) are \\c true.\n      * This expression can be assigned to a vector with entries of type \\c bool.\n      *\n      * \\sa DenseBase::all() */\n    EIGEN_DEVICE_FUNC\n    const AllReturnType all() const\n    { return AllReturnType(_expression()); }\n\n    /** \\returns a row (or column) vector expression representing\n      * whether \\b at \\b least one coefficient of each respective column (or row) is \\c true.\n      * This expression can be assigned to a vector with entries of type \\c bool.\n      *\n      * \\sa DenseBase::any() */\n    EIGEN_DEVICE_FUNC\n    const AnyReturnType any() const\n    { return AnyReturnType(_expression()); }\n\n    /** \\returns a row (or column) vector expression representing\n      * the number of \\c true coefficients of each respective column (or row).\n      * This expression can be assigned to a vector whose entries have the same type as is used to\n      * index entries of the original matrix; for dense matrices, this is \\c std::ptrdiff_t .\n      *\n      * Example: \\include PartialRedux_count.cpp\n      * Output: \\verbinclude PartialRedux_count.out\n      *\n      * \\sa DenseBase::count() */\n    EIGEN_DEVICE_FUNC\n    const CountReturnType count() const\n    { return CountReturnType(_expression()); }\n\n    /** \\returns a row (or column) vector expression of the product\n      * of each column (or row) of the referenced expression.\n      *\n      * Example: \\include PartialRedux_prod.cpp\n      * Output: \\verbinclude PartialRedux_prod.out\n      *\n      * \\sa DenseBase::prod() */\n    EIGEN_DEVICE_FUNC\n    const ProdReturnType prod() const\n    { return ProdReturnType(_expression()); }\n\n\n    /** \\returns a matrix expression\n      * where each column (or row) are reversed.\n      *\n      * Example: \\include Vectorwise_reverse.cpp\n      * Output: \\verbinclude Vectorwise_reverse.out\n      *\n      * \\sa DenseBase::reverse() */\n    EIGEN_DEVICE_FUNC\n    const ConstReverseReturnType reverse() const\n    { return ConstReverseReturnType( _expression() ); }\n\n    /** \\returns a writable matrix expression\n      * where each column (or row) are reversed.\n      *\n      * \\sa reverse() const */\n    EIGEN_DEVICE_FUNC\n    ReverseReturnType reverse()\n    { return ReverseReturnType( _expression() ); }\n\n    typedef Replicate<ExpressionType,(isVertical?Dynamic:1),(isHorizontal?Dynamic:1)> ReplicateReturnType;\n    EIGEN_DEVICE_FUNC\n    const ReplicateReturnType replicate(Index factor) const;\n\n    /**\n      * \\return an expression of the replication of each column (or row) of \\c *this\n      *\n      * Example: \\include DirectionWise_replicate.cpp\n      * Output: \\verbinclude DirectionWise_replicate.out\n      *\n      * \\sa VectorwiseOp::replicate(Index), DenseBase::replicate(), class Replicate\n      */\n    // NOTE implemented here because of sunstudio's compilation errors\n    // isVertical*Factor+isHorizontal instead of (isVertical?Factor:1) to handle CUDA bug with ternary operator\n    template<int Factor> const Replicate<ExpressionType,isVertical*Factor+isHorizontal,isHorizontal*Factor+isVertical>\n    EIGEN_DEVICE_FUNC\n    replicate(Index factor = Factor) const\n    {\n      return Replicate<ExpressionType,(isVertical?Factor:1),(isHorizontal?Factor:1)>\n          (_expression(),isVertical?factor:1,isHorizontal?factor:1);\n    }\n\n/////////// Artithmetic operators ///////////\n\n    /** Copies the vector \\a other to each subvector of \\c *this */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    ExpressionType& operator=(const DenseBase<OtherDerived>& other)\n    {\n      EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)\n      EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)\n      //eigen_assert((m_matrix.isNull()) == (other.isNull())); FIXME\n      return const_cast<ExpressionType&>(m_matrix = extendedTo(other.derived()));\n    }\n\n    /** Adds the vector \\a other to each subvector of \\c *this */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    ExpressionType& operator+=(const DenseBase<OtherDerived>& other)\n    {\n      EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)\n      EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)\n      return const_cast<ExpressionType&>(m_matrix += extendedTo(other.derived()));\n    }\n\n    /** Substracts the vector \\a other to each subvector of \\c *this */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    ExpressionType& operator-=(const DenseBase<OtherDerived>& other)\n    {\n      EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)\n      EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)\n      return const_cast<ExpressionType&>(m_matrix -= extendedTo(other.derived()));\n    }\n\n    /** Multiples each subvector of \\c *this by the vector \\a other */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    ExpressionType& operator*=(const DenseBase<OtherDerived>& other)\n    {\n      EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)\n      EIGEN_STATIC_ASSERT_ARRAYXPR(ExpressionType)\n      EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)\n      m_matrix *= extendedTo(other.derived());\n      return const_cast<ExpressionType&>(m_matrix);\n    }\n\n    /** Divides each subvector of \\c *this by the vector \\a other */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    ExpressionType& operator/=(const DenseBase<OtherDerived>& other)\n    {\n      EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)\n      EIGEN_STATIC_ASSERT_ARRAYXPR(ExpressionType)\n      EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)\n      m_matrix /= extendedTo(other.derived());\n      return const_cast<ExpressionType&>(m_matrix);\n    }\n\n    /** Returns the expression of the sum of the vector \\a other to each subvector of \\c *this */\n    template<typename OtherDerived> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC\n    CwiseBinaryOp<internal::scalar_sum_op<Scalar,typename OtherDerived::Scalar>,\n                  const ExpressionTypeNestedCleaned,\n                  const typename ExtendedType<OtherDerived>::Type>\n    operator+(const DenseBase<OtherDerived>& other) const\n    {\n      EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)\n      EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)\n      return m_matrix + extendedTo(other.derived());\n    }\n\n    /** Returns the expression of the difference between each subvector of \\c *this and the vector \\a other */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    CwiseBinaryOp<internal::scalar_difference_op<Scalar,typename OtherDerived::Scalar>,\n                  const ExpressionTypeNestedCleaned,\n                  const typename ExtendedType<OtherDerived>::Type>\n    operator-(const DenseBase<OtherDerived>& other) const\n    {\n      EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)\n      EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)\n      return m_matrix - extendedTo(other.derived());\n    }\n\n    /** Returns the expression where each subvector is the product of the vector \\a other\n      * by the corresponding subvector of \\c *this */\n    template<typename OtherDerived> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC\n    CwiseBinaryOp<internal::scalar_product_op<Scalar>,\n                  const ExpressionTypeNestedCleaned,\n                  const typename ExtendedType<OtherDerived>::Type>\n    EIGEN_DEVICE_FUNC\n    operator*(const DenseBase<OtherDerived>& other) const\n    {\n      EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)\n      EIGEN_STATIC_ASSERT_ARRAYXPR(ExpressionType)\n      EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)\n      return m_matrix * extendedTo(other.derived());\n    }\n\n    /** Returns the expression where each subvector is the quotient of the corresponding\n      * subvector of \\c *this by the vector \\a other */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    CwiseBinaryOp<internal::scalar_quotient_op<Scalar>,\n                  const ExpressionTypeNestedCleaned,\n                  const typename ExtendedType<OtherDerived>::Type>\n    operator/(const DenseBase<OtherDerived>& other) const\n    {\n      EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)\n      EIGEN_STATIC_ASSERT_ARRAYXPR(ExpressionType)\n      EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)\n      return m_matrix / extendedTo(other.derived());\n    }\n\n    /** \\returns an expression where each column (or row) of the referenced matrix are normalized.\n      * The referenced matrix is \\b not modified.\n      * \\sa MatrixBase::normalized(), normalize()\n      */\n    EIGEN_DEVICE_FUNC\n    CwiseBinaryOp<internal::scalar_quotient_op<Scalar>,\n                  const ExpressionTypeNestedCleaned,\n                  const typename OppositeExtendedType<typename ReturnType<internal::member_norm,RealScalar>::Type>::Type>\n    normalized() const { return m_matrix.cwiseQuotient(extendedToOpposite(this->norm())); }\n\n\n    /** Normalize in-place each row or columns of the referenced matrix.\n      * \\sa MatrixBase::normalize(), normalized()\n      */\n    EIGEN_DEVICE_FUNC void normalize() {\n      m_matrix = this->normalized();\n    }\n\n    EIGEN_DEVICE_FUNC inline void reverseInPlace();\n\n/////////// Geometry module ///////////\n\n    typedef Homogeneous<ExpressionType,Direction> HomogeneousReturnType;\n    EIGEN_DEVICE_FUNC\n    HomogeneousReturnType homogeneous() const;\n\n    typedef typename ExpressionType::PlainObject CrossReturnType;\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    const CrossReturnType cross(const MatrixBase<OtherDerived>& other) const;\n\n    enum {\n      HNormalized_Size = Direction==Vertical ? internal::traits<ExpressionType>::RowsAtCompileTime\n                                             : internal::traits<ExpressionType>::ColsAtCompileTime,\n      HNormalized_SizeMinusOne = HNormalized_Size==Dynamic ? Dynamic : HNormalized_Size-1\n    };\n    typedef Block<const ExpressionType,\n                  Direction==Vertical   ? int(HNormalized_SizeMinusOne)\n                                        : int(internal::traits<ExpressionType>::RowsAtCompileTime),\n                  Direction==Horizontal ? int(HNormalized_SizeMinusOne)\n                                        : int(internal::traits<ExpressionType>::ColsAtCompileTime)>\n            HNormalized_Block;\n    typedef Block<const ExpressionType,\n                  Direction==Vertical   ? 1 : int(internal::traits<ExpressionType>::RowsAtCompileTime),\n                  Direction==Horizontal ? 1 : int(internal::traits<ExpressionType>::ColsAtCompileTime)>\n            HNormalized_Factors;\n    typedef CwiseBinaryOp<internal::scalar_quotient_op<typename internal::traits<ExpressionType>::Scalar>,\n                const HNormalized_Block,\n                const Replicate<HNormalized_Factors,\n                  Direction==Vertical   ? HNormalized_SizeMinusOne : 1,\n                  Direction==Horizontal ? HNormalized_SizeMinusOne : 1> >\n            HNormalizedReturnType;\n\n    EIGEN_DEVICE_FUNC\n    const HNormalizedReturnType hnormalized() const;\n\n  protected:\n    ExpressionTypeNested m_matrix;\n};\n\n//const colwise moved to DenseBase.h due to CUDA compiler bug\n\n\n/** \\returns a writable VectorwiseOp wrapper of *this providing additional partial reduction operations\n  *\n  * \\sa rowwise(), class VectorwiseOp, \\ref TutorialReductionsVisitorsBroadcasting\n  */\ntemplate<typename Derived>\ninline typename DenseBase<Derived>::ColwiseReturnType\nDenseBase<Derived>::colwise()\n{\n  return ColwiseReturnType(derived());\n}\n\n//const rowwise moved to DenseBase.h due to CUDA compiler bug\n\n\n/** \\returns a writable VectorwiseOp wrapper of *this providing additional partial reduction operations\n  *\n  * \\sa colwise(), class VectorwiseOp, \\ref TutorialReductionsVisitorsBroadcasting\n  */\ntemplate<typename Derived>\ninline typename DenseBase<Derived>::RowwiseReturnType\nDenseBase<Derived>::rowwise()\n{\n  return RowwiseReturnType(derived());\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_PARTIAL_REDUX_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/Visitor.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_VISITOR_H\n#define EIGEN_VISITOR_H\n\nnamespace Eigen { \n\nnamespace internal {\n\ntemplate<typename Visitor, typename Derived, int UnrollCount>\nstruct visitor_impl\n{\n  enum {\n    col = (UnrollCount-1) / Derived::RowsAtCompileTime,\n    row = (UnrollCount-1) % Derived::RowsAtCompileTime\n  };\n\n  EIGEN_DEVICE_FUNC\n  static inline void run(const Derived &mat, Visitor& visitor)\n  {\n    visitor_impl<Visitor, Derived, UnrollCount-1>::run(mat, visitor);\n    visitor(mat.coeff(row, col), row, col);\n  }\n};\n\ntemplate<typename Visitor, typename Derived>\nstruct visitor_impl<Visitor, Derived, 1>\n{\n  EIGEN_DEVICE_FUNC\n  static inline void run(const Derived &mat, Visitor& visitor)\n  {\n    return visitor.init(mat.coeff(0, 0), 0, 0);\n  }\n};\n\ntemplate<typename Visitor, typename Derived>\nstruct visitor_impl<Visitor, Derived, Dynamic>\n{\n  EIGEN_DEVICE_FUNC\n  static inline void run(const Derived& mat, Visitor& visitor)\n  {\n    visitor.init(mat.coeff(0,0), 0, 0);\n    for(Index i = 1; i < mat.rows(); ++i)\n      visitor(mat.coeff(i, 0), i, 0);\n    for(Index j = 1; j < mat.cols(); ++j)\n      for(Index i = 0; i < mat.rows(); ++i)\n        visitor(mat.coeff(i, j), i, j);\n  }\n};\n\n// evaluator adaptor\ntemplate<typename XprType>\nclass visitor_evaluator\n{\npublic:\n  EIGEN_DEVICE_FUNC\n  explicit visitor_evaluator(const XprType &xpr) : m_evaluator(xpr), m_xpr(xpr) {}\n  \n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  \n  enum {\n    RowsAtCompileTime = XprType::RowsAtCompileTime,\n    CoeffReadCost = internal::evaluator<XprType>::CoeffReadCost\n  };\n  \n  EIGEN_DEVICE_FUNC Index rows() const { return m_xpr.rows(); }\n  EIGEN_DEVICE_FUNC Index cols() const { return m_xpr.cols(); }\n  EIGEN_DEVICE_FUNC Index size() const { return m_xpr.size(); }\n\n  EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index row, Index col) const\n  { return m_evaluator.coeff(row, col); }\n  \nprotected:\n  internal::evaluator<XprType> m_evaluator;\n  const XprType &m_xpr;\n};\n} // end namespace internal\n\n/** Applies the visitor \\a visitor to the whole coefficients of the matrix or vector.\n  *\n  * The template parameter \\a Visitor is the type of the visitor and provides the following interface:\n  * \\code\n  * struct MyVisitor {\n  *   // called for the first coefficient\n  *   void init(const Scalar& value, Index i, Index j);\n  *   // called for all other coefficients\n  *   void operator() (const Scalar& value, Index i, Index j);\n  * };\n  * \\endcode\n  *\n  * \\note compared to one or two \\em for \\em loops, visitors offer automatic\n  * unrolling for small fixed size matrix.\n  *\n  * \\sa minCoeff(Index*,Index*), maxCoeff(Index*,Index*), DenseBase::redux()\n  */\ntemplate<typename Derived>\ntemplate<typename Visitor>\nEIGEN_DEVICE_FUNC\nvoid DenseBase<Derived>::visit(Visitor& visitor) const\n{\n  typedef typename internal::visitor_evaluator<Derived> ThisEvaluator;\n  ThisEvaluator thisEval(derived());\n  \n  enum {\n    unroll =  SizeAtCompileTime != Dynamic\n           && SizeAtCompileTime * ThisEvaluator::CoeffReadCost + (SizeAtCompileTime-1) * internal::functor_traits<Visitor>::Cost <= EIGEN_UNROLLING_LIMIT\n  };\n  return internal::visitor_impl<Visitor, ThisEvaluator, unroll ? int(SizeAtCompileTime) : Dynamic>::run(thisEval, visitor);\n}\n\nnamespace internal {\n\n/** \\internal\n  * \\brief Base class to implement min and max visitors\n  */\ntemplate <typename Derived>\nstruct coeff_visitor\n{\n  typedef typename Derived::Scalar Scalar;\n  Index row, col;\n  Scalar res;\n  EIGEN_DEVICE_FUNC\n  inline void init(const Scalar& value, Index i, Index j)\n  {\n    res = value;\n    row = i;\n    col = j;\n  }\n};\n\n/** \\internal\n  * \\brief Visitor computing the min coefficient with its value and coordinates\n  *\n  * \\sa DenseBase::minCoeff(Index*, Index*)\n  */\ntemplate <typename Derived>\nstruct min_coeff_visitor : coeff_visitor<Derived>\n{\n  typedef typename Derived::Scalar Scalar;\n  EIGEN_DEVICE_FUNC\n  void operator() (const Scalar& value, Index i, Index j)\n  {\n    if(value < this->res)\n    {\n      this->res = value;\n      this->row = i;\n      this->col = j;\n    }\n  }\n};\n\ntemplate<typename Scalar>\nstruct functor_traits<min_coeff_visitor<Scalar> > {\n  enum {\n    Cost = NumTraits<Scalar>::AddCost\n  };\n};\n\n/** \\internal\n  * \\brief Visitor computing the max coefficient with its value and coordinates\n  *\n  * \\sa DenseBase::maxCoeff(Index*, Index*)\n  */\ntemplate <typename Derived>\nstruct max_coeff_visitor : coeff_visitor<Derived>\n{\n  typedef typename Derived::Scalar Scalar; \n  EIGEN_DEVICE_FUNC\n  void operator() (const Scalar& value, Index i, Index j)\n  {\n    if(value > this->res)\n    {\n      this->res = value;\n      this->row = i;\n      this->col = j;\n    }\n  }\n};\n\ntemplate<typename Scalar>\nstruct functor_traits<max_coeff_visitor<Scalar> > {\n  enum {\n    Cost = NumTraits<Scalar>::AddCost\n  };\n};\n\n} // end namespace internal\n\n/** \\fn DenseBase<Derived>::minCoeff(IndexType* rowId, IndexType* colId) const\n  * \\returns the minimum of all coefficients of *this and puts in *row and *col its location.\n  * \\warning the result is undefined if \\c *this contains NaN.\n  *\n  * \\sa DenseBase::minCoeff(Index*), DenseBase::maxCoeff(Index*,Index*), DenseBase::visit(), DenseBase::minCoeff()\n  */\ntemplate<typename Derived>\ntemplate<typename IndexType>\nEIGEN_DEVICE_FUNC\ntypename internal::traits<Derived>::Scalar\nDenseBase<Derived>::minCoeff(IndexType* rowId, IndexType* colId) const\n{\n  internal::min_coeff_visitor<Derived> minVisitor;\n  this->visit(minVisitor);\n  *rowId = minVisitor.row;\n  if (colId) *colId = minVisitor.col;\n  return minVisitor.res;\n}\n\n/** \\returns the minimum of all coefficients of *this and puts in *index its location.\n  * \\warning the result is undefined if \\c *this contains NaN. \n  *\n  * \\sa DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::maxCoeff(IndexType*,IndexType*), DenseBase::visit(), DenseBase::minCoeff()\n  */\ntemplate<typename Derived>\ntemplate<typename IndexType>\nEIGEN_DEVICE_FUNC\ntypename internal::traits<Derived>::Scalar\nDenseBase<Derived>::minCoeff(IndexType* index) const\n{\n  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)\n  internal::min_coeff_visitor<Derived> minVisitor;\n  this->visit(minVisitor);\n  *index = IndexType((RowsAtCompileTime==1) ? minVisitor.col : minVisitor.row);\n  return minVisitor.res;\n}\n\n/** \\fn DenseBase<Derived>::maxCoeff(IndexType* rowId, IndexType* colId) const\n  * \\returns the maximum of all coefficients of *this and puts in *row and *col its location.\n  * \\warning the result is undefined if \\c *this contains NaN. \n  *\n  * \\sa DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::visit(), DenseBase::maxCoeff()\n  */\ntemplate<typename Derived>\ntemplate<typename IndexType>\nEIGEN_DEVICE_FUNC\ntypename internal::traits<Derived>::Scalar\nDenseBase<Derived>::maxCoeff(IndexType* rowPtr, IndexType* colPtr) const\n{\n  internal::max_coeff_visitor<Derived> maxVisitor;\n  this->visit(maxVisitor);\n  *rowPtr = maxVisitor.row;\n  if (colPtr) *colPtr = maxVisitor.col;\n  return maxVisitor.res;\n}\n\n/** \\returns the maximum of all coefficients of *this and puts in *index its location.\n  * \\warning the result is undefined if \\c *this contains NaN.\n  *\n  * \\sa DenseBase::maxCoeff(IndexType*,IndexType*), DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::visitor(), DenseBase::maxCoeff()\n  */\ntemplate<typename Derived>\ntemplate<typename IndexType>\nEIGEN_DEVICE_FUNC\ntypename internal::traits<Derived>::Scalar\nDenseBase<Derived>::maxCoeff(IndexType* index) const\n{\n  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)\n  internal::max_coeff_visitor<Derived> maxVisitor;\n  this->visit(maxVisitor);\n  *index = (RowsAtCompileTime==1) ? maxVisitor.col : maxVisitor.row;\n  return maxVisitor.res;\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_VISITOR_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/arch/AVX/Complex.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner (benoit.steiner.goog@gmail.com)\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_COMPLEX_AVX_H\n#define EIGEN_COMPLEX_AVX_H\n\nnamespace Eigen {\n\nnamespace internal {\n\n//---------- float ----------\nstruct Packet4cf\n{\n  EIGEN_STRONG_INLINE Packet4cf() {}\n  EIGEN_STRONG_INLINE explicit Packet4cf(const __m256& a) : v(a) {}\n  __m256  v;\n};\n\ntemplate<> struct packet_traits<std::complex<float> >  : default_packet_traits\n{\n  typedef Packet4cf type;\n  typedef Packet2cf half;\n  enum {\n    Vectorizable = 1,\n    AlignedOnScalar = 1,\n    size = 4,\n    HasHalfPacket = 1,\n\n    HasAdd    = 1,\n    HasSub    = 1,\n    HasMul    = 1,\n    HasDiv    = 1,\n    HasNegate = 1,\n    HasAbs    = 0,\n    HasAbs2   = 0,\n    HasMin    = 0,\n    HasMax    = 0,\n    HasSetLinear = 0\n  };\n};\n\ntemplate<> struct unpacket_traits<Packet4cf> { typedef std::complex<float> type; enum {size=4, alignment=Aligned32}; typedef Packet2cf half; };\n\ntemplate<> EIGEN_STRONG_INLINE Packet4cf padd<Packet4cf>(const Packet4cf& a, const Packet4cf& b) { return Packet4cf(_mm256_add_ps(a.v,b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet4cf psub<Packet4cf>(const Packet4cf& a, const Packet4cf& b) { return Packet4cf(_mm256_sub_ps(a.v,b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet4cf pnegate(const Packet4cf& a)\n{\n  return Packet4cf(pnegate(a.v));\n}\ntemplate<> EIGEN_STRONG_INLINE Packet4cf pconj(const Packet4cf& a)\n{\n  const __m256 mask = _mm256_castsi256_ps(_mm256_setr_epi32(0x00000000,0x80000000,0x00000000,0x80000000,0x00000000,0x80000000,0x00000000,0x80000000));\n  return Packet4cf(_mm256_xor_ps(a.v,mask));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4cf pmul<Packet4cf>(const Packet4cf& a, const Packet4cf& b)\n{\n  __m256 tmp1 = _mm256_mul_ps(_mm256_moveldup_ps(a.v), b.v);\n  __m256 tmp2 = _mm256_mul_ps(_mm256_movehdup_ps(a.v), _mm256_permute_ps(b.v, _MM_SHUFFLE(2,3,0,1)));\n  __m256 result = _mm256_addsub_ps(tmp1, tmp2);\n  return Packet4cf(result);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4cf pand   <Packet4cf>(const Packet4cf& a, const Packet4cf& b) { return Packet4cf(_mm256_and_ps(a.v,b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet4cf por    <Packet4cf>(const Packet4cf& a, const Packet4cf& b) { return Packet4cf(_mm256_or_ps(a.v,b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet4cf pxor   <Packet4cf>(const Packet4cf& a, const Packet4cf& b) { return Packet4cf(_mm256_xor_ps(a.v,b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet4cf pandnot<Packet4cf>(const Packet4cf& a, const Packet4cf& b) { return Packet4cf(_mm256_andnot_ps(a.v,b.v)); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4cf pload <Packet4cf>(const std::complex<float>* from) { EIGEN_DEBUG_ALIGNED_LOAD return Packet4cf(pload<Packet8f>(&numext::real_ref(*from))); }\ntemplate<> EIGEN_STRONG_INLINE Packet4cf ploadu<Packet4cf>(const std::complex<float>* from) { EIGEN_DEBUG_UNALIGNED_LOAD return Packet4cf(ploadu<Packet8f>(&numext::real_ref(*from))); }\n\n\ntemplate<> EIGEN_STRONG_INLINE Packet4cf pset1<Packet4cf>(const std::complex<float>& from)\n{\n  return Packet4cf(_mm256_castpd_ps(_mm256_broadcast_sd((const double*)(const void*)&from)));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4cf ploaddup<Packet4cf>(const std::complex<float>* from)\n{\n  // FIXME The following might be optimized using _mm256_movedup_pd\n  Packet2cf a = ploaddup<Packet2cf>(from);\n  Packet2cf b = ploaddup<Packet2cf>(from+1);\n  return  Packet4cf(_mm256_insertf128_ps(_mm256_castps128_ps256(a.v), b.v, 1));\n}\n\ntemplate<> EIGEN_STRONG_INLINE void pstore <std::complex<float> >(std::complex<float>* to, const Packet4cf& from) { EIGEN_DEBUG_ALIGNED_STORE pstore(&numext::real_ref(*to), from.v); }\ntemplate<> EIGEN_STRONG_INLINE void pstoreu<std::complex<float> >(std::complex<float>* to, const Packet4cf& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu(&numext::real_ref(*to), from.v); }\n\ntemplate<> EIGEN_DEVICE_FUNC inline Packet4cf pgather<std::complex<float>, Packet4cf>(const std::complex<float>* from, Index stride)\n{\n  return Packet4cf(_mm256_set_ps(std::imag(from[3*stride]), std::real(from[3*stride]),\n                                 std::imag(from[2*stride]), std::real(from[2*stride]),\n                                 std::imag(from[1*stride]), std::real(from[1*stride]),\n                                 std::imag(from[0*stride]), std::real(from[0*stride])));\n}\n\ntemplate<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<float>, Packet4cf>(std::complex<float>* to, const Packet4cf& from, Index stride)\n{\n  __m128 low = _mm256_extractf128_ps(from.v, 0);\n  to[stride*0] = std::complex<float>(_mm_cvtss_f32(_mm_shuffle_ps(low, low, 0)),\n                                     _mm_cvtss_f32(_mm_shuffle_ps(low, low, 1)));\n  to[stride*1] = std::complex<float>(_mm_cvtss_f32(_mm_shuffle_ps(low, low, 2)),\n                                     _mm_cvtss_f32(_mm_shuffle_ps(low, low, 3)));\n\n  __m128 high = _mm256_extractf128_ps(from.v, 1);\n  to[stride*2] = std::complex<float>(_mm_cvtss_f32(_mm_shuffle_ps(high, high, 0)),\n                                     _mm_cvtss_f32(_mm_shuffle_ps(high, high, 1)));\n  to[stride*3] = std::complex<float>(_mm_cvtss_f32(_mm_shuffle_ps(high, high, 2)),\n                                     _mm_cvtss_f32(_mm_shuffle_ps(high, high, 3)));\n\n}\n\ntemplate<> EIGEN_STRONG_INLINE std::complex<float>  pfirst<Packet4cf>(const Packet4cf& a)\n{\n  return pfirst(Packet2cf(_mm256_castps256_ps128(a.v)));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4cf preverse(const Packet4cf& a) {\n  __m128 low  = _mm256_extractf128_ps(a.v, 0);\n  __m128 high = _mm256_extractf128_ps(a.v, 1);\n  __m128d lowd  = _mm_castps_pd(low);\n  __m128d highd = _mm_castps_pd(high);\n  low  = _mm_castpd_ps(_mm_shuffle_pd(lowd,lowd,0x1));\n  high = _mm_castpd_ps(_mm_shuffle_pd(highd,highd,0x1));\n  __m256 result = _mm256_setzero_ps();\n  result = _mm256_insertf128_ps(result, low, 1);\n  result = _mm256_insertf128_ps(result, high, 0);\n  return Packet4cf(result);\n}\n\ntemplate<> EIGEN_STRONG_INLINE std::complex<float> predux<Packet4cf>(const Packet4cf& a)\n{\n  return predux(padd(Packet2cf(_mm256_extractf128_ps(a.v,0)),\n                     Packet2cf(_mm256_extractf128_ps(a.v,1))));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4cf preduxp<Packet4cf>(const Packet4cf* vecs)\n{\n  Packet8f t0 = _mm256_shuffle_ps(vecs[0].v, vecs[0].v, _MM_SHUFFLE(3, 1, 2 ,0));\n  Packet8f t1 = _mm256_shuffle_ps(vecs[1].v, vecs[1].v, _MM_SHUFFLE(3, 1, 2 ,0));\n  t0 = _mm256_hadd_ps(t0,t1);\n  Packet8f t2 = _mm256_shuffle_ps(vecs[2].v, vecs[2].v, _MM_SHUFFLE(3, 1, 2 ,0));\n  Packet8f t3 = _mm256_shuffle_ps(vecs[3].v, vecs[3].v, _MM_SHUFFLE(3, 1, 2 ,0));\n  t2 = _mm256_hadd_ps(t2,t3);\n  \n  t1 = _mm256_permute2f128_ps(t0,t2, 0 + (2<<4));\n  t3 = _mm256_permute2f128_ps(t0,t2, 1 + (3<<4));\n\n  return Packet4cf(_mm256_add_ps(t1,t3));\n}\n\ntemplate<> EIGEN_STRONG_INLINE std::complex<float> predux_mul<Packet4cf>(const Packet4cf& a)\n{\n  return predux_mul(pmul(Packet2cf(_mm256_extractf128_ps(a.v, 0)),\n                         Packet2cf(_mm256_extractf128_ps(a.v, 1))));\n}\n\ntemplate<int Offset>\nstruct palign_impl<Offset,Packet4cf>\n{\n  static EIGEN_STRONG_INLINE void run(Packet4cf& first, const Packet4cf& second)\n  {\n    if (Offset==0) return;\n    palign_impl<Offset*2,Packet8f>::run(first.v, second.v);\n  }\n};\n\ntemplate<> struct conj_helper<Packet4cf, Packet4cf, false,true>\n{\n  EIGEN_STRONG_INLINE Packet4cf pmadd(const Packet4cf& x, const Packet4cf& y, const Packet4cf& c) const\n  { return padd(pmul(x,y),c); }\n\n  EIGEN_STRONG_INLINE Packet4cf pmul(const Packet4cf& a, const Packet4cf& b) const\n  {\n    return internal::pmul(a, pconj(b));\n  }\n};\n\ntemplate<> struct conj_helper<Packet4cf, Packet4cf, true,false>\n{\n  EIGEN_STRONG_INLINE Packet4cf pmadd(const Packet4cf& x, const Packet4cf& y, const Packet4cf& c) const\n  { return padd(pmul(x,y),c); }\n\n  EIGEN_STRONG_INLINE Packet4cf pmul(const Packet4cf& a, const Packet4cf& b) const\n  {\n    return internal::pmul(pconj(a), b);\n  }\n};\n\ntemplate<> struct conj_helper<Packet4cf, Packet4cf, true,true>\n{\n  EIGEN_STRONG_INLINE Packet4cf pmadd(const Packet4cf& x, const Packet4cf& y, const Packet4cf& c) const\n  { return padd(pmul(x,y),c); }\n\n  EIGEN_STRONG_INLINE Packet4cf pmul(const Packet4cf& a, const Packet4cf& b) const\n  {\n    return pconj(internal::pmul(a, b));\n  }\n};\n\nEIGEN_MAKE_CONJ_HELPER_CPLX_REAL(Packet4cf,Packet8f)\n\ntemplate<> EIGEN_STRONG_INLINE Packet4cf pdiv<Packet4cf>(const Packet4cf& a, const Packet4cf& b)\n{\n  Packet4cf num = pmul(a, pconj(b));\n  __m256 tmp = _mm256_mul_ps(b.v, b.v);\n  __m256 tmp2    = _mm256_shuffle_ps(tmp,tmp,0xB1);\n  __m256 denom = _mm256_add_ps(tmp, tmp2);\n  return Packet4cf(_mm256_div_ps(num.v, denom));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4cf pcplxflip<Packet4cf>(const Packet4cf& x)\n{\n  return Packet4cf(_mm256_shuffle_ps(x.v, x.v, _MM_SHUFFLE(2, 3, 0 ,1)));\n}\n\n//---------- double ----------\nstruct Packet2cd\n{\n  EIGEN_STRONG_INLINE Packet2cd() {}\n  EIGEN_STRONG_INLINE explicit Packet2cd(const __m256d& a) : v(a) {}\n  __m256d  v;\n};\n\ntemplate<> struct packet_traits<std::complex<double> >  : default_packet_traits\n{\n  typedef Packet2cd type;\n  typedef Packet1cd half;\n  enum {\n    Vectorizable = 1,\n    AlignedOnScalar = 0,\n    size = 2,\n    HasHalfPacket = 1,\n\n    HasAdd    = 1,\n    HasSub    = 1,\n    HasMul    = 1,\n    HasDiv    = 1,\n    HasNegate = 1,\n    HasAbs    = 0,\n    HasAbs2   = 0,\n    HasMin    = 0,\n    HasMax    = 0,\n    HasSetLinear = 0\n  };\n};\n\ntemplate<> struct unpacket_traits<Packet2cd> { typedef std::complex<double> type; enum {size=2, alignment=Aligned32}; typedef Packet1cd half; };\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cd padd<Packet2cd>(const Packet2cd& a, const Packet2cd& b) { return Packet2cd(_mm256_add_pd(a.v,b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet2cd psub<Packet2cd>(const Packet2cd& a, const Packet2cd& b) { return Packet2cd(_mm256_sub_pd(a.v,b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet2cd pnegate(const Packet2cd& a) { return Packet2cd(pnegate(a.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet2cd pconj(const Packet2cd& a)\n{\n  const __m256d mask = _mm256_castsi256_pd(_mm256_set_epi32(0x80000000,0x0,0x0,0x0,0x80000000,0x0,0x0,0x0));\n  return Packet2cd(_mm256_xor_pd(a.v,mask));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cd pmul<Packet2cd>(const Packet2cd& a, const Packet2cd& b)\n{\n  __m256d tmp1 = _mm256_shuffle_pd(a.v,a.v,0x0);\n  __m256d even = _mm256_mul_pd(tmp1, b.v);\n  __m256d tmp2 = _mm256_shuffle_pd(a.v,a.v,0xF);\n  __m256d tmp3 = _mm256_shuffle_pd(b.v,b.v,0x5);\n  __m256d odd  = _mm256_mul_pd(tmp2, tmp3);\n  return Packet2cd(_mm256_addsub_pd(even, odd));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cd pand   <Packet2cd>(const Packet2cd& a, const Packet2cd& b) { return Packet2cd(_mm256_and_pd(a.v,b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet2cd por    <Packet2cd>(const Packet2cd& a, const Packet2cd& b) { return Packet2cd(_mm256_or_pd(a.v,b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet2cd pxor   <Packet2cd>(const Packet2cd& a, const Packet2cd& b) { return Packet2cd(_mm256_xor_pd(a.v,b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet2cd pandnot<Packet2cd>(const Packet2cd& a, const Packet2cd& b) { return Packet2cd(_mm256_andnot_pd(a.v,b.v)); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cd pload <Packet2cd>(const std::complex<double>* from)\n{ EIGEN_DEBUG_ALIGNED_LOAD return Packet2cd(pload<Packet4d>((const double*)from)); }\ntemplate<> EIGEN_STRONG_INLINE Packet2cd ploadu<Packet2cd>(const std::complex<double>* from)\n{ EIGEN_DEBUG_UNALIGNED_LOAD return Packet2cd(ploadu<Packet4d>((const double*)from)); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cd pset1<Packet2cd>(const std::complex<double>& from)\n{\n  // in case casting to a __m128d* is really not safe, then we can still fallback to this version: (much slower though)\n//   return Packet2cd(_mm256_loadu2_m128d((const double*)&from,(const double*)&from));\n    return Packet2cd(_mm256_broadcast_pd((const __m128d*)(const void*)&from));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cd ploaddup<Packet2cd>(const std::complex<double>* from) { return pset1<Packet2cd>(*from); }\n\ntemplate<> EIGEN_STRONG_INLINE void pstore <std::complex<double> >(std::complex<double> *   to, const Packet2cd& from) { EIGEN_DEBUG_ALIGNED_STORE pstore((double*)to, from.v); }\ntemplate<> EIGEN_STRONG_INLINE void pstoreu<std::complex<double> >(std::complex<double> *   to, const Packet2cd& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu((double*)to, from.v); }\n\ntemplate<> EIGEN_DEVICE_FUNC inline Packet2cd pgather<std::complex<double>, Packet2cd>(const std::complex<double>* from, Index stride)\n{\n  return Packet2cd(_mm256_set_pd(std::imag(from[1*stride]), std::real(from[1*stride]),\n\t\t\t\t std::imag(from[0*stride]), std::real(from[0*stride])));\n}\n\ntemplate<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<double>, Packet2cd>(std::complex<double>* to, const Packet2cd& from, Index stride)\n{\n  __m128d low = _mm256_extractf128_pd(from.v, 0);\n  to[stride*0] = std::complex<double>(_mm_cvtsd_f64(low), _mm_cvtsd_f64(_mm_shuffle_pd(low, low, 1)));\n  __m128d high = _mm256_extractf128_pd(from.v, 1);\n  to[stride*1] = std::complex<double>(_mm_cvtsd_f64(high), _mm_cvtsd_f64(_mm_shuffle_pd(high, high, 1)));\n}\n\ntemplate<> EIGEN_STRONG_INLINE std::complex<double> pfirst<Packet2cd>(const Packet2cd& a)\n{\n  __m128d low = _mm256_extractf128_pd(a.v, 0);\n  EIGEN_ALIGN16 double res[2];\n  _mm_store_pd(res, low);\n  return std::complex<double>(res[0],res[1]);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cd preverse(const Packet2cd& a) {\n  __m256d result = _mm256_permute2f128_pd(a.v, a.v, 1);\n  return Packet2cd(result);\n}\n\ntemplate<> EIGEN_STRONG_INLINE std::complex<double> predux<Packet2cd>(const Packet2cd& a)\n{\n  return predux(padd(Packet1cd(_mm256_extractf128_pd(a.v,0)),\n                     Packet1cd(_mm256_extractf128_pd(a.v,1))));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cd preduxp<Packet2cd>(const Packet2cd* vecs)\n{\n  Packet4d t0 = _mm256_permute2f128_pd(vecs[0].v,vecs[1].v, 0 + (2<<4));\n  Packet4d t1 = _mm256_permute2f128_pd(vecs[0].v,vecs[1].v, 1 + (3<<4));\n\n  return Packet2cd(_mm256_add_pd(t0,t1));\n}\n\ntemplate<> EIGEN_STRONG_INLINE std::complex<double> predux_mul<Packet2cd>(const Packet2cd& a)\n{\n  return predux(pmul(Packet1cd(_mm256_extractf128_pd(a.v,0)),\n                     Packet1cd(_mm256_extractf128_pd(a.v,1))));\n}\n\ntemplate<int Offset>\nstruct palign_impl<Offset,Packet2cd>\n{\n  static EIGEN_STRONG_INLINE void run(Packet2cd& first, const Packet2cd& second)\n  {\n    if (Offset==0) return;\n    palign_impl<Offset*2,Packet4d>::run(first.v, second.v);\n  }\n};\n\ntemplate<> struct conj_helper<Packet2cd, Packet2cd, false,true>\n{\n  EIGEN_STRONG_INLINE Packet2cd pmadd(const Packet2cd& x, const Packet2cd& y, const Packet2cd& c) const\n  { return padd(pmul(x,y),c); }\n\n  EIGEN_STRONG_INLINE Packet2cd pmul(const Packet2cd& a, const Packet2cd& b) const\n  {\n    return internal::pmul(a, pconj(b));\n  }\n};\n\ntemplate<> struct conj_helper<Packet2cd, Packet2cd, true,false>\n{\n  EIGEN_STRONG_INLINE Packet2cd pmadd(const Packet2cd& x, const Packet2cd& y, const Packet2cd& c) const\n  { return padd(pmul(x,y),c); }\n\n  EIGEN_STRONG_INLINE Packet2cd pmul(const Packet2cd& a, const Packet2cd& b) const\n  {\n    return internal::pmul(pconj(a), b);\n  }\n};\n\ntemplate<> struct conj_helper<Packet2cd, Packet2cd, true,true>\n{\n  EIGEN_STRONG_INLINE Packet2cd pmadd(const Packet2cd& x, const Packet2cd& y, const Packet2cd& c) const\n  { return padd(pmul(x,y),c); }\n\n  EIGEN_STRONG_INLINE Packet2cd pmul(const Packet2cd& a, const Packet2cd& b) const\n  {\n    return pconj(internal::pmul(a, b));\n  }\n};\n\nEIGEN_MAKE_CONJ_HELPER_CPLX_REAL(Packet2cd,Packet4d)\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cd pdiv<Packet2cd>(const Packet2cd& a, const Packet2cd& b)\n{\n  Packet2cd num = pmul(a, pconj(b));\n  __m256d tmp = _mm256_mul_pd(b.v, b.v);\n  __m256d denom = _mm256_hadd_pd(tmp, tmp);\n  return Packet2cd(_mm256_div_pd(num.v, denom));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cd pcplxflip<Packet2cd>(const Packet2cd& x)\n{\n  return Packet2cd(_mm256_shuffle_pd(x.v, x.v, 0x5));\n}\n\nEIGEN_DEVICE_FUNC inline void\nptranspose(PacketBlock<Packet4cf,4>& kernel) {\n  __m256d P0 = _mm256_castps_pd(kernel.packet[0].v);\n  __m256d P1 = _mm256_castps_pd(kernel.packet[1].v);\n  __m256d P2 = _mm256_castps_pd(kernel.packet[2].v);\n  __m256d P3 = _mm256_castps_pd(kernel.packet[3].v);\n\n  __m256d T0 = _mm256_shuffle_pd(P0, P1, 15);\n  __m256d T1 = _mm256_shuffle_pd(P0, P1, 0);\n  __m256d T2 = _mm256_shuffle_pd(P2, P3, 15);\n  __m256d T3 = _mm256_shuffle_pd(P2, P3, 0);\n\n  kernel.packet[1].v = _mm256_castpd_ps(_mm256_permute2f128_pd(T0, T2, 32));\n  kernel.packet[3].v = _mm256_castpd_ps(_mm256_permute2f128_pd(T0, T2, 49));\n  kernel.packet[0].v = _mm256_castpd_ps(_mm256_permute2f128_pd(T1, T3, 32));\n  kernel.packet[2].v = _mm256_castpd_ps(_mm256_permute2f128_pd(T1, T3, 49));\n}\n\nEIGEN_DEVICE_FUNC inline void\nptranspose(PacketBlock<Packet2cd,2>& kernel) {\n  __m256d tmp = _mm256_permute2f128_pd(kernel.packet[0].v, kernel.packet[1].v, 0+(2<<4));\n  kernel.packet[1].v = _mm256_permute2f128_pd(kernel.packet[0].v, kernel.packet[1].v, 1+(3<<4));\n kernel.packet[0].v = tmp;\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4cf pinsertfirst(const Packet4cf& a, std::complex<float> b)\n{\n  return Packet4cf(_mm256_blend_ps(a.v,pset1<Packet4cf>(b).v,1|2));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cd pinsertfirst(const Packet2cd& a, std::complex<double> b)\n{\n  return Packet2cd(_mm256_blend_pd(a.v,pset1<Packet2cd>(b).v,1|2));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4cf pinsertlast(const Packet4cf& a, std::complex<float> b)\n{\n  return Packet4cf(_mm256_blend_ps(a.v,pset1<Packet4cf>(b).v,(1<<7)|(1<<6)));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cd pinsertlast(const Packet2cd& a, std::complex<double> b)\n{\n  return Packet2cd(_mm256_blend_pd(a.v,pset1<Packet2cd>(b).v,(1<<3)|(1<<2)));\n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_COMPLEX_AVX_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/arch/AVX/MathFunctions.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Pedro Gonnet (pedro.gonnet@gmail.com)\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_MATH_FUNCTIONS_AVX_H\n#define EIGEN_MATH_FUNCTIONS_AVX_H\n\n/* The sin, cos, exp, and log functions of this file are loosely derived from\n * Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/\n */\n\nnamespace Eigen {\n\nnamespace internal {\n\ninline Packet8i pshiftleft(Packet8i v, int n)\n{\n#ifdef EIGEN_VECTORIZE_AVX2\n  return _mm256_slli_epi32(v, n);\n#else\n  __m128i lo = _mm_slli_epi32(_mm256_extractf128_si256(v, 0), n);\n  __m128i hi = _mm_slli_epi32(_mm256_extractf128_si256(v, 1), n);\n  return _mm256_insertf128_si256(_mm256_castsi128_si256(lo), (hi), 1);\n#endif\n}\n\ninline Packet8f pshiftright(Packet8f v, int n)\n{\n#ifdef EIGEN_VECTORIZE_AVX2\n  return _mm256_cvtepi32_ps(_mm256_srli_epi32(_mm256_castps_si256(v), n));\n#else\n  __m128i lo = _mm_srli_epi32(_mm256_extractf128_si256(_mm256_castps_si256(v), 0), n);\n  __m128i hi = _mm_srli_epi32(_mm256_extractf128_si256(_mm256_castps_si256(v), 1), n);\n  return _mm256_cvtepi32_ps(_mm256_insertf128_si256(_mm256_castsi128_si256(lo), (hi), 1));\n#endif\n}\n\n// Sine function\n// Computes sin(x) by wrapping x to the interval [-Pi/4,3*Pi/4] and\n// evaluating interpolants in [-Pi/4,Pi/4] or [Pi/4,3*Pi/4]. The interpolants\n// are (anti-)symmetric and thus have only odd/even coefficients\ntemplate <>\nEIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8f\npsin<Packet8f>(const Packet8f& _x) {\n  Packet8f x = _x;\n\n  // Some useful values.\n  _EIGEN_DECLARE_CONST_Packet8i(one, 1);\n  _EIGEN_DECLARE_CONST_Packet8f(one, 1.0f);\n  _EIGEN_DECLARE_CONST_Packet8f(two, 2.0f);\n  _EIGEN_DECLARE_CONST_Packet8f(one_over_four, 0.25f);\n  _EIGEN_DECLARE_CONST_Packet8f(one_over_pi, 3.183098861837907e-01f);\n  _EIGEN_DECLARE_CONST_Packet8f(neg_pi_first, -3.140625000000000e+00f);\n  _EIGEN_DECLARE_CONST_Packet8f(neg_pi_second, -9.670257568359375e-04f);\n  _EIGEN_DECLARE_CONST_Packet8f(neg_pi_third, -6.278329571784980e-07f);\n  _EIGEN_DECLARE_CONST_Packet8f(four_over_pi, 1.273239544735163e+00f);\n\n  // Map x from [-Pi/4,3*Pi/4] to z in [-1,3] and subtract the shifted period.\n  Packet8f z = pmul(x, p8f_one_over_pi);\n  Packet8f shift = _mm256_floor_ps(padd(z, p8f_one_over_four));\n  x = pmadd(shift, p8f_neg_pi_first, x);\n  x = pmadd(shift, p8f_neg_pi_second, x);\n  x = pmadd(shift, p8f_neg_pi_third, x);\n  z = pmul(x, p8f_four_over_pi);\n\n  // Make a mask for the entries that need flipping, i.e. wherever the shift\n  // is odd.\n  Packet8i shift_ints = _mm256_cvtps_epi32(shift);\n  Packet8i shift_isodd = _mm256_castps_si256(_mm256_and_ps(_mm256_castsi256_ps(shift_ints), _mm256_castsi256_ps(p8i_one)));\n  Packet8i sign_flip_mask = pshiftleft(shift_isodd, 31);\n\n  // Create a mask for which interpolant to use, i.e. if z > 1, then the mask\n  // is set to ones for that entry.\n  Packet8f ival_mask = _mm256_cmp_ps(z, p8f_one, _CMP_GT_OQ);\n\n  // Evaluate the polynomial for the interval [1,3] in z.\n  _EIGEN_DECLARE_CONST_Packet8f(coeff_right_0, 9.999999724233232e-01f);\n  _EIGEN_DECLARE_CONST_Packet8f(coeff_right_2, -3.084242535619928e-01f);\n  _EIGEN_DECLARE_CONST_Packet8f(coeff_right_4, 1.584991525700324e-02f);\n  _EIGEN_DECLARE_CONST_Packet8f(coeff_right_6, -3.188805084631342e-04f);\n  Packet8f z_minus_two = psub(z, p8f_two);\n  Packet8f z_minus_two2 = pmul(z_minus_two, z_minus_two);\n  Packet8f right = pmadd(p8f_coeff_right_6, z_minus_two2, p8f_coeff_right_4);\n  right = pmadd(right, z_minus_two2, p8f_coeff_right_2);\n  right = pmadd(right, z_minus_two2, p8f_coeff_right_0);\n\n  // Evaluate the polynomial for the interval [-1,1] in z.\n  _EIGEN_DECLARE_CONST_Packet8f(coeff_left_1, 7.853981525427295e-01f);\n  _EIGEN_DECLARE_CONST_Packet8f(coeff_left_3, -8.074536727092352e-02f);\n  _EIGEN_DECLARE_CONST_Packet8f(coeff_left_5, 2.489871967827018e-03f);\n  _EIGEN_DECLARE_CONST_Packet8f(coeff_left_7, -3.587725841214251e-05f);\n  Packet8f z2 = pmul(z, z);\n  Packet8f left = pmadd(p8f_coeff_left_7, z2, p8f_coeff_left_5);\n  left = pmadd(left, z2, p8f_coeff_left_3);\n  left = pmadd(left, z2, p8f_coeff_left_1);\n  left = pmul(left, z);\n\n  // Assemble the results, i.e. select the left and right polynomials.\n  left = _mm256_andnot_ps(ival_mask, left);\n  right = _mm256_and_ps(ival_mask, right);\n  Packet8f res = _mm256_or_ps(left, right);\n\n  // Flip the sign on the odd intervals and return the result.\n  res = _mm256_xor_ps(res, _mm256_castsi256_ps(sign_flip_mask));\n  return res;\n}\n\n// Natural logarithm\n// Computes log(x) as log(2^e * m) = C*e + log(m), where the constant C =log(2)\n// and m is in the range [sqrt(1/2),sqrt(2)). In this range, the logarithm can\n// be easily approximated by a polynomial centered on m=1 for stability.\n// TODO(gonnet): Further reduce the interval allowing for lower-degree\n//               polynomial interpolants -> ... -> profit!\ntemplate <>\nEIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8f\nplog<Packet8f>(const Packet8f& _x) {\n  Packet8f x = _x;\n  _EIGEN_DECLARE_CONST_Packet8f(1, 1.0f);\n  _EIGEN_DECLARE_CONST_Packet8f(half, 0.5f);\n  _EIGEN_DECLARE_CONST_Packet8f(126f, 126.0f);\n\n  _EIGEN_DECLARE_CONST_Packet8f_FROM_INT(inv_mant_mask, ~0x7f800000);\n\n  // The smallest non denormalized float number.\n  _EIGEN_DECLARE_CONST_Packet8f_FROM_INT(min_norm_pos, 0x00800000);\n  _EIGEN_DECLARE_CONST_Packet8f_FROM_INT(minus_inf, 0xff800000);\n\n  // Polynomial coefficients.\n  _EIGEN_DECLARE_CONST_Packet8f(cephes_SQRTHF, 0.707106781186547524f);\n  _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p0, 7.0376836292E-2f);\n  _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p1, -1.1514610310E-1f);\n  _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p2, 1.1676998740E-1f);\n  _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p3, -1.2420140846E-1f);\n  _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p4, +1.4249322787E-1f);\n  _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p5, -1.6668057665E-1f);\n  _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p6, +2.0000714765E-1f);\n  _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p7, -2.4999993993E-1f);\n  _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p8, +3.3333331174E-1f);\n  _EIGEN_DECLARE_CONST_Packet8f(cephes_log_q1, -2.12194440e-4f);\n  _EIGEN_DECLARE_CONST_Packet8f(cephes_log_q2, 0.693359375f);\n\n  Packet8f invalid_mask = _mm256_cmp_ps(x, _mm256_setzero_ps(), _CMP_NGE_UQ); // not greater equal is true if x is NaN\n  Packet8f iszero_mask = _mm256_cmp_ps(x, _mm256_setzero_ps(), _CMP_EQ_OQ);\n\n  // Truncate input values to the minimum positive normal.\n  x = pmax(x, p8f_min_norm_pos);\n\n  Packet8f emm0 = pshiftright(x,23);\n  Packet8f e = _mm256_sub_ps(emm0, p8f_126f);\n\n  // Set the exponents to -1, i.e. x are in the range [0.5,1).\n  x = _mm256_and_ps(x, p8f_inv_mant_mask);\n  x = _mm256_or_ps(x, p8f_half);\n\n  // part2: Shift the inputs from the range [0.5,1) to [sqrt(1/2),sqrt(2))\n  // and shift by -1. The values are then centered around 0, which improves\n  // the stability of the polynomial evaluation.\n  //   if( x < SQRTHF ) {\n  //     e -= 1;\n  //     x = x + x - 1.0;\n  //   } else { x = x - 1.0; }\n  Packet8f mask = _mm256_cmp_ps(x, p8f_cephes_SQRTHF, _CMP_LT_OQ);\n  Packet8f tmp = _mm256_and_ps(x, mask);\n  x = psub(x, p8f_1);\n  e = psub(e, _mm256_and_ps(p8f_1, mask));\n  x = padd(x, tmp);\n\n  Packet8f x2 = pmul(x, x);\n  Packet8f x3 = pmul(x2, x);\n\n  // Evaluate the polynomial approximant of degree 8 in three parts, probably\n  // to improve instruction-level parallelism.\n  Packet8f y, y1, y2;\n  y = pmadd(p8f_cephes_log_p0, x, p8f_cephes_log_p1);\n  y1 = pmadd(p8f_cephes_log_p3, x, p8f_cephes_log_p4);\n  y2 = pmadd(p8f_cephes_log_p6, x, p8f_cephes_log_p7);\n  y = pmadd(y, x, p8f_cephes_log_p2);\n  y1 = pmadd(y1, x, p8f_cephes_log_p5);\n  y2 = pmadd(y2, x, p8f_cephes_log_p8);\n  y = pmadd(y, x3, y1);\n  y = pmadd(y, x3, y2);\n  y = pmul(y, x3);\n\n  // Add the logarithm of the exponent back to the result of the interpolation.\n  y1 = pmul(e, p8f_cephes_log_q1);\n  tmp = pmul(x2, p8f_half);\n  y = padd(y, y1);\n  x = psub(x, tmp);\n  y2 = pmul(e, p8f_cephes_log_q2);\n  x = padd(x, y);\n  x = padd(x, y2);\n\n  // Filter out invalid inputs, i.e. negative arg will be NAN, 0 will be -INF.\n  return _mm256_or_ps(\n      _mm256_andnot_ps(iszero_mask, _mm256_or_ps(x, invalid_mask)),\n      _mm256_and_ps(iszero_mask, p8f_minus_inf));\n}\n\n// Exponential function. Works by writing \"x = m*log(2) + r\" where\n// \"m = floor(x/log(2)+1/2)\" and \"r\" is the remainder. The result is then\n// \"exp(x) = 2^m*exp(r)\" where exp(r) is in the range [-1,1).\ntemplate <>\nEIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8f\npexp<Packet8f>(const Packet8f& _x) {\n  _EIGEN_DECLARE_CONST_Packet8f(1, 1.0f);\n  _EIGEN_DECLARE_CONST_Packet8f(half, 0.5f);\n  _EIGEN_DECLARE_CONST_Packet8f(127, 127.0f);\n\n  _EIGEN_DECLARE_CONST_Packet8f(exp_hi, 88.3762626647950f);\n  _EIGEN_DECLARE_CONST_Packet8f(exp_lo, -88.3762626647949f);\n\n  _EIGEN_DECLARE_CONST_Packet8f(cephes_LOG2EF, 1.44269504088896341f);\n\n  _EIGEN_DECLARE_CONST_Packet8f(cephes_exp_p0, 1.9875691500E-4f);\n  _EIGEN_DECLARE_CONST_Packet8f(cephes_exp_p1, 1.3981999507E-3f);\n  _EIGEN_DECLARE_CONST_Packet8f(cephes_exp_p2, 8.3334519073E-3f);\n  _EIGEN_DECLARE_CONST_Packet8f(cephes_exp_p3, 4.1665795894E-2f);\n  _EIGEN_DECLARE_CONST_Packet8f(cephes_exp_p4, 1.6666665459E-1f);\n  _EIGEN_DECLARE_CONST_Packet8f(cephes_exp_p5, 5.0000001201E-1f);\n\n  // Clamp x.\n  Packet8f x = pmax(pmin(_x, p8f_exp_hi), p8f_exp_lo);\n\n  // Express exp(x) as exp(m*ln(2) + r), start by extracting\n  // m = floor(x/ln(2) + 0.5).\n  Packet8f m = _mm256_floor_ps(pmadd(x, p8f_cephes_LOG2EF, p8f_half));\n\n// Get r = x - m*ln(2). If no FMA instructions are available, m*ln(2) is\n// subtracted out in two parts, m*C1+m*C2 = m*ln(2), to avoid accumulating\n// truncation errors. Note that we don't use the \"pmadd\" function here to\n// ensure that a precision-preserving FMA instruction is used.\n#ifdef EIGEN_VECTORIZE_FMA\n  _EIGEN_DECLARE_CONST_Packet8f(nln2, -0.6931471805599453f);\n  Packet8f r = _mm256_fmadd_ps(m, p8f_nln2, x);\n#else\n  _EIGEN_DECLARE_CONST_Packet8f(cephes_exp_C1, 0.693359375f);\n  _EIGEN_DECLARE_CONST_Packet8f(cephes_exp_C2, -2.12194440e-4f);\n  Packet8f r = psub(x, pmul(m, p8f_cephes_exp_C1));\n  r = psub(r, pmul(m, p8f_cephes_exp_C2));\n#endif\n\n  Packet8f r2 = pmul(r, r);\n\n  // TODO(gonnet): Split into odd/even polynomials and try to exploit\n  //               instruction-level parallelism.\n  Packet8f y = p8f_cephes_exp_p0;\n  y = pmadd(y, r, p8f_cephes_exp_p1);\n  y = pmadd(y, r, p8f_cephes_exp_p2);\n  y = pmadd(y, r, p8f_cephes_exp_p3);\n  y = pmadd(y, r, p8f_cephes_exp_p4);\n  y = pmadd(y, r, p8f_cephes_exp_p5);\n  y = pmadd(y, r2, r);\n  y = padd(y, p8f_1);\n\n  // Build emm0 = 2^m.\n  Packet8i emm0 = _mm256_cvttps_epi32(padd(m, p8f_127));\n  emm0 = pshiftleft(emm0, 23);\n\n  // Return 2^m * exp(r).\n  return pmax(pmul(y, _mm256_castsi256_ps(emm0)), _x);\n}\n\n// Hyperbolic Tangent function.\ntemplate <>\nEIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8f\nptanh<Packet8f>(const Packet8f& x) {\n  return internal::generic_fast_tanh_float(x);\n}\n\ntemplate <>\nEIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4d\npexp<Packet4d>(const Packet4d& _x) {\n  Packet4d x = _x;\n\n  _EIGEN_DECLARE_CONST_Packet4d(1, 1.0);\n  _EIGEN_DECLARE_CONST_Packet4d(2, 2.0);\n  _EIGEN_DECLARE_CONST_Packet4d(half, 0.5);\n\n  _EIGEN_DECLARE_CONST_Packet4d(exp_hi, 709.437);\n  _EIGEN_DECLARE_CONST_Packet4d(exp_lo, -709.436139303);\n\n  _EIGEN_DECLARE_CONST_Packet4d(cephes_LOG2EF, 1.4426950408889634073599);\n\n  _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_p0, 1.26177193074810590878e-4);\n  _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_p1, 3.02994407707441961300e-2);\n  _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_p2, 9.99999999999999999910e-1);\n\n  _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_q0, 3.00198505138664455042e-6);\n  _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_q1, 2.52448340349684104192e-3);\n  _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_q2, 2.27265548208155028766e-1);\n  _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_q3, 2.00000000000000000009e0);\n\n  _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_C1, 0.693145751953125);\n  _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_C2, 1.42860682030941723212e-6);\n  _EIGEN_DECLARE_CONST_Packet4i(1023, 1023);\n\n  Packet4d tmp, fx;\n\n  // clamp x\n  x = pmax(pmin(x, p4d_exp_hi), p4d_exp_lo);\n  // Express exp(x) as exp(g + n*log(2)).\n  fx = pmadd(p4d_cephes_LOG2EF, x, p4d_half);\n\n  // Get the integer modulus of log(2), i.e. the \"n\" described above.\n  fx = _mm256_floor_pd(fx);\n\n  // Get the remainder modulo log(2), i.e. the \"g\" described above. Subtract\n  // n*log(2) out in two steps, i.e. n*C1 + n*C2, C1+C2=log2 to get the last\n  // digits right.\n  tmp = pmul(fx, p4d_cephes_exp_C1);\n  Packet4d z = pmul(fx, p4d_cephes_exp_C2);\n  x = psub(x, tmp);\n  x = psub(x, z);\n\n  Packet4d x2 = pmul(x, x);\n\n  // Evaluate the numerator polynomial of the rational interpolant.\n  Packet4d px = p4d_cephes_exp_p0;\n  px = pmadd(px, x2, p4d_cephes_exp_p1);\n  px = pmadd(px, x2, p4d_cephes_exp_p2);\n  px = pmul(px, x);\n\n  // Evaluate the denominator polynomial of the rational interpolant.\n  Packet4d qx = p4d_cephes_exp_q0;\n  qx = pmadd(qx, x2, p4d_cephes_exp_q1);\n  qx = pmadd(qx, x2, p4d_cephes_exp_q2);\n  qx = pmadd(qx, x2, p4d_cephes_exp_q3);\n\n  // I don't really get this bit, copied from the SSE2 routines, so...\n  // TODO(gonnet): Figure out what is going on here, perhaps find a better\n  // rational interpolant?\n  x = _mm256_div_pd(px, psub(qx, px));\n  x = pmadd(p4d_2, x, p4d_1);\n\n  // Build e=2^n by constructing the exponents in a 128-bit vector and\n  // shifting them to where they belong in double-precision values.\n  __m128i emm0 = _mm256_cvtpd_epi32(fx);\n  emm0 = _mm_add_epi32(emm0, p4i_1023);\n  emm0 = _mm_shuffle_epi32(emm0, _MM_SHUFFLE(3, 1, 2, 0));\n  __m128i lo = _mm_slli_epi64(emm0, 52);\n  __m128i hi = _mm_slli_epi64(_mm_srli_epi64(emm0, 32), 52);\n  __m256i e = _mm256_insertf128_si256(_mm256_setzero_si256(), lo, 0);\n  e = _mm256_insertf128_si256(e, hi, 1);\n\n  // Construct the result 2^n * exp(g) = e * x. The max is used to catch\n  // non-finite values in the input.\n  return pmax(pmul(x, _mm256_castsi256_pd(e)), _x);\n}\n\n// Functions for sqrt.\n// The EIGEN_FAST_MATH version uses the _mm_rsqrt_ps approximation and one step\n// of Newton's method, at a cost of 1-2 bits of precision as opposed to the\n// exact solution. It does not handle +inf, or denormalized numbers correctly.\n// The main advantage of this approach is not just speed, but also the fact that\n// it can be inlined and pipelined with other computations, further reducing its\n// effective latency. This is similar to Quake3's fast inverse square root.\n// For detail see here: http://www.beyond3d.com/content/articles/8/\n#if EIGEN_FAST_MATH\ntemplate <>\nEIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8f\npsqrt<Packet8f>(const Packet8f& _x) {\n  Packet8f half = pmul(_x, pset1<Packet8f>(.5f));\n  Packet8f denormal_mask = _mm256_and_ps(\n      _mm256_cmp_ps(_x, pset1<Packet8f>((std::numeric_limits<float>::min)()),\n                    _CMP_LT_OQ),\n      _mm256_cmp_ps(_x, _mm256_setzero_ps(), _CMP_GE_OQ));\n\n  // Compute approximate reciprocal sqrt.\n  Packet8f x = _mm256_rsqrt_ps(_x);\n  // Do a single step of Newton's iteration.\n  x = pmul(x, psub(pset1<Packet8f>(1.5f), pmul(half, pmul(x,x))));\n  // Flush results for denormals to zero.\n  return _mm256_andnot_ps(denormal_mask, pmul(_x,x));\n}\n#else\ntemplate <> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED\nPacket8f psqrt<Packet8f>(const Packet8f& x) {\n  return _mm256_sqrt_ps(x);\n}\n#endif\ntemplate <> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED\nPacket4d psqrt<Packet4d>(const Packet4d& x) {\n  return _mm256_sqrt_pd(x);\n}\n#if EIGEN_FAST_MATH\n\ntemplate<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED\nPacket8f prsqrt<Packet8f>(const Packet8f& _x) {\n  _EIGEN_DECLARE_CONST_Packet8f_FROM_INT(inf, 0x7f800000);\n  _EIGEN_DECLARE_CONST_Packet8f_FROM_INT(nan, 0x7fc00000);\n  _EIGEN_DECLARE_CONST_Packet8f(one_point_five, 1.5f);\n  _EIGEN_DECLARE_CONST_Packet8f(minus_half, -0.5f);\n  _EIGEN_DECLARE_CONST_Packet8f_FROM_INT(flt_min, 0x00800000);\n\n  Packet8f neg_half = pmul(_x, p8f_minus_half);\n\n  // select only the inverse sqrt of positive normal inputs (denormals are\n  // flushed to zero and cause infs as well).\n  Packet8f le_zero_mask = _mm256_cmp_ps(_x, p8f_flt_min, _CMP_LT_OQ);\n  Packet8f x = _mm256_andnot_ps(le_zero_mask, _mm256_rsqrt_ps(_x));\n\n  // Fill in NaNs and Infs for the negative/zero entries.\n  Packet8f neg_mask = _mm256_cmp_ps(_x, _mm256_setzero_ps(), _CMP_LT_OQ);\n  Packet8f zero_mask = _mm256_andnot_ps(neg_mask, le_zero_mask);\n  Packet8f infs_and_nans = _mm256_or_ps(_mm256_and_ps(neg_mask, p8f_nan),\n                                        _mm256_and_ps(zero_mask, p8f_inf));\n\n  // Do a single step of Newton's iteration.\n  x = pmul(x, pmadd(neg_half, pmul(x, x), p8f_one_point_five));\n\n  // Insert NaNs and Infs in all the right places.\n  return _mm256_or_ps(x, infs_and_nans);\n}\n\n#else\ntemplate <> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED\nPacket8f prsqrt<Packet8f>(const Packet8f& x) {\n  _EIGEN_DECLARE_CONST_Packet8f(one, 1.0f);\n  return _mm256_div_ps(p8f_one, _mm256_sqrt_ps(x));\n}\n#endif\n\ntemplate <> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED\nPacket4d prsqrt<Packet4d>(const Packet4d& x) {\n  _EIGEN_DECLARE_CONST_Packet4d(one, 1.0);\n  return _mm256_div_pd(p4d_one, _mm256_sqrt_pd(x));\n}\n\n\n}  // end namespace internal\n\n}  // end namespace Eigen\n\n#endif  // EIGEN_MATH_FUNCTIONS_AVX_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/arch/AVX/PacketMath.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner (benoit.steiner.goog@gmail.com)\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_PACKET_MATH_AVX_H\n#define EIGEN_PACKET_MATH_AVX_H\n\nnamespace Eigen {\n\nnamespace internal {\n\n#ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD\n#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 8\n#endif\n\n#ifndef EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS\n#define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS (2*sizeof(void*))\n#endif\n\n#ifdef __FMA__\n#ifndef EIGEN_HAS_SINGLE_INSTRUCTION_MADD\n#define EIGEN_HAS_SINGLE_INSTRUCTION_MADD\n#endif\n#endif\n\ntypedef __m256  Packet8f;\ntypedef __m256i Packet8i;\ntypedef __m256d Packet4d;\n\ntemplate<> struct is_arithmetic<__m256>  { enum { value = true }; };\ntemplate<> struct is_arithmetic<__m256i> { enum { value = true }; };\ntemplate<> struct is_arithmetic<__m256d> { enum { value = true }; };\n\n#define _EIGEN_DECLARE_CONST_Packet8f(NAME,X) \\\n  const Packet8f p8f_##NAME = pset1<Packet8f>(X)\n\n#define _EIGEN_DECLARE_CONST_Packet4d(NAME,X) \\\n  const Packet4d p4d_##NAME = pset1<Packet4d>(X)\n\n#define _EIGEN_DECLARE_CONST_Packet8f_FROM_INT(NAME,X) \\\n  const Packet8f p8f_##NAME = _mm256_castsi256_ps(pset1<Packet8i>(X))\n\n#define _EIGEN_DECLARE_CONST_Packet8i(NAME,X) \\\n  const Packet8i p8i_##NAME = pset1<Packet8i>(X)\n\n// Use the packet_traits defined in AVX512/PacketMath.h instead if we're going\n// to leverage AVX512 instructions.\n#ifndef EIGEN_VECTORIZE_AVX512\ntemplate<> struct packet_traits<float>  : default_packet_traits\n{\n  typedef Packet8f type;\n  typedef Packet4f half;\n  enum {\n    Vectorizable = 1,\n    AlignedOnScalar = 1,\n    size=8,\n    HasHalfPacket = 1,\n\n    HasDiv  = 1,\n    HasSin  = EIGEN_FAST_MATH,\n    HasCos  = 0,\n    HasLog  = 1,\n    HasExp  = 1,\n    HasSqrt = 1,\n    HasRsqrt = 1,\n    HasTanh  = EIGEN_FAST_MATH,\n    HasBlend = 1,\n    HasRound = 1,\n    HasFloor = 1,\n    HasCeil = 1\n  };\n};\ntemplate<> struct packet_traits<double> : default_packet_traits\n{\n  typedef Packet4d type;\n  typedef Packet2d half;\n  enum {\n    Vectorizable = 1,\n    AlignedOnScalar = 1,\n    size=4,\n    HasHalfPacket = 1,\n\n    HasDiv  = 1,\n    HasExp  = 1,\n    HasSqrt = 1,\n    HasRsqrt = 1,\n    HasBlend = 1,\n    HasRound = 1,\n    HasFloor = 1,\n    HasCeil = 1\n  };\n};\n#endif\n\ntemplate<> struct scalar_div_cost<float,true> { enum { value = 14 }; };\ntemplate<> struct scalar_div_cost<double,true> { enum { value = 16 }; };\n\n/* Proper support for integers is only provided by AVX2. In the meantime, we'll\n   use SSE instructions and packets to deal with integers.\ntemplate<> struct packet_traits<int>    : default_packet_traits\n{\n  typedef Packet8i type;\n  enum {\n    Vectorizable = 1,\n    AlignedOnScalar = 1,\n    size=8\n  };\n};\n*/\n\ntemplate<> struct unpacket_traits<Packet8f> { typedef float  type; typedef Packet4f half; enum {size=8, alignment=Aligned32}; };\ntemplate<> struct unpacket_traits<Packet4d> { typedef double type; typedef Packet2d half; enum {size=4, alignment=Aligned32}; };\ntemplate<> struct unpacket_traits<Packet8i> { typedef int    type; typedef Packet4i half; enum {size=8, alignment=Aligned32}; };\n\ntemplate<> EIGEN_STRONG_INLINE Packet8f pset1<Packet8f>(const float&  from) { return _mm256_set1_ps(from); }\ntemplate<> EIGEN_STRONG_INLINE Packet4d pset1<Packet4d>(const double& from) { return _mm256_set1_pd(from); }\ntemplate<> EIGEN_STRONG_INLINE Packet8i pset1<Packet8i>(const int&    from) { return _mm256_set1_epi32(from); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet8f pload1<Packet8f>(const float*  from) { return _mm256_broadcast_ss(from); }\ntemplate<> EIGEN_STRONG_INLINE Packet4d pload1<Packet4d>(const double* from) { return _mm256_broadcast_sd(from); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet8f plset<Packet8f>(const float& a) { return _mm256_add_ps(_mm256_set1_ps(a), _mm256_set_ps(7.0,6.0,5.0,4.0,3.0,2.0,1.0,0.0)); }\ntemplate<> EIGEN_STRONG_INLINE Packet4d plset<Packet4d>(const double& a) { return _mm256_add_pd(_mm256_set1_pd(a), _mm256_set_pd(3.0,2.0,1.0,0.0)); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet8f padd<Packet8f>(const Packet8f& a, const Packet8f& b) { return _mm256_add_ps(a,b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4d padd<Packet4d>(const Packet4d& a, const Packet4d& b) { return _mm256_add_pd(a,b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet8f psub<Packet8f>(const Packet8f& a, const Packet8f& b) { return _mm256_sub_ps(a,b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4d psub<Packet4d>(const Packet4d& a, const Packet4d& b) { return _mm256_sub_pd(a,b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet8f pnegate(const Packet8f& a)\n{\n  return _mm256_sub_ps(_mm256_set1_ps(0.0),a);\n}\ntemplate<> EIGEN_STRONG_INLINE Packet4d pnegate(const Packet4d& a)\n{\n  return _mm256_sub_pd(_mm256_set1_pd(0.0),a);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet8f pconj(const Packet8f& a) { return a; }\ntemplate<> EIGEN_STRONG_INLINE Packet4d pconj(const Packet4d& a) { return a; }\ntemplate<> EIGEN_STRONG_INLINE Packet8i pconj(const Packet8i& a) { return a; }\n\ntemplate<> EIGEN_STRONG_INLINE Packet8f pmul<Packet8f>(const Packet8f& a, const Packet8f& b) { return _mm256_mul_ps(a,b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4d pmul<Packet4d>(const Packet4d& a, const Packet4d& b) { return _mm256_mul_pd(a,b); }\n\n\ntemplate<> EIGEN_STRONG_INLINE Packet8f pdiv<Packet8f>(const Packet8f& a, const Packet8f& b) { return _mm256_div_ps(a,b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4d pdiv<Packet4d>(const Packet4d& a, const Packet4d& b) { return _mm256_div_pd(a,b); }\ntemplate<> EIGEN_STRONG_INLINE Packet8i pdiv<Packet8i>(const Packet8i& /*a*/, const Packet8i& /*b*/)\n{ eigen_assert(false && \"packet integer division are not supported by AVX\");\n  return pset1<Packet8i>(0);\n}\n\n#ifdef __FMA__\ntemplate<> EIGEN_STRONG_INLINE Packet8f pmadd(const Packet8f& a, const Packet8f& b, const Packet8f& c) {\n#if ( EIGEN_COMP_GNUC_STRICT || (EIGEN_COMP_CLANG && (EIGEN_COMP_CLANG<308)) )\n  // clang stupidly generates a vfmadd213ps instruction plus some vmovaps on registers,\n  // and gcc stupidly generates a vfmadd132ps instruction,\n  // so let's enforce it to generate a vfmadd231ps instruction since the most common use case is to accumulate\n  // the result of the product.\n  Packet8f res = c;\n  __asm__(\"vfmadd231ps %[a], %[b], %[c]\" : [c] \"+x\" (res) : [a] \"x\" (a), [b] \"x\" (b));\n  return res;\n#else\n  return _mm256_fmadd_ps(a,b,c);\n#endif\n}\ntemplate<> EIGEN_STRONG_INLINE Packet4d pmadd(const Packet4d& a, const Packet4d& b, const Packet4d& c) {\n#if ( EIGEN_COMP_GNUC_STRICT || (EIGEN_COMP_CLANG && (EIGEN_COMP_CLANG<308)) )\n  // see above\n  Packet4d res = c;\n  __asm__(\"vfmadd231pd %[a], %[b], %[c]\" : [c] \"+x\" (res) : [a] \"x\" (a), [b] \"x\" (b));\n  return res;\n#else\n  return _mm256_fmadd_pd(a,b,c);\n#endif\n}\n#endif\n\ntemplate<> EIGEN_STRONG_INLINE Packet8f pmin<Packet8f>(const Packet8f& a, const Packet8f& b) { return _mm256_min_ps(a,b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4d pmin<Packet4d>(const Packet4d& a, const Packet4d& b) { return _mm256_min_pd(a,b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet8f pmax<Packet8f>(const Packet8f& a, const Packet8f& b) { return _mm256_max_ps(a,b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4d pmax<Packet4d>(const Packet4d& a, const Packet4d& b) { return _mm256_max_pd(a,b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet8f pround<Packet8f>(const Packet8f& a) { return _mm256_round_ps(a, _MM_FROUND_CUR_DIRECTION); }\ntemplate<> EIGEN_STRONG_INLINE Packet4d pround<Packet4d>(const Packet4d& a) { return _mm256_round_pd(a, _MM_FROUND_CUR_DIRECTION); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet8f pceil<Packet8f>(const Packet8f& a) { return _mm256_ceil_ps(a); }\ntemplate<> EIGEN_STRONG_INLINE Packet4d pceil<Packet4d>(const Packet4d& a) { return _mm256_ceil_pd(a); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet8f pfloor<Packet8f>(const Packet8f& a) { return _mm256_floor_ps(a); }\ntemplate<> EIGEN_STRONG_INLINE Packet4d pfloor<Packet4d>(const Packet4d& a) { return _mm256_floor_pd(a); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet8f pand<Packet8f>(const Packet8f& a, const Packet8f& b) { return _mm256_and_ps(a,b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4d pand<Packet4d>(const Packet4d& a, const Packet4d& b) { return _mm256_and_pd(a,b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet8f por<Packet8f>(const Packet8f& a, const Packet8f& b) { return _mm256_or_ps(a,b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4d por<Packet4d>(const Packet4d& a, const Packet4d& b) { return _mm256_or_pd(a,b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet8f pxor<Packet8f>(const Packet8f& a, const Packet8f& b) { return _mm256_xor_ps(a,b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4d pxor<Packet4d>(const Packet4d& a, const Packet4d& b) { return _mm256_xor_pd(a,b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet8f pandnot<Packet8f>(const Packet8f& a, const Packet8f& b) { return _mm256_andnot_ps(a,b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4d pandnot<Packet4d>(const Packet4d& a, const Packet4d& b) { return _mm256_andnot_pd(a,b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet8f pload<Packet8f>(const float*   from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm256_load_ps(from); }\ntemplate<> EIGEN_STRONG_INLINE Packet4d pload<Packet4d>(const double*  from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm256_load_pd(from); }\ntemplate<> EIGEN_STRONG_INLINE Packet8i pload<Packet8i>(const int*     from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm256_load_si256(reinterpret_cast<const __m256i*>(from)); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet8f ploadu<Packet8f>(const float* from) { EIGEN_DEBUG_UNALIGNED_LOAD return _mm256_loadu_ps(from); }\ntemplate<> EIGEN_STRONG_INLINE Packet4d ploadu<Packet4d>(const double* from) { EIGEN_DEBUG_UNALIGNED_LOAD return _mm256_loadu_pd(from); }\ntemplate<> EIGEN_STRONG_INLINE Packet8i ploadu<Packet8i>(const int* from) { EIGEN_DEBUG_UNALIGNED_LOAD return _mm256_loadu_si256(reinterpret_cast<const __m256i*>(from)); }\n\n// Loads 4 floats from memory a returns the packet {a0, a0  a1, a1, a2, a2, a3, a3}\ntemplate<> EIGEN_STRONG_INLINE Packet8f ploaddup<Packet8f>(const float* from)\n{\n  // TODO try to find a way to avoid the need of a temporary register\n//   Packet8f tmp  = _mm256_castps128_ps256(_mm_loadu_ps(from));\n//   tmp = _mm256_insertf128_ps(tmp, _mm_movehl_ps(_mm256_castps256_ps128(tmp),_mm256_castps256_ps128(tmp)), 1);\n//   return _mm256_unpacklo_ps(tmp,tmp);\n  \n  // _mm256_insertf128_ps is very slow on Haswell, thus:\n  Packet8f tmp = _mm256_broadcast_ps((const __m128*)(const void*)from);\n  // mimic an \"inplace\" permutation of the lower 128bits using a blend\n  tmp = _mm256_blend_ps(tmp,_mm256_castps128_ps256(_mm_permute_ps( _mm256_castps256_ps128(tmp), _MM_SHUFFLE(1,0,1,0))), 15);\n  // then we can perform a consistent permutation on the global register to get everything in shape:\n  return  _mm256_permute_ps(tmp, _MM_SHUFFLE(3,3,2,2));\n}\n// Loads 2 doubles from memory a returns the packet {a0, a0  a1, a1}\ntemplate<> EIGEN_STRONG_INLINE Packet4d ploaddup<Packet4d>(const double* from)\n{\n  Packet4d tmp = _mm256_broadcast_pd((const __m128d*)(const void*)from);\n  return  _mm256_permute_pd(tmp, 3<<2);\n}\n\n// Loads 2 floats from memory a returns the packet {a0, a0  a0, a0, a1, a1, a1, a1}\ntemplate<> EIGEN_STRONG_INLINE Packet8f ploadquad<Packet8f>(const float* from)\n{\n  Packet8f tmp = _mm256_castps128_ps256(_mm_broadcast_ss(from));\n  return _mm256_insertf128_ps(tmp, _mm_broadcast_ss(from+1), 1);\n}\n\ntemplate<> EIGEN_STRONG_INLINE void pstore<float>(float*   to, const Packet8f& from) { EIGEN_DEBUG_ALIGNED_STORE _mm256_store_ps(to, from); }\ntemplate<> EIGEN_STRONG_INLINE void pstore<double>(double* to, const Packet4d& from) { EIGEN_DEBUG_ALIGNED_STORE _mm256_store_pd(to, from); }\ntemplate<> EIGEN_STRONG_INLINE void pstore<int>(int*       to, const Packet8i& from) { EIGEN_DEBUG_ALIGNED_STORE _mm256_storeu_si256(reinterpret_cast<__m256i*>(to), from); }\n\ntemplate<> EIGEN_STRONG_INLINE void pstoreu<float>(float*   to, const Packet8f& from) { EIGEN_DEBUG_UNALIGNED_STORE _mm256_storeu_ps(to, from); }\ntemplate<> EIGEN_STRONG_INLINE void pstoreu<double>(double* to, const Packet4d& from) { EIGEN_DEBUG_UNALIGNED_STORE _mm256_storeu_pd(to, from); }\ntemplate<> EIGEN_STRONG_INLINE void pstoreu<int>(int*       to, const Packet8i& from) { EIGEN_DEBUG_UNALIGNED_STORE _mm256_storeu_si256(reinterpret_cast<__m256i*>(to), from); }\n\n// NOTE: leverage _mm256_i32gather_ps and _mm256_i32gather_pd if AVX2 instructions are available\n// NOTE: for the record the following seems to be slower: return _mm256_i32gather_ps(from, _mm256_set1_epi32(stride), 4);\ntemplate<> EIGEN_DEVICE_FUNC inline Packet8f pgather<float, Packet8f>(const float* from, Index stride)\n{\n  return _mm256_set_ps(from[7*stride], from[6*stride], from[5*stride], from[4*stride],\n                       from[3*stride], from[2*stride], from[1*stride], from[0*stride]);\n}\ntemplate<> EIGEN_DEVICE_FUNC inline Packet4d pgather<double, Packet4d>(const double* from, Index stride)\n{\n  return _mm256_set_pd(from[3*stride], from[2*stride], from[1*stride], from[0*stride]);\n}\n\ntemplate<> EIGEN_DEVICE_FUNC inline void pscatter<float, Packet8f>(float* to, const Packet8f& from, Index stride)\n{\n  __m128 low = _mm256_extractf128_ps(from, 0);\n  to[stride*0] = _mm_cvtss_f32(low);\n  to[stride*1] = _mm_cvtss_f32(_mm_shuffle_ps(low, low, 1));\n  to[stride*2] = _mm_cvtss_f32(_mm_shuffle_ps(low, low, 2));\n  to[stride*3] = _mm_cvtss_f32(_mm_shuffle_ps(low, low, 3));\n\n  __m128 high = _mm256_extractf128_ps(from, 1);\n  to[stride*4] = _mm_cvtss_f32(high);\n  to[stride*5] = _mm_cvtss_f32(_mm_shuffle_ps(high, high, 1));\n  to[stride*6] = _mm_cvtss_f32(_mm_shuffle_ps(high, high, 2));\n  to[stride*7] = _mm_cvtss_f32(_mm_shuffle_ps(high, high, 3));\n}\ntemplate<> EIGEN_DEVICE_FUNC inline void pscatter<double, Packet4d>(double* to, const Packet4d& from, Index stride)\n{\n  __m128d low = _mm256_extractf128_pd(from, 0);\n  to[stride*0] = _mm_cvtsd_f64(low);\n  to[stride*1] = _mm_cvtsd_f64(_mm_shuffle_pd(low, low, 1));\n  __m128d high = _mm256_extractf128_pd(from, 1);\n  to[stride*2] = _mm_cvtsd_f64(high);\n  to[stride*3] = _mm_cvtsd_f64(_mm_shuffle_pd(high, high, 1));\n}\n\ntemplate<> EIGEN_STRONG_INLINE void pstore1<Packet8f>(float* to, const float& a)\n{\n  Packet8f pa = pset1<Packet8f>(a);\n  pstore(to, pa);\n}\ntemplate<> EIGEN_STRONG_INLINE void pstore1<Packet4d>(double* to, const double& a)\n{\n  Packet4d pa = pset1<Packet4d>(a);\n  pstore(to, pa);\n}\ntemplate<> EIGEN_STRONG_INLINE void pstore1<Packet8i>(int* to, const int& a)\n{\n  Packet8i pa = pset1<Packet8i>(a);\n  pstore(to, pa);\n}\n\n#ifndef EIGEN_VECTORIZE_AVX512\ntemplate<> EIGEN_STRONG_INLINE void prefetch<float>(const float*   addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }\ntemplate<> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }\ntemplate<> EIGEN_STRONG_INLINE void prefetch<int>(const int*       addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }\n#endif\n\ntemplate<> EIGEN_STRONG_INLINE float  pfirst<Packet8f>(const Packet8f& a) {\n  return _mm_cvtss_f32(_mm256_castps256_ps128(a));\n}\ntemplate<> EIGEN_STRONG_INLINE double pfirst<Packet4d>(const Packet4d& a) {\n  return _mm_cvtsd_f64(_mm256_castpd256_pd128(a));\n}\ntemplate<> EIGEN_STRONG_INLINE int    pfirst<Packet8i>(const Packet8i& a) {\n  return _mm_cvtsi128_si32(_mm256_castsi256_si128(a));\n}\n\n\ntemplate<> EIGEN_STRONG_INLINE Packet8f preverse(const Packet8f& a)\n{\n  __m256 tmp = _mm256_shuffle_ps(a,a,0x1b);\n  return _mm256_permute2f128_ps(tmp, tmp, 1);\n}\ntemplate<> EIGEN_STRONG_INLINE Packet4d preverse(const Packet4d& a)\n{\n   __m256d tmp = _mm256_shuffle_pd(a,a,5);\n  return _mm256_permute2f128_pd(tmp, tmp, 1);\n  #if 0\n  // This version is unlikely to be faster as _mm256_shuffle_ps and _mm256_permute_pd\n  // exhibit the same latency/throughput, but it is here for future reference/benchmarking...\n  __m256d swap_halves = _mm256_permute2f128_pd(a,a,1);\n    return _mm256_permute_pd(swap_halves,5);\n  #endif\n}\n\n// pabs should be ok\ntemplate<> EIGEN_STRONG_INLINE Packet8f pabs(const Packet8f& a)\n{\n  const Packet8f mask = _mm256_castsi256_ps(_mm256_setr_epi32(0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF));\n  return _mm256_and_ps(a,mask);\n}\ntemplate<> EIGEN_STRONG_INLINE Packet4d pabs(const Packet4d& a)\n{\n  const Packet4d mask = _mm256_castsi256_pd(_mm256_setr_epi32(0xFFFFFFFF,0x7FFFFFFF,0xFFFFFFFF,0x7FFFFFFF,0xFFFFFFFF,0x7FFFFFFF,0xFFFFFFFF,0x7FFFFFFF));\n  return _mm256_and_pd(a,mask);\n}\n\n// preduxp should be ok\n// FIXME: why is this ok? why isn't the simply implementation working as expected?\ntemplate<> EIGEN_STRONG_INLINE Packet8f preduxp<Packet8f>(const Packet8f* vecs)\n{\n    __m256 hsum1 = _mm256_hadd_ps(vecs[0], vecs[1]);\n    __m256 hsum2 = _mm256_hadd_ps(vecs[2], vecs[3]);\n    __m256 hsum3 = _mm256_hadd_ps(vecs[4], vecs[5]);\n    __m256 hsum4 = _mm256_hadd_ps(vecs[6], vecs[7]);\n\n    __m256 hsum5 = _mm256_hadd_ps(hsum1, hsum1);\n    __m256 hsum6 = _mm256_hadd_ps(hsum2, hsum2);\n    __m256 hsum7 = _mm256_hadd_ps(hsum3, hsum3);\n    __m256 hsum8 = _mm256_hadd_ps(hsum4, hsum4);\n\n    __m256 perm1 =  _mm256_permute2f128_ps(hsum5, hsum5, 0x23);\n    __m256 perm2 =  _mm256_permute2f128_ps(hsum6, hsum6, 0x23);\n    __m256 perm3 =  _mm256_permute2f128_ps(hsum7, hsum7, 0x23);\n    __m256 perm4 =  _mm256_permute2f128_ps(hsum8, hsum8, 0x23);\n\n    __m256 sum1 = _mm256_add_ps(perm1, hsum5);\n    __m256 sum2 = _mm256_add_ps(perm2, hsum6);\n    __m256 sum3 = _mm256_add_ps(perm3, hsum7);\n    __m256 sum4 = _mm256_add_ps(perm4, hsum8);\n\n    __m256 blend1 = _mm256_blend_ps(sum1, sum2, 0xcc);\n    __m256 blend2 = _mm256_blend_ps(sum3, sum4, 0xcc);\n\n    __m256 final = _mm256_blend_ps(blend1, blend2, 0xf0);\n    return final;\n}\ntemplate<> EIGEN_STRONG_INLINE Packet4d preduxp<Packet4d>(const Packet4d* vecs)\n{\n Packet4d tmp0, tmp1;\n\n  tmp0 = _mm256_hadd_pd(vecs[0], vecs[1]);\n  tmp0 = _mm256_add_pd(tmp0, _mm256_permute2f128_pd(tmp0, tmp0, 1));\n\n  tmp1 = _mm256_hadd_pd(vecs[2], vecs[3]);\n  tmp1 = _mm256_add_pd(tmp1, _mm256_permute2f128_pd(tmp1, tmp1, 1));\n\n  return _mm256_blend_pd(tmp0, tmp1, 0xC);\n}\n\ntemplate<> EIGEN_STRONG_INLINE float predux<Packet8f>(const Packet8f& a)\n{\n  return predux(Packet4f(_mm_add_ps(_mm256_castps256_ps128(a),_mm256_extractf128_ps(a,1))));\n}\ntemplate<> EIGEN_STRONG_INLINE double predux<Packet4d>(const Packet4d& a)\n{\n  return predux(Packet2d(_mm_add_pd(_mm256_castpd256_pd128(a),_mm256_extractf128_pd(a,1))));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f predux_downto4<Packet8f>(const Packet8f& a)\n{\n  return _mm_add_ps(_mm256_castps256_ps128(a),_mm256_extractf128_ps(a,1));\n}\n\ntemplate<> EIGEN_STRONG_INLINE float predux_mul<Packet8f>(const Packet8f& a)\n{\n  Packet8f tmp;\n  tmp = _mm256_mul_ps(a, _mm256_permute2f128_ps(a,a,1));\n  tmp = _mm256_mul_ps(tmp, _mm256_shuffle_ps(tmp,tmp,_MM_SHUFFLE(1,0,3,2)));\n  return pfirst(_mm256_mul_ps(tmp, _mm256_shuffle_ps(tmp,tmp,1)));\n}\ntemplate<> EIGEN_STRONG_INLINE double predux_mul<Packet4d>(const Packet4d& a)\n{\n  Packet4d tmp;\n  tmp = _mm256_mul_pd(a, _mm256_permute2f128_pd(a,a,1));\n  return pfirst(_mm256_mul_pd(tmp, _mm256_shuffle_pd(tmp,tmp,1)));\n}\n\ntemplate<> EIGEN_STRONG_INLINE float predux_min<Packet8f>(const Packet8f& a)\n{\n  Packet8f tmp = _mm256_min_ps(a, _mm256_permute2f128_ps(a,a,1));\n  tmp = _mm256_min_ps(tmp, _mm256_shuffle_ps(tmp,tmp,_MM_SHUFFLE(1,0,3,2)));\n  return pfirst(_mm256_min_ps(tmp, _mm256_shuffle_ps(tmp,tmp,1)));\n}\ntemplate<> EIGEN_STRONG_INLINE double predux_min<Packet4d>(const Packet4d& a)\n{\n  Packet4d tmp = _mm256_min_pd(a, _mm256_permute2f128_pd(a,a,1));\n  return pfirst(_mm256_min_pd(tmp, _mm256_shuffle_pd(tmp, tmp, 1)));\n}\n\ntemplate<> EIGEN_STRONG_INLINE float predux_max<Packet8f>(const Packet8f& a)\n{\n  Packet8f tmp = _mm256_max_ps(a, _mm256_permute2f128_ps(a,a,1));\n  tmp = _mm256_max_ps(tmp, _mm256_shuffle_ps(tmp,tmp,_MM_SHUFFLE(1,0,3,2)));\n  return pfirst(_mm256_max_ps(tmp, _mm256_shuffle_ps(tmp,tmp,1)));\n}\n\ntemplate<> EIGEN_STRONG_INLINE double predux_max<Packet4d>(const Packet4d& a)\n{\n  Packet4d tmp = _mm256_max_pd(a, _mm256_permute2f128_pd(a,a,1));\n  return pfirst(_mm256_max_pd(tmp, _mm256_shuffle_pd(tmp, tmp, 1)));\n}\n\n\ntemplate<int Offset>\nstruct palign_impl<Offset,Packet8f>\n{\n  static EIGEN_STRONG_INLINE void run(Packet8f& first, const Packet8f& second)\n  {\n    if (Offset==1)\n    {\n      first = _mm256_blend_ps(first, second, 1);\n      Packet8f tmp1 = _mm256_permute_ps (first, _MM_SHUFFLE(0,3,2,1));\n      Packet8f tmp2 = _mm256_permute2f128_ps (tmp1, tmp1, 1);\n      first = _mm256_blend_ps(tmp1, tmp2, 0x88);\n    }\n    else if (Offset==2)\n    {\n      first = _mm256_blend_ps(first, second, 3);\n      Packet8f tmp1 = _mm256_permute_ps (first, _MM_SHUFFLE(1,0,3,2));\n      Packet8f tmp2 = _mm256_permute2f128_ps (tmp1, tmp1, 1);\n      first = _mm256_blend_ps(tmp1, tmp2, 0xcc);\n    }\n    else if (Offset==3)\n    {\n      first = _mm256_blend_ps(first, second, 7);\n      Packet8f tmp1 = _mm256_permute_ps (first, _MM_SHUFFLE(2,1,0,3));\n      Packet8f tmp2 = _mm256_permute2f128_ps (tmp1, tmp1, 1);\n      first = _mm256_blend_ps(tmp1, tmp2, 0xee);\n    }\n    else if (Offset==4)\n    {\n      first = _mm256_blend_ps(first, second, 15);\n      Packet8f tmp1 = _mm256_permute_ps (first, _MM_SHUFFLE(3,2,1,0));\n      Packet8f tmp2 = _mm256_permute2f128_ps (tmp1, tmp1, 1);\n      first = _mm256_permute_ps(tmp2, _MM_SHUFFLE(3,2,1,0));\n    }\n    else if (Offset==5)\n    {\n      first = _mm256_blend_ps(first, second, 31);\n      first = _mm256_permute2f128_ps(first, first, 1);\n      Packet8f tmp = _mm256_permute_ps (first, _MM_SHUFFLE(0,3,2,1));\n      first = _mm256_permute2f128_ps(tmp, tmp, 1);\n      first = _mm256_blend_ps(tmp, first, 0x88);\n    }\n    else if (Offset==6)\n    {\n      first = _mm256_blend_ps(first, second, 63);\n      first = _mm256_permute2f128_ps(first, first, 1);\n      Packet8f tmp = _mm256_permute_ps (first, _MM_SHUFFLE(1,0,3,2));\n      first = _mm256_permute2f128_ps(tmp, tmp, 1);\n      first = _mm256_blend_ps(tmp, first, 0xcc);\n    }\n    else if (Offset==7)\n    {\n      first = _mm256_blend_ps(first, second, 127);\n      first = _mm256_permute2f128_ps(first, first, 1);\n      Packet8f tmp = _mm256_permute_ps (first, _MM_SHUFFLE(2,1,0,3));\n      first = _mm256_permute2f128_ps(tmp, tmp, 1);\n      first = _mm256_blend_ps(tmp, first, 0xee);\n    }\n  }\n};\n\ntemplate<int Offset>\nstruct palign_impl<Offset,Packet4d>\n{\n  static EIGEN_STRONG_INLINE void run(Packet4d& first, const Packet4d& second)\n  {\n    if (Offset==1)\n    {\n      first = _mm256_blend_pd(first, second, 1);\n      __m256d tmp = _mm256_permute_pd(first, 5);\n      first = _mm256_permute2f128_pd(tmp, tmp, 1);\n      first = _mm256_blend_pd(tmp, first, 0xA);\n    }\n    else if (Offset==2)\n    {\n      first = _mm256_blend_pd(first, second, 3);\n      first = _mm256_permute2f128_pd(first, first, 1);\n    }\n    else if (Offset==3)\n    {\n      first = _mm256_blend_pd(first, second, 7);\n      __m256d tmp = _mm256_permute_pd(first, 5);\n      first = _mm256_permute2f128_pd(tmp, tmp, 1);\n      first = _mm256_blend_pd(tmp, first, 5);\n    }\n  }\n};\n\nEIGEN_DEVICE_FUNC inline void\nptranspose(PacketBlock<Packet8f,8>& kernel) {\n  __m256 T0 = _mm256_unpacklo_ps(kernel.packet[0], kernel.packet[1]);\n  __m256 T1 = _mm256_unpackhi_ps(kernel.packet[0], kernel.packet[1]);\n  __m256 T2 = _mm256_unpacklo_ps(kernel.packet[2], kernel.packet[3]);\n  __m256 T3 = _mm256_unpackhi_ps(kernel.packet[2], kernel.packet[3]);\n  __m256 T4 = _mm256_unpacklo_ps(kernel.packet[4], kernel.packet[5]);\n  __m256 T5 = _mm256_unpackhi_ps(kernel.packet[4], kernel.packet[5]);\n  __m256 T6 = _mm256_unpacklo_ps(kernel.packet[6], kernel.packet[7]);\n  __m256 T7 = _mm256_unpackhi_ps(kernel.packet[6], kernel.packet[7]);\n  __m256 S0 = _mm256_shuffle_ps(T0,T2,_MM_SHUFFLE(1,0,1,0));\n  __m256 S1 = _mm256_shuffle_ps(T0,T2,_MM_SHUFFLE(3,2,3,2));\n  __m256 S2 = _mm256_shuffle_ps(T1,T3,_MM_SHUFFLE(1,0,1,0));\n  __m256 S3 = _mm256_shuffle_ps(T1,T3,_MM_SHUFFLE(3,2,3,2));\n  __m256 S4 = _mm256_shuffle_ps(T4,T6,_MM_SHUFFLE(1,0,1,0));\n  __m256 S5 = _mm256_shuffle_ps(T4,T6,_MM_SHUFFLE(3,2,3,2));\n  __m256 S6 = _mm256_shuffle_ps(T5,T7,_MM_SHUFFLE(1,0,1,0));\n  __m256 S7 = _mm256_shuffle_ps(T5,T7,_MM_SHUFFLE(3,2,3,2));\n  kernel.packet[0] = _mm256_permute2f128_ps(S0, S4, 0x20);\n  kernel.packet[1] = _mm256_permute2f128_ps(S1, S5, 0x20);\n  kernel.packet[2] = _mm256_permute2f128_ps(S2, S6, 0x20);\n  kernel.packet[3] = _mm256_permute2f128_ps(S3, S7, 0x20);\n  kernel.packet[4] = _mm256_permute2f128_ps(S0, S4, 0x31);\n  kernel.packet[5] = _mm256_permute2f128_ps(S1, S5, 0x31);\n  kernel.packet[6] = _mm256_permute2f128_ps(S2, S6, 0x31);\n  kernel.packet[7] = _mm256_permute2f128_ps(S3, S7, 0x31);\n}\n\nEIGEN_DEVICE_FUNC inline void\nptranspose(PacketBlock<Packet8f,4>& kernel) {\n  __m256 T0 = _mm256_unpacklo_ps(kernel.packet[0], kernel.packet[1]);\n  __m256 T1 = _mm256_unpackhi_ps(kernel.packet[0], kernel.packet[1]);\n  __m256 T2 = _mm256_unpacklo_ps(kernel.packet[2], kernel.packet[3]);\n  __m256 T3 = _mm256_unpackhi_ps(kernel.packet[2], kernel.packet[3]);\n\n  __m256 S0 = _mm256_shuffle_ps(T0,T2,_MM_SHUFFLE(1,0,1,0));\n  __m256 S1 = _mm256_shuffle_ps(T0,T2,_MM_SHUFFLE(3,2,3,2));\n  __m256 S2 = _mm256_shuffle_ps(T1,T3,_MM_SHUFFLE(1,0,1,0));\n  __m256 S3 = _mm256_shuffle_ps(T1,T3,_MM_SHUFFLE(3,2,3,2));\n\n  kernel.packet[0] = _mm256_permute2f128_ps(S0, S1, 0x20);\n  kernel.packet[1] = _mm256_permute2f128_ps(S2, S3, 0x20);\n  kernel.packet[2] = _mm256_permute2f128_ps(S0, S1, 0x31);\n  kernel.packet[3] = _mm256_permute2f128_ps(S2, S3, 0x31);\n}\n\nEIGEN_DEVICE_FUNC inline void\nptranspose(PacketBlock<Packet4d,4>& kernel) {\n  __m256d T0 = _mm256_shuffle_pd(kernel.packet[0], kernel.packet[1], 15);\n  __m256d T1 = _mm256_shuffle_pd(kernel.packet[0], kernel.packet[1], 0);\n  __m256d T2 = _mm256_shuffle_pd(kernel.packet[2], kernel.packet[3], 15);\n  __m256d T3 = _mm256_shuffle_pd(kernel.packet[2], kernel.packet[3], 0);\n\n  kernel.packet[1] = _mm256_permute2f128_pd(T0, T2, 32);\n  kernel.packet[3] = _mm256_permute2f128_pd(T0, T2, 49);\n  kernel.packet[0] = _mm256_permute2f128_pd(T1, T3, 32);\n  kernel.packet[2] = _mm256_permute2f128_pd(T1, T3, 49);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet8f pblend(const Selector<8>& ifPacket, const Packet8f& thenPacket, const Packet8f& elsePacket) {\n  const __m256 zero = _mm256_setzero_ps();\n  const __m256 select = _mm256_set_ps(ifPacket.select[7], ifPacket.select[6], ifPacket.select[5], ifPacket.select[4], ifPacket.select[3], ifPacket.select[2], ifPacket.select[1], ifPacket.select[0]);\n  __m256 false_mask = _mm256_cmp_ps(select, zero, _CMP_EQ_UQ);\n  return _mm256_blendv_ps(thenPacket, elsePacket, false_mask);\n}\ntemplate<> EIGEN_STRONG_INLINE Packet4d pblend(const Selector<4>& ifPacket, const Packet4d& thenPacket, const Packet4d& elsePacket) {\n  const __m256d zero = _mm256_setzero_pd();\n  const __m256d select = _mm256_set_pd(ifPacket.select[3], ifPacket.select[2], ifPacket.select[1], ifPacket.select[0]);\n  __m256d false_mask = _mm256_cmp_pd(select, zero, _CMP_EQ_UQ);\n  return _mm256_blendv_pd(thenPacket, elsePacket, false_mask);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet8f pinsertfirst(const Packet8f& a, float b)\n{\n  return _mm256_blend_ps(a,pset1<Packet8f>(b),1);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4d pinsertfirst(const Packet4d& a, double b)\n{\n  return _mm256_blend_pd(a,pset1<Packet4d>(b),1);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet8f pinsertlast(const Packet8f& a, float b)\n{\n  return _mm256_blend_ps(a,pset1<Packet8f>(b),(1<<7));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4d pinsertlast(const Packet4d& a, double b)\n{\n  return _mm256_blend_pd(a,pset1<Packet4d>(b),(1<<3));\n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_PACKET_MATH_AVX_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/arch/AVX/TypeCasting.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_TYPE_CASTING_AVX_H\n#define EIGEN_TYPE_CASTING_AVX_H\n\nnamespace Eigen {\n\nnamespace internal {\n\n// For now we use SSE to handle integers, so we can't use AVX instructions to cast\n// from int to float\ntemplate <>\nstruct type_casting_traits<float, int> {\n  enum {\n    VectorizedCast = 0,\n    SrcCoeffRatio = 1,\n    TgtCoeffRatio = 1\n  };\n};\n\ntemplate <>\nstruct type_casting_traits<int, float> {\n  enum {\n    VectorizedCast = 0,\n    SrcCoeffRatio = 1,\n    TgtCoeffRatio = 1\n  };\n};\n\n\n\ntemplate<> EIGEN_STRONG_INLINE Packet8i pcast<Packet8f, Packet8i>(const Packet8f& a) {\n  return _mm256_cvtps_epi32(a);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet8f pcast<Packet8i, Packet8f>(const Packet8i& a) {\n  return _mm256_cvtepi32_ps(a);\n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_TYPE_CASTING_AVX_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/arch/AVX512/MathFunctions.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Pedro Gonnet (pedro.gonnet@gmail.com)\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef THIRD_PARTY_EIGEN3_EIGEN_SRC_CORE_ARCH_AVX512_MATHFUNCTIONS_H_\n#define THIRD_PARTY_EIGEN3_EIGEN_SRC_CORE_ARCH_AVX512_MATHFUNCTIONS_H_\n\nnamespace Eigen {\n\nnamespace internal {\n\n// Disable the code for older versions of gcc that don't support many of the required avx512 instrinsics.\n#if EIGEN_GNUC_AT_LEAST(5, 3)\n\n#define _EIGEN_DECLARE_CONST_Packet16f(NAME, X) \\\n  const Packet16f p16f_##NAME = pset1<Packet16f>(X)\n\n#define _EIGEN_DECLARE_CONST_Packet16f_FROM_INT(NAME, X) \\\n  const Packet16f p16f_##NAME = (__m512)pset1<Packet16i>(X)\n\n#define _EIGEN_DECLARE_CONST_Packet8d(NAME, X) \\\n  const Packet8d p8d_##NAME = pset1<Packet8d>(X)\n\n#define _EIGEN_DECLARE_CONST_Packet8d_FROM_INT64(NAME, X) \\\n  const Packet8d p8d_##NAME = _mm512_castsi512_pd(_mm512_set1_epi64(X))\n\n// Natural logarithm\n// Computes log(x) as log(2^e * m) = C*e + log(m), where the constant C =log(2)\n// and m is in the range [sqrt(1/2),sqrt(2)). In this range, the logarithm can\n// be easily approximated by a polynomial centered on m=1 for stability.\n#if defined(EIGEN_VECTORIZE_AVX512DQ)\ntemplate <>\nEIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet16f\nplog<Packet16f>(const Packet16f& _x) {\n  Packet16f x = _x;\n  _EIGEN_DECLARE_CONST_Packet16f(1, 1.0f);\n  _EIGEN_DECLARE_CONST_Packet16f(half, 0.5f);\n  _EIGEN_DECLARE_CONST_Packet16f(126f, 126.0f);\n\n  _EIGEN_DECLARE_CONST_Packet16f_FROM_INT(inv_mant_mask, ~0x7f800000);\n\n  // The smallest non denormalized float number.\n  _EIGEN_DECLARE_CONST_Packet16f_FROM_INT(min_norm_pos, 0x00800000);\n  _EIGEN_DECLARE_CONST_Packet16f_FROM_INT(minus_inf, 0xff800000);\n  _EIGEN_DECLARE_CONST_Packet16f_FROM_INT(nan, 0x7fc00000);\n\n  // Polynomial coefficients.\n  _EIGEN_DECLARE_CONST_Packet16f(cephes_SQRTHF, 0.707106781186547524f);\n  _EIGEN_DECLARE_CONST_Packet16f(cephes_log_p0, 7.0376836292E-2f);\n  _EIGEN_DECLARE_CONST_Packet16f(cephes_log_p1, -1.1514610310E-1f);\n  _EIGEN_DECLARE_CONST_Packet16f(cephes_log_p2, 1.1676998740E-1f);\n  _EIGEN_DECLARE_CONST_Packet16f(cephes_log_p3, -1.2420140846E-1f);\n  _EIGEN_DECLARE_CONST_Packet16f(cephes_log_p4, +1.4249322787E-1f);\n  _EIGEN_DECLARE_CONST_Packet16f(cephes_log_p5, -1.6668057665E-1f);\n  _EIGEN_DECLARE_CONST_Packet16f(cephes_log_p6, +2.0000714765E-1f);\n  _EIGEN_DECLARE_CONST_Packet16f(cephes_log_p7, -2.4999993993E-1f);\n  _EIGEN_DECLARE_CONST_Packet16f(cephes_log_p8, +3.3333331174E-1f);\n  _EIGEN_DECLARE_CONST_Packet16f(cephes_log_q1, -2.12194440e-4f);\n  _EIGEN_DECLARE_CONST_Packet16f(cephes_log_q2, 0.693359375f);\n\n  // invalid_mask is set to true when x is NaN\n  __mmask16 invalid_mask =\n      _mm512_cmp_ps_mask(x, _mm512_setzero_ps(), _CMP_NGE_UQ);\n  __mmask16 iszero_mask =\n      _mm512_cmp_ps_mask(x, _mm512_setzero_ps(), _CMP_EQ_UQ);\n\n  // Truncate input values to the minimum positive normal.\n  x = pmax(x, p16f_min_norm_pos);\n\n  // Extract the shifted exponents.\n  Packet16f emm0 = _mm512_cvtepi32_ps(_mm512_srli_epi32((__m512i)x, 23));\n  Packet16f e = _mm512_sub_ps(emm0, p16f_126f);\n\n  // Set the exponents to -1, i.e. x are in the range [0.5,1).\n  x = _mm512_and_ps(x, p16f_inv_mant_mask);\n  x = _mm512_or_ps(x, p16f_half);\n\n  // part2: Shift the inputs from the range [0.5,1) to [sqrt(1/2),sqrt(2))\n  // and shift by -1. The values are then centered around 0, which improves\n  // the stability of the polynomial evaluation.\n  //   if( x < SQRTHF ) {\n  //     e -= 1;\n  //     x = x + x - 1.0;\n  //   } else { x = x - 1.0; }\n  __mmask16 mask = _mm512_cmp_ps_mask(x, p16f_cephes_SQRTHF, _CMP_LT_OQ);\n  Packet16f tmp = _mm512_mask_blend_ps(mask, _mm512_setzero_ps(), x);\n  x = psub(x, p16f_1);\n  e = psub(e, _mm512_mask_blend_ps(mask, _mm512_setzero_ps(), p16f_1));\n  x = padd(x, tmp);\n\n  Packet16f x2 = pmul(x, x);\n  Packet16f x3 = pmul(x2, x);\n\n  // Evaluate the polynomial approximant of degree 8 in three parts, probably\n  // to improve instruction-level parallelism.\n  Packet16f y, y1, y2;\n  y = pmadd(p16f_cephes_log_p0, x, p16f_cephes_log_p1);\n  y1 = pmadd(p16f_cephes_log_p3, x, p16f_cephes_log_p4);\n  y2 = pmadd(p16f_cephes_log_p6, x, p16f_cephes_log_p7);\n  y = pmadd(y, x, p16f_cephes_log_p2);\n  y1 = pmadd(y1, x, p16f_cephes_log_p5);\n  y2 = pmadd(y2, x, p16f_cephes_log_p8);\n  y = pmadd(y, x3, y1);\n  y = pmadd(y, x3, y2);\n  y = pmul(y, x3);\n\n  // Add the logarithm of the exponent back to the result of the interpolation.\n  y1 = pmul(e, p16f_cephes_log_q1);\n  tmp = pmul(x2, p16f_half);\n  y = padd(y, y1);\n  x = psub(x, tmp);\n  y2 = pmul(e, p16f_cephes_log_q2);\n  x = padd(x, y);\n  x = padd(x, y2);\n\n  // Filter out invalid inputs, i.e. negative arg will be NAN, 0 will be -INF.\n  return _mm512_mask_blend_ps(iszero_mask,\n                              _mm512_mask_blend_ps(invalid_mask, x, p16f_nan),\n                              p16f_minus_inf);\n}\n#endif\n\n// Exponential function. Works by writing \"x = m*log(2) + r\" where\n// \"m = floor(x/log(2)+1/2)\" and \"r\" is the remainder. The result is then\n// \"exp(x) = 2^m*exp(r)\" where exp(r) is in the range [-1,1).\ntemplate <>\nEIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet16f\npexp<Packet16f>(const Packet16f& _x) {\n  _EIGEN_DECLARE_CONST_Packet16f(1, 1.0f);\n  _EIGEN_DECLARE_CONST_Packet16f(half, 0.5f);\n  _EIGEN_DECLARE_CONST_Packet16f(127, 127.0f);\n\n  _EIGEN_DECLARE_CONST_Packet16f(exp_hi, 88.3762626647950f);\n  _EIGEN_DECLARE_CONST_Packet16f(exp_lo, -88.3762626647949f);\n\n  _EIGEN_DECLARE_CONST_Packet16f(cephes_LOG2EF, 1.44269504088896341f);\n\n  _EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p0, 1.9875691500E-4f);\n  _EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p1, 1.3981999507E-3f);\n  _EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p2, 8.3334519073E-3f);\n  _EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p3, 4.1665795894E-2f);\n  _EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p4, 1.6666665459E-1f);\n  _EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p5, 5.0000001201E-1f);\n\n  // Clamp x.\n  Packet16f x = pmax(pmin(_x, p16f_exp_hi), p16f_exp_lo);\n\n  // Express exp(x) as exp(m*ln(2) + r), start by extracting\n  // m = floor(x/ln(2) + 0.5).\n  Packet16f m = _mm512_floor_ps(pmadd(x, p16f_cephes_LOG2EF, p16f_half));\n\n  // Get r = x - m*ln(2). Note that we can do this without losing more than one\n  // ulp precision due to the FMA instruction.\n  _EIGEN_DECLARE_CONST_Packet16f(nln2, -0.6931471805599453f);\n  Packet16f r = _mm512_fmadd_ps(m, p16f_nln2, x);\n  Packet16f r2 = pmul(r, r);\n\n  // TODO(gonnet): Split into odd/even polynomials and try to exploit\n  //               instruction-level parallelism.\n  Packet16f y = p16f_cephes_exp_p0;\n  y = pmadd(y, r, p16f_cephes_exp_p1);\n  y = pmadd(y, r, p16f_cephes_exp_p2);\n  y = pmadd(y, r, p16f_cephes_exp_p3);\n  y = pmadd(y, r, p16f_cephes_exp_p4);\n  y = pmadd(y, r, p16f_cephes_exp_p5);\n  y = pmadd(y, r2, r);\n  y = padd(y, p16f_1);\n\n  // Build emm0 = 2^m.\n  Packet16i emm0 = _mm512_cvttps_epi32(padd(m, p16f_127));\n  emm0 = _mm512_slli_epi32(emm0, 23);\n\n  // Return 2^m * exp(r).\n  return pmax(pmul(y, _mm512_castsi512_ps(emm0)), _x);\n}\n\n/*template <>\nEIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8d\npexp<Packet8d>(const Packet8d& _x) {\n  Packet8d x = _x;\n\n  _EIGEN_DECLARE_CONST_Packet8d(1, 1.0);\n  _EIGEN_DECLARE_CONST_Packet8d(2, 2.0);\n\n  _EIGEN_DECLARE_CONST_Packet8d(exp_hi, 709.437);\n  _EIGEN_DECLARE_CONST_Packet8d(exp_lo, -709.436139303);\n\n  _EIGEN_DECLARE_CONST_Packet8d(cephes_LOG2EF, 1.4426950408889634073599);\n\n  _EIGEN_DECLARE_CONST_Packet8d(cephes_exp_p0, 1.26177193074810590878e-4);\n  _EIGEN_DECLARE_CONST_Packet8d(cephes_exp_p1, 3.02994407707441961300e-2);\n  _EIGEN_DECLARE_CONST_Packet8d(cephes_exp_p2, 9.99999999999999999910e-1);\n\n  _EIGEN_DECLARE_CONST_Packet8d(cephes_exp_q0, 3.00198505138664455042e-6);\n  _EIGEN_DECLARE_CONST_Packet8d(cephes_exp_q1, 2.52448340349684104192e-3);\n  _EIGEN_DECLARE_CONST_Packet8d(cephes_exp_q2, 2.27265548208155028766e-1);\n  _EIGEN_DECLARE_CONST_Packet8d(cephes_exp_q3, 2.00000000000000000009e0);\n\n  _EIGEN_DECLARE_CONST_Packet8d(cephes_exp_C1, 0.693145751953125);\n  _EIGEN_DECLARE_CONST_Packet8d(cephes_exp_C2, 1.42860682030941723212e-6);\n\n  // clamp x\n  x = pmax(pmin(x, p8d_exp_hi), p8d_exp_lo);\n\n  // Express exp(x) as exp(g + n*log(2)).\n  const Packet8d n =\n      _mm512_mul_round_pd(p8d_cephes_LOG2EF, x, _MM_FROUND_TO_NEAREST_INT);\n\n  // Get the remainder modulo log(2), i.e. the \"g\" described above. Subtract\n  // n*log(2) out in two steps, i.e. n*C1 + n*C2, C1+C2=log2 to get the last\n  // digits right.\n  const Packet8d nC1 = pmul(n, p8d_cephes_exp_C1);\n  const Packet8d nC2 = pmul(n, p8d_cephes_exp_C2);\n  x = psub(x, nC1);\n  x = psub(x, nC2);\n\n  const Packet8d x2 = pmul(x, x);\n\n  // Evaluate the numerator polynomial of the rational interpolant.\n  Packet8d px = p8d_cephes_exp_p0;\n  px = pmadd(px, x2, p8d_cephes_exp_p1);\n  px = pmadd(px, x2, p8d_cephes_exp_p2);\n  px = pmul(px, x);\n\n  // Evaluate the denominator polynomial of the rational interpolant.\n  Packet8d qx = p8d_cephes_exp_q0;\n  qx = pmadd(qx, x2, p8d_cephes_exp_q1);\n  qx = pmadd(qx, x2, p8d_cephes_exp_q2);\n  qx = pmadd(qx, x2, p8d_cephes_exp_q3);\n\n  // I don't really get this bit, copied from the SSE2 routines, so...\n  // TODO(gonnet): Figure out what is going on here, perhaps find a better\n  // rational interpolant?\n  x = _mm512_div_pd(px, psub(qx, px));\n  x = pmadd(p8d_2, x, p8d_1);\n\n  // Build e=2^n.\n  const Packet8d e = _mm512_castsi512_pd(_mm512_slli_epi64(\n      _mm512_add_epi64(_mm512_cvtpd_epi64(n), _mm512_set1_epi64(1023)), 52));\n\n  // Construct the result 2^n * exp(g) = e * x. The max is used to catch\n  // non-finite values in the input.\n  return pmax(pmul(x, e), _x);\n  }*/\n\n// Functions for sqrt.\n// The EIGEN_FAST_MATH version uses the _mm_rsqrt_ps approximation and one step\n// of Newton's method, at a cost of 1-2 bits of precision as opposed to the\n// exact solution. The main advantage of this approach is not just speed, but\n// also the fact that it can be inlined and pipelined with other computations,\n// further reducing its effective latency.\n#if EIGEN_FAST_MATH\ntemplate <>\nEIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet16f\npsqrt<Packet16f>(const Packet16f& _x) {\n  _EIGEN_DECLARE_CONST_Packet16f(one_point_five, 1.5f);\n  _EIGEN_DECLARE_CONST_Packet16f(minus_half, -0.5f);\n  _EIGEN_DECLARE_CONST_Packet16f_FROM_INT(flt_min, 0x00800000);\n\n  Packet16f neg_half = pmul(_x, p16f_minus_half);\n\n  // select only the inverse sqrt of positive normal inputs (denormals are\n  // flushed to zero and cause infs as well).\n  __mmask16 non_zero_mask = _mm512_cmp_ps_mask(_x, p16f_flt_min, _CMP_GE_OQ);\n  Packet16f x = _mm512_mask_blend_ps(non_zero_mask, _mm512_setzero_ps(), _mm512_rsqrt14_ps(_x));\n\n  // Do a single step of Newton's iteration.\n  x = pmul(x, pmadd(neg_half, pmul(x, x), p16f_one_point_five));\n\n  // Multiply the original _x by it's reciprocal square root to extract the\n  // square root.\n  return pmul(_x, x);\n}\n\ntemplate <>\nEIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8d\npsqrt<Packet8d>(const Packet8d& _x) {\n  _EIGEN_DECLARE_CONST_Packet8d(one_point_five, 1.5);\n  _EIGEN_DECLARE_CONST_Packet8d(minus_half, -0.5);\n  _EIGEN_DECLARE_CONST_Packet8d_FROM_INT64(dbl_min, 0x0010000000000000LL);\n\n  Packet8d neg_half = pmul(_x, p8d_minus_half);\n\n  // select only the inverse sqrt of positive normal inputs (denormals are\n  // flushed to zero and cause infs as well).\n  __mmask8 non_zero_mask = _mm512_cmp_pd_mask(_x, p8d_dbl_min, _CMP_GE_OQ);\n  Packet8d x = _mm512_mask_blend_pd(non_zero_mask, _mm512_setzero_pd(), _mm512_rsqrt14_pd(_x));\n\n  // Do a first step of Newton's iteration.\n  x = pmul(x, pmadd(neg_half, pmul(x, x), p8d_one_point_five));\n\n  // Do a second step of Newton's iteration.\n  x = pmul(x, pmadd(neg_half, pmul(x, x), p8d_one_point_five));\n\n  // Multiply the original _x by it's reciprocal square root to extract the\n  // square root.\n  return pmul(_x, x);\n}\n#else\ntemplate <>\nEIGEN_STRONG_INLINE Packet16f psqrt<Packet16f>(const Packet16f& x) {\n  return _mm512_sqrt_ps(x);\n}\ntemplate <>\nEIGEN_STRONG_INLINE Packet8d psqrt<Packet8d>(const Packet8d& x) {\n  return _mm512_sqrt_pd(x);\n}\n#endif\n\n// Functions for rsqrt.\n// Almost identical to the sqrt routine, just leave out the last multiplication\n// and fill in NaN/Inf where needed. Note that this function only exists as an\n// iterative version for doubles since there is no instruction for diretly\n// computing the reciprocal square root in AVX-512.\n#ifdef EIGEN_FAST_MATH\ntemplate <>\nEIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet16f\nprsqrt<Packet16f>(const Packet16f& _x) {\n  _EIGEN_DECLARE_CONST_Packet16f_FROM_INT(inf, 0x7f800000);\n  _EIGEN_DECLARE_CONST_Packet16f_FROM_INT(nan, 0x7fc00000);\n  _EIGEN_DECLARE_CONST_Packet16f(one_point_five, 1.5f);\n  _EIGEN_DECLARE_CONST_Packet16f(minus_half, -0.5f);\n  _EIGEN_DECLARE_CONST_Packet16f_FROM_INT(flt_min, 0x00800000);\n\n  Packet16f neg_half = pmul(_x, p16f_minus_half);\n\n  // select only the inverse sqrt of positive normal inputs (denormals are\n  // flushed to zero and cause infs as well).\n  __mmask16 le_zero_mask = _mm512_cmp_ps_mask(_x, p16f_flt_min, _CMP_LT_OQ);\n  Packet16f x = _mm512_mask_blend_ps(le_zero_mask, _mm512_rsqrt14_ps(_x), _mm512_setzero_ps());\n\n  // Fill in NaNs and Infs for the negative/zero entries.\n  __mmask16 neg_mask = _mm512_cmp_ps_mask(_x, _mm512_setzero_ps(), _CMP_LT_OQ);\n  Packet16f infs_and_nans = _mm512_mask_blend_ps(\n      neg_mask, _mm512_mask_blend_ps(le_zero_mask, _mm512_setzero_ps(), p16f_inf), p16f_nan);\n\n  // Do a single step of Newton's iteration.\n  x = pmul(x, pmadd(neg_half, pmul(x, x), p16f_one_point_five));\n\n  // Insert NaNs and Infs in all the right places.\n  return _mm512_mask_blend_ps(le_zero_mask, x, infs_and_nans);\n}\n\ntemplate <>\nEIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8d\nprsqrt<Packet8d>(const Packet8d& _x) {\n  _EIGEN_DECLARE_CONST_Packet8d_FROM_INT64(inf, 0x7ff0000000000000LL);\n  _EIGEN_DECLARE_CONST_Packet8d_FROM_INT64(nan, 0x7ff1000000000000LL);\n  _EIGEN_DECLARE_CONST_Packet8d(one_point_five, 1.5);\n  _EIGEN_DECLARE_CONST_Packet8d(minus_half, -0.5);\n  _EIGEN_DECLARE_CONST_Packet8d_FROM_INT64(dbl_min, 0x0010000000000000LL);\n\n  Packet8d neg_half = pmul(_x, p8d_minus_half);\n\n  // select only the inverse sqrt of positive normal inputs (denormals are\n  // flushed to zero and cause infs as well).\n  __mmask8 le_zero_mask = _mm512_cmp_pd_mask(_x, p8d_dbl_min, _CMP_LT_OQ);\n  Packet8d x = _mm512_mask_blend_pd(le_zero_mask, _mm512_rsqrt14_pd(_x), _mm512_setzero_pd());\n\n  // Fill in NaNs and Infs for the negative/zero entries.\n  __mmask8 neg_mask = _mm512_cmp_pd_mask(_x, _mm512_setzero_pd(), _CMP_LT_OQ);\n  Packet8d infs_and_nans = _mm512_mask_blend_pd(\n      neg_mask, _mm512_mask_blend_pd(le_zero_mask, _mm512_setzero_pd(), p8d_inf), p8d_nan);\n\n  // Do a first step of Newton's iteration.\n  x = pmul(x, pmadd(neg_half, pmul(x, x), p8d_one_point_five));\n\n  // Do a second step of Newton's iteration.\n  x = pmul(x, pmadd(neg_half, pmul(x, x), p8d_one_point_five));\n\n  // Insert NaNs and Infs in all the right places.\n  return _mm512_mask_blend_pd(le_zero_mask, x, infs_and_nans);\n}\n#elif defined(EIGEN_VECTORIZE_AVX512ER)\ntemplate <>\nEIGEN_STRONG_INLINE Packet16f prsqrt<Packet16f>(const Packet16f& x) {\n  return _mm512_rsqrt28_ps(x);\n}\n#endif\n#endif\n\n}  // end namespace internal\n\n}  // end namespace Eigen\n\n#endif  // THIRD_PARTY_EIGEN3_EIGEN_SRC_CORE_ARCH_AVX512_MATHFUNCTIONS_H_\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/arch/AVX512/PacketMath.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Benoit Steiner (benoit.steiner.goog@gmail.com)\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_PACKET_MATH_AVX512_H\n#define EIGEN_PACKET_MATH_AVX512_H\n\nnamespace Eigen {\n\nnamespace internal {\n\n#ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD\n#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 8\n#endif\n\n#ifndef EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS\n#define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS (2*sizeof(void*))\n#endif\n\n#ifdef __FMA__\n#ifndef EIGEN_HAS_SINGLE_INSTRUCTION_MADD\n#define EIGEN_HAS_SINGLE_INSTRUCTION_MADD\n#endif\n#endif\n\ntypedef __m512 Packet16f;\ntypedef __m512i Packet16i;\ntypedef __m512d Packet8d;\n\ntemplate <>\nstruct is_arithmetic<__m512> {\n  enum { value = true };\n};\ntemplate <>\nstruct is_arithmetic<__m512i> {\n  enum { value = true };\n};\ntemplate <>\nstruct is_arithmetic<__m512d> {\n  enum { value = true };\n};\n\ntemplate<> struct packet_traits<float>  : default_packet_traits\n{\n  typedef Packet16f type;\n  typedef Packet8f half;\n  enum {\n    Vectorizable = 1,\n    AlignedOnScalar = 1,\n    size = 16,\n    HasHalfPacket = 1,\n#if EIGEN_GNUC_AT_LEAST(5, 3)\n#ifdef EIGEN_VECTORIZE_AVX512DQ\n    HasLog = 1,\n#endif\n    HasExp = 1,\n    HasSqrt = 1,\n    HasRsqrt = 1,\n#endif\n    HasDiv = 1\n  };\n };\ntemplate<> struct packet_traits<double> : default_packet_traits\n{\n  typedef Packet8d type;\n  typedef Packet4d half;\n  enum {\n    Vectorizable = 1,\n    AlignedOnScalar = 1,\n    size = 8,\n    HasHalfPacket = 1,\n#if EIGEN_GNUC_AT_LEAST(5, 3)\n    HasSqrt = 1,\n    HasRsqrt = EIGEN_FAST_MATH,\n#endif\n    HasDiv = 1\n  };\n};\n\n/* TODO Implement AVX512 for integers\ntemplate<> struct packet_traits<int>    : default_packet_traits\n{\n  typedef Packet16i type;\n  enum {\n    Vectorizable = 1,\n    AlignedOnScalar = 1,\n    size=8\n  };\n};\n*/\n\ntemplate <>\nstruct unpacket_traits<Packet16f> {\n  typedef float type;\n  typedef Packet8f half;\n  enum { size = 16, alignment=Aligned64 };\n};\ntemplate <>\nstruct unpacket_traits<Packet8d> {\n  typedef double type;\n  typedef Packet4d half;\n  enum { size = 8, alignment=Aligned64 };\n};\ntemplate <>\nstruct unpacket_traits<Packet16i> {\n  typedef int type;\n  typedef Packet8i half;\n  enum { size = 16, alignment=Aligned64 };\n};\n\ntemplate <>\nEIGEN_STRONG_INLINE Packet16f pset1<Packet16f>(const float& from) {\n  return _mm512_set1_ps(from);\n}\ntemplate <>\nEIGEN_STRONG_INLINE Packet8d pset1<Packet8d>(const double& from) {\n  return _mm512_set1_pd(from);\n}\ntemplate <>\nEIGEN_STRONG_INLINE Packet16i pset1<Packet16i>(const int& from) {\n  return _mm512_set1_epi32(from);\n}\n\ntemplate <>\nEIGEN_STRONG_INLINE Packet16f pload1<Packet16f>(const float* from) {\n  return _mm512_broadcastss_ps(_mm_load_ps1(from));\n}\ntemplate <>\nEIGEN_STRONG_INLINE Packet8d pload1<Packet8d>(const double* from) {\n  return _mm512_broadcastsd_pd(_mm_load_pd1(from));\n}\n\ntemplate <>\nEIGEN_STRONG_INLINE Packet16f plset<Packet16f>(const float& a) {\n  return _mm512_add_ps(\n      _mm512_set1_ps(a),\n      _mm512_set_ps(15.0f, 14.0f, 13.0f, 12.0f, 11.0f, 10.0f, 9.0f, 8.0f, 7.0f, 6.0f, 5.0f,\n                    4.0f, 3.0f, 2.0f, 1.0f, 0.0f));\n}\ntemplate <>\nEIGEN_STRONG_INLINE Packet8d plset<Packet8d>(const double& a) {\n  return _mm512_add_pd(_mm512_set1_pd(a),\n                       _mm512_set_pd(7.0, 6.0, 5.0, 4.0, 3.0, 2.0, 1.0, 0.0));\n}\n\ntemplate <>\nEIGEN_STRONG_INLINE Packet16f padd<Packet16f>(const Packet16f& a,\n                                              const Packet16f& b) {\n  return _mm512_add_ps(a, b);\n}\ntemplate <>\nEIGEN_STRONG_INLINE Packet8d padd<Packet8d>(const Packet8d& a,\n                                            const Packet8d& b) {\n  return _mm512_add_pd(a, b);\n}\n\ntemplate <>\nEIGEN_STRONG_INLINE Packet16f psub<Packet16f>(const Packet16f& a,\n                                              const Packet16f& b) {\n  return _mm512_sub_ps(a, b);\n}\ntemplate <>\nEIGEN_STRONG_INLINE Packet8d psub<Packet8d>(const Packet8d& a,\n                                            const Packet8d& b) {\n  return _mm512_sub_pd(a, b);\n}\n\ntemplate <>\nEIGEN_STRONG_INLINE Packet16f pnegate(const Packet16f& a) {\n  return _mm512_sub_ps(_mm512_set1_ps(0.0), a);\n}\ntemplate <>\nEIGEN_STRONG_INLINE Packet8d pnegate(const Packet8d& a) {\n  return _mm512_sub_pd(_mm512_set1_pd(0.0), a);\n}\n\ntemplate <>\nEIGEN_STRONG_INLINE Packet16f pconj(const Packet16f& a) {\n  return a;\n}\ntemplate <>\nEIGEN_STRONG_INLINE Packet8d pconj(const Packet8d& a) {\n  return a;\n}\ntemplate <>\nEIGEN_STRONG_INLINE Packet16i pconj(const Packet16i& a) {\n  return a;\n}\n\ntemplate <>\nEIGEN_STRONG_INLINE Packet16f pmul<Packet16f>(const Packet16f& a,\n                                              const Packet16f& b) {\n  return _mm512_mul_ps(a, b);\n}\ntemplate <>\nEIGEN_STRONG_INLINE Packet8d pmul<Packet8d>(const Packet8d& a,\n                                            const Packet8d& b) {\n  return _mm512_mul_pd(a, b);\n}\n\ntemplate <>\nEIGEN_STRONG_INLINE Packet16f pdiv<Packet16f>(const Packet16f& a,\n                                              const Packet16f& b) {\n  return _mm512_div_ps(a, b);\n}\ntemplate <>\nEIGEN_STRONG_INLINE Packet8d pdiv<Packet8d>(const Packet8d& a,\n                                            const Packet8d& b) {\n  return _mm512_div_pd(a, b);\n}\n\n#ifdef __FMA__\ntemplate <>\nEIGEN_STRONG_INLINE Packet16f pmadd(const Packet16f& a, const Packet16f& b,\n                                    const Packet16f& c) {\n  return _mm512_fmadd_ps(a, b, c);\n}\ntemplate <>\nEIGEN_STRONG_INLINE Packet8d pmadd(const Packet8d& a, const Packet8d& b,\n                                   const Packet8d& c) {\n  return _mm512_fmadd_pd(a, b, c);\n}\n#endif\n\ntemplate <>\nEIGEN_STRONG_INLINE Packet16f pmin<Packet16f>(const Packet16f& a,\n                                              const Packet16f& b) {\n  return _mm512_min_ps(a, b);\n}\ntemplate <>\nEIGEN_STRONG_INLINE Packet8d pmin<Packet8d>(const Packet8d& a,\n                                            const Packet8d& b) {\n  return _mm512_min_pd(a, b);\n}\n\ntemplate <>\nEIGEN_STRONG_INLINE Packet16f pmax<Packet16f>(const Packet16f& a,\n                                              const Packet16f& b) {\n  return _mm512_max_ps(a, b);\n}\ntemplate <>\nEIGEN_STRONG_INLINE Packet8d pmax<Packet8d>(const Packet8d& a,\n                                            const Packet8d& b) {\n  return _mm512_max_pd(a, b);\n}\n\ntemplate <>\nEIGEN_STRONG_INLINE Packet16f pand<Packet16f>(const Packet16f& a,\n                                              const Packet16f& b) {\n#ifdef EIGEN_VECTORIZE_AVX512DQ\n  return _mm512_and_ps(a, b);\n#else\n  Packet16f res = _mm512_undefined_ps();\n  Packet4f lane0_a = _mm512_extractf32x4_ps(a, 0);\n  Packet4f lane0_b = _mm512_extractf32x4_ps(b, 0);\n  res = _mm512_insertf32x4(res, _mm_and_ps(lane0_a, lane0_b), 0);\n\n  Packet4f lane1_a = _mm512_extractf32x4_ps(a, 1);\n  Packet4f lane1_b = _mm512_extractf32x4_ps(b, 1);\n  res = _mm512_insertf32x4(res, _mm_and_ps(lane1_a, lane1_b), 1);\n\n  Packet4f lane2_a = _mm512_extractf32x4_ps(a, 2);\n  Packet4f lane2_b = _mm512_extractf32x4_ps(b, 2);\n  res = _mm512_insertf32x4(res, _mm_and_ps(lane2_a, lane2_b), 2);\n\n  Packet4f lane3_a = _mm512_extractf32x4_ps(a, 3);\n  Packet4f lane3_b = _mm512_extractf32x4_ps(b, 3);\n  res = _mm512_insertf32x4(res, _mm_and_ps(lane3_a, lane3_b), 3);\n\n  return res;\n#endif\n}\ntemplate <>\nEIGEN_STRONG_INLINE Packet8d pand<Packet8d>(const Packet8d& a,\n                                            const Packet8d& b) {\n#ifdef EIGEN_VECTORIZE_AVX512DQ\n  return _mm512_and_pd(a, b);\n#else\n  Packet8d res = _mm512_undefined_pd();\n  Packet4d lane0_a = _mm512_extractf64x4_pd(a, 0);\n  Packet4d lane0_b = _mm512_extractf64x4_pd(b, 0);\n  res = _mm512_insertf64x4(res, _mm256_and_pd(lane0_a, lane0_b), 0);\n\n  Packet4d lane1_a = _mm512_extractf64x4_pd(a, 1);\n  Packet4d lane1_b = _mm512_extractf64x4_pd(b, 1);\n  res = _mm512_insertf64x4(res, _mm256_and_pd(lane1_a, lane1_b), 1);\n\n  return res;\n#endif\n}\ntemplate <>\nEIGEN_STRONG_INLINE Packet16f por<Packet16f>(const Packet16f& a,\n                                             const Packet16f& b) {\n#ifdef EIGEN_VECTORIZE_AVX512DQ\n  return _mm512_or_ps(a, b);\n#else\n  Packet16f res = _mm512_undefined_ps();\n  Packet4f lane0_a = _mm512_extractf32x4_ps(a, 0);\n  Packet4f lane0_b = _mm512_extractf32x4_ps(b, 0);\n  res = _mm512_insertf32x4(res, _mm_or_ps(lane0_a, lane0_b), 0);\n\n  Packet4f lane1_a = _mm512_extractf32x4_ps(a, 1);\n  Packet4f lane1_b = _mm512_extractf32x4_ps(b, 1);\n  res = _mm512_insertf32x4(res, _mm_or_ps(lane1_a, lane1_b), 1);\n\n  Packet4f lane2_a = _mm512_extractf32x4_ps(a, 2);\n  Packet4f lane2_b = _mm512_extractf32x4_ps(b, 2);\n  res = _mm512_insertf32x4(res, _mm_or_ps(lane2_a, lane2_b), 2);\n\n  Packet4f lane3_a = _mm512_extractf32x4_ps(a, 3);\n  Packet4f lane3_b = _mm512_extractf32x4_ps(b, 3);\n  res = _mm512_insertf32x4(res, _mm_or_ps(lane3_a, lane3_b), 3);\n\n  return res;\n#endif\n}\n\ntemplate <>\nEIGEN_STRONG_INLINE Packet8d por<Packet8d>(const Packet8d& a,\n                                           const Packet8d& b) {\n#ifdef EIGEN_VECTORIZE_AVX512DQ\n  return _mm512_or_pd(a, b);\n#else\n  Packet8d res = _mm512_undefined_pd();\n  Packet4d lane0_a = _mm512_extractf64x4_pd(a, 0);\n  Packet4d lane0_b = _mm512_extractf64x4_pd(b, 0);\n  res = _mm512_insertf64x4(res, _mm256_or_pd(lane0_a, lane0_b), 0);\n\n  Packet4d lane1_a = _mm512_extractf64x4_pd(a, 1);\n  Packet4d lane1_b = _mm512_extractf64x4_pd(b, 1);\n  res = _mm512_insertf64x4(res, _mm256_or_pd(lane1_a, lane1_b), 1);\n\n  return res;\n#endif\n}\n\ntemplate <>\nEIGEN_STRONG_INLINE Packet16f pxor<Packet16f>(const Packet16f& a,\n                                              const Packet16f& b) {\n#ifdef EIGEN_VECTORIZE_AVX512DQ\n  return _mm512_xor_ps(a, b);\n#else\n  Packet16f res = _mm512_undefined_ps();\n  Packet4f lane0_a = _mm512_extractf32x4_ps(a, 0);\n  Packet4f lane0_b = _mm512_extractf32x4_ps(b, 0);\n  res = _mm512_insertf32x4(res, _mm_xor_ps(lane0_a, lane0_b), 0);\n\n  Packet4f lane1_a = _mm512_extractf32x4_ps(a, 1);\n  Packet4f lane1_b = _mm512_extractf32x4_ps(b, 1);\n  res = _mm512_insertf32x4(res, _mm_xor_ps(lane1_a, lane1_b), 1);\n\n  Packet4f lane2_a = _mm512_extractf32x4_ps(a, 2);\n  Packet4f lane2_b = _mm512_extractf32x4_ps(b, 2);\n  res = _mm512_insertf32x4(res, _mm_xor_ps(lane2_a, lane2_b), 2);\n\n  Packet4f lane3_a = _mm512_extractf32x4_ps(a, 3);\n  Packet4f lane3_b = _mm512_extractf32x4_ps(b, 3);\n  res = _mm512_insertf32x4(res, _mm_xor_ps(lane3_a, lane3_b), 3);\n\n  return res;\n#endif\n}\ntemplate <>\nEIGEN_STRONG_INLINE Packet8d pxor<Packet8d>(const Packet8d& a,\n                                            const Packet8d& b) {\n#ifdef EIGEN_VECTORIZE_AVX512DQ\n  return _mm512_xor_pd(a, b);\n#else\n  Packet8d res = _mm512_undefined_pd();\n  Packet4d lane0_a = _mm512_extractf64x4_pd(a, 0);\n  Packet4d lane0_b = _mm512_extractf64x4_pd(b, 0);\n  res = _mm512_insertf64x4(res, _mm256_xor_pd(lane0_a, lane0_b), 0);\n\n  Packet4d lane1_a = _mm512_extractf64x4_pd(a, 1);\n  Packet4d lane1_b = _mm512_extractf64x4_pd(b, 1);\n  res = _mm512_insertf64x4(res, _mm256_xor_pd(lane1_a, lane1_b), 1);\n\n  return res;\n#endif\n}\n\ntemplate <>\nEIGEN_STRONG_INLINE Packet16f pandnot<Packet16f>(const Packet16f& a,\n                                                 const Packet16f& b) {\n#ifdef EIGEN_VECTORIZE_AVX512DQ\n  return _mm512_andnot_ps(a, b);\n#else\n  Packet16f res = _mm512_undefined_ps();\n  Packet4f lane0_a = _mm512_extractf32x4_ps(a, 0);\n  Packet4f lane0_b = _mm512_extractf32x4_ps(b, 0);\n  res = _mm512_insertf32x4(res, _mm_andnot_ps(lane0_a, lane0_b), 0);\n\n  Packet4f lane1_a = _mm512_extractf32x4_ps(a, 1);\n  Packet4f lane1_b = _mm512_extractf32x4_ps(b, 1);\n  res = _mm512_insertf32x4(res, _mm_andnot_ps(lane1_a, lane1_b), 1);\n\n  Packet4f lane2_a = _mm512_extractf32x4_ps(a, 2);\n  Packet4f lane2_b = _mm512_extractf32x4_ps(b, 2);\n  res = _mm512_insertf32x4(res, _mm_andnot_ps(lane2_a, lane2_b), 2);\n\n  Packet4f lane3_a = _mm512_extractf32x4_ps(a, 3);\n  Packet4f lane3_b = _mm512_extractf32x4_ps(b, 3);\n  res = _mm512_insertf32x4(res, _mm_andnot_ps(lane3_a, lane3_b), 3);\n\n  return res;\n#endif\n}\ntemplate <>\nEIGEN_STRONG_INLINE Packet8d pandnot<Packet8d>(const Packet8d& a,\n                                               const Packet8d& b) {\n#ifdef EIGEN_VECTORIZE_AVX512DQ\n  return _mm512_andnot_pd(a, b);\n#else\n  Packet8d res = _mm512_undefined_pd();\n  Packet4d lane0_a = _mm512_extractf64x4_pd(a, 0);\n  Packet4d lane0_b = _mm512_extractf64x4_pd(b, 0);\n  res = _mm512_insertf64x4(res, _mm256_andnot_pd(lane0_a, lane0_b), 0);\n\n  Packet4d lane1_a = _mm512_extractf64x4_pd(a, 1);\n  Packet4d lane1_b = _mm512_extractf64x4_pd(b, 1);\n  res = _mm512_insertf64x4(res, _mm256_andnot_pd(lane1_a, lane1_b), 1);\n\n  return res;\n#endif\n}\n\ntemplate <>\nEIGEN_STRONG_INLINE Packet16f pload<Packet16f>(const float* from) {\n  EIGEN_DEBUG_ALIGNED_LOAD return _mm512_load_ps(from);\n}\ntemplate <>\nEIGEN_STRONG_INLINE Packet8d pload<Packet8d>(const double* from) {\n  EIGEN_DEBUG_ALIGNED_LOAD return _mm512_load_pd(from);\n}\ntemplate <>\nEIGEN_STRONG_INLINE Packet16i pload<Packet16i>(const int* from) {\n  EIGEN_DEBUG_ALIGNED_LOAD return _mm512_load_si512(\n      reinterpret_cast<const __m512i*>(from));\n}\n\ntemplate <>\nEIGEN_STRONG_INLINE Packet16f ploadu<Packet16f>(const float* from) {\n  EIGEN_DEBUG_UNALIGNED_LOAD return _mm512_loadu_ps(from);\n}\ntemplate <>\nEIGEN_STRONG_INLINE Packet8d ploadu<Packet8d>(const double* from) {\n  EIGEN_DEBUG_UNALIGNED_LOAD return _mm512_loadu_pd(from);\n}\ntemplate <>\nEIGEN_STRONG_INLINE Packet16i ploadu<Packet16i>(const int* from) {\n  EIGEN_DEBUG_UNALIGNED_LOAD return _mm512_loadu_si512(\n      reinterpret_cast<const __m512i*>(from));\n}\n\n// Loads 8 floats from memory a returns the packet\n// {a0, a0  a1, a1, a2, a2, a3, a3, a4, a4, a5, a5, a6, a6, a7, a7}\ntemplate <>\nEIGEN_STRONG_INLINE Packet16f ploaddup<Packet16f>(const float* from) {\n  Packet8f lane0 = _mm256_broadcast_ps((const __m128*)(const void*)from);\n  // mimic an \"inplace\" permutation of the lower 128bits using a blend\n  lane0 = _mm256_blend_ps(\n      lane0, _mm256_castps128_ps256(_mm_permute_ps(\n                 _mm256_castps256_ps128(lane0), _MM_SHUFFLE(1, 0, 1, 0))),\n      15);\n  // then we can perform a consistent permutation on the global register to get\n  // everything in shape:\n  lane0 = _mm256_permute_ps(lane0, _MM_SHUFFLE(3, 3, 2, 2));\n\n  Packet8f lane1 = _mm256_broadcast_ps((const __m128*)(const void*)(from + 4));\n  // mimic an \"inplace\" permutation of the lower 128bits using a blend\n  lane1 = _mm256_blend_ps(\n      lane1, _mm256_castps128_ps256(_mm_permute_ps(\n                 _mm256_castps256_ps128(lane1), _MM_SHUFFLE(1, 0, 1, 0))),\n      15);\n  // then we can perform a consistent permutation on the global register to get\n  // everything in shape:\n  lane1 = _mm256_permute_ps(lane1, _MM_SHUFFLE(3, 3, 2, 2));\n\n#ifdef EIGEN_VECTORIZE_AVX512DQ\n  Packet16f res = _mm512_undefined_ps();\n  return _mm512_insertf32x8(res, lane0, 0);\n  return _mm512_insertf32x8(res, lane1, 1);\n  return res;\n#else\n  Packet16f res = _mm512_undefined_ps();\n  res = _mm512_insertf32x4(res, _mm256_extractf128_ps(lane0, 0), 0);\n  res = _mm512_insertf32x4(res, _mm256_extractf128_ps(lane0, 1), 1);\n  res = _mm512_insertf32x4(res, _mm256_extractf128_ps(lane1, 0), 2);\n  res = _mm512_insertf32x4(res, _mm256_extractf128_ps(lane1, 1), 3);\n  return res;\n#endif\n}\n// Loads 4 doubles from memory a returns the packet {a0, a0  a1, a1, a2, a2, a3,\n// a3}\ntemplate <>\nEIGEN_STRONG_INLINE Packet8d ploaddup<Packet8d>(const double* from) {\n  Packet4d lane0 = _mm256_broadcast_pd((const __m128d*)(const void*)from);\n  lane0 = _mm256_permute_pd(lane0, 3 << 2);\n\n  Packet4d lane1 = _mm256_broadcast_pd((const __m128d*)(const void*)(from + 2));\n  lane1 = _mm256_permute_pd(lane1, 3 << 2);\n\n  Packet8d res = _mm512_undefined_pd();\n  res = _mm512_insertf64x4(res, lane0, 0);\n  return _mm512_insertf64x4(res, lane1, 1);\n}\n\n// Loads 4 floats from memory a returns the packet\n// {a0, a0  a0, a0, a1, a1, a1, a1, a2, a2, a2, a2, a3, a3, a3, a3}\ntemplate <>\nEIGEN_STRONG_INLINE Packet16f ploadquad<Packet16f>(const float* from) {\n  Packet16f tmp = _mm512_undefined_ps();\n  tmp = _mm512_insertf32x4(tmp, _mm_load_ps1(from), 0);\n  tmp = _mm512_insertf32x4(tmp, _mm_load_ps1(from + 1), 1);\n  tmp = _mm512_insertf32x4(tmp, _mm_load_ps1(from + 2), 2);\n  tmp = _mm512_insertf32x4(tmp, _mm_load_ps1(from + 3), 3);\n  return tmp;\n}\n// Loads 2 doubles from memory a returns the packet\n// {a0, a0  a0, a0, a1, a1, a1, a1}\ntemplate <>\nEIGEN_STRONG_INLINE Packet8d ploadquad<Packet8d>(const double* from) {\n  Packet8d tmp = _mm512_undefined_pd();\n  Packet2d tmp0 = _mm_load_pd1(from);\n  Packet2d tmp1 = _mm_load_pd1(from + 1);\n  Packet4d lane0 = _mm256_broadcastsd_pd(tmp0);\n  Packet4d lane1 = _mm256_broadcastsd_pd(tmp1);\n  tmp = _mm512_insertf64x4(tmp, lane0, 0);\n  return _mm512_insertf64x4(tmp, lane1, 1);\n}\n\ntemplate <>\nEIGEN_STRONG_INLINE void pstore<float>(float* to, const Packet16f& from) {\n  EIGEN_DEBUG_ALIGNED_STORE _mm512_store_ps(to, from);\n}\ntemplate <>\nEIGEN_STRONG_INLINE void pstore<double>(double* to, const Packet8d& from) {\n  EIGEN_DEBUG_ALIGNED_STORE _mm512_store_pd(to, from);\n}\ntemplate <>\nEIGEN_STRONG_INLINE void pstore<int>(int* to, const Packet16i& from) {\n  EIGEN_DEBUG_ALIGNED_STORE _mm512_storeu_si512(reinterpret_cast<__m512i*>(to),\n                                                from);\n}\n\ntemplate <>\nEIGEN_STRONG_INLINE void pstoreu<float>(float* to, const Packet16f& from) {\n  EIGEN_DEBUG_UNALIGNED_STORE _mm512_storeu_ps(to, from);\n}\ntemplate <>\nEIGEN_STRONG_INLINE void pstoreu<double>(double* to, const Packet8d& from) {\n  EIGEN_DEBUG_UNALIGNED_STORE _mm512_storeu_pd(to, from);\n}\ntemplate <>\nEIGEN_STRONG_INLINE void pstoreu<int>(int* to, const Packet16i& from) {\n  EIGEN_DEBUG_UNALIGNED_STORE _mm512_storeu_si512(\n      reinterpret_cast<__m512i*>(to), from);\n}\n\ntemplate <>\nEIGEN_DEVICE_FUNC inline Packet16f pgather<float, Packet16f>(const float* from,\n                                                             Index stride) {\n  Packet16i stride_vector = _mm512_set1_epi32(stride);\n  Packet16i stride_multiplier =\n      _mm512_set_epi32(15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0);\n  Packet16i indices = _mm512_mullo_epi32(stride_vector, stride_multiplier);\n\n  return _mm512_i32gather_ps(indices, from, 4);\n}\ntemplate <>\nEIGEN_DEVICE_FUNC inline Packet8d pgather<double, Packet8d>(const double* from,\n                                                            Index stride) {\n  Packet8i stride_vector = _mm256_set1_epi32(stride);\n  Packet8i stride_multiplier = _mm256_set_epi32(7, 6, 5, 4, 3, 2, 1, 0);\n  Packet8i indices = _mm256_mullo_epi32(stride_vector, stride_multiplier);\n\n  return _mm512_i32gather_pd(indices, from, 8);\n}\n\ntemplate <>\nEIGEN_DEVICE_FUNC inline void pscatter<float, Packet16f>(float* to,\n                                                         const Packet16f& from,\n                                                         Index stride) {\n  Packet16i stride_vector = _mm512_set1_epi32(stride);\n  Packet16i stride_multiplier =\n      _mm512_set_epi32(15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0);\n  Packet16i indices = _mm512_mullo_epi32(stride_vector, stride_multiplier);\n  _mm512_i32scatter_ps(to, indices, from, 4);\n}\ntemplate <>\nEIGEN_DEVICE_FUNC inline void pscatter<double, Packet8d>(double* to,\n                                                         const Packet8d& from,\n                                                         Index stride) {\n  Packet8i stride_vector = _mm256_set1_epi32(stride);\n  Packet8i stride_multiplier = _mm256_set_epi32(7, 6, 5, 4, 3, 2, 1, 0);\n  Packet8i indices = _mm256_mullo_epi32(stride_vector, stride_multiplier);\n  _mm512_i32scatter_pd(to, indices, from, 8);\n}\n\ntemplate <>\nEIGEN_STRONG_INLINE void pstore1<Packet16f>(float* to, const float& a) {\n  Packet16f pa = pset1<Packet16f>(a);\n  pstore(to, pa);\n}\ntemplate <>\nEIGEN_STRONG_INLINE void pstore1<Packet8d>(double* to, const double& a) {\n  Packet8d pa = pset1<Packet8d>(a);\n  pstore(to, pa);\n}\ntemplate <>\nEIGEN_STRONG_INLINE void pstore1<Packet16i>(int* to, const int& a) {\n  Packet16i pa = pset1<Packet16i>(a);\n  pstore(to, pa);\n}\n\ntemplate<> EIGEN_STRONG_INLINE void prefetch<float>(const float*   addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }\ntemplate<> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }\ntemplate<> EIGEN_STRONG_INLINE void prefetch<int>(const int*       addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }\n\ntemplate <>\nEIGEN_STRONG_INLINE float pfirst<Packet16f>(const Packet16f& a) {\n  return _mm_cvtss_f32(_mm512_extractf32x4_ps(a, 0));\n}\ntemplate <>\nEIGEN_STRONG_INLINE double pfirst<Packet8d>(const Packet8d& a) {\n  return _mm_cvtsd_f64(_mm256_extractf128_pd(_mm512_extractf64x4_pd(a, 0), 0));\n}\ntemplate <>\nEIGEN_STRONG_INLINE int pfirst<Packet16i>(const Packet16i& a) {\n  return _mm_extract_epi32(_mm512_extracti32x4_epi32(a, 0), 0);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet16f preverse(const Packet16f& a)\n{\n  return _mm512_permutexvar_ps(_mm512_set_epi32(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15), a);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet8d preverse(const Packet8d& a)\n{\n  return _mm512_permutexvar_pd(_mm512_set_epi32(0, 0, 0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7), a);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet16f pabs(const Packet16f& a)\n{\n  // _mm512_abs_ps intrinsic not found, so hack around it\n  return (__m512)_mm512_and_si512((__m512i)a, _mm512_set1_epi32(0x7fffffff));\n}\ntemplate <>\nEIGEN_STRONG_INLINE Packet8d pabs(const Packet8d& a) {\n  // _mm512_abs_ps intrinsic not found, so hack around it\n  return (__m512d)_mm512_and_si512((__m512i)a,\n                                   _mm512_set1_epi64(0x7fffffffffffffff));\n}\n\n#ifdef EIGEN_VECTORIZE_AVX512DQ\n// AVX512F does not define _mm512_extractf32x8_ps to extract _m256 from _m512\n#define EIGEN_EXTRACT_8f_FROM_16f(INPUT, OUTPUT)                           \\\n  __m256 OUTPUT##_0 = _mm512_extractf32x8_ps(INPUT, 0) __m256 OUTPUT##_1 = \\\n      _mm512_extractf32x8_ps(INPUT, 1)\n#else\n#define EIGEN_EXTRACT_8f_FROM_16f(INPUT, OUTPUT)                \\\n  __m256 OUTPUT##_0 = _mm256_insertf128_ps(                     \\\n      _mm256_castps128_ps256(_mm512_extractf32x4_ps(INPUT, 0)), \\\n      _mm512_extractf32x4_ps(INPUT, 1), 1);                     \\\n  __m256 OUTPUT##_1 = _mm256_insertf128_ps(                     \\\n      _mm256_castps128_ps256(_mm512_extractf32x4_ps(INPUT, 2)), \\\n      _mm512_extractf32x4_ps(INPUT, 3), 1);\n#endif\n\n#ifdef EIGEN_VECTORIZE_AVX512DQ\n#define EIGEN_INSERT_8f_INTO_16f(OUTPUT, INPUTA, INPUTB) \\\n  OUTPUT = _mm512_insertf32x8(OUTPUT, INPUTA, 0);        \\\n  OUTPUT = _mm512_insertf32x8(OUTPUT, INPUTB, 1);\n#else\n#define EIGEN_INSERT_8f_INTO_16f(OUTPUT, INPUTA, INPUTB)                    \\\n  OUTPUT = _mm512_insertf32x4(OUTPUT, _mm256_extractf128_ps(INPUTA, 0), 0); \\\n  OUTPUT = _mm512_insertf32x4(OUTPUT, _mm256_extractf128_ps(INPUTA, 1), 1); \\\n  OUTPUT = _mm512_insertf32x4(OUTPUT, _mm256_extractf128_ps(INPUTB, 0), 2); \\\n  OUTPUT = _mm512_insertf32x4(OUTPUT, _mm256_extractf128_ps(INPUTB, 1), 3);\n#endif\ntemplate<> EIGEN_STRONG_INLINE Packet16f preduxp<Packet16f>(const Packet16f*\nvecs)\n{\n  EIGEN_EXTRACT_8f_FROM_16f(vecs[0], vecs0);\n  EIGEN_EXTRACT_8f_FROM_16f(vecs[1], vecs1);\n  EIGEN_EXTRACT_8f_FROM_16f(vecs[2], vecs2);\n  EIGEN_EXTRACT_8f_FROM_16f(vecs[3], vecs3);\n  EIGEN_EXTRACT_8f_FROM_16f(vecs[4], vecs4);\n  EIGEN_EXTRACT_8f_FROM_16f(vecs[5], vecs5);\n  EIGEN_EXTRACT_8f_FROM_16f(vecs[6], vecs6);\n  EIGEN_EXTRACT_8f_FROM_16f(vecs[7], vecs7);\n  EIGEN_EXTRACT_8f_FROM_16f(vecs[8], vecs8);\n  EIGEN_EXTRACT_8f_FROM_16f(vecs[9], vecs9);\n  EIGEN_EXTRACT_8f_FROM_16f(vecs[10], vecs10);\n  EIGEN_EXTRACT_8f_FROM_16f(vecs[11], vecs11);\n  EIGEN_EXTRACT_8f_FROM_16f(vecs[12], vecs12);\n  EIGEN_EXTRACT_8f_FROM_16f(vecs[13], vecs13);\n  EIGEN_EXTRACT_8f_FROM_16f(vecs[14], vecs14);\n  EIGEN_EXTRACT_8f_FROM_16f(vecs[15], vecs15);\n\n  __m256 hsum1 = _mm256_hadd_ps(vecs0_0, vecs1_0);\n  __m256 hsum2 = _mm256_hadd_ps(vecs2_0, vecs3_0);\n  __m256 hsum3 = _mm256_hadd_ps(vecs4_0, vecs5_0);\n  __m256 hsum4 = _mm256_hadd_ps(vecs6_0, vecs7_0);\n\n  __m256 hsum5 = _mm256_hadd_ps(hsum1, hsum1);\n  __m256 hsum6 = _mm256_hadd_ps(hsum2, hsum2);\n  __m256 hsum7 = _mm256_hadd_ps(hsum3, hsum3);\n  __m256 hsum8 = _mm256_hadd_ps(hsum4, hsum4);\n\n  __m256 perm1 = _mm256_permute2f128_ps(hsum5, hsum5, 0x23);\n  __m256 perm2 = _mm256_permute2f128_ps(hsum6, hsum6, 0x23);\n  __m256 perm3 = _mm256_permute2f128_ps(hsum7, hsum7, 0x23);\n  __m256 perm4 = _mm256_permute2f128_ps(hsum8, hsum8, 0x23);\n\n  __m256 sum1 = _mm256_add_ps(perm1, hsum5);\n  __m256 sum2 = _mm256_add_ps(perm2, hsum6);\n  __m256 sum3 = _mm256_add_ps(perm3, hsum7);\n  __m256 sum4 = _mm256_add_ps(perm4, hsum8);\n\n  __m256 blend1 = _mm256_blend_ps(sum1, sum2, 0xcc);\n  __m256 blend2 = _mm256_blend_ps(sum3, sum4, 0xcc);\n\n  __m256 final = _mm256_blend_ps(blend1, blend2, 0xf0);\n\n  hsum1 = _mm256_hadd_ps(vecs0_1, vecs1_1);\n  hsum2 = _mm256_hadd_ps(vecs2_1, vecs3_1);\n  hsum3 = _mm256_hadd_ps(vecs4_1, vecs5_1);\n  hsum4 = _mm256_hadd_ps(vecs6_1, vecs7_1);\n\n  hsum5 = _mm256_hadd_ps(hsum1, hsum1);\n  hsum6 = _mm256_hadd_ps(hsum2, hsum2);\n  hsum7 = _mm256_hadd_ps(hsum3, hsum3);\n  hsum8 = _mm256_hadd_ps(hsum4, hsum4);\n\n  perm1 = _mm256_permute2f128_ps(hsum5, hsum5, 0x23);\n  perm2 = _mm256_permute2f128_ps(hsum6, hsum6, 0x23);\n  perm3 = _mm256_permute2f128_ps(hsum7, hsum7, 0x23);\n  perm4 = _mm256_permute2f128_ps(hsum8, hsum8, 0x23);\n\n  sum1 = _mm256_add_ps(perm1, hsum5);\n  sum2 = _mm256_add_ps(perm2, hsum6);\n  sum3 = _mm256_add_ps(perm3, hsum7);\n  sum4 = _mm256_add_ps(perm4, hsum8);\n\n  blend1 = _mm256_blend_ps(sum1, sum2, 0xcc);\n  blend2 = _mm256_blend_ps(sum3, sum4, 0xcc);\n\n  final = padd(final, _mm256_blend_ps(blend1, blend2, 0xf0));\n\n  hsum1 = _mm256_hadd_ps(vecs8_0, vecs9_0);\n  hsum2 = _mm256_hadd_ps(vecs10_0, vecs11_0);\n  hsum3 = _mm256_hadd_ps(vecs12_0, vecs13_0);\n  hsum4 = _mm256_hadd_ps(vecs14_0, vecs15_0);\n\n  hsum5 = _mm256_hadd_ps(hsum1, hsum1);\n  hsum6 = _mm256_hadd_ps(hsum2, hsum2);\n  hsum7 = _mm256_hadd_ps(hsum3, hsum3);\n  hsum8 = _mm256_hadd_ps(hsum4, hsum4);\n\n  perm1 = _mm256_permute2f128_ps(hsum5, hsum5, 0x23);\n  perm2 = _mm256_permute2f128_ps(hsum6, hsum6, 0x23);\n  perm3 = _mm256_permute2f128_ps(hsum7, hsum7, 0x23);\n  perm4 = _mm256_permute2f128_ps(hsum8, hsum8, 0x23);\n\n  sum1 = _mm256_add_ps(perm1, hsum5);\n  sum2 = _mm256_add_ps(perm2, hsum6);\n  sum3 = _mm256_add_ps(perm3, hsum7);\n  sum4 = _mm256_add_ps(perm4, hsum8);\n\n  blend1 = _mm256_blend_ps(sum1, sum2, 0xcc);\n  blend2 = _mm256_blend_ps(sum3, sum4, 0xcc);\n\n  __m256 final_1 = _mm256_blend_ps(blend1, blend2, 0xf0);\n\n  hsum1 = _mm256_hadd_ps(vecs8_1, vecs9_1);\n  hsum2 = _mm256_hadd_ps(vecs10_1, vecs11_1);\n  hsum3 = _mm256_hadd_ps(vecs12_1, vecs13_1);\n  hsum4 = _mm256_hadd_ps(vecs14_1, vecs15_1);\n\n  hsum5 = _mm256_hadd_ps(hsum1, hsum1);\n  hsum6 = _mm256_hadd_ps(hsum2, hsum2);\n  hsum7 = _mm256_hadd_ps(hsum3, hsum3);\n  hsum8 = _mm256_hadd_ps(hsum4, hsum4);\n\n  perm1 = _mm256_permute2f128_ps(hsum5, hsum5, 0x23);\n  perm2 = _mm256_permute2f128_ps(hsum6, hsum6, 0x23);\n  perm3 = _mm256_permute2f128_ps(hsum7, hsum7, 0x23);\n  perm4 = _mm256_permute2f128_ps(hsum8, hsum8, 0x23);\n\n  sum1 = _mm256_add_ps(perm1, hsum5);\n  sum2 = _mm256_add_ps(perm2, hsum6);\n  sum3 = _mm256_add_ps(perm3, hsum7);\n  sum4 = _mm256_add_ps(perm4, hsum8);\n\n  blend1 = _mm256_blend_ps(sum1, sum2, 0xcc);\n  blend2 = _mm256_blend_ps(sum3, sum4, 0xcc);\n\n  final_1 = padd(final_1, _mm256_blend_ps(blend1, blend2, 0xf0));\n\n  __m512 final_output;\n\n  EIGEN_INSERT_8f_INTO_16f(final_output, final, final_1);\n  return final_output;\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet8d preduxp<Packet8d>(const Packet8d* vecs)\n{\n  Packet4d vecs0_0 = _mm512_extractf64x4_pd(vecs[0], 0);\n  Packet4d vecs0_1 = _mm512_extractf64x4_pd(vecs[0], 1);\n\n  Packet4d vecs1_0 = _mm512_extractf64x4_pd(vecs[1], 0);\n  Packet4d vecs1_1 = _mm512_extractf64x4_pd(vecs[1], 1);\n\n  Packet4d vecs2_0 = _mm512_extractf64x4_pd(vecs[2], 0);\n  Packet4d vecs2_1 = _mm512_extractf64x4_pd(vecs[2], 1);\n\n  Packet4d vecs3_0 = _mm512_extractf64x4_pd(vecs[3], 0);\n  Packet4d vecs3_1 = _mm512_extractf64x4_pd(vecs[3], 1);\n\n  Packet4d vecs4_0 = _mm512_extractf64x4_pd(vecs[4], 0);\n  Packet4d vecs4_1 = _mm512_extractf64x4_pd(vecs[4], 1);\n\n  Packet4d vecs5_0 = _mm512_extractf64x4_pd(vecs[5], 0);\n  Packet4d vecs5_1 = _mm512_extractf64x4_pd(vecs[5], 1);\n\n  Packet4d vecs6_0 = _mm512_extractf64x4_pd(vecs[6], 0);\n  Packet4d vecs6_1 = _mm512_extractf64x4_pd(vecs[6], 1);\n\n  Packet4d vecs7_0 = _mm512_extractf64x4_pd(vecs[7], 0);\n  Packet4d vecs7_1 = _mm512_extractf64x4_pd(vecs[7], 1);\n\n  Packet4d tmp0, tmp1;\n\n  tmp0 = _mm256_hadd_pd(vecs0_0, vecs1_0);\n  tmp0 = _mm256_add_pd(tmp0, _mm256_permute2f128_pd(tmp0, tmp0, 1));\n\n  tmp1 = _mm256_hadd_pd(vecs2_0, vecs3_0);\n  tmp1 = _mm256_add_pd(tmp1, _mm256_permute2f128_pd(tmp1, tmp1, 1));\n\n  __m256d final_0 = _mm256_blend_pd(tmp0, tmp1, 0xC);\n\n  tmp0 = _mm256_hadd_pd(vecs0_1, vecs1_1);\n  tmp0 = _mm256_add_pd(tmp0, _mm256_permute2f128_pd(tmp0, tmp0, 1));\n\n  tmp1 = _mm256_hadd_pd(vecs2_1, vecs3_1);\n  tmp1 = _mm256_add_pd(tmp1, _mm256_permute2f128_pd(tmp1, tmp1, 1));\n\n  final_0 = padd(final_0, _mm256_blend_pd(tmp0, tmp1, 0xC));\n\n  tmp0 = _mm256_hadd_pd(vecs4_0, vecs5_0);\n  tmp0 = _mm256_add_pd(tmp0, _mm256_permute2f128_pd(tmp0, tmp0, 1));\n\n  tmp1 = _mm256_hadd_pd(vecs6_0, vecs7_0);\n  tmp1 = _mm256_add_pd(tmp1, _mm256_permute2f128_pd(tmp1, tmp1, 1));\n\n  __m256d final_1 = _mm256_blend_pd(tmp0, tmp1, 0xC);\n\n  tmp0 = _mm256_hadd_pd(vecs4_1, vecs5_1);\n  tmp0 = _mm256_add_pd(tmp0, _mm256_permute2f128_pd(tmp0, tmp0, 1));\n\n  tmp1 = _mm256_hadd_pd(vecs6_1, vecs7_1);\n  tmp1 = _mm256_add_pd(tmp1, _mm256_permute2f128_pd(tmp1, tmp1, 1));\n\n  final_1 = padd(final_1, _mm256_blend_pd(tmp0, tmp1, 0xC));\n\n  __m512d final_output = _mm512_insertf64x4(final_output, final_0, 0);\n\n  return _mm512_insertf64x4(final_output, final_1, 1);\n}\n\ntemplate <>\nEIGEN_STRONG_INLINE float predux<Packet16f>(const Packet16f& a) {\n  //#ifdef EIGEN_VECTORIZE_AVX512DQ\n#if 0\n  Packet8f lane0 = _mm512_extractf32x8_ps(a, 0);\n  Packet8f lane1 = _mm512_extractf32x8_ps(a, 1);\n  Packet8f sum = padd(lane0, lane1);\n  Packet8f tmp0 = _mm256_hadd_ps(sum, _mm256_permute2f128_ps(a, a, 1));\n  tmp0 = _mm256_hadd_ps(tmp0, tmp0);\n  return pfirst(_mm256_hadd_ps(tmp0, tmp0));\n#else\n  Packet4f lane0 = _mm512_extractf32x4_ps(a, 0);\n  Packet4f lane1 = _mm512_extractf32x4_ps(a, 1);\n  Packet4f lane2 = _mm512_extractf32x4_ps(a, 2);\n  Packet4f lane3 = _mm512_extractf32x4_ps(a, 3);\n  Packet4f sum = padd(padd(lane0, lane1), padd(lane2, lane3));\n  sum = _mm_hadd_ps(sum, sum);\n  sum = _mm_hadd_ps(sum, _mm_permute_ps(sum, 1));\n  return pfirst(sum);\n#endif\n}\ntemplate <>\nEIGEN_STRONG_INLINE double predux<Packet8d>(const Packet8d& a) {\n  Packet4d lane0 = _mm512_extractf64x4_pd(a, 0);\n  Packet4d lane1 = _mm512_extractf64x4_pd(a, 1);\n  Packet4d sum = padd(lane0, lane1);\n  Packet4d tmp0 = _mm256_hadd_pd(sum, _mm256_permute2f128_pd(sum, sum, 1));\n  return pfirst(_mm256_hadd_pd(tmp0, tmp0));\n}\n\ntemplate <>\nEIGEN_STRONG_INLINE Packet8f predux_downto4<Packet16f>(const Packet16f& a) {\n#ifdef EIGEN_VECTORIZE_AVX512DQ\n  Packet8f lane0 = _mm512_extractf32x8_ps(a, 0);\n  Packet8f lane1 = _mm512_extractf32x8_ps(a, 1);\n  return padd(lane0, lane1);\n#else\n  Packet4f lane0 = _mm512_extractf32x4_ps(a, 0);\n  Packet4f lane1 = _mm512_extractf32x4_ps(a, 1);\n  Packet4f lane2 = _mm512_extractf32x4_ps(a, 2);\n  Packet4f lane3 = _mm512_extractf32x4_ps(a, 3);\n  Packet4f sum0 = padd(lane0, lane2);\n  Packet4f sum1 = padd(lane1, lane3);\n  return _mm256_insertf128_ps(_mm256_castps128_ps256(sum0), sum1, 1);\n#endif\n}\ntemplate <>\nEIGEN_STRONG_INLINE Packet4d predux_downto4<Packet8d>(const Packet8d& a) {\n  Packet4d lane0 = _mm512_extractf64x4_pd(a, 0);\n  Packet4d lane1 = _mm512_extractf64x4_pd(a, 1);\n  Packet4d res = padd(lane0, lane1);\n  return res;\n}\n\ntemplate <>\nEIGEN_STRONG_INLINE float predux_mul<Packet16f>(const Packet16f& a) {\n//#ifdef EIGEN_VECTORIZE_AVX512DQ\n#if 0\n  Packet8f lane0 = _mm512_extractf32x8_ps(a, 0);\n  Packet8f lane1 = _mm512_extractf32x8_ps(a, 1);\n  Packet8f res = pmul(lane0, lane1);\n  res = pmul(res, _mm256_permute2f128_ps(res, res, 1));\n  res = pmul(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 3, 2)));\n  return pfirst(pmul(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 0, 1))));\n#else\n  Packet4f lane0 = _mm512_extractf32x4_ps(a, 0);\n  Packet4f lane1 = _mm512_extractf32x4_ps(a, 1);\n  Packet4f lane2 = _mm512_extractf32x4_ps(a, 2);\n  Packet4f lane3 = _mm512_extractf32x4_ps(a, 3);\n  Packet4f res = pmul(pmul(lane0, lane1), pmul(lane2, lane3));\n  res = pmul(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 3, 2)));\n  return pfirst(pmul(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 0, 1))));\n#endif\n}\ntemplate <>\nEIGEN_STRONG_INLINE double predux_mul<Packet8d>(const Packet8d& a) {\n  Packet4d lane0 = _mm512_extractf64x4_pd(a, 0);\n  Packet4d lane1 = _mm512_extractf64x4_pd(a, 1);\n  Packet4d res = pmul(lane0, lane1);\n  res = pmul(res, _mm256_permute2f128_pd(res, res, 1));\n  return pfirst(pmul(res, _mm256_shuffle_pd(res, res, 1)));\n}\n\ntemplate <>\nEIGEN_STRONG_INLINE float predux_min<Packet16f>(const Packet16f& a) {\n  Packet4f lane0 = _mm512_extractf32x4_ps(a, 0);\n  Packet4f lane1 = _mm512_extractf32x4_ps(a, 1);\n  Packet4f lane2 = _mm512_extractf32x4_ps(a, 2);\n  Packet4f lane3 = _mm512_extractf32x4_ps(a, 3);\n  Packet4f res = _mm_min_ps(_mm_min_ps(lane0, lane1), _mm_min_ps(lane2, lane3));\n  res = _mm_min_ps(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 3, 2)));\n  return pfirst(_mm_min_ps(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 0, 1))));\n}\ntemplate <>\nEIGEN_STRONG_INLINE double predux_min<Packet8d>(const Packet8d& a) {\n  Packet4d lane0 = _mm512_extractf64x4_pd(a, 0);\n  Packet4d lane1 = _mm512_extractf64x4_pd(a, 1);\n  Packet4d res = _mm256_min_pd(lane0, lane1);\n  res = _mm256_min_pd(res, _mm256_permute2f128_pd(res, res, 1));\n  return pfirst(_mm256_min_pd(res, _mm256_shuffle_pd(res, res, 1)));\n}\n\ntemplate <>\nEIGEN_STRONG_INLINE float predux_max<Packet16f>(const Packet16f& a) {\n  Packet4f lane0 = _mm512_extractf32x4_ps(a, 0);\n  Packet4f lane1 = _mm512_extractf32x4_ps(a, 1);\n  Packet4f lane2 = _mm512_extractf32x4_ps(a, 2);\n  Packet4f lane3 = _mm512_extractf32x4_ps(a, 3);\n  Packet4f res = _mm_max_ps(_mm_max_ps(lane0, lane1), _mm_max_ps(lane2, lane3));\n  res = _mm_max_ps(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 3, 2)));\n  return pfirst(_mm_max_ps(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 0, 1))));\n}\ntemplate <>\nEIGEN_STRONG_INLINE double predux_max<Packet8d>(const Packet8d& a) {\n  Packet4d lane0 = _mm512_extractf64x4_pd(a, 0);\n  Packet4d lane1 = _mm512_extractf64x4_pd(a, 1);\n  Packet4d res = _mm256_max_pd(lane0, lane1);\n  res = _mm256_max_pd(res, _mm256_permute2f128_pd(res, res, 1));\n  return pfirst(_mm256_max_pd(res, _mm256_shuffle_pd(res, res, 1)));\n}\n\ntemplate <int Offset>\nstruct palign_impl<Offset, Packet16f> {\n  static EIGEN_STRONG_INLINE void run(Packet16f& first,\n                                      const Packet16f& second) {\n    if (Offset != 0) {\n      __m512i first_idx = _mm512_set_epi32(\n          Offset + 15, Offset + 14, Offset + 13, Offset + 12, Offset + 11,\n          Offset + 10, Offset + 9, Offset + 8, Offset + 7, Offset + 6,\n          Offset + 5, Offset + 4, Offset + 3, Offset + 2, Offset + 1, Offset);\n\n      __m512i second_idx =\n          _mm512_set_epi32(Offset - 1, Offset - 2, Offset - 3, Offset - 4,\n                           Offset - 5, Offset - 6, Offset - 7, Offset - 8,\n                           Offset - 9, Offset - 10, Offset - 11, Offset - 12,\n                           Offset - 13, Offset - 14, Offset - 15, Offset - 16);\n\n      unsigned short mask = 0xFFFF;\n      mask <<= (16 - Offset);\n\n      first = _mm512_permutexvar_ps(first_idx, first);\n      Packet16f tmp = _mm512_permutexvar_ps(second_idx, second);\n      first = _mm512_mask_blend_ps(mask, first, tmp);\n    }\n  }\n};\ntemplate <int Offset>\nstruct palign_impl<Offset, Packet8d> {\n  static EIGEN_STRONG_INLINE void run(Packet8d& first, const Packet8d& second) {\n    if (Offset != 0) {\n      __m512i first_idx = _mm512_set_epi32(\n          0, Offset + 7, 0, Offset + 6, 0, Offset + 5, 0, Offset + 4, 0,\n          Offset + 3, 0, Offset + 2, 0, Offset + 1, 0, Offset);\n\n      __m512i second_idx = _mm512_set_epi32(\n          0, Offset - 1, 0, Offset - 2, 0, Offset - 3, 0, Offset - 4, 0,\n          Offset - 5, 0, Offset - 6, 0, Offset - 7, 0, Offset - 8);\n\n      unsigned char mask = 0xFF;\n      mask <<= (8 - Offset);\n\n      first = _mm512_permutexvar_pd(first_idx, first);\n      Packet8d tmp = _mm512_permutexvar_pd(second_idx, second);\n      first = _mm512_mask_blend_pd(mask, first, tmp);\n    }\n  }\n};\n\n\n#define PACK_OUTPUT(OUTPUT, INPUT, INDEX, STRIDE) \\\n  EIGEN_INSERT_8f_INTO_16f(OUTPUT[INDEX], INPUT[INDEX], INPUT[INDEX + STRIDE]);\n\nEIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet16f, 16>& kernel) {\n  __m512 T0 = _mm512_unpacklo_ps(kernel.packet[0], kernel.packet[1]);\n  __m512 T1 = _mm512_unpackhi_ps(kernel.packet[0], kernel.packet[1]);\n  __m512 T2 = _mm512_unpacklo_ps(kernel.packet[2], kernel.packet[3]);\n  __m512 T3 = _mm512_unpackhi_ps(kernel.packet[2], kernel.packet[3]);\n  __m512 T4 = _mm512_unpacklo_ps(kernel.packet[4], kernel.packet[5]);\n  __m512 T5 = _mm512_unpackhi_ps(kernel.packet[4], kernel.packet[5]);\n  __m512 T6 = _mm512_unpacklo_ps(kernel.packet[6], kernel.packet[7]);\n  __m512 T7 = _mm512_unpackhi_ps(kernel.packet[6], kernel.packet[7]);\n  __m512 T8 = _mm512_unpacklo_ps(kernel.packet[8], kernel.packet[9]);\n  __m512 T9 = _mm512_unpackhi_ps(kernel.packet[8], kernel.packet[9]);\n  __m512 T10 = _mm512_unpacklo_ps(kernel.packet[10], kernel.packet[11]);\n  __m512 T11 = _mm512_unpackhi_ps(kernel.packet[10], kernel.packet[11]);\n  __m512 T12 = _mm512_unpacklo_ps(kernel.packet[12], kernel.packet[13]);\n  __m512 T13 = _mm512_unpackhi_ps(kernel.packet[12], kernel.packet[13]);\n  __m512 T14 = _mm512_unpacklo_ps(kernel.packet[14], kernel.packet[15]);\n  __m512 T15 = _mm512_unpackhi_ps(kernel.packet[14], kernel.packet[15]);\n  __m512 S0 = _mm512_shuffle_ps(T0, T2, _MM_SHUFFLE(1, 0, 1, 0));\n  __m512 S1 = _mm512_shuffle_ps(T0, T2, _MM_SHUFFLE(3, 2, 3, 2));\n  __m512 S2 = _mm512_shuffle_ps(T1, T3, _MM_SHUFFLE(1, 0, 1, 0));\n  __m512 S3 = _mm512_shuffle_ps(T1, T3, _MM_SHUFFLE(3, 2, 3, 2));\n  __m512 S4 = _mm512_shuffle_ps(T4, T6, _MM_SHUFFLE(1, 0, 1, 0));\n  __m512 S5 = _mm512_shuffle_ps(T4, T6, _MM_SHUFFLE(3, 2, 3, 2));\n  __m512 S6 = _mm512_shuffle_ps(T5, T7, _MM_SHUFFLE(1, 0, 1, 0));\n  __m512 S7 = _mm512_shuffle_ps(T5, T7, _MM_SHUFFLE(3, 2, 3, 2));\n  __m512 S8 = _mm512_shuffle_ps(T8, T10, _MM_SHUFFLE(1, 0, 1, 0));\n  __m512 S9 = _mm512_shuffle_ps(T8, T10, _MM_SHUFFLE(3, 2, 3, 2));\n  __m512 S10 = _mm512_shuffle_ps(T9, T11, _MM_SHUFFLE(1, 0, 1, 0));\n  __m512 S11 = _mm512_shuffle_ps(T9, T11, _MM_SHUFFLE(3, 2, 3, 2));\n  __m512 S12 = _mm512_shuffle_ps(T12, T14, _MM_SHUFFLE(1, 0, 1, 0));\n  __m512 S13 = _mm512_shuffle_ps(T12, T14, _MM_SHUFFLE(3, 2, 3, 2));\n  __m512 S14 = _mm512_shuffle_ps(T13, T15, _MM_SHUFFLE(1, 0, 1, 0));\n  __m512 S15 = _mm512_shuffle_ps(T13, T15, _MM_SHUFFLE(3, 2, 3, 2));\n\n  EIGEN_EXTRACT_8f_FROM_16f(S0, S0);\n  EIGEN_EXTRACT_8f_FROM_16f(S1, S1);\n  EIGEN_EXTRACT_8f_FROM_16f(S2, S2);\n  EIGEN_EXTRACT_8f_FROM_16f(S3, S3);\n  EIGEN_EXTRACT_8f_FROM_16f(S4, S4);\n  EIGEN_EXTRACT_8f_FROM_16f(S5, S5);\n  EIGEN_EXTRACT_8f_FROM_16f(S6, S6);\n  EIGEN_EXTRACT_8f_FROM_16f(S7, S7);\n  EIGEN_EXTRACT_8f_FROM_16f(S8, S8);\n  EIGEN_EXTRACT_8f_FROM_16f(S9, S9);\n  EIGEN_EXTRACT_8f_FROM_16f(S10, S10);\n  EIGEN_EXTRACT_8f_FROM_16f(S11, S11);\n  EIGEN_EXTRACT_8f_FROM_16f(S12, S12);\n  EIGEN_EXTRACT_8f_FROM_16f(S13, S13);\n  EIGEN_EXTRACT_8f_FROM_16f(S14, S14);\n  EIGEN_EXTRACT_8f_FROM_16f(S15, S15);\n\n  PacketBlock<Packet8f, 32> tmp;\n\n  tmp.packet[0] = _mm256_permute2f128_ps(S0_0, S4_0, 0x20);\n  tmp.packet[1] = _mm256_permute2f128_ps(S1_0, S5_0, 0x20);\n  tmp.packet[2] = _mm256_permute2f128_ps(S2_0, S6_0, 0x20);\n  tmp.packet[3] = _mm256_permute2f128_ps(S3_0, S7_0, 0x20);\n  tmp.packet[4] = _mm256_permute2f128_ps(S0_0, S4_0, 0x31);\n  tmp.packet[5] = _mm256_permute2f128_ps(S1_0, S5_0, 0x31);\n  tmp.packet[6] = _mm256_permute2f128_ps(S2_0, S6_0, 0x31);\n  tmp.packet[7] = _mm256_permute2f128_ps(S3_0, S7_0, 0x31);\n\n  tmp.packet[8] = _mm256_permute2f128_ps(S0_1, S4_1, 0x20);\n  tmp.packet[9] = _mm256_permute2f128_ps(S1_1, S5_1, 0x20);\n  tmp.packet[10] = _mm256_permute2f128_ps(S2_1, S6_1, 0x20);\n  tmp.packet[11] = _mm256_permute2f128_ps(S3_1, S7_1, 0x20);\n  tmp.packet[12] = _mm256_permute2f128_ps(S0_1, S4_1, 0x31);\n  tmp.packet[13] = _mm256_permute2f128_ps(S1_1, S5_1, 0x31);\n  tmp.packet[14] = _mm256_permute2f128_ps(S2_1, S6_1, 0x31);\n  tmp.packet[15] = _mm256_permute2f128_ps(S3_1, S7_1, 0x31);\n\n  // Second set of _m256 outputs\n  tmp.packet[16] = _mm256_permute2f128_ps(S8_0, S12_0, 0x20);\n  tmp.packet[17] = _mm256_permute2f128_ps(S9_0, S13_0, 0x20);\n  tmp.packet[18] = _mm256_permute2f128_ps(S10_0, S14_0, 0x20);\n  tmp.packet[19] = _mm256_permute2f128_ps(S11_0, S15_0, 0x20);\n  tmp.packet[20] = _mm256_permute2f128_ps(S8_0, S12_0, 0x31);\n  tmp.packet[21] = _mm256_permute2f128_ps(S9_0, S13_0, 0x31);\n  tmp.packet[22] = _mm256_permute2f128_ps(S10_0, S14_0, 0x31);\n  tmp.packet[23] = _mm256_permute2f128_ps(S11_0, S15_0, 0x31);\n\n  tmp.packet[24] = _mm256_permute2f128_ps(S8_1, S12_1, 0x20);\n  tmp.packet[25] = _mm256_permute2f128_ps(S9_1, S13_1, 0x20);\n  tmp.packet[26] = _mm256_permute2f128_ps(S10_1, S14_1, 0x20);\n  tmp.packet[27] = _mm256_permute2f128_ps(S11_1, S15_1, 0x20);\n  tmp.packet[28] = _mm256_permute2f128_ps(S8_1, S12_1, 0x31);\n  tmp.packet[29] = _mm256_permute2f128_ps(S9_1, S13_1, 0x31);\n  tmp.packet[30] = _mm256_permute2f128_ps(S10_1, S14_1, 0x31);\n  tmp.packet[31] = _mm256_permute2f128_ps(S11_1, S15_1, 0x31);\n\n  // Pack them into the output\n  PACK_OUTPUT(kernel.packet, tmp.packet, 0, 16);\n  PACK_OUTPUT(kernel.packet, tmp.packet, 1, 16);\n  PACK_OUTPUT(kernel.packet, tmp.packet, 2, 16);\n  PACK_OUTPUT(kernel.packet, tmp.packet, 3, 16);\n\n  PACK_OUTPUT(kernel.packet, tmp.packet, 4, 16);\n  PACK_OUTPUT(kernel.packet, tmp.packet, 5, 16);\n  PACK_OUTPUT(kernel.packet, tmp.packet, 6, 16);\n  PACK_OUTPUT(kernel.packet, tmp.packet, 7, 16);\n\n  PACK_OUTPUT(kernel.packet, tmp.packet, 8, 16);\n  PACK_OUTPUT(kernel.packet, tmp.packet, 9, 16);\n  PACK_OUTPUT(kernel.packet, tmp.packet, 10, 16);\n  PACK_OUTPUT(kernel.packet, tmp.packet, 11, 16);\n\n  PACK_OUTPUT(kernel.packet, tmp.packet, 12, 16);\n  PACK_OUTPUT(kernel.packet, tmp.packet, 13, 16);\n  PACK_OUTPUT(kernel.packet, tmp.packet, 14, 16);\n  PACK_OUTPUT(kernel.packet, tmp.packet, 15, 16);\n}\n#define PACK_OUTPUT_2(OUTPUT, INPUT, INDEX, STRIDE)         \\\n  EIGEN_INSERT_8f_INTO_16f(OUTPUT[INDEX], INPUT[2 * INDEX], \\\n                           INPUT[2 * INDEX + STRIDE]);\n\nEIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet16f, 4>& kernel) {\n  __m512 T0 = _mm512_unpacklo_ps(kernel.packet[0], kernel.packet[1]);\n  __m512 T1 = _mm512_unpackhi_ps(kernel.packet[0], kernel.packet[1]);\n  __m512 T2 = _mm512_unpacklo_ps(kernel.packet[2], kernel.packet[3]);\n  __m512 T3 = _mm512_unpackhi_ps(kernel.packet[2], kernel.packet[3]);\n\n  __m512 S0 = _mm512_shuffle_ps(T0, T2, _MM_SHUFFLE(1, 0, 1, 0));\n  __m512 S1 = _mm512_shuffle_ps(T0, T2, _MM_SHUFFLE(3, 2, 3, 2));\n  __m512 S2 = _mm512_shuffle_ps(T1, T3, _MM_SHUFFLE(1, 0, 1, 0));\n  __m512 S3 = _mm512_shuffle_ps(T1, T3, _MM_SHUFFLE(3, 2, 3, 2));\n\n  EIGEN_EXTRACT_8f_FROM_16f(S0, S0);\n  EIGEN_EXTRACT_8f_FROM_16f(S1, S1);\n  EIGEN_EXTRACT_8f_FROM_16f(S2, S2);\n  EIGEN_EXTRACT_8f_FROM_16f(S3, S3);\n\n  PacketBlock<Packet8f, 8> tmp;\n\n  tmp.packet[0] = _mm256_permute2f128_ps(S0_0, S1_0, 0x20);\n  tmp.packet[1] = _mm256_permute2f128_ps(S2_0, S3_0, 0x20);\n  tmp.packet[2] = _mm256_permute2f128_ps(S0_0, S1_0, 0x31);\n  tmp.packet[3] = _mm256_permute2f128_ps(S2_0, S3_0, 0x31);\n\n  tmp.packet[4] = _mm256_permute2f128_ps(S0_1, S1_1, 0x20);\n  tmp.packet[5] = _mm256_permute2f128_ps(S2_1, S3_1, 0x20);\n  tmp.packet[6] = _mm256_permute2f128_ps(S0_1, S1_1, 0x31);\n  tmp.packet[7] = _mm256_permute2f128_ps(S2_1, S3_1, 0x31);\n\n  PACK_OUTPUT_2(kernel.packet, tmp.packet, 0, 1);\n  PACK_OUTPUT_2(kernel.packet, tmp.packet, 1, 1);\n  PACK_OUTPUT_2(kernel.packet, tmp.packet, 2, 1);\n  PACK_OUTPUT_2(kernel.packet, tmp.packet, 3, 1);\n}\n\n#define PACK_OUTPUT_SQ_D(OUTPUT, INPUT, INDEX, STRIDE)                \\\n  OUTPUT[INDEX] = _mm512_insertf64x4(OUTPUT[INDEX], INPUT[INDEX], 0); \\\n  OUTPUT[INDEX] = _mm512_insertf64x4(OUTPUT[INDEX], INPUT[INDEX + STRIDE], 1);\n\n#define PACK_OUTPUT_D(OUTPUT, INPUT, INDEX, STRIDE)                         \\\n  OUTPUT[INDEX] = _mm512_insertf64x4(OUTPUT[INDEX], INPUT[(2 * INDEX)], 0); \\\n  OUTPUT[INDEX] =                                                           \\\n      _mm512_insertf64x4(OUTPUT[INDEX], INPUT[(2 * INDEX) + STRIDE], 1);\n\nEIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet8d, 4>& kernel) {\n  __m512d T0 = _mm512_shuffle_pd(kernel.packet[0], kernel.packet[1], 0);\n  __m512d T1 = _mm512_shuffle_pd(kernel.packet[0], kernel.packet[1], 0xff);\n  __m512d T2 = _mm512_shuffle_pd(kernel.packet[2], kernel.packet[3], 0);\n  __m512d T3 = _mm512_shuffle_pd(kernel.packet[2], kernel.packet[3], 0xff);\n\n  PacketBlock<Packet4d, 8> tmp;\n\n  tmp.packet[0] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 0),\n                                         _mm512_extractf64x4_pd(T2, 0), 0x20);\n  tmp.packet[1] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 0),\n                                         _mm512_extractf64x4_pd(T3, 0), 0x20);\n  tmp.packet[2] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 0),\n                                         _mm512_extractf64x4_pd(T2, 0), 0x31);\n  tmp.packet[3] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 0),\n                                         _mm512_extractf64x4_pd(T3, 0), 0x31);\n\n  tmp.packet[4] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 1),\n                                         _mm512_extractf64x4_pd(T2, 1), 0x20);\n  tmp.packet[5] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 1),\n                                         _mm512_extractf64x4_pd(T3, 1), 0x20);\n  tmp.packet[6] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 1),\n                                         _mm512_extractf64x4_pd(T2, 1), 0x31);\n  tmp.packet[7] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 1),\n                                         _mm512_extractf64x4_pd(T3, 1), 0x31);\n\n  PACK_OUTPUT_D(kernel.packet, tmp.packet, 0, 1);\n  PACK_OUTPUT_D(kernel.packet, tmp.packet, 1, 1);\n  PACK_OUTPUT_D(kernel.packet, tmp.packet, 2, 1);\n  PACK_OUTPUT_D(kernel.packet, tmp.packet, 3, 1);\n}\n\nEIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet8d, 8>& kernel) {\n  __m512d T0 = _mm512_unpacklo_pd(kernel.packet[0], kernel.packet[1]);\n  __m512d T1 = _mm512_unpackhi_pd(kernel.packet[0], kernel.packet[1]);\n  __m512d T2 = _mm512_unpacklo_pd(kernel.packet[2], kernel.packet[3]);\n  __m512d T3 = _mm512_unpackhi_pd(kernel.packet[2], kernel.packet[3]);\n  __m512d T4 = _mm512_unpacklo_pd(kernel.packet[4], kernel.packet[5]);\n  __m512d T5 = _mm512_unpackhi_pd(kernel.packet[4], kernel.packet[5]);\n  __m512d T6 = _mm512_unpacklo_pd(kernel.packet[6], kernel.packet[7]);\n  __m512d T7 = _mm512_unpackhi_pd(kernel.packet[6], kernel.packet[7]);\n\n  PacketBlock<Packet4d, 16> tmp;\n\n  tmp.packet[0] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 0),\n                                         _mm512_extractf64x4_pd(T2, 0), 0x20);\n  tmp.packet[1] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 0),\n                                         _mm512_extractf64x4_pd(T3, 0), 0x20);\n  tmp.packet[2] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 0),\n                                         _mm512_extractf64x4_pd(T2, 0), 0x31);\n  tmp.packet[3] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 0),\n                                         _mm512_extractf64x4_pd(T3, 0), 0x31);\n\n  tmp.packet[4] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 1),\n                                         _mm512_extractf64x4_pd(T2, 1), 0x20);\n  tmp.packet[5] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 1),\n                                         _mm512_extractf64x4_pd(T3, 1), 0x20);\n  tmp.packet[6] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 1),\n                                         _mm512_extractf64x4_pd(T2, 1), 0x31);\n  tmp.packet[7] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 1),\n                                         _mm512_extractf64x4_pd(T3, 1), 0x31);\n\n  tmp.packet[8] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T4, 0),\n                                         _mm512_extractf64x4_pd(T6, 0), 0x20);\n  tmp.packet[9] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T5, 0),\n                                         _mm512_extractf64x4_pd(T7, 0), 0x20);\n  tmp.packet[10] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T4, 0),\n                                          _mm512_extractf64x4_pd(T6, 0), 0x31);\n  tmp.packet[11] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T5, 0),\n                                          _mm512_extractf64x4_pd(T7, 0), 0x31);\n\n  tmp.packet[12] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T4, 1),\n                                          _mm512_extractf64x4_pd(T6, 1), 0x20);\n  tmp.packet[13] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T5, 1),\n                                          _mm512_extractf64x4_pd(T7, 1), 0x20);\n  tmp.packet[14] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T4, 1),\n                                          _mm512_extractf64x4_pd(T6, 1), 0x31);\n  tmp.packet[15] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T5, 1),\n                                          _mm512_extractf64x4_pd(T7, 1), 0x31);\n\n  PACK_OUTPUT_SQ_D(kernel.packet, tmp.packet, 0, 8);\n  PACK_OUTPUT_SQ_D(kernel.packet, tmp.packet, 1, 8);\n  PACK_OUTPUT_SQ_D(kernel.packet, tmp.packet, 2, 8);\n  PACK_OUTPUT_SQ_D(kernel.packet, tmp.packet, 3, 8);\n\n  PACK_OUTPUT_SQ_D(kernel.packet, tmp.packet, 4, 8);\n  PACK_OUTPUT_SQ_D(kernel.packet, tmp.packet, 5, 8);\n  PACK_OUTPUT_SQ_D(kernel.packet, tmp.packet, 6, 8);\n  PACK_OUTPUT_SQ_D(kernel.packet, tmp.packet, 7, 8);\n}\ntemplate <>\nEIGEN_STRONG_INLINE Packet16f pblend(const Selector<16>& /*ifPacket*/,\n                                     const Packet16f& /*thenPacket*/,\n                                     const Packet16f& /*elsePacket*/) {\n  assert(false && \"To be implemented\");\n  return Packet16f();\n}\ntemplate <>\nEIGEN_STRONG_INLINE Packet8d pblend(const Selector<8>& /*ifPacket*/,\n                                    const Packet8d& /*thenPacket*/,\n                                    const Packet8d& /*elsePacket*/) {\n  assert(false && \"To be implemented\");\n  return Packet8d();\n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_PACKET_MATH_AVX512_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/arch/AltiVec/Complex.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2010-2016 Konstantinos Margaritis <markos@freevec.org>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_COMPLEX32_ALTIVEC_H\n#define EIGEN_COMPLEX32_ALTIVEC_H\n\nnamespace Eigen {\n\nnamespace internal {\n\nstatic Packet4ui  p4ui_CONJ_XOR = vec_mergeh((Packet4ui)p4i_ZERO, (Packet4ui)p4f_MZERO);//{ 0x00000000, 0x80000000, 0x00000000, 0x80000000 };\n#ifdef __VSX__\n#if defined(_BIG_ENDIAN)\nstatic Packet2ul  p2ul_CONJ_XOR1 = (Packet2ul) vec_sld((Packet4ui) p2d_MZERO, (Packet4ui) p2l_ZERO, 8);//{ 0x8000000000000000, 0x0000000000000000 };\nstatic Packet2ul  p2ul_CONJ_XOR2 = (Packet2ul) vec_sld((Packet4ui) p2l_ZERO,  (Packet4ui) p2d_MZERO, 8);//{ 0x8000000000000000, 0x0000000000000000 };\n#else\nstatic Packet2ul  p2ul_CONJ_XOR1 = (Packet2ul) vec_sld((Packet4ui) p2l_ZERO,  (Packet4ui) p2d_MZERO, 8);//{ 0x8000000000000000, 0x0000000000000000 };\nstatic Packet2ul  p2ul_CONJ_XOR2 = (Packet2ul) vec_sld((Packet4ui) p2d_MZERO, (Packet4ui) p2l_ZERO, 8);//{ 0x8000000000000000, 0x0000000000000000 };\n#endif\n#endif\n\n//---------- float ----------\nstruct Packet2cf\n{\n  EIGEN_STRONG_INLINE explicit Packet2cf() : v(p4f_ZERO) {}\n  EIGEN_STRONG_INLINE explicit Packet2cf(const Packet4f& a) : v(a) {}\n  Packet4f  v;\n};\n\ntemplate<> struct packet_traits<std::complex<float> >  : default_packet_traits\n{\n  typedef Packet2cf type;\n  typedef Packet2cf half;\n  enum {\n    Vectorizable = 1,\n    AlignedOnScalar = 1,\n    size = 2,\n    HasHalfPacket = 0,\n\n    HasAdd    = 1,\n    HasSub    = 1,\n    HasMul    = 1,\n    HasDiv    = 1,\n    HasNegate = 1,\n    HasAbs    = 0,\n    HasAbs2   = 0,\n    HasMin    = 0,\n    HasMax    = 0,\n#ifdef __VSX__\n    HasBlend  = 1,\n#endif\n    HasSetLinear = 0\n  };\n};\n\ntemplate<> struct unpacket_traits<Packet2cf> { typedef std::complex<float> type; enum {size=2, alignment=Aligned16}; typedef Packet2cf half; };\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pset1<Packet2cf>(const std::complex<float>&  from)\n{\n  Packet2cf res;\n  if((std::ptrdiff_t(&from) % 16) == 0)\n    res.v = pload<Packet4f>((const float *)&from);\n  else\n    res.v = ploadu<Packet4f>((const float *)&from);\n  res.v = vec_perm(res.v, res.v, p16uc_PSET64_HI);\n  return res;\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pload<Packet2cf>(const std::complex<float>*        from) { return Packet2cf(pload<Packet4f>((const float *) from)); }\ntemplate<> EIGEN_STRONG_INLINE Packet2cf ploadu<Packet2cf>(const std::complex<float>*       from) { return Packet2cf(ploadu<Packet4f>((const float*) from)); }\ntemplate<> EIGEN_STRONG_INLINE Packet2cf ploaddup<Packet2cf>(const std::complex<float>*     from) { return pset1<Packet2cf>(*from); }\n\ntemplate<> EIGEN_STRONG_INLINE void pstore <std::complex<float> >(std::complex<float> *   to, const Packet2cf& from) { pstore((float*)to, from.v); }\ntemplate<> EIGEN_STRONG_INLINE void pstoreu<std::complex<float> >(std::complex<float> *   to, const Packet2cf& from) { pstoreu((float*)to, from.v); }\n\ntemplate<> EIGEN_DEVICE_FUNC inline Packet2cf pgather<std::complex<float>, Packet2cf>(const std::complex<float>* from, Index stride)\n{\n  std::complex<float> EIGEN_ALIGN16 af[2];\n  af[0] = from[0*stride];\n  af[1] = from[1*stride];\n  return pload<Packet2cf>(af);\n}\ntemplate<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<float>, Packet2cf>(std::complex<float>* to, const Packet2cf& from, Index stride)\n{\n  std::complex<float> EIGEN_ALIGN16 af[2];\n  pstore<std::complex<float> >((std::complex<float> *) af, from);\n  to[0*stride] = af[0];\n  to[1*stride] = af[1];\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cf padd<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(a.v + b.v); }\ntemplate<> EIGEN_STRONG_INLINE Packet2cf psub<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(a.v - b.v); }\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pnegate(const Packet2cf& a) { return Packet2cf(pnegate(a.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pconj(const Packet2cf& a) { return Packet2cf(pxor<Packet4f>(a.v, reinterpret_cast<Packet4f>(p4ui_CONJ_XOR))); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pmul<Packet2cf>(const Packet2cf& a, const Packet2cf& b)\n{\n  Packet4f v1, v2;\n\n  // Permute and multiply the real parts of a and b\n  v1 = vec_perm(a.v, a.v, p16uc_PSET32_WODD);\n  // Get the imaginary parts of a\n  v2 = vec_perm(a.v, a.v, p16uc_PSET32_WEVEN);\n  // multiply a_re * b \n  v1 = vec_madd(v1, b.v, p4f_ZERO);\n  // multiply a_im * b and get the conjugate result\n  v2 = vec_madd(v2, b.v, p4f_ZERO);\n  v2 = reinterpret_cast<Packet4f>(pxor(v2, reinterpret_cast<Packet4f>(p4ui_CONJ_XOR)));\n  // permute back to a proper order\n  v2 = vec_perm(v2, v2, p16uc_COMPLEX32_REV);\n  \n  return Packet2cf(padd<Packet4f>(v1, v2));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pand   <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(pand<Packet4f>(a.v, b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet2cf por    <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(por<Packet4f>(a.v, b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pxor   <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(pxor<Packet4f>(a.v, b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pandnot<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(pandnot<Packet4f>(a.v, b.v)); }\n\ntemplate<> EIGEN_STRONG_INLINE void prefetch<std::complex<float> >(const std::complex<float> * addr)    { EIGEN_PPC_PREFETCH(addr); }\n\ntemplate<> EIGEN_STRONG_INLINE std::complex<float>  pfirst<Packet2cf>(const Packet2cf& a)\n{\n  std::complex<float> EIGEN_ALIGN16 res[2];\n  pstore((float *)&res, a.v);\n\n  return res[0];\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cf preverse(const Packet2cf& a)\n{\n  Packet4f rev_a;\n  rev_a = vec_perm(a.v, a.v, p16uc_COMPLEX32_REV2);\n  return Packet2cf(rev_a);\n}\n\ntemplate<> EIGEN_STRONG_INLINE std::complex<float> predux<Packet2cf>(const Packet2cf& a)\n{\n  Packet4f b;\n  b = vec_sld(a.v, a.v, 8);\n  b = padd<Packet4f>(a.v, b);\n  return pfirst<Packet2cf>(Packet2cf(b));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cf preduxp<Packet2cf>(const Packet2cf* vecs)\n{\n  Packet4f b1, b2;\n#ifdef _BIG_ENDIAN  \n  b1 = vec_sld(vecs[0].v, vecs[1].v, 8);\n  b2 = vec_sld(vecs[1].v, vecs[0].v, 8);\n#else\n  b1 = vec_sld(vecs[1].v, vecs[0].v, 8);\n  b2 = vec_sld(vecs[0].v, vecs[1].v, 8);\n#endif\n  b2 = vec_sld(b2, b2, 8);\n  b2 = padd<Packet4f>(b1, b2);\n\n  return Packet2cf(b2);\n}\n\ntemplate<> EIGEN_STRONG_INLINE std::complex<float> predux_mul<Packet2cf>(const Packet2cf& a)\n{\n  Packet4f b;\n  Packet2cf prod;\n  b = vec_sld(a.v, a.v, 8);\n  prod = pmul<Packet2cf>(a, Packet2cf(b));\n\n  return pfirst<Packet2cf>(prod);\n}\n\ntemplate<int Offset>\nstruct palign_impl<Offset,Packet2cf>\n{\n  static EIGEN_STRONG_INLINE void run(Packet2cf& first, const Packet2cf& second)\n  {\n    if (Offset==1)\n    {\n#ifdef _BIG_ENDIAN\n      first.v = vec_sld(first.v, second.v, 8);\n#else\n      first.v = vec_sld(second.v, first.v, 8);\n#endif\n    }\n  }\n};\n\ntemplate<> struct conj_helper<Packet2cf, Packet2cf, false,true>\n{\n  EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const\n  { return padd(pmul(x,y),c); }\n\n  EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const\n  {\n    return internal::pmul(a, pconj(b));\n  }\n};\n\ntemplate<> struct conj_helper<Packet2cf, Packet2cf, true,false>\n{\n  EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const\n  { return padd(pmul(x,y),c); }\n\n  EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const\n  {\n    return internal::pmul(pconj(a), b);\n  }\n};\n\ntemplate<> struct conj_helper<Packet2cf, Packet2cf, true,true>\n{\n  EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const\n  { return padd(pmul(x,y),c); }\n\n  EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const\n  {\n    return pconj(internal::pmul(a, b));\n  }\n};\n\nEIGEN_MAKE_CONJ_HELPER_CPLX_REAL(Packet2cf,Packet4f)\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pdiv<Packet2cf>(const Packet2cf& a, const Packet2cf& b)\n{\n  // TODO optimize it for AltiVec\n  Packet2cf res = conj_helper<Packet2cf,Packet2cf,false,true>().pmul(a, b);\n  Packet4f s = pmul<Packet4f>(b.v, b.v);\n  return Packet2cf(pdiv(res.v, padd<Packet4f>(s, vec_perm(s, s, p16uc_COMPLEX32_REV))));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pcplxflip<Packet2cf>(const Packet2cf& x)\n{\n  return Packet2cf(vec_perm(x.v, x.v, p16uc_COMPLEX32_REV));\n}\n\nEIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet2cf,2>& kernel)\n{\n  Packet4f tmp = vec_perm(kernel.packet[0].v, kernel.packet[1].v, p16uc_TRANSPOSE64_HI);\n  kernel.packet[1].v = vec_perm(kernel.packet[0].v, kernel.packet[1].v, p16uc_TRANSPOSE64_LO);\n  kernel.packet[0].v = tmp;\n}\n\n#ifdef __VSX__\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pblend(const Selector<2>& ifPacket, const Packet2cf& thenPacket, const Packet2cf& elsePacket) {\n  Packet2cf result;\n  result.v = reinterpret_cast<Packet4f>(pblend<Packet2d>(ifPacket, reinterpret_cast<Packet2d>(thenPacket.v), reinterpret_cast<Packet2d>(elsePacket.v)));\n  return result;\n}\n#endif\n\n//---------- double ----------\n#ifdef __VSX__\nstruct Packet1cd\n{\n  EIGEN_STRONG_INLINE Packet1cd() {}\n  EIGEN_STRONG_INLINE explicit Packet1cd(const Packet2d& a) : v(a) {}\n  Packet2d v;\n};\n\ntemplate<> struct packet_traits<std::complex<double> >  : default_packet_traits\n{\n  typedef Packet1cd type;\n  typedef Packet1cd half;\n  enum {\n    Vectorizable = 1,\n    AlignedOnScalar = 0,\n    size = 1,\n    HasHalfPacket = 0,\n\n    HasAdd    = 1,\n    HasSub    = 1,\n    HasMul    = 1,\n    HasDiv    = 1,\n    HasNegate = 1,\n    HasAbs    = 0,\n    HasAbs2   = 0,\n    HasMin    = 0,\n    HasMax    = 0,\n    HasSetLinear = 0\n  };\n};\n\ntemplate<> struct unpacket_traits<Packet1cd> { typedef std::complex<double> type; enum {size=1, alignment=Aligned16}; typedef Packet1cd half; };\n\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pload <Packet1cd>(const std::complex<double>* from) { return Packet1cd(pload<Packet2d>((const double*)from)); }\ntemplate<> EIGEN_STRONG_INLINE Packet1cd ploadu<Packet1cd>(const std::complex<double>* from) { return Packet1cd(ploadu<Packet2d>((const double*)from)); }\ntemplate<> EIGEN_STRONG_INLINE void pstore <std::complex<double> >(std::complex<double> *   to, const Packet1cd& from) { pstore((double*)to, from.v); }\ntemplate<> EIGEN_STRONG_INLINE void pstoreu<std::complex<double> >(std::complex<double> *   to, const Packet1cd& from) { pstoreu((double*)to, from.v); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pset1<Packet1cd>(const std::complex<double>&  from)\n{ /* here we really have to use unaligned loads :( */ return ploadu<Packet1cd>(&from); }\n\ntemplate<> EIGEN_DEVICE_FUNC inline Packet1cd pgather<std::complex<double>, Packet1cd>(const std::complex<double>* from, Index stride)\n{\n  std::complex<double> EIGEN_ALIGN16 af[2];\n  af[0] = from[0*stride];\n  af[1] = from[1*stride];\n  return pload<Packet1cd>(af);\n}\ntemplate<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<double>, Packet1cd>(std::complex<double>* to, const Packet1cd& from, Index stride)\n{\n  std::complex<double> EIGEN_ALIGN16 af[2];\n  pstore<std::complex<double> >(af, from);\n  to[0*stride] = af[0];\n  to[1*stride] = af[1];\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet1cd padd<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(a.v + b.v); }\ntemplate<> EIGEN_STRONG_INLINE Packet1cd psub<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(a.v - b.v); }\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pnegate(const Packet1cd& a) { return Packet1cd(pnegate(Packet2d(a.v))); }\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pconj(const Packet1cd& a) { return Packet1cd(pxor(a.v, reinterpret_cast<Packet2d>(p2ul_CONJ_XOR2))); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pmul<Packet1cd>(const Packet1cd& a, const Packet1cd& b)\n{\n  Packet2d a_re, a_im, v1, v2;\n\n  // Permute and multiply the real parts of a and b\n  a_re = vec_perm(a.v, a.v, p16uc_PSET64_HI);\n  // Get the imaginary parts of a\n  a_im = vec_perm(a.v, a.v, p16uc_PSET64_LO);\n  // multiply a_re * b\n  v1 = vec_madd(a_re, b.v, p2d_ZERO);\n  // multiply a_im * b and get the conjugate result\n  v2 = vec_madd(a_im, b.v, p2d_ZERO);\n  v2 = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(v2), reinterpret_cast<Packet4ui>(v2), 8));\n  v2 = pxor(v2, reinterpret_cast<Packet2d>(p2ul_CONJ_XOR1));\n\n  return Packet1cd(padd<Packet2d>(v1, v2));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pand   <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(pand(a.v,b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet1cd por    <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(por(a.v,b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pxor   <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(pxor(a.v,b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pandnot<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(pandnot(a.v, b.v)); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet1cd ploaddup<Packet1cd>(const std::complex<double>*     from)  { return pset1<Packet1cd>(*from); }\n\ntemplate<> EIGEN_STRONG_INLINE void prefetch<std::complex<double> >(const std::complex<double> * addr)    { EIGEN_PPC_PREFETCH(addr); }\n\ntemplate<> EIGEN_STRONG_INLINE std::complex<double>  pfirst<Packet1cd>(const Packet1cd& a)\n{\n  std::complex<double> EIGEN_ALIGN16 res[2];\n  pstore<std::complex<double> >(res, a);\n\n  return res[0];\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet1cd preverse(const Packet1cd& a) { return a; }\n\ntemplate<> EIGEN_STRONG_INLINE std::complex<double> predux<Packet1cd>(const Packet1cd& a) { return pfirst(a); }\ntemplate<> EIGEN_STRONG_INLINE Packet1cd preduxp<Packet1cd>(const Packet1cd* vecs)        { return vecs[0]; }\n\ntemplate<> EIGEN_STRONG_INLINE std::complex<double> predux_mul<Packet1cd>(const Packet1cd& a) { return pfirst(a); }\n\ntemplate<int Offset>\nstruct palign_impl<Offset,Packet1cd>\n{\n  static EIGEN_STRONG_INLINE void run(Packet1cd& /*first*/, const Packet1cd& /*second*/)\n  {\n    // FIXME is it sure we never have to align a Packet1cd?\n    // Even though a std::complex<double> has 16 bytes, it is not necessarily aligned on a 16 bytes boundary...\n  }\n};\n\ntemplate<> struct conj_helper<Packet1cd, Packet1cd, false,true>\n{\n  EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet1cd& x, const Packet1cd& y, const Packet1cd& c) const\n  { return padd(pmul(x,y),c); }\n\n  EIGEN_STRONG_INLINE Packet1cd pmul(const Packet1cd& a, const Packet1cd& b) const\n  {\n    return internal::pmul(a, pconj(b));\n  }\n};\n\ntemplate<> struct conj_helper<Packet1cd, Packet1cd, true,false>\n{\n  EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet1cd& x, const Packet1cd& y, const Packet1cd& c) const\n  { return padd(pmul(x,y),c); }\n\n  EIGEN_STRONG_INLINE Packet1cd pmul(const Packet1cd& a, const Packet1cd& b) const\n  {\n    return internal::pmul(pconj(a), b);\n  }\n};\n\ntemplate<> struct conj_helper<Packet1cd, Packet1cd, true,true>\n{\n  EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet1cd& x, const Packet1cd& y, const Packet1cd& c) const\n  { return padd(pmul(x,y),c); }\n\n  EIGEN_STRONG_INLINE Packet1cd pmul(const Packet1cd& a, const Packet1cd& b) const\n  {\n    return pconj(internal::pmul(a, b));\n  }\n};\n\nEIGEN_MAKE_CONJ_HELPER_CPLX_REAL(Packet1cd,Packet2d)\n\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pdiv<Packet1cd>(const Packet1cd& a, const Packet1cd& b)\n{\n  // TODO optimize it for AltiVec\n  Packet1cd res = conj_helper<Packet1cd,Packet1cd,false,true>().pmul(a,b);\n  Packet2d s = pmul<Packet2d>(b.v, b.v);\n  return Packet1cd(pdiv(res.v, padd<Packet2d>(s, vec_perm(s, s, p16uc_REVERSE64))));\n}\n\nEIGEN_STRONG_INLINE Packet1cd pcplxflip/*<Packet1cd>*/(const Packet1cd& x)\n{\n  return Packet1cd(preverse(Packet2d(x.v)));\n}\n\nEIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet1cd,2>& kernel)\n{\n  Packet2d tmp = vec_perm(kernel.packet[0].v, kernel.packet[1].v, p16uc_TRANSPOSE64_HI);\n  kernel.packet[1].v = vec_perm(kernel.packet[0].v, kernel.packet[1].v, p16uc_TRANSPOSE64_LO);\n  kernel.packet[0].v = tmp;\n}\n#endif // __VSX__\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_COMPLEX32_ALTIVEC_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/arch/AltiVec/MathFunctions.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2007 Julien Pommier\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2016 Konstantinos Margaritis <markos@freevec.org>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n/* The sin, cos, exp, and log functions of this file come from\n * Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/\n */\n\n#ifndef EIGEN_MATH_FUNCTIONS_ALTIVEC_H\n#define EIGEN_MATH_FUNCTIONS_ALTIVEC_H\n\nnamespace Eigen {\n\nnamespace internal {\n\nstatic _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);\nstatic _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);\nstatic _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);\nstatic _EIGEN_DECLARE_CONST_Packet4i(23, 23);\n\nstatic _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(inv_mant_mask, ~0x7f800000);\n\n/* the smallest non denormalized float number */\nstatic _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(min_norm_pos,  0x00800000);\nstatic _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_inf,     0xff800000); // -1.f/0.f\nstatic _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_nan,     0xffffffff);\n  \n/* natural logarithm computed for 4 simultaneous float\n  return NaN for x <= 0\n*/\nstatic _EIGEN_DECLARE_CONST_Packet4f(cephes_SQRTHF, 0.707106781186547524f);\nstatic _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p0, 7.0376836292E-2f);\nstatic _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p1, - 1.1514610310E-1f);\nstatic _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p2, 1.1676998740E-1f);\nstatic _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p3, - 1.2420140846E-1f);\nstatic _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p4, + 1.4249322787E-1f);\nstatic _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p5, - 1.6668057665E-1f);\nstatic _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p6, + 2.0000714765E-1f);\nstatic _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p7, - 2.4999993993E-1f);\nstatic _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p8, + 3.3333331174E-1f);\nstatic _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q1, -2.12194440e-4f);\nstatic _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q2, 0.693359375f);\n\nstatic _EIGEN_DECLARE_CONST_Packet4f(exp_hi,  88.3762626647950f);\nstatic _EIGEN_DECLARE_CONST_Packet4f(exp_lo, -88.3762626647949f);\n\nstatic _EIGEN_DECLARE_CONST_Packet4f(cephes_LOG2EF, 1.44269504088896341f);\nstatic _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C1, 0.693359375f);\nstatic _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C2, -2.12194440e-4f);\n\nstatic _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p0, 1.9875691500E-4f);\nstatic _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p1, 1.3981999507E-3f);\nstatic _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p2, 8.3334519073E-3f);\nstatic _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p3, 4.1665795894E-2f);\nstatic _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459E-1f);\nstatic _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201E-1f);\n\n#ifdef __VSX__\nstatic _EIGEN_DECLARE_CONST_Packet2d(1 , 1.0);\nstatic _EIGEN_DECLARE_CONST_Packet2d(2 , 2.0);\nstatic _EIGEN_DECLARE_CONST_Packet2d(half, 0.5);\n\nstatic _EIGEN_DECLARE_CONST_Packet2d(exp_hi,  709.437);\nstatic _EIGEN_DECLARE_CONST_Packet2d(exp_lo, -709.436139303);\n\nstatic _EIGEN_DECLARE_CONST_Packet2d(cephes_LOG2EF, 1.4426950408889634073599);\n\nstatic _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p0, 1.26177193074810590878e-4);\nstatic _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p1, 3.02994407707441961300e-2);\nstatic _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p2, 9.99999999999999999910e-1);\n\nstatic _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q0, 3.00198505138664455042e-6);\nstatic _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q1, 2.52448340349684104192e-3);\nstatic _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q2, 2.27265548208155028766e-1);\nstatic _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q3, 2.00000000000000000009e0);\n\nstatic _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C1, 0.693145751953125);\nstatic _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C2, 1.42860682030941723212e-6);\n\n#ifdef __POWER8_VECTOR__\nstatic Packet2l p2l_1023 = { 1023, 1023 };\nstatic Packet2ul p2ul_52 = { 52, 52 };\n#endif\n\n#endif\n\ntemplate<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED\nPacket4f plog<Packet4f>(const Packet4f& _x)\n{\n  Packet4f x = _x;\n\n  Packet4i emm0;\n\n  /* isvalid_mask is 0 if x < 0 or x is NaN. */\n  Packet4ui isvalid_mask = reinterpret_cast<Packet4ui>(vec_cmpge(x, p4f_ZERO));\n  Packet4ui iszero_mask = reinterpret_cast<Packet4ui>(vec_cmpeq(x, p4f_ZERO));\n\n  x = pmax(x, p4f_min_norm_pos);  /* cut off denormalized stuff */\n  emm0 = vec_sr(reinterpret_cast<Packet4i>(x),\n                reinterpret_cast<Packet4ui>(p4i_23));\n\n  /* keep only the fractional part */\n  x = pand(x, p4f_inv_mant_mask);\n  x = por(x, p4f_half);\n\n  emm0 = psub(emm0, p4i_0x7f);\n  Packet4f e = padd(vec_ctf(emm0, 0), p4f_1);\n\n  /* part2:\n     if( x < SQRTHF ) {\n       e -= 1;\n       x = x + x - 1.0;\n     } else { x = x - 1.0; }\n  */\n  Packet4f mask = reinterpret_cast<Packet4f>(vec_cmplt(x, p4f_cephes_SQRTHF));\n  Packet4f tmp = pand(x, mask);\n  x = psub(x, p4f_1);\n  e = psub(e, pand(p4f_1, mask));\n  x = padd(x, tmp);\n\n  Packet4f x2 = pmul(x,x);\n  Packet4f x3 = pmul(x2,x);\n\n  Packet4f y, y1, y2;\n  y  = pmadd(p4f_cephes_log_p0, x, p4f_cephes_log_p1);\n  y1 = pmadd(p4f_cephes_log_p3, x, p4f_cephes_log_p4);\n  y2 = pmadd(p4f_cephes_log_p6, x, p4f_cephes_log_p7);\n  y  = pmadd(y , x, p4f_cephes_log_p2);\n  y1 = pmadd(y1, x, p4f_cephes_log_p5);\n  y2 = pmadd(y2, x, p4f_cephes_log_p8);\n  y = pmadd(y, x3, y1);\n  y = pmadd(y, x3, y2);\n  y = pmul(y, x3);\n\n  y1 = pmul(e, p4f_cephes_log_q1);\n  tmp = pmul(x2, p4f_half);\n  y = padd(y, y1);\n  x = psub(x, tmp);\n  y2 = pmul(e, p4f_cephes_log_q2);\n  x = padd(x, y);\n  x = padd(x, y2);\n  // negative arg will be NAN, 0 will be -INF\n  x = vec_sel(x, p4f_minus_inf, iszero_mask);\n  x = vec_sel(p4f_minus_nan, x, isvalid_mask);\n  return x;\n}\n\ntemplate<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED\nPacket4f pexp<Packet4f>(const Packet4f& _x)\n{\n  Packet4f x = _x;\n\n  Packet4f tmp, fx;\n  Packet4i emm0;\n\n  // clamp x\n  x = pmax(pmin(x, p4f_exp_hi), p4f_exp_lo);\n\n  // express exp(x) as exp(g + n*log(2))\n  fx = pmadd(x, p4f_cephes_LOG2EF, p4f_half);\n\n  fx = pfloor(fx);\n\n  tmp = pmul(fx, p4f_cephes_exp_C1);\n  Packet4f z = pmul(fx, p4f_cephes_exp_C2);\n  x = psub(x, tmp);\n  x = psub(x, z);\n\n  z = pmul(x,x);\n\n  Packet4f y = p4f_cephes_exp_p0;\n  y = pmadd(y, x, p4f_cephes_exp_p1);\n  y = pmadd(y, x, p4f_cephes_exp_p2);\n  y = pmadd(y, x, p4f_cephes_exp_p3);\n  y = pmadd(y, x, p4f_cephes_exp_p4);\n  y = pmadd(y, x, p4f_cephes_exp_p5);\n  y = pmadd(y, z, x);\n  y = padd(y, p4f_1);\n\n  // build 2^n\n  emm0 = vec_cts(fx, 0);\n  emm0 = vec_add(emm0, p4i_0x7f);\n  emm0 = vec_sl(emm0, reinterpret_cast<Packet4ui>(p4i_23));\n\n  // Altivec's max & min operators just drop silent NaNs. Check NaNs in \n  // inputs and return them unmodified.\n  Packet4ui isnumber_mask = reinterpret_cast<Packet4ui>(vec_cmpeq(_x, _x));\n  return vec_sel(_x, pmax(pmul(y, reinterpret_cast<Packet4f>(emm0)), _x),\n                 isnumber_mask);\n}\n\n#ifndef EIGEN_COMP_CLANG\ntemplate<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED\nPacket4f prsqrt<Packet4f>(const Packet4f& x)\n{\n  return  vec_rsqrt(x);\n}\n#endif\n\n#ifdef __VSX__\n#ifndef EIGEN_COMP_CLANG\ntemplate<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED\nPacket2d prsqrt<Packet2d>(const Packet2d& x)\n{\n  return  vec_rsqrt(x);\n}\n#endif\n\ntemplate<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED\nPacket4f psqrt<Packet4f>(const Packet4f& x)\n{\n  return  vec_sqrt(x);\n}\n\ntemplate<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED\nPacket2d psqrt<Packet2d>(const Packet2d& x)\n{\n  return  vec_sqrt(x);\n}\n\n// VSX support varies between different compilers and even different\n// versions of the same compiler.  For gcc version >= 4.9.3, we can use\n// vec_cts to efficiently convert Packet2d to Packet2l.  Otherwise, use\n// a slow version that works with older compilers. \n// Update: apparently vec_cts/vec_ctf intrinsics for 64-bit doubles\n// are buggy, https://gcc.gnu.org/bugzilla/show_bug.cgi?id=70963\nstatic inline Packet2l ConvertToPacket2l(const Packet2d& x) {\n#if EIGEN_GNUC_AT_LEAST(5, 4) || \\\n    (EIGEN_GNUC_AT(6, 1) && __GNUC_PATCHLEVEL__ >= 1)\n  return vec_cts(x, 0);    // TODO: check clang version.\n#else\n  double tmp[2];\n  memcpy(tmp, &x, sizeof(tmp));\n  Packet2l l = { static_cast<long long>(tmp[0]),\n                 static_cast<long long>(tmp[1]) };\n  return l;\n#endif\n}\n\ntemplate<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED\nPacket2d pexp<Packet2d>(const Packet2d& _x)\n{\n  Packet2d x = _x;\n\n  Packet2d tmp, fx;\n  Packet2l emm0;\n\n  // clamp x\n  x = pmax(pmin(x, p2d_exp_hi), p2d_exp_lo);\n\n  /* express exp(x) as exp(g + n*log(2)) */\n  fx = pmadd(x, p2d_cephes_LOG2EF, p2d_half);\n\n  fx = pfloor(fx);\n\n  tmp = pmul(fx, p2d_cephes_exp_C1);\n  Packet2d z = pmul(fx, p2d_cephes_exp_C2);\n  x = psub(x, tmp);\n  x = psub(x, z);\n\n  Packet2d x2 = pmul(x,x);\n\n  Packet2d px = p2d_cephes_exp_p0;\n  px = pmadd(px, x2, p2d_cephes_exp_p1);\n  px = pmadd(px, x2, p2d_cephes_exp_p2);\n  px = pmul (px, x);\n\n  Packet2d qx = p2d_cephes_exp_q0;\n  qx = pmadd(qx, x2, p2d_cephes_exp_q1);\n  qx = pmadd(qx, x2, p2d_cephes_exp_q2);\n  qx = pmadd(qx, x2, p2d_cephes_exp_q3);\n\n  x = pdiv(px,psub(qx,px));\n  x = pmadd(p2d_2,x,p2d_1);\n\n  // build 2^n\n  emm0 = ConvertToPacket2l(fx);\n\n#ifdef __POWER8_VECTOR__ \n  emm0 = vec_add(emm0, p2l_1023);\n  emm0 = vec_sl(emm0, p2ul_52);\n#else\n  // Code is a bit complex for POWER7.  There is actually a\n  // vec_xxsldi intrinsic but it is not supported by some gcc versions.\n  // So we shift (52-32) bits and do a word swap with zeros.\n  _EIGEN_DECLARE_CONST_Packet4i(1023, 1023);\n  _EIGEN_DECLARE_CONST_Packet4i(20, 20);    // 52 - 32\n\n  Packet4i emm04i = reinterpret_cast<Packet4i>(emm0);\n  emm04i = vec_add(emm04i, p4i_1023);\n  emm04i = vec_sl(emm04i, reinterpret_cast<Packet4ui>(p4i_20));\n  static const Packet16uc perm = {\n    0x14, 0x15, 0x16, 0x17, 0x00, 0x01, 0x02, 0x03, \n    0x1c, 0x1d, 0x1e, 0x1f, 0x08, 0x09, 0x0a, 0x0b };\n#ifdef  _BIG_ENDIAN\n  emm0 = reinterpret_cast<Packet2l>(vec_perm(p4i_ZERO, emm04i, perm));\n#else\n  emm0 = reinterpret_cast<Packet2l>(vec_perm(emm04i, p4i_ZERO, perm));\n#endif\n\n#endif\n\n  // Altivec's max & min operators just drop silent NaNs. Check NaNs in \n  // inputs and return them unmodified.\n  Packet2ul isnumber_mask = reinterpret_cast<Packet2ul>(vec_cmpeq(_x, _x));\n  return vec_sel(_x, pmax(pmul(x, reinterpret_cast<Packet2d>(emm0)), _x),\n                 isnumber_mask);\n}\n#endif\n\n}  // end namespace internal\n\n}  // end namespace Eigen\n\n#endif  // EIGEN_MATH_FUNCTIONS_ALTIVEC_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/arch/AltiVec/PacketMath.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2016 Konstantinos Margaritis <markos@freevec.org>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_PACKET_MATH_ALTIVEC_H\n#define EIGEN_PACKET_MATH_ALTIVEC_H\n\nnamespace Eigen {\n\nnamespace internal {\n\n#ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD\n#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 4\n#endif\n\n#ifndef EIGEN_HAS_SINGLE_INSTRUCTION_MADD\n#define EIGEN_HAS_SINGLE_INSTRUCTION_MADD\n#endif\n\n#ifndef EIGEN_HAS_SINGLE_INSTRUCTION_CJMADD\n#define EIGEN_HAS_SINGLE_INSTRUCTION_CJMADD\n#endif\n\n// NOTE Altivec has 32 registers, but Eigen only accepts a value of 8 or 16\n#ifndef EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS\n#define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS  32\n#endif\n\ntypedef __vector float          Packet4f;\ntypedef __vector int            Packet4i;\ntypedef __vector unsigned int   Packet4ui;\ntypedef __vector __bool int     Packet4bi;\ntypedef __vector short int      Packet8i;\ntypedef __vector unsigned char  Packet16uc;\n\n// We don't want to write the same code all the time, but we need to reuse the constants\n// and it doesn't really work to declare them global, so we define macros instead\n\n#define _EIGEN_DECLARE_CONST_FAST_Packet4f(NAME,X) \\\n  Packet4f p4f_##NAME = reinterpret_cast<Packet4f>(vec_splat_s32(X))\n\n#define _EIGEN_DECLARE_CONST_FAST_Packet4i(NAME,X) \\\n  Packet4i p4i_##NAME = vec_splat_s32(X)\n\n#define _EIGEN_DECLARE_CONST_Packet4f(NAME,X) \\\n  Packet4f p4f_##NAME = pset1<Packet4f>(X)\n\n#define _EIGEN_DECLARE_CONST_Packet4i(NAME,X) \\\n  Packet4i p4i_##NAME = pset1<Packet4i>(X)\n\n#define _EIGEN_DECLARE_CONST_Packet2d(NAME,X) \\\n  Packet2d p2d_##NAME = pset1<Packet2d>(X)\n\n#define _EIGEN_DECLARE_CONST_Packet2l(NAME,X) \\\n  Packet2l p2l_##NAME = pset1<Packet2l>(X)\n\n#define _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(NAME,X) \\\n  const Packet4f p4f_##NAME = reinterpret_cast<Packet4f>(pset1<Packet4i>(X))\n\n#define DST_CHAN 1\n#define DST_CTRL(size, count, stride) (((size) << 24) | ((count) << 16) | (stride))\n\n\n// These constants are endian-agnostic\nstatic _EIGEN_DECLARE_CONST_FAST_Packet4f(ZERO, 0); //{ 0.0, 0.0, 0.0, 0.0}\nstatic _EIGEN_DECLARE_CONST_FAST_Packet4i(ZERO, 0); //{ 0, 0, 0, 0,}\nstatic _EIGEN_DECLARE_CONST_FAST_Packet4i(ONE,1); //{ 1, 1, 1, 1}\nstatic _EIGEN_DECLARE_CONST_FAST_Packet4i(MINUS16,-16); //{ -16, -16, -16, -16}\nstatic _EIGEN_DECLARE_CONST_FAST_Packet4i(MINUS1,-1); //{ -1, -1, -1, -1}\nstatic Packet4f p4f_MZERO = (Packet4f) vec_sl((Packet4ui)p4i_MINUS1, (Packet4ui)p4i_MINUS1); //{ 0x80000000, 0x80000000, 0x80000000, 0x80000000}\n#ifndef __VSX__\nstatic Packet4f p4f_ONE = vec_ctf(p4i_ONE, 0); //{ 1.0, 1.0, 1.0, 1.0}\n#endif\n\nstatic Packet4f p4f_COUNTDOWN = { 0.0, 1.0, 2.0, 3.0 };\nstatic Packet4i p4i_COUNTDOWN = { 0, 1, 2, 3 };\n\nstatic Packet16uc p16uc_REVERSE32 = { 12,13,14,15, 8,9,10,11, 4,5,6,7, 0,1,2,3 };\nstatic Packet16uc p16uc_DUPLICATE32_HI = { 0,1,2,3, 0,1,2,3, 4,5,6,7, 4,5,6,7 };\n\n// Mask alignment\n#ifdef __PPC64__\n#define _EIGEN_MASK_ALIGNMENT\t0xfffffffffffffff0\n#else\n#define _EIGEN_MASK_ALIGNMENT\t0xfffffff0\n#endif\n\n#define _EIGEN_ALIGNED_PTR(x)\t((std::ptrdiff_t)(x) & _EIGEN_MASK_ALIGNMENT)\n\n// Handle endianness properly while loading constants\n// Define global static constants:\n#ifdef _BIG_ENDIAN\nstatic Packet16uc p16uc_FORWARD = vec_lvsl(0, (float*)0);\n#ifdef __VSX__\nstatic Packet16uc p16uc_REVERSE64 = { 8,9,10,11, 12,13,14,15, 0,1,2,3, 4,5,6,7 };\n#endif\nstatic Packet16uc p16uc_PSET32_WODD   = vec_sld((Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 0), (Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 2), 8);//{ 0,1,2,3, 0,1,2,3, 8,9,10,11, 8,9,10,11 };\nstatic Packet16uc p16uc_PSET32_WEVEN  = vec_sld(p16uc_DUPLICATE32_HI, (Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 3), 8);//{ 4,5,6,7, 4,5,6,7, 12,13,14,15, 12,13,14,15 };\nstatic Packet16uc p16uc_HALF64_0_16 = vec_sld((Packet16uc)p4i_ZERO, vec_splat((Packet16uc) vec_abs(p4i_MINUS16), 3), 8);      //{ 0,0,0,0, 0,0,0,0, 16,16,16,16, 16,16,16,16};\n#else\nstatic Packet16uc p16uc_FORWARD = p16uc_REVERSE32;\nstatic Packet16uc p16uc_REVERSE64 = { 8,9,10,11, 12,13,14,15, 0,1,2,3, 4,5,6,7 };\nstatic Packet16uc p16uc_PSET32_WODD = vec_sld((Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 1), (Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 3), 8);//{ 0,1,2,3, 0,1,2,3, 8,9,10,11, 8,9,10,11 };\nstatic Packet16uc p16uc_PSET32_WEVEN = vec_sld((Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 0), (Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 2), 8);//{ 4,5,6,7, 4,5,6,7, 12,13,14,15, 12,13,14,15 };\nstatic Packet16uc p16uc_HALF64_0_16 = vec_sld(vec_splat((Packet16uc) vec_abs(p4i_MINUS16), 0), (Packet16uc)p4i_ZERO, 8);      //{ 0,0,0,0, 0,0,0,0, 16,16,16,16, 16,16,16,16};\n#endif // _BIG_ENDIAN\n\nstatic Packet16uc p16uc_PSET64_HI = (Packet16uc) vec_mergeh((Packet4ui)p16uc_PSET32_WODD, (Packet4ui)p16uc_PSET32_WEVEN);     //{ 0,1,2,3, 4,5,6,7, 0,1,2,3, 4,5,6,7 };\nstatic Packet16uc p16uc_PSET64_LO = (Packet16uc) vec_mergel((Packet4ui)p16uc_PSET32_WODD, (Packet4ui)p16uc_PSET32_WEVEN);     //{ 8,9,10,11, 12,13,14,15, 8,9,10,11, 12,13,14,15 };\nstatic Packet16uc p16uc_TRANSPOSE64_HI = p16uc_PSET64_HI + p16uc_HALF64_0_16;                                         //{ 0,1,2,3, 4,5,6,7, 16,17,18,19, 20,21,22,23};\nstatic Packet16uc p16uc_TRANSPOSE64_LO = p16uc_PSET64_LO + p16uc_HALF64_0_16;                                         //{ 8,9,10,11, 12,13,14,15, 24,25,26,27, 28,29,30,31};\n\nstatic Packet16uc p16uc_COMPLEX32_REV = vec_sld(p16uc_REVERSE32, p16uc_REVERSE32, 8);                                         //{ 4,5,6,7, 0,1,2,3, 12,13,14,15, 8,9,10,11 };\n\n#ifdef _BIG_ENDIAN\nstatic Packet16uc p16uc_COMPLEX32_REV2 = vec_sld(p16uc_FORWARD, p16uc_FORWARD, 8);                                            //{ 8,9,10,11, 12,13,14,15, 0,1,2,3, 4,5,6,7 };\n#else\nstatic Packet16uc p16uc_COMPLEX32_REV2 = vec_sld(p16uc_PSET64_HI, p16uc_PSET64_LO, 8);                                            //{ 8,9,10,11, 12,13,14,15, 0,1,2,3, 4,5,6,7 };\n#endif // _BIG_ENDIAN\n\n#if EIGEN_HAS_BUILTIN(__builtin_prefetch) || EIGEN_COMP_GNUC\n  #define EIGEN_PPC_PREFETCH(ADDR) __builtin_prefetch(ADDR);\n#else\n  #define EIGEN_PPC_PREFETCH(ADDR) asm( \"   dcbt [%[addr]]\\n\" :: [addr] \"r\" (ADDR) : \"cc\" );\n#endif\n\ntemplate<> struct packet_traits<float>  : default_packet_traits\n{\n  typedef Packet4f type;\n  typedef Packet4f half;\n  enum {\n    Vectorizable = 1,\n    AlignedOnScalar = 1,\n    size=4,\n    HasHalfPacket = 1,\n\n    HasAdd  = 1,\n    HasSub  = 1,\n    HasMul  = 1,\n    HasDiv  = 1,\n    HasMin  = 1,\n    HasMax  = 1,\n    HasAbs  = 1,\n    HasSin  = 0,\n    HasCos  = 0,\n    HasLog  = 0,\n    HasExp  = 1,\n#ifdef __VSX__\n    HasSqrt = 1,\n#if !EIGEN_COMP_CLANG\n    HasRsqrt = 1,\n#else\n    HasRsqrt = 0,\n#endif\n#else\n    HasSqrt = 0,\n    HasRsqrt = 0,\n#endif\n    HasRound = 1,\n    HasFloor = 1,\n    HasCeil = 1,\n    HasNegate = 1,\n    HasBlend = 1\n  };\n};\ntemplate<> struct packet_traits<int>    : default_packet_traits\n{\n  typedef Packet4i type;\n  typedef Packet4i half;\n  enum {\n    Vectorizable = 1,\n    AlignedOnScalar = 1,\n    size = 4,\n    HasHalfPacket = 0,\n\n    HasAdd  = 1,\n    HasSub  = 1,\n    HasMul  = 1,\n    HasDiv  = 0,\n    HasBlend = 1\n  };\n};\n\n\ntemplate<> struct unpacket_traits<Packet4f> { typedef float  type; enum {size=4, alignment=Aligned16}; typedef Packet4f half; };\ntemplate<> struct unpacket_traits<Packet4i> { typedef int    type; enum {size=4, alignment=Aligned16}; typedef Packet4i half; };\n\ninline std::ostream & operator <<(std::ostream & s, const Packet16uc & v)\n{\n  union {\n    Packet16uc   v;\n    unsigned char n[16];\n  } vt;\n  vt.v = v;\n  for (int i=0; i< 16; i++)\n    s << (int)vt.n[i] << \", \";\n  return s;\n}\n\ninline std::ostream & operator <<(std::ostream & s, const Packet4f & v)\n{\n  union {\n    Packet4f   v;\n    float n[4];\n  } vt;\n  vt.v = v;\n  s << vt.n[0] << \", \" << vt.n[1] << \", \" << vt.n[2] << \", \" << vt.n[3];\n  return s;\n}\n\ninline std::ostream & operator <<(std::ostream & s, const Packet4i & v)\n{\n  union {\n    Packet4i   v;\n    int n[4];\n  } vt;\n  vt.v = v;\n  s << vt.n[0] << \", \" << vt.n[1] << \", \" << vt.n[2] << \", \" << vt.n[3];\n  return s;\n}\n\ninline std::ostream & operator <<(std::ostream & s, const Packet4ui & v)\n{\n  union {\n    Packet4ui   v;\n    unsigned int n[4];\n  } vt;\n  vt.v = v;\n  s << vt.n[0] << \", \" << vt.n[1] << \", \" << vt.n[2] << \", \" << vt.n[3];\n  return s;\n}\n\n// Need to define them first or we get specialization after instantiation errors\ntemplate<> EIGEN_STRONG_INLINE Packet4f pload<Packet4f>(const float* from)\n{\n  EIGEN_DEBUG_ALIGNED_LOAD\n#ifdef __VSX__\n  return vec_vsx_ld(0, from);\n#else\n  return vec_ld(0, from);\n#endif\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4i pload<Packet4i>(const int*     from)\n{\n  EIGEN_DEBUG_ALIGNED_LOAD\n#ifdef __VSX__\n  return vec_vsx_ld(0, from);\n#else\n  return vec_ld(0, from);\n#endif\n}\n\ntemplate<> EIGEN_STRONG_INLINE void pstore<float>(float*   to, const Packet4f& from)\n{\n  EIGEN_DEBUG_ALIGNED_STORE\n#ifdef __VSX__\n  vec_vsx_st(from, 0, to);\n#else\n  vec_st(from, 0, to);\n#endif\n}\n\ntemplate<> EIGEN_STRONG_INLINE void pstore<int>(int*       to, const Packet4i& from)\n{\n  EIGEN_DEBUG_ALIGNED_STORE\n#ifdef __VSX__\n  vec_vsx_st(from, 0, to);\n#else\n  vec_st(from, 0, to);\n#endif\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float&  from) {\n  Packet4f v = {from, from, from, from};\n  return v;\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int&    from)   {\n  Packet4i v = {from, from, from, from};\n  return v;\n}\ntemplate<> EIGEN_STRONG_INLINE void\npbroadcast4<Packet4f>(const float *a,\n                      Packet4f& a0, Packet4f& a1, Packet4f& a2, Packet4f& a3)\n{\n  a3 = pload<Packet4f>(a);\n  a0 = vec_splat(a3, 0);\n  a1 = vec_splat(a3, 1);\n  a2 = vec_splat(a3, 2);\n  a3 = vec_splat(a3, 3);\n}\ntemplate<> EIGEN_STRONG_INLINE void\npbroadcast4<Packet4i>(const int *a,\n                      Packet4i& a0, Packet4i& a1, Packet4i& a2, Packet4i& a3)\n{\n  a3 = pload<Packet4i>(a);\n  a0 = vec_splat(a3, 0);\n  a1 = vec_splat(a3, 1);\n  a2 = vec_splat(a3, 2);\n  a3 = vec_splat(a3, 3);\n}\n\ntemplate<> EIGEN_DEVICE_FUNC inline Packet4f pgather<float, Packet4f>(const float* from, Index stride)\n{\n  float EIGEN_ALIGN16 af[4];\n  af[0] = from[0*stride];\n  af[1] = from[1*stride];\n  af[2] = from[2*stride];\n  af[3] = from[3*stride];\n return pload<Packet4f>(af);\n}\ntemplate<> EIGEN_DEVICE_FUNC inline Packet4i pgather<int, Packet4i>(const int* from, Index stride)\n{\n  int EIGEN_ALIGN16 ai[4];\n  ai[0] = from[0*stride];\n  ai[1] = from[1*stride];\n  ai[2] = from[2*stride];\n  ai[3] = from[3*stride];\n return pload<Packet4i>(ai);\n}\ntemplate<> EIGEN_DEVICE_FUNC inline void pscatter<float, Packet4f>(float* to, const Packet4f& from, Index stride)\n{\n  float EIGEN_ALIGN16 af[4];\n  pstore<float>(af, from);\n  to[0*stride] = af[0];\n  to[1*stride] = af[1];\n  to[2*stride] = af[2];\n  to[3*stride] = af[3];\n}\ntemplate<> EIGEN_DEVICE_FUNC inline void pscatter<int, Packet4i>(int* to, const Packet4i& from, Index stride)\n{\n  int EIGEN_ALIGN16 ai[4];\n  pstore<int>((int *)ai, from);\n  to[0*stride] = ai[0];\n  to[1*stride] = ai[1];\n  to[2*stride] = ai[2];\n  to[3*stride] = ai[3];\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f plset<Packet4f>(const float& a) { return pset1<Packet4f>(a) + p4f_COUNTDOWN; }\ntemplate<> EIGEN_STRONG_INLINE Packet4i plset<Packet4i>(const int& a)   { return pset1<Packet4i>(a) + p4i_COUNTDOWN; }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f padd<Packet4f>(const Packet4f& a, const Packet4f& b) { return a + b; }\ntemplate<> EIGEN_STRONG_INLINE Packet4i padd<Packet4i>(const Packet4i& a, const Packet4i& b) { return a + b; }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f psub<Packet4f>(const Packet4f& a, const Packet4f& b) { return a - b; }\ntemplate<> EIGEN_STRONG_INLINE Packet4i psub<Packet4i>(const Packet4i& a, const Packet4i& b) { return a - b; }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pnegate(const Packet4f& a) { return p4f_ZERO - a; }\ntemplate<> EIGEN_STRONG_INLINE Packet4i pnegate(const Packet4i& a) { return p4i_ZERO - a; }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pconj(const Packet4f& a) { return a; }\ntemplate<> EIGEN_STRONG_INLINE Packet4i pconj(const Packet4i& a) { return a; }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pmul<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_madd(a,b, p4f_MZERO); }\ntemplate<> EIGEN_STRONG_INLINE Packet4i pmul<Packet4i>(const Packet4i& a, const Packet4i& b) { return a * b; }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pdiv<Packet4f>(const Packet4f& a, const Packet4f& b)\n{\n#ifndef __VSX__  // VSX actually provides a div instruction\n  Packet4f t, y_0, y_1;\n\n  // Altivec does not offer a divide instruction, we have to do a reciprocal approximation\n  y_0 = vec_re(b);\n\n  // Do one Newton-Raphson iteration to get the needed accuracy\n  t   = vec_nmsub(y_0, b, p4f_ONE);\n  y_1 = vec_madd(y_0, t, y_0);\n\n  return vec_madd(a, y_1, p4f_MZERO);\n#else\n  return vec_div(a, b);\n#endif\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4i pdiv<Packet4i>(const Packet4i& /*a*/, const Packet4i& /*b*/)\n{ eigen_assert(false && \"packet integer division are not supported by AltiVec\");\n  return pset1<Packet4i>(0);\n}\n\n// for some weird raisons, it has to be overloaded for packet of integers\ntemplate<> EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c) { return vec_madd(a,b,c); }\ntemplate<> EIGEN_STRONG_INLINE Packet4i pmadd(const Packet4i& a, const Packet4i& b, const Packet4i& c) { return a*b + c; }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pmin<Packet4f>(const Packet4f& a, const Packet4f& b)\n{\n  #ifdef __VSX__\n  Packet4f ret;\n  __asm__ (\"xvcmpgesp %x0,%x1,%x2\\n\\txxsel %x0,%x1,%x2,%x0\" : \"=&wa\" (ret) : \"wa\" (a), \"wa\" (b));\n  return ret;\n  #else\n  return vec_min(a, b);\n  #endif\n}\ntemplate<> EIGEN_STRONG_INLINE Packet4i pmin<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_min(a, b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pmax<Packet4f>(const Packet4f& a, const Packet4f& b)\n{\n  #ifdef __VSX__\n  Packet4f ret;\n  __asm__ (\"xvcmpgtsp %x0,%x2,%x1\\n\\txxsel %x0,%x1,%x2,%x0\" : \"=&wa\" (ret) : \"wa\" (a), \"wa\" (b));\n  return ret;\n  #else\n  return vec_max(a, b);\n  #endif\n}\ntemplate<> EIGEN_STRONG_INLINE Packet4i pmax<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_max(a, b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pand<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_and(a, b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4i pand<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_and(a, b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f por<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_or(a, b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4i por<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_or(a, b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pxor<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_xor(a, b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4i pxor<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_xor(a, b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pandnot<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_and(a, vec_nor(b, b)); }\ntemplate<> EIGEN_STRONG_INLINE Packet4i pandnot<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_and(a, vec_nor(b, b)); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pround<Packet4f>(const Packet4f& a) { return vec_round(a); }\ntemplate<> EIGEN_STRONG_INLINE Packet4f pceil<Packet4f>(const  Packet4f& a) { return vec_ceil(a); }\ntemplate<> EIGEN_STRONG_INLINE Packet4f pfloor<Packet4f>(const Packet4f& a) { return vec_floor(a); }\n\n#ifdef _BIG_ENDIAN\ntemplate<> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float* from)\n{\n  EIGEN_DEBUG_ALIGNED_LOAD\n  Packet16uc MSQ, LSQ;\n  Packet16uc mask;\n  MSQ = vec_ld(0, (unsigned char *)from);          // most significant quadword\n  LSQ = vec_ld(15, (unsigned char *)from);         // least significant quadword\n  mask = vec_lvsl(0, from);                        // create the permute mask\n  return (Packet4f) vec_perm(MSQ, LSQ, mask);           // align the data\n\n}\ntemplate<> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int* from)\n{\n  EIGEN_DEBUG_ALIGNED_LOAD\n  // Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html\n  Packet16uc MSQ, LSQ;\n  Packet16uc mask;\n  MSQ = vec_ld(0, (unsigned char *)from);          // most significant quadword\n  LSQ = vec_ld(15, (unsigned char *)from);         // least significant quadword\n  mask = vec_lvsl(0, from);                        // create the permute mask\n  return (Packet4i) vec_perm(MSQ, LSQ, mask);    // align the data\n}\n#else\n// We also need ot redefine little endian loading of Packet4i/Packet4f using VSX\ntemplate<> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int* from)\n{\n  EIGEN_DEBUG_UNALIGNED_LOAD\n  return (Packet4i) vec_vsx_ld((long)from & 15, (const int*) _EIGEN_ALIGNED_PTR(from));\n}\ntemplate<> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float* from)\n{\n  EIGEN_DEBUG_UNALIGNED_LOAD\n  return (Packet4f) vec_vsx_ld((long)from & 15, (const float*) _EIGEN_ALIGNED_PTR(from));\n}\n#endif\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f ploaddup<Packet4f>(const float*   from)\n{\n  Packet4f p;\n  if((std::ptrdiff_t(from) % 16) == 0)  p = pload<Packet4f>(from);\n  else                                  p = ploadu<Packet4f>(from);\n  return vec_perm(p, p, p16uc_DUPLICATE32_HI);\n}\ntemplate<> EIGEN_STRONG_INLINE Packet4i ploaddup<Packet4i>(const int*     from)\n{\n  Packet4i p;\n  if((std::ptrdiff_t(from) % 16) == 0)  p = pload<Packet4i>(from);\n  else                                  p = ploadu<Packet4i>(from);\n  return vec_perm(p, p, p16uc_DUPLICATE32_HI);\n}\n\n#ifdef _BIG_ENDIAN\ntemplate<> EIGEN_STRONG_INLINE void pstoreu<float>(float*  to, const Packet4f& from)\n{\n  EIGEN_DEBUG_UNALIGNED_STORE\n  // Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html\n  // Warning: not thread safe!\n  Packet16uc MSQ, LSQ, edges;\n  Packet16uc edgeAlign, align;\n\n  MSQ = vec_ld(0, (unsigned char *)to);                     // most significant quadword\n  LSQ = vec_ld(15, (unsigned char *)to);                    // least significant quadword\n  edgeAlign = vec_lvsl(0, to);                              // permute map to extract edges\n  edges=vec_perm(LSQ,MSQ,edgeAlign);                        // extract the edges\n  align = vec_lvsr( 0, to );                                // permute map to misalign data\n  MSQ = vec_perm(edges,(Packet16uc)from,align);             // misalign the data (MSQ)\n  LSQ = vec_perm((Packet16uc)from,edges,align);             // misalign the data (LSQ)\n  vec_st( LSQ, 15, (unsigned char *)to );                   // Store the LSQ part first\n  vec_st( MSQ, 0, (unsigned char *)to );                    // Store the MSQ part\n}\ntemplate<> EIGEN_STRONG_INLINE void pstoreu<int>(int*      to, const Packet4i& from)\n{\n  EIGEN_DEBUG_UNALIGNED_STORE\n  // Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html\n  // Warning: not thread safe!\n  Packet16uc MSQ, LSQ, edges;\n  Packet16uc edgeAlign, align;\n\n  MSQ = vec_ld(0, (unsigned char *)to);                     // most significant quadword\n  LSQ = vec_ld(15, (unsigned char *)to);                    // least significant quadword\n  edgeAlign = vec_lvsl(0, to);                              // permute map to extract edges\n  edges=vec_perm(LSQ, MSQ, edgeAlign);                      // extract the edges\n  align = vec_lvsr( 0, to );                                // permute map to misalign data\n  MSQ = vec_perm(edges, (Packet16uc) from, align);          // misalign the data (MSQ)\n  LSQ = vec_perm((Packet16uc) from, edges, align);          // misalign the data (LSQ)\n  vec_st( LSQ, 15, (unsigned char *)to );                   // Store the LSQ part first\n  vec_st( MSQ, 0, (unsigned char *)to );                    // Store the MSQ part\n}\n#else\n// We also need ot redefine little endian loading of Packet4i/Packet4f using VSX\ntemplate<> EIGEN_STRONG_INLINE void pstoreu<int>(int*       to, const Packet4i& from)\n{\n  EIGEN_DEBUG_ALIGNED_STORE\n  vec_vsx_st(from, (long)to & 15, (int*) _EIGEN_ALIGNED_PTR(to));\n}\ntemplate<> EIGEN_STRONG_INLINE void pstoreu<float>(float*   to, const Packet4f& from)\n{\n  EIGEN_DEBUG_ALIGNED_STORE\n  vec_vsx_st(from, (long)to & 15, (float*) _EIGEN_ALIGNED_PTR(to));\n}\n#endif\n\ntemplate<> EIGEN_STRONG_INLINE void prefetch<float>(const float* addr)    { EIGEN_PPC_PREFETCH(addr); }\ntemplate<> EIGEN_STRONG_INLINE void prefetch<int>(const int*     addr)    { EIGEN_PPC_PREFETCH(addr); }\n\ntemplate<> EIGEN_STRONG_INLINE float  pfirst<Packet4f>(const Packet4f& a) { float EIGEN_ALIGN16 x; vec_ste(a, 0, &x); return x; }\ntemplate<> EIGEN_STRONG_INLINE int    pfirst<Packet4i>(const Packet4i& a) { int   EIGEN_ALIGN16 x; vec_ste(a, 0, &x); return x; }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f preverse(const Packet4f& a)\n{\n  return reinterpret_cast<Packet4f>(vec_perm(reinterpret_cast<Packet16uc>(a), reinterpret_cast<Packet16uc>(a), p16uc_REVERSE32));\n}\ntemplate<> EIGEN_STRONG_INLINE Packet4i preverse(const Packet4i& a)\n{\n  return reinterpret_cast<Packet4i>(vec_perm(reinterpret_cast<Packet16uc>(a), reinterpret_cast<Packet16uc>(a), p16uc_REVERSE32)); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pabs(const Packet4f& a) { return vec_abs(a); }\ntemplate<> EIGEN_STRONG_INLINE Packet4i pabs(const Packet4i& a) { return vec_abs(a); }\n\ntemplate<> EIGEN_STRONG_INLINE float predux<Packet4f>(const Packet4f& a)\n{\n  Packet4f b, sum;\n  b   = vec_sld(a, a, 8);\n  sum = a + b;\n  b   = vec_sld(sum, sum, 4);\n  sum += b;\n  return pfirst(sum);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f preduxp<Packet4f>(const Packet4f* vecs)\n{\n  Packet4f v[4], sum[4];\n\n  // It's easier and faster to transpose then add as columns\n  // Check: http://www.freevec.org/function/matrix_4x4_transpose_floats for explanation\n  // Do the transpose, first set of moves\n  v[0] = vec_mergeh(vecs[0], vecs[2]);\n  v[1] = vec_mergel(vecs[0], vecs[2]);\n  v[2] = vec_mergeh(vecs[1], vecs[3]);\n  v[3] = vec_mergel(vecs[1], vecs[3]);\n  // Get the resulting vectors\n  sum[0] = vec_mergeh(v[0], v[2]);\n  sum[1] = vec_mergel(v[0], v[2]);\n  sum[2] = vec_mergeh(v[1], v[3]);\n  sum[3] = vec_mergel(v[1], v[3]);\n\n  // Now do the summation:\n  // Lines 0+1\n  sum[0] = sum[0] + sum[1];\n  // Lines 2+3\n  sum[1] = sum[2] + sum[3];\n  // Add the results\n  sum[0] = sum[0] + sum[1];\n\n  return sum[0];\n}\n\ntemplate<> EIGEN_STRONG_INLINE int predux<Packet4i>(const Packet4i& a)\n{\n  Packet4i sum;\n  sum = vec_sums(a, p4i_ZERO);\n#ifdef _BIG_ENDIAN\n  sum = vec_sld(sum, p4i_ZERO, 12);\n#else\n  sum = vec_sld(p4i_ZERO, sum, 4);\n#endif\n  return pfirst(sum);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4i preduxp<Packet4i>(const Packet4i* vecs)\n{\n  Packet4i v[4], sum[4];\n\n  // It's easier and faster to transpose then add as columns\n  // Check: http://www.freevec.org/function/matrix_4x4_transpose_floats for explanation\n  // Do the transpose, first set of moves\n  v[0] = vec_mergeh(vecs[0], vecs[2]);\n  v[1] = vec_mergel(vecs[0], vecs[2]);\n  v[2] = vec_mergeh(vecs[1], vecs[3]);\n  v[3] = vec_mergel(vecs[1], vecs[3]);\n  // Get the resulting vectors\n  sum[0] = vec_mergeh(v[0], v[2]);\n  sum[1] = vec_mergel(v[0], v[2]);\n  sum[2] = vec_mergeh(v[1], v[3]);\n  sum[3] = vec_mergel(v[1], v[3]);\n\n  // Now do the summation:\n  // Lines 0+1\n  sum[0] = sum[0] + sum[1];\n  // Lines 2+3\n  sum[1] = sum[2] + sum[3];\n  // Add the results\n  sum[0] = sum[0] + sum[1];\n\n  return sum[0];\n}\n\n// Other reduction functions:\n// mul\ntemplate<> EIGEN_STRONG_INLINE float predux_mul<Packet4f>(const Packet4f& a)\n{\n  Packet4f prod;\n  prod = pmul(a, vec_sld(a, a, 8));\n  return pfirst(pmul(prod, vec_sld(prod, prod, 4)));\n}\n\ntemplate<> EIGEN_STRONG_INLINE int predux_mul<Packet4i>(const Packet4i& a)\n{\n  EIGEN_ALIGN16 int aux[4];\n  pstore(aux, a);\n  return aux[0] * aux[1] * aux[2] * aux[3];\n}\n\n// min\ntemplate<> EIGEN_STRONG_INLINE float predux_min<Packet4f>(const Packet4f& a)\n{\n  Packet4f b, res;\n  b = vec_min(a, vec_sld(a, a, 8));\n  res = vec_min(b, vec_sld(b, b, 4));\n  return pfirst(res);\n}\n\ntemplate<> EIGEN_STRONG_INLINE int predux_min<Packet4i>(const Packet4i& a)\n{\n  Packet4i b, res;\n  b = vec_min(a, vec_sld(a, a, 8));\n  res = vec_min(b, vec_sld(b, b, 4));\n  return pfirst(res);\n}\n\n// max\ntemplate<> EIGEN_STRONG_INLINE float predux_max<Packet4f>(const Packet4f& a)\n{\n  Packet4f b, res;\n  b = vec_max(a, vec_sld(a, a, 8));\n  res = vec_max(b, vec_sld(b, b, 4));\n  return pfirst(res);\n}\n\ntemplate<> EIGEN_STRONG_INLINE int predux_max<Packet4i>(const Packet4i& a)\n{\n  Packet4i b, res;\n  b = vec_max(a, vec_sld(a, a, 8));\n  res = vec_max(b, vec_sld(b, b, 4));\n  return pfirst(res);\n}\n\ntemplate<int Offset>\nstruct palign_impl<Offset,Packet4f>\n{\n  static EIGEN_STRONG_INLINE void run(Packet4f& first, const Packet4f& second)\n  {\n#ifdef _BIG_ENDIAN\n    switch (Offset % 4) {\n    case 1:\n      first = vec_sld(first, second, 4); break;\n    case 2:\n      first = vec_sld(first, second, 8); break;\n    case 3:\n      first = vec_sld(first, second, 12); break;\n    }\n#else\n    switch (Offset % 4) {\n    case 1:\n      first = vec_sld(second, first, 12); break;\n    case 2:\n      first = vec_sld(second, first, 8); break;\n    case 3:\n      first = vec_sld(second, first, 4); break;\n    }\n#endif\n  }\n};\n\ntemplate<int Offset>\nstruct palign_impl<Offset,Packet4i>\n{\n  static EIGEN_STRONG_INLINE void run(Packet4i& first, const Packet4i& second)\n  {\n#ifdef _BIG_ENDIAN\n    switch (Offset % 4) {\n    case 1:\n      first = vec_sld(first, second, 4); break;\n    case 2:\n      first = vec_sld(first, second, 8); break;\n    case 3:\n      first = vec_sld(first, second, 12); break;\n    }\n#else\n    switch (Offset % 4) {\n    case 1:\n      first = vec_sld(second, first, 12); break;\n    case 2:\n      first = vec_sld(second, first, 8); break;\n    case 3:\n      first = vec_sld(second, first, 4); break;\n    }\n#endif\n  }\n};\n\nEIGEN_DEVICE_FUNC inline void\nptranspose(PacketBlock<Packet4f,4>& kernel) {\n  Packet4f t0, t1, t2, t3;\n  t0 = vec_mergeh(kernel.packet[0], kernel.packet[2]);\n  t1 = vec_mergel(kernel.packet[0], kernel.packet[2]);\n  t2 = vec_mergeh(kernel.packet[1], kernel.packet[3]);\n  t3 = vec_mergel(kernel.packet[1], kernel.packet[3]);\n  kernel.packet[0] = vec_mergeh(t0, t2);\n  kernel.packet[1] = vec_mergel(t0, t2);\n  kernel.packet[2] = vec_mergeh(t1, t3);\n  kernel.packet[3] = vec_mergel(t1, t3);\n}\n\nEIGEN_DEVICE_FUNC inline void\nptranspose(PacketBlock<Packet4i,4>& kernel) {\n  Packet4i t0, t1, t2, t3;\n  t0 = vec_mergeh(kernel.packet[0], kernel.packet[2]);\n  t1 = vec_mergel(kernel.packet[0], kernel.packet[2]);\n  t2 = vec_mergeh(kernel.packet[1], kernel.packet[3]);\n  t3 = vec_mergel(kernel.packet[1], kernel.packet[3]);\n  kernel.packet[0] = vec_mergeh(t0, t2);\n  kernel.packet[1] = vec_mergel(t0, t2);\n  kernel.packet[2] = vec_mergeh(t1, t3);\n  kernel.packet[3] = vec_mergel(t1, t3);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4i pblend(const Selector<4>& ifPacket, const Packet4i& thenPacket, const Packet4i& elsePacket) {\n  Packet4ui select = { ifPacket.select[0], ifPacket.select[1], ifPacket.select[2], ifPacket.select[3] };\n  Packet4ui mask = reinterpret_cast<Packet4ui>(vec_cmpeq(reinterpret_cast<Packet4ui>(select), reinterpret_cast<Packet4ui>(p4i_ONE)));\n  return vec_sel(elsePacket, thenPacket, mask);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pblend(const Selector<4>& ifPacket, const Packet4f& thenPacket, const Packet4f& elsePacket) {\n  Packet4ui select = { ifPacket.select[0], ifPacket.select[1], ifPacket.select[2], ifPacket.select[3] };\n  Packet4ui mask = reinterpret_cast<Packet4ui>(vec_cmpeq(reinterpret_cast<Packet4ui>(select), reinterpret_cast<Packet4ui>(p4i_ONE)));\n  return vec_sel(elsePacket, thenPacket, mask);\n}\n\n\n//---------- double ----------\n#ifdef __VSX__\ntypedef __vector double              Packet2d;\ntypedef __vector unsigned long long  Packet2ul;\ntypedef __vector long long           Packet2l;\n#if EIGEN_COMP_CLANG\ntypedef Packet2ul                    Packet2bl;\n#else\ntypedef __vector __bool long         Packet2bl;\n#endif\n\nstatic Packet2l  p2l_ONE  = { 1, 1 };\nstatic Packet2l  p2l_ZERO = reinterpret_cast<Packet2l>(p4i_ZERO);\nstatic Packet2d  p2d_ONE  = { 1.0, 1.0 };\nstatic Packet2d  p2d_ZERO = reinterpret_cast<Packet2d>(p4f_ZERO);\nstatic Packet2d  p2d_MZERO = { -0.0, -0.0 };\n\n#ifdef _BIG_ENDIAN\nstatic Packet2d p2d_COUNTDOWN = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(p2d_ZERO), reinterpret_cast<Packet4f>(p2d_ONE), 8));\n#else\nstatic Packet2d p2d_COUNTDOWN = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(p2d_ONE), reinterpret_cast<Packet4f>(p2d_ZERO), 8));\n#endif\n\ntemplate<int index> Packet2d vec_splat_dbl(Packet2d& a);\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d vec_splat_dbl<0>(Packet2d& a)\n{\n  return reinterpret_cast<Packet2d>(vec_perm(a, a, p16uc_PSET64_HI));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d vec_splat_dbl<1>(Packet2d& a)\n{\n  return reinterpret_cast<Packet2d>(vec_perm(a, a, p16uc_PSET64_LO));\n}\n\ntemplate<> struct packet_traits<double> : default_packet_traits\n{\n  typedef Packet2d type;\n  typedef Packet2d half;\n  enum {\n    Vectorizable = 1,\n    AlignedOnScalar = 1,\n    size=2,\n    HasHalfPacket = 1,\n\n    HasAdd  = 1,\n    HasSub  = 1,\n    HasMul  = 1,\n    HasDiv  = 1,\n    HasMin  = 1,\n    HasMax  = 1,\n    HasAbs  = 1,\n    HasSin  = 0,\n    HasCos  = 0,\n    HasLog  = 0,\n    HasExp  = 1,\n    HasSqrt = 1,\n    HasRsqrt = 1,\n    HasRound = 1,\n    HasFloor = 1,\n    HasCeil = 1,\n    HasNegate = 1,\n    HasBlend = 1\n  };\n};\n\ntemplate<> struct unpacket_traits<Packet2d> { typedef double type; enum {size=2, alignment=Aligned16}; typedef Packet2d half; };\n\ninline std::ostream & operator <<(std::ostream & s, const Packet2l & v)\n{\n  union {\n    Packet2l   v;\n    int64_t n[2];\n  } vt;\n  vt.v = v;\n  s << vt.n[0] << \", \" << vt.n[1];\n  return s;\n}\n\ninline std::ostream & operator <<(std::ostream & s, const Packet2d & v)\n{\n  union {\n    Packet2d   v;\n    double n[2];\n  } vt;\n  vt.v = v;\n  s << vt.n[0] << \", \" << vt.n[1];\n  return s;\n}\n\n// Need to define them first or we get specialization after instantiation errors\ntemplate<> EIGEN_STRONG_INLINE Packet2d pload<Packet2d>(const double* from)\n{\n  EIGEN_DEBUG_ALIGNED_LOAD\n#ifdef __VSX__\n  return vec_vsx_ld(0, from);\n#else\n  return vec_ld(0, from);\n#endif\n}\n\ntemplate<> EIGEN_STRONG_INLINE void pstore<double>(double*   to, const Packet2d& from)\n{\n  EIGEN_DEBUG_ALIGNED_STORE\n#ifdef __VSX__\n  vec_vsx_st(from, 0, to);\n#else\n  vec_st(from, 0, to);\n#endif\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d pset1<Packet2d>(const double&  from) {\n  Packet2d v = {from, from};\n  return v;\n}\n\ntemplate<> EIGEN_STRONG_INLINE void\npbroadcast4<Packet2d>(const double *a,\n                      Packet2d& a0, Packet2d& a1, Packet2d& a2, Packet2d& a3)\n{\n  a1 = pload<Packet2d>(a);\n  a0 = vec_splat_dbl<0>(a1);\n  a1 = vec_splat_dbl<1>(a1);\n  a3 = pload<Packet2d>(a+2);\n  a2 = vec_splat_dbl<0>(a3);\n  a3 = vec_splat_dbl<1>(a3);\n}\n\ntemplate<> EIGEN_DEVICE_FUNC inline Packet2d pgather<double, Packet2d>(const double* from, Index stride)\n{\n  double EIGEN_ALIGN16 af[2];\n  af[0] = from[0*stride];\n  af[1] = from[1*stride];\n return pload<Packet2d>(af);\n}\ntemplate<> EIGEN_DEVICE_FUNC inline void pscatter<double, Packet2d>(double* to, const Packet2d& from, Index stride)\n{\n  double EIGEN_ALIGN16 af[2];\n  pstore<double>(af, from);\n  to[0*stride] = af[0];\n  to[1*stride] = af[1];\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d plset<Packet2d>(const double& a) { return pset1<Packet2d>(a) + p2d_COUNTDOWN; }\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d padd<Packet2d>(const Packet2d& a, const Packet2d& b) { return a + b; }\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d psub<Packet2d>(const Packet2d& a, const Packet2d& b) { return a - b; }\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d pnegate(const Packet2d& a) { return p2d_ZERO - a; }\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d pconj(const Packet2d& a) { return a; }\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d pmul<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_madd(a,b,p2d_MZERO); }\ntemplate<> EIGEN_STRONG_INLINE Packet2d pdiv<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_div(a,b); }\n\n// for some weird raisons, it has to be overloaded for packet of integers\ntemplate<> EIGEN_STRONG_INLINE Packet2d pmadd(const Packet2d& a, const Packet2d& b, const Packet2d& c) { return vec_madd(a, b, c); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d pmin<Packet2d>(const Packet2d& a, const Packet2d& b)\n{\n  Packet2d ret;\n  __asm__ (\"xvcmpgedp %x0,%x1,%x2\\n\\txxsel %x0,%x1,%x2,%x0\" : \"=&wa\" (ret) : \"wa\" (a), \"wa\" (b));\n  return ret;\n }\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d pmax<Packet2d>(const Packet2d& a, const Packet2d& b)\n{\n  Packet2d ret;\n  __asm__ (\"xvcmpgtdp %x0,%x2,%x1\\n\\txxsel %x0,%x1,%x2,%x0\" : \"=&wa\" (ret) : \"wa\" (a), \"wa\" (b));\n  return ret;\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d pand<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_and(a, b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d por<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_or(a, b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d pxor<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_xor(a, b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d pandnot<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_and(a, vec_nor(b, b)); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d pround<Packet2d>(const Packet2d& a) { return vec_round(a); }\ntemplate<> EIGEN_STRONG_INLINE Packet2d pceil<Packet2d>(const  Packet2d& a) { return vec_ceil(a); }\ntemplate<> EIGEN_STRONG_INLINE Packet2d pfloor<Packet2d>(const Packet2d& a) { return vec_floor(a); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d ploadu<Packet2d>(const double* from)\n{\n  EIGEN_DEBUG_ALIGNED_LOAD\n  return (Packet2d) vec_vsx_ld((long)from & 15, (const double*) _EIGEN_ALIGNED_PTR(from));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d ploaddup<Packet2d>(const double*   from)\n{\n  Packet2d p;\n  if((std::ptrdiff_t(from) % 16) == 0)  p = pload<Packet2d>(from);\n  else                                  p = ploadu<Packet2d>(from);\n  return vec_splat_dbl<0>(p);\n}\n\ntemplate<> EIGEN_STRONG_INLINE void pstoreu<double>(double*  to, const Packet2d& from)\n{\n  EIGEN_DEBUG_ALIGNED_STORE\n  vec_vsx_st((Packet4f)from, (long)to & 15, (float*) _EIGEN_ALIGNED_PTR(to));\n}\n\ntemplate<> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { EIGEN_PPC_PREFETCH(addr); }\n\ntemplate<> EIGEN_STRONG_INLINE double  pfirst<Packet2d>(const Packet2d& a) { double EIGEN_ALIGN16 x[2]; pstore<double>(x, a); return x[0]; }\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d preverse(const Packet2d& a)\n{\n  return reinterpret_cast<Packet2d>(vec_perm(reinterpret_cast<Packet16uc>(a), reinterpret_cast<Packet16uc>(a), p16uc_REVERSE64));\n}\ntemplate<> EIGEN_STRONG_INLINE Packet2d pabs(const Packet2d& a) { return vec_abs(a); }\n\ntemplate<> EIGEN_STRONG_INLINE double predux<Packet2d>(const Packet2d& a)\n{\n  Packet2d b, sum;\n  b   = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(a), reinterpret_cast<Packet4f>(a), 8));\n  sum = a + b;\n  return pfirst<Packet2d>(sum);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d preduxp<Packet2d>(const Packet2d* vecs)\n{\n  Packet2d v[2], sum;\n  v[0] = vecs[0] + reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(vecs[0]), reinterpret_cast<Packet4f>(vecs[0]), 8));\n  v[1] = vecs[1] + reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(vecs[1]), reinterpret_cast<Packet4f>(vecs[1]), 8));\n\n#ifdef _BIG_ENDIAN\n  sum = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(v[0]), reinterpret_cast<Packet4f>(v[1]), 8));\n#else\n  sum = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(v[1]), reinterpret_cast<Packet4f>(v[0]), 8));\n#endif\n\n  return sum;\n}\n// Other reduction functions:\n// mul\ntemplate<> EIGEN_STRONG_INLINE double predux_mul<Packet2d>(const Packet2d& a)\n{\n  return pfirst(pmul(a, reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(a), reinterpret_cast<Packet4ui>(a), 8))));\n}\n\n// min\ntemplate<> EIGEN_STRONG_INLINE double predux_min<Packet2d>(const Packet2d& a)\n{\n  return pfirst(pmin(a, reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(a), reinterpret_cast<Packet4ui>(a), 8))));\n}\n\n// max\ntemplate<> EIGEN_STRONG_INLINE double predux_max<Packet2d>(const Packet2d& a)\n{\n  return pfirst(pmax(a, reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(a), reinterpret_cast<Packet4ui>(a), 8))));\n}\n\ntemplate<int Offset>\nstruct palign_impl<Offset,Packet2d>\n{\n  static EIGEN_STRONG_INLINE void run(Packet2d& first, const Packet2d& second)\n  {\n    if (Offset == 1)\n#ifdef _BIG_ENDIAN\n      first = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(first), reinterpret_cast<Packet4ui>(second), 8));\n#else\n      first = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(second), reinterpret_cast<Packet4ui>(first), 8));\n#endif\n  }\n};\n\nEIGEN_DEVICE_FUNC inline void\nptranspose(PacketBlock<Packet2d,2>& kernel) {\n  Packet2d t0, t1;\n  t0 = vec_perm(kernel.packet[0], kernel.packet[1], p16uc_TRANSPOSE64_HI);\n  t1 = vec_perm(kernel.packet[0], kernel.packet[1], p16uc_TRANSPOSE64_LO);\n  kernel.packet[0] = t0;\n  kernel.packet[1] = t1;\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d pblend(const Selector<2>& ifPacket, const Packet2d& thenPacket, const Packet2d& elsePacket) {\n  Packet2l select = { ifPacket.select[0], ifPacket.select[1] };\n  Packet2bl mask = reinterpret_cast<Packet2bl>( vec_cmpeq(reinterpret_cast<Packet2d>(select), reinterpret_cast<Packet2d>(p2l_ONE)) );\n  return vec_sel(elsePacket, thenPacket, mask);\n}\n#endif // __VSX__\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_PACKET_MATH_ALTIVEC_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/arch/CUDA/Complex.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_COMPLEX_CUDA_H\n#define EIGEN_COMPLEX_CUDA_H\n\n// clang-format off\n\nnamespace Eigen {\n\nnamespace internal {\n\n#if defined(__CUDACC__) && defined(EIGEN_USE_GPU)\n\n// Many std::complex methods such as operator+, operator-, operator* and\n// operator/ are not constexpr. Due to this, clang does not treat them as device\n// functions and thus Eigen functors making use of these operators fail to\n// compile. Here, we manually specialize these functors for complex types when\n// building for CUDA to avoid non-constexpr methods.\n\n// Sum\ntemplate<typename T> struct scalar_sum_op<const std::complex<T>, const std::complex<T> > : binary_op_base<const std::complex<T>, const std::complex<T> > {\n  typedef typename std::complex<T> result_type;\n\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_sum_op)\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::complex<T> operator() (const std::complex<T>& a, const std::complex<T>& b) const {\n    return std::complex<T>(numext::real(a) + numext::real(b),\n                           numext::imag(a) + numext::imag(b));\n  }\n};\n\ntemplate<typename T> struct scalar_sum_op<std::complex<T>, std::complex<T> > : scalar_sum_op<const std::complex<T>, const std::complex<T> > {};\n\n\n// Difference\ntemplate<typename T> struct scalar_difference_op<const std::complex<T>, const std::complex<T> >  : binary_op_base<const std::complex<T>, const std::complex<T> > {\n  typedef typename std::complex<T> result_type;\n\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_difference_op)\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::complex<T> operator() (const std::complex<T>& a, const std::complex<T>& b) const {\n    return std::complex<T>(numext::real(a) - numext::real(b),\n                           numext::imag(a) - numext::imag(b));\n  }\n};\n\ntemplate<typename T> struct scalar_difference_op<std::complex<T>, std::complex<T> > : scalar_difference_op<const std::complex<T>, const std::complex<T> > {};\n\n\n// Product\ntemplate<typename T> struct scalar_product_op<const std::complex<T>, const std::complex<T> >  : binary_op_base<const std::complex<T>, const std::complex<T> > {\n  enum {\n    Vectorizable = packet_traits<std::complex<T>>::HasMul\n  };\n  typedef typename std::complex<T> result_type;\n\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_product_op)\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::complex<T> operator() (const std::complex<T>& a, const std::complex<T>& b) const {\n    const T a_real = numext::real(a);\n    const T a_imag = numext::imag(a);\n    const T b_real = numext::real(b);\n    const T b_imag = numext::imag(b);\n    return std::complex<T>(a_real * b_real - a_imag * b_imag,\n                           a_real * b_imag + a_imag * b_real);\n  }\n};\n\ntemplate<typename T> struct scalar_product_op<std::complex<T>, std::complex<T> > : scalar_product_op<const std::complex<T>, const std::complex<T> > {};\n\n\n// Quotient\ntemplate<typename T> struct scalar_quotient_op<const std::complex<T>, const std::complex<T> > : binary_op_base<const std::complex<T>, const std::complex<T> > {\n  enum {\n    Vectorizable = packet_traits<std::complex<T>>::HasDiv\n  };\n  typedef typename std::complex<T> result_type;\n\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_quotient_op)\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::complex<T> operator() (const std::complex<T>& a, const std::complex<T>& b) const {\n    const T a_real = numext::real(a);\n    const T a_imag = numext::imag(a);\n    const T b_real = numext::real(b);\n    const T b_imag = numext::imag(b);\n    const T norm = T(1) / (b_real * b_real + b_imag * b_imag);\n    return std::complex<T>((a_real * b_real + a_imag * b_imag) * norm,\n                           (a_imag * b_real - a_real * b_imag) * norm);\n  }\n};\n\ntemplate<typename T> struct scalar_quotient_op<std::complex<T>, std::complex<T> > : scalar_quotient_op<const std::complex<T>, const std::complex<T> > {};\n\n#endif\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_COMPLEX_CUDA_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/arch/CUDA/Half.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n//\n// The conversion routines are Copyright (c) Fabian Giesen, 2016.\n// The original license follows:\n//\n// Copyright (c) Fabian Giesen, 2016\n// All rights reserved.\n// Redistribution and use in source and binary forms, with or without\n// modification, are permitted.\n// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS\n// \"AS IS\" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT\n// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR\n// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT\n// HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,\n// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT\n// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,\n// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY\n// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT\n// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE\n// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n\n\n// Standard 16-bit float type, mostly useful for GPUs. Defines a new\n// type Eigen::half (inheriting from CUDA's __half struct) with\n// operator overloads such that it behaves basically as an arithmetic\n// type. It will be quite slow on CPUs (so it is recommended to stay\n// in fp32 for CPUs, except for simple parameter conversions, I/O\n// to disk and the likes), but fast on GPUs.\n\n\n#ifndef EIGEN_HALF_CUDA_H\n#define EIGEN_HALF_CUDA_H\n\n#if __cplusplus > 199711L\n#define EIGEN_EXPLICIT_CAST(tgt_type) explicit operator tgt_type()\n#else\n#define EIGEN_EXPLICIT_CAST(tgt_type) operator tgt_type()\n#endif\n\n\nnamespace Eigen {\n\nstruct half;\n\nnamespace half_impl {\n\n#if !defined(EIGEN_HAS_CUDA_FP16)\n\n// Make our own __half definition that is similar to CUDA's.\nstruct __half {\n  EIGEN_DEVICE_FUNC __half() {}\n  explicit EIGEN_DEVICE_FUNC __half(unsigned short raw) : x(raw) {}\n  unsigned short x;\n};\n\n#endif\n\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __half raw_uint16_to_half(unsigned short x);\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __half float_to_half_rtne(float ff);\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC float half_to_float(__half h);\n\nstruct half_base : public __half {\n  EIGEN_DEVICE_FUNC half_base() {}\n  EIGEN_DEVICE_FUNC half_base(const half_base& h) : __half(h) {}\n  EIGEN_DEVICE_FUNC half_base(const __half& h) : __half(h) {}\n};\n\n} // namespace half_impl\n\n// Class definition.\nstruct half : public half_impl::half_base {\n  #if !defined(EIGEN_HAS_CUDA_FP16)\n    typedef half_impl::__half __half;\n  #endif\n\n  EIGEN_DEVICE_FUNC half() {}\n\n  EIGEN_DEVICE_FUNC half(const __half& h) : half_impl::half_base(h) {}\n  EIGEN_DEVICE_FUNC half(const half& h) : half_impl::half_base(h) {}\n\n  explicit EIGEN_DEVICE_FUNC half(bool b)\n      : half_impl::half_base(half_impl::raw_uint16_to_half(b ? 0x3c00 : 0)) {}\n  template<class T>\n  explicit EIGEN_DEVICE_FUNC half(const T& val)\n      : half_impl::half_base(half_impl::float_to_half_rtne(static_cast<float>(val))) {}\n  explicit EIGEN_DEVICE_FUNC half(float f)\n      : half_impl::half_base(half_impl::float_to_half_rtne(f)) {}\n\n  EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(bool) const {\n    // +0.0 and -0.0 become false, everything else becomes true.\n    return (x & 0x7fff) != 0;\n  }\n  EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(signed char) const {\n    return static_cast<signed char>(half_impl::half_to_float(*this));\n  }\n  EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(unsigned char) const {\n    return static_cast<unsigned char>(half_impl::half_to_float(*this));\n  }\n  EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(short) const {\n    return static_cast<short>(half_impl::half_to_float(*this));\n  }\n  EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(unsigned short) const {\n    return static_cast<unsigned short>(half_impl::half_to_float(*this));\n  }\n  EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(int) const {\n    return static_cast<int>(half_impl::half_to_float(*this));\n  }\n  EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(unsigned int) const {\n    return static_cast<unsigned int>(half_impl::half_to_float(*this));\n  }\n  EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(long) const {\n    return static_cast<long>(half_impl::half_to_float(*this));\n  }\n  EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(unsigned long) const {\n    return static_cast<unsigned long>(half_impl::half_to_float(*this));\n  }\n  EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(long long) const {\n    return static_cast<long long>(half_impl::half_to_float(*this));\n  }\n  EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(unsigned long long) const {\n    return static_cast<unsigned long long>(half_to_float(*this));\n  }\n  EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(float) const {\n    return half_impl::half_to_float(*this);\n  }\n  EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(double) const {\n    return static_cast<double>(half_impl::half_to_float(*this));\n  }\n\n  EIGEN_DEVICE_FUNC half& operator=(const half& other) {\n    x = other.x;\n    return *this;\n  }\n};\n\nnamespace half_impl {\n\n#if defined(EIGEN_HAS_CUDA_FP16) && defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 530\n\n// Intrinsics for native fp16 support. Note that on current hardware,\n// these are no faster than fp32 arithmetic (you need to use the half2\n// versions to get the ALU speed increased), but you do save the\n// conversion steps back and forth.\n\nEIGEN_STRONG_INLINE __device__ half operator + (const half& a, const half& b) {\n  return __hadd(a, b);\n}\nEIGEN_STRONG_INLINE __device__ half operator * (const half& a, const half& b) {\n  return __hmul(a, b);\n}\nEIGEN_STRONG_INLINE __device__ half operator - (const half& a, const half& b) {\n  return __hsub(a, b);\n}\nEIGEN_STRONG_INLINE __device__ half operator / (const half& a, const half& b) {\n  float num = __half2float(a);\n  float denom = __half2float(b);\n  return __float2half(num / denom);\n}\nEIGEN_STRONG_INLINE __device__ half operator - (const half& a) {\n  return __hneg(a);\n}\nEIGEN_STRONG_INLINE __device__ half& operator += (half& a, const half& b) {\n  a = a + b;\n  return a;\n}\nEIGEN_STRONG_INLINE __device__ half& operator *= (half& a, const half& b) {\n  a = a * b;\n  return a;\n}\nEIGEN_STRONG_INLINE __device__ half& operator -= (half& a, const half& b) {\n  a = a - b;\n  return a;\n}\nEIGEN_STRONG_INLINE __device__ half& operator /= (half& a, const half& b) {\n  a = a / b;\n  return a;\n}\nEIGEN_STRONG_INLINE __device__ bool operator == (const half& a, const half& b) {\n  return __heq(a, b);\n}\nEIGEN_STRONG_INLINE __device__ bool operator != (const half& a, const half& b) {\n  return __hne(a, b);\n}\nEIGEN_STRONG_INLINE __device__ bool operator < (const half& a, const half& b) {\n  return __hlt(a, b);\n}\nEIGEN_STRONG_INLINE __device__ bool operator <= (const half& a, const half& b) {\n  return __hle(a, b);\n}\nEIGEN_STRONG_INLINE __device__ bool operator > (const half& a, const half& b) {\n  return __hgt(a, b);\n}\nEIGEN_STRONG_INLINE __device__ bool operator >= (const half& a, const half& b) {\n  return __hge(a, b);\n}\n\n#else  // Emulate support for half floats\n\n// Definitions for CPUs and older CUDA, mostly working through conversion\n// to/from fp32.\n\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator + (const half& a, const half& b) {\n  return half(float(a) + float(b));\n}\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator * (const half& a, const half& b) {\n  return half(float(a) * float(b));\n}\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator - (const half& a, const half& b) {\n  return half(float(a) - float(b));\n}\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator / (const half& a, const half& b) {\n  return half(float(a) / float(b));\n}\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator - (const half& a) {\n  half result;\n  result.x = a.x ^ 0x8000;\n  return result;\n}\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half& operator += (half& a, const half& b) {\n  a = half(float(a) + float(b));\n  return a;\n}\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half& operator *= (half& a, const half& b) {\n  a = half(float(a) * float(b));\n  return a;\n}\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half& operator -= (half& a, const half& b) {\n  a = half(float(a) - float(b));\n  return a;\n}\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half& operator /= (half& a, const half& b) {\n  a = half(float(a) / float(b));\n  return a;\n}\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator == (const half& a, const half& b) {\n  return numext::equal_strict(float(a),float(b));\n}\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator != (const half& a, const half& b) {\n  return numext::not_equal_strict(float(a), float(b));\n}\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator < (const half& a, const half& b) {\n  return float(a) < float(b);\n}\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator <= (const half& a, const half& b) {\n  return float(a) <= float(b);\n}\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator > (const half& a, const half& b) {\n  return float(a) > float(b);\n}\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator >= (const half& a, const half& b) {\n  return float(a) >= float(b);\n}\n\n#endif  // Emulate support for half floats\n\n// Division by an index. Do it in full float precision to avoid accuracy\n// issues in converting the denominator to half.\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator / (const half& a, Index b) {\n  return half(static_cast<float>(a) / static_cast<float>(b));\n}\n\n// Conversion routines, including fallbacks for the host or older CUDA.\n// Note that newer Intel CPUs (Haswell or newer) have vectorized versions of\n// these in hardware. If we need more performance on older/other CPUs, they are\n// also possible to vectorize directly.\n\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __half raw_uint16_to_half(unsigned short x) {\n  __half h;\n  h.x = x;\n  return h;\n}\n\nunion FP32 {\n  unsigned int u;\n  float f;\n};\n\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __half float_to_half_rtne(float ff) {\n#if defined(EIGEN_HAS_CUDA_FP16) && defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 300\n  return __float2half(ff);\n\n#elif defined(EIGEN_HAS_FP16_C)\n  __half h;\n  h.x = _cvtss_sh(ff, 0);\n  return h;\n\n#else\n  FP32 f; f.f = ff;\n\n  const FP32 f32infty = { 255 << 23 };\n  const FP32 f16max = { (127 + 16) << 23 };\n  const FP32 denorm_magic = { ((127 - 15) + (23 - 10) + 1) << 23 };\n  unsigned int sign_mask = 0x80000000u;\n  __half o;\n  o.x = static_cast<unsigned short>(0x0u);\n\n  unsigned int sign = f.u & sign_mask;\n  f.u ^= sign;\n\n  // NOTE all the integer compares in this function can be safely\n  // compiled into signed compares since all operands are below\n  // 0x80000000. Important if you want fast straight SSE2 code\n  // (since there's no unsigned PCMPGTD).\n\n  if (f.u >= f16max.u) {  // result is Inf or NaN (all exponent bits set)\n    o.x = (f.u > f32infty.u) ? 0x7e00 : 0x7c00; // NaN->qNaN and Inf->Inf\n  } else {  // (De)normalized number or zero\n    if (f.u < (113 << 23)) {  // resulting FP16 is subnormal or zero\n      // use a magic value to align our 10 mantissa bits at the bottom of\n      // the float. as long as FP addition is round-to-nearest-even this\n      // just works.\n      f.f += denorm_magic.f;\n\n      // and one integer subtract of the bias later, we have our final float!\n      o.x = static_cast<unsigned short>(f.u - denorm_magic.u);\n    } else {\n      unsigned int mant_odd = (f.u >> 13) & 1; // resulting mantissa is odd\n\n      // update exponent, rounding bias part 1\n      f.u += ((unsigned int)(15 - 127) << 23) + 0xfff;\n      // rounding bias part 2\n      f.u += mant_odd;\n      // take the bits!\n      o.x = static_cast<unsigned short>(f.u >> 13);\n    }\n  }\n\n  o.x |= static_cast<unsigned short>(sign >> 16);\n  return o;\n#endif\n}\n\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC float half_to_float(__half h) {\n#if defined(EIGEN_HAS_CUDA_FP16) && defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 300\n  return __half2float(h);\n\n#elif defined(EIGEN_HAS_FP16_C)\n  return _cvtsh_ss(h.x);\n\n#else\n  const FP32 magic = { 113 << 23 };\n  const unsigned int shifted_exp = 0x7c00 << 13; // exponent mask after shift\n  FP32 o;\n\n  o.u = (h.x & 0x7fff) << 13;             // exponent/mantissa bits\n  unsigned int exp = shifted_exp & o.u;   // just the exponent\n  o.u += (127 - 15) << 23;                // exponent adjust\n\n  // handle exponent special cases\n  if (exp == shifted_exp) {     // Inf/NaN?\n    o.u += (128 - 16) << 23;    // extra exp adjust\n  } else if (exp == 0) {        // Zero/Denormal?\n    o.u += 1 << 23;             // extra exp adjust\n    o.f -= magic.f;             // renormalize\n  }\n\n  o.u |= (h.x & 0x8000) << 16;    // sign bit\n  return o.f;\n#endif\n}\n\n// --- standard functions ---\n\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool (isinf)(const half& a) {\n  return (a.x & 0x7fff) == 0x7c00;\n}\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool (isnan)(const half& a) {\n#if defined(EIGEN_HAS_CUDA_FP16) && defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 530\n  return __hisnan(a);\n#else\n  return (a.x & 0x7fff) > 0x7c00;\n#endif\n}\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool (isfinite)(const half& a) {\n  return !(isinf EIGEN_NOT_A_MACRO (a)) && !(isnan EIGEN_NOT_A_MACRO (a));\n}\n\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half abs(const half& a) {\n  half result;\n  result.x = a.x & 0x7FFF;\n  return result;\n}\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half exp(const half& a) {\n#if EIGEN_CUDACC_VER >= 80000 && defined EIGEN_CUDA_ARCH && EIGEN_CUDA_ARCH >= 530\n  return half(hexp(a));\n#else\n   return half(::expf(float(a)));\n#endif\n}\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half log(const half& a) {\n#if defined(EIGEN_HAS_CUDA_FP16) && EIGEN_CUDACC_VER >= 80000 && defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 530\n  return half(::hlog(a));\n#else\n  return half(::logf(float(a)));\n#endif\n}\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half log1p(const half& a) {\n  return half(numext::log1p(float(a)));\n}\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half log10(const half& a) {\n  return half(::log10f(float(a)));\n}\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half sqrt(const half& a) {\n#if EIGEN_CUDACC_VER >= 80000 && defined EIGEN_CUDA_ARCH && EIGEN_CUDA_ARCH >= 530\n  return half(hsqrt(a));\n#else\n    return half(::sqrtf(float(a)));\n#endif\n}\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half pow(const half& a, const half& b) {\n  return half(::powf(float(a), float(b)));\n}\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half sin(const half& a) {\n  return half(::sinf(float(a)));\n}\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half cos(const half& a) {\n  return half(::cosf(float(a)));\n}\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half tan(const half& a) {\n  return half(::tanf(float(a)));\n}\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half tanh(const half& a) {\n  return half(::tanhf(float(a)));\n}\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half floor(const half& a) {\n#if EIGEN_CUDACC_VER >= 80000 && defined EIGEN_CUDA_ARCH && EIGEN_CUDA_ARCH >= 300\n  return half(hfloor(a));\n#else\n  return half(::floorf(float(a)));\n#endif\n}\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half ceil(const half& a) {\n#if EIGEN_CUDACC_VER >= 80000 && defined EIGEN_CUDA_ARCH && EIGEN_CUDA_ARCH >= 300\n  return half(hceil(a));\n#else\n  return half(::ceilf(float(a)));\n#endif\n}\n\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half (min)(const half& a, const half& b) {\n#if defined(EIGEN_HAS_CUDA_FP16) && defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 530\n  return __hlt(b, a) ? b : a;\n#else\n  const float f1 = static_cast<float>(a);\n  const float f2 = static_cast<float>(b);\n  return f2 < f1 ? b : a;\n#endif\n}\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half (max)(const half& a, const half& b) {\n#if defined(EIGEN_HAS_CUDA_FP16) && defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 530\n  return __hlt(a, b) ? b : a;\n#else\n  const float f1 = static_cast<float>(a);\n  const float f2 = static_cast<float>(b);\n  return f1 < f2 ? b : a;\n#endif\n}\n\nEIGEN_ALWAYS_INLINE std::ostream& operator << (std::ostream& os, const half& v) {\n  os << static_cast<float>(v);\n  return os;\n}\n\n} // end namespace half_impl\n\n// import Eigen::half_impl::half into Eigen namespace\n// using half_impl::half;\n\nnamespace internal {\n\ntemplate<>\nstruct random_default_impl<half, false, false>\n{\n  static inline half run(const half& x, const half& y)\n  {\n    return x + (y-x) * half(float(std::rand()) / float(RAND_MAX));\n  }\n  static inline half run()\n  {\n    return run(half(-1.f), half(1.f));\n  }\n};\n\ntemplate<> struct is_arithmetic<half> { enum { value = true }; };\n\n} // end namespace internal\n\n}  // end namespace Eigen\n\nnamespace std {\ntemplate<>\nstruct numeric_limits<Eigen::half> {\n  static const bool is_specialized = true;\n  static const bool is_signed = true;\n  static const bool is_integer = false;\n  static const bool is_exact = false;\n  static const bool has_infinity = true;\n  static const bool has_quiet_NaN = true;\n  static const bool has_signaling_NaN = true;\n  static const float_denorm_style has_denorm = denorm_present;\n  static const bool has_denorm_loss = false;\n  static const std::float_round_style round_style = std::round_to_nearest;\n  static const bool is_iec559 = false;\n  static const bool is_bounded = false;\n  static const bool is_modulo = false;\n  static const int digits = 11;\n  static const int digits10 = 3;      // according to http://half.sourceforge.net/structstd_1_1numeric__limits_3_01half__float_1_1half_01_4.html\n  static const int max_digits10 = 5;  // according to http://half.sourceforge.net/structstd_1_1numeric__limits_3_01half__float_1_1half_01_4.html\n  static const int radix = 2;\n  static const int min_exponent = -13;\n  static const int min_exponent10 = -4;\n  static const int max_exponent = 16;\n  static const int max_exponent10 = 4;\n  static const bool traps = true;\n  static const bool tinyness_before = false;\n\n  static Eigen::half (min)() { return Eigen::half_impl::raw_uint16_to_half(0x400); }\n  static Eigen::half lowest() { return Eigen::half_impl::raw_uint16_to_half(0xfbff); }\n  static Eigen::half (max)() { return Eigen::half_impl::raw_uint16_to_half(0x7bff); }\n  static Eigen::half epsilon() { return Eigen::half_impl::raw_uint16_to_half(0x0800); }\n  static Eigen::half round_error() { return Eigen::half(0.5); }\n  static Eigen::half infinity() { return Eigen::half_impl::raw_uint16_to_half(0x7c00); }\n  static Eigen::half quiet_NaN() { return Eigen::half_impl::raw_uint16_to_half(0x7e00); }\n  static Eigen::half signaling_NaN() { return Eigen::half_impl::raw_uint16_to_half(0x7e00); }\n  static Eigen::half denorm_min() { return Eigen::half_impl::raw_uint16_to_half(0x1); }\n};\n}\n\nnamespace Eigen {\n\ntemplate<> struct NumTraits<Eigen::half>\n    : GenericNumTraits<Eigen::half>\n{\n  enum {\n    IsSigned = true,\n    IsInteger = false,\n    IsComplex = false,\n    RequireInitialization = false\n  };\n\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Eigen::half epsilon() {\n    return half_impl::raw_uint16_to_half(0x0800);\n  }\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Eigen::half dummy_precision() { return Eigen::half(1e-2f); }\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Eigen::half highest() {\n    return half_impl::raw_uint16_to_half(0x7bff);\n  }\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Eigen::half lowest() {\n    return half_impl::raw_uint16_to_half(0xfbff);\n  }\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Eigen::half infinity() {\n    return half_impl::raw_uint16_to_half(0x7c00);\n  }\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Eigen::half quiet_NaN() {\n    return half_impl::raw_uint16_to_half(0x7c01);\n  }\n};\n\n} // end namespace Eigen\n\n// C-like standard mathematical functions and trancendentals.\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half fabsh(const Eigen::half& a) {\n  Eigen::half result;\n  result.x = a.x & 0x7FFF;\n  return result;\n}\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half exph(const Eigen::half& a) {\n  return Eigen::half(::expf(float(a)));\n}\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half logh(const Eigen::half& a) {\n#if EIGEN_CUDACC_VER >= 80000 && defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 530\n  return Eigen::half(::hlog(a));\n#else\n  return Eigen::half(::logf(float(a)));\n#endif\n}\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half sqrth(const Eigen::half& a) {\n  return Eigen::half(::sqrtf(float(a)));\n}\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half powh(const Eigen::half& a, const Eigen::half& b) {\n  return Eigen::half(::powf(float(a), float(b)));\n}\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half floorh(const Eigen::half& a) {\n  return Eigen::half(::floorf(float(a)));\n}\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half ceilh(const Eigen::half& a) {\n  return Eigen::half(::ceilf(float(a)));\n}\n\nnamespace std {\n\n#if __cplusplus > 199711L\ntemplate <>\nstruct hash<Eigen::half> {\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::size_t operator()(const Eigen::half& a) const {\n    return static_cast<std::size_t>(a.x);\n  }\n};\n#endif\n\n} // end namespace std\n\n\n// Add the missing shfl_xor intrinsic\n#if defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 300\n__device__ EIGEN_STRONG_INLINE Eigen::half __shfl_xor(Eigen::half var, int laneMask, int width=warpSize) {\n  return static_cast<Eigen::half>(__shfl_xor(static_cast<float>(var), laneMask, width));\n}\n#endif\n\n// ldg() has an overload for __half, but we also need one for Eigen::half.\n#if defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 350\nEIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half __ldg(const Eigen::half* ptr) {\n  return Eigen::half_impl::raw_uint16_to_half(\n      __ldg(reinterpret_cast<const unsigned short*>(ptr)));\n}\n#endif\n\n\n#if defined(__CUDA_ARCH__)\nnamespace Eigen {\nnamespace numext {\n\ntemplate<>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nbool (isnan)(const Eigen::half& h) {\n  return (half_impl::isnan)(h);\n}\n\ntemplate<>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nbool (isinf)(const Eigen::half& h) {\n  return (half_impl::isinf)(h);\n}\n\ntemplate<>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nbool (isfinite)(const Eigen::half& h) {\n  return (half_impl::isfinite)(h);\n}\n\n} // namespace Eigen\n}  // namespace numext\n#endif\n\n#endif // EIGEN_HALF_CUDA_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/arch/CUDA/MathFunctions.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_MATH_FUNCTIONS_CUDA_H\n#define EIGEN_MATH_FUNCTIONS_CUDA_H\n\nnamespace Eigen {\n\nnamespace internal {\n\n// Make sure this is only available when targeting a GPU: we don't want to\n// introduce conflicts between these packet_traits definitions and the ones\n// we'll use on the host side (SSE, AVX, ...)\n#if defined(__CUDACC__) && defined(EIGEN_USE_GPU)\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nfloat4 plog<float4>(const float4& a)\n{\n  return make_float4(logf(a.x), logf(a.y), logf(a.z), logf(a.w));\n}\n\ntemplate<>  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\ndouble2 plog<double2>(const double2& a)\n{\n  using ::log;\n  return make_double2(log(a.x), log(a.y));\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nfloat4 plog1p<float4>(const float4& a)\n{\n  return make_float4(log1pf(a.x), log1pf(a.y), log1pf(a.z), log1pf(a.w));\n}\n\ntemplate<>  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\ndouble2 plog1p<double2>(const double2& a)\n{\n  return make_double2(log1p(a.x), log1p(a.y));\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nfloat4 pexp<float4>(const float4& a)\n{\n  return make_float4(expf(a.x), expf(a.y), expf(a.z), expf(a.w));\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\ndouble2 pexp<double2>(const double2& a)\n{\n  using ::exp;\n  return make_double2(exp(a.x), exp(a.y));\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nfloat4 psqrt<float4>(const float4& a)\n{\n  return make_float4(sqrtf(a.x), sqrtf(a.y), sqrtf(a.z), sqrtf(a.w));\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\ndouble2 psqrt<double2>(const double2& a)\n{\n  using ::sqrt;\n  return make_double2(sqrt(a.x), sqrt(a.y));\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nfloat4 prsqrt<float4>(const float4& a)\n{\n  return make_float4(rsqrtf(a.x), rsqrtf(a.y), rsqrtf(a.z), rsqrtf(a.w));\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\ndouble2 prsqrt<double2>(const double2& a)\n{\n  return make_double2(rsqrt(a.x), rsqrt(a.y));\n}\n\n\n#endif\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_MATH_FUNCTIONS_CUDA_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/arch/CUDA/PacketMath.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_PACKET_MATH_CUDA_H\n#define EIGEN_PACKET_MATH_CUDA_H\n\nnamespace Eigen {\n\nnamespace internal {\n\n// Make sure this is only available when targeting a GPU: we don't want to\n// introduce conflicts between these packet_traits definitions and the ones\n// we'll use on the host side (SSE, AVX, ...)\n#if defined(__CUDACC__) && defined(EIGEN_USE_GPU)\ntemplate<> struct is_arithmetic<float4>  { enum { value = true }; };\ntemplate<> struct is_arithmetic<double2> { enum { value = true }; };\n\ntemplate<> struct packet_traits<float> : default_packet_traits\n{\n  typedef float4 type;\n  typedef float4 half;\n  enum {\n    Vectorizable = 1,\n    AlignedOnScalar = 1,\n    size=4,\n    HasHalfPacket = 0,\n\n    HasDiv  = 1,\n    HasSin  = 0,\n    HasCos  = 0,\n    HasLog  = 1,\n    HasExp  = 1,\n    HasSqrt = 1,\n    HasRsqrt = 1,\n    HasLGamma = 1,\n    HasDiGamma = 1,\n    HasZeta = 1,\n    HasPolygamma = 1,\n    HasErf = 1,\n    HasErfc = 1,\n    HasIGamma = 1,\n    HasIGammac = 1,\n    HasBetaInc = 1,\n\n    HasBlend = 0,\n  };\n};\n\ntemplate<> struct packet_traits<double> : default_packet_traits\n{\n  typedef double2 type;\n  typedef double2 half;\n  enum {\n    Vectorizable = 1,\n    AlignedOnScalar = 1,\n    size=2,\n    HasHalfPacket = 0,\n\n    HasDiv  = 1,\n    HasLog  = 1,\n    HasExp  = 1,\n    HasSqrt = 1,\n    HasRsqrt = 1,\n    HasLGamma = 1,\n    HasDiGamma = 1,\n    HasZeta = 1,\n    HasPolygamma = 1,\n    HasErf = 1,\n    HasErfc = 1,\n    HasIGamma = 1,\n    HasIGammac = 1,\n    HasBetaInc = 1,\n\n    HasBlend = 0,\n  };\n};\n\n\ntemplate<> struct unpacket_traits<float4>  { typedef float  type; enum {size=4, alignment=Aligned16}; typedef float4 half; };\ntemplate<> struct unpacket_traits<double2> { typedef double type; enum {size=2, alignment=Aligned16}; typedef double2 half; };\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pset1<float4>(const float&  from) {\n  return make_float4(from, from, from, from);\n}\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 pset1<double2>(const double& from) {\n  return make_double2(from, from);\n}\n\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 plset<float4>(const float& a) {\n  return make_float4(a, a+1, a+2, a+3);\n}\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 plset<double2>(const double& a) {\n  return make_double2(a, a+1);\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 padd<float4>(const float4& a, const float4& b) {\n  return make_float4(a.x+b.x, a.y+b.y, a.z+b.z, a.w+b.w);\n}\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 padd<double2>(const double2& a, const double2& b) {\n  return make_double2(a.x+b.x, a.y+b.y);\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 psub<float4>(const float4& a, const float4& b) {\n  return make_float4(a.x-b.x, a.y-b.y, a.z-b.z, a.w-b.w);\n}\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 psub<double2>(const double2& a, const double2& b) {\n  return make_double2(a.x-b.x, a.y-b.y);\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pnegate(const float4& a) {\n  return make_float4(-a.x, -a.y, -a.z, -a.w);\n}\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 pnegate(const double2& a) {\n  return make_double2(-a.x, -a.y);\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pconj(const float4& a) { return a; }\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 pconj(const double2& a) { return a; }\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pmul<float4>(const float4& a, const float4& b) {\n  return make_float4(a.x*b.x, a.y*b.y, a.z*b.z, a.w*b.w);\n}\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 pmul<double2>(const double2& a, const double2& b) {\n  return make_double2(a.x*b.x, a.y*b.y);\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pdiv<float4>(const float4& a, const float4& b) {\n  return make_float4(a.x/b.x, a.y/b.y, a.z/b.z, a.w/b.w);\n}\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 pdiv<double2>(const double2& a, const double2& b) {\n  return make_double2(a.x/b.x, a.y/b.y);\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pmin<float4>(const float4& a, const float4& b) {\n  return make_float4(fminf(a.x, b.x), fminf(a.y, b.y), fminf(a.z, b.z), fminf(a.w, b.w));\n}\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 pmin<double2>(const double2& a, const double2& b) {\n  return make_double2(fmin(a.x, b.x), fmin(a.y, b.y));\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pmax<float4>(const float4& a, const float4& b) {\n  return make_float4(fmaxf(a.x, b.x), fmaxf(a.y, b.y), fmaxf(a.z, b.z), fmaxf(a.w, b.w));\n}\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 pmax<double2>(const double2& a, const double2& b) {\n  return make_double2(fmax(a.x, b.x), fmax(a.y, b.y));\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pload<float4>(const float* from) {\n  return *reinterpret_cast<const float4*>(from);\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 pload<double2>(const double* from) {\n  return *reinterpret_cast<const double2*>(from);\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 ploadu<float4>(const float* from) {\n  return make_float4(from[0], from[1], from[2], from[3]);\n}\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 ploadu<double2>(const double* from) {\n  return make_double2(from[0], from[1]);\n}\n\ntemplate<> EIGEN_STRONG_INLINE float4 ploaddup<float4>(const float*   from) {\n  return make_float4(from[0], from[0], from[1], from[1]);\n}\ntemplate<> EIGEN_STRONG_INLINE double2 ploaddup<double2>(const double*  from) {\n  return make_double2(from[0], from[0]);\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstore<float>(float*   to, const float4& from) {\n  *reinterpret_cast<float4*>(to) = from;\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstore<double>(double* to, const double2& from) {\n  *reinterpret_cast<double2*>(to) = from;\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstoreu<float>(float*  to, const float4& from) {\n  to[0] = from.x;\n  to[1] = from.y;\n  to[2] = from.z;\n  to[3] = from.w;\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstoreu<double>(double* to, const double2& from) {\n  to[0] = from.x;\n  to[1] = from.y;\n}\n\ntemplate<>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float4 ploadt_ro<float4, Aligned>(const float* from) {\n#if defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 350\n  return __ldg((const float4*)from);\n#else\n  return make_float4(from[0], from[1], from[2], from[3]);\n#endif\n}\ntemplate<>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double2 ploadt_ro<double2, Aligned>(const double* from) {\n#if defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 350\n  return __ldg((const double2*)from);\n#else\n  return make_double2(from[0], from[1]);\n#endif\n}\n\ntemplate<>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float4 ploadt_ro<float4, Unaligned>(const float* from) {\n#if defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 350\n  return make_float4(__ldg(from+0), __ldg(from+1), __ldg(from+2), __ldg(from+3));\n#else\n  return make_float4(from[0], from[1], from[2], from[3]);\n#endif\n}\ntemplate<>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double2 ploadt_ro<double2, Unaligned>(const double* from) {\n#if defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 350\n  return make_double2(__ldg(from+0), __ldg(from+1));\n#else\n  return make_double2(from[0], from[1]);\n#endif\n}\n\ntemplate<> EIGEN_DEVICE_FUNC inline float4 pgather<float, float4>(const float* from, Index stride) {\n  return make_float4(from[0*stride], from[1*stride], from[2*stride], from[3*stride]);\n}\n\ntemplate<> EIGEN_DEVICE_FUNC inline double2 pgather<double, double2>(const double* from, Index stride) {\n  return make_double2(from[0*stride], from[1*stride]);\n}\n\ntemplate<> EIGEN_DEVICE_FUNC inline void pscatter<float, float4>(float* to, const float4& from, Index stride) {\n  to[stride*0] = from.x;\n  to[stride*1] = from.y;\n  to[stride*2] = from.z;\n  to[stride*3] = from.w;\n}\ntemplate<> EIGEN_DEVICE_FUNC inline void pscatter<double, double2>(double* to, const double2& from, Index stride) {\n  to[stride*0] = from.x;\n  to[stride*1] = from.y;\n}\n\ntemplate<> EIGEN_DEVICE_FUNC inline float  pfirst<float4>(const float4& a) {\n  return a.x;\n}\ntemplate<> EIGEN_DEVICE_FUNC inline double pfirst<double2>(const double2& a) {\n  return a.x;\n}\n\ntemplate<> EIGEN_DEVICE_FUNC inline float  predux<float4>(const float4& a) {\n  return a.x + a.y + a.z + a.w;\n}\ntemplate<> EIGEN_DEVICE_FUNC inline double predux<double2>(const double2& a) {\n  return a.x + a.y;\n}\n\ntemplate<> EIGEN_DEVICE_FUNC inline float  predux_max<float4>(const float4& a) {\n  return fmaxf(fmaxf(a.x, a.y), fmaxf(a.z, a.w));\n}\ntemplate<> EIGEN_DEVICE_FUNC inline double predux_max<double2>(const double2& a) {\n  return fmax(a.x, a.y);\n}\n\ntemplate<> EIGEN_DEVICE_FUNC inline float  predux_min<float4>(const float4& a) {\n  return fminf(fminf(a.x, a.y), fminf(a.z, a.w));\n}\ntemplate<> EIGEN_DEVICE_FUNC inline double predux_min<double2>(const double2& a) {\n  return fmin(a.x, a.y);\n}\n\ntemplate<> EIGEN_DEVICE_FUNC inline float  predux_mul<float4>(const float4& a) {\n  return a.x * a.y * a.z * a.w;\n}\ntemplate<> EIGEN_DEVICE_FUNC inline double predux_mul<double2>(const double2& a) {\n  return a.x * a.y;\n}\n\ntemplate<> EIGEN_DEVICE_FUNC inline float4  pabs<float4>(const float4& a) {\n  return make_float4(fabsf(a.x), fabsf(a.y), fabsf(a.z), fabsf(a.w));\n}\ntemplate<> EIGEN_DEVICE_FUNC inline double2 pabs<double2>(const double2& a) {\n  return make_double2(fabs(a.x), fabs(a.y));\n}\n\nEIGEN_DEVICE_FUNC inline void\nptranspose(PacketBlock<float4,4>& kernel) {\n  float tmp = kernel.packet[0].y;\n  kernel.packet[0].y = kernel.packet[1].x;\n  kernel.packet[1].x = tmp;\n\n  tmp = kernel.packet[0].z;\n  kernel.packet[0].z = kernel.packet[2].x;\n  kernel.packet[2].x = tmp;\n\n  tmp = kernel.packet[0].w;\n  kernel.packet[0].w = kernel.packet[3].x;\n  kernel.packet[3].x = tmp;\n\n  tmp = kernel.packet[1].z;\n  kernel.packet[1].z = kernel.packet[2].y;\n  kernel.packet[2].y = tmp;\n\n  tmp = kernel.packet[1].w;\n  kernel.packet[1].w = kernel.packet[3].y;\n  kernel.packet[3].y = tmp;\n\n  tmp = kernel.packet[2].w;\n  kernel.packet[2].w = kernel.packet[3].z;\n  kernel.packet[3].z = tmp;\n}\n\nEIGEN_DEVICE_FUNC inline void\nptranspose(PacketBlock<double2,2>& kernel) {\n  double tmp = kernel.packet[0].y;\n  kernel.packet[0].y = kernel.packet[1].x;\n  kernel.packet[1].x = tmp;\n}\n\n#endif\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n\n#endif // EIGEN_PACKET_MATH_CUDA_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/arch/CUDA/PacketMathHalf.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_PACKET_MATH_HALF_CUDA_H\n#define EIGEN_PACKET_MATH_HALF_CUDA_H\n\n\nnamespace Eigen {\nnamespace internal {\n\n// Most of the following operations require arch >= 3.0\n#if defined(EIGEN_HAS_CUDA_FP16) && defined(__CUDACC__) && defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 300\n\ntemplate<> struct is_arithmetic<half2> { enum { value = true }; };\n\ntemplate<> struct packet_traits<Eigen::half> : default_packet_traits\n{\n  typedef half2 type;\n  typedef half2 half;\n  enum {\n    Vectorizable = 1,\n    AlignedOnScalar = 1,\n    size=2,\n    HasHalfPacket = 0,\n    HasAdd    = 1,\n    HasMul    = 1,\n    HasDiv    = 1,\n    HasSqrt   = 1,\n    HasRsqrt  = 1,\n    HasExp    = 1,\n    HasLog    = 1,\n    HasLog1p  = 1\n  };\n};\n\ntemplate<> struct unpacket_traits<half2> { typedef Eigen::half type; enum {size=2, alignment=Aligned16}; typedef half2 half; };\n\ntemplate<> __device__ EIGEN_STRONG_INLINE half2 pset1<half2>(const Eigen::half& from) {\n  return __half2half2(from);\n}\n\ntemplate<> __device__ EIGEN_STRONG_INLINE half2 pload<half2>(const Eigen::half* from) {\n  return *reinterpret_cast<const half2*>(from);\n}\n\ntemplate<> __device__ EIGEN_STRONG_INLINE half2 ploadu<half2>(const Eigen::half* from) {\n  return __halves2half2(from[0], from[1]);\n}\n\ntemplate<> EIGEN_STRONG_INLINE half2 ploaddup<half2>(const Eigen::half*  from) {\n  return __halves2half2(from[0], from[0]);\n}\n\ntemplate<> __device__ EIGEN_STRONG_INLINE void pstore<Eigen::half>(Eigen::half* to, const half2& from) {\n  *reinterpret_cast<half2*>(to) = from;\n}\n\ntemplate<> __device__ EIGEN_STRONG_INLINE void pstoreu<Eigen::half>(Eigen::half* to, const half2& from) {\n  to[0] = __low2half(from);\n  to[1] = __high2half(from);\n}\n\ntemplate<>\n __device__ EIGEN_ALWAYS_INLINE half2 ploadt_ro<half2, Aligned>(const Eigen::half* from) {\n#if __CUDA_ARCH__ >= 350\n   return __ldg((const half2*)from);\n#else\n  return __halves2half2(*(from+0), *(from+1));\n#endif\n}\n\ntemplate<>\n__device__ EIGEN_ALWAYS_INLINE half2 ploadt_ro<half2, Unaligned>(const Eigen::half* from) {\n#if __CUDA_ARCH__ >= 350\n   return __halves2half2(__ldg(from+0), __ldg(from+1));\n#else\n  return __halves2half2(*(from+0), *(from+1));\n#endif\n}\n\ntemplate<> __device__ EIGEN_STRONG_INLINE half2 pgather<Eigen::half, half2>(const Eigen::half* from, Index stride) {\n  return __halves2half2(from[0*stride], from[1*stride]);\n}\n\ntemplate<> __device__ EIGEN_STRONG_INLINE void pscatter<Eigen::half, half2>(Eigen::half* to, const half2& from, Index stride) {\n  to[stride*0] = __low2half(from);\n  to[stride*1] = __high2half(from);\n}\n\ntemplate<> __device__ EIGEN_STRONG_INLINE Eigen::half pfirst<half2>(const half2& a) {\n  return __low2half(a);\n}\n\ntemplate<> __device__ EIGEN_STRONG_INLINE half2 pabs<half2>(const half2& a) {\n  half2 result;\n  result.x = a.x & 0x7FFF7FFF;\n  return result;\n}\n\n\n__device__ EIGEN_STRONG_INLINE void\nptranspose(PacketBlock<half2,2>& kernel) {\n  __half a1 = __low2half(kernel.packet[0]);\n  __half a2 = __high2half(kernel.packet[0]);\n  __half b1 = __low2half(kernel.packet[1]);\n  __half b2 = __high2half(kernel.packet[1]);\n  kernel.packet[0] = __halves2half2(a1, b1);\n  kernel.packet[1] = __halves2half2(a2, b2);\n}\n\ntemplate<> __device__ EIGEN_STRONG_INLINE half2 plset<half2>(const Eigen::half& a) {\n#if __CUDA_ARCH__ >= 530\n  return __halves2half2(a, __hadd(a, __float2half(1.0f)));\n#else\n  float f = __half2float(a) + 1.0f;\n  return __halves2half2(a, __float2half(f));\n#endif\n}\n\ntemplate<> __device__ EIGEN_STRONG_INLINE half2 padd<half2>(const half2& a, const half2& b) {\n#if __CUDA_ARCH__ >= 530\n  return __hadd2(a, b);\n#else\n  float a1 = __low2float(a);\n  float a2 = __high2float(a);\n  float b1 = __low2float(b);\n  float b2 = __high2float(b);\n  float r1 = a1 + b1;\n  float r2 = a2 + b2;\n  return __floats2half2_rn(r1, r2);\n#endif\n}\n\ntemplate<> __device__ EIGEN_STRONG_INLINE half2 psub<half2>(const half2& a, const half2& b) {\n#if __CUDA_ARCH__ >= 530\n  return __hsub2(a, b);\n#else\n  float a1 = __low2float(a);\n  float a2 = __high2float(a);\n  float b1 = __low2float(b);\n  float b2 = __high2float(b);\n  float r1 = a1 - b1;\n  float r2 = a2 - b2;\n  return __floats2half2_rn(r1, r2);\n#endif\n}\n\ntemplate<> __device__ EIGEN_STRONG_INLINE half2 pnegate(const half2& a) {\n#if __CUDA_ARCH__ >= 530\n  return __hneg2(a);\n#else\n  float a1 = __low2float(a);\n  float a2 = __high2float(a);\n  return __floats2half2_rn(-a1, -a2);\n#endif\n}\n\ntemplate<> __device__ EIGEN_STRONG_INLINE half2 pconj(const half2& a) { return a; }\n\ntemplate<> __device__ EIGEN_STRONG_INLINE half2 pmul<half2>(const half2& a, const half2& b) {\n#if __CUDA_ARCH__ >= 530\n  return __hmul2(a, b);\n#else\n  float a1 = __low2float(a);\n  float a2 = __high2float(a);\n  float b1 = __low2float(b);\n  float b2 = __high2float(b);\n  float r1 = a1 * b1;\n  float r2 = a2 * b2;\n  return __floats2half2_rn(r1, r2);\n#endif\n}\n\ntemplate<> __device__ EIGEN_STRONG_INLINE half2 pmadd<half2>(const half2& a, const half2& b, const half2& c) {\n#if __CUDA_ARCH__ >= 530\n   return __hfma2(a, b, c);\n#else\n  float a1 = __low2float(a);\n  float a2 = __high2float(a);\n  float b1 = __low2float(b);\n  float b2 = __high2float(b);\n  float c1 = __low2float(c);\n  float c2 = __high2float(c);\n  float r1 = a1 * b1 + c1;\n  float r2 = a2 * b2 + c2;\n  return __floats2half2_rn(r1, r2);\n#endif\n}\n\ntemplate<> __device__ EIGEN_STRONG_INLINE half2 pdiv<half2>(const half2& a, const half2& b) {\n  float a1 = __low2float(a);\n  float a2 = __high2float(a);\n  float b1 = __low2float(b);\n  float b2 = __high2float(b);\n  float r1 = a1 / b1;\n  float r2 = a2 / b2;\n  return __floats2half2_rn(r1, r2);\n}\n\ntemplate<> __device__ EIGEN_STRONG_INLINE half2 pmin<half2>(const half2& a, const half2& b) {\n  float a1 = __low2float(a);\n  float a2 = __high2float(a);\n  float b1 = __low2float(b);\n  float b2 = __high2float(b);\n  __half r1 = a1 < b1 ? __low2half(a) : __low2half(b);\n  __half r2 = a2 < b2 ? __high2half(a) : __high2half(b);\n  return __halves2half2(r1, r2);\n}\n\ntemplate<> __device__ EIGEN_STRONG_INLINE half2 pmax<half2>(const half2& a, const half2& b) {\n  float a1 = __low2float(a);\n  float a2 = __high2float(a);\n  float b1 = __low2float(b);\n  float b2 = __high2float(b);\n  __half r1 = a1 > b1 ? __low2half(a) : __low2half(b);\n  __half r2 = a2 > b2 ? __high2half(a) : __high2half(b);\n  return __halves2half2(r1, r2);\n}\n\ntemplate<> __device__ EIGEN_STRONG_INLINE Eigen::half predux<half2>(const half2& a) {\n#if __CUDA_ARCH__ >= 530\n  return __hadd(__low2half(a), __high2half(a));\n#else\n  float a1 = __low2float(a);\n  float a2 = __high2float(a);\n  return Eigen::half(half_impl::raw_uint16_to_half(__float2half_rn(a1 + a2)));\n#endif\n}\n\ntemplate<> __device__ EIGEN_STRONG_INLINE Eigen::half predux_max<half2>(const half2& a) {\n#if __CUDA_ARCH__ >= 530\n  __half first = __low2half(a);\n  __half second = __high2half(a);\n  return __hgt(first, second) ? first : second;\n#else\n  float a1 = __low2float(a);\n  float a2 = __high2float(a);\n  return a1 > a2 ? __low2half(a) : __high2half(a);\n#endif\n}\n\ntemplate<> __device__ EIGEN_STRONG_INLINE Eigen::half predux_min<half2>(const half2& a) {\n#if __CUDA_ARCH__ >= 530\n  __half first = __low2half(a);\n  __half second = __high2half(a);\n  return __hlt(first, second) ? first : second;\n#else\n  float a1 = __low2float(a);\n  float a2 = __high2float(a);\n  return a1 < a2 ? __low2half(a) : __high2half(a);\n#endif\n}\n\ntemplate<> __device__ EIGEN_STRONG_INLINE Eigen::half predux_mul<half2>(const half2& a) {\n#if __CUDA_ARCH__ >= 530\n  return __hmul(__low2half(a), __high2half(a));\n#else\n  float a1 = __low2float(a);\n  float a2 = __high2float(a);\n  return Eigen::half(half_impl::raw_uint16_to_half(__float2half_rn(a1 * a2)));\n#endif\n}\n\ntemplate<> __device__ EIGEN_STRONG_INLINE half2 plog1p<half2>(const half2& a) {\n  float a1 = __low2float(a);\n  float a2 = __high2float(a);\n  float r1 = log1pf(a1);\n  float r2 = log1pf(a2);\n  return __floats2half2_rn(r1, r2);\n}\n\n#if EIGEN_CUDACC_VER >= 80000 && defined EIGEN_CUDA_ARCH && EIGEN_CUDA_ARCH >= 530\n\ntemplate<>  __device__ EIGEN_STRONG_INLINE\nhalf2 plog<half2>(const half2& a) {\n  return h2log(a);\n}\n\ntemplate<> __device__ EIGEN_STRONG_INLINE\nhalf2 pexp<half2>(const half2& a) {\n  return h2exp(a);\n}\n\ntemplate<> __device__ EIGEN_STRONG_INLINE\nhalf2 psqrt<half2>(const half2& a) {\n  return h2sqrt(a);\n}\n\ntemplate<> __device__ EIGEN_STRONG_INLINE\nhalf2 prsqrt<half2>(const half2& a) {\n  return h2rsqrt(a);\n}\n\n#else\n\ntemplate<> __device__ EIGEN_STRONG_INLINE half2 plog<half2>(const half2& a) {\n  float a1 = __low2float(a);\n  float a2 = __high2float(a);\n  float r1 = logf(a1);\n  float r2 = logf(a2);\n  return __floats2half2_rn(r1, r2);\n}\n\ntemplate<> __device__ EIGEN_STRONG_INLINE half2 pexp<half2>(const half2& a) {\n  float a1 = __low2float(a);\n  float a2 = __high2float(a);\n  float r1 = expf(a1);\n  float r2 = expf(a2);\n  return __floats2half2_rn(r1, r2);\n}\n\ntemplate<> __device__ EIGEN_STRONG_INLINE half2 psqrt<half2>(const half2& a) {\n  float a1 = __low2float(a);\n  float a2 = __high2float(a);\n  float r1 = sqrtf(a1);\n  float r2 = sqrtf(a2);\n  return __floats2half2_rn(r1, r2);\n}\n\ntemplate<> __device__ EIGEN_STRONG_INLINE half2 prsqrt<half2>(const half2& a) {\n  float a1 = __low2float(a);\n  float a2 = __high2float(a);\n  float r1 = rsqrtf(a1);\n  float r2 = rsqrtf(a2);\n  return __floats2half2_rn(r1, r2);\n}\n\n#endif\n\n#elif defined EIGEN_VECTORIZE_AVX512\n\ntypedef struct {\n  __m256i x;\n} Packet16h;\n\n\ntemplate<> struct is_arithmetic<Packet16h> { enum { value = true }; };\n\ntemplate <>\nstruct packet_traits<half> : default_packet_traits {\n  typedef Packet16h type;\n  // There is no half-size packet for Packet16h.\n  typedef Packet16h half;\n  enum {\n    Vectorizable = 1,\n    AlignedOnScalar = 1,\n    size = 16,\n    HasHalfPacket = 0,\n    HasAdd    = 0,\n    HasSub    = 0,\n    HasMul    = 0,\n    HasNegate = 0,\n    HasAbs    = 0,\n    HasAbs2   = 0,\n    HasMin    = 0,\n    HasMax    = 0,\n    HasConj   = 0,\n    HasSetLinear = 0,\n    HasDiv = 0,\n    HasSqrt = 0,\n    HasRsqrt = 0,\n    HasExp = 0,\n    HasLog = 0,\n    HasBlend = 0\n  };\n};\n\n\ntemplate<> struct unpacket_traits<Packet16h> { typedef Eigen::half type; enum {size=16, alignment=Aligned32}; typedef Packet16h half; };\n\ntemplate<> EIGEN_STRONG_INLINE Packet16h pset1<Packet16h>(const Eigen::half& from) {\n  Packet16h result;\n  result.x = _mm256_set1_epi16(from.x);\n  return result;\n}\n\ntemplate<> EIGEN_STRONG_INLINE Eigen::half pfirst<Packet16h>(const Packet16h& from) {\n  return half_impl::raw_uint16_to_half(static_cast<unsigned short>(_mm256_extract_epi16(from.x, 0)));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet16h pload<Packet16h>(const Eigen::half* from) {\n  Packet16h result;\n  result.x = _mm256_load_si256(reinterpret_cast<const __m256i*>(from));\n  return result;\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet16h ploadu<Packet16h>(const Eigen::half* from) {\n  Packet16h result;\n  result.x = _mm256_loadu_si256(reinterpret_cast<const __m256i*>(from));\n  return result;\n}\n\ntemplate<> EIGEN_STRONG_INLINE void pstore<half>(Eigen::half* to, const Packet16h& from) {\n  _mm256_store_si256((__m256i*)to, from.x);\n}\n\ntemplate<> EIGEN_STRONG_INLINE void pstoreu<half>(Eigen::half* to, const Packet16h& from) {\n  _mm256_storeu_si256((__m256i*)to, from.x);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet16h\nploadquad(const Eigen::half* from) {\n  Packet16h result;\n  unsigned short a = from[0].x;\n  unsigned short b = from[1].x;\n  unsigned short c = from[2].x;\n  unsigned short d = from[3].x;\n  result.x = _mm256_set_epi16(d, d, d, d, c, c, c, c, b, b, b, b, a, a, a, a);\n  return result;\n}\n\nEIGEN_STRONG_INLINE Packet16f half2float(const Packet16h& a) {\n#ifdef EIGEN_HAS_FP16_C\n  return _mm512_cvtph_ps(a.x);\n#else\n  EIGEN_ALIGN64 half aux[16];\n  pstore(aux, a);\n  float f0(aux[0]);\n  float f1(aux[1]);\n  float f2(aux[2]);\n  float f3(aux[3]);\n  float f4(aux[4]);\n  float f5(aux[5]);\n  float f6(aux[6]);\n  float f7(aux[7]);\n  float f8(aux[8]);\n  float f9(aux[9]);\n  float fa(aux[10]);\n  float fb(aux[11]);\n  float fc(aux[12]);\n  float fd(aux[13]);\n  float fe(aux[14]);\n  float ff(aux[15]);\n\n  return _mm512_set_ps(\n      ff, fe, fd, fc, fb, fa, f9, f8, f7, f6, f5, f4, f3, f2, f1, f0);\n#endif\n}\n\nEIGEN_STRONG_INLINE Packet16h float2half(const Packet16f& a) {\n#ifdef EIGEN_HAS_FP16_C\n  Packet16h result;\n  result.x = _mm512_cvtps_ph(a, _MM_FROUND_TO_NEAREST_INT|_MM_FROUND_NO_EXC);\n  return result;\n#else\n  EIGEN_ALIGN64 float aux[16];\n  pstore(aux, a);\n  half h0(aux[0]);\n  half h1(aux[1]);\n  half h2(aux[2]);\n  half h3(aux[3]);\n  half h4(aux[4]);\n  half h5(aux[5]);\n  half h6(aux[6]);\n  half h7(aux[7]);\n  half h8(aux[8]);\n  half h9(aux[9]);\n  half ha(aux[10]);\n  half hb(aux[11]);\n  half hc(aux[12]);\n  half hd(aux[13]);\n  half he(aux[14]);\n  half hf(aux[15]);\n\n  Packet16h result;\n  result.x = _mm256_set_epi16(\n      hf.x, he.x, hd.x, hc.x, hb.x, ha.x, h9.x, h8.x,\n      h7.x, h6.x, h5.x, h4.x, h3.x, h2.x, h1.x, h0.x);\n  return result;\n#endif\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet16h padd<Packet16h>(const Packet16h& a, const Packet16h& b) {\n  Packet16f af = half2float(a);\n  Packet16f bf = half2float(b);\n  Packet16f rf = padd(af, bf);\n  return float2half(rf);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet16h pmul<Packet16h>(const Packet16h& a, const Packet16h& b) {\n  Packet16f af = half2float(a);\n  Packet16f bf = half2float(b);\n  Packet16f rf = pmul(af, bf);\n  return float2half(rf);\n}\n\ntemplate<> EIGEN_STRONG_INLINE half predux<Packet16h>(const Packet16h& from) {\n  Packet16f from_float = half2float(from);\n  return half(predux(from_float));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet16h pgather<Eigen::half, Packet16h>(const Eigen::half* from, Index stride)\n{\n  Packet16h result;\n  result.x = _mm256_set_epi16(\n      from[15*stride].x, from[14*stride].x, from[13*stride].x, from[12*stride].x,\n      from[11*stride].x, from[10*stride].x, from[9*stride].x, from[8*stride].x,\n      from[7*stride].x, from[6*stride].x, from[5*stride].x, from[4*stride].x,\n      from[3*stride].x, from[2*stride].x, from[1*stride].x, from[0*stride].x);\n  return result;\n}\n\ntemplate<> EIGEN_STRONG_INLINE void pscatter<half, Packet16h>(half* to, const Packet16h& from, Index stride)\n{\n  EIGEN_ALIGN64 half aux[16];\n  pstore(aux, from);\n  to[stride*0].x = aux[0].x;\n  to[stride*1].x = aux[1].x;\n  to[stride*2].x = aux[2].x;\n  to[stride*3].x = aux[3].x;\n  to[stride*4].x = aux[4].x;\n  to[stride*5].x = aux[5].x;\n  to[stride*6].x = aux[6].x;\n  to[stride*7].x = aux[7].x;\n  to[stride*8].x = aux[8].x;\n  to[stride*9].x = aux[9].x;\n  to[stride*10].x = aux[10].x;\n  to[stride*11].x = aux[11].x;\n  to[stride*12].x = aux[12].x;\n  to[stride*13].x = aux[13].x;\n  to[stride*14].x = aux[14].x;\n  to[stride*15].x = aux[15].x;\n}\n\nEIGEN_STRONG_INLINE void\nptranspose(PacketBlock<Packet16h,16>& kernel) {\n  __m256i a = kernel.packet[0].x;\n  __m256i b = kernel.packet[1].x;\n  __m256i c = kernel.packet[2].x;\n  __m256i d = kernel.packet[3].x;\n  __m256i e = kernel.packet[4].x;\n  __m256i f = kernel.packet[5].x;\n  __m256i g = kernel.packet[6].x;\n  __m256i h = kernel.packet[7].x;\n  __m256i i = kernel.packet[8].x;\n  __m256i j = kernel.packet[9].x;\n  __m256i k = kernel.packet[10].x;\n  __m256i l = kernel.packet[11].x;\n  __m256i m = kernel.packet[12].x;\n  __m256i n = kernel.packet[13].x;\n  __m256i o = kernel.packet[14].x;\n  __m256i p = kernel.packet[15].x;\n\n  __m256i ab_07 = _mm256_unpacklo_epi16(a, b);\n  __m256i cd_07 = _mm256_unpacklo_epi16(c, d);\n  __m256i ef_07 = _mm256_unpacklo_epi16(e, f);\n  __m256i gh_07 = _mm256_unpacklo_epi16(g, h);\n  __m256i ij_07 = _mm256_unpacklo_epi16(i, j);\n  __m256i kl_07 = _mm256_unpacklo_epi16(k, l);\n  __m256i mn_07 = _mm256_unpacklo_epi16(m, n);\n  __m256i op_07 = _mm256_unpacklo_epi16(o, p);\n\n  __m256i ab_8f = _mm256_unpackhi_epi16(a, b);\n  __m256i cd_8f = _mm256_unpackhi_epi16(c, d);\n  __m256i ef_8f = _mm256_unpackhi_epi16(e, f);\n  __m256i gh_8f = _mm256_unpackhi_epi16(g, h);\n  __m256i ij_8f = _mm256_unpackhi_epi16(i, j);\n  __m256i kl_8f = _mm256_unpackhi_epi16(k, l);\n  __m256i mn_8f = _mm256_unpackhi_epi16(m, n);\n  __m256i op_8f = _mm256_unpackhi_epi16(o, p);\n\n  __m256i abcd_03 = _mm256_unpacklo_epi32(ab_07, cd_07);\n  __m256i abcd_47 = _mm256_unpackhi_epi32(ab_07, cd_07);\n  __m256i efgh_03 = _mm256_unpacklo_epi32(ef_07, gh_07);\n  __m256i efgh_47 = _mm256_unpackhi_epi32(ef_07, gh_07);\n  __m256i ijkl_03 = _mm256_unpacklo_epi32(ij_07, kl_07);\n  __m256i ijkl_47 = _mm256_unpackhi_epi32(ij_07, kl_07);\n  __m256i mnop_03 = _mm256_unpacklo_epi32(mn_07, op_07);\n  __m256i mnop_47 = _mm256_unpackhi_epi32(mn_07, op_07);\n\n  __m256i abcd_8b = _mm256_unpacklo_epi32(ab_8f, cd_8f);\n  __m256i abcd_cf = _mm256_unpackhi_epi32(ab_8f, cd_8f);\n  __m256i efgh_8b = _mm256_unpacklo_epi32(ef_8f, gh_8f);\n  __m256i efgh_cf = _mm256_unpackhi_epi32(ef_8f, gh_8f);\n  __m256i ijkl_8b = _mm256_unpacklo_epi32(ij_8f, kl_8f);\n  __m256i ijkl_cf = _mm256_unpackhi_epi32(ij_8f, kl_8f);\n  __m256i mnop_8b = _mm256_unpacklo_epi32(mn_8f, op_8f);\n  __m256i mnop_cf = _mm256_unpackhi_epi32(mn_8f, op_8f);\n\n  __m256i abcdefgh_01 = _mm256_unpacklo_epi64(abcd_03, efgh_03);\n  __m256i abcdefgh_23 = _mm256_unpackhi_epi64(abcd_03, efgh_03);\n  __m256i ijklmnop_01 = _mm256_unpacklo_epi64(ijkl_03, mnop_03);\n  __m256i ijklmnop_23 = _mm256_unpackhi_epi64(ijkl_03, mnop_03);\n  __m256i abcdefgh_45 = _mm256_unpacklo_epi64(abcd_47, efgh_47);\n  __m256i abcdefgh_67 = _mm256_unpackhi_epi64(abcd_47, efgh_47);\n  __m256i ijklmnop_45 = _mm256_unpacklo_epi64(ijkl_47, mnop_47);\n  __m256i ijklmnop_67 = _mm256_unpackhi_epi64(ijkl_47, mnop_47);\n  __m256i abcdefgh_89 = _mm256_unpacklo_epi64(abcd_8b, efgh_8b);\n  __m256i abcdefgh_ab = _mm256_unpackhi_epi64(abcd_8b, efgh_8b);\n  __m256i ijklmnop_89 = _mm256_unpacklo_epi64(ijkl_8b, mnop_8b);\n  __m256i ijklmnop_ab = _mm256_unpackhi_epi64(ijkl_8b, mnop_8b);\n  __m256i abcdefgh_cd = _mm256_unpacklo_epi64(abcd_cf, efgh_cf);\n  __m256i abcdefgh_ef = _mm256_unpackhi_epi64(abcd_cf, efgh_cf);\n  __m256i ijklmnop_cd = _mm256_unpacklo_epi64(ijkl_cf, mnop_cf);\n  __m256i ijklmnop_ef = _mm256_unpackhi_epi64(ijkl_cf, mnop_cf);\n\n  // NOTE: no unpacklo/hi instr in this case, so using permute instr.\n  __m256i a_p_0 = _mm256_permute2x128_si256(abcdefgh_01, ijklmnop_01, 0x20);\n  __m256i a_p_1 = _mm256_permute2x128_si256(abcdefgh_01, ijklmnop_01, 0x31);\n  __m256i a_p_2 = _mm256_permute2x128_si256(abcdefgh_23, ijklmnop_23, 0x20);\n  __m256i a_p_3 = _mm256_permute2x128_si256(abcdefgh_23, ijklmnop_23, 0x31);\n  __m256i a_p_4 = _mm256_permute2x128_si256(abcdefgh_45, ijklmnop_45, 0x20);\n  __m256i a_p_5 = _mm256_permute2x128_si256(abcdefgh_45, ijklmnop_45, 0x31);\n  __m256i a_p_6 = _mm256_permute2x128_si256(abcdefgh_67, ijklmnop_67, 0x20);\n  __m256i a_p_7 = _mm256_permute2x128_si256(abcdefgh_67, ijklmnop_67, 0x31);\n  __m256i a_p_8 = _mm256_permute2x128_si256(abcdefgh_89, ijklmnop_89, 0x20);\n  __m256i a_p_9 = _mm256_permute2x128_si256(abcdefgh_89, ijklmnop_89, 0x31);\n  __m256i a_p_a = _mm256_permute2x128_si256(abcdefgh_ab, ijklmnop_ab, 0x20);\n  __m256i a_p_b = _mm256_permute2x128_si256(abcdefgh_ab, ijklmnop_ab, 0x31);\n  __m256i a_p_c = _mm256_permute2x128_si256(abcdefgh_cd, ijklmnop_cd, 0x20);\n  __m256i a_p_d = _mm256_permute2x128_si256(abcdefgh_cd, ijklmnop_cd, 0x31);\n  __m256i a_p_e = _mm256_permute2x128_si256(abcdefgh_ef, ijklmnop_ef, 0x20);\n  __m256i a_p_f = _mm256_permute2x128_si256(abcdefgh_ef, ijklmnop_ef, 0x31);\n\n  kernel.packet[0].x = a_p_0;\n  kernel.packet[1].x = a_p_1;\n  kernel.packet[2].x = a_p_2;\n  kernel.packet[3].x = a_p_3;\n  kernel.packet[4].x = a_p_4;\n  kernel.packet[5].x = a_p_5;\n  kernel.packet[6].x = a_p_6;\n  kernel.packet[7].x = a_p_7;\n  kernel.packet[8].x = a_p_8;\n  kernel.packet[9].x = a_p_9;\n  kernel.packet[10].x = a_p_a;\n  kernel.packet[11].x = a_p_b;\n  kernel.packet[12].x = a_p_c;\n  kernel.packet[13].x = a_p_d;\n  kernel.packet[14].x = a_p_e;\n  kernel.packet[15].x = a_p_f;\n}\n\nEIGEN_STRONG_INLINE void\nptranspose(PacketBlock<Packet16h,8>& kernel) {\n  EIGEN_ALIGN64 half in[8][16];\n  pstore<half>(in[0], kernel.packet[0]);\n  pstore<half>(in[1], kernel.packet[1]);\n  pstore<half>(in[2], kernel.packet[2]);\n  pstore<half>(in[3], kernel.packet[3]);\n  pstore<half>(in[4], kernel.packet[4]);\n  pstore<half>(in[5], kernel.packet[5]);\n  pstore<half>(in[6], kernel.packet[6]);\n  pstore<half>(in[7], kernel.packet[7]);\n\n  EIGEN_ALIGN64 half out[8][16];\n\n  for (int i = 0; i < 8; ++i) {\n    for (int j = 0; j < 8; ++j) {\n      out[i][j] = in[j][2*i];\n    }\n    for (int j = 0; j < 8; ++j) {\n      out[i][j+8] = in[j][2*i+1];\n    }\n  }\n\n  kernel.packet[0] = pload<Packet16h>(out[0]);\n  kernel.packet[1] = pload<Packet16h>(out[1]);\n  kernel.packet[2] = pload<Packet16h>(out[2]);\n  kernel.packet[3] = pload<Packet16h>(out[3]);\n  kernel.packet[4] = pload<Packet16h>(out[4]);\n  kernel.packet[5] = pload<Packet16h>(out[5]);\n  kernel.packet[6] = pload<Packet16h>(out[6]);\n  kernel.packet[7] = pload<Packet16h>(out[7]);\n}\n\nEIGEN_STRONG_INLINE void\nptranspose(PacketBlock<Packet16h,4>& kernel) {\n  EIGEN_ALIGN64 half in[4][16];\n  pstore<half>(in[0], kernel.packet[0]);\n  pstore<half>(in[1], kernel.packet[1]);\n  pstore<half>(in[2], kernel.packet[2]);\n  pstore<half>(in[3], kernel.packet[3]);\n\n  EIGEN_ALIGN64 half out[4][16];\n\n  for (int i = 0; i < 4; ++i) {\n    for (int j = 0; j < 4; ++j) {\n      out[i][j] = in[j][4*i];\n    }\n    for (int j = 0; j < 4; ++j) {\n      out[i][j+4] = in[j][4*i+1];\n    }\n    for (int j = 0; j < 4; ++j) {\n      out[i][j+8] = in[j][4*i+2];\n    }\n    for (int j = 0; j < 4; ++j) {\n      out[i][j+12] = in[j][4*i+3];\n    }\n  }\n\n  kernel.packet[0] = pload<Packet16h>(out[0]);\n  kernel.packet[1] = pload<Packet16h>(out[1]);\n  kernel.packet[2] = pload<Packet16h>(out[2]);\n  kernel.packet[3] = pload<Packet16h>(out[3]);\n}\n\n\n#elif defined EIGEN_VECTORIZE_AVX\n\ntypedef struct {\n  __m128i x;\n} Packet8h;\n\n\ntemplate<> struct is_arithmetic<Packet8h> { enum { value = true }; };\n\ntemplate <>\nstruct packet_traits<Eigen::half> : default_packet_traits {\n  typedef Packet8h type;\n  // There is no half-size packet for Packet8h.\n  typedef Packet8h half;\n  enum {\n    Vectorizable = 1,\n    AlignedOnScalar = 1,\n    size = 8,\n    HasHalfPacket = 0,\n    HasAdd    = 0,\n    HasSub    = 0,\n    HasMul    = 0,\n    HasNegate = 0,\n    HasAbs    = 0,\n    HasAbs2   = 0,\n    HasMin    = 0,\n    HasMax    = 0,\n    HasConj   = 0,\n    HasSetLinear = 0,\n    HasDiv = 0,\n    HasSqrt = 0,\n    HasRsqrt = 0,\n    HasExp = 0,\n    HasLog = 0,\n    HasBlend = 0\n  };\n};\n\n\ntemplate<> struct unpacket_traits<Packet8h> { typedef Eigen::half type; enum {size=8, alignment=Aligned16}; typedef Packet8h half; };\n\ntemplate<> EIGEN_STRONG_INLINE Packet8h pset1<Packet8h>(const Eigen::half& from) {\n  Packet8h result;\n  result.x = _mm_set1_epi16(from.x);\n  return result;\n}\n\ntemplate<> EIGEN_STRONG_INLINE Eigen::half pfirst<Packet8h>(const Packet8h& from) {\n  return half_impl::raw_uint16_to_half(static_cast<unsigned short>(_mm_extract_epi16(from.x, 0)));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet8h pload<Packet8h>(const Eigen::half* from) {\n  Packet8h result;\n  result.x = _mm_load_si128(reinterpret_cast<const __m128i*>(from));\n  return result;\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet8h ploadu<Packet8h>(const Eigen::half* from) {\n  Packet8h result;\n  result.x = _mm_loadu_si128(reinterpret_cast<const __m128i*>(from));\n  return result;\n}\n\ntemplate<> EIGEN_STRONG_INLINE void pstore<Eigen::half>(Eigen::half* to, const Packet8h& from) {\n  _mm_store_si128(reinterpret_cast<__m128i*>(to), from.x);\n}\n\ntemplate<> EIGEN_STRONG_INLINE void pstoreu<Eigen::half>(Eigen::half* to, const Packet8h& from) {\n  _mm_storeu_si128(reinterpret_cast<__m128i*>(to), from.x);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet8h\nploadquad<Packet8h>(const Eigen::half* from) {\n  Packet8h result;\n  unsigned short a = from[0].x;\n  unsigned short b = from[1].x;\n  result.x = _mm_set_epi16(b, b, b, b, a, a, a, a);\n  return result;\n}\n\nEIGEN_STRONG_INLINE Packet8f half2float(const Packet8h& a) {\n#ifdef EIGEN_HAS_FP16_C\n  return _mm256_cvtph_ps(a.x);\n#else\n  EIGEN_ALIGN32 Eigen::half aux[8];\n  pstore(aux, a);\n  float f0(aux[0]);\n  float f1(aux[1]);\n  float f2(aux[2]);\n  float f3(aux[3]);\n  float f4(aux[4]);\n  float f5(aux[5]);\n  float f6(aux[6]);\n  float f7(aux[7]);\n\n  return _mm256_set_ps(f7, f6, f5, f4, f3, f2, f1, f0);\n#endif\n}\n\nEIGEN_STRONG_INLINE Packet8h float2half(const Packet8f& a) {\n#ifdef EIGEN_HAS_FP16_C\n  Packet8h result;\n  result.x = _mm256_cvtps_ph(a, _MM_FROUND_TO_NEAREST_INT|_MM_FROUND_NO_EXC);\n  return result;\n#else\n  EIGEN_ALIGN32 float aux[8];\n  pstore(aux, a);\n  Eigen::half h0(aux[0]);\n  Eigen::half h1(aux[1]);\n  Eigen::half h2(aux[2]);\n  Eigen::half h3(aux[3]);\n  Eigen::half h4(aux[4]);\n  Eigen::half h5(aux[5]);\n  Eigen::half h6(aux[6]);\n  Eigen::half h7(aux[7]);\n\n  Packet8h result;\n  result.x = _mm_set_epi16(h7.x, h6.x, h5.x, h4.x, h3.x, h2.x, h1.x, h0.x);\n  return result;\n#endif\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet8h pconj(const Packet8h& a) { return a; }\n\ntemplate<> EIGEN_STRONG_INLINE Packet8h padd<Packet8h>(const Packet8h& a, const Packet8h& b) {\n  Packet8f af = half2float(a);\n  Packet8f bf = half2float(b);\n  Packet8f rf = padd(af, bf);\n  return float2half(rf);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet8h pmul<Packet8h>(const Packet8h& a, const Packet8h& b) {\n  Packet8f af = half2float(a);\n  Packet8f bf = half2float(b);\n  Packet8f rf = pmul(af, bf);\n  return float2half(rf);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet8h pgather<Eigen::half, Packet8h>(const Eigen::half* from, Index stride)\n{\n  Packet8h result;\n  result.x = _mm_set_epi16(from[7*stride].x, from[6*stride].x, from[5*stride].x, from[4*stride].x, from[3*stride].x, from[2*stride].x, from[1*stride].x, from[0*stride].x);\n  return result;\n}\n\ntemplate<> EIGEN_STRONG_INLINE void pscatter<Eigen::half, Packet8h>(Eigen::half* to, const Packet8h& from, Index stride)\n{\n  EIGEN_ALIGN32 Eigen::half aux[8];\n  pstore(aux, from);\n  to[stride*0].x = aux[0].x;\n  to[stride*1].x = aux[1].x;\n  to[stride*2].x = aux[2].x;\n  to[stride*3].x = aux[3].x;\n  to[stride*4].x = aux[4].x;\n  to[stride*5].x = aux[5].x;\n  to[stride*6].x = aux[6].x;\n  to[stride*7].x = aux[7].x;\n}\n\ntemplate<> EIGEN_STRONG_INLINE Eigen::half predux<Packet8h>(const Packet8h& a) {\n  Packet8f af = half2float(a);\n  float reduced = predux<Packet8f>(af);\n  return Eigen::half(reduced);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Eigen::half predux_max<Packet8h>(const Packet8h& a) {\n  Packet8f af = half2float(a);\n  float reduced = predux_max<Packet8f>(af);\n  return Eigen::half(reduced);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Eigen::half predux_min<Packet8h>(const Packet8h& a) {\n  Packet8f af = half2float(a);\n  float reduced = predux_min<Packet8f>(af);\n  return Eigen::half(reduced);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Eigen::half predux_mul<Packet8h>(const Packet8h& a) {\n  Packet8f af = half2float(a);\n  float reduced = predux_mul<Packet8f>(af);\n  return Eigen::half(reduced);\n}\n\nEIGEN_STRONG_INLINE void\nptranspose(PacketBlock<Packet8h,8>& kernel) {\n  __m128i a = kernel.packet[0].x;\n  __m128i b = kernel.packet[1].x;\n  __m128i c = kernel.packet[2].x;\n  __m128i d = kernel.packet[3].x;\n  __m128i e = kernel.packet[4].x;\n  __m128i f = kernel.packet[5].x;\n  __m128i g = kernel.packet[6].x;\n  __m128i h = kernel.packet[7].x;\n\n  __m128i a03b03 = _mm_unpacklo_epi16(a, b);\n  __m128i c03d03 = _mm_unpacklo_epi16(c, d);\n  __m128i e03f03 = _mm_unpacklo_epi16(e, f);\n  __m128i g03h03 = _mm_unpacklo_epi16(g, h);\n  __m128i a47b47 = _mm_unpackhi_epi16(a, b);\n  __m128i c47d47 = _mm_unpackhi_epi16(c, d);\n  __m128i e47f47 = _mm_unpackhi_epi16(e, f);\n  __m128i g47h47 = _mm_unpackhi_epi16(g, h);\n\n  __m128i a01b01c01d01 = _mm_unpacklo_epi32(a03b03, c03d03);\n  __m128i a23b23c23d23 = _mm_unpackhi_epi32(a03b03, c03d03);\n  __m128i e01f01g01h01 = _mm_unpacklo_epi32(e03f03, g03h03);\n  __m128i e23f23g23h23 = _mm_unpackhi_epi32(e03f03, g03h03);\n  __m128i a45b45c45d45 = _mm_unpacklo_epi32(a47b47, c47d47);\n  __m128i a67b67c67d67 = _mm_unpackhi_epi32(a47b47, c47d47);\n  __m128i e45f45g45h45 = _mm_unpacklo_epi32(e47f47, g47h47);\n  __m128i e67f67g67h67 = _mm_unpackhi_epi32(e47f47, g47h47);\n\n  __m128i a0b0c0d0e0f0g0h0 = _mm_unpacklo_epi64(a01b01c01d01, e01f01g01h01);\n  __m128i a1b1c1d1e1f1g1h1 = _mm_unpackhi_epi64(a01b01c01d01, e01f01g01h01);\n  __m128i a2b2c2d2e2f2g2h2 = _mm_unpacklo_epi64(a23b23c23d23, e23f23g23h23);\n  __m128i a3b3c3d3e3f3g3h3 = _mm_unpackhi_epi64(a23b23c23d23, e23f23g23h23);\n  __m128i a4b4c4d4e4f4g4h4 = _mm_unpacklo_epi64(a45b45c45d45, e45f45g45h45);\n  __m128i a5b5c5d5e5f5g5h5 = _mm_unpackhi_epi64(a45b45c45d45, e45f45g45h45);\n  __m128i a6b6c6d6e6f6g6h6 = _mm_unpacklo_epi64(a67b67c67d67, e67f67g67h67);\n  __m128i a7b7c7d7e7f7g7h7 = _mm_unpackhi_epi64(a67b67c67d67, e67f67g67h67);\n\n  kernel.packet[0].x = a0b0c0d0e0f0g0h0;\n  kernel.packet[1].x = a1b1c1d1e1f1g1h1;\n  kernel.packet[2].x = a2b2c2d2e2f2g2h2;\n  kernel.packet[3].x = a3b3c3d3e3f3g3h3;\n  kernel.packet[4].x = a4b4c4d4e4f4g4h4;\n  kernel.packet[5].x = a5b5c5d5e5f5g5h5;\n  kernel.packet[6].x = a6b6c6d6e6f6g6h6;\n  kernel.packet[7].x = a7b7c7d7e7f7g7h7;\n}\n\nEIGEN_STRONG_INLINE void\nptranspose(PacketBlock<Packet8h,4>& kernel) {\n  EIGEN_ALIGN32 Eigen::half in[4][8];\n  pstore<Eigen::half>(in[0], kernel.packet[0]);\n  pstore<Eigen::half>(in[1], kernel.packet[1]);\n  pstore<Eigen::half>(in[2], kernel.packet[2]);\n  pstore<Eigen::half>(in[3], kernel.packet[3]);\n\n  EIGEN_ALIGN32 Eigen::half out[4][8];\n\n  for (int i = 0; i < 4; ++i) {\n    for (int j = 0; j < 4; ++j) {\n      out[i][j] = in[j][2*i];\n    }\n    for (int j = 0; j < 4; ++j) {\n      out[i][j+4] = in[j][2*i+1];\n    }\n  }\n\n  kernel.packet[0] = pload<Packet8h>(out[0]);\n  kernel.packet[1] = pload<Packet8h>(out[1]);\n  kernel.packet[2] = pload<Packet8h>(out[2]);\n  kernel.packet[3] = pload<Packet8h>(out[3]);\n}\n\n\n// Disable the following code since it's broken on too many platforms / compilers.\n//#elif defined(EIGEN_VECTORIZE_SSE) && (!EIGEN_ARCH_x86_64) && (!EIGEN_COMP_MSVC)\n#elif 0\n\ntypedef struct {\n  __m64 x;\n} Packet4h;\n\n\ntemplate<> struct is_arithmetic<Packet4h> { enum { value = true }; };\n\ntemplate <>\nstruct packet_traits<Eigen::half> : default_packet_traits {\n  typedef Packet4h type;\n  // There is no half-size packet for Packet4h.\n  typedef Packet4h half;\n  enum {\n    Vectorizable = 1,\n    AlignedOnScalar = 1,\n    size = 4,\n    HasHalfPacket = 0,\n    HasAdd    = 0,\n    HasSub    = 0,\n    HasMul    = 0,\n    HasNegate = 0,\n    HasAbs    = 0,\n    HasAbs2   = 0,\n    HasMin    = 0,\n    HasMax    = 0,\n    HasConj   = 0,\n    HasSetLinear = 0,\n    HasDiv = 0,\n    HasSqrt = 0,\n    HasRsqrt = 0,\n    HasExp = 0,\n    HasLog = 0,\n    HasBlend = 0\n  };\n};\n\n\ntemplate<> struct unpacket_traits<Packet4h> { typedef Eigen::half type; enum {size=4, alignment=Aligned16}; typedef Packet4h half; };\n\ntemplate<> EIGEN_STRONG_INLINE Packet4h pset1<Packet4h>(const Eigen::half& from) {\n  Packet4h result;\n  result.x = _mm_set1_pi16(from.x);\n  return result;\n}\n\ntemplate<> EIGEN_STRONG_INLINE Eigen::half pfirst<Packet4h>(const Packet4h& from) {\n  return half_impl::raw_uint16_to_half(static_cast<unsigned short>(_mm_cvtsi64_si32(from.x)));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4h pconj(const Packet4h& a) { return a; }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4h padd<Packet4h>(const Packet4h& a, const Packet4h& b) {\n  __int64_t a64 = _mm_cvtm64_si64(a.x);\n  __int64_t b64 = _mm_cvtm64_si64(b.x);\n\n  Eigen::half h[4];\n\n  Eigen::half ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64));\n  Eigen::half hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64));\n  h[0] = ha + hb;\n  ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 16));\n  hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 16));\n  h[1] = ha + hb;\n  ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 32));\n  hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 32));\n  h[2] = ha + hb;\n  ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 48));\n  hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 48));\n  h[3] = ha + hb;\n  Packet4h result;\n  result.x = _mm_set_pi16(h[3].x, h[2].x, h[1].x, h[0].x);\n  return result;\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4h pmul<Packet4h>(const Packet4h& a, const Packet4h& b) {\n  __int64_t a64 = _mm_cvtm64_si64(a.x);\n  __int64_t b64 = _mm_cvtm64_si64(b.x);\n\n  Eigen::half h[4];\n\n  Eigen::half ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64));\n  Eigen::half hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64));\n  h[0] = ha * hb;\n  ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 16));\n  hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 16));\n  h[1] = ha * hb;\n  ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 32));\n  hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 32));\n  h[2] = ha * hb;\n  ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 48));\n  hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 48));\n  h[3] = ha * hb;\n  Packet4h result;\n  result.x = _mm_set_pi16(h[3].x, h[2].x, h[1].x, h[0].x);\n  return result;\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4h pload<Packet4h>(const Eigen::half* from) {\n  Packet4h result;\n  result.x = _mm_cvtsi64_m64(*reinterpret_cast<const __int64_t*>(from));\n  return result;\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4h ploadu<Packet4h>(const Eigen::half* from) {\n  Packet4h result;\n  result.x = _mm_cvtsi64_m64(*reinterpret_cast<const __int64_t*>(from));\n  return result;\n}\n\ntemplate<> EIGEN_STRONG_INLINE void pstore<Eigen::half>(Eigen::half* to, const Packet4h& from) {\n  __int64_t r = _mm_cvtm64_si64(from.x);\n  *(reinterpret_cast<__int64_t*>(to)) = r;\n}\n\ntemplate<> EIGEN_STRONG_INLINE void pstoreu<Eigen::half>(Eigen::half* to, const Packet4h& from) {\n  __int64_t r = _mm_cvtm64_si64(from.x);\n  *(reinterpret_cast<__int64_t*>(to)) = r;\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4h\nploadquad<Packet4h>(const Eigen::half* from) {\n  return pset1<Packet4h>(*from);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4h pgather<Eigen::half, Packet4h>(const Eigen::half* from, Index stride)\n{\n  Packet4h result;\n  result.x = _mm_set_pi16(from[3*stride].x, from[2*stride].x, from[1*stride].x, from[0*stride].x);\n  return result;\n}\n\ntemplate<> EIGEN_STRONG_INLINE void pscatter<Eigen::half, Packet4h>(Eigen::half* to, const Packet4h& from, Index stride)\n{\n  __int64_t a = _mm_cvtm64_si64(from.x);\n  to[stride*0].x = static_cast<unsigned short>(a);\n  to[stride*1].x = static_cast<unsigned short>(a >> 16);\n  to[stride*2].x = static_cast<unsigned short>(a >> 32);\n  to[stride*3].x = static_cast<unsigned short>(a >> 48);\n}\n\nEIGEN_STRONG_INLINE void\nptranspose(PacketBlock<Packet4h,4>& kernel) {\n  __m64 T0 = _mm_unpacklo_pi16(kernel.packet[0].x, kernel.packet[1].x);\n  __m64 T1 = _mm_unpacklo_pi16(kernel.packet[2].x, kernel.packet[3].x);\n  __m64 T2 = _mm_unpackhi_pi16(kernel.packet[0].x, kernel.packet[1].x);\n  __m64 T3 = _mm_unpackhi_pi16(kernel.packet[2].x, kernel.packet[3].x);\n\n  kernel.packet[0].x = _mm_unpacklo_pi32(T0, T1);\n  kernel.packet[1].x = _mm_unpackhi_pi32(T0, T1);\n  kernel.packet[2].x = _mm_unpacklo_pi32(T2, T3);\n  kernel.packet[3].x = _mm_unpackhi_pi32(T2, T3);\n}\n\n#endif\n\n}\n}\n\n#endif // EIGEN_PACKET_MATH_HALF_CUDA_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/arch/CUDA/TypeCasting.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_TYPE_CASTING_CUDA_H\n#define EIGEN_TYPE_CASTING_CUDA_H\n\nnamespace Eigen {\n\nnamespace internal {\n\ntemplate<>\nstruct scalar_cast_op<float, Eigen::half> {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_cast_op)\n  typedef Eigen::half result_type;\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half operator() (const float& a) const {\n    #if defined(EIGEN_HAS_CUDA_FP16) && defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 300\n      return __float2half(a);\n    #else\n      return Eigen::half(a);\n    #endif\n  }\n};\n\ntemplate<>\nstruct functor_traits<scalar_cast_op<float, Eigen::half> >\n{ enum { Cost = NumTraits<float>::AddCost, PacketAccess = false }; };\n\n\ntemplate<>\nstruct scalar_cast_op<int, Eigen::half> {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_cast_op)\n  typedef Eigen::half result_type;\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half operator() (const int& a) const {\n    #if defined(EIGEN_HAS_CUDA_FP16) && defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 300\n      return __float2half(static_cast<float>(a));\n    #else\n      return Eigen::half(static_cast<float>(a));\n    #endif\n  }\n};\n\ntemplate<>\nstruct functor_traits<scalar_cast_op<int, Eigen::half> >\n{ enum { Cost = NumTraits<float>::AddCost, PacketAccess = false }; };\n\n\ntemplate<>\nstruct scalar_cast_op<Eigen::half, float> {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_cast_op)\n  typedef float result_type;\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float operator() (const Eigen::half& a) const {\n    #if defined(EIGEN_HAS_CUDA_FP16) && defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 300\n      return __half2float(a);\n    #else\n      return static_cast<float>(a);\n    #endif\n  }\n};\n\ntemplate<>\nstruct functor_traits<scalar_cast_op<Eigen::half, float> >\n{ enum { Cost = NumTraits<float>::AddCost, PacketAccess = false }; };\n\n\n\n#if defined(EIGEN_HAS_CUDA_FP16) && defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 300\n\ntemplate <>\nstruct type_casting_traits<Eigen::half, float> {\n  enum {\n    VectorizedCast = 1,\n    SrcCoeffRatio = 2,\n    TgtCoeffRatio = 1\n  };\n};\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pcast<half2, float4>(const half2& a, const half2& b) {\n  float2 r1 = __half22float2(a);\n  float2 r2 = __half22float2(b);\n  return make_float4(r1.x, r1.y, r2.x, r2.y);\n}\n\ntemplate <>\nstruct type_casting_traits<float, Eigen::half> {\n  enum {\n    VectorizedCast = 1,\n    SrcCoeffRatio = 1,\n    TgtCoeffRatio = 2\n  };\n};\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pcast<float4, half2>(const float4& a) {\n  // Simply discard the second half of the input\n  return __floats2half2_rn(a.x, a.y);\n}\n\n#elif defined EIGEN_VECTORIZE_AVX512\ntemplate <>\nstruct type_casting_traits<half, float> {\n  enum {\n    VectorizedCast = 1,\n    SrcCoeffRatio = 1,\n    TgtCoeffRatio = 1\n  };\n};\n\ntemplate<> EIGEN_STRONG_INLINE Packet16f pcast<Packet16h, Packet16f>(const Packet16h& a) {\n  return half2float(a);\n}\n\ntemplate <>\nstruct type_casting_traits<float, half> {\n  enum {\n    VectorizedCast = 1,\n    SrcCoeffRatio = 1,\n    TgtCoeffRatio = 1\n  };\n};\n\ntemplate<> EIGEN_STRONG_INLINE Packet16h pcast<Packet16f, Packet16h>(const Packet16f& a) {\n  return float2half(a);\n}\n\n#elif defined EIGEN_VECTORIZE_AVX\n\ntemplate <>\nstruct type_casting_traits<Eigen::half, float> {\n  enum {\n    VectorizedCast = 1,\n    SrcCoeffRatio = 1,\n    TgtCoeffRatio = 1\n  };\n};\n\ntemplate<> EIGEN_STRONG_INLINE Packet8f pcast<Packet8h, Packet8f>(const Packet8h& a) {\n  return half2float(a);\n}\n\ntemplate <>\nstruct type_casting_traits<float, Eigen::half> {\n  enum {\n    VectorizedCast = 1,\n    SrcCoeffRatio = 1,\n    TgtCoeffRatio = 1\n  };\n};\n\ntemplate<> EIGEN_STRONG_INLINE Packet8h pcast<Packet8f, Packet8h>(const Packet8f& a) {\n  return float2half(a);\n}\n\n// Disable the following code since it's broken on too many platforms / compilers.\n//#elif defined(EIGEN_VECTORIZE_SSE) && (!EIGEN_ARCH_x86_64) && (!EIGEN_COMP_MSVC)\n#elif 0\n\ntemplate <>\nstruct type_casting_traits<Eigen::half, float> {\n  enum {\n    VectorizedCast = 1,\n    SrcCoeffRatio = 1,\n    TgtCoeffRatio = 1\n  };\n};\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pcast<Packet4h, Packet4f>(const Packet4h& a) {\n  __int64_t a64 = _mm_cvtm64_si64(a.x);\n  Eigen::half h = raw_uint16_to_half(static_cast<unsigned short>(a64));\n  float f1 = static_cast<float>(h);\n  h = raw_uint16_to_half(static_cast<unsigned short>(a64 >> 16));\n  float f2 = static_cast<float>(h);\n  h = raw_uint16_to_half(static_cast<unsigned short>(a64 >> 32));\n  float f3 = static_cast<float>(h);\n  h = raw_uint16_to_half(static_cast<unsigned short>(a64 >> 48));\n  float f4 = static_cast<float>(h);\n  return _mm_set_ps(f4, f3, f2, f1);\n}\n\ntemplate <>\nstruct type_casting_traits<float, Eigen::half> {\n  enum {\n    VectorizedCast = 1,\n    SrcCoeffRatio = 1,\n    TgtCoeffRatio = 1\n  };\n};\n\ntemplate<> EIGEN_STRONG_INLINE Packet4h pcast<Packet4f, Packet4h>(const Packet4f& a) {\n  EIGEN_ALIGN16 float aux[4];\n  pstore(aux, a);\n  Eigen::half h0(aux[0]);\n  Eigen::half h1(aux[1]);\n  Eigen::half h2(aux[2]);\n  Eigen::half h3(aux[3]);\n\n  Packet4h result;\n  result.x = _mm_set_pi16(h3.x, h2.x, h1.x, h0.x);\n  return result;\n}\n\n#endif\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_TYPE_CASTING_CUDA_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/arch/Default/ConjHelper.h",
    "content": "\n// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2017 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_ARCH_CONJ_HELPER_H\n#define EIGEN_ARCH_CONJ_HELPER_H\n\n#define EIGEN_MAKE_CONJ_HELPER_CPLX_REAL(PACKET_CPLX, PACKET_REAL)                                                          \\\n  template<> struct conj_helper<PACKET_REAL, PACKET_CPLX, false,false> {                                          \\\n    EIGEN_STRONG_INLINE PACKET_CPLX pmadd(const PACKET_REAL& x, const PACKET_CPLX& y, const PACKET_CPLX& c) const \\\n    { return padd(c, pmul(x,y)); }                                                                                \\\n    EIGEN_STRONG_INLINE PACKET_CPLX pmul(const PACKET_REAL& x, const PACKET_CPLX& y) const                        \\\n    { return PACKET_CPLX(Eigen::internal::pmul<PACKET_REAL>(x, y.v)); }                                           \\\n  };                                                                                                              \\\n                                                                                                                  \\\n  template<> struct conj_helper<PACKET_CPLX, PACKET_REAL, false,false> {                                          \\\n    EIGEN_STRONG_INLINE PACKET_CPLX pmadd(const PACKET_CPLX& x, const PACKET_REAL& y, const PACKET_CPLX& c) const \\\n    { return padd(c, pmul(x,y)); }                                                                                \\\n    EIGEN_STRONG_INLINE PACKET_CPLX pmul(const PACKET_CPLX& x, const PACKET_REAL& y) const                        \\\n    { return PACKET_CPLX(Eigen::internal::pmul<PACKET_REAL>(x.v, y)); }                                           \\\n  };\n\n#endif // EIGEN_ARCH_CONJ_HELPER_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/arch/Default/Settings.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n\n/* All the parameters defined in this file can be specialized in the\n * architecture specific files, and/or by the user.\n * More to come... */\n\n#ifndef EIGEN_DEFAULT_SETTINGS_H\n#define EIGEN_DEFAULT_SETTINGS_H\n\n/** Defines the maximal loop size to enable meta unrolling of loops.\n  * Note that the value here is expressed in Eigen's own notion of \"number of FLOPS\",\n  * it does not correspond to the number of iterations or the number of instructions\n  */\n#ifndef EIGEN_UNROLLING_LIMIT\n#define EIGEN_UNROLLING_LIMIT 100\n#endif\n\n/** Defines the threshold between a \"small\" and a \"large\" matrix.\n  * This threshold is mainly used to select the proper product implementation.\n  */\n#ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD\n#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 8\n#endif\n\n/** Defines the maximal width of the blocks used in the triangular product and solver\n  * for vectors (level 2 blas xTRMV and xTRSV). The default is 8.\n  */\n#ifndef EIGEN_TUNE_TRIANGULAR_PANEL_WIDTH\n#define EIGEN_TUNE_TRIANGULAR_PANEL_WIDTH 8\n#endif\n\n\n/** Defines the default number of registers available for that architecture.\n  * Currently it must be 8 or 16. Other values will fail.\n  */\n#ifndef EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS\n#define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS 8\n#endif\n\n#endif // EIGEN_DEFAULT_SETTINGS_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/arch/NEON/Complex.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2010 Konstantinos Margaritis <markos@freevec.org>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_COMPLEX_NEON_H\n#define EIGEN_COMPLEX_NEON_H\n\nnamespace Eigen {\n\nnamespace internal {\n\ninline uint32x4_t p4ui_CONJ_XOR() {\n// See bug 1325, clang fails to call vld1q_u64.\n#if EIGEN_COMP_CLANG\n  uint32x4_t ret = { 0x00000000, 0x80000000, 0x00000000, 0x80000000 };\n  return ret;\n#else\n  static const uint32_t conj_XOR_DATA[] = { 0x00000000, 0x80000000, 0x00000000, 0x80000000 };\n  return vld1q_u32( conj_XOR_DATA );\n#endif\n}\n\ninline uint32x2_t p2ui_CONJ_XOR() {\n  static const uint32_t conj_XOR_DATA[] = { 0x00000000, 0x80000000 };\n  return vld1_u32( conj_XOR_DATA );\n}\n\n//---------- float ----------\nstruct Packet2cf\n{\n  EIGEN_STRONG_INLINE Packet2cf() {}\n  EIGEN_STRONG_INLINE explicit Packet2cf(const Packet4f& a) : v(a) {}\n  Packet4f  v;\n};\n\ntemplate<> struct packet_traits<std::complex<float> >  : default_packet_traits\n{\n  typedef Packet2cf type;\n  typedef Packet2cf half;\n  enum {\n    Vectorizable = 1,\n    AlignedOnScalar = 1,\n    size = 2,\n    HasHalfPacket = 0,\n\n    HasAdd    = 1,\n    HasSub    = 1,\n    HasMul    = 1,\n    HasDiv    = 1,\n    HasNegate = 1,\n    HasAbs    = 0,\n    HasAbs2   = 0,\n    HasMin    = 0,\n    HasMax    = 0,\n    HasSetLinear = 0\n  };\n};\n\ntemplate<> struct unpacket_traits<Packet2cf> { typedef std::complex<float> type; enum {size=2, alignment=Aligned16}; typedef Packet2cf half; };\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pset1<Packet2cf>(const std::complex<float>&  from)\n{\n  float32x2_t r64;\n  r64 = vld1_f32((const float *)&from);\n\n  return Packet2cf(vcombine_f32(r64, r64));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cf padd<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(padd<Packet4f>(a.v,b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet2cf psub<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(psub<Packet4f>(a.v,b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pnegate(const Packet2cf& a) { return Packet2cf(pnegate<Packet4f>(a.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pconj(const Packet2cf& a)\n{\n  Packet4ui b = vreinterpretq_u32_f32(a.v);\n  return Packet2cf(vreinterpretq_f32_u32(veorq_u32(b, p4ui_CONJ_XOR())));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pmul<Packet2cf>(const Packet2cf& a, const Packet2cf& b)\n{\n  Packet4f v1, v2;\n\n  // Get the real values of a | a1_re | a1_re | a2_re | a2_re |\n  v1 = vcombine_f32(vdup_lane_f32(vget_low_f32(a.v), 0), vdup_lane_f32(vget_high_f32(a.v), 0));\n  // Get the imag values of a | a1_im | a1_im | a2_im | a2_im |\n  v2 = vcombine_f32(vdup_lane_f32(vget_low_f32(a.v), 1), vdup_lane_f32(vget_high_f32(a.v), 1));\n  // Multiply the real a with b\n  v1 = vmulq_f32(v1, b.v);\n  // Multiply the imag a with b\n  v2 = vmulq_f32(v2, b.v);\n  // Conjugate v2 \n  v2 = vreinterpretq_f32_u32(veorq_u32(vreinterpretq_u32_f32(v2), p4ui_CONJ_XOR()));\n  // Swap real/imag elements in v2.\n  v2 = vrev64q_f32(v2);\n  // Add and return the result\n  return Packet2cf(vaddq_f32(v1, v2));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pand   <Packet2cf>(const Packet2cf& a, const Packet2cf& b)\n{\n  return Packet2cf(vreinterpretq_f32_u32(vandq_u32(vreinterpretq_u32_f32(a.v),vreinterpretq_u32_f32(b.v))));\n}\ntemplate<> EIGEN_STRONG_INLINE Packet2cf por    <Packet2cf>(const Packet2cf& a, const Packet2cf& b)\n{\n  return Packet2cf(vreinterpretq_f32_u32(vorrq_u32(vreinterpretq_u32_f32(a.v),vreinterpretq_u32_f32(b.v))));\n}\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pxor   <Packet2cf>(const Packet2cf& a, const Packet2cf& b)\n{\n  return Packet2cf(vreinterpretq_f32_u32(veorq_u32(vreinterpretq_u32_f32(a.v),vreinterpretq_u32_f32(b.v))));\n}\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pandnot<Packet2cf>(const Packet2cf& a, const Packet2cf& b)\n{\n  return Packet2cf(vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(a.v),vreinterpretq_u32_f32(b.v))));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pload<Packet2cf>(const std::complex<float>* from) { EIGEN_DEBUG_ALIGNED_LOAD return Packet2cf(pload<Packet4f>((const float*)from)); }\ntemplate<> EIGEN_STRONG_INLINE Packet2cf ploadu<Packet2cf>(const std::complex<float>* from) { EIGEN_DEBUG_UNALIGNED_LOAD return Packet2cf(ploadu<Packet4f>((const float*)from)); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cf ploaddup<Packet2cf>(const std::complex<float>* from) { return pset1<Packet2cf>(*from); }\n\ntemplate<> EIGEN_STRONG_INLINE void pstore <std::complex<float> >(std::complex<float> *   to, const Packet2cf& from) { EIGEN_DEBUG_ALIGNED_STORE pstore((float*)to, from.v); }\ntemplate<> EIGEN_STRONG_INLINE void pstoreu<std::complex<float> >(std::complex<float> *   to, const Packet2cf& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu((float*)to, from.v); }\n\ntemplate<> EIGEN_DEVICE_FUNC inline Packet2cf pgather<std::complex<float>, Packet2cf>(const std::complex<float>* from, Index stride)\n{\n  Packet4f res = pset1<Packet4f>(0.f);\n  res = vsetq_lane_f32(std::real(from[0*stride]), res, 0);\n  res = vsetq_lane_f32(std::imag(from[0*stride]), res, 1);\n  res = vsetq_lane_f32(std::real(from[1*stride]), res, 2);\n  res = vsetq_lane_f32(std::imag(from[1*stride]), res, 3);\n  return Packet2cf(res);\n}\n\ntemplate<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<float>, Packet2cf>(std::complex<float>* to, const Packet2cf& from, Index stride)\n{\n  to[stride*0] = std::complex<float>(vgetq_lane_f32(from.v, 0), vgetq_lane_f32(from.v, 1));\n  to[stride*1] = std::complex<float>(vgetq_lane_f32(from.v, 2), vgetq_lane_f32(from.v, 3));\n}\n\ntemplate<> EIGEN_STRONG_INLINE void prefetch<std::complex<float> >(const std::complex<float> *   addr) { EIGEN_ARM_PREFETCH((const float *)addr); }\n\ntemplate<> EIGEN_STRONG_INLINE std::complex<float>  pfirst<Packet2cf>(const Packet2cf& a)\n{\n  std::complex<float> EIGEN_ALIGN16 x[2];\n  vst1q_f32((float *)x, a.v);\n  return x[0];\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cf preverse(const Packet2cf& a)\n{\n  float32x2_t a_lo, a_hi;\n  Packet4f a_r128;\n\n  a_lo = vget_low_f32(a.v);\n  a_hi = vget_high_f32(a.v);\n  a_r128 = vcombine_f32(a_hi, a_lo);\n\n  return Packet2cf(a_r128);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pcplxflip<Packet2cf>(const Packet2cf& a)\n{\n  return Packet2cf(vrev64q_f32(a.v));\n}\n\ntemplate<> EIGEN_STRONG_INLINE std::complex<float> predux<Packet2cf>(const Packet2cf& a)\n{\n  float32x2_t a1, a2;\n  std::complex<float> s;\n\n  a1 = vget_low_f32(a.v);\n  a2 = vget_high_f32(a.v);\n  a2 = vadd_f32(a1, a2);\n  vst1_f32((float *)&s, a2);\n\n  return s;\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cf preduxp<Packet2cf>(const Packet2cf* vecs)\n{\n  Packet4f sum1, sum2, sum;\n\n  // Add the first two 64-bit float32x2_t of vecs[0]\n  sum1 = vcombine_f32(vget_low_f32(vecs[0].v), vget_low_f32(vecs[1].v));\n  sum2 = vcombine_f32(vget_high_f32(vecs[0].v), vget_high_f32(vecs[1].v));\n  sum = vaddq_f32(sum1, sum2);\n\n  return Packet2cf(sum);\n}\n\ntemplate<> EIGEN_STRONG_INLINE std::complex<float> predux_mul<Packet2cf>(const Packet2cf& a)\n{\n  float32x2_t a1, a2, v1, v2, prod;\n  std::complex<float> s;\n\n  a1 = vget_low_f32(a.v);\n  a2 = vget_high_f32(a.v);\n   // Get the real values of a | a1_re | a1_re | a2_re | a2_re |\n  v1 = vdup_lane_f32(a1, 0);\n  // Get the real values of a | a1_im | a1_im | a2_im | a2_im |\n  v2 = vdup_lane_f32(a1, 1);\n  // Multiply the real a with b\n  v1 = vmul_f32(v1, a2);\n  // Multiply the imag a with b\n  v2 = vmul_f32(v2, a2);\n  // Conjugate v2 \n  v2 = vreinterpret_f32_u32(veor_u32(vreinterpret_u32_f32(v2), p2ui_CONJ_XOR()));\n  // Swap real/imag elements in v2.\n  v2 = vrev64_f32(v2);\n  // Add v1, v2\n  prod = vadd_f32(v1, v2);\n\n  vst1_f32((float *)&s, prod);\n\n  return s;\n}\n\ntemplate<int Offset>\nstruct palign_impl<Offset,Packet2cf>\n{\n  EIGEN_STRONG_INLINE static void run(Packet2cf& first, const Packet2cf& second)\n  {\n    if (Offset==1)\n    {\n      first.v = vextq_f32(first.v, second.v, 2);\n    }\n  }\n};\n\ntemplate<> struct conj_helper<Packet2cf, Packet2cf, false,true>\n{\n  EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const\n  { return padd(pmul(x,y),c); }\n\n  EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const\n  {\n    return internal::pmul(a, pconj(b));\n  }\n};\n\ntemplate<> struct conj_helper<Packet2cf, Packet2cf, true,false>\n{\n  EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const\n  { return padd(pmul(x,y),c); }\n\n  EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const\n  {\n    return internal::pmul(pconj(a), b);\n  }\n};\n\ntemplate<> struct conj_helper<Packet2cf, Packet2cf, true,true>\n{\n  EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const\n  { return padd(pmul(x,y),c); }\n\n  EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const\n  {\n    return pconj(internal::pmul(a, b));\n  }\n};\n\nEIGEN_MAKE_CONJ_HELPER_CPLX_REAL(Packet2cf,Packet4f)\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pdiv<Packet2cf>(const Packet2cf& a, const Packet2cf& b)\n{\n  // TODO optimize it for NEON\n  Packet2cf res = conj_helper<Packet2cf,Packet2cf,false,true>().pmul(a,b);\n  Packet4f s, rev_s;\n\n  // this computes the norm\n  s = vmulq_f32(b.v, b.v);\n  rev_s = vrev64q_f32(s);\n\n  return Packet2cf(pdiv<Packet4f>(res.v, vaddq_f32(s,rev_s)));\n}\n\nEIGEN_DEVICE_FUNC inline void\nptranspose(PacketBlock<Packet2cf,2>& kernel) {\n  Packet4f tmp = vcombine_f32(vget_high_f32(kernel.packet[0].v), vget_high_f32(kernel.packet[1].v));\n  kernel.packet[0].v = vcombine_f32(vget_low_f32(kernel.packet[0].v), vget_low_f32(kernel.packet[1].v));\n  kernel.packet[1].v = tmp;\n}\n\n//---------- double ----------\n#if EIGEN_ARCH_ARM64 && !EIGEN_APPLE_DOUBLE_NEON_BUG\n\n// See bug 1325, clang fails to call vld1q_u64.\n#if EIGEN_COMP_CLANG\n  static uint64x2_t p2ul_CONJ_XOR = {0x0, 0x8000000000000000};\n#else\n  const uint64_t  p2ul_conj_XOR_DATA[] = { 0x0, 0x8000000000000000 };\n  static uint64x2_t p2ul_CONJ_XOR = vld1q_u64( p2ul_conj_XOR_DATA );\n#endif\n\nstruct Packet1cd\n{\n  EIGEN_STRONG_INLINE Packet1cd() {}\n  EIGEN_STRONG_INLINE explicit Packet1cd(const Packet2d& a) : v(a) {}\n  Packet2d v;\n};\n\ntemplate<> struct packet_traits<std::complex<double> >  : default_packet_traits\n{\n  typedef Packet1cd type;\n  typedef Packet1cd half;\n  enum {\n    Vectorizable = 1,\n    AlignedOnScalar = 0,\n    size = 1,\n    HasHalfPacket = 0,\n\n    HasAdd    = 1,\n    HasSub    = 1,\n    HasMul    = 1,\n    HasDiv    = 1,\n    HasNegate = 1,\n    HasAbs    = 0,\n    HasAbs2   = 0,\n    HasMin    = 0,\n    HasMax    = 0,\n    HasSetLinear = 0\n  };\n};\n\ntemplate<> struct unpacket_traits<Packet1cd> { typedef std::complex<double> type; enum {size=1, alignment=Aligned16}; typedef Packet1cd half; };\n\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pload<Packet1cd>(const std::complex<double>* from) { EIGEN_DEBUG_ALIGNED_LOAD return Packet1cd(pload<Packet2d>((const double*)from)); }\ntemplate<> EIGEN_STRONG_INLINE Packet1cd ploadu<Packet1cd>(const std::complex<double>* from) { EIGEN_DEBUG_UNALIGNED_LOAD return Packet1cd(ploadu<Packet2d>((const double*)from)); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pset1<Packet1cd>(const std::complex<double>&  from)\n{ /* here we really have to use unaligned loads :( */ return ploadu<Packet1cd>(&from); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet1cd padd<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(padd<Packet2d>(a.v,b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet1cd psub<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(psub<Packet2d>(a.v,b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pnegate(const Packet1cd& a) { return Packet1cd(pnegate<Packet2d>(a.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pconj(const Packet1cd& a) { return Packet1cd(vreinterpretq_f64_u64(veorq_u64(vreinterpretq_u64_f64(a.v), p2ul_CONJ_XOR))); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pmul<Packet1cd>(const Packet1cd& a, const Packet1cd& b)\n{\n  Packet2d v1, v2;\n\n  // Get the real values of a \n  v1 = vdupq_lane_f64(vget_low_f64(a.v), 0);\n  // Get the imag values of a\n  v2 = vdupq_lane_f64(vget_high_f64(a.v), 0);\n  // Multiply the real a with b\n  v1 = vmulq_f64(v1, b.v);\n  // Multiply the imag a with b\n  v2 = vmulq_f64(v2, b.v);\n  // Conjugate v2 \n  v2 = vreinterpretq_f64_u64(veorq_u64(vreinterpretq_u64_f64(v2), p2ul_CONJ_XOR));\n  // Swap real/imag elements in v2.\n  v2 = preverse<Packet2d>(v2);\n  // Add and return the result\n  return Packet1cd(vaddq_f64(v1, v2));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pand   <Packet1cd>(const Packet1cd& a, const Packet1cd& b)\n{\n  return Packet1cd(vreinterpretq_f64_u64(vandq_u64(vreinterpretq_u64_f64(a.v),vreinterpretq_u64_f64(b.v))));\n}\ntemplate<> EIGEN_STRONG_INLINE Packet1cd por    <Packet1cd>(const Packet1cd& a, const Packet1cd& b)\n{\n  return Packet1cd(vreinterpretq_f64_u64(vorrq_u64(vreinterpretq_u64_f64(a.v),vreinterpretq_u64_f64(b.v))));\n}\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pxor   <Packet1cd>(const Packet1cd& a, const Packet1cd& b)\n{\n  return Packet1cd(vreinterpretq_f64_u64(veorq_u64(vreinterpretq_u64_f64(a.v),vreinterpretq_u64_f64(b.v))));\n}\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pandnot<Packet1cd>(const Packet1cd& a, const Packet1cd& b)\n{\n  return Packet1cd(vreinterpretq_f64_u64(vbicq_u64(vreinterpretq_u64_f64(a.v),vreinterpretq_u64_f64(b.v))));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet1cd ploaddup<Packet1cd>(const std::complex<double>* from) { return pset1<Packet1cd>(*from); }\n\ntemplate<> EIGEN_STRONG_INLINE void pstore <std::complex<double> >(std::complex<double> *   to, const Packet1cd& from) { EIGEN_DEBUG_ALIGNED_STORE pstore((double*)to, from.v); }\ntemplate<> EIGEN_STRONG_INLINE void pstoreu<std::complex<double> >(std::complex<double> *   to, const Packet1cd& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu((double*)to, from.v); }\n\ntemplate<> EIGEN_STRONG_INLINE void prefetch<std::complex<double> >(const std::complex<double> *   addr) { EIGEN_ARM_PREFETCH((const double *)addr); }\n\ntemplate<> EIGEN_DEVICE_FUNC inline Packet1cd pgather<std::complex<double>, Packet1cd>(const std::complex<double>* from, Index stride)\n{\n  Packet2d res = pset1<Packet2d>(0.0);\n  res = vsetq_lane_f64(std::real(from[0*stride]), res, 0);\n  res = vsetq_lane_f64(std::imag(from[0*stride]), res, 1);\n  return Packet1cd(res);\n}\n\ntemplate<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<double>, Packet1cd>(std::complex<double>* to, const Packet1cd& from, Index stride)\n{\n  to[stride*0] = std::complex<double>(vgetq_lane_f64(from.v, 0), vgetq_lane_f64(from.v, 1));\n}\n\n\ntemplate<> EIGEN_STRONG_INLINE std::complex<double>  pfirst<Packet1cd>(const Packet1cd& a)\n{\n  std::complex<double> EIGEN_ALIGN16 res;\n  pstore<std::complex<double> >(&res, a);\n\n  return res;\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet1cd preverse(const Packet1cd& a) { return a; }\n\ntemplate<> EIGEN_STRONG_INLINE std::complex<double> predux<Packet1cd>(const Packet1cd& a) { return pfirst(a); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet1cd preduxp<Packet1cd>(const Packet1cd* vecs) { return vecs[0]; }\n\ntemplate<> EIGEN_STRONG_INLINE std::complex<double> predux_mul<Packet1cd>(const Packet1cd& a) { return pfirst(a); }\n\ntemplate<int Offset>\nstruct palign_impl<Offset,Packet1cd>\n{\n  static EIGEN_STRONG_INLINE void run(Packet1cd& /*first*/, const Packet1cd& /*second*/)\n  {\n    // FIXME is it sure we never have to align a Packet1cd?\n    // Even though a std::complex<double> has 16 bytes, it is not necessarily aligned on a 16 bytes boundary...\n  }\n};\n\ntemplate<> struct conj_helper<Packet1cd, Packet1cd, false,true>\n{\n  EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet1cd& x, const Packet1cd& y, const Packet1cd& c) const\n  { return padd(pmul(x,y),c); }\n\n  EIGEN_STRONG_INLINE Packet1cd pmul(const Packet1cd& a, const Packet1cd& b) const\n  {\n    return internal::pmul(a, pconj(b));\n  }\n};\n\ntemplate<> struct conj_helper<Packet1cd, Packet1cd, true,false>\n{\n  EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet1cd& x, const Packet1cd& y, const Packet1cd& c) const\n  { return padd(pmul(x,y),c); }\n\n  EIGEN_STRONG_INLINE Packet1cd pmul(const Packet1cd& a, const Packet1cd& b) const\n  {\n    return internal::pmul(pconj(a), b);\n  }\n};\n\ntemplate<> struct conj_helper<Packet1cd, Packet1cd, true,true>\n{\n  EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet1cd& x, const Packet1cd& y, const Packet1cd& c) const\n  { return padd(pmul(x,y),c); }\n\n  EIGEN_STRONG_INLINE Packet1cd pmul(const Packet1cd& a, const Packet1cd& b) const\n  {\n    return pconj(internal::pmul(a, b));\n  }\n};\n\nEIGEN_MAKE_CONJ_HELPER_CPLX_REAL(Packet1cd,Packet2d)\n\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pdiv<Packet1cd>(const Packet1cd& a, const Packet1cd& b)\n{\n  // TODO optimize it for NEON\n  Packet1cd res = conj_helper<Packet1cd,Packet1cd,false,true>().pmul(a,b);\n  Packet2d s = pmul<Packet2d>(b.v, b.v);\n  Packet2d rev_s = preverse<Packet2d>(s);\n\n  return Packet1cd(pdiv(res.v, padd<Packet2d>(s,rev_s)));\n}\n\nEIGEN_STRONG_INLINE Packet1cd pcplxflip/*<Packet1cd>*/(const Packet1cd& x)\n{\n  return Packet1cd(preverse(Packet2d(x.v)));\n}\n\nEIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet1cd,2>& kernel)\n{\n  Packet2d tmp = vcombine_f64(vget_high_f64(kernel.packet[0].v), vget_high_f64(kernel.packet[1].v));\n  kernel.packet[0].v = vcombine_f64(vget_low_f64(kernel.packet[0].v), vget_low_f64(kernel.packet[1].v));\n  kernel.packet[1].v = tmp;\n}\n#endif // EIGEN_ARCH_ARM64\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_COMPLEX_NEON_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/arch/NEON/MathFunctions.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n/* The sin, cos, exp, and log functions of this file come from\n * Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/\n */\n\n#ifndef EIGEN_MATH_FUNCTIONS_NEON_H\n#define EIGEN_MATH_FUNCTIONS_NEON_H\n\nnamespace Eigen {\n\nnamespace internal {\n\ntemplate<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED\nPacket4f pexp<Packet4f>(const Packet4f& _x)\n{\n  Packet4f x = _x;\n  Packet4f tmp, fx;\n\n  _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);\n  _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);\n  _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);\n  _EIGEN_DECLARE_CONST_Packet4f(exp_hi,  88.3762626647950f);\n  _EIGEN_DECLARE_CONST_Packet4f(exp_lo, -88.3762626647949f);\n  _EIGEN_DECLARE_CONST_Packet4f(cephes_LOG2EF, 1.44269504088896341f);\n  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C1, 0.693359375f);\n  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C2, -2.12194440e-4f);\n  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p0, 1.9875691500E-4f);\n  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p1, 1.3981999507E-3f);\n  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p2, 8.3334519073E-3f);\n  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p3, 4.1665795894E-2f);\n  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459E-1f);\n  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201E-1f);\n\n  x = vminq_f32(x, p4f_exp_hi);\n  x = vmaxq_f32(x, p4f_exp_lo);\n\n  /* express exp(x) as exp(g + n*log(2)) */\n  fx = vmlaq_f32(p4f_half, x, p4f_cephes_LOG2EF);\n\n  /* perform a floorf */\n  tmp = vcvtq_f32_s32(vcvtq_s32_f32(fx));\n\n  /* if greater, substract 1 */\n  Packet4ui mask = vcgtq_f32(tmp, fx);\n  mask = vandq_u32(mask, vreinterpretq_u32_f32(p4f_1));\n\n  fx = vsubq_f32(tmp, vreinterpretq_f32_u32(mask));\n\n  tmp = vmulq_f32(fx, p4f_cephes_exp_C1);\n  Packet4f z = vmulq_f32(fx, p4f_cephes_exp_C2);\n  x = vsubq_f32(x, tmp);\n  x = vsubq_f32(x, z);\n\n  Packet4f y = vmulq_f32(p4f_cephes_exp_p0, x);\n  z = vmulq_f32(x, x);\n  y = vaddq_f32(y, p4f_cephes_exp_p1);\n  y = vmulq_f32(y, x);\n  y = vaddq_f32(y, p4f_cephes_exp_p2);\n  y = vmulq_f32(y, x);\n  y = vaddq_f32(y, p4f_cephes_exp_p3);\n  y = vmulq_f32(y, x);\n  y = vaddq_f32(y, p4f_cephes_exp_p4);\n  y = vmulq_f32(y, x);\n  y = vaddq_f32(y, p4f_cephes_exp_p5);\n\n  y = vmulq_f32(y, z);\n  y = vaddq_f32(y, x);\n  y = vaddq_f32(y, p4f_1);\n\n  /* build 2^n */\n  int32x4_t mm;\n  mm = vcvtq_s32_f32(fx);\n  mm = vaddq_s32(mm, p4i_0x7f);\n  mm = vshlq_n_s32(mm, 23);\n  Packet4f pow2n = vreinterpretq_f32_s32(mm);\n\n  y = vmulq_f32(y, pow2n);\n  return y;\n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_MATH_FUNCTIONS_NEON_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/arch/NEON/PacketMath.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2010 Konstantinos Margaritis <markos@freevec.org>\n// Heavily based on Gael's SSE version.\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_PACKET_MATH_NEON_H\n#define EIGEN_PACKET_MATH_NEON_H\n\nnamespace Eigen {\n\nnamespace internal {\n\n#ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD\n#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 8\n#endif\n\n#ifndef EIGEN_HAS_SINGLE_INSTRUCTION_MADD\n#define EIGEN_HAS_SINGLE_INSTRUCTION_MADD\n#endif\n\n#ifndef EIGEN_HAS_SINGLE_INSTRUCTION_CJMADD\n#define EIGEN_HAS_SINGLE_INSTRUCTION_CJMADD\n#endif\n\n#ifndef EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS\n#if EIGEN_ARCH_ARM64\n#define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS 32\n#else\n#define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS 16 \n#endif\n#endif\n\n#if EIGEN_COMP_MSVC\n\n// In MSVC's arm_neon.h header file, all NEON vector types\n// are aliases to the same underlying type __n128.\n// We thus have to wrap them to make them different C++ types.\n// (See also bug 1428)\n\ntemplate<typename T,int unique_id>\nstruct eigen_packet_wrapper\n{\n  operator T&() { return m_val; }\n  operator const T&() const { return m_val; }\n  eigen_packet_wrapper() {}\n  eigen_packet_wrapper(const T &v) : m_val(v) {}\n  eigen_packet_wrapper& operator=(const T &v) {\n    m_val = v;\n    return *this;\n  }\n\n  T m_val;\n};\ntypedef eigen_packet_wrapper<float32x2_t,0> Packet2f;\ntypedef eigen_packet_wrapper<float32x4_t,1> Packet4f;\ntypedef eigen_packet_wrapper<int32x4_t  ,2> Packet4i;\ntypedef eigen_packet_wrapper<int32x2_t  ,3> Packet2i;\ntypedef eigen_packet_wrapper<uint32x4_t ,4> Packet4ui;\n\n#else\n\ntypedef float32x2_t Packet2f;\ntypedef float32x4_t Packet4f;\ntypedef int32x4_t   Packet4i;\ntypedef int32x2_t   Packet2i;\ntypedef uint32x4_t  Packet4ui;\n\n#endif // EIGEN_COMP_MSVC\n\n#define _EIGEN_DECLARE_CONST_Packet4f(NAME,X) \\\n  const Packet4f p4f_##NAME = pset1<Packet4f>(X)\n\n#define _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(NAME,X) \\\n  const Packet4f p4f_##NAME = vreinterpretq_f32_u32(pset1<int32_t>(X))\n\n#define _EIGEN_DECLARE_CONST_Packet4i(NAME,X) \\\n  const Packet4i p4i_##NAME = pset1<Packet4i>(X)\n\n#if EIGEN_ARCH_ARM64\n  // __builtin_prefetch tends to do nothing on ARM64 compilers because the\n  // prefetch instructions there are too detailed for __builtin_prefetch to map\n  // meaningfully to them.\n  #define EIGEN_ARM_PREFETCH(ADDR)  __asm__ __volatile__(\"prfm pldl1keep, [%[addr]]\\n\" ::[addr] \"r\"(ADDR) : );\n#elif EIGEN_HAS_BUILTIN(__builtin_prefetch) || EIGEN_COMP_GNUC\n  #define EIGEN_ARM_PREFETCH(ADDR) __builtin_prefetch(ADDR);\n#elif defined __pld\n  #define EIGEN_ARM_PREFETCH(ADDR) __pld(ADDR)\n#elif EIGEN_ARCH_ARM32\n  #define EIGEN_ARM_PREFETCH(ADDR) __asm__ __volatile__ (\"pld [%[addr]]\\n\" :: [addr] \"r\" (ADDR) : );\n#else\n  // by default no explicit prefetching\n  #define EIGEN_ARM_PREFETCH(ADDR)\n#endif\n\ntemplate<> struct packet_traits<float>  : default_packet_traits\n{\n  typedef Packet4f type;\n  typedef Packet4f half; // Packet2f intrinsics not implemented yet\n  enum {\n    Vectorizable = 1,\n    AlignedOnScalar = 1,\n    size = 4,\n    HasHalfPacket=0, // Packet2f intrinsics not implemented yet\n   \n    HasDiv  = 1,\n    // FIXME check the Has*\n    HasSin  = 0,\n    HasCos  = 0,\n    HasLog  = 0,\n    HasExp  = 1,\n    HasSqrt = 0\n  };\n};\ntemplate<> struct packet_traits<int32_t>    : default_packet_traits\n{\n  typedef Packet4i type;\n  typedef Packet4i half; // Packet2i intrinsics not implemented yet\n  enum {\n    Vectorizable = 1,\n    AlignedOnScalar = 1,\n    size=4,\n    HasHalfPacket=0 // Packet2i intrinsics not implemented yet\n    // FIXME check the Has*\n  };\n};\n\n#if EIGEN_GNUC_AT_MOST(4,4) && !EIGEN_COMP_LLVM\n// workaround gcc 4.2, 4.3 and 4.4 compilatin issue\nEIGEN_STRONG_INLINE float32x4_t vld1q_f32(const float* x) { return ::vld1q_f32((const float32_t*)x); }\nEIGEN_STRONG_INLINE float32x2_t vld1_f32 (const float* x) { return ::vld1_f32 ((const float32_t*)x); }\nEIGEN_STRONG_INLINE float32x2_t vld1_dup_f32 (const float* x) { return ::vld1_dup_f32 ((const float32_t*)x); }\nEIGEN_STRONG_INLINE void        vst1q_f32(float* to, float32x4_t from) { ::vst1q_f32((float32_t*)to,from); }\nEIGEN_STRONG_INLINE void        vst1_f32 (float* to, float32x2_t from) { ::vst1_f32 ((float32_t*)to,from); }\n#endif\n\ntemplate<> struct unpacket_traits<Packet4f> { typedef float   type; enum {size=4, alignment=Aligned16}; typedef Packet4f half; };\ntemplate<> struct unpacket_traits<Packet4i> { typedef int32_t type; enum {size=4, alignment=Aligned16}; typedef Packet4i half; };\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float&  from) { return vdupq_n_f32(from); }\ntemplate<> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int32_t&    from)   { return vdupq_n_s32(from); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f plset<Packet4f>(const float& a)\n{\n  const float f[] = {0, 1, 2, 3};\n  Packet4f countdown = vld1q_f32(f);\n  return vaddq_f32(pset1<Packet4f>(a), countdown);\n}\ntemplate<> EIGEN_STRONG_INLINE Packet4i plset<Packet4i>(const int32_t& a)\n{\n  const int32_t i[] = {0, 1, 2, 3};\n  Packet4i countdown = vld1q_s32(i);\n  return vaddq_s32(pset1<Packet4i>(a), countdown);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f padd<Packet4f>(const Packet4f& a, const Packet4f& b) { return vaddq_f32(a,b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4i padd<Packet4i>(const Packet4i& a, const Packet4i& b) { return vaddq_s32(a,b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f psub<Packet4f>(const Packet4f& a, const Packet4f& b) { return vsubq_f32(a,b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4i psub<Packet4i>(const Packet4i& a, const Packet4i& b) { return vsubq_s32(a,b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pnegate(const Packet4f& a) { return vnegq_f32(a); }\ntemplate<> EIGEN_STRONG_INLINE Packet4i pnegate(const Packet4i& a) { return vnegq_s32(a); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pconj(const Packet4f& a) { return a; }\ntemplate<> EIGEN_STRONG_INLINE Packet4i pconj(const Packet4i& a) { return a; }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pmul<Packet4f>(const Packet4f& a, const Packet4f& b) { return vmulq_f32(a,b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4i pmul<Packet4i>(const Packet4i& a, const Packet4i& b) { return vmulq_s32(a,b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pdiv<Packet4f>(const Packet4f& a, const Packet4f& b)\n{\n#if EIGEN_ARCH_ARM64\n  return vdivq_f32(a,b);\n#else\n  Packet4f inv, restep, div;\n\n  // NEON does not offer a divide instruction, we have to do a reciprocal approximation\n  // However NEON in contrast to other SIMD engines (AltiVec/SSE), offers\n  // a reciprocal estimate AND a reciprocal step -which saves a few instructions\n  // vrecpeq_f32() returns an estimate to 1/b, which we will finetune with\n  // Newton-Raphson and vrecpsq_f32()\n  inv = vrecpeq_f32(b);\n\n  // This returns a differential, by which we will have to multiply inv to get a better\n  // approximation of 1/b.\n  restep = vrecpsq_f32(b, inv);\n  inv = vmulq_f32(restep, inv);\n\n  // Finally, multiply a by 1/b and get the wanted result of the division.\n  div = vmulq_f32(a, inv);\n\n  return div;\n#endif\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4i pdiv<Packet4i>(const Packet4i& /*a*/, const Packet4i& /*b*/)\n{ eigen_assert(false && \"packet integer division are not supported by NEON\");\n  return pset1<Packet4i>(0);\n}\n\n// Clang/ARM wrongly advertises __ARM_FEATURE_FMA even when it's not available,\n// then implements a slow software scalar fallback calling fmaf()!\n// Filed LLVM bug:\n//     https://llvm.org/bugs/show_bug.cgi?id=27216\n#if (defined __ARM_FEATURE_FMA) && !(EIGEN_COMP_CLANG && EIGEN_ARCH_ARM)\n// See bug 936.\n// FMA is available on VFPv4 i.e. when compiling with -mfpu=neon-vfpv4.\n// FMA is a true fused multiply-add i.e. only 1 rounding at the end, no intermediate rounding.\n// MLA is not fused i.e. does 2 roundings.\n// In addition to giving better accuracy, FMA also gives better performance here on a Krait (Nexus 4):\n// MLA: 10 GFlop/s ; FMA: 12 GFlops/s.\ntemplate<> EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c) { return vfmaq_f32(c,a,b); }\n#else\ntemplate<> EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c) {\n#if EIGEN_COMP_CLANG && EIGEN_ARCH_ARM\n  // Clang/ARM will replace VMLA by VMUL+VADD at least for some values of -mcpu,\n  // at least -mcpu=cortex-a8 and -mcpu=cortex-a7. Since the former is the default on\n  // -march=armv7-a, that is a very common case.\n  // See e.g. this thread:\n  //     http://lists.llvm.org/pipermail/llvm-dev/2013-December/068806.html\n  // Filed LLVM bug:\n  //     https://llvm.org/bugs/show_bug.cgi?id=27219\n  Packet4f r = c;\n  asm volatile(\n    \"vmla.f32 %q[r], %q[a], %q[b]\"\n    : [r] \"+w\" (r)\n    : [a] \"w\" (a),\n      [b] \"w\" (b)\n    : );\n  return r;\n#else\n  return vmlaq_f32(c,a,b);\n#endif\n}\n#endif\n\n// No FMA instruction for int, so use MLA unconditionally.\ntemplate<> EIGEN_STRONG_INLINE Packet4i pmadd(const Packet4i& a, const Packet4i& b, const Packet4i& c) { return vmlaq_s32(c,a,b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pmin<Packet4f>(const Packet4f& a, const Packet4f& b) { return vminq_f32(a,b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4i pmin<Packet4i>(const Packet4i& a, const Packet4i& b) { return vminq_s32(a,b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pmax<Packet4f>(const Packet4f& a, const Packet4f& b) { return vmaxq_f32(a,b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4i pmax<Packet4i>(const Packet4i& a, const Packet4i& b) { return vmaxq_s32(a,b); }\n\n// Logical Operations are not supported for float, so we have to reinterpret casts using NEON intrinsics\ntemplate<> EIGEN_STRONG_INLINE Packet4f pand<Packet4f>(const Packet4f& a, const Packet4f& b)\n{\n  return vreinterpretq_f32_u32(vandq_u32(vreinterpretq_u32_f32(a),vreinterpretq_u32_f32(b)));\n}\ntemplate<> EIGEN_STRONG_INLINE Packet4i pand<Packet4i>(const Packet4i& a, const Packet4i& b) { return vandq_s32(a,b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f por<Packet4f>(const Packet4f& a, const Packet4f& b)\n{\n  return vreinterpretq_f32_u32(vorrq_u32(vreinterpretq_u32_f32(a),vreinterpretq_u32_f32(b)));\n}\ntemplate<> EIGEN_STRONG_INLINE Packet4i por<Packet4i>(const Packet4i& a, const Packet4i& b) { return vorrq_s32(a,b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pxor<Packet4f>(const Packet4f& a, const Packet4f& b)\n{\n  return vreinterpretq_f32_u32(veorq_u32(vreinterpretq_u32_f32(a),vreinterpretq_u32_f32(b)));\n}\ntemplate<> EIGEN_STRONG_INLINE Packet4i pxor<Packet4i>(const Packet4i& a, const Packet4i& b) { return veorq_s32(a,b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pandnot<Packet4f>(const Packet4f& a, const Packet4f& b)\n{\n  return vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(a),vreinterpretq_u32_f32(b)));\n}\ntemplate<> EIGEN_STRONG_INLINE Packet4i pandnot<Packet4i>(const Packet4i& a, const Packet4i& b) { return vbicq_s32(a,b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pload<Packet4f>(const float*    from) { EIGEN_DEBUG_ALIGNED_LOAD return vld1q_f32(from); }\ntemplate<> EIGEN_STRONG_INLINE Packet4i pload<Packet4i>(const int32_t*  from) { EIGEN_DEBUG_ALIGNED_LOAD return vld1q_s32(from); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float*   from) { EIGEN_DEBUG_UNALIGNED_LOAD return vld1q_f32(from); }\ntemplate<> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int32_t* from) { EIGEN_DEBUG_UNALIGNED_LOAD return vld1q_s32(from); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f ploaddup<Packet4f>(const float* from)\n{\n  float32x2_t lo, hi;\n  lo = vld1_dup_f32(from);\n  hi = vld1_dup_f32(from+1);\n  return vcombine_f32(lo, hi);\n}\ntemplate<> EIGEN_STRONG_INLINE Packet4i ploaddup<Packet4i>(const int32_t* from)\n{\n  int32x2_t lo, hi;\n  lo = vld1_dup_s32(from);\n  hi = vld1_dup_s32(from+1);\n  return vcombine_s32(lo, hi);\n}\n\ntemplate<> EIGEN_STRONG_INLINE void pstore<float>  (float*    to, const Packet4f& from) { EIGEN_DEBUG_ALIGNED_STORE vst1q_f32(to, from); }\ntemplate<> EIGEN_STRONG_INLINE void pstore<int32_t>(int32_t*  to, const Packet4i& from) { EIGEN_DEBUG_ALIGNED_STORE vst1q_s32(to, from); }\n\ntemplate<> EIGEN_STRONG_INLINE void pstoreu<float>  (float*   to, const Packet4f& from) { EIGEN_DEBUG_UNALIGNED_STORE vst1q_f32(to, from); }\ntemplate<> EIGEN_STRONG_INLINE void pstoreu<int32_t>(int32_t* to, const Packet4i& from) { EIGEN_DEBUG_UNALIGNED_STORE vst1q_s32(to, from); }\n\ntemplate<> EIGEN_DEVICE_FUNC inline Packet4f pgather<float, Packet4f>(const float* from, Index stride)\n{\n  Packet4f res = pset1<Packet4f>(0.f);\n  res = vsetq_lane_f32(from[0*stride], res, 0);\n  res = vsetq_lane_f32(from[1*stride], res, 1);\n  res = vsetq_lane_f32(from[2*stride], res, 2);\n  res = vsetq_lane_f32(from[3*stride], res, 3);\n  return res;\n}\ntemplate<> EIGEN_DEVICE_FUNC inline Packet4i pgather<int32_t, Packet4i>(const int32_t* from, Index stride)\n{\n  Packet4i res = pset1<Packet4i>(0);\n  res = vsetq_lane_s32(from[0*stride], res, 0);\n  res = vsetq_lane_s32(from[1*stride], res, 1);\n  res = vsetq_lane_s32(from[2*stride], res, 2);\n  res = vsetq_lane_s32(from[3*stride], res, 3);\n  return res;\n}\n\ntemplate<> EIGEN_DEVICE_FUNC inline void pscatter<float, Packet4f>(float* to, const Packet4f& from, Index stride)\n{\n  to[stride*0] = vgetq_lane_f32(from, 0);\n  to[stride*1] = vgetq_lane_f32(from, 1);\n  to[stride*2] = vgetq_lane_f32(from, 2);\n  to[stride*3] = vgetq_lane_f32(from, 3);\n}\ntemplate<> EIGEN_DEVICE_FUNC inline void pscatter<int32_t, Packet4i>(int32_t* to, const Packet4i& from, Index stride)\n{\n  to[stride*0] = vgetq_lane_s32(from, 0);\n  to[stride*1] = vgetq_lane_s32(from, 1);\n  to[stride*2] = vgetq_lane_s32(from, 2);\n  to[stride*3] = vgetq_lane_s32(from, 3);\n}\n\ntemplate<> EIGEN_STRONG_INLINE void prefetch<float>  (const float*    addr) { EIGEN_ARM_PREFETCH(addr); }\ntemplate<> EIGEN_STRONG_INLINE void prefetch<int32_t>(const int32_t*  addr) { EIGEN_ARM_PREFETCH(addr); }\n\n// FIXME only store the 2 first elements ?\ntemplate<> EIGEN_STRONG_INLINE float   pfirst<Packet4f>(const Packet4f& a) { float   EIGEN_ALIGN16 x[4]; vst1q_f32(x, a); return x[0]; }\ntemplate<> EIGEN_STRONG_INLINE int32_t pfirst<Packet4i>(const Packet4i& a) { int32_t EIGEN_ALIGN16 x[4]; vst1q_s32(x, a); return x[0]; }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f preverse(const Packet4f& a) {\n  float32x2_t a_lo, a_hi;\n  Packet4f a_r64;\n\n  a_r64 = vrev64q_f32(a);\n  a_lo = vget_low_f32(a_r64);\n  a_hi = vget_high_f32(a_r64);\n  return vcombine_f32(a_hi, a_lo);\n}\ntemplate<> EIGEN_STRONG_INLINE Packet4i preverse(const Packet4i& a) {\n  int32x2_t a_lo, a_hi;\n  Packet4i a_r64;\n\n  a_r64 = vrev64q_s32(a);\n  a_lo = vget_low_s32(a_r64);\n  a_hi = vget_high_s32(a_r64);\n  return vcombine_s32(a_hi, a_lo);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pabs(const Packet4f& a) { return vabsq_f32(a); }\ntemplate<> EIGEN_STRONG_INLINE Packet4i pabs(const Packet4i& a) { return vabsq_s32(a); }\n\ntemplate<> EIGEN_STRONG_INLINE float predux<Packet4f>(const Packet4f& a)\n{\n  float32x2_t a_lo, a_hi, sum;\n\n  a_lo = vget_low_f32(a);\n  a_hi = vget_high_f32(a);\n  sum = vpadd_f32(a_lo, a_hi);\n  sum = vpadd_f32(sum, sum);\n  return vget_lane_f32(sum, 0);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f preduxp<Packet4f>(const Packet4f* vecs)\n{\n  float32x4x2_t vtrn1, vtrn2, res1, res2;\n  Packet4f sum1, sum2, sum;\n\n  // NEON zip performs interleaving of the supplied vectors.\n  // We perform two interleaves in a row to acquire the transposed vector\n  vtrn1 = vzipq_f32(vecs[0], vecs[2]);\n  vtrn2 = vzipq_f32(vecs[1], vecs[3]);\n  res1 = vzipq_f32(vtrn1.val[0], vtrn2.val[0]);\n  res2 = vzipq_f32(vtrn1.val[1], vtrn2.val[1]);\n\n  // Do the addition of the resulting vectors\n  sum1 = vaddq_f32(res1.val[0], res1.val[1]);\n  sum2 = vaddq_f32(res2.val[0], res2.val[1]);\n  sum = vaddq_f32(sum1, sum2);\n\n  return sum;\n}\n\ntemplate<> EIGEN_STRONG_INLINE int32_t predux<Packet4i>(const Packet4i& a)\n{\n  int32x2_t a_lo, a_hi, sum;\n\n  a_lo = vget_low_s32(a);\n  a_hi = vget_high_s32(a);\n  sum = vpadd_s32(a_lo, a_hi);\n  sum = vpadd_s32(sum, sum);\n  return vget_lane_s32(sum, 0);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4i preduxp<Packet4i>(const Packet4i* vecs)\n{\n  int32x4x2_t vtrn1, vtrn2, res1, res2;\n  Packet4i sum1, sum2, sum;\n\n  // NEON zip performs interleaving of the supplied vectors.\n  // We perform two interleaves in a row to acquire the transposed vector\n  vtrn1 = vzipq_s32(vecs[0], vecs[2]);\n  vtrn2 = vzipq_s32(vecs[1], vecs[3]);\n  res1 = vzipq_s32(vtrn1.val[0], vtrn2.val[0]);\n  res2 = vzipq_s32(vtrn1.val[1], vtrn2.val[1]);\n\n  // Do the addition of the resulting vectors\n  sum1 = vaddq_s32(res1.val[0], res1.val[1]);\n  sum2 = vaddq_s32(res2.val[0], res2.val[1]);\n  sum = vaddq_s32(sum1, sum2);\n\n  return sum;\n}\n\n// Other reduction functions:\n// mul\ntemplate<> EIGEN_STRONG_INLINE float predux_mul<Packet4f>(const Packet4f& a)\n{\n  float32x2_t a_lo, a_hi, prod;\n\n  // Get a_lo = |a1|a2| and a_hi = |a3|a4|\n  a_lo = vget_low_f32(a);\n  a_hi = vget_high_f32(a);\n  // Get the product of a_lo * a_hi -> |a1*a3|a2*a4|\n  prod = vmul_f32(a_lo, a_hi);\n  // Multiply prod with its swapped value |a2*a4|a1*a3|\n  prod = vmul_f32(prod, vrev64_f32(prod));\n\n  return vget_lane_f32(prod, 0);\n}\ntemplate<> EIGEN_STRONG_INLINE int32_t predux_mul<Packet4i>(const Packet4i& a)\n{\n  int32x2_t a_lo, a_hi, prod;\n\n  // Get a_lo = |a1|a2| and a_hi = |a3|a4|\n  a_lo = vget_low_s32(a);\n  a_hi = vget_high_s32(a);\n  // Get the product of a_lo * a_hi -> |a1*a3|a2*a4|\n  prod = vmul_s32(a_lo, a_hi);\n  // Multiply prod with its swapped value |a2*a4|a1*a3|\n  prod = vmul_s32(prod, vrev64_s32(prod));\n\n  return vget_lane_s32(prod, 0);\n}\n\n// min\ntemplate<> EIGEN_STRONG_INLINE float predux_min<Packet4f>(const Packet4f& a)\n{\n  float32x2_t a_lo, a_hi, min;\n\n  a_lo = vget_low_f32(a);\n  a_hi = vget_high_f32(a);\n  min = vpmin_f32(a_lo, a_hi);\n  min = vpmin_f32(min, min);\n\n  return vget_lane_f32(min, 0);\n}\n\ntemplate<> EIGEN_STRONG_INLINE int32_t predux_min<Packet4i>(const Packet4i& a)\n{\n  int32x2_t a_lo, a_hi, min;\n\n  a_lo = vget_low_s32(a);\n  a_hi = vget_high_s32(a);\n  min = vpmin_s32(a_lo, a_hi);\n  min = vpmin_s32(min, min);\n  \n  return vget_lane_s32(min, 0);\n}\n\n// max\ntemplate<> EIGEN_STRONG_INLINE float predux_max<Packet4f>(const Packet4f& a)\n{\n  float32x2_t a_lo, a_hi, max;\n\n  a_lo = vget_low_f32(a);\n  a_hi = vget_high_f32(a);\n  max = vpmax_f32(a_lo, a_hi);\n  max = vpmax_f32(max, max);\n\n  return vget_lane_f32(max, 0);\n}\n\ntemplate<> EIGEN_STRONG_INLINE int32_t predux_max<Packet4i>(const Packet4i& a)\n{\n  int32x2_t a_lo, a_hi, max;\n\n  a_lo = vget_low_s32(a);\n  a_hi = vget_high_s32(a);\n  max = vpmax_s32(a_lo, a_hi);\n  max = vpmax_s32(max, max);\n\n  return vget_lane_s32(max, 0);\n}\n\n// this PALIGN_NEON business is to work around a bug in LLVM Clang 3.0 causing incorrect compilation errors,\n// see bug 347 and this LLVM bug: http://llvm.org/bugs/show_bug.cgi?id=11074\n#define PALIGN_NEON(Offset,Type,Command) \\\ntemplate<>\\\nstruct palign_impl<Offset,Type>\\\n{\\\n    EIGEN_STRONG_INLINE static void run(Type& first, const Type& second)\\\n    {\\\n        if (Offset!=0)\\\n            first = Command(first, second, Offset);\\\n    }\\\n};\\\n\nPALIGN_NEON(0,Packet4f,vextq_f32)\nPALIGN_NEON(1,Packet4f,vextq_f32)\nPALIGN_NEON(2,Packet4f,vextq_f32)\nPALIGN_NEON(3,Packet4f,vextq_f32)\nPALIGN_NEON(0,Packet4i,vextq_s32)\nPALIGN_NEON(1,Packet4i,vextq_s32)\nPALIGN_NEON(2,Packet4i,vextq_s32)\nPALIGN_NEON(3,Packet4i,vextq_s32)\n\n#undef PALIGN_NEON\n\nEIGEN_DEVICE_FUNC inline void\nptranspose(PacketBlock<Packet4f,4>& kernel) {\n  float32x4x2_t tmp1 = vzipq_f32(kernel.packet[0], kernel.packet[1]);\n  float32x4x2_t tmp2 = vzipq_f32(kernel.packet[2], kernel.packet[3]);\n\n  kernel.packet[0] = vcombine_f32(vget_low_f32(tmp1.val[0]), vget_low_f32(tmp2.val[0]));\n  kernel.packet[1] = vcombine_f32(vget_high_f32(tmp1.val[0]), vget_high_f32(tmp2.val[0]));\n  kernel.packet[2] = vcombine_f32(vget_low_f32(tmp1.val[1]), vget_low_f32(tmp2.val[1]));\n  kernel.packet[3] = vcombine_f32(vget_high_f32(tmp1.val[1]), vget_high_f32(tmp2.val[1]));\n}\n\nEIGEN_DEVICE_FUNC inline void\nptranspose(PacketBlock<Packet4i,4>& kernel) {\n  int32x4x2_t tmp1 = vzipq_s32(kernel.packet[0], kernel.packet[1]);\n  int32x4x2_t tmp2 = vzipq_s32(kernel.packet[2], kernel.packet[3]);\n  kernel.packet[0] = vcombine_s32(vget_low_s32(tmp1.val[0]), vget_low_s32(tmp2.val[0]));\n  kernel.packet[1] = vcombine_s32(vget_high_s32(tmp1.val[0]), vget_high_s32(tmp2.val[0]));\n  kernel.packet[2] = vcombine_s32(vget_low_s32(tmp1.val[1]), vget_low_s32(tmp2.val[1]));\n  kernel.packet[3] = vcombine_s32(vget_high_s32(tmp1.val[1]), vget_high_s32(tmp2.val[1]));\n}\n\n//---------- double ----------\n\n// Clang 3.5 in the iOS toolchain has an ICE triggered by NEON intrisics for double.\n// Confirmed at least with __apple_build_version__ = 6000054.\n#ifdef __apple_build_version__\n// Let's hope that by the time __apple_build_version__ hits the 601* range, the bug will be fixed.\n// https://gist.github.com/yamaya/2924292 suggests that the 3 first digits are only updated with\n// major toolchain updates.\n#define EIGEN_APPLE_DOUBLE_NEON_BUG (__apple_build_version__ < 6010000)\n#else\n#define EIGEN_APPLE_DOUBLE_NEON_BUG 0\n#endif\n\n#if EIGEN_ARCH_ARM64 && !EIGEN_APPLE_DOUBLE_NEON_BUG\n\n// Bug 907: workaround missing declarations of the following two functions in the ADK\n// Defining these functions as templates ensures that if these intrinsics are\n// already defined in arm_neon.h, then our workaround doesn't cause a conflict\n// and has lower priority in overload resolution.\ntemplate <typename T>\nuint64x2_t vreinterpretq_u64_f64(T a)\n{\n  return (uint64x2_t) a;\n}\n\ntemplate <typename T>\nfloat64x2_t vreinterpretq_f64_u64(T a)\n{\n  return (float64x2_t) a;\n}\n\ntypedef float64x2_t Packet2d;\ntypedef float64x1_t Packet1d;\n\ntemplate<> struct packet_traits<double>  : default_packet_traits\n{\n  typedef Packet2d type;\n  typedef Packet2d half;\n  enum {\n    Vectorizable = 1,\n    AlignedOnScalar = 1,\n    size = 2,\n    HasHalfPacket=0,\n   \n    HasDiv  = 1,\n    // FIXME check the Has*\n    HasSin  = 0,\n    HasCos  = 0,\n    HasLog  = 0,\n    HasExp  = 0,\n    HasSqrt = 0\n  };\n};\n\ntemplate<> struct unpacket_traits<Packet2d> { typedef double  type; enum {size=2, alignment=Aligned16}; typedef Packet2d half; };\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d pset1<Packet2d>(const double&  from) { return vdupq_n_f64(from); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d plset<Packet2d>(const double& a)\n{\n  const double countdown_raw[] = {0.0,1.0};\n  const Packet2d countdown = vld1q_f64(countdown_raw);\n  return vaddq_f64(pset1<Packet2d>(a), countdown);\n}\ntemplate<> EIGEN_STRONG_INLINE Packet2d padd<Packet2d>(const Packet2d& a, const Packet2d& b) { return vaddq_f64(a,b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d psub<Packet2d>(const Packet2d& a, const Packet2d& b) { return vsubq_f64(a,b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d pnegate(const Packet2d& a) { return vnegq_f64(a); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d pconj(const Packet2d& a) { return a; }\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d pmul<Packet2d>(const Packet2d& a, const Packet2d& b) { return vmulq_f64(a,b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d pdiv<Packet2d>(const Packet2d& a, const Packet2d& b) { return vdivq_f64(a,b); }\n\n#ifdef __ARM_FEATURE_FMA\n// See bug 936. See above comment about FMA for float.\ntemplate<> EIGEN_STRONG_INLINE Packet2d pmadd(const Packet2d& a, const Packet2d& b, const Packet2d& c) { return vfmaq_f64(c,a,b); }\n#else\ntemplate<> EIGEN_STRONG_INLINE Packet2d pmadd(const Packet2d& a, const Packet2d& b, const Packet2d& c) { return vmlaq_f64(c,a,b); }\n#endif\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d pmin<Packet2d>(const Packet2d& a, const Packet2d& b) { return vminq_f64(a,b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d pmax<Packet2d>(const Packet2d& a, const Packet2d& b) { return vmaxq_f64(a,b); }\n\n// Logical Operations are not supported for float, so we have to reinterpret casts using NEON intrinsics\ntemplate<> EIGEN_STRONG_INLINE Packet2d pand<Packet2d>(const Packet2d& a, const Packet2d& b)\n{\n  return vreinterpretq_f64_u64(vandq_u64(vreinterpretq_u64_f64(a),vreinterpretq_u64_f64(b)));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d por<Packet2d>(const Packet2d& a, const Packet2d& b)\n{\n  return vreinterpretq_f64_u64(vorrq_u64(vreinterpretq_u64_f64(a),vreinterpretq_u64_f64(b)));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d pxor<Packet2d>(const Packet2d& a, const Packet2d& b)\n{\n  return vreinterpretq_f64_u64(veorq_u64(vreinterpretq_u64_f64(a),vreinterpretq_u64_f64(b)));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d pandnot<Packet2d>(const Packet2d& a, const Packet2d& b)\n{\n  return vreinterpretq_f64_u64(vbicq_u64(vreinterpretq_u64_f64(a),vreinterpretq_u64_f64(b)));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d pload<Packet2d>(const double* from) { EIGEN_DEBUG_ALIGNED_LOAD return vld1q_f64(from); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d ploadu<Packet2d>(const double* from) { EIGEN_DEBUG_UNALIGNED_LOAD return vld1q_f64(from); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d ploaddup<Packet2d>(const double*   from)\n{\n  return vld1q_dup_f64(from);\n}\ntemplate<> EIGEN_STRONG_INLINE void pstore<double>(double*   to, const Packet2d& from) { EIGEN_DEBUG_ALIGNED_STORE vst1q_f64(to, from); }\n\ntemplate<> EIGEN_STRONG_INLINE void pstoreu<double>(double*  to, const Packet2d& from) { EIGEN_DEBUG_UNALIGNED_STORE vst1q_f64(to, from); }\n\ntemplate<> EIGEN_DEVICE_FUNC inline Packet2d pgather<double, Packet2d>(const double* from, Index stride)\n{\n  Packet2d res = pset1<Packet2d>(0.0);\n  res = vsetq_lane_f64(from[0*stride], res, 0);\n  res = vsetq_lane_f64(from[1*stride], res, 1);\n  return res;\n}\ntemplate<> EIGEN_DEVICE_FUNC inline void pscatter<double, Packet2d>(double* to, const Packet2d& from, Index stride)\n{\n  to[stride*0] = vgetq_lane_f64(from, 0);\n  to[stride*1] = vgetq_lane_f64(from, 1);\n}\ntemplate<> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { EIGEN_ARM_PREFETCH(addr); }\n\n// FIXME only store the 2 first elements ?\ntemplate<> EIGEN_STRONG_INLINE double pfirst<Packet2d>(const Packet2d& a) { return vgetq_lane_f64(a, 0); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d preverse(const Packet2d& a) { return vcombine_f64(vget_high_f64(a), vget_low_f64(a)); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d pabs(const Packet2d& a) { return vabsq_f64(a); }\n\n#if EIGEN_COMP_CLANG && defined(__apple_build_version__)\n// workaround ICE, see bug 907\ntemplate<> EIGEN_STRONG_INLINE double predux<Packet2d>(const Packet2d& a) { return (vget_low_f64(a) + vget_high_f64(a))[0]; }\n#else\ntemplate<> EIGEN_STRONG_INLINE double predux<Packet2d>(const Packet2d& a) { return vget_lane_f64(vget_low_f64(a) + vget_high_f64(a), 0); }\n#endif\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d preduxp<Packet2d>(const Packet2d* vecs)\n{\n  float64x2_t trn1, trn2;\n\n  // NEON zip performs interleaving of the supplied vectors.\n  // We perform two interleaves in a row to acquire the transposed vector\n  trn1 = vzip1q_f64(vecs[0], vecs[1]);\n  trn2 = vzip2q_f64(vecs[0], vecs[1]);\n\n  // Do the addition of the resulting vectors\n  return vaddq_f64(trn1, trn2);\n}\n// Other reduction functions:\n// mul\n#if EIGEN_COMP_CLANG && defined(__apple_build_version__)\ntemplate<> EIGEN_STRONG_INLINE double predux_mul<Packet2d>(const Packet2d& a) { return (vget_low_f64(a) * vget_high_f64(a))[0]; }\n#else\ntemplate<> EIGEN_STRONG_INLINE double predux_mul<Packet2d>(const Packet2d& a) { return vget_lane_f64(vget_low_f64(a) * vget_high_f64(a), 0); }\n#endif\n\n// min\ntemplate<> EIGEN_STRONG_INLINE double predux_min<Packet2d>(const Packet2d& a) { return vgetq_lane_f64(vpminq_f64(a, a), 0); }\n\n// max\ntemplate<> EIGEN_STRONG_INLINE double predux_max<Packet2d>(const Packet2d& a) { return vgetq_lane_f64(vpmaxq_f64(a, a), 0); }\n\n// this PALIGN_NEON business is to work around a bug in LLVM Clang 3.0 causing incorrect compilation errors,\n// see bug 347 and this LLVM bug: http://llvm.org/bugs/show_bug.cgi?id=11074\n#define PALIGN_NEON(Offset,Type,Command) \\\ntemplate<>\\\nstruct palign_impl<Offset,Type>\\\n{\\\n    EIGEN_STRONG_INLINE static void run(Type& first, const Type& second)\\\n    {\\\n        if (Offset!=0)\\\n            first = Command(first, second, Offset);\\\n    }\\\n};\\\n\nPALIGN_NEON(0,Packet2d,vextq_f64)\nPALIGN_NEON(1,Packet2d,vextq_f64)\n#undef PALIGN_NEON\n\nEIGEN_DEVICE_FUNC inline void\nptranspose(PacketBlock<Packet2d,2>& kernel) {\n  float64x2_t trn1 = vzip1q_f64(kernel.packet[0], kernel.packet[1]);\n  float64x2_t trn2 = vzip2q_f64(kernel.packet[0], kernel.packet[1]);\n\n  kernel.packet[0] = trn1;\n  kernel.packet[1] = trn2;\n}\n#endif // EIGEN_ARCH_ARM64 \n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_PACKET_MATH_NEON_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/arch/SSE/Complex.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_COMPLEX_SSE_H\n#define EIGEN_COMPLEX_SSE_H\n\nnamespace Eigen {\n\nnamespace internal {\n\n//---------- float ----------\nstruct Packet2cf\n{\n  EIGEN_STRONG_INLINE Packet2cf() {}\n  EIGEN_STRONG_INLINE explicit Packet2cf(const __m128& a) : v(a) {}\n  __m128  v;\n};\n\n// Use the packet_traits defined in AVX/PacketMath.h instead if we're going\n// to leverage AVX instructions.\n#ifndef EIGEN_VECTORIZE_AVX\ntemplate<> struct packet_traits<std::complex<float> >  : default_packet_traits\n{\n  typedef Packet2cf type;\n  typedef Packet2cf half;\n  enum {\n    Vectorizable = 1,\n    AlignedOnScalar = 1,\n    size = 2,\n    HasHalfPacket = 0,\n\n    HasAdd    = 1,\n    HasSub    = 1,\n    HasMul    = 1,\n    HasDiv    = 1,\n    HasNegate = 1,\n    HasAbs    = 0,\n    HasAbs2   = 0,\n    HasMin    = 0,\n    HasMax    = 0,\n    HasSetLinear = 0,\n    HasBlend = 1\n  };\n};\n#endif\n\ntemplate<> struct unpacket_traits<Packet2cf> { typedef std::complex<float> type; enum {size=2, alignment=Aligned16}; typedef Packet2cf half; };\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cf padd<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_add_ps(a.v,b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet2cf psub<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_sub_ps(a.v,b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pnegate(const Packet2cf& a)\n{\n  const __m128 mask = _mm_castsi128_ps(_mm_setr_epi32(0x80000000,0x80000000,0x80000000,0x80000000));\n  return Packet2cf(_mm_xor_ps(a.v,mask));\n}\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pconj(const Packet2cf& a)\n{\n  const __m128 mask = _mm_castsi128_ps(_mm_setr_epi32(0x00000000,0x80000000,0x00000000,0x80000000));\n  return Packet2cf(_mm_xor_ps(a.v,mask));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pmul<Packet2cf>(const Packet2cf& a, const Packet2cf& b)\n{\n  #ifdef EIGEN_VECTORIZE_SSE3\n  return Packet2cf(_mm_addsub_ps(_mm_mul_ps(_mm_moveldup_ps(a.v), b.v),\n                                 _mm_mul_ps(_mm_movehdup_ps(a.v),\n                                            vec4f_swizzle1(b.v, 1, 0, 3, 2))));\n//   return Packet2cf(_mm_addsub_ps(_mm_mul_ps(vec4f_swizzle1(a.v, 0, 0, 2, 2), b.v),\n//                                  _mm_mul_ps(vec4f_swizzle1(a.v, 1, 1, 3, 3),\n//                                             vec4f_swizzle1(b.v, 1, 0, 3, 2))));\n  #else\n  const __m128 mask = _mm_castsi128_ps(_mm_setr_epi32(0x80000000,0x00000000,0x80000000,0x00000000));\n  return Packet2cf(_mm_add_ps(_mm_mul_ps(vec4f_swizzle1(a.v, 0, 0, 2, 2), b.v),\n                              _mm_xor_ps(_mm_mul_ps(vec4f_swizzle1(a.v, 1, 1, 3, 3),\n                                                    vec4f_swizzle1(b.v, 1, 0, 3, 2)), mask)));\n  #endif\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pand   <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_and_ps(a.v,b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet2cf por    <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_or_ps(a.v,b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pxor   <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_xor_ps(a.v,b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pandnot<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_andnot_ps(a.v,b.v)); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pload <Packet2cf>(const std::complex<float>* from) { EIGEN_DEBUG_ALIGNED_LOAD return Packet2cf(pload<Packet4f>(&numext::real_ref(*from))); }\ntemplate<> EIGEN_STRONG_INLINE Packet2cf ploadu<Packet2cf>(const std::complex<float>* from) { EIGEN_DEBUG_UNALIGNED_LOAD return Packet2cf(ploadu<Packet4f>(&numext::real_ref(*from))); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pset1<Packet2cf>(const std::complex<float>&  from)\n{\n  Packet2cf res;\n#if EIGEN_GNUC_AT_MOST(4,2)\n  // Workaround annoying \"may be used uninitialized in this function\" warning with gcc 4.2\n  res.v = _mm_loadl_pi(_mm_set1_ps(0.0f), reinterpret_cast<const __m64*>(&from));\n#elif EIGEN_GNUC_AT_LEAST(4,6)\n  // Suppress annoying \"may be used uninitialized in this function\" warning with gcc >= 4.6\n  #pragma GCC diagnostic push\n  #pragma GCC diagnostic ignored \"-Wuninitialized\"\n  res.v = _mm_loadl_pi(res.v, (const __m64*)&from);\n  #pragma GCC diagnostic pop\n#else\n  res.v = _mm_loadl_pi(res.v, (const __m64*)&from);\n#endif\n  return Packet2cf(_mm_movelh_ps(res.v,res.v));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cf ploaddup<Packet2cf>(const std::complex<float>* from) { return pset1<Packet2cf>(*from); }\n\ntemplate<> EIGEN_STRONG_INLINE void pstore <std::complex<float> >(std::complex<float> *   to, const Packet2cf& from) { EIGEN_DEBUG_ALIGNED_STORE pstore(&numext::real_ref(*to), Packet4f(from.v)); }\ntemplate<> EIGEN_STRONG_INLINE void pstoreu<std::complex<float> >(std::complex<float> *   to, const Packet2cf& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu(&numext::real_ref(*to), Packet4f(from.v)); }\n\n\ntemplate<> EIGEN_DEVICE_FUNC inline Packet2cf pgather<std::complex<float>, Packet2cf>(const std::complex<float>* from, Index stride)\n{\n  return Packet2cf(_mm_set_ps(std::imag(from[1*stride]), std::real(from[1*stride]),\n                              std::imag(from[0*stride]), std::real(from[0*stride])));\n}\n\ntemplate<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<float>, Packet2cf>(std::complex<float>* to, const Packet2cf& from, Index stride)\n{\n  to[stride*0] = std::complex<float>(_mm_cvtss_f32(_mm_shuffle_ps(from.v, from.v, 0)),\n                                     _mm_cvtss_f32(_mm_shuffle_ps(from.v, from.v, 1)));\n  to[stride*1] = std::complex<float>(_mm_cvtss_f32(_mm_shuffle_ps(from.v, from.v, 2)),\n                                     _mm_cvtss_f32(_mm_shuffle_ps(from.v, from.v, 3)));\n}\n\ntemplate<> EIGEN_STRONG_INLINE void prefetch<std::complex<float> >(const std::complex<float> *   addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }\n\ntemplate<> EIGEN_STRONG_INLINE std::complex<float>  pfirst<Packet2cf>(const Packet2cf& a)\n{\n  #if EIGEN_GNUC_AT_MOST(4,3)\n  // Workaround gcc 4.2 ICE - this is not performance wise ideal, but who cares...\n  // This workaround also fix invalid code generation with gcc 4.3\n  EIGEN_ALIGN16 std::complex<float> res[2];\n  _mm_store_ps((float*)res, a.v);\n  return res[0];\n  #else\n  std::complex<float> res;\n  _mm_storel_pi((__m64*)&res, a.v);\n  return res;\n  #endif\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cf preverse(const Packet2cf& a) { return Packet2cf(_mm_castpd_ps(preverse(Packet2d(_mm_castps_pd(a.v))))); }\n\ntemplate<> EIGEN_STRONG_INLINE std::complex<float> predux<Packet2cf>(const Packet2cf& a)\n{\n  return pfirst(Packet2cf(_mm_add_ps(a.v, _mm_movehl_ps(a.v,a.v))));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cf preduxp<Packet2cf>(const Packet2cf* vecs)\n{\n  return Packet2cf(_mm_add_ps(_mm_movelh_ps(vecs[0].v,vecs[1].v), _mm_movehl_ps(vecs[1].v,vecs[0].v)));\n}\n\ntemplate<> EIGEN_STRONG_INLINE std::complex<float> predux_mul<Packet2cf>(const Packet2cf& a)\n{\n  return pfirst(pmul(a, Packet2cf(_mm_movehl_ps(a.v,a.v))));\n}\n\ntemplate<int Offset>\nstruct palign_impl<Offset,Packet2cf>\n{\n  static EIGEN_STRONG_INLINE void run(Packet2cf& first, const Packet2cf& second)\n  {\n    if (Offset==1)\n    {\n      first.v = _mm_movehl_ps(first.v, first.v);\n      first.v = _mm_movelh_ps(first.v, second.v);\n    }\n  }\n};\n\ntemplate<> struct conj_helper<Packet2cf, Packet2cf, false,true>\n{\n  EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const\n  { return padd(pmul(x,y),c); }\n\n  EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const\n  {\n    #ifdef EIGEN_VECTORIZE_SSE3\n    return internal::pmul(a, pconj(b));\n    #else\n    const __m128 mask = _mm_castsi128_ps(_mm_setr_epi32(0x00000000,0x80000000,0x00000000,0x80000000));\n    return Packet2cf(_mm_add_ps(_mm_xor_ps(_mm_mul_ps(vec4f_swizzle1(a.v, 0, 0, 2, 2), b.v), mask),\n                                _mm_mul_ps(vec4f_swizzle1(a.v, 1, 1, 3, 3),\n                                           vec4f_swizzle1(b.v, 1, 0, 3, 2))));\n    #endif\n  }\n};\n\ntemplate<> struct conj_helper<Packet2cf, Packet2cf, true,false>\n{\n  EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const\n  { return padd(pmul(x,y),c); }\n\n  EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const\n  {\n    #ifdef EIGEN_VECTORIZE_SSE3\n    return internal::pmul(pconj(a), b);\n    #else\n    const __m128 mask = _mm_castsi128_ps(_mm_setr_epi32(0x00000000,0x80000000,0x00000000,0x80000000));\n    return Packet2cf(_mm_add_ps(_mm_mul_ps(vec4f_swizzle1(a.v, 0, 0, 2, 2), b.v),\n                                _mm_xor_ps(_mm_mul_ps(vec4f_swizzle1(a.v, 1, 1, 3, 3),\n                                                      vec4f_swizzle1(b.v, 1, 0, 3, 2)), mask)));\n    #endif\n  }\n};\n\ntemplate<> struct conj_helper<Packet2cf, Packet2cf, true,true>\n{\n  EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const\n  { return padd(pmul(x,y),c); }\n\n  EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const\n  {\n    #ifdef EIGEN_VECTORIZE_SSE3\n    return pconj(internal::pmul(a, b));\n    #else\n    const __m128 mask = _mm_castsi128_ps(_mm_setr_epi32(0x00000000,0x80000000,0x00000000,0x80000000));\n    return Packet2cf(_mm_sub_ps(_mm_xor_ps(_mm_mul_ps(vec4f_swizzle1(a.v, 0, 0, 2, 2), b.v), mask),\n                                _mm_mul_ps(vec4f_swizzle1(a.v, 1, 1, 3, 3),\n                                           vec4f_swizzle1(b.v, 1, 0, 3, 2))));\n    #endif\n  }\n};\n\nEIGEN_MAKE_CONJ_HELPER_CPLX_REAL(Packet2cf,Packet4f)\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pdiv<Packet2cf>(const Packet2cf& a, const Packet2cf& b)\n{\n  // TODO optimize it for SSE3 and 4\n  Packet2cf res = conj_helper<Packet2cf,Packet2cf,false,true>().pmul(a,b);\n  __m128 s = _mm_mul_ps(b.v,b.v);\n  return Packet2cf(_mm_div_ps(res.v,_mm_add_ps(s,_mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(s), 0xb1)))));\n}\n\nEIGEN_STRONG_INLINE Packet2cf pcplxflip/* <Packet2cf> */(const Packet2cf& x)\n{\n  return Packet2cf(vec4f_swizzle1(x.v, 1, 0, 3, 2));\n}\n\n\n//---------- double ----------\nstruct Packet1cd\n{\n  EIGEN_STRONG_INLINE Packet1cd() {}\n  EIGEN_STRONG_INLINE explicit Packet1cd(const __m128d& a) : v(a) {}\n  __m128d  v;\n};\n\n// Use the packet_traits defined in AVX/PacketMath.h instead if we're going\n// to leverage AVX instructions.\n#ifndef EIGEN_VECTORIZE_AVX\ntemplate<> struct packet_traits<std::complex<double> >  : default_packet_traits\n{\n  typedef Packet1cd type;\n  typedef Packet1cd half;\n  enum {\n    Vectorizable = 1,\n    AlignedOnScalar = 0,\n    size = 1,\n    HasHalfPacket = 0,\n\n    HasAdd    = 1,\n    HasSub    = 1,\n    HasMul    = 1,\n    HasDiv    = 1,\n    HasNegate = 1,\n    HasAbs    = 0,\n    HasAbs2   = 0,\n    HasMin    = 0,\n    HasMax    = 0,\n    HasSetLinear = 0\n  };\n};\n#endif\n\ntemplate<> struct unpacket_traits<Packet1cd> { typedef std::complex<double> type; enum {size=1, alignment=Aligned16}; typedef Packet1cd half; };\n\ntemplate<> EIGEN_STRONG_INLINE Packet1cd padd<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(_mm_add_pd(a.v,b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet1cd psub<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(_mm_sub_pd(a.v,b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pnegate(const Packet1cd& a) { return Packet1cd(pnegate(Packet2d(a.v))); }\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pconj(const Packet1cd& a)\n{\n  const __m128d mask = _mm_castsi128_pd(_mm_set_epi32(0x80000000,0x0,0x0,0x0));\n  return Packet1cd(_mm_xor_pd(a.v,mask));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pmul<Packet1cd>(const Packet1cd& a, const Packet1cd& b)\n{\n  #ifdef EIGEN_VECTORIZE_SSE3\n  return Packet1cd(_mm_addsub_pd(_mm_mul_pd(_mm_movedup_pd(a.v), b.v),\n                                 _mm_mul_pd(vec2d_swizzle1(a.v, 1, 1),\n                                            vec2d_swizzle1(b.v, 1, 0))));\n  #else\n  const __m128d mask = _mm_castsi128_pd(_mm_set_epi32(0x0,0x0,0x80000000,0x0));\n  return Packet1cd(_mm_add_pd(_mm_mul_pd(vec2d_swizzle1(a.v, 0, 0), b.v),\n                              _mm_xor_pd(_mm_mul_pd(vec2d_swizzle1(a.v, 1, 1),\n                                                    vec2d_swizzle1(b.v, 1, 0)), mask)));\n  #endif\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pand   <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(_mm_and_pd(a.v,b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet1cd por    <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(_mm_or_pd(a.v,b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pxor   <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(_mm_xor_pd(a.v,b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pandnot<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(_mm_andnot_pd(a.v,b.v)); }\n\n// FIXME force unaligned load, this is a temporary fix\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pload <Packet1cd>(const std::complex<double>* from)\n{ EIGEN_DEBUG_ALIGNED_LOAD return Packet1cd(pload<Packet2d>((const double*)from)); }\ntemplate<> EIGEN_STRONG_INLINE Packet1cd ploadu<Packet1cd>(const std::complex<double>* from)\n{ EIGEN_DEBUG_UNALIGNED_LOAD return Packet1cd(ploadu<Packet2d>((const double*)from)); }\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pset1<Packet1cd>(const std::complex<double>&  from)\n{ /* here we really have to use unaligned loads :( */ return ploadu<Packet1cd>(&from); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet1cd ploaddup<Packet1cd>(const std::complex<double>* from) { return pset1<Packet1cd>(*from); }\n\n// FIXME force unaligned store, this is a temporary fix\ntemplate<> EIGEN_STRONG_INLINE void pstore <std::complex<double> >(std::complex<double> *   to, const Packet1cd& from) { EIGEN_DEBUG_ALIGNED_STORE pstore((double*)to, Packet2d(from.v)); }\ntemplate<> EIGEN_STRONG_INLINE void pstoreu<std::complex<double> >(std::complex<double> *   to, const Packet1cd& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu((double*)to, Packet2d(from.v)); }\n\ntemplate<> EIGEN_STRONG_INLINE void prefetch<std::complex<double> >(const std::complex<double> *   addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }\n\ntemplate<> EIGEN_STRONG_INLINE std::complex<double>  pfirst<Packet1cd>(const Packet1cd& a)\n{\n  EIGEN_ALIGN16 double res[2];\n  _mm_store_pd(res, a.v);\n  return std::complex<double>(res[0],res[1]);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet1cd preverse(const Packet1cd& a) { return a; }\n\ntemplate<> EIGEN_STRONG_INLINE std::complex<double> predux<Packet1cd>(const Packet1cd& a)\n{\n  return pfirst(a);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet1cd preduxp<Packet1cd>(const Packet1cd* vecs)\n{\n  return vecs[0];\n}\n\ntemplate<> EIGEN_STRONG_INLINE std::complex<double> predux_mul<Packet1cd>(const Packet1cd& a)\n{\n  return pfirst(a);\n}\n\ntemplate<int Offset>\nstruct palign_impl<Offset,Packet1cd>\n{\n  static EIGEN_STRONG_INLINE void run(Packet1cd& /*first*/, const Packet1cd& /*second*/)\n  {\n    // FIXME is it sure we never have to align a Packet1cd?\n    // Even though a std::complex<double> has 16 bytes, it is not necessarily aligned on a 16 bytes boundary...\n  }\n};\n\ntemplate<> struct conj_helper<Packet1cd, Packet1cd, false,true>\n{\n  EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet1cd& x, const Packet1cd& y, const Packet1cd& c) const\n  { return padd(pmul(x,y),c); }\n\n  EIGEN_STRONG_INLINE Packet1cd pmul(const Packet1cd& a, const Packet1cd& b) const\n  {\n    #ifdef EIGEN_VECTORIZE_SSE3\n    return internal::pmul(a, pconj(b));\n    #else\n    const __m128d mask = _mm_castsi128_pd(_mm_set_epi32(0x80000000,0x0,0x0,0x0));\n    return Packet1cd(_mm_add_pd(_mm_xor_pd(_mm_mul_pd(vec2d_swizzle1(a.v, 0, 0), b.v), mask),\n                                _mm_mul_pd(vec2d_swizzle1(a.v, 1, 1),\n                                           vec2d_swizzle1(b.v, 1, 0))));\n    #endif\n  }\n};\n\ntemplate<> struct conj_helper<Packet1cd, Packet1cd, true,false>\n{\n  EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet1cd& x, const Packet1cd& y, const Packet1cd& c) const\n  { return padd(pmul(x,y),c); }\n\n  EIGEN_STRONG_INLINE Packet1cd pmul(const Packet1cd& a, const Packet1cd& b) const\n  {\n    #ifdef EIGEN_VECTORIZE_SSE3\n    return internal::pmul(pconj(a), b);\n    #else\n    const __m128d mask = _mm_castsi128_pd(_mm_set_epi32(0x80000000,0x0,0x0,0x0));\n    return Packet1cd(_mm_add_pd(_mm_mul_pd(vec2d_swizzle1(a.v, 0, 0), b.v),\n                                _mm_xor_pd(_mm_mul_pd(vec2d_swizzle1(a.v, 1, 1),\n                                                      vec2d_swizzle1(b.v, 1, 0)), mask)));\n    #endif\n  }\n};\n\ntemplate<> struct conj_helper<Packet1cd, Packet1cd, true,true>\n{\n  EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet1cd& x, const Packet1cd& y, const Packet1cd& c) const\n  { return padd(pmul(x,y),c); }\n\n  EIGEN_STRONG_INLINE Packet1cd pmul(const Packet1cd& a, const Packet1cd& b) const\n  {\n    #ifdef EIGEN_VECTORIZE_SSE3\n    return pconj(internal::pmul(a, b));\n    #else\n    const __m128d mask = _mm_castsi128_pd(_mm_set_epi32(0x80000000,0x0,0x0,0x0));\n    return Packet1cd(_mm_sub_pd(_mm_xor_pd(_mm_mul_pd(vec2d_swizzle1(a.v, 0, 0), b.v), mask),\n                                _mm_mul_pd(vec2d_swizzle1(a.v, 1, 1),\n                                           vec2d_swizzle1(b.v, 1, 0))));\n    #endif\n  }\n};\n\nEIGEN_MAKE_CONJ_HELPER_CPLX_REAL(Packet1cd,Packet2d)\n\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pdiv<Packet1cd>(const Packet1cd& a, const Packet1cd& b)\n{\n  // TODO optimize it for SSE3 and 4\n  Packet1cd res = conj_helper<Packet1cd,Packet1cd,false,true>().pmul(a,b);\n  __m128d s = _mm_mul_pd(b.v,b.v);\n  return Packet1cd(_mm_div_pd(res.v, _mm_add_pd(s,_mm_shuffle_pd(s, s, 0x1))));\n}\n\nEIGEN_STRONG_INLINE Packet1cd pcplxflip/* <Packet1cd> */(const Packet1cd& x)\n{\n  return Packet1cd(preverse(Packet2d(x.v)));\n}\n\nEIGEN_DEVICE_FUNC inline void\nptranspose(PacketBlock<Packet2cf,2>& kernel) {\n  __m128d w1 = _mm_castps_pd(kernel.packet[0].v);\n  __m128d w2 = _mm_castps_pd(kernel.packet[1].v);\n\n  __m128 tmp = _mm_castpd_ps(_mm_unpackhi_pd(w1, w2));\n  kernel.packet[0].v = _mm_castpd_ps(_mm_unpacklo_pd(w1, w2));\n  kernel.packet[1].v = tmp;\n}\n\ntemplate<>  EIGEN_STRONG_INLINE Packet2cf pblend(const Selector<2>& ifPacket, const Packet2cf& thenPacket, const Packet2cf& elsePacket) {\n  __m128d result = pblend<Packet2d>(ifPacket, _mm_castps_pd(thenPacket.v), _mm_castps_pd(elsePacket.v));\n  return Packet2cf(_mm_castpd_ps(result));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pinsertfirst(const Packet2cf& a, std::complex<float> b)\n{\n  return Packet2cf(_mm_loadl_pi(a.v, reinterpret_cast<const __m64*>(&b)));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pinsertfirst(const Packet1cd&, std::complex<double> b)\n{\n  return pset1<Packet1cd>(b);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pinsertlast(const Packet2cf& a, std::complex<float> b)\n{\n  return Packet2cf(_mm_loadh_pi(a.v, reinterpret_cast<const __m64*>(&b)));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pinsertlast(const Packet1cd&, std::complex<double> b)\n{\n  return pset1<Packet1cd>(b);\n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_COMPLEX_SSE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/arch/SSE/MathFunctions.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2007 Julien Pommier\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n/* The sin, cos, exp, and log functions of this file come from\n * Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/\n */\n\n#ifndef EIGEN_MATH_FUNCTIONS_SSE_H\n#define EIGEN_MATH_FUNCTIONS_SSE_H\n\nnamespace Eigen {\n\nnamespace internal {\n\ntemplate<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED\nPacket4f plog<Packet4f>(const Packet4f& _x)\n{\n  Packet4f x = _x;\n  _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);\n  _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);\n  _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);\n\n  _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(inv_mant_mask, ~0x7f800000);\n\n  /* the smallest non denormalized float number */\n  _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(min_norm_pos,  0x00800000);\n  _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_inf,     0xff800000);//-1.f/0.f);\n\n  /* natural logarithm computed for 4 simultaneous float\n    return NaN for x <= 0\n  */\n  _EIGEN_DECLARE_CONST_Packet4f(cephes_SQRTHF, 0.707106781186547524f);\n  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p0, 7.0376836292E-2f);\n  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p1, - 1.1514610310E-1f);\n  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p2, 1.1676998740E-1f);\n  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p3, - 1.2420140846E-1f);\n  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p4, + 1.4249322787E-1f);\n  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p5, - 1.6668057665E-1f);\n  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p6, + 2.0000714765E-1f);\n  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p7, - 2.4999993993E-1f);\n  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p8, + 3.3333331174E-1f);\n  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q1, -2.12194440e-4f);\n  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q2, 0.693359375f);\n\n\n  Packet4i emm0;\n\n  Packet4f invalid_mask = _mm_cmpnge_ps(x, _mm_setzero_ps()); // not greater equal is true if x is NaN\n  Packet4f iszero_mask = _mm_cmpeq_ps(x, _mm_setzero_ps());\n\n  x = pmax(x, p4f_min_norm_pos);  /* cut off denormalized stuff */\n  emm0 = _mm_srli_epi32(_mm_castps_si128(x), 23);\n\n  /* keep only the fractional part */\n  x = _mm_and_ps(x, p4f_inv_mant_mask);\n  x = _mm_or_ps(x, p4f_half);\n\n  emm0 = _mm_sub_epi32(emm0, p4i_0x7f);\n  Packet4f e = padd(Packet4f(_mm_cvtepi32_ps(emm0)), p4f_1);\n\n  /* part2:\n     if( x < SQRTHF ) {\n       e -= 1;\n       x = x + x - 1.0;\n     } else { x = x - 1.0; }\n  */\n  Packet4f mask = _mm_cmplt_ps(x, p4f_cephes_SQRTHF);\n  Packet4f tmp = pand(x, mask);\n  x = psub(x, p4f_1);\n  e = psub(e, pand(p4f_1, mask));\n  x = padd(x, tmp);\n\n  Packet4f x2 = pmul(x,x);\n  Packet4f x3 = pmul(x2,x);\n\n  Packet4f y, y1, y2;\n  y  = pmadd(p4f_cephes_log_p0, x, p4f_cephes_log_p1);\n  y1 = pmadd(p4f_cephes_log_p3, x, p4f_cephes_log_p4);\n  y2 = pmadd(p4f_cephes_log_p6, x, p4f_cephes_log_p7);\n  y  = pmadd(y , x, p4f_cephes_log_p2);\n  y1 = pmadd(y1, x, p4f_cephes_log_p5);\n  y2 = pmadd(y2, x, p4f_cephes_log_p8);\n  y = pmadd(y, x3, y1);\n  y = pmadd(y, x3, y2);\n  y = pmul(y, x3);\n\n  y1 = pmul(e, p4f_cephes_log_q1);\n  tmp = pmul(x2, p4f_half);\n  y = padd(y, y1);\n  x = psub(x, tmp);\n  y2 = pmul(e, p4f_cephes_log_q2);\n  x = padd(x, y);\n  x = padd(x, y2);\n  // negative arg will be NAN, 0 will be -INF\n  return _mm_or_ps(_mm_andnot_ps(iszero_mask, _mm_or_ps(x, invalid_mask)),\n                   _mm_and_ps(iszero_mask, p4f_minus_inf));\n}\n\ntemplate<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED\nPacket4f pexp<Packet4f>(const Packet4f& _x)\n{\n  Packet4f x = _x;\n  _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);\n  _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);\n  _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);\n\n\n  _EIGEN_DECLARE_CONST_Packet4f(exp_hi,  88.3762626647950f);\n  _EIGEN_DECLARE_CONST_Packet4f(exp_lo, -88.3762626647949f);\n\n  _EIGEN_DECLARE_CONST_Packet4f(cephes_LOG2EF, 1.44269504088896341f);\n  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C1, 0.693359375f);\n  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C2, -2.12194440e-4f);\n\n  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p0, 1.9875691500E-4f);\n  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p1, 1.3981999507E-3f);\n  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p2, 8.3334519073E-3f);\n  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p3, 4.1665795894E-2f);\n  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459E-1f);\n  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201E-1f);\n\n  Packet4f tmp, fx;\n  Packet4i emm0;\n\n  // clamp x\n  x = pmax(pmin(x, p4f_exp_hi), p4f_exp_lo);\n\n  /* express exp(x) as exp(g + n*log(2)) */\n  fx = pmadd(x, p4f_cephes_LOG2EF, p4f_half);\n\n#ifdef EIGEN_VECTORIZE_SSE4_1\n  fx = _mm_floor_ps(fx);\n#else\n  emm0 = _mm_cvttps_epi32(fx);\n  tmp  = _mm_cvtepi32_ps(emm0);\n  /* if greater, substract 1 */\n  Packet4f mask = _mm_cmpgt_ps(tmp, fx);\n  mask = _mm_and_ps(mask, p4f_1);\n  fx = psub(tmp, mask);\n#endif\n\n  tmp = pmul(fx, p4f_cephes_exp_C1);\n  Packet4f z = pmul(fx, p4f_cephes_exp_C2);\n  x = psub(x, tmp);\n  x = psub(x, z);\n\n  z = pmul(x,x);\n\n  Packet4f y = p4f_cephes_exp_p0;\n  y = pmadd(y, x, p4f_cephes_exp_p1);\n  y = pmadd(y, x, p4f_cephes_exp_p2);\n  y = pmadd(y, x, p4f_cephes_exp_p3);\n  y = pmadd(y, x, p4f_cephes_exp_p4);\n  y = pmadd(y, x, p4f_cephes_exp_p5);\n  y = pmadd(y, z, x);\n  y = padd(y, p4f_1);\n\n  // build 2^n\n  emm0 = _mm_cvttps_epi32(fx);\n  emm0 = _mm_add_epi32(emm0, p4i_0x7f);\n  emm0 = _mm_slli_epi32(emm0, 23);\n  return pmax(pmul(y, Packet4f(_mm_castsi128_ps(emm0))), _x);\n}\ntemplate<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED\nPacket2d pexp<Packet2d>(const Packet2d& _x)\n{\n  Packet2d x = _x;\n\n  _EIGEN_DECLARE_CONST_Packet2d(1 , 1.0);\n  _EIGEN_DECLARE_CONST_Packet2d(2 , 2.0);\n  _EIGEN_DECLARE_CONST_Packet2d(half, 0.5);\n\n  _EIGEN_DECLARE_CONST_Packet2d(exp_hi,  709.437);\n  _EIGEN_DECLARE_CONST_Packet2d(exp_lo, -709.436139303);\n\n  _EIGEN_DECLARE_CONST_Packet2d(cephes_LOG2EF, 1.4426950408889634073599);\n\n  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p0, 1.26177193074810590878e-4);\n  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p1, 3.02994407707441961300e-2);\n  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p2, 9.99999999999999999910e-1);\n\n  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q0, 3.00198505138664455042e-6);\n  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q1, 2.52448340349684104192e-3);\n  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q2, 2.27265548208155028766e-1);\n  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q3, 2.00000000000000000009e0);\n\n  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C1, 0.693145751953125);\n  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C2, 1.42860682030941723212e-6);\n  static const __m128i p4i_1023_0 = _mm_setr_epi32(1023, 1023, 0, 0);\n\n  Packet2d tmp, fx;\n  Packet4i emm0;\n\n  // clamp x\n  x = pmax(pmin(x, p2d_exp_hi), p2d_exp_lo);\n  /* express exp(x) as exp(g + n*log(2)) */\n  fx = pmadd(p2d_cephes_LOG2EF, x, p2d_half);\n\n#ifdef EIGEN_VECTORIZE_SSE4_1\n  fx = _mm_floor_pd(fx);\n#else\n  emm0 = _mm_cvttpd_epi32(fx);\n  tmp  = _mm_cvtepi32_pd(emm0);\n  /* if greater, substract 1 */\n  Packet2d mask = _mm_cmpgt_pd(tmp, fx);\n  mask = _mm_and_pd(mask, p2d_1);\n  fx = psub(tmp, mask);\n#endif\n\n  tmp = pmul(fx, p2d_cephes_exp_C1);\n  Packet2d z = pmul(fx, p2d_cephes_exp_C2);\n  x = psub(x, tmp);\n  x = psub(x, z);\n\n  Packet2d x2 = pmul(x,x);\n\n  Packet2d px = p2d_cephes_exp_p0;\n  px = pmadd(px, x2, p2d_cephes_exp_p1);\n  px = pmadd(px, x2, p2d_cephes_exp_p2);\n  px = pmul (px, x);\n\n  Packet2d qx = p2d_cephes_exp_q0;\n  qx = pmadd(qx, x2, p2d_cephes_exp_q1);\n  qx = pmadd(qx, x2, p2d_cephes_exp_q2);\n  qx = pmadd(qx, x2, p2d_cephes_exp_q3);\n\n  x = pdiv(px,psub(qx,px));\n  x = pmadd(p2d_2,x,p2d_1);\n\n  // build 2^n\n  emm0 = _mm_cvttpd_epi32(fx);\n  emm0 = _mm_add_epi32(emm0, p4i_1023_0);\n  emm0 = _mm_slli_epi32(emm0, 20);\n  emm0 = _mm_shuffle_epi32(emm0, _MM_SHUFFLE(1,2,0,3));\n  return pmax(pmul(x, Packet2d(_mm_castsi128_pd(emm0))), _x);\n}\n\n/* evaluation of 4 sines at onces, using SSE2 intrinsics.\n\n   The code is the exact rewriting of the cephes sinf function.\n   Precision is excellent as long as x < 8192 (I did not bother to\n   take into account the special handling they have for greater values\n   -- it does not return garbage for arguments over 8192, though, but\n   the extra precision is missing).\n\n   Note that it is such that sinf((float)M_PI) = 8.74e-8, which is the\n   surprising but correct result.\n*/\n\ntemplate<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED\nPacket4f psin<Packet4f>(const Packet4f& _x)\n{\n  Packet4f x = _x;\n  _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);\n  _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);\n\n  _EIGEN_DECLARE_CONST_Packet4i(1, 1);\n  _EIGEN_DECLARE_CONST_Packet4i(not1, ~1);\n  _EIGEN_DECLARE_CONST_Packet4i(2, 2);\n  _EIGEN_DECLARE_CONST_Packet4i(4, 4);\n\n  _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(sign_mask, 0x80000000);\n\n  _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP1,-0.78515625f);\n  _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP2, -2.4187564849853515625e-4f);\n  _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP3, -3.77489497744594108e-8f);\n  _EIGEN_DECLARE_CONST_Packet4f(sincof_p0, -1.9515295891E-4f);\n  _EIGEN_DECLARE_CONST_Packet4f(sincof_p1,  8.3321608736E-3f);\n  _EIGEN_DECLARE_CONST_Packet4f(sincof_p2, -1.6666654611E-1f);\n  _EIGEN_DECLARE_CONST_Packet4f(coscof_p0,  2.443315711809948E-005f);\n  _EIGEN_DECLARE_CONST_Packet4f(coscof_p1, -1.388731625493765E-003f);\n  _EIGEN_DECLARE_CONST_Packet4f(coscof_p2,  4.166664568298827E-002f);\n  _EIGEN_DECLARE_CONST_Packet4f(cephes_FOPI, 1.27323954473516f); // 4 / M_PI\n\n  Packet4f xmm1, xmm2, xmm3, sign_bit, y;\n\n  Packet4i emm0, emm2;\n  sign_bit = x;\n  /* take the absolute value */\n  x = pabs(x);\n\n  /* take the modulo */\n\n  /* extract the sign bit (upper one) */\n  sign_bit = _mm_and_ps(sign_bit, p4f_sign_mask);\n\n  /* scale by 4/Pi */\n  y = pmul(x, p4f_cephes_FOPI);\n\n  /* store the integer part of y in mm0 */\n  emm2 = _mm_cvttps_epi32(y);\n  /* j=(j+1) & (~1) (see the cephes sources) */\n  emm2 = _mm_add_epi32(emm2, p4i_1);\n  emm2 = _mm_and_si128(emm2, p4i_not1);\n  y = _mm_cvtepi32_ps(emm2);\n  /* get the swap sign flag */\n  emm0 = _mm_and_si128(emm2, p4i_4);\n  emm0 = _mm_slli_epi32(emm0, 29);\n  /* get the polynom selection mask\n     there is one polynom for 0 <= x <= Pi/4\n     and another one for Pi/4<x<=Pi/2\n\n     Both branches will be computed.\n  */\n  emm2 = _mm_and_si128(emm2, p4i_2);\n  emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());\n\n  Packet4f swap_sign_bit = _mm_castsi128_ps(emm0);\n  Packet4f poly_mask = _mm_castsi128_ps(emm2);\n  sign_bit = _mm_xor_ps(sign_bit, swap_sign_bit);\n\n  /* The magic pass: \"Extended precision modular arithmetic\"\n     x = ((x - y * DP1) - y * DP2) - y * DP3; */\n  xmm1 = pmul(y, p4f_minus_cephes_DP1);\n  xmm2 = pmul(y, p4f_minus_cephes_DP2);\n  xmm3 = pmul(y, p4f_minus_cephes_DP3);\n  x = padd(x, xmm1);\n  x = padd(x, xmm2);\n  x = padd(x, xmm3);\n\n  /* Evaluate the first polynom  (0 <= x <= Pi/4) */\n  y = p4f_coscof_p0;\n  Packet4f z = _mm_mul_ps(x,x);\n\n  y = pmadd(y, z, p4f_coscof_p1);\n  y = pmadd(y, z, p4f_coscof_p2);\n  y = pmul(y, z);\n  y = pmul(y, z);\n  Packet4f tmp = pmul(z, p4f_half);\n  y = psub(y, tmp);\n  y = padd(y, p4f_1);\n\n  /* Evaluate the second polynom  (Pi/4 <= x <= 0) */\n\n  Packet4f y2 = p4f_sincof_p0;\n  y2 = pmadd(y2, z, p4f_sincof_p1);\n  y2 = pmadd(y2, z, p4f_sincof_p2);\n  y2 = pmul(y2, z);\n  y2 = pmul(y2, x);\n  y2 = padd(y2, x);\n\n  /* select the correct result from the two polynoms */\n  y2 = _mm_and_ps(poly_mask, y2);\n  y = _mm_andnot_ps(poly_mask, y);\n  y = _mm_or_ps(y,y2);\n  /* update the sign */\n  return _mm_xor_ps(y, sign_bit);\n}\n\n/* almost the same as psin */\ntemplate<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED\nPacket4f pcos<Packet4f>(const Packet4f& _x)\n{\n  Packet4f x = _x;\n  _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);\n  _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);\n\n  _EIGEN_DECLARE_CONST_Packet4i(1, 1);\n  _EIGEN_DECLARE_CONST_Packet4i(not1, ~1);\n  _EIGEN_DECLARE_CONST_Packet4i(2, 2);\n  _EIGEN_DECLARE_CONST_Packet4i(4, 4);\n\n  _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP1,-0.78515625f);\n  _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP2, -2.4187564849853515625e-4f);\n  _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP3, -3.77489497744594108e-8f);\n  _EIGEN_DECLARE_CONST_Packet4f(sincof_p0, -1.9515295891E-4f);\n  _EIGEN_DECLARE_CONST_Packet4f(sincof_p1,  8.3321608736E-3f);\n  _EIGEN_DECLARE_CONST_Packet4f(sincof_p2, -1.6666654611E-1f);\n  _EIGEN_DECLARE_CONST_Packet4f(coscof_p0,  2.443315711809948E-005f);\n  _EIGEN_DECLARE_CONST_Packet4f(coscof_p1, -1.388731625493765E-003f);\n  _EIGEN_DECLARE_CONST_Packet4f(coscof_p2,  4.166664568298827E-002f);\n  _EIGEN_DECLARE_CONST_Packet4f(cephes_FOPI, 1.27323954473516f); // 4 / M_PI\n\n  Packet4f xmm1, xmm2, xmm3, y;\n  Packet4i emm0, emm2;\n\n  x = pabs(x);\n\n  /* scale by 4/Pi */\n  y = pmul(x, p4f_cephes_FOPI);\n\n  /* get the integer part of y */\n  emm2 = _mm_cvttps_epi32(y);\n  /* j=(j+1) & (~1) (see the cephes sources) */\n  emm2 = _mm_add_epi32(emm2, p4i_1);\n  emm2 = _mm_and_si128(emm2, p4i_not1);\n  y = _mm_cvtepi32_ps(emm2);\n\n  emm2 = _mm_sub_epi32(emm2, p4i_2);\n\n  /* get the swap sign flag */\n  emm0 = _mm_andnot_si128(emm2, p4i_4);\n  emm0 = _mm_slli_epi32(emm0, 29);\n  /* get the polynom selection mask */\n  emm2 = _mm_and_si128(emm2, p4i_2);\n  emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());\n\n  Packet4f sign_bit = _mm_castsi128_ps(emm0);\n  Packet4f poly_mask = _mm_castsi128_ps(emm2);\n\n  /* The magic pass: \"Extended precision modular arithmetic\"\n     x = ((x - y * DP1) - y * DP2) - y * DP3; */\n  xmm1 = pmul(y, p4f_minus_cephes_DP1);\n  xmm2 = pmul(y, p4f_minus_cephes_DP2);\n  xmm3 = pmul(y, p4f_minus_cephes_DP3);\n  x = padd(x, xmm1);\n  x = padd(x, xmm2);\n  x = padd(x, xmm3);\n\n  /* Evaluate the first polynom  (0 <= x <= Pi/4) */\n  y = p4f_coscof_p0;\n  Packet4f z = pmul(x,x);\n\n  y = pmadd(y,z,p4f_coscof_p1);\n  y = pmadd(y,z,p4f_coscof_p2);\n  y = pmul(y, z);\n  y = pmul(y, z);\n  Packet4f tmp = _mm_mul_ps(z, p4f_half);\n  y = psub(y, tmp);\n  y = padd(y, p4f_1);\n\n  /* Evaluate the second polynom  (Pi/4 <= x <= 0) */\n  Packet4f y2 = p4f_sincof_p0;\n  y2 = pmadd(y2, z, p4f_sincof_p1);\n  y2 = pmadd(y2, z, p4f_sincof_p2);\n  y2 = pmul(y2, z);\n  y2 = pmadd(y2, x, x);\n\n  /* select the correct result from the two polynoms */\n  y2 = _mm_and_ps(poly_mask, y2);\n  y  = _mm_andnot_ps(poly_mask, y);\n  y  = _mm_or_ps(y,y2);\n\n  /* update the sign */\n  return _mm_xor_ps(y, sign_bit);\n}\n\n#if EIGEN_FAST_MATH\n\n// Functions for sqrt.\n// The EIGEN_FAST_MATH version uses the _mm_rsqrt_ps approximation and one step\n// of Newton's method, at a cost of 1-2 bits of precision as opposed to the\n// exact solution. It does not handle +inf, or denormalized numbers correctly.\n// The main advantage of this approach is not just speed, but also the fact that\n// it can be inlined and pipelined with other computations, further reducing its\n// effective latency. This is similar to Quake3's fast inverse square root.\n// For detail see here: http://www.beyond3d.com/content/articles/8/\ntemplate<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED\nPacket4f psqrt<Packet4f>(const Packet4f& _x)\n{\n  Packet4f half = pmul(_x, pset1<Packet4f>(.5f));\n  Packet4f denormal_mask = _mm_and_ps(\n      _mm_cmpge_ps(_x, _mm_setzero_ps()),\n      _mm_cmplt_ps(_x, pset1<Packet4f>((std::numeric_limits<float>::min)())));\n\n  // Compute approximate reciprocal sqrt.\n  Packet4f x = _mm_rsqrt_ps(_x);\n  // Do a single step of Newton's iteration.\n  x = pmul(x, psub(pset1<Packet4f>(1.5f), pmul(half, pmul(x,x))));\n  // Flush results for denormals to zero.\n  return _mm_andnot_ps(denormal_mask, pmul(_x,x));\n}\n\n#else\n\ntemplate<>EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED\nPacket4f psqrt<Packet4f>(const Packet4f& x) { return _mm_sqrt_ps(x); }\n\n#endif\n\ntemplate<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED\nPacket2d psqrt<Packet2d>(const Packet2d& x) { return _mm_sqrt_pd(x); }\n\n#if EIGEN_FAST_MATH\n\ntemplate<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED\nPacket4f prsqrt<Packet4f>(const Packet4f& _x) {\n  _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(inf, 0x7f800000);\n  _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(nan, 0x7fc00000);\n  _EIGEN_DECLARE_CONST_Packet4f(one_point_five, 1.5f);\n  _EIGEN_DECLARE_CONST_Packet4f(minus_half, -0.5f);\n  _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(flt_min, 0x00800000);\n\n  Packet4f neg_half = pmul(_x, p4f_minus_half);\n\n  // select only the inverse sqrt of positive normal inputs (denormals are\n  // flushed to zero and cause infs as well).\n  Packet4f le_zero_mask = _mm_cmple_ps(_x, p4f_flt_min);\n  Packet4f x = _mm_andnot_ps(le_zero_mask, _mm_rsqrt_ps(_x));\n\n  // Fill in NaNs and Infs for the negative/zero entries.\n  Packet4f neg_mask = _mm_cmplt_ps(_x, _mm_setzero_ps());\n  Packet4f zero_mask = _mm_andnot_ps(neg_mask, le_zero_mask);\n  Packet4f infs_and_nans = _mm_or_ps(_mm_and_ps(neg_mask, p4f_nan),\n                                     _mm_and_ps(zero_mask, p4f_inf));\n\n  // Do a single step of Newton's iteration.\n  x = pmul(x, pmadd(neg_half, pmul(x, x), p4f_one_point_five));\n\n  // Insert NaNs and Infs in all the right places.\n  return _mm_or_ps(x, infs_and_nans);\n}\n\n#else\n\ntemplate<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED\nPacket4f prsqrt<Packet4f>(const Packet4f& x) {\n  // Unfortunately we can't use the much faster mm_rqsrt_ps since it only provides an approximation.\n  return _mm_div_ps(pset1<Packet4f>(1.0f), _mm_sqrt_ps(x));\n}\n\n#endif\n\ntemplate<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED\nPacket2d prsqrt<Packet2d>(const Packet2d& x) {\n  // Unfortunately we can't use the much faster mm_rqsrt_pd since it only provides an approximation.\n  return _mm_div_pd(pset1<Packet2d>(1.0), _mm_sqrt_pd(x));\n}\n\n// Hyperbolic Tangent function.\ntemplate <>\nEIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4f\nptanh<Packet4f>(const Packet4f& x) {\n  return internal::generic_fast_tanh_float(x);\n}\n\n} // end namespace internal\n\nnamespace numext {\n\ntemplate<>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nfloat sqrt(const float &x)\n{\n  return internal::pfirst(internal::Packet4f(_mm_sqrt_ss(_mm_set_ss(x))));\n}\n\ntemplate<>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\ndouble sqrt(const double &x)\n{\n#if EIGEN_COMP_GNUC_STRICT\n  // This works around a GCC bug generating poor code for _mm_sqrt_pd\n  // See https://bitbucket.org/eigen/eigen/commits/14f468dba4d350d7c19c9b93072e19f7b3df563b\n  return internal::pfirst(internal::Packet2d(__builtin_ia32_sqrtsd(_mm_set_sd(x))));\n#else\n  return internal::pfirst(internal::Packet2d(_mm_sqrt_pd(_mm_set_sd(x))));\n#endif\n}\n\n} // end namespace numex\n\n} // end namespace Eigen\n\n#endif // EIGEN_MATH_FUNCTIONS_SSE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/arch/SSE/PacketMath.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_PACKET_MATH_SSE_H\n#define EIGEN_PACKET_MATH_SSE_H\n\nnamespace Eigen {\n\nnamespace internal {\n\n#ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD\n#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 8\n#endif\n\n#ifndef EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS\n#define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS (2*sizeof(void*))\n#endif\n\n#ifdef __FMA__\n#ifndef EIGEN_HAS_SINGLE_INSTRUCTION_MADD\n#define EIGEN_HAS_SINGLE_INSTRUCTION_MADD 1\n#endif\n#endif\n\n#if (defined EIGEN_VECTORIZE_AVX) && (EIGEN_COMP_GNUC_STRICT || EIGEN_COMP_MINGW) && (__GXX_ABI_VERSION < 1004)\n// With GCC's default ABI version, a __m128 or __m256 are the same types and therefore we cannot\n// have overloads for both types without linking error.\n// One solution is to increase ABI version using -fabi-version=4 (or greater).\n// Otherwise, we workaround this inconvenience by wrapping 128bit types into the following helper\n// structure:\ntemplate<typename T>\nstruct eigen_packet_wrapper\n{\n  EIGEN_ALWAYS_INLINE operator T&() { return m_val; }\n  EIGEN_ALWAYS_INLINE operator const T&() const { return m_val; }\n  EIGEN_ALWAYS_INLINE eigen_packet_wrapper() {}\n  EIGEN_ALWAYS_INLINE eigen_packet_wrapper(const T &v) : m_val(v) {}\n  EIGEN_ALWAYS_INLINE eigen_packet_wrapper& operator=(const T &v) {\n    m_val = v;\n    return *this;\n  }\n  \n  T m_val;\n};\ntypedef eigen_packet_wrapper<__m128>  Packet4f;\ntypedef eigen_packet_wrapper<__m128i> Packet4i;\ntypedef eigen_packet_wrapper<__m128d> Packet2d;\n#else\ntypedef __m128  Packet4f;\ntypedef __m128i Packet4i;\ntypedef __m128d Packet2d;\n#endif\n\ntemplate<> struct is_arithmetic<__m128>  { enum { value = true }; };\ntemplate<> struct is_arithmetic<__m128i> { enum { value = true }; };\ntemplate<> struct is_arithmetic<__m128d> { enum { value = true }; };\n\n#define vec4f_swizzle1(v,p,q,r,s) \\\n  (_mm_castsi128_ps(_mm_shuffle_epi32( _mm_castps_si128(v), ((s)<<6|(r)<<4|(q)<<2|(p)))))\n\n#define vec4i_swizzle1(v,p,q,r,s) \\\n  (_mm_shuffle_epi32( v, ((s)<<6|(r)<<4|(q)<<2|(p))))\n\n#define vec2d_swizzle1(v,p,q) \\\n  (_mm_castsi128_pd(_mm_shuffle_epi32( _mm_castpd_si128(v), ((q*2+1)<<6|(q*2)<<4|(p*2+1)<<2|(p*2)))))\n  \n#define vec4f_swizzle2(a,b,p,q,r,s) \\\n  (_mm_shuffle_ps( (a), (b), ((s)<<6|(r)<<4|(q)<<2|(p))))\n\n#define vec4i_swizzle2(a,b,p,q,r,s) \\\n  (_mm_castps_si128( (_mm_shuffle_ps( _mm_castsi128_ps(a), _mm_castsi128_ps(b), ((s)<<6|(r)<<4|(q)<<2|(p))))))\n\n#define _EIGEN_DECLARE_CONST_Packet4f(NAME,X) \\\n  const Packet4f p4f_##NAME = pset1<Packet4f>(X)\n\n#define _EIGEN_DECLARE_CONST_Packet2d(NAME,X) \\\n  const Packet2d p2d_##NAME = pset1<Packet2d>(X)\n\n#define _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(NAME,X) \\\n  const Packet4f p4f_##NAME = _mm_castsi128_ps(pset1<Packet4i>(X))\n\n#define _EIGEN_DECLARE_CONST_Packet4i(NAME,X) \\\n  const Packet4i p4i_##NAME = pset1<Packet4i>(X)\n\n\n// Use the packet_traits defined in AVX/PacketMath.h instead if we're going\n// to leverage AVX instructions.\n#ifndef EIGEN_VECTORIZE_AVX\ntemplate<> struct packet_traits<float>  : default_packet_traits\n{\n  typedef Packet4f type;\n  typedef Packet4f half;\n  enum {\n    Vectorizable = 1,\n    AlignedOnScalar = 1,\n    size=4,\n    HasHalfPacket = 0,\n\n    HasDiv  = 1,\n    HasSin  = EIGEN_FAST_MATH,\n    HasCos  = EIGEN_FAST_MATH,\n    HasLog  = 1,\n    HasExp  = 1,\n    HasSqrt = 1,\n    HasRsqrt = 1,\n    HasTanh  = EIGEN_FAST_MATH,\n    HasBlend = 1\n\n#ifdef EIGEN_VECTORIZE_SSE4_1\n    ,\n    HasRound = 1,\n    HasFloor = 1,\n    HasCeil = 1\n#endif\n  };\n};\ntemplate<> struct packet_traits<double> : default_packet_traits\n{\n  typedef Packet2d type;\n  typedef Packet2d half;\n  enum {\n    Vectorizable = 1,\n    AlignedOnScalar = 1,\n    size=2,\n    HasHalfPacket = 0,\n\n    HasDiv  = 1,\n    HasExp  = 1,\n    HasSqrt = 1,\n    HasRsqrt = 1,\n    HasBlend = 1\n\n#ifdef EIGEN_VECTORIZE_SSE4_1\n    ,\n    HasRound = 1,\n    HasFloor = 1,\n    HasCeil = 1\n#endif\n  };\n};\n#endif\ntemplate<> struct packet_traits<int>    : default_packet_traits\n{\n  typedef Packet4i type;\n  typedef Packet4i half;\n  enum {\n    Vectorizable = 1,\n    AlignedOnScalar = 1,\n    size=4,\n\n    HasBlend = 1\n  };\n};\n\ntemplate<> struct unpacket_traits<Packet4f> { typedef float  type; enum {size=4, alignment=Aligned16}; typedef Packet4f half; };\ntemplate<> struct unpacket_traits<Packet2d> { typedef double type; enum {size=2, alignment=Aligned16}; typedef Packet2d half; };\ntemplate<> struct unpacket_traits<Packet4i> { typedef int    type; enum {size=4, alignment=Aligned16}; typedef Packet4i half; };\n\n#ifndef EIGEN_VECTORIZE_AVX\ntemplate<> struct scalar_div_cost<float,true> { enum { value = 7 }; };\ntemplate<> struct scalar_div_cost<double,true> { enum { value = 8 }; };\n#endif\n\n#if EIGEN_COMP_MSVC==1500\n// Workaround MSVC 9 internal compiler error.\n// TODO: It has been detected with win64 builds (amd64), so let's check whether it also happens in 32bits+SSE mode\n// TODO: let's check whether there does not exist a better fix, like adding a pset0() function. (it crashed on pset1(0)).\ntemplate<> EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float&  from) { return _mm_set_ps(from,from,from,from); }\ntemplate<> EIGEN_STRONG_INLINE Packet2d pset1<Packet2d>(const double& from) { return _mm_set_pd(from,from); }\ntemplate<> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int&    from) { return _mm_set_epi32(from,from,from,from); }\n#else\ntemplate<> EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float&  from) { return _mm_set_ps1(from); }\ntemplate<> EIGEN_STRONG_INLINE Packet2d pset1<Packet2d>(const double& from) { return _mm_set1_pd(from); }\ntemplate<> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int&    from) { return _mm_set1_epi32(from); }\n#endif\n\n// GCC generates a shufps instruction for _mm_set1_ps/_mm_load1_ps instead of the more efficient pshufd instruction.\n// However, using inrinsics for pset1 makes gcc to generate crappy code in some cases (see bug 203)\n// Using inline assembly is also not an option because then gcc fails to reorder properly the instructions.\n// Therefore, we introduced the pload1 functions to be used in product kernels for which bug 203 does not apply.\n// Also note that with AVX, we want it to generate a vbroadcastss.\n#if EIGEN_COMP_GNUC_STRICT && (!defined __AVX__)\ntemplate<> EIGEN_STRONG_INLINE Packet4f pload1<Packet4f>(const float *from) {\n  return vec4f_swizzle1(_mm_load_ss(from),0,0,0,0);\n}\n#endif\n  \ntemplate<> EIGEN_STRONG_INLINE Packet4f plset<Packet4f>(const float& a) { return _mm_add_ps(pset1<Packet4f>(a), _mm_set_ps(3,2,1,0)); }\ntemplate<> EIGEN_STRONG_INLINE Packet2d plset<Packet2d>(const double& a) { return _mm_add_pd(pset1<Packet2d>(a),_mm_set_pd(1,0)); }\ntemplate<> EIGEN_STRONG_INLINE Packet4i plset<Packet4i>(const int& a) { return _mm_add_epi32(pset1<Packet4i>(a),_mm_set_epi32(3,2,1,0)); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f padd<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_add_ps(a,b); }\ntemplate<> EIGEN_STRONG_INLINE Packet2d padd<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_add_pd(a,b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4i padd<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_add_epi32(a,b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f psub<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_sub_ps(a,b); }\ntemplate<> EIGEN_STRONG_INLINE Packet2d psub<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_sub_pd(a,b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4i psub<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_sub_epi32(a,b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pnegate(const Packet4f& a)\n{\n  const Packet4f mask = _mm_castsi128_ps(_mm_setr_epi32(0x80000000,0x80000000,0x80000000,0x80000000));\n  return _mm_xor_ps(a,mask);\n}\ntemplate<> EIGEN_STRONG_INLINE Packet2d pnegate(const Packet2d& a)\n{\n  const Packet2d mask = _mm_castsi128_pd(_mm_setr_epi32(0x0,0x80000000,0x0,0x80000000));\n  return _mm_xor_pd(a,mask);\n}\ntemplate<> EIGEN_STRONG_INLINE Packet4i pnegate(const Packet4i& a)\n{\n  return psub(Packet4i(_mm_setr_epi32(0,0,0,0)), a);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pconj(const Packet4f& a) { return a; }\ntemplate<> EIGEN_STRONG_INLINE Packet2d pconj(const Packet2d& a) { return a; }\ntemplate<> EIGEN_STRONG_INLINE Packet4i pconj(const Packet4i& a) { return a; }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pmul<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_mul_ps(a,b); }\ntemplate<> EIGEN_STRONG_INLINE Packet2d pmul<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_mul_pd(a,b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4i pmul<Packet4i>(const Packet4i& a, const Packet4i& b)\n{\n#ifdef EIGEN_VECTORIZE_SSE4_1\n  return _mm_mullo_epi32(a,b);\n#else\n  // this version is slightly faster than 4 scalar products\n  return vec4i_swizzle1(\n            vec4i_swizzle2(\n              _mm_mul_epu32(a,b),\n              _mm_mul_epu32(vec4i_swizzle1(a,1,0,3,2),\n                            vec4i_swizzle1(b,1,0,3,2)),\n              0,2,0,2),\n            0,2,1,3);\n#endif\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pdiv<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_div_ps(a,b); }\ntemplate<> EIGEN_STRONG_INLINE Packet2d pdiv<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_div_pd(a,b); }\n\n// for some weird raisons, it has to be overloaded for packet of integers\ntemplate<> EIGEN_STRONG_INLINE Packet4i pmadd(const Packet4i& a, const Packet4i& b, const Packet4i& c) { return padd(pmul(a,b), c); }\n#ifdef __FMA__\ntemplate<> EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c) { return _mm_fmadd_ps(a,b,c); }\ntemplate<> EIGEN_STRONG_INLINE Packet2d pmadd(const Packet2d& a, const Packet2d& b, const Packet2d& c) { return _mm_fmadd_pd(a,b,c); }\n#endif\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pmin<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_min_ps(a,b); }\ntemplate<> EIGEN_STRONG_INLINE Packet2d pmin<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_min_pd(a,b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4i pmin<Packet4i>(const Packet4i& a, const Packet4i& b)\n{\n#ifdef EIGEN_VECTORIZE_SSE4_1\n  return _mm_min_epi32(a,b);\n#else\n  // after some bench, this version *is* faster than a scalar implementation\n  Packet4i mask = _mm_cmplt_epi32(a,b);\n  return _mm_or_si128(_mm_and_si128(mask,a),_mm_andnot_si128(mask,b));\n#endif\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pmax<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_max_ps(a,b); }\ntemplate<> EIGEN_STRONG_INLINE Packet2d pmax<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_max_pd(a,b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4i pmax<Packet4i>(const Packet4i& a, const Packet4i& b)\n{\n#ifdef EIGEN_VECTORIZE_SSE4_1\n  return _mm_max_epi32(a,b);\n#else\n  // after some bench, this version *is* faster than a scalar implementation\n  Packet4i mask = _mm_cmpgt_epi32(a,b);\n  return _mm_or_si128(_mm_and_si128(mask,a),_mm_andnot_si128(mask,b));\n#endif\n}\n\n#ifdef EIGEN_VECTORIZE_SSE4_1\ntemplate<> EIGEN_STRONG_INLINE Packet4f pround<Packet4f>(const Packet4f& a) { return _mm_round_ps(a, 0); }\ntemplate<> EIGEN_STRONG_INLINE Packet2d pround<Packet2d>(const Packet2d& a) { return _mm_round_pd(a, 0); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pceil<Packet4f>(const Packet4f& a) { return _mm_ceil_ps(a); }\ntemplate<> EIGEN_STRONG_INLINE Packet2d pceil<Packet2d>(const Packet2d& a) { return _mm_ceil_pd(a); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pfloor<Packet4f>(const Packet4f& a) { return _mm_floor_ps(a); }\ntemplate<> EIGEN_STRONG_INLINE Packet2d pfloor<Packet2d>(const Packet2d& a) { return _mm_floor_pd(a); }\n#endif\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pand<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_and_ps(a,b); }\ntemplate<> EIGEN_STRONG_INLINE Packet2d pand<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_and_pd(a,b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4i pand<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_and_si128(a,b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f por<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_or_ps(a,b); }\ntemplate<> EIGEN_STRONG_INLINE Packet2d por<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_or_pd(a,b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4i por<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_or_si128(a,b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pxor<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_xor_ps(a,b); }\ntemplate<> EIGEN_STRONG_INLINE Packet2d pxor<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_xor_pd(a,b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4i pxor<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_xor_si128(a,b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pandnot<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_andnot_ps(a,b); }\ntemplate<> EIGEN_STRONG_INLINE Packet2d pandnot<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_andnot_pd(a,b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4i pandnot<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_andnot_si128(a,b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pload<Packet4f>(const float*   from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm_load_ps(from); }\ntemplate<> EIGEN_STRONG_INLINE Packet2d pload<Packet2d>(const double*  from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm_load_pd(from); }\ntemplate<> EIGEN_STRONG_INLINE Packet4i pload<Packet4i>(const int*     from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm_load_si128(reinterpret_cast<const __m128i*>(from)); }\n\n#if EIGEN_COMP_MSVC\n  template<> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float*  from) {\n    EIGEN_DEBUG_UNALIGNED_LOAD\n    #if (EIGEN_COMP_MSVC==1600)\n    // NOTE Some version of MSVC10 generates bad code when using _mm_loadu_ps\n    // (i.e., it does not generate an unaligned load!!\n    __m128 res = _mm_loadl_pi(_mm_set1_ps(0.0f), (const __m64*)(from));\n    res = _mm_loadh_pi(res, (const __m64*)(from+2));\n    return res;\n    #else\n    return _mm_loadu_ps(from);\n    #endif\n  }\n#else\n// NOTE: with the code below, MSVC's compiler crashes!\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float* from)\n{\n  EIGEN_DEBUG_UNALIGNED_LOAD\n  return _mm_loadu_ps(from);\n}\n#endif\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d ploadu<Packet2d>(const double* from)\n{\n  EIGEN_DEBUG_UNALIGNED_LOAD\n  return _mm_loadu_pd(from);\n}\ntemplate<> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int* from)\n{\n  EIGEN_DEBUG_UNALIGNED_LOAD\n  return _mm_loadu_si128(reinterpret_cast<const __m128i*>(from));\n}\n\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f ploaddup<Packet4f>(const float*   from)\n{\n  return vec4f_swizzle1(_mm_castpd_ps(_mm_load_sd(reinterpret_cast<const double*>(from))), 0, 0, 1, 1);\n}\ntemplate<> EIGEN_STRONG_INLINE Packet2d ploaddup<Packet2d>(const double*  from)\n{ return pset1<Packet2d>(from[0]); }\ntemplate<> EIGEN_STRONG_INLINE Packet4i ploaddup<Packet4i>(const int*     from)\n{\n  Packet4i tmp;\n  tmp = _mm_loadl_epi64(reinterpret_cast<const __m128i*>(from));\n  return vec4i_swizzle1(tmp, 0, 0, 1, 1);\n}\n\ntemplate<> EIGEN_STRONG_INLINE void pstore<float>(float*   to, const Packet4f& from) { EIGEN_DEBUG_ALIGNED_STORE _mm_store_ps(to, from); }\ntemplate<> EIGEN_STRONG_INLINE void pstore<double>(double* to, const Packet2d& from) { EIGEN_DEBUG_ALIGNED_STORE _mm_store_pd(to, from); }\ntemplate<> EIGEN_STRONG_INLINE void pstore<int>(int*       to, const Packet4i& from) { EIGEN_DEBUG_ALIGNED_STORE _mm_store_si128(reinterpret_cast<__m128i*>(to), from); }\n\ntemplate<> EIGEN_STRONG_INLINE void pstoreu<double>(double* to, const Packet2d& from) { EIGEN_DEBUG_UNALIGNED_STORE _mm_storeu_pd(to, from); }\ntemplate<> EIGEN_STRONG_INLINE void pstoreu<float>(float*   to, const Packet4f& from) { EIGEN_DEBUG_UNALIGNED_STORE _mm_storeu_ps(to, from); }\ntemplate<> EIGEN_STRONG_INLINE void pstoreu<int>(int*       to, const Packet4i& from) { EIGEN_DEBUG_UNALIGNED_STORE _mm_storeu_si128(reinterpret_cast<__m128i*>(to), from); }\n\ntemplate<> EIGEN_DEVICE_FUNC inline Packet4f pgather<float, Packet4f>(const float* from, Index stride)\n{\n return _mm_set_ps(from[3*stride], from[2*stride], from[1*stride], from[0*stride]);\n}\ntemplate<> EIGEN_DEVICE_FUNC inline Packet2d pgather<double, Packet2d>(const double* from, Index stride)\n{\n return _mm_set_pd(from[1*stride], from[0*stride]);\n}\ntemplate<> EIGEN_DEVICE_FUNC inline Packet4i pgather<int, Packet4i>(const int* from, Index stride)\n{\n return _mm_set_epi32(from[3*stride], from[2*stride], from[1*stride], from[0*stride]);\n }\n\ntemplate<> EIGEN_DEVICE_FUNC inline void pscatter<float, Packet4f>(float* to, const Packet4f& from, Index stride)\n{\n  to[stride*0] = _mm_cvtss_f32(from);\n  to[stride*1] = _mm_cvtss_f32(_mm_shuffle_ps(from, from, 1));\n  to[stride*2] = _mm_cvtss_f32(_mm_shuffle_ps(from, from, 2));\n  to[stride*3] = _mm_cvtss_f32(_mm_shuffle_ps(from, from, 3));\n}\ntemplate<> EIGEN_DEVICE_FUNC inline void pscatter<double, Packet2d>(double* to, const Packet2d& from, Index stride)\n{\n  to[stride*0] = _mm_cvtsd_f64(from);\n  to[stride*1] = _mm_cvtsd_f64(_mm_shuffle_pd(from, from, 1));\n}\ntemplate<> EIGEN_DEVICE_FUNC inline void pscatter<int, Packet4i>(int* to, const Packet4i& from, Index stride)\n{\n  to[stride*0] = _mm_cvtsi128_si32(from);\n  to[stride*1] = _mm_cvtsi128_si32(_mm_shuffle_epi32(from, 1));\n  to[stride*2] = _mm_cvtsi128_si32(_mm_shuffle_epi32(from, 2));\n  to[stride*3] = _mm_cvtsi128_si32(_mm_shuffle_epi32(from, 3));\n}\n\n// some compilers might be tempted to perform multiple moves instead of using a vector path.\ntemplate<> EIGEN_STRONG_INLINE void pstore1<Packet4f>(float* to, const float& a)\n{\n  Packet4f pa = _mm_set_ss(a);\n  pstore(to, Packet4f(vec4f_swizzle1(pa,0,0,0,0)));\n}\n// some compilers might be tempted to perform multiple moves instead of using a vector path.\ntemplate<> EIGEN_STRONG_INLINE void pstore1<Packet2d>(double* to, const double& a)\n{\n  Packet2d pa = _mm_set_sd(a);\n  pstore(to, Packet2d(vec2d_swizzle1(pa,0,0)));\n}\n\n#if EIGEN_COMP_PGI\ntypedef const void * SsePrefetchPtrType;\n#else\ntypedef const char * SsePrefetchPtrType;\n#endif\n\n#ifndef EIGEN_VECTORIZE_AVX\ntemplate<> EIGEN_STRONG_INLINE void prefetch<float>(const float*   addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }\ntemplate<> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }\ntemplate<> EIGEN_STRONG_INLINE void prefetch<int>(const int*       addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }\n#endif\n\n#if EIGEN_COMP_MSVC_STRICT && EIGEN_OS_WIN64\n// The temporary variable fixes an internal compilation error in vs <= 2008 and a wrong-result bug in vs 2010\n// Direct of the struct members fixed bug #62.\ntemplate<> EIGEN_STRONG_INLINE float  pfirst<Packet4f>(const Packet4f& a) { return a.m128_f32[0]; }\ntemplate<> EIGEN_STRONG_INLINE double pfirst<Packet2d>(const Packet2d& a) { return a.m128d_f64[0]; }\ntemplate<> EIGEN_STRONG_INLINE int    pfirst<Packet4i>(const Packet4i& a) { int x = _mm_cvtsi128_si32(a); return x; }\n#elif EIGEN_COMP_MSVC_STRICT\n// The temporary variable fixes an internal compilation error in vs <= 2008 and a wrong-result bug in vs 2010\ntemplate<> EIGEN_STRONG_INLINE float  pfirst<Packet4f>(const Packet4f& a) { float x = _mm_cvtss_f32(a); return x; }\ntemplate<> EIGEN_STRONG_INLINE double pfirst<Packet2d>(const Packet2d& a) { double x = _mm_cvtsd_f64(a); return x; }\ntemplate<> EIGEN_STRONG_INLINE int    pfirst<Packet4i>(const Packet4i& a) { int x = _mm_cvtsi128_si32(a); return x; }\n#else\ntemplate<> EIGEN_STRONG_INLINE float  pfirst<Packet4f>(const Packet4f& a) { return _mm_cvtss_f32(a); }\ntemplate<> EIGEN_STRONG_INLINE double pfirst<Packet2d>(const Packet2d& a) { return _mm_cvtsd_f64(a); }\ntemplate<> EIGEN_STRONG_INLINE int    pfirst<Packet4i>(const Packet4i& a) { return _mm_cvtsi128_si32(a); }\n#endif\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f preverse(const Packet4f& a)\n{ return _mm_shuffle_ps(a,a,0x1B); }\ntemplate<> EIGEN_STRONG_INLINE Packet2d preverse(const Packet2d& a)\n{ return _mm_shuffle_pd(a,a,0x1); }\ntemplate<> EIGEN_STRONG_INLINE Packet4i preverse(const Packet4i& a)\n{ return _mm_shuffle_epi32(a,0x1B); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pabs(const Packet4f& a)\n{\n  const Packet4f mask = _mm_castsi128_ps(_mm_setr_epi32(0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF));\n  return _mm_and_ps(a,mask);\n}\ntemplate<> EIGEN_STRONG_INLINE Packet2d pabs(const Packet2d& a)\n{\n  const Packet2d mask = _mm_castsi128_pd(_mm_setr_epi32(0xFFFFFFFF,0x7FFFFFFF,0xFFFFFFFF,0x7FFFFFFF));\n  return _mm_and_pd(a,mask);\n}\ntemplate<> EIGEN_STRONG_INLINE Packet4i pabs(const Packet4i& a)\n{\n  #ifdef EIGEN_VECTORIZE_SSSE3\n  return _mm_abs_epi32(a);\n  #else\n  Packet4i aux = _mm_srai_epi32(a,31);\n  return _mm_sub_epi32(_mm_xor_si128(a,aux),aux);\n  #endif\n}\n\n// with AVX, the default implementations based on pload1 are faster\n#ifndef __AVX__\ntemplate<> EIGEN_STRONG_INLINE void\npbroadcast4<Packet4f>(const float *a,\n                      Packet4f& a0, Packet4f& a1, Packet4f& a2, Packet4f& a3)\n{\n  a3 = pload<Packet4f>(a);\n  a0 = vec4f_swizzle1(a3, 0,0,0,0);\n  a1 = vec4f_swizzle1(a3, 1,1,1,1);\n  a2 = vec4f_swizzle1(a3, 2,2,2,2);\n  a3 = vec4f_swizzle1(a3, 3,3,3,3);\n}\ntemplate<> EIGEN_STRONG_INLINE void\npbroadcast4<Packet2d>(const double *a,\n                      Packet2d& a0, Packet2d& a1, Packet2d& a2, Packet2d& a3)\n{\n#ifdef EIGEN_VECTORIZE_SSE3\n  a0 = _mm_loaddup_pd(a+0);\n  a1 = _mm_loaddup_pd(a+1);\n  a2 = _mm_loaddup_pd(a+2);\n  a3 = _mm_loaddup_pd(a+3);\n#else\n  a1 = pload<Packet2d>(a);\n  a0 = vec2d_swizzle1(a1, 0,0);\n  a1 = vec2d_swizzle1(a1, 1,1);\n  a3 = pload<Packet2d>(a+2);\n  a2 = vec2d_swizzle1(a3, 0,0);\n  a3 = vec2d_swizzle1(a3, 1,1);\n#endif\n}\n#endif\n\nEIGEN_STRONG_INLINE void punpackp(Packet4f* vecs)\n{\n  vecs[1] = _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(vecs[0]), 0x55));\n  vecs[2] = _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(vecs[0]), 0xAA));\n  vecs[3] = _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(vecs[0]), 0xFF));\n  vecs[0] = _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(vecs[0]), 0x00));\n}\n\n#ifdef EIGEN_VECTORIZE_SSE3\ntemplate<> EIGEN_STRONG_INLINE Packet4f preduxp<Packet4f>(const Packet4f* vecs)\n{\n  return _mm_hadd_ps(_mm_hadd_ps(vecs[0], vecs[1]),_mm_hadd_ps(vecs[2], vecs[3]));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d preduxp<Packet2d>(const Packet2d* vecs)\n{\n  return _mm_hadd_pd(vecs[0], vecs[1]);\n}\n\n#else\ntemplate<> EIGEN_STRONG_INLINE Packet4f preduxp<Packet4f>(const Packet4f* vecs)\n{\n  Packet4f tmp0, tmp1, tmp2;\n  tmp0 = _mm_unpacklo_ps(vecs[0], vecs[1]);\n  tmp1 = _mm_unpackhi_ps(vecs[0], vecs[1]);\n  tmp2 = _mm_unpackhi_ps(vecs[2], vecs[3]);\n  tmp0 = _mm_add_ps(tmp0, tmp1);\n  tmp1 = _mm_unpacklo_ps(vecs[2], vecs[3]);\n  tmp1 = _mm_add_ps(tmp1, tmp2);\n  tmp2 = _mm_movehl_ps(tmp1, tmp0);\n  tmp0 = _mm_movelh_ps(tmp0, tmp1);\n  return _mm_add_ps(tmp0, tmp2);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d preduxp<Packet2d>(const Packet2d* vecs)\n{\n  return _mm_add_pd(_mm_unpacklo_pd(vecs[0], vecs[1]), _mm_unpackhi_pd(vecs[0], vecs[1]));\n}\n#endif  // SSE3\n\ntemplate<> EIGEN_STRONG_INLINE float predux<Packet4f>(const Packet4f& a)\n{\n  // Disable SSE3 _mm_hadd_pd that is extremely slow on all existing Intel's architectures\n  // (from Nehalem to Haswell)\n// #ifdef EIGEN_VECTORIZE_SSE3\n//   Packet4f tmp = _mm_add_ps(a, vec4f_swizzle1(a,2,3,2,3));\n//   return pfirst<Packet4f>(_mm_hadd_ps(tmp, tmp));\n// #else\n  Packet4f tmp = _mm_add_ps(a, _mm_movehl_ps(a,a));\n  return pfirst<Packet4f>(_mm_add_ss(tmp, _mm_shuffle_ps(tmp,tmp, 1)));\n// #endif\n}\n\ntemplate<> EIGEN_STRONG_INLINE double predux<Packet2d>(const Packet2d& a)\n{\n  // Disable SSE3 _mm_hadd_pd that is extremely slow on all existing Intel's architectures\n  // (from Nehalem to Haswell)\n// #ifdef EIGEN_VECTORIZE_SSE3\n//   return pfirst<Packet2d>(_mm_hadd_pd(a, a));\n// #else\n  return pfirst<Packet2d>(_mm_add_sd(a, _mm_unpackhi_pd(a,a)));\n// #endif\n}\n\n#ifdef EIGEN_VECTORIZE_SSSE3\ntemplate<> EIGEN_STRONG_INLINE Packet4i preduxp<Packet4i>(const Packet4i* vecs)\n{\n  return _mm_hadd_epi32(_mm_hadd_epi32(vecs[0], vecs[1]),_mm_hadd_epi32(vecs[2], vecs[3]));\n}\ntemplate<> EIGEN_STRONG_INLINE int predux<Packet4i>(const Packet4i& a)\n{\n  Packet4i tmp0 = _mm_hadd_epi32(a,a);\n  return pfirst<Packet4i>(_mm_hadd_epi32(tmp0,tmp0));\n}\n#else\ntemplate<> EIGEN_STRONG_INLINE int predux<Packet4i>(const Packet4i& a)\n{\n  Packet4i tmp = _mm_add_epi32(a, _mm_unpackhi_epi64(a,a));\n  return pfirst(tmp) + pfirst<Packet4i>(_mm_shuffle_epi32(tmp, 1));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4i preduxp<Packet4i>(const Packet4i* vecs)\n{\n  Packet4i tmp0, tmp1, tmp2;\n  tmp0 = _mm_unpacklo_epi32(vecs[0], vecs[1]);\n  tmp1 = _mm_unpackhi_epi32(vecs[0], vecs[1]);\n  tmp2 = _mm_unpackhi_epi32(vecs[2], vecs[3]);\n  tmp0 = _mm_add_epi32(tmp0, tmp1);\n  tmp1 = _mm_unpacklo_epi32(vecs[2], vecs[3]);\n  tmp1 = _mm_add_epi32(tmp1, tmp2);\n  tmp2 = _mm_unpacklo_epi64(tmp0, tmp1);\n  tmp0 = _mm_unpackhi_epi64(tmp0, tmp1);\n  return _mm_add_epi32(tmp0, tmp2);\n}\n#endif\n// Other reduction functions:\n\n// mul\ntemplate<> EIGEN_STRONG_INLINE float predux_mul<Packet4f>(const Packet4f& a)\n{\n  Packet4f tmp = _mm_mul_ps(a, _mm_movehl_ps(a,a));\n  return pfirst<Packet4f>(_mm_mul_ss(tmp, _mm_shuffle_ps(tmp,tmp, 1)));\n}\ntemplate<> EIGEN_STRONG_INLINE double predux_mul<Packet2d>(const Packet2d& a)\n{\n  return pfirst<Packet2d>(_mm_mul_sd(a, _mm_unpackhi_pd(a,a)));\n}\ntemplate<> EIGEN_STRONG_INLINE int predux_mul<Packet4i>(const Packet4i& a)\n{\n  // after some experiments, it is seems this is the fastest way to implement it\n  // for GCC (eg., reusing pmul is very slow !)\n  // TODO try to call _mm_mul_epu32 directly\n  EIGEN_ALIGN16 int aux[4];\n  pstore(aux, a);\n  return  (aux[0] * aux[1]) * (aux[2] * aux[3]);;\n}\n\n// min\ntemplate<> EIGEN_STRONG_INLINE float predux_min<Packet4f>(const Packet4f& a)\n{\n  Packet4f tmp = _mm_min_ps(a, _mm_movehl_ps(a,a));\n  return pfirst<Packet4f>(_mm_min_ss(tmp, _mm_shuffle_ps(tmp,tmp, 1)));\n}\ntemplate<> EIGEN_STRONG_INLINE double predux_min<Packet2d>(const Packet2d& a)\n{\n  return pfirst<Packet2d>(_mm_min_sd(a, _mm_unpackhi_pd(a,a)));\n}\ntemplate<> EIGEN_STRONG_INLINE int predux_min<Packet4i>(const Packet4i& a)\n{\n#ifdef EIGEN_VECTORIZE_SSE4_1\n  Packet4i tmp = _mm_min_epi32(a, _mm_shuffle_epi32(a, _MM_SHUFFLE(0,0,3,2)));\n  return pfirst<Packet4i>(_mm_min_epi32(tmp,_mm_shuffle_epi32(tmp, 1)));\n#else\n  // after some experiments, it is seems this is the fastest way to implement it\n  // for GCC (eg., it does not like using std::min after the pstore !!)\n  EIGEN_ALIGN16 int aux[4];\n  pstore(aux, a);\n  int aux0 = aux[0]<aux[1] ? aux[0] : aux[1];\n  int aux2 = aux[2]<aux[3] ? aux[2] : aux[3];\n  return aux0<aux2 ? aux0 : aux2;\n#endif // EIGEN_VECTORIZE_SSE4_1\n}\n\n// max\ntemplate<> EIGEN_STRONG_INLINE float predux_max<Packet4f>(const Packet4f& a)\n{\n  Packet4f tmp = _mm_max_ps(a, _mm_movehl_ps(a,a));\n  return pfirst<Packet4f>(_mm_max_ss(tmp, _mm_shuffle_ps(tmp,tmp, 1)));\n}\ntemplate<> EIGEN_STRONG_INLINE double predux_max<Packet2d>(const Packet2d& a)\n{\n  return pfirst<Packet2d>(_mm_max_sd(a, _mm_unpackhi_pd(a,a)));\n}\ntemplate<> EIGEN_STRONG_INLINE int predux_max<Packet4i>(const Packet4i& a)\n{\n#ifdef EIGEN_VECTORIZE_SSE4_1\n  Packet4i tmp = _mm_max_epi32(a, _mm_shuffle_epi32(a, _MM_SHUFFLE(0,0,3,2)));\n  return pfirst<Packet4i>(_mm_max_epi32(tmp,_mm_shuffle_epi32(tmp, 1)));\n#else\n  // after some experiments, it is seems this is the fastest way to implement it\n  // for GCC (eg., it does not like using std::min after the pstore !!)\n  EIGEN_ALIGN16 int aux[4];\n  pstore(aux, a);\n  int aux0 = aux[0]>aux[1] ? aux[0] : aux[1];\n  int aux2 = aux[2]>aux[3] ? aux[2] : aux[3];\n  return aux0>aux2 ? aux0 : aux2;\n#endif // EIGEN_VECTORIZE_SSE4_1\n}\n\n#if EIGEN_COMP_GNUC\n// template <> EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f&  a, const Packet4f&  b, const Packet4f&  c)\n// {\n//   Packet4f res = b;\n//   asm(\"mulps %[a], %[b] \\n\\taddps %[c], %[b]\" : [b] \"+x\" (res) : [a] \"x\" (a), [c] \"x\" (c));\n//   return res;\n// }\n// EIGEN_STRONG_INLINE Packet4i _mm_alignr_epi8(const Packet4i&  a, const Packet4i&  b, const int i)\n// {\n//   Packet4i res = a;\n//   asm(\"palignr %[i], %[a], %[b] \" : [b] \"+x\" (res) : [a] \"x\" (a), [i] \"i\" (i));\n//   return res;\n// }\n#endif\n\n#ifdef EIGEN_VECTORIZE_SSSE3\n// SSSE3 versions\ntemplate<int Offset>\nstruct palign_impl<Offset,Packet4f>\n{\n  static EIGEN_STRONG_INLINE void run(Packet4f& first, const Packet4f& second)\n  {\n    if (Offset!=0)\n      first = _mm_castsi128_ps(_mm_alignr_epi8(_mm_castps_si128(second), _mm_castps_si128(first), Offset*4));\n  }\n};\n\ntemplate<int Offset>\nstruct palign_impl<Offset,Packet4i>\n{\n  static EIGEN_STRONG_INLINE void run(Packet4i& first, const Packet4i& second)\n  {\n    if (Offset!=0)\n      first = _mm_alignr_epi8(second,first, Offset*4);\n  }\n};\n\ntemplate<int Offset>\nstruct palign_impl<Offset,Packet2d>\n{\n  static EIGEN_STRONG_INLINE void run(Packet2d& first, const Packet2d& second)\n  {\n    if (Offset==1)\n      first = _mm_castsi128_pd(_mm_alignr_epi8(_mm_castpd_si128(second), _mm_castpd_si128(first), 8));\n  }\n};\n#else\n// SSE2 versions\ntemplate<int Offset>\nstruct palign_impl<Offset,Packet4f>\n{\n  static EIGEN_STRONG_INLINE void run(Packet4f& first, const Packet4f& second)\n  {\n    if (Offset==1)\n    {\n      first = _mm_move_ss(first,second);\n      first = _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(first),0x39));\n    }\n    else if (Offset==2)\n    {\n      first = _mm_movehl_ps(first,first);\n      first = _mm_movelh_ps(first,second);\n    }\n    else if (Offset==3)\n    {\n      first = _mm_move_ss(first,second);\n      first = _mm_shuffle_ps(first,second,0x93);\n    }\n  }\n};\n\ntemplate<int Offset>\nstruct palign_impl<Offset,Packet4i>\n{\n  static EIGEN_STRONG_INLINE void run(Packet4i& first, const Packet4i& second)\n  {\n    if (Offset==1)\n    {\n      first = _mm_castps_si128(_mm_move_ss(_mm_castsi128_ps(first),_mm_castsi128_ps(second)));\n      first = _mm_shuffle_epi32(first,0x39);\n    }\n    else if (Offset==2)\n    {\n      first = _mm_castps_si128(_mm_movehl_ps(_mm_castsi128_ps(first),_mm_castsi128_ps(first)));\n      first = _mm_castps_si128(_mm_movelh_ps(_mm_castsi128_ps(first),_mm_castsi128_ps(second)));\n    }\n    else if (Offset==3)\n    {\n      first = _mm_castps_si128(_mm_move_ss(_mm_castsi128_ps(first),_mm_castsi128_ps(second)));\n      first = _mm_castps_si128(_mm_shuffle_ps(_mm_castsi128_ps(first),_mm_castsi128_ps(second),0x93));\n    }\n  }\n};\n\ntemplate<int Offset>\nstruct palign_impl<Offset,Packet2d>\n{\n  static EIGEN_STRONG_INLINE void run(Packet2d& first, const Packet2d& second)\n  {\n    if (Offset==1)\n    {\n      first = _mm_castps_pd(_mm_movehl_ps(_mm_castpd_ps(first),_mm_castpd_ps(first)));\n      first = _mm_castps_pd(_mm_movelh_ps(_mm_castpd_ps(first),_mm_castpd_ps(second)));\n    }\n  }\n};\n#endif\n\nEIGEN_DEVICE_FUNC inline void\nptranspose(PacketBlock<Packet4f,4>& kernel) {\n  _MM_TRANSPOSE4_PS(kernel.packet[0], kernel.packet[1], kernel.packet[2], kernel.packet[3]);\n}\n\nEIGEN_DEVICE_FUNC inline void\nptranspose(PacketBlock<Packet2d,2>& kernel) {\n  __m128d tmp = _mm_unpackhi_pd(kernel.packet[0], kernel.packet[1]);\n  kernel.packet[0] = _mm_unpacklo_pd(kernel.packet[0], kernel.packet[1]);\n  kernel.packet[1] = tmp;\n}\n\nEIGEN_DEVICE_FUNC inline void\nptranspose(PacketBlock<Packet4i,4>& kernel) {\n  __m128i T0 = _mm_unpacklo_epi32(kernel.packet[0], kernel.packet[1]);\n  __m128i T1 = _mm_unpacklo_epi32(kernel.packet[2], kernel.packet[3]);\n  __m128i T2 = _mm_unpackhi_epi32(kernel.packet[0], kernel.packet[1]);\n  __m128i T3 = _mm_unpackhi_epi32(kernel.packet[2], kernel.packet[3]);\n\n  kernel.packet[0] = _mm_unpacklo_epi64(T0, T1);\n  kernel.packet[1] = _mm_unpackhi_epi64(T0, T1);\n  kernel.packet[2] = _mm_unpacklo_epi64(T2, T3);\n  kernel.packet[3] = _mm_unpackhi_epi64(T2, T3);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4i pblend(const Selector<4>& ifPacket, const Packet4i& thenPacket, const Packet4i& elsePacket) {\n  const __m128i zero = _mm_setzero_si128();\n  const __m128i select = _mm_set_epi32(ifPacket.select[3], ifPacket.select[2], ifPacket.select[1], ifPacket.select[0]);\n  __m128i false_mask = _mm_cmpeq_epi32(select, zero);\n#ifdef EIGEN_VECTORIZE_SSE4_1\n  return _mm_blendv_epi8(thenPacket, elsePacket, false_mask);\n#else\n  return _mm_or_si128(_mm_andnot_si128(false_mask, thenPacket), _mm_and_si128(false_mask, elsePacket));\n#endif\n}\ntemplate<> EIGEN_STRONG_INLINE Packet4f pblend(const Selector<4>& ifPacket, const Packet4f& thenPacket, const Packet4f& elsePacket) {\n  const __m128 zero = _mm_setzero_ps();\n  const __m128 select = _mm_set_ps(ifPacket.select[3], ifPacket.select[2], ifPacket.select[1], ifPacket.select[0]);\n  __m128 false_mask = _mm_cmpeq_ps(select, zero);\n#ifdef EIGEN_VECTORIZE_SSE4_1\n  return _mm_blendv_ps(thenPacket, elsePacket, false_mask);\n#else\n  return _mm_or_ps(_mm_andnot_ps(false_mask, thenPacket), _mm_and_ps(false_mask, elsePacket));\n#endif\n}\ntemplate<> EIGEN_STRONG_INLINE Packet2d pblend(const Selector<2>& ifPacket, const Packet2d& thenPacket, const Packet2d& elsePacket) {\n  const __m128d zero = _mm_setzero_pd();\n  const __m128d select = _mm_set_pd(ifPacket.select[1], ifPacket.select[0]);\n  __m128d false_mask = _mm_cmpeq_pd(select, zero);\n#ifdef EIGEN_VECTORIZE_SSE4_1\n  return _mm_blendv_pd(thenPacket, elsePacket, false_mask);\n#else\n  return _mm_or_pd(_mm_andnot_pd(false_mask, thenPacket), _mm_and_pd(false_mask, elsePacket));\n#endif\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pinsertfirst(const Packet4f& a, float b)\n{\n#ifdef EIGEN_VECTORIZE_SSE4_1\n  return _mm_blend_ps(a,pset1<Packet4f>(b),1);\n#else\n  return _mm_move_ss(a, _mm_load_ss(&b));\n#endif\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d pinsertfirst(const Packet2d& a, double b)\n{\n#ifdef EIGEN_VECTORIZE_SSE4_1\n  return _mm_blend_pd(a,pset1<Packet2d>(b),1);\n#else\n  return _mm_move_sd(a, _mm_load_sd(&b));\n#endif\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pinsertlast(const Packet4f& a, float b)\n{\n#ifdef EIGEN_VECTORIZE_SSE4_1\n  return _mm_blend_ps(a,pset1<Packet4f>(b),(1<<3));\n#else\n  const Packet4f mask = _mm_castsi128_ps(_mm_setr_epi32(0x0,0x0,0x0,0xFFFFFFFF));\n  return _mm_or_ps(_mm_andnot_ps(mask, a), _mm_and_ps(mask, pset1<Packet4f>(b)));\n#endif\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d pinsertlast(const Packet2d& a, double b)\n{\n#ifdef EIGEN_VECTORIZE_SSE4_1\n  return _mm_blend_pd(a,pset1<Packet2d>(b),(1<<1));\n#else\n  const Packet2d mask = _mm_castsi128_pd(_mm_setr_epi32(0x0,0x0,0xFFFFFFFF,0xFFFFFFFF));\n  return _mm_or_pd(_mm_andnot_pd(mask, a), _mm_and_pd(mask, pset1<Packet2d>(b)));\n#endif\n}\n\n// Scalar path for pmadd with FMA to ensure consistency with vectorized path.\n#ifdef __FMA__\ntemplate<> EIGEN_STRONG_INLINE float pmadd(const float& a, const float& b, const float& c) {\n  return ::fmaf(a,b,c);\n}\ntemplate<> EIGEN_STRONG_INLINE double pmadd(const double& a, const double& b, const double& c) {\n  return ::fma(a,b,c);\n}\n#endif\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#if EIGEN_COMP_PGI\n// PGI++ does not define the following intrinsics in C++ mode.\nstatic inline __m128  _mm_castpd_ps   (__m128d x) { return reinterpret_cast<__m128&>(x);  }\nstatic inline __m128i _mm_castpd_si128(__m128d x) { return reinterpret_cast<__m128i&>(x); }\nstatic inline __m128d _mm_castps_pd   (__m128  x) { return reinterpret_cast<__m128d&>(x); }\nstatic inline __m128i _mm_castps_si128(__m128  x) { return reinterpret_cast<__m128i&>(x); }\nstatic inline __m128  _mm_castsi128_ps(__m128i x) { return reinterpret_cast<__m128&>(x);  }\nstatic inline __m128d _mm_castsi128_pd(__m128i x) { return reinterpret_cast<__m128d&>(x); }\n#endif\n\n#endif // EIGEN_PACKET_MATH_SSE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/arch/SSE/TypeCasting.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_TYPE_CASTING_SSE_H\n#define EIGEN_TYPE_CASTING_SSE_H\n\nnamespace Eigen {\n\nnamespace internal {\n\n#ifndef EIGEN_VECTORIZE_AVX\ntemplate <>\nstruct type_casting_traits<float, int> {\n  enum {\n    VectorizedCast = 1,\n    SrcCoeffRatio = 1,\n    TgtCoeffRatio = 1\n  };\n};\n\ntemplate <>\nstruct type_casting_traits<int, float> {\n  enum {\n    VectorizedCast = 1,\n    SrcCoeffRatio = 1,\n    TgtCoeffRatio = 1\n  };\n};\n\ntemplate <>\nstruct type_casting_traits<double, float> {\n  enum {\n    VectorizedCast = 1,\n    SrcCoeffRatio = 2,\n    TgtCoeffRatio = 1\n  };\n};\n\ntemplate <>\nstruct type_casting_traits<float, double> {\n  enum {\n    VectorizedCast = 1,\n    SrcCoeffRatio = 1,\n    TgtCoeffRatio = 2\n  };\n};\n#endif\n\ntemplate<> EIGEN_STRONG_INLINE Packet4i pcast<Packet4f, Packet4i>(const Packet4f& a) {\n  return _mm_cvttps_epi32(a);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pcast<Packet4i, Packet4f>(const Packet4i& a) {\n  return _mm_cvtepi32_ps(a);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pcast<Packet2d, Packet4f>(const Packet2d& a, const Packet2d& b) {\n  return _mm_shuffle_ps(_mm_cvtpd_ps(a), _mm_cvtpd_ps(b), (1 << 2) | (1 << 6));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d pcast<Packet4f, Packet2d>(const Packet4f& a) {\n  // Simply discard the second half of the input\n  return _mm_cvtps_pd(a);\n}\n\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_TYPE_CASTING_SSE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/arch/ZVector/Complex.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2016 Konstantinos Margaritis <markos@freevec.org>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_COMPLEX32_ALTIVEC_H\n#define EIGEN_COMPLEX32_ALTIVEC_H\n\nnamespace Eigen {\n\nnamespace internal {\n\nstatic Packet2ul  p2ul_CONJ_XOR1 = (Packet2ul) vec_sld((Packet4ui) p2d_ZERO_, (Packet4ui) p2l_ZERO, 8);//{ 0x8000000000000000, 0x0000000000000000 };\nstatic Packet2ul  p2ul_CONJ_XOR2 = (Packet2ul) vec_sld((Packet4ui) p2l_ZERO,  (Packet4ui) p2d_ZERO_, 8);//{ 0x8000000000000000, 0x0000000000000000 };\n\nstruct Packet1cd\n{\n  EIGEN_STRONG_INLINE Packet1cd() {}\n  EIGEN_STRONG_INLINE explicit Packet1cd(const Packet2d& a) : v(a) {}\n  Packet2d v;\n};\n\nstruct Packet2cf\n{\n  EIGEN_STRONG_INLINE Packet2cf() {}\n  EIGEN_STRONG_INLINE explicit Packet2cf(const Packet4f& a) : v(a) {}\n  union {\n    Packet4f v;\n    Packet1cd cd[2];\n  };\n};\n\ntemplate<> struct packet_traits<std::complex<float> >  : default_packet_traits\n{\n  typedef Packet2cf type;\n  typedef Packet2cf half;\n  enum {\n    Vectorizable = 1,\n    AlignedOnScalar = 1,\n    size = 2,\n    HasHalfPacket = 0,\n\n    HasAdd    = 1,\n    HasSub    = 1,\n    HasMul    = 1,\n    HasDiv    = 1,\n    HasNegate = 1,\n    HasAbs    = 0,\n    HasAbs2   = 0,\n    HasMin    = 0,\n    HasMax    = 0,\n    HasBlend  = 1,\n    HasSetLinear = 0\n  };\n};\n\n\ntemplate<> struct packet_traits<std::complex<double> >  : default_packet_traits\n{\n  typedef Packet1cd type;\n  typedef Packet1cd half;\n  enum {\n    Vectorizable = 1,\n    AlignedOnScalar = 1,\n    size = 1,\n    HasHalfPacket = 0,\n\n    HasAdd    = 1,\n    HasSub    = 1,\n    HasMul    = 1,\n    HasDiv    = 1,\n    HasNegate = 1,\n    HasAbs    = 0,\n    HasAbs2   = 0,\n    HasMin    = 0,\n    HasMax    = 0,\n    HasSetLinear = 0\n  };\n};\n\ntemplate<> struct unpacket_traits<Packet2cf> { typedef std::complex<float>  type; enum {size=2, alignment=Aligned16}; typedef Packet2cf half; };\ntemplate<> struct unpacket_traits<Packet1cd> { typedef std::complex<double> type; enum {size=1, alignment=Aligned16}; typedef Packet1cd half; };\n\n/* Forward declaration */\nEIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet2cf,2>& kernel);\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pload <Packet2cf>(const std::complex<float>* from)  { EIGEN_DEBUG_ALIGNED_LOAD return Packet2cf(pload<Packet4f>((const float*)from)); }\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pload <Packet1cd>(const std::complex<double>* from) { EIGEN_DEBUG_ALIGNED_LOAD return Packet1cd(pload<Packet2d>((const double*)from)); }\ntemplate<> EIGEN_STRONG_INLINE Packet2cf ploadu<Packet2cf>(const std::complex<float>* from)  { EIGEN_DEBUG_UNALIGNED_LOAD return Packet2cf(ploadu<Packet4f>((const float*)from)); }\ntemplate<> EIGEN_STRONG_INLINE Packet1cd ploadu<Packet1cd>(const std::complex<double>* from) { EIGEN_DEBUG_UNALIGNED_LOAD return Packet1cd(ploadu<Packet2d>((const double*)from)); }\ntemplate<> EIGEN_STRONG_INLINE void pstore <std::complex<float> >(std::complex<float> *     to, const Packet2cf& from) { EIGEN_DEBUG_ALIGNED_STORE pstore((float*)to, from.v); }\ntemplate<> EIGEN_STRONG_INLINE void pstore <std::complex<double> >(std::complex<double> *   to, const Packet1cd& from) { EIGEN_DEBUG_ALIGNED_STORE pstore((double*)to, from.v); }\ntemplate<> EIGEN_STRONG_INLINE void pstoreu<std::complex<float> >(std::complex<float> *     to, const Packet2cf& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu((float*)to, from.v); }\ntemplate<> EIGEN_STRONG_INLINE void pstoreu<std::complex<double> >(std::complex<double> *   to, const Packet1cd& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu((double*)to, from.v); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pset1<Packet1cd>(const std::complex<double>&  from)\n{ /* here we really have to use unaligned loads :( */ return ploadu<Packet1cd>(&from); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pset1<Packet2cf>(const std::complex<float>&  from)\n{\n  Packet2cf res;\n  res.cd[0] = Packet1cd(vec_ld2f((const float *)&from));\n  res.cd[1] = res.cd[0];\n  return res;\n}\ntemplate<> EIGEN_DEVICE_FUNC inline Packet2cf pgather<std::complex<float>, Packet2cf>(const std::complex<float>* from, Index stride)\n{\n  std::complex<float> EIGEN_ALIGN16 af[2];\n  af[0] = from[0*stride];\n  af[1] = from[1*stride];\n  return pload<Packet2cf>(af);\n}\ntemplate<> EIGEN_DEVICE_FUNC inline Packet1cd pgather<std::complex<double>, Packet1cd>(const std::complex<double>* from, Index stride EIGEN_UNUSED)\n{\n  return pload<Packet1cd>(from);\n}\ntemplate<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<float>, Packet2cf>(std::complex<float>* to, const Packet2cf& from, Index stride)\n{\n  std::complex<float> EIGEN_ALIGN16 af[2];\n  pstore<std::complex<float> >((std::complex<float> *) af, from);\n  to[0*stride] = af[0];\n  to[1*stride] = af[1];\n}\ntemplate<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<double>, Packet1cd>(std::complex<double>* to, const Packet1cd& from, Index stride EIGEN_UNUSED)\n{\n  pstore<std::complex<double> >(to, from);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cf padd<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(padd<Packet4f>(a.v, b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet1cd padd<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(a.v + b.v); }\ntemplate<> EIGEN_STRONG_INLINE Packet2cf psub<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(psub<Packet4f>(a.v, b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet1cd psub<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(a.v - b.v); }\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pnegate(const Packet1cd& a) { return Packet1cd(pnegate(Packet2d(a.v))); }\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pnegate(const Packet2cf& a) { return Packet2cf(pnegate(Packet4f(a.v))); }\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pconj(const Packet1cd& a) { return Packet1cd((Packet2d)vec_xor((Packet2d)a.v, (Packet2d)p2ul_CONJ_XOR2)); }\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pconj(const Packet2cf& a)\n{\n  Packet2cf res;\n  res.v.v4f[0] = pconj(Packet1cd(reinterpret_cast<Packet2d>(a.v.v4f[0]))).v;\n  res.v.v4f[1] = pconj(Packet1cd(reinterpret_cast<Packet2d>(a.v.v4f[1]))).v;\n  return res;\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pmul<Packet1cd>(const Packet1cd& a, const Packet1cd& b)\n{\n  Packet2d a_re, a_im, v1, v2;\n\n  // Permute and multiply the real parts of a and b\n  a_re = vec_perm(a.v, a.v, p16uc_PSET64_HI);\n  // Get the imaginary parts of a\n  a_im = vec_perm(a.v, a.v, p16uc_PSET64_LO);\n  // multiply a_re * b\n  v1 = vec_madd(a_re, b.v, p2d_ZERO);\n  // multiply a_im * b and get the conjugate result\n  v2 = vec_madd(a_im, b.v, p2d_ZERO);\n  v2 = (Packet2d) vec_sld((Packet4ui)v2, (Packet4ui)v2, 8);\n  v2 = (Packet2d) vec_xor((Packet2d)v2, (Packet2d) p2ul_CONJ_XOR1);\n\n  return Packet1cd(v1 + v2);\n}\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pmul<Packet2cf>(const Packet2cf& a, const Packet2cf& b)\n{\n  Packet2cf res;\n  res.v.v4f[0] = pmul(Packet1cd(reinterpret_cast<Packet2d>(a.v.v4f[0])), Packet1cd(reinterpret_cast<Packet2d>(b.v.v4f[0]))).v;\n  res.v.v4f[1] = pmul(Packet1cd(reinterpret_cast<Packet2d>(a.v.v4f[1])), Packet1cd(reinterpret_cast<Packet2d>(b.v.v4f[1]))).v;\n  return res;\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pand   <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(vec_and(a.v,b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pand   <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(pand<Packet4f>(a.v,b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet1cd por    <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(vec_or(a.v,b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet2cf por    <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(por<Packet4f>(a.v,b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pxor   <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(vec_xor(a.v,b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pxor   <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(pxor<Packet4f>(a.v,b.v)); }\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pandnot<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(vec_and(a.v, vec_nor(b.v,b.v))); }\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pandnot<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(pandnot<Packet4f>(a.v,b.v)); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet1cd ploaddup<Packet1cd>(const std::complex<double>*     from) {  return pset1<Packet1cd>(*from); }\ntemplate<> EIGEN_STRONG_INLINE Packet2cf ploaddup<Packet2cf>(const std::complex<float>*      from) {  return pset1<Packet2cf>(*from); }\n\ntemplate<> EIGEN_STRONG_INLINE void prefetch<std::complex<float> >(const std::complex<float> *     addr) { EIGEN_ZVECTOR_PREFETCH(addr); }\ntemplate<> EIGEN_STRONG_INLINE void prefetch<std::complex<double> >(const std::complex<double> *   addr) { EIGEN_ZVECTOR_PREFETCH(addr); }\n\ntemplate<> EIGEN_STRONG_INLINE std::complex<double>  pfirst<Packet1cd>(const Packet1cd& a)\n{\n  std::complex<double> EIGEN_ALIGN16 res;\n  pstore<std::complex<double> >(&res, a);\n\n  return res;\n}\ntemplate<> EIGEN_STRONG_INLINE std::complex<float>  pfirst<Packet2cf>(const Packet2cf& a)\n{\n  std::complex<float> EIGEN_ALIGN16 res[2];\n  pstore<std::complex<float> >(res, a);\n\n  return res[0];\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet1cd preverse(const Packet1cd& a) { return a; }\ntemplate<> EIGEN_STRONG_INLINE Packet2cf preverse(const Packet2cf& a)\n{\n  Packet2cf res;\n  res.cd[0] = a.cd[1];\n  res.cd[1] = a.cd[0];\n  return res;\n}\n\ntemplate<> EIGEN_STRONG_INLINE std::complex<double> predux<Packet1cd>(const Packet1cd& a)\n{\n  return pfirst(a);\n}\ntemplate<> EIGEN_STRONG_INLINE std::complex<float> predux<Packet2cf>(const Packet2cf& a)\n{\n  std::complex<float> res;\n  Packet1cd b = padd<Packet1cd>(a.cd[0], a.cd[1]);\n  vec_st2f(b.v, (float*)&res);\n  return res;\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet1cd preduxp<Packet1cd>(const Packet1cd* vecs)\n{\n  return vecs[0];\n}\ntemplate<> EIGEN_STRONG_INLINE Packet2cf preduxp<Packet2cf>(const Packet2cf* vecs)\n{\n  PacketBlock<Packet2cf,2> transpose;\n  transpose.packet[0] = vecs[0];\n  transpose.packet[1] = vecs[1];\n  ptranspose(transpose);\n\n  return padd<Packet2cf>(transpose.packet[0], transpose.packet[1]);\n} \n\ntemplate<> EIGEN_STRONG_INLINE std::complex<double> predux_mul<Packet1cd>(const Packet1cd& a)\n{\n  return pfirst(a);\n}\ntemplate<> EIGEN_STRONG_INLINE std::complex<float> predux_mul<Packet2cf>(const Packet2cf& a)\n{\n  std::complex<float> res;\n  Packet1cd b = pmul<Packet1cd>(a.cd[0], a.cd[1]);\n  vec_st2f(b.v, (float*)&res);\n  return res;\n}\n\ntemplate<int Offset>\nstruct palign_impl<Offset,Packet1cd>\n{\n  static EIGEN_STRONG_INLINE void run(Packet1cd& /*first*/, const Packet1cd& /*second*/)\n  {\n    // FIXME is it sure we never have to align a Packet1cd?\n    // Even though a std::complex<double> has 16 bytes, it is not necessarily aligned on a 16 bytes boundary...\n  }\n};\n\ntemplate<int Offset>\nstruct palign_impl<Offset,Packet2cf>\n{\n  static EIGEN_STRONG_INLINE void run(Packet2cf& first, const Packet2cf& second)\n  {\n    if (Offset == 1) {\n      first.cd[0] = first.cd[1];\n      first.cd[1] = second.cd[0];\n    }\n  }\n};\n\ntemplate<> struct conj_helper<Packet1cd, Packet1cd, false,true>\n{\n  EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet1cd& x, const Packet1cd& y, const Packet1cd& c) const\n  { return padd(pmul(x,y),c); }\n\n  EIGEN_STRONG_INLINE Packet1cd pmul(const Packet1cd& a, const Packet1cd& b) const\n  {\n    return internal::pmul(a, pconj(b));\n  }\n};\n\ntemplate<> struct conj_helper<Packet1cd, Packet1cd, true,false>\n{\n  EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet1cd& x, const Packet1cd& y, const Packet1cd& c) const\n  { return padd(pmul(x,y),c); }\n\n  EIGEN_STRONG_INLINE Packet1cd pmul(const Packet1cd& a, const Packet1cd& b) const\n  {\n    return internal::pmul(pconj(a), b);\n  }\n};\n\ntemplate<> struct conj_helper<Packet1cd, Packet1cd, true,true>\n{\n  EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet1cd& x, const Packet1cd& y, const Packet1cd& c) const\n  { return padd(pmul(x,y),c); }\n\n  EIGEN_STRONG_INLINE Packet1cd pmul(const Packet1cd& a, const Packet1cd& b) const\n  {\n    return pconj(internal::pmul(a, b));\n  }\n};\n\ntemplate<> struct conj_helper<Packet2cf, Packet2cf, false,true>\n{\n  EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const\n  { return padd(pmul(x,y),c); }\n\n  EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const\n  {\n    return internal::pmul(a, pconj(b));\n  }\n};\n\ntemplate<> struct conj_helper<Packet2cf, Packet2cf, true,false>\n{\n  EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const\n  { return padd(pmul(x,y),c); }\n\n  EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const\n  {\n    return internal::pmul(pconj(a), b);\n  }\n};\n\ntemplate<> struct conj_helper<Packet2cf, Packet2cf, true,true>\n{\n  EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const\n  { return padd(pmul(x,y),c); }\n\n  EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const\n  {\n    return pconj(internal::pmul(a, b));\n  }\n};\n\nEIGEN_MAKE_CONJ_HELPER_CPLX_REAL(Packet2cf,Packet4f)\nEIGEN_MAKE_CONJ_HELPER_CPLX_REAL(Packet1cd,Packet2d)\n\ntemplate<> EIGEN_STRONG_INLINE Packet1cd pdiv<Packet1cd>(const Packet1cd& a, const Packet1cd& b)\n{\n  // TODO optimize it for AltiVec\n  Packet1cd res = conj_helper<Packet1cd,Packet1cd,false,true>().pmul(a,b);\n  Packet2d s = vec_madd(b.v, b.v, p2d_ZERO_);\n  return Packet1cd(pdiv(res.v, s + vec_perm(s, s, p16uc_REVERSE64)));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pdiv<Packet2cf>(const Packet2cf& a, const Packet2cf& b)\n{\n  // TODO optimize it for AltiVec\n  Packet2cf res;\n  res.cd[0] = pdiv<Packet1cd>(a.cd[0], b.cd[0]);\n  res.cd[1] = pdiv<Packet1cd>(a.cd[1], b.cd[1]);\n  return res;\n}\n\nEIGEN_STRONG_INLINE Packet1cd pcplxflip/*<Packet1cd>*/(const Packet1cd& x)\n{\n  return Packet1cd(preverse(Packet2d(x.v)));\n}\n\nEIGEN_STRONG_INLINE Packet2cf pcplxflip/*<Packet2cf>*/(const Packet2cf& x)\n{\n  Packet2cf res;\n  res.cd[0] = pcplxflip(x.cd[0]);\n  res.cd[1] = pcplxflip(x.cd[1]);\n  return res;\n}\n\nEIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet1cd,2>& kernel)\n{\n  Packet2d tmp = vec_perm(kernel.packet[0].v, kernel.packet[1].v, p16uc_TRANSPOSE64_HI);\n  kernel.packet[1].v = vec_perm(kernel.packet[0].v, kernel.packet[1].v, p16uc_TRANSPOSE64_LO);\n  kernel.packet[0].v = tmp;\n}\n\nEIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet2cf,2>& kernel)\n{\n  Packet1cd tmp = kernel.packet[0].cd[1];\n  kernel.packet[0].cd[1] = kernel.packet[1].cd[0];\n  kernel.packet[1].cd[0] = tmp;\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2cf pblend(const Selector<2>& ifPacket, const Packet2cf& thenPacket, const Packet2cf& elsePacket) {\n  Packet2cf result;\n  const Selector<4> ifPacket4 = { ifPacket.select[0], ifPacket.select[0], ifPacket.select[1], ifPacket.select[1] };\n  result.v = pblend<Packet4f>(ifPacket4, thenPacket.v, elsePacket.v);\n  return result;\n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_COMPLEX32_ALTIVEC_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/arch/ZVector/MathFunctions.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2007 Julien Pommier\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2016 Konstantinos Margaritis <markos@freevec.org>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n/* The sin, cos, exp, and log functions of this file come from\n * Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/\n */\n\n#ifndef EIGEN_MATH_FUNCTIONS_ALTIVEC_H\n#define EIGEN_MATH_FUNCTIONS_ALTIVEC_H\n\nnamespace Eigen {\n\nnamespace internal {\n\nstatic _EIGEN_DECLARE_CONST_Packet2d(1 , 1.0);\nstatic _EIGEN_DECLARE_CONST_Packet2d(2 , 2.0);\nstatic _EIGEN_DECLARE_CONST_Packet2d(half, 0.5);\n\nstatic _EIGEN_DECLARE_CONST_Packet2d(exp_hi,  709.437);\nstatic _EIGEN_DECLARE_CONST_Packet2d(exp_lo, -709.436139303);\n\nstatic _EIGEN_DECLARE_CONST_Packet2d(cephes_LOG2EF, 1.4426950408889634073599);\n\nstatic _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p0, 1.26177193074810590878e-4);\nstatic _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p1, 3.02994407707441961300e-2);\nstatic _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p2, 9.99999999999999999910e-1);\n\nstatic _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q0, 3.00198505138664455042e-6);\nstatic _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q1, 2.52448340349684104192e-3);\nstatic _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q2, 2.27265548208155028766e-1);\nstatic _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q3, 2.00000000000000000009e0);\n\nstatic _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C1, 0.693145751953125);\nstatic _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C2, 1.42860682030941723212e-6);\n\ntemplate<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED\nPacket2d pexp<Packet2d>(const Packet2d& _x)\n{\n  Packet2d x = _x;\n\n  Packet2d tmp, fx;\n  Packet2l emm0;\n\n  // clamp x\n  x = pmax(pmin(x, p2d_exp_hi), p2d_exp_lo);\n  /* express exp(x) as exp(g + n*log(2)) */\n  fx = pmadd(p2d_cephes_LOG2EF, x, p2d_half);\n\n  fx = vec_floor(fx);\n\n  tmp = pmul(fx, p2d_cephes_exp_C1);\n  Packet2d z = pmul(fx, p2d_cephes_exp_C2);\n  x = psub(x, tmp);\n  x = psub(x, z);\n\n  Packet2d x2 = pmul(x,x);\n\n  Packet2d px = p2d_cephes_exp_p0;\n  px = pmadd(px, x2, p2d_cephes_exp_p1);\n  px = pmadd(px, x2, p2d_cephes_exp_p2);\n  px = pmul (px, x);\n\n  Packet2d qx = p2d_cephes_exp_q0;\n  qx = pmadd(qx, x2, p2d_cephes_exp_q1);\n  qx = pmadd(qx, x2, p2d_cephes_exp_q2);\n  qx = pmadd(qx, x2, p2d_cephes_exp_q3);\n\n  x = pdiv(px,psub(qx,px));\n  x = pmadd(p2d_2,x,p2d_1);\n\n  // build 2^n\n  emm0 = vec_ctsl(fx, 0);\n\n  static const Packet2l p2l_1023 = { 1023, 1023 };\n  static const Packet2ul p2ul_52 = { 52, 52 };\n\n  emm0 = emm0 + p2l_1023;\n  emm0 = emm0 << reinterpret_cast<Packet2l>(p2ul_52);\n\n  // Altivec's max & min operators just drop silent NaNs. Check NaNs in \n  // inputs and return them unmodified.\n  Packet2ul isnumber_mask = reinterpret_cast<Packet2ul>(vec_cmpeq(_x, _x));\n  return vec_sel(_x, pmax(pmul(x, reinterpret_cast<Packet2d>(emm0)), _x),\n                 isnumber_mask);\n}\n\ntemplate<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED\nPacket4f pexp<Packet4f>(const Packet4f& x)\n{\n  Packet4f res;\n  res.v4f[0] = pexp<Packet2d>(x.v4f[0]);\n  res.v4f[1] = pexp<Packet2d>(x.v4f[1]);\n  return res;\n}\n\ntemplate<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED\nPacket2d psqrt<Packet2d>(const Packet2d& x)\n{\n  return  __builtin_s390_vfsqdb(x);\n}\n\ntemplate<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED\nPacket4f psqrt<Packet4f>(const Packet4f& x)\n{\n  Packet4f res;\n  res.v4f[0] = psqrt<Packet2d>(x.v4f[0]);\n  res.v4f[1] = psqrt<Packet2d>(x.v4f[1]);\n  return res;\n}\n\ntemplate<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED\nPacket2d prsqrt<Packet2d>(const Packet2d& x) {\n  // Unfortunately we can't use the much faster mm_rqsrt_pd since it only provides an approximation.\n  return pset1<Packet2d>(1.0) / psqrt<Packet2d>(x);\n}\n\ntemplate<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED\nPacket4f prsqrt<Packet4f>(const Packet4f& x) {\n  Packet4f res;\n  res.v4f[0] = prsqrt<Packet2d>(x.v4f[0]);\n  res.v4f[1] = prsqrt<Packet2d>(x.v4f[1]);\n  return res;\n}\n\n}  // end namespace internal\n\n}  // end namespace Eigen\n\n#endif  // EIGEN_MATH_FUNCTIONS_ALTIVEC_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/arch/ZVector/PacketMath.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Konstantinos Margaritis <markos@freevec.org>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_PACKET_MATH_ZVECTOR_H\n#define EIGEN_PACKET_MATH_ZVECTOR_H\n\n#include <stdint.h>\n\nnamespace Eigen {\n\nnamespace internal {\n\n#ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD\n#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 4\n#endif\n\n#ifndef EIGEN_HAS_SINGLE_INSTRUCTION_MADD\n#define EIGEN_HAS_SINGLE_INSTRUCTION_MADD\n#endif\n\n#ifndef EIGEN_HAS_SINGLE_INSTRUCTION_CJMADD\n#define EIGEN_HAS_SINGLE_INSTRUCTION_CJMADD\n#endif\n\n#ifndef EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS\n#define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS  16\n#endif\n\ntypedef __vector int                 Packet4i;\ntypedef __vector unsigned int        Packet4ui;\ntypedef __vector __bool int          Packet4bi;\ntypedef __vector short int           Packet8i;\ntypedef __vector unsigned char       Packet16uc;\ntypedef __vector double              Packet2d;\ntypedef __vector unsigned long long  Packet2ul;\ntypedef __vector long long           Packet2l;\n\ntypedef struct {\n\tPacket2d  v4f[2];\n} Packet4f;\n\ntypedef union {\n  int32_t   i[4];\n  uint32_t ui[4];\n  int64_t   l[2];\n  uint64_t ul[2];\n  double    d[2];\n  Packet4i  v4i;\n  Packet4ui v4ui;\n  Packet2l  v2l;\n  Packet2ul v2ul;\n  Packet2d  v2d;\n} Packet;\n\n// We don't want to write the same code all the time, but we need to reuse the constants\n// and it doesn't really work to declare them global, so we define macros instead\n\n#define _EIGEN_DECLARE_CONST_FAST_Packet4i(NAME,X) \\\n  Packet4i p4i_##NAME = reinterpret_cast<Packet4i>(vec_splat_s32(X))\n\n#define _EIGEN_DECLARE_CONST_FAST_Packet2d(NAME,X) \\\n  Packet2d p2d_##NAME = reinterpret_cast<Packet2d>(vec_splat_s64(X))\n\n#define _EIGEN_DECLARE_CONST_FAST_Packet2l(NAME,X) \\\n  Packet2l p2l_##NAME = reinterpret_cast<Packet2l>(vec_splat_s64(X))\n\n#define _EIGEN_DECLARE_CONST_Packet4i(NAME,X) \\\n  Packet4i p4i_##NAME = pset1<Packet4i>(X)\n\n#define _EIGEN_DECLARE_CONST_Packet2d(NAME,X) \\\n  Packet2d p2d_##NAME = pset1<Packet2d>(X)\n\n#define _EIGEN_DECLARE_CONST_Packet2l(NAME,X) \\\n  Packet2l p2l_##NAME = pset1<Packet2l>(X)\n\n// These constants are endian-agnostic\n//static _EIGEN_DECLARE_CONST_FAST_Packet4i(ZERO, 0); //{ 0, 0, 0, 0,}\nstatic _EIGEN_DECLARE_CONST_FAST_Packet4i(ONE, 1); //{ 1, 1, 1, 1}\n\nstatic _EIGEN_DECLARE_CONST_FAST_Packet2d(ZERO, 0);\nstatic _EIGEN_DECLARE_CONST_FAST_Packet2l(ZERO, 0);\nstatic _EIGEN_DECLARE_CONST_FAST_Packet2l(ONE, 1);\n\nstatic Packet2d p2d_ONE = { 1.0, 1.0 }; \nstatic Packet2d p2d_ZERO_ = { -0.0, -0.0 };\n\nstatic Packet4i p4i_COUNTDOWN = { 0, 1, 2, 3 };\nstatic Packet4f p4f_COUNTDOWN = { 0.0, 1.0, 2.0, 3.0 };\nstatic Packet2d p2d_COUNTDOWN = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet16uc>(p2d_ZERO), reinterpret_cast<Packet16uc>(p2d_ONE), 8));\n\nstatic Packet16uc p16uc_PSET64_HI = { 0,1,2,3, 4,5,6,7, 0,1,2,3, 4,5,6,7 };\nstatic Packet16uc p16uc_DUPLICATE32_HI = { 0,1,2,3, 0,1,2,3, 4,5,6,7, 4,5,6,7 };\n\n// Mask alignment\n#define _EIGEN_MASK_ALIGNMENT\t0xfffffffffffffff0\n\n#define _EIGEN_ALIGNED_PTR(x)\t((std::ptrdiff_t)(x) & _EIGEN_MASK_ALIGNMENT)\n\n// Handle endianness properly while loading constants\n// Define global static constants:\n\nstatic Packet16uc p16uc_FORWARD =   { 0,1,2,3, 4,5,6,7, 8,9,10,11, 12,13,14,15 };\nstatic Packet16uc p16uc_REVERSE32 = { 12,13,14,15, 8,9,10,11, 4,5,6,7, 0,1,2,3 };\nstatic Packet16uc p16uc_REVERSE64 = { 8,9,10,11, 12,13,14,15, 0,1,2,3, 4,5,6,7 };\n\nstatic Packet16uc p16uc_PSET32_WODD   = vec_sld((Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 0), (Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 2), 8);//{ 0,1,2,3, 0,1,2,3, 8,9,10,11, 8,9,10,11 };\nstatic Packet16uc p16uc_PSET32_WEVEN  = vec_sld(p16uc_DUPLICATE32_HI, (Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 3), 8);//{ 4,5,6,7, 4,5,6,7, 12,13,14,15, 12,13,14,15 };\n/*static Packet16uc p16uc_HALF64_0_16 = vec_sld((Packet16uc)p4i_ZERO, vec_splat((Packet16uc) vec_abs(p4i_MINUS16), 3), 8);      //{ 0,0,0,0, 0,0,0,0, 16,16,16,16, 16,16,16,16};\n\nstatic Packet16uc p16uc_PSET64_HI = (Packet16uc) vec_mergeh((Packet4ui)p16uc_PSET32_WODD, (Packet4ui)p16uc_PSET32_WEVEN);     //{ 0,1,2,3, 4,5,6,7, 0,1,2,3, 4,5,6,7 };*/\nstatic Packet16uc p16uc_PSET64_LO = (Packet16uc) vec_mergel((Packet4ui)p16uc_PSET32_WODD, (Packet4ui)p16uc_PSET32_WEVEN);     //{ 8,9,10,11, 12,13,14,15, 8,9,10,11, 12,13,14,15 };\n/*static Packet16uc p16uc_TRANSPOSE64_HI = vec_add(p16uc_PSET64_HI, p16uc_HALF64_0_16);                                         //{ 0,1,2,3, 4,5,6,7, 16,17,18,19, 20,21,22,23};\nstatic Packet16uc p16uc_TRANSPOSE64_LO = vec_add(p16uc_PSET64_LO, p16uc_HALF64_0_16);                                         //{ 8,9,10,11, 12,13,14,15, 24,25,26,27, 28,29,30,31};*/\nstatic Packet16uc p16uc_TRANSPOSE64_HI = { 0,1,2,3, 4,5,6,7, 16,17,18,19, 20,21,22,23};\nstatic Packet16uc p16uc_TRANSPOSE64_LO = { 8,9,10,11, 12,13,14,15, 24,25,26,27, 28,29,30,31};\n\n//static Packet16uc p16uc_COMPLEX32_REV = vec_sld(p16uc_REVERSE32, p16uc_REVERSE32, 8);                                         //{ 4,5,6,7, 0,1,2,3, 12,13,14,15, 8,9,10,11 };\n\n//static Packet16uc p16uc_COMPLEX32_REV2 = vec_sld(p16uc_FORWARD, p16uc_FORWARD, 8);                                            //{ 8,9,10,11, 12,13,14,15, 0,1,2,3, 4,5,6,7 };\n\n\n#if EIGEN_HAS_BUILTIN(__builtin_prefetch) || EIGEN_COMP_GNUC\n  #define EIGEN_ZVECTOR_PREFETCH(ADDR) __builtin_prefetch(ADDR);\n#else\n  #define EIGEN_ZVECTOR_PREFETCH(ADDR) asm( \"   pfd [%[addr]]\\n\" :: [addr] \"r\" (ADDR) : \"cc\" );\n#endif\n\ntemplate<> struct packet_traits<int>    : default_packet_traits\n{\n  typedef Packet4i type;\n  typedef Packet4i half;\n  enum {\n    Vectorizable = 1,\n    AlignedOnScalar = 1,\n    size = 4,\n    HasHalfPacket = 0,\n\n    HasAdd  = 1,\n    HasSub  = 1,\n    HasMul  = 1,\n    HasDiv  = 1,\n    HasBlend = 1\n  };\n};\n\ntemplate<> struct packet_traits<float> : default_packet_traits\n{\n  typedef Packet4f type;\n  typedef Packet4f half;\n  enum {\n    Vectorizable = 1,\n    AlignedOnScalar = 1,\n    size=4,\n    HasHalfPacket = 0,\n\n    HasAdd  = 1,\n    HasSub  = 1,\n    HasMul  = 1,\n    HasDiv  = 1,\n    HasMin  = 1,\n    HasMax  = 1,\n    HasAbs  = 1,\n    HasSin  = 0,\n    HasCos  = 0,\n    HasLog  = 0,\n    HasExp  = 1,\n    HasSqrt = 1,\n    HasRsqrt = 1,\n    HasRound = 1,\n    HasFloor = 1,\n    HasCeil = 1,\n    HasNegate = 1,\n    HasBlend = 1\n  };\n};\n\ntemplate<> struct packet_traits<double> : default_packet_traits\n{\n  typedef Packet2d type;\n  typedef Packet2d half;\n  enum {\n    Vectorizable = 1,\n    AlignedOnScalar = 1,\n    size=2,\n    HasHalfPacket = 1,\n\n    HasAdd  = 1,\n    HasSub  = 1,\n    HasMul  = 1,\n    HasDiv  = 1,\n    HasMin  = 1,\n    HasMax  = 1,\n    HasAbs  = 1,\n    HasSin  = 0,\n    HasCos  = 0,\n    HasLog  = 0,\n    HasExp  = 1,\n    HasSqrt = 1,\n    HasRsqrt = 1,\n    HasRound = 1,\n    HasFloor = 1,\n    HasCeil = 1,\n    HasNegate = 1,\n    HasBlend = 1\n  };\n};\n\ntemplate<> struct unpacket_traits<Packet4i> { typedef int    type; enum {size=4, alignment=Aligned16}; typedef Packet4i half; };\ntemplate<> struct unpacket_traits<Packet4f> { typedef float  type; enum {size=4, alignment=Aligned16}; typedef Packet4f half; };\ntemplate<> struct unpacket_traits<Packet2d> { typedef double type; enum {size=2, alignment=Aligned16}; typedef Packet2d half; };\n\n/* Forward declaration */\nEIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet4f,4>& kernel);\n \ninline std::ostream & operator <<(std::ostream & s, const Packet4i & v)\n{\n  Packet vt;\n  vt.v4i = v;\n  s << vt.i[0] << \", \" << vt.i[1] << \", \" << vt.i[2] << \", \" << vt.i[3];\n  return s;\n}\n\ninline std::ostream & operator <<(std::ostream & s, const Packet4ui & v)\n{\n  Packet vt;\n  vt.v4ui = v;\n  s << vt.ui[0] << \", \" << vt.ui[1] << \", \" << vt.ui[2] << \", \" << vt.ui[3];\n  return s;\n}\n\ninline std::ostream & operator <<(std::ostream & s, const Packet2l & v)\n{\n  Packet vt;\n  vt.v2l = v;\n  s << vt.l[0] << \", \" << vt.l[1];\n  return s;\n}\n\ninline std::ostream & operator <<(std::ostream & s, const Packet2ul & v)\n{\n  Packet vt;\n  vt.v2ul = v;\n  s << vt.ul[0] << \", \" << vt.ul[1] ;\n  return s;\n}\n\ninline std::ostream & operator <<(std::ostream & s, const Packet2d & v)\n{\n  Packet vt;\n  vt.v2d = v;\n  s << vt.d[0] << \", \" << vt.d[1];\n  return s;\n}\n\n/* Helper function to simulate a vec_splat_packet4f\n */\ntemplate<int element> EIGEN_STRONG_INLINE Packet4f vec_splat_packet4f(const Packet4f&   from)\n{\n  Packet4f splat;\n  switch (element) {\n  case 0:\n    splat.v4f[0] = vec_splat(from.v4f[0], 0);\n    splat.v4f[1] = splat.v4f[0];\n    break;\n  case 1:\n    splat.v4f[0] = vec_splat(from.v4f[0], 1);\n    splat.v4f[1] = splat.v4f[0];\n    break;\n  case 2:\n    splat.v4f[0] = vec_splat(from.v4f[1], 0);\n    splat.v4f[1] = splat.v4f[0];\n    break;\n  case 3:\n    splat.v4f[0] = vec_splat(from.v4f[1], 1);\n    splat.v4f[1] = splat.v4f[0];\n    break;\n  }\n  return splat;\n}\n\ntemplate<int Offset>\nstruct palign_impl<Offset,Packet4i>\n{\n  static EIGEN_STRONG_INLINE void run(Packet4i& first, const Packet4i& second)\n  {\n    switch (Offset % 4) {\n    case 1:\n      first = vec_sld(first, second, 4); break;\n    case 2:\n      first = vec_sld(first, second, 8); break;\n    case 3:\n      first = vec_sld(first, second, 12); break;\n    }\n  }\n};\n\n/* This is a tricky one, we have to translate float alignment to vector elements of sizeof double\n */\ntemplate<int Offset>\nstruct palign_impl<Offset,Packet4f>\n{\n  static EIGEN_STRONG_INLINE void run(Packet4f& first, const Packet4f& second)\n  {\n    switch (Offset % 4) {\n    case 1:\n      first.v4f[0] = vec_sld(first.v4f[0], first.v4f[1], 8);\n      first.v4f[1] = vec_sld(first.v4f[1], second.v4f[0], 8);\n      break;\n    case 2:\n      first.v4f[0] = first.v4f[1];\n      first.v4f[1] = second.v4f[0];\n      break;\n    case 3:\n      first.v4f[0] = vec_sld(first.v4f[1],  second.v4f[0], 8);\n      first.v4f[1] = vec_sld(second.v4f[0], second.v4f[1], 8);\n      break;\n    }\n  }\n};\n\n\ntemplate<int Offset>\nstruct palign_impl<Offset,Packet2d>\n{\n  static EIGEN_STRONG_INLINE void run(Packet2d& first, const Packet2d& second)\n  {\n    if (Offset == 1)\n      first = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4i>(first), reinterpret_cast<Packet4i>(second), 8));\n  }\n};\n\ntemplate<> EIGEN_STRONG_INLINE Packet4i pload<Packet4i>(const int*     from)\n{\n  // FIXME: No intrinsic yet\n  EIGEN_DEBUG_ALIGNED_LOAD\n  Packet *vfrom;\n  vfrom = (Packet *) from;\n  return vfrom->v4i;\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pload<Packet4f>(const float*   from)\n{\n  // FIXME: No intrinsic yet\n  EIGEN_DEBUG_ALIGNED_LOAD\n  Packet4f vfrom;\n  vfrom.v4f[0] = vec_ld2f(&from[0]);\n  vfrom.v4f[1] = vec_ld2f(&from[2]);\n  return vfrom;\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d pload<Packet2d>(const double* from)\n{\n  // FIXME: No intrinsic yet\n  EIGEN_DEBUG_ALIGNED_LOAD\n  Packet *vfrom;\n  vfrom = (Packet *) from;\n  return vfrom->v2d;\n}\n\ntemplate<> EIGEN_STRONG_INLINE void pstore<int>(int*       to, const Packet4i& from)\n{\n  // FIXME: No intrinsic yet\n  EIGEN_DEBUG_ALIGNED_STORE\n  Packet *vto;\n  vto = (Packet *) to;\n  vto->v4i = from;\n}\n\ntemplate<> EIGEN_STRONG_INLINE void pstore<float>(float*   to, const Packet4f& from)\n{\n  // FIXME: No intrinsic yet\n  EIGEN_DEBUG_ALIGNED_STORE\n  vec_st2f(from.v4f[0], &to[0]);\n  vec_st2f(from.v4f[1], &to[2]);\n}\n\n\ntemplate<> EIGEN_STRONG_INLINE void pstore<double>(double*   to, const Packet2d& from)\n{\n  // FIXME: No intrinsic yet\n  EIGEN_DEBUG_ALIGNED_STORE\n  Packet *vto;\n  vto = (Packet *) to;\n  vto->v2d = from;\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int&    from)\n{\n  return vec_splats(from);\n}\ntemplate<> EIGEN_STRONG_INLINE Packet2d pset1<Packet2d>(const double& from) {\n  return vec_splats(from);\n}\ntemplate<> EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float&    from)\n{\n  Packet4f to;\n  to.v4f[0] = pset1<Packet2d>(static_cast<const double&>(from));\n  to.v4f[1] = to.v4f[0];\n  return to;\n}\n\ntemplate<> EIGEN_STRONG_INLINE void\npbroadcast4<Packet4i>(const int *a,\n                      Packet4i& a0, Packet4i& a1, Packet4i& a2, Packet4i& a3)\n{\n  a3 = pload<Packet4i>(a);\n  a0 = vec_splat(a3, 0);\n  a1 = vec_splat(a3, 1);\n  a2 = vec_splat(a3, 2);\n  a3 = vec_splat(a3, 3);\n}\n\ntemplate<> EIGEN_STRONG_INLINE void\npbroadcast4<Packet4f>(const float *a,\n                      Packet4f& a0, Packet4f& a1, Packet4f& a2, Packet4f& a3)\n{\n  a3 = pload<Packet4f>(a);\n  a0 = vec_splat_packet4f<0>(a3);\n  a1 = vec_splat_packet4f<1>(a3);\n  a2 = vec_splat_packet4f<2>(a3);\n  a3 = vec_splat_packet4f<3>(a3);\n}\n\ntemplate<> EIGEN_STRONG_INLINE void\npbroadcast4<Packet2d>(const double *a,\n                      Packet2d& a0, Packet2d& a1, Packet2d& a2, Packet2d& a3)\n{\n  a1 = pload<Packet2d>(a);\n  a0 = vec_splat(a1, 0);\n  a1 = vec_splat(a1, 1);\n  a3 = pload<Packet2d>(a+2);\n  a2 = vec_splat(a3, 0);\n  a3 = vec_splat(a3, 1);\n}\n\ntemplate<> EIGEN_DEVICE_FUNC inline Packet4i pgather<int, Packet4i>(const int* from, Index stride)\n{\n  int EIGEN_ALIGN16 ai[4];\n  ai[0] = from[0*stride];\n  ai[1] = from[1*stride];\n  ai[2] = from[2*stride];\n  ai[3] = from[3*stride];\n return pload<Packet4i>(ai);\n}\n\ntemplate<> EIGEN_DEVICE_FUNC inline Packet4f pgather<float, Packet4f>(const float* from, Index stride)\n{\n  float EIGEN_ALIGN16 ai[4];\n  ai[0] = from[0*stride];\n  ai[1] = from[1*stride];\n  ai[2] = from[2*stride];\n  ai[3] = from[3*stride];\n return pload<Packet4f>(ai);\n}\n\ntemplate<> EIGEN_DEVICE_FUNC inline Packet2d pgather<double, Packet2d>(const double* from, Index stride)\n{\n  double EIGEN_ALIGN16 af[2];\n  af[0] = from[0*stride];\n  af[1] = from[1*stride];\n return pload<Packet2d>(af);\n}\n\ntemplate<> EIGEN_DEVICE_FUNC inline void pscatter<int, Packet4i>(int* to, const Packet4i& from, Index stride)\n{\n  int EIGEN_ALIGN16 ai[4];\n  pstore<int>((int *)ai, from);\n  to[0*stride] = ai[0];\n  to[1*stride] = ai[1];\n  to[2*stride] = ai[2];\n  to[3*stride] = ai[3];\n}\n\ntemplate<> EIGEN_DEVICE_FUNC inline void pscatter<float, Packet4f>(float* to, const Packet4f& from, Index stride)\n{\n  float EIGEN_ALIGN16 ai[4];\n  pstore<float>((float *)ai, from);\n  to[0*stride] = ai[0];\n  to[1*stride] = ai[1];\n  to[2*stride] = ai[2];\n  to[3*stride] = ai[3];\n}\n\ntemplate<> EIGEN_DEVICE_FUNC inline void pscatter<double, Packet2d>(double* to, const Packet2d& from, Index stride)\n{\n  double EIGEN_ALIGN16 af[2];\n  pstore<double>(af, from);\n  to[0*stride] = af[0];\n  to[1*stride] = af[1];\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4i padd<Packet4i>(const Packet4i& a, const Packet4i& b) { return (a + b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4f padd<Packet4f>(const Packet4f& a, const Packet4f& b)\n{\n  Packet4f c;\n  c.v4f[0] = a.v4f[0] + b.v4f[0];\n  c.v4f[1] = a.v4f[1] + b.v4f[1];\n  return c;\n}\ntemplate<> EIGEN_STRONG_INLINE Packet2d padd<Packet2d>(const Packet2d& a, const Packet2d& b) { return (a + b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4i psub<Packet4i>(const Packet4i& a, const Packet4i& b) { return (a - b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4f psub<Packet4f>(const Packet4f& a, const Packet4f& b)\n{\n  Packet4f c;\n  c.v4f[0] = a.v4f[0] - b.v4f[0];\n  c.v4f[1] = a.v4f[1] - b.v4f[1];\n  return c;\n}\ntemplate<> EIGEN_STRONG_INLINE Packet2d psub<Packet2d>(const Packet2d& a, const Packet2d& b) { return (a - b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4i pmul<Packet4i>(const Packet4i& a, const Packet4i& b) { return (a * b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4f pmul<Packet4f>(const Packet4f& a, const Packet4f& b)\n{\n  Packet4f c;\n  c.v4f[0] = a.v4f[0] * b.v4f[0];\n  c.v4f[1] = a.v4f[1] * b.v4f[1];\n  return c;\n}\ntemplate<> EIGEN_STRONG_INLINE Packet2d pmul<Packet2d>(const Packet2d& a, const Packet2d& b) { return (a * b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4i pdiv<Packet4i>(const Packet4i& a, const Packet4i& b) { return (a / b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4f pdiv<Packet4f>(const Packet4f& a, const Packet4f& b)\n{\n  Packet4f c;\n  c.v4f[0] = a.v4f[0] / b.v4f[0];\n  c.v4f[1] = a.v4f[1] / b.v4f[1];\n  return c;\n}\ntemplate<> EIGEN_STRONG_INLINE Packet2d pdiv<Packet2d>(const Packet2d& a, const Packet2d& b) { return (a / b); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4i pnegate(const Packet4i& a) { return (-a); }\ntemplate<> EIGEN_STRONG_INLINE Packet4f pnegate(const Packet4f& a)\n{\n  Packet4f c;\n  c.v4f[0] = -a.v4f[0];\n  c.v4f[1] = -a.v4f[1];\n  return c;\n}\ntemplate<> EIGEN_STRONG_INLINE Packet2d pnegate(const Packet2d& a) { return (-a); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4i pconj(const Packet4i& a) { return a; }\ntemplate<> EIGEN_STRONG_INLINE Packet4f pconj(const Packet4f& a) { return a; }\ntemplate<> EIGEN_STRONG_INLINE Packet2d pconj(const Packet2d& a) { return a; }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4i pmadd(const Packet4i& a, const Packet4i& b, const Packet4i& c) { return padd<Packet4i>(pmul<Packet4i>(a, b), c); }\ntemplate<> EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c)\n{\n  Packet4f res;\n  res.v4f[0] = vec_madd(a.v4f[0], b.v4f[0], c.v4f[0]);\n  res.v4f[1] = vec_madd(a.v4f[1], b.v4f[1], c.v4f[1]);\n  return res;\n}\ntemplate<> EIGEN_STRONG_INLINE Packet2d pmadd(const Packet2d& a, const Packet2d& b, const Packet2d& c) { return vec_madd(a, b, c); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4i plset<Packet4i>(const int& a)    { return padd<Packet4i>(pset1<Packet4i>(a), p4i_COUNTDOWN); }\ntemplate<> EIGEN_STRONG_INLINE Packet4f plset<Packet4f>(const float& a)  { return padd<Packet4f>(pset1<Packet4f>(a), p4f_COUNTDOWN); }\ntemplate<> EIGEN_STRONG_INLINE Packet2d plset<Packet2d>(const double& a) { return padd<Packet2d>(pset1<Packet2d>(a), p2d_COUNTDOWN); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4i pmin<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_min(a, b); }\ntemplate<> EIGEN_STRONG_INLINE Packet2d pmin<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_min(a, b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4f pmin<Packet4f>(const Packet4f& a, const Packet4f& b)\n{\n  Packet4f res;\n  res.v4f[0] = pmin(a.v4f[0], b.v4f[0]);\n  res.v4f[1] = pmin(a.v4f[1], b.v4f[1]);\n  return res;\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4i pmax<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_max(a, b); }\ntemplate<> EIGEN_STRONG_INLINE Packet2d pmax<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_max(a, b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4f pmax<Packet4f>(const Packet4f& a, const Packet4f& b)\n{\n  Packet4f res;\n  res.v4f[0] = pmax(a.v4f[0], b.v4f[0]);\n  res.v4f[1] = pmax(a.v4f[1], b.v4f[1]);\n  return res;\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4i pand<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_and(a, b); }\ntemplate<> EIGEN_STRONG_INLINE Packet2d pand<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_and(a, b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4f pand<Packet4f>(const Packet4f& a, const Packet4f& b)\n{\n  Packet4f res;\n  res.v4f[0] = pand(a.v4f[0], b.v4f[0]);\n  res.v4f[1] = pand(a.v4f[1], b.v4f[1]);\n  return res;\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4i por<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_or(a, b); }\ntemplate<> EIGEN_STRONG_INLINE Packet2d por<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_or(a, b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4f por<Packet4f>(const Packet4f& a, const Packet4f& b)\n{\n  Packet4f res;\n  res.v4f[0] = pand(a.v4f[0], b.v4f[0]);\n  res.v4f[1] = pand(a.v4f[1], b.v4f[1]);\n  return res;\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4i pxor<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_xor(a, b); }\ntemplate<> EIGEN_STRONG_INLINE Packet2d pxor<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_xor(a, b); }\ntemplate<> EIGEN_STRONG_INLINE Packet4f pxor<Packet4f>(const Packet4f& a, const Packet4f& b)\n{\n  Packet4f res;\n  res.v4f[0] = pand(a.v4f[0], b.v4f[0]);\n  res.v4f[1] = pand(a.v4f[1], b.v4f[1]);\n  return res;\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4i pandnot<Packet4i>(const Packet4i& a, const Packet4i& b) { return pand<Packet4i>(a, vec_nor(b, b)); }\ntemplate<> EIGEN_STRONG_INLINE Packet2d pandnot<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_and(a, vec_nor(b, b)); }\ntemplate<> EIGEN_STRONG_INLINE Packet4f pandnot<Packet4f>(const Packet4f& a, const Packet4f& b)\n{\n  Packet4f res;\n  res.v4f[0] = pandnot(a.v4f[0], b.v4f[0]);\n  res.v4f[1] = pandnot(a.v4f[1], b.v4f[1]);\n  return res;\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pround<Packet4f>(const Packet4f& a)\n{\n  Packet4f res;\n  res.v4f[0] = vec_round(a.v4f[0]);\n  res.v4f[1] = vec_round(a.v4f[1]);\n  return res;\n}\ntemplate<> EIGEN_STRONG_INLINE Packet2d pround<Packet2d>(const Packet2d& a) { return vec_round(a); }\ntemplate<> EIGEN_STRONG_INLINE Packet4f pceil<Packet4f>(const  Packet4f& a)\n{\n  Packet4f res;\n  res.v4f[0] = vec_ceil(a.v4f[0]);\n  res.v4f[1] = vec_ceil(a.v4f[1]);\n  return res;\n}\ntemplate<> EIGEN_STRONG_INLINE Packet2d pceil<Packet2d>(const  Packet2d& a) { return vec_ceil(a); }\ntemplate<> EIGEN_STRONG_INLINE Packet4f pfloor<Packet4f>(const Packet4f& a)\n{\n  Packet4f res;\n  res.v4f[0] = vec_floor(a.v4f[0]);\n  res.v4f[1] = vec_floor(a.v4f[1]);\n  return res;\n}\ntemplate<> EIGEN_STRONG_INLINE Packet2d pfloor<Packet2d>(const Packet2d& a) { return vec_floor(a); }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int*       from) { return pload<Packet4i>(from); }\ntemplate<> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float*     from) { return pload<Packet4f>(from); }\ntemplate<> EIGEN_STRONG_INLINE Packet2d ploadu<Packet2d>(const double*    from) { return pload<Packet2d>(from); }\n\n\ntemplate<> EIGEN_STRONG_INLINE Packet4i ploaddup<Packet4i>(const int*     from)\n{\n  Packet4i p = pload<Packet4i>(from);\n  return vec_perm(p, p, p16uc_DUPLICATE32_HI);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f ploaddup<Packet4f>(const float*    from)\n{\n  Packet4f p = pload<Packet4f>(from);\n  p.v4f[1] = vec_splat(p.v4f[0], 1);\n  p.v4f[0] = vec_splat(p.v4f[0], 0);\n  return p;\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d ploaddup<Packet2d>(const double*   from)\n{\n  Packet2d p = pload<Packet2d>(from);\n  return vec_perm(p, p, p16uc_PSET64_HI);\n}\n\ntemplate<> EIGEN_STRONG_INLINE void pstoreu<int>(int*        to, const Packet4i& from) { pstore<int>(to, from); }\ntemplate<> EIGEN_STRONG_INLINE void pstoreu<float>(float*    to, const Packet4f& from) { pstore<float>(to, from); }\ntemplate<> EIGEN_STRONG_INLINE void pstoreu<double>(double*  to, const Packet2d& from) { pstore<double>(to, from); }\n\ntemplate<> EIGEN_STRONG_INLINE void prefetch<int>(const int*       addr) { EIGEN_ZVECTOR_PREFETCH(addr); }\ntemplate<> EIGEN_STRONG_INLINE void prefetch<float>(const float*   addr) { EIGEN_ZVECTOR_PREFETCH(addr); }\ntemplate<> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { EIGEN_ZVECTOR_PREFETCH(addr); }\n\ntemplate<> EIGEN_STRONG_INLINE int    pfirst<Packet4i>(const Packet4i& a) { int    EIGEN_ALIGN16 x[4]; pstore(x, a); return x[0]; }\ntemplate<> EIGEN_STRONG_INLINE float  pfirst<Packet4f>(const Packet4f& a) { float  EIGEN_ALIGN16 x[2]; vec_st2f(a.v4f[0], &x[0]); return x[0]; }\ntemplate<> EIGEN_STRONG_INLINE double pfirst<Packet2d>(const Packet2d& a) { double EIGEN_ALIGN16 x[2]; pstore(x, a); return x[0]; }\n\ntemplate<> EIGEN_STRONG_INLINE Packet4i preverse(const Packet4i& a)\n{\n  return reinterpret_cast<Packet4i>(vec_perm(reinterpret_cast<Packet16uc>(a), reinterpret_cast<Packet16uc>(a), p16uc_REVERSE32));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d preverse(const Packet2d& a)\n{\n  return reinterpret_cast<Packet2d>(vec_perm(reinterpret_cast<Packet16uc>(a), reinterpret_cast<Packet16uc>(a), p16uc_REVERSE64));\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f preverse(const Packet4f& a)\n{\n  Packet4f rev;\n  rev.v4f[0] = preverse<Packet2d>(a.v4f[1]);\n  rev.v4f[1] = preverse<Packet2d>(a.v4f[0]);\n  return rev;\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4i pabs<Packet4i>(const Packet4i& a) { return vec_abs(a); }\ntemplate<> EIGEN_STRONG_INLINE Packet2d pabs<Packet2d>(const Packet2d& a) { return vec_abs(a); }\ntemplate<> EIGEN_STRONG_INLINE Packet4f pabs<Packet4f>(const Packet4f& a)\n{\n  Packet4f res;\n  res.v4f[0] = pabs(a.v4f[0]);\n  res.v4f[1] = pabs(a.v4f[1]);\n  return res;\n}\n\ntemplate<> EIGEN_STRONG_INLINE int predux<Packet4i>(const Packet4i& a)\n{\n  Packet4i b, sum;\n  b   = vec_sld(a, a, 8);\n  sum = padd<Packet4i>(a, b);\n  b   = vec_sld(sum, sum, 4);\n  sum = padd<Packet4i>(sum, b);\n  return pfirst(sum);\n}\n\ntemplate<> EIGEN_STRONG_INLINE double predux<Packet2d>(const Packet2d& a)\n{\n  Packet2d b, sum;\n  b   = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4i>(a), reinterpret_cast<Packet4i>(a), 8));\n  sum = padd<Packet2d>(a, b);\n  return pfirst(sum);\n}\ntemplate<> EIGEN_STRONG_INLINE float predux<Packet4f>(const Packet4f& a)\n{\n  Packet2d sum;\n  sum = padd<Packet2d>(a.v4f[0], a.v4f[1]);\n  double first = predux<Packet2d>(sum);\n  return static_cast<float>(first);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4i preduxp<Packet4i>(const Packet4i* vecs)\n{\n  Packet4i v[4], sum[4];\n\n  // It's easier and faster to transpose then add as columns\n  // Check: http://www.freevec.org/function/matrix_4x4_transpose_floats for explanation\n  // Do the transpose, first set of moves\n  v[0] = vec_mergeh(vecs[0], vecs[2]);\n  v[1] = vec_mergel(vecs[0], vecs[2]);\n  v[2] = vec_mergeh(vecs[1], vecs[3]);\n  v[3] = vec_mergel(vecs[1], vecs[3]);\n  // Get the resulting vectors\n  sum[0] = vec_mergeh(v[0], v[2]);\n  sum[1] = vec_mergel(v[0], v[2]);\n  sum[2] = vec_mergeh(v[1], v[3]);\n  sum[3] = vec_mergel(v[1], v[3]);\n\n  // Now do the summation:\n  // Lines 0+1\n  sum[0] = padd<Packet4i>(sum[0], sum[1]);\n  // Lines 2+3\n  sum[1] = padd<Packet4i>(sum[2], sum[3]);\n  // Add the results\n  sum[0] = padd<Packet4i>(sum[0], sum[1]);\n\n  return sum[0];\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d preduxp<Packet2d>(const Packet2d* vecs)\n{\n  Packet2d v[2], sum;\n  v[0] = padd<Packet2d>(vecs[0], reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(vecs[0]), reinterpret_cast<Packet4ui>(vecs[0]), 8)));\n  v[1] = padd<Packet2d>(vecs[1], reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(vecs[1]), reinterpret_cast<Packet4ui>(vecs[1]), 8)));\n \n  sum = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(v[0]), reinterpret_cast<Packet4ui>(v[1]), 8));\n\n  return sum;\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f preduxp<Packet4f>(const Packet4f* vecs)\n{\n  PacketBlock<Packet4f,4> transpose;\n  transpose.packet[0] = vecs[0];\n  transpose.packet[1] = vecs[1];\n  transpose.packet[2] = vecs[2];\n  transpose.packet[3] = vecs[3];\n  ptranspose(transpose);\n\n  Packet4f sum = padd(transpose.packet[0], transpose.packet[1]);\n  sum = padd(sum, transpose.packet[2]);\n  sum = padd(sum, transpose.packet[3]);\n  return sum;\n}\n\n// Other reduction functions:\n// mul\ntemplate<> EIGEN_STRONG_INLINE int predux_mul<Packet4i>(const Packet4i& a)\n{\n  EIGEN_ALIGN16 int aux[4];\n  pstore(aux, a);\n  return aux[0] * aux[1] * aux[2] * aux[3];\n}\n\ntemplate<> EIGEN_STRONG_INLINE double predux_mul<Packet2d>(const Packet2d& a)\n{\n  return pfirst(pmul(a, reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4i>(a), reinterpret_cast<Packet4i>(a), 8))));\n}\n\ntemplate<> EIGEN_STRONG_INLINE float predux_mul<Packet4f>(const Packet4f& a)\n{\n  // Return predux_mul<Packet2d> of the subvectors product\n  return static_cast<float>(pfirst(predux_mul(pmul(a.v4f[0], a.v4f[1]))));\n}\n\n// min\ntemplate<> EIGEN_STRONG_INLINE int predux_min<Packet4i>(const Packet4i& a)\n{\n  Packet4i b, res;\n  b   = pmin<Packet4i>(a, vec_sld(a, a, 8));\n  res = pmin<Packet4i>(b, vec_sld(b, b, 4));\n  return pfirst(res);\n}\n\ntemplate<> EIGEN_STRONG_INLINE double predux_min<Packet2d>(const Packet2d& a)\n{\n  return pfirst(pmin<Packet2d>(a, reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4i>(a), reinterpret_cast<Packet4i>(a), 8))));\n}\n\ntemplate<> EIGEN_STRONG_INLINE float predux_min<Packet4f>(const Packet4f& a)\n{\n  Packet2d b, res;\n  b   = pmin<Packet2d>(a.v4f[0], a.v4f[1]);\n  res = pmin<Packet2d>(b, reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4i>(b), reinterpret_cast<Packet4i>(b), 8)));\n  return static_cast<float>(pfirst(res));\n}\n\n// max\ntemplate<> EIGEN_STRONG_INLINE int predux_max<Packet4i>(const Packet4i& a)\n{\n  Packet4i b, res;\n  b = pmax<Packet4i>(a, vec_sld(a, a, 8));\n  res = pmax<Packet4i>(b, vec_sld(b, b, 4));\n  return pfirst(res);\n}\n\n// max\ntemplate<> EIGEN_STRONG_INLINE double predux_max<Packet2d>(const Packet2d& a)\n{\n  return pfirst(pmax<Packet2d>(a, reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4i>(a), reinterpret_cast<Packet4i>(a), 8))));\n}\n\ntemplate<> EIGEN_STRONG_INLINE float predux_max<Packet4f>(const Packet4f& a)\n{\n  Packet2d b, res;\n  b   = pmax<Packet2d>(a.v4f[0], a.v4f[1]);\n  res = pmax<Packet2d>(b, reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4i>(b), reinterpret_cast<Packet4i>(b), 8)));\n  return static_cast<float>(pfirst(res));\n}\n\nEIGEN_DEVICE_FUNC inline void\nptranspose(PacketBlock<Packet4i,4>& kernel) {\n  Packet4i t0 = vec_mergeh(kernel.packet[0], kernel.packet[2]);\n  Packet4i t1 = vec_mergel(kernel.packet[0], kernel.packet[2]);\n  Packet4i t2 = vec_mergeh(kernel.packet[1], kernel.packet[3]);\n  Packet4i t3 = vec_mergel(kernel.packet[1], kernel.packet[3]);\n  kernel.packet[0] = vec_mergeh(t0, t2);\n  kernel.packet[1] = vec_mergel(t0, t2);\n  kernel.packet[2] = vec_mergeh(t1, t3);\n  kernel.packet[3] = vec_mergel(t1, t3);\n}\n\nEIGEN_DEVICE_FUNC inline void\nptranspose(PacketBlock<Packet2d,2>& kernel) {\n  Packet2d t0 = vec_perm(kernel.packet[0], kernel.packet[1], p16uc_TRANSPOSE64_HI);\n  Packet2d t1 = vec_perm(kernel.packet[0], kernel.packet[1], p16uc_TRANSPOSE64_LO);\n  kernel.packet[0] = t0;\n  kernel.packet[1] = t1;\n}\n\n/* Split the Packet4f PacketBlock into 4 Packet2d PacketBlocks and transpose each one\n */\nEIGEN_DEVICE_FUNC inline void\nptranspose(PacketBlock<Packet4f,4>& kernel) {\n  PacketBlock<Packet2d,2> t0,t1,t2,t3;\n  // copy top-left 2x2 Packet2d block\n  t0.packet[0] = kernel.packet[0].v4f[0];\n  t0.packet[1] = kernel.packet[1].v4f[0];\n\n  // copy top-right 2x2 Packet2d block\n  t1.packet[0] = kernel.packet[0].v4f[1];\n  t1.packet[1] = kernel.packet[1].v4f[1];\n\n  // copy bottom-left 2x2 Packet2d block\n  t2.packet[0] = kernel.packet[2].v4f[0];\n  t2.packet[1] = kernel.packet[3].v4f[0];\n\n  // copy bottom-right 2x2 Packet2d block\n  t3.packet[0] = kernel.packet[2].v4f[1];\n  t3.packet[1] = kernel.packet[3].v4f[1];\n\n  // Transpose all 2x2 blocks\n  ptranspose(t0);\n  ptranspose(t1);\n  ptranspose(t2);\n  ptranspose(t3);\n\n  // Copy back transposed blocks, but exchange t1 and t2 due to transposition\n  kernel.packet[0].v4f[0] = t0.packet[0];\n  kernel.packet[0].v4f[1] = t2.packet[0];\n  kernel.packet[1].v4f[0] = t0.packet[1];\n  kernel.packet[1].v4f[1] = t2.packet[1];\n  kernel.packet[2].v4f[0] = t1.packet[0];\n  kernel.packet[2].v4f[1] = t3.packet[0];\n  kernel.packet[3].v4f[0] = t1.packet[1];\n  kernel.packet[3].v4f[1] = t3.packet[1];\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4i pblend(const Selector<4>& ifPacket, const Packet4i& thenPacket, const Packet4i& elsePacket) {\n  Packet4ui select = { ifPacket.select[0], ifPacket.select[1], ifPacket.select[2], ifPacket.select[3] };\n  Packet4ui mask = vec_cmpeq(select, reinterpret_cast<Packet4ui>(p4i_ONE));\n  return vec_sel(elsePacket, thenPacket, mask);\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet4f pblend(const Selector<4>& ifPacket, const Packet4f& thenPacket, const Packet4f& elsePacket) {\n  Packet2ul select_hi = { ifPacket.select[0], ifPacket.select[1] };\n  Packet2ul select_lo = { ifPacket.select[2], ifPacket.select[3] };\n  Packet2ul mask_hi = vec_cmpeq(select_hi, reinterpret_cast<Packet2ul>(p2l_ONE));\n  Packet2ul mask_lo = vec_cmpeq(select_lo, reinterpret_cast<Packet2ul>(p2l_ONE));\n  Packet4f result;\n  result.v4f[0] = vec_sel(elsePacket.v4f[0], thenPacket.v4f[0], mask_hi);\n  result.v4f[1] = vec_sel(elsePacket.v4f[1], thenPacket.v4f[1], mask_lo);\n  return result;\n}\n\ntemplate<> EIGEN_STRONG_INLINE Packet2d pblend(const Selector<2>& ifPacket, const Packet2d& thenPacket, const Packet2d& elsePacket) {\n  Packet2ul select = { ifPacket.select[0], ifPacket.select[1] };\n  Packet2ul mask = vec_cmpeq(select, reinterpret_cast<Packet2ul>(p2l_ONE));\n  return vec_sel(elsePacket, thenPacket, mask);\n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_PACKET_MATH_ZVECTOR_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/functors/AssignmentFunctors.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_ASSIGNMENT_FUNCTORS_H\n#define EIGEN_ASSIGNMENT_FUNCTORS_H\n\nnamespace Eigen {\n\nnamespace internal {\n  \n/** \\internal\n  * \\brief Template functor for scalar/packet assignment\n  *\n  */\ntemplate<typename DstScalar,typename SrcScalar> struct assign_op {\n\n  EIGEN_EMPTY_STRUCT_CTOR(assign_op)\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignCoeff(DstScalar& a, const SrcScalar& b) const { a = b; }\n  \n  template<int Alignment, typename Packet>\n  EIGEN_STRONG_INLINE void assignPacket(DstScalar* a, const Packet& b) const\n  { internal::pstoret<DstScalar,Packet,Alignment>(a,b); }\n};\n\n// Empty overload for void type (used by PermutationMatrix)\ntemplate<typename DstScalar> struct assign_op<DstScalar,void> {};\n\ntemplate<typename DstScalar,typename SrcScalar>\nstruct functor_traits<assign_op<DstScalar,SrcScalar> > {\n  enum {\n    Cost = NumTraits<DstScalar>::ReadCost,\n    PacketAccess = is_same<DstScalar,SrcScalar>::value && packet_traits<DstScalar>::Vectorizable && packet_traits<SrcScalar>::Vectorizable\n  };\n};\n\n/** \\internal\n  * \\brief Template functor for scalar/packet assignment with addition\n  *\n  */\ntemplate<typename DstScalar,typename SrcScalar> struct add_assign_op {\n\n  EIGEN_EMPTY_STRUCT_CTOR(add_assign_op)\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignCoeff(DstScalar& a, const SrcScalar& b) const { a += b; }\n  \n  template<int Alignment, typename Packet>\n  EIGEN_STRONG_INLINE void assignPacket(DstScalar* a, const Packet& b) const\n  { internal::pstoret<DstScalar,Packet,Alignment>(a,internal::padd(internal::ploadt<Packet,Alignment>(a),b)); }\n};\ntemplate<typename DstScalar,typename SrcScalar>\nstruct functor_traits<add_assign_op<DstScalar,SrcScalar> > {\n  enum {\n    Cost = NumTraits<DstScalar>::ReadCost + NumTraits<DstScalar>::AddCost,\n    PacketAccess = is_same<DstScalar,SrcScalar>::value && packet_traits<DstScalar>::HasAdd\n  };\n};\n\n/** \\internal\n  * \\brief Template functor for scalar/packet assignment with subtraction\n  *\n  */\ntemplate<typename DstScalar,typename SrcScalar> struct sub_assign_op {\n\n  EIGEN_EMPTY_STRUCT_CTOR(sub_assign_op)\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignCoeff(DstScalar& a, const SrcScalar& b) const { a -= b; }\n  \n  template<int Alignment, typename Packet>\n  EIGEN_STRONG_INLINE void assignPacket(DstScalar* a, const Packet& b) const\n  { internal::pstoret<DstScalar,Packet,Alignment>(a,internal::psub(internal::ploadt<Packet,Alignment>(a),b)); }\n};\ntemplate<typename DstScalar,typename SrcScalar>\nstruct functor_traits<sub_assign_op<DstScalar,SrcScalar> > {\n  enum {\n    Cost = NumTraits<DstScalar>::ReadCost + NumTraits<DstScalar>::AddCost,\n    PacketAccess = is_same<DstScalar,SrcScalar>::value && packet_traits<DstScalar>::HasSub\n  };\n};\n\n/** \\internal\n  * \\brief Template functor for scalar/packet assignment with multiplication\n  *\n  */\ntemplate<typename DstScalar, typename SrcScalar=DstScalar>\nstruct mul_assign_op {\n\n  EIGEN_EMPTY_STRUCT_CTOR(mul_assign_op)\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignCoeff(DstScalar& a, const SrcScalar& b) const { a *= b; }\n  \n  template<int Alignment, typename Packet>\n  EIGEN_STRONG_INLINE void assignPacket(DstScalar* a, const Packet& b) const\n  { internal::pstoret<DstScalar,Packet,Alignment>(a,internal::pmul(internal::ploadt<Packet,Alignment>(a),b)); }\n};\ntemplate<typename DstScalar, typename SrcScalar>\nstruct functor_traits<mul_assign_op<DstScalar,SrcScalar> > {\n  enum {\n    Cost = NumTraits<DstScalar>::ReadCost + NumTraits<DstScalar>::MulCost,\n    PacketAccess = is_same<DstScalar,SrcScalar>::value && packet_traits<DstScalar>::HasMul\n  };\n};\n\n/** \\internal\n  * \\brief Template functor for scalar/packet assignment with diviving\n  *\n  */\ntemplate<typename DstScalar, typename SrcScalar=DstScalar> struct div_assign_op {\n\n  EIGEN_EMPTY_STRUCT_CTOR(div_assign_op)\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignCoeff(DstScalar& a, const SrcScalar& b) const { a /= b; }\n  \n  template<int Alignment, typename Packet>\n  EIGEN_STRONG_INLINE void assignPacket(DstScalar* a, const Packet& b) const\n  { internal::pstoret<DstScalar,Packet,Alignment>(a,internal::pdiv(internal::ploadt<Packet,Alignment>(a),b)); }\n};\ntemplate<typename DstScalar, typename SrcScalar>\nstruct functor_traits<div_assign_op<DstScalar,SrcScalar> > {\n  enum {\n    Cost = NumTraits<DstScalar>::ReadCost + NumTraits<DstScalar>::MulCost,\n    PacketAccess = is_same<DstScalar,SrcScalar>::value && packet_traits<DstScalar>::HasDiv\n  };\n};\n\n/** \\internal\n  * \\brief Template functor for scalar/packet assignment with swapping\n  *\n  * It works as follow. For a non-vectorized evaluation loop, we have:\n  *   for(i) func(A.coeffRef(i), B.coeff(i));\n  * where B is a SwapWrapper expression. The trick is to make SwapWrapper::coeff behaves like a non-const coeffRef.\n  * Actually, SwapWrapper might not even be needed since even if B is a plain expression, since it has to be writable\n  * B.coeff already returns a const reference to the underlying scalar value.\n  * \n  * The case of a vectorized loop is more tricky:\n  *   for(i,j) func.assignPacket<A_Align>(&A.coeffRef(i,j), B.packet<B_Align>(i,j));\n  * Here, B must be a SwapWrapper whose packet function actually returns a proxy object holding a Scalar*,\n  * the actual alignment and Packet type.\n  *\n  */\ntemplate<typename Scalar> struct swap_assign_op {\n\n  EIGEN_EMPTY_STRUCT_CTOR(swap_assign_op)\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignCoeff(Scalar& a, const Scalar& b) const\n  {\n#ifdef __CUDACC__\n    // FIXME is there some kind of cuda::swap?\n    Scalar t=b; const_cast<Scalar&>(b)=a; a=t;\n#else\n    using std::swap;\n    swap(a,const_cast<Scalar&>(b));\n#endif\n  }\n};\ntemplate<typename Scalar>\nstruct functor_traits<swap_assign_op<Scalar> > {\n  enum {\n    Cost = 3 * NumTraits<Scalar>::ReadCost,\n    PacketAccess = packet_traits<Scalar>::Vectorizable\n  };\n};\n\n} // namespace internal\n\n} // namespace Eigen\n\n#endif // EIGEN_ASSIGNMENT_FUNCTORS_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/functors/BinaryFunctors.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_BINARY_FUNCTORS_H\n#define EIGEN_BINARY_FUNCTORS_H\n\nnamespace Eigen {\n\nnamespace internal {\n\n//---------- associative binary functors ----------\n\ntemplate<typename Arg1, typename Arg2>\nstruct binary_op_base\n{\n  typedef Arg1 first_argument_type;\n  typedef Arg2 second_argument_type;\n};\n\n/** \\internal\n  * \\brief Template functor to compute the sum of two scalars\n  *\n  * \\sa class CwiseBinaryOp, MatrixBase::operator+, class VectorwiseOp, DenseBase::sum()\n  */\ntemplate<typename LhsScalar,typename RhsScalar>\nstruct scalar_sum_op : binary_op_base<LhsScalar,RhsScalar>\n{\n  typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_sum_op>::ReturnType result_type;\n#ifndef EIGEN_SCALAR_BINARY_OP_PLUGIN\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_sum_op)\n#else\n  scalar_sum_op() {\n    EIGEN_SCALAR_BINARY_OP_PLUGIN\n  }\n#endif\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return a + b; }\n  template<typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const\n  { return internal::padd(a,b); }\n  template<typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type predux(const Packet& a) const\n  { return internal::predux(a); }\n};\ntemplate<typename LhsScalar,typename RhsScalar>\nstruct functor_traits<scalar_sum_op<LhsScalar,RhsScalar> > {\n  enum {\n    Cost = (NumTraits<LhsScalar>::AddCost+NumTraits<RhsScalar>::AddCost)/2, // rough estimate!\n    PacketAccess = is_same<LhsScalar,RhsScalar>::value && packet_traits<LhsScalar>::HasAdd && packet_traits<RhsScalar>::HasAdd\n    // TODO vectorize mixed sum\n  };\n};\n\n/** \\internal\n  * \\brief Template specialization to deprecate the summation of boolean expressions.\n  * This is required to solve Bug 426.\n  * \\sa DenseBase::count(), DenseBase::any(), ArrayBase::cast(), MatrixBase::cast()\n  */\ntemplate<> struct scalar_sum_op<bool,bool> : scalar_sum_op<int,int> {\n  EIGEN_DEPRECATED\n  scalar_sum_op() {}\n};\n\n\n/** \\internal\n  * \\brief Template functor to compute the product of two scalars\n  *\n  * \\sa class CwiseBinaryOp, Cwise::operator*(), class VectorwiseOp, MatrixBase::redux()\n  */\ntemplate<typename LhsScalar,typename RhsScalar>\nstruct scalar_product_op  : binary_op_base<LhsScalar,RhsScalar>\n{\n  typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_product_op>::ReturnType result_type;\n#ifndef EIGEN_SCALAR_BINARY_OP_PLUGIN\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_product_op)\n#else\n  scalar_product_op() {\n    EIGEN_SCALAR_BINARY_OP_PLUGIN\n  }\n#endif\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return a * b; }\n  template<typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const\n  { return internal::pmul(a,b); }\n  template<typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type predux(const Packet& a) const\n  { return internal::predux_mul(a); }\n};\ntemplate<typename LhsScalar,typename RhsScalar>\nstruct functor_traits<scalar_product_op<LhsScalar,RhsScalar> > {\n  enum {\n    Cost = (NumTraits<LhsScalar>::MulCost + NumTraits<RhsScalar>::MulCost)/2, // rough estimate!\n    PacketAccess = is_same<LhsScalar,RhsScalar>::value && packet_traits<LhsScalar>::HasMul && packet_traits<RhsScalar>::HasMul\n    // TODO vectorize mixed product\n  };\n};\n\n/** \\internal\n  * \\brief Template functor to compute the conjugate product of two scalars\n  *\n  * This is a short cut for conj(x) * y which is needed for optimization purpose; in Eigen2 support mode, this becomes x * conj(y)\n  */\ntemplate<typename LhsScalar,typename RhsScalar>\nstruct scalar_conj_product_op  : binary_op_base<LhsScalar,RhsScalar>\n{\n\n  enum {\n    Conj = NumTraits<LhsScalar>::IsComplex\n  };\n  \n  typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_conj_product_op>::ReturnType result_type;\n  \n  EIGEN_EMPTY_STRUCT_CTOR(scalar_conj_product_op)\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const\n  { return conj_helper<LhsScalar,RhsScalar,Conj,false>().pmul(a,b); }\n  \n  template<typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const\n  { return conj_helper<Packet,Packet,Conj,false>().pmul(a,b); }\n};\ntemplate<typename LhsScalar,typename RhsScalar>\nstruct functor_traits<scalar_conj_product_op<LhsScalar,RhsScalar> > {\n  enum {\n    Cost = NumTraits<LhsScalar>::MulCost,\n    PacketAccess = internal::is_same<LhsScalar, RhsScalar>::value && packet_traits<LhsScalar>::HasMul\n  };\n};\n\n/** \\internal\n  * \\brief Template functor to compute the min of two scalars\n  *\n  * \\sa class CwiseBinaryOp, MatrixBase::cwiseMin, class VectorwiseOp, MatrixBase::minCoeff()\n  */\ntemplate<typename LhsScalar,typename RhsScalar>\nstruct scalar_min_op : binary_op_base<LhsScalar,RhsScalar>\n{\n  typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_min_op>::ReturnType result_type;\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_min_op)\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return numext::mini(a, b); }\n  template<typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const\n  { return internal::pmin(a,b); }\n  template<typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type predux(const Packet& a) const\n  { return internal::predux_min(a); }\n};\ntemplate<typename LhsScalar,typename RhsScalar>\nstruct functor_traits<scalar_min_op<LhsScalar,RhsScalar> > {\n  enum {\n    Cost = (NumTraits<LhsScalar>::AddCost+NumTraits<RhsScalar>::AddCost)/2,\n    PacketAccess = internal::is_same<LhsScalar, RhsScalar>::value && packet_traits<LhsScalar>::HasMin\n  };\n};\n\n/** \\internal\n  * \\brief Template functor to compute the max of two scalars\n  *\n  * \\sa class CwiseBinaryOp, MatrixBase::cwiseMax, class VectorwiseOp, MatrixBase::maxCoeff()\n  */\ntemplate<typename LhsScalar,typename RhsScalar>\nstruct scalar_max_op  : binary_op_base<LhsScalar,RhsScalar>\n{\n  typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_max_op>::ReturnType result_type;\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_max_op)\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return numext::maxi(a, b); }\n  template<typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const\n  { return internal::pmax(a,b); }\n  template<typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type predux(const Packet& a) const\n  { return internal::predux_max(a); }\n};\ntemplate<typename LhsScalar,typename RhsScalar>\nstruct functor_traits<scalar_max_op<LhsScalar,RhsScalar> > {\n  enum {\n    Cost = (NumTraits<LhsScalar>::AddCost+NumTraits<RhsScalar>::AddCost)/2,\n    PacketAccess = internal::is_same<LhsScalar, RhsScalar>::value && packet_traits<LhsScalar>::HasMax\n  };\n};\n\n/** \\internal\n  * \\brief Template functors for comparison of two scalars\n  * \\todo Implement packet-comparisons\n  */\ntemplate<typename LhsScalar, typename RhsScalar, ComparisonName cmp> struct scalar_cmp_op;\n\ntemplate<typename LhsScalar, typename RhsScalar, ComparisonName cmp>\nstruct functor_traits<scalar_cmp_op<LhsScalar,RhsScalar, cmp> > {\n  enum {\n    Cost = (NumTraits<LhsScalar>::AddCost+NumTraits<RhsScalar>::AddCost)/2,\n    PacketAccess = false\n  };\n};\n\ntemplate<ComparisonName Cmp, typename LhsScalar, typename RhsScalar>\nstruct result_of<scalar_cmp_op<LhsScalar, RhsScalar, Cmp>(LhsScalar,RhsScalar)> {\n  typedef bool type;\n};\n\n\ntemplate<typename LhsScalar, typename RhsScalar>\nstruct scalar_cmp_op<LhsScalar,RhsScalar, cmp_EQ> : binary_op_base<LhsScalar,RhsScalar>\n{\n  typedef bool result_type;\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const LhsScalar& a, const RhsScalar& b) const {return a==b;}\n};\ntemplate<typename LhsScalar, typename RhsScalar>\nstruct scalar_cmp_op<LhsScalar,RhsScalar, cmp_LT> : binary_op_base<LhsScalar,RhsScalar>\n{\n  typedef bool result_type;\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const LhsScalar& a, const RhsScalar& b) const {return a<b;}\n};\ntemplate<typename LhsScalar, typename RhsScalar>\nstruct scalar_cmp_op<LhsScalar,RhsScalar, cmp_LE> : binary_op_base<LhsScalar,RhsScalar>\n{\n  typedef bool result_type;\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const LhsScalar& a, const RhsScalar& b) const {return a<=b;}\n};\ntemplate<typename LhsScalar, typename RhsScalar>\nstruct scalar_cmp_op<LhsScalar,RhsScalar, cmp_GT> : binary_op_base<LhsScalar,RhsScalar>\n{\n  typedef bool result_type;\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const LhsScalar& a, const RhsScalar& b) const {return a>b;}\n};\ntemplate<typename LhsScalar, typename RhsScalar>\nstruct scalar_cmp_op<LhsScalar,RhsScalar, cmp_GE> : binary_op_base<LhsScalar,RhsScalar>\n{\n  typedef bool result_type;\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const LhsScalar& a, const RhsScalar& b) const {return a>=b;}\n};\ntemplate<typename LhsScalar, typename RhsScalar>\nstruct scalar_cmp_op<LhsScalar,RhsScalar, cmp_UNORD> : binary_op_base<LhsScalar,RhsScalar>\n{\n  typedef bool result_type;\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const LhsScalar& a, const RhsScalar& b) const {return !(a<=b || b<=a);}\n};\ntemplate<typename LhsScalar, typename RhsScalar>\nstruct scalar_cmp_op<LhsScalar,RhsScalar, cmp_NEQ> : binary_op_base<LhsScalar,RhsScalar>\n{\n  typedef bool result_type;\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const LhsScalar& a, const RhsScalar& b) const {return a!=b;}\n};\n\n\n/** \\internal\n  * \\brief Template functor to compute the hypot of two \\b positive \\b and \\b real scalars\n  *\n  * \\sa MatrixBase::stableNorm(), class Redux\n  */\ntemplate<typename Scalar>\nstruct scalar_hypot_op<Scalar,Scalar> : binary_op_base<Scalar,Scalar>\n{\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_hypot_op)\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar &x, const Scalar &y) const\n  {\n    // This functor is used by hypotNorm only for which it is faster to first apply abs\n    // on all coefficients prior to reduction through hypot.\n    // This way we avoid calling abs on positive and real entries, and this also permits\n    // to seamlessly handle complexes. Otherwise we would have to handle both real and complexes\n    // through the same functor...\n    return internal::positive_real_hypot(x,y);\n  }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_hypot_op<Scalar,Scalar> > {\n  enum\n  {\n    Cost = 3 * NumTraits<Scalar>::AddCost +\n           2 * NumTraits<Scalar>::MulCost +\n           2 * scalar_div_cost<Scalar,false>::value,\n    PacketAccess = false\n  };\n};\n\n/** \\internal\n  * \\brief Template functor to compute the pow of two scalars\n  */\ntemplate<typename Scalar, typename Exponent>\nstruct scalar_pow_op  : binary_op_base<Scalar,Exponent>\n{\n  typedef typename ScalarBinaryOpTraits<Scalar,Exponent,scalar_pow_op>::ReturnType result_type;\n#ifndef EIGEN_SCALAR_BINARY_OP_PLUGIN\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_pow_op)\n#else\n  scalar_pow_op() {\n    typedef Scalar LhsScalar;\n    typedef Exponent RhsScalar;\n    EIGEN_SCALAR_BINARY_OP_PLUGIN\n  }\n#endif\n  EIGEN_DEVICE_FUNC\n  inline result_type operator() (const Scalar& a, const Exponent& b) const { return numext::pow(a, b); }\n};\ntemplate<typename Scalar, typename Exponent>\nstruct functor_traits<scalar_pow_op<Scalar,Exponent> > {\n  enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = false };\n};\n\n\n\n//---------- non associative binary functors ----------\n\n/** \\internal\n  * \\brief Template functor to compute the difference of two scalars\n  *\n  * \\sa class CwiseBinaryOp, MatrixBase::operator-\n  */\ntemplate<typename LhsScalar,typename RhsScalar>\nstruct scalar_difference_op : binary_op_base<LhsScalar,RhsScalar>\n{\n  typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_difference_op>::ReturnType result_type;\n#ifndef EIGEN_SCALAR_BINARY_OP_PLUGIN\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_difference_op)\n#else\n  scalar_difference_op() {\n    EIGEN_SCALAR_BINARY_OP_PLUGIN\n  }\n#endif\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return a - b; }\n  template<typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const\n  { return internal::psub(a,b); }\n};\ntemplate<typename LhsScalar,typename RhsScalar>\nstruct functor_traits<scalar_difference_op<LhsScalar,RhsScalar> > {\n  enum {\n    Cost = (NumTraits<LhsScalar>::AddCost+NumTraits<RhsScalar>::AddCost)/2,\n    PacketAccess = is_same<LhsScalar,RhsScalar>::value && packet_traits<LhsScalar>::HasSub && packet_traits<RhsScalar>::HasSub\n  };\n};\n\n/** \\internal\n  * \\brief Template functor to compute the quotient of two scalars\n  *\n  * \\sa class CwiseBinaryOp, Cwise::operator/()\n  */\ntemplate<typename LhsScalar,typename RhsScalar>\nstruct scalar_quotient_op  : binary_op_base<LhsScalar,RhsScalar>\n{\n  typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_quotient_op>::ReturnType result_type;\n#ifndef EIGEN_SCALAR_BINARY_OP_PLUGIN\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_quotient_op)\n#else\n  scalar_quotient_op() {\n    EIGEN_SCALAR_BINARY_OP_PLUGIN\n  }\n#endif\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return a / b; }\n  template<typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const\n  { return internal::pdiv(a,b); }\n};\ntemplate<typename LhsScalar,typename RhsScalar>\nstruct functor_traits<scalar_quotient_op<LhsScalar,RhsScalar> > {\n  typedef typename scalar_quotient_op<LhsScalar,RhsScalar>::result_type result_type;\n  enum {\n    PacketAccess = is_same<LhsScalar,RhsScalar>::value && packet_traits<LhsScalar>::HasDiv && packet_traits<RhsScalar>::HasDiv,\n    Cost = scalar_div_cost<result_type,PacketAccess>::value\n  };\n};\n\n\n\n/** \\internal\n  * \\brief Template functor to compute the and of two booleans\n  *\n  * \\sa class CwiseBinaryOp, ArrayBase::operator&&\n  */\nstruct scalar_boolean_and_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_boolean_and_op)\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator() (const bool& a, const bool& b) const { return a && b; }\n};\ntemplate<> struct functor_traits<scalar_boolean_and_op> {\n  enum {\n    Cost = NumTraits<bool>::AddCost,\n    PacketAccess = false\n  };\n};\n\n/** \\internal\n  * \\brief Template functor to compute the or of two booleans\n  *\n  * \\sa class CwiseBinaryOp, ArrayBase::operator||\n  */\nstruct scalar_boolean_or_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_boolean_or_op)\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator() (const bool& a, const bool& b) const { return a || b; }\n};\ntemplate<> struct functor_traits<scalar_boolean_or_op> {\n  enum {\n    Cost = NumTraits<bool>::AddCost,\n    PacketAccess = false\n  };\n};\n\n/** \\internal\n * \\brief Template functor to compute the xor of two booleans\n *\n * \\sa class CwiseBinaryOp, ArrayBase::operator^\n */\nstruct scalar_boolean_xor_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_boolean_xor_op)\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator() (const bool& a, const bool& b) const { return a ^ b; }\n};\ntemplate<> struct functor_traits<scalar_boolean_xor_op> {\n  enum {\n    Cost = NumTraits<bool>::AddCost,\n    PacketAccess = false\n  };\n};\n\n\n\n//---------- binary functors bound to a constant, thus appearing as a unary functor ----------\n\n// The following two classes permits to turn any binary functor into a unary one with one argument bound to a constant value.\n// They are analogues to std::binder1st/binder2nd but with the following differences:\n//  - they are compatible with packetOp\n//  - they are portable across C++ versions (the std::binder* are deprecated in C++11)\ntemplate<typename BinaryOp> struct bind1st_op : BinaryOp {\n\n  typedef typename BinaryOp::first_argument_type  first_argument_type;\n  typedef typename BinaryOp::second_argument_type second_argument_type;\n  typedef typename BinaryOp::result_type          result_type;\n\n  bind1st_op(const first_argument_type &val) : m_value(val) {}\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const second_argument_type& b) const { return BinaryOp::operator()(m_value,b); }\n\n  template<typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& b) const\n  { return BinaryOp::packetOp(internal::pset1<Packet>(m_value), b); }\n\n  first_argument_type m_value;\n};\ntemplate<typename BinaryOp> struct functor_traits<bind1st_op<BinaryOp> > : functor_traits<BinaryOp> {};\n\n\ntemplate<typename BinaryOp> struct bind2nd_op : BinaryOp {\n\n  typedef typename BinaryOp::first_argument_type  first_argument_type;\n  typedef typename BinaryOp::second_argument_type second_argument_type;\n  typedef typename BinaryOp::result_type          result_type;\n\n  bind2nd_op(const second_argument_type &val) : m_value(val) {}\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const first_argument_type& a) const { return BinaryOp::operator()(a,m_value); }\n\n  template<typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const\n  { return BinaryOp::packetOp(a,internal::pset1<Packet>(m_value)); }\n\n  second_argument_type m_value;\n};\ntemplate<typename BinaryOp> struct functor_traits<bind2nd_op<BinaryOp> > : functor_traits<BinaryOp> {};\n\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_BINARY_FUNCTORS_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/functors/NullaryFunctors.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2016 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_NULLARY_FUNCTORS_H\n#define EIGEN_NULLARY_FUNCTORS_H\n\nnamespace Eigen {\n\nnamespace internal {\n\ntemplate<typename Scalar>\nstruct scalar_constant_op {\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE scalar_constant_op(const scalar_constant_op& other) : m_other(other.m_other) { }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE scalar_constant_op(const Scalar& other) : m_other(other) { }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() () const { return m_other; }\n  template<typename PacketType>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const PacketType packetOp() const { return internal::pset1<PacketType>(m_other); }\n  const Scalar m_other;\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_constant_op<Scalar> >\n{ enum { Cost = 0 /* as the constant value should be loaded in register only once for the whole expression */,\n         PacketAccess = packet_traits<Scalar>::Vectorizable, IsRepeatable = true }; };\n\ntemplate<typename Scalar> struct scalar_identity_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_identity_op)\n  template<typename IndexType>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (IndexType row, IndexType col) const { return row==col ? Scalar(1) : Scalar(0); }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_identity_op<Scalar> >\n{ enum { Cost = NumTraits<Scalar>::AddCost, PacketAccess = false, IsRepeatable = true }; };\n\ntemplate <typename Scalar, typename Packet, bool IsInteger> struct linspaced_op_impl;\n\ntemplate <typename Scalar, typename Packet>\nstruct linspaced_op_impl<Scalar,Packet,/*IsInteger*/false>\n{\n  linspaced_op_impl(const Scalar& low, const Scalar& high, Index num_steps) :\n    m_low(low), m_high(high), m_size1(num_steps==1 ? 1 : num_steps-1), m_step(num_steps==1 ? Scalar() : (high-low)/Scalar(num_steps-1)),\n    m_flip(numext::abs(high)<numext::abs(low))\n  {}\n\n  template<typename IndexType>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (IndexType i) const {\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n    if(m_flip)\n      return (i==0)? m_low : (m_high - RealScalar(m_size1-i)*m_step);\n    else\n      return (i==m_size1)? m_high : (m_low + RealScalar(i)*m_step);\n  }\n\n  template<typename IndexType>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(IndexType i) const\n  {\n    // Principle:\n    // [low, ..., low] + ( [step, ..., step] * ( [i, ..., i] + [0, ..., size] ) )\n    if(m_flip)\n    {\n      Packet pi = plset<Packet>(Scalar(i-m_size1));\n      Packet res = padd(pset1<Packet>(m_high), pmul(pset1<Packet>(m_step), pi));\n      if(i==0)\n        res = pinsertfirst(res, m_low);\n      return res;\n    }\n    else\n    {\n      Packet pi = plset<Packet>(Scalar(i));\n      Packet res = padd(pset1<Packet>(m_low), pmul(pset1<Packet>(m_step), pi));\n      if(i==m_size1-unpacket_traits<Packet>::size+1)\n        res = pinsertlast(res, m_high);\n      return res;\n    }\n  }\n\n  const Scalar m_low;\n  const Scalar m_high;\n  const Index m_size1;\n  const Scalar m_step;\n  const bool m_flip;\n};\n\ntemplate <typename Scalar, typename Packet>\nstruct linspaced_op_impl<Scalar,Packet,/*IsInteger*/true>\n{\n  linspaced_op_impl(const Scalar& low, const Scalar& high, Index num_steps) :\n    m_low(low),\n    m_multiplier((high-low)/convert_index<Scalar>(num_steps<=1 ? 1 : num_steps-1)),\n    m_divisor(convert_index<Scalar>((high>=low?num_steps:-num_steps)+(high-low))/((numext::abs(high-low)+1)==0?1:(numext::abs(high-low)+1))),\n    m_use_divisor(num_steps>1 && (numext::abs(high-low)+1)<num_steps)\n  {}\n\n  template<typename IndexType>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  const Scalar operator() (IndexType i) const\n  {\n    if(m_use_divisor) return m_low + convert_index<Scalar>(i)/m_divisor;\n    else              return m_low + convert_index<Scalar>(i)*m_multiplier;\n  }\n\n  const Scalar m_low;\n  const Scalar m_multiplier;\n  const Scalar m_divisor;\n  const bool m_use_divisor;\n};\n\n// ----- Linspace functor ----------------------------------------------------------------\n\n// Forward declaration (we default to random access which does not really give\n// us a speed gain when using packet access but it allows to use the functor in\n// nested expressions).\ntemplate <typename Scalar, typename PacketType> struct linspaced_op;\ntemplate <typename Scalar, typename PacketType> struct functor_traits< linspaced_op<Scalar,PacketType> >\n{\n  enum\n  {\n    Cost = 1,\n    PacketAccess =   (!NumTraits<Scalar>::IsInteger) && packet_traits<Scalar>::HasSetLinear && packet_traits<Scalar>::HasBlend,\n                  /*&& ((!NumTraits<Scalar>::IsInteger) || packet_traits<Scalar>::HasDiv),*/ // <- vectorization for integer is currently disabled\n    IsRepeatable = true\n  };\n};\ntemplate <typename Scalar, typename PacketType> struct linspaced_op\n{\n  linspaced_op(const Scalar& low, const Scalar& high, Index num_steps)\n    : impl((num_steps==1 ? high : low),high,num_steps)\n  {}\n\n  template<typename IndexType>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (IndexType i) const { return impl(i); }\n\n  template<typename Packet,typename IndexType>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(IndexType i) const { return impl.packetOp(i); }\n\n  // This proxy object handles the actual required temporaries and the different\n  // implementations (integer vs. floating point).\n  const linspaced_op_impl<Scalar,PacketType,NumTraits<Scalar>::IsInteger> impl;\n};\n\n// Linear access is automatically determined from the operator() prototypes available for the given functor.\n// If it exposes an operator()(i,j), then we assume the i and j coefficients are required independently\n// and linear access is not possible. In all other cases, linear access is enabled.\n// Users should not have to deal with this structure.\ntemplate<typename Functor> struct functor_has_linear_access { enum { ret = !has_binary_operator<Functor>::value }; };\n\n// For unreliable compilers, let's specialize the has_*ary_operator\n// helpers so that at least built-in nullary functors work fine.\n#if !( (EIGEN_COMP_MSVC>1600) || (EIGEN_GNUC_AT_LEAST(4,8)) || (EIGEN_COMP_ICC>=1600))\ntemplate<typename Scalar,typename IndexType>\nstruct has_nullary_operator<scalar_constant_op<Scalar>,IndexType> { enum { value = 1}; };\ntemplate<typename Scalar,typename IndexType>\nstruct has_unary_operator<scalar_constant_op<Scalar>,IndexType> { enum { value = 0}; };\ntemplate<typename Scalar,typename IndexType>\nstruct has_binary_operator<scalar_constant_op<Scalar>,IndexType> { enum { value = 0}; };\n\ntemplate<typename Scalar,typename IndexType>\nstruct has_nullary_operator<scalar_identity_op<Scalar>,IndexType> { enum { value = 0}; };\ntemplate<typename Scalar,typename IndexType>\nstruct has_unary_operator<scalar_identity_op<Scalar>,IndexType> { enum { value = 0}; };\ntemplate<typename Scalar,typename IndexType>\nstruct has_binary_operator<scalar_identity_op<Scalar>,IndexType> { enum { value = 1}; };\n\ntemplate<typename Scalar, typename PacketType,typename IndexType>\nstruct has_nullary_operator<linspaced_op<Scalar,PacketType>,IndexType> { enum { value = 0}; };\ntemplate<typename Scalar, typename PacketType,typename IndexType>\nstruct has_unary_operator<linspaced_op<Scalar,PacketType>,IndexType> { enum { value = 1}; };\ntemplate<typename Scalar, typename PacketType,typename IndexType>\nstruct has_binary_operator<linspaced_op<Scalar,PacketType>,IndexType> { enum { value = 0}; };\n\ntemplate<typename Scalar,typename IndexType>\nstruct has_nullary_operator<scalar_random_op<Scalar>,IndexType> { enum { value = 1}; };\ntemplate<typename Scalar,typename IndexType>\nstruct has_unary_operator<scalar_random_op<Scalar>,IndexType> { enum { value = 0}; };\ntemplate<typename Scalar,typename IndexType>\nstruct has_binary_operator<scalar_random_op<Scalar>,IndexType> { enum { value = 0}; };\n#endif\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_NULLARY_FUNCTORS_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/functors/StlFunctors.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_STL_FUNCTORS_H\n#define EIGEN_STL_FUNCTORS_H\n\nnamespace Eigen {\n\nnamespace internal {\n\n// default functor traits for STL functors:\n\ntemplate<typename T>\nstruct functor_traits<std::multiplies<T> >\n{ enum { Cost = NumTraits<T>::MulCost, PacketAccess = false }; };\n\ntemplate<typename T>\nstruct functor_traits<std::divides<T> >\n{ enum { Cost = NumTraits<T>::MulCost, PacketAccess = false }; };\n\ntemplate<typename T>\nstruct functor_traits<std::plus<T> >\n{ enum { Cost = NumTraits<T>::AddCost, PacketAccess = false }; };\n\ntemplate<typename T>\nstruct functor_traits<std::minus<T> >\n{ enum { Cost = NumTraits<T>::AddCost, PacketAccess = false }; };\n\ntemplate<typename T>\nstruct functor_traits<std::negate<T> >\n{ enum { Cost = NumTraits<T>::AddCost, PacketAccess = false }; };\n\ntemplate<typename T>\nstruct functor_traits<std::logical_or<T> >\n{ enum { Cost = 1, PacketAccess = false }; };\n\ntemplate<typename T>\nstruct functor_traits<std::logical_and<T> >\n{ enum { Cost = 1, PacketAccess = false }; };\n\ntemplate<typename T>\nstruct functor_traits<std::logical_not<T> >\n{ enum { Cost = 1, PacketAccess = false }; };\n\ntemplate<typename T>\nstruct functor_traits<std::greater<T> >\n{ enum { Cost = 1, PacketAccess = false }; };\n\ntemplate<typename T>\nstruct functor_traits<std::less<T> >\n{ enum { Cost = 1, PacketAccess = false }; };\n\ntemplate<typename T>\nstruct functor_traits<std::greater_equal<T> >\n{ enum { Cost = 1, PacketAccess = false }; };\n\ntemplate<typename T>\nstruct functor_traits<std::less_equal<T> >\n{ enum { Cost = 1, PacketAccess = false }; };\n\ntemplate<typename T>\nstruct functor_traits<std::equal_to<T> >\n{ enum { Cost = 1, PacketAccess = false }; };\n\ntemplate<typename T>\nstruct functor_traits<std::not_equal_to<T> >\n{ enum { Cost = 1, PacketAccess = false }; };\n\n#if (__cplusplus < 201103L) && (EIGEN_COMP_MSVC <= 1900)\n// std::binder* are deprecated since c++11 and will be removed in c++17\ntemplate<typename T>\nstruct functor_traits<std::binder2nd<T> >\n{ enum { Cost = functor_traits<T>::Cost, PacketAccess = false }; };\n\ntemplate<typename T>\nstruct functor_traits<std::binder1st<T> >\n{ enum { Cost = functor_traits<T>::Cost, PacketAccess = false }; };\n#endif\n\n#if (__cplusplus < 201703L) && (EIGEN_COMP_MSVC < 1910)\n// std::unary_negate is deprecated since c++17 and will be removed in c++20\ntemplate<typename T>\nstruct functor_traits<std::unary_negate<T> >\n{ enum { Cost = 1 + functor_traits<T>::Cost, PacketAccess = false }; };\n\n// std::binary_negate is deprecated since c++17 and will be removed in c++20\ntemplate<typename T>\nstruct functor_traits<std::binary_negate<T> >\n{ enum { Cost = 1 + functor_traits<T>::Cost, PacketAccess = false }; };\n#endif\n\n#ifdef EIGEN_STDEXT_SUPPORT\n\ntemplate<typename T0,typename T1>\nstruct functor_traits<std::project1st<T0,T1> >\n{ enum { Cost = 0, PacketAccess = false }; };\n\ntemplate<typename T0,typename T1>\nstruct functor_traits<std::project2nd<T0,T1> >\n{ enum { Cost = 0, PacketAccess = false }; };\n\ntemplate<typename T0,typename T1>\nstruct functor_traits<std::select2nd<std::pair<T0,T1> > >\n{ enum { Cost = 0, PacketAccess = false }; };\n\ntemplate<typename T0,typename T1>\nstruct functor_traits<std::select1st<std::pair<T0,T1> > >\n{ enum { Cost = 0, PacketAccess = false }; };\n\ntemplate<typename T0,typename T1>\nstruct functor_traits<std::unary_compose<T0,T1> >\n{ enum { Cost = functor_traits<T0>::Cost + functor_traits<T1>::Cost, PacketAccess = false }; };\n\ntemplate<typename T0,typename T1,typename T2>\nstruct functor_traits<std::binary_compose<T0,T1,T2> >\n{ enum { Cost = functor_traits<T0>::Cost + functor_traits<T1>::Cost + functor_traits<T2>::Cost, PacketAccess = false }; };\n\n#endif // EIGEN_STDEXT_SUPPORT\n\n// allow to add new functors and specializations of functor_traits from outside Eigen.\n// this macro is really needed because functor_traits must be specialized after it is declared but before it is used...\n#ifdef EIGEN_FUNCTORS_PLUGIN\n#include EIGEN_FUNCTORS_PLUGIN\n#endif\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_STL_FUNCTORS_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/functors/TernaryFunctors.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Eugene Brevdo <ebrevdo@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_TERNARY_FUNCTORS_H\n#define EIGEN_TERNARY_FUNCTORS_H\n\nnamespace Eigen {\n\nnamespace internal {\n\n//---------- associative ternary functors ----------\n\n\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_TERNARY_FUNCTORS_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/functors/UnaryFunctors.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2016 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_UNARY_FUNCTORS_H\n#define EIGEN_UNARY_FUNCTORS_H\n\nnamespace Eigen {\n\nnamespace internal {\n\n/** \\internal\n  * \\brief Template functor to compute the opposite of a scalar\n  *\n  * \\sa class CwiseUnaryOp, MatrixBase::operator-\n  */\ntemplate<typename Scalar> struct scalar_opposite_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_opposite_op)\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { return -a; }\n  template<typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const\n  { return internal::pnegate(a); }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_opposite_op<Scalar> >\n{ enum {\n    Cost = NumTraits<Scalar>::AddCost,\n    PacketAccess = packet_traits<Scalar>::HasNegate };\n};\n\n/** \\internal\n  * \\brief Template functor to compute the absolute value of a scalar\n  *\n  * \\sa class CwiseUnaryOp, Cwise::abs\n  */\ntemplate<typename Scalar> struct scalar_abs_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_abs_op)\n  typedef typename NumTraits<Scalar>::Real result_type;\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a) const { return numext::abs(a); }\n  template<typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const\n  { return internal::pabs(a); }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_abs_op<Scalar> >\n{\n  enum {\n    Cost = NumTraits<Scalar>::AddCost,\n    PacketAccess = packet_traits<Scalar>::HasAbs\n  };\n};\n\n/** \\internal\n  * \\brief Template functor to compute the score of a scalar, to chose a pivot\n  *\n  * \\sa class CwiseUnaryOp\n  */\ntemplate<typename Scalar> struct scalar_score_coeff_op : scalar_abs_op<Scalar>\n{\n  typedef void Score_is_abs;\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_score_coeff_op<Scalar> > : functor_traits<scalar_abs_op<Scalar> > {};\n\n/* Avoid recomputing abs when we know the score and they are the same. Not a true Eigen functor.  */\ntemplate<typename Scalar, typename=void> struct abs_knowing_score\n{\n  EIGEN_EMPTY_STRUCT_CTOR(abs_knowing_score)\n  typedef typename NumTraits<Scalar>::Real result_type;\n  template<typename Score>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a, const Score&) const { return numext::abs(a); }\n};\ntemplate<typename Scalar> struct abs_knowing_score<Scalar, typename scalar_score_coeff_op<Scalar>::Score_is_abs>\n{\n  EIGEN_EMPTY_STRUCT_CTOR(abs_knowing_score)\n  typedef typename NumTraits<Scalar>::Real result_type;\n  template<typename Scal>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const Scal&, const result_type& a) const { return a; }\n};\n\n/** \\internal\n  * \\brief Template functor to compute the squared absolute value of a scalar\n  *\n  * \\sa class CwiseUnaryOp, Cwise::abs2\n  */\ntemplate<typename Scalar> struct scalar_abs2_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_abs2_op)\n  typedef typename NumTraits<Scalar>::Real result_type;\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a) const { return numext::abs2(a); }\n  template<typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const\n  { return internal::pmul(a,a); }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_abs2_op<Scalar> >\n{ enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasAbs2 }; };\n\n/** \\internal\n  * \\brief Template functor to compute the conjugate of a complex value\n  *\n  * \\sa class CwiseUnaryOp, MatrixBase::conjugate()\n  */\ntemplate<typename Scalar> struct scalar_conjugate_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_conjugate_op)\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { using numext::conj; return conj(a); }\n  template<typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const { return internal::pconj(a); }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_conjugate_op<Scalar> >\n{\n  enum {\n    Cost = NumTraits<Scalar>::IsComplex ? NumTraits<Scalar>::AddCost : 0,\n    PacketAccess = packet_traits<Scalar>::HasConj\n  };\n};\n\n/** \\internal\n  * \\brief Template functor to compute the phase angle of a complex\n  *\n  * \\sa class CwiseUnaryOp, Cwise::arg\n  */\ntemplate<typename Scalar> struct scalar_arg_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_arg_op)\n  typedef typename NumTraits<Scalar>::Real result_type;\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a) const { using numext::arg; return arg(a); }\n  template<typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const\n  { return internal::parg(a); }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_arg_op<Scalar> >\n{\n  enum {\n    Cost = NumTraits<Scalar>::IsComplex ? 5 * NumTraits<Scalar>::MulCost : NumTraits<Scalar>::AddCost,\n    PacketAccess = packet_traits<Scalar>::HasArg\n  };\n};\n/** \\internal\n  * \\brief Template functor to cast a scalar to another type\n  *\n  * \\sa class CwiseUnaryOp, MatrixBase::cast()\n  */\ntemplate<typename Scalar, typename NewType>\nstruct scalar_cast_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_cast_op)\n  typedef NewType result_type;\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const NewType operator() (const Scalar& a) const { return cast<Scalar, NewType>(a); }\n};\ntemplate<typename Scalar, typename NewType>\nstruct functor_traits<scalar_cast_op<Scalar,NewType> >\n{ enum { Cost = is_same<Scalar, NewType>::value ? 0 : NumTraits<NewType>::AddCost, PacketAccess = false }; };\n\n/** \\internal\n  * \\brief Template functor to extract the real part of a complex\n  *\n  * \\sa class CwiseUnaryOp, MatrixBase::real()\n  */\ntemplate<typename Scalar>\nstruct scalar_real_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_real_op)\n  typedef typename NumTraits<Scalar>::Real result_type;\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const { return numext::real(a); }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_real_op<Scalar> >\n{ enum { Cost = 0, PacketAccess = false }; };\n\n/** \\internal\n  * \\brief Template functor to extract the imaginary part of a complex\n  *\n  * \\sa class CwiseUnaryOp, MatrixBase::imag()\n  */\ntemplate<typename Scalar>\nstruct scalar_imag_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_imag_op)\n  typedef typename NumTraits<Scalar>::Real result_type;\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const { return numext::imag(a); }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_imag_op<Scalar> >\n{ enum { Cost = 0, PacketAccess = false }; };\n\n/** \\internal\n  * \\brief Template functor to extract the real part of a complex as a reference\n  *\n  * \\sa class CwiseUnaryOp, MatrixBase::real()\n  */\ntemplate<typename Scalar>\nstruct scalar_real_ref_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_real_ref_op)\n  typedef typename NumTraits<Scalar>::Real result_type;\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE result_type& operator() (const Scalar& a) const { return numext::real_ref(*const_cast<Scalar*>(&a)); }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_real_ref_op<Scalar> >\n{ enum { Cost = 0, PacketAccess = false }; };\n\n/** \\internal\n  * \\brief Template functor to extract the imaginary part of a complex as a reference\n  *\n  * \\sa class CwiseUnaryOp, MatrixBase::imag()\n  */\ntemplate<typename Scalar>\nstruct scalar_imag_ref_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_imag_ref_op)\n  typedef typename NumTraits<Scalar>::Real result_type;\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE result_type& operator() (const Scalar& a) const { return numext::imag_ref(*const_cast<Scalar*>(&a)); }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_imag_ref_op<Scalar> >\n{ enum { Cost = 0, PacketAccess = false }; };\n\n/** \\internal\n  *\n  * \\brief Template functor to compute the exponential of a scalar\n  *\n  * \\sa class CwiseUnaryOp, Cwise::exp()\n  */\ntemplate<typename Scalar> struct scalar_exp_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_exp_op)\n  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::exp(a); }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pexp(a); }\n};\ntemplate <typename Scalar>\nstruct functor_traits<scalar_exp_op<Scalar> > {\n  enum {\n    PacketAccess = packet_traits<Scalar>::HasExp,\n    // The following numbers are based on the AVX implementation.\n#ifdef EIGEN_VECTORIZE_FMA\n    // Haswell can issue 2 add/mul/madd per cycle.\n    Cost =\n    (sizeof(Scalar) == 4\n     // float: 8 pmadd, 4 pmul, 2 padd/psub, 6 other\n     ? (8 * NumTraits<Scalar>::AddCost + 6 * NumTraits<Scalar>::MulCost)\n     // double: 7 pmadd, 5 pmul, 3 padd/psub, 1 div,  13 other\n     : (14 * NumTraits<Scalar>::AddCost +\n        6 * NumTraits<Scalar>::MulCost +\n        scalar_div_cost<Scalar,packet_traits<Scalar>::HasDiv>::value))\n#else\n    Cost =\n    (sizeof(Scalar) == 4\n     // float: 7 pmadd, 6 pmul, 4 padd/psub, 10 other\n     ? (21 * NumTraits<Scalar>::AddCost + 13 * NumTraits<Scalar>::MulCost)\n     // double: 7 pmadd, 5 pmul, 3 padd/psub, 1 div,  13 other\n     : (23 * NumTraits<Scalar>::AddCost +\n        12 * NumTraits<Scalar>::MulCost +\n        scalar_div_cost<Scalar,packet_traits<Scalar>::HasDiv>::value))\n#endif\n  };\n};\n\n/** \\internal\n  *\n  * \\brief Template functor to compute the logarithm of a scalar\n  *\n  * \\sa class CwiseUnaryOp, ArrayBase::log()\n  */\ntemplate<typename Scalar> struct scalar_log_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_log_op)\n  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::log(a); }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::plog(a); }\n};\ntemplate <typename Scalar>\nstruct functor_traits<scalar_log_op<Scalar> > {\n  enum {\n    PacketAccess = packet_traits<Scalar>::HasLog,\n    Cost =\n    (PacketAccess\n     // The following numbers are based on the AVX implementation.\n#ifdef EIGEN_VECTORIZE_FMA\n     // 8 pmadd, 6 pmul, 8 padd/psub, 16 other, can issue 2 add/mul/madd per cycle.\n     ? (20 * NumTraits<Scalar>::AddCost + 7 * NumTraits<Scalar>::MulCost)\n#else\n     // 8 pmadd, 6 pmul, 8 padd/psub, 20 other\n     ? (36 * NumTraits<Scalar>::AddCost + 14 * NumTraits<Scalar>::MulCost)\n#endif\n     // Measured cost of std::log.\n     : sizeof(Scalar)==4 ? 40 : 85)\n  };\n};\n\n/** \\internal\n  *\n  * \\brief Template functor to compute the logarithm of 1 plus a scalar value\n  *\n  * \\sa class CwiseUnaryOp, ArrayBase::log1p()\n  */\ntemplate<typename Scalar> struct scalar_log1p_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_log1p_op)\n  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::log1p(a); }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::plog1p(a); }\n};\ntemplate <typename Scalar>\nstruct functor_traits<scalar_log1p_op<Scalar> > {\n  enum {\n    PacketAccess = packet_traits<Scalar>::HasLog1p,\n    Cost = functor_traits<scalar_log_op<Scalar> >::Cost // TODO measure cost of log1p\n  };\n};\n\n/** \\internal\n  *\n  * \\brief Template functor to compute the base-10 logarithm of a scalar\n  *\n  * \\sa class CwiseUnaryOp, Cwise::log10()\n  */\ntemplate<typename Scalar> struct scalar_log10_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_log10_op)\n  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { EIGEN_USING_STD_MATH(log10) return log10(a); }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::plog10(a); }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_log10_op<Scalar> >\n{ enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasLog10 }; };\n\n/** \\internal\n  * \\brief Template functor to compute the square root of a scalar\n  * \\sa class CwiseUnaryOp, Cwise::sqrt()\n  */\ntemplate<typename Scalar> struct scalar_sqrt_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_sqrt_op)\n  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::sqrt(a); }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::psqrt(a); }\n};\ntemplate <typename Scalar>\nstruct functor_traits<scalar_sqrt_op<Scalar> > {\n  enum {\n#if EIGEN_FAST_MATH\n    // The following numbers are based on the AVX implementation.\n    Cost = (sizeof(Scalar) == 8 ? 28\n                                // 4 pmul, 1 pmadd, 3 other\n                                : (3 * NumTraits<Scalar>::AddCost +\n                                   5 * NumTraits<Scalar>::MulCost)),\n#else\n    // The following numbers are based on min VSQRT throughput on Haswell.\n    Cost = (sizeof(Scalar) == 8 ? 28 : 14),\n#endif\n    PacketAccess = packet_traits<Scalar>::HasSqrt\n  };\n};\n\n/** \\internal\n  * \\brief Template functor to compute the reciprocal square root of a scalar\n  * \\sa class CwiseUnaryOp, Cwise::rsqrt()\n  */\ntemplate<typename Scalar> struct scalar_rsqrt_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_rsqrt_op)\n  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return Scalar(1)/numext::sqrt(a); }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::prsqrt(a); }\n};\n\ntemplate<typename Scalar>\nstruct functor_traits<scalar_rsqrt_op<Scalar> >\n{ enum {\n    Cost = 5 * NumTraits<Scalar>::MulCost,\n    PacketAccess = packet_traits<Scalar>::HasRsqrt\n  };\n};\n\n/** \\internal\n  * \\brief Template functor to compute the cosine of a scalar\n  * \\sa class CwiseUnaryOp, ArrayBase::cos()\n  */\ntemplate<typename Scalar> struct scalar_cos_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_cos_op)\n  EIGEN_DEVICE_FUNC inline Scalar operator() (const Scalar& a) const { return numext::cos(a); }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pcos(a); }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_cos_op<Scalar> >\n{\n  enum {\n    Cost = 5 * NumTraits<Scalar>::MulCost,\n    PacketAccess = packet_traits<Scalar>::HasCos\n  };\n};\n\n/** \\internal\n  * \\brief Template functor to compute the sine of a scalar\n  * \\sa class CwiseUnaryOp, ArrayBase::sin()\n  */\ntemplate<typename Scalar> struct scalar_sin_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_sin_op)\n  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::sin(a); }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::psin(a); }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_sin_op<Scalar> >\n{\n  enum {\n    Cost = 5 * NumTraits<Scalar>::MulCost,\n    PacketAccess = packet_traits<Scalar>::HasSin\n  };\n};\n\n\n/** \\internal\n  * \\brief Template functor to compute the tan of a scalar\n  * \\sa class CwiseUnaryOp, ArrayBase::tan()\n  */\ntemplate<typename Scalar> struct scalar_tan_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_tan_op)\n  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::tan(a); }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::ptan(a); }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_tan_op<Scalar> >\n{\n  enum {\n    Cost = 5 * NumTraits<Scalar>::MulCost,\n    PacketAccess = packet_traits<Scalar>::HasTan\n  };\n};\n\n/** \\internal\n  * \\brief Template functor to compute the arc cosine of a scalar\n  * \\sa class CwiseUnaryOp, ArrayBase::acos()\n  */\ntemplate<typename Scalar> struct scalar_acos_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_acos_op)\n  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::acos(a); }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pacos(a); }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_acos_op<Scalar> >\n{\n  enum {\n    Cost = 5 * NumTraits<Scalar>::MulCost,\n    PacketAccess = packet_traits<Scalar>::HasACos\n  };\n};\n\n/** \\internal\n  * \\brief Template functor to compute the arc sine of a scalar\n  * \\sa class CwiseUnaryOp, ArrayBase::asin()\n  */\ntemplate<typename Scalar> struct scalar_asin_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_asin_op)\n  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::asin(a); }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pasin(a); }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_asin_op<Scalar> >\n{\n  enum {\n    Cost = 5 * NumTraits<Scalar>::MulCost,\n    PacketAccess = packet_traits<Scalar>::HasASin\n  };\n};\n\n\n/** \\internal\n  * \\brief Template functor to compute the atan of a scalar\n  * \\sa class CwiseUnaryOp, ArrayBase::atan()\n  */\ntemplate<typename Scalar> struct scalar_atan_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_atan_op)\n  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::atan(a); }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::patan(a); }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_atan_op<Scalar> >\n{\n  enum {\n    Cost = 5 * NumTraits<Scalar>::MulCost,\n    PacketAccess = packet_traits<Scalar>::HasATan\n  };\n};\n\n/** \\internal\n  * \\brief Template functor to compute the tanh of a scalar\n  * \\sa class CwiseUnaryOp, ArrayBase::tanh()\n  */\ntemplate <typename Scalar>\nstruct scalar_tanh_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_tanh_op)\n  EIGEN_DEVICE_FUNC inline const Scalar operator()(const Scalar& a) const { return numext::tanh(a); }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& x) const { return ptanh(x); }\n};\n\ntemplate <typename Scalar>\nstruct functor_traits<scalar_tanh_op<Scalar> > {\n  enum {\n    PacketAccess = packet_traits<Scalar>::HasTanh,\n    Cost = ( (EIGEN_FAST_MATH && is_same<Scalar,float>::value)\n// The following numbers are based on the AVX implementation,\n#ifdef EIGEN_VECTORIZE_FMA\n                // Haswell can issue 2 add/mul/madd per cycle.\n                // 9 pmadd, 2 pmul, 1 div, 2 other\n                ? (2 * NumTraits<Scalar>::AddCost +\n                   6 * NumTraits<Scalar>::MulCost +\n                   scalar_div_cost<Scalar,packet_traits<Scalar>::HasDiv>::value)\n#else\n                ? (11 * NumTraits<Scalar>::AddCost +\n                   11 * NumTraits<Scalar>::MulCost +\n                   scalar_div_cost<Scalar,packet_traits<Scalar>::HasDiv>::value)\n#endif\n                // This number assumes a naive implementation of tanh\n                : (6 * NumTraits<Scalar>::AddCost +\n                   3 * NumTraits<Scalar>::MulCost +\n                   2 * scalar_div_cost<Scalar,packet_traits<Scalar>::HasDiv>::value +\n                   functor_traits<scalar_exp_op<Scalar> >::Cost))\n  };\n};\n\n/** \\internal\n  * \\brief Template functor to compute the sinh of a scalar\n  * \\sa class CwiseUnaryOp, ArrayBase::sinh()\n  */\ntemplate<typename Scalar> struct scalar_sinh_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_sinh_op)\n  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::sinh(a); }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::psinh(a); }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_sinh_op<Scalar> >\n{\n  enum {\n    Cost = 5 * NumTraits<Scalar>::MulCost,\n    PacketAccess = packet_traits<Scalar>::HasSinh\n  };\n};\n\n/** \\internal\n  * \\brief Template functor to compute the cosh of a scalar\n  * \\sa class CwiseUnaryOp, ArrayBase::cosh()\n  */\ntemplate<typename Scalar> struct scalar_cosh_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_cosh_op)\n  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::cosh(a); }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pcosh(a); }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_cosh_op<Scalar> >\n{\n  enum {\n    Cost = 5 * NumTraits<Scalar>::MulCost,\n    PacketAccess = packet_traits<Scalar>::HasCosh\n  };\n};\n\n/** \\internal\n  * \\brief Template functor to compute the inverse of a scalar\n  * \\sa class CwiseUnaryOp, Cwise::inverse()\n  */\ntemplate<typename Scalar>\nstruct scalar_inverse_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_inverse_op)\n  EIGEN_DEVICE_FUNC inline Scalar operator() (const Scalar& a) const { return Scalar(1)/a; }\n  template<typename Packet>\n  EIGEN_DEVICE_FUNC inline const Packet packetOp(const Packet& a) const\n  { return internal::pdiv(pset1<Packet>(Scalar(1)),a); }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_inverse_op<Scalar> >\n{ enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasDiv }; };\n\n/** \\internal\n  * \\brief Template functor to compute the square of a scalar\n  * \\sa class CwiseUnaryOp, Cwise::square()\n  */\ntemplate<typename Scalar>\nstruct scalar_square_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_square_op)\n  EIGEN_DEVICE_FUNC inline Scalar operator() (const Scalar& a) const { return a*a; }\n  template<typename Packet>\n  EIGEN_DEVICE_FUNC inline const Packet packetOp(const Packet& a) const\n  { return internal::pmul(a,a); }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_square_op<Scalar> >\n{ enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasMul }; };\n\n/** \\internal\n  * \\brief Template functor to compute the cube of a scalar\n  * \\sa class CwiseUnaryOp, Cwise::cube()\n  */\ntemplate<typename Scalar>\nstruct scalar_cube_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_cube_op)\n  EIGEN_DEVICE_FUNC inline Scalar operator() (const Scalar& a) const { return a*a*a; }\n  template<typename Packet>\n  EIGEN_DEVICE_FUNC inline const Packet packetOp(const Packet& a) const\n  { return internal::pmul(a,pmul(a,a)); }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_cube_op<Scalar> >\n{ enum { Cost = 2*NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasMul }; };\n\n/** \\internal\n  * \\brief Template functor to compute the rounded value of a scalar\n  * \\sa class CwiseUnaryOp, ArrayBase::round()\n  */\ntemplate<typename Scalar> struct scalar_round_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_round_op)\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { return numext::round(a); }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pround(a); }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_round_op<Scalar> >\n{\n  enum {\n    Cost = NumTraits<Scalar>::MulCost,\n    PacketAccess = packet_traits<Scalar>::HasRound\n  };\n};\n\n/** \\internal\n  * \\brief Template functor to compute the floor of a scalar\n  * \\sa class CwiseUnaryOp, ArrayBase::floor()\n  */\ntemplate<typename Scalar> struct scalar_floor_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_floor_op)\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { return numext::floor(a); }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pfloor(a); }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_floor_op<Scalar> >\n{\n  enum {\n    Cost = NumTraits<Scalar>::MulCost,\n    PacketAccess = packet_traits<Scalar>::HasFloor\n  };\n};\n\n/** \\internal\n  * \\brief Template functor to compute the ceil of a scalar\n  * \\sa class CwiseUnaryOp, ArrayBase::ceil()\n  */\ntemplate<typename Scalar> struct scalar_ceil_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_ceil_op)\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { return numext::ceil(a); }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pceil(a); }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_ceil_op<Scalar> >\n{\n  enum {\n    Cost = NumTraits<Scalar>::MulCost,\n    PacketAccess = packet_traits<Scalar>::HasCeil\n  };\n};\n\n/** \\internal\n  * \\brief Template functor to compute whether a scalar is NaN\n  * \\sa class CwiseUnaryOp, ArrayBase::isnan()\n  */\ntemplate<typename Scalar> struct scalar_isnan_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_isnan_op)\n  typedef bool result_type;\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const { return (numext::isnan)(a); }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_isnan_op<Scalar> >\n{\n  enum {\n    Cost = NumTraits<Scalar>::MulCost,\n    PacketAccess = false\n  };\n};\n\n/** \\internal\n  * \\brief Template functor to check whether a scalar is +/-inf\n  * \\sa class CwiseUnaryOp, ArrayBase::isinf()\n  */\ntemplate<typename Scalar> struct scalar_isinf_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_isinf_op)\n  typedef bool result_type;\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const { return (numext::isinf)(a); }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_isinf_op<Scalar> >\n{\n  enum {\n    Cost = NumTraits<Scalar>::MulCost,\n    PacketAccess = false\n  };\n};\n\n/** \\internal\n  * \\brief Template functor to check whether a scalar has a finite value\n  * \\sa class CwiseUnaryOp, ArrayBase::isfinite()\n  */\ntemplate<typename Scalar> struct scalar_isfinite_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_isfinite_op)\n  typedef bool result_type;\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const { return (numext::isfinite)(a); }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_isfinite_op<Scalar> >\n{\n  enum {\n    Cost = NumTraits<Scalar>::MulCost,\n    PacketAccess = false\n  };\n};\n\n/** \\internal\n  * \\brief Template functor to compute the logical not of a boolean\n  *\n  * \\sa class CwiseUnaryOp, ArrayBase::operator!\n  */\ntemplate<typename Scalar> struct scalar_boolean_not_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_boolean_not_op)\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator() (const bool& a) const { return !a; }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_boolean_not_op<Scalar> > {\n  enum {\n    Cost = NumTraits<bool>::AddCost,\n    PacketAccess = false\n  };\n};\n\n/** \\internal\n  * \\brief Template functor to compute the signum of a scalar\n  * \\sa class CwiseUnaryOp, Cwise::sign()\n  */\ntemplate<typename Scalar,bool iscpx=(NumTraits<Scalar>::IsComplex!=0) > struct scalar_sign_op;\ntemplate<typename Scalar>\nstruct scalar_sign_op<Scalar,false> {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_sign_op)\n  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const\n  {\n      return Scalar( (a>Scalar(0)) - (a<Scalar(0)) );\n  }\n  //TODO\n  //template <typename Packet>\n  //EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::psign(a); }\n};\ntemplate<typename Scalar>\nstruct scalar_sign_op<Scalar,true> {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_sign_op)\n  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const\n  {\n    typedef typename NumTraits<Scalar>::Real real_type;\n    real_type aa = numext::abs(a);\n    if (aa==real_type(0))\n      return Scalar(0);\n    aa = real_type(1)/aa;\n    return Scalar(real(a)*aa, imag(a)*aa );\n  }\n  //TODO\n  //template <typename Packet>\n  //EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::psign(a); }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_sign_op<Scalar> >\n{ enum {\n    Cost = \n        NumTraits<Scalar>::IsComplex\n        ? ( 8*NumTraits<Scalar>::MulCost  ) // roughly\n        : ( 3*NumTraits<Scalar>::AddCost),\n    PacketAccess = packet_traits<Scalar>::HasSign\n  };\n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_FUNCTORS_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/products/GeneralBlockPanelKernel.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_GENERAL_BLOCK_PANEL_H\n#define EIGEN_GENERAL_BLOCK_PANEL_H\n\n\nnamespace Eigen {\n\nnamespace internal {\n\ntemplate<typename _LhsScalar, typename _RhsScalar, bool _ConjLhs=false, bool _ConjRhs=false>\nclass gebp_traits;\n\n\n/** \\internal \\returns b if a<=0, and returns a otherwise. */\ninline std::ptrdiff_t manage_caching_sizes_helper(std::ptrdiff_t a, std::ptrdiff_t b)\n{\n  return a<=0 ? b : a;\n}\n\n#if EIGEN_ARCH_i386_OR_x86_64\nconst std::ptrdiff_t defaultL1CacheSize = 32*1024;\nconst std::ptrdiff_t defaultL2CacheSize = 256*1024;\nconst std::ptrdiff_t defaultL3CacheSize = 2*1024*1024;\n#else\nconst std::ptrdiff_t defaultL1CacheSize = 16*1024;\nconst std::ptrdiff_t defaultL2CacheSize = 512*1024;\nconst std::ptrdiff_t defaultL3CacheSize = 512*1024;\n#endif\n\n/** \\internal */\nstruct CacheSizes {\n  CacheSizes(): m_l1(-1),m_l2(-1),m_l3(-1) {\n    int l1CacheSize, l2CacheSize, l3CacheSize;\n    queryCacheSizes(l1CacheSize, l2CacheSize, l3CacheSize);\n    m_l1 = manage_caching_sizes_helper(l1CacheSize, defaultL1CacheSize);\n    m_l2 = manage_caching_sizes_helper(l2CacheSize, defaultL2CacheSize);\n    m_l3 = manage_caching_sizes_helper(l3CacheSize, defaultL3CacheSize);\n  }\n\n  std::ptrdiff_t m_l1;\n  std::ptrdiff_t m_l2;\n  std::ptrdiff_t m_l3;\n};\n\n\n/** \\internal */\ninline void manage_caching_sizes(Action action, std::ptrdiff_t* l1, std::ptrdiff_t* l2, std::ptrdiff_t* l3)\n{\n  static CacheSizes m_cacheSizes;\n\n  if(action==SetAction)\n  {\n    // set the cpu cache size and cache all block sizes from a global cache size in byte\n    eigen_internal_assert(l1!=0 && l2!=0);\n    m_cacheSizes.m_l1 = *l1;\n    m_cacheSizes.m_l2 = *l2;\n    m_cacheSizes.m_l3 = *l3;\n  }\n  else if(action==GetAction)\n  {\n    eigen_internal_assert(l1!=0 && l2!=0);\n    *l1 = m_cacheSizes.m_l1;\n    *l2 = m_cacheSizes.m_l2;\n    *l3 = m_cacheSizes.m_l3;\n  }\n  else\n  {\n    eigen_internal_assert(false);\n  }\n}\n\n/* Helper for computeProductBlockingSizes.\n *\n * Given a m x k times k x n matrix product of scalar types \\c LhsScalar and \\c RhsScalar,\n * this function computes the blocking size parameters along the respective dimensions\n * for matrix products and related algorithms. The blocking sizes depends on various\n * parameters:\n * - the L1 and L2 cache sizes,\n * - the register level blocking sizes defined by gebp_traits,\n * - the number of scalars that fit into a packet (when vectorization is enabled).\n *\n * \\sa setCpuCacheSizes */\n\ntemplate<typename LhsScalar, typename RhsScalar, int KcFactor, typename Index>\nvoid evaluateProductBlockingSizesHeuristic(Index& k, Index& m, Index& n, Index num_threads = 1)\n{\n  typedef gebp_traits<LhsScalar,RhsScalar> Traits;\n\n  // Explanations:\n  // Let's recall that the product algorithms form mc x kc vertical panels A' on the lhs and\n  // kc x nc blocks B' on the rhs. B' has to fit into L2/L3 cache. Moreover, A' is processed\n  // per mr x kc horizontal small panels where mr is the blocking size along the m dimension\n  // at the register level. This small horizontal panel has to stay within L1 cache.\n  std::ptrdiff_t l1, l2, l3;\n  manage_caching_sizes(GetAction, &l1, &l2, &l3);\n\n  if (num_threads > 1) {\n    typedef typename Traits::ResScalar ResScalar;\n    enum {\n      kdiv = KcFactor * (Traits::mr * sizeof(LhsScalar) + Traits::nr * sizeof(RhsScalar)),\n      ksub = Traits::mr * Traits::nr * sizeof(ResScalar),\n      kr = 8,\n      mr = Traits::mr,\n      nr = Traits::nr\n    };\n    // Increasing k gives us more time to prefetch the content of the \"C\"\n    // registers. However once the latency is hidden there is no point in\n    // increasing the value of k, so we'll cap it at 320 (value determined\n    // experimentally).\n    const Index k_cache = (numext::mini<Index>)((l1-ksub)/kdiv, 320);\n    if (k_cache < k) {\n      k = k_cache - (k_cache % kr);\n      eigen_internal_assert(k > 0);\n    }\n\n    const Index n_cache = (l2-l1) / (nr * sizeof(RhsScalar) * k);\n    const Index n_per_thread = numext::div_ceil(n, num_threads);\n    if (n_cache <= n_per_thread) {\n      // Don't exceed the capacity of the l2 cache.\n      eigen_internal_assert(n_cache >= static_cast<Index>(nr));\n      n = n_cache - (n_cache % nr);\n      eigen_internal_assert(n > 0);\n    } else {\n      n = (numext::mini<Index>)(n, (n_per_thread + nr - 1) - ((n_per_thread + nr - 1) % nr));\n    }\n\n    if (l3 > l2) {\n      // l3 is shared between all cores, so we'll give each thread its own chunk of l3.\n      const Index m_cache = (l3-l2) / (sizeof(LhsScalar) * k * num_threads);\n      const Index m_per_thread = numext::div_ceil(m, num_threads);\n      if(m_cache < m_per_thread && m_cache >= static_cast<Index>(mr)) {\n        m = m_cache - (m_cache % mr);\n        eigen_internal_assert(m > 0);\n      } else {\n        m = (numext::mini<Index>)(m, (m_per_thread + mr - 1) - ((m_per_thread + mr - 1) % mr));\n      }\n    }\n  }\n  else {\n    // In unit tests we do not want to use extra large matrices,\n    // so we reduce the cache size to check the blocking strategy is not flawed\n#ifdef EIGEN_DEBUG_SMALL_PRODUCT_BLOCKS\n    l1 = 9*1024;\n    l2 = 32*1024;\n    l3 = 512*1024;\n#endif\n\n    // Early return for small problems because the computation below are time consuming for small problems.\n    // Perhaps it would make more sense to consider k*n*m??\n    // Note that for very tiny problem, this function should be bypassed anyway\n    // because we use the coefficient-based implementation for them.\n    if((numext::maxi)(k,(numext::maxi)(m,n))<48)\n      return;\n\n    typedef typename Traits::ResScalar ResScalar;\n    enum {\n      k_peeling = 8,\n      k_div = KcFactor * (Traits::mr * sizeof(LhsScalar) + Traits::nr * sizeof(RhsScalar)),\n      k_sub = Traits::mr * Traits::nr * sizeof(ResScalar)\n    };\n\n    // ---- 1st level of blocking on L1, yields kc ----\n\n    // Blocking on the third dimension (i.e., k) is chosen so that an horizontal panel\n    // of size mr x kc of the lhs plus a vertical panel of kc x nr of the rhs both fits within L1 cache.\n    // We also include a register-level block of the result (mx x nr).\n    // (In an ideal world only the lhs panel would stay in L1)\n    // Moreover, kc has to be a multiple of 8 to be compatible with loop peeling, leading to a maximum blocking size of:\n    const Index max_kc = numext::maxi<Index>(((l1-k_sub)/k_div) & (~(k_peeling-1)),1);\n    const Index old_k = k;\n    if(k>max_kc)\n    {\n      // We are really blocking on the third dimension:\n      // -> reduce blocking size to make sure the last block is as large as possible\n      //    while keeping the same number of sweeps over the result.\n      k = (k%max_kc)==0 ? max_kc\n                        : max_kc - k_peeling * ((max_kc-1-(k%max_kc))/(k_peeling*(k/max_kc+1)));\n\n      eigen_internal_assert(((old_k/k) == (old_k/max_kc)) && \"the number of sweeps has to remain the same\");\n    }\n\n    // ---- 2nd level of blocking on max(L2,L3), yields nc ----\n\n    // TODO find a reliable way to get the actual amount of cache per core to use for 2nd level blocking, that is:\n    //      actual_l2 = max(l2, l3/nb_core_sharing_l3)\n    // The number below is quite conservative: it is better to underestimate the cache size rather than overestimating it)\n    // For instance, it corresponds to 6MB of L3 shared among 4 cores.\n    #ifdef EIGEN_DEBUG_SMALL_PRODUCT_BLOCKS\n    const Index actual_l2 = l3;\n    #else\n    const Index actual_l2 = 1572864; // == 1.5 MB\n    #endif\n\n    // Here, nc is chosen such that a block of kc x nc of the rhs fit within half of L2.\n    // The second half is implicitly reserved to access the result and lhs coefficients.\n    // When k<max_kc, then nc can arbitrarily growth. In practice, it seems to be fruitful\n    // to limit this growth: we bound nc to growth by a factor x1.5.\n    // However, if the entire lhs block fit within L1, then we are not going to block on the rows at all,\n    // and it becomes fruitful to keep the packed rhs blocks in L1 if there is enough remaining space.\n    Index max_nc;\n    const Index lhs_bytes = m * k * sizeof(LhsScalar);\n    const Index remaining_l1 = l1- k_sub - lhs_bytes;\n    if(remaining_l1 >= Index(Traits::nr*sizeof(RhsScalar))*k)\n    {\n      // L1 blocking\n      max_nc = remaining_l1 / (k*sizeof(RhsScalar));\n    }\n    else\n    {\n      // L2 blocking\n      max_nc = (3*actual_l2)/(2*2*max_kc*sizeof(RhsScalar));\n    }\n    // WARNING Below, we assume that Traits::nr is a power of two.\n    Index nc = numext::mini<Index>(actual_l2/(2*k*sizeof(RhsScalar)), max_nc) & (~(Traits::nr-1));\n    if(n>nc)\n    {\n      // We are really blocking over the columns:\n      // -> reduce blocking size to make sure the last block is as large as possible\n      //    while keeping the same number of sweeps over the packed lhs.\n      //    Here we allow one more sweep if this gives us a perfect match, thus the commented \"-1\"\n      n = (n%nc)==0 ? nc\n                    : (nc - Traits::nr * ((nc/*-1*/-(n%nc))/(Traits::nr*(n/nc+1))));\n    }\n    else if(old_k==k)\n    {\n      // So far, no blocking at all, i.e., kc==k, and nc==n.\n      // In this case, let's perform a blocking over the rows such that the packed lhs data is kept in cache L1/L2\n      // TODO: part of this blocking strategy is now implemented within the kernel itself, so the L1-based heuristic here should be obsolete.\n      Index problem_size = k*n*sizeof(LhsScalar);\n      Index actual_lm = actual_l2;\n      Index max_mc = m;\n      if(problem_size<=1024)\n      {\n        // problem is small enough to keep in L1\n        // Let's choose m such that lhs's block fit in 1/3 of L1\n        actual_lm = l1;\n      }\n      else if(l3!=0 && problem_size<=32768)\n      {\n        // we have both L2 and L3, and problem is small enough to be kept in L2\n        // Let's choose m such that lhs's block fit in 1/3 of L2\n        actual_lm = l2;\n        max_mc = (numext::mini<Index>)(576,max_mc);\n      }\n      Index mc = (numext::mini<Index>)(actual_lm/(3*k*sizeof(LhsScalar)), max_mc);\n      if (mc > Traits::mr) mc -= mc % Traits::mr;\n      else if (mc==0) return;\n      m = (m%mc)==0 ? mc\n                    : (mc - Traits::mr * ((mc/*-1*/-(m%mc))/(Traits::mr*(m/mc+1))));\n    }\n  }\n}\n\ntemplate <typename Index>\ninline bool useSpecificBlockingSizes(Index& k, Index& m, Index& n)\n{\n#ifdef EIGEN_TEST_SPECIFIC_BLOCKING_SIZES\n  if (EIGEN_TEST_SPECIFIC_BLOCKING_SIZES) {\n    k = numext::mini<Index>(k, EIGEN_TEST_SPECIFIC_BLOCKING_SIZE_K);\n    m = numext::mini<Index>(m, EIGEN_TEST_SPECIFIC_BLOCKING_SIZE_M);\n    n = numext::mini<Index>(n, EIGEN_TEST_SPECIFIC_BLOCKING_SIZE_N);\n    return true;\n  }\n#else\n  EIGEN_UNUSED_VARIABLE(k)\n  EIGEN_UNUSED_VARIABLE(m)\n  EIGEN_UNUSED_VARIABLE(n)\n#endif\n  return false;\n}\n\n/** \\brief Computes the blocking parameters for a m x k times k x n matrix product\n  *\n  * \\param[in,out] k Input: the third dimension of the product. Output: the blocking size along the same dimension.\n  * \\param[in,out] m Input: the number of rows of the left hand side. Output: the blocking size along the same dimension.\n  * \\param[in,out] n Input: the number of columns of the right hand side. Output: the blocking size along the same dimension.\n  *\n  * Given a m x k times k x n matrix product of scalar types \\c LhsScalar and \\c RhsScalar,\n  * this function computes the blocking size parameters along the respective dimensions\n  * for matrix products and related algorithms.\n  *\n  * The blocking size parameters may be evaluated:\n  *   - either by a heuristic based on cache sizes;\n  *   - or using fixed prescribed values (for testing purposes).\n  *\n  * \\sa setCpuCacheSizes */\n\ntemplate<typename LhsScalar, typename RhsScalar, int KcFactor, typename Index>\nvoid computeProductBlockingSizes(Index& k, Index& m, Index& n, Index num_threads = 1)\n{\n  if (!useSpecificBlockingSizes(k, m, n)) {\n    evaluateProductBlockingSizesHeuristic<LhsScalar, RhsScalar, KcFactor, Index>(k, m, n, num_threads);\n  }\n}\n\ntemplate<typename LhsScalar, typename RhsScalar, typename Index>\ninline void computeProductBlockingSizes(Index& k, Index& m, Index& n, Index num_threads = 1)\n{\n  computeProductBlockingSizes<LhsScalar,RhsScalar,1,Index>(k, m, n, num_threads);\n}\n\n#ifdef EIGEN_HAS_SINGLE_INSTRUCTION_CJMADD\n  #define CJMADD(CJ,A,B,C,T)  C = CJ.pmadd(A,B,C);\n#else\n\n  // FIXME (a bit overkill maybe ?)\n\n  template<typename CJ, typename A, typename B, typename C, typename T> struct gebp_madd_selector {\n    EIGEN_ALWAYS_INLINE static void run(const CJ& cj, A& a, B& b, C& c, T& /*t*/)\n    {\n      c = cj.pmadd(a,b,c);\n    }\n  };\n\n  template<typename CJ, typename T> struct gebp_madd_selector<CJ,T,T,T,T> {\n    EIGEN_ALWAYS_INLINE static void run(const CJ& cj, T& a, T& b, T& c, T& t)\n    {\n      t = b; t = cj.pmul(a,t); c = padd(c,t);\n    }\n  };\n\n  template<typename CJ, typename A, typename B, typename C, typename T>\n  EIGEN_STRONG_INLINE void gebp_madd(const CJ& cj, A& a, B& b, C& c, T& t)\n  {\n    gebp_madd_selector<CJ,A,B,C,T>::run(cj,a,b,c,t);\n  }\n\n  #define CJMADD(CJ,A,B,C,T)  gebp_madd(CJ,A,B,C,T);\n//   #define CJMADD(CJ,A,B,C,T)  T = B; T = CJ.pmul(A,T); C = padd(C,T);\n#endif\n\n/* Vectorization logic\n *  real*real: unpack rhs to constant packets, ...\n * \n *  cd*cd : unpack rhs to (b_r,b_r), (b_i,b_i), mul to get (a_r b_r,a_i b_r) (a_r b_i,a_i b_i),\n *          storing each res packet into two packets (2x2),\n *          at the end combine them: swap the second and addsub them \n *  cf*cf : same but with 2x4 blocks\n *  cplx*real : unpack rhs to constant packets, ...\n *  real*cplx : load lhs as (a0,a0,a1,a1), and mul as usual\n */\ntemplate<typename _LhsScalar, typename _RhsScalar, bool _ConjLhs, bool _ConjRhs>\nclass gebp_traits\n{\npublic:\n  typedef _LhsScalar LhsScalar;\n  typedef _RhsScalar RhsScalar;\n  typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;\n\n  enum {\n    ConjLhs = _ConjLhs,\n    ConjRhs = _ConjRhs,\n    Vectorizable = packet_traits<LhsScalar>::Vectorizable && packet_traits<RhsScalar>::Vectorizable,\n    LhsPacketSize = Vectorizable ? packet_traits<LhsScalar>::size : 1,\n    RhsPacketSize = Vectorizable ? packet_traits<RhsScalar>::size : 1,\n    ResPacketSize = Vectorizable ? packet_traits<ResScalar>::size : 1,\n    \n    NumberOfRegisters = EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS,\n\n    // register block size along the N direction must be 1 or 4\n    nr = 4,\n\n    // register block size along the M direction (currently, this one cannot be modified)\n    default_mr = (EIGEN_PLAIN_ENUM_MIN(16,NumberOfRegisters)/2/nr)*LhsPacketSize,\n#if defined(EIGEN_HAS_SINGLE_INSTRUCTION_MADD) && !defined(EIGEN_VECTORIZE_ALTIVEC) && !defined(EIGEN_VECTORIZE_VSX)\n    // we assume 16 registers\n    // See bug 992, if the scalar type is not vectorizable but that EIGEN_HAS_SINGLE_INSTRUCTION_MADD is defined,\n    // then using 3*LhsPacketSize triggers non-implemented paths in syrk.\n    mr = Vectorizable ? 3*LhsPacketSize : default_mr,\n#else\n    mr = default_mr,\n#endif\n    \n    LhsProgress = LhsPacketSize,\n    RhsProgress = 1\n  };\n\n  typedef typename packet_traits<LhsScalar>::type  _LhsPacket;\n  typedef typename packet_traits<RhsScalar>::type  _RhsPacket;\n  typedef typename packet_traits<ResScalar>::type  _ResPacket;\n\n  typedef typename conditional<Vectorizable,_LhsPacket,LhsScalar>::type LhsPacket;\n  typedef typename conditional<Vectorizable,_RhsPacket,RhsScalar>::type RhsPacket;\n  typedef typename conditional<Vectorizable,_ResPacket,ResScalar>::type ResPacket;\n\n  typedef ResPacket AccPacket;\n  \n  EIGEN_STRONG_INLINE void initAcc(AccPacket& p)\n  {\n    p = pset1<ResPacket>(ResScalar(0));\n  }\n  \n  EIGEN_STRONG_INLINE void broadcastRhs(const RhsScalar* b, RhsPacket& b0, RhsPacket& b1, RhsPacket& b2, RhsPacket& b3)\n  {\n    pbroadcast4(b, b0, b1, b2, b3);\n  }\n  \n//   EIGEN_STRONG_INLINE void broadcastRhs(const RhsScalar* b, RhsPacket& b0, RhsPacket& b1)\n//   {\n//     pbroadcast2(b, b0, b1);\n//   }\n  \n  template<typename RhsPacketType>\n  EIGEN_STRONG_INLINE void loadRhs(const RhsScalar* b, RhsPacketType& dest) const\n  {\n    dest = pset1<RhsPacketType>(*b);\n  }\n  \n  EIGEN_STRONG_INLINE void loadRhsQuad(const RhsScalar* b, RhsPacket& dest) const\n  {\n    dest = ploadquad<RhsPacket>(b);\n  }\n\n  template<typename LhsPacketType>\n  EIGEN_STRONG_INLINE void loadLhs(const LhsScalar* a, LhsPacketType& dest) const\n  {\n    dest = pload<LhsPacketType>(a);\n  }\n\n  template<typename LhsPacketType>\n  EIGEN_STRONG_INLINE void loadLhsUnaligned(const LhsScalar* a, LhsPacketType& dest) const\n  {\n    dest = ploadu<LhsPacketType>(a);\n  }\n\n  template<typename LhsPacketType, typename RhsPacketType, typename AccPacketType>\n  EIGEN_STRONG_INLINE void madd(const LhsPacketType& a, const RhsPacketType& b, AccPacketType& c, AccPacketType& tmp) const\n  {\n    conj_helper<LhsPacketType,RhsPacketType,ConjLhs,ConjRhs> cj;\n    // It would be a lot cleaner to call pmadd all the time. Unfortunately if we\n    // let gcc allocate the register in which to store the result of the pmul\n    // (in the case where there is no FMA) gcc fails to figure out how to avoid\n    // spilling register.\n#ifdef EIGEN_HAS_SINGLE_INSTRUCTION_MADD\n    EIGEN_UNUSED_VARIABLE(tmp);\n    c = cj.pmadd(a,b,c);\n#else\n    tmp = b; tmp = cj.pmul(a,tmp); c = padd(c,tmp);\n#endif\n  }\n\n  EIGEN_STRONG_INLINE void acc(const AccPacket& c, const ResPacket& alpha, ResPacket& r) const\n  {\n    r = pmadd(c,alpha,r);\n  }\n  \n  template<typename ResPacketHalf>\n  EIGEN_STRONG_INLINE void acc(const ResPacketHalf& c, const ResPacketHalf& alpha, ResPacketHalf& r) const\n  {\n    r = pmadd(c,alpha,r);\n  }\n\n};\n\ntemplate<typename RealScalar, bool _ConjLhs>\nclass gebp_traits<std::complex<RealScalar>, RealScalar, _ConjLhs, false>\n{\npublic:\n  typedef std::complex<RealScalar> LhsScalar;\n  typedef RealScalar RhsScalar;\n  typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;\n\n  enum {\n    ConjLhs = _ConjLhs,\n    ConjRhs = false,\n    Vectorizable = packet_traits<LhsScalar>::Vectorizable && packet_traits<RhsScalar>::Vectorizable,\n    LhsPacketSize = Vectorizable ? packet_traits<LhsScalar>::size : 1,\n    RhsPacketSize = Vectorizable ? packet_traits<RhsScalar>::size : 1,\n    ResPacketSize = Vectorizable ? packet_traits<ResScalar>::size : 1,\n    \n    NumberOfRegisters = EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS,\n    nr = 4,\n#if defined(EIGEN_HAS_SINGLE_INSTRUCTION_MADD) && !defined(EIGEN_VECTORIZE_ALTIVEC) && !defined(EIGEN_VECTORIZE_VSX)\n    // we assume 16 registers\n    mr = 3*LhsPacketSize,\n#else\n    mr = (EIGEN_PLAIN_ENUM_MIN(16,NumberOfRegisters)/2/nr)*LhsPacketSize,\n#endif\n\n    LhsProgress = LhsPacketSize,\n    RhsProgress = 1\n  };\n\n  typedef typename packet_traits<LhsScalar>::type  _LhsPacket;\n  typedef typename packet_traits<RhsScalar>::type  _RhsPacket;\n  typedef typename packet_traits<ResScalar>::type  _ResPacket;\n\n  typedef typename conditional<Vectorizable,_LhsPacket,LhsScalar>::type LhsPacket;\n  typedef typename conditional<Vectorizable,_RhsPacket,RhsScalar>::type RhsPacket;\n  typedef typename conditional<Vectorizable,_ResPacket,ResScalar>::type ResPacket;\n\n  typedef ResPacket AccPacket;\n\n  EIGEN_STRONG_INLINE void initAcc(AccPacket& p)\n  {\n    p = pset1<ResPacket>(ResScalar(0));\n  }\n\n  EIGEN_STRONG_INLINE void loadRhs(const RhsScalar* b, RhsPacket& dest) const\n  {\n    dest = pset1<RhsPacket>(*b);\n  }\n  \n  EIGEN_STRONG_INLINE void loadRhsQuad(const RhsScalar* b, RhsPacket& dest) const\n  {\n    dest = pset1<RhsPacket>(*b);\n  }\n\n  EIGEN_STRONG_INLINE void loadLhs(const LhsScalar* a, LhsPacket& dest) const\n  {\n    dest = pload<LhsPacket>(a);\n  }\n\n  EIGEN_STRONG_INLINE void loadLhsUnaligned(const LhsScalar* a, LhsPacket& dest) const\n  {\n    dest = ploadu<LhsPacket>(a);\n  }\n\n  EIGEN_STRONG_INLINE void broadcastRhs(const RhsScalar* b, RhsPacket& b0, RhsPacket& b1, RhsPacket& b2, RhsPacket& b3)\n  {\n    pbroadcast4(b, b0, b1, b2, b3);\n  }\n  \n//   EIGEN_STRONG_INLINE void broadcastRhs(const RhsScalar* b, RhsPacket& b0, RhsPacket& b1)\n//   {\n//     pbroadcast2(b, b0, b1);\n//   }\n\n  EIGEN_STRONG_INLINE void madd(const LhsPacket& a, const RhsPacket& b, AccPacket& c, RhsPacket& tmp) const\n  {\n    madd_impl(a, b, c, tmp, typename conditional<Vectorizable,true_type,false_type>::type());\n  }\n\n  EIGEN_STRONG_INLINE void madd_impl(const LhsPacket& a, const RhsPacket& b, AccPacket& c, RhsPacket& tmp, const true_type&) const\n  {\n#ifdef EIGEN_HAS_SINGLE_INSTRUCTION_MADD\n    EIGEN_UNUSED_VARIABLE(tmp);\n    c.v = pmadd(a.v,b,c.v);\n#else\n    tmp = b; tmp = pmul(a.v,tmp); c.v = padd(c.v,tmp);\n#endif\n  }\n\n  EIGEN_STRONG_INLINE void madd_impl(const LhsScalar& a, const RhsScalar& b, ResScalar& c, RhsScalar& /*tmp*/, const false_type&) const\n  {\n    c += a * b;\n  }\n\n  EIGEN_STRONG_INLINE void acc(const AccPacket& c, const ResPacket& alpha, ResPacket& r) const\n  {\n    r = cj.pmadd(c,alpha,r);\n  }\n\nprotected:\n  conj_helper<ResPacket,ResPacket,ConjLhs,false> cj;\n};\n\ntemplate<typename Packet>\nstruct DoublePacket\n{\n  Packet first;\n  Packet second;\n};\n\ntemplate<typename Packet>\nDoublePacket<Packet> padd(const DoublePacket<Packet> &a, const DoublePacket<Packet> &b)\n{\n  DoublePacket<Packet> res;\n  res.first  = padd(a.first, b.first);\n  res.second = padd(a.second,b.second);\n  return res;\n}\n\ntemplate<typename Packet>\nconst DoublePacket<Packet>& predux_downto4(const DoublePacket<Packet> &a)\n{\n  return a;\n}\n\ntemplate<typename Packet> struct unpacket_traits<DoublePacket<Packet> > { typedef DoublePacket<Packet> half; };\n// template<typename Packet>\n// DoublePacket<Packet> pmadd(const DoublePacket<Packet> &a, const DoublePacket<Packet> &b)\n// {\n//   DoublePacket<Packet> res;\n//   res.first  = padd(a.first, b.first);\n//   res.second = padd(a.second,b.second);\n//   return res;\n// }\n\ntemplate<typename RealScalar, bool _ConjLhs, bool _ConjRhs>\nclass gebp_traits<std::complex<RealScalar>, std::complex<RealScalar>, _ConjLhs, _ConjRhs >\n{\npublic:\n  typedef std::complex<RealScalar>  Scalar;\n  typedef std::complex<RealScalar>  LhsScalar;\n  typedef std::complex<RealScalar>  RhsScalar;\n  typedef std::complex<RealScalar>  ResScalar;\n  \n  enum {\n    ConjLhs = _ConjLhs,\n    ConjRhs = _ConjRhs,\n    Vectorizable = packet_traits<RealScalar>::Vectorizable\n                && packet_traits<Scalar>::Vectorizable,\n    RealPacketSize  = Vectorizable ? packet_traits<RealScalar>::size : 1,\n    ResPacketSize   = Vectorizable ? packet_traits<ResScalar>::size : 1,\n    LhsPacketSize = Vectorizable ? packet_traits<LhsScalar>::size : 1,\n    RhsPacketSize = Vectorizable ? packet_traits<RhsScalar>::size : 1,\n\n    // FIXME: should depend on NumberOfRegisters\n    nr = 4,\n    mr = ResPacketSize,\n\n    LhsProgress = ResPacketSize,\n    RhsProgress = 1\n  };\n  \n  typedef typename packet_traits<RealScalar>::type RealPacket;\n  typedef typename packet_traits<Scalar>::type     ScalarPacket;\n  typedef DoublePacket<RealPacket> DoublePacketType;\n\n  typedef typename conditional<Vectorizable,RealPacket,  Scalar>::type LhsPacket;\n  typedef typename conditional<Vectorizable,DoublePacketType,Scalar>::type RhsPacket;\n  typedef typename conditional<Vectorizable,ScalarPacket,Scalar>::type ResPacket;\n  typedef typename conditional<Vectorizable,DoublePacketType,Scalar>::type AccPacket;\n  \n  EIGEN_STRONG_INLINE void initAcc(Scalar& p) { p = Scalar(0); }\n\n  EIGEN_STRONG_INLINE void initAcc(DoublePacketType& p)\n  {\n    p.first   = pset1<RealPacket>(RealScalar(0));\n    p.second  = pset1<RealPacket>(RealScalar(0));\n  }\n\n  // Scalar path\n  EIGEN_STRONG_INLINE void loadRhs(const RhsScalar* b, ResPacket& dest) const\n  {\n    dest = pset1<ResPacket>(*b);\n  }\n\n  // Vectorized path\n  EIGEN_STRONG_INLINE void loadRhs(const RhsScalar* b, DoublePacketType& dest) const\n  {\n    dest.first  = pset1<RealPacket>(real(*b));\n    dest.second = pset1<RealPacket>(imag(*b));\n  }\n  \n  EIGEN_STRONG_INLINE void loadRhsQuad(const RhsScalar* b, ResPacket& dest) const\n  {\n    loadRhs(b,dest);\n  }\n  EIGEN_STRONG_INLINE void loadRhsQuad(const RhsScalar* b, DoublePacketType& dest) const\n  {\n    eigen_internal_assert(unpacket_traits<ScalarPacket>::size<=4);\n    loadRhs(b,dest);\n  }\n  \n  EIGEN_STRONG_INLINE void broadcastRhs(const RhsScalar* b, RhsPacket& b0, RhsPacket& b1, RhsPacket& b2, RhsPacket& b3)\n  {\n    // FIXME not sure that's the best way to implement it!\n    loadRhs(b+0, b0);\n    loadRhs(b+1, b1);\n    loadRhs(b+2, b2);\n    loadRhs(b+3, b3);\n  }\n  \n  // Vectorized path\n  EIGEN_STRONG_INLINE void broadcastRhs(const RhsScalar* b, DoublePacketType& b0, DoublePacketType& b1)\n  {\n    // FIXME not sure that's the best way to implement it!\n    loadRhs(b+0, b0);\n    loadRhs(b+1, b1);\n  }\n  \n  // Scalar path\n  EIGEN_STRONG_INLINE void broadcastRhs(const RhsScalar* b, RhsScalar& b0, RhsScalar& b1)\n  {\n    // FIXME not sure that's the best way to implement it!\n    loadRhs(b+0, b0);\n    loadRhs(b+1, b1);\n  }\n\n  // nothing special here\n  EIGEN_STRONG_INLINE void loadLhs(const LhsScalar* a, LhsPacket& dest) const\n  {\n    dest = pload<LhsPacket>((const typename unpacket_traits<LhsPacket>::type*)(a));\n  }\n\n  EIGEN_STRONG_INLINE void loadLhsUnaligned(const LhsScalar* a, LhsPacket& dest) const\n  {\n    dest = ploadu<LhsPacket>((const typename unpacket_traits<LhsPacket>::type*)(a));\n  }\n\n  EIGEN_STRONG_INLINE void madd(const LhsPacket& a, const RhsPacket& b, DoublePacketType& c, RhsPacket& /*tmp*/) const\n  {\n    c.first   = padd(pmul(a,b.first), c.first);\n    c.second  = padd(pmul(a,b.second),c.second);\n  }\n\n  EIGEN_STRONG_INLINE void madd(const LhsPacket& a, const RhsPacket& b, ResPacket& c, RhsPacket& /*tmp*/) const\n  {\n    c = cj.pmadd(a,b,c);\n  }\n  \n  EIGEN_STRONG_INLINE void acc(const Scalar& c, const Scalar& alpha, Scalar& r) const { r += alpha * c; }\n  \n  EIGEN_STRONG_INLINE void acc(const DoublePacketType& c, const ResPacket& alpha, ResPacket& r) const\n  {\n    // assemble c\n    ResPacket tmp;\n    if((!ConjLhs)&&(!ConjRhs))\n    {\n      tmp = pcplxflip(pconj(ResPacket(c.second)));\n      tmp = padd(ResPacket(c.first),tmp);\n    }\n    else if((!ConjLhs)&&(ConjRhs))\n    {\n      tmp = pconj(pcplxflip(ResPacket(c.second)));\n      tmp = padd(ResPacket(c.first),tmp);\n    }\n    else if((ConjLhs)&&(!ConjRhs))\n    {\n      tmp = pcplxflip(ResPacket(c.second));\n      tmp = padd(pconj(ResPacket(c.first)),tmp);\n    }\n    else if((ConjLhs)&&(ConjRhs))\n    {\n      tmp = pcplxflip(ResPacket(c.second));\n      tmp = psub(pconj(ResPacket(c.first)),tmp);\n    }\n    \n    r = pmadd(tmp,alpha,r);\n  }\n\nprotected:\n  conj_helper<LhsScalar,RhsScalar,ConjLhs,ConjRhs> cj;\n};\n\ntemplate<typename RealScalar, bool _ConjRhs>\nclass gebp_traits<RealScalar, std::complex<RealScalar>, false, _ConjRhs >\n{\npublic:\n  typedef std::complex<RealScalar>  Scalar;\n  typedef RealScalar  LhsScalar;\n  typedef Scalar      RhsScalar;\n  typedef Scalar      ResScalar;\n\n  enum {\n    ConjLhs = false,\n    ConjRhs = _ConjRhs,\n    Vectorizable = packet_traits<RealScalar>::Vectorizable\n                && packet_traits<Scalar>::Vectorizable,\n    LhsPacketSize = Vectorizable ? packet_traits<LhsScalar>::size : 1,\n    RhsPacketSize = Vectorizable ? packet_traits<RhsScalar>::size : 1,\n    ResPacketSize = Vectorizable ? packet_traits<ResScalar>::size : 1,\n    \n    NumberOfRegisters = EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS,\n    // FIXME: should depend on NumberOfRegisters\n    nr = 4,\n    mr = (EIGEN_PLAIN_ENUM_MIN(16,NumberOfRegisters)/2/nr)*ResPacketSize,\n\n    LhsProgress = ResPacketSize,\n    RhsProgress = 1\n  };\n\n  typedef typename packet_traits<LhsScalar>::type  _LhsPacket;\n  typedef typename packet_traits<RhsScalar>::type  _RhsPacket;\n  typedef typename packet_traits<ResScalar>::type  _ResPacket;\n\n  typedef typename conditional<Vectorizable,_LhsPacket,LhsScalar>::type LhsPacket;\n  typedef typename conditional<Vectorizable,_RhsPacket,RhsScalar>::type RhsPacket;\n  typedef typename conditional<Vectorizable,_ResPacket,ResScalar>::type ResPacket;\n\n  typedef ResPacket AccPacket;\n\n  EIGEN_STRONG_INLINE void initAcc(AccPacket& p)\n  {\n    p = pset1<ResPacket>(ResScalar(0));\n  }\n\n  EIGEN_STRONG_INLINE void loadRhs(const RhsScalar* b, RhsPacket& dest) const\n  {\n    dest = pset1<RhsPacket>(*b);\n  }\n  \n  void broadcastRhs(const RhsScalar* b, RhsPacket& b0, RhsPacket& b1, RhsPacket& b2, RhsPacket& b3)\n  {\n    pbroadcast4(b, b0, b1, b2, b3);\n  }\n  \n//   EIGEN_STRONG_INLINE void broadcastRhs(const RhsScalar* b, RhsPacket& b0, RhsPacket& b1)\n//   {\n//     // FIXME not sure that's the best way to implement it!\n//     b0 = pload1<RhsPacket>(b+0);\n//     b1 = pload1<RhsPacket>(b+1);\n//   }\n\n  EIGEN_STRONG_INLINE void loadLhs(const LhsScalar* a, LhsPacket& dest) const\n  {\n    dest = ploaddup<LhsPacket>(a);\n  }\n  \n  EIGEN_STRONG_INLINE void loadRhsQuad(const RhsScalar* b, RhsPacket& dest) const\n  {\n    eigen_internal_assert(unpacket_traits<RhsPacket>::size<=4);\n    loadRhs(b,dest);\n  }\n\n  EIGEN_STRONG_INLINE void loadLhsUnaligned(const LhsScalar* a, LhsPacket& dest) const\n  {\n    dest = ploaddup<LhsPacket>(a);\n  }\n\n  EIGEN_STRONG_INLINE void madd(const LhsPacket& a, const RhsPacket& b, AccPacket& c, RhsPacket& tmp) const\n  {\n    madd_impl(a, b, c, tmp, typename conditional<Vectorizable,true_type,false_type>::type());\n  }\n\n  EIGEN_STRONG_INLINE void madd_impl(const LhsPacket& a, const RhsPacket& b, AccPacket& c, RhsPacket& tmp, const true_type&) const\n  {\n#ifdef EIGEN_HAS_SINGLE_INSTRUCTION_MADD\n    EIGEN_UNUSED_VARIABLE(tmp);\n    c.v = pmadd(a,b.v,c.v);\n#else\n    tmp = b; tmp.v = pmul(a,tmp.v); c = padd(c,tmp);\n#endif\n    \n  }\n\n  EIGEN_STRONG_INLINE void madd_impl(const LhsScalar& a, const RhsScalar& b, ResScalar& c, RhsScalar& /*tmp*/, const false_type&) const\n  {\n    c += a * b;\n  }\n\n  EIGEN_STRONG_INLINE void acc(const AccPacket& c, const ResPacket& alpha, ResPacket& r) const\n  {\n    r = cj.pmadd(alpha,c,r);\n  }\n\nprotected:\n  conj_helper<ResPacket,ResPacket,false,ConjRhs> cj;\n};\n\n/* optimized GEneral packed Block * packed Panel product kernel\n *\n * Mixing type logic: C += A * B\n *  |  A  |  B  | comments\n *  |real |cplx | no vectorization yet, would require to pack A with duplication\n *  |cplx |real | easy vectorization\n */\ntemplate<typename LhsScalar, typename RhsScalar, typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>\nstruct gebp_kernel\n{\n  typedef gebp_traits<LhsScalar,RhsScalar,ConjugateLhs,ConjugateRhs> Traits;\n  typedef typename Traits::ResScalar ResScalar;\n  typedef typename Traits::LhsPacket LhsPacket;\n  typedef typename Traits::RhsPacket RhsPacket;\n  typedef typename Traits::ResPacket ResPacket;\n  typedef typename Traits::AccPacket AccPacket;\n\n  typedef gebp_traits<RhsScalar,LhsScalar,ConjugateRhs,ConjugateLhs> SwappedTraits;\n  typedef typename SwappedTraits::ResScalar SResScalar;\n  typedef typename SwappedTraits::LhsPacket SLhsPacket;\n  typedef typename SwappedTraits::RhsPacket SRhsPacket;\n  typedef typename SwappedTraits::ResPacket SResPacket;\n  typedef typename SwappedTraits::AccPacket SAccPacket;\n\n  typedef typename DataMapper::LinearMapper LinearMapper;\n\n  enum {\n    Vectorizable  = Traits::Vectorizable,\n    LhsProgress   = Traits::LhsProgress,\n    RhsProgress   = Traits::RhsProgress,\n    ResPacketSize = Traits::ResPacketSize\n  };\n\n  EIGEN_DONT_INLINE\n  void operator()(const DataMapper& res, const LhsScalar* blockA, const RhsScalar* blockB,\n                  Index rows, Index depth, Index cols, ResScalar alpha,\n                  Index strideA=-1, Index strideB=-1, Index offsetA=0, Index offsetB=0);\n};\n\ntemplate<typename LhsScalar, typename RhsScalar, typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>\nEIGEN_DONT_INLINE\nvoid gebp_kernel<LhsScalar,RhsScalar,Index,DataMapper,mr,nr,ConjugateLhs,ConjugateRhs>\n  ::operator()(const DataMapper& res, const LhsScalar* blockA, const RhsScalar* blockB,\n               Index rows, Index depth, Index cols, ResScalar alpha,\n               Index strideA, Index strideB, Index offsetA, Index offsetB)\n  {\n    Traits traits;\n    SwappedTraits straits;\n    \n    if(strideA==-1) strideA = depth;\n    if(strideB==-1) strideB = depth;\n    conj_helper<LhsScalar,RhsScalar,ConjugateLhs,ConjugateRhs> cj;\n    Index packet_cols4 = nr>=4 ? (cols/4) * 4 : 0;\n    const Index peeled_mc3 = mr>=3*Traits::LhsProgress ? (rows/(3*LhsProgress))*(3*LhsProgress) : 0;\n    const Index peeled_mc2 = mr>=2*Traits::LhsProgress ? peeled_mc3+((rows-peeled_mc3)/(2*LhsProgress))*(2*LhsProgress) : 0;\n    const Index peeled_mc1 = mr>=1*Traits::LhsProgress ? (rows/(1*LhsProgress))*(1*LhsProgress) : 0;\n    enum { pk = 8 }; // NOTE Such a large peeling factor is important for large matrices (~ +5% when >1000 on Haswell)\n    const Index peeled_kc  = depth & ~(pk-1);\n    const Index prefetch_res_offset = 32/sizeof(ResScalar);    \n//     const Index depth2     = depth & ~1;\n\n    //---------- Process 3 * LhsProgress rows at once ----------\n    // This corresponds to 3*LhsProgress x nr register blocks.\n    // Usually, make sense only with FMA\n    if(mr>=3*Traits::LhsProgress)\n    {\n      // Here, the general idea is to loop on each largest micro horizontal panel of the lhs (3*Traits::LhsProgress x depth)\n      // and on each largest micro vertical panel of the rhs (depth * nr).\n      // Blocking sizes, i.e., 'depth' has been computed so that the micro horizontal panel of the lhs fit in L1.\n      // However, if depth is too small, we can extend the number of rows of these horizontal panels.\n      // This actual number of rows is computed as follow:\n      const Index l1 = defaultL1CacheSize; // in Bytes, TODO, l1 should be passed to this function.\n      // The max(1, ...) here is needed because we may be using blocking params larger than what our known l1 cache size\n      // suggests we should be using: either because our known l1 cache size is inaccurate (e.g. on Android, we can only guess),\n      // or because we are testing specific blocking sizes.\n      const Index actual_panel_rows = (3*LhsProgress) * std::max<Index>(1,( (l1 - sizeof(ResScalar)*mr*nr - depth*nr*sizeof(RhsScalar)) / (depth * sizeof(LhsScalar) * 3*LhsProgress) ));\n      for(Index i1=0; i1<peeled_mc3; i1+=actual_panel_rows)\n      {\n        const Index actual_panel_end = (std::min)(i1+actual_panel_rows, peeled_mc3);\n        for(Index j2=0; j2<packet_cols4; j2+=nr)\n        {\n          for(Index i=i1; i<actual_panel_end; i+=3*LhsProgress)\n          {\n          \n          // We selected a 3*Traits::LhsProgress x nr micro block of res which is entirely\n          // stored into 3 x nr registers.\n          \n          const LhsScalar* blA = &blockA[i*strideA+offsetA*(3*LhsProgress)];\n          prefetch(&blA[0]);\n\n          // gets res block as register\n          AccPacket C0, C1, C2,  C3,\n                    C4, C5, C6,  C7,\n                    C8, C9, C10, C11;\n          traits.initAcc(C0);  traits.initAcc(C1);  traits.initAcc(C2);  traits.initAcc(C3);\n          traits.initAcc(C4);  traits.initAcc(C5);  traits.initAcc(C6);  traits.initAcc(C7);\n          traits.initAcc(C8);  traits.initAcc(C9);  traits.initAcc(C10); traits.initAcc(C11);\n\n          LinearMapper r0 = res.getLinearMapper(i, j2 + 0);\n          LinearMapper r1 = res.getLinearMapper(i, j2 + 1);\n          LinearMapper r2 = res.getLinearMapper(i, j2 + 2);\n          LinearMapper r3 = res.getLinearMapper(i, j2 + 3);\n\n          r0.prefetch(0);\n          r1.prefetch(0);\n          r2.prefetch(0);\n          r3.prefetch(0);\n\n          // performs \"inner\" products\n          const RhsScalar* blB = &blockB[j2*strideB+offsetB*nr];\n          prefetch(&blB[0]);\n          LhsPacket A0, A1;\n\n          for(Index k=0; k<peeled_kc; k+=pk)\n          {\n            EIGEN_ASM_COMMENT(\"begin gebp micro kernel 3pX4\");\n            RhsPacket B_0, T0;\n            LhsPacket A2;\n\n#define EIGEN_GEBP_ONESTEP(K) \\\n            do { \\\n              EIGEN_ASM_COMMENT(\"begin step of gebp micro kernel 3pX4\"); \\\n              EIGEN_ASM_COMMENT(\"Note: these asm comments work around bug 935!\"); \\\n              internal::prefetch(blA+(3*K+16)*LhsProgress); \\\n              if (EIGEN_ARCH_ARM) { internal::prefetch(blB+(4*K+16)*RhsProgress); } /* Bug 953 */ \\\n              traits.loadLhs(&blA[(0+3*K)*LhsProgress], A0);  \\\n              traits.loadLhs(&blA[(1+3*K)*LhsProgress], A1);  \\\n              traits.loadLhs(&blA[(2+3*K)*LhsProgress], A2);  \\\n              traits.loadRhs(blB + (0+4*K)*Traits::RhsProgress, B_0); \\\n              traits.madd(A0, B_0, C0, T0); \\\n              traits.madd(A1, B_0, C4, T0); \\\n              traits.madd(A2, B_0, C8, B_0); \\\n              traits.loadRhs(blB + (1+4*K)*Traits::RhsProgress, B_0); \\\n              traits.madd(A0, B_0, C1, T0); \\\n              traits.madd(A1, B_0, C5, T0); \\\n              traits.madd(A2, B_0, C9, B_0); \\\n              traits.loadRhs(blB + (2+4*K)*Traits::RhsProgress, B_0); \\\n              traits.madd(A0, B_0, C2,  T0); \\\n              traits.madd(A1, B_0, C6,  T0); \\\n              traits.madd(A2, B_0, C10, B_0); \\\n              traits.loadRhs(blB + (3+4*K)*Traits::RhsProgress, B_0); \\\n              traits.madd(A0, B_0, C3 , T0); \\\n              traits.madd(A1, B_0, C7,  T0); \\\n              traits.madd(A2, B_0, C11, B_0); \\\n              EIGEN_ASM_COMMENT(\"end step of gebp micro kernel 3pX4\"); \\\n            } while(false)\n\n            internal::prefetch(blB);\n            EIGEN_GEBP_ONESTEP(0);\n            EIGEN_GEBP_ONESTEP(1);\n            EIGEN_GEBP_ONESTEP(2);\n            EIGEN_GEBP_ONESTEP(3);\n            EIGEN_GEBP_ONESTEP(4);\n            EIGEN_GEBP_ONESTEP(5);\n            EIGEN_GEBP_ONESTEP(6);\n            EIGEN_GEBP_ONESTEP(7);\n\n            blB += pk*4*RhsProgress;\n            blA += pk*3*Traits::LhsProgress;\n\n            EIGEN_ASM_COMMENT(\"end gebp micro kernel 3pX4\");\n          }\n          // process remaining peeled loop\n          for(Index k=peeled_kc; k<depth; k++)\n          {\n            RhsPacket B_0, T0;\n            LhsPacket A2;\n            EIGEN_GEBP_ONESTEP(0);\n            blB += 4*RhsProgress;\n            blA += 3*Traits::LhsProgress;\n          }\n\n#undef EIGEN_GEBP_ONESTEP\n\n          ResPacket R0, R1, R2;\n          ResPacket alphav = pset1<ResPacket>(alpha);\n\n          R0 = r0.loadPacket(0 * Traits::ResPacketSize);\n          R1 = r0.loadPacket(1 * Traits::ResPacketSize);\n          R2 = r0.loadPacket(2 * Traits::ResPacketSize);\n          traits.acc(C0, alphav, R0);\n          traits.acc(C4, alphav, R1);\n          traits.acc(C8, alphav, R2);\n          r0.storePacket(0 * Traits::ResPacketSize, R0);\n          r0.storePacket(1 * Traits::ResPacketSize, R1);\n          r0.storePacket(2 * Traits::ResPacketSize, R2);\n\n          R0 = r1.loadPacket(0 * Traits::ResPacketSize);\n          R1 = r1.loadPacket(1 * Traits::ResPacketSize);\n          R2 = r1.loadPacket(2 * Traits::ResPacketSize);\n          traits.acc(C1, alphav, R0);\n          traits.acc(C5, alphav, R1);\n          traits.acc(C9, alphav, R2);\n          r1.storePacket(0 * Traits::ResPacketSize, R0);\n          r1.storePacket(1 * Traits::ResPacketSize, R1);\n          r1.storePacket(2 * Traits::ResPacketSize, R2);\n\n          R0 = r2.loadPacket(0 * Traits::ResPacketSize);\n          R1 = r2.loadPacket(1 * Traits::ResPacketSize);\n          R2 = r2.loadPacket(2 * Traits::ResPacketSize);\n          traits.acc(C2, alphav, R0);\n          traits.acc(C6, alphav, R1);\n          traits.acc(C10, alphav, R2);\n          r2.storePacket(0 * Traits::ResPacketSize, R0);\n          r2.storePacket(1 * Traits::ResPacketSize, R1);\n          r2.storePacket(2 * Traits::ResPacketSize, R2);\n\n          R0 = r3.loadPacket(0 * Traits::ResPacketSize);\n          R1 = r3.loadPacket(1 * Traits::ResPacketSize);\n          R2 = r3.loadPacket(2 * Traits::ResPacketSize);\n          traits.acc(C3, alphav, R0);\n          traits.acc(C7, alphav, R1);\n          traits.acc(C11, alphav, R2);\n          r3.storePacket(0 * Traits::ResPacketSize, R0);\n          r3.storePacket(1 * Traits::ResPacketSize, R1);\n          r3.storePacket(2 * Traits::ResPacketSize, R2);          \n          }\n        }\n\n        // Deal with remaining columns of the rhs\n        for(Index j2=packet_cols4; j2<cols; j2++)\n        {\n          for(Index i=i1; i<actual_panel_end; i+=3*LhsProgress)\n          {\n          // One column at a time\n          const LhsScalar* blA = &blockA[i*strideA+offsetA*(3*Traits::LhsProgress)];\n          prefetch(&blA[0]);\n\n          // gets res block as register\n          AccPacket C0, C4, C8;\n          traits.initAcc(C0);\n          traits.initAcc(C4);\n          traits.initAcc(C8);\n\n          LinearMapper r0 = res.getLinearMapper(i, j2);\n          r0.prefetch(0);\n\n          // performs \"inner\" products\n          const RhsScalar* blB = &blockB[j2*strideB+offsetB];\n          LhsPacket A0, A1, A2;\n          \n          for(Index k=0; k<peeled_kc; k+=pk)\n          {\n            EIGEN_ASM_COMMENT(\"begin gebp micro kernel 3pX1\");\n            RhsPacket B_0;\n#define EIGEN_GEBGP_ONESTEP(K) \\\n            do { \\\n              EIGEN_ASM_COMMENT(\"begin step of gebp micro kernel 3pX1\"); \\\n              EIGEN_ASM_COMMENT(\"Note: these asm comments work around bug 935!\"); \\\n              traits.loadLhs(&blA[(0+3*K)*LhsProgress], A0);  \\\n              traits.loadLhs(&blA[(1+3*K)*LhsProgress], A1);  \\\n              traits.loadLhs(&blA[(2+3*K)*LhsProgress], A2);  \\\n              traits.loadRhs(&blB[(0+K)*RhsProgress], B_0);   \\\n              traits.madd(A0, B_0, C0, B_0); \\\n              traits.madd(A1, B_0, C4, B_0); \\\n              traits.madd(A2, B_0, C8, B_0); \\\n              EIGEN_ASM_COMMENT(\"end step of gebp micro kernel 3pX1\"); \\\n            } while(false)\n        \n            EIGEN_GEBGP_ONESTEP(0);\n            EIGEN_GEBGP_ONESTEP(1);\n            EIGEN_GEBGP_ONESTEP(2);\n            EIGEN_GEBGP_ONESTEP(3);\n            EIGEN_GEBGP_ONESTEP(4);\n            EIGEN_GEBGP_ONESTEP(5);\n            EIGEN_GEBGP_ONESTEP(6);\n            EIGEN_GEBGP_ONESTEP(7);\n\n            blB += pk*RhsProgress;\n            blA += pk*3*Traits::LhsProgress;\n\n            EIGEN_ASM_COMMENT(\"end gebp micro kernel 3pX1\");\n          }\n\n          // process remaining peeled loop\n          for(Index k=peeled_kc; k<depth; k++)\n          {\n            RhsPacket B_0;\n            EIGEN_GEBGP_ONESTEP(0);\n            blB += RhsProgress;\n            blA += 3*Traits::LhsProgress;\n          }\n#undef EIGEN_GEBGP_ONESTEP\n          ResPacket R0, R1, R2;\n          ResPacket alphav = pset1<ResPacket>(alpha);\n\n          R0 = r0.loadPacket(0 * Traits::ResPacketSize);\n          R1 = r0.loadPacket(1 * Traits::ResPacketSize);\n          R2 = r0.loadPacket(2 * Traits::ResPacketSize);\n          traits.acc(C0, alphav, R0);\n          traits.acc(C4, alphav, R1);\n          traits.acc(C8, alphav, R2);\n          r0.storePacket(0 * Traits::ResPacketSize, R0);\n          r0.storePacket(1 * Traits::ResPacketSize, R1);\n          r0.storePacket(2 * Traits::ResPacketSize, R2);          \n          }\n        }\n      }\n    }\n\n    //---------- Process 2 * LhsProgress rows at once ----------\n    if(mr>=2*Traits::LhsProgress)\n    {\n      const Index l1 = defaultL1CacheSize; // in Bytes, TODO, l1 should be passed to this function.\n      // The max(1, ...) here is needed because we may be using blocking params larger than what our known l1 cache size\n      // suggests we should be using: either because our known l1 cache size is inaccurate (e.g. on Android, we can only guess),\n      // or because we are testing specific blocking sizes.\n      Index actual_panel_rows = (2*LhsProgress) * std::max<Index>(1,( (l1 - sizeof(ResScalar)*mr*nr - depth*nr*sizeof(RhsScalar)) / (depth * sizeof(LhsScalar) * 2*LhsProgress) ));\n\n      for(Index i1=peeled_mc3; i1<peeled_mc2; i1+=actual_panel_rows)\n      {\n        Index actual_panel_end = (std::min)(i1+actual_panel_rows, peeled_mc2);\n        for(Index j2=0; j2<packet_cols4; j2+=nr)\n        {\n          for(Index i=i1; i<actual_panel_end; i+=2*LhsProgress)\n          {\n          \n          // We selected a 2*Traits::LhsProgress x nr micro block of res which is entirely\n          // stored into 2 x nr registers.\n          \n          const LhsScalar* blA = &blockA[i*strideA+offsetA*(2*Traits::LhsProgress)];\n          prefetch(&blA[0]);\n\n          // gets res block as register\n          AccPacket C0, C1, C2, C3,\n                    C4, C5, C6, C7;\n          traits.initAcc(C0); traits.initAcc(C1); traits.initAcc(C2); traits.initAcc(C3);\n          traits.initAcc(C4); traits.initAcc(C5); traits.initAcc(C6); traits.initAcc(C7);\n\n          LinearMapper r0 = res.getLinearMapper(i, j2 + 0);\n          LinearMapper r1 = res.getLinearMapper(i, j2 + 1);\n          LinearMapper r2 = res.getLinearMapper(i, j2 + 2);\n          LinearMapper r3 = res.getLinearMapper(i, j2 + 3);\n\n          r0.prefetch(prefetch_res_offset);\n          r1.prefetch(prefetch_res_offset);\n          r2.prefetch(prefetch_res_offset);\n          r3.prefetch(prefetch_res_offset);\n\n          // performs \"inner\" products\n          const RhsScalar* blB = &blockB[j2*strideB+offsetB*nr];\n          prefetch(&blB[0]);\n          LhsPacket A0, A1;\n\n          for(Index k=0; k<peeled_kc; k+=pk)\n          {\n            EIGEN_ASM_COMMENT(\"begin gebp micro kernel 2pX4\");\n            RhsPacket B_0, B1, B2, B3, T0;\n\n   #define EIGEN_GEBGP_ONESTEP(K) \\\n            do {                                                                \\\n              EIGEN_ASM_COMMENT(\"begin step of gebp micro kernel 2pX4\");        \\\n              EIGEN_ASM_COMMENT(\"Note: these asm comments work around bug 935!\"); \\\n              traits.loadLhs(&blA[(0+2*K)*LhsProgress], A0);                    \\\n              traits.loadLhs(&blA[(1+2*K)*LhsProgress], A1);                    \\\n              traits.broadcastRhs(&blB[(0+4*K)*RhsProgress], B_0, B1, B2, B3);  \\\n              traits.madd(A0, B_0, C0, T0);                                     \\\n              traits.madd(A1, B_0, C4, B_0);                                    \\\n              traits.madd(A0, B1,  C1, T0);                                     \\\n              traits.madd(A1, B1,  C5, B1);                                     \\\n              traits.madd(A0, B2,  C2, T0);                                     \\\n              traits.madd(A1, B2,  C6, B2);                                     \\\n              traits.madd(A0, B3,  C3, T0);                                     \\\n              traits.madd(A1, B3,  C7, B3);                                     \\\n              EIGEN_ASM_COMMENT(\"end step of gebp micro kernel 2pX4\");          \\\n            } while(false)\n            \n            internal::prefetch(blB+(48+0));\n            EIGEN_GEBGP_ONESTEP(0);\n            EIGEN_GEBGP_ONESTEP(1);\n            EIGEN_GEBGP_ONESTEP(2);\n            EIGEN_GEBGP_ONESTEP(3);\n            internal::prefetch(blB+(48+16));\n            EIGEN_GEBGP_ONESTEP(4);\n            EIGEN_GEBGP_ONESTEP(5);\n            EIGEN_GEBGP_ONESTEP(6);\n            EIGEN_GEBGP_ONESTEP(7);\n\n            blB += pk*4*RhsProgress;\n            blA += pk*(2*Traits::LhsProgress);\n\n            EIGEN_ASM_COMMENT(\"end gebp micro kernel 2pX4\");\n          }\n          // process remaining peeled loop\n          for(Index k=peeled_kc; k<depth; k++)\n          {\n            RhsPacket B_0, B1, B2, B3, T0;\n            EIGEN_GEBGP_ONESTEP(0);\n            blB += 4*RhsProgress;\n            blA += 2*Traits::LhsProgress;\n          }\n#undef EIGEN_GEBGP_ONESTEP\n\n          ResPacket R0, R1, R2, R3;\n          ResPacket alphav = pset1<ResPacket>(alpha);\n\n          R0 = r0.loadPacket(0 * Traits::ResPacketSize);\n          R1 = r0.loadPacket(1 * Traits::ResPacketSize);\n          R2 = r1.loadPacket(0 * Traits::ResPacketSize);\n          R3 = r1.loadPacket(1 * Traits::ResPacketSize);\n          traits.acc(C0, alphav, R0);\n          traits.acc(C4, alphav, R1);\n          traits.acc(C1, alphav, R2);\n          traits.acc(C5, alphav, R3);\n          r0.storePacket(0 * Traits::ResPacketSize, R0);\n          r0.storePacket(1 * Traits::ResPacketSize, R1);\n          r1.storePacket(0 * Traits::ResPacketSize, R2);\n          r1.storePacket(1 * Traits::ResPacketSize, R3);\n\n          R0 = r2.loadPacket(0 * Traits::ResPacketSize);\n          R1 = r2.loadPacket(1 * Traits::ResPacketSize);\n          R2 = r3.loadPacket(0 * Traits::ResPacketSize);\n          R3 = r3.loadPacket(1 * Traits::ResPacketSize);\n          traits.acc(C2,  alphav, R0);\n          traits.acc(C6,  alphav, R1);\n          traits.acc(C3,  alphav, R2);\n          traits.acc(C7,  alphav, R3);\n          r2.storePacket(0 * Traits::ResPacketSize, R0);\n          r2.storePacket(1 * Traits::ResPacketSize, R1);\n          r3.storePacket(0 * Traits::ResPacketSize, R2);\n          r3.storePacket(1 * Traits::ResPacketSize, R3);\n          }\n        }\n      \n        // Deal with remaining columns of the rhs\n        for(Index j2=packet_cols4; j2<cols; j2++)\n        {\n          for(Index i=i1; i<actual_panel_end; i+=2*LhsProgress)\n          {\n          // One column at a time\n          const LhsScalar* blA = &blockA[i*strideA+offsetA*(2*Traits::LhsProgress)];\n          prefetch(&blA[0]);\n\n          // gets res block as register\n          AccPacket C0, C4;\n          traits.initAcc(C0);\n          traits.initAcc(C4);\n\n          LinearMapper r0 = res.getLinearMapper(i, j2);\n          r0.prefetch(prefetch_res_offset);\n\n          // performs \"inner\" products\n          const RhsScalar* blB = &blockB[j2*strideB+offsetB];\n          LhsPacket A0, A1;\n\n          for(Index k=0; k<peeled_kc; k+=pk)\n          {\n            EIGEN_ASM_COMMENT(\"begin gebp micro kernel 2pX1\");\n            RhsPacket B_0, B1;\n        \n#define EIGEN_GEBGP_ONESTEP(K) \\\n            do {                                                                  \\\n              EIGEN_ASM_COMMENT(\"begin step of gebp micro kernel 2pX1\");          \\\n              EIGEN_ASM_COMMENT(\"Note: these asm comments work around bug 935!\"); \\\n              traits.loadLhs(&blA[(0+2*K)*LhsProgress], A0);                      \\\n              traits.loadLhs(&blA[(1+2*K)*LhsProgress], A1);                      \\\n              traits.loadRhs(&blB[(0+K)*RhsProgress], B_0);                       \\\n              traits.madd(A0, B_0, C0, B1);                                       \\\n              traits.madd(A1, B_0, C4, B_0);                                      \\\n              EIGEN_ASM_COMMENT(\"end step of gebp micro kernel 2pX1\");            \\\n            } while(false)\n        \n            EIGEN_GEBGP_ONESTEP(0);\n            EIGEN_GEBGP_ONESTEP(1);\n            EIGEN_GEBGP_ONESTEP(2);\n            EIGEN_GEBGP_ONESTEP(3);\n            EIGEN_GEBGP_ONESTEP(4);\n            EIGEN_GEBGP_ONESTEP(5);\n            EIGEN_GEBGP_ONESTEP(6);\n            EIGEN_GEBGP_ONESTEP(7);\n\n            blB += pk*RhsProgress;\n            blA += pk*2*Traits::LhsProgress;\n\n            EIGEN_ASM_COMMENT(\"end gebp micro kernel 2pX1\");\n          }\n\n          // process remaining peeled loop\n          for(Index k=peeled_kc; k<depth; k++)\n          {\n            RhsPacket B_0, B1;\n            EIGEN_GEBGP_ONESTEP(0);\n            blB += RhsProgress;\n            blA += 2*Traits::LhsProgress;\n          }\n#undef EIGEN_GEBGP_ONESTEP\n          ResPacket R0, R1;\n          ResPacket alphav = pset1<ResPacket>(alpha);\n\n          R0 = r0.loadPacket(0 * Traits::ResPacketSize);\n          R1 = r0.loadPacket(1 * Traits::ResPacketSize);\n          traits.acc(C0, alphav, R0);\n          traits.acc(C4, alphav, R1);\n          r0.storePacket(0 * Traits::ResPacketSize, R0);\n          r0.storePacket(1 * Traits::ResPacketSize, R1);\n          }\n        }\n      }\n    }\n    //---------- Process 1 * LhsProgress rows at once ----------\n    if(mr>=1*Traits::LhsProgress)\n    {\n      // loops on each largest micro horizontal panel of lhs (1*LhsProgress x depth)\n      for(Index i=peeled_mc2; i<peeled_mc1; i+=1*LhsProgress)\n      {\n        // loops on each largest micro vertical panel of rhs (depth * nr)\n        for(Index j2=0; j2<packet_cols4; j2+=nr)\n        {\n          // We select a 1*Traits::LhsProgress x nr micro block of res which is entirely\n          // stored into 1 x nr registers.\n          \n          const LhsScalar* blA = &blockA[i*strideA+offsetA*(1*Traits::LhsProgress)];\n          prefetch(&blA[0]);\n\n          // gets res block as register\n          AccPacket C0, C1, C2, C3;\n          traits.initAcc(C0);\n          traits.initAcc(C1);\n          traits.initAcc(C2);\n          traits.initAcc(C3);\n\n          LinearMapper r0 = res.getLinearMapper(i, j2 + 0);\n          LinearMapper r1 = res.getLinearMapper(i, j2 + 1);\n          LinearMapper r2 = res.getLinearMapper(i, j2 + 2);\n          LinearMapper r3 = res.getLinearMapper(i, j2 + 3);\n\n          r0.prefetch(prefetch_res_offset);\n          r1.prefetch(prefetch_res_offset);\n          r2.prefetch(prefetch_res_offset);\n          r3.prefetch(prefetch_res_offset);\n\n          // performs \"inner\" products\n          const RhsScalar* blB = &blockB[j2*strideB+offsetB*nr];\n          prefetch(&blB[0]);\n          LhsPacket A0;\n\n          for(Index k=0; k<peeled_kc; k+=pk)\n          {\n            EIGEN_ASM_COMMENT(\"begin gebp micro kernel 1pX4\");\n            RhsPacket B_0, B1, B2, B3;\n               \n#define EIGEN_GEBGP_ONESTEP(K) \\\n            do {                                                                \\\n              EIGEN_ASM_COMMENT(\"begin step of gebp micro kernel 1pX4\");        \\\n              EIGEN_ASM_COMMENT(\"Note: these asm comments work around bug 935!\"); \\\n              traits.loadLhs(&blA[(0+1*K)*LhsProgress], A0);                    \\\n              traits.broadcastRhs(&blB[(0+4*K)*RhsProgress], B_0, B1, B2, B3);  \\\n              traits.madd(A0, B_0, C0, B_0);                                    \\\n              traits.madd(A0, B1,  C1, B1);                                     \\\n              traits.madd(A0, B2,  C2, B2);                                     \\\n              traits.madd(A0, B3,  C3, B3);                                     \\\n              EIGEN_ASM_COMMENT(\"end step of gebp micro kernel 1pX4\");          \\\n            } while(false)\n            \n            internal::prefetch(blB+(48+0));\n            EIGEN_GEBGP_ONESTEP(0);\n            EIGEN_GEBGP_ONESTEP(1);\n            EIGEN_GEBGP_ONESTEP(2);\n            EIGEN_GEBGP_ONESTEP(3);\n            internal::prefetch(blB+(48+16));\n            EIGEN_GEBGP_ONESTEP(4);\n            EIGEN_GEBGP_ONESTEP(5);\n            EIGEN_GEBGP_ONESTEP(6);\n            EIGEN_GEBGP_ONESTEP(7);\n\n            blB += pk*4*RhsProgress;\n            blA += pk*1*LhsProgress;\n\n            EIGEN_ASM_COMMENT(\"end gebp micro kernel 1pX4\");\n          }\n          // process remaining peeled loop\n          for(Index k=peeled_kc; k<depth; k++)\n          {\n            RhsPacket B_0, B1, B2, B3;\n            EIGEN_GEBGP_ONESTEP(0);\n            blB += 4*RhsProgress;\n            blA += 1*LhsProgress;\n          }\n#undef EIGEN_GEBGP_ONESTEP\n\n          ResPacket R0, R1;\n          ResPacket alphav = pset1<ResPacket>(alpha);\n\n          R0 = r0.loadPacket(0 * Traits::ResPacketSize);\n          R1 = r1.loadPacket(0 * Traits::ResPacketSize);\n          traits.acc(C0, alphav, R0);\n          traits.acc(C1,  alphav, R1);\n          r0.storePacket(0 * Traits::ResPacketSize, R0);\n          r1.storePacket(0 * Traits::ResPacketSize, R1);\n\n          R0 = r2.loadPacket(0 * Traits::ResPacketSize);\n          R1 = r3.loadPacket(0 * Traits::ResPacketSize);\n          traits.acc(C2,  alphav, R0);\n          traits.acc(C3,  alphav, R1);\n          r2.storePacket(0 * Traits::ResPacketSize, R0);\n          r3.storePacket(0 * Traits::ResPacketSize, R1);\n        }\n\n        // Deal with remaining columns of the rhs\n        for(Index j2=packet_cols4; j2<cols; j2++)\n        {\n          // One column at a time\n          const LhsScalar* blA = &blockA[i*strideA+offsetA*(1*Traits::LhsProgress)];\n          prefetch(&blA[0]);\n\n          // gets res block as register\n          AccPacket C0;\n          traits.initAcc(C0);\n\n          LinearMapper r0 = res.getLinearMapper(i, j2);\n\n          // performs \"inner\" products\n          const RhsScalar* blB = &blockB[j2*strideB+offsetB];\n          LhsPacket A0;\n\n          for(Index k=0; k<peeled_kc; k+=pk)\n          {\n            EIGEN_ASM_COMMENT(\"begin gebp micro kernel 1pX1\");\n            RhsPacket B_0;\n        \n#define EIGEN_GEBGP_ONESTEP(K) \\\n            do {                                                                \\\n              EIGEN_ASM_COMMENT(\"begin step of gebp micro kernel 1pX1\");        \\\n              EIGEN_ASM_COMMENT(\"Note: these asm comments work around bug 935!\"); \\\n              traits.loadLhs(&blA[(0+1*K)*LhsProgress], A0);                    \\\n              traits.loadRhs(&blB[(0+K)*RhsProgress], B_0);                     \\\n              traits.madd(A0, B_0, C0, B_0);                                    \\\n              EIGEN_ASM_COMMENT(\"end step of gebp micro kernel 1pX1\");          \\\n            } while(false);\n\n            EIGEN_GEBGP_ONESTEP(0);\n            EIGEN_GEBGP_ONESTEP(1);\n            EIGEN_GEBGP_ONESTEP(2);\n            EIGEN_GEBGP_ONESTEP(3);\n            EIGEN_GEBGP_ONESTEP(4);\n            EIGEN_GEBGP_ONESTEP(5);\n            EIGEN_GEBGP_ONESTEP(6);\n            EIGEN_GEBGP_ONESTEP(7);\n\n            blB += pk*RhsProgress;\n            blA += pk*1*Traits::LhsProgress;\n\n            EIGEN_ASM_COMMENT(\"end gebp micro kernel 1pX1\");\n          }\n\n          // process remaining peeled loop\n          for(Index k=peeled_kc; k<depth; k++)\n          {\n            RhsPacket B_0;\n            EIGEN_GEBGP_ONESTEP(0);\n            blB += RhsProgress;\n            blA += 1*Traits::LhsProgress;\n          }\n#undef EIGEN_GEBGP_ONESTEP\n          ResPacket R0;\n          ResPacket alphav = pset1<ResPacket>(alpha);\n          R0 = r0.loadPacket(0 * Traits::ResPacketSize);\n          traits.acc(C0, alphav, R0);\n          r0.storePacket(0 * Traits::ResPacketSize, R0);\n        }\n      }\n    }\n    //---------- Process remaining rows, 1 at once ----------\n    if(peeled_mc1<rows)\n    {\n      // loop on each panel of the rhs\n      for(Index j2=0; j2<packet_cols4; j2+=nr)\n      {\n        // loop on each row of the lhs (1*LhsProgress x depth)\n        for(Index i=peeled_mc1; i<rows; i+=1)\n        {\n          const LhsScalar* blA = &blockA[i*strideA+offsetA];\n          prefetch(&blA[0]);\n          const RhsScalar* blB = &blockB[j2*strideB+offsetB*nr];\n\n          // The following piece of code wont work for 512 bit registers\n          // Moreover, if LhsProgress==8 it assumes that there is a half packet of the same size\n          // as nr (which is currently 4) for the return type.\n          typedef typename unpacket_traits<SResPacket>::half SResPacketHalf;\n          if ((SwappedTraits::LhsProgress % 4) == 0 &&\n              (SwappedTraits::LhsProgress <= 8) &&\n              (SwappedTraits::LhsProgress!=8 || unpacket_traits<SResPacketHalf>::size==nr))\n          {\n            SAccPacket C0, C1, C2, C3;\n            straits.initAcc(C0);\n            straits.initAcc(C1);\n            straits.initAcc(C2);\n            straits.initAcc(C3);\n\n            const Index spk   = (std::max)(1,SwappedTraits::LhsProgress/4);\n            const Index endk  = (depth/spk)*spk;\n            const Index endk4 = (depth/(spk*4))*(spk*4);\n\n            Index k=0;\n            for(; k<endk4; k+=4*spk)\n            {\n              SLhsPacket A0,A1;\n              SRhsPacket B_0,B_1;\n\n              straits.loadLhsUnaligned(blB+0*SwappedTraits::LhsProgress, A0);\n              straits.loadLhsUnaligned(blB+1*SwappedTraits::LhsProgress, A1);\n\n              straits.loadRhsQuad(blA+0*spk, B_0);\n              straits.loadRhsQuad(blA+1*spk, B_1);\n              straits.madd(A0,B_0,C0,B_0);\n              straits.madd(A1,B_1,C1,B_1);\n\n              straits.loadLhsUnaligned(blB+2*SwappedTraits::LhsProgress, A0);\n              straits.loadLhsUnaligned(blB+3*SwappedTraits::LhsProgress, A1);\n              straits.loadRhsQuad(blA+2*spk, B_0);\n              straits.loadRhsQuad(blA+3*spk, B_1);\n              straits.madd(A0,B_0,C2,B_0);\n              straits.madd(A1,B_1,C3,B_1);\n\n              blB += 4*SwappedTraits::LhsProgress;\n              blA += 4*spk;\n            }\n            C0 = padd(padd(C0,C1),padd(C2,C3));\n            for(; k<endk; k+=spk)\n            {\n              SLhsPacket A0;\n              SRhsPacket B_0;\n\n              straits.loadLhsUnaligned(blB, A0);\n              straits.loadRhsQuad(blA, B_0);\n              straits.madd(A0,B_0,C0,B_0);\n\n              blB += SwappedTraits::LhsProgress;\n              blA += spk;\n            }\n            if(SwappedTraits::LhsProgress==8)\n            {\n              // Special case where we have to first reduce the accumulation register C0\n              typedef typename conditional<SwappedTraits::LhsProgress>=8,typename unpacket_traits<SResPacket>::half,SResPacket>::type SResPacketHalf;\n              typedef typename conditional<SwappedTraits::LhsProgress>=8,typename unpacket_traits<SLhsPacket>::half,SLhsPacket>::type SLhsPacketHalf;\n              typedef typename conditional<SwappedTraits::LhsProgress>=8,typename unpacket_traits<SLhsPacket>::half,SRhsPacket>::type SRhsPacketHalf;\n              typedef typename conditional<SwappedTraits::LhsProgress>=8,typename unpacket_traits<SAccPacket>::half,SAccPacket>::type SAccPacketHalf;\n\n              SResPacketHalf R = res.template gatherPacket<SResPacketHalf>(i, j2);\n              SResPacketHalf alphav = pset1<SResPacketHalf>(alpha);\n\n              if(depth-endk>0)\n              {\n                // We have to handle the last row of the rhs which corresponds to a half-packet\n                SLhsPacketHalf a0;\n                SRhsPacketHalf b0;\n                straits.loadLhsUnaligned(blB, a0);\n                straits.loadRhs(blA, b0);\n                SAccPacketHalf c0 = predux_downto4(C0);\n                straits.madd(a0,b0,c0,b0);\n                straits.acc(c0, alphav, R);\n              }\n              else\n              {\n                straits.acc(predux_downto4(C0), alphav, R);\n              }\n              res.scatterPacket(i, j2, R);\n            }\n            else\n            {\n              SResPacket R = res.template gatherPacket<SResPacket>(i, j2);\n              SResPacket alphav = pset1<SResPacket>(alpha);\n              straits.acc(C0, alphav, R);\n              res.scatterPacket(i, j2, R);\n            }\n          }\n          else // scalar path\n          {\n            // get a 1 x 4 res block as registers\n            ResScalar C0(0), C1(0), C2(0), C3(0);\n\n            for(Index k=0; k<depth; k++)\n            {\n              LhsScalar A0;\n              RhsScalar B_0, B_1;\n\n              A0 = blA[k];\n\n              B_0 = blB[0];\n              B_1 = blB[1];\n              CJMADD(cj,A0,B_0,C0,  B_0);\n              CJMADD(cj,A0,B_1,C1,  B_1);\n              \n              B_0 = blB[2];\n              B_1 = blB[3];\n              CJMADD(cj,A0,B_0,C2,  B_0);\n              CJMADD(cj,A0,B_1,C3,  B_1);\n              \n              blB += 4;\n            }\n            res(i, j2 + 0) += alpha * C0;\n            res(i, j2 + 1) += alpha * C1;\n            res(i, j2 + 2) += alpha * C2;\n            res(i, j2 + 3) += alpha * C3;\n          }\n        }\n      }\n      // remaining columns\n      for(Index j2=packet_cols4; j2<cols; j2++)\n      {\n        // loop on each row of the lhs (1*LhsProgress x depth)\n        for(Index i=peeled_mc1; i<rows; i+=1)\n        {\n          const LhsScalar* blA = &blockA[i*strideA+offsetA];\n          prefetch(&blA[0]);\n          // gets a 1 x 1 res block as registers\n          ResScalar C0(0);\n          const RhsScalar* blB = &blockB[j2*strideB+offsetB];\n          for(Index k=0; k<depth; k++)\n          {\n            LhsScalar A0 = blA[k];\n            RhsScalar B_0 = blB[k];\n            CJMADD(cj, A0, B_0, C0, B_0);\n          }\n          res(i, j2) += alpha * C0;\n        }\n      }\n    }\n  }\n\n\n#undef CJMADD\n\n// pack a block of the lhs\n// The traversal is as follow (mr==4):\n//   0  4  8 12 ...\n//   1  5  9 13 ...\n//   2  6 10 14 ...\n//   3  7 11 15 ...\n//\n//  16 20 24 28 ...\n//  17 21 25 29 ...\n//  18 22 26 30 ...\n//  19 23 27 31 ...\n//\n//  32 33 34 35 ...\n//  36 36 38 39 ...\ntemplate<typename Scalar, typename Index, typename DataMapper, int Pack1, int Pack2, bool Conjugate, bool PanelMode>\nstruct gemm_pack_lhs<Scalar, Index, DataMapper, Pack1, Pack2, ColMajor, Conjugate, PanelMode>\n{\n  typedef typename DataMapper::LinearMapper LinearMapper;\n  EIGEN_DONT_INLINE void operator()(Scalar* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride=0, Index offset=0);\n};\n\ntemplate<typename Scalar, typename Index, typename DataMapper, int Pack1, int Pack2, bool Conjugate, bool PanelMode>\nEIGEN_DONT_INLINE void gemm_pack_lhs<Scalar, Index, DataMapper, Pack1, Pack2, ColMajor, Conjugate, PanelMode>\n  ::operator()(Scalar* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride, Index offset)\n{\n  typedef typename packet_traits<Scalar>::type Packet;\n  enum { PacketSize = packet_traits<Scalar>::size };\n\n  EIGEN_ASM_COMMENT(\"EIGEN PRODUCT PACK LHS\");\n  EIGEN_UNUSED_VARIABLE(stride);\n  EIGEN_UNUSED_VARIABLE(offset);\n  eigen_assert(((!PanelMode) && stride==0 && offset==0) || (PanelMode && stride>=depth && offset<=stride));\n  eigen_assert( ((Pack1%PacketSize)==0 && Pack1<=4*PacketSize) || (Pack1<=4) );\n  conj_if<NumTraits<Scalar>::IsComplex && Conjugate> cj;\n  Index count = 0;\n\n  const Index peeled_mc3 = Pack1>=3*PacketSize ? (rows/(3*PacketSize))*(3*PacketSize) : 0;\n  const Index peeled_mc2 = Pack1>=2*PacketSize ? peeled_mc3+((rows-peeled_mc3)/(2*PacketSize))*(2*PacketSize) : 0;\n  const Index peeled_mc1 = Pack1>=1*PacketSize ? (rows/(1*PacketSize))*(1*PacketSize) : 0;\n  const Index peeled_mc0 = Pack2>=1*PacketSize ? peeled_mc1\n                         : Pack2>1             ? (rows/Pack2)*Pack2 : 0;\n\n  Index i=0;\n\n  // Pack 3 packets\n  if(Pack1>=3*PacketSize)\n  {\n    for(; i<peeled_mc3; i+=3*PacketSize)\n    {\n      if(PanelMode) count += (3*PacketSize) * offset;\n\n      for(Index k=0; k<depth; k++)\n      {\n        Packet A, B, C;\n        A = lhs.loadPacket(i+0*PacketSize, k);\n        B = lhs.loadPacket(i+1*PacketSize, k);\n        C = lhs.loadPacket(i+2*PacketSize, k);\n        pstore(blockA+count, cj.pconj(A)); count+=PacketSize;\n        pstore(blockA+count, cj.pconj(B)); count+=PacketSize;\n        pstore(blockA+count, cj.pconj(C)); count+=PacketSize;\n      }\n      if(PanelMode) count += (3*PacketSize) * (stride-offset-depth);\n    }\n  }\n  // Pack 2 packets\n  if(Pack1>=2*PacketSize)\n  {\n    for(; i<peeled_mc2; i+=2*PacketSize)\n    {\n      if(PanelMode) count += (2*PacketSize) * offset;\n\n      for(Index k=0; k<depth; k++)\n      {\n        Packet A, B;\n        A = lhs.loadPacket(i+0*PacketSize, k);\n        B = lhs.loadPacket(i+1*PacketSize, k);\n        pstore(blockA+count, cj.pconj(A)); count+=PacketSize;\n        pstore(blockA+count, cj.pconj(B)); count+=PacketSize;\n      }\n      if(PanelMode) count += (2*PacketSize) * (stride-offset-depth);\n    }\n  }\n  // Pack 1 packets\n  if(Pack1>=1*PacketSize)\n  {\n    for(; i<peeled_mc1; i+=1*PacketSize)\n    {\n      if(PanelMode) count += (1*PacketSize) * offset;\n\n      for(Index k=0; k<depth; k++)\n      {\n        Packet A;\n        A = lhs.loadPacket(i+0*PacketSize, k);\n        pstore(blockA+count, cj.pconj(A));\n        count+=PacketSize;\n      }\n      if(PanelMode) count += (1*PacketSize) * (stride-offset-depth);\n    }\n  }\n  // Pack scalars\n  if(Pack2<PacketSize && Pack2>1)\n  {\n    for(; i<peeled_mc0; i+=Pack2)\n    {\n      if(PanelMode) count += Pack2 * offset;\n\n      for(Index k=0; k<depth; k++)\n        for(Index w=0; w<Pack2; w++)\n          blockA[count++] = cj(lhs(i+w, k));\n\n      if(PanelMode) count += Pack2 * (stride-offset-depth);\n    }\n  }\n  for(; i<rows; i++)\n  {\n    if(PanelMode) count += offset;\n    for(Index k=0; k<depth; k++)\n      blockA[count++] = cj(lhs(i, k));\n    if(PanelMode) count += (stride-offset-depth);\n  }\n}\n\ntemplate<typename Scalar, typename Index, typename DataMapper, int Pack1, int Pack2, bool Conjugate, bool PanelMode>\nstruct gemm_pack_lhs<Scalar, Index, DataMapper, Pack1, Pack2, RowMajor, Conjugate, PanelMode>\n{\n  typedef typename DataMapper::LinearMapper LinearMapper;\n  EIGEN_DONT_INLINE void operator()(Scalar* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride=0, Index offset=0);\n};\n\ntemplate<typename Scalar, typename Index, typename DataMapper, int Pack1, int Pack2, bool Conjugate, bool PanelMode>\nEIGEN_DONT_INLINE void gemm_pack_lhs<Scalar, Index, DataMapper, Pack1, Pack2, RowMajor, Conjugate, PanelMode>\n  ::operator()(Scalar* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride, Index offset)\n{\n  typedef typename packet_traits<Scalar>::type Packet;\n  enum { PacketSize = packet_traits<Scalar>::size };\n\n  EIGEN_ASM_COMMENT(\"EIGEN PRODUCT PACK LHS\");\n  EIGEN_UNUSED_VARIABLE(stride);\n  EIGEN_UNUSED_VARIABLE(offset);\n  eigen_assert(((!PanelMode) && stride==0 && offset==0) || (PanelMode && stride>=depth && offset<=stride));\n  conj_if<NumTraits<Scalar>::IsComplex && Conjugate> cj;\n  Index count = 0;\n\n//   const Index peeled_mc3 = Pack1>=3*PacketSize ? (rows/(3*PacketSize))*(3*PacketSize) : 0;\n//   const Index peeled_mc2 = Pack1>=2*PacketSize ? peeled_mc3+((rows-peeled_mc3)/(2*PacketSize))*(2*PacketSize) : 0;\n//   const Index peeled_mc1 = Pack1>=1*PacketSize ? (rows/(1*PacketSize))*(1*PacketSize) : 0;\n\n  int pack = Pack1;\n  Index i = 0;\n  while(pack>0)\n  {\n    Index remaining_rows = rows-i;\n    Index peeled_mc = i+(remaining_rows/pack)*pack;\n    for(; i<peeled_mc; i+=pack)\n    {\n      if(PanelMode) count += pack * offset;\n\n      const Index peeled_k = (depth/PacketSize)*PacketSize;\n      Index k=0;\n      if(pack>=PacketSize)\n      {\n        for(; k<peeled_k; k+=PacketSize)\n        {\n          for (Index m = 0; m < pack; m += PacketSize)\n          {\n            PacketBlock<Packet> kernel;\n            for (int p = 0; p < PacketSize; ++p) kernel.packet[p] = lhs.loadPacket(i+p+m, k);\n            ptranspose(kernel);\n            for (int p = 0; p < PacketSize; ++p) pstore(blockA+count+m+(pack)*p, cj.pconj(kernel.packet[p]));\n          }\n          count += PacketSize*pack;\n        }\n      }\n      for(; k<depth; k++)\n      {\n        Index w=0;\n        for(; w<pack-3; w+=4)\n        {\n          Scalar a(cj(lhs(i+w+0, k))),\n                 b(cj(lhs(i+w+1, k))),\n                 c(cj(lhs(i+w+2, k))),\n                 d(cj(lhs(i+w+3, k)));\n          blockA[count++] = a;\n          blockA[count++] = b;\n          blockA[count++] = c;\n          blockA[count++] = d;\n        }\n        if(pack%4)\n          for(;w<pack;++w)\n            blockA[count++] = cj(lhs(i+w, k));\n      }\n\n      if(PanelMode) count += pack * (stride-offset-depth);\n    }\n\n    pack -= PacketSize;\n    if(pack<Pack2 && (pack+PacketSize)!=Pack2)\n      pack = Pack2;\n  }\n\n  for(; i<rows; i++)\n  {\n    if(PanelMode) count += offset;\n    for(Index k=0; k<depth; k++)\n      blockA[count++] = cj(lhs(i, k));\n    if(PanelMode) count += (stride-offset-depth);\n  }\n}\n\n// copy a complete panel of the rhs\n// this version is optimized for column major matrices\n// The traversal order is as follow: (nr==4):\n//  0  1  2  3   12 13 14 15   24 27\n//  4  5  6  7   16 17 18 19   25 28\n//  8  9 10 11   20 21 22 23   26 29\n//  .  .  .  .    .  .  .  .    .  .\ntemplate<typename Scalar, typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>\nstruct gemm_pack_rhs<Scalar, Index, DataMapper, nr, ColMajor, Conjugate, PanelMode>\n{\n  typedef typename packet_traits<Scalar>::type Packet;\n  typedef typename DataMapper::LinearMapper LinearMapper;\n  enum { PacketSize = packet_traits<Scalar>::size };\n  EIGEN_DONT_INLINE void operator()(Scalar* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride=0, Index offset=0);\n};\n\ntemplate<typename Scalar, typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>\nEIGEN_DONT_INLINE void gemm_pack_rhs<Scalar, Index, DataMapper, nr, ColMajor, Conjugate, PanelMode>\n  ::operator()(Scalar* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride, Index offset)\n{\n  EIGEN_ASM_COMMENT(\"EIGEN PRODUCT PACK RHS COLMAJOR\");\n  EIGEN_UNUSED_VARIABLE(stride);\n  EIGEN_UNUSED_VARIABLE(offset);\n  eigen_assert(((!PanelMode) && stride==0 && offset==0) || (PanelMode && stride>=depth && offset<=stride));\n  conj_if<NumTraits<Scalar>::IsComplex && Conjugate> cj;\n  Index packet_cols8 = nr>=8 ? (cols/8) * 8 : 0;\n  Index packet_cols4 = nr>=4 ? (cols/4) * 4 : 0;\n  Index count = 0;\n  const Index peeled_k = (depth/PacketSize)*PacketSize;\n//   if(nr>=8)\n//   {\n//     for(Index j2=0; j2<packet_cols8; j2+=8)\n//     {\n//       // skip what we have before\n//       if(PanelMode) count += 8 * offset;\n//       const Scalar* b0 = &rhs[(j2+0)*rhsStride];\n//       const Scalar* b1 = &rhs[(j2+1)*rhsStride];\n//       const Scalar* b2 = &rhs[(j2+2)*rhsStride];\n//       const Scalar* b3 = &rhs[(j2+3)*rhsStride];\n//       const Scalar* b4 = &rhs[(j2+4)*rhsStride];\n//       const Scalar* b5 = &rhs[(j2+5)*rhsStride];\n//       const Scalar* b6 = &rhs[(j2+6)*rhsStride];\n//       const Scalar* b7 = &rhs[(j2+7)*rhsStride];\n//       Index k=0;\n//       if(PacketSize==8) // TODO enbale vectorized transposition for PacketSize==4\n//       {\n//         for(; k<peeled_k; k+=PacketSize) {\n//           PacketBlock<Packet> kernel;\n//           for (int p = 0; p < PacketSize; ++p) {\n//             kernel.packet[p] = ploadu<Packet>(&rhs[(j2+p)*rhsStride+k]);\n//           }\n//           ptranspose(kernel);\n//           for (int p = 0; p < PacketSize; ++p) {\n//             pstoreu(blockB+count, cj.pconj(kernel.packet[p]));\n//             count+=PacketSize;\n//           }\n//         }\n//       }\n//       for(; k<depth; k++)\n//       {\n//         blockB[count+0] = cj(b0[k]);\n//         blockB[count+1] = cj(b1[k]);\n//         blockB[count+2] = cj(b2[k]);\n//         blockB[count+3] = cj(b3[k]);\n//         blockB[count+4] = cj(b4[k]);\n//         blockB[count+5] = cj(b5[k]);\n//         blockB[count+6] = cj(b6[k]);\n//         blockB[count+7] = cj(b7[k]);\n//         count += 8;\n//       }\n//       // skip what we have after\n//       if(PanelMode) count += 8 * (stride-offset-depth);\n//     }\n//   }\n\n  if(nr>=4)\n  {\n    for(Index j2=packet_cols8; j2<packet_cols4; j2+=4)\n    {\n      // skip what we have before\n      if(PanelMode) count += 4 * offset;\n      const LinearMapper dm0 = rhs.getLinearMapper(0, j2 + 0);\n      const LinearMapper dm1 = rhs.getLinearMapper(0, j2 + 1);\n      const LinearMapper dm2 = rhs.getLinearMapper(0, j2 + 2);\n      const LinearMapper dm3 = rhs.getLinearMapper(0, j2 + 3);\n\n      Index k=0;\n      if((PacketSize%4)==0) // TODO enable vectorized transposition for PacketSize==2 ??\n      {\n        for(; k<peeled_k; k+=PacketSize) {\n          PacketBlock<Packet,(PacketSize%4)==0?4:PacketSize> kernel;\n          kernel.packet[0] = dm0.loadPacket(k);\n          kernel.packet[1%PacketSize] = dm1.loadPacket(k);\n          kernel.packet[2%PacketSize] = dm2.loadPacket(k);\n          kernel.packet[3%PacketSize] = dm3.loadPacket(k);\n          ptranspose(kernel);\n          pstoreu(blockB+count+0*PacketSize, cj.pconj(kernel.packet[0]));\n          pstoreu(blockB+count+1*PacketSize, cj.pconj(kernel.packet[1%PacketSize]));\n          pstoreu(blockB+count+2*PacketSize, cj.pconj(kernel.packet[2%PacketSize]));\n          pstoreu(blockB+count+3*PacketSize, cj.pconj(kernel.packet[3%PacketSize]));\n          count+=4*PacketSize;\n        }\n      }\n      for(; k<depth; k++)\n      {\n        blockB[count+0] = cj(dm0(k));\n        blockB[count+1] = cj(dm1(k));\n        blockB[count+2] = cj(dm2(k));\n        blockB[count+3] = cj(dm3(k));\n        count += 4;\n      }\n      // skip what we have after\n      if(PanelMode) count += 4 * (stride-offset-depth);\n    }\n  }\n\n  // copy the remaining columns one at a time (nr==1)\n  for(Index j2=packet_cols4; j2<cols; ++j2)\n  {\n    if(PanelMode) count += offset;\n    const LinearMapper dm0 = rhs.getLinearMapper(0, j2);\n    for(Index k=0; k<depth; k++)\n    {\n      blockB[count] = cj(dm0(k));\n      count += 1;\n    }\n    if(PanelMode) count += (stride-offset-depth);\n  }\n}\n\n// this version is optimized for row major matrices\ntemplate<typename Scalar, typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>\nstruct gemm_pack_rhs<Scalar, Index, DataMapper, nr, RowMajor, Conjugate, PanelMode>\n{\n  typedef typename packet_traits<Scalar>::type Packet;\n  typedef typename DataMapper::LinearMapper LinearMapper;\n  enum { PacketSize = packet_traits<Scalar>::size };\n  EIGEN_DONT_INLINE void operator()(Scalar* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride=0, Index offset=0);\n};\n\ntemplate<typename Scalar, typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>\nEIGEN_DONT_INLINE void gemm_pack_rhs<Scalar, Index, DataMapper, nr, RowMajor, Conjugate, PanelMode>\n  ::operator()(Scalar* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride, Index offset)\n{\n  EIGEN_ASM_COMMENT(\"EIGEN PRODUCT PACK RHS ROWMAJOR\");\n  EIGEN_UNUSED_VARIABLE(stride);\n  EIGEN_UNUSED_VARIABLE(offset);\n  eigen_assert(((!PanelMode) && stride==0 && offset==0) || (PanelMode && stride>=depth && offset<=stride));\n  conj_if<NumTraits<Scalar>::IsComplex && Conjugate> cj;\n  Index packet_cols8 = nr>=8 ? (cols/8) * 8 : 0;\n  Index packet_cols4 = nr>=4 ? (cols/4) * 4 : 0;\n  Index count = 0;\n\n//   if(nr>=8)\n//   {\n//     for(Index j2=0; j2<packet_cols8; j2+=8)\n//     {\n//       // skip what we have before\n//       if(PanelMode) count += 8 * offset;\n//       for(Index k=0; k<depth; k++)\n//       {\n//         if (PacketSize==8) {\n//           Packet A = ploadu<Packet>(&rhs[k*rhsStride + j2]);\n//           pstoreu(blockB+count, cj.pconj(A));\n//         } else if (PacketSize==4) {\n//           Packet A = ploadu<Packet>(&rhs[k*rhsStride + j2]);\n//           Packet B = ploadu<Packet>(&rhs[k*rhsStride + j2 + PacketSize]);\n//           pstoreu(blockB+count, cj.pconj(A));\n//           pstoreu(blockB+count+PacketSize, cj.pconj(B));\n//         } else {\n//           const Scalar* b0 = &rhs[k*rhsStride + j2];\n//           blockB[count+0] = cj(b0[0]);\n//           blockB[count+1] = cj(b0[1]);\n//           blockB[count+2] = cj(b0[2]);\n//           blockB[count+3] = cj(b0[3]);\n//           blockB[count+4] = cj(b0[4]);\n//           blockB[count+5] = cj(b0[5]);\n//           blockB[count+6] = cj(b0[6]);\n//           blockB[count+7] = cj(b0[7]);\n//         }\n//         count += 8;\n//       }\n//       // skip what we have after\n//       if(PanelMode) count += 8 * (stride-offset-depth);\n//     }\n//   }\n  if(nr>=4)\n  {\n    for(Index j2=packet_cols8; j2<packet_cols4; j2+=4)\n    {\n      // skip what we have before\n      if(PanelMode) count += 4 * offset;\n      for(Index k=0; k<depth; k++)\n      {\n        if (PacketSize==4) {\n          Packet A = rhs.loadPacket(k, j2);\n          pstoreu(blockB+count, cj.pconj(A));\n          count += PacketSize;\n        } else {\n          const LinearMapper dm0 = rhs.getLinearMapper(k, j2);\n          blockB[count+0] = cj(dm0(0));\n          blockB[count+1] = cj(dm0(1));\n          blockB[count+2] = cj(dm0(2));\n          blockB[count+3] = cj(dm0(3));\n          count += 4;\n        }\n      }\n      // skip what we have after\n      if(PanelMode) count += 4 * (stride-offset-depth);\n    }\n  }\n  // copy the remaining columns one at a time (nr==1)\n  for(Index j2=packet_cols4; j2<cols; ++j2)\n  {\n    if(PanelMode) count += offset;\n    for(Index k=0; k<depth; k++)\n    {\n      blockB[count] = cj(rhs(k, j2));\n      count += 1;\n    }\n    if(PanelMode) count += stride-offset-depth;\n  }\n}\n\n} // end namespace internal\n\n/** \\returns the currently set level 1 cpu cache size (in bytes) used to estimate the ideal blocking size parameters.\n  * \\sa setCpuCacheSize */\ninline std::ptrdiff_t l1CacheSize()\n{\n  std::ptrdiff_t l1, l2, l3;\n  internal::manage_caching_sizes(GetAction, &l1, &l2, &l3);\n  return l1;\n}\n\n/** \\returns the currently set level 2 cpu cache size (in bytes) used to estimate the ideal blocking size parameters.\n  * \\sa setCpuCacheSize */\ninline std::ptrdiff_t l2CacheSize()\n{\n  std::ptrdiff_t l1, l2, l3;\n  internal::manage_caching_sizes(GetAction, &l1, &l2, &l3);\n  return l2;\n}\n\n/** \\returns the currently set level 3 cpu cache size (in bytes) used to estimate the ideal blocking size paramete\\\nrs.                                                                                                                \n* \\sa setCpuCacheSize */\ninline std::ptrdiff_t l3CacheSize()\n{\n  std::ptrdiff_t l1, l2, l3;\n  internal::manage_caching_sizes(GetAction, &l1, &l2, &l3);\n  return l3;\n}\n\n/** Set the cpu L1 and L2 cache sizes (in bytes).\n  * These values are use to adjust the size of the blocks\n  * for the algorithms working per blocks.\n  *\n  * \\sa computeProductBlockingSizes */\ninline void setCpuCacheSizes(std::ptrdiff_t l1, std::ptrdiff_t l2, std::ptrdiff_t l3)\n{\n  internal::manage_caching_sizes(SetAction, &l1, &l2, &l3);\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_GENERAL_BLOCK_PANEL_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/products/GeneralMatrixMatrix.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_GENERAL_MATRIX_MATRIX_H\n#define EIGEN_GENERAL_MATRIX_MATRIX_H\n\nnamespace Eigen {\n\nnamespace internal {\n\ntemplate<typename _LhsScalar, typename _RhsScalar> class level3_blocking;\n\n/* Specialization for a row-major destination matrix => simple transposition of the product */\ntemplate<\n  typename Index,\n  typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,\n  typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs>\nstruct general_matrix_matrix_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,RowMajor>\n{\n  typedef gebp_traits<RhsScalar,LhsScalar> Traits;\n\n  typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;\n  static EIGEN_STRONG_INLINE void run(\n    Index rows, Index cols, Index depth,\n    const LhsScalar* lhs, Index lhsStride,\n    const RhsScalar* rhs, Index rhsStride,\n    ResScalar* res, Index resStride,\n    ResScalar alpha,\n    level3_blocking<RhsScalar,LhsScalar>& blocking,\n    GemmParallelInfo<Index>* info = 0)\n  {\n    // transpose the product such that the result is column major\n    general_matrix_matrix_product<Index,\n      RhsScalar, RhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateRhs,\n      LhsScalar, LhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateLhs,\n      ColMajor>\n    ::run(cols,rows,depth,rhs,rhsStride,lhs,lhsStride,res,resStride,alpha,blocking,info);\n  }\n};\n\n/*  Specialization for a col-major destination matrix\n *    => Blocking algorithm following Goto's paper */\ntemplate<\n  typename Index,\n  typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,\n  typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs>\nstruct general_matrix_matrix_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,ColMajor>\n{\n\ntypedef gebp_traits<LhsScalar,RhsScalar> Traits;\n\ntypedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;\nstatic void run(Index rows, Index cols, Index depth,\n  const LhsScalar* _lhs, Index lhsStride,\n  const RhsScalar* _rhs, Index rhsStride,\n  ResScalar* _res, Index resStride,\n  ResScalar alpha,\n  level3_blocking<LhsScalar,RhsScalar>& blocking,\n  GemmParallelInfo<Index>* info = 0)\n{\n  typedef const_blas_data_mapper<LhsScalar, Index, LhsStorageOrder> LhsMapper;\n  typedef const_blas_data_mapper<RhsScalar, Index, RhsStorageOrder> RhsMapper;\n  typedef blas_data_mapper<typename Traits::ResScalar, Index, ColMajor> ResMapper;\n  LhsMapper lhs(_lhs,lhsStride);\n  RhsMapper rhs(_rhs,rhsStride);\n  ResMapper res(_res, resStride);\n\n  Index kc = blocking.kc();                   // cache block size along the K direction\n  Index mc = (std::min)(rows,blocking.mc());  // cache block size along the M direction\n  Index nc = (std::min)(cols,blocking.nc());  // cache block size along the N direction\n\n  gemm_pack_lhs<LhsScalar, Index, LhsMapper, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;\n  gemm_pack_rhs<RhsScalar, Index, RhsMapper, Traits::nr, RhsStorageOrder> pack_rhs;\n  gebp_kernel<LhsScalar, RhsScalar, Index, ResMapper, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp;\n\n#ifdef EIGEN_HAS_OPENMP\n  if(info)\n  {\n    // this is the parallel version!\n    int tid = omp_get_thread_num();\n    int threads = omp_get_num_threads();\n\n    LhsScalar* blockA = blocking.blockA();\n    eigen_internal_assert(blockA!=0);\n\n    std::size_t sizeB = kc*nc;\n    ei_declare_aligned_stack_constructed_variable(RhsScalar, blockB, sizeB, 0);\n\n    // For each horizontal panel of the rhs, and corresponding vertical panel of the lhs...\n    for(Index k=0; k<depth; k+=kc)\n    {\n      const Index actual_kc = (std::min)(k+kc,depth)-k; // => rows of B', and cols of the A'\n\n      // In order to reduce the chance that a thread has to wait for the other,\n      // let's start by packing B'.\n      pack_rhs(blockB, rhs.getSubMapper(k,0), actual_kc, nc);\n\n      // Pack A_k to A' in a parallel fashion:\n      // each thread packs the sub block A_k,i to A'_i where i is the thread id.\n\n      // However, before copying to A'_i, we have to make sure that no other thread is still using it,\n      // i.e., we test that info[tid].users equals 0.\n      // Then, we set info[tid].users to the number of threads to mark that all other threads are going to use it.\n      while(info[tid].users!=0) {}\n      info[tid].users += threads;\n\n      pack_lhs(blockA+info[tid].lhs_start*actual_kc, lhs.getSubMapper(info[tid].lhs_start,k), actual_kc, info[tid].lhs_length);\n\n      // Notify the other threads that the part A'_i is ready to go.\n      info[tid].sync = k;\n\n      // Computes C_i += A' * B' per A'_i\n      for(int shift=0; shift<threads; ++shift)\n      {\n        int i = (tid+shift)%threads;\n\n        // At this point we have to make sure that A'_i has been updated by the thread i,\n        // we use testAndSetOrdered to mimic a volatile access.\n        // However, no need to wait for the B' part which has been updated by the current thread!\n        if (shift>0) {\n          while(info[i].sync!=k) {\n          }\n        }\n\n        gebp(res.getSubMapper(info[i].lhs_start, 0), blockA+info[i].lhs_start*actual_kc, blockB, info[i].lhs_length, actual_kc, nc, alpha);\n      }\n\n      // Then keep going as usual with the remaining B'\n      for(Index j=nc; j<cols; j+=nc)\n      {\n        const Index actual_nc = (std::min)(j+nc,cols)-j;\n\n        // pack B_k,j to B'\n        pack_rhs(blockB, rhs.getSubMapper(k,j), actual_kc, actual_nc);\n\n        // C_j += A' * B'\n        gebp(res.getSubMapper(0, j), blockA, blockB, rows, actual_kc, actual_nc, alpha);\n      }\n\n      // Release all the sub blocks A'_i of A' for the current thread,\n      // i.e., we simply decrement the number of users by 1\n      for(Index i=0; i<threads; ++i)\n        #pragma omp atomic\n        info[i].users -= 1;\n    }\n  }\n  else\n#endif // EIGEN_HAS_OPENMP\n  {\n    EIGEN_UNUSED_VARIABLE(info);\n\n    // this is the sequential version!\n    std::size_t sizeA = kc*mc;\n    std::size_t sizeB = kc*nc;\n\n    ei_declare_aligned_stack_constructed_variable(LhsScalar, blockA, sizeA, blocking.blockA());\n    ei_declare_aligned_stack_constructed_variable(RhsScalar, blockB, sizeB, blocking.blockB());\n\n    const bool pack_rhs_once = mc!=rows && kc==depth && nc==cols;\n\n    // For each horizontal panel of the rhs, and corresponding panel of the lhs...\n    for(Index i2=0; i2<rows; i2+=mc)\n    {\n      const Index actual_mc = (std::min)(i2+mc,rows)-i2;\n\n      for(Index k2=0; k2<depth; k2+=kc)\n      {\n        const Index actual_kc = (std::min)(k2+kc,depth)-k2;\n\n        // OK, here we have selected one horizontal panel of rhs and one vertical panel of lhs.\n        // => Pack lhs's panel into a sequential chunk of memory (L2/L3 caching)\n        // Note that this panel will be read as many times as the number of blocks in the rhs's\n        // horizontal panel which is, in practice, a very low number.\n        pack_lhs(blockA, lhs.getSubMapper(i2,k2), actual_kc, actual_mc);\n\n        // For each kc x nc block of the rhs's horizontal panel...\n        for(Index j2=0; j2<cols; j2+=nc)\n        {\n          const Index actual_nc = (std::min)(j2+nc,cols)-j2;\n\n          // We pack the rhs's block into a sequential chunk of memory (L2 caching)\n          // Note that this block will be read a very high number of times, which is equal to the number of\n          // micro horizontal panel of the large rhs's panel (e.g., rows/12 times).\n          if((!pack_rhs_once) || i2==0)\n            pack_rhs(blockB, rhs.getSubMapper(k2,j2), actual_kc, actual_nc);\n\n          // Everything is packed, we can now call the panel * block kernel:\n          gebp(res.getSubMapper(i2, j2), blockA, blockB, actual_mc, actual_kc, actual_nc, alpha);\n        }\n      }\n    }\n  }\n}\n\n};\n\n/*********************************************************************************\n*  Specialization of generic_product_impl for \"large\" GEMM, i.e.,\n*  implementation of the high level wrapper to general_matrix_matrix_product\n**********************************************************************************/\n\ntemplate<typename Scalar, typename Index, typename Gemm, typename Lhs, typename Rhs, typename Dest, typename BlockingType>\nstruct gemm_functor\n{\n  gemm_functor(const Lhs& lhs, const Rhs& rhs, Dest& dest, const Scalar& actualAlpha, BlockingType& blocking)\n    : m_lhs(lhs), m_rhs(rhs), m_dest(dest), m_actualAlpha(actualAlpha), m_blocking(blocking)\n  {}\n\n  void initParallelSession(Index num_threads) const\n  {\n    m_blocking.initParallel(m_lhs.rows(), m_rhs.cols(), m_lhs.cols(), num_threads);\n    m_blocking.allocateA();\n  }\n\n  void operator() (Index row, Index rows, Index col=0, Index cols=-1, GemmParallelInfo<Index>* info=0) const\n  {\n    if(cols==-1)\n      cols = m_rhs.cols();\n\n    Gemm::run(rows, cols, m_lhs.cols(),\n              &m_lhs.coeffRef(row,0), m_lhs.outerStride(),\n              &m_rhs.coeffRef(0,col), m_rhs.outerStride(),\n              (Scalar*)&(m_dest.coeffRef(row,col)), m_dest.outerStride(),\n              m_actualAlpha, m_blocking, info);\n  }\n\n  typedef typename Gemm::Traits Traits;\n\n  protected:\n    const Lhs& m_lhs;\n    const Rhs& m_rhs;\n    Dest& m_dest;\n    Scalar m_actualAlpha;\n    BlockingType& m_blocking;\n};\n\ntemplate<int StorageOrder, typename LhsScalar, typename RhsScalar, int MaxRows, int MaxCols, int MaxDepth, int KcFactor=1,\nbool FiniteAtCompileTime = MaxRows!=Dynamic && MaxCols!=Dynamic && MaxDepth != Dynamic> class gemm_blocking_space;\n\ntemplate<typename _LhsScalar, typename _RhsScalar>\nclass level3_blocking\n{\n    typedef _LhsScalar LhsScalar;\n    typedef _RhsScalar RhsScalar;\n\n  protected:\n    LhsScalar* m_blockA;\n    RhsScalar* m_blockB;\n\n    Index m_mc;\n    Index m_nc;\n    Index m_kc;\n\n  public:\n\n    level3_blocking()\n      : m_blockA(0), m_blockB(0), m_mc(0), m_nc(0), m_kc(0)\n    {}\n\n    inline Index mc() const { return m_mc; }\n    inline Index nc() const { return m_nc; }\n    inline Index kc() const { return m_kc; }\n\n    inline LhsScalar* blockA() { return m_blockA; }\n    inline RhsScalar* blockB() { return m_blockB; }\n};\n\ntemplate<int StorageOrder, typename _LhsScalar, typename _RhsScalar, int MaxRows, int MaxCols, int MaxDepth, int KcFactor>\nclass gemm_blocking_space<StorageOrder,_LhsScalar,_RhsScalar,MaxRows, MaxCols, MaxDepth, KcFactor, true /* == FiniteAtCompileTime */>\n  : public level3_blocking<\n      typename conditional<StorageOrder==RowMajor,_RhsScalar,_LhsScalar>::type,\n      typename conditional<StorageOrder==RowMajor,_LhsScalar,_RhsScalar>::type>\n{\n    enum {\n      Transpose = StorageOrder==RowMajor,\n      ActualRows = Transpose ? MaxCols : MaxRows,\n      ActualCols = Transpose ? MaxRows : MaxCols\n    };\n    typedef typename conditional<Transpose,_RhsScalar,_LhsScalar>::type LhsScalar;\n    typedef typename conditional<Transpose,_LhsScalar,_RhsScalar>::type RhsScalar;\n    typedef gebp_traits<LhsScalar,RhsScalar> Traits;\n    enum {\n      SizeA = ActualRows * MaxDepth,\n      SizeB = ActualCols * MaxDepth\n    };\n\n#if EIGEN_MAX_STATIC_ALIGN_BYTES >= EIGEN_DEFAULT_ALIGN_BYTES\n    EIGEN_ALIGN_MAX LhsScalar m_staticA[SizeA];\n    EIGEN_ALIGN_MAX RhsScalar m_staticB[SizeB];\n#else\n    EIGEN_ALIGN_MAX char m_staticA[SizeA * sizeof(LhsScalar) + EIGEN_DEFAULT_ALIGN_BYTES-1];\n    EIGEN_ALIGN_MAX char m_staticB[SizeB * sizeof(RhsScalar) + EIGEN_DEFAULT_ALIGN_BYTES-1];\n#endif\n\n  public:\n\n    gemm_blocking_space(Index /*rows*/, Index /*cols*/, Index /*depth*/, Index /*num_threads*/, bool /*full_rows = false*/)\n    {\n      this->m_mc = ActualRows;\n      this->m_nc = ActualCols;\n      this->m_kc = MaxDepth;\n#if EIGEN_MAX_STATIC_ALIGN_BYTES >= EIGEN_DEFAULT_ALIGN_BYTES\n      this->m_blockA = m_staticA;\n      this->m_blockB = m_staticB;\n#else\n      this->m_blockA = reinterpret_cast<LhsScalar*>((internal::UIntPtr(m_staticA) + (EIGEN_DEFAULT_ALIGN_BYTES-1)) & ~std::size_t(EIGEN_DEFAULT_ALIGN_BYTES-1));\n      this->m_blockB = reinterpret_cast<RhsScalar*>((internal::UIntPtr(m_staticB) + (EIGEN_DEFAULT_ALIGN_BYTES-1)) & ~std::size_t(EIGEN_DEFAULT_ALIGN_BYTES-1));\n#endif\n    }\n\n    void initParallel(Index, Index, Index, Index)\n    {}\n\n    inline void allocateA() {}\n    inline void allocateB() {}\n    inline void allocateAll() {}\n};\n\ntemplate<int StorageOrder, typename _LhsScalar, typename _RhsScalar, int MaxRows, int MaxCols, int MaxDepth, int KcFactor>\nclass gemm_blocking_space<StorageOrder,_LhsScalar,_RhsScalar,MaxRows, MaxCols, MaxDepth, KcFactor, false>\n  : public level3_blocking<\n      typename conditional<StorageOrder==RowMajor,_RhsScalar,_LhsScalar>::type,\n      typename conditional<StorageOrder==RowMajor,_LhsScalar,_RhsScalar>::type>\n{\n    enum {\n      Transpose = StorageOrder==RowMajor\n    };\n    typedef typename conditional<Transpose,_RhsScalar,_LhsScalar>::type LhsScalar;\n    typedef typename conditional<Transpose,_LhsScalar,_RhsScalar>::type RhsScalar;\n    typedef gebp_traits<LhsScalar,RhsScalar> Traits;\n\n    Index m_sizeA;\n    Index m_sizeB;\n\n  public:\n\n    gemm_blocking_space(Index rows, Index cols, Index depth, Index num_threads, bool l3_blocking)\n    {\n      this->m_mc = Transpose ? cols : rows;\n      this->m_nc = Transpose ? rows : cols;\n      this->m_kc = depth;\n\n      if(l3_blocking)\n      {\n        computeProductBlockingSizes<LhsScalar,RhsScalar,KcFactor>(this->m_kc, this->m_mc, this->m_nc, num_threads);\n      }\n      else  // no l3 blocking\n      {\n        Index n = this->m_nc;\n        computeProductBlockingSizes<LhsScalar,RhsScalar,KcFactor>(this->m_kc, this->m_mc, n, num_threads);\n      }\n\n      m_sizeA = this->m_mc * this->m_kc;\n      m_sizeB = this->m_kc * this->m_nc;\n    }\n\n    void initParallel(Index rows, Index cols, Index depth, Index num_threads)\n    {\n      this->m_mc = Transpose ? cols : rows;\n      this->m_nc = Transpose ? rows : cols;\n      this->m_kc = depth;\n\n      eigen_internal_assert(this->m_blockA==0 && this->m_blockB==0);\n      Index m = this->m_mc;\n      computeProductBlockingSizes<LhsScalar,RhsScalar,KcFactor>(this->m_kc, m, this->m_nc, num_threads);\n      m_sizeA = this->m_mc * this->m_kc;\n      m_sizeB = this->m_kc * this->m_nc;\n    }\n\n    void allocateA()\n    {\n      if(this->m_blockA==0)\n        this->m_blockA = aligned_new<LhsScalar>(m_sizeA);\n    }\n\n    void allocateB()\n    {\n      if(this->m_blockB==0)\n        this->m_blockB = aligned_new<RhsScalar>(m_sizeB);\n    }\n\n    void allocateAll()\n    {\n      allocateA();\n      allocateB();\n    }\n\n    ~gemm_blocking_space()\n    {\n      aligned_delete(this->m_blockA, m_sizeA);\n      aligned_delete(this->m_blockB, m_sizeB);\n    }\n};\n\n} // end namespace internal\n\nnamespace internal {\n\ntemplate<typename Lhs, typename Rhs>\nstruct generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,GemmProduct>\n  : generic_product_impl_base<Lhs,Rhs,generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,GemmProduct> >\n{\n  typedef typename Product<Lhs,Rhs>::Scalar Scalar;\n  typedef typename Lhs::Scalar LhsScalar;\n  typedef typename Rhs::Scalar RhsScalar;\n\n  typedef internal::blas_traits<Lhs> LhsBlasTraits;\n  typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;\n  typedef typename internal::remove_all<ActualLhsType>::type ActualLhsTypeCleaned;\n\n  typedef internal::blas_traits<Rhs> RhsBlasTraits;\n  typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;\n  typedef typename internal::remove_all<ActualRhsType>::type ActualRhsTypeCleaned;\n\n  enum {\n    MaxDepthAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(Lhs::MaxColsAtCompileTime,Rhs::MaxRowsAtCompileTime)\n  };\n\n  typedef generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,CoeffBasedProductMode> lazyproduct;\n\n  template<typename Dst>\n  static void evalTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)\n  {\n    if((rhs.rows()+dst.rows()+dst.cols())<20 && rhs.rows()>0)\n      lazyproduct::evalTo(dst, lhs, rhs);\n    else\n    {\n      dst.setZero();\n      scaleAndAddTo(dst, lhs, rhs, Scalar(1));\n    }\n  }\n\n  template<typename Dst>\n  static void addTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)\n  {\n    if((rhs.rows()+dst.rows()+dst.cols())<20 && rhs.rows()>0)\n      lazyproduct::addTo(dst, lhs, rhs);\n    else\n      scaleAndAddTo(dst,lhs, rhs, Scalar(1));\n  }\n\n  template<typename Dst>\n  static void subTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)\n  {\n    if((rhs.rows()+dst.rows()+dst.cols())<20 && rhs.rows()>0)\n      lazyproduct::subTo(dst, lhs, rhs);\n    else\n      scaleAndAddTo(dst, lhs, rhs, Scalar(-1));\n  }\n\n  template<typename Dest>\n  static void scaleAndAddTo(Dest& dst, const Lhs& a_lhs, const Rhs& a_rhs, const Scalar& alpha)\n  {\n    eigen_assert(dst.rows()==a_lhs.rows() && dst.cols()==a_rhs.cols());\n    if(a_lhs.cols()==0 || a_lhs.rows()==0 || a_rhs.cols()==0)\n      return;\n\n    typename internal::add_const_on_value_type<ActualLhsType>::type lhs = LhsBlasTraits::extract(a_lhs);\n    typename internal::add_const_on_value_type<ActualRhsType>::type rhs = RhsBlasTraits::extract(a_rhs);\n\n    Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(a_lhs)\n                               * RhsBlasTraits::extractScalarFactor(a_rhs);\n\n    typedef internal::gemm_blocking_space<(Dest::Flags&RowMajorBit) ? RowMajor : ColMajor,LhsScalar,RhsScalar,\n            Dest::MaxRowsAtCompileTime,Dest::MaxColsAtCompileTime,MaxDepthAtCompileTime> BlockingType;\n\n    typedef internal::gemm_functor<\n      Scalar, Index,\n      internal::general_matrix_matrix_product<\n        Index,\n        LhsScalar, (ActualLhsTypeCleaned::Flags&RowMajorBit) ? RowMajor : ColMajor, bool(LhsBlasTraits::NeedToConjugate),\n        RhsScalar, (ActualRhsTypeCleaned::Flags&RowMajorBit) ? RowMajor : ColMajor, bool(RhsBlasTraits::NeedToConjugate),\n        (Dest::Flags&RowMajorBit) ? RowMajor : ColMajor>,\n      ActualLhsTypeCleaned, ActualRhsTypeCleaned, Dest, BlockingType> GemmFunctor;\n\n    BlockingType blocking(dst.rows(), dst.cols(), lhs.cols(), 1, true);\n    internal::parallelize_gemm<(Dest::MaxRowsAtCompileTime>32 || Dest::MaxRowsAtCompileTime==Dynamic)>\n        (GemmFunctor(lhs, rhs, dst, actualAlpha, blocking), a_lhs.rows(), a_rhs.cols(), a_lhs.cols(), Dest::Flags&RowMajorBit);\n  }\n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_GENERAL_MATRIX_MATRIX_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/products/GeneralMatrixMatrixTriangular.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H\n#define EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H\n\nnamespace Eigen { \n\ntemplate<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjLhs, bool ConjRhs>\nstruct selfadjoint_rank1_update;\n\nnamespace internal {\n\n/**********************************************************************\n* This file implements a general A * B product while\n* evaluating only one triangular part of the product.\n* This is a more general version of self adjoint product (C += A A^T)\n* as the level 3 SYRK Blas routine.\n**********************************************************************/\n\n// forward declarations (defined at the end of this file)\ntemplate<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjLhs, bool ConjRhs, int UpLo>\nstruct tribb_kernel;\n  \n/* Optimized matrix-matrix product evaluating only one triangular half */\ntemplate <typename Index,\n          typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,\n          typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs,\n                              int ResStorageOrder, int  UpLo, int Version = Specialized>\nstruct general_matrix_matrix_triangular_product;\n\n// as usual if the result is row major => we transpose the product\ntemplate <typename Index, typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,\n                          typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs, int  UpLo, int Version>\nstruct general_matrix_matrix_triangular_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,RowMajor,UpLo,Version>\n{\n  typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;\n  static EIGEN_STRONG_INLINE void run(Index size, Index depth,const LhsScalar* lhs, Index lhsStride,\n                                      const RhsScalar* rhs, Index rhsStride, ResScalar* res, Index resStride,\n                                      const ResScalar& alpha, level3_blocking<RhsScalar,LhsScalar>& blocking)\n  {\n    general_matrix_matrix_triangular_product<Index,\n        RhsScalar, RhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateRhs,\n        LhsScalar, LhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateLhs,\n        ColMajor, UpLo==Lower?Upper:Lower>\n      ::run(size,depth,rhs,rhsStride,lhs,lhsStride,res,resStride,alpha,blocking);\n  }\n};\n\ntemplate <typename Index, typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,\n                          typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs, int  UpLo, int Version>\nstruct general_matrix_matrix_triangular_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,ColMajor,UpLo,Version>\n{\n  typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;\n  static EIGEN_STRONG_INLINE void run(Index size, Index depth,const LhsScalar* _lhs, Index lhsStride,\n                                      const RhsScalar* _rhs, Index rhsStride, ResScalar* _res, Index resStride,\n                                      const ResScalar& alpha, level3_blocking<LhsScalar,RhsScalar>& blocking)\n  {\n    typedef gebp_traits<LhsScalar,RhsScalar> Traits;\n\n    typedef const_blas_data_mapper<LhsScalar, Index, LhsStorageOrder> LhsMapper;\n    typedef const_blas_data_mapper<RhsScalar, Index, RhsStorageOrder> RhsMapper;\n    typedef blas_data_mapper<typename Traits::ResScalar, Index, ColMajor> ResMapper;\n    LhsMapper lhs(_lhs,lhsStride);\n    RhsMapper rhs(_rhs,rhsStride);\n    ResMapper res(_res, resStride);\n\n    Index kc = blocking.kc();\n    Index mc = (std::min)(size,blocking.mc());\n\n    // !!! mc must be a multiple of nr:\n    if(mc > Traits::nr)\n      mc = (mc/Traits::nr)*Traits::nr;\n\n    std::size_t sizeA = kc*mc;\n    std::size_t sizeB = kc*size;\n\n    ei_declare_aligned_stack_constructed_variable(LhsScalar, blockA, sizeA, blocking.blockA());\n    ei_declare_aligned_stack_constructed_variable(RhsScalar, blockB, sizeB, blocking.blockB());\n\n    gemm_pack_lhs<LhsScalar, Index, LhsMapper, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;\n    gemm_pack_rhs<RhsScalar, Index, RhsMapper, Traits::nr, RhsStorageOrder> pack_rhs;\n    gebp_kernel<LhsScalar, RhsScalar, Index, ResMapper, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp;\n    tribb_kernel<LhsScalar, RhsScalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs, UpLo> sybb;\n\n    for(Index k2=0; k2<depth; k2+=kc)\n    {\n      const Index actual_kc = (std::min)(k2+kc,depth)-k2;\n\n      // note that the actual rhs is the transpose/adjoint of mat\n      pack_rhs(blockB, rhs.getSubMapper(k2,0), actual_kc, size);\n\n      for(Index i2=0; i2<size; i2+=mc)\n      {\n        const Index actual_mc = (std::min)(i2+mc,size)-i2;\n\n        pack_lhs(blockA, lhs.getSubMapper(i2, k2), actual_kc, actual_mc);\n\n        // the selected actual_mc * size panel of res is split into three different part:\n        //  1 - before the diagonal => processed with gebp or skipped\n        //  2 - the actual_mc x actual_mc symmetric block => processed with a special kernel\n        //  3 - after the diagonal => processed with gebp or skipped\n        if (UpLo==Lower)\n          gebp(res.getSubMapper(i2, 0), blockA, blockB, actual_mc, actual_kc,\n               (std::min)(size,i2), alpha, -1, -1, 0, 0);\n\n\n        sybb(_res+resStride*i2 + i2, resStride, blockA, blockB + actual_kc*i2, actual_mc, actual_kc, alpha);\n\n        if (UpLo==Upper)\n        {\n          Index j2 = i2+actual_mc;\n          gebp(res.getSubMapper(i2, j2), blockA, blockB+actual_kc*j2, actual_mc,\n               actual_kc, (std::max)(Index(0), size-j2), alpha, -1, -1, 0, 0);\n        }\n      }\n    }\n  }\n};\n\n// Optimized packed Block * packed Block product kernel evaluating only one given triangular part\n// This kernel is built on top of the gebp kernel:\n// - the current destination block is processed per panel of actual_mc x BlockSize\n//   where BlockSize is set to the minimal value allowing gebp to be as fast as possible\n// - then, as usual, each panel is split into three parts along the diagonal,\n//   the sub blocks above and below the diagonal are processed as usual,\n//   while the triangular block overlapping the diagonal is evaluated into a\n//   small temporary buffer which is then accumulated into the result using a\n//   triangular traversal.\ntemplate<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjLhs, bool ConjRhs, int UpLo>\nstruct tribb_kernel\n{\n  typedef gebp_traits<LhsScalar,RhsScalar,ConjLhs,ConjRhs> Traits;\n  typedef typename Traits::ResScalar ResScalar;\n\n  enum {\n    BlockSize  = meta_least_common_multiple<EIGEN_PLAIN_ENUM_MAX(mr,nr),EIGEN_PLAIN_ENUM_MIN(mr,nr)>::ret\n  };\n  void operator()(ResScalar* _res, Index resStride, const LhsScalar* blockA, const RhsScalar* blockB, Index size, Index depth, const ResScalar& alpha)\n  {\n    typedef blas_data_mapper<ResScalar, Index, ColMajor> ResMapper;\n    ResMapper res(_res, resStride);\n    gebp_kernel<LhsScalar, RhsScalar, Index, ResMapper, mr, nr, ConjLhs, ConjRhs> gebp_kernel;\n\n    Matrix<ResScalar,BlockSize,BlockSize,ColMajor> buffer((internal::constructor_without_unaligned_array_assert()));\n\n    // let's process the block per panel of actual_mc x BlockSize,\n    // again, each is split into three parts, etc.\n    for (Index j=0; j<size; j+=BlockSize)\n    {\n      Index actualBlockSize = std::min<Index>(BlockSize,size - j);\n      const RhsScalar* actual_b = blockB+j*depth;\n\n      if(UpLo==Upper)\n        gebp_kernel(res.getSubMapper(0, j), blockA, actual_b, j, depth, actualBlockSize, alpha,\n                    -1, -1, 0, 0);\n\n      // selfadjoint micro block\n      {\n        Index i = j;\n        buffer.setZero();\n        // 1 - apply the kernel on the temporary buffer\n        gebp_kernel(ResMapper(buffer.data(), BlockSize), blockA+depth*i, actual_b, actualBlockSize, depth, actualBlockSize, alpha,\n                    -1, -1, 0, 0);\n        // 2 - triangular accumulation\n        for(Index j1=0; j1<actualBlockSize; ++j1)\n        {\n          ResScalar* r = &res(i, j + j1);\n          for(Index i1=UpLo==Lower ? j1 : 0;\n              UpLo==Lower ? i1<actualBlockSize : i1<=j1; ++i1)\n            r[i1] += buffer(i1,j1);\n        }\n      }\n\n      if(UpLo==Lower)\n      {\n        Index i = j+actualBlockSize;\n        gebp_kernel(res.getSubMapper(i, j), blockA+depth*i, actual_b, size-i, \n                    depth, actualBlockSize, alpha, -1, -1, 0, 0);\n      }\n    }\n  }\n};\n\n} // end namespace internal\n\n// high level API\n\ntemplate<typename MatrixType, typename ProductType, int UpLo, bool IsOuterProduct>\nstruct general_product_to_triangular_selector;\n\n\ntemplate<typename MatrixType, typename ProductType, int UpLo>\nstruct general_product_to_triangular_selector<MatrixType,ProductType,UpLo,true>\n{\n  static void run(MatrixType& mat, const ProductType& prod, const typename MatrixType::Scalar& alpha, bool beta)\n  {\n    typedef typename MatrixType::Scalar Scalar;\n    \n    typedef typename internal::remove_all<typename ProductType::LhsNested>::type Lhs;\n    typedef internal::blas_traits<Lhs> LhsBlasTraits;\n    typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhs;\n    typedef typename internal::remove_all<ActualLhs>::type _ActualLhs;\n    typename internal::add_const_on_value_type<ActualLhs>::type actualLhs = LhsBlasTraits::extract(prod.lhs());\n    \n    typedef typename internal::remove_all<typename ProductType::RhsNested>::type Rhs;\n    typedef internal::blas_traits<Rhs> RhsBlasTraits;\n    typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhs;\n    typedef typename internal::remove_all<ActualRhs>::type _ActualRhs;\n    typename internal::add_const_on_value_type<ActualRhs>::type actualRhs = RhsBlasTraits::extract(prod.rhs());\n\n    Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs().derived()) * RhsBlasTraits::extractScalarFactor(prod.rhs().derived());\n\n    if(!beta)\n      mat.template triangularView<UpLo>().setZero();\n\n    enum {\n      StorageOrder = (internal::traits<MatrixType>::Flags&RowMajorBit) ? RowMajor : ColMajor,\n      UseLhsDirectly = _ActualLhs::InnerStrideAtCompileTime==1,\n      UseRhsDirectly = _ActualRhs::InnerStrideAtCompileTime==1\n    };\n    \n    internal::gemv_static_vector_if<Scalar,Lhs::SizeAtCompileTime,Lhs::MaxSizeAtCompileTime,!UseLhsDirectly> static_lhs;\n    ei_declare_aligned_stack_constructed_variable(Scalar, actualLhsPtr, actualLhs.size(),\n      (UseLhsDirectly ? const_cast<Scalar*>(actualLhs.data()) : static_lhs.data()));\n    if(!UseLhsDirectly) Map<typename _ActualLhs::PlainObject>(actualLhsPtr, actualLhs.size()) = actualLhs;\n    \n    internal::gemv_static_vector_if<Scalar,Rhs::SizeAtCompileTime,Rhs::MaxSizeAtCompileTime,!UseRhsDirectly> static_rhs;\n    ei_declare_aligned_stack_constructed_variable(Scalar, actualRhsPtr, actualRhs.size(),\n      (UseRhsDirectly ? const_cast<Scalar*>(actualRhs.data()) : static_rhs.data()));\n    if(!UseRhsDirectly) Map<typename _ActualRhs::PlainObject>(actualRhsPtr, actualRhs.size()) = actualRhs;\n    \n    \n    selfadjoint_rank1_update<Scalar,Index,StorageOrder,UpLo,\n                              LhsBlasTraits::NeedToConjugate && NumTraits<Scalar>::IsComplex,\n                              RhsBlasTraits::NeedToConjugate && NumTraits<Scalar>::IsComplex>\n          ::run(actualLhs.size(), mat.data(), mat.outerStride(), actualLhsPtr, actualRhsPtr, actualAlpha);\n  }\n};\n\ntemplate<typename MatrixType, typename ProductType, int UpLo>\nstruct general_product_to_triangular_selector<MatrixType,ProductType,UpLo,false>\n{\n  static void run(MatrixType& mat, const ProductType& prod, const typename MatrixType::Scalar& alpha, bool beta)\n  {\n    typedef typename internal::remove_all<typename ProductType::LhsNested>::type Lhs;\n    typedef internal::blas_traits<Lhs> LhsBlasTraits;\n    typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhs;\n    typedef typename internal::remove_all<ActualLhs>::type _ActualLhs;\n    typename internal::add_const_on_value_type<ActualLhs>::type actualLhs = LhsBlasTraits::extract(prod.lhs());\n    \n    typedef typename internal::remove_all<typename ProductType::RhsNested>::type Rhs;\n    typedef internal::blas_traits<Rhs> RhsBlasTraits;\n    typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhs;\n    typedef typename internal::remove_all<ActualRhs>::type _ActualRhs;\n    typename internal::add_const_on_value_type<ActualRhs>::type actualRhs = RhsBlasTraits::extract(prod.rhs());\n\n    typename ProductType::Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs().derived()) * RhsBlasTraits::extractScalarFactor(prod.rhs().derived());\n\n    if(!beta)\n      mat.template triangularView<UpLo>().setZero();\n\n    enum {\n      IsRowMajor = (internal::traits<MatrixType>::Flags&RowMajorBit) ? 1 : 0,\n      LhsIsRowMajor = _ActualLhs::Flags&RowMajorBit ? 1 : 0,\n      RhsIsRowMajor = _ActualRhs::Flags&RowMajorBit ? 1 : 0,\n      SkipDiag = (UpLo&(UnitDiag|ZeroDiag))!=0\n    };\n\n    Index size = mat.cols();\n    if(SkipDiag)\n      size--;\n    Index depth = actualLhs.cols();\n\n    typedef internal::gemm_blocking_space<IsRowMajor ? RowMajor : ColMajor,typename Lhs::Scalar,typename Rhs::Scalar,\n          MatrixType::MaxColsAtCompileTime, MatrixType::MaxColsAtCompileTime, _ActualRhs::MaxColsAtCompileTime> BlockingType;\n\n    BlockingType blocking(size, size, depth, 1, false);\n\n    internal::general_matrix_matrix_triangular_product<Index,\n      typename Lhs::Scalar, LhsIsRowMajor ? RowMajor : ColMajor, LhsBlasTraits::NeedToConjugate,\n      typename Rhs::Scalar, RhsIsRowMajor ? RowMajor : ColMajor, RhsBlasTraits::NeedToConjugate,\n      IsRowMajor ? RowMajor : ColMajor, UpLo&(Lower|Upper)>\n      ::run(size, depth,\n            &actualLhs.coeffRef(SkipDiag&&(UpLo&Lower)==Lower ? 1 : 0,0), actualLhs.outerStride(),\n            &actualRhs.coeffRef(0,SkipDiag&&(UpLo&Upper)==Upper ? 1 : 0), actualRhs.outerStride(),\n            mat.data() + (SkipDiag ? (bool(IsRowMajor) != ((UpLo&Lower)==Lower) ? 1 : mat.outerStride() ) : 0), mat.outerStride(), actualAlpha, blocking);\n  }\n};\n\ntemplate<typename MatrixType, unsigned int UpLo>\ntemplate<typename ProductType>\nTriangularView<MatrixType,UpLo>& TriangularViewImpl<MatrixType,UpLo,Dense>::_assignProduct(const ProductType& prod, const Scalar& alpha, bool beta)\n{\n  EIGEN_STATIC_ASSERT((UpLo&UnitDiag)==0, WRITING_TO_TRIANGULAR_PART_WITH_UNIT_DIAGONAL_IS_NOT_SUPPORTED);\n  eigen_assert(derived().nestedExpression().rows() == prod.rows() && derived().cols() == prod.cols());\n  \n  general_product_to_triangular_selector<MatrixType, ProductType, UpLo, internal::traits<ProductType>::InnerSize==1>::run(derived().nestedExpression().const_cast_derived(), prod, alpha, beta);\n  \n  return derived();\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/products/GeneralMatrixMatrixTriangular_BLAS.h",
    "content": "/*\n Copyright (c) 2011, Intel Corporation. All rights reserved.\n\n Redistribution and use in source and binary forms, with or without modification,\n are permitted provided that the following conditions are met:\n\n * Redistributions of source code must retain the above copyright notice, this\n   list of conditions and the following disclaimer.\n * Redistributions in binary form must reproduce the above copyright notice,\n   this list of conditions and the following disclaimer in the documentation\n   and/or other materials provided with the distribution.\n * Neither the name of Intel Corporation nor the names of its contributors may\n   be used to endorse or promote products derived from this software without\n   specific prior written permission.\n\n THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\" AND\n ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED\n WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\n DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR\n ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES\n (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;\n LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON\n ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT\n (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS\n SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n\n ********************************************************************************\n *   Content : Eigen bindings to BLAS F77\n *   Level 3 BLAS SYRK/HERK implementation.\n ********************************************************************************\n*/\n\n#ifndef EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_BLAS_H\n#define EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_BLAS_H\n\nnamespace Eigen {\n\nnamespace internal {\n\ntemplate <typename Index, typename Scalar, int AStorageOrder, bool ConjugateA, int ResStorageOrder, int  UpLo>\nstruct general_matrix_matrix_rankupdate :\n       general_matrix_matrix_triangular_product<\n         Index,Scalar,AStorageOrder,ConjugateA,Scalar,AStorageOrder,ConjugateA,ResStorageOrder,UpLo,BuiltIn> {};\n\n\n// try to go to BLAS specialization\n#define EIGEN_BLAS_RANKUPDATE_SPECIALIZE(Scalar) \\\ntemplate <typename Index, int LhsStorageOrder, bool ConjugateLhs, \\\n                          int RhsStorageOrder, bool ConjugateRhs, int  UpLo> \\\nstruct general_matrix_matrix_triangular_product<Index,Scalar,LhsStorageOrder,ConjugateLhs, \\\n               Scalar,RhsStorageOrder,ConjugateRhs,ColMajor,UpLo,Specialized> { \\\n  static EIGEN_STRONG_INLINE void run(Index size, Index depth,const Scalar* lhs, Index lhsStride, \\\n                          const Scalar* rhs, Index rhsStride, Scalar* res, Index resStride, Scalar alpha, level3_blocking<Scalar, Scalar>& blocking) \\\n  { \\\n    if ( lhs==rhs && ((UpLo&(Lower|Upper)==UpLo)) ) { \\\n      general_matrix_matrix_rankupdate<Index,Scalar,LhsStorageOrder,ConjugateLhs,ColMajor,UpLo> \\\n      ::run(size,depth,lhs,lhsStride,rhs,rhsStride,res,resStride,alpha,blocking); \\\n    } else { \\\n      general_matrix_matrix_triangular_product<Index, \\\n        Scalar, LhsStorageOrder, ConjugateLhs, \\\n        Scalar, RhsStorageOrder, ConjugateRhs, \\\n        ColMajor, UpLo, BuiltIn> \\\n      ::run(size,depth,lhs,lhsStride,rhs,rhsStride,res,resStride,alpha,blocking); \\\n    } \\\n  } \\\n};\n\nEIGEN_BLAS_RANKUPDATE_SPECIALIZE(double)\nEIGEN_BLAS_RANKUPDATE_SPECIALIZE(float)\n// TODO handle complex cases\n// EIGEN_BLAS_RANKUPDATE_SPECIALIZE(dcomplex)\n// EIGEN_BLAS_RANKUPDATE_SPECIALIZE(scomplex)\n\n// SYRK for float/double\n#define EIGEN_BLAS_RANKUPDATE_R(EIGTYPE, BLASTYPE, BLASFUNC) \\\ntemplate <typename Index, int AStorageOrder, bool ConjugateA, int  UpLo> \\\nstruct general_matrix_matrix_rankupdate<Index,EIGTYPE,AStorageOrder,ConjugateA,ColMajor,UpLo> { \\\n  enum { \\\n    IsLower = (UpLo&Lower) == Lower, \\\n    LowUp = IsLower ? Lower : Upper, \\\n    conjA = ((AStorageOrder==ColMajor) && ConjugateA) ? 1 : 0 \\\n  }; \\\n  static EIGEN_STRONG_INLINE void run(Index size, Index depth,const EIGTYPE* lhs, Index lhsStride, \\\n                          const EIGTYPE* /*rhs*/, Index /*rhsStride*/, EIGTYPE* res, Index resStride, EIGTYPE alpha, level3_blocking<EIGTYPE, EIGTYPE>& /*blocking*/) \\\n  { \\\n  /* typedef Matrix<EIGTYPE, Dynamic, Dynamic, RhsStorageOrder> MatrixRhs;*/ \\\n\\\n   BlasIndex lda=convert_index<BlasIndex>(lhsStride), ldc=convert_index<BlasIndex>(resStride), n=convert_index<BlasIndex>(size), k=convert_index<BlasIndex>(depth); \\\n   char uplo=((IsLower) ? 'L' : 'U'), trans=((AStorageOrder==RowMajor) ? 'T':'N'); \\\n   EIGTYPE beta(1); \\\n   BLASFUNC(&uplo, &trans, &n, &k, (const BLASTYPE*)&numext::real_ref(alpha), lhs, &lda, (const BLASTYPE*)&numext::real_ref(beta), res, &ldc); \\\n  } \\\n};\n\n// HERK for complex data\n#define EIGEN_BLAS_RANKUPDATE_C(EIGTYPE, BLASTYPE, RTYPE, BLASFUNC) \\\ntemplate <typename Index, int AStorageOrder, bool ConjugateA, int  UpLo> \\\nstruct general_matrix_matrix_rankupdate<Index,EIGTYPE,AStorageOrder,ConjugateA,ColMajor,UpLo> { \\\n  enum { \\\n    IsLower = (UpLo&Lower) == Lower, \\\n    LowUp = IsLower ? Lower : Upper, \\\n    conjA = (((AStorageOrder==ColMajor) && ConjugateA) || ((AStorageOrder==RowMajor) && !ConjugateA)) ? 1 : 0 \\\n  }; \\\n  static EIGEN_STRONG_INLINE void run(Index size, Index depth,const EIGTYPE* lhs, Index lhsStride, \\\n                          const EIGTYPE* /*rhs*/, Index /*rhsStride*/, EIGTYPE* res, Index resStride, EIGTYPE alpha, level3_blocking<EIGTYPE, EIGTYPE>& /*blocking*/) \\\n  { \\\n   typedef Matrix<EIGTYPE, Dynamic, Dynamic, AStorageOrder> MatrixType; \\\n\\\n   BlasIndex lda=convert_index<BlasIndex>(lhsStride), ldc=convert_index<BlasIndex>(resStride), n=convert_index<BlasIndex>(size), k=convert_index<BlasIndex>(depth); \\\n   char uplo=((IsLower) ? 'L' : 'U'), trans=((AStorageOrder==RowMajor) ? 'C':'N'); \\\n   RTYPE alpha_, beta_; \\\n   const EIGTYPE* a_ptr; \\\n\\\n   alpha_ = alpha.real(); \\\n   beta_ = 1.0; \\\n/* Copy with conjugation in some cases*/ \\\n   MatrixType a; \\\n   if (conjA) { \\\n     Map<const MatrixType, 0, OuterStride<> > mapA(lhs,n,k,OuterStride<>(lhsStride)); \\\n     a = mapA.conjugate(); \\\n     lda = a.outerStride(); \\\n     a_ptr = a.data(); \\\n   } else a_ptr=lhs; \\\n   BLASFUNC(&uplo, &trans, &n, &k, &alpha_, (BLASTYPE*)a_ptr, &lda, &beta_, (BLASTYPE*)res, &ldc); \\\n  } \\\n};\n\n#ifdef EIGEN_USE_MKL\nEIGEN_BLAS_RANKUPDATE_R(double, double, dsyrk)\nEIGEN_BLAS_RANKUPDATE_R(float,  float,  ssyrk)\n#else\nEIGEN_BLAS_RANKUPDATE_R(double, double, dsyrk_)\nEIGEN_BLAS_RANKUPDATE_R(float,  float,  ssyrk_)\n#endif\n\n// TODO hanlde complex cases\n// EIGEN_BLAS_RANKUPDATE_C(dcomplex, double, double, zherk_)\n// EIGEN_BLAS_RANKUPDATE_C(scomplex, float,  float, cherk_)\n\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_BLAS_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/products/GeneralMatrixMatrix_BLAS.h",
    "content": "/*\n Copyright (c) 2011, Intel Corporation. All rights reserved.\n\n Redistribution and use in source and binary forms, with or without modification,\n are permitted provided that the following conditions are met:\n\n * Redistributions of source code must retain the above copyright notice, this\n   list of conditions and the following disclaimer.\n * Redistributions in binary form must reproduce the above copyright notice,\n   this list of conditions and the following disclaimer in the documentation\n   and/or other materials provided with the distribution.\n * Neither the name of Intel Corporation nor the names of its contributors may\n   be used to endorse or promote products derived from this software without\n   specific prior written permission.\n\n THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\" AND\n ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED\n WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\n DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR\n ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES\n (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;\n LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON\n ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT\n (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS\n SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n\n ********************************************************************************\n *   Content : Eigen bindings to BLAS F77\n *   General matrix-matrix product functionality based on ?GEMM.\n ********************************************************************************\n*/\n\n#ifndef EIGEN_GENERAL_MATRIX_MATRIX_BLAS_H\n#define EIGEN_GENERAL_MATRIX_MATRIX_BLAS_H\n\nnamespace Eigen { \n\nnamespace internal {\n\n/**********************************************************************\n* This file implements general matrix-matrix multiplication using BLAS\n* gemm function via partial specialization of\n* general_matrix_matrix_product::run(..) method for float, double,\n* std::complex<float> and std::complex<double> types\n**********************************************************************/\n\n// gemm specialization\n\n#define GEMM_SPECIALIZATION(EIGTYPE, EIGPREFIX, BLASTYPE, BLASFUNC) \\\ntemplate< \\\n  typename Index, \\\n  int LhsStorageOrder, bool ConjugateLhs, \\\n  int RhsStorageOrder, bool ConjugateRhs> \\\nstruct general_matrix_matrix_product<Index,EIGTYPE,LhsStorageOrder,ConjugateLhs,EIGTYPE,RhsStorageOrder,ConjugateRhs,ColMajor> \\\n{ \\\ntypedef gebp_traits<EIGTYPE,EIGTYPE> Traits; \\\n\\\nstatic void run(Index rows, Index cols, Index depth, \\\n  const EIGTYPE* _lhs, Index lhsStride, \\\n  const EIGTYPE* _rhs, Index rhsStride, \\\n  EIGTYPE* res, Index resStride, \\\n  EIGTYPE alpha, \\\n  level3_blocking<EIGTYPE, EIGTYPE>& /*blocking*/, \\\n  GemmParallelInfo<Index>* /*info = 0*/) \\\n{ \\\n  using std::conj; \\\n\\\n  char transa, transb; \\\n  BlasIndex m, n, k, lda, ldb, ldc; \\\n  const EIGTYPE *a, *b; \\\n  EIGTYPE beta(1); \\\n  MatrixX##EIGPREFIX a_tmp, b_tmp; \\\n\\\n/* Set transpose options */ \\\n  transa = (LhsStorageOrder==RowMajor) ? ((ConjugateLhs) ? 'C' : 'T') : 'N'; \\\n  transb = (RhsStorageOrder==RowMajor) ? ((ConjugateRhs) ? 'C' : 'T') : 'N'; \\\n\\\n/* Set m, n, k */ \\\n  m = convert_index<BlasIndex>(rows);  \\\n  n = convert_index<BlasIndex>(cols);  \\\n  k = convert_index<BlasIndex>(depth); \\\n\\\n/* Set lda, ldb, ldc */ \\\n  lda = convert_index<BlasIndex>(lhsStride); \\\n  ldb = convert_index<BlasIndex>(rhsStride); \\\n  ldc = convert_index<BlasIndex>(resStride); \\\n\\\n/* Set a, b, c */ \\\n  if ((LhsStorageOrder==ColMajor) && (ConjugateLhs)) { \\\n    Map<const MatrixX##EIGPREFIX, 0, OuterStride<> > lhs(_lhs,m,k,OuterStride<>(lhsStride)); \\\n    a_tmp = lhs.conjugate(); \\\n    a = a_tmp.data(); \\\n    lda = convert_index<BlasIndex>(a_tmp.outerStride()); \\\n  } else a = _lhs; \\\n\\\n  if ((RhsStorageOrder==ColMajor) && (ConjugateRhs)) { \\\n    Map<const MatrixX##EIGPREFIX, 0, OuterStride<> > rhs(_rhs,k,n,OuterStride<>(rhsStride)); \\\n    b_tmp = rhs.conjugate(); \\\n    b = b_tmp.data(); \\\n    ldb = convert_index<BlasIndex>(b_tmp.outerStride()); \\\n  } else b = _rhs; \\\n\\\n  BLASFUNC(&transa, &transb, &m, &n, &k, (const BLASTYPE*)&numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (const BLASTYPE*)b, &ldb, (const BLASTYPE*)&numext::real_ref(beta), (BLASTYPE*)res, &ldc); \\\n}};\n\n#ifdef EIGEN_USE_MKL\nGEMM_SPECIALIZATION(double,   d,  double, dgemm)\nGEMM_SPECIALIZATION(float,    f,  float,  sgemm)\nGEMM_SPECIALIZATION(dcomplex, cd, MKL_Complex16, zgemm)\nGEMM_SPECIALIZATION(scomplex, cf, MKL_Complex8,  cgemm)\n#else\nGEMM_SPECIALIZATION(double,   d,  double, dgemm_)\nGEMM_SPECIALIZATION(float,    f,  float,  sgemm_)\nGEMM_SPECIALIZATION(dcomplex, cd, double, zgemm_)\nGEMM_SPECIALIZATION(scomplex, cf, float,  cgemm_)\n#endif\n\n} // end namespase internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_GENERAL_MATRIX_MATRIX_BLAS_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/products/GeneralMatrixVector.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_GENERAL_MATRIX_VECTOR_H\n#define EIGEN_GENERAL_MATRIX_VECTOR_H\n\nnamespace Eigen {\n\nnamespace internal {\n\n/* Optimized col-major matrix * vector product:\n * This algorithm processes 4 columns at onces that allows to both reduce\n * the number of load/stores of the result by a factor 4 and to reduce\n * the instruction dependency. Moreover, we know that all bands have the\n * same alignment pattern.\n *\n * Mixing type logic: C += alpha * A * B\n *  |  A  |  B  |alpha| comments\n *  |real |cplx |cplx | no vectorization\n *  |real |cplx |real | alpha is converted to a cplx when calling the run function, no vectorization\n *  |cplx |real |cplx | invalid, the caller has to do tmp: = A * B; C += alpha*tmp\n *  |cplx |real |real | optimal case, vectorization possible via real-cplx mul\n *\n * Accesses to the matrix coefficients follow the following logic:\n *\n * - if all columns have the same alignment then\n *   - if the columns have the same alignment as the result vector, then easy! (-> AllAligned case)\n *   - otherwise perform unaligned loads only (-> NoneAligned case)\n * - otherwise\n *   - if even columns have the same alignment then\n *     // odd columns are guaranteed to have the same alignment too\n *     - if even or odd columns have the same alignment as the result, then\n *       // for a register size of 2 scalars, this is guarantee to be the case (e.g., SSE with double)\n *       - perform half aligned and half unaligned loads (-> EvenAligned case)\n *     - otherwise perform unaligned loads only (-> NoneAligned case)\n *   - otherwise, if the register size is 4 scalars (e.g., SSE with float) then\n *     - one over 4 consecutive columns is guaranteed to be aligned with the result vector,\n *       perform simple aligned loads for this column and aligned loads plus re-alignment for the other. (-> FirstAligned case)\n *       // this re-alignment is done by the palign function implemented for SSE in Eigen/src/Core/arch/SSE/PacketMath.h\n *   - otherwise,\n *     // if we get here, this means the register size is greater than 4 (e.g., AVX with floats),\n *     // we currently fall back to the NoneAligned case\n *\n * The same reasoning apply for the transposed case.\n *\n * The last case (PacketSize>4) could probably be improved by generalizing the FirstAligned case, but since we do not support AVX yet...\n * One might also wonder why in the EvenAligned case we perform unaligned loads instead of using the aligned-loads plus re-alignment\n * strategy as in the FirstAligned case. The reason is that we observed that unaligned loads on a 8 byte boundary are not too slow\n * compared to unaligned loads on a 4 byte boundary.\n *\n */\ntemplate<typename Index, typename LhsScalar, typename LhsMapper, bool ConjugateLhs, typename RhsScalar, typename RhsMapper, bool ConjugateRhs, int Version>\nstruct general_matrix_vector_product<Index,LhsScalar,LhsMapper,ColMajor,ConjugateLhs,RhsScalar,RhsMapper,ConjugateRhs,Version>\n{\n  typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;\n\nenum {\n  Vectorizable = packet_traits<LhsScalar>::Vectorizable && packet_traits<RhsScalar>::Vectorizable\n              && int(packet_traits<LhsScalar>::size)==int(packet_traits<RhsScalar>::size),\n  LhsPacketSize = Vectorizable ? packet_traits<LhsScalar>::size : 1,\n  RhsPacketSize = Vectorizable ? packet_traits<RhsScalar>::size : 1,\n  ResPacketSize = Vectorizable ? packet_traits<ResScalar>::size : 1\n};\n\ntypedef typename packet_traits<LhsScalar>::type  _LhsPacket;\ntypedef typename packet_traits<RhsScalar>::type  _RhsPacket;\ntypedef typename packet_traits<ResScalar>::type  _ResPacket;\n\ntypedef typename conditional<Vectorizable,_LhsPacket,LhsScalar>::type LhsPacket;\ntypedef typename conditional<Vectorizable,_RhsPacket,RhsScalar>::type RhsPacket;\ntypedef typename conditional<Vectorizable,_ResPacket,ResScalar>::type ResPacket;\n\nEIGEN_DONT_INLINE static void run(\n  Index rows, Index cols,\n  const LhsMapper& lhs,\n  const RhsMapper& rhs,\n        ResScalar* res, Index resIncr,\n  RhsScalar alpha);\n};\n\ntemplate<typename Index, typename LhsScalar, typename LhsMapper, bool ConjugateLhs, typename RhsScalar, typename RhsMapper, bool ConjugateRhs, int Version>\nEIGEN_DONT_INLINE void general_matrix_vector_product<Index,LhsScalar,LhsMapper,ColMajor,ConjugateLhs,RhsScalar,RhsMapper,ConjugateRhs,Version>::run(\n  Index rows, Index cols,\n  const LhsMapper& lhs,\n  const RhsMapper& rhs,\n        ResScalar* res, Index resIncr,\n  RhsScalar alpha)\n{\n  EIGEN_UNUSED_VARIABLE(resIncr);\n  eigen_internal_assert(resIncr==1);\n  #ifdef _EIGEN_ACCUMULATE_PACKETS\n  #error _EIGEN_ACCUMULATE_PACKETS has already been defined\n  #endif\n  #define _EIGEN_ACCUMULATE_PACKETS(Alignment0,Alignment13,Alignment2) \\\n    pstore(&res[j], \\\n      padd(pload<ResPacket>(&res[j]), \\\n        padd( \\\n      padd(pcj.pmul(lhs0.template load<LhsPacket, Alignment0>(j),    ptmp0), \\\n      pcj.pmul(lhs1.template load<LhsPacket, Alignment13>(j),   ptmp1)),   \\\n      padd(pcj.pmul(lhs2.template load<LhsPacket, Alignment2>(j),    ptmp2), \\\n      pcj.pmul(lhs3.template load<LhsPacket, Alignment13>(j),   ptmp3)) )))\n\n  typedef typename LhsMapper::VectorMapper LhsScalars;\n\n  conj_helper<LhsScalar,RhsScalar,ConjugateLhs,ConjugateRhs> cj;\n  conj_helper<LhsPacket,RhsPacket,ConjugateLhs,ConjugateRhs> pcj;\n  if(ConjugateRhs)\n    alpha = numext::conj(alpha);\n\n  enum { AllAligned = 0, EvenAligned, FirstAligned, NoneAligned };\n  const Index columnsAtOnce = 4;\n  const Index peels = 2;\n  const Index LhsPacketAlignedMask = LhsPacketSize-1;\n  const Index ResPacketAlignedMask = ResPacketSize-1;\n//  const Index PeelAlignedMask = ResPacketSize*peels-1;\n  const Index size = rows;\n\n  const Index lhsStride = lhs.stride();\n\n  // How many coeffs of the result do we have to skip to be aligned.\n  // Here we assume data are at least aligned on the base scalar type.\n  Index alignedStart = internal::first_default_aligned(res,size);\n  Index alignedSize = ResPacketSize>1 ? alignedStart + ((size-alignedStart) & ~ResPacketAlignedMask) : 0;\n  const Index peeledSize = alignedSize - RhsPacketSize*peels - RhsPacketSize + 1;\n\n  const Index alignmentStep = LhsPacketSize>1 ? (LhsPacketSize - lhsStride % LhsPacketSize) & LhsPacketAlignedMask : 0;\n  Index alignmentPattern = alignmentStep==0 ? AllAligned\n                       : alignmentStep==(LhsPacketSize/2) ? EvenAligned\n                       : FirstAligned;\n\n  // we cannot assume the first element is aligned because of sub-matrices\n  const Index lhsAlignmentOffset = lhs.firstAligned(size);\n\n  // find how many columns do we have to skip to be aligned with the result (if possible)\n  Index skipColumns = 0;\n  // if the data cannot be aligned (TODO add some compile time tests when possible, e.g. for floats)\n  if( (lhsAlignmentOffset < 0) || (lhsAlignmentOffset == size) || (UIntPtr(res)%sizeof(ResScalar)) )\n  {\n    alignedSize = 0;\n    alignedStart = 0;\n    alignmentPattern = NoneAligned;\n  }\n  else if(LhsPacketSize > 4)\n  {\n    // TODO: extend the code to support aligned loads whenever possible when LhsPacketSize > 4.\n    // Currently, it seems to be better to perform unaligned loads anyway\n    alignmentPattern = NoneAligned;\n  }\n  else if (LhsPacketSize>1)\n  {\n  //    eigen_internal_assert(size_t(firstLhs+lhsAlignmentOffset)%sizeof(LhsPacket)==0 || size<LhsPacketSize);\n\n    while (skipColumns<LhsPacketSize &&\n          alignedStart != ((lhsAlignmentOffset + alignmentStep*skipColumns)%LhsPacketSize))\n      ++skipColumns;\n    if (skipColumns==LhsPacketSize)\n    {\n      // nothing can be aligned, no need to skip any column\n      alignmentPattern = NoneAligned;\n      skipColumns = 0;\n    }\n    else\n    {\n      skipColumns = (std::min)(skipColumns,cols);\n      // note that the skiped columns are processed later.\n    }\n\n    /*    eigen_internal_assert(  (alignmentPattern==NoneAligned)\n                      || (skipColumns + columnsAtOnce >= cols)\n                      || LhsPacketSize > size\n                      || (size_t(firstLhs+alignedStart+lhsStride*skipColumns)%sizeof(LhsPacket))==0);*/\n  }\n  else if(Vectorizable)\n  {\n    alignedStart = 0;\n    alignedSize = size;\n    alignmentPattern = AllAligned;\n  }\n\n  const Index offset1 = (alignmentPattern==FirstAligned && alignmentStep==1)?3:1;\n  const Index offset3 = (alignmentPattern==FirstAligned && alignmentStep==1)?1:3;\n\n  Index columnBound = ((cols-skipColumns)/columnsAtOnce)*columnsAtOnce + skipColumns;\n  for (Index i=skipColumns; i<columnBound; i+=columnsAtOnce)\n  {\n    RhsPacket ptmp0 = pset1<RhsPacket>(alpha*rhs(i, 0)),\n              ptmp1 = pset1<RhsPacket>(alpha*rhs(i+offset1, 0)),\n              ptmp2 = pset1<RhsPacket>(alpha*rhs(i+2, 0)),\n              ptmp3 = pset1<RhsPacket>(alpha*rhs(i+offset3, 0));\n\n    // this helps a lot generating better binary code\n    const LhsScalars lhs0 = lhs.getVectorMapper(0, i+0),   lhs1 = lhs.getVectorMapper(0, i+offset1),\n                     lhs2 = lhs.getVectorMapper(0, i+2),   lhs3 = lhs.getVectorMapper(0, i+offset3);\n\n    if (Vectorizable)\n    {\n      /* explicit vectorization */\n      // process initial unaligned coeffs\n      for (Index j=0; j<alignedStart; ++j)\n      {\n        res[j] = cj.pmadd(lhs0(j), pfirst(ptmp0), res[j]);\n        res[j] = cj.pmadd(lhs1(j), pfirst(ptmp1), res[j]);\n        res[j] = cj.pmadd(lhs2(j), pfirst(ptmp2), res[j]);\n        res[j] = cj.pmadd(lhs3(j), pfirst(ptmp3), res[j]);\n      }\n\n      if (alignedSize>alignedStart)\n      {\n        switch(alignmentPattern)\n        {\n          case AllAligned:\n            for (Index j = alignedStart; j<alignedSize; j+=ResPacketSize)\n              _EIGEN_ACCUMULATE_PACKETS(Aligned,Aligned,Aligned);\n            break;\n          case EvenAligned:\n            for (Index j = alignedStart; j<alignedSize; j+=ResPacketSize)\n              _EIGEN_ACCUMULATE_PACKETS(Aligned,Unaligned,Aligned);\n            break;\n          case FirstAligned:\n          {\n            Index j = alignedStart;\n            if(peels>1)\n            {\n              LhsPacket A00, A01, A02, A03, A10, A11, A12, A13;\n              ResPacket T0, T1;\n\n              A01 = lhs1.template load<LhsPacket, Aligned>(alignedStart-1);\n              A02 = lhs2.template load<LhsPacket, Aligned>(alignedStart-2);\n              A03 = lhs3.template load<LhsPacket, Aligned>(alignedStart-3);\n\n              for (; j<peeledSize; j+=peels*ResPacketSize)\n              {\n                A11 = lhs1.template load<LhsPacket, Aligned>(j-1+LhsPacketSize);  palign<1>(A01,A11);\n                A12 = lhs2.template load<LhsPacket, Aligned>(j-2+LhsPacketSize);  palign<2>(A02,A12);\n                A13 = lhs3.template load<LhsPacket, Aligned>(j-3+LhsPacketSize);  palign<3>(A03,A13);\n\n                A00 = lhs0.template load<LhsPacket, Aligned>(j);\n                A10 = lhs0.template load<LhsPacket, Aligned>(j+LhsPacketSize);\n                T0  = pcj.pmadd(A00, ptmp0, pload<ResPacket>(&res[j]));\n                T1  = pcj.pmadd(A10, ptmp0, pload<ResPacket>(&res[j+ResPacketSize]));\n\n                T0  = pcj.pmadd(A01, ptmp1, T0);\n                A01 = lhs1.template load<LhsPacket, Aligned>(j-1+2*LhsPacketSize);  palign<1>(A11,A01);\n                T0  = pcj.pmadd(A02, ptmp2, T0);\n                A02 = lhs2.template load<LhsPacket, Aligned>(j-2+2*LhsPacketSize);  palign<2>(A12,A02);\n                T0  = pcj.pmadd(A03, ptmp3, T0);\n                pstore(&res[j],T0);\n                A03 = lhs3.template load<LhsPacket, Aligned>(j-3+2*LhsPacketSize);  palign<3>(A13,A03);\n                T1  = pcj.pmadd(A11, ptmp1, T1);\n                T1  = pcj.pmadd(A12, ptmp2, T1);\n                T1  = pcj.pmadd(A13, ptmp3, T1);\n                pstore(&res[j+ResPacketSize],T1);\n              }\n            }\n            for (; j<alignedSize; j+=ResPacketSize)\n              _EIGEN_ACCUMULATE_PACKETS(Aligned,Unaligned,Unaligned);\n            break;\n          }\n          default:\n            for (Index j = alignedStart; j<alignedSize; j+=ResPacketSize)\n              _EIGEN_ACCUMULATE_PACKETS(Unaligned,Unaligned,Unaligned);\n            break;\n        }\n      }\n    } // end explicit vectorization\n\n    /* process remaining coeffs (or all if there is no explicit vectorization) */\n    for (Index j=alignedSize; j<size; ++j)\n    {\n      res[j] = cj.pmadd(lhs0(j), pfirst(ptmp0), res[j]);\n      res[j] = cj.pmadd(lhs1(j), pfirst(ptmp1), res[j]);\n      res[j] = cj.pmadd(lhs2(j), pfirst(ptmp2), res[j]);\n      res[j] = cj.pmadd(lhs3(j), pfirst(ptmp3), res[j]);\n    }\n  }\n\n  // process remaining first and last columns (at most columnsAtOnce-1)\n  Index end = cols;\n  Index start = columnBound;\n  do\n  {\n    for (Index k=start; k<end; ++k)\n    {\n      RhsPacket ptmp0 = pset1<RhsPacket>(alpha*rhs(k, 0));\n      const LhsScalars lhs0 = lhs.getVectorMapper(0, k);\n\n      if (Vectorizable)\n      {\n        /* explicit vectorization */\n        // process first unaligned result's coeffs\n        for (Index j=0; j<alignedStart; ++j)\n          res[j] += cj.pmul(lhs0(j), pfirst(ptmp0));\n        // process aligned result's coeffs\n        if (lhs0.template aligned<LhsPacket>(alignedStart))\n          for (Index i = alignedStart;i<alignedSize;i+=ResPacketSize)\n            pstore(&res[i], pcj.pmadd(lhs0.template load<LhsPacket, Aligned>(i), ptmp0, pload<ResPacket>(&res[i])));\n        else\n          for (Index i = alignedStart;i<alignedSize;i+=ResPacketSize)\n            pstore(&res[i], pcj.pmadd(lhs0.template load<LhsPacket, Unaligned>(i), ptmp0, pload<ResPacket>(&res[i])));\n      }\n\n      // process remaining scalars (or all if no explicit vectorization)\n      for (Index i=alignedSize; i<size; ++i)\n        res[i] += cj.pmul(lhs0(i), pfirst(ptmp0));\n    }\n    if (skipColumns)\n    {\n      start = 0;\n      end = skipColumns;\n      skipColumns = 0;\n    }\n    else\n      break;\n  } while(Vectorizable);\n  #undef _EIGEN_ACCUMULATE_PACKETS\n}\n\n/* Optimized row-major matrix * vector product:\n * This algorithm processes 4 rows at onces that allows to both reduce\n * the number of load/stores of the result by a factor 4 and to reduce\n * the instruction dependency. Moreover, we know that all bands have the\n * same alignment pattern.\n *\n * Mixing type logic:\n *  - alpha is always a complex (or converted to a complex)\n *  - no vectorization\n */\ntemplate<typename Index, typename LhsScalar, typename LhsMapper, bool ConjugateLhs, typename RhsScalar, typename RhsMapper, bool ConjugateRhs, int Version>\nstruct general_matrix_vector_product<Index,LhsScalar,LhsMapper,RowMajor,ConjugateLhs,RhsScalar,RhsMapper,ConjugateRhs,Version>\n{\ntypedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;\n\nenum {\n  Vectorizable = packet_traits<LhsScalar>::Vectorizable && packet_traits<RhsScalar>::Vectorizable\n              && int(packet_traits<LhsScalar>::size)==int(packet_traits<RhsScalar>::size),\n  LhsPacketSize = Vectorizable ? packet_traits<LhsScalar>::size : 1,\n  RhsPacketSize = Vectorizable ? packet_traits<RhsScalar>::size : 1,\n  ResPacketSize = Vectorizable ? packet_traits<ResScalar>::size : 1\n};\n\ntypedef typename packet_traits<LhsScalar>::type  _LhsPacket;\ntypedef typename packet_traits<RhsScalar>::type  _RhsPacket;\ntypedef typename packet_traits<ResScalar>::type  _ResPacket;\n\ntypedef typename conditional<Vectorizable,_LhsPacket,LhsScalar>::type LhsPacket;\ntypedef typename conditional<Vectorizable,_RhsPacket,RhsScalar>::type RhsPacket;\ntypedef typename conditional<Vectorizable,_ResPacket,ResScalar>::type ResPacket;\n\nEIGEN_DONT_INLINE static void run(\n  Index rows, Index cols,\n  const LhsMapper& lhs,\n  const RhsMapper& rhs,\n        ResScalar* res, Index resIncr,\n  ResScalar alpha);\n};\n\ntemplate<typename Index, typename LhsScalar, typename LhsMapper, bool ConjugateLhs, typename RhsScalar, typename RhsMapper, bool ConjugateRhs, int Version>\nEIGEN_DONT_INLINE void general_matrix_vector_product<Index,LhsScalar,LhsMapper,RowMajor,ConjugateLhs,RhsScalar,RhsMapper,ConjugateRhs,Version>::run(\n  Index rows, Index cols,\n  const LhsMapper& lhs,\n  const RhsMapper& rhs,\n  ResScalar* res, Index resIncr,\n  ResScalar alpha)\n{\n  eigen_internal_assert(rhs.stride()==1);\n\n  #ifdef _EIGEN_ACCUMULATE_PACKETS\n  #error _EIGEN_ACCUMULATE_PACKETS has already been defined\n  #endif\n\n  #define _EIGEN_ACCUMULATE_PACKETS(Alignment0,Alignment13,Alignment2) {\\\n    RhsPacket b = rhs.getVectorMapper(j, 0).template load<RhsPacket, Aligned>(0);  \\\n    ptmp0 = pcj.pmadd(lhs0.template load<LhsPacket, Alignment0>(j), b, ptmp0); \\\n    ptmp1 = pcj.pmadd(lhs1.template load<LhsPacket, Alignment13>(j), b, ptmp1); \\\n    ptmp2 = pcj.pmadd(lhs2.template load<LhsPacket, Alignment2>(j), b, ptmp2); \\\n    ptmp3 = pcj.pmadd(lhs3.template load<LhsPacket, Alignment13>(j), b, ptmp3); }\n\n  conj_helper<LhsScalar,RhsScalar,ConjugateLhs,ConjugateRhs> cj;\n  conj_helper<LhsPacket,RhsPacket,ConjugateLhs,ConjugateRhs> pcj;\n\n  typedef typename LhsMapper::VectorMapper LhsScalars;\n\n  enum { AllAligned=0, EvenAligned=1, FirstAligned=2, NoneAligned=3 };\n  const Index rowsAtOnce = 4;\n  const Index peels = 2;\n  const Index RhsPacketAlignedMask = RhsPacketSize-1;\n  const Index LhsPacketAlignedMask = LhsPacketSize-1;\n  const Index depth = cols;\n  const Index lhsStride = lhs.stride();\n\n  // How many coeffs of the result do we have to skip to be aligned.\n  // Here we assume data are at least aligned on the base scalar type\n  // if that's not the case then vectorization is discarded, see below.\n  Index alignedStart = rhs.firstAligned(depth);\n  Index alignedSize = RhsPacketSize>1 ? alignedStart + ((depth-alignedStart) & ~RhsPacketAlignedMask) : 0;\n  const Index peeledSize = alignedSize - RhsPacketSize*peels - RhsPacketSize + 1;\n\n  const Index alignmentStep = LhsPacketSize>1 ? (LhsPacketSize - lhsStride % LhsPacketSize) & LhsPacketAlignedMask : 0;\n  Index alignmentPattern = alignmentStep==0 ? AllAligned\n                           : alignmentStep==(LhsPacketSize/2) ? EvenAligned\n                           : FirstAligned;\n\n  // we cannot assume the first element is aligned because of sub-matrices\n  const Index lhsAlignmentOffset = lhs.firstAligned(depth);\n  const Index rhsAlignmentOffset = rhs.firstAligned(rows);\n\n  // find how many rows do we have to skip to be aligned with rhs (if possible)\n  Index skipRows = 0;\n  // if the data cannot be aligned (TODO add some compile time tests when possible, e.g. for floats)\n  if( (sizeof(LhsScalar)!=sizeof(RhsScalar)) ||\n      (lhsAlignmentOffset < 0) || (lhsAlignmentOffset == depth) ||\n      (rhsAlignmentOffset < 0) || (rhsAlignmentOffset == rows) )\n  {\n    alignedSize = 0;\n    alignedStart = 0;\n    alignmentPattern = NoneAligned;\n  }\n  else if(LhsPacketSize > 4)\n  {\n    // TODO: extend the code to support aligned loads whenever possible when LhsPacketSize > 4.\n    alignmentPattern = NoneAligned;\n  }\n  else if (LhsPacketSize>1)\n  {\n  //    eigen_internal_assert(size_t(firstLhs+lhsAlignmentOffset)%sizeof(LhsPacket)==0  || depth<LhsPacketSize);\n\n    while (skipRows<LhsPacketSize &&\n           alignedStart != ((lhsAlignmentOffset + alignmentStep*skipRows)%LhsPacketSize))\n      ++skipRows;\n    if (skipRows==LhsPacketSize)\n    {\n      // nothing can be aligned, no need to skip any column\n      alignmentPattern = NoneAligned;\n      skipRows = 0;\n    }\n    else\n    {\n      skipRows = (std::min)(skipRows,Index(rows));\n      // note that the skiped columns are processed later.\n    }\n    /*    eigen_internal_assert(  alignmentPattern==NoneAligned\n                      || LhsPacketSize==1\n                      || (skipRows + rowsAtOnce >= rows)\n                      || LhsPacketSize > depth\n                      || (size_t(firstLhs+alignedStart+lhsStride*skipRows)%sizeof(LhsPacket))==0);*/\n  }\n  else if(Vectorizable)\n  {\n    alignedStart = 0;\n    alignedSize = depth;\n    alignmentPattern = AllAligned;\n  }\n\n  const Index offset1 = (alignmentPattern==FirstAligned && alignmentStep==1)?3:1;\n  const Index offset3 = (alignmentPattern==FirstAligned && alignmentStep==1)?1:3;\n\n  Index rowBound = ((rows-skipRows)/rowsAtOnce)*rowsAtOnce + skipRows;\n  for (Index i=skipRows; i<rowBound; i+=rowsAtOnce)\n  {\n    // FIXME: what is the purpose of this EIGEN_ALIGN_DEFAULT ??\n    EIGEN_ALIGN_MAX ResScalar tmp0 = ResScalar(0);\n    ResScalar tmp1 = ResScalar(0), tmp2 = ResScalar(0), tmp3 = ResScalar(0);\n\n    // this helps the compiler generating good binary code\n    const LhsScalars lhs0 = lhs.getVectorMapper(i+0, 0),    lhs1 = lhs.getVectorMapper(i+offset1, 0),\n                     lhs2 = lhs.getVectorMapper(i+2, 0),    lhs3 = lhs.getVectorMapper(i+offset3, 0);\n\n    if (Vectorizable)\n    {\n      /* explicit vectorization */\n      ResPacket ptmp0 = pset1<ResPacket>(ResScalar(0)), ptmp1 = pset1<ResPacket>(ResScalar(0)),\n                ptmp2 = pset1<ResPacket>(ResScalar(0)), ptmp3 = pset1<ResPacket>(ResScalar(0));\n\n      // process initial unaligned coeffs\n      // FIXME this loop get vectorized by the compiler !\n      for (Index j=0; j<alignedStart; ++j)\n      {\n        RhsScalar b = rhs(j, 0);\n        tmp0 += cj.pmul(lhs0(j),b); tmp1 += cj.pmul(lhs1(j),b);\n        tmp2 += cj.pmul(lhs2(j),b); tmp3 += cj.pmul(lhs3(j),b);\n      }\n\n      if (alignedSize>alignedStart)\n      {\n        switch(alignmentPattern)\n        {\n          case AllAligned:\n            for (Index j = alignedStart; j<alignedSize; j+=RhsPacketSize)\n              _EIGEN_ACCUMULATE_PACKETS(Aligned,Aligned,Aligned);\n            break;\n          case EvenAligned:\n            for (Index j = alignedStart; j<alignedSize; j+=RhsPacketSize)\n              _EIGEN_ACCUMULATE_PACKETS(Aligned,Unaligned,Aligned);\n            break;\n          case FirstAligned:\n          {\n            Index j = alignedStart;\n            if (peels>1)\n            {\n              /* Here we proccess 4 rows with with two peeled iterations to hide\n               * the overhead of unaligned loads. Moreover unaligned loads are handled\n               * using special shift/move operations between the two aligned packets\n               * overlaping the desired unaligned packet. This is *much* more efficient\n               * than basic unaligned loads.\n               */\n              LhsPacket A01, A02, A03, A11, A12, A13;\n              A01 = lhs1.template load<LhsPacket, Aligned>(alignedStart-1);\n              A02 = lhs2.template load<LhsPacket, Aligned>(alignedStart-2);\n              A03 = lhs3.template load<LhsPacket, Aligned>(alignedStart-3);\n\n              for (; j<peeledSize; j+=peels*RhsPacketSize)\n              {\n                RhsPacket b = rhs.getVectorMapper(j, 0).template load<RhsPacket, Aligned>(0);\n                A11 = lhs1.template load<LhsPacket, Aligned>(j-1+LhsPacketSize);  palign<1>(A01,A11);\n                A12 = lhs2.template load<LhsPacket, Aligned>(j-2+LhsPacketSize);  palign<2>(A02,A12);\n                A13 = lhs3.template load<LhsPacket, Aligned>(j-3+LhsPacketSize);  palign<3>(A03,A13);\n\n                ptmp0 = pcj.pmadd(lhs0.template load<LhsPacket, Aligned>(j), b, ptmp0);\n                ptmp1 = pcj.pmadd(A01, b, ptmp1);\n                A01 = lhs1.template load<LhsPacket, Aligned>(j-1+2*LhsPacketSize);  palign<1>(A11,A01);\n                ptmp2 = pcj.pmadd(A02, b, ptmp2);\n                A02 = lhs2.template load<LhsPacket, Aligned>(j-2+2*LhsPacketSize);  palign<2>(A12,A02);\n                ptmp3 = pcj.pmadd(A03, b, ptmp3);\n                A03 = lhs3.template load<LhsPacket, Aligned>(j-3+2*LhsPacketSize);  palign<3>(A13,A03);\n\n                b = rhs.getVectorMapper(j+RhsPacketSize, 0).template load<RhsPacket, Aligned>(0);\n                ptmp0 = pcj.pmadd(lhs0.template load<LhsPacket, Aligned>(j+LhsPacketSize), b, ptmp0);\n                ptmp1 = pcj.pmadd(A11, b, ptmp1);\n                ptmp2 = pcj.pmadd(A12, b, ptmp2);\n                ptmp3 = pcj.pmadd(A13, b, ptmp3);\n              }\n            }\n            for (; j<alignedSize; j+=RhsPacketSize)\n              _EIGEN_ACCUMULATE_PACKETS(Aligned,Unaligned,Unaligned);\n            break;\n          }\n          default:\n            for (Index j = alignedStart; j<alignedSize; j+=RhsPacketSize)\n              _EIGEN_ACCUMULATE_PACKETS(Unaligned,Unaligned,Unaligned);\n            break;\n        }\n        tmp0 += predux(ptmp0);\n        tmp1 += predux(ptmp1);\n        tmp2 += predux(ptmp2);\n        tmp3 += predux(ptmp3);\n      }\n    } // end explicit vectorization\n\n    // process remaining coeffs (or all if no explicit vectorization)\n    // FIXME this loop get vectorized by the compiler !\n    for (Index j=alignedSize; j<depth; ++j)\n    {\n      RhsScalar b = rhs(j, 0);\n      tmp0 += cj.pmul(lhs0(j),b); tmp1 += cj.pmul(lhs1(j),b);\n      tmp2 += cj.pmul(lhs2(j),b); tmp3 += cj.pmul(lhs3(j),b);\n    }\n    res[i*resIncr]            += alpha*tmp0;\n    res[(i+offset1)*resIncr]  += alpha*tmp1;\n    res[(i+2)*resIncr]        += alpha*tmp2;\n    res[(i+offset3)*resIncr]  += alpha*tmp3;\n  }\n\n  // process remaining first and last rows (at most columnsAtOnce-1)\n  Index end = rows;\n  Index start = rowBound;\n  do\n  {\n    for (Index i=start; i<end; ++i)\n    {\n      EIGEN_ALIGN_MAX ResScalar tmp0 = ResScalar(0);\n      ResPacket ptmp0 = pset1<ResPacket>(tmp0);\n      const LhsScalars lhs0 = lhs.getVectorMapper(i, 0);\n      // process first unaligned result's coeffs\n      // FIXME this loop get vectorized by the compiler !\n      for (Index j=0; j<alignedStart; ++j)\n        tmp0 += cj.pmul(lhs0(j), rhs(j, 0));\n\n      if (alignedSize>alignedStart)\n      {\n        // process aligned rhs coeffs\n        if (lhs0.template aligned<LhsPacket>(alignedStart))\n          for (Index j = alignedStart;j<alignedSize;j+=RhsPacketSize)\n            ptmp0 = pcj.pmadd(lhs0.template load<LhsPacket, Aligned>(j), rhs.getVectorMapper(j, 0).template load<RhsPacket, Aligned>(0), ptmp0);\n        else\n          for (Index j = alignedStart;j<alignedSize;j+=RhsPacketSize)\n            ptmp0 = pcj.pmadd(lhs0.template load<LhsPacket, Unaligned>(j), rhs.getVectorMapper(j, 0).template load<RhsPacket, Aligned>(0), ptmp0);\n        tmp0 += predux(ptmp0);\n      }\n\n      // process remaining scalars\n      // FIXME this loop get vectorized by the compiler !\n      for (Index j=alignedSize; j<depth; ++j)\n        tmp0 += cj.pmul(lhs0(j), rhs(j, 0));\n      res[i*resIncr] += alpha*tmp0;\n    }\n    if (skipRows)\n    {\n      start = 0;\n      end = skipRows;\n      skipRows = 0;\n    }\n    else\n      break;\n  } while(Vectorizable);\n\n  #undef _EIGEN_ACCUMULATE_PACKETS\n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_GENERAL_MATRIX_VECTOR_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/products/GeneralMatrixVector_BLAS.h",
    "content": "/*\n Copyright (c) 2011, Intel Corporation. All rights reserved.\n\n Redistribution and use in source and binary forms, with or without modification,\n are permitted provided that the following conditions are met:\n\n * Redistributions of source code must retain the above copyright notice, this\n   list of conditions and the following disclaimer.\n * Redistributions in binary form must reproduce the above copyright notice,\n   this list of conditions and the following disclaimer in the documentation\n   and/or other materials provided with the distribution.\n * Neither the name of Intel Corporation nor the names of its contributors may\n   be used to endorse or promote products derived from this software without\n   specific prior written permission.\n\n THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\" AND\n ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED\n WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\n DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR\n ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES\n (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;\n LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON\n ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT\n (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS\n SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n\n ********************************************************************************\n *   Content : Eigen bindings to BLAS F77\n *   General matrix-vector product functionality based on ?GEMV.\n ********************************************************************************\n*/\n\n#ifndef EIGEN_GENERAL_MATRIX_VECTOR_BLAS_H\n#define EIGEN_GENERAL_MATRIX_VECTOR_BLAS_H\n\nnamespace Eigen { \n\nnamespace internal {\n\n/**********************************************************************\n* This file implements general matrix-vector multiplication using BLAS\n* gemv function via partial specialization of\n* general_matrix_vector_product::run(..) method for float, double,\n* std::complex<float> and std::complex<double> types\n**********************************************************************/\n\n// gemv specialization\n\ntemplate<typename Index, typename LhsScalar, int StorageOrder, bool ConjugateLhs, typename RhsScalar, bool ConjugateRhs>\nstruct general_matrix_vector_product_gemv;\n\n#define EIGEN_BLAS_GEMV_SPECIALIZE(Scalar) \\\ntemplate<typename Index, bool ConjugateLhs, bool ConjugateRhs> \\\nstruct general_matrix_vector_product<Index,Scalar,const_blas_data_mapper<Scalar,Index,ColMajor>,ColMajor,ConjugateLhs,Scalar,const_blas_data_mapper<Scalar,Index,RowMajor>,ConjugateRhs,Specialized> { \\\nstatic void run( \\\n  Index rows, Index cols, \\\n  const const_blas_data_mapper<Scalar,Index,ColMajor> &lhs, \\\n  const const_blas_data_mapper<Scalar,Index,RowMajor> &rhs, \\\n  Scalar* res, Index resIncr, Scalar alpha) \\\n{ \\\n  if (ConjugateLhs) { \\\n    general_matrix_vector_product<Index,Scalar,const_blas_data_mapper<Scalar,Index,ColMajor>,ColMajor,ConjugateLhs,Scalar,const_blas_data_mapper<Scalar,Index,RowMajor>,ConjugateRhs,BuiltIn>::run( \\\n      rows, cols, lhs, rhs, res, resIncr, alpha); \\\n  } else { \\\n    general_matrix_vector_product_gemv<Index,Scalar,ColMajor,ConjugateLhs,Scalar,ConjugateRhs>::run( \\\n      rows, cols, lhs.data(), lhs.stride(), rhs.data(), rhs.stride(), res, resIncr, alpha); \\\n  } \\\n} \\\n}; \\\ntemplate<typename Index, bool ConjugateLhs, bool ConjugateRhs> \\\nstruct general_matrix_vector_product<Index,Scalar,const_blas_data_mapper<Scalar,Index,RowMajor>,RowMajor,ConjugateLhs,Scalar,const_blas_data_mapper<Scalar,Index,ColMajor>,ConjugateRhs,Specialized> { \\\nstatic void run( \\\n  Index rows, Index cols, \\\n  const const_blas_data_mapper<Scalar,Index,RowMajor> &lhs, \\\n  const const_blas_data_mapper<Scalar,Index,ColMajor> &rhs, \\\n  Scalar* res, Index resIncr, Scalar alpha) \\\n{ \\\n    general_matrix_vector_product_gemv<Index,Scalar,RowMajor,ConjugateLhs,Scalar,ConjugateRhs>::run( \\\n      rows, cols, lhs.data(), lhs.stride(), rhs.data(), rhs.stride(), res, resIncr, alpha); \\\n} \\\n}; \\\n\nEIGEN_BLAS_GEMV_SPECIALIZE(double)\nEIGEN_BLAS_GEMV_SPECIALIZE(float)\nEIGEN_BLAS_GEMV_SPECIALIZE(dcomplex)\nEIGEN_BLAS_GEMV_SPECIALIZE(scomplex)\n\n#define EIGEN_BLAS_GEMV_SPECIALIZATION(EIGTYPE,BLASTYPE,BLASFUNC) \\\ntemplate<typename Index, int LhsStorageOrder, bool ConjugateLhs, bool ConjugateRhs> \\\nstruct general_matrix_vector_product_gemv<Index,EIGTYPE,LhsStorageOrder,ConjugateLhs,EIGTYPE,ConjugateRhs> \\\n{ \\\ntypedef Matrix<EIGTYPE,Dynamic,1,ColMajor> GEMVVector;\\\n\\\nstatic void run( \\\n  Index rows, Index cols, \\\n  const EIGTYPE* lhs, Index lhsStride, \\\n  const EIGTYPE* rhs, Index rhsIncr, \\\n  EIGTYPE* res, Index resIncr, EIGTYPE alpha) \\\n{ \\\n  BlasIndex m=convert_index<BlasIndex>(rows), n=convert_index<BlasIndex>(cols), \\\n            lda=convert_index<BlasIndex>(lhsStride), incx=convert_index<BlasIndex>(rhsIncr), incy=convert_index<BlasIndex>(resIncr); \\\n  const EIGTYPE beta(1); \\\n  const EIGTYPE *x_ptr; \\\n  char trans=(LhsStorageOrder==ColMajor) ? 'N' : (ConjugateLhs) ? 'C' : 'T'; \\\n  if (LhsStorageOrder==RowMajor) { \\\n    m = convert_index<BlasIndex>(cols); \\\n    n = convert_index<BlasIndex>(rows); \\\n  }\\\n  GEMVVector x_tmp; \\\n  if (ConjugateRhs) { \\\n    Map<const GEMVVector, 0, InnerStride<> > map_x(rhs,cols,1,InnerStride<>(incx)); \\\n    x_tmp=map_x.conjugate(); \\\n    x_ptr=x_tmp.data(); \\\n    incx=1; \\\n  } else x_ptr=rhs; \\\n  BLASFUNC(&trans, &m, &n, (const BLASTYPE*)&numext::real_ref(alpha), (const BLASTYPE*)lhs, &lda, (const BLASTYPE*)x_ptr, &incx, (const BLASTYPE*)&numext::real_ref(beta), (BLASTYPE*)res, &incy); \\\n}\\\n};\n\n#ifdef EIGEN_USE_MKL\nEIGEN_BLAS_GEMV_SPECIALIZATION(double,   double, dgemv)\nEIGEN_BLAS_GEMV_SPECIALIZATION(float,    float,  sgemv)\nEIGEN_BLAS_GEMV_SPECIALIZATION(dcomplex, MKL_Complex16, zgemv)\nEIGEN_BLAS_GEMV_SPECIALIZATION(scomplex, MKL_Complex8 , cgemv)\n#else\nEIGEN_BLAS_GEMV_SPECIALIZATION(double,   double, dgemv_)\nEIGEN_BLAS_GEMV_SPECIALIZATION(float,    float,  sgemv_)\nEIGEN_BLAS_GEMV_SPECIALIZATION(dcomplex, double, zgemv_)\nEIGEN_BLAS_GEMV_SPECIALIZATION(scomplex, float,  cgemv_)\n#endif\n\n} // end namespase internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_GENERAL_MATRIX_VECTOR_BLAS_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/products/Parallelizer.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_PARALLELIZER_H\n#define EIGEN_PARALLELIZER_H\n\nnamespace Eigen {\n\nnamespace internal {\n\n/** \\internal */\ninline void manage_multi_threading(Action action, int* v)\n{\n  static EIGEN_UNUSED int m_maxThreads = -1;\n\n  if(action==SetAction)\n  {\n    eigen_internal_assert(v!=0);\n    m_maxThreads = *v;\n  }\n  else if(action==GetAction)\n  {\n    eigen_internal_assert(v!=0);\n    #ifdef EIGEN_HAS_OPENMP\n    if(m_maxThreads>0)\n      *v = m_maxThreads;\n    else\n      *v = omp_get_max_threads();\n    #else\n    *v = 1;\n    #endif\n  }\n  else\n  {\n    eigen_internal_assert(false);\n  }\n}\n\n}\n\n/** Must be call first when calling Eigen from multiple threads */\ninline void initParallel()\n{\n  int nbt;\n  internal::manage_multi_threading(GetAction, &nbt);\n  std::ptrdiff_t l1, l2, l3;\n  internal::manage_caching_sizes(GetAction, &l1, &l2, &l3);\n}\n\n/** \\returns the max number of threads reserved for Eigen\n  * \\sa setNbThreads */\ninline int nbThreads()\n{\n  int ret;\n  internal::manage_multi_threading(GetAction, &ret);\n  return ret;\n}\n\n/** Sets the max number of threads reserved for Eigen\n  * \\sa nbThreads */\ninline void setNbThreads(int v)\n{\n  internal::manage_multi_threading(SetAction, &v);\n}\n\nnamespace internal {\n\ntemplate<typename Index> struct GemmParallelInfo\n{\n  GemmParallelInfo() : sync(-1), users(0), lhs_start(0), lhs_length(0) {}\n\n  Index volatile sync;\n  int volatile users;\n\n  Index lhs_start;\n  Index lhs_length;\n};\n\ntemplate<bool Condition, typename Functor, typename Index>\nvoid parallelize_gemm(const Functor& func, Index rows, Index cols, Index depth, bool transpose)\n{\n  // TODO when EIGEN_USE_BLAS is defined,\n  // we should still enable OMP for other scalar types\n#if !(defined (EIGEN_HAS_OPENMP)) || defined (EIGEN_USE_BLAS)\n  // FIXME the transpose variable is only needed to properly split\n  // the matrix product when multithreading is enabled. This is a temporary\n  // fix to support row-major destination matrices. This whole\n  // parallelizer mechanism has to be redisigned anyway.\n  EIGEN_UNUSED_VARIABLE(depth);\n  EIGEN_UNUSED_VARIABLE(transpose);\n  func(0,rows, 0,cols);\n#else\n\n  // Dynamically check whether we should enable or disable OpenMP.\n  // The conditions are:\n  // - the max number of threads we can create is greater than 1\n  // - we are not already in a parallel code\n  // - the sizes are large enough\n\n  // compute the maximal number of threads from the size of the product:\n  // This first heuristic takes into account that the product kernel is fully optimized when working with nr columns at once.\n  Index size = transpose ? rows : cols;\n  Index pb_max_threads = std::max<Index>(1,size / Functor::Traits::nr);\n\n  // compute the maximal number of threads from the total amount of work:\n  double work = static_cast<double>(rows) * static_cast<double>(cols) *\n      static_cast<double>(depth);\n  double kMinTaskSize = 50000;  // FIXME improve this heuristic.\n  pb_max_threads = std::max<Index>(1, std::min<Index>(pb_max_threads, work / kMinTaskSize));\n\n  // compute the number of threads we are going to use\n  Index threads = std::min<Index>(nbThreads(), pb_max_threads);\n\n  // if multi-threading is explicitely disabled, not useful, or if we already are in a parallel session,\n  // then abort multi-threading\n  // FIXME omp_get_num_threads()>1 only works for openmp, what if the user does not use openmp?\n  if((!Condition) || (threads==1) || (omp_get_num_threads()>1))\n    return func(0,rows, 0,cols);\n\n  Eigen::initParallel();\n  func.initParallelSession(threads);\n\n  if(transpose)\n    std::swap(rows,cols);\n\n  ei_declare_aligned_stack_constructed_variable(GemmParallelInfo<Index>,info,threads,0);\n\n  #pragma omp parallel num_threads(threads)\n  {\n    Index i = omp_get_thread_num();\n    // Note that the actual number of threads might be lower than the number of request ones.\n    Index actual_threads = omp_get_num_threads();\n\n    Index blockCols = (cols / actual_threads) & ~Index(0x3);\n    Index blockRows = (rows / actual_threads);\n    blockRows = (blockRows/Functor::Traits::mr)*Functor::Traits::mr;\n\n    Index r0 = i*blockRows;\n    Index actualBlockRows = (i+1==actual_threads) ? rows-r0 : blockRows;\n\n    Index c0 = i*blockCols;\n    Index actualBlockCols = (i+1==actual_threads) ? cols-c0 : blockCols;\n\n    info[i].lhs_start = r0;\n    info[i].lhs_length = actualBlockRows;\n\n    if(transpose) func(c0, actualBlockCols, 0, rows, info);\n    else          func(0, rows, c0, actualBlockCols, info);\n  }\n#endif\n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_PARALLELIZER_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/products/SelfadjointMatrixMatrix.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SELFADJOINT_MATRIX_MATRIX_H\n#define EIGEN_SELFADJOINT_MATRIX_MATRIX_H\n\nnamespace Eigen { \n\nnamespace internal {\n\n// pack a selfadjoint block diagonal for use with the gebp_kernel\ntemplate<typename Scalar, typename Index, int Pack1, int Pack2_dummy, int StorageOrder>\nstruct symm_pack_lhs\n{\n  template<int BlockRows> inline\n  void pack(Scalar* blockA, const const_blas_data_mapper<Scalar,Index,StorageOrder>& lhs, Index cols, Index i, Index& count)\n  {\n    // normal copy\n    for(Index k=0; k<i; k++)\n      for(Index w=0; w<BlockRows; w++)\n        blockA[count++] = lhs(i+w,k);           // normal\n    // symmetric copy\n    Index h = 0;\n    for(Index k=i; k<i+BlockRows; k++)\n    {\n      for(Index w=0; w<h; w++)\n        blockA[count++] = numext::conj(lhs(k, i+w)); // transposed\n\n      blockA[count++] = numext::real(lhs(k,k));   // real (diagonal)\n\n      for(Index w=h+1; w<BlockRows; w++)\n        blockA[count++] = lhs(i+w, k);          // normal\n      ++h;\n    }\n    // transposed copy\n    for(Index k=i+BlockRows; k<cols; k++)\n      for(Index w=0; w<BlockRows; w++)\n        blockA[count++] = numext::conj(lhs(k, i+w)); // transposed\n  }\n  void operator()(Scalar* blockA, const Scalar* _lhs, Index lhsStride, Index cols, Index rows)\n  {\n    enum { PacketSize = packet_traits<Scalar>::size };\n    const_blas_data_mapper<Scalar,Index,StorageOrder> lhs(_lhs,lhsStride);\n    Index count = 0;\n    //Index peeled_mc3 = (rows/Pack1)*Pack1;\n    \n    const Index peeled_mc3 = Pack1>=3*PacketSize ? (rows/(3*PacketSize))*(3*PacketSize) : 0;\n    const Index peeled_mc2 = Pack1>=2*PacketSize ? peeled_mc3+((rows-peeled_mc3)/(2*PacketSize))*(2*PacketSize) : 0;\n    const Index peeled_mc1 = Pack1>=1*PacketSize ? (rows/(1*PacketSize))*(1*PacketSize) : 0;\n    \n    if(Pack1>=3*PacketSize)\n      for(Index i=0; i<peeled_mc3; i+=3*PacketSize)\n        pack<3*PacketSize>(blockA, lhs, cols, i, count);\n    \n    if(Pack1>=2*PacketSize)\n      for(Index i=peeled_mc3; i<peeled_mc2; i+=2*PacketSize)\n        pack<2*PacketSize>(blockA, lhs, cols, i, count);\n    \n    if(Pack1>=1*PacketSize)\n      for(Index i=peeled_mc2; i<peeled_mc1; i+=1*PacketSize)\n        pack<1*PacketSize>(blockA, lhs, cols, i, count);\n\n    // do the same with mr==1\n    for(Index i=peeled_mc1; i<rows; i++)\n    {\n      for(Index k=0; k<i; k++)\n        blockA[count++] = lhs(i, k);                   // normal\n\n      blockA[count++] = numext::real(lhs(i, i));       // real (diagonal)\n\n      for(Index k=i+1; k<cols; k++)\n        blockA[count++] = numext::conj(lhs(k, i));     // transposed\n    }\n  }\n};\n\ntemplate<typename Scalar, typename Index, int nr, int StorageOrder>\nstruct symm_pack_rhs\n{\n  enum { PacketSize = packet_traits<Scalar>::size };\n  void operator()(Scalar* blockB, const Scalar* _rhs, Index rhsStride, Index rows, Index cols, Index k2)\n  {\n    Index end_k = k2 + rows;\n    Index count = 0;\n    const_blas_data_mapper<Scalar,Index,StorageOrder> rhs(_rhs,rhsStride);\n    Index packet_cols8 = nr>=8 ? (cols/8) * 8 : 0;\n    Index packet_cols4 = nr>=4 ? (cols/4) * 4 : 0;\n\n    // first part: normal case\n    for(Index j2=0; j2<k2; j2+=nr)\n    {\n      for(Index k=k2; k<end_k; k++)\n      {\n        blockB[count+0] = rhs(k,j2+0);\n        blockB[count+1] = rhs(k,j2+1);\n        if (nr>=4)\n        {\n          blockB[count+2] = rhs(k,j2+2);\n          blockB[count+3] = rhs(k,j2+3);\n        }\n        if (nr>=8)\n        {\n          blockB[count+4] = rhs(k,j2+4);\n          blockB[count+5] = rhs(k,j2+5);\n          blockB[count+6] = rhs(k,j2+6);\n          blockB[count+7] = rhs(k,j2+7);\n        }\n        count += nr;\n      }\n    }\n\n    // second part: diagonal block\n    Index end8 = nr>=8 ? (std::min)(k2+rows,packet_cols8) : k2;\n    if(nr>=8)\n    {\n      for(Index j2=k2; j2<end8; j2+=8)\n      {\n        // again we can split vertically in three different parts (transpose, symmetric, normal)\n        // transpose\n        for(Index k=k2; k<j2; k++)\n        {\n          blockB[count+0] = numext::conj(rhs(j2+0,k));\n          blockB[count+1] = numext::conj(rhs(j2+1,k));\n          blockB[count+2] = numext::conj(rhs(j2+2,k));\n          blockB[count+3] = numext::conj(rhs(j2+3,k));\n          blockB[count+4] = numext::conj(rhs(j2+4,k));\n          blockB[count+5] = numext::conj(rhs(j2+5,k));\n          blockB[count+6] = numext::conj(rhs(j2+6,k));\n          blockB[count+7] = numext::conj(rhs(j2+7,k));\n          count += 8;\n        }\n        // symmetric\n        Index h = 0;\n        for(Index k=j2; k<j2+8; k++)\n        {\n          // normal\n          for (Index w=0 ; w<h; ++w)\n            blockB[count+w] = rhs(k,j2+w);\n\n          blockB[count+h] = numext::real(rhs(k,k));\n\n          // transpose\n          for (Index w=h+1 ; w<8; ++w)\n            blockB[count+w] = numext::conj(rhs(j2+w,k));\n          count += 8;\n          ++h;\n        }\n        // normal\n        for(Index k=j2+8; k<end_k; k++)\n        {\n          blockB[count+0] = rhs(k,j2+0);\n          blockB[count+1] = rhs(k,j2+1);\n          blockB[count+2] = rhs(k,j2+2);\n          blockB[count+3] = rhs(k,j2+3);\n          blockB[count+4] = rhs(k,j2+4);\n          blockB[count+5] = rhs(k,j2+5);\n          blockB[count+6] = rhs(k,j2+6);\n          blockB[count+7] = rhs(k,j2+7);\n          count += 8;\n        }\n      }\n    }\n    if(nr>=4)\n    {\n      for(Index j2=end8; j2<(std::min)(k2+rows,packet_cols4); j2+=4)\n      {\n        // again we can split vertically in three different parts (transpose, symmetric, normal)\n        // transpose\n        for(Index k=k2; k<j2; k++)\n        {\n          blockB[count+0] = numext::conj(rhs(j2+0,k));\n          blockB[count+1] = numext::conj(rhs(j2+1,k));\n          blockB[count+2] = numext::conj(rhs(j2+2,k));\n          blockB[count+3] = numext::conj(rhs(j2+3,k));\n          count += 4;\n        }\n        // symmetric\n        Index h = 0;\n        for(Index k=j2; k<j2+4; k++)\n        {\n          // normal\n          for (Index w=0 ; w<h; ++w)\n            blockB[count+w] = rhs(k,j2+w);\n\n          blockB[count+h] = numext::real(rhs(k,k));\n\n          // transpose\n          for (Index w=h+1 ; w<4; ++w)\n            blockB[count+w] = numext::conj(rhs(j2+w,k));\n          count += 4;\n          ++h;\n        }\n        // normal\n        for(Index k=j2+4; k<end_k; k++)\n        {\n          blockB[count+0] = rhs(k,j2+0);\n          blockB[count+1] = rhs(k,j2+1);\n          blockB[count+2] = rhs(k,j2+2);\n          blockB[count+3] = rhs(k,j2+3);\n          count += 4;\n        }\n      }\n    }\n\n    // third part: transposed\n    if(nr>=8)\n    {\n      for(Index j2=k2+rows; j2<packet_cols8; j2+=8)\n      {\n        for(Index k=k2; k<end_k; k++)\n        {\n          blockB[count+0] = numext::conj(rhs(j2+0,k));\n          blockB[count+1] = numext::conj(rhs(j2+1,k));\n          blockB[count+2] = numext::conj(rhs(j2+2,k));\n          blockB[count+3] = numext::conj(rhs(j2+3,k));\n          blockB[count+4] = numext::conj(rhs(j2+4,k));\n          blockB[count+5] = numext::conj(rhs(j2+5,k));\n          blockB[count+6] = numext::conj(rhs(j2+6,k));\n          blockB[count+7] = numext::conj(rhs(j2+7,k));\n          count += 8;\n        }\n      }\n    }\n    if(nr>=4)\n    {\n      for(Index j2=(std::max)(packet_cols8,k2+rows); j2<packet_cols4; j2+=4)\n      {\n        for(Index k=k2; k<end_k; k++)\n        {\n          blockB[count+0] = numext::conj(rhs(j2+0,k));\n          blockB[count+1] = numext::conj(rhs(j2+1,k));\n          blockB[count+2] = numext::conj(rhs(j2+2,k));\n          blockB[count+3] = numext::conj(rhs(j2+3,k));\n          count += 4;\n        }\n      }\n    }\n\n    // copy the remaining columns one at a time (=> the same with nr==1)\n    for(Index j2=packet_cols4; j2<cols; ++j2)\n    {\n      // transpose\n      Index half = (std::min)(end_k,j2);\n      for(Index k=k2; k<half; k++)\n      {\n        blockB[count] = numext::conj(rhs(j2,k));\n        count += 1;\n      }\n\n      if(half==j2 && half<k2+rows)\n      {\n        blockB[count] = numext::real(rhs(j2,j2));\n        count += 1;\n      }\n      else\n        half--;\n\n      // normal\n      for(Index k=half+1; k<k2+rows; k++)\n      {\n        blockB[count] = rhs(k,j2);\n        count += 1;\n      }\n    }\n  }\n};\n\n/* Optimized selfadjoint matrix * matrix (_SYMM) product built on top of\n * the general matrix matrix product.\n */\ntemplate <typename Scalar, typename Index,\n          int LhsStorageOrder, bool LhsSelfAdjoint, bool ConjugateLhs,\n          int RhsStorageOrder, bool RhsSelfAdjoint, bool ConjugateRhs,\n          int ResStorageOrder>\nstruct product_selfadjoint_matrix;\n\ntemplate <typename Scalar, typename Index,\n          int LhsStorageOrder, bool LhsSelfAdjoint, bool ConjugateLhs,\n          int RhsStorageOrder, bool RhsSelfAdjoint, bool ConjugateRhs>\nstruct product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,LhsSelfAdjoint,ConjugateLhs, RhsStorageOrder,RhsSelfAdjoint,ConjugateRhs,RowMajor>\n{\n\n  static EIGEN_STRONG_INLINE void run(\n    Index rows, Index cols,\n    const Scalar* lhs, Index lhsStride,\n    const Scalar* rhs, Index rhsStride,\n    Scalar* res,       Index resStride,\n    const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking)\n  {\n    product_selfadjoint_matrix<Scalar, Index,\n      EIGEN_LOGICAL_XOR(RhsSelfAdjoint,RhsStorageOrder==RowMajor) ? ColMajor : RowMajor,\n      RhsSelfAdjoint, NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(RhsSelfAdjoint,ConjugateRhs),\n      EIGEN_LOGICAL_XOR(LhsSelfAdjoint,LhsStorageOrder==RowMajor) ? ColMajor : RowMajor,\n      LhsSelfAdjoint, NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(LhsSelfAdjoint,ConjugateLhs),\n      ColMajor>\n      ::run(cols, rows,  rhs, rhsStride,  lhs, lhsStride,  res, resStride,  alpha, blocking);\n  }\n};\n\ntemplate <typename Scalar, typename Index,\n          int LhsStorageOrder, bool ConjugateLhs,\n          int RhsStorageOrder, bool ConjugateRhs>\nstruct product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,true,ConjugateLhs, RhsStorageOrder,false,ConjugateRhs,ColMajor>\n{\n\n  static EIGEN_DONT_INLINE void run(\n    Index rows, Index cols,\n    const Scalar* _lhs, Index lhsStride,\n    const Scalar* _rhs, Index rhsStride,\n    Scalar* res,        Index resStride,\n    const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking);\n};\n\ntemplate <typename Scalar, typename Index,\n          int LhsStorageOrder, bool ConjugateLhs,\n          int RhsStorageOrder, bool ConjugateRhs>\nEIGEN_DONT_INLINE void product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,true,ConjugateLhs, RhsStorageOrder,false,ConjugateRhs,ColMajor>::run(\n    Index rows, Index cols,\n    const Scalar* _lhs, Index lhsStride,\n    const Scalar* _rhs, Index rhsStride,\n    Scalar* _res,        Index resStride,\n    const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking)\n  {\n    Index size = rows;\n\n    typedef gebp_traits<Scalar,Scalar> Traits;\n\n    typedef const_blas_data_mapper<Scalar, Index, LhsStorageOrder> LhsMapper;\n    typedef const_blas_data_mapper<Scalar, Index, (LhsStorageOrder == RowMajor) ? ColMajor : RowMajor> LhsTransposeMapper;\n    typedef const_blas_data_mapper<Scalar, Index, RhsStorageOrder> RhsMapper;\n    typedef blas_data_mapper<typename Traits::ResScalar, Index, ColMajor> ResMapper;\n    LhsMapper lhs(_lhs,lhsStride);\n    LhsTransposeMapper lhs_transpose(_lhs,lhsStride);\n    RhsMapper rhs(_rhs,rhsStride);\n    ResMapper res(_res, resStride);\n\n    Index kc = blocking.kc();                   // cache block size along the K direction\n    Index mc = (std::min)(rows,blocking.mc());  // cache block size along the M direction\n    // kc must be smaller than mc\n    kc = (std::min)(kc,mc);\n    std::size_t sizeA = kc*mc;\n    std::size_t sizeB = kc*cols;\n    ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());\n    ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());\n\n    gebp_kernel<Scalar, Scalar, Index, ResMapper, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;\n    symm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;\n    gemm_pack_rhs<Scalar, Index, RhsMapper, Traits::nr,RhsStorageOrder> pack_rhs;\n    gemm_pack_lhs<Scalar, Index, LhsTransposeMapper, Traits::mr, Traits::LhsProgress, LhsStorageOrder==RowMajor?ColMajor:RowMajor, true> pack_lhs_transposed;\n\n    for(Index k2=0; k2<size; k2+=kc)\n    {\n      const Index actual_kc = (std::min)(k2+kc,size)-k2;\n\n      // we have selected one row panel of rhs and one column panel of lhs\n      // pack rhs's panel into a sequential chunk of memory\n      // and expand each coeff to a constant packet for further reuse\n      pack_rhs(blockB, rhs.getSubMapper(k2,0), actual_kc, cols);\n\n      // the select lhs's panel has to be split in three different parts:\n      //  1 - the transposed panel above the diagonal block => transposed packed copy\n      //  2 - the diagonal block => special packed copy\n      //  3 - the panel below the diagonal block => generic packed copy\n      for(Index i2=0; i2<k2; i2+=mc)\n      {\n        const Index actual_mc = (std::min)(i2+mc,k2)-i2;\n        // transposed packed copy\n        pack_lhs_transposed(blockA, lhs_transpose.getSubMapper(i2, k2), actual_kc, actual_mc);\n\n        gebp_kernel(res.getSubMapper(i2, 0), blockA, blockB, actual_mc, actual_kc, cols, alpha);\n      }\n      // the block diagonal\n      {\n        const Index actual_mc = (std::min)(k2+kc,size)-k2;\n        // symmetric packed copy\n        pack_lhs(blockA, &lhs(k2,k2), lhsStride, actual_kc, actual_mc);\n\n        gebp_kernel(res.getSubMapper(k2, 0), blockA, blockB, actual_mc, actual_kc, cols, alpha);\n      }\n\n      for(Index i2=k2+kc; i2<size; i2+=mc)\n      {\n        const Index actual_mc = (std::min)(i2+mc,size)-i2;\n        gemm_pack_lhs<Scalar, Index, LhsMapper, Traits::mr, Traits::LhsProgress, LhsStorageOrder,false>()\n          (blockA, lhs.getSubMapper(i2, k2), actual_kc, actual_mc);\n\n        gebp_kernel(res.getSubMapper(i2, 0), blockA, blockB, actual_mc, actual_kc, cols, alpha);\n      }\n    }\n  }\n\n// matrix * selfadjoint product\ntemplate <typename Scalar, typename Index,\n          int LhsStorageOrder, bool ConjugateLhs,\n          int RhsStorageOrder, bool ConjugateRhs>\nstruct product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,false,ConjugateLhs, RhsStorageOrder,true,ConjugateRhs,ColMajor>\n{\n\n  static EIGEN_DONT_INLINE void run(\n    Index rows, Index cols,\n    const Scalar* _lhs, Index lhsStride,\n    const Scalar* _rhs, Index rhsStride,\n    Scalar* res,        Index resStride,\n    const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking);\n};\n\ntemplate <typename Scalar, typename Index,\n          int LhsStorageOrder, bool ConjugateLhs,\n          int RhsStorageOrder, bool ConjugateRhs>\nEIGEN_DONT_INLINE void product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,false,ConjugateLhs, RhsStorageOrder,true,ConjugateRhs,ColMajor>::run(\n    Index rows, Index cols,\n    const Scalar* _lhs, Index lhsStride,\n    const Scalar* _rhs, Index rhsStride,\n    Scalar* _res,        Index resStride,\n    const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking)\n  {\n    Index size = cols;\n\n    typedef gebp_traits<Scalar,Scalar> Traits;\n\n    typedef const_blas_data_mapper<Scalar, Index, LhsStorageOrder> LhsMapper;\n    typedef blas_data_mapper<typename Traits::ResScalar, Index, ColMajor> ResMapper;\n    LhsMapper lhs(_lhs,lhsStride);\n    ResMapper res(_res,resStride);\n\n    Index kc = blocking.kc();                   // cache block size along the K direction\n    Index mc = (std::min)(rows,blocking.mc());  // cache block size along the M direction\n    std::size_t sizeA = kc*mc;\n    std::size_t sizeB = kc*cols;\n    ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());\n    ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());\n\n    gebp_kernel<Scalar, Scalar, Index, ResMapper, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;\n    gemm_pack_lhs<Scalar, Index, LhsMapper, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;\n    symm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder> pack_rhs;\n\n    for(Index k2=0; k2<size; k2+=kc)\n    {\n      const Index actual_kc = (std::min)(k2+kc,size)-k2;\n\n      pack_rhs(blockB, _rhs, rhsStride, actual_kc, cols, k2);\n\n      // => GEPP\n      for(Index i2=0; i2<rows; i2+=mc)\n      {\n        const Index actual_mc = (std::min)(i2+mc,rows)-i2;\n        pack_lhs(blockA, lhs.getSubMapper(i2, k2), actual_kc, actual_mc);\n\n        gebp_kernel(res.getSubMapper(i2, 0), blockA, blockB, actual_mc, actual_kc, cols, alpha);\n      }\n    }\n  }\n\n} // end namespace internal\n\n/***************************************************************************\n* Wrapper to product_selfadjoint_matrix\n***************************************************************************/\n\nnamespace internal {\n  \ntemplate<typename Lhs, int LhsMode, typename Rhs, int RhsMode>\nstruct selfadjoint_product_impl<Lhs,LhsMode,false,Rhs,RhsMode,false>\n{\n  typedef typename Product<Lhs,Rhs>::Scalar Scalar;\n  \n  typedef internal::blas_traits<Lhs> LhsBlasTraits;\n  typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;\n  typedef internal::blas_traits<Rhs> RhsBlasTraits;\n  typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;\n  \n  enum {\n    LhsIsUpper = (LhsMode&(Upper|Lower))==Upper,\n    LhsIsSelfAdjoint = (LhsMode&SelfAdjoint)==SelfAdjoint,\n    RhsIsUpper = (RhsMode&(Upper|Lower))==Upper,\n    RhsIsSelfAdjoint = (RhsMode&SelfAdjoint)==SelfAdjoint\n  };\n  \n  template<typename Dest>\n  static void run(Dest &dst, const Lhs &a_lhs, const Rhs &a_rhs, const Scalar& alpha)\n  {\n    eigen_assert(dst.rows()==a_lhs.rows() && dst.cols()==a_rhs.cols());\n\n    typename internal::add_const_on_value_type<ActualLhsType>::type lhs = LhsBlasTraits::extract(a_lhs);\n    typename internal::add_const_on_value_type<ActualRhsType>::type rhs = RhsBlasTraits::extract(a_rhs);\n\n    Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(a_lhs)\n                               * RhsBlasTraits::extractScalarFactor(a_rhs);\n\n    typedef internal::gemm_blocking_space<(Dest::Flags&RowMajorBit) ? RowMajor : ColMajor,Scalar,Scalar,\n              Lhs::MaxRowsAtCompileTime, Rhs::MaxColsAtCompileTime, Lhs::MaxColsAtCompileTime,1> BlockingType;\n\n    BlockingType blocking(lhs.rows(), rhs.cols(), lhs.cols(), 1, false);\n\n    internal::product_selfadjoint_matrix<Scalar, Index,\n      EIGEN_LOGICAL_XOR(LhsIsUpper,internal::traits<Lhs>::Flags &RowMajorBit) ? RowMajor : ColMajor, LhsIsSelfAdjoint,\n      NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(LhsIsUpper,bool(LhsBlasTraits::NeedToConjugate)),\n      EIGEN_LOGICAL_XOR(RhsIsUpper,internal::traits<Rhs>::Flags &RowMajorBit) ? RowMajor : ColMajor, RhsIsSelfAdjoint,\n      NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(RhsIsUpper,bool(RhsBlasTraits::NeedToConjugate)),\n      internal::traits<Dest>::Flags&RowMajorBit  ? RowMajor : ColMajor>\n      ::run(\n        lhs.rows(), rhs.cols(),                 // sizes\n        &lhs.coeffRef(0,0), lhs.outerStride(),  // lhs info\n        &rhs.coeffRef(0,0), rhs.outerStride(),  // rhs info\n        &dst.coeffRef(0,0), dst.outerStride(),  // result info\n        actualAlpha, blocking                   // alpha\n      );\n  }\n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_SELFADJOINT_MATRIX_MATRIX_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/products/SelfadjointMatrixMatrix_BLAS.h",
    "content": "/*\n Copyright (c) 2011, Intel Corporation. All rights reserved.\n\n Redistribution and use in source and binary forms, with or without modification,\n are permitted provided that the following conditions are met:\n\n * Redistributions of source code must retain the above copyright notice, this\n   list of conditions and the following disclaimer.\n * Redistributions in binary form must reproduce the above copyright notice,\n   this list of conditions and the following disclaimer in the documentation\n   and/or other materials provided with the distribution.\n * Neither the name of Intel Corporation nor the names of its contributors may\n   be used to endorse or promote products derived from this software without\n   specific prior written permission.\n\n THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\" AND\n ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED\n WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\n DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR\n ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES\n (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;\n LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON\n ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT\n (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS\n SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n//\n ********************************************************************************\n *   Content : Eigen bindings to BLAS F77\n *   Self adjoint matrix * matrix product functionality based on ?SYMM/?HEMM.\n ********************************************************************************\n*/\n\n#ifndef EIGEN_SELFADJOINT_MATRIX_MATRIX_BLAS_H\n#define EIGEN_SELFADJOINT_MATRIX_MATRIX_BLAS_H\n\nnamespace Eigen { \n\nnamespace internal {\n\n\n/* Optimized selfadjoint matrix * matrix (?SYMM/?HEMM) product */\n\n#define EIGEN_BLAS_SYMM_L(EIGTYPE, BLASTYPE, EIGPREFIX, BLASFUNC) \\\ntemplate <typename Index, \\\n          int LhsStorageOrder, bool ConjugateLhs, \\\n          int RhsStorageOrder, bool ConjugateRhs> \\\nstruct product_selfadjoint_matrix<EIGTYPE,Index,LhsStorageOrder,true,ConjugateLhs,RhsStorageOrder,false,ConjugateRhs,ColMajor> \\\n{\\\n\\\n  static void run( \\\n    Index rows, Index cols, \\\n    const EIGTYPE* _lhs, Index lhsStride, \\\n    const EIGTYPE* _rhs, Index rhsStride, \\\n    EIGTYPE* res,        Index resStride, \\\n    EIGTYPE alpha, level3_blocking<EIGTYPE, EIGTYPE>& /*blocking*/) \\\n  { \\\n    char side='L', uplo='L'; \\\n    BlasIndex m, n, lda, ldb, ldc; \\\n    const EIGTYPE *a, *b; \\\n    EIGTYPE beta(1); \\\n    MatrixX##EIGPREFIX b_tmp; \\\n\\\n/* Set transpose options */ \\\n/* Set m, n, k */ \\\n    m = convert_index<BlasIndex>(rows);  \\\n    n = convert_index<BlasIndex>(cols);  \\\n\\\n/* Set lda, ldb, ldc */ \\\n    lda = convert_index<BlasIndex>(lhsStride); \\\n    ldb = convert_index<BlasIndex>(rhsStride); \\\n    ldc = convert_index<BlasIndex>(resStride); \\\n\\\n/* Set a, b, c */ \\\n    if (LhsStorageOrder==RowMajor) uplo='U'; \\\n    a = _lhs; \\\n\\\n    if (RhsStorageOrder==RowMajor) { \\\n      Map<const MatrixX##EIGPREFIX, 0, OuterStride<> > rhs(_rhs,n,m,OuterStride<>(rhsStride)); \\\n      b_tmp = rhs.adjoint(); \\\n      b = b_tmp.data(); \\\n      ldb = convert_index<BlasIndex>(b_tmp.outerStride()); \\\n    } else b = _rhs; \\\n\\\n    BLASFUNC(&side, &uplo, &m, &n, (const BLASTYPE*)&numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (const BLASTYPE*)b, &ldb, (const BLASTYPE*)&numext::real_ref(beta), (BLASTYPE*)res, &ldc); \\\n\\\n  } \\\n};\n\n\n#define EIGEN_BLAS_HEMM_L(EIGTYPE, BLASTYPE, EIGPREFIX, BLASFUNC) \\\ntemplate <typename Index, \\\n          int LhsStorageOrder, bool ConjugateLhs, \\\n          int RhsStorageOrder, bool ConjugateRhs> \\\nstruct product_selfadjoint_matrix<EIGTYPE,Index,LhsStorageOrder,true,ConjugateLhs,RhsStorageOrder,false,ConjugateRhs,ColMajor> \\\n{\\\n  static void run( \\\n    Index rows, Index cols, \\\n    const EIGTYPE* _lhs, Index lhsStride, \\\n    const EIGTYPE* _rhs, Index rhsStride, \\\n    EIGTYPE* res,        Index resStride, \\\n    EIGTYPE alpha, level3_blocking<EIGTYPE, EIGTYPE>& /*blocking*/) \\\n  { \\\n    char side='L', uplo='L'; \\\n    BlasIndex m, n, lda, ldb, ldc; \\\n    const EIGTYPE *a, *b; \\\n    EIGTYPE beta(1); \\\n    MatrixX##EIGPREFIX b_tmp; \\\n    Matrix<EIGTYPE, Dynamic, Dynamic, LhsStorageOrder> a_tmp; \\\n\\\n/* Set transpose options */ \\\n/* Set m, n, k */ \\\n    m = convert_index<BlasIndex>(rows); \\\n    n = convert_index<BlasIndex>(cols); \\\n\\\n/* Set lda, ldb, ldc */ \\\n    lda = convert_index<BlasIndex>(lhsStride); \\\n    ldb = convert_index<BlasIndex>(rhsStride); \\\n    ldc = convert_index<BlasIndex>(resStride); \\\n\\\n/* Set a, b, c */ \\\n    if (((LhsStorageOrder==ColMajor) && ConjugateLhs) || ((LhsStorageOrder==RowMajor) && (!ConjugateLhs))) { \\\n      Map<const Matrix<EIGTYPE, Dynamic, Dynamic, LhsStorageOrder>, 0, OuterStride<> > lhs(_lhs,m,m,OuterStride<>(lhsStride)); \\\n      a_tmp = lhs.conjugate(); \\\n      a = a_tmp.data(); \\\n      lda = convert_index<BlasIndex>(a_tmp.outerStride()); \\\n    } else a = _lhs; \\\n    if (LhsStorageOrder==RowMajor) uplo='U'; \\\n\\\n    if (RhsStorageOrder==ColMajor && (!ConjugateRhs)) { \\\n       b = _rhs; } \\\n    else { \\\n      if (RhsStorageOrder==ColMajor && ConjugateRhs) { \\\n        Map<const MatrixX##EIGPREFIX, 0, OuterStride<> > rhs(_rhs,m,n,OuterStride<>(rhsStride)); \\\n        b_tmp = rhs.conjugate(); \\\n      } else \\\n      if (ConjugateRhs) { \\\n        Map<const MatrixX##EIGPREFIX, 0, OuterStride<> > rhs(_rhs,n,m,OuterStride<>(rhsStride)); \\\n        b_tmp = rhs.adjoint(); \\\n      } else { \\\n        Map<const MatrixX##EIGPREFIX, 0, OuterStride<> > rhs(_rhs,n,m,OuterStride<>(rhsStride)); \\\n        b_tmp = rhs.transpose(); \\\n      } \\\n      b = b_tmp.data(); \\\n      ldb = convert_index<BlasIndex>(b_tmp.outerStride()); \\\n    } \\\n\\\n    BLASFUNC(&side, &uplo, &m, &n, (const BLASTYPE*)&numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (const BLASTYPE*)b, &ldb, (const BLASTYPE*)&numext::real_ref(beta), (BLASTYPE*)res, &ldc); \\\n\\\n  } \\\n};\n\n#ifdef EIGEN_USE_MKL\nEIGEN_BLAS_SYMM_L(double, double, d, dsymm)\nEIGEN_BLAS_SYMM_L(float, float, f, ssymm)\nEIGEN_BLAS_HEMM_L(dcomplex, MKL_Complex16, cd, zhemm)\nEIGEN_BLAS_HEMM_L(scomplex, MKL_Complex8, cf, chemm)\n#else\nEIGEN_BLAS_SYMM_L(double, double, d, dsymm_)\nEIGEN_BLAS_SYMM_L(float, float, f, ssymm_)\nEIGEN_BLAS_HEMM_L(dcomplex, double, cd, zhemm_)\nEIGEN_BLAS_HEMM_L(scomplex, float, cf, chemm_)\n#endif\n\n/* Optimized matrix * selfadjoint matrix (?SYMM/?HEMM) product */\n\n#define EIGEN_BLAS_SYMM_R(EIGTYPE, BLASTYPE, EIGPREFIX, BLASFUNC) \\\ntemplate <typename Index, \\\n          int LhsStorageOrder, bool ConjugateLhs, \\\n          int RhsStorageOrder, bool ConjugateRhs> \\\nstruct product_selfadjoint_matrix<EIGTYPE,Index,LhsStorageOrder,false,ConjugateLhs,RhsStorageOrder,true,ConjugateRhs,ColMajor> \\\n{\\\n\\\n  static void run( \\\n    Index rows, Index cols, \\\n    const EIGTYPE* _lhs, Index lhsStride, \\\n    const EIGTYPE* _rhs, Index rhsStride, \\\n    EIGTYPE* res,        Index resStride, \\\n    EIGTYPE alpha, level3_blocking<EIGTYPE, EIGTYPE>& /*blocking*/) \\\n  { \\\n    char side='R', uplo='L'; \\\n    BlasIndex m, n, lda, ldb, ldc; \\\n    const EIGTYPE *a, *b; \\\n    EIGTYPE beta(1); \\\n    MatrixX##EIGPREFIX b_tmp; \\\n\\\n/* Set m, n, k */ \\\n    m = convert_index<BlasIndex>(rows);  \\\n    n = convert_index<BlasIndex>(cols);  \\\n\\\n/* Set lda, ldb, ldc */ \\\n    lda = convert_index<BlasIndex>(rhsStride); \\\n    ldb = convert_index<BlasIndex>(lhsStride); \\\n    ldc = convert_index<BlasIndex>(resStride); \\\n\\\n/* Set a, b, c */ \\\n    if (RhsStorageOrder==RowMajor) uplo='U'; \\\n    a = _rhs; \\\n\\\n    if (LhsStorageOrder==RowMajor) { \\\n      Map<const MatrixX##EIGPREFIX, 0, OuterStride<> > lhs(_lhs,n,m,OuterStride<>(rhsStride)); \\\n      b_tmp = lhs.adjoint(); \\\n      b = b_tmp.data(); \\\n      ldb = convert_index<BlasIndex>(b_tmp.outerStride()); \\\n    } else b = _lhs; \\\n\\\n    BLASFUNC(&side, &uplo, &m, &n, (const BLASTYPE*)&numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (const BLASTYPE*)b, &ldb, (const BLASTYPE*)&numext::real_ref(beta), (BLASTYPE*)res, &ldc); \\\n\\\n  } \\\n};\n\n\n#define EIGEN_BLAS_HEMM_R(EIGTYPE, BLASTYPE, EIGPREFIX, BLASFUNC) \\\ntemplate <typename Index, \\\n          int LhsStorageOrder, bool ConjugateLhs, \\\n          int RhsStorageOrder, bool ConjugateRhs> \\\nstruct product_selfadjoint_matrix<EIGTYPE,Index,LhsStorageOrder,false,ConjugateLhs,RhsStorageOrder,true,ConjugateRhs,ColMajor> \\\n{\\\n  static void run( \\\n    Index rows, Index cols, \\\n    const EIGTYPE* _lhs, Index lhsStride, \\\n    const EIGTYPE* _rhs, Index rhsStride, \\\n    EIGTYPE* res,        Index resStride, \\\n    EIGTYPE alpha, level3_blocking<EIGTYPE, EIGTYPE>& /*blocking*/) \\\n  { \\\n    char side='R', uplo='L'; \\\n    BlasIndex m, n, lda, ldb, ldc; \\\n    const EIGTYPE *a, *b; \\\n    EIGTYPE beta(1); \\\n    MatrixX##EIGPREFIX b_tmp; \\\n    Matrix<EIGTYPE, Dynamic, Dynamic, RhsStorageOrder> a_tmp; \\\n\\\n/* Set m, n, k */ \\\n    m = convert_index<BlasIndex>(rows); \\\n    n = convert_index<BlasIndex>(cols); \\\n\\\n/* Set lda, ldb, ldc */ \\\n    lda = convert_index<BlasIndex>(rhsStride); \\\n    ldb = convert_index<BlasIndex>(lhsStride); \\\n    ldc = convert_index<BlasIndex>(resStride); \\\n\\\n/* Set a, b, c */ \\\n    if (((RhsStorageOrder==ColMajor) && ConjugateRhs) || ((RhsStorageOrder==RowMajor) && (!ConjugateRhs))) { \\\n      Map<const Matrix<EIGTYPE, Dynamic, Dynamic, RhsStorageOrder>, 0, OuterStride<> > rhs(_rhs,n,n,OuterStride<>(rhsStride)); \\\n      a_tmp = rhs.conjugate(); \\\n      a = a_tmp.data(); \\\n      lda = convert_index<BlasIndex>(a_tmp.outerStride()); \\\n    } else a = _rhs; \\\n    if (RhsStorageOrder==RowMajor) uplo='U'; \\\n\\\n    if (LhsStorageOrder==ColMajor && (!ConjugateLhs)) { \\\n       b = _lhs; } \\\n    else { \\\n      if (LhsStorageOrder==ColMajor && ConjugateLhs) { \\\n        Map<const MatrixX##EIGPREFIX, 0, OuterStride<> > lhs(_lhs,m,n,OuterStride<>(lhsStride)); \\\n        b_tmp = lhs.conjugate(); \\\n      } else \\\n      if (ConjugateLhs) { \\\n        Map<const MatrixX##EIGPREFIX, 0, OuterStride<> > lhs(_lhs,n,m,OuterStride<>(lhsStride)); \\\n        b_tmp = lhs.adjoint(); \\\n      } else { \\\n        Map<const MatrixX##EIGPREFIX, 0, OuterStride<> > lhs(_lhs,n,m,OuterStride<>(lhsStride)); \\\n        b_tmp = lhs.transpose(); \\\n      } \\\n      b = b_tmp.data(); \\\n      ldb = convert_index<BlasIndex>(b_tmp.outerStride()); \\\n    } \\\n\\\n    BLASFUNC(&side, &uplo, &m, &n, (const BLASTYPE*)&numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (const BLASTYPE*)b, &ldb, (const BLASTYPE*)&numext::real_ref(beta), (BLASTYPE*)res, &ldc); \\\n  } \\\n};\n\n#ifdef EIGEN_USE_MKL\nEIGEN_BLAS_SYMM_R(double, double, d, dsymm)\nEIGEN_BLAS_SYMM_R(float, float, f, ssymm)\nEIGEN_BLAS_HEMM_R(dcomplex, MKL_Complex16, cd, zhemm)\nEIGEN_BLAS_HEMM_R(scomplex, MKL_Complex8, cf, chemm)\n#else\nEIGEN_BLAS_SYMM_R(double, double, d, dsymm_)\nEIGEN_BLAS_SYMM_R(float, float, f, ssymm_)\nEIGEN_BLAS_HEMM_R(dcomplex, double, cd, zhemm_)\nEIGEN_BLAS_HEMM_R(scomplex, float, cf, chemm_)\n#endif\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_SELFADJOINT_MATRIX_MATRIX_BLAS_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/products/SelfadjointMatrixVector.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SELFADJOINT_MATRIX_VECTOR_H\n#define EIGEN_SELFADJOINT_MATRIX_VECTOR_H\n\nnamespace Eigen { \n\nnamespace internal {\n\n/* Optimized selfadjoint matrix * vector product:\n * This algorithm processes 2 columns at onces that allows to both reduce\n * the number of load/stores of the result by a factor 2 and to reduce\n * the instruction dependency.\n */\n\ntemplate<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjugateLhs, bool ConjugateRhs, int Version=Specialized>\nstruct selfadjoint_matrix_vector_product;\n\ntemplate<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjugateLhs, bool ConjugateRhs, int Version>\nstruct selfadjoint_matrix_vector_product\n\n{\nstatic EIGEN_DONT_INLINE void run(\n  Index size,\n  const Scalar*  lhs, Index lhsStride,\n  const Scalar*  rhs,\n  Scalar* res,\n  Scalar alpha);\n};\n\ntemplate<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjugateLhs, bool ConjugateRhs, int Version>\nEIGEN_DONT_INLINE void selfadjoint_matrix_vector_product<Scalar,Index,StorageOrder,UpLo,ConjugateLhs,ConjugateRhs,Version>::run(\n  Index size,\n  const Scalar*  lhs, Index lhsStride,\n  const Scalar*  rhs,\n  Scalar* res,\n  Scalar alpha)\n{\n  typedef typename packet_traits<Scalar>::type Packet;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  const Index PacketSize = sizeof(Packet)/sizeof(Scalar);\n\n  enum {\n    IsRowMajor = StorageOrder==RowMajor ? 1 : 0,\n    IsLower = UpLo == Lower ? 1 : 0,\n    FirstTriangular = IsRowMajor == IsLower\n  };\n\n  conj_helper<Scalar,Scalar,NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(ConjugateLhs,  IsRowMajor), ConjugateRhs> cj0;\n  conj_helper<Scalar,Scalar,NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(ConjugateLhs, !IsRowMajor), ConjugateRhs> cj1;\n  conj_helper<RealScalar,Scalar,false, ConjugateRhs> cjd;\n\n  conj_helper<Packet,Packet,NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(ConjugateLhs,  IsRowMajor), ConjugateRhs> pcj0;\n  conj_helper<Packet,Packet,NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(ConjugateLhs, !IsRowMajor), ConjugateRhs> pcj1;\n\n  Scalar cjAlpha = ConjugateRhs ? numext::conj(alpha) : alpha;\n\n\n  Index bound = (std::max)(Index(0),size-8) & 0xfffffffe;\n  if (FirstTriangular)\n    bound = size - bound;\n\n  for (Index j=FirstTriangular ? bound : 0;\n       j<(FirstTriangular ? size : bound);j+=2)\n  {\n    const Scalar* EIGEN_RESTRICT A0 = lhs + j*lhsStride;\n    const Scalar* EIGEN_RESTRICT A1 = lhs + (j+1)*lhsStride;\n\n    Scalar t0 = cjAlpha * rhs[j];\n    Packet ptmp0 = pset1<Packet>(t0);\n    Scalar t1 = cjAlpha * rhs[j+1];\n    Packet ptmp1 = pset1<Packet>(t1);\n\n    Scalar t2(0);\n    Packet ptmp2 = pset1<Packet>(t2);\n    Scalar t3(0);\n    Packet ptmp3 = pset1<Packet>(t3);\n\n    Index starti = FirstTriangular ? 0 : j+2;\n    Index endi   = FirstTriangular ? j : size;\n    Index alignedStart = (starti) + internal::first_default_aligned(&res[starti], endi-starti);\n    Index alignedEnd = alignedStart + ((endi-alignedStart)/(PacketSize))*(PacketSize);\n\n    res[j]   += cjd.pmul(numext::real(A0[j]), t0);\n    res[j+1] += cjd.pmul(numext::real(A1[j+1]), t1);\n    if(FirstTriangular)\n    {\n      res[j]   += cj0.pmul(A1[j],   t1);\n      t3       += cj1.pmul(A1[j],   rhs[j]);\n    }\n    else\n    {\n      res[j+1] += cj0.pmul(A0[j+1],t0);\n      t2 += cj1.pmul(A0[j+1], rhs[j+1]);\n    }\n\n    for (Index i=starti; i<alignedStart; ++i)\n    {\n      res[i] += cj0.pmul(A0[i], t0) + cj0.pmul(A1[i],t1);\n      t2 += cj1.pmul(A0[i], rhs[i]);\n      t3 += cj1.pmul(A1[i], rhs[i]);\n    }\n    // Yes this an optimization for gcc 4.3 and 4.4 (=> huge speed up)\n    // gcc 4.2 does this optimization automatically.\n    const Scalar* EIGEN_RESTRICT a0It  = A0  + alignedStart;\n    const Scalar* EIGEN_RESTRICT a1It  = A1  + alignedStart;\n    const Scalar* EIGEN_RESTRICT rhsIt = rhs + alignedStart;\n          Scalar* EIGEN_RESTRICT resIt = res + alignedStart;\n    for (Index i=alignedStart; i<alignedEnd; i+=PacketSize)\n    {\n      Packet A0i = ploadu<Packet>(a0It);  a0It  += PacketSize;\n      Packet A1i = ploadu<Packet>(a1It);  a1It  += PacketSize;\n      Packet Bi  = ploadu<Packet>(rhsIt); rhsIt += PacketSize; // FIXME should be aligned in most cases\n      Packet Xi  = pload <Packet>(resIt);\n\n      Xi    = pcj0.pmadd(A0i,ptmp0, pcj0.pmadd(A1i,ptmp1,Xi));\n      ptmp2 = pcj1.pmadd(A0i,  Bi, ptmp2);\n      ptmp3 = pcj1.pmadd(A1i,  Bi, ptmp3);\n      pstore(resIt,Xi); resIt += PacketSize;\n    }\n    for (Index i=alignedEnd; i<endi; i++)\n    {\n      res[i] += cj0.pmul(A0[i], t0) + cj0.pmul(A1[i],t1);\n      t2 += cj1.pmul(A0[i], rhs[i]);\n      t3 += cj1.pmul(A1[i], rhs[i]);\n    }\n\n    res[j]   += alpha * (t2 + predux(ptmp2));\n    res[j+1] += alpha * (t3 + predux(ptmp3));\n  }\n  for (Index j=FirstTriangular ? 0 : bound;j<(FirstTriangular ? bound : size);j++)\n  {\n    const Scalar* EIGEN_RESTRICT A0 = lhs + j*lhsStride;\n\n    Scalar t1 = cjAlpha * rhs[j];\n    Scalar t2(0);\n    res[j] += cjd.pmul(numext::real(A0[j]), t1);\n    for (Index i=FirstTriangular ? 0 : j+1; i<(FirstTriangular ? j : size); i++)\n    {\n      res[i] += cj0.pmul(A0[i], t1);\n      t2 += cj1.pmul(A0[i], rhs[i]);\n    }\n    res[j] += alpha * t2;\n  }\n}\n\n} // end namespace internal \n\n/***************************************************************************\n* Wrapper to product_selfadjoint_vector\n***************************************************************************/\n\nnamespace internal {\n\ntemplate<typename Lhs, int LhsMode, typename Rhs>\nstruct selfadjoint_product_impl<Lhs,LhsMode,false,Rhs,0,true>\n{\n  typedef typename Product<Lhs,Rhs>::Scalar Scalar;\n  \n  typedef internal::blas_traits<Lhs> LhsBlasTraits;\n  typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;\n  typedef typename internal::remove_all<ActualLhsType>::type ActualLhsTypeCleaned;\n  \n  typedef internal::blas_traits<Rhs> RhsBlasTraits;\n  typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;\n  typedef typename internal::remove_all<ActualRhsType>::type ActualRhsTypeCleaned;\n\n  enum { LhsUpLo = LhsMode&(Upper|Lower) };\n\n  template<typename Dest>\n  static void run(Dest& dest, const Lhs &a_lhs, const Rhs &a_rhs, const Scalar& alpha)\n  {\n    typedef typename Dest::Scalar ResScalar;\n    typedef typename Rhs::Scalar RhsScalar;\n    typedef Map<Matrix<ResScalar,Dynamic,1>, EIGEN_PLAIN_ENUM_MIN(AlignedMax,internal::packet_traits<ResScalar>::size)> MappedDest;\n    \n    eigen_assert(dest.rows()==a_lhs.rows() && dest.cols()==a_rhs.cols());\n\n    typename internal::add_const_on_value_type<ActualLhsType>::type lhs = LhsBlasTraits::extract(a_lhs);\n    typename internal::add_const_on_value_type<ActualRhsType>::type rhs = RhsBlasTraits::extract(a_rhs);\n\n    Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(a_lhs)\n                               * RhsBlasTraits::extractScalarFactor(a_rhs);\n\n    enum {\n      EvalToDest = (Dest::InnerStrideAtCompileTime==1),\n      UseRhs = (ActualRhsTypeCleaned::InnerStrideAtCompileTime==1)\n    };\n    \n    internal::gemv_static_vector_if<ResScalar,Dest::SizeAtCompileTime,Dest::MaxSizeAtCompileTime,!EvalToDest> static_dest;\n    internal::gemv_static_vector_if<RhsScalar,ActualRhsTypeCleaned::SizeAtCompileTime,ActualRhsTypeCleaned::MaxSizeAtCompileTime,!UseRhs> static_rhs;\n\n    ei_declare_aligned_stack_constructed_variable(ResScalar,actualDestPtr,dest.size(),\n                                                  EvalToDest ? dest.data() : static_dest.data());\n                                                  \n    ei_declare_aligned_stack_constructed_variable(RhsScalar,actualRhsPtr,rhs.size(),\n        UseRhs ? const_cast<RhsScalar*>(rhs.data()) : static_rhs.data());\n    \n    if(!EvalToDest)\n    {\n      #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN\n      Index size = dest.size();\n      EIGEN_DENSE_STORAGE_CTOR_PLUGIN\n      #endif\n      MappedDest(actualDestPtr, dest.size()) = dest;\n    }\n      \n    if(!UseRhs)\n    {\n      #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN\n      Index size = rhs.size();\n      EIGEN_DENSE_STORAGE_CTOR_PLUGIN\n      #endif\n      Map<typename ActualRhsTypeCleaned::PlainObject>(actualRhsPtr, rhs.size()) = rhs;\n    }\n      \n      \n    internal::selfadjoint_matrix_vector_product<Scalar, Index, (internal::traits<ActualLhsTypeCleaned>::Flags&RowMajorBit) ? RowMajor : ColMajor,\n                                                int(LhsUpLo), bool(LhsBlasTraits::NeedToConjugate), bool(RhsBlasTraits::NeedToConjugate)>::run\n      (\n        lhs.rows(),                             // size\n        &lhs.coeffRef(0,0),  lhs.outerStride(), // lhs info\n        actualRhsPtr,                           // rhs info\n        actualDestPtr,                          // result info\n        actualAlpha                             // scale factor\n      );\n    \n    if(!EvalToDest)\n      dest = MappedDest(actualDestPtr, dest.size());\n  }\n};\n\ntemplate<typename Lhs, typename Rhs, int RhsMode>\nstruct selfadjoint_product_impl<Lhs,0,true,Rhs,RhsMode,false>\n{\n  typedef typename Product<Lhs,Rhs>::Scalar Scalar;\n  enum { RhsUpLo = RhsMode&(Upper|Lower)  };\n\n  template<typename Dest>\n  static void run(Dest& dest, const Lhs &a_lhs, const Rhs &a_rhs, const Scalar& alpha)\n  {\n    // let's simply transpose the product\n    Transpose<Dest> destT(dest);\n    selfadjoint_product_impl<Transpose<const Rhs>, int(RhsUpLo)==Upper ? Lower : Upper, false,\n                             Transpose<const Lhs>, 0, true>::run(destT, a_rhs.transpose(), a_lhs.transpose(), alpha);\n  }\n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_SELFADJOINT_MATRIX_VECTOR_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/products/SelfadjointMatrixVector_BLAS.h",
    "content": "/*\n Copyright (c) 2011, Intel Corporation. All rights reserved.\n\n Redistribution and use in source and binary forms, with or without modification,\n are permitted provided that the following conditions are met:\n\n * Redistributions of source code must retain the above copyright notice, this\n   list of conditions and the following disclaimer.\n * Redistributions in binary form must reproduce the above copyright notice,\n   this list of conditions and the following disclaimer in the documentation\n   and/or other materials provided with the distribution.\n * Neither the name of Intel Corporation nor the names of its contributors may\n   be used to endorse or promote products derived from this software without\n   specific prior written permission.\n\n THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\" AND\n ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED\n WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\n DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR\n ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES\n (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;\n LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON\n ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT\n (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS\n SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n\n ********************************************************************************\n *   Content : Eigen bindings to BLAS F77\n *   Selfadjoint matrix-vector product functionality based on ?SYMV/HEMV.\n ********************************************************************************\n*/\n\n#ifndef EIGEN_SELFADJOINT_MATRIX_VECTOR_BLAS_H\n#define EIGEN_SELFADJOINT_MATRIX_VECTOR_BLAS_H\n\nnamespace Eigen { \n\nnamespace internal {\n\n/**********************************************************************\n* This file implements selfadjoint matrix-vector multiplication using BLAS\n**********************************************************************/\n\n// symv/hemv specialization\n\ntemplate<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjugateLhs, bool ConjugateRhs>\nstruct selfadjoint_matrix_vector_product_symv :\n  selfadjoint_matrix_vector_product<Scalar,Index,StorageOrder,UpLo,ConjugateLhs,ConjugateRhs,BuiltIn> {};\n\n#define EIGEN_BLAS_SYMV_SPECIALIZE(Scalar) \\\ntemplate<typename Index, int StorageOrder, int UpLo, bool ConjugateLhs, bool ConjugateRhs> \\\nstruct selfadjoint_matrix_vector_product<Scalar,Index,StorageOrder,UpLo,ConjugateLhs,ConjugateRhs,Specialized> { \\\nstatic void run( \\\n  Index size, const Scalar*  lhs, Index lhsStride, \\\n  const Scalar* _rhs, Scalar* res, Scalar alpha) { \\\n    enum {\\\n      IsColMajor = StorageOrder==ColMajor \\\n    }; \\\n    if (IsColMajor == ConjugateLhs) {\\\n      selfadjoint_matrix_vector_product<Scalar,Index,StorageOrder,UpLo,ConjugateLhs,ConjugateRhs,BuiltIn>::run( \\\n        size, lhs, lhsStride, _rhs, res, alpha);  \\\n    } else {\\\n      selfadjoint_matrix_vector_product_symv<Scalar,Index,StorageOrder,UpLo,ConjugateLhs,ConjugateRhs>::run( \\\n        size, lhs, lhsStride, _rhs, res, alpha);  \\\n    }\\\n  } \\\n}; \\\n\nEIGEN_BLAS_SYMV_SPECIALIZE(double)\nEIGEN_BLAS_SYMV_SPECIALIZE(float)\nEIGEN_BLAS_SYMV_SPECIALIZE(dcomplex)\nEIGEN_BLAS_SYMV_SPECIALIZE(scomplex)\n\n#define EIGEN_BLAS_SYMV_SPECIALIZATION(EIGTYPE,BLASTYPE,BLASFUNC) \\\ntemplate<typename Index, int StorageOrder, int UpLo, bool ConjugateLhs, bool ConjugateRhs> \\\nstruct selfadjoint_matrix_vector_product_symv<EIGTYPE,Index,StorageOrder,UpLo,ConjugateLhs,ConjugateRhs> \\\n{ \\\ntypedef Matrix<EIGTYPE,Dynamic,1,ColMajor> SYMVVector;\\\n\\\nstatic void run( \\\nIndex size, const EIGTYPE*  lhs, Index lhsStride, \\\nconst EIGTYPE* _rhs, EIGTYPE* res, EIGTYPE alpha) \\\n{ \\\n  enum {\\\n    IsRowMajor = StorageOrder==RowMajor ? 1 : 0, \\\n    IsLower = UpLo == Lower ? 1 : 0 \\\n  }; \\\n  BlasIndex n=convert_index<BlasIndex>(size), lda=convert_index<BlasIndex>(lhsStride), incx=1, incy=1; \\\n  EIGTYPE beta(1); \\\n  const EIGTYPE *x_ptr; \\\n  char uplo=(IsRowMajor) ? (IsLower ? 'U' : 'L') : (IsLower ? 'L' : 'U'); \\\n  SYMVVector x_tmp; \\\n  if (ConjugateRhs) { \\\n    Map<const SYMVVector, 0 > map_x(_rhs,size,1); \\\n    x_tmp=map_x.conjugate(); \\\n    x_ptr=x_tmp.data(); \\\n  } else x_ptr=_rhs; \\\n  BLASFUNC(&uplo, &n, (const BLASTYPE*)&numext::real_ref(alpha), (const BLASTYPE*)lhs, &lda, (const BLASTYPE*)x_ptr, &incx, (const BLASTYPE*)&numext::real_ref(beta), (BLASTYPE*)res, &incy); \\\n}\\\n};\n\n#ifdef EIGEN_USE_MKL\nEIGEN_BLAS_SYMV_SPECIALIZATION(double,   double, dsymv)\nEIGEN_BLAS_SYMV_SPECIALIZATION(float,    float,  ssymv)\nEIGEN_BLAS_SYMV_SPECIALIZATION(dcomplex, MKL_Complex16, zhemv)\nEIGEN_BLAS_SYMV_SPECIALIZATION(scomplex, MKL_Complex8,  chemv)\n#else\nEIGEN_BLAS_SYMV_SPECIALIZATION(double,   double, dsymv_)\nEIGEN_BLAS_SYMV_SPECIALIZATION(float,    float,  ssymv_)\nEIGEN_BLAS_SYMV_SPECIALIZATION(dcomplex, double, zhemv_)\nEIGEN_BLAS_SYMV_SPECIALIZATION(scomplex, float,  chemv_)\n#endif\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_SELFADJOINT_MATRIX_VECTOR_BLAS_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/products/SelfadjointProduct.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SELFADJOINT_PRODUCT_H\n#define EIGEN_SELFADJOINT_PRODUCT_H\n\n/**********************************************************************\n* This file implements a self adjoint product: C += A A^T updating only\n* half of the selfadjoint matrix C.\n* It corresponds to the level 3 SYRK and level 2 SYR Blas routines.\n**********************************************************************/\n\nnamespace Eigen { \n\n\ntemplate<typename Scalar, typename Index, int UpLo, bool ConjLhs, bool ConjRhs>\nstruct selfadjoint_rank1_update<Scalar,Index,ColMajor,UpLo,ConjLhs,ConjRhs>\n{\n  static void run(Index size, Scalar* mat, Index stride, const Scalar* vecX, const Scalar* vecY, const Scalar& alpha)\n  {\n    internal::conj_if<ConjRhs> cj;\n    typedef Map<const Matrix<Scalar,Dynamic,1> > OtherMap;\n    typedef typename internal::conditional<ConjLhs,typename OtherMap::ConjugateReturnType,const OtherMap&>::type ConjLhsType;\n    for (Index i=0; i<size; ++i)\n    {\n      Map<Matrix<Scalar,Dynamic,1> >(mat+stride*i+(UpLo==Lower ? i : 0), (UpLo==Lower ? size-i : (i+1)))\n          += (alpha * cj(vecY[i])) * ConjLhsType(OtherMap(vecX+(UpLo==Lower ? i : 0),UpLo==Lower ? size-i : (i+1)));\n    }\n  }\n};\n\ntemplate<typename Scalar, typename Index, int UpLo, bool ConjLhs, bool ConjRhs>\nstruct selfadjoint_rank1_update<Scalar,Index,RowMajor,UpLo,ConjLhs,ConjRhs>\n{\n  static void run(Index size, Scalar* mat, Index stride, const Scalar* vecX, const Scalar* vecY, const Scalar& alpha)\n  {\n    selfadjoint_rank1_update<Scalar,Index,ColMajor,UpLo==Lower?Upper:Lower,ConjRhs,ConjLhs>::run(size,mat,stride,vecY,vecX,alpha);\n  }\n};\n\ntemplate<typename MatrixType, typename OtherType, int UpLo, bool OtherIsVector = OtherType::IsVectorAtCompileTime>\nstruct selfadjoint_product_selector;\n\ntemplate<typename MatrixType, typename OtherType, int UpLo>\nstruct selfadjoint_product_selector<MatrixType,OtherType,UpLo,true>\n{\n  static void run(MatrixType& mat, const OtherType& other, const typename MatrixType::Scalar& alpha)\n  {\n    typedef typename MatrixType::Scalar Scalar;\n    typedef internal::blas_traits<OtherType> OtherBlasTraits;\n    typedef typename OtherBlasTraits::DirectLinearAccessType ActualOtherType;\n    typedef typename internal::remove_all<ActualOtherType>::type _ActualOtherType;\n    typename internal::add_const_on_value_type<ActualOtherType>::type actualOther = OtherBlasTraits::extract(other.derived());\n\n    Scalar actualAlpha = alpha * OtherBlasTraits::extractScalarFactor(other.derived());\n\n    enum {\n      StorageOrder = (internal::traits<MatrixType>::Flags&RowMajorBit) ? RowMajor : ColMajor,\n      UseOtherDirectly = _ActualOtherType::InnerStrideAtCompileTime==1\n    };\n    internal::gemv_static_vector_if<Scalar,OtherType::SizeAtCompileTime,OtherType::MaxSizeAtCompileTime,!UseOtherDirectly> static_other;\n\n    ei_declare_aligned_stack_constructed_variable(Scalar, actualOtherPtr, other.size(),\n      (UseOtherDirectly ? const_cast<Scalar*>(actualOther.data()) : static_other.data()));\n      \n    if(!UseOtherDirectly)\n      Map<typename _ActualOtherType::PlainObject>(actualOtherPtr, actualOther.size()) = actualOther;\n    \n    selfadjoint_rank1_update<Scalar,Index,StorageOrder,UpLo,\n                              OtherBlasTraits::NeedToConjugate  && NumTraits<Scalar>::IsComplex,\n                            (!OtherBlasTraits::NeedToConjugate) && NumTraits<Scalar>::IsComplex>\n          ::run(other.size(), mat.data(), mat.outerStride(), actualOtherPtr, actualOtherPtr, actualAlpha);\n  }\n};\n\ntemplate<typename MatrixType, typename OtherType, int UpLo>\nstruct selfadjoint_product_selector<MatrixType,OtherType,UpLo,false>\n{\n  static void run(MatrixType& mat, const OtherType& other, const typename MatrixType::Scalar& alpha)\n  {\n    typedef typename MatrixType::Scalar Scalar;\n    typedef internal::blas_traits<OtherType> OtherBlasTraits;\n    typedef typename OtherBlasTraits::DirectLinearAccessType ActualOtherType;\n    typedef typename internal::remove_all<ActualOtherType>::type _ActualOtherType;\n    typename internal::add_const_on_value_type<ActualOtherType>::type actualOther = OtherBlasTraits::extract(other.derived());\n\n    Scalar actualAlpha = alpha * OtherBlasTraits::extractScalarFactor(other.derived());\n\n    enum {\n      IsRowMajor = (internal::traits<MatrixType>::Flags&RowMajorBit) ? 1 : 0,\n      OtherIsRowMajor = _ActualOtherType::Flags&RowMajorBit ? 1 : 0\n    };\n\n    Index size = mat.cols();\n    Index depth = actualOther.cols();\n\n    typedef internal::gemm_blocking_space<IsRowMajor ? RowMajor : ColMajor,Scalar,Scalar,\n              MatrixType::MaxColsAtCompileTime, MatrixType::MaxColsAtCompileTime, _ActualOtherType::MaxColsAtCompileTime> BlockingType;\n\n    BlockingType blocking(size, size, depth, 1, false);\n\n\n    internal::general_matrix_matrix_triangular_product<Index,\n      Scalar, OtherIsRowMajor ? RowMajor : ColMajor,   OtherBlasTraits::NeedToConjugate  && NumTraits<Scalar>::IsComplex,\n      Scalar, OtherIsRowMajor ? ColMajor : RowMajor, (!OtherBlasTraits::NeedToConjugate) && NumTraits<Scalar>::IsComplex,\n      IsRowMajor ? RowMajor : ColMajor, UpLo>\n      ::run(size, depth,\n            &actualOther.coeffRef(0,0), actualOther.outerStride(), &actualOther.coeffRef(0,0), actualOther.outerStride(),\n            mat.data(), mat.outerStride(), actualAlpha, blocking);\n  }\n};\n\n// high level API\n\ntemplate<typename MatrixType, unsigned int UpLo>\ntemplate<typename DerivedU>\nSelfAdjointView<MatrixType,UpLo>& SelfAdjointView<MatrixType,UpLo>\n::rankUpdate(const MatrixBase<DerivedU>& u, const Scalar& alpha)\n{\n  selfadjoint_product_selector<MatrixType,DerivedU,UpLo>::run(_expression().const_cast_derived(), u.derived(), alpha);\n\n  return *this;\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_SELFADJOINT_PRODUCT_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/products/SelfadjointRank2Update.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SELFADJOINTRANK2UPTADE_H\n#define EIGEN_SELFADJOINTRANK2UPTADE_H\n\nnamespace Eigen { \n\nnamespace internal {\n\n/* Optimized selfadjoint matrix += alpha * uv' + conj(alpha)*vu'\n * It corresponds to the Level2 syr2 BLAS routine\n */\n\ntemplate<typename Scalar, typename Index, typename UType, typename VType, int UpLo>\nstruct selfadjoint_rank2_update_selector;\n\ntemplate<typename Scalar, typename Index, typename UType, typename VType>\nstruct selfadjoint_rank2_update_selector<Scalar,Index,UType,VType,Lower>\n{\n  static void run(Scalar* mat, Index stride, const UType& u, const VType& v, const Scalar& alpha)\n  {\n    const Index size = u.size();\n    for (Index i=0; i<size; ++i)\n    {\n      Map<Matrix<Scalar,Dynamic,1> >(mat+stride*i+i, size-i) +=\n                        (numext::conj(alpha) * numext::conj(u.coeff(i))) * v.tail(size-i)\n                      + (alpha * numext::conj(v.coeff(i))) * u.tail(size-i);\n    }\n  }\n};\n\ntemplate<typename Scalar, typename Index, typename UType, typename VType>\nstruct selfadjoint_rank2_update_selector<Scalar,Index,UType,VType,Upper>\n{\n  static void run(Scalar* mat, Index stride, const UType& u, const VType& v, const Scalar& alpha)\n  {\n    const Index size = u.size();\n    for (Index i=0; i<size; ++i)\n      Map<Matrix<Scalar,Dynamic,1> >(mat+stride*i, i+1) +=\n                        (numext::conj(alpha)  * numext::conj(u.coeff(i))) * v.head(i+1)\n                      + (alpha * numext::conj(v.coeff(i))) * u.head(i+1);\n  }\n};\n\ntemplate<bool Cond, typename T> struct conj_expr_if\n  : conditional<!Cond, const T&,\n      CwiseUnaryOp<scalar_conjugate_op<typename traits<T>::Scalar>,T> > {};\n\n} // end namespace internal\n\ntemplate<typename MatrixType, unsigned int UpLo>\ntemplate<typename DerivedU, typename DerivedV>\nSelfAdjointView<MatrixType,UpLo>& SelfAdjointView<MatrixType,UpLo>\n::rankUpdate(const MatrixBase<DerivedU>& u, const MatrixBase<DerivedV>& v, const Scalar& alpha)\n{\n  typedef internal::blas_traits<DerivedU> UBlasTraits;\n  typedef typename UBlasTraits::DirectLinearAccessType ActualUType;\n  typedef typename internal::remove_all<ActualUType>::type _ActualUType;\n  typename internal::add_const_on_value_type<ActualUType>::type actualU = UBlasTraits::extract(u.derived());\n\n  typedef internal::blas_traits<DerivedV> VBlasTraits;\n  typedef typename VBlasTraits::DirectLinearAccessType ActualVType;\n  typedef typename internal::remove_all<ActualVType>::type _ActualVType;\n  typename internal::add_const_on_value_type<ActualVType>::type actualV = VBlasTraits::extract(v.derived());\n\n  // If MatrixType is row major, then we use the routine for lower triangular in the upper triangular case and\n  // vice versa, and take the complex conjugate of all coefficients and vector entries.\n\n  enum { IsRowMajor = (internal::traits<MatrixType>::Flags&RowMajorBit) ? 1 : 0 };\n  Scalar actualAlpha = alpha * UBlasTraits::extractScalarFactor(u.derived())\n                             * numext::conj(VBlasTraits::extractScalarFactor(v.derived()));\n  if (IsRowMajor)\n    actualAlpha = numext::conj(actualAlpha);\n\n  typedef typename internal::remove_all<typename internal::conj_expr_if<IsRowMajor ^ UBlasTraits::NeedToConjugate,_ActualUType>::type>::type UType;\n  typedef typename internal::remove_all<typename internal::conj_expr_if<IsRowMajor ^ VBlasTraits::NeedToConjugate,_ActualVType>::type>::type VType;\n  internal::selfadjoint_rank2_update_selector<Scalar, Index, UType, VType,\n    (IsRowMajor ? int(UpLo==Upper ? Lower : Upper) : UpLo)>\n    ::run(_expression().const_cast_derived().data(),_expression().outerStride(),UType(actualU),VType(actualV),actualAlpha);\n\n  return *this;\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_SELFADJOINTRANK2UPTADE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/products/TriangularMatrixMatrix.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_TRIANGULAR_MATRIX_MATRIX_H\n#define EIGEN_TRIANGULAR_MATRIX_MATRIX_H\n\nnamespace Eigen { \n\nnamespace internal {\n\n// template<typename Scalar, int mr, int StorageOrder, bool Conjugate, int Mode>\n// struct gemm_pack_lhs_triangular\n// {\n//   Matrix<Scalar,mr,mr,\n//   void operator()(Scalar* blockA, const EIGEN_RESTRICT Scalar* _lhs, int lhsStride, int depth, int rows)\n//   {\n//     conj_if<NumTraits<Scalar>::IsComplex && Conjugate> cj;\n//     const_blas_data_mapper<Scalar, StorageOrder> lhs(_lhs,lhsStride);\n//     int count = 0;\n//     const int peeled_mc = (rows/mr)*mr;\n//     for(int i=0; i<peeled_mc; i+=mr)\n//     {\n//       for(int k=0; k<depth; k++)\n//         for(int w=0; w<mr; w++)\n//           blockA[count++] = cj(lhs(i+w, k));\n//     }\n//     for(int i=peeled_mc; i<rows; i++)\n//     {\n//       for(int k=0; k<depth; k++)\n//         blockA[count++] = cj(lhs(i, k));\n//     }\n//   }\n// };\n\n/* Optimized triangular matrix * matrix (_TRMM++) product built on top of\n * the general matrix matrix product.\n */\ntemplate <typename Scalar, typename Index,\n          int Mode, bool LhsIsTriangular,\n          int LhsStorageOrder, bool ConjugateLhs,\n          int RhsStorageOrder, bool ConjugateRhs,\n          int ResStorageOrder, int Version = Specialized>\nstruct product_triangular_matrix_matrix;\n\ntemplate <typename Scalar, typename Index,\n          int Mode, bool LhsIsTriangular,\n          int LhsStorageOrder, bool ConjugateLhs,\n          int RhsStorageOrder, bool ConjugateRhs, int Version>\nstruct product_triangular_matrix_matrix<Scalar,Index,Mode,LhsIsTriangular,\n                                           LhsStorageOrder,ConjugateLhs,\n                                           RhsStorageOrder,ConjugateRhs,RowMajor,Version>\n{\n  static EIGEN_STRONG_INLINE void run(\n    Index rows, Index cols, Index depth,\n    const Scalar* lhs, Index lhsStride,\n    const Scalar* rhs, Index rhsStride,\n    Scalar* res,       Index resStride,\n    const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking)\n  {\n    product_triangular_matrix_matrix<Scalar, Index,\n      (Mode&(UnitDiag|ZeroDiag)) | ((Mode&Upper) ? Lower : Upper),\n      (!LhsIsTriangular),\n      RhsStorageOrder==RowMajor ? ColMajor : RowMajor,\n      ConjugateRhs,\n      LhsStorageOrder==RowMajor ? ColMajor : RowMajor,\n      ConjugateLhs,\n      ColMajor>\n      ::run(cols, rows, depth, rhs, rhsStride, lhs, lhsStride, res, resStride, alpha, blocking);\n  }\n};\n\n// implements col-major += alpha * op(triangular) * op(general)\ntemplate <typename Scalar, typename Index, int Mode,\n          int LhsStorageOrder, bool ConjugateLhs,\n          int RhsStorageOrder, bool ConjugateRhs, int Version>\nstruct product_triangular_matrix_matrix<Scalar,Index,Mode,true,\n                                           LhsStorageOrder,ConjugateLhs,\n                                           RhsStorageOrder,ConjugateRhs,ColMajor,Version>\n{\n  \n  typedef gebp_traits<Scalar,Scalar> Traits;\n  enum {\n    SmallPanelWidth   = 2 * EIGEN_PLAIN_ENUM_MAX(Traits::mr,Traits::nr),\n    IsLower = (Mode&Lower) == Lower,\n    SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1\n  };\n\n  static EIGEN_DONT_INLINE void run(\n    Index _rows, Index _cols, Index _depth,\n    const Scalar* _lhs, Index lhsStride,\n    const Scalar* _rhs, Index rhsStride,\n    Scalar* res,        Index resStride,\n    const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking);\n};\n\ntemplate <typename Scalar, typename Index, int Mode,\n          int LhsStorageOrder, bool ConjugateLhs,\n          int RhsStorageOrder, bool ConjugateRhs, int Version>\nEIGEN_DONT_INLINE void product_triangular_matrix_matrix<Scalar,Index,Mode,true,\n                                                        LhsStorageOrder,ConjugateLhs,\n                                                        RhsStorageOrder,ConjugateRhs,ColMajor,Version>::run(\n    Index _rows, Index _cols, Index _depth,\n    const Scalar* _lhs, Index lhsStride,\n    const Scalar* _rhs, Index rhsStride,\n    Scalar* _res,        Index resStride,\n    const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking)\n  {\n    // strip zeros\n    Index diagSize  = (std::min)(_rows,_depth);\n    Index rows      = IsLower ? _rows : diagSize;\n    Index depth     = IsLower ? diagSize : _depth;\n    Index cols      = _cols;\n    \n    typedef const_blas_data_mapper<Scalar, Index, LhsStorageOrder> LhsMapper;\n    typedef const_blas_data_mapper<Scalar, Index, RhsStorageOrder> RhsMapper;\n    typedef blas_data_mapper<typename Traits::ResScalar, Index, ColMajor> ResMapper;\n    LhsMapper lhs(_lhs,lhsStride);\n    RhsMapper rhs(_rhs,rhsStride);\n    ResMapper res(_res, resStride);\n\n    Index kc = blocking.kc();                   // cache block size along the K direction\n    Index mc = (std::min)(rows,blocking.mc());  // cache block size along the M direction\n    // The small panel size must not be larger than blocking size.\n    // Usually this should never be the case because SmallPanelWidth^2 is very small\n    // compared to L2 cache size, but let's be safe:\n    Index panelWidth = (std::min)(Index(SmallPanelWidth),(std::min)(kc,mc));\n\n    std::size_t sizeA = kc*mc;\n    std::size_t sizeB = kc*cols;\n\n    ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());\n    ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());\n\n    // To work around an \"error: member reference base type 'Matrix<...>\n    // (Eigen::internal::constructor_without_unaligned_array_assert (*)())' is\n    // not a structure or union\" compilation error in nvcc (tested V8.0.61),\n    // create a dummy internal::constructor_without_unaligned_array_assert\n    // object to pass to the Matrix constructor.\n    internal::constructor_without_unaligned_array_assert a;\n    Matrix<Scalar,SmallPanelWidth,SmallPanelWidth,LhsStorageOrder> triangularBuffer(a);\n    triangularBuffer.setZero();\n    if((Mode&ZeroDiag)==ZeroDiag)\n      triangularBuffer.diagonal().setZero();\n    else\n      triangularBuffer.diagonal().setOnes();\n\n    gebp_kernel<Scalar, Scalar, Index, ResMapper, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;\n    gemm_pack_lhs<Scalar, Index, LhsMapper, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;\n    gemm_pack_rhs<Scalar, Index, RhsMapper, Traits::nr,RhsStorageOrder> pack_rhs;\n\n    for(Index k2=IsLower ? depth : 0;\n        IsLower ? k2>0 : k2<depth;\n        IsLower ? k2-=kc : k2+=kc)\n    {\n      Index actual_kc = (std::min)(IsLower ? k2 : depth-k2, kc);\n      Index actual_k2 = IsLower ? k2-actual_kc : k2;\n\n      // align blocks with the end of the triangular part for trapezoidal lhs\n      if((!IsLower)&&(k2<rows)&&(k2+actual_kc>rows))\n      {\n        actual_kc = rows-k2;\n        k2 = k2+actual_kc-kc;\n      }\n\n      pack_rhs(blockB, rhs.getSubMapper(actual_k2,0), actual_kc, cols);\n\n      // the selected lhs's panel has to be split in three different parts:\n      //  1 - the part which is zero => skip it\n      //  2 - the diagonal block => special kernel\n      //  3 - the dense panel below (lower case) or above (upper case) the diagonal block => GEPP\n\n      // the block diagonal, if any:\n      if(IsLower || actual_k2<rows)\n      {\n        // for each small vertical panels of lhs\n        for (Index k1=0; k1<actual_kc; k1+=panelWidth)\n        {\n          Index actualPanelWidth = std::min<Index>(actual_kc-k1, panelWidth);\n          Index lengthTarget = IsLower ? actual_kc-k1-actualPanelWidth : k1;\n          Index startBlock   = actual_k2+k1;\n          Index blockBOffset = k1;\n\n          // => GEBP with the micro triangular block\n          // The trick is to pack this micro block while filling the opposite triangular part with zeros.\n          // To this end we do an extra triangular copy to a small temporary buffer\n          for (Index k=0;k<actualPanelWidth;++k)\n          {\n            if (SetDiag)\n              triangularBuffer.coeffRef(k,k) = lhs(startBlock+k,startBlock+k);\n            for (Index i=IsLower ? k+1 : 0; IsLower ? i<actualPanelWidth : i<k; ++i)\n              triangularBuffer.coeffRef(i,k) = lhs(startBlock+i,startBlock+k);\n          }\n          pack_lhs(blockA, LhsMapper(triangularBuffer.data(), triangularBuffer.outerStride()), actualPanelWidth, actualPanelWidth);\n\n          gebp_kernel(res.getSubMapper(startBlock, 0), blockA, blockB,\n                      actualPanelWidth, actualPanelWidth, cols, alpha,\n                      actualPanelWidth, actual_kc, 0, blockBOffset);\n\n          // GEBP with remaining micro panel\n          if (lengthTarget>0)\n          {\n            Index startTarget  = IsLower ? actual_k2+k1+actualPanelWidth : actual_k2;\n\n            pack_lhs(blockA, lhs.getSubMapper(startTarget,startBlock), actualPanelWidth, lengthTarget);\n\n            gebp_kernel(res.getSubMapper(startTarget, 0), blockA, blockB,\n                        lengthTarget, actualPanelWidth, cols, alpha,\n                        actualPanelWidth, actual_kc, 0, blockBOffset);\n          }\n        }\n      }\n      // the part below (lower case) or above (upper case) the diagonal => GEPP\n      {\n        Index start = IsLower ? k2 : 0;\n        Index end   = IsLower ? rows : (std::min)(actual_k2,rows);\n        for(Index i2=start; i2<end; i2+=mc)\n        {\n          const Index actual_mc = (std::min)(i2+mc,end)-i2;\n          gemm_pack_lhs<Scalar, Index, LhsMapper, Traits::mr,Traits::LhsProgress, LhsStorageOrder,false>()\n            (blockA, lhs.getSubMapper(i2, actual_k2), actual_kc, actual_mc);\n\n          gebp_kernel(res.getSubMapper(i2, 0), blockA, blockB, actual_mc,\n                      actual_kc, cols, alpha, -1, -1, 0, 0);\n        }\n      }\n    }\n  }\n\n// implements col-major += alpha * op(general) * op(triangular)\ntemplate <typename Scalar, typename Index, int Mode,\n          int LhsStorageOrder, bool ConjugateLhs,\n          int RhsStorageOrder, bool ConjugateRhs, int Version>\nstruct product_triangular_matrix_matrix<Scalar,Index,Mode,false,\n                                        LhsStorageOrder,ConjugateLhs,\n                                        RhsStorageOrder,ConjugateRhs,ColMajor,Version>\n{\n  typedef gebp_traits<Scalar,Scalar> Traits;\n  enum {\n    SmallPanelWidth   = EIGEN_PLAIN_ENUM_MAX(Traits::mr,Traits::nr),\n    IsLower = (Mode&Lower) == Lower,\n    SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1\n  };\n\n  static EIGEN_DONT_INLINE void run(\n    Index _rows, Index _cols, Index _depth,\n    const Scalar* _lhs, Index lhsStride,\n    const Scalar* _rhs, Index rhsStride,\n    Scalar* res,        Index resStride,\n    const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking);\n};\n\ntemplate <typename Scalar, typename Index, int Mode,\n          int LhsStorageOrder, bool ConjugateLhs,\n          int RhsStorageOrder, bool ConjugateRhs, int Version>\nEIGEN_DONT_INLINE void product_triangular_matrix_matrix<Scalar,Index,Mode,false,\n                                                        LhsStorageOrder,ConjugateLhs,\n                                                        RhsStorageOrder,ConjugateRhs,ColMajor,Version>::run(\n    Index _rows, Index _cols, Index _depth,\n    const Scalar* _lhs, Index lhsStride,\n    const Scalar* _rhs, Index rhsStride,\n    Scalar* _res,        Index resStride,\n    const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking)\n  {\n    const Index PacketBytes = packet_traits<Scalar>::size*sizeof(Scalar);\n    // strip zeros\n    Index diagSize  = (std::min)(_cols,_depth);\n    Index rows      = _rows;\n    Index depth     = IsLower ? _depth : diagSize;\n    Index cols      = IsLower ? diagSize : _cols;\n    \n    typedef const_blas_data_mapper<Scalar, Index, LhsStorageOrder> LhsMapper;\n    typedef const_blas_data_mapper<Scalar, Index, RhsStorageOrder> RhsMapper;\n    typedef blas_data_mapper<typename Traits::ResScalar, Index, ColMajor> ResMapper;\n    LhsMapper lhs(_lhs,lhsStride);\n    RhsMapper rhs(_rhs,rhsStride);\n    ResMapper res(_res, resStride);\n\n    Index kc = blocking.kc();                   // cache block size along the K direction\n    Index mc = (std::min)(rows,blocking.mc());  // cache block size along the M direction\n\n    std::size_t sizeA = kc*mc;\n    std::size_t sizeB = kc*cols+EIGEN_MAX_ALIGN_BYTES/sizeof(Scalar);\n\n    ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());\n    ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());\n\n    internal::constructor_without_unaligned_array_assert a;\n    Matrix<Scalar,SmallPanelWidth,SmallPanelWidth,RhsStorageOrder> triangularBuffer(a);\n    triangularBuffer.setZero();\n    if((Mode&ZeroDiag)==ZeroDiag)\n      triangularBuffer.diagonal().setZero();\n    else\n      triangularBuffer.diagonal().setOnes();\n\n    gebp_kernel<Scalar, Scalar, Index, ResMapper, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;\n    gemm_pack_lhs<Scalar, Index, LhsMapper, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;\n    gemm_pack_rhs<Scalar, Index, RhsMapper, Traits::nr,RhsStorageOrder> pack_rhs;\n    gemm_pack_rhs<Scalar, Index, RhsMapper, Traits::nr,RhsStorageOrder,false,true> pack_rhs_panel;\n\n    for(Index k2=IsLower ? 0 : depth;\n        IsLower ? k2<depth  : k2>0;\n        IsLower ? k2+=kc   : k2-=kc)\n    {\n      Index actual_kc = (std::min)(IsLower ? depth-k2 : k2, kc);\n      Index actual_k2 = IsLower ? k2 : k2-actual_kc;\n\n      // align blocks with the end of the triangular part for trapezoidal rhs\n      if(IsLower && (k2<cols) && (actual_k2+actual_kc>cols))\n      {\n        actual_kc = cols-k2;\n        k2 = actual_k2 + actual_kc - kc;\n      }\n\n      // remaining size\n      Index rs = IsLower ? (std::min)(cols,actual_k2) : cols - k2;\n      // size of the triangular part\n      Index ts = (IsLower && actual_k2>=cols) ? 0 : actual_kc;\n\n      Scalar* geb = blockB+ts*ts;\n      geb = geb + internal::first_aligned<PacketBytes>(geb,PacketBytes/sizeof(Scalar));\n\n      pack_rhs(geb, rhs.getSubMapper(actual_k2,IsLower ? 0 : k2), actual_kc, rs);\n\n      // pack the triangular part of the rhs padding the unrolled blocks with zeros\n      if(ts>0)\n      {\n        for (Index j2=0; j2<actual_kc; j2+=SmallPanelWidth)\n        {\n          Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth);\n          Index actual_j2 = actual_k2 + j2;\n          Index panelOffset = IsLower ? j2+actualPanelWidth : 0;\n          Index panelLength = IsLower ? actual_kc-j2-actualPanelWidth : j2;\n          // general part\n          pack_rhs_panel(blockB+j2*actual_kc,\n                         rhs.getSubMapper(actual_k2+panelOffset, actual_j2),\n                         panelLength, actualPanelWidth,\n                         actual_kc, panelOffset);\n\n          // append the triangular part via a temporary buffer\n          for (Index j=0;j<actualPanelWidth;++j)\n          {\n            if (SetDiag)\n              triangularBuffer.coeffRef(j,j) = rhs(actual_j2+j,actual_j2+j);\n            for (Index k=IsLower ? j+1 : 0; IsLower ? k<actualPanelWidth : k<j; ++k)\n              triangularBuffer.coeffRef(k,j) = rhs(actual_j2+k,actual_j2+j);\n          }\n\n          pack_rhs_panel(blockB+j2*actual_kc,\n                         RhsMapper(triangularBuffer.data(), triangularBuffer.outerStride()),\n                         actualPanelWidth, actualPanelWidth,\n                         actual_kc, j2);\n        }\n      }\n\n      for (Index i2=0; i2<rows; i2+=mc)\n      {\n        const Index actual_mc = (std::min)(mc,rows-i2);\n        pack_lhs(blockA, lhs.getSubMapper(i2, actual_k2), actual_kc, actual_mc);\n\n        // triangular kernel\n        if(ts>0)\n        {\n          for (Index j2=0; j2<actual_kc; j2+=SmallPanelWidth)\n          {\n            Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth);\n            Index panelLength = IsLower ? actual_kc-j2 : j2+actualPanelWidth;\n            Index blockOffset = IsLower ? j2 : 0;\n\n            gebp_kernel(res.getSubMapper(i2, actual_k2 + j2),\n                        blockA, blockB+j2*actual_kc,\n                        actual_mc, panelLength, actualPanelWidth,\n                        alpha,\n                        actual_kc, actual_kc,  // strides\n                        blockOffset, blockOffset);// offsets\n          }\n        }\n        gebp_kernel(res.getSubMapper(i2, IsLower ? 0 : k2),\n                    blockA, geb, actual_mc, actual_kc, rs,\n                    alpha,\n                    -1, -1, 0, 0);\n      }\n    }\n  }\n\n/***************************************************************************\n* Wrapper to product_triangular_matrix_matrix\n***************************************************************************/\n\n} // end namespace internal\n\nnamespace internal {\ntemplate<int Mode, bool LhsIsTriangular, typename Lhs, typename Rhs>\nstruct triangular_product_impl<Mode,LhsIsTriangular,Lhs,false,Rhs,false>\n{\n  template<typename Dest> static void run(Dest& dst, const Lhs &a_lhs, const Rhs &a_rhs, const typename Dest::Scalar& alpha)\n  {\n    typedef typename Lhs::Scalar  LhsScalar;\n    typedef typename Rhs::Scalar  RhsScalar;\n    typedef typename Dest::Scalar Scalar;\n    \n    typedef internal::blas_traits<Lhs> LhsBlasTraits;\n    typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;\n    typedef typename internal::remove_all<ActualLhsType>::type ActualLhsTypeCleaned;\n    typedef internal::blas_traits<Rhs> RhsBlasTraits;\n    typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;\n    typedef typename internal::remove_all<ActualRhsType>::type ActualRhsTypeCleaned;\n    \n    typename internal::add_const_on_value_type<ActualLhsType>::type lhs = LhsBlasTraits::extract(a_lhs);\n    typename internal::add_const_on_value_type<ActualRhsType>::type rhs = RhsBlasTraits::extract(a_rhs);\n\n    LhsScalar lhs_alpha = LhsBlasTraits::extractScalarFactor(a_lhs);\n    RhsScalar rhs_alpha = RhsBlasTraits::extractScalarFactor(a_rhs);\n    Scalar actualAlpha = alpha * lhs_alpha * rhs_alpha;\n\n    typedef internal::gemm_blocking_space<(Dest::Flags&RowMajorBit) ? RowMajor : ColMajor,Scalar,Scalar,\n              Lhs::MaxRowsAtCompileTime, Rhs::MaxColsAtCompileTime, Lhs::MaxColsAtCompileTime,4> BlockingType;\n\n    enum { IsLower = (Mode&Lower) == Lower };\n    Index stripedRows  = ((!LhsIsTriangular) || (IsLower))  ? lhs.rows() : (std::min)(lhs.rows(),lhs.cols());\n    Index stripedCols  = ((LhsIsTriangular)  || (!IsLower)) ? rhs.cols() : (std::min)(rhs.cols(),rhs.rows());\n    Index stripedDepth = LhsIsTriangular ? ((!IsLower) ? lhs.cols() : (std::min)(lhs.cols(),lhs.rows()))\n                                         : ((IsLower)  ? rhs.rows() : (std::min)(rhs.rows(),rhs.cols()));\n\n    BlockingType blocking(stripedRows, stripedCols, stripedDepth, 1, false);\n\n    internal::product_triangular_matrix_matrix<Scalar, Index,\n      Mode, LhsIsTriangular,\n      (internal::traits<ActualLhsTypeCleaned>::Flags&RowMajorBit) ? RowMajor : ColMajor, LhsBlasTraits::NeedToConjugate,\n      (internal::traits<ActualRhsTypeCleaned>::Flags&RowMajorBit) ? RowMajor : ColMajor, RhsBlasTraits::NeedToConjugate,\n      (internal::traits<Dest          >::Flags&RowMajorBit) ? RowMajor : ColMajor>\n      ::run(\n        stripedRows, stripedCols, stripedDepth,   // sizes\n        &lhs.coeffRef(0,0), lhs.outerStride(),    // lhs info\n        &rhs.coeffRef(0,0), rhs.outerStride(),    // rhs info\n        &dst.coeffRef(0,0), dst.outerStride(),    // result info\n        actualAlpha, blocking\n      );\n\n    // Apply correction if the diagonal is unit and a scalar factor was nested:\n    if ((Mode&UnitDiag)==UnitDiag)\n    {\n      if (LhsIsTriangular && lhs_alpha!=LhsScalar(1))\n      {\n        Index diagSize = (std::min)(lhs.rows(),lhs.cols());\n        dst.topRows(diagSize) -= ((lhs_alpha-LhsScalar(1))*a_rhs).topRows(diagSize);\n      }\n      else if ((!LhsIsTriangular) && rhs_alpha!=RhsScalar(1))\n      {\n        Index diagSize = (std::min)(rhs.rows(),rhs.cols());\n        dst.leftCols(diagSize) -= (rhs_alpha-RhsScalar(1))*a_lhs.leftCols(diagSize);\n      }\n    }\n  }\n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_TRIANGULAR_MATRIX_MATRIX_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/products/TriangularMatrixMatrix_BLAS.h",
    "content": "/*\n Copyright (c) 2011, Intel Corporation. All rights reserved.\n\n Redistribution and use in source and binary forms, with or without modification,\n are permitted provided that the following conditions are met:\n\n * Redistributions of source code must retain the above copyright notice, this\n   list of conditions and the following disclaimer.\n * Redistributions in binary form must reproduce the above copyright notice,\n   this list of conditions and the following disclaimer in the documentation\n   and/or other materials provided with the distribution.\n * Neither the name of Intel Corporation nor the names of its contributors may\n   be used to endorse or promote products derived from this software without\n   specific prior written permission.\n\n THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\" AND\n ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED\n WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\n DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR\n ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES\n (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;\n LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON\n ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT\n (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS\n SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n\n ********************************************************************************\n *   Content : Eigen bindings to BLAS F77\n *   Triangular matrix * matrix product functionality based on ?TRMM.\n ********************************************************************************\n*/\n\n#ifndef EIGEN_TRIANGULAR_MATRIX_MATRIX_BLAS_H\n#define EIGEN_TRIANGULAR_MATRIX_MATRIX_BLAS_H\n\nnamespace Eigen { \n\nnamespace internal {\n\n\ntemplate <typename Scalar, typename Index,\n          int Mode, bool LhsIsTriangular,\n          int LhsStorageOrder, bool ConjugateLhs,\n          int RhsStorageOrder, bool ConjugateRhs,\n          int ResStorageOrder>\nstruct product_triangular_matrix_matrix_trmm :\n       product_triangular_matrix_matrix<Scalar,Index,Mode,\n          LhsIsTriangular,LhsStorageOrder,ConjugateLhs,\n          RhsStorageOrder, ConjugateRhs, ResStorageOrder, BuiltIn> {};\n\n\n// try to go to BLAS specialization\n#define EIGEN_BLAS_TRMM_SPECIALIZE(Scalar, LhsIsTriangular) \\\ntemplate <typename Index, int Mode, \\\n          int LhsStorageOrder, bool ConjugateLhs, \\\n          int RhsStorageOrder, bool ConjugateRhs> \\\nstruct product_triangular_matrix_matrix<Scalar,Index, Mode, LhsIsTriangular, \\\n           LhsStorageOrder,ConjugateLhs, RhsStorageOrder,ConjugateRhs,ColMajor,Specialized> { \\\n  static inline void run(Index _rows, Index _cols, Index _depth, const Scalar* _lhs, Index lhsStride,\\\n    const Scalar* _rhs, Index rhsStride, Scalar* res, Index resStride, Scalar alpha, level3_blocking<Scalar,Scalar>& blocking) { \\\n      product_triangular_matrix_matrix_trmm<Scalar,Index,Mode, \\\n        LhsIsTriangular,LhsStorageOrder,ConjugateLhs, \\\n        RhsStorageOrder, ConjugateRhs, ColMajor>::run( \\\n        _rows, _cols, _depth, _lhs, lhsStride, _rhs, rhsStride, res, resStride, alpha, blocking); \\\n  } \\\n};\n\nEIGEN_BLAS_TRMM_SPECIALIZE(double, true)\nEIGEN_BLAS_TRMM_SPECIALIZE(double, false)\nEIGEN_BLAS_TRMM_SPECIALIZE(dcomplex, true)\nEIGEN_BLAS_TRMM_SPECIALIZE(dcomplex, false)\nEIGEN_BLAS_TRMM_SPECIALIZE(float, true)\nEIGEN_BLAS_TRMM_SPECIALIZE(float, false)\nEIGEN_BLAS_TRMM_SPECIALIZE(scomplex, true)\nEIGEN_BLAS_TRMM_SPECIALIZE(scomplex, false)\n\n// implements col-major += alpha * op(triangular) * op(general)\n#define EIGEN_BLAS_TRMM_L(EIGTYPE, BLASTYPE, EIGPREFIX, BLASFUNC) \\\ntemplate <typename Index, int Mode, \\\n          int LhsStorageOrder, bool ConjugateLhs, \\\n          int RhsStorageOrder, bool ConjugateRhs> \\\nstruct product_triangular_matrix_matrix_trmm<EIGTYPE,Index,Mode,true, \\\n         LhsStorageOrder,ConjugateLhs,RhsStorageOrder,ConjugateRhs,ColMajor> \\\n{ \\\n  enum { \\\n    IsLower = (Mode&Lower) == Lower, \\\n    SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1, \\\n    IsUnitDiag  = (Mode&UnitDiag) ? 1 : 0, \\\n    IsZeroDiag  = (Mode&ZeroDiag) ? 1 : 0, \\\n    LowUp = IsLower ? Lower : Upper, \\\n    conjA = ((LhsStorageOrder==ColMajor) && ConjugateLhs) ? 1 : 0 \\\n  }; \\\n\\\n  static void run( \\\n    Index _rows, Index _cols, Index _depth, \\\n    const EIGTYPE* _lhs, Index lhsStride, \\\n    const EIGTYPE* _rhs, Index rhsStride, \\\n    EIGTYPE* res,        Index resStride, \\\n    EIGTYPE alpha, level3_blocking<EIGTYPE,EIGTYPE>& blocking) \\\n  { \\\n   Index diagSize  = (std::min)(_rows,_depth); \\\n   Index rows      = IsLower ? _rows : diagSize; \\\n   Index depth     = IsLower ? diagSize : _depth; \\\n   Index cols      = _cols; \\\n\\\n   typedef Matrix<EIGTYPE, Dynamic, Dynamic, LhsStorageOrder> MatrixLhs; \\\n   typedef Matrix<EIGTYPE, Dynamic, Dynamic, RhsStorageOrder> MatrixRhs; \\\n\\\n/* Non-square case - doesn't fit to BLAS ?TRMM. Fall to default triangular product or call BLAS ?GEMM*/ \\\n   if (rows != depth) { \\\n\\\n     /* FIXME handle mkl_domain_get_max_threads */ \\\n     /*int nthr = mkl_domain_get_max_threads(EIGEN_BLAS_DOMAIN_BLAS);*/ int nthr = 1;\\\n\\\n     if (((nthr==1) && (((std::max)(rows,depth)-diagSize)/(double)diagSize < 0.5))) { \\\n     /* Most likely no benefit to call TRMM or GEMM from BLAS */ \\\n       product_triangular_matrix_matrix<EIGTYPE,Index,Mode,true, \\\n       LhsStorageOrder,ConjugateLhs, RhsStorageOrder, ConjugateRhs, ColMajor, BuiltIn>::run( \\\n           _rows, _cols, _depth, _lhs, lhsStride, _rhs, rhsStride, res, resStride, alpha, blocking); \\\n     /*std::cout << \"TRMM_L: A is not square! Go to Eigen TRMM implementation!\\n\";*/ \\\n     } else { \\\n     /* Make sense to call GEMM */ \\\n       Map<const MatrixLhs, 0, OuterStride<> > lhsMap(_lhs,rows,depth,OuterStride<>(lhsStride)); \\\n       MatrixLhs aa_tmp=lhsMap.template triangularView<Mode>(); \\\n       BlasIndex aStride = convert_index<BlasIndex>(aa_tmp.outerStride()); \\\n       gemm_blocking_space<ColMajor,EIGTYPE,EIGTYPE,Dynamic,Dynamic,Dynamic> gemm_blocking(_rows,_cols,_depth, 1, true); \\\n       general_matrix_matrix_product<Index,EIGTYPE,LhsStorageOrder,ConjugateLhs,EIGTYPE,RhsStorageOrder,ConjugateRhs,ColMajor>::run( \\\n       rows, cols, depth, aa_tmp.data(), aStride, _rhs, rhsStride, res, resStride, alpha, gemm_blocking, 0); \\\n\\\n     /*std::cout << \"TRMM_L: A is not square! Go to BLAS GEMM implementation! \" << nthr<<\" \\n\";*/ \\\n     } \\\n     return; \\\n   } \\\n   char side = 'L', transa, uplo, diag = 'N'; \\\n   EIGTYPE *b; \\\n   const EIGTYPE *a; \\\n   BlasIndex m, n, lda, ldb; \\\n\\\n/* Set m, n */ \\\n   m = convert_index<BlasIndex>(diagSize); \\\n   n = convert_index<BlasIndex>(cols); \\\n\\\n/* Set trans */ \\\n   transa = (LhsStorageOrder==RowMajor) ? ((ConjugateLhs) ? 'C' : 'T') : 'N'; \\\n\\\n/* Set b, ldb */ \\\n   Map<const MatrixRhs, 0, OuterStride<> > rhs(_rhs,depth,cols,OuterStride<>(rhsStride)); \\\n   MatrixX##EIGPREFIX b_tmp; \\\n\\\n   if (ConjugateRhs) b_tmp = rhs.conjugate(); else b_tmp = rhs; \\\n   b = b_tmp.data(); \\\n   ldb = convert_index<BlasIndex>(b_tmp.outerStride()); \\\n\\\n/* Set uplo */ \\\n   uplo = IsLower ? 'L' : 'U'; \\\n   if (LhsStorageOrder==RowMajor) uplo = (uplo == 'L') ? 'U' : 'L'; \\\n/* Set a, lda */ \\\n   Map<const MatrixLhs, 0, OuterStride<> > lhs(_lhs,rows,depth,OuterStride<>(lhsStride)); \\\n   MatrixLhs a_tmp; \\\n\\\n   if ((conjA!=0) || (SetDiag==0)) { \\\n     if (conjA) a_tmp = lhs.conjugate(); else a_tmp = lhs; \\\n     if (IsZeroDiag) \\\n       a_tmp.diagonal().setZero(); \\\n     else if (IsUnitDiag) \\\n       a_tmp.diagonal().setOnes();\\\n     a = a_tmp.data(); \\\n     lda = convert_index<BlasIndex>(a_tmp.outerStride()); \\\n   } else { \\\n     a = _lhs; \\\n     lda = convert_index<BlasIndex>(lhsStride); \\\n   } \\\n   /*std::cout << \"TRMM_L: A is square! Go to BLAS TRMM implementation! \\n\";*/ \\\n/* call ?trmm*/ \\\n   BLASFUNC(&side, &uplo, &transa, &diag, &m, &n, (const BLASTYPE*)&numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (BLASTYPE*)b, &ldb); \\\n\\\n/* Add op(a_triangular)*b into res*/ \\\n   Map<MatrixX##EIGPREFIX, 0, OuterStride<> > res_tmp(res,rows,cols,OuterStride<>(resStride)); \\\n   res_tmp=res_tmp+b_tmp; \\\n  } \\\n};\n\n#ifdef EIGEN_USE_MKL\nEIGEN_BLAS_TRMM_L(double, double, d, dtrmm)\nEIGEN_BLAS_TRMM_L(dcomplex, MKL_Complex16, cd, ztrmm)\nEIGEN_BLAS_TRMM_L(float, float, f, strmm)\nEIGEN_BLAS_TRMM_L(scomplex, MKL_Complex8, cf, ctrmm)\n#else\nEIGEN_BLAS_TRMM_L(double, double, d, dtrmm_)\nEIGEN_BLAS_TRMM_L(dcomplex, double, cd, ztrmm_)\nEIGEN_BLAS_TRMM_L(float, float, f, strmm_)\nEIGEN_BLAS_TRMM_L(scomplex, float, cf, ctrmm_)\n#endif\n\n// implements col-major += alpha * op(general) * op(triangular)\n#define EIGEN_BLAS_TRMM_R(EIGTYPE, BLASTYPE, EIGPREFIX, BLASFUNC) \\\ntemplate <typename Index, int Mode, \\\n          int LhsStorageOrder, bool ConjugateLhs, \\\n          int RhsStorageOrder, bool ConjugateRhs> \\\nstruct product_triangular_matrix_matrix_trmm<EIGTYPE,Index,Mode,false, \\\n         LhsStorageOrder,ConjugateLhs,RhsStorageOrder,ConjugateRhs,ColMajor> \\\n{ \\\n  enum { \\\n    IsLower = (Mode&Lower) == Lower, \\\n    SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1, \\\n    IsUnitDiag  = (Mode&UnitDiag) ? 1 : 0, \\\n    IsZeroDiag  = (Mode&ZeroDiag) ? 1 : 0, \\\n    LowUp = IsLower ? Lower : Upper, \\\n    conjA = ((RhsStorageOrder==ColMajor) && ConjugateRhs) ? 1 : 0 \\\n  }; \\\n\\\n  static void run( \\\n    Index _rows, Index _cols, Index _depth, \\\n    const EIGTYPE* _lhs, Index lhsStride, \\\n    const EIGTYPE* _rhs, Index rhsStride, \\\n    EIGTYPE* res,        Index resStride, \\\n    EIGTYPE alpha, level3_blocking<EIGTYPE,EIGTYPE>& blocking) \\\n  { \\\n   Index diagSize  = (std::min)(_cols,_depth); \\\n   Index rows      = _rows; \\\n   Index depth     = IsLower ? _depth : diagSize; \\\n   Index cols      = IsLower ? diagSize : _cols; \\\n\\\n   typedef Matrix<EIGTYPE, Dynamic, Dynamic, LhsStorageOrder> MatrixLhs; \\\n   typedef Matrix<EIGTYPE, Dynamic, Dynamic, RhsStorageOrder> MatrixRhs; \\\n\\\n/* Non-square case - doesn't fit to BLAS ?TRMM. Fall to default triangular product or call BLAS ?GEMM*/ \\\n   if (cols != depth) { \\\n\\\n     int nthr = 1 /*mkl_domain_get_max_threads(EIGEN_BLAS_DOMAIN_BLAS)*/; \\\n\\\n     if ((nthr==1) && (((std::max)(cols,depth)-diagSize)/(double)diagSize < 0.5)) { \\\n     /* Most likely no benefit to call TRMM or GEMM from BLAS*/ \\\n       product_triangular_matrix_matrix<EIGTYPE,Index,Mode,false, \\\n       LhsStorageOrder,ConjugateLhs, RhsStorageOrder, ConjugateRhs, ColMajor, BuiltIn>::run( \\\n           _rows, _cols, _depth, _lhs, lhsStride, _rhs, rhsStride, res, resStride, alpha, blocking); \\\n       /*std::cout << \"TRMM_R: A is not square! Go to Eigen TRMM implementation!\\n\";*/ \\\n     } else { \\\n     /* Make sense to call GEMM */ \\\n       Map<const MatrixRhs, 0, OuterStride<> > rhsMap(_rhs,depth,cols, OuterStride<>(rhsStride)); \\\n       MatrixRhs aa_tmp=rhsMap.template triangularView<Mode>(); \\\n       BlasIndex aStride = convert_index<BlasIndex>(aa_tmp.outerStride()); \\\n       gemm_blocking_space<ColMajor,EIGTYPE,EIGTYPE,Dynamic,Dynamic,Dynamic> gemm_blocking(_rows,_cols,_depth, 1, true); \\\n       general_matrix_matrix_product<Index,EIGTYPE,LhsStorageOrder,ConjugateLhs,EIGTYPE,RhsStorageOrder,ConjugateRhs,ColMajor>::run( \\\n       rows, cols, depth, _lhs, lhsStride, aa_tmp.data(), aStride, res, resStride, alpha, gemm_blocking, 0); \\\n\\\n     /*std::cout << \"TRMM_R: A is not square! Go to BLAS GEMM implementation! \" << nthr<<\" \\n\";*/ \\\n     } \\\n     return; \\\n   } \\\n   char side = 'R', transa, uplo, diag = 'N'; \\\n   EIGTYPE *b; \\\n   const EIGTYPE *a; \\\n   BlasIndex m, n, lda, ldb; \\\n\\\n/* Set m, n */ \\\n   m = convert_index<BlasIndex>(rows); \\\n   n = convert_index<BlasIndex>(diagSize); \\\n\\\n/* Set trans */ \\\n   transa = (RhsStorageOrder==RowMajor) ? ((ConjugateRhs) ? 'C' : 'T') : 'N'; \\\n\\\n/* Set b, ldb */ \\\n   Map<const MatrixLhs, 0, OuterStride<> > lhs(_lhs,rows,depth,OuterStride<>(lhsStride)); \\\n   MatrixX##EIGPREFIX b_tmp; \\\n\\\n   if (ConjugateLhs) b_tmp = lhs.conjugate(); else b_tmp = lhs; \\\n   b = b_tmp.data(); \\\n   ldb = convert_index<BlasIndex>(b_tmp.outerStride()); \\\n\\\n/* Set uplo */ \\\n   uplo = IsLower ? 'L' : 'U'; \\\n   if (RhsStorageOrder==RowMajor) uplo = (uplo == 'L') ? 'U' : 'L'; \\\n/* Set a, lda */ \\\n   Map<const MatrixRhs, 0, OuterStride<> > rhs(_rhs,depth,cols, OuterStride<>(rhsStride)); \\\n   MatrixRhs a_tmp; \\\n\\\n   if ((conjA!=0) || (SetDiag==0)) { \\\n     if (conjA) a_tmp = rhs.conjugate(); else a_tmp = rhs; \\\n     if (IsZeroDiag) \\\n       a_tmp.diagonal().setZero(); \\\n     else if (IsUnitDiag) \\\n       a_tmp.diagonal().setOnes();\\\n     a = a_tmp.data(); \\\n     lda = convert_index<BlasIndex>(a_tmp.outerStride()); \\\n   } else { \\\n     a = _rhs; \\\n     lda = convert_index<BlasIndex>(rhsStride); \\\n   } \\\n   /*std::cout << \"TRMM_R: A is square! Go to BLAS TRMM implementation! \\n\";*/ \\\n/* call ?trmm*/ \\\n   BLASFUNC(&side, &uplo, &transa, &diag, &m, &n, (const BLASTYPE*)&numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (BLASTYPE*)b, &ldb); \\\n\\\n/* Add op(a_triangular)*b into res*/ \\\n   Map<MatrixX##EIGPREFIX, 0, OuterStride<> > res_tmp(res,rows,cols,OuterStride<>(resStride)); \\\n   res_tmp=res_tmp+b_tmp; \\\n  } \\\n};\n\n#ifdef EIGEN_USE_MKL\nEIGEN_BLAS_TRMM_R(double, double, d, dtrmm)\nEIGEN_BLAS_TRMM_R(dcomplex, MKL_Complex16, cd, ztrmm)\nEIGEN_BLAS_TRMM_R(float, float, f, strmm)\nEIGEN_BLAS_TRMM_R(scomplex, MKL_Complex8, cf, ctrmm)\n#else\nEIGEN_BLAS_TRMM_R(double, double, d, dtrmm_)\nEIGEN_BLAS_TRMM_R(dcomplex, double, cd, ztrmm_)\nEIGEN_BLAS_TRMM_R(float, float, f, strmm_)\nEIGEN_BLAS_TRMM_R(scomplex, float, cf, ctrmm_)\n#endif\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_TRIANGULAR_MATRIX_MATRIX_BLAS_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/products/TriangularMatrixVector.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_TRIANGULARMATRIXVECTOR_H\n#define EIGEN_TRIANGULARMATRIXVECTOR_H\n\nnamespace Eigen {\n\nnamespace internal {\n\ntemplate<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, bool ConjRhs, int StorageOrder, int Version=Specialized>\nstruct triangular_matrix_vector_product;\n\ntemplate<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, bool ConjRhs, int Version>\nstruct triangular_matrix_vector_product<Index,Mode,LhsScalar,ConjLhs,RhsScalar,ConjRhs,ColMajor,Version>\n{\n  typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;\n  enum {\n    IsLower = ((Mode&Lower)==Lower),\n    HasUnitDiag = (Mode & UnitDiag)==UnitDiag,\n    HasZeroDiag = (Mode & ZeroDiag)==ZeroDiag\n  };\n  static EIGEN_DONT_INLINE  void run(Index _rows, Index _cols, const LhsScalar* _lhs, Index lhsStride,\n                                     const RhsScalar* _rhs, Index rhsIncr, ResScalar* _res, Index resIncr, const RhsScalar& alpha);\n};\n\ntemplate<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, bool ConjRhs, int Version>\nEIGEN_DONT_INLINE void triangular_matrix_vector_product<Index,Mode,LhsScalar,ConjLhs,RhsScalar,ConjRhs,ColMajor,Version>\n  ::run(Index _rows, Index _cols, const LhsScalar* _lhs, Index lhsStride,\n        const RhsScalar* _rhs, Index rhsIncr, ResScalar* _res, Index resIncr, const RhsScalar& alpha)\n  {\n    static const Index PanelWidth = EIGEN_TUNE_TRIANGULAR_PANEL_WIDTH;\n    Index size = (std::min)(_rows,_cols);\n    Index rows = IsLower ? _rows : (std::min)(_rows,_cols);\n    Index cols = IsLower ? (std::min)(_rows,_cols) : _cols;\n\n    typedef Map<const Matrix<LhsScalar,Dynamic,Dynamic,ColMajor>, 0, OuterStride<> > LhsMap;\n    const LhsMap lhs(_lhs,rows,cols,OuterStride<>(lhsStride));\n    typename conj_expr_if<ConjLhs,LhsMap>::type cjLhs(lhs);\n\n    typedef Map<const Matrix<RhsScalar,Dynamic,1>, 0, InnerStride<> > RhsMap;\n    const RhsMap rhs(_rhs,cols,InnerStride<>(rhsIncr));\n    typename conj_expr_if<ConjRhs,RhsMap>::type cjRhs(rhs);\n\n    typedef Map<Matrix<ResScalar,Dynamic,1> > ResMap;\n    ResMap res(_res,rows);\n\n    typedef const_blas_data_mapper<LhsScalar,Index,ColMajor> LhsMapper;\n    typedef const_blas_data_mapper<RhsScalar,Index,RowMajor> RhsMapper;\n\n    for (Index pi=0; pi<size; pi+=PanelWidth)\n    {\n      Index actualPanelWidth = (std::min)(PanelWidth, size-pi);\n      for (Index k=0; k<actualPanelWidth; ++k)\n      {\n        Index i = pi + k;\n        Index s = IsLower ? ((HasUnitDiag||HasZeroDiag) ? i+1 : i ) : pi;\n        Index r = IsLower ? actualPanelWidth-k : k+1;\n        if ((!(HasUnitDiag||HasZeroDiag)) || (--r)>0)\n          res.segment(s,r) += (alpha * cjRhs.coeff(i)) * cjLhs.col(i).segment(s,r);\n        if (HasUnitDiag)\n          res.coeffRef(i) += alpha * cjRhs.coeff(i);\n      }\n      Index r = IsLower ? rows - pi - actualPanelWidth : pi;\n      if (r>0)\n      {\n        Index s = IsLower ? pi+actualPanelWidth : 0;\n        general_matrix_vector_product<Index,LhsScalar,LhsMapper,ColMajor,ConjLhs,RhsScalar,RhsMapper,ConjRhs,BuiltIn>::run(\n            r, actualPanelWidth,\n            LhsMapper(&lhs.coeffRef(s,pi), lhsStride),\n            RhsMapper(&rhs.coeffRef(pi), rhsIncr),\n            &res.coeffRef(s), resIncr, alpha);\n      }\n    }\n    if((!IsLower) && cols>size)\n    {\n      general_matrix_vector_product<Index,LhsScalar,LhsMapper,ColMajor,ConjLhs,RhsScalar,RhsMapper,ConjRhs>::run(\n          rows, cols-size,\n          LhsMapper(&lhs.coeffRef(0,size), lhsStride),\n          RhsMapper(&rhs.coeffRef(size), rhsIncr),\n          _res, resIncr, alpha);\n    }\n  }\n\ntemplate<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, bool ConjRhs,int Version>\nstruct triangular_matrix_vector_product<Index,Mode,LhsScalar,ConjLhs,RhsScalar,ConjRhs,RowMajor,Version>\n{\n  typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;\n  enum {\n    IsLower = ((Mode&Lower)==Lower),\n    HasUnitDiag = (Mode & UnitDiag)==UnitDiag,\n    HasZeroDiag = (Mode & ZeroDiag)==ZeroDiag\n  };\n  static EIGEN_DONT_INLINE void run(Index _rows, Index _cols, const LhsScalar* _lhs, Index lhsStride,\n                                    const RhsScalar* _rhs, Index rhsIncr, ResScalar* _res, Index resIncr, const ResScalar& alpha);\n};\n\ntemplate<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, bool ConjRhs,int Version>\nEIGEN_DONT_INLINE void triangular_matrix_vector_product<Index,Mode,LhsScalar,ConjLhs,RhsScalar,ConjRhs,RowMajor,Version>\n  ::run(Index _rows, Index _cols, const LhsScalar* _lhs, Index lhsStride,\n        const RhsScalar* _rhs, Index rhsIncr, ResScalar* _res, Index resIncr, const ResScalar& alpha)\n  {\n    static const Index PanelWidth = EIGEN_TUNE_TRIANGULAR_PANEL_WIDTH;\n    Index diagSize = (std::min)(_rows,_cols);\n    Index rows = IsLower ? _rows : diagSize;\n    Index cols = IsLower ? diagSize : _cols;\n\n    typedef Map<const Matrix<LhsScalar,Dynamic,Dynamic,RowMajor>, 0, OuterStride<> > LhsMap;\n    const LhsMap lhs(_lhs,rows,cols,OuterStride<>(lhsStride));\n    typename conj_expr_if<ConjLhs,LhsMap>::type cjLhs(lhs);\n\n    typedef Map<const Matrix<RhsScalar,Dynamic,1> > RhsMap;\n    const RhsMap rhs(_rhs,cols);\n    typename conj_expr_if<ConjRhs,RhsMap>::type cjRhs(rhs);\n\n    typedef Map<Matrix<ResScalar,Dynamic,1>, 0, InnerStride<> > ResMap;\n    ResMap res(_res,rows,InnerStride<>(resIncr));\n\n    typedef const_blas_data_mapper<LhsScalar,Index,RowMajor> LhsMapper;\n    typedef const_blas_data_mapper<RhsScalar,Index,RowMajor> RhsMapper;\n\n    for (Index pi=0; pi<diagSize; pi+=PanelWidth)\n    {\n      Index actualPanelWidth = (std::min)(PanelWidth, diagSize-pi);\n      for (Index k=0; k<actualPanelWidth; ++k)\n      {\n        Index i = pi + k;\n        Index s = IsLower ? pi  : ((HasUnitDiag||HasZeroDiag) ? i+1 : i);\n        Index r = IsLower ? k+1 : actualPanelWidth-k;\n        if ((!(HasUnitDiag||HasZeroDiag)) || (--r)>0)\n          res.coeffRef(i) += alpha * (cjLhs.row(i).segment(s,r).cwiseProduct(cjRhs.segment(s,r).transpose())).sum();\n        if (HasUnitDiag)\n          res.coeffRef(i) += alpha * cjRhs.coeff(i);\n      }\n      Index r = IsLower ? pi : cols - pi - actualPanelWidth;\n      if (r>0)\n      {\n        Index s = IsLower ? 0 : pi + actualPanelWidth;\n        general_matrix_vector_product<Index,LhsScalar,LhsMapper,RowMajor,ConjLhs,RhsScalar,RhsMapper,ConjRhs,BuiltIn>::run(\n            actualPanelWidth, r,\n            LhsMapper(&lhs.coeffRef(pi,s), lhsStride),\n            RhsMapper(&rhs.coeffRef(s), rhsIncr),\n            &res.coeffRef(pi), resIncr, alpha);\n      }\n    }\n    if(IsLower && rows>diagSize)\n    {\n      general_matrix_vector_product<Index,LhsScalar,LhsMapper,RowMajor,ConjLhs,RhsScalar,RhsMapper,ConjRhs>::run(\n            rows-diagSize, cols,\n            LhsMapper(&lhs.coeffRef(diagSize,0), lhsStride),\n            RhsMapper(&rhs.coeffRef(0), rhsIncr),\n            &res.coeffRef(diagSize), resIncr, alpha);\n    }\n  }\n\n/***************************************************************************\n* Wrapper to product_triangular_vector\n***************************************************************************/\n\ntemplate<int Mode,int StorageOrder>\nstruct trmv_selector;\n\n} // end namespace internal\n\nnamespace internal {\n\ntemplate<int Mode, typename Lhs, typename Rhs>\nstruct triangular_product_impl<Mode,true,Lhs,false,Rhs,true>\n{\n  template<typename Dest> static void run(Dest& dst, const Lhs &lhs, const Rhs &rhs, const typename Dest::Scalar& alpha)\n  {\n    eigen_assert(dst.rows()==lhs.rows() && dst.cols()==rhs.cols());\n  \n    internal::trmv_selector<Mode,(int(internal::traits<Lhs>::Flags)&RowMajorBit) ? RowMajor : ColMajor>::run(lhs, rhs, dst, alpha);\n  }\n};\n\ntemplate<int Mode, typename Lhs, typename Rhs>\nstruct triangular_product_impl<Mode,false,Lhs,true,Rhs,false>\n{\n  template<typename Dest> static void run(Dest& dst, const Lhs &lhs, const Rhs &rhs, const typename Dest::Scalar& alpha)\n  {\n    eigen_assert(dst.rows()==lhs.rows() && dst.cols()==rhs.cols());\n\n    Transpose<Dest> dstT(dst);\n    internal::trmv_selector<(Mode & (UnitDiag|ZeroDiag)) | ((Mode & Lower) ? Upper : Lower),\n                            (int(internal::traits<Rhs>::Flags)&RowMajorBit) ? ColMajor : RowMajor>\n            ::run(rhs.transpose(),lhs.transpose(), dstT, alpha);\n  }\n};\n\n} // end namespace internal\n\nnamespace internal {\n\n// TODO: find a way to factorize this piece of code with gemv_selector since the logic is exactly the same.\n  \ntemplate<int Mode> struct trmv_selector<Mode,ColMajor>\n{\n  template<typename Lhs, typename Rhs, typename Dest>\n  static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)\n  {\n    typedef typename Lhs::Scalar      LhsScalar;\n    typedef typename Rhs::Scalar      RhsScalar;\n    typedef typename Dest::Scalar     ResScalar;\n    typedef typename Dest::RealScalar RealScalar;\n    \n    typedef internal::blas_traits<Lhs> LhsBlasTraits;\n    typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;\n    typedef internal::blas_traits<Rhs> RhsBlasTraits;\n    typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;\n    \n    typedef Map<Matrix<ResScalar,Dynamic,1>, EIGEN_PLAIN_ENUM_MIN(AlignedMax,internal::packet_traits<ResScalar>::size)> MappedDest;\n\n    typename internal::add_const_on_value_type<ActualLhsType>::type actualLhs = LhsBlasTraits::extract(lhs);\n    typename internal::add_const_on_value_type<ActualRhsType>::type actualRhs = RhsBlasTraits::extract(rhs);\n\n    LhsScalar lhs_alpha = LhsBlasTraits::extractScalarFactor(lhs);\n    RhsScalar rhs_alpha = RhsBlasTraits::extractScalarFactor(rhs);\n    ResScalar actualAlpha = alpha * lhs_alpha * rhs_alpha;\n\n    enum {\n      // FIXME find a way to allow an inner stride on the result if packet_traits<Scalar>::size==1\n      // on, the other hand it is good for the cache to pack the vector anyways...\n      EvalToDestAtCompileTime = Dest::InnerStrideAtCompileTime==1,\n      ComplexByReal = (NumTraits<LhsScalar>::IsComplex) && (!NumTraits<RhsScalar>::IsComplex),\n      MightCannotUseDest = (Dest::InnerStrideAtCompileTime!=1) || ComplexByReal\n    };\n\n    gemv_static_vector_if<ResScalar,Dest::SizeAtCompileTime,Dest::MaxSizeAtCompileTime,MightCannotUseDest> static_dest;\n\n    bool alphaIsCompatible = (!ComplexByReal) || (numext::imag(actualAlpha)==RealScalar(0));\n    bool evalToDest = EvalToDestAtCompileTime && alphaIsCompatible;\n\n    RhsScalar compatibleAlpha = get_factor<ResScalar,RhsScalar>::run(actualAlpha);\n\n    ei_declare_aligned_stack_constructed_variable(ResScalar,actualDestPtr,dest.size(),\n                                                  evalToDest ? dest.data() : static_dest.data());\n\n    if(!evalToDest)\n    {\n      #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN\n      Index size = dest.size();\n      EIGEN_DENSE_STORAGE_CTOR_PLUGIN\n      #endif\n      if(!alphaIsCompatible)\n      {\n        MappedDest(actualDestPtr, dest.size()).setZero();\n        compatibleAlpha = RhsScalar(1);\n      }\n      else\n        MappedDest(actualDestPtr, dest.size()) = dest;\n    }\n\n    internal::triangular_matrix_vector_product\n      <Index,Mode,\n       LhsScalar, LhsBlasTraits::NeedToConjugate,\n       RhsScalar, RhsBlasTraits::NeedToConjugate,\n       ColMajor>\n      ::run(actualLhs.rows(),actualLhs.cols(),\n            actualLhs.data(),actualLhs.outerStride(),\n            actualRhs.data(),actualRhs.innerStride(),\n            actualDestPtr,1,compatibleAlpha);\n\n    if (!evalToDest)\n    {\n      if(!alphaIsCompatible)\n        dest += actualAlpha * MappedDest(actualDestPtr, dest.size());\n      else\n        dest = MappedDest(actualDestPtr, dest.size());\n    }\n\n    if ( ((Mode&UnitDiag)==UnitDiag) && (lhs_alpha!=LhsScalar(1)) )\n    {\n      Index diagSize = (std::min)(lhs.rows(),lhs.cols());\n      dest.head(diagSize) -= (lhs_alpha-LhsScalar(1))*rhs.head(diagSize);\n    }\n  }\n};\n\ntemplate<int Mode> struct trmv_selector<Mode,RowMajor>\n{\n  template<typename Lhs, typename Rhs, typename Dest>\n  static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)\n  {\n    typedef typename Lhs::Scalar      LhsScalar;\n    typedef typename Rhs::Scalar      RhsScalar;\n    typedef typename Dest::Scalar     ResScalar;\n    \n    typedef internal::blas_traits<Lhs> LhsBlasTraits;\n    typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;\n    typedef internal::blas_traits<Rhs> RhsBlasTraits;\n    typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;\n    typedef typename internal::remove_all<ActualRhsType>::type ActualRhsTypeCleaned;\n\n    typename add_const<ActualLhsType>::type actualLhs = LhsBlasTraits::extract(lhs);\n    typename add_const<ActualRhsType>::type actualRhs = RhsBlasTraits::extract(rhs);\n\n    LhsScalar lhs_alpha = LhsBlasTraits::extractScalarFactor(lhs);\n    RhsScalar rhs_alpha = RhsBlasTraits::extractScalarFactor(rhs);\n    ResScalar actualAlpha = alpha * lhs_alpha * rhs_alpha;\n\n    enum {\n      DirectlyUseRhs = ActualRhsTypeCleaned::InnerStrideAtCompileTime==1\n    };\n\n    gemv_static_vector_if<RhsScalar,ActualRhsTypeCleaned::SizeAtCompileTime,ActualRhsTypeCleaned::MaxSizeAtCompileTime,!DirectlyUseRhs> static_rhs;\n\n    ei_declare_aligned_stack_constructed_variable(RhsScalar,actualRhsPtr,actualRhs.size(),\n        DirectlyUseRhs ? const_cast<RhsScalar*>(actualRhs.data()) : static_rhs.data());\n\n    if(!DirectlyUseRhs)\n    {\n      #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN\n      Index size = actualRhs.size();\n      EIGEN_DENSE_STORAGE_CTOR_PLUGIN\n      #endif\n      Map<typename ActualRhsTypeCleaned::PlainObject>(actualRhsPtr, actualRhs.size()) = actualRhs;\n    }\n\n    internal::triangular_matrix_vector_product\n      <Index,Mode,\n       LhsScalar, LhsBlasTraits::NeedToConjugate,\n       RhsScalar, RhsBlasTraits::NeedToConjugate,\n       RowMajor>\n      ::run(actualLhs.rows(),actualLhs.cols(),\n            actualLhs.data(),actualLhs.outerStride(),\n            actualRhsPtr,1,\n            dest.data(),dest.innerStride(),\n            actualAlpha);\n\n    if ( ((Mode&UnitDiag)==UnitDiag) && (lhs_alpha!=LhsScalar(1)) )\n    {\n      Index diagSize = (std::min)(lhs.rows(),lhs.cols());\n      dest.head(diagSize) -= (lhs_alpha-LhsScalar(1))*rhs.head(diagSize);\n    }\n  }\n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_TRIANGULARMATRIXVECTOR_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/products/TriangularMatrixVector_BLAS.h",
    "content": "/*\n Copyright (c) 2011, Intel Corporation. All rights reserved.\n\n Redistribution and use in source and binary forms, with or without modification,\n are permitted provided that the following conditions are met:\n\n * Redistributions of source code must retain the above copyright notice, this\n   list of conditions and the following disclaimer.\n * Redistributions in binary form must reproduce the above copyright notice,\n   this list of conditions and the following disclaimer in the documentation\n   and/or other materials provided with the distribution.\n * Neither the name of Intel Corporation nor the names of its contributors may\n   be used to endorse or promote products derived from this software without\n   specific prior written permission.\n\n THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\" AND\n ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED\n WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\n DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR\n ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES\n (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;\n LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON\n ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT\n (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS\n SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n\n ********************************************************************************\n *   Content : Eigen bindings to BLAS F77\n *   Triangular matrix-vector product functionality based on ?TRMV.\n ********************************************************************************\n*/\n\n#ifndef EIGEN_TRIANGULAR_MATRIX_VECTOR_BLAS_H\n#define EIGEN_TRIANGULAR_MATRIX_VECTOR_BLAS_H\n\nnamespace Eigen { \n\nnamespace internal {\n\n/**********************************************************************\n* This file implements triangular matrix-vector multiplication using BLAS\n**********************************************************************/\n\n// trmv/hemv specialization\n\ntemplate<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, bool ConjRhs, int StorageOrder>\nstruct triangular_matrix_vector_product_trmv :\n  triangular_matrix_vector_product<Index,Mode,LhsScalar,ConjLhs,RhsScalar,ConjRhs,StorageOrder,BuiltIn> {};\n\n#define EIGEN_BLAS_TRMV_SPECIALIZE(Scalar) \\\ntemplate<typename Index, int Mode, bool ConjLhs, bool ConjRhs> \\\nstruct triangular_matrix_vector_product<Index,Mode,Scalar,ConjLhs,Scalar,ConjRhs,ColMajor,Specialized> { \\\n static void run(Index _rows, Index _cols, const Scalar* _lhs, Index lhsStride, \\\n                                     const Scalar* _rhs, Index rhsIncr, Scalar* _res, Index resIncr, Scalar alpha) { \\\n      triangular_matrix_vector_product_trmv<Index,Mode,Scalar,ConjLhs,Scalar,ConjRhs,ColMajor>::run( \\\n        _rows, _cols, _lhs, lhsStride, _rhs, rhsIncr, _res, resIncr, alpha); \\\n  } \\\n}; \\\ntemplate<typename Index, int Mode, bool ConjLhs, bool ConjRhs> \\\nstruct triangular_matrix_vector_product<Index,Mode,Scalar,ConjLhs,Scalar,ConjRhs,RowMajor,Specialized> { \\\n static void run(Index _rows, Index _cols, const Scalar* _lhs, Index lhsStride, \\\n                                     const Scalar* _rhs, Index rhsIncr, Scalar* _res, Index resIncr, Scalar alpha) { \\\n      triangular_matrix_vector_product_trmv<Index,Mode,Scalar,ConjLhs,Scalar,ConjRhs,RowMajor>::run( \\\n        _rows, _cols, _lhs, lhsStride, _rhs, rhsIncr, _res, resIncr, alpha); \\\n  } \\\n};\n\nEIGEN_BLAS_TRMV_SPECIALIZE(double)\nEIGEN_BLAS_TRMV_SPECIALIZE(float)\nEIGEN_BLAS_TRMV_SPECIALIZE(dcomplex)\nEIGEN_BLAS_TRMV_SPECIALIZE(scomplex)\n\n// implements col-major: res += alpha * op(triangular) * vector\n#define EIGEN_BLAS_TRMV_CM(EIGTYPE, BLASTYPE, EIGPREFIX, BLASPREFIX, BLASPOSTFIX) \\\ntemplate<typename Index, int Mode, bool ConjLhs, bool ConjRhs> \\\nstruct triangular_matrix_vector_product_trmv<Index,Mode,EIGTYPE,ConjLhs,EIGTYPE,ConjRhs,ColMajor> { \\\n  enum { \\\n    IsLower = (Mode&Lower) == Lower, \\\n    SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1, \\\n    IsUnitDiag  = (Mode&UnitDiag) ? 1 : 0, \\\n    IsZeroDiag  = (Mode&ZeroDiag) ? 1 : 0, \\\n    LowUp = IsLower ? Lower : Upper \\\n  }; \\\n static void run(Index _rows, Index _cols, const EIGTYPE* _lhs, Index lhsStride, \\\n                 const EIGTYPE* _rhs, Index rhsIncr, EIGTYPE* _res, Index resIncr, EIGTYPE alpha) \\\n { \\\n   if (ConjLhs || IsZeroDiag) { \\\n     triangular_matrix_vector_product<Index,Mode,EIGTYPE,ConjLhs,EIGTYPE,ConjRhs,ColMajor,BuiltIn>::run( \\\n       _rows, _cols, _lhs, lhsStride, _rhs, rhsIncr, _res, resIncr, alpha); \\\n     return; \\\n   }\\\n   Index size = (std::min)(_rows,_cols); \\\n   Index rows = IsLower ? _rows : size; \\\n   Index cols = IsLower ? size : _cols; \\\n\\\n   typedef VectorX##EIGPREFIX VectorRhs; \\\n   EIGTYPE *x, *y;\\\n\\\n/* Set x*/ \\\n   Map<const VectorRhs, 0, InnerStride<> > rhs(_rhs,cols,InnerStride<>(rhsIncr)); \\\n   VectorRhs x_tmp; \\\n   if (ConjRhs) x_tmp = rhs.conjugate(); else x_tmp = rhs; \\\n   x = x_tmp.data(); \\\n\\\n/* Square part handling */\\\n\\\n   char trans, uplo, diag; \\\n   BlasIndex m, n, lda, incx, incy; \\\n   EIGTYPE const *a; \\\n   EIGTYPE beta(1); \\\n\\\n/* Set m, n */ \\\n   n = convert_index<BlasIndex>(size); \\\n   lda = convert_index<BlasIndex>(lhsStride); \\\n   incx = 1; \\\n   incy = convert_index<BlasIndex>(resIncr); \\\n\\\n/* Set uplo, trans and diag*/ \\\n   trans = 'N'; \\\n   uplo = IsLower ? 'L' : 'U'; \\\n   diag = IsUnitDiag ? 'U' : 'N'; \\\n\\\n/* call ?TRMV*/ \\\n   BLASPREFIX##trmv##BLASPOSTFIX(&uplo, &trans, &diag, &n, (const BLASTYPE*)_lhs, &lda, (BLASTYPE*)x, &incx); \\\n\\\n/* Add op(a_tr)rhs into res*/ \\\n   BLASPREFIX##axpy##BLASPOSTFIX(&n, (const BLASTYPE*)&numext::real_ref(alpha),(const BLASTYPE*)x, &incx, (BLASTYPE*)_res, &incy); \\\n/* Non-square case - doesn't fit to BLAS ?TRMV. Fall to default triangular product*/ \\\n   if (size<(std::max)(rows,cols)) { \\\n     if (ConjRhs) x_tmp = rhs.conjugate(); else x_tmp = rhs; \\\n     x = x_tmp.data(); \\\n     if (size<rows) { \\\n       y = _res + size*resIncr; \\\n       a = _lhs + size; \\\n       m = convert_index<BlasIndex>(rows-size); \\\n       n = convert_index<BlasIndex>(size); \\\n     } \\\n     else { \\\n       x += size; \\\n       y = _res; \\\n       a = _lhs + size*lda; \\\n       m = convert_index<BlasIndex>(size); \\\n       n = convert_index<BlasIndex>(cols-size); \\\n     } \\\n     BLASPREFIX##gemv##BLASPOSTFIX(&trans, &m, &n, (const BLASTYPE*)&numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (const BLASTYPE*)x, &incx, (const BLASTYPE*)&numext::real_ref(beta), (BLASTYPE*)y, &incy); \\\n   } \\\n  } \\\n};\n\n#ifdef EIGEN_USE_MKL\nEIGEN_BLAS_TRMV_CM(double,   double, d,  d,)\nEIGEN_BLAS_TRMV_CM(dcomplex, MKL_Complex16, cd, z,)\nEIGEN_BLAS_TRMV_CM(float,    float,  f,  s,)\nEIGEN_BLAS_TRMV_CM(scomplex, MKL_Complex8,  cf, c,)\n#else\nEIGEN_BLAS_TRMV_CM(double,   double, d,  d, _)\nEIGEN_BLAS_TRMV_CM(dcomplex, double, cd, z, _)\nEIGEN_BLAS_TRMV_CM(float,    float,  f,  s, _)\nEIGEN_BLAS_TRMV_CM(scomplex, float,  cf, c, _)\n#endif\n\n// implements row-major: res += alpha * op(triangular) * vector\n#define EIGEN_BLAS_TRMV_RM(EIGTYPE, BLASTYPE, EIGPREFIX, BLASPREFIX, BLASPOSTFIX) \\\ntemplate<typename Index, int Mode, bool ConjLhs, bool ConjRhs> \\\nstruct triangular_matrix_vector_product_trmv<Index,Mode,EIGTYPE,ConjLhs,EIGTYPE,ConjRhs,RowMajor> { \\\n  enum { \\\n    IsLower = (Mode&Lower) == Lower, \\\n    SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1, \\\n    IsUnitDiag  = (Mode&UnitDiag) ? 1 : 0, \\\n    IsZeroDiag  = (Mode&ZeroDiag) ? 1 : 0, \\\n    LowUp = IsLower ? Lower : Upper \\\n  }; \\\n static void run(Index _rows, Index _cols, const EIGTYPE* _lhs, Index lhsStride, \\\n                 const EIGTYPE* _rhs, Index rhsIncr, EIGTYPE* _res, Index resIncr, EIGTYPE alpha) \\\n { \\\n   if (IsZeroDiag) { \\\n     triangular_matrix_vector_product<Index,Mode,EIGTYPE,ConjLhs,EIGTYPE,ConjRhs,RowMajor,BuiltIn>::run( \\\n       _rows, _cols, _lhs, lhsStride, _rhs, rhsIncr, _res, resIncr, alpha); \\\n     return; \\\n   }\\\n   Index size = (std::min)(_rows,_cols); \\\n   Index rows = IsLower ? _rows : size; \\\n   Index cols = IsLower ? size : _cols; \\\n\\\n   typedef VectorX##EIGPREFIX VectorRhs; \\\n   EIGTYPE *x, *y;\\\n\\\n/* Set x*/ \\\n   Map<const VectorRhs, 0, InnerStride<> > rhs(_rhs,cols,InnerStride<>(rhsIncr)); \\\n   VectorRhs x_tmp; \\\n   if (ConjRhs) x_tmp = rhs.conjugate(); else x_tmp = rhs; \\\n   x = x_tmp.data(); \\\n\\\n/* Square part handling */\\\n\\\n   char trans, uplo, diag; \\\n   BlasIndex m, n, lda, incx, incy; \\\n   EIGTYPE const *a; \\\n   EIGTYPE beta(1); \\\n\\\n/* Set m, n */ \\\n   n = convert_index<BlasIndex>(size); \\\n   lda = convert_index<BlasIndex>(lhsStride); \\\n   incx = 1; \\\n   incy = convert_index<BlasIndex>(resIncr); \\\n\\\n/* Set uplo, trans and diag*/ \\\n   trans = ConjLhs ? 'C' : 'T'; \\\n   uplo = IsLower ? 'U' : 'L'; \\\n   diag = IsUnitDiag ? 'U' : 'N'; \\\n\\\n/* call ?TRMV*/ \\\n   BLASPREFIX##trmv##BLASPOSTFIX(&uplo, &trans, &diag, &n, (const BLASTYPE*)_lhs, &lda, (BLASTYPE*)x, &incx); \\\n\\\n/* Add op(a_tr)rhs into res*/ \\\n   BLASPREFIX##axpy##BLASPOSTFIX(&n, (const BLASTYPE*)&numext::real_ref(alpha),(const BLASTYPE*)x, &incx, (BLASTYPE*)_res, &incy); \\\n/* Non-square case - doesn't fit to BLAS ?TRMV. Fall to default triangular product*/ \\\n   if (size<(std::max)(rows,cols)) { \\\n     if (ConjRhs) x_tmp = rhs.conjugate(); else x_tmp = rhs; \\\n     x = x_tmp.data(); \\\n     if (size<rows) { \\\n       y = _res + size*resIncr; \\\n       a = _lhs + size*lda; \\\n       m = convert_index<BlasIndex>(rows-size); \\\n       n = convert_index<BlasIndex>(size); \\\n     } \\\n     else { \\\n       x += size; \\\n       y = _res; \\\n       a = _lhs + size; \\\n       m = convert_index<BlasIndex>(size); \\\n       n = convert_index<BlasIndex>(cols-size); \\\n     } \\\n     BLASPREFIX##gemv##BLASPOSTFIX(&trans, &n, &m, (const BLASTYPE*)&numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (const BLASTYPE*)x, &incx, (const BLASTYPE*)&numext::real_ref(beta), (BLASTYPE*)y, &incy); \\\n   } \\\n  } \\\n};\n\n#ifdef EIGEN_USE_MKL\nEIGEN_BLAS_TRMV_RM(double,   double, d,  d,)\nEIGEN_BLAS_TRMV_RM(dcomplex, MKL_Complex16, cd, z,)\nEIGEN_BLAS_TRMV_RM(float,    float,  f,  s,)\nEIGEN_BLAS_TRMV_RM(scomplex, MKL_Complex8,  cf, c,)\n#else\nEIGEN_BLAS_TRMV_RM(double,   double, d,  d,_)\nEIGEN_BLAS_TRMV_RM(dcomplex, double, cd, z,_)\nEIGEN_BLAS_TRMV_RM(float,    float,  f,  s,_)\nEIGEN_BLAS_TRMV_RM(scomplex, float,  cf, c,_)\n#endif\n\n} // end namespase internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_TRIANGULAR_MATRIX_VECTOR_BLAS_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/products/TriangularSolverMatrix.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_TRIANGULAR_SOLVER_MATRIX_H\n#define EIGEN_TRIANGULAR_SOLVER_MATRIX_H\n\nnamespace Eigen { \n\nnamespace internal {\n\n// if the rhs is row major, let's transpose the product\ntemplate <typename Scalar, typename Index, int Side, int Mode, bool Conjugate, int TriStorageOrder>\nstruct triangular_solve_matrix<Scalar,Index,Side,Mode,Conjugate,TriStorageOrder,RowMajor>\n{\n  static void run(\n    Index size, Index cols,\n    const Scalar*  tri, Index triStride,\n    Scalar* _other, Index otherStride,\n    level3_blocking<Scalar,Scalar>& blocking)\n  {\n    triangular_solve_matrix<\n      Scalar, Index, Side==OnTheLeft?OnTheRight:OnTheLeft,\n      (Mode&UnitDiag) | ((Mode&Upper) ? Lower : Upper),\n      NumTraits<Scalar>::IsComplex && Conjugate,\n      TriStorageOrder==RowMajor ? ColMajor : RowMajor, ColMajor>\n      ::run(size, cols, tri, triStride, _other, otherStride, blocking);\n  }\n};\n\n/* Optimized triangular solver with multiple right hand side and the triangular matrix on the left\n */\ntemplate <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder>\nstruct triangular_solve_matrix<Scalar,Index,OnTheLeft,Mode,Conjugate,TriStorageOrder,ColMajor>\n{\n  static EIGEN_DONT_INLINE void run(\n    Index size, Index otherSize,\n    const Scalar* _tri, Index triStride,\n    Scalar* _other, Index otherStride,\n    level3_blocking<Scalar,Scalar>& blocking);\n};\ntemplate <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder>\nEIGEN_DONT_INLINE void triangular_solve_matrix<Scalar,Index,OnTheLeft,Mode,Conjugate,TriStorageOrder,ColMajor>::run(\n    Index size, Index otherSize,\n    const Scalar* _tri, Index triStride,\n    Scalar* _other, Index otherStride,\n    level3_blocking<Scalar,Scalar>& blocking)\n  {\n    Index cols = otherSize;\n\n    typedef const_blas_data_mapper<Scalar, Index, TriStorageOrder> TriMapper;\n    typedef blas_data_mapper<Scalar, Index, ColMajor> OtherMapper;\n    TriMapper tri(_tri, triStride);\n    OtherMapper other(_other, otherStride);\n\n    typedef gebp_traits<Scalar,Scalar> Traits;\n\n    enum {\n      SmallPanelWidth   = EIGEN_PLAIN_ENUM_MAX(Traits::mr,Traits::nr),\n      IsLower = (Mode&Lower) == Lower\n    };\n\n    Index kc = blocking.kc();                   // cache block size along the K direction\n    Index mc = (std::min)(size,blocking.mc());  // cache block size along the M direction\n\n    std::size_t sizeA = kc*mc;\n    std::size_t sizeB = kc*cols;\n\n    ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());\n    ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());\n\n    conj_if<Conjugate> conj;\n    gebp_kernel<Scalar, Scalar, Index, OtherMapper, Traits::mr, Traits::nr, Conjugate, false> gebp_kernel;\n    gemm_pack_lhs<Scalar, Index, TriMapper, Traits::mr, Traits::LhsProgress, TriStorageOrder> pack_lhs;\n    gemm_pack_rhs<Scalar, Index, OtherMapper, Traits::nr, ColMajor, false, true> pack_rhs;\n\n    // the goal here is to subdivise the Rhs panels such that we keep some cache\n    // coherence when accessing the rhs elements\n    std::ptrdiff_t l1, l2, l3;\n    manage_caching_sizes(GetAction, &l1, &l2, &l3);\n    Index subcols = cols>0 ? l2/(4 * sizeof(Scalar) * std::max<Index>(otherStride,size)) : 0;\n    subcols = std::max<Index>((subcols/Traits::nr)*Traits::nr, Traits::nr);\n\n    for(Index k2=IsLower ? 0 : size;\n        IsLower ? k2<size : k2>0;\n        IsLower ? k2+=kc : k2-=kc)\n    {\n      const Index actual_kc = (std::min)(IsLower ? size-k2 : k2, kc);\n\n      // We have selected and packed a big horizontal panel R1 of rhs. Let B be the packed copy of this panel,\n      // and R2 the remaining part of rhs. The corresponding vertical panel of lhs is split into\n      // A11 (the triangular part) and A21 the remaining rectangular part.\n      // Then the high level algorithm is:\n      //  - B = R1                    => general block copy (done during the next step)\n      //  - R1 = A11^-1 B             => tricky part\n      //  - update B from the new R1  => actually this has to be performed continuously during the above step\n      //  - R2 -= A21 * B             => GEPP\n\n      // The tricky part: compute R1 = A11^-1 B while updating B from R1\n      // The idea is to split A11 into multiple small vertical panels.\n      // Each panel can be split into a small triangular part T1k which is processed without optimization,\n      // and the remaining small part T2k which is processed using gebp with appropriate block strides\n      for(Index j2=0; j2<cols; j2+=subcols)\n      {\n        Index actual_cols = (std::min)(cols-j2,subcols);\n        // for each small vertical panels [T1k^T, T2k^T]^T of lhs\n        for (Index k1=0; k1<actual_kc; k1+=SmallPanelWidth)\n        {\n          Index actualPanelWidth = std::min<Index>(actual_kc-k1, SmallPanelWidth);\n          // tr solve\n          for (Index k=0; k<actualPanelWidth; ++k)\n          {\n            // TODO write a small kernel handling this (can be shared with trsv)\n            Index i  = IsLower ? k2+k1+k : k2-k1-k-1;\n            Index rs = actualPanelWidth - k - 1; // remaining size\n            Index s  = TriStorageOrder==RowMajor ? (IsLower ? k2+k1 : i+1)\n                                                 :  IsLower ? i+1 : i-rs;\n\n            Scalar a = (Mode & UnitDiag) ? Scalar(1) : Scalar(1)/conj(tri(i,i));\n            for (Index j=j2; j<j2+actual_cols; ++j)\n            {\n              if (TriStorageOrder==RowMajor)\n              {\n                Scalar b(0);\n                const Scalar* l = &tri(i,s);\n                Scalar* r = &other(s,j);\n                for (Index i3=0; i3<k; ++i3)\n                  b += conj(l[i3]) * r[i3];\n\n                other(i,j) = (other(i,j) - b)*a;\n              }\n              else\n              {\n                Scalar b = (other(i,j) *= a);\n                Scalar* r = &other(s,j);\n                const Scalar* l = &tri(s,i);\n                for (Index i3=0;i3<rs;++i3)\n                  r[i3] -= b * conj(l[i3]);\n              }\n            }\n          }\n\n          Index lengthTarget = actual_kc-k1-actualPanelWidth;\n          Index startBlock   = IsLower ? k2+k1 : k2-k1-actualPanelWidth;\n          Index blockBOffset = IsLower ? k1 : lengthTarget;\n\n          // update the respective rows of B from other\n          pack_rhs(blockB+actual_kc*j2, other.getSubMapper(startBlock,j2), actualPanelWidth, actual_cols, actual_kc, blockBOffset);\n\n          // GEBP\n          if (lengthTarget>0)\n          {\n            Index startTarget  = IsLower ? k2+k1+actualPanelWidth : k2-actual_kc;\n\n            pack_lhs(blockA, tri.getSubMapper(startTarget,startBlock), actualPanelWidth, lengthTarget);\n\n            gebp_kernel(other.getSubMapper(startTarget,j2), blockA, blockB+actual_kc*j2, lengthTarget, actualPanelWidth, actual_cols, Scalar(-1),\n                        actualPanelWidth, actual_kc, 0, blockBOffset);\n          }\n        }\n      }\n      \n      // R2 -= A21 * B => GEPP\n      {\n        Index start = IsLower ? k2+kc : 0;\n        Index end   = IsLower ? size : k2-kc;\n        for(Index i2=start; i2<end; i2+=mc)\n        {\n          const Index actual_mc = (std::min)(mc,end-i2);\n          if (actual_mc>0)\n          {\n            pack_lhs(blockA, tri.getSubMapper(i2, IsLower ? k2 : k2-kc), actual_kc, actual_mc);\n\n            gebp_kernel(other.getSubMapper(i2, 0), blockA, blockB, actual_mc, actual_kc, cols, Scalar(-1), -1, -1, 0, 0);\n          }\n        }\n      }\n    }\n  }\n\n/* Optimized triangular solver with multiple left hand sides and the triangular matrix on the right\n */\ntemplate <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder>\nstruct triangular_solve_matrix<Scalar,Index,OnTheRight,Mode,Conjugate,TriStorageOrder,ColMajor>\n{\n  static EIGEN_DONT_INLINE void run(\n    Index size, Index otherSize,\n    const Scalar* _tri, Index triStride,\n    Scalar* _other, Index otherStride,\n    level3_blocking<Scalar,Scalar>& blocking);\n};\ntemplate <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder>\nEIGEN_DONT_INLINE void triangular_solve_matrix<Scalar,Index,OnTheRight,Mode,Conjugate,TriStorageOrder,ColMajor>::run(\n    Index size, Index otherSize,\n    const Scalar* _tri, Index triStride,\n    Scalar* _other, Index otherStride,\n    level3_blocking<Scalar,Scalar>& blocking)\n  {\n    Index rows = otherSize;\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n\n    typedef blas_data_mapper<Scalar, Index, ColMajor> LhsMapper;\n    typedef const_blas_data_mapper<Scalar, Index, TriStorageOrder> RhsMapper;\n    LhsMapper lhs(_other, otherStride);\n    RhsMapper rhs(_tri, triStride);\n\n    typedef gebp_traits<Scalar,Scalar> Traits;\n    enum {\n      RhsStorageOrder   = TriStorageOrder,\n      SmallPanelWidth   = EIGEN_PLAIN_ENUM_MAX(Traits::mr,Traits::nr),\n      IsLower = (Mode&Lower) == Lower\n    };\n\n    Index kc = blocking.kc();                   // cache block size along the K direction\n    Index mc = (std::min)(rows,blocking.mc());  // cache block size along the M direction\n\n    std::size_t sizeA = kc*mc;\n    std::size_t sizeB = kc*size;\n\n    ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());\n    ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());\n\n    conj_if<Conjugate> conj;\n    gebp_kernel<Scalar, Scalar, Index, LhsMapper, Traits::mr, Traits::nr, false, Conjugate> gebp_kernel;\n    gemm_pack_rhs<Scalar, Index, RhsMapper, Traits::nr, RhsStorageOrder> pack_rhs;\n    gemm_pack_rhs<Scalar, Index, RhsMapper, Traits::nr, RhsStorageOrder,false,true> pack_rhs_panel;\n    gemm_pack_lhs<Scalar, Index, LhsMapper, Traits::mr, Traits::LhsProgress, ColMajor, false, true> pack_lhs_panel;\n\n    for(Index k2=IsLower ? size : 0;\n        IsLower ? k2>0 : k2<size;\n        IsLower ? k2-=kc : k2+=kc)\n    {\n      const Index actual_kc = (std::min)(IsLower ? k2 : size-k2, kc);\n      Index actual_k2 = IsLower ? k2-actual_kc : k2 ;\n\n      Index startPanel = IsLower ? 0 : k2+actual_kc;\n      Index rs = IsLower ? actual_k2 : size - actual_k2 - actual_kc;\n      Scalar* geb = blockB+actual_kc*actual_kc;\n\n      if (rs>0) pack_rhs(geb, rhs.getSubMapper(actual_k2,startPanel), actual_kc, rs);\n\n      // triangular packing (we only pack the panels off the diagonal,\n      // neglecting the blocks overlapping the diagonal\n      {\n        for (Index j2=0; j2<actual_kc; j2+=SmallPanelWidth)\n        {\n          Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth);\n          Index actual_j2 = actual_k2 + j2;\n          Index panelOffset = IsLower ? j2+actualPanelWidth : 0;\n          Index panelLength = IsLower ? actual_kc-j2-actualPanelWidth : j2;\n\n          if (panelLength>0)\n          pack_rhs_panel(blockB+j2*actual_kc,\n                         rhs.getSubMapper(actual_k2+panelOffset, actual_j2),\n                         panelLength, actualPanelWidth,\n                         actual_kc, panelOffset);\n        }\n      }\n\n      for(Index i2=0; i2<rows; i2+=mc)\n      {\n        const Index actual_mc = (std::min)(mc,rows-i2);\n\n        // triangular solver kernel\n        {\n          // for each small block of the diagonal (=> vertical panels of rhs)\n          for (Index j2 = IsLower\n                      ? (actual_kc - ((actual_kc%SmallPanelWidth) ? Index(actual_kc%SmallPanelWidth)\n                                                                  : Index(SmallPanelWidth)))\n                      : 0;\n               IsLower ? j2>=0 : j2<actual_kc;\n               IsLower ? j2-=SmallPanelWidth : j2+=SmallPanelWidth)\n          {\n            Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth);\n            Index absolute_j2 = actual_k2 + j2;\n            Index panelOffset = IsLower ? j2+actualPanelWidth : 0;\n            Index panelLength = IsLower ? actual_kc - j2 - actualPanelWidth : j2;\n\n            // GEBP\n            if(panelLength>0)\n            {\n              gebp_kernel(lhs.getSubMapper(i2,absolute_j2),\n                          blockA, blockB+j2*actual_kc,\n                          actual_mc, panelLength, actualPanelWidth,\n                          Scalar(-1),\n                          actual_kc, actual_kc, // strides\n                          panelOffset, panelOffset); // offsets\n            }\n\n            // unblocked triangular solve\n            for (Index k=0; k<actualPanelWidth; ++k)\n            {\n              Index j = IsLower ? absolute_j2+actualPanelWidth-k-1 : absolute_j2+k;\n\n              Scalar* r = &lhs(i2,j);\n              for (Index k3=0; k3<k; ++k3)\n              {\n                Scalar b = conj(rhs(IsLower ? j+1+k3 : absolute_j2+k3,j));\n                Scalar* a = &lhs(i2,IsLower ? j+1+k3 : absolute_j2+k3);\n                for (Index i=0; i<actual_mc; ++i)\n                  r[i] -= a[i] * b;\n              }\n              if((Mode & UnitDiag)==0)\n              {\n                Scalar inv_rjj = RealScalar(1)/conj(rhs(j,j));\n                for (Index i=0; i<actual_mc; ++i)\n                  r[i] *= inv_rjj;\n              }\n            }\n\n            // pack the just computed part of lhs to A\n            pack_lhs_panel(blockA, LhsMapper(_other+absolute_j2*otherStride+i2, otherStride),\n                           actualPanelWidth, actual_mc,\n                           actual_kc, j2);\n          }\n        }\n\n        if (rs>0)\n          gebp_kernel(lhs.getSubMapper(i2, startPanel), blockA, geb,\n                      actual_mc, actual_kc, rs, Scalar(-1),\n                      -1, -1, 0, 0);\n      }\n    }\n  }\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_TRIANGULAR_SOLVER_MATRIX_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/products/TriangularSolverMatrix_BLAS.h",
    "content": "/*\n Copyright (c) 2011, Intel Corporation. All rights reserved.\n\n Redistribution and use in source and binary forms, with or without modification,\n are permitted provided that the following conditions are met:\n\n * Redistributions of source code must retain the above copyright notice, this\n   list of conditions and the following disclaimer.\n * Redistributions in binary form must reproduce the above copyright notice,\n   this list of conditions and the following disclaimer in the documentation\n   and/or other materials provided with the distribution.\n * Neither the name of Intel Corporation nor the names of its contributors may\n   be used to endorse or promote products derived from this software without\n   specific prior written permission.\n\n THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\" AND\n ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED\n WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\n DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR\n ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES\n (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;\n LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON\n ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT\n (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS\n SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n\n ********************************************************************************\n *   Content : Eigen bindings to BLAS F77\n *   Triangular matrix * matrix product functionality based on ?TRMM.\n ********************************************************************************\n*/\n\n#ifndef EIGEN_TRIANGULAR_SOLVER_MATRIX_BLAS_H\n#define EIGEN_TRIANGULAR_SOLVER_MATRIX_BLAS_H\n\nnamespace Eigen {\n\nnamespace internal {\n\n// implements LeftSide op(triangular)^-1 * general\n#define EIGEN_BLAS_TRSM_L(EIGTYPE, BLASTYPE, BLASFUNC) \\\ntemplate <typename Index, int Mode, bool Conjugate, int TriStorageOrder> \\\nstruct triangular_solve_matrix<EIGTYPE,Index,OnTheLeft,Mode,Conjugate,TriStorageOrder,ColMajor> \\\n{ \\\n  enum { \\\n    IsLower = (Mode&Lower) == Lower, \\\n    IsUnitDiag  = (Mode&UnitDiag) ? 1 : 0, \\\n    IsZeroDiag  = (Mode&ZeroDiag) ? 1 : 0, \\\n    conjA = ((TriStorageOrder==ColMajor) && Conjugate) ? 1 : 0 \\\n  }; \\\n  static void run( \\\n      Index size, Index otherSize, \\\n      const EIGTYPE* _tri, Index triStride, \\\n      EIGTYPE* _other, Index otherStride, level3_blocking<EIGTYPE,EIGTYPE>& /*blocking*/) \\\n  { \\\n   BlasIndex m = convert_index<BlasIndex>(size), n = convert_index<BlasIndex>(otherSize), lda, ldb; \\\n   char side = 'L', uplo, diag='N', transa; \\\n   /* Set alpha_ */ \\\n   EIGTYPE alpha(1); \\\n   ldb = convert_index<BlasIndex>(otherStride);\\\n\\\n   const EIGTYPE *a; \\\n/* Set trans */ \\\n   transa = (TriStorageOrder==RowMajor) ? ((Conjugate) ? 'C' : 'T') : 'N'; \\\n/* Set uplo */ \\\n   uplo = IsLower ? 'L' : 'U'; \\\n   if (TriStorageOrder==RowMajor) uplo = (uplo == 'L') ? 'U' : 'L'; \\\n/* Set a, lda */ \\\n   typedef Matrix<EIGTYPE, Dynamic, Dynamic, TriStorageOrder> MatrixTri; \\\n   Map<const MatrixTri, 0, OuterStride<> > tri(_tri,size,size,OuterStride<>(triStride)); \\\n   MatrixTri a_tmp; \\\n\\\n   if (conjA) { \\\n     a_tmp = tri.conjugate(); \\\n     a = a_tmp.data(); \\\n     lda = convert_index<BlasIndex>(a_tmp.outerStride()); \\\n   } else { \\\n     a = _tri; \\\n     lda = convert_index<BlasIndex>(triStride); \\\n   } \\\n   if (IsUnitDiag) diag='U'; \\\n/* call ?trsm*/ \\\n   BLASFUNC(&side, &uplo, &transa, &diag, &m, &n, (const BLASTYPE*)&numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (BLASTYPE*)_other, &ldb); \\\n } \\\n};\n\n#ifdef EIGEN_USE_MKL\nEIGEN_BLAS_TRSM_L(double,   double, dtrsm)\nEIGEN_BLAS_TRSM_L(dcomplex, MKL_Complex16, ztrsm)\nEIGEN_BLAS_TRSM_L(float,    float,  strsm)\nEIGEN_BLAS_TRSM_L(scomplex, MKL_Complex8, ctrsm)\n#else\nEIGEN_BLAS_TRSM_L(double,   double, dtrsm_)\nEIGEN_BLAS_TRSM_L(dcomplex, double, ztrsm_)\nEIGEN_BLAS_TRSM_L(float,    float,  strsm_)\nEIGEN_BLAS_TRSM_L(scomplex, float,  ctrsm_)\n#endif\n\n// implements RightSide general * op(triangular)^-1\n#define EIGEN_BLAS_TRSM_R(EIGTYPE, BLASTYPE, BLASFUNC) \\\ntemplate <typename Index, int Mode, bool Conjugate, int TriStorageOrder> \\\nstruct triangular_solve_matrix<EIGTYPE,Index,OnTheRight,Mode,Conjugate,TriStorageOrder,ColMajor> \\\n{ \\\n  enum { \\\n    IsLower = (Mode&Lower) == Lower, \\\n    IsUnitDiag  = (Mode&UnitDiag) ? 1 : 0, \\\n    IsZeroDiag  = (Mode&ZeroDiag) ? 1 : 0, \\\n    conjA = ((TriStorageOrder==ColMajor) && Conjugate) ? 1 : 0 \\\n  }; \\\n  static void run( \\\n      Index size, Index otherSize, \\\n      const EIGTYPE* _tri, Index triStride, \\\n      EIGTYPE* _other, Index otherStride, level3_blocking<EIGTYPE,EIGTYPE>& /*blocking*/) \\\n  { \\\n   BlasIndex m = convert_index<BlasIndex>(otherSize), n = convert_index<BlasIndex>(size), lda, ldb; \\\n   char side = 'R', uplo, diag='N', transa; \\\n   /* Set alpha_ */ \\\n   EIGTYPE alpha(1); \\\n   ldb = convert_index<BlasIndex>(otherStride);\\\n\\\n   const EIGTYPE *a; \\\n/* Set trans */ \\\n   transa = (TriStorageOrder==RowMajor) ? ((Conjugate) ? 'C' : 'T') : 'N'; \\\n/* Set uplo */ \\\n   uplo = IsLower ? 'L' : 'U'; \\\n   if (TriStorageOrder==RowMajor) uplo = (uplo == 'L') ? 'U' : 'L'; \\\n/* Set a, lda */ \\\n   typedef Matrix<EIGTYPE, Dynamic, Dynamic, TriStorageOrder> MatrixTri; \\\n   Map<const MatrixTri, 0, OuterStride<> > tri(_tri,size,size,OuterStride<>(triStride)); \\\n   MatrixTri a_tmp; \\\n\\\n   if (conjA) { \\\n     a_tmp = tri.conjugate(); \\\n     a = a_tmp.data(); \\\n     lda = convert_index<BlasIndex>(a_tmp.outerStride()); \\\n   } else { \\\n     a = _tri; \\\n     lda = convert_index<BlasIndex>(triStride); \\\n   } \\\n   if (IsUnitDiag) diag='U'; \\\n/* call ?trsm*/ \\\n   BLASFUNC(&side, &uplo, &transa, &diag, &m, &n, (const BLASTYPE*)&numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (BLASTYPE*)_other, &ldb); \\\n   /*std::cout << \"TRMS_L specialization!\\n\";*/ \\\n } \\\n};\n\n#ifdef EIGEN_USE_MKL\nEIGEN_BLAS_TRSM_R(double,   double, dtrsm)\nEIGEN_BLAS_TRSM_R(dcomplex, MKL_Complex16, ztrsm)\nEIGEN_BLAS_TRSM_R(float,    float,  strsm)\nEIGEN_BLAS_TRSM_R(scomplex, MKL_Complex8,  ctrsm)\n#else\nEIGEN_BLAS_TRSM_R(double,   double, dtrsm_)\nEIGEN_BLAS_TRSM_R(dcomplex, double, ztrsm_)\nEIGEN_BLAS_TRSM_R(float,    float,  strsm_)\nEIGEN_BLAS_TRSM_R(scomplex, float,  ctrsm_)\n#endif\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_TRIANGULAR_SOLVER_MATRIX_BLAS_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/products/TriangularSolverVector.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_TRIANGULAR_SOLVER_VECTOR_H\n#define EIGEN_TRIANGULAR_SOLVER_VECTOR_H\n\nnamespace Eigen {\n\nnamespace internal {\n\ntemplate<typename LhsScalar, typename RhsScalar, typename Index, int Mode, bool Conjugate, int StorageOrder>\nstruct triangular_solve_vector<LhsScalar, RhsScalar, Index, OnTheRight, Mode, Conjugate, StorageOrder>\n{\n  static void run(Index size, const LhsScalar* _lhs, Index lhsStride, RhsScalar* rhs)\n  {\n    triangular_solve_vector<LhsScalar,RhsScalar,Index,OnTheLeft,\n        ((Mode&Upper)==Upper ? Lower : Upper) | (Mode&UnitDiag),\n        Conjugate,StorageOrder==RowMajor?ColMajor:RowMajor\n      >::run(size, _lhs, lhsStride, rhs);\n  }\n};\n\n// forward and backward substitution, row-major, rhs is a vector\ntemplate<typename LhsScalar, typename RhsScalar, typename Index, int Mode, bool Conjugate>\nstruct triangular_solve_vector<LhsScalar, RhsScalar, Index, OnTheLeft, Mode, Conjugate, RowMajor>\n{\n  enum {\n    IsLower = ((Mode&Lower)==Lower)\n  };\n  static void run(Index size, const LhsScalar* _lhs, Index lhsStride, RhsScalar* rhs)\n  {\n    typedef Map<const Matrix<LhsScalar,Dynamic,Dynamic,RowMajor>, 0, OuterStride<> > LhsMap;\n    const LhsMap lhs(_lhs,size,size,OuterStride<>(lhsStride));\n\n    typedef const_blas_data_mapper<LhsScalar,Index,RowMajor> LhsMapper;\n    typedef const_blas_data_mapper<RhsScalar,Index,ColMajor> RhsMapper;\n\n    typename internal::conditional<\n                          Conjugate,\n                          const CwiseUnaryOp<typename internal::scalar_conjugate_op<LhsScalar>,LhsMap>,\n                          const LhsMap&>\n                        ::type cjLhs(lhs);\n    static const Index PanelWidth = EIGEN_TUNE_TRIANGULAR_PANEL_WIDTH;\n    for(Index pi=IsLower ? 0 : size;\n        IsLower ? pi<size : pi>0;\n        IsLower ? pi+=PanelWidth : pi-=PanelWidth)\n    {\n      Index actualPanelWidth = (std::min)(IsLower ? size - pi : pi, PanelWidth);\n\n      Index r = IsLower ? pi : size - pi; // remaining size\n      if (r > 0)\n      {\n        // let's directly call the low level product function because:\n        // 1 - it is faster to compile\n        // 2 - it is slighlty faster at runtime\n        Index startRow = IsLower ? pi : pi-actualPanelWidth;\n        Index startCol = IsLower ? 0 : pi;\n\n        general_matrix_vector_product<Index,LhsScalar,LhsMapper,RowMajor,Conjugate,RhsScalar,RhsMapper,false>::run(\n          actualPanelWidth, r,\n          LhsMapper(&lhs.coeffRef(startRow,startCol), lhsStride),\n          RhsMapper(rhs + startCol, 1),\n          rhs + startRow, 1,\n          RhsScalar(-1));\n      }\n\n      for(Index k=0; k<actualPanelWidth; ++k)\n      {\n        Index i = IsLower ? pi+k : pi-k-1;\n        Index s = IsLower ? pi   : i+1;\n        if (k>0)\n          rhs[i] -= (cjLhs.row(i).segment(s,k).transpose().cwiseProduct(Map<const Matrix<RhsScalar,Dynamic,1> >(rhs+s,k))).sum();\n\n        if(!(Mode & UnitDiag))\n          rhs[i] /= cjLhs(i,i);\n      }\n    }\n  }\n};\n\n// forward and backward substitution, column-major, rhs is a vector\ntemplate<typename LhsScalar, typename RhsScalar, typename Index, int Mode, bool Conjugate>\nstruct triangular_solve_vector<LhsScalar, RhsScalar, Index, OnTheLeft, Mode, Conjugate, ColMajor>\n{\n  enum {\n    IsLower = ((Mode&Lower)==Lower)\n  };\n  static void run(Index size, const LhsScalar* _lhs, Index lhsStride, RhsScalar* rhs)\n  {\n    typedef Map<const Matrix<LhsScalar,Dynamic,Dynamic,ColMajor>, 0, OuterStride<> > LhsMap;\n    const LhsMap lhs(_lhs,size,size,OuterStride<>(lhsStride));\n    typedef const_blas_data_mapper<LhsScalar,Index,ColMajor> LhsMapper;\n    typedef const_blas_data_mapper<RhsScalar,Index,ColMajor> RhsMapper;\n    typename internal::conditional<Conjugate,\n                                   const CwiseUnaryOp<typename internal::scalar_conjugate_op<LhsScalar>,LhsMap>,\n                                   const LhsMap&\n                                  >::type cjLhs(lhs);\n    static const Index PanelWidth = EIGEN_TUNE_TRIANGULAR_PANEL_WIDTH;\n\n    for(Index pi=IsLower ? 0 : size;\n        IsLower ? pi<size : pi>0;\n        IsLower ? pi+=PanelWidth : pi-=PanelWidth)\n    {\n      Index actualPanelWidth = (std::min)(IsLower ? size - pi : pi, PanelWidth);\n      Index startBlock = IsLower ? pi : pi-actualPanelWidth;\n      Index endBlock = IsLower ? pi + actualPanelWidth : 0;\n\n      for(Index k=0; k<actualPanelWidth; ++k)\n      {\n        Index i = IsLower ? pi+k : pi-k-1;\n        if(!(Mode & UnitDiag))\n          rhs[i] /= cjLhs.coeff(i,i);\n\n        Index r = actualPanelWidth - k - 1; // remaining size\n        Index s = IsLower ? i+1 : i-r;\n        if (r>0)\n          Map<Matrix<RhsScalar,Dynamic,1> >(rhs+s,r) -= rhs[i] * cjLhs.col(i).segment(s,r);\n      }\n      Index r = IsLower ? size - endBlock : startBlock; // remaining size\n      if (r > 0)\n      {\n        // let's directly call the low level product function because:\n        // 1 - it is faster to compile\n        // 2 - it is slighlty faster at runtime\n        general_matrix_vector_product<Index,LhsScalar,LhsMapper,ColMajor,Conjugate,RhsScalar,RhsMapper,false>::run(\n            r, actualPanelWidth,\n            LhsMapper(&lhs.coeffRef(endBlock,startBlock), lhsStride),\n            RhsMapper(rhs+startBlock, 1),\n            rhs+endBlock, 1, RhsScalar(-1));\n      }\n    }\n  }\n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_TRIANGULAR_SOLVER_VECTOR_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/util/BlasUtil.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_BLASUTIL_H\n#define EIGEN_BLASUTIL_H\n\n// This file contains many lightweight helper classes used to\n// implement and control fast level 2 and level 3 BLAS-like routines.\n\nnamespace Eigen {\n\nnamespace internal {\n\n// forward declarations\ntemplate<typename LhsScalar, typename RhsScalar, typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs=false, bool ConjugateRhs=false>\nstruct gebp_kernel;\n\ntemplate<typename Scalar, typename Index, typename DataMapper, int nr, int StorageOrder, bool Conjugate = false, bool PanelMode=false>\nstruct gemm_pack_rhs;\n\ntemplate<typename Scalar, typename Index, typename DataMapper, int Pack1, int Pack2, int StorageOrder, bool Conjugate = false, bool PanelMode = false>\nstruct gemm_pack_lhs;\n\ntemplate<\n  typename Index,\n  typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,\n  typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs,\n  int ResStorageOrder>\nstruct general_matrix_matrix_product;\n\ntemplate<typename Index,\n         typename LhsScalar, typename LhsMapper, int LhsStorageOrder, bool ConjugateLhs,\n         typename RhsScalar, typename RhsMapper, bool ConjugateRhs, int Version=Specialized>\nstruct general_matrix_vector_product;\n\n\ntemplate<bool Conjugate> struct conj_if;\n\ntemplate<> struct conj_if<true> {\n  template<typename T>\n  inline T operator()(const T& x) const { return numext::conj(x); }\n  template<typename T>\n  inline T pconj(const T& x) const { return internal::pconj(x); }\n};\n\ntemplate<> struct conj_if<false> {\n  template<typename T>\n  inline const T& operator()(const T& x) const { return x; }\n  template<typename T>\n  inline const T& pconj(const T& x) const { return x; }\n};\n\n// Generic implementation for custom complex types.\ntemplate<typename LhsScalar, typename RhsScalar, bool ConjLhs, bool ConjRhs>\nstruct conj_helper\n{\n  typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar>::ReturnType Scalar;\n\n  EIGEN_STRONG_INLINE Scalar pmadd(const LhsScalar& x, const RhsScalar& y, const Scalar& c) const\n  { return padd(c, pmul(x,y)); }\n\n  EIGEN_STRONG_INLINE Scalar pmul(const LhsScalar& x, const RhsScalar& y) const\n  { return conj_if<ConjLhs>()(x) *  conj_if<ConjRhs>()(y); }\n};\n\ntemplate<typename Scalar> struct conj_helper<Scalar,Scalar,false,false>\n{\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar pmadd(const Scalar& x, const Scalar& y, const Scalar& c) const { return internal::pmadd(x,y,c); }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar pmul(const Scalar& x, const Scalar& y) const { return internal::pmul(x,y); }\n};\n\ntemplate<typename RealScalar> struct conj_helper<std::complex<RealScalar>, std::complex<RealScalar>, false,true>\n{\n  typedef std::complex<RealScalar> Scalar;\n  EIGEN_STRONG_INLINE Scalar pmadd(const Scalar& x, const Scalar& y, const Scalar& c) const\n  { return c + pmul(x,y); }\n\n  EIGEN_STRONG_INLINE Scalar pmul(const Scalar& x, const Scalar& y) const\n  { return Scalar(numext::real(x)*numext::real(y) + numext::imag(x)*numext::imag(y), numext::imag(x)*numext::real(y) - numext::real(x)*numext::imag(y)); }\n};\n\ntemplate<typename RealScalar> struct conj_helper<std::complex<RealScalar>, std::complex<RealScalar>, true,false>\n{\n  typedef std::complex<RealScalar> Scalar;\n  EIGEN_STRONG_INLINE Scalar pmadd(const Scalar& x, const Scalar& y, const Scalar& c) const\n  { return c + pmul(x,y); }\n\n  EIGEN_STRONG_INLINE Scalar pmul(const Scalar& x, const Scalar& y) const\n  { return Scalar(numext::real(x)*numext::real(y) + numext::imag(x)*numext::imag(y), numext::real(x)*numext::imag(y) - numext::imag(x)*numext::real(y)); }\n};\n\ntemplate<typename RealScalar> struct conj_helper<std::complex<RealScalar>, std::complex<RealScalar>, true,true>\n{\n  typedef std::complex<RealScalar> Scalar;\n  EIGEN_STRONG_INLINE Scalar pmadd(const Scalar& x, const Scalar& y, const Scalar& c) const\n  { return c + pmul(x,y); }\n\n  EIGEN_STRONG_INLINE Scalar pmul(const Scalar& x, const Scalar& y) const\n  { return Scalar(numext::real(x)*numext::real(y) - numext::imag(x)*numext::imag(y), - numext::real(x)*numext::imag(y) - numext::imag(x)*numext::real(y)); }\n};\n\ntemplate<typename RealScalar,bool Conj> struct conj_helper<std::complex<RealScalar>, RealScalar, Conj,false>\n{\n  typedef std::complex<RealScalar> Scalar;\n  EIGEN_STRONG_INLINE Scalar pmadd(const Scalar& x, const RealScalar& y, const Scalar& c) const\n  { return padd(c, pmul(x,y)); }\n  EIGEN_STRONG_INLINE Scalar pmul(const Scalar& x, const RealScalar& y) const\n  { return conj_if<Conj>()(x)*y; }\n};\n\ntemplate<typename RealScalar,bool Conj> struct conj_helper<RealScalar, std::complex<RealScalar>, false,Conj>\n{\n  typedef std::complex<RealScalar> Scalar;\n  EIGEN_STRONG_INLINE Scalar pmadd(const RealScalar& x, const Scalar& y, const Scalar& c) const\n  { return padd(c, pmul(x,y)); }\n  EIGEN_STRONG_INLINE Scalar pmul(const RealScalar& x, const Scalar& y) const\n  { return x*conj_if<Conj>()(y); }\n};\n\ntemplate<typename From,typename To> struct get_factor {\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE To run(const From& x) { return To(x); }\n};\n\ntemplate<typename Scalar> struct get_factor<Scalar,typename NumTraits<Scalar>::Real> {\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE typename NumTraits<Scalar>::Real run(const Scalar& x) { return numext::real(x); }\n};\n\n\ntemplate<typename Scalar, typename Index>\nclass BlasVectorMapper {\n  public:\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE BlasVectorMapper(Scalar *data) : m_data(data) {}\n\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Scalar operator()(Index i) const {\n    return m_data[i];\n  }\n  template <typename Packet, int AlignmentType>\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet load(Index i) const {\n    return ploadt<Packet, AlignmentType>(m_data + i);\n  }\n\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC bool aligned(Index i) const {\n    return (UIntPtr(m_data+i)%sizeof(Packet))==0;\n  }\n\n  protected:\n  Scalar* m_data;\n};\n\ntemplate<typename Scalar, typename Index, int AlignmentType>\nclass BlasLinearMapper {\n  public:\n  typedef typename packet_traits<Scalar>::type Packet;\n  typedef typename packet_traits<Scalar>::half HalfPacket;\n\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE BlasLinearMapper(Scalar *data) : m_data(data) {}\n\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void prefetch(int i) const {\n    internal::prefetch(&operator()(i));\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Scalar& operator()(Index i) const {\n    return m_data[i];\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet loadPacket(Index i) const {\n    return ploadt<Packet, AlignmentType>(m_data + i);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE HalfPacket loadHalfPacket(Index i) const {\n    return ploadt<HalfPacket, AlignmentType>(m_data + i);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void storePacket(Index i, const Packet &p) const {\n    pstoret<Scalar, Packet, AlignmentType>(m_data + i, p);\n  }\n\n  protected:\n  Scalar *m_data;\n};\n\n// Lightweight helper class to access matrix coefficients.\ntemplate<typename Scalar, typename Index, int StorageOrder, int AlignmentType = Unaligned>\nclass blas_data_mapper {\n  public:\n  typedef typename packet_traits<Scalar>::type Packet;\n  typedef typename packet_traits<Scalar>::half HalfPacket;\n\n  typedef BlasLinearMapper<Scalar, Index, AlignmentType> LinearMapper;\n  typedef BlasVectorMapper<Scalar, Index> VectorMapper;\n\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE blas_data_mapper(Scalar* data, Index stride) : m_data(data), m_stride(stride) {}\n\n  EIGEN_DEVICE_FUNC  EIGEN_ALWAYS_INLINE blas_data_mapper<Scalar, Index, StorageOrder, AlignmentType>\n  getSubMapper(Index i, Index j) const {\n    return blas_data_mapper<Scalar, Index, StorageOrder, AlignmentType>(&operator()(i, j), m_stride);\n  }\n\n  EIGEN_DEVICE_FUNC  EIGEN_ALWAYS_INLINE LinearMapper getLinearMapper(Index i, Index j) const {\n    return LinearMapper(&operator()(i, j));\n  }\n\n  EIGEN_DEVICE_FUNC  EIGEN_ALWAYS_INLINE VectorMapper getVectorMapper(Index i, Index j) const {\n    return VectorMapper(&operator()(i, j));\n  }\n\n\n  EIGEN_DEVICE_FUNC\n  EIGEN_ALWAYS_INLINE Scalar& operator()(Index i, Index j) const {\n    return m_data[StorageOrder==RowMajor ? j + i*m_stride : i + j*m_stride];\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet loadPacket(Index i, Index j) const {\n    return ploadt<Packet, AlignmentType>(&operator()(i, j));\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE HalfPacket loadHalfPacket(Index i, Index j) const {\n    return ploadt<HalfPacket, AlignmentType>(&operator()(i, j));\n  }\n\n  template<typename SubPacket>\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void scatterPacket(Index i, Index j, const SubPacket &p) const {\n    pscatter<Scalar, SubPacket>(&operator()(i, j), p, m_stride);\n  }\n\n  template<typename SubPacket>\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE SubPacket gatherPacket(Index i, Index j) const {\n    return pgather<Scalar, SubPacket>(&operator()(i, j), m_stride);\n  }\n\n  EIGEN_DEVICE_FUNC const Index stride() const { return m_stride; }\n  EIGEN_DEVICE_FUNC const Scalar* data() const { return m_data; }\n\n  EIGEN_DEVICE_FUNC Index firstAligned(Index size) const {\n    if (UIntPtr(m_data)%sizeof(Scalar)) {\n      return -1;\n    }\n    return internal::first_default_aligned(m_data, size);\n  }\n\n  protected:\n  Scalar* EIGEN_RESTRICT m_data;\n  const Index m_stride;\n};\n\n// lightweight helper class to access matrix coefficients (const version)\ntemplate<typename Scalar, typename Index, int StorageOrder>\nclass const_blas_data_mapper : public blas_data_mapper<const Scalar, Index, StorageOrder> {\n  public:\n  EIGEN_ALWAYS_INLINE const_blas_data_mapper(const Scalar *data, Index stride) : blas_data_mapper<const Scalar, Index, StorageOrder>(data, stride) {}\n\n  EIGEN_ALWAYS_INLINE const_blas_data_mapper<Scalar, Index, StorageOrder> getSubMapper(Index i, Index j) const {\n    return const_blas_data_mapper<Scalar, Index, StorageOrder>(&(this->operator()(i, j)), this->m_stride);\n  }\n};\n\n\n/* Helper class to analyze the factors of a Product expression.\n * In particular it allows to pop out operator-, scalar multiples,\n * and conjugate */\ntemplate<typename XprType> struct blas_traits\n{\n  typedef typename traits<XprType>::Scalar Scalar;\n  typedef const XprType& ExtractType;\n  typedef XprType _ExtractType;\n  enum {\n    IsComplex = NumTraits<Scalar>::IsComplex,\n    IsTransposed = false,\n    NeedToConjugate = false,\n    HasUsableDirectAccess = (    (int(XprType::Flags)&DirectAccessBit)\n                              && (   bool(XprType::IsVectorAtCompileTime)\n                                  || int(inner_stride_at_compile_time<XprType>::ret) == 1)\n                             ) ?  1 : 0\n  };\n  typedef typename conditional<bool(HasUsableDirectAccess),\n    ExtractType,\n    typename _ExtractType::PlainObject\n    >::type DirectLinearAccessType;\n  static inline ExtractType extract(const XprType& x) { return x; }\n  static inline const Scalar extractScalarFactor(const XprType&) { return Scalar(1); }\n};\n\n// pop conjugate\ntemplate<typename Scalar, typename NestedXpr>\nstruct blas_traits<CwiseUnaryOp<scalar_conjugate_op<Scalar>, NestedXpr> >\n : blas_traits<NestedXpr>\n{\n  typedef blas_traits<NestedXpr> Base;\n  typedef CwiseUnaryOp<scalar_conjugate_op<Scalar>, NestedXpr> XprType;\n  typedef typename Base::ExtractType ExtractType;\n\n  enum {\n    IsComplex = NumTraits<Scalar>::IsComplex,\n    NeedToConjugate = Base::NeedToConjugate ? 0 : IsComplex\n  };\n  static inline ExtractType extract(const XprType& x) { return Base::extract(x.nestedExpression()); }\n  static inline Scalar extractScalarFactor(const XprType& x) { return conj(Base::extractScalarFactor(x.nestedExpression())); }\n};\n\n// pop scalar multiple\ntemplate<typename Scalar, typename NestedXpr, typename Plain>\nstruct blas_traits<CwiseBinaryOp<scalar_product_op<Scalar>, const CwiseNullaryOp<scalar_constant_op<Scalar>,Plain>, NestedXpr> >\n : blas_traits<NestedXpr>\n{\n  typedef blas_traits<NestedXpr> Base;\n  typedef CwiseBinaryOp<scalar_product_op<Scalar>, const CwiseNullaryOp<scalar_constant_op<Scalar>,Plain>, NestedXpr> XprType;\n  typedef typename Base::ExtractType ExtractType;\n  static inline ExtractType extract(const XprType& x) { return Base::extract(x.rhs()); }\n  static inline Scalar extractScalarFactor(const XprType& x)\n  { return x.lhs().functor().m_other * Base::extractScalarFactor(x.rhs()); }\n};\ntemplate<typename Scalar, typename NestedXpr, typename Plain>\nstruct blas_traits<CwiseBinaryOp<scalar_product_op<Scalar>, NestedXpr, const CwiseNullaryOp<scalar_constant_op<Scalar>,Plain> > >\n : blas_traits<NestedXpr>\n{\n  typedef blas_traits<NestedXpr> Base;\n  typedef CwiseBinaryOp<scalar_product_op<Scalar>, NestedXpr, const CwiseNullaryOp<scalar_constant_op<Scalar>,Plain> > XprType;\n  typedef typename Base::ExtractType ExtractType;\n  static inline ExtractType extract(const XprType& x) { return Base::extract(x.lhs()); }\n  static inline Scalar extractScalarFactor(const XprType& x)\n  { return Base::extractScalarFactor(x.lhs()) * x.rhs().functor().m_other; }\n};\ntemplate<typename Scalar, typename Plain1, typename Plain2>\nstruct blas_traits<CwiseBinaryOp<scalar_product_op<Scalar>, const CwiseNullaryOp<scalar_constant_op<Scalar>,Plain1>,\n                                                            const CwiseNullaryOp<scalar_constant_op<Scalar>,Plain2> > >\n : blas_traits<CwiseNullaryOp<scalar_constant_op<Scalar>,Plain1> >\n{};\n\n// pop opposite\ntemplate<typename Scalar, typename NestedXpr>\nstruct blas_traits<CwiseUnaryOp<scalar_opposite_op<Scalar>, NestedXpr> >\n : blas_traits<NestedXpr>\n{\n  typedef blas_traits<NestedXpr> Base;\n  typedef CwiseUnaryOp<scalar_opposite_op<Scalar>, NestedXpr> XprType;\n  typedef typename Base::ExtractType ExtractType;\n  static inline ExtractType extract(const XprType& x) { return Base::extract(x.nestedExpression()); }\n  static inline Scalar extractScalarFactor(const XprType& x)\n  { return - Base::extractScalarFactor(x.nestedExpression()); }\n};\n\n// pop/push transpose\ntemplate<typename NestedXpr>\nstruct blas_traits<Transpose<NestedXpr> >\n : blas_traits<NestedXpr>\n{\n  typedef typename NestedXpr::Scalar Scalar;\n  typedef blas_traits<NestedXpr> Base;\n  typedef Transpose<NestedXpr> XprType;\n  typedef Transpose<const typename Base::_ExtractType>  ExtractType; // const to get rid of a compile error; anyway blas traits are only used on the RHS\n  typedef Transpose<const typename Base::_ExtractType> _ExtractType;\n  typedef typename conditional<bool(Base::HasUsableDirectAccess),\n    ExtractType,\n    typename ExtractType::PlainObject\n    >::type DirectLinearAccessType;\n  enum {\n    IsTransposed = Base::IsTransposed ? 0 : 1\n  };\n  static inline ExtractType extract(const XprType& x) { return ExtractType(Base::extract(x.nestedExpression())); }\n  static inline Scalar extractScalarFactor(const XprType& x) { return Base::extractScalarFactor(x.nestedExpression()); }\n};\n\ntemplate<typename T>\nstruct blas_traits<const T>\n     : blas_traits<T>\n{};\n\ntemplate<typename T, bool HasUsableDirectAccess=blas_traits<T>::HasUsableDirectAccess>\nstruct extract_data_selector {\n  static const typename T::Scalar* run(const T& m)\n  {\n    return blas_traits<T>::extract(m).data();\n  }\n};\n\ntemplate<typename T>\nstruct extract_data_selector<T,false> {\n  static typename T::Scalar* run(const T&) { return 0; }\n};\n\ntemplate<typename T> const typename T::Scalar* extract_data(const T& m)\n{\n  return extract_data_selector<T>::run(m);\n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_BLASUTIL_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/util/Constants.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CONSTANTS_H\n#define EIGEN_CONSTANTS_H\n\nnamespace Eigen {\n\n/** This value means that a positive quantity (e.g., a size) is not known at compile-time, and that instead the value is\n  * stored in some runtime variable.\n  *\n  * Changing the value of Dynamic breaks the ABI, as Dynamic is often used as a template parameter for Matrix.\n  */\nconst int Dynamic = -1;\n\n/** This value means that a signed quantity (e.g., a signed index) is not known at compile-time, and that instead its value\n  * has to be specified at runtime.\n  */\nconst int DynamicIndex = 0xffffff;\n\n/** This value means +Infinity; it is currently used only as the p parameter to MatrixBase::lpNorm<int>().\n  * The value Infinity there means the L-infinity norm.\n  */\nconst int Infinity = -1;\n\n/** This value means that the cost to evaluate an expression coefficient is either very expensive or\n  * cannot be known at compile time.\n  *\n  * This value has to be positive to (1) simplify cost computation, and (2) allow to distinguish between a very expensive and very very expensive expressions.\n  * It thus must also be large enough to make sure unrolling won't happen and that sub expressions will be evaluated, but not too large to avoid overflow.\n  */\nconst int HugeCost = 10000;\n\n/** \\defgroup flags Flags\n  * \\ingroup Core_Module\n  *\n  * These are the possible bits which can be OR'ed to constitute the flags of a matrix or\n  * expression.\n  *\n  * It is important to note that these flags are a purely compile-time notion. They are a compile-time property of\n  * an expression type, implemented as enum's. They are not stored in memory at runtime, and they do not incur any\n  * runtime overhead.\n  *\n  * \\sa MatrixBase::Flags\n  */\n\n/** \\ingroup flags\n  *\n  * for a matrix, this means that the storage order is row-major.\n  * If this bit is not set, the storage order is column-major.\n  * For an expression, this determines the storage order of\n  * the matrix created by evaluation of that expression.\n  * \\sa \\blank  \\ref TopicStorageOrders */\nconst unsigned int RowMajorBit = 0x1;\n\n/** \\ingroup flags\n  * means the expression should be evaluated by the calling expression */\nconst unsigned int EvalBeforeNestingBit = 0x2;\n\n/** \\ingroup flags\n  * \\deprecated\n  * means the expression should be evaluated before any assignment */\nEIGEN_DEPRECATED\nconst unsigned int EvalBeforeAssigningBit = 0x4; // FIXME deprecated\n\n/** \\ingroup flags\n  *\n  * Short version: means the expression might be vectorized\n  *\n  * Long version: means that the coefficients can be handled by packets\n  * and start at a memory location whose alignment meets the requirements\n  * of the present CPU architecture for optimized packet access. In the fixed-size\n  * case, there is the additional condition that it be possible to access all the\n  * coefficients by packets (this implies the requirement that the size be a multiple of 16 bytes,\n  * and that any nontrivial strides don't break the alignment). In the dynamic-size case,\n  * there is no such condition on the total size and strides, so it might not be possible to access\n  * all coeffs by packets.\n  *\n  * \\note This bit can be set regardless of whether vectorization is actually enabled.\n  *       To check for actual vectorizability, see \\a ActualPacketAccessBit.\n  */\nconst unsigned int PacketAccessBit = 0x8;\n\n#ifdef EIGEN_VECTORIZE\n/** \\ingroup flags\n  *\n  * If vectorization is enabled (EIGEN_VECTORIZE is defined) this constant\n  * is set to the value \\a PacketAccessBit.\n  *\n  * If vectorization is not enabled (EIGEN_VECTORIZE is not defined) this constant\n  * is set to the value 0.\n  */\nconst unsigned int ActualPacketAccessBit = PacketAccessBit;\n#else\nconst unsigned int ActualPacketAccessBit = 0x0;\n#endif\n\n/** \\ingroup flags\n  *\n  * Short version: means the expression can be seen as 1D vector.\n  *\n  * Long version: means that one can access the coefficients\n  * of this expression by coeff(int), and coeffRef(int) in the case of a lvalue expression. These\n  * index-based access methods are guaranteed\n  * to not have to do any runtime computation of a (row, col)-pair from the index, so that it\n  * is guaranteed that whenever it is available, index-based access is at least as fast as\n  * (row,col)-based access. Expressions for which that isn't possible don't have the LinearAccessBit.\n  *\n  * If both PacketAccessBit and LinearAccessBit are set, then the\n  * packets of this expression can be accessed by packet(int), and writePacket(int) in the case of a\n  * lvalue expression.\n  *\n  * Typically, all vector expressions have the LinearAccessBit, but there is one exception:\n  * Product expressions don't have it, because it would be troublesome for vectorization, even when the\n  * Product is a vector expression. Thus, vector Product expressions allow index-based coefficient access but\n  * not index-based packet access, so they don't have the LinearAccessBit.\n  */\nconst unsigned int LinearAccessBit = 0x10;\n\n/** \\ingroup flags\n  *\n  * Means the expression has a coeffRef() method, i.e. is writable as its individual coefficients are directly addressable.\n  * This rules out read-only expressions.\n  *\n  * Note that DirectAccessBit and LvalueBit are mutually orthogonal, as there are examples of expression having one but note\n  * the other:\n  *   \\li writable expressions that don't have a very simple memory layout as a strided array, have LvalueBit but not DirectAccessBit\n  *   \\li Map-to-const expressions, for example Map<const Matrix>, have DirectAccessBit but not LvalueBit\n  *\n  * Expressions having LvalueBit also have their coeff() method returning a const reference instead of returning a new value.\n  */\nconst unsigned int LvalueBit = 0x20;\n\n/** \\ingroup flags\n  *\n  * Means that the underlying array of coefficients can be directly accessed as a plain strided array. The memory layout\n  * of the array of coefficients must be exactly the natural one suggested by rows(), cols(),\n  * outerStride(), innerStride(), and the RowMajorBit. This rules out expressions such as Diagonal, whose coefficients,\n  * though referencable, do not have such a regular memory layout.\n  *\n  * See the comment on LvalueBit for an explanation of how LvalueBit and DirectAccessBit are mutually orthogonal.\n  */\nconst unsigned int DirectAccessBit = 0x40;\n\n/** \\deprecated \\ingroup flags\n  *\n  * means the first coefficient packet is guaranteed to be aligned.\n  * An expression cannot has the AlignedBit without the PacketAccessBit flag.\n  * In other words, this means we are allow to perform an aligned packet access to the first element regardless\n  * of the expression kind:\n  * \\code\n  * expression.packet<Aligned>(0);\n  * \\endcode\n  */\nEIGEN_DEPRECATED const unsigned int AlignedBit = 0x80;\n\nconst unsigned int NestByRefBit = 0x100;\n\n/** \\ingroup flags\n  *\n  * for an expression, this means that the storage order\n  * can be either row-major or column-major.\n  * The precise choice will be decided at evaluation time or when\n  * combined with other expressions.\n  * \\sa \\blank  \\ref RowMajorBit, \\ref TopicStorageOrders */\nconst unsigned int NoPreferredStorageOrderBit = 0x200;\n\n/** \\ingroup flags\n  *\n  * Means that the underlying coefficients can be accessed through pointers to the sparse (un)compressed storage format,\n  * that is, the expression provides:\n  * \\code\n    inline const Scalar* valuePtr() const;\n    inline const Index* innerIndexPtr() const;\n    inline const Index* outerIndexPtr() const;\n    inline const Index* innerNonZeroPtr() const;\n    \\endcode\n  */\nconst unsigned int CompressedAccessBit = 0x400;\n\n\n// list of flags that are inherited by default\nconst unsigned int HereditaryBits = RowMajorBit\n                                  | EvalBeforeNestingBit;\n\n/** \\defgroup enums Enumerations\n  * \\ingroup Core_Module\n  *\n  * Various enumerations used in %Eigen. Many of these are used as template parameters.\n  */\n\n/** \\ingroup enums\n  * Enum containing possible values for the \\c Mode or \\c UpLo parameter of\n  * MatrixBase::selfadjointView() and MatrixBase::triangularView(), and selfadjoint solvers. */\nenum UpLoType {\n  /** View matrix as a lower triangular matrix. */\n  Lower=0x1,                      \n  /** View matrix as an upper triangular matrix. */\n  Upper=0x2,                      \n  /** %Matrix has ones on the diagonal; to be used in combination with #Lower or #Upper. */\n  UnitDiag=0x4, \n  /** %Matrix has zeros on the diagonal; to be used in combination with #Lower or #Upper. */\n  ZeroDiag=0x8,\n  /** View matrix as a lower triangular matrix with ones on the diagonal. */\n  UnitLower=UnitDiag|Lower, \n  /** View matrix as an upper triangular matrix with ones on the diagonal. */\n  UnitUpper=UnitDiag|Upper,\n  /** View matrix as a lower triangular matrix with zeros on the diagonal. */\n  StrictlyLower=ZeroDiag|Lower, \n  /** View matrix as an upper triangular matrix with zeros on the diagonal. */\n  StrictlyUpper=ZeroDiag|Upper,\n  /** Used in BandMatrix and SelfAdjointView to indicate that the matrix is self-adjoint. */\n  SelfAdjoint=0x10,\n  /** Used to support symmetric, non-selfadjoint, complex matrices. */\n  Symmetric=0x20\n};\n\n/** \\ingroup enums\n  * Enum for indicating whether a buffer is aligned or not. */\nenum AlignmentType {\n  Unaligned=0,        /**< Data pointer has no specific alignment. */\n  Aligned8=8,         /**< Data pointer is aligned on a 8 bytes boundary. */\n  Aligned16=16,       /**< Data pointer is aligned on a 16 bytes boundary. */\n  Aligned32=32,       /**< Data pointer is aligned on a 32 bytes boundary. */\n  Aligned64=64,       /**< Data pointer is aligned on a 64 bytes boundary. */\n  Aligned128=128,     /**< Data pointer is aligned on a 128 bytes boundary. */\n  AlignedMask=255,\n  Aligned=16,         /**< \\deprecated Synonym for Aligned16. */\n#if EIGEN_MAX_ALIGN_BYTES==128\n  AlignedMax = Aligned128\n#elif EIGEN_MAX_ALIGN_BYTES==64\n  AlignedMax = Aligned64\n#elif EIGEN_MAX_ALIGN_BYTES==32\n  AlignedMax = Aligned32\n#elif EIGEN_MAX_ALIGN_BYTES==16\n  AlignedMax = Aligned16\n#elif EIGEN_MAX_ALIGN_BYTES==8\n  AlignedMax = Aligned8\n#elif EIGEN_MAX_ALIGN_BYTES==0\n  AlignedMax = Unaligned\n#else\n#error Invalid value for EIGEN_MAX_ALIGN_BYTES\n#endif\n};\n\n/** \\ingroup enums\n * Enum used by DenseBase::corner() in Eigen2 compatibility mode. */\n// FIXME after the corner() API change, this was not needed anymore, except by AlignedBox\n// TODO: find out what to do with that. Adapt the AlignedBox API ?\nenum CornerType { TopLeft, TopRight, BottomLeft, BottomRight };\n\n/** \\ingroup enums\n  * Enum containing possible values for the \\p Direction parameter of\n  * Reverse, PartialReduxExpr and VectorwiseOp. */\nenum DirectionType { \n  /** For Reverse, all columns are reversed; \n    * for PartialReduxExpr and VectorwiseOp, act on columns. */\n  Vertical, \n  /** For Reverse, all rows are reversed; \n    * for PartialReduxExpr and VectorwiseOp, act on rows. */\n  Horizontal, \n  /** For Reverse, both rows and columns are reversed; \n    * not used for PartialReduxExpr and VectorwiseOp. */\n  BothDirections \n};\n\n/** \\internal \\ingroup enums\n  * Enum to specify how to traverse the entries of a matrix. */\nenum TraversalType {\n  /** \\internal Default traversal, no vectorization, no index-based access */\n  DefaultTraversal,\n  /** \\internal No vectorization, use index-based access to have only one for loop instead of 2 nested loops */\n  LinearTraversal,\n  /** \\internal Equivalent to a slice vectorization for fixed-size matrices having good alignment\n    * and good size */\n  InnerVectorizedTraversal,\n  /** \\internal Vectorization path using a single loop plus scalar loops for the\n    * unaligned boundaries */\n  LinearVectorizedTraversal,\n  /** \\internal Generic vectorization path using one vectorized loop per row/column with some\n    * scalar loops to handle the unaligned boundaries */\n  SliceVectorizedTraversal,\n  /** \\internal Special case to properly handle incompatible scalar types or other defecting cases*/\n  InvalidTraversal,\n  /** \\internal Evaluate all entries at once */\n  AllAtOnceTraversal\n};\n\n/** \\internal \\ingroup enums\n  * Enum to specify whether to unroll loops when traversing over the entries of a matrix. */\nenum UnrollingType {\n  /** \\internal Do not unroll loops. */\n  NoUnrolling,\n  /** \\internal Unroll only the inner loop, but not the outer loop. */\n  InnerUnrolling,\n  /** \\internal Unroll both the inner and the outer loop. If there is only one loop, \n    * because linear traversal is used, then unroll that loop. */\n  CompleteUnrolling\n};\n\n/** \\internal \\ingroup enums\n  * Enum to specify whether to use the default (built-in) implementation or the specialization. */\nenum SpecializedType {\n  Specialized,\n  BuiltIn\n};\n\n/** \\ingroup enums\n  * Enum containing possible values for the \\p _Options template parameter of\n  * Matrix, Array and BandMatrix. */\nenum StorageOptions {\n  /** Storage order is column major (see \\ref TopicStorageOrders). */\n  ColMajor = 0,\n  /** Storage order is row major (see \\ref TopicStorageOrders). */\n  RowMajor = 0x1,  // it is only a coincidence that this is equal to RowMajorBit -- don't rely on that\n  /** Align the matrix itself if it is vectorizable fixed-size */\n  AutoAlign = 0,\n  /** Don't require alignment for the matrix itself (the array of coefficients, if dynamically allocated, may still be requested to be aligned) */ // FIXME --- clarify the situation\n  DontAlign = 0x2\n};\n\n/** \\ingroup enums\n  * Enum for specifying whether to apply or solve on the left or right. */\nenum SideType {\n  /** Apply transformation on the left. */\n  OnTheLeft = 1,  \n  /** Apply transformation on the right. */\n  OnTheRight = 2  \n};\n\n/* the following used to be written as:\n *\n *   struct NoChange_t {};\n *   namespace {\n *     EIGEN_UNUSED NoChange_t NoChange;\n *   }\n *\n * on the ground that it feels dangerous to disambiguate overloaded functions on enum/integer types.  \n * However, this leads to \"variable declared but never referenced\" warnings on Intel Composer XE,\n * and we do not know how to get rid of them (bug 450).\n */\n\nenum NoChange_t   { NoChange };\nenum Sequential_t { Sequential };\nenum Default_t    { Default };\n\n/** \\internal \\ingroup enums\n  * Used in AmbiVector. */\nenum AmbiVectorMode {\n  IsDense         = 0,\n  IsSparse\n};\n\n/** \\ingroup enums\n  * Used as template parameter in DenseCoeffBase and MapBase to indicate \n  * which accessors should be provided. */\nenum AccessorLevels {\n  /** Read-only access via a member function. */\n  ReadOnlyAccessors, \n  /** Read/write access via member functions. */\n  WriteAccessors, \n  /** Direct read-only access to the coefficients. */\n  DirectAccessors, \n  /** Direct read/write access to the coefficients. */\n  DirectWriteAccessors\n};\n\n/** \\ingroup enums\n  * Enum with options to give to various decompositions. */\nenum DecompositionOptions {\n  /** \\internal Not used (meant for LDLT?). */\n  Pivoting            = 0x01, \n  /** \\internal Not used (meant for LDLT?). */\n  NoPivoting          = 0x02, \n  /** Used in JacobiSVD to indicate that the square matrix U is to be computed. */\n  ComputeFullU        = 0x04,\n  /** Used in JacobiSVD to indicate that the thin matrix U is to be computed. */\n  ComputeThinU        = 0x08,\n  /** Used in JacobiSVD to indicate that the square matrix V is to be computed. */\n  ComputeFullV        = 0x10,\n  /** Used in JacobiSVD to indicate that the thin matrix V is to be computed. */\n  ComputeThinV        = 0x20,\n  /** Used in SelfAdjointEigenSolver and GeneralizedSelfAdjointEigenSolver to specify\n    * that only the eigenvalues are to be computed and not the eigenvectors. */\n  EigenvaluesOnly     = 0x40,\n  /** Used in SelfAdjointEigenSolver and GeneralizedSelfAdjointEigenSolver to specify\n    * that both the eigenvalues and the eigenvectors are to be computed. */\n  ComputeEigenvectors = 0x80,\n  /** \\internal */\n  EigVecMask = EigenvaluesOnly | ComputeEigenvectors,\n  /** Used in GeneralizedSelfAdjointEigenSolver to indicate that it should\n    * solve the generalized eigenproblem \\f$ Ax = \\lambda B x \\f$. */\n  Ax_lBx              = 0x100,\n  /** Used in GeneralizedSelfAdjointEigenSolver to indicate that it should\n    * solve the generalized eigenproblem \\f$ ABx = \\lambda x \\f$. */\n  ABx_lx              = 0x200,\n  /** Used in GeneralizedSelfAdjointEigenSolver to indicate that it should\n    * solve the generalized eigenproblem \\f$ BAx = \\lambda x \\f$. */\n  BAx_lx              = 0x400,\n  /** \\internal */\n  GenEigMask = Ax_lBx | ABx_lx | BAx_lx\n};\n\n/** \\ingroup enums\n  * Possible values for the \\p QRPreconditioner template parameter of JacobiSVD. */\nenum QRPreconditioners {\n  /** Do not specify what is to be done if the SVD of a non-square matrix is asked for. */\n  NoQRPreconditioner,\n  /** Use a QR decomposition without pivoting as the first step. */\n  HouseholderQRPreconditioner,\n  /** Use a QR decomposition with column pivoting as the first step. */\n  ColPivHouseholderQRPreconditioner,\n  /** Use a QR decomposition with full pivoting as the first step. */\n  FullPivHouseholderQRPreconditioner\n};\n\n#ifdef Success\n#error The preprocessor symbol 'Success' is defined, possibly by the X11 header file X.h\n#endif\n\n/** \\ingroup enums\n  * Enum for reporting the status of a computation. */\nenum ComputationInfo {\n  /** Computation was successful. */\n  Success = 0,        \n  /** The provided data did not satisfy the prerequisites. */\n  NumericalIssue = 1, \n  /** Iterative procedure did not converge. */\n  NoConvergence = 2,\n  /** The inputs are invalid, or the algorithm has been improperly called.\n    * When assertions are enabled, such errors trigger an assert. */\n  InvalidInput = 3\n};\n\n/** \\ingroup enums\n  * Enum used to specify how a particular transformation is stored in a matrix.\n  * \\sa Transform, Hyperplane::transform(). */\nenum TransformTraits {\n  /** Transformation is an isometry. */\n  Isometry      = 0x1,\n  /** Transformation is an affine transformation stored as a (Dim+1)^2 matrix whose last row is \n    * assumed to be [0 ... 0 1]. */\n  Affine        = 0x2,\n  /** Transformation is an affine transformation stored as a (Dim) x (Dim+1) matrix. */\n  AffineCompact = 0x10 | Affine,\n  /** Transformation is a general projective transformation stored as a (Dim+1)^2 matrix. */\n  Projective    = 0x20\n};\n\n/** \\internal \\ingroup enums\n  * Enum used to choose between implementation depending on the computer architecture. */\nnamespace Architecture\n{\n  enum Type {\n    Generic = 0x0,\n    SSE = 0x1,\n    AltiVec = 0x2,\n    VSX = 0x3,\n    NEON = 0x4,\n#if defined EIGEN_VECTORIZE_SSE\n    Target = SSE\n#elif defined EIGEN_VECTORIZE_ALTIVEC\n    Target = AltiVec\n#elif defined EIGEN_VECTORIZE_VSX\n    Target = VSX\n#elif defined EIGEN_VECTORIZE_NEON\n    Target = NEON\n#else\n    Target = Generic\n#endif\n  };\n}\n\n/** \\internal \\ingroup enums\n  * Enum used as template parameter in Product and product evaluators. */\nenum ProductImplType\n{ DefaultProduct=0, LazyProduct, AliasFreeProduct, CoeffBasedProductMode, LazyCoeffBasedProductMode, OuterProduct, InnerProduct, GemvProduct, GemmProduct };\n\n/** \\internal \\ingroup enums\n  * Enum used in experimental parallel implementation. */\nenum Action {GetAction, SetAction};\n\n/** The type used to identify a dense storage. */\nstruct Dense {};\n\n/** The type used to identify a general sparse storage. */\nstruct Sparse {};\n\n/** The type used to identify a general solver (factored) storage. */\nstruct SolverStorage {};\n\n/** The type used to identify a permutation storage. */\nstruct PermutationStorage {};\n\n/** The type used to identify a permutation storage. */\nstruct TranspositionsStorage {};\n\n/** The type used to identify a matrix expression */\nstruct MatrixXpr {};\n\n/** The type used to identify an array expression */\nstruct ArrayXpr {};\n\n// An evaluator must define its shape. By default, it can be one of the following:\nstruct DenseShape             { static std::string debugName() { return \"DenseShape\"; } };\nstruct SolverShape            { static std::string debugName() { return \"SolverShape\"; } };\nstruct HomogeneousShape       { static std::string debugName() { return \"HomogeneousShape\"; } };\nstruct DiagonalShape          { static std::string debugName() { return \"DiagonalShape\"; } };\nstruct BandShape              { static std::string debugName() { return \"BandShape\"; } };\nstruct TriangularShape        { static std::string debugName() { return \"TriangularShape\"; } };\nstruct SelfAdjointShape       { static std::string debugName() { return \"SelfAdjointShape\"; } };\nstruct PermutationShape       { static std::string debugName() { return \"PermutationShape\"; } };\nstruct TranspositionsShape    { static std::string debugName() { return \"TranspositionsShape\"; } };\nstruct SparseShape            { static std::string debugName() { return \"SparseShape\"; } };\n\nnamespace internal {\n\n  // random access iterators based on coeff*() accessors.\nstruct IndexBased {};\n\n// evaluator based on iterators to access coefficients. \nstruct IteratorBased {};\n\n/** \\internal\n * Constants for comparison functors\n */\nenum ComparisonName {\n  cmp_EQ = 0,\n  cmp_LT = 1,\n  cmp_LE = 2,\n  cmp_UNORD = 3,\n  cmp_NEQ = 4,\n  cmp_GT = 5,\n  cmp_GE = 6\n};\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_CONSTANTS_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/util/DisableStupidWarnings.h",
    "content": "#ifndef EIGEN_WARNINGS_DISABLED\n#define EIGEN_WARNINGS_DISABLED\n\n#ifdef _MSC_VER\n  // 4100 - unreferenced formal parameter (occurred e.g. in aligned_allocator::destroy(pointer p))\n  // 4101 - unreferenced local variable\n  // 4127 - conditional expression is constant\n  // 4181 - qualifier applied to reference type ignored\n  // 4211 - nonstandard extension used : redefined extern to static\n  // 4244 - 'argument' : conversion from 'type1' to 'type2', possible loss of data\n  // 4273 - QtAlignedMalloc, inconsistent DLL linkage\n  // 4324 - structure was padded due to declspec(align())\n  // 4503 - decorated name length exceeded, name was truncated\n  // 4512 - assignment operator could not be generated\n  // 4522 - 'class' : multiple assignment operators specified\n  // 4700 - uninitialized local variable 'xyz' used\n  // 4714 - function marked as __forceinline not inlined\n  // 4717 - 'function' : recursive on all control paths, function will cause runtime stack overflow\n  // 4800 - 'type' : forcing value to bool 'true' or 'false' (performance warning)\n  #ifndef EIGEN_PERMANENTLY_DISABLE_STUPID_WARNINGS\n    #pragma warning( push )\n  #endif\n  #pragma warning( disable : 4100 4101 4127 4181 4211 4244 4273 4324 4503 4512 4522 4700 4714 4717 4800)\n\n#elif defined __INTEL_COMPILER\n  // 2196 - routine is both \"inline\" and \"noinline\" (\"noinline\" assumed)\n  //        ICC 12 generates this warning even without any inline keyword, when defining class methods 'inline' i.e. inside of class body\n  //        typedef that may be a reference type.\n  // 279  - controlling expression is constant\n  //        ICC 12 generates this warning on assert(constant_expression_depending_on_template_params) and frankly this is a legitimate use case.\n  // 1684 - conversion from pointer to same-sized integral type (potential portability problem)\n  // 2259 - non-pointer conversion from \"Eigen::Index={ptrdiff_t={long}}\" to \"int\" may lose significant bits\n  #ifndef EIGEN_PERMANENTLY_DISABLE_STUPID_WARNINGS\n    #pragma warning push\n  #endif\n  #pragma warning disable 2196 279 1684 2259\n\n#elif defined __clang__\n  // -Wconstant-logical-operand - warning: use of logical && with constant operand; switch to bitwise & or remove constant\n  //     this is really a stupid warning as it warns on compile-time expressions involving enums\n  #ifndef EIGEN_PERMANENTLY_DISABLE_STUPID_WARNINGS\n    #pragma clang diagnostic push\n  #endif\n  #pragma clang diagnostic ignored \"-Wconstant-logical-operand\"\n\n#elif defined __GNUC__ && __GNUC__>=6\n\n  #ifndef EIGEN_PERMANENTLY_DISABLE_STUPID_WARNINGS\n    #pragma GCC diagnostic push\n  #endif\n  #pragma GCC diagnostic ignored \"-Wignored-attributes\"\n\n#endif\n\n#if defined __NVCC__\n  // Disable the \"statement is unreachable\" message\n  #pragma diag_suppress code_is_unreachable\n  // Disable the \"dynamic initialization in unreachable code\" message\n  #pragma diag_suppress initialization_not_reachable\n  // Disable the \"invalid error number\" message that we get with older versions of nvcc\n  #pragma diag_suppress 1222\n  // Disable the \"calling a __host__ function from a __host__ __device__ function is not allowed\" messages (yes, there are many of them and they seem to change with every version of the compiler)\n  #pragma diag_suppress 2527\n  #pragma diag_suppress 2529\n  #pragma diag_suppress 2651\n  #pragma diag_suppress 2653\n  #pragma diag_suppress 2668\n  #pragma diag_suppress 2669\n  #pragma diag_suppress 2670\n  #pragma diag_suppress 2671\n  #pragma diag_suppress 2735\n  #pragma diag_suppress 2737\n#endif\n\n#endif // not EIGEN_WARNINGS_DISABLED\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/util/ForwardDeclarations.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2007-2010 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_FORWARDDECLARATIONS_H\n#define EIGEN_FORWARDDECLARATIONS_H\n\nnamespace Eigen {\nnamespace internal {\n\ntemplate<typename T> struct traits;\n\n// here we say once and for all that traits<const T> == traits<T>\n// When constness must affect traits, it has to be constness on template parameters on which T itself depends.\n// For example, traits<Map<const T> > != traits<Map<T> >, but\n//              traits<const Map<T> > == traits<Map<T> >\ntemplate<typename T> struct traits<const T> : traits<T> {};\n\ntemplate<typename Derived> struct has_direct_access\n{\n  enum { ret = (traits<Derived>::Flags & DirectAccessBit) ? 1 : 0 };\n};\n\ntemplate<typename Derived> struct accessors_level\n{\n  enum { has_direct_access = (traits<Derived>::Flags & DirectAccessBit) ? 1 : 0,\n         has_write_access = (traits<Derived>::Flags & LvalueBit) ? 1 : 0,\n         value = has_direct_access ? (has_write_access ? DirectWriteAccessors : DirectAccessors)\n                                   : (has_write_access ? WriteAccessors       : ReadOnlyAccessors)\n  };\n};\n\ntemplate<typename T> struct evaluator_traits;\n\ntemplate< typename T> struct evaluator;\n\n} // end namespace internal\n\ntemplate<typename T> struct NumTraits;\n\ntemplate<typename Derived> struct EigenBase;\ntemplate<typename Derived> class DenseBase;\ntemplate<typename Derived> class PlainObjectBase;\n\n\ntemplate<typename Derived,\n         int Level = internal::accessors_level<Derived>::value >\nclass DenseCoeffsBase;\n\ntemplate<typename _Scalar, int _Rows, int _Cols,\n         int _Options = AutoAlign |\n#if EIGEN_GNUC_AT(3,4)\n    // workaround a bug in at least gcc 3.4.6\n    // the innermost ?: ternary operator is misparsed. We write it slightly\n    // differently and this makes gcc 3.4.6 happy, but it's ugly.\n    // The error would only show up with EIGEN_DEFAULT_TO_ROW_MAJOR is defined\n    // (when EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION is RowMajor)\n                          ( (_Rows==1 && _Cols!=1) ? Eigen::RowMajor\n                          : !(_Cols==1 && _Rows!=1) ?  EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION\n                          : Eigen::ColMajor ),\n#else\n                          ( (_Rows==1 && _Cols!=1) ? Eigen::RowMajor\n                          : (_Cols==1 && _Rows!=1) ? Eigen::ColMajor\n                          : EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION ),\n#endif\n         int _MaxRows = _Rows,\n         int _MaxCols = _Cols\n> class Matrix;\n\ntemplate<typename Derived> class MatrixBase;\ntemplate<typename Derived> class ArrayBase;\n\ntemplate<typename ExpressionType, unsigned int Added, unsigned int Removed> class Flagged;\ntemplate<typename ExpressionType, template <typename> class StorageBase > class NoAlias;\ntemplate<typename ExpressionType> class NestByValue;\ntemplate<typename ExpressionType> class ForceAlignedAccess;\ntemplate<typename ExpressionType> class SwapWrapper;\n\ntemplate<typename XprType, int BlockRows=Dynamic, int BlockCols=Dynamic, bool InnerPanel = false> class Block;\n\ntemplate<typename MatrixType, int Size=Dynamic> class VectorBlock;\ntemplate<typename MatrixType> class Transpose;\ntemplate<typename MatrixType> class Conjugate;\ntemplate<typename NullaryOp, typename MatrixType>         class CwiseNullaryOp;\ntemplate<typename UnaryOp,   typename MatrixType>         class CwiseUnaryOp;\ntemplate<typename ViewOp,    typename MatrixType>         class CwiseUnaryView;\ntemplate<typename BinaryOp,  typename Lhs, typename Rhs>  class CwiseBinaryOp;\ntemplate<typename TernaryOp, typename Arg1, typename Arg2, typename Arg3>  class CwiseTernaryOp;\ntemplate<typename Decomposition, typename Rhstype>        class Solve;\ntemplate<typename XprType>                                class Inverse;\n\ntemplate<typename Lhs, typename Rhs, int Option = DefaultProduct> class Product;\n\ntemplate<typename Derived> class DiagonalBase;\ntemplate<typename _DiagonalVectorType> class DiagonalWrapper;\ntemplate<typename _Scalar, int SizeAtCompileTime, int MaxSizeAtCompileTime=SizeAtCompileTime> class DiagonalMatrix;\ntemplate<typename MatrixType, typename DiagonalType, int ProductOrder> class DiagonalProduct;\ntemplate<typename MatrixType, int Index = 0> class Diagonal;\ntemplate<int SizeAtCompileTime, int MaxSizeAtCompileTime = SizeAtCompileTime, typename IndexType=int> class PermutationMatrix;\ntemplate<int SizeAtCompileTime, int MaxSizeAtCompileTime = SizeAtCompileTime, typename IndexType=int> class Transpositions;\ntemplate<typename Derived> class PermutationBase;\ntemplate<typename Derived> class TranspositionsBase;\ntemplate<typename _IndicesType> class PermutationWrapper;\ntemplate<typename _IndicesType> class TranspositionsWrapper;\n\ntemplate<typename Derived,\n         int Level = internal::accessors_level<Derived>::has_write_access ? WriteAccessors : ReadOnlyAccessors\n> class MapBase;\ntemplate<int InnerStrideAtCompileTime, int OuterStrideAtCompileTime> class Stride;\ntemplate<int Value = Dynamic> class InnerStride;\ntemplate<int Value = Dynamic> class OuterStride;\ntemplate<typename MatrixType, int MapOptions=Unaligned, typename StrideType = Stride<0,0> > class Map;\ntemplate<typename Derived> class RefBase;\ntemplate<typename PlainObjectType, int Options = 0,\n         typename StrideType = typename internal::conditional<PlainObjectType::IsVectorAtCompileTime,InnerStride<1>,OuterStride<> >::type > class Ref;\n\ntemplate<typename Derived> class TriangularBase;\ntemplate<typename MatrixType, unsigned int Mode> class TriangularView;\ntemplate<typename MatrixType, unsigned int Mode> class SelfAdjointView;\ntemplate<typename MatrixType> class SparseView;\ntemplate<typename ExpressionType> class WithFormat;\ntemplate<typename MatrixType> struct CommaInitializer;\ntemplate<typename Derived> class ReturnByValue;\ntemplate<typename ExpressionType> class ArrayWrapper;\ntemplate<typename ExpressionType> class MatrixWrapper;\ntemplate<typename Derived> class SolverBase;\ntemplate<typename XprType> class InnerIterator;\n\nnamespace internal {\ntemplate<typename DecompositionType> struct kernel_retval_base;\ntemplate<typename DecompositionType> struct kernel_retval;\ntemplate<typename DecompositionType> struct image_retval_base;\ntemplate<typename DecompositionType> struct image_retval;\n} // end namespace internal\n\nnamespace internal {\ntemplate<typename _Scalar, int Rows=Dynamic, int Cols=Dynamic, int Supers=Dynamic, int Subs=Dynamic, int Options=0> class BandMatrix;\n}\n\nnamespace internal {\ntemplate<typename Lhs, typename Rhs> struct product_type;\n\ntemplate<bool> struct EnableIf;\n\n/** \\internal\n  * \\class product_evaluator\n  * Products need their own evaluator with more template arguments allowing for\n  * easier partial template specializations.\n  */\ntemplate< typename T,\n          int ProductTag = internal::product_type<typename T::Lhs,typename T::Rhs>::ret,\n          typename LhsShape = typename evaluator_traits<typename T::Lhs>::Shape,\n          typename RhsShape = typename evaluator_traits<typename T::Rhs>::Shape,\n          typename LhsScalar = typename traits<typename T::Lhs>::Scalar,\n          typename RhsScalar = typename traits<typename T::Rhs>::Scalar\n        > struct product_evaluator;\n}\n\ntemplate<typename Lhs, typename Rhs,\n         int ProductType = internal::product_type<Lhs,Rhs>::value>\nstruct ProductReturnType;\n\n// this is a workaround for sun CC\ntemplate<typename Lhs, typename Rhs> struct LazyProductReturnType;\n\nnamespace internal {\n\n// Provides scalar/packet-wise product and product with accumulation\n// with optional conjugation of the arguments.\ntemplate<typename LhsScalar, typename RhsScalar, bool ConjLhs=false, bool ConjRhs=false> struct conj_helper;\n\ntemplate<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_sum_op;\ntemplate<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_difference_op;\ntemplate<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_conj_product_op;\ntemplate<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_min_op;\ntemplate<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_max_op;\ntemplate<typename Scalar> struct scalar_opposite_op;\ntemplate<typename Scalar> struct scalar_conjugate_op;\ntemplate<typename Scalar> struct scalar_real_op;\ntemplate<typename Scalar> struct scalar_imag_op;\ntemplate<typename Scalar> struct scalar_abs_op;\ntemplate<typename Scalar> struct scalar_abs2_op;\ntemplate<typename Scalar> struct scalar_sqrt_op;\ntemplate<typename Scalar> struct scalar_rsqrt_op;\ntemplate<typename Scalar> struct scalar_exp_op;\ntemplate<typename Scalar> struct scalar_log_op;\ntemplate<typename Scalar> struct scalar_cos_op;\ntemplate<typename Scalar> struct scalar_sin_op;\ntemplate<typename Scalar> struct scalar_acos_op;\ntemplate<typename Scalar> struct scalar_asin_op;\ntemplate<typename Scalar> struct scalar_tan_op;\ntemplate<typename Scalar> struct scalar_inverse_op;\ntemplate<typename Scalar> struct scalar_square_op;\ntemplate<typename Scalar> struct scalar_cube_op;\ntemplate<typename Scalar, typename NewType> struct scalar_cast_op;\ntemplate<typename Scalar> struct scalar_random_op;\ntemplate<typename Scalar> struct scalar_constant_op;\ntemplate<typename Scalar> struct scalar_identity_op;\ntemplate<typename Scalar,bool iscpx> struct scalar_sign_op;\ntemplate<typename Scalar,typename ScalarExponent> struct scalar_pow_op;\ntemplate<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_hypot_op;\ntemplate<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_product_op;\ntemplate<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_quotient_op;\n\n// SpecialFunctions module\ntemplate<typename Scalar> struct scalar_lgamma_op;\ntemplate<typename Scalar> struct scalar_digamma_op;\ntemplate<typename Scalar> struct scalar_erf_op;\ntemplate<typename Scalar> struct scalar_erfc_op;\ntemplate<typename Scalar> struct scalar_igamma_op;\ntemplate<typename Scalar> struct scalar_igammac_op;\ntemplate<typename Scalar> struct scalar_zeta_op;\ntemplate<typename Scalar> struct scalar_betainc_op;\n\n} // end namespace internal\n\nstruct IOFormat;\n\n// Array module\ntemplate<typename _Scalar, int _Rows, int _Cols,\n         int _Options = AutoAlign |\n#if EIGEN_GNUC_AT(3,4)\n    // workaround a bug in at least gcc 3.4.6\n    // the innermost ?: ternary operator is misparsed. We write it slightly\n    // differently and this makes gcc 3.4.6 happy, but it's ugly.\n    // The error would only show up with EIGEN_DEFAULT_TO_ROW_MAJOR is defined\n    // (when EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION is RowMajor)\n                          ( (_Rows==1 && _Cols!=1) ? Eigen::RowMajor\n                          : !(_Cols==1 && _Rows!=1) ?  EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION\n                          : Eigen::ColMajor ),\n#else\n                          ( (_Rows==1 && _Cols!=1) ? Eigen::RowMajor\n                          : (_Cols==1 && _Rows!=1) ? Eigen::ColMajor\n                          : EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION ),\n#endif\n         int _MaxRows = _Rows, int _MaxCols = _Cols> class Array;\ntemplate<typename ConditionMatrixType, typename ThenMatrixType, typename ElseMatrixType> class Select;\ntemplate<typename MatrixType, typename BinaryOp, int Direction> class PartialReduxExpr;\ntemplate<typename ExpressionType, int Direction> class VectorwiseOp;\ntemplate<typename MatrixType,int RowFactor,int ColFactor> class Replicate;\ntemplate<typename MatrixType, int Direction = BothDirections> class Reverse;\n\ntemplate<typename MatrixType> class FullPivLU;\ntemplate<typename MatrixType> class PartialPivLU;\nnamespace internal {\ntemplate<typename MatrixType> struct inverse_impl;\n}\ntemplate<typename MatrixType> class HouseholderQR;\ntemplate<typename MatrixType> class ColPivHouseholderQR;\ntemplate<typename MatrixType> class FullPivHouseholderQR;\ntemplate<typename MatrixType> class CompleteOrthogonalDecomposition;\ntemplate<typename MatrixType, int QRPreconditioner = ColPivHouseholderQRPreconditioner> class JacobiSVD;\ntemplate<typename MatrixType> class BDCSVD;\ntemplate<typename MatrixType, int UpLo = Lower> class LLT;\ntemplate<typename MatrixType, int UpLo = Lower> class LDLT;\ntemplate<typename VectorsType, typename CoeffsType, int Side=OnTheLeft> class HouseholderSequence;\ntemplate<typename Scalar>     class JacobiRotation;\n\n// Geometry module:\ntemplate<typename Derived, int _Dim> class RotationBase;\ntemplate<typename Lhs, typename Rhs> class Cross;\ntemplate<typename Derived> class QuaternionBase;\ntemplate<typename Scalar> class Rotation2D;\ntemplate<typename Scalar> class AngleAxis;\ntemplate<typename Scalar,int Dim> class Translation;\ntemplate<typename Scalar,int Dim> class AlignedBox;\ntemplate<typename Scalar, int Options = AutoAlign> class Quaternion;\ntemplate<typename Scalar,int Dim,int Mode,int _Options=AutoAlign> class Transform;\ntemplate <typename _Scalar, int _AmbientDim, int Options=AutoAlign> class ParametrizedLine;\ntemplate <typename _Scalar, int _AmbientDim, int Options=AutoAlign> class Hyperplane;\ntemplate<typename Scalar> class UniformScaling;\ntemplate<typename MatrixType,int Direction> class Homogeneous;\n\n// Sparse module:\ntemplate<typename Derived> class SparseMatrixBase;\n\n// MatrixFunctions module\ntemplate<typename Derived> struct MatrixExponentialReturnValue;\ntemplate<typename Derived> class MatrixFunctionReturnValue;\ntemplate<typename Derived> class MatrixSquareRootReturnValue;\ntemplate<typename Derived> class MatrixLogarithmReturnValue;\ntemplate<typename Derived> class MatrixPowerReturnValue;\ntemplate<typename Derived> class MatrixComplexPowerReturnValue;\n\nnamespace internal {\ntemplate <typename Scalar>\nstruct stem_function\n{\n  typedef std::complex<typename NumTraits<Scalar>::Real> ComplexScalar;\n  typedef ComplexScalar type(ComplexScalar, int);\n};\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_FORWARDDECLARATIONS_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/util/MKL_support.h",
    "content": "/*\n Copyright (c) 2011, Intel Corporation. All rights reserved.\n\n Redistribution and use in source and binary forms, with or without modification,\n are permitted provided that the following conditions are met:\n\n * Redistributions of source code must retain the above copyright notice, this\n   list of conditions and the following disclaimer.\n * Redistributions in binary form must reproduce the above copyright notice,\n   this list of conditions and the following disclaimer in the documentation\n   and/or other materials provided with the distribution.\n * Neither the name of Intel Corporation nor the names of its contributors may\n   be used to endorse or promote products derived from this software without\n   specific prior written permission.\n\n THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\" AND\n ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED\n WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\n DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR\n ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES\n (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;\n LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON\n ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT\n (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS\n SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n\n ********************************************************************************\n *   Content : Eigen bindings to Intel(R) MKL\n *   Include file with common MKL declarations\n ********************************************************************************\n*/\n\n#ifndef EIGEN_MKL_SUPPORT_H\n#define EIGEN_MKL_SUPPORT_H\n\n#ifdef EIGEN_USE_MKL_ALL\n  #ifndef EIGEN_USE_BLAS\n    #define EIGEN_USE_BLAS\n  #endif\n  #ifndef EIGEN_USE_LAPACKE\n    #define EIGEN_USE_LAPACKE\n  #endif\n  #ifndef EIGEN_USE_MKL_VML\n    #define EIGEN_USE_MKL_VML\n  #endif\n#endif\n\n#ifdef EIGEN_USE_LAPACKE_STRICT\n  #define EIGEN_USE_LAPACKE\n#endif\n\n#if defined(EIGEN_USE_MKL_VML) && !defined(EIGEN_USE_MKL)\n  #define EIGEN_USE_MKL\n#endif\n\n\n#if defined EIGEN_USE_MKL\n#   include <mkl.h> \n/*Check IMKL version for compatibility: < 10.3 is not usable with Eigen*/\n#   ifndef INTEL_MKL_VERSION\n#       undef EIGEN_USE_MKL /* INTEL_MKL_VERSION is not even defined on older versions */\n#   elif INTEL_MKL_VERSION < 100305    /* the intel-mkl-103-release-notes say this was when the lapacke.h interface was added*/\n#       undef EIGEN_USE_MKL\n#   endif\n#   ifndef EIGEN_USE_MKL\n    /*If the MKL version is too old, undef everything*/\n#       undef   EIGEN_USE_MKL_ALL\n#       undef   EIGEN_USE_LAPACKE\n#       undef   EIGEN_USE_MKL_VML\n#       undef   EIGEN_USE_LAPACKE_STRICT\n#       undef   EIGEN_USE_LAPACKE\n#   endif\n#endif\n\n#if defined EIGEN_USE_MKL\n\n#define EIGEN_MKL_VML_THRESHOLD 128\n\n/* MKL_DOMAIN_BLAS, etc are defined only in 10.3 update 7 */\n/* MKL_BLAS, etc are not defined in 11.2 */\n#ifdef MKL_DOMAIN_ALL\n#define EIGEN_MKL_DOMAIN_ALL MKL_DOMAIN_ALL\n#else\n#define EIGEN_MKL_DOMAIN_ALL MKL_ALL\n#endif\n\n#ifdef MKL_DOMAIN_BLAS\n#define EIGEN_MKL_DOMAIN_BLAS MKL_DOMAIN_BLAS\n#else\n#define EIGEN_MKL_DOMAIN_BLAS MKL_BLAS\n#endif\n\n#ifdef MKL_DOMAIN_FFT\n#define EIGEN_MKL_DOMAIN_FFT MKL_DOMAIN_FFT\n#else\n#define EIGEN_MKL_DOMAIN_FFT MKL_FFT\n#endif\n\n#ifdef MKL_DOMAIN_VML\n#define EIGEN_MKL_DOMAIN_VML MKL_DOMAIN_VML\n#else\n#define EIGEN_MKL_DOMAIN_VML MKL_VML\n#endif\n\n#ifdef MKL_DOMAIN_PARDISO\n#define EIGEN_MKL_DOMAIN_PARDISO MKL_DOMAIN_PARDISO\n#else\n#define EIGEN_MKL_DOMAIN_PARDISO MKL_PARDISO\n#endif\n#endif\n\n#if defined(EIGEN_USE_BLAS) && !defined(EIGEN_USE_MKL)\n#include \"../../misc/blas.h\"\n#endif\n\nnamespace Eigen {\n\ntypedef std::complex<double> dcomplex;\ntypedef std::complex<float>  scomplex;\n\n#if defined(EIGEN_USE_MKL)\ntypedef MKL_INT BlasIndex;\n#else\ntypedef int BlasIndex;\n#endif\n\n} // end namespace Eigen\n\n\n#endif // EIGEN_MKL_SUPPORT_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/util/Macros.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_MACROS_H\n#define EIGEN_MACROS_H\n\n#define EIGEN_WORLD_VERSION 3\n#define EIGEN_MAJOR_VERSION 3\n#define EIGEN_MINOR_VERSION 5\n\n#define EIGEN_VERSION_AT_LEAST(x,y,z) (EIGEN_WORLD_VERSION>x || (EIGEN_WORLD_VERSION>=x && \\\n                                      (EIGEN_MAJOR_VERSION>y || (EIGEN_MAJOR_VERSION>=y && \\\n                                                                 EIGEN_MINOR_VERSION>=z))))\n\n// Compiler identification, EIGEN_COMP_*\n\n/// \\internal EIGEN_COMP_GNUC set to 1 for all compilers compatible with GCC\n#ifdef __GNUC__\n  #define EIGEN_COMP_GNUC 1\n#else\n  #define EIGEN_COMP_GNUC 0\n#endif\n\n/// \\internal EIGEN_COMP_CLANG set to major+minor version (e.g., 307 for clang 3.7) if the compiler is clang\n#if defined(__clang__)\n  #define EIGEN_COMP_CLANG (__clang_major__*100+__clang_minor__)\n#else\n  #define EIGEN_COMP_CLANG 0\n#endif\n\n\n/// \\internal EIGEN_COMP_LLVM set to 1 if the compiler backend is llvm\n#if defined(__llvm__)\n  #define EIGEN_COMP_LLVM 1\n#else\n  #define EIGEN_COMP_LLVM 0\n#endif\n\n/// \\internal EIGEN_COMP_ICC set to __INTEL_COMPILER if the compiler is Intel compiler, 0 otherwise\n#if defined(__INTEL_COMPILER)\n  #define EIGEN_COMP_ICC __INTEL_COMPILER\n#else\n  #define EIGEN_COMP_ICC 0\n#endif\n\n/// \\internal EIGEN_COMP_MINGW set to 1 if the compiler is mingw\n#if defined(__MINGW32__)\n  #define EIGEN_COMP_MINGW 1\n#else\n  #define EIGEN_COMP_MINGW 0\n#endif\n\n/// \\internal EIGEN_COMP_SUNCC set to 1 if the compiler is Solaris Studio\n#if defined(__SUNPRO_CC)\n  #define EIGEN_COMP_SUNCC 1\n#else\n  #define EIGEN_COMP_SUNCC 0\n#endif\n\n/// \\internal EIGEN_COMP_MSVC set to _MSC_VER if the compiler is Microsoft Visual C++, 0 otherwise.\n#if defined(_MSC_VER)\n  #define EIGEN_COMP_MSVC _MSC_VER\n#else\n  #define EIGEN_COMP_MSVC 0\n#endif\n\n// For the record, here is a table summarizing the possible values for EIGEN_COMP_MSVC:\n//  name  ver   MSC_VER\n//  2008    9      1500\n//  2010   10      1600\n//  2012   11      1700\n//  2013   12      1800\n//  2015   14      1900\n//  \"15\"   15      1900\n\n/// \\internal EIGEN_COMP_MSVC_STRICT set to 1 if the compiler is really Microsoft Visual C++ and not ,e.g., ICC or clang-cl\n#if EIGEN_COMP_MSVC && !(EIGEN_COMP_ICC || EIGEN_COMP_LLVM || EIGEN_COMP_CLANG)\n  #define EIGEN_COMP_MSVC_STRICT _MSC_VER\n#else\n  #define EIGEN_COMP_MSVC_STRICT 0\n#endif\n\n/// \\internal EIGEN_COMP_IBM set to 1 if the compiler is IBM XL C++\n#if defined(__IBMCPP__) || defined(__xlc__)\n  #define EIGEN_COMP_IBM 1\n#else\n  #define EIGEN_COMP_IBM 0\n#endif\n\n/// \\internal EIGEN_COMP_PGI set to 1 if the compiler is Portland Group Compiler\n#if defined(__PGI)\n  #define EIGEN_COMP_PGI 1\n#else\n  #define EIGEN_COMP_PGI 0\n#endif\n\n/// \\internal EIGEN_COMP_ARM set to 1 if the compiler is ARM Compiler\n#if defined(__CC_ARM) || defined(__ARMCC_VERSION)\n  #define EIGEN_COMP_ARM 1\n#else\n  #define EIGEN_COMP_ARM 0\n#endif\n\n/// \\internal EIGEN_COMP_ARM set to 1 if the compiler is ARM Compiler\n#if defined(__EMSCRIPTEN__)\n  #define EIGEN_COMP_EMSCRIPTEN 1\n#else\n  #define EIGEN_COMP_EMSCRIPTEN 0\n#endif\n\n\n/// \\internal EIGEN_GNUC_STRICT set to 1 if the compiler is really GCC and not a compatible compiler (e.g., ICC, clang, mingw, etc.)\n#if EIGEN_COMP_GNUC && !(EIGEN_COMP_CLANG || EIGEN_COMP_ICC || EIGEN_COMP_MINGW || EIGEN_COMP_PGI || EIGEN_COMP_IBM || EIGEN_COMP_ARM || EIGEN_COMP_EMSCRIPTEN)\n  #define EIGEN_COMP_GNUC_STRICT 1\n#else\n  #define EIGEN_COMP_GNUC_STRICT 0\n#endif\n\n\n#if EIGEN_COMP_GNUC\n  #define EIGEN_GNUC_AT_LEAST(x,y) ((__GNUC__==x && __GNUC_MINOR__>=y) || __GNUC__>x)\n  #define EIGEN_GNUC_AT_MOST(x,y)  ((__GNUC__==x && __GNUC_MINOR__<=y) || __GNUC__<x)\n  #define EIGEN_GNUC_AT(x,y)       ( __GNUC__==x && __GNUC_MINOR__==y )\n#else\n  #define EIGEN_GNUC_AT_LEAST(x,y) 0\n  #define EIGEN_GNUC_AT_MOST(x,y)  0\n  #define EIGEN_GNUC_AT(x,y)       0\n#endif\n\n// FIXME: could probably be removed as we do not support gcc 3.x anymore\n#if EIGEN_COMP_GNUC && (__GNUC__ <= 3)\n#define EIGEN_GCC3_OR_OLDER 1\n#else\n#define EIGEN_GCC3_OR_OLDER 0\n#endif\n\n\n// Architecture identification, EIGEN_ARCH_*\n\n#if defined(__x86_64__) || defined(_M_X64) || defined(__amd64)\n  #define EIGEN_ARCH_x86_64 1\n#else\n  #define EIGEN_ARCH_x86_64 0\n#endif\n\n#if defined(__i386__) || defined(_M_IX86) || defined(_X86_) || defined(__i386)\n  #define EIGEN_ARCH_i386 1\n#else\n  #define EIGEN_ARCH_i386 0\n#endif\n\n#if EIGEN_ARCH_x86_64 || EIGEN_ARCH_i386\n  #define EIGEN_ARCH_i386_OR_x86_64 1\n#else\n  #define EIGEN_ARCH_i386_OR_x86_64 0\n#endif\n\n/// \\internal EIGEN_ARCH_ARM set to 1 if the architecture is ARM\n#if defined(__arm__)\n  #define EIGEN_ARCH_ARM 1\n#else\n  #define EIGEN_ARCH_ARM 0\n#endif\n\n/// \\internal EIGEN_ARCH_ARM64 set to 1 if the architecture is ARM64\n#if defined(__aarch64__)\n  #define EIGEN_ARCH_ARM64 1\n#else\n  #define EIGEN_ARCH_ARM64 0\n#endif\n\n#if EIGEN_ARCH_ARM || EIGEN_ARCH_ARM64\n  #define EIGEN_ARCH_ARM_OR_ARM64 1\n#else\n  #define EIGEN_ARCH_ARM_OR_ARM64 0\n#endif\n\n/// \\internal EIGEN_ARCH_MIPS set to 1 if the architecture is MIPS\n#if defined(__mips__) || defined(__mips)\n  #define EIGEN_ARCH_MIPS 1\n#else\n  #define EIGEN_ARCH_MIPS 0\n#endif\n\n/// \\internal EIGEN_ARCH_SPARC set to 1 if the architecture is SPARC\n#if defined(__sparc__) || defined(__sparc)\n  #define EIGEN_ARCH_SPARC 1\n#else\n  #define EIGEN_ARCH_SPARC 0\n#endif\n\n/// \\internal EIGEN_ARCH_IA64 set to 1 if the architecture is Intel Itanium\n#if defined(__ia64__)\n  #define EIGEN_ARCH_IA64 1\n#else\n  #define EIGEN_ARCH_IA64 0\n#endif\n\n/// \\internal EIGEN_ARCH_PPC set to 1 if the architecture is PowerPC\n#if defined(__powerpc__) || defined(__ppc__) || defined(_M_PPC)\n  #define EIGEN_ARCH_PPC 1\n#else\n  #define EIGEN_ARCH_PPC 0\n#endif\n\n\n\n// Operating system identification, EIGEN_OS_*\n\n/// \\internal EIGEN_OS_UNIX set to 1 if the OS is a unix variant\n#if defined(__unix__) || defined(__unix)\n  #define EIGEN_OS_UNIX 1\n#else\n  #define EIGEN_OS_UNIX 0\n#endif\n\n/// \\internal EIGEN_OS_LINUX set to 1 if the OS is based on Linux kernel\n#if defined(__linux__)\n  #define EIGEN_OS_LINUX 1\n#else\n  #define EIGEN_OS_LINUX 0\n#endif\n\n/// \\internal EIGEN_OS_ANDROID set to 1 if the OS is Android\n// note: ANDROID is defined when using ndk_build, __ANDROID__ is defined when using a standalone toolchain.\n#if defined(__ANDROID__) || defined(ANDROID)\n  #define EIGEN_OS_ANDROID 1\n#else\n  #define EIGEN_OS_ANDROID 0\n#endif\n\n/// \\internal EIGEN_OS_GNULINUX set to 1 if the OS is GNU Linux and not Linux-based OS (e.g., not android)\n#if defined(__gnu_linux__) && !(EIGEN_OS_ANDROID)\n  #define EIGEN_OS_GNULINUX 1\n#else\n  #define EIGEN_OS_GNULINUX 0\n#endif\n\n/// \\internal EIGEN_OS_BSD set to 1 if the OS is a BSD variant\n#if defined(__FreeBSD__) || defined(__NetBSD__) || defined(__OpenBSD__) || defined(__bsdi__) || defined(__DragonFly__)\n  #define EIGEN_OS_BSD 1\n#else\n  #define EIGEN_OS_BSD 0\n#endif\n\n/// \\internal EIGEN_OS_MAC set to 1 if the OS is MacOS\n#if defined(__APPLE__)\n  #define EIGEN_OS_MAC 1\n#else\n  #define EIGEN_OS_MAC 0\n#endif\n\n/// \\internal EIGEN_OS_QNX set to 1 if the OS is QNX\n#if defined(__QNX__)\n  #define EIGEN_OS_QNX 1\n#else\n  #define EIGEN_OS_QNX 0\n#endif\n\n/// \\internal EIGEN_OS_WIN set to 1 if the OS is Windows based\n#if defined(_WIN32)\n  #define EIGEN_OS_WIN 1\n#else\n  #define EIGEN_OS_WIN 0\n#endif\n\n/// \\internal EIGEN_OS_WIN64 set to 1 if the OS is Windows 64bits\n#if defined(_WIN64)\n  #define EIGEN_OS_WIN64 1\n#else\n  #define EIGEN_OS_WIN64 0\n#endif\n\n/// \\internal EIGEN_OS_WINCE set to 1 if the OS is Windows CE\n#if defined(_WIN32_WCE)\n  #define EIGEN_OS_WINCE 1\n#else\n  #define EIGEN_OS_WINCE 0\n#endif\n\n/// \\internal EIGEN_OS_CYGWIN set to 1 if the OS is Windows/Cygwin\n#if defined(__CYGWIN__)\n  #define EIGEN_OS_CYGWIN 1\n#else\n  #define EIGEN_OS_CYGWIN 0\n#endif\n\n/// \\internal EIGEN_OS_WIN_STRICT set to 1 if the OS is really Windows and not some variants\n#if EIGEN_OS_WIN && !( EIGEN_OS_WINCE || EIGEN_OS_CYGWIN )\n  #define EIGEN_OS_WIN_STRICT 1\n#else\n  #define EIGEN_OS_WIN_STRICT 0\n#endif\n\n/// \\internal EIGEN_OS_SUN set to 1 if the OS is SUN\n#if (defined(sun) || defined(__sun)) && !(defined(__SVR4) || defined(__svr4__))\n  #define EIGEN_OS_SUN 1\n#else\n  #define EIGEN_OS_SUN 0\n#endif\n\n/// \\internal EIGEN_OS_SOLARIS set to 1 if the OS is Solaris\n#if (defined(sun) || defined(__sun)) && (defined(__SVR4) || defined(__svr4__))\n  #define EIGEN_OS_SOLARIS 1\n#else\n  #define EIGEN_OS_SOLARIS 0\n#endif\n\n\n\n#if EIGEN_GNUC_AT_MOST(4,3) && !EIGEN_COMP_CLANG\n  // see bug 89\n  #define EIGEN_SAFE_TO_USE_STANDARD_ASSERT_MACRO 0\n#else\n  #define EIGEN_SAFE_TO_USE_STANDARD_ASSERT_MACRO 1\n#endif\n\n// This macro can be used to prevent from macro expansion, e.g.:\n//   std::max EIGEN_NOT_A_MACRO(a,b)\n#define EIGEN_NOT_A_MACRO\n\n#ifdef EIGEN_DEFAULT_TO_ROW_MAJOR\n#define EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION Eigen::RowMajor\n#else\n#define EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION Eigen::ColMajor\n#endif\n\n#ifndef EIGEN_DEFAULT_DENSE_INDEX_TYPE\n#define EIGEN_DEFAULT_DENSE_INDEX_TYPE std::ptrdiff_t\n#endif\n\n// Cross compiler wrapper around LLVM's __has_builtin\n#ifdef __has_builtin\n#  define EIGEN_HAS_BUILTIN(x) __has_builtin(x)\n#else\n#  define EIGEN_HAS_BUILTIN(x) 0\n#endif\n\n// A Clang feature extension to determine compiler features.\n// We use it to determine 'cxx_rvalue_references'\n#ifndef __has_feature\n# define __has_feature(x) 0\n#endif\n\n// Upperbound on the C++ version to use.\n// Expected values are 03, 11, 14, 17, etc.\n// By default, let's use an arbitrarily large C++ version.\n#ifndef EIGEN_MAX_CPP_VER\n#define EIGEN_MAX_CPP_VER 99\n#endif\n\n#if EIGEN_MAX_CPP_VER>=11 && (defined(__cplusplus) && (__cplusplus >= 201103L) || EIGEN_COMP_MSVC >= 1900)\n#define EIGEN_HAS_CXX11 1\n#else\n#define EIGEN_HAS_CXX11 0\n#endif\n\n\n// Do we support r-value references?\n#ifndef EIGEN_HAS_RVALUE_REFERENCES\n#if EIGEN_MAX_CPP_VER>=11 && \\\n    (__has_feature(cxx_rvalue_references) || \\\n    (defined(__cplusplus) && __cplusplus >= 201103L) || \\\n    (EIGEN_COMP_MSVC >= 1600))\n  #define EIGEN_HAS_RVALUE_REFERENCES 1\n#else\n  #define EIGEN_HAS_RVALUE_REFERENCES 0\n#endif\n#endif\n\n// Does the compiler support C99?\n#ifndef EIGEN_HAS_C99_MATH\n#if EIGEN_MAX_CPP_VER>=11 && \\\n    ((defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 199901))       \\\n  || (defined(__GNUC__) && defined(_GLIBCXX_USE_C99)) \\\n  || (defined(_LIBCPP_VERSION) && !defined(_MSC_VER)))\n  #define EIGEN_HAS_C99_MATH 1\n#else\n  #define EIGEN_HAS_C99_MATH 0\n#endif\n#endif\n\n// Does the compiler support result_of?\n#ifndef EIGEN_HAS_STD_RESULT_OF\n#if EIGEN_MAX_CPP_VER>=11 && ((__has_feature(cxx_lambdas) || (defined(__cplusplus) && __cplusplus >= 201103L)))\n#define EIGEN_HAS_STD_RESULT_OF 1\n#else\n#define EIGEN_HAS_STD_RESULT_OF 0\n#endif\n#endif\n\n// Does the compiler support variadic templates?\n#ifndef EIGEN_HAS_VARIADIC_TEMPLATES\n#if EIGEN_MAX_CPP_VER>=11 && (__cplusplus > 199711L || EIGEN_COMP_MSVC >= 1900) \\\n  && (!defined(__NVCC__) || !EIGEN_ARCH_ARM_OR_ARM64 || (EIGEN_CUDACC_VER >= 80000) )\n    // ^^ Disable the use of variadic templates when compiling with versions of nvcc older than 8.0 on ARM devices:\n    //    this prevents nvcc from crashing when compiling Eigen on Tegra X1\n#define EIGEN_HAS_VARIADIC_TEMPLATES 1\n#else\n#define EIGEN_HAS_VARIADIC_TEMPLATES 0\n#endif\n#endif\n\n// Does the compiler fully support const expressions? (as in c++14)\n#ifndef EIGEN_HAS_CONSTEXPR\n\n#ifdef __CUDACC__\n// Const expressions are supported provided that c++11 is enabled and we're using either clang or nvcc 7.5 or above\n#if EIGEN_MAX_CPP_VER>=14 && (__cplusplus > 199711L && (EIGEN_COMP_CLANG || EIGEN_CUDACC_VER >= 70500))\n  #define EIGEN_HAS_CONSTEXPR 1\n#endif\n#elif EIGEN_MAX_CPP_VER>=14 && (__has_feature(cxx_relaxed_constexpr) || (defined(__cplusplus) && __cplusplus >= 201402L) || \\\n  (EIGEN_GNUC_AT_LEAST(4,8) && (__cplusplus > 199711L)))\n#define EIGEN_HAS_CONSTEXPR 1\n#endif\n\n#ifndef EIGEN_HAS_CONSTEXPR\n#define EIGEN_HAS_CONSTEXPR 0\n#endif\n\n#endif\n\n// Does the compiler support C++11 math?\n// Let's be conservative and enable the default C++11 implementation only if we are sure it exists\n#ifndef EIGEN_HAS_CXX11_MATH\n  #if EIGEN_MAX_CPP_VER>=11 && ((__cplusplus > 201103L) || (__cplusplus >= 201103L) && (EIGEN_COMP_GNUC_STRICT || EIGEN_COMP_CLANG || EIGEN_COMP_MSVC || EIGEN_COMP_ICC)  \\\n      && (EIGEN_ARCH_i386_OR_x86_64) && (EIGEN_OS_GNULINUX || EIGEN_OS_WIN_STRICT || EIGEN_OS_MAC))\n    #define EIGEN_HAS_CXX11_MATH 1\n  #else\n    #define EIGEN_HAS_CXX11_MATH 0\n  #endif\n#endif\n\n// Does the compiler support proper C++11 containers?\n#ifndef EIGEN_HAS_CXX11_CONTAINERS\n  #if    EIGEN_MAX_CPP_VER>=11 && \\\n         ((__cplusplus > 201103L) \\\n      || ((__cplusplus >= 201103L) && (EIGEN_COMP_GNUC_STRICT || EIGEN_COMP_CLANG || EIGEN_COMP_ICC>=1400)) \\\n      || EIGEN_COMP_MSVC >= 1900)\n    #define EIGEN_HAS_CXX11_CONTAINERS 1\n  #else\n    #define EIGEN_HAS_CXX11_CONTAINERS 0\n  #endif\n#endif\n\n// Does the compiler support C++11 noexcept?\n#ifndef EIGEN_HAS_CXX11_NOEXCEPT\n  #if    EIGEN_MAX_CPP_VER>=11 && \\\n         (__has_feature(cxx_noexcept) \\\n      || (__cplusplus > 201103L) \\\n      || ((__cplusplus >= 201103L) && (EIGEN_COMP_GNUC_STRICT || EIGEN_COMP_CLANG || EIGEN_COMP_ICC>=1400)) \\\n      || EIGEN_COMP_MSVC >= 1900)\n    #define EIGEN_HAS_CXX11_NOEXCEPT 1\n  #else\n    #define EIGEN_HAS_CXX11_NOEXCEPT 0\n  #endif\n#endif\n\n/** Allows to disable some optimizations which might affect the accuracy of the result.\n  * Such optimization are enabled by default, and set EIGEN_FAST_MATH to 0 to disable them.\n  * They currently include:\n  *   - single precision ArrayBase::sin() and ArrayBase::cos() for SSE and AVX vectorization.\n  */\n#ifndef EIGEN_FAST_MATH\n#define EIGEN_FAST_MATH 1\n#endif\n\n#define EIGEN_DEBUG_VAR(x) std::cerr << #x << \" = \" << x << std::endl;\n\n// concatenate two tokens\n#define EIGEN_CAT2(a,b) a ## b\n#define EIGEN_CAT(a,b) EIGEN_CAT2(a,b)\n\n#define EIGEN_COMMA ,\n\n// convert a token to a string\n#define EIGEN_MAKESTRING2(a) #a\n#define EIGEN_MAKESTRING(a) EIGEN_MAKESTRING2(a)\n\n// EIGEN_STRONG_INLINE is a stronger version of the inline, using __forceinline on MSVC,\n// but it still doesn't use GCC's always_inline. This is useful in (common) situations where MSVC needs forceinline\n// but GCC is still doing fine with just inline.\n#ifndef EIGEN_STRONG_INLINE\n#if EIGEN_COMP_MSVC || EIGEN_COMP_ICC\n#define EIGEN_STRONG_INLINE __forceinline\n#else\n#define EIGEN_STRONG_INLINE inline\n#endif\n#endif\n\n// EIGEN_ALWAYS_INLINE is the stronget, it has the effect of making the function inline and adding every possible\n// attribute to maximize inlining. This should only be used when really necessary: in particular,\n// it uses __attribute__((always_inline)) on GCC, which most of the time is useless and can severely harm compile times.\n// FIXME with the always_inline attribute,\n// gcc 3.4.x and 4.1 reports the following compilation error:\n//   Eval.h:91: sorry, unimplemented: inlining failed in call to 'const Eigen::Eval<Derived> Eigen::MatrixBase<Scalar, Derived>::eval() const'\n//    : function body not available\n//   See also bug 1367\n#if EIGEN_GNUC_AT_LEAST(4,2)\n#define EIGEN_ALWAYS_INLINE __attribute__((always_inline)) inline\n#else\n#define EIGEN_ALWAYS_INLINE EIGEN_STRONG_INLINE\n#endif\n\n#if EIGEN_COMP_GNUC\n#define EIGEN_DONT_INLINE __attribute__((noinline))\n#elif EIGEN_COMP_MSVC\n#define EIGEN_DONT_INLINE __declspec(noinline)\n#else\n#define EIGEN_DONT_INLINE\n#endif\n\n#if EIGEN_COMP_GNUC\n#define EIGEN_PERMISSIVE_EXPR __extension__\n#else\n#define EIGEN_PERMISSIVE_EXPR\n#endif\n\n// this macro allows to get rid of linking errors about multiply defined functions.\n//  - static is not very good because it prevents definitions from different object files to be merged.\n//           So static causes the resulting linked executable to be bloated with multiple copies of the same function.\n//  - inline is not perfect either as it unwantedly hints the compiler toward inlining the function.\n#define EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS\n#define EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS inline\n\n#ifdef NDEBUG\n# ifndef EIGEN_NO_DEBUG\n#  define EIGEN_NO_DEBUG\n# endif\n#endif\n\n// eigen_plain_assert is where we implement the workaround for the assert() bug in GCC <= 4.3, see bug 89\n#ifdef EIGEN_NO_DEBUG\n  #define eigen_plain_assert(x)\n#else\n  #if EIGEN_SAFE_TO_USE_STANDARD_ASSERT_MACRO\n    namespace Eigen {\n    namespace internal {\n    inline bool copy_bool(bool b) { return b; }\n    }\n    }\n    #define eigen_plain_assert(x) assert(x)\n  #else\n    // work around bug 89\n    #include <cstdlib>   // for abort\n    #include <iostream>  // for std::cerr\n\n    namespace Eigen {\n    namespace internal {\n    // trivial function copying a bool. Must be EIGEN_DONT_INLINE, so we implement it after including Eigen headers.\n    // see bug 89.\n    namespace {\n    EIGEN_DONT_INLINE bool copy_bool(bool b) { return b; }\n    }\n    inline void assert_fail(const char *condition, const char *function, const char *file, int line)\n    {\n      std::cerr << \"assertion failed: \" << condition << \" in function \" << function << \" at \" << file << \":\" << line << std::endl;\n      abort();\n    }\n    }\n    }\n    #define eigen_plain_assert(x) \\\n      do { \\\n        if(!Eigen::internal::copy_bool(x)) \\\n          Eigen::internal::assert_fail(EIGEN_MAKESTRING(x), __PRETTY_FUNCTION__, __FILE__, __LINE__); \\\n      } while(false)\n  #endif\n#endif\n\n// eigen_assert can be overridden\n#ifndef eigen_assert\n#define eigen_assert(x) eigen_plain_assert(x)\n#endif\n\n#ifdef EIGEN_INTERNAL_DEBUGGING\n#define eigen_internal_assert(x) eigen_assert(x)\n#else\n#define eigen_internal_assert(x)\n#endif\n\n#ifdef EIGEN_NO_DEBUG\n#define EIGEN_ONLY_USED_FOR_DEBUG(x) EIGEN_UNUSED_VARIABLE(x)\n#else\n#define EIGEN_ONLY_USED_FOR_DEBUG(x)\n#endif\n\n#ifndef EIGEN_NO_DEPRECATED_WARNING\n  #if EIGEN_COMP_GNUC\n    #define EIGEN_DEPRECATED __attribute__((deprecated))\n  #elif EIGEN_COMP_MSVC\n    #define EIGEN_DEPRECATED __declspec(deprecated)\n  #else\n    #define EIGEN_DEPRECATED\n  #endif\n#else\n  #define EIGEN_DEPRECATED\n#endif\n\n#if EIGEN_COMP_GNUC\n#define EIGEN_UNUSED __attribute__((unused))\n#else\n#define EIGEN_UNUSED\n#endif\n\n// Suppresses 'unused variable' warnings.\nnamespace Eigen {\n  namespace internal {\n    template<typename T> EIGEN_DEVICE_FUNC void ignore_unused_variable(const T&) {}\n  }\n}\n#define EIGEN_UNUSED_VARIABLE(var) Eigen::internal::ignore_unused_variable(var);\n\n#if !defined(EIGEN_ASM_COMMENT)\n  #if EIGEN_COMP_GNUC && (EIGEN_ARCH_i386_OR_x86_64 || EIGEN_ARCH_ARM_OR_ARM64)\n    #define EIGEN_ASM_COMMENT(X)  __asm__(\"#\" X)\n  #else\n    #define EIGEN_ASM_COMMENT(X)\n  #endif\n#endif\n\n\n//------------------------------------------------------------------------------------------\n// Static and dynamic alignment control\n//\n// The main purpose of this section is to define EIGEN_MAX_ALIGN_BYTES and EIGEN_MAX_STATIC_ALIGN_BYTES\n// as the maximal boundary in bytes on which dynamically and statically allocated data may be alignment respectively.\n// The values of EIGEN_MAX_ALIGN_BYTES and EIGEN_MAX_STATIC_ALIGN_BYTES can be specified by the user. If not,\n// a default value is automatically computed based on architecture, compiler, and OS.\n//\n// This section also defines macros EIGEN_ALIGN_TO_BOUNDARY(N) and the shortcuts EIGEN_ALIGN{8,16,32,_MAX}\n// to be used to declare statically aligned buffers.\n//------------------------------------------------------------------------------------------\n\n\n/* EIGEN_ALIGN_TO_BOUNDARY(n) forces data to be n-byte aligned. This is used to satisfy SIMD requirements.\n * However, we do that EVEN if vectorization (EIGEN_VECTORIZE) is disabled,\n * so that vectorization doesn't affect binary compatibility.\n *\n * If we made alignment depend on whether or not EIGEN_VECTORIZE is defined, it would be impossible to link\n * vectorized and non-vectorized code.\n */\n#if (defined __CUDACC__)\n  #define EIGEN_ALIGN_TO_BOUNDARY(n) __align__(n)\n#elif EIGEN_COMP_GNUC || EIGEN_COMP_PGI || EIGEN_COMP_IBM || EIGEN_COMP_ARM\n  #define EIGEN_ALIGN_TO_BOUNDARY(n) __attribute__((aligned(n)))\n#elif EIGEN_COMP_MSVC\n  #define EIGEN_ALIGN_TO_BOUNDARY(n) __declspec(align(n))\n#elif EIGEN_COMP_SUNCC\n  // FIXME not sure about this one:\n  #define EIGEN_ALIGN_TO_BOUNDARY(n) __attribute__((aligned(n)))\n#else\n  #error Please tell me what is the equivalent of __attribute__((aligned(n))) for your compiler\n#endif\n\n// If the user explicitly disable vectorization, then we also disable alignment\n#if defined(EIGEN_DONT_VECTORIZE)\n  #define EIGEN_IDEAL_MAX_ALIGN_BYTES 0\n#elif defined(EIGEN_VECTORIZE_AVX512)\n  // 64 bytes static alignmeent is preferred only if really required\n  #define EIGEN_IDEAL_MAX_ALIGN_BYTES 64\n#elif defined(__AVX__)\n  // 32 bytes static alignmeent is preferred only if really required\n  #define EIGEN_IDEAL_MAX_ALIGN_BYTES 32\n#else\n  #define EIGEN_IDEAL_MAX_ALIGN_BYTES 16\n#endif\n\n\n// EIGEN_MIN_ALIGN_BYTES defines the minimal value for which the notion of explicit alignment makes sense\n#define EIGEN_MIN_ALIGN_BYTES 16\n\n// Defined the boundary (in bytes) on which the data needs to be aligned. Note\n// that unless EIGEN_ALIGN is defined and not equal to 0, the data may not be\n// aligned at all regardless of the value of this #define.\n\n#if (defined(EIGEN_DONT_ALIGN_STATICALLY) || defined(EIGEN_DONT_ALIGN))  && defined(EIGEN_MAX_STATIC_ALIGN_BYTES) && EIGEN_MAX_STATIC_ALIGN_BYTES>0\n#error EIGEN_MAX_STATIC_ALIGN_BYTES and EIGEN_DONT_ALIGN[_STATICALLY] are both defined with EIGEN_MAX_STATIC_ALIGN_BYTES!=0. Use EIGEN_MAX_STATIC_ALIGN_BYTES=0 as a synonym of EIGEN_DONT_ALIGN_STATICALLY.\n#endif\n\n// EIGEN_DONT_ALIGN_STATICALLY and EIGEN_DONT_ALIGN are deprectated\n// They imply EIGEN_MAX_STATIC_ALIGN_BYTES=0\n#if defined(EIGEN_DONT_ALIGN_STATICALLY) || defined(EIGEN_DONT_ALIGN)\n  #ifdef EIGEN_MAX_STATIC_ALIGN_BYTES\n    #undef EIGEN_MAX_STATIC_ALIGN_BYTES\n  #endif\n  #define EIGEN_MAX_STATIC_ALIGN_BYTES 0\n#endif\n\n#ifndef EIGEN_MAX_STATIC_ALIGN_BYTES\n\n  // Try to automatically guess what is the best default value for EIGEN_MAX_STATIC_ALIGN_BYTES\n\n  // 16 byte alignment is only useful for vectorization. Since it affects the ABI, we need to enable\n  // 16 byte alignment on all platforms where vectorization might be enabled. In theory we could always\n  // enable alignment, but it can be a cause of problems on some platforms, so we just disable it in\n  // certain common platform (compiler+architecture combinations) to avoid these problems.\n  // Only static alignment is really problematic (relies on nonstandard compiler extensions),\n  // try to keep heap alignment even when we have to disable static alignment.\n  #if EIGEN_COMP_GNUC && !(EIGEN_ARCH_i386_OR_x86_64 || EIGEN_ARCH_ARM_OR_ARM64 || EIGEN_ARCH_PPC || EIGEN_ARCH_IA64)\n  #define EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT 1\n  #elif EIGEN_ARCH_ARM_OR_ARM64 && EIGEN_COMP_GNUC_STRICT && EIGEN_GNUC_AT_MOST(4, 6)\n  // Old versions of GCC on ARM, at least 4.4, were once seen to have buggy static alignment support.\n  // Not sure which version fixed it, hopefully it doesn't affect 4.7, which is still somewhat in use.\n  // 4.8 and newer seem definitely unaffected.\n  #define EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT 1\n  #else\n  #define EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT 0\n  #endif\n\n  // static alignment is completely disabled with GCC 3, Sun Studio, and QCC/QNX\n  #if !EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT \\\n  && !EIGEN_GCC3_OR_OLDER \\\n  && !EIGEN_COMP_SUNCC \\\n  && !EIGEN_OS_QNX\n    #define EIGEN_ARCH_WANTS_STACK_ALIGNMENT 1\n  #else\n    #define EIGEN_ARCH_WANTS_STACK_ALIGNMENT 0\n  #endif\n\n  #if EIGEN_ARCH_WANTS_STACK_ALIGNMENT\n    #define EIGEN_MAX_STATIC_ALIGN_BYTES EIGEN_IDEAL_MAX_ALIGN_BYTES\n  #else\n    #define EIGEN_MAX_STATIC_ALIGN_BYTES 0\n  #endif\n\n#endif\n\n// If EIGEN_MAX_ALIGN_BYTES is defined, then it is considered as an upper bound for EIGEN_MAX_ALIGN_BYTES\n#if defined(EIGEN_MAX_ALIGN_BYTES) && EIGEN_MAX_ALIGN_BYTES<EIGEN_MAX_STATIC_ALIGN_BYTES\n#undef EIGEN_MAX_STATIC_ALIGN_BYTES\n#define EIGEN_MAX_STATIC_ALIGN_BYTES EIGEN_MAX_ALIGN_BYTES\n#endif\n\n#if EIGEN_MAX_STATIC_ALIGN_BYTES==0 && !defined(EIGEN_DISABLE_UNALIGNED_ARRAY_ASSERT)\n  #define EIGEN_DISABLE_UNALIGNED_ARRAY_ASSERT\n#endif\n\n// At this stage, EIGEN_MAX_STATIC_ALIGN_BYTES>0 is the true test whether we want to align arrays on the stack or not.\n// It takes into account both the user choice to explicitly enable/disable alignment (by settting EIGEN_MAX_STATIC_ALIGN_BYTES)\n// and the architecture config (EIGEN_ARCH_WANTS_STACK_ALIGNMENT).\n// Henceforth, only EIGEN_MAX_STATIC_ALIGN_BYTES should be used.\n\n\n// Shortcuts to EIGEN_ALIGN_TO_BOUNDARY\n#define EIGEN_ALIGN8  EIGEN_ALIGN_TO_BOUNDARY(8)\n#define EIGEN_ALIGN16 EIGEN_ALIGN_TO_BOUNDARY(16)\n#define EIGEN_ALIGN32 EIGEN_ALIGN_TO_BOUNDARY(32)\n#define EIGEN_ALIGN64 EIGEN_ALIGN_TO_BOUNDARY(64)\n#if EIGEN_MAX_STATIC_ALIGN_BYTES>0\n#define EIGEN_ALIGN_MAX EIGEN_ALIGN_TO_BOUNDARY(EIGEN_MAX_STATIC_ALIGN_BYTES)\n#else\n#define EIGEN_ALIGN_MAX\n#endif\n\n\n// Dynamic alignment control\n\n#if defined(EIGEN_DONT_ALIGN) && defined(EIGEN_MAX_ALIGN_BYTES) && EIGEN_MAX_ALIGN_BYTES>0\n#error EIGEN_MAX_ALIGN_BYTES and EIGEN_DONT_ALIGN are both defined with EIGEN_MAX_ALIGN_BYTES!=0. Use EIGEN_MAX_ALIGN_BYTES=0 as a synonym of EIGEN_DONT_ALIGN.\n#endif\n\n#ifdef EIGEN_DONT_ALIGN\n  #ifdef EIGEN_MAX_ALIGN_BYTES\n    #undef EIGEN_MAX_ALIGN_BYTES\n  #endif\n  #define EIGEN_MAX_ALIGN_BYTES 0\n#elif !defined(EIGEN_MAX_ALIGN_BYTES)\n  #define EIGEN_MAX_ALIGN_BYTES EIGEN_IDEAL_MAX_ALIGN_BYTES\n#endif\n\n#if EIGEN_IDEAL_MAX_ALIGN_BYTES > EIGEN_MAX_ALIGN_BYTES\n#define EIGEN_DEFAULT_ALIGN_BYTES EIGEN_IDEAL_MAX_ALIGN_BYTES\n#else\n#define EIGEN_DEFAULT_ALIGN_BYTES EIGEN_MAX_ALIGN_BYTES\n#endif\n\n\n#ifndef EIGEN_UNALIGNED_VECTORIZE\n#define EIGEN_UNALIGNED_VECTORIZE 1\n#endif\n\n//----------------------------------------------------------------------\n\n\n#ifdef EIGEN_DONT_USE_RESTRICT_KEYWORD\n  #define EIGEN_RESTRICT\n#endif\n#ifndef EIGEN_RESTRICT\n  #define EIGEN_RESTRICT __restrict\n#endif\n\n#ifndef EIGEN_STACK_ALLOCATION_LIMIT\n// 131072 == 128 KB\n#define EIGEN_STACK_ALLOCATION_LIMIT 131072\n#endif\n\n#ifndef EIGEN_DEFAULT_IO_FORMAT\n#ifdef EIGEN_MAKING_DOCS\n// format used in Eigen's documentation\n// needed to define it here as escaping characters in CMake add_definition's argument seems very problematic.\n#define EIGEN_DEFAULT_IO_FORMAT Eigen::IOFormat(3, 0, \" \", \"\\n\", \"\", \"\")\n#else\n#define EIGEN_DEFAULT_IO_FORMAT Eigen::IOFormat()\n#endif\n#endif\n\n// just an empty macro !\n#define EIGEN_EMPTY\n\n#if EIGEN_COMP_MSVC_STRICT && (EIGEN_COMP_MSVC < 1900 || EIGEN_CUDACC_VER>0)\n  // for older MSVC versions, as well as 1900 && CUDA 8, using the base operator is sufficient (cf Bugs 1000, 1324)\n  #define EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \\\n    using Base::operator =;\n#elif EIGEN_COMP_CLANG // workaround clang bug (see http://forum.kde.org/viewtopic.php?f=74&t=102653)\n  #define EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \\\n    using Base::operator =; \\\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const Derived& other) { Base::operator=(other); return *this; } \\\n    template <typename OtherDerived> \\\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const DenseBase<OtherDerived>& other) { Base::operator=(other.derived()); return *this; }\n#else\n  #define EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \\\n    using Base::operator =; \\\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const Derived& other) \\\n    { \\\n      Base::operator=(other); \\\n      return *this; \\\n    }\n#endif\n\n\n/** \\internal\n * \\brief Macro to manually inherit assignment operators.\n * This is necessary, because the implicitly defined assignment operator gets deleted when a custom operator= is defined.\n */\n#define EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Derived) EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived)\n\n/**\n* Just a side note. Commenting within defines works only by documenting\n* behind the object (via '!<'). Comments cannot be multi-line and thus\n* we have these extra long lines. What is confusing doxygen over here is\n* that we use '\\' and basically have a bunch of typedefs with their\n* documentation in a single line.\n**/\n\n#define EIGEN_GENERIC_PUBLIC_INTERFACE(Derived) \\\n  typedef typename Eigen::internal::traits<Derived>::Scalar Scalar; /*!< \\brief Numeric type, e.g. float, double, int or std::complex<float>. */ \\\n  typedef typename Eigen::NumTraits<Scalar>::Real RealScalar; /*!< \\brief The underlying numeric type for composed scalar types. \\details In cases where Scalar is e.g. std::complex<T>, T were corresponding to RealScalar. */ \\\n  typedef typename Base::CoeffReturnType CoeffReturnType; /*!< \\brief The return type for coefficient access. \\details Depending on whether the object allows direct coefficient access (e.g. for a MatrixXd), this type is either 'const Scalar&' or simply 'Scalar' for objects that do not allow direct coefficient access. */ \\\n  typedef typename Eigen::internal::ref_selector<Derived>::type Nested; \\\n  typedef typename Eigen::internal::traits<Derived>::StorageKind StorageKind; \\\n  typedef typename Eigen::internal::traits<Derived>::StorageIndex StorageIndex; \\\n  enum { RowsAtCompileTime = Eigen::internal::traits<Derived>::RowsAtCompileTime, \\\n        ColsAtCompileTime = Eigen::internal::traits<Derived>::ColsAtCompileTime, \\\n        Flags = Eigen::internal::traits<Derived>::Flags, \\\n        SizeAtCompileTime = Base::SizeAtCompileTime, \\\n        MaxSizeAtCompileTime = Base::MaxSizeAtCompileTime, \\\n        IsVectorAtCompileTime = Base::IsVectorAtCompileTime }; \\\n  using Base::derived; \\\n  using Base::const_cast_derived;\n\n\n// FIXME Maybe the EIGEN_DENSE_PUBLIC_INTERFACE could be removed as importing PacketScalar is rarely needed\n#define EIGEN_DENSE_PUBLIC_INTERFACE(Derived) \\\n  EIGEN_GENERIC_PUBLIC_INTERFACE(Derived) \\\n  typedef typename Base::PacketScalar PacketScalar;\n\n\n#define EIGEN_PLAIN_ENUM_MIN(a,b) (((int)a <= (int)b) ? (int)a : (int)b)\n#define EIGEN_PLAIN_ENUM_MAX(a,b) (((int)a >= (int)b) ? (int)a : (int)b)\n\n// EIGEN_SIZE_MIN_PREFER_DYNAMIC gives the min between compile-time sizes. 0 has absolute priority, followed by 1,\n// followed by Dynamic, followed by other finite values. The reason for giving Dynamic the priority over\n// finite values is that min(3, Dynamic) should be Dynamic, since that could be anything between 0 and 3.\n#define EIGEN_SIZE_MIN_PREFER_DYNAMIC(a,b) (((int)a == 0 || (int)b == 0) ? 0 \\\n                           : ((int)a == 1 || (int)b == 1) ? 1 \\\n                           : ((int)a == Dynamic || (int)b == Dynamic) ? Dynamic \\\n                           : ((int)a <= (int)b) ? (int)a : (int)b)\n\n// EIGEN_SIZE_MIN_PREFER_FIXED is a variant of EIGEN_SIZE_MIN_PREFER_DYNAMIC comparing MaxSizes. The difference is that finite values\n// now have priority over Dynamic, so that min(3, Dynamic) gives 3. Indeed, whatever the actual value is\n// (between 0 and 3), it is not more than 3.\n#define EIGEN_SIZE_MIN_PREFER_FIXED(a,b)  (((int)a == 0 || (int)b == 0) ? 0 \\\n                           : ((int)a == 1 || (int)b == 1) ? 1 \\\n                           : ((int)a == Dynamic && (int)b == Dynamic) ? Dynamic \\\n                           : ((int)a == Dynamic) ? (int)b \\\n                           : ((int)b == Dynamic) ? (int)a \\\n                           : ((int)a <= (int)b) ? (int)a : (int)b)\n\n// see EIGEN_SIZE_MIN_PREFER_DYNAMIC. No need for a separate variant for MaxSizes here.\n#define EIGEN_SIZE_MAX(a,b) (((int)a == Dynamic || (int)b == Dynamic) ? Dynamic \\\n                           : ((int)a >= (int)b) ? (int)a : (int)b)\n\n#define EIGEN_LOGICAL_XOR(a,b) (((a) || (b)) && !((a) && (b)))\n\n#define EIGEN_IMPLIES(a,b) (!(a) || (b))\n\n// the expression type of a standard coefficient wise binary operation\n#define EIGEN_CWISE_BINARY_RETURN_TYPE(LHS,RHS,OPNAME) \\\n    CwiseBinaryOp< \\\n      EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)< \\\n          typename internal::traits<LHS>::Scalar, \\\n          typename internal::traits<RHS>::Scalar \\\n      >, \\\n      const LHS, \\\n      const RHS \\\n    >\n\n#define EIGEN_MAKE_CWISE_BINARY_OP(METHOD,OPNAME) \\\n  template<typename OtherDerived> \\\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,OPNAME) \\\n  (METHOD)(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const \\\n  { \\\n    return EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,OPNAME)(derived(), other.derived()); \\\n  }\n\n#define EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,TYPEA,TYPEB) \\\n  (Eigen::internal::has_ReturnType<Eigen::ScalarBinaryOpTraits<TYPEA,TYPEB,EIGEN_CAT(EIGEN_CAT(Eigen::internal::scalar_,OPNAME),_op)<TYPEA,TYPEB>  > >::value)\n\n#define EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(EXPR,SCALAR,OPNAME) \\\n  CwiseBinaryOp<EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)<typename internal::traits<EXPR>::Scalar,SCALAR>, const EXPR, \\\n                const typename internal::plain_constant_type<EXPR,SCALAR>::type>\n\n#define EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(SCALAR,EXPR,OPNAME) \\\n  CwiseBinaryOp<EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)<SCALAR,typename internal::traits<EXPR>::Scalar>, \\\n                const typename internal::plain_constant_type<EXPR,SCALAR>::type, const EXPR>\n\n// Workaround for MSVC 2010 (see ML thread \"patch with compile for for MSVC 2010\")\n#if EIGEN_COMP_MSVC_STRICT<=1600\n#define EIGEN_MSVC10_WORKAROUND_BINARYOP_RETURN_TYPE(X) typename internal::enable_if<true,X>::type\n#else\n#define EIGEN_MSVC10_WORKAROUND_BINARYOP_RETURN_TYPE(X) X\n#endif\n\n#define EIGEN_MAKE_SCALAR_BINARY_OP_ONTHERIGHT(METHOD,OPNAME) \\\n  template <typename T> EIGEN_DEVICE_FUNC inline \\\n  EIGEN_MSVC10_WORKAROUND_BINARYOP_RETURN_TYPE(const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,typename internal::promote_scalar_arg<Scalar EIGEN_COMMA T EIGEN_COMMA EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,Scalar,T)>::type,OPNAME))\\\n  (METHOD)(const T& scalar) const { \\\n    typedef typename internal::promote_scalar_arg<Scalar,T,EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,Scalar,T)>::type PromotedT; \\\n    return EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,PromotedT,OPNAME)(derived(), \\\n           typename internal::plain_constant_type<Derived,PromotedT>::type(derived().rows(), derived().cols(), internal::scalar_constant_op<PromotedT>(scalar))); \\\n  }\n\n#define EIGEN_MAKE_SCALAR_BINARY_OP_ONTHELEFT(METHOD,OPNAME) \\\n  template <typename T> EIGEN_DEVICE_FUNC inline friend \\\n  EIGEN_MSVC10_WORKAROUND_BINARYOP_RETURN_TYPE(const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(typename internal::promote_scalar_arg<Scalar EIGEN_COMMA T EIGEN_COMMA EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,T,Scalar)>::type,Derived,OPNAME)) \\\n  (METHOD)(const T& scalar, const StorageBaseType& matrix) { \\\n    typedef typename internal::promote_scalar_arg<Scalar,T,EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,T,Scalar)>::type PromotedT; \\\n    return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(PromotedT,Derived,OPNAME)( \\\n           typename internal::plain_constant_type<Derived,PromotedT>::type(matrix.derived().rows(), matrix.derived().cols(), internal::scalar_constant_op<PromotedT>(scalar)), matrix.derived()); \\\n  }\n\n#define EIGEN_MAKE_SCALAR_BINARY_OP(METHOD,OPNAME) \\\n  EIGEN_MAKE_SCALAR_BINARY_OP_ONTHELEFT(METHOD,OPNAME) \\\n  EIGEN_MAKE_SCALAR_BINARY_OP_ONTHERIGHT(METHOD,OPNAME)\n\n\n#ifdef EIGEN_EXCEPTIONS\n#  define EIGEN_THROW_X(X) throw X\n#  define EIGEN_THROW throw\n#  define EIGEN_TRY try\n#  define EIGEN_CATCH(X) catch (X)\n#else\n#  ifdef __CUDA_ARCH__\n#    define EIGEN_THROW_X(X) asm(\"trap;\")\n#    define EIGEN_THROW asm(\"trap;\")\n#  else\n#    define EIGEN_THROW_X(X) std::abort()\n#    define EIGEN_THROW std::abort()\n#  endif\n#  define EIGEN_TRY if (true)\n#  define EIGEN_CATCH(X) else\n#endif\n\n\n#if EIGEN_HAS_CXX11_NOEXCEPT\n#   define EIGEN_INCLUDE_TYPE_TRAITS\n#   define EIGEN_NOEXCEPT noexcept\n#   define EIGEN_NOEXCEPT_IF(x) noexcept(x)\n#   define EIGEN_NO_THROW noexcept(true)\n#   define EIGEN_EXCEPTION_SPEC(X) noexcept(false)\n#else\n#   define EIGEN_NOEXCEPT\n#   define EIGEN_NOEXCEPT_IF(x)\n#   define EIGEN_NO_THROW throw()\n#   if EIGEN_COMP_MSVC\n      // MSVC does not support exception specifications (warning C4290),\n      // and they are deprecated in c++11 anyway.\n#     define EIGEN_EXCEPTION_SPEC(X) throw()\n#   else\n#     define EIGEN_EXCEPTION_SPEC(X) throw(X)\n#   endif\n#endif\n\n#endif // EIGEN_MACROS_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/util/Memory.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2008-2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2009 Kenneth Riddile <kfriddile@yahoo.com>\n// Copyright (C) 2010 Hauke Heibel <hauke.heibel@gmail.com>\n// Copyright (C) 2010 Thomas Capricelli <orzel@freehackers.org>\n// Copyright (C) 2013 Pavel Holoborodko <pavel@holoborodko.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n\n/*****************************************************************************\n*** Platform checks for aligned malloc functions                           ***\n*****************************************************************************/\n\n#ifndef EIGEN_MEMORY_H\n#define EIGEN_MEMORY_H\n\n#ifndef EIGEN_MALLOC_ALREADY_ALIGNED\n\n// Try to determine automatically if malloc is already aligned.\n\n// On 64-bit systems, glibc's malloc returns 16-byte-aligned pointers, see:\n//   http://www.gnu.org/s/libc/manual/html_node/Aligned-Memory-Blocks.html\n// This is true at least since glibc 2.8.\n// This leaves the question how to detect 64-bit. According to this document,\n//   http://gcc.fyxm.net/summit/2003/Porting%20to%2064%20bit.pdf\n// page 114, \"[The] LP64 model [...] is used by all 64-bit UNIX ports\" so it's indeed\n// quite safe, at least within the context of glibc, to equate 64-bit with LP64.\n#if defined(__GLIBC__) && ((__GLIBC__>=2 && __GLIBC_MINOR__ >= 8) || __GLIBC__>2) \\\n && defined(__LP64__) && ! defined( __SANITIZE_ADDRESS__ ) && (EIGEN_DEFAULT_ALIGN_BYTES == 16)\n  #define EIGEN_GLIBC_MALLOC_ALREADY_ALIGNED 1\n#else\n  #define EIGEN_GLIBC_MALLOC_ALREADY_ALIGNED 0\n#endif\n\n// FreeBSD 6 seems to have 16-byte aligned malloc\n//   See http://svn.freebsd.org/viewvc/base/stable/6/lib/libc/stdlib/malloc.c?view=markup\n// FreeBSD 7 seems to have 16-byte aligned malloc except on ARM and MIPS architectures\n//   See http://svn.freebsd.org/viewvc/base/stable/7/lib/libc/stdlib/malloc.c?view=markup\n#if defined(__FreeBSD__) && !(EIGEN_ARCH_ARM || EIGEN_ARCH_MIPS) && (EIGEN_DEFAULT_ALIGN_BYTES == 16)\n  #define EIGEN_FREEBSD_MALLOC_ALREADY_ALIGNED 1\n#else\n  #define EIGEN_FREEBSD_MALLOC_ALREADY_ALIGNED 0\n#endif\n\n#if (EIGEN_OS_MAC && (EIGEN_DEFAULT_ALIGN_BYTES == 16))     \\\n || (EIGEN_OS_WIN64 && (EIGEN_DEFAULT_ALIGN_BYTES == 16))   \\\n || EIGEN_GLIBC_MALLOC_ALREADY_ALIGNED              \\\n || EIGEN_FREEBSD_MALLOC_ALREADY_ALIGNED\n  #define EIGEN_MALLOC_ALREADY_ALIGNED 1\n#else\n  #define EIGEN_MALLOC_ALREADY_ALIGNED 0\n#endif\n\n#endif\n\nnamespace Eigen {\n\nnamespace internal {\n\nEIGEN_DEVICE_FUNC \ninline void throw_std_bad_alloc()\n{\n  #ifdef EIGEN_EXCEPTIONS\n    throw std::bad_alloc();\n  #else\n    std::size_t huge = static_cast<std::size_t>(-1);\n    ::operator new(huge);\n  #endif\n}\n\n/*****************************************************************************\n*** Implementation of handmade aligned functions                           ***\n*****************************************************************************/\n\n/* ----- Hand made implementations of aligned malloc/free and realloc ----- */\n\n/** \\internal Like malloc, but the returned pointer is guaranteed to be 16-byte aligned.\n  * Fast, but wastes 16 additional bytes of memory. Does not throw any exception.\n  */\ninline void* handmade_aligned_malloc(std::size_t size)\n{\n  void *original = std::malloc(size+EIGEN_DEFAULT_ALIGN_BYTES);\n  if (original == 0) return 0;\n  void *aligned = reinterpret_cast<void*>((reinterpret_cast<std::size_t>(original) & ~(std::size_t(EIGEN_DEFAULT_ALIGN_BYTES-1))) + EIGEN_DEFAULT_ALIGN_BYTES);\n  *(reinterpret_cast<void**>(aligned) - 1) = original;\n  return aligned;\n}\n\n/** \\internal Frees memory allocated with handmade_aligned_malloc */\ninline void handmade_aligned_free(void *ptr)\n{\n  if (ptr) std::free(*(reinterpret_cast<void**>(ptr) - 1));\n}\n\n/** \\internal\n  * \\brief Reallocates aligned memory.\n  * Since we know that our handmade version is based on std::malloc\n  * we can use std::realloc to implement efficient reallocation.\n  */\ninline void* handmade_aligned_realloc(void* ptr, std::size_t size, std::size_t = 0)\n{\n  if (ptr == 0) return handmade_aligned_malloc(size);\n  void *original = *(reinterpret_cast<void**>(ptr) - 1);\n  std::ptrdiff_t previous_offset = static_cast<char *>(ptr)-static_cast<char *>(original);\n  original = std::realloc(original,size+EIGEN_DEFAULT_ALIGN_BYTES);\n  if (original == 0) return 0;\n  void *aligned = reinterpret_cast<void*>((reinterpret_cast<std::size_t>(original) & ~(std::size_t(EIGEN_DEFAULT_ALIGN_BYTES-1))) + EIGEN_DEFAULT_ALIGN_BYTES);\n  void *previous_aligned = static_cast<char *>(original)+previous_offset;\n  if(aligned!=previous_aligned)\n    std::memmove(aligned, previous_aligned, size);\n  \n  *(reinterpret_cast<void**>(aligned) - 1) = original;\n  return aligned;\n}\n\n/*****************************************************************************\n*** Implementation of portable aligned versions of malloc/free/realloc     ***\n*****************************************************************************/\n\n#ifdef EIGEN_NO_MALLOC\nEIGEN_DEVICE_FUNC inline void check_that_malloc_is_allowed()\n{\n  eigen_assert(false && \"heap allocation is forbidden (EIGEN_NO_MALLOC is defined)\");\n}\n#elif defined EIGEN_RUNTIME_NO_MALLOC\nEIGEN_DEVICE_FUNC inline bool is_malloc_allowed_impl(bool update, bool new_value = false)\n{\n  static bool value = true;\n  if (update == 1)\n    value = new_value;\n  return value;\n}\nEIGEN_DEVICE_FUNC inline bool is_malloc_allowed() { return is_malloc_allowed_impl(false); }\nEIGEN_DEVICE_FUNC inline bool set_is_malloc_allowed(bool new_value) { return is_malloc_allowed_impl(true, new_value); }\nEIGEN_DEVICE_FUNC inline void check_that_malloc_is_allowed()\n{\n  eigen_assert(is_malloc_allowed() && \"heap allocation is forbidden (EIGEN_RUNTIME_NO_MALLOC is defined and g_is_malloc_allowed is false)\");\n}\n#else \nEIGEN_DEVICE_FUNC inline void check_that_malloc_is_allowed()\n{}\n#endif\n\n/** \\internal Allocates \\a size bytes. The returned pointer is guaranteed to have 16 or 32 bytes alignment depending on the requirements.\n  * On allocation error, the returned pointer is null, and std::bad_alloc is thrown.\n  */\nEIGEN_DEVICE_FUNC inline void* aligned_malloc(std::size_t size)\n{\n  check_that_malloc_is_allowed();\n\n  void *result;\n  #if (EIGEN_DEFAULT_ALIGN_BYTES==0) || EIGEN_MALLOC_ALREADY_ALIGNED\n    result = std::malloc(size);\n    #if EIGEN_DEFAULT_ALIGN_BYTES==16\n    eigen_assert((size<16 || (std::size_t(result)%16)==0) && \"System's malloc returned an unaligned pointer. Compile with EIGEN_MALLOC_ALREADY_ALIGNED=0 to fallback to handmade alignd memory allocator.\");\n    #endif\n  #else\n    result = handmade_aligned_malloc(size);\n  #endif\n\n  if(!result && size)\n    throw_std_bad_alloc();\n\n  return result;\n}\n\n/** \\internal Frees memory allocated with aligned_malloc. */\nEIGEN_DEVICE_FUNC inline void aligned_free(void *ptr)\n{\n  #if (EIGEN_DEFAULT_ALIGN_BYTES==0) || EIGEN_MALLOC_ALREADY_ALIGNED\n    std::free(ptr);\n  #else\n    handmade_aligned_free(ptr);\n  #endif\n}\n\n/**\n  * \\internal\n  * \\brief Reallocates an aligned block of memory.\n  * \\throws std::bad_alloc on allocation failure\n  */\ninline void* aligned_realloc(void *ptr, std::size_t new_size, std::size_t old_size)\n{\n  EIGEN_UNUSED_VARIABLE(old_size);\n\n  void *result;\n#if (EIGEN_DEFAULT_ALIGN_BYTES==0) || EIGEN_MALLOC_ALREADY_ALIGNED\n  result = std::realloc(ptr,new_size);\n#else\n  result = handmade_aligned_realloc(ptr,new_size,old_size);\n#endif\n\n  if (!result && new_size)\n    throw_std_bad_alloc();\n\n  return result;\n}\n\n/*****************************************************************************\n*** Implementation of conditionally aligned functions                      ***\n*****************************************************************************/\n\n/** \\internal Allocates \\a size bytes. If Align is true, then the returned ptr is 16-byte-aligned.\n  * On allocation error, the returned pointer is null, and a std::bad_alloc is thrown.\n  */\ntemplate<bool Align> EIGEN_DEVICE_FUNC inline void* conditional_aligned_malloc(std::size_t size)\n{\n  return aligned_malloc(size);\n}\n\ntemplate<> EIGEN_DEVICE_FUNC inline void* conditional_aligned_malloc<false>(std::size_t size)\n{\n  check_that_malloc_is_allowed();\n\n  void *result = std::malloc(size);\n  if(!result && size)\n    throw_std_bad_alloc();\n  return result;\n}\n\n/** \\internal Frees memory allocated with conditional_aligned_malloc */\ntemplate<bool Align> EIGEN_DEVICE_FUNC inline void conditional_aligned_free(void *ptr)\n{\n  aligned_free(ptr);\n}\n\ntemplate<> EIGEN_DEVICE_FUNC inline void conditional_aligned_free<false>(void *ptr)\n{\n  std::free(ptr);\n}\n\ntemplate<bool Align> inline void* conditional_aligned_realloc(void* ptr, std::size_t new_size, std::size_t old_size)\n{\n  return aligned_realloc(ptr, new_size, old_size);\n}\n\ntemplate<> inline void* conditional_aligned_realloc<false>(void* ptr, std::size_t new_size, std::size_t)\n{\n  return std::realloc(ptr, new_size);\n}\n\n/*****************************************************************************\n*** Construction/destruction of array elements                             ***\n*****************************************************************************/\n\n/** \\internal Destructs the elements of an array.\n  * The \\a size parameters tells on how many objects to call the destructor of T.\n  */\ntemplate<typename T> EIGEN_DEVICE_FUNC inline void destruct_elements_of_array(T *ptr, std::size_t size)\n{\n  // always destruct an array starting from the end.\n  if(ptr)\n    while(size) ptr[--size].~T();\n}\n\n/** \\internal Constructs the elements of an array.\n  * The \\a size parameter tells on how many objects to call the constructor of T.\n  */\ntemplate<typename T> EIGEN_DEVICE_FUNC inline T* construct_elements_of_array(T *ptr, std::size_t size)\n{\n  std::size_t i;\n  EIGEN_TRY\n  {\n      for (i = 0; i < size; ++i) ::new (ptr + i) T;\n      return ptr;\n  }\n  EIGEN_CATCH(...)\n  {\n    destruct_elements_of_array(ptr, i);\n    EIGEN_THROW;\n  }\n  return NULL;\n}\n\n/*****************************************************************************\n*** Implementation of aligned new/delete-like functions                    ***\n*****************************************************************************/\n\ntemplate<typename T>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void check_size_for_overflow(std::size_t size)\n{\n  if(size > std::size_t(-1) / sizeof(T))\n    throw_std_bad_alloc();\n}\n\n/** \\internal Allocates \\a size objects of type T. The returned pointer is guaranteed to have 16 bytes alignment.\n  * On allocation error, the returned pointer is undefined, but a std::bad_alloc is thrown.\n  * The default constructor of T is called.\n  */\ntemplate<typename T> EIGEN_DEVICE_FUNC inline T* aligned_new(std::size_t size)\n{\n  check_size_for_overflow<T>(size);\n  T *result = reinterpret_cast<T*>(aligned_malloc(sizeof(T)*size));\n  EIGEN_TRY\n  {\n    return construct_elements_of_array(result, size);\n  }\n  EIGEN_CATCH(...)\n  {\n    aligned_free(result);\n    EIGEN_THROW;\n  }\n  return result;\n}\n\ntemplate<typename T, bool Align> EIGEN_DEVICE_FUNC inline T* conditional_aligned_new(std::size_t size)\n{\n  check_size_for_overflow<T>(size);\n  T *result = reinterpret_cast<T*>(conditional_aligned_malloc<Align>(sizeof(T)*size));\n  EIGEN_TRY\n  {\n    return construct_elements_of_array(result, size);\n  }\n  EIGEN_CATCH(...)\n  {\n    conditional_aligned_free<Align>(result);\n    EIGEN_THROW;\n  }\n  return result;\n}\n\n/** \\internal Deletes objects constructed with aligned_new\n  * The \\a size parameters tells on how many objects to call the destructor of T.\n  */\ntemplate<typename T> EIGEN_DEVICE_FUNC inline void aligned_delete(T *ptr, std::size_t size)\n{\n  destruct_elements_of_array<T>(ptr, size);\n  aligned_free(ptr);\n}\n\n/** \\internal Deletes objects constructed with conditional_aligned_new\n  * The \\a size parameters tells on how many objects to call the destructor of T.\n  */\ntemplate<typename T, bool Align> EIGEN_DEVICE_FUNC inline void conditional_aligned_delete(T *ptr, std::size_t size)\n{\n  destruct_elements_of_array<T>(ptr, size);\n  conditional_aligned_free<Align>(ptr);\n}\n\ntemplate<typename T, bool Align> EIGEN_DEVICE_FUNC inline T* conditional_aligned_realloc_new(T* pts, std::size_t new_size, std::size_t old_size)\n{\n  check_size_for_overflow<T>(new_size);\n  check_size_for_overflow<T>(old_size);\n  if(new_size < old_size)\n    destruct_elements_of_array(pts+new_size, old_size-new_size);\n  T *result = reinterpret_cast<T*>(conditional_aligned_realloc<Align>(reinterpret_cast<void*>(pts), sizeof(T)*new_size, sizeof(T)*old_size));\n  if(new_size > old_size)\n  {\n    EIGEN_TRY\n    {\n      construct_elements_of_array(result+old_size, new_size-old_size);\n    }\n    EIGEN_CATCH(...)\n    {\n      conditional_aligned_free<Align>(result);\n      EIGEN_THROW;\n    }\n  }\n  return result;\n}\n\n\ntemplate<typename T, bool Align> EIGEN_DEVICE_FUNC inline T* conditional_aligned_new_auto(std::size_t size)\n{\n  if(size==0)\n    return 0; // short-cut. Also fixes Bug 884\n  check_size_for_overflow<T>(size);\n  T *result = reinterpret_cast<T*>(conditional_aligned_malloc<Align>(sizeof(T)*size));\n  if(NumTraits<T>::RequireInitialization)\n  {\n    EIGEN_TRY\n    {\n      construct_elements_of_array(result, size);\n    }\n    EIGEN_CATCH(...)\n    {\n      conditional_aligned_free<Align>(result);\n      EIGEN_THROW;\n    }\n  }\n  return result;\n}\n\ntemplate<typename T, bool Align> inline T* conditional_aligned_realloc_new_auto(T* pts, std::size_t new_size, std::size_t old_size)\n{\n  check_size_for_overflow<T>(new_size);\n  check_size_for_overflow<T>(old_size);\n  if(NumTraits<T>::RequireInitialization && (new_size < old_size))\n    destruct_elements_of_array(pts+new_size, old_size-new_size);\n  T *result = reinterpret_cast<T*>(conditional_aligned_realloc<Align>(reinterpret_cast<void*>(pts), sizeof(T)*new_size, sizeof(T)*old_size));\n  if(NumTraits<T>::RequireInitialization && (new_size > old_size))\n  {\n    EIGEN_TRY\n    {\n      construct_elements_of_array(result+old_size, new_size-old_size);\n    }\n    EIGEN_CATCH(...)\n    {\n      conditional_aligned_free<Align>(result);\n      EIGEN_THROW;\n    }\n  }\n  return result;\n}\n\ntemplate<typename T, bool Align> EIGEN_DEVICE_FUNC inline void conditional_aligned_delete_auto(T *ptr, std::size_t size)\n{\n  if(NumTraits<T>::RequireInitialization)\n    destruct_elements_of_array<T>(ptr, size);\n  conditional_aligned_free<Align>(ptr);\n}\n\n/****************************************************************************/\n\n/** \\internal Returns the index of the first element of the array that is well aligned with respect to the requested \\a Alignment.\n  *\n  * \\tparam Alignment requested alignment in Bytes.\n  * \\param array the address of the start of the array\n  * \\param size the size of the array\n  *\n  * \\note If no element of the array is well aligned or the requested alignment is not a multiple of a scalar,\n  * the size of the array is returned. For example with SSE, the requested alignment is typically 16-bytes. If\n  * packet size for the given scalar type is 1, then everything is considered well-aligned.\n  *\n  * \\note Otherwise, if the Alignment is larger that the scalar size, we rely on the assumptions that sizeof(Scalar) is a\n  * power of 2. On the other hand, we do not assume that the array address is a multiple of sizeof(Scalar), as that fails for\n  * example with Scalar=double on certain 32-bit platforms, see bug #79.\n  *\n  * There is also the variant first_aligned(const MatrixBase&) defined in DenseCoeffsBase.h.\n  * \\sa first_default_aligned()\n  */\ntemplate<int Alignment, typename Scalar, typename Index>\nEIGEN_DEVICE_FUNC inline Index first_aligned(const Scalar* array, Index size)\n{\n  const Index ScalarSize = sizeof(Scalar);\n  const Index AlignmentSize = Alignment / ScalarSize;\n  const Index AlignmentMask = AlignmentSize-1;\n\n  if(AlignmentSize<=1)\n  {\n    // Either the requested alignment if smaller than a scalar, or it exactly match a 1 scalar\n    // so that all elements of the array have the same alignment.\n    return 0;\n  }\n  else if( (UIntPtr(array) & (sizeof(Scalar)-1)) || (Alignment%ScalarSize)!=0)\n  {\n    // The array is not aligned to the size of a single scalar, or the requested alignment is not a multiple of the scalar size.\n    // Consequently, no element of the array is well aligned.\n    return size;\n  }\n  else\n  {\n    Index first = (AlignmentSize - (Index((UIntPtr(array)/sizeof(Scalar))) & AlignmentMask)) & AlignmentMask;\n    return (first < size) ? first : size;\n  }\n}\n\n/** \\internal Returns the index of the first element of the array that is well aligned with respect the largest packet requirement.\n   * \\sa first_aligned(Scalar*,Index) and first_default_aligned(DenseBase<Derived>) */\ntemplate<typename Scalar, typename Index>\nEIGEN_DEVICE_FUNC inline Index first_default_aligned(const Scalar* array, Index size)\n{\n  typedef typename packet_traits<Scalar>::type DefaultPacketType;\n  return first_aligned<unpacket_traits<DefaultPacketType>::alignment>(array, size);\n}\n\n/** \\internal Returns the smallest integer multiple of \\a base and greater or equal to \\a size\n  */ \ntemplate<typename Index> \ninline Index first_multiple(Index size, Index base)\n{\n  return ((size+base-1)/base)*base;\n}\n\n// std::copy is much slower than memcpy, so let's introduce a smart_copy which\n// use memcpy on trivial types, i.e., on types that does not require an initialization ctor.\ntemplate<typename T, bool UseMemcpy> struct smart_copy_helper;\n\ntemplate<typename T> EIGEN_DEVICE_FUNC void smart_copy(const T* start, const T* end, T* target)\n{\n  smart_copy_helper<T,!NumTraits<T>::RequireInitialization>::run(start, end, target);\n}\n\ntemplate<typename T> struct smart_copy_helper<T,true> {\n  EIGEN_DEVICE_FUNC static inline void run(const T* start, const T* end, T* target)\n  {\n    IntPtr size = IntPtr(end)-IntPtr(start);\n    if(size==0) return;\n    eigen_internal_assert(start!=0 && end!=0 && target!=0);\n    std::memcpy(target, start, size);\n  }\n};\n\ntemplate<typename T> struct smart_copy_helper<T,false> {\n  EIGEN_DEVICE_FUNC static inline void run(const T* start, const T* end, T* target)\n  { std::copy(start, end, target); }\n};\n\n// intelligent memmove. falls back to std::memmove for POD types, uses std::copy otherwise. \ntemplate<typename T, bool UseMemmove> struct smart_memmove_helper;\n\ntemplate<typename T> void smart_memmove(const T* start, const T* end, T* target)\n{\n  smart_memmove_helper<T,!NumTraits<T>::RequireInitialization>::run(start, end, target);\n}\n\ntemplate<typename T> struct smart_memmove_helper<T,true> {\n  static inline void run(const T* start, const T* end, T* target)\n  {\n    IntPtr size = IntPtr(end)-IntPtr(start);\n    if(size==0) return;\n    eigen_internal_assert(start!=0 && end!=0 && target!=0);\n    std::memmove(target, start, size);\n  }\n};\n\ntemplate<typename T> struct smart_memmove_helper<T,false> {\n  static inline void run(const T* start, const T* end, T* target)\n  { \n    if (UIntPtr(target) < UIntPtr(start))\n    {\n      std::copy(start, end, target);\n    }\n    else                                 \n    {\n      std::ptrdiff_t count = (std::ptrdiff_t(end)-std::ptrdiff_t(start)) / sizeof(T);\n      std::copy_backward(start, end, target + count); \n    }\n  }\n};\n\n\n/*****************************************************************************\n*** Implementation of runtime stack allocation (falling back to malloc)    ***\n*****************************************************************************/\n\n// you can overwrite Eigen's default behavior regarding alloca by defining EIGEN_ALLOCA\n// to the appropriate stack allocation function\n#ifndef EIGEN_ALLOCA\n  #if EIGEN_OS_LINUX || EIGEN_OS_MAC || (defined alloca)\n    #define EIGEN_ALLOCA alloca\n  #elif EIGEN_COMP_MSVC\n    #define EIGEN_ALLOCA _alloca\n  #endif\n#endif\n\n// This helper class construct the allocated memory, and takes care of destructing and freeing the handled data\n// at destruction time. In practice this helper class is mainly useful to avoid memory leak in case of exceptions.\ntemplate<typename T> class aligned_stack_memory_handler : noncopyable\n{\n  public:\n    /* Creates a stack_memory_handler responsible for the buffer \\a ptr of size \\a size.\n     * Note that \\a ptr can be 0 regardless of the other parameters.\n     * This constructor takes care of constructing/initializing the elements of the buffer if required by the scalar type T (see NumTraits<T>::RequireInitialization).\n     * In this case, the buffer elements will also be destructed when this handler will be destructed.\n     * Finally, if \\a dealloc is true, then the pointer \\a ptr is freed.\n     **/\n    aligned_stack_memory_handler(T* ptr, std::size_t size, bool dealloc)\n      : m_ptr(ptr), m_size(size), m_deallocate(dealloc)\n    {\n      if(NumTraits<T>::RequireInitialization && m_ptr)\n        Eigen::internal::construct_elements_of_array(m_ptr, size);\n    }\n    ~aligned_stack_memory_handler()\n    {\n      if(NumTraits<T>::RequireInitialization && m_ptr)\n        Eigen::internal::destruct_elements_of_array<T>(m_ptr, m_size);\n      if(m_deallocate)\n        Eigen::internal::aligned_free(m_ptr);\n    }\n  protected:\n    T* m_ptr;\n    std::size_t m_size;\n    bool m_deallocate;\n};\n\ntemplate<typename T> class scoped_array : noncopyable\n{\n  T* m_ptr;\npublic:\n  explicit scoped_array(std::ptrdiff_t size)\n  {\n    m_ptr = new T[size];\n  }\n  ~scoped_array()\n  {\n    delete[] m_ptr;\n  }\n  T& operator[](std::ptrdiff_t i) { return m_ptr[i]; }\n  const T& operator[](std::ptrdiff_t i) const { return m_ptr[i]; }\n  T* &ptr() { return m_ptr; }\n  const T* ptr() const { return m_ptr; }\n  operator const T*() const { return m_ptr; }\n};\n\ntemplate<typename T> void swap(scoped_array<T> &a,scoped_array<T> &b)\n{\n  std::swap(a.ptr(),b.ptr());\n}\n    \n} // end namespace internal\n\n/** \\internal\n  * Declares, allocates and construct an aligned buffer named NAME of SIZE elements of type TYPE on the stack\n  * if SIZE is smaller than EIGEN_STACK_ALLOCATION_LIMIT, and if stack allocation is supported by the platform\n  * (currently, this is Linux and Visual Studio only). Otherwise the memory is allocated on the heap.\n  * The allocated buffer is automatically deleted when exiting the scope of this declaration.\n  * If BUFFER is non null, then the declared variable is simply an alias for BUFFER, and no allocation/deletion occurs.\n  * Here is an example:\n  * \\code\n  * {\n  *   ei_declare_aligned_stack_constructed_variable(float,data,size,0);\n  *   // use data[0] to data[size-1]\n  * }\n  * \\endcode\n  * The underlying stack allocation function can controlled with the EIGEN_ALLOCA preprocessor token.\n  */\n#ifdef EIGEN_ALLOCA\n  \n  #if EIGEN_DEFAULT_ALIGN_BYTES>0\n    // We always manually re-align the result of EIGEN_ALLOCA.\n    // If alloca is already aligned, the compiler should be smart enough to optimize away the re-alignment.\n    #define EIGEN_ALIGNED_ALLOCA(SIZE) reinterpret_cast<void*>((internal::UIntPtr(EIGEN_ALLOCA(SIZE+EIGEN_DEFAULT_ALIGN_BYTES-1)) + EIGEN_DEFAULT_ALIGN_BYTES-1) & ~(std::size_t(EIGEN_DEFAULT_ALIGN_BYTES-1)))\n  #else\n    #define EIGEN_ALIGNED_ALLOCA(SIZE) EIGEN_ALLOCA(SIZE)\n  #endif\n\n  #define ei_declare_aligned_stack_constructed_variable(TYPE,NAME,SIZE,BUFFER) \\\n    Eigen::internal::check_size_for_overflow<TYPE>(SIZE); \\\n    TYPE* NAME = (BUFFER)!=0 ? (BUFFER) \\\n               : reinterpret_cast<TYPE*>( \\\n                      (sizeof(TYPE)*SIZE<=EIGEN_STACK_ALLOCATION_LIMIT) ? EIGEN_ALIGNED_ALLOCA(sizeof(TYPE)*SIZE) \\\n                    : Eigen::internal::aligned_malloc(sizeof(TYPE)*SIZE) );  \\\n    Eigen::internal::aligned_stack_memory_handler<TYPE> EIGEN_CAT(NAME,_stack_memory_destructor)((BUFFER)==0 ? NAME : 0,SIZE,sizeof(TYPE)*SIZE>EIGEN_STACK_ALLOCATION_LIMIT)\n\n#else\n\n  #define ei_declare_aligned_stack_constructed_variable(TYPE,NAME,SIZE,BUFFER) \\\n    Eigen::internal::check_size_for_overflow<TYPE>(SIZE); \\\n    TYPE* NAME = (BUFFER)!=0 ? BUFFER : reinterpret_cast<TYPE*>(Eigen::internal::aligned_malloc(sizeof(TYPE)*SIZE));    \\\n    Eigen::internal::aligned_stack_memory_handler<TYPE> EIGEN_CAT(NAME,_stack_memory_destructor)((BUFFER)==0 ? NAME : 0,SIZE,true)\n    \n#endif\n\n\n/*****************************************************************************\n*** Implementation of EIGEN_MAKE_ALIGNED_OPERATOR_NEW [_IF]                ***\n*****************************************************************************/\n\n#if EIGEN_MAX_ALIGN_BYTES!=0\n  #define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_NOTHROW(NeedsToAlign) \\\n      void* operator new(std::size_t size, const std::nothrow_t&) EIGEN_NO_THROW { \\\n        EIGEN_TRY { return Eigen::internal::conditional_aligned_malloc<NeedsToAlign>(size); } \\\n        EIGEN_CATCH (...) { return 0; } \\\n      }\n  #define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(NeedsToAlign) \\\n      void *operator new(std::size_t size) { \\\n        return Eigen::internal::conditional_aligned_malloc<NeedsToAlign>(size); \\\n      } \\\n      void *operator new[](std::size_t size) { \\\n        return Eigen::internal::conditional_aligned_malloc<NeedsToAlign>(size); \\\n      } \\\n      void operator delete(void * ptr) EIGEN_NO_THROW { Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr); } \\\n      void operator delete[](void * ptr) EIGEN_NO_THROW { Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr); } \\\n      void operator delete(void * ptr, std::size_t /* sz */) EIGEN_NO_THROW { Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr); } \\\n      void operator delete[](void * ptr, std::size_t /* sz */) EIGEN_NO_THROW { Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr); } \\\n      /* in-place new and delete. since (at least afaik) there is no actual   */ \\\n      /* memory allocated we can safely let the default implementation handle */ \\\n      /* this particular case. */ \\\n      static void *operator new(std::size_t size, void *ptr) { return ::operator new(size,ptr); } \\\n      static void *operator new[](std::size_t size, void* ptr) { return ::operator new[](size,ptr); } \\\n      void operator delete(void * memory, void *ptr) EIGEN_NO_THROW { return ::operator delete(memory,ptr); } \\\n      void operator delete[](void * memory, void *ptr) EIGEN_NO_THROW { return ::operator delete[](memory,ptr); } \\\n      /* nothrow-new (returns zero instead of std::bad_alloc) */ \\\n      EIGEN_MAKE_ALIGNED_OPERATOR_NEW_NOTHROW(NeedsToAlign) \\\n      void operator delete(void *ptr, const std::nothrow_t&) EIGEN_NO_THROW { \\\n        Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr); \\\n      } \\\n      typedef void eigen_aligned_operator_new_marker_type;\n#else\n  #define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(NeedsToAlign)\n#endif\n\n#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(true)\n#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(Scalar,Size) \\\n  EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(bool(((Size)!=Eigen::Dynamic) && ((sizeof(Scalar)*(Size))%EIGEN_MAX_ALIGN_BYTES==0)))\n\n/****************************************************************************/\n\n/** \\class aligned_allocator\n* \\ingroup Core_Module\n*\n* \\brief STL compatible allocator to use with types requiring a non standrad alignment.\n*\n* The memory is aligned as for dynamically aligned matrix/array types such as MatrixXd.\n* By default, it will thus provide at least 16 bytes alignment and more in following cases:\n*  - 32 bytes alignment if AVX is enabled.\n*  - 64 bytes alignment if AVX512 is enabled.\n*\n* This can be controled using the \\c EIGEN_MAX_ALIGN_BYTES macro as documented\n* \\link TopicPreprocessorDirectivesPerformance there \\endlink.\n*\n* Example:\n* \\code\n* // Matrix4f requires 16 bytes alignment:\n* std::map< int, Matrix4f, std::less<int>, \n*           aligned_allocator<std::pair<const int, Matrix4f> > > my_map_mat4;\n* // Vector3f does not require 16 bytes alignment, no need to use Eigen's allocator:\n* std::map< int, Vector3f > my_map_vec3;\n* \\endcode\n*\n* \\sa \\blank \\ref TopicStlContainers.\n*/\ntemplate<class T>\nclass aligned_allocator : public std::allocator<T>\n{\npublic:\n  typedef std::size_t     size_type;\n  typedef std::ptrdiff_t  difference_type;\n  typedef T*              pointer;\n  typedef const T*        const_pointer;\n  typedef T&              reference;\n  typedef const T&        const_reference;\n  typedef T               value_type;\n\n  template<class U>\n  struct rebind\n  {\n    typedef aligned_allocator<U> other;\n  };\n\n  aligned_allocator() : std::allocator<T>() {}\n\n  aligned_allocator(const aligned_allocator& other) : std::allocator<T>(other) {}\n\n  template<class U>\n  aligned_allocator(const aligned_allocator<U>& other) : std::allocator<T>(other) {}\n\n  ~aligned_allocator() {}\n\n  pointer allocate(size_type num, const void* /*hint*/ = 0)\n  {\n    internal::check_size_for_overflow<T>(num);\n    return static_cast<pointer>( internal::aligned_malloc(num * sizeof(T)) );\n  }\n\n  void deallocate(pointer p, size_type /*num*/)\n  {\n    internal::aligned_free(p);\n  }\n};\n\n//---------- Cache sizes ----------\n\n#if !defined(EIGEN_NO_CPUID)\n#  if EIGEN_COMP_GNUC && EIGEN_ARCH_i386_OR_x86_64\n#    if defined(__PIC__) && EIGEN_ARCH_i386\n       // Case for x86 with PIC\n#      define EIGEN_CPUID(abcd,func,id) \\\n         __asm__ __volatile__ (\"xchgl %%ebx, %k1;cpuid; xchgl %%ebx,%k1\": \"=a\" (abcd[0]), \"=&r\" (abcd[1]), \"=c\" (abcd[2]), \"=d\" (abcd[3]) : \"a\" (func), \"c\" (id));\n#    elif defined(__PIC__) && EIGEN_ARCH_x86_64\n       // Case for x64 with PIC. In theory this is only a problem with recent gcc and with medium or large code model, not with the default small code model.\n       // However, we cannot detect which code model is used, and the xchg overhead is negligible anyway.\n#      define EIGEN_CPUID(abcd,func,id) \\\n        __asm__ __volatile__ (\"xchg{q}\\t{%%}rbx, %q1; cpuid; xchg{q}\\t{%%}rbx, %q1\": \"=a\" (abcd[0]), \"=&r\" (abcd[1]), \"=c\" (abcd[2]), \"=d\" (abcd[3]) : \"0\" (func), \"2\" (id));\n#    else\n       // Case for x86_64 or x86 w/o PIC\n#      define EIGEN_CPUID(abcd,func,id) \\\n         __asm__ __volatile__ (\"cpuid\": \"=a\" (abcd[0]), \"=b\" (abcd[1]), \"=c\" (abcd[2]), \"=d\" (abcd[3]) : \"0\" (func), \"2\" (id) );\n#    endif\n#  elif EIGEN_COMP_MSVC\n#    if (EIGEN_COMP_MSVC > 1500) && EIGEN_ARCH_i386_OR_x86_64\n#      define EIGEN_CPUID(abcd,func,id) __cpuidex((int*)abcd,func,id)\n#    endif\n#  endif\n#endif\n\nnamespace internal {\n\n#ifdef EIGEN_CPUID\n\ninline bool cpuid_is_vendor(int abcd[4], const int vendor[3])\n{\n  return abcd[1]==vendor[0] && abcd[3]==vendor[1] && abcd[2]==vendor[2];\n}\n\ninline void queryCacheSizes_intel_direct(int& l1, int& l2, int& l3)\n{\n  int abcd[4];\n  l1 = l2 = l3 = 0;\n  int cache_id = 0;\n  int cache_type = 0;\n  do {\n    abcd[0] = abcd[1] = abcd[2] = abcd[3] = 0;\n    EIGEN_CPUID(abcd,0x4,cache_id);\n    cache_type  = (abcd[0] & 0x0F) >> 0;\n    if(cache_type==1||cache_type==3) // data or unified cache\n    {\n      int cache_level = (abcd[0] & 0xE0) >> 5;  // A[7:5]\n      int ways        = (abcd[1] & 0xFFC00000) >> 22; // B[31:22]\n      int partitions  = (abcd[1] & 0x003FF000) >> 12; // B[21:12]\n      int line_size   = (abcd[1] & 0x00000FFF) >>  0; // B[11:0]\n      int sets        = (abcd[2]);                    // C[31:0]\n\n      int cache_size = (ways+1) * (partitions+1) * (line_size+1) * (sets+1);\n\n      switch(cache_level)\n      {\n        case 1: l1 = cache_size; break;\n        case 2: l2 = cache_size; break;\n        case 3: l3 = cache_size; break;\n        default: break;\n      }\n    }\n    cache_id++;\n  } while(cache_type>0 && cache_id<16);\n}\n\ninline void queryCacheSizes_intel_codes(int& l1, int& l2, int& l3)\n{\n  int abcd[4];\n  abcd[0] = abcd[1] = abcd[2] = abcd[3] = 0;\n  l1 = l2 = l3 = 0;\n  EIGEN_CPUID(abcd,0x00000002,0);\n  unsigned char * bytes = reinterpret_cast<unsigned char *>(abcd)+2;\n  bool check_for_p2_core2 = false;\n  for(int i=0; i<14; ++i)\n  {\n    switch(bytes[i])\n    {\n      case 0x0A: l1 = 8; break;   // 0Ah   data L1 cache, 8 KB, 2 ways, 32 byte lines\n      case 0x0C: l1 = 16; break;  // 0Ch   data L1 cache, 16 KB, 4 ways, 32 byte lines\n      case 0x0E: l1 = 24; break;  // 0Eh   data L1 cache, 24 KB, 6 ways, 64 byte lines\n      case 0x10: l1 = 16; break;  // 10h   data L1 cache, 16 KB, 4 ways, 32 byte lines (IA-64)\n      case 0x15: l1 = 16; break;  // 15h   code L1 cache, 16 KB, 4 ways, 32 byte lines (IA-64)\n      case 0x2C: l1 = 32; break;  // 2Ch   data L1 cache, 32 KB, 8 ways, 64 byte lines\n      case 0x30: l1 = 32; break;  // 30h   code L1 cache, 32 KB, 8 ways, 64 byte lines\n      case 0x60: l1 = 16; break;  // 60h   data L1 cache, 16 KB, 8 ways, 64 byte lines, sectored\n      case 0x66: l1 = 8; break;   // 66h   data L1 cache, 8 KB, 4 ways, 64 byte lines, sectored\n      case 0x67: l1 = 16; break;  // 67h   data L1 cache, 16 KB, 4 ways, 64 byte lines, sectored\n      case 0x68: l1 = 32; break;  // 68h   data L1 cache, 32 KB, 4 ways, 64 byte lines, sectored\n      case 0x1A: l2 = 96; break;   // code and data L2 cache, 96 KB, 6 ways, 64 byte lines (IA-64)\n      case 0x22: l3 = 512; break;   // code and data L3 cache, 512 KB, 4 ways (!), 64 byte lines, dual-sectored\n      case 0x23: l3 = 1024; break;   // code and data L3 cache, 1024 KB, 8 ways, 64 byte lines, dual-sectored\n      case 0x25: l3 = 2048; break;   // code and data L3 cache, 2048 KB, 8 ways, 64 byte lines, dual-sectored\n      case 0x29: l3 = 4096; break;   // code and data L3 cache, 4096 KB, 8 ways, 64 byte lines, dual-sectored\n      case 0x39: l2 = 128; break;   // code and data L2 cache, 128 KB, 4 ways, 64 byte lines, sectored\n      case 0x3A: l2 = 192; break;   // code and data L2 cache, 192 KB, 6 ways, 64 byte lines, sectored\n      case 0x3B: l2 = 128; break;   // code and data L2 cache, 128 KB, 2 ways, 64 byte lines, sectored\n      case 0x3C: l2 = 256; break;   // code and data L2 cache, 256 KB, 4 ways, 64 byte lines, sectored\n      case 0x3D: l2 = 384; break;   // code and data L2 cache, 384 KB, 6 ways, 64 byte lines, sectored\n      case 0x3E: l2 = 512; break;   // code and data L2 cache, 512 KB, 4 ways, 64 byte lines, sectored\n      case 0x40: l2 = 0; break;   // no integrated L2 cache (P6 core) or L3 cache (P4 core)\n      case 0x41: l2 = 128; break;   // code and data L2 cache, 128 KB, 4 ways, 32 byte lines\n      case 0x42: l2 = 256; break;   // code and data L2 cache, 256 KB, 4 ways, 32 byte lines\n      case 0x43: l2 = 512; break;   // code and data L2 cache, 512 KB, 4 ways, 32 byte lines\n      case 0x44: l2 = 1024; break;   // code and data L2 cache, 1024 KB, 4 ways, 32 byte lines\n      case 0x45: l2 = 2048; break;   // code and data L2 cache, 2048 KB, 4 ways, 32 byte lines\n      case 0x46: l3 = 4096; break;   // code and data L3 cache, 4096 KB, 4 ways, 64 byte lines\n      case 0x47: l3 = 8192; break;   // code and data L3 cache, 8192 KB, 8 ways, 64 byte lines\n      case 0x48: l2 = 3072; break;   // code and data L2 cache, 3072 KB, 12 ways, 64 byte lines\n      case 0x49: if(l2!=0) l3 = 4096; else {check_for_p2_core2=true; l3 = l2 = 4096;} break;// code and data L3 cache, 4096 KB, 16 ways, 64 byte lines (P4) or L2 for core2\n      case 0x4A: l3 = 6144; break;   // code and data L3 cache, 6144 KB, 12 ways, 64 byte lines\n      case 0x4B: l3 = 8192; break;   // code and data L3 cache, 8192 KB, 16 ways, 64 byte lines\n      case 0x4C: l3 = 12288; break;   // code and data L3 cache, 12288 KB, 12 ways, 64 byte lines\n      case 0x4D: l3 = 16384; break;   // code and data L3 cache, 16384 KB, 16 ways, 64 byte lines\n      case 0x4E: l2 = 6144; break;   // code and data L2 cache, 6144 KB, 24 ways, 64 byte lines\n      case 0x78: l2 = 1024; break;   // code and data L2 cache, 1024 KB, 4 ways, 64 byte lines\n      case 0x79: l2 = 128; break;   // code and data L2 cache, 128 KB, 8 ways, 64 byte lines, dual-sectored\n      case 0x7A: l2 = 256; break;   // code and data L2 cache, 256 KB, 8 ways, 64 byte lines, dual-sectored\n      case 0x7B: l2 = 512; break;   // code and data L2 cache, 512 KB, 8 ways, 64 byte lines, dual-sectored\n      case 0x7C: l2 = 1024; break;   // code and data L2 cache, 1024 KB, 8 ways, 64 byte lines, dual-sectored\n      case 0x7D: l2 = 2048; break;   // code and data L2 cache, 2048 KB, 8 ways, 64 byte lines\n      case 0x7E: l2 = 256; break;   // code and data L2 cache, 256 KB, 8 ways, 128 byte lines, sect. (IA-64)\n      case 0x7F: l2 = 512; break;   // code and data L2 cache, 512 KB, 2 ways, 64 byte lines\n      case 0x80: l2 = 512; break;   // code and data L2 cache, 512 KB, 8 ways, 64 byte lines\n      case 0x81: l2 = 128; break;   // code and data L2 cache, 128 KB, 8 ways, 32 byte lines\n      case 0x82: l2 = 256; break;   // code and data L2 cache, 256 KB, 8 ways, 32 byte lines\n      case 0x83: l2 = 512; break;   // code and data L2 cache, 512 KB, 8 ways, 32 byte lines\n      case 0x84: l2 = 1024; break;   // code and data L2 cache, 1024 KB, 8 ways, 32 byte lines\n      case 0x85: l2 = 2048; break;   // code and data L2 cache, 2048 KB, 8 ways, 32 byte lines\n      case 0x86: l2 = 512; break;   // code and data L2 cache, 512 KB, 4 ways, 64 byte lines\n      case 0x87: l2 = 1024; break;   // code and data L2 cache, 1024 KB, 8 ways, 64 byte lines\n      case 0x88: l3 = 2048; break;   // code and data L3 cache, 2048 KB, 4 ways, 64 byte lines (IA-64)\n      case 0x89: l3 = 4096; break;   // code and data L3 cache, 4096 KB, 4 ways, 64 byte lines (IA-64)\n      case 0x8A: l3 = 8192; break;   // code and data L3 cache, 8192 KB, 4 ways, 64 byte lines (IA-64)\n      case 0x8D: l3 = 3072; break;   // code and data L3 cache, 3072 KB, 12 ways, 128 byte lines (IA-64)\n\n      default: break;\n    }\n  }\n  if(check_for_p2_core2 && l2 == l3)\n    l3 = 0;\n  l1 *= 1024;\n  l2 *= 1024;\n  l3 *= 1024;\n}\n\ninline void queryCacheSizes_intel(int& l1, int& l2, int& l3, int max_std_funcs)\n{\n  if(max_std_funcs>=4)\n    queryCacheSizes_intel_direct(l1,l2,l3);\n  else\n    queryCacheSizes_intel_codes(l1,l2,l3);\n}\n\ninline void queryCacheSizes_amd(int& l1, int& l2, int& l3)\n{\n  int abcd[4];\n  abcd[0] = abcd[1] = abcd[2] = abcd[3] = 0;\n  EIGEN_CPUID(abcd,0x80000005,0);\n  l1 = (abcd[2] >> 24) * 1024; // C[31:24] = L1 size in KB\n  abcd[0] = abcd[1] = abcd[2] = abcd[3] = 0;\n  EIGEN_CPUID(abcd,0x80000006,0);\n  l2 = (abcd[2] >> 16) * 1024; // C[31;16] = l2 cache size in KB\n  l3 = ((abcd[3] & 0xFFFC000) >> 18) * 512 * 1024; // D[31;18] = l3 cache size in 512KB\n}\n#endif\n\n/** \\internal\n * Queries and returns the cache sizes in Bytes of the L1, L2, and L3 data caches respectively */\ninline void queryCacheSizes(int& l1, int& l2, int& l3)\n{\n  #ifdef EIGEN_CPUID\n  int abcd[4];\n  const int GenuineIntel[] = {0x756e6547, 0x49656e69, 0x6c65746e};\n  const int AuthenticAMD[] = {0x68747541, 0x69746e65, 0x444d4163};\n  const int AMDisbetter_[] = {0x69444d41, 0x74656273, 0x21726574}; // \"AMDisbetter!\"\n\n  // identify the CPU vendor\n  EIGEN_CPUID(abcd,0x0,0);\n  int max_std_funcs = abcd[1];\n  if(cpuid_is_vendor(abcd,GenuineIntel))\n    queryCacheSizes_intel(l1,l2,l3,max_std_funcs);\n  else if(cpuid_is_vendor(abcd,AuthenticAMD) || cpuid_is_vendor(abcd,AMDisbetter_))\n    queryCacheSizes_amd(l1,l2,l3);\n  else\n    // by default let's use Intel's API\n    queryCacheSizes_intel(l1,l2,l3,max_std_funcs);\n\n  // here is the list of other vendors:\n//   ||cpuid_is_vendor(abcd,\"VIA VIA VIA \")\n//   ||cpuid_is_vendor(abcd,\"CyrixInstead\")\n//   ||cpuid_is_vendor(abcd,\"CentaurHauls\")\n//   ||cpuid_is_vendor(abcd,\"GenuineTMx86\")\n//   ||cpuid_is_vendor(abcd,\"TransmetaCPU\")\n//   ||cpuid_is_vendor(abcd,\"RiseRiseRise\")\n//   ||cpuid_is_vendor(abcd,\"Geode by NSC\")\n//   ||cpuid_is_vendor(abcd,\"SiS SiS SiS \")\n//   ||cpuid_is_vendor(abcd,\"UMC UMC UMC \")\n//   ||cpuid_is_vendor(abcd,\"NexGenDriven\")\n  #else\n  l1 = l2 = l3 = -1;\n  #endif\n}\n\n/** \\internal\n * \\returns the size in Bytes of the L1 data cache */\ninline int queryL1CacheSize()\n{\n  int l1(-1), l2, l3;\n  queryCacheSizes(l1,l2,l3);\n  return l1;\n}\n\n/** \\internal\n * \\returns the size in Bytes of the L2 or L3 cache if this later is present */\ninline int queryTopLevelCacheSize()\n{\n  int l1, l2(-1), l3(-1);\n  queryCacheSizes(l1,l2,l3);\n  return (std::max)(l2,l3);\n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_MEMORY_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/util/Meta.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_META_H\n#define EIGEN_META_H\n\n#if defined(__CUDA_ARCH__)\n#include <cfloat>\n#include <math_constants.h>\n#endif\n\n#if EIGEN_COMP_ICC>=1600 &&  __cplusplus >= 201103L\n#include <cstdint>\n#endif\n\nnamespace Eigen {\n\ntypedef EIGEN_DEFAULT_DENSE_INDEX_TYPE DenseIndex;\n\n/**\n * \\brief The Index type as used for the API.\n * \\details To change this, \\c \\#define the preprocessor symbol \\c EIGEN_DEFAULT_DENSE_INDEX_TYPE.\n * \\sa \\blank \\ref TopicPreprocessorDirectives, StorageIndex.\n */\n\ntypedef EIGEN_DEFAULT_DENSE_INDEX_TYPE Index;\n\nnamespace internal {\n\n/** \\internal\n  * \\file Meta.h\n  * This file contains generic metaprogramming classes which are not specifically related to Eigen.\n  * \\note In case you wonder, yes we're aware that Boost already provides all these features,\n  * we however don't want to add a dependency to Boost.\n  */\n\n// Only recent versions of ICC complain about using ptrdiff_t to hold pointers,\n// and older versions do not provide *intptr_t types.\n#if EIGEN_COMP_ICC>=1600 &&  __cplusplus >= 201103L\ntypedef std::intptr_t  IntPtr;\ntypedef std::uintptr_t UIntPtr;\n#else\ntypedef std::ptrdiff_t IntPtr;\ntypedef std::size_t UIntPtr;\n#endif\n\nstruct true_type {  enum { value = 1 }; };\nstruct false_type { enum { value = 0 }; };\n\ntemplate<bool Condition, typename Then, typename Else>\nstruct conditional { typedef Then type; };\n\ntemplate<typename Then, typename Else>\nstruct conditional <false, Then, Else> { typedef Else type; };\n\ntemplate<typename T, typename U> struct is_same { enum { value = 0 }; };\ntemplate<typename T> struct is_same<T,T> { enum { value = 1 }; };\n\ntemplate<typename T> struct remove_reference { typedef T type; };\ntemplate<typename T> struct remove_reference<T&> { typedef T type; };\n\ntemplate<typename T> struct remove_pointer { typedef T type; };\ntemplate<typename T> struct remove_pointer<T*> { typedef T type; };\ntemplate<typename T> struct remove_pointer<T*const> { typedef T type; };\n\ntemplate <class T> struct remove_const { typedef T type; };\ntemplate <class T> struct remove_const<const T> { typedef T type; };\ntemplate <class T> struct remove_const<const T[]> { typedef T type[]; };\ntemplate <class T, unsigned int Size> struct remove_const<const T[Size]> { typedef T type[Size]; };\n\ntemplate<typename T> struct remove_all { typedef T type; };\ntemplate<typename T> struct remove_all<const T>   { typedef typename remove_all<T>::type type; };\ntemplate<typename T> struct remove_all<T const&>  { typedef typename remove_all<T>::type type; };\ntemplate<typename T> struct remove_all<T&>        { typedef typename remove_all<T>::type type; };\ntemplate<typename T> struct remove_all<T const*>  { typedef typename remove_all<T>::type type; };\ntemplate<typename T> struct remove_all<T*>        { typedef typename remove_all<T>::type type; };\n\ntemplate<typename T> struct is_arithmetic      { enum { value = false }; };\ntemplate<> struct is_arithmetic<float>         { enum { value = true }; };\ntemplate<> struct is_arithmetic<double>        { enum { value = true }; };\ntemplate<> struct is_arithmetic<long double>   { enum { value = true }; };\ntemplate<> struct is_arithmetic<bool>          { enum { value = true }; };\ntemplate<> struct is_arithmetic<char>          { enum { value = true }; };\ntemplate<> struct is_arithmetic<signed char>   { enum { value = true }; };\ntemplate<> struct is_arithmetic<unsigned char> { enum { value = true }; };\ntemplate<> struct is_arithmetic<signed short>  { enum { value = true }; };\ntemplate<> struct is_arithmetic<unsigned short>{ enum { value = true }; };\ntemplate<> struct is_arithmetic<signed int>    { enum { value = true }; };\ntemplate<> struct is_arithmetic<unsigned int>  { enum { value = true }; };\ntemplate<> struct is_arithmetic<signed long>   { enum { value = true }; };\ntemplate<> struct is_arithmetic<unsigned long> { enum { value = true }; };\n\ntemplate<typename T> struct is_integral        { enum { value = false }; };\ntemplate<> struct is_integral<bool>            { enum { value = true }; };\ntemplate<> struct is_integral<char>            { enum { value = true }; };\ntemplate<> struct is_integral<signed char>     { enum { value = true }; };\ntemplate<> struct is_integral<unsigned char>   { enum { value = true }; };\ntemplate<> struct is_integral<signed short>    { enum { value = true }; };\ntemplate<> struct is_integral<unsigned short>  { enum { value = true }; };\ntemplate<> struct is_integral<signed int>      { enum { value = true }; };\ntemplate<> struct is_integral<unsigned int>    { enum { value = true }; };\ntemplate<> struct is_integral<signed long>     { enum { value = true }; };\ntemplate<> struct is_integral<unsigned long>   { enum { value = true }; };\n\ntemplate <typename T> struct add_const { typedef const T type; };\ntemplate <typename T> struct add_const<T&> { typedef T& type; };\n\ntemplate <typename T> struct is_const { enum { value = 0 }; };\ntemplate <typename T> struct is_const<T const> { enum { value = 1 }; };\n\ntemplate<typename T> struct add_const_on_value_type            { typedef const T type;  };\ntemplate<typename T> struct add_const_on_value_type<T&>        { typedef T const& type; };\ntemplate<typename T> struct add_const_on_value_type<T*>        { typedef T const* type; };\ntemplate<typename T> struct add_const_on_value_type<T* const>  { typedef T const* const type; };\ntemplate<typename T> struct add_const_on_value_type<T const* const>  { typedef T const* const type; };\n\n\ntemplate<typename From, typename To>\nstruct is_convertible_impl\n{\nprivate:\n  struct any_conversion\n  {\n    template <typename T> any_conversion(const volatile T&);\n    template <typename T> any_conversion(T&);\n  };\n  struct yes {int a[1];};\n  struct no  {int a[2];};\n\n  static yes test(const To&, int);\n  static no  test(any_conversion, ...);\n\npublic:\n  static From ms_from;\n#ifdef __INTEL_COMPILER\n  #pragma warning push\n  #pragma warning ( disable : 2259 )\n#endif\n  enum { value = sizeof(test(ms_from, 0))==sizeof(yes) };\n#ifdef __INTEL_COMPILER\n  #pragma warning pop\n#endif\n};\n\ntemplate<typename From, typename To>\nstruct is_convertible\n{\n  enum { value = is_convertible_impl<typename remove_all<From>::type,\n                                     typename remove_all<To  >::type>::value };\n};\n\n/** \\internal Allows to enable/disable an overload\n  * according to a compile time condition.\n  */\ntemplate<bool Condition, typename T=void> struct enable_if;\n\ntemplate<typename T> struct enable_if<true,T>\n{ typedef T type; };\n\n#if defined(__CUDA_ARCH__)\n#if !defined(__FLT_EPSILON__)\n#define __FLT_EPSILON__ FLT_EPSILON\n#define __DBL_EPSILON__ DBL_EPSILON\n#endif\n\nnamespace device {\n\ntemplate<typename T> struct numeric_limits\n{\n  EIGEN_DEVICE_FUNC\n  static T epsilon() { return 0; }\n  static T (max)() { assert(false && \"Highest not supported for this type\"); }\n  static T (min)() { assert(false && \"Lowest not supported for this type\"); }\n  static T infinity() { assert(false && \"Infinity not supported for this type\"); }\n  static T quiet_NaN() { assert(false && \"quiet_NaN not supported for this type\"); }\n};\ntemplate<> struct numeric_limits<float>\n{\n  EIGEN_DEVICE_FUNC\n  static float epsilon() { return __FLT_EPSILON__; }\n  EIGEN_DEVICE_FUNC\n  static float (max)() { return CUDART_MAX_NORMAL_F; }\n  EIGEN_DEVICE_FUNC\n  static float (min)() { return FLT_MIN; }\n  EIGEN_DEVICE_FUNC\n  static float infinity() { return CUDART_INF_F; }\n  EIGEN_DEVICE_FUNC\n  static float quiet_NaN() { return CUDART_NAN_F; }\n};\ntemplate<> struct numeric_limits<double>\n{\n  EIGEN_DEVICE_FUNC\n  static double epsilon() { return __DBL_EPSILON__; }\n  EIGEN_DEVICE_FUNC\n  static double (max)() { return DBL_MAX; }\n  EIGEN_DEVICE_FUNC\n  static double (min)() { return DBL_MIN; }\n  EIGEN_DEVICE_FUNC\n  static double infinity() { return CUDART_INF; }\n  EIGEN_DEVICE_FUNC\n  static double quiet_NaN() { return CUDART_NAN; }\n};\ntemplate<> struct numeric_limits<int>\n{\n  EIGEN_DEVICE_FUNC\n  static int epsilon() { return 0; }\n  EIGEN_DEVICE_FUNC\n  static int (max)() { return INT_MAX; }\n  EIGEN_DEVICE_FUNC\n  static int (min)() { return INT_MIN; }\n};\ntemplate<> struct numeric_limits<unsigned int>\n{\n  EIGEN_DEVICE_FUNC\n  static unsigned int epsilon() { return 0; }\n  EIGEN_DEVICE_FUNC\n  static unsigned int (max)() { return UINT_MAX; }\n  EIGEN_DEVICE_FUNC\n  static unsigned int (min)() { return 0; }\n};\ntemplate<> struct numeric_limits<long>\n{\n  EIGEN_DEVICE_FUNC\n  static long epsilon() { return 0; }\n  EIGEN_DEVICE_FUNC\n  static long (max)() { return LONG_MAX; }\n  EIGEN_DEVICE_FUNC\n  static long (min)() { return LONG_MIN; }\n};\ntemplate<> struct numeric_limits<unsigned long>\n{\n  EIGEN_DEVICE_FUNC\n  static unsigned long epsilon() { return 0; }\n  EIGEN_DEVICE_FUNC\n  static unsigned long (max)() { return ULONG_MAX; }\n  EIGEN_DEVICE_FUNC\n  static unsigned long (min)() { return 0; }\n};\ntemplate<> struct numeric_limits<long long>\n{\n  EIGEN_DEVICE_FUNC\n  static long long epsilon() { return 0; }\n  EIGEN_DEVICE_FUNC\n  static long long (max)() { return LLONG_MAX; }\n  EIGEN_DEVICE_FUNC\n  static long long (min)() { return LLONG_MIN; }\n};\ntemplate<> struct numeric_limits<unsigned long long>\n{\n  EIGEN_DEVICE_FUNC\n  static unsigned long long epsilon() { return 0; }\n  EIGEN_DEVICE_FUNC\n  static unsigned long long (max)() { return ULLONG_MAX; }\n  EIGEN_DEVICE_FUNC\n  static unsigned long long (min)() { return 0; }\n};\n\n}\n\n#endif\n\n/** \\internal\n  * A base class do disable default copy ctor and copy assignement operator.\n  */\nclass noncopyable\n{\n  EIGEN_DEVICE_FUNC noncopyable(const noncopyable&);\n  EIGEN_DEVICE_FUNC const noncopyable& operator=(const noncopyable&);\nprotected:\n  EIGEN_DEVICE_FUNC noncopyable() {}\n  EIGEN_DEVICE_FUNC ~noncopyable() {}\n};\n\n/** \\internal\n  * Convenient struct to get the result type of a unary or binary functor.\n  *\n  * It supports both the current STL mechanism (using the result_type member) as well as\n  * upcoming next STL generation (using a templated result member).\n  * If none of these members is provided, then the type of the first argument is returned. FIXME, that behavior is a pretty bad hack.\n  */\n#if EIGEN_HAS_STD_RESULT_OF\ntemplate<typename T> struct result_of {\n  typedef typename std::result_of<T>::type type1;\n  typedef typename remove_all<type1>::type type;\n};\n#else\ntemplate<typename T> struct result_of { };\n\nstruct has_none {int a[1];};\nstruct has_std_result_type {int a[2];};\nstruct has_tr1_result {int a[3];};\n\ntemplate<typename Func, typename ArgType, int SizeOf=sizeof(has_none)>\nstruct unary_result_of_select {typedef typename internal::remove_all<ArgType>::type type;};\n\ntemplate<typename Func, typename ArgType>\nstruct unary_result_of_select<Func, ArgType, sizeof(has_std_result_type)> {typedef typename Func::result_type type;};\n\ntemplate<typename Func, typename ArgType>\nstruct unary_result_of_select<Func, ArgType, sizeof(has_tr1_result)> {typedef typename Func::template result<Func(ArgType)>::type type;};\n\ntemplate<typename Func, typename ArgType>\nstruct result_of<Func(ArgType)> {\n    template<typename T>\n    static has_std_result_type    testFunctor(T const *, typename T::result_type const * = 0);\n    template<typename T>\n    static has_tr1_result         testFunctor(T const *, typename T::template result<T(ArgType)>::type const * = 0);\n    static has_none               testFunctor(...);\n\n    // note that the following indirection is needed for gcc-3.3\n    enum {FunctorType = sizeof(testFunctor(static_cast<Func*>(0)))};\n    typedef typename unary_result_of_select<Func, ArgType, FunctorType>::type type;\n};\n\ntemplate<typename Func, typename ArgType0, typename ArgType1, int SizeOf=sizeof(has_none)>\nstruct binary_result_of_select {typedef typename internal::remove_all<ArgType0>::type type;};\n\ntemplate<typename Func, typename ArgType0, typename ArgType1>\nstruct binary_result_of_select<Func, ArgType0, ArgType1, sizeof(has_std_result_type)>\n{typedef typename Func::result_type type;};\n\ntemplate<typename Func, typename ArgType0, typename ArgType1>\nstruct binary_result_of_select<Func, ArgType0, ArgType1, sizeof(has_tr1_result)>\n{typedef typename Func::template result<Func(ArgType0,ArgType1)>::type type;};\n\ntemplate<typename Func, typename ArgType0, typename ArgType1>\nstruct result_of<Func(ArgType0,ArgType1)> {\n    template<typename T>\n    static has_std_result_type    testFunctor(T const *, typename T::result_type const * = 0);\n    template<typename T>\n    static has_tr1_result         testFunctor(T const *, typename T::template result<T(ArgType0,ArgType1)>::type const * = 0);\n    static has_none               testFunctor(...);\n\n    // note that the following indirection is needed for gcc-3.3\n    enum {FunctorType = sizeof(testFunctor(static_cast<Func*>(0)))};\n    typedef typename binary_result_of_select<Func, ArgType0, ArgType1, FunctorType>::type type;\n};\n\ntemplate<typename Func, typename ArgType0, typename ArgType1, typename ArgType2, int SizeOf=sizeof(has_none)>\nstruct ternary_result_of_select {typedef typename internal::remove_all<ArgType0>::type type;};\n\ntemplate<typename Func, typename ArgType0, typename ArgType1, typename ArgType2>\nstruct ternary_result_of_select<Func, ArgType0, ArgType1, ArgType2, sizeof(has_std_result_type)>\n{typedef typename Func::result_type type;};\n\ntemplate<typename Func, typename ArgType0, typename ArgType1, typename ArgType2>\nstruct ternary_result_of_select<Func, ArgType0, ArgType1, ArgType2, sizeof(has_tr1_result)>\n{typedef typename Func::template result<Func(ArgType0,ArgType1,ArgType2)>::type type;};\n\ntemplate<typename Func, typename ArgType0, typename ArgType1, typename ArgType2>\nstruct result_of<Func(ArgType0,ArgType1,ArgType2)> {\n    template<typename T>\n    static has_std_result_type    testFunctor(T const *, typename T::result_type const * = 0);\n    template<typename T>\n    static has_tr1_result         testFunctor(T const *, typename T::template result<T(ArgType0,ArgType1,ArgType2)>::type const * = 0);\n    static has_none               testFunctor(...);\n\n    // note that the following indirection is needed for gcc-3.3\n    enum {FunctorType = sizeof(testFunctor(static_cast<Func*>(0)))};\n    typedef typename ternary_result_of_select<Func, ArgType0, ArgType1, ArgType2, FunctorType>::type type;\n};\n#endif\n\nstruct meta_yes { char a[1]; };\nstruct meta_no  { char a[2]; };\n\n// Check whether T::ReturnType does exist\ntemplate <typename T>\nstruct has_ReturnType\n{\n  template <typename C> static meta_yes testFunctor(typename C::ReturnType const *);\n  template <typename C> static meta_no testFunctor(...);\n\n  enum { value = sizeof(testFunctor<T>(0)) == sizeof(meta_yes) };\n};\n\ntemplate<typename T> const T* return_ptr();\n\ntemplate <typename T, typename IndexType=Index>\nstruct has_nullary_operator\n{\n  template <typename C> static meta_yes testFunctor(C const *,typename enable_if<(sizeof(return_ptr<C>()->operator()())>0)>::type * = 0);\n  static meta_no testFunctor(...);\n\n  enum { value = sizeof(testFunctor(static_cast<T*>(0))) == sizeof(meta_yes) };\n};\n\ntemplate <typename T, typename IndexType=Index>\nstruct has_unary_operator\n{\n  template <typename C> static meta_yes testFunctor(C const *,typename enable_if<(sizeof(return_ptr<C>()->operator()(IndexType(0)))>0)>::type * = 0);\n  static meta_no testFunctor(...);\n\n  enum { value = sizeof(testFunctor(static_cast<T*>(0))) == sizeof(meta_yes) };\n};\n\ntemplate <typename T, typename IndexType=Index>\nstruct has_binary_operator\n{\n  template <typename C> static meta_yes testFunctor(C const *,typename enable_if<(sizeof(return_ptr<C>()->operator()(IndexType(0),IndexType(0)))>0)>::type * = 0);\n  static meta_no testFunctor(...);\n\n  enum { value = sizeof(testFunctor(static_cast<T*>(0))) == sizeof(meta_yes) };\n};\n\n/** \\internal In short, it computes int(sqrt(\\a Y)) with \\a Y an integer.\n  * Usage example: \\code meta_sqrt<1023>::ret \\endcode\n  */\ntemplate<int Y,\n         int InfX = 0,\n         int SupX = ((Y==1) ? 1 : Y/2),\n         bool Done = ((SupX-InfX)<=1 ? true : ((SupX*SupX <= Y) && ((SupX+1)*(SupX+1) > Y))) >\n                                // use ?: instead of || just to shut up a stupid gcc 4.3 warning\nclass meta_sqrt\n{\n    enum {\n      MidX = (InfX+SupX)/2,\n      TakeInf = MidX*MidX > Y ? 1 : 0,\n      NewInf = int(TakeInf) ? InfX : int(MidX),\n      NewSup = int(TakeInf) ? int(MidX) : SupX\n    };\n  public:\n    enum { ret = meta_sqrt<Y,NewInf,NewSup>::ret };\n};\n\ntemplate<int Y, int InfX, int SupX>\nclass meta_sqrt<Y, InfX, SupX, true> { public:  enum { ret = (SupX*SupX <= Y) ? SupX : InfX }; };\n\n\n/** \\internal Computes the least common multiple of two positive integer A and B\n  * at compile-time. It implements a naive algorithm testing all multiples of A.\n  * It thus works better if A>=B.\n  */\ntemplate<int A, int B, int K=1, bool Done = ((A*K)%B)==0>\nstruct meta_least_common_multiple\n{\n  enum { ret = meta_least_common_multiple<A,B,K+1>::ret };\n};\ntemplate<int A, int B, int K>\nstruct meta_least_common_multiple<A,B,K,true>\n{\n  enum { ret = A*K };\n};\n\n/** \\internal determines whether the product of two numeric types is allowed and what the return type is */\ntemplate<typename T, typename U> struct scalar_product_traits\n{\n  enum { Defined = 0 };\n};\n\n// FIXME quick workaround around current limitation of result_of\n// template<typename Scalar, typename ArgType0, typename ArgType1>\n// struct result_of<scalar_product_op<Scalar>(ArgType0,ArgType1)> {\n// typedef typename scalar_product_traits<typename remove_all<ArgType0>::type, typename remove_all<ArgType1>::type>::ReturnType type;\n// };\n\n} // end namespace internal\n\nnamespace numext {\n  \n#if defined(__CUDA_ARCH__)\ntemplate<typename T> EIGEN_DEVICE_FUNC   void swap(T &a, T &b) { T tmp = b; b = a; a = tmp; }\n#else\ntemplate<typename T> EIGEN_STRONG_INLINE void swap(T &a, T &b) { std::swap(a,b); }\n#endif\n\n#if defined(__CUDA_ARCH__)\nusing internal::device::numeric_limits;\n#else\nusing std::numeric_limits;\n#endif\n\n// Integer division with rounding up.\n// T is assumed to be an integer type with a>=0, and b>0\ntemplate<typename T>\nT div_ceil(const T &a, const T &b)\n{\n  return (a+b-1) / b;\n}\n\n// The aim of the following functions is to bypass -Wfloat-equal warnings\n// when we really want a strict equality comparison on floating points.\ntemplate<typename X, typename Y> EIGEN_STRONG_INLINE\nbool equal_strict(const X& x,const Y& y) { return x == y; }\n\ntemplate<> EIGEN_STRONG_INLINE\nbool equal_strict(const float& x,const float& y) { return std::equal_to<float>()(x,y); }\n\ntemplate<> EIGEN_STRONG_INLINE\nbool equal_strict(const double& x,const double& y) { return std::equal_to<double>()(x,y); }\n\ntemplate<typename X, typename Y> EIGEN_STRONG_INLINE\nbool not_equal_strict(const X& x,const Y& y) { return x != y; }\n\ntemplate<> EIGEN_STRONG_INLINE\nbool not_equal_strict(const float& x,const float& y) { return std::not_equal_to<float>()(x,y); }\n\ntemplate<> EIGEN_STRONG_INLINE\nbool not_equal_strict(const double& x,const double& y) { return std::not_equal_to<double>()(x,y); }\n\n} // end namespace numext\n\n} // end namespace Eigen\n\n#endif // EIGEN_META_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/util/NonMPL2.h",
    "content": "#ifdef EIGEN_MPL2_ONLY\n#error Including non-MPL2 code in EIGEN_MPL2_ONLY mode\n#endif\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/util/ReenableStupidWarnings.h",
    "content": "#ifdef EIGEN_WARNINGS_DISABLED\n#undef EIGEN_WARNINGS_DISABLED\n\n#ifndef EIGEN_PERMANENTLY_DISABLE_STUPID_WARNINGS\n  #ifdef _MSC_VER\n    #pragma warning( pop )\n  #elif defined __INTEL_COMPILER\n    #pragma warning pop\n  #elif defined __clang__\n    #pragma clang diagnostic pop\n  #elif defined __GNUC__ && __GNUC__>=6\n    #pragma GCC diagnostic pop\n  #endif\n\n  #if defined __NVCC__\n//    Don't reenable the diagnostic messages, as it turns out these messages need\n//    to be disabled at the point of the template instantiation (i.e the user code)\n//    otherwise they'll be triggered by nvcc.\n//    #pragma diag_default code_is_unreachable\n//    #pragma diag_default initialization_not_reachable\n//    #pragma diag_default 2651\n//    #pragma diag_default 2653\n  #endif\n\n#endif\n\n#endif // EIGEN_WARNINGS_DISABLED\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/util/StaticAssert.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_STATIC_ASSERT_H\n#define EIGEN_STATIC_ASSERT_H\n\n/* Some notes on Eigen's static assertion mechanism:\n *\n *  - in EIGEN_STATIC_ASSERT(CONDITION,MSG) the parameter CONDITION must be a compile time boolean\n *    expression, and MSG an enum listed in struct internal::static_assertion<true>\n *\n *  - define EIGEN_NO_STATIC_ASSERT to disable them (and save compilation time)\n *    in that case, the static assertion is converted to the following runtime assert:\n *      eigen_assert(CONDITION && \"MSG\")\n *\n *  - currently EIGEN_STATIC_ASSERT can only be used in function scope\n *\n */\n\n#ifndef EIGEN_STATIC_ASSERT\n#ifndef EIGEN_NO_STATIC_ASSERT\n\n  #if EIGEN_MAX_CPP_VER>=11 && (__has_feature(cxx_static_assert) || (defined(__cplusplus) && __cplusplus >= 201103L) || (EIGEN_COMP_MSVC >= 1600))\n\n    // if native static_assert is enabled, let's use it\n    #define EIGEN_STATIC_ASSERT(X,MSG) static_assert(X,#MSG);\n\n  #else // not CXX0X\n\n    namespace Eigen {\n\n    namespace internal {\n\n    template<bool condition>\n    struct static_assertion {};\n\n    template<>\n    struct static_assertion<true>\n    {\n      enum {\n        YOU_TRIED_CALLING_A_VECTOR_METHOD_ON_A_MATRIX=1,\n        YOU_MIXED_VECTORS_OF_DIFFERENT_SIZES=1,\n        YOU_MIXED_MATRICES_OF_DIFFERENT_SIZES=1,\n        THIS_METHOD_IS_ONLY_FOR_VECTORS_OF_A_SPECIFIC_SIZE=1,\n        THIS_METHOD_IS_ONLY_FOR_MATRICES_OF_A_SPECIFIC_SIZE=1,\n        THIS_METHOD_IS_ONLY_FOR_OBJECTS_OF_A_SPECIFIC_SIZE=1,\n        OUT_OF_RANGE_ACCESS=1,\n        YOU_MADE_A_PROGRAMMING_MISTAKE=1,\n        EIGEN_INTERNAL_ERROR_PLEASE_FILE_A_BUG_REPORT=1,\n        EIGEN_INTERNAL_COMPILATION_ERROR_OR_YOU_MADE_A_PROGRAMMING_MISTAKE=1,\n        YOU_CALLED_A_FIXED_SIZE_METHOD_ON_A_DYNAMIC_SIZE_MATRIX_OR_VECTOR=1,\n        YOU_CALLED_A_DYNAMIC_SIZE_METHOD_ON_A_FIXED_SIZE_MATRIX_OR_VECTOR=1,\n        UNALIGNED_LOAD_AND_STORE_OPERATIONS_UNIMPLEMENTED_ON_ALTIVEC=1,\n        THIS_FUNCTION_IS_NOT_FOR_INTEGER_NUMERIC_TYPES=1,\n        FLOATING_POINT_ARGUMENT_PASSED__INTEGER_WAS_EXPECTED=1,\n        NUMERIC_TYPE_MUST_BE_REAL=1,\n        COEFFICIENT_WRITE_ACCESS_TO_SELFADJOINT_NOT_SUPPORTED=1,\n        WRITING_TO_TRIANGULAR_PART_WITH_UNIT_DIAGONAL_IS_NOT_SUPPORTED=1,\n        THIS_METHOD_IS_ONLY_FOR_FIXED_SIZE=1,\n        INVALID_MATRIX_PRODUCT=1,\n        INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS=1,\n        INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION=1,\n        YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY=1,\n        THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES=1,\n        THIS_METHOD_IS_ONLY_FOR_ROW_MAJOR_MATRICES=1,\n        INVALID_MATRIX_TEMPLATE_PARAMETERS=1,\n        INVALID_MATRIXBASE_TEMPLATE_PARAMETERS=1,\n        BOTH_MATRICES_MUST_HAVE_THE_SAME_STORAGE_ORDER=1,\n        THIS_METHOD_IS_ONLY_FOR_DIAGONAL_MATRIX=1,\n        THE_MATRIX_OR_EXPRESSION_THAT_YOU_PASSED_DOES_NOT_HAVE_THE_EXPECTED_TYPE=1,\n        THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_WITH_DIRECT_MEMORY_ACCESS_SUCH_AS_MAP_OR_PLAIN_MATRICES=1,\n        YOU_ALREADY_SPECIFIED_THIS_STRIDE=1,\n        INVALID_STORAGE_ORDER_FOR_THIS_VECTOR_EXPRESSION=1,\n        THE_BRACKET_OPERATOR_IS_ONLY_FOR_VECTORS__USE_THE_PARENTHESIS_OPERATOR_INSTEAD=1,\n        PACKET_ACCESS_REQUIRES_TO_HAVE_INNER_STRIDE_FIXED_TO_1=1,\n        THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS=1,\n        YOU_CANNOT_MIX_ARRAYS_AND_MATRICES=1,\n        YOU_PERFORMED_AN_INVALID_TRANSFORMATION_CONVERSION=1,\n        THIS_EXPRESSION_IS_NOT_A_LVALUE__IT_IS_READ_ONLY=1,\n        YOU_ARE_TRYING_TO_USE_AN_INDEX_BASED_ACCESSOR_ON_AN_EXPRESSION_THAT_DOES_NOT_SUPPORT_THAT=1,\n        THIS_METHOD_IS_ONLY_FOR_1x1_EXPRESSIONS=1,\n        THIS_METHOD_IS_ONLY_FOR_INNER_OR_LAZY_PRODUCTS=1,\n        THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_OF_BOOL=1,\n        THIS_METHOD_IS_ONLY_FOR_ARRAYS_NOT_MATRICES=1,\n        YOU_PASSED_A_ROW_VECTOR_BUT_A_COLUMN_VECTOR_WAS_EXPECTED=1,\n        YOU_PASSED_A_COLUMN_VECTOR_BUT_A_ROW_VECTOR_WAS_EXPECTED=1,\n        THE_INDEX_TYPE_MUST_BE_A_SIGNED_TYPE=1,\n        THE_STORAGE_ORDER_OF_BOTH_SIDES_MUST_MATCH=1,\n        OBJECT_ALLOCATED_ON_STACK_IS_TOO_BIG=1,\n        IMPLICIT_CONVERSION_TO_SCALAR_IS_FOR_INNER_PRODUCT_ONLY=1,\n        STORAGE_LAYOUT_DOES_NOT_MATCH=1,\n        EIGEN_INTERNAL_ERROR_PLEASE_FILE_A_BUG_REPORT__INVALID_COST_VALUE=1,\n        THIS_COEFFICIENT_ACCESSOR_TAKING_ONE_ACCESS_IS_ONLY_FOR_EXPRESSIONS_ALLOWING_LINEAR_ACCESS=1,\n        MATRIX_FREE_CONJUGATE_GRADIENT_IS_COMPATIBLE_WITH_UPPER_UNION_LOWER_MODE_ONLY=1,\n        THIS_TYPE_IS_NOT_SUPPORTED=1,\n        STORAGE_KIND_MUST_MATCH=1,\n        STORAGE_INDEX_MUST_MATCH=1,\n        CHOLMOD_SUPPORTS_DOUBLE_PRECISION_ONLY=1,\n        SELFADJOINTVIEW_ACCEPTS_UPPER_AND_LOWER_MODE_ONLY=1\n      };\n    };\n\n    } // end namespace internal\n\n    } // end namespace Eigen\n\n    // Specialized implementation for MSVC to avoid \"conditional\n    // expression is constant\" warnings.  This implementation doesn't\n    // appear to work under GCC, hence the multiple implementations.\n    #if EIGEN_COMP_MSVC\n\n      #define EIGEN_STATIC_ASSERT(CONDITION,MSG) \\\n        {Eigen::internal::static_assertion<bool(CONDITION)>::MSG;}\n\n    #else\n      // In some cases clang interprets bool(CONDITION) as function declaration\n      #define EIGEN_STATIC_ASSERT(CONDITION,MSG) \\\n        if (Eigen::internal::static_assertion<static_cast<bool>(CONDITION)>::MSG) {}\n\n    #endif\n\n  #endif // not CXX0X\n\n#else // EIGEN_NO_STATIC_ASSERT\n\n  #define EIGEN_STATIC_ASSERT(CONDITION,MSG) eigen_assert((CONDITION) && #MSG);\n\n#endif // EIGEN_NO_STATIC_ASSERT\n#endif // EIGEN_STATIC_ASSERT\n\n// static assertion failing if the type \\a TYPE is not a vector type\n#define EIGEN_STATIC_ASSERT_VECTOR_ONLY(TYPE) \\\n  EIGEN_STATIC_ASSERT(TYPE::IsVectorAtCompileTime, \\\n                      YOU_TRIED_CALLING_A_VECTOR_METHOD_ON_A_MATRIX)\n\n// static assertion failing if the type \\a TYPE is not fixed-size\n#define EIGEN_STATIC_ASSERT_FIXED_SIZE(TYPE) \\\n  EIGEN_STATIC_ASSERT(TYPE::SizeAtCompileTime!=Eigen::Dynamic, \\\n                      YOU_CALLED_A_FIXED_SIZE_METHOD_ON_A_DYNAMIC_SIZE_MATRIX_OR_VECTOR)\n\n// static assertion failing if the type \\a TYPE is not dynamic-size\n#define EIGEN_STATIC_ASSERT_DYNAMIC_SIZE(TYPE) \\\n  EIGEN_STATIC_ASSERT(TYPE::SizeAtCompileTime==Eigen::Dynamic, \\\n                      YOU_CALLED_A_DYNAMIC_SIZE_METHOD_ON_A_FIXED_SIZE_MATRIX_OR_VECTOR)\n\n// static assertion failing if the type \\a TYPE is not a vector type of the given size\n#define EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(TYPE, SIZE) \\\n  EIGEN_STATIC_ASSERT(TYPE::IsVectorAtCompileTime && TYPE::SizeAtCompileTime==SIZE, \\\n                      THIS_METHOD_IS_ONLY_FOR_VECTORS_OF_A_SPECIFIC_SIZE)\n\n// static assertion failing if the type \\a TYPE is not a vector type of the given size\n#define EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(TYPE, ROWS, COLS) \\\n  EIGEN_STATIC_ASSERT(TYPE::RowsAtCompileTime==ROWS && TYPE::ColsAtCompileTime==COLS, \\\n                      THIS_METHOD_IS_ONLY_FOR_MATRICES_OF_A_SPECIFIC_SIZE)\n\n// static assertion failing if the two vector expression types are not compatible (same fixed-size or dynamic size)\n#define EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(TYPE0,TYPE1) \\\n  EIGEN_STATIC_ASSERT( \\\n      (int(TYPE0::SizeAtCompileTime)==Eigen::Dynamic \\\n    || int(TYPE1::SizeAtCompileTime)==Eigen::Dynamic \\\n    || int(TYPE0::SizeAtCompileTime)==int(TYPE1::SizeAtCompileTime)),\\\n    YOU_MIXED_VECTORS_OF_DIFFERENT_SIZES)\n\n#define EIGEN_PREDICATE_SAME_MATRIX_SIZE(TYPE0,TYPE1) \\\n     ( \\\n        (int(Eigen::internal::size_of_xpr_at_compile_time<TYPE0>::ret)==0 && int(Eigen::internal::size_of_xpr_at_compile_time<TYPE1>::ret)==0) \\\n    || (\\\n          (int(TYPE0::RowsAtCompileTime)==Eigen::Dynamic \\\n        || int(TYPE1::RowsAtCompileTime)==Eigen::Dynamic \\\n        || int(TYPE0::RowsAtCompileTime)==int(TYPE1::RowsAtCompileTime)) \\\n      &&  (int(TYPE0::ColsAtCompileTime)==Eigen::Dynamic \\\n        || int(TYPE1::ColsAtCompileTime)==Eigen::Dynamic \\\n        || int(TYPE0::ColsAtCompileTime)==int(TYPE1::ColsAtCompileTime))\\\n       ) \\\n     )\n\n#define EIGEN_STATIC_ASSERT_NON_INTEGER(TYPE) \\\n    EIGEN_STATIC_ASSERT(!NumTraits<TYPE>::IsInteger, THIS_FUNCTION_IS_NOT_FOR_INTEGER_NUMERIC_TYPES)\n\n\n// static assertion failing if it is guaranteed at compile-time that the two matrix expression types have different sizes\n#define EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(TYPE0,TYPE1) \\\n  EIGEN_STATIC_ASSERT( \\\n     EIGEN_PREDICATE_SAME_MATRIX_SIZE(TYPE0,TYPE1),\\\n    YOU_MIXED_MATRICES_OF_DIFFERENT_SIZES)\n\n#define EIGEN_STATIC_ASSERT_SIZE_1x1(TYPE) \\\n      EIGEN_STATIC_ASSERT((TYPE::RowsAtCompileTime == 1 || TYPE::RowsAtCompileTime == Dynamic) && \\\n                          (TYPE::ColsAtCompileTime == 1 || TYPE::ColsAtCompileTime == Dynamic), \\\n                          THIS_METHOD_IS_ONLY_FOR_1x1_EXPRESSIONS)\n\n#define EIGEN_STATIC_ASSERT_LVALUE(Derived) \\\n      EIGEN_STATIC_ASSERT(Eigen::internal::is_lvalue<Derived>::value, \\\n                          THIS_EXPRESSION_IS_NOT_A_LVALUE__IT_IS_READ_ONLY)\n\n#define EIGEN_STATIC_ASSERT_ARRAYXPR(Derived) \\\n      EIGEN_STATIC_ASSERT((Eigen::internal::is_same<typename Eigen::internal::traits<Derived>::XprKind, ArrayXpr>::value), \\\n                          THIS_METHOD_IS_ONLY_FOR_ARRAYS_NOT_MATRICES)\n\n#define EIGEN_STATIC_ASSERT_SAME_XPR_KIND(Derived1, Derived2) \\\n      EIGEN_STATIC_ASSERT((Eigen::internal::is_same<typename Eigen::internal::traits<Derived1>::XprKind, \\\n                                             typename Eigen::internal::traits<Derived2>::XprKind \\\n                                            >::value), \\\n                          YOU_CANNOT_MIX_ARRAYS_AND_MATRICES)\n\n// Check that a cost value is positive, and that is stay within a reasonable range\n// TODO this check could be enabled for internal debugging only\n#define EIGEN_INTERNAL_CHECK_COST_VALUE(C) \\\n      EIGEN_STATIC_ASSERT((C)>=0 && (C)<=HugeCost*HugeCost, EIGEN_INTERNAL_ERROR_PLEASE_FILE_A_BUG_REPORT__INVALID_COST_VALUE);\n\n#endif // EIGEN_STATIC_ASSERT_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Core/util/XprHelper.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_XPRHELPER_H\n#define EIGEN_XPRHELPER_H\n\n// just a workaround because GCC seems to not really like empty structs\n// FIXME: gcc 4.3 generates bad code when strict-aliasing is enabled\n// so currently we simply disable this optimization for gcc 4.3\n#if EIGEN_COMP_GNUC && !EIGEN_GNUC_AT(4,3)\n  #define EIGEN_EMPTY_STRUCT_CTOR(X) \\\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE X() {} \\\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE X(const X& ) {}\n#else\n  #define EIGEN_EMPTY_STRUCT_CTOR(X)\n#endif\n\nnamespace Eigen {\n\nnamespace internal {\n\ntemplate<typename IndexDest, typename IndexSrc>\nEIGEN_DEVICE_FUNC\ninline IndexDest convert_index(const IndexSrc& idx) {\n  // for sizeof(IndexDest)>=sizeof(IndexSrc) compilers should be able to optimize this away:\n  eigen_internal_assert(idx <= NumTraits<IndexDest>::highest() && \"Index value to big for target type\");\n  return IndexDest(idx);\n}\n\n\n// promote_scalar_arg is an helper used in operation between an expression and a scalar, like:\n//    expression * scalar\n// Its role is to determine how the type T of the scalar operand should be promoted given the scalar type ExprScalar of the given expression.\n// The IsSupported template parameter must be provided by the caller as: internal::has_ReturnType<ScalarBinaryOpTraits<ExprScalar,T,op> >::value using the proper order for ExprScalar and T.\n// Then the logic is as follows:\n//  - if the operation is natively supported as defined by IsSupported, then the scalar type is not promoted, and T is returned.\n//  - otherwise, NumTraits<ExprScalar>::Literal is returned if T is implicitly convertible to NumTraits<ExprScalar>::Literal AND that this does not imply a float to integer conversion.\n//  - otherwise, ExprScalar is returned if T is implicitly convertible to ExprScalar AND that this does not imply a float to integer conversion.\n//  - In all other cases, the promoted type is not defined, and the respective operation is thus invalid and not available (SFINAE).\ntemplate<typename ExprScalar,typename T, bool IsSupported>\nstruct promote_scalar_arg;\n\ntemplate<typename S,typename T>\nstruct promote_scalar_arg<S,T,true>\n{\n  typedef T type;\n};\n\n// Recursively check safe conversion to PromotedType, and then ExprScalar if they are different.\ntemplate<typename ExprScalar,typename T,typename PromotedType,\n  bool ConvertibleToLiteral = internal::is_convertible<T,PromotedType>::value,\n  bool IsSafe = NumTraits<T>::IsInteger || !NumTraits<PromotedType>::IsInteger>\nstruct promote_scalar_arg_unsupported;\n\n// Start recursion with NumTraits<ExprScalar>::Literal\ntemplate<typename S,typename T>\nstruct promote_scalar_arg<S,T,false> : promote_scalar_arg_unsupported<S,T,typename NumTraits<S>::Literal> {};\n\n// We found a match!\ntemplate<typename S,typename T, typename PromotedType>\nstruct promote_scalar_arg_unsupported<S,T,PromotedType,true,true>\n{\n  typedef PromotedType type;\n};\n\n// No match, but no real-to-integer issues, and ExprScalar and current PromotedType are different,\n// so let's try to promote to ExprScalar\ntemplate<typename ExprScalar,typename T, typename PromotedType>\nstruct promote_scalar_arg_unsupported<ExprScalar,T,PromotedType,false,true>\n   : promote_scalar_arg_unsupported<ExprScalar,T,ExprScalar>\n{};\n\n// Unsafe real-to-integer, let's stop.\ntemplate<typename S,typename T, typename PromotedType, bool ConvertibleToLiteral>\nstruct promote_scalar_arg_unsupported<S,T,PromotedType,ConvertibleToLiteral,false> {};\n\n// T is not even convertible to ExprScalar, let's stop.\ntemplate<typename S,typename T>\nstruct promote_scalar_arg_unsupported<S,T,S,false,true> {};\n\n//classes inheriting no_assignment_operator don't generate a default operator=.\nclass no_assignment_operator\n{\n  private:\n    no_assignment_operator& operator=(const no_assignment_operator&);\n};\n\n/** \\internal return the index type with the largest number of bits */\ntemplate<typename I1, typename I2>\nstruct promote_index_type\n{\n  typedef typename conditional<(sizeof(I1)<sizeof(I2)), I2, I1>::type type;\n};\n\n/** \\internal If the template parameter Value is Dynamic, this class is just a wrapper around a T variable that\n  * can be accessed using value() and setValue().\n  * Otherwise, this class is an empty structure and value() just returns the template parameter Value.\n  */\ntemplate<typename T, int Value> class variable_if_dynamic\n{\n  public:\n    EIGEN_EMPTY_STRUCT_CTOR(variable_if_dynamic)\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit variable_if_dynamic(T v) { EIGEN_ONLY_USED_FOR_DEBUG(v); eigen_assert(v == T(Value)); }\n    EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE T value() { return T(Value); }\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void setValue(T) {}\n};\n\ntemplate<typename T> class variable_if_dynamic<T, Dynamic>\n{\n    T m_value;\n    EIGEN_DEVICE_FUNC variable_if_dynamic() { eigen_assert(false); }\n  public:\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit variable_if_dynamic(T value) : m_value(value) {}\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T value() const { return m_value; }\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void setValue(T value) { m_value = value; }\n};\n\n/** \\internal like variable_if_dynamic but for DynamicIndex\n  */\ntemplate<typename T, int Value> class variable_if_dynamicindex\n{\n  public:\n    EIGEN_EMPTY_STRUCT_CTOR(variable_if_dynamicindex)\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit variable_if_dynamicindex(T v) { EIGEN_ONLY_USED_FOR_DEBUG(v); eigen_assert(v == T(Value)); }\n    EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE T value() { return T(Value); }\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void setValue(T) {}\n};\n\ntemplate<typename T> class variable_if_dynamicindex<T, DynamicIndex>\n{\n    T m_value;\n    EIGEN_DEVICE_FUNC variable_if_dynamicindex() { eigen_assert(false); }\n  public:\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit variable_if_dynamicindex(T value) : m_value(value) {}\n    EIGEN_DEVICE_FUNC T EIGEN_STRONG_INLINE value() const { return m_value; }\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void setValue(T value) { m_value = value; }\n};\n\ntemplate<typename T> struct functor_traits\n{\n  enum\n  {\n    Cost = 10,\n    PacketAccess = false,\n    IsRepeatable = false\n  };\n};\n\ntemplate<typename T> struct packet_traits;\n\ntemplate<typename T> struct unpacket_traits\n{\n  typedef T type;\n  typedef T half;\n  enum\n  {\n    size = 1,\n    alignment = 1\n  };\n};\n\ntemplate<int Size, typename PacketType,\n         bool Stop = Size==Dynamic || (Size%unpacket_traits<PacketType>::size)==0 || is_same<PacketType,typename unpacket_traits<PacketType>::half>::value>\nstruct find_best_packet_helper;\n\ntemplate< int Size, typename PacketType>\nstruct find_best_packet_helper<Size,PacketType,true>\n{\n  typedef PacketType type;\n};\n\ntemplate<int Size, typename PacketType>\nstruct find_best_packet_helper<Size,PacketType,false>\n{\n  typedef typename find_best_packet_helper<Size,typename unpacket_traits<PacketType>::half>::type type;\n};\n\ntemplate<typename T, int Size>\nstruct find_best_packet\n{\n  typedef typename find_best_packet_helper<Size,typename packet_traits<T>::type>::type type;\n};\n\n#if EIGEN_MAX_STATIC_ALIGN_BYTES>0\ntemplate<int ArrayBytes, int AlignmentBytes,\n         bool Match     =  bool((ArrayBytes%AlignmentBytes)==0),\n         bool TryHalf   =  bool(EIGEN_MIN_ALIGN_BYTES<AlignmentBytes) >\nstruct compute_default_alignment_helper\n{\n  enum { value = 0 };\n};\n\ntemplate<int ArrayBytes, int AlignmentBytes, bool TryHalf>\nstruct compute_default_alignment_helper<ArrayBytes, AlignmentBytes, true, TryHalf> // Match\n{\n  enum { value = AlignmentBytes };\n};\n\ntemplate<int ArrayBytes, int AlignmentBytes>\nstruct compute_default_alignment_helper<ArrayBytes, AlignmentBytes, false, true> // Try-half\n{\n  // current packet too large, try with an half-packet\n  enum { value = compute_default_alignment_helper<ArrayBytes, AlignmentBytes/2>::value };\n};\n#else\n// If static alignment is disabled, no need to bother.\n// This also avoids a division by zero in \"bool Match =  bool((ArrayBytes%AlignmentBytes)==0)\"\ntemplate<int ArrayBytes, int AlignmentBytes>\nstruct compute_default_alignment_helper\n{\n  enum { value = 0 };\n};\n#endif\n\ntemplate<typename T, int Size> struct compute_default_alignment {\n  enum { value = compute_default_alignment_helper<Size*sizeof(T),EIGEN_MAX_STATIC_ALIGN_BYTES>::value };\n};\n\ntemplate<typename T> struct compute_default_alignment<T,Dynamic> {\n  enum { value = EIGEN_MAX_ALIGN_BYTES };\n};\n\ntemplate<typename _Scalar, int _Rows, int _Cols,\n         int _Options = AutoAlign |\n                          ( (_Rows==1 && _Cols!=1) ? RowMajor\n                          : (_Cols==1 && _Rows!=1) ? ColMajor\n                          : EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION ),\n         int _MaxRows = _Rows,\n         int _MaxCols = _Cols\n> class make_proper_matrix_type\n{\n    enum {\n      IsColVector = _Cols==1 && _Rows!=1,\n      IsRowVector = _Rows==1 && _Cols!=1,\n      Options = IsColVector ? (_Options | ColMajor) & ~RowMajor\n              : IsRowVector ? (_Options | RowMajor) & ~ColMajor\n              : _Options\n    };\n  public:\n    typedef Matrix<_Scalar, _Rows, _Cols, Options, _MaxRows, _MaxCols> type;\n};\n\ntemplate<typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>\nclass compute_matrix_flags\n{\n    enum { row_major_bit = Options&RowMajor ? RowMajorBit : 0 };\n  public:\n    // FIXME currently we still have to handle DirectAccessBit at the expression level to handle DenseCoeffsBase<>\n    // and then propagate this information to the evaluator's flags.\n    // However, I (Gael) think that DirectAccessBit should only matter at the evaluation stage.\n    enum { ret = DirectAccessBit | LvalueBit | NestByRefBit | row_major_bit };\n};\n\ntemplate<int _Rows, int _Cols> struct size_at_compile_time\n{\n  enum { ret = (_Rows==Dynamic || _Cols==Dynamic) ? Dynamic : _Rows * _Cols };\n};\n\ntemplate<typename XprType> struct size_of_xpr_at_compile_time\n{\n  enum { ret = size_at_compile_time<traits<XprType>::RowsAtCompileTime,traits<XprType>::ColsAtCompileTime>::ret };\n};\n\n/* plain_matrix_type : the difference from eval is that plain_matrix_type is always a plain matrix type,\n * whereas eval is a const reference in the case of a matrix\n */\n\ntemplate<typename T, typename StorageKind = typename traits<T>::StorageKind> struct plain_matrix_type;\ntemplate<typename T, typename BaseClassType, int Flags> struct plain_matrix_type_dense;\ntemplate<typename T> struct plain_matrix_type<T,Dense>\n{\n  typedef typename plain_matrix_type_dense<T,typename traits<T>::XprKind, traits<T>::Flags>::type type;\n};\ntemplate<typename T> struct plain_matrix_type<T,DiagonalShape>\n{\n  typedef typename T::PlainObject type;\n};\n\ntemplate<typename T, int Flags> struct plain_matrix_type_dense<T,MatrixXpr,Flags>\n{\n  typedef Matrix<typename traits<T>::Scalar,\n                traits<T>::RowsAtCompileTime,\n                traits<T>::ColsAtCompileTime,\n                AutoAlign | (Flags&RowMajorBit ? RowMajor : ColMajor),\n                traits<T>::MaxRowsAtCompileTime,\n                traits<T>::MaxColsAtCompileTime\n          > type;\n};\n\ntemplate<typename T, int Flags> struct plain_matrix_type_dense<T,ArrayXpr,Flags>\n{\n  typedef Array<typename traits<T>::Scalar,\n                traits<T>::RowsAtCompileTime,\n                traits<T>::ColsAtCompileTime,\n                AutoAlign | (Flags&RowMajorBit ? RowMajor : ColMajor),\n                traits<T>::MaxRowsAtCompileTime,\n                traits<T>::MaxColsAtCompileTime\n          > type;\n};\n\n/* eval : the return type of eval(). For matrices, this is just a const reference\n * in order to avoid a useless copy\n */\n\ntemplate<typename T, typename StorageKind = typename traits<T>::StorageKind> struct eval;\n\ntemplate<typename T> struct eval<T,Dense>\n{\n  typedef typename plain_matrix_type<T>::type type;\n//   typedef typename T::PlainObject type;\n//   typedef T::Matrix<typename traits<T>::Scalar,\n//                 traits<T>::RowsAtCompileTime,\n//                 traits<T>::ColsAtCompileTime,\n//                 AutoAlign | (traits<T>::Flags&RowMajorBit ? RowMajor : ColMajor),\n//                 traits<T>::MaxRowsAtCompileTime,\n//                 traits<T>::MaxColsAtCompileTime\n//           > type;\n};\n\ntemplate<typename T> struct eval<T,DiagonalShape>\n{\n  typedef typename plain_matrix_type<T>::type type;\n};\n\n// for matrices, no need to evaluate, just use a const reference to avoid a useless copy\ntemplate<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>\nstruct eval<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>, Dense>\n{\n  typedef const Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>& type;\n};\n\ntemplate<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>\nstruct eval<Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>, Dense>\n{\n  typedef const Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>& type;\n};\n\n\n/* similar to plain_matrix_type, but using the evaluator's Flags */\ntemplate<typename T, typename StorageKind = typename traits<T>::StorageKind> struct plain_object_eval;\n\ntemplate<typename T>\nstruct plain_object_eval<T,Dense>\n{\n  typedef typename plain_matrix_type_dense<T,typename traits<T>::XprKind, evaluator<T>::Flags>::type type;\n};\n\n\n/* plain_matrix_type_column_major : same as plain_matrix_type but guaranteed to be column-major\n */\ntemplate<typename T> struct plain_matrix_type_column_major\n{\n  enum { Rows = traits<T>::RowsAtCompileTime,\n         Cols = traits<T>::ColsAtCompileTime,\n         MaxRows = traits<T>::MaxRowsAtCompileTime,\n         MaxCols = traits<T>::MaxColsAtCompileTime\n  };\n  typedef Matrix<typename traits<T>::Scalar,\n                Rows,\n                Cols,\n                (MaxRows==1&&MaxCols!=1) ? RowMajor : ColMajor,\n                MaxRows,\n                MaxCols\n          > type;\n};\n\n/* plain_matrix_type_row_major : same as plain_matrix_type but guaranteed to be row-major\n */\ntemplate<typename T> struct plain_matrix_type_row_major\n{\n  enum { Rows = traits<T>::RowsAtCompileTime,\n         Cols = traits<T>::ColsAtCompileTime,\n         MaxRows = traits<T>::MaxRowsAtCompileTime,\n         MaxCols = traits<T>::MaxColsAtCompileTime\n  };\n  typedef Matrix<typename traits<T>::Scalar,\n                Rows,\n                Cols,\n                (MaxCols==1&&MaxRows!=1) ? RowMajor : ColMajor,\n                MaxRows,\n                MaxCols\n          > type;\n};\n\n/** \\internal The reference selector for template expressions. The idea is that we don't\n  * need to use references for expressions since they are light weight proxy\n  * objects which should generate no copying overhead. */\ntemplate <typename T>\nstruct ref_selector\n{\n  typedef typename conditional<\n    bool(traits<T>::Flags & NestByRefBit),\n    T const&,\n    const T\n  >::type type;\n  \n  typedef typename conditional<\n    bool(traits<T>::Flags & NestByRefBit),\n    T &,\n    T\n  >::type non_const_type;\n};\n\n/** \\internal Adds the const qualifier on the value-type of T2 if and only if T1 is a const type */\ntemplate<typename T1, typename T2>\nstruct transfer_constness\n{\n  typedef typename conditional<\n    bool(internal::is_const<T1>::value),\n    typename internal::add_const_on_value_type<T2>::type,\n    T2\n  >::type type;\n};\n\n\n// However, we still need a mechanism to detect whether an expression which is evaluated multiple time\n// has to be evaluated into a temporary.\n// That's the purpose of this new nested_eval helper:\n/** \\internal Determines how a given expression should be nested when evaluated multiple times.\n  * For example, when you do a * (b+c), Eigen will determine how the expression b+c should be\n  * evaluated into the bigger product expression. The choice is between nesting the expression b+c as-is, or\n  * evaluating that expression b+c into a temporary variable d, and nest d so that the resulting expression is\n  * a*d. Evaluating can be beneficial for example if every coefficient access in the resulting expression causes\n  * many coefficient accesses in the nested expressions -- as is the case with matrix product for example.\n  *\n  * \\tparam T the type of the expression being nested.\n  * \\tparam n the number of coefficient accesses in the nested expression for each coefficient access in the bigger expression.\n  * \\tparam PlainObject the type of the temporary if needed.\n  */\ntemplate<typename T, int n, typename PlainObject = typename plain_object_eval<T>::type> struct nested_eval\n{\n  enum {\n    ScalarReadCost = NumTraits<typename traits<T>::Scalar>::ReadCost,\n    CoeffReadCost = evaluator<T>::CoeffReadCost,  // NOTE What if an evaluator evaluate itself into a tempory?\n                                                  //      Then CoeffReadCost will be small (e.g., 1) but we still have to evaluate, especially if n>1.\n                                                  //      This situation is already taken care by the EvalBeforeNestingBit flag, which is turned ON\n                                                  //      for all evaluator creating a temporary. This flag is then propagated by the parent evaluators.\n                                                  //      Another solution could be to count the number of temps?\n    NAsInteger = n == Dynamic ? HugeCost : n,\n    CostEval   = (NAsInteger+1) * ScalarReadCost + CoeffReadCost,\n    CostNoEval = NAsInteger * CoeffReadCost,\n    Evaluate = (int(evaluator<T>::Flags) & EvalBeforeNestingBit) || (int(CostEval) < int(CostNoEval))\n  };\n\n  typedef typename conditional<Evaluate, PlainObject, typename ref_selector<T>::type>::type type;\n};\n\ntemplate<typename T>\nEIGEN_DEVICE_FUNC\ninline T* const_cast_ptr(const T* ptr)\n{\n  return const_cast<T*>(ptr);\n}\n\ntemplate<typename Derived, typename XprKind = typename traits<Derived>::XprKind>\nstruct dense_xpr_base\n{\n  /* dense_xpr_base should only ever be used on dense expressions, thus falling either into the MatrixXpr or into the ArrayXpr cases */\n};\n\ntemplate<typename Derived>\nstruct dense_xpr_base<Derived, MatrixXpr>\n{\n  typedef MatrixBase<Derived> type;\n};\n\ntemplate<typename Derived>\nstruct dense_xpr_base<Derived, ArrayXpr>\n{\n  typedef ArrayBase<Derived> type;\n};\n\ntemplate<typename Derived, typename XprKind = typename traits<Derived>::XprKind, typename StorageKind = typename traits<Derived>::StorageKind>\nstruct generic_xpr_base;\n\ntemplate<typename Derived, typename XprKind>\nstruct generic_xpr_base<Derived, XprKind, Dense>\n{\n  typedef typename dense_xpr_base<Derived,XprKind>::type type;\n};\n\ntemplate<typename XprType, typename CastType> struct cast_return_type\n{\n  typedef typename XprType::Scalar CurrentScalarType;\n  typedef typename remove_all<CastType>::type _CastType;\n  typedef typename _CastType::Scalar NewScalarType;\n  typedef typename conditional<is_same<CurrentScalarType,NewScalarType>::value,\n                              const XprType&,CastType>::type type;\n};\n\ntemplate <typename A, typename B> struct promote_storage_type;\n\ntemplate <typename A> struct promote_storage_type<A,A>\n{\n  typedef A ret;\n};\ntemplate <typename A> struct promote_storage_type<A, const A>\n{\n  typedef A ret;\n};\ntemplate <typename A> struct promote_storage_type<const A, A>\n{\n  typedef A ret;\n};\n\n/** \\internal Specify the \"storage kind\" of applying a coefficient-wise\n  * binary operations between two expressions of kinds A and B respectively.\n  * The template parameter Functor permits to specialize the resulting storage kind wrt to\n  * the functor.\n  * The default rules are as follows:\n  * \\code\n  * A      op A      -> A\n  * A      op dense  -> dense\n  * dense  op B      -> dense\n  * sparse op dense  -> sparse\n  * dense  op sparse -> sparse\n  * \\endcode\n  */\ntemplate <typename A, typename B, typename Functor> struct cwise_promote_storage_type;\n\ntemplate <typename A, typename Functor>                   struct cwise_promote_storage_type<A,A,Functor>                                      { typedef A      ret; };\ntemplate <typename Functor>                               struct cwise_promote_storage_type<Dense,Dense,Functor>                              { typedef Dense  ret; };\ntemplate <typename A, typename Functor>                   struct cwise_promote_storage_type<A,Dense,Functor>                                  { typedef Dense  ret; };\ntemplate <typename B, typename Functor>                   struct cwise_promote_storage_type<Dense,B,Functor>                                  { typedef Dense  ret; };\ntemplate <typename Functor>                               struct cwise_promote_storage_type<Sparse,Dense,Functor>                             { typedef Sparse ret; };\ntemplate <typename Functor>                               struct cwise_promote_storage_type<Dense,Sparse,Functor>                             { typedef Sparse ret; };\n\ntemplate <typename LhsKind, typename RhsKind, int LhsOrder, int RhsOrder> struct cwise_promote_storage_order {\n  enum { value = LhsOrder };\n};\n\ntemplate <typename LhsKind, int LhsOrder, int RhsOrder>   struct cwise_promote_storage_order<LhsKind,Sparse,LhsOrder,RhsOrder>                { enum { value = RhsOrder }; };\ntemplate <typename RhsKind, int LhsOrder, int RhsOrder>   struct cwise_promote_storage_order<Sparse,RhsKind,LhsOrder,RhsOrder>                { enum { value = LhsOrder }; };\ntemplate <int Order>                                      struct cwise_promote_storage_order<Sparse,Sparse,Order,Order>                       { enum { value = Order }; };\n\n\n/** \\internal Specify the \"storage kind\" of multiplying an expression of kind A with kind B.\n  * The template parameter ProductTag permits to specialize the resulting storage kind wrt to\n  * some compile-time properties of the product: GemmProduct, GemvProduct, OuterProduct, InnerProduct.\n  * The default rules are as follows:\n  * \\code\n  *  K * K            -> K\n  *  dense * K        -> dense\n  *  K * dense        -> dense\n  *  diag * K         -> K\n  *  K * diag         -> K\n  *  Perm * K         -> K\n  * K * Perm          -> K\n  * \\endcode\n  */\ntemplate <typename A, typename B, int ProductTag> struct product_promote_storage_type;\n\ntemplate <typename A, int ProductTag> struct product_promote_storage_type<A,                  A,                  ProductTag> { typedef A     ret;};\ntemplate <int ProductTag>             struct product_promote_storage_type<Dense,              Dense,              ProductTag> { typedef Dense ret;};\ntemplate <typename A, int ProductTag> struct product_promote_storage_type<A,                  Dense,              ProductTag> { typedef Dense ret; };\ntemplate <typename B, int ProductTag> struct product_promote_storage_type<Dense,              B,                  ProductTag> { typedef Dense ret; };\n\ntemplate <typename A, int ProductTag> struct product_promote_storage_type<A,                  DiagonalShape,      ProductTag> { typedef A ret; };\ntemplate <typename B, int ProductTag> struct product_promote_storage_type<DiagonalShape,      B,                  ProductTag> { typedef B ret; };\ntemplate <int ProductTag>             struct product_promote_storage_type<Dense,              DiagonalShape,      ProductTag> { typedef Dense ret; };\ntemplate <int ProductTag>             struct product_promote_storage_type<DiagonalShape,      Dense,              ProductTag> { typedef Dense ret; };\n\ntemplate <typename A, int ProductTag> struct product_promote_storage_type<A,                  PermutationStorage, ProductTag> { typedef A ret; };\ntemplate <typename B, int ProductTag> struct product_promote_storage_type<PermutationStorage, B,                  ProductTag> { typedef B ret; };\ntemplate <int ProductTag>             struct product_promote_storage_type<Dense,              PermutationStorage, ProductTag> { typedef Dense ret; };\ntemplate <int ProductTag>             struct product_promote_storage_type<PermutationStorage, Dense,              ProductTag> { typedef Dense ret; };\n\n/** \\internal gives the plain matrix or array type to store a row/column/diagonal of a matrix type.\n  * \\tparam Scalar optional parameter allowing to pass a different scalar type than the one of the MatrixType.\n  */\ntemplate<typename ExpressionType, typename Scalar = typename ExpressionType::Scalar>\nstruct plain_row_type\n{\n  typedef Matrix<Scalar, 1, ExpressionType::ColsAtCompileTime,\n                 ExpressionType::PlainObject::Options | RowMajor, 1, ExpressionType::MaxColsAtCompileTime> MatrixRowType;\n  typedef Array<Scalar, 1, ExpressionType::ColsAtCompileTime,\n                 ExpressionType::PlainObject::Options | RowMajor, 1, ExpressionType::MaxColsAtCompileTime> ArrayRowType;\n\n  typedef typename conditional<\n    is_same< typename traits<ExpressionType>::XprKind, MatrixXpr >::value,\n    MatrixRowType,\n    ArrayRowType \n  >::type type;\n};\n\ntemplate<typename ExpressionType, typename Scalar = typename ExpressionType::Scalar>\nstruct plain_col_type\n{\n  typedef Matrix<Scalar, ExpressionType::RowsAtCompileTime, 1,\n                 ExpressionType::PlainObject::Options & ~RowMajor, ExpressionType::MaxRowsAtCompileTime, 1> MatrixColType;\n  typedef Array<Scalar, ExpressionType::RowsAtCompileTime, 1,\n                 ExpressionType::PlainObject::Options & ~RowMajor, ExpressionType::MaxRowsAtCompileTime, 1> ArrayColType;\n\n  typedef typename conditional<\n    is_same< typename traits<ExpressionType>::XprKind, MatrixXpr >::value,\n    MatrixColType,\n    ArrayColType \n  >::type type;\n};\n\ntemplate<typename ExpressionType, typename Scalar = typename ExpressionType::Scalar>\nstruct plain_diag_type\n{\n  enum { diag_size = EIGEN_SIZE_MIN_PREFER_DYNAMIC(ExpressionType::RowsAtCompileTime, ExpressionType::ColsAtCompileTime),\n         max_diag_size = EIGEN_SIZE_MIN_PREFER_FIXED(ExpressionType::MaxRowsAtCompileTime, ExpressionType::MaxColsAtCompileTime)\n  };\n  typedef Matrix<Scalar, diag_size, 1, ExpressionType::PlainObject::Options & ~RowMajor, max_diag_size, 1> MatrixDiagType;\n  typedef Array<Scalar, diag_size, 1, ExpressionType::PlainObject::Options & ~RowMajor, max_diag_size, 1> ArrayDiagType;\n\n  typedef typename conditional<\n    is_same< typename traits<ExpressionType>::XprKind, MatrixXpr >::value,\n    MatrixDiagType,\n    ArrayDiagType \n  >::type type;\n};\n\ntemplate<typename Expr,typename Scalar = typename Expr::Scalar>\nstruct plain_constant_type\n{\n  enum { Options = (traits<Expr>::Flags&RowMajorBit)?RowMajor:0 };\n\n  typedef Array<Scalar,  traits<Expr>::RowsAtCompileTime,   traits<Expr>::ColsAtCompileTime,\n                Options, traits<Expr>::MaxRowsAtCompileTime,traits<Expr>::MaxColsAtCompileTime> array_type;\n\n  typedef Matrix<Scalar,  traits<Expr>::RowsAtCompileTime,   traits<Expr>::ColsAtCompileTime,\n                 Options, traits<Expr>::MaxRowsAtCompileTime,traits<Expr>::MaxColsAtCompileTime> matrix_type;\n\n  typedef CwiseNullaryOp<scalar_constant_op<Scalar>, const typename conditional<is_same< typename traits<Expr>::XprKind, MatrixXpr >::value, matrix_type, array_type>::type > type;\n};\n\ntemplate<typename ExpressionType>\nstruct is_lvalue\n{\n  enum { value = (!bool(is_const<ExpressionType>::value)) &&\n                 bool(traits<ExpressionType>::Flags & LvalueBit) };\n};\n\ntemplate<typename T> struct is_diagonal\n{ enum { ret = false }; };\n\ntemplate<typename T> struct is_diagonal<DiagonalBase<T> >\n{ enum { ret = true }; };\n\ntemplate<typename T> struct is_diagonal<DiagonalWrapper<T> >\n{ enum { ret = true }; };\n\ntemplate<typename T, int S> struct is_diagonal<DiagonalMatrix<T,S> >\n{ enum { ret = true }; };\n\ntemplate<typename S1, typename S2> struct glue_shapes;\ntemplate<> struct glue_shapes<DenseShape,TriangularShape> { typedef TriangularShape type;  };\n\ntemplate<typename T1, typename T2>\nbool is_same_dense(const T1 &mat1, const T2 &mat2, typename enable_if<has_direct_access<T1>::ret&&has_direct_access<T2>::ret, T1>::type * = 0)\n{\n  return (mat1.data()==mat2.data()) && (mat1.innerStride()==mat2.innerStride()) && (mat1.outerStride()==mat2.outerStride());\n}\n\ntemplate<typename T1, typename T2>\nbool is_same_dense(const T1 &, const T2 &, typename enable_if<!(has_direct_access<T1>::ret&&has_direct_access<T2>::ret), T1>::type * = 0)\n{\n  return false;\n}\n\n// Internal helper defining the cost of a scalar division for the type T.\n// The default heuristic can be specialized for each scalar type and architecture.\ntemplate<typename T,bool Vectorized=false,typename EnaleIf = void>\nstruct scalar_div_cost {\n  enum { value = 8*NumTraits<T>::MulCost };\n};\n\ntemplate<typename T,bool Vectorized>\nstruct scalar_div_cost<std::complex<T>, Vectorized> {\n  enum { value = 2*scalar_div_cost<T>::value\n               + 6*NumTraits<T>::MulCost\n               + 3*NumTraits<T>::AddCost\n  };\n};\n\n\ntemplate<bool Vectorized>\nstruct scalar_div_cost<signed long,Vectorized,typename conditional<sizeof(long)==8,void,false_type>::type> { enum { value = 24 }; };\ntemplate<bool Vectorized>\nstruct scalar_div_cost<unsigned long,Vectorized,typename conditional<sizeof(long)==8,void,false_type>::type> { enum { value = 21 }; };\n\n\n#ifdef EIGEN_DEBUG_ASSIGN\nstd::string demangle_traversal(int t)\n{\n  if(t==DefaultTraversal) return \"DefaultTraversal\";\n  if(t==LinearTraversal) return \"LinearTraversal\";\n  if(t==InnerVectorizedTraversal) return \"InnerVectorizedTraversal\";\n  if(t==LinearVectorizedTraversal) return \"LinearVectorizedTraversal\";\n  if(t==SliceVectorizedTraversal) return \"SliceVectorizedTraversal\";\n  return \"?\";\n}\nstd::string demangle_unrolling(int t)\n{\n  if(t==NoUnrolling) return \"NoUnrolling\";\n  if(t==InnerUnrolling) return \"InnerUnrolling\";\n  if(t==CompleteUnrolling) return \"CompleteUnrolling\";\n  return \"?\";\n}\nstd::string demangle_flags(int f)\n{\n  std::string res;\n  if(f&RowMajorBit)                 res += \" | RowMajor\";\n  if(f&PacketAccessBit)             res += \" | Packet\";\n  if(f&LinearAccessBit)             res += \" | Linear\";\n  if(f&LvalueBit)                   res += \" | Lvalue\";\n  if(f&DirectAccessBit)             res += \" | Direct\";\n  if(f&NestByRefBit)                res += \" | NestByRef\";\n  if(f&NoPreferredStorageOrderBit)  res += \" | NoPreferredStorageOrderBit\";\n  \n  return res;\n}\n#endif\n\n} // end namespace internal\n\n\n/** \\class ScalarBinaryOpTraits\n  * \\ingroup Core_Module\n  *\n  * \\brief Determines whether the given binary operation of two numeric types is allowed and what the scalar return type is.\n  *\n  * This class permits to control the scalar return type of any binary operation performed on two different scalar types through (partial) template specializations.\n  *\n  * For instance, let \\c U1, \\c U2 and \\c U3 be three user defined scalar types for which most operations between instances of \\c U1 and \\c U2 returns an \\c U3.\n  * You can let %Eigen knows that by defining:\n    \\code\n    template<typename BinaryOp>\n    struct ScalarBinaryOpTraits<U1,U2,BinaryOp> { typedef U3 ReturnType;  };\n    template<typename BinaryOp>\n    struct ScalarBinaryOpTraits<U2,U1,BinaryOp> { typedef U3 ReturnType;  };\n    \\endcode\n  * You can then explicitly disable some particular operations to get more explicit error messages:\n    \\code\n    template<>\n    struct ScalarBinaryOpTraits<U1,U2,internal::scalar_max_op<U1,U2> > {};\n    \\endcode\n  * Or customize the return type for individual operation:\n    \\code\n    template<>\n    struct ScalarBinaryOpTraits<U1,U2,internal::scalar_sum_op<U1,U2> > { typedef U1 ReturnType; };\n    \\endcode\n  *\n  * By default, the following generic combinations are supported:\n  <table class=\"manual\">\n  <tr><th>ScalarA</th><th>ScalarB</th><th>BinaryOp</th><th>ReturnType</th><th>Note</th></tr>\n  <tr            ><td>\\c T </td><td>\\c T </td><td>\\c * </td><td>\\c T </td><td></td></tr>\n  <tr class=\"alt\"><td>\\c NumTraits<T>::Real </td><td>\\c T </td><td>\\c * </td><td>\\c T </td><td>Only if \\c NumTraits<T>::IsComplex </td></tr>\n  <tr            ><td>\\c T </td><td>\\c NumTraits<T>::Real </td><td>\\c * </td><td>\\c T </td><td>Only if \\c NumTraits<T>::IsComplex </td></tr>\n  </table>\n  *\n  * \\sa CwiseBinaryOp\n  */\ntemplate<typename ScalarA, typename ScalarB, typename BinaryOp=internal::scalar_product_op<ScalarA,ScalarB> >\nstruct ScalarBinaryOpTraits\n#ifndef EIGEN_PARSED_BY_DOXYGEN\n  // for backward compatibility, use the hints given by the (deprecated) internal::scalar_product_traits class.\n  : internal::scalar_product_traits<ScalarA,ScalarB>\n#endif // EIGEN_PARSED_BY_DOXYGEN\n{};\n\ntemplate<typename T, typename BinaryOp>\nstruct ScalarBinaryOpTraits<T,T,BinaryOp>\n{\n  typedef T ReturnType;\n};\n\ntemplate <typename T, typename BinaryOp>\nstruct ScalarBinaryOpTraits<T, typename NumTraits<typename internal::enable_if<NumTraits<T>::IsComplex,T>::type>::Real, BinaryOp>\n{\n  typedef T ReturnType;\n};\ntemplate <typename T, typename BinaryOp>\nstruct ScalarBinaryOpTraits<typename NumTraits<typename internal::enable_if<NumTraits<T>::IsComplex,T>::type>::Real, T, BinaryOp>\n{\n  typedef T ReturnType;\n};\n\n// For Matrix * Permutation\ntemplate<typename T, typename BinaryOp>\nstruct ScalarBinaryOpTraits<T,void,BinaryOp>\n{\n  typedef T ReturnType;\n};\n\n// For Permutation * Matrix\ntemplate<typename T, typename BinaryOp>\nstruct ScalarBinaryOpTraits<void,T,BinaryOp>\n{\n  typedef T ReturnType;\n};\n\n// for Permutation*Permutation\ntemplate<typename BinaryOp>\nstruct ScalarBinaryOpTraits<void,void,BinaryOp>\n{\n  typedef void ReturnType;\n};\n\n// We require Lhs and Rhs to have \"compatible\" scalar types.\n// It is tempting to always allow mixing different types but remember that this is often impossible in the vectorized paths.\n// So allowing mixing different types gives very unexpected errors when enabling vectorization, when the user tries to\n// add together a float matrix and a double matrix.\n#define EIGEN_CHECK_BINARY_COMPATIBILIY(BINOP,LHS,RHS) \\\n  EIGEN_STATIC_ASSERT((Eigen::internal::has_ReturnType<ScalarBinaryOpTraits<LHS, RHS,BINOP> >::value), \\\n    YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)\n    \n} // end namespace Eigen\n\n#endif // EIGEN_XPRHELPER_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Eigenvalues/ComplexEigenSolver.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Claire Maurice\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_COMPLEX_EIGEN_SOLVER_H\n#define EIGEN_COMPLEX_EIGEN_SOLVER_H\n\n#include \"./ComplexSchur.h\"\n\nnamespace Eigen { \n\n/** \\eigenvalues_module \\ingroup Eigenvalues_Module\n  *\n  *\n  * \\class ComplexEigenSolver\n  *\n  * \\brief Computes eigenvalues and eigenvectors of general complex matrices\n  *\n  * \\tparam _MatrixType the type of the matrix of which we are\n  * computing the eigendecomposition; this is expected to be an\n  * instantiation of the Matrix class template.\n  *\n  * The eigenvalues and eigenvectors of a matrix \\f$ A \\f$ are scalars\n  * \\f$ \\lambda \\f$ and vectors \\f$ v \\f$ such that \\f$ Av = \\lambda v\n  * \\f$.  If \\f$ D \\f$ is a diagonal matrix with the eigenvalues on\n  * the diagonal, and \\f$ V \\f$ is a matrix with the eigenvectors as\n  * its columns, then \\f$ A V = V D \\f$. The matrix \\f$ V \\f$ is\n  * almost always invertible, in which case we have \\f$ A = V D V^{-1}\n  * \\f$. This is called the eigendecomposition.\n  *\n  * The main function in this class is compute(), which computes the\n  * eigenvalues and eigenvectors of a given function. The\n  * documentation for that function contains an example showing the\n  * main features of the class.\n  *\n  * \\sa class EigenSolver, class SelfAdjointEigenSolver\n  */\ntemplate<typename _MatrixType> class ComplexEigenSolver\n{\n  public:\n\n    /** \\brief Synonym for the template parameter \\p _MatrixType. */\n    typedef _MatrixType MatrixType;\n\n    enum {\n      RowsAtCompileTime = MatrixType::RowsAtCompileTime,\n      ColsAtCompileTime = MatrixType::ColsAtCompileTime,\n      Options = MatrixType::Options,\n      MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,\n      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime\n    };\n\n    /** \\brief Scalar type for matrices of type #MatrixType. */\n    typedef typename MatrixType::Scalar Scalar;\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n    typedef Eigen::Index Index; ///< \\deprecated since Eigen 3.3\n\n    /** \\brief Complex scalar type for #MatrixType.\n      *\n      * This is \\c std::complex<Scalar> if #Scalar is real (e.g.,\n      * \\c float or \\c double) and just \\c Scalar if #Scalar is\n      * complex.\n      */\n    typedef std::complex<RealScalar> ComplexScalar;\n\n    /** \\brief Type for vector of eigenvalues as returned by eigenvalues().\n      *\n      * This is a column vector with entries of type #ComplexScalar.\n      * The length of the vector is the size of #MatrixType.\n      */\n    typedef Matrix<ComplexScalar, ColsAtCompileTime, 1, Options&(~RowMajor), MaxColsAtCompileTime, 1> EigenvalueType;\n\n    /** \\brief Type for matrix of eigenvectors as returned by eigenvectors().\n      *\n      * This is a square matrix with entries of type #ComplexScalar.\n      * The size is the same as the size of #MatrixType.\n      */\n    typedef Matrix<ComplexScalar, RowsAtCompileTime, ColsAtCompileTime, Options, MaxRowsAtCompileTime, MaxColsAtCompileTime> EigenvectorType;\n\n    /** \\brief Default constructor.\n      *\n      * The default constructor is useful in cases in which the user intends to\n      * perform decompositions via compute().\n      */\n    ComplexEigenSolver()\n            : m_eivec(),\n              m_eivalues(),\n              m_schur(),\n              m_isInitialized(false),\n              m_eigenvectorsOk(false),\n              m_matX()\n    {}\n\n    /** \\brief Default Constructor with memory preallocation\n      *\n      * Like the default constructor but with preallocation of the internal data\n      * according to the specified problem \\a size.\n      * \\sa ComplexEigenSolver()\n      */\n    explicit ComplexEigenSolver(Index size)\n            : m_eivec(size, size),\n              m_eivalues(size),\n              m_schur(size),\n              m_isInitialized(false),\n              m_eigenvectorsOk(false),\n              m_matX(size, size)\n    {}\n\n    /** \\brief Constructor; computes eigendecomposition of given matrix.\n      *\n      * \\param[in]  matrix  Square matrix whose eigendecomposition is to be computed.\n      * \\param[in]  computeEigenvectors  If true, both the eigenvectors and the\n      *    eigenvalues are computed; if false, only the eigenvalues are\n      *    computed.\n      *\n      * This constructor calls compute() to compute the eigendecomposition.\n      */\n    template<typename InputType>\n    explicit ComplexEigenSolver(const EigenBase<InputType>& matrix, bool computeEigenvectors = true)\n            : m_eivec(matrix.rows(),matrix.cols()),\n              m_eivalues(matrix.cols()),\n              m_schur(matrix.rows()),\n              m_isInitialized(false),\n              m_eigenvectorsOk(false),\n              m_matX(matrix.rows(),matrix.cols())\n    {\n      compute(matrix.derived(), computeEigenvectors);\n    }\n\n    /** \\brief Returns the eigenvectors of given matrix.\n      *\n      * \\returns  A const reference to the matrix whose columns are the eigenvectors.\n      *\n      * \\pre Either the constructor\n      * ComplexEigenSolver(const MatrixType& matrix, bool) or the member\n      * function compute(const MatrixType& matrix, bool) has been called before\n      * to compute the eigendecomposition of a matrix, and\n      * \\p computeEigenvectors was set to true (the default).\n      *\n      * This function returns a matrix whose columns are the eigenvectors. Column\n      * \\f$ k \\f$ is an eigenvector corresponding to eigenvalue number \\f$ k\n      * \\f$ as returned by eigenvalues().  The eigenvectors are normalized to\n      * have (Euclidean) norm equal to one. The matrix returned by this\n      * function is the matrix \\f$ V \\f$ in the eigendecomposition \\f$ A = V D\n      * V^{-1} \\f$, if it exists.\n      *\n      * Example: \\include ComplexEigenSolver_eigenvectors.cpp\n      * Output: \\verbinclude ComplexEigenSolver_eigenvectors.out\n      */\n    const EigenvectorType& eigenvectors() const\n    {\n      eigen_assert(m_isInitialized && \"ComplexEigenSolver is not initialized.\");\n      eigen_assert(m_eigenvectorsOk && \"The eigenvectors have not been computed together with the eigenvalues.\");\n      return m_eivec;\n    }\n\n    /** \\brief Returns the eigenvalues of given matrix.\n      *\n      * \\returns A const reference to the column vector containing the eigenvalues.\n      *\n      * \\pre Either the constructor\n      * ComplexEigenSolver(const MatrixType& matrix, bool) or the member\n      * function compute(const MatrixType& matrix, bool) has been called before\n      * to compute the eigendecomposition of a matrix.\n      *\n      * This function returns a column vector containing the\n      * eigenvalues. Eigenvalues are repeated according to their\n      * algebraic multiplicity, so there are as many eigenvalues as\n      * rows in the matrix. The eigenvalues are not sorted in any particular\n      * order.\n      *\n      * Example: \\include ComplexEigenSolver_eigenvalues.cpp\n      * Output: \\verbinclude ComplexEigenSolver_eigenvalues.out\n      */\n    const EigenvalueType& eigenvalues() const\n    {\n      eigen_assert(m_isInitialized && \"ComplexEigenSolver is not initialized.\");\n      return m_eivalues;\n    }\n\n    /** \\brief Computes eigendecomposition of given matrix.\n      *\n      * \\param[in]  matrix  Square matrix whose eigendecomposition is to be computed.\n      * \\param[in]  computeEigenvectors  If true, both the eigenvectors and the\n      *    eigenvalues are computed; if false, only the eigenvalues are\n      *    computed.\n      * \\returns    Reference to \\c *this\n      *\n      * This function computes the eigenvalues of the complex matrix \\p matrix.\n      * The eigenvalues() function can be used to retrieve them.  If\n      * \\p computeEigenvectors is true, then the eigenvectors are also computed\n      * and can be retrieved by calling eigenvectors().\n      *\n      * The matrix is first reduced to Schur form using the\n      * ComplexSchur class. The Schur decomposition is then used to\n      * compute the eigenvalues and eigenvectors.\n      *\n      * The cost of the computation is dominated by the cost of the\n      * Schur decomposition, which is \\f$ O(n^3) \\f$ where \\f$ n \\f$\n      * is the size of the matrix.\n      *\n      * Example: \\include ComplexEigenSolver_compute.cpp\n      * Output: \\verbinclude ComplexEigenSolver_compute.out\n      */\n    template<typename InputType>\n    ComplexEigenSolver& compute(const EigenBase<InputType>& matrix, bool computeEigenvectors = true);\n\n    /** \\brief Reports whether previous computation was successful.\n      *\n      * \\returns \\c Success if computation was succesful, \\c NoConvergence otherwise.\n      */\n    ComputationInfo info() const\n    {\n      eigen_assert(m_isInitialized && \"ComplexEigenSolver is not initialized.\");\n      return m_schur.info();\n    }\n\n    /** \\brief Sets the maximum number of iterations allowed. */\n    ComplexEigenSolver& setMaxIterations(Index maxIters)\n    {\n      m_schur.setMaxIterations(maxIters);\n      return *this;\n    }\n\n    /** \\brief Returns the maximum number of iterations. */\n    Index getMaxIterations()\n    {\n      return m_schur.getMaxIterations();\n    }\n\n  protected:\n    \n    static void check_template_parameters()\n    {\n      EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);\n    }\n    \n    EigenvectorType m_eivec;\n    EigenvalueType m_eivalues;\n    ComplexSchur<MatrixType> m_schur;\n    bool m_isInitialized;\n    bool m_eigenvectorsOk;\n    EigenvectorType m_matX;\n\n  private:\n    void doComputeEigenvectors(RealScalar matrixnorm);\n    void sortEigenvalues(bool computeEigenvectors);\n};\n\n\ntemplate<typename MatrixType>\ntemplate<typename InputType>\nComplexEigenSolver<MatrixType>& \nComplexEigenSolver<MatrixType>::compute(const EigenBase<InputType>& matrix, bool computeEigenvectors)\n{\n  check_template_parameters();\n  \n  // this code is inspired from Jampack\n  eigen_assert(matrix.cols() == matrix.rows());\n\n  // Do a complex Schur decomposition, A = U T U^*\n  // The eigenvalues are on the diagonal of T.\n  m_schur.compute(matrix.derived(), computeEigenvectors);\n\n  if(m_schur.info() == Success)\n  {\n    m_eivalues = m_schur.matrixT().diagonal();\n    if(computeEigenvectors)\n      doComputeEigenvectors(m_schur.matrixT().norm());\n    sortEigenvalues(computeEigenvectors);\n  }\n\n  m_isInitialized = true;\n  m_eigenvectorsOk = computeEigenvectors;\n  return *this;\n}\n\n\ntemplate<typename MatrixType>\nvoid ComplexEigenSolver<MatrixType>::doComputeEigenvectors(RealScalar matrixnorm)\n{\n  const Index n = m_eivalues.size();\n\n  matrixnorm = numext::maxi(matrixnorm,(std::numeric_limits<RealScalar>::min)());\n\n  // Compute X such that T = X D X^(-1), where D is the diagonal of T.\n  // The matrix X is unit triangular.\n  m_matX = EigenvectorType::Zero(n, n);\n  for(Index k=n-1 ; k>=0 ; k--)\n  {\n    m_matX.coeffRef(k,k) = ComplexScalar(1.0,0.0);\n    // Compute X(i,k) using the (i,k) entry of the equation X T = D X\n    for(Index i=k-1 ; i>=0 ; i--)\n    {\n      m_matX.coeffRef(i,k) = -m_schur.matrixT().coeff(i,k);\n      if(k-i-1>0)\n        m_matX.coeffRef(i,k) -= (m_schur.matrixT().row(i).segment(i+1,k-i-1) * m_matX.col(k).segment(i+1,k-i-1)).value();\n      ComplexScalar z = m_schur.matrixT().coeff(i,i) - m_schur.matrixT().coeff(k,k);\n      if(z==ComplexScalar(0))\n      {\n        // If the i-th and k-th eigenvalue are equal, then z equals 0.\n        // Use a small value instead, to prevent division by zero.\n        numext::real_ref(z) = NumTraits<RealScalar>::epsilon() * matrixnorm;\n      }\n      m_matX.coeffRef(i,k) = m_matX.coeff(i,k) / z;\n    }\n  }\n\n  // Compute V as V = U X; now A = U T U^* = U X D X^(-1) U^* = V D V^(-1)\n  m_eivec.noalias() = m_schur.matrixU() * m_matX;\n  // .. and normalize the eigenvectors\n  for(Index k=0 ; k<n ; k++)\n  {\n    m_eivec.col(k).normalize();\n  }\n}\n\n\ntemplate<typename MatrixType>\nvoid ComplexEigenSolver<MatrixType>::sortEigenvalues(bool computeEigenvectors)\n{\n  const Index n =  m_eivalues.size();\n  for (Index i=0; i<n; i++)\n  {\n    Index k;\n    m_eivalues.cwiseAbs().tail(n-i).minCoeff(&k);\n    if (k != 0)\n    {\n      k += i;\n      std::swap(m_eivalues[k],m_eivalues[i]);\n      if(computeEigenvectors)\n\tm_eivec.col(i).swap(m_eivec.col(k));\n    }\n  }\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_COMPLEX_EIGEN_SOLVER_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Eigenvalues/ComplexSchur.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Claire Maurice\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_COMPLEX_SCHUR_H\n#define EIGEN_COMPLEX_SCHUR_H\n\n#include \"./HessenbergDecomposition.h\"\n\nnamespace Eigen { \n\nnamespace internal {\ntemplate<typename MatrixType, bool IsComplex> struct complex_schur_reduce_to_hessenberg;\n}\n\n/** \\eigenvalues_module \\ingroup Eigenvalues_Module\n  *\n  *\n  * \\class ComplexSchur\n  *\n  * \\brief Performs a complex Schur decomposition of a real or complex square matrix\n  *\n  * \\tparam _MatrixType the type of the matrix of which we are\n  * computing the Schur decomposition; this is expected to be an\n  * instantiation of the Matrix class template.\n  *\n  * Given a real or complex square matrix A, this class computes the\n  * Schur decomposition: \\f$ A = U T U^*\\f$ where U is a unitary\n  * complex matrix, and T is a complex upper triangular matrix.  The\n  * diagonal of the matrix T corresponds to the eigenvalues of the\n  * matrix A.\n  *\n  * Call the function compute() to compute the Schur decomposition of\n  * a given matrix. Alternatively, you can use the \n  * ComplexSchur(const MatrixType&, bool) constructor which computes\n  * the Schur decomposition at construction time. Once the\n  * decomposition is computed, you can use the matrixU() and matrixT()\n  * functions to retrieve the matrices U and V in the decomposition.\n  *\n  * \\note This code is inspired from Jampack\n  *\n  * \\sa class RealSchur, class EigenSolver, class ComplexEigenSolver\n  */\ntemplate<typename _MatrixType> class ComplexSchur\n{\n  public:\n    typedef _MatrixType MatrixType;\n    enum {\n      RowsAtCompileTime = MatrixType::RowsAtCompileTime,\n      ColsAtCompileTime = MatrixType::ColsAtCompileTime,\n      Options = MatrixType::Options,\n      MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,\n      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime\n    };\n\n    /** \\brief Scalar type for matrices of type \\p _MatrixType. */\n    typedef typename MatrixType::Scalar Scalar;\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n    typedef Eigen::Index Index; ///< \\deprecated since Eigen 3.3\n\n    /** \\brief Complex scalar type for \\p _MatrixType. \n      *\n      * This is \\c std::complex<Scalar> if #Scalar is real (e.g.,\n      * \\c float or \\c double) and just \\c Scalar if #Scalar is\n      * complex.\n      */\n    typedef std::complex<RealScalar> ComplexScalar;\n\n    /** \\brief Type for the matrices in the Schur decomposition.\n      *\n      * This is a square matrix with entries of type #ComplexScalar. \n      * The size is the same as the size of \\p _MatrixType.\n      */\n    typedef Matrix<ComplexScalar, RowsAtCompileTime, ColsAtCompileTime, Options, MaxRowsAtCompileTime, MaxColsAtCompileTime> ComplexMatrixType;\n\n    /** \\brief Default constructor.\n      *\n      * \\param [in] size  Positive integer, size of the matrix whose Schur decomposition will be computed.\n      *\n      * The default constructor is useful in cases in which the user\n      * intends to perform decompositions via compute().  The \\p size\n      * parameter is only used as a hint. It is not an error to give a\n      * wrong \\p size, but it may impair performance.\n      *\n      * \\sa compute() for an example.\n      */\n    explicit ComplexSchur(Index size = RowsAtCompileTime==Dynamic ? 1 : RowsAtCompileTime)\n      : m_matT(size,size),\n        m_matU(size,size),\n        m_hess(size),\n        m_isInitialized(false),\n        m_matUisUptodate(false),\n        m_maxIters(-1)\n    {}\n\n    /** \\brief Constructor; computes Schur decomposition of given matrix. \n      * \n      * \\param[in]  matrix    Square matrix whose Schur decomposition is to be computed.\n      * \\param[in]  computeU  If true, both T and U are computed; if false, only T is computed.\n      *\n      * This constructor calls compute() to compute the Schur decomposition.\n      *\n      * \\sa matrixT() and matrixU() for examples.\n      */\n    template<typename InputType>\n    explicit ComplexSchur(const EigenBase<InputType>& matrix, bool computeU = true)\n      : m_matT(matrix.rows(),matrix.cols()),\n        m_matU(matrix.rows(),matrix.cols()),\n        m_hess(matrix.rows()),\n        m_isInitialized(false),\n        m_matUisUptodate(false),\n        m_maxIters(-1)\n    {\n      compute(matrix.derived(), computeU);\n    }\n\n    /** \\brief Returns the unitary matrix in the Schur decomposition. \n      *\n      * \\returns A const reference to the matrix U.\n      *\n      * It is assumed that either the constructor\n      * ComplexSchur(const MatrixType& matrix, bool computeU) or the\n      * member function compute(const MatrixType& matrix, bool computeU)\n      * has been called before to compute the Schur decomposition of a\n      * matrix, and that \\p computeU was set to true (the default\n      * value).\n      *\n      * Example: \\include ComplexSchur_matrixU.cpp\n      * Output: \\verbinclude ComplexSchur_matrixU.out\n      */\n    const ComplexMatrixType& matrixU() const\n    {\n      eigen_assert(m_isInitialized && \"ComplexSchur is not initialized.\");\n      eigen_assert(m_matUisUptodate && \"The matrix U has not been computed during the ComplexSchur decomposition.\");\n      return m_matU;\n    }\n\n    /** \\brief Returns the triangular matrix in the Schur decomposition. \n      *\n      * \\returns A const reference to the matrix T.\n      *\n      * It is assumed that either the constructor\n      * ComplexSchur(const MatrixType& matrix, bool computeU) or the\n      * member function compute(const MatrixType& matrix, bool computeU)\n      * has been called before to compute the Schur decomposition of a\n      * matrix.\n      *\n      * Note that this function returns a plain square matrix. If you want to reference\n      * only the upper triangular part, use:\n      * \\code schur.matrixT().triangularView<Upper>() \\endcode \n      *\n      * Example: \\include ComplexSchur_matrixT.cpp\n      * Output: \\verbinclude ComplexSchur_matrixT.out\n      */\n    const ComplexMatrixType& matrixT() const\n    {\n      eigen_assert(m_isInitialized && \"ComplexSchur is not initialized.\");\n      return m_matT;\n    }\n\n    /** \\brief Computes Schur decomposition of given matrix. \n      * \n      * \\param[in]  matrix  Square matrix whose Schur decomposition is to be computed.\n      * \\param[in]  computeU  If true, both T and U are computed; if false, only T is computed.\n\n      * \\returns    Reference to \\c *this\n      *\n      * The Schur decomposition is computed by first reducing the\n      * matrix to Hessenberg form using the class\n      * HessenbergDecomposition. The Hessenberg matrix is then reduced\n      * to triangular form by performing QR iterations with a single\n      * shift. The cost of computing the Schur decomposition depends\n      * on the number of iterations; as a rough guide, it may be taken\n      * on the number of iterations; as a rough guide, it may be taken\n      * to be \\f$25n^3\\f$ complex flops, or \\f$10n^3\\f$ complex flops\n      * if \\a computeU is false.\n      *\n      * Example: \\include ComplexSchur_compute.cpp\n      * Output: \\verbinclude ComplexSchur_compute.out\n      *\n      * \\sa compute(const MatrixType&, bool, Index)\n      */\n    template<typename InputType>\n    ComplexSchur& compute(const EigenBase<InputType>& matrix, bool computeU = true);\n    \n    /** \\brief Compute Schur decomposition from a given Hessenberg matrix\n     *  \\param[in] matrixH Matrix in Hessenberg form H\n     *  \\param[in] matrixQ orthogonal matrix Q that transform a matrix A to H : A = Q H Q^T\n     *  \\param computeU Computes the matriX U of the Schur vectors\n     * \\return Reference to \\c *this\n     * \n     *  This routine assumes that the matrix is already reduced in Hessenberg form matrixH\n     *  using either the class HessenbergDecomposition or another mean. \n     *  It computes the upper quasi-triangular matrix T of the Schur decomposition of H\n     *  When computeU is true, this routine computes the matrix U such that \n     *  A = U T U^T =  (QZ) T (QZ)^T = Q H Q^T where A is the initial matrix\n     * \n     * NOTE Q is referenced if computeU is true; so, if the initial orthogonal matrix\n     * is not available, the user should give an identity matrix (Q.setIdentity())\n     * \n     * \\sa compute(const MatrixType&, bool)\n     */\n    template<typename HessMatrixType, typename OrthMatrixType>\n    ComplexSchur& computeFromHessenberg(const HessMatrixType& matrixH, const OrthMatrixType& matrixQ,  bool computeU=true);\n\n    /** \\brief Reports whether previous computation was successful.\n      *\n      * \\returns \\c Success if computation was succesful, \\c NoConvergence otherwise.\n      */\n    ComputationInfo info() const\n    {\n      eigen_assert(m_isInitialized && \"ComplexSchur is not initialized.\");\n      return m_info;\n    }\n\n    /** \\brief Sets the maximum number of iterations allowed. \n      *\n      * If not specified by the user, the maximum number of iterations is m_maxIterationsPerRow times the size\n      * of the matrix.\n      */\n    ComplexSchur& setMaxIterations(Index maxIters)\n    {\n      m_maxIters = maxIters;\n      return *this;\n    }\n\n    /** \\brief Returns the maximum number of iterations. */\n    Index getMaxIterations()\n    {\n      return m_maxIters;\n    }\n\n    /** \\brief Maximum number of iterations per row.\n      *\n      * If not otherwise specified, the maximum number of iterations is this number times the size of the\n      * matrix. It is currently set to 30.\n      */\n    static const int m_maxIterationsPerRow = 30;\n\n  protected:\n    ComplexMatrixType m_matT, m_matU;\n    HessenbergDecomposition<MatrixType> m_hess;\n    ComputationInfo m_info;\n    bool m_isInitialized;\n    bool m_matUisUptodate;\n    Index m_maxIters;\n\n  private:  \n    bool subdiagonalEntryIsNeglegible(Index i);\n    ComplexScalar computeShift(Index iu, Index iter);\n    void reduceToTriangularForm(bool computeU);\n    friend struct internal::complex_schur_reduce_to_hessenberg<MatrixType, NumTraits<Scalar>::IsComplex>;\n};\n\n/** If m_matT(i+1,i) is neglegible in floating point arithmetic\n  * compared to m_matT(i,i) and m_matT(j,j), then set it to zero and\n  * return true, else return false. */\ntemplate<typename MatrixType>\ninline bool ComplexSchur<MatrixType>::subdiagonalEntryIsNeglegible(Index i)\n{\n  RealScalar d = numext::norm1(m_matT.coeff(i,i)) + numext::norm1(m_matT.coeff(i+1,i+1));\n  RealScalar sd = numext::norm1(m_matT.coeff(i+1,i));\n  if (internal::isMuchSmallerThan(sd, d, NumTraits<RealScalar>::epsilon()))\n  {\n    m_matT.coeffRef(i+1,i) = ComplexScalar(0);\n    return true;\n  }\n  return false;\n}\n\n\n/** Compute the shift in the current QR iteration. */\ntemplate<typename MatrixType>\ntypename ComplexSchur<MatrixType>::ComplexScalar ComplexSchur<MatrixType>::computeShift(Index iu, Index iter)\n{\n  using std::abs;\n  if (iter == 10 || iter == 20) \n  {\n    // exceptional shift, taken from http://www.netlib.org/eispack/comqr.f\n    return abs(numext::real(m_matT.coeff(iu,iu-1))) + abs(numext::real(m_matT.coeff(iu-1,iu-2)));\n  }\n\n  // compute the shift as one of the eigenvalues of t, the 2x2\n  // diagonal block on the bottom of the active submatrix\n  Matrix<ComplexScalar,2,2> t = m_matT.template block<2,2>(iu-1,iu-1);\n  RealScalar normt = t.cwiseAbs().sum();\n  t /= normt;     // the normalization by sf is to avoid under/overflow\n\n  ComplexScalar b = t.coeff(0,1) * t.coeff(1,0);\n  ComplexScalar c = t.coeff(0,0) - t.coeff(1,1);\n  ComplexScalar disc = sqrt(c*c + RealScalar(4)*b);\n  ComplexScalar det = t.coeff(0,0) * t.coeff(1,1) - b;\n  ComplexScalar trace = t.coeff(0,0) + t.coeff(1,1);\n  ComplexScalar eival1 = (trace + disc) / RealScalar(2);\n  ComplexScalar eival2 = (trace - disc) / RealScalar(2);\n\n  if(numext::norm1(eival1) > numext::norm1(eival2))\n    eival2 = det / eival1;\n  else\n    eival1 = det / eival2;\n\n  // choose the eigenvalue closest to the bottom entry of the diagonal\n  if(numext::norm1(eival1-t.coeff(1,1)) < numext::norm1(eival2-t.coeff(1,1)))\n    return normt * eival1;\n  else\n    return normt * eival2;\n}\n\n\ntemplate<typename MatrixType>\ntemplate<typename InputType>\nComplexSchur<MatrixType>& ComplexSchur<MatrixType>::compute(const EigenBase<InputType>& matrix, bool computeU)\n{\n  m_matUisUptodate = false;\n  eigen_assert(matrix.cols() == matrix.rows());\n\n  if(matrix.cols() == 1)\n  {\n    m_matT = matrix.derived().template cast<ComplexScalar>();\n    if(computeU)  m_matU = ComplexMatrixType::Identity(1,1);\n    m_info = Success;\n    m_isInitialized = true;\n    m_matUisUptodate = computeU;\n    return *this;\n  }\n\n  internal::complex_schur_reduce_to_hessenberg<MatrixType, NumTraits<Scalar>::IsComplex>::run(*this, matrix.derived(), computeU);\n  computeFromHessenberg(m_matT, m_matU, computeU);\n  return *this;\n}\n\ntemplate<typename MatrixType>\ntemplate<typename HessMatrixType, typename OrthMatrixType>\nComplexSchur<MatrixType>& ComplexSchur<MatrixType>::computeFromHessenberg(const HessMatrixType& matrixH, const OrthMatrixType& matrixQ, bool computeU)\n{\n  m_matT = matrixH;\n  if(computeU)\n    m_matU = matrixQ;\n  reduceToTriangularForm(computeU);\n  return *this;\n}\nnamespace internal {\n\n/* Reduce given matrix to Hessenberg form */\ntemplate<typename MatrixType, bool IsComplex>\nstruct complex_schur_reduce_to_hessenberg\n{\n  // this is the implementation for the case IsComplex = true\n  static void run(ComplexSchur<MatrixType>& _this, const MatrixType& matrix, bool computeU)\n  {\n    _this.m_hess.compute(matrix);\n    _this.m_matT = _this.m_hess.matrixH();\n    if(computeU)  _this.m_matU = _this.m_hess.matrixQ();\n  }\n};\n\ntemplate<typename MatrixType>\nstruct complex_schur_reduce_to_hessenberg<MatrixType, false>\n{\n  static void run(ComplexSchur<MatrixType>& _this, const MatrixType& matrix, bool computeU)\n  {\n    typedef typename ComplexSchur<MatrixType>::ComplexScalar ComplexScalar;\n\n    // Note: m_hess is over RealScalar; m_matT and m_matU is over ComplexScalar\n    _this.m_hess.compute(matrix);\n    _this.m_matT = _this.m_hess.matrixH().template cast<ComplexScalar>();\n    if(computeU)  \n    {\n      // This may cause an allocation which seems to be avoidable\n      MatrixType Q = _this.m_hess.matrixQ(); \n      _this.m_matU = Q.template cast<ComplexScalar>();\n    }\n  }\n};\n\n} // end namespace internal\n\n// Reduce the Hessenberg matrix m_matT to triangular form by QR iteration.\ntemplate<typename MatrixType>\nvoid ComplexSchur<MatrixType>::reduceToTriangularForm(bool computeU)\n{  \n  Index maxIters = m_maxIters;\n  if (maxIters == -1)\n    maxIters = m_maxIterationsPerRow * m_matT.rows();\n\n  // The matrix m_matT is divided in three parts. \n  // Rows 0,...,il-1 are decoupled from the rest because m_matT(il,il-1) is zero. \n  // Rows il,...,iu is the part we are working on (the active submatrix).\n  // Rows iu+1,...,end are already brought in triangular form.\n  Index iu = m_matT.cols() - 1;\n  Index il;\n  Index iter = 0; // number of iterations we are working on the (iu,iu) element\n  Index totalIter = 0; // number of iterations for whole matrix\n\n  while(true)\n  {\n    // find iu, the bottom row of the active submatrix\n    while(iu > 0)\n    {\n      if(!subdiagonalEntryIsNeglegible(iu-1)) break;\n      iter = 0;\n      --iu;\n    }\n\n    // if iu is zero then we are done; the whole matrix is triangularized\n    if(iu==0) break;\n\n    // if we spent too many iterations, we give up\n    iter++;\n    totalIter++;\n    if(totalIter > maxIters) break;\n\n    // find il, the top row of the active submatrix\n    il = iu-1;\n    while(il > 0 && !subdiagonalEntryIsNeglegible(il-1))\n    {\n      --il;\n    }\n\n    /* perform the QR step using Givens rotations. The first rotation\n       creates a bulge; the (il+2,il) element becomes nonzero. This\n       bulge is chased down to the bottom of the active submatrix. */\n\n    ComplexScalar shift = computeShift(iu, iter);\n    JacobiRotation<ComplexScalar> rot;\n    rot.makeGivens(m_matT.coeff(il,il) - shift, m_matT.coeff(il+1,il));\n    m_matT.rightCols(m_matT.cols()-il).applyOnTheLeft(il, il+1, rot.adjoint());\n    m_matT.topRows((std::min)(il+2,iu)+1).applyOnTheRight(il, il+1, rot);\n    if(computeU) m_matU.applyOnTheRight(il, il+1, rot);\n\n    for(Index i=il+1 ; i<iu ; i++)\n    {\n      rot.makeGivens(m_matT.coeffRef(i,i-1), m_matT.coeffRef(i+1,i-1), &m_matT.coeffRef(i,i-1));\n      m_matT.coeffRef(i+1,i-1) = ComplexScalar(0);\n      m_matT.rightCols(m_matT.cols()-i).applyOnTheLeft(i, i+1, rot.adjoint());\n      m_matT.topRows((std::min)(i+2,iu)+1).applyOnTheRight(i, i+1, rot);\n      if(computeU) m_matU.applyOnTheRight(i, i+1, rot);\n    }\n  }\n\n  if(totalIter <= maxIters)\n    m_info = Success;\n  else\n    m_info = NoConvergence;\n\n  m_isInitialized = true;\n  m_matUisUptodate = computeU;\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_COMPLEX_SCHUR_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Eigenvalues/ComplexSchur_LAPACKE.h",
    "content": "/*\n Copyright (c) 2011, Intel Corporation. All rights reserved.\n\n Redistribution and use in source and binary forms, with or without modification,\n are permitted provided that the following conditions are met:\n\n * Redistributions of source code must retain the above copyright notice, this\n   list of conditions and the following disclaimer.\n * Redistributions in binary form must reproduce the above copyright notice,\n   this list of conditions and the following disclaimer in the documentation\n   and/or other materials provided with the distribution.\n * Neither the name of Intel Corporation nor the names of its contributors may\n   be used to endorse or promote products derived from this software without\n   specific prior written permission.\n\n THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\" AND\n ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED\n WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\n DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR\n ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES\n (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;\n LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON\n ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT\n (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS\n SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n\n ********************************************************************************\n *   Content : Eigen bindings to LAPACKe\n *    Complex Schur needed to complex unsymmetrical eigenvalues/eigenvectors.\n ********************************************************************************\n*/\n\n#ifndef EIGEN_COMPLEX_SCHUR_LAPACKE_H\n#define EIGEN_COMPLEX_SCHUR_LAPACKE_H\n\nnamespace Eigen { \n\n/** \\internal Specialization for the data types supported by LAPACKe */\n\n#define EIGEN_LAPACKE_SCHUR_COMPLEX(EIGTYPE, LAPACKE_TYPE, LAPACKE_PREFIX, LAPACKE_PREFIX_U, EIGCOLROW, LAPACKE_COLROW) \\\ntemplate<> template<typename InputType> inline \\\nComplexSchur<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >& \\\nComplexSchur<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >::compute(const EigenBase<InputType>& matrix, bool computeU) \\\n{ \\\n  typedef Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> MatrixType; \\\n  typedef MatrixType::RealScalar RealScalar; \\\n  typedef std::complex<RealScalar> ComplexScalar; \\\n\\\n  eigen_assert(matrix.cols() == matrix.rows()); \\\n\\\n  m_matUisUptodate = false; \\\n  if(matrix.cols() == 1) \\\n  { \\\n    m_matT = matrix.derived().template cast<ComplexScalar>(); \\\n    if(computeU)  m_matU = ComplexMatrixType::Identity(1,1); \\\n      m_info = Success; \\\n      m_isInitialized = true; \\\n      m_matUisUptodate = computeU; \\\n      return *this; \\\n  } \\\n  lapack_int n = internal::convert_index<lapack_int>(matrix.cols()), sdim, info; \\\n  lapack_int matrix_order = LAPACKE_COLROW; \\\n  char jobvs, sort='N'; \\\n  LAPACK_##LAPACKE_PREFIX_U##_SELECT1 select = 0; \\\n  jobvs = (computeU) ? 'V' : 'N'; \\\n  m_matU.resize(n, n); \\\n  lapack_int ldvs  = internal::convert_index<lapack_int>(m_matU.outerStride()); \\\n  m_matT = matrix; \\\n  lapack_int lda = internal::convert_index<lapack_int>(m_matT.outerStride()); \\\n  Matrix<EIGTYPE, Dynamic, Dynamic> w; \\\n  w.resize(n, 1);\\\n  info = LAPACKE_##LAPACKE_PREFIX##gees( matrix_order, jobvs, sort, select, n, (LAPACKE_TYPE*)m_matT.data(), lda, &sdim, (LAPACKE_TYPE*)w.data(), (LAPACKE_TYPE*)m_matU.data(), ldvs ); \\\n  if(info == 0) \\\n    m_info = Success; \\\n  else \\\n    m_info = NoConvergence; \\\n\\\n  m_isInitialized = true; \\\n  m_matUisUptodate = computeU; \\\n  return *this; \\\n\\\n}\n\nEIGEN_LAPACKE_SCHUR_COMPLEX(dcomplex, lapack_complex_double, z, Z, ColMajor, LAPACK_COL_MAJOR)\nEIGEN_LAPACKE_SCHUR_COMPLEX(scomplex, lapack_complex_float,  c, C, ColMajor, LAPACK_COL_MAJOR)\nEIGEN_LAPACKE_SCHUR_COMPLEX(dcomplex, lapack_complex_double, z, Z, RowMajor, LAPACK_ROW_MAJOR)\nEIGEN_LAPACKE_SCHUR_COMPLEX(scomplex, lapack_complex_float,  c, C, RowMajor, LAPACK_ROW_MAJOR)\n\n} // end namespace Eigen\n\n#endif // EIGEN_COMPLEX_SCHUR_LAPACKE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Eigenvalues/EigenSolver.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_EIGENSOLVER_H\n#define EIGEN_EIGENSOLVER_H\n\n#include \"./RealSchur.h\"\n\nnamespace Eigen { \n\n/** \\eigenvalues_module \\ingroup Eigenvalues_Module\n  *\n  *\n  * \\class EigenSolver\n  *\n  * \\brief Computes eigenvalues and eigenvectors of general matrices\n  *\n  * \\tparam _MatrixType the type of the matrix of which we are computing the\n  * eigendecomposition; this is expected to be an instantiation of the Matrix\n  * class template. Currently, only real matrices are supported.\n  *\n  * The eigenvalues and eigenvectors of a matrix \\f$ A \\f$ are scalars\n  * \\f$ \\lambda \\f$ and vectors \\f$ v \\f$ such that \\f$ Av = \\lambda v \\f$.  If\n  * \\f$ D \\f$ is a diagonal matrix with the eigenvalues on the diagonal, and\n  * \\f$ V \\f$ is a matrix with the eigenvectors as its columns, then \\f$ A V =\n  * V D \\f$. The matrix \\f$ V \\f$ is almost always invertible, in which case we\n  * have \\f$ A = V D V^{-1} \\f$. This is called the eigendecomposition.\n  *\n  * The eigenvalues and eigenvectors of a matrix may be complex, even when the\n  * matrix is real. However, we can choose real matrices \\f$ V \\f$ and \\f$ D\n  * \\f$ satisfying \\f$ A V = V D \\f$, just like the eigendecomposition, if the\n  * matrix \\f$ D \\f$ is not required to be diagonal, but if it is allowed to\n  * have blocks of the form\n  * \\f[ \\begin{bmatrix} u & v \\\\ -v & u \\end{bmatrix} \\f]\n  * (where \\f$ u \\f$ and \\f$ v \\f$ are real numbers) on the diagonal.  These\n  * blocks correspond to complex eigenvalue pairs \\f$ u \\pm iv \\f$. We call\n  * this variant of the eigendecomposition the pseudo-eigendecomposition.\n  *\n  * Call the function compute() to compute the eigenvalues and eigenvectors of\n  * a given matrix. Alternatively, you can use the \n  * EigenSolver(const MatrixType&, bool) constructor which computes the\n  * eigenvalues and eigenvectors at construction time. Once the eigenvalue and\n  * eigenvectors are computed, they can be retrieved with the eigenvalues() and\n  * eigenvectors() functions. The pseudoEigenvalueMatrix() and\n  * pseudoEigenvectors() methods allow the construction of the\n  * pseudo-eigendecomposition.\n  *\n  * The documentation for EigenSolver(const MatrixType&, bool) contains an\n  * example of the typical use of this class.\n  *\n  * \\note The implementation is adapted from\n  * <a href=\"http://math.nist.gov/javanumerics/jama/\">JAMA</a> (public domain).\n  * Their code is based on EISPACK.\n  *\n  * \\sa MatrixBase::eigenvalues(), class ComplexEigenSolver, class SelfAdjointEigenSolver\n  */\ntemplate<typename _MatrixType> class EigenSolver\n{\n  public:\n\n    /** \\brief Synonym for the template parameter \\p _MatrixType. */\n    typedef _MatrixType MatrixType;\n\n    enum {\n      RowsAtCompileTime = MatrixType::RowsAtCompileTime,\n      ColsAtCompileTime = MatrixType::ColsAtCompileTime,\n      Options = MatrixType::Options,\n      MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,\n      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime\n    };\n\n    /** \\brief Scalar type for matrices of type #MatrixType. */\n    typedef typename MatrixType::Scalar Scalar;\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n    typedef Eigen::Index Index; ///< \\deprecated since Eigen 3.3\n\n    /** \\brief Complex scalar type for #MatrixType. \n      *\n      * This is \\c std::complex<Scalar> if #Scalar is real (e.g.,\n      * \\c float or \\c double) and just \\c Scalar if #Scalar is\n      * complex.\n      */\n    typedef std::complex<RealScalar> ComplexScalar;\n\n    /** \\brief Type for vector of eigenvalues as returned by eigenvalues(). \n      *\n      * This is a column vector with entries of type #ComplexScalar.\n      * The length of the vector is the size of #MatrixType.\n      */\n    typedef Matrix<ComplexScalar, ColsAtCompileTime, 1, Options & ~RowMajor, MaxColsAtCompileTime, 1> EigenvalueType;\n\n    /** \\brief Type for matrix of eigenvectors as returned by eigenvectors(). \n      *\n      * This is a square matrix with entries of type #ComplexScalar. \n      * The size is the same as the size of #MatrixType.\n      */\n    typedef Matrix<ComplexScalar, RowsAtCompileTime, ColsAtCompileTime, Options, MaxRowsAtCompileTime, MaxColsAtCompileTime> EigenvectorsType;\n\n    /** \\brief Default constructor.\n      *\n      * The default constructor is useful in cases in which the user intends to\n      * perform decompositions via EigenSolver::compute(const MatrixType&, bool).\n      *\n      * \\sa compute() for an example.\n      */\n    EigenSolver() : m_eivec(), m_eivalues(), m_isInitialized(false), m_realSchur(), m_matT(), m_tmp() {}\n\n    /** \\brief Default constructor with memory preallocation\n      *\n      * Like the default constructor but with preallocation of the internal data\n      * according to the specified problem \\a size.\n      * \\sa EigenSolver()\n      */\n    explicit EigenSolver(Index size)\n      : m_eivec(size, size),\n        m_eivalues(size),\n        m_isInitialized(false),\n        m_eigenvectorsOk(false),\n        m_realSchur(size),\n        m_matT(size, size), \n        m_tmp(size)\n    {}\n\n    /** \\brief Constructor; computes eigendecomposition of given matrix. \n      * \n      * \\param[in]  matrix  Square matrix whose eigendecomposition is to be computed.\n      * \\param[in]  computeEigenvectors  If true, both the eigenvectors and the\n      *    eigenvalues are computed; if false, only the eigenvalues are\n      *    computed. \n      *\n      * This constructor calls compute() to compute the eigenvalues\n      * and eigenvectors.\n      *\n      * Example: \\include EigenSolver_EigenSolver_MatrixType.cpp\n      * Output: \\verbinclude EigenSolver_EigenSolver_MatrixType.out\n      *\n      * \\sa compute()\n      */\n    template<typename InputType>\n    explicit EigenSolver(const EigenBase<InputType>& matrix, bool computeEigenvectors = true)\n      : m_eivec(matrix.rows(), matrix.cols()),\n        m_eivalues(matrix.cols()),\n        m_isInitialized(false),\n        m_eigenvectorsOk(false),\n        m_realSchur(matrix.cols()),\n        m_matT(matrix.rows(), matrix.cols()), \n        m_tmp(matrix.cols())\n    {\n      compute(matrix.derived(), computeEigenvectors);\n    }\n\n    /** \\brief Returns the eigenvectors of given matrix. \n      *\n      * \\returns  %Matrix whose columns are the (possibly complex) eigenvectors.\n      *\n      * \\pre Either the constructor \n      * EigenSolver(const MatrixType&,bool) or the member function\n      * compute(const MatrixType&, bool) has been called before, and\n      * \\p computeEigenvectors was set to true (the default).\n      *\n      * Column \\f$ k \\f$ of the returned matrix is an eigenvector corresponding\n      * to eigenvalue number \\f$ k \\f$ as returned by eigenvalues().  The\n      * eigenvectors are normalized to have (Euclidean) norm equal to one. The\n      * matrix returned by this function is the matrix \\f$ V \\f$ in the\n      * eigendecomposition \\f$ A = V D V^{-1} \\f$, if it exists.\n      *\n      * Example: \\include EigenSolver_eigenvectors.cpp\n      * Output: \\verbinclude EigenSolver_eigenvectors.out\n      *\n      * \\sa eigenvalues(), pseudoEigenvectors()\n      */\n    EigenvectorsType eigenvectors() const;\n\n    /** \\brief Returns the pseudo-eigenvectors of given matrix. \n      *\n      * \\returns  Const reference to matrix whose columns are the pseudo-eigenvectors.\n      *\n      * \\pre Either the constructor \n      * EigenSolver(const MatrixType&,bool) or the member function\n      * compute(const MatrixType&, bool) has been called before, and\n      * \\p computeEigenvectors was set to true (the default).\n      *\n      * The real matrix \\f$ V \\f$ returned by this function and the\n      * block-diagonal matrix \\f$ D \\f$ returned by pseudoEigenvalueMatrix()\n      * satisfy \\f$ AV = VD \\f$.\n      *\n      * Example: \\include EigenSolver_pseudoEigenvectors.cpp\n      * Output: \\verbinclude EigenSolver_pseudoEigenvectors.out\n      *\n      * \\sa pseudoEigenvalueMatrix(), eigenvectors()\n      */\n    const MatrixType& pseudoEigenvectors() const\n    {\n      eigen_assert(m_isInitialized && \"EigenSolver is not initialized.\");\n      eigen_assert(m_eigenvectorsOk && \"The eigenvectors have not been computed together with the eigenvalues.\");\n      return m_eivec;\n    }\n\n    /** \\brief Returns the block-diagonal matrix in the pseudo-eigendecomposition.\n      *\n      * \\returns  A block-diagonal matrix.\n      *\n      * \\pre Either the constructor \n      * EigenSolver(const MatrixType&,bool) or the member function\n      * compute(const MatrixType&, bool) has been called before.\n      *\n      * The matrix \\f$ D \\f$ returned by this function is real and\n      * block-diagonal. The blocks on the diagonal are either 1-by-1 or 2-by-2\n      * blocks of the form\n      * \\f$ \\begin{bmatrix} u & v \\\\ -v & u \\end{bmatrix} \\f$.\n      * These blocks are not sorted in any particular order.\n      * The matrix \\f$ D \\f$ and the matrix \\f$ V \\f$ returned by\n      * pseudoEigenvectors() satisfy \\f$ AV = VD \\f$.\n      *\n      * \\sa pseudoEigenvectors() for an example, eigenvalues()\n      */\n    MatrixType pseudoEigenvalueMatrix() const;\n\n    /** \\brief Returns the eigenvalues of given matrix. \n      *\n      * \\returns A const reference to the column vector containing the eigenvalues.\n      *\n      * \\pre Either the constructor \n      * EigenSolver(const MatrixType&,bool) or the member function\n      * compute(const MatrixType&, bool) has been called before.\n      *\n      * The eigenvalues are repeated according to their algebraic multiplicity,\n      * so there are as many eigenvalues as rows in the matrix. The eigenvalues \n      * are not sorted in any particular order.\n      *\n      * Example: \\include EigenSolver_eigenvalues.cpp\n      * Output: \\verbinclude EigenSolver_eigenvalues.out\n      *\n      * \\sa eigenvectors(), pseudoEigenvalueMatrix(),\n      *     MatrixBase::eigenvalues()\n      */\n    const EigenvalueType& eigenvalues() const\n    {\n      eigen_assert(m_isInitialized && \"EigenSolver is not initialized.\");\n      return m_eivalues;\n    }\n\n    /** \\brief Computes eigendecomposition of given matrix. \n      * \n      * \\param[in]  matrix  Square matrix whose eigendecomposition is to be computed.\n      * \\param[in]  computeEigenvectors  If true, both the eigenvectors and the\n      *    eigenvalues are computed; if false, only the eigenvalues are\n      *    computed. \n      * \\returns    Reference to \\c *this\n      *\n      * This function computes the eigenvalues of the real matrix \\p matrix.\n      * The eigenvalues() function can be used to retrieve them.  If \n      * \\p computeEigenvectors is true, then the eigenvectors are also computed\n      * and can be retrieved by calling eigenvectors().\n      *\n      * The matrix is first reduced to real Schur form using the RealSchur\n      * class. The Schur decomposition is then used to compute the eigenvalues\n      * and eigenvectors.\n      *\n      * The cost of the computation is dominated by the cost of the\n      * Schur decomposition, which is very approximately \\f$ 25n^3 \\f$\n      * (where \\f$ n \\f$ is the size of the matrix) if \\p computeEigenvectors \n      * is true, and \\f$ 10n^3 \\f$ if \\p computeEigenvectors is false.\n      *\n      * This method reuses of the allocated data in the EigenSolver object.\n      *\n      * Example: \\include EigenSolver_compute.cpp\n      * Output: \\verbinclude EigenSolver_compute.out\n      */\n    template<typename InputType>\n    EigenSolver& compute(const EigenBase<InputType>& matrix, bool computeEigenvectors = true);\n\n    /** \\returns NumericalIssue if the input contains INF or NaN values or overflow occured. Returns Success otherwise. */\n    ComputationInfo info() const\n    {\n      eigen_assert(m_isInitialized && \"EigenSolver is not initialized.\");\n      return m_info;\n    }\n\n    /** \\brief Sets the maximum number of iterations allowed. */\n    EigenSolver& setMaxIterations(Index maxIters)\n    {\n      m_realSchur.setMaxIterations(maxIters);\n      return *this;\n    }\n\n    /** \\brief Returns the maximum number of iterations. */\n    Index getMaxIterations()\n    {\n      return m_realSchur.getMaxIterations();\n    }\n\n  private:\n    void doComputeEigenvectors();\n\n  protected:\n    \n    static void check_template_parameters()\n    {\n      EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);\n      EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsComplex, NUMERIC_TYPE_MUST_BE_REAL);\n    }\n    \n    MatrixType m_eivec;\n    EigenvalueType m_eivalues;\n    bool m_isInitialized;\n    bool m_eigenvectorsOk;\n    ComputationInfo m_info;\n    RealSchur<MatrixType> m_realSchur;\n    MatrixType m_matT;\n\n    typedef Matrix<Scalar, ColsAtCompileTime, 1, Options & ~RowMajor, MaxColsAtCompileTime, 1> ColumnVectorType;\n    ColumnVectorType m_tmp;\n};\n\ntemplate<typename MatrixType>\nMatrixType EigenSolver<MatrixType>::pseudoEigenvalueMatrix() const\n{\n  eigen_assert(m_isInitialized && \"EigenSolver is not initialized.\");\n  const RealScalar precision = RealScalar(2)*NumTraits<RealScalar>::epsilon();\n  Index n = m_eivalues.rows();\n  MatrixType matD = MatrixType::Zero(n,n);\n  for (Index i=0; i<n; ++i)\n  {\n    if (internal::isMuchSmallerThan(numext::imag(m_eivalues.coeff(i)), numext::real(m_eivalues.coeff(i)), precision))\n      matD.coeffRef(i,i) = numext::real(m_eivalues.coeff(i));\n    else\n    {\n      matD.template block<2,2>(i,i) <<  numext::real(m_eivalues.coeff(i)), numext::imag(m_eivalues.coeff(i)),\n                                       -numext::imag(m_eivalues.coeff(i)), numext::real(m_eivalues.coeff(i));\n      ++i;\n    }\n  }\n  return matD;\n}\n\ntemplate<typename MatrixType>\ntypename EigenSolver<MatrixType>::EigenvectorsType EigenSolver<MatrixType>::eigenvectors() const\n{\n  eigen_assert(m_isInitialized && \"EigenSolver is not initialized.\");\n  eigen_assert(m_eigenvectorsOk && \"The eigenvectors have not been computed together with the eigenvalues.\");\n  const RealScalar precision = RealScalar(2)*NumTraits<RealScalar>::epsilon();\n  Index n = m_eivec.cols();\n  EigenvectorsType matV(n,n);\n  for (Index j=0; j<n; ++j)\n  {\n    if (internal::isMuchSmallerThan(numext::imag(m_eivalues.coeff(j)), numext::real(m_eivalues.coeff(j)), precision) || j+1==n)\n    {\n      // we have a real eigen value\n      matV.col(j) = m_eivec.col(j).template cast<ComplexScalar>();\n      matV.col(j).normalize();\n    }\n    else\n    {\n      // we have a pair of complex eigen values\n      for (Index i=0; i<n; ++i)\n      {\n        matV.coeffRef(i,j)   = ComplexScalar(m_eivec.coeff(i,j),  m_eivec.coeff(i,j+1));\n        matV.coeffRef(i,j+1) = ComplexScalar(m_eivec.coeff(i,j), -m_eivec.coeff(i,j+1));\n      }\n      matV.col(j).normalize();\n      matV.col(j+1).normalize();\n      ++j;\n    }\n  }\n  return matV;\n}\n\ntemplate<typename MatrixType>\ntemplate<typename InputType>\nEigenSolver<MatrixType>& \nEigenSolver<MatrixType>::compute(const EigenBase<InputType>& matrix, bool computeEigenvectors)\n{\n  check_template_parameters();\n  \n  using std::sqrt;\n  using std::abs;\n  using numext::isfinite;\n  eigen_assert(matrix.cols() == matrix.rows());\n\n  // Reduce to real Schur form.\n  m_realSchur.compute(matrix.derived(), computeEigenvectors);\n  \n  m_info = m_realSchur.info();\n\n  if (m_info == Success)\n  {\n    m_matT = m_realSchur.matrixT();\n    if (computeEigenvectors)\n      m_eivec = m_realSchur.matrixU();\n  \n    // Compute eigenvalues from matT\n    m_eivalues.resize(matrix.cols());\n    Index i = 0;\n    while (i < matrix.cols()) \n    {\n      if (i == matrix.cols() - 1 || m_matT.coeff(i+1, i) == Scalar(0)) \n      {\n        m_eivalues.coeffRef(i) = m_matT.coeff(i, i);\n        if(!(isfinite)(m_eivalues.coeffRef(i)))\n        {\n          m_isInitialized = true;\n          m_eigenvectorsOk = false;\n          m_info = NumericalIssue;\n          return *this;\n        }\n        ++i;\n      }\n      else\n      {\n        Scalar p = Scalar(0.5) * (m_matT.coeff(i, i) - m_matT.coeff(i+1, i+1));\n        Scalar z;\n        // Compute z = sqrt(abs(p * p + m_matT.coeff(i+1, i) * m_matT.coeff(i, i+1)));\n        // without overflow\n        {\n          Scalar t0 = m_matT.coeff(i+1, i);\n          Scalar t1 = m_matT.coeff(i, i+1);\n          Scalar maxval = numext::maxi<Scalar>(abs(p),numext::maxi<Scalar>(abs(t0),abs(t1)));\n          t0 /= maxval;\n          t1 /= maxval;\n          Scalar p0 = p/maxval;\n          z = maxval * sqrt(abs(p0 * p0 + t0 * t1));\n        }\n        \n        m_eivalues.coeffRef(i)   = ComplexScalar(m_matT.coeff(i+1, i+1) + p, z);\n        m_eivalues.coeffRef(i+1) = ComplexScalar(m_matT.coeff(i+1, i+1) + p, -z);\n        if(!((isfinite)(m_eivalues.coeffRef(i)) && (isfinite)(m_eivalues.coeffRef(i+1))))\n        {\n          m_isInitialized = true;\n          m_eigenvectorsOk = false;\n          m_info = NumericalIssue;\n          return *this;\n        }\n        i += 2;\n      }\n    }\n    \n    // Compute eigenvectors.\n    if (computeEigenvectors)\n      doComputeEigenvectors();\n  }\n\n  m_isInitialized = true;\n  m_eigenvectorsOk = computeEigenvectors;\n\n  return *this;\n}\n\n\ntemplate<typename MatrixType>\nvoid EigenSolver<MatrixType>::doComputeEigenvectors()\n{\n  using std::abs;\n  const Index size = m_eivec.cols();\n  const Scalar eps = NumTraits<Scalar>::epsilon();\n\n  // inefficient! this is already computed in RealSchur\n  Scalar norm(0);\n  for (Index j = 0; j < size; ++j)\n  {\n    norm += m_matT.row(j).segment((std::max)(j-1,Index(0)), size-(std::max)(j-1,Index(0))).cwiseAbs().sum();\n  }\n  \n  // Backsubstitute to find vectors of upper triangular form\n  if (norm == Scalar(0))\n  {\n    return;\n  }\n\n  for (Index n = size-1; n >= 0; n--)\n  {\n    Scalar p = m_eivalues.coeff(n).real();\n    Scalar q = m_eivalues.coeff(n).imag();\n\n    // Scalar vector\n    if (q == Scalar(0))\n    {\n      Scalar lastr(0), lastw(0);\n      Index l = n;\n\n      m_matT.coeffRef(n,n) = Scalar(1);\n      for (Index i = n-1; i >= 0; i--)\n      {\n        Scalar w = m_matT.coeff(i,i) - p;\n        Scalar r = m_matT.row(i).segment(l,n-l+1).dot(m_matT.col(n).segment(l, n-l+1));\n\n        if (m_eivalues.coeff(i).imag() < Scalar(0))\n        {\n          lastw = w;\n          lastr = r;\n        }\n        else\n        {\n          l = i;\n          if (m_eivalues.coeff(i).imag() == Scalar(0))\n          {\n            if (w != Scalar(0))\n              m_matT.coeffRef(i,n) = -r / w;\n            else\n              m_matT.coeffRef(i,n) = -r / (eps * norm);\n          }\n          else // Solve real equations\n          {\n            Scalar x = m_matT.coeff(i,i+1);\n            Scalar y = m_matT.coeff(i+1,i);\n            Scalar denom = (m_eivalues.coeff(i).real() - p) * (m_eivalues.coeff(i).real() - p) + m_eivalues.coeff(i).imag() * m_eivalues.coeff(i).imag();\n            Scalar t = (x * lastr - lastw * r) / denom;\n            m_matT.coeffRef(i,n) = t;\n            if (abs(x) > abs(lastw))\n              m_matT.coeffRef(i+1,n) = (-r - w * t) / x;\n            else\n              m_matT.coeffRef(i+1,n) = (-lastr - y * t) / lastw;\n          }\n\n          // Overflow control\n          Scalar t = abs(m_matT.coeff(i,n));\n          if ((eps * t) * t > Scalar(1))\n            m_matT.col(n).tail(size-i) /= t;\n        }\n      }\n    }\n    else if (q < Scalar(0) && n > 0) // Complex vector\n    {\n      Scalar lastra(0), lastsa(0), lastw(0);\n      Index l = n-1;\n\n      // Last vector component imaginary so matrix is triangular\n      if (abs(m_matT.coeff(n,n-1)) > abs(m_matT.coeff(n-1,n)))\n      {\n        m_matT.coeffRef(n-1,n-1) = q / m_matT.coeff(n,n-1);\n        m_matT.coeffRef(n-1,n) = -(m_matT.coeff(n,n) - p) / m_matT.coeff(n,n-1);\n      }\n      else\n      {\n        ComplexScalar cc = ComplexScalar(Scalar(0),-m_matT.coeff(n-1,n)) / ComplexScalar(m_matT.coeff(n-1,n-1)-p,q);\n        m_matT.coeffRef(n-1,n-1) = numext::real(cc);\n        m_matT.coeffRef(n-1,n) = numext::imag(cc);\n      }\n      m_matT.coeffRef(n,n-1) = Scalar(0);\n      m_matT.coeffRef(n,n) = Scalar(1);\n      for (Index i = n-2; i >= 0; i--)\n      {\n        Scalar ra = m_matT.row(i).segment(l, n-l+1).dot(m_matT.col(n-1).segment(l, n-l+1));\n        Scalar sa = m_matT.row(i).segment(l, n-l+1).dot(m_matT.col(n).segment(l, n-l+1));\n        Scalar w = m_matT.coeff(i,i) - p;\n\n        if (m_eivalues.coeff(i).imag() < Scalar(0))\n        {\n          lastw = w;\n          lastra = ra;\n          lastsa = sa;\n        }\n        else\n        {\n          l = i;\n          if (m_eivalues.coeff(i).imag() == RealScalar(0))\n          {\n            ComplexScalar cc = ComplexScalar(-ra,-sa) / ComplexScalar(w,q);\n            m_matT.coeffRef(i,n-1) = numext::real(cc);\n            m_matT.coeffRef(i,n) = numext::imag(cc);\n          }\n          else\n          {\n            // Solve complex equations\n            Scalar x = m_matT.coeff(i,i+1);\n            Scalar y = m_matT.coeff(i+1,i);\n            Scalar vr = (m_eivalues.coeff(i).real() - p) * (m_eivalues.coeff(i).real() - p) + m_eivalues.coeff(i).imag() * m_eivalues.coeff(i).imag() - q * q;\n            Scalar vi = (m_eivalues.coeff(i).real() - p) * Scalar(2) * q;\n            if ((vr == Scalar(0)) && (vi == Scalar(0)))\n              vr = eps * norm * (abs(w) + abs(q) + abs(x) + abs(y) + abs(lastw));\n\n            ComplexScalar cc = ComplexScalar(x*lastra-lastw*ra+q*sa,x*lastsa-lastw*sa-q*ra) / ComplexScalar(vr,vi);\n            m_matT.coeffRef(i,n-1) = numext::real(cc);\n            m_matT.coeffRef(i,n) = numext::imag(cc);\n            if (abs(x) > (abs(lastw) + abs(q)))\n            {\n              m_matT.coeffRef(i+1,n-1) = (-ra - w * m_matT.coeff(i,n-1) + q * m_matT.coeff(i,n)) / x;\n              m_matT.coeffRef(i+1,n) = (-sa - w * m_matT.coeff(i,n) - q * m_matT.coeff(i,n-1)) / x;\n            }\n            else\n            {\n              cc = ComplexScalar(-lastra-y*m_matT.coeff(i,n-1),-lastsa-y*m_matT.coeff(i,n)) / ComplexScalar(lastw,q);\n              m_matT.coeffRef(i+1,n-1) = numext::real(cc);\n              m_matT.coeffRef(i+1,n) = numext::imag(cc);\n            }\n          }\n\n          // Overflow control\n          Scalar t = numext::maxi<Scalar>(abs(m_matT.coeff(i,n-1)),abs(m_matT.coeff(i,n)));\n          if ((eps * t) * t > Scalar(1))\n            m_matT.block(i, n-1, size-i, 2) /= t;\n\n        }\n      }\n      \n      // We handled a pair of complex conjugate eigenvalues, so need to skip them both\n      n--;\n    }\n    else\n    {\n      eigen_assert(0 && \"Internal bug in EigenSolver (INF or NaN has not been detected)\"); // this should not happen\n    }\n  }\n\n  // Back transformation to get eigenvectors of original matrix\n  for (Index j = size-1; j >= 0; j--)\n  {\n    m_tmp.noalias() = m_eivec.leftCols(j+1) * m_matT.col(j).segment(0, j+1);\n    m_eivec.col(j) = m_tmp;\n  }\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_EIGENSOLVER_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Eigenvalues/GeneralizedEigenSolver.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012-2016 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>\n// Copyright (C) 2016 Tobias Wood <tobias@spinicist.org.uk>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_GENERALIZEDEIGENSOLVER_H\n#define EIGEN_GENERALIZEDEIGENSOLVER_H\n\n#include \"./RealQZ.h\"\n\nnamespace Eigen { \n\n/** \\eigenvalues_module \\ingroup Eigenvalues_Module\n  *\n  *\n  * \\class GeneralizedEigenSolver\n  *\n  * \\brief Computes the generalized eigenvalues and eigenvectors of a pair of general matrices\n  *\n  * \\tparam _MatrixType the type of the matrices of which we are computing the\n  * eigen-decomposition; this is expected to be an instantiation of the Matrix\n  * class template. Currently, only real matrices are supported.\n  *\n  * The generalized eigenvalues and eigenvectors of a matrix pair \\f$ A \\f$ and \\f$ B \\f$ are scalars\n  * \\f$ \\lambda \\f$ and vectors \\f$ v \\f$ such that \\f$ Av = \\lambda Bv \\f$.  If\n  * \\f$ D \\f$ is a diagonal matrix with the eigenvalues on the diagonal, and\n  * \\f$ V \\f$ is a matrix with the eigenvectors as its columns, then \\f$ A V =\n  * B V D \\f$. The matrix \\f$ V \\f$ is almost always invertible, in which case we\n  * have \\f$ A = B V D V^{-1} \\f$. This is called the generalized eigen-decomposition.\n  *\n  * The generalized eigenvalues and eigenvectors of a matrix pair may be complex, even when the\n  * matrices are real. Moreover, the generalized eigenvalue might be infinite if the matrix B is\n  * singular. To workaround this difficulty, the eigenvalues are provided as a pair of complex \\f$ \\alpha \\f$\n  * and real \\f$ \\beta \\f$ such that: \\f$ \\lambda_i = \\alpha_i / \\beta_i \\f$. If \\f$ \\beta_i \\f$ is (nearly) zero,\n  * then one can consider the well defined left eigenvalue \\f$ \\mu = \\beta_i / \\alpha_i\\f$ such that:\n  * \\f$ \\mu_i A v_i = B v_i \\f$, or even \\f$ \\mu_i u_i^T A  = u_i^T B \\f$ where \\f$ u_i \\f$ is\n  * called the left eigenvector.\n  *\n  * Call the function compute() to compute the generalized eigenvalues and eigenvectors of\n  * a given matrix pair. Alternatively, you can use the\n  * GeneralizedEigenSolver(const MatrixType&, const MatrixType&, bool) constructor which computes the\n  * eigenvalues and eigenvectors at construction time. Once the eigenvalue and\n  * eigenvectors are computed, they can be retrieved with the eigenvalues() and\n  * eigenvectors() functions.\n  *\n  * Here is an usage example of this class:\n  * Example: \\include GeneralizedEigenSolver.cpp\n  * Output: \\verbinclude GeneralizedEigenSolver.out\n  *\n  * \\sa MatrixBase::eigenvalues(), class ComplexEigenSolver, class SelfAdjointEigenSolver\n  */\ntemplate<typename _MatrixType> class GeneralizedEigenSolver\n{\n  public:\n\n    /** \\brief Synonym for the template parameter \\p _MatrixType. */\n    typedef _MatrixType MatrixType;\n\n    enum {\n      RowsAtCompileTime = MatrixType::RowsAtCompileTime,\n      ColsAtCompileTime = MatrixType::ColsAtCompileTime,\n      Options = MatrixType::Options,\n      MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,\n      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime\n    };\n\n    /** \\brief Scalar type for matrices of type #MatrixType. */\n    typedef typename MatrixType::Scalar Scalar;\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n    typedef Eigen::Index Index; ///< \\deprecated since Eigen 3.3\n\n    /** \\brief Complex scalar type for #MatrixType. \n      *\n      * This is \\c std::complex<Scalar> if #Scalar is real (e.g.,\n      * \\c float or \\c double) and just \\c Scalar if #Scalar is\n      * complex.\n      */\n    typedef std::complex<RealScalar> ComplexScalar;\n\n    /** \\brief Type for vector of real scalar values eigenvalues as returned by betas().\n      *\n      * This is a column vector with entries of type #Scalar.\n      * The length of the vector is the size of #MatrixType.\n      */\n    typedef Matrix<Scalar, ColsAtCompileTime, 1, Options & ~RowMajor, MaxColsAtCompileTime, 1> VectorType;\n\n    /** \\brief Type for vector of complex scalar values eigenvalues as returned by alphas().\n      *\n      * This is a column vector with entries of type #ComplexScalar.\n      * The length of the vector is the size of #MatrixType.\n      */\n    typedef Matrix<ComplexScalar, ColsAtCompileTime, 1, Options & ~RowMajor, MaxColsAtCompileTime, 1> ComplexVectorType;\n\n    /** \\brief Expression type for the eigenvalues as returned by eigenvalues().\n      */\n    typedef CwiseBinaryOp<internal::scalar_quotient_op<ComplexScalar,Scalar>,ComplexVectorType,VectorType> EigenvalueType;\n\n    /** \\brief Type for matrix of eigenvectors as returned by eigenvectors(). \n      *\n      * This is a square matrix with entries of type #ComplexScalar. \n      * The size is the same as the size of #MatrixType.\n      */\n    typedef Matrix<ComplexScalar, RowsAtCompileTime, ColsAtCompileTime, Options, MaxRowsAtCompileTime, MaxColsAtCompileTime> EigenvectorsType;\n\n    /** \\brief Default constructor.\n      *\n      * The default constructor is useful in cases in which the user intends to\n      * perform decompositions via EigenSolver::compute(const MatrixType&, bool).\n      *\n      * \\sa compute() for an example.\n      */\n    GeneralizedEigenSolver()\n      : m_eivec(),\n        m_alphas(),\n        m_betas(),\n        m_valuesOkay(false),\n        m_vectorsOkay(false),\n        m_realQZ()\n    {}\n\n    /** \\brief Default constructor with memory preallocation\n      *\n      * Like the default constructor but with preallocation of the internal data\n      * according to the specified problem \\a size.\n      * \\sa GeneralizedEigenSolver()\n      */\n    explicit GeneralizedEigenSolver(Index size)\n      : m_eivec(size, size),\n        m_alphas(size),\n        m_betas(size),\n        m_valuesOkay(false),\n        m_vectorsOkay(false),\n        m_realQZ(size),\n        m_tmp(size)\n    {}\n\n    /** \\brief Constructor; computes the generalized eigendecomposition of given matrix pair.\n      * \n      * \\param[in]  A  Square matrix whose eigendecomposition is to be computed.\n      * \\param[in]  B  Square matrix whose eigendecomposition is to be computed.\n      * \\param[in]  computeEigenvectors  If true, both the eigenvectors and the\n      *    eigenvalues are computed; if false, only the eigenvalues are computed.\n      *\n      * This constructor calls compute() to compute the generalized eigenvalues\n      * and eigenvectors.\n      *\n      * \\sa compute()\n      */\n    GeneralizedEigenSolver(const MatrixType& A, const MatrixType& B, bool computeEigenvectors = true)\n      : m_eivec(A.rows(), A.cols()),\n        m_alphas(A.cols()),\n        m_betas(A.cols()),\n        m_valuesOkay(false),\n        m_vectorsOkay(false),\n        m_realQZ(A.cols()),\n        m_tmp(A.cols())\n    {\n      compute(A, B, computeEigenvectors);\n    }\n\n    /* \\brief Returns the computed generalized eigenvectors.\n      *\n      * \\returns  %Matrix whose columns are the (possibly complex) right eigenvectors.\n      * i.e. the eigenvectors that solve (A - l*B)x = 0. The ordering matches the eigenvalues.\n      *\n      * \\pre Either the constructor \n      * GeneralizedEigenSolver(const MatrixType&,const MatrixType&, bool) or the member function\n      * compute(const MatrixType&, const MatrixType& bool) has been called before, and\n      * \\p computeEigenvectors was set to true (the default).\n      *\n      * \\sa eigenvalues()\n      */\n    EigenvectorsType eigenvectors() const {\n      eigen_assert(m_vectorsOkay && \"Eigenvectors for GeneralizedEigenSolver were not calculated.\");\n      return m_eivec;\n    }\n\n    /** \\brief Returns an expression of the computed generalized eigenvalues.\n      *\n      * \\returns An expression of the column vector containing the eigenvalues.\n      *\n      * It is a shortcut for \\code this->alphas().cwiseQuotient(this->betas()); \\endcode\n      * Not that betas might contain zeros. It is therefore not recommended to use this function,\n      * but rather directly deal with the alphas and betas vectors.\n      *\n      * \\pre Either the constructor \n      * GeneralizedEigenSolver(const MatrixType&,const MatrixType&,bool) or the member function\n      * compute(const MatrixType&,const MatrixType&,bool) has been called before.\n      *\n      * The eigenvalues are repeated according to their algebraic multiplicity,\n      * so there are as many eigenvalues as rows in the matrix. The eigenvalues \n      * are not sorted in any particular order.\n      *\n      * \\sa alphas(), betas(), eigenvectors()\n      */\n    EigenvalueType eigenvalues() const\n    {\n      eigen_assert(m_valuesOkay && \"GeneralizedEigenSolver is not initialized.\");\n      return EigenvalueType(m_alphas,m_betas);\n    }\n\n    /** \\returns A const reference to the vectors containing the alpha values\n      *\n      * This vector permits to reconstruct the j-th eigenvalues as alphas(i)/betas(j).\n      *\n      * \\sa betas(), eigenvalues() */\n    ComplexVectorType alphas() const\n    {\n      eigen_assert(m_valuesOkay && \"GeneralizedEigenSolver is not initialized.\");\n      return m_alphas;\n    }\n\n    /** \\returns A const reference to the vectors containing the beta values\n      *\n      * This vector permits to reconstruct the j-th eigenvalues as alphas(i)/betas(j).\n      *\n      * \\sa alphas(), eigenvalues() */\n    VectorType betas() const\n    {\n      eigen_assert(m_valuesOkay && \"GeneralizedEigenSolver is not initialized.\");\n      return m_betas;\n    }\n\n    /** \\brief Computes generalized eigendecomposition of given matrix.\n      * \n      * \\param[in]  A  Square matrix whose eigendecomposition is to be computed.\n      * \\param[in]  B  Square matrix whose eigendecomposition is to be computed.\n      * \\param[in]  computeEigenvectors  If true, both the eigenvectors and the\n      *    eigenvalues are computed; if false, only the eigenvalues are\n      *    computed. \n      * \\returns    Reference to \\c *this\n      *\n      * This function computes the eigenvalues of the real matrix \\p matrix.\n      * The eigenvalues() function can be used to retrieve them.  If \n      * \\p computeEigenvectors is true, then the eigenvectors are also computed\n      * and can be retrieved by calling eigenvectors().\n      *\n      * The matrix is first reduced to real generalized Schur form using the RealQZ\n      * class. The generalized Schur decomposition is then used to compute the eigenvalues\n      * and eigenvectors.\n      *\n      * The cost of the computation is dominated by the cost of the\n      * generalized Schur decomposition.\n      *\n      * This method reuses of the allocated data in the GeneralizedEigenSolver object.\n      */\n    GeneralizedEigenSolver& compute(const MatrixType& A, const MatrixType& B, bool computeEigenvectors = true);\n\n    ComputationInfo info() const\n    {\n      eigen_assert(m_valuesOkay && \"EigenSolver is not initialized.\");\n      return m_realQZ.info();\n    }\n\n    /** Sets the maximal number of iterations allowed.\n    */\n    GeneralizedEigenSolver& setMaxIterations(Index maxIters)\n    {\n      m_realQZ.setMaxIterations(maxIters);\n      return *this;\n    }\n\n  protected:\n    \n    static void check_template_parameters()\n    {\n      EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);\n      EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsComplex, NUMERIC_TYPE_MUST_BE_REAL);\n    }\n    \n    EigenvectorsType m_eivec;\n    ComplexVectorType m_alphas;\n    VectorType m_betas;\n    bool m_valuesOkay, m_vectorsOkay;\n    RealQZ<MatrixType> m_realQZ;\n    ComplexVectorType m_tmp;\n};\n\ntemplate<typename MatrixType>\nGeneralizedEigenSolver<MatrixType>&\nGeneralizedEigenSolver<MatrixType>::compute(const MatrixType& A, const MatrixType& B, bool computeEigenvectors)\n{\n  check_template_parameters();\n  \n  using std::sqrt;\n  using std::abs;\n  eigen_assert(A.cols() == A.rows() && B.cols() == A.rows() && B.cols() == B.rows());\n  Index size = A.cols();\n  m_valuesOkay = false;\n  m_vectorsOkay = false;\n  // Reduce to generalized real Schur form:\n  // A = Q S Z and B = Q T Z\n  m_realQZ.compute(A, B, computeEigenvectors);\n  if (m_realQZ.info() == Success)\n  {\n    // Resize storage\n    m_alphas.resize(size);\n    m_betas.resize(size);\n    if (computeEigenvectors)\n    {\n      m_eivec.resize(size,size);\n      m_tmp.resize(size);\n    }\n\n    // Aliases:\n    Map<VectorType> v(reinterpret_cast<Scalar*>(m_tmp.data()), size);\n    ComplexVectorType &cv = m_tmp;\n    const MatrixType &mS = m_realQZ.matrixS();\n    const MatrixType &mT = m_realQZ.matrixT();\n\n    Index i = 0;\n    while (i < size)\n    {\n      if (i == size - 1 || mS.coeff(i+1, i) == Scalar(0))\n      {\n        // Real eigenvalue\n        m_alphas.coeffRef(i) = mS.diagonal().coeff(i);\n        m_betas.coeffRef(i)  = mT.diagonal().coeff(i);\n        if (computeEigenvectors)\n        {\n          v.setConstant(Scalar(0.0));\n          v.coeffRef(i) = Scalar(1.0);\n          // For singular eigenvalues do nothing more\n          if(abs(m_betas.coeffRef(i)) >= (std::numeric_limits<RealScalar>::min)())\n          {\n            // Non-singular eigenvalue\n            const Scalar alpha = real(m_alphas.coeffRef(i));\n            const Scalar beta = m_betas.coeffRef(i);\n            for (Index j = i-1; j >= 0; j--)\n            {\n              const Index st = j+1;\n              const Index sz = i-j;\n              if (j > 0 && mS.coeff(j, j-1) != Scalar(0))\n              {\n                // 2x2 block\n                Matrix<Scalar, 2, 1> rhs = (alpha*mT.template block<2,Dynamic>(j-1,st,2,sz) - beta*mS.template block<2,Dynamic>(j-1,st,2,sz)) .lazyProduct( v.segment(st,sz) );\n                Matrix<Scalar, 2, 2> lhs = beta * mS.template block<2,2>(j-1,j-1) - alpha * mT.template block<2,2>(j-1,j-1);\n                v.template segment<2>(j-1) = lhs.partialPivLu().solve(rhs);\n                j--;\n              }\n              else\n              {\n                v.coeffRef(j) = -v.segment(st,sz).transpose().cwiseProduct(beta*mS.block(j,st,1,sz) - alpha*mT.block(j,st,1,sz)).sum() / (beta*mS.coeffRef(j,j) - alpha*mT.coeffRef(j,j));\n              }\n            }\n          }\n          m_eivec.col(i).real().noalias() = m_realQZ.matrixZ().transpose() * v;\n          m_eivec.col(i).real().normalize();\n          m_eivec.col(i).imag().setConstant(0);\n        }\n        ++i;\n      }\n      else\n      {\n        // We need to extract the generalized eigenvalues of the pair of a general 2x2 block S and a positive diagonal 2x2 block T\n        // Then taking beta=T_00*T_11, we can avoid any division, and alpha is the eigenvalues of A = (U^-1 * S * U) * diag(T_11,T_00):\n\n        // T =  [a 0]\n        //      [0 b]\n        RealScalar a = mT.diagonal().coeff(i),\n                   b = mT.diagonal().coeff(i+1);\n        const RealScalar beta = m_betas.coeffRef(i) = m_betas.coeffRef(i+1) = a*b;\n\n        // ^^ NOTE: using diagonal()(i) instead of coeff(i,i) workarounds a MSVC bug.\n        Matrix<RealScalar,2,2> S2 = mS.template block<2,2>(i,i) * Matrix<Scalar,2,1>(b,a).asDiagonal();\n\n        Scalar p = Scalar(0.5) * (S2.coeff(0,0) - S2.coeff(1,1));\n        Scalar z = sqrt(abs(p * p + S2.coeff(1,0) * S2.coeff(0,1)));\n        const ComplexScalar alpha = ComplexScalar(S2.coeff(1,1) + p, (beta > 0) ? z : -z);\n        m_alphas.coeffRef(i)   = conj(alpha);\n        m_alphas.coeffRef(i+1) = alpha;\n\n        if (computeEigenvectors) {\n          // Compute eigenvector in position (i+1) and then position (i) is just the conjugate\n          cv.setZero();\n          cv.coeffRef(i+1) = Scalar(1.0);\n          // here, the \"static_cast\" workaound expression template issues.\n          cv.coeffRef(i) = -(static_cast<Scalar>(beta*mS.coeffRef(i,i+1)) - alpha*mT.coeffRef(i,i+1))\n                          / (static_cast<Scalar>(beta*mS.coeffRef(i,i))   - alpha*mT.coeffRef(i,i));\n          for (Index j = i-1; j >= 0; j--)\n          {\n            const Index st = j+1;\n            const Index sz = i+1-j;\n            if (j > 0 && mS.coeff(j, j-1) != Scalar(0))\n            {\n              // 2x2 block\n              Matrix<ComplexScalar, 2, 1> rhs = (alpha*mT.template block<2,Dynamic>(j-1,st,2,sz) - beta*mS.template block<2,Dynamic>(j-1,st,2,sz)) .lazyProduct( cv.segment(st,sz) );\n              Matrix<ComplexScalar, 2, 2> lhs = beta * mS.template block<2,2>(j-1,j-1) - alpha * mT.template block<2,2>(j-1,j-1);\n              cv.template segment<2>(j-1) = lhs.partialPivLu().solve(rhs);\n              j--;\n            } else {\n              cv.coeffRef(j) =  cv.segment(st,sz).transpose().cwiseProduct(beta*mS.block(j,st,1,sz) - alpha*mT.block(j,st,1,sz)).sum()\n                              / (alpha*mT.coeffRef(j,j) - static_cast<Scalar>(beta*mS.coeffRef(j,j)));\n            }\n          }\n          m_eivec.col(i+1).noalias() = (m_realQZ.matrixZ().transpose() * cv);\n          m_eivec.col(i+1).normalize();\n          m_eivec.col(i) = m_eivec.col(i+1).conjugate();\n        }\n        i += 2;\n      }\n    }\n\n    m_valuesOkay = true;\n    m_vectorsOkay = computeEigenvectors;\n  }\n  return *this;\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_GENERALIZEDEIGENSOLVER_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Eigenvalues/GeneralizedSelfAdjointEigenSolver.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_GENERALIZEDSELFADJOINTEIGENSOLVER_H\n#define EIGEN_GENERALIZEDSELFADJOINTEIGENSOLVER_H\n\n#include \"./Tridiagonalization.h\"\n\nnamespace Eigen { \n\n/** \\eigenvalues_module \\ingroup Eigenvalues_Module\n  *\n  *\n  * \\class GeneralizedSelfAdjointEigenSolver\n  *\n  * \\brief Computes eigenvalues and eigenvectors of the generalized selfadjoint eigen problem\n  *\n  * \\tparam _MatrixType the type of the matrix of which we are computing the\n  * eigendecomposition; this is expected to be an instantiation of the Matrix\n  * class template.\n  *\n  * This class solves the generalized eigenvalue problem\n  * \\f$ Av = \\lambda Bv \\f$. In this case, the matrix \\f$ A \\f$ should be\n  * selfadjoint and the matrix \\f$ B \\f$ should be positive definite.\n  *\n  * Only the \\b lower \\b triangular \\b part of the input matrix is referenced.\n  *\n  * Call the function compute() to compute the eigenvalues and eigenvectors of\n  * a given matrix. Alternatively, you can use the\n  * GeneralizedSelfAdjointEigenSolver(const MatrixType&, const MatrixType&, int)\n  * constructor which computes the eigenvalues and eigenvectors at construction time.\n  * Once the eigenvalue and eigenvectors are computed, they can be retrieved with the eigenvalues()\n  * and eigenvectors() functions.\n  *\n  * The documentation for GeneralizedSelfAdjointEigenSolver(const MatrixType&, const MatrixType&, int)\n  * contains an example of the typical use of this class.\n  *\n  * \\sa class SelfAdjointEigenSolver, class EigenSolver, class ComplexEigenSolver\n  */\ntemplate<typename _MatrixType>\nclass GeneralizedSelfAdjointEigenSolver : public SelfAdjointEigenSolver<_MatrixType>\n{\n    typedef SelfAdjointEigenSolver<_MatrixType> Base;\n  public:\n\n    typedef _MatrixType MatrixType;\n\n    /** \\brief Default constructor for fixed-size matrices.\n      *\n      * The default constructor is useful in cases in which the user intends to\n      * perform decompositions via compute(). This constructor\n      * can only be used if \\p _MatrixType is a fixed-size matrix; use\n      * GeneralizedSelfAdjointEigenSolver(Index) for dynamic-size matrices.\n      */\n    GeneralizedSelfAdjointEigenSolver() : Base() {}\n\n    /** \\brief Constructor, pre-allocates memory for dynamic-size matrices.\n      *\n      * \\param [in]  size  Positive integer, size of the matrix whose\n      * eigenvalues and eigenvectors will be computed.\n      *\n      * This constructor is useful for dynamic-size matrices, when the user\n      * intends to perform decompositions via compute(). The \\p size\n      * parameter is only used as a hint. It is not an error to give a wrong\n      * \\p size, but it may impair performance.\n      *\n      * \\sa compute() for an example\n      */\n    explicit GeneralizedSelfAdjointEigenSolver(Index size)\n        : Base(size)\n    {}\n\n    /** \\brief Constructor; computes generalized eigendecomposition of given matrix pencil.\n      *\n      * \\param[in]  matA  Selfadjoint matrix in matrix pencil.\n      *                   Only the lower triangular part of the matrix is referenced.\n      * \\param[in]  matB  Positive-definite matrix in matrix pencil.\n      *                   Only the lower triangular part of the matrix is referenced.\n      * \\param[in]  options A or-ed set of flags {#ComputeEigenvectors,#EigenvaluesOnly} | {#Ax_lBx,#ABx_lx,#BAx_lx}.\n      *                     Default is #ComputeEigenvectors|#Ax_lBx.\n      *\n      * This constructor calls compute(const MatrixType&, const MatrixType&, int)\n      * to compute the eigenvalues and (if requested) the eigenvectors of the\n      * generalized eigenproblem \\f$ Ax = \\lambda B x \\f$ with \\a matA the\n      * selfadjoint matrix \\f$ A \\f$ and \\a matB the positive definite matrix\n      * \\f$ B \\f$. Each eigenvector \\f$ x \\f$ satisfies the property\n      * \\f$ x^* B x = 1 \\f$. The eigenvectors are computed if\n      * \\a options contains ComputeEigenvectors.\n      *\n      * In addition, the two following variants can be solved via \\p options:\n      * - \\c ABx_lx: \\f$ ABx = \\lambda x \\f$\n      * - \\c BAx_lx: \\f$ BAx = \\lambda x \\f$\n      *\n      * Example: \\include SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType2.cpp\n      * Output: \\verbinclude SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType2.out\n      *\n      * \\sa compute(const MatrixType&, const MatrixType&, int)\n      */\n    GeneralizedSelfAdjointEigenSolver(const MatrixType& matA, const MatrixType& matB,\n                                      int options = ComputeEigenvectors|Ax_lBx)\n      : Base(matA.cols())\n    {\n      compute(matA, matB, options);\n    }\n\n    /** \\brief Computes generalized eigendecomposition of given matrix pencil.\n      *\n      * \\param[in]  matA  Selfadjoint matrix in matrix pencil.\n      *                   Only the lower triangular part of the matrix is referenced.\n      * \\param[in]  matB  Positive-definite matrix in matrix pencil.\n      *                   Only the lower triangular part of the matrix is referenced.\n      * \\param[in]  options A or-ed set of flags {#ComputeEigenvectors,#EigenvaluesOnly} | {#Ax_lBx,#ABx_lx,#BAx_lx}.\n      *                     Default is #ComputeEigenvectors|#Ax_lBx.\n      *\n      * \\returns    Reference to \\c *this\n      *\n      * Accoring to \\p options, this function computes eigenvalues and (if requested)\n      * the eigenvectors of one of the following three generalized eigenproblems:\n      * - \\c Ax_lBx: \\f$ Ax = \\lambda B x \\f$\n      * - \\c ABx_lx: \\f$ ABx = \\lambda x \\f$\n      * - \\c BAx_lx: \\f$ BAx = \\lambda x \\f$\n      * with \\a matA the selfadjoint matrix \\f$ A \\f$ and \\a matB the positive definite\n      * matrix \\f$ B \\f$.\n      * In addition, each eigenvector \\f$ x \\f$ satisfies the property \\f$ x^* B x = 1 \\f$.\n      *\n      * The eigenvalues() function can be used to retrieve\n      * the eigenvalues. If \\p options contains ComputeEigenvectors, then the\n      * eigenvectors are also computed and can be retrieved by calling\n      * eigenvectors().\n      *\n      * The implementation uses LLT to compute the Cholesky decomposition\n      * \\f$ B = LL^* \\f$ and computes the classical eigendecomposition\n      * of the selfadjoint matrix \\f$ L^{-1} A (L^*)^{-1} \\f$ if \\p options contains Ax_lBx\n      * and of \\f$ L^{*} A L \\f$ otherwise. This solves the\n      * generalized eigenproblem, because any solution of the generalized\n      * eigenproblem \\f$ Ax = \\lambda B x \\f$ corresponds to a solution\n      * \\f$ L^{-1} A (L^*)^{-1} (L^* x) = \\lambda (L^* x) \\f$ of the\n      * eigenproblem for \\f$ L^{-1} A (L^*)^{-1} \\f$. Similar statements\n      * can be made for the two other variants.\n      *\n      * Example: \\include SelfAdjointEigenSolver_compute_MatrixType2.cpp\n      * Output: \\verbinclude SelfAdjointEigenSolver_compute_MatrixType2.out\n      *\n      * \\sa GeneralizedSelfAdjointEigenSolver(const MatrixType&, const MatrixType&, int)\n      */\n    GeneralizedSelfAdjointEigenSolver& compute(const MatrixType& matA, const MatrixType& matB,\n                                               int options = ComputeEigenvectors|Ax_lBx);\n\n  protected:\n\n};\n\n\ntemplate<typename MatrixType>\nGeneralizedSelfAdjointEigenSolver<MatrixType>& GeneralizedSelfAdjointEigenSolver<MatrixType>::\ncompute(const MatrixType& matA, const MatrixType& matB, int options)\n{\n  eigen_assert(matA.cols()==matA.rows() && matB.rows()==matA.rows() && matB.cols()==matB.rows());\n  eigen_assert((options&~(EigVecMask|GenEigMask))==0\n          && (options&EigVecMask)!=EigVecMask\n          && ((options&GenEigMask)==0 || (options&GenEigMask)==Ax_lBx\n           || (options&GenEigMask)==ABx_lx || (options&GenEigMask)==BAx_lx)\n          && \"invalid option parameter\");\n\n  bool computeEigVecs = ((options&EigVecMask)==0) || ((options&EigVecMask)==ComputeEigenvectors);\n\n  // Compute the cholesky decomposition of matB = L L' = U'U\n  LLT<MatrixType> cholB(matB);\n\n  int type = (options&GenEigMask);\n  if(type==0)\n    type = Ax_lBx;\n\n  if(type==Ax_lBx)\n  {\n    // compute C = inv(L) A inv(L')\n    MatrixType matC = matA.template selfadjointView<Lower>();\n    cholB.matrixL().template solveInPlace<OnTheLeft>(matC);\n    cholB.matrixU().template solveInPlace<OnTheRight>(matC);\n\n    Base::compute(matC, computeEigVecs ? ComputeEigenvectors : EigenvaluesOnly );\n\n    // transform back the eigen vectors: evecs = inv(U) * evecs\n    if(computeEigVecs)\n      cholB.matrixU().solveInPlace(Base::m_eivec);\n  }\n  else if(type==ABx_lx)\n  {\n    // compute C = L' A L\n    MatrixType matC = matA.template selfadjointView<Lower>();\n    matC = matC * cholB.matrixL();\n    matC = cholB.matrixU() * matC;\n\n    Base::compute(matC, computeEigVecs ? ComputeEigenvectors : EigenvaluesOnly);\n\n    // transform back the eigen vectors: evecs = inv(U) * evecs\n    if(computeEigVecs)\n      cholB.matrixU().solveInPlace(Base::m_eivec);\n  }\n  else if(type==BAx_lx)\n  {\n    // compute C = L' A L\n    MatrixType matC = matA.template selfadjointView<Lower>();\n    matC = matC * cholB.matrixL();\n    matC = cholB.matrixU() * matC;\n\n    Base::compute(matC, computeEigVecs ? ComputeEigenvectors : EigenvaluesOnly);\n\n    // transform back the eigen vectors: evecs = L * evecs\n    if(computeEigVecs)\n      Base::m_eivec = cholB.matrixL() * Base::m_eivec;\n  }\n\n  return *this;\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_GENERALIZEDSELFADJOINTEIGENSOLVER_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Eigenvalues/HessenbergDecomposition.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_HESSENBERGDECOMPOSITION_H\n#define EIGEN_HESSENBERGDECOMPOSITION_H\n\nnamespace Eigen { \n\nnamespace internal {\n  \ntemplate<typename MatrixType> struct HessenbergDecompositionMatrixHReturnType;\ntemplate<typename MatrixType>\nstruct traits<HessenbergDecompositionMatrixHReturnType<MatrixType> >\n{\n  typedef MatrixType ReturnType;\n};\n\n}\n\n/** \\eigenvalues_module \\ingroup Eigenvalues_Module\n  *\n  *\n  * \\class HessenbergDecomposition\n  *\n  * \\brief Reduces a square matrix to Hessenberg form by an orthogonal similarity transformation\n  *\n  * \\tparam _MatrixType the type of the matrix of which we are computing the Hessenberg decomposition\n  *\n  * This class performs an Hessenberg decomposition of a matrix \\f$ A \\f$. In\n  * the real case, the Hessenberg decomposition consists of an orthogonal\n  * matrix \\f$ Q \\f$ and a Hessenberg matrix \\f$ H \\f$ such that \\f$ A = Q H\n  * Q^T \\f$. An orthogonal matrix is a matrix whose inverse equals its\n  * transpose (\\f$ Q^{-1} = Q^T \\f$). A Hessenberg matrix has zeros below the\n  * subdiagonal, so it is almost upper triangular. The Hessenberg decomposition\n  * of a complex matrix is \\f$ A = Q H Q^* \\f$ with \\f$ Q \\f$ unitary (that is,\n  * \\f$ Q^{-1} = Q^* \\f$).\n  *\n  * Call the function compute() to compute the Hessenberg decomposition of a\n  * given matrix. Alternatively, you can use the\n  * HessenbergDecomposition(const MatrixType&) constructor which computes the\n  * Hessenberg decomposition at construction time. Once the decomposition is\n  * computed, you can use the matrixH() and matrixQ() functions to construct\n  * the matrices H and Q in the decomposition.\n  *\n  * The documentation for matrixH() contains an example of the typical use of\n  * this class.\n  *\n  * \\sa class ComplexSchur, class Tridiagonalization, \\ref QR_Module \"QR Module\"\n  */\ntemplate<typename _MatrixType> class HessenbergDecomposition\n{\n  public:\n\n    /** \\brief Synonym for the template parameter \\p _MatrixType. */\n    typedef _MatrixType MatrixType;\n\n    enum {\n      Size = MatrixType::RowsAtCompileTime,\n      SizeMinusOne = Size == Dynamic ? Dynamic : Size - 1,\n      Options = MatrixType::Options,\n      MaxSize = MatrixType::MaxRowsAtCompileTime,\n      MaxSizeMinusOne = MaxSize == Dynamic ? Dynamic : MaxSize - 1\n    };\n\n    /** \\brief Scalar type for matrices of type #MatrixType. */\n    typedef typename MatrixType::Scalar Scalar;\n    typedef Eigen::Index Index; ///< \\deprecated since Eigen 3.3\n\n    /** \\brief Type for vector of Householder coefficients.\n      *\n      * This is column vector with entries of type #Scalar. The length of the\n      * vector is one less than the size of #MatrixType, if it is a fixed-side\n      * type.\n      */\n    typedef Matrix<Scalar, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> CoeffVectorType;\n\n    /** \\brief Return type of matrixQ() */\n    typedef HouseholderSequence<MatrixType,typename internal::remove_all<typename CoeffVectorType::ConjugateReturnType>::type> HouseholderSequenceType;\n    \n    typedef internal::HessenbergDecompositionMatrixHReturnType<MatrixType> MatrixHReturnType;\n\n    /** \\brief Default constructor; the decomposition will be computed later.\n      *\n      * \\param [in] size  The size of the matrix whose Hessenberg decomposition will be computed.\n      *\n      * The default constructor is useful in cases in which the user intends to\n      * perform decompositions via compute().  The \\p size parameter is only\n      * used as a hint. It is not an error to give a wrong \\p size, but it may\n      * impair performance.\n      *\n      * \\sa compute() for an example.\n      */\n    explicit HessenbergDecomposition(Index size = Size==Dynamic ? 2 : Size)\n      : m_matrix(size,size),\n        m_temp(size),\n        m_isInitialized(false)\n    {\n      if(size>1)\n        m_hCoeffs.resize(size-1);\n    }\n\n    /** \\brief Constructor; computes Hessenberg decomposition of given matrix.\n      *\n      * \\param[in]  matrix  Square matrix whose Hessenberg decomposition is to be computed.\n      *\n      * This constructor calls compute() to compute the Hessenberg\n      * decomposition.\n      *\n      * \\sa matrixH() for an example.\n      */\n    template<typename InputType>\n    explicit HessenbergDecomposition(const EigenBase<InputType>& matrix)\n      : m_matrix(matrix.derived()),\n        m_temp(matrix.rows()),\n        m_isInitialized(false)\n    {\n      if(matrix.rows()<2)\n      {\n        m_isInitialized = true;\n        return;\n      }\n      m_hCoeffs.resize(matrix.rows()-1,1);\n      _compute(m_matrix, m_hCoeffs, m_temp);\n      m_isInitialized = true;\n    }\n\n    /** \\brief Computes Hessenberg decomposition of given matrix.\n      *\n      * \\param[in]  matrix  Square matrix whose Hessenberg decomposition is to be computed.\n      * \\returns    Reference to \\c *this\n      *\n      * The Hessenberg decomposition is computed by bringing the columns of the\n      * matrix successively in the required form using Householder reflections\n      * (see, e.g., Algorithm 7.4.2 in Golub \\& Van Loan, <i>%Matrix\n      * Computations</i>). The cost is \\f$ 10n^3/3 \\f$ flops, where \\f$ n \\f$\n      * denotes the size of the given matrix.\n      *\n      * This method reuses of the allocated data in the HessenbergDecomposition\n      * object.\n      *\n      * Example: \\include HessenbergDecomposition_compute.cpp\n      * Output: \\verbinclude HessenbergDecomposition_compute.out\n      */\n    template<typename InputType>\n    HessenbergDecomposition& compute(const EigenBase<InputType>& matrix)\n    {\n      m_matrix = matrix.derived();\n      if(matrix.rows()<2)\n      {\n        m_isInitialized = true;\n        return *this;\n      }\n      m_hCoeffs.resize(matrix.rows()-1,1);\n      _compute(m_matrix, m_hCoeffs, m_temp);\n      m_isInitialized = true;\n      return *this;\n    }\n\n    /** \\brief Returns the Householder coefficients.\n      *\n      * \\returns a const reference to the vector of Householder coefficients\n      *\n      * \\pre Either the constructor HessenbergDecomposition(const MatrixType&)\n      * or the member function compute(const MatrixType&) has been called\n      * before to compute the Hessenberg decomposition of a matrix.\n      *\n      * The Householder coefficients allow the reconstruction of the matrix\n      * \\f$ Q \\f$ in the Hessenberg decomposition from the packed data.\n      *\n      * \\sa packedMatrix(), \\ref Householder_Module \"Householder module\"\n      */\n    const CoeffVectorType& householderCoefficients() const\n    {\n      eigen_assert(m_isInitialized && \"HessenbergDecomposition is not initialized.\");\n      return m_hCoeffs;\n    }\n\n    /** \\brief Returns the internal representation of the decomposition\n      *\n      *\t\\returns a const reference to a matrix with the internal representation\n      *\t         of the decomposition.\n      *\n      * \\pre Either the constructor HessenbergDecomposition(const MatrixType&)\n      * or the member function compute(const MatrixType&) has been called\n      * before to compute the Hessenberg decomposition of a matrix.\n      *\n      * The returned matrix contains the following information:\n      *  - the upper part and lower sub-diagonal represent the Hessenberg matrix H\n      *  - the rest of the lower part contains the Householder vectors that, combined with\n      *    Householder coefficients returned by householderCoefficients(),\n      *    allows to reconstruct the matrix Q as\n      *       \\f$ Q = H_{N-1} \\ldots H_1 H_0 \\f$.\n      *    Here, the matrices \\f$ H_i \\f$ are the Householder transformations\n      *       \\f$ H_i = (I - h_i v_i v_i^T) \\f$\n      *    where \\f$ h_i \\f$ is the \\f$ i \\f$th Householder coefficient and\n      *    \\f$ v_i \\f$ is the Householder vector defined by\n      *       \\f$ v_i = [ 0, \\ldots, 0, 1, M(i+2,i), \\ldots, M(N-1,i) ]^T \\f$\n      *    with M the matrix returned by this function.\n      *\n      * See LAPACK for further details on this packed storage.\n      *\n      * Example: \\include HessenbergDecomposition_packedMatrix.cpp\n      * Output: \\verbinclude HessenbergDecomposition_packedMatrix.out\n      *\n      * \\sa householderCoefficients()\n      */\n    const MatrixType& packedMatrix() const\n    {\n      eigen_assert(m_isInitialized && \"HessenbergDecomposition is not initialized.\");\n      return m_matrix;\n    }\n\n    /** \\brief Reconstructs the orthogonal matrix Q in the decomposition\n      *\n      * \\returns object representing the matrix Q\n      *\n      * \\pre Either the constructor HessenbergDecomposition(const MatrixType&)\n      * or the member function compute(const MatrixType&) has been called\n      * before to compute the Hessenberg decomposition of a matrix.\n      *\n      * This function returns a light-weight object of template class\n      * HouseholderSequence. You can either apply it directly to a matrix or\n      * you can convert it to a matrix of type #MatrixType.\n      *\n      * \\sa matrixH() for an example, class HouseholderSequence\n      */\n    HouseholderSequenceType matrixQ() const\n    {\n      eigen_assert(m_isInitialized && \"HessenbergDecomposition is not initialized.\");\n      return HouseholderSequenceType(m_matrix, m_hCoeffs.conjugate())\n             .setLength(m_matrix.rows() - 1)\n             .setShift(1);\n    }\n\n    /** \\brief Constructs the Hessenberg matrix H in the decomposition\n      *\n      * \\returns expression object representing the matrix H\n      *\n      * \\pre Either the constructor HessenbergDecomposition(const MatrixType&)\n      * or the member function compute(const MatrixType&) has been called\n      * before to compute the Hessenberg decomposition of a matrix.\n      *\n      * The object returned by this function constructs the Hessenberg matrix H\n      * when it is assigned to a matrix or otherwise evaluated. The matrix H is\n      * constructed from the packed matrix as returned by packedMatrix(): The\n      * upper part (including the subdiagonal) of the packed matrix contains\n      * the matrix H. It may sometimes be better to directly use the packed\n      * matrix instead of constructing the matrix H.\n      *\n      * Example: \\include HessenbergDecomposition_matrixH.cpp\n      * Output: \\verbinclude HessenbergDecomposition_matrixH.out\n      *\n      * \\sa matrixQ(), packedMatrix()\n      */\n    MatrixHReturnType matrixH() const\n    {\n      eigen_assert(m_isInitialized && \"HessenbergDecomposition is not initialized.\");\n      return MatrixHReturnType(*this);\n    }\n\n  private:\n\n    typedef Matrix<Scalar, 1, Size, Options | RowMajor, 1, MaxSize> VectorType;\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n    static void _compute(MatrixType& matA, CoeffVectorType& hCoeffs, VectorType& temp);\n\n  protected:\n    MatrixType m_matrix;\n    CoeffVectorType m_hCoeffs;\n    VectorType m_temp;\n    bool m_isInitialized;\n};\n\n/** \\internal\n  * Performs a tridiagonal decomposition of \\a matA in place.\n  *\n  * \\param matA the input selfadjoint matrix\n  * \\param hCoeffs returned Householder coefficients\n  *\n  * The result is written in the lower triangular part of \\a matA.\n  *\n  * Implemented from Golub's \"%Matrix Computations\", algorithm 8.3.1.\n  *\n  * \\sa packedMatrix()\n  */\ntemplate<typename MatrixType>\nvoid HessenbergDecomposition<MatrixType>::_compute(MatrixType& matA, CoeffVectorType& hCoeffs, VectorType& temp)\n{\n  eigen_assert(matA.rows()==matA.cols());\n  Index n = matA.rows();\n  temp.resize(n);\n  for (Index i = 0; i<n-1; ++i)\n  {\n    // let's consider the vector v = i-th column starting at position i+1\n    Index remainingSize = n-i-1;\n    RealScalar beta;\n    Scalar h;\n    matA.col(i).tail(remainingSize).makeHouseholderInPlace(h, beta);\n    matA.col(i).coeffRef(i+1) = beta;\n    hCoeffs.coeffRef(i) = h;\n\n    // Apply similarity transformation to remaining columns,\n    // i.e., compute A = H A H'\n\n    // A = H A\n    matA.bottomRightCorner(remainingSize, remainingSize)\n        .applyHouseholderOnTheLeft(matA.col(i).tail(remainingSize-1), h, &temp.coeffRef(0));\n\n    // A = A H'\n    matA.rightCols(remainingSize)\n        .applyHouseholderOnTheRight(matA.col(i).tail(remainingSize-1).conjugate(), numext::conj(h), &temp.coeffRef(0));\n  }\n}\n\nnamespace internal {\n\n/** \\eigenvalues_module \\ingroup Eigenvalues_Module\n  *\n  *\n  * \\brief Expression type for return value of HessenbergDecomposition::matrixH()\n  *\n  * \\tparam MatrixType type of matrix in the Hessenberg decomposition\n  *\n  * Objects of this type represent the Hessenberg matrix in the Hessenberg\n  * decomposition of some matrix. The object holds a reference to the\n  * HessenbergDecomposition class until the it is assigned or evaluated for\n  * some other reason (the reference should remain valid during the life time\n  * of this object). This class is the return type of\n  * HessenbergDecomposition::matrixH(); there is probably no other use for this\n  * class.\n  */\ntemplate<typename MatrixType> struct HessenbergDecompositionMatrixHReturnType\n: public ReturnByValue<HessenbergDecompositionMatrixHReturnType<MatrixType> >\n{\n  public:\n    /** \\brief Constructor.\n      *\n      * \\param[in] hess  Hessenberg decomposition\n      */\n    HessenbergDecompositionMatrixHReturnType(const HessenbergDecomposition<MatrixType>& hess) : m_hess(hess) { }\n\n    /** \\brief Hessenberg matrix in decomposition.\n      *\n      * \\param[out] result  Hessenberg matrix in decomposition \\p hess which\n      *                     was passed to the constructor\n      */\n    template <typename ResultType>\n    inline void evalTo(ResultType& result) const\n    {\n      result = m_hess.packedMatrix();\n      Index n = result.rows();\n      if (n>2)\n        result.bottomLeftCorner(n-2, n-2).template triangularView<Lower>().setZero();\n    }\n\n    Index rows() const { return m_hess.packedMatrix().rows(); }\n    Index cols() const { return m_hess.packedMatrix().cols(); }\n\n  protected:\n    const HessenbergDecomposition<MatrixType>& m_hess;\n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_HESSENBERGDECOMPOSITION_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Eigenvalues/MatrixBaseEigenvalues.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_MATRIXBASEEIGENVALUES_H\n#define EIGEN_MATRIXBASEEIGENVALUES_H\n\nnamespace Eigen { \n\nnamespace internal {\n\ntemplate<typename Derived, bool IsComplex>\nstruct eigenvalues_selector\n{\n  // this is the implementation for the case IsComplex = true\n  static inline typename MatrixBase<Derived>::EigenvaluesReturnType const\n  run(const MatrixBase<Derived>& m)\n  {\n    typedef typename Derived::PlainObject PlainObject;\n    PlainObject m_eval(m);\n    return ComplexEigenSolver<PlainObject>(m_eval, false).eigenvalues();\n  }\n};\n\ntemplate<typename Derived>\nstruct eigenvalues_selector<Derived, false>\n{\n  static inline typename MatrixBase<Derived>::EigenvaluesReturnType const\n  run(const MatrixBase<Derived>& m)\n  {\n    typedef typename Derived::PlainObject PlainObject;\n    PlainObject m_eval(m);\n    return EigenSolver<PlainObject>(m_eval, false).eigenvalues();\n  }\n};\n\n} // end namespace internal\n\n/** \\brief Computes the eigenvalues of a matrix \n  * \\returns Column vector containing the eigenvalues.\n  *\n  * \\eigenvalues_module\n  * This function computes the eigenvalues with the help of the EigenSolver\n  * class (for real matrices) or the ComplexEigenSolver class (for complex\n  * matrices). \n  *\n  * The eigenvalues are repeated according to their algebraic multiplicity,\n  * so there are as many eigenvalues as rows in the matrix.\n  *\n  * The SelfAdjointView class provides a better algorithm for selfadjoint\n  * matrices.\n  *\n  * Example: \\include MatrixBase_eigenvalues.cpp\n  * Output: \\verbinclude MatrixBase_eigenvalues.out\n  *\n  * \\sa EigenSolver::eigenvalues(), ComplexEigenSolver::eigenvalues(),\n  *     SelfAdjointView::eigenvalues()\n  */\ntemplate<typename Derived>\ninline typename MatrixBase<Derived>::EigenvaluesReturnType\nMatrixBase<Derived>::eigenvalues() const\n{\n  typedef typename internal::traits<Derived>::Scalar Scalar;\n  return internal::eigenvalues_selector<Derived, NumTraits<Scalar>::IsComplex>::run(derived());\n}\n\n/** \\brief Computes the eigenvalues of a matrix\n  * \\returns Column vector containing the eigenvalues.\n  *\n  * \\eigenvalues_module\n  * This function computes the eigenvalues with the help of the\n  * SelfAdjointEigenSolver class.  The eigenvalues are repeated according to\n  * their algebraic multiplicity, so there are as many eigenvalues as rows in\n  * the matrix.\n  *\n  * Example: \\include SelfAdjointView_eigenvalues.cpp\n  * Output: \\verbinclude SelfAdjointView_eigenvalues.out\n  *\n  * \\sa SelfAdjointEigenSolver::eigenvalues(), MatrixBase::eigenvalues()\n  */\ntemplate<typename MatrixType, unsigned int UpLo> \ninline typename SelfAdjointView<MatrixType, UpLo>::EigenvaluesReturnType\nSelfAdjointView<MatrixType, UpLo>::eigenvalues() const\n{\n  typedef typename SelfAdjointView<MatrixType, UpLo>::PlainObject PlainObject;\n  PlainObject thisAsMatrix(*this);\n  return SelfAdjointEigenSolver<PlainObject>(thisAsMatrix, false).eigenvalues();\n}\n\n\n\n/** \\brief Computes the L2 operator norm\n  * \\returns Operator norm of the matrix.\n  *\n  * \\eigenvalues_module\n  * This function computes the L2 operator norm of a matrix, which is also\n  * known as the spectral norm. The norm of a matrix \\f$ A \\f$ is defined to be\n  * \\f[ \\|A\\|_2 = \\max_x \\frac{\\|Ax\\|_2}{\\|x\\|_2} \\f]\n  * where the maximum is over all vectors and the norm on the right is the\n  * Euclidean vector norm. The norm equals the largest singular value, which is\n  * the square root of the largest eigenvalue of the positive semi-definite\n  * matrix \\f$ A^*A \\f$.\n  *\n  * The current implementation uses the eigenvalues of \\f$ A^*A \\f$, as computed\n  * by SelfAdjointView::eigenvalues(), to compute the operator norm of a\n  * matrix.  The SelfAdjointView class provides a better algorithm for\n  * selfadjoint matrices.\n  *\n  * Example: \\include MatrixBase_operatorNorm.cpp\n  * Output: \\verbinclude MatrixBase_operatorNorm.out\n  *\n  * \\sa SelfAdjointView::eigenvalues(), SelfAdjointView::operatorNorm()\n  */\ntemplate<typename Derived>\ninline typename MatrixBase<Derived>::RealScalar\nMatrixBase<Derived>::operatorNorm() const\n{\n  using std::sqrt;\n  typename Derived::PlainObject m_eval(derived());\n  // FIXME if it is really guaranteed that the eigenvalues are already sorted,\n  // then we don't need to compute a maxCoeff() here, comparing the 1st and last ones is enough.\n  return sqrt((m_eval*m_eval.adjoint())\n                 .eval()\n\t\t .template selfadjointView<Lower>()\n\t\t .eigenvalues()\n\t\t .maxCoeff()\n\t\t );\n}\n\n/** \\brief Computes the L2 operator norm\n  * \\returns Operator norm of the matrix.\n  *\n  * \\eigenvalues_module\n  * This function computes the L2 operator norm of a self-adjoint matrix. For a\n  * self-adjoint matrix, the operator norm is the largest eigenvalue.\n  *\n  * The current implementation uses the eigenvalues of the matrix, as computed\n  * by eigenvalues(), to compute the operator norm of the matrix.\n  *\n  * Example: \\include SelfAdjointView_operatorNorm.cpp\n  * Output: \\verbinclude SelfAdjointView_operatorNorm.out\n  *\n  * \\sa eigenvalues(), MatrixBase::operatorNorm()\n  */\ntemplate<typename MatrixType, unsigned int UpLo>\ninline typename SelfAdjointView<MatrixType, UpLo>::RealScalar\nSelfAdjointView<MatrixType, UpLo>::operatorNorm() const\n{\n  return eigenvalues().cwiseAbs().maxCoeff();\n}\n\n} // end namespace Eigen\n\n#endif\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Eigenvalues/RealQZ.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Alexey Korepanov <kaikaikai@yandex.ru>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_REAL_QZ_H\n#define EIGEN_REAL_QZ_H\n\nnamespace Eigen {\n\n  /** \\eigenvalues_module \\ingroup Eigenvalues_Module\n   *\n   *\n   * \\class RealQZ\n   *\n   * \\brief Performs a real QZ decomposition of a pair of square matrices\n   *\n   * \\tparam _MatrixType the type of the matrix of which we are computing the\n   * real QZ decomposition; this is expected to be an instantiation of the\n   * Matrix class template.\n   *\n   * Given a real square matrices A and B, this class computes the real QZ\n   * decomposition: \\f$ A = Q S Z \\f$, \\f$ B = Q T Z \\f$ where Q and Z are\n   * real orthogonal matrixes, T is upper-triangular matrix, and S is upper\n   * quasi-triangular matrix. An orthogonal matrix is a matrix whose\n   * inverse is equal to its transpose, \\f$ U^{-1} = U^T \\f$. A quasi-triangular\n   * matrix is a block-triangular matrix whose diagonal consists of 1-by-1\n   * blocks and 2-by-2 blocks where further reduction is impossible due to\n   * complex eigenvalues. \n   *\n   * The eigenvalues of the pencil \\f$ A - z B \\f$ can be obtained from\n   * 1x1 and 2x2 blocks on the diagonals of S and T.\n   *\n   * Call the function compute() to compute the real QZ decomposition of a\n   * given pair of matrices. Alternatively, you can use the \n   * RealQZ(const MatrixType& B, const MatrixType& B, bool computeQZ)\n   * constructor which computes the real QZ decomposition at construction\n   * time. Once the decomposition is computed, you can use the matrixS(),\n   * matrixT(), matrixQ() and matrixZ() functions to retrieve the matrices\n   * S, T, Q and Z in the decomposition. If computeQZ==false, some time\n   * is saved by not computing matrices Q and Z.\n   *\n   * Example: \\include RealQZ_compute.cpp\n   * Output: \\include RealQZ_compute.out\n   *\n   * \\note The implementation is based on the algorithm in \"Matrix Computations\"\n   * by Gene H. Golub and Charles F. Van Loan, and a paper \"An algorithm for\n   * generalized eigenvalue problems\" by C.B.Moler and G.W.Stewart.\n   *\n   * \\sa class RealSchur, class ComplexSchur, class EigenSolver, class ComplexEigenSolver\n   */\n\n  template<typename _MatrixType> class RealQZ\n  {\n    public:\n      typedef _MatrixType MatrixType;\n      enum {\n        RowsAtCompileTime = MatrixType::RowsAtCompileTime,\n        ColsAtCompileTime = MatrixType::ColsAtCompileTime,\n        Options = MatrixType::Options,\n        MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,\n        MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime\n      };\n      typedef typename MatrixType::Scalar Scalar;\n      typedef std::complex<typename NumTraits<Scalar>::Real> ComplexScalar;\n      typedef Eigen::Index Index; ///< \\deprecated since Eigen 3.3\n\n      typedef Matrix<ComplexScalar, ColsAtCompileTime, 1, Options & ~RowMajor, MaxColsAtCompileTime, 1> EigenvalueType;\n      typedef Matrix<Scalar, ColsAtCompileTime, 1, Options & ~RowMajor, MaxColsAtCompileTime, 1> ColumnVectorType;\n\n      /** \\brief Default constructor.\n       *\n       * \\param [in] size  Positive integer, size of the matrix whose QZ decomposition will be computed.\n       *\n       * The default constructor is useful in cases in which the user intends to\n       * perform decompositions via compute().  The \\p size parameter is only\n       * used as a hint. It is not an error to give a wrong \\p size, but it may\n       * impair performance.\n       *\n       * \\sa compute() for an example.\n       */\n      explicit RealQZ(Index size = RowsAtCompileTime==Dynamic ? 1 : RowsAtCompileTime) :\n        m_S(size, size),\n        m_T(size, size),\n        m_Q(size, size),\n        m_Z(size, size),\n        m_workspace(size*2),\n        m_maxIters(400),\n        m_isInitialized(false)\n        { }\n\n      /** \\brief Constructor; computes real QZ decomposition of given matrices\n       * \n       * \\param[in]  A          Matrix A.\n       * \\param[in]  B          Matrix B.\n       * \\param[in]  computeQZ  If false, A and Z are not computed.\n       *\n       * This constructor calls compute() to compute the QZ decomposition.\n       */\n      RealQZ(const MatrixType& A, const MatrixType& B, bool computeQZ = true) :\n        m_S(A.rows(),A.cols()),\n        m_T(A.rows(),A.cols()),\n        m_Q(A.rows(),A.cols()),\n        m_Z(A.rows(),A.cols()),\n        m_workspace(A.rows()*2),\n        m_maxIters(400),\n        m_isInitialized(false) {\n          compute(A, B, computeQZ);\n        }\n\n      /** \\brief Returns matrix Q in the QZ decomposition. \n       *\n       * \\returns A const reference to the matrix Q.\n       */\n      const MatrixType& matrixQ() const {\n        eigen_assert(m_isInitialized && \"RealQZ is not initialized.\");\n        eigen_assert(m_computeQZ && \"The matrices Q and Z have not been computed during the QZ decomposition.\");\n        return m_Q;\n      }\n\n      /** \\brief Returns matrix Z in the QZ decomposition. \n       *\n       * \\returns A const reference to the matrix Z.\n       */\n      const MatrixType& matrixZ() const {\n        eigen_assert(m_isInitialized && \"RealQZ is not initialized.\");\n        eigen_assert(m_computeQZ && \"The matrices Q and Z have not been computed during the QZ decomposition.\");\n        return m_Z;\n      }\n\n      /** \\brief Returns matrix S in the QZ decomposition. \n       *\n       * \\returns A const reference to the matrix S.\n       */\n      const MatrixType& matrixS() const {\n        eigen_assert(m_isInitialized && \"RealQZ is not initialized.\");\n        return m_S;\n      }\n\n      /** \\brief Returns matrix S in the QZ decomposition. \n       *\n       * \\returns A const reference to the matrix S.\n       */\n      const MatrixType& matrixT() const {\n        eigen_assert(m_isInitialized && \"RealQZ is not initialized.\");\n        return m_T;\n      }\n\n      /** \\brief Computes QZ decomposition of given matrix. \n       * \n       * \\param[in]  A          Matrix A.\n       * \\param[in]  B          Matrix B.\n       * \\param[in]  computeQZ  If false, A and Z are not computed.\n       * \\returns    Reference to \\c *this\n       */\n      RealQZ& compute(const MatrixType& A, const MatrixType& B, bool computeQZ = true);\n\n      /** \\brief Reports whether previous computation was successful.\n       *\n       * \\returns \\c Success if computation was succesful, \\c NoConvergence otherwise.\n       */\n      ComputationInfo info() const\n      {\n        eigen_assert(m_isInitialized && \"RealQZ is not initialized.\");\n        return m_info;\n      }\n\n      /** \\brief Returns number of performed QR-like iterations.\n      */\n      Index iterations() const\n      {\n        eigen_assert(m_isInitialized && \"RealQZ is not initialized.\");\n        return m_global_iter;\n      }\n\n      /** Sets the maximal number of iterations allowed to converge to one eigenvalue\n       * or decouple the problem.\n      */\n      RealQZ& setMaxIterations(Index maxIters)\n      {\n        m_maxIters = maxIters;\n        return *this;\n      }\n\n    private:\n\n      MatrixType m_S, m_T, m_Q, m_Z;\n      Matrix<Scalar,Dynamic,1> m_workspace;\n      ComputationInfo m_info;\n      Index m_maxIters;\n      bool m_isInitialized;\n      bool m_computeQZ;\n      Scalar m_normOfT, m_normOfS;\n      Index m_global_iter;\n\n      typedef Matrix<Scalar,3,1> Vector3s;\n      typedef Matrix<Scalar,2,1> Vector2s;\n      typedef Matrix<Scalar,2,2> Matrix2s;\n      typedef JacobiRotation<Scalar> JRs;\n\n      void hessenbergTriangular();\n      void computeNorms();\n      Index findSmallSubdiagEntry(Index iu);\n      Index findSmallDiagEntry(Index f, Index l);\n      void splitOffTwoRows(Index i);\n      void pushDownZero(Index z, Index f, Index l);\n      void step(Index f, Index l, Index iter);\n\n  }; // RealQZ\n\n  /** \\internal Reduces S and T to upper Hessenberg - triangular form */\n  template<typename MatrixType>\n    void RealQZ<MatrixType>::hessenbergTriangular()\n    {\n\n      const Index dim = m_S.cols();\n\n      // perform QR decomposition of T, overwrite T with R, save Q\n      HouseholderQR<MatrixType> qrT(m_T);\n      m_T = qrT.matrixQR();\n      m_T.template triangularView<StrictlyLower>().setZero();\n      m_Q = qrT.householderQ();\n      // overwrite S with Q* S\n      m_S.applyOnTheLeft(m_Q.adjoint());\n      // init Z as Identity\n      if (m_computeQZ)\n        m_Z = MatrixType::Identity(dim,dim);\n      // reduce S to upper Hessenberg with Givens rotations\n      for (Index j=0; j<=dim-3; j++) {\n        for (Index i=dim-1; i>=j+2; i--) {\n          JRs G;\n          // kill S(i,j)\n          if(m_S.coeff(i,j) != 0)\n          {\n            G.makeGivens(m_S.coeff(i-1,j), m_S.coeff(i,j), &m_S.coeffRef(i-1, j));\n            m_S.coeffRef(i,j) = Scalar(0.0);\n            m_S.rightCols(dim-j-1).applyOnTheLeft(i-1,i,G.adjoint());\n            m_T.rightCols(dim-i+1).applyOnTheLeft(i-1,i,G.adjoint());\n            // update Q\n            if (m_computeQZ)\n              m_Q.applyOnTheRight(i-1,i,G);\n          }\n          // kill T(i,i-1)\n          if(m_T.coeff(i,i-1)!=Scalar(0))\n          {\n            G.makeGivens(m_T.coeff(i,i), m_T.coeff(i,i-1), &m_T.coeffRef(i,i));\n            m_T.coeffRef(i,i-1) = Scalar(0.0);\n            m_S.applyOnTheRight(i,i-1,G);\n            m_T.topRows(i).applyOnTheRight(i,i-1,G);\n            // update Z\n            if (m_computeQZ)\n              m_Z.applyOnTheLeft(i,i-1,G.adjoint());\n          }\n        }\n      }\n    }\n\n  /** \\internal Computes vector L1 norms of S and T when in Hessenberg-Triangular form already */\n  template<typename MatrixType>\n    inline void RealQZ<MatrixType>::computeNorms()\n    {\n      const Index size = m_S.cols();\n      m_normOfS = Scalar(0.0);\n      m_normOfT = Scalar(0.0);\n      for (Index j = 0; j < size; ++j)\n      {\n        m_normOfS += m_S.col(j).segment(0, (std::min)(size,j+2)).cwiseAbs().sum();\n        m_normOfT += m_T.row(j).segment(j, size - j).cwiseAbs().sum();\n      }\n    }\n\n\n  /** \\internal Look for single small sub-diagonal element S(res, res-1) and return res (or 0) */\n  template<typename MatrixType>\n    inline Index RealQZ<MatrixType>::findSmallSubdiagEntry(Index iu)\n    {\n      using std::abs;\n      Index res = iu;\n      while (res > 0)\n      {\n        Scalar s = abs(m_S.coeff(res-1,res-1)) + abs(m_S.coeff(res,res));\n        if (s == Scalar(0.0))\n          s = m_normOfS;\n        if (abs(m_S.coeff(res,res-1)) < NumTraits<Scalar>::epsilon() * s)\n          break;\n        res--;\n      }\n      return res;\n    }\n\n  /** \\internal Look for single small diagonal element T(res, res) for res between f and l, and return res (or f-1)  */\n  template<typename MatrixType>\n    inline Index RealQZ<MatrixType>::findSmallDiagEntry(Index f, Index l)\n    {\n      using std::abs;\n      Index res = l;\n      while (res >= f) {\n        if (abs(m_T.coeff(res,res)) <= NumTraits<Scalar>::epsilon() * m_normOfT)\n          break;\n        res--;\n      }\n      return res;\n    }\n\n  /** \\internal decouple 2x2 diagonal block in rows i, i+1 if eigenvalues are real */\n  template<typename MatrixType>\n    inline void RealQZ<MatrixType>::splitOffTwoRows(Index i)\n    {\n      using std::abs;\n      using std::sqrt;\n      const Index dim=m_S.cols();\n      if (abs(m_S.coeff(i+1,i))==Scalar(0))\n        return;\n      Index j = findSmallDiagEntry(i,i+1);\n      if (j==i-1)\n      {\n        // block of (S T^{-1})\n        Matrix2s STi = m_T.template block<2,2>(i,i).template triangularView<Upper>().\n          template solve<OnTheRight>(m_S.template block<2,2>(i,i));\n        Scalar p = Scalar(0.5)*(STi(0,0)-STi(1,1));\n        Scalar q = p*p + STi(1,0)*STi(0,1);\n        if (q>=0) {\n          Scalar z = sqrt(q);\n          // one QR-like iteration for ABi - lambda I\n          // is enough - when we know exact eigenvalue in advance,\n          // convergence is immediate\n          JRs G;\n          if (p>=0)\n            G.makeGivens(p + z, STi(1,0));\n          else\n            G.makeGivens(p - z, STi(1,0));\n          m_S.rightCols(dim-i).applyOnTheLeft(i,i+1,G.adjoint());\n          m_T.rightCols(dim-i).applyOnTheLeft(i,i+1,G.adjoint());\n          // update Q\n          if (m_computeQZ)\n            m_Q.applyOnTheRight(i,i+1,G);\n\n          G.makeGivens(m_T.coeff(i+1,i+1), m_T.coeff(i+1,i));\n          m_S.topRows(i+2).applyOnTheRight(i+1,i,G);\n          m_T.topRows(i+2).applyOnTheRight(i+1,i,G);\n          // update Z\n          if (m_computeQZ)\n            m_Z.applyOnTheLeft(i+1,i,G.adjoint());\n\n          m_S.coeffRef(i+1,i) = Scalar(0.0);\n          m_T.coeffRef(i+1,i) = Scalar(0.0);\n        }\n      }\n      else\n      {\n        pushDownZero(j,i,i+1);\n      }\n    }\n\n  /** \\internal use zero in T(z,z) to zero S(l,l-1), working in block f..l */\n  template<typename MatrixType>\n    inline void RealQZ<MatrixType>::pushDownZero(Index z, Index f, Index l)\n    {\n      JRs G;\n      const Index dim = m_S.cols();\n      for (Index zz=z; zz<l; zz++)\n      {\n        // push 0 down\n        Index firstColS = zz>f ? (zz-1) : zz;\n        G.makeGivens(m_T.coeff(zz, zz+1), m_T.coeff(zz+1, zz+1));\n        m_S.rightCols(dim-firstColS).applyOnTheLeft(zz,zz+1,G.adjoint());\n        m_T.rightCols(dim-zz).applyOnTheLeft(zz,zz+1,G.adjoint());\n        m_T.coeffRef(zz+1,zz+1) = Scalar(0.0);\n        // update Q\n        if (m_computeQZ)\n          m_Q.applyOnTheRight(zz,zz+1,G);\n        // kill S(zz+1, zz-1)\n        if (zz>f)\n        {\n          G.makeGivens(m_S.coeff(zz+1, zz), m_S.coeff(zz+1,zz-1));\n          m_S.topRows(zz+2).applyOnTheRight(zz, zz-1,G);\n          m_T.topRows(zz+1).applyOnTheRight(zz, zz-1,G);\n          m_S.coeffRef(zz+1,zz-1) = Scalar(0.0);\n          // update Z\n          if (m_computeQZ)\n            m_Z.applyOnTheLeft(zz,zz-1,G.adjoint());\n        }\n      }\n      // finally kill S(l,l-1)\n      G.makeGivens(m_S.coeff(l,l), m_S.coeff(l,l-1));\n      m_S.applyOnTheRight(l,l-1,G);\n      m_T.applyOnTheRight(l,l-1,G);\n      m_S.coeffRef(l,l-1)=Scalar(0.0);\n      // update Z\n      if (m_computeQZ)\n        m_Z.applyOnTheLeft(l,l-1,G.adjoint());\n    }\n\n  /** \\internal QR-like iterative step for block f..l */\n  template<typename MatrixType>\n    inline void RealQZ<MatrixType>::step(Index f, Index l, Index iter)\n    {\n      using std::abs;\n      const Index dim = m_S.cols();\n\n      // x, y, z\n      Scalar x, y, z;\n      if (iter==10)\n      {\n        // Wilkinson ad hoc shift\n        const Scalar\n          a11=m_S.coeff(f+0,f+0), a12=m_S.coeff(f+0,f+1),\n          a21=m_S.coeff(f+1,f+0), a22=m_S.coeff(f+1,f+1), a32=m_S.coeff(f+2,f+1),\n          b12=m_T.coeff(f+0,f+1),\n          b11i=Scalar(1.0)/m_T.coeff(f+0,f+0),\n          b22i=Scalar(1.0)/m_T.coeff(f+1,f+1),\n          a87=m_S.coeff(l-1,l-2),\n          a98=m_S.coeff(l-0,l-1),\n          b77i=Scalar(1.0)/m_T.coeff(l-2,l-2),\n          b88i=Scalar(1.0)/m_T.coeff(l-1,l-1);\n        Scalar ss = abs(a87*b77i) + abs(a98*b88i),\n               lpl = Scalar(1.5)*ss,\n               ll = ss*ss;\n        x = ll + a11*a11*b11i*b11i - lpl*a11*b11i + a12*a21*b11i*b22i\n          - a11*a21*b12*b11i*b11i*b22i;\n        y = a11*a21*b11i*b11i - lpl*a21*b11i + a21*a22*b11i*b22i \n          - a21*a21*b12*b11i*b11i*b22i;\n        z = a21*a32*b11i*b22i;\n      }\n      else if (iter==16)\n      {\n        // another exceptional shift\n        x = m_S.coeff(f,f)/m_T.coeff(f,f)-m_S.coeff(l,l)/m_T.coeff(l,l) + m_S.coeff(l,l-1)*m_T.coeff(l-1,l) /\n          (m_T.coeff(l-1,l-1)*m_T.coeff(l,l));\n        y = m_S.coeff(f+1,f)/m_T.coeff(f,f);\n        z = 0;\n      }\n      else if (iter>23 && !(iter%8))\n      {\n        // extremely exceptional shift\n        x = internal::random<Scalar>(-1.0,1.0);\n        y = internal::random<Scalar>(-1.0,1.0);\n        z = internal::random<Scalar>(-1.0,1.0);\n      }\n      else\n      {\n        // Compute the shifts: (x,y,z,0...) = (AB^-1 - l1 I) (AB^-1 - l2 I) e1\n        // where l1 and l2 are the eigenvalues of the 2x2 matrix C = U V^-1 where\n        // U and V are 2x2 bottom right sub matrices of A and B. Thus:\n        //  = AB^-1AB^-1 + l1 l2 I - (l1+l2)(AB^-1)\n        //  = AB^-1AB^-1 + det(M) - tr(M)(AB^-1)\n        // Since we are only interested in having x, y, z with a correct ratio, we have:\n        const Scalar\n          a11 = m_S.coeff(f,f),     a12 = m_S.coeff(f,f+1),\n          a21 = m_S.coeff(f+1,f),   a22 = m_S.coeff(f+1,f+1),\n                                    a32 = m_S.coeff(f+2,f+1),\n\n          a88 = m_S.coeff(l-1,l-1), a89 = m_S.coeff(l-1,l),\n          a98 = m_S.coeff(l,l-1),   a99 = m_S.coeff(l,l),\n\n          b11 = m_T.coeff(f,f),     b12 = m_T.coeff(f,f+1),\n                                    b22 = m_T.coeff(f+1,f+1),\n\n          b88 = m_T.coeff(l-1,l-1), b89 = m_T.coeff(l-1,l),\n                                    b99 = m_T.coeff(l,l);\n\n        x = ( (a88/b88 - a11/b11)*(a99/b99 - a11/b11) - (a89/b99)*(a98/b88) + (a98/b88)*(b89/b99)*(a11/b11) ) * (b11/a21)\n          + a12/b22 - (a11/b11)*(b12/b22);\n        y = (a22/b22-a11/b11) - (a21/b11)*(b12/b22) - (a88/b88-a11/b11) - (a99/b99-a11/b11) + (a98/b88)*(b89/b99);\n        z = a32/b22;\n      }\n\n      JRs G;\n\n      for (Index k=f; k<=l-2; k++)\n      {\n        // variables for Householder reflections\n        Vector2s essential2;\n        Scalar tau, beta;\n\n        Vector3s hr(x,y,z);\n\n        // Q_k to annihilate S(k+1,k-1) and S(k+2,k-1)\n        hr.makeHouseholderInPlace(tau, beta);\n        essential2 = hr.template bottomRows<2>();\n        Index fc=(std::max)(k-1,Index(0));  // first col to update\n        m_S.template middleRows<3>(k).rightCols(dim-fc).applyHouseholderOnTheLeft(essential2, tau, m_workspace.data());\n        m_T.template middleRows<3>(k).rightCols(dim-fc).applyHouseholderOnTheLeft(essential2, tau, m_workspace.data());\n        if (m_computeQZ)\n          m_Q.template middleCols<3>(k).applyHouseholderOnTheRight(essential2, tau, m_workspace.data());\n        if (k>f)\n          m_S.coeffRef(k+2,k-1) = m_S.coeffRef(k+1,k-1) = Scalar(0.0);\n\n        // Z_{k1} to annihilate T(k+2,k+1) and T(k+2,k)\n        hr << m_T.coeff(k+2,k+2),m_T.coeff(k+2,k),m_T.coeff(k+2,k+1);\n        hr.makeHouseholderInPlace(tau, beta);\n        essential2 = hr.template bottomRows<2>();\n        {\n          Index lr = (std::min)(k+4,dim); // last row to update\n          Map<Matrix<Scalar,Dynamic,1> > tmp(m_workspace.data(),lr);\n          // S\n          tmp = m_S.template middleCols<2>(k).topRows(lr) * essential2;\n          tmp += m_S.col(k+2).head(lr);\n          m_S.col(k+2).head(lr) -= tau*tmp;\n          m_S.template middleCols<2>(k).topRows(lr) -= (tau*tmp) * essential2.adjoint();\n          // T\n          tmp = m_T.template middleCols<2>(k).topRows(lr) * essential2;\n          tmp += m_T.col(k+2).head(lr);\n          m_T.col(k+2).head(lr) -= tau*tmp;\n          m_T.template middleCols<2>(k).topRows(lr) -= (tau*tmp) * essential2.adjoint();\n        }\n        if (m_computeQZ)\n        {\n          // Z\n          Map<Matrix<Scalar,1,Dynamic> > tmp(m_workspace.data(),dim);\n          tmp = essential2.adjoint()*(m_Z.template middleRows<2>(k));\n          tmp += m_Z.row(k+2);\n          m_Z.row(k+2) -= tau*tmp;\n          m_Z.template middleRows<2>(k) -= essential2 * (tau*tmp);\n        }\n        m_T.coeffRef(k+2,k) = m_T.coeffRef(k+2,k+1) = Scalar(0.0);\n\n        // Z_{k2} to annihilate T(k+1,k)\n        G.makeGivens(m_T.coeff(k+1,k+1), m_T.coeff(k+1,k));\n        m_S.applyOnTheRight(k+1,k,G);\n        m_T.applyOnTheRight(k+1,k,G);\n        // update Z\n        if (m_computeQZ)\n          m_Z.applyOnTheLeft(k+1,k,G.adjoint());\n        m_T.coeffRef(k+1,k) = Scalar(0.0);\n\n        // update x,y,z\n        x = m_S.coeff(k+1,k);\n        y = m_S.coeff(k+2,k);\n        if (k < l-2)\n          z = m_S.coeff(k+3,k);\n      } // loop over k\n\n      // Q_{n-1} to annihilate y = S(l,l-2)\n      G.makeGivens(x,y);\n      m_S.applyOnTheLeft(l-1,l,G.adjoint());\n      m_T.applyOnTheLeft(l-1,l,G.adjoint());\n      if (m_computeQZ)\n        m_Q.applyOnTheRight(l-1,l,G);\n      m_S.coeffRef(l,l-2) = Scalar(0.0);\n\n      // Z_{n-1} to annihilate T(l,l-1)\n      G.makeGivens(m_T.coeff(l,l),m_T.coeff(l,l-1));\n      m_S.applyOnTheRight(l,l-1,G);\n      m_T.applyOnTheRight(l,l-1,G);\n      if (m_computeQZ)\n        m_Z.applyOnTheLeft(l,l-1,G.adjoint());\n      m_T.coeffRef(l,l-1) = Scalar(0.0);\n    }\n\n  template<typename MatrixType>\n    RealQZ<MatrixType>& RealQZ<MatrixType>::compute(const MatrixType& A_in, const MatrixType& B_in, bool computeQZ)\n    {\n\n      const Index dim = A_in.cols();\n\n      eigen_assert (A_in.rows()==dim && A_in.cols()==dim \n          && B_in.rows()==dim && B_in.cols()==dim \n          && \"Need square matrices of the same dimension\");\n\n      m_isInitialized = true;\n      m_computeQZ = computeQZ;\n      m_S = A_in; m_T = B_in;\n      m_workspace.resize(dim*2);\n      m_global_iter = 0;\n\n      // entrance point: hessenberg triangular decomposition\n      hessenbergTriangular();\n      // compute L1 vector norms of T, S into m_normOfS, m_normOfT\n      computeNorms();\n\n      Index l = dim-1, \n            f, \n            local_iter = 0;\n\n      while (l>0 && local_iter<m_maxIters)\n      {\n        f = findSmallSubdiagEntry(l);\n        // now rows and columns f..l (including) decouple from the rest of the problem\n        if (f>0) m_S.coeffRef(f,f-1) = Scalar(0.0);\n        if (f == l) // One root found\n        {\n          l--;\n          local_iter = 0;\n        }\n        else if (f == l-1) // Two roots found\n        {\n          splitOffTwoRows(f);\n          l -= 2;\n          local_iter = 0;\n        }\n        else // No convergence yet\n        {\n          // if there's zero on diagonal of T, we can isolate an eigenvalue with Givens rotations\n          Index z = findSmallDiagEntry(f,l);\n          if (z>=f)\n          {\n            // zero found\n            pushDownZero(z,f,l);\n          }\n          else\n          {\n            // We are sure now that S.block(f,f, l-f+1,l-f+1) is underuced upper-Hessenberg \n            // and T.block(f,f, l-f+1,l-f+1) is invertible uper-triangular, which allows to\n            // apply a QR-like iteration to rows and columns f..l.\n            step(f,l, local_iter);\n            local_iter++;\n            m_global_iter++;\n          }\n        }\n      }\n      // check if we converged before reaching iterations limit\n      m_info = (local_iter<m_maxIters) ? Success : NoConvergence;\n\n      // For each non triangular 2x2 diagonal block of S,\n      //    reduce the respective 2x2 diagonal block of T to positive diagonal form using 2x2 SVD.\n      // This step is not mandatory for QZ, but it does help further extraction of eigenvalues/eigenvectors,\n      // and is in par with Lapack/Matlab QZ.\n      if(m_info==Success)\n      {\n        for(Index i=0; i<dim-1; ++i)\n        {\n          if(m_S.coeff(i+1, i) != Scalar(0))\n          {\n            JacobiRotation<Scalar> j_left, j_right;\n            internal::real_2x2_jacobi_svd(m_T, i, i+1, &j_left, &j_right);\n\n            // Apply resulting Jacobi rotations\n            m_S.applyOnTheLeft(i,i+1,j_left);\n            m_S.applyOnTheRight(i,i+1,j_right);\n            m_T.applyOnTheLeft(i,i+1,j_left);\n            m_T.applyOnTheRight(i,i+1,j_right);\n            m_T(i+1,i) = m_T(i,i+1) = Scalar(0);\n\n            if(m_computeQZ) {\n              m_Q.applyOnTheRight(i,i+1,j_left.transpose());\n              m_Z.applyOnTheLeft(i,i+1,j_right.transpose());\n            }\n\n            i++;\n          }\n        }\n      }\n\n      return *this;\n    } // end compute\n\n} // end namespace Eigen\n\n#endif //EIGEN_REAL_QZ\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Eigenvalues/RealSchur.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_REAL_SCHUR_H\n#define EIGEN_REAL_SCHUR_H\n\n#include \"./HessenbergDecomposition.h\"\n\nnamespace Eigen { \n\n/** \\eigenvalues_module \\ingroup Eigenvalues_Module\n  *\n  *\n  * \\class RealSchur\n  *\n  * \\brief Performs a real Schur decomposition of a square matrix\n  *\n  * \\tparam _MatrixType the type of the matrix of which we are computing the\n  * real Schur decomposition; this is expected to be an instantiation of the\n  * Matrix class template.\n  *\n  * Given a real square matrix A, this class computes the real Schur\n  * decomposition: \\f$ A = U T U^T \\f$ where U is a real orthogonal matrix and\n  * T is a real quasi-triangular matrix. An orthogonal matrix is a matrix whose\n  * inverse is equal to its transpose, \\f$ U^{-1} = U^T \\f$. A quasi-triangular\n  * matrix is a block-triangular matrix whose diagonal consists of 1-by-1\n  * blocks and 2-by-2 blocks with complex eigenvalues. The eigenvalues of the\n  * blocks on the diagonal of T are the same as the eigenvalues of the matrix\n  * A, and thus the real Schur decomposition is used in EigenSolver to compute\n  * the eigendecomposition of a matrix.\n  *\n  * Call the function compute() to compute the real Schur decomposition of a\n  * given matrix. Alternatively, you can use the RealSchur(const MatrixType&, bool)\n  * constructor which computes the real Schur decomposition at construction\n  * time. Once the decomposition is computed, you can use the matrixU() and\n  * matrixT() functions to retrieve the matrices U and T in the decomposition.\n  *\n  * The documentation of RealSchur(const MatrixType&, bool) contains an example\n  * of the typical use of this class.\n  *\n  * \\note The implementation is adapted from\n  * <a href=\"http://math.nist.gov/javanumerics/jama/\">JAMA</a> (public domain).\n  * Their code is based on EISPACK.\n  *\n  * \\sa class ComplexSchur, class EigenSolver, class ComplexEigenSolver\n  */\ntemplate<typename _MatrixType> class RealSchur\n{\n  public:\n    typedef _MatrixType MatrixType;\n    enum {\n      RowsAtCompileTime = MatrixType::RowsAtCompileTime,\n      ColsAtCompileTime = MatrixType::ColsAtCompileTime,\n      Options = MatrixType::Options,\n      MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,\n      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime\n    };\n    typedef typename MatrixType::Scalar Scalar;\n    typedef std::complex<typename NumTraits<Scalar>::Real> ComplexScalar;\n    typedef Eigen::Index Index; ///< \\deprecated since Eigen 3.3\n\n    typedef Matrix<ComplexScalar, ColsAtCompileTime, 1, Options & ~RowMajor, MaxColsAtCompileTime, 1> EigenvalueType;\n    typedef Matrix<Scalar, ColsAtCompileTime, 1, Options & ~RowMajor, MaxColsAtCompileTime, 1> ColumnVectorType;\n\n    /** \\brief Default constructor.\n      *\n      * \\param [in] size  Positive integer, size of the matrix whose Schur decomposition will be computed.\n      *\n      * The default constructor is useful in cases in which the user intends to\n      * perform decompositions via compute().  The \\p size parameter is only\n      * used as a hint. It is not an error to give a wrong \\p size, but it may\n      * impair performance.\n      *\n      * \\sa compute() for an example.\n      */\n    explicit RealSchur(Index size = RowsAtCompileTime==Dynamic ? 1 : RowsAtCompileTime)\n            : m_matT(size, size),\n              m_matU(size, size),\n              m_workspaceVector(size),\n              m_hess(size),\n              m_isInitialized(false),\n              m_matUisUptodate(false),\n              m_maxIters(-1)\n    { }\n\n    /** \\brief Constructor; computes real Schur decomposition of given matrix. \n      * \n      * \\param[in]  matrix    Square matrix whose Schur decomposition is to be computed.\n      * \\param[in]  computeU  If true, both T and U are computed; if false, only T is computed.\n      *\n      * This constructor calls compute() to compute the Schur decomposition.\n      *\n      * Example: \\include RealSchur_RealSchur_MatrixType.cpp\n      * Output: \\verbinclude RealSchur_RealSchur_MatrixType.out\n      */\n    template<typename InputType>\n    explicit RealSchur(const EigenBase<InputType>& matrix, bool computeU = true)\n            : m_matT(matrix.rows(),matrix.cols()),\n              m_matU(matrix.rows(),matrix.cols()),\n              m_workspaceVector(matrix.rows()),\n              m_hess(matrix.rows()),\n              m_isInitialized(false),\n              m_matUisUptodate(false),\n              m_maxIters(-1)\n    {\n      compute(matrix.derived(), computeU);\n    }\n\n    /** \\brief Returns the orthogonal matrix in the Schur decomposition. \n      *\n      * \\returns A const reference to the matrix U.\n      *\n      * \\pre Either the constructor RealSchur(const MatrixType&, bool) or the\n      * member function compute(const MatrixType&, bool) has been called before\n      * to compute the Schur decomposition of a matrix, and \\p computeU was set\n      * to true (the default value).\n      *\n      * \\sa RealSchur(const MatrixType&, bool) for an example\n      */\n    const MatrixType& matrixU() const\n    {\n      eigen_assert(m_isInitialized && \"RealSchur is not initialized.\");\n      eigen_assert(m_matUisUptodate && \"The matrix U has not been computed during the RealSchur decomposition.\");\n      return m_matU;\n    }\n\n    /** \\brief Returns the quasi-triangular matrix in the Schur decomposition. \n      *\n      * \\returns A const reference to the matrix T.\n      *\n      * \\pre Either the constructor RealSchur(const MatrixType&, bool) or the\n      * member function compute(const MatrixType&, bool) has been called before\n      * to compute the Schur decomposition of a matrix.\n      *\n      * \\sa RealSchur(const MatrixType&, bool) for an example\n      */\n    const MatrixType& matrixT() const\n    {\n      eigen_assert(m_isInitialized && \"RealSchur is not initialized.\");\n      return m_matT;\n    }\n  \n    /** \\brief Computes Schur decomposition of given matrix. \n      * \n      * \\param[in]  matrix    Square matrix whose Schur decomposition is to be computed.\n      * \\param[in]  computeU  If true, both T and U are computed; if false, only T is computed.\n      * \\returns    Reference to \\c *this\n      *\n      * The Schur decomposition is computed by first reducing the matrix to\n      * Hessenberg form using the class HessenbergDecomposition. The Hessenberg\n      * matrix is then reduced to triangular form by performing Francis QR\n      * iterations with implicit double shift. The cost of computing the Schur\n      * decomposition depends on the number of iterations; as a rough guide, it\n      * may be taken to be \\f$25n^3\\f$ flops if \\a computeU is true and\n      * \\f$10n^3\\f$ flops if \\a computeU is false.\n      *\n      * Example: \\include RealSchur_compute.cpp\n      * Output: \\verbinclude RealSchur_compute.out\n      *\n      * \\sa compute(const MatrixType&, bool, Index)\n      */\n    template<typename InputType>\n    RealSchur& compute(const EigenBase<InputType>& matrix, bool computeU = true);\n\n    /** \\brief Computes Schur decomposition of a Hessenberg matrix H = Z T Z^T\n     *  \\param[in] matrixH Matrix in Hessenberg form H\n     *  \\param[in] matrixQ orthogonal matrix Q that transform a matrix A to H : A = Q H Q^T\n     *  \\param computeU Computes the matriX U of the Schur vectors\n     * \\return Reference to \\c *this\n     * \n     *  This routine assumes that the matrix is already reduced in Hessenberg form matrixH\n     *  using either the class HessenbergDecomposition or another mean. \n     *  It computes the upper quasi-triangular matrix T of the Schur decomposition of H\n     *  When computeU is true, this routine computes the matrix U such that \n     *  A = U T U^T =  (QZ) T (QZ)^T = Q H Q^T where A is the initial matrix\n     * \n     * NOTE Q is referenced if computeU is true; so, if the initial orthogonal matrix\n     * is not available, the user should give an identity matrix (Q.setIdentity())\n     * \n     * \\sa compute(const MatrixType&, bool)\n     */\n    template<typename HessMatrixType, typename OrthMatrixType>\n    RealSchur& computeFromHessenberg(const HessMatrixType& matrixH, const OrthMatrixType& matrixQ,  bool computeU);\n    /** \\brief Reports whether previous computation was successful.\n      *\n      * \\returns \\c Success if computation was succesful, \\c NoConvergence otherwise.\n      */\n    ComputationInfo info() const\n    {\n      eigen_assert(m_isInitialized && \"RealSchur is not initialized.\");\n      return m_info;\n    }\n\n    /** \\brief Sets the maximum number of iterations allowed. \n      *\n      * If not specified by the user, the maximum number of iterations is m_maxIterationsPerRow times the size\n      * of the matrix.\n      */\n    RealSchur& setMaxIterations(Index maxIters)\n    {\n      m_maxIters = maxIters;\n      return *this;\n    }\n\n    /** \\brief Returns the maximum number of iterations. */\n    Index getMaxIterations()\n    {\n      return m_maxIters;\n    }\n\n    /** \\brief Maximum number of iterations per row.\n      *\n      * If not otherwise specified, the maximum number of iterations is this number times the size of the\n      * matrix. It is currently set to 40.\n      */\n    static const int m_maxIterationsPerRow = 40;\n\n  private:\n    \n    MatrixType m_matT;\n    MatrixType m_matU;\n    ColumnVectorType m_workspaceVector;\n    HessenbergDecomposition<MatrixType> m_hess;\n    ComputationInfo m_info;\n    bool m_isInitialized;\n    bool m_matUisUptodate;\n    Index m_maxIters;\n\n    typedef Matrix<Scalar,3,1> Vector3s;\n\n    Scalar computeNormOfT();\n    Index findSmallSubdiagEntry(Index iu);\n    void splitOffTwoRows(Index iu, bool computeU, const Scalar& exshift);\n    void computeShift(Index iu, Index iter, Scalar& exshift, Vector3s& shiftInfo);\n    void initFrancisQRStep(Index il, Index iu, const Vector3s& shiftInfo, Index& im, Vector3s& firstHouseholderVector);\n    void performFrancisQRStep(Index il, Index im, Index iu, bool computeU, const Vector3s& firstHouseholderVector, Scalar* workspace);\n};\n\n\ntemplate<typename MatrixType>\ntemplate<typename InputType>\nRealSchur<MatrixType>& RealSchur<MatrixType>::compute(const EigenBase<InputType>& matrix, bool computeU)\n{\n  const Scalar considerAsZero = (std::numeric_limits<Scalar>::min)();\n\n  eigen_assert(matrix.cols() == matrix.rows());\n  Index maxIters = m_maxIters;\n  if (maxIters == -1)\n    maxIters = m_maxIterationsPerRow * matrix.rows();\n\n  Scalar scale = matrix.derived().cwiseAbs().maxCoeff();\n  if(scale<considerAsZero)\n  {\n    m_matT.setZero(matrix.rows(),matrix.cols());\n    if(computeU)\n      m_matU.setIdentity(matrix.rows(),matrix.cols());\n    m_info = Success;\n    m_isInitialized = true;\n    m_matUisUptodate = computeU;\n    return *this;\n  }\n\n  // Step 1. Reduce to Hessenberg form\n  m_hess.compute(matrix.derived()/scale);\n\n  // Step 2. Reduce to real Schur form  \n  computeFromHessenberg(m_hess.matrixH(), m_hess.matrixQ(), computeU);\n\n  m_matT *= scale;\n  \n  return *this;\n}\ntemplate<typename MatrixType>\ntemplate<typename HessMatrixType, typename OrthMatrixType>\nRealSchur<MatrixType>& RealSchur<MatrixType>::computeFromHessenberg(const HessMatrixType& matrixH, const OrthMatrixType& matrixQ,  bool computeU)\n{\n  using std::abs;\n\n  m_matT = matrixH;\n  if(computeU)\n    m_matU = matrixQ;\n  \n  Index maxIters = m_maxIters;\n  if (maxIters == -1)\n    maxIters = m_maxIterationsPerRow * matrixH.rows();\n  m_workspaceVector.resize(m_matT.cols());\n  Scalar* workspace = &m_workspaceVector.coeffRef(0);\n\n  // The matrix m_matT is divided in three parts. \n  // Rows 0,...,il-1 are decoupled from the rest because m_matT(il,il-1) is zero. \n  // Rows il,...,iu is the part we are working on (the active window).\n  // Rows iu+1,...,end are already brought in triangular form.\n  Index iu = m_matT.cols() - 1;\n  Index iter = 0;      // iteration count for current eigenvalue\n  Index totalIter = 0; // iteration count for whole matrix\n  Scalar exshift(0);   // sum of exceptional shifts\n  Scalar norm = computeNormOfT();\n\n  if(norm!=Scalar(0))\n  {\n    while (iu >= 0)\n    {\n      Index il = findSmallSubdiagEntry(iu);\n\n      // Check for convergence\n      if (il == iu) // One root found\n      {\n        m_matT.coeffRef(iu,iu) = m_matT.coeff(iu,iu) + exshift;\n        if (iu > 0)\n          m_matT.coeffRef(iu, iu-1) = Scalar(0);\n        iu--;\n        iter = 0;\n      }\n      else if (il == iu-1) // Two roots found\n      {\n        splitOffTwoRows(iu, computeU, exshift);\n        iu -= 2;\n        iter = 0;\n      }\n      else // No convergence yet\n      {\n        // The firstHouseholderVector vector has to be initialized to something to get rid of a silly GCC warning (-O1 -Wall -DNDEBUG )\n        Vector3s firstHouseholderVector = Vector3s::Zero(), shiftInfo;\n        computeShift(iu, iter, exshift, shiftInfo);\n        iter = iter + 1;\n        totalIter = totalIter + 1;\n        if (totalIter > maxIters) break;\n        Index im;\n        initFrancisQRStep(il, iu, shiftInfo, im, firstHouseholderVector);\n        performFrancisQRStep(il, im, iu, computeU, firstHouseholderVector, workspace);\n      }\n    }\n  }\n  if(totalIter <= maxIters)\n    m_info = Success;\n  else\n    m_info = NoConvergence;\n\n  m_isInitialized = true;\n  m_matUisUptodate = computeU;\n  return *this;\n}\n\n/** \\internal Computes and returns vector L1 norm of T */\ntemplate<typename MatrixType>\ninline typename MatrixType::Scalar RealSchur<MatrixType>::computeNormOfT()\n{\n  const Index size = m_matT.cols();\n  // FIXME to be efficient the following would requires a triangular reduxion code\n  // Scalar norm = m_matT.upper().cwiseAbs().sum() \n  //               + m_matT.bottomLeftCorner(size-1,size-1).diagonal().cwiseAbs().sum();\n  Scalar norm(0);\n  for (Index j = 0; j < size; ++j)\n    norm += m_matT.col(j).segment(0, (std::min)(size,j+2)).cwiseAbs().sum();\n  return norm;\n}\n\n/** \\internal Look for single small sub-diagonal element and returns its index */\ntemplate<typename MatrixType>\ninline Index RealSchur<MatrixType>::findSmallSubdiagEntry(Index iu)\n{\n  using std::abs;\n  Index res = iu;\n  while (res > 0)\n  {\n    Scalar s = abs(m_matT.coeff(res-1,res-1)) + abs(m_matT.coeff(res,res));\n    if (abs(m_matT.coeff(res,res-1)) <= NumTraits<Scalar>::epsilon() * s)\n      break;\n    res--;\n  }\n  return res;\n}\n\n/** \\internal Update T given that rows iu-1 and iu decouple from the rest. */\ntemplate<typename MatrixType>\ninline void RealSchur<MatrixType>::splitOffTwoRows(Index iu, bool computeU, const Scalar& exshift)\n{\n  using std::sqrt;\n  using std::abs;\n  const Index size = m_matT.cols();\n\n  // The eigenvalues of the 2x2 matrix [a b; c d] are \n  // trace +/- sqrt(discr/4) where discr = tr^2 - 4*det, tr = a + d, det = ad - bc\n  Scalar p = Scalar(0.5) * (m_matT.coeff(iu-1,iu-1) - m_matT.coeff(iu,iu));\n  Scalar q = p * p + m_matT.coeff(iu,iu-1) * m_matT.coeff(iu-1,iu);   // q = tr^2 / 4 - det = discr/4\n  m_matT.coeffRef(iu,iu) += exshift;\n  m_matT.coeffRef(iu-1,iu-1) += exshift;\n\n  if (q >= Scalar(0)) // Two real eigenvalues\n  {\n    Scalar z = sqrt(abs(q));\n    JacobiRotation<Scalar> rot;\n    if (p >= Scalar(0))\n      rot.makeGivens(p + z, m_matT.coeff(iu, iu-1));\n    else\n      rot.makeGivens(p - z, m_matT.coeff(iu, iu-1));\n\n    m_matT.rightCols(size-iu+1).applyOnTheLeft(iu-1, iu, rot.adjoint());\n    m_matT.topRows(iu+1).applyOnTheRight(iu-1, iu, rot);\n    m_matT.coeffRef(iu, iu-1) = Scalar(0); \n    if (computeU)\n      m_matU.applyOnTheRight(iu-1, iu, rot);\n  }\n\n  if (iu > 1) \n    m_matT.coeffRef(iu-1, iu-2) = Scalar(0);\n}\n\n/** \\internal Form shift in shiftInfo, and update exshift if an exceptional shift is performed. */\ntemplate<typename MatrixType>\ninline void RealSchur<MatrixType>::computeShift(Index iu, Index iter, Scalar& exshift, Vector3s& shiftInfo)\n{\n  using std::sqrt;\n  using std::abs;\n  shiftInfo.coeffRef(0) = m_matT.coeff(iu,iu);\n  shiftInfo.coeffRef(1) = m_matT.coeff(iu-1,iu-1);\n  shiftInfo.coeffRef(2) = m_matT.coeff(iu,iu-1) * m_matT.coeff(iu-1,iu);\n\n  // Wilkinson's original ad hoc shift\n  if (iter == 10)\n  {\n    exshift += shiftInfo.coeff(0);\n    for (Index i = 0; i <= iu; ++i)\n      m_matT.coeffRef(i,i) -= shiftInfo.coeff(0);\n    Scalar s = abs(m_matT.coeff(iu,iu-1)) + abs(m_matT.coeff(iu-1,iu-2));\n    shiftInfo.coeffRef(0) = Scalar(0.75) * s;\n    shiftInfo.coeffRef(1) = Scalar(0.75) * s;\n    shiftInfo.coeffRef(2) = Scalar(-0.4375) * s * s;\n  }\n\n  // MATLAB's new ad hoc shift\n  if (iter == 30)\n  {\n    Scalar s = (shiftInfo.coeff(1) - shiftInfo.coeff(0)) / Scalar(2.0);\n    s = s * s + shiftInfo.coeff(2);\n    if (s > Scalar(0))\n    {\n      s = sqrt(s);\n      if (shiftInfo.coeff(1) < shiftInfo.coeff(0))\n        s = -s;\n      s = s + (shiftInfo.coeff(1) - shiftInfo.coeff(0)) / Scalar(2.0);\n      s = shiftInfo.coeff(0) - shiftInfo.coeff(2) / s;\n      exshift += s;\n      for (Index i = 0; i <= iu; ++i)\n        m_matT.coeffRef(i,i) -= s;\n      shiftInfo.setConstant(Scalar(0.964));\n    }\n  }\n}\n\n/** \\internal Compute index im at which Francis QR step starts and the first Householder vector. */\ntemplate<typename MatrixType>\ninline void RealSchur<MatrixType>::initFrancisQRStep(Index il, Index iu, const Vector3s& shiftInfo, Index& im, Vector3s& firstHouseholderVector)\n{\n  using std::abs;\n  Vector3s& v = firstHouseholderVector; // alias to save typing\n\n  for (im = iu-2; im >= il; --im)\n  {\n    const Scalar Tmm = m_matT.coeff(im,im);\n    const Scalar r = shiftInfo.coeff(0) - Tmm;\n    const Scalar s = shiftInfo.coeff(1) - Tmm;\n    v.coeffRef(0) = (r * s - shiftInfo.coeff(2)) / m_matT.coeff(im+1,im) + m_matT.coeff(im,im+1);\n    v.coeffRef(1) = m_matT.coeff(im+1,im+1) - Tmm - r - s;\n    v.coeffRef(2) = m_matT.coeff(im+2,im+1);\n    if (im == il) {\n      break;\n    }\n    const Scalar lhs = m_matT.coeff(im,im-1) * (abs(v.coeff(1)) + abs(v.coeff(2)));\n    const Scalar rhs = v.coeff(0) * (abs(m_matT.coeff(im-1,im-1)) + abs(Tmm) + abs(m_matT.coeff(im+1,im+1)));\n    if (abs(lhs) < NumTraits<Scalar>::epsilon() * rhs)\n      break;\n  }\n}\n\n/** \\internal Perform a Francis QR step involving rows il:iu and columns im:iu. */\ntemplate<typename MatrixType>\ninline void RealSchur<MatrixType>::performFrancisQRStep(Index il, Index im, Index iu, bool computeU, const Vector3s& firstHouseholderVector, Scalar* workspace)\n{\n  eigen_assert(im >= il);\n  eigen_assert(im <= iu-2);\n\n  const Index size = m_matT.cols();\n\n  for (Index k = im; k <= iu-2; ++k)\n  {\n    bool firstIteration = (k == im);\n\n    Vector3s v;\n    if (firstIteration)\n      v = firstHouseholderVector;\n    else\n      v = m_matT.template block<3,1>(k,k-1);\n\n    Scalar tau, beta;\n    Matrix<Scalar, 2, 1> ess;\n    v.makeHouseholder(ess, tau, beta);\n    \n    if (beta != Scalar(0)) // if v is not zero\n    {\n      if (firstIteration && k > il)\n        m_matT.coeffRef(k,k-1) = -m_matT.coeff(k,k-1);\n      else if (!firstIteration)\n        m_matT.coeffRef(k,k-1) = beta;\n\n      // These Householder transformations form the O(n^3) part of the algorithm\n      m_matT.block(k, k, 3, size-k).applyHouseholderOnTheLeft(ess, tau, workspace);\n      m_matT.block(0, k, (std::min)(iu,k+3) + 1, 3).applyHouseholderOnTheRight(ess, tau, workspace);\n      if (computeU)\n        m_matU.block(0, k, size, 3).applyHouseholderOnTheRight(ess, tau, workspace);\n    }\n  }\n\n  Matrix<Scalar, 2, 1> v = m_matT.template block<2,1>(iu-1, iu-2);\n  Scalar tau, beta;\n  Matrix<Scalar, 1, 1> ess;\n  v.makeHouseholder(ess, tau, beta);\n\n  if (beta != Scalar(0)) // if v is not zero\n  {\n    m_matT.coeffRef(iu-1, iu-2) = beta;\n    m_matT.block(iu-1, iu-1, 2, size-iu+1).applyHouseholderOnTheLeft(ess, tau, workspace);\n    m_matT.block(0, iu-1, iu+1, 2).applyHouseholderOnTheRight(ess, tau, workspace);\n    if (computeU)\n      m_matU.block(0, iu-1, size, 2).applyHouseholderOnTheRight(ess, tau, workspace);\n  }\n\n  // clean up pollution due to round-off errors\n  for (Index i = im+2; i <= iu; ++i)\n  {\n    m_matT.coeffRef(i,i-2) = Scalar(0);\n    if (i > im+2)\n      m_matT.coeffRef(i,i-3) = Scalar(0);\n  }\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_REAL_SCHUR_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Eigenvalues/RealSchur_LAPACKE.h",
    "content": "/*\n Copyright (c) 2011, Intel Corporation. All rights reserved.\n\n Redistribution and use in source and binary forms, with or without modification,\n are permitted provided that the following conditions are met:\n\n * Redistributions of source code must retain the above copyright notice, this\n   list of conditions and the following disclaimer.\n * Redistributions in binary form must reproduce the above copyright notice,\n   this list of conditions and the following disclaimer in the documentation\n   and/or other materials provided with the distribution.\n * Neither the name of Intel Corporation nor the names of its contributors may\n   be used to endorse or promote products derived from this software without\n   specific prior written permission.\n\n THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\" AND\n ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED\n WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\n DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR\n ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES\n (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;\n LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON\n ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT\n (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS\n SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n\n ********************************************************************************\n *   Content : Eigen bindings to LAPACKe\n *    Real Schur needed to real unsymmetrical eigenvalues/eigenvectors.\n ********************************************************************************\n*/\n\n#ifndef EIGEN_REAL_SCHUR_LAPACKE_H\n#define EIGEN_REAL_SCHUR_LAPACKE_H\n\nnamespace Eigen { \n\n/** \\internal Specialization for the data types supported by LAPACKe */\n\n#define EIGEN_LAPACKE_SCHUR_REAL(EIGTYPE, LAPACKE_TYPE, LAPACKE_PREFIX, LAPACKE_PREFIX_U, EIGCOLROW, LAPACKE_COLROW) \\\ntemplate<> template<typename InputType> inline \\\nRealSchur<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >& \\\nRealSchur<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >::compute(const EigenBase<InputType>& matrix, bool computeU) \\\n{ \\\n  eigen_assert(matrix.cols() == matrix.rows()); \\\n\\\n  lapack_int n = internal::convert_index<lapack_int>(matrix.cols()), sdim, info; \\\n  lapack_int matrix_order = LAPACKE_COLROW; \\\n  char jobvs, sort='N'; \\\n  LAPACK_##LAPACKE_PREFIX_U##_SELECT2 select = 0; \\\n  jobvs = (computeU) ? 'V' : 'N'; \\\n  m_matU.resize(n, n); \\\n  lapack_int ldvs  = internal::convert_index<lapack_int>(m_matU.outerStride()); \\\n  m_matT = matrix; \\\n  lapack_int lda = internal::convert_index<lapack_int>(m_matT.outerStride()); \\\n  Matrix<EIGTYPE, Dynamic, Dynamic> wr, wi; \\\n  wr.resize(n, 1); wi.resize(n, 1); \\\n  info = LAPACKE_##LAPACKE_PREFIX##gees( matrix_order, jobvs, sort, select, n, (LAPACKE_TYPE*)m_matT.data(), lda, &sdim, (LAPACKE_TYPE*)wr.data(), (LAPACKE_TYPE*)wi.data(), (LAPACKE_TYPE*)m_matU.data(), ldvs ); \\\n  if(info == 0) \\\n    m_info = Success; \\\n  else \\\n    m_info = NoConvergence; \\\n\\\n  m_isInitialized = true; \\\n  m_matUisUptodate = computeU; \\\n  return *this; \\\n\\\n}\n\nEIGEN_LAPACKE_SCHUR_REAL(double,   double, d, D, ColMajor, LAPACK_COL_MAJOR)\nEIGEN_LAPACKE_SCHUR_REAL(float,    float,  s, S, ColMajor, LAPACK_COL_MAJOR)\nEIGEN_LAPACKE_SCHUR_REAL(double,   double, d, D, RowMajor, LAPACK_ROW_MAJOR)\nEIGEN_LAPACKE_SCHUR_REAL(float,    float,  s, S, RowMajor, LAPACK_ROW_MAJOR)\n\n} // end namespace Eigen\n\n#endif // EIGEN_REAL_SCHUR_LAPACKE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SELFADJOINTEIGENSOLVER_H\n#define EIGEN_SELFADJOINTEIGENSOLVER_H\n\n#include \"./Tridiagonalization.h\"\n\nnamespace Eigen { \n\ntemplate<typename _MatrixType>\nclass GeneralizedSelfAdjointEigenSolver;\n\nnamespace internal {\ntemplate<typename SolverType,int Size,bool IsComplex> struct direct_selfadjoint_eigenvalues;\ntemplate<typename MatrixType, typename DiagType, typename SubDiagType>\nComputationInfo computeFromTridiagonal_impl(DiagType& diag, SubDiagType& subdiag, const Index maxIterations, bool computeEigenvectors, MatrixType& eivec);\n}\n\n/** \\eigenvalues_module \\ingroup Eigenvalues_Module\n  *\n  *\n  * \\class SelfAdjointEigenSolver\n  *\n  * \\brief Computes eigenvalues and eigenvectors of selfadjoint matrices\n  *\n  * \\tparam _MatrixType the type of the matrix of which we are computing the\n  * eigendecomposition; this is expected to be an instantiation of the Matrix\n  * class template.\n  *\n  * A matrix \\f$ A \\f$ is selfadjoint if it equals its adjoint. For real\n  * matrices, this means that the matrix is symmetric: it equals its\n  * transpose. This class computes the eigenvalues and eigenvectors of a\n  * selfadjoint matrix. These are the scalars \\f$ \\lambda \\f$ and vectors\n  * \\f$ v \\f$ such that \\f$ Av = \\lambda v \\f$.  The eigenvalues of a\n  * selfadjoint matrix are always real. If \\f$ D \\f$ is a diagonal matrix with\n  * the eigenvalues on the diagonal, and \\f$ V \\f$ is a matrix with the\n  * eigenvectors as its columns, then \\f$ A = V D V^{-1} \\f$ (for selfadjoint\n  * matrices, the matrix \\f$ V \\f$ is always invertible). This is called the\n  * eigendecomposition.\n  *\n  * The algorithm exploits the fact that the matrix is selfadjoint, making it\n  * faster and more accurate than the general purpose eigenvalue algorithms\n  * implemented in EigenSolver and ComplexEigenSolver.\n  *\n  * Only the \\b lower \\b triangular \\b part of the input matrix is referenced.\n  *\n  * Call the function compute() to compute the eigenvalues and eigenvectors of\n  * a given matrix. Alternatively, you can use the\n  * SelfAdjointEigenSolver(const MatrixType&, int) constructor which computes\n  * the eigenvalues and eigenvectors at construction time. Once the eigenvalue\n  * and eigenvectors are computed, they can be retrieved with the eigenvalues()\n  * and eigenvectors() functions.\n  *\n  * The documentation for SelfAdjointEigenSolver(const MatrixType&, int)\n  * contains an example of the typical use of this class.\n  *\n  * To solve the \\em generalized eigenvalue problem \\f$ Av = \\lambda Bv \\f$ and\n  * the likes, see the class GeneralizedSelfAdjointEigenSolver.\n  *\n  * \\sa MatrixBase::eigenvalues(), class EigenSolver, class ComplexEigenSolver\n  */\ntemplate<typename _MatrixType> class SelfAdjointEigenSolver\n{\n  public:\n\n    typedef _MatrixType MatrixType;\n    enum {\n      Size = MatrixType::RowsAtCompileTime,\n      ColsAtCompileTime = MatrixType::ColsAtCompileTime,\n      Options = MatrixType::Options,\n      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime\n    };\n    \n    /** \\brief Scalar type for matrices of type \\p _MatrixType. */\n    typedef typename MatrixType::Scalar Scalar;\n    typedef Eigen::Index Index; ///< \\deprecated since Eigen 3.3\n    \n    typedef Matrix<Scalar,Size,Size,ColMajor,MaxColsAtCompileTime,MaxColsAtCompileTime> EigenvectorsType;\n\n    /** \\brief Real scalar type for \\p _MatrixType.\n      *\n      * This is just \\c Scalar if #Scalar is real (e.g., \\c float or\n      * \\c double), and the type of the real part of \\c Scalar if #Scalar is\n      * complex.\n      */\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n    \n    friend struct internal::direct_selfadjoint_eigenvalues<SelfAdjointEigenSolver,Size,NumTraits<Scalar>::IsComplex>;\n\n    /** \\brief Type for vector of eigenvalues as returned by eigenvalues().\n      *\n      * This is a column vector with entries of type #RealScalar.\n      * The length of the vector is the size of \\p _MatrixType.\n      */\n    typedef typename internal::plain_col_type<MatrixType, RealScalar>::type RealVectorType;\n    typedef Tridiagonalization<MatrixType> TridiagonalizationType;\n    typedef typename TridiagonalizationType::SubDiagonalType SubDiagonalType;\n\n    /** \\brief Default constructor for fixed-size matrices.\n      *\n      * The default constructor is useful in cases in which the user intends to\n      * perform decompositions via compute(). This constructor\n      * can only be used if \\p _MatrixType is a fixed-size matrix; use\n      * SelfAdjointEigenSolver(Index) for dynamic-size matrices.\n      *\n      * Example: \\include SelfAdjointEigenSolver_SelfAdjointEigenSolver.cpp\n      * Output: \\verbinclude SelfAdjointEigenSolver_SelfAdjointEigenSolver.out\n      */\n    EIGEN_DEVICE_FUNC\n    SelfAdjointEigenSolver()\n        : m_eivec(),\n          m_eivalues(),\n          m_subdiag(),\n          m_isInitialized(false)\n    { }\n\n    /** \\brief Constructor, pre-allocates memory for dynamic-size matrices.\n      *\n      * \\param [in]  size  Positive integer, size of the matrix whose\n      * eigenvalues and eigenvectors will be computed.\n      *\n      * This constructor is useful for dynamic-size matrices, when the user\n      * intends to perform decompositions via compute(). The \\p size\n      * parameter is only used as a hint. It is not an error to give a wrong\n      * \\p size, but it may impair performance.\n      *\n      * \\sa compute() for an example\n      */\n    EIGEN_DEVICE_FUNC\n    explicit SelfAdjointEigenSolver(Index size)\n        : m_eivec(size, size),\n          m_eivalues(size),\n          m_subdiag(size > 1 ? size - 1 : 1),\n          m_isInitialized(false)\n    {}\n\n    /** \\brief Constructor; computes eigendecomposition of given matrix.\n      *\n      * \\param[in]  matrix  Selfadjoint matrix whose eigendecomposition is to\n      *    be computed. Only the lower triangular part of the matrix is referenced.\n      * \\param[in]  options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly.\n      *\n      * This constructor calls compute(const MatrixType&, int) to compute the\n      * eigenvalues of the matrix \\p matrix. The eigenvectors are computed if\n      * \\p options equals #ComputeEigenvectors.\n      *\n      * Example: \\include SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType.cpp\n      * Output: \\verbinclude SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType.out\n      *\n      * \\sa compute(const MatrixType&, int)\n      */\n    template<typename InputType>\n    EIGEN_DEVICE_FUNC\n    explicit SelfAdjointEigenSolver(const EigenBase<InputType>& matrix, int options = ComputeEigenvectors)\n      : m_eivec(matrix.rows(), matrix.cols()),\n        m_eivalues(matrix.cols()),\n        m_subdiag(matrix.rows() > 1 ? matrix.rows() - 1 : 1),\n        m_isInitialized(false)\n    {\n      compute(matrix.derived(), options);\n    }\n\n    /** \\brief Computes eigendecomposition of given matrix.\n      *\n      * \\param[in]  matrix  Selfadjoint matrix whose eigendecomposition is to\n      *    be computed. Only the lower triangular part of the matrix is referenced.\n      * \\param[in]  options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly.\n      * \\returns    Reference to \\c *this\n      *\n      * This function computes the eigenvalues of \\p matrix.  The eigenvalues()\n      * function can be used to retrieve them.  If \\p options equals #ComputeEigenvectors,\n      * then the eigenvectors are also computed and can be retrieved by\n      * calling eigenvectors().\n      *\n      * This implementation uses a symmetric QR algorithm. The matrix is first\n      * reduced to tridiagonal form using the Tridiagonalization class. The\n      * tridiagonal matrix is then brought to diagonal form with implicit\n      * symmetric QR steps with Wilkinson shift. Details can be found in\n      * Section 8.3 of Golub \\& Van Loan, <i>%Matrix Computations</i>.\n      *\n      * The cost of the computation is about \\f$ 9n^3 \\f$ if the eigenvectors\n      * are required and \\f$ 4n^3/3 \\f$ if they are not required.\n      *\n      * This method reuses the memory in the SelfAdjointEigenSolver object that\n      * was allocated when the object was constructed, if the size of the\n      * matrix does not change.\n      *\n      * Example: \\include SelfAdjointEigenSolver_compute_MatrixType.cpp\n      * Output: \\verbinclude SelfAdjointEigenSolver_compute_MatrixType.out\n      *\n      * \\sa SelfAdjointEigenSolver(const MatrixType&, int)\n      */\n    template<typename InputType>\n    EIGEN_DEVICE_FUNC\n    SelfAdjointEigenSolver& compute(const EigenBase<InputType>& matrix, int options = ComputeEigenvectors);\n    \n    /** \\brief Computes eigendecomposition of given matrix using a closed-form algorithm\n      *\n      * This is a variant of compute(const MatrixType&, int options) which\n      * directly solves the underlying polynomial equation.\n      * \n      * Currently only 2x2 and 3x3 matrices for which the sizes are known at compile time are supported (e.g., Matrix3d).\n      * \n      * This method is usually significantly faster than the QR iterative algorithm\n      * but it might also be less accurate. It is also worth noting that\n      * for 3x3 matrices it involves trigonometric operations which are\n      * not necessarily available for all scalar types.\n      * \n      * For the 3x3 case, we observed the following worst case relative error regarding the eigenvalues:\n      *   - double: 1e-8\n      *   - float:  1e-3\n      *\n      * \\sa compute(const MatrixType&, int options)\n      */\n    EIGEN_DEVICE_FUNC\n    SelfAdjointEigenSolver& computeDirect(const MatrixType& matrix, int options = ComputeEigenvectors);\n\n    /**\n      *\\brief Computes the eigen decomposition from a tridiagonal symmetric matrix\n      *\n      * \\param[in] diag The vector containing the diagonal of the matrix.\n      * \\param[in] subdiag The subdiagonal of the matrix.\n      * \\param[in] options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly.\n      * \\returns Reference to \\c *this\n      *\n      * This function assumes that the matrix has been reduced to tridiagonal form.\n      *\n      * \\sa compute(const MatrixType&, int) for more information\n      */\n    SelfAdjointEigenSolver& computeFromTridiagonal(const RealVectorType& diag, const SubDiagonalType& subdiag , int options=ComputeEigenvectors);\n\n    /** \\brief Returns the eigenvectors of given matrix.\n      *\n      * \\returns  A const reference to the matrix whose columns are the eigenvectors.\n      *\n      * \\pre The eigenvectors have been computed before.\n      *\n      * Column \\f$ k \\f$ of the returned matrix is an eigenvector corresponding\n      * to eigenvalue number \\f$ k \\f$ as returned by eigenvalues().  The\n      * eigenvectors are normalized to have (Euclidean) norm equal to one. If\n      * this object was used to solve the eigenproblem for the selfadjoint\n      * matrix \\f$ A \\f$, then the matrix returned by this function is the\n      * matrix \\f$ V \\f$ in the eigendecomposition \\f$ A = V D V^{-1} \\f$.\n      *\n      * Example: \\include SelfAdjointEigenSolver_eigenvectors.cpp\n      * Output: \\verbinclude SelfAdjointEigenSolver_eigenvectors.out\n      *\n      * \\sa eigenvalues()\n      */\n    EIGEN_DEVICE_FUNC\n    const EigenvectorsType& eigenvectors() const\n    {\n      eigen_assert(m_isInitialized && \"SelfAdjointEigenSolver is not initialized.\");\n      eigen_assert(m_eigenvectorsOk && \"The eigenvectors have not been computed together with the eigenvalues.\");\n      return m_eivec;\n    }\n\n    /** \\brief Returns the eigenvalues of given matrix.\n      *\n      * \\returns A const reference to the column vector containing the eigenvalues.\n      *\n      * \\pre The eigenvalues have been computed before.\n      *\n      * The eigenvalues are repeated according to their algebraic multiplicity,\n      * so there are as many eigenvalues as rows in the matrix. The eigenvalues\n      * are sorted in increasing order.\n      *\n      * Example: \\include SelfAdjointEigenSolver_eigenvalues.cpp\n      * Output: \\verbinclude SelfAdjointEigenSolver_eigenvalues.out\n      *\n      * \\sa eigenvectors(), MatrixBase::eigenvalues()\n      */\n    EIGEN_DEVICE_FUNC\n    const RealVectorType& eigenvalues() const\n    {\n      eigen_assert(m_isInitialized && \"SelfAdjointEigenSolver is not initialized.\");\n      return m_eivalues;\n    }\n\n    /** \\brief Computes the positive-definite square root of the matrix.\n      *\n      * \\returns the positive-definite square root of the matrix\n      *\n      * \\pre The eigenvalues and eigenvectors of a positive-definite matrix\n      * have been computed before.\n      *\n      * The square root of a positive-definite matrix \\f$ A \\f$ is the\n      * positive-definite matrix whose square equals \\f$ A \\f$. This function\n      * uses the eigendecomposition \\f$ A = V D V^{-1} \\f$ to compute the\n      * square root as \\f$ A^{1/2} = V D^{1/2} V^{-1} \\f$.\n      *\n      * Example: \\include SelfAdjointEigenSolver_operatorSqrt.cpp\n      * Output: \\verbinclude SelfAdjointEigenSolver_operatorSqrt.out\n      *\n      * \\sa operatorInverseSqrt(), <a href=\"unsupported/group__MatrixFunctions__Module.html\">MatrixFunctions Module</a>\n      */\n    EIGEN_DEVICE_FUNC\n    MatrixType operatorSqrt() const\n    {\n      eigen_assert(m_isInitialized && \"SelfAdjointEigenSolver is not initialized.\");\n      eigen_assert(m_eigenvectorsOk && \"The eigenvectors have not been computed together with the eigenvalues.\");\n      return m_eivec * m_eivalues.cwiseSqrt().asDiagonal() * m_eivec.adjoint();\n    }\n\n    /** \\brief Computes the inverse square root of the matrix.\n      *\n      * \\returns the inverse positive-definite square root of the matrix\n      *\n      * \\pre The eigenvalues and eigenvectors of a positive-definite matrix\n      * have been computed before.\n      *\n      * This function uses the eigendecomposition \\f$ A = V D V^{-1} \\f$ to\n      * compute the inverse square root as \\f$ V D^{-1/2} V^{-1} \\f$. This is\n      * cheaper than first computing the square root with operatorSqrt() and\n      * then its inverse with MatrixBase::inverse().\n      *\n      * Example: \\include SelfAdjointEigenSolver_operatorInverseSqrt.cpp\n      * Output: \\verbinclude SelfAdjointEigenSolver_operatorInverseSqrt.out\n      *\n      * \\sa operatorSqrt(), MatrixBase::inverse(), <a href=\"unsupported/group__MatrixFunctions__Module.html\">MatrixFunctions Module</a>\n      */\n    EIGEN_DEVICE_FUNC\n    MatrixType operatorInverseSqrt() const\n    {\n      eigen_assert(m_isInitialized && \"SelfAdjointEigenSolver is not initialized.\");\n      eigen_assert(m_eigenvectorsOk && \"The eigenvectors have not been computed together with the eigenvalues.\");\n      return m_eivec * m_eivalues.cwiseInverse().cwiseSqrt().asDiagonal() * m_eivec.adjoint();\n    }\n\n    /** \\brief Reports whether previous computation was successful.\n      *\n      * \\returns \\c Success if computation was succesful, \\c NoConvergence otherwise.\n      */\n    EIGEN_DEVICE_FUNC\n    ComputationInfo info() const\n    {\n      eigen_assert(m_isInitialized && \"SelfAdjointEigenSolver is not initialized.\");\n      return m_info;\n    }\n\n    /** \\brief Maximum number of iterations.\n      *\n      * The algorithm terminates if it does not converge within m_maxIterations * n iterations, where n\n      * denotes the size of the matrix. This value is currently set to 30 (copied from LAPACK).\n      */\n    static const int m_maxIterations = 30;\n\n  protected:\n    static void check_template_parameters()\n    {\n      EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);\n    }\n    \n    EigenvectorsType m_eivec;\n    RealVectorType m_eivalues;\n    typename TridiagonalizationType::SubDiagonalType m_subdiag;\n    ComputationInfo m_info;\n    bool m_isInitialized;\n    bool m_eigenvectorsOk;\n};\n\nnamespace internal {\n/** \\internal\n  *\n  * \\eigenvalues_module \\ingroup Eigenvalues_Module\n  *\n  * Performs a QR step on a tridiagonal symmetric matrix represented as a\n  * pair of two vectors \\a diag and \\a subdiag.\n  *\n  * \\param diag the diagonal part of the input selfadjoint tridiagonal matrix\n  * \\param subdiag the sub-diagonal part of the input selfadjoint tridiagonal matrix\n  * \\param start starting index of the submatrix to work on\n  * \\param end last+1 index of the submatrix to work on\n  * \\param matrixQ pointer to the column-major matrix holding the eigenvectors, can be 0\n  * \\param n size of the input matrix\n  *\n  * For compilation efficiency reasons, this procedure does not use eigen expression\n  * for its arguments.\n  *\n  * Implemented from Golub's \"Matrix Computations\", algorithm 8.3.2:\n  * \"implicit symmetric QR step with Wilkinson shift\"\n  */\ntemplate<int StorageOrder,typename RealScalar, typename Scalar, typename Index>\nEIGEN_DEVICE_FUNC\nstatic void tridiagonal_qr_step(RealScalar* diag, RealScalar* subdiag, Index start, Index end, Scalar* matrixQ, Index n);\n}\n\ntemplate<typename MatrixType>\ntemplate<typename InputType>\nEIGEN_DEVICE_FUNC\nSelfAdjointEigenSolver<MatrixType>& SelfAdjointEigenSolver<MatrixType>\n::compute(const EigenBase<InputType>& a_matrix, int options)\n{\n  check_template_parameters();\n  \n  const InputType &matrix(a_matrix.derived());\n  \n  using std::abs;\n  eigen_assert(matrix.cols() == matrix.rows());\n  eigen_assert((options&~(EigVecMask|GenEigMask))==0\n          && (options&EigVecMask)!=EigVecMask\n          && \"invalid option parameter\");\n  bool computeEigenvectors = (options&ComputeEigenvectors)==ComputeEigenvectors;\n  Index n = matrix.cols();\n  m_eivalues.resize(n,1);\n\n  if(n==1)\n  {\n    m_eivec = matrix;\n    m_eivalues.coeffRef(0,0) = numext::real(m_eivec.coeff(0,0));\n    if(computeEigenvectors)\n      m_eivec.setOnes(n,n);\n    m_info = Success;\n    m_isInitialized = true;\n    m_eigenvectorsOk = computeEigenvectors;\n    return *this;\n  }\n\n  // declare some aliases\n  RealVectorType& diag = m_eivalues;\n  EigenvectorsType& mat = m_eivec;\n\n  // map the matrix coefficients to [-1:1] to avoid over- and underflow.\n  mat = matrix.template triangularView<Lower>();\n  RealScalar scale = mat.cwiseAbs().maxCoeff();\n  if(scale==RealScalar(0)) scale = RealScalar(1);\n  mat.template triangularView<Lower>() /= scale;\n  m_subdiag.resize(n-1);\n  internal::tridiagonalization_inplace(mat, diag, m_subdiag, computeEigenvectors);\n\n  m_info = internal::computeFromTridiagonal_impl(diag, m_subdiag, m_maxIterations, computeEigenvectors, m_eivec);\n  \n  // scale back the eigen values\n  m_eivalues *= scale;\n\n  m_isInitialized = true;\n  m_eigenvectorsOk = computeEigenvectors;\n  return *this;\n}\n\ntemplate<typename MatrixType>\nSelfAdjointEigenSolver<MatrixType>& SelfAdjointEigenSolver<MatrixType>\n::computeFromTridiagonal(const RealVectorType& diag, const SubDiagonalType& subdiag , int options)\n{\n  //TODO : Add an option to scale the values beforehand\n  bool computeEigenvectors = (options&ComputeEigenvectors)==ComputeEigenvectors;\n\n  m_eivalues = diag;\n  m_subdiag = subdiag;\n  if (computeEigenvectors)\n  {\n    m_eivec.setIdentity(diag.size(), diag.size());\n  }\n  m_info = internal::computeFromTridiagonal_impl(m_eivalues, m_subdiag, m_maxIterations, computeEigenvectors, m_eivec);\n\n  m_isInitialized = true;\n  m_eigenvectorsOk = computeEigenvectors;\n  return *this;\n}\n\nnamespace internal {\n/**\n  * \\internal\n  * \\brief Compute the eigendecomposition from a tridiagonal matrix\n  *\n  * \\param[in,out] diag : On input, the diagonal of the matrix, on output the eigenvalues\n  * \\param[in,out] subdiag : The subdiagonal part of the matrix (entries are modified during the decomposition)\n  * \\param[in] maxIterations : the maximum number of iterations\n  * \\param[in] computeEigenvectors : whether the eigenvectors have to be computed or not\n  * \\param[out] eivec : The matrix to store the eigenvectors if computeEigenvectors==true. Must be allocated on input.\n  * \\returns \\c Success or \\c NoConvergence\n  */\ntemplate<typename MatrixType, typename DiagType, typename SubDiagType>\nComputationInfo computeFromTridiagonal_impl(DiagType& diag, SubDiagType& subdiag, const Index maxIterations, bool computeEigenvectors, MatrixType& eivec)\n{\n  using std::abs;\n\n  ComputationInfo info;\n  typedef typename MatrixType::Scalar Scalar;\n\n  Index n = diag.size();\n  Index end = n-1;\n  Index start = 0;\n  Index iter = 0; // total number of iterations\n  \n  typedef typename DiagType::RealScalar RealScalar;\n  const RealScalar considerAsZero = (std::numeric_limits<RealScalar>::min)();\n  const RealScalar precision = RealScalar(2)*NumTraits<RealScalar>::epsilon();\n  \n  while (end>0)\n  {\n    for (Index i = start; i<end; ++i)\n      if (internal::isMuchSmallerThan(abs(subdiag[i]),(abs(diag[i])+abs(diag[i+1])),precision) || abs(subdiag[i]) <= considerAsZero)\n        subdiag[i] = 0;\n\n    // find the largest unreduced block\n    while (end>0 && subdiag[end-1]==RealScalar(0))\n    {\n      end--;\n    }\n    if (end<=0)\n      break;\n\n    // if we spent too many iterations, we give up\n    iter++;\n    if(iter > maxIterations * n) break;\n\n    start = end - 1;\n    while (start>0 && subdiag[start-1]!=0)\n      start--;\n\n    internal::tridiagonal_qr_step<MatrixType::Flags&RowMajorBit ? RowMajor : ColMajor>(diag.data(), subdiag.data(), start, end, computeEigenvectors ? eivec.data() : (Scalar*)0, n);\n  }\n  if (iter <= maxIterations * n)\n    info = Success;\n  else\n    info = NoConvergence;\n\n  // Sort eigenvalues and corresponding vectors.\n  // TODO make the sort optional ?\n  // TODO use a better sort algorithm !!\n  if (info == Success)\n  {\n    for (Index i = 0; i < n-1; ++i)\n    {\n      Index k;\n      diag.segment(i,n-i).minCoeff(&k);\n      if (k > 0)\n      {\n        std::swap(diag[i], diag[k+i]);\n        if(computeEigenvectors)\n          eivec.col(i).swap(eivec.col(k+i));\n      }\n    }\n  }\n  return info;\n}\n  \ntemplate<typename SolverType,int Size,bool IsComplex> struct direct_selfadjoint_eigenvalues\n{\n  EIGEN_DEVICE_FUNC\n  static inline void run(SolverType& eig, const typename SolverType::MatrixType& A, int options)\n  { eig.compute(A,options); }\n};\n\ntemplate<typename SolverType> struct direct_selfadjoint_eigenvalues<SolverType,3,false>\n{\n  typedef typename SolverType::MatrixType MatrixType;\n  typedef typename SolverType::RealVectorType VectorType;\n  typedef typename SolverType::Scalar Scalar;\n  typedef typename SolverType::EigenvectorsType EigenvectorsType;\n  \n\n  /** \\internal\n   * Computes the roots of the characteristic polynomial of \\a m.\n   * For numerical stability m.trace() should be near zero and to avoid over- or underflow m should be normalized.\n   */\n  EIGEN_DEVICE_FUNC\n  static inline void computeRoots(const MatrixType& m, VectorType& roots)\n  {\n    EIGEN_USING_STD_MATH(sqrt)\n    EIGEN_USING_STD_MATH(atan2)\n    EIGEN_USING_STD_MATH(cos)\n    EIGEN_USING_STD_MATH(sin)\n    const Scalar s_inv3 = Scalar(1)/Scalar(3);\n    const Scalar s_sqrt3 = sqrt(Scalar(3));\n\n    // The characteristic equation is x^3 - c2*x^2 + c1*x - c0 = 0.  The\n    // eigenvalues are the roots to this equation, all guaranteed to be\n    // real-valued, because the matrix is symmetric.\n    Scalar c0 = m(0,0)*m(1,1)*m(2,2) + Scalar(2)*m(1,0)*m(2,0)*m(2,1) - m(0,0)*m(2,1)*m(2,1) - m(1,1)*m(2,0)*m(2,0) - m(2,2)*m(1,0)*m(1,0);\n    Scalar c1 = m(0,0)*m(1,1) - m(1,0)*m(1,0) + m(0,0)*m(2,2) - m(2,0)*m(2,0) + m(1,1)*m(2,2) - m(2,1)*m(2,1);\n    Scalar c2 = m(0,0) + m(1,1) + m(2,2);\n\n    // Construct the parameters used in classifying the roots of the equation\n    // and in solving the equation for the roots in closed form.\n    Scalar c2_over_3 = c2*s_inv3;\n    Scalar a_over_3 = (c2*c2_over_3 - c1)*s_inv3;\n    a_over_3 = numext::maxi(a_over_3, Scalar(0));\n\n    Scalar half_b = Scalar(0.5)*(c0 + c2_over_3*(Scalar(2)*c2_over_3*c2_over_3 - c1));\n\n    Scalar q = a_over_3*a_over_3*a_over_3 - half_b*half_b;\n    q = numext::maxi(q, Scalar(0));\n\n    // Compute the eigenvalues by solving for the roots of the polynomial.\n    Scalar rho = sqrt(a_over_3);\n    Scalar theta = atan2(sqrt(q),half_b)*s_inv3;  // since sqrt(q) > 0, atan2 is in [0, pi] and theta is in [0, pi/3]\n    Scalar cos_theta = cos(theta);\n    Scalar sin_theta = sin(theta);\n    // roots are already sorted, since cos is monotonically decreasing on [0, pi]\n    roots(0) = c2_over_3 - rho*(cos_theta + s_sqrt3*sin_theta); // == 2*rho*cos(theta+2pi/3)\n    roots(1) = c2_over_3 - rho*(cos_theta - s_sqrt3*sin_theta); // == 2*rho*cos(theta+ pi/3)\n    roots(2) = c2_over_3 + Scalar(2)*rho*cos_theta;\n  }\n\n  EIGEN_DEVICE_FUNC\n  static inline bool extract_kernel(MatrixType& mat, Ref<VectorType> res, Ref<VectorType> representative)\n  {\n    using std::abs;\n    Index i0;\n    // Find non-zero column i0 (by construction, there must exist a non zero coefficient on the diagonal):\n    mat.diagonal().cwiseAbs().maxCoeff(&i0);\n    // mat.col(i0) is a good candidate for an orthogonal vector to the current eigenvector,\n    // so let's save it:\n    representative = mat.col(i0);\n    Scalar n0, n1;\n    VectorType c0, c1;\n    n0 = (c0 = representative.cross(mat.col((i0+1)%3))).squaredNorm();\n    n1 = (c1 = representative.cross(mat.col((i0+2)%3))).squaredNorm();\n    if(n0>n1) res = c0/std::sqrt(n0);\n    else      res = c1/std::sqrt(n1);\n\n    return true;\n  }\n\n  EIGEN_DEVICE_FUNC\n  static inline void run(SolverType& solver, const MatrixType& mat, int options)\n  {\n    eigen_assert(mat.cols() == 3 && mat.cols() == mat.rows());\n    eigen_assert((options&~(EigVecMask|GenEigMask))==0\n            && (options&EigVecMask)!=EigVecMask\n            && \"invalid option parameter\");\n    bool computeEigenvectors = (options&ComputeEigenvectors)==ComputeEigenvectors;\n    \n    EigenvectorsType& eivecs = solver.m_eivec;\n    VectorType& eivals = solver.m_eivalues;\n  \n    // Shift the matrix to the mean eigenvalue and map the matrix coefficients to [-1:1] to avoid over- and underflow.\n    Scalar shift = mat.trace() / Scalar(3);\n    // TODO Avoid this copy. Currently it is necessary to suppress bogus values when determining maxCoeff and for computing the eigenvectors later\n    MatrixType scaledMat = mat.template selfadjointView<Lower>();\n    scaledMat.diagonal().array() -= shift;\n    Scalar scale = scaledMat.cwiseAbs().maxCoeff();\n    if(scale > 0) scaledMat /= scale;   // TODO for scale==0 we could save the remaining operations\n\n    // compute the eigenvalues\n    computeRoots(scaledMat,eivals);\n\n    // compute the eigenvectors\n    if(computeEigenvectors)\n    {\n      if((eivals(2)-eivals(0))<=Eigen::NumTraits<Scalar>::epsilon())\n      {\n        // All three eigenvalues are numerically the same\n        eivecs.setIdentity();\n      }\n      else\n      {\n        MatrixType tmp;\n        tmp = scaledMat;\n\n        // Compute the eigenvector of the most distinct eigenvalue\n        Scalar d0 = eivals(2) - eivals(1);\n        Scalar d1 = eivals(1) - eivals(0);\n        Index k(0), l(2);\n        if(d0 > d1)\n        {\n          numext::swap(k,l);\n          d0 = d1;\n        }\n\n        // Compute the eigenvector of index k\n        {\n          tmp.diagonal().array () -= eivals(k);\n          // By construction, 'tmp' is of rank 2, and its kernel corresponds to the respective eigenvector.\n          extract_kernel(tmp, eivecs.col(k), eivecs.col(l));\n        }\n\n        // Compute eigenvector of index l\n        if(d0<=2*Eigen::NumTraits<Scalar>::epsilon()*d1)\n        {\n          // If d0 is too small, then the two other eigenvalues are numerically the same,\n          // and thus we only have to ortho-normalize the near orthogonal vector we saved above.\n          eivecs.col(l) -= eivecs.col(k).dot(eivecs.col(l))*eivecs.col(l);\n          eivecs.col(l).normalize();\n        }\n        else\n        {\n          tmp = scaledMat;\n          tmp.diagonal().array () -= eivals(l);\n\n          VectorType dummy;\n          extract_kernel(tmp, eivecs.col(l), dummy);\n        }\n\n        // Compute last eigenvector from the other two\n        eivecs.col(1) = eivecs.col(2).cross(eivecs.col(0)).normalized();\n      }\n    }\n\n    // Rescale back to the original size.\n    eivals *= scale;\n    eivals.array() += shift;\n    \n    solver.m_info = Success;\n    solver.m_isInitialized = true;\n    solver.m_eigenvectorsOk = computeEigenvectors;\n  }\n};\n\n// 2x2 direct eigenvalues decomposition, code from Hauke Heibel\ntemplate<typename SolverType> \nstruct direct_selfadjoint_eigenvalues<SolverType,2,false>\n{\n  typedef typename SolverType::MatrixType MatrixType;\n  typedef typename SolverType::RealVectorType VectorType;\n  typedef typename SolverType::Scalar Scalar;\n  typedef typename SolverType::EigenvectorsType EigenvectorsType;\n  \n  EIGEN_DEVICE_FUNC\n  static inline void computeRoots(const MatrixType& m, VectorType& roots)\n  {\n    using std::sqrt;\n    const Scalar t0 = Scalar(0.5) * sqrt( numext::abs2(m(0,0)-m(1,1)) + Scalar(4)*numext::abs2(m(1,0)));\n    const Scalar t1 = Scalar(0.5) * (m(0,0) + m(1,1));\n    roots(0) = t1 - t0;\n    roots(1) = t1 + t0;\n  }\n  \n  EIGEN_DEVICE_FUNC\n  static inline void run(SolverType& solver, const MatrixType& mat, int options)\n  {\n    EIGEN_USING_STD_MATH(sqrt);\n    EIGEN_USING_STD_MATH(abs);\n    \n    eigen_assert(mat.cols() == 2 && mat.cols() == mat.rows());\n    eigen_assert((options&~(EigVecMask|GenEigMask))==0\n            && (options&EigVecMask)!=EigVecMask\n            && \"invalid option parameter\");\n    bool computeEigenvectors = (options&ComputeEigenvectors)==ComputeEigenvectors;\n    \n    EigenvectorsType& eivecs = solver.m_eivec;\n    VectorType& eivals = solver.m_eivalues;\n  \n    // Shift the matrix to the mean eigenvalue and map the matrix coefficients to [-1:1] to avoid over- and underflow.\n    Scalar shift = mat.trace() / Scalar(2);\n    MatrixType scaledMat = mat;\n    scaledMat.coeffRef(0,1) = mat.coeff(1,0);\n    scaledMat.diagonal().array() -= shift;\n    Scalar scale = scaledMat.cwiseAbs().maxCoeff();\n    if(scale > Scalar(0))\n      scaledMat /= scale;\n\n    // Compute the eigenvalues\n    computeRoots(scaledMat,eivals);\n\n    // compute the eigen vectors\n    if(computeEigenvectors)\n    {\n      if((eivals(1)-eivals(0))<=abs(eivals(1))*Eigen::NumTraits<Scalar>::epsilon())\n      {\n        eivecs.setIdentity();\n      }\n      else\n      {\n        scaledMat.diagonal().array () -= eivals(1);\n        Scalar a2 = numext::abs2(scaledMat(0,0));\n        Scalar c2 = numext::abs2(scaledMat(1,1));\n        Scalar b2 = numext::abs2(scaledMat(1,0));\n        if(a2>c2)\n        {\n          eivecs.col(1) << -scaledMat(1,0), scaledMat(0,0);\n          eivecs.col(1) /= sqrt(a2+b2);\n        }\n        else\n        {\n          eivecs.col(1) << -scaledMat(1,1), scaledMat(1,0);\n          eivecs.col(1) /= sqrt(c2+b2);\n        }\n\n        eivecs.col(0) << eivecs.col(1).unitOrthogonal();\n      }\n    }\n\n    // Rescale back to the original size.\n    eivals *= scale;\n    eivals.array() += shift;\n\n    solver.m_info = Success;\n    solver.m_isInitialized = true;\n    solver.m_eigenvectorsOk = computeEigenvectors;\n  }\n};\n\n}\n\ntemplate<typename MatrixType>\nEIGEN_DEVICE_FUNC\nSelfAdjointEigenSolver<MatrixType>& SelfAdjointEigenSolver<MatrixType>\n::computeDirect(const MatrixType& matrix, int options)\n{\n  internal::direct_selfadjoint_eigenvalues<SelfAdjointEigenSolver,Size,NumTraits<Scalar>::IsComplex>::run(*this,matrix,options);\n  return *this;\n}\n\nnamespace internal {\ntemplate<int StorageOrder,typename RealScalar, typename Scalar, typename Index>\nEIGEN_DEVICE_FUNC\nstatic void tridiagonal_qr_step(RealScalar* diag, RealScalar* subdiag, Index start, Index end, Scalar* matrixQ, Index n)\n{\n  using std::abs;\n  RealScalar td = (diag[end-1] - diag[end])*RealScalar(0.5);\n  RealScalar e = subdiag[end-1];\n  // Note that thanks to scaling, e^2 or td^2 cannot overflow, however they can still\n  // underflow thus leading to inf/NaN values when using the following commented code:\n//   RealScalar e2 = numext::abs2(subdiag[end-1]);\n//   RealScalar mu = diag[end] - e2 / (td + (td>0 ? 1 : -1) * sqrt(td*td + e2));\n  // This explain the following, somewhat more complicated, version:\n  RealScalar mu = diag[end];\n  if(td==RealScalar(0))\n    mu -= abs(e);\n  else\n  {\n    RealScalar e2 = numext::abs2(subdiag[end-1]);\n    RealScalar h = numext::hypot(td,e);\n    if(e2==RealScalar(0)) mu -= (e / (td + (td>RealScalar(0) ? RealScalar(1) : RealScalar(-1)))) * (e / h);\n    else                  mu -= e2 / (td + (td>RealScalar(0) ? h : -h));\n  }\n  \n  RealScalar x = diag[start] - mu;\n  RealScalar z = subdiag[start];\n  for (Index k = start; k < end; ++k)\n  {\n    JacobiRotation<RealScalar> rot;\n    rot.makeGivens(x, z);\n\n    // do T = G' T G\n    RealScalar sdk = rot.s() * diag[k] + rot.c() * subdiag[k];\n    RealScalar dkp1 = rot.s() * subdiag[k] + rot.c() * diag[k+1];\n\n    diag[k] = rot.c() * (rot.c() * diag[k] - rot.s() * subdiag[k]) - rot.s() * (rot.c() * subdiag[k] - rot.s() * diag[k+1]);\n    diag[k+1] = rot.s() * sdk + rot.c() * dkp1;\n    subdiag[k] = rot.c() * sdk - rot.s() * dkp1;\n    \n\n    if (k > start)\n      subdiag[k - 1] = rot.c() * subdiag[k-1] - rot.s() * z;\n\n    x = subdiag[k];\n\n    if (k < end - 1)\n    {\n      z = -rot.s() * subdiag[k+1];\n      subdiag[k + 1] = rot.c() * subdiag[k+1];\n    }\n    \n    // apply the givens rotation to the unit matrix Q = Q * G\n    if (matrixQ)\n    {\n      // FIXME if StorageOrder == RowMajor this operation is not very efficient\n      Map<Matrix<Scalar,Dynamic,Dynamic,StorageOrder> > q(matrixQ,n,n);\n      q.applyOnTheRight(k,k+1,rot);\n    }\n  }\n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_SELFADJOINTEIGENSOLVER_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Eigenvalues/SelfAdjointEigenSolver_LAPACKE.h",
    "content": "/*\n Copyright (c) 2011, Intel Corporation. All rights reserved.\n\n Redistribution and use in source and binary forms, with or without modification,\n are permitted provided that the following conditions are met:\n\n * Redistributions of source code must retain the above copyright notice, this\n   list of conditions and the following disclaimer.\n * Redistributions in binary form must reproduce the above copyright notice,\n   this list of conditions and the following disclaimer in the documentation\n   and/or other materials provided with the distribution.\n * Neither the name of Intel Corporation nor the names of its contributors may\n   be used to endorse or promote products derived from this software without\n   specific prior written permission.\n\n THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\" AND\n ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED\n WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\n DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR\n ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES\n (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;\n LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON\n ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT\n (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS\n SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n\n ********************************************************************************\n *   Content : Eigen bindings to LAPACKe\n *    Self-adjoint eigenvalues/eigenvectors.\n ********************************************************************************\n*/\n\n#ifndef EIGEN_SAEIGENSOLVER_LAPACKE_H\n#define EIGEN_SAEIGENSOLVER_LAPACKE_H\n\nnamespace Eigen { \n\n/** \\internal Specialization for the data types supported by LAPACKe */\n\n#define EIGEN_LAPACKE_EIG_SELFADJ_2(EIGTYPE, LAPACKE_TYPE, LAPACKE_RTYPE, LAPACKE_NAME, EIGCOLROW ) \\\ntemplate<> template<typename InputType> inline \\\nSelfAdjointEigenSolver<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >& \\\nSelfAdjointEigenSolver<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >::compute(const EigenBase<InputType>& matrix, int options) \\\n{ \\\n  eigen_assert(matrix.cols() == matrix.rows()); \\\n  eigen_assert((options&~(EigVecMask|GenEigMask))==0 \\\n          && (options&EigVecMask)!=EigVecMask \\\n          && \"invalid option parameter\"); \\\n  bool computeEigenvectors = (options&ComputeEigenvectors)==ComputeEigenvectors; \\\n  lapack_int n = internal::convert_index<lapack_int>(matrix.cols()), lda, info; \\\n  m_eivalues.resize(n,1); \\\n  m_subdiag.resize(n-1); \\\n  m_eivec = matrix; \\\n\\\n  if(n==1) \\\n  { \\\n    m_eivalues.coeffRef(0,0) = numext::real(m_eivec.coeff(0,0)); \\\n    if(computeEigenvectors) m_eivec.setOnes(n,n); \\\n    m_info = Success; \\\n    m_isInitialized = true; \\\n    m_eigenvectorsOk = computeEigenvectors; \\\n    return *this; \\\n  } \\\n\\\n  lda = internal::convert_index<lapack_int>(m_eivec.outerStride()); \\\n  char jobz, uplo='L'/*, range='A'*/; \\\n  jobz = computeEigenvectors ? 'V' : 'N'; \\\n\\\n  info = LAPACKE_##LAPACKE_NAME( LAPACK_COL_MAJOR, jobz, uplo, n, (LAPACKE_TYPE*)m_eivec.data(), lda, (LAPACKE_RTYPE*)m_eivalues.data() ); \\\n  m_info = (info==0) ? Success : NoConvergence; \\\n  m_isInitialized = true; \\\n  m_eigenvectorsOk = computeEigenvectors; \\\n  return *this; \\\n}\n\n#define EIGEN_LAPACKE_EIG_SELFADJ(EIGTYPE, LAPACKE_TYPE, LAPACKE_RTYPE, LAPACKE_NAME )              \\\n        EIGEN_LAPACKE_EIG_SELFADJ_2(EIGTYPE, LAPACKE_TYPE, LAPACKE_RTYPE, LAPACKE_NAME, ColMajor )  \\\n        EIGEN_LAPACKE_EIG_SELFADJ_2(EIGTYPE, LAPACKE_TYPE, LAPACKE_RTYPE, LAPACKE_NAME, RowMajor ) \n\nEIGEN_LAPACKE_EIG_SELFADJ(double,   double,                double, dsyev)\nEIGEN_LAPACKE_EIG_SELFADJ(float,    float,                 float,  ssyev)\nEIGEN_LAPACKE_EIG_SELFADJ(dcomplex, lapack_complex_double, double, zheev)\nEIGEN_LAPACKE_EIG_SELFADJ(scomplex, lapack_complex_float,  float,  cheev)\n\n} // end namespace Eigen\n\n#endif // EIGEN_SAEIGENSOLVER_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Eigenvalues/Tridiagonalization.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_TRIDIAGONALIZATION_H\n#define EIGEN_TRIDIAGONALIZATION_H\n\nnamespace Eigen { \n\nnamespace internal {\n  \ntemplate<typename MatrixType> struct TridiagonalizationMatrixTReturnType;\ntemplate<typename MatrixType>\nstruct traits<TridiagonalizationMatrixTReturnType<MatrixType> >\n  : public traits<typename MatrixType::PlainObject>\n{\n  typedef typename MatrixType::PlainObject ReturnType; // FIXME shall it be a BandMatrix?\n  enum { Flags = 0 };\n};\n\ntemplate<typename MatrixType, typename CoeffVectorType>\nvoid tridiagonalization_inplace(MatrixType& matA, CoeffVectorType& hCoeffs);\n}\n\n/** \\eigenvalues_module \\ingroup Eigenvalues_Module\n  *\n  *\n  * \\class Tridiagonalization\n  *\n  * \\brief Tridiagonal decomposition of a selfadjoint matrix\n  *\n  * \\tparam _MatrixType the type of the matrix of which we are computing the\n  * tridiagonal decomposition; this is expected to be an instantiation of the\n  * Matrix class template.\n  *\n  * This class performs a tridiagonal decomposition of a selfadjoint matrix \\f$ A \\f$ such that:\n  * \\f$ A = Q T Q^* \\f$ where \\f$ Q \\f$ is unitary and \\f$ T \\f$ a real symmetric tridiagonal matrix.\n  *\n  * A tridiagonal matrix is a matrix which has nonzero elements only on the\n  * main diagonal and the first diagonal below and above it. The Hessenberg\n  * decomposition of a selfadjoint matrix is in fact a tridiagonal\n  * decomposition. This class is used in SelfAdjointEigenSolver to compute the\n  * eigenvalues and eigenvectors of a selfadjoint matrix.\n  *\n  * Call the function compute() to compute the tridiagonal decomposition of a\n  * given matrix. Alternatively, you can use the Tridiagonalization(const MatrixType&)\n  * constructor which computes the tridiagonal Schur decomposition at\n  * construction time. Once the decomposition is computed, you can use the\n  * matrixQ() and matrixT() functions to retrieve the matrices Q and T in the\n  * decomposition.\n  *\n  * The documentation of Tridiagonalization(const MatrixType&) contains an\n  * example of the typical use of this class.\n  *\n  * \\sa class HessenbergDecomposition, class SelfAdjointEigenSolver\n  */\ntemplate<typename _MatrixType> class Tridiagonalization\n{\n  public:\n\n    /** \\brief Synonym for the template parameter \\p _MatrixType. */\n    typedef _MatrixType MatrixType;\n\n    typedef typename MatrixType::Scalar Scalar;\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n    typedef Eigen::Index Index; ///< \\deprecated since Eigen 3.3\n\n    enum {\n      Size = MatrixType::RowsAtCompileTime,\n      SizeMinusOne = Size == Dynamic ? Dynamic : (Size > 1 ? Size - 1 : 1),\n      Options = MatrixType::Options,\n      MaxSize = MatrixType::MaxRowsAtCompileTime,\n      MaxSizeMinusOne = MaxSize == Dynamic ? Dynamic : (MaxSize > 1 ? MaxSize - 1 : 1)\n    };\n\n    typedef Matrix<Scalar, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> CoeffVectorType;\n    typedef typename internal::plain_col_type<MatrixType, RealScalar>::type DiagonalType;\n    typedef Matrix<RealScalar, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> SubDiagonalType;\n    typedef typename internal::remove_all<typename MatrixType::RealReturnType>::type MatrixTypeRealView;\n    typedef internal::TridiagonalizationMatrixTReturnType<MatrixTypeRealView> MatrixTReturnType;\n\n    typedef typename internal::conditional<NumTraits<Scalar>::IsComplex,\n              typename internal::add_const_on_value_type<typename Diagonal<const MatrixType>::RealReturnType>::type,\n              const Diagonal<const MatrixType>\n            >::type DiagonalReturnType;\n\n    typedef typename internal::conditional<NumTraits<Scalar>::IsComplex,\n              typename internal::add_const_on_value_type<typename Diagonal<const MatrixType, -1>::RealReturnType>::type,\n              const Diagonal<const MatrixType, -1>\n            >::type SubDiagonalReturnType;\n\n    /** \\brief Return type of matrixQ() */\n    typedef HouseholderSequence<MatrixType,typename internal::remove_all<typename CoeffVectorType::ConjugateReturnType>::type> HouseholderSequenceType;\n\n    /** \\brief Default constructor.\n      *\n      * \\param [in]  size  Positive integer, size of the matrix whose tridiagonal\n      * decomposition will be computed.\n      *\n      * The default constructor is useful in cases in which the user intends to\n      * perform decompositions via compute().  The \\p size parameter is only\n      * used as a hint. It is not an error to give a wrong \\p size, but it may\n      * impair performance.\n      *\n      * \\sa compute() for an example.\n      */\n    explicit Tridiagonalization(Index size = Size==Dynamic ? 2 : Size)\n      : m_matrix(size,size),\n        m_hCoeffs(size > 1 ? size-1 : 1),\n        m_isInitialized(false)\n    {}\n\n    /** \\brief Constructor; computes tridiagonal decomposition of given matrix.\n      *\n      * \\param[in]  matrix  Selfadjoint matrix whose tridiagonal decomposition\n      * is to be computed.\n      *\n      * This constructor calls compute() to compute the tridiagonal decomposition.\n      *\n      * Example: \\include Tridiagonalization_Tridiagonalization_MatrixType.cpp\n      * Output: \\verbinclude Tridiagonalization_Tridiagonalization_MatrixType.out\n      */\n    template<typename InputType>\n    explicit Tridiagonalization(const EigenBase<InputType>& matrix)\n      : m_matrix(matrix.derived()),\n        m_hCoeffs(matrix.cols() > 1 ? matrix.cols()-1 : 1),\n        m_isInitialized(false)\n    {\n      internal::tridiagonalization_inplace(m_matrix, m_hCoeffs);\n      m_isInitialized = true;\n    }\n\n    /** \\brief Computes tridiagonal decomposition of given matrix.\n      *\n      * \\param[in]  matrix  Selfadjoint matrix whose tridiagonal decomposition\n      * is to be computed.\n      * \\returns    Reference to \\c *this\n      *\n      * The tridiagonal decomposition is computed by bringing the columns of\n      * the matrix successively in the required form using Householder\n      * reflections. The cost is \\f$ 4n^3/3 \\f$ flops, where \\f$ n \\f$ denotes\n      * the size of the given matrix.\n      *\n      * This method reuses of the allocated data in the Tridiagonalization\n      * object, if the size of the matrix does not change.\n      *\n      * Example: \\include Tridiagonalization_compute.cpp\n      * Output: \\verbinclude Tridiagonalization_compute.out\n      */\n    template<typename InputType>\n    Tridiagonalization& compute(const EigenBase<InputType>& matrix)\n    {\n      m_matrix = matrix.derived();\n      m_hCoeffs.resize(matrix.rows()-1, 1);\n      internal::tridiagonalization_inplace(m_matrix, m_hCoeffs);\n      m_isInitialized = true;\n      return *this;\n    }\n\n    /** \\brief Returns the Householder coefficients.\n      *\n      * \\returns a const reference to the vector of Householder coefficients\n      *\n      * \\pre Either the constructor Tridiagonalization(const MatrixType&) or\n      * the member function compute(const MatrixType&) has been called before\n      * to compute the tridiagonal decomposition of a matrix.\n      *\n      * The Householder coefficients allow the reconstruction of the matrix\n      * \\f$ Q \\f$ in the tridiagonal decomposition from the packed data.\n      *\n      * Example: \\include Tridiagonalization_householderCoefficients.cpp\n      * Output: \\verbinclude Tridiagonalization_householderCoefficients.out\n      *\n      * \\sa packedMatrix(), \\ref Householder_Module \"Householder module\"\n      */\n    inline CoeffVectorType householderCoefficients() const\n    {\n      eigen_assert(m_isInitialized && \"Tridiagonalization is not initialized.\");\n      return m_hCoeffs;\n    }\n\n    /** \\brief Returns the internal representation of the decomposition\n      *\n      *\t\\returns a const reference to a matrix with the internal representation\n      *\t         of the decomposition.\n      *\n      * \\pre Either the constructor Tridiagonalization(const MatrixType&) or\n      * the member function compute(const MatrixType&) has been called before\n      * to compute the tridiagonal decomposition of a matrix.\n      *\n      * The returned matrix contains the following information:\n      *  - the strict upper triangular part is equal to the input matrix A.\n      *  - the diagonal and lower sub-diagonal represent the real tridiagonal\n      *    symmetric matrix T.\n      *  - the rest of the lower part contains the Householder vectors that,\n      *    combined with Householder coefficients returned by\n      *    householderCoefficients(), allows to reconstruct the matrix Q as\n      *       \\f$ Q = H_{N-1} \\ldots H_1 H_0 \\f$.\n      *    Here, the matrices \\f$ H_i \\f$ are the Householder transformations\n      *       \\f$ H_i = (I - h_i v_i v_i^T) \\f$\n      *    where \\f$ h_i \\f$ is the \\f$ i \\f$th Householder coefficient and\n      *    \\f$ v_i \\f$ is the Householder vector defined by\n      *       \\f$ v_i = [ 0, \\ldots, 0, 1, M(i+2,i), \\ldots, M(N-1,i) ]^T \\f$\n      *    with M the matrix returned by this function.\n      *\n      * See LAPACK for further details on this packed storage.\n      *\n      * Example: \\include Tridiagonalization_packedMatrix.cpp\n      * Output: \\verbinclude Tridiagonalization_packedMatrix.out\n      *\n      * \\sa householderCoefficients()\n      */\n    inline const MatrixType& packedMatrix() const\n    {\n      eigen_assert(m_isInitialized && \"Tridiagonalization is not initialized.\");\n      return m_matrix;\n    }\n\n    /** \\brief Returns the unitary matrix Q in the decomposition\n      *\n      * \\returns object representing the matrix Q\n      *\n      * \\pre Either the constructor Tridiagonalization(const MatrixType&) or\n      * the member function compute(const MatrixType&) has been called before\n      * to compute the tridiagonal decomposition of a matrix.\n      *\n      * This function returns a light-weight object of template class\n      * HouseholderSequence. You can either apply it directly to a matrix or\n      * you can convert it to a matrix of type #MatrixType.\n      *\n      * \\sa Tridiagonalization(const MatrixType&) for an example,\n      *     matrixT(), class HouseholderSequence\n      */\n    HouseholderSequenceType matrixQ() const\n    {\n      eigen_assert(m_isInitialized && \"Tridiagonalization is not initialized.\");\n      return HouseholderSequenceType(m_matrix, m_hCoeffs.conjugate())\n             .setLength(m_matrix.rows() - 1)\n             .setShift(1);\n    }\n\n    /** \\brief Returns an expression of the tridiagonal matrix T in the decomposition\n      *\n      * \\returns expression object representing the matrix T\n      *\n      * \\pre Either the constructor Tridiagonalization(const MatrixType&) or\n      * the member function compute(const MatrixType&) has been called before\n      * to compute the tridiagonal decomposition of a matrix.\n      *\n      * Currently, this function can be used to extract the matrix T from internal\n      * data and copy it to a dense matrix object. In most cases, it may be\n      * sufficient to directly use the packed matrix or the vector expressions\n      * returned by diagonal() and subDiagonal() instead of creating a new\n      * dense copy matrix with this function.\n      *\n      * \\sa Tridiagonalization(const MatrixType&) for an example,\n      * matrixQ(), packedMatrix(), diagonal(), subDiagonal()\n      */\n    MatrixTReturnType matrixT() const\n    {\n      eigen_assert(m_isInitialized && \"Tridiagonalization is not initialized.\");\n      return MatrixTReturnType(m_matrix.real());\n    }\n\n    /** \\brief Returns the diagonal of the tridiagonal matrix T in the decomposition.\n      *\n      * \\returns expression representing the diagonal of T\n      *\n      * \\pre Either the constructor Tridiagonalization(const MatrixType&) or\n      * the member function compute(const MatrixType&) has been called before\n      * to compute the tridiagonal decomposition of a matrix.\n      *\n      * Example: \\include Tridiagonalization_diagonal.cpp\n      * Output: \\verbinclude Tridiagonalization_diagonal.out\n      *\n      * \\sa matrixT(), subDiagonal()\n      */\n    DiagonalReturnType diagonal() const;\n\n    /** \\brief Returns the subdiagonal of the tridiagonal matrix T in the decomposition.\n      *\n      * \\returns expression representing the subdiagonal of T\n      *\n      * \\pre Either the constructor Tridiagonalization(const MatrixType&) or\n      * the member function compute(const MatrixType&) has been called before\n      * to compute the tridiagonal decomposition of a matrix.\n      *\n      * \\sa diagonal() for an example, matrixT()\n      */\n    SubDiagonalReturnType subDiagonal() const;\n\n  protected:\n\n    MatrixType m_matrix;\n    CoeffVectorType m_hCoeffs;\n    bool m_isInitialized;\n};\n\ntemplate<typename MatrixType>\ntypename Tridiagonalization<MatrixType>::DiagonalReturnType\nTridiagonalization<MatrixType>::diagonal() const\n{\n  eigen_assert(m_isInitialized && \"Tridiagonalization is not initialized.\");\n  return m_matrix.diagonal().real();\n}\n\ntemplate<typename MatrixType>\ntypename Tridiagonalization<MatrixType>::SubDiagonalReturnType\nTridiagonalization<MatrixType>::subDiagonal() const\n{\n  eigen_assert(m_isInitialized && \"Tridiagonalization is not initialized.\");\n  return m_matrix.template diagonal<-1>().real();\n}\n\nnamespace internal {\n\n/** \\internal\n  * Performs a tridiagonal decomposition of the selfadjoint matrix \\a matA in-place.\n  *\n  * \\param[in,out] matA On input the selfadjoint matrix. Only the \\b lower triangular part is referenced.\n  *                     On output, the strict upper part is left unchanged, and the lower triangular part\n  *                     represents the T and Q matrices in packed format has detailed below.\n  * \\param[out]    hCoeffs returned Householder coefficients (see below)\n  *\n  * On output, the tridiagonal selfadjoint matrix T is stored in the diagonal\n  * and lower sub-diagonal of the matrix \\a matA.\n  * The unitary matrix Q is represented in a compact way as a product of\n  * Householder reflectors \\f$ H_i \\f$ such that:\n  *       \\f$ Q = H_{N-1} \\ldots H_1 H_0 \\f$.\n  * The Householder reflectors are defined as\n  *       \\f$ H_i = (I - h_i v_i v_i^T) \\f$\n  * where \\f$ h_i = hCoeffs[i]\\f$ is the \\f$ i \\f$th Householder coefficient and\n  * \\f$ v_i \\f$ is the Householder vector defined by\n  *       \\f$ v_i = [ 0, \\ldots, 0, 1, matA(i+2,i), \\ldots, matA(N-1,i) ]^T \\f$.\n  *\n  * Implemented from Golub's \"Matrix Computations\", algorithm 8.3.1.\n  *\n  * \\sa Tridiagonalization::packedMatrix()\n  */\ntemplate<typename MatrixType, typename CoeffVectorType>\nvoid tridiagonalization_inplace(MatrixType& matA, CoeffVectorType& hCoeffs)\n{\n  using numext::conj;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename MatrixType::RealScalar RealScalar;\n  Index n = matA.rows();\n  eigen_assert(n==matA.cols());\n  eigen_assert(n==hCoeffs.size()+1 || n==1);\n  \n  for (Index i = 0; i<n-1; ++i)\n  {\n    Index remainingSize = n-i-1;\n    RealScalar beta;\n    Scalar h;\n    matA.col(i).tail(remainingSize).makeHouseholderInPlace(h, beta);\n\n    // Apply similarity transformation to remaining columns,\n    // i.e., A = H A H' where H = I - h v v' and v = matA.col(i).tail(n-i-1)\n    matA.col(i).coeffRef(i+1) = 1;\n\n    hCoeffs.tail(n-i-1).noalias() = (matA.bottomRightCorner(remainingSize,remainingSize).template selfadjointView<Lower>()\n                                  * (conj(h) * matA.col(i).tail(remainingSize)));\n\n    hCoeffs.tail(n-i-1) += (conj(h)*RealScalar(-0.5)*(hCoeffs.tail(remainingSize).dot(matA.col(i).tail(remainingSize)))) * matA.col(i).tail(n-i-1);\n\n    matA.bottomRightCorner(remainingSize, remainingSize).template selfadjointView<Lower>()\n      .rankUpdate(matA.col(i).tail(remainingSize), hCoeffs.tail(remainingSize), Scalar(-1));\n\n    matA.col(i).coeffRef(i+1) = beta;\n    hCoeffs.coeffRef(i) = h;\n  }\n}\n\n// forward declaration, implementation at the end of this file\ntemplate<typename MatrixType,\n         int Size=MatrixType::ColsAtCompileTime,\n         bool IsComplex=NumTraits<typename MatrixType::Scalar>::IsComplex>\nstruct tridiagonalization_inplace_selector;\n\n/** \\brief Performs a full tridiagonalization in place\n  *\n  * \\param[in,out]  mat  On input, the selfadjoint matrix whose tridiagonal\n  *    decomposition is to be computed. Only the lower triangular part referenced.\n  *    The rest is left unchanged. On output, the orthogonal matrix Q\n  *    in the decomposition if \\p extractQ is true.\n  * \\param[out]  diag  The diagonal of the tridiagonal matrix T in the\n  *    decomposition.\n  * \\param[out]  subdiag  The subdiagonal of the tridiagonal matrix T in\n  *    the decomposition.\n  * \\param[in]  extractQ  If true, the orthogonal matrix Q in the\n  *    decomposition is computed and stored in \\p mat.\n  *\n  * Computes the tridiagonal decomposition of the selfadjoint matrix \\p mat in place\n  * such that \\f$ mat = Q T Q^* \\f$ where \\f$ Q \\f$ is unitary and \\f$ T \\f$ a real\n  * symmetric tridiagonal matrix.\n  *\n  * The tridiagonal matrix T is passed to the output parameters \\p diag and \\p subdiag. If\n  * \\p extractQ is true, then the orthogonal matrix Q is passed to \\p mat. Otherwise the lower\n  * part of the matrix \\p mat is destroyed.\n  *\n  * The vectors \\p diag and \\p subdiag are not resized. The function\n  * assumes that they are already of the correct size. The length of the\n  * vector \\p diag should equal the number of rows in \\p mat, and the\n  * length of the vector \\p subdiag should be one left.\n  *\n  * This implementation contains an optimized path for 3-by-3 matrices\n  * which is especially useful for plane fitting.\n  *\n  * \\note Currently, it requires two temporary vectors to hold the intermediate\n  * Householder coefficients, and to reconstruct the matrix Q from the Householder\n  * reflectors.\n  *\n  * Example (this uses the same matrix as the example in\n  *    Tridiagonalization::Tridiagonalization(const MatrixType&)):\n  *    \\include Tridiagonalization_decomposeInPlace.cpp\n  * Output: \\verbinclude Tridiagonalization_decomposeInPlace.out\n  *\n  * \\sa class Tridiagonalization\n  */\ntemplate<typename MatrixType, typename DiagonalType, typename SubDiagonalType>\nvoid tridiagonalization_inplace(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag, bool extractQ)\n{\n  eigen_assert(mat.cols()==mat.rows() && diag.size()==mat.rows() && subdiag.size()==mat.rows()-1);\n  tridiagonalization_inplace_selector<MatrixType>::run(mat, diag, subdiag, extractQ);\n}\n\n/** \\internal\n  * General full tridiagonalization\n  */\ntemplate<typename MatrixType, int Size, bool IsComplex>\nstruct tridiagonalization_inplace_selector\n{\n  typedef typename Tridiagonalization<MatrixType>::CoeffVectorType CoeffVectorType;\n  typedef typename Tridiagonalization<MatrixType>::HouseholderSequenceType HouseholderSequenceType;\n  template<typename DiagonalType, typename SubDiagonalType>\n  static void run(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag, bool extractQ)\n  {\n    CoeffVectorType hCoeffs(mat.cols()-1);\n    tridiagonalization_inplace(mat,hCoeffs);\n    diag = mat.diagonal().real();\n    subdiag = mat.template diagonal<-1>().real();\n    if(extractQ)\n      mat = HouseholderSequenceType(mat, hCoeffs.conjugate())\n            .setLength(mat.rows() - 1)\n            .setShift(1);\n  }\n};\n\n/** \\internal\n  * Specialization for 3x3 real matrices.\n  * Especially useful for plane fitting.\n  */\ntemplate<typename MatrixType>\nstruct tridiagonalization_inplace_selector<MatrixType,3,false>\n{\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename MatrixType::RealScalar RealScalar;\n\n  template<typename DiagonalType, typename SubDiagonalType>\n  static void run(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag, bool extractQ)\n  {\n    using std::sqrt;\n    const RealScalar tol = (std::numeric_limits<RealScalar>::min)();\n    diag[0] = mat(0,0);\n    RealScalar v1norm2 = numext::abs2(mat(2,0));\n    if(v1norm2 <= tol)\n    {\n      diag[1] = mat(1,1);\n      diag[2] = mat(2,2);\n      subdiag[0] = mat(1,0);\n      subdiag[1] = mat(2,1);\n      if (extractQ)\n        mat.setIdentity();\n    }\n    else\n    {\n      RealScalar beta = sqrt(numext::abs2(mat(1,0)) + v1norm2);\n      RealScalar invBeta = RealScalar(1)/beta;\n      Scalar m01 = mat(1,0) * invBeta;\n      Scalar m02 = mat(2,0) * invBeta;\n      Scalar q = RealScalar(2)*m01*mat(2,1) + m02*(mat(2,2) - mat(1,1));\n      diag[1] = mat(1,1) + m02*q;\n      diag[2] = mat(2,2) - m02*q;\n      subdiag[0] = beta;\n      subdiag[1] = mat(2,1) - m01 * q;\n      if (extractQ)\n      {\n        mat << 1,   0,    0,\n               0, m01,  m02,\n               0, m02, -m01;\n      }\n    }\n  }\n};\n\n/** \\internal\n  * Trivial specialization for 1x1 matrices\n  */\ntemplate<typename MatrixType, bool IsComplex>\nstruct tridiagonalization_inplace_selector<MatrixType,1,IsComplex>\n{\n  typedef typename MatrixType::Scalar Scalar;\n\n  template<typename DiagonalType, typename SubDiagonalType>\n  static void run(MatrixType& mat, DiagonalType& diag, SubDiagonalType&, bool extractQ)\n  {\n    diag(0,0) = numext::real(mat(0,0));\n    if(extractQ)\n      mat(0,0) = Scalar(1);\n  }\n};\n\n/** \\internal\n  * \\eigenvalues_module \\ingroup Eigenvalues_Module\n  *\n  * \\brief Expression type for return value of Tridiagonalization::matrixT()\n  *\n  * \\tparam MatrixType type of underlying dense matrix\n  */\ntemplate<typename MatrixType> struct TridiagonalizationMatrixTReturnType\n: public ReturnByValue<TridiagonalizationMatrixTReturnType<MatrixType> >\n{\n  public:\n    /** \\brief Constructor.\n      *\n      * \\param[in] mat The underlying dense matrix\n      */\n    TridiagonalizationMatrixTReturnType(const MatrixType& mat) : m_matrix(mat) { }\n\n    template <typename ResultType>\n    inline void evalTo(ResultType& result) const\n    {\n      result.setZero();\n      result.template diagonal<1>() = m_matrix.template diagonal<-1>().conjugate();\n      result.diagonal() = m_matrix.diagonal();\n      result.template diagonal<-1>() = m_matrix.template diagonal<-1>();\n    }\n\n    Index rows() const { return m_matrix.rows(); }\n    Index cols() const { return m_matrix.cols(); }\n\n  protected:\n    typename MatrixType::Nested m_matrix;\n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_TRIDIAGONALIZATION_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Geometry/AlignedBox.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_ALIGNEDBOX_H\n#define EIGEN_ALIGNEDBOX_H\n\nnamespace Eigen { \n\n/** \\geometry_module \\ingroup Geometry_Module\n  *\n  *\n  * \\class AlignedBox\n  *\n  * \\brief An axis aligned box\n  *\n  * \\tparam _Scalar the type of the scalar coefficients\n  * \\tparam _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.\n  *\n  * This class represents an axis aligned box as a pair of the minimal and maximal corners.\n  * \\warning The result of most methods is undefined when applied to an empty box. You can check for empty boxes using isEmpty().\n  * \\sa alignedboxtypedefs\n  */\ntemplate <typename _Scalar, int _AmbientDim>\nclass AlignedBox\n{\npublic:\nEIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)\n  enum { AmbientDimAtCompileTime = _AmbientDim };\n  typedef _Scalar                                   Scalar;\n  typedef NumTraits<Scalar>                         ScalarTraits;\n  typedef Eigen::Index                              Index; ///< \\deprecated since Eigen 3.3\n  typedef typename ScalarTraits::Real               RealScalar;\n  typedef typename ScalarTraits::NonInteger         NonInteger;\n  typedef Matrix<Scalar,AmbientDimAtCompileTime,1>  VectorType;\n  typedef CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const VectorType, const VectorType> VectorTypeSum;\n\n  /** Define constants to name the corners of a 1D, 2D or 3D axis aligned bounding box */\n  enum CornerType\n  {\n    /** 1D names @{ */\n    Min=0, Max=1,\n    /** @} */\n\n    /** Identifier for 2D corner @{ */\n    BottomLeft=0, BottomRight=1,\n    TopLeft=2, TopRight=3,\n    /** @} */\n\n    /** Identifier for 3D corner  @{ */\n    BottomLeftFloor=0, BottomRightFloor=1,\n    TopLeftFloor=2, TopRightFloor=3,\n    BottomLeftCeil=4, BottomRightCeil=5,\n    TopLeftCeil=6, TopRightCeil=7\n    /** @} */\n  };\n\n\n  /** Default constructor initializing a null box. */\n  EIGEN_DEVICE_FUNC inline AlignedBox()\n  { if (AmbientDimAtCompileTime!=Dynamic) setEmpty(); }\n\n  /** Constructs a null box with \\a _dim the dimension of the ambient space. */\n  EIGEN_DEVICE_FUNC inline explicit AlignedBox(Index _dim) : m_min(_dim), m_max(_dim)\n  { setEmpty(); }\n\n  /** Constructs a box with extremities \\a _min and \\a _max.\n   * \\warning If either component of \\a _min is larger than the same component of \\a _max, the constructed box is empty. */\n  template<typename OtherVectorType1, typename OtherVectorType2>\n  EIGEN_DEVICE_FUNC inline AlignedBox(const OtherVectorType1& _min, const OtherVectorType2& _max) : m_min(_min), m_max(_max) {}\n\n  /** Constructs a box containing a single point \\a p. */\n  template<typename Derived>\n  EIGEN_DEVICE_FUNC inline explicit AlignedBox(const MatrixBase<Derived>& p) : m_min(p), m_max(m_min)\n  { }\n\n  EIGEN_DEVICE_FUNC ~AlignedBox() {}\n\n  /** \\returns the dimension in which the box holds */\n  EIGEN_DEVICE_FUNC inline Index dim() const { return AmbientDimAtCompileTime==Dynamic ? m_min.size() : Index(AmbientDimAtCompileTime); }\n\n  /** \\deprecated use isEmpty() */\n  EIGEN_DEVICE_FUNC inline bool isNull() const { return isEmpty(); }\n\n  /** \\deprecated use setEmpty() */\n  EIGEN_DEVICE_FUNC inline void setNull() { setEmpty(); }\n\n  /** \\returns true if the box is empty.\n   * \\sa setEmpty */\n  EIGEN_DEVICE_FUNC inline bool isEmpty() const { return (m_min.array() > m_max.array()).any(); }\n\n  /** Makes \\c *this an empty box.\n   * \\sa isEmpty */\n  EIGEN_DEVICE_FUNC inline void setEmpty()\n  {\n    m_min.setConstant( ScalarTraits::highest() );\n    m_max.setConstant( ScalarTraits::lowest() );\n  }\n\n  /** \\returns the minimal corner */\n  EIGEN_DEVICE_FUNC inline const VectorType& (min)() const { return m_min; }\n  /** \\returns a non const reference to the minimal corner */\n  EIGEN_DEVICE_FUNC inline VectorType& (min)() { return m_min; }\n  /** \\returns the maximal corner */\n  EIGEN_DEVICE_FUNC inline const VectorType& (max)() const { return m_max; }\n  /** \\returns a non const reference to the maximal corner */\n  EIGEN_DEVICE_FUNC inline VectorType& (max)() { return m_max; }\n\n  /** \\returns the center of the box */\n  EIGEN_DEVICE_FUNC inline const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(VectorTypeSum, RealScalar, quotient)\n  center() const\n  { return (m_min+m_max)/RealScalar(2); }\n\n  /** \\returns the lengths of the sides of the bounding box.\n    * Note that this function does not get the same\n    * result for integral or floating scalar types: see\n    */\n  EIGEN_DEVICE_FUNC inline const CwiseBinaryOp< internal::scalar_difference_op<Scalar,Scalar>, const VectorType, const VectorType> sizes() const\n  { return m_max - m_min; }\n\n  /** \\returns the volume of the bounding box */\n  EIGEN_DEVICE_FUNC inline Scalar volume() const\n  { return sizes().prod(); }\n\n  /** \\returns an expression for the bounding box diagonal vector\n    * if the length of the diagonal is needed: diagonal().norm()\n    * will provide it.\n    */\n  EIGEN_DEVICE_FUNC inline CwiseBinaryOp< internal::scalar_difference_op<Scalar,Scalar>, const VectorType, const VectorType> diagonal() const\n  { return sizes(); }\n\n  /** \\returns the vertex of the bounding box at the corner defined by\n    * the corner-id corner. It works only for a 1D, 2D or 3D bounding box.\n    * For 1D bounding boxes corners are named by 2 enum constants:\n    * BottomLeft and BottomRight.\n    * For 2D bounding boxes, corners are named by 4 enum constants:\n    * BottomLeft, BottomRight, TopLeft, TopRight.\n    * For 3D bounding boxes, the following names are added:\n    * BottomLeftCeil, BottomRightCeil, TopLeftCeil, TopRightCeil.\n    */\n  EIGEN_DEVICE_FUNC inline VectorType corner(CornerType corner) const\n  {\n    EIGEN_STATIC_ASSERT(_AmbientDim <= 3, THIS_METHOD_IS_ONLY_FOR_VECTORS_OF_A_SPECIFIC_SIZE);\n\n    VectorType res;\n\n    Index mult = 1;\n    for(Index d=0; d<dim(); ++d)\n    {\n      if( mult & corner ) res[d] = m_max[d];\n      else                res[d] = m_min[d];\n      mult *= 2;\n    }\n    return res;\n  }\n\n  /** \\returns a random point inside the bounding box sampled with\n   * a uniform distribution */\n  EIGEN_DEVICE_FUNC inline VectorType sample() const\n  {\n    VectorType r(dim());\n    for(Index d=0; d<dim(); ++d)\n    {\n      if(!ScalarTraits::IsInteger)\n      {\n        r[d] = m_min[d] + (m_max[d]-m_min[d])\n             * internal::random<Scalar>(Scalar(0), Scalar(1));\n      }\n      else\n        r[d] = internal::random(m_min[d], m_max[d]);\n    }\n    return r;\n  }\n\n  /** \\returns true if the point \\a p is inside the box \\c *this. */\n  template<typename Derived>\n  EIGEN_DEVICE_FUNC inline bool contains(const MatrixBase<Derived>& p) const\n  {\n    typename internal::nested_eval<Derived,2>::type p_n(p.derived());\n    return (m_min.array()<=p_n.array()).all() && (p_n.array()<=m_max.array()).all();\n  }\n\n  /** \\returns true if the box \\a b is entirely inside the box \\c *this. */\n  EIGEN_DEVICE_FUNC inline bool contains(const AlignedBox& b) const\n  { return (m_min.array()<=(b.min)().array()).all() && ((b.max)().array()<=m_max.array()).all(); }\n\n  /** \\returns true if the box \\a b is intersecting the box \\c *this.\n   * \\sa intersection, clamp */\n  EIGEN_DEVICE_FUNC inline bool intersects(const AlignedBox& b) const\n  { return (m_min.array()<=(b.max)().array()).all() && ((b.min)().array()<=m_max.array()).all(); }\n\n  /** Extends \\c *this such that it contains the point \\a p and returns a reference to \\c *this.\n   * \\sa extend(const AlignedBox&) */\n  template<typename Derived>\n  EIGEN_DEVICE_FUNC inline AlignedBox& extend(const MatrixBase<Derived>& p)\n  {\n    typename internal::nested_eval<Derived,2>::type p_n(p.derived());\n    m_min = m_min.cwiseMin(p_n);\n    m_max = m_max.cwiseMax(p_n);\n    return *this;\n  }\n\n  /** Extends \\c *this such that it contains the box \\a b and returns a reference to \\c *this.\n   * \\sa merged, extend(const MatrixBase&) */\n  EIGEN_DEVICE_FUNC inline AlignedBox& extend(const AlignedBox& b)\n  {\n    m_min = m_min.cwiseMin(b.m_min);\n    m_max = m_max.cwiseMax(b.m_max);\n    return *this;\n  }\n\n  /** Clamps \\c *this by the box \\a b and returns a reference to \\c *this.\n   * \\note If the boxes don't intersect, the resulting box is empty.\n   * \\sa intersection(), intersects() */\n  EIGEN_DEVICE_FUNC inline AlignedBox& clamp(const AlignedBox& b)\n  {\n    m_min = m_min.cwiseMax(b.m_min);\n    m_max = m_max.cwiseMin(b.m_max);\n    return *this;\n  }\n\n  /** Returns an AlignedBox that is the intersection of \\a b and \\c *this\n   * \\note If the boxes don't intersect, the resulting box is empty.\n   * \\sa intersects(), clamp, contains()  */\n  EIGEN_DEVICE_FUNC inline AlignedBox intersection(const AlignedBox& b) const\n  {return AlignedBox(m_min.cwiseMax(b.m_min), m_max.cwiseMin(b.m_max)); }\n\n  /** Returns an AlignedBox that is the union of \\a b and \\c *this.\n   * \\note Merging with an empty box may result in a box bigger than \\c *this. \n   * \\sa extend(const AlignedBox&) */\n  EIGEN_DEVICE_FUNC inline AlignedBox merged(const AlignedBox& b) const\n  { return AlignedBox(m_min.cwiseMin(b.m_min), m_max.cwiseMax(b.m_max)); }\n\n  /** Translate \\c *this by the vector \\a t and returns a reference to \\c *this. */\n  template<typename Derived>\n  EIGEN_DEVICE_FUNC inline AlignedBox& translate(const MatrixBase<Derived>& a_t)\n  {\n    const typename internal::nested_eval<Derived,2>::type t(a_t.derived());\n    m_min += t;\n    m_max += t;\n    return *this;\n  }\n\n  /** \\returns the squared distance between the point \\a p and the box \\c *this,\n    * and zero if \\a p is inside the box.\n    * \\sa exteriorDistance(const MatrixBase&), squaredExteriorDistance(const AlignedBox&)\n    */\n  template<typename Derived>\n  EIGEN_DEVICE_FUNC inline Scalar squaredExteriorDistance(const MatrixBase<Derived>& p) const;\n\n  /** \\returns the squared distance between the boxes \\a b and \\c *this,\n    * and zero if the boxes intersect.\n    * \\sa exteriorDistance(const AlignedBox&), squaredExteriorDistance(const MatrixBase&)\n    */\n  EIGEN_DEVICE_FUNC inline Scalar squaredExteriorDistance(const AlignedBox& b) const;\n\n  /** \\returns the distance between the point \\a p and the box \\c *this,\n    * and zero if \\a p is inside the box.\n    * \\sa squaredExteriorDistance(const MatrixBase&), exteriorDistance(const AlignedBox&)\n    */\n  template<typename Derived>\n  EIGEN_DEVICE_FUNC inline NonInteger exteriorDistance(const MatrixBase<Derived>& p) const\n  { EIGEN_USING_STD_MATH(sqrt) return sqrt(NonInteger(squaredExteriorDistance(p))); }\n\n  /** \\returns the distance between the boxes \\a b and \\c *this,\n    * and zero if the boxes intersect.\n    * \\sa squaredExteriorDistance(const AlignedBox&), exteriorDistance(const MatrixBase&)\n    */\n  EIGEN_DEVICE_FUNC inline NonInteger exteriorDistance(const AlignedBox& b) const\n  { EIGEN_USING_STD_MATH(sqrt) return sqrt(NonInteger(squaredExteriorDistance(b))); }\n\n  /** \\returns \\c *this with scalar type casted to \\a NewScalarType\n    *\n    * Note that if \\a NewScalarType is equal to the current scalar type of \\c *this\n    * then this function smartly returns a const reference to \\c *this.\n    */\n  template<typename NewScalarType>\n  EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<AlignedBox,\n           AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type cast() const\n  {\n    return typename internal::cast_return_type<AlignedBox,\n                    AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type(*this);\n  }\n\n  /** Copy constructor with scalar type conversion */\n  template<typename OtherScalarType>\n  EIGEN_DEVICE_FUNC inline explicit AlignedBox(const AlignedBox<OtherScalarType,AmbientDimAtCompileTime>& other)\n  {\n    m_min = (other.min)().template cast<Scalar>();\n    m_max = (other.max)().template cast<Scalar>();\n  }\n\n  /** \\returns \\c true if \\c *this is approximately equal to \\a other, within the precision\n    * determined by \\a prec.\n    *\n    * \\sa MatrixBase::isApprox() */\n  EIGEN_DEVICE_FUNC bool isApprox(const AlignedBox& other, const RealScalar& prec = ScalarTraits::dummy_precision()) const\n  { return m_min.isApprox(other.m_min, prec) && m_max.isApprox(other.m_max, prec); }\n\nprotected:\n\n  VectorType m_min, m_max;\n};\n\n\n\ntemplate<typename Scalar,int AmbientDim>\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC inline Scalar AlignedBox<Scalar,AmbientDim>::squaredExteriorDistance(const MatrixBase<Derived>& a_p) const\n{\n  typename internal::nested_eval<Derived,2*AmbientDim>::type p(a_p.derived());\n  Scalar dist2(0);\n  Scalar aux;\n  for (Index k=0; k<dim(); ++k)\n  {\n    if( m_min[k] > p[k] )\n    {\n      aux = m_min[k] - p[k];\n      dist2 += aux*aux;\n    }\n    else if( p[k] > m_max[k] )\n    {\n      aux = p[k] - m_max[k];\n      dist2 += aux*aux;\n    }\n  }\n  return dist2;\n}\n\ntemplate<typename Scalar,int AmbientDim>\nEIGEN_DEVICE_FUNC inline Scalar AlignedBox<Scalar,AmbientDim>::squaredExteriorDistance(const AlignedBox& b) const\n{\n  Scalar dist2(0);\n  Scalar aux;\n  for (Index k=0; k<dim(); ++k)\n  {\n    if( m_min[k] > b.m_max[k] )\n    {\n      aux = m_min[k] - b.m_max[k];\n      dist2 += aux*aux;\n    }\n    else if( b.m_min[k] > m_max[k] )\n    {\n      aux = b.m_min[k] - m_max[k];\n      dist2 += aux*aux;\n    }\n  }\n  return dist2;\n}\n\n/** \\defgroup alignedboxtypedefs Global aligned box typedefs\n  *\n  * \\ingroup Geometry_Module\n  *\n  * Eigen defines several typedef shortcuts for most common aligned box types.\n  *\n  * The general patterns are the following:\n  *\n  * \\c AlignedBoxSizeType where \\c Size can be \\c 1, \\c 2,\\c 3,\\c 4 for fixed size boxes or \\c X for dynamic size,\n  * and where \\c Type can be \\c i for integer, \\c f for float, \\c d for double.\n  *\n  * For example, \\c AlignedBox3d is a fixed-size 3x3 aligned box type of doubles, and \\c AlignedBoxXf is a dynamic-size aligned box of floats.\n  *\n  * \\sa class AlignedBox\n  */\n\n#define EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix)    \\\n/** \\ingroup alignedboxtypedefs */                                 \\\ntypedef AlignedBox<Type, Size>   AlignedBox##SizeSuffix##TypeSuffix;\n\n#define EIGEN_MAKE_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \\\nEIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 1, 1) \\\nEIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 2, 2) \\\nEIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 3, 3) \\\nEIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 4, 4) \\\nEIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Dynamic, X)\n\nEIGEN_MAKE_TYPEDEFS_ALL_SIZES(int,                  i)\nEIGEN_MAKE_TYPEDEFS_ALL_SIZES(float,                f)\nEIGEN_MAKE_TYPEDEFS_ALL_SIZES(double,               d)\n\n#undef EIGEN_MAKE_TYPEDEFS_ALL_SIZES\n#undef EIGEN_MAKE_TYPEDEFS\n\n} // end namespace Eigen\n\n#endif // EIGEN_ALIGNEDBOX_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Geometry/AngleAxis.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_ANGLEAXIS_H\n#define EIGEN_ANGLEAXIS_H\n\nnamespace Eigen { \n\n/** \\geometry_module \\ingroup Geometry_Module\n  *\n  * \\class AngleAxis\n  *\n  * \\brief Represents a 3D rotation as a rotation angle around an arbitrary 3D axis\n  *\n  * \\param _Scalar the scalar type, i.e., the type of the coefficients.\n  *\n  * \\warning When setting up an AngleAxis object, the axis vector \\b must \\b be \\b normalized.\n  *\n  * The following two typedefs are provided for convenience:\n  * \\li \\c AngleAxisf for \\c float\n  * \\li \\c AngleAxisd for \\c double\n  *\n  * Combined with MatrixBase::Unit{X,Y,Z}, AngleAxis can be used to easily\n  * mimic Euler-angles. Here is an example:\n  * \\include AngleAxis_mimic_euler.cpp\n  * Output: \\verbinclude AngleAxis_mimic_euler.out\n  *\n  * \\note This class is not aimed to be used to store a rotation transformation,\n  * but rather to make easier the creation of other rotation (Quaternion, rotation Matrix)\n  * and transformation objects.\n  *\n  * \\sa class Quaternion, class Transform, MatrixBase::UnitX()\n  */\n\nnamespace internal {\ntemplate<typename _Scalar> struct traits<AngleAxis<_Scalar> >\n{\n  typedef _Scalar Scalar;\n};\n}\n\ntemplate<typename _Scalar>\nclass AngleAxis : public RotationBase<AngleAxis<_Scalar>,3>\n{\n  typedef RotationBase<AngleAxis<_Scalar>,3> Base;\n\npublic:\n\n  using Base::operator*;\n\n  enum { Dim = 3 };\n  /** the scalar type of the coefficients */\n  typedef _Scalar Scalar;\n  typedef Matrix<Scalar,3,3> Matrix3;\n  typedef Matrix<Scalar,3,1> Vector3;\n  typedef Quaternion<Scalar> QuaternionType;\n\nprotected:\n\n  Vector3 m_axis;\n  Scalar m_angle;\n\npublic:\n\n  /** Default constructor without initialization. */\n  EIGEN_DEVICE_FUNC AngleAxis() {}\n  /** Constructs and initialize the angle-axis rotation from an \\a angle in radian\n    * and an \\a axis which \\b must \\b be \\b normalized.\n    *\n    * \\warning If the \\a axis vector is not normalized, then the angle-axis object\n    *          represents an invalid rotation. */\n  template<typename Derived>\n  EIGEN_DEVICE_FUNC \n  inline AngleAxis(const Scalar& angle, const MatrixBase<Derived>& axis) : m_axis(axis), m_angle(angle) {}\n  /** Constructs and initialize the angle-axis rotation from a quaternion \\a q.\n    * This function implicitly normalizes the quaternion \\a q.\n    */\n  template<typename QuatDerived> \n  EIGEN_DEVICE_FUNC inline explicit AngleAxis(const QuaternionBase<QuatDerived>& q) { *this = q; }\n  /** Constructs and initialize the angle-axis rotation from a 3x3 rotation matrix. */\n  template<typename Derived>\n  EIGEN_DEVICE_FUNC inline explicit AngleAxis(const MatrixBase<Derived>& m) { *this = m; }\n\n  /** \\returns the value of the rotation angle in radian */\n  EIGEN_DEVICE_FUNC Scalar angle() const { return m_angle; }\n  /** \\returns a read-write reference to the stored angle in radian */\n  EIGEN_DEVICE_FUNC Scalar& angle() { return m_angle; }\n\n  /** \\returns the rotation axis */\n  EIGEN_DEVICE_FUNC const Vector3& axis() const { return m_axis; }\n  /** \\returns a read-write reference to the stored rotation axis.\n    *\n    * \\warning The rotation axis must remain a \\b unit vector.\n    */\n  EIGEN_DEVICE_FUNC Vector3& axis() { return m_axis; }\n\n  /** Concatenates two rotations */\n  EIGEN_DEVICE_FUNC inline QuaternionType operator* (const AngleAxis& other) const\n  { return QuaternionType(*this) * QuaternionType(other); }\n\n  /** Concatenates two rotations */\n  EIGEN_DEVICE_FUNC inline QuaternionType operator* (const QuaternionType& other) const\n  { return QuaternionType(*this) * other; }\n\n  /** Concatenates two rotations */\n  friend EIGEN_DEVICE_FUNC inline QuaternionType operator* (const QuaternionType& a, const AngleAxis& b)\n  { return a * QuaternionType(b); }\n\n  /** \\returns the inverse rotation, i.e., an angle-axis with opposite rotation angle */\n  EIGEN_DEVICE_FUNC AngleAxis inverse() const\n  { return AngleAxis(-m_angle, m_axis); }\n\n  template<class QuatDerived>\n  EIGEN_DEVICE_FUNC AngleAxis& operator=(const QuaternionBase<QuatDerived>& q);\n  template<typename Derived>\n  EIGEN_DEVICE_FUNC AngleAxis& operator=(const MatrixBase<Derived>& m);\n\n  template<typename Derived>\n  EIGEN_DEVICE_FUNC AngleAxis& fromRotationMatrix(const MatrixBase<Derived>& m);\n  EIGEN_DEVICE_FUNC Matrix3 toRotationMatrix(void) const;\n\n  /** \\returns \\c *this with scalar type casted to \\a NewScalarType\n    *\n    * Note that if \\a NewScalarType is equal to the current scalar type of \\c *this\n    * then this function smartly returns a const reference to \\c *this.\n    */\n  template<typename NewScalarType>\n  EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type cast() const\n  { return typename internal::cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type(*this); }\n\n  /** Copy constructor with scalar type conversion */\n  template<typename OtherScalarType>\n  EIGEN_DEVICE_FUNC inline explicit AngleAxis(const AngleAxis<OtherScalarType>& other)\n  {\n    m_axis = other.axis().template cast<Scalar>();\n    m_angle = Scalar(other.angle());\n  }\n\n  EIGEN_DEVICE_FUNC static inline const AngleAxis Identity() { return AngleAxis(Scalar(0), Vector3::UnitX()); }\n\n  /** \\returns \\c true if \\c *this is approximately equal to \\a other, within the precision\n    * determined by \\a prec.\n    *\n    * \\sa MatrixBase::isApprox() */\n  EIGEN_DEVICE_FUNC bool isApprox(const AngleAxis& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const\n  { return m_axis.isApprox(other.m_axis, prec) && internal::isApprox(m_angle,other.m_angle, prec); }\n};\n\n/** \\ingroup Geometry_Module\n  * single precision angle-axis type */\ntypedef AngleAxis<float> AngleAxisf;\n/** \\ingroup Geometry_Module\n  * double precision angle-axis type */\ntypedef AngleAxis<double> AngleAxisd;\n\n/** Set \\c *this from a \\b unit quaternion.\n  *\n  * The resulting axis is normalized, and the computed angle is in the [0,pi] range.\n  * \n  * This function implicitly normalizes the quaternion \\a q.\n  */\ntemplate<typename Scalar>\ntemplate<typename QuatDerived>\nEIGEN_DEVICE_FUNC AngleAxis<Scalar>& AngleAxis<Scalar>::operator=(const QuaternionBase<QuatDerived>& q)\n{\n  EIGEN_USING_STD_MATH(atan2)\n  EIGEN_USING_STD_MATH(abs)\n  Scalar n = q.vec().norm();\n  if(n<NumTraits<Scalar>::epsilon())\n    n = q.vec().stableNorm();\n\n  if (n != Scalar(0))\n  {\n    m_angle = Scalar(2)*atan2(n, abs(q.w()));\n    if(q.w() < Scalar(0))\n      n = -n;\n    m_axis  = q.vec() / n;\n  }\n  else\n  {\n    m_angle = Scalar(0);\n    m_axis << Scalar(1), Scalar(0), Scalar(0);\n  }\n  return *this;\n}\n\n/** Set \\c *this from a 3x3 rotation matrix \\a mat.\n  */\ntemplate<typename Scalar>\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC AngleAxis<Scalar>& AngleAxis<Scalar>::operator=(const MatrixBase<Derived>& mat)\n{\n  // Since a direct conversion would not be really faster,\n  // let's use the robust Quaternion implementation:\n  return *this = QuaternionType(mat);\n}\n\n/**\n* \\brief Sets \\c *this from a 3x3 rotation matrix.\n**/\ntemplate<typename Scalar>\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC AngleAxis<Scalar>& AngleAxis<Scalar>::fromRotationMatrix(const MatrixBase<Derived>& mat)\n{\n  return *this = QuaternionType(mat);\n}\n\n/** Constructs and \\returns an equivalent 3x3 rotation matrix.\n  */\ntemplate<typename Scalar>\ntypename AngleAxis<Scalar>::Matrix3\nEIGEN_DEVICE_FUNC AngleAxis<Scalar>::toRotationMatrix(void) const\n{\n  EIGEN_USING_STD_MATH(sin)\n  EIGEN_USING_STD_MATH(cos)\n  Matrix3 res;\n  Vector3 sin_axis  = sin(m_angle) * m_axis;\n  Scalar c = cos(m_angle);\n  Vector3 cos1_axis = (Scalar(1)-c) * m_axis;\n\n  Scalar tmp;\n  tmp = cos1_axis.x() * m_axis.y();\n  res.coeffRef(0,1) = tmp - sin_axis.z();\n  res.coeffRef(1,0) = tmp + sin_axis.z();\n\n  tmp = cos1_axis.x() * m_axis.z();\n  res.coeffRef(0,2) = tmp + sin_axis.y();\n  res.coeffRef(2,0) = tmp - sin_axis.y();\n\n  tmp = cos1_axis.y() * m_axis.z();\n  res.coeffRef(1,2) = tmp - sin_axis.x();\n  res.coeffRef(2,1) = tmp + sin_axis.x();\n\n  res.diagonal() = (cos1_axis.cwiseProduct(m_axis)).array() + c;\n\n  return res;\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_ANGLEAXIS_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Geometry/EulerAngles.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_EULERANGLES_H\n#define EIGEN_EULERANGLES_H\n\nnamespace Eigen { \n\n/** \\geometry_module \\ingroup Geometry_Module\n  *\n  *\n  * \\returns the Euler-angles of the rotation matrix \\c *this using the convention defined by the triplet (\\a a0,\\a a1,\\a a2)\n  *\n  * Each of the three parameters \\a a0,\\a a1,\\a a2 represents the respective rotation axis as an integer in {0,1,2}.\n  * For instance, in:\n  * \\code Vector3f ea = mat.eulerAngles(2, 0, 2); \\endcode\n  * \"2\" represents the z axis and \"0\" the x axis, etc. The returned angles are such that\n  * we have the following equality:\n  * \\code\n  * mat == AngleAxisf(ea[0], Vector3f::UnitZ())\n  *      * AngleAxisf(ea[1], Vector3f::UnitX())\n  *      * AngleAxisf(ea[2], Vector3f::UnitZ()); \\endcode\n  * This corresponds to the right-multiply conventions (with right hand side frames).\n  * \n  * The returned angles are in the ranges [0:pi]x[-pi:pi]x[-pi:pi].\n  * \n  * \\sa class AngleAxis\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC inline Matrix<typename MatrixBase<Derived>::Scalar,3,1>\nMatrixBase<Derived>::eulerAngles(Index a0, Index a1, Index a2) const\n{\n  EIGEN_USING_STD_MATH(atan2)\n  EIGEN_USING_STD_MATH(sin)\n  EIGEN_USING_STD_MATH(cos)\n  /* Implemented from Graphics Gems IV */\n  EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived,3,3)\n\n  Matrix<Scalar,3,1> res;\n  typedef Matrix<typename Derived::Scalar,2,1> Vector2;\n\n  const Index odd = ((a0+1)%3 == a1) ? 0 : 1;\n  const Index i = a0;\n  const Index j = (a0 + 1 + odd)%3;\n  const Index k = (a0 + 2 - odd)%3;\n  \n  if (a0==a2)\n  {\n    res[0] = atan2(coeff(j,i), coeff(k,i));\n    if((odd && res[0]<Scalar(0)) || ((!odd) && res[0]>Scalar(0)))\n    {\n      if(res[0] > Scalar(0)) {\n        res[0] -= Scalar(EIGEN_PI);\n      }\n      else {\n        res[0] += Scalar(EIGEN_PI);\n      }\n      Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm();\n      res[1] = -atan2(s2, coeff(i,i));\n    }\n    else\n    {\n      Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm();\n      res[1] = atan2(s2, coeff(i,i));\n    }\n    \n    // With a=(0,1,0), we have i=0; j=1; k=2, and after computing the first two angles,\n    // we can compute their respective rotation, and apply its inverse to M. Since the result must\n    // be a rotation around x, we have:\n    //\n    //  c2  s1.s2 c1.s2                   1  0   0 \n    //  0   c1    -s1       *    M    =   0  c3  s3\n    //  -s2 s1.c2 c1.c2                   0 -s3  c3\n    //\n    //  Thus:  m11.c1 - m21.s1 = c3  &   m12.c1 - m22.s1 = s3\n    \n    Scalar s1 = sin(res[0]);\n    Scalar c1 = cos(res[0]);\n    res[2] = atan2(c1*coeff(j,k)-s1*coeff(k,k), c1*coeff(j,j) - s1 * coeff(k,j));\n  } \n  else\n  {\n    res[0] = atan2(coeff(j,k), coeff(k,k));\n    Scalar c2 = Vector2(coeff(i,i), coeff(i,j)).norm();\n    if((odd && res[0]<Scalar(0)) || ((!odd) && res[0]>Scalar(0))) {\n      if(res[0] > Scalar(0)) {\n        res[0] -= Scalar(EIGEN_PI);\n      }\n      else {\n        res[0] += Scalar(EIGEN_PI);\n      }\n      res[1] = atan2(-coeff(i,k), -c2);\n    }\n    else\n      res[1] = atan2(-coeff(i,k), c2);\n    Scalar s1 = sin(res[0]);\n    Scalar c1 = cos(res[0]);\n    res[2] = atan2(s1*coeff(k,i)-c1*coeff(j,i), c1*coeff(j,j) - s1 * coeff(k,j));\n  }\n  if (!odd)\n    res = -res;\n  \n  return res;\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_EULERANGLES_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Geometry/Homogeneous.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_HOMOGENEOUS_H\n#define EIGEN_HOMOGENEOUS_H\n\nnamespace Eigen { \n\n/** \\geometry_module \\ingroup Geometry_Module\n  *\n  * \\class Homogeneous\n  *\n  * \\brief Expression of one (or a set of) homogeneous vector(s)\n  *\n  * \\param MatrixType the type of the object in which we are making homogeneous\n  *\n  * This class represents an expression of one (or a set of) homogeneous vector(s).\n  * It is the return type of MatrixBase::homogeneous() and most of the time\n  * this is the only way it is used.\n  *\n  * \\sa MatrixBase::homogeneous()\n  */\n\nnamespace internal {\n\ntemplate<typename MatrixType,int Direction>\nstruct traits<Homogeneous<MatrixType,Direction> >\n : traits<MatrixType>\n{\n  typedef typename traits<MatrixType>::StorageKind StorageKind;\n  typedef typename ref_selector<MatrixType>::type MatrixTypeNested;\n  typedef typename remove_reference<MatrixTypeNested>::type _MatrixTypeNested;\n  enum {\n    RowsPlusOne = (MatrixType::RowsAtCompileTime != Dynamic) ?\n                  int(MatrixType::RowsAtCompileTime) + 1 : Dynamic,\n    ColsPlusOne = (MatrixType::ColsAtCompileTime != Dynamic) ?\n                  int(MatrixType::ColsAtCompileTime) + 1 : Dynamic,\n    RowsAtCompileTime = Direction==Vertical  ?  RowsPlusOne : MatrixType::RowsAtCompileTime,\n    ColsAtCompileTime = Direction==Horizontal ? ColsPlusOne : MatrixType::ColsAtCompileTime,\n    MaxRowsAtCompileTime = RowsAtCompileTime,\n    MaxColsAtCompileTime = ColsAtCompileTime,\n    TmpFlags = _MatrixTypeNested::Flags & HereditaryBits,\n    Flags = ColsAtCompileTime==1 ? (TmpFlags & ~RowMajorBit)\n          : RowsAtCompileTime==1 ? (TmpFlags | RowMajorBit)\n          : TmpFlags\n  };\n};\n\ntemplate<typename MatrixType,typename Lhs> struct homogeneous_left_product_impl;\ntemplate<typename MatrixType,typename Rhs> struct homogeneous_right_product_impl;\n\n} // end namespace internal\n\ntemplate<typename MatrixType,int _Direction> class Homogeneous\n  : public MatrixBase<Homogeneous<MatrixType,_Direction> >, internal::no_assignment_operator\n{\n  public:\n\n    typedef MatrixType NestedExpression;\n    enum { Direction = _Direction };\n\n    typedef MatrixBase<Homogeneous> Base;\n    EIGEN_DENSE_PUBLIC_INTERFACE(Homogeneous)\n\n    EIGEN_DEVICE_FUNC explicit inline Homogeneous(const MatrixType& matrix)\n      : m_matrix(matrix)\n    {}\n\n    EIGEN_DEVICE_FUNC inline Index rows() const { return m_matrix.rows() + (int(Direction)==Vertical   ? 1 : 0); }\n    EIGEN_DEVICE_FUNC inline Index cols() const { return m_matrix.cols() + (int(Direction)==Horizontal ? 1 : 0); }\n    \n    EIGEN_DEVICE_FUNC const NestedExpression& nestedExpression() const { return m_matrix; }\n\n    template<typename Rhs>\n    EIGEN_DEVICE_FUNC inline const Product<Homogeneous,Rhs>\n    operator* (const MatrixBase<Rhs>& rhs) const\n    {\n      eigen_assert(int(Direction)==Horizontal);\n      return Product<Homogeneous,Rhs>(*this,rhs.derived());\n    }\n\n    template<typename Lhs> friend\n    EIGEN_DEVICE_FUNC inline const Product<Lhs,Homogeneous>\n    operator* (const MatrixBase<Lhs>& lhs, const Homogeneous& rhs)\n    {\n      eigen_assert(int(Direction)==Vertical);\n      return Product<Lhs,Homogeneous>(lhs.derived(),rhs);\n    }\n\n    template<typename Scalar, int Dim, int Mode, int Options> friend\n    EIGEN_DEVICE_FUNC inline const Product<Transform<Scalar,Dim,Mode,Options>, Homogeneous >\n    operator* (const Transform<Scalar,Dim,Mode,Options>& lhs, const Homogeneous& rhs)\n    {\n      eigen_assert(int(Direction)==Vertical);\n      return Product<Transform<Scalar,Dim,Mode,Options>, Homogeneous>(lhs,rhs);\n    }\n\n    template<typename Func>\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::result_of<Func(Scalar,Scalar)>::type\n    redux(const Func& func) const\n    {\n      return func(m_matrix.redux(func), Scalar(1));\n    }\n\n  protected:\n    typename MatrixType::Nested m_matrix;\n};\n\n/** \\geometry_module \\ingroup Geometry_Module\n  *\n  * \\returns a vector expression that is one longer than the vector argument, with the value 1 symbolically appended as the last coefficient.\n  *\n  * This can be used to convert affine coordinates to homogeneous coordinates.\n  *\n  * \\only_for_vectors\n  *\n  * Example: \\include MatrixBase_homogeneous.cpp\n  * Output: \\verbinclude MatrixBase_homogeneous.out\n  *\n  * \\sa VectorwiseOp::homogeneous(), class Homogeneous\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::HomogeneousReturnType\nMatrixBase<Derived>::homogeneous() const\n{\n  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);\n  return HomogeneousReturnType(derived());\n}\n\n/** \\geometry_module \\ingroup Geometry_Module\n  *\n  * \\returns an expression where the value 1 is symbolically appended as the final coefficient to each column (or row) of the matrix.\n  *\n  * This can be used to convert affine coordinates to homogeneous coordinates.\n  *\n  * Example: \\include VectorwiseOp_homogeneous.cpp\n  * Output: \\verbinclude VectorwiseOp_homogeneous.out\n  *\n  * \\sa MatrixBase::homogeneous(), class Homogeneous */\ntemplate<typename ExpressionType, int Direction>\nEIGEN_DEVICE_FUNC inline Homogeneous<ExpressionType,Direction>\nVectorwiseOp<ExpressionType,Direction>::homogeneous() const\n{\n  return HomogeneousReturnType(_expression());\n}\n\n/** \\geometry_module \\ingroup Geometry_Module\n  *\n  * \\brief homogeneous normalization\n  *\n  * \\returns a vector expression of the N-1 first coefficients of \\c *this divided by that last coefficient.\n  *\n  * This can be used to convert homogeneous coordinates to affine coordinates.\n  *\n  * It is essentially a shortcut for:\n  * \\code\n    this->head(this->size()-1)/this->coeff(this->size()-1);\n    \\endcode\n  *\n  * Example: \\include MatrixBase_hnormalized.cpp\n  * Output: \\verbinclude MatrixBase_hnormalized.out\n  *\n  * \\sa VectorwiseOp::hnormalized() */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC inline const typename MatrixBase<Derived>::HNormalizedReturnType\nMatrixBase<Derived>::hnormalized() const\n{\n  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);\n  return ConstStartMinusOne(derived(),0,0,\n    ColsAtCompileTime==1?size()-1:1,\n    ColsAtCompileTime==1?1:size()-1) / coeff(size()-1);\n}\n\n/** \\geometry_module \\ingroup Geometry_Module\n  *\n  * \\brief column or row-wise homogeneous normalization\n  *\n  * \\returns an expression of the first N-1 coefficients of each column (or row) of \\c *this divided by the last coefficient of each column (or row).\n  *\n  * This can be used to convert homogeneous coordinates to affine coordinates.\n  *\n  * It is conceptually equivalent to calling MatrixBase::hnormalized() to each column (or row) of \\c *this.\n  *\n  * Example: \\include DirectionWise_hnormalized.cpp\n  * Output: \\verbinclude DirectionWise_hnormalized.out\n  *\n  * \\sa MatrixBase::hnormalized() */\ntemplate<typename ExpressionType, int Direction>\nEIGEN_DEVICE_FUNC inline const typename VectorwiseOp<ExpressionType,Direction>::HNormalizedReturnType\nVectorwiseOp<ExpressionType,Direction>::hnormalized() const\n{\n  return HNormalized_Block(_expression(),0,0,\n      Direction==Vertical   ? _expression().rows()-1 : _expression().rows(),\n      Direction==Horizontal ? _expression().cols()-1 : _expression().cols()).cwiseQuotient(\n      Replicate<HNormalized_Factors,\n                Direction==Vertical   ? HNormalized_SizeMinusOne : 1,\n                Direction==Horizontal ? HNormalized_SizeMinusOne : 1>\n        (HNormalized_Factors(_expression(),\n          Direction==Vertical    ? _expression().rows()-1:0,\n          Direction==Horizontal  ? _expression().cols()-1:0,\n          Direction==Vertical    ? 1 : _expression().rows(),\n          Direction==Horizontal  ? 1 : _expression().cols()),\n         Direction==Vertical   ? _expression().rows()-1 : 1,\n         Direction==Horizontal ? _expression().cols()-1 : 1));\n}\n\nnamespace internal {\n\ntemplate<typename MatrixOrTransformType>\nstruct take_matrix_for_product\n{\n  typedef MatrixOrTransformType type;\n  EIGEN_DEVICE_FUNC static const type& run(const type &x) { return x; }\n};\n\ntemplate<typename Scalar, int Dim, int Mode,int Options>\nstruct take_matrix_for_product<Transform<Scalar, Dim, Mode, Options> >\n{\n  typedef Transform<Scalar, Dim, Mode, Options> TransformType;\n  typedef typename internal::add_const<typename TransformType::ConstAffinePart>::type type;\n  EIGEN_DEVICE_FUNC static type run (const TransformType& x) { return x.affine(); }\n};\n\ntemplate<typename Scalar, int Dim, int Options>\nstruct take_matrix_for_product<Transform<Scalar, Dim, Projective, Options> >\n{\n  typedef Transform<Scalar, Dim, Projective, Options> TransformType;\n  typedef typename TransformType::MatrixType type;\n  EIGEN_DEVICE_FUNC static const type& run (const TransformType& x) { return x.matrix(); }\n};\n\ntemplate<typename MatrixType,typename Lhs>\nstruct traits<homogeneous_left_product_impl<Homogeneous<MatrixType,Vertical>,Lhs> >\n{\n  typedef typename take_matrix_for_product<Lhs>::type LhsMatrixType;\n  typedef typename remove_all<MatrixType>::type MatrixTypeCleaned;\n  typedef typename remove_all<LhsMatrixType>::type LhsMatrixTypeCleaned;\n  typedef typename make_proper_matrix_type<\n                 typename traits<MatrixTypeCleaned>::Scalar,\n                 LhsMatrixTypeCleaned::RowsAtCompileTime,\n                 MatrixTypeCleaned::ColsAtCompileTime,\n                 MatrixTypeCleaned::PlainObject::Options,\n                 LhsMatrixTypeCleaned::MaxRowsAtCompileTime,\n                 MatrixTypeCleaned::MaxColsAtCompileTime>::type ReturnType;\n};\n\ntemplate<typename MatrixType,typename Lhs>\nstruct homogeneous_left_product_impl<Homogeneous<MatrixType,Vertical>,Lhs>\n  : public ReturnByValue<homogeneous_left_product_impl<Homogeneous<MatrixType,Vertical>,Lhs> >\n{\n  typedef typename traits<homogeneous_left_product_impl>::LhsMatrixType LhsMatrixType;\n  typedef typename remove_all<LhsMatrixType>::type LhsMatrixTypeCleaned;\n  typedef typename remove_all<typename LhsMatrixTypeCleaned::Nested>::type LhsMatrixTypeNested;\n  EIGEN_DEVICE_FUNC homogeneous_left_product_impl(const Lhs& lhs, const MatrixType& rhs)\n    : m_lhs(take_matrix_for_product<Lhs>::run(lhs)),\n      m_rhs(rhs)\n  {}\n\n  EIGEN_DEVICE_FUNC inline Index rows() const { return m_lhs.rows(); }\n  EIGEN_DEVICE_FUNC inline Index cols() const { return m_rhs.cols(); }\n\n  template<typename Dest> EIGEN_DEVICE_FUNC void evalTo(Dest& dst) const\n  {\n    // FIXME investigate how to allow lazy evaluation of this product when possible\n    dst = Block<const LhsMatrixTypeNested,\n              LhsMatrixTypeNested::RowsAtCompileTime,\n              LhsMatrixTypeNested::ColsAtCompileTime==Dynamic?Dynamic:LhsMatrixTypeNested::ColsAtCompileTime-1>\n            (m_lhs,0,0,m_lhs.rows(),m_lhs.cols()-1) * m_rhs;\n    dst += m_lhs.col(m_lhs.cols()-1).rowwise()\n            .template replicate<MatrixType::ColsAtCompileTime>(m_rhs.cols());\n  }\n\n  typename LhsMatrixTypeCleaned::Nested m_lhs;\n  typename MatrixType::Nested m_rhs;\n};\n\ntemplate<typename MatrixType,typename Rhs>\nstruct traits<homogeneous_right_product_impl<Homogeneous<MatrixType,Horizontal>,Rhs> >\n{\n  typedef typename make_proper_matrix_type<typename traits<MatrixType>::Scalar,\n                 MatrixType::RowsAtCompileTime,\n                 Rhs::ColsAtCompileTime,\n                 MatrixType::PlainObject::Options,\n                 MatrixType::MaxRowsAtCompileTime,\n                 Rhs::MaxColsAtCompileTime>::type ReturnType;\n};\n\ntemplate<typename MatrixType,typename Rhs>\nstruct homogeneous_right_product_impl<Homogeneous<MatrixType,Horizontal>,Rhs>\n  : public ReturnByValue<homogeneous_right_product_impl<Homogeneous<MatrixType,Horizontal>,Rhs> >\n{\n  typedef typename remove_all<typename Rhs::Nested>::type RhsNested;\n  EIGEN_DEVICE_FUNC homogeneous_right_product_impl(const MatrixType& lhs, const Rhs& rhs)\n    : m_lhs(lhs), m_rhs(rhs)\n  {}\n\n  EIGEN_DEVICE_FUNC inline Index rows() const { return m_lhs.rows(); }\n  EIGEN_DEVICE_FUNC inline Index cols() const { return m_rhs.cols(); }\n\n  template<typename Dest> EIGEN_DEVICE_FUNC void evalTo(Dest& dst) const\n  {\n    // FIXME investigate how to allow lazy evaluation of this product when possible\n    dst = m_lhs * Block<const RhsNested,\n                        RhsNested::RowsAtCompileTime==Dynamic?Dynamic:RhsNested::RowsAtCompileTime-1,\n                        RhsNested::ColsAtCompileTime>\n            (m_rhs,0,0,m_rhs.rows()-1,m_rhs.cols());\n    dst += m_rhs.row(m_rhs.rows()-1).colwise()\n            .template replicate<MatrixType::RowsAtCompileTime>(m_lhs.rows());\n  }\n\n  typename MatrixType::Nested m_lhs;\n  typename Rhs::Nested m_rhs;\n};\n\ntemplate<typename ArgType,int Direction>\nstruct evaluator_traits<Homogeneous<ArgType,Direction> >\n{\n  typedef typename storage_kind_to_evaluator_kind<typename ArgType::StorageKind>::Kind Kind;\n  typedef HomogeneousShape Shape;  \n};\n\ntemplate<> struct AssignmentKind<DenseShape,HomogeneousShape> { typedef Dense2Dense Kind; };\n\n\ntemplate<typename ArgType,int Direction>\nstruct unary_evaluator<Homogeneous<ArgType,Direction>, IndexBased>\n  : evaluator<typename Homogeneous<ArgType,Direction>::PlainObject >\n{\n  typedef Homogeneous<ArgType,Direction> XprType;\n  typedef typename XprType::PlainObject PlainObject;\n  typedef evaluator<PlainObject> Base;\n\n  EIGEN_DEVICE_FUNC explicit unary_evaluator(const XprType& op)\n    : Base(), m_temp(op)\n  {\n    ::new (static_cast<Base*>(this)) Base(m_temp);\n  }\n\nprotected:\n  PlainObject m_temp;\n};\n\n// dense = homogeneous\ntemplate< typename DstXprType, typename ArgType, typename Scalar>\nstruct Assignment<DstXprType, Homogeneous<ArgType,Vertical>, internal::assign_op<Scalar,typename ArgType::Scalar>, Dense2Dense>\n{\n  typedef Homogeneous<ArgType,Vertical> SrcXprType;\n  EIGEN_DEVICE_FUNC static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,typename ArgType::Scalar> &)\n  {\n    Index dstRows = src.rows();\n    Index dstCols = src.cols();\n    if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))\n      dst.resize(dstRows, dstCols);\n\n    dst.template topRows<ArgType::RowsAtCompileTime>(src.nestedExpression().rows()) = src.nestedExpression();\n    dst.row(dst.rows()-1).setOnes();\n  }\n};\n\n// dense = homogeneous\ntemplate< typename DstXprType, typename ArgType, typename Scalar>\nstruct Assignment<DstXprType, Homogeneous<ArgType,Horizontal>, internal::assign_op<Scalar,typename ArgType::Scalar>, Dense2Dense>\n{\n  typedef Homogeneous<ArgType,Horizontal> SrcXprType;\n  EIGEN_DEVICE_FUNC static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,typename ArgType::Scalar> &)\n  {\n    Index dstRows = src.rows();\n    Index dstCols = src.cols();\n    if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))\n      dst.resize(dstRows, dstCols);\n\n    dst.template leftCols<ArgType::ColsAtCompileTime>(src.nestedExpression().cols()) = src.nestedExpression();\n    dst.col(dst.cols()-1).setOnes();\n  }\n};\n\ntemplate<typename LhsArg, typename Rhs, int ProductTag>\nstruct generic_product_impl<Homogeneous<LhsArg,Horizontal>, Rhs, HomogeneousShape, DenseShape, ProductTag>\n{\n  template<typename Dest>\n  EIGEN_DEVICE_FUNC static void evalTo(Dest& dst, const Homogeneous<LhsArg,Horizontal>& lhs, const Rhs& rhs)\n  {\n    homogeneous_right_product_impl<Homogeneous<LhsArg,Horizontal>, Rhs>(lhs.nestedExpression(), rhs).evalTo(dst);\n  }\n};\n\ntemplate<typename Lhs,typename Rhs>\nstruct homogeneous_right_product_refactoring_helper\n{\n  enum {\n    Dim  = Lhs::ColsAtCompileTime,\n    Rows = Lhs::RowsAtCompileTime\n  };\n  typedef typename Rhs::template ConstNRowsBlockXpr<Dim>::Type          LinearBlockConst;\n  typedef typename remove_const<LinearBlockConst>::type                 LinearBlock;\n  typedef typename Rhs::ConstRowXpr                                     ConstantColumn;\n  typedef Replicate<const ConstantColumn,Rows,1>                        ConstantBlock;\n  typedef Product<Lhs,LinearBlock,LazyProduct>                          LinearProduct;\n  typedef CwiseBinaryOp<internal::scalar_sum_op<typename Lhs::Scalar,typename Rhs::Scalar>, const LinearProduct, const ConstantBlock> Xpr;\n};\n\ntemplate<typename Lhs, typename Rhs, int ProductTag>\nstruct product_evaluator<Product<Lhs, Rhs, LazyProduct>, ProductTag, HomogeneousShape, DenseShape>\n : public evaluator<typename homogeneous_right_product_refactoring_helper<typename Lhs::NestedExpression,Rhs>::Xpr>\n{\n  typedef Product<Lhs, Rhs, LazyProduct> XprType;\n  typedef homogeneous_right_product_refactoring_helper<typename Lhs::NestedExpression,Rhs> helper;\n  typedef typename helper::ConstantBlock ConstantBlock;\n  typedef typename helper::Xpr RefactoredXpr;\n  typedef evaluator<RefactoredXpr> Base;\n  \n  EIGEN_DEVICE_FUNC explicit product_evaluator(const XprType& xpr)\n    : Base(  xpr.lhs().nestedExpression() .lazyProduct(  xpr.rhs().template topRows<helper::Dim>(xpr.lhs().nestedExpression().cols()) )\n            + ConstantBlock(xpr.rhs().row(xpr.rhs().rows()-1),xpr.lhs().rows(), 1) )\n  {}\n};\n\ntemplate<typename Lhs, typename RhsArg, int ProductTag>\nstruct generic_product_impl<Lhs, Homogeneous<RhsArg,Vertical>, DenseShape, HomogeneousShape, ProductTag>\n{\n  template<typename Dest>\n  EIGEN_DEVICE_FUNC static void evalTo(Dest& dst, const Lhs& lhs, const Homogeneous<RhsArg,Vertical>& rhs)\n  {\n    homogeneous_left_product_impl<Homogeneous<RhsArg,Vertical>, Lhs>(lhs, rhs.nestedExpression()).evalTo(dst);\n  }\n};\n\n// TODO: the following specialization is to address a regression from 3.2 to 3.3\n// In the future, this path should be optimized.\ntemplate<typename Lhs, typename RhsArg, int ProductTag>\nstruct generic_product_impl<Lhs, Homogeneous<RhsArg,Vertical>, TriangularShape, HomogeneousShape, ProductTag>\n{\n  template<typename Dest>\n  static void evalTo(Dest& dst, const Lhs& lhs, const Homogeneous<RhsArg,Vertical>& rhs)\n  {\n    dst.noalias() = lhs * rhs.eval();\n  }\n};\n\ntemplate<typename Lhs,typename Rhs>\nstruct homogeneous_left_product_refactoring_helper\n{\n  enum {\n    Dim = Rhs::RowsAtCompileTime,\n    Cols = Rhs::ColsAtCompileTime\n  };\n  typedef typename Lhs::template ConstNColsBlockXpr<Dim>::Type          LinearBlockConst;\n  typedef typename remove_const<LinearBlockConst>::type                 LinearBlock;\n  typedef typename Lhs::ConstColXpr                                     ConstantColumn;\n  typedef Replicate<const ConstantColumn,1,Cols>                        ConstantBlock;\n  typedef Product<LinearBlock,Rhs,LazyProduct>                          LinearProduct;\n  typedef CwiseBinaryOp<internal::scalar_sum_op<typename Lhs::Scalar,typename Rhs::Scalar>, const LinearProduct, const ConstantBlock> Xpr;\n};\n\ntemplate<typename Lhs, typename Rhs, int ProductTag>\nstruct product_evaluator<Product<Lhs, Rhs, LazyProduct>, ProductTag, DenseShape, HomogeneousShape>\n : public evaluator<typename homogeneous_left_product_refactoring_helper<Lhs,typename Rhs::NestedExpression>::Xpr>\n{\n  typedef Product<Lhs, Rhs, LazyProduct> XprType;\n  typedef homogeneous_left_product_refactoring_helper<Lhs,typename Rhs::NestedExpression> helper;\n  typedef typename helper::ConstantBlock ConstantBlock;\n  typedef typename helper::Xpr RefactoredXpr;\n  typedef evaluator<RefactoredXpr> Base;\n  \n  EIGEN_DEVICE_FUNC explicit product_evaluator(const XprType& xpr)\n    : Base(   xpr.lhs().template leftCols<helper::Dim>(xpr.rhs().nestedExpression().rows()) .lazyProduct( xpr.rhs().nestedExpression() )\n            + ConstantBlock(xpr.lhs().col(xpr.lhs().cols()-1),1,xpr.rhs().cols()) )\n  {}\n};\n\ntemplate<typename Scalar, int Dim, int Mode,int Options, typename RhsArg, int ProductTag>\nstruct generic_product_impl<Transform<Scalar,Dim,Mode,Options>, Homogeneous<RhsArg,Vertical>, DenseShape, HomogeneousShape, ProductTag>\n{\n  typedef Transform<Scalar,Dim,Mode,Options> TransformType;\n  template<typename Dest>\n  EIGEN_DEVICE_FUNC static void evalTo(Dest& dst, const TransformType& lhs, const Homogeneous<RhsArg,Vertical>& rhs)\n  {\n    homogeneous_left_product_impl<Homogeneous<RhsArg,Vertical>, TransformType>(lhs, rhs.nestedExpression()).evalTo(dst);\n  }\n};\n\ntemplate<typename ExpressionType, int Side, bool Transposed>\nstruct permutation_matrix_product<ExpressionType, Side, Transposed, HomogeneousShape>\n  : public permutation_matrix_product<ExpressionType, Side, Transposed, DenseShape>\n{};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_HOMOGENEOUS_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Geometry/Hyperplane.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_HYPERPLANE_H\n#define EIGEN_HYPERPLANE_H\n\nnamespace Eigen { \n\n/** \\geometry_module \\ingroup Geometry_Module\n  *\n  * \\class Hyperplane\n  *\n  * \\brief A hyperplane\n  *\n  * A hyperplane is an affine subspace of dimension n-1 in a space of dimension n.\n  * For example, a hyperplane in a plane is a line; a hyperplane in 3-space is a plane.\n  *\n  * \\tparam _Scalar the scalar type, i.e., the type of the coefficients\n  * \\tparam _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.\n  *             Notice that the dimension of the hyperplane is _AmbientDim-1.\n  *\n  * This class represents an hyperplane as the zero set of the implicit equation\n  * \\f$ n \\cdot x + d = 0 \\f$ where \\f$ n \\f$ is a unit normal vector of the plane (linear part)\n  * and \\f$ d \\f$ is the distance (offset) to the origin.\n  */\ntemplate <typename _Scalar, int _AmbientDim, int _Options>\nclass Hyperplane\n{\npublic:\n  EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim==Dynamic ? Dynamic : _AmbientDim+1)\n  enum {\n    AmbientDimAtCompileTime = _AmbientDim,\n    Options = _Options\n  };\n  typedef _Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  typedef Eigen::Index Index; ///< \\deprecated since Eigen 3.3\n  typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType;\n  typedef Matrix<Scalar,Index(AmbientDimAtCompileTime)==Dynamic\n                        ? Dynamic\n                        : Index(AmbientDimAtCompileTime)+1,1,Options> Coefficients;\n  typedef Block<Coefficients,AmbientDimAtCompileTime,1> NormalReturnType;\n  typedef const Block<const Coefficients,AmbientDimAtCompileTime,1> ConstNormalReturnType;\n\n  /** Default constructor without initialization */\n  EIGEN_DEVICE_FUNC inline Hyperplane() {}\n  \n  template<int OtherOptions>\n  EIGEN_DEVICE_FUNC Hyperplane(const Hyperplane<Scalar,AmbientDimAtCompileTime,OtherOptions>& other)\n   : m_coeffs(other.coeffs())\n  {}\n\n  /** Constructs a dynamic-size hyperplane with \\a _dim the dimension\n    * of the ambient space */\n  EIGEN_DEVICE_FUNC inline explicit Hyperplane(Index _dim) : m_coeffs(_dim+1) {}\n\n  /** Construct a plane from its normal \\a n and a point \\a e onto the plane.\n    * \\warning the vector normal is assumed to be normalized.\n    */\n  EIGEN_DEVICE_FUNC inline Hyperplane(const VectorType& n, const VectorType& e)\n    : m_coeffs(n.size()+1)\n  {\n    normal() = n;\n    offset() = -n.dot(e);\n  }\n\n  /** Constructs a plane from its normal \\a n and distance to the origin \\a d\n    * such that the algebraic equation of the plane is \\f$ n \\cdot x + d = 0 \\f$.\n    * \\warning the vector normal is assumed to be normalized.\n    */\n  EIGEN_DEVICE_FUNC inline Hyperplane(const VectorType& n, const Scalar& d)\n    : m_coeffs(n.size()+1)\n  {\n    normal() = n;\n    offset() = d;\n  }\n\n  /** Constructs a hyperplane passing through the two points. If the dimension of the ambient space\n    * is greater than 2, then there isn't uniqueness, so an arbitrary choice is made.\n    */\n  EIGEN_DEVICE_FUNC static inline Hyperplane Through(const VectorType& p0, const VectorType& p1)\n  {\n    Hyperplane result(p0.size());\n    result.normal() = (p1 - p0).unitOrthogonal();\n    result.offset() = -p0.dot(result.normal());\n    return result;\n  }\n\n  /** Constructs a hyperplane passing through the three points. The dimension of the ambient space\n    * is required to be exactly 3.\n    */\n  EIGEN_DEVICE_FUNC static inline Hyperplane Through(const VectorType& p0, const VectorType& p1, const VectorType& p2)\n  {\n    EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 3)\n    Hyperplane result(p0.size());\n    VectorType v0(p2 - p0), v1(p1 - p0);\n    result.normal() = v0.cross(v1);\n    RealScalar norm = result.normal().norm();\n    if(norm <= v0.norm() * v1.norm() * NumTraits<RealScalar>::epsilon())\n    {\n      Matrix<Scalar,2,3> m; m << v0.transpose(), v1.transpose();\n      JacobiSVD<Matrix<Scalar,2,3> > svd(m, ComputeFullV);\n      result.normal() = svd.matrixV().col(2);\n    }\n    else\n      result.normal() /= norm;\n    result.offset() = -p0.dot(result.normal());\n    return result;\n  }\n\n  /** Constructs a hyperplane passing through the parametrized line \\a parametrized.\n    * If the dimension of the ambient space is greater than 2, then there isn't uniqueness,\n    * so an arbitrary choice is made.\n    */\n  // FIXME to be consitent with the rest this could be implemented as a static Through function ??\n  EIGEN_DEVICE_FUNC explicit Hyperplane(const ParametrizedLine<Scalar, AmbientDimAtCompileTime>& parametrized)\n  {\n    normal() = parametrized.direction().unitOrthogonal();\n    offset() = -parametrized.origin().dot(normal());\n  }\n\n  EIGEN_DEVICE_FUNC ~Hyperplane() {}\n\n  /** \\returns the dimension in which the plane holds */\n  EIGEN_DEVICE_FUNC inline Index dim() const { return AmbientDimAtCompileTime==Dynamic ? m_coeffs.size()-1 : Index(AmbientDimAtCompileTime); }\n\n  /** normalizes \\c *this */\n  EIGEN_DEVICE_FUNC void normalize(void)\n  {\n    m_coeffs /= normal().norm();\n  }\n\n  /** \\returns the signed distance between the plane \\c *this and a point \\a p.\n    * \\sa absDistance()\n    */\n  EIGEN_DEVICE_FUNC inline Scalar signedDistance(const VectorType& p) const { return normal().dot(p) + offset(); }\n\n  /** \\returns the absolute distance between the plane \\c *this and a point \\a p.\n    * \\sa signedDistance()\n    */\n  EIGEN_DEVICE_FUNC inline Scalar absDistance(const VectorType& p) const { return numext::abs(signedDistance(p)); }\n\n  /** \\returns the projection of a point \\a p onto the plane \\c *this.\n    */\n  EIGEN_DEVICE_FUNC inline VectorType projection(const VectorType& p) const { return p - signedDistance(p) * normal(); }\n\n  /** \\returns a constant reference to the unit normal vector of the plane, which corresponds\n    * to the linear part of the implicit equation.\n    */\n  EIGEN_DEVICE_FUNC inline ConstNormalReturnType normal() const { return ConstNormalReturnType(m_coeffs,0,0,dim(),1); }\n\n  /** \\returns a non-constant reference to the unit normal vector of the plane, which corresponds\n    * to the linear part of the implicit equation.\n    */\n  EIGEN_DEVICE_FUNC inline NormalReturnType normal() { return NormalReturnType(m_coeffs,0,0,dim(),1); }\n\n  /** \\returns the distance to the origin, which is also the \"constant term\" of the implicit equation\n    * \\warning the vector normal is assumed to be normalized.\n    */\n  EIGEN_DEVICE_FUNC inline const Scalar& offset() const { return m_coeffs.coeff(dim()); }\n\n  /** \\returns a non-constant reference to the distance to the origin, which is also the constant part\n    * of the implicit equation */\n  EIGEN_DEVICE_FUNC inline Scalar& offset() { return m_coeffs(dim()); }\n\n  /** \\returns a constant reference to the coefficients c_i of the plane equation:\n    * \\f$ c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0 \\f$\n    */\n  EIGEN_DEVICE_FUNC inline const Coefficients& coeffs() const { return m_coeffs; }\n\n  /** \\returns a non-constant reference to the coefficients c_i of the plane equation:\n    * \\f$ c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0 \\f$\n    */\n  EIGEN_DEVICE_FUNC inline Coefficients& coeffs() { return m_coeffs; }\n\n  /** \\returns the intersection of *this with \\a other.\n    *\n    * \\warning The ambient space must be a plane, i.e. have dimension 2, so that \\c *this and \\a other are lines.\n    *\n    * \\note If \\a other is approximately parallel to *this, this method will return any point on *this.\n    */\n  EIGEN_DEVICE_FUNC VectorType intersection(const Hyperplane& other) const\n  {\n    EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2)\n    Scalar det = coeffs().coeff(0) * other.coeffs().coeff(1) - coeffs().coeff(1) * other.coeffs().coeff(0);\n    // since the line equations ax+by=c are normalized with a^2+b^2=1, the following tests\n    // whether the two lines are approximately parallel.\n    if(internal::isMuchSmallerThan(det, Scalar(1)))\n    {   // special case where the two lines are approximately parallel. Pick any point on the first line.\n        if(numext::abs(coeffs().coeff(1))>numext::abs(coeffs().coeff(0)))\n            return VectorType(coeffs().coeff(1), -coeffs().coeff(2)/coeffs().coeff(1)-coeffs().coeff(0));\n        else\n            return VectorType(-coeffs().coeff(2)/coeffs().coeff(0)-coeffs().coeff(1), coeffs().coeff(0));\n    }\n    else\n    {   // general case\n        Scalar invdet = Scalar(1) / det;\n        return VectorType(invdet*(coeffs().coeff(1)*other.coeffs().coeff(2)-other.coeffs().coeff(1)*coeffs().coeff(2)),\n                          invdet*(other.coeffs().coeff(0)*coeffs().coeff(2)-coeffs().coeff(0)*other.coeffs().coeff(2)));\n    }\n  }\n\n  /** Applies the transformation matrix \\a mat to \\c *this and returns a reference to \\c *this.\n    *\n    * \\param mat the Dim x Dim transformation matrix\n    * \\param traits specifies whether the matrix \\a mat represents an #Isometry\n    *               or a more generic #Affine transformation. The default is #Affine.\n    */\n  template<typename XprType>\n  EIGEN_DEVICE_FUNC inline Hyperplane& transform(const MatrixBase<XprType>& mat, TransformTraits traits = Affine)\n  {\n    if (traits==Affine)\n    {\n      normal() = mat.inverse().transpose() * normal();\n      m_coeffs /= normal().norm();\n    }\n    else if (traits==Isometry)\n      normal() = mat * normal();\n    else\n    {\n      eigen_assert(0 && \"invalid traits value in Hyperplane::transform()\");\n    }\n    return *this;\n  }\n\n  /** Applies the transformation \\a t to \\c *this and returns a reference to \\c *this.\n    *\n    * \\param t the transformation of dimension Dim\n    * \\param traits specifies whether the transformation \\a t represents an #Isometry\n    *               or a more generic #Affine transformation. The default is #Affine.\n    *               Other kind of transformations are not supported.\n    */\n  template<int TrOptions>\n  EIGEN_DEVICE_FUNC inline Hyperplane& transform(const Transform<Scalar,AmbientDimAtCompileTime,Affine,TrOptions>& t,\n                                TransformTraits traits = Affine)\n  {\n    transform(t.linear(), traits);\n    offset() -= normal().dot(t.translation());\n    return *this;\n  }\n\n  /** \\returns \\c *this with scalar type casted to \\a NewScalarType\n    *\n    * Note that if \\a NewScalarType is equal to the current scalar type of \\c *this\n    * then this function smartly returns a const reference to \\c *this.\n    */\n  template<typename NewScalarType>\n  EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<Hyperplane,\n           Hyperplane<NewScalarType,AmbientDimAtCompileTime,Options> >::type cast() const\n  {\n    return typename internal::cast_return_type<Hyperplane,\n                    Hyperplane<NewScalarType,AmbientDimAtCompileTime,Options> >::type(*this);\n  }\n\n  /** Copy constructor with scalar type conversion */\n  template<typename OtherScalarType,int OtherOptions>\n  EIGEN_DEVICE_FUNC inline explicit Hyperplane(const Hyperplane<OtherScalarType,AmbientDimAtCompileTime,OtherOptions>& other)\n  { m_coeffs = other.coeffs().template cast<Scalar>(); }\n\n  /** \\returns \\c true if \\c *this is approximately equal to \\a other, within the precision\n    * determined by \\a prec.\n    *\n    * \\sa MatrixBase::isApprox() */\n  template<int OtherOptions>\n  EIGEN_DEVICE_FUNC bool isApprox(const Hyperplane<Scalar,AmbientDimAtCompileTime,OtherOptions>& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const\n  { return m_coeffs.isApprox(other.m_coeffs, prec); }\n\nprotected:\n\n  Coefficients m_coeffs;\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_HYPERPLANE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Geometry/OrthoMethods.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_ORTHOMETHODS_H\n#define EIGEN_ORTHOMETHODS_H\n\nnamespace Eigen { \n\n/** \\geometry_module \\ingroup Geometry_Module\n  *\n  * \\returns the cross product of \\c *this and \\a other\n  *\n  * Here is a very good explanation of cross-product: http://xkcd.com/199/\n  * \n  * With complex numbers, the cross product is implemented as\n  * \\f$ (\\mathbf{a}+i\\mathbf{b}) \\times (\\mathbf{c}+i\\mathbf{d}) = (\\mathbf{a} \\times \\mathbf{c} - \\mathbf{b} \\times \\mathbf{d}) - i(\\mathbf{a} \\times \\mathbf{d} - \\mathbf{b} \\times \\mathbf{c})\\f$\n  * \n  * \\sa MatrixBase::cross3()\n  */\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\n#ifndef EIGEN_PARSED_BY_DOXYGEN\nEIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::template cross_product_return_type<OtherDerived>::type\n#else\ninline typename MatrixBase<Derived>::PlainObject\n#endif\nMatrixBase<Derived>::cross(const MatrixBase<OtherDerived>& other) const\n{\n  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived,3)\n  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,3)\n\n  // Note that there is no need for an expression here since the compiler\n  // optimize such a small temporary very well (even within a complex expression)\n  typename internal::nested_eval<Derived,2>::type lhs(derived());\n  typename internal::nested_eval<OtherDerived,2>::type rhs(other.derived());\n  return typename cross_product_return_type<OtherDerived>::type(\n    numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),\n    numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),\n    numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0))\n  );\n}\n\nnamespace internal {\n\ntemplate< int Arch,typename VectorLhs,typename VectorRhs,\n          typename Scalar = typename VectorLhs::Scalar,\n          bool Vectorizable = bool((VectorLhs::Flags&VectorRhs::Flags)&PacketAccessBit)>\nstruct cross3_impl {\n  EIGEN_DEVICE_FUNC static inline typename internal::plain_matrix_type<VectorLhs>::type\n  run(const VectorLhs& lhs, const VectorRhs& rhs)\n  {\n    return typename internal::plain_matrix_type<VectorLhs>::type(\n      numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),\n      numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),\n      numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0)),\n      0\n    );\n  }\n};\n\n}\n\n/** \\geometry_module \\ingroup Geometry_Module\n  *\n  * \\returns the cross product of \\c *this and \\a other using only the x, y, and z coefficients\n  *\n  * The size of \\c *this and \\a other must be four. This function is especially useful\n  * when using 4D vectors instead of 3D ones to get advantage of SSE/AltiVec vectorization.\n  *\n  * \\sa MatrixBase::cross()\n  */\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\nEIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::PlainObject\nMatrixBase<Derived>::cross3(const MatrixBase<OtherDerived>& other) const\n{\n  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived,4)\n  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,4)\n\n  typedef typename internal::nested_eval<Derived,2>::type DerivedNested;\n  typedef typename internal::nested_eval<OtherDerived,2>::type OtherDerivedNested;\n  DerivedNested lhs(derived());\n  OtherDerivedNested rhs(other.derived());\n\n  return internal::cross3_impl<Architecture::Target,\n                        typename internal::remove_all<DerivedNested>::type,\n                        typename internal::remove_all<OtherDerivedNested>::type>::run(lhs,rhs);\n}\n\n/** \\geometry_module \\ingroup Geometry_Module\n  *\n  * \\returns a matrix expression of the cross product of each column or row\n  * of the referenced expression with the \\a other vector.\n  *\n  * The referenced matrix must have one dimension equal to 3.\n  * The result matrix has the same dimensions than the referenced one.\n  *\n  * \\sa MatrixBase::cross() */\ntemplate<typename ExpressionType, int Direction>\ntemplate<typename OtherDerived>\nEIGEN_DEVICE_FUNC \nconst typename VectorwiseOp<ExpressionType,Direction>::CrossReturnType\nVectorwiseOp<ExpressionType,Direction>::cross(const MatrixBase<OtherDerived>& other) const\n{\n  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,3)\n  EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),\n    YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)\n  \n  typename internal::nested_eval<ExpressionType,2>::type mat(_expression());\n  typename internal::nested_eval<OtherDerived,2>::type vec(other.derived());\n\n  CrossReturnType res(_expression().rows(),_expression().cols());\n  if(Direction==Vertical)\n  {\n    eigen_assert(CrossReturnType::RowsAtCompileTime==3 && \"the matrix must have exactly 3 rows\");\n    res.row(0) = (mat.row(1) * vec.coeff(2) - mat.row(2) * vec.coeff(1)).conjugate();\n    res.row(1) = (mat.row(2) * vec.coeff(0) - mat.row(0) * vec.coeff(2)).conjugate();\n    res.row(2) = (mat.row(0) * vec.coeff(1) - mat.row(1) * vec.coeff(0)).conjugate();\n  }\n  else\n  {\n    eigen_assert(CrossReturnType::ColsAtCompileTime==3 && \"the matrix must have exactly 3 columns\");\n    res.col(0) = (mat.col(1) * vec.coeff(2) - mat.col(2) * vec.coeff(1)).conjugate();\n    res.col(1) = (mat.col(2) * vec.coeff(0) - mat.col(0) * vec.coeff(2)).conjugate();\n    res.col(2) = (mat.col(0) * vec.coeff(1) - mat.col(1) * vec.coeff(0)).conjugate();\n  }\n  return res;\n}\n\nnamespace internal {\n\ntemplate<typename Derived, int Size = Derived::SizeAtCompileTime>\nstruct unitOrthogonal_selector\n{\n  typedef typename plain_matrix_type<Derived>::type VectorType;\n  typedef typename traits<Derived>::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  typedef Matrix<Scalar,2,1> Vector2;\n  EIGEN_DEVICE_FUNC\n  static inline VectorType run(const Derived& src)\n  {\n    VectorType perp = VectorType::Zero(src.size());\n    Index maxi = 0;\n    Index sndi = 0;\n    src.cwiseAbs().maxCoeff(&maxi);\n    if (maxi==0)\n      sndi = 1;\n    RealScalar invnm = RealScalar(1)/(Vector2() << src.coeff(sndi),src.coeff(maxi)).finished().norm();\n    perp.coeffRef(maxi) = -numext::conj(src.coeff(sndi)) * invnm;\n    perp.coeffRef(sndi) =  numext::conj(src.coeff(maxi)) * invnm;\n\n    return perp;\n   }\n};\n\ntemplate<typename Derived>\nstruct unitOrthogonal_selector<Derived,3>\n{\n  typedef typename plain_matrix_type<Derived>::type VectorType;\n  typedef typename traits<Derived>::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  EIGEN_DEVICE_FUNC\n  static inline VectorType run(const Derived& src)\n  {\n    VectorType perp;\n    /* Let us compute the crossed product of *this with a vector\n     * that is not too close to being colinear to *this.\n     */\n\n    /* unless the x and y coords are both close to zero, we can\n     * simply take ( -y, x, 0 ) and normalize it.\n     */\n    if((!isMuchSmallerThan(src.x(), src.z()))\n    || (!isMuchSmallerThan(src.y(), src.z())))\n    {\n      RealScalar invnm = RealScalar(1)/src.template head<2>().norm();\n      perp.coeffRef(0) = -numext::conj(src.y())*invnm;\n      perp.coeffRef(1) = numext::conj(src.x())*invnm;\n      perp.coeffRef(2) = 0;\n    }\n    /* if both x and y are close to zero, then the vector is close\n     * to the z-axis, so it's far from colinear to the x-axis for instance.\n     * So we take the crossed product with (1,0,0) and normalize it.\n     */\n    else\n    {\n      RealScalar invnm = RealScalar(1)/src.template tail<2>().norm();\n      perp.coeffRef(0) = 0;\n      perp.coeffRef(1) = -numext::conj(src.z())*invnm;\n      perp.coeffRef(2) = numext::conj(src.y())*invnm;\n    }\n\n    return perp;\n   }\n};\n\ntemplate<typename Derived>\nstruct unitOrthogonal_selector<Derived,2>\n{\n  typedef typename plain_matrix_type<Derived>::type VectorType;\n  EIGEN_DEVICE_FUNC\n  static inline VectorType run(const Derived& src)\n  { return VectorType(-numext::conj(src.y()), numext::conj(src.x())).normalized(); }\n};\n\n} // end namespace internal\n\n/** \\geometry_module \\ingroup Geometry_Module\n  *\n  * \\returns a unit vector which is orthogonal to \\c *this\n  *\n  * The size of \\c *this must be at least 2. If the size is exactly 2,\n  * then the returned vector is a counter clock wise rotation of \\c *this, i.e., (-y,x).normalized().\n  *\n  * \\sa cross()\n  */\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC typename MatrixBase<Derived>::PlainObject\nMatrixBase<Derived>::unitOrthogonal() const\n{\n  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)\n  return internal::unitOrthogonal_selector<Derived>::run(derived());\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_ORTHOMETHODS_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Geometry/ParametrizedLine.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_PARAMETRIZEDLINE_H\n#define EIGEN_PARAMETRIZEDLINE_H\n\nnamespace Eigen { \n\n/** \\geometry_module \\ingroup Geometry_Module\n  *\n  * \\class ParametrizedLine\n  *\n  * \\brief A parametrized line\n  *\n  * A parametrized line is defined by an origin point \\f$ \\mathbf{o} \\f$ and a unit\n  * direction vector \\f$ \\mathbf{d} \\f$ such that the line corresponds to\n  * the set \\f$ l(t) = \\mathbf{o} + t \\mathbf{d} \\f$, \\f$ t \\in \\mathbf{R} \\f$.\n  *\n  * \\tparam _Scalar the scalar type, i.e., the type of the coefficients\n  * \\tparam _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.\n  */\ntemplate <typename _Scalar, int _AmbientDim, int _Options>\nclass ParametrizedLine\n{\npublic:\n  EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)\n  enum {\n    AmbientDimAtCompileTime = _AmbientDim,\n    Options = _Options\n  };\n  typedef _Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  typedef Eigen::Index Index; ///< \\deprecated since Eigen 3.3\n  typedef Matrix<Scalar,AmbientDimAtCompileTime,1,Options> VectorType;\n\n  /** Default constructor without initialization */\n  EIGEN_DEVICE_FUNC inline ParametrizedLine() {}\n  \n  template<int OtherOptions>\n  EIGEN_DEVICE_FUNC ParametrizedLine(const ParametrizedLine<Scalar,AmbientDimAtCompileTime,OtherOptions>& other)\n   : m_origin(other.origin()), m_direction(other.direction())\n  {}\n\n  /** Constructs a dynamic-size line with \\a _dim the dimension\n    * of the ambient space */\n  EIGEN_DEVICE_FUNC inline explicit ParametrizedLine(Index _dim) : m_origin(_dim), m_direction(_dim) {}\n\n  /** Initializes a parametrized line of direction \\a direction and origin \\a origin.\n    * \\warning the vector direction is assumed to be normalized.\n    */\n  EIGEN_DEVICE_FUNC ParametrizedLine(const VectorType& origin, const VectorType& direction)\n    : m_origin(origin), m_direction(direction) {}\n\n  template <int OtherOptions>\n  EIGEN_DEVICE_FUNC explicit ParametrizedLine(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane);\n\n  /** Constructs a parametrized line going from \\a p0 to \\a p1. */\n  EIGEN_DEVICE_FUNC static inline ParametrizedLine Through(const VectorType& p0, const VectorType& p1)\n  { return ParametrizedLine(p0, (p1-p0).normalized()); }\n\n  EIGEN_DEVICE_FUNC ~ParametrizedLine() {}\n\n  /** \\returns the dimension in which the line holds */\n  EIGEN_DEVICE_FUNC inline Index dim() const { return m_direction.size(); }\n\n  EIGEN_DEVICE_FUNC const VectorType& origin() const { return m_origin; }\n  EIGEN_DEVICE_FUNC VectorType& origin() { return m_origin; }\n\n  EIGEN_DEVICE_FUNC const VectorType& direction() const { return m_direction; }\n  EIGEN_DEVICE_FUNC VectorType& direction() { return m_direction; }\n\n  /** \\returns the squared distance of a point \\a p to its projection onto the line \\c *this.\n    * \\sa distance()\n    */\n  EIGEN_DEVICE_FUNC RealScalar squaredDistance(const VectorType& p) const\n  {\n    VectorType diff = p - origin();\n    return (diff - direction().dot(diff) * direction()).squaredNorm();\n  }\n  /** \\returns the distance of a point \\a p to its projection onto the line \\c *this.\n    * \\sa squaredDistance()\n    */\n  EIGEN_DEVICE_FUNC RealScalar distance(const VectorType& p) const { EIGEN_USING_STD_MATH(sqrt) return sqrt(squaredDistance(p)); }\n\n  /** \\returns the projection of a point \\a p onto the line \\c *this. */\n  EIGEN_DEVICE_FUNC VectorType projection(const VectorType& p) const\n  { return origin() + direction().dot(p-origin()) * direction(); }\n\n  EIGEN_DEVICE_FUNC VectorType pointAt(const Scalar& t) const;\n  \n  template <int OtherOptions>\n  EIGEN_DEVICE_FUNC Scalar intersectionParameter(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const;\n \n  template <int OtherOptions>\n  EIGEN_DEVICE_FUNC Scalar intersection(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const;\n  \n  template <int OtherOptions>\n  EIGEN_DEVICE_FUNC VectorType intersectionPoint(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const;\n\n  /** \\returns \\c *this with scalar type casted to \\a NewScalarType\n    *\n    * Note that if \\a NewScalarType is equal to the current scalar type of \\c *this\n    * then this function smartly returns a const reference to \\c *this.\n    */\n  template<typename NewScalarType>\n  EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<ParametrizedLine,\n           ParametrizedLine<NewScalarType,AmbientDimAtCompileTime,Options> >::type cast() const\n  {\n    return typename internal::cast_return_type<ParametrizedLine,\n                    ParametrizedLine<NewScalarType,AmbientDimAtCompileTime,Options> >::type(*this);\n  }\n\n  /** Copy constructor with scalar type conversion */\n  template<typename OtherScalarType,int OtherOptions>\n  EIGEN_DEVICE_FUNC inline explicit ParametrizedLine(const ParametrizedLine<OtherScalarType,AmbientDimAtCompileTime,OtherOptions>& other)\n  {\n    m_origin = other.origin().template cast<Scalar>();\n    m_direction = other.direction().template cast<Scalar>();\n  }\n\n  /** \\returns \\c true if \\c *this is approximately equal to \\a other, within the precision\n    * determined by \\a prec.\n    *\n    * \\sa MatrixBase::isApprox() */\n  EIGEN_DEVICE_FUNC bool isApprox(const ParametrizedLine& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const\n  { return m_origin.isApprox(other.m_origin, prec) && m_direction.isApprox(other.m_direction, prec); }\n\nprotected:\n\n  VectorType m_origin, m_direction;\n};\n\n/** Constructs a parametrized line from a 2D hyperplane\n  *\n  * \\warning the ambient space must have dimension 2 such that the hyperplane actually describes a line\n  */\ntemplate <typename _Scalar, int _AmbientDim, int _Options>\ntemplate <int OtherOptions>\nEIGEN_DEVICE_FUNC inline ParametrizedLine<_Scalar, _AmbientDim,_Options>::ParametrizedLine(const Hyperplane<_Scalar, _AmbientDim,OtherOptions>& hyperplane)\n{\n  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2)\n  direction() = hyperplane.normal().unitOrthogonal();\n  origin() = -hyperplane.normal()*hyperplane.offset();\n}\n\n/** \\returns the point at \\a t along this line\n  */\ntemplate <typename _Scalar, int _AmbientDim, int _Options>\nEIGEN_DEVICE_FUNC inline typename ParametrizedLine<_Scalar, _AmbientDim,_Options>::VectorType\nParametrizedLine<_Scalar, _AmbientDim,_Options>::pointAt(const _Scalar& t) const\n{\n  return origin() + (direction()*t); \n}\n\n/** \\returns the parameter value of the intersection between \\c *this and the given \\a hyperplane\n  */\ntemplate <typename _Scalar, int _AmbientDim, int _Options>\ntemplate <int OtherOptions>\nEIGEN_DEVICE_FUNC inline _Scalar ParametrizedLine<_Scalar, _AmbientDim,_Options>::intersectionParameter(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const\n{\n  return -(hyperplane.offset()+hyperplane.normal().dot(origin()))\n          / hyperplane.normal().dot(direction());\n}\n\n\n/** \\deprecated use intersectionParameter()\n  * \\returns the parameter value of the intersection between \\c *this and the given \\a hyperplane\n  */\ntemplate <typename _Scalar, int _AmbientDim, int _Options>\ntemplate <int OtherOptions>\nEIGEN_DEVICE_FUNC inline _Scalar ParametrizedLine<_Scalar, _AmbientDim,_Options>::intersection(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const\n{\n  return intersectionParameter(hyperplane);\n}\n\n/** \\returns the point of the intersection between \\c *this and the given hyperplane\n  */\ntemplate <typename _Scalar, int _AmbientDim, int _Options>\ntemplate <int OtherOptions>\nEIGEN_DEVICE_FUNC inline typename ParametrizedLine<_Scalar, _AmbientDim,_Options>::VectorType\nParametrizedLine<_Scalar, _AmbientDim,_Options>::intersectionPoint(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const\n{\n  return pointAt(intersectionParameter(hyperplane));\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_PARAMETRIZEDLINE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Geometry/Quaternion.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2009 Mathieu Gautier <mathieu.gautier@cea.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_QUATERNION_H\n#define EIGEN_QUATERNION_H\nnamespace Eigen { \n\n\n/***************************************************************************\n* Definition of QuaternionBase<Derived>\n* The implementation is at the end of the file\n***************************************************************************/\n\nnamespace internal {\ntemplate<typename Other,\n         int OtherRows=Other::RowsAtCompileTime,\n         int OtherCols=Other::ColsAtCompileTime>\nstruct quaternionbase_assign_impl;\n}\n\n/** \\geometry_module \\ingroup Geometry_Module\n  * \\class QuaternionBase\n  * \\brief Base class for quaternion expressions\n  * \\tparam Derived derived type (CRTP)\n  * \\sa class Quaternion\n  */\ntemplate<class Derived>\nclass QuaternionBase : public RotationBase<Derived, 3>\n{\n public:\n  typedef RotationBase<Derived, 3> Base;\n\n  using Base::operator*;\n  using Base::derived;\n\n  typedef typename internal::traits<Derived>::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  typedef typename internal::traits<Derived>::Coefficients Coefficients;\n  typedef typename Coefficients::CoeffReturnType CoeffReturnType;\n  typedef typename internal::conditional<bool(internal::traits<Derived>::Flags&LvalueBit),\n                                        Scalar&, CoeffReturnType>::type NonConstCoeffReturnType;\n\n\n  enum {\n    Flags = Eigen::internal::traits<Derived>::Flags\n  };\n\n // typedef typename Matrix<Scalar,4,1> Coefficients;\n  /** the type of a 3D vector */\n  typedef Matrix<Scalar,3,1> Vector3;\n  /** the equivalent rotation matrix type */\n  typedef Matrix<Scalar,3,3> Matrix3;\n  /** the equivalent angle-axis type */\n  typedef AngleAxis<Scalar> AngleAxisType;\n\n\n\n  /** \\returns the \\c x coefficient */\n  EIGEN_DEVICE_FUNC inline CoeffReturnType x() const { return this->derived().coeffs().coeff(0); }\n  /** \\returns the \\c y coefficient */\n  EIGEN_DEVICE_FUNC inline CoeffReturnType y() const { return this->derived().coeffs().coeff(1); }\n  /** \\returns the \\c z coefficient */\n  EIGEN_DEVICE_FUNC inline CoeffReturnType z() const { return this->derived().coeffs().coeff(2); }\n  /** \\returns the \\c w coefficient */\n  EIGEN_DEVICE_FUNC inline CoeffReturnType w() const { return this->derived().coeffs().coeff(3); }\n\n  /** \\returns a reference to the \\c x coefficient (if Derived is a non-const lvalue) */\n  EIGEN_DEVICE_FUNC inline NonConstCoeffReturnType x() { return this->derived().coeffs().x(); }\n  /** \\returns a reference to the \\c y coefficient (if Derived is a non-const lvalue) */\n  EIGEN_DEVICE_FUNC inline NonConstCoeffReturnType y() { return this->derived().coeffs().y(); }\n  /** \\returns a reference to the \\c z coefficient (if Derived is a non-const lvalue) */\n  EIGEN_DEVICE_FUNC inline NonConstCoeffReturnType z() { return this->derived().coeffs().z(); }\n  /** \\returns a reference to the \\c w coefficient (if Derived is a non-const lvalue) */\n  EIGEN_DEVICE_FUNC inline NonConstCoeffReturnType w() { return this->derived().coeffs().w(); }\n\n  /** \\returns a read-only vector expression of the imaginary part (x,y,z) */\n  EIGEN_DEVICE_FUNC inline const VectorBlock<const Coefficients,3> vec() const { return coeffs().template head<3>(); }\n\n  /** \\returns a vector expression of the imaginary part (x,y,z) */\n  EIGEN_DEVICE_FUNC inline VectorBlock<Coefficients,3> vec() { return coeffs().template head<3>(); }\n\n  /** \\returns a read-only vector expression of the coefficients (x,y,z,w) */\n  EIGEN_DEVICE_FUNC inline const typename internal::traits<Derived>::Coefficients& coeffs() const { return derived().coeffs(); }\n\n  /** \\returns a vector expression of the coefficients (x,y,z,w) */\n  EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Coefficients& coeffs() { return derived().coeffs(); }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE QuaternionBase<Derived>& operator=(const QuaternionBase<Derived>& other);\n  template<class OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const QuaternionBase<OtherDerived>& other);\n\n// disabled this copy operator as it is giving very strange compilation errors when compiling\n// test_stdvector with GCC 4.4.2. This looks like a GCC bug though, so feel free to re-enable it if it's\n// useful; however notice that we already have the templated operator= above and e.g. in MatrixBase\n// we didn't have to add, in addition to templated operator=, such a non-templated copy operator.\n//  Derived& operator=(const QuaternionBase& other)\n//  { return operator=<Derived>(other); }\n\n  EIGEN_DEVICE_FUNC Derived& operator=(const AngleAxisType& aa);\n  template<class OtherDerived> EIGEN_DEVICE_FUNC Derived& operator=(const MatrixBase<OtherDerived>& m);\n\n  /** \\returns a quaternion representing an identity rotation\n    * \\sa MatrixBase::Identity()\n    */\n  EIGEN_DEVICE_FUNC static inline Quaternion<Scalar> Identity() { return Quaternion<Scalar>(Scalar(1), Scalar(0), Scalar(0), Scalar(0)); }\n\n  /** \\sa QuaternionBase::Identity(), MatrixBase::setIdentity()\n    */\n  EIGEN_DEVICE_FUNC inline QuaternionBase& setIdentity() { coeffs() << Scalar(0), Scalar(0), Scalar(0), Scalar(1); return *this; }\n\n  /** \\returns the squared norm of the quaternion's coefficients\n    * \\sa QuaternionBase::norm(), MatrixBase::squaredNorm()\n    */\n  EIGEN_DEVICE_FUNC inline Scalar squaredNorm() const { return coeffs().squaredNorm(); }\n\n  /** \\returns the norm of the quaternion's coefficients\n    * \\sa QuaternionBase::squaredNorm(), MatrixBase::norm()\n    */\n  EIGEN_DEVICE_FUNC inline Scalar norm() const { return coeffs().norm(); }\n\n  /** Normalizes the quaternion \\c *this\n    * \\sa normalized(), MatrixBase::normalize() */\n  EIGEN_DEVICE_FUNC inline void normalize() { coeffs().normalize(); }\n  /** \\returns a normalized copy of \\c *this\n    * \\sa normalize(), MatrixBase::normalized() */\n  EIGEN_DEVICE_FUNC inline Quaternion<Scalar> normalized() const { return Quaternion<Scalar>(coeffs().normalized()); }\n\n    /** \\returns the dot product of \\c *this and \\a other\n    * Geometrically speaking, the dot product of two unit quaternions\n    * corresponds to the cosine of half the angle between the two rotations.\n    * \\sa angularDistance()\n    */\n  template<class OtherDerived> EIGEN_DEVICE_FUNC inline Scalar dot(const QuaternionBase<OtherDerived>& other) const { return coeffs().dot(other.coeffs()); }\n\n  template<class OtherDerived> EIGEN_DEVICE_FUNC Scalar angularDistance(const QuaternionBase<OtherDerived>& other) const;\n\n  /** \\returns an equivalent 3x3 rotation matrix */\n  EIGEN_DEVICE_FUNC Matrix3 toRotationMatrix() const;\n\n  /** \\returns the quaternion which transform \\a a into \\a b through a rotation */\n  template<typename Derived1, typename Derived2>\n  EIGEN_DEVICE_FUNC Derived& setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b);\n\n  template<class OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Quaternion<Scalar> operator* (const QuaternionBase<OtherDerived>& q) const;\n  template<class OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator*= (const QuaternionBase<OtherDerived>& q);\n\n  /** \\returns the quaternion describing the inverse rotation */\n  EIGEN_DEVICE_FUNC Quaternion<Scalar> inverse() const;\n\n  /** \\returns the conjugated quaternion */\n  EIGEN_DEVICE_FUNC Quaternion<Scalar> conjugate() const;\n\n  template<class OtherDerived> EIGEN_DEVICE_FUNC Quaternion<Scalar> slerp(const Scalar& t, const QuaternionBase<OtherDerived>& other) const;\n\n  /** \\returns \\c true if \\c *this is approximately equal to \\a other, within the precision\n    * determined by \\a prec.\n    *\n    * \\sa MatrixBase::isApprox() */\n  template<class OtherDerived>\n  EIGEN_DEVICE_FUNC bool isApprox(const QuaternionBase<OtherDerived>& other, const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const\n  { return coeffs().isApprox(other.coeffs(), prec); }\n\n  /** return the result vector of \\a v through the rotation*/\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Vector3 _transformVector(const Vector3& v) const;\n\n  /** \\returns \\c *this with scalar type casted to \\a NewScalarType\n    *\n    * Note that if \\a NewScalarType is equal to the current scalar type of \\c *this\n    * then this function smartly returns a const reference to \\c *this.\n    */\n  template<typename NewScalarType>\n  EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<Derived,Quaternion<NewScalarType> >::type cast() const\n  {\n    return typename internal::cast_return_type<Derived,Quaternion<NewScalarType> >::type(derived());\n  }\n\n#ifdef EIGEN_QUATERNIONBASE_PLUGIN\n# include EIGEN_QUATERNIONBASE_PLUGIN\n#endif\n};\n\n/***************************************************************************\n* Definition/implementation of Quaternion<Scalar>\n***************************************************************************/\n\n/** \\geometry_module \\ingroup Geometry_Module\n  *\n  * \\class Quaternion\n  *\n  * \\brief The quaternion class used to represent 3D orientations and rotations\n  *\n  * \\tparam _Scalar the scalar type, i.e., the type of the coefficients\n  * \\tparam _Options controls the memory alignment of the coefficients. Can be \\# AutoAlign or \\# DontAlign. Default is AutoAlign.\n  *\n  * This class represents a quaternion \\f$ w+xi+yj+zk \\f$ that is a convenient representation of\n  * orientations and rotations of objects in three dimensions. Compared to other representations\n  * like Euler angles or 3x3 matrices, quaternions offer the following advantages:\n  * \\li \\b compact storage (4 scalars)\n  * \\li \\b efficient to compose (28 flops),\n  * \\li \\b stable spherical interpolation\n  *\n  * The following two typedefs are provided for convenience:\n  * \\li \\c Quaternionf for \\c float\n  * \\li \\c Quaterniond for \\c double\n  *\n  * \\warning Operations interpreting the quaternion as rotation have undefined behavior if the quaternion is not normalized.\n  *\n  * \\sa  class AngleAxis, class Transform\n  */\n\nnamespace internal {\ntemplate<typename _Scalar,int _Options>\nstruct traits<Quaternion<_Scalar,_Options> >\n{\n  typedef Quaternion<_Scalar,_Options> PlainObject;\n  typedef _Scalar Scalar;\n  typedef Matrix<_Scalar,4,1,_Options> Coefficients;\n  enum{\n    Alignment = internal::traits<Coefficients>::Alignment,\n    Flags = LvalueBit\n  };\n};\n}\n\ntemplate<typename _Scalar, int _Options>\nclass Quaternion : public QuaternionBase<Quaternion<_Scalar,_Options> >\n{\npublic:\n  typedef QuaternionBase<Quaternion<_Scalar,_Options> > Base;\n  enum { NeedsAlignment = internal::traits<Quaternion>::Alignment>0 };\n\n  typedef _Scalar Scalar;\n\n  EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Quaternion)\n  using Base::operator*=;\n\n  typedef typename internal::traits<Quaternion>::Coefficients Coefficients;\n  typedef typename Base::AngleAxisType AngleAxisType;\n\n  /** Default constructor leaving the quaternion uninitialized. */\n  EIGEN_DEVICE_FUNC inline Quaternion() {}\n\n  /** Constructs and initializes the quaternion \\f$ w+xi+yj+zk \\f$ from\n    * its four coefficients \\a w, \\a x, \\a y and \\a z.\n    *\n    * \\warning Note the order of the arguments: the real \\a w coefficient first,\n    * while internally the coefficients are stored in the following order:\n    * [\\c x, \\c y, \\c z, \\c w]\n    */\n  EIGEN_DEVICE_FUNC inline Quaternion(const Scalar& w, const Scalar& x, const Scalar& y, const Scalar& z) : m_coeffs(x, y, z, w){}\n\n  /** Constructs and initialize a quaternion from the array data */\n  EIGEN_DEVICE_FUNC explicit inline Quaternion(const Scalar* data) : m_coeffs(data) {}\n\n  /** Copy constructor */\n  template<class Derived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Quaternion(const QuaternionBase<Derived>& other) { this->Base::operator=(other); }\n\n  /** Constructs and initializes a quaternion from the angle-axis \\a aa */\n  EIGEN_DEVICE_FUNC explicit inline Quaternion(const AngleAxisType& aa) { *this = aa; }\n\n  /** Constructs and initializes a quaternion from either:\n    *  - a rotation matrix expression,\n    *  - a 4D vector expression representing quaternion coefficients.\n    */\n  template<typename Derived>\n  EIGEN_DEVICE_FUNC explicit inline Quaternion(const MatrixBase<Derived>& other) { *this = other; }\n\n  /** Explicit copy constructor with scalar conversion */\n  template<typename OtherScalar, int OtherOptions>\n  EIGEN_DEVICE_FUNC explicit inline Quaternion(const Quaternion<OtherScalar, OtherOptions>& other)\n  { m_coeffs = other.coeffs().template cast<Scalar>(); }\n\n  EIGEN_DEVICE_FUNC static Quaternion UnitRandom();\n\n  template<typename Derived1, typename Derived2>\n  EIGEN_DEVICE_FUNC static Quaternion FromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b);\n\n  EIGEN_DEVICE_FUNC inline Coefficients& coeffs() { return m_coeffs;}\n  EIGEN_DEVICE_FUNC inline const Coefficients& coeffs() const { return m_coeffs;}\n\n  EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(bool(NeedsAlignment))\n  \n#ifdef EIGEN_QUATERNION_PLUGIN\n# include EIGEN_QUATERNION_PLUGIN\n#endif\n\nprotected:\n  Coefficients m_coeffs;\n  \n#ifndef EIGEN_PARSED_BY_DOXYGEN\n    static EIGEN_STRONG_INLINE void _check_template_params()\n    {\n      EIGEN_STATIC_ASSERT( (_Options & DontAlign) == _Options,\n        INVALID_MATRIX_TEMPLATE_PARAMETERS)\n    }\n#endif\n};\n\n/** \\ingroup Geometry_Module\n  * single precision quaternion type */\ntypedef Quaternion<float> Quaternionf;\n/** \\ingroup Geometry_Module\n  * double precision quaternion type */\ntypedef Quaternion<double> Quaterniond;\n\n/***************************************************************************\n* Specialization of Map<Quaternion<Scalar>>\n***************************************************************************/\n\nnamespace internal {\n  template<typename _Scalar, int _Options>\n  struct traits<Map<Quaternion<_Scalar>, _Options> > : traits<Quaternion<_Scalar, (int(_Options)&Aligned)==Aligned ? AutoAlign : DontAlign> >\n  {\n    typedef Map<Matrix<_Scalar,4,1>, _Options> Coefficients;\n  };\n}\n\nnamespace internal {\n  template<typename _Scalar, int _Options>\n  struct traits<Map<const Quaternion<_Scalar>, _Options> > : traits<Quaternion<_Scalar, (int(_Options)&Aligned)==Aligned ? AutoAlign : DontAlign> >\n  {\n    typedef Map<const Matrix<_Scalar,4,1>, _Options> Coefficients;\n    typedef traits<Quaternion<_Scalar, (int(_Options)&Aligned)==Aligned ? AutoAlign : DontAlign> > TraitsBase;\n    enum {\n      Flags = TraitsBase::Flags & ~LvalueBit\n    };\n  };\n}\n\n/** \\ingroup Geometry_Module\n  * \\brief Quaternion expression mapping a constant memory buffer\n  *\n  * \\tparam _Scalar the type of the Quaternion coefficients\n  * \\tparam _Options see class Map\n  *\n  * This is a specialization of class Map for Quaternion. This class allows to view\n  * a 4 scalar memory buffer as an Eigen's Quaternion object.\n  *\n  * \\sa class Map, class Quaternion, class QuaternionBase\n  */\ntemplate<typename _Scalar, int _Options>\nclass Map<const Quaternion<_Scalar>, _Options >\n  : public QuaternionBase<Map<const Quaternion<_Scalar>, _Options> >\n{\n  public:\n    typedef QuaternionBase<Map<const Quaternion<_Scalar>, _Options> > Base;\n\n    typedef _Scalar Scalar;\n    typedef typename internal::traits<Map>::Coefficients Coefficients;\n    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Map)\n    using Base::operator*=;\n\n    /** Constructs a Mapped Quaternion object from the pointer \\a coeffs\n      *\n      * The pointer \\a coeffs must reference the four coefficients of Quaternion in the following order:\n      * \\code *coeffs == {x, y, z, w} \\endcode\n      *\n      * If the template parameter _Options is set to #Aligned, then the pointer coeffs must be aligned. */\n    EIGEN_DEVICE_FUNC explicit EIGEN_STRONG_INLINE Map(const Scalar* coeffs) : m_coeffs(coeffs) {}\n\n    EIGEN_DEVICE_FUNC inline const Coefficients& coeffs() const { return m_coeffs;}\n\n  protected:\n    const Coefficients m_coeffs;\n};\n\n/** \\ingroup Geometry_Module\n  * \\brief Expression of a quaternion from a memory buffer\n  *\n  * \\tparam _Scalar the type of the Quaternion coefficients\n  * \\tparam _Options see class Map\n  *\n  * This is a specialization of class Map for Quaternion. This class allows to view\n  * a 4 scalar memory buffer as an Eigen's  Quaternion object.\n  *\n  * \\sa class Map, class Quaternion, class QuaternionBase\n  */\ntemplate<typename _Scalar, int _Options>\nclass Map<Quaternion<_Scalar>, _Options >\n  : public QuaternionBase<Map<Quaternion<_Scalar>, _Options> >\n{\n  public:\n    typedef QuaternionBase<Map<Quaternion<_Scalar>, _Options> > Base;\n\n    typedef _Scalar Scalar;\n    typedef typename internal::traits<Map>::Coefficients Coefficients;\n    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Map)\n    using Base::operator*=;\n\n    /** Constructs a Mapped Quaternion object from the pointer \\a coeffs\n      *\n      * The pointer \\a coeffs must reference the four coefficients of Quaternion in the following order:\n      * \\code *coeffs == {x, y, z, w} \\endcode\n      *\n      * If the template parameter _Options is set to #Aligned, then the pointer coeffs must be aligned. */\n    EIGEN_DEVICE_FUNC explicit EIGEN_STRONG_INLINE Map(Scalar* coeffs) : m_coeffs(coeffs) {}\n\n    EIGEN_DEVICE_FUNC inline Coefficients& coeffs() { return m_coeffs; }\n    EIGEN_DEVICE_FUNC inline const Coefficients& coeffs() const { return m_coeffs; }\n\n  protected:\n    Coefficients m_coeffs;\n};\n\n/** \\ingroup Geometry_Module\n  * Map an unaligned array of single precision scalars as a quaternion */\ntypedef Map<Quaternion<float>, 0>         QuaternionMapf;\n/** \\ingroup Geometry_Module\n  * Map an unaligned array of double precision scalars as a quaternion */\ntypedef Map<Quaternion<double>, 0>        QuaternionMapd;\n/** \\ingroup Geometry_Module\n  * Map a 16-byte aligned array of single precision scalars as a quaternion */\ntypedef Map<Quaternion<float>, Aligned>   QuaternionMapAlignedf;\n/** \\ingroup Geometry_Module\n  * Map a 16-byte aligned array of double precision scalars as a quaternion */\ntypedef Map<Quaternion<double>, Aligned>  QuaternionMapAlignedd;\n\n/***************************************************************************\n* Implementation of QuaternionBase methods\n***************************************************************************/\n\n// Generic Quaternion * Quaternion product\n// This product can be specialized for a given architecture via the Arch template argument.\nnamespace internal {\ntemplate<int Arch, class Derived1, class Derived2, typename Scalar> struct quat_product\n{\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Quaternion<Scalar> run(const QuaternionBase<Derived1>& a, const QuaternionBase<Derived2>& b){\n    return Quaternion<Scalar>\n    (\n      a.w() * b.w() - a.x() * b.x() - a.y() * b.y() - a.z() * b.z(),\n      a.w() * b.x() + a.x() * b.w() + a.y() * b.z() - a.z() * b.y(),\n      a.w() * b.y() + a.y() * b.w() + a.z() * b.x() - a.x() * b.z(),\n      a.w() * b.z() + a.z() * b.w() + a.x() * b.y() - a.y() * b.x()\n    );\n  }\n};\n}\n\n/** \\returns the concatenation of two rotations as a quaternion-quaternion product */\ntemplate <class Derived>\ntemplate <class OtherDerived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Quaternion<typename internal::traits<Derived>::Scalar>\nQuaternionBase<Derived>::operator* (const QuaternionBase<OtherDerived>& other) const\n{\n  EIGEN_STATIC_ASSERT((internal::is_same<typename Derived::Scalar, typename OtherDerived::Scalar>::value),\n   YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)\n  return internal::quat_product<Architecture::Target, Derived, OtherDerived,\n                         typename internal::traits<Derived>::Scalar>::run(*this, other);\n}\n\n/** \\sa operator*(Quaternion) */\ntemplate <class Derived>\ntemplate <class OtherDerived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator*= (const QuaternionBase<OtherDerived>& other)\n{\n  derived() = derived() * other.derived();\n  return derived();\n}\n\n/** Rotation of a vector by a quaternion.\n  * \\remarks If the quaternion is used to rotate several points (>1)\n  * then it is much more efficient to first convert it to a 3x3 Matrix.\n  * Comparison of the operation cost for n transformations:\n  *   - Quaternion2:    30n\n  *   - Via a Matrix3: 24 + 15n\n  */\ntemplate <class Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename QuaternionBase<Derived>::Vector3\nQuaternionBase<Derived>::_transformVector(const Vector3& v) const\n{\n    // Note that this algorithm comes from the optimization by hand\n    // of the conversion to a Matrix followed by a Matrix/Vector product.\n    // It appears to be much faster than the common algorithm found\n    // in the literature (30 versus 39 flops). It also requires two\n    // Vector3 as temporaries.\n    Vector3 uv = this->vec().cross(v);\n    uv += uv;\n    return v + this->w() * uv + this->vec().cross(uv);\n}\n\ntemplate<class Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE QuaternionBase<Derived>& QuaternionBase<Derived>::operator=(const QuaternionBase<Derived>& other)\n{\n  coeffs() = other.coeffs();\n  return derived();\n}\n\ntemplate<class Derived>\ntemplate<class OtherDerived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator=(const QuaternionBase<OtherDerived>& other)\n{\n  coeffs() = other.coeffs();\n  return derived();\n}\n\n/** Set \\c *this from an angle-axis \\a aa and returns a reference to \\c *this\n  */\ntemplate<class Derived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator=(const AngleAxisType& aa)\n{\n  EIGEN_USING_STD_MATH(cos)\n  EIGEN_USING_STD_MATH(sin)\n  Scalar ha = Scalar(0.5)*aa.angle(); // Scalar(0.5) to suppress precision loss warnings\n  this->w() = cos(ha);\n  this->vec() = sin(ha) * aa.axis();\n  return derived();\n}\n\n/** Set \\c *this from the expression \\a xpr:\n  *   - if \\a xpr is a 4x1 vector, then \\a xpr is assumed to be a quaternion\n  *   - if \\a xpr is a 3x3 matrix, then \\a xpr is assumed to be rotation matrix\n  *     and \\a xpr is converted to a quaternion\n  */\n\ntemplate<class Derived>\ntemplate<class MatrixDerived>\nEIGEN_DEVICE_FUNC inline Derived& QuaternionBase<Derived>::operator=(const MatrixBase<MatrixDerived>& xpr)\n{\n  EIGEN_STATIC_ASSERT((internal::is_same<typename Derived::Scalar, typename MatrixDerived::Scalar>::value),\n   YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)\n  internal::quaternionbase_assign_impl<MatrixDerived>::run(*this, xpr.derived());\n  return derived();\n}\n\n/** Convert the quaternion to a 3x3 rotation matrix. The quaternion is required to\n  * be normalized, otherwise the result is undefined.\n  */\ntemplate<class Derived>\nEIGEN_DEVICE_FUNC inline typename QuaternionBase<Derived>::Matrix3\nQuaternionBase<Derived>::toRotationMatrix(void) const\n{\n  // NOTE if inlined, then gcc 4.2 and 4.4 get rid of the temporary (not gcc 4.3 !!)\n  // if not inlined then the cost of the return by value is huge ~ +35%,\n  // however, not inlining this function is an order of magnitude slower, so\n  // it has to be inlined, and so the return by value is not an issue\n  Matrix3 res;\n\n  const Scalar tx  = Scalar(2)*this->x();\n  const Scalar ty  = Scalar(2)*this->y();\n  const Scalar tz  = Scalar(2)*this->z();\n  const Scalar twx = tx*this->w();\n  const Scalar twy = ty*this->w();\n  const Scalar twz = tz*this->w();\n  const Scalar txx = tx*this->x();\n  const Scalar txy = ty*this->x();\n  const Scalar txz = tz*this->x();\n  const Scalar tyy = ty*this->y();\n  const Scalar tyz = tz*this->y();\n  const Scalar tzz = tz*this->z();\n\n  res.coeffRef(0,0) = Scalar(1)-(tyy+tzz);\n  res.coeffRef(0,1) = txy-twz;\n  res.coeffRef(0,2) = txz+twy;\n  res.coeffRef(1,0) = txy+twz;\n  res.coeffRef(1,1) = Scalar(1)-(txx+tzz);\n  res.coeffRef(1,2) = tyz-twx;\n  res.coeffRef(2,0) = txz-twy;\n  res.coeffRef(2,1) = tyz+twx;\n  res.coeffRef(2,2) = Scalar(1)-(txx+tyy);\n\n  return res;\n}\n\n/** Sets \\c *this to be a quaternion representing a rotation between\n  * the two arbitrary vectors \\a a and \\a b. In other words, the built\n  * rotation represent a rotation sending the line of direction \\a a\n  * to the line of direction \\a b, both lines passing through the origin.\n  *\n  * \\returns a reference to \\c *this.\n  *\n  * Note that the two input vectors do \\b not have to be normalized, and\n  * do not need to have the same norm.\n  */\ntemplate<class Derived>\ntemplate<typename Derived1, typename Derived2>\nEIGEN_DEVICE_FUNC inline Derived& QuaternionBase<Derived>::setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b)\n{\n  EIGEN_USING_STD_MATH(sqrt)\n  Vector3 v0 = a.normalized();\n  Vector3 v1 = b.normalized();\n  Scalar c = v1.dot(v0);\n\n  // if dot == -1, vectors are nearly opposites\n  // => accurately compute the rotation axis by computing the\n  //    intersection of the two planes. This is done by solving:\n  //       x^T v0 = 0\n  //       x^T v1 = 0\n  //    under the constraint:\n  //       ||x|| = 1\n  //    which yields a singular value problem\n  if (c < Scalar(-1)+NumTraits<Scalar>::dummy_precision())\n  {\n    c = numext::maxi(c,Scalar(-1));\n    Matrix<Scalar,2,3> m; m << v0.transpose(), v1.transpose();\n    JacobiSVD<Matrix<Scalar,2,3> > svd(m, ComputeFullV);\n    Vector3 axis = svd.matrixV().col(2);\n\n    Scalar w2 = (Scalar(1)+c)*Scalar(0.5);\n    this->w() = sqrt(w2);\n    this->vec() = axis * sqrt(Scalar(1) - w2);\n    return derived();\n  }\n  Vector3 axis = v0.cross(v1);\n  Scalar s = sqrt((Scalar(1)+c)*Scalar(2));\n  Scalar invs = Scalar(1)/s;\n  this->vec() = axis * invs;\n  this->w() = s * Scalar(0.5);\n\n  return derived();\n}\n\n/** \\returns a random unit quaternion following a uniform distribution law on SO(3)\n  *\n  * \\note The implementation is based on http://planning.cs.uiuc.edu/node198.html\n  */\ntemplate<typename Scalar, int Options>\nEIGEN_DEVICE_FUNC Quaternion<Scalar,Options> Quaternion<Scalar,Options>::UnitRandom()\n{\n  EIGEN_USING_STD_MATH(sqrt)\n  EIGEN_USING_STD_MATH(sin)\n  EIGEN_USING_STD_MATH(cos)\n  const Scalar u1 = internal::random<Scalar>(0, 1),\n               u2 = internal::random<Scalar>(0, 2*EIGEN_PI),\n               u3 = internal::random<Scalar>(0, 2*EIGEN_PI);\n  const Scalar a = sqrt(1 - u1),\n               b = sqrt(u1);\n  return Quaternion (a * sin(u2), a * cos(u2), b * sin(u3), b * cos(u3));\n}\n\n\n/** Returns a quaternion representing a rotation between\n  * the two arbitrary vectors \\a a and \\a b. In other words, the built\n  * rotation represent a rotation sending the line of direction \\a a\n  * to the line of direction \\a b, both lines passing through the origin.\n  *\n  * \\returns resulting quaternion\n  *\n  * Note that the two input vectors do \\b not have to be normalized, and\n  * do not need to have the same norm.\n  */\ntemplate<typename Scalar, int Options>\ntemplate<typename Derived1, typename Derived2>\nEIGEN_DEVICE_FUNC Quaternion<Scalar,Options> Quaternion<Scalar,Options>::FromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b)\n{\n    Quaternion quat;\n    quat.setFromTwoVectors(a, b);\n    return quat;\n}\n\n\n/** \\returns the multiplicative inverse of \\c *this\n  * Note that in most cases, i.e., if you simply want the opposite rotation,\n  * and/or the quaternion is normalized, then it is enough to use the conjugate.\n  *\n  * \\sa QuaternionBase::conjugate()\n  */\ntemplate <class Derived>\nEIGEN_DEVICE_FUNC inline Quaternion<typename internal::traits<Derived>::Scalar> QuaternionBase<Derived>::inverse() const\n{\n  // FIXME should this function be called multiplicativeInverse and conjugate() be called inverse() or opposite()  ??\n  Scalar n2 = this->squaredNorm();\n  if (n2 > Scalar(0))\n    return Quaternion<Scalar>(conjugate().coeffs() / n2);\n  else\n  {\n    // return an invalid result to flag the error\n    return Quaternion<Scalar>(Coefficients::Zero());\n  }\n}\n\n// Generic conjugate of a Quaternion\nnamespace internal {\ntemplate<int Arch, class Derived, typename Scalar> struct quat_conj\n{\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Quaternion<Scalar> run(const QuaternionBase<Derived>& q){\n    return Quaternion<Scalar>(q.w(),-q.x(),-q.y(),-q.z());\n  }\n};\n}\n                         \n/** \\returns the conjugate of the \\c *this which is equal to the multiplicative inverse\n  * if the quaternion is normalized.\n  * The conjugate of a quaternion represents the opposite rotation.\n  *\n  * \\sa Quaternion2::inverse()\n  */\ntemplate <class Derived>\nEIGEN_DEVICE_FUNC inline Quaternion<typename internal::traits<Derived>::Scalar>\nQuaternionBase<Derived>::conjugate() const\n{\n  return internal::quat_conj<Architecture::Target, Derived,\n                         typename internal::traits<Derived>::Scalar>::run(*this);\n                         \n}\n\n/** \\returns the angle (in radian) between two rotations\n  * \\sa dot()\n  */\ntemplate <class Derived>\ntemplate <class OtherDerived>\nEIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Scalar\nQuaternionBase<Derived>::angularDistance(const QuaternionBase<OtherDerived>& other) const\n{\n  EIGEN_USING_STD_MATH(atan2)\n  Quaternion<Scalar> d = (*this) * other.conjugate();\n  return Scalar(2) * atan2( d.vec().norm(), numext::abs(d.w()) );\n}\n\n \n    \n/** \\returns the spherical linear interpolation between the two quaternions\n  * \\c *this and \\a other at the parameter \\a t in [0;1].\n  * \n  * This represents an interpolation for a constant motion between \\c *this and \\a other,\n  * see also http://en.wikipedia.org/wiki/Slerp.\n  */\ntemplate <class Derived>\ntemplate <class OtherDerived>\nEIGEN_DEVICE_FUNC Quaternion<typename internal::traits<Derived>::Scalar>\nQuaternionBase<Derived>::slerp(const Scalar& t, const QuaternionBase<OtherDerived>& other) const\n{\n  EIGEN_USING_STD_MATH(acos)\n  EIGEN_USING_STD_MATH(sin)\n  const Scalar one = Scalar(1) - NumTraits<Scalar>::epsilon();\n  Scalar d = this->dot(other);\n  Scalar absD = numext::abs(d);\n\n  Scalar scale0;\n  Scalar scale1;\n\n  if(absD>=one)\n  {\n    scale0 = Scalar(1) - t;\n    scale1 = t;\n  }\n  else\n  {\n    // theta is the angle between the 2 quaternions\n    Scalar theta = acos(absD);\n    Scalar sinTheta = sin(theta);\n\n    scale0 = sin( ( Scalar(1) - t ) * theta) / sinTheta;\n    scale1 = sin( ( t * theta) ) / sinTheta;\n  }\n  if(d<Scalar(0)) scale1 = -scale1;\n\n  return Quaternion<Scalar>(scale0 * coeffs() + scale1 * other.coeffs());\n}\n\nnamespace internal {\n\n// set from a rotation matrix\ntemplate<typename Other>\nstruct quaternionbase_assign_impl<Other,3,3>\n{\n  typedef typename Other::Scalar Scalar;\n  template<class Derived> EIGEN_DEVICE_FUNC static inline void run(QuaternionBase<Derived>& q, const Other& a_mat)\n  {\n    const typename internal::nested_eval<Other,2>::type mat(a_mat);\n    EIGEN_USING_STD_MATH(sqrt)\n    // This algorithm comes from  \"Quaternion Calculus and Fast Animation\",\n    // Ken Shoemake, 1987 SIGGRAPH course notes\n    Scalar t = mat.trace();\n    if (t > Scalar(0))\n    {\n      t = sqrt(t + Scalar(1.0));\n      q.w() = Scalar(0.5)*t;\n      t = Scalar(0.5)/t;\n      q.x() = (mat.coeff(2,1) - mat.coeff(1,2)) * t;\n      q.y() = (mat.coeff(0,2) - mat.coeff(2,0)) * t;\n      q.z() = (mat.coeff(1,0) - mat.coeff(0,1)) * t;\n    }\n    else\n    {\n      Index i = 0;\n      if (mat.coeff(1,1) > mat.coeff(0,0))\n        i = 1;\n      if (mat.coeff(2,2) > mat.coeff(i,i))\n        i = 2;\n      Index j = (i+1)%3;\n      Index k = (j+1)%3;\n\n      t = sqrt(mat.coeff(i,i)-mat.coeff(j,j)-mat.coeff(k,k) + Scalar(1.0));\n      q.coeffs().coeffRef(i) = Scalar(0.5) * t;\n      t = Scalar(0.5)/t;\n      q.w() = (mat.coeff(k,j)-mat.coeff(j,k))*t;\n      q.coeffs().coeffRef(j) = (mat.coeff(j,i)+mat.coeff(i,j))*t;\n      q.coeffs().coeffRef(k) = (mat.coeff(k,i)+mat.coeff(i,k))*t;\n    }\n  }\n};\n\n// set from a vector of coefficients assumed to be a quaternion\ntemplate<typename Other>\nstruct quaternionbase_assign_impl<Other,4,1>\n{\n  typedef typename Other::Scalar Scalar;\n  template<class Derived> EIGEN_DEVICE_FUNC static inline void run(QuaternionBase<Derived>& q, const Other& vec)\n  {\n    q.coeffs() = vec;\n  }\n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_QUATERNION_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Geometry/Rotation2D.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_ROTATION2D_H\n#define EIGEN_ROTATION2D_H\n\nnamespace Eigen { \n\n/** \\geometry_module \\ingroup Geometry_Module\n  *\n  * \\class Rotation2D\n  *\n  * \\brief Represents a rotation/orientation in a 2 dimensional space.\n  *\n  * \\tparam _Scalar the scalar type, i.e., the type of the coefficients\n  *\n  * This class is equivalent to a single scalar representing a counter clock wise rotation\n  * as a single angle in radian. It provides some additional features such as the automatic\n  * conversion from/to a 2x2 rotation matrix. Moreover this class aims to provide a similar\n  * interface to Quaternion in order to facilitate the writing of generic algorithms\n  * dealing with rotations.\n  *\n  * \\sa class Quaternion, class Transform\n  */\n\nnamespace internal {\n\ntemplate<typename _Scalar> struct traits<Rotation2D<_Scalar> >\n{\n  typedef _Scalar Scalar;\n};\n} // end namespace internal\n\ntemplate<typename _Scalar>\nclass Rotation2D : public RotationBase<Rotation2D<_Scalar>,2>\n{\n  typedef RotationBase<Rotation2D<_Scalar>,2> Base;\n\npublic:\n\n  using Base::operator*;\n\n  enum { Dim = 2 };\n  /** the scalar type of the coefficients */\n  typedef _Scalar Scalar;\n  typedef Matrix<Scalar,2,1> Vector2;\n  typedef Matrix<Scalar,2,2> Matrix2;\n\nprotected:\n\n  Scalar m_angle;\n\npublic:\n\n  /** Construct a 2D counter clock wise rotation from the angle \\a a in radian. */\n  EIGEN_DEVICE_FUNC explicit inline Rotation2D(const Scalar& a) : m_angle(a) {}\n  \n  /** Default constructor wihtout initialization. The represented rotation is undefined. */\n  EIGEN_DEVICE_FUNC Rotation2D() {}\n\n  /** Construct a 2D rotation from a 2x2 rotation matrix \\a mat.\n    *\n    * \\sa fromRotationMatrix()\n    */\n  template<typename Derived>\n  EIGEN_DEVICE_FUNC explicit Rotation2D(const MatrixBase<Derived>& m)\n  {\n    fromRotationMatrix(m.derived());\n  }\n\n  /** \\returns the rotation angle */\n  EIGEN_DEVICE_FUNC inline Scalar angle() const { return m_angle; }\n\n  /** \\returns a read-write reference to the rotation angle */\n  EIGEN_DEVICE_FUNC inline Scalar& angle() { return m_angle; }\n  \n  /** \\returns the rotation angle in [0,2pi] */\n  EIGEN_DEVICE_FUNC inline Scalar smallestPositiveAngle() const {\n    Scalar tmp = numext::fmod(m_angle,Scalar(2*EIGEN_PI));\n    return tmp<Scalar(0) ? tmp + Scalar(2*EIGEN_PI) : tmp;\n  }\n  \n  /** \\returns the rotation angle in [-pi,pi] */\n  EIGEN_DEVICE_FUNC inline Scalar smallestAngle() const {\n    Scalar tmp = numext::fmod(m_angle,Scalar(2*EIGEN_PI));\n    if(tmp>Scalar(EIGEN_PI))       tmp -= Scalar(2*EIGEN_PI);\n    else if(tmp<-Scalar(EIGEN_PI)) tmp += Scalar(2*EIGEN_PI);\n    return tmp;\n  }\n\n  /** \\returns the inverse rotation */\n  EIGEN_DEVICE_FUNC inline Rotation2D inverse() const { return Rotation2D(-m_angle); }\n\n  /** Concatenates two rotations */\n  EIGEN_DEVICE_FUNC inline Rotation2D operator*(const Rotation2D& other) const\n  { return Rotation2D(m_angle + other.m_angle); }\n\n  /** Concatenates two rotations */\n  EIGEN_DEVICE_FUNC inline Rotation2D& operator*=(const Rotation2D& other)\n  { m_angle += other.m_angle; return *this; }\n\n  /** Applies the rotation to a 2D vector */\n  EIGEN_DEVICE_FUNC Vector2 operator* (const Vector2& vec) const\n  { return toRotationMatrix() * vec; }\n  \n  template<typename Derived>\n  EIGEN_DEVICE_FUNC Rotation2D& fromRotationMatrix(const MatrixBase<Derived>& m);\n  EIGEN_DEVICE_FUNC Matrix2 toRotationMatrix() const;\n\n  /** Set \\c *this from a 2x2 rotation matrix \\a mat.\n    * In other words, this function extract the rotation angle from the rotation matrix.\n    *\n    * This method is an alias for fromRotationMatrix()\n    *\n    * \\sa fromRotationMatrix()\n    */\n  template<typename Derived>\n  EIGEN_DEVICE_FUNC Rotation2D& operator=(const  MatrixBase<Derived>& m)\n  { return fromRotationMatrix(m.derived()); }\n\n  /** \\returns the spherical interpolation between \\c *this and \\a other using\n    * parameter \\a t. It is in fact equivalent to a linear interpolation.\n    */\n  EIGEN_DEVICE_FUNC inline Rotation2D slerp(const Scalar& t, const Rotation2D& other) const\n  {\n    Scalar dist = Rotation2D(other.m_angle-m_angle).smallestAngle();\n    return Rotation2D(m_angle + dist*t);\n  }\n\n  /** \\returns \\c *this with scalar type casted to \\a NewScalarType\n    *\n    * Note that if \\a NewScalarType is equal to the current scalar type of \\c *this\n    * then this function smartly returns a const reference to \\c *this.\n    */\n  template<typename NewScalarType>\n  EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<Rotation2D,Rotation2D<NewScalarType> >::type cast() const\n  { return typename internal::cast_return_type<Rotation2D,Rotation2D<NewScalarType> >::type(*this); }\n\n  /** Copy constructor with scalar type conversion */\n  template<typename OtherScalarType>\n  EIGEN_DEVICE_FUNC inline explicit Rotation2D(const Rotation2D<OtherScalarType>& other)\n  {\n    m_angle = Scalar(other.angle());\n  }\n\n  EIGEN_DEVICE_FUNC static inline Rotation2D Identity() { return Rotation2D(0); }\n\n  /** \\returns \\c true if \\c *this is approximately equal to \\a other, within the precision\n    * determined by \\a prec.\n    *\n    * \\sa MatrixBase::isApprox() */\n  EIGEN_DEVICE_FUNC bool isApprox(const Rotation2D& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const\n  { return internal::isApprox(m_angle,other.m_angle, prec); }\n  \n};\n\n/** \\ingroup Geometry_Module\n  * single precision 2D rotation type */\ntypedef Rotation2D<float> Rotation2Df;\n/** \\ingroup Geometry_Module\n  * double precision 2D rotation type */\ntypedef Rotation2D<double> Rotation2Dd;\n\n/** Set \\c *this from a 2x2 rotation matrix \\a mat.\n  * In other words, this function extract the rotation angle\n  * from the rotation matrix.\n  */\ntemplate<typename Scalar>\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC Rotation2D<Scalar>& Rotation2D<Scalar>::fromRotationMatrix(const MatrixBase<Derived>& mat)\n{\n  EIGEN_USING_STD_MATH(atan2)\n  EIGEN_STATIC_ASSERT(Derived::RowsAtCompileTime==2 && Derived::ColsAtCompileTime==2,YOU_MADE_A_PROGRAMMING_MISTAKE)\n  m_angle = atan2(mat.coeff(1,0), mat.coeff(0,0));\n  return *this;\n}\n\n/** Constructs and \\returns an equivalent 2x2 rotation matrix.\n  */\ntemplate<typename Scalar>\ntypename Rotation2D<Scalar>::Matrix2\nEIGEN_DEVICE_FUNC Rotation2D<Scalar>::toRotationMatrix(void) const\n{\n  EIGEN_USING_STD_MATH(sin)\n  EIGEN_USING_STD_MATH(cos)\n  Scalar sinA = sin(m_angle);\n  Scalar cosA = cos(m_angle);\n  return (Matrix2() << cosA, -sinA, sinA, cosA).finished();\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_ROTATION2D_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Geometry/RotationBase.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_ROTATIONBASE_H\n#define EIGEN_ROTATIONBASE_H\n\nnamespace Eigen { \n\n// forward declaration\nnamespace internal {\ntemplate<typename RotationDerived, typename MatrixType, bool IsVector=MatrixType::IsVectorAtCompileTime>\nstruct rotation_base_generic_product_selector;\n}\n\n/** \\class RotationBase\n  *\n  * \\brief Common base class for compact rotation representations\n  *\n  * \\tparam Derived is the derived type, i.e., a rotation type\n  * \\tparam _Dim the dimension of the space\n  */\ntemplate<typename Derived, int _Dim>\nclass RotationBase\n{\n  public:\n    enum { Dim = _Dim };\n    /** the scalar type of the coefficients */\n    typedef typename internal::traits<Derived>::Scalar Scalar;\n\n    /** corresponding linear transformation matrix type */\n    typedef Matrix<Scalar,Dim,Dim> RotationMatrixType;\n    typedef Matrix<Scalar,Dim,1> VectorType;\n\n  public:\n    EIGEN_DEVICE_FUNC inline const Derived& derived() const { return *static_cast<const Derived*>(this); }\n    EIGEN_DEVICE_FUNC inline Derived& derived() { return *static_cast<Derived*>(this); }\n\n    /** \\returns an equivalent rotation matrix */\n    EIGEN_DEVICE_FUNC inline RotationMatrixType toRotationMatrix() const { return derived().toRotationMatrix(); }\n\n    /** \\returns an equivalent rotation matrix \n      * This function is added to be conform with the Transform class' naming scheme.\n      */\n    EIGEN_DEVICE_FUNC inline RotationMatrixType matrix() const { return derived().toRotationMatrix(); }\n\n    /** \\returns the inverse rotation */\n    EIGEN_DEVICE_FUNC inline Derived inverse() const { return derived().inverse(); }\n\n    /** \\returns the concatenation of the rotation \\c *this with a translation \\a t */\n    EIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Isometry> operator*(const Translation<Scalar,Dim>& t) const\n    { return Transform<Scalar,Dim,Isometry>(*this) * t; }\n\n    /** \\returns the concatenation of the rotation \\c *this with a uniform scaling \\a s */\n    EIGEN_DEVICE_FUNC inline RotationMatrixType operator*(const UniformScaling<Scalar>& s) const\n    { return toRotationMatrix() * s.factor(); }\n\n    /** \\returns the concatenation of the rotation \\c *this with a generic expression \\a e\n      * \\a e can be:\n      *  - a DimxDim linear transformation matrix\n      *  - a DimxDim diagonal matrix (axis aligned scaling)\n      *  - a vector of size Dim\n      */\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::rotation_base_generic_product_selector<Derived,OtherDerived,OtherDerived::IsVectorAtCompileTime>::ReturnType\n    operator*(const EigenBase<OtherDerived>& e) const\n    { return internal::rotation_base_generic_product_selector<Derived,OtherDerived>::run(derived(), e.derived()); }\n\n    /** \\returns the concatenation of a linear transformation \\a l with the rotation \\a r */\n    template<typename OtherDerived> friend\n    EIGEN_DEVICE_FUNC inline RotationMatrixType operator*(const EigenBase<OtherDerived>& l, const Derived& r)\n    { return l.derived() * r.toRotationMatrix(); }\n\n    /** \\returns the concatenation of a scaling \\a l with the rotation \\a r */\n    EIGEN_DEVICE_FUNC friend inline Transform<Scalar,Dim,Affine> operator*(const DiagonalMatrix<Scalar,Dim>& l, const Derived& r)\n    { \n      Transform<Scalar,Dim,Affine> res(r);\n      res.linear().applyOnTheLeft(l);\n      return res;\n    }\n\n    /** \\returns the concatenation of the rotation \\c *this with a transformation \\a t */\n    template<int Mode, int Options>\n    EIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode> operator*(const Transform<Scalar,Dim,Mode,Options>& t) const\n    { return toRotationMatrix() * t; }\n\n    template<typename OtherVectorType>\n    EIGEN_DEVICE_FUNC inline VectorType _transformVector(const OtherVectorType& v) const\n    { return toRotationMatrix() * v; }\n};\n\nnamespace internal {\n\n// implementation of the generic product rotation * matrix\ntemplate<typename RotationDerived, typename MatrixType>\nstruct rotation_base_generic_product_selector<RotationDerived,MatrixType,false>\n{\n  enum { Dim = RotationDerived::Dim };\n  typedef Matrix<typename RotationDerived::Scalar,Dim,Dim> ReturnType;\n  EIGEN_DEVICE_FUNC static inline ReturnType run(const RotationDerived& r, const MatrixType& m)\n  { return r.toRotationMatrix() * m; }\n};\n\ntemplate<typename RotationDerived, typename Scalar, int Dim, int MaxDim>\nstruct rotation_base_generic_product_selector< RotationDerived, DiagonalMatrix<Scalar,Dim,MaxDim>, false >\n{\n  typedef Transform<Scalar,Dim,Affine> ReturnType;\n  EIGEN_DEVICE_FUNC static inline ReturnType run(const RotationDerived& r, const DiagonalMatrix<Scalar,Dim,MaxDim>& m)\n  {\n    ReturnType res(r);\n    res.linear() *= m;\n    return res;\n  }\n};\n\ntemplate<typename RotationDerived,typename OtherVectorType>\nstruct rotation_base_generic_product_selector<RotationDerived,OtherVectorType,true>\n{\n  enum { Dim = RotationDerived::Dim };\n  typedef Matrix<typename RotationDerived::Scalar,Dim,1> ReturnType;\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE ReturnType run(const RotationDerived& r, const OtherVectorType& v)\n  {\n    return r._transformVector(v);\n  }\n};\n\n} // end namespace internal\n\n/** \\geometry_module\n  *\n  * \\brief Constructs a Dim x Dim rotation matrix from the rotation \\a r\n  */\ntemplate<typename _Scalar, int _Rows, int _Cols, int _Storage, int _MaxRows, int _MaxCols>\ntemplate<typename OtherDerived>\nEIGEN_DEVICE_FUNC Matrix<_Scalar, _Rows, _Cols, _Storage, _MaxRows, _MaxCols>\n::Matrix(const RotationBase<OtherDerived,ColsAtCompileTime>& r)\n{\n  EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix,int(OtherDerived::Dim),int(OtherDerived::Dim))\n  *this = r.toRotationMatrix();\n}\n\n/** \\geometry_module\n  *\n  * \\brief Set a Dim x Dim rotation matrix from the rotation \\a r\n  */\ntemplate<typename _Scalar, int _Rows, int _Cols, int _Storage, int _MaxRows, int _MaxCols>\ntemplate<typename OtherDerived>\nEIGEN_DEVICE_FUNC Matrix<_Scalar, _Rows, _Cols, _Storage, _MaxRows, _MaxCols>&\nMatrix<_Scalar, _Rows, _Cols, _Storage, _MaxRows, _MaxCols>\n::operator=(const RotationBase<OtherDerived,ColsAtCompileTime>& r)\n{\n  EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix,int(OtherDerived::Dim),int(OtherDerived::Dim))\n  return *this = r.toRotationMatrix();\n}\n\nnamespace internal {\n\n/** \\internal\n  *\n  * Helper function to return an arbitrary rotation object to a rotation matrix.\n  *\n  * \\tparam Scalar the numeric type of the matrix coefficients\n  * \\tparam Dim the dimension of the current space\n  *\n  * It returns a Dim x Dim fixed size matrix.\n  *\n  * Default specializations are provided for:\n  *   - any scalar type (2D),\n  *   - any matrix expression,\n  *   - any type based on RotationBase (e.g., Quaternion, AngleAxis, Rotation2D)\n  *\n  * Currently toRotationMatrix is only used by Transform.\n  *\n  * \\sa class Transform, class Rotation2D, class Quaternion, class AngleAxis\n  */\ntemplate<typename Scalar, int Dim>\nEIGEN_DEVICE_FUNC static inline Matrix<Scalar,2,2> toRotationMatrix(const Scalar& s)\n{\n  EIGEN_STATIC_ASSERT(Dim==2,YOU_MADE_A_PROGRAMMING_MISTAKE)\n  return Rotation2D<Scalar>(s).toRotationMatrix();\n}\n\ntemplate<typename Scalar, int Dim, typename OtherDerived>\nEIGEN_DEVICE_FUNC static inline Matrix<Scalar,Dim,Dim> toRotationMatrix(const RotationBase<OtherDerived,Dim>& r)\n{\n  return r.toRotationMatrix();\n}\n\ntemplate<typename Scalar, int Dim, typename OtherDerived>\nEIGEN_DEVICE_FUNC static inline const MatrixBase<OtherDerived>& toRotationMatrix(const MatrixBase<OtherDerived>& mat)\n{\n  EIGEN_STATIC_ASSERT(OtherDerived::RowsAtCompileTime==Dim && OtherDerived::ColsAtCompileTime==Dim,\n    YOU_MADE_A_PROGRAMMING_MISTAKE)\n  return mat;\n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_ROTATIONBASE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Geometry/Scaling.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SCALING_H\n#define EIGEN_SCALING_H\n\nnamespace Eigen { \n\n/** \\geometry_module \\ingroup Geometry_Module\n  *\n  * \\class Scaling\n  *\n  * \\brief Represents a generic uniform scaling transformation\n  *\n  * \\tparam _Scalar the scalar type, i.e., the type of the coefficients.\n  *\n  * This class represent a uniform scaling transformation. It is the return\n  * type of Scaling(Scalar), and most of the time this is the only way it\n  * is used. In particular, this class is not aimed to be used to store a scaling transformation,\n  * but rather to make easier the constructions and updates of Transform objects.\n  *\n  * To represent an axis aligned scaling, use the DiagonalMatrix class.\n  *\n  * \\sa Scaling(), class DiagonalMatrix, MatrixBase::asDiagonal(), class Translation, class Transform\n  */\ntemplate<typename _Scalar>\nclass UniformScaling\n{\npublic:\n  /** the scalar type of the coefficients */\n  typedef _Scalar Scalar;\n\nprotected:\n\n  Scalar m_factor;\n\npublic:\n\n  /** Default constructor without initialization. */\n  UniformScaling() {}\n  /** Constructs and initialize a uniform scaling transformation */\n  explicit inline UniformScaling(const Scalar& s) : m_factor(s) {}\n\n  inline const Scalar& factor() const { return m_factor; }\n  inline Scalar& factor() { return m_factor; }\n\n  /** Concatenates two uniform scaling */\n  inline UniformScaling operator* (const UniformScaling& other) const\n  { return UniformScaling(m_factor * other.factor()); }\n\n  /** Concatenates a uniform scaling and a translation */\n  template<int Dim>\n  inline Transform<Scalar,Dim,Affine> operator* (const Translation<Scalar,Dim>& t) const;\n\n  /** Concatenates a uniform scaling and an affine transformation */\n  template<int Dim, int Mode, int Options>\n  inline Transform<Scalar,Dim,(int(Mode)==int(Isometry)?Affine:Mode)> operator* (const Transform<Scalar,Dim, Mode, Options>& t) const\n  {\n    Transform<Scalar,Dim,(int(Mode)==int(Isometry)?Affine:Mode)> res = t;\n    res.prescale(factor());\n    return res;\n  }\n\n  /** Concatenates a uniform scaling and a linear transformation matrix */\n  // TODO returns an expression\n  template<typename Derived>\n  inline typename internal::plain_matrix_type<Derived>::type operator* (const MatrixBase<Derived>& other) const\n  { return other * m_factor; }\n\n  template<typename Derived,int Dim>\n  inline Matrix<Scalar,Dim,Dim> operator*(const RotationBase<Derived,Dim>& r) const\n  { return r.toRotationMatrix() * m_factor; }\n\n  /** \\returns the inverse scaling */\n  inline UniformScaling inverse() const\n  { return UniformScaling(Scalar(1)/m_factor); }\n\n  /** \\returns \\c *this with scalar type casted to \\a NewScalarType\n    *\n    * Note that if \\a NewScalarType is equal to the current scalar type of \\c *this\n    * then this function smartly returns a const reference to \\c *this.\n    */\n  template<typename NewScalarType>\n  inline UniformScaling<NewScalarType> cast() const\n  { return UniformScaling<NewScalarType>(NewScalarType(m_factor)); }\n\n  /** Copy constructor with scalar type conversion */\n  template<typename OtherScalarType>\n  inline explicit UniformScaling(const UniformScaling<OtherScalarType>& other)\n  { m_factor = Scalar(other.factor()); }\n\n  /** \\returns \\c true if \\c *this is approximately equal to \\a other, within the precision\n    * determined by \\a prec.\n    *\n    * \\sa MatrixBase::isApprox() */\n  bool isApprox(const UniformScaling& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const\n  { return internal::isApprox(m_factor, other.factor(), prec); }\n\n};\n\n/** \\addtogroup Geometry_Module */\n//@{\n\n/** Concatenates a linear transformation matrix and a uniform scaling\n  * \\relates UniformScaling\n  */\n// NOTE this operator is defiend in MatrixBase and not as a friend function\n// of UniformScaling to fix an internal crash of Intel's ICC\ntemplate<typename Derived,typename Scalar>\nEIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,Scalar,product)\noperator*(const MatrixBase<Derived>& matrix, const UniformScaling<Scalar>& s)\n{ return matrix.derived() * s.factor(); }\n\n/** Constructs a uniform scaling from scale factor \\a s */\ninline UniformScaling<float> Scaling(float s) { return UniformScaling<float>(s); }\n/** Constructs a uniform scaling from scale factor \\a s */\ninline UniformScaling<double> Scaling(double s) { return UniformScaling<double>(s); }\n/** Constructs a uniform scaling from scale factor \\a s */\ntemplate<typename RealScalar>\ninline UniformScaling<std::complex<RealScalar> > Scaling(const std::complex<RealScalar>& s)\n{ return UniformScaling<std::complex<RealScalar> >(s); }\n\n/** Constructs a 2D axis aligned scaling */\ntemplate<typename Scalar>\ninline DiagonalMatrix<Scalar,2> Scaling(const Scalar& sx, const Scalar& sy)\n{ return DiagonalMatrix<Scalar,2>(sx, sy); }\n/** Constructs a 3D axis aligned scaling */\ntemplate<typename Scalar>\ninline DiagonalMatrix<Scalar,3> Scaling(const Scalar& sx, const Scalar& sy, const Scalar& sz)\n{ return DiagonalMatrix<Scalar,3>(sx, sy, sz); }\n\n/** Constructs an axis aligned scaling expression from vector expression \\a coeffs\n  * This is an alias for coeffs.asDiagonal()\n  */\ntemplate<typename Derived>\ninline const DiagonalWrapper<const Derived> Scaling(const MatrixBase<Derived>& coeffs)\n{ return coeffs.asDiagonal(); }\n\n/** \\deprecated */\ntypedef DiagonalMatrix<float, 2> AlignedScaling2f;\n/** \\deprecated */\ntypedef DiagonalMatrix<double,2> AlignedScaling2d;\n/** \\deprecated */\ntypedef DiagonalMatrix<float, 3> AlignedScaling3f;\n/** \\deprecated */\ntypedef DiagonalMatrix<double,3> AlignedScaling3d;\n//@}\n\ntemplate<typename Scalar>\ntemplate<int Dim>\ninline Transform<Scalar,Dim,Affine>\nUniformScaling<Scalar>::operator* (const Translation<Scalar,Dim>& t) const\n{\n  Transform<Scalar,Dim,Affine> res;\n  res.matrix().setZero();\n  res.linear().diagonal().fill(factor());\n  res.translation() = factor() * t.vector();\n  res(Dim,Dim) = Scalar(1);\n  return res;\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_SCALING_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Geometry/Transform.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2010 Hauke Heibel <hauke.heibel@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_TRANSFORM_H\n#define EIGEN_TRANSFORM_H\n\nnamespace Eigen { \n\nnamespace internal {\n\ntemplate<typename Transform>\nstruct transform_traits\n{\n  enum\n  {\n    Dim = Transform::Dim,\n    HDim = Transform::HDim,\n    Mode = Transform::Mode,\n    IsProjective = (int(Mode)==int(Projective))\n  };\n};\n\ntemplate< typename TransformType,\n          typename MatrixType,\n          int Case = transform_traits<TransformType>::IsProjective ? 0\n                   : int(MatrixType::RowsAtCompileTime) == int(transform_traits<TransformType>::HDim) ? 1\n                   : 2,\n          int RhsCols = MatrixType::ColsAtCompileTime>\nstruct transform_right_product_impl;\n\ntemplate< typename Other,\n          int Mode,\n          int Options,\n          int Dim,\n          int HDim,\n          int OtherRows=Other::RowsAtCompileTime,\n          int OtherCols=Other::ColsAtCompileTime>\nstruct transform_left_product_impl;\n\ntemplate< typename Lhs,\n          typename Rhs,\n          bool AnyProjective = \n            transform_traits<Lhs>::IsProjective ||\n            transform_traits<Rhs>::IsProjective>\nstruct transform_transform_product_impl;\n\ntemplate< typename Other,\n          int Mode,\n          int Options,\n          int Dim,\n          int HDim,\n          int OtherRows=Other::RowsAtCompileTime,\n          int OtherCols=Other::ColsAtCompileTime>\nstruct transform_construct_from_matrix;\n\ntemplate<typename TransformType> struct transform_take_affine_part;\n\ntemplate<typename _Scalar, int _Dim, int _Mode, int _Options>\nstruct traits<Transform<_Scalar,_Dim,_Mode,_Options> >\n{\n  typedef _Scalar Scalar;\n  typedef Eigen::Index StorageIndex;\n  typedef Dense StorageKind;\n  enum {\n    Dim1 = _Dim==Dynamic ? _Dim : _Dim + 1,\n    RowsAtCompileTime = _Mode==Projective ? Dim1 : _Dim,\n    ColsAtCompileTime = Dim1,\n    MaxRowsAtCompileTime = RowsAtCompileTime,\n    MaxColsAtCompileTime = ColsAtCompileTime,\n    Flags = 0\n  };\n};\n\ntemplate<int Mode> struct transform_make_affine;\n\n} // end namespace internal\n\n/** \\geometry_module \\ingroup Geometry_Module\n  *\n  * \\class Transform\n  *\n  * \\brief Represents an homogeneous transformation in a N dimensional space\n  *\n  * \\tparam _Scalar the scalar type, i.e., the type of the coefficients\n  * \\tparam _Dim the dimension of the space\n  * \\tparam _Mode the type of the transformation. Can be:\n  *              - #Affine: the transformation is stored as a (Dim+1)^2 matrix,\n  *                         where the last row is assumed to be [0 ... 0 1].\n  *              - #AffineCompact: the transformation is stored as a (Dim)x(Dim+1) matrix.\n  *              - #Projective: the transformation is stored as a (Dim+1)^2 matrix\n  *                             without any assumption.\n  * \\tparam _Options has the same meaning as in class Matrix. It allows to specify DontAlign and/or RowMajor.\n  *                  These Options are passed directly to the underlying matrix type.\n  *\n  * The homography is internally represented and stored by a matrix which\n  * is available through the matrix() method. To understand the behavior of\n  * this class you have to think a Transform object as its internal\n  * matrix representation. The chosen convention is right multiply:\n  *\n  * \\code v' = T * v \\endcode\n  *\n  * Therefore, an affine transformation matrix M is shaped like this:\n  *\n  * \\f$ \\left( \\begin{array}{cc}\n  * linear & translation\\\\\n  * 0 ... 0 & 1\n  * \\end{array} \\right) \\f$\n  *\n  * Note that for a projective transformation the last row can be anything,\n  * and then the interpretation of different parts might be sightly different.\n  *\n  * However, unlike a plain matrix, the Transform class provides many features\n  * simplifying both its assembly and usage. In particular, it can be composed\n  * with any other transformations (Transform,Translation,RotationBase,DiagonalMatrix)\n  * and can be directly used to transform implicit homogeneous vectors. All these\n  * operations are handled via the operator*. For the composition of transformations,\n  * its principle consists to first convert the right/left hand sides of the product\n  * to a compatible (Dim+1)^2 matrix and then perform a pure matrix product.\n  * Of course, internally, operator* tries to perform the minimal number of operations\n  * according to the nature of each terms. Likewise, when applying the transform\n  * to points, the latters are automatically promoted to homogeneous vectors\n  * before doing the matrix product. The conventions to homogeneous representations\n  * are performed as follow:\n  *\n  * \\b Translation t (Dim)x(1):\n  * \\f$ \\left( \\begin{array}{cc}\n  * I & t \\\\\n  * 0\\,...\\,0 & 1\n  * \\end{array} \\right) \\f$\n  *\n  * \\b Rotation R (Dim)x(Dim):\n  * \\f$ \\left( \\begin{array}{cc}\n  * R & 0\\\\\n  * 0\\,...\\,0 & 1\n  * \\end{array} \\right) \\f$\n  *<!--\n  * \\b Linear \\b Matrix L (Dim)x(Dim):\n  * \\f$ \\left( \\begin{array}{cc}\n  * L & 0\\\\\n  * 0\\,...\\,0 & 1\n  * \\end{array} \\right) \\f$\n  *\n  * \\b Affine \\b Matrix A (Dim)x(Dim+1):\n  * \\f$ \\left( \\begin{array}{c}\n  * A\\\\\n  * 0\\,...\\,0\\,1\n  * \\end{array} \\right) \\f$\n  *-->\n  * \\b Scaling \\b DiagonalMatrix S (Dim)x(Dim):\n  * \\f$ \\left( \\begin{array}{cc}\n  * S & 0\\\\\n  * 0\\,...\\,0 & 1\n  * \\end{array} \\right) \\f$\n  *\n  * \\b Column \\b point v (Dim)x(1):\n  * \\f$ \\left( \\begin{array}{c}\n  * v\\\\\n  * 1\n  * \\end{array} \\right) \\f$\n  *\n  * \\b Set \\b of \\b column \\b points V1...Vn (Dim)x(n):\n  * \\f$ \\left( \\begin{array}{ccc}\n  * v_1 & ... & v_n\\\\\n  * 1 & ... & 1\n  * \\end{array} \\right) \\f$\n  *\n  * The concatenation of a Transform object with any kind of other transformation\n  * always returns a Transform object.\n  *\n  * A little exception to the \"as pure matrix product\" rule is the case of the\n  * transformation of non homogeneous vectors by an affine transformation. In\n  * that case the last matrix row can be ignored, and the product returns non\n  * homogeneous vectors.\n  *\n  * Since, for instance, a Dim x Dim matrix is interpreted as a linear transformation,\n  * it is not possible to directly transform Dim vectors stored in a Dim x Dim matrix.\n  * The solution is either to use a Dim x Dynamic matrix or explicitly request a\n  * vector transformation by making the vector homogeneous:\n  * \\code\n  * m' = T * m.colwise().homogeneous();\n  * \\endcode\n  * Note that there is zero overhead.\n  *\n  * Conversion methods from/to Qt's QMatrix and QTransform are available if the\n  * preprocessor token EIGEN_QT_SUPPORT is defined.\n  *\n  * This class can be extended with the help of the plugin mechanism described on the page\n  * \\ref TopicCustomizing_Plugins by defining the preprocessor symbol \\c EIGEN_TRANSFORM_PLUGIN.\n  *\n  * \\sa class Matrix, class Quaternion\n  */\ntemplate<typename _Scalar, int _Dim, int _Mode, int _Options>\nclass Transform\n{\npublic:\n  EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Dim==Dynamic ? Dynamic : (_Dim+1)*(_Dim+1))\n  enum {\n    Mode = _Mode,\n    Options = _Options,\n    Dim = _Dim,     ///< space dimension in which the transformation holds\n    HDim = _Dim+1,  ///< size of a respective homogeneous vector\n    Rows = int(Mode)==(AffineCompact) ? Dim : HDim\n  };\n  /** the scalar type of the coefficients */\n  typedef _Scalar Scalar;\n  typedef Eigen::Index StorageIndex;\n  typedef Eigen::Index Index; ///< \\deprecated since Eigen 3.3\n  /** type of the matrix used to represent the transformation */\n  typedef typename internal::make_proper_matrix_type<Scalar,Rows,HDim,Options>::type MatrixType;\n  /** constified MatrixType */\n  typedef const MatrixType ConstMatrixType;\n  /** type of the matrix used to represent the linear part of the transformation */\n  typedef Matrix<Scalar,Dim,Dim,Options> LinearMatrixType;\n  /** type of read/write reference to the linear part of the transformation */\n  typedef Block<MatrixType,Dim,Dim,int(Mode)==(AffineCompact) && (Options&RowMajor)==0> LinearPart;\n  /** type of read reference to the linear part of the transformation */\n  typedef const Block<ConstMatrixType,Dim,Dim,int(Mode)==(AffineCompact) && (Options&RowMajor)==0> ConstLinearPart;\n  /** type of read/write reference to the affine part of the transformation */\n  typedef typename internal::conditional<int(Mode)==int(AffineCompact),\n                              MatrixType&,\n                              Block<MatrixType,Dim,HDim> >::type AffinePart;\n  /** type of read reference to the affine part of the transformation */\n  typedef typename internal::conditional<int(Mode)==int(AffineCompact),\n                              const MatrixType&,\n                              const Block<const MatrixType,Dim,HDim> >::type ConstAffinePart;\n  /** type of a vector */\n  typedef Matrix<Scalar,Dim,1> VectorType;\n  /** type of a read/write reference to the translation part of the rotation */\n  typedef Block<MatrixType,Dim,1,!(internal::traits<MatrixType>::Flags & RowMajorBit)> TranslationPart;\n  /** type of a read reference to the translation part of the rotation */\n  typedef const Block<ConstMatrixType,Dim,1,!(internal::traits<MatrixType>::Flags & RowMajorBit)> ConstTranslationPart;\n  /** corresponding translation type */\n  typedef Translation<Scalar,Dim> TranslationType;\n  \n  // this intermediate enum is needed to avoid an ICE with gcc 3.4 and 4.0\n  enum { TransformTimeDiagonalMode = ((Mode==int(Isometry))?Affine:int(Mode)) };\n  /** The return type of the product between a diagonal matrix and a transform */\n  typedef Transform<Scalar,Dim,TransformTimeDiagonalMode> TransformTimeDiagonalReturnType;\n\nprotected:\n\n  MatrixType m_matrix;\n\npublic:\n\n  /** Default constructor without initialization of the meaningful coefficients.\n    * If Mode==Affine, then the last row is set to [0 ... 0 1] */\n  EIGEN_DEVICE_FUNC inline Transform()\n  {\n    check_template_params();\n    internal::transform_make_affine<(int(Mode)==Affine) ? Affine : AffineCompact>::run(m_matrix);\n  }\n\n  EIGEN_DEVICE_FUNC inline Transform(const Transform& other)\n  {\n    check_template_params();\n    m_matrix = other.m_matrix;\n  }\n\n  EIGEN_DEVICE_FUNC inline explicit Transform(const TranslationType& t)\n  {\n    check_template_params();\n    *this = t;\n  }\n  EIGEN_DEVICE_FUNC inline explicit Transform(const UniformScaling<Scalar>& s)\n  {\n    check_template_params();\n    *this = s;\n  }\n  template<typename Derived>\n  EIGEN_DEVICE_FUNC inline explicit Transform(const RotationBase<Derived, Dim>& r)\n  {\n    check_template_params();\n    *this = r;\n  }\n\n  EIGEN_DEVICE_FUNC inline Transform& operator=(const Transform& other)\n  { m_matrix = other.m_matrix; return *this; }\n\n  typedef internal::transform_take_affine_part<Transform> take_affine_part;\n\n  /** Constructs and initializes a transformation from a Dim^2 or a (Dim+1)^2 matrix. */\n  template<typename OtherDerived>\n  EIGEN_DEVICE_FUNC inline explicit Transform(const EigenBase<OtherDerived>& other)\n  {\n    EIGEN_STATIC_ASSERT((internal::is_same<Scalar,typename OtherDerived::Scalar>::value),\n      YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY);\n\n    check_template_params();\n    internal::transform_construct_from_matrix<OtherDerived,Mode,Options,Dim,HDim>::run(this, other.derived());\n  }\n\n  /** Set \\c *this from a Dim^2 or (Dim+1)^2 matrix. */\n  template<typename OtherDerived>\n  EIGEN_DEVICE_FUNC inline Transform& operator=(const EigenBase<OtherDerived>& other)\n  {\n    EIGEN_STATIC_ASSERT((internal::is_same<Scalar,typename OtherDerived::Scalar>::value),\n      YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY);\n\n    internal::transform_construct_from_matrix<OtherDerived,Mode,Options,Dim,HDim>::run(this, other.derived());\n    return *this;\n  }\n  \n  template<int OtherOptions>\n  EIGEN_DEVICE_FUNC inline Transform(const Transform<Scalar,Dim,Mode,OtherOptions>& other)\n  {\n    check_template_params();\n    // only the options change, we can directly copy the matrices\n    m_matrix = other.matrix();\n  }\n\n  template<int OtherMode,int OtherOptions>\n  EIGEN_DEVICE_FUNC inline Transform(const Transform<Scalar,Dim,OtherMode,OtherOptions>& other)\n  {\n    check_template_params();\n    // prevent conversions as:\n    // Affine | AffineCompact | Isometry = Projective\n    EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(OtherMode==int(Projective), Mode==int(Projective)),\n                        YOU_PERFORMED_AN_INVALID_TRANSFORMATION_CONVERSION)\n\n    // prevent conversions as:\n    // Isometry = Affine | AffineCompact\n    EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(OtherMode==int(Affine)||OtherMode==int(AffineCompact), Mode!=int(Isometry)),\n                        YOU_PERFORMED_AN_INVALID_TRANSFORMATION_CONVERSION)\n\n    enum { ModeIsAffineCompact = Mode == int(AffineCompact),\n           OtherModeIsAffineCompact = OtherMode == int(AffineCompact)\n    };\n\n    if(ModeIsAffineCompact == OtherModeIsAffineCompact)\n    {\n      // We need the block expression because the code is compiled for all\n      // combinations of transformations and will trigger a compile time error\n      // if one tries to assign the matrices directly\n      m_matrix.template block<Dim,Dim+1>(0,0) = other.matrix().template block<Dim,Dim+1>(0,0);\n      makeAffine();\n    }\n    else if(OtherModeIsAffineCompact)\n    {\n      typedef typename Transform<Scalar,Dim,OtherMode,OtherOptions>::MatrixType OtherMatrixType;\n      internal::transform_construct_from_matrix<OtherMatrixType,Mode,Options,Dim,HDim>::run(this, other.matrix());\n    }\n    else\n    {\n      // here we know that Mode == AffineCompact and OtherMode != AffineCompact.\n      // if OtherMode were Projective, the static assert above would already have caught it.\n      // So the only possibility is that OtherMode == Affine\n      linear() = other.linear();\n      translation() = other.translation();\n    }\n  }\n\n  template<typename OtherDerived>\n  EIGEN_DEVICE_FUNC Transform(const ReturnByValue<OtherDerived>& other)\n  {\n    check_template_params();\n    other.evalTo(*this);\n  }\n\n  template<typename OtherDerived>\n  EIGEN_DEVICE_FUNC Transform& operator=(const ReturnByValue<OtherDerived>& other)\n  {\n    other.evalTo(*this);\n    return *this;\n  }\n\n  #ifdef EIGEN_QT_SUPPORT\n  inline Transform(const QMatrix& other);\n  inline Transform& operator=(const QMatrix& other);\n  inline QMatrix toQMatrix(void) const;\n  inline Transform(const QTransform& other);\n  inline Transform& operator=(const QTransform& other);\n  inline QTransform toQTransform(void) const;\n  #endif\n  \n  EIGEN_DEVICE_FUNC Index rows() const { return int(Mode)==int(Projective) ? m_matrix.cols() : (m_matrix.cols()-1); }\n  EIGEN_DEVICE_FUNC Index cols() const { return m_matrix.cols(); }\n\n  /** shortcut for m_matrix(row,col);\n    * \\sa MatrixBase::operator(Index,Index) const */\n  EIGEN_DEVICE_FUNC inline Scalar operator() (Index row, Index col) const { return m_matrix(row,col); }\n  /** shortcut for m_matrix(row,col);\n    * \\sa MatrixBase::operator(Index,Index) */\n  EIGEN_DEVICE_FUNC inline Scalar& operator() (Index row, Index col) { return m_matrix(row,col); }\n\n  /** \\returns a read-only expression of the transformation matrix */\n  EIGEN_DEVICE_FUNC inline const MatrixType& matrix() const { return m_matrix; }\n  /** \\returns a writable expression of the transformation matrix */\n  EIGEN_DEVICE_FUNC inline MatrixType& matrix() { return m_matrix; }\n\n  /** \\returns a read-only expression of the linear part of the transformation */\n  EIGEN_DEVICE_FUNC inline ConstLinearPart linear() const { return ConstLinearPart(m_matrix,0,0); }\n  /** \\returns a writable expression of the linear part of the transformation */\n  EIGEN_DEVICE_FUNC inline LinearPart linear() { return LinearPart(m_matrix,0,0); }\n\n  /** \\returns a read-only expression of the Dim x HDim affine part of the transformation */\n  EIGEN_DEVICE_FUNC inline ConstAffinePart affine() const { return take_affine_part::run(m_matrix); }\n  /** \\returns a writable expression of the Dim x HDim affine part of the transformation */\n  EIGEN_DEVICE_FUNC inline AffinePart affine() { return take_affine_part::run(m_matrix); }\n\n  /** \\returns a read-only expression of the translation vector of the transformation */\n  EIGEN_DEVICE_FUNC inline ConstTranslationPart translation() const { return ConstTranslationPart(m_matrix,0,Dim); }\n  /** \\returns a writable expression of the translation vector of the transformation */\n  EIGEN_DEVICE_FUNC inline TranslationPart translation() { return TranslationPart(m_matrix,0,Dim); }\n\n  /** \\returns an expression of the product between the transform \\c *this and a matrix expression \\a other.\n    *\n    * The right-hand-side \\a other can be either:\n    * \\li an homogeneous vector of size Dim+1,\n    * \\li a set of homogeneous vectors of size Dim+1 x N,\n    * \\li a transformation matrix of size Dim+1 x Dim+1.\n    *\n    * Moreover, if \\c *this represents an affine transformation (i.e., Mode!=Projective), then \\a other can also be:\n    * \\li a point of size Dim (computes: \\code this->linear() * other + this->translation()\\endcode),\n    * \\li a set of N points as a Dim x N matrix (computes: \\code (this->linear() * other).colwise() + this->translation()\\endcode),\n    *\n    * In all cases, the return type is a matrix or vector of same sizes as the right-hand-side \\a other.\n    *\n    * If you want to interpret \\a other as a linear or affine transformation, then first convert it to a Transform<> type,\n    * or do your own cooking.\n    *\n    * Finally, if you want to apply Affine transformations to vectors, then explicitly apply the linear part only:\n    * \\code\n    * Affine3f A;\n    * Vector3f v1, v2;\n    * v2 = A.linear() * v1;\n    * \\endcode\n    *\n    */\n  // note: this function is defined here because some compilers cannot find the respective declaration\n  template<typename OtherDerived>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename internal::transform_right_product_impl<Transform, OtherDerived>::ResultType\n  operator * (const EigenBase<OtherDerived> &other) const\n  { return internal::transform_right_product_impl<Transform, OtherDerived>::run(*this,other.derived()); }\n\n  /** \\returns the product expression of a transformation matrix \\a a times a transform \\a b\n    *\n    * The left hand side \\a other can be either:\n    * \\li a linear transformation matrix of size Dim x Dim,\n    * \\li an affine transformation matrix of size Dim x Dim+1,\n    * \\li a general transformation matrix of size Dim+1 x Dim+1.\n    */\n  template<typename OtherDerived> friend\n  EIGEN_DEVICE_FUNC inline const typename internal::transform_left_product_impl<OtherDerived,Mode,Options,_Dim,_Dim+1>::ResultType\n    operator * (const EigenBase<OtherDerived> &a, const Transform &b)\n  { return internal::transform_left_product_impl<OtherDerived,Mode,Options,Dim,HDim>::run(a.derived(),b); }\n\n  /** \\returns The product expression of a transform \\a a times a diagonal matrix \\a b\n    *\n    * The rhs diagonal matrix is interpreted as an affine scaling transformation. The\n    * product results in a Transform of the same type (mode) as the lhs only if the lhs \n    * mode is no isometry. In that case, the returned transform is an affinity.\n    */\n  template<typename DiagonalDerived>\n  EIGEN_DEVICE_FUNC inline const TransformTimeDiagonalReturnType\n    operator * (const DiagonalBase<DiagonalDerived> &b) const\n  {\n    TransformTimeDiagonalReturnType res(*this);\n    res.linearExt() *= b;\n    return res;\n  }\n\n  /** \\returns The product expression of a diagonal matrix \\a a times a transform \\a b\n    *\n    * The lhs diagonal matrix is interpreted as an affine scaling transformation. The\n    * product results in a Transform of the same type (mode) as the lhs only if the lhs \n    * mode is no isometry. In that case, the returned transform is an affinity.\n    */\n  template<typename DiagonalDerived>\n  EIGEN_DEVICE_FUNC friend inline TransformTimeDiagonalReturnType\n    operator * (const DiagonalBase<DiagonalDerived> &a, const Transform &b)\n  {\n    TransformTimeDiagonalReturnType res;\n    res.linear().noalias() = a*b.linear();\n    res.translation().noalias() = a*b.translation();\n    if (Mode!=int(AffineCompact))\n      res.matrix().row(Dim) = b.matrix().row(Dim);\n    return res;\n  }\n\n  template<typename OtherDerived>\n  EIGEN_DEVICE_FUNC inline Transform& operator*=(const EigenBase<OtherDerived>& other) { return *this = *this * other; }\n\n  /** Concatenates two transformations */\n  EIGEN_DEVICE_FUNC inline const Transform operator * (const Transform& other) const\n  {\n    return internal::transform_transform_product_impl<Transform,Transform>::run(*this,other);\n  }\n  \n  #if EIGEN_COMP_ICC\nprivate:\n  // this intermediate structure permits to workaround a bug in ICC 11:\n  //   error: template instantiation resulted in unexpected function type of \"Eigen::Transform<double, 3, 32, 0>\n  //             (const Eigen::Transform<double, 3, 2, 0> &) const\"\n  //  (the meaning of a name may have changed since the template declaration -- the type of the template is:\n  // \"Eigen::internal::transform_transform_product_impl<Eigen::Transform<double, 3, 32, 0>,\n  //     Eigen::Transform<double, 3, Mode, Options>, <expression>>::ResultType (const Eigen::Transform<double, 3, Mode, Options> &) const\")\n  // \n  template<int OtherMode,int OtherOptions> struct icc_11_workaround\n  {\n    typedef internal::transform_transform_product_impl<Transform,Transform<Scalar,Dim,OtherMode,OtherOptions> > ProductType;\n    typedef typename ProductType::ResultType ResultType;\n  };\n  \npublic:\n  /** Concatenates two different transformations */\n  template<int OtherMode,int OtherOptions>\n  inline typename icc_11_workaround<OtherMode,OtherOptions>::ResultType\n    operator * (const Transform<Scalar,Dim,OtherMode,OtherOptions>& other) const\n  {\n    typedef typename icc_11_workaround<OtherMode,OtherOptions>::ProductType ProductType;\n    return ProductType::run(*this,other);\n  }\n  #else\n  /** Concatenates two different transformations */\n  template<int OtherMode,int OtherOptions>\n  EIGEN_DEVICE_FUNC inline typename internal::transform_transform_product_impl<Transform,Transform<Scalar,Dim,OtherMode,OtherOptions> >::ResultType\n    operator * (const Transform<Scalar,Dim,OtherMode,OtherOptions>& other) const\n  {\n    return internal::transform_transform_product_impl<Transform,Transform<Scalar,Dim,OtherMode,OtherOptions> >::run(*this,other);\n  }\n  #endif\n\n  /** \\sa MatrixBase::setIdentity() */\n  EIGEN_DEVICE_FUNC void setIdentity() { m_matrix.setIdentity(); }\n\n  /**\n   * \\brief Returns an identity transformation.\n   * \\todo In the future this function should be returning a Transform expression.\n   */\n  EIGEN_DEVICE_FUNC static const Transform Identity()\n  {\n    return Transform(MatrixType::Identity());\n  }\n\n  template<typename OtherDerived>\n  EIGEN_DEVICE_FUNC \n  inline Transform& scale(const MatrixBase<OtherDerived> &other);\n\n  template<typename OtherDerived>\n  EIGEN_DEVICE_FUNC\n  inline Transform& prescale(const MatrixBase<OtherDerived> &other);\n\n  EIGEN_DEVICE_FUNC inline Transform& scale(const Scalar& s);\n  EIGEN_DEVICE_FUNC inline Transform& prescale(const Scalar& s);\n\n  template<typename OtherDerived>\n  EIGEN_DEVICE_FUNC\n  inline Transform& translate(const MatrixBase<OtherDerived> &other);\n\n  template<typename OtherDerived>\n  EIGEN_DEVICE_FUNC\n  inline Transform& pretranslate(const MatrixBase<OtherDerived> &other);\n\n  template<typename RotationType>\n  EIGEN_DEVICE_FUNC\n  inline Transform& rotate(const RotationType& rotation);\n\n  template<typename RotationType>\n  EIGEN_DEVICE_FUNC\n  inline Transform& prerotate(const RotationType& rotation);\n\n  EIGEN_DEVICE_FUNC Transform& shear(const Scalar& sx, const Scalar& sy);\n  EIGEN_DEVICE_FUNC Transform& preshear(const Scalar& sx, const Scalar& sy);\n\n  EIGEN_DEVICE_FUNC inline Transform& operator=(const TranslationType& t);\n  \n  EIGEN_DEVICE_FUNC\n  inline Transform& operator*=(const TranslationType& t) { return translate(t.vector()); }\n  \n  EIGEN_DEVICE_FUNC inline Transform operator*(const TranslationType& t) const;\n\n  EIGEN_DEVICE_FUNC \n  inline Transform& operator=(const UniformScaling<Scalar>& t);\n  \n  EIGEN_DEVICE_FUNC\n  inline Transform& operator*=(const UniformScaling<Scalar>& s) { return scale(s.factor()); }\n  \n  EIGEN_DEVICE_FUNC\n  inline TransformTimeDiagonalReturnType operator*(const UniformScaling<Scalar>& s) const\n  {\n    TransformTimeDiagonalReturnType res = *this;\n    res.scale(s.factor());\n    return res;\n  }\n\n  EIGEN_DEVICE_FUNC\n  inline Transform& operator*=(const DiagonalMatrix<Scalar,Dim>& s) { linearExt() *= s; return *this; }\n\n  template<typename Derived>\n  EIGEN_DEVICE_FUNC inline Transform& operator=(const RotationBase<Derived,Dim>& r);\n  template<typename Derived>\n  EIGEN_DEVICE_FUNC inline Transform& operator*=(const RotationBase<Derived,Dim>& r) { return rotate(r.toRotationMatrix()); }\n  template<typename Derived>\n  EIGEN_DEVICE_FUNC inline Transform operator*(const RotationBase<Derived,Dim>& r) const;\n\n  EIGEN_DEVICE_FUNC const LinearMatrixType rotation() const;\n  template<typename RotationMatrixType, typename ScalingMatrixType>\n  EIGEN_DEVICE_FUNC\n  void computeRotationScaling(RotationMatrixType *rotation, ScalingMatrixType *scaling) const;\n  template<typename ScalingMatrixType, typename RotationMatrixType>\n  EIGEN_DEVICE_FUNC\n  void computeScalingRotation(ScalingMatrixType *scaling, RotationMatrixType *rotation) const;\n\n  template<typename PositionDerived, typename OrientationType, typename ScaleDerived>\n  EIGEN_DEVICE_FUNC\n  Transform& fromPositionOrientationScale(const MatrixBase<PositionDerived> &position,\n    const OrientationType& orientation, const MatrixBase<ScaleDerived> &scale);\n\n  EIGEN_DEVICE_FUNC\n  inline Transform inverse(TransformTraits traits = (TransformTraits)Mode) const;\n\n  /** \\returns a const pointer to the column major internal matrix */\n  EIGEN_DEVICE_FUNC const Scalar* data() const { return m_matrix.data(); }\n  /** \\returns a non-const pointer to the column major internal matrix */\n  EIGEN_DEVICE_FUNC Scalar* data() { return m_matrix.data(); }\n\n  /** \\returns \\c *this with scalar type casted to \\a NewScalarType\n    *\n    * Note that if \\a NewScalarType is equal to the current scalar type of \\c *this\n    * then this function smartly returns a const reference to \\c *this.\n    */\n  template<typename NewScalarType>\n  EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<Transform,Transform<NewScalarType,Dim,Mode,Options> >::type cast() const\n  { return typename internal::cast_return_type<Transform,Transform<NewScalarType,Dim,Mode,Options> >::type(*this); }\n\n  /** Copy constructor with scalar type conversion */\n  template<typename OtherScalarType>\n  EIGEN_DEVICE_FUNC inline explicit Transform(const Transform<OtherScalarType,Dim,Mode,Options>& other)\n  {\n    check_template_params();\n    m_matrix = other.matrix().template cast<Scalar>();\n  }\n\n  /** \\returns \\c true if \\c *this is approximately equal to \\a other, within the precision\n    * determined by \\a prec.\n    *\n    * \\sa MatrixBase::isApprox() */\n  EIGEN_DEVICE_FUNC bool isApprox(const Transform& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const\n  { return m_matrix.isApprox(other.m_matrix, prec); }\n\n  /** Sets the last row to [0 ... 0 1]\n    */\n  EIGEN_DEVICE_FUNC void makeAffine()\n  {\n    internal::transform_make_affine<int(Mode)>::run(m_matrix);\n  }\n\n  /** \\internal\n    * \\returns the Dim x Dim linear part if the transformation is affine,\n    *          and the HDim x Dim part for projective transformations.\n    */\n  EIGEN_DEVICE_FUNC inline Block<MatrixType,int(Mode)==int(Projective)?HDim:Dim,Dim> linearExt()\n  { return m_matrix.template block<int(Mode)==int(Projective)?HDim:Dim,Dim>(0,0); }\n  /** \\internal\n    * \\returns the Dim x Dim linear part if the transformation is affine,\n    *          and the HDim x Dim part for projective transformations.\n    */\n  EIGEN_DEVICE_FUNC inline const Block<MatrixType,int(Mode)==int(Projective)?HDim:Dim,Dim> linearExt() const\n  { return m_matrix.template block<int(Mode)==int(Projective)?HDim:Dim,Dim>(0,0); }\n\n  /** \\internal\n    * \\returns the translation part if the transformation is affine,\n    *          and the last column for projective transformations.\n    */\n  EIGEN_DEVICE_FUNC inline Block<MatrixType,int(Mode)==int(Projective)?HDim:Dim,1> translationExt()\n  { return m_matrix.template block<int(Mode)==int(Projective)?HDim:Dim,1>(0,Dim); }\n  /** \\internal\n    * \\returns the translation part if the transformation is affine,\n    *          and the last column for projective transformations.\n    */\n  EIGEN_DEVICE_FUNC inline const Block<MatrixType,int(Mode)==int(Projective)?HDim:Dim,1> translationExt() const\n  { return m_matrix.template block<int(Mode)==int(Projective)?HDim:Dim,1>(0,Dim); }\n\n\n  #ifdef EIGEN_TRANSFORM_PLUGIN\n  #include EIGEN_TRANSFORM_PLUGIN\n  #endif\n  \nprotected:\n  #ifndef EIGEN_PARSED_BY_DOXYGEN\n    EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void check_template_params()\n    {\n      EIGEN_STATIC_ASSERT((Options & (DontAlign|RowMajor)) == Options, INVALID_MATRIX_TEMPLATE_PARAMETERS)\n    }\n  #endif\n\n};\n\n/** \\ingroup Geometry_Module */\ntypedef Transform<float,2,Isometry> Isometry2f;\n/** \\ingroup Geometry_Module */\ntypedef Transform<float,3,Isometry> Isometry3f;\n/** \\ingroup Geometry_Module */\ntypedef Transform<double,2,Isometry> Isometry2d;\n/** \\ingroup Geometry_Module */\ntypedef Transform<double,3,Isometry> Isometry3d;\n\n/** \\ingroup Geometry_Module */\ntypedef Transform<float,2,Affine> Affine2f;\n/** \\ingroup Geometry_Module */\ntypedef Transform<float,3,Affine> Affine3f;\n/** \\ingroup Geometry_Module */\ntypedef Transform<double,2,Affine> Affine2d;\n/** \\ingroup Geometry_Module */\ntypedef Transform<double,3,Affine> Affine3d;\n\n/** \\ingroup Geometry_Module */\ntypedef Transform<float,2,AffineCompact> AffineCompact2f;\n/** \\ingroup Geometry_Module */\ntypedef Transform<float,3,AffineCompact> AffineCompact3f;\n/** \\ingroup Geometry_Module */\ntypedef Transform<double,2,AffineCompact> AffineCompact2d;\n/** \\ingroup Geometry_Module */\ntypedef Transform<double,3,AffineCompact> AffineCompact3d;\n\n/** \\ingroup Geometry_Module */\ntypedef Transform<float,2,Projective> Projective2f;\n/** \\ingroup Geometry_Module */\ntypedef Transform<float,3,Projective> Projective3f;\n/** \\ingroup Geometry_Module */\ntypedef Transform<double,2,Projective> Projective2d;\n/** \\ingroup Geometry_Module */\ntypedef Transform<double,3,Projective> Projective3d;\n\n/**************************\n*** Optional QT support ***\n**************************/\n\n#ifdef EIGEN_QT_SUPPORT\n/** Initializes \\c *this from a QMatrix assuming the dimension is 2.\n  *\n  * This function is available only if the token EIGEN_QT_SUPPORT is defined.\n  */\ntemplate<typename Scalar, int Dim, int Mode,int Options>\nTransform<Scalar,Dim,Mode,Options>::Transform(const QMatrix& other)\n{\n  check_template_params();\n  *this = other;\n}\n\n/** Set \\c *this from a QMatrix assuming the dimension is 2.\n  *\n  * This function is available only if the token EIGEN_QT_SUPPORT is defined.\n  */\ntemplate<typename Scalar, int Dim, int Mode,int Options>\nTransform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::operator=(const QMatrix& other)\n{\n  EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)\n  if (Mode == int(AffineCompact))\n    m_matrix << other.m11(), other.m21(), other.dx(),\n                other.m12(), other.m22(), other.dy();\n  else\n    m_matrix << other.m11(), other.m21(), other.dx(),\n                other.m12(), other.m22(), other.dy(),\n                0, 0, 1;\n  return *this;\n}\n\n/** \\returns a QMatrix from \\c *this assuming the dimension is 2.\n  *\n  * \\warning this conversion might loss data if \\c *this is not affine\n  *\n  * This function is available only if the token EIGEN_QT_SUPPORT is defined.\n  */\ntemplate<typename Scalar, int Dim, int Mode, int Options>\nQMatrix Transform<Scalar,Dim,Mode,Options>::toQMatrix(void) const\n{\n  check_template_params();\n  EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)\n  return QMatrix(m_matrix.coeff(0,0), m_matrix.coeff(1,0),\n                 m_matrix.coeff(0,1), m_matrix.coeff(1,1),\n                 m_matrix.coeff(0,2), m_matrix.coeff(1,2));\n}\n\n/** Initializes \\c *this from a QTransform assuming the dimension is 2.\n  *\n  * This function is available only if the token EIGEN_QT_SUPPORT is defined.\n  */\ntemplate<typename Scalar, int Dim, int Mode,int Options>\nTransform<Scalar,Dim,Mode,Options>::Transform(const QTransform& other)\n{\n  check_template_params();\n  *this = other;\n}\n\n/** Set \\c *this from a QTransform assuming the dimension is 2.\n  *\n  * This function is available only if the token EIGEN_QT_SUPPORT is defined.\n  */\ntemplate<typename Scalar, int Dim, int Mode, int Options>\nTransform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::operator=(const QTransform& other)\n{\n  check_template_params();\n  EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)\n  if (Mode == int(AffineCompact))\n    m_matrix << other.m11(), other.m21(), other.dx(),\n                other.m12(), other.m22(), other.dy();\n  else\n    m_matrix << other.m11(), other.m21(), other.dx(),\n                other.m12(), other.m22(), other.dy(),\n                other.m13(), other.m23(), other.m33();\n  return *this;\n}\n\n/** \\returns a QTransform from \\c *this assuming the dimension is 2.\n  *\n  * This function is available only if the token EIGEN_QT_SUPPORT is defined.\n  */\ntemplate<typename Scalar, int Dim, int Mode, int Options>\nQTransform Transform<Scalar,Dim,Mode,Options>::toQTransform(void) const\n{\n  EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)\n  if (Mode == int(AffineCompact))\n    return QTransform(m_matrix.coeff(0,0), m_matrix.coeff(1,0),\n                      m_matrix.coeff(0,1), m_matrix.coeff(1,1),\n                      m_matrix.coeff(0,2), m_matrix.coeff(1,2));\n  else\n    return QTransform(m_matrix.coeff(0,0), m_matrix.coeff(1,0), m_matrix.coeff(2,0),\n                      m_matrix.coeff(0,1), m_matrix.coeff(1,1), m_matrix.coeff(2,1),\n                      m_matrix.coeff(0,2), m_matrix.coeff(1,2), m_matrix.coeff(2,2));\n}\n#endif\n\n/*********************\n*** Procedural API ***\n*********************/\n\n/** Applies on the right the non uniform scale transformation represented\n  * by the vector \\a other to \\c *this and returns a reference to \\c *this.\n  * \\sa prescale()\n  */\ntemplate<typename Scalar, int Dim, int Mode, int Options>\ntemplate<typename OtherDerived>\nEIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&\nTransform<Scalar,Dim,Mode,Options>::scale(const MatrixBase<OtherDerived> &other)\n{\n  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))\n  EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)\n  linearExt().noalias() = (linearExt() * other.asDiagonal());\n  return *this;\n}\n\n/** Applies on the right a uniform scale of a factor \\a c to \\c *this\n  * and returns a reference to \\c *this.\n  * \\sa prescale(Scalar)\n  */\ntemplate<typename Scalar, int Dim, int Mode, int Options>\nEIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::scale(const Scalar& s)\n{\n  EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)\n  linearExt() *= s;\n  return *this;\n}\n\n/** Applies on the left the non uniform scale transformation represented\n  * by the vector \\a other to \\c *this and returns a reference to \\c *this.\n  * \\sa scale()\n  */\ntemplate<typename Scalar, int Dim, int Mode, int Options>\ntemplate<typename OtherDerived>\nEIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&\nTransform<Scalar,Dim,Mode,Options>::prescale(const MatrixBase<OtherDerived> &other)\n{\n  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))\n  EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)\n  affine().noalias() = (other.asDiagonal() * affine());\n  return *this;\n}\n\n/** Applies on the left a uniform scale of a factor \\a c to \\c *this\n  * and returns a reference to \\c *this.\n  * \\sa scale(Scalar)\n  */\ntemplate<typename Scalar, int Dim, int Mode, int Options>\nEIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::prescale(const Scalar& s)\n{\n  EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)\n  m_matrix.template topRows<Dim>() *= s;\n  return *this;\n}\n\n/** Applies on the right the translation matrix represented by the vector \\a other\n  * to \\c *this and returns a reference to \\c *this.\n  * \\sa pretranslate()\n  */\ntemplate<typename Scalar, int Dim, int Mode, int Options>\ntemplate<typename OtherDerived>\nEIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&\nTransform<Scalar,Dim,Mode,Options>::translate(const MatrixBase<OtherDerived> &other)\n{\n  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))\n  translationExt() += linearExt() * other;\n  return *this;\n}\n\n/** Applies on the left the translation matrix represented by the vector \\a other\n  * to \\c *this and returns a reference to \\c *this.\n  * \\sa translate()\n  */\ntemplate<typename Scalar, int Dim, int Mode, int Options>\ntemplate<typename OtherDerived>\nEIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&\nTransform<Scalar,Dim,Mode,Options>::pretranslate(const MatrixBase<OtherDerived> &other)\n{\n  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))\n  if(int(Mode)==int(Projective))\n    affine() += other * m_matrix.row(Dim);\n  else\n    translation() += other;\n  return *this;\n}\n\n/** Applies on the right the rotation represented by the rotation \\a rotation\n  * to \\c *this and returns a reference to \\c *this.\n  *\n  * The template parameter \\a RotationType is the type of the rotation which\n  * must be known by internal::toRotationMatrix<>.\n  *\n  * Natively supported types includes:\n  *   - any scalar (2D),\n  *   - a Dim x Dim matrix expression,\n  *   - a Quaternion (3D),\n  *   - a AngleAxis (3D)\n  *\n  * This mechanism is easily extendable to support user types such as Euler angles,\n  * or a pair of Quaternion for 4D rotations.\n  *\n  * \\sa rotate(Scalar), class Quaternion, class AngleAxis, prerotate(RotationType)\n  */\ntemplate<typename Scalar, int Dim, int Mode, int Options>\ntemplate<typename RotationType>\nEIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&\nTransform<Scalar,Dim,Mode,Options>::rotate(const RotationType& rotation)\n{\n  linearExt() *= internal::toRotationMatrix<Scalar,Dim>(rotation);\n  return *this;\n}\n\n/** Applies on the left the rotation represented by the rotation \\a rotation\n  * to \\c *this and returns a reference to \\c *this.\n  *\n  * See rotate() for further details.\n  *\n  * \\sa rotate()\n  */\ntemplate<typename Scalar, int Dim, int Mode, int Options>\ntemplate<typename RotationType>\nEIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&\nTransform<Scalar,Dim,Mode,Options>::prerotate(const RotationType& rotation)\n{\n  m_matrix.template block<Dim,HDim>(0,0) = internal::toRotationMatrix<Scalar,Dim>(rotation)\n                                         * m_matrix.template block<Dim,HDim>(0,0);\n  return *this;\n}\n\n/** Applies on the right the shear transformation represented\n  * by the vector \\a other to \\c *this and returns a reference to \\c *this.\n  * \\warning 2D only.\n  * \\sa preshear()\n  */\ntemplate<typename Scalar, int Dim, int Mode, int Options>\nEIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&\nTransform<Scalar,Dim,Mode,Options>::shear(const Scalar& sx, const Scalar& sy)\n{\n  EIGEN_STATIC_ASSERT(int(Dim)==2, YOU_MADE_A_PROGRAMMING_MISTAKE)\n  EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)\n  VectorType tmp = linear().col(0)*sy + linear().col(1);\n  linear() << linear().col(0) + linear().col(1)*sx, tmp;\n  return *this;\n}\n\n/** Applies on the left the shear transformation represented\n  * by the vector \\a other to \\c *this and returns a reference to \\c *this.\n  * \\warning 2D only.\n  * \\sa shear()\n  */\ntemplate<typename Scalar, int Dim, int Mode, int Options>\nEIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&\nTransform<Scalar,Dim,Mode,Options>::preshear(const Scalar& sx, const Scalar& sy)\n{\n  EIGEN_STATIC_ASSERT(int(Dim)==2, YOU_MADE_A_PROGRAMMING_MISTAKE)\n  EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)\n  m_matrix.template block<Dim,HDim>(0,0) = LinearMatrixType(1, sx, sy, 1) * m_matrix.template block<Dim,HDim>(0,0);\n  return *this;\n}\n\n/******************************************************\n*** Scaling, Translation and Rotation compatibility ***\n******************************************************/\n\ntemplate<typename Scalar, int Dim, int Mode, int Options>\nEIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::operator=(const TranslationType& t)\n{\n  linear().setIdentity();\n  translation() = t.vector();\n  makeAffine();\n  return *this;\n}\n\ntemplate<typename Scalar, int Dim, int Mode, int Options>\nEIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode,Options> Transform<Scalar,Dim,Mode,Options>::operator*(const TranslationType& t) const\n{\n  Transform res = *this;\n  res.translate(t.vector());\n  return res;\n}\n\ntemplate<typename Scalar, int Dim, int Mode, int Options>\nEIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::operator=(const UniformScaling<Scalar>& s)\n{\n  m_matrix.setZero();\n  linear().diagonal().fill(s.factor());\n  makeAffine();\n  return *this;\n}\n\ntemplate<typename Scalar, int Dim, int Mode, int Options>\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::operator=(const RotationBase<Derived,Dim>& r)\n{\n  linear() = internal::toRotationMatrix<Scalar,Dim>(r);\n  translation().setZero();\n  makeAffine();\n  return *this;\n}\n\ntemplate<typename Scalar, int Dim, int Mode, int Options>\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode,Options> Transform<Scalar,Dim,Mode,Options>::operator*(const RotationBase<Derived,Dim>& r) const\n{\n  Transform res = *this;\n  res.rotate(r.derived());\n  return res;\n}\n\n/************************\n*** Special functions ***\n************************/\n\n/** \\returns the rotation part of the transformation\n  *\n  *\n  * \\svd_module\n  *\n  * \\sa computeRotationScaling(), computeScalingRotation(), class SVD\n  */\ntemplate<typename Scalar, int Dim, int Mode, int Options>\nEIGEN_DEVICE_FUNC const typename Transform<Scalar,Dim,Mode,Options>::LinearMatrixType\nTransform<Scalar,Dim,Mode,Options>::rotation() const\n{\n  LinearMatrixType result;\n  computeRotationScaling(&result, (LinearMatrixType*)0);\n  return result;\n}\n\n\n/** decomposes the linear part of the transformation as a product rotation x scaling, the scaling being\n  * not necessarily positive.\n  *\n  * If either pointer is zero, the corresponding computation is skipped.\n  *\n  *\n  *\n  * \\svd_module\n  *\n  * \\sa computeScalingRotation(), rotation(), class SVD\n  */\ntemplate<typename Scalar, int Dim, int Mode, int Options>\ntemplate<typename RotationMatrixType, typename ScalingMatrixType>\nEIGEN_DEVICE_FUNC void Transform<Scalar,Dim,Mode,Options>::computeRotationScaling(RotationMatrixType *rotation, ScalingMatrixType *scaling) const\n{\n  JacobiSVD<LinearMatrixType> svd(linear(), ComputeFullU | ComputeFullV);\n\n  Scalar x = (svd.matrixU() * svd.matrixV().adjoint()).determinant(); // so x has absolute value 1\n  VectorType sv(svd.singularValues());\n  sv.coeffRef(0) *= x;\n  if(scaling) scaling->lazyAssign(svd.matrixV() * sv.asDiagonal() * svd.matrixV().adjoint());\n  if(rotation)\n  {\n    LinearMatrixType m(svd.matrixU());\n    m.col(0) /= x;\n    rotation->lazyAssign(m * svd.matrixV().adjoint());\n  }\n}\n\n/** decomposes the linear part of the transformation as a product scaling x rotation, the scaling being\n  * not necessarily positive.\n  *\n  * If either pointer is zero, the corresponding computation is skipped.\n  *\n  *\n  *\n  * \\svd_module\n  *\n  * \\sa computeRotationScaling(), rotation(), class SVD\n  */\ntemplate<typename Scalar, int Dim, int Mode, int Options>\ntemplate<typename ScalingMatrixType, typename RotationMatrixType>\nEIGEN_DEVICE_FUNC void Transform<Scalar,Dim,Mode,Options>::computeScalingRotation(ScalingMatrixType *scaling, RotationMatrixType *rotation) const\n{\n  JacobiSVD<LinearMatrixType> svd(linear(), ComputeFullU | ComputeFullV);\n\n  Scalar x = (svd.matrixU() * svd.matrixV().adjoint()).determinant(); // so x has absolute value 1\n  VectorType sv(svd.singularValues());\n  sv.coeffRef(0) *= x;\n  if(scaling) scaling->lazyAssign(svd.matrixU() * sv.asDiagonal() * svd.matrixU().adjoint());\n  if(rotation)\n  {\n    LinearMatrixType m(svd.matrixU());\n    m.col(0) /= x;\n    rotation->lazyAssign(m * svd.matrixV().adjoint());\n  }\n}\n\n/** Convenient method to set \\c *this from a position, orientation and scale\n  * of a 3D object.\n  */\ntemplate<typename Scalar, int Dim, int Mode, int Options>\ntemplate<typename PositionDerived, typename OrientationType, typename ScaleDerived>\nEIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&\nTransform<Scalar,Dim,Mode,Options>::fromPositionOrientationScale(const MatrixBase<PositionDerived> &position,\n  const OrientationType& orientation, const MatrixBase<ScaleDerived> &scale)\n{\n  linear() = internal::toRotationMatrix<Scalar,Dim>(orientation);\n  linear() *= scale.asDiagonal();\n  translation() = position;\n  makeAffine();\n  return *this;\n}\n\nnamespace internal {\n\ntemplate<int Mode>\nstruct transform_make_affine\n{\n  template<typename MatrixType>\n  EIGEN_DEVICE_FUNC static void run(MatrixType &mat)\n  {\n    static const int Dim = MatrixType::ColsAtCompileTime-1;\n    mat.template block<1,Dim>(Dim,0).setZero();\n    mat.coeffRef(Dim,Dim) = typename MatrixType::Scalar(1);\n  }\n};\n\ntemplate<>\nstruct transform_make_affine<AffineCompact>\n{\n  template<typename MatrixType> EIGEN_DEVICE_FUNC static void run(MatrixType &) { }\n};\n    \n// selector needed to avoid taking the inverse of a 3x4 matrix\ntemplate<typename TransformType, int Mode=TransformType::Mode>\nstruct projective_transform_inverse\n{\n  EIGEN_DEVICE_FUNC static inline void run(const TransformType&, TransformType&)\n  {}\n};\n\ntemplate<typename TransformType>\nstruct projective_transform_inverse<TransformType, Projective>\n{\n  EIGEN_DEVICE_FUNC static inline void run(const TransformType& m, TransformType& res)\n  {\n    res.matrix() = m.matrix().inverse();\n  }\n};\n\n} // end namespace internal\n\n\n/**\n  *\n  * \\returns the inverse transformation according to some given knowledge\n  * on \\c *this.\n  *\n  * \\param hint allows to optimize the inversion process when the transformation\n  * is known to be not a general transformation (optional). The possible values are:\n  *  - #Projective if the transformation is not necessarily affine, i.e., if the\n  *    last row is not guaranteed to be [0 ... 0 1]\n  *  - #Affine if the last row can be assumed to be [0 ... 0 1]\n  *  - #Isometry if the transformation is only a concatenations of translations\n  *    and rotations.\n  *  The default is the template class parameter \\c Mode.\n  *\n  * \\warning unless \\a traits is always set to NoShear or NoScaling, this function\n  * requires the generic inverse method of MatrixBase defined in the LU module. If\n  * you forget to include this module, then you will get hard to debug linking errors.\n  *\n  * \\sa MatrixBase::inverse()\n  */\ntemplate<typename Scalar, int Dim, int Mode, int Options>\nEIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>\nTransform<Scalar,Dim,Mode,Options>::inverse(TransformTraits hint) const\n{\n  Transform res;\n  if (hint == Projective)\n  {\n    internal::projective_transform_inverse<Transform>::run(*this, res);\n  }\n  else\n  {\n    if (hint == Isometry)\n    {\n      res.matrix().template topLeftCorner<Dim,Dim>() = linear().transpose();\n    }\n    else if(hint&Affine)\n    {\n      res.matrix().template topLeftCorner<Dim,Dim>() = linear().inverse();\n    }\n    else\n    {\n      eigen_assert(false && \"Invalid transform traits in Transform::Inverse\");\n    }\n    // translation and remaining parts\n    res.matrix().template topRightCorner<Dim,1>()\n      = - res.matrix().template topLeftCorner<Dim,Dim>() * translation();\n    res.makeAffine(); // we do need this, because in the beginning res is uninitialized\n  }\n  return res;\n}\n\nnamespace internal {\n\n/*****************************************************\n*** Specializations of take affine part            ***\n*****************************************************/\n\ntemplate<typename TransformType> struct transform_take_affine_part {\n  typedef typename TransformType::MatrixType MatrixType;\n  typedef typename TransformType::AffinePart AffinePart;\n  typedef typename TransformType::ConstAffinePart ConstAffinePart;\n  static inline AffinePart run(MatrixType& m)\n  { return m.template block<TransformType::Dim,TransformType::HDim>(0,0); }\n  static inline ConstAffinePart run(const MatrixType& m)\n  { return m.template block<TransformType::Dim,TransformType::HDim>(0,0); }\n};\n\ntemplate<typename Scalar, int Dim, int Options>\nstruct transform_take_affine_part<Transform<Scalar,Dim,AffineCompact, Options> > {\n  typedef typename Transform<Scalar,Dim,AffineCompact,Options>::MatrixType MatrixType;\n  static inline MatrixType& run(MatrixType& m) { return m; }\n  static inline const MatrixType& run(const MatrixType& m) { return m; }\n};\n\n/*****************************************************\n*** Specializations of construct from matrix       ***\n*****************************************************/\n\ntemplate<typename Other, int Mode, int Options, int Dim, int HDim>\nstruct transform_construct_from_matrix<Other, Mode,Options,Dim,HDim, Dim,Dim>\n{\n  static inline void run(Transform<typename Other::Scalar,Dim,Mode,Options> *transform, const Other& other)\n  {\n    transform->linear() = other;\n    transform->translation().setZero();\n    transform->makeAffine();\n  }\n};\n\ntemplate<typename Other, int Mode, int Options, int Dim, int HDim>\nstruct transform_construct_from_matrix<Other, Mode,Options,Dim,HDim, Dim,HDim>\n{\n  static inline void run(Transform<typename Other::Scalar,Dim,Mode,Options> *transform, const Other& other)\n  {\n    transform->affine() = other;\n    transform->makeAffine();\n  }\n};\n\ntemplate<typename Other, int Mode, int Options, int Dim, int HDim>\nstruct transform_construct_from_matrix<Other, Mode,Options,Dim,HDim, HDim,HDim>\n{\n  static inline void run(Transform<typename Other::Scalar,Dim,Mode,Options> *transform, const Other& other)\n  { transform->matrix() = other; }\n};\n\ntemplate<typename Other, int Options, int Dim, int HDim>\nstruct transform_construct_from_matrix<Other, AffineCompact,Options,Dim,HDim, HDim,HDim>\n{\n  static inline void run(Transform<typename Other::Scalar,Dim,AffineCompact,Options> *transform, const Other& other)\n  { transform->matrix() = other.template block<Dim,HDim>(0,0); }\n};\n\n/**********************************************************\n***   Specializations of operator* with rhs EigenBase   ***\n**********************************************************/\n\ntemplate<int LhsMode,int RhsMode>\nstruct transform_product_result\n{\n  enum \n  { \n    Mode =\n      (LhsMode == (int)Projective    || RhsMode == (int)Projective    ) ? Projective :\n      (LhsMode == (int)Affine        || RhsMode == (int)Affine        ) ? Affine :\n      (LhsMode == (int)AffineCompact || RhsMode == (int)AffineCompact ) ? AffineCompact :\n      (LhsMode == (int)Isometry      || RhsMode == (int)Isometry      ) ? Isometry : Projective\n  };\n};\n\ntemplate< typename TransformType, typename MatrixType, int RhsCols>\nstruct transform_right_product_impl< TransformType, MatrixType, 0, RhsCols>\n{\n  typedef typename MatrixType::PlainObject ResultType;\n\n  static EIGEN_STRONG_INLINE ResultType run(const TransformType& T, const MatrixType& other)\n  {\n    return T.matrix() * other;\n  }\n};\n\ntemplate< typename TransformType, typename MatrixType, int RhsCols>\nstruct transform_right_product_impl< TransformType, MatrixType, 1, RhsCols>\n{\n  enum { \n    Dim = TransformType::Dim, \n    HDim = TransformType::HDim,\n    OtherRows = MatrixType::RowsAtCompileTime,\n    OtherCols = MatrixType::ColsAtCompileTime\n  };\n\n  typedef typename MatrixType::PlainObject ResultType;\n\n  static EIGEN_STRONG_INLINE ResultType run(const TransformType& T, const MatrixType& other)\n  {\n    EIGEN_STATIC_ASSERT(OtherRows==HDim, YOU_MIXED_MATRICES_OF_DIFFERENT_SIZES);\n\n    typedef Block<ResultType, Dim, OtherCols, int(MatrixType::RowsAtCompileTime)==Dim> TopLeftLhs;\n\n    ResultType res(other.rows(),other.cols());\n    TopLeftLhs(res, 0, 0, Dim, other.cols()).noalias() = T.affine() * other;\n    res.row(OtherRows-1) = other.row(OtherRows-1);\n    \n    return res;\n  }\n};\n\ntemplate< typename TransformType, typename MatrixType, int RhsCols>\nstruct transform_right_product_impl< TransformType, MatrixType, 2, RhsCols>\n{\n  enum { \n    Dim = TransformType::Dim, \n    HDim = TransformType::HDim,\n    OtherRows = MatrixType::RowsAtCompileTime,\n    OtherCols = MatrixType::ColsAtCompileTime\n  };\n\n  typedef typename MatrixType::PlainObject ResultType;\n\n  static EIGEN_STRONG_INLINE ResultType run(const TransformType& T, const MatrixType& other)\n  {\n    EIGEN_STATIC_ASSERT(OtherRows==Dim, YOU_MIXED_MATRICES_OF_DIFFERENT_SIZES);\n\n    typedef Block<ResultType, Dim, OtherCols, true> TopLeftLhs;\n    ResultType res(Replicate<typename TransformType::ConstTranslationPart, 1, OtherCols>(T.translation(),1,other.cols()));\n    TopLeftLhs(res, 0, 0, Dim, other.cols()).noalias() += T.linear() * other;\n\n    return res;\n  }\n};\n\ntemplate< typename TransformType, typename MatrixType >\nstruct transform_right_product_impl< TransformType, MatrixType, 2, 1> // rhs is a vector of size Dim\n{\n  typedef typename TransformType::MatrixType TransformMatrix;\n  enum {\n    Dim = TransformType::Dim,\n    HDim = TransformType::HDim,\n    OtherRows = MatrixType::RowsAtCompileTime,\n    WorkingRows = EIGEN_PLAIN_ENUM_MIN(TransformMatrix::RowsAtCompileTime,HDim)\n  };\n\n  typedef typename MatrixType::PlainObject ResultType;\n\n  static EIGEN_STRONG_INLINE ResultType run(const TransformType& T, const MatrixType& other)\n  {\n    EIGEN_STATIC_ASSERT(OtherRows==Dim, YOU_MIXED_MATRICES_OF_DIFFERENT_SIZES);\n\n    Matrix<typename ResultType::Scalar, Dim+1, 1> rhs;\n    rhs.template head<Dim>() = other; rhs[Dim] = typename ResultType::Scalar(1);\n    Matrix<typename ResultType::Scalar, WorkingRows, 1> res(T.matrix() * rhs);\n    return res.template head<Dim>();\n  }\n};\n\n/**********************************************************\n***   Specializations of operator* with lhs EigenBase   ***\n**********************************************************/\n\n// generic HDim x HDim matrix * T => Projective\ntemplate<typename Other,int Mode, int Options, int Dim, int HDim>\nstruct transform_left_product_impl<Other,Mode,Options,Dim,HDim, HDim,HDim>\n{\n  typedef Transform<typename Other::Scalar,Dim,Mode,Options> TransformType;\n  typedef typename TransformType::MatrixType MatrixType;\n  typedef Transform<typename Other::Scalar,Dim,Projective,Options> ResultType;\n  static ResultType run(const Other& other,const TransformType& tr)\n  { return ResultType(other * tr.matrix()); }\n};\n\n// generic HDim x HDim matrix * AffineCompact => Projective\ntemplate<typename Other, int Options, int Dim, int HDim>\nstruct transform_left_product_impl<Other,AffineCompact,Options,Dim,HDim, HDim,HDim>\n{\n  typedef Transform<typename Other::Scalar,Dim,AffineCompact,Options> TransformType;\n  typedef typename TransformType::MatrixType MatrixType;\n  typedef Transform<typename Other::Scalar,Dim,Projective,Options> ResultType;\n  static ResultType run(const Other& other,const TransformType& tr)\n  {\n    ResultType res;\n    res.matrix().noalias() = other.template block<HDim,Dim>(0,0) * tr.matrix();\n    res.matrix().col(Dim) += other.col(Dim);\n    return res;\n  }\n};\n\n// affine matrix * T\ntemplate<typename Other,int Mode, int Options, int Dim, int HDim>\nstruct transform_left_product_impl<Other,Mode,Options,Dim,HDim, Dim,HDim>\n{\n  typedef Transform<typename Other::Scalar,Dim,Mode,Options> TransformType;\n  typedef typename TransformType::MatrixType MatrixType;\n  typedef TransformType ResultType;\n  static ResultType run(const Other& other,const TransformType& tr)\n  {\n    ResultType res;\n    res.affine().noalias() = other * tr.matrix();\n    res.matrix().row(Dim) = tr.matrix().row(Dim);\n    return res;\n  }\n};\n\n// affine matrix * AffineCompact\ntemplate<typename Other, int Options, int Dim, int HDim>\nstruct transform_left_product_impl<Other,AffineCompact,Options,Dim,HDim, Dim,HDim>\n{\n  typedef Transform<typename Other::Scalar,Dim,AffineCompact,Options> TransformType;\n  typedef typename TransformType::MatrixType MatrixType;\n  typedef TransformType ResultType;\n  static ResultType run(const Other& other,const TransformType& tr)\n  {\n    ResultType res;\n    res.matrix().noalias() = other.template block<Dim,Dim>(0,0) * tr.matrix();\n    res.translation() += other.col(Dim);\n    return res;\n  }\n};\n\n// linear matrix * T\ntemplate<typename Other,int Mode, int Options, int Dim, int HDim>\nstruct transform_left_product_impl<Other,Mode,Options,Dim,HDim, Dim,Dim>\n{\n  typedef Transform<typename Other::Scalar,Dim,Mode,Options> TransformType;\n  typedef typename TransformType::MatrixType MatrixType;\n  typedef TransformType ResultType;\n  static ResultType run(const Other& other, const TransformType& tr)\n  {\n    TransformType res;\n    if(Mode!=int(AffineCompact))\n      res.matrix().row(Dim) = tr.matrix().row(Dim);\n    res.matrix().template topRows<Dim>().noalias()\n      = other * tr.matrix().template topRows<Dim>();\n    return res;\n  }\n};\n\n/**********************************************************\n*** Specializations of operator* with another Transform ***\n**********************************************************/\n\ntemplate<typename Scalar, int Dim, int LhsMode, int LhsOptions, int RhsMode, int RhsOptions>\nstruct transform_transform_product_impl<Transform<Scalar,Dim,LhsMode,LhsOptions>,Transform<Scalar,Dim,RhsMode,RhsOptions>,false >\n{\n  enum { ResultMode = transform_product_result<LhsMode,RhsMode>::Mode };\n  typedef Transform<Scalar,Dim,LhsMode,LhsOptions> Lhs;\n  typedef Transform<Scalar,Dim,RhsMode,RhsOptions> Rhs;\n  typedef Transform<Scalar,Dim,ResultMode,LhsOptions> ResultType;\n  static ResultType run(const Lhs& lhs, const Rhs& rhs)\n  {\n    ResultType res;\n    res.linear() = lhs.linear() * rhs.linear();\n    res.translation() = lhs.linear() * rhs.translation() + lhs.translation();\n    res.makeAffine();\n    return res;\n  }\n};\n\ntemplate<typename Scalar, int Dim, int LhsMode, int LhsOptions, int RhsMode, int RhsOptions>\nstruct transform_transform_product_impl<Transform<Scalar,Dim,LhsMode,LhsOptions>,Transform<Scalar,Dim,RhsMode,RhsOptions>,true >\n{\n  typedef Transform<Scalar,Dim,LhsMode,LhsOptions> Lhs;\n  typedef Transform<Scalar,Dim,RhsMode,RhsOptions> Rhs;\n  typedef Transform<Scalar,Dim,Projective> ResultType;\n  static ResultType run(const Lhs& lhs, const Rhs& rhs)\n  {\n    return ResultType( lhs.matrix() * rhs.matrix() );\n  }\n};\n\ntemplate<typename Scalar, int Dim, int LhsOptions, int RhsOptions>\nstruct transform_transform_product_impl<Transform<Scalar,Dim,AffineCompact,LhsOptions>,Transform<Scalar,Dim,Projective,RhsOptions>,true >\n{\n  typedef Transform<Scalar,Dim,AffineCompact,LhsOptions> Lhs;\n  typedef Transform<Scalar,Dim,Projective,RhsOptions> Rhs;\n  typedef Transform<Scalar,Dim,Projective> ResultType;\n  static ResultType run(const Lhs& lhs, const Rhs& rhs)\n  {\n    ResultType res;\n    res.matrix().template topRows<Dim>() = lhs.matrix() * rhs.matrix();\n    res.matrix().row(Dim) = rhs.matrix().row(Dim);\n    return res;\n  }\n};\n\ntemplate<typename Scalar, int Dim, int LhsOptions, int RhsOptions>\nstruct transform_transform_product_impl<Transform<Scalar,Dim,Projective,LhsOptions>,Transform<Scalar,Dim,AffineCompact,RhsOptions>,true >\n{\n  typedef Transform<Scalar,Dim,Projective,LhsOptions> Lhs;\n  typedef Transform<Scalar,Dim,AffineCompact,RhsOptions> Rhs;\n  typedef Transform<Scalar,Dim,Projective> ResultType;\n  static ResultType run(const Lhs& lhs, const Rhs& rhs)\n  {\n    ResultType res(lhs.matrix().template leftCols<Dim>() * rhs.matrix());\n    res.matrix().col(Dim) += lhs.matrix().col(Dim);\n    return res;\n  }\n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_TRANSFORM_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Geometry/Translation.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_TRANSLATION_H\n#define EIGEN_TRANSLATION_H\n\nnamespace Eigen { \n\n/** \\geometry_module \\ingroup Geometry_Module\n  *\n  * \\class Translation\n  *\n  * \\brief Represents a translation transformation\n  *\n  * \\tparam _Scalar the scalar type, i.e., the type of the coefficients.\n  * \\tparam _Dim the  dimension of the space, can be a compile time value or Dynamic\n  *\n  * \\note This class is not aimed to be used to store a translation transformation,\n  * but rather to make easier the constructions and updates of Transform objects.\n  *\n  * \\sa class Scaling, class Transform\n  */\ntemplate<typename _Scalar, int _Dim>\nclass Translation\n{\npublic:\n  EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Dim)\n  /** dimension of the space */\n  enum { Dim = _Dim };\n  /** the scalar type of the coefficients */\n  typedef _Scalar Scalar;\n  /** corresponding vector type */\n  typedef Matrix<Scalar,Dim,1> VectorType;\n  /** corresponding linear transformation matrix type */\n  typedef Matrix<Scalar,Dim,Dim> LinearMatrixType;\n  /** corresponding affine transformation type */\n  typedef Transform<Scalar,Dim,Affine> AffineTransformType;\n  /** corresponding isometric transformation type */\n  typedef Transform<Scalar,Dim,Isometry> IsometryTransformType;\n\nprotected:\n\n  VectorType m_coeffs;\n\npublic:\n\n  /** Default constructor without initialization. */\n  EIGEN_DEVICE_FUNC Translation() {}\n  /**  */\n  EIGEN_DEVICE_FUNC inline Translation(const Scalar& sx, const Scalar& sy)\n  {\n    eigen_assert(Dim==2);\n    m_coeffs.x() = sx;\n    m_coeffs.y() = sy;\n  }\n  /**  */\n  EIGEN_DEVICE_FUNC inline Translation(const Scalar& sx, const Scalar& sy, const Scalar& sz)\n  {\n    eigen_assert(Dim==3);\n    m_coeffs.x() = sx;\n    m_coeffs.y() = sy;\n    m_coeffs.z() = sz;\n  }\n  /** Constructs and initialize the translation transformation from a vector of translation coefficients */\n  EIGEN_DEVICE_FUNC explicit inline Translation(const VectorType& vector) : m_coeffs(vector) {}\n\n  /** \\brief Retruns the x-translation by value. **/\n  EIGEN_DEVICE_FUNC inline Scalar x() const { return m_coeffs.x(); }\n  /** \\brief Retruns the y-translation by value. **/\n  EIGEN_DEVICE_FUNC inline Scalar y() const { return m_coeffs.y(); }\n  /** \\brief Retruns the z-translation by value. **/\n  EIGEN_DEVICE_FUNC inline Scalar z() const { return m_coeffs.z(); }\n\n  /** \\brief Retruns the x-translation as a reference. **/\n  EIGEN_DEVICE_FUNC inline Scalar& x() { return m_coeffs.x(); }\n  /** \\brief Retruns the y-translation as a reference. **/\n  EIGEN_DEVICE_FUNC inline Scalar& y() { return m_coeffs.y(); }\n  /** \\brief Retruns the z-translation as a reference. **/\n  EIGEN_DEVICE_FUNC inline Scalar& z() { return m_coeffs.z(); }\n\n  EIGEN_DEVICE_FUNC const VectorType& vector() const { return m_coeffs; }\n  EIGEN_DEVICE_FUNC VectorType& vector() { return m_coeffs; }\n\n  EIGEN_DEVICE_FUNC const VectorType& translation() const { return m_coeffs; }\n  EIGEN_DEVICE_FUNC VectorType& translation() { return m_coeffs; }\n\n  /** Concatenates two translation */\n  EIGEN_DEVICE_FUNC inline Translation operator* (const Translation& other) const\n  { return Translation(m_coeffs + other.m_coeffs); }\n\n  /** Concatenates a translation and a uniform scaling */\n  EIGEN_DEVICE_FUNC inline AffineTransformType operator* (const UniformScaling<Scalar>& other) const;\n\n  /** Concatenates a translation and a linear transformation */\n  template<typename OtherDerived>\n  EIGEN_DEVICE_FUNC inline AffineTransformType operator* (const EigenBase<OtherDerived>& linear) const;\n\n  /** Concatenates a translation and a rotation */\n  template<typename Derived>\n  EIGEN_DEVICE_FUNC inline IsometryTransformType operator*(const RotationBase<Derived,Dim>& r) const\n  { return *this * IsometryTransformType(r); }\n\n  /** \\returns the concatenation of a linear transformation \\a l with the translation \\a t */\n  // its a nightmare to define a templated friend function outside its declaration\n  template<typename OtherDerived> friend\n  EIGEN_DEVICE_FUNC inline AffineTransformType operator*(const EigenBase<OtherDerived>& linear, const Translation& t)\n  {\n    AffineTransformType res;\n    res.matrix().setZero();\n    res.linear() = linear.derived();\n    res.translation() = linear.derived() * t.m_coeffs;\n    res.matrix().row(Dim).setZero();\n    res(Dim,Dim) = Scalar(1);\n    return res;\n  }\n\n  /** Concatenates a translation and a transformation */\n  template<int Mode, int Options>\n  EIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode> operator* (const Transform<Scalar,Dim,Mode,Options>& t) const\n  {\n    Transform<Scalar,Dim,Mode> res = t;\n    res.pretranslate(m_coeffs);\n    return res;\n  }\n\n  /** Applies translation to vector */\n  template<typename Derived>\n  inline typename internal::enable_if<Derived::IsVectorAtCompileTime,VectorType>::type\n  operator* (const MatrixBase<Derived>& vec) const\n  { return m_coeffs + vec.derived(); }\n\n  /** \\returns the inverse translation (opposite) */\n  Translation inverse() const { return Translation(-m_coeffs); }\n\n  Translation& operator=(const Translation& other)\n  {\n    m_coeffs = other.m_coeffs;\n    return *this;\n  }\n\n  static const Translation Identity() { return Translation(VectorType::Zero()); }\n\n  /** \\returns \\c *this with scalar type casted to \\a NewScalarType\n    *\n    * Note that if \\a NewScalarType is equal to the current scalar type of \\c *this\n    * then this function smartly returns a const reference to \\c *this.\n    */\n  template<typename NewScalarType>\n  EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<Translation,Translation<NewScalarType,Dim> >::type cast() const\n  { return typename internal::cast_return_type<Translation,Translation<NewScalarType,Dim> >::type(*this); }\n\n  /** Copy constructor with scalar type conversion */\n  template<typename OtherScalarType>\n  EIGEN_DEVICE_FUNC inline explicit Translation(const Translation<OtherScalarType,Dim>& other)\n  { m_coeffs = other.vector().template cast<Scalar>(); }\n\n  /** \\returns \\c true if \\c *this is approximately equal to \\a other, within the precision\n    * determined by \\a prec.\n    *\n    * \\sa MatrixBase::isApprox() */\n  EIGEN_DEVICE_FUNC bool isApprox(const Translation& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const\n  { return m_coeffs.isApprox(other.m_coeffs, prec); }\n\n};\n\n/** \\addtogroup Geometry_Module */\n//@{\ntypedef Translation<float, 2> Translation2f;\ntypedef Translation<double,2> Translation2d;\ntypedef Translation<float, 3> Translation3f;\ntypedef Translation<double,3> Translation3d;\n//@}\n\ntemplate<typename Scalar, int Dim>\nEIGEN_DEVICE_FUNC inline typename Translation<Scalar,Dim>::AffineTransformType\nTranslation<Scalar,Dim>::operator* (const UniformScaling<Scalar>& other) const\n{\n  AffineTransformType res;\n  res.matrix().setZero();\n  res.linear().diagonal().fill(other.factor());\n  res.translation() = m_coeffs;\n  res(Dim,Dim) = Scalar(1);\n  return res;\n}\n\ntemplate<typename Scalar, int Dim>\ntemplate<typename OtherDerived>\nEIGEN_DEVICE_FUNC inline typename Translation<Scalar,Dim>::AffineTransformType\nTranslation<Scalar,Dim>::operator* (const EigenBase<OtherDerived>& linear) const\n{\n  AffineTransformType res;\n  res.matrix().setZero();\n  res.linear() = linear.derived();\n  res.translation() = m_coeffs;\n  res.matrix().row(Dim).setZero();\n  res(Dim,Dim) = Scalar(1);\n  return res;\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_TRANSLATION_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Geometry/Umeyama.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Hauke Heibel <hauke.heibel@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_UMEYAMA_H\n#define EIGEN_UMEYAMA_H\n\n// This file requires the user to include \n// * Eigen/Core\n// * Eigen/LU \n// * Eigen/SVD\n// * Eigen/Array\n\nnamespace Eigen { \n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\n\n// These helpers are required since it allows to use mixed types as parameters\n// for the Umeyama. The problem with mixed parameters is that the return type\n// cannot trivially be deduced when float and double types are mixed.\nnamespace internal {\n\n// Compile time return type deduction for different MatrixBase types.\n// Different means here different alignment and parameters but the same underlying\n// real scalar type.\ntemplate<typename MatrixType, typename OtherMatrixType>\nstruct umeyama_transform_matrix_type\n{\n  enum {\n    MinRowsAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(MatrixType::RowsAtCompileTime, OtherMatrixType::RowsAtCompileTime),\n\n    // When possible we want to choose some small fixed size value since the result\n    // is likely to fit on the stack. So here, EIGEN_SIZE_MIN_PREFER_DYNAMIC is not what we want.\n    HomogeneousDimension = int(MinRowsAtCompileTime) == Dynamic ? Dynamic : int(MinRowsAtCompileTime)+1\n  };\n\n  typedef Matrix<typename traits<MatrixType>::Scalar,\n    HomogeneousDimension,\n    HomogeneousDimension,\n    AutoAlign | (traits<MatrixType>::Flags & RowMajorBit ? RowMajor : ColMajor),\n    HomogeneousDimension,\n    HomogeneousDimension\n  > type;\n};\n\n}\n\n#endif\n\n/**\n* \\geometry_module \\ingroup Geometry_Module\n*\n* \\brief Returns the transformation between two point sets.\n*\n* The algorithm is based on:\n* \"Least-squares estimation of transformation parameters between two point patterns\",\n* Shinji Umeyama, PAMI 1991, DOI: 10.1109/34.88573\n*\n* It estimates parameters \\f$ c, \\mathbf{R}, \\f$ and \\f$ \\mathbf{t} \\f$ such that\n* \\f{align*}\n*   \\frac{1}{n} \\sum_{i=1}^n \\vert\\vert y_i - (c\\mathbf{R}x_i + \\mathbf{t}) \\vert\\vert_2^2\n* \\f}\n* is minimized.\n*\n* The algorithm is based on the analysis of the covariance matrix\n* \\f$ \\Sigma_{\\mathbf{x}\\mathbf{y}} \\in \\mathbb{R}^{d \\times d} \\f$\n* of the input point sets \\f$ \\mathbf{x} \\f$ and \\f$ \\mathbf{y} \\f$ where \n* \\f$d\\f$ is corresponding to the dimension (which is typically small).\n* The analysis is involving the SVD having a complexity of \\f$O(d^3)\\f$\n* though the actual computational effort lies in the covariance\n* matrix computation which has an asymptotic lower bound of \\f$O(dm)\\f$ when \n* the input point sets have dimension \\f$d \\times m\\f$.\n*\n* Currently the method is working only for floating point matrices.\n*\n* \\todo Should the return type of umeyama() become a Transform?\n*\n* \\param src Source points \\f$ \\mathbf{x} = \\left( x_1, \\hdots, x_n \\right) \\f$.\n* \\param dst Destination points \\f$ \\mathbf{y} = \\left( y_1, \\hdots, y_n \\right) \\f$.\n* \\param with_scaling Sets \\f$ c=1 \\f$ when <code>false</code> is passed.\n* \\return The homogeneous transformation \n* \\f{align*}\n*   T = \\begin{bmatrix} c\\mathbf{R} & \\mathbf{t} \\\\ \\mathbf{0} & 1 \\end{bmatrix}\n* \\f}\n* minimizing the resudiual above. This transformation is always returned as an \n* Eigen::Matrix.\n*/\ntemplate <typename Derived, typename OtherDerived>\ntypename internal::umeyama_transform_matrix_type<Derived, OtherDerived>::type\numeyama(const MatrixBase<Derived>& src, const MatrixBase<OtherDerived>& dst, bool with_scaling = true)\n{\n  typedef typename internal::umeyama_transform_matrix_type<Derived, OtherDerived>::type TransformationMatrixType;\n  typedef typename internal::traits<TransformationMatrixType>::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n\n  EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsComplex, NUMERIC_TYPE_MUST_BE_REAL)\n  EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename internal::traits<OtherDerived>::Scalar>::value),\n    YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)\n\n  enum { Dimension = EIGEN_SIZE_MIN_PREFER_DYNAMIC(Derived::RowsAtCompileTime, OtherDerived::RowsAtCompileTime) };\n\n  typedef Matrix<Scalar, Dimension, 1> VectorType;\n  typedef Matrix<Scalar, Dimension, Dimension> MatrixType;\n  typedef typename internal::plain_matrix_type_row_major<Derived>::type RowMajorMatrixType;\n\n  const Index m = src.rows(); // dimension\n  const Index n = src.cols(); // number of measurements\n\n  // required for demeaning ...\n  const RealScalar one_over_n = RealScalar(1) / static_cast<RealScalar>(n);\n\n  // computation of mean\n  const VectorType src_mean = src.rowwise().sum() * one_over_n;\n  const VectorType dst_mean = dst.rowwise().sum() * one_over_n;\n\n  // demeaning of src and dst points\n  const RowMajorMatrixType src_demean = src.colwise() - src_mean;\n  const RowMajorMatrixType dst_demean = dst.colwise() - dst_mean;\n\n  // Eq. (36)-(37)\n  const Scalar src_var = src_demean.rowwise().squaredNorm().sum() * one_over_n;\n\n  // Eq. (38)\n  const MatrixType sigma = one_over_n * dst_demean * src_demean.transpose();\n\n  JacobiSVD<MatrixType> svd(sigma, ComputeFullU | ComputeFullV);\n\n  // Initialize the resulting transformation with an identity matrix...\n  TransformationMatrixType Rt = TransformationMatrixType::Identity(m+1,m+1);\n\n  // Eq. (39)\n  VectorType S = VectorType::Ones(m);\n\n  if  ( svd.matrixU().determinant() * svd.matrixV().determinant() < 0 )\n    S(m-1) = -1;\n\n  // Eq. (40) and (43)\n  Rt.block(0,0,m,m).noalias() = svd.matrixU() * S.asDiagonal() * svd.matrixV().transpose();\n\n  if (with_scaling)\n  {\n    // Eq. (42)\n    const Scalar c = Scalar(1)/src_var * svd.singularValues().dot(S);\n\n    // Eq. (41)\n    Rt.col(m).head(m) = dst_mean;\n    Rt.col(m).head(m).noalias() -= c*Rt.topLeftCorner(m,m)*src_mean;\n    Rt.block(0,0,m,m) *= c;\n  }\n  else\n  {\n    Rt.col(m).head(m) = dst_mean;\n    Rt.col(m).head(m).noalias() -= Rt.topLeftCorner(m,m)*src_mean;\n  }\n\n  return Rt;\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_UMEYAMA_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Geometry/arch/Geometry_SSE.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Rohit Garg <rpg.314@gmail.com>\n// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_GEOMETRY_SSE_H\n#define EIGEN_GEOMETRY_SSE_H\n\nnamespace Eigen { \n\nnamespace internal {\n\ntemplate<class Derived, class OtherDerived>\nstruct quat_product<Architecture::SSE, Derived, OtherDerived, float>\n{\n  enum {\n    AAlignment = traits<Derived>::Alignment,\n    BAlignment = traits<OtherDerived>::Alignment,\n    ResAlignment = traits<Quaternion<float> >::Alignment\n  };\n  static inline Quaternion<float> run(const QuaternionBase<Derived>& _a, const QuaternionBase<OtherDerived>& _b)\n  {\n    Quaternion<float> res;\n    const __m128 mask = _mm_setr_ps(0.f,0.f,0.f,-0.f);\n    __m128 a = _a.coeffs().template packet<AAlignment>(0);\n    __m128 b = _b.coeffs().template packet<BAlignment>(0);\n    __m128 s1 = _mm_mul_ps(vec4f_swizzle1(a,1,2,0,2),vec4f_swizzle1(b,2,0,1,2));\n    __m128 s2 = _mm_mul_ps(vec4f_swizzle1(a,3,3,3,1),vec4f_swizzle1(b,0,1,2,1));\n    pstoret<float,Packet4f,ResAlignment>(\n              &res.x(),\n              _mm_add_ps(_mm_sub_ps(_mm_mul_ps(a,vec4f_swizzle1(b,3,3,3,3)),\n                                    _mm_mul_ps(vec4f_swizzle1(a,2,0,1,0),\n                                               vec4f_swizzle1(b,1,2,0,0))),\n                         _mm_xor_ps(mask,_mm_add_ps(s1,s2))));\n    \n    return res;\n  }\n};\n\ntemplate<class Derived>\nstruct quat_conj<Architecture::SSE, Derived, float>\n{\n  enum {\n    ResAlignment = traits<Quaternion<float> >::Alignment\n  };\n  static inline Quaternion<float> run(const QuaternionBase<Derived>& q)\n  {\n    Quaternion<float> res;\n    const __m128 mask = _mm_setr_ps(-0.f,-0.f,-0.f,0.f);\n    pstoret<float,Packet4f,ResAlignment>(&res.x(), _mm_xor_ps(mask, q.coeffs().template packet<traits<Derived>::Alignment>(0)));\n    return res;\n  }\n};\n\n\ntemplate<typename VectorLhs,typename VectorRhs>\nstruct cross3_impl<Architecture::SSE,VectorLhs,VectorRhs,float,true>\n{\n  enum {\n    ResAlignment = traits<typename plain_matrix_type<VectorLhs>::type>::Alignment\n  };\n  static inline typename plain_matrix_type<VectorLhs>::type\n  run(const VectorLhs& lhs, const VectorRhs& rhs)\n  {\n    __m128 a = lhs.template packet<traits<VectorLhs>::Alignment>(0);\n    __m128 b = rhs.template packet<traits<VectorRhs>::Alignment>(0);\n    __m128 mul1=_mm_mul_ps(vec4f_swizzle1(a,1,2,0,3),vec4f_swizzle1(b,2,0,1,3));\n    __m128 mul2=_mm_mul_ps(vec4f_swizzle1(a,2,0,1,3),vec4f_swizzle1(b,1,2,0,3));\n    typename plain_matrix_type<VectorLhs>::type res;\n    pstoret<float,Packet4f,ResAlignment>(&res.x(),_mm_sub_ps(mul1,mul2));\n    return res;\n  }\n};\n\n\n\n\ntemplate<class Derived, class OtherDerived>\nstruct quat_product<Architecture::SSE, Derived, OtherDerived, double>\n{\n  enum {\n    BAlignment = traits<OtherDerived>::Alignment,\n    ResAlignment = traits<Quaternion<double> >::Alignment\n  };\n\n  static inline Quaternion<double> run(const QuaternionBase<Derived>& _a, const QuaternionBase<OtherDerived>& _b)\n  {\n  const Packet2d mask = _mm_castsi128_pd(_mm_set_epi32(0x0,0x0,0x80000000,0x0));\n\n  Quaternion<double> res;\n\n  const double* a = _a.coeffs().data();\n  Packet2d b_xy = _b.coeffs().template packet<BAlignment>(0);\n  Packet2d b_zw = _b.coeffs().template packet<BAlignment>(2);\n  Packet2d a_xx = pset1<Packet2d>(a[0]);\n  Packet2d a_yy = pset1<Packet2d>(a[1]);\n  Packet2d a_zz = pset1<Packet2d>(a[2]);\n  Packet2d a_ww = pset1<Packet2d>(a[3]);\n\n  // two temporaries:\n  Packet2d t1, t2;\n\n  /*\n   * t1 = ww*xy + yy*zw\n   * t2 = zz*xy - xx*zw\n   * res.xy = t1 +/- swap(t2)\n   */\n  t1 = padd(pmul(a_ww, b_xy), pmul(a_yy, b_zw));\n  t2 = psub(pmul(a_zz, b_xy), pmul(a_xx, b_zw));\n#ifdef EIGEN_VECTORIZE_SSE3\n  EIGEN_UNUSED_VARIABLE(mask)\n  pstoret<double,Packet2d,ResAlignment>(&res.x(), _mm_addsub_pd(t1, preverse(t2)));\n#else\n  pstoret<double,Packet2d,ResAlignment>(&res.x(), padd(t1, pxor(mask,preverse(t2))));\n#endif\n  \n  /*\n   * t1 = ww*zw - yy*xy\n   * t2 = zz*zw + xx*xy\n   * res.zw = t1 -/+ swap(t2) = swap( swap(t1) +/- t2)\n   */\n  t1 = psub(pmul(a_ww, b_zw), pmul(a_yy, b_xy));\n  t2 = padd(pmul(a_zz, b_zw), pmul(a_xx, b_xy));\n#ifdef EIGEN_VECTORIZE_SSE3\n  EIGEN_UNUSED_VARIABLE(mask)\n  pstoret<double,Packet2d,ResAlignment>(&res.z(), preverse(_mm_addsub_pd(preverse(t1), t2)));\n#else\n  pstoret<double,Packet2d,ResAlignment>(&res.z(), psub(t1, pxor(mask,preverse(t2))));\n#endif\n\n  return res;\n}\n};\n\ntemplate<class Derived>\nstruct quat_conj<Architecture::SSE, Derived, double>\n{\n  enum {\n    ResAlignment = traits<Quaternion<double> >::Alignment\n  };\n  static inline Quaternion<double> run(const QuaternionBase<Derived>& q)\n  {\n    Quaternion<double> res;\n    const __m128d mask0 = _mm_setr_pd(-0.,-0.);\n    const __m128d mask2 = _mm_setr_pd(-0.,0.);\n    pstoret<double,Packet2d,ResAlignment>(&res.x(), _mm_xor_pd(mask0, q.coeffs().template packet<traits<Derived>::Alignment>(0)));\n    pstoret<double,Packet2d,ResAlignment>(&res.z(), _mm_xor_pd(mask2, q.coeffs().template packet<traits<Derived>::Alignment>(2)));\n    return res;\n  }\n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_GEOMETRY_SSE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Householder/BlockHouseholder.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2010 Vincent Lejeune\n// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_BLOCK_HOUSEHOLDER_H\n#define EIGEN_BLOCK_HOUSEHOLDER_H\n\n// This file contains some helper function to deal with block householder reflectors\n\nnamespace Eigen { \n\nnamespace internal {\n  \n/** \\internal */\n// template<typename TriangularFactorType,typename VectorsType,typename CoeffsType>\n// void make_block_householder_triangular_factor(TriangularFactorType& triFactor, const VectorsType& vectors, const CoeffsType& hCoeffs)\n// {\n//   typedef typename VectorsType::Scalar Scalar;\n//   const Index nbVecs = vectors.cols();\n//   eigen_assert(triFactor.rows() == nbVecs && triFactor.cols() == nbVecs && vectors.rows()>=nbVecs);\n// \n//   for(Index i = 0; i < nbVecs; i++)\n//   {\n//     Index rs = vectors.rows() - i;\n//     // Warning, note that hCoeffs may alias with vectors.\n//     // It is then necessary to copy it before modifying vectors(i,i). \n//     typename CoeffsType::Scalar h = hCoeffs(i);\n//     // This hack permits to pass trough nested Block<> and Transpose<> expressions.\n//     Scalar *Vii_ptr = const_cast<Scalar*>(vectors.data() + vectors.outerStride()*i + vectors.innerStride()*i);\n//     Scalar Vii = *Vii_ptr;\n//     *Vii_ptr = Scalar(1);\n//     triFactor.col(i).head(i).noalias() = -h * vectors.block(i, 0, rs, i).adjoint()\n//                                        * vectors.col(i).tail(rs);\n//     *Vii_ptr = Vii;\n//     // FIXME add .noalias() once the triangular product can work inplace\n//     triFactor.col(i).head(i) = triFactor.block(0,0,i,i).template triangularView<Upper>()\n//                              * triFactor.col(i).head(i);\n//     triFactor(i,i) = hCoeffs(i);\n//   }\n// }\n\n/** \\internal */\n// This variant avoid modifications in vectors\ntemplate<typename TriangularFactorType,typename VectorsType,typename CoeffsType>\nvoid make_block_householder_triangular_factor(TriangularFactorType& triFactor, const VectorsType& vectors, const CoeffsType& hCoeffs)\n{\n  const Index nbVecs = vectors.cols();\n  eigen_assert(triFactor.rows() == nbVecs && triFactor.cols() == nbVecs && vectors.rows()>=nbVecs);\n\n  for(Index i = nbVecs-1; i >=0 ; --i)\n  {\n    Index rs = vectors.rows() - i - 1;\n    Index rt = nbVecs-i-1;\n\n    if(rt>0)\n    {\n      triFactor.row(i).tail(rt).noalias() = -hCoeffs(i) * vectors.col(i).tail(rs).adjoint()\n                                                        * vectors.bottomRightCorner(rs, rt).template triangularView<UnitLower>();\n            \n      // FIXME add .noalias() once the triangular product can work inplace\n      triFactor.row(i).tail(rt) = triFactor.row(i).tail(rt) * triFactor.bottomRightCorner(rt,rt).template triangularView<Upper>();\n      \n    }\n    triFactor(i,i) = hCoeffs(i);\n  }\n}\n\n/** \\internal\n  * if forward then perform   mat = H0 * H1 * H2 * mat\n  * otherwise perform         mat = H2 * H1 * H0 * mat\n  */\ntemplate<typename MatrixType,typename VectorsType,typename CoeffsType>\nvoid apply_block_householder_on_the_left(MatrixType& mat, const VectorsType& vectors, const CoeffsType& hCoeffs, bool forward)\n{\n  enum { TFactorSize = MatrixType::ColsAtCompileTime };\n  Index nbVecs = vectors.cols();\n  Matrix<typename MatrixType::Scalar, TFactorSize, TFactorSize, RowMajor> T(nbVecs,nbVecs);\n  \n  if(forward) make_block_householder_triangular_factor(T, vectors, hCoeffs);\n  else        make_block_householder_triangular_factor(T, vectors, hCoeffs.conjugate());  \n  const TriangularView<const VectorsType, UnitLower> V(vectors);\n\n  // A -= V T V^* A\n  Matrix<typename MatrixType::Scalar,VectorsType::ColsAtCompileTime,MatrixType::ColsAtCompileTime,\n         (VectorsType::MaxColsAtCompileTime==1 && MatrixType::MaxColsAtCompileTime!=1)?RowMajor:ColMajor,\n         VectorsType::MaxColsAtCompileTime,MatrixType::MaxColsAtCompileTime> tmp = V.adjoint() * mat;\n  // FIXME add .noalias() once the triangular product can work inplace\n  if(forward) tmp = T.template triangularView<Upper>()           * tmp;\n  else        tmp = T.template triangularView<Upper>().adjoint() * tmp;\n  mat.noalias() -= V * tmp;\n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_BLOCK_HOUSEHOLDER_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Householder/Householder.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_HOUSEHOLDER_H\n#define EIGEN_HOUSEHOLDER_H\n\nnamespace Eigen { \n\nnamespace internal {\ntemplate<int n> struct decrement_size\n{\n  enum {\n    ret = n==Dynamic ? n : n-1\n  };\n};\n}\n\n/** Computes the elementary reflector H such that:\n  * \\f$ H *this = [ beta 0 ... 0]^T \\f$\n  * where the transformation H is:\n  * \\f$ H = I - tau v v^*\\f$\n  * and the vector v is:\n  * \\f$ v^T = [1 essential^T] \\f$\n  *\n  * The essential part of the vector \\c v is stored in *this.\n  * \n  * On output:\n  * \\param tau the scaling factor of the Householder transformation\n  * \\param beta the result of H * \\c *this\n  *\n  * \\sa MatrixBase::makeHouseholder(), MatrixBase::applyHouseholderOnTheLeft(),\n  *     MatrixBase::applyHouseholderOnTheRight()\n  */\ntemplate<typename Derived>\nvoid MatrixBase<Derived>::makeHouseholderInPlace(Scalar& tau, RealScalar& beta)\n{\n  VectorBlock<Derived, internal::decrement_size<Base::SizeAtCompileTime>::ret> essentialPart(derived(), 1, size()-1);\n  makeHouseholder(essentialPart, tau, beta);\n}\n\n/** Computes the elementary reflector H such that:\n  * \\f$ H *this = [ beta 0 ... 0]^T \\f$\n  * where the transformation H is:\n  * \\f$ H = I - tau v v^*\\f$\n  * and the vector v is:\n  * \\f$ v^T = [1 essential^T] \\f$\n  *\n  * On output:\n  * \\param essential the essential part of the vector \\c v\n  * \\param tau the scaling factor of the Householder transformation\n  * \\param beta the result of H * \\c *this\n  *\n  * \\sa MatrixBase::makeHouseholderInPlace(), MatrixBase::applyHouseholderOnTheLeft(),\n  *     MatrixBase::applyHouseholderOnTheRight()\n  */\ntemplate<typename Derived>\ntemplate<typename EssentialPart>\nvoid MatrixBase<Derived>::makeHouseholder(\n  EssentialPart& essential,\n  Scalar& tau,\n  RealScalar& beta) const\n{\n  using std::sqrt;\n  using numext::conj;\n  \n  EIGEN_STATIC_ASSERT_VECTOR_ONLY(EssentialPart)\n  VectorBlock<const Derived, EssentialPart::SizeAtCompileTime> tail(derived(), 1, size()-1);\n  \n  RealScalar tailSqNorm = size()==1 ? RealScalar(0) : tail.squaredNorm();\n  Scalar c0 = coeff(0);\n  const RealScalar tol = (std::numeric_limits<RealScalar>::min)();\n\n  if(tailSqNorm <= tol && numext::abs2(numext::imag(c0))<=tol)\n  {\n    tau = RealScalar(0);\n    beta = numext::real(c0);\n    essential.setZero();\n  }\n  else\n  {\n    beta = sqrt(numext::abs2(c0) + tailSqNorm);\n    if (numext::real(c0)>=RealScalar(0))\n      beta = -beta;\n    essential = tail / (c0 - beta);\n    tau = conj((beta - c0) / beta);\n  }\n}\n\n/** Apply the elementary reflector H given by\n  * \\f$ H = I - tau v v^*\\f$\n  * with\n  * \\f$ v^T = [1 essential^T] \\f$\n  * from the left to a vector or matrix.\n  *\n  * On input:\n  * \\param essential the essential part of the vector \\c v\n  * \\param tau the scaling factor of the Householder transformation\n  * \\param workspace a pointer to working space with at least\n  *                  this->cols() * essential.size() entries\n  *\n  * \\sa MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(), \n  *     MatrixBase::applyHouseholderOnTheRight()\n  */\ntemplate<typename Derived>\ntemplate<typename EssentialPart>\nvoid MatrixBase<Derived>::applyHouseholderOnTheLeft(\n  const EssentialPart& essential,\n  const Scalar& tau,\n  Scalar* workspace)\n{\n  if(rows() == 1)\n  {\n    *this *= Scalar(1)-tau;\n  }\n  else if(tau!=Scalar(0))\n  {\n    Map<typename internal::plain_row_type<PlainObject>::type> tmp(workspace,cols());\n    Block<Derived, EssentialPart::SizeAtCompileTime, Derived::ColsAtCompileTime> bottom(derived(), 1, 0, rows()-1, cols());\n    tmp.noalias() = essential.adjoint() * bottom;\n    tmp += this->row(0);\n    this->row(0) -= tau * tmp;\n    bottom.noalias() -= tau * essential * tmp;\n  }\n}\n\n/** Apply the elementary reflector H given by\n  * \\f$ H = I - tau v v^*\\f$\n  * with\n  * \\f$ v^T = [1 essential^T] \\f$\n  * from the right to a vector or matrix.\n  *\n  * On input:\n  * \\param essential the essential part of the vector \\c v\n  * \\param tau the scaling factor of the Householder transformation\n  * \\param workspace a pointer to working space with at least\n  *                  this->cols() * essential.size() entries\n  *\n  * \\sa MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(), \n  *     MatrixBase::applyHouseholderOnTheLeft()\n  */\ntemplate<typename Derived>\ntemplate<typename EssentialPart>\nvoid MatrixBase<Derived>::applyHouseholderOnTheRight(\n  const EssentialPart& essential,\n  const Scalar& tau,\n  Scalar* workspace)\n{\n  if(cols() == 1)\n  {\n    *this *= Scalar(1)-tau;\n  }\n  else if(tau!=Scalar(0))\n  {\n    Map<typename internal::plain_col_type<PlainObject>::type> tmp(workspace,rows());\n    Block<Derived, Derived::RowsAtCompileTime, EssentialPart::SizeAtCompileTime> right(derived(), 0, 1, rows(), cols()-1);\n    tmp.noalias() = right * essential.conjugate();\n    tmp += this->col(0);\n    this->col(0) -= tau * tmp;\n    right.noalias() -= tau * tmp * essential.transpose();\n  }\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_HOUSEHOLDER_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Householder/HouseholderSequence.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_HOUSEHOLDER_SEQUENCE_H\n#define EIGEN_HOUSEHOLDER_SEQUENCE_H\n\nnamespace Eigen { \n\n/** \\ingroup Householder_Module\n  * \\householder_module\n  * \\class HouseholderSequence\n  * \\brief Sequence of Householder reflections acting on subspaces with decreasing size\n  * \\tparam VectorsType type of matrix containing the Householder vectors\n  * \\tparam CoeffsType  type of vector containing the Householder coefficients\n  * \\tparam Side        either OnTheLeft (the default) or OnTheRight\n  *\n  * This class represents a product sequence of Householder reflections where the first Householder reflection\n  * acts on the whole space, the second Householder reflection leaves the one-dimensional subspace spanned by\n  * the first unit vector invariant, the third Householder reflection leaves the two-dimensional subspace\n  * spanned by the first two unit vectors invariant, and so on up to the last reflection which leaves all but\n  * one dimensions invariant and acts only on the last dimension. Such sequences of Householder reflections\n  * are used in several algorithms to zero out certain parts of a matrix. Indeed, the methods\n  * HessenbergDecomposition::matrixQ(), Tridiagonalization::matrixQ(), HouseholderQR::householderQ(),\n  * and ColPivHouseholderQR::householderQ() all return a %HouseholderSequence.\n  *\n  * More precisely, the class %HouseholderSequence represents an \\f$ n \\times n \\f$ matrix \\f$ H \\f$ of the\n  * form \\f$ H = \\prod_{i=0}^{n-1} H_i \\f$ where the i-th Householder reflection is \\f$ H_i = I - h_i v_i\n  * v_i^* \\f$. The i-th Householder coefficient \\f$ h_i \\f$ is a scalar and the i-th Householder vector \\f$\n  * v_i \\f$ is a vector of the form\n  * \\f[ \n  * v_i = [\\underbrace{0, \\ldots, 0}_{i-1\\mbox{ zeros}}, 1, \\underbrace{*, \\ldots,*}_{n-i\\mbox{ arbitrary entries}} ]. \n  * \\f]\n  * The last \\f$ n-i \\f$ entries of \\f$ v_i \\f$ are called the essential part of the Householder vector.\n  *\n  * Typical usages are listed below, where H is a HouseholderSequence:\n  * \\code\n  * A.applyOnTheRight(H);             // A = A * H\n  * A.applyOnTheLeft(H);              // A = H * A\n  * A.applyOnTheRight(H.adjoint());   // A = A * H^*\n  * A.applyOnTheLeft(H.adjoint());    // A = H^* * A\n  * MatrixXd Q = H;                   // conversion to a dense matrix\n  * \\endcode\n  * In addition to the adjoint, you can also apply the inverse (=adjoint), the transpose, and the conjugate operators.\n  *\n  * See the documentation for HouseholderSequence(const VectorsType&, const CoeffsType&) for an example.\n  *\n  * \\sa MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()\n  */\n\nnamespace internal {\n\ntemplate<typename VectorsType, typename CoeffsType, int Side>\nstruct traits<HouseholderSequence<VectorsType,CoeffsType,Side> >\n{\n  typedef typename VectorsType::Scalar Scalar;\n  typedef typename VectorsType::StorageIndex StorageIndex;\n  typedef typename VectorsType::StorageKind StorageKind;\n  enum {\n    RowsAtCompileTime = Side==OnTheLeft ? traits<VectorsType>::RowsAtCompileTime\n                                        : traits<VectorsType>::ColsAtCompileTime,\n    ColsAtCompileTime = RowsAtCompileTime,\n    MaxRowsAtCompileTime = Side==OnTheLeft ? traits<VectorsType>::MaxRowsAtCompileTime\n                                           : traits<VectorsType>::MaxColsAtCompileTime,\n    MaxColsAtCompileTime = MaxRowsAtCompileTime,\n    Flags = 0\n  };\n};\n\nstruct HouseholderSequenceShape {};\n\ntemplate<typename VectorsType, typename CoeffsType, int Side>\nstruct evaluator_traits<HouseholderSequence<VectorsType,CoeffsType,Side> >\n  : public evaluator_traits_base<HouseholderSequence<VectorsType,CoeffsType,Side> >\n{\n  typedef HouseholderSequenceShape Shape;\n};\n\ntemplate<typename VectorsType, typename CoeffsType, int Side>\nstruct hseq_side_dependent_impl\n{\n  typedef Block<const VectorsType, Dynamic, 1> EssentialVectorType;\n  typedef HouseholderSequence<VectorsType, CoeffsType, OnTheLeft> HouseholderSequenceType;\n  static inline const EssentialVectorType essentialVector(const HouseholderSequenceType& h, Index k)\n  {\n    Index start = k+1+h.m_shift;\n    return Block<const VectorsType,Dynamic,1>(h.m_vectors, start, k, h.rows()-start, 1);\n  }\n};\n\ntemplate<typename VectorsType, typename CoeffsType>\nstruct hseq_side_dependent_impl<VectorsType, CoeffsType, OnTheRight>\n{\n  typedef Transpose<Block<const VectorsType, 1, Dynamic> > EssentialVectorType;\n  typedef HouseholderSequence<VectorsType, CoeffsType, OnTheRight> HouseholderSequenceType;\n  static inline const EssentialVectorType essentialVector(const HouseholderSequenceType& h, Index k)\n  {\n    Index start = k+1+h.m_shift;\n    return Block<const VectorsType,1,Dynamic>(h.m_vectors, k, start, 1, h.rows()-start).transpose();\n  }\n};\n\ntemplate<typename OtherScalarType, typename MatrixType> struct matrix_type_times_scalar_type\n{\n  typedef typename ScalarBinaryOpTraits<OtherScalarType, typename MatrixType::Scalar>::ReturnType\n    ResultScalar;\n  typedef Matrix<ResultScalar, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime,\n                 0, MatrixType::MaxRowsAtCompileTime, MatrixType::MaxColsAtCompileTime> Type;\n};\n\n} // end namespace internal\n\ntemplate<typename VectorsType, typename CoeffsType, int Side> class HouseholderSequence\n  : public EigenBase<HouseholderSequence<VectorsType,CoeffsType,Side> >\n{\n    typedef typename internal::hseq_side_dependent_impl<VectorsType,CoeffsType,Side>::EssentialVectorType EssentialVectorType;\n  \n  public:\n    enum {\n      RowsAtCompileTime = internal::traits<HouseholderSequence>::RowsAtCompileTime,\n      ColsAtCompileTime = internal::traits<HouseholderSequence>::ColsAtCompileTime,\n      MaxRowsAtCompileTime = internal::traits<HouseholderSequence>::MaxRowsAtCompileTime,\n      MaxColsAtCompileTime = internal::traits<HouseholderSequence>::MaxColsAtCompileTime\n    };\n    typedef typename internal::traits<HouseholderSequence>::Scalar Scalar;\n\n    typedef HouseholderSequence<\n      typename internal::conditional<NumTraits<Scalar>::IsComplex,\n        typename internal::remove_all<typename VectorsType::ConjugateReturnType>::type,\n        VectorsType>::type,\n      typename internal::conditional<NumTraits<Scalar>::IsComplex,\n        typename internal::remove_all<typename CoeffsType::ConjugateReturnType>::type,\n        CoeffsType>::type,\n      Side\n    > ConjugateReturnType;\n\n    /** \\brief Constructor.\n      * \\param[in]  v      %Matrix containing the essential parts of the Householder vectors\n      * \\param[in]  h      Vector containing the Householder coefficients\n      *\n      * Constructs the Householder sequence with coefficients given by \\p h and vectors given by \\p v. The\n      * i-th Householder coefficient \\f$ h_i \\f$ is given by \\p h(i) and the essential part of the i-th\n      * Householder vector \\f$ v_i \\f$ is given by \\p v(k,i) with \\p k > \\p i (the subdiagonal part of the\n      * i-th column). If \\p v has fewer columns than rows, then the Householder sequence contains as many\n      * Householder reflections as there are columns.\n      *\n      * \\note The %HouseholderSequence object stores \\p v and \\p h by reference.\n      *\n      * Example: \\include HouseholderSequence_HouseholderSequence.cpp\n      * Output: \\verbinclude HouseholderSequence_HouseholderSequence.out\n      *\n      * \\sa setLength(), setShift()\n      */\n    HouseholderSequence(const VectorsType& v, const CoeffsType& h)\n      : m_vectors(v), m_coeffs(h), m_trans(false), m_length(v.diagonalSize()),\n        m_shift(0)\n    {\n    }\n\n    /** \\brief Copy constructor. */\n    HouseholderSequence(const HouseholderSequence& other)\n      : m_vectors(other.m_vectors),\n        m_coeffs(other.m_coeffs),\n        m_trans(other.m_trans),\n        m_length(other.m_length),\n        m_shift(other.m_shift)\n    {\n    }\n\n    /** \\brief Number of rows of transformation viewed as a matrix.\n      * \\returns Number of rows \n      * \\details This equals the dimension of the space that the transformation acts on.\n      */\n    Index rows() const { return Side==OnTheLeft ? m_vectors.rows() : m_vectors.cols(); }\n\n    /** \\brief Number of columns of transformation viewed as a matrix.\n      * \\returns Number of columns\n      * \\details This equals the dimension of the space that the transformation acts on.\n      */\n    Index cols() const { return rows(); }\n\n    /** \\brief Essential part of a Householder vector.\n      * \\param[in]  k  Index of Householder reflection\n      * \\returns    Vector containing non-trivial entries of k-th Householder vector\n      *\n      * This function returns the essential part of the Householder vector \\f$ v_i \\f$. This is a vector of\n      * length \\f$ n-i \\f$ containing the last \\f$ n-i \\f$ entries of the vector\n      * \\f[ \n      * v_i = [\\underbrace{0, \\ldots, 0}_{i-1\\mbox{ zeros}}, 1, \\underbrace{*, \\ldots,*}_{n-i\\mbox{ arbitrary entries}} ]. \n      * \\f]\n      * The index \\f$ i \\f$ equals \\p k + shift(), corresponding to the k-th column of the matrix \\p v\n      * passed to the constructor.\n      *\n      * \\sa setShift(), shift()\n      */\n    const EssentialVectorType essentialVector(Index k) const\n    {\n      eigen_assert(k >= 0 && k < m_length);\n      return internal::hseq_side_dependent_impl<VectorsType,CoeffsType,Side>::essentialVector(*this, k);\n    }\n\n    /** \\brief %Transpose of the Householder sequence. */\n    HouseholderSequence transpose() const\n    {\n      return HouseholderSequence(*this).setTrans(!m_trans);\n    }\n\n    /** \\brief Complex conjugate of the Householder sequence. */\n    ConjugateReturnType conjugate() const\n    {\n      return ConjugateReturnType(m_vectors.conjugate(), m_coeffs.conjugate())\n             .setTrans(m_trans)\n             .setLength(m_length)\n             .setShift(m_shift);\n    }\n\n    /** \\brief Adjoint (conjugate transpose) of the Householder sequence. */\n    ConjugateReturnType adjoint() const\n    {\n      return conjugate().setTrans(!m_trans);\n    }\n\n    /** \\brief Inverse of the Householder sequence (equals the adjoint). */\n    ConjugateReturnType inverse() const { return adjoint(); }\n\n    /** \\internal */\n    template<typename DestType> inline void evalTo(DestType& dst) const\n    {\n      Matrix<Scalar, DestType::RowsAtCompileTime, 1,\n             AutoAlign|ColMajor, DestType::MaxRowsAtCompileTime, 1> workspace(rows());\n      evalTo(dst, workspace);\n    }\n\n    /** \\internal */\n    template<typename Dest, typename Workspace>\n    void evalTo(Dest& dst, Workspace& workspace) const\n    {\n      workspace.resize(rows());\n      Index vecs = m_length;\n      if(internal::is_same_dense(dst,m_vectors))\n      {\n        // in-place\n        dst.diagonal().setOnes();\n        dst.template triangularView<StrictlyUpper>().setZero();\n        for(Index k = vecs-1; k >= 0; --k)\n        {\n          Index cornerSize = rows() - k - m_shift;\n          if(m_trans)\n            dst.bottomRightCorner(cornerSize, cornerSize)\n               .applyHouseholderOnTheRight(essentialVector(k), m_coeffs.coeff(k), workspace.data());\n          else\n            dst.bottomRightCorner(cornerSize, cornerSize)\n               .applyHouseholderOnTheLeft(essentialVector(k), m_coeffs.coeff(k), workspace.data());\n\n          // clear the off diagonal vector\n          dst.col(k).tail(rows()-k-1).setZero();\n        }\n        // clear the remaining columns if needed\n        for(Index k = 0; k<cols()-vecs ; ++k)\n          dst.col(k).tail(rows()-k-1).setZero();\n      }\n      else\n      {\n        dst.setIdentity(rows(), rows());\n        for(Index k = vecs-1; k >= 0; --k)\n        {\n          Index cornerSize = rows() - k - m_shift;\n          if(m_trans)\n            dst.bottomRightCorner(cornerSize, cornerSize)\n               .applyHouseholderOnTheRight(essentialVector(k), m_coeffs.coeff(k), &workspace.coeffRef(0));\n          else\n            dst.bottomRightCorner(cornerSize, cornerSize)\n               .applyHouseholderOnTheLeft(essentialVector(k), m_coeffs.coeff(k), &workspace.coeffRef(0));\n        }\n      }\n    }\n\n    /** \\internal */\n    template<typename Dest> inline void applyThisOnTheRight(Dest& dst) const\n    {\n      Matrix<Scalar,1,Dest::RowsAtCompileTime,RowMajor,1,Dest::MaxRowsAtCompileTime> workspace(dst.rows());\n      applyThisOnTheRight(dst, workspace);\n    }\n\n    /** \\internal */\n    template<typename Dest, typename Workspace>\n    inline void applyThisOnTheRight(Dest& dst, Workspace& workspace) const\n    {\n      workspace.resize(dst.rows());\n      for(Index k = 0; k < m_length; ++k)\n      {\n        Index actual_k = m_trans ? m_length-k-1 : k;\n        dst.rightCols(rows()-m_shift-actual_k)\n           .applyHouseholderOnTheRight(essentialVector(actual_k), m_coeffs.coeff(actual_k), workspace.data());\n      }\n    }\n\n    /** \\internal */\n    template<typename Dest> inline void applyThisOnTheLeft(Dest& dst) const\n    {\n      Matrix<Scalar,1,Dest::ColsAtCompileTime,RowMajor,1,Dest::MaxColsAtCompileTime> workspace;\n      applyThisOnTheLeft(dst, workspace);\n    }\n\n    /** \\internal */\n    template<typename Dest, typename Workspace>\n    inline void applyThisOnTheLeft(Dest& dst, Workspace& workspace) const\n    {\n      const Index BlockSize = 48;\n      // if the entries are large enough, then apply the reflectors by block\n      if(m_length>=BlockSize && dst.cols()>1)\n      {\n        for(Index i = 0; i < m_length; i+=BlockSize)\n        {\n          Index end = m_trans ? (std::min)(m_length,i+BlockSize) : m_length-i;\n          Index k = m_trans ? i : (std::max)(Index(0),end-BlockSize);\n          Index bs = end-k;\n          Index start = k + m_shift;\n          \n          typedef Block<typename internal::remove_all<VectorsType>::type,Dynamic,Dynamic> SubVectorsType;\n          SubVectorsType sub_vecs1(m_vectors.const_cast_derived(), Side==OnTheRight ? k : start,\n                                                                   Side==OnTheRight ? start : k,\n                                                                   Side==OnTheRight ? bs : m_vectors.rows()-start,\n                                                                   Side==OnTheRight ? m_vectors.cols()-start : bs);\n          typename internal::conditional<Side==OnTheRight, Transpose<SubVectorsType>, SubVectorsType&>::type sub_vecs(sub_vecs1);\n          Block<Dest,Dynamic,Dynamic> sub_dst(dst,dst.rows()-rows()+m_shift+k,0, rows()-m_shift-k,dst.cols());\n          apply_block_householder_on_the_left(sub_dst, sub_vecs, m_coeffs.segment(k, bs), !m_trans);\n        }\n      }\n      else\n      {\n        workspace.resize(dst.cols());\n        for(Index k = 0; k < m_length; ++k)\n        {\n          Index actual_k = m_trans ? k : m_length-k-1;\n          dst.bottomRows(rows()-m_shift-actual_k)\n            .applyHouseholderOnTheLeft(essentialVector(actual_k), m_coeffs.coeff(actual_k), workspace.data());\n        }\n      }\n    }\n\n    /** \\brief Computes the product of a Householder sequence with a matrix.\n      * \\param[in]  other  %Matrix being multiplied.\n      * \\returns    Expression object representing the product.\n      *\n      * This function computes \\f$ HM \\f$ where \\f$ H \\f$ is the Householder sequence represented by \\p *this\n      * and \\f$ M \\f$ is the matrix \\p other.\n      */\n    template<typename OtherDerived>\n    typename internal::matrix_type_times_scalar_type<Scalar, OtherDerived>::Type operator*(const MatrixBase<OtherDerived>& other) const\n    {\n      typename internal::matrix_type_times_scalar_type<Scalar, OtherDerived>::Type\n        res(other.template cast<typename internal::matrix_type_times_scalar_type<Scalar,OtherDerived>::ResultScalar>());\n      applyThisOnTheLeft(res);\n      return res;\n    }\n\n    template<typename _VectorsType, typename _CoeffsType, int _Side> friend struct internal::hseq_side_dependent_impl;\n\n    /** \\brief Sets the length of the Householder sequence.\n      * \\param [in]  length  New value for the length.\n      *\n      * By default, the length \\f$ n \\f$ of the Householder sequence \\f$ H = H_0 H_1 \\ldots H_{n-1} \\f$ is set\n      * to the number of columns of the matrix \\p v passed to the constructor, or the number of rows if that\n      * is smaller. After this function is called, the length equals \\p length.\n      *\n      * \\sa length()\n      */\n    HouseholderSequence& setLength(Index length)\n    {\n      m_length = length;\n      return *this;\n    }\n\n    /** \\brief Sets the shift of the Householder sequence.\n      * \\param [in]  shift  New value for the shift.\n      *\n      * By default, a %HouseholderSequence object represents \\f$ H = H_0 H_1 \\ldots H_{n-1} \\f$ and the i-th\n      * column of the matrix \\p v passed to the constructor corresponds to the i-th Householder\n      * reflection. After this function is called, the object represents \\f$ H = H_{\\mathrm{shift}}\n      * H_{\\mathrm{shift}+1} \\ldots H_{n-1} \\f$ and the i-th column of \\p v corresponds to the (shift+i)-th\n      * Householder reflection.\n      *\n      * \\sa shift()\n      */\n    HouseholderSequence& setShift(Index shift)\n    {\n      m_shift = shift;\n      return *this;\n    }\n\n    Index length() const { return m_length; }  /**< \\brief Returns the length of the Householder sequence. */\n    Index shift() const { return m_shift; }    /**< \\brief Returns the shift of the Householder sequence. */\n\n    /* Necessary for .adjoint() and .conjugate() */\n    template <typename VectorsType2, typename CoeffsType2, int Side2> friend class HouseholderSequence;\n\n  protected:\n\n    /** \\brief Sets the transpose flag.\n      * \\param [in]  trans  New value of the transpose flag.\n      *\n      * By default, the transpose flag is not set. If the transpose flag is set, then this object represents \n      * \\f$ H^T = H_{n-1}^T \\ldots H_1^T H_0^T \\f$ instead of \\f$ H = H_0 H_1 \\ldots H_{n-1} \\f$.\n      *\n      * \\sa trans()\n      */\n    HouseholderSequence& setTrans(bool trans)\n    {\n      m_trans = trans;\n      return *this;\n    }\n\n    bool trans() const { return m_trans; }     /**< \\brief Returns the transpose flag. */\n\n    typename VectorsType::Nested m_vectors;\n    typename CoeffsType::Nested m_coeffs;\n    bool m_trans;\n    Index m_length;\n    Index m_shift;\n};\n\n/** \\brief Computes the product of a matrix with a Householder sequence.\n  * \\param[in]  other  %Matrix being multiplied.\n  * \\param[in]  h      %HouseholderSequence being multiplied.\n  * \\returns    Expression object representing the product.\n  *\n  * This function computes \\f$ MH \\f$ where \\f$ M \\f$ is the matrix \\p other and \\f$ H \\f$ is the\n  * Householder sequence represented by \\p h.\n  */\ntemplate<typename OtherDerived, typename VectorsType, typename CoeffsType, int Side>\ntypename internal::matrix_type_times_scalar_type<typename VectorsType::Scalar,OtherDerived>::Type operator*(const MatrixBase<OtherDerived>& other, const HouseholderSequence<VectorsType,CoeffsType,Side>& h)\n{\n  typename internal::matrix_type_times_scalar_type<typename VectorsType::Scalar,OtherDerived>::Type\n    res(other.template cast<typename internal::matrix_type_times_scalar_type<typename VectorsType::Scalar,OtherDerived>::ResultScalar>());\n  h.applyThisOnTheRight(res);\n  return res;\n}\n\n/** \\ingroup Householder_Module \\householder_module\n  * \\brief Convenience function for constructing a Householder sequence. \n  * \\returns A HouseholderSequence constructed from the specified arguments.\n  */\ntemplate<typename VectorsType, typename CoeffsType>\nHouseholderSequence<VectorsType,CoeffsType> householderSequence(const VectorsType& v, const CoeffsType& h)\n{\n  return HouseholderSequence<VectorsType,CoeffsType,OnTheLeft>(v, h);\n}\n\n/** \\ingroup Householder_Module \\householder_module\n  * \\brief Convenience function for constructing a Householder sequence. \n  * \\returns A HouseholderSequence constructed from the specified arguments.\n  * \\details This function differs from householderSequence() in that the template argument \\p OnTheSide of\n  * the constructed HouseholderSequence is set to OnTheRight, instead of the default OnTheLeft.\n  */\ntemplate<typename VectorsType, typename CoeffsType>\nHouseholderSequence<VectorsType,CoeffsType,OnTheRight> rightHouseholderSequence(const VectorsType& v, const CoeffsType& h)\n{\n  return HouseholderSequence<VectorsType,CoeffsType,OnTheRight>(v, h);\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_HOUSEHOLDER_SEQUENCE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/IterativeLinearSolvers/BasicPreconditioners.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2011-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_BASIC_PRECONDITIONERS_H\n#define EIGEN_BASIC_PRECONDITIONERS_H\n\nnamespace Eigen { \n\n/** \\ingroup IterativeLinearSolvers_Module\n  * \\brief A preconditioner based on the digonal entries\n  *\n  * This class allows to approximately solve for A.x = b problems assuming A is a diagonal matrix.\n  * In other words, this preconditioner neglects all off diagonal entries and, in Eigen's language, solves for:\n    \\code\n    A.diagonal().asDiagonal() . x = b\n    \\endcode\n  *\n  * \\tparam _Scalar the type of the scalar.\n  *\n  * \\implsparsesolverconcept\n  *\n  * This preconditioner is suitable for both selfadjoint and general problems.\n  * The diagonal entries are pre-inverted and stored into a dense vector.\n  *\n  * \\note A variant that has yet to be implemented would attempt to preserve the norm of each column.\n  *\n  * \\sa class LeastSquareDiagonalPreconditioner, class ConjugateGradient\n  */\ntemplate <typename _Scalar>\nclass DiagonalPreconditioner\n{\n    typedef _Scalar Scalar;\n    typedef Matrix<Scalar,Dynamic,1> Vector;\n  public:\n    typedef typename Vector::StorageIndex StorageIndex;\n    enum {\n      ColsAtCompileTime = Dynamic,\n      MaxColsAtCompileTime = Dynamic\n    };\n\n    DiagonalPreconditioner() : m_isInitialized(false) {}\n\n    template<typename MatType>\n    explicit DiagonalPreconditioner(const MatType& mat) : m_invdiag(mat.cols())\n    {\n      compute(mat);\n    }\n\n    Index rows() const { return m_invdiag.size(); }\n    Index cols() const { return m_invdiag.size(); }\n    \n    template<typename MatType>\n    DiagonalPreconditioner& analyzePattern(const MatType& )\n    {\n      return *this;\n    }\n    \n    template<typename MatType>\n    DiagonalPreconditioner& factorize(const MatType& mat)\n    {\n      m_invdiag.resize(mat.cols());\n      for(int j=0; j<mat.outerSize(); ++j)\n      {\n        typename MatType::InnerIterator it(mat,j);\n        while(it && it.index()!=j) ++it;\n        if(it && it.index()==j && it.value()!=Scalar(0))\n          m_invdiag(j) = Scalar(1)/it.value();\n        else\n          m_invdiag(j) = Scalar(1);\n      }\n      m_isInitialized = true;\n      return *this;\n    }\n    \n    template<typename MatType>\n    DiagonalPreconditioner& compute(const MatType& mat)\n    {\n      return factorize(mat);\n    }\n\n    /** \\internal */\n    template<typename Rhs, typename Dest>\n    void _solve_impl(const Rhs& b, Dest& x) const\n    {\n      x = m_invdiag.array() * b.array() ;\n    }\n\n    template<typename Rhs> inline const Solve<DiagonalPreconditioner, Rhs>\n    solve(const MatrixBase<Rhs>& b) const\n    {\n      eigen_assert(m_isInitialized && \"DiagonalPreconditioner is not initialized.\");\n      eigen_assert(m_invdiag.size()==b.rows()\n                && \"DiagonalPreconditioner::solve(): invalid number of rows of the right hand side matrix b\");\n      return Solve<DiagonalPreconditioner, Rhs>(*this, b.derived());\n    }\n    \n    ComputationInfo info() { return Success; }\n\n  protected:\n    Vector m_invdiag;\n    bool m_isInitialized;\n};\n\n/** \\ingroup IterativeLinearSolvers_Module\n  * \\brief Jacobi preconditioner for LeastSquaresConjugateGradient\n  *\n  * This class allows to approximately solve for A' A x  = A' b problems assuming A' A is a diagonal matrix.\n  * In other words, this preconditioner neglects all off diagonal entries and, in Eigen's language, solves for:\n    \\code\n    (A.adjoint() * A).diagonal().asDiagonal() * x = b\n    \\endcode\n  *\n  * \\tparam _Scalar the type of the scalar.\n  *\n  * \\implsparsesolverconcept\n  *\n  * The diagonal entries are pre-inverted and stored into a dense vector.\n  * \n  * \\sa class LeastSquaresConjugateGradient, class DiagonalPreconditioner\n  */\ntemplate <typename _Scalar>\nclass LeastSquareDiagonalPreconditioner : public DiagonalPreconditioner<_Scalar>\n{\n    typedef _Scalar Scalar;\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n    typedef DiagonalPreconditioner<_Scalar> Base;\n    using Base::m_invdiag;\n  public:\n\n    LeastSquareDiagonalPreconditioner() : Base() {}\n\n    template<typename MatType>\n    explicit LeastSquareDiagonalPreconditioner(const MatType& mat) : Base()\n    {\n      compute(mat);\n    }\n\n    template<typename MatType>\n    LeastSquareDiagonalPreconditioner& analyzePattern(const MatType& )\n    {\n      return *this;\n    }\n    \n    template<typename MatType>\n    LeastSquareDiagonalPreconditioner& factorize(const MatType& mat)\n    {\n      // Compute the inverse squared-norm of each column of mat\n      m_invdiag.resize(mat.cols());\n      if(MatType::IsRowMajor)\n      {\n        m_invdiag.setZero();\n        for(Index j=0; j<mat.outerSize(); ++j)\n        {\n          for(typename MatType::InnerIterator it(mat,j); it; ++it)\n            m_invdiag(it.index()) += numext::abs2(it.value());\n        }\n        for(Index j=0; j<mat.cols(); ++j)\n          if(numext::real(m_invdiag(j))>RealScalar(0))\n            m_invdiag(j) = RealScalar(1)/numext::real(m_invdiag(j));\n      }\n      else\n      {\n        for(Index j=0; j<mat.outerSize(); ++j)\n        {\n          RealScalar sum = mat.col(j).squaredNorm();\n          if(sum>RealScalar(0))\n            m_invdiag(j) = RealScalar(1)/sum;\n          else\n            m_invdiag(j) = RealScalar(1);\n        }\n      }\n      Base::m_isInitialized = true;\n      return *this;\n    }\n    \n    template<typename MatType>\n    LeastSquareDiagonalPreconditioner& compute(const MatType& mat)\n    {\n      return factorize(mat);\n    }\n    \n    ComputationInfo info() { return Success; }\n\n  protected:\n};\n\n/** \\ingroup IterativeLinearSolvers_Module\n  * \\brief A naive preconditioner which approximates any matrix as the identity matrix\n  *\n  * \\implsparsesolverconcept\n  *\n  * \\sa class DiagonalPreconditioner\n  */\nclass IdentityPreconditioner\n{\n  public:\n\n    IdentityPreconditioner() {}\n\n    template<typename MatrixType>\n    explicit IdentityPreconditioner(const MatrixType& ) {}\n    \n    template<typename MatrixType>\n    IdentityPreconditioner& analyzePattern(const MatrixType& ) { return *this; }\n    \n    template<typename MatrixType>\n    IdentityPreconditioner& factorize(const MatrixType& ) { return *this; }\n\n    template<typename MatrixType>\n    IdentityPreconditioner& compute(const MatrixType& ) { return *this; }\n    \n    template<typename Rhs>\n    inline const Rhs& solve(const Rhs& b) const { return b; }\n    \n    ComputationInfo info() { return Success; }\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_BASIC_PRECONDITIONERS_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/IterativeLinearSolvers/BiCGSTAB.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2011-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_BICGSTAB_H\n#define EIGEN_BICGSTAB_H\n\nnamespace Eigen { \n\nnamespace internal {\n\n/** \\internal Low-level bi conjugate gradient stabilized algorithm\n  * \\param mat The matrix A\n  * \\param rhs The right hand side vector b\n  * \\param x On input and initial solution, on output the computed solution.\n  * \\param precond A preconditioner being able to efficiently solve for an\n  *                approximation of Ax=b (regardless of b)\n  * \\param iters On input the max number of iteration, on output the number of performed iterations.\n  * \\param tol_error On input the tolerance error, on output an estimation of the relative error.\n  * \\return false in the case of numerical issue, for example a break down of BiCGSTAB. \n  */\ntemplate<typename MatrixType, typename Rhs, typename Dest, typename Preconditioner>\nbool bicgstab(const MatrixType& mat, const Rhs& rhs, Dest& x,\n              const Preconditioner& precond, Index& iters,\n              typename Dest::RealScalar& tol_error)\n{\n  using std::sqrt;\n  using std::abs;\n  typedef typename Dest::RealScalar RealScalar;\n  typedef typename Dest::Scalar Scalar;\n  typedef Matrix<Scalar,Dynamic,1> VectorType;\n  RealScalar tol = tol_error;\n  Index maxIters = iters;\n\n  Index n = mat.cols();\n  VectorType r  = rhs - mat * x;\n  VectorType r0 = r;\n  \n  RealScalar r0_sqnorm = r0.squaredNorm();\n  RealScalar rhs_sqnorm = rhs.squaredNorm();\n  if(rhs_sqnorm == 0)\n  {\n    x.setZero();\n    return true;\n  }\n  Scalar rho    = 1;\n  Scalar alpha  = 1;\n  Scalar w      = 1;\n  \n  VectorType v = VectorType::Zero(n), p = VectorType::Zero(n);\n  VectorType y(n),  z(n);\n  VectorType kt(n), ks(n);\n\n  VectorType s(n), t(n);\n\n  RealScalar tol2 = tol*tol*rhs_sqnorm;\n  RealScalar eps2 = NumTraits<Scalar>::epsilon()*NumTraits<Scalar>::epsilon();\n  Index i = 0;\n  Index restarts = 0;\n\n  while ( r.squaredNorm() > tol2 && i<maxIters )\n  {\n    Scalar rho_old = rho;\n\n    rho = r0.dot(r);\n    if (abs(rho) < eps2*r0_sqnorm)\n    {\n      // The new residual vector became too orthogonal to the arbitrarily chosen direction r0\n      // Let's restart with a new r0:\n      r  = rhs - mat * x;\n      r0 = r;\n      rho = r0_sqnorm = r.squaredNorm();\n      if(restarts++ == 0)\n        i = 0;\n    }\n    Scalar beta = (rho/rho_old) * (alpha / w);\n    p = r + beta * (p - w * v);\n    \n    y = precond.solve(p);\n    \n    v.noalias() = mat * y;\n\n    alpha = rho / r0.dot(v);\n    s = r - alpha * v;\n\n    z = precond.solve(s);\n    t.noalias() = mat * z;\n\n    RealScalar tmp = t.squaredNorm();\n    if(tmp>RealScalar(0))\n      w = t.dot(s) / tmp;\n    else\n      w = Scalar(0);\n    x += alpha * y + w * z;\n    r = s - w * t;\n    ++i;\n  }\n  tol_error = sqrt(r.squaredNorm()/rhs_sqnorm);\n  iters = i;\n  return true; \n}\n\n}\n\ntemplate< typename _MatrixType,\n          typename _Preconditioner = DiagonalPreconditioner<typename _MatrixType::Scalar> >\nclass BiCGSTAB;\n\nnamespace internal {\n\ntemplate< typename _MatrixType, typename _Preconditioner>\nstruct traits<BiCGSTAB<_MatrixType,_Preconditioner> >\n{\n  typedef _MatrixType MatrixType;\n  typedef _Preconditioner Preconditioner;\n};\n\n}\n\n/** \\ingroup IterativeLinearSolvers_Module\n  * \\brief A bi conjugate gradient stabilized solver for sparse square problems\n  *\n  * This class allows to solve for A.x = b sparse linear problems using a bi conjugate gradient\n  * stabilized algorithm. The vectors x and b can be either dense or sparse.\n  *\n  * \\tparam _MatrixType the type of the sparse matrix A, can be a dense or a sparse matrix.\n  * \\tparam _Preconditioner the type of the preconditioner. Default is DiagonalPreconditioner\n  *\n  * \\implsparsesolverconcept\n  *\n  * The maximal number of iterations and tolerance value can be controlled via the setMaxIterations()\n  * and setTolerance() methods. The defaults are the size of the problem for the maximal number of iterations\n  * and NumTraits<Scalar>::epsilon() for the tolerance.\n  * \n  * The tolerance corresponds to the relative residual error: |Ax-b|/|b|\n  * \n  * \\b Performance: when using sparse matrices, best performance is achied for a row-major sparse matrix format.\n  * Moreover, in this case multi-threading can be exploited if the user code is compiled with OpenMP enabled.\n  * See \\ref TopicMultiThreading for details.\n  * \n  * This class can be used as the direct solver classes. Here is a typical usage example:\n  * \\include BiCGSTAB_simple.cpp\n  * \n  * By default the iterations start with x=0 as an initial guess of the solution.\n  * One can control the start using the solveWithGuess() method.\n  * \n  * BiCGSTAB can also be used in a matrix-free context, see the following \\link MatrixfreeSolverExample example \\endlink.\n  *\n  * \\sa class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner\n  */\ntemplate< typename _MatrixType, typename _Preconditioner>\nclass BiCGSTAB : public IterativeSolverBase<BiCGSTAB<_MatrixType,_Preconditioner> >\n{\n  typedef IterativeSolverBase<BiCGSTAB> Base;\n  using Base::matrix;\n  using Base::m_error;\n  using Base::m_iterations;\n  using Base::m_info;\n  using Base::m_isInitialized;\npublic:\n  typedef _MatrixType MatrixType;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename MatrixType::RealScalar RealScalar;\n  typedef _Preconditioner Preconditioner;\n\npublic:\n\n  /** Default constructor. */\n  BiCGSTAB() : Base() {}\n\n  /** Initialize the solver with matrix \\a A for further \\c Ax=b solving.\n    * \n    * This constructor is a shortcut for the default constructor followed\n    * by a call to compute().\n    * \n    * \\warning this class stores a reference to the matrix A as well as some\n    * precomputed values that depend on it. Therefore, if \\a A is changed\n    * this class becomes invalid. Call compute() to update it with the new\n    * matrix A, or modify a copy of A.\n    */\n  template<typename MatrixDerived>\n  explicit BiCGSTAB(const EigenBase<MatrixDerived>& A) : Base(A.derived()) {}\n\n  ~BiCGSTAB() {}\n\n  /** \\internal */\n  template<typename Rhs,typename Dest>\n  void _solve_with_guess_impl(const Rhs& b, Dest& x) const\n  {    \n    bool failed = false;\n    for(Index j=0; j<b.cols(); ++j)\n    {\n      m_iterations = Base::maxIterations();\n      m_error = Base::m_tolerance;\n      \n      typename Dest::ColXpr xj(x,j);\n      if(!internal::bicgstab(matrix(), b.col(j), xj, Base::m_preconditioner, m_iterations, m_error))\n        failed = true;\n    }\n    m_info = failed ? NumericalIssue\n           : m_error <= Base::m_tolerance ? Success\n           : NoConvergence;\n    m_isInitialized = true;\n  }\n\n  /** \\internal */\n  using Base::_solve_impl;\n  template<typename Rhs,typename Dest>\n  void _solve_impl(const MatrixBase<Rhs>& b, Dest& x) const\n  {\n    x.resize(this->rows(),b.cols());\n    x.setZero();\n    _solve_with_guess_impl(b,x);\n  }\n\nprotected:\n\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_BICGSTAB_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/IterativeLinearSolvers/ConjugateGradient.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2011-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CONJUGATE_GRADIENT_H\n#define EIGEN_CONJUGATE_GRADIENT_H\n\nnamespace Eigen { \n\nnamespace internal {\n\n/** \\internal Low-level conjugate gradient algorithm\n  * \\param mat The matrix A\n  * \\param rhs The right hand side vector b\n  * \\param x On input and initial solution, on output the computed solution.\n  * \\param precond A preconditioner being able to efficiently solve for an\n  *                approximation of Ax=b (regardless of b)\n  * \\param iters On input the max number of iteration, on output the number of performed iterations.\n  * \\param tol_error On input the tolerance error, on output an estimation of the relative error.\n  */\ntemplate<typename MatrixType, typename Rhs, typename Dest, typename Preconditioner>\nEIGEN_DONT_INLINE\nvoid conjugate_gradient(const MatrixType& mat, const Rhs& rhs, Dest& x,\n                        const Preconditioner& precond, Index& iters,\n                        typename Dest::RealScalar& tol_error)\n{\n  using std::sqrt;\n  using std::abs;\n  typedef typename Dest::RealScalar RealScalar;\n  typedef typename Dest::Scalar Scalar;\n  typedef Matrix<Scalar,Dynamic,1> VectorType;\n  \n  RealScalar tol = tol_error;\n  Index maxIters = iters;\n  \n  Index n = mat.cols();\n\n  VectorType residual = rhs - mat * x; //initial residual\n\n  RealScalar rhsNorm2 = rhs.squaredNorm();\n  if(rhsNorm2 == 0) \n  {\n    x.setZero();\n    iters = 0;\n    tol_error = 0;\n    return;\n  }\n  RealScalar threshold = tol*tol*rhsNorm2;\n  RealScalar residualNorm2 = residual.squaredNorm();\n  if (residualNorm2 < threshold)\n  {\n    iters = 0;\n    tol_error = sqrt(residualNorm2 / rhsNorm2);\n    return;\n  }\n  \n  VectorType p(n);\n  p = precond.solve(residual);      // initial search direction\n\n  VectorType z(n), tmp(n);\n  RealScalar absNew = numext::real(residual.dot(p));  // the square of the absolute value of r scaled by invM\n  Index i = 0;\n  while(i < maxIters)\n  {\n    tmp.noalias() = mat * p;                    // the bottleneck of the algorithm\n\n    Scalar alpha = absNew / p.dot(tmp);         // the amount we travel on dir\n    x += alpha * p;                             // update solution\n    residual -= alpha * tmp;                    // update residual\n    \n    residualNorm2 = residual.squaredNorm();\n    if(residualNorm2 < threshold)\n      break;\n    \n    z = precond.solve(residual);                // approximately solve for \"A z = residual\"\n\n    RealScalar absOld = absNew;\n    absNew = numext::real(residual.dot(z));     // update the absolute value of r\n    RealScalar beta = absNew / absOld;          // calculate the Gram-Schmidt value used to create the new search direction\n    p = z + beta * p;                           // update search direction\n    i++;\n  }\n  tol_error = sqrt(residualNorm2 / rhsNorm2);\n  iters = i;\n}\n\n}\n\ntemplate< typename _MatrixType, int _UpLo=Lower,\n          typename _Preconditioner = DiagonalPreconditioner<typename _MatrixType::Scalar> >\nclass ConjugateGradient;\n\nnamespace internal {\n\ntemplate< typename _MatrixType, int _UpLo, typename _Preconditioner>\nstruct traits<ConjugateGradient<_MatrixType,_UpLo,_Preconditioner> >\n{\n  typedef _MatrixType MatrixType;\n  typedef _Preconditioner Preconditioner;\n};\n\n}\n\n/** \\ingroup IterativeLinearSolvers_Module\n  * \\brief A conjugate gradient solver for sparse (or dense) self-adjoint problems\n  *\n  * This class allows to solve for A.x = b linear problems using an iterative conjugate gradient algorithm.\n  * The matrix A must be selfadjoint. The matrix A and the vectors x and b can be either dense or sparse.\n  *\n  * \\tparam _MatrixType the type of the matrix A, can be a dense or a sparse matrix.\n  * \\tparam _UpLo the triangular part that will be used for the computations. It can be Lower,\n  *               \\c Upper, or \\c Lower|Upper in which the full matrix entries will be considered.\n  *               Default is \\c Lower, best performance is \\c Lower|Upper.\n  * \\tparam _Preconditioner the type of the preconditioner. Default is DiagonalPreconditioner\n  *\n  * \\implsparsesolverconcept\n  *\n  * The maximal number of iterations and tolerance value can be controlled via the setMaxIterations()\n  * and setTolerance() methods. The defaults are the size of the problem for the maximal number of iterations\n  * and NumTraits<Scalar>::epsilon() for the tolerance.\n  * \n  * The tolerance corresponds to the relative residual error: |Ax-b|/|b|\n  * \n  * \\b Performance: Even though the default value of \\c _UpLo is \\c Lower, significantly higher performance is\n  * achieved when using a complete matrix and \\b Lower|Upper as the \\a _UpLo template parameter. Moreover, in this\n  * case multi-threading can be exploited if the user code is compiled with OpenMP enabled.\n  * See \\ref TopicMultiThreading for details.\n  * \n  * This class can be used as the direct solver classes. Here is a typical usage example:\n    \\code\n    int n = 10000;\n    VectorXd x(n), b(n);\n    SparseMatrix<double> A(n,n);\n    // fill A and b\n    ConjugateGradient<SparseMatrix<double>, Lower|Upper> cg;\n    cg.compute(A);\n    x = cg.solve(b);\n    std::cout << \"#iterations:     \" << cg.iterations() << std::endl;\n    std::cout << \"estimated error: \" << cg.error()      << std::endl;\n    // update b, and solve again\n    x = cg.solve(b);\n    \\endcode\n  * \n  * By default the iterations start with x=0 as an initial guess of the solution.\n  * One can control the start using the solveWithGuess() method.\n  * \n  * ConjugateGradient can also be used in a matrix-free context, see the following \\link MatrixfreeSolverExample example \\endlink.\n  *\n  * \\sa class LeastSquaresConjugateGradient, class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner\n  */\ntemplate< typename _MatrixType, int _UpLo, typename _Preconditioner>\nclass ConjugateGradient : public IterativeSolverBase<ConjugateGradient<_MatrixType,_UpLo,_Preconditioner> >\n{\n  typedef IterativeSolverBase<ConjugateGradient> Base;\n  using Base::matrix;\n  using Base::m_error;\n  using Base::m_iterations;\n  using Base::m_info;\n  using Base::m_isInitialized;\npublic:\n  typedef _MatrixType MatrixType;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename MatrixType::RealScalar RealScalar;\n  typedef _Preconditioner Preconditioner;\n\n  enum {\n    UpLo = _UpLo\n  };\n\npublic:\n\n  /** Default constructor. */\n  ConjugateGradient() : Base() {}\n\n  /** Initialize the solver with matrix \\a A for further \\c Ax=b solving.\n    * \n    * This constructor is a shortcut for the default constructor followed\n    * by a call to compute().\n    * \n    * \\warning this class stores a reference to the matrix A as well as some\n    * precomputed values that depend on it. Therefore, if \\a A is changed\n    * this class becomes invalid. Call compute() to update it with the new\n    * matrix A, or modify a copy of A.\n    */\n  template<typename MatrixDerived>\n  explicit ConjugateGradient(const EigenBase<MatrixDerived>& A) : Base(A.derived()) {}\n\n  ~ConjugateGradient() {}\n\n  /** \\internal */\n  template<typename Rhs,typename Dest>\n  void _solve_with_guess_impl(const Rhs& b, Dest& x) const\n  {\n    typedef typename Base::MatrixWrapper MatrixWrapper;\n    typedef typename Base::ActualMatrixType ActualMatrixType;\n    enum {\n      TransposeInput  =   (!MatrixWrapper::MatrixFree)\n                      &&  (UpLo==(Lower|Upper))\n                      &&  (!MatrixType::IsRowMajor)\n                      &&  (!NumTraits<Scalar>::IsComplex)\n    };\n    typedef typename internal::conditional<TransposeInput,Transpose<const ActualMatrixType>, ActualMatrixType const&>::type RowMajorWrapper;\n    EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(MatrixWrapper::MatrixFree,UpLo==(Lower|Upper)),MATRIX_FREE_CONJUGATE_GRADIENT_IS_COMPATIBLE_WITH_UPPER_UNION_LOWER_MODE_ONLY);\n    typedef typename internal::conditional<UpLo==(Lower|Upper),\n                                           RowMajorWrapper,\n                                           typename MatrixWrapper::template ConstSelfAdjointViewReturnType<UpLo>::Type\n                                          >::type SelfAdjointWrapper;\n    m_iterations = Base::maxIterations();\n    m_error = Base::m_tolerance;\n\n    for(Index j=0; j<b.cols(); ++j)\n    {\n      m_iterations = Base::maxIterations();\n      m_error = Base::m_tolerance;\n\n      typename Dest::ColXpr xj(x,j);\n      RowMajorWrapper row_mat(matrix());\n      internal::conjugate_gradient(SelfAdjointWrapper(row_mat), b.col(j), xj, Base::m_preconditioner, m_iterations, m_error);\n    }\n\n    m_isInitialized = true;\n    m_info = m_error <= Base::m_tolerance ? Success : NoConvergence;\n  }\n  \n  /** \\internal */\n  using Base::_solve_impl;\n  template<typename Rhs,typename Dest>\n  void _solve_impl(const MatrixBase<Rhs>& b, Dest& x) const\n  {\n    x.setZero();\n    _solve_with_guess_impl(b.derived(),x);\n  }\n\nprotected:\n\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_CONJUGATE_GRADIENT_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/IterativeLinearSolvers/IncompleteCholesky.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>\n// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_INCOMPLETE_CHOlESKY_H\n#define EIGEN_INCOMPLETE_CHOlESKY_H\n\n#include <vector>\n#include <list>\n\nnamespace Eigen {  \n/** \n  * \\brief Modified Incomplete Cholesky with dual threshold\n  *\n  * References : C-J. Lin and J. J. Moré, Incomplete Cholesky Factorizations with\n  *              Limited memory, SIAM J. Sci. Comput.  21(1), pp. 24-45, 1999\n  *\n  * \\tparam Scalar the scalar type of the input matrices\n  * \\tparam _UpLo The triangular part that will be used for the computations. It can be Lower\n    *               or Upper. Default is Lower.\n  * \\tparam _OrderingType The ordering method to use, either AMDOrdering<> or NaturalOrdering<>. Default is AMDOrdering<int>,\n  *                       unless EIGEN_MPL2_ONLY is defined, in which case the default is NaturalOrdering<int>.\n  *\n  * \\implsparsesolverconcept\n  *\n  * It performs the following incomplete factorization: \\f$ S P A P' S \\approx L L' \\f$\n  * where L is a lower triangular factor, S is a diagonal scaling matrix, and P is a\n  * fill-in reducing permutation as computed by the ordering method.\n  *\n  * \\b Shifting \\b strategy: Let \\f$ B = S P A P' S \\f$  be the scaled matrix on which the factorization is carried out,\n  * and \\f$ \\beta \\f$ be the minimum value of the diagonal. If \\f$ \\beta > 0 \\f$ then, the factorization is directly performed\n  * on the matrix B. Otherwise, the factorization is performed on the shifted matrix \\f$ B + (\\sigma+|\\beta| I \\f$ where\n  * \\f$ \\sigma \\f$ is the initial shift value as returned and set by setInitialShift() method. The default value is \\f$ \\sigma = 10^{-3} \\f$.\n  * If the factorization fails, then the shift in doubled until it succeed or a maximum of ten attempts. If it still fails, as returned by\n  * the info() method, then you can either increase the initial shift, or better use another preconditioning technique.\n  *\n  */\ntemplate <typename Scalar, int _UpLo = Lower, typename _OrderingType =\n#ifndef EIGEN_MPL2_ONLY\nAMDOrdering<int>\n#else\nNaturalOrdering<int>\n#endif\n>\nclass IncompleteCholesky : public SparseSolverBase<IncompleteCholesky<Scalar,_UpLo,_OrderingType> >\n{\n  protected:\n    typedef SparseSolverBase<IncompleteCholesky<Scalar,_UpLo,_OrderingType> > Base;\n    using Base::m_isInitialized;\n  public:\n    typedef typename NumTraits<Scalar>::Real RealScalar; \n    typedef _OrderingType OrderingType;\n    typedef typename OrderingType::PermutationType PermutationType;\n    typedef typename PermutationType::StorageIndex StorageIndex; \n    typedef SparseMatrix<Scalar,ColMajor,StorageIndex> FactorType;\n    typedef Matrix<Scalar,Dynamic,1> VectorSx;\n    typedef Matrix<RealScalar,Dynamic,1> VectorRx;\n    typedef Matrix<StorageIndex,Dynamic, 1> VectorIx;\n    typedef std::vector<std::list<StorageIndex> > VectorList; \n    enum { UpLo = _UpLo };\n    enum {\n      ColsAtCompileTime = Dynamic,\n      MaxColsAtCompileTime = Dynamic\n    };\n  public:\n\n    /** Default constructor leaving the object in a partly non-initialized stage.\n      *\n      * You must call compute() or the pair analyzePattern()/factorize() to make it valid.\n      *\n      * \\sa IncompleteCholesky(const MatrixType&)\n      */\n    IncompleteCholesky() : m_initialShift(1e-3),m_factorizationIsOk(false) {}\n    \n    /** Constructor computing the incomplete factorization for the given matrix \\a matrix.\n      */\n    template<typename MatrixType>\n    IncompleteCholesky(const MatrixType& matrix) : m_initialShift(1e-3),m_factorizationIsOk(false)\n    {\n      compute(matrix);\n    }\n    \n    /** \\returns number of rows of the factored matrix */\n    Index rows() const { return m_L.rows(); }\n    \n    /** \\returns number of columns of the factored matrix */\n    Index cols() const { return m_L.cols(); }\n    \n\n    /** \\brief Reports whether previous computation was successful.\n      *\n      * It triggers an assertion if \\c *this has not been initialized through the respective constructor,\n      * or a call to compute() or analyzePattern().\n      *\n      * \\returns \\c Success if computation was successful,\n      *          \\c NumericalIssue if the matrix appears to be negative.\n      */\n    ComputationInfo info() const\n    {\n      eigen_assert(m_isInitialized && \"IncompleteCholesky is not initialized.\");\n      return m_info;\n    }\n    \n    /** \\brief Set the initial shift parameter \\f$ \\sigma \\f$.\n      */\n    void setInitialShift(RealScalar shift) { m_initialShift = shift; }\n    \n    /** \\brief Computes the fill reducing permutation vector using the sparsity pattern of \\a mat\n      */\n    template<typename MatrixType>\n    void analyzePattern(const MatrixType& mat)\n    {\n      OrderingType ord; \n      PermutationType pinv;\n      ord(mat.template selfadjointView<UpLo>(), pinv); \n      if(pinv.size()>0) m_perm = pinv.inverse();\n      else              m_perm.resize(0);\n      m_L.resize(mat.rows(), mat.cols());\n      m_analysisIsOk = true;\n      m_isInitialized = true;\n      m_info = Success;\n    }\n    \n    /** \\brief Performs the numerical factorization of the input matrix \\a mat\n      *\n      * The method analyzePattern() or compute() must have been called beforehand\n      * with a matrix having the same pattern.\n      *\n      * \\sa compute(), analyzePattern()\n      */\n    template<typename MatrixType>\n    void factorize(const MatrixType& mat);\n    \n    /** Computes or re-computes the incomplete Cholesky factorization of the input matrix \\a mat\n      *\n      * It is a shortcut for a sequential call to the analyzePattern() and factorize() methods.\n      *\n      * \\sa analyzePattern(), factorize()\n      */\n    template<typename MatrixType>\n    void compute(const MatrixType& mat)\n    {\n      analyzePattern(mat);\n      factorize(mat);\n    }\n    \n    // internal\n    template<typename Rhs, typename Dest>\n    void _solve_impl(const Rhs& b, Dest& x) const\n    {\n      eigen_assert(m_factorizationIsOk && \"factorize() should be called first\");\n      if (m_perm.rows() == b.rows())  x = m_perm * b;\n      else                            x = b;\n      x = m_scale.asDiagonal() * x;\n      x = m_L.template triangularView<Lower>().solve(x);\n      x = m_L.adjoint().template triangularView<Upper>().solve(x);\n      x = m_scale.asDiagonal() * x;\n      if (m_perm.rows() == b.rows())\n        x = m_perm.inverse() * x;\n    }\n\n    /** \\returns the sparse lower triangular factor L */\n    const FactorType& matrixL() const { eigen_assert(\"m_factorizationIsOk\"); return m_L; }\n\n    /** \\returns a vector representing the scaling factor S */\n    const VectorRx& scalingS() const { eigen_assert(\"m_factorizationIsOk\"); return m_scale; }\n\n    /** \\returns the fill-in reducing permutation P (can be empty for a natural ordering) */\n    const PermutationType& permutationP() const { eigen_assert(\"m_analysisIsOk\"); return m_perm; }\n\n  protected:\n    FactorType m_L;              // The lower part stored in CSC\n    VectorRx m_scale;            // The vector for scaling the matrix \n    RealScalar m_initialShift;   // The initial shift parameter\n    bool m_analysisIsOk; \n    bool m_factorizationIsOk; \n    ComputationInfo m_info;\n    PermutationType m_perm; \n\n  private:\n    inline void updateList(Ref<const VectorIx> colPtr, Ref<VectorIx> rowIdx, Ref<VectorSx> vals, const Index& col, const Index& jk, VectorIx& firstElt, VectorList& listCol); \n}; \n\n// Based on the following paper:\n//   C-J. Lin and J. J. Moré, Incomplete Cholesky Factorizations with\n//   Limited memory, SIAM J. Sci. Comput.  21(1), pp. 24-45, 1999\n//   http://ftp.mcs.anl.gov/pub/tech_reports/reports/P682.pdf\ntemplate<typename Scalar, int _UpLo, typename OrderingType>\ntemplate<typename _MatrixType>\nvoid IncompleteCholesky<Scalar,_UpLo, OrderingType>::factorize(const _MatrixType& mat)\n{\n  using std::sqrt;\n  eigen_assert(m_analysisIsOk && \"analyzePattern() should be called first\"); \n    \n  // Dropping strategy : Keep only the p largest elements per column, where p is the number of elements in the column of the original matrix. Other strategies will be added\n  \n  // Apply the fill-reducing permutation computed in analyzePattern()\n  if (m_perm.rows() == mat.rows() ) // To detect the null permutation\n  {\n    // The temporary is needed to make sure that the diagonal entry is properly sorted\n    FactorType tmp(mat.rows(), mat.cols());\n    tmp = mat.template selfadjointView<_UpLo>().twistedBy(m_perm);\n    m_L.template selfadjointView<Lower>() = tmp.template selfadjointView<Lower>();\n  }\n  else\n  {\n    m_L.template selfadjointView<Lower>() = mat.template selfadjointView<_UpLo>();\n  }\n  \n  Index n = m_L.cols(); \n  Index nnz = m_L.nonZeros();\n  Map<VectorSx> vals(m_L.valuePtr(), nnz);         //values\n  Map<VectorIx> rowIdx(m_L.innerIndexPtr(), nnz);  //Row indices\n  Map<VectorIx> colPtr( m_L.outerIndexPtr(), n+1); // Pointer to the beginning of each row\n  VectorIx firstElt(n-1); // for each j, points to the next entry in vals that will be used in the factorization\n  VectorList listCol(n);  // listCol(j) is a linked list of columns to update column j\n  VectorSx col_vals(n);   // Store a  nonzero values in each column\n  VectorIx col_irow(n);   // Row indices of nonzero elements in each column\n  VectorIx col_pattern(n);\n  col_pattern.fill(-1);\n  StorageIndex col_nnz;\n  \n  \n  // Computes the scaling factors \n  m_scale.resize(n);\n  m_scale.setZero();\n  for (Index j = 0; j < n; j++)\n    for (Index k = colPtr[j]; k < colPtr[j+1]; k++)\n    {\n      m_scale(j) += numext::abs2(vals(k));\n      if(rowIdx[k]!=j)\n        m_scale(rowIdx[k]) += numext::abs2(vals(k));\n    }\n  \n  m_scale = m_scale.cwiseSqrt().cwiseSqrt();\n\n  for (Index j = 0; j < n; ++j)\n    if(m_scale(j)>(std::numeric_limits<RealScalar>::min)())\n      m_scale(j) = RealScalar(1)/m_scale(j);\n    else\n      m_scale(j) = 1;\n\n  // TODO disable scaling if not needed, i.e., if it is roughly uniform? (this will make solve() faster)\n  \n  // Scale and compute the shift for the matrix \n  RealScalar mindiag = NumTraits<RealScalar>::highest();\n  for (Index j = 0; j < n; j++)\n  {\n    for (Index k = colPtr[j]; k < colPtr[j+1]; k++)\n      vals[k] *= (m_scale(j)*m_scale(rowIdx[k]));\n    eigen_internal_assert(rowIdx[colPtr[j]]==j && \"IncompleteCholesky: only the lower triangular part must be stored\");\n    mindiag = numext::mini(numext::real(vals[colPtr[j]]), mindiag);\n  }\n\n  FactorType L_save = m_L;\n  \n  RealScalar shift = 0;\n  if(mindiag <= RealScalar(0.))\n    shift = m_initialShift - mindiag;\n\n  m_info = NumericalIssue;\n\n  // Try to perform the incomplete factorization using the current shift\n  int iter = 0;\n  do\n  {\n    // Apply the shift to the diagonal elements of the matrix\n    for (Index j = 0; j < n; j++)\n      vals[colPtr[j]] += shift;\n\n    // jki version of the Cholesky factorization\n    Index j=0;\n    for (; j < n; ++j)\n    {\n      // Left-looking factorization of the j-th column\n      // First, load the j-th column into col_vals\n      Scalar diag = vals[colPtr[j]];  // It is assumed that only the lower part is stored\n      col_nnz = 0;\n      for (Index i = colPtr[j] + 1; i < colPtr[j+1]; i++)\n      {\n        StorageIndex l = rowIdx[i];\n        col_vals(col_nnz) = vals[i];\n        col_irow(col_nnz) = l;\n        col_pattern(l) = col_nnz;\n        col_nnz++;\n      }\n      {\n        typename std::list<StorageIndex>::iterator k;\n        // Browse all previous columns that will update column j\n        for(k = listCol[j].begin(); k != listCol[j].end(); k++)\n        {\n          Index jk = firstElt(*k); // First element to use in the column\n          eigen_internal_assert(rowIdx[jk]==j);\n          Scalar v_j_jk = numext::conj(vals[jk]);\n\n          jk += 1;\n          for (Index i = jk; i < colPtr[*k+1]; i++)\n          {\n            StorageIndex l = rowIdx[i];\n            if(col_pattern[l]<0)\n            {\n              col_vals(col_nnz) = vals[i] * v_j_jk;\n              col_irow[col_nnz] = l;\n              col_pattern(l) = col_nnz;\n              col_nnz++;\n            }\n            else\n              col_vals(col_pattern[l]) -= vals[i] * v_j_jk;\n          }\n          updateList(colPtr,rowIdx,vals, *k, jk, firstElt, listCol);\n        }\n      }\n\n      // Scale the current column\n      if(numext::real(diag) <= 0)\n      {\n        if(++iter>=10)\n          return;\n\n        // increase shift\n        shift = numext::maxi(m_initialShift,RealScalar(2)*shift);\n        // restore m_L, col_pattern, and listCol\n        vals = Map<const VectorSx>(L_save.valuePtr(), nnz);\n        rowIdx = Map<const VectorIx>(L_save.innerIndexPtr(), nnz);\n        colPtr = Map<const VectorIx>(L_save.outerIndexPtr(), n+1);\n        col_pattern.fill(-1);\n        for(Index i=0; i<n; ++i)\n          listCol[i].clear();\n\n        break;\n      }\n\n      RealScalar rdiag = sqrt(numext::real(diag));\n      vals[colPtr[j]] = rdiag;\n      for (Index k = 0; k<col_nnz; ++k)\n      {\n        Index i = col_irow[k];\n        //Scale\n        col_vals(k) /= rdiag;\n        //Update the remaining diagonals with col_vals\n        vals[colPtr[i]] -= numext::abs2(col_vals(k));\n      }\n      // Select the largest p elements\n      // p is the original number of elements in the column (without the diagonal)\n      Index p = colPtr[j+1] - colPtr[j] - 1 ;\n      Ref<VectorSx> cvals = col_vals.head(col_nnz);\n      Ref<VectorIx> cirow = col_irow.head(col_nnz);\n      internal::QuickSplit(cvals,cirow, p);\n      // Insert the largest p elements in the matrix\n      Index cpt = 0;\n      for (Index i = colPtr[j]+1; i < colPtr[j+1]; i++)\n      {\n        vals[i] = col_vals(cpt);\n        rowIdx[i] = col_irow(cpt);\n        // restore col_pattern:\n        col_pattern(col_irow(cpt)) = -1;\n        cpt++;\n      }\n      // Get the first smallest row index and put it after the diagonal element\n      Index jk = colPtr(j)+1;\n      updateList(colPtr,rowIdx,vals,j,jk,firstElt,listCol);\n    }\n\n    if(j==n)\n    {\n      m_factorizationIsOk = true;\n      m_info = Success;\n    }\n  } while(m_info!=Success);\n}\n\ntemplate<typename Scalar, int _UpLo, typename OrderingType>\ninline void IncompleteCholesky<Scalar,_UpLo, OrderingType>::updateList(Ref<const VectorIx> colPtr, Ref<VectorIx> rowIdx, Ref<VectorSx> vals, const Index& col, const Index& jk, VectorIx& firstElt, VectorList& listCol)\n{\n  if (jk < colPtr(col+1) )\n  {\n    Index p = colPtr(col+1) - jk;\n    Index minpos; \n    rowIdx.segment(jk,p).minCoeff(&minpos);\n    minpos += jk;\n    if (rowIdx(minpos) != rowIdx(jk))\n    {\n      //Swap\n      std::swap(rowIdx(jk),rowIdx(minpos));\n      std::swap(vals(jk),vals(minpos));\n    }\n    firstElt(col) = internal::convert_index<StorageIndex,Index>(jk);\n    listCol[rowIdx(jk)].push_back(internal::convert_index<StorageIndex,Index>(col));\n  }\n}\n\n} // end namespace Eigen \n\n#endif\n"
  },
  {
    "path": "include/eigen3/Eigen/src/IterativeLinearSolvers/IncompleteLUT.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>\n// Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_INCOMPLETE_LUT_H\n#define EIGEN_INCOMPLETE_LUT_H\n\n\nnamespace Eigen { \n\nnamespace internal {\n    \n/** \\internal\n  * Compute a quick-sort split of a vector \n  * On output, the vector row is permuted such that its elements satisfy\n  * abs(row(i)) >= abs(row(ncut)) if i<ncut\n  * abs(row(i)) <= abs(row(ncut)) if i>ncut \n  * \\param row The vector of values\n  * \\param ind The array of index for the elements in @p row\n  * \\param ncut  The number of largest elements to keep\n  **/ \ntemplate <typename VectorV, typename VectorI>\nIndex QuickSplit(VectorV &row, VectorI &ind, Index ncut)\n{\n  typedef typename VectorV::RealScalar RealScalar;\n  using std::swap;\n  using std::abs;\n  Index mid;\n  Index n = row.size(); /* length of the vector */\n  Index first, last ;\n  \n  ncut--; /* to fit the zero-based indices */\n  first = 0; \n  last = n-1; \n  if (ncut < first || ncut > last ) return 0;\n  \n  do {\n    mid = first; \n    RealScalar abskey = abs(row(mid)); \n    for (Index j = first + 1; j <= last; j++) {\n      if ( abs(row(j)) > abskey) {\n        ++mid;\n        swap(row(mid), row(j));\n        swap(ind(mid), ind(j));\n      }\n    }\n    /* Interchange for the pivot element */\n    swap(row(mid), row(first));\n    swap(ind(mid), ind(first));\n    \n    if (mid > ncut) last = mid - 1;\n    else if (mid < ncut ) first = mid + 1; \n  } while (mid != ncut );\n  \n  return 0; /* mid is equal to ncut */ \n}\n\n}// end namespace internal\n\n/** \\ingroup IterativeLinearSolvers_Module\n  * \\class IncompleteLUT\n  * \\brief Incomplete LU factorization with dual-threshold strategy\n  *\n  * \\implsparsesolverconcept\n  *\n  * During the numerical factorization, two dropping rules are used :\n  *  1) any element whose magnitude is less than some tolerance is dropped.\n  *    This tolerance is obtained by multiplying the input tolerance @p droptol \n  *    by the average magnitude of all the original elements in the current row.\n  *  2) After the elimination of the row, only the @p fill largest elements in \n  *    the L part and the @p fill largest elements in the U part are kept \n  *    (in addition to the diagonal element ). Note that @p fill is computed from \n  *    the input parameter @p fillfactor which is used the ratio to control the fill_in \n  *    relatively to the initial number of nonzero elements.\n  * \n  * The two extreme cases are when @p droptol=0 (to keep all the @p fill*2 largest elements)\n  * and when @p fill=n/2 with @p droptol being different to zero. \n  * \n  * References : Yousef Saad, ILUT: A dual threshold incomplete LU factorization, \n  *              Numerical Linear Algebra with Applications, 1(4), pp 387-402, 1994.\n  * \n  * NOTE : The following implementation is derived from the ILUT implementation\n  * in the SPARSKIT package, Copyright (C) 2005, the Regents of the University of Minnesota \n  *  released under the terms of the GNU LGPL: \n  *    http://www-users.cs.umn.edu/~saad/software/SPARSKIT/README\n  * However, Yousef Saad gave us permission to relicense his ILUT code to MPL2.\n  * See the Eigen mailing list archive, thread: ILUT, date: July 8, 2012:\n  *   http://listengine.tuxfamily.org/lists.tuxfamily.org/eigen/2012/07/msg00064.html\n  * alternatively, on GMANE:\n  *   http://comments.gmane.org/gmane.comp.lib.eigen/3302\n  */\ntemplate <typename _Scalar, typename _StorageIndex = int>\nclass IncompleteLUT : public SparseSolverBase<IncompleteLUT<_Scalar, _StorageIndex> >\n{\n  protected:\n    typedef SparseSolverBase<IncompleteLUT> Base;\n    using Base::m_isInitialized;\n  public:\n    typedef _Scalar Scalar;\n    typedef _StorageIndex StorageIndex;\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n    typedef Matrix<Scalar,Dynamic,1> Vector;\n    typedef Matrix<StorageIndex,Dynamic,1> VectorI;\n    typedef SparseMatrix<Scalar,RowMajor,StorageIndex> FactorType;\n\n    enum {\n      ColsAtCompileTime = Dynamic,\n      MaxColsAtCompileTime = Dynamic\n    };\n\n  public:\n    \n    IncompleteLUT()\n      : m_droptol(NumTraits<Scalar>::dummy_precision()), m_fillfactor(10),\n        m_analysisIsOk(false), m_factorizationIsOk(false)\n    {}\n    \n    template<typename MatrixType>\n    explicit IncompleteLUT(const MatrixType& mat, const RealScalar& droptol=NumTraits<Scalar>::dummy_precision(), int fillfactor = 10)\n      : m_droptol(droptol),m_fillfactor(fillfactor),\n        m_analysisIsOk(false),m_factorizationIsOk(false)\n    {\n      eigen_assert(fillfactor != 0);\n      compute(mat); \n    }\n    \n    Index rows() const { return m_lu.rows(); }\n    \n    Index cols() const { return m_lu.cols(); }\n\n    /** \\brief Reports whether previous computation was successful.\n      *\n      * \\returns \\c Success if computation was succesful,\n      *          \\c NumericalIssue if the matrix.appears to be negative.\n      */\n    ComputationInfo info() const\n    {\n      eigen_assert(m_isInitialized && \"IncompleteLUT is not initialized.\");\n      return m_info;\n    }\n    \n    template<typename MatrixType>\n    void analyzePattern(const MatrixType& amat);\n    \n    template<typename MatrixType>\n    void factorize(const MatrixType& amat);\n    \n    /**\n      * Compute an incomplete LU factorization with dual threshold on the matrix mat\n      * No pivoting is done in this version\n      * \n      **/\n    template<typename MatrixType>\n    IncompleteLUT& compute(const MatrixType& amat)\n    {\n      analyzePattern(amat); \n      factorize(amat);\n      return *this;\n    }\n\n    void setDroptol(const RealScalar& droptol); \n    void setFillfactor(int fillfactor); \n    \n    template<typename Rhs, typename Dest>\n    void _solve_impl(const Rhs& b, Dest& x) const\n    {\n      x = m_Pinv * b;\n      x = m_lu.template triangularView<UnitLower>().solve(x);\n      x = m_lu.template triangularView<Upper>().solve(x);\n      x = m_P * x; \n    }\n\nprotected:\n\n    /** keeps off-diagonal entries; drops diagonal entries */\n    struct keep_diag {\n      inline bool operator() (const Index& row, const Index& col, const Scalar&) const\n      {\n        return row!=col;\n      }\n    };\n\nprotected:\n\n    FactorType m_lu;\n    RealScalar m_droptol;\n    int m_fillfactor;\n    bool m_analysisIsOk;\n    bool m_factorizationIsOk;\n    ComputationInfo m_info;\n    PermutationMatrix<Dynamic,Dynamic,StorageIndex> m_P;     // Fill-reducing permutation\n    PermutationMatrix<Dynamic,Dynamic,StorageIndex> m_Pinv;  // Inverse permutation\n};\n\n/**\n * Set control parameter droptol\n *  \\param droptol   Drop any element whose magnitude is less than this tolerance \n **/ \ntemplate<typename Scalar, typename StorageIndex>\nvoid IncompleteLUT<Scalar,StorageIndex>::setDroptol(const RealScalar& droptol)\n{\n  this->m_droptol = droptol;   \n}\n\n/**\n * Set control parameter fillfactor\n * \\param fillfactor  This is used to compute the  number @p fill_in of largest elements to keep on each row. \n **/ \ntemplate<typename Scalar, typename StorageIndex>\nvoid IncompleteLUT<Scalar,StorageIndex>::setFillfactor(int fillfactor)\n{\n  this->m_fillfactor = fillfactor;   \n}\n\ntemplate <typename Scalar, typename StorageIndex>\ntemplate<typename _MatrixType>\nvoid IncompleteLUT<Scalar,StorageIndex>::analyzePattern(const _MatrixType& amat)\n{\n  // Compute the Fill-reducing permutation\n  // Since ILUT does not perform any numerical pivoting,\n  // it is highly preferable to keep the diagonal through symmetric permutations.\n#ifndef EIGEN_MPL2_ONLY\n  // To this end, let's symmetrize the pattern and perform AMD on it.\n  SparseMatrix<Scalar,ColMajor, StorageIndex> mat1 = amat;\n  SparseMatrix<Scalar,ColMajor, StorageIndex> mat2 = amat.transpose();\n  // FIXME for a matrix with nearly symmetric pattern, mat2+mat1 is the appropriate choice.\n  //       on the other hand for a really non-symmetric pattern, mat2*mat1 should be prefered...\n  SparseMatrix<Scalar,ColMajor, StorageIndex> AtA = mat2 + mat1;\n  AMDOrdering<StorageIndex> ordering;\n  ordering(AtA,m_P);\n  m_Pinv  = m_P.inverse(); // cache the inverse permutation\n#else\n  // If AMD is not available, (MPL2-only), then let's use the slower COLAMD routine.\n  SparseMatrix<Scalar,ColMajor, StorageIndex> mat1 = amat;\n  COLAMDOrdering<StorageIndex> ordering;\n  ordering(mat1,m_Pinv);\n  m_P = m_Pinv.inverse();\n#endif\n\n  m_analysisIsOk = true;\n  m_factorizationIsOk = false;\n  m_isInitialized = true;\n}\n\ntemplate <typename Scalar, typename StorageIndex>\ntemplate<typename _MatrixType>\nvoid IncompleteLUT<Scalar,StorageIndex>::factorize(const _MatrixType& amat)\n{\n  using std::sqrt;\n  using std::swap;\n  using std::abs;\n  using internal::convert_index;\n\n  eigen_assert((amat.rows() == amat.cols()) && \"The factorization should be done on a square matrix\");\n  Index n = amat.cols();  // Size of the matrix\n  m_lu.resize(n,n);\n  // Declare Working vectors and variables\n  Vector u(n) ;     // real values of the row -- maximum size is n --\n  VectorI ju(n);   // column position of the values in u -- maximum size  is n\n  VectorI jr(n);   // Indicate the position of the nonzero elements in the vector u -- A zero location is indicated by -1\n\n  // Apply the fill-reducing permutation\n  eigen_assert(m_analysisIsOk && \"You must first call analyzePattern()\");\n  SparseMatrix<Scalar,RowMajor, StorageIndex> mat;\n  mat = amat.twistedBy(m_Pinv);\n\n  // Initialization\n  jr.fill(-1);\n  ju.fill(0);\n  u.fill(0);\n\n  // number of largest elements to keep in each row:\n  Index fill_in = (amat.nonZeros()*m_fillfactor)/n + 1;\n  if (fill_in > n) fill_in = n;\n\n  // number of largest nonzero elements to keep in the L and the U part of the current row:\n  Index nnzL = fill_in/2;\n  Index nnzU = nnzL;\n  m_lu.reserve(n * (nnzL + nnzU + 1));\n\n  // global loop over the rows of the sparse matrix\n  for (Index ii = 0; ii < n; ii++)\n  {\n    // 1 - copy the lower and the upper part of the row i of mat in the working vector u\n\n    Index sizeu = 1; // number of nonzero elements in the upper part of the current row\n    Index sizel = 0; // number of nonzero elements in the lower part of the current row\n    ju(ii)    = convert_index<StorageIndex>(ii);\n    u(ii)     = 0;\n    jr(ii)    = convert_index<StorageIndex>(ii);\n    RealScalar rownorm = 0;\n\n    typename FactorType::InnerIterator j_it(mat, ii); // Iterate through the current row ii\n    for (; j_it; ++j_it)\n    {\n      Index k = j_it.index();\n      if (k < ii)\n      {\n        // copy the lower part\n        ju(sizel) = convert_index<StorageIndex>(k);\n        u(sizel) = j_it.value();\n        jr(k) = convert_index<StorageIndex>(sizel);\n        ++sizel;\n      }\n      else if (k == ii)\n      {\n        u(ii) = j_it.value();\n      }\n      else\n      {\n        // copy the upper part\n        Index jpos = ii + sizeu;\n        ju(jpos) = convert_index<StorageIndex>(k);\n        u(jpos) = j_it.value();\n        jr(k) = convert_index<StorageIndex>(jpos);\n        ++sizeu;\n      }\n      rownorm += numext::abs2(j_it.value());\n    }\n\n    // 2 - detect possible zero row\n    if(rownorm==0)\n    {\n      m_info = NumericalIssue;\n      return;\n    }\n    // Take the 2-norm of the current row as a relative tolerance\n    rownorm = sqrt(rownorm);\n\n    // 3 - eliminate the previous nonzero rows\n    Index jj = 0;\n    Index len = 0;\n    while (jj < sizel)\n    {\n      // In order to eliminate in the correct order,\n      // we must select first the smallest column index among  ju(jj:sizel)\n      Index k;\n      Index minrow = ju.segment(jj,sizel-jj).minCoeff(&k); // k is relative to the segment\n      k += jj;\n      if (minrow != ju(jj))\n      {\n        // swap the two locations\n        Index j = ju(jj);\n        swap(ju(jj), ju(k));\n        jr(minrow) = convert_index<StorageIndex>(jj);\n        jr(j) = convert_index<StorageIndex>(k);\n        swap(u(jj), u(k));\n      }\n      // Reset this location\n      jr(minrow) = -1;\n\n      // Start elimination\n      typename FactorType::InnerIterator ki_it(m_lu, minrow);\n      while (ki_it && ki_it.index() < minrow) ++ki_it;\n      eigen_internal_assert(ki_it && ki_it.col()==minrow);\n      Scalar fact = u(jj) / ki_it.value();\n\n      // drop too small elements\n      if(abs(fact) <= m_droptol)\n      {\n        jj++;\n        continue;\n      }\n\n      // linear combination of the current row ii and the row minrow\n      ++ki_it;\n      for (; ki_it; ++ki_it)\n      {\n        Scalar prod = fact * ki_it.value();\n        Index j     = ki_it.index();\n        Index jpos  = jr(j);\n        if (jpos == -1) // fill-in element\n        {\n          Index newpos;\n          if (j >= ii) // dealing with the upper part\n          {\n            newpos = ii + sizeu;\n            sizeu++;\n            eigen_internal_assert(sizeu<=n);\n          }\n          else // dealing with the lower part\n          {\n            newpos = sizel;\n            sizel++;\n            eigen_internal_assert(sizel<=ii);\n          }\n          ju(newpos) = convert_index<StorageIndex>(j);\n          u(newpos) = -prod;\n          jr(j) = convert_index<StorageIndex>(newpos);\n        }\n        else\n          u(jpos) -= prod;\n      }\n      // store the pivot element\n      u(len)  = fact;\n      ju(len) = convert_index<StorageIndex>(minrow);\n      ++len;\n\n      jj++;\n    } // end of the elimination on the row ii\n\n    // reset the upper part of the pointer jr to zero\n    for(Index k = 0; k <sizeu; k++) jr(ju(ii+k)) = -1;\n\n    // 4 - partially sort and insert the elements in the m_lu matrix\n\n    // sort the L-part of the row\n    sizel = len;\n    len = (std::min)(sizel, nnzL);\n    typename Vector::SegmentReturnType ul(u.segment(0, sizel));\n    typename VectorI::SegmentReturnType jul(ju.segment(0, sizel));\n    internal::QuickSplit(ul, jul, len);\n\n    // store the largest m_fill elements of the L part\n    m_lu.startVec(ii);\n    for(Index k = 0; k < len; k++)\n      m_lu.insertBackByOuterInnerUnordered(ii,ju(k)) = u(k);\n\n    // store the diagonal element\n    // apply a shifting rule to avoid zero pivots (we are doing an incomplete factorization)\n    if (u(ii) == Scalar(0))\n      u(ii) = sqrt(m_droptol) * rownorm;\n    m_lu.insertBackByOuterInnerUnordered(ii, ii) = u(ii);\n\n    // sort the U-part of the row\n    // apply the dropping rule first\n    len = 0;\n    for(Index k = 1; k < sizeu; k++)\n    {\n      if(abs(u(ii+k)) > m_droptol * rownorm )\n      {\n        ++len;\n        u(ii + len)  = u(ii + k);\n        ju(ii + len) = ju(ii + k);\n      }\n    }\n    sizeu = len + 1; // +1 to take into account the diagonal element\n    len = (std::min)(sizeu, nnzU);\n    typename Vector::SegmentReturnType uu(u.segment(ii+1, sizeu-1));\n    typename VectorI::SegmentReturnType juu(ju.segment(ii+1, sizeu-1));\n    internal::QuickSplit(uu, juu, len);\n\n    // store the largest elements of the U part\n    for(Index k = ii + 1; k < ii + len; k++)\n      m_lu.insertBackByOuterInnerUnordered(ii,ju(k)) = u(k);\n  }\n  m_lu.finalize();\n  m_lu.makeCompressed();\n\n  m_factorizationIsOk = true;\n  m_info = Success;\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_INCOMPLETE_LUT_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/IterativeLinearSolvers/IterativeSolverBase.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2011-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_ITERATIVE_SOLVER_BASE_H\n#define EIGEN_ITERATIVE_SOLVER_BASE_H\n\nnamespace Eigen { \n\nnamespace internal {\n\ntemplate<typename MatrixType>\nstruct is_ref_compatible_impl\n{\nprivate:\n  template <typename T0>\n  struct any_conversion\n  {\n    template <typename T> any_conversion(const volatile T&);\n    template <typename T> any_conversion(T&);\n  };\n  struct yes {int a[1];};\n  struct no  {int a[2];};\n\n  template<typename T>\n  static yes test(const Ref<const T>&, int);\n  template<typename T>\n  static no  test(any_conversion<T>, ...);\n\npublic:\n  static MatrixType ms_from;\n  enum { value = sizeof(test<MatrixType>(ms_from, 0))==sizeof(yes) };\n};\n\ntemplate<typename MatrixType>\nstruct is_ref_compatible\n{\n  enum { value = is_ref_compatible_impl<typename remove_all<MatrixType>::type>::value };\n};\n\ntemplate<typename MatrixType, bool MatrixFree = !internal::is_ref_compatible<MatrixType>::value>\nclass generic_matrix_wrapper;\n\n// We have an explicit matrix at hand, compatible with Ref<>\ntemplate<typename MatrixType>\nclass generic_matrix_wrapper<MatrixType,false>\n{\npublic:\n  typedef Ref<const MatrixType> ActualMatrixType;\n  template<int UpLo> struct ConstSelfAdjointViewReturnType {\n    typedef typename ActualMatrixType::template ConstSelfAdjointViewReturnType<UpLo>::Type Type;\n  };\n\n  enum {\n    MatrixFree = false\n  };\n\n  generic_matrix_wrapper()\n    : m_dummy(0,0), m_matrix(m_dummy)\n  {}\n\n  template<typename InputType>\n  generic_matrix_wrapper(const InputType &mat)\n    : m_matrix(mat)\n  {}\n\n  const ActualMatrixType& matrix() const\n  {\n    return m_matrix;\n  }\n\n  template<typename MatrixDerived>\n  void grab(const EigenBase<MatrixDerived> &mat)\n  {\n    m_matrix.~Ref<const MatrixType>();\n    ::new (&m_matrix) Ref<const MatrixType>(mat.derived());\n  }\n\n  void grab(const Ref<const MatrixType> &mat)\n  {\n    if(&(mat.derived()) != &m_matrix)\n    {\n      m_matrix.~Ref<const MatrixType>();\n      ::new (&m_matrix) Ref<const MatrixType>(mat);\n    }\n  }\n\nprotected:\n  MatrixType m_dummy; // used to default initialize the Ref<> object\n  ActualMatrixType m_matrix;\n};\n\n// MatrixType is not compatible with Ref<> -> matrix-free wrapper\ntemplate<typename MatrixType>\nclass generic_matrix_wrapper<MatrixType,true>\n{\npublic:\n  typedef MatrixType ActualMatrixType;\n  template<int UpLo> struct ConstSelfAdjointViewReturnType\n  {\n    typedef ActualMatrixType Type;\n  };\n\n  enum {\n    MatrixFree = true\n  };\n\n  generic_matrix_wrapper()\n    : mp_matrix(0)\n  {}\n\n  generic_matrix_wrapper(const MatrixType &mat)\n    : mp_matrix(&mat)\n  {}\n\n  const ActualMatrixType& matrix() const\n  {\n    return *mp_matrix;\n  }\n\n  void grab(const MatrixType &mat)\n  {\n    mp_matrix = &mat;\n  }\n\nprotected:\n  const ActualMatrixType *mp_matrix;\n};\n\n}\n\n/** \\ingroup IterativeLinearSolvers_Module\n  * \\brief Base class for linear iterative solvers\n  *\n  * \\sa class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner\n  */\ntemplate< typename Derived>\nclass IterativeSolverBase : public SparseSolverBase<Derived>\n{\nprotected:\n  typedef SparseSolverBase<Derived> Base;\n  using Base::m_isInitialized;\n  \npublic:\n  typedef typename internal::traits<Derived>::MatrixType MatrixType;\n  typedef typename internal::traits<Derived>::Preconditioner Preconditioner;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename MatrixType::StorageIndex StorageIndex;\n  typedef typename MatrixType::RealScalar RealScalar;\n\n  enum {\n    ColsAtCompileTime = MatrixType::ColsAtCompileTime,\n    MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime\n  };\n\npublic:\n\n  using Base::derived;\n\n  /** Default constructor. */\n  IterativeSolverBase()\n  {\n    init();\n  }\n\n  /** Initialize the solver with matrix \\a A for further \\c Ax=b solving.\n    * \n    * This constructor is a shortcut for the default constructor followed\n    * by a call to compute().\n    * \n    * \\warning this class stores a reference to the matrix A as well as some\n    * precomputed values that depend on it. Therefore, if \\a A is changed\n    * this class becomes invalid. Call compute() to update it with the new\n    * matrix A, or modify a copy of A.\n    */\n  template<typename MatrixDerived>\n  explicit IterativeSolverBase(const EigenBase<MatrixDerived>& A)\n    : m_matrixWrapper(A.derived())\n  {\n    init();\n    compute(matrix());\n  }\n\n  ~IterativeSolverBase() {}\n  \n  /** Initializes the iterative solver for the sparsity pattern of the matrix \\a A for further solving \\c Ax=b problems.\n    *\n    * Currently, this function mostly calls analyzePattern on the preconditioner. In the future\n    * we might, for instance, implement column reordering for faster matrix vector products.\n    */\n  template<typename MatrixDerived>\n  Derived& analyzePattern(const EigenBase<MatrixDerived>& A)\n  {\n    grab(A.derived());\n    m_preconditioner.analyzePattern(matrix());\n    m_isInitialized = true;\n    m_analysisIsOk = true;\n    m_info = m_preconditioner.info();\n    return derived();\n  }\n  \n  /** Initializes the iterative solver with the numerical values of the matrix \\a A for further solving \\c Ax=b problems.\n    *\n    * Currently, this function mostly calls factorize on the preconditioner.\n    *\n    * \\warning this class stores a reference to the matrix A as well as some\n    * precomputed values that depend on it. Therefore, if \\a A is changed\n    * this class becomes invalid. Call compute() to update it with the new\n    * matrix A, or modify a copy of A.\n    */\n  template<typename MatrixDerived>\n  Derived& factorize(const EigenBase<MatrixDerived>& A)\n  {\n    eigen_assert(m_analysisIsOk && \"You must first call analyzePattern()\"); \n    grab(A.derived());\n    m_preconditioner.factorize(matrix());\n    m_factorizationIsOk = true;\n    m_info = m_preconditioner.info();\n    return derived();\n  }\n\n  /** Initializes the iterative solver with the matrix \\a A for further solving \\c Ax=b problems.\n    *\n    * Currently, this function mostly initializes/computes the preconditioner. In the future\n    * we might, for instance, implement column reordering for faster matrix vector products.\n    *\n    * \\warning this class stores a reference to the matrix A as well as some\n    * precomputed values that depend on it. Therefore, if \\a A is changed\n    * this class becomes invalid. Call compute() to update it with the new\n    * matrix A, or modify a copy of A.\n    */\n  template<typename MatrixDerived>\n  Derived& compute(const EigenBase<MatrixDerived>& A)\n  {\n    grab(A.derived());\n    m_preconditioner.compute(matrix());\n    m_isInitialized = true;\n    m_analysisIsOk = true;\n    m_factorizationIsOk = true;\n    m_info = m_preconditioner.info();\n    return derived();\n  }\n\n  /** \\internal */\n  Index rows() const { return matrix().rows(); }\n\n  /** \\internal */\n  Index cols() const { return matrix().cols(); }\n\n  /** \\returns the tolerance threshold used by the stopping criteria.\n    * \\sa setTolerance()\n    */\n  RealScalar tolerance() const { return m_tolerance; }\n  \n  /** Sets the tolerance threshold used by the stopping criteria.\n    *\n    * This value is used as an upper bound to the relative residual error: |Ax-b|/|b|.\n    * The default value is the machine precision given by NumTraits<Scalar>::epsilon()\n    */\n  Derived& setTolerance(const RealScalar& tolerance)\n  {\n    m_tolerance = tolerance;\n    return derived();\n  }\n\n  /** \\returns a read-write reference to the preconditioner for custom configuration. */\n  Preconditioner& preconditioner() { return m_preconditioner; }\n  \n  /** \\returns a read-only reference to the preconditioner. */\n  const Preconditioner& preconditioner() const { return m_preconditioner; }\n\n  /** \\returns the max number of iterations.\n    * It is either the value setted by setMaxIterations or, by default,\n    * twice the number of columns of the matrix.\n    */\n  Index maxIterations() const\n  {\n    return (m_maxIterations<0) ? 2*matrix().cols() : m_maxIterations;\n  }\n  \n  /** Sets the max number of iterations.\n    * Default is twice the number of columns of the matrix.\n    */\n  Derived& setMaxIterations(Index maxIters)\n  {\n    m_maxIterations = maxIters;\n    return derived();\n  }\n\n  /** \\returns the number of iterations performed during the last solve */\n  Index iterations() const\n  {\n    eigen_assert(m_isInitialized && \"ConjugateGradient is not initialized.\");\n    return m_iterations;\n  }\n\n  /** \\returns the tolerance error reached during the last solve.\n    * It is a close approximation of the true relative residual error |Ax-b|/|b|.\n    */\n  RealScalar error() const\n  {\n    eigen_assert(m_isInitialized && \"ConjugateGradient is not initialized.\");\n    return m_error;\n  }\n\n  /** \\returns the solution x of \\f$ A x = b \\f$ using the current decomposition of A\n    * and \\a x0 as an initial solution.\n    *\n    * \\sa solve(), compute()\n    */\n  template<typename Rhs,typename Guess>\n  inline const SolveWithGuess<Derived, Rhs, Guess>\n  solveWithGuess(const MatrixBase<Rhs>& b, const Guess& x0) const\n  {\n    eigen_assert(m_isInitialized && \"Solver is not initialized.\");\n    eigen_assert(derived().rows()==b.rows() && \"solve(): invalid number of rows of the right hand side matrix b\");\n    return SolveWithGuess<Derived, Rhs, Guess>(derived(), b.derived(), x0);\n  }\n\n  /** \\returns Success if the iterations converged, and NoConvergence otherwise. */\n  ComputationInfo info() const\n  {\n    eigen_assert(m_isInitialized && \"IterativeSolverBase is not initialized.\");\n    return m_info;\n  }\n  \n  /** \\internal */\n  template<typename Rhs, typename DestDerived>\n  void _solve_impl(const Rhs& b, SparseMatrixBase<DestDerived> &aDest) const\n  {\n    eigen_assert(rows()==b.rows());\n    \n    Index rhsCols = b.cols();\n    Index size = b.rows();\n    DestDerived& dest(aDest.derived());\n    typedef typename DestDerived::Scalar DestScalar;\n    Eigen::Matrix<DestScalar,Dynamic,1> tb(size);\n    Eigen::Matrix<DestScalar,Dynamic,1> tx(cols());\n    // We do not directly fill dest because sparse expressions have to be free of aliasing issue.\n    // For non square least-square problems, b and dest might not have the same size whereas they might alias each-other.\n    typename DestDerived::PlainObject tmp(cols(),rhsCols);\n    for(Index k=0; k<rhsCols; ++k)\n    {\n      tb = b.col(k);\n      tx = derived().solve(tb);\n      tmp.col(k) = tx.sparseView(0);\n    }\n    dest.swap(tmp);\n  }\n\nprotected:\n  void init()\n  {\n    m_isInitialized = false;\n    m_analysisIsOk = false;\n    m_factorizationIsOk = false;\n    m_maxIterations = -1;\n    m_tolerance = NumTraits<Scalar>::epsilon();\n  }\n\n  typedef internal::generic_matrix_wrapper<MatrixType> MatrixWrapper;\n  typedef typename MatrixWrapper::ActualMatrixType ActualMatrixType;\n\n  const ActualMatrixType& matrix() const\n  {\n    return m_matrixWrapper.matrix();\n  }\n  \n  template<typename InputType>\n  void grab(const InputType &A)\n  {\n    m_matrixWrapper.grab(A);\n  }\n  \n  MatrixWrapper m_matrixWrapper;\n  Preconditioner m_preconditioner;\n\n  Index m_maxIterations;\n  RealScalar m_tolerance;\n  \n  mutable RealScalar m_error;\n  mutable Index m_iterations;\n  mutable ComputationInfo m_info;\n  mutable bool m_analysisIsOk, m_factorizationIsOk;\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_ITERATIVE_SOLVER_BASE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/IterativeLinearSolvers/LeastSquareConjugateGradient.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_LEAST_SQUARE_CONJUGATE_GRADIENT_H\n#define EIGEN_LEAST_SQUARE_CONJUGATE_GRADIENT_H\n\nnamespace Eigen { \n\nnamespace internal {\n\n/** \\internal Low-level conjugate gradient algorithm for least-square problems\n  * \\param mat The matrix A\n  * \\param rhs The right hand side vector b\n  * \\param x On input and initial solution, on output the computed solution.\n  * \\param precond A preconditioner being able to efficiently solve for an\n  *                approximation of A'Ax=b (regardless of b)\n  * \\param iters On input the max number of iteration, on output the number of performed iterations.\n  * \\param tol_error On input the tolerance error, on output an estimation of the relative error.\n  */\ntemplate<typename MatrixType, typename Rhs, typename Dest, typename Preconditioner>\nEIGEN_DONT_INLINE\nvoid least_square_conjugate_gradient(const MatrixType& mat, const Rhs& rhs, Dest& x,\n                                     const Preconditioner& precond, Index& iters,\n                                     typename Dest::RealScalar& tol_error)\n{\n  using std::sqrt;\n  using std::abs;\n  typedef typename Dest::RealScalar RealScalar;\n  typedef typename Dest::Scalar Scalar;\n  typedef Matrix<Scalar,Dynamic,1> VectorType;\n  \n  RealScalar tol = tol_error;\n  Index maxIters = iters;\n  \n  Index m = mat.rows(), n = mat.cols();\n\n  VectorType residual        = rhs - mat * x;\n  VectorType normal_residual = mat.adjoint() * residual;\n\n  RealScalar rhsNorm2 = (mat.adjoint()*rhs).squaredNorm();\n  if(rhsNorm2 == 0) \n  {\n    x.setZero();\n    iters = 0;\n    tol_error = 0;\n    return;\n  }\n  RealScalar threshold = tol*tol*rhsNorm2;\n  RealScalar residualNorm2 = normal_residual.squaredNorm();\n  if (residualNorm2 < threshold)\n  {\n    iters = 0;\n    tol_error = sqrt(residualNorm2 / rhsNorm2);\n    return;\n  }\n  \n  VectorType p(n);\n  p = precond.solve(normal_residual);                         // initial search direction\n\n  VectorType z(n), tmp(m);\n  RealScalar absNew = numext::real(normal_residual.dot(p));  // the square of the absolute value of r scaled by invM\n  Index i = 0;\n  while(i < maxIters)\n  {\n    tmp.noalias() = mat * p;\n\n    Scalar alpha = absNew / tmp.squaredNorm();      // the amount we travel on dir\n    x += alpha * p;                                 // update solution\n    residual -= alpha * tmp;                        // update residual\n    normal_residual = mat.adjoint() * residual;     // update residual of the normal equation\n    \n    residualNorm2 = normal_residual.squaredNorm();\n    if(residualNorm2 < threshold)\n      break;\n    \n    z = precond.solve(normal_residual);             // approximately solve for \"A'A z = normal_residual\"\n\n    RealScalar absOld = absNew;\n    absNew = numext::real(normal_residual.dot(z));  // update the absolute value of r\n    RealScalar beta = absNew / absOld;              // calculate the Gram-Schmidt value used to create the new search direction\n    p = z + beta * p;                               // update search direction\n    i++;\n  }\n  tol_error = sqrt(residualNorm2 / rhsNorm2);\n  iters = i;\n}\n\n}\n\ntemplate< typename _MatrixType,\n          typename _Preconditioner = LeastSquareDiagonalPreconditioner<typename _MatrixType::Scalar> >\nclass LeastSquaresConjugateGradient;\n\nnamespace internal {\n\ntemplate< typename _MatrixType, typename _Preconditioner>\nstruct traits<LeastSquaresConjugateGradient<_MatrixType,_Preconditioner> >\n{\n  typedef _MatrixType MatrixType;\n  typedef _Preconditioner Preconditioner;\n};\n\n}\n\n/** \\ingroup IterativeLinearSolvers_Module\n  * \\brief A conjugate gradient solver for sparse (or dense) least-square problems\n  *\n  * This class allows to solve for A x = b linear problems using an iterative conjugate gradient algorithm.\n  * The matrix A can be non symmetric and rectangular, but the matrix A' A should be positive-definite to guaranty stability.\n  * Otherwise, the SparseLU or SparseQR classes might be preferable.\n  * The matrix A and the vectors x and b can be either dense or sparse.\n  *\n  * \\tparam _MatrixType the type of the matrix A, can be a dense or a sparse matrix.\n  * \\tparam _Preconditioner the type of the preconditioner. Default is LeastSquareDiagonalPreconditioner\n  *\n  * \\implsparsesolverconcept\n  * \n  * The maximal number of iterations and tolerance value can be controlled via the setMaxIterations()\n  * and setTolerance() methods. The defaults are the size of the problem for the maximal number of iterations\n  * and NumTraits<Scalar>::epsilon() for the tolerance.\n  * \n  * This class can be used as the direct solver classes. Here is a typical usage example:\n    \\code\n    int m=1000000, n = 10000;\n    VectorXd x(n), b(m);\n    SparseMatrix<double> A(m,n);\n    // fill A and b\n    LeastSquaresConjugateGradient<SparseMatrix<double> > lscg;\n    lscg.compute(A);\n    x = lscg.solve(b);\n    std::cout << \"#iterations:     \" << lscg.iterations() << std::endl;\n    std::cout << \"estimated error: \" << lscg.error()      << std::endl;\n    // update b, and solve again\n    x = lscg.solve(b);\n    \\endcode\n  * \n  * By default the iterations start with x=0 as an initial guess of the solution.\n  * One can control the start using the solveWithGuess() method.\n  * \n  * \\sa class ConjugateGradient, SparseLU, SparseQR\n  */\ntemplate< typename _MatrixType, typename _Preconditioner>\nclass LeastSquaresConjugateGradient : public IterativeSolverBase<LeastSquaresConjugateGradient<_MatrixType,_Preconditioner> >\n{\n  typedef IterativeSolverBase<LeastSquaresConjugateGradient> Base;\n  using Base::matrix;\n  using Base::m_error;\n  using Base::m_iterations;\n  using Base::m_info;\n  using Base::m_isInitialized;\npublic:\n  typedef _MatrixType MatrixType;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename MatrixType::RealScalar RealScalar;\n  typedef _Preconditioner Preconditioner;\n\npublic:\n\n  /** Default constructor. */\n  LeastSquaresConjugateGradient() : Base() {}\n\n  /** Initialize the solver with matrix \\a A for further \\c Ax=b solving.\n    * \n    * This constructor is a shortcut for the default constructor followed\n    * by a call to compute().\n    * \n    * \\warning this class stores a reference to the matrix A as well as some\n    * precomputed values that depend on it. Therefore, if \\a A is changed\n    * this class becomes invalid. Call compute() to update it with the new\n    * matrix A, or modify a copy of A.\n    */\n  template<typename MatrixDerived>\n  explicit LeastSquaresConjugateGradient(const EigenBase<MatrixDerived>& A) : Base(A.derived()) {}\n\n  ~LeastSquaresConjugateGradient() {}\n\n  /** \\internal */\n  template<typename Rhs,typename Dest>\n  void _solve_with_guess_impl(const Rhs& b, Dest& x) const\n  {\n    m_iterations = Base::maxIterations();\n    m_error = Base::m_tolerance;\n\n    for(Index j=0; j<b.cols(); ++j)\n    {\n      m_iterations = Base::maxIterations();\n      m_error = Base::m_tolerance;\n\n      typename Dest::ColXpr xj(x,j);\n      internal::least_square_conjugate_gradient(matrix(), b.col(j), xj, Base::m_preconditioner, m_iterations, m_error);\n    }\n\n    m_isInitialized = true;\n    m_info = m_error <= Base::m_tolerance ? Success : NoConvergence;\n  }\n  \n  /** \\internal */\n  using Base::_solve_impl;\n  template<typename Rhs,typename Dest>\n  void _solve_impl(const MatrixBase<Rhs>& b, Dest& x) const\n  {\n    x.setZero();\n    _solve_with_guess_impl(b.derived(),x);\n  }\n\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_LEAST_SQUARE_CONJUGATE_GRADIENT_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/IterativeLinearSolvers/SolveWithGuess.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SOLVEWITHGUESS_H\n#define EIGEN_SOLVEWITHGUESS_H\n\nnamespace Eigen {\n\ntemplate<typename Decomposition, typename RhsType, typename GuessType> class SolveWithGuess;\n  \n/** \\class SolveWithGuess\n  * \\ingroup IterativeLinearSolvers_Module\n  *\n  * \\brief Pseudo expression representing a solving operation\n  *\n  * \\tparam Decomposition the type of the matrix or decomposion object\n  * \\tparam Rhstype the type of the right-hand side\n  *\n  * This class represents an expression of A.solve(B)\n  * and most of the time this is the only way it is used.\n  *\n  */\nnamespace internal {\n\n\ntemplate<typename Decomposition, typename RhsType, typename GuessType>\nstruct traits<SolveWithGuess<Decomposition, RhsType, GuessType> >\n  : traits<Solve<Decomposition,RhsType> >\n{};\n\n}\n\n\ntemplate<typename Decomposition, typename RhsType, typename GuessType>\nclass SolveWithGuess : public internal::generic_xpr_base<SolveWithGuess<Decomposition,RhsType,GuessType>, MatrixXpr, typename internal::traits<RhsType>::StorageKind>::type\n{\npublic:\n  typedef typename internal::traits<SolveWithGuess>::Scalar Scalar;\n  typedef typename internal::traits<SolveWithGuess>::PlainObject PlainObject;\n  typedef typename internal::generic_xpr_base<SolveWithGuess<Decomposition,RhsType,GuessType>, MatrixXpr, typename internal::traits<RhsType>::StorageKind>::type Base;\n  typedef typename internal::ref_selector<SolveWithGuess>::type Nested;\n  \n  SolveWithGuess(const Decomposition &dec, const RhsType &rhs, const GuessType &guess)\n    : m_dec(dec), m_rhs(rhs), m_guess(guess)\n  {}\n  \n  EIGEN_DEVICE_FUNC Index rows() const { return m_dec.cols(); }\n  EIGEN_DEVICE_FUNC Index cols() const { return m_rhs.cols(); }\n\n  EIGEN_DEVICE_FUNC const Decomposition& dec()   const { return m_dec; }\n  EIGEN_DEVICE_FUNC const RhsType&       rhs()   const { return m_rhs; }\n  EIGEN_DEVICE_FUNC const GuessType&     guess() const { return m_guess; }\n\nprotected:\n  const Decomposition &m_dec;\n  const RhsType       &m_rhs;\n  const GuessType     &m_guess;\n  \nprivate:\n  Scalar coeff(Index row, Index col) const;\n  Scalar coeff(Index i) const;\n};\n\nnamespace internal {\n\n// Evaluator of SolveWithGuess -> eval into a temporary\ntemplate<typename Decomposition, typename RhsType, typename GuessType>\nstruct evaluator<SolveWithGuess<Decomposition,RhsType, GuessType> >\n  : public evaluator<typename SolveWithGuess<Decomposition,RhsType,GuessType>::PlainObject>\n{\n  typedef SolveWithGuess<Decomposition,RhsType,GuessType> SolveType;\n  typedef typename SolveType::PlainObject PlainObject;\n  typedef evaluator<PlainObject> Base;\n\n  evaluator(const SolveType& solve)\n    : m_result(solve.rows(), solve.cols())\n  {\n    ::new (static_cast<Base*>(this)) Base(m_result);\n    m_result = solve.guess();\n    solve.dec()._solve_with_guess_impl(solve.rhs(), m_result);\n  }\n  \nprotected:  \n  PlainObject m_result;\n};\n\n// Specialization for \"dst = dec.solveWithGuess(rhs)\"\n// NOTE we need to specialize it for Dense2Dense to avoid ambiguous specialization error and a Sparse2Sparse specialization must exist somewhere\ntemplate<typename DstXprType, typename DecType, typename RhsType, typename GuessType, typename Scalar>\nstruct Assignment<DstXprType, SolveWithGuess<DecType,RhsType,GuessType>, internal::assign_op<Scalar,Scalar>, Dense2Dense>\n{\n  typedef SolveWithGuess<DecType,RhsType,GuessType> SrcXprType;\n  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &)\n  {\n    Index dstRows = src.rows();\n    Index dstCols = src.cols();\n    if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))\n      dst.resize(dstRows, dstCols);\n\n    dst = src.guess();\n    src.dec()._solve_with_guess_impl(src.rhs(), dst/*, src.guess()*/);\n  }\n};\n\n} // end namepsace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_SOLVEWITHGUESS_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/Jacobi/Jacobi.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_JACOBI_H\n#define EIGEN_JACOBI_H\n\nnamespace Eigen { \n\n/** \\ingroup Jacobi_Module\n  * \\jacobi_module\n  * \\class JacobiRotation\n  * \\brief Rotation given by a cosine-sine pair.\n  *\n  * This class represents a Jacobi or Givens rotation.\n  * This is a 2D rotation in the plane \\c J of angle \\f$ \\theta \\f$ defined by\n  * its cosine \\c c and sine \\c s as follow:\n  * \\f$ J = \\left ( \\begin{array}{cc} c & \\overline s \\\\ -s  & \\overline c \\end{array} \\right ) \\f$\n  *\n  * You can apply the respective counter-clockwise rotation to a column vector \\c v by\n  * applying its adjoint on the left: \\f$ v = J^* v \\f$ that translates to the following Eigen code:\n  * \\code\n  * v.applyOnTheLeft(J.adjoint());\n  * \\endcode\n  *\n  * \\sa MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()\n  */\ntemplate<typename Scalar> class JacobiRotation\n{\n  public:\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n\n    /** Default constructor without any initialization. */\n    JacobiRotation() {}\n\n    /** Construct a planar rotation from a cosine-sine pair (\\a c, \\c s). */\n    JacobiRotation(const Scalar& c, const Scalar& s) : m_c(c), m_s(s) {}\n\n    Scalar& c() { return m_c; }\n    Scalar c() const { return m_c; }\n    Scalar& s() { return m_s; }\n    Scalar s() const { return m_s; }\n\n    /** Concatenates two planar rotation */\n    JacobiRotation operator*(const JacobiRotation& other)\n    {\n      using numext::conj;\n      return JacobiRotation(m_c * other.m_c - conj(m_s) * other.m_s,\n                            conj(m_c * conj(other.m_s) + conj(m_s) * conj(other.m_c)));\n    }\n\n    /** Returns the transposed transformation */\n    JacobiRotation transpose() const { using numext::conj; return JacobiRotation(m_c, -conj(m_s)); }\n\n    /** Returns the adjoint transformation */\n    JacobiRotation adjoint() const { using numext::conj; return JacobiRotation(conj(m_c), -m_s); }\n\n    template<typename Derived>\n    bool makeJacobi(const MatrixBase<Derived>&, Index p, Index q);\n    bool makeJacobi(const RealScalar& x, const Scalar& y, const RealScalar& z);\n\n    void makeGivens(const Scalar& p, const Scalar& q, Scalar* z=0);\n\n  protected:\n    void makeGivens(const Scalar& p, const Scalar& q, Scalar* z, internal::true_type);\n    void makeGivens(const Scalar& p, const Scalar& q, Scalar* z, internal::false_type);\n\n    Scalar m_c, m_s;\n};\n\n/** Makes \\c *this as a Jacobi rotation \\a J such that applying \\a J on both the right and left sides of the selfadjoint 2x2 matrix\n  * \\f$ B = \\left ( \\begin{array}{cc} x & y \\\\ \\overline y & z \\end{array} \\right )\\f$ yields a diagonal matrix \\f$ A = J^* B J \\f$\n  *\n  * \\sa MatrixBase::makeJacobi(const MatrixBase<Derived>&, Index, Index), MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()\n  */\ntemplate<typename Scalar>\nbool JacobiRotation<Scalar>::makeJacobi(const RealScalar& x, const Scalar& y, const RealScalar& z)\n{\n  using std::sqrt;\n  using std::abs;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  RealScalar deno = RealScalar(2)*abs(y);\n  if(deno < (std::numeric_limits<RealScalar>::min)())\n  {\n    m_c = Scalar(1);\n    m_s = Scalar(0);\n    return false;\n  }\n  else\n  {\n    RealScalar tau = (x-z)/deno;\n    RealScalar w = sqrt(numext::abs2(tau) + RealScalar(1));\n    RealScalar t;\n    if(tau>RealScalar(0))\n    {\n      t = RealScalar(1) / (tau + w);\n    }\n    else\n    {\n      t = RealScalar(1) / (tau - w);\n    }\n    RealScalar sign_t = t > RealScalar(0) ? RealScalar(1) : RealScalar(-1);\n    RealScalar n = RealScalar(1) / sqrt(numext::abs2(t)+RealScalar(1));\n    m_s = - sign_t * (numext::conj(y) / abs(y)) * abs(t) * n;\n    m_c = n;\n    return true;\n  }\n}\n\n/** Makes \\c *this as a Jacobi rotation \\c J such that applying \\a J on both the right and left sides of the 2x2 selfadjoint matrix\n  * \\f$ B = \\left ( \\begin{array}{cc} \\text{this}_{pp} & \\text{this}_{pq} \\\\ (\\text{this}_{pq})^* & \\text{this}_{qq} \\end{array} \\right )\\f$ yields\n  * a diagonal matrix \\f$ A = J^* B J \\f$\n  *\n  * Example: \\include Jacobi_makeJacobi.cpp\n  * Output: \\verbinclude Jacobi_makeJacobi.out\n  *\n  * \\sa JacobiRotation::makeJacobi(RealScalar, Scalar, RealScalar), MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()\n  */\ntemplate<typename Scalar>\ntemplate<typename Derived>\ninline bool JacobiRotation<Scalar>::makeJacobi(const MatrixBase<Derived>& m, Index p, Index q)\n{\n  return makeJacobi(numext::real(m.coeff(p,p)), m.coeff(p,q), numext::real(m.coeff(q,q)));\n}\n\n/** Makes \\c *this as a Givens rotation \\c G such that applying \\f$ G^* \\f$ to the left of the vector\n  * \\f$ V = \\left ( \\begin{array}{c} p \\\\ q \\end{array} \\right )\\f$ yields:\n  * \\f$ G^* V = \\left ( \\begin{array}{c} r \\\\ 0 \\end{array} \\right )\\f$.\n  *\n  * The value of \\a z is returned if \\a z is not null (the default is null).\n  * Also note that G is built such that the cosine is always real.\n  *\n  * Example: \\include Jacobi_makeGivens.cpp\n  * Output: \\verbinclude Jacobi_makeGivens.out\n  *\n  * This function implements the continuous Givens rotation generation algorithm\n  * found in Anderson (2000), Discontinuous Plane Rotations and the Symmetric Eigenvalue Problem.\n  * LAPACK Working Note 150, University of Tennessee, UT-CS-00-454, December 4, 2000.\n  *\n  * \\sa MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()\n  */\ntemplate<typename Scalar>\nvoid JacobiRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar* z)\n{\n  makeGivens(p, q, z, typename internal::conditional<NumTraits<Scalar>::IsComplex, internal::true_type, internal::false_type>::type());\n}\n\n\n// specialization for complexes\ntemplate<typename Scalar>\nvoid JacobiRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar* r, internal::true_type)\n{\n  using std::sqrt;\n  using std::abs;\n  using numext::conj;\n  \n  if(q==Scalar(0))\n  {\n    m_c = numext::real(p)<0 ? Scalar(-1) : Scalar(1);\n    m_s = 0;\n    if(r) *r = m_c * p;\n  }\n  else if(p==Scalar(0))\n  {\n    m_c = 0;\n    m_s = -q/abs(q);\n    if(r) *r = abs(q);\n  }\n  else\n  {\n    RealScalar p1 = numext::norm1(p);\n    RealScalar q1 = numext::norm1(q);\n    if(p1>=q1)\n    {\n      Scalar ps = p / p1;\n      RealScalar p2 = numext::abs2(ps);\n      Scalar qs = q / p1;\n      RealScalar q2 = numext::abs2(qs);\n\n      RealScalar u = sqrt(RealScalar(1) + q2/p2);\n      if(numext::real(p)<RealScalar(0))\n        u = -u;\n\n      m_c = Scalar(1)/u;\n      m_s = -qs*conj(ps)*(m_c/p2);\n      if(r) *r = p * u;\n    }\n    else\n    {\n      Scalar ps = p / q1;\n      RealScalar p2 = numext::abs2(ps);\n      Scalar qs = q / q1;\n      RealScalar q2 = numext::abs2(qs);\n\n      RealScalar u = q1 * sqrt(p2 + q2);\n      if(numext::real(p)<RealScalar(0))\n        u = -u;\n\n      p1 = abs(p);\n      ps = p/p1;\n      m_c = p1/u;\n      m_s = -conj(ps) * (q/u);\n      if(r) *r = ps * u;\n    }\n  }\n}\n\n// specialization for reals\ntemplate<typename Scalar>\nvoid JacobiRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar* r, internal::false_type)\n{\n  using std::sqrt;\n  using std::abs;\n  if(q==Scalar(0))\n  {\n    m_c = p<Scalar(0) ? Scalar(-1) : Scalar(1);\n    m_s = Scalar(0);\n    if(r) *r = abs(p);\n  }\n  else if(p==Scalar(0))\n  {\n    m_c = Scalar(0);\n    m_s = q<Scalar(0) ? Scalar(1) : Scalar(-1);\n    if(r) *r = abs(q);\n  }\n  else if(abs(p) > abs(q))\n  {\n    Scalar t = q/p;\n    Scalar u = sqrt(Scalar(1) + numext::abs2(t));\n    if(p<Scalar(0))\n      u = -u;\n    m_c = Scalar(1)/u;\n    m_s = -t * m_c;\n    if(r) *r = p * u;\n  }\n  else\n  {\n    Scalar t = p/q;\n    Scalar u = sqrt(Scalar(1) + numext::abs2(t));\n    if(q<Scalar(0))\n      u = -u;\n    m_s = -Scalar(1)/u;\n    m_c = -t * m_s;\n    if(r) *r = q * u;\n  }\n\n}\n\n/****************************************************************************************\n*   Implementation of MatrixBase methods\n****************************************************************************************/\n\nnamespace internal {\n/** \\jacobi_module\n  * Applies the clock wise 2D rotation \\a j to the set of 2D vectors of cordinates \\a x and \\a y:\n  * \\f$ \\left ( \\begin{array}{cc} x \\\\ y \\end{array} \\right )  =  J \\left ( \\begin{array}{cc} x \\\\ y \\end{array} \\right ) \\f$\n  *\n  * \\sa MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()\n  */\ntemplate<typename VectorX, typename VectorY, typename OtherScalar>\nvoid apply_rotation_in_the_plane(DenseBase<VectorX>& xpr_x, DenseBase<VectorY>& xpr_y, const JacobiRotation<OtherScalar>& j);\n}\n\n/** \\jacobi_module\n  * Applies the rotation in the plane \\a j to the rows \\a p and \\a q of \\c *this, i.e., it computes B = J * B,\n  * with \\f$ B = \\left ( \\begin{array}{cc} \\text{*this.row}(p) \\\\ \\text{*this.row}(q) \\end{array} \\right ) \\f$.\n  *\n  * \\sa class JacobiRotation, MatrixBase::applyOnTheRight(), internal::apply_rotation_in_the_plane()\n  */\ntemplate<typename Derived>\ntemplate<typename OtherScalar>\ninline void MatrixBase<Derived>::applyOnTheLeft(Index p, Index q, const JacobiRotation<OtherScalar>& j)\n{\n  RowXpr x(this->row(p));\n  RowXpr y(this->row(q));\n  internal::apply_rotation_in_the_plane(x, y, j);\n}\n\n/** \\ingroup Jacobi_Module\n  * Applies the rotation in the plane \\a j to the columns \\a p and \\a q of \\c *this, i.e., it computes B = B * J\n  * with \\f$ B = \\left ( \\begin{array}{cc} \\text{*this.col}(p) & \\text{*this.col}(q) \\end{array} \\right ) \\f$.\n  *\n  * \\sa class JacobiRotation, MatrixBase::applyOnTheLeft(), internal::apply_rotation_in_the_plane()\n  */\ntemplate<typename Derived>\ntemplate<typename OtherScalar>\ninline void MatrixBase<Derived>::applyOnTheRight(Index p, Index q, const JacobiRotation<OtherScalar>& j)\n{\n  ColXpr x(this->col(p));\n  ColXpr y(this->col(q));\n  internal::apply_rotation_in_the_plane(x, y, j.transpose());\n}\n\nnamespace internal {\n\ntemplate<typename Scalar, typename OtherScalar,\n         int SizeAtCompileTime, int MinAlignment, bool Vectorizable>\nstruct apply_rotation_in_the_plane_selector\n{\n  static inline void run(Scalar *x, Index incrx, Scalar *y, Index incry, Index size, OtherScalar c, OtherScalar s)\n  {\n    for(Index i=0; i<size; ++i)\n    {\n      Scalar xi = *x;\n      Scalar yi = *y;\n      *x =  c * xi + numext::conj(s) * yi;\n      *y = -s * xi + numext::conj(c) * yi;\n      x += incrx;\n      y += incry;\n    }\n  }\n};\n\ntemplate<typename Scalar, typename OtherScalar,\n         int SizeAtCompileTime, int MinAlignment>\nstruct apply_rotation_in_the_plane_selector<Scalar,OtherScalar,SizeAtCompileTime,MinAlignment,true /* vectorizable */>\n{\n  static inline void run(Scalar *x, Index incrx, Scalar *y, Index incry, Index size, OtherScalar c, OtherScalar s)\n  {\n    enum {\n      PacketSize = packet_traits<Scalar>::size,\n      OtherPacketSize = packet_traits<OtherScalar>::size\n    };\n    typedef typename packet_traits<Scalar>::type Packet;\n    typedef typename packet_traits<OtherScalar>::type OtherPacket;\n\n    /*** dynamic-size vectorized paths ***/\n    if(SizeAtCompileTime == Dynamic && ((incrx==1 && incry==1) || PacketSize == 1))\n    {\n      // both vectors are sequentially stored in memory => vectorization\n      enum { Peeling = 2 };\n\n      Index alignedStart = internal::first_default_aligned(y, size);\n      Index alignedEnd = alignedStart + ((size-alignedStart)/PacketSize)*PacketSize;\n\n      const OtherPacket pc = pset1<OtherPacket>(c);\n      const OtherPacket ps = pset1<OtherPacket>(s);\n      conj_helper<OtherPacket,Packet,NumTraits<OtherScalar>::IsComplex,false> pcj;\n      conj_helper<OtherPacket,Packet,false,false> pm;\n\n      for(Index i=0; i<alignedStart; ++i)\n      {\n        Scalar xi = x[i];\n        Scalar yi = y[i];\n        x[i] =  c * xi + numext::conj(s) * yi;\n        y[i] = -s * xi + numext::conj(c) * yi;\n      }\n\n      Scalar* EIGEN_RESTRICT px = x + alignedStart;\n      Scalar* EIGEN_RESTRICT py = y + alignedStart;\n\n      if(internal::first_default_aligned(x, size)==alignedStart)\n      {\n        for(Index i=alignedStart; i<alignedEnd; i+=PacketSize)\n        {\n          Packet xi = pload<Packet>(px);\n          Packet yi = pload<Packet>(py);\n          pstore(px, padd(pm.pmul(pc,xi),pcj.pmul(ps,yi)));\n          pstore(py, psub(pcj.pmul(pc,yi),pm.pmul(ps,xi)));\n          px += PacketSize;\n          py += PacketSize;\n        }\n      }\n      else\n      {\n        Index peelingEnd = alignedStart + ((size-alignedStart)/(Peeling*PacketSize))*(Peeling*PacketSize);\n        for(Index i=alignedStart; i<peelingEnd; i+=Peeling*PacketSize)\n        {\n          Packet xi   = ploadu<Packet>(px);\n          Packet xi1  = ploadu<Packet>(px+PacketSize);\n          Packet yi   = pload <Packet>(py);\n          Packet yi1  = pload <Packet>(py+PacketSize);\n          pstoreu(px, padd(pm.pmul(pc,xi),pcj.pmul(ps,yi)));\n          pstoreu(px+PacketSize, padd(pm.pmul(pc,xi1),pcj.pmul(ps,yi1)));\n          pstore (py, psub(pcj.pmul(pc,yi),pm.pmul(ps,xi)));\n          pstore (py+PacketSize, psub(pcj.pmul(pc,yi1),pm.pmul(ps,xi1)));\n          px += Peeling*PacketSize;\n          py += Peeling*PacketSize;\n        }\n        if(alignedEnd!=peelingEnd)\n        {\n          Packet xi = ploadu<Packet>(x+peelingEnd);\n          Packet yi = pload <Packet>(y+peelingEnd);\n          pstoreu(x+peelingEnd, padd(pm.pmul(pc,xi),pcj.pmul(ps,yi)));\n          pstore (y+peelingEnd, psub(pcj.pmul(pc,yi),pm.pmul(ps,xi)));\n        }\n      }\n\n      for(Index i=alignedEnd; i<size; ++i)\n      {\n        Scalar xi = x[i];\n        Scalar yi = y[i];\n        x[i] =  c * xi + numext::conj(s) * yi;\n        y[i] = -s * xi + numext::conj(c) * yi;\n      }\n    }\n\n    /*** fixed-size vectorized path ***/\n    else if(SizeAtCompileTime != Dynamic && MinAlignment>0) // FIXME should be compared to the required alignment\n    {\n      const OtherPacket pc = pset1<OtherPacket>(c);\n      const OtherPacket ps = pset1<OtherPacket>(s);\n      conj_helper<OtherPacket,Packet,NumTraits<OtherPacket>::IsComplex,false> pcj;\n      conj_helper<OtherPacket,Packet,false,false> pm;\n      Scalar* EIGEN_RESTRICT px = x;\n      Scalar* EIGEN_RESTRICT py = y;\n      for(Index i=0; i<size; i+=PacketSize)\n      {\n        Packet xi = pload<Packet>(px);\n        Packet yi = pload<Packet>(py);\n        pstore(px, padd(pm.pmul(pc,xi),pcj.pmul(ps,yi)));\n        pstore(py, psub(pcj.pmul(pc,yi),pm.pmul(ps,xi)));\n        px += PacketSize;\n        py += PacketSize;\n      }\n    }\n\n    /*** non-vectorized path ***/\n    else\n    {\n      apply_rotation_in_the_plane_selector<Scalar,OtherScalar,SizeAtCompileTime,MinAlignment,false>::run(x,incrx,y,incry,size,c,s);\n    }\n  }\n};\n\ntemplate<typename VectorX, typename VectorY, typename OtherScalar>\nvoid /*EIGEN_DONT_INLINE*/ apply_rotation_in_the_plane(DenseBase<VectorX>& xpr_x, DenseBase<VectorY>& xpr_y, const JacobiRotation<OtherScalar>& j)\n{\n  typedef typename VectorX::Scalar Scalar;\n  const bool Vectorizable =    (VectorX::Flags & VectorY::Flags & PacketAccessBit)\n                            && (int(packet_traits<Scalar>::size) == int(packet_traits<OtherScalar>::size));\n\n  eigen_assert(xpr_x.size() == xpr_y.size());\n  Index size = xpr_x.size();\n  Index incrx = xpr_x.derived().innerStride();\n  Index incry = xpr_y.derived().innerStride();\n\n  Scalar* EIGEN_RESTRICT x = &xpr_x.derived().coeffRef(0);\n  Scalar* EIGEN_RESTRICT y = &xpr_y.derived().coeffRef(0);\n  \n  OtherScalar c = j.c();\n  OtherScalar s = j.s();\n  if (c==OtherScalar(1) && s==OtherScalar(0))\n    return;\n\n  apply_rotation_in_the_plane_selector<\n    Scalar,OtherScalar,\n    VectorX::SizeAtCompileTime,\n    EIGEN_PLAIN_ENUM_MIN(evaluator<VectorX>::Alignment, evaluator<VectorY>::Alignment),\n    Vectorizable>::run(x,incrx,y,incry,size,c,s);\n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_JACOBI_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/LU/Determinant.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_DETERMINANT_H\n#define EIGEN_DETERMINANT_H\n\nnamespace Eigen { \n\nnamespace internal {\n\ntemplate<typename Derived>\ninline const typename Derived::Scalar bruteforce_det3_helper\n(const MatrixBase<Derived>& matrix, int a, int b, int c)\n{\n  return matrix.coeff(0,a)\n         * (matrix.coeff(1,b) * matrix.coeff(2,c) - matrix.coeff(1,c) * matrix.coeff(2,b));\n}\n\ntemplate<typename Derived>\nconst typename Derived::Scalar bruteforce_det4_helper\n(const MatrixBase<Derived>& matrix, int j, int k, int m, int n)\n{\n  return (matrix.coeff(j,0) * matrix.coeff(k,1) - matrix.coeff(k,0) * matrix.coeff(j,1))\n       * (matrix.coeff(m,2) * matrix.coeff(n,3) - matrix.coeff(n,2) * matrix.coeff(m,3));\n}\n\ntemplate<typename Derived,\n         int DeterminantType = Derived::RowsAtCompileTime\n> struct determinant_impl\n{\n  static inline typename traits<Derived>::Scalar run(const Derived& m)\n  {\n    if(Derived::ColsAtCompileTime==Dynamic && m.rows()==0)\n      return typename traits<Derived>::Scalar(1);\n    return m.partialPivLu().determinant();\n  }\n};\n\ntemplate<typename Derived> struct determinant_impl<Derived, 1>\n{\n  static inline typename traits<Derived>::Scalar run(const Derived& m)\n  {\n    return m.coeff(0,0);\n  }\n};\n\ntemplate<typename Derived> struct determinant_impl<Derived, 2>\n{\n  static inline typename traits<Derived>::Scalar run(const Derived& m)\n  {\n    return m.coeff(0,0) * m.coeff(1,1) - m.coeff(1,0) * m.coeff(0,1);\n  }\n};\n\ntemplate<typename Derived> struct determinant_impl<Derived, 3>\n{\n  static inline typename traits<Derived>::Scalar run(const Derived& m)\n  {\n    return bruteforce_det3_helper(m,0,1,2)\n          - bruteforce_det3_helper(m,1,0,2)\n          + bruteforce_det3_helper(m,2,0,1);\n  }\n};\n\ntemplate<typename Derived> struct determinant_impl<Derived, 4>\n{\n  static typename traits<Derived>::Scalar run(const Derived& m)\n  {\n    // trick by Martin Costabel to compute 4x4 det with only 30 muls\n    return bruteforce_det4_helper(m,0,1,2,3)\n          - bruteforce_det4_helper(m,0,2,1,3)\n          + bruteforce_det4_helper(m,0,3,1,2)\n          + bruteforce_det4_helper(m,1,2,0,3)\n          - bruteforce_det4_helper(m,1,3,0,2)\n          + bruteforce_det4_helper(m,2,3,0,1);\n  }\n};\n\n} // end namespace internal\n\n/** \\lu_module\n  *\n  * \\returns the determinant of this matrix\n  */\ntemplate<typename Derived>\ninline typename internal::traits<Derived>::Scalar MatrixBase<Derived>::determinant() const\n{\n  eigen_assert(rows() == cols());\n  typedef typename internal::nested_eval<Derived,Base::RowsAtCompileTime>::type Nested;\n  return internal::determinant_impl<typename internal::remove_all<Nested>::type>::run(derived());\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_DETERMINANT_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/LU/FullPivLU.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2006-2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_LU_H\n#define EIGEN_LU_H\n\nnamespace Eigen {\n\nnamespace internal {\ntemplate<typename _MatrixType> struct traits<FullPivLU<_MatrixType> >\n : traits<_MatrixType>\n{\n  typedef MatrixXpr XprKind;\n  typedef SolverStorage StorageKind;\n  enum { Flags = 0 };\n};\n\n} // end namespace internal\n\n/** \\ingroup LU_Module\n  *\n  * \\class FullPivLU\n  *\n  * \\brief LU decomposition of a matrix with complete pivoting, and related features\n  *\n  * \\tparam _MatrixType the type of the matrix of which we are computing the LU decomposition\n  *\n  * This class represents a LU decomposition of any matrix, with complete pivoting: the matrix A is\n  * decomposed as \\f$ A = P^{-1} L U Q^{-1} \\f$ where L is unit-lower-triangular, U is\n  * upper-triangular, and P and Q are permutation matrices. This is a rank-revealing LU\n  * decomposition. The eigenvalues (diagonal coefficients) of U are sorted in such a way that any\n  * zeros are at the end.\n  *\n  * This decomposition provides the generic approach to solving systems of linear equations, computing\n  * the rank, invertibility, inverse, kernel, and determinant.\n  *\n  * This LU decomposition is very stable and well tested with large matrices. However there are use cases where the SVD\n  * decomposition is inherently more stable and/or flexible. For example, when computing the kernel of a matrix,\n  * working with the SVD allows to select the smallest singular values of the matrix, something that\n  * the LU decomposition doesn't see.\n  *\n  * The data of the LU decomposition can be directly accessed through the methods matrixLU(),\n  * permutationP(), permutationQ().\n  *\n  * As an exemple, here is how the original matrix can be retrieved:\n  * \\include class_FullPivLU.cpp\n  * Output: \\verbinclude class_FullPivLU.out\n  *\n  * This class supports the \\link InplaceDecomposition inplace decomposition \\endlink mechanism.\n  * \n  * \\sa MatrixBase::fullPivLu(), MatrixBase::determinant(), MatrixBase::inverse()\n  */\ntemplate<typename _MatrixType> class FullPivLU\n  : public SolverBase<FullPivLU<_MatrixType> >\n{\n  public:\n    typedef _MatrixType MatrixType;\n    typedef SolverBase<FullPivLU> Base;\n\n    EIGEN_GENERIC_PUBLIC_INTERFACE(FullPivLU)\n    // FIXME StorageIndex defined in EIGEN_GENERIC_PUBLIC_INTERFACE should be int\n    enum {\n      MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,\n      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime\n    };\n    typedef typename internal::plain_row_type<MatrixType, StorageIndex>::type IntRowVectorType;\n    typedef typename internal::plain_col_type<MatrixType, StorageIndex>::type IntColVectorType;\n    typedef PermutationMatrix<ColsAtCompileTime, MaxColsAtCompileTime> PermutationQType;\n    typedef PermutationMatrix<RowsAtCompileTime, MaxRowsAtCompileTime> PermutationPType;\n    typedef typename MatrixType::PlainObject PlainObject;\n\n    /**\n      * \\brief Default Constructor.\n      *\n      * The default constructor is useful in cases in which the user intends to\n      * perform decompositions via LU::compute(const MatrixType&).\n      */\n    FullPivLU();\n\n    /** \\brief Default Constructor with memory preallocation\n      *\n      * Like the default constructor but with preallocation of the internal data\n      * according to the specified problem \\a size.\n      * \\sa FullPivLU()\n      */\n    FullPivLU(Index rows, Index cols);\n\n    /** Constructor.\n      *\n      * \\param matrix the matrix of which to compute the LU decomposition.\n      *               It is required to be nonzero.\n      */\n    template<typename InputType>\n    explicit FullPivLU(const EigenBase<InputType>& matrix);\n\n    /** \\brief Constructs a LU factorization from a given matrix\n      *\n      * This overloaded constructor is provided for \\link InplaceDecomposition inplace decomposition \\endlink when \\c MatrixType is a Eigen::Ref.\n      *\n      * \\sa FullPivLU(const EigenBase&)\n      */\n    template<typename InputType>\n    explicit FullPivLU(EigenBase<InputType>& matrix);\n\n    /** Computes the LU decomposition of the given matrix.\n      *\n      * \\param matrix the matrix of which to compute the LU decomposition.\n      *               It is required to be nonzero.\n      *\n      * \\returns a reference to *this\n      */\n    template<typename InputType>\n    FullPivLU& compute(const EigenBase<InputType>& matrix) {\n      m_lu = matrix.derived();\n      computeInPlace();\n      return *this;\n    }\n\n    /** \\returns the LU decomposition matrix: the upper-triangular part is U, the\n      * unit-lower-triangular part is L (at least for square matrices; in the non-square\n      * case, special care is needed, see the documentation of class FullPivLU).\n      *\n      * \\sa matrixL(), matrixU()\n      */\n    inline const MatrixType& matrixLU() const\n    {\n      eigen_assert(m_isInitialized && \"LU is not initialized.\");\n      return m_lu;\n    }\n\n    /** \\returns the number of nonzero pivots in the LU decomposition.\n      * Here nonzero is meant in the exact sense, not in a fuzzy sense.\n      * So that notion isn't really intrinsically interesting, but it is\n      * still useful when implementing algorithms.\n      *\n      * \\sa rank()\n      */\n    inline Index nonzeroPivots() const\n    {\n      eigen_assert(m_isInitialized && \"LU is not initialized.\");\n      return m_nonzero_pivots;\n    }\n\n    /** \\returns the absolute value of the biggest pivot, i.e. the biggest\n      *          diagonal coefficient of U.\n      */\n    RealScalar maxPivot() const { return m_maxpivot; }\n\n    /** \\returns the permutation matrix P\n      *\n      * \\sa permutationQ()\n      */\n    EIGEN_DEVICE_FUNC inline const PermutationPType& permutationP() const\n    {\n      eigen_assert(m_isInitialized && \"LU is not initialized.\");\n      return m_p;\n    }\n\n    /** \\returns the permutation matrix Q\n      *\n      * \\sa permutationP()\n      */\n    inline const PermutationQType& permutationQ() const\n    {\n      eigen_assert(m_isInitialized && \"LU is not initialized.\");\n      return m_q;\n    }\n\n    /** \\returns the kernel of the matrix, also called its null-space. The columns of the returned matrix\n      * will form a basis of the kernel.\n      *\n      * \\note If the kernel has dimension zero, then the returned matrix is a column-vector filled with zeros.\n      *\n      * \\note This method has to determine which pivots should be considered nonzero.\n      *       For that, it uses the threshold value that you can control by calling\n      *       setThreshold(const RealScalar&).\n      *\n      * Example: \\include FullPivLU_kernel.cpp\n      * Output: \\verbinclude FullPivLU_kernel.out\n      *\n      * \\sa image()\n      */\n    inline const internal::kernel_retval<FullPivLU> kernel() const\n    {\n      eigen_assert(m_isInitialized && \"LU is not initialized.\");\n      return internal::kernel_retval<FullPivLU>(*this);\n    }\n\n    /** \\returns the image of the matrix, also called its column-space. The columns of the returned matrix\n      * will form a basis of the image (column-space).\n      *\n      * \\param originalMatrix the original matrix, of which *this is the LU decomposition.\n      *                       The reason why it is needed to pass it here, is that this allows\n      *                       a large optimization, as otherwise this method would need to reconstruct it\n      *                       from the LU decomposition.\n      *\n      * \\note If the image has dimension zero, then the returned matrix is a column-vector filled with zeros.\n      *\n      * \\note This method has to determine which pivots should be considered nonzero.\n      *       For that, it uses the threshold value that you can control by calling\n      *       setThreshold(const RealScalar&).\n      *\n      * Example: \\include FullPivLU_image.cpp\n      * Output: \\verbinclude FullPivLU_image.out\n      *\n      * \\sa kernel()\n      */\n    inline const internal::image_retval<FullPivLU>\n      image(const MatrixType& originalMatrix) const\n    {\n      eigen_assert(m_isInitialized && \"LU is not initialized.\");\n      return internal::image_retval<FullPivLU>(*this, originalMatrix);\n    }\n\n    /** \\return a solution x to the equation Ax=b, where A is the matrix of which\n      * *this is the LU decomposition.\n      *\n      * \\param b the right-hand-side of the equation to solve. Can be a vector or a matrix,\n      *          the only requirement in order for the equation to make sense is that\n      *          b.rows()==A.rows(), where A is the matrix of which *this is the LU decomposition.\n      *\n      * \\returns a solution.\n      *\n      * \\note_about_checking_solutions\n      *\n      * \\note_about_arbitrary_choice_of_solution\n      * \\note_about_using_kernel_to_study_multiple_solutions\n      *\n      * Example: \\include FullPivLU_solve.cpp\n      * Output: \\verbinclude FullPivLU_solve.out\n      *\n      * \\sa TriangularView::solve(), kernel(), inverse()\n      */\n    // FIXME this is a copy-paste of the base-class member to add the isInitialized assertion.\n    template<typename Rhs>\n    inline const Solve<FullPivLU, Rhs>\n    solve(const MatrixBase<Rhs>& b) const\n    {\n      eigen_assert(m_isInitialized && \"LU is not initialized.\");\n      return Solve<FullPivLU, Rhs>(*this, b.derived());\n    }\n\n    /** \\returns an estimate of the reciprocal condition number of the matrix of which \\c *this is\n        the LU decomposition.\n      */\n    inline RealScalar rcond() const\n    {\n      eigen_assert(m_isInitialized && \"PartialPivLU is not initialized.\");\n      return internal::rcond_estimate_helper(m_l1_norm, *this);\n    }\n\n    /** \\returns the determinant of the matrix of which\n      * *this is the LU decomposition. It has only linear complexity\n      * (that is, O(n) where n is the dimension of the square matrix)\n      * as the LU decomposition has already been computed.\n      *\n      * \\note This is only for square matrices.\n      *\n      * \\note For fixed-size matrices of size up to 4, MatrixBase::determinant() offers\n      *       optimized paths.\n      *\n      * \\warning a determinant can be very big or small, so for matrices\n      * of large enough dimension, there is a risk of overflow/underflow.\n      *\n      * \\sa MatrixBase::determinant()\n      */\n    typename internal::traits<MatrixType>::Scalar determinant() const;\n\n    /** Allows to prescribe a threshold to be used by certain methods, such as rank(),\n      * who need to determine when pivots are to be considered nonzero. This is not used for the\n      * LU decomposition itself.\n      *\n      * When it needs to get the threshold value, Eigen calls threshold(). By default, this\n      * uses a formula to automatically determine a reasonable threshold.\n      * Once you have called the present method setThreshold(const RealScalar&),\n      * your value is used instead.\n      *\n      * \\param threshold The new value to use as the threshold.\n      *\n      * A pivot will be considered nonzero if its absolute value is strictly greater than\n      *  \\f$ \\vert pivot \\vert \\leqslant threshold \\times \\vert maxpivot \\vert \\f$\n      * where maxpivot is the biggest pivot.\n      *\n      * If you want to come back to the default behavior, call setThreshold(Default_t)\n      */\n    FullPivLU& setThreshold(const RealScalar& threshold)\n    {\n      m_usePrescribedThreshold = true;\n      m_prescribedThreshold = threshold;\n      return *this;\n    }\n\n    /** Allows to come back to the default behavior, letting Eigen use its default formula for\n      * determining the threshold.\n      *\n      * You should pass the special object Eigen::Default as parameter here.\n      * \\code lu.setThreshold(Eigen::Default); \\endcode\n      *\n      * See the documentation of setThreshold(const RealScalar&).\n      */\n    FullPivLU& setThreshold(Default_t)\n    {\n      m_usePrescribedThreshold = false;\n      return *this;\n    }\n\n    /** Returns the threshold that will be used by certain methods such as rank().\n      *\n      * See the documentation of setThreshold(const RealScalar&).\n      */\n    RealScalar threshold() const\n    {\n      eigen_assert(m_isInitialized || m_usePrescribedThreshold);\n      return m_usePrescribedThreshold ? m_prescribedThreshold\n      // this formula comes from experimenting (see \"LU precision tuning\" thread on the list)\n      // and turns out to be identical to Higham's formula used already in LDLt.\n                                      : NumTraits<Scalar>::epsilon() * m_lu.diagonalSize();\n    }\n\n    /** \\returns the rank of the matrix of which *this is the LU decomposition.\n      *\n      * \\note This method has to determine which pivots should be considered nonzero.\n      *       For that, it uses the threshold value that you can control by calling\n      *       setThreshold(const RealScalar&).\n      */\n    inline Index rank() const\n    {\n      using std::abs;\n      eigen_assert(m_isInitialized && \"LU is not initialized.\");\n      RealScalar premultiplied_threshold = abs(m_maxpivot) * threshold();\n      Index result = 0;\n      for(Index i = 0; i < m_nonzero_pivots; ++i)\n        result += (abs(m_lu.coeff(i,i)) > premultiplied_threshold);\n      return result;\n    }\n\n    /** \\returns the dimension of the kernel of the matrix of which *this is the LU decomposition.\n      *\n      * \\note This method has to determine which pivots should be considered nonzero.\n      *       For that, it uses the threshold value that you can control by calling\n      *       setThreshold(const RealScalar&).\n      */\n    inline Index dimensionOfKernel() const\n    {\n      eigen_assert(m_isInitialized && \"LU is not initialized.\");\n      return cols() - rank();\n    }\n\n    /** \\returns true if the matrix of which *this is the LU decomposition represents an injective\n      *          linear map, i.e. has trivial kernel; false otherwise.\n      *\n      * \\note This method has to determine which pivots should be considered nonzero.\n      *       For that, it uses the threshold value that you can control by calling\n      *       setThreshold(const RealScalar&).\n      */\n    inline bool isInjective() const\n    {\n      eigen_assert(m_isInitialized && \"LU is not initialized.\");\n      return rank() == cols();\n    }\n\n    /** \\returns true if the matrix of which *this is the LU decomposition represents a surjective\n      *          linear map; false otherwise.\n      *\n      * \\note This method has to determine which pivots should be considered nonzero.\n      *       For that, it uses the threshold value that you can control by calling\n      *       setThreshold(const RealScalar&).\n      */\n    inline bool isSurjective() const\n    {\n      eigen_assert(m_isInitialized && \"LU is not initialized.\");\n      return rank() == rows();\n    }\n\n    /** \\returns true if the matrix of which *this is the LU decomposition is invertible.\n      *\n      * \\note This method has to determine which pivots should be considered nonzero.\n      *       For that, it uses the threshold value that you can control by calling\n      *       setThreshold(const RealScalar&).\n      */\n    inline bool isInvertible() const\n    {\n      eigen_assert(m_isInitialized && \"LU is not initialized.\");\n      return isInjective() && (m_lu.rows() == m_lu.cols());\n    }\n\n    /** \\returns the inverse of the matrix of which *this is the LU decomposition.\n      *\n      * \\note If this matrix is not invertible, the returned matrix has undefined coefficients.\n      *       Use isInvertible() to first determine whether this matrix is invertible.\n      *\n      * \\sa MatrixBase::inverse()\n      */\n    inline const Inverse<FullPivLU> inverse() const\n    {\n      eigen_assert(m_isInitialized && \"LU is not initialized.\");\n      eigen_assert(m_lu.rows() == m_lu.cols() && \"You can't take the inverse of a non-square matrix!\");\n      return Inverse<FullPivLU>(*this);\n    }\n\n    MatrixType reconstructedMatrix() const;\n\n    EIGEN_DEVICE_FUNC inline Index rows() const { return m_lu.rows(); }\n    EIGEN_DEVICE_FUNC inline Index cols() const { return m_lu.cols(); }\n\n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    template<typename RhsType, typename DstType>\n    EIGEN_DEVICE_FUNC\n    void _solve_impl(const RhsType &rhs, DstType &dst) const;\n\n    template<bool Conjugate, typename RhsType, typename DstType>\n    EIGEN_DEVICE_FUNC\n    void _solve_impl_transposed(const RhsType &rhs, DstType &dst) const;\n    #endif\n\n  protected:\n\n    static void check_template_parameters()\n    {\n      EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);\n    }\n\n    void computeInPlace();\n\n    MatrixType m_lu;\n    PermutationPType m_p;\n    PermutationQType m_q;\n    IntColVectorType m_rowsTranspositions;\n    IntRowVectorType m_colsTranspositions;\n    Index m_nonzero_pivots;\n    RealScalar m_l1_norm;\n    RealScalar m_maxpivot, m_prescribedThreshold;\n    signed char m_det_pq;\n    bool m_isInitialized, m_usePrescribedThreshold;\n};\n\ntemplate<typename MatrixType>\nFullPivLU<MatrixType>::FullPivLU()\n  : m_isInitialized(false), m_usePrescribedThreshold(false)\n{\n}\n\ntemplate<typename MatrixType>\nFullPivLU<MatrixType>::FullPivLU(Index rows, Index cols)\n  : m_lu(rows, cols),\n    m_p(rows),\n    m_q(cols),\n    m_rowsTranspositions(rows),\n    m_colsTranspositions(cols),\n    m_isInitialized(false),\n    m_usePrescribedThreshold(false)\n{\n}\n\ntemplate<typename MatrixType>\ntemplate<typename InputType>\nFullPivLU<MatrixType>::FullPivLU(const EigenBase<InputType>& matrix)\n  : m_lu(matrix.rows(), matrix.cols()),\n    m_p(matrix.rows()),\n    m_q(matrix.cols()),\n    m_rowsTranspositions(matrix.rows()),\n    m_colsTranspositions(matrix.cols()),\n    m_isInitialized(false),\n    m_usePrescribedThreshold(false)\n{\n  compute(matrix.derived());\n}\n\ntemplate<typename MatrixType>\ntemplate<typename InputType>\nFullPivLU<MatrixType>::FullPivLU(EigenBase<InputType>& matrix)\n  : m_lu(matrix.derived()),\n    m_p(matrix.rows()),\n    m_q(matrix.cols()),\n    m_rowsTranspositions(matrix.rows()),\n    m_colsTranspositions(matrix.cols()),\n    m_isInitialized(false),\n    m_usePrescribedThreshold(false)\n{\n  computeInPlace();\n}\n\ntemplate<typename MatrixType>\nvoid FullPivLU<MatrixType>::computeInPlace()\n{\n  check_template_parameters();\n\n  // the permutations are stored as int indices, so just to be sure:\n  eigen_assert(m_lu.rows()<=NumTraits<int>::highest() && m_lu.cols()<=NumTraits<int>::highest());\n\n  m_l1_norm = m_lu.cwiseAbs().colwise().sum().maxCoeff();\n\n  const Index size = m_lu.diagonalSize();\n  const Index rows = m_lu.rows();\n  const Index cols = m_lu.cols();\n\n  // will store the transpositions, before we accumulate them at the end.\n  // can't accumulate on-the-fly because that will be done in reverse order for the rows.\n  m_rowsTranspositions.resize(m_lu.rows());\n  m_colsTranspositions.resize(m_lu.cols());\n  Index number_of_transpositions = 0; // number of NONTRIVIAL transpositions, i.e. m_rowsTranspositions[i]!=i\n\n  m_nonzero_pivots = size; // the generic case is that in which all pivots are nonzero (invertible case)\n  m_maxpivot = RealScalar(0);\n\n  for(Index k = 0; k < size; ++k)\n  {\n    // First, we need to find the pivot.\n\n    // biggest coefficient in the remaining bottom-right corner (starting at row k, col k)\n    Index row_of_biggest_in_corner, col_of_biggest_in_corner;\n    typedef internal::scalar_score_coeff_op<Scalar> Scoring;\n    typedef typename Scoring::result_type Score;\n    Score biggest_in_corner;\n    biggest_in_corner = m_lu.bottomRightCorner(rows-k, cols-k)\n                        .unaryExpr(Scoring())\n                        .maxCoeff(&row_of_biggest_in_corner, &col_of_biggest_in_corner);\n    row_of_biggest_in_corner += k; // correct the values! since they were computed in the corner,\n    col_of_biggest_in_corner += k; // need to add k to them.\n\n    if(biggest_in_corner==Score(0))\n    {\n      // before exiting, make sure to initialize the still uninitialized transpositions\n      // in a sane state without destroying what we already have.\n      m_nonzero_pivots = k;\n      for(Index i = k; i < size; ++i)\n      {\n        m_rowsTranspositions.coeffRef(i) = i;\n        m_colsTranspositions.coeffRef(i) = i;\n      }\n      break;\n    }\n\n    RealScalar abs_pivot = internal::abs_knowing_score<Scalar>()(m_lu(row_of_biggest_in_corner, col_of_biggest_in_corner), biggest_in_corner);\n    if(abs_pivot > m_maxpivot) m_maxpivot = abs_pivot;\n\n    // Now that we've found the pivot, we need to apply the row/col swaps to\n    // bring it to the location (k,k).\n\n    m_rowsTranspositions.coeffRef(k) = row_of_biggest_in_corner;\n    m_colsTranspositions.coeffRef(k) = col_of_biggest_in_corner;\n    if(k != row_of_biggest_in_corner) {\n      m_lu.row(k).swap(m_lu.row(row_of_biggest_in_corner));\n      ++number_of_transpositions;\n    }\n    if(k != col_of_biggest_in_corner) {\n      m_lu.col(k).swap(m_lu.col(col_of_biggest_in_corner));\n      ++number_of_transpositions;\n    }\n\n    // Now that the pivot is at the right location, we update the remaining\n    // bottom-right corner by Gaussian elimination.\n\n    if(k<rows-1)\n      m_lu.col(k).tail(rows-k-1) /= m_lu.coeff(k,k);\n    if(k<size-1)\n      m_lu.block(k+1,k+1,rows-k-1,cols-k-1).noalias() -= m_lu.col(k).tail(rows-k-1) * m_lu.row(k).tail(cols-k-1);\n  }\n\n  // the main loop is over, we still have to accumulate the transpositions to find the\n  // permutations P and Q\n\n  m_p.setIdentity(rows);\n  for(Index k = size-1; k >= 0; --k)\n    m_p.applyTranspositionOnTheRight(k, m_rowsTranspositions.coeff(k));\n\n  m_q.setIdentity(cols);\n  for(Index k = 0; k < size; ++k)\n    m_q.applyTranspositionOnTheRight(k, m_colsTranspositions.coeff(k));\n\n  m_det_pq = (number_of_transpositions%2) ? -1 : 1;\n\n  m_isInitialized = true;\n}\n\ntemplate<typename MatrixType>\ntypename internal::traits<MatrixType>::Scalar FullPivLU<MatrixType>::determinant() const\n{\n  eigen_assert(m_isInitialized && \"LU is not initialized.\");\n  eigen_assert(m_lu.rows() == m_lu.cols() && \"You can't take the determinant of a non-square matrix!\");\n  return Scalar(m_det_pq) * Scalar(m_lu.diagonal().prod());\n}\n\n/** \\returns the matrix represented by the decomposition,\n * i.e., it returns the product: \\f$ P^{-1} L U Q^{-1} \\f$.\n * This function is provided for debug purposes. */\ntemplate<typename MatrixType>\nMatrixType FullPivLU<MatrixType>::reconstructedMatrix() const\n{\n  eigen_assert(m_isInitialized && \"LU is not initialized.\");\n  const Index smalldim = (std::min)(m_lu.rows(), m_lu.cols());\n  // LU\n  MatrixType res(m_lu.rows(),m_lu.cols());\n  // FIXME the .toDenseMatrix() should not be needed...\n  res = m_lu.leftCols(smalldim)\n            .template triangularView<UnitLower>().toDenseMatrix()\n      * m_lu.topRows(smalldim)\n            .template triangularView<Upper>().toDenseMatrix();\n\n  // P^{-1}(LU)\n  res = m_p.inverse() * res;\n\n  // (P^{-1}LU)Q^{-1}\n  res = res * m_q.inverse();\n\n  return res;\n}\n\n/********* Implementation of kernel() **************************************************/\n\nnamespace internal {\ntemplate<typename _MatrixType>\nstruct kernel_retval<FullPivLU<_MatrixType> >\n  : kernel_retval_base<FullPivLU<_MatrixType> >\n{\n  EIGEN_MAKE_KERNEL_HELPERS(FullPivLU<_MatrixType>)\n\n  enum { MaxSmallDimAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(\n            MatrixType::MaxColsAtCompileTime,\n            MatrixType::MaxRowsAtCompileTime)\n  };\n\n  template<typename Dest> void evalTo(Dest& dst) const\n  {\n    using std::abs;\n    const Index cols = dec().matrixLU().cols(), dimker = cols - rank();\n    if(dimker == 0)\n    {\n      // The Kernel is just {0}, so it doesn't have a basis properly speaking, but let's\n      // avoid crashing/asserting as that depends on floating point calculations. Let's\n      // just return a single column vector filled with zeros.\n      dst.setZero();\n      return;\n    }\n\n    /* Let us use the following lemma:\n      *\n      * Lemma: If the matrix A has the LU decomposition PAQ = LU,\n      * then Ker A = Q(Ker U).\n      *\n      * Proof: trivial: just keep in mind that P, Q, L are invertible.\n      */\n\n    /* Thus, all we need to do is to compute Ker U, and then apply Q.\n      *\n      * U is upper triangular, with eigenvalues sorted so that any zeros appear at the end.\n      * Thus, the diagonal of U ends with exactly\n      * dimKer zero's. Let us use that to construct dimKer linearly\n      * independent vectors in Ker U.\n      */\n\n    Matrix<Index, Dynamic, 1, 0, MaxSmallDimAtCompileTime, 1> pivots(rank());\n    RealScalar premultiplied_threshold = dec().maxPivot() * dec().threshold();\n    Index p = 0;\n    for(Index i = 0; i < dec().nonzeroPivots(); ++i)\n      if(abs(dec().matrixLU().coeff(i,i)) > premultiplied_threshold)\n        pivots.coeffRef(p++) = i;\n    eigen_internal_assert(p == rank());\n\n    // we construct a temporaty trapezoid matrix m, by taking the U matrix and\n    // permuting the rows and cols to bring the nonnegligible pivots to the top of\n    // the main diagonal. We need that to be able to apply our triangular solvers.\n    // FIXME when we get triangularView-for-rectangular-matrices, this can be simplified\n    Matrix<typename MatrixType::Scalar, Dynamic, Dynamic, MatrixType::Options,\n           MaxSmallDimAtCompileTime, MatrixType::MaxColsAtCompileTime>\n      m(dec().matrixLU().block(0, 0, rank(), cols));\n    for(Index i = 0; i < rank(); ++i)\n    {\n      if(i) m.row(i).head(i).setZero();\n      m.row(i).tail(cols-i) = dec().matrixLU().row(pivots.coeff(i)).tail(cols-i);\n    }\n    m.block(0, 0, rank(), rank());\n    m.block(0, 0, rank(), rank()).template triangularView<StrictlyLower>().setZero();\n    for(Index i = 0; i < rank(); ++i)\n      m.col(i).swap(m.col(pivots.coeff(i)));\n\n    // ok, we have our trapezoid matrix, we can apply the triangular solver.\n    // notice that the math behind this suggests that we should apply this to the\n    // negative of the RHS, but for performance we just put the negative sign elsewhere, see below.\n    m.topLeftCorner(rank(), rank())\n     .template triangularView<Upper>().solveInPlace(\n        m.topRightCorner(rank(), dimker)\n      );\n\n    // now we must undo the column permutation that we had applied!\n    for(Index i = rank()-1; i >= 0; --i)\n      m.col(i).swap(m.col(pivots.coeff(i)));\n\n    // see the negative sign in the next line, that's what we were talking about above.\n    for(Index i = 0; i < rank(); ++i) dst.row(dec().permutationQ().indices().coeff(i)) = -m.row(i).tail(dimker);\n    for(Index i = rank(); i < cols; ++i) dst.row(dec().permutationQ().indices().coeff(i)).setZero();\n    for(Index k = 0; k < dimker; ++k) dst.coeffRef(dec().permutationQ().indices().coeff(rank()+k), k) = Scalar(1);\n  }\n};\n\n/***** Implementation of image() *****************************************************/\n\ntemplate<typename _MatrixType>\nstruct image_retval<FullPivLU<_MatrixType> >\n  : image_retval_base<FullPivLU<_MatrixType> >\n{\n  EIGEN_MAKE_IMAGE_HELPERS(FullPivLU<_MatrixType>)\n\n  enum { MaxSmallDimAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(\n            MatrixType::MaxColsAtCompileTime,\n            MatrixType::MaxRowsAtCompileTime)\n  };\n\n  template<typename Dest> void evalTo(Dest& dst) const\n  {\n    using std::abs;\n    if(rank() == 0)\n    {\n      // The Image is just {0}, so it doesn't have a basis properly speaking, but let's\n      // avoid crashing/asserting as that depends on floating point calculations. Let's\n      // just return a single column vector filled with zeros.\n      dst.setZero();\n      return;\n    }\n\n    Matrix<Index, Dynamic, 1, 0, MaxSmallDimAtCompileTime, 1> pivots(rank());\n    RealScalar premultiplied_threshold = dec().maxPivot() * dec().threshold();\n    Index p = 0;\n    for(Index i = 0; i < dec().nonzeroPivots(); ++i)\n      if(abs(dec().matrixLU().coeff(i,i)) > premultiplied_threshold)\n        pivots.coeffRef(p++) = i;\n    eigen_internal_assert(p == rank());\n\n    for(Index i = 0; i < rank(); ++i)\n      dst.col(i) = originalMatrix().col(dec().permutationQ().indices().coeff(pivots.coeff(i)));\n  }\n};\n\n/***** Implementation of solve() *****************************************************/\n\n} // end namespace internal\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\ntemplate<typename _MatrixType>\ntemplate<typename RhsType, typename DstType>\nvoid FullPivLU<_MatrixType>::_solve_impl(const RhsType &rhs, DstType &dst) const\n{\n  /* The decomposition PAQ = LU can be rewritten as A = P^{-1} L U Q^{-1}.\n  * So we proceed as follows:\n  * Step 1: compute c = P * rhs.\n  * Step 2: replace c by the solution x to Lx = c. Exists because L is invertible.\n  * Step 3: replace c by the solution x to Ux = c. May or may not exist.\n  * Step 4: result = Q * c;\n  */\n\n  const Index rows = this->rows(),\n              cols = this->cols(),\n              nonzero_pivots = this->rank();\n  eigen_assert(rhs.rows() == rows);\n  const Index smalldim = (std::min)(rows, cols);\n\n  if(nonzero_pivots == 0)\n  {\n    dst.setZero();\n    return;\n  }\n\n  typename RhsType::PlainObject c(rhs.rows(), rhs.cols());\n\n  // Step 1\n  c = permutationP() * rhs;\n\n  // Step 2\n  m_lu.topLeftCorner(smalldim,smalldim)\n      .template triangularView<UnitLower>()\n      .solveInPlace(c.topRows(smalldim));\n  if(rows>cols)\n    c.bottomRows(rows-cols) -= m_lu.bottomRows(rows-cols) * c.topRows(cols);\n\n  // Step 3\n  m_lu.topLeftCorner(nonzero_pivots, nonzero_pivots)\n      .template triangularView<Upper>()\n      .solveInPlace(c.topRows(nonzero_pivots));\n\n  // Step 4\n  for(Index i = 0; i < nonzero_pivots; ++i)\n    dst.row(permutationQ().indices().coeff(i)) = c.row(i);\n  for(Index i = nonzero_pivots; i < m_lu.cols(); ++i)\n    dst.row(permutationQ().indices().coeff(i)).setZero();\n}\n\ntemplate<typename _MatrixType>\ntemplate<bool Conjugate, typename RhsType, typename DstType>\nvoid FullPivLU<_MatrixType>::_solve_impl_transposed(const RhsType &rhs, DstType &dst) const\n{\n  /* The decomposition PAQ = LU can be rewritten as A = P^{-1} L U Q^{-1},\n   * and since permutations are real and unitary, we can write this\n   * as   A^T = Q U^T L^T P,\n   * So we proceed as follows:\n   * Step 1: compute c = Q^T rhs.\n   * Step 2: replace c by the solution x to U^T x = c. May or may not exist.\n   * Step 3: replace c by the solution x to L^T x = c.\n   * Step 4: result = P^T c.\n   * If Conjugate is true, replace \"^T\" by \"^*\" above.\n   */\n\n  const Index rows = this->rows(), cols = this->cols(),\n    nonzero_pivots = this->rank();\n   eigen_assert(rhs.rows() == cols);\n  const Index smalldim = (std::min)(rows, cols);\n\n  if(nonzero_pivots == 0)\n  {\n    dst.setZero();\n    return;\n  }\n\n  typename RhsType::PlainObject c(rhs.rows(), rhs.cols());\n\n  // Step 1\n  c = permutationQ().inverse() * rhs;\n\n  if (Conjugate) {\n    // Step 2\n    m_lu.topLeftCorner(nonzero_pivots, nonzero_pivots)\n        .template triangularView<Upper>()\n        .adjoint()\n        .solveInPlace(c.topRows(nonzero_pivots));\n    // Step 3\n    m_lu.topLeftCorner(smalldim, smalldim)\n        .template triangularView<UnitLower>()\n        .adjoint()\n        .solveInPlace(c.topRows(smalldim));\n  } else {\n    // Step 2\n    m_lu.topLeftCorner(nonzero_pivots, nonzero_pivots)\n        .template triangularView<Upper>()\n        .transpose()\n        .solveInPlace(c.topRows(nonzero_pivots));\n    // Step 3\n    m_lu.topLeftCorner(smalldim, smalldim)\n        .template triangularView<UnitLower>()\n        .transpose()\n        .solveInPlace(c.topRows(smalldim));\n  }\n\n  // Step 4\n  PermutationPType invp = permutationP().inverse().eval();\n  for(Index i = 0; i < smalldim; ++i)\n    dst.row(invp.indices().coeff(i)) = c.row(i);\n  for(Index i = smalldim; i < rows; ++i)\n    dst.row(invp.indices().coeff(i)).setZero();\n}\n\n#endif\n\nnamespace internal {\n\n\n/***** Implementation of inverse() *****************************************************/\ntemplate<typename DstXprType, typename MatrixType>\nstruct Assignment<DstXprType, Inverse<FullPivLU<MatrixType> >, internal::assign_op<typename DstXprType::Scalar,typename FullPivLU<MatrixType>::Scalar>, Dense2Dense>\n{\n  typedef FullPivLU<MatrixType> LuType;\n  typedef Inverse<LuType> SrcXprType;\n  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename MatrixType::Scalar> &)\n  {\n    dst = src.nestedExpression().solve(MatrixType::Identity(src.rows(), src.cols()));\n  }\n};\n} // end namespace internal\n\n/******* MatrixBase methods *****************************************************************/\n\n/** \\lu_module\n  *\n  * \\return the full-pivoting LU decomposition of \\c *this.\n  *\n  * \\sa class FullPivLU\n  */\ntemplate<typename Derived>\ninline const FullPivLU<typename MatrixBase<Derived>::PlainObject>\nMatrixBase<Derived>::fullPivLu() const\n{\n  return FullPivLU<PlainObject>(eval());\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_LU_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/LU/InverseImpl.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2010 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_INVERSE_IMPL_H\n#define EIGEN_INVERSE_IMPL_H\n\nnamespace Eigen { \n\nnamespace internal {\n\n/**********************************\n*** General case implementation ***\n**********************************/\n\ntemplate<typename MatrixType, typename ResultType, int Size = MatrixType::RowsAtCompileTime>\nstruct compute_inverse\n{\n  EIGEN_DEVICE_FUNC\n  static inline void run(const MatrixType& matrix, ResultType& result)\n  {\n    result = matrix.partialPivLu().inverse();\n  }\n};\n\ntemplate<typename MatrixType, typename ResultType, int Size = MatrixType::RowsAtCompileTime>\nstruct compute_inverse_and_det_with_check { /* nothing! general case not supported. */ };\n\n/****************************\n*** Size 1 implementation ***\n****************************/\n\ntemplate<typename MatrixType, typename ResultType>\nstruct compute_inverse<MatrixType, ResultType, 1>\n{\n  EIGEN_DEVICE_FUNC\n  static inline void run(const MatrixType& matrix, ResultType& result)\n  {\n    typedef typename MatrixType::Scalar Scalar;\n    internal::evaluator<MatrixType> matrixEval(matrix);\n    result.coeffRef(0,0) = Scalar(1) / matrixEval.coeff(0,0);\n  }\n};\n\ntemplate<typename MatrixType, typename ResultType>\nstruct compute_inverse_and_det_with_check<MatrixType, ResultType, 1>\n{\n  EIGEN_DEVICE_FUNC\n  static inline void run(\n    const MatrixType& matrix,\n    const typename MatrixType::RealScalar& absDeterminantThreshold,\n    ResultType& result,\n    typename ResultType::Scalar& determinant,\n    bool& invertible\n  )\n  {\n    using std::abs;\n    determinant = matrix.coeff(0,0);\n    invertible = abs(determinant) > absDeterminantThreshold;\n    if(invertible) result.coeffRef(0,0) = typename ResultType::Scalar(1) / determinant;\n  }\n};\n\n/****************************\n*** Size 2 implementation ***\n****************************/\n\ntemplate<typename MatrixType, typename ResultType>\nEIGEN_DEVICE_FUNC \ninline void compute_inverse_size2_helper(\n    const MatrixType& matrix, const typename ResultType::Scalar& invdet,\n    ResultType& result)\n{\n  result.coeffRef(0,0) =  matrix.coeff(1,1) * invdet;\n  result.coeffRef(1,0) = -matrix.coeff(1,0) * invdet;\n  result.coeffRef(0,1) = -matrix.coeff(0,1) * invdet;\n  result.coeffRef(1,1) =  matrix.coeff(0,0) * invdet;\n}\n\ntemplate<typename MatrixType, typename ResultType>\nstruct compute_inverse<MatrixType, ResultType, 2>\n{\n  EIGEN_DEVICE_FUNC\n  static inline void run(const MatrixType& matrix, ResultType& result)\n  {\n    typedef typename ResultType::Scalar Scalar;\n    const Scalar invdet = typename MatrixType::Scalar(1) / matrix.determinant();\n    compute_inverse_size2_helper(matrix, invdet, result);\n  }\n};\n\ntemplate<typename MatrixType, typename ResultType>\nstruct compute_inverse_and_det_with_check<MatrixType, ResultType, 2>\n{\n  EIGEN_DEVICE_FUNC\n  static inline void run(\n    const MatrixType& matrix,\n    const typename MatrixType::RealScalar& absDeterminantThreshold,\n    ResultType& inverse,\n    typename ResultType::Scalar& determinant,\n    bool& invertible\n  )\n  {\n    using std::abs;\n    typedef typename ResultType::Scalar Scalar;\n    determinant = matrix.determinant();\n    invertible = abs(determinant) > absDeterminantThreshold;\n    if(!invertible) return;\n    const Scalar invdet = Scalar(1) / determinant;\n    compute_inverse_size2_helper(matrix, invdet, inverse);\n  }\n};\n\n/****************************\n*** Size 3 implementation ***\n****************************/\n\ntemplate<typename MatrixType, int i, int j>\nEIGEN_DEVICE_FUNC \ninline typename MatrixType::Scalar cofactor_3x3(const MatrixType& m)\n{\n  enum {\n    i1 = (i+1) % 3,\n    i2 = (i+2) % 3,\n    j1 = (j+1) % 3,\n    j2 = (j+2) % 3\n  };\n  return m.coeff(i1, j1) * m.coeff(i2, j2)\n       - m.coeff(i1, j2) * m.coeff(i2, j1);\n}\n\ntemplate<typename MatrixType, typename ResultType>\nEIGEN_DEVICE_FUNC\ninline void compute_inverse_size3_helper(\n    const MatrixType& matrix,\n    const typename ResultType::Scalar& invdet,\n    const Matrix<typename ResultType::Scalar,3,1>& cofactors_col0,\n    ResultType& result)\n{\n  result.row(0) = cofactors_col0 * invdet;\n  result.coeffRef(1,0) =  cofactor_3x3<MatrixType,0,1>(matrix) * invdet;\n  result.coeffRef(1,1) =  cofactor_3x3<MatrixType,1,1>(matrix) * invdet;\n  result.coeffRef(1,2) =  cofactor_3x3<MatrixType,2,1>(matrix) * invdet;\n  result.coeffRef(2,0) =  cofactor_3x3<MatrixType,0,2>(matrix) * invdet;\n  result.coeffRef(2,1) =  cofactor_3x3<MatrixType,1,2>(matrix) * invdet;\n  result.coeffRef(2,2) =  cofactor_3x3<MatrixType,2,2>(matrix) * invdet;\n}\n\ntemplate<typename MatrixType, typename ResultType>\nstruct compute_inverse<MatrixType, ResultType, 3>\n{\n  EIGEN_DEVICE_FUNC\n  static inline void run(const MatrixType& matrix, ResultType& result)\n  {\n    typedef typename ResultType::Scalar Scalar;\n    Matrix<typename MatrixType::Scalar,3,1> cofactors_col0;\n    cofactors_col0.coeffRef(0) =  cofactor_3x3<MatrixType,0,0>(matrix);\n    cofactors_col0.coeffRef(1) =  cofactor_3x3<MatrixType,1,0>(matrix);\n    cofactors_col0.coeffRef(2) =  cofactor_3x3<MatrixType,2,0>(matrix);\n    const Scalar det = (cofactors_col0.cwiseProduct(matrix.col(0))).sum();\n    const Scalar invdet = Scalar(1) / det;\n    compute_inverse_size3_helper(matrix, invdet, cofactors_col0, result);\n  }\n};\n\ntemplate<typename MatrixType, typename ResultType>\nstruct compute_inverse_and_det_with_check<MatrixType, ResultType, 3>\n{\n  EIGEN_DEVICE_FUNC\n  static inline void run(\n    const MatrixType& matrix,\n    const typename MatrixType::RealScalar& absDeterminantThreshold,\n    ResultType& inverse,\n    typename ResultType::Scalar& determinant,\n    bool& invertible\n  )\n  {\n    using std::abs;\n    typedef typename ResultType::Scalar Scalar;\n    Matrix<Scalar,3,1> cofactors_col0;\n    cofactors_col0.coeffRef(0) =  cofactor_3x3<MatrixType,0,0>(matrix);\n    cofactors_col0.coeffRef(1) =  cofactor_3x3<MatrixType,1,0>(matrix);\n    cofactors_col0.coeffRef(2) =  cofactor_3x3<MatrixType,2,0>(matrix);\n    determinant = (cofactors_col0.cwiseProduct(matrix.col(0))).sum();\n    invertible = abs(determinant) > absDeterminantThreshold;\n    if(!invertible) return;\n    const Scalar invdet = Scalar(1) / determinant;\n    compute_inverse_size3_helper(matrix, invdet, cofactors_col0, inverse);\n  }\n};\n\n/****************************\n*** Size 4 implementation ***\n****************************/\n\ntemplate<typename Derived>\nEIGEN_DEVICE_FUNC \ninline const typename Derived::Scalar general_det3_helper\n(const MatrixBase<Derived>& matrix, int i1, int i2, int i3, int j1, int j2, int j3)\n{\n  return matrix.coeff(i1,j1)\n         * (matrix.coeff(i2,j2) * matrix.coeff(i3,j3) - matrix.coeff(i2,j3) * matrix.coeff(i3,j2));\n}\n\ntemplate<typename MatrixType, int i, int j>\nEIGEN_DEVICE_FUNC \ninline typename MatrixType::Scalar cofactor_4x4(const MatrixType& matrix)\n{\n  enum {\n    i1 = (i+1) % 4,\n    i2 = (i+2) % 4,\n    i3 = (i+3) % 4,\n    j1 = (j+1) % 4,\n    j2 = (j+2) % 4,\n    j3 = (j+3) % 4\n  };\n  return general_det3_helper(matrix, i1, i2, i3, j1, j2, j3)\n       + general_det3_helper(matrix, i2, i3, i1, j1, j2, j3)\n       + general_det3_helper(matrix, i3, i1, i2, j1, j2, j3);\n}\n\ntemplate<int Arch, typename Scalar, typename MatrixType, typename ResultType>\nstruct compute_inverse_size4\n{\n  EIGEN_DEVICE_FUNC\n  static void run(const MatrixType& matrix, ResultType& result)\n  {\n    result.coeffRef(0,0) =  cofactor_4x4<MatrixType,0,0>(matrix);\n    result.coeffRef(1,0) = -cofactor_4x4<MatrixType,0,1>(matrix);\n    result.coeffRef(2,0) =  cofactor_4x4<MatrixType,0,2>(matrix);\n    result.coeffRef(3,0) = -cofactor_4x4<MatrixType,0,3>(matrix);\n    result.coeffRef(0,2) =  cofactor_4x4<MatrixType,2,0>(matrix);\n    result.coeffRef(1,2) = -cofactor_4x4<MatrixType,2,1>(matrix);\n    result.coeffRef(2,2) =  cofactor_4x4<MatrixType,2,2>(matrix);\n    result.coeffRef(3,2) = -cofactor_4x4<MatrixType,2,3>(matrix);\n    result.coeffRef(0,1) = -cofactor_4x4<MatrixType,1,0>(matrix);\n    result.coeffRef(1,1) =  cofactor_4x4<MatrixType,1,1>(matrix);\n    result.coeffRef(2,1) = -cofactor_4x4<MatrixType,1,2>(matrix);\n    result.coeffRef(3,1) =  cofactor_4x4<MatrixType,1,3>(matrix);\n    result.coeffRef(0,3) = -cofactor_4x4<MatrixType,3,0>(matrix);\n    result.coeffRef(1,3) =  cofactor_4x4<MatrixType,3,1>(matrix);\n    result.coeffRef(2,3) = -cofactor_4x4<MatrixType,3,2>(matrix);\n    result.coeffRef(3,3) =  cofactor_4x4<MatrixType,3,3>(matrix);\n    result /= (matrix.col(0).cwiseProduct(result.row(0).transpose())).sum();\n  }\n};\n\ntemplate<typename MatrixType, typename ResultType>\nstruct compute_inverse<MatrixType, ResultType, 4>\n : compute_inverse_size4<Architecture::Target, typename MatrixType::Scalar,\n                            MatrixType, ResultType>\n{\n};\n\ntemplate<typename MatrixType, typename ResultType>\nstruct compute_inverse_and_det_with_check<MatrixType, ResultType, 4>\n{\n  EIGEN_DEVICE_FUNC\n  static inline void run(\n    const MatrixType& matrix,\n    const typename MatrixType::RealScalar& absDeterminantThreshold,\n    ResultType& inverse,\n    typename ResultType::Scalar& determinant,\n    bool& invertible\n  )\n  {\n    using std::abs;\n    determinant = matrix.determinant();\n    invertible = abs(determinant) > absDeterminantThreshold;\n    if(invertible) compute_inverse<MatrixType, ResultType>::run(matrix, inverse);\n  }\n};\n\n/*************************\n*** MatrixBase methods ***\n*************************/\n\n} // end namespace internal\n\nnamespace internal {\n\n// Specialization for \"dense = dense_xpr.inverse()\"\ntemplate<typename DstXprType, typename XprType>\nstruct Assignment<DstXprType, Inverse<XprType>, internal::assign_op<typename DstXprType::Scalar,typename XprType::Scalar>, Dense2Dense>\n{\n  typedef Inverse<XprType> SrcXprType;\n  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename XprType::Scalar> &)\n  {\n    Index dstRows = src.rows();\n    Index dstCols = src.cols();\n    if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))\n      dst.resize(dstRows, dstCols);\n    \n    const int Size = EIGEN_PLAIN_ENUM_MIN(XprType::ColsAtCompileTime,DstXprType::ColsAtCompileTime);\n    EIGEN_ONLY_USED_FOR_DEBUG(Size);\n    eigen_assert(( (Size<=1) || (Size>4) || (extract_data(src.nestedExpression())!=extract_data(dst)))\n              && \"Aliasing problem detected in inverse(), you need to do inverse().eval() here.\");\n\n    typedef typename internal::nested_eval<XprType,XprType::ColsAtCompileTime>::type  ActualXprType;\n    typedef typename internal::remove_all<ActualXprType>::type                        ActualXprTypeCleanded;\n    \n    ActualXprType actual_xpr(src.nestedExpression());\n    \n    compute_inverse<ActualXprTypeCleanded, DstXprType>::run(actual_xpr, dst);\n  }\n};\n\n  \n} // end namespace internal\n\n/** \\lu_module\n  *\n  * \\returns the matrix inverse of this matrix.\n  *\n  * For small fixed sizes up to 4x4, this method uses cofactors.\n  * In the general case, this method uses class PartialPivLU.\n  *\n  * \\note This matrix must be invertible, otherwise the result is undefined. If you need an\n  * invertibility check, do the following:\n  * \\li for fixed sizes up to 4x4, use computeInverseAndDetWithCheck().\n  * \\li for the general case, use class FullPivLU.\n  *\n  * Example: \\include MatrixBase_inverse.cpp\n  * Output: \\verbinclude MatrixBase_inverse.out\n  *\n  * \\sa computeInverseAndDetWithCheck()\n  */\ntemplate<typename Derived>\ninline const Inverse<Derived> MatrixBase<Derived>::inverse() const\n{\n  EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsInteger,THIS_FUNCTION_IS_NOT_FOR_INTEGER_NUMERIC_TYPES)\n  eigen_assert(rows() == cols());\n  return Inverse<Derived>(derived());\n}\n\n/** \\lu_module\n  *\n  * Computation of matrix inverse and determinant, with invertibility check.\n  *\n  * This is only for fixed-size square matrices of size up to 4x4.\n  *\n  * \\param inverse Reference to the matrix in which to store the inverse.\n  * \\param determinant Reference to the variable in which to store the determinant.\n  * \\param invertible Reference to the bool variable in which to store whether the matrix is invertible.\n  * \\param absDeterminantThreshold Optional parameter controlling the invertibility check.\n  *                                The matrix will be declared invertible if the absolute value of its\n  *                                determinant is greater than this threshold.\n  *\n  * Example: \\include MatrixBase_computeInverseAndDetWithCheck.cpp\n  * Output: \\verbinclude MatrixBase_computeInverseAndDetWithCheck.out\n  *\n  * \\sa inverse(), computeInverseWithCheck()\n  */\ntemplate<typename Derived>\ntemplate<typename ResultType>\ninline void MatrixBase<Derived>::computeInverseAndDetWithCheck(\n    ResultType& inverse,\n    typename ResultType::Scalar& determinant,\n    bool& invertible,\n    const RealScalar& absDeterminantThreshold\n  ) const\n{\n  // i'd love to put some static assertions there, but SFINAE means that they have no effect...\n  eigen_assert(rows() == cols());\n  // for 2x2, it's worth giving a chance to avoid evaluating.\n  // for larger sizes, evaluating has negligible cost and limits code size.\n  typedef typename internal::conditional<\n    RowsAtCompileTime == 2,\n    typename internal::remove_all<typename internal::nested_eval<Derived, 2>::type>::type,\n    PlainObject\n  >::type MatrixType;\n  internal::compute_inverse_and_det_with_check<MatrixType, ResultType>::run\n    (derived(), absDeterminantThreshold, inverse, determinant, invertible);\n}\n\n/** \\lu_module\n  *\n  * Computation of matrix inverse, with invertibility check.\n  *\n  * This is only for fixed-size square matrices of size up to 4x4.\n  *\n  * \\param inverse Reference to the matrix in which to store the inverse.\n  * \\param invertible Reference to the bool variable in which to store whether the matrix is invertible.\n  * \\param absDeterminantThreshold Optional parameter controlling the invertibility check.\n  *                                The matrix will be declared invertible if the absolute value of its\n  *                                determinant is greater than this threshold.\n  *\n  * Example: \\include MatrixBase_computeInverseWithCheck.cpp\n  * Output: \\verbinclude MatrixBase_computeInverseWithCheck.out\n  *\n  * \\sa inverse(), computeInverseAndDetWithCheck()\n  */\ntemplate<typename Derived>\ntemplate<typename ResultType>\ninline void MatrixBase<Derived>::computeInverseWithCheck(\n    ResultType& inverse,\n    bool& invertible,\n    const RealScalar& absDeterminantThreshold\n  ) const\n{\n  Scalar determinant;\n  // i'd love to put some static assertions there, but SFINAE means that they have no effect...\n  eigen_assert(rows() == cols());\n  computeInverseAndDetWithCheck(inverse,determinant,invertible,absDeterminantThreshold);\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_INVERSE_IMPL_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/LU/PartialPivLU.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2006-2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_PARTIALLU_H\n#define EIGEN_PARTIALLU_H\n\nnamespace Eigen {\n\nnamespace internal {\ntemplate<typename _MatrixType> struct traits<PartialPivLU<_MatrixType> >\n : traits<_MatrixType>\n{\n  typedef MatrixXpr XprKind;\n  typedef SolverStorage StorageKind;\n  typedef traits<_MatrixType> BaseTraits;\n  enum {\n    Flags = BaseTraits::Flags & RowMajorBit,\n    CoeffReadCost = Dynamic\n  };\n};\n\ntemplate<typename T,typename Derived>\nstruct enable_if_ref;\n// {\n//   typedef Derived type;\n// };\n\ntemplate<typename T,typename Derived>\nstruct enable_if_ref<Ref<T>,Derived> {\n  typedef Derived type;\n};\n\n} // end namespace internal\n\n/** \\ingroup LU_Module\n  *\n  * \\class PartialPivLU\n  *\n  * \\brief LU decomposition of a matrix with partial pivoting, and related features\n  *\n  * \\tparam _MatrixType the type of the matrix of which we are computing the LU decomposition\n  *\n  * This class represents a LU decomposition of a \\b square \\b invertible matrix, with partial pivoting: the matrix A\n  * is decomposed as A = PLU where L is unit-lower-triangular, U is upper-triangular, and P\n  * is a permutation matrix.\n  *\n  * Typically, partial pivoting LU decomposition is only considered numerically stable for square invertible\n  * matrices. Thus LAPACK's dgesv and dgesvx require the matrix to be square and invertible. The present class\n  * does the same. It will assert that the matrix is square, but it won't (actually it can't) check that the\n  * matrix is invertible: it is your task to check that you only use this decomposition on invertible matrices.\n  *\n  * The guaranteed safe alternative, working for all matrices, is the full pivoting LU decomposition, provided\n  * by class FullPivLU.\n  *\n  * This is \\b not a rank-revealing LU decomposition. Many features are intentionally absent from this class,\n  * such as rank computation. If you need these features, use class FullPivLU.\n  *\n  * This LU decomposition is suitable to invert invertible matrices. It is what MatrixBase::inverse() uses\n  * in the general case.\n  * On the other hand, it is \\b not suitable to determine whether a given matrix is invertible.\n  *\n  * The data of the LU decomposition can be directly accessed through the methods matrixLU(), permutationP().\n  *\n  * This class supports the \\link InplaceDecomposition inplace decomposition \\endlink mechanism.\n  * \n  * \\sa MatrixBase::partialPivLu(), MatrixBase::determinant(), MatrixBase::inverse(), MatrixBase::computeInverse(), class FullPivLU\n  */\ntemplate<typename _MatrixType> class PartialPivLU\n  : public SolverBase<PartialPivLU<_MatrixType> >\n{\n  public:\n\n    typedef _MatrixType MatrixType;\n    typedef SolverBase<PartialPivLU> Base;\n    EIGEN_GENERIC_PUBLIC_INTERFACE(PartialPivLU)\n    // FIXME StorageIndex defined in EIGEN_GENERIC_PUBLIC_INTERFACE should be int\n    enum {\n      MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,\n      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime\n    };\n    typedef PermutationMatrix<RowsAtCompileTime, MaxRowsAtCompileTime> PermutationType;\n    typedef Transpositions<RowsAtCompileTime, MaxRowsAtCompileTime> TranspositionType;\n    typedef typename MatrixType::PlainObject PlainObject;\n\n    /**\n      * \\brief Default Constructor.\n      *\n      * The default constructor is useful in cases in which the user intends to\n      * perform decompositions via PartialPivLU::compute(const MatrixType&).\n      */\n    PartialPivLU();\n\n    /** \\brief Default Constructor with memory preallocation\n      *\n      * Like the default constructor but with preallocation of the internal data\n      * according to the specified problem \\a size.\n      * \\sa PartialPivLU()\n      */\n    explicit PartialPivLU(Index size);\n\n    /** Constructor.\n      *\n      * \\param matrix the matrix of which to compute the LU decomposition.\n      *\n      * \\warning The matrix should have full rank (e.g. if it's square, it should be invertible).\n      * If you need to deal with non-full rank, use class FullPivLU instead.\n      */\n    template<typename InputType>\n    explicit PartialPivLU(const EigenBase<InputType>& matrix);\n\n    /** Constructor for \\link InplaceDecomposition inplace decomposition \\endlink\n      *\n      * \\param matrix the matrix of which to compute the LU decomposition.\n      *\n      * \\warning The matrix should have full rank (e.g. if it's square, it should be invertible).\n      * If you need to deal with non-full rank, use class FullPivLU instead.\n      */\n    template<typename InputType>\n    explicit PartialPivLU(EigenBase<InputType>& matrix);\n\n    template<typename InputType>\n    PartialPivLU& compute(const EigenBase<InputType>& matrix) {\n      m_lu = matrix.derived();\n      compute();\n      return *this;\n    }\n\n    /** \\returns the LU decomposition matrix: the upper-triangular part is U, the\n      * unit-lower-triangular part is L (at least for square matrices; in the non-square\n      * case, special care is needed, see the documentation of class FullPivLU).\n      *\n      * \\sa matrixL(), matrixU()\n      */\n    inline const MatrixType& matrixLU() const\n    {\n      eigen_assert(m_isInitialized && \"PartialPivLU is not initialized.\");\n      return m_lu;\n    }\n\n    /** \\returns the permutation matrix P.\n      */\n    inline const PermutationType& permutationP() const\n    {\n      eigen_assert(m_isInitialized && \"PartialPivLU is not initialized.\");\n      return m_p;\n    }\n\n    /** This method returns the solution x to the equation Ax=b, where A is the matrix of which\n      * *this is the LU decomposition.\n      *\n      * \\param b the right-hand-side of the equation to solve. Can be a vector or a matrix,\n      *          the only requirement in order for the equation to make sense is that\n      *          b.rows()==A.rows(), where A is the matrix of which *this is the LU decomposition.\n      *\n      * \\returns the solution.\n      *\n      * Example: \\include PartialPivLU_solve.cpp\n      * Output: \\verbinclude PartialPivLU_solve.out\n      *\n      * Since this PartialPivLU class assumes anyway that the matrix A is invertible, the solution\n      * theoretically exists and is unique regardless of b.\n      *\n      * \\sa TriangularView::solve(), inverse(), computeInverse()\n      */\n    // FIXME this is a copy-paste of the base-class member to add the isInitialized assertion.\n    template<typename Rhs>\n    inline const Solve<PartialPivLU, Rhs>\n    solve(const MatrixBase<Rhs>& b) const\n    {\n      eigen_assert(m_isInitialized && \"PartialPivLU is not initialized.\");\n      return Solve<PartialPivLU, Rhs>(*this, b.derived());\n    }\n\n    /** \\returns an estimate of the reciprocal condition number of the matrix of which \\c *this is\n        the LU decomposition.\n      */\n    inline RealScalar rcond() const\n    {\n      eigen_assert(m_isInitialized && \"PartialPivLU is not initialized.\");\n      return internal::rcond_estimate_helper(m_l1_norm, *this);\n    }\n\n    /** \\returns the inverse of the matrix of which *this is the LU decomposition.\n      *\n      * \\warning The matrix being decomposed here is assumed to be invertible. If you need to check for\n      *          invertibility, use class FullPivLU instead.\n      *\n      * \\sa MatrixBase::inverse(), LU::inverse()\n      */\n    inline const Inverse<PartialPivLU> inverse() const\n    {\n      eigen_assert(m_isInitialized && \"PartialPivLU is not initialized.\");\n      return Inverse<PartialPivLU>(*this);\n    }\n\n    /** \\returns the determinant of the matrix of which\n      * *this is the LU decomposition. It has only linear complexity\n      * (that is, O(n) where n is the dimension of the square matrix)\n      * as the LU decomposition has already been computed.\n      *\n      * \\note For fixed-size matrices of size up to 4, MatrixBase::determinant() offers\n      *       optimized paths.\n      *\n      * \\warning a determinant can be very big or small, so for matrices\n      * of large enough dimension, there is a risk of overflow/underflow.\n      *\n      * \\sa MatrixBase::determinant()\n      */\n    Scalar determinant() const;\n\n    MatrixType reconstructedMatrix() const;\n\n    inline Index rows() const { return m_lu.rows(); }\n    inline Index cols() const { return m_lu.cols(); }\n\n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    template<typename RhsType, typename DstType>\n    EIGEN_DEVICE_FUNC\n    void _solve_impl(const RhsType &rhs, DstType &dst) const {\n     /* The decomposition PA = LU can be rewritten as A = P^{-1} L U.\n      * So we proceed as follows:\n      * Step 1: compute c = Pb.\n      * Step 2: replace c by the solution x to Lx = c.\n      * Step 3: replace c by the solution x to Ux = c.\n      */\n\n      eigen_assert(rhs.rows() == m_lu.rows());\n\n      // Step 1\n      dst = permutationP() * rhs;\n\n      // Step 2\n      m_lu.template triangularView<UnitLower>().solveInPlace(dst);\n\n      // Step 3\n      m_lu.template triangularView<Upper>().solveInPlace(dst);\n    }\n\n    template<bool Conjugate, typename RhsType, typename DstType>\n    EIGEN_DEVICE_FUNC\n    void _solve_impl_transposed(const RhsType &rhs, DstType &dst) const {\n     /* The decomposition PA = LU can be rewritten as A = P^{-1} L U.\n      * So we proceed as follows:\n      * Step 1: compute c = Pb.\n      * Step 2: replace c by the solution x to Lx = c.\n      * Step 3: replace c by the solution x to Ux = c.\n      */\n\n      eigen_assert(rhs.rows() == m_lu.cols());\n\n      if (Conjugate) {\n        // Step 1\n        dst = m_lu.template triangularView<Upper>().adjoint().solve(rhs);\n        // Step 2\n        m_lu.template triangularView<UnitLower>().adjoint().solveInPlace(dst);\n      } else {\n        // Step 1\n        dst = m_lu.template triangularView<Upper>().transpose().solve(rhs);\n        // Step 2\n        m_lu.template triangularView<UnitLower>().transpose().solveInPlace(dst);\n      }\n      // Step 3\n      dst = permutationP().transpose() * dst;\n    }\n    #endif\n\n  protected:\n\n    static void check_template_parameters()\n    {\n      EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);\n    }\n\n    void compute();\n\n    MatrixType m_lu;\n    PermutationType m_p;\n    TranspositionType m_rowsTranspositions;\n    RealScalar m_l1_norm;\n    signed char m_det_p;\n    bool m_isInitialized;\n};\n\ntemplate<typename MatrixType>\nPartialPivLU<MatrixType>::PartialPivLU()\n  : m_lu(),\n    m_p(),\n    m_rowsTranspositions(),\n    m_l1_norm(0),\n    m_det_p(0),\n    m_isInitialized(false)\n{\n}\n\ntemplate<typename MatrixType>\nPartialPivLU<MatrixType>::PartialPivLU(Index size)\n  : m_lu(size, size),\n    m_p(size),\n    m_rowsTranspositions(size),\n    m_l1_norm(0),\n    m_det_p(0),\n    m_isInitialized(false)\n{\n}\n\ntemplate<typename MatrixType>\ntemplate<typename InputType>\nPartialPivLU<MatrixType>::PartialPivLU(const EigenBase<InputType>& matrix)\n  : m_lu(matrix.rows(),matrix.cols()),\n    m_p(matrix.rows()),\n    m_rowsTranspositions(matrix.rows()),\n    m_l1_norm(0),\n    m_det_p(0),\n    m_isInitialized(false)\n{\n  compute(matrix.derived());\n}\n\ntemplate<typename MatrixType>\ntemplate<typename InputType>\nPartialPivLU<MatrixType>::PartialPivLU(EigenBase<InputType>& matrix)\n  : m_lu(matrix.derived()),\n    m_p(matrix.rows()),\n    m_rowsTranspositions(matrix.rows()),\n    m_l1_norm(0),\n    m_det_p(0),\n    m_isInitialized(false)\n{\n  compute();\n}\n\nnamespace internal {\n\n/** \\internal This is the blocked version of fullpivlu_unblocked() */\ntemplate<typename Scalar, int StorageOrder, typename PivIndex>\nstruct partial_lu_impl\n{\n  // FIXME add a stride to Map, so that the following mapping becomes easier,\n  // another option would be to create an expression being able to automatically\n  // warp any Map, Matrix, and Block expressions as a unique type, but since that's exactly\n  // a Map + stride, why not adding a stride to Map, and convenient ctors from a Matrix,\n  // and Block.\n  typedef Map<Matrix<Scalar, Dynamic, Dynamic, StorageOrder> > MapLU;\n  typedef Block<MapLU, Dynamic, Dynamic> MatrixType;\n  typedef Block<MatrixType,Dynamic,Dynamic> BlockType;\n  typedef typename MatrixType::RealScalar RealScalar;\n\n  /** \\internal performs the LU decomposition in-place of the matrix \\a lu\n    * using an unblocked algorithm.\n    *\n    * In addition, this function returns the row transpositions in the\n    * vector \\a row_transpositions which must have a size equal to the number\n    * of columns of the matrix \\a lu, and an integer \\a nb_transpositions\n    * which returns the actual number of transpositions.\n    *\n    * \\returns The index of the first pivot which is exactly zero if any, or a negative number otherwise.\n    */\n  static Index unblocked_lu(MatrixType& lu, PivIndex* row_transpositions, PivIndex& nb_transpositions)\n  {\n    typedef scalar_score_coeff_op<Scalar> Scoring;\n    typedef typename Scoring::result_type Score;\n    const Index rows = lu.rows();\n    const Index cols = lu.cols();\n    const Index size = (std::min)(rows,cols);\n    nb_transpositions = 0;\n    Index first_zero_pivot = -1;\n    for(Index k = 0; k < size; ++k)\n    {\n      Index rrows = rows-k-1;\n      Index rcols = cols-k-1;\n\n      Index row_of_biggest_in_col;\n      Score biggest_in_corner\n        = lu.col(k).tail(rows-k).unaryExpr(Scoring()).maxCoeff(&row_of_biggest_in_col);\n      row_of_biggest_in_col += k;\n\n      row_transpositions[k] = PivIndex(row_of_biggest_in_col);\n\n      if(biggest_in_corner != Score(0))\n      {\n        if(k != row_of_biggest_in_col)\n        {\n          lu.row(k).swap(lu.row(row_of_biggest_in_col));\n          ++nb_transpositions;\n        }\n\n        // FIXME shall we introduce a safe quotient expression in cas 1/lu.coeff(k,k)\n        // overflow but not the actual quotient?\n        lu.col(k).tail(rrows) /= lu.coeff(k,k);\n      }\n      else if(first_zero_pivot==-1)\n      {\n        // the pivot is exactly zero, we record the index of the first pivot which is exactly 0,\n        // and continue the factorization such we still have A = PLU\n        first_zero_pivot = k;\n      }\n\n      if(k<rows-1)\n        lu.bottomRightCorner(rrows,rcols).noalias() -= lu.col(k).tail(rrows) * lu.row(k).tail(rcols);\n    }\n    return first_zero_pivot;\n  }\n\n  /** \\internal performs the LU decomposition in-place of the matrix represented\n    * by the variables \\a rows, \\a cols, \\a lu_data, and \\a lu_stride using a\n    * recursive, blocked algorithm.\n    *\n    * In addition, this function returns the row transpositions in the\n    * vector \\a row_transpositions which must have a size equal to the number\n    * of columns of the matrix \\a lu, and an integer \\a nb_transpositions\n    * which returns the actual number of transpositions.\n    *\n    * \\returns The index of the first pivot which is exactly zero if any, or a negative number otherwise.\n    *\n    * \\note This very low level interface using pointers, etc. is to:\n    *   1 - reduce the number of instanciations to the strict minimum\n    *   2 - avoid infinite recursion of the instanciations with Block<Block<Block<...> > >\n    */\n  static Index blocked_lu(Index rows, Index cols, Scalar* lu_data, Index luStride, PivIndex* row_transpositions, PivIndex& nb_transpositions, Index maxBlockSize=256)\n  {\n    MapLU lu1(lu_data,StorageOrder==RowMajor?rows:luStride,StorageOrder==RowMajor?luStride:cols);\n    MatrixType lu(lu1,0,0,rows,cols);\n\n    const Index size = (std::min)(rows,cols);\n\n    // if the matrix is too small, no blocking:\n    if(size<=16)\n    {\n      return unblocked_lu(lu, row_transpositions, nb_transpositions);\n    }\n\n    // automatically adjust the number of subdivisions to the size\n    // of the matrix so that there is enough sub blocks:\n    Index blockSize;\n    {\n      blockSize = size/8;\n      blockSize = (blockSize/16)*16;\n      blockSize = (std::min)((std::max)(blockSize,Index(8)), maxBlockSize);\n    }\n\n    nb_transpositions = 0;\n    Index first_zero_pivot = -1;\n    for(Index k = 0; k < size; k+=blockSize)\n    {\n      Index bs = (std::min)(size-k,blockSize); // actual size of the block\n      Index trows = rows - k - bs; // trailing rows\n      Index tsize = size - k - bs; // trailing size\n\n      // partition the matrix:\n      //                          A00 | A01 | A02\n      // lu  = A_0 | A_1 | A_2 =  A10 | A11 | A12\n      //                          A20 | A21 | A22\n      BlockType A_0(lu,0,0,rows,k);\n      BlockType A_2(lu,0,k+bs,rows,tsize);\n      BlockType A11(lu,k,k,bs,bs);\n      BlockType A12(lu,k,k+bs,bs,tsize);\n      BlockType A21(lu,k+bs,k,trows,bs);\n      BlockType A22(lu,k+bs,k+bs,trows,tsize);\n\n      PivIndex nb_transpositions_in_panel;\n      // recursively call the blocked LU algorithm on [A11^T A21^T]^T\n      // with a very small blocking size:\n      Index ret = blocked_lu(trows+bs, bs, &lu.coeffRef(k,k), luStride,\n                   row_transpositions+k, nb_transpositions_in_panel, 16);\n      if(ret>=0 && first_zero_pivot==-1)\n        first_zero_pivot = k+ret;\n\n      nb_transpositions += nb_transpositions_in_panel;\n      // update permutations and apply them to A_0\n      for(Index i=k; i<k+bs; ++i)\n      {\n        Index piv = (row_transpositions[i] += internal::convert_index<PivIndex>(k));\n        A_0.row(i).swap(A_0.row(piv));\n      }\n\n      if(trows)\n      {\n        // apply permutations to A_2\n        for(Index i=k;i<k+bs; ++i)\n          A_2.row(i).swap(A_2.row(row_transpositions[i]));\n\n        // A12 = A11^-1 A12\n        A11.template triangularView<UnitLower>().solveInPlace(A12);\n\n        A22.noalias() -= A21 * A12;\n      }\n    }\n    return first_zero_pivot;\n  }\n};\n\n/** \\internal performs the LU decomposition with partial pivoting in-place.\n  */\ntemplate<typename MatrixType, typename TranspositionType>\nvoid partial_lu_inplace(MatrixType& lu, TranspositionType& row_transpositions, typename TranspositionType::StorageIndex& nb_transpositions)\n{\n  eigen_assert(lu.cols() == row_transpositions.size());\n  eigen_assert((&row_transpositions.coeffRef(1)-&row_transpositions.coeffRef(0)) == 1);\n\n  partial_lu_impl\n    <typename MatrixType::Scalar, MatrixType::Flags&RowMajorBit?RowMajor:ColMajor, typename TranspositionType::StorageIndex>\n    ::blocked_lu(lu.rows(), lu.cols(), &lu.coeffRef(0,0), lu.outerStride(), &row_transpositions.coeffRef(0), nb_transpositions);\n}\n\n} // end namespace internal\n\ntemplate<typename MatrixType>\nvoid PartialPivLU<MatrixType>::compute()\n{\n  check_template_parameters();\n\n  // the row permutation is stored as int indices, so just to be sure:\n  eigen_assert(m_lu.rows()<NumTraits<int>::highest());\n\n  m_l1_norm = m_lu.cwiseAbs().colwise().sum().maxCoeff();\n\n  eigen_assert(m_lu.rows() == m_lu.cols() && \"PartialPivLU is only for square (and moreover invertible) matrices\");\n  const Index size = m_lu.rows();\n\n  m_rowsTranspositions.resize(size);\n\n  typename TranspositionType::StorageIndex nb_transpositions;\n  internal::partial_lu_inplace(m_lu, m_rowsTranspositions, nb_transpositions);\n  m_det_p = (nb_transpositions%2) ? -1 : 1;\n\n  m_p = m_rowsTranspositions;\n\n  m_isInitialized = true;\n}\n\ntemplate<typename MatrixType>\ntypename PartialPivLU<MatrixType>::Scalar PartialPivLU<MatrixType>::determinant() const\n{\n  eigen_assert(m_isInitialized && \"PartialPivLU is not initialized.\");\n  return Scalar(m_det_p) * m_lu.diagonal().prod();\n}\n\n/** \\returns the matrix represented by the decomposition,\n * i.e., it returns the product: P^{-1} L U.\n * This function is provided for debug purpose. */\ntemplate<typename MatrixType>\nMatrixType PartialPivLU<MatrixType>::reconstructedMatrix() const\n{\n  eigen_assert(m_isInitialized && \"LU is not initialized.\");\n  // LU\n  MatrixType res = m_lu.template triangularView<UnitLower>().toDenseMatrix()\n                 * m_lu.template triangularView<Upper>();\n\n  // P^{-1}(LU)\n  res = m_p.inverse() * res;\n\n  return res;\n}\n\n/***** Implementation details *****************************************************/\n\nnamespace internal {\n\n/***** Implementation of inverse() *****************************************************/\ntemplate<typename DstXprType, typename MatrixType>\nstruct Assignment<DstXprType, Inverse<PartialPivLU<MatrixType> >, internal::assign_op<typename DstXprType::Scalar,typename PartialPivLU<MatrixType>::Scalar>, Dense2Dense>\n{\n  typedef PartialPivLU<MatrixType> LuType;\n  typedef Inverse<LuType> SrcXprType;\n  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename LuType::Scalar> &)\n  {\n    dst = src.nestedExpression().solve(MatrixType::Identity(src.rows(), src.cols()));\n  }\n};\n} // end namespace internal\n\n/******** MatrixBase methods *******/\n\n/** \\lu_module\n  *\n  * \\return the partial-pivoting LU decomposition of \\c *this.\n  *\n  * \\sa class PartialPivLU\n  */\ntemplate<typename Derived>\ninline const PartialPivLU<typename MatrixBase<Derived>::PlainObject>\nMatrixBase<Derived>::partialPivLu() const\n{\n  return PartialPivLU<PlainObject>(eval());\n}\n\n/** \\lu_module\n  *\n  * Synonym of partialPivLu().\n  *\n  * \\return the partial-pivoting LU decomposition of \\c *this.\n  *\n  * \\sa class PartialPivLU\n  */\ntemplate<typename Derived>\ninline const PartialPivLU<typename MatrixBase<Derived>::PlainObject>\nMatrixBase<Derived>::lu() const\n{\n  return PartialPivLU<PlainObject>(eval());\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_PARTIALLU_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/LU/PartialPivLU_LAPACKE.h",
    "content": "/*\n Copyright (c) 2011, Intel Corporation. All rights reserved.\n\n Redistribution and use in source and binary forms, with or without modification,\n are permitted provided that the following conditions are met:\n\n * Redistributions of source code must retain the above copyright notice, this\n   list of conditions and the following disclaimer.\n * Redistributions in binary form must reproduce the above copyright notice,\n   this list of conditions and the following disclaimer in the documentation\n   and/or other materials provided with the distribution.\n * Neither the name of Intel Corporation nor the names of its contributors may\n   be used to endorse or promote products derived from this software without\n   specific prior written permission.\n\n THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\" AND\n ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED\n WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\n DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR\n ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES\n (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;\n LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON\n ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT\n (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS\n SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n\n ********************************************************************************\n *   Content : Eigen bindings to LAPACKe\n *     LU decomposition with partial pivoting based on LAPACKE_?getrf function.\n ********************************************************************************\n*/\n\n#ifndef EIGEN_PARTIALLU_LAPACK_H\n#define EIGEN_PARTIALLU_LAPACK_H\n\nnamespace Eigen { \n\nnamespace internal {\n\n/** \\internal Specialization for the data types supported by LAPACKe */\n\n#define EIGEN_LAPACKE_LU_PARTPIV(EIGTYPE, LAPACKE_TYPE, LAPACKE_PREFIX) \\\ntemplate<int StorageOrder> \\\nstruct partial_lu_impl<EIGTYPE, StorageOrder, lapack_int> \\\n{ \\\n  /* \\internal performs the LU decomposition in-place of the matrix represented */ \\\n  static lapack_int blocked_lu(Index rows, Index cols, EIGTYPE* lu_data, Index luStride, lapack_int* row_transpositions, lapack_int& nb_transpositions, lapack_int maxBlockSize=256) \\\n  { \\\n    EIGEN_UNUSED_VARIABLE(maxBlockSize);\\\n    lapack_int matrix_order, first_zero_pivot; \\\n    lapack_int m, n, lda, *ipiv, info; \\\n    EIGTYPE* a; \\\n/* Set up parameters for ?getrf */ \\\n    matrix_order = StorageOrder==RowMajor ? LAPACK_ROW_MAJOR : LAPACK_COL_MAJOR; \\\n    lda = convert_index<lapack_int>(luStride); \\\n    a = lu_data; \\\n    ipiv = row_transpositions; \\\n    m = convert_index<lapack_int>(rows); \\\n    n = convert_index<lapack_int>(cols); \\\n    nb_transpositions = 0; \\\n\\\n    info = LAPACKE_##LAPACKE_PREFIX##getrf( matrix_order, m, n, (LAPACKE_TYPE*)a, lda, ipiv ); \\\n\\\n    for(int i=0;i<m;i++) { ipiv[i]--; if (ipiv[i]!=i) nb_transpositions++; } \\\n\\\n    eigen_assert(info >= 0); \\\n/* something should be done with nb_transpositions */ \\\n\\\n    first_zero_pivot = info; \\\n    return first_zero_pivot; \\\n  } \\\n};\n\nEIGEN_LAPACKE_LU_PARTPIV(double, double, d)\nEIGEN_LAPACKE_LU_PARTPIV(float, float, s)\nEIGEN_LAPACKE_LU_PARTPIV(dcomplex, lapack_complex_double, z)\nEIGEN_LAPACKE_LU_PARTPIV(scomplex, lapack_complex_float,  c)\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_PARTIALLU_LAPACK_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/LU/arch/Inverse_SSE.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2001 Intel Corporation\n// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n// The SSE code for the 4x4 float and double matrix inverse in this file\n// comes from the following Intel's library:\n// http://software.intel.com/en-us/articles/optimized-matrix-library-for-use-with-the-intel-pentiumr-4-processors-sse2-instructions/\n//\n// Here is the respective copyright and license statement:\n//\n//   Copyright (c) 2001 Intel Corporation.\n//\n// Permition is granted to use, copy, distribute and prepare derivative works\n// of this library for any purpose and without fee, provided, that the above\n// copyright notice and this statement appear in all copies.\n// Intel makes no representations about the suitability of this software for\n// any purpose, and specifically disclaims all warranties.\n// See LEGAL.TXT for all the legal information.\n\n#ifndef EIGEN_INVERSE_SSE_H\n#define EIGEN_INVERSE_SSE_H\n\nnamespace Eigen { \n\nnamespace internal {\n\ntemplate<typename MatrixType, typename ResultType>\nstruct compute_inverse_size4<Architecture::SSE, float, MatrixType, ResultType>\n{\n  enum {\n    MatrixAlignment     = traits<MatrixType>::Alignment,\n    ResultAlignment     = traits<ResultType>::Alignment,\n    StorageOrdersMatch  = (MatrixType::Flags&RowMajorBit) == (ResultType::Flags&RowMajorBit)\n  };\n  typedef typename conditional<(MatrixType::Flags&LinearAccessBit),MatrixType const &,typename MatrixType::PlainObject>::type ActualMatrixType;\n  \n  static void run(const MatrixType& mat, ResultType& result)\n  {\n    ActualMatrixType matrix(mat);\n    EIGEN_ALIGN16 const unsigned int _Sign_PNNP[4] = { 0x00000000, 0x80000000, 0x80000000, 0x00000000 };\n\n    // Load the full matrix into registers\n    __m128 _L1 = matrix.template packet<MatrixAlignment>( 0);\n    __m128 _L2 = matrix.template packet<MatrixAlignment>( 4);\n    __m128 _L3 = matrix.template packet<MatrixAlignment>( 8);\n    __m128 _L4 = matrix.template packet<MatrixAlignment>(12);\n\n    // The inverse is calculated using \"Divide and Conquer\" technique. The\n    // original matrix is divide into four 2x2 sub-matrices. Since each\n    // register holds four matrix element, the smaller matrices are\n    // represented as a registers. Hence we get a better locality of the\n    // calculations.\n\n    __m128 A, B, C, D; // the four sub-matrices\n    if(!StorageOrdersMatch)\n    {\n      A = _mm_unpacklo_ps(_L1, _L2);\n      B = _mm_unpacklo_ps(_L3, _L4);\n      C = _mm_unpackhi_ps(_L1, _L2);\n      D = _mm_unpackhi_ps(_L3, _L4);\n    }\n    else\n    {\n      A = _mm_movelh_ps(_L1, _L2);\n      B = _mm_movehl_ps(_L2, _L1);\n      C = _mm_movelh_ps(_L3, _L4);\n      D = _mm_movehl_ps(_L4, _L3);\n    }\n\n    __m128 iA, iB, iC, iD,                 // partial inverse of the sub-matrices\n            DC, AB;\n    __m128 dA, dB, dC, dD;                 // determinant of the sub-matrices\n    __m128 det, d, d1, d2;\n    __m128 rd;                             // reciprocal of the determinant\n\n    //  AB = A# * B\n    AB = _mm_mul_ps(_mm_shuffle_ps(A,A,0x0F), B);\n    AB = _mm_sub_ps(AB,_mm_mul_ps(_mm_shuffle_ps(A,A,0xA5), _mm_shuffle_ps(B,B,0x4E)));\n    //  DC = D# * C\n    DC = _mm_mul_ps(_mm_shuffle_ps(D,D,0x0F), C);\n    DC = _mm_sub_ps(DC,_mm_mul_ps(_mm_shuffle_ps(D,D,0xA5), _mm_shuffle_ps(C,C,0x4E)));\n\n    //  dA = |A|\n    dA = _mm_mul_ps(_mm_shuffle_ps(A, A, 0x5F),A);\n    dA = _mm_sub_ss(dA, _mm_movehl_ps(dA,dA));\n    //  dB = |B|\n    dB = _mm_mul_ps(_mm_shuffle_ps(B, B, 0x5F),B);\n    dB = _mm_sub_ss(dB, _mm_movehl_ps(dB,dB));\n\n    //  dC = |C|\n    dC = _mm_mul_ps(_mm_shuffle_ps(C, C, 0x5F),C);\n    dC = _mm_sub_ss(dC, _mm_movehl_ps(dC,dC));\n    //  dD = |D|\n    dD = _mm_mul_ps(_mm_shuffle_ps(D, D, 0x5F),D);\n    dD = _mm_sub_ss(dD, _mm_movehl_ps(dD,dD));\n\n    //  d = trace(AB*DC) = trace(A#*B*D#*C)\n    d = _mm_mul_ps(_mm_shuffle_ps(DC,DC,0xD8),AB);\n\n    //  iD = C*A#*B\n    iD = _mm_mul_ps(_mm_shuffle_ps(C,C,0xA0), _mm_movelh_ps(AB,AB));\n    iD = _mm_add_ps(iD,_mm_mul_ps(_mm_shuffle_ps(C,C,0xF5), _mm_movehl_ps(AB,AB)));\n    //  iA = B*D#*C\n    iA = _mm_mul_ps(_mm_shuffle_ps(B,B,0xA0), _mm_movelh_ps(DC,DC));\n    iA = _mm_add_ps(iA,_mm_mul_ps(_mm_shuffle_ps(B,B,0xF5), _mm_movehl_ps(DC,DC)));\n\n    //  d = trace(AB*DC) = trace(A#*B*D#*C) [continue]\n    d  = _mm_add_ps(d, _mm_movehl_ps(d, d));\n    d  = _mm_add_ss(d, _mm_shuffle_ps(d, d, 1));\n    d1 = _mm_mul_ss(dA,dD);\n    d2 = _mm_mul_ss(dB,dC);\n\n    //  iD = D*|A| - C*A#*B\n    iD = _mm_sub_ps(_mm_mul_ps(D,_mm_shuffle_ps(dA,dA,0)), iD);\n\n    //  iA = A*|D| - B*D#*C;\n    iA = _mm_sub_ps(_mm_mul_ps(A,_mm_shuffle_ps(dD,dD,0)), iA);\n\n    //  det = |A|*|D| + |B|*|C| - trace(A#*B*D#*C)\n    det = _mm_sub_ss(_mm_add_ss(d1,d2),d);\n    rd  = _mm_div_ss(_mm_set_ss(1.0f), det);\n\n//     #ifdef ZERO_SINGULAR\n//         rd = _mm_and_ps(_mm_cmpneq_ss(det,_mm_setzero_ps()), rd);\n//     #endif\n\n    //  iB = D * (A#B)# = D*B#*A\n    iB = _mm_mul_ps(D, _mm_shuffle_ps(AB,AB,0x33));\n    iB = _mm_sub_ps(iB, _mm_mul_ps(_mm_shuffle_ps(D,D,0xB1), _mm_shuffle_ps(AB,AB,0x66)));\n    //  iC = A * (D#C)# = A*C#*D\n    iC = _mm_mul_ps(A, _mm_shuffle_ps(DC,DC,0x33));\n    iC = _mm_sub_ps(iC, _mm_mul_ps(_mm_shuffle_ps(A,A,0xB1), _mm_shuffle_ps(DC,DC,0x66)));\n\n    rd = _mm_shuffle_ps(rd,rd,0);\n    rd = _mm_xor_ps(rd, _mm_load_ps((float*)_Sign_PNNP));\n\n    //  iB = C*|B| - D*B#*A\n    iB = _mm_sub_ps(_mm_mul_ps(C,_mm_shuffle_ps(dB,dB,0)), iB);\n\n    //  iC = B*|C| - A*C#*D;\n    iC = _mm_sub_ps(_mm_mul_ps(B,_mm_shuffle_ps(dC,dC,0)), iC);\n\n    //  iX = iX / det\n    iA = _mm_mul_ps(rd,iA);\n    iB = _mm_mul_ps(rd,iB);\n    iC = _mm_mul_ps(rd,iC);\n    iD = _mm_mul_ps(rd,iD);\n\n    Index res_stride = result.outerStride();\n    float* res = result.data();\n    pstoret<float, Packet4f, ResultAlignment>(res+0,            _mm_shuffle_ps(iA,iB,0x77));\n    pstoret<float, Packet4f, ResultAlignment>(res+res_stride,   _mm_shuffle_ps(iA,iB,0x22));\n    pstoret<float, Packet4f, ResultAlignment>(res+2*res_stride, _mm_shuffle_ps(iC,iD,0x77));\n    pstoret<float, Packet4f, ResultAlignment>(res+3*res_stride, _mm_shuffle_ps(iC,iD,0x22));\n  }\n\n};\n\ntemplate<typename MatrixType, typename ResultType>\nstruct compute_inverse_size4<Architecture::SSE, double, MatrixType, ResultType>\n{\n  enum {\n    MatrixAlignment     = traits<MatrixType>::Alignment,\n    ResultAlignment     = traits<ResultType>::Alignment,\n    StorageOrdersMatch  = (MatrixType::Flags&RowMajorBit) == (ResultType::Flags&RowMajorBit)\n  };\n  typedef typename conditional<(MatrixType::Flags&LinearAccessBit),MatrixType const &,typename MatrixType::PlainObject>::type ActualMatrixType;\n  \n  static void run(const MatrixType& mat, ResultType& result)\n  {\n    ActualMatrixType matrix(mat);\n    const __m128d _Sign_NP = _mm_castsi128_pd(_mm_set_epi32(0x0,0x0,0x80000000,0x0));\n    const __m128d _Sign_PN = _mm_castsi128_pd(_mm_set_epi32(0x80000000,0x0,0x0,0x0));\n\n    // The inverse is calculated using \"Divide and Conquer\" technique. The\n    // original matrix is divide into four 2x2 sub-matrices. Since each\n    // register of the matrix holds two elements, the smaller matrices are\n    // consisted of two registers. Hence we get a better locality of the\n    // calculations.\n\n    // the four sub-matrices\n    __m128d A1, A2, B1, B2, C1, C2, D1, D2;\n    \n    if(StorageOrdersMatch)\n    {\n      A1 = matrix.template packet<MatrixAlignment>( 0); B1 = matrix.template packet<MatrixAlignment>( 2);\n      A2 = matrix.template packet<MatrixAlignment>( 4); B2 = matrix.template packet<MatrixAlignment>( 6);\n      C1 = matrix.template packet<MatrixAlignment>( 8); D1 = matrix.template packet<MatrixAlignment>(10);\n      C2 = matrix.template packet<MatrixAlignment>(12); D2 = matrix.template packet<MatrixAlignment>(14);\n    }\n    else\n    {\n      __m128d tmp;\n      A1 = matrix.template packet<MatrixAlignment>( 0); C1 = matrix.template packet<MatrixAlignment>( 2);\n      A2 = matrix.template packet<MatrixAlignment>( 4); C2 = matrix.template packet<MatrixAlignment>( 6);\n      tmp = A1;\n      A1 = _mm_unpacklo_pd(A1,A2);\n      A2 = _mm_unpackhi_pd(tmp,A2);\n      tmp = C1;\n      C1 = _mm_unpacklo_pd(C1,C2);\n      C2 = _mm_unpackhi_pd(tmp,C2);\n      \n      B1 = matrix.template packet<MatrixAlignment>( 8); D1 = matrix.template packet<MatrixAlignment>(10);\n      B2 = matrix.template packet<MatrixAlignment>(12); D2 = matrix.template packet<MatrixAlignment>(14);\n      tmp = B1;\n      B1 = _mm_unpacklo_pd(B1,B2);\n      B2 = _mm_unpackhi_pd(tmp,B2);\n      tmp = D1;\n      D1 = _mm_unpacklo_pd(D1,D2);\n      D2 = _mm_unpackhi_pd(tmp,D2);\n    }\n    \n    __m128d iA1, iA2, iB1, iB2, iC1, iC2, iD1, iD2,     // partial invese of the sub-matrices\n            DC1, DC2, AB1, AB2;\n    __m128d dA, dB, dC, dD;     // determinant of the sub-matrices\n    __m128d det, d1, d2, rd;\n\n    //  dA = |A|\n    dA = _mm_shuffle_pd(A2, A2, 1);\n    dA = _mm_mul_pd(A1, dA);\n    dA = _mm_sub_sd(dA, _mm_shuffle_pd(dA,dA,3));\n    //  dB = |B|\n    dB = _mm_shuffle_pd(B2, B2, 1);\n    dB = _mm_mul_pd(B1, dB);\n    dB = _mm_sub_sd(dB, _mm_shuffle_pd(dB,dB,3));\n\n    //  AB = A# * B\n    AB1 = _mm_mul_pd(B1, _mm_shuffle_pd(A2,A2,3));\n    AB2 = _mm_mul_pd(B2, _mm_shuffle_pd(A1,A1,0));\n    AB1 = _mm_sub_pd(AB1, _mm_mul_pd(B2, _mm_shuffle_pd(A1,A1,3)));\n    AB2 = _mm_sub_pd(AB2, _mm_mul_pd(B1, _mm_shuffle_pd(A2,A2,0)));\n\n    //  dC = |C|\n    dC = _mm_shuffle_pd(C2, C2, 1);\n    dC = _mm_mul_pd(C1, dC);\n    dC = _mm_sub_sd(dC, _mm_shuffle_pd(dC,dC,3));\n    //  dD = |D|\n    dD = _mm_shuffle_pd(D2, D2, 1);\n    dD = _mm_mul_pd(D1, dD);\n    dD = _mm_sub_sd(dD, _mm_shuffle_pd(dD,dD,3));\n\n    //  DC = D# * C\n    DC1 = _mm_mul_pd(C1, _mm_shuffle_pd(D2,D2,3));\n    DC2 = _mm_mul_pd(C2, _mm_shuffle_pd(D1,D1,0));\n    DC1 = _mm_sub_pd(DC1, _mm_mul_pd(C2, _mm_shuffle_pd(D1,D1,3)));\n    DC2 = _mm_sub_pd(DC2, _mm_mul_pd(C1, _mm_shuffle_pd(D2,D2,0)));\n\n    //  rd = trace(AB*DC) = trace(A#*B*D#*C)\n    d1 = _mm_mul_pd(AB1, _mm_shuffle_pd(DC1, DC2, 0));\n    d2 = _mm_mul_pd(AB2, _mm_shuffle_pd(DC1, DC2, 3));\n    rd = _mm_add_pd(d1, d2);\n    rd = _mm_add_sd(rd, _mm_shuffle_pd(rd, rd,3));\n\n    //  iD = C*A#*B\n    iD1 = _mm_mul_pd(AB1, _mm_shuffle_pd(C1,C1,0));\n    iD2 = _mm_mul_pd(AB1, _mm_shuffle_pd(C2,C2,0));\n    iD1 = _mm_add_pd(iD1, _mm_mul_pd(AB2, _mm_shuffle_pd(C1,C1,3)));\n    iD2 = _mm_add_pd(iD2, _mm_mul_pd(AB2, _mm_shuffle_pd(C2,C2,3)));\n\n    //  iA = B*D#*C\n    iA1 = _mm_mul_pd(DC1, _mm_shuffle_pd(B1,B1,0));\n    iA2 = _mm_mul_pd(DC1, _mm_shuffle_pd(B2,B2,0));\n    iA1 = _mm_add_pd(iA1, _mm_mul_pd(DC2, _mm_shuffle_pd(B1,B1,3)));\n    iA2 = _mm_add_pd(iA2, _mm_mul_pd(DC2, _mm_shuffle_pd(B2,B2,3)));\n\n    //  iD = D*|A| - C*A#*B\n    dA = _mm_shuffle_pd(dA,dA,0);\n    iD1 = _mm_sub_pd(_mm_mul_pd(D1, dA), iD1);\n    iD2 = _mm_sub_pd(_mm_mul_pd(D2, dA), iD2);\n\n    //  iA = A*|D| - B*D#*C;\n    dD = _mm_shuffle_pd(dD,dD,0);\n    iA1 = _mm_sub_pd(_mm_mul_pd(A1, dD), iA1);\n    iA2 = _mm_sub_pd(_mm_mul_pd(A2, dD), iA2);\n\n    d1 = _mm_mul_sd(dA, dD);\n    d2 = _mm_mul_sd(dB, dC);\n\n    //  iB = D * (A#B)# = D*B#*A\n    iB1 = _mm_mul_pd(D1, _mm_shuffle_pd(AB2,AB1,1));\n    iB2 = _mm_mul_pd(D2, _mm_shuffle_pd(AB2,AB1,1));\n    iB1 = _mm_sub_pd(iB1, _mm_mul_pd(_mm_shuffle_pd(D1,D1,1), _mm_shuffle_pd(AB2,AB1,2)));\n    iB2 = _mm_sub_pd(iB2, _mm_mul_pd(_mm_shuffle_pd(D2,D2,1), _mm_shuffle_pd(AB2,AB1,2)));\n\n    //  det = |A|*|D| + |B|*|C| - trace(A#*B*D#*C)\n    det = _mm_add_sd(d1, d2);\n    det = _mm_sub_sd(det, rd);\n\n    //  iC = A * (D#C)# = A*C#*D\n    iC1 = _mm_mul_pd(A1, _mm_shuffle_pd(DC2,DC1,1));\n    iC2 = _mm_mul_pd(A2, _mm_shuffle_pd(DC2,DC1,1));\n    iC1 = _mm_sub_pd(iC1, _mm_mul_pd(_mm_shuffle_pd(A1,A1,1), _mm_shuffle_pd(DC2,DC1,2)));\n    iC2 = _mm_sub_pd(iC2, _mm_mul_pd(_mm_shuffle_pd(A2,A2,1), _mm_shuffle_pd(DC2,DC1,2)));\n\n    rd = _mm_div_sd(_mm_set_sd(1.0), det);\n//     #ifdef ZERO_SINGULAR\n//         rd = _mm_and_pd(_mm_cmpneq_sd(det,_mm_setzero_pd()), rd);\n//     #endif\n    rd = _mm_shuffle_pd(rd,rd,0);\n\n    //  iB = C*|B| - D*B#*A\n    dB = _mm_shuffle_pd(dB,dB,0);\n    iB1 = _mm_sub_pd(_mm_mul_pd(C1, dB), iB1);\n    iB2 = _mm_sub_pd(_mm_mul_pd(C2, dB), iB2);\n\n    d1 = _mm_xor_pd(rd, _Sign_PN);\n    d2 = _mm_xor_pd(rd, _Sign_NP);\n\n    //  iC = B*|C| - A*C#*D;\n    dC = _mm_shuffle_pd(dC,dC,0);\n    iC1 = _mm_sub_pd(_mm_mul_pd(B1, dC), iC1);\n    iC2 = _mm_sub_pd(_mm_mul_pd(B2, dC), iC2);\n\n    Index res_stride = result.outerStride();\n    double* res = result.data();\n    pstoret<double, Packet2d, ResultAlignment>(res+0,             _mm_mul_pd(_mm_shuffle_pd(iA2, iA1, 3), d1));\n    pstoret<double, Packet2d, ResultAlignment>(res+res_stride,    _mm_mul_pd(_mm_shuffle_pd(iA2, iA1, 0), d2));\n    pstoret<double, Packet2d, ResultAlignment>(res+2,             _mm_mul_pd(_mm_shuffle_pd(iB2, iB1, 3), d1));\n    pstoret<double, Packet2d, ResultAlignment>(res+res_stride+2,  _mm_mul_pd(_mm_shuffle_pd(iB2, iB1, 0), d2));\n    pstoret<double, Packet2d, ResultAlignment>(res+2*res_stride,  _mm_mul_pd(_mm_shuffle_pd(iC2, iC1, 3), d1));\n    pstoret<double, Packet2d, ResultAlignment>(res+3*res_stride,  _mm_mul_pd(_mm_shuffle_pd(iC2, iC1, 0), d2));\n    pstoret<double, Packet2d, ResultAlignment>(res+2*res_stride+2,_mm_mul_pd(_mm_shuffle_pd(iD2, iD1, 3), d1));\n    pstoret<double, Packet2d, ResultAlignment>(res+3*res_stride+2,_mm_mul_pd(_mm_shuffle_pd(iD2, iD1, 0), d2));\n  }\n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_INVERSE_SSE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/MetisSupport/MetisSupport.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n#ifndef METIS_SUPPORT_H\n#define METIS_SUPPORT_H\n\nnamespace Eigen {\n/**\n * Get the fill-reducing ordering from the METIS package\n * \n * If A is the original matrix and Ap is the permuted matrix, \n * the fill-reducing permutation is defined as follows :\n * Row (column) i of A is the matperm(i) row (column) of Ap. \n * WARNING: As computed by METIS, this corresponds to the vector iperm (instead of perm)\n */\ntemplate <typename StorageIndex>\nclass MetisOrdering\n{\npublic:\n  typedef PermutationMatrix<Dynamic,Dynamic,StorageIndex> PermutationType;\n  typedef Matrix<StorageIndex,Dynamic,1> IndexVector; \n  \n  template <typename MatrixType>\n  void get_symmetrized_graph(const MatrixType& A)\n  {\n    Index m = A.cols(); \n    eigen_assert((A.rows() == A.cols()) && \"ONLY FOR SQUARED MATRICES\");\n    // Get the transpose of the input matrix \n    MatrixType At = A.transpose(); \n    // Get the number of nonzeros elements in each row/col of At+A\n    Index TotNz = 0; \n    IndexVector visited(m); \n    visited.setConstant(-1); \n    for (StorageIndex j = 0; j < m; j++)\n    {\n      // Compute the union structure of of A(j,:) and At(j,:)\n      visited(j) = j; // Do not include the diagonal element\n      // Get the nonzeros in row/column j of A\n      for (typename MatrixType::InnerIterator it(A, j); it; ++it)\n      {\n        Index idx = it.index(); // Get the row index (for column major) or column index (for row major)\n        if (visited(idx) != j ) \n        {\n          visited(idx) = j; \n          ++TotNz; \n        }\n      }\n      //Get the nonzeros in row/column j of At\n      for (typename MatrixType::InnerIterator it(At, j); it; ++it)\n      {\n        Index idx = it.index(); \n        if(visited(idx) != j)\n        {\n          visited(idx) = j; \n          ++TotNz; \n        }\n      }\n    }\n    // Reserve place for A + At\n    m_indexPtr.resize(m+1);\n    m_innerIndices.resize(TotNz); \n\n    // Now compute the real adjacency list of each column/row \n    visited.setConstant(-1); \n    StorageIndex CurNz = 0; \n    for (StorageIndex j = 0; j < m; j++)\n    {\n      m_indexPtr(j) = CurNz; \n      \n      visited(j) = j; // Do not include the diagonal element\n      // Add the pattern of row/column j of A to A+At\n      for (typename MatrixType::InnerIterator it(A,j); it; ++it)\n      {\n        StorageIndex idx = it.index(); // Get the row index (for column major) or column index (for row major)\n        if (visited(idx) != j ) \n        {\n          visited(idx) = j; \n          m_innerIndices(CurNz) = idx; \n          CurNz++; \n        }\n      }\n      //Add the pattern of row/column j of At to A+At\n      for (typename MatrixType::InnerIterator it(At, j); it; ++it)\n      {\n        StorageIndex idx = it.index(); \n        if(visited(idx) != j)\n        {\n          visited(idx) = j; \n          m_innerIndices(CurNz) = idx; \n          ++CurNz; \n        }\n      }\n    }\n    m_indexPtr(m) = CurNz;    \n  }\n  \n  template <typename MatrixType>\n  void operator() (const MatrixType& A, PermutationType& matperm)\n  {\n     StorageIndex m = internal::convert_index<StorageIndex>(A.cols()); // must be StorageIndex, because it is passed by address to METIS\n     IndexVector perm(m),iperm(m); \n    // First, symmetrize the matrix graph. \n     get_symmetrized_graph(A); \n     int output_error;\n     \n     // Call the fill-reducing routine from METIS \n     output_error = METIS_NodeND(&m, m_indexPtr.data(), m_innerIndices.data(), NULL, NULL, perm.data(), iperm.data());\n     \n    if(output_error != METIS_OK) \n    {\n      //FIXME The ordering interface should define a class of possible errors \n     std::cerr << \"ERROR WHILE CALLING THE METIS PACKAGE \\n\"; \n     return; \n    }\n    \n    // Get the fill-reducing permutation \n    //NOTE:  If Ap is the permuted matrix then perm and iperm vectors are defined as follows \n    // Row (column) i of Ap is the perm(i) row(column) of A, and row (column) i of A is the iperm(i) row(column) of Ap\n    \n     matperm.resize(m);\n     for (int j = 0; j < m; j++)\n       matperm.indices()(iperm(j)) = j;\n   \n  }\n  \n  protected:\n    IndexVector m_indexPtr; // Pointer to the adjacenccy list of each row/column\n    IndexVector m_innerIndices; // Adjacency list \n};\n\n}// end namespace eigen \n#endif\n"
  },
  {
    "path": "include/eigen3/Eigen/src/OrderingMethods/Amd.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n\n/*\n\nNOTE: this routine has been adapted from the CSparse library:\n\nCopyright (c) 2006, Timothy A. Davis.\nhttp://www.suitesparse.com\n\nCSparse is free software; you can redistribute it and/or\nmodify it under the terms of the GNU Lesser General Public\nLicense as published by the Free Software Foundation; either\nversion 2.1 of the License, or (at your option) any later version.\n\nCSparse is distributed in the hope that it will be useful,\nbut WITHOUT ANY WARRANTY; without even the implied warranty of\nMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU\nLesser General Public License for more details.\n\nYou should have received a copy of the GNU Lesser General Public\nLicense along with this Module; if not, write to the Free Software\nFoundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA\n\n*/\n\n#include \"../Core/util/NonMPL2.h\"\n\n#ifndef EIGEN_SPARSE_AMD_H\n#define EIGEN_SPARSE_AMD_H\n\nnamespace Eigen { \n\nnamespace internal {\n  \ntemplate<typename T> inline T amd_flip(const T& i) { return -i-2; }\ntemplate<typename T> inline T amd_unflip(const T& i) { return i<0 ? amd_flip(i) : i; }\ntemplate<typename T0, typename T1> inline bool amd_marked(const T0* w, const T1& j) { return w[j]<0; }\ntemplate<typename T0, typename T1> inline void amd_mark(const T0* w, const T1& j) { return w[j] = amd_flip(w[j]); }\n\n/* clear w */\ntemplate<typename StorageIndex>\nstatic StorageIndex cs_wclear (StorageIndex mark, StorageIndex lemax, StorageIndex *w, StorageIndex n)\n{\n  StorageIndex k;\n  if(mark < 2 || (mark + lemax < 0))\n  {\n    for(k = 0; k < n; k++)\n      if(w[k] != 0)\n        w[k] = 1;\n    mark = 2;\n  }\n  return (mark);     /* at this point, w[0..n-1] < mark holds */\n}\n\n/* depth-first search and postorder of a tree rooted at node j */\ntemplate<typename StorageIndex>\nStorageIndex cs_tdfs(StorageIndex j, StorageIndex k, StorageIndex *head, const StorageIndex *next, StorageIndex *post, StorageIndex *stack)\n{\n  StorageIndex i, p, top = 0;\n  if(!head || !next || !post || !stack) return (-1);    /* check inputs */\n  stack[0] = j;                 /* place j on the stack */\n  while (top >= 0)                /* while (stack is not empty) */\n  {\n    p = stack[top];           /* p = top of stack */\n    i = head[p];              /* i = youngest child of p */\n    if(i == -1)\n    {\n      top--;                 /* p has no unordered children left */\n      post[k++] = p;        /* node p is the kth postordered node */\n    }\n    else\n    {\n      head[p] = next[i];   /* remove i from children of p */\n      stack[++top] = i;     /* start dfs on child node i */\n    }\n  }\n  return k;\n}\n\n\n/** \\internal\n  * \\ingroup OrderingMethods_Module \n  * Approximate minimum degree ordering algorithm.\n  *\n  * \\param[in] C the input selfadjoint matrix stored in compressed column major format.\n  * \\param[out] perm the permutation P reducing the fill-in of the input matrix \\a C\n  *\n  * Note that the input matrix \\a C must be complete, that is both the upper and lower parts have to be stored, as well as the diagonal entries.\n  * On exit the values of C are destroyed */\ntemplate<typename Scalar, typename StorageIndex>\nvoid minimum_degree_ordering(SparseMatrix<Scalar,ColMajor,StorageIndex>& C, PermutationMatrix<Dynamic,Dynamic,StorageIndex>& perm)\n{\n  using std::sqrt;\n  \n  StorageIndex d, dk, dext, lemax = 0, e, elenk, eln, i, j, k, k1,\n                k2, k3, jlast, ln, dense, nzmax, mindeg = 0, nvi, nvj, nvk, mark, wnvi,\n                ok, nel = 0, p, p1, p2, p3, p4, pj, pk, pk1, pk2, pn, q, t, h;\n  \n  StorageIndex n = StorageIndex(C.cols());\n  dense = std::max<StorageIndex> (16, StorageIndex(10 * sqrt(double(n))));   /* find dense threshold */\n  dense = (std::min)(n-2, dense);\n  \n  StorageIndex cnz = StorageIndex(C.nonZeros());\n  perm.resize(n+1);\n  t = cnz + cnz/5 + 2*n;                 /* add elbow room to C */\n  C.resizeNonZeros(t);\n  \n  // get workspace\n  ei_declare_aligned_stack_constructed_variable(StorageIndex,W,8*(n+1),0);\n  StorageIndex* len     = W;\n  StorageIndex* nv      = W +   (n+1);\n  StorageIndex* next    = W + 2*(n+1);\n  StorageIndex* head    = W + 3*(n+1);\n  StorageIndex* elen    = W + 4*(n+1);\n  StorageIndex* degree  = W + 5*(n+1);\n  StorageIndex* w       = W + 6*(n+1);\n  StorageIndex* hhead   = W + 7*(n+1);\n  StorageIndex* last    = perm.indices().data();                              /* use P as workspace for last */\n  \n  /* --- Initialize quotient graph ---------------------------------------- */\n  StorageIndex* Cp = C.outerIndexPtr();\n  StorageIndex* Ci = C.innerIndexPtr();\n  for(k = 0; k < n; k++)\n    len[k] = Cp[k+1] - Cp[k];\n  len[n] = 0;\n  nzmax = t;\n  \n  for(i = 0; i <= n; i++)\n  {\n    head[i]   = -1;                     // degree list i is empty\n    last[i]   = -1;\n    next[i]   = -1;\n    hhead[i]  = -1;                     // hash list i is empty \n    nv[i]     = 1;                      // node i is just one node\n    w[i]      = 1;                      // node i is alive\n    elen[i]   = 0;                      // Ek of node i is empty\n    degree[i] = len[i];                 // degree of node i\n  }\n  mark = internal::cs_wclear<StorageIndex>(0, 0, w, n);         /* clear w */\n  \n  /* --- Initialize degree lists ------------------------------------------ */\n  for(i = 0; i < n; i++)\n  {\n    bool has_diag = false;\n    for(p = Cp[i]; p<Cp[i+1]; ++p)\n      if(Ci[p]==i)\n      {\n        has_diag = true;\n        break;\n      }\n   \n    d = degree[i];\n    if(d == 1 && has_diag)           /* node i is empty */\n    {\n      elen[i] = -2;                 /* element i is dead */\n      nel++;\n      Cp[i] = -1;                   /* i is a root of assembly tree */\n      w[i] = 0;\n    }\n    else if(d > dense || !has_diag)  /* node i is dense or has no structural diagonal element */\n    {\n      nv[i] = 0;                    /* absorb i into element n */\n      elen[i] = -1;                 /* node i is dead */\n      nel++;\n      Cp[i] = amd_flip (n);\n      nv[n]++;\n    }\n    else\n    {\n      if(head[d] != -1) last[head[d]] = i;\n      next[i] = head[d];           /* put node i in degree list d */\n      head[d] = i;\n    }\n  }\n  \n  elen[n] = -2;                         /* n is a dead element */\n  Cp[n] = -1;                           /* n is a root of assembly tree */\n  w[n] = 0;                             /* n is a dead element */\n  \n  while (nel < n)                         /* while (selecting pivots) do */\n  {\n    /* --- Select node of minimum approximate degree -------------------- */\n    for(k = -1; mindeg < n && (k = head[mindeg]) == -1; mindeg++) {}\n    if(next[k] != -1) last[next[k]] = -1;\n    head[mindeg] = next[k];          /* remove k from degree list */\n    elenk = elen[k];                  /* elenk = |Ek| */\n    nvk = nv[k];                      /* # of nodes k represents */\n    nel += nvk;                        /* nv[k] nodes of A eliminated */\n    \n    /* --- Garbage collection ------------------------------------------- */\n    if(elenk > 0 && cnz + mindeg >= nzmax)\n    {\n      for(j = 0; j < n; j++)\n      {\n        if((p = Cp[j]) >= 0)      /* j is a live node or element */\n        {\n          Cp[j] = Ci[p];          /* save first entry of object */\n          Ci[p] = amd_flip (j);    /* first entry is now amd_flip(j) */\n        }\n      }\n      for(q = 0, p = 0; p < cnz; ) /* scan all of memory */\n      {\n        if((j = amd_flip (Ci[p++])) >= 0)  /* found object j */\n        {\n          Ci[q] = Cp[j];       /* restore first entry of object */\n          Cp[j] = q++;          /* new pointer to object j */\n          for(k3 = 0; k3 < len[j]-1; k3++) Ci[q++] = Ci[p++];\n        }\n      }\n      cnz = q;                       /* Ci[cnz...nzmax-1] now free */\n    }\n    \n    /* --- Construct new element ---------------------------------------- */\n    dk = 0;\n    nv[k] = -nvk;                     /* flag k as in Lk */\n    p = Cp[k];\n    pk1 = (elenk == 0) ? p : cnz;      /* do in place if elen[k] == 0 */\n    pk2 = pk1;\n    for(k1 = 1; k1 <= elenk + 1; k1++)\n    {\n      if(k1 > elenk)\n      {\n        e = k;                     /* search the nodes in k */\n        pj = p;                    /* list of nodes starts at Ci[pj]*/\n        ln = len[k] - elenk;      /* length of list of nodes in k */\n      }\n      else\n      {\n        e = Ci[p++];              /* search the nodes in e */\n        pj = Cp[e];\n        ln = len[e];              /* length of list of nodes in e */\n      }\n      for(k2 = 1; k2 <= ln; k2++)\n      {\n        i = Ci[pj++];\n        if((nvi = nv[i]) <= 0) continue; /* node i dead, or seen */\n        dk += nvi;                 /* degree[Lk] += size of node i */\n        nv[i] = -nvi;             /* negate nv[i] to denote i in Lk*/\n        Ci[pk2++] = i;            /* place i in Lk */\n        if(next[i] != -1) last[next[i]] = last[i];\n        if(last[i] != -1)         /* remove i from degree list */\n        {\n          next[last[i]] = next[i];\n        }\n        else\n        {\n          head[degree[i]] = next[i];\n        }\n      }\n      if(e != k)\n      {\n        Cp[e] = amd_flip (k);      /* absorb e into k */\n        w[e] = 0;                 /* e is now a dead element */\n      }\n    }\n    if(elenk != 0) cnz = pk2;         /* Ci[cnz...nzmax] is free */\n    degree[k] = dk;                   /* external degree of k - |Lk\\i| */\n    Cp[k] = pk1;                      /* element k is in Ci[pk1..pk2-1] */\n    len[k] = pk2 - pk1;\n    elen[k] = -2;                     /* k is now an element */\n    \n    /* --- Find set differences ----------------------------------------- */\n    mark = internal::cs_wclear<StorageIndex>(mark, lemax, w, n);  /* clear w if necessary */\n    for(pk = pk1; pk < pk2; pk++)    /* scan 1: find |Le\\Lk| */\n    {\n      i = Ci[pk];\n      if((eln = elen[i]) <= 0) continue;/* skip if elen[i] empty */\n      nvi = -nv[i];                      /* nv[i] was negated */\n      wnvi = mark - nvi;\n      for(p = Cp[i]; p <= Cp[i] + eln - 1; p++)  /* scan Ei */\n      {\n        e = Ci[p];\n        if(w[e] >= mark)\n        {\n          w[e] -= nvi;          /* decrement |Le\\Lk| */\n        }\n        else if(w[e] != 0)        /* ensure e is a live element */\n        {\n          w[e] = degree[e] + wnvi; /* 1st time e seen in scan 1 */\n        }\n      }\n    }\n    \n    /* --- Degree update ------------------------------------------------ */\n    for(pk = pk1; pk < pk2; pk++)    /* scan2: degree update */\n    {\n      i = Ci[pk];                   /* consider node i in Lk */\n      p1 = Cp[i];\n      p2 = p1 + elen[i] - 1;\n      pn = p1;\n      for(h = 0, d = 0, p = p1; p <= p2; p++)    /* scan Ei */\n      {\n        e = Ci[p];\n        if(w[e] != 0)             /* e is an unabsorbed element */\n        {\n          dext = w[e] - mark;   /* dext = |Le\\Lk| */\n          if(dext > 0)\n          {\n            d += dext;         /* sum up the set differences */\n            Ci[pn++] = e;     /* keep e in Ei */\n            h += e;            /* compute the hash of node i */\n          }\n          else\n          {\n            Cp[e] = amd_flip (k);  /* aggressive absorb. e->k */\n            w[e] = 0;             /* e is a dead element */\n          }\n        }\n      }\n      elen[i] = pn - p1 + 1;        /* elen[i] = |Ei| */\n      p3 = pn;\n      p4 = p1 + len[i];\n      for(p = p2 + 1; p < p4; p++) /* prune edges in Ai */\n      {\n        j = Ci[p];\n        if((nvj = nv[j]) <= 0) continue; /* node j dead or in Lk */\n        d += nvj;                  /* degree(i) += |j| */\n        Ci[pn++] = j;             /* place j in node list of i */\n        h += j;                    /* compute hash for node i */\n      }\n      if(d == 0)                     /* check for mass elimination */\n      {\n        Cp[i] = amd_flip (k);      /* absorb i into k */\n        nvi = -nv[i];\n        dk -= nvi;                 /* |Lk| -= |i| */\n        nvk += nvi;                /* |k| += nv[i] */\n        nel += nvi;\n        nv[i] = 0;\n        elen[i] = -1;             /* node i is dead */\n      }\n      else\n      {\n        degree[i] = std::min<StorageIndex> (degree[i], d);   /* update degree(i) */\n        Ci[pn] = Ci[p3];         /* move first node to end */\n        Ci[p3] = Ci[p1];         /* move 1st el. to end of Ei */\n        Ci[p1] = k;               /* add k as 1st element in of Ei */\n        len[i] = pn - p1 + 1;     /* new len of adj. list of node i */\n        h %= n;                    /* finalize hash of i */\n        next[i] = hhead[h];      /* place i in hash bucket */\n        hhead[h] = i;\n        last[i] = h;      /* save hash of i in last[i] */\n      }\n    }                                   /* scan2 is done */\n    degree[k] = dk;                   /* finalize |Lk| */\n    lemax = std::max<StorageIndex>(lemax, dk);\n    mark = internal::cs_wclear<StorageIndex>(mark+lemax, lemax, w, n);    /* clear w */\n    \n    /* --- Supernode detection ------------------------------------------ */\n    for(pk = pk1; pk < pk2; pk++)\n    {\n      i = Ci[pk];\n      if(nv[i] >= 0) continue;         /* skip if i is dead */\n      h = last[i];                      /* scan hash bucket of node i */\n      i = hhead[h];\n      hhead[h] = -1;                    /* hash bucket will be empty */\n      for(; i != -1 && next[i] != -1; i = next[i], mark++)\n      {\n        ln = len[i];\n        eln = elen[i];\n        for(p = Cp[i]+1; p <= Cp[i] + ln-1; p++) w[Ci[p]] = mark;\n        jlast = i;\n        for(j = next[i]; j != -1; ) /* compare i with all j */\n        {\n          ok = (len[j] == ln) && (elen[j] == eln);\n          for(p = Cp[j] + 1; ok && p <= Cp[j] + ln - 1; p++)\n          {\n            if(w[Ci[p]] != mark) ok = 0;    /* compare i and j*/\n          }\n          if(ok)                     /* i and j are identical */\n          {\n            Cp[j] = amd_flip (i);  /* absorb j into i */\n            nv[i] += nv[j];\n            nv[j] = 0;\n            elen[j] = -1;         /* node j is dead */\n            j = next[j];          /* delete j from hash bucket */\n            next[jlast] = j;\n          }\n          else\n          {\n            jlast = j;             /* j and i are different */\n            j = next[j];\n          }\n        }\n      }\n    }\n    \n    /* --- Finalize new element------------------------------------------ */\n    for(p = pk1, pk = pk1; pk < pk2; pk++)   /* finalize Lk */\n    {\n      i = Ci[pk];\n      if((nvi = -nv[i]) <= 0) continue;/* skip if i is dead */\n      nv[i] = nvi;                      /* restore nv[i] */\n      d = degree[i] + dk - nvi;         /* compute external degree(i) */\n      d = std::min<StorageIndex> (d, n - nel - nvi);\n      if(head[d] != -1) last[head[d]] = i;\n      next[i] = head[d];               /* put i back in degree list */\n      last[i] = -1;\n      head[d] = i;\n      mindeg = std::min<StorageIndex> (mindeg, d);       /* find new minimum degree */\n      degree[i] = d;\n      Ci[p++] = i;                      /* place i in Lk */\n    }\n    nv[k] = nvk;                      /* # nodes absorbed into k */\n    if((len[k] = p-pk1) == 0)         /* length of adj list of element k*/\n    {\n      Cp[k] = -1;                   /* k is a root of the tree */\n      w[k] = 0;                     /* k is now a dead element */\n    }\n    if(elenk != 0) cnz = p;           /* free unused space in Lk */\n  }\n  \n  /* --- Postordering ----------------------------------------------------- */\n  for(i = 0; i < n; i++) Cp[i] = amd_flip (Cp[i]);/* fix assembly tree */\n  for(j = 0; j <= n; j++) head[j] = -1;\n  for(j = n; j >= 0; j--)              /* place unordered nodes in lists */\n  {\n    if(nv[j] > 0) continue;          /* skip if j is an element */\n    next[j] = head[Cp[j]];          /* place j in list of its parent */\n    head[Cp[j]] = j;\n  }\n  for(e = n; e >= 0; e--)              /* place elements in lists */\n  {\n    if(nv[e] <= 0) continue;         /* skip unless e is an element */\n    if(Cp[e] != -1)\n    {\n      next[e] = head[Cp[e]];      /* place e in list of its parent */\n      head[Cp[e]] = e;\n    }\n  }\n  for(k = 0, i = 0; i <= n; i++)       /* postorder the assembly tree */\n  {\n    if(Cp[i] == -1) k = internal::cs_tdfs<StorageIndex>(i, k, head, next, perm.indices().data(), w);\n  }\n  \n  perm.indices().conservativeResize(n);\n}\n\n} // namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_SPARSE_AMD_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/OrderingMethods/Eigen_Colamd.h",
    "content": "// // This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Desire Nuentsa Wakam <desire.nuentsa_wakam@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n// This file is modified from the colamd/symamd library. The copyright is below\n\n//   The authors of the code itself are Stefan I. Larimore and Timothy A.\n//   Davis (davis@cise.ufl.edu), University of Florida.  The algorithm was\n//   developed in collaboration with John Gilbert, Xerox PARC, and Esmond\n//   Ng, Oak Ridge National Laboratory.\n// \n//     Date:\n// \n//   September 8, 2003.  Version 2.3.\n// \n//     Acknowledgements:\n// \n//   This work was supported by the National Science Foundation, under\n//   grants DMS-9504974 and DMS-9803599.\n// \n//     Notice:\n// \n//   Copyright (c) 1998-2003 by the University of Florida.\n//   All Rights Reserved.\n// \n//   THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY\n//   EXPRESSED OR IMPLIED.  ANY USE IS AT YOUR OWN RISK.\n// \n//   Permission is hereby granted to use, copy, modify, and/or distribute\n//   this program, provided that the Copyright, this License, and the\n//   Availability of the original version is retained on all copies and made\n//   accessible to the end-user of any code or package that includes COLAMD\n//   or any modified version of COLAMD. \n// \n//     Availability:\n// \n//   The colamd/symamd library is available at\n// \n//       http://www.suitesparse.com\n\n  \n#ifndef EIGEN_COLAMD_H\n#define EIGEN_COLAMD_H\n\nnamespace internal {\n/* Ensure that debugging is turned off: */\n#ifndef COLAMD_NDEBUG\n#define COLAMD_NDEBUG\n#endif /* NDEBUG */\n/* ========================================================================== */\n/* === Knob and statistics definitions ====================================== */\n/* ========================================================================== */\n\n/* size of the knobs [ ] array.  Only knobs [0..1] are currently used. */\n#define COLAMD_KNOBS 20\n\n/* number of output statistics.  Only stats [0..6] are currently used. */\n#define COLAMD_STATS 20 \n\n/* knobs [0] and stats [0]: dense row knob and output statistic. */\n#define COLAMD_DENSE_ROW 0\n\n/* knobs [1] and stats [1]: dense column knob and output statistic. */\n#define COLAMD_DENSE_COL 1\n\n/* stats [2]: memory defragmentation count output statistic */\n#define COLAMD_DEFRAG_COUNT 2\n\n/* stats [3]: colamd status:  zero OK, > 0 warning or notice, < 0 error */\n#define COLAMD_STATUS 3\n\n/* stats [4..6]: error info, or info on jumbled columns */ \n#define COLAMD_INFO1 4\n#define COLAMD_INFO2 5\n#define COLAMD_INFO3 6\n\n/* error codes returned in stats [3]: */\n#define COLAMD_OK       (0)\n#define COLAMD_OK_BUT_JUMBLED     (1)\n#define COLAMD_ERROR_A_not_present    (-1)\n#define COLAMD_ERROR_p_not_present    (-2)\n#define COLAMD_ERROR_nrow_negative    (-3)\n#define COLAMD_ERROR_ncol_negative    (-4)\n#define COLAMD_ERROR_nnz_negative   (-5)\n#define COLAMD_ERROR_p0_nonzero     (-6)\n#define COLAMD_ERROR_A_too_small    (-7)\n#define COLAMD_ERROR_col_length_negative  (-8)\n#define COLAMD_ERROR_row_index_out_of_bounds  (-9)\n#define COLAMD_ERROR_out_of_memory    (-10)\n#define COLAMD_ERROR_internal_error   (-999)\n\n/* ========================================================================== */\n/* === Definitions ========================================================== */\n/* ========================================================================== */\n\n#define ONES_COMPLEMENT(r) (-(r)-1)\n\n/* -------------------------------------------------------------------------- */\n\n#define COLAMD_EMPTY (-1)\n\n/* Row and column status */\n#define ALIVE (0)\n#define DEAD  (-1)\n\n/* Column status */\n#define DEAD_PRINCIPAL    (-1)\n#define DEAD_NON_PRINCIPAL  (-2)\n\n/* Macros for row and column status update and checking. */\n#define ROW_IS_DEAD(r)      ROW_IS_MARKED_DEAD (Row[r].shared2.mark)\n#define ROW_IS_MARKED_DEAD(row_mark)  (row_mark < ALIVE)\n#define ROW_IS_ALIVE(r)     (Row [r].shared2.mark >= ALIVE)\n#define COL_IS_DEAD(c)      (Col [c].start < ALIVE)\n#define COL_IS_ALIVE(c)     (Col [c].start >= ALIVE)\n#define COL_IS_DEAD_PRINCIPAL(c)  (Col [c].start == DEAD_PRINCIPAL)\n#define KILL_ROW(r)     { Row [r].shared2.mark = DEAD ; }\n#define KILL_PRINCIPAL_COL(c)   { Col [c].start = DEAD_PRINCIPAL ; }\n#define KILL_NON_PRINCIPAL_COL(c) { Col [c].start = DEAD_NON_PRINCIPAL ; }\n\n/* ========================================================================== */\n/* === Colamd reporting mechanism =========================================== */\n/* ========================================================================== */\n\n// == Row and Column structures ==\ntemplate <typename IndexType>\nstruct colamd_col\n{\n  IndexType start ;   /* index for A of first row in this column, or DEAD */\n  /* if column is dead */\n  IndexType length ;  /* number of rows in this column */\n  union\n  {\n    IndexType thickness ; /* number of original columns represented by this */\n    /* col, if the column is alive */\n    IndexType parent ;  /* parent in parent tree super-column structure, if */\n    /* the column is dead */\n  } shared1 ;\n  union\n  {\n    IndexType score ; /* the score used to maintain heap, if col is alive */\n    IndexType order ; /* pivot ordering of this column, if col is dead */\n  } shared2 ;\n  union\n  {\n    IndexType headhash ;  /* head of a hash bucket, if col is at the head of */\n    /* a degree list */\n    IndexType hash ;  /* hash value, if col is not in a degree list */\n    IndexType prev ;  /* previous column in degree list, if col is in a */\n    /* degree list (but not at the head of a degree list) */\n  } shared3 ;\n  union\n  {\n    IndexType degree_next ; /* next column, if col is in a degree list */\n    IndexType hash_next ;   /* next column, if col is in a hash list */\n  } shared4 ;\n  \n};\n \ntemplate <typename IndexType>\nstruct Colamd_Row\n{\n  IndexType start ;   /* index for A of first col in this row */\n  IndexType length ;  /* number of principal columns in this row */\n  union\n  {\n    IndexType degree ;  /* number of principal & non-principal columns in row */\n    IndexType p ;   /* used as a row pointer in init_rows_cols () */\n  } shared1 ;\n  union\n  {\n    IndexType mark ;  /* for computing set differences and marking dead rows*/\n    IndexType first_column ;/* first column in row (used in garbage collection) */\n  } shared2 ;\n  \n};\n \n/* ========================================================================== */\n/* === Colamd recommended memory size ======================================= */\n/* ========================================================================== */\n \n/*\n  The recommended length Alen of the array A passed to colamd is given by\n  the COLAMD_RECOMMENDED (nnz, n_row, n_col) macro.  It returns -1 if any\n  argument is negative.  2*nnz space is required for the row and column\n  indices of the matrix. colamd_c (n_col) + colamd_r (n_row) space is\n  required for the Col and Row arrays, respectively, which are internal to\n  colamd.  An additional n_col space is the minimal amount of \"elbow room\",\n  and nnz/5 more space is recommended for run time efficiency.\n  \n  This macro is not needed when using symamd.\n  \n  Explicit typecast to IndexType added Sept. 23, 2002, COLAMD version 2.2, to avoid\n  gcc -pedantic warning messages.\n*/\ntemplate <typename IndexType>\ninline IndexType colamd_c(IndexType n_col) \n{ return IndexType( ((n_col) + 1) * sizeof (colamd_col<IndexType>) / sizeof (IndexType) ) ; }\n\ntemplate <typename IndexType>\ninline IndexType  colamd_r(IndexType n_row)\n{ return IndexType(((n_row) + 1) * sizeof (Colamd_Row<IndexType>) / sizeof (IndexType)); }\n\n// Prototypes of non-user callable routines\ntemplate <typename IndexType>\nstatic IndexType init_rows_cols (IndexType n_row, IndexType n_col, Colamd_Row<IndexType> Row [], colamd_col<IndexType> col [], IndexType A [], IndexType p [], IndexType stats[COLAMD_STATS] ); \n\ntemplate <typename IndexType>\nstatic void init_scoring (IndexType n_row, IndexType n_col, Colamd_Row<IndexType> Row [], colamd_col<IndexType> Col [], IndexType A [], IndexType head [], double knobs[COLAMD_KNOBS], IndexType *p_n_row2, IndexType *p_n_col2, IndexType *p_max_deg);\n\ntemplate <typename IndexType>\nstatic IndexType find_ordering (IndexType n_row, IndexType n_col, IndexType Alen, Colamd_Row<IndexType> Row [], colamd_col<IndexType> Col [], IndexType A [], IndexType head [], IndexType n_col2, IndexType max_deg, IndexType pfree);\n\ntemplate <typename IndexType>\nstatic void order_children (IndexType n_col, colamd_col<IndexType> Col [], IndexType p []);\n\ntemplate <typename IndexType>\nstatic void detect_super_cols (colamd_col<IndexType> Col [], IndexType A [], IndexType head [], IndexType row_start, IndexType row_length ) ;\n\ntemplate <typename IndexType>\nstatic IndexType garbage_collection (IndexType n_row, IndexType n_col, Colamd_Row<IndexType> Row [], colamd_col<IndexType> Col [], IndexType A [], IndexType *pfree) ;\n\ntemplate <typename IndexType>\nstatic inline  IndexType clear_mark (IndexType n_row, Colamd_Row<IndexType> Row [] ) ;\n\n/* === No debugging ========================================================= */\n\n#define COLAMD_DEBUG0(params) ;\n#define COLAMD_DEBUG1(params) ;\n#define COLAMD_DEBUG2(params) ;\n#define COLAMD_DEBUG3(params) ;\n#define COLAMD_DEBUG4(params) ;\n\n#define COLAMD_ASSERT(expression) ((void) 0)\n\n\n/**\n * \\brief Returns the recommended value of Alen \n * \n * Returns recommended value of Alen for use by colamd.  \n * Returns -1 if any input argument is negative.  \n * The use of this routine or macro is optional.  \n * Note that the macro uses its arguments   more than once, \n * so be careful for side effects, if you pass expressions as arguments to COLAMD_RECOMMENDED.  \n * \n * \\param nnz nonzeros in A\n * \\param n_row number of rows in A\n * \\param n_col number of columns in A\n * \\return recommended value of Alen for use by colamd\n */\ntemplate <typename IndexType>\ninline IndexType colamd_recommended ( IndexType nnz, IndexType n_row, IndexType n_col)\n{\n  if ((nnz) < 0 || (n_row) < 0 || (n_col) < 0)\n    return (-1);\n  else\n    return (2 * (nnz) + colamd_c (n_col) + colamd_r (n_row) + (n_col) + ((nnz) / 5)); \n}\n\n/**\n * \\brief set default parameters  The use of this routine is optional.\n * \n * Colamd: rows with more than (knobs [COLAMD_DENSE_ROW] * n_col)\n * entries are removed prior to ordering.  Columns with more than\n * (knobs [COLAMD_DENSE_COL] * n_row) entries are removed prior to\n * ordering, and placed last in the output column ordering. \n *\n * COLAMD_DENSE_ROW and COLAMD_DENSE_COL are defined as 0 and 1,\n * respectively, in colamd.h.  Default values of these two knobs\n * are both 0.5.  Currently, only knobs [0] and knobs [1] are\n * used, but future versions may use more knobs.  If so, they will\n * be properly set to their defaults by the future version of\n * colamd_set_defaults, so that the code that calls colamd will\n * not need to change, assuming that you either use\n * colamd_set_defaults, or pass a (double *) NULL pointer as the\n * knobs array to colamd or symamd.\n * \n * \\param knobs parameter settings for colamd\n */\n\nstatic inline void colamd_set_defaults(double knobs[COLAMD_KNOBS])\n{\n  /* === Local variables ================================================== */\n  \n  int i ;\n\n  if (!knobs)\n  {\n    return ;      /* no knobs to initialize */\n  }\n  for (i = 0 ; i < COLAMD_KNOBS ; i++)\n  {\n    knobs [i] = 0 ;\n  }\n  knobs [COLAMD_DENSE_ROW] = 0.5 ;  /* ignore rows over 50% dense */\n  knobs [COLAMD_DENSE_COL] = 0.5 ;  /* ignore columns over 50% dense */\n}\n\n/** \n * \\brief  Computes a column ordering using the column approximate minimum degree ordering\n * \n * Computes a column ordering (Q) of A such that P(AQ)=LU or\n * (AQ)'AQ=LL' have less fill-in and require fewer floating point\n * operations than factorizing the unpermuted matrix A or A'A,\n * respectively.\n * \n * \n * \\param n_row number of rows in A\n * \\param n_col number of columns in A\n * \\param Alen, size of the array A\n * \\param A row indices of the matrix, of size ALen\n * \\param p column pointers of A, of size n_col+1\n * \\param knobs parameter settings for colamd\n * \\param stats colamd output statistics and error codes\n */\ntemplate <typename IndexType>\nstatic bool colamd(IndexType n_row, IndexType n_col, IndexType Alen, IndexType *A, IndexType *p, double knobs[COLAMD_KNOBS], IndexType stats[COLAMD_STATS])\n{\n  /* === Local variables ================================================== */\n  \n  IndexType i ;     /* loop index */\n  IndexType nnz ;     /* nonzeros in A */\n  IndexType Row_size ;    /* size of Row [], in integers */\n  IndexType Col_size ;    /* size of Col [], in integers */\n  IndexType need ;      /* minimum required length of A */\n  Colamd_Row<IndexType> *Row ;   /* pointer into A of Row [0..n_row] array */\n  colamd_col<IndexType> *Col ;   /* pointer into A of Col [0..n_col] array */\n  IndexType n_col2 ;    /* number of non-dense, non-empty columns */\n  IndexType n_row2 ;    /* number of non-dense, non-empty rows */\n  IndexType ngarbage ;    /* number of garbage collections performed */\n  IndexType max_deg ;   /* maximum row degree */\n  double default_knobs [COLAMD_KNOBS] ; /* default knobs array */\n  \n  \n  /* === Check the input arguments ======================================== */\n  \n  if (!stats)\n  {\n    COLAMD_DEBUG0 ((\"colamd: stats not present\\n\")) ;\n    return (false) ;\n  }\n  for (i = 0 ; i < COLAMD_STATS ; i++)\n  {\n    stats [i] = 0 ;\n  }\n  stats [COLAMD_STATUS] = COLAMD_OK ;\n  stats [COLAMD_INFO1] = -1 ;\n  stats [COLAMD_INFO2] = -1 ;\n  \n  if (!A)   /* A is not present */\n  {\n    stats [COLAMD_STATUS] = COLAMD_ERROR_A_not_present ;\n    COLAMD_DEBUG0 ((\"colamd: A not present\\n\")) ;\n    return (false) ;\n  }\n  \n  if (!p)   /* p is not present */\n  {\n    stats [COLAMD_STATUS] = COLAMD_ERROR_p_not_present ;\n    COLAMD_DEBUG0 ((\"colamd: p not present\\n\")) ;\n    return (false) ;\n  }\n  \n  if (n_row < 0)  /* n_row must be >= 0 */\n  {\n    stats [COLAMD_STATUS] = COLAMD_ERROR_nrow_negative ;\n    stats [COLAMD_INFO1] = n_row ;\n    COLAMD_DEBUG0 ((\"colamd: nrow negative %d\\n\", n_row)) ;\n    return (false) ;\n  }\n  \n  if (n_col < 0)  /* n_col must be >= 0 */\n  {\n    stats [COLAMD_STATUS] = COLAMD_ERROR_ncol_negative ;\n    stats [COLAMD_INFO1] = n_col ;\n    COLAMD_DEBUG0 ((\"colamd: ncol negative %d\\n\", n_col)) ;\n    return (false) ;\n  }\n  \n  nnz = p [n_col] ;\n  if (nnz < 0)  /* nnz must be >= 0 */\n  {\n    stats [COLAMD_STATUS] = COLAMD_ERROR_nnz_negative ;\n    stats [COLAMD_INFO1] = nnz ;\n    COLAMD_DEBUG0 ((\"colamd: number of entries negative %d\\n\", nnz)) ;\n    return (false) ;\n  }\n  \n  if (p [0] != 0)\n  {\n    stats [COLAMD_STATUS] = COLAMD_ERROR_p0_nonzero ;\n    stats [COLAMD_INFO1] = p [0] ;\n    COLAMD_DEBUG0 ((\"colamd: p[0] not zero %d\\n\", p [0])) ;\n    return (false) ;\n  }\n  \n  /* === If no knobs, set default knobs =================================== */\n  \n  if (!knobs)\n  {\n    colamd_set_defaults (default_knobs) ;\n    knobs = default_knobs ;\n  }\n  \n  /* === Allocate the Row and Col arrays from array A ===================== */\n  \n  Col_size = colamd_c (n_col) ;\n  Row_size = colamd_r (n_row) ;\n  need = 2*nnz + n_col + Col_size + Row_size ;\n  \n  if (need > Alen)\n  {\n    /* not enough space in array A to perform the ordering */\n    stats [COLAMD_STATUS] = COLAMD_ERROR_A_too_small ;\n    stats [COLAMD_INFO1] = need ;\n    stats [COLAMD_INFO2] = Alen ;\n    COLAMD_DEBUG0 ((\"colamd: Need Alen >= %d, given only Alen = %d\\n\", need,Alen));\n    return (false) ;\n  }\n  \n  Alen -= Col_size + Row_size ;\n  Col = (colamd_col<IndexType> *) &A [Alen] ;\n  Row = (Colamd_Row<IndexType> *) &A [Alen + Col_size] ;\n\n  /* === Construct the row and column data structures ===================== */\n  \n  if (!Eigen::internal::init_rows_cols (n_row, n_col, Row, Col, A, p, stats))\n  {\n    /* input matrix is invalid */\n    COLAMD_DEBUG0 ((\"colamd: Matrix invalid\\n\")) ;\n    return (false) ;\n  }\n  \n  /* === Initialize scores, kill dense rows/columns ======================= */\n\n  Eigen::internal::init_scoring (n_row, n_col, Row, Col, A, p, knobs,\n\t\t&n_row2, &n_col2, &max_deg) ;\n  \n  /* === Order the supercolumns =========================================== */\n  \n  ngarbage = Eigen::internal::find_ordering (n_row, n_col, Alen, Row, Col, A, p,\n\t\t\t    n_col2, max_deg, 2*nnz) ;\n  \n  /* === Order the non-principal columns ================================== */\n  \n  Eigen::internal::order_children (n_col, Col, p) ;\n  \n  /* === Return statistics in stats ======================================= */\n  \n  stats [COLAMD_DENSE_ROW] = n_row - n_row2 ;\n  stats [COLAMD_DENSE_COL] = n_col - n_col2 ;\n  stats [COLAMD_DEFRAG_COUNT] = ngarbage ;\n  COLAMD_DEBUG0 ((\"colamd: done.\\n\")) ; \n  return (true) ;\n}\n\n/* ========================================================================== */\n/* === NON-USER-CALLABLE ROUTINES: ========================================== */\n/* ========================================================================== */\n\n/* There are no user-callable routines beyond this point in the file */\n\n\n/* ========================================================================== */\n/* === init_rows_cols ======================================================= */\n/* ========================================================================== */\n\n/*\n  Takes the column form of the matrix in A and creates the row form of the\n  matrix.  Also, row and column attributes are stored in the Col and Row\n  structs.  If the columns are un-sorted or contain duplicate row indices,\n  this routine will also sort and remove duplicate row indices from the\n  column form of the matrix.  Returns false if the matrix is invalid,\n  true otherwise.  Not user-callable.\n*/\ntemplate <typename IndexType>\nstatic IndexType init_rows_cols  /* returns true if OK, or false otherwise */\n  (\n    /* === Parameters ======================================================= */\n\n    IndexType n_row,      /* number of rows of A */\n    IndexType n_col,      /* number of columns of A */\n    Colamd_Row<IndexType> Row [],    /* of size n_row+1 */\n    colamd_col<IndexType> Col [],    /* of size n_col+1 */\n    IndexType A [],     /* row indices of A, of size Alen */\n    IndexType p [],     /* pointers to columns in A, of size n_col+1 */\n    IndexType stats [COLAMD_STATS]  /* colamd statistics */ \n    )\n{\n  /* === Local variables ================================================== */\n\n  IndexType col ;     /* a column index */\n  IndexType row ;     /* a row index */\n  IndexType *cp ;     /* a column pointer */\n  IndexType *cp_end ;   /* a pointer to the end of a column */\n  IndexType *rp ;     /* a row pointer */\n  IndexType *rp_end ;   /* a pointer to the end of a row */\n  IndexType last_row ;    /* previous row */\n\n  /* === Initialize columns, and check column pointers ==================== */\n\n  for (col = 0 ; col < n_col ; col++)\n  {\n    Col [col].start = p [col] ;\n    Col [col].length = p [col+1] - p [col] ;\n\n    if ((Col [col].length) < 0) // extra parentheses to work-around gcc bug 10200\n    {\n      /* column pointers must be non-decreasing */\n      stats [COLAMD_STATUS] = COLAMD_ERROR_col_length_negative ;\n      stats [COLAMD_INFO1] = col ;\n      stats [COLAMD_INFO2] = Col [col].length ;\n      COLAMD_DEBUG0 ((\"colamd: col %d length %d < 0\\n\", col, Col [col].length)) ;\n      return (false) ;\n    }\n\n    Col [col].shared1.thickness = 1 ;\n    Col [col].shared2.score = 0 ;\n    Col [col].shared3.prev = COLAMD_EMPTY ;\n    Col [col].shared4.degree_next = COLAMD_EMPTY ;\n  }\n\n  /* p [0..n_col] no longer needed, used as \"head\" in subsequent routines */\n\n  /* === Scan columns, compute row degrees, and check row indices ========= */\n\n  stats [COLAMD_INFO3] = 0 ;  /* number of duplicate or unsorted row indices*/\n\n  for (row = 0 ; row < n_row ; row++)\n  {\n    Row [row].length = 0 ;\n    Row [row].shared2.mark = -1 ;\n  }\n\n  for (col = 0 ; col < n_col ; col++)\n  {\n    last_row = -1 ;\n\n    cp = &A [p [col]] ;\n    cp_end = &A [p [col+1]] ;\n\n    while (cp < cp_end)\n    {\n      row = *cp++ ;\n\n      /* make sure row indices within range */\n      if (row < 0 || row >= n_row)\n      {\n\tstats [COLAMD_STATUS] = COLAMD_ERROR_row_index_out_of_bounds ;\n\tstats [COLAMD_INFO1] = col ;\n\tstats [COLAMD_INFO2] = row ;\n\tstats [COLAMD_INFO3] = n_row ;\n\tCOLAMD_DEBUG0 ((\"colamd: row %d col %d out of bounds\\n\", row, col)) ;\n\treturn (false) ;\n      }\n\n      if (row <= last_row || Row [row].shared2.mark == col)\n      {\n\t/* row index are unsorted or repeated (or both), thus col */\n\t/* is jumbled.  This is a notice, not an error condition. */\n\tstats [COLAMD_STATUS] = COLAMD_OK_BUT_JUMBLED ;\n\tstats [COLAMD_INFO1] = col ;\n\tstats [COLAMD_INFO2] = row ;\n\t(stats [COLAMD_INFO3]) ++ ;\n\tCOLAMD_DEBUG1 ((\"colamd: row %d col %d unsorted/duplicate\\n\",row,col));\n      }\n\n      if (Row [row].shared2.mark != col)\n      {\n\tRow [row].length++ ;\n      }\n      else\n      {\n\t/* this is a repeated entry in the column, */\n\t/* it will be removed */\n\tCol [col].length-- ;\n      }\n\n      /* mark the row as having been seen in this column */\n      Row [row].shared2.mark = col ;\n\n      last_row = row ;\n    }\n  }\n\n  /* === Compute row pointers ============================================= */\n\n  /* row form of the matrix starts directly after the column */\n  /* form of matrix in A */\n  Row [0].start = p [n_col] ;\n  Row [0].shared1.p = Row [0].start ;\n  Row [0].shared2.mark = -1 ;\n  for (row = 1 ; row < n_row ; row++)\n  {\n    Row [row].start = Row [row-1].start + Row [row-1].length ;\n    Row [row].shared1.p = Row [row].start ;\n    Row [row].shared2.mark = -1 ;\n  }\n\n  /* === Create row form ================================================== */\n\n  if (stats [COLAMD_STATUS] == COLAMD_OK_BUT_JUMBLED)\n  {\n    /* if cols jumbled, watch for repeated row indices */\n    for (col = 0 ; col < n_col ; col++)\n    {\n      cp = &A [p [col]] ;\n      cp_end = &A [p [col+1]] ;\n      while (cp < cp_end)\n      {\n\trow = *cp++ ;\n\tif (Row [row].shared2.mark != col)\n\t{\n\t  A [(Row [row].shared1.p)++] = col ;\n\t  Row [row].shared2.mark = col ;\n\t}\n      }\n    }\n  }\n  else\n  {\n    /* if cols not jumbled, we don't need the mark (this is faster) */\n    for (col = 0 ; col < n_col ; col++)\n    {\n      cp = &A [p [col]] ;\n      cp_end = &A [p [col+1]] ;\n      while (cp < cp_end)\n      {\n\tA [(Row [*cp++].shared1.p)++] = col ;\n      }\n    }\n  }\n\n  /* === Clear the row marks and set row degrees ========================== */\n\n  for (row = 0 ; row < n_row ; row++)\n  {\n    Row [row].shared2.mark = 0 ;\n    Row [row].shared1.degree = Row [row].length ;\n  }\n\n  /* === See if we need to re-create columns ============================== */\n\n  if (stats [COLAMD_STATUS] == COLAMD_OK_BUT_JUMBLED)\n  {\n    COLAMD_DEBUG0 ((\"colamd: reconstructing column form, matrix jumbled\\n\")) ;\n\n\n    /* === Compute col pointers ========================================= */\n\n    /* col form of the matrix starts at A [0]. */\n    /* Note, we may have a gap between the col form and the row */\n    /* form if there were duplicate entries, if so, it will be */\n    /* removed upon the first garbage collection */\n    Col [0].start = 0 ;\n    p [0] = Col [0].start ;\n    for (col = 1 ; col < n_col ; col++)\n    {\n      /* note that the lengths here are for pruned columns, i.e. */\n      /* no duplicate row indices will exist for these columns */\n      Col [col].start = Col [col-1].start + Col [col-1].length ;\n      p [col] = Col [col].start ;\n    }\n\n    /* === Re-create col form =========================================== */\n\n    for (row = 0 ; row < n_row ; row++)\n    {\n      rp = &A [Row [row].start] ;\n      rp_end = rp + Row [row].length ;\n      while (rp < rp_end)\n      {\n\tA [(p [*rp++])++] = row ;\n      }\n    }\n  }\n\n  /* === Done.  Matrix is not (or no longer) jumbled ====================== */\n\n  return (true) ;\n}\n\n\n/* ========================================================================== */\n/* === init_scoring ========================================================= */\n/* ========================================================================== */\n\n/*\n  Kills dense or empty columns and rows, calculates an initial score for\n  each column, and places all columns in the degree lists.  Not user-callable.\n*/\ntemplate <typename IndexType>\nstatic void init_scoring\n  (\n    /* === Parameters ======================================================= */\n\n    IndexType n_row,      /* number of rows of A */\n    IndexType n_col,      /* number of columns of A */\n    Colamd_Row<IndexType> Row [],    /* of size n_row+1 */\n    colamd_col<IndexType> Col [],    /* of size n_col+1 */\n    IndexType A [],     /* column form and row form of A */\n    IndexType head [],    /* of size n_col+1 */\n    double knobs [COLAMD_KNOBS],/* parameters */\n    IndexType *p_n_row2,    /* number of non-dense, non-empty rows */\n    IndexType *p_n_col2,    /* number of non-dense, non-empty columns */\n    IndexType *p_max_deg    /* maximum row degree */\n    )\n{\n  /* === Local variables ================================================== */\n\n  IndexType c ;     /* a column index */\n  IndexType r, row ;    /* a row index */\n  IndexType *cp ;     /* a column pointer */\n  IndexType deg ;     /* degree of a row or column */\n  IndexType *cp_end ;   /* a pointer to the end of a column */\n  IndexType *new_cp ;   /* new column pointer */\n  IndexType col_length ;    /* length of pruned column */\n  IndexType score ;     /* current column score */\n  IndexType n_col2 ;    /* number of non-dense, non-empty columns */\n  IndexType n_row2 ;    /* number of non-dense, non-empty rows */\n  IndexType dense_row_count ; /* remove rows with more entries than this */\n  IndexType dense_col_count ; /* remove cols with more entries than this */\n  IndexType min_score ;   /* smallest column score */\n  IndexType max_deg ;   /* maximum row degree */\n  IndexType next_col ;    /* Used to add to degree list.*/\n\n\n  /* === Extract knobs ==================================================== */\n\n  dense_row_count = numext::maxi(IndexType(0), numext::mini(IndexType(knobs [COLAMD_DENSE_ROW] * n_col), n_col)) ;\n  dense_col_count = numext::maxi(IndexType(0), numext::mini(IndexType(knobs [COLAMD_DENSE_COL] * n_row), n_row)) ;\n  COLAMD_DEBUG1 ((\"colamd: densecount: %d %d\\n\", dense_row_count, dense_col_count)) ;\n  max_deg = 0 ;\n  n_col2 = n_col ;\n  n_row2 = n_row ;\n\n  /* === Kill empty columns =============================================== */\n\n  /* Put the empty columns at the end in their natural order, so that LU */\n  /* factorization can proceed as far as possible. */\n  for (c = n_col-1 ; c >= 0 ; c--)\n  {\n    deg = Col [c].length ;\n    if (deg == 0)\n    {\n      /* this is a empty column, kill and order it last */\n      Col [c].shared2.order = --n_col2 ;\n      KILL_PRINCIPAL_COL (c) ;\n    }\n  }\n  COLAMD_DEBUG1 ((\"colamd: null columns killed: %d\\n\", n_col - n_col2)) ;\n\n  /* === Kill dense columns =============================================== */\n\n  /* Put the dense columns at the end, in their natural order */\n  for (c = n_col-1 ; c >= 0 ; c--)\n  {\n    /* skip any dead columns */\n    if (COL_IS_DEAD (c))\n    {\n      continue ;\n    }\n    deg = Col [c].length ;\n    if (deg > dense_col_count)\n    {\n      /* this is a dense column, kill and order it last */\n      Col [c].shared2.order = --n_col2 ;\n      /* decrement the row degrees */\n      cp = &A [Col [c].start] ;\n      cp_end = cp + Col [c].length ;\n      while (cp < cp_end)\n      {\n\tRow [*cp++].shared1.degree-- ;\n      }\n      KILL_PRINCIPAL_COL (c) ;\n    }\n  }\n  COLAMD_DEBUG1 ((\"colamd: Dense and null columns killed: %d\\n\", n_col - n_col2)) ;\n\n  /* === Kill dense and empty rows ======================================== */\n\n  for (r = 0 ; r < n_row ; r++)\n  {\n    deg = Row [r].shared1.degree ;\n    COLAMD_ASSERT (deg >= 0 && deg <= n_col) ;\n    if (deg > dense_row_count || deg == 0)\n    {\n      /* kill a dense or empty row */\n      KILL_ROW (r) ;\n      --n_row2 ;\n    }\n    else\n    {\n      /* keep track of max degree of remaining rows */\n      max_deg = numext::maxi(max_deg, deg) ;\n    }\n  }\n  COLAMD_DEBUG1 ((\"colamd: Dense and null rows killed: %d\\n\", n_row - n_row2)) ;\n\n  /* === Compute initial column scores ==================================== */\n\n  /* At this point the row degrees are accurate.  They reflect the number */\n  /* of \"live\" (non-dense) columns in each row.  No empty rows exist. */\n  /* Some \"live\" columns may contain only dead rows, however.  These are */\n  /* pruned in the code below. */\n\n  /* now find the initial matlab score for each column */\n  for (c = n_col-1 ; c >= 0 ; c--)\n  {\n    /* skip dead column */\n    if (COL_IS_DEAD (c))\n    {\n      continue ;\n    }\n    score = 0 ;\n    cp = &A [Col [c].start] ;\n    new_cp = cp ;\n    cp_end = cp + Col [c].length ;\n    while (cp < cp_end)\n    {\n      /* get a row */\n      row = *cp++ ;\n      /* skip if dead */\n      if (ROW_IS_DEAD (row))\n      {\n\tcontinue ;\n      }\n      /* compact the column */\n      *new_cp++ = row ;\n      /* add row's external degree */\n      score += Row [row].shared1.degree - 1 ;\n      /* guard against integer overflow */\n      score = numext::mini(score, n_col) ;\n    }\n    /* determine pruned column length */\n    col_length = (IndexType) (new_cp - &A [Col [c].start]) ;\n    if (col_length == 0)\n    {\n      /* a newly-made null column (all rows in this col are \"dense\" */\n      /* and have already been killed) */\n      COLAMD_DEBUG2 ((\"Newly null killed: %d\\n\", c)) ;\n      Col [c].shared2.order = --n_col2 ;\n      KILL_PRINCIPAL_COL (c) ;\n    }\n    else\n    {\n      /* set column length and set score */\n      COLAMD_ASSERT (score >= 0) ;\n      COLAMD_ASSERT (score <= n_col) ;\n      Col [c].length = col_length ;\n      Col [c].shared2.score = score ;\n    }\n  }\n  COLAMD_DEBUG1 ((\"colamd: Dense, null, and newly-null columns killed: %d\\n\",\n\t\t  n_col-n_col2)) ;\n\n  /* At this point, all empty rows and columns are dead.  All live columns */\n  /* are \"clean\" (containing no dead rows) and simplicial (no supercolumns */\n  /* yet).  Rows may contain dead columns, but all live rows contain at */\n  /* least one live column. */\n\n  /* === Initialize degree lists ========================================== */\n\n\n  /* clear the hash buckets */\n  for (c = 0 ; c <= n_col ; c++)\n  {\n    head [c] = COLAMD_EMPTY ;\n  }\n  min_score = n_col ;\n  /* place in reverse order, so low column indices are at the front */\n  /* of the lists.  This is to encourage natural tie-breaking */\n  for (c = n_col-1 ; c >= 0 ; c--)\n  {\n    /* only add principal columns to degree lists */\n    if (COL_IS_ALIVE (c))\n    {\n      COLAMD_DEBUG4 ((\"place %d score %d minscore %d ncol %d\\n\",\n\t\t      c, Col [c].shared2.score, min_score, n_col)) ;\n\n      /* === Add columns score to DList =============================== */\n\n      score = Col [c].shared2.score ;\n\n      COLAMD_ASSERT (min_score >= 0) ;\n      COLAMD_ASSERT (min_score <= n_col) ;\n      COLAMD_ASSERT (score >= 0) ;\n      COLAMD_ASSERT (score <= n_col) ;\n      COLAMD_ASSERT (head [score] >= COLAMD_EMPTY) ;\n\n      /* now add this column to dList at proper score location */\n      next_col = head [score] ;\n      Col [c].shared3.prev = COLAMD_EMPTY ;\n      Col [c].shared4.degree_next = next_col ;\n\n      /* if there already was a column with the same score, set its */\n      /* previous pointer to this new column */\n      if (next_col != COLAMD_EMPTY)\n      {\n\tCol [next_col].shared3.prev = c ;\n      }\n      head [score] = c ;\n\n      /* see if this score is less than current min */\n      min_score = numext::mini(min_score, score) ;\n\n\n    }\n  }\n\n\n  /* === Return number of remaining columns, and max row degree =========== */\n\n  *p_n_col2 = n_col2 ;\n  *p_n_row2 = n_row2 ;\n  *p_max_deg = max_deg ;\n}\n\n\n/* ========================================================================== */\n/* === find_ordering ======================================================== */\n/* ========================================================================== */\n\n/*\n  Order the principal columns of the supercolumn form of the matrix\n  (no supercolumns on input).  Uses a minimum approximate column minimum\n  degree ordering method.  Not user-callable.\n*/\ntemplate <typename IndexType>\nstatic IndexType find_ordering /* return the number of garbage collections */\n  (\n    /* === Parameters ======================================================= */\n\n    IndexType n_row,      /* number of rows of A */\n    IndexType n_col,      /* number of columns of A */\n    IndexType Alen,     /* size of A, 2*nnz + n_col or larger */\n    Colamd_Row<IndexType> Row [],    /* of size n_row+1 */\n    colamd_col<IndexType> Col [],    /* of size n_col+1 */\n    IndexType A [],     /* column form and row form of A */\n    IndexType head [],    /* of size n_col+1 */\n    IndexType n_col2,     /* Remaining columns to order */\n    IndexType max_deg,    /* Maximum row degree */\n    IndexType pfree     /* index of first free slot (2*nnz on entry) */\n    )\n{\n  /* === Local variables ================================================== */\n\n  IndexType k ;     /* current pivot ordering step */\n  IndexType pivot_col ;   /* current pivot column */\n  IndexType *cp ;     /* a column pointer */\n  IndexType *rp ;     /* a row pointer */\n  IndexType pivot_row ;   /* current pivot row */\n  IndexType *new_cp ;   /* modified column pointer */\n  IndexType *new_rp ;   /* modified row pointer */\n  IndexType pivot_row_start ; /* pointer to start of pivot row */\n  IndexType pivot_row_degree ;  /* number of columns in pivot row */\n  IndexType pivot_row_length ;  /* number of supercolumns in pivot row */\n  IndexType pivot_col_score ; /* score of pivot column */\n  IndexType needed_memory ;   /* free space needed for pivot row */\n  IndexType *cp_end ;   /* pointer to the end of a column */\n  IndexType *rp_end ;   /* pointer to the end of a row */\n  IndexType row ;     /* a row index */\n  IndexType col ;     /* a column index */\n  IndexType max_score ;   /* maximum possible score */\n  IndexType cur_score ;   /* score of current column */\n  unsigned int hash ;   /* hash value for supernode detection */\n  IndexType head_column ;   /* head of hash bucket */\n  IndexType first_col ;   /* first column in hash bucket */\n  IndexType tag_mark ;    /* marker value for mark array */\n  IndexType row_mark ;    /* Row [row].shared2.mark */\n  IndexType set_difference ;  /* set difference size of row with pivot row */\n  IndexType min_score ;   /* smallest column score */\n  IndexType col_thickness ;   /* \"thickness\" (no. of columns in a supercol) */\n  IndexType max_mark ;    /* maximum value of tag_mark */\n  IndexType pivot_col_thickness ; /* number of columns represented by pivot col */\n  IndexType prev_col ;    /* Used by Dlist operations. */\n  IndexType next_col ;    /* Used by Dlist operations. */\n  IndexType ngarbage ;    /* number of garbage collections performed */\n\n\n  /* === Initialization and clear mark ==================================== */\n\n  max_mark = INT_MAX - n_col ;  /* INT_MAX defined in <limits.h> */\n  tag_mark = Eigen::internal::clear_mark (n_row, Row) ;\n  min_score = 0 ;\n  ngarbage = 0 ;\n  COLAMD_DEBUG1 ((\"colamd: Ordering, n_col2=%d\\n\", n_col2)) ;\n\n  /* === Order the columns ================================================ */\n\n  for (k = 0 ; k < n_col2 ; /* 'k' is incremented below */)\n  {\n\n    /* === Select pivot column, and order it ============================ */\n\n    /* make sure degree list isn't empty */\n    COLAMD_ASSERT (min_score >= 0) ;\n    COLAMD_ASSERT (min_score <= n_col) ;\n    COLAMD_ASSERT (head [min_score] >= COLAMD_EMPTY) ;\n\n    /* get pivot column from head of minimum degree list */\n    while (min_score < n_col && head [min_score] == COLAMD_EMPTY)\n    {\n      min_score++ ;\n    }\n    pivot_col = head [min_score] ;\n    COLAMD_ASSERT (pivot_col >= 0 && pivot_col <= n_col) ;\n    next_col = Col [pivot_col].shared4.degree_next ;\n    head [min_score] = next_col ;\n    if (next_col != COLAMD_EMPTY)\n    {\n      Col [next_col].shared3.prev = COLAMD_EMPTY ;\n    }\n\n    COLAMD_ASSERT (COL_IS_ALIVE (pivot_col)) ;\n    COLAMD_DEBUG3 ((\"Pivot col: %d\\n\", pivot_col)) ;\n\n    /* remember score for defrag check */\n    pivot_col_score = Col [pivot_col].shared2.score ;\n\n    /* the pivot column is the kth column in the pivot order */\n    Col [pivot_col].shared2.order = k ;\n\n    /* increment order count by column thickness */\n    pivot_col_thickness = Col [pivot_col].shared1.thickness ;\n    k += pivot_col_thickness ;\n    COLAMD_ASSERT (pivot_col_thickness > 0) ;\n\n    /* === Garbage_collection, if necessary ============================= */\n\n    needed_memory = numext::mini(pivot_col_score, n_col - k) ;\n    if (pfree + needed_memory >= Alen)\n    {\n      pfree = Eigen::internal::garbage_collection (n_row, n_col, Row, Col, A, &A [pfree]) ;\n      ngarbage++ ;\n      /* after garbage collection we will have enough */\n      COLAMD_ASSERT (pfree + needed_memory < Alen) ;\n      /* garbage collection has wiped out the Row[].shared2.mark array */\n      tag_mark = Eigen::internal::clear_mark (n_row, Row) ;\n\n    }\n\n    /* === Compute pivot row pattern ==================================== */\n\n    /* get starting location for this new merged row */\n    pivot_row_start = pfree ;\n\n    /* initialize new row counts to zero */\n    pivot_row_degree = 0 ;\n\n    /* tag pivot column as having been visited so it isn't included */\n    /* in merged pivot row */\n    Col [pivot_col].shared1.thickness = -pivot_col_thickness ;\n\n    /* pivot row is the union of all rows in the pivot column pattern */\n    cp = &A [Col [pivot_col].start] ;\n    cp_end = cp + Col [pivot_col].length ;\n    while (cp < cp_end)\n    {\n      /* get a row */\n      row = *cp++ ;\n      COLAMD_DEBUG4 ((\"Pivot col pattern %d %d\\n\", ROW_IS_ALIVE (row), row)) ;\n      /* skip if row is dead */\n      if (ROW_IS_DEAD (row))\n      {\n\tcontinue ;\n      }\n      rp = &A [Row [row].start] ;\n      rp_end = rp + Row [row].length ;\n      while (rp < rp_end)\n      {\n\t/* get a column */\n\tcol = *rp++ ;\n\t/* add the column, if alive and untagged */\n\tcol_thickness = Col [col].shared1.thickness ;\n\tif (col_thickness > 0 && COL_IS_ALIVE (col))\n\t{\n\t  /* tag column in pivot row */\n\t  Col [col].shared1.thickness = -col_thickness ;\n\t  COLAMD_ASSERT (pfree < Alen) ;\n\t  /* place column in pivot row */\n\t  A [pfree++] = col ;\n\t  pivot_row_degree += col_thickness ;\n\t}\n      }\n    }\n\n    /* clear tag on pivot column */\n    Col [pivot_col].shared1.thickness = pivot_col_thickness ;\n    max_deg = numext::maxi(max_deg, pivot_row_degree) ;\n\n\n    /* === Kill all rows used to construct pivot row ==================== */\n\n    /* also kill pivot row, temporarily */\n    cp = &A [Col [pivot_col].start] ;\n    cp_end = cp + Col [pivot_col].length ;\n    while (cp < cp_end)\n    {\n      /* may be killing an already dead row */\n      row = *cp++ ;\n      COLAMD_DEBUG3 ((\"Kill row in pivot col: %d\\n\", row)) ;\n      KILL_ROW (row) ;\n    }\n\n    /* === Select a row index to use as the new pivot row =============== */\n\n    pivot_row_length = pfree - pivot_row_start ;\n    if (pivot_row_length > 0)\n    {\n      /* pick the \"pivot\" row arbitrarily (first row in col) */\n      pivot_row = A [Col [pivot_col].start] ;\n      COLAMD_DEBUG3 ((\"Pivotal row is %d\\n\", pivot_row)) ;\n    }\n    else\n    {\n      /* there is no pivot row, since it is of zero length */\n      pivot_row = COLAMD_EMPTY ;\n      COLAMD_ASSERT (pivot_row_length == 0) ;\n    }\n    COLAMD_ASSERT (Col [pivot_col].length > 0 || pivot_row_length == 0) ;\n\n    /* === Approximate degree computation =============================== */\n\n    /* Here begins the computation of the approximate degree.  The column */\n    /* score is the sum of the pivot row \"length\", plus the size of the */\n    /* set differences of each row in the column minus the pattern of the */\n    /* pivot row itself.  The column (\"thickness\") itself is also */\n    /* excluded from the column score (we thus use an approximate */\n    /* external degree). */\n\n    /* The time taken by the following code (compute set differences, and */\n    /* add them up) is proportional to the size of the data structure */\n    /* being scanned - that is, the sum of the sizes of each column in */\n    /* the pivot row.  Thus, the amortized time to compute a column score */\n    /* is proportional to the size of that column (where size, in this */\n    /* context, is the column \"length\", or the number of row indices */\n    /* in that column).  The number of row indices in a column is */\n    /* monotonically non-decreasing, from the length of the original */\n    /* column on input to colamd. */\n\n    /* === Compute set differences ====================================== */\n\n    COLAMD_DEBUG3 ((\"** Computing set differences phase. **\\n\")) ;\n\n    /* pivot row is currently dead - it will be revived later. */\n\n    COLAMD_DEBUG3 ((\"Pivot row: \")) ;\n    /* for each column in pivot row */\n    rp = &A [pivot_row_start] ;\n    rp_end = rp + pivot_row_length ;\n    while (rp < rp_end)\n    {\n      col = *rp++ ;\n      COLAMD_ASSERT (COL_IS_ALIVE (col) && col != pivot_col) ;\n      COLAMD_DEBUG3 ((\"Col: %d\\n\", col)) ;\n\n      /* clear tags used to construct pivot row pattern */\n      col_thickness = -Col [col].shared1.thickness ;\n      COLAMD_ASSERT (col_thickness > 0) ;\n      Col [col].shared1.thickness = col_thickness ;\n\n      /* === Remove column from degree list =========================== */\n\n      cur_score = Col [col].shared2.score ;\n      prev_col = Col [col].shared3.prev ;\n      next_col = Col [col].shared4.degree_next ;\n      COLAMD_ASSERT (cur_score >= 0) ;\n      COLAMD_ASSERT (cur_score <= n_col) ;\n      COLAMD_ASSERT (cur_score >= COLAMD_EMPTY) ;\n      if (prev_col == COLAMD_EMPTY)\n      {\n\thead [cur_score] = next_col ;\n      }\n      else\n      {\n\tCol [prev_col].shared4.degree_next = next_col ;\n      }\n      if (next_col != COLAMD_EMPTY)\n      {\n\tCol [next_col].shared3.prev = prev_col ;\n      }\n\n      /* === Scan the column ========================================== */\n\n      cp = &A [Col [col].start] ;\n      cp_end = cp + Col [col].length ;\n      while (cp < cp_end)\n      {\n\t/* get a row */\n\trow = *cp++ ;\n\trow_mark = Row [row].shared2.mark ;\n\t/* skip if dead */\n\tif (ROW_IS_MARKED_DEAD (row_mark))\n\t{\n\t  continue ;\n\t}\n\tCOLAMD_ASSERT (row != pivot_row) ;\n\tset_difference = row_mark - tag_mark ;\n\t/* check if the row has been seen yet */\n\tif (set_difference < 0)\n\t{\n\t  COLAMD_ASSERT (Row [row].shared1.degree <= max_deg) ;\n\t  set_difference = Row [row].shared1.degree ;\n\t}\n\t/* subtract column thickness from this row's set difference */\n\tset_difference -= col_thickness ;\n\tCOLAMD_ASSERT (set_difference >= 0) ;\n\t/* absorb this row if the set difference becomes zero */\n\tif (set_difference == 0)\n\t{\n\t  COLAMD_DEBUG3 ((\"aggressive absorption. Row: %d\\n\", row)) ;\n\t  KILL_ROW (row) ;\n\t}\n\telse\n\t{\n\t  /* save the new mark */\n\t  Row [row].shared2.mark = set_difference + tag_mark ;\n\t}\n      }\n    }\n\n\n    /* === Add up set differences for each column ======================= */\n\n    COLAMD_DEBUG3 ((\"** Adding set differences phase. **\\n\")) ;\n\n    /* for each column in pivot row */\n    rp = &A [pivot_row_start] ;\n    rp_end = rp + pivot_row_length ;\n    while (rp < rp_end)\n    {\n      /* get a column */\n      col = *rp++ ;\n      COLAMD_ASSERT (COL_IS_ALIVE (col) && col != pivot_col) ;\n      hash = 0 ;\n      cur_score = 0 ;\n      cp = &A [Col [col].start] ;\n      /* compact the column */\n      new_cp = cp ;\n      cp_end = cp + Col [col].length ;\n\n      COLAMD_DEBUG4 ((\"Adding set diffs for Col: %d.\\n\", col)) ;\n\n      while (cp < cp_end)\n      {\n\t/* get a row */\n\trow = *cp++ ;\n\tCOLAMD_ASSERT(row >= 0 && row < n_row) ;\n\trow_mark = Row [row].shared2.mark ;\n\t/* skip if dead */\n\tif (ROW_IS_MARKED_DEAD (row_mark))\n\t{\n\t  continue ;\n\t}\n\tCOLAMD_ASSERT (row_mark > tag_mark) ;\n\t/* compact the column */\n\t*new_cp++ = row ;\n\t/* compute hash function */\n\thash += row ;\n\t/* add set difference */\n\tcur_score += row_mark - tag_mark ;\n\t/* integer overflow... */\n\tcur_score = numext::mini(cur_score, n_col) ;\n      }\n\n      /* recompute the column's length */\n      Col [col].length = (IndexType) (new_cp - &A [Col [col].start]) ;\n\n      /* === Further mass elimination ================================= */\n\n      if (Col [col].length == 0)\n      {\n\tCOLAMD_DEBUG4 ((\"further mass elimination. Col: %d\\n\", col)) ;\n\t/* nothing left but the pivot row in this column */\n\tKILL_PRINCIPAL_COL (col) ;\n\tpivot_row_degree -= Col [col].shared1.thickness ;\n\tCOLAMD_ASSERT (pivot_row_degree >= 0) ;\n\t/* order it */\n\tCol [col].shared2.order = k ;\n\t/* increment order count by column thickness */\n\tk += Col [col].shared1.thickness ;\n      }\n      else\n      {\n\t/* === Prepare for supercolumn detection ==================== */\n\n\tCOLAMD_DEBUG4 ((\"Preparing supercol detection for Col: %d.\\n\", col)) ;\n\n\t/* save score so far */\n\tCol [col].shared2.score = cur_score ;\n\n\t/* add column to hash table, for supercolumn detection */\n\thash %= n_col + 1 ;\n\n\tCOLAMD_DEBUG4 ((\" Hash = %d, n_col = %d.\\n\", hash, n_col)) ;\n\tCOLAMD_ASSERT (hash <= n_col) ;\n\n\thead_column = head [hash] ;\n\tif (head_column > COLAMD_EMPTY)\n\t{\n\t  /* degree list \"hash\" is non-empty, use prev (shared3) of */\n\t  /* first column in degree list as head of hash bucket */\n\t  first_col = Col [head_column].shared3.headhash ;\n\t  Col [head_column].shared3.headhash = col ;\n\t}\n\telse\n\t{\n\t  /* degree list \"hash\" is empty, use head as hash bucket */\n\t  first_col = - (head_column + 2) ;\n\t  head [hash] = - (col + 2) ;\n\t}\n\tCol [col].shared4.hash_next = first_col ;\n\n\t/* save hash function in Col [col].shared3.hash */\n\tCol [col].shared3.hash = (IndexType) hash ;\n\tCOLAMD_ASSERT (COL_IS_ALIVE (col)) ;\n      }\n    }\n\n    /* The approximate external column degree is now computed.  */\n\n    /* === Supercolumn detection ======================================== */\n\n    COLAMD_DEBUG3 ((\"** Supercolumn detection phase. **\\n\")) ;\n\n    Eigen::internal::detect_super_cols (Col, A, head, pivot_row_start, pivot_row_length) ;\n\n    /* === Kill the pivotal column ====================================== */\n\n    KILL_PRINCIPAL_COL (pivot_col) ;\n\n    /* === Clear mark =================================================== */\n\n    tag_mark += (max_deg + 1) ;\n    if (tag_mark >= max_mark)\n    {\n      COLAMD_DEBUG2 ((\"clearing tag_mark\\n\")) ;\n      tag_mark = Eigen::internal::clear_mark (n_row, Row) ;\n    }\n\n    /* === Finalize the new pivot row, and column scores ================ */\n\n    COLAMD_DEBUG3 ((\"** Finalize scores phase. **\\n\")) ;\n\n    /* for each column in pivot row */\n    rp = &A [pivot_row_start] ;\n    /* compact the pivot row */\n    new_rp = rp ;\n    rp_end = rp + pivot_row_length ;\n    while (rp < rp_end)\n    {\n      col = *rp++ ;\n      /* skip dead columns */\n      if (COL_IS_DEAD (col))\n      {\n\tcontinue ;\n      }\n      *new_rp++ = col ;\n      /* add new pivot row to column */\n      A [Col [col].start + (Col [col].length++)] = pivot_row ;\n\n      /* retrieve score so far and add on pivot row's degree. */\n      /* (we wait until here for this in case the pivot */\n      /* row's degree was reduced due to mass elimination). */\n      cur_score = Col [col].shared2.score + pivot_row_degree ;\n\n      /* calculate the max possible score as the number of */\n      /* external columns minus the 'k' value minus the */\n      /* columns thickness */\n      max_score = n_col - k - Col [col].shared1.thickness ;\n\n      /* make the score the external degree of the union-of-rows */\n      cur_score -= Col [col].shared1.thickness ;\n\n      /* make sure score is less or equal than the max score */\n      cur_score = numext::mini(cur_score, max_score) ;\n      COLAMD_ASSERT (cur_score >= 0) ;\n\n      /* store updated score */\n      Col [col].shared2.score = cur_score ;\n\n      /* === Place column back in degree list ========================= */\n\n      COLAMD_ASSERT (min_score >= 0) ;\n      COLAMD_ASSERT (min_score <= n_col) ;\n      COLAMD_ASSERT (cur_score >= 0) ;\n      COLAMD_ASSERT (cur_score <= n_col) ;\n      COLAMD_ASSERT (head [cur_score] >= COLAMD_EMPTY) ;\n      next_col = head [cur_score] ;\n      Col [col].shared4.degree_next = next_col ;\n      Col [col].shared3.prev = COLAMD_EMPTY ;\n      if (next_col != COLAMD_EMPTY)\n      {\n\tCol [next_col].shared3.prev = col ;\n      }\n      head [cur_score] = col ;\n\n      /* see if this score is less than current min */\n      min_score = numext::mini(min_score, cur_score) ;\n\n    }\n\n    /* === Resurrect the new pivot row ================================== */\n\n    if (pivot_row_degree > 0)\n    {\n      /* update pivot row length to reflect any cols that were killed */\n      /* during super-col detection and mass elimination */\n      Row [pivot_row].start  = pivot_row_start ;\n      Row [pivot_row].length = (IndexType) (new_rp - &A[pivot_row_start]) ;\n      Row [pivot_row].shared1.degree = pivot_row_degree ;\n      Row [pivot_row].shared2.mark = 0 ;\n      /* pivot row is no longer dead */\n    }\n  }\n\n  /* === All principal columns have now been ordered ====================== */\n\n  return (ngarbage) ;\n}\n\n\n/* ========================================================================== */\n/* === order_children ======================================================= */\n/* ========================================================================== */\n\n/*\n  The find_ordering routine has ordered all of the principal columns (the\n  representatives of the supercolumns).  The non-principal columns have not\n  yet been ordered.  This routine orders those columns by walking up the\n  parent tree (a column is a child of the column which absorbed it).  The\n  final permutation vector is then placed in p [0 ... n_col-1], with p [0]\n  being the first column, and p [n_col-1] being the last.  It doesn't look\n  like it at first glance, but be assured that this routine takes time linear\n  in the number of columns.  Although not immediately obvious, the time\n  taken by this routine is O (n_col), that is, linear in the number of\n  columns.  Not user-callable.\n*/\ntemplate <typename IndexType>\nstatic inline  void order_children\n(\n  /* === Parameters ======================================================= */\n\n  IndexType n_col,      /* number of columns of A */\n  colamd_col<IndexType> Col [],    /* of size n_col+1 */\n  IndexType p []      /* p [0 ... n_col-1] is the column permutation*/\n  )\n{\n  /* === Local variables ================================================== */\n\n  IndexType i ;     /* loop counter for all columns */\n  IndexType c ;     /* column index */\n  IndexType parent ;    /* index of column's parent */\n  IndexType order ;     /* column's order */\n\n  /* === Order each non-principal column ================================== */\n\n  for (i = 0 ; i < n_col ; i++)\n  {\n    /* find an un-ordered non-principal column */\n    COLAMD_ASSERT (COL_IS_DEAD (i)) ;\n    if (!COL_IS_DEAD_PRINCIPAL (i) && Col [i].shared2.order == COLAMD_EMPTY)\n    {\n      parent = i ;\n      /* once found, find its principal parent */\n      do\n      {\n\tparent = Col [parent].shared1.parent ;\n      } while (!COL_IS_DEAD_PRINCIPAL (parent)) ;\n\n      /* now, order all un-ordered non-principal columns along path */\n      /* to this parent.  collapse tree at the same time */\n      c = i ;\n      /* get order of parent */\n      order = Col [parent].shared2.order ;\n\n      do\n      {\n\tCOLAMD_ASSERT (Col [c].shared2.order == COLAMD_EMPTY) ;\n\n\t/* order this column */\n\tCol [c].shared2.order = order++ ;\n\t/* collaps tree */\n\tCol [c].shared1.parent = parent ;\n\n\t/* get immediate parent of this column */\n\tc = Col [c].shared1.parent ;\n\n\t/* continue until we hit an ordered column.  There are */\n\t/* guarranteed not to be anymore unordered columns */\n\t/* above an ordered column */\n      } while (Col [c].shared2.order == COLAMD_EMPTY) ;\n\n      /* re-order the super_col parent to largest order for this group */\n      Col [parent].shared2.order = order ;\n    }\n  }\n\n  /* === Generate the permutation ========================================= */\n\n  for (c = 0 ; c < n_col ; c++)\n  {\n    p [Col [c].shared2.order] = c ;\n  }\n}\n\n\n/* ========================================================================== */\n/* === detect_super_cols ==================================================== */\n/* ========================================================================== */\n\n/*\n  Detects supercolumns by finding matches between columns in the hash buckets.\n  Check amongst columns in the set A [row_start ... row_start + row_length-1].\n  The columns under consideration are currently *not* in the degree lists,\n  and have already been placed in the hash buckets.\n\n  The hash bucket for columns whose hash function is equal to h is stored\n  as follows:\n\n  if head [h] is >= 0, then head [h] contains a degree list, so:\n\n  head [h] is the first column in degree bucket h.\n  Col [head [h]].headhash gives the first column in hash bucket h.\n\n  otherwise, the degree list is empty, and:\n\n  -(head [h] + 2) is the first column in hash bucket h.\n\n  For a column c in a hash bucket, Col [c].shared3.prev is NOT a \"previous\n  column\" pointer.  Col [c].shared3.hash is used instead as the hash number\n  for that column.  The value of Col [c].shared4.hash_next is the next column\n  in the same hash bucket.\n\n  Assuming no, or \"few\" hash collisions, the time taken by this routine is\n  linear in the sum of the sizes (lengths) of each column whose score has\n  just been computed in the approximate degree computation.\n  Not user-callable.\n*/\ntemplate <typename IndexType>\nstatic void detect_super_cols\n(\n  /* === Parameters ======================================================= */\n  \n  colamd_col<IndexType> Col [],    /* of size n_col+1 */\n  IndexType A [],     /* row indices of A */\n  IndexType head [],    /* head of degree lists and hash buckets */\n  IndexType row_start,    /* pointer to set of columns to check */\n  IndexType row_length    /* number of columns to check */\n)\n{\n  /* === Local variables ================================================== */\n\n  IndexType hash ;      /* hash value for a column */\n  IndexType *rp ;     /* pointer to a row */\n  IndexType c ;     /* a column index */\n  IndexType super_c ;   /* column index of the column to absorb into */\n  IndexType *cp1 ;      /* column pointer for column super_c */\n  IndexType *cp2 ;      /* column pointer for column c */\n  IndexType length ;    /* length of column super_c */\n  IndexType prev_c ;    /* column preceding c in hash bucket */\n  IndexType i ;     /* loop counter */\n  IndexType *rp_end ;   /* pointer to the end of the row */\n  IndexType col ;     /* a column index in the row to check */\n  IndexType head_column ;   /* first column in hash bucket or degree list */\n  IndexType first_col ;   /* first column in hash bucket */\n\n  /* === Consider each column in the row ================================== */\n\n  rp = &A [row_start] ;\n  rp_end = rp + row_length ;\n  while (rp < rp_end)\n  {\n    col = *rp++ ;\n    if (COL_IS_DEAD (col))\n    {\n      continue ;\n    }\n\n    /* get hash number for this column */\n    hash = Col [col].shared3.hash ;\n    COLAMD_ASSERT (hash <= n_col) ;\n\n    /* === Get the first column in this hash bucket ===================== */\n\n    head_column = head [hash] ;\n    if (head_column > COLAMD_EMPTY)\n    {\n      first_col = Col [head_column].shared3.headhash ;\n    }\n    else\n    {\n      first_col = - (head_column + 2) ;\n    }\n\n    /* === Consider each column in the hash bucket ====================== */\n\n    for (super_c = first_col ; super_c != COLAMD_EMPTY ;\n\t super_c = Col [super_c].shared4.hash_next)\n    {\n      COLAMD_ASSERT (COL_IS_ALIVE (super_c)) ;\n      COLAMD_ASSERT (Col [super_c].shared3.hash == hash) ;\n      length = Col [super_c].length ;\n\n      /* prev_c is the column preceding column c in the hash bucket */\n      prev_c = super_c ;\n\n      /* === Compare super_c with all columns after it ================ */\n\n      for (c = Col [super_c].shared4.hash_next ;\n\t   c != COLAMD_EMPTY ; c = Col [c].shared4.hash_next)\n      {\n\tCOLAMD_ASSERT (c != super_c) ;\n\tCOLAMD_ASSERT (COL_IS_ALIVE (c)) ;\n\tCOLAMD_ASSERT (Col [c].shared3.hash == hash) ;\n\n\t/* not identical if lengths or scores are different */\n\tif (Col [c].length != length ||\n\t    Col [c].shared2.score != Col [super_c].shared2.score)\n\t{\n\t  prev_c = c ;\n\t  continue ;\n\t}\n\n\t/* compare the two columns */\n\tcp1 = &A [Col [super_c].start] ;\n\tcp2 = &A [Col [c].start] ;\n\n\tfor (i = 0 ; i < length ; i++)\n\t{\n\t  /* the columns are \"clean\" (no dead rows) */\n\t  COLAMD_ASSERT (ROW_IS_ALIVE (*cp1))  ;\n\t  COLAMD_ASSERT (ROW_IS_ALIVE (*cp2))  ;\n\t  /* row indices will same order for both supercols, */\n\t  /* no gather scatter nessasary */\n\t  if (*cp1++ != *cp2++)\n\t  {\n\t    break ;\n\t  }\n\t}\n\n\t/* the two columns are different if the for-loop \"broke\" */\n\tif (i != length)\n\t{\n\t  prev_c = c ;\n\t  continue ;\n\t}\n\n\t/* === Got it!  two columns are identical =================== */\n\n\tCOLAMD_ASSERT (Col [c].shared2.score == Col [super_c].shared2.score) ;\n\n\tCol [super_c].shared1.thickness += Col [c].shared1.thickness ;\n\tCol [c].shared1.parent = super_c ;\n\tKILL_NON_PRINCIPAL_COL (c) ;\n\t/* order c later, in order_children() */\n\tCol [c].shared2.order = COLAMD_EMPTY ;\n\t/* remove c from hash bucket */\n\tCol [prev_c].shared4.hash_next = Col [c].shared4.hash_next ;\n      }\n    }\n\n    /* === Empty this hash bucket ======================================= */\n\n    if (head_column > COLAMD_EMPTY)\n    {\n      /* corresponding degree list \"hash\" is not empty */\n      Col [head_column].shared3.headhash = COLAMD_EMPTY ;\n    }\n    else\n    {\n      /* corresponding degree list \"hash\" is empty */\n      head [hash] = COLAMD_EMPTY ;\n    }\n  }\n}\n\n\n/* ========================================================================== */\n/* === garbage_collection =================================================== */\n/* ========================================================================== */\n\n/*\n  Defragments and compacts columns and rows in the workspace A.  Used when\n  all avaliable memory has been used while performing row merging.  Returns\n  the index of the first free position in A, after garbage collection.  The\n  time taken by this routine is linear is the size of the array A, which is\n  itself linear in the number of nonzeros in the input matrix.\n  Not user-callable.\n*/\ntemplate <typename IndexType>\nstatic IndexType garbage_collection  /* returns the new value of pfree */\n  (\n    /* === Parameters ======================================================= */\n    \n    IndexType n_row,      /* number of rows */\n    IndexType n_col,      /* number of columns */\n    Colamd_Row<IndexType> Row [],    /* row info */\n    colamd_col<IndexType> Col [],    /* column info */\n    IndexType A [],     /* A [0 ... Alen-1] holds the matrix */\n    IndexType *pfree      /* &A [0] ... pfree is in use */\n    )\n{\n  /* === Local variables ================================================== */\n\n  IndexType *psrc ;     /* source pointer */\n  IndexType *pdest ;    /* destination pointer */\n  IndexType j ;     /* counter */\n  IndexType r ;     /* a row index */\n  IndexType c ;     /* a column index */\n  IndexType length ;    /* length of a row or column */\n\n  /* === Defragment the columns =========================================== */\n\n  pdest = &A[0] ;\n  for (c = 0 ; c < n_col ; c++)\n  {\n    if (COL_IS_ALIVE (c))\n    {\n      psrc = &A [Col [c].start] ;\n\n      /* move and compact the column */\n      COLAMD_ASSERT (pdest <= psrc) ;\n      Col [c].start = (IndexType) (pdest - &A [0]) ;\n      length = Col [c].length ;\n      for (j = 0 ; j < length ; j++)\n      {\n\tr = *psrc++ ;\n\tif (ROW_IS_ALIVE (r))\n\t{\n\t  *pdest++ = r ;\n\t}\n      }\n      Col [c].length = (IndexType) (pdest - &A [Col [c].start]) ;\n    }\n  }\n\n  /* === Prepare to defragment the rows =================================== */\n\n  for (r = 0 ; r < n_row ; r++)\n  {\n    if (ROW_IS_ALIVE (r))\n    {\n      if (Row [r].length == 0)\n      {\n\t/* this row is of zero length.  cannot compact it, so kill it */\n\tCOLAMD_DEBUG3 ((\"Defrag row kill\\n\")) ;\n\tKILL_ROW (r) ;\n      }\n      else\n      {\n\t/* save first column index in Row [r].shared2.first_column */\n\tpsrc = &A [Row [r].start] ;\n\tRow [r].shared2.first_column = *psrc ;\n\tCOLAMD_ASSERT (ROW_IS_ALIVE (r)) ;\n\t/* flag the start of the row with the one's complement of row */\n\t*psrc = ONES_COMPLEMENT (r) ;\n\n      }\n    }\n  }\n\n  /* === Defragment the rows ============================================== */\n\n  psrc = pdest ;\n  while (psrc < pfree)\n  {\n    /* find a negative number ... the start of a row */\n    if (*psrc++ < 0)\n    {\n      psrc-- ;\n      /* get the row index */\n      r = ONES_COMPLEMENT (*psrc) ;\n      COLAMD_ASSERT (r >= 0 && r < n_row) ;\n      /* restore first column index */\n      *psrc = Row [r].shared2.first_column ;\n      COLAMD_ASSERT (ROW_IS_ALIVE (r)) ;\n\n      /* move and compact the row */\n      COLAMD_ASSERT (pdest <= psrc) ;\n      Row [r].start = (IndexType) (pdest - &A [0]) ;\n      length = Row [r].length ;\n      for (j = 0 ; j < length ; j++)\n      {\n\tc = *psrc++ ;\n\tif (COL_IS_ALIVE (c))\n\t{\n\t  *pdest++ = c ;\n\t}\n      }\n      Row [r].length = (IndexType) (pdest - &A [Row [r].start]) ;\n\n    }\n  }\n  /* ensure we found all the rows */\n  COLAMD_ASSERT (debug_rows == 0) ;\n\n  /* === Return the new value of pfree ==================================== */\n\n  return ((IndexType) (pdest - &A [0])) ;\n}\n\n\n/* ========================================================================== */\n/* === clear_mark =========================================================== */\n/* ========================================================================== */\n\n/*\n  Clears the Row [].shared2.mark array, and returns the new tag_mark.\n  Return value is the new tag_mark.  Not user-callable.\n*/\ntemplate <typename IndexType>\nstatic inline  IndexType clear_mark  /* return the new value for tag_mark */\n  (\n      /* === Parameters ======================================================= */\n\n    IndexType n_row,    /* number of rows in A */\n    Colamd_Row<IndexType> Row [] /* Row [0 ... n_row-1].shared2.mark is set to zero */\n    )\n{\n  /* === Local variables ================================================== */\n\n  IndexType r ;\n\n  for (r = 0 ; r < n_row ; r++)\n  {\n    if (ROW_IS_ALIVE (r))\n    {\n      Row [r].shared2.mark = 0 ;\n    }\n  }\n  return (1) ;\n}\n\n\n} // namespace internal \n#endif\n"
  },
  {
    "path": "include/eigen3/Eigen/src/OrderingMethods/Ordering.h",
    "content": " \n// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012  Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_ORDERING_H\n#define EIGEN_ORDERING_H\n\nnamespace Eigen {\n  \n#include \"Eigen_Colamd.h\"\n\nnamespace internal {\n    \n/** \\internal\n  * \\ingroup OrderingMethods_Module\n  * \\param[in] A the input non-symmetric matrix\n  * \\param[out] symmat the symmetric pattern A^T+A from the input matrix \\a A.\n  * FIXME: The values should not be considered here\n  */\ntemplate<typename MatrixType> \nvoid ordering_helper_at_plus_a(const MatrixType& A, MatrixType& symmat)\n{\n  MatrixType C;\n  C = A.transpose(); // NOTE: Could be  costly\n  for (int i = 0; i < C.rows(); i++) \n  {\n      for (typename MatrixType::InnerIterator it(C, i); it; ++it)\n        it.valueRef() = 0.0;\n  }\n  symmat = C + A;\n}\n    \n}\n\n#ifndef EIGEN_MPL2_ONLY\n\n/** \\ingroup OrderingMethods_Module\n  * \\class AMDOrdering\n  *\n  * Functor computing the \\em approximate \\em minimum \\em degree ordering\n  * If the matrix is not structurally symmetric, an ordering of A^T+A is computed\n  * \\tparam  StorageIndex The type of indices of the matrix \n  * \\sa COLAMDOrdering\n  */\ntemplate <typename StorageIndex>\nclass AMDOrdering\n{\n  public:\n    typedef PermutationMatrix<Dynamic, Dynamic, StorageIndex> PermutationType;\n    \n    /** Compute the permutation vector from a sparse matrix\n     * This routine is much faster if the input matrix is column-major     \n     */\n    template <typename MatrixType>\n    void operator()(const MatrixType& mat, PermutationType& perm)\n    {\n      // Compute the symmetric pattern\n      SparseMatrix<typename MatrixType::Scalar, ColMajor, StorageIndex> symm;\n      internal::ordering_helper_at_plus_a(mat,symm); \n    \n      // Call the AMD routine \n      //m_mat.prune(keep_diag());\n      internal::minimum_degree_ordering(symm, perm);\n    }\n    \n    /** Compute the permutation with a selfadjoint matrix */\n    template <typename SrcType, unsigned int SrcUpLo> \n    void operator()(const SparseSelfAdjointView<SrcType, SrcUpLo>& mat, PermutationType& perm)\n    { \n      SparseMatrix<typename SrcType::Scalar, ColMajor, StorageIndex> C; C = mat;\n      \n      // Call the AMD routine \n      // m_mat.prune(keep_diag()); //Remove the diagonal elements \n      internal::minimum_degree_ordering(C, perm);\n    }\n};\n\n#endif // EIGEN_MPL2_ONLY\n\n/** \\ingroup OrderingMethods_Module\n  * \\class NaturalOrdering\n  *\n  * Functor computing the natural ordering (identity)\n  * \n  * \\note Returns an empty permutation matrix\n  * \\tparam  StorageIndex The type of indices of the matrix \n  */\ntemplate <typename StorageIndex>\nclass NaturalOrdering\n{\n  public:\n    typedef PermutationMatrix<Dynamic, Dynamic, StorageIndex> PermutationType;\n    \n    /** Compute the permutation vector from a column-major sparse matrix */\n    template <typename MatrixType>\n    void operator()(const MatrixType& /*mat*/, PermutationType& perm)\n    {\n      perm.resize(0); \n    }\n    \n};\n\n/** \\ingroup OrderingMethods_Module\n  * \\class COLAMDOrdering\n  *\n  * \\tparam  StorageIndex The type of indices of the matrix \n  * \n  * Functor computing the \\em column \\em approximate \\em minimum \\em degree ordering \n  * The matrix should be in column-major and \\b compressed format (see SparseMatrix::makeCompressed()).\n  */\ntemplate<typename StorageIndex>\nclass COLAMDOrdering\n{\n  public:\n    typedef PermutationMatrix<Dynamic, Dynamic, StorageIndex> PermutationType; \n    typedef Matrix<StorageIndex, Dynamic, 1> IndexVector;\n    \n    /** Compute the permutation vector \\a perm form the sparse matrix \\a mat\n      * \\warning The input sparse matrix \\a mat must be in compressed mode (see SparseMatrix::makeCompressed()).\n      */\n    template <typename MatrixType>\n    void operator() (const MatrixType& mat, PermutationType& perm)\n    {\n      eigen_assert(mat.isCompressed() && \"COLAMDOrdering requires a sparse matrix in compressed mode. Call .makeCompressed() before passing it to COLAMDOrdering\");\n      \n      StorageIndex m = StorageIndex(mat.rows());\n      StorageIndex n = StorageIndex(mat.cols());\n      StorageIndex nnz = StorageIndex(mat.nonZeros());\n      // Get the recommended value of Alen to be used by colamd\n      StorageIndex Alen = internal::colamd_recommended(nnz, m, n); \n      // Set the default parameters\n      double knobs [COLAMD_KNOBS]; \n      StorageIndex stats [COLAMD_STATS];\n      internal::colamd_set_defaults(knobs);\n      \n      IndexVector p(n+1), A(Alen); \n      for(StorageIndex i=0; i <= n; i++)   p(i) = mat.outerIndexPtr()[i];\n      for(StorageIndex i=0; i < nnz; i++)  A(i) = mat.innerIndexPtr()[i];\n      // Call Colamd routine to compute the ordering \n      StorageIndex info = internal::colamd(m, n, Alen, A.data(), p.data(), knobs, stats); \n      EIGEN_UNUSED_VARIABLE(info);\n      eigen_assert( info && \"COLAMD failed \" );\n      \n      perm.resize(n);\n      for (StorageIndex i = 0; i < n; i++) perm.indices()(p(i)) = i;\n    }\n};\n\n} // end namespace Eigen\n\n#endif\n"
  },
  {
    "path": "include/eigen3/Eigen/src/PaStiXSupport/PaStiXSupport.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_PASTIXSUPPORT_H\n#define EIGEN_PASTIXSUPPORT_H\n\nnamespace Eigen { \n\n#if defined(DCOMPLEX)\n  #define PASTIX_COMPLEX  COMPLEX\n  #define PASTIX_DCOMPLEX DCOMPLEX\n#else\n  #define PASTIX_COMPLEX  std::complex<float>\n  #define PASTIX_DCOMPLEX std::complex<double>\n#endif\n\n/** \\ingroup PaStiXSupport_Module\n  * \\brief Interface to the PaStix solver\n  * \n  * This class is used to solve the linear systems A.X = B via the PaStix library. \n  * The matrix can be either real or complex, symmetric or not.\n  *\n  * \\sa TutorialSparseDirectSolvers\n  */\ntemplate<typename _MatrixType, bool IsStrSym = false> class PastixLU;\ntemplate<typename _MatrixType, int Options> class PastixLLT;\ntemplate<typename _MatrixType, int Options> class PastixLDLT;\n\nnamespace internal\n{\n    \n  template<class Pastix> struct pastix_traits;\n\n  template<typename _MatrixType>\n  struct pastix_traits< PastixLU<_MatrixType> >\n  {\n    typedef _MatrixType MatrixType;\n    typedef typename _MatrixType::Scalar Scalar;\n    typedef typename _MatrixType::RealScalar RealScalar;\n    typedef typename _MatrixType::StorageIndex StorageIndex;\n  };\n\n  template<typename _MatrixType, int Options>\n  struct pastix_traits< PastixLLT<_MatrixType,Options> >\n  {\n    typedef _MatrixType MatrixType;\n    typedef typename _MatrixType::Scalar Scalar;\n    typedef typename _MatrixType::RealScalar RealScalar;\n    typedef typename _MatrixType::StorageIndex StorageIndex;\n  };\n\n  template<typename _MatrixType, int Options>\n  struct pastix_traits< PastixLDLT<_MatrixType,Options> >\n  {\n    typedef _MatrixType MatrixType;\n    typedef typename _MatrixType::Scalar Scalar;\n    typedef typename _MatrixType::RealScalar RealScalar;\n    typedef typename _MatrixType::StorageIndex StorageIndex;\n  };\n  \n  inline void eigen_pastix(pastix_data_t **pastix_data, int pastix_comm, int n, int *ptr, int *idx, float *vals, int *perm, int * invp, float *x, int nbrhs, int *iparm, double *dparm)\n  {\n    if (n == 0) { ptr = NULL; idx = NULL; vals = NULL; }\n    if (nbrhs == 0) {x = NULL; nbrhs=1;}\n    s_pastix(pastix_data, pastix_comm, n, ptr, idx, vals, perm, invp, x, nbrhs, iparm, dparm); \n  }\n  \n  inline void eigen_pastix(pastix_data_t **pastix_data, int pastix_comm, int n, int *ptr, int *idx, double *vals, int *perm, int * invp, double *x, int nbrhs, int *iparm, double *dparm)\n  {\n    if (n == 0) { ptr = NULL; idx = NULL; vals = NULL; }\n    if (nbrhs == 0) {x = NULL; nbrhs=1;}\n    d_pastix(pastix_data, pastix_comm, n, ptr, idx, vals, perm, invp, x, nbrhs, iparm, dparm); \n  }\n  \n  inline void eigen_pastix(pastix_data_t **pastix_data, int pastix_comm, int n, int *ptr, int *idx, std::complex<float> *vals, int *perm, int * invp, std::complex<float> *x, int nbrhs, int *iparm, double *dparm)\n  {\n    if (n == 0) { ptr = NULL; idx = NULL; vals = NULL; }\n    if (nbrhs == 0) {x = NULL; nbrhs=1;}\n    c_pastix(pastix_data, pastix_comm, n, ptr, idx, reinterpret_cast<PASTIX_COMPLEX*>(vals), perm, invp, reinterpret_cast<PASTIX_COMPLEX*>(x), nbrhs, iparm, dparm); \n  }\n  \n  inline void eigen_pastix(pastix_data_t **pastix_data, int pastix_comm, int n, int *ptr, int *idx, std::complex<double> *vals, int *perm, int * invp, std::complex<double> *x, int nbrhs, int *iparm, double *dparm)\n  {\n    if (n == 0) { ptr = NULL; idx = NULL; vals = NULL; }\n    if (nbrhs == 0) {x = NULL; nbrhs=1;}\n    z_pastix(pastix_data, pastix_comm, n, ptr, idx, reinterpret_cast<PASTIX_DCOMPLEX*>(vals), perm, invp, reinterpret_cast<PASTIX_DCOMPLEX*>(x), nbrhs, iparm, dparm); \n  }\n\n  // Convert the matrix  to Fortran-style Numbering\n  template <typename MatrixType>\n  void c_to_fortran_numbering (MatrixType& mat)\n  {\n    if ( !(mat.outerIndexPtr()[0]) ) \n    { \n      int i;\n      for(i = 0; i <= mat.rows(); ++i)\n        ++mat.outerIndexPtr()[i];\n      for(i = 0; i < mat.nonZeros(); ++i)\n        ++mat.innerIndexPtr()[i];\n    }\n  }\n  \n  // Convert to C-style Numbering\n  template <typename MatrixType>\n  void fortran_to_c_numbering (MatrixType& mat)\n  {\n    // Check the Numbering\n    if ( mat.outerIndexPtr()[0] == 1 ) \n    { // Convert to C-style numbering\n      int i;\n      for(i = 0; i <= mat.rows(); ++i)\n        --mat.outerIndexPtr()[i];\n      for(i = 0; i < mat.nonZeros(); ++i)\n        --mat.innerIndexPtr()[i];\n    }\n  }\n}\n\n// This is the base class to interface with PaStiX functions. \n// Users should not used this class directly. \ntemplate <class Derived>\nclass PastixBase : public SparseSolverBase<Derived>\n{\n  protected:\n    typedef SparseSolverBase<Derived> Base;\n    using Base::derived;\n    using Base::m_isInitialized;\n  public:\n    using Base::_solve_impl;\n    \n    typedef typename internal::pastix_traits<Derived>::MatrixType _MatrixType;\n    typedef _MatrixType MatrixType;\n    typedef typename MatrixType::Scalar Scalar;\n    typedef typename MatrixType::RealScalar RealScalar;\n    typedef typename MatrixType::StorageIndex StorageIndex;\n    typedef Matrix<Scalar,Dynamic,1> Vector;\n    typedef SparseMatrix<Scalar, ColMajor> ColSpMatrix;\n    enum {\n      ColsAtCompileTime = MatrixType::ColsAtCompileTime,\n      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime\n    };\n    \n  public:\n    \n    PastixBase() : m_initisOk(false), m_analysisIsOk(false), m_factorizationIsOk(false), m_pastixdata(0), m_size(0)\n    {\n      init();\n    }\n    \n    ~PastixBase() \n    {\n      clean();\n    }\n    \n    template<typename Rhs,typename Dest>\n    bool _solve_impl(const MatrixBase<Rhs> &b, MatrixBase<Dest> &x) const;\n    \n    /** Returns a reference to the integer vector IPARM of PaStiX parameters\n      * to modify the default parameters. \n      * The statistics related to the different phases of factorization and solve are saved here as well\n      * \\sa analyzePattern() factorize()\n      */\n    Array<StorageIndex,IPARM_SIZE,1>& iparm()\n    {\n      return m_iparm; \n    }\n    \n    /** Return a reference to a particular index parameter of the IPARM vector \n     * \\sa iparm()\n     */\n    \n    int& iparm(int idxparam)\n    {\n      return m_iparm(idxparam);\n    }\n    \n     /** Returns a reference to the double vector DPARM of PaStiX parameters \n      * The statistics related to the different phases of factorization and solve are saved here as well\n      * \\sa analyzePattern() factorize()\n      */\n    Array<double,DPARM_SIZE,1>& dparm()\n    {\n      return m_dparm; \n    }\n    \n    \n    /** Return a reference to a particular index parameter of the DPARM vector \n     * \\sa dparm()\n     */\n    double& dparm(int idxparam)\n    {\n      return m_dparm(idxparam);\n    }\n    \n    inline Index cols() const { return m_size; }\n    inline Index rows() const { return m_size; }\n    \n     /** \\brief Reports whether previous computation was successful.\n      *\n      * \\returns \\c Success if computation was succesful,\n      *          \\c NumericalIssue if the PaStiX reports a problem\n      *          \\c InvalidInput if the input matrix is invalid\n      *\n      * \\sa iparm()          \n      */\n    ComputationInfo info() const\n    {\n      eigen_assert(m_isInitialized && \"Decomposition is not initialized.\");\n      return m_info;\n    }\n    \n  protected:\n\n    // Initialize the Pastix data structure, check the matrix\n    void init(); \n    \n    // Compute the ordering and the symbolic factorization\n    void analyzePattern(ColSpMatrix& mat);\n    \n    // Compute the numerical factorization\n    void factorize(ColSpMatrix& mat);\n    \n    // Free all the data allocated by Pastix\n    void clean()\n    {\n      eigen_assert(m_initisOk && \"The Pastix structure should be allocated first\"); \n      m_iparm(IPARM_START_TASK) = API_TASK_CLEAN;\n      m_iparm(IPARM_END_TASK) = API_TASK_CLEAN;\n      internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, 0, 0, 0, (Scalar*)0,\n                             m_perm.data(), m_invp.data(), 0, 0, m_iparm.data(), m_dparm.data());\n    }\n    \n    void compute(ColSpMatrix& mat);\n    \n    int m_initisOk; \n    int m_analysisIsOk;\n    int m_factorizationIsOk;\n    mutable ComputationInfo m_info; \n    mutable pastix_data_t *m_pastixdata; // Data structure for pastix\n    mutable int m_comm; // The MPI communicator identifier\n    mutable Array<int,IPARM_SIZE,1> m_iparm; // integer vector for the input parameters\n    mutable Array<double,DPARM_SIZE,1> m_dparm; // Scalar vector for the input parameters\n    mutable Matrix<StorageIndex,Dynamic,1> m_perm;  // Permutation vector\n    mutable Matrix<StorageIndex,Dynamic,1> m_invp;  // Inverse permutation vector\n    mutable int m_size; // Size of the matrix \n}; \n\n /** Initialize the PaStiX data structure. \n   *A first call to this function fills iparm and dparm with the default PaStiX parameters\n   * \\sa iparm() dparm()\n   */\ntemplate <class Derived>\nvoid PastixBase<Derived>::init()\n{\n  m_size = 0; \n  m_iparm.setZero(IPARM_SIZE);\n  m_dparm.setZero(DPARM_SIZE);\n  \n  m_iparm(IPARM_MODIFY_PARAMETER) = API_NO;\n  pastix(&m_pastixdata, MPI_COMM_WORLD,\n         0, 0, 0, 0,\n         0, 0, 0, 1, m_iparm.data(), m_dparm.data());\n  \n  m_iparm[IPARM_MATRIX_VERIFICATION] = API_NO;\n  m_iparm[IPARM_VERBOSE]             = API_VERBOSE_NOT;\n  m_iparm[IPARM_ORDERING]            = API_ORDER_SCOTCH;\n  m_iparm[IPARM_INCOMPLETE]          = API_NO;\n  m_iparm[IPARM_OOC_LIMIT]           = 2000;\n  m_iparm[IPARM_RHS_MAKING]          = API_RHS_B;\n  m_iparm(IPARM_MATRIX_VERIFICATION) = API_NO;\n  \n  m_iparm(IPARM_START_TASK) = API_TASK_INIT;\n  m_iparm(IPARM_END_TASK) = API_TASK_INIT;\n  internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, 0, 0, 0, (Scalar*)0,\n                         0, 0, 0, 0, m_iparm.data(), m_dparm.data());\n  \n  // Check the returned error\n  if(m_iparm(IPARM_ERROR_NUMBER)) {\n    m_info = InvalidInput;\n    m_initisOk = false;\n  }\n  else { \n    m_info = Success;\n    m_initisOk = true;\n  }\n}\n\ntemplate <class Derived>\nvoid PastixBase<Derived>::compute(ColSpMatrix& mat)\n{\n  eigen_assert(mat.rows() == mat.cols() && \"The input matrix should be squared\");\n  \n  analyzePattern(mat);  \n  factorize(mat);\n  \n  m_iparm(IPARM_MATRIX_VERIFICATION) = API_NO;\n}\n\n\ntemplate <class Derived>\nvoid PastixBase<Derived>::analyzePattern(ColSpMatrix& mat)\n{                         \n  eigen_assert(m_initisOk && \"The initialization of PaSTiX failed\");\n  \n  // clean previous calls\n  if(m_size>0)\n    clean();\n  \n  m_size = internal::convert_index<int>(mat.rows());\n  m_perm.resize(m_size);\n  m_invp.resize(m_size);\n  \n  m_iparm(IPARM_START_TASK) = API_TASK_ORDERING;\n  m_iparm(IPARM_END_TASK) = API_TASK_ANALYSE;\n  internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, m_size, mat.outerIndexPtr(), mat.innerIndexPtr(),\n               mat.valuePtr(), m_perm.data(), m_invp.data(), 0, 0, m_iparm.data(), m_dparm.data());\n  \n  // Check the returned error\n  if(m_iparm(IPARM_ERROR_NUMBER))\n  {\n    m_info = NumericalIssue;\n    m_analysisIsOk = false;\n  }\n  else\n  { \n    m_info = Success;\n    m_analysisIsOk = true;\n  }\n}\n\ntemplate <class Derived>\nvoid PastixBase<Derived>::factorize(ColSpMatrix& mat)\n{\n//   if(&m_cpyMat != &mat) m_cpyMat = mat;\n  eigen_assert(m_analysisIsOk && \"The analysis phase should be called before the factorization phase\");\n  m_iparm(IPARM_START_TASK) = API_TASK_NUMFACT;\n  m_iparm(IPARM_END_TASK) = API_TASK_NUMFACT;\n  m_size = internal::convert_index<int>(mat.rows());\n  \n  internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, m_size, mat.outerIndexPtr(), mat.innerIndexPtr(),\n               mat.valuePtr(), m_perm.data(), m_invp.data(), 0, 0, m_iparm.data(), m_dparm.data());\n  \n  // Check the returned error\n  if(m_iparm(IPARM_ERROR_NUMBER))\n  {\n    m_info = NumericalIssue;\n    m_factorizationIsOk = false;\n    m_isInitialized = false;\n  }\n  else\n  {\n    m_info = Success;\n    m_factorizationIsOk = true;\n    m_isInitialized = true;\n  }\n}\n\n/* Solve the system */\ntemplate<typename Base>\ntemplate<typename Rhs,typename Dest>\nbool PastixBase<Base>::_solve_impl(const MatrixBase<Rhs> &b, MatrixBase<Dest> &x) const\n{\n  eigen_assert(m_isInitialized && \"The matrix should be factorized first\");\n  EIGEN_STATIC_ASSERT((Dest::Flags&RowMajorBit)==0,\n                     THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);\n  int rhs = 1;\n  \n  x = b; /* on return, x is overwritten by the computed solution */\n  \n  for (int i = 0; i < b.cols(); i++){\n    m_iparm[IPARM_START_TASK]          = API_TASK_SOLVE;\n    m_iparm[IPARM_END_TASK]            = API_TASK_REFINE;\n  \n    internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, internal::convert_index<int>(x.rows()), 0, 0, 0,\n                           m_perm.data(), m_invp.data(), &x(0, i), rhs, m_iparm.data(), m_dparm.data());\n  }\n  \n  // Check the returned error\n  m_info = m_iparm(IPARM_ERROR_NUMBER)==0 ? Success : NumericalIssue;\n  \n  return m_iparm(IPARM_ERROR_NUMBER)==0;\n}\n\n/** \\ingroup PaStiXSupport_Module\n  * \\class PastixLU\n  * \\brief Sparse direct LU solver based on PaStiX library\n  * \n  * This class is used to solve the linear systems A.X = B with a supernodal LU \n  * factorization in the PaStiX library. The matrix A should be squared and nonsingular\n  * PaStiX requires that the matrix A has a symmetric structural pattern. \n  * This interface can symmetrize the input matrix otherwise. \n  * The vectors or matrices X and B can be either dense or sparse.\n  * \n  * \\tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>\n  * \\tparam IsStrSym Indicates if the input matrix has a symmetric pattern, default is false\n  * NOTE : Note that if the analysis and factorization phase are called separately, \n  * the input matrix will be symmetrized at each call, hence it is advised to \n  * symmetrize the matrix in a end-user program and set \\p IsStrSym to true\n  *\n  * \\implsparsesolverconcept\n  *\n  * \\sa \\ref TutorialSparseSolverConcept, class SparseLU\n  * \n  */\ntemplate<typename _MatrixType, bool IsStrSym>\nclass PastixLU : public PastixBase< PastixLU<_MatrixType> >\n{\n  public:\n    typedef _MatrixType MatrixType;\n    typedef PastixBase<PastixLU<MatrixType> > Base;\n    typedef typename Base::ColSpMatrix ColSpMatrix;\n    typedef typename MatrixType::StorageIndex StorageIndex;\n    \n  public:\n    PastixLU() : Base()\n    {\n      init();\n    }\n    \n    explicit PastixLU(const MatrixType& matrix):Base()\n    {\n      init();\n      compute(matrix);\n    }\n    /** Compute the LU supernodal factorization of \\p matrix. \n      * iparm and dparm can be used to tune the PaStiX parameters. \n      * see the PaStiX user's manual\n      * \\sa analyzePattern() factorize()\n      */\n    void compute (const MatrixType& matrix)\n    {\n      m_structureIsUptodate = false;\n      ColSpMatrix temp;\n      grabMatrix(matrix, temp);\n      Base::compute(temp);\n    }\n    /** Compute the LU symbolic factorization of \\p matrix using its sparsity pattern. \n      * Several ordering methods can be used at this step. See the PaStiX user's manual. \n      * The result of this operation can be used with successive matrices having the same pattern as \\p matrix\n      * \\sa factorize()\n      */\n    void analyzePattern(const MatrixType& matrix)\n    {\n      m_structureIsUptodate = false;\n      ColSpMatrix temp;\n      grabMatrix(matrix, temp);\n      Base::analyzePattern(temp);\n    }\n\n    /** Compute the LU supernodal factorization of \\p matrix\n      * WARNING The matrix \\p matrix should have the same structural pattern \n      * as the same used in the analysis phase.\n      * \\sa analyzePattern()\n      */ \n    void factorize(const MatrixType& matrix)\n    {\n      ColSpMatrix temp;\n      grabMatrix(matrix, temp);\n      Base::factorize(temp);\n    }\n  protected:\n    \n    void init()\n    {\n      m_structureIsUptodate = false;\n      m_iparm(IPARM_SYM) = API_SYM_NO;\n      m_iparm(IPARM_FACTORIZATION) = API_FACT_LU;\n    }\n    \n    void grabMatrix(const MatrixType& matrix, ColSpMatrix& out)\n    {\n      if(IsStrSym)\n        out = matrix;\n      else\n      {\n        if(!m_structureIsUptodate)\n        {\n          // update the transposed structure\n          m_transposedStructure = matrix.transpose();\n          \n          // Set the elements of the matrix to zero \n          for (Index j=0; j<m_transposedStructure.outerSize(); ++j) \n            for(typename ColSpMatrix::InnerIterator it(m_transposedStructure, j); it; ++it)\n              it.valueRef() = 0.0;\n\n          m_structureIsUptodate = true;\n        }\n        \n        out = m_transposedStructure + matrix;\n      }\n      internal::c_to_fortran_numbering(out);\n    }\n    \n    using Base::m_iparm;\n    using Base::m_dparm;\n    \n    ColSpMatrix m_transposedStructure;\n    bool m_structureIsUptodate;\n};\n\n/** \\ingroup PaStiXSupport_Module\n  * \\class PastixLLT\n  * \\brief A sparse direct supernodal Cholesky (LLT) factorization and solver based on the PaStiX library\n  * \n  * This class is used to solve the linear systems A.X = B via a LL^T supernodal Cholesky factorization\n  * available in the PaStiX library. The matrix A should be symmetric and positive definite\n  * WARNING Selfadjoint complex matrices are not supported in the current version of PaStiX\n  * The vectors or matrices X and B can be either dense or sparse\n  * \n  * \\tparam MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>\n  * \\tparam UpLo The part of the matrix to use : Lower or Upper. The default is Lower as required by PaStiX\n  *\n  * \\implsparsesolverconcept\n  *\n  * \\sa \\ref TutorialSparseSolverConcept, class SimplicialLLT\n  */\ntemplate<typename _MatrixType, int _UpLo>\nclass PastixLLT : public PastixBase< PastixLLT<_MatrixType, _UpLo> >\n{\n  public:\n    typedef _MatrixType MatrixType;\n    typedef PastixBase<PastixLLT<MatrixType, _UpLo> > Base;\n    typedef typename Base::ColSpMatrix ColSpMatrix;\n    \n  public:\n    enum { UpLo = _UpLo };\n    PastixLLT() : Base()\n    {\n      init();\n    }\n    \n    explicit PastixLLT(const MatrixType& matrix):Base()\n    {\n      init();\n      compute(matrix);\n    }\n\n    /** Compute the L factor of the LL^T supernodal factorization of \\p matrix \n      * \\sa analyzePattern() factorize()\n      */\n    void compute (const MatrixType& matrix)\n    {\n      ColSpMatrix temp;\n      grabMatrix(matrix, temp);\n      Base::compute(temp);\n    }\n\n     /** Compute the LL^T symbolic factorization of \\p matrix using its sparsity pattern\n      * The result of this operation can be used with successive matrices having the same pattern as \\p matrix\n      * \\sa factorize()\n      */\n    void analyzePattern(const MatrixType& matrix)\n    {\n      ColSpMatrix temp;\n      grabMatrix(matrix, temp);\n      Base::analyzePattern(temp);\n    }\n      /** Compute the LL^T supernodal numerical factorization of \\p matrix \n        * \\sa analyzePattern()\n        */\n    void factorize(const MatrixType& matrix)\n    {\n      ColSpMatrix temp;\n      grabMatrix(matrix, temp);\n      Base::factorize(temp);\n    }\n  protected:\n    using Base::m_iparm;\n    \n    void init()\n    {\n      m_iparm(IPARM_SYM) = API_SYM_YES;\n      m_iparm(IPARM_FACTORIZATION) = API_FACT_LLT;\n    }\n    \n    void grabMatrix(const MatrixType& matrix, ColSpMatrix& out)\n    {\n      out.resize(matrix.rows(), matrix.cols());\n      // Pastix supports only lower, column-major matrices \n      out.template selfadjointView<Lower>() = matrix.template selfadjointView<UpLo>();\n      internal::c_to_fortran_numbering(out);\n    }\n};\n\n/** \\ingroup PaStiXSupport_Module\n  * \\class PastixLDLT\n  * \\brief A sparse direct supernodal Cholesky (LLT) factorization and solver based on the PaStiX library\n  * \n  * This class is used to solve the linear systems A.X = B via a LDL^T supernodal Cholesky factorization\n  * available in the PaStiX library. The matrix A should be symmetric and positive definite\n  * WARNING Selfadjoint complex matrices are not supported in the current version of PaStiX\n  * The vectors or matrices X and B can be either dense or sparse\n  * \n  * \\tparam MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>\n  * \\tparam UpLo The part of the matrix to use : Lower or Upper. The default is Lower as required by PaStiX\n  *\n  * \\implsparsesolverconcept\n  *\n  * \\sa \\ref TutorialSparseSolverConcept, class SimplicialLDLT\n  */\ntemplate<typename _MatrixType, int _UpLo>\nclass PastixLDLT : public PastixBase< PastixLDLT<_MatrixType, _UpLo> >\n{\n  public:\n    typedef _MatrixType MatrixType;\n    typedef PastixBase<PastixLDLT<MatrixType, _UpLo> > Base; \n    typedef typename Base::ColSpMatrix ColSpMatrix;\n    \n  public:\n    enum { UpLo = _UpLo };\n    PastixLDLT():Base()\n    {\n      init();\n    }\n    \n    explicit PastixLDLT(const MatrixType& matrix):Base()\n    {\n      init();\n      compute(matrix);\n    }\n\n    /** Compute the L and D factors of the LDL^T factorization of \\p matrix \n      * \\sa analyzePattern() factorize()\n      */\n    void compute (const MatrixType& matrix)\n    {\n      ColSpMatrix temp;\n      grabMatrix(matrix, temp);\n      Base::compute(temp);\n    }\n\n    /** Compute the LDL^T symbolic factorization of \\p matrix using its sparsity pattern\n      * The result of this operation can be used with successive matrices having the same pattern as \\p matrix\n      * \\sa factorize()\n      */\n    void analyzePattern(const MatrixType& matrix)\n    { \n      ColSpMatrix temp;\n      grabMatrix(matrix, temp);\n      Base::analyzePattern(temp);\n    }\n    /** Compute the LDL^T supernodal numerical factorization of \\p matrix \n      * \n      */\n    void factorize(const MatrixType& matrix)\n    {\n      ColSpMatrix temp;\n      grabMatrix(matrix, temp);\n      Base::factorize(temp);\n    }\n\n  protected:\n    using Base::m_iparm;\n    \n    void init()\n    {\n      m_iparm(IPARM_SYM) = API_SYM_YES;\n      m_iparm(IPARM_FACTORIZATION) = API_FACT_LDLT;\n    }\n    \n    void grabMatrix(const MatrixType& matrix, ColSpMatrix& out)\n    {\n      // Pastix supports only lower, column-major matrices \n      out.resize(matrix.rows(), matrix.cols());\n      out.template selfadjointView<Lower>() = matrix.template selfadjointView<UpLo>();\n      internal::c_to_fortran_numbering(out);\n    }\n};\n\n} // end namespace Eigen\n\n#endif\n"
  },
  {
    "path": "include/eigen3/Eigen/src/PardisoSupport/PardisoSupport.h",
    "content": "/*\n Copyright (c) 2011, Intel Corporation. All rights reserved.\n\n Redistribution and use in source and binary forms, with or without modification,\n are permitted provided that the following conditions are met:\n\n * Redistributions of source code must retain the above copyright notice, this\n   list of conditions and the following disclaimer.\n * Redistributions in binary form must reproduce the above copyright notice,\n   this list of conditions and the following disclaimer in the documentation\n   and/or other materials provided with the distribution.\n * Neither the name of Intel Corporation nor the names of its contributors may\n   be used to endorse or promote products derived from this software without\n   specific prior written permission.\n\n THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\" AND\n ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED\n WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\n DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR\n ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES\n (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;\n LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON\n ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT\n (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS\n SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n\n ********************************************************************************\n *   Content : Eigen bindings to Intel(R) MKL PARDISO\n ********************************************************************************\n*/\n\n#ifndef EIGEN_PARDISOSUPPORT_H\n#define EIGEN_PARDISOSUPPORT_H\n\nnamespace Eigen { \n\ntemplate<typename _MatrixType> class PardisoLU;\ntemplate<typename _MatrixType, int Options=Upper> class PardisoLLT;\ntemplate<typename _MatrixType, int Options=Upper> class PardisoLDLT;\n\nnamespace internal\n{\n  template<typename IndexType>\n  struct pardiso_run_selector\n  {\n    static IndexType run( _MKL_DSS_HANDLE_t pt, IndexType maxfct, IndexType mnum, IndexType type, IndexType phase, IndexType n, void *a,\n                      IndexType *ia, IndexType *ja, IndexType *perm, IndexType nrhs, IndexType *iparm, IndexType msglvl, void *b, void *x)\n    {\n      IndexType error = 0;\n      ::pardiso(pt, &maxfct, &mnum, &type, &phase, &n, a, ia, ja, perm, &nrhs, iparm, &msglvl, b, x, &error);\n      return error;\n    }\n  };\n  template<>\n  struct pardiso_run_selector<long long int>\n  {\n    typedef long long int IndexType;\n    static IndexType run( _MKL_DSS_HANDLE_t pt, IndexType maxfct, IndexType mnum, IndexType type, IndexType phase, IndexType n, void *a,\n                      IndexType *ia, IndexType *ja, IndexType *perm, IndexType nrhs, IndexType *iparm, IndexType msglvl, void *b, void *x)\n    {\n      IndexType error = 0;\n      ::pardiso_64(pt, &maxfct, &mnum, &type, &phase, &n, a, ia, ja, perm, &nrhs, iparm, &msglvl, b, x, &error);\n      return error;\n    }\n  };\n\n  template<class Pardiso> struct pardiso_traits;\n\n  template<typename _MatrixType>\n  struct pardiso_traits< PardisoLU<_MatrixType> >\n  {\n    typedef _MatrixType MatrixType;\n    typedef typename _MatrixType::Scalar Scalar;\n    typedef typename _MatrixType::RealScalar RealScalar;\n    typedef typename _MatrixType::StorageIndex StorageIndex;\n  };\n\n  template<typename _MatrixType, int Options>\n  struct pardiso_traits< PardisoLLT<_MatrixType, Options> >\n  {\n    typedef _MatrixType MatrixType;\n    typedef typename _MatrixType::Scalar Scalar;\n    typedef typename _MatrixType::RealScalar RealScalar;\n    typedef typename _MatrixType::StorageIndex StorageIndex;\n  };\n\n  template<typename _MatrixType, int Options>\n  struct pardiso_traits< PardisoLDLT<_MatrixType, Options> >\n  {\n    typedef _MatrixType MatrixType;\n    typedef typename _MatrixType::Scalar Scalar;\n    typedef typename _MatrixType::RealScalar RealScalar;\n    typedef typename _MatrixType::StorageIndex StorageIndex;    \n  };\n\n} // end namespace internal\n\ntemplate<class Derived>\nclass PardisoImpl : public SparseSolverBase<Derived>\n{\n  protected:\n    typedef SparseSolverBase<Derived> Base;\n    using Base::derived;\n    using Base::m_isInitialized;\n    \n    typedef internal::pardiso_traits<Derived> Traits;\n  public:\n    using Base::_solve_impl;\n    \n    typedef typename Traits::MatrixType MatrixType;\n    typedef typename Traits::Scalar Scalar;\n    typedef typename Traits::RealScalar RealScalar;\n    typedef typename Traits::StorageIndex StorageIndex;\n    typedef SparseMatrix<Scalar,RowMajor,StorageIndex> SparseMatrixType;\n    typedef Matrix<Scalar,Dynamic,1> VectorType;\n    typedef Matrix<StorageIndex, 1, MatrixType::ColsAtCompileTime> IntRowVectorType;\n    typedef Matrix<StorageIndex, MatrixType::RowsAtCompileTime, 1> IntColVectorType;\n    typedef Array<StorageIndex,64,1,DontAlign> ParameterType;\n    enum {\n      ScalarIsComplex = NumTraits<Scalar>::IsComplex,\n      ColsAtCompileTime = Dynamic,\n      MaxColsAtCompileTime = Dynamic\n    };\n\n    PardisoImpl()\n    {\n      eigen_assert((sizeof(StorageIndex) >= sizeof(_INTEGER_t) && sizeof(StorageIndex) <= 8) && \"Non-supported index type\");\n      m_iparm.setZero();\n      m_msglvl = 0; // No output\n      m_isInitialized = false;\n    }\n\n    ~PardisoImpl()\n    {\n      pardisoRelease();\n    }\n\n    inline Index cols() const { return m_size; }\n    inline Index rows() const { return m_size; }\n  \n    /** \\brief Reports whether previous computation was successful.\n      *\n      * \\returns \\c Success if computation was succesful,\n      *          \\c NumericalIssue if the matrix appears to be negative.\n      */\n    ComputationInfo info() const\n    {\n      eigen_assert(m_isInitialized && \"Decomposition is not initialized.\");\n      return m_info;\n    }\n\n    /** \\warning for advanced usage only.\n      * \\returns a reference to the parameter array controlling PARDISO.\n      * See the PARDISO manual to know how to use it. */\n    ParameterType& pardisoParameterArray()\n    {\n      return m_iparm;\n    }\n    \n    /** Performs a symbolic decomposition on the sparcity of \\a matrix.\n      *\n      * This function is particularly useful when solving for several problems having the same structure.\n      * \n      * \\sa factorize()\n      */\n    Derived& analyzePattern(const MatrixType& matrix);\n    \n    /** Performs a numeric decomposition of \\a matrix\n      *\n      * The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed.\n      *\n      * \\sa analyzePattern()\n      */\n    Derived& factorize(const MatrixType& matrix);\n\n    Derived& compute(const MatrixType& matrix);\n\n    template<typename Rhs,typename Dest>\n    void _solve_impl(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const;\n\n  protected:\n    void pardisoRelease()\n    {\n      if(m_isInitialized) // Factorization ran at least once\n      {\n        internal::pardiso_run_selector<StorageIndex>::run(m_pt, 1, 1, m_type, -1, internal::convert_index<StorageIndex>(m_size),0, 0, 0, m_perm.data(), 0,\n                                                          m_iparm.data(), m_msglvl, NULL, NULL);\n        m_isInitialized = false;\n      }\n    }\n\n    void pardisoInit(int type)\n    {\n      m_type = type;\n      bool symmetric = std::abs(m_type) < 10;\n      m_iparm[0] = 1;   // No solver default\n      m_iparm[1] = 2;   // use Metis for the ordering\n      m_iparm[2] = 0;   // Reserved. Set to zero. (??Numbers of processors, value of OMP_NUM_THREADS??)\n      m_iparm[3] = 0;   // No iterative-direct algorithm\n      m_iparm[4] = 0;   // No user fill-in reducing permutation\n      m_iparm[5] = 0;   // Write solution into x, b is left unchanged\n      m_iparm[6] = 0;   // Not in use\n      m_iparm[7] = 2;   // Max numbers of iterative refinement steps\n      m_iparm[8] = 0;   // Not in use\n      m_iparm[9] = 13;  // Perturb the pivot elements with 1E-13\n      m_iparm[10] = symmetric ? 0 : 1; // Use nonsymmetric permutation and scaling MPS\n      m_iparm[11] = 0;  // Not in use\n      m_iparm[12] = symmetric ? 0 : 1;  // Maximum weighted matching algorithm is switched-off (default for symmetric).\n                                        // Try m_iparm[12] = 1 in case of inappropriate accuracy\n      m_iparm[13] = 0;  // Output: Number of perturbed pivots\n      m_iparm[14] = 0;  // Not in use\n      m_iparm[15] = 0;  // Not in use\n      m_iparm[16] = 0;  // Not in use\n      m_iparm[17] = -1; // Output: Number of nonzeros in the factor LU\n      m_iparm[18] = -1; // Output: Mflops for LU factorization\n      m_iparm[19] = 0;  // Output: Numbers of CG Iterations\n      \n      m_iparm[20] = 0;  // 1x1 pivoting\n      m_iparm[26] = 0;  // No matrix checker\n      m_iparm[27] = (sizeof(RealScalar) == 4) ? 1 : 0;\n      m_iparm[34] = 1;  // C indexing\n      m_iparm[36] = 0;  // CSR\n      m_iparm[59] = 0;  // 0 - In-Core ; 1 - Automatic switch between In-Core and Out-of-Core modes ; 2 - Out-of-Core\n      \n      memset(m_pt, 0, sizeof(m_pt));\n    }\n\n  protected:\n    // cached data to reduce reallocation, etc.\n    \n    void manageErrorCode(Index error) const\n    {\n      switch(error)\n      {\n        case 0:\n          m_info = Success;\n          break;\n        case -4:\n        case -7:\n          m_info = NumericalIssue;\n          break;\n        default:\n          m_info = InvalidInput;\n      }\n    }\n\n    mutable SparseMatrixType m_matrix;\n    mutable ComputationInfo m_info;\n    bool m_analysisIsOk, m_factorizationIsOk;\n    StorageIndex m_type, m_msglvl;\n    mutable void *m_pt[64];\n    mutable ParameterType m_iparm;\n    mutable IntColVectorType m_perm;\n    Index m_size;\n    \n};\n\ntemplate<class Derived>\nDerived& PardisoImpl<Derived>::compute(const MatrixType& a)\n{\n  m_size = a.rows();\n  eigen_assert(a.rows() == a.cols());\n\n  pardisoRelease();\n  m_perm.setZero(m_size);\n  derived().getMatrix(a);\n  \n  Index error;\n  error = internal::pardiso_run_selector<StorageIndex>::run(m_pt, 1, 1, m_type, 12, internal::convert_index<StorageIndex>(m_size),\n                                                            m_matrix.valuePtr(), m_matrix.outerIndexPtr(), m_matrix.innerIndexPtr(),\n                                                            m_perm.data(), 0, m_iparm.data(), m_msglvl, NULL, NULL);\n  manageErrorCode(error);\n  m_analysisIsOk = true;\n  m_factorizationIsOk = true;\n  m_isInitialized = true;\n  return derived();\n}\n\ntemplate<class Derived>\nDerived& PardisoImpl<Derived>::analyzePattern(const MatrixType& a)\n{\n  m_size = a.rows();\n  eigen_assert(m_size == a.cols());\n\n  pardisoRelease();\n  m_perm.setZero(m_size);\n  derived().getMatrix(a);\n  \n  Index error;\n  error = internal::pardiso_run_selector<StorageIndex>::run(m_pt, 1, 1, m_type, 11, internal::convert_index<StorageIndex>(m_size),\n                                                            m_matrix.valuePtr(), m_matrix.outerIndexPtr(), m_matrix.innerIndexPtr(),\n                                                            m_perm.data(), 0, m_iparm.data(), m_msglvl, NULL, NULL);\n  \n  manageErrorCode(error);\n  m_analysisIsOk = true;\n  m_factorizationIsOk = false;\n  m_isInitialized = true;\n  return derived();\n}\n\ntemplate<class Derived>\nDerived& PardisoImpl<Derived>::factorize(const MatrixType& a)\n{\n  eigen_assert(m_analysisIsOk && \"You must first call analyzePattern()\");\n  eigen_assert(m_size == a.rows() && m_size == a.cols());\n  \n  derived().getMatrix(a);\n\n  Index error;\n  error = internal::pardiso_run_selector<StorageIndex>::run(m_pt, 1, 1, m_type, 22, internal::convert_index<StorageIndex>(m_size),\n                                                            m_matrix.valuePtr(), m_matrix.outerIndexPtr(), m_matrix.innerIndexPtr(),\n                                                            m_perm.data(), 0, m_iparm.data(), m_msglvl, NULL, NULL);\n  \n  manageErrorCode(error);\n  m_factorizationIsOk = true;\n  return derived();\n}\n\ntemplate<class Derived>\ntemplate<typename BDerived,typename XDerived>\nvoid PardisoImpl<Derived>::_solve_impl(const MatrixBase<BDerived> &b, MatrixBase<XDerived>& x) const\n{\n  if(m_iparm[0] == 0) // Factorization was not computed\n  {\n    m_info = InvalidInput;\n    return;\n  }\n\n  //Index n = m_matrix.rows();\n  Index nrhs = Index(b.cols());\n  eigen_assert(m_size==b.rows());\n  eigen_assert(((MatrixBase<BDerived>::Flags & RowMajorBit) == 0 || nrhs == 1) && \"Row-major right hand sides are not supported\");\n  eigen_assert(((MatrixBase<XDerived>::Flags & RowMajorBit) == 0 || nrhs == 1) && \"Row-major matrices of unknowns are not supported\");\n  eigen_assert(((nrhs == 1) || b.outerStride() == b.rows()));\n\n\n//  switch (transposed) {\n//    case SvNoTrans    : m_iparm[11] = 0 ; break;\n//    case SvTranspose  : m_iparm[11] = 2 ; break;\n//    case SvAdjoint    : m_iparm[11] = 1 ; break;\n//    default:\n//      //std::cerr << \"Eigen: transposition  option \\\"\" << transposed << \"\\\" not supported by the PARDISO backend\\n\";\n//      m_iparm[11] = 0;\n//  }\n\n  Scalar* rhs_ptr = const_cast<Scalar*>(b.derived().data());\n  Matrix<Scalar,Dynamic,Dynamic,ColMajor> tmp;\n  \n  // Pardiso cannot solve in-place\n  if(rhs_ptr == x.derived().data())\n  {\n    tmp = b;\n    rhs_ptr = tmp.data();\n  }\n  \n  Index error;\n  error = internal::pardiso_run_selector<StorageIndex>::run(m_pt, 1, 1, m_type, 33, internal::convert_index<StorageIndex>(m_size),\n                                                            m_matrix.valuePtr(), m_matrix.outerIndexPtr(), m_matrix.innerIndexPtr(),\n                                                            m_perm.data(), internal::convert_index<StorageIndex>(nrhs), m_iparm.data(), m_msglvl,\n                                                            rhs_ptr, x.derived().data());\n\n  manageErrorCode(error);\n}\n\n\n/** \\ingroup PardisoSupport_Module\n  * \\class PardisoLU\n  * \\brief A sparse direct LU factorization and solver based on the PARDISO library\n  *\n  * This class allows to solve for A.X = B sparse linear problems via a direct LU factorization\n  * using the Intel MKL PARDISO library. The sparse matrix A must be squared and invertible.\n  * The vectors or matrices X and B can be either dense or sparse.\n  *\n  * By default, it runs in in-core mode. To enable PARDISO's out-of-core feature, set:\n  * \\code solver.pardisoParameterArray()[59] = 1; \\endcode\n  *\n  * \\tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>\n  *\n  * \\implsparsesolverconcept\n  *\n  * \\sa \\ref TutorialSparseSolverConcept, class SparseLU\n  */\ntemplate<typename MatrixType>\nclass PardisoLU : public PardisoImpl< PardisoLU<MatrixType> >\n{\n  protected:\n    typedef PardisoImpl<PardisoLU> Base;\n    typedef typename Base::Scalar Scalar;\n    typedef typename Base::RealScalar RealScalar;\n    using Base::pardisoInit;\n    using Base::m_matrix;\n    friend class PardisoImpl< PardisoLU<MatrixType> >;\n\n  public:\n\n    using Base::compute;\n    using Base::solve;\n\n    PardisoLU()\n      : Base()\n    {\n      pardisoInit(Base::ScalarIsComplex ? 13 : 11);\n    }\n\n    explicit PardisoLU(const MatrixType& matrix)\n      : Base()\n    {\n      pardisoInit(Base::ScalarIsComplex ? 13 : 11);\n      compute(matrix);\n    }\n  protected:\n    void getMatrix(const MatrixType& matrix)\n    {\n      m_matrix = matrix;\n      m_matrix.makeCompressed();\n    }\n};\n\n/** \\ingroup PardisoSupport_Module\n  * \\class PardisoLLT\n  * \\brief A sparse direct Cholesky (LLT) factorization and solver based on the PARDISO library\n  *\n  * This class allows to solve for A.X = B sparse linear problems via a LL^T Cholesky factorization\n  * using the Intel MKL PARDISO library. The sparse matrix A must be selfajoint and positive definite.\n  * The vectors or matrices X and B can be either dense or sparse.\n  *\n  * By default, it runs in in-core mode. To enable PARDISO's out-of-core feature, set:\n  * \\code solver.pardisoParameterArray()[59] = 1; \\endcode\n  *\n  * \\tparam MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>\n  * \\tparam UpLo can be any bitwise combination of Upper, Lower. The default is Upper, meaning only the upper triangular part has to be used.\n  *         Upper|Lower can be used to tell both triangular parts can be used as input.\n  *\n  * \\implsparsesolverconcept\n  *\n  * \\sa \\ref TutorialSparseSolverConcept, class SimplicialLLT\n  */\ntemplate<typename MatrixType, int _UpLo>\nclass PardisoLLT : public PardisoImpl< PardisoLLT<MatrixType,_UpLo> >\n{\n  protected:\n    typedef PardisoImpl< PardisoLLT<MatrixType,_UpLo> > Base;\n    typedef typename Base::Scalar Scalar;\n    typedef typename Base::RealScalar RealScalar;\n    using Base::pardisoInit;\n    using Base::m_matrix;\n    friend class PardisoImpl< PardisoLLT<MatrixType,_UpLo> >;\n\n  public:\n\n    typedef typename Base::StorageIndex StorageIndex;\n    enum { UpLo = _UpLo };\n    using Base::compute;\n\n    PardisoLLT()\n      : Base()\n    {\n      pardisoInit(Base::ScalarIsComplex ? 4 : 2);\n    }\n\n    explicit PardisoLLT(const MatrixType& matrix)\n      : Base()\n    {\n      pardisoInit(Base::ScalarIsComplex ? 4 : 2);\n      compute(matrix);\n    }\n    \n  protected:\n    \n    void getMatrix(const MatrixType& matrix)\n    {\n      // PARDISO supports only upper, row-major matrices\n      PermutationMatrix<Dynamic,Dynamic,StorageIndex> p_null;\n      m_matrix.resize(matrix.rows(), matrix.cols());\n      m_matrix.template selfadjointView<Upper>() = matrix.template selfadjointView<UpLo>().twistedBy(p_null);\n      m_matrix.makeCompressed();\n    }\n};\n\n/** \\ingroup PardisoSupport_Module\n  * \\class PardisoLDLT\n  * \\brief A sparse direct Cholesky (LDLT) factorization and solver based on the PARDISO library\n  *\n  * This class allows to solve for A.X = B sparse linear problems via a LDL^T Cholesky factorization\n  * using the Intel MKL PARDISO library. The sparse matrix A is assumed to be selfajoint and positive definite.\n  * For complex matrices, A can also be symmetric only, see the \\a Options template parameter.\n  * The vectors or matrices X and B can be either dense or sparse.\n  *\n  * By default, it runs in in-core mode. To enable PARDISO's out-of-core feature, set:\n  * \\code solver.pardisoParameterArray()[59] = 1; \\endcode\n  *\n  * \\tparam MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>\n  * \\tparam Options can be any bitwise combination of Upper, Lower, and Symmetric. The default is Upper, meaning only the upper triangular part has to be used.\n  *         Symmetric can be used for symmetric, non-selfadjoint complex matrices, the default being to assume a selfadjoint matrix.\n  *         Upper|Lower can be used to tell both triangular parts can be used as input.\n  *\n  * \\implsparsesolverconcept\n  *\n  * \\sa \\ref TutorialSparseSolverConcept, class SimplicialLDLT\n  */\ntemplate<typename MatrixType, int Options>\nclass PardisoLDLT : public PardisoImpl< PardisoLDLT<MatrixType,Options> >\n{\n  protected:\n    typedef PardisoImpl< PardisoLDLT<MatrixType,Options> > Base;\n    typedef typename Base::Scalar Scalar;\n    typedef typename Base::RealScalar RealScalar;\n    using Base::pardisoInit;\n    using Base::m_matrix;\n    friend class PardisoImpl< PardisoLDLT<MatrixType,Options> >;\n\n  public:\n\n    typedef typename Base::StorageIndex StorageIndex;\n    using Base::compute;\n    enum { UpLo = Options&(Upper|Lower) };\n\n    PardisoLDLT()\n      : Base()\n    {\n      pardisoInit(Base::ScalarIsComplex ? ( bool(Options&Symmetric) ? 6 : -4 ) : -2);\n    }\n\n    explicit PardisoLDLT(const MatrixType& matrix)\n      : Base()\n    {\n      pardisoInit(Base::ScalarIsComplex ? ( bool(Options&Symmetric) ? 6 : -4 ) : -2);\n      compute(matrix);\n    }\n    \n    void getMatrix(const MatrixType& matrix)\n    {\n      // PARDISO supports only upper, row-major matrices\n      PermutationMatrix<Dynamic,Dynamic,StorageIndex> p_null;\n      m_matrix.resize(matrix.rows(), matrix.cols());\n      m_matrix.template selfadjointView<Upper>() = matrix.template selfadjointView<UpLo>().twistedBy(p_null);\n      m_matrix.makeCompressed();\n    }\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_PARDISOSUPPORT_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/QR/ColPivHouseholderQR.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_COLPIVOTINGHOUSEHOLDERQR_H\n#define EIGEN_COLPIVOTINGHOUSEHOLDERQR_H\n\nnamespace Eigen {\n\nnamespace internal {\ntemplate<typename _MatrixType> struct traits<ColPivHouseholderQR<_MatrixType> >\n : traits<_MatrixType>\n{\n  enum { Flags = 0 };\n};\n\n} // end namespace internal\n\n/** \\ingroup QR_Module\n  *\n  * \\class ColPivHouseholderQR\n  *\n  * \\brief Householder rank-revealing QR decomposition of a matrix with column-pivoting\n  *\n  * \\tparam _MatrixType the type of the matrix of which we are computing the QR decomposition\n  *\n  * This class performs a rank-revealing QR decomposition of a matrix \\b A into matrices \\b P, \\b Q and \\b R\n  * such that\n  * \\f[\n  *  \\mathbf{A} \\, \\mathbf{P} = \\mathbf{Q} \\, \\mathbf{R}\n  * \\f]\n  * by using Householder transformations. Here, \\b P is a permutation matrix, \\b Q a unitary matrix and \\b R an\n  * upper triangular matrix.\n  *\n  * This decomposition performs column pivoting in order to be rank-revealing and improve\n  * numerical stability. It is slower than HouseholderQR, and faster than FullPivHouseholderQR.\n  *\n  * This class supports the \\link InplaceDecomposition inplace decomposition \\endlink mechanism.\n  * \n  * \\sa MatrixBase::colPivHouseholderQr()\n  */\ntemplate<typename _MatrixType> class ColPivHouseholderQR\n{\n  public:\n\n    typedef _MatrixType MatrixType;\n    enum {\n      RowsAtCompileTime = MatrixType::RowsAtCompileTime,\n      ColsAtCompileTime = MatrixType::ColsAtCompileTime,\n      MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,\n      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime\n    };\n    typedef typename MatrixType::Scalar Scalar;\n    typedef typename MatrixType::RealScalar RealScalar;\n    // FIXME should be int\n    typedef typename MatrixType::StorageIndex StorageIndex;\n    typedef typename internal::plain_diag_type<MatrixType>::type HCoeffsType;\n    typedef PermutationMatrix<ColsAtCompileTime, MaxColsAtCompileTime> PermutationType;\n    typedef typename internal::plain_row_type<MatrixType, Index>::type IntRowVectorType;\n    typedef typename internal::plain_row_type<MatrixType>::type RowVectorType;\n    typedef typename internal::plain_row_type<MatrixType, RealScalar>::type RealRowVectorType;\n    typedef HouseholderSequence<MatrixType,typename internal::remove_all<typename HCoeffsType::ConjugateReturnType>::type> HouseholderSequenceType;\n    typedef typename MatrixType::PlainObject PlainObject;\n\n  private:\n\n    typedef typename PermutationType::StorageIndex PermIndexType;\n\n  public:\n\n    /**\n    * \\brief Default Constructor.\n    *\n    * The default constructor is useful in cases in which the user intends to\n    * perform decompositions via ColPivHouseholderQR::compute(const MatrixType&).\n    */\n    ColPivHouseholderQR()\n      : m_qr(),\n        m_hCoeffs(),\n        m_colsPermutation(),\n        m_colsTranspositions(),\n        m_temp(),\n        m_colNormsUpdated(),\n        m_colNormsDirect(),\n        m_isInitialized(false),\n        m_usePrescribedThreshold(false) {}\n\n    /** \\brief Default Constructor with memory preallocation\n      *\n      * Like the default constructor but with preallocation of the internal data\n      * according to the specified problem \\a size.\n      * \\sa ColPivHouseholderQR()\n      */\n    ColPivHouseholderQR(Index rows, Index cols)\n      : m_qr(rows, cols),\n        m_hCoeffs((std::min)(rows,cols)),\n        m_colsPermutation(PermIndexType(cols)),\n        m_colsTranspositions(cols),\n        m_temp(cols),\n        m_colNormsUpdated(cols),\n        m_colNormsDirect(cols),\n        m_isInitialized(false),\n        m_usePrescribedThreshold(false) {}\n\n    /** \\brief Constructs a QR factorization from a given matrix\n      *\n      * This constructor computes the QR factorization of the matrix \\a matrix by calling\n      * the method compute(). It is a short cut for:\n      *\n      * \\code\n      * ColPivHouseholderQR<MatrixType> qr(matrix.rows(), matrix.cols());\n      * qr.compute(matrix);\n      * \\endcode\n      *\n      * \\sa compute()\n      */\n    template<typename InputType>\n    explicit ColPivHouseholderQR(const EigenBase<InputType>& matrix)\n      : m_qr(matrix.rows(), matrix.cols()),\n        m_hCoeffs((std::min)(matrix.rows(),matrix.cols())),\n        m_colsPermutation(PermIndexType(matrix.cols())),\n        m_colsTranspositions(matrix.cols()),\n        m_temp(matrix.cols()),\n        m_colNormsUpdated(matrix.cols()),\n        m_colNormsDirect(matrix.cols()),\n        m_isInitialized(false),\n        m_usePrescribedThreshold(false)\n    {\n      compute(matrix.derived());\n    }\n\n    /** \\brief Constructs a QR factorization from a given matrix\n      *\n      * This overloaded constructor is provided for \\link InplaceDecomposition inplace decomposition \\endlink when \\c MatrixType is a Eigen::Ref.\n      *\n      * \\sa ColPivHouseholderQR(const EigenBase&)\n      */\n    template<typename InputType>\n    explicit ColPivHouseholderQR(EigenBase<InputType>& matrix)\n      : m_qr(matrix.derived()),\n        m_hCoeffs((std::min)(matrix.rows(),matrix.cols())),\n        m_colsPermutation(PermIndexType(matrix.cols())),\n        m_colsTranspositions(matrix.cols()),\n        m_temp(matrix.cols()),\n        m_colNormsUpdated(matrix.cols()),\n        m_colNormsDirect(matrix.cols()),\n        m_isInitialized(false),\n        m_usePrescribedThreshold(false)\n    {\n      computeInPlace();\n    }\n\n    /** This method finds a solution x to the equation Ax=b, where A is the matrix of which\n      * *this is the QR decomposition, if any exists.\n      *\n      * \\param b the right-hand-side of the equation to solve.\n      *\n      * \\returns a solution.\n      *\n      * \\note_about_checking_solutions\n      *\n      * \\note_about_arbitrary_choice_of_solution\n      *\n      * Example: \\include ColPivHouseholderQR_solve.cpp\n      * Output: \\verbinclude ColPivHouseholderQR_solve.out\n      */\n    template<typename Rhs>\n    inline const Solve<ColPivHouseholderQR, Rhs>\n    solve(const MatrixBase<Rhs>& b) const\n    {\n      eigen_assert(m_isInitialized && \"ColPivHouseholderQR is not initialized.\");\n      return Solve<ColPivHouseholderQR, Rhs>(*this, b.derived());\n    }\n\n    HouseholderSequenceType householderQ() const;\n    HouseholderSequenceType matrixQ() const\n    {\n      return householderQ();\n    }\n\n    /** \\returns a reference to the matrix where the Householder QR decomposition is stored\n      */\n    const MatrixType& matrixQR() const\n    {\n      eigen_assert(m_isInitialized && \"ColPivHouseholderQR is not initialized.\");\n      return m_qr;\n    }\n\n    /** \\returns a reference to the matrix where the result Householder QR is stored\n     * \\warning The strict lower part of this matrix contains internal values.\n     * Only the upper triangular part should be referenced. To get it, use\n     * \\code matrixR().template triangularView<Upper>() \\endcode\n     * For rank-deficient matrices, use\n     * \\code\n     * matrixR().topLeftCorner(rank(), rank()).template triangularView<Upper>()\n     * \\endcode\n     */\n    const MatrixType& matrixR() const\n    {\n      eigen_assert(m_isInitialized && \"ColPivHouseholderQR is not initialized.\");\n      return m_qr;\n    }\n\n    template<typename InputType>\n    ColPivHouseholderQR& compute(const EigenBase<InputType>& matrix);\n\n    /** \\returns a const reference to the column permutation matrix */\n    const PermutationType& colsPermutation() const\n    {\n      eigen_assert(m_isInitialized && \"ColPivHouseholderQR is not initialized.\");\n      return m_colsPermutation;\n    }\n\n    /** \\returns the absolute value of the determinant of the matrix of which\n      * *this is the QR decomposition. It has only linear complexity\n      * (that is, O(n) where n is the dimension of the square matrix)\n      * as the QR decomposition has already been computed.\n      *\n      * \\note This is only for square matrices.\n      *\n      * \\warning a determinant can be very big or small, so for matrices\n      * of large enough dimension, there is a risk of overflow/underflow.\n      * One way to work around that is to use logAbsDeterminant() instead.\n      *\n      * \\sa logAbsDeterminant(), MatrixBase::determinant()\n      */\n    typename MatrixType::RealScalar absDeterminant() const;\n\n    /** \\returns the natural log of the absolute value of the determinant of the matrix of which\n      * *this is the QR decomposition. It has only linear complexity\n      * (that is, O(n) where n is the dimension of the square matrix)\n      * as the QR decomposition has already been computed.\n      *\n      * \\note This is only for square matrices.\n      *\n      * \\note This method is useful to work around the risk of overflow/underflow that's inherent\n      * to determinant computation.\n      *\n      * \\sa absDeterminant(), MatrixBase::determinant()\n      */\n    typename MatrixType::RealScalar logAbsDeterminant() const;\n\n    /** \\returns the rank of the matrix of which *this is the QR decomposition.\n      *\n      * \\note This method has to determine which pivots should be considered nonzero.\n      *       For that, it uses the threshold value that you can control by calling\n      *       setThreshold(const RealScalar&).\n      */\n    inline Index rank() const\n    {\n      using std::abs;\n      eigen_assert(m_isInitialized && \"ColPivHouseholderQR is not initialized.\");\n      RealScalar premultiplied_threshold = abs(m_maxpivot) * threshold();\n      Index result = 0;\n      for(Index i = 0; i < m_nonzero_pivots; ++i)\n        result += (abs(m_qr.coeff(i,i)) > premultiplied_threshold);\n      return result;\n    }\n\n    /** \\returns the dimension of the kernel of the matrix of which *this is the QR decomposition.\n      *\n      * \\note This method has to determine which pivots should be considered nonzero.\n      *       For that, it uses the threshold value that you can control by calling\n      *       setThreshold(const RealScalar&).\n      */\n    inline Index dimensionOfKernel() const\n    {\n      eigen_assert(m_isInitialized && \"ColPivHouseholderQR is not initialized.\");\n      return cols() - rank();\n    }\n\n    /** \\returns true if the matrix of which *this is the QR decomposition represents an injective\n      *          linear map, i.e. has trivial kernel; false otherwise.\n      *\n      * \\note This method has to determine which pivots should be considered nonzero.\n      *       For that, it uses the threshold value that you can control by calling\n      *       setThreshold(const RealScalar&).\n      */\n    inline bool isInjective() const\n    {\n      eigen_assert(m_isInitialized && \"ColPivHouseholderQR is not initialized.\");\n      return rank() == cols();\n    }\n\n    /** \\returns true if the matrix of which *this is the QR decomposition represents a surjective\n      *          linear map; false otherwise.\n      *\n      * \\note This method has to determine which pivots should be considered nonzero.\n      *       For that, it uses the threshold value that you can control by calling\n      *       setThreshold(const RealScalar&).\n      */\n    inline bool isSurjective() const\n    {\n      eigen_assert(m_isInitialized && \"ColPivHouseholderQR is not initialized.\");\n      return rank() == rows();\n    }\n\n    /** \\returns true if the matrix of which *this is the QR decomposition is invertible.\n      *\n      * \\note This method has to determine which pivots should be considered nonzero.\n      *       For that, it uses the threshold value that you can control by calling\n      *       setThreshold(const RealScalar&).\n      */\n    inline bool isInvertible() const\n    {\n      eigen_assert(m_isInitialized && \"ColPivHouseholderQR is not initialized.\");\n      return isInjective() && isSurjective();\n    }\n\n    /** \\returns the inverse of the matrix of which *this is the QR decomposition.\n      *\n      * \\note If this matrix is not invertible, the returned matrix has undefined coefficients.\n      *       Use isInvertible() to first determine whether this matrix is invertible.\n      */\n    inline const Inverse<ColPivHouseholderQR> inverse() const\n    {\n      eigen_assert(m_isInitialized && \"ColPivHouseholderQR is not initialized.\");\n      return Inverse<ColPivHouseholderQR>(*this);\n    }\n\n    inline Index rows() const { return m_qr.rows(); }\n    inline Index cols() const { return m_qr.cols(); }\n\n    /** \\returns a const reference to the vector of Householder coefficients used to represent the factor \\c Q.\n      *\n      * For advanced uses only.\n      */\n    const HCoeffsType& hCoeffs() const { return m_hCoeffs; }\n\n    /** Allows to prescribe a threshold to be used by certain methods, such as rank(),\n      * who need to determine when pivots are to be considered nonzero. This is not used for the\n      * QR decomposition itself.\n      *\n      * When it needs to get the threshold value, Eigen calls threshold(). By default, this\n      * uses a formula to automatically determine a reasonable threshold.\n      * Once you have called the present method setThreshold(const RealScalar&),\n      * your value is used instead.\n      *\n      * \\param threshold The new value to use as the threshold.\n      *\n      * A pivot will be considered nonzero if its absolute value is strictly greater than\n      *  \\f$ \\vert pivot \\vert \\leqslant threshold \\times \\vert maxpivot \\vert \\f$\n      * where maxpivot is the biggest pivot.\n      *\n      * If you want to come back to the default behavior, call setThreshold(Default_t)\n      */\n    ColPivHouseholderQR& setThreshold(const RealScalar& threshold)\n    {\n      m_usePrescribedThreshold = true;\n      m_prescribedThreshold = threshold;\n      return *this;\n    }\n\n    /** Allows to come back to the default behavior, letting Eigen use its default formula for\n      * determining the threshold.\n      *\n      * You should pass the special object Eigen::Default as parameter here.\n      * \\code qr.setThreshold(Eigen::Default); \\endcode\n      *\n      * See the documentation of setThreshold(const RealScalar&).\n      */\n    ColPivHouseholderQR& setThreshold(Default_t)\n    {\n      m_usePrescribedThreshold = false;\n      return *this;\n    }\n\n    /** Returns the threshold that will be used by certain methods such as rank().\n      *\n      * See the documentation of setThreshold(const RealScalar&).\n      */\n    RealScalar threshold() const\n    {\n      eigen_assert(m_isInitialized || m_usePrescribedThreshold);\n      return m_usePrescribedThreshold ? m_prescribedThreshold\n      // this formula comes from experimenting (see \"LU precision tuning\" thread on the list)\n      // and turns out to be identical to Higham's formula used already in LDLt.\n                                      : NumTraits<Scalar>::epsilon() * RealScalar(m_qr.diagonalSize());\n    }\n\n    /** \\returns the number of nonzero pivots in the QR decomposition.\n      * Here nonzero is meant in the exact sense, not in a fuzzy sense.\n      * So that notion isn't really intrinsically interesting, but it is\n      * still useful when implementing algorithms.\n      *\n      * \\sa rank()\n      */\n    inline Index nonzeroPivots() const\n    {\n      eigen_assert(m_isInitialized && \"ColPivHouseholderQR is not initialized.\");\n      return m_nonzero_pivots;\n    }\n\n    /** \\returns the absolute value of the biggest pivot, i.e. the biggest\n      *          diagonal coefficient of R.\n      */\n    RealScalar maxPivot() const { return m_maxpivot; }\n\n    /** \\brief Reports whether the QR factorization was succesful.\n      *\n      * \\note This function always returns \\c Success. It is provided for compatibility\n      * with other factorization routines.\n      * \\returns \\c Success\n      */\n    ComputationInfo info() const\n    {\n      eigen_assert(m_isInitialized && \"Decomposition is not initialized.\");\n      return Success;\n    }\n\n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    template<typename RhsType, typename DstType>\n    EIGEN_DEVICE_FUNC\n    void _solve_impl(const RhsType &rhs, DstType &dst) const;\n    #endif\n\n  protected:\n\n    friend class CompleteOrthogonalDecomposition<MatrixType>;\n\n    static void check_template_parameters()\n    {\n      EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);\n    }\n\n    void computeInPlace();\n\n    MatrixType m_qr;\n    HCoeffsType m_hCoeffs;\n    PermutationType m_colsPermutation;\n    IntRowVectorType m_colsTranspositions;\n    RowVectorType m_temp;\n    RealRowVectorType m_colNormsUpdated;\n    RealRowVectorType m_colNormsDirect;\n    bool m_isInitialized, m_usePrescribedThreshold;\n    RealScalar m_prescribedThreshold, m_maxpivot;\n    Index m_nonzero_pivots;\n    Index m_det_pq;\n};\n\ntemplate<typename MatrixType>\ntypename MatrixType::RealScalar ColPivHouseholderQR<MatrixType>::absDeterminant() const\n{\n  using std::abs;\n  eigen_assert(m_isInitialized && \"ColPivHouseholderQR is not initialized.\");\n  eigen_assert(m_qr.rows() == m_qr.cols() && \"You can't take the determinant of a non-square matrix!\");\n  return abs(m_qr.diagonal().prod());\n}\n\ntemplate<typename MatrixType>\ntypename MatrixType::RealScalar ColPivHouseholderQR<MatrixType>::logAbsDeterminant() const\n{\n  eigen_assert(m_isInitialized && \"ColPivHouseholderQR is not initialized.\");\n  eigen_assert(m_qr.rows() == m_qr.cols() && \"You can't take the determinant of a non-square matrix!\");\n  return m_qr.diagonal().cwiseAbs().array().log().sum();\n}\n\n/** Performs the QR factorization of the given matrix \\a matrix. The result of\n  * the factorization is stored into \\c *this, and a reference to \\c *this\n  * is returned.\n  *\n  * \\sa class ColPivHouseholderQR, ColPivHouseholderQR(const MatrixType&)\n  */\ntemplate<typename MatrixType>\ntemplate<typename InputType>\nColPivHouseholderQR<MatrixType>& ColPivHouseholderQR<MatrixType>::compute(const EigenBase<InputType>& matrix)\n{\n  m_qr = matrix.derived();\n  computeInPlace();\n  return *this;\n}\n\ntemplate<typename MatrixType>\nvoid ColPivHouseholderQR<MatrixType>::computeInPlace()\n{\n  check_template_parameters();\n\n  // the column permutation is stored as int indices, so just to be sure:\n  eigen_assert(m_qr.cols()<=NumTraits<int>::highest());\n\n  using std::abs;\n\n  Index rows = m_qr.rows();\n  Index cols = m_qr.cols();\n  Index size = m_qr.diagonalSize();\n\n  m_hCoeffs.resize(size);\n\n  m_temp.resize(cols);\n\n  m_colsTranspositions.resize(m_qr.cols());\n  Index number_of_transpositions = 0;\n\n  m_colNormsUpdated.resize(cols);\n  m_colNormsDirect.resize(cols);\n  for (Index k = 0; k < cols; ++k) {\n    // colNormsDirect(k) caches the most recent directly computed norm of\n    // column k.\n    m_colNormsDirect.coeffRef(k) = m_qr.col(k).norm();\n    m_colNormsUpdated.coeffRef(k) = m_colNormsDirect.coeffRef(k);\n  }\n\n  RealScalar threshold_helper =  numext::abs2<RealScalar>(m_colNormsUpdated.maxCoeff() * NumTraits<RealScalar>::epsilon()) / RealScalar(rows);\n  RealScalar norm_downdate_threshold = numext::sqrt(NumTraits<RealScalar>::epsilon());\n\n  m_nonzero_pivots = size; // the generic case is that in which all pivots are nonzero (invertible case)\n  m_maxpivot = RealScalar(0);\n\n  for(Index k = 0; k < size; ++k)\n  {\n    // first, we look up in our table m_colNormsUpdated which column has the biggest norm\n    Index biggest_col_index;\n    RealScalar biggest_col_sq_norm = numext::abs2(m_colNormsUpdated.tail(cols-k).maxCoeff(&biggest_col_index));\n    biggest_col_index += k;\n\n    // Track the number of meaningful pivots but do not stop the decomposition to make\n    // sure that the initial matrix is properly reproduced. See bug 941.\n    if(m_nonzero_pivots==size && biggest_col_sq_norm < threshold_helper * RealScalar(rows-k))\n      m_nonzero_pivots = k;\n\n    // apply the transposition to the columns\n    m_colsTranspositions.coeffRef(k) = biggest_col_index;\n    if(k != biggest_col_index) {\n      m_qr.col(k).swap(m_qr.col(biggest_col_index));\n      std::swap(m_colNormsUpdated.coeffRef(k), m_colNormsUpdated.coeffRef(biggest_col_index));\n      std::swap(m_colNormsDirect.coeffRef(k), m_colNormsDirect.coeffRef(biggest_col_index));\n      ++number_of_transpositions;\n    }\n\n    // generate the householder vector, store it below the diagonal\n    RealScalar beta;\n    m_qr.col(k).tail(rows-k).makeHouseholderInPlace(m_hCoeffs.coeffRef(k), beta);\n\n    // apply the householder transformation to the diagonal coefficient\n    m_qr.coeffRef(k,k) = beta;\n\n    // remember the maximum absolute value of diagonal coefficients\n    if(abs(beta) > m_maxpivot) m_maxpivot = abs(beta);\n\n    // apply the householder transformation\n    m_qr.bottomRightCorner(rows-k, cols-k-1)\n        .applyHouseholderOnTheLeft(m_qr.col(k).tail(rows-k-1), m_hCoeffs.coeffRef(k), &m_temp.coeffRef(k+1));\n\n    // update our table of norms of the columns\n    for (Index j = k + 1; j < cols; ++j) {\n      // The following implements the stable norm downgrade step discussed in\n      // http://www.netlib.org/lapack/lawnspdf/lawn176.pdf\n      // and used in LAPACK routines xGEQPF and xGEQP3.\n      // See lines 278-297 in http://www.netlib.org/lapack/explore-html/dc/df4/sgeqpf_8f_source.html\n      if (m_colNormsUpdated.coeffRef(j) != RealScalar(0)) {\n        RealScalar temp = abs(m_qr.coeffRef(k, j)) / m_colNormsUpdated.coeffRef(j);\n        temp = (RealScalar(1) + temp) * (RealScalar(1) - temp);\n        temp = temp <  RealScalar(0) ? RealScalar(0) : temp;\n        RealScalar temp2 = temp * numext::abs2<RealScalar>(m_colNormsUpdated.coeffRef(j) /\n                                                           m_colNormsDirect.coeffRef(j));\n        if (temp2 <= norm_downdate_threshold) {\n          // The updated norm has become too inaccurate so re-compute the column\n          // norm directly.\n          m_colNormsDirect.coeffRef(j) = m_qr.col(j).tail(rows - k - 1).norm();\n          m_colNormsUpdated.coeffRef(j) = m_colNormsDirect.coeffRef(j);\n        } else {\n          m_colNormsUpdated.coeffRef(j) *= numext::sqrt(temp);\n        }\n      }\n    }\n  }\n\n  m_colsPermutation.setIdentity(PermIndexType(cols));\n  for(PermIndexType k = 0; k < size/*m_nonzero_pivots*/; ++k)\n    m_colsPermutation.applyTranspositionOnTheRight(k, PermIndexType(m_colsTranspositions.coeff(k)));\n\n  m_det_pq = (number_of_transpositions%2) ? -1 : 1;\n  m_isInitialized = true;\n}\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\ntemplate<typename _MatrixType>\ntemplate<typename RhsType, typename DstType>\nvoid ColPivHouseholderQR<_MatrixType>::_solve_impl(const RhsType &rhs, DstType &dst) const\n{\n  eigen_assert(rhs.rows() == rows());\n\n  const Index nonzero_pivots = nonzeroPivots();\n\n  if(nonzero_pivots == 0)\n  {\n    dst.setZero();\n    return;\n  }\n\n  typename RhsType::PlainObject c(rhs);\n\n  // Note that the matrix Q = H_0^* H_1^*... so its inverse is Q^* = (H_0 H_1 ...)^T\n  c.applyOnTheLeft(householderSequence(m_qr, m_hCoeffs)\n                    .setLength(nonzero_pivots)\n                    .transpose()\n    );\n\n  m_qr.topLeftCorner(nonzero_pivots, nonzero_pivots)\n      .template triangularView<Upper>()\n      .solveInPlace(c.topRows(nonzero_pivots));\n\n  for(Index i = 0; i < nonzero_pivots; ++i) dst.row(m_colsPermutation.indices().coeff(i)) = c.row(i);\n  for(Index i = nonzero_pivots; i < cols(); ++i) dst.row(m_colsPermutation.indices().coeff(i)).setZero();\n}\n#endif\n\nnamespace internal {\n\ntemplate<typename DstXprType, typename MatrixType>\nstruct Assignment<DstXprType, Inverse<ColPivHouseholderQR<MatrixType> >, internal::assign_op<typename DstXprType::Scalar,typename ColPivHouseholderQR<MatrixType>::Scalar>, Dense2Dense>\n{\n  typedef ColPivHouseholderQR<MatrixType> QrType;\n  typedef Inverse<QrType> SrcXprType;\n  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename QrType::Scalar> &)\n  {\n    dst = src.nestedExpression().solve(MatrixType::Identity(src.rows(), src.cols()));\n  }\n};\n\n} // end namespace internal\n\n/** \\returns the matrix Q as a sequence of householder transformations.\n  * You can extract the meaningful part only by using:\n  * \\code qr.householderQ().setLength(qr.nonzeroPivots()) \\endcode*/\ntemplate<typename MatrixType>\ntypename ColPivHouseholderQR<MatrixType>::HouseholderSequenceType ColPivHouseholderQR<MatrixType>\n  ::householderQ() const\n{\n  eigen_assert(m_isInitialized && \"ColPivHouseholderQR is not initialized.\");\n  return HouseholderSequenceType(m_qr, m_hCoeffs.conjugate());\n}\n\n/** \\return the column-pivoting Householder QR decomposition of \\c *this.\n  *\n  * \\sa class ColPivHouseholderQR\n  */\ntemplate<typename Derived>\nconst ColPivHouseholderQR<typename MatrixBase<Derived>::PlainObject>\nMatrixBase<Derived>::colPivHouseholderQr() const\n{\n  return ColPivHouseholderQR<PlainObject>(eval());\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_COLPIVOTINGHOUSEHOLDERQR_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/QR/ColPivHouseholderQR_LAPACKE.h",
    "content": "/*\n Copyright (c) 2011, Intel Corporation. All rights reserved.\n\n Redistribution and use in source and binary forms, with or without modification,\n are permitted provided that the following conditions are met:\n\n * Redistributions of source code must retain the above copyright notice, this\n   list of conditions and the following disclaimer.\n * Redistributions in binary form must reproduce the above copyright notice,\n   this list of conditions and the following disclaimer in the documentation\n   and/or other materials provided with the distribution.\n * Neither the name of Intel Corporation nor the names of its contributors may\n   be used to endorse or promote products derived from this software without\n   specific prior written permission.\n\n THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\" AND\n ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED\n WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\n DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR\n ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES\n (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;\n LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON\n ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT\n (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS\n SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n\n ********************************************************************************\n *   Content : Eigen bindings to LAPACKe\n *    Householder QR decomposition of a matrix with column pivoting based on\n *    LAPACKE_?geqp3 function.\n ********************************************************************************\n*/\n\n#ifndef EIGEN_COLPIVOTINGHOUSEHOLDERQR_LAPACKE_H\n#define EIGEN_COLPIVOTINGHOUSEHOLDERQR_LAPACKE_H\n\nnamespace Eigen { \n\n/** \\internal Specialization for the data types supported by LAPACKe */\n\n#define EIGEN_LAPACKE_QR_COLPIV(EIGTYPE, LAPACKE_TYPE, LAPACKE_PREFIX, EIGCOLROW, LAPACKE_COLROW) \\\ntemplate<> template<typename InputType> inline \\\nColPivHouseholderQR<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic> >& \\\nColPivHouseholderQR<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic> >::compute( \\\n              const EigenBase<InputType>& matrix) \\\n\\\n{ \\\n  using std::abs; \\\n  typedef Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic> MatrixType; \\\n  typedef MatrixType::RealScalar RealScalar; \\\n  Index rows = matrix.rows();\\\n  Index cols = matrix.cols();\\\n\\\n  m_qr = matrix;\\\n  Index size = m_qr.diagonalSize();\\\n  m_hCoeffs.resize(size);\\\n\\\n  m_colsTranspositions.resize(cols);\\\n  /*Index number_of_transpositions = 0;*/ \\\n\\\n  m_nonzero_pivots = 0; \\\n  m_maxpivot = RealScalar(0);\\\n  m_colsPermutation.resize(cols); \\\n  m_colsPermutation.indices().setZero(); \\\n\\\n  lapack_int lda = internal::convert_index<lapack_int,Index>(m_qr.outerStride()); \\\n  lapack_int matrix_order = LAPACKE_COLROW; \\\n  LAPACKE_##LAPACKE_PREFIX##geqp3( matrix_order, internal::convert_index<lapack_int,Index>(rows), internal::convert_index<lapack_int,Index>(cols), \\\n                              (LAPACKE_TYPE*)m_qr.data(), lda, (lapack_int*)m_colsPermutation.indices().data(), (LAPACKE_TYPE*)m_hCoeffs.data()); \\\n  m_isInitialized = true; \\\n  m_maxpivot=m_qr.diagonal().cwiseAbs().maxCoeff(); \\\n  m_hCoeffs.adjointInPlace(); \\\n  RealScalar premultiplied_threshold = abs(m_maxpivot) * threshold(); \\\n  lapack_int *perm = m_colsPermutation.indices().data(); \\\n  for(Index i=0;i<size;i++) { \\\n    m_nonzero_pivots += (abs(m_qr.coeff(i,i)) > premultiplied_threshold);\\\n  } \\\n  for(Index i=0;i<cols;i++) perm[i]--;\\\n\\\n  /*m_det_pq = (number_of_transpositions%2) ? -1 : 1;  // TODO: It's not needed now; fix upon availability in Eigen */ \\\n\\\n  return *this; \\\n}\n\nEIGEN_LAPACKE_QR_COLPIV(double,   double,        d, ColMajor, LAPACK_COL_MAJOR)\nEIGEN_LAPACKE_QR_COLPIV(float,    float,         s, ColMajor, LAPACK_COL_MAJOR)\nEIGEN_LAPACKE_QR_COLPIV(dcomplex, lapack_complex_double, z, ColMajor, LAPACK_COL_MAJOR)\nEIGEN_LAPACKE_QR_COLPIV(scomplex, lapack_complex_float,  c, ColMajor, LAPACK_COL_MAJOR)\n\nEIGEN_LAPACKE_QR_COLPIV(double,   double,        d, RowMajor, LAPACK_ROW_MAJOR)\nEIGEN_LAPACKE_QR_COLPIV(float,    float,         s, RowMajor, LAPACK_ROW_MAJOR)\nEIGEN_LAPACKE_QR_COLPIV(dcomplex, lapack_complex_double, z, RowMajor, LAPACK_ROW_MAJOR)\nEIGEN_LAPACKE_QR_COLPIV(scomplex, lapack_complex_float,  c, RowMajor, LAPACK_ROW_MAJOR)\n\n} // end namespace Eigen\n\n#endif // EIGEN_COLPIVOTINGHOUSEHOLDERQR_LAPACKE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/QR/CompleteOrthogonalDecomposition.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Rasmus Munk Larsen <rmlarsen@google.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_COMPLETEORTHOGONALDECOMPOSITION_H\n#define EIGEN_COMPLETEORTHOGONALDECOMPOSITION_H\n\nnamespace Eigen {\n\nnamespace internal {\ntemplate <typename _MatrixType>\nstruct traits<CompleteOrthogonalDecomposition<_MatrixType> >\n    : traits<_MatrixType> {\n  enum { Flags = 0 };\n};\n\n}  // end namespace internal\n\n/** \\ingroup QR_Module\n  *\n  * \\class CompleteOrthogonalDecomposition\n  *\n  * \\brief Complete orthogonal decomposition (COD) of a matrix.\n  *\n  * \\param MatrixType the type of the matrix of which we are computing the COD.\n  *\n  * This class performs a rank-revealing complete orthogonal decomposition of a\n  * matrix  \\b A into matrices \\b P, \\b Q, \\b T, and \\b Z such that\n  * \\f[\n  *  \\mathbf{A} \\, \\mathbf{P} = \\mathbf{Q} \\,\n  *                     \\begin{bmatrix} \\mathbf{T} &  \\mathbf{0} \\\\\n  *                                     \\mathbf{0} & \\mathbf{0} \\end{bmatrix} \\, \\mathbf{Z}\n  * \\f]\n  * by using Householder transformations. Here, \\b P is a permutation matrix,\n  * \\b Q and \\b Z are unitary matrices and \\b T an upper triangular matrix of\n  * size rank-by-rank. \\b A may be rank deficient.\n  *\n  * This class supports the \\link InplaceDecomposition inplace decomposition \\endlink mechanism.\n  * \n  * \\sa MatrixBase::completeOrthogonalDecomposition()\n  */\ntemplate <typename _MatrixType>\nclass CompleteOrthogonalDecomposition {\n public:\n  typedef _MatrixType MatrixType;\n  enum {\n    RowsAtCompileTime = MatrixType::RowsAtCompileTime,\n    ColsAtCompileTime = MatrixType::ColsAtCompileTime,\n    MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,\n    MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime\n  };\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename MatrixType::RealScalar RealScalar;\n  typedef typename MatrixType::StorageIndex StorageIndex;\n  typedef typename internal::plain_diag_type<MatrixType>::type HCoeffsType;\n  typedef PermutationMatrix<ColsAtCompileTime, MaxColsAtCompileTime>\n      PermutationType;\n  typedef typename internal::plain_row_type<MatrixType, Index>::type\n      IntRowVectorType;\n  typedef typename internal::plain_row_type<MatrixType>::type RowVectorType;\n  typedef typename internal::plain_row_type<MatrixType, RealScalar>::type\n      RealRowVectorType;\n  typedef HouseholderSequence<\n      MatrixType, typename internal::remove_all<\n                      typename HCoeffsType::ConjugateReturnType>::type>\n      HouseholderSequenceType;\n  typedef typename MatrixType::PlainObject PlainObject;\n\n private:\n  typedef typename PermutationType::Index PermIndexType;\n\n public:\n  /**\n   * \\brief Default Constructor.\n   *\n   * The default constructor is useful in cases in which the user intends to\n   * perform decompositions via\n   * \\c CompleteOrthogonalDecomposition::compute(const* MatrixType&).\n   */\n  CompleteOrthogonalDecomposition() : m_cpqr(), m_zCoeffs(), m_temp() {}\n\n  /** \\brief Default Constructor with memory preallocation\n   *\n   * Like the default constructor but with preallocation of the internal data\n   * according to the specified problem \\a size.\n   * \\sa CompleteOrthogonalDecomposition()\n   */\n  CompleteOrthogonalDecomposition(Index rows, Index cols)\n      : m_cpqr(rows, cols), m_zCoeffs((std::min)(rows, cols)), m_temp(cols) {}\n\n  /** \\brief Constructs a complete orthogonal decomposition from a given\n   * matrix.\n   *\n   * This constructor computes the complete orthogonal decomposition of the\n   * matrix \\a matrix by calling the method compute(). The default\n   * threshold for rank determination will be used. It is a short cut for:\n   *\n   * \\code\n   * CompleteOrthogonalDecomposition<MatrixType> cod(matrix.rows(),\n   *                                                 matrix.cols());\n   * cod.setThreshold(Default);\n   * cod.compute(matrix);\n   * \\endcode\n   *\n   * \\sa compute()\n   */\n  template <typename InputType>\n  explicit CompleteOrthogonalDecomposition(const EigenBase<InputType>& matrix)\n      : m_cpqr(matrix.rows(), matrix.cols()),\n        m_zCoeffs((std::min)(matrix.rows(), matrix.cols())),\n        m_temp(matrix.cols())\n  {\n    compute(matrix.derived());\n  }\n\n  /** \\brief Constructs a complete orthogonal decomposition from a given matrix\n    *\n    * This overloaded constructor is provided for \\link InplaceDecomposition inplace decomposition \\endlink when \\c MatrixType is a Eigen::Ref.\n    *\n    * \\sa CompleteOrthogonalDecomposition(const EigenBase&)\n    */\n  template<typename InputType>\n  explicit CompleteOrthogonalDecomposition(EigenBase<InputType>& matrix)\n    : m_cpqr(matrix.derived()),\n      m_zCoeffs((std::min)(matrix.rows(), matrix.cols())),\n      m_temp(matrix.cols())\n  {\n    computeInPlace();\n  }\n\n\n  /** This method computes the minimum-norm solution X to a least squares\n   * problem \\f[\\mathrm{minimize} \\|A X - B\\|, \\f] where \\b A is the matrix of\n   * which \\c *this is the complete orthogonal decomposition.\n   *\n   * \\param b the right-hand sides of the problem to solve.\n   *\n   * \\returns a solution.\n   *\n   */\n  template <typename Rhs>\n  inline const Solve<CompleteOrthogonalDecomposition, Rhs> solve(\n      const MatrixBase<Rhs>& b) const {\n    eigen_assert(m_cpqr.m_isInitialized &&\n                 \"CompleteOrthogonalDecomposition is not initialized.\");\n    return Solve<CompleteOrthogonalDecomposition, Rhs>(*this, b.derived());\n  }\n\n  HouseholderSequenceType householderQ(void) const;\n  HouseholderSequenceType matrixQ(void) const { return m_cpqr.householderQ(); }\n\n  /** \\returns the matrix \\b Z.\n   */\n  MatrixType matrixZ() const {\n    MatrixType Z = MatrixType::Identity(m_cpqr.cols(), m_cpqr.cols());\n    applyZAdjointOnTheLeftInPlace(Z);\n    return Z.adjoint();\n  }\n\n  /** \\returns a reference to the matrix where the complete orthogonal\n   * decomposition is stored\n   */\n  const MatrixType& matrixQTZ() const { return m_cpqr.matrixQR(); }\n\n  /** \\returns a reference to the matrix where the complete orthogonal\n   * decomposition is stored.\n   * \\warning The strict lower part and \\code cols() - rank() \\endcode right\n   * columns of this matrix contains internal values.\n   * Only the upper triangular part should be referenced. To get it, use\n   * \\code matrixT().template triangularView<Upper>() \\endcode\n   * For rank-deficient matrices, use\n   * \\code\n   * matrixR().topLeftCorner(rank(), rank()).template triangularView<Upper>()\n   * \\endcode\n   */\n  const MatrixType& matrixT() const { return m_cpqr.matrixQR(); }\n\n  template <typename InputType>\n  CompleteOrthogonalDecomposition& compute(const EigenBase<InputType>& matrix) {\n    // Compute the column pivoted QR factorization A P = Q R.\n    m_cpqr.compute(matrix);\n    computeInPlace();\n    return *this;\n  }\n\n  /** \\returns a const reference to the column permutation matrix */\n  const PermutationType& colsPermutation() const {\n    return m_cpqr.colsPermutation();\n  }\n\n  /** \\returns the absolute value of the determinant of the matrix of which\n   * *this is the complete orthogonal decomposition. It has only linear\n   * complexity (that is, O(n) where n is the dimension of the square matrix)\n   * as the complete orthogonal decomposition has already been computed.\n   *\n   * \\note This is only for square matrices.\n   *\n   * \\warning a determinant can be very big or small, so for matrices\n   * of large enough dimension, there is a risk of overflow/underflow.\n   * One way to work around that is to use logAbsDeterminant() instead.\n   *\n   * \\sa logAbsDeterminant(), MatrixBase::determinant()\n   */\n  typename MatrixType::RealScalar absDeterminant() const;\n\n  /** \\returns the natural log of the absolute value of the determinant of the\n   * matrix of which *this is the complete orthogonal decomposition. It has\n   * only linear complexity (that is, O(n) where n is the dimension of the\n   * square matrix) as the complete orthogonal decomposition has already been\n   * computed.\n   *\n   * \\note This is only for square matrices.\n   *\n   * \\note This method is useful to work around the risk of overflow/underflow\n   * that's inherent to determinant computation.\n   *\n   * \\sa absDeterminant(), MatrixBase::determinant()\n   */\n  typename MatrixType::RealScalar logAbsDeterminant() const;\n\n  /** \\returns the rank of the matrix of which *this is the complete orthogonal\n   * decomposition.\n   *\n   * \\note This method has to determine which pivots should be considered\n   * nonzero. For that, it uses the threshold value that you can control by\n   * calling setThreshold(const RealScalar&).\n   */\n  inline Index rank() const { return m_cpqr.rank(); }\n\n  /** \\returns the dimension of the kernel of the matrix of which *this is the\n   * complete orthogonal decomposition.\n   *\n   * \\note This method has to determine which pivots should be considered\n   * nonzero. For that, it uses the threshold value that you can control by\n   * calling setThreshold(const RealScalar&).\n   */\n  inline Index dimensionOfKernel() const { return m_cpqr.dimensionOfKernel(); }\n\n  /** \\returns true if the matrix of which *this is the decomposition represents\n   * an injective linear map, i.e. has trivial kernel; false otherwise.\n   *\n   * \\note This method has to determine which pivots should be considered\n   * nonzero. For that, it uses the threshold value that you can control by\n   * calling setThreshold(const RealScalar&).\n   */\n  inline bool isInjective() const { return m_cpqr.isInjective(); }\n\n  /** \\returns true if the matrix of which *this is the decomposition represents\n   * a surjective linear map; false otherwise.\n   *\n   * \\note This method has to determine which pivots should be considered\n   * nonzero. For that, it uses the threshold value that you can control by\n   * calling setThreshold(const RealScalar&).\n   */\n  inline bool isSurjective() const { return m_cpqr.isSurjective(); }\n\n  /** \\returns true if the matrix of which *this is the complete orthogonal\n   * decomposition is invertible.\n   *\n   * \\note This method has to determine which pivots should be considered\n   * nonzero. For that, it uses the threshold value that you can control by\n   * calling setThreshold(const RealScalar&).\n   */\n  inline bool isInvertible() const { return m_cpqr.isInvertible(); }\n\n  /** \\returns the pseudo-inverse of the matrix of which *this is the complete\n   * orthogonal decomposition.\n   * \\warning: Do not compute \\c this->pseudoInverse()*rhs to solve a linear systems.\n   * It is more efficient and numerically stable to call \\c this->solve(rhs).\n   */\n  inline const Inverse<CompleteOrthogonalDecomposition> pseudoInverse() const\n  {\n    return Inverse<CompleteOrthogonalDecomposition>(*this);\n  }\n\n  inline Index rows() const { return m_cpqr.rows(); }\n  inline Index cols() const { return m_cpqr.cols(); }\n\n  /** \\returns a const reference to the vector of Householder coefficients used\n   * to represent the factor \\c Q.\n   *\n   * For advanced uses only.\n   */\n  inline const HCoeffsType& hCoeffs() const { return m_cpqr.hCoeffs(); }\n\n  /** \\returns a const reference to the vector of Householder coefficients\n   * used to represent the factor \\c Z.\n   *\n   * For advanced uses only.\n   */\n  const HCoeffsType& zCoeffs() const { return m_zCoeffs; }\n\n  /** Allows to prescribe a threshold to be used by certain methods, such as\n   * rank(), who need to determine when pivots are to be considered nonzero.\n   * Most be called before calling compute().\n   *\n   * When it needs to get the threshold value, Eigen calls threshold(). By\n   * default, this uses a formula to automatically determine a reasonable\n   * threshold. Once you have called the present method\n   * setThreshold(const RealScalar&), your value is used instead.\n   *\n   * \\param threshold The new value to use as the threshold.\n   *\n   * A pivot will be considered nonzero if its absolute value is strictly\n   * greater than\n   *  \\f$ \\vert pivot \\vert \\leqslant threshold \\times \\vert maxpivot \\vert \\f$\n   * where maxpivot is the biggest pivot.\n   *\n   * If you want to come back to the default behavior, call\n   * setThreshold(Default_t)\n   */\n  CompleteOrthogonalDecomposition& setThreshold(const RealScalar& threshold) {\n    m_cpqr.setThreshold(threshold);\n    return *this;\n  }\n\n  /** Allows to come back to the default behavior, letting Eigen use its default\n   * formula for determining the threshold.\n   *\n   * You should pass the special object Eigen::Default as parameter here.\n   * \\code qr.setThreshold(Eigen::Default); \\endcode\n   *\n   * See the documentation of setThreshold(const RealScalar&).\n   */\n  CompleteOrthogonalDecomposition& setThreshold(Default_t) {\n    m_cpqr.setThreshold(Default);\n    return *this;\n  }\n\n  /** Returns the threshold that will be used by certain methods such as rank().\n   *\n   * See the documentation of setThreshold(const RealScalar&).\n   */\n  RealScalar threshold() const { return m_cpqr.threshold(); }\n\n  /** \\returns the number of nonzero pivots in the complete orthogonal\n   * decomposition. Here nonzero is meant in the exact sense, not in a\n   * fuzzy sense. So that notion isn't really intrinsically interesting,\n   * but it is still useful when implementing algorithms.\n   *\n   * \\sa rank()\n   */\n  inline Index nonzeroPivots() const { return m_cpqr.nonzeroPivots(); }\n\n  /** \\returns the absolute value of the biggest pivot, i.e. the biggest\n   *          diagonal coefficient of R.\n   */\n  inline RealScalar maxPivot() const { return m_cpqr.maxPivot(); }\n\n  /** \\brief Reports whether the complete orthogonal decomposition was\n   * succesful.\n   *\n   * \\note This function always returns \\c Success. It is provided for\n   * compatibility\n   * with other factorization routines.\n   * \\returns \\c Success\n   */\n  ComputationInfo info() const {\n    eigen_assert(m_cpqr.m_isInitialized && \"Decomposition is not initialized.\");\n    return Success;\n  }\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\n  template <typename RhsType, typename DstType>\n  EIGEN_DEVICE_FUNC void _solve_impl(const RhsType& rhs, DstType& dst) const;\n#endif\n\n protected:\n  static void check_template_parameters() {\n    EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);\n  }\n\n  void computeInPlace();\n\n  /** Overwrites \\b rhs with \\f$ \\mathbf{Z}^* * \\mathbf{rhs} \\f$.\n   */\n  template <typename Rhs>\n  void applyZAdjointOnTheLeftInPlace(Rhs& rhs) const;\n\n  ColPivHouseholderQR<MatrixType> m_cpqr;\n  HCoeffsType m_zCoeffs;\n  RowVectorType m_temp;\n};\n\ntemplate <typename MatrixType>\ntypename MatrixType::RealScalar\nCompleteOrthogonalDecomposition<MatrixType>::absDeterminant() const {\n  return m_cpqr.absDeterminant();\n}\n\ntemplate <typename MatrixType>\ntypename MatrixType::RealScalar\nCompleteOrthogonalDecomposition<MatrixType>::logAbsDeterminant() const {\n  return m_cpqr.logAbsDeterminant();\n}\n\n/** Performs the complete orthogonal decomposition of the given matrix \\a\n * matrix. The result of the factorization is stored into \\c *this, and a\n * reference to \\c *this is returned.\n *\n * \\sa class CompleteOrthogonalDecomposition,\n * CompleteOrthogonalDecomposition(const MatrixType&)\n */\ntemplate <typename MatrixType>\nvoid CompleteOrthogonalDecomposition<MatrixType>::computeInPlace()\n{\n  check_template_parameters();\n\n  // the column permutation is stored as int indices, so just to be sure:\n  eigen_assert(m_cpqr.cols() <= NumTraits<int>::highest());\n\n  const Index rank = m_cpqr.rank();\n  const Index cols = m_cpqr.cols();\n  const Index rows = m_cpqr.rows();\n  m_zCoeffs.resize((std::min)(rows, cols));\n  m_temp.resize(cols);\n\n  if (rank < cols) {\n    // We have reduced the (permuted) matrix to the form\n    //   [R11 R12]\n    //   [ 0  R22]\n    // where R11 is r-by-r (r = rank) upper triangular, R12 is\n    // r-by-(n-r), and R22 is empty or the norm of R22 is negligible.\n    // We now compute the complete orthogonal decomposition by applying\n    // Householder transformations from the right to the upper trapezoidal\n    // matrix X = [R11 R12] to zero out R12 and obtain the factorization\n    // [R11 R12] = [T11 0] * Z, where T11 is r-by-r upper triangular and\n    // Z = Z(0) * Z(1) ... Z(r-1) is an n-by-n orthogonal matrix.\n    // We store the data representing Z in R12 and m_zCoeffs.\n    for (Index k = rank - 1; k >= 0; --k) {\n      if (k != rank - 1) {\n        // Given the API for Householder reflectors, it is more convenient if\n        // we swap the leading parts of columns k and r-1 (zero-based) to form\n        // the matrix X_k = [X(0:k, k), X(0:k, r:n)]\n        m_cpqr.m_qr.col(k).head(k + 1).swap(\n            m_cpqr.m_qr.col(rank - 1).head(k + 1));\n      }\n      // Construct Householder reflector Z(k) to zero out the last row of X_k,\n      // i.e. choose Z(k) such that\n      // [X(k, k), X(k, r:n)] * Z(k) = [beta, 0, .., 0].\n      RealScalar beta;\n      m_cpqr.m_qr.row(k)\n          .tail(cols - rank + 1)\n          .makeHouseholderInPlace(m_zCoeffs(k), beta);\n      m_cpqr.m_qr(k, rank - 1) = beta;\n      if (k > 0) {\n        // Apply Z(k) to the first k rows of X_k\n        m_cpqr.m_qr.topRightCorner(k, cols - rank + 1)\n            .applyHouseholderOnTheRight(\n                m_cpqr.m_qr.row(k).tail(cols - rank).transpose(), m_zCoeffs(k),\n                &m_temp(0));\n      }\n      if (k != rank - 1) {\n        // Swap X(0:k,k) back to its proper location.\n        m_cpqr.m_qr.col(k).head(k + 1).swap(\n            m_cpqr.m_qr.col(rank - 1).head(k + 1));\n      }\n    }\n  }\n}\n\ntemplate <typename MatrixType>\ntemplate <typename Rhs>\nvoid CompleteOrthogonalDecomposition<MatrixType>::applyZAdjointOnTheLeftInPlace(\n    Rhs& rhs) const {\n  const Index cols = this->cols();\n  const Index nrhs = rhs.cols();\n  const Index rank = this->rank();\n  Matrix<typename MatrixType::Scalar, Dynamic, 1> temp((std::max)(cols, nrhs));\n  for (Index k = 0; k < rank; ++k) {\n    if (k != rank - 1) {\n      rhs.row(k).swap(rhs.row(rank - 1));\n    }\n    rhs.middleRows(rank - 1, cols - rank + 1)\n        .applyHouseholderOnTheLeft(\n            matrixQTZ().row(k).tail(cols - rank).adjoint(), zCoeffs()(k),\n            &temp(0));\n    if (k != rank - 1) {\n      rhs.row(k).swap(rhs.row(rank - 1));\n    }\n  }\n}\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\ntemplate <typename _MatrixType>\ntemplate <typename RhsType, typename DstType>\nvoid CompleteOrthogonalDecomposition<_MatrixType>::_solve_impl(\n    const RhsType& rhs, DstType& dst) const {\n  eigen_assert(rhs.rows() == this->rows());\n\n  const Index rank = this->rank();\n  if (rank == 0) {\n    dst.setZero();\n    return;\n  }\n\n  // Compute c = Q^* * rhs\n  // Note that the matrix Q = H_0^* H_1^*... so its inverse is\n  // Q^* = (H_0 H_1 ...)^T\n  typename RhsType::PlainObject c(rhs);\n  c.applyOnTheLeft(\n      householderSequence(matrixQTZ(), hCoeffs()).setLength(rank).transpose());\n\n  // Solve T z = c(1:rank, :)\n  dst.topRows(rank) = matrixT()\n                          .topLeftCorner(rank, rank)\n                          .template triangularView<Upper>()\n                          .solve(c.topRows(rank));\n\n  const Index cols = this->cols();\n  if (rank < cols) {\n    // Compute y = Z^* * [ z ]\n    //                   [ 0 ]\n    dst.bottomRows(cols - rank).setZero();\n    applyZAdjointOnTheLeftInPlace(dst);\n  }\n\n  // Undo permutation to get x = P^{-1} * y.\n  dst = colsPermutation() * dst;\n}\n#endif\n\nnamespace internal {\n\ntemplate<typename DstXprType, typename MatrixType>\nstruct Assignment<DstXprType, Inverse<CompleteOrthogonalDecomposition<MatrixType> >, internal::assign_op<typename DstXprType::Scalar,typename CompleteOrthogonalDecomposition<MatrixType>::Scalar>, Dense2Dense>\n{\n  typedef CompleteOrthogonalDecomposition<MatrixType> CodType;\n  typedef Inverse<CodType> SrcXprType;\n  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename CodType::Scalar> &)\n  {\n    dst = src.nestedExpression().solve(MatrixType::Identity(src.rows(), src.rows()));\n  }\n};\n\n} // end namespace internal\n\n/** \\returns the matrix Q as a sequence of householder transformations */\ntemplate <typename MatrixType>\ntypename CompleteOrthogonalDecomposition<MatrixType>::HouseholderSequenceType\nCompleteOrthogonalDecomposition<MatrixType>::householderQ() const {\n  return m_cpqr.householderQ();\n}\n\n/** \\return the complete orthogonal decomposition of \\c *this.\n  *\n  * \\sa class CompleteOrthogonalDecomposition\n  */\ntemplate <typename Derived>\nconst CompleteOrthogonalDecomposition<typename MatrixBase<Derived>::PlainObject>\nMatrixBase<Derived>::completeOrthogonalDecomposition() const {\n  return CompleteOrthogonalDecomposition<PlainObject>(eval());\n}\n\n}  // end namespace Eigen\n\n#endif  // EIGEN_COMPLETEORTHOGONALDECOMPOSITION_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/QR/FullPivHouseholderQR.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_FULLPIVOTINGHOUSEHOLDERQR_H\n#define EIGEN_FULLPIVOTINGHOUSEHOLDERQR_H\n\nnamespace Eigen { \n\nnamespace internal {\n\ntemplate<typename _MatrixType> struct traits<FullPivHouseholderQR<_MatrixType> >\n : traits<_MatrixType>\n{\n  enum { Flags = 0 };\n};\n\ntemplate<typename MatrixType> struct FullPivHouseholderQRMatrixQReturnType;\n\ntemplate<typename MatrixType>\nstruct traits<FullPivHouseholderQRMatrixQReturnType<MatrixType> >\n{\n  typedef typename MatrixType::PlainObject ReturnType;\n};\n\n} // end namespace internal\n\n/** \\ingroup QR_Module\n  *\n  * \\class FullPivHouseholderQR\n  *\n  * \\brief Householder rank-revealing QR decomposition of a matrix with full pivoting\n  *\n  * \\tparam _MatrixType the type of the matrix of which we are computing the QR decomposition\n  *\n  * This class performs a rank-revealing QR decomposition of a matrix \\b A into matrices \\b P, \\b P', \\b Q and \\b R\n  * such that \n  * \\f[\n  *  \\mathbf{P} \\, \\mathbf{A} \\, \\mathbf{P}' = \\mathbf{Q} \\, \\mathbf{R}\n  * \\f]\n  * by using Householder transformations. Here, \\b P and \\b P' are permutation matrices, \\b Q a unitary matrix \n  * and \\b R an upper triangular matrix.\n  *\n  * This decomposition performs a very prudent full pivoting in order to be rank-revealing and achieve optimal\n  * numerical stability. The trade-off is that it is slower than HouseholderQR and ColPivHouseholderQR.\n  *\n  * This class supports the \\link InplaceDecomposition inplace decomposition \\endlink mechanism.\n  * \n  * \\sa MatrixBase::fullPivHouseholderQr()\n  */\ntemplate<typename _MatrixType> class FullPivHouseholderQR\n{\n  public:\n\n    typedef _MatrixType MatrixType;\n    enum {\n      RowsAtCompileTime = MatrixType::RowsAtCompileTime,\n      ColsAtCompileTime = MatrixType::ColsAtCompileTime,\n      MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,\n      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime\n    };\n    typedef typename MatrixType::Scalar Scalar;\n    typedef typename MatrixType::RealScalar RealScalar;\n    // FIXME should be int\n    typedef typename MatrixType::StorageIndex StorageIndex;\n    typedef internal::FullPivHouseholderQRMatrixQReturnType<MatrixType> MatrixQReturnType;\n    typedef typename internal::plain_diag_type<MatrixType>::type HCoeffsType;\n    typedef Matrix<StorageIndex, 1,\n                   EIGEN_SIZE_MIN_PREFER_DYNAMIC(ColsAtCompileTime,RowsAtCompileTime), RowMajor, 1,\n                   EIGEN_SIZE_MIN_PREFER_FIXED(MaxColsAtCompileTime,MaxRowsAtCompileTime)> IntDiagSizeVectorType;\n    typedef PermutationMatrix<ColsAtCompileTime, MaxColsAtCompileTime> PermutationType;\n    typedef typename internal::plain_row_type<MatrixType>::type RowVectorType;\n    typedef typename internal::plain_col_type<MatrixType>::type ColVectorType;\n    typedef typename MatrixType::PlainObject PlainObject;\n\n    /** \\brief Default Constructor.\n      *\n      * The default constructor is useful in cases in which the user intends to\n      * perform decompositions via FullPivHouseholderQR::compute(const MatrixType&).\n      */\n    FullPivHouseholderQR()\n      : m_qr(),\n        m_hCoeffs(),\n        m_rows_transpositions(),\n        m_cols_transpositions(),\n        m_cols_permutation(),\n        m_temp(),\n        m_isInitialized(false),\n        m_usePrescribedThreshold(false) {}\n\n    /** \\brief Default Constructor with memory preallocation\n      *\n      * Like the default constructor but with preallocation of the internal data\n      * according to the specified problem \\a size.\n      * \\sa FullPivHouseholderQR()\n      */\n    FullPivHouseholderQR(Index rows, Index cols)\n      : m_qr(rows, cols),\n        m_hCoeffs((std::min)(rows,cols)),\n        m_rows_transpositions((std::min)(rows,cols)),\n        m_cols_transpositions((std::min)(rows,cols)),\n        m_cols_permutation(cols),\n        m_temp(cols),\n        m_isInitialized(false),\n        m_usePrescribedThreshold(false) {}\n\n    /** \\brief Constructs a QR factorization from a given matrix\n      *\n      * This constructor computes the QR factorization of the matrix \\a matrix by calling\n      * the method compute(). It is a short cut for:\n      * \n      * \\code\n      * FullPivHouseholderQR<MatrixType> qr(matrix.rows(), matrix.cols());\n      * qr.compute(matrix);\n      * \\endcode\n      * \n      * \\sa compute()\n      */\n    template<typename InputType>\n    explicit FullPivHouseholderQR(const EigenBase<InputType>& matrix)\n      : m_qr(matrix.rows(), matrix.cols()),\n        m_hCoeffs((std::min)(matrix.rows(), matrix.cols())),\n        m_rows_transpositions((std::min)(matrix.rows(), matrix.cols())),\n        m_cols_transpositions((std::min)(matrix.rows(), matrix.cols())),\n        m_cols_permutation(matrix.cols()),\n        m_temp(matrix.cols()),\n        m_isInitialized(false),\n        m_usePrescribedThreshold(false)\n    {\n      compute(matrix.derived());\n    }\n\n    /** \\brief Constructs a QR factorization from a given matrix\n      *\n      * This overloaded constructor is provided for \\link InplaceDecomposition inplace decomposition \\endlink when \\c MatrixType is a Eigen::Ref.\n      *\n      * \\sa FullPivHouseholderQR(const EigenBase&)\n      */\n    template<typename InputType>\n    explicit FullPivHouseholderQR(EigenBase<InputType>& matrix)\n      : m_qr(matrix.derived()),\n        m_hCoeffs((std::min)(matrix.rows(), matrix.cols())),\n        m_rows_transpositions((std::min)(matrix.rows(), matrix.cols())),\n        m_cols_transpositions((std::min)(matrix.rows(), matrix.cols())),\n        m_cols_permutation(matrix.cols()),\n        m_temp(matrix.cols()),\n        m_isInitialized(false),\n        m_usePrescribedThreshold(false)\n    {\n      computeInPlace();\n    }\n\n    /** This method finds a solution x to the equation Ax=b, where A is the matrix of which\n      * \\c *this is the QR decomposition.\n      *\n      * \\param b the right-hand-side of the equation to solve.\n      *\n      * \\returns the exact or least-square solution if the rank is greater or equal to the number of columns of A,\n      * and an arbitrary solution otherwise.\n      *\n      * \\note_about_checking_solutions\n      *\n      * \\note_about_arbitrary_choice_of_solution\n      *\n      * Example: \\include FullPivHouseholderQR_solve.cpp\n      * Output: \\verbinclude FullPivHouseholderQR_solve.out\n      */\n    template<typename Rhs>\n    inline const Solve<FullPivHouseholderQR, Rhs>\n    solve(const MatrixBase<Rhs>& b) const\n    {\n      eigen_assert(m_isInitialized && \"FullPivHouseholderQR is not initialized.\");\n      return Solve<FullPivHouseholderQR, Rhs>(*this, b.derived());\n    }\n\n    /** \\returns Expression object representing the matrix Q\n      */\n    MatrixQReturnType matrixQ(void) const;\n\n    /** \\returns a reference to the matrix where the Householder QR decomposition is stored\n      */\n    const MatrixType& matrixQR() const\n    {\n      eigen_assert(m_isInitialized && \"FullPivHouseholderQR is not initialized.\");\n      return m_qr;\n    }\n\n    template<typename InputType>\n    FullPivHouseholderQR& compute(const EigenBase<InputType>& matrix);\n\n    /** \\returns a const reference to the column permutation matrix */\n    const PermutationType& colsPermutation() const\n    {\n      eigen_assert(m_isInitialized && \"FullPivHouseholderQR is not initialized.\");\n      return m_cols_permutation;\n    }\n\n    /** \\returns a const reference to the vector of indices representing the rows transpositions */\n    const IntDiagSizeVectorType& rowsTranspositions() const\n    {\n      eigen_assert(m_isInitialized && \"FullPivHouseholderQR is not initialized.\");\n      return m_rows_transpositions;\n    }\n\n    /** \\returns the absolute value of the determinant of the matrix of which\n      * *this is the QR decomposition. It has only linear complexity\n      * (that is, O(n) where n is the dimension of the square matrix)\n      * as the QR decomposition has already been computed.\n      *\n      * \\note This is only for square matrices.\n      *\n      * \\warning a determinant can be very big or small, so for matrices\n      * of large enough dimension, there is a risk of overflow/underflow.\n      * One way to work around that is to use logAbsDeterminant() instead.\n      *\n      * \\sa logAbsDeterminant(), MatrixBase::determinant()\n      */\n    typename MatrixType::RealScalar absDeterminant() const;\n\n    /** \\returns the natural log of the absolute value of the determinant of the matrix of which\n      * *this is the QR decomposition. It has only linear complexity\n      * (that is, O(n) where n is the dimension of the square matrix)\n      * as the QR decomposition has already been computed.\n      *\n      * \\note This is only for square matrices.\n      *\n      * \\note This method is useful to work around the risk of overflow/underflow that's inherent\n      * to determinant computation.\n      *\n      * \\sa absDeterminant(), MatrixBase::determinant()\n      */\n    typename MatrixType::RealScalar logAbsDeterminant() const;\n\n    /** \\returns the rank of the matrix of which *this is the QR decomposition.\n      *\n      * \\note This method has to determine which pivots should be considered nonzero.\n      *       For that, it uses the threshold value that you can control by calling\n      *       setThreshold(const RealScalar&).\n      */\n    inline Index rank() const\n    {\n      using std::abs;\n      eigen_assert(m_isInitialized && \"FullPivHouseholderQR is not initialized.\");\n      RealScalar premultiplied_threshold = abs(m_maxpivot) * threshold();\n      Index result = 0;\n      for(Index i = 0; i < m_nonzero_pivots; ++i)\n        result += (abs(m_qr.coeff(i,i)) > premultiplied_threshold);\n      return result;\n    }\n\n    /** \\returns the dimension of the kernel of the matrix of which *this is the QR decomposition.\n      *\n      * \\note This method has to determine which pivots should be considered nonzero.\n      *       For that, it uses the threshold value that you can control by calling\n      *       setThreshold(const RealScalar&).\n      */\n    inline Index dimensionOfKernel() const\n    {\n      eigen_assert(m_isInitialized && \"FullPivHouseholderQR is not initialized.\");\n      return cols() - rank();\n    }\n\n    /** \\returns true if the matrix of which *this is the QR decomposition represents an injective\n      *          linear map, i.e. has trivial kernel; false otherwise.\n      *\n      * \\note This method has to determine which pivots should be considered nonzero.\n      *       For that, it uses the threshold value that you can control by calling\n      *       setThreshold(const RealScalar&).\n      */\n    inline bool isInjective() const\n    {\n      eigen_assert(m_isInitialized && \"FullPivHouseholderQR is not initialized.\");\n      return rank() == cols();\n    }\n\n    /** \\returns true if the matrix of which *this is the QR decomposition represents a surjective\n      *          linear map; false otherwise.\n      *\n      * \\note This method has to determine which pivots should be considered nonzero.\n      *       For that, it uses the threshold value that you can control by calling\n      *       setThreshold(const RealScalar&).\n      */\n    inline bool isSurjective() const\n    {\n      eigen_assert(m_isInitialized && \"FullPivHouseholderQR is not initialized.\");\n      return rank() == rows();\n    }\n\n    /** \\returns true if the matrix of which *this is the QR decomposition is invertible.\n      *\n      * \\note This method has to determine which pivots should be considered nonzero.\n      *       For that, it uses the threshold value that you can control by calling\n      *       setThreshold(const RealScalar&).\n      */\n    inline bool isInvertible() const\n    {\n      eigen_assert(m_isInitialized && \"FullPivHouseholderQR is not initialized.\");\n      return isInjective() && isSurjective();\n    }\n\n    /** \\returns the inverse of the matrix of which *this is the QR decomposition.\n      *\n      * \\note If this matrix is not invertible, the returned matrix has undefined coefficients.\n      *       Use isInvertible() to first determine whether this matrix is invertible.\n      */\n    inline const Inverse<FullPivHouseholderQR> inverse() const\n    {\n      eigen_assert(m_isInitialized && \"FullPivHouseholderQR is not initialized.\");\n      return Inverse<FullPivHouseholderQR>(*this);\n    }\n\n    inline Index rows() const { return m_qr.rows(); }\n    inline Index cols() const { return m_qr.cols(); }\n    \n    /** \\returns a const reference to the vector of Householder coefficients used to represent the factor \\c Q.\n      * \n      * For advanced uses only.\n      */\n    const HCoeffsType& hCoeffs() const { return m_hCoeffs; }\n\n    /** Allows to prescribe a threshold to be used by certain methods, such as rank(),\n      * who need to determine when pivots are to be considered nonzero. This is not used for the\n      * QR decomposition itself.\n      *\n      * When it needs to get the threshold value, Eigen calls threshold(). By default, this\n      * uses a formula to automatically determine a reasonable threshold.\n      * Once you have called the present method setThreshold(const RealScalar&),\n      * your value is used instead.\n      *\n      * \\param threshold The new value to use as the threshold.\n      *\n      * A pivot will be considered nonzero if its absolute value is strictly greater than\n      *  \\f$ \\vert pivot \\vert \\leqslant threshold \\times \\vert maxpivot \\vert \\f$\n      * where maxpivot is the biggest pivot.\n      *\n      * If you want to come back to the default behavior, call setThreshold(Default_t)\n      */\n    FullPivHouseholderQR& setThreshold(const RealScalar& threshold)\n    {\n      m_usePrescribedThreshold = true;\n      m_prescribedThreshold = threshold;\n      return *this;\n    }\n\n    /** Allows to come back to the default behavior, letting Eigen use its default formula for\n      * determining the threshold.\n      *\n      * You should pass the special object Eigen::Default as parameter here.\n      * \\code qr.setThreshold(Eigen::Default); \\endcode\n      *\n      * See the documentation of setThreshold(const RealScalar&).\n      */\n    FullPivHouseholderQR& setThreshold(Default_t)\n    {\n      m_usePrescribedThreshold = false;\n      return *this;\n    }\n\n    /** Returns the threshold that will be used by certain methods such as rank().\n      *\n      * See the documentation of setThreshold(const RealScalar&).\n      */\n    RealScalar threshold() const\n    {\n      eigen_assert(m_isInitialized || m_usePrescribedThreshold);\n      return m_usePrescribedThreshold ? m_prescribedThreshold\n      // this formula comes from experimenting (see \"LU precision tuning\" thread on the list)\n      // and turns out to be identical to Higham's formula used already in LDLt.\n                                      : NumTraits<Scalar>::epsilon() * RealScalar(m_qr.diagonalSize());\n    }\n\n    /** \\returns the number of nonzero pivots in the QR decomposition.\n      * Here nonzero is meant in the exact sense, not in a fuzzy sense.\n      * So that notion isn't really intrinsically interesting, but it is\n      * still useful when implementing algorithms.\n      *\n      * \\sa rank()\n      */\n    inline Index nonzeroPivots() const\n    {\n      eigen_assert(m_isInitialized && \"LU is not initialized.\");\n      return m_nonzero_pivots;\n    }\n\n    /** \\returns the absolute value of the biggest pivot, i.e. the biggest\n      *          diagonal coefficient of U.\n      */\n    RealScalar maxPivot() const { return m_maxpivot; }\n    \n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    template<typename RhsType, typename DstType>\n    EIGEN_DEVICE_FUNC\n    void _solve_impl(const RhsType &rhs, DstType &dst) const;\n    #endif\n\n  protected:\n    \n    static void check_template_parameters()\n    {\n      EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);\n    }\n    \n    void computeInPlace();\n    \n    MatrixType m_qr;\n    HCoeffsType m_hCoeffs;\n    IntDiagSizeVectorType m_rows_transpositions;\n    IntDiagSizeVectorType m_cols_transpositions;\n    PermutationType m_cols_permutation;\n    RowVectorType m_temp;\n    bool m_isInitialized, m_usePrescribedThreshold;\n    RealScalar m_prescribedThreshold, m_maxpivot;\n    Index m_nonzero_pivots;\n    RealScalar m_precision;\n    Index m_det_pq;\n};\n\ntemplate<typename MatrixType>\ntypename MatrixType::RealScalar FullPivHouseholderQR<MatrixType>::absDeterminant() const\n{\n  using std::abs;\n  eigen_assert(m_isInitialized && \"FullPivHouseholderQR is not initialized.\");\n  eigen_assert(m_qr.rows() == m_qr.cols() && \"You can't take the determinant of a non-square matrix!\");\n  return abs(m_qr.diagonal().prod());\n}\n\ntemplate<typename MatrixType>\ntypename MatrixType::RealScalar FullPivHouseholderQR<MatrixType>::logAbsDeterminant() const\n{\n  eigen_assert(m_isInitialized && \"FullPivHouseholderQR is not initialized.\");\n  eigen_assert(m_qr.rows() == m_qr.cols() && \"You can't take the determinant of a non-square matrix!\");\n  return m_qr.diagonal().cwiseAbs().array().log().sum();\n}\n\n/** Performs the QR factorization of the given matrix \\a matrix. The result of\n  * the factorization is stored into \\c *this, and a reference to \\c *this\n  * is returned.\n  *\n  * \\sa class FullPivHouseholderQR, FullPivHouseholderQR(const MatrixType&)\n  */\ntemplate<typename MatrixType>\ntemplate<typename InputType>\nFullPivHouseholderQR<MatrixType>& FullPivHouseholderQR<MatrixType>::compute(const EigenBase<InputType>& matrix)\n{\n  m_qr = matrix.derived();\n  computeInPlace();\n  return *this;\n}\n\ntemplate<typename MatrixType>\nvoid FullPivHouseholderQR<MatrixType>::computeInPlace()\n{\n  check_template_parameters();\n\n  using std::abs;\n  Index rows = m_qr.rows();\n  Index cols = m_qr.cols();\n  Index size = (std::min)(rows,cols);\n\n  \n  m_hCoeffs.resize(size);\n\n  m_temp.resize(cols);\n\n  m_precision = NumTraits<Scalar>::epsilon() * RealScalar(size);\n\n  m_rows_transpositions.resize(size);\n  m_cols_transpositions.resize(size);\n  Index number_of_transpositions = 0;\n\n  RealScalar biggest(0);\n\n  m_nonzero_pivots = size; // the generic case is that in which all pivots are nonzero (invertible case)\n  m_maxpivot = RealScalar(0);\n\n  for (Index k = 0; k < size; ++k)\n  {\n    Index row_of_biggest_in_corner, col_of_biggest_in_corner;\n    typedef internal::scalar_score_coeff_op<Scalar> Scoring;\n    typedef typename Scoring::result_type Score;\n\n    Score score = m_qr.bottomRightCorner(rows-k, cols-k)\n                      .unaryExpr(Scoring())\n                      .maxCoeff(&row_of_biggest_in_corner, &col_of_biggest_in_corner);\n    row_of_biggest_in_corner += k;\n    col_of_biggest_in_corner += k;\n    RealScalar biggest_in_corner = internal::abs_knowing_score<Scalar>()(m_qr(row_of_biggest_in_corner, col_of_biggest_in_corner), score);\n    if(k==0) biggest = biggest_in_corner;\n\n    // if the corner is negligible, then we have less than full rank, and we can finish early\n    if(internal::isMuchSmallerThan(biggest_in_corner, biggest, m_precision))\n    {\n      m_nonzero_pivots = k;\n      for(Index i = k; i < size; i++)\n      {\n        m_rows_transpositions.coeffRef(i) = i;\n        m_cols_transpositions.coeffRef(i) = i;\n        m_hCoeffs.coeffRef(i) = Scalar(0);\n      }\n      break;\n    }\n\n    m_rows_transpositions.coeffRef(k) = row_of_biggest_in_corner;\n    m_cols_transpositions.coeffRef(k) = col_of_biggest_in_corner;\n    if(k != row_of_biggest_in_corner) {\n      m_qr.row(k).tail(cols-k).swap(m_qr.row(row_of_biggest_in_corner).tail(cols-k));\n      ++number_of_transpositions;\n    }\n    if(k != col_of_biggest_in_corner) {\n      m_qr.col(k).swap(m_qr.col(col_of_biggest_in_corner));\n      ++number_of_transpositions;\n    }\n\n    RealScalar beta;\n    m_qr.col(k).tail(rows-k).makeHouseholderInPlace(m_hCoeffs.coeffRef(k), beta);\n    m_qr.coeffRef(k,k) = beta;\n\n    // remember the maximum absolute value of diagonal coefficients\n    if(abs(beta) > m_maxpivot) m_maxpivot = abs(beta);\n\n    m_qr.bottomRightCorner(rows-k, cols-k-1)\n        .applyHouseholderOnTheLeft(m_qr.col(k).tail(rows-k-1), m_hCoeffs.coeffRef(k), &m_temp.coeffRef(k+1));\n  }\n\n  m_cols_permutation.setIdentity(cols);\n  for(Index k = 0; k < size; ++k)\n    m_cols_permutation.applyTranspositionOnTheRight(k, m_cols_transpositions.coeff(k));\n\n  m_det_pq = (number_of_transpositions%2) ? -1 : 1;\n  m_isInitialized = true;\n}\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\ntemplate<typename _MatrixType>\ntemplate<typename RhsType, typename DstType>\nvoid FullPivHouseholderQR<_MatrixType>::_solve_impl(const RhsType &rhs, DstType &dst) const\n{\n  eigen_assert(rhs.rows() == rows());\n  const Index l_rank = rank();\n\n  // FIXME introduce nonzeroPivots() and use it here. and more generally,\n  // make the same improvements in this dec as in FullPivLU.\n  if(l_rank==0)\n  {\n    dst.setZero();\n    return;\n  }\n\n  typename RhsType::PlainObject c(rhs);\n\n  Matrix<Scalar,1,RhsType::ColsAtCompileTime> temp(rhs.cols());\n  for (Index k = 0; k < l_rank; ++k)\n  {\n    Index remainingSize = rows()-k;\n    c.row(k).swap(c.row(m_rows_transpositions.coeff(k)));\n    c.bottomRightCorner(remainingSize, rhs.cols())\n      .applyHouseholderOnTheLeft(m_qr.col(k).tail(remainingSize-1),\n                               m_hCoeffs.coeff(k), &temp.coeffRef(0));\n  }\n\n  m_qr.topLeftCorner(l_rank, l_rank)\n      .template triangularView<Upper>()\n      .solveInPlace(c.topRows(l_rank));\n\n  for(Index i = 0; i < l_rank; ++i) dst.row(m_cols_permutation.indices().coeff(i)) = c.row(i);\n  for(Index i = l_rank; i < cols(); ++i) dst.row(m_cols_permutation.indices().coeff(i)).setZero();\n}\n#endif\n\nnamespace internal {\n  \ntemplate<typename DstXprType, typename MatrixType>\nstruct Assignment<DstXprType, Inverse<FullPivHouseholderQR<MatrixType> >, internal::assign_op<typename DstXprType::Scalar,typename FullPivHouseholderQR<MatrixType>::Scalar>, Dense2Dense>\n{\n  typedef FullPivHouseholderQR<MatrixType> QrType;\n  typedef Inverse<QrType> SrcXprType;\n  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename QrType::Scalar> &)\n  {    \n    dst = src.nestedExpression().solve(MatrixType::Identity(src.rows(), src.cols()));\n  }\n};\n\n/** \\ingroup QR_Module\n  *\n  * \\brief Expression type for return value of FullPivHouseholderQR::matrixQ()\n  *\n  * \\tparam MatrixType type of underlying dense matrix\n  */\ntemplate<typename MatrixType> struct FullPivHouseholderQRMatrixQReturnType\n  : public ReturnByValue<FullPivHouseholderQRMatrixQReturnType<MatrixType> >\n{\npublic:\n  typedef typename FullPivHouseholderQR<MatrixType>::IntDiagSizeVectorType IntDiagSizeVectorType;\n  typedef typename internal::plain_diag_type<MatrixType>::type HCoeffsType;\n  typedef Matrix<typename MatrixType::Scalar, 1, MatrixType::RowsAtCompileTime, RowMajor, 1,\n                 MatrixType::MaxRowsAtCompileTime> WorkVectorType;\n\n  FullPivHouseholderQRMatrixQReturnType(const MatrixType&       qr,\n                                        const HCoeffsType&      hCoeffs,\n                                        const IntDiagSizeVectorType& rowsTranspositions)\n    : m_qr(qr),\n      m_hCoeffs(hCoeffs),\n      m_rowsTranspositions(rowsTranspositions)\n  {}\n\n  template <typename ResultType>\n  void evalTo(ResultType& result) const\n  {\n    const Index rows = m_qr.rows();\n    WorkVectorType workspace(rows);\n    evalTo(result, workspace);\n  }\n\n  template <typename ResultType>\n  void evalTo(ResultType& result, WorkVectorType& workspace) const\n  {\n    using numext::conj;\n    // compute the product H'_0 H'_1 ... H'_n-1,\n    // where H_k is the k-th Householder transformation I - h_k v_k v_k'\n    // and v_k is the k-th Householder vector [1,m_qr(k+1,k), m_qr(k+2,k), ...]\n    const Index rows = m_qr.rows();\n    const Index cols = m_qr.cols();\n    const Index size = (std::min)(rows, cols);\n    workspace.resize(rows);\n    result.setIdentity(rows, rows);\n    for (Index k = size-1; k >= 0; k--)\n    {\n      result.block(k, k, rows-k, rows-k)\n            .applyHouseholderOnTheLeft(m_qr.col(k).tail(rows-k-1), conj(m_hCoeffs.coeff(k)), &workspace.coeffRef(k));\n      result.row(k).swap(result.row(m_rowsTranspositions.coeff(k)));\n    }\n  }\n\n  Index rows() const { return m_qr.rows(); }\n  Index cols() const { return m_qr.rows(); }\n\nprotected:\n  typename MatrixType::Nested m_qr;\n  typename HCoeffsType::Nested m_hCoeffs;\n  typename IntDiagSizeVectorType::Nested m_rowsTranspositions;\n};\n\n// template<typename MatrixType>\n// struct evaluator<FullPivHouseholderQRMatrixQReturnType<MatrixType> >\n//  : public evaluator<ReturnByValue<FullPivHouseholderQRMatrixQReturnType<MatrixType> > >\n// {};\n\n} // end namespace internal\n\ntemplate<typename MatrixType>\ninline typename FullPivHouseholderQR<MatrixType>::MatrixQReturnType FullPivHouseholderQR<MatrixType>::matrixQ() const\n{\n  eigen_assert(m_isInitialized && \"FullPivHouseholderQR is not initialized.\");\n  return MatrixQReturnType(m_qr, m_hCoeffs, m_rows_transpositions);\n}\n\n/** \\return the full-pivoting Householder QR decomposition of \\c *this.\n  *\n  * \\sa class FullPivHouseholderQR\n  */\ntemplate<typename Derived>\nconst FullPivHouseholderQR<typename MatrixBase<Derived>::PlainObject>\nMatrixBase<Derived>::fullPivHouseholderQr() const\n{\n  return FullPivHouseholderQR<PlainObject>(eval());\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_FULLPIVOTINGHOUSEHOLDERQR_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/QR/HouseholderQR.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2010 Vincent Lejeune\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_QR_H\n#define EIGEN_QR_H\n\nnamespace Eigen { \n\n/** \\ingroup QR_Module\n  *\n  *\n  * \\class HouseholderQR\n  *\n  * \\brief Householder QR decomposition of a matrix\n  *\n  * \\tparam _MatrixType the type of the matrix of which we are computing the QR decomposition\n  *\n  * This class performs a QR decomposition of a matrix \\b A into matrices \\b Q and \\b R\n  * such that \n  * \\f[\n  *  \\mathbf{A} = \\mathbf{Q} \\, \\mathbf{R}\n  * \\f]\n  * by using Householder transformations. Here, \\b Q a unitary matrix and \\b R an upper triangular matrix.\n  * The result is stored in a compact way compatible with LAPACK.\n  *\n  * Note that no pivoting is performed. This is \\b not a rank-revealing decomposition.\n  * If you want that feature, use FullPivHouseholderQR or ColPivHouseholderQR instead.\n  *\n  * This Householder QR decomposition is faster, but less numerically stable and less feature-full than\n  * FullPivHouseholderQR or ColPivHouseholderQR.\n  *\n  * This class supports the \\link InplaceDecomposition inplace decomposition \\endlink mechanism.\n  *\n  * \\sa MatrixBase::householderQr()\n  */\ntemplate<typename _MatrixType> class HouseholderQR\n{\n  public:\n\n    typedef _MatrixType MatrixType;\n    enum {\n      RowsAtCompileTime = MatrixType::RowsAtCompileTime,\n      ColsAtCompileTime = MatrixType::ColsAtCompileTime,\n      MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,\n      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime\n    };\n    typedef typename MatrixType::Scalar Scalar;\n    typedef typename MatrixType::RealScalar RealScalar;\n    // FIXME should be int\n    typedef typename MatrixType::StorageIndex StorageIndex;\n    typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime, (MatrixType::Flags&RowMajorBit) ? RowMajor : ColMajor, MaxRowsAtCompileTime, MaxRowsAtCompileTime> MatrixQType;\n    typedef typename internal::plain_diag_type<MatrixType>::type HCoeffsType;\n    typedef typename internal::plain_row_type<MatrixType>::type RowVectorType;\n    typedef HouseholderSequence<MatrixType,typename internal::remove_all<typename HCoeffsType::ConjugateReturnType>::type> HouseholderSequenceType;\n\n    /**\n      * \\brief Default Constructor.\n      *\n      * The default constructor is useful in cases in which the user intends to\n      * perform decompositions via HouseholderQR::compute(const MatrixType&).\n      */\n    HouseholderQR() : m_qr(), m_hCoeffs(), m_temp(), m_isInitialized(false) {}\n\n    /** \\brief Default Constructor with memory preallocation\n      *\n      * Like the default constructor but with preallocation of the internal data\n      * according to the specified problem \\a size.\n      * \\sa HouseholderQR()\n      */\n    HouseholderQR(Index rows, Index cols)\n      : m_qr(rows, cols),\n        m_hCoeffs((std::min)(rows,cols)),\n        m_temp(cols),\n        m_isInitialized(false) {}\n\n    /** \\brief Constructs a QR factorization from a given matrix\n      *\n      * This constructor computes the QR factorization of the matrix \\a matrix by calling\n      * the method compute(). It is a short cut for:\n      * \n      * \\code\n      * HouseholderQR<MatrixType> qr(matrix.rows(), matrix.cols());\n      * qr.compute(matrix);\n      * \\endcode\n      * \n      * \\sa compute()\n      */\n    template<typename InputType>\n    explicit HouseholderQR(const EigenBase<InputType>& matrix)\n      : m_qr(matrix.rows(), matrix.cols()),\n        m_hCoeffs((std::min)(matrix.rows(),matrix.cols())),\n        m_temp(matrix.cols()),\n        m_isInitialized(false)\n    {\n      compute(matrix.derived());\n    }\n\n\n    /** \\brief Constructs a QR factorization from a given matrix\n      *\n      * This overloaded constructor is provided for \\link InplaceDecomposition inplace decomposition \\endlink when\n      * \\c MatrixType is a Eigen::Ref.\n      *\n      * \\sa HouseholderQR(const EigenBase&)\n      */\n    template<typename InputType>\n    explicit HouseholderQR(EigenBase<InputType>& matrix)\n      : m_qr(matrix.derived()),\n        m_hCoeffs((std::min)(matrix.rows(),matrix.cols())),\n        m_temp(matrix.cols()),\n        m_isInitialized(false)\n    {\n      computeInPlace();\n    }\n\n    /** This method finds a solution x to the equation Ax=b, where A is the matrix of which\n      * *this is the QR decomposition, if any exists.\n      *\n      * \\param b the right-hand-side of the equation to solve.\n      *\n      * \\returns a solution.\n      *\n      * \\note_about_checking_solutions\n      *\n      * \\note_about_arbitrary_choice_of_solution\n      *\n      * Example: \\include HouseholderQR_solve.cpp\n      * Output: \\verbinclude HouseholderQR_solve.out\n      */\n    template<typename Rhs>\n    inline const Solve<HouseholderQR, Rhs>\n    solve(const MatrixBase<Rhs>& b) const\n    {\n      eigen_assert(m_isInitialized && \"HouseholderQR is not initialized.\");\n      return Solve<HouseholderQR, Rhs>(*this, b.derived());\n    }\n\n    /** This method returns an expression of the unitary matrix Q as a sequence of Householder transformations.\n      *\n      * The returned expression can directly be used to perform matrix products. It can also be assigned to a dense Matrix object.\n      * Here is an example showing how to recover the full or thin matrix Q, as well as how to perform matrix products using operator*:\n      *\n      * Example: \\include HouseholderQR_householderQ.cpp\n      * Output: \\verbinclude HouseholderQR_householderQ.out\n      */\n    HouseholderSequenceType householderQ() const\n    {\n      eigen_assert(m_isInitialized && \"HouseholderQR is not initialized.\");\n      return HouseholderSequenceType(m_qr, m_hCoeffs.conjugate());\n    }\n\n    /** \\returns a reference to the matrix where the Householder QR decomposition is stored\n      * in a LAPACK-compatible way.\n      */\n    const MatrixType& matrixQR() const\n    {\n        eigen_assert(m_isInitialized && \"HouseholderQR is not initialized.\");\n        return m_qr;\n    }\n\n    template<typename InputType>\n    HouseholderQR& compute(const EigenBase<InputType>& matrix) {\n      m_qr = matrix.derived();\n      computeInPlace();\n      return *this;\n    }\n\n    /** \\returns the absolute value of the determinant of the matrix of which\n      * *this is the QR decomposition. It has only linear complexity\n      * (that is, O(n) where n is the dimension of the square matrix)\n      * as the QR decomposition has already been computed.\n      *\n      * \\note This is only for square matrices.\n      *\n      * \\warning a determinant can be very big or small, so for matrices\n      * of large enough dimension, there is a risk of overflow/underflow.\n      * One way to work around that is to use logAbsDeterminant() instead.\n      *\n      * \\sa logAbsDeterminant(), MatrixBase::determinant()\n      */\n    typename MatrixType::RealScalar absDeterminant() const;\n\n    /** \\returns the natural log of the absolute value of the determinant of the matrix of which\n      * *this is the QR decomposition. It has only linear complexity\n      * (that is, O(n) where n is the dimension of the square matrix)\n      * as the QR decomposition has already been computed.\n      *\n      * \\note This is only for square matrices.\n      *\n      * \\note This method is useful to work around the risk of overflow/underflow that's inherent\n      * to determinant computation.\n      *\n      * \\sa absDeterminant(), MatrixBase::determinant()\n      */\n    typename MatrixType::RealScalar logAbsDeterminant() const;\n\n    inline Index rows() const { return m_qr.rows(); }\n    inline Index cols() const { return m_qr.cols(); }\n    \n    /** \\returns a const reference to the vector of Householder coefficients used to represent the factor \\c Q.\n      * \n      * For advanced uses only.\n      */\n    const HCoeffsType& hCoeffs() const { return m_hCoeffs; }\n    \n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    template<typename RhsType, typename DstType>\n    EIGEN_DEVICE_FUNC\n    void _solve_impl(const RhsType &rhs, DstType &dst) const;\n    #endif\n\n  protected:\n    \n    static void check_template_parameters()\n    {\n      EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);\n    }\n\n    void computeInPlace();\n    \n    MatrixType m_qr;\n    HCoeffsType m_hCoeffs;\n    RowVectorType m_temp;\n    bool m_isInitialized;\n};\n\ntemplate<typename MatrixType>\ntypename MatrixType::RealScalar HouseholderQR<MatrixType>::absDeterminant() const\n{\n  using std::abs;\n  eigen_assert(m_isInitialized && \"HouseholderQR is not initialized.\");\n  eigen_assert(m_qr.rows() == m_qr.cols() && \"You can't take the determinant of a non-square matrix!\");\n  return abs(m_qr.diagonal().prod());\n}\n\ntemplate<typename MatrixType>\ntypename MatrixType::RealScalar HouseholderQR<MatrixType>::logAbsDeterminant() const\n{\n  eigen_assert(m_isInitialized && \"HouseholderQR is not initialized.\");\n  eigen_assert(m_qr.rows() == m_qr.cols() && \"You can't take the determinant of a non-square matrix!\");\n  return m_qr.diagonal().cwiseAbs().array().log().sum();\n}\n\nnamespace internal {\n\n/** \\internal */\ntemplate<typename MatrixQR, typename HCoeffs>\nvoid householder_qr_inplace_unblocked(MatrixQR& mat, HCoeffs& hCoeffs, typename MatrixQR::Scalar* tempData = 0)\n{\n  typedef typename MatrixQR::Scalar Scalar;\n  typedef typename MatrixQR::RealScalar RealScalar;\n  Index rows = mat.rows();\n  Index cols = mat.cols();\n  Index size = (std::min)(rows,cols);\n\n  eigen_assert(hCoeffs.size() == size);\n\n  typedef Matrix<Scalar,MatrixQR::ColsAtCompileTime,1> TempType;\n  TempType tempVector;\n  if(tempData==0)\n  {\n    tempVector.resize(cols);\n    tempData = tempVector.data();\n  }\n\n  for(Index k = 0; k < size; ++k)\n  {\n    Index remainingRows = rows - k;\n    Index remainingCols = cols - k - 1;\n\n    RealScalar beta;\n    mat.col(k).tail(remainingRows).makeHouseholderInPlace(hCoeffs.coeffRef(k), beta);\n    mat.coeffRef(k,k) = beta;\n\n    // apply H to remaining part of m_qr from the left\n    mat.bottomRightCorner(remainingRows, remainingCols)\n        .applyHouseholderOnTheLeft(mat.col(k).tail(remainingRows-1), hCoeffs.coeffRef(k), tempData+k+1);\n  }\n}\n\n/** \\internal */\ntemplate<typename MatrixQR, typename HCoeffs,\n  typename MatrixQRScalar = typename MatrixQR::Scalar,\n  bool InnerStrideIsOne = (MatrixQR::InnerStrideAtCompileTime == 1 && HCoeffs::InnerStrideAtCompileTime == 1)>\nstruct householder_qr_inplace_blocked\n{\n  // This is specialized for MKL-supported Scalar types in HouseholderQR_MKL.h\n  static void run(MatrixQR& mat, HCoeffs& hCoeffs, Index maxBlockSize=32,\n      typename MatrixQR::Scalar* tempData = 0)\n  {\n    typedef typename MatrixQR::Scalar Scalar;\n    typedef Block<MatrixQR,Dynamic,Dynamic> BlockType;\n\n    Index rows = mat.rows();\n    Index cols = mat.cols();\n    Index size = (std::min)(rows, cols);\n\n    typedef Matrix<Scalar,Dynamic,1,ColMajor,MatrixQR::MaxColsAtCompileTime,1> TempType;\n    TempType tempVector;\n    if(tempData==0)\n    {\n      tempVector.resize(cols);\n      tempData = tempVector.data();\n    }\n\n    Index blockSize = (std::min)(maxBlockSize,size);\n\n    Index k = 0;\n    for (k = 0; k < size; k += blockSize)\n    {\n      Index bs = (std::min)(size-k,blockSize);  // actual size of the block\n      Index tcols = cols - k - bs;              // trailing columns\n      Index brows = rows-k;                     // rows of the block\n\n      // partition the matrix:\n      //        A00 | A01 | A02\n      // mat  = A10 | A11 | A12\n      //        A20 | A21 | A22\n      // and performs the qr dec of [A11^T A12^T]^T\n      // and update [A21^T A22^T]^T using level 3 operations.\n      // Finally, the algorithm continue on A22\n\n      BlockType A11_21 = mat.block(k,k,brows,bs);\n      Block<HCoeffs,Dynamic,1> hCoeffsSegment = hCoeffs.segment(k,bs);\n\n      householder_qr_inplace_unblocked(A11_21, hCoeffsSegment, tempData);\n\n      if(tcols)\n      {\n        BlockType A21_22 = mat.block(k,k+bs,brows,tcols);\n        apply_block_householder_on_the_left(A21_22,A11_21,hCoeffsSegment, false); // false == backward\n      }\n    }\n  }\n};\n\n} // end namespace internal\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\ntemplate<typename _MatrixType>\ntemplate<typename RhsType, typename DstType>\nvoid HouseholderQR<_MatrixType>::_solve_impl(const RhsType &rhs, DstType &dst) const\n{\n  const Index rank = (std::min)(rows(), cols());\n  eigen_assert(rhs.rows() == rows());\n\n  typename RhsType::PlainObject c(rhs);\n\n  // Note that the matrix Q = H_0^* H_1^*... so its inverse is Q^* = (H_0 H_1 ...)^T\n  c.applyOnTheLeft(householderSequence(\n    m_qr.leftCols(rank),\n    m_hCoeffs.head(rank)).transpose()\n  );\n\n  m_qr.topLeftCorner(rank, rank)\n      .template triangularView<Upper>()\n      .solveInPlace(c.topRows(rank));\n\n  dst.topRows(rank) = c.topRows(rank);\n  dst.bottomRows(cols()-rank).setZero();\n}\n#endif\n\n/** Performs the QR factorization of the given matrix \\a matrix. The result of\n  * the factorization is stored into \\c *this, and a reference to \\c *this\n  * is returned.\n  *\n  * \\sa class HouseholderQR, HouseholderQR(const MatrixType&)\n  */\ntemplate<typename MatrixType>\nvoid HouseholderQR<MatrixType>::computeInPlace()\n{\n  check_template_parameters();\n  \n  Index rows = m_qr.rows();\n  Index cols = m_qr.cols();\n  Index size = (std::min)(rows,cols);\n\n  m_hCoeffs.resize(size);\n\n  m_temp.resize(cols);\n\n  internal::householder_qr_inplace_blocked<MatrixType, HCoeffsType>::run(m_qr, m_hCoeffs, 48, m_temp.data());\n\n  m_isInitialized = true;\n}\n\n/** \\return the Householder QR decomposition of \\c *this.\n  *\n  * \\sa class HouseholderQR\n  */\ntemplate<typename Derived>\nconst HouseholderQR<typename MatrixBase<Derived>::PlainObject>\nMatrixBase<Derived>::householderQr() const\n{\n  return HouseholderQR<PlainObject>(eval());\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_QR_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/QR/HouseholderQR_LAPACKE.h",
    "content": "/*\n Copyright (c) 2011, Intel Corporation. All rights reserved.\n\n Redistribution and use in source and binary forms, with or without modification,\n are permitted provided that the following conditions are met:\n\n * Redistributions of source code must retain the above copyright notice, this\n   list of conditions and the following disclaimer.\n * Redistributions in binary form must reproduce the above copyright notice,\n   this list of conditions and the following disclaimer in the documentation\n   and/or other materials provided with the distribution.\n * Neither the name of Intel Corporation nor the names of its contributors may\n   be used to endorse or promote products derived from this software without\n   specific prior written permission.\n\n THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\" AND\n ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED\n WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\n DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR\n ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES\n (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;\n LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON\n ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT\n (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS\n SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n\n ********************************************************************************\n *   Content : Eigen bindings to LAPACKe\n *    Householder QR decomposition of a matrix w/o pivoting based on\n *    LAPACKE_?geqrf function.\n ********************************************************************************\n*/\n\n#ifndef EIGEN_QR_LAPACKE_H\n#define EIGEN_QR_LAPACKE_H\n\nnamespace Eigen { \n\nnamespace internal {\n\n/** \\internal Specialization for the data types supported by LAPACKe */\n\n#define EIGEN_LAPACKE_QR_NOPIV(EIGTYPE, LAPACKE_TYPE, LAPACKE_PREFIX) \\\ntemplate<typename MatrixQR, typename HCoeffs> \\\nstruct householder_qr_inplace_blocked<MatrixQR, HCoeffs, EIGTYPE, true> \\\n{ \\\n  static void run(MatrixQR& mat, HCoeffs& hCoeffs, Index = 32, \\\n      typename MatrixQR::Scalar* = 0) \\\n  { \\\n    lapack_int m = (lapack_int) mat.rows(); \\\n    lapack_int n = (lapack_int) mat.cols(); \\\n    lapack_int lda = (lapack_int) mat.outerStride(); \\\n    lapack_int matrix_order = (MatrixQR::IsRowMajor) ? LAPACK_ROW_MAJOR : LAPACK_COL_MAJOR; \\\n    LAPACKE_##LAPACKE_PREFIX##geqrf( matrix_order, m, n, (LAPACKE_TYPE*)mat.data(), lda, (LAPACKE_TYPE*)hCoeffs.data()); \\\n    hCoeffs.adjointInPlace(); \\\n  } \\\n};\n\nEIGEN_LAPACKE_QR_NOPIV(double, double, d)\nEIGEN_LAPACKE_QR_NOPIV(float, float, s)\nEIGEN_LAPACKE_QR_NOPIV(dcomplex, lapack_complex_double, z)\nEIGEN_LAPACKE_QR_NOPIV(scomplex, lapack_complex_float, c)\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_QR_LAPACKE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SPQRSupport/SuiteSparseQRSupport.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Desire Nuentsa <desire.nuentsa_wakam@inria.fr>\n// Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SUITESPARSEQRSUPPORT_H\n#define EIGEN_SUITESPARSEQRSUPPORT_H\n\nnamespace Eigen {\n  \n  template<typename MatrixType> class SPQR; \n  template<typename SPQRType> struct SPQRMatrixQReturnType; \n  template<typename SPQRType> struct SPQRMatrixQTransposeReturnType; \n  template <typename SPQRType, typename Derived> struct SPQR_QProduct;\n  namespace internal {\n    template <typename SPQRType> struct traits<SPQRMatrixQReturnType<SPQRType> >\n    {\n      typedef typename SPQRType::MatrixType ReturnType;\n    };\n    template <typename SPQRType> struct traits<SPQRMatrixQTransposeReturnType<SPQRType> >\n    {\n      typedef typename SPQRType::MatrixType ReturnType;\n    };\n    template <typename SPQRType, typename Derived> struct traits<SPQR_QProduct<SPQRType, Derived> >\n    {\n      typedef typename Derived::PlainObject ReturnType;\n    };\n  } // End namespace internal\n  \n/**\n  * \\ingroup SPQRSupport_Module\n  * \\class SPQR\n  * \\brief Sparse QR factorization based on SuiteSparseQR library\n  *\n  * This class is used to perform a multithreaded and multifrontal rank-revealing QR decomposition\n  * of sparse matrices. The result is then used to solve linear leasts_square systems.\n  * Clearly, a QR factorization is returned such that A*P = Q*R where :\n  *\n  * P is the column permutation. Use colsPermutation() to get it.\n  *\n  * Q is the orthogonal matrix represented as Householder reflectors.\n  * Use matrixQ() to get an expression and matrixQ().transpose() to get the transpose.\n  * You can then apply it to a vector.\n  *\n  * R is the sparse triangular factor. Use matrixQR() to get it as SparseMatrix.\n  * NOTE : The Index type of R is always SuiteSparse_long. You can get it with SPQR::Index\n  *\n  * \\tparam _MatrixType The type of the sparse matrix A, must be a column-major SparseMatrix<>\n  *\n  * \\implsparsesolverconcept\n  *\n  *\n  */\ntemplate<typename _MatrixType>\nclass SPQR : public SparseSolverBase<SPQR<_MatrixType> >\n{\n  protected:\n    typedef SparseSolverBase<SPQR<_MatrixType> > Base;\n    using Base::m_isInitialized;\n  public:\n    typedef typename _MatrixType::Scalar Scalar;\n    typedef typename _MatrixType::RealScalar RealScalar;\n    typedef SuiteSparse_long StorageIndex ;\n    typedef SparseMatrix<Scalar, ColMajor, StorageIndex> MatrixType;\n    typedef Map<PermutationMatrix<Dynamic, Dynamic, StorageIndex> > PermutationType;\n    enum {\n      ColsAtCompileTime = Dynamic,\n      MaxColsAtCompileTime = Dynamic\n    };\n  public:\n    SPQR() \n      : m_ordering(SPQR_ORDERING_DEFAULT), m_allow_tol(SPQR_DEFAULT_TOL), m_tolerance (NumTraits<Scalar>::epsilon()), m_useDefaultThreshold(true)\n    { \n      cholmod_l_start(&m_cc);\n    }\n    \n    explicit SPQR(const _MatrixType& matrix)\n    : m_ordering(SPQR_ORDERING_DEFAULT), m_allow_tol(SPQR_DEFAULT_TOL), m_tolerance (NumTraits<Scalar>::epsilon()), m_useDefaultThreshold(true)\n    {\n      cholmod_l_start(&m_cc);\n      compute(matrix);\n    }\n    \n    ~SPQR()\n    {\n      SPQR_free();\n      cholmod_l_finish(&m_cc);\n    }\n    void SPQR_free()\n    {\n      cholmod_l_free_sparse(&m_H, &m_cc);\n      cholmod_l_free_sparse(&m_cR, &m_cc);\n      cholmod_l_free_dense(&m_HTau, &m_cc);\n      std::free(m_E);\n      std::free(m_HPinv);\n    }\n\n    void compute(const _MatrixType& matrix)\n    {\n      if(m_isInitialized) SPQR_free();\n\n      MatrixType mat(matrix);\n      \n      /* Compute the default threshold as in MatLab, see:\n       * Tim Davis, \"Algorithm 915, SuiteSparseQR: Multifrontal Multithreaded Rank-Revealing\n       * Sparse QR Factorization, ACM Trans. on Math. Soft. 38(1), 2011, Page 8:3 \n       */\n      RealScalar pivotThreshold = m_tolerance;\n      if(m_useDefaultThreshold) \n      {\n        RealScalar max2Norm = 0.0;\n        for (int j = 0; j < mat.cols(); j++) max2Norm = numext::maxi(max2Norm, mat.col(j).norm());\n        if(max2Norm==RealScalar(0))\n          max2Norm = RealScalar(1);\n        pivotThreshold = 20 * (mat.rows() + mat.cols()) * max2Norm * NumTraits<RealScalar>::epsilon();\n      }\n      cholmod_sparse A; \n      A = viewAsCholmod(mat);\n      m_rows = matrix.rows();\n      Index col = matrix.cols();\n      m_rank = SuiteSparseQR<Scalar>(m_ordering, pivotThreshold, col, &A, \n                             &m_cR, &m_E, &m_H, &m_HPinv, &m_HTau, &m_cc);\n\n      if (!m_cR)\n      {\n        m_info = NumericalIssue;\n        m_isInitialized = false;\n        return;\n      }\n      m_info = Success;\n      m_isInitialized = true;\n      m_isRUpToDate = false;\n    }\n    /** \n     * Get the number of rows of the input matrix and the Q matrix\n     */\n    inline Index rows() const {return m_rows; }\n    \n    /** \n     * Get the number of columns of the input matrix. \n     */\n    inline Index cols() const { return m_cR->ncol; }\n    \n    template<typename Rhs, typename Dest>\n    void _solve_impl(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const\n    {\n      eigen_assert(m_isInitialized && \" The QR factorization should be computed first, call compute()\");\n      eigen_assert(b.cols()==1 && \"This method is for vectors only\");\n\n      //Compute Q^T * b\n      typename Dest::PlainObject y, y2;\n      y = matrixQ().transpose() * b;\n      \n      // Solves with the triangular matrix R\n      Index rk = this->rank();\n      y2 = y;\n      y.resize((std::max)(cols(),Index(y.rows())),y.cols());\n      y.topRows(rk) = this->matrixR().topLeftCorner(rk, rk).template triangularView<Upper>().solve(y2.topRows(rk));\n\n      // Apply the column permutation \n      // colsPermutation() performs a copy of the permutation,\n      // so let's apply it manually:\n      for(Index i = 0; i < rk; ++i) dest.row(m_E[i]) = y.row(i);\n      for(Index i = rk; i < cols(); ++i) dest.row(m_E[i]).setZero();\n      \n//       y.bottomRows(y.rows()-rk).setZero();\n//       dest = colsPermutation() * y.topRows(cols());\n      \n      m_info = Success;\n    }\n    \n    /** \\returns the sparse triangular factor R. It is a sparse matrix\n     */\n    const MatrixType matrixR() const\n    {\n      eigen_assert(m_isInitialized && \" The QR factorization should be computed first, call compute()\");\n      if(!m_isRUpToDate) {\n        m_R = viewAsEigen<Scalar,ColMajor, typename MatrixType::StorageIndex>(*m_cR);\n        m_isRUpToDate = true;\n      }\n      return m_R;\n    }\n    /// Get an expression of the matrix Q\n    SPQRMatrixQReturnType<SPQR> matrixQ() const\n    {\n      return SPQRMatrixQReturnType<SPQR>(*this);\n    }\n    /// Get the permutation that was applied to columns of A\n    PermutationType colsPermutation() const\n    { \n      eigen_assert(m_isInitialized && \"Decomposition is not initialized.\");\n      return PermutationType(m_E, m_cR->ncol);\n    }\n    /**\n     * Gets the rank of the matrix. \n     * It should be equal to matrixQR().cols if the matrix is full-rank\n     */\n    Index rank() const\n    {\n      eigen_assert(m_isInitialized && \"Decomposition is not initialized.\");\n      return m_cc.SPQR_istat[4];\n    }\n    /// Set the fill-reducing ordering method to be used\n    void setSPQROrdering(int ord) { m_ordering = ord;}\n    /// Set the tolerance tol to treat columns with 2-norm < =tol as zero\n    void setPivotThreshold(const RealScalar& tol)\n    {\n      m_useDefaultThreshold = false;\n      m_tolerance = tol;\n    }\n    \n    /** \\returns a pointer to the SPQR workspace */\n    cholmod_common *cholmodCommon() const { return &m_cc; }\n    \n    \n    /** \\brief Reports whether previous computation was successful.\n      *\n      * \\returns \\c Success if computation was succesful,\n      *          \\c NumericalIssue if the sparse QR can not be computed\n      */\n    ComputationInfo info() const\n    {\n      eigen_assert(m_isInitialized && \"Decomposition is not initialized.\");\n      return m_info;\n    }\n  protected:\n    bool m_analysisIsOk;\n    bool m_factorizationIsOk;\n    mutable bool m_isRUpToDate;\n    mutable ComputationInfo m_info;\n    int m_ordering; // Ordering method to use, see SPQR's manual\n    int m_allow_tol; // Allow to use some tolerance during numerical factorization.\n    RealScalar m_tolerance; // treat columns with 2-norm below this tolerance as zero\n    mutable cholmod_sparse *m_cR; // The sparse R factor in cholmod format\n    mutable MatrixType m_R; // The sparse matrix R in Eigen format\n    mutable StorageIndex *m_E; // The permutation applied to columns\n    mutable cholmod_sparse *m_H;  //The householder vectors\n    mutable StorageIndex *m_HPinv; // The row permutation of H\n    mutable cholmod_dense *m_HTau; // The Householder coefficients\n    mutable Index m_rank; // The rank of the matrix\n    mutable cholmod_common m_cc; // Workspace and parameters\n    bool m_useDefaultThreshold;     // Use default threshold\n    Index m_rows;\n    template<typename ,typename > friend struct SPQR_QProduct;\n};\n\ntemplate <typename SPQRType, typename Derived>\nstruct SPQR_QProduct : ReturnByValue<SPQR_QProduct<SPQRType,Derived> >\n{\n  typedef typename SPQRType::Scalar Scalar;\n  typedef typename SPQRType::StorageIndex StorageIndex;\n  //Define the constructor to get reference to argument types\n  SPQR_QProduct(const SPQRType& spqr, const Derived& other, bool transpose) : m_spqr(spqr),m_other(other),m_transpose(transpose) {}\n  \n  inline Index rows() const { return m_transpose ? m_spqr.rows() : m_spqr.cols(); }\n  inline Index cols() const { return m_other.cols(); }\n  // Assign to a vector\n  template<typename ResType>\n  void evalTo(ResType& res) const\n  {\n    cholmod_dense y_cd;\n    cholmod_dense *x_cd; \n    int method = m_transpose ? SPQR_QTX : SPQR_QX; \n    cholmod_common *cc = m_spqr.cholmodCommon();\n    y_cd = viewAsCholmod(m_other.const_cast_derived());\n    x_cd = SuiteSparseQR_qmult<Scalar>(method, m_spqr.m_H, m_spqr.m_HTau, m_spqr.m_HPinv, &y_cd, cc);\n    res = Matrix<Scalar,ResType::RowsAtCompileTime,ResType::ColsAtCompileTime>::Map(reinterpret_cast<Scalar*>(x_cd->x), x_cd->nrow, x_cd->ncol);\n    cholmod_l_free_dense(&x_cd, cc);\n  }\n  const SPQRType& m_spqr; \n  const Derived& m_other; \n  bool m_transpose; \n  \n};\ntemplate<typename SPQRType>\nstruct SPQRMatrixQReturnType{\n  \n  SPQRMatrixQReturnType(const SPQRType& spqr) : m_spqr(spqr) {}\n  template<typename Derived>\n  SPQR_QProduct<SPQRType, Derived> operator*(const MatrixBase<Derived>& other)\n  {\n    return SPQR_QProduct<SPQRType,Derived>(m_spqr,other.derived(),false);\n  }\n  SPQRMatrixQTransposeReturnType<SPQRType> adjoint() const\n  {\n    return SPQRMatrixQTransposeReturnType<SPQRType>(m_spqr);\n  }\n  // To use for operations with the transpose of Q\n  SPQRMatrixQTransposeReturnType<SPQRType> transpose() const\n  {\n    return SPQRMatrixQTransposeReturnType<SPQRType>(m_spqr);\n  }\n  const SPQRType& m_spqr;\n};\n\ntemplate<typename SPQRType>\nstruct SPQRMatrixQTransposeReturnType{\n  SPQRMatrixQTransposeReturnType(const SPQRType& spqr) : m_spqr(spqr) {}\n  template<typename Derived>\n  SPQR_QProduct<SPQRType,Derived> operator*(const MatrixBase<Derived>& other)\n  {\n    return SPQR_QProduct<SPQRType,Derived>(m_spqr,other.derived(), true);\n  }\n  const SPQRType& m_spqr;\n};\n\n}// End namespace Eigen\n#endif\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SVD/BDCSVD.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n// \n// We used the \"A Divide-And-Conquer Algorithm for the Bidiagonal SVD\"\n// research report written by Ming Gu and Stanley C.Eisenstat\n// The code variable names correspond to the names they used in their \n// report\n//\n// Copyright (C) 2013 Gauthier Brun <brun.gauthier@gmail.com>\n// Copyright (C) 2013 Nicolas Carre <nicolas.carre@ensimag.fr>\n// Copyright (C) 2013 Jean Ceccato <jean.ceccato@ensimag.fr>\n// Copyright (C) 2013 Pierre Zoppitelli <pierre.zoppitelli@ensimag.fr>\n// Copyright (C) 2013 Jitse Niesen <jitse@maths.leeds.ac.uk>\n// Copyright (C) 2014-2017 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_BDCSVD_H\n#define EIGEN_BDCSVD_H\n// #define EIGEN_BDCSVD_DEBUG_VERBOSE\n// #define EIGEN_BDCSVD_SANITY_CHECKS\n\nnamespace Eigen {\n\n#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE\nIOFormat bdcsvdfmt(8, 0, \", \", \"\\n\", \"  [\", \"]\");\n#endif\n  \ntemplate<typename _MatrixType> class BDCSVD;\n\nnamespace internal {\n\ntemplate<typename _MatrixType> \nstruct traits<BDCSVD<_MatrixType> >\n{\n  typedef _MatrixType MatrixType;\n};  \n\n} // end namespace internal\n  \n  \n/** \\ingroup SVD_Module\n *\n *\n * \\class BDCSVD\n *\n * \\brief class Bidiagonal Divide and Conquer SVD\n *\n * \\tparam _MatrixType the type of the matrix of which we are computing the SVD decomposition\n *\n * This class first reduces the input matrix to bi-diagonal form using class UpperBidiagonalization,\n * and then performs a divide-and-conquer diagonalization. Small blocks are diagonalized using class JacobiSVD.\n * You can control the switching size with the setSwitchSize() method, default is 16.\n * For small matrice (<16), it is thus preferable to directly use JacobiSVD. For larger ones, BDCSVD is highly\n * recommended and can several order of magnitude faster.\n *\n * \\warning this algorithm is unlikely to provide accurate result when compiled with unsafe math optimizations.\n * For instance, this concerns Intel's compiler (ICC), which perfroms such optimization by default unless\n * you compile with the \\c -fp-model \\c precise option. Likewise, the \\c -ffast-math option of GCC or clang will\n * significantly degrade the accuracy.\n *\n * \\sa class JacobiSVD\n */\ntemplate<typename _MatrixType> \nclass BDCSVD : public SVDBase<BDCSVD<_MatrixType> >\n{\n  typedef SVDBase<BDCSVD> Base;\n    \npublic:\n  using Base::rows;\n  using Base::cols;\n  using Base::computeU;\n  using Base::computeV;\n  \n  typedef _MatrixType MatrixType;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;\n  typedef typename NumTraits<RealScalar>::Literal Literal;\n  enum {\n    RowsAtCompileTime = MatrixType::RowsAtCompileTime, \n    ColsAtCompileTime = MatrixType::ColsAtCompileTime, \n    DiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime, ColsAtCompileTime), \n    MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime, \n    MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime, \n    MaxDiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(MaxRowsAtCompileTime, MaxColsAtCompileTime), \n    MatrixOptions = MatrixType::Options\n  };\n\n  typedef typename Base::MatrixUType MatrixUType;\n  typedef typename Base::MatrixVType MatrixVType;\n  typedef typename Base::SingularValuesType SingularValuesType;\n  \n  typedef Matrix<Scalar, Dynamic, Dynamic, ColMajor> MatrixX;\n  typedef Matrix<RealScalar, Dynamic, Dynamic, ColMajor> MatrixXr;\n  typedef Matrix<RealScalar, Dynamic, 1> VectorType;\n  typedef Array<RealScalar, Dynamic, 1> ArrayXr;\n  typedef Array<Index,1,Dynamic> ArrayXi;\n  typedef Ref<ArrayXr> ArrayRef;\n  typedef Ref<ArrayXi> IndicesRef;\n\n  /** \\brief Default Constructor.\n   *\n   * The default constructor is useful in cases in which the user intends to\n   * perform decompositions via BDCSVD::compute(const MatrixType&).\n   */\n  BDCSVD() : m_algoswap(16), m_numIters(0)\n  {}\n\n\n  /** \\brief Default Constructor with memory preallocation\n   *\n   * Like the default constructor but with preallocation of the internal data\n   * according to the specified problem size.\n   * \\sa BDCSVD()\n   */\n  BDCSVD(Index rows, Index cols, unsigned int computationOptions = 0)\n    : m_algoswap(16), m_numIters(0)\n  {\n    allocate(rows, cols, computationOptions);\n  }\n\n  /** \\brief Constructor performing the decomposition of given matrix.\n   *\n   * \\param matrix the matrix to decompose\n   * \\param computationOptions optional parameter allowing to specify if you want full or thin U or V unitaries to be computed.\n   *                           By default, none is computed. This is a bit - field, the possible bits are #ComputeFullU, #ComputeThinU, \n   *                           #ComputeFullV, #ComputeThinV.\n   *\n   * Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not\n   * available with the (non - default) FullPivHouseholderQR preconditioner.\n   */\n  BDCSVD(const MatrixType& matrix, unsigned int computationOptions = 0)\n    : m_algoswap(16), m_numIters(0)\n  {\n    compute(matrix, computationOptions);\n  }\n\n  ~BDCSVD() \n  {\n  }\n  \n  /** \\brief Method performing the decomposition of given matrix using custom options.\n   *\n   * \\param matrix the matrix to decompose\n   * \\param computationOptions optional parameter allowing to specify if you want full or thin U or V unitaries to be computed.\n   *                           By default, none is computed. This is a bit - field, the possible bits are #ComputeFullU, #ComputeThinU, \n   *                           #ComputeFullV, #ComputeThinV.\n   *\n   * Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not\n   * available with the (non - default) FullPivHouseholderQR preconditioner.\n   */\n  BDCSVD& compute(const MatrixType& matrix, unsigned int computationOptions);\n\n  /** \\brief Method performing the decomposition of given matrix using current options.\n   *\n   * \\param matrix the matrix to decompose\n   *\n   * This method uses the current \\a computationOptions, as already passed to the constructor or to compute(const MatrixType&, unsigned int).\n   */\n  BDCSVD& compute(const MatrixType& matrix)\n  {\n    return compute(matrix, this->m_computationOptions);\n  }\n\n  void setSwitchSize(int s) \n  {\n    eigen_assert(s>3 && \"BDCSVD the size of the algo switch has to be greater than 3\");\n    m_algoswap = s;\n  }\n \nprivate:\n  void allocate(Index rows, Index cols, unsigned int computationOptions);\n  void divide(Index firstCol, Index lastCol, Index firstRowW, Index firstColW, Index shift);\n  void computeSVDofM(Index firstCol, Index n, MatrixXr& U, VectorType& singVals, MatrixXr& V);\n  void computeSingVals(const ArrayRef& col0, const ArrayRef& diag, const IndicesRef& perm, VectorType& singVals, ArrayRef shifts, ArrayRef mus);\n  void perturbCol0(const ArrayRef& col0, const ArrayRef& diag, const IndicesRef& perm, const VectorType& singVals, const ArrayRef& shifts, const ArrayRef& mus, ArrayRef zhat);\n  void computeSingVecs(const ArrayRef& zhat, const ArrayRef& diag, const IndicesRef& perm, const VectorType& singVals, const ArrayRef& shifts, const ArrayRef& mus, MatrixXr& U, MatrixXr& V);\n  void deflation43(Index firstCol, Index shift, Index i, Index size);\n  void deflation44(Index firstColu , Index firstColm, Index firstRowW, Index firstColW, Index i, Index j, Index size);\n  void deflation(Index firstCol, Index lastCol, Index k, Index firstRowW, Index firstColW, Index shift);\n  template<typename HouseholderU, typename HouseholderV, typename NaiveU, typename NaiveV>\n  void copyUV(const HouseholderU &householderU, const HouseholderV &householderV, const NaiveU &naiveU, const NaiveV &naivev);\n  void structured_update(Block<MatrixXr,Dynamic,Dynamic> A, const MatrixXr &B, Index n1);\n  static RealScalar secularEq(RealScalar x, const ArrayRef& col0, const ArrayRef& diag, const IndicesRef &perm, const ArrayRef& diagShifted, RealScalar shift);\n\nprotected:\n  MatrixXr m_naiveU, m_naiveV;\n  MatrixXr m_computed;\n  Index m_nRec;\n  ArrayXr m_workspace;\n  ArrayXi m_workspaceI;\n  int m_algoswap;\n  bool m_isTranspose, m_compU, m_compV;\n  \n  using Base::m_singularValues;\n  using Base::m_diagSize;\n  using Base::m_computeFullU;\n  using Base::m_computeFullV;\n  using Base::m_computeThinU;\n  using Base::m_computeThinV;\n  using Base::m_matrixU;\n  using Base::m_matrixV;\n  using Base::m_isInitialized;\n  using Base::m_nonzeroSingularValues;\n\npublic:  \n  int m_numIters;\n}; //end class BDCSVD\n\n\n// Method to allocate and initialize matrix and attributes\ntemplate<typename MatrixType>\nvoid BDCSVD<MatrixType>::allocate(Index rows, Index cols, unsigned int computationOptions)\n{\n  m_isTranspose = (cols > rows);\n\n  if (Base::allocate(rows, cols, computationOptions))\n    return;\n  \n  m_computed = MatrixXr::Zero(m_diagSize + 1, m_diagSize );\n  m_compU = computeV();\n  m_compV = computeU();\n  if (m_isTranspose)\n    std::swap(m_compU, m_compV);\n  \n  if (m_compU) m_naiveU = MatrixXr::Zero(m_diagSize + 1, m_diagSize + 1 );\n  else         m_naiveU = MatrixXr::Zero(2, m_diagSize + 1 );\n  \n  if (m_compV) m_naiveV = MatrixXr::Zero(m_diagSize, m_diagSize);\n  \n  m_workspace.resize((m_diagSize+1)*(m_diagSize+1)*3);\n  m_workspaceI.resize(3*m_diagSize);\n}// end allocate\n\ntemplate<typename MatrixType>\nBDCSVD<MatrixType>& BDCSVD<MatrixType>::compute(const MatrixType& matrix, unsigned int computationOptions) \n{\n#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE\n  std::cout << \"\\n\\n\\n======================================================================================================================\\n\\n\\n\";\n#endif\n  allocate(matrix.rows(), matrix.cols(), computationOptions);\n  using std::abs;\n\n  const RealScalar considerZero = (std::numeric_limits<RealScalar>::min)();\n  \n  //**** step -1 - If the problem is too small, directly falls back to JacobiSVD and return\n  if(matrix.cols() < m_algoswap)\n  {\n    // FIXME this line involves temporaries\n    JacobiSVD<MatrixType> jsvd(matrix,computationOptions);\n    if(computeU()) m_matrixU = jsvd.matrixU();\n    if(computeV()) m_matrixV = jsvd.matrixV();\n    m_singularValues = jsvd.singularValues();\n    m_nonzeroSingularValues = jsvd.nonzeroSingularValues();\n    m_isInitialized = true;\n    return *this;\n  }\n  \n  //**** step 0 - Copy the input matrix and apply scaling to reduce over/under-flows\n  RealScalar scale = matrix.cwiseAbs().maxCoeff();\n  if(scale==Literal(0)) scale = Literal(1);\n  MatrixX copy;\n  if (m_isTranspose) copy = matrix.adjoint()/scale;\n  else               copy = matrix/scale;\n  \n  //**** step 1 - Bidiagonalization\n  // FIXME this line involves temporaries\n  internal::UpperBidiagonalization<MatrixX> bid(copy);\n\n  //**** step 2 - Divide & Conquer\n  m_naiveU.setZero();\n  m_naiveV.setZero();\n  // FIXME this line involves a temporary matrix\n  m_computed.topRows(m_diagSize) = bid.bidiagonal().toDenseMatrix().transpose();\n  m_computed.template bottomRows<1>().setZero();\n  divide(0, m_diagSize - 1, 0, 0, 0);\n\n  //**** step 3 - Copy singular values and vectors\n  for (int i=0; i<m_diagSize; i++)\n  {\n    RealScalar a = abs(m_computed.coeff(i, i));\n    m_singularValues.coeffRef(i) = a * scale;\n    if (a<considerZero)\n    {\n      m_nonzeroSingularValues = i;\n      m_singularValues.tail(m_diagSize - i - 1).setZero();\n      break;\n    }\n    else if (i == m_diagSize - 1)\n    {\n      m_nonzeroSingularValues = i + 1;\n      break;\n    }\n  }\n\n#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE\n//   std::cout << \"m_naiveU\\n\" << m_naiveU << \"\\n\\n\";\n//   std::cout << \"m_naiveV\\n\" << m_naiveV << \"\\n\\n\";\n#endif\n  if(m_isTranspose) copyUV(bid.householderV(), bid.householderU(), m_naiveV, m_naiveU);\n  else              copyUV(bid.householderU(), bid.householderV(), m_naiveU, m_naiveV);\n\n  m_isInitialized = true;\n  return *this;\n}// end compute\n\n\ntemplate<typename MatrixType>\ntemplate<typename HouseholderU, typename HouseholderV, typename NaiveU, typename NaiveV>\nvoid BDCSVD<MatrixType>::copyUV(const HouseholderU &householderU, const HouseholderV &householderV, const NaiveU &naiveU, const NaiveV &naiveV)\n{\n  // Note exchange of U and V: m_matrixU is set from m_naiveV and vice versa\n  if (computeU())\n  {\n    Index Ucols = m_computeThinU ? m_diagSize : householderU.cols();\n    m_matrixU = MatrixX::Identity(householderU.cols(), Ucols);\n    m_matrixU.topLeftCorner(m_diagSize, m_diagSize) = naiveV.template cast<Scalar>().topLeftCorner(m_diagSize, m_diagSize);\n    householderU.applyThisOnTheLeft(m_matrixU); // FIXME this line involves a temporary buffer\n  }\n  if (computeV())\n  {\n    Index Vcols = m_computeThinV ? m_diagSize : householderV.cols();\n    m_matrixV = MatrixX::Identity(householderV.cols(), Vcols);\n    m_matrixV.topLeftCorner(m_diagSize, m_diagSize) = naiveU.template cast<Scalar>().topLeftCorner(m_diagSize, m_diagSize);\n    householderV.applyThisOnTheLeft(m_matrixV); // FIXME this line involves a temporary buffer\n  }\n}\n\n/** \\internal\n  * Performs A = A * B exploiting the special structure of the matrix A. Splitting A as:\n  *  A = [A1]\n  *      [A2]\n  * such that A1.rows()==n1, then we assume that at least half of the columns of A1 and A2 are zeros.\n  * We can thus pack them prior to the the matrix product. However, this is only worth the effort if the matrix is large\n  * enough.\n  */\ntemplate<typename MatrixType>\nvoid BDCSVD<MatrixType>::structured_update(Block<MatrixXr,Dynamic,Dynamic> A, const MatrixXr &B, Index n1)\n{\n  Index n = A.rows();\n  if(n>100)\n  {\n    // If the matrices are large enough, let's exploit the sparse structure of A by\n    // splitting it in half (wrt n1), and packing the non-zero columns.\n    Index n2 = n - n1;\n    Map<MatrixXr> A1(m_workspace.data()      , n1, n);\n    Map<MatrixXr> A2(m_workspace.data()+ n1*n, n2, n);\n    Map<MatrixXr> B1(m_workspace.data()+  n*n, n,  n);\n    Map<MatrixXr> B2(m_workspace.data()+2*n*n, n,  n);\n    Index k1=0, k2=0;\n    for(Index j=0; j<n; ++j)\n    {\n      if( (A.col(j).head(n1).array()!=Literal(0)).any() )\n      {\n        A1.col(k1) = A.col(j).head(n1);\n        B1.row(k1) = B.row(j);\n        ++k1;\n      }\n      if( (A.col(j).tail(n2).array()!=Literal(0)).any() )\n      {\n        A2.col(k2) = A.col(j).tail(n2);\n        B2.row(k2) = B.row(j);\n        ++k2;\n      }\n    }\n  \n    A.topRows(n1).noalias()    = A1.leftCols(k1) * B1.topRows(k1);\n    A.bottomRows(n2).noalias() = A2.leftCols(k2) * B2.topRows(k2);\n  }\n  else\n  {\n    Map<MatrixXr,Aligned> tmp(m_workspace.data(),n,n);\n    tmp.noalias() = A*B;\n    A = tmp;\n  }\n}\n\n// The divide algorithm is done \"in place\", we are always working on subsets of the same matrix. The divide methods takes as argument the \n// place of the submatrix we are currently working on.\n\n//@param firstCol : The Index of the first column of the submatrix of m_computed and for m_naiveU;\n//@param lastCol : The Index of the last column of the submatrix of m_computed and for m_naiveU; \n// lastCol + 1 - firstCol is the size of the submatrix.\n//@param firstRowW : The Index of the first row of the matrix W that we are to change. (see the reference paper section 1 for more information on W)\n//@param firstRowW : Same as firstRowW with the column.\n//@param shift : Each time one takes the left submatrix, one must add 1 to the shift. Why? Because! We actually want the last column of the U submatrix \n// to become the first column (*coeff) and to shift all the other columns to the right. There are more details on the reference paper.\ntemplate<typename MatrixType>\nvoid BDCSVD<MatrixType>::divide (Index firstCol, Index lastCol, Index firstRowW, Index firstColW, Index shift)\n{\n  // requires rows = cols + 1;\n  using std::pow;\n  using std::sqrt;\n  using std::abs;\n  const Index n = lastCol - firstCol + 1;\n  const Index k = n/2;\n  const RealScalar considerZero = (std::numeric_limits<RealScalar>::min)();\n  RealScalar alphaK;\n  RealScalar betaK; \n  RealScalar r0; \n  RealScalar lambda, phi, c0, s0;\n  VectorType l, f;\n  // We use the other algorithm which is more efficient for small \n  // matrices.\n  if (n < m_algoswap)\n  {\n    // FIXME this line involves temporaries\n    JacobiSVD<MatrixXr> b(m_computed.block(firstCol, firstCol, n + 1, n), ComputeFullU | (m_compV ? ComputeFullV : 0));\n    if (m_compU)\n      m_naiveU.block(firstCol, firstCol, n + 1, n + 1).real() = b.matrixU();\n    else \n    {\n      m_naiveU.row(0).segment(firstCol, n + 1).real() = b.matrixU().row(0);\n      m_naiveU.row(1).segment(firstCol, n + 1).real() = b.matrixU().row(n);\n    }\n    if (m_compV) m_naiveV.block(firstRowW, firstColW, n, n).real() = b.matrixV();\n    m_computed.block(firstCol + shift, firstCol + shift, n + 1, n).setZero();\n    m_computed.diagonal().segment(firstCol + shift, n) = b.singularValues().head(n);\n    return;\n  }\n  // We use the divide and conquer algorithm\n  alphaK =  m_computed(firstCol + k, firstCol + k);\n  betaK = m_computed(firstCol + k + 1, firstCol + k);\n  // The divide must be done in that order in order to have good results. Divide change the data inside the submatrices\n  // and the divide of the right submatrice reads one column of the left submatrice. That's why we need to treat the \n  // right submatrix before the left one. \n  divide(k + 1 + firstCol, lastCol, k + 1 + firstRowW, k + 1 + firstColW, shift);\n  divide(firstCol, k - 1 + firstCol, firstRowW, firstColW + 1, shift + 1);\n\n  if (m_compU)\n  {\n    lambda = m_naiveU(firstCol + k, firstCol + k);\n    phi = m_naiveU(firstCol + k + 1, lastCol + 1);\n  } \n  else \n  {\n    lambda = m_naiveU(1, firstCol + k);\n    phi = m_naiveU(0, lastCol + 1);\n  }\n  r0 = sqrt((abs(alphaK * lambda) * abs(alphaK * lambda)) + abs(betaK * phi) * abs(betaK * phi));\n  if (m_compU)\n  {\n    l = m_naiveU.row(firstCol + k).segment(firstCol, k);\n    f = m_naiveU.row(firstCol + k + 1).segment(firstCol + k + 1, n - k - 1);\n  } \n  else \n  {\n    l = m_naiveU.row(1).segment(firstCol, k);\n    f = m_naiveU.row(0).segment(firstCol + k + 1, n - k - 1);\n  }\n  if (m_compV) m_naiveV(firstRowW+k, firstColW) = Literal(1);\n  if (r0<considerZero)\n  {\n    c0 = Literal(1);\n    s0 = Literal(0);\n  }\n  else\n  {\n    c0 = alphaK * lambda / r0;\n    s0 = betaK * phi / r0;\n  }\n  \n#ifdef EIGEN_BDCSVD_SANITY_CHECKS\n  assert(m_naiveU.allFinite());\n  assert(m_naiveV.allFinite());\n  assert(m_computed.allFinite());\n#endif\n  \n  if (m_compU)\n  {\n    MatrixXr q1 (m_naiveU.col(firstCol + k).segment(firstCol, k + 1));     \n    // we shiftW Q1 to the right\n    for (Index i = firstCol + k - 1; i >= firstCol; i--) \n      m_naiveU.col(i + 1).segment(firstCol, k + 1) = m_naiveU.col(i).segment(firstCol, k + 1);\n    // we shift q1 at the left with a factor c0\n    m_naiveU.col(firstCol).segment( firstCol, k + 1) = (q1 * c0);\n    // last column = q1 * - s0\n    m_naiveU.col(lastCol + 1).segment(firstCol, k + 1) = (q1 * ( - s0));\n    // first column = q2 * s0\n    m_naiveU.col(firstCol).segment(firstCol + k + 1, n - k) = m_naiveU.col(lastCol + 1).segment(firstCol + k + 1, n - k) * s0; \n    // q2 *= c0\n    m_naiveU.col(lastCol + 1).segment(firstCol + k + 1, n - k) *= c0;\n  } \n  else \n  {\n    RealScalar q1 = m_naiveU(0, firstCol + k);\n    // we shift Q1 to the right\n    for (Index i = firstCol + k - 1; i >= firstCol; i--) \n      m_naiveU(0, i + 1) = m_naiveU(0, i);\n    // we shift q1 at the left with a factor c0\n    m_naiveU(0, firstCol) = (q1 * c0);\n    // last column = q1 * - s0\n    m_naiveU(0, lastCol + 1) = (q1 * ( - s0));\n    // first column = q2 * s0\n    m_naiveU(1, firstCol) = m_naiveU(1, lastCol + 1) *s0; \n    // q2 *= c0\n    m_naiveU(1, lastCol + 1) *= c0;\n    m_naiveU.row(1).segment(firstCol + 1, k).setZero();\n    m_naiveU.row(0).segment(firstCol + k + 1, n - k - 1).setZero();\n  }\n  \n#ifdef EIGEN_BDCSVD_SANITY_CHECKS\n  assert(m_naiveU.allFinite());\n  assert(m_naiveV.allFinite());\n  assert(m_computed.allFinite());\n#endif\n  \n  m_computed(firstCol + shift, firstCol + shift) = r0;\n  m_computed.col(firstCol + shift).segment(firstCol + shift + 1, k) = alphaK * l.transpose().real();\n  m_computed.col(firstCol + shift).segment(firstCol + shift + k + 1, n - k - 1) = betaK * f.transpose().real();\n\n#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE\n  ArrayXr tmp1 = (m_computed.block(firstCol+shift, firstCol+shift, n, n)).jacobiSvd().singularValues();\n#endif\n  // Second part: try to deflate singular values in combined matrix\n  deflation(firstCol, lastCol, k, firstRowW, firstColW, shift);\n#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE\n  ArrayXr tmp2 = (m_computed.block(firstCol+shift, firstCol+shift, n, n)).jacobiSvd().singularValues();\n  std::cout << \"\\n\\nj1 = \" << tmp1.transpose().format(bdcsvdfmt) << \"\\n\";\n  std::cout << \"j2 = \" << tmp2.transpose().format(bdcsvdfmt) << \"\\n\\n\";\n  std::cout << \"err:      \" << ((tmp1-tmp2).abs()>1e-12*tmp2.abs()).transpose() << \"\\n\";\n  static int count = 0;\n  std::cout << \"# \" << ++count << \"\\n\\n\";\n  assert((tmp1-tmp2).matrix().norm() < 1e-14*tmp2.matrix().norm());\n//   assert(count<681);\n//   assert(((tmp1-tmp2).abs()<1e-13*tmp2.abs()).all());\n#endif\n  \n  // Third part: compute SVD of combined matrix\n  MatrixXr UofSVD, VofSVD;\n  VectorType singVals;\n  computeSVDofM(firstCol + shift, n, UofSVD, singVals, VofSVD);\n  \n#ifdef EIGEN_BDCSVD_SANITY_CHECKS\n  assert(UofSVD.allFinite());\n  assert(VofSVD.allFinite());\n#endif\n  \n  if (m_compU)\n    structured_update(m_naiveU.block(firstCol, firstCol, n + 1, n + 1), UofSVD, (n+2)/2);\n  else\n  {\n    Map<Matrix<RealScalar,2,Dynamic>,Aligned> tmp(m_workspace.data(),2,n+1);\n    tmp.noalias() = m_naiveU.middleCols(firstCol, n+1) * UofSVD;\n    m_naiveU.middleCols(firstCol, n + 1) = tmp;\n  }\n  \n  if (m_compV)  structured_update(m_naiveV.block(firstRowW, firstColW, n, n), VofSVD, (n+1)/2);\n  \n#ifdef EIGEN_BDCSVD_SANITY_CHECKS\n  assert(m_naiveU.allFinite());\n  assert(m_naiveV.allFinite());\n  assert(m_computed.allFinite());\n#endif\n  \n  m_computed.block(firstCol + shift, firstCol + shift, n, n).setZero();\n  m_computed.block(firstCol + shift, firstCol + shift, n, n).diagonal() = singVals;\n}// end divide\n\n// Compute SVD of m_computed.block(firstCol, firstCol, n + 1, n); this block only has non-zeros in\n// the first column and on the diagonal and has undergone deflation, so diagonal is in increasing\n// order except for possibly the (0,0) entry. The computed SVD is stored U, singVals and V, except\n// that if m_compV is false, then V is not computed. Singular values are sorted in decreasing order.\n//\n// TODO Opportunities for optimization: better root finding algo, better stopping criterion, better\n// handling of round-off errors, be consistent in ordering\n// For instance, to solve the secular equation using FMM, see http://www.stat.uchicago.edu/~lekheng/courses/302/classics/greengard-rokhlin.pdf\ntemplate <typename MatrixType>\nvoid BDCSVD<MatrixType>::computeSVDofM(Index firstCol, Index n, MatrixXr& U, VectorType& singVals, MatrixXr& V)\n{\n  const RealScalar considerZero = (std::numeric_limits<RealScalar>::min)();\n  using std::abs;\n  ArrayRef col0 = m_computed.col(firstCol).segment(firstCol, n);\n  m_workspace.head(n) =  m_computed.block(firstCol, firstCol, n, n).diagonal();\n  ArrayRef diag = m_workspace.head(n);\n  diag(0) = Literal(0);\n\n  // Allocate space for singular values and vectors\n  singVals.resize(n);\n  U.resize(n+1, n+1);\n  if (m_compV) V.resize(n, n);\n\n#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE\n  if (col0.hasNaN() || diag.hasNaN())\n    std::cout << \"\\n\\nHAS NAN\\n\\n\";\n#endif\n  \n  // Many singular values might have been deflated, the zero ones have been moved to the end,\n  // but others are interleaved and we must ignore them at this stage.\n  // To this end, let's compute a permutation skipping them:\n  Index actual_n = n;\n  while(actual_n>1 && diag(actual_n-1)==Literal(0)) --actual_n;\n  Index m = 0; // size of the deflated problem\n  for(Index k=0;k<actual_n;++k)\n    if(abs(col0(k))>considerZero)\n      m_workspaceI(m++) = k;\n  Map<ArrayXi> perm(m_workspaceI.data(),m);\n  \n  Map<ArrayXr> shifts(m_workspace.data()+1*n, n);\n  Map<ArrayXr> mus(m_workspace.data()+2*n, n);\n  Map<ArrayXr> zhat(m_workspace.data()+3*n, n);\n\n#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE\n  std::cout << \"computeSVDofM using:\\n\";\n  std::cout << \"  z: \" << col0.transpose() << \"\\n\";\n  std::cout << \"  d: \" << diag.transpose() << \"\\n\";\n#endif\n  \n  // Compute singVals, shifts, and mus\n  computeSingVals(col0, diag, perm, singVals, shifts, mus);\n  \n#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE\n  std::cout << \"  j:        \" << (m_computed.block(firstCol, firstCol, n, n)).jacobiSvd().singularValues().transpose().reverse() << \"\\n\\n\";\n  std::cout << \"  sing-val: \" << singVals.transpose() << \"\\n\";\n  std::cout << \"  mu:       \" << mus.transpose() << \"\\n\";\n  std::cout << \"  shift:    \" << shifts.transpose() << \"\\n\";\n  \n  {\n    Index actual_n = n;\n    while(actual_n>1 && abs(col0(actual_n-1))<considerZero) --actual_n;\n    std::cout << \"\\n\\n    mus:    \" << mus.head(actual_n).transpose() << \"\\n\\n\";\n    std::cout << \"    check1 (expect0) : \" << ((singVals.array()-(shifts+mus)) / singVals.array()).head(actual_n).transpose() << \"\\n\\n\";\n    std::cout << \"    check2 (>0)      : \" << ((singVals.array()-diag) / singVals.array()).head(actual_n).transpose() << \"\\n\\n\";\n    std::cout << \"    check3 (>0)      : \" << ((diag.segment(1,actual_n-1)-singVals.head(actual_n-1).array()) / singVals.head(actual_n-1).array()).transpose() << \"\\n\\n\\n\";\n    std::cout << \"    check4 (>0)      : \" << ((singVals.segment(1,actual_n-1)-singVals.head(actual_n-1))).transpose() << \"\\n\\n\\n\";\n  }\n#endif\n  \n#ifdef EIGEN_BDCSVD_SANITY_CHECKS\n  assert(singVals.allFinite());\n  assert(mus.allFinite());\n  assert(shifts.allFinite());\n#endif\n  \n  // Compute zhat\n  perturbCol0(col0, diag, perm, singVals, shifts, mus, zhat);\n#ifdef  EIGEN_BDCSVD_DEBUG_VERBOSE\n  std::cout << \"  zhat: \" << zhat.transpose() << \"\\n\";\n#endif\n  \n#ifdef EIGEN_BDCSVD_SANITY_CHECKS\n  assert(zhat.allFinite());\n#endif\n  \n  computeSingVecs(zhat, diag, perm, singVals, shifts, mus, U, V);\n  \n#ifdef  EIGEN_BDCSVD_DEBUG_VERBOSE\n  std::cout << \"U^T U: \" << (U.transpose() * U - MatrixXr(MatrixXr::Identity(U.cols(),U.cols()))).norm() << \"\\n\";\n  std::cout << \"V^T V: \" << (V.transpose() * V - MatrixXr(MatrixXr::Identity(V.cols(),V.cols()))).norm() << \"\\n\";\n#endif\n  \n#ifdef EIGEN_BDCSVD_SANITY_CHECKS\n  assert(U.allFinite());\n  assert(V.allFinite());\n  assert((U.transpose() * U - MatrixXr(MatrixXr::Identity(U.cols(),U.cols()))).norm() < 1e-14 * n);\n  assert((V.transpose() * V - MatrixXr(MatrixXr::Identity(V.cols(),V.cols()))).norm() < 1e-14 * n);\n  assert(m_naiveU.allFinite());\n  assert(m_naiveV.allFinite());\n  assert(m_computed.allFinite());\n#endif\n  \n  // Because of deflation, the singular values might not be completely sorted.\n  // Fortunately, reordering them is a O(n) problem\n  for(Index i=0; i<actual_n-1; ++i)\n  {\n    if(singVals(i)>singVals(i+1))\n    {\n      using std::swap;\n      swap(singVals(i),singVals(i+1));\n      U.col(i).swap(U.col(i+1));\n      if(m_compV) V.col(i).swap(V.col(i+1));\n    }\n  }\n  \n  // Reverse order so that singular values in increased order\n  // Because of deflation, the zeros singular-values are already at the end\n  singVals.head(actual_n).reverseInPlace();\n  U.leftCols(actual_n).rowwise().reverseInPlace();\n  if (m_compV) V.leftCols(actual_n).rowwise().reverseInPlace();\n  \n#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE\n  JacobiSVD<MatrixXr> jsvd(m_computed.block(firstCol, firstCol, n, n) );\n  std::cout << \"  * j:        \" << jsvd.singularValues().transpose() << \"\\n\\n\";\n  std::cout << \"  * sing-val: \" << singVals.transpose() << \"\\n\";\n//   std::cout << \"  * err:      \" << ((jsvd.singularValues()-singVals)>1e-13*singVals.norm()).transpose() << \"\\n\";\n#endif\n}\n\ntemplate <typename MatrixType>\ntypename BDCSVD<MatrixType>::RealScalar BDCSVD<MatrixType>::secularEq(RealScalar mu, const ArrayRef& col0, const ArrayRef& diag, const IndicesRef &perm, const ArrayRef& diagShifted, RealScalar shift)\n{\n  Index m = perm.size();\n  RealScalar res = Literal(1);\n  for(Index i=0; i<m; ++i)\n  {\n    Index j = perm(i);\n    // The following expression could be rewritten to involve only a single division,\n    // but this would make the expression more sensitive to overflow.\n    res += (col0(j) / (diagShifted(j) - mu)) * (col0(j) / (diag(j) + shift + mu));\n  }\n  return res;\n\n}\n\ntemplate <typename MatrixType>\nvoid BDCSVD<MatrixType>::computeSingVals(const ArrayRef& col0, const ArrayRef& diag, const IndicesRef &perm,\n                                         VectorType& singVals, ArrayRef shifts, ArrayRef mus)\n{\n  using std::abs;\n  using std::swap;\n  using std::sqrt;\n\n  Index n = col0.size();\n  Index actual_n = n;\n  // Note that here actual_n is computed based on col0(i)==0 instead of diag(i)==0 as above\n  // because 1) we have diag(i)==0 => col0(i)==0 and 2) if col0(i)==0, then diag(i) is already a singular value.\n  while(actual_n>1 && col0(actual_n-1)==Literal(0)) --actual_n;\n\n  for (Index k = 0; k < n; ++k)\n  {\n    if (col0(k) == Literal(0) || actual_n==1)\n    {\n      // if col0(k) == 0, then entry is deflated, so singular value is on diagonal\n      // if actual_n==1, then the deflated problem is already diagonalized\n      singVals(k) = k==0 ? col0(0) : diag(k);\n      mus(k) = Literal(0);\n      shifts(k) = k==0 ? col0(0) : diag(k);\n      continue;\n    } \n\n    // otherwise, use secular equation to find singular value\n    RealScalar left = diag(k);\n    RealScalar right; // was: = (k != actual_n-1) ? diag(k+1) : (diag(actual_n-1) + col0.matrix().norm());\n    if(k==actual_n-1)\n      right = (diag(actual_n-1) + col0.matrix().norm());\n    else\n    {\n      // Skip deflated singular values,\n      // recall that at this stage we assume that z[j]!=0 and all entries for which z[j]==0 have been put aside.\n      // This should be equivalent to using perm[]\n      Index l = k+1;\n      while(col0(l)==Literal(0)) { ++l; eigen_internal_assert(l<actual_n); }\n      right = diag(l);\n    }\n\n    // first decide whether it's closer to the left end or the right end\n    RealScalar mid = left + (right-left) / Literal(2);\n    RealScalar fMid = secularEq(mid, col0, diag, perm, diag, Literal(0));\n#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE\n    std::cout << right-left << \"\\n\";\n    std::cout << \"fMid = \" << fMid << \" \" << secularEq(mid-left, col0, diag, perm, diag-left, left) << \" \" << secularEq(mid-right, col0, diag, perm, diag-right, right)   << \"\\n\";\n    std::cout << \"     = \" << secularEq(0.1*(left+right), col0, diag, perm, diag, 0)\n              << \" \"       << secularEq(0.2*(left+right), col0, diag, perm, diag, 0)\n              << \" \"       << secularEq(0.3*(left+right), col0, diag, perm, diag, 0)\n              << \" \"       << secularEq(0.4*(left+right), col0, diag, perm, diag, 0)\n              << \" \"       << secularEq(0.49*(left+right), col0, diag, perm, diag, 0)\n              << \" \"       << secularEq(0.5*(left+right), col0, diag, perm, diag, 0)\n              << \" \"       << secularEq(0.51*(left+right), col0, diag, perm, diag, 0)\n              << \" \"       << secularEq(0.6*(left+right), col0, diag, perm, diag, 0)\n              << \" \"       << secularEq(0.7*(left+right), col0, diag, perm, diag, 0)\n              << \" \"       << secularEq(0.8*(left+right), col0, diag, perm, diag, 0)\n              << \" \"       << secularEq(0.9*(left+right), col0, diag, perm, diag, 0) << \"\\n\";\n#endif\n    RealScalar shift = (k == actual_n-1 || fMid > Literal(0)) ? left : right;\n    \n    // measure everything relative to shift\n    Map<ArrayXr> diagShifted(m_workspace.data()+4*n, n);\n    diagShifted = diag - shift;\n    \n    // initial guess\n    RealScalar muPrev, muCur;\n    if (shift == left)\n    {\n      muPrev = (right - left) * RealScalar(0.1);\n      if (k == actual_n-1) muCur = right - left;\n      else                 muCur = (right - left) * RealScalar(0.5);\n    }\n    else\n    {\n      muPrev = -(right - left) * RealScalar(0.1);\n      muCur = -(right - left) * RealScalar(0.5);\n    }\n\n    RealScalar fPrev = secularEq(muPrev, col0, diag, perm, diagShifted, shift);\n    RealScalar fCur = secularEq(muCur, col0, diag, perm, diagShifted, shift);\n    if (abs(fPrev) < abs(fCur))\n    {\n      swap(fPrev, fCur);\n      swap(muPrev, muCur);\n    }\n\n    // rational interpolation: fit a function of the form a / mu + b through the two previous\n    // iterates and use its zero to compute the next iterate\n    bool useBisection = fPrev*fCur>Literal(0);\n    while (fCur!=Literal(0) && abs(muCur - muPrev) > Literal(8) * NumTraits<RealScalar>::epsilon() * numext::maxi<RealScalar>(abs(muCur), abs(muPrev)) && abs(fCur - fPrev)>NumTraits<RealScalar>::epsilon() && !useBisection)\n    {\n      ++m_numIters;\n\n      // Find a and b such that the function f(mu) = a / mu + b matches the current and previous samples.\n      RealScalar a = (fCur - fPrev) / (Literal(1)/muCur - Literal(1)/muPrev);\n      RealScalar b = fCur - a / muCur;\n      // And find mu such that f(mu)==0:\n      RealScalar muZero = -a/b;\n      RealScalar fZero = secularEq(muZero, col0, diag, perm, diagShifted, shift);\n      \n      muPrev = muCur;\n      fPrev = fCur;\n      muCur = muZero;\n      fCur = fZero;\n      \n      \n      if (shift == left  && (muCur < Literal(0) || muCur > right - left)) useBisection = true;\n      if (shift == right && (muCur < -(right - left) || muCur > Literal(0))) useBisection = true;\n      if (abs(fCur)>abs(fPrev)) useBisection = true;\n    }\n\n    // fall back on bisection method if rational interpolation did not work\n    if (useBisection)\n    {\n#ifdef  EIGEN_BDCSVD_DEBUG_VERBOSE\n      std::cout << \"useBisection for k = \" << k << \", actual_n = \" << actual_n << \"\\n\";\n#endif\n      RealScalar leftShifted, rightShifted;\n      if (shift == left)\n      {\n        // to avoid overflow, we must have mu > max(real_min, |z(k)|/sqrt(real_max)),\n        // the factor 2 is to be more conservative\n        leftShifted = numext::maxi<RealScalar>( (std::numeric_limits<RealScalar>::min)(), Literal(2) * abs(col0(k)) / sqrt((std::numeric_limits<RealScalar>::max)()) );\n\n        // check that we did it right:\n        eigen_internal_assert( (numext::isfinite)( (col0(k)/leftShifted)*(col0(k)/(diag(k)+shift+leftShifted)) ) );\n        // I don't understand why the case k==0 would be special there:\n        // if (k == 0) rightShifted = right - left; else\n        rightShifted = (k==actual_n-1) ? right : ((right - left) * RealScalar(0.51)); // theoretically we can take 0.5, but let's be safe\n      }\n      else\n      {\n        leftShifted = -(right - left) * RealScalar(0.51);\n        if(k+1<n)\n          rightShifted = -numext::maxi<RealScalar>( (std::numeric_limits<RealScalar>::min)(), abs(col0(k+1)) / sqrt((std::numeric_limits<RealScalar>::max)()) );\n        else\n          rightShifted = -(std::numeric_limits<RealScalar>::min)();\n      }\n      \n      RealScalar fLeft = secularEq(leftShifted, col0, diag, perm, diagShifted, shift);\n\n#if defined EIGEN_INTERNAL_DEBUGGING || defined EIGEN_BDCSVD_DEBUG_VERBOSE\n      RealScalar fRight = secularEq(rightShifted, col0, diag, perm, diagShifted, shift);\n#endif\n\n#ifdef  EIGEN_BDCSVD_DEBUG_VERBOSE\n      if(!(fLeft * fRight<0))\n      {\n        std::cout << \"fLeft: \" << leftShifted << \" - \" << diagShifted.head(10).transpose()  << \"\\n ; \" << bool(left==shift) << \" \" << (left-shift) << \"\\n\";\n        std::cout << k << \" : \" <<  fLeft << \" * \" << fRight << \" == \" << fLeft * fRight << \"  ;  \" << left << \" - \" << right << \" -> \" <<  leftShifted << \" \" << rightShifted << \"   shift=\" << shift << \"\\n\";\n      }\n#endif\n      eigen_internal_assert(fLeft * fRight < Literal(0));\n      \n      while (rightShifted - leftShifted > Literal(2) * NumTraits<RealScalar>::epsilon() * numext::maxi<RealScalar>(abs(leftShifted), abs(rightShifted)))\n      {\n        RealScalar midShifted = (leftShifted + rightShifted) / Literal(2);\n        fMid = secularEq(midShifted, col0, diag, perm, diagShifted, shift);\n        if (fLeft * fMid < Literal(0))\n        {\n          rightShifted = midShifted;\n        }\n        else\n        {\n          leftShifted = midShifted;\n          fLeft = fMid;\n        }\n      }\n\n      muCur = (leftShifted + rightShifted) / Literal(2);\n    }\n      \n    singVals[k] = shift + muCur;\n    shifts[k] = shift;\n    mus[k] = muCur;\n\n    // perturb singular value slightly if it equals diagonal entry to avoid division by zero later\n    // (deflation is supposed to avoid this from happening)\n    // - this does no seem to be necessary anymore -\n//     if (singVals[k] == left) singVals[k] *= 1 + NumTraits<RealScalar>::epsilon();\n//     if (singVals[k] == right) singVals[k] *= 1 - NumTraits<RealScalar>::epsilon();\n  }\n}\n\n\n// zhat is perturbation of col0 for which singular vectors can be computed stably (see Section 3.1)\ntemplate <typename MatrixType>\nvoid BDCSVD<MatrixType>::perturbCol0\n   (const ArrayRef& col0, const ArrayRef& diag, const IndicesRef &perm, const VectorType& singVals,\n    const ArrayRef& shifts, const ArrayRef& mus, ArrayRef zhat)\n{\n  using std::sqrt;\n  Index n = col0.size();\n  Index m = perm.size();\n  if(m==0)\n  {\n    zhat.setZero();\n    return;\n  }\n  Index last = perm(m-1);\n  // The offset permits to skip deflated entries while computing zhat\n  for (Index k = 0; k < n; ++k)\n  {\n    if (col0(k) == Literal(0)) // deflated\n      zhat(k) = Literal(0);\n    else\n    {\n      // see equation (3.6)\n      RealScalar dk = diag(k);\n      RealScalar prod = (singVals(last) + dk) * (mus(last) + (shifts(last) - dk));\n\n      for(Index l = 0; l<m; ++l)\n      {\n        Index i = perm(l);\n        if(i!=k)\n        {\n          Index j = i<k ? i : perm(l-1);\n          prod *= ((singVals(j)+dk) / ((diag(i)+dk))) * ((mus(j)+(shifts(j)-dk)) / ((diag(i)-dk)));\n#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE\n          if(i!=k && std::abs(((singVals(j)+dk)*(mus(j)+(shifts(j)-dk)))/((diag(i)+dk)*(diag(i)-dk)) - 1) > 0.9 )\n            std::cout << \"     \" << ((singVals(j)+dk)*(mus(j)+(shifts(j)-dk)))/((diag(i)+dk)*(diag(i)-dk)) << \" == (\" << (singVals(j)+dk) << \" * \" << (mus(j)+(shifts(j)-dk))\n                       << \") / (\" << (diag(i)+dk) << \" * \" << (diag(i)-dk) << \")\\n\";\n#endif\n        }\n      }\n#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE\n      std::cout << \"zhat(\" << k << \") =  sqrt( \" << prod << \")  ;  \" << (singVals(last) + dk) << \" * \" << mus(last) + shifts(last) << \" - \" << dk << \"\\n\";\n#endif\n      RealScalar tmp = sqrt(prod);\n      zhat(k) = col0(k) > Literal(0) ? tmp : -tmp;\n    }\n  }\n}\n\n// compute singular vectors\ntemplate <typename MatrixType>\nvoid BDCSVD<MatrixType>::computeSingVecs\n   (const ArrayRef& zhat, const ArrayRef& diag, const IndicesRef &perm, const VectorType& singVals,\n    const ArrayRef& shifts, const ArrayRef& mus, MatrixXr& U, MatrixXr& V)\n{\n  Index n = zhat.size();\n  Index m = perm.size();\n  \n  for (Index k = 0; k < n; ++k)\n  {\n    if (zhat(k) == Literal(0))\n    {\n      U.col(k) = VectorType::Unit(n+1, k);\n      if (m_compV) V.col(k) = VectorType::Unit(n, k);\n    }\n    else\n    {\n      U.col(k).setZero();\n      for(Index l=0;l<m;++l)\n      {\n        Index i = perm(l);\n        U(i,k) = zhat(i)/(((diag(i) - shifts(k)) - mus(k)) )/( (diag(i) + singVals[k]));\n      }\n      U(n,k) = Literal(0);\n      U.col(k).normalize();\n    \n      if (m_compV)\n      {\n        V.col(k).setZero();\n        for(Index l=1;l<m;++l)\n        {\n          Index i = perm(l);\n          V(i,k) = diag(i) * zhat(i) / (((diag(i) - shifts(k)) - mus(k)) )/( (diag(i) + singVals[k]));\n        }\n        V(0,k) = Literal(-1);\n        V.col(k).normalize();\n      }\n    }\n  }\n  U.col(n) = VectorType::Unit(n+1, n);\n}\n\n\n// page 12_13\n// i >= 1, di almost null and zi non null.\n// We use a rotation to zero out zi applied to the left of M\ntemplate <typename MatrixType>\nvoid BDCSVD<MatrixType>::deflation43(Index firstCol, Index shift, Index i, Index size)\n{\n  using std::abs;\n  using std::sqrt;\n  using std::pow;\n  Index start = firstCol + shift;\n  RealScalar c = m_computed(start, start);\n  RealScalar s = m_computed(start+i, start);\n  RealScalar r = numext::hypot(c,s);\n  if (r == Literal(0))\n  {\n    m_computed(start+i, start+i) = Literal(0);\n    return;\n  }\n  m_computed(start,start) = r;  \n  m_computed(start+i, start) = Literal(0);\n  m_computed(start+i, start+i) = Literal(0);\n  \n  JacobiRotation<RealScalar> J(c/r,-s/r);\n  if (m_compU)  m_naiveU.middleRows(firstCol, size+1).applyOnTheRight(firstCol, firstCol+i, J);\n  else          m_naiveU.applyOnTheRight(firstCol, firstCol+i, J);\n}// end deflation 43\n\n\n// page 13\n// i,j >= 1, i!=j and |di - dj| < epsilon * norm2(M)\n// We apply two rotations to have zj = 0;\n// TODO deflation44 is still broken and not properly tested\ntemplate <typename MatrixType>\nvoid BDCSVD<MatrixType>::deflation44(Index firstColu , Index firstColm, Index firstRowW, Index firstColW, Index i, Index j, Index size)\n{\n  using std::abs;\n  using std::sqrt;\n  using std::conj;\n  using std::pow;\n  RealScalar c = m_computed(firstColm+i, firstColm);\n  RealScalar s = m_computed(firstColm+j, firstColm);\n  RealScalar r = sqrt(numext::abs2(c) + numext::abs2(s));\n#ifdef  EIGEN_BDCSVD_DEBUG_VERBOSE\n  std::cout << \"deflation 4.4: \" << i << \",\" << j << \" -> \" << c << \" \" << s << \" \" << r << \" ; \"\n    << m_computed(firstColm + i-1, firstColm)  << \" \"\n    << m_computed(firstColm + i, firstColm)  << \" \"\n    << m_computed(firstColm + i+1, firstColm) << \" \"\n    << m_computed(firstColm + i+2, firstColm) << \"\\n\";\n  std::cout << m_computed(firstColm + i-1, firstColm + i-1)  << \" \"\n    << m_computed(firstColm + i, firstColm+i)  << \" \"\n    << m_computed(firstColm + i+1, firstColm+i+1) << \" \"\n    << m_computed(firstColm + i+2, firstColm+i+2) << \"\\n\";\n#endif\n  if (r==Literal(0))\n  {\n    m_computed(firstColm + i, firstColm + i) = m_computed(firstColm + j, firstColm + j);\n    return;\n  }\n  c/=r;\n  s/=r;\n  m_computed(firstColm + i, firstColm) = r;  \n  m_computed(firstColm + j, firstColm + j) = m_computed(firstColm + i, firstColm + i);\n  m_computed(firstColm + j, firstColm) = Literal(0);\n\n  JacobiRotation<RealScalar> J(c,-s);\n  if (m_compU)  m_naiveU.middleRows(firstColu, size+1).applyOnTheRight(firstColu + i, firstColu + j, J);\n  else          m_naiveU.applyOnTheRight(firstColu+i, firstColu+j, J);\n  if (m_compV)  m_naiveV.middleRows(firstRowW, size).applyOnTheRight(firstColW + i, firstColW + j, J);\n}// end deflation 44\n\n\n// acts on block from (firstCol+shift, firstCol+shift) to (lastCol+shift, lastCol+shift) [inclusive]\ntemplate <typename MatrixType>\nvoid BDCSVD<MatrixType>::deflation(Index firstCol, Index lastCol, Index k, Index firstRowW, Index firstColW, Index shift)\n{\n  using std::sqrt;\n  using std::abs;\n  const Index length = lastCol + 1 - firstCol;\n  \n  Block<MatrixXr,Dynamic,1> col0(m_computed, firstCol+shift, firstCol+shift, length, 1);\n  Diagonal<MatrixXr> fulldiag(m_computed);\n  VectorBlock<Diagonal<MatrixXr>,Dynamic> diag(fulldiag, firstCol+shift, length);\n  \n  const RealScalar considerZero = (std::numeric_limits<RealScalar>::min)();\n  RealScalar maxDiag = diag.tail((std::max)(Index(1),length-1)).cwiseAbs().maxCoeff();\n  RealScalar epsilon_strict = numext::maxi<RealScalar>(considerZero,NumTraits<RealScalar>::epsilon() * maxDiag);\n  RealScalar epsilon_coarse = Literal(8) * NumTraits<RealScalar>::epsilon() * numext::maxi<RealScalar>(col0.cwiseAbs().maxCoeff(), maxDiag);\n  \n#ifdef EIGEN_BDCSVD_SANITY_CHECKS\n  assert(m_naiveU.allFinite());\n  assert(m_naiveV.allFinite());\n  assert(m_computed.allFinite());\n#endif\n\n#ifdef  EIGEN_BDCSVD_DEBUG_VERBOSE  \n  std::cout << \"\\ndeflate:\" << diag.head(k+1).transpose() << \"  |  \" << diag.segment(k+1,length-k-1).transpose() << \"\\n\";\n#endif\n  \n  //condition 4.1\n  if (diag(0) < epsilon_coarse)\n  { \n#ifdef  EIGEN_BDCSVD_DEBUG_VERBOSE\n    std::cout << \"deflation 4.1, because \" << diag(0) << \" < \" << epsilon_coarse << \"\\n\";\n#endif\n    diag(0) = epsilon_coarse;\n  }\n\n  //condition 4.2\n  for (Index i=1;i<length;++i)\n    if (abs(col0(i)) < epsilon_strict)\n    {\n#ifdef  EIGEN_BDCSVD_DEBUG_VERBOSE\n      std::cout << \"deflation 4.2, set z(\" << i << \") to zero because \" << abs(col0(i)) << \" < \" << epsilon_strict << \"  (diag(\" << i << \")=\" << diag(i) << \")\\n\";\n#endif\n      col0(i) = Literal(0);\n    }\n\n  //condition 4.3\n  for (Index i=1;i<length; i++)\n    if (diag(i) < epsilon_coarse)\n    {\n#ifdef  EIGEN_BDCSVD_DEBUG_VERBOSE\n      std::cout << \"deflation 4.3, cancel z(\" << i << \")=\" << col0(i) << \" because diag(\" << i << \")=\" << diag(i) << \" < \" << epsilon_coarse << \"\\n\";\n#endif\n      deflation43(firstCol, shift, i, length);\n    }\n\n#ifdef EIGEN_BDCSVD_SANITY_CHECKS\n  assert(m_naiveU.allFinite());\n  assert(m_naiveV.allFinite());\n  assert(m_computed.allFinite());\n#endif\n#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE\n  std::cout << \"to be sorted: \" << diag.transpose() << \"\\n\\n\";\n#endif\n  {\n    // Check for total deflation\n    // If we have a total deflation, then we have to consider col0(0)==diag(0) as a singular value during sorting\n    bool total_deflation = (col0.tail(length-1).array()<considerZero).all();\n    \n    // Sort the diagonal entries, since diag(1:k-1) and diag(k:length) are already sorted, let's do a sorted merge.\n    // First, compute the respective permutation.\n    Index *permutation = m_workspaceI.data();\n    {\n      permutation[0] = 0;\n      Index p = 1;\n      \n      // Move deflated diagonal entries at the end.\n      for(Index i=1; i<length; ++i)\n        if(abs(diag(i))<considerZero)\n          permutation[p++] = i;\n        \n      Index i=1, j=k+1;\n      for( ; p < length; ++p)\n      {\n             if (i > k)             permutation[p] = j++;\n        else if (j >= length)       permutation[p] = i++;\n        else if (diag(i) < diag(j)) permutation[p] = j++;\n        else                        permutation[p] = i++;\n      }\n    }\n    \n    // If we have a total deflation, then we have to insert diag(0) at the right place\n    if(total_deflation)\n    {\n      for(Index i=1; i<length; ++i)\n      {\n        Index pi = permutation[i];\n        if(abs(diag(pi))<considerZero || diag(0)<diag(pi))\n          permutation[i-1] = permutation[i];\n        else\n        {\n          permutation[i-1] = 0;\n          break;\n        }\n      }\n    }\n    \n    // Current index of each col, and current column of each index\n    Index *realInd = m_workspaceI.data()+length;\n    Index *realCol = m_workspaceI.data()+2*length;\n    \n    for(int pos = 0; pos< length; pos++)\n    {\n      realCol[pos] = pos;\n      realInd[pos] = pos;\n    }\n    \n    for(Index i = total_deflation?0:1; i < length; i++)\n    {\n      const Index pi = permutation[length - (total_deflation ? i+1 : i)];\n      const Index J = realCol[pi];\n      \n      using std::swap;\n      // swap diagonal and first column entries:\n      swap(diag(i), diag(J));\n      if(i!=0 && J!=0) swap(col0(i), col0(J));\n\n      // change columns\n      if (m_compU) m_naiveU.col(firstCol+i).segment(firstCol, length + 1).swap(m_naiveU.col(firstCol+J).segment(firstCol, length + 1));\n      else         m_naiveU.col(firstCol+i).segment(0, 2)                .swap(m_naiveU.col(firstCol+J).segment(0, 2));\n      if (m_compV) m_naiveV.col(firstColW + i).segment(firstRowW, length).swap(m_naiveV.col(firstColW + J).segment(firstRowW, length));\n\n      //update real pos\n      const Index realI = realInd[i];\n      realCol[realI] = J;\n      realCol[pi] = i;\n      realInd[J] = realI;\n      realInd[i] = pi;\n    }\n  }\n#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE\n  std::cout << \"sorted: \" << diag.transpose().format(bdcsvdfmt) << \"\\n\";\n  std::cout << \"      : \" << col0.transpose() << \"\\n\\n\";\n#endif\n    \n  //condition 4.4\n  {\n    Index i = length-1;\n    while(i>0 && (abs(diag(i))<considerZero || abs(col0(i))<considerZero)) --i;\n    for(; i>1;--i)\n       if( (diag(i) - diag(i-1)) < NumTraits<RealScalar>::epsilon()*maxDiag )\n      {\n#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE\n        std::cout << \"deflation 4.4 with i = \" << i << \" because \" << (diag(i) - diag(i-1)) << \" < \" << NumTraits<RealScalar>::epsilon()*diag(i) << \"\\n\";\n#endif\n        eigen_internal_assert(abs(diag(i) - diag(i-1))<epsilon_coarse && \" diagonal entries are not properly sorted\");\n        deflation44(firstCol, firstCol + shift, firstRowW, firstColW, i-1, i, length);\n      }\n  }\n  \n#ifdef EIGEN_BDCSVD_SANITY_CHECKS\n  for(Index j=2;j<length;++j)\n    assert(diag(j-1)<=diag(j) || abs(diag(j))<considerZero);\n#endif\n  \n#ifdef EIGEN_BDCSVD_SANITY_CHECKS\n  assert(m_naiveU.allFinite());\n  assert(m_naiveV.allFinite());\n  assert(m_computed.allFinite());\n#endif\n}//end deflation\n\n#ifndef __CUDACC__\n/** \\svd_module\n  *\n  * \\return the singular value decomposition of \\c *this computed by Divide & Conquer algorithm\n  *\n  * \\sa class BDCSVD\n  */\ntemplate<typename Derived>\nBDCSVD<typename MatrixBase<Derived>::PlainObject>\nMatrixBase<Derived>::bdcSvd(unsigned int computationOptions) const\n{\n  return BDCSVD<PlainObject>(*this, computationOptions);\n}\n#endif\n\n} // end namespace Eigen\n\n#endif\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SVD/JacobiSVD.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2013-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_JACOBISVD_H\n#define EIGEN_JACOBISVD_H\n\nnamespace Eigen { \n\nnamespace internal {\n// forward declaration (needed by ICC)\n// the empty body is required by MSVC\ntemplate<typename MatrixType, int QRPreconditioner,\n         bool IsComplex = NumTraits<typename MatrixType::Scalar>::IsComplex>\nstruct svd_precondition_2x2_block_to_be_real {};\n\n/*** QR preconditioners (R-SVD)\n ***\n *** Their role is to reduce the problem of computing the SVD to the case of a square matrix.\n *** This approach, known as R-SVD, is an optimization for rectangular-enough matrices, and is a requirement for\n *** JacobiSVD which by itself is only able to work on square matrices.\n ***/\n\nenum { PreconditionIfMoreColsThanRows, PreconditionIfMoreRowsThanCols };\n\ntemplate<typename MatrixType, int QRPreconditioner, int Case>\nstruct qr_preconditioner_should_do_anything\n{\n  enum { a = MatrixType::RowsAtCompileTime != Dynamic &&\n             MatrixType::ColsAtCompileTime != Dynamic &&\n             MatrixType::ColsAtCompileTime <= MatrixType::RowsAtCompileTime,\n         b = MatrixType::RowsAtCompileTime != Dynamic &&\n             MatrixType::ColsAtCompileTime != Dynamic &&\n             MatrixType::RowsAtCompileTime <= MatrixType::ColsAtCompileTime,\n         ret = !( (QRPreconditioner == NoQRPreconditioner) ||\n                  (Case == PreconditionIfMoreColsThanRows && bool(a)) ||\n                  (Case == PreconditionIfMoreRowsThanCols && bool(b)) )\n  };\n};\n\ntemplate<typename MatrixType, int QRPreconditioner, int Case,\n         bool DoAnything = qr_preconditioner_should_do_anything<MatrixType, QRPreconditioner, Case>::ret\n> struct qr_preconditioner_impl {};\n\ntemplate<typename MatrixType, int QRPreconditioner, int Case>\nclass qr_preconditioner_impl<MatrixType, QRPreconditioner, Case, false>\n{\npublic:\n  void allocate(const JacobiSVD<MatrixType, QRPreconditioner>&) {}\n  bool run(JacobiSVD<MatrixType, QRPreconditioner>&, const MatrixType&)\n  {\n    return false;\n  }\n};\n\n/*** preconditioner using FullPivHouseholderQR ***/\n\ntemplate<typename MatrixType>\nclass qr_preconditioner_impl<MatrixType, FullPivHouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true>\n{\npublic:\n  typedef typename MatrixType::Scalar Scalar;\n  enum\n  {\n    RowsAtCompileTime = MatrixType::RowsAtCompileTime,\n    MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime\n  };\n  typedef Matrix<Scalar, 1, RowsAtCompileTime, RowMajor, 1, MaxRowsAtCompileTime> WorkspaceType;\n\n  void allocate(const JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner>& svd)\n  {\n    if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols())\n    {\n      m_qr.~QRType();\n      ::new (&m_qr) QRType(svd.rows(), svd.cols());\n    }\n    if (svd.m_computeFullU) m_workspace.resize(svd.rows());\n  }\n\n  bool run(JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner>& svd, const MatrixType& matrix)\n  {\n    if(matrix.rows() > matrix.cols())\n    {\n      m_qr.compute(matrix);\n      svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.cols(),matrix.cols()).template triangularView<Upper>();\n      if(svd.m_computeFullU) m_qr.matrixQ().evalTo(svd.m_matrixU, m_workspace);\n      if(svd.computeV()) svd.m_matrixV = m_qr.colsPermutation();\n      return true;\n    }\n    return false;\n  }\nprivate:\n  typedef FullPivHouseholderQR<MatrixType> QRType;\n  QRType m_qr;\n  WorkspaceType m_workspace;\n};\n\ntemplate<typename MatrixType>\nclass qr_preconditioner_impl<MatrixType, FullPivHouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true>\n{\npublic:\n  typedef typename MatrixType::Scalar Scalar;\n  enum\n  {\n    RowsAtCompileTime = MatrixType::RowsAtCompileTime,\n    ColsAtCompileTime = MatrixType::ColsAtCompileTime,\n    MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,\n    MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,\n    TrOptions = RowsAtCompileTime==1 ? (MatrixType::Options & ~(RowMajor))\n              : ColsAtCompileTime==1 ? (MatrixType::Options |   RowMajor)\n              : MatrixType::Options\n  };\n  typedef Matrix<Scalar, ColsAtCompileTime, RowsAtCompileTime, TrOptions, MaxColsAtCompileTime, MaxRowsAtCompileTime>\n          TransposeTypeWithSameStorageOrder;\n\n  void allocate(const JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner>& svd)\n  {\n    if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols())\n    {\n      m_qr.~QRType();\n      ::new (&m_qr) QRType(svd.cols(), svd.rows());\n    }\n    m_adjoint.resize(svd.cols(), svd.rows());\n    if (svd.m_computeFullV) m_workspace.resize(svd.cols());\n  }\n\n  bool run(JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner>& svd, const MatrixType& matrix)\n  {\n    if(matrix.cols() > matrix.rows())\n    {\n      m_adjoint = matrix.adjoint();\n      m_qr.compute(m_adjoint);\n      svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).template triangularView<Upper>().adjoint();\n      if(svd.m_computeFullV) m_qr.matrixQ().evalTo(svd.m_matrixV, m_workspace);\n      if(svd.computeU()) svd.m_matrixU = m_qr.colsPermutation();\n      return true;\n    }\n    else return false;\n  }\nprivate:\n  typedef FullPivHouseholderQR<TransposeTypeWithSameStorageOrder> QRType;\n  QRType m_qr;\n  TransposeTypeWithSameStorageOrder m_adjoint;\n  typename internal::plain_row_type<MatrixType>::type m_workspace;\n};\n\n/*** preconditioner using ColPivHouseholderQR ***/\n\ntemplate<typename MatrixType>\nclass qr_preconditioner_impl<MatrixType, ColPivHouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true>\n{\npublic:\n  void allocate(const JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>& svd)\n  {\n    if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols())\n    {\n      m_qr.~QRType();\n      ::new (&m_qr) QRType(svd.rows(), svd.cols());\n    }\n    if (svd.m_computeFullU) m_workspace.resize(svd.rows());\n    else if (svd.m_computeThinU) m_workspace.resize(svd.cols());\n  }\n\n  bool run(JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>& svd, const MatrixType& matrix)\n  {\n    if(matrix.rows() > matrix.cols())\n    {\n      m_qr.compute(matrix);\n      svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.cols(),matrix.cols()).template triangularView<Upper>();\n      if(svd.m_computeFullU) m_qr.householderQ().evalTo(svd.m_matrixU, m_workspace);\n      else if(svd.m_computeThinU)\n      {\n        svd.m_matrixU.setIdentity(matrix.rows(), matrix.cols());\n        m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixU, m_workspace);\n      }\n      if(svd.computeV()) svd.m_matrixV = m_qr.colsPermutation();\n      return true;\n    }\n    return false;\n  }\n\nprivate:\n  typedef ColPivHouseholderQR<MatrixType> QRType;\n  QRType m_qr;\n  typename internal::plain_col_type<MatrixType>::type m_workspace;\n};\n\ntemplate<typename MatrixType>\nclass qr_preconditioner_impl<MatrixType, ColPivHouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true>\n{\npublic:\n  typedef typename MatrixType::Scalar Scalar;\n  enum\n  {\n    RowsAtCompileTime = MatrixType::RowsAtCompileTime,\n    ColsAtCompileTime = MatrixType::ColsAtCompileTime,\n    MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,\n    MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,\n    TrOptions = RowsAtCompileTime==1 ? (MatrixType::Options & ~(RowMajor))\n              : ColsAtCompileTime==1 ? (MatrixType::Options |   RowMajor)\n              : MatrixType::Options\n  };\n\n  typedef Matrix<Scalar, ColsAtCompileTime, RowsAtCompileTime, TrOptions, MaxColsAtCompileTime, MaxRowsAtCompileTime>\n          TransposeTypeWithSameStorageOrder;\n\n  void allocate(const JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>& svd)\n  {\n    if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols())\n    {\n      m_qr.~QRType();\n      ::new (&m_qr) QRType(svd.cols(), svd.rows());\n    }\n    if (svd.m_computeFullV) m_workspace.resize(svd.cols());\n    else if (svd.m_computeThinV) m_workspace.resize(svd.rows());\n    m_adjoint.resize(svd.cols(), svd.rows());\n  }\n\n  bool run(JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>& svd, const MatrixType& matrix)\n  {\n    if(matrix.cols() > matrix.rows())\n    {\n      m_adjoint = matrix.adjoint();\n      m_qr.compute(m_adjoint);\n\n      svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).template triangularView<Upper>().adjoint();\n      if(svd.m_computeFullV) m_qr.householderQ().evalTo(svd.m_matrixV, m_workspace);\n      else if(svd.m_computeThinV)\n      {\n        svd.m_matrixV.setIdentity(matrix.cols(), matrix.rows());\n        m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixV, m_workspace);\n      }\n      if(svd.computeU()) svd.m_matrixU = m_qr.colsPermutation();\n      return true;\n    }\n    else return false;\n  }\n\nprivate:\n  typedef ColPivHouseholderQR<TransposeTypeWithSameStorageOrder> QRType;\n  QRType m_qr;\n  TransposeTypeWithSameStorageOrder m_adjoint;\n  typename internal::plain_row_type<MatrixType>::type m_workspace;\n};\n\n/*** preconditioner using HouseholderQR ***/\n\ntemplate<typename MatrixType>\nclass qr_preconditioner_impl<MatrixType, HouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true>\n{\npublic:\n  void allocate(const JacobiSVD<MatrixType, HouseholderQRPreconditioner>& svd)\n  {\n    if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols())\n    {\n      m_qr.~QRType();\n      ::new (&m_qr) QRType(svd.rows(), svd.cols());\n    }\n    if (svd.m_computeFullU) m_workspace.resize(svd.rows());\n    else if (svd.m_computeThinU) m_workspace.resize(svd.cols());\n  }\n\n  bool run(JacobiSVD<MatrixType, HouseholderQRPreconditioner>& svd, const MatrixType& matrix)\n  {\n    if(matrix.rows() > matrix.cols())\n    {\n      m_qr.compute(matrix);\n      svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.cols(),matrix.cols()).template triangularView<Upper>();\n      if(svd.m_computeFullU) m_qr.householderQ().evalTo(svd.m_matrixU, m_workspace);\n      else if(svd.m_computeThinU)\n      {\n        svd.m_matrixU.setIdentity(matrix.rows(), matrix.cols());\n        m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixU, m_workspace);\n      }\n      if(svd.computeV()) svd.m_matrixV.setIdentity(matrix.cols(), matrix.cols());\n      return true;\n    }\n    return false;\n  }\nprivate:\n  typedef HouseholderQR<MatrixType> QRType;\n  QRType m_qr;\n  typename internal::plain_col_type<MatrixType>::type m_workspace;\n};\n\ntemplate<typename MatrixType>\nclass qr_preconditioner_impl<MatrixType, HouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true>\n{\npublic:\n  typedef typename MatrixType::Scalar Scalar;\n  enum\n  {\n    RowsAtCompileTime = MatrixType::RowsAtCompileTime,\n    ColsAtCompileTime = MatrixType::ColsAtCompileTime,\n    MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,\n    MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,\n    Options = MatrixType::Options\n  };\n\n  typedef Matrix<Scalar, ColsAtCompileTime, RowsAtCompileTime, Options, MaxColsAtCompileTime, MaxRowsAtCompileTime>\n          TransposeTypeWithSameStorageOrder;\n\n  void allocate(const JacobiSVD<MatrixType, HouseholderQRPreconditioner>& svd)\n  {\n    if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols())\n    {\n      m_qr.~QRType();\n      ::new (&m_qr) QRType(svd.cols(), svd.rows());\n    }\n    if (svd.m_computeFullV) m_workspace.resize(svd.cols());\n    else if (svd.m_computeThinV) m_workspace.resize(svd.rows());\n    m_adjoint.resize(svd.cols(), svd.rows());\n  }\n\n  bool run(JacobiSVD<MatrixType, HouseholderQRPreconditioner>& svd, const MatrixType& matrix)\n  {\n    if(matrix.cols() > matrix.rows())\n    {\n      m_adjoint = matrix.adjoint();\n      m_qr.compute(m_adjoint);\n\n      svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).template triangularView<Upper>().adjoint();\n      if(svd.m_computeFullV) m_qr.householderQ().evalTo(svd.m_matrixV, m_workspace);\n      else if(svd.m_computeThinV)\n      {\n        svd.m_matrixV.setIdentity(matrix.cols(), matrix.rows());\n        m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixV, m_workspace);\n      }\n      if(svd.computeU()) svd.m_matrixU.setIdentity(matrix.rows(), matrix.rows());\n      return true;\n    }\n    else return false;\n  }\n\nprivate:\n  typedef HouseholderQR<TransposeTypeWithSameStorageOrder> QRType;\n  QRType m_qr;\n  TransposeTypeWithSameStorageOrder m_adjoint;\n  typename internal::plain_row_type<MatrixType>::type m_workspace;\n};\n\n/*** 2x2 SVD implementation\n ***\n *** JacobiSVD consists in performing a series of 2x2 SVD subproblems\n ***/\n\ntemplate<typename MatrixType, int QRPreconditioner>\nstruct svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner, false>\n{\n  typedef JacobiSVD<MatrixType, QRPreconditioner> SVD;\n  typedef typename MatrixType::RealScalar RealScalar;\n  static bool run(typename SVD::WorkMatrixType&, SVD&, Index, Index, RealScalar&) { return true; }\n};\n\ntemplate<typename MatrixType, int QRPreconditioner>\nstruct svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner, true>\n{\n  typedef JacobiSVD<MatrixType, QRPreconditioner> SVD;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename MatrixType::RealScalar RealScalar;\n  static bool run(typename SVD::WorkMatrixType& work_matrix, SVD& svd, Index p, Index q, RealScalar& maxDiagEntry)\n  {\n    using std::sqrt;\n    using std::abs;\n    Scalar z;\n    JacobiRotation<Scalar> rot;\n    RealScalar n = sqrt(numext::abs2(work_matrix.coeff(p,p)) + numext::abs2(work_matrix.coeff(q,p)));\n\n    const RealScalar considerAsZero = (std::numeric_limits<RealScalar>::min)();\n    const RealScalar precision = NumTraits<Scalar>::epsilon();\n\n    if(n==0)\n    {\n      // make sure first column is zero\n      work_matrix.coeffRef(p,p) = work_matrix.coeffRef(q,p) = Scalar(0);\n\n      if(abs(numext::imag(work_matrix.coeff(p,q)))>considerAsZero)\n      {\n        // work_matrix.coeff(p,q) can be zero if work_matrix.coeff(q,p) is not zero but small enough to underflow when computing n\n        z = abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q);\n        work_matrix.row(p) *= z;\n        if(svd.computeU()) svd.m_matrixU.col(p) *= conj(z);\n      }\n      if(abs(numext::imag(work_matrix.coeff(q,q)))>considerAsZero)\n      {\n        z = abs(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q);\n        work_matrix.row(q) *= z;\n        if(svd.computeU()) svd.m_matrixU.col(q) *= conj(z);\n      }\n      // otherwise the second row is already zero, so we have nothing to do.\n    }\n    else\n    {\n      rot.c() = conj(work_matrix.coeff(p,p)) / n;\n      rot.s() = work_matrix.coeff(q,p) / n;\n      work_matrix.applyOnTheLeft(p,q,rot);\n      if(svd.computeU()) svd.m_matrixU.applyOnTheRight(p,q,rot.adjoint());\n      if(abs(numext::imag(work_matrix.coeff(p,q)))>considerAsZero)\n      {\n        z = abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q);\n        work_matrix.col(q) *= z;\n        if(svd.computeV()) svd.m_matrixV.col(q) *= z;\n      }\n      if(abs(numext::imag(work_matrix.coeff(q,q)))>considerAsZero)\n      {\n        z = abs(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q);\n        work_matrix.row(q) *= z;\n        if(svd.computeU()) svd.m_matrixU.col(q) *= conj(z);\n      }\n    }\n\n    // update largest diagonal entry\n    maxDiagEntry = numext::maxi<RealScalar>(maxDiagEntry,numext::maxi<RealScalar>(abs(work_matrix.coeff(p,p)), abs(work_matrix.coeff(q,q))));\n    // and check whether the 2x2 block is already diagonal\n    RealScalar threshold = numext::maxi<RealScalar>(considerAsZero, precision * maxDiagEntry);\n    return abs(work_matrix.coeff(p,q))>threshold || abs(work_matrix.coeff(q,p)) > threshold;\n  }\n};\n\ntemplate<typename _MatrixType, int QRPreconditioner> \nstruct traits<JacobiSVD<_MatrixType,QRPreconditioner> >\n{\n  typedef _MatrixType MatrixType;\n};\n\n} // end namespace internal\n\n/** \\ingroup SVD_Module\n  *\n  *\n  * \\class JacobiSVD\n  *\n  * \\brief Two-sided Jacobi SVD decomposition of a rectangular matrix\n  *\n  * \\tparam _MatrixType the type of the matrix of which we are computing the SVD decomposition\n  * \\tparam QRPreconditioner this optional parameter allows to specify the type of QR decomposition that will be used internally\n  *                        for the R-SVD step for non-square matrices. See discussion of possible values below.\n  *\n  * SVD decomposition consists in decomposing any n-by-p matrix \\a A as a product\n  *   \\f[ A = U S V^* \\f]\n  * where \\a U is a n-by-n unitary, \\a V is a p-by-p unitary, and \\a S is a n-by-p real positive matrix which is zero outside of its main diagonal;\n  * the diagonal entries of S are known as the \\em singular \\em values of \\a A and the columns of \\a U and \\a V are known as the left\n  * and right \\em singular \\em vectors of \\a A respectively.\n  *\n  * Singular values are always sorted in decreasing order.\n  *\n  * This JacobiSVD decomposition computes only the singular values by default. If you want \\a U or \\a V, you need to ask for them explicitly.\n  *\n  * You can ask for only \\em thin \\a U or \\a V to be computed, meaning the following. In case of a rectangular n-by-p matrix, letting \\a m be the\n  * smaller value among \\a n and \\a p, there are only \\a m singular vectors; the remaining columns of \\a U and \\a V do not correspond to actual\n  * singular vectors. Asking for \\em thin \\a U or \\a V means asking for only their \\a m first columns to be formed. So \\a U is then a n-by-m matrix,\n  * and \\a V is then a p-by-m matrix. Notice that thin \\a U and \\a V are all you need for (least squares) solving.\n  *\n  * Here's an example demonstrating basic usage:\n  * \\include JacobiSVD_basic.cpp\n  * Output: \\verbinclude JacobiSVD_basic.out\n  *\n  * This JacobiSVD class is a two-sided Jacobi R-SVD decomposition, ensuring optimal reliability and accuracy. The downside is that it's slower than\n  * bidiagonalizing SVD algorithms for large square matrices; however its complexity is still \\f$ O(n^2p) \\f$ where \\a n is the smaller dimension and\n  * \\a p is the greater dimension, meaning that it is still of the same order of complexity as the faster bidiagonalizing R-SVD algorithms.\n  * In particular, like any R-SVD, it takes advantage of non-squareness in that its complexity is only linear in the greater dimension.\n  *\n  * If the input matrix has inf or nan coefficients, the result of the computation is undefined, but the computation is guaranteed to\n  * terminate in finite (and reasonable) time.\n  *\n  * The possible values for QRPreconditioner are:\n  * \\li ColPivHouseholderQRPreconditioner is the default. In practice it's very safe. It uses column-pivoting QR.\n  * \\li FullPivHouseholderQRPreconditioner, is the safest and slowest. It uses full-pivoting QR.\n  *     Contrary to other QRs, it doesn't allow computing thin unitaries.\n  * \\li HouseholderQRPreconditioner is the fastest, and less safe and accurate than the pivoting variants. It uses non-pivoting QR.\n  *     This is very similar in safety and accuracy to the bidiagonalization process used by bidiagonalizing SVD algorithms (since bidiagonalization\n  *     is inherently non-pivoting). However the resulting SVD is still more reliable than bidiagonalizing SVDs because the Jacobi-based iterarive\n  *     process is more reliable than the optimized bidiagonal SVD iterations.\n  * \\li NoQRPreconditioner allows not to use a QR preconditioner at all. This is useful if you know that you will only be computing\n  *     JacobiSVD decompositions of square matrices. Non-square matrices require a QR preconditioner. Using this option will result in\n  *     faster compilation and smaller executable code. It won't significantly speed up computation, since JacobiSVD is always checking\n  *     if QR preconditioning is needed before applying it anyway.\n  *\n  * \\sa MatrixBase::jacobiSvd()\n  */\ntemplate<typename _MatrixType, int QRPreconditioner> class JacobiSVD\n : public SVDBase<JacobiSVD<_MatrixType,QRPreconditioner> >\n{\n    typedef SVDBase<JacobiSVD> Base;\n  public:\n\n    typedef _MatrixType MatrixType;\n    typedef typename MatrixType::Scalar Scalar;\n    typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;\n    enum {\n      RowsAtCompileTime = MatrixType::RowsAtCompileTime,\n      ColsAtCompileTime = MatrixType::ColsAtCompileTime,\n      DiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime,ColsAtCompileTime),\n      MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,\n      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,\n      MaxDiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(MaxRowsAtCompileTime,MaxColsAtCompileTime),\n      MatrixOptions = MatrixType::Options\n    };\n\n    typedef typename Base::MatrixUType MatrixUType;\n    typedef typename Base::MatrixVType MatrixVType;\n    typedef typename Base::SingularValuesType SingularValuesType;\n    \n    typedef typename internal::plain_row_type<MatrixType>::type RowType;\n    typedef typename internal::plain_col_type<MatrixType>::type ColType;\n    typedef Matrix<Scalar, DiagSizeAtCompileTime, DiagSizeAtCompileTime,\n                   MatrixOptions, MaxDiagSizeAtCompileTime, MaxDiagSizeAtCompileTime>\n            WorkMatrixType;\n\n    /** \\brief Default Constructor.\n      *\n      * The default constructor is useful in cases in which the user intends to\n      * perform decompositions via JacobiSVD::compute(const MatrixType&).\n      */\n    JacobiSVD()\n    {}\n\n\n    /** \\brief Default Constructor with memory preallocation\n      *\n      * Like the default constructor but with preallocation of the internal data\n      * according to the specified problem size.\n      * \\sa JacobiSVD()\n      */\n    JacobiSVD(Index rows, Index cols, unsigned int computationOptions = 0)\n    {\n      allocate(rows, cols, computationOptions);\n    }\n\n    /** \\brief Constructor performing the decomposition of given matrix.\n     *\n     * \\param matrix the matrix to decompose\n     * \\param computationOptions optional parameter allowing to specify if you want full or thin U or V unitaries to be computed.\n     *                           By default, none is computed. This is a bit-field, the possible bits are #ComputeFullU, #ComputeThinU,\n     *                           #ComputeFullV, #ComputeThinV.\n     *\n     * Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not\n     * available with the (non-default) FullPivHouseholderQR preconditioner.\n     */\n    explicit JacobiSVD(const MatrixType& matrix, unsigned int computationOptions = 0)\n    {\n      compute(matrix, computationOptions);\n    }\n\n    /** \\brief Method performing the decomposition of given matrix using custom options.\n     *\n     * \\param matrix the matrix to decompose\n     * \\param computationOptions optional parameter allowing to specify if you want full or thin U or V unitaries to be computed.\n     *                           By default, none is computed. This is a bit-field, the possible bits are #ComputeFullU, #ComputeThinU,\n     *                           #ComputeFullV, #ComputeThinV.\n     *\n     * Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not\n     * available with the (non-default) FullPivHouseholderQR preconditioner.\n     */\n    JacobiSVD& compute(const MatrixType& matrix, unsigned int computationOptions);\n\n    /** \\brief Method performing the decomposition of given matrix using current options.\n     *\n     * \\param matrix the matrix to decompose\n     *\n     * This method uses the current \\a computationOptions, as already passed to the constructor or to compute(const MatrixType&, unsigned int).\n     */\n    JacobiSVD& compute(const MatrixType& matrix)\n    {\n      return compute(matrix, m_computationOptions);\n    }\n\n    using Base::computeU;\n    using Base::computeV;\n    using Base::rows;\n    using Base::cols;\n    using Base::rank;\n\n  private:\n    void allocate(Index rows, Index cols, unsigned int computationOptions);\n\n  protected:\n    using Base::m_matrixU;\n    using Base::m_matrixV;\n    using Base::m_singularValues;\n    using Base::m_isInitialized;\n    using Base::m_isAllocated;\n    using Base::m_usePrescribedThreshold;\n    using Base::m_computeFullU;\n    using Base::m_computeThinU;\n    using Base::m_computeFullV;\n    using Base::m_computeThinV;\n    using Base::m_computationOptions;\n    using Base::m_nonzeroSingularValues;\n    using Base::m_rows;\n    using Base::m_cols;\n    using Base::m_diagSize;\n    using Base::m_prescribedThreshold;\n    WorkMatrixType m_workMatrix;\n\n    template<typename __MatrixType, int _QRPreconditioner, bool _IsComplex>\n    friend struct internal::svd_precondition_2x2_block_to_be_real;\n    template<typename __MatrixType, int _QRPreconditioner, int _Case, bool _DoAnything>\n    friend struct internal::qr_preconditioner_impl;\n\n    internal::qr_preconditioner_impl<MatrixType, QRPreconditioner, internal::PreconditionIfMoreColsThanRows> m_qr_precond_morecols;\n    internal::qr_preconditioner_impl<MatrixType, QRPreconditioner, internal::PreconditionIfMoreRowsThanCols> m_qr_precond_morerows;\n    MatrixType m_scaledMatrix;\n};\n\ntemplate<typename MatrixType, int QRPreconditioner>\nvoid JacobiSVD<MatrixType, QRPreconditioner>::allocate(Index rows, Index cols, unsigned int computationOptions)\n{\n  eigen_assert(rows >= 0 && cols >= 0);\n\n  if (m_isAllocated &&\n      rows == m_rows &&\n      cols == m_cols &&\n      computationOptions == m_computationOptions)\n  {\n    return;\n  }\n\n  m_rows = rows;\n  m_cols = cols;\n  m_isInitialized = false;\n  m_isAllocated = true;\n  m_computationOptions = computationOptions;\n  m_computeFullU = (computationOptions & ComputeFullU) != 0;\n  m_computeThinU = (computationOptions & ComputeThinU) != 0;\n  m_computeFullV = (computationOptions & ComputeFullV) != 0;\n  m_computeThinV = (computationOptions & ComputeThinV) != 0;\n  eigen_assert(!(m_computeFullU && m_computeThinU) && \"JacobiSVD: you can't ask for both full and thin U\");\n  eigen_assert(!(m_computeFullV && m_computeThinV) && \"JacobiSVD: you can't ask for both full and thin V\");\n  eigen_assert(EIGEN_IMPLIES(m_computeThinU || m_computeThinV, MatrixType::ColsAtCompileTime==Dynamic) &&\n              \"JacobiSVD: thin U and V are only available when your matrix has a dynamic number of columns.\");\n  if (QRPreconditioner == FullPivHouseholderQRPreconditioner)\n  {\n      eigen_assert(!(m_computeThinU || m_computeThinV) &&\n              \"JacobiSVD: can't compute thin U or thin V with the FullPivHouseholderQR preconditioner. \"\n              \"Use the ColPivHouseholderQR preconditioner instead.\");\n  }\n  m_diagSize = (std::min)(m_rows, m_cols);\n  m_singularValues.resize(m_diagSize);\n  if(RowsAtCompileTime==Dynamic)\n    m_matrixU.resize(m_rows, m_computeFullU ? m_rows\n                            : m_computeThinU ? m_diagSize\n                            : 0);\n  if(ColsAtCompileTime==Dynamic)\n    m_matrixV.resize(m_cols, m_computeFullV ? m_cols\n                            : m_computeThinV ? m_diagSize\n                            : 0);\n  m_workMatrix.resize(m_diagSize, m_diagSize);\n  \n  if(m_cols>m_rows)   m_qr_precond_morecols.allocate(*this);\n  if(m_rows>m_cols)   m_qr_precond_morerows.allocate(*this);\n  if(m_rows!=m_cols)  m_scaledMatrix.resize(rows,cols);\n}\n\ntemplate<typename MatrixType, int QRPreconditioner>\nJacobiSVD<MatrixType, QRPreconditioner>&\nJacobiSVD<MatrixType, QRPreconditioner>::compute(const MatrixType& matrix, unsigned int computationOptions)\n{\n  using std::abs;\n  allocate(matrix.rows(), matrix.cols(), computationOptions);\n\n  // currently we stop when we reach precision 2*epsilon as the last bit of precision can require an unreasonable number of iterations,\n  // only worsening the precision of U and V as we accumulate more rotations\n  const RealScalar precision = RealScalar(2) * NumTraits<Scalar>::epsilon();\n\n  // limit for denormal numbers to be considered zero in order to avoid infinite loops (see bug 286)\n  const RealScalar considerAsZero = (std::numeric_limits<RealScalar>::min)();\n\n  // Scaling factor to reduce over/under-flows\n  RealScalar scale = matrix.cwiseAbs().maxCoeff();\n  if(scale==RealScalar(0)) scale = RealScalar(1);\n  \n  /*** step 1. The R-SVD step: we use a QR decomposition to reduce to the case of a square matrix */\n\n  if(m_rows!=m_cols)\n  {\n    m_scaledMatrix = matrix / scale;\n    m_qr_precond_morecols.run(*this, m_scaledMatrix);\n    m_qr_precond_morerows.run(*this, m_scaledMatrix);\n  }\n  else\n  {\n    m_workMatrix = matrix.block(0,0,m_diagSize,m_diagSize) / scale;\n    if(m_computeFullU) m_matrixU.setIdentity(m_rows,m_rows);\n    if(m_computeThinU) m_matrixU.setIdentity(m_rows,m_diagSize);\n    if(m_computeFullV) m_matrixV.setIdentity(m_cols,m_cols);\n    if(m_computeThinV) m_matrixV.setIdentity(m_cols, m_diagSize);\n  }\n\n  /*** step 2. The main Jacobi SVD iteration. ***/\n  RealScalar maxDiagEntry = m_workMatrix.cwiseAbs().diagonal().maxCoeff();\n\n  bool finished = false;\n  while(!finished)\n  {\n    finished = true;\n\n    // do a sweep: for all index pairs (p,q), perform SVD of the corresponding 2x2 sub-matrix\n\n    for(Index p = 1; p < m_diagSize; ++p)\n    {\n      for(Index q = 0; q < p; ++q)\n      {\n        // if this 2x2 sub-matrix is not diagonal already...\n        // notice that this comparison will evaluate to false if any NaN is involved, ensuring that NaN's don't\n        // keep us iterating forever. Similarly, small denormal numbers are considered zero.\n        RealScalar threshold = numext::maxi<RealScalar>(considerAsZero, precision * maxDiagEntry);\n        if(abs(m_workMatrix.coeff(p,q))>threshold || abs(m_workMatrix.coeff(q,p)) > threshold)\n        {\n          finished = false;\n          // perform SVD decomposition of 2x2 sub-matrix corresponding to indices p,q to make it diagonal\n          // the complex to real operation returns true if the updated 2x2 block is not already diagonal\n          if(internal::svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner>::run(m_workMatrix, *this, p, q, maxDiagEntry))\n          {\n            JacobiRotation<RealScalar> j_left, j_right;\n            internal::real_2x2_jacobi_svd(m_workMatrix, p, q, &j_left, &j_right);\n\n            // accumulate resulting Jacobi rotations\n            m_workMatrix.applyOnTheLeft(p,q,j_left);\n            if(computeU()) m_matrixU.applyOnTheRight(p,q,j_left.transpose());\n\n            m_workMatrix.applyOnTheRight(p,q,j_right);\n            if(computeV()) m_matrixV.applyOnTheRight(p,q,j_right);\n\n            // keep track of the largest diagonal coefficient\n            maxDiagEntry = numext::maxi<RealScalar>(maxDiagEntry,numext::maxi<RealScalar>(abs(m_workMatrix.coeff(p,p)), abs(m_workMatrix.coeff(q,q))));\n          }\n        }\n      }\n    }\n  }\n\n  /*** step 3. The work matrix is now diagonal, so ensure it's positive so its diagonal entries are the singular values ***/\n\n  for(Index i = 0; i < m_diagSize; ++i)\n  {\n    // For a complex matrix, some diagonal coefficients might note have been\n    // treated by svd_precondition_2x2_block_to_be_real, and the imaginary part\n    // of some diagonal entry might not be null.\n    if(NumTraits<Scalar>::IsComplex && abs(numext::imag(m_workMatrix.coeff(i,i)))>considerAsZero)\n    {\n      RealScalar a = abs(m_workMatrix.coeff(i,i));\n      m_singularValues.coeffRef(i) = abs(a);\n      if(computeU()) m_matrixU.col(i) *= m_workMatrix.coeff(i,i)/a;\n    }\n    else\n    {\n      // m_workMatrix.coeff(i,i) is already real, no difficulty:\n      RealScalar a = numext::real(m_workMatrix.coeff(i,i));\n      m_singularValues.coeffRef(i) = abs(a);\n      if(computeU() && (a<RealScalar(0))) m_matrixU.col(i) = -m_matrixU.col(i);\n    }\n  }\n  \n  m_singularValues *= scale;\n\n  /*** step 4. Sort singular values in descending order and compute the number of nonzero singular values ***/\n\n  m_nonzeroSingularValues = m_diagSize;\n  for(Index i = 0; i < m_diagSize; i++)\n  {\n    Index pos;\n    RealScalar maxRemainingSingularValue = m_singularValues.tail(m_diagSize-i).maxCoeff(&pos);\n    if(maxRemainingSingularValue == RealScalar(0))\n    {\n      m_nonzeroSingularValues = i;\n      break;\n    }\n    if(pos)\n    {\n      pos += i;\n      std::swap(m_singularValues.coeffRef(i), m_singularValues.coeffRef(pos));\n      if(computeU()) m_matrixU.col(pos).swap(m_matrixU.col(i));\n      if(computeV()) m_matrixV.col(pos).swap(m_matrixV.col(i));\n    }\n  }\n\n  m_isInitialized = true;\n  return *this;\n}\n\n/** \\svd_module\n  *\n  * \\return the singular value decomposition of \\c *this computed by two-sided\n  * Jacobi transformations.\n  *\n  * \\sa class JacobiSVD\n  */\ntemplate<typename Derived>\nJacobiSVD<typename MatrixBase<Derived>::PlainObject>\nMatrixBase<Derived>::jacobiSvd(unsigned int computationOptions) const\n{\n  return JacobiSVD<PlainObject>(*this, computationOptions);\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_JACOBISVD_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SVD/JacobiSVD_LAPACKE.h",
    "content": "/*\n Copyright (c) 2011, Intel Corporation. All rights reserved.\n\n Redistribution and use in source and binary forms, with or without modification,\n are permitted provided that the following conditions are met:\n\n * Redistributions of source code must retain the above copyright notice, this\n   list of conditions and the following disclaimer.\n * Redistributions in binary form must reproduce the above copyright notice,\n   this list of conditions and the following disclaimer in the documentation\n   and/or other materials provided with the distribution.\n * Neither the name of Intel Corporation nor the names of its contributors may\n   be used to endorse or promote products derived from this software without\n   specific prior written permission.\n\n THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\" AND\n ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED\n WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\n DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR\n ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES\n (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;\n LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON\n ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT\n (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS\n SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n\n ********************************************************************************\n *   Content : Eigen bindings to LAPACKe\n *    Singular Value Decomposition - SVD.\n ********************************************************************************\n*/\n\n#ifndef EIGEN_JACOBISVD_LAPACKE_H\n#define EIGEN_JACOBISVD_LAPACKE_H\n\nnamespace Eigen { \n\n/** \\internal Specialization for the data types supported by LAPACKe */\n\n#define EIGEN_LAPACKE_SVD(EIGTYPE, LAPACKE_TYPE, LAPACKE_RTYPE, LAPACKE_PREFIX, EIGCOLROW, LAPACKE_COLROW) \\\ntemplate<> inline \\\nJacobiSVD<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>, ColPivHouseholderQRPreconditioner>& \\\nJacobiSVD<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>, ColPivHouseholderQRPreconditioner>::compute(const Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>& matrix, unsigned int computationOptions) \\\n{ \\\n  typedef Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic> MatrixType; \\\n  /*typedef MatrixType::Scalar Scalar;*/ \\\n  /*typedef MatrixType::RealScalar RealScalar;*/ \\\n  allocate(matrix.rows(), matrix.cols(), computationOptions); \\\n\\\n  /*const RealScalar precision = RealScalar(2) * NumTraits<Scalar>::epsilon();*/ \\\n  m_nonzeroSingularValues = m_diagSize; \\\n\\\n  lapack_int lda = internal::convert_index<lapack_int>(matrix.outerStride()), ldu, ldvt; \\\n  lapack_int matrix_order = LAPACKE_COLROW; \\\n  char jobu, jobvt; \\\n  LAPACKE_TYPE *u, *vt, dummy; \\\n  jobu  = (m_computeFullU) ? 'A' : (m_computeThinU) ? 'S' : 'N'; \\\n  jobvt = (m_computeFullV) ? 'A' : (m_computeThinV) ? 'S' : 'N'; \\\n  if (computeU()) { \\\n    ldu  = internal::convert_index<lapack_int>(m_matrixU.outerStride()); \\\n    u    = (LAPACKE_TYPE*)m_matrixU.data(); \\\n  } else { ldu=1; u=&dummy; }\\\n  MatrixType localV; \\\n  lapack_int vt_rows = (m_computeFullV) ? internal::convert_index<lapack_int>(m_cols) : (m_computeThinV) ? internal::convert_index<lapack_int>(m_diagSize) : 1; \\\n  if (computeV()) { \\\n    localV.resize(vt_rows, m_cols); \\\n    ldvt  = internal::convert_index<lapack_int>(localV.outerStride()); \\\n    vt   = (LAPACKE_TYPE*)localV.data(); \\\n  } else { ldvt=1; vt=&dummy; }\\\n  Matrix<LAPACKE_RTYPE, Dynamic, Dynamic> superb; superb.resize(m_diagSize, 1); \\\n  MatrixType m_temp; m_temp = matrix; \\\n  LAPACKE_##LAPACKE_PREFIX##gesvd( matrix_order, jobu, jobvt, internal::convert_index<lapack_int>(m_rows), internal::convert_index<lapack_int>(m_cols), (LAPACKE_TYPE*)m_temp.data(), lda, (LAPACKE_RTYPE*)m_singularValues.data(), u, ldu, vt, ldvt, superb.data()); \\\n  if (computeV()) m_matrixV = localV.adjoint(); \\\n /* for(int i=0;i<m_diagSize;i++) if (m_singularValues.coeffRef(i) < precision) { m_nonzeroSingularValues--; m_singularValues.coeffRef(i)=RealScalar(0);}*/ \\\n  m_isInitialized = true; \\\n  return *this; \\\n}\n\nEIGEN_LAPACKE_SVD(double,   double,                double, d, ColMajor, LAPACK_COL_MAJOR)\nEIGEN_LAPACKE_SVD(float,    float,                 float , s, ColMajor, LAPACK_COL_MAJOR)\nEIGEN_LAPACKE_SVD(dcomplex, lapack_complex_double, double, z, ColMajor, LAPACK_COL_MAJOR)\nEIGEN_LAPACKE_SVD(scomplex, lapack_complex_float,  float , c, ColMajor, LAPACK_COL_MAJOR)\n\nEIGEN_LAPACKE_SVD(double,   double,                double, d, RowMajor, LAPACK_ROW_MAJOR)\nEIGEN_LAPACKE_SVD(float,    float,                 float , s, RowMajor, LAPACK_ROW_MAJOR)\nEIGEN_LAPACKE_SVD(dcomplex, lapack_complex_double, double, z, RowMajor, LAPACK_ROW_MAJOR)\nEIGEN_LAPACKE_SVD(scomplex, lapack_complex_float,  float , c, RowMajor, LAPACK_ROW_MAJOR)\n\n} // end namespace Eigen\n\n#endif // EIGEN_JACOBISVD_LAPACKE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SVD/SVDBase.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// Copyright (C) 2013 Gauthier Brun <brun.gauthier@gmail.com>\n// Copyright (C) 2013 Nicolas Carre <nicolas.carre@ensimag.fr>\n// Copyright (C) 2013 Jean Ceccato <jean.ceccato@ensimag.fr>\n// Copyright (C) 2013 Pierre Zoppitelli <pierre.zoppitelli@ensimag.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SVDBASE_H\n#define EIGEN_SVDBASE_H\n\nnamespace Eigen {\n/** \\ingroup SVD_Module\n *\n *\n * \\class SVDBase\n *\n * \\brief Base class of SVD algorithms\n *\n * \\tparam Derived the type of the actual SVD decomposition\n *\n * SVD decomposition consists in decomposing any n-by-p matrix \\a A as a product\n *   \\f[ A = U S V^* \\f]\n * where \\a U is a n-by-n unitary, \\a V is a p-by-p unitary, and \\a S is a n-by-p real positive matrix which is zero outside of its main diagonal;\n * the diagonal entries of S are known as the \\em singular \\em values of \\a A and the columns of \\a U and \\a V are known as the left\n * and right \\em singular \\em vectors of \\a A respectively.\n *\n * Singular values are always sorted in decreasing order.\n *\n * \n * You can ask for only \\em thin \\a U or \\a V to be computed, meaning the following. In case of a rectangular n-by-p matrix, letting \\a m be the\n * smaller value among \\a n and \\a p, there are only \\a m singular vectors; the remaining columns of \\a U and \\a V do not correspond to actual\n * singular vectors. Asking for \\em thin \\a U or \\a V means asking for only their \\a m first columns to be formed. So \\a U is then a n-by-m matrix,\n * and \\a V is then a p-by-m matrix. Notice that thin \\a U and \\a V are all you need for (least squares) solving.\n *  \n * If the input matrix has inf or nan coefficients, the result of the computation is undefined, but the computation is guaranteed to\n * terminate in finite (and reasonable) time.\n * \\sa class BDCSVD, class JacobiSVD\n */\ntemplate<typename Derived>\nclass SVDBase\n{\n\npublic:\n  typedef typename internal::traits<Derived>::MatrixType MatrixType;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;\n  typedef typename MatrixType::StorageIndex StorageIndex;\n  typedef Eigen::Index Index; ///< \\deprecated since Eigen 3.3\n  enum {\n    RowsAtCompileTime = MatrixType::RowsAtCompileTime,\n    ColsAtCompileTime = MatrixType::ColsAtCompileTime,\n    DiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime,ColsAtCompileTime),\n    MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,\n    MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,\n    MaxDiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(MaxRowsAtCompileTime,MaxColsAtCompileTime),\n    MatrixOptions = MatrixType::Options\n  };\n\n  typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime, MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime> MatrixUType;\n  typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime, MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime> MatrixVType;\n  typedef typename internal::plain_diag_type<MatrixType, RealScalar>::type SingularValuesType;\n  \n  Derived& derived() { return *static_cast<Derived*>(this); }\n  const Derived& derived() const { return *static_cast<const Derived*>(this); }\n\n  /** \\returns the \\a U matrix.\n   *\n   * For the SVD decomposition of a n-by-p matrix, letting \\a m be the minimum of \\a n and \\a p,\n   * the U matrix is n-by-n if you asked for \\link Eigen::ComputeFullU ComputeFullU \\endlink, and is n-by-m if you asked for \\link Eigen::ComputeThinU ComputeThinU \\endlink.\n   *\n   * The \\a m first columns of \\a U are the left singular vectors of the matrix being decomposed.\n   *\n   * This method asserts that you asked for \\a U to be computed.\n   */\n  const MatrixUType& matrixU() const\n  {\n    eigen_assert(m_isInitialized && \"SVD is not initialized.\");\n    eigen_assert(computeU() && \"This SVD decomposition didn't compute U. Did you ask for it?\");\n    return m_matrixU;\n  }\n\n  /** \\returns the \\a V matrix.\n   *\n   * For the SVD decomposition of a n-by-p matrix, letting \\a m be the minimum of \\a n and \\a p,\n   * the V matrix is p-by-p if you asked for \\link Eigen::ComputeFullV ComputeFullV \\endlink, and is p-by-m if you asked for \\link Eigen::ComputeThinV ComputeThinV \\endlink.\n   *\n   * The \\a m first columns of \\a V are the right singular vectors of the matrix being decomposed.\n   *\n   * This method asserts that you asked for \\a V to be computed.\n   */\n  const MatrixVType& matrixV() const\n  {\n    eigen_assert(m_isInitialized && \"SVD is not initialized.\");\n    eigen_assert(computeV() && \"This SVD decomposition didn't compute V. Did you ask for it?\");\n    return m_matrixV;\n  }\n\n  /** \\returns the vector of singular values.\n   *\n   * For the SVD decomposition of a n-by-p matrix, letting \\a m be the minimum of \\a n and \\a p, the\n   * returned vector has size \\a m.  Singular values are always sorted in decreasing order.\n   */\n  const SingularValuesType& singularValues() const\n  {\n    eigen_assert(m_isInitialized && \"SVD is not initialized.\");\n    return m_singularValues;\n  }\n\n  /** \\returns the number of singular values that are not exactly 0 */\n  Index nonzeroSingularValues() const\n  {\n    eigen_assert(m_isInitialized && \"SVD is not initialized.\");\n    return m_nonzeroSingularValues;\n  }\n  \n  /** \\returns the rank of the matrix of which \\c *this is the SVD.\n    *\n    * \\note This method has to determine which singular values should be considered nonzero.\n    *       For that, it uses the threshold value that you can control by calling\n    *       setThreshold(const RealScalar&).\n    */\n  inline Index rank() const\n  {\n    using std::abs;\n    eigen_assert(m_isInitialized && \"JacobiSVD is not initialized.\");\n    if(m_singularValues.size()==0) return 0;\n    RealScalar premultiplied_threshold = numext::maxi<RealScalar>(m_singularValues.coeff(0) * threshold(), (std::numeric_limits<RealScalar>::min)());\n    Index i = m_nonzeroSingularValues-1;\n    while(i>=0 && m_singularValues.coeff(i) < premultiplied_threshold) --i;\n    return i+1;\n  }\n  \n  /** Allows to prescribe a threshold to be used by certain methods, such as rank() and solve(),\n    * which need to determine when singular values are to be considered nonzero.\n    * This is not used for the SVD decomposition itself.\n    *\n    * When it needs to get the threshold value, Eigen calls threshold().\n    * The default is \\c NumTraits<Scalar>::epsilon()\n    *\n    * \\param threshold The new value to use as the threshold.\n    *\n    * A singular value will be considered nonzero if its value is strictly greater than\n    *  \\f$ \\vert singular value \\vert \\leqslant threshold \\times \\vert max singular value \\vert \\f$.\n    *\n    * If you want to come back to the default behavior, call setThreshold(Default_t)\n    */\n  Derived& setThreshold(const RealScalar& threshold)\n  {\n    m_usePrescribedThreshold = true;\n    m_prescribedThreshold = threshold;\n    return derived();\n  }\n\n  /** Allows to come back to the default behavior, letting Eigen use its default formula for\n    * determining the threshold.\n    *\n    * You should pass the special object Eigen::Default as parameter here.\n    * \\code svd.setThreshold(Eigen::Default); \\endcode\n    *\n    * See the documentation of setThreshold(const RealScalar&).\n    */\n  Derived& setThreshold(Default_t)\n  {\n    m_usePrescribedThreshold = false;\n    return derived();\n  }\n\n  /** Returns the threshold that will be used by certain methods such as rank().\n    *\n    * See the documentation of setThreshold(const RealScalar&).\n    */\n  RealScalar threshold() const\n  {\n    eigen_assert(m_isInitialized || m_usePrescribedThreshold);\n    return m_usePrescribedThreshold ? m_prescribedThreshold\n                                    : (std::max<Index>)(1,m_diagSize)*NumTraits<Scalar>::epsilon();\n  }\n\n  /** \\returns true if \\a U (full or thin) is asked for in this SVD decomposition */\n  inline bool computeU() const { return m_computeFullU || m_computeThinU; }\n  /** \\returns true if \\a V (full or thin) is asked for in this SVD decomposition */\n  inline bool computeV() const { return m_computeFullV || m_computeThinV; }\n\n  inline Index rows() const { return m_rows; }\n  inline Index cols() const { return m_cols; }\n  \n  /** \\returns a (least squares) solution of \\f$ A x = b \\f$ using the current SVD decomposition of A.\n    *\n    * \\param b the right-hand-side of the equation to solve.\n    *\n    * \\note Solving requires both U and V to be computed. Thin U and V are enough, there is no need for full U or V.\n    *\n    * \\note SVD solving is implicitly least-squares. Thus, this method serves both purposes of exact solving and least-squares solving.\n    * In other words, the returned solution is guaranteed to minimize the Euclidean norm \\f$ \\Vert A x - b \\Vert \\f$.\n    */\n  template<typename Rhs>\n  inline const Solve<Derived, Rhs>\n  solve(const MatrixBase<Rhs>& b) const\n  {\n    eigen_assert(m_isInitialized && \"SVD is not initialized.\");\n    eigen_assert(computeU() && computeV() && \"SVD::solve() requires both unitaries U and V to be computed (thin unitaries suffice).\");\n    return Solve<Derived, Rhs>(derived(), b.derived());\n  }\n  \n  #ifndef EIGEN_PARSED_BY_DOXYGEN\n  template<typename RhsType, typename DstType>\n  EIGEN_DEVICE_FUNC\n  void _solve_impl(const RhsType &rhs, DstType &dst) const;\n  #endif\n\nprotected:\n  \n  static void check_template_parameters()\n  {\n    EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);\n  }\n  \n  // return true if already allocated\n  bool allocate(Index rows, Index cols, unsigned int computationOptions) ;\n\n  MatrixUType m_matrixU;\n  MatrixVType m_matrixV;\n  SingularValuesType m_singularValues;\n  bool m_isInitialized, m_isAllocated, m_usePrescribedThreshold;\n  bool m_computeFullU, m_computeThinU;\n  bool m_computeFullV, m_computeThinV;\n  unsigned int m_computationOptions;\n  Index m_nonzeroSingularValues, m_rows, m_cols, m_diagSize;\n  RealScalar m_prescribedThreshold;\n\n  /** \\brief Default Constructor.\n   *\n   * Default constructor of SVDBase\n   */\n  SVDBase()\n    : m_isInitialized(false),\n      m_isAllocated(false),\n      m_usePrescribedThreshold(false),\n      m_computationOptions(0),\n      m_rows(-1), m_cols(-1), m_diagSize(0)\n  {\n    check_template_parameters();\n  }\n\n\n};\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\ntemplate<typename Derived>\ntemplate<typename RhsType, typename DstType>\nvoid SVDBase<Derived>::_solve_impl(const RhsType &rhs, DstType &dst) const\n{\n  eigen_assert(rhs.rows() == rows());\n\n  // A = U S V^*\n  // So A^{-1} = V S^{-1} U^*\n\n  Matrix<Scalar, Dynamic, RhsType::ColsAtCompileTime, 0, MatrixType::MaxRowsAtCompileTime, RhsType::MaxColsAtCompileTime> tmp;\n  Index l_rank = rank();\n  tmp.noalias() =  m_matrixU.leftCols(l_rank).adjoint() * rhs;\n  tmp = m_singularValues.head(l_rank).asDiagonal().inverse() * tmp;\n  dst = m_matrixV.leftCols(l_rank) * tmp;\n}\n#endif\n\ntemplate<typename MatrixType>\nbool SVDBase<MatrixType>::allocate(Index rows, Index cols, unsigned int computationOptions)\n{\n  eigen_assert(rows >= 0 && cols >= 0);\n\n  if (m_isAllocated &&\n      rows == m_rows &&\n      cols == m_cols &&\n      computationOptions == m_computationOptions)\n  {\n    return true;\n  }\n\n  m_rows = rows;\n  m_cols = cols;\n  m_isInitialized = false;\n  m_isAllocated = true;\n  m_computationOptions = computationOptions;\n  m_computeFullU = (computationOptions & ComputeFullU) != 0;\n  m_computeThinU = (computationOptions & ComputeThinU) != 0;\n  m_computeFullV = (computationOptions & ComputeFullV) != 0;\n  m_computeThinV = (computationOptions & ComputeThinV) != 0;\n  eigen_assert(!(m_computeFullU && m_computeThinU) && \"SVDBase: you can't ask for both full and thin U\");\n  eigen_assert(!(m_computeFullV && m_computeThinV) && \"SVDBase: you can't ask for both full and thin V\");\n  eigen_assert(EIGEN_IMPLIES(m_computeThinU || m_computeThinV, MatrixType::ColsAtCompileTime==Dynamic) &&\n\t       \"SVDBase: thin U and V are only available when your matrix has a dynamic number of columns.\");\n\n  m_diagSize = (std::min)(m_rows, m_cols);\n  m_singularValues.resize(m_diagSize);\n  if(RowsAtCompileTime==Dynamic)\n    m_matrixU.resize(m_rows, m_computeFullU ? m_rows : m_computeThinU ? m_diagSize : 0);\n  if(ColsAtCompileTime==Dynamic)\n    m_matrixV.resize(m_cols, m_computeFullV ? m_cols : m_computeThinV ? m_diagSize : 0);\n\n  return false;\n}\n\n}// end namespace\n\n#endif // EIGEN_SVDBASE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SVD/UpperBidiagonalization.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2013-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_BIDIAGONALIZATION_H\n#define EIGEN_BIDIAGONALIZATION_H\n\nnamespace Eigen { \n\nnamespace internal {\n// UpperBidiagonalization will probably be replaced by a Bidiagonalization class, don't want to make it stable API.\n// At the same time, it's useful to keep for now as it's about the only thing that is testing the BandMatrix class.\n\ntemplate<typename _MatrixType> class UpperBidiagonalization\n{\n  public:\n\n    typedef _MatrixType MatrixType;\n    enum {\n      RowsAtCompileTime = MatrixType::RowsAtCompileTime,\n      ColsAtCompileTime = MatrixType::ColsAtCompileTime,\n      ColsAtCompileTimeMinusOne = internal::decrement_size<ColsAtCompileTime>::ret\n    };\n    typedef typename MatrixType::Scalar Scalar;\n    typedef typename MatrixType::RealScalar RealScalar;\n    typedef Eigen::Index Index; ///< \\deprecated since Eigen 3.3\n    typedef Matrix<Scalar, 1, ColsAtCompileTime> RowVectorType;\n    typedef Matrix<Scalar, RowsAtCompileTime, 1> ColVectorType;\n    typedef BandMatrix<RealScalar, ColsAtCompileTime, ColsAtCompileTime, 1, 0, RowMajor> BidiagonalType;\n    typedef Matrix<Scalar, ColsAtCompileTime, 1> DiagVectorType;\n    typedef Matrix<Scalar, ColsAtCompileTimeMinusOne, 1> SuperDiagVectorType;\n    typedef HouseholderSequence<\n              const MatrixType,\n              const typename internal::remove_all<typename Diagonal<const MatrixType,0>::ConjugateReturnType>::type\n            > HouseholderUSequenceType;\n    typedef HouseholderSequence<\n              const typename internal::remove_all<typename MatrixType::ConjugateReturnType>::type,\n              Diagonal<const MatrixType,1>,\n              OnTheRight\n            > HouseholderVSequenceType;\n    \n    /**\n    * \\brief Default Constructor.\n    *\n    * The default constructor is useful in cases in which the user intends to\n    * perform decompositions via Bidiagonalization::compute(const MatrixType&).\n    */\n    UpperBidiagonalization() : m_householder(), m_bidiagonal(), m_isInitialized(false) {}\n\n    explicit UpperBidiagonalization(const MatrixType& matrix)\n      : m_householder(matrix.rows(), matrix.cols()),\n        m_bidiagonal(matrix.cols(), matrix.cols()),\n        m_isInitialized(false)\n    {\n      compute(matrix);\n    }\n    \n    UpperBidiagonalization& compute(const MatrixType& matrix);\n    UpperBidiagonalization& computeUnblocked(const MatrixType& matrix);\n    \n    const MatrixType& householder() const { return m_householder; }\n    const BidiagonalType& bidiagonal() const { return m_bidiagonal; }\n    \n    const HouseholderUSequenceType householderU() const\n    {\n      eigen_assert(m_isInitialized && \"UpperBidiagonalization is not initialized.\");\n      return HouseholderUSequenceType(m_householder, m_householder.diagonal().conjugate());\n    }\n\n    const HouseholderVSequenceType householderV() // const here gives nasty errors and i'm lazy\n    {\n      eigen_assert(m_isInitialized && \"UpperBidiagonalization is not initialized.\");\n      return HouseholderVSequenceType(m_householder.conjugate(), m_householder.const_derived().template diagonal<1>())\n             .setLength(m_householder.cols()-1)\n             .setShift(1);\n    }\n    \n  protected:\n    MatrixType m_householder;\n    BidiagonalType m_bidiagonal;\n    bool m_isInitialized;\n};\n\n// Standard upper bidiagonalization without fancy optimizations\n// This version should be faster for small matrix size\ntemplate<typename MatrixType>\nvoid upperbidiagonalization_inplace_unblocked(MatrixType& mat,\n                                              typename MatrixType::RealScalar *diagonal,\n                                              typename MatrixType::RealScalar *upper_diagonal,\n                                              typename MatrixType::Scalar* tempData = 0)\n{\n  typedef typename MatrixType::Scalar Scalar;\n\n  Index rows = mat.rows();\n  Index cols = mat.cols();\n\n  typedef Matrix<Scalar,Dynamic,1,ColMajor,MatrixType::MaxRowsAtCompileTime,1> TempType;\n  TempType tempVector;\n  if(tempData==0)\n  {\n    tempVector.resize(rows);\n    tempData = tempVector.data();\n  }\n\n  for (Index k = 0; /* breaks at k==cols-1 below */ ; ++k)\n  {\n    Index remainingRows = rows - k;\n    Index remainingCols = cols - k - 1;\n\n    // construct left householder transform in-place in A\n    mat.col(k).tail(remainingRows)\n       .makeHouseholderInPlace(mat.coeffRef(k,k), diagonal[k]);\n    // apply householder transform to remaining part of A on the left\n    mat.bottomRightCorner(remainingRows, remainingCols)\n       .applyHouseholderOnTheLeft(mat.col(k).tail(remainingRows-1), mat.coeff(k,k), tempData);\n\n    if(k == cols-1) break;\n\n    // construct right householder transform in-place in mat\n    mat.row(k).tail(remainingCols)\n       .makeHouseholderInPlace(mat.coeffRef(k,k+1), upper_diagonal[k]);\n    // apply householder transform to remaining part of mat on the left\n    mat.bottomRightCorner(remainingRows-1, remainingCols)\n       .applyHouseholderOnTheRight(mat.row(k).tail(remainingCols-1).transpose(), mat.coeff(k,k+1), tempData);\n  }\n}\n\n/** \\internal\n  * Helper routine for the block reduction to upper bidiagonal form.\n  *\n  * Let's partition the matrix A:\n  * \n  *      | A00 A01 |\n  *  A = |         |\n  *      | A10 A11 |\n  *\n  * This function reduces to bidiagonal form the left \\c rows x \\a blockSize vertical panel [A00/A10]\n  * and the \\a blockSize x \\c cols horizontal panel [A00 A01] of the matrix \\a A. The bottom-right block A11\n  * is updated using matrix-matrix products:\n  *   A22 -= V * Y^T - X * U^T\n  * where V and U contains the left and right Householder vectors. U and V are stored in A10, and A01\n  * respectively, and the update matrices X and Y are computed during the reduction.\n  * \n  */\ntemplate<typename MatrixType>\nvoid upperbidiagonalization_blocked_helper(MatrixType& A,\n                                           typename MatrixType::RealScalar *diagonal,\n                                           typename MatrixType::RealScalar *upper_diagonal,\n                                           Index bs,\n                                           Ref<Matrix<typename MatrixType::Scalar, Dynamic, Dynamic,\n                                                      traits<MatrixType>::Flags & RowMajorBit> > X,\n                                           Ref<Matrix<typename MatrixType::Scalar, Dynamic, Dynamic,\n                                                      traits<MatrixType>::Flags & RowMajorBit> > Y)\n{\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename MatrixType::RealScalar RealScalar;\n  typedef typename NumTraits<RealScalar>::Literal Literal;\n  enum { StorageOrder = traits<MatrixType>::Flags & RowMajorBit };\n  typedef InnerStride<int(StorageOrder) == int(ColMajor) ? 1 : Dynamic> ColInnerStride;\n  typedef InnerStride<int(StorageOrder) == int(ColMajor) ? Dynamic : 1> RowInnerStride;\n  typedef Ref<Matrix<Scalar, Dynamic, 1>, 0, ColInnerStride>    SubColumnType;\n  typedef Ref<Matrix<Scalar, 1, Dynamic>, 0, RowInnerStride>    SubRowType;\n  typedef Ref<Matrix<Scalar, Dynamic, Dynamic, StorageOrder > > SubMatType;\n  \n  Index brows = A.rows();\n  Index bcols = A.cols();\n\n  Scalar tau_u, tau_u_prev(0), tau_v;\n\n  for(Index k = 0; k < bs; ++k)\n  {\n    Index remainingRows = brows - k;\n    Index remainingCols = bcols - k - 1;\n\n    SubMatType X_k1( X.block(k,0, remainingRows,k) );\n    SubMatType V_k1( A.block(k,0, remainingRows,k) );\n\n    // 1 - update the k-th column of A\n    SubColumnType v_k = A.col(k).tail(remainingRows);\n          v_k -= V_k1 * Y.row(k).head(k).adjoint();\n    if(k) v_k -= X_k1 * A.col(k).head(k);\n    \n    // 2 - construct left Householder transform in-place\n    v_k.makeHouseholderInPlace(tau_v, diagonal[k]);\n       \n    if(k+1<bcols)\n    {\n      SubMatType Y_k  ( Y.block(k+1,0, remainingCols, k+1) );\n      SubMatType U_k1 ( A.block(0,k+1, k,remainingCols) );\n      \n      // this eases the application of Householder transforAions\n      // A(k,k) will store tau_v later\n      A(k,k) = Scalar(1);\n\n      // 3 - Compute y_k^T = tau_v * ( A^T*v_k - Y_k-1*V_k-1^T*v_k - U_k-1*X_k-1^T*v_k )\n      {\n        SubColumnType y_k( Y.col(k).tail(remainingCols) );\n        \n        // let's use the begining of column k of Y as a temporary vector\n        SubColumnType tmp( Y.col(k).head(k) );\n        y_k.noalias()  = A.block(k,k+1, remainingRows,remainingCols).adjoint() * v_k; // bottleneck\n        tmp.noalias()  = V_k1.adjoint()  * v_k;\n        y_k.noalias() -= Y_k.leftCols(k) * tmp;\n        tmp.noalias()  = X_k1.adjoint()  * v_k;\n        y_k.noalias() -= U_k1.adjoint()  * tmp;\n        y_k *= numext::conj(tau_v);\n      }\n\n      // 4 - update k-th row of A (it will become u_k)\n      SubRowType u_k( A.row(k).tail(remainingCols) );\n      u_k = u_k.conjugate();\n      {\n        u_k -= Y_k * A.row(k).head(k+1).adjoint();\n        if(k) u_k -= U_k1.adjoint() * X.row(k).head(k).adjoint();\n      }\n\n      // 5 - construct right Householder transform in-place\n      u_k.makeHouseholderInPlace(tau_u, upper_diagonal[k]);\n\n      // this eases the application of Householder transformations\n      // A(k,k+1) will store tau_u later\n      A(k,k+1) = Scalar(1);\n\n      // 6 - Compute x_k = tau_u * ( A*u_k - X_k-1*U_k-1^T*u_k - V_k*Y_k^T*u_k )\n      {\n        SubColumnType x_k ( X.col(k).tail(remainingRows-1) );\n        \n        // let's use the begining of column k of X as a temporary vectors\n        // note that tmp0 and tmp1 overlaps\n        SubColumnType tmp0 ( X.col(k).head(k) ),\n                      tmp1 ( X.col(k).head(k+1) );\n                    \n        x_k.noalias()   = A.block(k+1,k+1, remainingRows-1,remainingCols) * u_k.transpose(); // bottleneck\n        tmp0.noalias()  = U_k1 * u_k.transpose();\n        x_k.noalias()  -= X_k1.bottomRows(remainingRows-1) * tmp0;\n        tmp1.noalias()  = Y_k.adjoint() * u_k.transpose();\n        x_k.noalias()  -= A.block(k+1,0, remainingRows-1,k+1) * tmp1;\n        x_k *= numext::conj(tau_u);\n        tau_u = numext::conj(tau_u);\n        u_k = u_k.conjugate();\n      }\n\n      if(k>0) A.coeffRef(k-1,k) = tau_u_prev;\n      tau_u_prev = tau_u;\n    }\n    else\n      A.coeffRef(k-1,k) = tau_u_prev;\n\n    A.coeffRef(k,k) = tau_v;\n  }\n  \n  if(bs<bcols)\n    A.coeffRef(bs-1,bs) = tau_u_prev;\n\n  // update A22\n  if(bcols>bs && brows>bs)\n  {\n    SubMatType A11( A.bottomRightCorner(brows-bs,bcols-bs) );\n    SubMatType A10( A.block(bs,0, brows-bs,bs) );\n    SubMatType A01( A.block(0,bs, bs,bcols-bs) );\n    Scalar tmp = A01(bs-1,0);\n    A01(bs-1,0) = Literal(1);\n    A11.noalias() -= A10 * Y.topLeftCorner(bcols,bs).bottomRows(bcols-bs).adjoint();\n    A11.noalias() -= X.topLeftCorner(brows,bs).bottomRows(brows-bs) * A01;\n    A01(bs-1,0) = tmp;\n  }\n}\n\n/** \\internal\n  *\n  * Implementation of a block-bidiagonal reduction.\n  * It is based on the following paper:\n  *   The Design of a Parallel Dense Linear Algebra Software Library: Reduction to Hessenberg, Tridiagonal, and Bidiagonal Form.\n  *   by Jaeyoung Choi, Jack J. Dongarra, David W. Walker. (1995)\n  *   section 3.3\n  */\ntemplate<typename MatrixType, typename BidiagType>\nvoid upperbidiagonalization_inplace_blocked(MatrixType& A, BidiagType& bidiagonal,\n                                            Index maxBlockSize=32,\n                                            typename MatrixType::Scalar* /*tempData*/ = 0)\n{\n  typedef typename MatrixType::Scalar Scalar;\n  typedef Block<MatrixType,Dynamic,Dynamic> BlockType;\n\n  Index rows = A.rows();\n  Index cols = A.cols();\n  Index size = (std::min)(rows, cols);\n\n  // X and Y are work space\n  enum { StorageOrder = traits<MatrixType>::Flags & RowMajorBit };\n  Matrix<Scalar,\n         MatrixType::RowsAtCompileTime,\n         Dynamic,\n         StorageOrder,\n         MatrixType::MaxRowsAtCompileTime> X(rows,maxBlockSize);\n  Matrix<Scalar,\n         MatrixType::ColsAtCompileTime,\n         Dynamic,\n         StorageOrder,\n         MatrixType::MaxColsAtCompileTime> Y(cols,maxBlockSize);\n  Index blockSize = (std::min)(maxBlockSize,size);\n\n  Index k = 0;\n  for(k = 0; k < size; k += blockSize)\n  {\n    Index bs = (std::min)(size-k,blockSize);  // actual size of the block\n    Index brows = rows - k;                   // rows of the block\n    Index bcols = cols - k;                   // columns of the block\n\n    // partition the matrix A:\n    // \n    //      | A00 A01 A02 |\n    //      |             |\n    // A  = | A10 A11 A12 |\n    //      |             |\n    //      | A20 A21 A22 |\n    //\n    // where A11 is a bs x bs diagonal block,\n    // and let:\n    //      | A11 A12 |\n    //  B = |         |\n    //      | A21 A22 |\n\n    BlockType B = A.block(k,k,brows,bcols);\n    \n    // This stage performs the bidiagonalization of A11, A21, A12, and updating of A22.\n    // Finally, the algorithm continue on the updated A22.\n    //\n    // However, if B is too small, or A22 empty, then let's use an unblocked strategy\n    if(k+bs==cols || bcols<48) // somewhat arbitrary threshold\n    {\n      upperbidiagonalization_inplace_unblocked(B,\n                                               &(bidiagonal.template diagonal<0>().coeffRef(k)),\n                                               &(bidiagonal.template diagonal<1>().coeffRef(k)),\n                                               X.data()\n                                              );\n      break; // We're done\n    }\n    else\n    {\n      upperbidiagonalization_blocked_helper<BlockType>( B,\n                                                        &(bidiagonal.template diagonal<0>().coeffRef(k)),\n                                                        &(bidiagonal.template diagonal<1>().coeffRef(k)),\n                                                        bs,\n                                                        X.topLeftCorner(brows,bs),\n                                                        Y.topLeftCorner(bcols,bs)\n                                                      );\n    }\n  }\n}\n\ntemplate<typename _MatrixType>\nUpperBidiagonalization<_MatrixType>& UpperBidiagonalization<_MatrixType>::computeUnblocked(const _MatrixType& matrix)\n{\n  Index rows = matrix.rows();\n  Index cols = matrix.cols();\n  EIGEN_ONLY_USED_FOR_DEBUG(cols);\n\n  eigen_assert(rows >= cols && \"UpperBidiagonalization is only for Arices satisfying rows>=cols.\");\n\n  m_householder = matrix;\n\n  ColVectorType temp(rows);\n\n  upperbidiagonalization_inplace_unblocked(m_householder,\n                                           &(m_bidiagonal.template diagonal<0>().coeffRef(0)),\n                                           &(m_bidiagonal.template diagonal<1>().coeffRef(0)),\n                                           temp.data());\n\n  m_isInitialized = true;\n  return *this;\n}\n\ntemplate<typename _MatrixType>\nUpperBidiagonalization<_MatrixType>& UpperBidiagonalization<_MatrixType>::compute(const _MatrixType& matrix)\n{\n  Index rows = matrix.rows();\n  Index cols = matrix.cols();\n  EIGEN_ONLY_USED_FOR_DEBUG(rows);\n  EIGEN_ONLY_USED_FOR_DEBUG(cols);\n\n  eigen_assert(rows >= cols && \"UpperBidiagonalization is only for Arices satisfying rows>=cols.\");\n\n  m_householder = matrix;\n  upperbidiagonalization_inplace_blocked(m_householder, m_bidiagonal);\n            \n  m_isInitialized = true;\n  return *this;\n}\n\n#if 0\n/** \\return the Householder QR decomposition of \\c *this.\n  *\n  * \\sa class Bidiagonalization\n  */\ntemplate<typename Derived>\nconst UpperBidiagonalization<typename MatrixBase<Derived>::PlainObject>\nMatrixBase<Derived>::bidiagonalization() const\n{\n  return UpperBidiagonalization<PlainObject>(eval());\n}\n#endif\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_BIDIAGONALIZATION_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseCholesky/SimplicialCholesky.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2012 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SIMPLICIAL_CHOLESKY_H\n#define EIGEN_SIMPLICIAL_CHOLESKY_H\n\nnamespace Eigen { \n\nenum SimplicialCholeskyMode {\n  SimplicialCholeskyLLT,\n  SimplicialCholeskyLDLT\n};\n\nnamespace internal {\n  template<typename CholMatrixType, typename InputMatrixType>\n  struct simplicial_cholesky_grab_input {\n    typedef CholMatrixType const * ConstCholMatrixPtr;\n    static void run(const InputMatrixType& input, ConstCholMatrixPtr &pmat, CholMatrixType &tmp)\n    {\n      tmp = input;\n      pmat = &tmp;\n    }\n  };\n  \n  template<typename MatrixType>\n  struct simplicial_cholesky_grab_input<MatrixType,MatrixType> {\n    typedef MatrixType const * ConstMatrixPtr;\n    static void run(const MatrixType& input, ConstMatrixPtr &pmat, MatrixType &/*tmp*/)\n    {\n      pmat = &input;\n    }\n  };\n} // end namespace internal\n\n/** \\ingroup SparseCholesky_Module\n  * \\brief A base class for direct sparse Cholesky factorizations\n  *\n  * This is a base class for LL^T and LDL^T Cholesky factorizations of sparse matrices that are\n  * selfadjoint and positive definite. These factorizations allow for solving A.X = B where\n  * X and B can be either dense or sparse.\n  * \n  * In order to reduce the fill-in, a symmetric permutation P is applied prior to the factorization\n  * such that the factorized matrix is P A P^-1.\n  *\n  * \\tparam Derived the type of the derived class, that is the actual factorization type.\n  *\n  */\ntemplate<typename Derived>\nclass SimplicialCholeskyBase : public SparseSolverBase<Derived>\n{\n    typedef SparseSolverBase<Derived> Base;\n    using Base::m_isInitialized;\n    \n  public:\n    typedef typename internal::traits<Derived>::MatrixType MatrixType;\n    typedef typename internal::traits<Derived>::OrderingType OrderingType;\n    enum { UpLo = internal::traits<Derived>::UpLo };\n    typedef typename MatrixType::Scalar Scalar;\n    typedef typename MatrixType::RealScalar RealScalar;\n    typedef typename MatrixType::StorageIndex StorageIndex;\n    typedef SparseMatrix<Scalar,ColMajor,StorageIndex> CholMatrixType;\n    typedef CholMatrixType const * ConstCholMatrixPtr;\n    typedef Matrix<Scalar,Dynamic,1> VectorType;\n    typedef Matrix<StorageIndex,Dynamic,1> VectorI;\n\n    enum {\n      ColsAtCompileTime = MatrixType::ColsAtCompileTime,\n      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime\n    };\n\n  public:\n    \n    using Base::derived;\n\n    /** Default constructor */\n    SimplicialCholeskyBase()\n      : m_info(Success), m_shiftOffset(0), m_shiftScale(1)\n    {}\n\n    explicit SimplicialCholeskyBase(const MatrixType& matrix)\n      : m_info(Success), m_shiftOffset(0), m_shiftScale(1)\n    {\n      derived().compute(matrix);\n    }\n\n    ~SimplicialCholeskyBase()\n    {\n    }\n\n    Derived& derived() { return *static_cast<Derived*>(this); }\n    const Derived& derived() const { return *static_cast<const Derived*>(this); }\n    \n    inline Index cols() const { return m_matrix.cols(); }\n    inline Index rows() const { return m_matrix.rows(); }\n    \n    /** \\brief Reports whether previous computation was successful.\n      *\n      * \\returns \\c Success if computation was succesful,\n      *          \\c NumericalIssue if the matrix.appears to be negative.\n      */\n    ComputationInfo info() const\n    {\n      eigen_assert(m_isInitialized && \"Decomposition is not initialized.\");\n      return m_info;\n    }\n    \n    /** \\returns the permutation P\n      * \\sa permutationPinv() */\n    const PermutationMatrix<Dynamic,Dynamic,StorageIndex>& permutationP() const\n    { return m_P; }\n    \n    /** \\returns the inverse P^-1 of the permutation P\n      * \\sa permutationP() */\n    const PermutationMatrix<Dynamic,Dynamic,StorageIndex>& permutationPinv() const\n    { return m_Pinv; }\n\n    /** Sets the shift parameters that will be used to adjust the diagonal coefficients during the numerical factorization.\n      *\n      * During the numerical factorization, the diagonal coefficients are transformed by the following linear model:\\n\n      * \\c d_ii = \\a offset + \\a scale * \\c d_ii\n      *\n      * The default is the identity transformation with \\a offset=0, and \\a scale=1.\n      *\n      * \\returns a reference to \\c *this.\n      */\n    Derived& setShift(const RealScalar& offset, const RealScalar& scale = 1)\n    {\n      m_shiftOffset = offset;\n      m_shiftScale = scale;\n      return derived();\n    }\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\n    /** \\internal */\n    template<typename Stream>\n    void dumpMemory(Stream& s)\n    {\n      int total = 0;\n      s << \"  L:        \" << ((total+=(m_matrix.cols()+1) * sizeof(int) + m_matrix.nonZeros()*(sizeof(int)+sizeof(Scalar))) >> 20) << \"Mb\" << \"\\n\";\n      s << \"  diag:     \" << ((total+=m_diag.size() * sizeof(Scalar)) >> 20) << \"Mb\" << \"\\n\";\n      s << \"  tree:     \" << ((total+=m_parent.size() * sizeof(int)) >> 20) << \"Mb\" << \"\\n\";\n      s << \"  nonzeros: \" << ((total+=m_nonZerosPerCol.size() * sizeof(int)) >> 20) << \"Mb\" << \"\\n\";\n      s << \"  perm:     \" << ((total+=m_P.size() * sizeof(int)) >> 20) << \"Mb\" << \"\\n\";\n      s << \"  perm^-1:  \" << ((total+=m_Pinv.size() * sizeof(int)) >> 20) << \"Mb\" << \"\\n\";\n      s << \"  TOTAL:    \" << (total>> 20) << \"Mb\" << \"\\n\";\n    }\n\n    /** \\internal */\n    template<typename Rhs,typename Dest>\n    void _solve_impl(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const\n    {\n      eigen_assert(m_factorizationIsOk && \"The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()\");\n      eigen_assert(m_matrix.rows()==b.rows());\n\n      if(m_info!=Success)\n        return;\n\n      if(m_P.size()>0)\n        dest = m_P * b;\n      else\n        dest = b;\n\n      if(m_matrix.nonZeros()>0) // otherwise L==I\n        derived().matrixL().solveInPlace(dest);\n\n      if(m_diag.size()>0)\n        dest = m_diag.asDiagonal().inverse() * dest;\n\n      if (m_matrix.nonZeros()>0) // otherwise U==I\n        derived().matrixU().solveInPlace(dest);\n\n      if(m_P.size()>0)\n        dest = m_Pinv * dest;\n    }\n    \n    template<typename Rhs,typename Dest>\n    void _solve_impl(const SparseMatrixBase<Rhs> &b, SparseMatrixBase<Dest> &dest) const\n    {\n      internal::solve_sparse_through_dense_panels(derived(), b, dest);\n    }\n\n#endif // EIGEN_PARSED_BY_DOXYGEN\n\n  protected:\n    \n    /** Computes the sparse Cholesky decomposition of \\a matrix */\n    template<bool DoLDLT>\n    void compute(const MatrixType& matrix)\n    {\n      eigen_assert(matrix.rows()==matrix.cols());\n      Index size = matrix.cols();\n      CholMatrixType tmp(size,size);\n      ConstCholMatrixPtr pmat;\n      ordering(matrix, pmat, tmp);\n      analyzePattern_preordered(*pmat, DoLDLT);\n      factorize_preordered<DoLDLT>(*pmat);\n    }\n    \n    template<bool DoLDLT>\n    void factorize(const MatrixType& a)\n    {\n      eigen_assert(a.rows()==a.cols());\n      Index size = a.cols();\n      CholMatrixType tmp(size,size);\n      ConstCholMatrixPtr pmat;\n      \n      if(m_P.size()==0 && (UpLo&Upper)==Upper)\n      {\n        // If there is no ordering, try to directly use the input matrix without any copy\n        internal::simplicial_cholesky_grab_input<CholMatrixType,MatrixType>::run(a, pmat, tmp);\n      }\n      else\n      {\n        tmp.template selfadjointView<Upper>() = a.template selfadjointView<UpLo>().twistedBy(m_P);\n        pmat = &tmp;\n      }\n      \n      factorize_preordered<DoLDLT>(*pmat);\n    }\n\n    template<bool DoLDLT>\n    void factorize_preordered(const CholMatrixType& a);\n\n    void analyzePattern(const MatrixType& a, bool doLDLT)\n    {\n      eigen_assert(a.rows()==a.cols());\n      Index size = a.cols();\n      CholMatrixType tmp(size,size);\n      ConstCholMatrixPtr pmat;\n      ordering(a, pmat, tmp);\n      analyzePattern_preordered(*pmat,doLDLT);\n    }\n    void analyzePattern_preordered(const CholMatrixType& a, bool doLDLT);\n    \n    void ordering(const MatrixType& a, ConstCholMatrixPtr &pmat, CholMatrixType& ap);\n\n    /** keeps off-diagonal entries; drops diagonal entries */\n    struct keep_diag {\n      inline bool operator() (const Index& row, const Index& col, const Scalar&) const\n      {\n        return row!=col;\n      }\n    };\n\n    mutable ComputationInfo m_info;\n    bool m_factorizationIsOk;\n    bool m_analysisIsOk;\n    \n    CholMatrixType m_matrix;\n    VectorType m_diag;                                // the diagonal coefficients (LDLT mode)\n    VectorI m_parent;                                 // elimination tree\n    VectorI m_nonZerosPerCol;\n    PermutationMatrix<Dynamic,Dynamic,StorageIndex> m_P;     // the permutation\n    PermutationMatrix<Dynamic,Dynamic,StorageIndex> m_Pinv;  // the inverse permutation\n\n    RealScalar m_shiftOffset;\n    RealScalar m_shiftScale;\n};\n\ntemplate<typename _MatrixType, int _UpLo = Lower, typename _Ordering = AMDOrdering<typename _MatrixType::StorageIndex> > class SimplicialLLT;\ntemplate<typename _MatrixType, int _UpLo = Lower, typename _Ordering = AMDOrdering<typename _MatrixType::StorageIndex> > class SimplicialLDLT;\ntemplate<typename _MatrixType, int _UpLo = Lower, typename _Ordering = AMDOrdering<typename _MatrixType::StorageIndex> > class SimplicialCholesky;\n\nnamespace internal {\n\ntemplate<typename _MatrixType, int _UpLo, typename _Ordering> struct traits<SimplicialLLT<_MatrixType,_UpLo,_Ordering> >\n{\n  typedef _MatrixType MatrixType;\n  typedef _Ordering OrderingType;\n  enum { UpLo = _UpLo };\n  typedef typename MatrixType::Scalar                         Scalar;\n  typedef typename MatrixType::StorageIndex                   StorageIndex;\n  typedef SparseMatrix<Scalar, ColMajor, StorageIndex>        CholMatrixType;\n  typedef TriangularView<const CholMatrixType, Eigen::Lower>  MatrixL;\n  typedef TriangularView<const typename CholMatrixType::AdjointReturnType, Eigen::Upper>   MatrixU;\n  static inline MatrixL getL(const MatrixType& m) { return MatrixL(m); }\n  static inline MatrixU getU(const MatrixType& m) { return MatrixU(m.adjoint()); }\n};\n\ntemplate<typename _MatrixType,int _UpLo, typename _Ordering> struct traits<SimplicialLDLT<_MatrixType,_UpLo,_Ordering> >\n{\n  typedef _MatrixType MatrixType;\n  typedef _Ordering OrderingType;\n  enum { UpLo = _UpLo };\n  typedef typename MatrixType::Scalar                             Scalar;\n  typedef typename MatrixType::StorageIndex                       StorageIndex;\n  typedef SparseMatrix<Scalar, ColMajor, StorageIndex>            CholMatrixType;\n  typedef TriangularView<const CholMatrixType, Eigen::UnitLower>  MatrixL;\n  typedef TriangularView<const typename CholMatrixType::AdjointReturnType, Eigen::UnitUpper> MatrixU;\n  static inline MatrixL getL(const MatrixType& m) { return MatrixL(m); }\n  static inline MatrixU getU(const MatrixType& m) { return MatrixU(m.adjoint()); }\n};\n\ntemplate<typename _MatrixType, int _UpLo, typename _Ordering> struct traits<SimplicialCholesky<_MatrixType,_UpLo,_Ordering> >\n{\n  typedef _MatrixType MatrixType;\n  typedef _Ordering OrderingType;\n  enum { UpLo = _UpLo };\n};\n\n}\n\n/** \\ingroup SparseCholesky_Module\n  * \\class SimplicialLLT\n  * \\brief A direct sparse LLT Cholesky factorizations\n  *\n  * This class provides a LL^T Cholesky factorizations of sparse matrices that are\n  * selfadjoint and positive definite. The factorization allows for solving A.X = B where\n  * X and B can be either dense or sparse.\n  * \n  * In order to reduce the fill-in, a symmetric permutation P is applied prior to the factorization\n  * such that the factorized matrix is P A P^-1.\n  *\n  * \\tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>\n  * \\tparam _UpLo the triangular part that will be used for the computations. It can be Lower\n  *               or Upper. Default is Lower.\n  * \\tparam _Ordering The ordering method to use, either AMDOrdering<> or NaturalOrdering<>. Default is AMDOrdering<>\n  *\n  * \\implsparsesolverconcept\n  *\n  * \\sa class SimplicialLDLT, class AMDOrdering, class NaturalOrdering\n  */\ntemplate<typename _MatrixType, int _UpLo, typename _Ordering>\n    class SimplicialLLT : public SimplicialCholeskyBase<SimplicialLLT<_MatrixType,_UpLo,_Ordering> >\n{\npublic:\n    typedef _MatrixType MatrixType;\n    enum { UpLo = _UpLo };\n    typedef SimplicialCholeskyBase<SimplicialLLT> Base;\n    typedef typename MatrixType::Scalar Scalar;\n    typedef typename MatrixType::RealScalar RealScalar;\n    typedef typename MatrixType::StorageIndex StorageIndex;\n    typedef SparseMatrix<Scalar,ColMajor,Index> CholMatrixType;\n    typedef Matrix<Scalar,Dynamic,1> VectorType;\n    typedef internal::traits<SimplicialLLT> Traits;\n    typedef typename Traits::MatrixL  MatrixL;\n    typedef typename Traits::MatrixU  MatrixU;\npublic:\n    /** Default constructor */\n    SimplicialLLT() : Base() {}\n    /** Constructs and performs the LLT factorization of \\a matrix */\n    explicit SimplicialLLT(const MatrixType& matrix)\n        : Base(matrix) {}\n\n    /** \\returns an expression of the factor L */\n    inline const MatrixL matrixL() const {\n        eigen_assert(Base::m_factorizationIsOk && \"Simplicial LLT not factorized\");\n        return Traits::getL(Base::m_matrix);\n    }\n\n    /** \\returns an expression of the factor U (= L^*) */\n    inline const MatrixU matrixU() const {\n        eigen_assert(Base::m_factorizationIsOk && \"Simplicial LLT not factorized\");\n        return Traits::getU(Base::m_matrix);\n    }\n    \n    /** Computes the sparse Cholesky decomposition of \\a matrix */\n    SimplicialLLT& compute(const MatrixType& matrix)\n    {\n      Base::template compute<false>(matrix);\n      return *this;\n    }\n\n    /** Performs a symbolic decomposition on the sparcity of \\a matrix.\n      *\n      * This function is particularly useful when solving for several problems having the same structure.\n      *\n      * \\sa factorize()\n      */\n    void analyzePattern(const MatrixType& a)\n    {\n      Base::analyzePattern(a, false);\n    }\n\n    /** Performs a numeric decomposition of \\a matrix\n      *\n      * The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed.\n      *\n      * \\sa analyzePattern()\n      */\n    void factorize(const MatrixType& a)\n    {\n      Base::template factorize<false>(a);\n    }\n\n    /** \\returns the determinant of the underlying matrix from the current factorization */\n    Scalar determinant() const\n    {\n      Scalar detL = Base::m_matrix.diagonal().prod();\n      return numext::abs2(detL);\n    }\n};\n\n/** \\ingroup SparseCholesky_Module\n  * \\class SimplicialLDLT\n  * \\brief A direct sparse LDLT Cholesky factorizations without square root.\n  *\n  * This class provides a LDL^T Cholesky factorizations without square root of sparse matrices that are\n  * selfadjoint and positive definite. The factorization allows for solving A.X = B where\n  * X and B can be either dense or sparse.\n  * \n  * In order to reduce the fill-in, a symmetric permutation P is applied prior to the factorization\n  * such that the factorized matrix is P A P^-1.\n  *\n  * \\tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>\n  * \\tparam _UpLo the triangular part that will be used for the computations. It can be Lower\n  *               or Upper. Default is Lower.\n  * \\tparam _Ordering The ordering method to use, either AMDOrdering<> or NaturalOrdering<>. Default is AMDOrdering<>\n  *\n  * \\implsparsesolverconcept\n  *\n  * \\sa class SimplicialLLT, class AMDOrdering, class NaturalOrdering\n  */\ntemplate<typename _MatrixType, int _UpLo, typename _Ordering>\n    class SimplicialLDLT : public SimplicialCholeskyBase<SimplicialLDLT<_MatrixType,_UpLo,_Ordering> >\n{\npublic:\n    typedef _MatrixType MatrixType;\n    enum { UpLo = _UpLo };\n    typedef SimplicialCholeskyBase<SimplicialLDLT> Base;\n    typedef typename MatrixType::Scalar Scalar;\n    typedef typename MatrixType::RealScalar RealScalar;\n    typedef typename MatrixType::StorageIndex StorageIndex;\n    typedef SparseMatrix<Scalar,ColMajor,StorageIndex> CholMatrixType;\n    typedef Matrix<Scalar,Dynamic,1> VectorType;\n    typedef internal::traits<SimplicialLDLT> Traits;\n    typedef typename Traits::MatrixL  MatrixL;\n    typedef typename Traits::MatrixU  MatrixU;\npublic:\n    /** Default constructor */\n    SimplicialLDLT() : Base() {}\n\n    /** Constructs and performs the LLT factorization of \\a matrix */\n    explicit SimplicialLDLT(const MatrixType& matrix)\n        : Base(matrix) {}\n\n    /** \\returns a vector expression of the diagonal D */\n    inline const VectorType vectorD() const {\n        eigen_assert(Base::m_factorizationIsOk && \"Simplicial LDLT not factorized\");\n        return Base::m_diag;\n    }\n    /** \\returns an expression of the factor L */\n    inline const MatrixL matrixL() const {\n        eigen_assert(Base::m_factorizationIsOk && \"Simplicial LDLT not factorized\");\n        return Traits::getL(Base::m_matrix);\n    }\n\n    /** \\returns an expression of the factor U (= L^*) */\n    inline const MatrixU matrixU() const {\n        eigen_assert(Base::m_factorizationIsOk && \"Simplicial LDLT not factorized\");\n        return Traits::getU(Base::m_matrix);\n    }\n\n    /** Computes the sparse Cholesky decomposition of \\a matrix */\n    SimplicialLDLT& compute(const MatrixType& matrix)\n    {\n      Base::template compute<true>(matrix);\n      return *this;\n    }\n    \n    /** Performs a symbolic decomposition on the sparcity of \\a matrix.\n      *\n      * This function is particularly useful when solving for several problems having the same structure.\n      *\n      * \\sa factorize()\n      */\n    void analyzePattern(const MatrixType& a)\n    {\n      Base::analyzePattern(a, true);\n    }\n\n    /** Performs a numeric decomposition of \\a matrix\n      *\n      * The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed.\n      *\n      * \\sa analyzePattern()\n      */\n    void factorize(const MatrixType& a)\n    {\n      Base::template factorize<true>(a);\n    }\n\n    /** \\returns the determinant of the underlying matrix from the current factorization */\n    Scalar determinant() const\n    {\n      return Base::m_diag.prod();\n    }\n};\n\n/** \\deprecated use SimplicialLDLT or class SimplicialLLT\n  * \\ingroup SparseCholesky_Module\n  * \\class SimplicialCholesky\n  *\n  * \\sa class SimplicialLDLT, class SimplicialLLT\n  */\ntemplate<typename _MatrixType, int _UpLo, typename _Ordering>\n    class SimplicialCholesky : public SimplicialCholeskyBase<SimplicialCholesky<_MatrixType,_UpLo,_Ordering> >\n{\npublic:\n    typedef _MatrixType MatrixType;\n    enum { UpLo = _UpLo };\n    typedef SimplicialCholeskyBase<SimplicialCholesky> Base;\n    typedef typename MatrixType::Scalar Scalar;\n    typedef typename MatrixType::RealScalar RealScalar;\n    typedef typename MatrixType::StorageIndex StorageIndex;\n    typedef SparseMatrix<Scalar,ColMajor,StorageIndex> CholMatrixType;\n    typedef Matrix<Scalar,Dynamic,1> VectorType;\n    typedef internal::traits<SimplicialCholesky> Traits;\n    typedef internal::traits<SimplicialLDLT<MatrixType,UpLo> > LDLTTraits;\n    typedef internal::traits<SimplicialLLT<MatrixType,UpLo>  > LLTTraits;\n  public:\n    SimplicialCholesky() : Base(), m_LDLT(true) {}\n\n    explicit SimplicialCholesky(const MatrixType& matrix)\n      : Base(), m_LDLT(true)\n    {\n      compute(matrix);\n    }\n\n    SimplicialCholesky& setMode(SimplicialCholeskyMode mode)\n    {\n      switch(mode)\n      {\n      case SimplicialCholeskyLLT:\n        m_LDLT = false;\n        break;\n      case SimplicialCholeskyLDLT:\n        m_LDLT = true;\n        break;\n      default:\n        break;\n      }\n\n      return *this;\n    }\n\n    inline const VectorType vectorD() const {\n        eigen_assert(Base::m_factorizationIsOk && \"Simplicial Cholesky not factorized\");\n        return Base::m_diag;\n    }\n    inline const CholMatrixType rawMatrix() const {\n        eigen_assert(Base::m_factorizationIsOk && \"Simplicial Cholesky not factorized\");\n        return Base::m_matrix;\n    }\n    \n    /** Computes the sparse Cholesky decomposition of \\a matrix */\n    SimplicialCholesky& compute(const MatrixType& matrix)\n    {\n      if(m_LDLT)\n        Base::template compute<true>(matrix);\n      else\n        Base::template compute<false>(matrix);\n      return *this;\n    }\n\n    /** Performs a symbolic decomposition on the sparcity of \\a matrix.\n      *\n      * This function is particularly useful when solving for several problems having the same structure.\n      *\n      * \\sa factorize()\n      */\n    void analyzePattern(const MatrixType& a)\n    {\n      Base::analyzePattern(a, m_LDLT);\n    }\n\n    /** Performs a numeric decomposition of \\a matrix\n      *\n      * The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed.\n      *\n      * \\sa analyzePattern()\n      */\n    void factorize(const MatrixType& a)\n    {\n      if(m_LDLT)\n        Base::template factorize<true>(a);\n      else\n        Base::template factorize<false>(a);\n    }\n\n    /** \\internal */\n    template<typename Rhs,typename Dest>\n    void _solve_impl(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const\n    {\n      eigen_assert(Base::m_factorizationIsOk && \"The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()\");\n      eigen_assert(Base::m_matrix.rows()==b.rows());\n\n      if(Base::m_info!=Success)\n        return;\n\n      if(Base::m_P.size()>0)\n        dest = Base::m_P * b;\n      else\n        dest = b;\n\n      if(Base::m_matrix.nonZeros()>0) // otherwise L==I\n      {\n        if(m_LDLT)\n          LDLTTraits::getL(Base::m_matrix).solveInPlace(dest);\n        else\n          LLTTraits::getL(Base::m_matrix).solveInPlace(dest);\n      }\n\n      if(Base::m_diag.size()>0)\n        dest = Base::m_diag.asDiagonal().inverse() * dest;\n\n      if (Base::m_matrix.nonZeros()>0) // otherwise I==I\n      {\n        if(m_LDLT)\n          LDLTTraits::getU(Base::m_matrix).solveInPlace(dest);\n        else\n          LLTTraits::getU(Base::m_matrix).solveInPlace(dest);\n      }\n\n      if(Base::m_P.size()>0)\n        dest = Base::m_Pinv * dest;\n    }\n    \n    /** \\internal */\n    template<typename Rhs,typename Dest>\n    void _solve_impl(const SparseMatrixBase<Rhs> &b, SparseMatrixBase<Dest> &dest) const\n    {\n      internal::solve_sparse_through_dense_panels(*this, b, dest);\n    }\n    \n    Scalar determinant() const\n    {\n      if(m_LDLT)\n      {\n        return Base::m_diag.prod();\n      }\n      else\n      {\n        Scalar detL = Diagonal<const CholMatrixType>(Base::m_matrix).prod();\n        return numext::abs2(detL);\n      }\n    }\n    \n  protected:\n    bool m_LDLT;\n};\n\ntemplate<typename Derived>\nvoid SimplicialCholeskyBase<Derived>::ordering(const MatrixType& a, ConstCholMatrixPtr &pmat, CholMatrixType& ap)\n{\n  eigen_assert(a.rows()==a.cols());\n  const Index size = a.rows();\n  pmat = &ap;\n  // Note that ordering methods compute the inverse permutation\n  if(!internal::is_same<OrderingType,NaturalOrdering<Index> >::value)\n  {\n    {\n      CholMatrixType C;\n      C = a.template selfadjointView<UpLo>();\n      \n      OrderingType ordering;\n      ordering(C,m_Pinv);\n    }\n\n    if(m_Pinv.size()>0) m_P = m_Pinv.inverse();\n    else                m_P.resize(0);\n    \n    ap.resize(size,size);\n    ap.template selfadjointView<Upper>() = a.template selfadjointView<UpLo>().twistedBy(m_P);\n  }\n  else\n  {\n    m_Pinv.resize(0);\n    m_P.resize(0);\n    if(int(UpLo)==int(Lower) || MatrixType::IsRowMajor)\n    {\n      // we have to transpose the lower part to to the upper one\n      ap.resize(size,size);\n      ap.template selfadjointView<Upper>() = a.template selfadjointView<UpLo>();\n    }\n    else\n      internal::simplicial_cholesky_grab_input<CholMatrixType,MatrixType>::run(a, pmat, ap);\n  }  \n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_SIMPLICIAL_CHOLESKY_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseCholesky/SimplicialCholesky_impl.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2012 Gael Guennebaud <gael.guennebaud@inria.fr>\n\n/*\n\nNOTE: thes functions vave been adapted from the LDL library:\n\nLDL Copyright (c) 2005 by Timothy A. Davis.  All Rights Reserved.\n\nLDL License:\n\n    Your use or distribution of LDL or any modified version of\n    LDL implies that you agree to this License.\n\n    This library is free software; you can redistribute it and/or\n    modify it under the terms of the GNU Lesser General Public\n    License as published by the Free Software Foundation; either\n    version 2.1 of the License, or (at your option) any later version.\n\n    This library is distributed in the hope that it will be useful,\n    but WITHOUT ANY WARRANTY; without even the implied warranty of\n    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU\n    Lesser General Public License for more details.\n\n    You should have received a copy of the GNU Lesser General Public\n    License along with this library; if not, write to the Free Software\n    Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301\n    USA\n\n    Permission is hereby granted to use or copy this program under the\n    terms of the GNU LGPL, provided that the Copyright, this License,\n    and the Availability of the original version is retained on all copies.\n    User documentation of any code that uses this code or any modified\n    version of this code must cite the Copyright, this License, the\n    Availability note, and \"Used by permission.\" Permission to modify\n    the code and to distribute modified code is granted, provided the\n    Copyright, this License, and the Availability note are retained,\n    and a notice that the code was modified is included.\n */\n\n#include \"../Core/util/NonMPL2.h\"\n\n#ifndef EIGEN_SIMPLICIAL_CHOLESKY_IMPL_H\n#define EIGEN_SIMPLICIAL_CHOLESKY_IMPL_H\n\nnamespace Eigen {\n\ntemplate<typename Derived>\nvoid SimplicialCholeskyBase<Derived>::analyzePattern_preordered(const CholMatrixType& ap, bool doLDLT)\n{\n  const StorageIndex size = StorageIndex(ap.rows());\n  m_matrix.resize(size, size);\n  m_parent.resize(size);\n  m_nonZerosPerCol.resize(size);\n\n  ei_declare_aligned_stack_constructed_variable(StorageIndex, tags, size, 0);\n\n  for(StorageIndex k = 0; k < size; ++k)\n  {\n    /* L(k,:) pattern: all nodes reachable in etree from nz in A(0:k-1,k) */\n    m_parent[k] = -1;             /* parent of k is not yet known */\n    tags[k] = k;                  /* mark node k as visited */\n    m_nonZerosPerCol[k] = 0;      /* count of nonzeros in column k of L */\n    for(typename CholMatrixType::InnerIterator it(ap,k); it; ++it)\n    {\n      StorageIndex i = it.index();\n      if(i < k)\n      {\n        /* follow path from i to root of etree, stop at flagged node */\n        for(; tags[i] != k; i = m_parent[i])\n        {\n          /* find parent of i if not yet determined */\n          if (m_parent[i] == -1)\n            m_parent[i] = k;\n          m_nonZerosPerCol[i]++;        /* L (k,i) is nonzero */\n          tags[i] = k;                  /* mark i as visited */\n        }\n      }\n    }\n  }\n\n  /* construct Lp index array from m_nonZerosPerCol column counts */\n  StorageIndex* Lp = m_matrix.outerIndexPtr();\n  Lp[0] = 0;\n  for(StorageIndex k = 0; k < size; ++k)\n    Lp[k+1] = Lp[k] + m_nonZerosPerCol[k] + (doLDLT ? 0 : 1);\n\n  m_matrix.resizeNonZeros(Lp[size]);\n\n  m_isInitialized     = true;\n  m_info              = Success;\n  m_analysisIsOk      = true;\n  m_factorizationIsOk = false;\n}\n\n\ntemplate<typename Derived>\ntemplate<bool DoLDLT>\nvoid SimplicialCholeskyBase<Derived>::factorize_preordered(const CholMatrixType& ap)\n{\n  using std::sqrt;\n\n  eigen_assert(m_analysisIsOk && \"You must first call analyzePattern()\");\n  eigen_assert(ap.rows()==ap.cols());\n  eigen_assert(m_parent.size()==ap.rows());\n  eigen_assert(m_nonZerosPerCol.size()==ap.rows());\n\n  const StorageIndex size = StorageIndex(ap.rows());\n  const StorageIndex* Lp = m_matrix.outerIndexPtr();\n  StorageIndex* Li = m_matrix.innerIndexPtr();\n  Scalar* Lx = m_matrix.valuePtr();\n\n  ei_declare_aligned_stack_constructed_variable(Scalar, y, size, 0);\n  ei_declare_aligned_stack_constructed_variable(StorageIndex,  pattern, size, 0);\n  ei_declare_aligned_stack_constructed_variable(StorageIndex,  tags, size, 0);\n\n  bool ok = true;\n  m_diag.resize(DoLDLT ? size : 0);\n\n  for(StorageIndex k = 0; k < size; ++k)\n  {\n    // compute nonzero pattern of kth row of L, in topological order\n    y[k] = 0.0;                     // Y(0:k) is now all zero\n    StorageIndex top = size;               // stack for pattern is empty\n    tags[k] = k;                    // mark node k as visited\n    m_nonZerosPerCol[k] = 0;        // count of nonzeros in column k of L\n    for(typename CholMatrixType::InnerIterator it(ap,k); it; ++it)\n    {\n      StorageIndex i = it.index();\n      if(i <= k)\n      {\n        y[i] += numext::conj(it.value());            /* scatter A(i,k) into Y (sum duplicates) */\n        Index len;\n        for(len = 0; tags[i] != k; i = m_parent[i])\n        {\n          pattern[len++] = i;     /* L(k,i) is nonzero */\n          tags[i] = k;            /* mark i as visited */\n        }\n        while(len > 0)\n          pattern[--top] = pattern[--len];\n      }\n    }\n\n    /* compute numerical values kth row of L (a sparse triangular solve) */\n\n    RealScalar d = numext::real(y[k]) * m_shiftScale + m_shiftOffset;    // get D(k,k), apply the shift function, and clear Y(k)\n    y[k] = 0.0;\n    for(; top < size; ++top)\n    {\n      Index i = pattern[top];       /* pattern[top:n-1] is pattern of L(:,k) */\n      Scalar yi = y[i];             /* get and clear Y(i) */\n      y[i] = 0.0;\n\n      /* the nonzero entry L(k,i) */\n      Scalar l_ki;\n      if(DoLDLT)\n        l_ki = yi / m_diag[i];\n      else\n        yi = l_ki = yi / Lx[Lp[i]];\n\n      Index p2 = Lp[i] + m_nonZerosPerCol[i];\n      Index p;\n      for(p = Lp[i] + (DoLDLT ? 0 : 1); p < p2; ++p)\n        y[Li[p]] -= numext::conj(Lx[p]) * yi;\n      d -= numext::real(l_ki * numext::conj(yi));\n      Li[p] = k;                          /* store L(k,i) in column form of L */\n      Lx[p] = l_ki;\n      ++m_nonZerosPerCol[i];              /* increment count of nonzeros in col i */\n    }\n    if(DoLDLT)\n    {\n      m_diag[k] = d;\n      if(d == RealScalar(0))\n      {\n        ok = false;                         /* failure, D(k,k) is zero */\n        break;\n      }\n    }\n    else\n    {\n      Index p = Lp[k] + m_nonZerosPerCol[k]++;\n      Li[p] = k ;                /* store L(k,k) = sqrt (d) in column k */\n      if(d <= RealScalar(0)) {\n        ok = false;              /* failure, matrix is not positive definite */\n        break;\n      }\n      Lx[p] = sqrt(d) ;\n    }\n  }\n\n  m_info = ok ? Success : NumericalIssue;\n  m_factorizationIsOk = true;\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_SIMPLICIAL_CHOLESKY_IMPL_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseCore/AmbiVector.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_AMBIVECTOR_H\n#define EIGEN_AMBIVECTOR_H\n\nnamespace Eigen { \n\nnamespace internal {\n\n/** \\internal\n  * Hybrid sparse/dense vector class designed for intensive read-write operations.\n  *\n  * See BasicSparseLLT and SparseProduct for usage examples.\n  */\ntemplate<typename _Scalar, typename _StorageIndex>\nclass AmbiVector\n{\n  public:\n    typedef _Scalar Scalar;\n    typedef _StorageIndex StorageIndex;\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n\n    explicit AmbiVector(Index size)\n      : m_buffer(0), m_zero(0), m_size(0), m_allocatedSize(0), m_allocatedElements(0), m_mode(-1)\n    {\n      resize(size);\n    }\n\n    void init(double estimatedDensity);\n    void init(int mode);\n\n    Index nonZeros() const;\n\n    /** Specifies a sub-vector to work on */\n    void setBounds(Index start, Index end) { m_start = convert_index(start); m_end = convert_index(end); }\n\n    void setZero();\n\n    void restart();\n    Scalar& coeffRef(Index i);\n    Scalar& coeff(Index i);\n\n    class Iterator;\n\n    ~AmbiVector() { delete[] m_buffer; }\n\n    void resize(Index size)\n    {\n      if (m_allocatedSize < size)\n        reallocate(size);\n      m_size = convert_index(size);\n    }\n\n    StorageIndex size() const { return m_size; }\n\n  protected:\n    StorageIndex convert_index(Index idx)\n    {\n      return internal::convert_index<StorageIndex>(idx);\n    }\n\n    void reallocate(Index size)\n    {\n      // if the size of the matrix is not too large, let's allocate a bit more than needed such\n      // that we can handle dense vector even in sparse mode.\n      delete[] m_buffer;\n      if (size<1000)\n      {\n        Index allocSize = (size * sizeof(ListEl) + sizeof(Scalar) - 1)/sizeof(Scalar);\n        m_allocatedElements = convert_index((allocSize*sizeof(Scalar))/sizeof(ListEl));\n        m_buffer = new Scalar[allocSize];\n      }\n      else\n      {\n        m_allocatedElements = convert_index((size*sizeof(Scalar))/sizeof(ListEl));\n        m_buffer = new Scalar[size];\n      }\n      m_size = convert_index(size);\n      m_start = 0;\n      m_end = m_size;\n    }\n\n    void reallocateSparse()\n    {\n      Index copyElements = m_allocatedElements;\n      m_allocatedElements = (std::min)(StorageIndex(m_allocatedElements*1.5),m_size);\n      Index allocSize = m_allocatedElements * sizeof(ListEl);\n      allocSize = (allocSize + sizeof(Scalar) - 1)/sizeof(Scalar);\n      Scalar* newBuffer = new Scalar[allocSize];\n      std::memcpy(newBuffer,  m_buffer,  copyElements * sizeof(ListEl));\n      delete[] m_buffer;\n      m_buffer = newBuffer;\n    }\n\n  protected:\n    // element type of the linked list\n    struct ListEl\n    {\n      StorageIndex next;\n      StorageIndex index;\n      Scalar value;\n    };\n\n    // used to store data in both mode\n    Scalar* m_buffer;\n    Scalar m_zero;\n    StorageIndex m_size;\n    StorageIndex m_start;\n    StorageIndex m_end;\n    StorageIndex m_allocatedSize;\n    StorageIndex m_allocatedElements;\n    StorageIndex m_mode;\n\n    // linked list mode\n    StorageIndex m_llStart;\n    StorageIndex m_llCurrent;\n    StorageIndex m_llSize;\n};\n\n/** \\returns the number of non zeros in the current sub vector */\ntemplate<typename _Scalar,typename _StorageIndex>\nIndex AmbiVector<_Scalar,_StorageIndex>::nonZeros() const\n{\n  if (m_mode==IsSparse)\n    return m_llSize;\n  else\n    return m_end - m_start;\n}\n\ntemplate<typename _Scalar,typename _StorageIndex>\nvoid AmbiVector<_Scalar,_StorageIndex>::init(double estimatedDensity)\n{\n  if (estimatedDensity>0.1)\n    init(IsDense);\n  else\n    init(IsSparse);\n}\n\ntemplate<typename _Scalar,typename _StorageIndex>\nvoid AmbiVector<_Scalar,_StorageIndex>::init(int mode)\n{\n  m_mode = mode;\n  if (m_mode==IsSparse)\n  {\n    m_llSize = 0;\n    m_llStart = -1;\n  }\n}\n\n/** Must be called whenever we might perform a write access\n  * with an index smaller than the previous one.\n  *\n  * Don't worry, this function is extremely cheap.\n  */\ntemplate<typename _Scalar,typename _StorageIndex>\nvoid AmbiVector<_Scalar,_StorageIndex>::restart()\n{\n  m_llCurrent = m_llStart;\n}\n\n/** Set all coefficients of current subvector to zero */\ntemplate<typename _Scalar,typename _StorageIndex>\nvoid AmbiVector<_Scalar,_StorageIndex>::setZero()\n{\n  if (m_mode==IsDense)\n  {\n    for (Index i=m_start; i<m_end; ++i)\n      m_buffer[i] = Scalar(0);\n  }\n  else\n  {\n    eigen_assert(m_mode==IsSparse);\n    m_llSize = 0;\n    m_llStart = -1;\n  }\n}\n\ntemplate<typename _Scalar,typename _StorageIndex>\n_Scalar& AmbiVector<_Scalar,_StorageIndex>::coeffRef(Index i)\n{\n  if (m_mode==IsDense)\n    return m_buffer[i];\n  else\n  {\n    ListEl* EIGEN_RESTRICT llElements = reinterpret_cast<ListEl*>(m_buffer);\n    // TODO factorize the following code to reduce code generation\n    eigen_assert(m_mode==IsSparse);\n    if (m_llSize==0)\n    {\n      // this is the first element\n      m_llStart = 0;\n      m_llCurrent = 0;\n      ++m_llSize;\n      llElements[0].value = Scalar(0);\n      llElements[0].index = convert_index(i);\n      llElements[0].next = -1;\n      return llElements[0].value;\n    }\n    else if (i<llElements[m_llStart].index)\n    {\n      // this is going to be the new first element of the list\n      ListEl& el = llElements[m_llSize];\n      el.value = Scalar(0);\n      el.index = convert_index(i);\n      el.next = m_llStart;\n      m_llStart = m_llSize;\n      ++m_llSize;\n      m_llCurrent = m_llStart;\n      return el.value;\n    }\n    else\n    {\n      StorageIndex nextel = llElements[m_llCurrent].next;\n      eigen_assert(i>=llElements[m_llCurrent].index && \"you must call restart() before inserting an element with lower or equal index\");\n      while (nextel >= 0 && llElements[nextel].index<=i)\n      {\n        m_llCurrent = nextel;\n        nextel = llElements[nextel].next;\n      }\n\n      if (llElements[m_llCurrent].index==i)\n      {\n        // the coefficient already exists and we found it !\n        return llElements[m_llCurrent].value;\n      }\n      else\n      {\n        if (m_llSize>=m_allocatedElements)\n        {\n          reallocateSparse();\n          llElements = reinterpret_cast<ListEl*>(m_buffer);\n        }\n        eigen_internal_assert(m_llSize<m_allocatedElements && \"internal error: overflow in sparse mode\");\n        // let's insert a new coefficient\n        ListEl& el = llElements[m_llSize];\n        el.value = Scalar(0);\n        el.index = convert_index(i);\n        el.next = llElements[m_llCurrent].next;\n        llElements[m_llCurrent].next = m_llSize;\n        ++m_llSize;\n        return el.value;\n      }\n    }\n  }\n}\n\ntemplate<typename _Scalar,typename _StorageIndex>\n_Scalar& AmbiVector<_Scalar,_StorageIndex>::coeff(Index i)\n{\n  if (m_mode==IsDense)\n    return m_buffer[i];\n  else\n  {\n    ListEl* EIGEN_RESTRICT llElements = reinterpret_cast<ListEl*>(m_buffer);\n    eigen_assert(m_mode==IsSparse);\n    if ((m_llSize==0) || (i<llElements[m_llStart].index))\n    {\n      return m_zero;\n    }\n    else\n    {\n      Index elid = m_llStart;\n      while (elid >= 0 && llElements[elid].index<i)\n        elid = llElements[elid].next;\n\n      if (llElements[elid].index==i)\n        return llElements[m_llCurrent].value;\n      else\n        return m_zero;\n    }\n  }\n}\n\n/** Iterator over the nonzero coefficients */\ntemplate<typename _Scalar,typename _StorageIndex>\nclass AmbiVector<_Scalar,_StorageIndex>::Iterator\n{\n  public:\n    typedef _Scalar Scalar;\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n\n    /** Default constructor\n      * \\param vec the vector on which we iterate\n      * \\param epsilon the minimal value used to prune zero coefficients.\n      * In practice, all coefficients having a magnitude smaller than \\a epsilon\n      * are skipped.\n      */\n    explicit Iterator(const AmbiVector& vec, const RealScalar& epsilon = 0)\n      : m_vector(vec)\n    {\n      using std::abs;\n      m_epsilon = epsilon;\n      m_isDense = m_vector.m_mode==IsDense;\n      if (m_isDense)\n      {\n        m_currentEl = 0;   // this is to avoid a compilation warning\n        m_cachedValue = 0; // this is to avoid a compilation warning\n        m_cachedIndex = m_vector.m_start-1;\n        ++(*this);\n      }\n      else\n      {\n        ListEl* EIGEN_RESTRICT llElements = reinterpret_cast<ListEl*>(m_vector.m_buffer);\n        m_currentEl = m_vector.m_llStart;\n        while (m_currentEl>=0 && abs(llElements[m_currentEl].value)<=m_epsilon)\n          m_currentEl = llElements[m_currentEl].next;\n        if (m_currentEl<0)\n        {\n          m_cachedValue = 0; // this is to avoid a compilation warning\n          m_cachedIndex = -1;\n        }\n        else\n        {\n          m_cachedIndex = llElements[m_currentEl].index;\n          m_cachedValue = llElements[m_currentEl].value;\n        }\n      }\n    }\n\n    StorageIndex index() const { return m_cachedIndex; }\n    Scalar value() const { return m_cachedValue; }\n\n    operator bool() const { return m_cachedIndex>=0; }\n\n    Iterator& operator++()\n    {\n      using std::abs;\n      if (m_isDense)\n      {\n        do {\n          ++m_cachedIndex;\n        } while (m_cachedIndex<m_vector.m_end && abs(m_vector.m_buffer[m_cachedIndex])<=m_epsilon);\n        if (m_cachedIndex<m_vector.m_end)\n          m_cachedValue = m_vector.m_buffer[m_cachedIndex];\n        else\n          m_cachedIndex=-1;\n      }\n      else\n      {\n        ListEl* EIGEN_RESTRICT llElements = reinterpret_cast<ListEl*>(m_vector.m_buffer);\n        do {\n          m_currentEl = llElements[m_currentEl].next;\n        } while (m_currentEl>=0 && abs(llElements[m_currentEl].value)<=m_epsilon);\n        if (m_currentEl<0)\n        {\n          m_cachedIndex = -1;\n        }\n        else\n        {\n          m_cachedIndex = llElements[m_currentEl].index;\n          m_cachedValue = llElements[m_currentEl].value;\n        }\n      }\n      return *this;\n    }\n\n  protected:\n    const AmbiVector& m_vector; // the target vector\n    StorageIndex m_currentEl;   // the current element in sparse/linked-list mode\n    RealScalar m_epsilon;       // epsilon used to prune zero coefficients\n    StorageIndex m_cachedIndex; // current coordinate\n    Scalar m_cachedValue;       // current value\n    bool m_isDense;             // mode of the vector\n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_AMBIVECTOR_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseCore/CompressedStorage.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_COMPRESSED_STORAGE_H\n#define EIGEN_COMPRESSED_STORAGE_H\n\nnamespace Eigen { \n\nnamespace internal {\n\n/** \\internal\n  * Stores a sparse set of values as a list of values and a list of indices.\n  *\n  */\ntemplate<typename _Scalar,typename _StorageIndex>\nclass CompressedStorage\n{\n  public:\n\n    typedef _Scalar Scalar;\n    typedef _StorageIndex StorageIndex;\n\n  protected:\n\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n\n  public:\n\n    CompressedStorage()\n      : m_values(0), m_indices(0), m_size(0), m_allocatedSize(0)\n    {}\n\n    explicit CompressedStorage(Index size)\n      : m_values(0), m_indices(0), m_size(0), m_allocatedSize(0)\n    {\n      resize(size);\n    }\n\n    CompressedStorage(const CompressedStorage& other)\n      : m_values(0), m_indices(0), m_size(0), m_allocatedSize(0)\n    {\n      *this = other;\n    }\n\n    CompressedStorage& operator=(const CompressedStorage& other)\n    {\n      resize(other.size());\n      if(other.size()>0)\n      {\n        internal::smart_copy(other.m_values,  other.m_values  + m_size, m_values);\n        internal::smart_copy(other.m_indices, other.m_indices + m_size, m_indices);\n      }\n      return *this;\n    }\n\n    void swap(CompressedStorage& other)\n    {\n      std::swap(m_values, other.m_values);\n      std::swap(m_indices, other.m_indices);\n      std::swap(m_size, other.m_size);\n      std::swap(m_allocatedSize, other.m_allocatedSize);\n    }\n\n    ~CompressedStorage()\n    {\n      delete[] m_values;\n      delete[] m_indices;\n    }\n\n    void reserve(Index size)\n    {\n      Index newAllocatedSize = m_size + size;\n      if (newAllocatedSize > m_allocatedSize)\n        reallocate(newAllocatedSize);\n    }\n\n    void squeeze()\n    {\n      if (m_allocatedSize>m_size)\n        reallocate(m_size);\n    }\n\n    void resize(Index size, double reserveSizeFactor = 0)\n    {\n      if (m_allocatedSize<size)\n      {\n        Index realloc_size = (std::min<Index>)(NumTraits<StorageIndex>::highest(),  size + Index(reserveSizeFactor*double(size)));\n        if(realloc_size<size)\n          internal::throw_std_bad_alloc();\n        reallocate(realloc_size);\n      }\n      m_size = size;\n    }\n\n    void append(const Scalar& v, Index i)\n    {\n      Index id = m_size;\n      resize(m_size+1, 1);\n      m_values[id] = v;\n      m_indices[id] = internal::convert_index<StorageIndex>(i);\n    }\n\n    inline Index size() const { return m_size; }\n    inline Index allocatedSize() const { return m_allocatedSize; }\n    inline void clear() { m_size = 0; }\n\n    const Scalar* valuePtr() const { return m_values; }\n    Scalar* valuePtr() { return m_values; }\n    const StorageIndex* indexPtr() const { return m_indices; }\n    StorageIndex* indexPtr() { return m_indices; }\n\n    inline Scalar& value(Index i) { eigen_internal_assert(m_values!=0); return m_values[i]; }\n    inline const Scalar& value(Index i) const { eigen_internal_assert(m_values!=0); return m_values[i]; }\n\n    inline StorageIndex& index(Index i) { eigen_internal_assert(m_indices!=0); return m_indices[i]; }\n    inline const StorageIndex& index(Index i) const { eigen_internal_assert(m_indices!=0); return m_indices[i]; }\n\n    /** \\returns the largest \\c k such that for all \\c j in [0,k) index[\\c j]\\<\\a key */\n    inline Index searchLowerIndex(Index key) const\n    {\n      return searchLowerIndex(0, m_size, key);\n    }\n\n    /** \\returns the largest \\c k in [start,end) such that for all \\c j in [start,k) index[\\c j]\\<\\a key */\n    inline Index searchLowerIndex(Index start, Index end, Index key) const\n    {\n      while(end>start)\n      {\n        Index mid = (end+start)>>1;\n        if (m_indices[mid]<key)\n          start = mid+1;\n        else\n          end = mid;\n      }\n      return start;\n    }\n\n    /** \\returns the stored value at index \\a key\n      * If the value does not exist, then the value \\a defaultValue is returned without any insertion. */\n    inline Scalar at(Index key, const Scalar& defaultValue = Scalar(0)) const\n    {\n      if (m_size==0)\n        return defaultValue;\n      else if (key==m_indices[m_size-1])\n        return m_values[m_size-1];\n      // ^^  optimization: let's first check if it is the last coefficient\n      // (very common in high level algorithms)\n      const Index id = searchLowerIndex(0,m_size-1,key);\n      return ((id<m_size) && (m_indices[id]==key)) ? m_values[id] : defaultValue;\n    }\n\n    /** Like at(), but the search is performed in the range [start,end) */\n    inline Scalar atInRange(Index start, Index end, Index key, const Scalar &defaultValue = Scalar(0)) const\n    {\n      if (start>=end)\n        return defaultValue;\n      else if (end>start && key==m_indices[end-1])\n        return m_values[end-1];\n      // ^^  optimization: let's first check if it is the last coefficient\n      // (very common in high level algorithms)\n      const Index id = searchLowerIndex(start,end-1,key);\n      return ((id<end) && (m_indices[id]==key)) ? m_values[id] : defaultValue;\n    }\n\n    /** \\returns a reference to the value at index \\a key\n      * If the value does not exist, then the value \\a defaultValue is inserted\n      * such that the keys are sorted. */\n    inline Scalar& atWithInsertion(Index key, const Scalar& defaultValue = Scalar(0))\n    {\n      Index id = searchLowerIndex(0,m_size,key);\n      if (id>=m_size || m_indices[id]!=key)\n      {\n        if (m_allocatedSize<m_size+1)\n        {\n          m_allocatedSize = 2*(m_size+1);\n          internal::scoped_array<Scalar> newValues(m_allocatedSize);\n          internal::scoped_array<StorageIndex> newIndices(m_allocatedSize);\n\n          // copy first chunk\n          internal::smart_copy(m_values,  m_values +id, newValues.ptr());\n          internal::smart_copy(m_indices, m_indices+id, newIndices.ptr());\n\n          // copy the rest\n          if(m_size>id)\n          {\n            internal::smart_copy(m_values +id,  m_values +m_size, newValues.ptr() +id+1);\n            internal::smart_copy(m_indices+id,  m_indices+m_size, newIndices.ptr()+id+1);\n          }\n          std::swap(m_values,newValues.ptr());\n          std::swap(m_indices,newIndices.ptr());\n        }\n        else if(m_size>id)\n        {\n          internal::smart_memmove(m_values +id, m_values +m_size, m_values +id+1);\n          internal::smart_memmove(m_indices+id, m_indices+m_size, m_indices+id+1);\n        }\n        m_size++;\n        m_indices[id] = internal::convert_index<StorageIndex>(key);\n        m_values[id] = defaultValue;\n      }\n      return m_values[id];\n    }\n\n    void prune(const Scalar& reference, const RealScalar& epsilon = NumTraits<RealScalar>::dummy_precision())\n    {\n      Index k = 0;\n      Index n = size();\n      for (Index i=0; i<n; ++i)\n      {\n        if (!internal::isMuchSmallerThan(value(i), reference, epsilon))\n        {\n          value(k) = value(i);\n          index(k) = index(i);\n          ++k;\n        }\n      }\n      resize(k,0);\n    }\n\n  protected:\n\n    inline void reallocate(Index size)\n    {\n      #ifdef EIGEN_SPARSE_COMPRESSED_STORAGE_REALLOCATE_PLUGIN\n        EIGEN_SPARSE_COMPRESSED_STORAGE_REALLOCATE_PLUGIN\n      #endif\n      eigen_internal_assert(size!=m_allocatedSize);\n      internal::scoped_array<Scalar> newValues(size);\n      internal::scoped_array<StorageIndex> newIndices(size);\n      Index copySize = (std::min)(size, m_size);\n      if (copySize>0) {\n        internal::smart_copy(m_values, m_values+copySize, newValues.ptr());\n        internal::smart_copy(m_indices, m_indices+copySize, newIndices.ptr());\n      }\n      std::swap(m_values,newValues.ptr());\n      std::swap(m_indices,newIndices.ptr());\n      m_allocatedSize = size;\n    }\n\n  protected:\n    Scalar* m_values;\n    StorageIndex* m_indices;\n    Index m_size;\n    Index m_allocatedSize;\n\n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_COMPRESSED_STORAGE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseCore/ConservativeSparseSparseProduct.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CONSERVATIVESPARSESPARSEPRODUCT_H\n#define EIGEN_CONSERVATIVESPARSESPARSEPRODUCT_H\n\nnamespace Eigen { \n\nnamespace internal {\n\ntemplate<typename Lhs, typename Rhs, typename ResultType>\nstatic void conservative_sparse_sparse_product_impl(const Lhs& lhs, const Rhs& rhs, ResultType& res, bool sortedInsertion = false)\n{\n  typedef typename remove_all<Lhs>::type::Scalar LhsScalar;\n  typedef typename remove_all<Rhs>::type::Scalar RhsScalar;\n  typedef typename remove_all<ResultType>::type::Scalar ResScalar;\n\n  // make sure to call innerSize/outerSize since we fake the storage order.\n  Index rows = lhs.innerSize();\n  Index cols = rhs.outerSize();\n  eigen_assert(lhs.outerSize() == rhs.innerSize());\n  \n  ei_declare_aligned_stack_constructed_variable(bool,   mask,     rows, 0);\n  ei_declare_aligned_stack_constructed_variable(ResScalar, values,   rows, 0);\n  ei_declare_aligned_stack_constructed_variable(Index,  indices,  rows, 0);\n  \n  std::memset(mask,0,sizeof(bool)*rows);\n\n  evaluator<Lhs> lhsEval(lhs);\n  evaluator<Rhs> rhsEval(rhs);\n  \n  // estimate the number of non zero entries\n  // given a rhs column containing Y non zeros, we assume that the respective Y columns\n  // of the lhs differs in average of one non zeros, thus the number of non zeros for\n  // the product of a rhs column with the lhs is X+Y where X is the average number of non zero\n  // per column of the lhs.\n  // Therefore, we have nnz(lhs*rhs) = nnz(lhs) + nnz(rhs)\n  Index estimated_nnz_prod = lhsEval.nonZerosEstimate() + rhsEval.nonZerosEstimate();\n\n  res.setZero();\n  res.reserve(Index(estimated_nnz_prod));\n  // we compute each column of the result, one after the other\n  for (Index j=0; j<cols; ++j)\n  {\n\n    res.startVec(j);\n    Index nnz = 0;\n    for (typename evaluator<Rhs>::InnerIterator rhsIt(rhsEval, j); rhsIt; ++rhsIt)\n    {\n      RhsScalar y = rhsIt.value();\n      Index k = rhsIt.index();\n      for (typename evaluator<Lhs>::InnerIterator lhsIt(lhsEval, k); lhsIt; ++lhsIt)\n      {\n        Index i = lhsIt.index();\n        LhsScalar x = lhsIt.value();\n        if(!mask[i])\n        {\n          mask[i] = true;\n          values[i] = x * y;\n          indices[nnz] = i;\n          ++nnz;\n        }\n        else\n          values[i] += x * y;\n      }\n    }\n    if(!sortedInsertion)\n    {\n      // unordered insertion\n      for(Index k=0; k<nnz; ++k)\n      {\n        Index i = indices[k];\n        res.insertBackByOuterInnerUnordered(j,i) = values[i];\n        mask[i] = false;\n      }\n    }\n    else\n    {\n      // alternative ordered insertion code:\n      const Index t200 = rows/11; // 11 == (log2(200)*1.39)\n      const Index t = (rows*100)/139;\n\n      // FIXME reserve nnz non zeros\n      // FIXME implement faster sorting algorithms for very small nnz\n      // if the result is sparse enough => use a quick sort\n      // otherwise => loop through the entire vector\n      // In order to avoid to perform an expensive log2 when the\n      // result is clearly very sparse we use a linear bound up to 200.\n      if((nnz<200 && nnz<t200) || nnz * numext::log2(int(nnz)) < t)\n      {\n        if(nnz>1) std::sort(indices,indices+nnz);\n        for(Index k=0; k<nnz; ++k)\n        {\n          Index i = indices[k];\n          res.insertBackByOuterInner(j,i) = values[i];\n          mask[i] = false;\n        }\n      }\n      else\n      {\n        // dense path\n        for(Index i=0; i<rows; ++i)\n        {\n          if(mask[i])\n          {\n            mask[i] = false;\n            res.insertBackByOuterInner(j,i) = values[i];\n          }\n        }\n      }\n    }\n  }\n  res.finalize();\n}\n\n\n} // end namespace internal\n\nnamespace internal {\n\ntemplate<typename Lhs, typename Rhs, typename ResultType,\n  int LhsStorageOrder = (traits<Lhs>::Flags&RowMajorBit) ? RowMajor : ColMajor,\n  int RhsStorageOrder = (traits<Rhs>::Flags&RowMajorBit) ? RowMajor : ColMajor,\n  int ResStorageOrder = (traits<ResultType>::Flags&RowMajorBit) ? RowMajor : ColMajor>\nstruct conservative_sparse_sparse_product_selector;\n\ntemplate<typename Lhs, typename Rhs, typename ResultType>\nstruct conservative_sparse_sparse_product_selector<Lhs,Rhs,ResultType,ColMajor,ColMajor,ColMajor>\n{\n  typedef typename remove_all<Lhs>::type LhsCleaned;\n  typedef typename LhsCleaned::Scalar Scalar;\n\n  static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)\n  {\n    typedef SparseMatrix<typename ResultType::Scalar,RowMajor,typename ResultType::StorageIndex> RowMajorMatrix;\n    typedef SparseMatrix<typename ResultType::Scalar,ColMajor,typename ResultType::StorageIndex> ColMajorMatrixAux;\n    typedef typename sparse_eval<ColMajorMatrixAux,ResultType::RowsAtCompileTime,ResultType::ColsAtCompileTime,ColMajorMatrixAux::Flags>::type ColMajorMatrix;\n    \n    // If the result is tall and thin (in the extreme case a column vector)\n    // then it is faster to sort the coefficients inplace instead of transposing twice.\n    // FIXME, the following heuristic is probably not very good.\n    if(lhs.rows()>rhs.cols())\n    {\n      ColMajorMatrix resCol(lhs.rows(),rhs.cols());\n      // perform sorted insertion\n      internal::conservative_sparse_sparse_product_impl<Lhs,Rhs,ColMajorMatrix>(lhs, rhs, resCol, true);\n      res = resCol.markAsRValue();\n    }\n    else\n    {\n      ColMajorMatrixAux resCol(lhs.rows(),rhs.cols());\n      // ressort to transpose to sort the entries\n      internal::conservative_sparse_sparse_product_impl<Lhs,Rhs,ColMajorMatrixAux>(lhs, rhs, resCol, false);\n      RowMajorMatrix resRow(resCol);\n      res = resRow.markAsRValue();\n    }\n  }\n};\n\ntemplate<typename Lhs, typename Rhs, typename ResultType>\nstruct conservative_sparse_sparse_product_selector<Lhs,Rhs,ResultType,RowMajor,ColMajor,ColMajor>\n{\n  static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)\n  {\n    typedef SparseMatrix<typename Rhs::Scalar,RowMajor,typename ResultType::StorageIndex> RowMajorRhs;\n    typedef SparseMatrix<typename ResultType::Scalar,RowMajor,typename ResultType::StorageIndex> RowMajorRes;\n    RowMajorRhs rhsRow = rhs;\n    RowMajorRes resRow(lhs.rows(), rhs.cols());\n    internal::conservative_sparse_sparse_product_impl<RowMajorRhs,Lhs,RowMajorRes>(rhsRow, lhs, resRow);\n    res = resRow;\n  }\n};\n\ntemplate<typename Lhs, typename Rhs, typename ResultType>\nstruct conservative_sparse_sparse_product_selector<Lhs,Rhs,ResultType,ColMajor,RowMajor,ColMajor>\n{\n  static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)\n  {\n    typedef SparseMatrix<typename Lhs::Scalar,RowMajor,typename ResultType::StorageIndex> RowMajorLhs;\n    typedef SparseMatrix<typename ResultType::Scalar,RowMajor,typename ResultType::StorageIndex> RowMajorRes;\n    RowMajorLhs lhsRow = lhs;\n    RowMajorRes resRow(lhs.rows(), rhs.cols());\n    internal::conservative_sparse_sparse_product_impl<Rhs,RowMajorLhs,RowMajorRes>(rhs, lhsRow, resRow);\n    res = resRow;\n  }\n};\n\ntemplate<typename Lhs, typename Rhs, typename ResultType>\nstruct conservative_sparse_sparse_product_selector<Lhs,Rhs,ResultType,RowMajor,RowMajor,ColMajor>\n{\n  static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)\n  {\n    typedef SparseMatrix<typename ResultType::Scalar,RowMajor,typename ResultType::StorageIndex> RowMajorMatrix;\n    RowMajorMatrix resRow(lhs.rows(), rhs.cols());\n    internal::conservative_sparse_sparse_product_impl<Rhs,Lhs,RowMajorMatrix>(rhs, lhs, resRow);\n    res = resRow;\n  }\n};\n\n\ntemplate<typename Lhs, typename Rhs, typename ResultType>\nstruct conservative_sparse_sparse_product_selector<Lhs,Rhs,ResultType,ColMajor,ColMajor,RowMajor>\n{\n  typedef typename traits<typename remove_all<Lhs>::type>::Scalar Scalar;\n\n  static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)\n  {\n    typedef SparseMatrix<typename ResultType::Scalar,ColMajor,typename ResultType::StorageIndex> ColMajorMatrix;\n    ColMajorMatrix resCol(lhs.rows(), rhs.cols());\n    internal::conservative_sparse_sparse_product_impl<Lhs,Rhs,ColMajorMatrix>(lhs, rhs, resCol);\n    res = resCol;\n  }\n};\n\ntemplate<typename Lhs, typename Rhs, typename ResultType>\nstruct conservative_sparse_sparse_product_selector<Lhs,Rhs,ResultType,RowMajor,ColMajor,RowMajor>\n{\n  static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)\n  {\n    typedef SparseMatrix<typename Lhs::Scalar,ColMajor,typename ResultType::StorageIndex> ColMajorLhs;\n    typedef SparseMatrix<typename ResultType::Scalar,ColMajor,typename ResultType::StorageIndex> ColMajorRes;\n    ColMajorLhs lhsCol = lhs;\n    ColMajorRes resCol(lhs.rows(), rhs.cols());\n    internal::conservative_sparse_sparse_product_impl<ColMajorLhs,Rhs,ColMajorRes>(lhsCol, rhs, resCol);\n    res = resCol;\n  }\n};\n\ntemplate<typename Lhs, typename Rhs, typename ResultType>\nstruct conservative_sparse_sparse_product_selector<Lhs,Rhs,ResultType,ColMajor,RowMajor,RowMajor>\n{\n  static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)\n  {\n    typedef SparseMatrix<typename Rhs::Scalar,ColMajor,typename ResultType::StorageIndex> ColMajorRhs;\n    typedef SparseMatrix<typename ResultType::Scalar,ColMajor,typename ResultType::StorageIndex> ColMajorRes;\n    ColMajorRhs rhsCol = rhs;\n    ColMajorRes resCol(lhs.rows(), rhs.cols());\n    internal::conservative_sparse_sparse_product_impl<Lhs,ColMajorRhs,ColMajorRes>(lhs, rhsCol, resCol);\n    res = resCol;\n  }\n};\n\ntemplate<typename Lhs, typename Rhs, typename ResultType>\nstruct conservative_sparse_sparse_product_selector<Lhs,Rhs,ResultType,RowMajor,RowMajor,RowMajor>\n{\n  static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)\n  {\n    typedef SparseMatrix<typename ResultType::Scalar,RowMajor,typename ResultType::StorageIndex> RowMajorMatrix;\n    typedef SparseMatrix<typename ResultType::Scalar,ColMajor,typename ResultType::StorageIndex> ColMajorMatrix;\n    RowMajorMatrix resRow(lhs.rows(),rhs.cols());\n    internal::conservative_sparse_sparse_product_impl<Rhs,Lhs,RowMajorMatrix>(rhs, lhs, resRow);\n    // sort the non zeros:\n    ColMajorMatrix resCol(resRow);\n    res = resCol;\n  }\n};\n\n} // end namespace internal\n\n\nnamespace internal {\n\ntemplate<typename Lhs, typename Rhs, typename ResultType>\nstatic void sparse_sparse_to_dense_product_impl(const Lhs& lhs, const Rhs& rhs, ResultType& res)\n{\n  typedef typename remove_all<Lhs>::type::Scalar LhsScalar;\n  typedef typename remove_all<Rhs>::type::Scalar RhsScalar;\n  Index cols = rhs.outerSize();\n  eigen_assert(lhs.outerSize() == rhs.innerSize());\n\n  evaluator<Lhs> lhsEval(lhs);\n  evaluator<Rhs> rhsEval(rhs);\n\n  for (Index j=0; j<cols; ++j)\n  {\n    for (typename evaluator<Rhs>::InnerIterator rhsIt(rhsEval, j); rhsIt; ++rhsIt)\n    {\n      RhsScalar y = rhsIt.value();\n      Index k = rhsIt.index();\n      for (typename evaluator<Lhs>::InnerIterator lhsIt(lhsEval, k); lhsIt; ++lhsIt)\n      {\n        Index i = lhsIt.index();\n        LhsScalar x = lhsIt.value();\n        res.coeffRef(i,j) += x * y;\n      }\n    }\n  }\n}\n\n\n} // end namespace internal\n\nnamespace internal {\n\ntemplate<typename Lhs, typename Rhs, typename ResultType,\n  int LhsStorageOrder = (traits<Lhs>::Flags&RowMajorBit) ? RowMajor : ColMajor,\n  int RhsStorageOrder = (traits<Rhs>::Flags&RowMajorBit) ? RowMajor : ColMajor>\nstruct sparse_sparse_to_dense_product_selector;\n\ntemplate<typename Lhs, typename Rhs, typename ResultType>\nstruct sparse_sparse_to_dense_product_selector<Lhs,Rhs,ResultType,ColMajor,ColMajor>\n{\n  static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)\n  {\n    internal::sparse_sparse_to_dense_product_impl<Lhs,Rhs,ResultType>(lhs, rhs, res);\n  }\n};\n\ntemplate<typename Lhs, typename Rhs, typename ResultType>\nstruct sparse_sparse_to_dense_product_selector<Lhs,Rhs,ResultType,RowMajor,ColMajor>\n{\n  static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)\n  {\n    typedef SparseMatrix<typename Lhs::Scalar,ColMajor,typename ResultType::StorageIndex> ColMajorLhs;\n    ColMajorLhs lhsCol(lhs);\n    internal::sparse_sparse_to_dense_product_impl<ColMajorLhs,Rhs,ResultType>(lhsCol, rhs, res);\n  }\n};\n\ntemplate<typename Lhs, typename Rhs, typename ResultType>\nstruct sparse_sparse_to_dense_product_selector<Lhs,Rhs,ResultType,ColMajor,RowMajor>\n{\n  static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)\n  {\n    typedef SparseMatrix<typename Rhs::Scalar,ColMajor,typename ResultType::StorageIndex> ColMajorRhs;\n    ColMajorRhs rhsCol(rhs);\n    internal::sparse_sparse_to_dense_product_impl<Lhs,ColMajorRhs,ResultType>(lhs, rhsCol, res);\n  }\n};\n\ntemplate<typename Lhs, typename Rhs, typename ResultType>\nstruct sparse_sparse_to_dense_product_selector<Lhs,Rhs,ResultType,RowMajor,RowMajor>\n{\n  static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)\n  {\n    Transpose<ResultType> trRes(res);\n    internal::sparse_sparse_to_dense_product_impl<Rhs,Lhs,Transpose<ResultType> >(rhs, lhs, trRes);\n  }\n};\n\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_CONSERVATIVESPARSESPARSEPRODUCT_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseCore/MappedSparseMatrix.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_MAPPED_SPARSEMATRIX_H\n#define EIGEN_MAPPED_SPARSEMATRIX_H\n\nnamespace Eigen {\n\n/** \\deprecated Use Map<SparseMatrix<> >\n  * \\class MappedSparseMatrix\n  *\n  * \\brief Sparse matrix\n  *\n  * \\param _Scalar the scalar type, i.e. the type of the coefficients\n  *\n  * See http://www.netlib.org/linalg/html_templates/node91.html for details on the storage scheme.\n  *\n  */\nnamespace internal {\ntemplate<typename _Scalar, int _Flags, typename _StorageIndex>\nstruct traits<MappedSparseMatrix<_Scalar, _Flags, _StorageIndex> > : traits<SparseMatrix<_Scalar, _Flags, _StorageIndex> >\n{};\n} // end namespace internal\n\ntemplate<typename _Scalar, int _Flags, typename _StorageIndex>\nclass MappedSparseMatrix\n  : public Map<SparseMatrix<_Scalar, _Flags, _StorageIndex> >\n{\n    typedef Map<SparseMatrix<_Scalar, _Flags, _StorageIndex> > Base;\n\n  public:\n    \n    typedef typename Base::StorageIndex StorageIndex;\n    typedef typename Base::Scalar Scalar;\n\n    inline MappedSparseMatrix(Index rows, Index cols, Index nnz, StorageIndex* outerIndexPtr, StorageIndex* innerIndexPtr, Scalar* valuePtr, StorageIndex* innerNonZeroPtr = 0)\n      : Base(rows, cols, nnz, outerIndexPtr, innerIndexPtr, valuePtr, innerNonZeroPtr)\n    {}\n\n    /** Empty destructor */\n    inline ~MappedSparseMatrix() {}\n};\n\nnamespace internal {\n\ntemplate<typename _Scalar, int _Options, typename _StorageIndex>\nstruct evaluator<MappedSparseMatrix<_Scalar,_Options,_StorageIndex> >\n  : evaluator<SparseCompressedBase<MappedSparseMatrix<_Scalar,_Options,_StorageIndex> > >\n{\n  typedef MappedSparseMatrix<_Scalar,_Options,_StorageIndex> XprType;\n  typedef evaluator<SparseCompressedBase<XprType> > Base;\n  \n  evaluator() : Base() {}\n  explicit evaluator(const XprType &mat) : Base(mat) {}\n};\n\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_MAPPED_SPARSEMATRIX_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseCore/SparseAssign.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSEASSIGN_H\n#define EIGEN_SPARSEASSIGN_H\n\nnamespace Eigen { \n\ntemplate<typename Derived>    \ntemplate<typename OtherDerived>\nDerived& SparseMatrixBase<Derived>::operator=(const EigenBase<OtherDerived> &other)\n{\n  internal::call_assignment_no_alias(derived(), other.derived());\n  return derived();\n}\n\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\nDerived& SparseMatrixBase<Derived>::operator=(const ReturnByValue<OtherDerived>& other)\n{\n  // TODO use the evaluator mechanism\n  other.evalTo(derived());\n  return derived();\n}\n\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\ninline Derived& SparseMatrixBase<Derived>::operator=(const SparseMatrixBase<OtherDerived>& other)\n{\n  // by default sparse evaluation do not alias, so we can safely bypass the generic call_assignment routine\n  internal::Assignment<Derived,OtherDerived,internal::assign_op<Scalar,typename OtherDerived::Scalar> >\n          ::run(derived(), other.derived(), internal::assign_op<Scalar,typename OtherDerived::Scalar>());\n  return derived();\n}\n\ntemplate<typename Derived>\ninline Derived& SparseMatrixBase<Derived>::operator=(const Derived& other)\n{\n  internal::call_assignment_no_alias(derived(), other.derived());\n  return derived();\n}\n\nnamespace internal {\n\ntemplate<>\nstruct storage_kind_to_evaluator_kind<Sparse> {\n  typedef IteratorBased Kind;\n};\n\ntemplate<>\nstruct storage_kind_to_shape<Sparse> {\n  typedef SparseShape Shape;\n};\n\nstruct Sparse2Sparse {};\nstruct Sparse2Dense  {};\n\ntemplate<> struct AssignmentKind<SparseShape, SparseShape>           { typedef Sparse2Sparse Kind; };\ntemplate<> struct AssignmentKind<SparseShape, SparseTriangularShape> { typedef Sparse2Sparse Kind; };\ntemplate<> struct AssignmentKind<DenseShape,  SparseShape>           { typedef Sparse2Dense  Kind; };\ntemplate<> struct AssignmentKind<DenseShape,  SparseTriangularShape> { typedef Sparse2Dense  Kind; };\n\n\ntemplate<typename DstXprType, typename SrcXprType>\nvoid assign_sparse_to_sparse(DstXprType &dst, const SrcXprType &src)\n{\n  typedef typename DstXprType::Scalar Scalar;\n  typedef internal::evaluator<DstXprType> DstEvaluatorType;\n  typedef internal::evaluator<SrcXprType> SrcEvaluatorType;\n\n  SrcEvaluatorType srcEvaluator(src);\n\n  const bool transpose = (DstEvaluatorType::Flags & RowMajorBit) != (SrcEvaluatorType::Flags & RowMajorBit);\n  const Index outerEvaluationSize = (SrcEvaluatorType::Flags&RowMajorBit) ? src.rows() : src.cols();\n  if ((!transpose) && src.isRValue())\n  {\n    // eval without temporary\n    dst.resize(src.rows(), src.cols());\n    dst.setZero();\n    dst.reserve((std::max)(src.rows(),src.cols())*2);\n    for (Index j=0; j<outerEvaluationSize; ++j)\n    {\n      dst.startVec(j);\n      for (typename SrcEvaluatorType::InnerIterator it(srcEvaluator, j); it; ++it)\n      {\n        Scalar v = it.value();\n        dst.insertBackByOuterInner(j,it.index()) = v;\n      }\n    }\n    dst.finalize();\n  }\n  else\n  {\n    // eval through a temporary\n    eigen_assert(( ((internal::traits<DstXprType>::SupportedAccessPatterns & OuterRandomAccessPattern)==OuterRandomAccessPattern) ||\n              (!((DstEvaluatorType::Flags & RowMajorBit) != (SrcEvaluatorType::Flags & RowMajorBit)))) &&\n              \"the transpose operation is supposed to be handled in SparseMatrix::operator=\");\n\n    enum { Flip = (DstEvaluatorType::Flags & RowMajorBit) != (SrcEvaluatorType::Flags & RowMajorBit) };\n\n    \n    DstXprType temp(src.rows(), src.cols());\n\n    temp.reserve((std::max)(src.rows(),src.cols())*2);\n    for (Index j=0; j<outerEvaluationSize; ++j)\n    {\n      temp.startVec(j);\n      for (typename SrcEvaluatorType::InnerIterator it(srcEvaluator, j); it; ++it)\n      {\n        Scalar v = it.value();\n        temp.insertBackByOuterInner(Flip?it.index():j,Flip?j:it.index()) = v;\n      }\n    }\n    temp.finalize();\n\n    dst = temp.markAsRValue();\n  }\n}\n\n// Generic Sparse to Sparse assignment\ntemplate< typename DstXprType, typename SrcXprType, typename Functor>\nstruct Assignment<DstXprType, SrcXprType, Functor, Sparse2Sparse>\n{\n  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)\n  {\n    assign_sparse_to_sparse(dst.derived(), src.derived());\n  }\n};\n\n// Generic Sparse to Dense assignment\ntemplate< typename DstXprType, typename SrcXprType, typename Functor>\nstruct Assignment<DstXprType, SrcXprType, Functor, Sparse2Dense>\n{\n  static void run(DstXprType &dst, const SrcXprType &src, const Functor &func)\n  {\n    if(internal::is_same<Functor,internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> >::value)\n      dst.setZero();\n    \n    internal::evaluator<SrcXprType> srcEval(src);\n    resize_if_allowed(dst, src, func);\n    internal::evaluator<DstXprType> dstEval(dst);\n    \n    const Index outerEvaluationSize = (internal::evaluator<SrcXprType>::Flags&RowMajorBit) ? src.rows() : src.cols();\n    for (Index j=0; j<outerEvaluationSize; ++j)\n      for (typename internal::evaluator<SrcXprType>::InnerIterator i(srcEval,j); i; ++i)\n        func.assignCoeff(dstEval.coeffRef(i.row(),i.col()), i.value());\n  }\n};\n\n// Specialization for \"dst = dec.solve(rhs)\"\n// NOTE we need to specialize it for Sparse2Sparse to avoid ambiguous specialization error\ntemplate<typename DstXprType, typename DecType, typename RhsType, typename Scalar>\nstruct Assignment<DstXprType, Solve<DecType,RhsType>, internal::assign_op<Scalar,Scalar>, Sparse2Sparse>\n{\n  typedef Solve<DecType,RhsType> SrcXprType;\n  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &)\n  {\n    Index dstRows = src.rows();\n    Index dstCols = src.cols();\n    if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))\n      dst.resize(dstRows, dstCols);\n\n    src.dec()._solve_impl(src.rhs(), dst);\n  }\n};\n\nstruct Diagonal2Sparse {};\n\ntemplate<> struct AssignmentKind<SparseShape,DiagonalShape> { typedef Diagonal2Sparse Kind; };\n\ntemplate< typename DstXprType, typename SrcXprType, typename Functor>\nstruct Assignment<DstXprType, SrcXprType, Functor, Diagonal2Sparse>\n{\n  typedef typename DstXprType::StorageIndex StorageIndex;\n  typedef typename DstXprType::Scalar Scalar;\n  typedef Array<StorageIndex,Dynamic,1> ArrayXI;\n  typedef Array<Scalar,Dynamic,1> ArrayXS;\n  template<int Options>\n  static void run(SparseMatrix<Scalar,Options,StorageIndex> &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)\n  {\n    Index dstRows = src.rows();\n    Index dstCols = src.cols();\n    if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))\n      dst.resize(dstRows, dstCols);\n\n    Index size = src.diagonal().size();\n    dst.makeCompressed();\n    dst.resizeNonZeros(size);\n    Map<ArrayXI>(dst.innerIndexPtr(), size).setLinSpaced(0,StorageIndex(size)-1);\n    Map<ArrayXI>(dst.outerIndexPtr(), size+1).setLinSpaced(0,StorageIndex(size));\n    Map<ArrayXS>(dst.valuePtr(), size) = src.diagonal();\n  }\n  \n  template<typename DstDerived>\n  static void run(SparseMatrixBase<DstDerived> &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)\n  {\n    dst.diagonal() = src.diagonal();\n  }\n  \n  static void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)\n  { dst.diagonal() += src.diagonal(); }\n  \n  static void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)\n  { dst.diagonal() -= src.diagonal(); }\n};\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_SPARSEASSIGN_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseCore/SparseBlock.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSE_BLOCK_H\n#define EIGEN_SPARSE_BLOCK_H\n\nnamespace Eigen {\n\n// Subset of columns or rows\ntemplate<typename XprType, int BlockRows, int BlockCols>\nclass BlockImpl<XprType,BlockRows,BlockCols,true,Sparse>\n  : public SparseMatrixBase<Block<XprType,BlockRows,BlockCols,true> >\n{\n    typedef typename internal::remove_all<typename XprType::Nested>::type _MatrixTypeNested;\n    typedef Block<XprType, BlockRows, BlockCols, true> BlockType;\npublic:\n    enum { IsRowMajor = internal::traits<BlockType>::IsRowMajor };\nprotected:\n    enum { OuterSize = IsRowMajor ? BlockRows : BlockCols };\n    typedef SparseMatrixBase<BlockType> Base;\n    using Base::convert_index;\npublic:\n    EIGEN_SPARSE_PUBLIC_INTERFACE(BlockType)\n\n    inline BlockImpl(XprType& xpr, Index i)\n      : m_matrix(xpr), m_outerStart(convert_index(i)), m_outerSize(OuterSize)\n    {}\n\n    inline BlockImpl(XprType& xpr, Index startRow, Index startCol, Index blockRows, Index blockCols)\n      : m_matrix(xpr), m_outerStart(convert_index(IsRowMajor ? startRow : startCol)), m_outerSize(convert_index(IsRowMajor ? blockRows : blockCols))\n    {}\n\n    EIGEN_STRONG_INLINE Index rows() const { return IsRowMajor ? m_outerSize.value() : m_matrix.rows(); }\n    EIGEN_STRONG_INLINE Index cols() const { return IsRowMajor ? m_matrix.cols() : m_outerSize.value(); }\n\n    Index nonZeros() const\n    {\n      typedef internal::evaluator<XprType> EvaluatorType;\n      EvaluatorType matEval(m_matrix);\n      Index nnz = 0;\n      Index end = m_outerStart + m_outerSize.value();\n      for(Index j=m_outerStart; j<end; ++j)\n        for(typename EvaluatorType::InnerIterator it(matEval, j); it; ++it)\n          ++nnz;\n      return nnz;\n    }\n\n    inline const Scalar coeff(Index row, Index col) const\n    {\n      return m_matrix.coeff(row + (IsRowMajor ? m_outerStart : 0), col + (IsRowMajor ? 0 :  m_outerStart));\n    }\n\n    inline const Scalar coeff(Index index) const\n    {\n      return m_matrix.coeff(IsRowMajor ? m_outerStart : index, IsRowMajor ? index :  m_outerStart);\n    }\n\n    inline const XprType& nestedExpression() const { return m_matrix; }\n    inline XprType& nestedExpression() { return m_matrix; }\n    Index startRow() const { return IsRowMajor ? m_outerStart : 0; }\n    Index startCol() const { return IsRowMajor ? 0 : m_outerStart; }\n    Index blockRows() const { return IsRowMajor ? m_outerSize.value() : m_matrix.rows(); }\n    Index blockCols() const { return IsRowMajor ? m_matrix.cols() : m_outerSize.value(); }\n\n  protected:\n\n    typename internal::ref_selector<XprType>::non_const_type m_matrix;\n    Index m_outerStart;\n    const internal::variable_if_dynamic<Index, OuterSize> m_outerSize;\n\n  protected:\n    // Disable assignment with clear error message.\n    // Note that simply removing operator= yields compilation errors with ICC+MSVC\n    template<typename T>\n    BlockImpl& operator=(const T&)\n    {\n      EIGEN_STATIC_ASSERT(sizeof(T)==0, THIS_SPARSE_BLOCK_SUBEXPRESSION_IS_READ_ONLY);\n      return *this;\n    }\n};\n\n\n/***************************************************************************\n* specialization for SparseMatrix\n***************************************************************************/\n\nnamespace internal {\n\ntemplate<typename SparseMatrixType, int BlockRows, int BlockCols>\nclass sparse_matrix_block_impl\n  : public SparseCompressedBase<Block<SparseMatrixType,BlockRows,BlockCols,true> >\n{\n    typedef typename internal::remove_all<typename SparseMatrixType::Nested>::type _MatrixTypeNested;\n    typedef Block<SparseMatrixType, BlockRows, BlockCols, true> BlockType;\n    typedef SparseCompressedBase<Block<SparseMatrixType,BlockRows,BlockCols,true> > Base;\n    using Base::convert_index;\npublic:\n    enum { IsRowMajor = internal::traits<BlockType>::IsRowMajor };\n    EIGEN_SPARSE_PUBLIC_INTERFACE(BlockType)\nprotected:\n    typedef typename Base::IndexVector IndexVector;\n    enum { OuterSize = IsRowMajor ? BlockRows : BlockCols };\npublic:\n\n    inline sparse_matrix_block_impl(SparseMatrixType& xpr, Index i)\n      : m_matrix(xpr), m_outerStart(convert_index(i)), m_outerSize(OuterSize)\n    {}\n\n    inline sparse_matrix_block_impl(SparseMatrixType& xpr, Index startRow, Index startCol, Index blockRows, Index blockCols)\n      : m_matrix(xpr), m_outerStart(convert_index(IsRowMajor ? startRow : startCol)), m_outerSize(convert_index(IsRowMajor ? blockRows : blockCols))\n    {}\n\n    template<typename OtherDerived>\n    inline BlockType& operator=(const SparseMatrixBase<OtherDerived>& other)\n    {\n      typedef typename internal::remove_all<typename SparseMatrixType::Nested>::type _NestedMatrixType;\n      _NestedMatrixType& matrix = m_matrix;\n      // This assignment is slow if this vector set is not empty\n      // and/or it is not at the end of the nonzeros of the underlying matrix.\n\n      // 1 - eval to a temporary to avoid transposition and/or aliasing issues\n      Ref<const SparseMatrix<Scalar, IsRowMajor ? RowMajor : ColMajor, StorageIndex> > tmp(other.derived());\n      eigen_internal_assert(tmp.outerSize()==m_outerSize.value());\n\n      // 2 - let's check whether there is enough allocated memory\n      Index nnz           = tmp.nonZeros();\n      Index start         = m_outerStart==0 ? 0 : m_matrix.outerIndexPtr()[m_outerStart]; // starting position of the current block\n      Index end           = m_matrix.outerIndexPtr()[m_outerStart+m_outerSize.value()]; // ending position of the current block\n      Index block_size    = end - start;                                                // available room in the current block\n      Index tail_size     = m_matrix.outerIndexPtr()[m_matrix.outerSize()] - end;\n\n      Index free_size     = m_matrix.isCompressed()\n                          ? Index(matrix.data().allocatedSize()) + block_size\n                          : block_size;\n\n      Index tmp_start = tmp.outerIndexPtr()[0];\n\n      bool update_trailing_pointers = false;\n      if(nnz>free_size)\n      {\n        // realloc manually to reduce copies\n        typename SparseMatrixType::Storage newdata(m_matrix.data().allocatedSize() - block_size + nnz);\n\n        internal::smart_copy(m_matrix.valuePtr(),       m_matrix.valuePtr() + start,      newdata.valuePtr());\n        internal::smart_copy(m_matrix.innerIndexPtr(),  m_matrix.innerIndexPtr() + start, newdata.indexPtr());\n\n        internal::smart_copy(tmp.valuePtr() + tmp_start,      tmp.valuePtr() + tmp_start + nnz,       newdata.valuePtr() + start);\n        internal::smart_copy(tmp.innerIndexPtr() + tmp_start, tmp.innerIndexPtr() + tmp_start + nnz,  newdata.indexPtr() + start);\n\n        internal::smart_copy(matrix.valuePtr()+end,       matrix.valuePtr()+end + tail_size,      newdata.valuePtr()+start+nnz);\n        internal::smart_copy(matrix.innerIndexPtr()+end,  matrix.innerIndexPtr()+end + tail_size, newdata.indexPtr()+start+nnz);\n\n        newdata.resize(m_matrix.outerIndexPtr()[m_matrix.outerSize()] - block_size + nnz);\n\n        matrix.data().swap(newdata);\n\n        update_trailing_pointers = true;\n      }\n      else\n      {\n        if(m_matrix.isCompressed())\n        {\n          // no need to realloc, simply copy the tail at its respective position and insert tmp\n          matrix.data().resize(start + nnz + tail_size);\n\n          internal::smart_memmove(matrix.valuePtr()+end,      matrix.valuePtr() + end+tail_size,      matrix.valuePtr() + start+nnz);\n          internal::smart_memmove(matrix.innerIndexPtr()+end, matrix.innerIndexPtr() + end+tail_size, matrix.innerIndexPtr() + start+nnz);\n\n          update_trailing_pointers = true;\n        }\n\n        internal::smart_copy(tmp.valuePtr() + tmp_start,      tmp.valuePtr() + tmp_start + nnz,       matrix.valuePtr() + start);\n        internal::smart_copy(tmp.innerIndexPtr() + tmp_start, tmp.innerIndexPtr() + tmp_start + nnz,  matrix.innerIndexPtr() + start);\n      }\n\n      // update outer index pointers and innerNonZeros\n      if(IsVectorAtCompileTime)\n      {\n        if(!m_matrix.isCompressed())\n          matrix.innerNonZeroPtr()[m_outerStart] = StorageIndex(nnz);\n        matrix.outerIndexPtr()[m_outerStart] = StorageIndex(start);\n      }\n      else\n      {\n        StorageIndex p = StorageIndex(start);\n        for(Index k=0; k<m_outerSize.value(); ++k)\n        {\n          StorageIndex nnz_k = internal::convert_index<StorageIndex>(tmp.innerVector(k).nonZeros());\n          if(!m_matrix.isCompressed())\n            matrix.innerNonZeroPtr()[m_outerStart+k] = nnz_k;\n          matrix.outerIndexPtr()[m_outerStart+k] = p;\n          p += nnz_k;\n        }\n      }\n\n      if(update_trailing_pointers)\n      {\n        StorageIndex offset = internal::convert_index<StorageIndex>(nnz - block_size);\n        for(Index k = m_outerStart + m_outerSize.value(); k<=matrix.outerSize(); ++k)\n        {\n          matrix.outerIndexPtr()[k] += offset;\n        }\n      }\n\n      return derived();\n    }\n\n    inline BlockType& operator=(const BlockType& other)\n    {\n      return operator=<BlockType>(other);\n    }\n\n    inline const Scalar* valuePtr() const\n    { return m_matrix.valuePtr(); }\n    inline Scalar* valuePtr()\n    { return m_matrix.valuePtr(); }\n\n    inline const StorageIndex* innerIndexPtr() const\n    { return m_matrix.innerIndexPtr(); }\n    inline StorageIndex* innerIndexPtr()\n    { return m_matrix.innerIndexPtr(); }\n\n    inline const StorageIndex* outerIndexPtr() const\n    { return m_matrix.outerIndexPtr() + m_outerStart; }\n    inline StorageIndex* outerIndexPtr()\n    { return m_matrix.outerIndexPtr() + m_outerStart; }\n\n    inline const StorageIndex* innerNonZeroPtr() const\n    { return isCompressed() ? 0 : (m_matrix.innerNonZeroPtr()+m_outerStart); }\n    inline StorageIndex* innerNonZeroPtr()\n    { return isCompressed() ? 0 : (m_matrix.innerNonZeroPtr()+m_outerStart); }\n\n    bool isCompressed() const { return m_matrix.innerNonZeroPtr()==0; }\n\n    inline Scalar& coeffRef(Index row, Index col)\n    {\n      return m_matrix.coeffRef(row + (IsRowMajor ? m_outerStart : 0), col + (IsRowMajor ? 0 :  m_outerStart));\n    }\n\n    inline const Scalar coeff(Index row, Index col) const\n    {\n      return m_matrix.coeff(row + (IsRowMajor ? m_outerStart : 0), col + (IsRowMajor ? 0 :  m_outerStart));\n    }\n\n    inline const Scalar coeff(Index index) const\n    {\n      return m_matrix.coeff(IsRowMajor ? m_outerStart : index, IsRowMajor ? index :  m_outerStart);\n    }\n\n    const Scalar& lastCoeff() const\n    {\n      EIGEN_STATIC_ASSERT_VECTOR_ONLY(sparse_matrix_block_impl);\n      eigen_assert(Base::nonZeros()>0);\n      if(m_matrix.isCompressed())\n        return m_matrix.valuePtr()[m_matrix.outerIndexPtr()[m_outerStart+1]-1];\n      else\n        return m_matrix.valuePtr()[m_matrix.outerIndexPtr()[m_outerStart]+m_matrix.innerNonZeroPtr()[m_outerStart]-1];\n    }\n\n    EIGEN_STRONG_INLINE Index rows() const { return IsRowMajor ? m_outerSize.value() : m_matrix.rows(); }\n    EIGEN_STRONG_INLINE Index cols() const { return IsRowMajor ? m_matrix.cols() : m_outerSize.value(); }\n\n    inline const SparseMatrixType& nestedExpression() const { return m_matrix; }\n    inline SparseMatrixType& nestedExpression() { return m_matrix; }\n    Index startRow() const { return IsRowMajor ? m_outerStart : 0; }\n    Index startCol() const { return IsRowMajor ? 0 : m_outerStart; }\n    Index blockRows() const { return IsRowMajor ? m_outerSize.value() : m_matrix.rows(); }\n    Index blockCols() const { return IsRowMajor ? m_matrix.cols() : m_outerSize.value(); }\n\n  protected:\n\n    typename internal::ref_selector<SparseMatrixType>::non_const_type m_matrix;\n    Index m_outerStart;\n    const internal::variable_if_dynamic<Index, OuterSize> m_outerSize;\n\n};\n\n} // namespace internal\n\ntemplate<typename _Scalar, int _Options, typename _StorageIndex, int BlockRows, int BlockCols>\nclass BlockImpl<SparseMatrix<_Scalar, _Options, _StorageIndex>,BlockRows,BlockCols,true,Sparse>\n  : public internal::sparse_matrix_block_impl<SparseMatrix<_Scalar, _Options, _StorageIndex>,BlockRows,BlockCols>\n{\npublic:\n  typedef _StorageIndex StorageIndex;\n  typedef SparseMatrix<_Scalar, _Options, _StorageIndex> SparseMatrixType;\n  typedef internal::sparse_matrix_block_impl<SparseMatrixType,BlockRows,BlockCols> Base;\n  inline BlockImpl(SparseMatrixType& xpr, Index i)\n    : Base(xpr, i)\n  {}\n\n  inline BlockImpl(SparseMatrixType& xpr, Index startRow, Index startCol, Index blockRows, Index blockCols)\n    : Base(xpr, startRow, startCol, blockRows, blockCols)\n  {}\n\n  using Base::operator=;\n};\n\ntemplate<typename _Scalar, int _Options, typename _StorageIndex, int BlockRows, int BlockCols>\nclass BlockImpl<const SparseMatrix<_Scalar, _Options, _StorageIndex>,BlockRows,BlockCols,true,Sparse>\n  : public internal::sparse_matrix_block_impl<const SparseMatrix<_Scalar, _Options, _StorageIndex>,BlockRows,BlockCols>\n{\npublic:\n  typedef _StorageIndex StorageIndex;\n  typedef const SparseMatrix<_Scalar, _Options, _StorageIndex> SparseMatrixType;\n  typedef internal::sparse_matrix_block_impl<SparseMatrixType,BlockRows,BlockCols> Base;\n  inline BlockImpl(SparseMatrixType& xpr, Index i)\n    : Base(xpr, i)\n  {}\n\n  inline BlockImpl(SparseMatrixType& xpr, Index startRow, Index startCol, Index blockRows, Index blockCols)\n    : Base(xpr, startRow, startCol, blockRows, blockCols)\n  {}\n\n  using Base::operator=;\nprivate:\n  template<typename Derived> BlockImpl(const SparseMatrixBase<Derived>& xpr, Index i);\n  template<typename Derived> BlockImpl(const SparseMatrixBase<Derived>& xpr);\n};\n\n//----------\n\n/** \\returns the \\a outer -th column (resp. row) of the matrix \\c *this if \\c *this\n  * is col-major (resp. row-major).\n  */\ntemplate<typename Derived>\ntypename SparseMatrixBase<Derived>::InnerVectorReturnType SparseMatrixBase<Derived>::innerVector(Index outer)\n{ return InnerVectorReturnType(derived(), outer); }\n\n/** \\returns the \\a outer -th column (resp. row) of the matrix \\c *this if \\c *this\n  * is col-major (resp. row-major). Read-only.\n  */\ntemplate<typename Derived>\nconst typename SparseMatrixBase<Derived>::ConstInnerVectorReturnType SparseMatrixBase<Derived>::innerVector(Index outer) const\n{ return ConstInnerVectorReturnType(derived(), outer); }\n\n/** \\returns the \\a outer -th column (resp. row) of the matrix \\c *this if \\c *this\n  * is col-major (resp. row-major).\n  */\ntemplate<typename Derived>\ntypename SparseMatrixBase<Derived>::InnerVectorsReturnType\nSparseMatrixBase<Derived>::innerVectors(Index outerStart, Index outerSize)\n{\n  return Block<Derived,Dynamic,Dynamic,true>(derived(),\n                                             IsRowMajor ? outerStart : 0, IsRowMajor ? 0 : outerStart,\n                                             IsRowMajor ? outerSize : rows(), IsRowMajor ? cols() : outerSize);\n\n}\n\n/** \\returns the \\a outer -th column (resp. row) of the matrix \\c *this if \\c *this\n  * is col-major (resp. row-major). Read-only.\n  */\ntemplate<typename Derived>\nconst typename SparseMatrixBase<Derived>::ConstInnerVectorsReturnType\nSparseMatrixBase<Derived>::innerVectors(Index outerStart, Index outerSize) const\n{\n  return Block<const Derived,Dynamic,Dynamic,true>(derived(),\n                                                  IsRowMajor ? outerStart : 0, IsRowMajor ? 0 : outerStart,\n                                                  IsRowMajor ? outerSize : rows(), IsRowMajor ? cols() : outerSize);\n\n}\n\n/** Generic implementation of sparse Block expression.\n  * Real-only.\n  */\ntemplate<typename XprType, int BlockRows, int BlockCols, bool InnerPanel>\nclass BlockImpl<XprType,BlockRows,BlockCols,InnerPanel,Sparse>\n  : public SparseMatrixBase<Block<XprType,BlockRows,BlockCols,InnerPanel> >, internal::no_assignment_operator\n{\n    typedef Block<XprType, BlockRows, BlockCols, InnerPanel> BlockType;\n    typedef SparseMatrixBase<BlockType> Base;\n    using Base::convert_index;\npublic:\n    enum { IsRowMajor = internal::traits<BlockType>::IsRowMajor };\n    EIGEN_SPARSE_PUBLIC_INTERFACE(BlockType)\n\n    typedef typename internal::remove_all<typename XprType::Nested>::type _MatrixTypeNested;\n\n    /** Column or Row constructor\n      */\n    inline BlockImpl(XprType& xpr, Index i)\n      : m_matrix(xpr),\n        m_startRow( (BlockRows==1) && (BlockCols==XprType::ColsAtCompileTime) ? convert_index(i) : 0),\n        m_startCol( (BlockRows==XprType::RowsAtCompileTime) && (BlockCols==1) ? convert_index(i) : 0),\n        m_blockRows(BlockRows==1 ? 1 : xpr.rows()),\n        m_blockCols(BlockCols==1 ? 1 : xpr.cols())\n    {}\n\n    /** Dynamic-size constructor\n      */\n    inline BlockImpl(XprType& xpr, Index startRow, Index startCol, Index blockRows, Index blockCols)\n      : m_matrix(xpr), m_startRow(convert_index(startRow)), m_startCol(convert_index(startCol)), m_blockRows(convert_index(blockRows)), m_blockCols(convert_index(blockCols))\n    {}\n\n    inline Index rows() const { return m_blockRows.value(); }\n    inline Index cols() const { return m_blockCols.value(); }\n\n    inline Scalar& coeffRef(Index row, Index col)\n    {\n      return m_matrix.coeffRef(row + m_startRow.value(), col + m_startCol.value());\n    }\n\n    inline const Scalar coeff(Index row, Index col) const\n    {\n      return m_matrix.coeff(row + m_startRow.value(), col + m_startCol.value());\n    }\n\n    inline Scalar& coeffRef(Index index)\n    {\n      return m_matrix.coeffRef(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),\n                               m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));\n    }\n\n    inline const Scalar coeff(Index index) const\n    {\n      return m_matrix.coeff(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),\n                            m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));\n    }\n\n    inline const XprType& nestedExpression() const { return m_matrix; }\n    inline XprType& nestedExpression() { return m_matrix; }\n    Index startRow() const { return m_startRow.value(); }\n    Index startCol() const { return m_startCol.value(); }\n    Index blockRows() const { return m_blockRows.value(); }\n    Index blockCols() const { return m_blockCols.value(); }\n\n  protected:\n//     friend class internal::GenericSparseBlockInnerIteratorImpl<XprType,BlockRows,BlockCols,InnerPanel>;\n    friend struct internal::unary_evaluator<Block<XprType,BlockRows,BlockCols,InnerPanel>, internal::IteratorBased, Scalar >;\n\n    Index nonZeros() const { return Dynamic; }\n\n    typename internal::ref_selector<XprType>::non_const_type m_matrix;\n    const internal::variable_if_dynamic<Index, XprType::RowsAtCompileTime == 1 ? 0 : Dynamic> m_startRow;\n    const internal::variable_if_dynamic<Index, XprType::ColsAtCompileTime == 1 ? 0 : Dynamic> m_startCol;\n    const internal::variable_if_dynamic<Index, RowsAtCompileTime> m_blockRows;\n    const internal::variable_if_dynamic<Index, ColsAtCompileTime> m_blockCols;\n\n  protected:\n    // Disable assignment with clear error message.\n    // Note that simply removing operator= yields compilation errors with ICC+MSVC\n    template<typename T>\n    BlockImpl& operator=(const T&)\n    {\n      EIGEN_STATIC_ASSERT(sizeof(T)==0, THIS_SPARSE_BLOCK_SUBEXPRESSION_IS_READ_ONLY);\n      return *this;\n    }\n\n};\n\nnamespace internal {\n\ntemplate<typename ArgType, int BlockRows, int BlockCols, bool InnerPanel>\nstruct unary_evaluator<Block<ArgType,BlockRows,BlockCols,InnerPanel>, IteratorBased >\n : public evaluator_base<Block<ArgType,BlockRows,BlockCols,InnerPanel> >\n{\n    class InnerVectorInnerIterator;\n    class OuterVectorInnerIterator;\n  public:\n    typedef Block<ArgType,BlockRows,BlockCols,InnerPanel> XprType;\n    typedef typename XprType::StorageIndex StorageIndex;\n    typedef typename XprType::Scalar Scalar;\n\n    enum {\n      IsRowMajor = XprType::IsRowMajor,\n\n      OuterVector =  (BlockCols==1 && ArgType::IsRowMajor)\n                    | // FIXME | instead of || to please GCC 4.4.0 stupid warning \"suggest parentheses around &&\".\n                      // revert to || as soon as not needed anymore.\n                     (BlockRows==1 && !ArgType::IsRowMajor),\n\n      CoeffReadCost = evaluator<ArgType>::CoeffReadCost,\n      Flags = XprType::Flags\n    };\n\n    typedef typename internal::conditional<OuterVector,OuterVectorInnerIterator,InnerVectorInnerIterator>::type InnerIterator;\n\n    explicit unary_evaluator(const XprType& op)\n      : m_argImpl(op.nestedExpression()), m_block(op)\n    {}\n\n    inline Index nonZerosEstimate() const {\n      Index nnz = m_block.nonZeros();\n      if(nnz<0)\n        return m_argImpl.nonZerosEstimate() * m_block.size() / m_block.nestedExpression().size();\n      return nnz;\n    }\n\n  protected:\n    typedef typename evaluator<ArgType>::InnerIterator EvalIterator;\n\n    evaluator<ArgType> m_argImpl;\n    const XprType &m_block;\n};\n\ntemplate<typename ArgType, int BlockRows, int BlockCols, bool InnerPanel>\nclass unary_evaluator<Block<ArgType,BlockRows,BlockCols,InnerPanel>, IteratorBased>::InnerVectorInnerIterator\n : public EvalIterator\n{\n  enum { IsRowMajor = unary_evaluator::IsRowMajor };\n  const XprType& m_block;\n  Index m_end;\npublic:\n\n  EIGEN_STRONG_INLINE InnerVectorInnerIterator(const unary_evaluator& aEval, Index outer)\n    : EvalIterator(aEval.m_argImpl, outer + (IsRowMajor ? aEval.m_block.startRow() : aEval.m_block.startCol())),\n      m_block(aEval.m_block),\n      m_end(IsRowMajor ? aEval.m_block.startCol()+aEval.m_block.blockCols() : aEval.m_block.startRow()+aEval.m_block.blockRows())\n  {\n    while( (EvalIterator::operator bool()) && (EvalIterator::index() < (IsRowMajor ? m_block.startCol() : m_block.startRow())) )\n      EvalIterator::operator++();\n  }\n\n  inline StorageIndex index() const { return EvalIterator::index() - convert_index<StorageIndex>(IsRowMajor ? m_block.startCol() : m_block.startRow()); }\n  inline Index outer()  const { return EvalIterator::outer() - (IsRowMajor ? m_block.startRow() : m_block.startCol()); }\n  inline Index row()    const { return EvalIterator::row()   - m_block.startRow(); }\n  inline Index col()    const { return EvalIterator::col()   - m_block.startCol(); }\n\n  inline operator bool() const { return EvalIterator::operator bool() && EvalIterator::index() < m_end; }\n};\n\ntemplate<typename ArgType, int BlockRows, int BlockCols, bool InnerPanel>\nclass unary_evaluator<Block<ArgType,BlockRows,BlockCols,InnerPanel>, IteratorBased>::OuterVectorInnerIterator\n{\n  enum { IsRowMajor = unary_evaluator::IsRowMajor };\n  const unary_evaluator& m_eval;\n  Index m_outerPos;\n  const Index m_innerIndex;\n  Index m_end;\n  EvalIterator m_it;\npublic:\n\n  EIGEN_STRONG_INLINE OuterVectorInnerIterator(const unary_evaluator& aEval, Index outer)\n    : m_eval(aEval),\n      m_outerPos( (IsRowMajor ? aEval.m_block.startCol() : aEval.m_block.startRow()) ),\n      m_innerIndex(IsRowMajor ? aEval.m_block.startRow() : aEval.m_block.startCol()),\n      m_end(IsRowMajor ? aEval.m_block.startCol()+aEval.m_block.blockCols() : aEval.m_block.startRow()+aEval.m_block.blockRows()),\n      m_it(m_eval.m_argImpl, m_outerPos)\n  {\n    EIGEN_UNUSED_VARIABLE(outer);\n    eigen_assert(outer==0);\n\n    while(m_it && m_it.index() < m_innerIndex) ++m_it;\n    if((!m_it) || (m_it.index()!=m_innerIndex))\n      ++(*this);\n  }\n\n  inline StorageIndex index() const { return convert_index<StorageIndex>(m_outerPos - (IsRowMajor ? m_eval.m_block.startCol() : m_eval.m_block.startRow())); }\n  inline Index outer()  const { return 0; }\n  inline Index row()    const { return IsRowMajor ? 0 : index(); }\n  inline Index col()    const { return IsRowMajor ? index() : 0; }\n\n  inline Scalar value() const { return m_it.value(); }\n  inline Scalar& valueRef() { return m_it.valueRef(); }\n\n  inline OuterVectorInnerIterator& operator++()\n  {\n    // search next non-zero entry\n    while(++m_outerPos<m_end)\n    {\n      // Restart iterator at the next inner-vector:\n      m_it.~EvalIterator();\n      ::new (&m_it) EvalIterator(m_eval.m_argImpl, m_outerPos);\n      // search for the key m_innerIndex in the current outer-vector\n      while(m_it && m_it.index() < m_innerIndex) ++m_it;\n      if(m_it && m_it.index()==m_innerIndex) break;\n    }\n    return *this;\n  }\n\n  inline operator bool() const { return m_outerPos < m_end; }\n};\n\ntemplate<typename _Scalar, int _Options, typename _StorageIndex, int BlockRows, int BlockCols>\nstruct unary_evaluator<Block<SparseMatrix<_Scalar, _Options, _StorageIndex>,BlockRows,BlockCols,true>, IteratorBased>\n  : evaluator<SparseCompressedBase<Block<SparseMatrix<_Scalar, _Options, _StorageIndex>,BlockRows,BlockCols,true> > >\n{\n  typedef Block<SparseMatrix<_Scalar, _Options, _StorageIndex>,BlockRows,BlockCols,true> XprType;\n  typedef evaluator<SparseCompressedBase<XprType> > Base;\n  explicit unary_evaluator(const XprType &xpr) : Base(xpr) {}\n};\n\ntemplate<typename _Scalar, int _Options, typename _StorageIndex, int BlockRows, int BlockCols>\nstruct unary_evaluator<Block<const SparseMatrix<_Scalar, _Options, _StorageIndex>,BlockRows,BlockCols,true>, IteratorBased>\n  : evaluator<SparseCompressedBase<Block<const SparseMatrix<_Scalar, _Options, _StorageIndex>,BlockRows,BlockCols,true> > >\n{\n  typedef Block<const SparseMatrix<_Scalar, _Options, _StorageIndex>,BlockRows,BlockCols,true> XprType;\n  typedef evaluator<SparseCompressedBase<XprType> > Base;\n  explicit unary_evaluator(const XprType &xpr) : Base(xpr) {}\n};\n\n} // end namespace internal\n\n\n} // end namespace Eigen\n\n#endif // EIGEN_SPARSE_BLOCK_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseCore/SparseColEtree.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n\n/* \n \n * NOTE: This file is the modified version of sp_coletree.c file in SuperLU \n \n * -- SuperLU routine (version 3.1) --\n * Univ. of California Berkeley, Xerox Palo Alto Research Center,\n * and Lawrence Berkeley National Lab.\n * August 1, 2008\n *\n * Copyright (c) 1994 by Xerox Corporation.  All rights reserved.\n *\n * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY\n * EXPRESSED OR IMPLIED.  ANY USE IS AT YOUR OWN RISK.\n *\n * Permission is hereby granted to use or copy this program for any\n * purpose, provided the above notices are retained on all copies.\n * Permission to modify the code and to distribute modified code is\n * granted, provided the above notices are retained, and a notice that\n * the code was modified is included with the above copyright notice.\n */\n#ifndef SPARSE_COLETREE_H\n#define SPARSE_COLETREE_H\n\nnamespace Eigen {\n\nnamespace internal {\n\n/** Find the root of the tree/set containing the vertex i : Use Path halving */ \ntemplate<typename Index, typename IndexVector>\nIndex etree_find (Index i, IndexVector& pp)\n{\n  Index p = pp(i); // Parent \n  Index gp = pp(p); // Grand parent \n  while (gp != p) \n  {\n    pp(i) = gp; // Parent pointer on find path is changed to former grand parent\n    i = gp; \n    p = pp(i);\n    gp = pp(p);\n  }\n  return p; \n}\n\n/** Compute the column elimination tree of a sparse matrix\n  * \\param mat The matrix in column-major format. \n  * \\param parent The elimination tree\n  * \\param firstRowElt The column index of the first element in each row\n  * \\param perm The permutation to apply to the column of \\b mat\n  */\ntemplate <typename MatrixType, typename IndexVector>\nint coletree(const MatrixType& mat, IndexVector& parent, IndexVector& firstRowElt, typename MatrixType::StorageIndex *perm=0)\n{\n  typedef typename MatrixType::StorageIndex StorageIndex;\n  StorageIndex nc = convert_index<StorageIndex>(mat.cols()); // Number of columns\n  StorageIndex m = convert_index<StorageIndex>(mat.rows());\n  StorageIndex diagSize = (std::min)(nc,m);\n  IndexVector root(nc); // root of subtree of etree \n  root.setZero();\n  IndexVector pp(nc); // disjoint sets \n  pp.setZero(); // Initialize disjoint sets \n  parent.resize(mat.cols());\n  //Compute first nonzero column in each row \n  firstRowElt.resize(m);\n  firstRowElt.setConstant(nc);\n  firstRowElt.segment(0, diagSize).setLinSpaced(diagSize, 0, diagSize-1);\n  bool found_diag;\n  for (StorageIndex col = 0; col < nc; col++)\n  {\n    StorageIndex pcol = col;\n    if(perm) pcol  = perm[col];\n    for (typename MatrixType::InnerIterator it(mat, pcol); it; ++it)\n    { \n      Index row = it.row();\n      firstRowElt(row) = (std::min)(firstRowElt(row), col);\n    }\n  }\n  /* Compute etree by Liu's algorithm for symmetric matrices,\n          except use (firstRowElt[r],c) in place of an edge (r,c) of A.\n    Thus each row clique in A'*A is replaced by a star\n    centered at its first vertex, which has the same fill. */\n  StorageIndex rset, cset, rroot;\n  for (StorageIndex col = 0; col < nc; col++) \n  {\n    found_diag = col>=m;\n    pp(col) = col; \n    cset = col; \n    root(cset) = col; \n    parent(col) = nc; \n    /* The diagonal element is treated here even if it does not exist in the matrix\n     * hence the loop is executed once more */ \n    StorageIndex pcol = col;\n    if(perm) pcol  = perm[col];\n    for (typename MatrixType::InnerIterator it(mat, pcol); it||!found_diag; ++it)\n    { //  A sequence of interleaved find and union is performed \n      Index i = col;\n      if(it) i = it.index();\n      if (i == col) found_diag = true;\n      \n      StorageIndex row = firstRowElt(i);\n      if (row >= col) continue; \n      rset = internal::etree_find(row, pp); // Find the name of the set containing row\n      rroot = root(rset);\n      if (rroot != col) \n      {\n        parent(rroot) = col; \n        pp(cset) = rset; \n        cset = rset; \n        root(cset) = col; \n      }\n    }\n  }\n  return 0;  \n}\n\n/** \n  * Depth-first search from vertex n.  No recursion.\n  * This routine was contributed by Cédric Doucet, CEDRAT Group, Meylan, France.\n*/\ntemplate <typename IndexVector>\nvoid nr_etdfs (typename IndexVector::Scalar n, IndexVector& parent, IndexVector& first_kid, IndexVector& next_kid, IndexVector& post, typename IndexVector::Scalar postnum)\n{\n  typedef typename IndexVector::Scalar StorageIndex;\n  StorageIndex current = n, first, next;\n  while (postnum != n) \n  {\n    // No kid for the current node\n    first = first_kid(current);\n    \n    // no kid for the current node\n    if (first == -1) \n    {\n      // Numbering this node because it has no kid \n      post(current) = postnum++;\n      \n      // looking for the next kid \n      next = next_kid(current); \n      while (next == -1) \n      {\n        // No more kids : back to the parent node\n        current = parent(current); \n        // numbering the parent node \n        post(current) = postnum++;\n        \n        // Get the next kid \n        next = next_kid(current); \n      }\n      // stopping criterion \n      if (postnum == n+1) return; \n      \n      // Updating current node \n      current = next; \n    }\n    else \n    {\n      current = first; \n    }\n  }\n}\n\n\n/**\n  * \\brief Post order a tree \n  * \\param n the number of nodes\n  * \\param parent Input tree\n  * \\param post postordered tree\n  */\ntemplate <typename IndexVector>\nvoid treePostorder(typename IndexVector::Scalar n, IndexVector& parent, IndexVector& post)\n{\n  typedef typename IndexVector::Scalar StorageIndex;\n  IndexVector first_kid, next_kid; // Linked list of children \n  StorageIndex postnum; \n  // Allocate storage for working arrays and results \n  first_kid.resize(n+1); \n  next_kid.setZero(n+1);\n  post.setZero(n+1);\n  \n  // Set up structure describing children\n  first_kid.setConstant(-1); \n  for (StorageIndex v = n-1; v >= 0; v--) \n  {\n    StorageIndex dad = parent(v);\n    next_kid(v) = first_kid(dad); \n    first_kid(dad) = v; \n  }\n  \n  // Depth-first search from dummy root vertex #n\n  postnum = 0; \n  internal::nr_etdfs(n, parent, first_kid, next_kid, post, postnum);\n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // SPARSE_COLETREE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseCore/SparseCompressedBase.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSE_COMPRESSED_BASE_H\n#define EIGEN_SPARSE_COMPRESSED_BASE_H\n\nnamespace Eigen { \n\ntemplate<typename Derived> class SparseCompressedBase;\n  \nnamespace internal {\n\ntemplate<typename Derived>\nstruct traits<SparseCompressedBase<Derived> > : traits<Derived>\n{};\n\n} // end namespace internal\n\n/** \\ingroup SparseCore_Module\n  * \\class SparseCompressedBase\n  * \\brief Common base class for sparse [compressed]-{row|column}-storage format.\n  *\n  * This class defines the common interface for all derived classes implementing the compressed sparse storage format, such as:\n  *  - SparseMatrix\n  *  - Ref<SparseMatrixType,Options>\n  *  - Map<SparseMatrixType>\n  *\n  */\ntemplate<typename Derived>\nclass SparseCompressedBase\n  : public SparseMatrixBase<Derived>\n{\n  public:\n    typedef SparseMatrixBase<Derived> Base;\n    EIGEN_SPARSE_PUBLIC_INTERFACE(SparseCompressedBase)\n    using Base::operator=;\n    using Base::IsRowMajor;\n    \n    class InnerIterator;\n    class ReverseInnerIterator;\n    \n  protected:\n    typedef typename Base::IndexVector IndexVector;\n    Eigen::Map<IndexVector> innerNonZeros() { return Eigen::Map<IndexVector>(innerNonZeroPtr(), isCompressed()?0:derived().outerSize()); }\n    const  Eigen::Map<const IndexVector> innerNonZeros() const { return Eigen::Map<const IndexVector>(innerNonZeroPtr(), isCompressed()?0:derived().outerSize()); }\n        \n  public:\n    \n    /** \\returns the number of non zero coefficients */\n    inline Index nonZeros() const\n    {\n      if(Derived::IsVectorAtCompileTime && outerIndexPtr()==0)\n        return derived().nonZeros();\n      else if(isCompressed())\n        return outerIndexPtr()[derived().outerSize()]-outerIndexPtr()[0];\n      else if(derived().outerSize()==0)\n        return 0;\n      else\n        return innerNonZeros().sum();\n    }\n    \n    /** \\returns a const pointer to the array of values.\n      * This function is aimed at interoperability with other libraries.\n      * \\sa innerIndexPtr(), outerIndexPtr() */\n    inline const Scalar* valuePtr() const { return derived().valuePtr(); }\n    /** \\returns a non-const pointer to the array of values.\n      * This function is aimed at interoperability with other libraries.\n      * \\sa innerIndexPtr(), outerIndexPtr() */\n    inline Scalar* valuePtr() { return derived().valuePtr(); }\n\n    /** \\returns a const pointer to the array of inner indices.\n      * This function is aimed at interoperability with other libraries.\n      * \\sa valuePtr(), outerIndexPtr() */\n    inline const StorageIndex* innerIndexPtr() const { return derived().innerIndexPtr(); }\n    /** \\returns a non-const pointer to the array of inner indices.\n      * This function is aimed at interoperability with other libraries.\n      * \\sa valuePtr(), outerIndexPtr() */\n    inline StorageIndex* innerIndexPtr() { return derived().innerIndexPtr(); }\n\n    /** \\returns a const pointer to the array of the starting positions of the inner vectors.\n      * This function is aimed at interoperability with other libraries.\n      * \\warning it returns the null pointer 0 for SparseVector\n      * \\sa valuePtr(), innerIndexPtr() */\n    inline const StorageIndex* outerIndexPtr() const { return derived().outerIndexPtr(); }\n    /** \\returns a non-const pointer to the array of the starting positions of the inner vectors.\n      * This function is aimed at interoperability with other libraries.\n      * \\warning it returns the null pointer 0 for SparseVector\n      * \\sa valuePtr(), innerIndexPtr() */\n    inline StorageIndex* outerIndexPtr() { return derived().outerIndexPtr(); }\n\n    /** \\returns a const pointer to the array of the number of non zeros of the inner vectors.\n      * This function is aimed at interoperability with other libraries.\n      * \\warning it returns the null pointer 0 in compressed mode */\n    inline const StorageIndex* innerNonZeroPtr() const { return derived().innerNonZeroPtr(); }\n    /** \\returns a non-const pointer to the array of the number of non zeros of the inner vectors.\n      * This function is aimed at interoperability with other libraries.\n      * \\warning it returns the null pointer 0 in compressed mode */\n    inline StorageIndex* innerNonZeroPtr() { return derived().innerNonZeroPtr(); }\n    \n    /** \\returns whether \\c *this is in compressed form. */\n    inline bool isCompressed() const { return innerNonZeroPtr()==0; }\n\n    /** \\returns a read-only view of the stored coefficients as a 1D array expression.\n      *\n      * \\warning this method is for \\b compressed \\b storage \\b only, and it will trigger an assertion otherwise.\n      *\n      * \\sa valuePtr(), isCompressed() */\n    const Map<const Array<Scalar,Dynamic,1> > coeffs() const { eigen_assert(isCompressed()); return Array<Scalar,Dynamic,1>::Map(valuePtr(),nonZeros()); }\n\n    /** \\returns a read-write view of the stored coefficients as a 1D array expression\n      *\n      * \\warning this method is for \\b compressed \\b storage \\b only, and it will trigger an assertion otherwise.\n      *\n      * Here is an example:\n      * \\include SparseMatrix_coeffs.cpp\n      * and the output is:\n      * \\include SparseMatrix_coeffs.out\n      *\n      * \\sa valuePtr(), isCompressed() */\n    Map<Array<Scalar,Dynamic,1> > coeffs() { eigen_assert(isCompressed()); return Array<Scalar,Dynamic,1>::Map(valuePtr(),nonZeros()); }\n\n  protected:\n    /** Default constructor. Do nothing. */\n    SparseCompressedBase() {}\n  private:\n    template<typename OtherDerived> explicit SparseCompressedBase(const SparseCompressedBase<OtherDerived>&);\n};\n\ntemplate<typename Derived>\nclass SparseCompressedBase<Derived>::InnerIterator\n{\n  public:\n    InnerIterator()\n      : m_values(0), m_indices(0), m_outer(0), m_id(0), m_end(0)\n    {}\n\n    InnerIterator(const InnerIterator& other)\n      : m_values(other.m_values), m_indices(other.m_indices), m_outer(other.m_outer), m_id(other.m_id), m_end(other.m_end)\n    {}\n\n    InnerIterator& operator=(const InnerIterator& other)\n    {\n      m_values = other.m_values;\n      m_indices = other.m_indices;\n      const_cast<OuterType&>(m_outer).setValue(other.m_outer.value());\n      m_id = other.m_id;\n      m_end = other.m_end;\n      return *this;\n    }\n\n    InnerIterator(const SparseCompressedBase& mat, Index outer)\n      : m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(outer)\n    {\n      if(Derived::IsVectorAtCompileTime && mat.outerIndexPtr()==0)\n      {\n        m_id = 0;\n        m_end = mat.nonZeros();\n      }\n      else\n      {\n        m_id = mat.outerIndexPtr()[outer];\n        if(mat.isCompressed())\n          m_end = mat.outerIndexPtr()[outer+1];\n        else\n          m_end = m_id + mat.innerNonZeroPtr()[outer];\n      }\n    }\n\n    explicit InnerIterator(const SparseCompressedBase& mat)\n      : m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(0), m_id(0), m_end(mat.nonZeros())\n    {\n      EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);\n    }\n\n    explicit InnerIterator(const internal::CompressedStorage<Scalar,StorageIndex>& data)\n      : m_values(data.valuePtr()), m_indices(data.indexPtr()), m_outer(0), m_id(0), m_end(data.size())\n    {\n      EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);\n    }\n\n    inline InnerIterator& operator++() { m_id++; return *this; }\n\n    inline const Scalar& value() const { return m_values[m_id]; }\n    inline Scalar& valueRef() { return const_cast<Scalar&>(m_values[m_id]); }\n\n    inline StorageIndex index() const { return m_indices[m_id]; }\n    inline Index outer() const { return m_outer.value(); }\n    inline Index row() const { return IsRowMajor ? m_outer.value() : index(); }\n    inline Index col() const { return IsRowMajor ? index() : m_outer.value(); }\n\n    inline operator bool() const { return (m_id < m_end); }\n\n  protected:\n    const Scalar* m_values;\n    const StorageIndex* m_indices;\n    typedef internal::variable_if_dynamic<Index,Derived::IsVectorAtCompileTime?0:Dynamic> OuterType;\n    const OuterType m_outer;\n    Index m_id;\n    Index m_end;\n  private:\n    // If you get here, then you're not using the right InnerIterator type, e.g.:\n    //   SparseMatrix<double,RowMajor> A;\n    //   SparseMatrix<double>::InnerIterator it(A,0);\n    template<typename T> InnerIterator(const SparseMatrixBase<T>&, Index outer);\n};\n\ntemplate<typename Derived>\nclass SparseCompressedBase<Derived>::ReverseInnerIterator\n{\n  public:\n    ReverseInnerIterator(const SparseCompressedBase& mat, Index outer)\n      : m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(outer)\n    {\n      if(Derived::IsVectorAtCompileTime && mat.outerIndexPtr()==0)\n      {\n        m_start = 0;\n        m_id = mat.nonZeros();\n      }\n      else\n      {\n        m_start = mat.outerIndexPtr()[outer];\n        if(mat.isCompressed())\n          m_id = mat.outerIndexPtr()[outer+1];\n        else\n          m_id = m_start + mat.innerNonZeroPtr()[outer];\n      }\n    }\n\n    explicit ReverseInnerIterator(const SparseCompressedBase& mat)\n      : m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(0), m_start(0), m_id(mat.nonZeros())\n    {\n      EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);\n    }\n\n    explicit ReverseInnerIterator(const internal::CompressedStorage<Scalar,StorageIndex>& data)\n      : m_values(data.valuePtr()), m_indices(data.indexPtr()), m_outer(0), m_start(0), m_id(data.size())\n    {\n      EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);\n    }\n\n    inline ReverseInnerIterator& operator--() { --m_id; return *this; }\n\n    inline const Scalar& value() const { return m_values[m_id-1]; }\n    inline Scalar& valueRef() { return const_cast<Scalar&>(m_values[m_id-1]); }\n\n    inline StorageIndex index() const { return m_indices[m_id-1]; }\n    inline Index outer() const { return m_outer.value(); }\n    inline Index row() const { return IsRowMajor ? m_outer.value() : index(); }\n    inline Index col() const { return IsRowMajor ? index() : m_outer.value(); }\n\n    inline operator bool() const { return (m_id > m_start); }\n\n  protected:\n    const Scalar* m_values;\n    const StorageIndex* m_indices;\n    typedef internal::variable_if_dynamic<Index,Derived::IsVectorAtCompileTime?0:Dynamic> OuterType;\n    const OuterType m_outer;\n    Index m_start;\n    Index m_id;\n};\n\nnamespace internal {\n\ntemplate<typename Derived>\nstruct evaluator<SparseCompressedBase<Derived> >\n  : evaluator_base<Derived>\n{\n  typedef typename Derived::Scalar Scalar;\n  typedef typename Derived::InnerIterator InnerIterator;\n  \n  enum {\n    CoeffReadCost = NumTraits<Scalar>::ReadCost,\n    Flags = Derived::Flags\n  };\n  \n  evaluator() : m_matrix(0), m_zero(0)\n  {\n    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);\n  }\n  explicit evaluator(const Derived &mat) : m_matrix(&mat), m_zero(0)\n  {\n    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);\n  }\n  \n  inline Index nonZerosEstimate() const {\n    return m_matrix->nonZeros();\n  }\n  \n  operator Derived&() { return m_matrix->const_cast_derived(); }\n  operator const Derived&() const { return *m_matrix; }\n  \n  typedef typename DenseCoeffsBase<Derived,ReadOnlyAccessors>::CoeffReturnType CoeffReturnType;\n  const Scalar& coeff(Index row, Index col) const\n  {\n    Index p = find(row,col);\n\n    if(p==Dynamic)\n      return m_zero;\n    else\n      return m_matrix->const_cast_derived().valuePtr()[p];\n  }\n\n  Scalar& coeffRef(Index row, Index col)\n  {\n    Index p = find(row,col);\n    eigen_assert(p!=Dynamic && \"written coefficient does not exist\");\n    return m_matrix->const_cast_derived().valuePtr()[p];\n  }\n\nprotected:\n\n  Index find(Index row, Index col) const\n  {\n    eigen_internal_assert(row>=0 && row<m_matrix->rows() && col>=0 && col<m_matrix->cols());\n\n    const Index outer = Derived::IsRowMajor ? row : col;\n    const Index inner = Derived::IsRowMajor ? col : row;\n\n    Index start = m_matrix->outerIndexPtr()[outer];\n    Index end = m_matrix->isCompressed() ? m_matrix->outerIndexPtr()[outer+1] : m_matrix->outerIndexPtr()[outer] + m_matrix->innerNonZeroPtr()[outer];\n    eigen_assert(end>=start && \"you are using a non finalized sparse matrix or written coefficient does not exist\");\n    const Index p = std::lower_bound(m_matrix->innerIndexPtr()+start, m_matrix->innerIndexPtr()+end,inner) - m_matrix->innerIndexPtr();\n\n    return ((p<end) && (m_matrix->innerIndexPtr()[p]==inner)) ? p : Dynamic;\n  }\n\n  const Derived *m_matrix;\n  const Scalar m_zero;\n};\n\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_SPARSE_COMPRESSED_BASE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseCore/SparseCwiseBinaryOp.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSE_CWISE_BINARY_OP_H\n#define EIGEN_SPARSE_CWISE_BINARY_OP_H\n\nnamespace Eigen { \n\n// Here we have to handle 3 cases:\n//  1 - sparse op dense\n//  2 - dense op sparse\n//  3 - sparse op sparse\n// We also need to implement a 4th iterator for:\n//  4 - dense op dense\n// Finally, we also need to distinguish between the product and other operations :\n//                configuration      returned mode\n//  1 - sparse op dense    product      sparse\n//                         generic      dense\n//  2 - dense op sparse    product      sparse\n//                         generic      dense\n//  3 - sparse op sparse   product      sparse\n//                         generic      sparse\n//  4 - dense op dense     product      dense\n//                         generic      dense\n//\n// TODO to ease compiler job, we could specialize product/quotient with a scalar\n//      and fallback to cwise-unary evaluator using bind1st_op and bind2nd_op.\n\ntemplate<typename BinaryOp, typename Lhs, typename Rhs>\nclass CwiseBinaryOpImpl<BinaryOp, Lhs, Rhs, Sparse>\n  : public SparseMatrixBase<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >\n{\n  public:\n    typedef CwiseBinaryOp<BinaryOp, Lhs, Rhs> Derived;\n    typedef SparseMatrixBase<Derived> Base;\n    EIGEN_SPARSE_PUBLIC_INTERFACE(Derived)\n    CwiseBinaryOpImpl()\n    {\n      EIGEN_STATIC_ASSERT((\n                (!internal::is_same<typename internal::traits<Lhs>::StorageKind,\n                                    typename internal::traits<Rhs>::StorageKind>::value)\n            ||  ((internal::evaluator<Lhs>::Flags&RowMajorBit) == (internal::evaluator<Rhs>::Flags&RowMajorBit))),\n            THE_STORAGE_ORDER_OF_BOTH_SIDES_MUST_MATCH);\n    }\n};\n\nnamespace internal {\n\n  \n// Generic \"sparse OP sparse\"\ntemplate<typename XprType> struct binary_sparse_evaluator;\n\ntemplate<typename BinaryOp, typename Lhs, typename Rhs>\nstruct binary_evaluator<CwiseBinaryOp<BinaryOp, Lhs, Rhs>, IteratorBased, IteratorBased>\n  : evaluator_base<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >\n{\nprotected:\n  typedef typename evaluator<Lhs>::InnerIterator  LhsIterator;\n  typedef typename evaluator<Rhs>::InnerIterator  RhsIterator;\n  typedef CwiseBinaryOp<BinaryOp, Lhs, Rhs> XprType;\n  typedef typename traits<XprType>::Scalar Scalar;\n  typedef typename XprType::StorageIndex StorageIndex;\npublic:\n\n  class InnerIterator\n  {\n  public:\n    \n    EIGEN_STRONG_INLINE InnerIterator(const binary_evaluator& aEval, Index outer)\n      : m_lhsIter(aEval.m_lhsImpl,outer), m_rhsIter(aEval.m_rhsImpl,outer), m_functor(aEval.m_functor)\n    {\n      this->operator++();\n    }\n\n    EIGEN_STRONG_INLINE InnerIterator& operator++()\n    {\n      if (m_lhsIter && m_rhsIter && (m_lhsIter.index() == m_rhsIter.index()))\n      {\n        m_id = m_lhsIter.index();\n        m_value = m_functor(m_lhsIter.value(), m_rhsIter.value());\n        ++m_lhsIter;\n        ++m_rhsIter;\n      }\n      else if (m_lhsIter && (!m_rhsIter || (m_lhsIter.index() < m_rhsIter.index())))\n      {\n        m_id = m_lhsIter.index();\n        m_value = m_functor(m_lhsIter.value(), Scalar(0));\n        ++m_lhsIter;\n      }\n      else if (m_rhsIter && (!m_lhsIter || (m_lhsIter.index() > m_rhsIter.index())))\n      {\n        m_id = m_rhsIter.index();\n        m_value = m_functor(Scalar(0), m_rhsIter.value());\n        ++m_rhsIter;\n      }\n      else\n      {\n        m_value = 0; // this is to avoid a compilation warning\n        m_id = -1;\n      }\n      return *this;\n    }\n\n    EIGEN_STRONG_INLINE Scalar value() const { return m_value; }\n\n    EIGEN_STRONG_INLINE StorageIndex index() const { return m_id; }\n    EIGEN_STRONG_INLINE Index outer() const { return m_lhsIter.outer(); }\n    EIGEN_STRONG_INLINE Index row() const { return Lhs::IsRowMajor ? m_lhsIter.row() : index(); }\n    EIGEN_STRONG_INLINE Index col() const { return Lhs::IsRowMajor ? index() : m_lhsIter.col(); }\n\n    EIGEN_STRONG_INLINE operator bool() const { return m_id>=0; }\n\n  protected:\n    LhsIterator m_lhsIter;\n    RhsIterator m_rhsIter;\n    const BinaryOp& m_functor;\n    Scalar m_value;\n    StorageIndex m_id;\n  };\n  \n  \n  enum {\n    CoeffReadCost = evaluator<Lhs>::CoeffReadCost + evaluator<Rhs>::CoeffReadCost + functor_traits<BinaryOp>::Cost,\n    Flags = XprType::Flags\n  };\n  \n  explicit binary_evaluator(const XprType& xpr)\n    : m_functor(xpr.functor()),\n      m_lhsImpl(xpr.lhs()), \n      m_rhsImpl(xpr.rhs())  \n  {\n    EIGEN_INTERNAL_CHECK_COST_VALUE(functor_traits<BinaryOp>::Cost);\n    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);\n  }\n  \n  inline Index nonZerosEstimate() const {\n    return m_lhsImpl.nonZerosEstimate() + m_rhsImpl.nonZerosEstimate();\n  }\n\nprotected:\n  const BinaryOp m_functor;\n  evaluator<Lhs> m_lhsImpl;\n  evaluator<Rhs> m_rhsImpl;\n};\n\n// dense op sparse\ntemplate<typename BinaryOp, typename Lhs, typename Rhs>\nstruct binary_evaluator<CwiseBinaryOp<BinaryOp, Lhs, Rhs>, IndexBased, IteratorBased>\n  : evaluator_base<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >\n{\nprotected:\n  typedef typename evaluator<Rhs>::InnerIterator  RhsIterator;\n  typedef CwiseBinaryOp<BinaryOp, Lhs, Rhs> XprType;\n  typedef typename traits<XprType>::Scalar Scalar;\n  typedef typename XprType::StorageIndex StorageIndex;\npublic:\n\n  class InnerIterator\n  {\n    enum { IsRowMajor = (int(Rhs::Flags)&RowMajorBit)==RowMajorBit };\n  public:\n\n    EIGEN_STRONG_INLINE InnerIterator(const binary_evaluator& aEval, Index outer)\n      : m_lhsEval(aEval.m_lhsImpl), m_rhsIter(aEval.m_rhsImpl,outer), m_functor(aEval.m_functor), m_value(0), m_id(-1), m_innerSize(aEval.m_expr.rhs().innerSize())\n    {\n      this->operator++();\n    }\n\n    EIGEN_STRONG_INLINE InnerIterator& operator++()\n    {\n      ++m_id;\n      if(m_id<m_innerSize)\n      {\n        Scalar lhsVal = m_lhsEval.coeff(IsRowMajor?m_rhsIter.outer():m_id,\n                                        IsRowMajor?m_id:m_rhsIter.outer());\n        if(m_rhsIter && m_rhsIter.index()==m_id)\n        {\n          m_value = m_functor(lhsVal, m_rhsIter.value());\n          ++m_rhsIter;\n        }\n        else\n          m_value = m_functor(lhsVal, Scalar(0));\n      }\n\n      return *this;\n    }\n\n    EIGEN_STRONG_INLINE Scalar value() const { eigen_internal_assert(m_id<m_innerSize); return m_value; }\n\n    EIGEN_STRONG_INLINE StorageIndex index() const { return m_id; }\n    EIGEN_STRONG_INLINE Index outer() const { return m_rhsIter.outer(); }\n    EIGEN_STRONG_INLINE Index row() const { return IsRowMajor ? m_rhsIter.outer() : m_id; }\n    EIGEN_STRONG_INLINE Index col() const { return IsRowMajor ? m_id : m_rhsIter.outer(); }\n\n    EIGEN_STRONG_INLINE operator bool() const { return m_id<m_innerSize; }\n\n  protected:\n    const evaluator<Lhs> &m_lhsEval;\n    RhsIterator m_rhsIter;\n    const BinaryOp& m_functor;\n    Scalar m_value;\n    StorageIndex m_id;\n    StorageIndex m_innerSize;\n  };\n\n\n  enum {\n    CoeffReadCost = evaluator<Lhs>::CoeffReadCost + evaluator<Rhs>::CoeffReadCost + functor_traits<BinaryOp>::Cost,\n    // Expose storage order of the sparse expression\n    Flags = (XprType::Flags & ~RowMajorBit) | (int(Rhs::Flags)&RowMajorBit)\n  };\n\n  explicit binary_evaluator(const XprType& xpr)\n    : m_functor(xpr.functor()),\n      m_lhsImpl(xpr.lhs()),\n      m_rhsImpl(xpr.rhs()),\n      m_expr(xpr)\n  {\n    EIGEN_INTERNAL_CHECK_COST_VALUE(functor_traits<BinaryOp>::Cost);\n    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);\n  }\n\n  inline Index nonZerosEstimate() const {\n    return m_expr.size();\n  }\n\nprotected:\n  const BinaryOp m_functor;\n  evaluator<Lhs> m_lhsImpl;\n  evaluator<Rhs> m_rhsImpl;\n  const XprType &m_expr;\n};\n\n// sparse op dense\ntemplate<typename BinaryOp, typename Lhs, typename Rhs>\nstruct binary_evaluator<CwiseBinaryOp<BinaryOp, Lhs, Rhs>, IteratorBased, IndexBased>\n  : evaluator_base<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >\n{\nprotected:\n  typedef typename evaluator<Lhs>::InnerIterator  LhsIterator;\n  typedef CwiseBinaryOp<BinaryOp, Lhs, Rhs> XprType;\n  typedef typename traits<XprType>::Scalar Scalar;\n  typedef typename XprType::StorageIndex StorageIndex;\npublic:\n\n  class InnerIterator\n  {\n    enum { IsRowMajor = (int(Lhs::Flags)&RowMajorBit)==RowMajorBit };\n  public:\n\n    EIGEN_STRONG_INLINE InnerIterator(const binary_evaluator& aEval, Index outer)\n      : m_lhsIter(aEval.m_lhsImpl,outer), m_rhsEval(aEval.m_rhsImpl), m_functor(aEval.m_functor), m_value(0), m_id(-1), m_innerSize(aEval.m_expr.lhs().innerSize())\n    {\n      this->operator++();\n    }\n\n    EIGEN_STRONG_INLINE InnerIterator& operator++()\n    {\n      ++m_id;\n      if(m_id<m_innerSize)\n      {\n        Scalar rhsVal = m_rhsEval.coeff(IsRowMajor?m_lhsIter.outer():m_id,\n                                        IsRowMajor?m_id:m_lhsIter.outer());\n        if(m_lhsIter && m_lhsIter.index()==m_id)\n        {\n          m_value = m_functor(m_lhsIter.value(), rhsVal);\n          ++m_lhsIter;\n        }\n        else\n          m_value = m_functor(Scalar(0),rhsVal);\n      }\n\n      return *this;\n    }\n\n    EIGEN_STRONG_INLINE Scalar value() const { eigen_internal_assert(m_id<m_innerSize); return m_value; }\n\n    EIGEN_STRONG_INLINE StorageIndex index() const { return m_id; }\n    EIGEN_STRONG_INLINE Index outer() const { return m_lhsIter.outer(); }\n    EIGEN_STRONG_INLINE Index row() const { return IsRowMajor ? m_lhsIter.outer() : m_id; }\n    EIGEN_STRONG_INLINE Index col() const { return IsRowMajor ? m_id : m_lhsIter.outer(); }\n\n    EIGEN_STRONG_INLINE operator bool() const { return m_id<m_innerSize; }\n\n  protected:\n    LhsIterator m_lhsIter;\n    const evaluator<Rhs> &m_rhsEval;\n    const BinaryOp& m_functor;\n    Scalar m_value;\n    StorageIndex m_id;\n    StorageIndex m_innerSize;\n  };\n\n\n  enum {\n    CoeffReadCost = evaluator<Lhs>::CoeffReadCost + evaluator<Rhs>::CoeffReadCost + functor_traits<BinaryOp>::Cost,\n    // Expose storage order of the sparse expression\n    Flags = (XprType::Flags & ~RowMajorBit) | (int(Lhs::Flags)&RowMajorBit)\n  };\n\n  explicit binary_evaluator(const XprType& xpr)\n    : m_functor(xpr.functor()),\n      m_lhsImpl(xpr.lhs()),\n      m_rhsImpl(xpr.rhs()),\n      m_expr(xpr)\n  {\n    EIGEN_INTERNAL_CHECK_COST_VALUE(functor_traits<BinaryOp>::Cost);\n    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);\n  }\n\n  inline Index nonZerosEstimate() const {\n    return m_expr.size();\n  }\n\nprotected:\n  const BinaryOp m_functor;\n  evaluator<Lhs> m_lhsImpl;\n  evaluator<Rhs> m_rhsImpl;\n  const XprType &m_expr;\n};\n\ntemplate<typename T,\n         typename LhsKind   = typename evaluator_traits<typename T::Lhs>::Kind,\n         typename RhsKind   = typename evaluator_traits<typename T::Rhs>::Kind,\n         typename LhsScalar = typename traits<typename T::Lhs>::Scalar,\n         typename RhsScalar = typename traits<typename T::Rhs>::Scalar> struct sparse_conjunction_evaluator;\n\n// \"sparse .* sparse\"\ntemplate<typename T1, typename T2, typename Lhs, typename Rhs>\nstruct binary_evaluator<CwiseBinaryOp<scalar_product_op<T1,T2>, Lhs, Rhs>, IteratorBased, IteratorBased>\n  : sparse_conjunction_evaluator<CwiseBinaryOp<scalar_product_op<T1,T2>, Lhs, Rhs> >\n{\n  typedef CwiseBinaryOp<scalar_product_op<T1,T2>, Lhs, Rhs> XprType;\n  typedef sparse_conjunction_evaluator<XprType> Base;\n  explicit binary_evaluator(const XprType& xpr) : Base(xpr) {}\n};\n// \"dense .* sparse\"\ntemplate<typename T1, typename T2, typename Lhs, typename Rhs>\nstruct binary_evaluator<CwiseBinaryOp<scalar_product_op<T1,T2>, Lhs, Rhs>, IndexBased, IteratorBased>\n  : sparse_conjunction_evaluator<CwiseBinaryOp<scalar_product_op<T1,T2>, Lhs, Rhs> >\n{\n  typedef CwiseBinaryOp<scalar_product_op<T1,T2>, Lhs, Rhs> XprType;\n  typedef sparse_conjunction_evaluator<XprType> Base;\n  explicit binary_evaluator(const XprType& xpr) : Base(xpr) {}\n};\n// \"sparse .* dense\"\ntemplate<typename T1, typename T2, typename Lhs, typename Rhs>\nstruct binary_evaluator<CwiseBinaryOp<scalar_product_op<T1,T2>, Lhs, Rhs>, IteratorBased, IndexBased>\n  : sparse_conjunction_evaluator<CwiseBinaryOp<scalar_product_op<T1,T2>, Lhs, Rhs> >\n{\n  typedef CwiseBinaryOp<scalar_product_op<T1,T2>, Lhs, Rhs> XprType;\n  typedef sparse_conjunction_evaluator<XprType> Base;\n  explicit binary_evaluator(const XprType& xpr) : Base(xpr) {}\n};\n\n// \"sparse ./ dense\"\ntemplate<typename T1, typename T2, typename Lhs, typename Rhs>\nstruct binary_evaluator<CwiseBinaryOp<scalar_quotient_op<T1,T2>, Lhs, Rhs>, IteratorBased, IndexBased>\n  : sparse_conjunction_evaluator<CwiseBinaryOp<scalar_quotient_op<T1,T2>, Lhs, Rhs> >\n{\n  typedef CwiseBinaryOp<scalar_quotient_op<T1,T2>, Lhs, Rhs> XprType;\n  typedef sparse_conjunction_evaluator<XprType> Base;\n  explicit binary_evaluator(const XprType& xpr) : Base(xpr) {}\n};\n\n// \"sparse && sparse\"\ntemplate<typename Lhs, typename Rhs>\nstruct binary_evaluator<CwiseBinaryOp<scalar_boolean_and_op, Lhs, Rhs>, IteratorBased, IteratorBased>\n  : sparse_conjunction_evaluator<CwiseBinaryOp<scalar_boolean_and_op, Lhs, Rhs> >\n{\n  typedef CwiseBinaryOp<scalar_boolean_and_op, Lhs, Rhs> XprType;\n  typedef sparse_conjunction_evaluator<XprType> Base;\n  explicit binary_evaluator(const XprType& xpr) : Base(xpr) {}\n};\n// \"dense && sparse\"\ntemplate<typename Lhs, typename Rhs>\nstruct binary_evaluator<CwiseBinaryOp<scalar_boolean_and_op, Lhs, Rhs>, IndexBased, IteratorBased>\n  : sparse_conjunction_evaluator<CwiseBinaryOp<scalar_boolean_and_op, Lhs, Rhs> >\n{\n  typedef CwiseBinaryOp<scalar_boolean_and_op, Lhs, Rhs> XprType;\n  typedef sparse_conjunction_evaluator<XprType> Base;\n  explicit binary_evaluator(const XprType& xpr) : Base(xpr) {}\n};\n// \"sparse && dense\"\ntemplate<typename Lhs, typename Rhs>\nstruct binary_evaluator<CwiseBinaryOp<scalar_boolean_and_op, Lhs, Rhs>, IteratorBased, IndexBased>\n  : sparse_conjunction_evaluator<CwiseBinaryOp<scalar_boolean_and_op, Lhs, Rhs> >\n{\n  typedef CwiseBinaryOp<scalar_boolean_and_op, Lhs, Rhs> XprType;\n  typedef sparse_conjunction_evaluator<XprType> Base;\n  explicit binary_evaluator(const XprType& xpr) : Base(xpr) {}\n};\n\n// \"sparse ^ sparse\"\ntemplate<typename XprType>\nstruct sparse_conjunction_evaluator<XprType, IteratorBased, IteratorBased>\n  : evaluator_base<XprType>\n{\nprotected:\n  typedef typename XprType::Functor BinaryOp;\n  typedef typename XprType::Lhs LhsArg;\n  typedef typename XprType::Rhs RhsArg;\n  typedef typename evaluator<LhsArg>::InnerIterator  LhsIterator;\n  typedef typename evaluator<RhsArg>::InnerIterator  RhsIterator;\n  typedef typename XprType::StorageIndex StorageIndex;\n  typedef typename traits<XprType>::Scalar Scalar;\npublic:\n\n  class InnerIterator\n  {\n  public:\n    \n    EIGEN_STRONG_INLINE InnerIterator(const sparse_conjunction_evaluator& aEval, Index outer)\n      : m_lhsIter(aEval.m_lhsImpl,outer), m_rhsIter(aEval.m_rhsImpl,outer), m_functor(aEval.m_functor)\n    {\n      while (m_lhsIter && m_rhsIter && (m_lhsIter.index() != m_rhsIter.index()))\n      {\n        if (m_lhsIter.index() < m_rhsIter.index())\n          ++m_lhsIter;\n        else\n          ++m_rhsIter;\n      }\n    }\n\n    EIGEN_STRONG_INLINE InnerIterator& operator++()\n    {\n      ++m_lhsIter;\n      ++m_rhsIter;\n      while (m_lhsIter && m_rhsIter && (m_lhsIter.index() != m_rhsIter.index()))\n      {\n        if (m_lhsIter.index() < m_rhsIter.index())\n          ++m_lhsIter;\n        else\n          ++m_rhsIter;\n      }\n      return *this;\n    }\n    \n    EIGEN_STRONG_INLINE Scalar value() const { return m_functor(m_lhsIter.value(), m_rhsIter.value()); }\n\n    EIGEN_STRONG_INLINE StorageIndex index() const { return m_lhsIter.index(); }\n    EIGEN_STRONG_INLINE Index outer() const { return m_lhsIter.outer(); }\n    EIGEN_STRONG_INLINE Index row() const { return m_lhsIter.row(); }\n    EIGEN_STRONG_INLINE Index col() const { return m_lhsIter.col(); }\n\n    EIGEN_STRONG_INLINE operator bool() const { return (m_lhsIter && m_rhsIter); }\n\n  protected:\n    LhsIterator m_lhsIter;\n    RhsIterator m_rhsIter;\n    const BinaryOp& m_functor;\n  };\n  \n  \n  enum {\n    CoeffReadCost = evaluator<LhsArg>::CoeffReadCost + evaluator<RhsArg>::CoeffReadCost + functor_traits<BinaryOp>::Cost,\n    Flags = XprType::Flags\n  };\n  \n  explicit sparse_conjunction_evaluator(const XprType& xpr)\n    : m_functor(xpr.functor()),\n      m_lhsImpl(xpr.lhs()), \n      m_rhsImpl(xpr.rhs())  \n  {\n    EIGEN_INTERNAL_CHECK_COST_VALUE(functor_traits<BinaryOp>::Cost);\n    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);\n  }\n  \n  inline Index nonZerosEstimate() const {\n    return (std::min)(m_lhsImpl.nonZerosEstimate(), m_rhsImpl.nonZerosEstimate());\n  }\n\nprotected:\n  const BinaryOp m_functor;\n  evaluator<LhsArg> m_lhsImpl;\n  evaluator<RhsArg> m_rhsImpl;\n};\n\n// \"dense ^ sparse\"\ntemplate<typename XprType>\nstruct sparse_conjunction_evaluator<XprType, IndexBased, IteratorBased>\n  : evaluator_base<XprType>\n{\nprotected:\n  typedef typename XprType::Functor BinaryOp;\n  typedef typename XprType::Lhs LhsArg;\n  typedef typename XprType::Rhs RhsArg;\n  typedef evaluator<LhsArg> LhsEvaluator;\n  typedef typename evaluator<RhsArg>::InnerIterator  RhsIterator;\n  typedef typename XprType::StorageIndex StorageIndex;\n  typedef typename traits<XprType>::Scalar Scalar;\npublic:\n\n  class InnerIterator\n  {\n    enum { IsRowMajor = (int(RhsArg::Flags)&RowMajorBit)==RowMajorBit };\n\n  public:\n    \n    EIGEN_STRONG_INLINE InnerIterator(const sparse_conjunction_evaluator& aEval, Index outer)\n      : m_lhsEval(aEval.m_lhsImpl), m_rhsIter(aEval.m_rhsImpl,outer), m_functor(aEval.m_functor), m_outer(outer)\n    {}\n\n    EIGEN_STRONG_INLINE InnerIterator& operator++()\n    {\n      ++m_rhsIter;\n      return *this;\n    }\n\n    EIGEN_STRONG_INLINE Scalar value() const\n    { return m_functor(m_lhsEval.coeff(IsRowMajor?m_outer:m_rhsIter.index(),IsRowMajor?m_rhsIter.index():m_outer), m_rhsIter.value()); }\n\n    EIGEN_STRONG_INLINE StorageIndex index() const { return m_rhsIter.index(); }\n    EIGEN_STRONG_INLINE Index outer() const { return m_rhsIter.outer(); }\n    EIGEN_STRONG_INLINE Index row() const { return m_rhsIter.row(); }\n    EIGEN_STRONG_INLINE Index col() const { return m_rhsIter.col(); }\n\n    EIGEN_STRONG_INLINE operator bool() const { return m_rhsIter; }\n    \n  protected:\n    const LhsEvaluator &m_lhsEval;\n    RhsIterator m_rhsIter;\n    const BinaryOp& m_functor;\n    const Index m_outer;\n  };\n  \n  \n  enum {\n    CoeffReadCost = evaluator<LhsArg>::CoeffReadCost + evaluator<RhsArg>::CoeffReadCost + functor_traits<BinaryOp>::Cost,\n    // Expose storage order of the sparse expression\n    Flags = (XprType::Flags & ~RowMajorBit) | (int(RhsArg::Flags)&RowMajorBit)\n  };\n  \n  explicit sparse_conjunction_evaluator(const XprType& xpr)\n    : m_functor(xpr.functor()),\n      m_lhsImpl(xpr.lhs()), \n      m_rhsImpl(xpr.rhs())  \n  {\n    EIGEN_INTERNAL_CHECK_COST_VALUE(functor_traits<BinaryOp>::Cost);\n    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);\n  }\n  \n  inline Index nonZerosEstimate() const {\n    return m_rhsImpl.nonZerosEstimate();\n  }\n\nprotected:\n  const BinaryOp m_functor;\n  evaluator<LhsArg> m_lhsImpl;\n  evaluator<RhsArg> m_rhsImpl;\n};\n\n// \"sparse ^ dense\"\ntemplate<typename XprType>\nstruct sparse_conjunction_evaluator<XprType, IteratorBased, IndexBased>\n  : evaluator_base<XprType>\n{\nprotected:\n  typedef typename XprType::Functor BinaryOp;\n  typedef typename XprType::Lhs LhsArg;\n  typedef typename XprType::Rhs RhsArg;\n  typedef typename evaluator<LhsArg>::InnerIterator LhsIterator;\n  typedef evaluator<RhsArg> RhsEvaluator;\n  typedef typename XprType::StorageIndex StorageIndex;\n  typedef typename traits<XprType>::Scalar Scalar;\npublic:\n\n  class InnerIterator\n  {\n    enum { IsRowMajor = (int(LhsArg::Flags)&RowMajorBit)==RowMajorBit };\n\n  public:\n    \n    EIGEN_STRONG_INLINE InnerIterator(const sparse_conjunction_evaluator& aEval, Index outer)\n      : m_lhsIter(aEval.m_lhsImpl,outer), m_rhsEval(aEval.m_rhsImpl), m_functor(aEval.m_functor), m_outer(outer)\n    {}\n\n    EIGEN_STRONG_INLINE InnerIterator& operator++()\n    {\n      ++m_lhsIter;\n      return *this;\n    }\n\n    EIGEN_STRONG_INLINE Scalar value() const\n    { return m_functor(m_lhsIter.value(),\n                       m_rhsEval.coeff(IsRowMajor?m_outer:m_lhsIter.index(),IsRowMajor?m_lhsIter.index():m_outer)); }\n\n    EIGEN_STRONG_INLINE StorageIndex index() const { return m_lhsIter.index(); }\n    EIGEN_STRONG_INLINE Index outer() const { return m_lhsIter.outer(); }\n    EIGEN_STRONG_INLINE Index row() const { return m_lhsIter.row(); }\n    EIGEN_STRONG_INLINE Index col() const { return m_lhsIter.col(); }\n\n    EIGEN_STRONG_INLINE operator bool() const { return m_lhsIter; }\n    \n  protected:\n    LhsIterator m_lhsIter;\n    const evaluator<RhsArg> &m_rhsEval;\n    const BinaryOp& m_functor;\n    const Index m_outer;\n  };\n  \n  \n  enum {\n    CoeffReadCost = evaluator<LhsArg>::CoeffReadCost + evaluator<RhsArg>::CoeffReadCost + functor_traits<BinaryOp>::Cost,\n    // Expose storage order of the sparse expression\n    Flags = (XprType::Flags & ~RowMajorBit) | (int(LhsArg::Flags)&RowMajorBit)\n  };\n  \n  explicit sparse_conjunction_evaluator(const XprType& xpr)\n    : m_functor(xpr.functor()),\n      m_lhsImpl(xpr.lhs()), \n      m_rhsImpl(xpr.rhs())  \n  {\n    EIGEN_INTERNAL_CHECK_COST_VALUE(functor_traits<BinaryOp>::Cost);\n    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);\n  }\n  \n  inline Index nonZerosEstimate() const {\n    return m_lhsImpl.nonZerosEstimate();\n  }\n\nprotected:\n  const BinaryOp m_functor;\n  evaluator<LhsArg> m_lhsImpl;\n  evaluator<RhsArg> m_rhsImpl;\n};\n\n}\n\n/***************************************************************************\n* Implementation of SparseMatrixBase and SparseCwise functions/operators\n***************************************************************************/\n\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\nDerived& SparseMatrixBase<Derived>::operator+=(const EigenBase<OtherDerived> &other)\n{\n  call_assignment(derived(), other.derived(), internal::add_assign_op<Scalar,typename OtherDerived::Scalar>());\n  return derived();\n}\n\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\nDerived& SparseMatrixBase<Derived>::operator-=(const EigenBase<OtherDerived> &other)\n{\n  call_assignment(derived(), other.derived(), internal::assign_op<Scalar,typename OtherDerived::Scalar>());\n  return derived();\n}\n\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\nEIGEN_STRONG_INLINE Derived &\nSparseMatrixBase<Derived>::operator-=(const SparseMatrixBase<OtherDerived> &other)\n{\n  return derived() = derived() - other.derived();\n}\n\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\nEIGEN_STRONG_INLINE Derived &\nSparseMatrixBase<Derived>::operator+=(const SparseMatrixBase<OtherDerived>& other)\n{\n  return derived() = derived() + other.derived();\n}\n\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\nDerived& SparseMatrixBase<Derived>::operator+=(const DiagonalBase<OtherDerived>& other)\n{\n  call_assignment_no_alias(derived(), other.derived(), internal::add_assign_op<Scalar,typename OtherDerived::Scalar>());\n  return derived();\n}\n\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\nDerived& SparseMatrixBase<Derived>::operator-=(const DiagonalBase<OtherDerived>& other)\n{\n  call_assignment_no_alias(derived(), other.derived(), internal::sub_assign_op<Scalar,typename OtherDerived::Scalar>());\n  return derived();\n}\n    \ntemplate<typename Derived>\ntemplate<typename OtherDerived>\nEIGEN_STRONG_INLINE const typename SparseMatrixBase<Derived>::template CwiseProductDenseReturnType<OtherDerived>::Type\nSparseMatrixBase<Derived>::cwiseProduct(const MatrixBase<OtherDerived> &other) const\n{\n  return typename CwiseProductDenseReturnType<OtherDerived>::Type(derived(), other.derived());\n}\n\ntemplate<typename DenseDerived, typename SparseDerived>\nEIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_sum_op<typename DenseDerived::Scalar,typename SparseDerived::Scalar>, const DenseDerived, const SparseDerived>\noperator+(const MatrixBase<DenseDerived> &a, const SparseMatrixBase<SparseDerived> &b)\n{\n  return CwiseBinaryOp<internal::scalar_sum_op<typename DenseDerived::Scalar,typename SparseDerived::Scalar>, const DenseDerived, const SparseDerived>(a.derived(), b.derived());\n}\n\ntemplate<typename SparseDerived, typename DenseDerived>\nEIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_sum_op<typename SparseDerived::Scalar,typename DenseDerived::Scalar>, const SparseDerived, const DenseDerived>\noperator+(const SparseMatrixBase<SparseDerived> &a, const MatrixBase<DenseDerived> &b)\n{\n  return CwiseBinaryOp<internal::scalar_sum_op<typename SparseDerived::Scalar,typename DenseDerived::Scalar>, const SparseDerived, const DenseDerived>(a.derived(), b.derived());\n}\n\ntemplate<typename DenseDerived, typename SparseDerived>\nEIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_difference_op<typename DenseDerived::Scalar,typename SparseDerived::Scalar>, const DenseDerived, const SparseDerived>\noperator-(const MatrixBase<DenseDerived> &a, const SparseMatrixBase<SparseDerived> &b)\n{\n  return CwiseBinaryOp<internal::scalar_difference_op<typename DenseDerived::Scalar,typename SparseDerived::Scalar>, const DenseDerived, const SparseDerived>(a.derived(), b.derived());\n}\n\ntemplate<typename SparseDerived, typename DenseDerived>\nEIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_difference_op<typename SparseDerived::Scalar,typename DenseDerived::Scalar>, const SparseDerived, const DenseDerived>\noperator-(const SparseMatrixBase<SparseDerived> &a, const MatrixBase<DenseDerived> &b)\n{\n  return CwiseBinaryOp<internal::scalar_difference_op<typename SparseDerived::Scalar,typename DenseDerived::Scalar>, const SparseDerived, const DenseDerived>(a.derived(), b.derived());\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_SPARSE_CWISE_BINARY_OP_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseCore/SparseCwiseUnaryOp.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSE_CWISE_UNARY_OP_H\n#define EIGEN_SPARSE_CWISE_UNARY_OP_H\n\nnamespace Eigen { \n\nnamespace internal {\n  \ntemplate<typename UnaryOp, typename ArgType>\nstruct unary_evaluator<CwiseUnaryOp<UnaryOp,ArgType>, IteratorBased>\n  : public evaluator_base<CwiseUnaryOp<UnaryOp,ArgType> >\n{\n  public:\n    typedef CwiseUnaryOp<UnaryOp, ArgType> XprType;\n\n    class InnerIterator;\n    \n    enum {\n      CoeffReadCost = evaluator<ArgType>::CoeffReadCost + functor_traits<UnaryOp>::Cost,\n      Flags = XprType::Flags\n    };\n    \n    explicit unary_evaluator(const XprType& op) : m_functor(op.functor()), m_argImpl(op.nestedExpression())\n    {\n      EIGEN_INTERNAL_CHECK_COST_VALUE(functor_traits<UnaryOp>::Cost);\n      EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);\n    }\n    \n    inline Index nonZerosEstimate() const {\n      return m_argImpl.nonZerosEstimate();\n    }\n\n  protected:\n    typedef typename evaluator<ArgType>::InnerIterator        EvalIterator;\n    \n    const UnaryOp m_functor;\n    evaluator<ArgType> m_argImpl;\n};\n\ntemplate<typename UnaryOp, typename ArgType>\nclass unary_evaluator<CwiseUnaryOp<UnaryOp,ArgType>, IteratorBased>::InnerIterator\n    : public unary_evaluator<CwiseUnaryOp<UnaryOp,ArgType>, IteratorBased>::EvalIterator\n{\n    typedef typename XprType::Scalar Scalar;\n    typedef typename unary_evaluator<CwiseUnaryOp<UnaryOp,ArgType>, IteratorBased>::EvalIterator Base;\n  public:\n\n    EIGEN_STRONG_INLINE InnerIterator(const unary_evaluator& unaryOp, Index outer)\n      : Base(unaryOp.m_argImpl,outer), m_functor(unaryOp.m_functor)\n    {}\n\n    EIGEN_STRONG_INLINE InnerIterator& operator++()\n    { Base::operator++(); return *this; }\n\n    EIGEN_STRONG_INLINE Scalar value() const { return m_functor(Base::value()); }\n\n  protected:\n    const UnaryOp m_functor;\n  private:\n    Scalar& valueRef();\n};\n\ntemplate<typename ViewOp, typename ArgType>\nstruct unary_evaluator<CwiseUnaryView<ViewOp,ArgType>, IteratorBased>\n  : public evaluator_base<CwiseUnaryView<ViewOp,ArgType> >\n{\n  public:\n    typedef CwiseUnaryView<ViewOp, ArgType> XprType;\n\n    class InnerIterator;\n    \n    enum {\n      CoeffReadCost = evaluator<ArgType>::CoeffReadCost + functor_traits<ViewOp>::Cost,\n      Flags = XprType::Flags\n    };\n    \n    explicit unary_evaluator(const XprType& op) : m_functor(op.functor()), m_argImpl(op.nestedExpression())\n    {\n      EIGEN_INTERNAL_CHECK_COST_VALUE(functor_traits<ViewOp>::Cost);\n      EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);\n    }\n\n  protected:\n    typedef typename evaluator<ArgType>::InnerIterator        EvalIterator;\n    \n    const ViewOp m_functor;\n    evaluator<ArgType> m_argImpl;\n};\n\ntemplate<typename ViewOp, typename ArgType>\nclass unary_evaluator<CwiseUnaryView<ViewOp,ArgType>, IteratorBased>::InnerIterator\n    : public unary_evaluator<CwiseUnaryView<ViewOp,ArgType>, IteratorBased>::EvalIterator\n{\n    typedef typename XprType::Scalar Scalar;\n    typedef typename unary_evaluator<CwiseUnaryView<ViewOp,ArgType>, IteratorBased>::EvalIterator Base;\n  public:\n\n    EIGEN_STRONG_INLINE InnerIterator(const unary_evaluator& unaryOp, Index outer)\n      : Base(unaryOp.m_argImpl,outer), m_functor(unaryOp.m_functor)\n    {}\n\n    EIGEN_STRONG_INLINE InnerIterator& operator++()\n    { Base::operator++(); return *this; }\n\n    EIGEN_STRONG_INLINE Scalar value() const { return m_functor(Base::value()); }\n    EIGEN_STRONG_INLINE Scalar& valueRef() { return m_functor(Base::valueRef()); }\n\n  protected:\n    const ViewOp m_functor;\n};\n\n} // end namespace internal\n\ntemplate<typename Derived>\nEIGEN_STRONG_INLINE Derived&\nSparseMatrixBase<Derived>::operator*=(const Scalar& other)\n{\n  typedef typename internal::evaluator<Derived>::InnerIterator EvalIterator;\n  internal::evaluator<Derived> thisEval(derived());\n  for (Index j=0; j<outerSize(); ++j)\n    for (EvalIterator i(thisEval,j); i; ++i)\n      i.valueRef() *= other;\n  return derived();\n}\n\ntemplate<typename Derived>\nEIGEN_STRONG_INLINE Derived&\nSparseMatrixBase<Derived>::operator/=(const Scalar& other)\n{\n  typedef typename internal::evaluator<Derived>::InnerIterator EvalIterator;\n  internal::evaluator<Derived> thisEval(derived());\n  for (Index j=0; j<outerSize(); ++j)\n    for (EvalIterator i(thisEval,j); i; ++i)\n      i.valueRef() /= other;\n  return derived();\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_SPARSE_CWISE_UNARY_OP_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseCore/SparseDenseProduct.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSEDENSEPRODUCT_H\n#define EIGEN_SPARSEDENSEPRODUCT_H\n\nnamespace Eigen { \n\nnamespace internal {\n\ntemplate <> struct product_promote_storage_type<Sparse,Dense, OuterProduct> { typedef Sparse ret; };\ntemplate <> struct product_promote_storage_type<Dense,Sparse, OuterProduct> { typedef Sparse ret; };\n\ntemplate<typename SparseLhsType, typename DenseRhsType, typename DenseResType,\n         typename AlphaType,\n         int LhsStorageOrder = ((SparseLhsType::Flags&RowMajorBit)==RowMajorBit) ? RowMajor : ColMajor,\n         bool ColPerCol = ((DenseRhsType::Flags&RowMajorBit)==0) || DenseRhsType::ColsAtCompileTime==1>\nstruct sparse_time_dense_product_impl;\n\ntemplate<typename SparseLhsType, typename DenseRhsType, typename DenseResType>\nstruct sparse_time_dense_product_impl<SparseLhsType,DenseRhsType,DenseResType, typename DenseResType::Scalar, RowMajor, true>\n{\n  typedef typename internal::remove_all<SparseLhsType>::type Lhs;\n  typedef typename internal::remove_all<DenseRhsType>::type Rhs;\n  typedef typename internal::remove_all<DenseResType>::type Res;\n  typedef typename evaluator<Lhs>::InnerIterator LhsInnerIterator;\n  typedef evaluator<Lhs> LhsEval;\n  static void run(const SparseLhsType& lhs, const DenseRhsType& rhs, DenseResType& res, const typename Res::Scalar& alpha)\n  {\n    LhsEval lhsEval(lhs);\n    \n    Index n = lhs.outerSize();\n#ifdef EIGEN_HAS_OPENMP\n    Eigen::initParallel();\n    Index threads = Eigen::nbThreads();\n#endif\n    \n    for(Index c=0; c<rhs.cols(); ++c)\n    {\n#ifdef EIGEN_HAS_OPENMP\n      // This 20000 threshold has been found experimentally on 2D and 3D Poisson problems.\n      // It basically represents the minimal amount of work to be done to be worth it.\n      if(threads>1 && lhsEval.nonZerosEstimate() > 20000)\n      {\n        #pragma omp parallel for schedule(dynamic,(n+threads*4-1)/(threads*4)) num_threads(threads)\n        for(Index i=0; i<n; ++i)\n          processRow(lhsEval,rhs,res,alpha,i,c);\n      }\n      else\n#endif\n      {\n        for(Index i=0; i<n; ++i)\n          processRow(lhsEval,rhs,res,alpha,i,c);\n      }\n    }\n  }\n  \n  static void processRow(const LhsEval& lhsEval, const DenseRhsType& rhs, DenseResType& res, const typename Res::Scalar& alpha, Index i, Index col)\n  {\n    typename Res::Scalar tmp(0);\n    for(LhsInnerIterator it(lhsEval,i); it ;++it)\n      tmp += it.value() * rhs.coeff(it.index(),col);\n    res.coeffRef(i,col) += alpha * tmp;\n  }\n  \n};\n\n// FIXME: what is the purpose of the following specialization? Is it for the BlockedSparse format?\n// -> let's disable it for now as it is conflicting with generic scalar*matrix and matrix*scalar operators\n// template<typename T1, typename T2/*, int _Options, typename _StrideType*/>\n// struct ScalarBinaryOpTraits<T1, Ref<T2/*, _Options, _StrideType*/> >\n// {\n//   enum {\n//     Defined = 1\n//   };\n//   typedef typename CwiseUnaryOp<scalar_multiple2_op<T1, typename T2::Scalar>, T2>::PlainObject ReturnType;\n// };\n\ntemplate<typename SparseLhsType, typename DenseRhsType, typename DenseResType, typename AlphaType>\nstruct sparse_time_dense_product_impl<SparseLhsType,DenseRhsType,DenseResType, AlphaType, ColMajor, true>\n{\n  typedef typename internal::remove_all<SparseLhsType>::type Lhs;\n  typedef typename internal::remove_all<DenseRhsType>::type Rhs;\n  typedef typename internal::remove_all<DenseResType>::type Res;\n  typedef typename evaluator<Lhs>::InnerIterator LhsInnerIterator;\n  static void run(const SparseLhsType& lhs, const DenseRhsType& rhs, DenseResType& res, const AlphaType& alpha)\n  {\n    evaluator<Lhs> lhsEval(lhs);\n    for(Index c=0; c<rhs.cols(); ++c)\n    {\n      for(Index j=0; j<lhs.outerSize(); ++j)\n      {\n//        typename Res::Scalar rhs_j = alpha * rhs.coeff(j,c);\n        typename ScalarBinaryOpTraits<AlphaType, typename Rhs::Scalar>::ReturnType rhs_j(alpha * rhs.coeff(j,c));\n        for(LhsInnerIterator it(lhsEval,j); it ;++it)\n          res.coeffRef(it.index(),c) += it.value() * rhs_j;\n      }\n    }\n  }\n};\n\ntemplate<typename SparseLhsType, typename DenseRhsType, typename DenseResType>\nstruct sparse_time_dense_product_impl<SparseLhsType,DenseRhsType,DenseResType, typename DenseResType::Scalar, RowMajor, false>\n{\n  typedef typename internal::remove_all<SparseLhsType>::type Lhs;\n  typedef typename internal::remove_all<DenseRhsType>::type Rhs;\n  typedef typename internal::remove_all<DenseResType>::type Res;\n  typedef typename evaluator<Lhs>::InnerIterator LhsInnerIterator;\n  static void run(const SparseLhsType& lhs, const DenseRhsType& rhs, DenseResType& res, const typename Res::Scalar& alpha)\n  {\n    evaluator<Lhs> lhsEval(lhs);\n    for(Index j=0; j<lhs.outerSize(); ++j)\n    {\n      typename Res::RowXpr res_j(res.row(j));\n      for(LhsInnerIterator it(lhsEval,j); it ;++it)\n        res_j += (alpha*it.value()) * rhs.row(it.index());\n    }\n  }\n};\n\ntemplate<typename SparseLhsType, typename DenseRhsType, typename DenseResType>\nstruct sparse_time_dense_product_impl<SparseLhsType,DenseRhsType,DenseResType, typename DenseResType::Scalar, ColMajor, false>\n{\n  typedef typename internal::remove_all<SparseLhsType>::type Lhs;\n  typedef typename internal::remove_all<DenseRhsType>::type Rhs;\n  typedef typename internal::remove_all<DenseResType>::type Res;\n  typedef typename evaluator<Lhs>::InnerIterator LhsInnerIterator;\n  static void run(const SparseLhsType& lhs, const DenseRhsType& rhs, DenseResType& res, const typename Res::Scalar& alpha)\n  {\n    evaluator<Lhs> lhsEval(lhs);\n    for(Index j=0; j<lhs.outerSize(); ++j)\n    {\n      typename Rhs::ConstRowXpr rhs_j(rhs.row(j));\n      for(LhsInnerIterator it(lhsEval,j); it ;++it)\n        res.row(it.index()) += (alpha*it.value()) * rhs_j;\n    }\n  }\n};\n\ntemplate<typename SparseLhsType, typename DenseRhsType, typename DenseResType,typename AlphaType>\ninline void sparse_time_dense_product(const SparseLhsType& lhs, const DenseRhsType& rhs, DenseResType& res, const AlphaType& alpha)\n{\n  sparse_time_dense_product_impl<SparseLhsType,DenseRhsType,DenseResType, AlphaType>::run(lhs, rhs, res, alpha);\n}\n\n} // end namespace internal\n\nnamespace internal {\n\ntemplate<typename Lhs, typename Rhs, int ProductType>\nstruct generic_product_impl<Lhs, Rhs, SparseShape, DenseShape, ProductType>\n : generic_product_impl_base<Lhs,Rhs,generic_product_impl<Lhs,Rhs,SparseShape,DenseShape,ProductType> >\n{\n  typedef typename Product<Lhs,Rhs>::Scalar Scalar;\n  \n  template<typename Dest>\n  static void scaleAndAddTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)\n  {\n    typedef typename nested_eval<Lhs,((Rhs::Flags&RowMajorBit)==0) ? 1 : Rhs::ColsAtCompileTime>::type LhsNested;\n    typedef typename nested_eval<Rhs,((Lhs::Flags&RowMajorBit)==0) ? 1 : Dynamic>::type RhsNested;\n    LhsNested lhsNested(lhs);\n    RhsNested rhsNested(rhs);\n    internal::sparse_time_dense_product(lhsNested, rhsNested, dst, alpha);\n  }\n};\n\ntemplate<typename Lhs, typename Rhs, int ProductType>\nstruct generic_product_impl<Lhs, Rhs, SparseTriangularShape, DenseShape, ProductType>\n  : generic_product_impl<Lhs, Rhs, SparseShape, DenseShape, ProductType>\n{};\n\ntemplate<typename Lhs, typename Rhs, int ProductType>\nstruct generic_product_impl<Lhs, Rhs, DenseShape, SparseShape, ProductType>\n  : generic_product_impl_base<Lhs,Rhs,generic_product_impl<Lhs,Rhs,DenseShape,SparseShape,ProductType> >\n{\n  typedef typename Product<Lhs,Rhs>::Scalar Scalar;\n  \n  template<typename Dst>\n  static void scaleAndAddTo(Dst& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)\n  {\n    typedef typename nested_eval<Lhs,((Rhs::Flags&RowMajorBit)==0) ? Dynamic : 1>::type LhsNested;\n    typedef typename nested_eval<Rhs,((Lhs::Flags&RowMajorBit)==RowMajorBit) ? 1 : Lhs::RowsAtCompileTime>::type RhsNested;\n    LhsNested lhsNested(lhs);\n    RhsNested rhsNested(rhs);\n    \n    // transpose everything\n    Transpose<Dst> dstT(dst);\n    internal::sparse_time_dense_product(rhsNested.transpose(), lhsNested.transpose(), dstT, alpha);\n  }\n};\n\ntemplate<typename Lhs, typename Rhs, int ProductType>\nstruct generic_product_impl<Lhs, Rhs, DenseShape, SparseTriangularShape, ProductType>\n  : generic_product_impl<Lhs, Rhs, DenseShape, SparseShape, ProductType>\n{};\n\ntemplate<typename LhsT, typename RhsT, bool NeedToTranspose>\nstruct sparse_dense_outer_product_evaluator\n{\nprotected:\n  typedef typename conditional<NeedToTranspose,RhsT,LhsT>::type Lhs1;\n  typedef typename conditional<NeedToTranspose,LhsT,RhsT>::type ActualRhs;\n  typedef Product<LhsT,RhsT,DefaultProduct> ProdXprType;\n  \n  // if the actual left-hand side is a dense vector,\n  // then build a sparse-view so that we can seamlessly iterate over it.\n  typedef typename conditional<is_same<typename internal::traits<Lhs1>::StorageKind,Sparse>::value,\n            Lhs1, SparseView<Lhs1> >::type ActualLhs;\n  typedef typename conditional<is_same<typename internal::traits<Lhs1>::StorageKind,Sparse>::value,\n            Lhs1 const&, SparseView<Lhs1> >::type LhsArg;\n            \n  typedef evaluator<ActualLhs> LhsEval;\n  typedef evaluator<ActualRhs> RhsEval;\n  typedef typename evaluator<ActualLhs>::InnerIterator LhsIterator;\n  typedef typename ProdXprType::Scalar Scalar;\n  \npublic:\n  enum {\n    Flags = NeedToTranspose ? RowMajorBit : 0,\n    CoeffReadCost = HugeCost\n  };\n  \n  class InnerIterator : public LhsIterator\n  {\n  public:\n    InnerIterator(const sparse_dense_outer_product_evaluator &xprEval, Index outer)\n      : LhsIterator(xprEval.m_lhsXprImpl, 0),\n        m_outer(outer),\n        m_empty(false),\n        m_factor(get(xprEval.m_rhsXprImpl, outer, typename internal::traits<ActualRhs>::StorageKind() ))\n    {}\n    \n    EIGEN_STRONG_INLINE Index outer() const { return m_outer; }\n    EIGEN_STRONG_INLINE Index row()   const { return NeedToTranspose ? m_outer : LhsIterator::index(); }\n    EIGEN_STRONG_INLINE Index col()   const { return NeedToTranspose ? LhsIterator::index() : m_outer; }\n\n    EIGEN_STRONG_INLINE Scalar value() const { return LhsIterator::value() * m_factor; }\n    EIGEN_STRONG_INLINE operator bool() const { return LhsIterator::operator bool() && (!m_empty); }\n    \n  protected:\n    Scalar get(const RhsEval &rhs, Index outer, Dense = Dense()) const\n    {\n      return rhs.coeff(outer);\n    }\n    \n    Scalar get(const RhsEval &rhs, Index outer, Sparse = Sparse())\n    {\n      typename RhsEval::InnerIterator it(rhs, outer);\n      if (it && it.index()==0 && it.value()!=Scalar(0))\n        return it.value();\n      m_empty = true;\n      return Scalar(0);\n    }\n    \n    Index m_outer;\n    bool m_empty;\n    Scalar m_factor;\n  };\n  \n  sparse_dense_outer_product_evaluator(const Lhs1 &lhs, const ActualRhs &rhs)\n     : m_lhs(lhs), m_lhsXprImpl(m_lhs), m_rhsXprImpl(rhs)\n  {\n    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);\n  }\n  \n  // transpose case\n  sparse_dense_outer_product_evaluator(const ActualRhs &rhs, const Lhs1 &lhs)\n     : m_lhs(lhs), m_lhsXprImpl(m_lhs), m_rhsXprImpl(rhs)\n  {\n    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);\n  }\n    \nprotected:\n  const LhsArg m_lhs;\n  evaluator<ActualLhs> m_lhsXprImpl;\n  evaluator<ActualRhs> m_rhsXprImpl;\n};\n\n// sparse * dense outer product\ntemplate<typename Lhs, typename Rhs>\nstruct product_evaluator<Product<Lhs, Rhs, DefaultProduct>, OuterProduct, SparseShape, DenseShape>\n  : sparse_dense_outer_product_evaluator<Lhs,Rhs, Lhs::IsRowMajor>\n{\n  typedef sparse_dense_outer_product_evaluator<Lhs,Rhs, Lhs::IsRowMajor> Base;\n  \n  typedef Product<Lhs, Rhs> XprType;\n  typedef typename XprType::PlainObject PlainObject;\n\n  explicit product_evaluator(const XprType& xpr)\n    : Base(xpr.lhs(), xpr.rhs())\n  {}\n  \n};\n\ntemplate<typename Lhs, typename Rhs>\nstruct product_evaluator<Product<Lhs, Rhs, DefaultProduct>, OuterProduct, DenseShape, SparseShape>\n  : sparse_dense_outer_product_evaluator<Lhs,Rhs, Rhs::IsRowMajor>\n{\n  typedef sparse_dense_outer_product_evaluator<Lhs,Rhs, Rhs::IsRowMajor> Base;\n  \n  typedef Product<Lhs, Rhs> XprType;\n  typedef typename XprType::PlainObject PlainObject;\n\n  explicit product_evaluator(const XprType& xpr)\n    : Base(xpr.lhs(), xpr.rhs())\n  {}\n  \n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_SPARSEDENSEPRODUCT_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseCore/SparseDiagonalProduct.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009-2015 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSE_DIAGONAL_PRODUCT_H\n#define EIGEN_SPARSE_DIAGONAL_PRODUCT_H\n\nnamespace Eigen { \n\n// The product of a diagonal matrix with a sparse matrix can be easily\n// implemented using expression template.\n// We have two consider very different cases:\n// 1 - diag * row-major sparse\n//     => each inner vector <=> scalar * sparse vector product\n//     => so we can reuse CwiseUnaryOp::InnerIterator\n// 2 - diag * col-major sparse\n//     => each inner vector <=> densevector * sparse vector cwise product\n//     => again, we can reuse specialization of CwiseBinaryOp::InnerIterator\n//        for that particular case\n// The two other cases are symmetric.\n\nnamespace internal {\n\nenum {\n  SDP_AsScalarProduct,\n  SDP_AsCwiseProduct\n};\n  \ntemplate<typename SparseXprType, typename DiagonalCoeffType, int SDP_Tag>\nstruct sparse_diagonal_product_evaluator;\n\ntemplate<typename Lhs, typename Rhs, int ProductTag>\nstruct product_evaluator<Product<Lhs, Rhs, DefaultProduct>, ProductTag, DiagonalShape, SparseShape>\n  : public sparse_diagonal_product_evaluator<Rhs, typename Lhs::DiagonalVectorType, Rhs::Flags&RowMajorBit?SDP_AsScalarProduct:SDP_AsCwiseProduct>\n{\n  typedef Product<Lhs, Rhs, DefaultProduct> XprType;\n  enum { CoeffReadCost = HugeCost, Flags = Rhs::Flags&RowMajorBit, Alignment = 0 }; // FIXME CoeffReadCost & Flags\n  \n  typedef sparse_diagonal_product_evaluator<Rhs, typename Lhs::DiagonalVectorType, Rhs::Flags&RowMajorBit?SDP_AsScalarProduct:SDP_AsCwiseProduct> Base;\n  explicit product_evaluator(const XprType& xpr) : Base(xpr.rhs(), xpr.lhs().diagonal()) {}\n};\n\ntemplate<typename Lhs, typename Rhs, int ProductTag>\nstruct product_evaluator<Product<Lhs, Rhs, DefaultProduct>, ProductTag, SparseShape, DiagonalShape>\n  : public sparse_diagonal_product_evaluator<Lhs, Transpose<const typename Rhs::DiagonalVectorType>, Lhs::Flags&RowMajorBit?SDP_AsCwiseProduct:SDP_AsScalarProduct>\n{\n  typedef Product<Lhs, Rhs, DefaultProduct> XprType;\n  enum { CoeffReadCost = HugeCost, Flags = Lhs::Flags&RowMajorBit, Alignment = 0 }; // FIXME CoeffReadCost & Flags\n  \n  typedef sparse_diagonal_product_evaluator<Lhs, Transpose<const typename Rhs::DiagonalVectorType>, Lhs::Flags&RowMajorBit?SDP_AsCwiseProduct:SDP_AsScalarProduct> Base;\n  explicit product_evaluator(const XprType& xpr) : Base(xpr.lhs(), xpr.rhs().diagonal().transpose()) {}\n};\n\ntemplate<typename SparseXprType, typename DiagonalCoeffType>\nstruct sparse_diagonal_product_evaluator<SparseXprType, DiagonalCoeffType, SDP_AsScalarProduct>\n{\nprotected:\n  typedef typename evaluator<SparseXprType>::InnerIterator SparseXprInnerIterator;\n  typedef typename SparseXprType::Scalar Scalar;\n  \npublic:\n  class InnerIterator : public SparseXprInnerIterator\n  {\n  public:\n    InnerIterator(const sparse_diagonal_product_evaluator &xprEval, Index outer)\n      : SparseXprInnerIterator(xprEval.m_sparseXprImpl, outer),\n        m_coeff(xprEval.m_diagCoeffImpl.coeff(outer))\n    {}\n    \n    EIGEN_STRONG_INLINE Scalar value() const { return m_coeff * SparseXprInnerIterator::value(); }\n  protected:\n    typename DiagonalCoeffType::Scalar m_coeff;\n  };\n  \n  sparse_diagonal_product_evaluator(const SparseXprType &sparseXpr, const DiagonalCoeffType &diagCoeff)\n    : m_sparseXprImpl(sparseXpr), m_diagCoeffImpl(diagCoeff)\n  {}\n\n  Index nonZerosEstimate() const { return m_sparseXprImpl.nonZerosEstimate(); }\n    \nprotected:\n  evaluator<SparseXprType> m_sparseXprImpl;\n  evaluator<DiagonalCoeffType> m_diagCoeffImpl;\n};\n\n\ntemplate<typename SparseXprType, typename DiagCoeffType>\nstruct sparse_diagonal_product_evaluator<SparseXprType, DiagCoeffType, SDP_AsCwiseProduct>\n{\n  typedef typename SparseXprType::Scalar Scalar;\n  typedef typename SparseXprType::StorageIndex StorageIndex;\n  \n  typedef typename nested_eval<DiagCoeffType,SparseXprType::IsRowMajor ? SparseXprType::RowsAtCompileTime\n                                                                       : SparseXprType::ColsAtCompileTime>::type DiagCoeffNested;\n  \n  class InnerIterator\n  {\n    typedef typename evaluator<SparseXprType>::InnerIterator SparseXprIter;\n  public:\n    InnerIterator(const sparse_diagonal_product_evaluator &xprEval, Index outer)\n      : m_sparseIter(xprEval.m_sparseXprEval, outer), m_diagCoeffNested(xprEval.m_diagCoeffNested)\n    {}\n    \n    inline Scalar value() const { return m_sparseIter.value() * m_diagCoeffNested.coeff(index()); }\n    inline StorageIndex index() const  { return m_sparseIter.index(); }\n    inline Index outer() const  { return m_sparseIter.outer(); }\n    inline Index col() const    { return SparseXprType::IsRowMajor ? m_sparseIter.index() : m_sparseIter.outer(); }\n    inline Index row() const    { return SparseXprType::IsRowMajor ? m_sparseIter.outer() : m_sparseIter.index(); }\n    \n    EIGEN_STRONG_INLINE InnerIterator& operator++() { ++m_sparseIter; return *this; }\n    inline operator bool() const  { return m_sparseIter; }\n    \n  protected:\n    SparseXprIter m_sparseIter;\n    DiagCoeffNested m_diagCoeffNested;\n  };\n  \n  sparse_diagonal_product_evaluator(const SparseXprType &sparseXpr, const DiagCoeffType &diagCoeff)\n    : m_sparseXprEval(sparseXpr), m_diagCoeffNested(diagCoeff)\n  {}\n\n  Index nonZerosEstimate() const { return m_sparseXprEval.nonZerosEstimate(); }\n    \nprotected:\n  evaluator<SparseXprType> m_sparseXprEval;\n  DiagCoeffNested m_diagCoeffNested;\n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_SPARSE_DIAGONAL_PRODUCT_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseCore/SparseDot.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSE_DOT_H\n#define EIGEN_SPARSE_DOT_H\n\nnamespace Eigen { \n\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\ntypename internal::traits<Derived>::Scalar\nSparseMatrixBase<Derived>::dot(const MatrixBase<OtherDerived>& other) const\n{\n  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)\n  EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)\n  EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)\n  EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),\n    YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)\n\n  eigen_assert(size() == other.size());\n  eigen_assert(other.size()>0 && \"you are using a non initialized vector\");\n\n  internal::evaluator<Derived> thisEval(derived());\n  typename internal::evaluator<Derived>::InnerIterator i(thisEval, 0);\n  Scalar res(0);\n  while (i)\n  {\n    res += numext::conj(i.value()) * other.coeff(i.index());\n    ++i;\n  }\n  return res;\n}\n\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\ntypename internal::traits<Derived>::Scalar\nSparseMatrixBase<Derived>::dot(const SparseMatrixBase<OtherDerived>& other) const\n{\n  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)\n  EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)\n  EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)\n  EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),\n    YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)\n\n  eigen_assert(size() == other.size());\n\n  internal::evaluator<Derived> thisEval(derived());\n  typename internal::evaluator<Derived>::InnerIterator i(thisEval, 0);\n  \n  internal::evaluator<OtherDerived>  otherEval(other.derived());\n  typename internal::evaluator<OtherDerived>::InnerIterator j(otherEval, 0);\n\n  Scalar res(0);\n  while (i && j)\n  {\n    if (i.index()==j.index())\n    {\n      res += numext::conj(i.value()) * j.value();\n      ++i; ++j;\n    }\n    else if (i.index()<j.index())\n      ++i;\n    else\n      ++j;\n  }\n  return res;\n}\n\ntemplate<typename Derived>\ninline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real\nSparseMatrixBase<Derived>::squaredNorm() const\n{\n  return numext::real((*this).cwiseAbs2().sum());\n}\n\ntemplate<typename Derived>\ninline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real\nSparseMatrixBase<Derived>::norm() const\n{\n  using std::sqrt;\n  return sqrt(squaredNorm());\n}\n\ntemplate<typename Derived>\ninline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real\nSparseMatrixBase<Derived>::blueNorm() const\n{\n  return internal::blueNorm_impl(*this);\n}\n} // end namespace Eigen\n\n#endif // EIGEN_SPARSE_DOT_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseCore/SparseFuzzy.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSE_FUZZY_H\n#define EIGEN_SPARSE_FUZZY_H\n\nnamespace Eigen {\n  \ntemplate<typename Derived>\ntemplate<typename OtherDerived>\nbool SparseMatrixBase<Derived>::isApprox(const SparseMatrixBase<OtherDerived>& other, const RealScalar &prec) const\n{\n  const typename internal::nested_eval<Derived,2,PlainObject>::type actualA(derived());\n  typename internal::conditional<bool(IsRowMajor)==bool(OtherDerived::IsRowMajor),\n    const typename internal::nested_eval<OtherDerived,2,PlainObject>::type,\n    const PlainObject>::type actualB(other.derived());\n\n  return (actualA - actualB).squaredNorm() <= prec * prec * numext::mini(actualA.squaredNorm(), actualB.squaredNorm());\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_SPARSE_FUZZY_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseCore/SparseMap.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSE_MAP_H\n#define EIGEN_SPARSE_MAP_H\n\nnamespace Eigen {\n\nnamespace internal {\n\ntemplate<typename MatScalar, int MatOptions, typename MatIndex, int Options, typename StrideType>\nstruct traits<Map<SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> >\n  : public traits<SparseMatrix<MatScalar,MatOptions,MatIndex> >\n{\n  typedef SparseMatrix<MatScalar,MatOptions,MatIndex> PlainObjectType;\n  typedef traits<PlainObjectType> TraitsBase;\n  enum {\n    Flags = TraitsBase::Flags & (~NestByRefBit)\n  };\n};\n\ntemplate<typename MatScalar, int MatOptions, typename MatIndex, int Options, typename StrideType>\nstruct traits<Map<const SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> >\n  : public traits<SparseMatrix<MatScalar,MatOptions,MatIndex> >\n{\n  typedef SparseMatrix<MatScalar,MatOptions,MatIndex> PlainObjectType;\n  typedef traits<PlainObjectType> TraitsBase;\n  enum {\n    Flags = TraitsBase::Flags & (~ (NestByRefBit | LvalueBit))\n  };\n};\n\n} // end namespace internal\n\ntemplate<typename Derived,\n         int Level = internal::accessors_level<Derived>::has_write_access ? WriteAccessors : ReadOnlyAccessors\n> class SparseMapBase;\n\n/** \\ingroup SparseCore_Module\n  * class SparseMapBase\n  * \\brief Common base class for Map and Ref instance of sparse matrix and vector.\n  */\ntemplate<typename Derived>\nclass SparseMapBase<Derived,ReadOnlyAccessors>\n  : public SparseCompressedBase<Derived>\n{\n  public:\n    typedef SparseCompressedBase<Derived> Base;\n    typedef typename Base::Scalar Scalar;\n    typedef typename Base::StorageIndex StorageIndex;\n    enum { IsRowMajor = Base::IsRowMajor };\n    using Base::operator=;\n  protected:\n    \n    typedef typename internal::conditional<\n                         bool(internal::is_lvalue<Derived>::value),\n                         Scalar *, const Scalar *>::type ScalarPointer;\n    typedef typename internal::conditional<\n                         bool(internal::is_lvalue<Derived>::value),\n                         StorageIndex *, const StorageIndex *>::type IndexPointer;\n\n    Index   m_outerSize;\n    Index   m_innerSize;\n    Array<StorageIndex,2,1>  m_zero_nnz;\n    IndexPointer  m_outerIndex;\n    IndexPointer  m_innerIndices;\n    ScalarPointer m_values;\n    IndexPointer  m_innerNonZeros;\n\n  public:\n\n    /** \\copydoc SparseMatrixBase::rows() */\n    inline Index rows() const { return IsRowMajor ? m_outerSize : m_innerSize; }\n    /** \\copydoc SparseMatrixBase::cols() */\n    inline Index cols() const { return IsRowMajor ? m_innerSize : m_outerSize; }\n    /** \\copydoc SparseMatrixBase::innerSize() */\n    inline Index innerSize() const { return m_innerSize; }\n    /** \\copydoc SparseMatrixBase::outerSize() */\n    inline Index outerSize() const { return m_outerSize; }\n    /** \\copydoc SparseCompressedBase::nonZeros */\n    inline Index nonZeros() const { return m_zero_nnz[1]; }\n    \n    /** \\copydoc SparseCompressedBase::isCompressed */\n    bool isCompressed() const { return m_innerNonZeros==0; }\n\n    //----------------------------------------\n    // direct access interface\n    /** \\copydoc SparseMatrix::valuePtr */\n    inline const Scalar* valuePtr() const { return m_values; }\n    /** \\copydoc SparseMatrix::innerIndexPtr */\n    inline const StorageIndex* innerIndexPtr() const { return m_innerIndices; }\n    /** \\copydoc SparseMatrix::outerIndexPtr */\n    inline const StorageIndex* outerIndexPtr() const { return m_outerIndex; }\n    /** \\copydoc SparseMatrix::innerNonZeroPtr */\n    inline const StorageIndex* innerNonZeroPtr() const { return m_innerNonZeros; }\n    //----------------------------------------\n\n    /** \\copydoc SparseMatrix::coeff */\n    inline Scalar coeff(Index row, Index col) const\n    {\n      const Index outer = IsRowMajor ? row : col;\n      const Index inner = IsRowMajor ? col : row;\n\n      Index start = m_outerIndex[outer];\n      Index end = isCompressed() ? m_outerIndex[outer+1] : start + m_innerNonZeros[outer];\n      if (start==end)\n        return Scalar(0);\n      else if (end>0 && inner==m_innerIndices[end-1])\n        return m_values[end-1];\n      // ^^  optimization: let's first check if it is the last coefficient\n      // (very common in high level algorithms)\n\n      const StorageIndex* r = std::lower_bound(&m_innerIndices[start],&m_innerIndices[end-1],inner);\n      const Index id = r-&m_innerIndices[0];\n      return ((*r==inner) && (id<end)) ? m_values[id] : Scalar(0);\n    }\n\n    inline SparseMapBase(Index rows, Index cols, Index nnz, IndexPointer outerIndexPtr, IndexPointer innerIndexPtr,\n                              ScalarPointer valuePtr, IndexPointer innerNonZerosPtr = 0)\n      : m_outerSize(IsRowMajor?rows:cols), m_innerSize(IsRowMajor?cols:rows), m_zero_nnz(0,internal::convert_index<StorageIndex>(nnz)), m_outerIndex(outerIndexPtr),\n        m_innerIndices(innerIndexPtr), m_values(valuePtr), m_innerNonZeros(innerNonZerosPtr)\n    {}\n\n    // for vectors\n    inline SparseMapBase(Index size, Index nnz, IndexPointer innerIndexPtr, ScalarPointer valuePtr)\n      : m_outerSize(1), m_innerSize(size), m_zero_nnz(0,internal::convert_index<StorageIndex>(nnz)), m_outerIndex(m_zero_nnz.data()),\n        m_innerIndices(innerIndexPtr), m_values(valuePtr), m_innerNonZeros(0)\n    {}\n\n    /** Empty destructor */\n    inline ~SparseMapBase() {}\n\n  protected:\n    inline SparseMapBase() {}\n};\n\n/** \\ingroup SparseCore_Module\n  * class SparseMapBase\n  * \\brief Common base class for writable Map and Ref instance of sparse matrix and vector.\n  */\ntemplate<typename Derived>\nclass SparseMapBase<Derived,WriteAccessors>\n  : public SparseMapBase<Derived,ReadOnlyAccessors>\n{\n    typedef MapBase<Derived, ReadOnlyAccessors> ReadOnlyMapBase;\n    \n  public:\n    typedef SparseMapBase<Derived, ReadOnlyAccessors> Base;\n    typedef typename Base::Scalar Scalar;\n    typedef typename Base::StorageIndex StorageIndex;\n    enum { IsRowMajor = Base::IsRowMajor };\n    \n    using Base::operator=;\n\n  public:\n    \n    //----------------------------------------\n    // direct access interface\n    using Base::valuePtr;\n    using Base::innerIndexPtr;\n    using Base::outerIndexPtr;\n    using Base::innerNonZeroPtr;\n    /** \\copydoc SparseMatrix::valuePtr */\n    inline Scalar* valuePtr()              { return Base::m_values; }\n    /** \\copydoc SparseMatrix::innerIndexPtr */\n    inline StorageIndex* innerIndexPtr()   { return Base::m_innerIndices; }\n    /** \\copydoc SparseMatrix::outerIndexPtr */\n    inline StorageIndex* outerIndexPtr()   { return Base::m_outerIndex; }\n    /** \\copydoc SparseMatrix::innerNonZeroPtr */\n    inline StorageIndex* innerNonZeroPtr() { return Base::m_innerNonZeros; }\n    //----------------------------------------\n\n    /** \\copydoc SparseMatrix::coeffRef */\n    inline Scalar& coeffRef(Index row, Index col)\n    {\n      const Index outer = IsRowMajor ? row : col;\n      const Index inner = IsRowMajor ? col : row;\n\n      Index start = Base::m_outerIndex[outer];\n      Index end = Base::isCompressed() ? Base::m_outerIndex[outer+1] : start + Base::m_innerNonZeros[outer];\n      eigen_assert(end>=start && \"you probably called coeffRef on a non finalized matrix\");\n      eigen_assert(end>start && \"coeffRef cannot be called on a zero coefficient\");\n      StorageIndex* r = std::lower_bound(&Base::m_innerIndices[start],&Base::m_innerIndices[end],inner);\n      const Index id = r - &Base::m_innerIndices[0];\n      eigen_assert((*r==inner) && (id<end) && \"coeffRef cannot be called on a zero coefficient\");\n      return const_cast<Scalar*>(Base::m_values)[id];\n    }\n    \n    inline SparseMapBase(Index rows, Index cols, Index nnz, StorageIndex* outerIndexPtr, StorageIndex* innerIndexPtr,\n                         Scalar* valuePtr, StorageIndex* innerNonZerosPtr = 0)\n      : Base(rows, cols, nnz, outerIndexPtr, innerIndexPtr, valuePtr, innerNonZerosPtr)\n    {}\n\n    // for vectors\n    inline SparseMapBase(Index size, Index nnz, StorageIndex* innerIndexPtr, Scalar* valuePtr)\n      : Base(size, nnz, innerIndexPtr, valuePtr)\n    {}\n\n    /** Empty destructor */\n    inline ~SparseMapBase() {}\n\n  protected:\n    inline SparseMapBase() {}\n};\n\n/** \\ingroup SparseCore_Module\n  *\n  * \\brief Specialization of class Map for SparseMatrix-like storage.\n  *\n  * \\tparam SparseMatrixType the equivalent sparse matrix type of the referenced data, it must be a template instance of class SparseMatrix.\n  *\n  * \\sa class Map, class SparseMatrix, class Ref<SparseMatrixType,Options>\n  */\n#ifndef EIGEN_PARSED_BY_DOXYGEN\ntemplate<typename MatScalar, int MatOptions, typename MatIndex, int Options, typename StrideType>\nclass Map<SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType>\n  : public SparseMapBase<Map<SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> >\n#else\ntemplate<typename SparseMatrixType>\nclass Map<SparseMatrixType>\n  : public SparseMapBase<Derived,WriteAccessors>\n#endif\n{\n  public:\n    typedef SparseMapBase<Map> Base;\n    EIGEN_SPARSE_PUBLIC_INTERFACE(Map)\n    enum { IsRowMajor = Base::IsRowMajor };\n\n  public:\n\n    /** Constructs a read-write Map to a sparse matrix of size \\a rows x \\a cols, containing \\a nnz non-zero coefficients,\n      * stored as a sparse format as defined by the pointers \\a outerIndexPtr, \\a innerIndexPtr, and \\a valuePtr.\n      * If the optional parameter \\a innerNonZerosPtr is the null pointer, then a standard compressed format is assumed.\n      *\n      * This constructor is available only if \\c SparseMatrixType is non-const.\n      *\n      * More details on the expected storage schemes are given in the \\ref TutorialSparse \"manual pages\".\n      */\n    inline Map(Index rows, Index cols, Index nnz, StorageIndex* outerIndexPtr,\n               StorageIndex* innerIndexPtr, Scalar* valuePtr, StorageIndex* innerNonZerosPtr = 0)\n      : Base(rows, cols, nnz, outerIndexPtr, innerIndexPtr, valuePtr, innerNonZerosPtr)\n    {}\n#ifndef EIGEN_PARSED_BY_DOXYGEN\n    /** Empty destructor */\n    inline ~Map() {}\n};\n\ntemplate<typename MatScalar, int MatOptions, typename MatIndex, int Options, typename StrideType>\nclass Map<const SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType>\n  : public SparseMapBase<Map<const SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> >\n{\n  public:\n    typedef SparseMapBase<Map> Base;\n    EIGEN_SPARSE_PUBLIC_INTERFACE(Map)\n    enum { IsRowMajor = Base::IsRowMajor };\n\n  public:\n#endif\n    /** This is the const version of the above constructor.\n      *\n      * This constructor is available only if \\c SparseMatrixType is const, e.g.:\n      * \\code Map<const SparseMatrix<double> >  \\endcode\n      */\n    inline Map(Index rows, Index cols, Index nnz, const StorageIndex* outerIndexPtr,\n               const StorageIndex* innerIndexPtr, const Scalar* valuePtr, const StorageIndex* innerNonZerosPtr = 0)\n      : Base(rows, cols, nnz, outerIndexPtr, innerIndexPtr, valuePtr, innerNonZerosPtr)\n    {}\n\n    /** Empty destructor */\n    inline ~Map() {}\n};\n\nnamespace internal {\n\ntemplate<typename MatScalar, int MatOptions, typename MatIndex, int Options, typename StrideType>\nstruct evaluator<Map<SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> >\n  : evaluator<SparseCompressedBase<Map<SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> > >\n{\n  typedef evaluator<SparseCompressedBase<Map<SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> > > Base;\n  typedef Map<SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> XprType;  \n  evaluator() : Base() {}\n  explicit evaluator(const XprType &mat) : Base(mat) {}\n};\n\ntemplate<typename MatScalar, int MatOptions, typename MatIndex, int Options, typename StrideType>\nstruct evaluator<Map<const SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> >\n  : evaluator<SparseCompressedBase<Map<const SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> > >\n{\n  typedef evaluator<SparseCompressedBase<Map<const SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> > > Base;\n  typedef Map<const SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> XprType;  \n  evaluator() : Base() {}\n  explicit evaluator(const XprType &mat) : Base(mat) {}\n};\n\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_SPARSE_MAP_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseCore/SparseMatrix.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSEMATRIX_H\n#define EIGEN_SPARSEMATRIX_H\n\nnamespace Eigen { \n\n/** \\ingroup SparseCore_Module\n  *\n  * \\class SparseMatrix\n  *\n  * \\brief A versatible sparse matrix representation\n  *\n  * This class implements a more versatile variants of the common \\em compressed row/column storage format.\n  * Each colmun's (resp. row) non zeros are stored as a pair of value with associated row (resp. colmiun) index.\n  * All the non zeros are stored in a single large buffer. Unlike the \\em compressed format, there might be extra\n  * space inbetween the nonzeros of two successive colmuns (resp. rows) such that insertion of new non-zero\n  * can be done with limited memory reallocation and copies.\n  *\n  * A call to the function makeCompressed() turns the matrix into the standard \\em compressed format\n  * compatible with many library.\n  *\n  * More details on this storage sceheme are given in the \\ref TutorialSparse \"manual pages\".\n  *\n  * \\tparam _Scalar the scalar type, i.e. the type of the coefficients\n  * \\tparam _Options Union of bit flags controlling the storage scheme. Currently the only possibility\n  *                 is ColMajor or RowMajor. The default is 0 which means column-major.\n  * \\tparam _StorageIndex the type of the indices. It has to be a \\b signed type (e.g., short, int, std::ptrdiff_t). Default is \\c int.\n  *\n  * \\warning In %Eigen 3.2, the undocumented type \\c SparseMatrix::Index was improperly defined as the storage index type (e.g., int),\n  *          whereas it is now (starting from %Eigen 3.3) deprecated and always defined as Eigen::Index.\n  *          Codes making use of \\c SparseMatrix::Index, might thus likely have to be changed to use \\c SparseMatrix::StorageIndex instead.\n  *\n  * This class can be extended with the help of the plugin mechanism described on the page\n  * \\ref TopicCustomizing_Plugins by defining the preprocessor symbol \\c EIGEN_SPARSEMATRIX_PLUGIN.\n  */\n\nnamespace internal {\ntemplate<typename _Scalar, int _Options, typename _StorageIndex>\nstruct traits<SparseMatrix<_Scalar, _Options, _StorageIndex> >\n{\n  typedef _Scalar Scalar;\n  typedef _StorageIndex StorageIndex;\n  typedef Sparse StorageKind;\n  typedef MatrixXpr XprKind;\n  enum {\n    RowsAtCompileTime = Dynamic,\n    ColsAtCompileTime = Dynamic,\n    MaxRowsAtCompileTime = Dynamic,\n    MaxColsAtCompileTime = Dynamic,\n    Flags = _Options | NestByRefBit | LvalueBit | CompressedAccessBit,\n    SupportedAccessPatterns = InnerRandomAccessPattern\n  };\n};\n\ntemplate<typename _Scalar, int _Options, typename _StorageIndex, int DiagIndex>\nstruct traits<Diagonal<SparseMatrix<_Scalar, _Options, _StorageIndex>, DiagIndex> >\n{\n  typedef SparseMatrix<_Scalar, _Options, _StorageIndex> MatrixType;\n  typedef typename ref_selector<MatrixType>::type MatrixTypeNested;\n  typedef typename remove_reference<MatrixTypeNested>::type _MatrixTypeNested;\n\n  typedef _Scalar Scalar;\n  typedef Dense StorageKind;\n  typedef _StorageIndex StorageIndex;\n  typedef MatrixXpr XprKind;\n\n  enum {\n    RowsAtCompileTime = Dynamic,\n    ColsAtCompileTime = 1,\n    MaxRowsAtCompileTime = Dynamic,\n    MaxColsAtCompileTime = 1,\n    Flags = LvalueBit\n  };\n};\n\ntemplate<typename _Scalar, int _Options, typename _StorageIndex, int DiagIndex>\nstruct traits<Diagonal<const SparseMatrix<_Scalar, _Options, _StorageIndex>, DiagIndex> >\n : public traits<Diagonal<SparseMatrix<_Scalar, _Options, _StorageIndex>, DiagIndex> >\n{\n  enum {\n    Flags = 0\n  };\n};\n\n} // end namespace internal\n\ntemplate<typename _Scalar, int _Options, typename _StorageIndex>\nclass SparseMatrix\n  : public SparseCompressedBase<SparseMatrix<_Scalar, _Options, _StorageIndex> >\n{\n    typedef SparseCompressedBase<SparseMatrix> Base;\n    using Base::convert_index;\n    friend class SparseVector<_Scalar,0,_StorageIndex>;\n  public:\n    using Base::isCompressed;\n    using Base::nonZeros;\n    EIGEN_SPARSE_PUBLIC_INTERFACE(SparseMatrix)\n    using Base::operator+=;\n    using Base::operator-=;\n\n    typedef MappedSparseMatrix<Scalar,Flags> Map;\n    typedef Diagonal<SparseMatrix> DiagonalReturnType;\n    typedef Diagonal<const SparseMatrix> ConstDiagonalReturnType;\n    typedef typename Base::InnerIterator InnerIterator;\n    typedef typename Base::ReverseInnerIterator ReverseInnerIterator;\n    \n\n    using Base::IsRowMajor;\n    typedef internal::CompressedStorage<Scalar,StorageIndex> Storage;\n    enum {\n      Options = _Options\n    };\n\n    typedef typename Base::IndexVector IndexVector;\n    typedef typename Base::ScalarVector ScalarVector;\n  protected:\n    typedef SparseMatrix<Scalar,(Flags&~RowMajorBit)|(IsRowMajor?RowMajorBit:0)> TransposedSparseMatrix;\n\n    Index m_outerSize;\n    Index m_innerSize;\n    StorageIndex* m_outerIndex;\n    StorageIndex* m_innerNonZeros;     // optional, if null then the data is compressed\n    Storage m_data;\n\n  public:\n    \n    /** \\returns the number of rows of the matrix */\n    inline Index rows() const { return IsRowMajor ? m_outerSize : m_innerSize; }\n    /** \\returns the number of columns of the matrix */\n    inline Index cols() const { return IsRowMajor ? m_innerSize : m_outerSize; }\n\n    /** \\returns the number of rows (resp. columns) of the matrix if the storage order column major (resp. row major) */\n    inline Index innerSize() const { return m_innerSize; }\n    /** \\returns the number of columns (resp. rows) of the matrix if the storage order column major (resp. row major) */\n    inline Index outerSize() const { return m_outerSize; }\n    \n    /** \\returns a const pointer to the array of values.\n      * This function is aimed at interoperability with other libraries.\n      * \\sa innerIndexPtr(), outerIndexPtr() */\n    inline const Scalar* valuePtr() const { return m_data.valuePtr(); }\n    /** \\returns a non-const pointer to the array of values.\n      * This function is aimed at interoperability with other libraries.\n      * \\sa innerIndexPtr(), outerIndexPtr() */\n    inline Scalar* valuePtr() { return m_data.valuePtr(); }\n\n    /** \\returns a const pointer to the array of inner indices.\n      * This function is aimed at interoperability with other libraries.\n      * \\sa valuePtr(), outerIndexPtr() */\n    inline const StorageIndex* innerIndexPtr() const { return m_data.indexPtr(); }\n    /** \\returns a non-const pointer to the array of inner indices.\n      * This function is aimed at interoperability with other libraries.\n      * \\sa valuePtr(), outerIndexPtr() */\n    inline StorageIndex* innerIndexPtr() { return m_data.indexPtr(); }\n\n    /** \\returns a const pointer to the array of the starting positions of the inner vectors.\n      * This function is aimed at interoperability with other libraries.\n      * \\sa valuePtr(), innerIndexPtr() */\n    inline const StorageIndex* outerIndexPtr() const { return m_outerIndex; }\n    /** \\returns a non-const pointer to the array of the starting positions of the inner vectors.\n      * This function is aimed at interoperability with other libraries.\n      * \\sa valuePtr(), innerIndexPtr() */\n    inline StorageIndex* outerIndexPtr() { return m_outerIndex; }\n\n    /** \\returns a const pointer to the array of the number of non zeros of the inner vectors.\n      * This function is aimed at interoperability with other libraries.\n      * \\warning it returns the null pointer 0 in compressed mode */\n    inline const StorageIndex* innerNonZeroPtr() const { return m_innerNonZeros; }\n    /** \\returns a non-const pointer to the array of the number of non zeros of the inner vectors.\n      * This function is aimed at interoperability with other libraries.\n      * \\warning it returns the null pointer 0 in compressed mode */\n    inline StorageIndex* innerNonZeroPtr() { return m_innerNonZeros; }\n\n    /** \\internal */\n    inline Storage& data() { return m_data; }\n    /** \\internal */\n    inline const Storage& data() const { return m_data; }\n\n    /** \\returns the value of the matrix at position \\a i, \\a j\n      * This function returns Scalar(0) if the element is an explicit \\em zero */\n    inline Scalar coeff(Index row, Index col) const\n    {\n      eigen_assert(row>=0 && row<rows() && col>=0 && col<cols());\n      \n      const Index outer = IsRowMajor ? row : col;\n      const Index inner = IsRowMajor ? col : row;\n      Index end = m_innerNonZeros ? m_outerIndex[outer] + m_innerNonZeros[outer] : m_outerIndex[outer+1];\n      return m_data.atInRange(m_outerIndex[outer], end, StorageIndex(inner));\n    }\n\n    /** \\returns a non-const reference to the value of the matrix at position \\a i, \\a j\n      *\n      * If the element does not exist then it is inserted via the insert(Index,Index) function\n      * which itself turns the matrix into a non compressed form if that was not the case.\n      *\n      * This is a O(log(nnz_j)) operation (binary search) plus the cost of insert(Index,Index)\n      * function if the element does not already exist.\n      */\n    inline Scalar& coeffRef(Index row, Index col)\n    {\n      eigen_assert(row>=0 && row<rows() && col>=0 && col<cols());\n      \n      const Index outer = IsRowMajor ? row : col;\n      const Index inner = IsRowMajor ? col : row;\n\n      Index start = m_outerIndex[outer];\n      Index end = m_innerNonZeros ? m_outerIndex[outer] + m_innerNonZeros[outer] : m_outerIndex[outer+1];\n      eigen_assert(end>=start && \"you probably called coeffRef on a non finalized matrix\");\n      if(end<=start)\n        return insert(row,col);\n      const Index p = m_data.searchLowerIndex(start,end-1,StorageIndex(inner));\n      if((p<end) && (m_data.index(p)==inner))\n        return m_data.value(p);\n      else\n        return insert(row,col);\n    }\n\n    /** \\returns a reference to a novel non zero coefficient with coordinates \\a row x \\a col.\n      * The non zero coefficient must \\b not already exist.\n      *\n      * If the matrix \\c *this is in compressed mode, then \\c *this is turned into uncompressed\n      * mode while reserving room for 2 x this->innerSize() non zeros if reserve(Index) has not been called earlier.\n      * In this case, the insertion procedure is optimized for a \\e sequential insertion mode where elements are assumed to be\n      * inserted by increasing outer-indices.\n      * \n      * If that's not the case, then it is strongly recommended to either use a triplet-list to assemble the matrix, or to first\n      * call reserve(const SizesType &) to reserve the appropriate number of non-zero elements per inner vector.\n      *\n      * Assuming memory has been appropriately reserved, this function performs a sorted insertion in O(1)\n      * if the elements of each inner vector are inserted in increasing inner index order, and in O(nnz_j) for a random insertion.\n      *\n      */\n    Scalar& insert(Index row, Index col);\n\n  public:\n\n    /** Removes all non zeros but keep allocated memory\n      *\n      * This function does not free the currently allocated memory. To release as much as memory as possible,\n      * call \\code mat.data().squeeze(); \\endcode after resizing it.\n      * \n      * \\sa resize(Index,Index), data()\n      */\n    inline void setZero()\n    {\n      m_data.clear();\n      memset(m_outerIndex, 0, (m_outerSize+1)*sizeof(StorageIndex));\n      if(m_innerNonZeros)\n        memset(m_innerNonZeros, 0, (m_outerSize)*sizeof(StorageIndex));\n    }\n\n    /** Preallocates \\a reserveSize non zeros.\n      *\n      * Precondition: the matrix must be in compressed mode. */\n    inline void reserve(Index reserveSize)\n    {\n      eigen_assert(isCompressed() && \"This function does not make sense in non compressed mode.\");\n      m_data.reserve(reserveSize);\n    }\n    \n    #ifdef EIGEN_PARSED_BY_DOXYGEN\n    /** Preallocates \\a reserveSize[\\c j] non zeros for each column (resp. row) \\c j.\n      *\n      * This function turns the matrix in non-compressed mode.\n      * \n      * The type \\c SizesType must expose the following interface:\n        \\code\n        typedef value_type;\n        const value_type& operator[](i) const;\n        \\endcode\n      * for \\c i in the [0,this->outerSize()[ range.\n      * Typical choices include std::vector<int>, Eigen::VectorXi, Eigen::VectorXi::Constant, etc.\n      */\n    template<class SizesType>\n    inline void reserve(const SizesType& reserveSizes);\n    #else\n    template<class SizesType>\n    inline void reserve(const SizesType& reserveSizes, const typename SizesType::value_type& enableif =\n    #if (!EIGEN_COMP_MSVC) || (EIGEN_COMP_MSVC>=1500) // MSVC 2005 fails to compile with this typename\n        typename\n    #endif\n        SizesType::value_type())\n    {\n      EIGEN_UNUSED_VARIABLE(enableif);\n      reserveInnerVectors(reserveSizes);\n    }\n    #endif // EIGEN_PARSED_BY_DOXYGEN\n  protected:\n    template<class SizesType>\n    inline void reserveInnerVectors(const SizesType& reserveSizes)\n    {\n      if(isCompressed())\n      {\n        Index totalReserveSize = 0;\n        // turn the matrix into non-compressed mode\n        m_innerNonZeros = static_cast<StorageIndex*>(std::malloc(m_outerSize * sizeof(StorageIndex)));\n        if (!m_innerNonZeros) internal::throw_std_bad_alloc();\n        \n        // temporarily use m_innerSizes to hold the new starting points.\n        StorageIndex* newOuterIndex = m_innerNonZeros;\n        \n        StorageIndex count = 0;\n        for(Index j=0; j<m_outerSize; ++j)\n        {\n          newOuterIndex[j] = count;\n          count += reserveSizes[j] + (m_outerIndex[j+1]-m_outerIndex[j]);\n          totalReserveSize += reserveSizes[j];\n        }\n        m_data.reserve(totalReserveSize);\n        StorageIndex previousOuterIndex = m_outerIndex[m_outerSize];\n        for(Index j=m_outerSize-1; j>=0; --j)\n        {\n          StorageIndex innerNNZ = previousOuterIndex - m_outerIndex[j];\n          for(Index i=innerNNZ-1; i>=0; --i)\n          {\n            m_data.index(newOuterIndex[j]+i) = m_data.index(m_outerIndex[j]+i);\n            m_data.value(newOuterIndex[j]+i) = m_data.value(m_outerIndex[j]+i);\n          }\n          previousOuterIndex = m_outerIndex[j];\n          m_outerIndex[j] = newOuterIndex[j];\n          m_innerNonZeros[j] = innerNNZ;\n        }\n        m_outerIndex[m_outerSize] = m_outerIndex[m_outerSize-1] + m_innerNonZeros[m_outerSize-1] + reserveSizes[m_outerSize-1];\n        \n        m_data.resize(m_outerIndex[m_outerSize]);\n      }\n      else\n      {\n        StorageIndex* newOuterIndex = static_cast<StorageIndex*>(std::malloc((m_outerSize+1)*sizeof(StorageIndex)));\n        if (!newOuterIndex) internal::throw_std_bad_alloc();\n        \n        StorageIndex count = 0;\n        for(Index j=0; j<m_outerSize; ++j)\n        {\n          newOuterIndex[j] = count;\n          StorageIndex alreadyReserved = (m_outerIndex[j+1]-m_outerIndex[j]) - m_innerNonZeros[j];\n          StorageIndex toReserve = std::max<StorageIndex>(reserveSizes[j], alreadyReserved);\n          count += toReserve + m_innerNonZeros[j];\n        }\n        newOuterIndex[m_outerSize] = count;\n        \n        m_data.resize(count);\n        for(Index j=m_outerSize-1; j>=0; --j)\n        {\n          Index offset = newOuterIndex[j] - m_outerIndex[j];\n          if(offset>0)\n          {\n            StorageIndex innerNNZ = m_innerNonZeros[j];\n            for(Index i=innerNNZ-1; i>=0; --i)\n            {\n              m_data.index(newOuterIndex[j]+i) = m_data.index(m_outerIndex[j]+i);\n              m_data.value(newOuterIndex[j]+i) = m_data.value(m_outerIndex[j]+i);\n            }\n          }\n        }\n        \n        std::swap(m_outerIndex, newOuterIndex);\n        std::free(newOuterIndex);\n      }\n      \n    }\n  public:\n\n    //--- low level purely coherent filling ---\n\n    /** \\internal\n      * \\returns a reference to the non zero coefficient at position \\a row, \\a col assuming that:\n      * - the nonzero does not already exist\n      * - the new coefficient is the last one according to the storage order\n      *\n      * Before filling a given inner vector you must call the statVec(Index) function.\n      *\n      * After an insertion session, you should call the finalize() function.\n      *\n      * \\sa insert, insertBackByOuterInner, startVec */\n    inline Scalar& insertBack(Index row, Index col)\n    {\n      return insertBackByOuterInner(IsRowMajor?row:col, IsRowMajor?col:row);\n    }\n\n    /** \\internal\n      * \\sa insertBack, startVec */\n    inline Scalar& insertBackByOuterInner(Index outer, Index inner)\n    {\n      eigen_assert(Index(m_outerIndex[outer+1]) == m_data.size() && \"Invalid ordered insertion (invalid outer index)\");\n      eigen_assert( (m_outerIndex[outer+1]-m_outerIndex[outer]==0 || m_data.index(m_data.size()-1)<inner) && \"Invalid ordered insertion (invalid inner index)\");\n      Index p = m_outerIndex[outer+1];\n      ++m_outerIndex[outer+1];\n      m_data.append(Scalar(0), inner);\n      return m_data.value(p);\n    }\n\n    /** \\internal\n      * \\warning use it only if you know what you are doing */\n    inline Scalar& insertBackByOuterInnerUnordered(Index outer, Index inner)\n    {\n      Index p = m_outerIndex[outer+1];\n      ++m_outerIndex[outer+1];\n      m_data.append(Scalar(0), inner);\n      return m_data.value(p);\n    }\n\n    /** \\internal\n      * \\sa insertBack, insertBackByOuterInner */\n    inline void startVec(Index outer)\n    {\n      eigen_assert(m_outerIndex[outer]==Index(m_data.size()) && \"You must call startVec for each inner vector sequentially\");\n      eigen_assert(m_outerIndex[outer+1]==0 && \"You must call startVec for each inner vector sequentially\");\n      m_outerIndex[outer+1] = m_outerIndex[outer];\n    }\n\n    /** \\internal\n      * Must be called after inserting a set of non zero entries using the low level compressed API.\n      */\n    inline void finalize()\n    {\n      if(isCompressed())\n      {\n        StorageIndex size = internal::convert_index<StorageIndex>(m_data.size());\n        Index i = m_outerSize;\n        // find the last filled column\n        while (i>=0 && m_outerIndex[i]==0)\n          --i;\n        ++i;\n        while (i<=m_outerSize)\n        {\n          m_outerIndex[i] = size;\n          ++i;\n        }\n      }\n    }\n\n    //---\n\n    template<typename InputIterators>\n    void setFromTriplets(const InputIterators& begin, const InputIterators& end);\n\n    template<typename InputIterators,typename DupFunctor>\n    void setFromTriplets(const InputIterators& begin, const InputIterators& end, DupFunctor dup_func);\n\n    void sumupDuplicates() { collapseDuplicates(internal::scalar_sum_op<Scalar,Scalar>()); }\n\n    template<typename DupFunctor>\n    void collapseDuplicates(DupFunctor dup_func = DupFunctor());\n\n    //---\n    \n    /** \\internal\n      * same as insert(Index,Index) except that the indices are given relative to the storage order */\n    Scalar& insertByOuterInner(Index j, Index i)\n    {\n      return insert(IsRowMajor ? j : i, IsRowMajor ? i : j);\n    }\n\n    /** Turns the matrix into the \\em compressed format.\n      */\n    void makeCompressed()\n    {\n      if(isCompressed())\n        return;\n      \n      eigen_internal_assert(m_outerIndex!=0 && m_outerSize>0);\n      \n      Index oldStart = m_outerIndex[1];\n      m_outerIndex[1] = m_innerNonZeros[0];\n      for(Index j=1; j<m_outerSize; ++j)\n      {\n        Index nextOldStart = m_outerIndex[j+1];\n        Index offset = oldStart - m_outerIndex[j];\n        if(offset>0)\n        {\n          for(Index k=0; k<m_innerNonZeros[j]; ++k)\n          {\n            m_data.index(m_outerIndex[j]+k) = m_data.index(oldStart+k);\n            m_data.value(m_outerIndex[j]+k) = m_data.value(oldStart+k);\n          }\n        }\n        m_outerIndex[j+1] = m_outerIndex[j] + m_innerNonZeros[j];\n        oldStart = nextOldStart;\n      }\n      std::free(m_innerNonZeros);\n      m_innerNonZeros = 0;\n      m_data.resize(m_outerIndex[m_outerSize]);\n      m_data.squeeze();\n    }\n\n    /** Turns the matrix into the uncompressed mode */\n    void uncompress()\n    {\n      if(m_innerNonZeros != 0)\n        return; \n      m_innerNonZeros = static_cast<StorageIndex*>(std::malloc(m_outerSize * sizeof(StorageIndex)));\n      for (Index i = 0; i < m_outerSize; i++)\n      {\n        m_innerNonZeros[i] = m_outerIndex[i+1] - m_outerIndex[i]; \n      }\n    }\n    \n    /** Suppresses all nonzeros which are \\b much \\b smaller \\b than \\a reference under the tolerence \\a epsilon */\n    void prune(const Scalar& reference, const RealScalar& epsilon = NumTraits<RealScalar>::dummy_precision())\n    {\n      prune(default_prunning_func(reference,epsilon));\n    }\n    \n    /** Turns the matrix into compressed format, and suppresses all nonzeros which do not satisfy the predicate \\a keep.\n      * The functor type \\a KeepFunc must implement the following function:\n      * \\code\n      * bool operator() (const Index& row, const Index& col, const Scalar& value) const;\n      * \\endcode\n      * \\sa prune(Scalar,RealScalar)\n      */\n    template<typename KeepFunc>\n    void prune(const KeepFunc& keep = KeepFunc())\n    {\n      // TODO optimize the uncompressed mode to avoid moving and allocating the data twice\n      makeCompressed();\n\n      StorageIndex k = 0;\n      for(Index j=0; j<m_outerSize; ++j)\n      {\n        Index previousStart = m_outerIndex[j];\n        m_outerIndex[j] = k;\n        Index end = m_outerIndex[j+1];\n        for(Index i=previousStart; i<end; ++i)\n        {\n          if(keep(IsRowMajor?j:m_data.index(i), IsRowMajor?m_data.index(i):j, m_data.value(i)))\n          {\n            m_data.value(k) = m_data.value(i);\n            m_data.index(k) = m_data.index(i);\n            ++k;\n          }\n        }\n      }\n      m_outerIndex[m_outerSize] = k;\n      m_data.resize(k,0);\n    }\n\n    /** Resizes the matrix to a \\a rows x \\a cols matrix leaving old values untouched.\n      *\n      * If the sizes of the matrix are decreased, then the matrix is turned to \\b uncompressed-mode\n      * and the storage of the out of bounds coefficients is kept and reserved.\n      * Call makeCompressed() to pack the entries and squeeze extra memory.\n      *\n      * \\sa reserve(), setZero(), makeCompressed()\n      */\n    void conservativeResize(Index rows, Index cols) \n    {\n      // No change\n      if (this->rows() == rows && this->cols() == cols) return;\n      \n      // If one dimension is null, then there is nothing to be preserved\n      if(rows==0 || cols==0) return resize(rows,cols);\n\n      Index innerChange = IsRowMajor ? cols - this->cols() : rows - this->rows();\n      Index outerChange = IsRowMajor ? rows - this->rows() : cols - this->cols();\n      StorageIndex newInnerSize = convert_index(IsRowMajor ? cols : rows);\n\n      // Deals with inner non zeros\n      if (m_innerNonZeros)\n      {\n        // Resize m_innerNonZeros\n        StorageIndex *newInnerNonZeros = static_cast<StorageIndex*>(std::realloc(m_innerNonZeros, (m_outerSize + outerChange) * sizeof(StorageIndex)));\n        if (!newInnerNonZeros) internal::throw_std_bad_alloc();\n        m_innerNonZeros = newInnerNonZeros;\n        \n        for(Index i=m_outerSize; i<m_outerSize+outerChange; i++)          \n          m_innerNonZeros[i] = 0;\n      } \n      else if (innerChange < 0) \n      {\n        // Inner size decreased: allocate a new m_innerNonZeros\n        m_innerNonZeros = static_cast<StorageIndex*>(std::malloc((m_outerSize+outerChange+1) * sizeof(StorageIndex)));\n        if (!m_innerNonZeros) internal::throw_std_bad_alloc();\n        for(Index i = 0; i < m_outerSize; i++)\n          m_innerNonZeros[i] = m_outerIndex[i+1] - m_outerIndex[i];\n      }\n      \n      // Change the m_innerNonZeros in case of a decrease of inner size\n      if (m_innerNonZeros && innerChange < 0)\n      {\n        for(Index i = 0; i < m_outerSize + (std::min)(outerChange, Index(0)); i++)\n        {\n          StorageIndex &n = m_innerNonZeros[i];\n          StorageIndex start = m_outerIndex[i];\n          while (n > 0 && m_data.index(start+n-1) >= newInnerSize) --n; \n        }\n      }\n      \n      m_innerSize = newInnerSize;\n\n      // Re-allocate outer index structure if necessary\n      if (outerChange == 0)\n        return;\n          \n      StorageIndex *newOuterIndex = static_cast<StorageIndex*>(std::realloc(m_outerIndex, (m_outerSize + outerChange + 1) * sizeof(StorageIndex)));\n      if (!newOuterIndex) internal::throw_std_bad_alloc();\n      m_outerIndex = newOuterIndex;\n      if (outerChange > 0)\n      {\n        StorageIndex last = m_outerSize == 0 ? 0 : m_outerIndex[m_outerSize];\n        for(Index i=m_outerSize; i<m_outerSize+outerChange+1; i++)          \n          m_outerIndex[i] = last; \n      }\n      m_outerSize += outerChange;\n    }\n    \n    /** Resizes the matrix to a \\a rows x \\a cols matrix and initializes it to zero.\n      * \n      * This function does not free the currently allocated memory. To release as much as memory as possible,\n      * call \\code mat.data().squeeze(); \\endcode after resizing it.\n      * \n      * \\sa reserve(), setZero()\n      */\n    void resize(Index rows, Index cols)\n    {\n      const Index outerSize = IsRowMajor ? rows : cols;\n      m_innerSize = IsRowMajor ? cols : rows;\n      m_data.clear();\n      if (m_outerSize != outerSize || m_outerSize==0)\n      {\n        std::free(m_outerIndex);\n        m_outerIndex = static_cast<StorageIndex*>(std::malloc((outerSize + 1) * sizeof(StorageIndex)));\n        if (!m_outerIndex) internal::throw_std_bad_alloc();\n        \n        m_outerSize = outerSize;\n      }\n      if(m_innerNonZeros)\n      {\n        std::free(m_innerNonZeros);\n        m_innerNonZeros = 0;\n      }\n      memset(m_outerIndex, 0, (m_outerSize+1)*sizeof(StorageIndex));\n    }\n\n    /** \\internal\n      * Resize the nonzero vector to \\a size */\n    void resizeNonZeros(Index size)\n    {\n      m_data.resize(size);\n    }\n\n    /** \\returns a const expression of the diagonal coefficients. */\n    const ConstDiagonalReturnType diagonal() const { return ConstDiagonalReturnType(*this); }\n    \n    /** \\returns a read-write expression of the diagonal coefficients.\n      * \\warning If the diagonal entries are written, then all diagonal\n      * entries \\b must already exist, otherwise an assertion will be raised.\n      */\n    DiagonalReturnType diagonal() { return DiagonalReturnType(*this); }\n\n    /** Default constructor yielding an empty \\c 0 \\c x \\c 0 matrix */\n    inline SparseMatrix()\n      : m_outerSize(-1), m_innerSize(0), m_outerIndex(0), m_innerNonZeros(0)\n    {\n      check_template_parameters();\n      resize(0, 0);\n    }\n\n    /** Constructs a \\a rows \\c x \\a cols empty matrix */\n    inline SparseMatrix(Index rows, Index cols)\n      : m_outerSize(0), m_innerSize(0), m_outerIndex(0), m_innerNonZeros(0)\n    {\n      check_template_parameters();\n      resize(rows, cols);\n    }\n\n    /** Constructs a sparse matrix from the sparse expression \\a other */\n    template<typename OtherDerived>\n    inline SparseMatrix(const SparseMatrixBase<OtherDerived>& other)\n      : m_outerSize(0), m_innerSize(0), m_outerIndex(0), m_innerNonZeros(0)\n    {\n      EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),\n        YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)\n      check_template_parameters();\n      const bool needToTranspose = (Flags & RowMajorBit) != (internal::evaluator<OtherDerived>::Flags & RowMajorBit);\n      if (needToTranspose)\n        *this = other.derived();\n      else\n      {\n        #ifdef EIGEN_SPARSE_CREATE_TEMPORARY_PLUGIN\n          EIGEN_SPARSE_CREATE_TEMPORARY_PLUGIN\n        #endif\n        internal::call_assignment_no_alias(*this, other.derived());\n      }\n    }\n    \n    /** Constructs a sparse matrix from the sparse selfadjoint view \\a other */\n    template<typename OtherDerived, unsigned int UpLo>\n    inline SparseMatrix(const SparseSelfAdjointView<OtherDerived, UpLo>& other)\n      : m_outerSize(0), m_innerSize(0), m_outerIndex(0), m_innerNonZeros(0)\n    {\n      check_template_parameters();\n      Base::operator=(other);\n    }\n\n    /** Copy constructor (it performs a deep copy) */\n    inline SparseMatrix(const SparseMatrix& other)\n      : Base(), m_outerSize(0), m_innerSize(0), m_outerIndex(0), m_innerNonZeros(0)\n    {\n      check_template_parameters();\n      *this = other.derived();\n    }\n\n    /** \\brief Copy constructor with in-place evaluation */\n    template<typename OtherDerived>\n    SparseMatrix(const ReturnByValue<OtherDerived>& other)\n      : Base(), m_outerSize(0), m_innerSize(0), m_outerIndex(0), m_innerNonZeros(0)\n    {\n      check_template_parameters();\n      initAssignment(other);\n      other.evalTo(*this);\n    }\n    \n    /** \\brief Copy constructor with in-place evaluation */\n    template<typename OtherDerived>\n    explicit SparseMatrix(const DiagonalBase<OtherDerived>& other)\n      : Base(), m_outerSize(0), m_innerSize(0), m_outerIndex(0), m_innerNonZeros(0)\n    {\n      check_template_parameters();\n      *this = other.derived();\n    }\n\n    /** Swaps the content of two sparse matrices of the same type.\n      * This is a fast operation that simply swaps the underlying pointers and parameters. */\n    inline void swap(SparseMatrix& other)\n    {\n      //EIGEN_DBG_SPARSE(std::cout << \"SparseMatrix:: swap\\n\");\n      std::swap(m_outerIndex, other.m_outerIndex);\n      std::swap(m_innerSize, other.m_innerSize);\n      std::swap(m_outerSize, other.m_outerSize);\n      std::swap(m_innerNonZeros, other.m_innerNonZeros);\n      m_data.swap(other.m_data);\n    }\n\n    /** Sets *this to the identity matrix.\n      * This function also turns the matrix into compressed mode, and drop any reserved memory. */\n    inline void setIdentity()\n    {\n      eigen_assert(rows() == cols() && \"ONLY FOR SQUARED MATRICES\");\n      this->m_data.resize(rows());\n      Eigen::Map<IndexVector>(this->m_data.indexPtr(), rows()).setLinSpaced(0, StorageIndex(rows()-1));\n      Eigen::Map<ScalarVector>(this->m_data.valuePtr(), rows()).setOnes();\n      Eigen::Map<IndexVector>(this->m_outerIndex, rows()+1).setLinSpaced(0, StorageIndex(rows()));\n      std::free(m_innerNonZeros);\n      m_innerNonZeros = 0;\n    }\n    inline SparseMatrix& operator=(const SparseMatrix& other)\n    {\n      if (other.isRValue())\n      {\n        swap(other.const_cast_derived());\n      }\n      else if(this!=&other)\n      {\n        #ifdef EIGEN_SPARSE_CREATE_TEMPORARY_PLUGIN\n          EIGEN_SPARSE_CREATE_TEMPORARY_PLUGIN\n        #endif\n        initAssignment(other);\n        if(other.isCompressed())\n        {\n          internal::smart_copy(other.m_outerIndex, other.m_outerIndex + m_outerSize + 1, m_outerIndex);\n          m_data = other.m_data;\n        }\n        else\n        {\n          Base::operator=(other);\n        }\n      }\n      return *this;\n    }\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\n    template<typename OtherDerived>\n    inline SparseMatrix& operator=(const EigenBase<OtherDerived>& other)\n    { return Base::operator=(other.derived()); }\n#endif // EIGEN_PARSED_BY_DOXYGEN\n\n    template<typename OtherDerived>\n    EIGEN_DONT_INLINE SparseMatrix& operator=(const SparseMatrixBase<OtherDerived>& other);\n\n    friend std::ostream & operator << (std::ostream & s, const SparseMatrix& m)\n    {\n      EIGEN_DBG_SPARSE(\n        s << \"Nonzero entries:\\n\";\n        if(m.isCompressed())\n        {\n          for (Index i=0; i<m.nonZeros(); ++i)\n            s << \"(\" << m.m_data.value(i) << \",\" << m.m_data.index(i) << \") \";\n        }\n        else\n        {\n          for (Index i=0; i<m.outerSize(); ++i)\n          {\n            Index p = m.m_outerIndex[i];\n            Index pe = m.m_outerIndex[i]+m.m_innerNonZeros[i];\n            Index k=p;\n            for (; k<pe; ++k) {\n              s << \"(\" << m.m_data.value(k) << \",\" << m.m_data.index(k) << \") \";\n            }\n            for (; k<m.m_outerIndex[i+1]; ++k) {\n              s << \"(_,_) \";\n            }\n          }\n        }\n        s << std::endl;\n        s << std::endl;\n        s << \"Outer pointers:\\n\";\n        for (Index i=0; i<m.outerSize(); ++i) {\n          s << m.m_outerIndex[i] << \" \";\n        }\n        s << \" $\" << std::endl;\n        if(!m.isCompressed())\n        {\n          s << \"Inner non zeros:\\n\";\n          for (Index i=0; i<m.outerSize(); ++i) {\n            s << m.m_innerNonZeros[i] << \" \";\n          }\n          s << \" $\" << std::endl;\n        }\n        s << std::endl;\n      );\n      s << static_cast<const SparseMatrixBase<SparseMatrix>&>(m);\n      return s;\n    }\n\n    /** Destructor */\n    inline ~SparseMatrix()\n    {\n      std::free(m_outerIndex);\n      std::free(m_innerNonZeros);\n    }\n\n    /** Overloaded for performance */\n    Scalar sum() const;\n    \n#   ifdef EIGEN_SPARSEMATRIX_PLUGIN\n#     include EIGEN_SPARSEMATRIX_PLUGIN\n#   endif\n\nprotected:\n\n    template<typename Other>\n    void initAssignment(const Other& other)\n    {\n      resize(other.rows(), other.cols());\n      if(m_innerNonZeros)\n      {\n        std::free(m_innerNonZeros);\n        m_innerNonZeros = 0;\n      }\n    }\n\n    /** \\internal\n      * \\sa insert(Index,Index) */\n    EIGEN_DONT_INLINE Scalar& insertCompressed(Index row, Index col);\n\n    /** \\internal\n      * A vector object that is equal to 0 everywhere but v at the position i */\n    class SingletonVector\n    {\n        StorageIndex m_index;\n        StorageIndex m_value;\n      public:\n        typedef StorageIndex value_type;\n        SingletonVector(Index i, Index v)\n          : m_index(convert_index(i)), m_value(convert_index(v))\n        {}\n\n        StorageIndex operator[](Index i) const { return i==m_index ? m_value : 0; }\n    };\n\n    /** \\internal\n      * \\sa insert(Index,Index) */\n    EIGEN_DONT_INLINE Scalar& insertUncompressed(Index row, Index col);\n\npublic:\n    /** \\internal\n      * \\sa insert(Index,Index) */\n    EIGEN_STRONG_INLINE Scalar& insertBackUncompressed(Index row, Index col)\n    {\n      const Index outer = IsRowMajor ? row : col;\n      const Index inner = IsRowMajor ? col : row;\n\n      eigen_assert(!isCompressed());\n      eigen_assert(m_innerNonZeros[outer]<=(m_outerIndex[outer+1] - m_outerIndex[outer]));\n\n      Index p = m_outerIndex[outer] + m_innerNonZeros[outer]++;\n      m_data.index(p) = convert_index(inner);\n      return (m_data.value(p) = 0);\n    }\n\nprivate:\n  static void check_template_parameters()\n  {\n    EIGEN_STATIC_ASSERT(NumTraits<StorageIndex>::IsSigned,THE_INDEX_TYPE_MUST_BE_A_SIGNED_TYPE);\n    EIGEN_STATIC_ASSERT((Options&(ColMajor|RowMajor))==Options,INVALID_MATRIX_TEMPLATE_PARAMETERS);\n  }\n\n  struct default_prunning_func {\n    default_prunning_func(const Scalar& ref, const RealScalar& eps) : reference(ref), epsilon(eps) {}\n    inline bool operator() (const Index&, const Index&, const Scalar& value) const\n    {\n      return !internal::isMuchSmallerThan(value, reference, epsilon);\n    }\n    Scalar reference;\n    RealScalar epsilon;\n  };\n};\n\nnamespace internal {\n\ntemplate<typename InputIterator, typename SparseMatrixType, typename DupFunctor>\nvoid set_from_triplets(const InputIterator& begin, const InputIterator& end, SparseMatrixType& mat, DupFunctor dup_func)\n{\n  enum { IsRowMajor = SparseMatrixType::IsRowMajor };\n  typedef typename SparseMatrixType::Scalar Scalar;\n  typedef typename SparseMatrixType::StorageIndex StorageIndex;\n  SparseMatrix<Scalar,IsRowMajor?ColMajor:RowMajor,StorageIndex> trMat(mat.rows(),mat.cols());\n\n  if(begin!=end)\n  {\n    // pass 1: count the nnz per inner-vector\n    typename SparseMatrixType::IndexVector wi(trMat.outerSize());\n    wi.setZero();\n    for(InputIterator it(begin); it!=end; ++it)\n    {\n      eigen_assert(it->row()>=0 && it->row()<mat.rows() && it->col()>=0 && it->col()<mat.cols());\n      wi(IsRowMajor ? it->col() : it->row())++;\n    }\n\n    // pass 2: insert all the elements into trMat\n    trMat.reserve(wi);\n    for(InputIterator it(begin); it!=end; ++it)\n      trMat.insertBackUncompressed(it->row(),it->col()) = it->value();\n\n    // pass 3:\n    trMat.collapseDuplicates(dup_func);\n  }\n\n  // pass 4: transposed copy -> implicit sorting\n  mat = trMat;\n}\n\n}\n\n\n/** Fill the matrix \\c *this with the list of \\em triplets defined by the iterator range \\a begin - \\a end.\n  *\n  * A \\em triplet is a tuple (i,j,value) defining a non-zero element.\n  * The input list of triplets does not have to be sorted, and can contains duplicated elements.\n  * In any case, the result is a \\b sorted and \\b compressed sparse matrix where the duplicates have been summed up.\n  * This is a \\em O(n) operation, with \\em n the number of triplet elements.\n  * The initial contents of \\c *this is destroyed.\n  * The matrix \\c *this must be properly resized beforehand using the SparseMatrix(Index,Index) constructor,\n  * or the resize(Index,Index) method. The sizes are not extracted from the triplet list.\n  *\n  * The \\a InputIterators value_type must provide the following interface:\n  * \\code\n  * Scalar value() const; // the value\n  * Scalar row() const;   // the row index i\n  * Scalar col() const;   // the column index j\n  * \\endcode\n  * See for instance the Eigen::Triplet template class.\n  *\n  * Here is a typical usage example:\n  * \\code\n    typedef Triplet<double> T;\n    std::vector<T> tripletList;\n    triplets.reserve(estimation_of_entries);\n    for(...)\n    {\n      // ...\n      tripletList.push_back(T(i,j,v_ij));\n    }\n    SparseMatrixType m(rows,cols);\n    m.setFromTriplets(tripletList.begin(), tripletList.end());\n    // m is ready to go!\n  * \\endcode\n  *\n  * \\warning The list of triplets is read multiple times (at least twice). Therefore, it is not recommended to define\n  * an abstract iterator over a complex data-structure that would be expensive to evaluate. The triplets should rather\n  * be explicitely stored into a std::vector for instance.\n  */\ntemplate<typename Scalar, int _Options, typename _StorageIndex>\ntemplate<typename InputIterators>\nvoid SparseMatrix<Scalar,_Options,_StorageIndex>::setFromTriplets(const InputIterators& begin, const InputIterators& end)\n{\n  internal::set_from_triplets<InputIterators, SparseMatrix<Scalar,_Options,_StorageIndex> >(begin, end, *this, internal::scalar_sum_op<Scalar,Scalar>());\n}\n\n/** The same as setFromTriplets but when duplicates are met the functor \\a dup_func is applied:\n  * \\code\n  * value = dup_func(OldValue, NewValue)\n  * \\endcode \n  * Here is a C++11 example keeping the latest entry only:\n  * \\code\n  * mat.setFromTriplets(triplets.begin(), triplets.end(), [] (const Scalar&,const Scalar &b) { return b; });\n  * \\endcode\n  */\ntemplate<typename Scalar, int _Options, typename _StorageIndex>\ntemplate<typename InputIterators,typename DupFunctor>\nvoid SparseMatrix<Scalar,_Options,_StorageIndex>::setFromTriplets(const InputIterators& begin, const InputIterators& end, DupFunctor dup_func)\n{\n  internal::set_from_triplets<InputIterators, SparseMatrix<Scalar,_Options,_StorageIndex>, DupFunctor>(begin, end, *this, dup_func);\n}\n\n/** \\internal */\ntemplate<typename Scalar, int _Options, typename _StorageIndex>\ntemplate<typename DupFunctor>\nvoid SparseMatrix<Scalar,_Options,_StorageIndex>::collapseDuplicates(DupFunctor dup_func)\n{\n  eigen_assert(!isCompressed());\n  // TODO, in practice we should be able to use m_innerNonZeros for that task\n  IndexVector wi(innerSize());\n  wi.fill(-1);\n  StorageIndex count = 0;\n  // for each inner-vector, wi[inner_index] will hold the position of first element into the index/value buffers\n  for(Index j=0; j<outerSize(); ++j)\n  {\n    StorageIndex start   = count;\n    Index oldEnd  = m_outerIndex[j]+m_innerNonZeros[j];\n    for(Index k=m_outerIndex[j]; k<oldEnd; ++k)\n    {\n      Index i = m_data.index(k);\n      if(wi(i)>=start)\n      {\n        // we already meet this entry => accumulate it\n        m_data.value(wi(i)) = dup_func(m_data.value(wi(i)), m_data.value(k));\n      }\n      else\n      {\n        m_data.value(count) = m_data.value(k);\n        m_data.index(count) = m_data.index(k);\n        wi(i) = count;\n        ++count;\n      }\n    }\n    m_outerIndex[j] = start;\n  }\n  m_outerIndex[m_outerSize] = count;\n\n  // turn the matrix into compressed form\n  std::free(m_innerNonZeros);\n  m_innerNonZeros = 0;\n  m_data.resize(m_outerIndex[m_outerSize]);\n}\n\ntemplate<typename Scalar, int _Options, typename _StorageIndex>\ntemplate<typename OtherDerived>\nEIGEN_DONT_INLINE SparseMatrix<Scalar,_Options,_StorageIndex>& SparseMatrix<Scalar,_Options,_StorageIndex>::operator=(const SparseMatrixBase<OtherDerived>& other)\n{\n  EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),\n        YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)\n\n  #ifdef EIGEN_SPARSE_CREATE_TEMPORARY_PLUGIN\n    EIGEN_SPARSE_CREATE_TEMPORARY_PLUGIN\n  #endif\n      \n  const bool needToTranspose = (Flags & RowMajorBit) != (internal::evaluator<OtherDerived>::Flags & RowMajorBit);\n  if (needToTranspose)\n  {\n    #ifdef EIGEN_SPARSE_TRANSPOSED_COPY_PLUGIN\n      EIGEN_SPARSE_TRANSPOSED_COPY_PLUGIN\n    #endif\n    // two passes algorithm:\n    //  1 - compute the number of coeffs per dest inner vector\n    //  2 - do the actual copy/eval\n    // Since each coeff of the rhs has to be evaluated twice, let's evaluate it if needed\n    typedef typename internal::nested_eval<OtherDerived,2,typename internal::plain_matrix_type<OtherDerived>::type >::type OtherCopy;\n    typedef typename internal::remove_all<OtherCopy>::type _OtherCopy;\n    typedef internal::evaluator<_OtherCopy> OtherCopyEval;\n    OtherCopy otherCopy(other.derived());\n    OtherCopyEval otherCopyEval(otherCopy);\n\n    SparseMatrix dest(other.rows(),other.cols());\n    Eigen::Map<IndexVector> (dest.m_outerIndex,dest.outerSize()).setZero();\n\n    // pass 1\n    // FIXME the above copy could be merged with that pass\n    for (Index j=0; j<otherCopy.outerSize(); ++j)\n      for (typename OtherCopyEval::InnerIterator it(otherCopyEval, j); it; ++it)\n        ++dest.m_outerIndex[it.index()];\n\n    // prefix sum\n    StorageIndex count = 0;\n    IndexVector positions(dest.outerSize());\n    for (Index j=0; j<dest.outerSize(); ++j)\n    {\n      StorageIndex tmp = dest.m_outerIndex[j];\n      dest.m_outerIndex[j] = count;\n      positions[j] = count;\n      count += tmp;\n    }\n    dest.m_outerIndex[dest.outerSize()] = count;\n    // alloc\n    dest.m_data.resize(count);\n    // pass 2\n    for (StorageIndex j=0; j<otherCopy.outerSize(); ++j)\n    {\n      for (typename OtherCopyEval::InnerIterator it(otherCopyEval, j); it; ++it)\n      {\n        Index pos = positions[it.index()]++;\n        dest.m_data.index(pos) = j;\n        dest.m_data.value(pos) = it.value();\n      }\n    }\n    this->swap(dest);\n    return *this;\n  }\n  else\n  {\n    if(other.isRValue())\n    {\n      initAssignment(other.derived());\n    }\n    // there is no special optimization\n    return Base::operator=(other.derived());\n  }\n}\n\ntemplate<typename _Scalar, int _Options, typename _StorageIndex>\ntypename SparseMatrix<_Scalar,_Options,_StorageIndex>::Scalar& SparseMatrix<_Scalar,_Options,_StorageIndex>::insert(Index row, Index col)\n{\n  eigen_assert(row>=0 && row<rows() && col>=0 && col<cols());\n  \n  const Index outer = IsRowMajor ? row : col;\n  const Index inner = IsRowMajor ? col : row;\n  \n  if(isCompressed())\n  {\n    if(nonZeros()==0)\n    {\n      // reserve space if not already done\n      if(m_data.allocatedSize()==0)\n        m_data.reserve(2*m_innerSize);\n      \n      // turn the matrix into non-compressed mode\n      m_innerNonZeros = static_cast<StorageIndex*>(std::malloc(m_outerSize * sizeof(StorageIndex)));\n      if(!m_innerNonZeros) internal::throw_std_bad_alloc();\n      \n      memset(m_innerNonZeros, 0, (m_outerSize)*sizeof(StorageIndex));\n      \n      // pack all inner-vectors to the end of the pre-allocated space\n      // and allocate the entire free-space to the first inner-vector\n      StorageIndex end = convert_index(m_data.allocatedSize());\n      for(Index j=1; j<=m_outerSize; ++j)\n        m_outerIndex[j] = end;\n    }\n    else\n    {\n      // turn the matrix into non-compressed mode\n      m_innerNonZeros = static_cast<StorageIndex*>(std::malloc(m_outerSize * sizeof(StorageIndex)));\n      if(!m_innerNonZeros) internal::throw_std_bad_alloc();\n      for(Index j=0; j<m_outerSize; ++j)\n        m_innerNonZeros[j] = m_outerIndex[j+1]-m_outerIndex[j];\n    }\n  }\n  \n  // check whether we can do a fast \"push back\" insertion\n  Index data_end = m_data.allocatedSize();\n  \n  // First case: we are filling a new inner vector which is packed at the end.\n  // We assume that all remaining inner-vectors are also empty and packed to the end.\n  if(m_outerIndex[outer]==data_end)\n  {\n    eigen_internal_assert(m_innerNonZeros[outer]==0);\n    \n    // pack previous empty inner-vectors to end of the used-space\n    // and allocate the entire free-space to the current inner-vector.\n    StorageIndex p = convert_index(m_data.size());\n    Index j = outer;\n    while(j>=0 && m_innerNonZeros[j]==0)\n      m_outerIndex[j--] = p;\n    \n    // push back the new element\n    ++m_innerNonZeros[outer];\n    m_data.append(Scalar(0), inner);\n    \n    // check for reallocation\n    if(data_end != m_data.allocatedSize())\n    {\n      // m_data has been reallocated\n      //  -> move remaining inner-vectors back to the end of the free-space\n      //     so that the entire free-space is allocated to the current inner-vector.\n      eigen_internal_assert(data_end < m_data.allocatedSize());\n      StorageIndex new_end = convert_index(m_data.allocatedSize());\n      for(Index k=outer+1; k<=m_outerSize; ++k)\n        if(m_outerIndex[k]==data_end)\n          m_outerIndex[k] = new_end;\n    }\n    return m_data.value(p);\n  }\n  \n  // Second case: the next inner-vector is packed to the end\n  // and the current inner-vector end match the used-space.\n  if(m_outerIndex[outer+1]==data_end && m_outerIndex[outer]+m_innerNonZeros[outer]==m_data.size())\n  {\n    eigen_internal_assert(outer+1==m_outerSize || m_innerNonZeros[outer+1]==0);\n    \n    // add space for the new element\n    ++m_innerNonZeros[outer];\n    m_data.resize(m_data.size()+1);\n    \n    // check for reallocation\n    if(data_end != m_data.allocatedSize())\n    {\n      // m_data has been reallocated\n      //  -> move remaining inner-vectors back to the end of the free-space\n      //     so that the entire free-space is allocated to the current inner-vector.\n      eigen_internal_assert(data_end < m_data.allocatedSize());\n      StorageIndex new_end = convert_index(m_data.allocatedSize());\n      for(Index k=outer+1; k<=m_outerSize; ++k)\n        if(m_outerIndex[k]==data_end)\n          m_outerIndex[k] = new_end;\n    }\n    \n    // and insert it at the right position (sorted insertion)\n    Index startId = m_outerIndex[outer];\n    Index p = m_outerIndex[outer]+m_innerNonZeros[outer]-1;\n    while ( (p > startId) && (m_data.index(p-1) > inner) )\n    {\n      m_data.index(p) = m_data.index(p-1);\n      m_data.value(p) = m_data.value(p-1);\n      --p;\n    }\n    \n    m_data.index(p) = convert_index(inner);\n    return (m_data.value(p) = 0);\n  }\n  \n  if(m_data.size() != m_data.allocatedSize())\n  {\n    // make sure the matrix is compatible to random un-compressed insertion:\n    m_data.resize(m_data.allocatedSize());\n    this->reserveInnerVectors(Array<StorageIndex,Dynamic,1>::Constant(m_outerSize, 2));\n  }\n  \n  return insertUncompressed(row,col);\n}\n    \ntemplate<typename _Scalar, int _Options, typename _StorageIndex>\nEIGEN_DONT_INLINE typename SparseMatrix<_Scalar,_Options,_StorageIndex>::Scalar& SparseMatrix<_Scalar,_Options,_StorageIndex>::insertUncompressed(Index row, Index col)\n{\n  eigen_assert(!isCompressed());\n\n  const Index outer = IsRowMajor ? row : col;\n  const StorageIndex inner = convert_index(IsRowMajor ? col : row);\n\n  Index room = m_outerIndex[outer+1] - m_outerIndex[outer];\n  StorageIndex innerNNZ = m_innerNonZeros[outer];\n  if(innerNNZ>=room)\n  {\n    // this inner vector is full, we need to reallocate the whole buffer :(\n    reserve(SingletonVector(outer,std::max<StorageIndex>(2,innerNNZ)));\n  }\n\n  Index startId = m_outerIndex[outer];\n  Index p = startId + m_innerNonZeros[outer];\n  while ( (p > startId) && (m_data.index(p-1) > inner) )\n  {\n    m_data.index(p) = m_data.index(p-1);\n    m_data.value(p) = m_data.value(p-1);\n    --p;\n  }\n  eigen_assert((p<=startId || m_data.index(p-1)!=inner) && \"you cannot insert an element that already exists, you must call coeffRef to this end\");\n\n  m_innerNonZeros[outer]++;\n\n  m_data.index(p) = inner;\n  return (m_data.value(p) = 0);\n}\n\ntemplate<typename _Scalar, int _Options, typename _StorageIndex>\nEIGEN_DONT_INLINE typename SparseMatrix<_Scalar,_Options,_StorageIndex>::Scalar& SparseMatrix<_Scalar,_Options,_StorageIndex>::insertCompressed(Index row, Index col)\n{\n  eigen_assert(isCompressed());\n\n  const Index outer = IsRowMajor ? row : col;\n  const Index inner = IsRowMajor ? col : row;\n\n  Index previousOuter = outer;\n  if (m_outerIndex[outer+1]==0)\n  {\n    // we start a new inner vector\n    while (previousOuter>=0 && m_outerIndex[previousOuter]==0)\n    {\n      m_outerIndex[previousOuter] = convert_index(m_data.size());\n      --previousOuter;\n    }\n    m_outerIndex[outer+1] = m_outerIndex[outer];\n  }\n\n  // here we have to handle the tricky case where the outerIndex array\n  // starts with: [ 0 0 0 0 0 1 ...] and we are inserted in, e.g.,\n  // the 2nd inner vector...\n  bool isLastVec = (!(previousOuter==-1 && m_data.size()!=0))\n                && (std::size_t(m_outerIndex[outer+1]) == m_data.size());\n\n  std::size_t startId = m_outerIndex[outer];\n  // FIXME let's make sure sizeof(long int) == sizeof(std::size_t)\n  std::size_t p = m_outerIndex[outer+1];\n  ++m_outerIndex[outer+1];\n\n  double reallocRatio = 1;\n  if (m_data.allocatedSize()<=m_data.size())\n  {\n    // if there is no preallocated memory, let's reserve a minimum of 32 elements\n    if (m_data.size()==0)\n    {\n      m_data.reserve(32);\n    }\n    else\n    {\n      // we need to reallocate the data, to reduce multiple reallocations\n      // we use a smart resize algorithm based on the current filling ratio\n      // in addition, we use double to avoid integers overflows\n      double nnzEstimate = double(m_outerIndex[outer])*double(m_outerSize)/double(outer+1);\n      reallocRatio = (nnzEstimate-double(m_data.size()))/double(m_data.size());\n      // furthermore we bound the realloc ratio to:\n      //   1) reduce multiple minor realloc when the matrix is almost filled\n      //   2) avoid to allocate too much memory when the matrix is almost empty\n      reallocRatio = (std::min)((std::max)(reallocRatio,1.5),8.);\n    }\n  }\n  m_data.resize(m_data.size()+1,reallocRatio);\n\n  if (!isLastVec)\n  {\n    if (previousOuter==-1)\n    {\n      // oops wrong guess.\n      // let's correct the outer offsets\n      for (Index k=0; k<=(outer+1); ++k)\n        m_outerIndex[k] = 0;\n      Index k=outer+1;\n      while(m_outerIndex[k]==0)\n        m_outerIndex[k++] = 1;\n      while (k<=m_outerSize && m_outerIndex[k]!=0)\n        m_outerIndex[k++]++;\n      p = 0;\n      --k;\n      k = m_outerIndex[k]-1;\n      while (k>0)\n      {\n        m_data.index(k) = m_data.index(k-1);\n        m_data.value(k) = m_data.value(k-1);\n        k--;\n      }\n    }\n    else\n    {\n      // we are not inserting into the last inner vec\n      // update outer indices:\n      Index j = outer+2;\n      while (j<=m_outerSize && m_outerIndex[j]!=0)\n        m_outerIndex[j++]++;\n      --j;\n      // shift data of last vecs:\n      Index k = m_outerIndex[j]-1;\n      while (k>=Index(p))\n      {\n        m_data.index(k) = m_data.index(k-1);\n        m_data.value(k) = m_data.value(k-1);\n        k--;\n      }\n    }\n  }\n\n  while ( (p > startId) && (m_data.index(p-1) > inner) )\n  {\n    m_data.index(p) = m_data.index(p-1);\n    m_data.value(p) = m_data.value(p-1);\n    --p;\n  }\n\n  m_data.index(p) = inner;\n  return (m_data.value(p) = 0);\n}\n\nnamespace internal {\n\ntemplate<typename _Scalar, int _Options, typename _StorageIndex>\nstruct evaluator<SparseMatrix<_Scalar,_Options,_StorageIndex> >\n  : evaluator<SparseCompressedBase<SparseMatrix<_Scalar,_Options,_StorageIndex> > >\n{\n  typedef evaluator<SparseCompressedBase<SparseMatrix<_Scalar,_Options,_StorageIndex> > > Base;\n  typedef SparseMatrix<_Scalar,_Options,_StorageIndex> SparseMatrixType;\n  evaluator() : Base() {}\n  explicit evaluator(const SparseMatrixType &mat) : Base(mat) {}\n};\n\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_SPARSEMATRIX_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseCore/SparseMatrixBase.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSEMATRIXBASE_H\n#define EIGEN_SPARSEMATRIXBASE_H\n\nnamespace Eigen { \n\n/** \\ingroup SparseCore_Module\n  *\n  * \\class SparseMatrixBase\n  *\n  * \\brief Base class of any sparse matrices or sparse expressions\n  *\n  * \\tparam Derived is the derived type, e.g. a sparse matrix type, or an expression, etc.\n  *\n  * This class can be extended with the help of the plugin mechanism described on the page\n  * \\ref TopicCustomizing_Plugins by defining the preprocessor symbol \\c EIGEN_SPARSEMATRIXBASE_PLUGIN.\n  */\ntemplate<typename Derived> class SparseMatrixBase\n  : public EigenBase<Derived>\n{\n  public:\n\n    typedef typename internal::traits<Derived>::Scalar Scalar;\n    \n    /** The numeric type of the expression' coefficients, e.g. float, double, int or std::complex<float>, etc.\n      *\n      * It is an alias for the Scalar type */\n    typedef Scalar value_type;\n    \n    typedef typename internal::packet_traits<Scalar>::type PacketScalar;\n    typedef typename internal::traits<Derived>::StorageKind StorageKind;\n\n    /** The integer type used to \\b store indices within a SparseMatrix.\n      * For a \\c SparseMatrix<Scalar,Options,IndexType> it an alias of the third template parameter \\c IndexType. */\n    typedef typename internal::traits<Derived>::StorageIndex StorageIndex;\n\n    typedef typename internal::add_const_on_value_type_if_arithmetic<\n                         typename internal::packet_traits<Scalar>::type\n                     >::type PacketReturnType;\n\n    typedef SparseMatrixBase StorageBaseType;\n\n    typedef Matrix<StorageIndex,Dynamic,1> IndexVector;\n    typedef Matrix<Scalar,Dynamic,1> ScalarVector;\n    \n    template<typename OtherDerived>\n    Derived& operator=(const EigenBase<OtherDerived> &other);\n\n    enum {\n\n      RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,\n        /**< The number of rows at compile-time. This is just a copy of the value provided\n          * by the \\a Derived type. If a value is not known at compile-time,\n          * it is set to the \\a Dynamic constant.\n          * \\sa MatrixBase::rows(), MatrixBase::cols(), ColsAtCompileTime, SizeAtCompileTime */\n\n      ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,\n        /**< The number of columns at compile-time. This is just a copy of the value provided\n          * by the \\a Derived type. If a value is not known at compile-time,\n          * it is set to the \\a Dynamic constant.\n          * \\sa MatrixBase::rows(), MatrixBase::cols(), RowsAtCompileTime, SizeAtCompileTime */\n\n\n      SizeAtCompileTime = (internal::size_at_compile_time<internal::traits<Derived>::RowsAtCompileTime,\n                                                   internal::traits<Derived>::ColsAtCompileTime>::ret),\n        /**< This is equal to the number of coefficients, i.e. the number of\n          * rows times the number of columns, or to \\a Dynamic if this is not\n          * known at compile-time. \\sa RowsAtCompileTime, ColsAtCompileTime */\n\n      MaxRowsAtCompileTime = RowsAtCompileTime,\n      MaxColsAtCompileTime = ColsAtCompileTime,\n\n      MaxSizeAtCompileTime = (internal::size_at_compile_time<MaxRowsAtCompileTime,\n                                                      MaxColsAtCompileTime>::ret),\n\n      IsVectorAtCompileTime = RowsAtCompileTime == 1 || ColsAtCompileTime == 1,\n        /**< This is set to true if either the number of rows or the number of\n          * columns is known at compile-time to be equal to 1. Indeed, in that case,\n          * we are dealing with a column-vector (if there is only one column) or with\n          * a row-vector (if there is only one row). */\n\n      Flags = internal::traits<Derived>::Flags,\n        /**< This stores expression \\ref flags flags which may or may not be inherited by new expressions\n          * constructed from this one. See the \\ref flags \"list of flags\".\n          */\n\n      IsRowMajor = Flags&RowMajorBit ? 1 : 0,\n      \n      InnerSizeAtCompileTime = int(IsVectorAtCompileTime) ? int(SizeAtCompileTime)\n                             : int(IsRowMajor) ? int(ColsAtCompileTime) : int(RowsAtCompileTime),\n\n      #ifndef EIGEN_PARSED_BY_DOXYGEN\n      _HasDirectAccess = (int(Flags)&DirectAccessBit) ? 1 : 0 // workaround sunCC\n      #endif\n    };\n\n    /** \\internal the return type of MatrixBase::adjoint() */\n    typedef typename internal::conditional<NumTraits<Scalar>::IsComplex,\n                        CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>, Eigen::Transpose<const Derived> >,\n                        Transpose<const Derived>\n                     >::type AdjointReturnType;\n    typedef Transpose<Derived> TransposeReturnType;\n    typedef typename internal::add_const<Transpose<const Derived> >::type ConstTransposeReturnType;\n\n    // FIXME storage order do not match evaluator storage order\n    typedef SparseMatrix<Scalar, Flags&RowMajorBit ? RowMajor : ColMajor, StorageIndex> PlainObject;\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\n    /** This is the \"real scalar\" type; if the \\a Scalar type is already real numbers\n      * (e.g. int, float or double) then \\a RealScalar is just the same as \\a Scalar. If\n      * \\a Scalar is \\a std::complex<T> then RealScalar is \\a T.\n      *\n      * \\sa class NumTraits\n      */\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n\n    /** \\internal the return type of coeff()\n      */\n    typedef typename internal::conditional<_HasDirectAccess, const Scalar&, Scalar>::type CoeffReturnType;\n\n    /** \\internal Represents a matrix with all coefficients equal to one another*/\n    typedef CwiseNullaryOp<internal::scalar_constant_op<Scalar>,Matrix<Scalar,Dynamic,Dynamic> > ConstantReturnType;\n\n    /** type of the equivalent dense matrix */\n    typedef Matrix<Scalar,RowsAtCompileTime,ColsAtCompileTime> DenseMatrixType;\n    /** type of the equivalent square matrix */\n    typedef Matrix<Scalar,EIGEN_SIZE_MAX(RowsAtCompileTime,ColsAtCompileTime),\n                          EIGEN_SIZE_MAX(RowsAtCompileTime,ColsAtCompileTime)> SquareMatrixType;\n\n    inline const Derived& derived() const { return *static_cast<const Derived*>(this); }\n    inline Derived& derived() { return *static_cast<Derived*>(this); }\n    inline Derived& const_cast_derived() const\n    { return *static_cast<Derived*>(const_cast<SparseMatrixBase*>(this)); }\n\n    typedef EigenBase<Derived> Base;\n\n#endif // not EIGEN_PARSED_BY_DOXYGEN\n\n#define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::SparseMatrixBase\n#ifdef EIGEN_PARSED_BY_DOXYGEN\n#define EIGEN_DOC_UNARY_ADDONS(METHOD,OP)           /** <p>This method does not change the sparsity of \\c *this: the OP is applied to explicitly stored coefficients only. \\sa SparseCompressedBase::coeffs() </p> */\n#define EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL      /** <p> \\warning This method returns a read-only expression for any sparse matrices. \\sa \\ref TutorialSparse_SubMatrices \"Sparse block operations\" </p> */\n#define EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(COND) /** <p> \\warning This method returns a read-write expression for COND sparse matrices only. Otherwise, the returned expression is read-only. \\sa \\ref TutorialSparse_SubMatrices \"Sparse block operations\" </p> */\n#else\n#define EIGEN_DOC_UNARY_ADDONS(X,Y)\n#define EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL\n#define EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(COND)\n#endif\n#   include \"../plugins/CommonCwiseUnaryOps.h\"\n#   include \"../plugins/CommonCwiseBinaryOps.h\"\n#   include \"../plugins/MatrixCwiseUnaryOps.h\"\n#   include \"../plugins/MatrixCwiseBinaryOps.h\"\n#   include \"../plugins/BlockMethods.h\"\n#   ifdef EIGEN_SPARSEMATRIXBASE_PLUGIN\n#     include EIGEN_SPARSEMATRIXBASE_PLUGIN\n#   endif\n#undef EIGEN_CURRENT_STORAGE_BASE_CLASS\n#undef EIGEN_DOC_UNARY_ADDONS\n#undef EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL\n#undef EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF\n\n    /** \\returns the number of rows. \\sa cols() */\n    inline Index rows() const { return derived().rows(); }\n    /** \\returns the number of columns. \\sa rows() */\n    inline Index cols() const { return derived().cols(); }\n    /** \\returns the number of coefficients, which is \\a rows()*cols().\n      * \\sa rows(), cols(). */\n    inline Index size() const { return rows() * cols(); }\n    /** \\returns true if either the number of rows or the number of columns is equal to 1.\n      * In other words, this function returns\n      * \\code rows()==1 || cols()==1 \\endcode\n      * \\sa rows(), cols(), IsVectorAtCompileTime. */\n    inline bool isVector() const { return rows()==1 || cols()==1; }\n    /** \\returns the size of the storage major dimension,\n      * i.e., the number of columns for a columns major matrix, and the number of rows otherwise */\n    Index outerSize() const { return (int(Flags)&RowMajorBit) ? this->rows() : this->cols(); }\n    /** \\returns the size of the inner dimension according to the storage order,\n      * i.e., the number of rows for a columns major matrix, and the number of cols otherwise */\n    Index innerSize() const { return (int(Flags)&RowMajorBit) ? this->cols() : this->rows(); }\n\n    bool isRValue() const { return m_isRValue; }\n    Derived& markAsRValue() { m_isRValue = true; return derived(); }\n\n    SparseMatrixBase() : m_isRValue(false) { /* TODO check flags */ }\n\n    \n    template<typename OtherDerived>\n    Derived& operator=(const ReturnByValue<OtherDerived>& other);\n\n    template<typename OtherDerived>\n    inline Derived& operator=(const SparseMatrixBase<OtherDerived>& other);\n\n    inline Derived& operator=(const Derived& other);\n\n  protected:\n\n    template<typename OtherDerived>\n    inline Derived& assign(const OtherDerived& other);\n\n    template<typename OtherDerived>\n    inline void assignGeneric(const OtherDerived& other);\n\n  public:\n\n    friend std::ostream & operator << (std::ostream & s, const SparseMatrixBase& m)\n    {\n      typedef typename Derived::Nested Nested;\n      typedef typename internal::remove_all<Nested>::type NestedCleaned;\n\n      if (Flags&RowMajorBit)\n      {\n        Nested nm(m.derived());\n        internal::evaluator<NestedCleaned> thisEval(nm);\n        for (Index row=0; row<nm.outerSize(); ++row)\n        {\n          Index col = 0;\n          for (typename internal::evaluator<NestedCleaned>::InnerIterator it(thisEval, row); it; ++it)\n          {\n            for ( ; col<it.index(); ++col)\n              s << \"0 \";\n            s << it.value() << \" \";\n            ++col;\n          }\n          for ( ; col<m.cols(); ++col)\n            s << \"0 \";\n          s << std::endl;\n        }\n      }\n      else\n      {\n        Nested nm(m.derived());\n        internal::evaluator<NestedCleaned> thisEval(nm);\n        if (m.cols() == 1) {\n          Index row = 0;\n          for (typename internal::evaluator<NestedCleaned>::InnerIterator it(thisEval, 0); it; ++it)\n          {\n            for ( ; row<it.index(); ++row)\n              s << \"0\" << std::endl;\n            s << it.value() << std::endl;\n            ++row;\n          }\n          for ( ; row<m.rows(); ++row)\n            s << \"0\" << std::endl;\n        }\n        else\n        {\n          SparseMatrix<Scalar, RowMajorBit, StorageIndex> trans = m;\n          s << static_cast<const SparseMatrixBase<SparseMatrix<Scalar, RowMajorBit, StorageIndex> >&>(trans);\n        }\n      }\n      return s;\n    }\n\n    template<typename OtherDerived>\n    Derived& operator+=(const SparseMatrixBase<OtherDerived>& other);\n    template<typename OtherDerived>\n    Derived& operator-=(const SparseMatrixBase<OtherDerived>& other);\n    \n    template<typename OtherDerived>\n    Derived& operator+=(const DiagonalBase<OtherDerived>& other);\n    template<typename OtherDerived>\n    Derived& operator-=(const DiagonalBase<OtherDerived>& other);\n\n    template<typename OtherDerived>\n    Derived& operator+=(const EigenBase<OtherDerived> &other);\n    template<typename OtherDerived>\n    Derived& operator-=(const EigenBase<OtherDerived> &other);\n\n    Derived& operator*=(const Scalar& other);\n    Derived& operator/=(const Scalar& other);\n\n    template<typename OtherDerived> struct CwiseProductDenseReturnType {\n      typedef CwiseBinaryOp<internal::scalar_product_op<typename ScalarBinaryOpTraits<\n                                                          typename internal::traits<Derived>::Scalar,\n                                                          typename internal::traits<OtherDerived>::Scalar\n                                                        >::ReturnType>,\n                            const Derived,\n                            const OtherDerived\n                          > Type;\n    };\n\n    template<typename OtherDerived>\n    EIGEN_STRONG_INLINE const typename CwiseProductDenseReturnType<OtherDerived>::Type\n    cwiseProduct(const MatrixBase<OtherDerived> &other) const;\n\n    // sparse * diagonal\n    template<typename OtherDerived>\n    const Product<Derived,OtherDerived>\n    operator*(const DiagonalBase<OtherDerived> &other) const\n    { return Product<Derived,OtherDerived>(derived(), other.derived()); }\n\n    // diagonal * sparse\n    template<typename OtherDerived> friend\n    const Product<OtherDerived,Derived>\n    operator*(const DiagonalBase<OtherDerived> &lhs, const SparseMatrixBase& rhs)\n    { return Product<OtherDerived,Derived>(lhs.derived(), rhs.derived()); }\n    \n    // sparse * sparse\n    template<typename OtherDerived>\n    const Product<Derived,OtherDerived,AliasFreeProduct>\n    operator*(const SparseMatrixBase<OtherDerived> &other) const;\n    \n    // sparse * dense\n    template<typename OtherDerived>\n    const Product<Derived,OtherDerived>\n    operator*(const MatrixBase<OtherDerived> &other) const\n    { return Product<Derived,OtherDerived>(derived(), other.derived()); }\n    \n    // dense * sparse\n    template<typename OtherDerived> friend\n    const Product<OtherDerived,Derived>\n    operator*(const MatrixBase<OtherDerived> &lhs, const SparseMatrixBase& rhs)\n    { return Product<OtherDerived,Derived>(lhs.derived(), rhs.derived()); }\n    \n     /** \\returns an expression of P H P^-1 where H is the matrix represented by \\c *this */\n    SparseSymmetricPermutationProduct<Derived,Upper|Lower> twistedBy(const PermutationMatrix<Dynamic,Dynamic,StorageIndex>& perm) const\n    {\n      return SparseSymmetricPermutationProduct<Derived,Upper|Lower>(derived(), perm);\n    }\n\n    template<typename OtherDerived>\n    Derived& operator*=(const SparseMatrixBase<OtherDerived>& other);\n\n    template<int Mode>\n    inline const TriangularView<const Derived, Mode> triangularView() const;\n    \n    template<unsigned int UpLo> struct SelfAdjointViewReturnType { typedef SparseSelfAdjointView<Derived, UpLo> Type; };\n    template<unsigned int UpLo> struct ConstSelfAdjointViewReturnType { typedef const SparseSelfAdjointView<const Derived, UpLo> Type; };\n\n    template<unsigned int UpLo> inline \n    typename ConstSelfAdjointViewReturnType<UpLo>::Type selfadjointView() const;\n    template<unsigned int UpLo> inline\n    typename SelfAdjointViewReturnType<UpLo>::Type selfadjointView();\n\n    template<typename OtherDerived> Scalar dot(const MatrixBase<OtherDerived>& other) const;\n    template<typename OtherDerived> Scalar dot(const SparseMatrixBase<OtherDerived>& other) const;\n    RealScalar squaredNorm() const;\n    RealScalar norm()  const;\n    RealScalar blueNorm() const;\n\n    TransposeReturnType transpose() { return TransposeReturnType(derived()); }\n    const ConstTransposeReturnType transpose() const { return ConstTransposeReturnType(derived()); }\n    const AdjointReturnType adjoint() const { return AdjointReturnType(transpose()); }\n\n    // inner-vector\n    typedef Block<Derived,IsRowMajor?1:Dynamic,IsRowMajor?Dynamic:1,true>       InnerVectorReturnType;\n    typedef Block<const Derived,IsRowMajor?1:Dynamic,IsRowMajor?Dynamic:1,true> ConstInnerVectorReturnType;\n    InnerVectorReturnType innerVector(Index outer);\n    const ConstInnerVectorReturnType innerVector(Index outer) const;\n\n    // set of inner-vectors\n    typedef Block<Derived,Dynamic,Dynamic,true> InnerVectorsReturnType;\n    typedef Block<const Derived,Dynamic,Dynamic,true> ConstInnerVectorsReturnType;\n    InnerVectorsReturnType innerVectors(Index outerStart, Index outerSize);\n    const ConstInnerVectorsReturnType innerVectors(Index outerStart, Index outerSize) const;\n\n    DenseMatrixType toDense() const\n    {\n      return DenseMatrixType(derived());\n    }\n\n    template<typename OtherDerived>\n    bool isApprox(const SparseMatrixBase<OtherDerived>& other,\n                  const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;\n\n    template<typename OtherDerived>\n    bool isApprox(const MatrixBase<OtherDerived>& other,\n                  const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const\n    { return toDense().isApprox(other,prec); }\n\n    /** \\returns the matrix or vector obtained by evaluating this expression.\n      *\n      * Notice that in the case of a plain matrix or vector (not an expression) this function just returns\n      * a const reference, in order to avoid a useless copy.\n      */\n    inline const typename internal::eval<Derived>::type eval() const\n    { return typename internal::eval<Derived>::type(derived()); }\n\n    Scalar sum() const;\n    \n    inline const SparseView<Derived>\n    pruned(const Scalar& reference = Scalar(0), const RealScalar& epsilon = NumTraits<Scalar>::dummy_precision()) const;\n\n  protected:\n\n    bool m_isRValue;\n\n    static inline StorageIndex convert_index(const Index idx) {\n      return internal::convert_index<StorageIndex>(idx);\n    }\n  private:\n    template<typename Dest> void evalTo(Dest &) const;\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_SPARSEMATRIXBASE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseCore/SparsePermutation.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSE_PERMUTATION_H\n#define EIGEN_SPARSE_PERMUTATION_H\n\n// This file implements sparse * permutation products\n\nnamespace Eigen { \n\nnamespace internal {\n\ntemplate<typename ExpressionType, int Side, bool Transposed>\nstruct permutation_matrix_product<ExpressionType, Side, Transposed, SparseShape>\n{\n    typedef typename nested_eval<ExpressionType, 1>::type MatrixType;\n    typedef typename remove_all<MatrixType>::type MatrixTypeCleaned;\n\n    typedef typename MatrixTypeCleaned::Scalar Scalar;\n    typedef typename MatrixTypeCleaned::StorageIndex StorageIndex;\n\n    enum {\n      SrcStorageOrder = MatrixTypeCleaned::Flags&RowMajorBit ? RowMajor : ColMajor,\n      MoveOuter = SrcStorageOrder==RowMajor ? Side==OnTheLeft : Side==OnTheRight\n    };\n    \n    typedef typename internal::conditional<MoveOuter,\n        SparseMatrix<Scalar,SrcStorageOrder,StorageIndex>,\n        SparseMatrix<Scalar,int(SrcStorageOrder)==RowMajor?ColMajor:RowMajor,StorageIndex> >::type ReturnType;\n\n    template<typename Dest,typename PermutationType>\n    static inline void run(Dest& dst, const PermutationType& perm, const ExpressionType& xpr)\n    {\n      MatrixType mat(xpr);\n      if(MoveOuter)\n      {\n        SparseMatrix<Scalar,SrcStorageOrder,StorageIndex> tmp(mat.rows(), mat.cols());\n        Matrix<StorageIndex,Dynamic,1> sizes(mat.outerSize());\n        for(Index j=0; j<mat.outerSize(); ++j)\n        {\n          Index jp = perm.indices().coeff(j);\n          sizes[((Side==OnTheLeft) ^ Transposed) ? jp : j] = StorageIndex(mat.innerVector(((Side==OnTheRight) ^ Transposed) ? jp : j).nonZeros());\n        }\n        tmp.reserve(sizes);\n        for(Index j=0; j<mat.outerSize(); ++j)\n        {\n          Index jp = perm.indices().coeff(j);\n          Index jsrc = ((Side==OnTheRight) ^ Transposed) ? jp : j;\n          Index jdst = ((Side==OnTheLeft) ^ Transposed) ? jp : j;\n          for(typename MatrixTypeCleaned::InnerIterator it(mat,jsrc); it; ++it)\n            tmp.insertByOuterInner(jdst,it.index()) = it.value();\n        }\n        dst = tmp;\n      }\n      else\n      {\n        SparseMatrix<Scalar,int(SrcStorageOrder)==RowMajor?ColMajor:RowMajor,StorageIndex> tmp(mat.rows(), mat.cols());\n        Matrix<StorageIndex,Dynamic,1> sizes(tmp.outerSize());\n        sizes.setZero();\n        PermutationMatrix<Dynamic,Dynamic,StorageIndex> perm_cpy;\n        if((Side==OnTheLeft) ^ Transposed)\n          perm_cpy = perm;\n        else\n          perm_cpy = perm.transpose();\n\n        for(Index j=0; j<mat.outerSize(); ++j)\n          for(typename MatrixTypeCleaned::InnerIterator it(mat,j); it; ++it)\n            sizes[perm_cpy.indices().coeff(it.index())]++;\n        tmp.reserve(sizes);\n        for(Index j=0; j<mat.outerSize(); ++j)\n          for(typename MatrixTypeCleaned::InnerIterator it(mat,j); it; ++it)\n            tmp.insertByOuterInner(perm_cpy.indices().coeff(it.index()),j) = it.value();\n        dst = tmp;\n      }\n    }\n};\n\n}\n\nnamespace internal {\n\ntemplate <int ProductTag> struct product_promote_storage_type<Sparse,             PermutationStorage, ProductTag> { typedef Sparse ret; };\ntemplate <int ProductTag> struct product_promote_storage_type<PermutationStorage, Sparse,             ProductTag> { typedef Sparse ret; };\n\n// TODO, the following two overloads are only needed to define the right temporary type through \n// typename traits<permutation_sparse_matrix_product<Rhs,Lhs,OnTheRight,false> >::ReturnType\n// whereas it should be correctly handled by traits<Product<> >::PlainObject\n\ntemplate<typename Lhs, typename Rhs, int ProductTag>\nstruct product_evaluator<Product<Lhs, Rhs, AliasFreeProduct>, ProductTag, PermutationShape, SparseShape>\n  : public evaluator<typename permutation_matrix_product<Rhs,OnTheLeft,false,SparseShape>::ReturnType>\n{\n  typedef Product<Lhs, Rhs, AliasFreeProduct> XprType;\n  typedef typename permutation_matrix_product<Rhs,OnTheLeft,false,SparseShape>::ReturnType PlainObject;\n  typedef evaluator<PlainObject> Base;\n\n  enum {\n    Flags = Base::Flags | EvalBeforeNestingBit\n  };\n\n  explicit product_evaluator(const XprType& xpr)\n    : m_result(xpr.rows(), xpr.cols())\n  {\n    ::new (static_cast<Base*>(this)) Base(m_result);\n    generic_product_impl<Lhs, Rhs, PermutationShape, SparseShape, ProductTag>::evalTo(m_result, xpr.lhs(), xpr.rhs());\n  }\n\nprotected:\n  PlainObject m_result;\n};\n\ntemplate<typename Lhs, typename Rhs, int ProductTag>\nstruct product_evaluator<Product<Lhs, Rhs, AliasFreeProduct>, ProductTag, SparseShape, PermutationShape >\n  : public evaluator<typename permutation_matrix_product<Lhs,OnTheRight,false,SparseShape>::ReturnType>\n{\n  typedef Product<Lhs, Rhs, AliasFreeProduct> XprType;\n  typedef typename permutation_matrix_product<Lhs,OnTheRight,false,SparseShape>::ReturnType PlainObject;\n  typedef evaluator<PlainObject> Base;\n\n  enum {\n    Flags = Base::Flags | EvalBeforeNestingBit\n  };\n\n  explicit product_evaluator(const XprType& xpr)\n    : m_result(xpr.rows(), xpr.cols())\n  {\n    ::new (static_cast<Base*>(this)) Base(m_result);\n    generic_product_impl<Lhs, Rhs, SparseShape, PermutationShape, ProductTag>::evalTo(m_result, xpr.lhs(), xpr.rhs());\n  }\n\nprotected:\n  PlainObject m_result;\n};\n\n} // end namespace internal\n\n/** \\returns the matrix with the permutation applied to the columns\n  */\ntemplate<typename SparseDerived, typename PermDerived>\ninline const Product<SparseDerived, PermDerived, AliasFreeProduct>\noperator*(const SparseMatrixBase<SparseDerived>& matrix, const PermutationBase<PermDerived>& perm)\n{ return Product<SparseDerived, PermDerived, AliasFreeProduct>(matrix.derived(), perm.derived()); }\n\n/** \\returns the matrix with the permutation applied to the rows\n  */\ntemplate<typename SparseDerived, typename PermDerived>\ninline const Product<PermDerived, SparseDerived, AliasFreeProduct>\noperator*( const PermutationBase<PermDerived>& perm, const SparseMatrixBase<SparseDerived>& matrix)\n{ return  Product<PermDerived, SparseDerived, AliasFreeProduct>(perm.derived(), matrix.derived()); }\n\n\n/** \\returns the matrix with the inverse permutation applied to the columns.\n  */\ntemplate<typename SparseDerived, typename PermutationType>\ninline const Product<SparseDerived, Inverse<PermutationType>, AliasFreeProduct>\noperator*(const SparseMatrixBase<SparseDerived>& matrix, const InverseImpl<PermutationType, PermutationStorage>& tperm)\n{\n  return Product<SparseDerived, Inverse<PermutationType>, AliasFreeProduct>(matrix.derived(), tperm.derived());\n}\n\n/** \\returns the matrix with the inverse permutation applied to the rows.\n  */\ntemplate<typename SparseDerived, typename PermutationType>\ninline const Product<Inverse<PermutationType>, SparseDerived, AliasFreeProduct>\noperator*(const InverseImpl<PermutationType,PermutationStorage>& tperm, const SparseMatrixBase<SparseDerived>& matrix)\n{\n  return Product<Inverse<PermutationType>, SparseDerived, AliasFreeProduct>(tperm.derived(), matrix.derived());\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_SPARSE_SELFADJOINTVIEW_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseCore/SparseProduct.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSEPRODUCT_H\n#define EIGEN_SPARSEPRODUCT_H\n\nnamespace Eigen { \n\n/** \\returns an expression of the product of two sparse matrices.\n  * By default a conservative product preserving the symbolic non zeros is performed.\n  * The automatic pruning of the small values can be achieved by calling the pruned() function\n  * in which case a totally different product algorithm is employed:\n  * \\code\n  * C = (A*B).pruned();             // supress numerical zeros (exact)\n  * C = (A*B).pruned(ref);\n  * C = (A*B).pruned(ref,epsilon);\n  * \\endcode\n  * where \\c ref is a meaningful non zero reference value.\n  * */\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\ninline const Product<Derived,OtherDerived,AliasFreeProduct>\nSparseMatrixBase<Derived>::operator*(const SparseMatrixBase<OtherDerived> &other) const\n{\n  return Product<Derived,OtherDerived,AliasFreeProduct>(derived(), other.derived());\n}\n\nnamespace internal {\n\n// sparse * sparse\ntemplate<typename Lhs, typename Rhs, int ProductType>\nstruct generic_product_impl<Lhs, Rhs, SparseShape, SparseShape, ProductType>\n{\n  template<typename Dest>\n  static void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs)\n  {\n    evalTo(dst, lhs, rhs, typename evaluator_traits<Dest>::Shape());\n  }\n\n  // dense += sparse * sparse\n  template<typename Dest,typename ActualLhs>\n  static void addTo(Dest& dst, const ActualLhs& lhs, const Rhs& rhs, typename enable_if<is_same<typename evaluator_traits<Dest>::Shape,DenseShape>::value,int*>::type* = 0)\n  {\n    typedef typename nested_eval<ActualLhs,Dynamic>::type LhsNested;\n    typedef typename nested_eval<Rhs,Dynamic>::type RhsNested;\n    LhsNested lhsNested(lhs);\n    RhsNested rhsNested(rhs);\n    internal::sparse_sparse_to_dense_product_selector<typename remove_all<LhsNested>::type,\n                                                      typename remove_all<RhsNested>::type, Dest>::run(lhsNested,rhsNested,dst);\n  }\n\n  // dense -= sparse * sparse\n  template<typename Dest>\n  static void subTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, typename enable_if<is_same<typename evaluator_traits<Dest>::Shape,DenseShape>::value,int*>::type* = 0)\n  {\n    addTo(dst, -lhs, rhs);\n  }\n\nprotected:\n\n  // sparse = sparse * sparse\n  template<typename Dest>\n  static void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, SparseShape)\n  {\n    typedef typename nested_eval<Lhs,Dynamic>::type LhsNested;\n    typedef typename nested_eval<Rhs,Dynamic>::type RhsNested;\n    LhsNested lhsNested(lhs);\n    RhsNested rhsNested(rhs);\n    internal::conservative_sparse_sparse_product_selector<typename remove_all<LhsNested>::type,\n                                                          typename remove_all<RhsNested>::type, Dest>::run(lhsNested,rhsNested,dst);\n  }\n\n  // dense = sparse * sparse\n  template<typename Dest>\n  static void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, DenseShape)\n  {\n    dst.setZero();\n    addTo(dst, lhs, rhs);\n  }\n};\n\n// sparse * sparse-triangular\ntemplate<typename Lhs, typename Rhs, int ProductType>\nstruct generic_product_impl<Lhs, Rhs, SparseShape, SparseTriangularShape, ProductType>\n : public generic_product_impl<Lhs, Rhs, SparseShape, SparseShape, ProductType>\n{};\n\n// sparse-triangular * sparse\ntemplate<typename Lhs, typename Rhs, int ProductType>\nstruct generic_product_impl<Lhs, Rhs, SparseTriangularShape, SparseShape, ProductType>\n : public generic_product_impl<Lhs, Rhs, SparseShape, SparseShape, ProductType>\n{};\n\n// dense = sparse-product (can be sparse*sparse, sparse*perm, etc.)\ntemplate< typename DstXprType, typename Lhs, typename Rhs>\nstruct Assignment<DstXprType, Product<Lhs,Rhs,AliasFreeProduct>, internal::assign_op<typename DstXprType::Scalar,typename Product<Lhs,Rhs,AliasFreeProduct>::Scalar>, Sparse2Dense>\n{\n  typedef Product<Lhs,Rhs,AliasFreeProduct> SrcXprType;\n  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &)\n  {\n    Index dstRows = src.rows();\n    Index dstCols = src.cols();\n    if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))\n      dst.resize(dstRows, dstCols);\n    \n    generic_product_impl<Lhs, Rhs>::evalTo(dst,src.lhs(),src.rhs());\n  }\n};\n\n// dense += sparse-product (can be sparse*sparse, sparse*perm, etc.)\ntemplate< typename DstXprType, typename Lhs, typename Rhs>\nstruct Assignment<DstXprType, Product<Lhs,Rhs,AliasFreeProduct>, internal::add_assign_op<typename DstXprType::Scalar,typename Product<Lhs,Rhs,AliasFreeProduct>::Scalar>, Sparse2Dense>\n{\n  typedef Product<Lhs,Rhs,AliasFreeProduct> SrcXprType;\n  static void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &)\n  {\n    generic_product_impl<Lhs, Rhs>::addTo(dst,src.lhs(),src.rhs());\n  }\n};\n\n// dense -= sparse-product (can be sparse*sparse, sparse*perm, etc.)\ntemplate< typename DstXprType, typename Lhs, typename Rhs>\nstruct Assignment<DstXprType, Product<Lhs,Rhs,AliasFreeProduct>, internal::sub_assign_op<typename DstXprType::Scalar,typename Product<Lhs,Rhs,AliasFreeProduct>::Scalar>, Sparse2Dense>\n{\n  typedef Product<Lhs,Rhs,AliasFreeProduct> SrcXprType;\n  static void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &)\n  {\n    generic_product_impl<Lhs, Rhs>::subTo(dst,src.lhs(),src.rhs());\n  }\n};\n\ntemplate<typename Lhs, typename Rhs, int Options>\nstruct unary_evaluator<SparseView<Product<Lhs, Rhs, Options> >, IteratorBased>\n : public evaluator<typename Product<Lhs, Rhs, DefaultProduct>::PlainObject>\n{\n  typedef SparseView<Product<Lhs, Rhs, Options> > XprType;\n  typedef typename XprType::PlainObject PlainObject;\n  typedef evaluator<PlainObject> Base;\n\n  explicit unary_evaluator(const XprType& xpr)\n    : m_result(xpr.rows(), xpr.cols())\n  {\n    using std::abs;\n    ::new (static_cast<Base*>(this)) Base(m_result);\n    typedef typename nested_eval<Lhs,Dynamic>::type LhsNested;\n    typedef typename nested_eval<Rhs,Dynamic>::type RhsNested;\n    LhsNested lhsNested(xpr.nestedExpression().lhs());\n    RhsNested rhsNested(xpr.nestedExpression().rhs());\n\n    internal::sparse_sparse_product_with_pruning_selector<typename remove_all<LhsNested>::type,\n                                                          typename remove_all<RhsNested>::type, PlainObject>::run(lhsNested,rhsNested,m_result,\n                                                                                                                  abs(xpr.reference())*xpr.epsilon());\n  }\n\nprotected:\n  PlainObject m_result;\n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_SPARSEPRODUCT_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseCore/SparseRedux.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSEREDUX_H\n#define EIGEN_SPARSEREDUX_H\n\nnamespace Eigen { \n\ntemplate<typename Derived>\ntypename internal::traits<Derived>::Scalar\nSparseMatrixBase<Derived>::sum() const\n{\n  eigen_assert(rows()>0 && cols()>0 && \"you are using a non initialized matrix\");\n  Scalar res(0);\n  internal::evaluator<Derived> thisEval(derived());\n  for (Index j=0; j<outerSize(); ++j)\n    for (typename internal::evaluator<Derived>::InnerIterator iter(thisEval,j); iter; ++iter)\n      res += iter.value();\n  return res;\n}\n\ntemplate<typename _Scalar, int _Options, typename _Index>\ntypename internal::traits<SparseMatrix<_Scalar,_Options,_Index> >::Scalar\nSparseMatrix<_Scalar,_Options,_Index>::sum() const\n{\n  eigen_assert(rows()>0 && cols()>0 && \"you are using a non initialized matrix\");\n  if(this->isCompressed())\n    return Matrix<Scalar,1,Dynamic>::Map(m_data.valuePtr(), m_data.size()).sum();\n  else\n    return Base::sum();\n}\n\ntemplate<typename _Scalar, int _Options, typename _Index>\ntypename internal::traits<SparseVector<_Scalar,_Options, _Index> >::Scalar\nSparseVector<_Scalar,_Options,_Index>::sum() const\n{\n  eigen_assert(rows()>0 && cols()>0 && \"you are using a non initialized matrix\");\n  return Matrix<Scalar,1,Dynamic>::Map(m_data.valuePtr(), m_data.size()).sum();\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_SPARSEREDUX_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseCore/SparseRef.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSE_REF_H\n#define EIGEN_SPARSE_REF_H\n\nnamespace Eigen {\n\nenum {\n  StandardCompressedFormat = 2 /**< used by Ref<SparseMatrix> to specify whether the input storage must be in standard compressed form */\n};\n  \nnamespace internal {\n\ntemplate<typename Derived> class SparseRefBase;\n\ntemplate<typename MatScalar, int MatOptions, typename MatIndex, int _Options, typename _StrideType>\nstruct traits<Ref<SparseMatrix<MatScalar,MatOptions,MatIndex>, _Options, _StrideType> >\n  : public traits<SparseMatrix<MatScalar,MatOptions,MatIndex> >\n{\n  typedef SparseMatrix<MatScalar,MatOptions,MatIndex> PlainObjectType;\n  enum {\n    Options = _Options,\n    Flags = traits<PlainObjectType>::Flags | CompressedAccessBit | NestByRefBit\n  };\n\n  template<typename Derived> struct match {\n    enum {\n      StorageOrderMatch = PlainObjectType::IsVectorAtCompileTime || Derived::IsVectorAtCompileTime || ((PlainObjectType::Flags&RowMajorBit)==(Derived::Flags&RowMajorBit)),\n      MatchAtCompileTime = (Derived::Flags&CompressedAccessBit) && StorageOrderMatch\n    };\n    typedef typename internal::conditional<MatchAtCompileTime,internal::true_type,internal::false_type>::type type;\n  };\n  \n};\n\ntemplate<typename MatScalar, int MatOptions, typename MatIndex, int _Options, typename _StrideType>\nstruct traits<Ref<const SparseMatrix<MatScalar,MatOptions,MatIndex>, _Options, _StrideType> >\n  : public traits<Ref<SparseMatrix<MatScalar,MatOptions,MatIndex>, _Options, _StrideType> >\n{\n  enum {\n    Flags = (traits<SparseMatrix<MatScalar,MatOptions,MatIndex> >::Flags | CompressedAccessBit | NestByRefBit) & ~LvalueBit\n  };\n};\n\ntemplate<typename MatScalar, int MatOptions, typename MatIndex, int _Options, typename _StrideType>\nstruct traits<Ref<SparseVector<MatScalar,MatOptions,MatIndex>, _Options, _StrideType> >\n  : public traits<SparseVector<MatScalar,MatOptions,MatIndex> >\n{\n  typedef SparseVector<MatScalar,MatOptions,MatIndex> PlainObjectType;\n  enum {\n    Options = _Options,\n    Flags = traits<PlainObjectType>::Flags | CompressedAccessBit | NestByRefBit\n  };\n\n  template<typename Derived> struct match {\n    enum {\n      MatchAtCompileTime = (Derived::Flags&CompressedAccessBit) && Derived::IsVectorAtCompileTime\n    };\n    typedef typename internal::conditional<MatchAtCompileTime,internal::true_type,internal::false_type>::type type;\n  };\n\n};\n\ntemplate<typename MatScalar, int MatOptions, typename MatIndex, int _Options, typename _StrideType>\nstruct traits<Ref<const SparseVector<MatScalar,MatOptions,MatIndex>, _Options, _StrideType> >\n  : public traits<Ref<SparseVector<MatScalar,MatOptions,MatIndex>, _Options, _StrideType> >\n{\n  enum {\n    Flags = (traits<SparseVector<MatScalar,MatOptions,MatIndex> >::Flags | CompressedAccessBit | NestByRefBit) & ~LvalueBit\n  };\n};\n\ntemplate<typename Derived>\nstruct traits<SparseRefBase<Derived> > : public traits<Derived> {};\n\ntemplate<typename Derived> class SparseRefBase\n  : public SparseMapBase<Derived>\n{\npublic:\n\n  typedef SparseMapBase<Derived> Base;\n  EIGEN_SPARSE_PUBLIC_INTERFACE(SparseRefBase)\n\n  SparseRefBase()\n    : Base(RowsAtCompileTime==Dynamic?0:RowsAtCompileTime,ColsAtCompileTime==Dynamic?0:ColsAtCompileTime, 0, 0, 0, 0, 0)\n  {}\n  \nprotected:\n\n  template<typename Expression>\n  void construct(Expression& expr)\n  {\n    if(expr.outerIndexPtr()==0)\n      ::new (static_cast<Base*>(this)) Base(expr.size(), expr.nonZeros(), expr.innerIndexPtr(), expr.valuePtr());\n    else\n      ::new (static_cast<Base*>(this)) Base(expr.rows(), expr.cols(), expr.nonZeros(), expr.outerIndexPtr(), expr.innerIndexPtr(), expr.valuePtr(), expr.innerNonZeroPtr());\n  }\n};\n\n} // namespace internal\n\n\n/** \n  * \\ingroup SparseCore_Module\n  *\n  * \\brief A sparse matrix expression referencing an existing sparse expression\n  *\n  * \\tparam SparseMatrixType the equivalent sparse matrix type of the referenced data, it must be a template instance of class SparseMatrix.\n  * \\tparam Options specifies whether the a standard compressed format is required \\c Options is  \\c #StandardCompressedFormat, or \\c 0.\n  *                The default is \\c 0.\n  *\n  * \\sa class Ref\n  */\n#ifndef EIGEN_PARSED_BY_DOXYGEN\ntemplate<typename MatScalar, int MatOptions, typename MatIndex, int Options, typename StrideType>\nclass Ref<SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType >\n  : public internal::SparseRefBase<Ref<SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType > >\n#else\ntemplate<typename SparseMatrixType, int Options>\nclass Ref<SparseMatrixType, Options>\n  : public SparseMapBase<Derived,WriteAccessors> // yes, that's weird to use Derived here, but that works!\n#endif\n{\n    typedef SparseMatrix<MatScalar,MatOptions,MatIndex> PlainObjectType;\n    typedef internal::traits<Ref> Traits;\n    template<int OtherOptions>\n    inline Ref(const SparseMatrix<MatScalar,OtherOptions,MatIndex>& expr);\n    template<int OtherOptions>\n    inline Ref(const MappedSparseMatrix<MatScalar,OtherOptions,MatIndex>& expr);\n  public:\n\n    typedef internal::SparseRefBase<Ref> Base;\n    EIGEN_SPARSE_PUBLIC_INTERFACE(Ref)\n\n\n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    template<int OtherOptions>\n    inline Ref(SparseMatrix<MatScalar,OtherOptions,MatIndex>& expr)\n    {\n      EIGEN_STATIC_ASSERT(bool(Traits::template match<SparseMatrix<MatScalar,OtherOptions,MatIndex> >::MatchAtCompileTime), STORAGE_LAYOUT_DOES_NOT_MATCH);\n      eigen_assert( ((Options & int(StandardCompressedFormat))==0) || (expr.isCompressed()) );\n      Base::construct(expr.derived());\n    }\n    \n    template<int OtherOptions>\n    inline Ref(MappedSparseMatrix<MatScalar,OtherOptions,MatIndex>& expr)\n    {\n      EIGEN_STATIC_ASSERT(bool(Traits::template match<SparseMatrix<MatScalar,OtherOptions,MatIndex> >::MatchAtCompileTime), STORAGE_LAYOUT_DOES_NOT_MATCH);\n      eigen_assert( ((Options & int(StandardCompressedFormat))==0) || (expr.isCompressed()) );\n      Base::construct(expr.derived());\n    }\n    \n    template<typename Derived>\n    inline Ref(const SparseCompressedBase<Derived>& expr)\n    #else\n    /** Implicit constructor from any sparse expression (2D matrix or 1D vector) */\n    template<typename Derived>\n    inline Ref(SparseCompressedBase<Derived>& expr)\n    #endif\n    {\n      EIGEN_STATIC_ASSERT(bool(internal::is_lvalue<Derived>::value), THIS_EXPRESSION_IS_NOT_A_LVALUE__IT_IS_READ_ONLY);\n      EIGEN_STATIC_ASSERT(bool(Traits::template match<Derived>::MatchAtCompileTime), STORAGE_LAYOUT_DOES_NOT_MATCH);\n      eigen_assert( ((Options & int(StandardCompressedFormat))==0) || (expr.isCompressed()) );\n      Base::construct(expr.const_cast_derived());\n    }\n};\n\n// this is the const ref version\ntemplate<typename MatScalar, int MatOptions, typename MatIndex, int Options, typename StrideType>\nclass Ref<const SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType>\n  : public internal::SparseRefBase<Ref<const SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> >\n{\n    typedef SparseMatrix<MatScalar,MatOptions,MatIndex> TPlainObjectType;\n    typedef internal::traits<Ref> Traits;\n  public:\n\n    typedef internal::SparseRefBase<Ref> Base;\n    EIGEN_SPARSE_PUBLIC_INTERFACE(Ref)\n\n    template<typename Derived>\n    inline Ref(const SparseMatrixBase<Derived>& expr) : m_hasCopy(false)\n    {\n      construct(expr.derived(), typename Traits::template match<Derived>::type());\n    }\n\n    inline Ref(const Ref& other) : Base(other), m_hasCopy(false) {\n      // copy constructor shall not copy the m_object, to avoid unnecessary malloc and copy\n    }\n\n    template<typename OtherRef>\n    inline Ref(const RefBase<OtherRef>& other) : m_hasCopy(false) {\n      construct(other.derived(), typename Traits::template match<OtherRef>::type());\n    }\n\n    ~Ref() {\n      if(m_hasCopy) {\n        TPlainObjectType* obj = reinterpret_cast<TPlainObjectType*>(m_object_bytes);\n        obj->~TPlainObjectType();\n      }\n    }\n\n  protected:\n\n    template<typename Expression>\n    void construct(const Expression& expr,internal::true_type)\n    {\n      if((Options & int(StandardCompressedFormat)) && (!expr.isCompressed()))\n      {\n        TPlainObjectType* obj = reinterpret_cast<TPlainObjectType*>(m_object_bytes);\n        ::new (obj) TPlainObjectType(expr);\n        m_hasCopy = true;\n        Base::construct(*obj);\n      }\n      else\n      {\n        Base::construct(expr);\n      }\n    }\n\n    template<typename Expression>\n    void construct(const Expression& expr, internal::false_type)\n    {\n      TPlainObjectType* obj = reinterpret_cast<TPlainObjectType*>(m_object_bytes);\n      ::new (obj) TPlainObjectType(expr);\n      m_hasCopy = true;\n      Base::construct(*obj);\n    }\n\n  protected:\n    char m_object_bytes[sizeof(TPlainObjectType)];\n    bool m_hasCopy;\n};\n\n\n\n/**\n  * \\ingroup SparseCore_Module\n  *\n  * \\brief A sparse vector expression referencing an existing sparse vector expression\n  *\n  * \\tparam SparseVectorType the equivalent sparse vector type of the referenced data, it must be a template instance of class SparseVector.\n  *\n  * \\sa class Ref\n  */\n#ifndef EIGEN_PARSED_BY_DOXYGEN\ntemplate<typename MatScalar, int MatOptions, typename MatIndex, int Options, typename StrideType>\nclass Ref<SparseVector<MatScalar,MatOptions,MatIndex>, Options, StrideType >\n  : public internal::SparseRefBase<Ref<SparseVector<MatScalar,MatOptions,MatIndex>, Options, StrideType > >\n#else\ntemplate<typename SparseVectorType>\nclass Ref<SparseVectorType>\n  : public SparseMapBase<Derived,WriteAccessors>\n#endif\n{\n    typedef SparseVector<MatScalar,MatOptions,MatIndex> PlainObjectType;\n    typedef internal::traits<Ref> Traits;\n    template<int OtherOptions>\n    inline Ref(const SparseVector<MatScalar,OtherOptions,MatIndex>& expr);\n  public:\n\n    typedef internal::SparseRefBase<Ref> Base;\n    EIGEN_SPARSE_PUBLIC_INTERFACE(Ref)\n\n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    template<int OtherOptions>\n    inline Ref(SparseVector<MatScalar,OtherOptions,MatIndex>& expr)\n    {\n      EIGEN_STATIC_ASSERT(bool(Traits::template match<SparseVector<MatScalar,OtherOptions,MatIndex> >::MatchAtCompileTime), STORAGE_LAYOUT_DOES_NOT_MATCH);\n      Base::construct(expr.derived());\n    }\n\n    template<typename Derived>\n    inline Ref(const SparseCompressedBase<Derived>& expr)\n    #else\n    /** Implicit constructor from any 1D sparse vector expression */\n    template<typename Derived>\n    inline Ref(SparseCompressedBase<Derived>& expr)\n    #endif\n    {\n      EIGEN_STATIC_ASSERT(bool(internal::is_lvalue<Derived>::value), THIS_EXPRESSION_IS_NOT_A_LVALUE__IT_IS_READ_ONLY);\n      EIGEN_STATIC_ASSERT(bool(Traits::template match<Derived>::MatchAtCompileTime), STORAGE_LAYOUT_DOES_NOT_MATCH);\n      Base::construct(expr.const_cast_derived());\n    }\n};\n\n// this is the const ref version\ntemplate<typename MatScalar, int MatOptions, typename MatIndex, int Options, typename StrideType>\nclass Ref<const SparseVector<MatScalar,MatOptions,MatIndex>, Options, StrideType>\n  : public internal::SparseRefBase<Ref<const SparseVector<MatScalar,MatOptions,MatIndex>, Options, StrideType> >\n{\n    typedef SparseVector<MatScalar,MatOptions,MatIndex> TPlainObjectType;\n    typedef internal::traits<Ref> Traits;\n  public:\n\n    typedef internal::SparseRefBase<Ref> Base;\n    EIGEN_SPARSE_PUBLIC_INTERFACE(Ref)\n\n    template<typename Derived>\n    inline Ref(const SparseMatrixBase<Derived>& expr) : m_hasCopy(false)\n    {\n      construct(expr.derived(), typename Traits::template match<Derived>::type());\n    }\n\n    inline Ref(const Ref& other) : Base(other), m_hasCopy(false) {\n      // copy constructor shall not copy the m_object, to avoid unnecessary malloc and copy\n    }\n\n    template<typename OtherRef>\n    inline Ref(const RefBase<OtherRef>& other) : m_hasCopy(false) {\n      construct(other.derived(), typename Traits::template match<OtherRef>::type());\n    }\n\n    ~Ref() {\n      if(m_hasCopy) {\n        TPlainObjectType* obj = reinterpret_cast<TPlainObjectType*>(m_object_bytes);\n        obj->~TPlainObjectType();\n      }\n    }\n\n  protected:\n\n    template<typename Expression>\n    void construct(const Expression& expr,internal::true_type)\n    {\n      Base::construct(expr);\n    }\n\n    template<typename Expression>\n    void construct(const Expression& expr, internal::false_type)\n    {\n      TPlainObjectType* obj = reinterpret_cast<TPlainObjectType*>(m_object_bytes);\n      ::new (obj) TPlainObjectType(expr);\n      m_hasCopy = true;\n      Base::construct(*obj);\n    }\n\n  protected:\n    char m_object_bytes[sizeof(TPlainObjectType)];\n    bool m_hasCopy;\n};\n\nnamespace internal {\n\n// FIXME shall we introduce a general evaluatior_ref that we can specialize for any sparse object once, and thus remove this copy-pasta thing...\n\ntemplate<typename MatScalar, int MatOptions, typename MatIndex, int Options, typename StrideType>\nstruct evaluator<Ref<SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> >\n  : evaluator<SparseCompressedBase<Ref<SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> > >\n{\n  typedef evaluator<SparseCompressedBase<Ref<SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> > > Base;\n  typedef Ref<SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> XprType;  \n  evaluator() : Base() {}\n  explicit evaluator(const XprType &mat) : Base(mat) {}\n};\n\ntemplate<typename MatScalar, int MatOptions, typename MatIndex, int Options, typename StrideType>\nstruct evaluator<Ref<const SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> >\n  : evaluator<SparseCompressedBase<Ref<const SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> > >\n{\n  typedef evaluator<SparseCompressedBase<Ref<const SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> > > Base;\n  typedef Ref<const SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> XprType;  \n  evaluator() : Base() {}\n  explicit evaluator(const XprType &mat) : Base(mat) {}\n};\n\ntemplate<typename MatScalar, int MatOptions, typename MatIndex, int Options, typename StrideType>\nstruct evaluator<Ref<SparseVector<MatScalar,MatOptions,MatIndex>, Options, StrideType> >\n  : evaluator<SparseCompressedBase<Ref<SparseVector<MatScalar,MatOptions,MatIndex>, Options, StrideType> > >\n{\n  typedef evaluator<SparseCompressedBase<Ref<SparseVector<MatScalar,MatOptions,MatIndex>, Options, StrideType> > > Base;\n  typedef Ref<SparseVector<MatScalar,MatOptions,MatIndex>, Options, StrideType> XprType;\n  evaluator() : Base() {}\n  explicit evaluator(const XprType &mat) : Base(mat) {}\n};\n\ntemplate<typename MatScalar, int MatOptions, typename MatIndex, int Options, typename StrideType>\nstruct evaluator<Ref<const SparseVector<MatScalar,MatOptions,MatIndex>, Options, StrideType> >\n  : evaluator<SparseCompressedBase<Ref<const SparseVector<MatScalar,MatOptions,MatIndex>, Options, StrideType> > >\n{\n  typedef evaluator<SparseCompressedBase<Ref<const SparseVector<MatScalar,MatOptions,MatIndex>, Options, StrideType> > > Base;\n  typedef Ref<const SparseVector<MatScalar,MatOptions,MatIndex>, Options, StrideType> XprType;\n  evaluator() : Base() {}\n  explicit evaluator(const XprType &mat) : Base(mat) {}\n};\n\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_SPARSE_REF_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseCore/SparseSelfAdjointView.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSE_SELFADJOINTVIEW_H\n#define EIGEN_SPARSE_SELFADJOINTVIEW_H\n\nnamespace Eigen { \n  \n/** \\ingroup SparseCore_Module\n  * \\class SparseSelfAdjointView\n  *\n  * \\brief Pseudo expression to manipulate a triangular sparse matrix as a selfadjoint matrix.\n  *\n  * \\param MatrixType the type of the dense matrix storing the coefficients\n  * \\param Mode can be either \\c #Lower or \\c #Upper\n  *\n  * This class is an expression of a sefladjoint matrix from a triangular part of a matrix\n  * with given dense storage of the coefficients. It is the return type of MatrixBase::selfadjointView()\n  * and most of the time this is the only way that it is used.\n  *\n  * \\sa SparseMatrixBase::selfadjointView()\n  */\nnamespace internal {\n  \ntemplate<typename MatrixType, unsigned int Mode>\nstruct traits<SparseSelfAdjointView<MatrixType,Mode> > : traits<MatrixType> {\n};\n\ntemplate<int SrcMode,int DstMode,typename MatrixType,int DestOrder>\nvoid permute_symm_to_symm(const MatrixType& mat, SparseMatrix<typename MatrixType::Scalar,DestOrder,typename MatrixType::StorageIndex>& _dest, const typename MatrixType::StorageIndex* perm = 0);\n\ntemplate<int Mode,typename MatrixType,int DestOrder>\nvoid permute_symm_to_fullsymm(const MatrixType& mat, SparseMatrix<typename MatrixType::Scalar,DestOrder,typename MatrixType::StorageIndex>& _dest, const typename MatrixType::StorageIndex* perm = 0);\n\n}\n\ntemplate<typename MatrixType, unsigned int _Mode> class SparseSelfAdjointView\n  : public EigenBase<SparseSelfAdjointView<MatrixType,_Mode> >\n{\n  public:\n    \n    enum {\n      Mode = _Mode,\n      TransposeMode = ((Mode & Upper) ? Lower : 0) | ((Mode & Lower) ? Upper : 0),\n      RowsAtCompileTime = internal::traits<SparseSelfAdjointView>::RowsAtCompileTime,\n      ColsAtCompileTime = internal::traits<SparseSelfAdjointView>::ColsAtCompileTime\n    };\n\n    typedef EigenBase<SparseSelfAdjointView> Base;\n    typedef typename MatrixType::Scalar Scalar;\n    typedef typename MatrixType::StorageIndex StorageIndex;\n    typedef Matrix<StorageIndex,Dynamic,1> VectorI;\n    typedef typename internal::ref_selector<MatrixType>::non_const_type MatrixTypeNested;\n    typedef typename internal::remove_all<MatrixTypeNested>::type _MatrixTypeNested;\n    \n    explicit inline SparseSelfAdjointView(MatrixType& matrix) : m_matrix(matrix)\n    {\n      eigen_assert(rows()==cols() && \"SelfAdjointView is only for squared matrices\");\n    }\n\n    inline Index rows() const { return m_matrix.rows(); }\n    inline Index cols() const { return m_matrix.cols(); }\n\n    /** \\internal \\returns a reference to the nested matrix */\n    const _MatrixTypeNested& matrix() const { return m_matrix; }\n    typename internal::remove_reference<MatrixTypeNested>::type& matrix() { return m_matrix; }\n\n    /** \\returns an expression of the matrix product between a sparse self-adjoint matrix \\c *this and a sparse matrix \\a rhs.\n      *\n      * Note that there is no algorithmic advantage of performing such a product compared to a general sparse-sparse matrix product.\n      * Indeed, the SparseSelfadjointView operand is first copied into a temporary SparseMatrix before computing the product.\n      */\n    template<typename OtherDerived>\n    Product<SparseSelfAdjointView, OtherDerived>\n    operator*(const SparseMatrixBase<OtherDerived>& rhs) const\n    {\n      return Product<SparseSelfAdjointView, OtherDerived>(*this, rhs.derived());\n    }\n\n    /** \\returns an expression of the matrix product between a sparse matrix \\a lhs and a sparse self-adjoint matrix \\a rhs.\n      *\n      * Note that there is no algorithmic advantage of performing such a product compared to a general sparse-sparse matrix product.\n      * Indeed, the SparseSelfadjointView operand is first copied into a temporary SparseMatrix before computing the product.\n      */\n    template<typename OtherDerived> friend\n    Product<OtherDerived, SparseSelfAdjointView>\n    operator*(const SparseMatrixBase<OtherDerived>& lhs, const SparseSelfAdjointView& rhs)\n    {\n      return Product<OtherDerived, SparseSelfAdjointView>(lhs.derived(), rhs);\n    }\n    \n    /** Efficient sparse self-adjoint matrix times dense vector/matrix product */\n    template<typename OtherDerived>\n    Product<SparseSelfAdjointView,OtherDerived>\n    operator*(const MatrixBase<OtherDerived>& rhs) const\n    {\n      return Product<SparseSelfAdjointView,OtherDerived>(*this, rhs.derived());\n    }\n\n    /** Efficient dense vector/matrix times sparse self-adjoint matrix product */\n    template<typename OtherDerived> friend\n    Product<OtherDerived,SparseSelfAdjointView>\n    operator*(const MatrixBase<OtherDerived>& lhs, const SparseSelfAdjointView& rhs)\n    {\n      return Product<OtherDerived,SparseSelfAdjointView>(lhs.derived(), rhs);\n    }\n\n    /** Perform a symmetric rank K update of the selfadjoint matrix \\c *this:\n      * \\f$ this = this + \\alpha ( u u^* ) \\f$ where \\a u is a vector or matrix.\n      *\n      * \\returns a reference to \\c *this\n      *\n      * To perform \\f$ this = this + \\alpha ( u^* u ) \\f$ you can simply\n      * call this function with u.adjoint().\n      */\n    template<typename DerivedU>\n    SparseSelfAdjointView& rankUpdate(const SparseMatrixBase<DerivedU>& u, const Scalar& alpha = Scalar(1));\n    \n    /** \\returns an expression of P H P^-1 */\n    // TODO implement twists in a more evaluator friendly fashion\n    SparseSymmetricPermutationProduct<_MatrixTypeNested,Mode> twistedBy(const PermutationMatrix<Dynamic,Dynamic,StorageIndex>& perm) const\n    {\n      return SparseSymmetricPermutationProduct<_MatrixTypeNested,Mode>(m_matrix, perm);\n    }\n\n    template<typename SrcMatrixType,int SrcMode>\n    SparseSelfAdjointView& operator=(const SparseSymmetricPermutationProduct<SrcMatrixType,SrcMode>& permutedMatrix)\n    {\n      internal::call_assignment_no_alias_no_transpose(*this, permutedMatrix);\n      return *this;\n    }\n\n    SparseSelfAdjointView& operator=(const SparseSelfAdjointView& src)\n    {\n      PermutationMatrix<Dynamic,Dynamic,StorageIndex> pnull;\n      return *this = src.twistedBy(pnull);\n    }\n\n    template<typename SrcMatrixType,unsigned int SrcMode>\n    SparseSelfAdjointView& operator=(const SparseSelfAdjointView<SrcMatrixType,SrcMode>& src)\n    {\n      PermutationMatrix<Dynamic,Dynamic,StorageIndex> pnull;\n      return *this = src.twistedBy(pnull);\n    }\n    \n    void resize(Index rows, Index cols)\n    {\n      EIGEN_ONLY_USED_FOR_DEBUG(rows);\n      EIGEN_ONLY_USED_FOR_DEBUG(cols);\n      eigen_assert(rows == this->rows() && cols == this->cols()\n                && \"SparseSelfadjointView::resize() does not actually allow to resize.\");\n    }\n    \n  protected:\n\n    MatrixTypeNested m_matrix;\n    //mutable VectorI m_countPerRow;\n    //mutable VectorI m_countPerCol;\n  private:\n    template<typename Dest> void evalTo(Dest &) const;\n};\n\n/***************************************************************************\n* Implementation of SparseMatrixBase methods\n***************************************************************************/\n\ntemplate<typename Derived>\ntemplate<unsigned int UpLo>\ntypename SparseMatrixBase<Derived>::template ConstSelfAdjointViewReturnType<UpLo>::Type SparseMatrixBase<Derived>::selfadjointView() const\n{\n  return SparseSelfAdjointView<const Derived, UpLo>(derived());\n}\n\ntemplate<typename Derived>\ntemplate<unsigned int UpLo>\ntypename SparseMatrixBase<Derived>::template SelfAdjointViewReturnType<UpLo>::Type SparseMatrixBase<Derived>::selfadjointView()\n{\n  return SparseSelfAdjointView<Derived, UpLo>(derived());\n}\n\n/***************************************************************************\n* Implementation of SparseSelfAdjointView methods\n***************************************************************************/\n\ntemplate<typename MatrixType, unsigned int Mode>\ntemplate<typename DerivedU>\nSparseSelfAdjointView<MatrixType,Mode>&\nSparseSelfAdjointView<MatrixType,Mode>::rankUpdate(const SparseMatrixBase<DerivedU>& u, const Scalar& alpha)\n{\n  SparseMatrix<Scalar,(MatrixType::Flags&RowMajorBit)?RowMajor:ColMajor> tmp = u * u.adjoint();\n  if(alpha==Scalar(0))\n    m_matrix = tmp.template triangularView<Mode>();\n  else\n    m_matrix += alpha * tmp.template triangularView<Mode>();\n\n  return *this;\n}\n\nnamespace internal {\n  \n// TODO currently a selfadjoint expression has the form SelfAdjointView<.,.>\n//      in the future selfadjoint-ness should be defined by the expression traits\n//      such that Transpose<SelfAdjointView<.,.> > is valid. (currently TriangularBase::transpose() is overloaded to make it work)\ntemplate<typename MatrixType, unsigned int Mode>\nstruct evaluator_traits<SparseSelfAdjointView<MatrixType,Mode> >\n{\n  typedef typename storage_kind_to_evaluator_kind<typename MatrixType::StorageKind>::Kind Kind;\n  typedef SparseSelfAdjointShape Shape;\n};\n\nstruct SparseSelfAdjoint2Sparse {};\n\ntemplate<> struct AssignmentKind<SparseShape,SparseSelfAdjointShape> { typedef SparseSelfAdjoint2Sparse Kind; };\ntemplate<> struct AssignmentKind<SparseSelfAdjointShape,SparseShape> { typedef Sparse2Sparse Kind; };\n\ntemplate< typename DstXprType, typename SrcXprType, typename Functor>\nstruct Assignment<DstXprType, SrcXprType, Functor, SparseSelfAdjoint2Sparse>\n{\n  typedef typename DstXprType::StorageIndex StorageIndex;\n  typedef internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> AssignOpType;\n\n  template<typename DestScalar,int StorageOrder>\n  static void run(SparseMatrix<DestScalar,StorageOrder,StorageIndex> &dst, const SrcXprType &src, const AssignOpType&/*func*/)\n  {\n    internal::permute_symm_to_fullsymm<SrcXprType::Mode>(src.matrix(), dst);\n  }\n\n  // FIXME: the handling of += and -= in sparse matrices should be cleanup so that next two overloads could be reduced to:\n  template<typename DestScalar,int StorageOrder,typename AssignFunc>\n  static void run(SparseMatrix<DestScalar,StorageOrder,StorageIndex> &dst, const SrcXprType &src, const AssignFunc& func)\n  {\n    SparseMatrix<DestScalar,StorageOrder,StorageIndex> tmp(src.rows(),src.cols());\n    run(tmp, src, AssignOpType());\n    call_assignment_no_alias_no_transpose(dst, tmp, func);\n  }\n\n  template<typename DestScalar,int StorageOrder>\n  static void run(SparseMatrix<DestScalar,StorageOrder,StorageIndex> &dst, const SrcXprType &src,\n                  const internal::add_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar>& /* func */)\n  {\n    SparseMatrix<DestScalar,StorageOrder,StorageIndex> tmp(src.rows(),src.cols());\n    run(tmp, src, AssignOpType());\n    dst += tmp;\n  }\n\n  template<typename DestScalar,int StorageOrder>\n  static void run(SparseMatrix<DestScalar,StorageOrder,StorageIndex> &dst, const SrcXprType &src,\n                  const internal::sub_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar>& /* func */)\n  {\n    SparseMatrix<DestScalar,StorageOrder,StorageIndex> tmp(src.rows(),src.cols());\n    run(tmp, src, AssignOpType());\n    dst -= tmp;\n  }\n  \n  template<typename DestScalar>\n  static void run(DynamicSparseMatrix<DestScalar,ColMajor,StorageIndex>& dst, const SrcXprType &src, const AssignOpType&/*func*/)\n  {\n    // TODO directly evaluate into dst;\n    SparseMatrix<DestScalar,ColMajor,StorageIndex> tmp(dst.rows(),dst.cols());\n    internal::permute_symm_to_fullsymm<SrcXprType::Mode>(src.matrix(), tmp);\n    dst = tmp;\n  }\n};\n\n} // end namespace internal\n\n/***************************************************************************\n* Implementation of sparse self-adjoint time dense matrix\n***************************************************************************/\n\nnamespace internal {\n\ntemplate<int Mode, typename SparseLhsType, typename DenseRhsType, typename DenseResType, typename AlphaType>\ninline void sparse_selfadjoint_time_dense_product(const SparseLhsType& lhs, const DenseRhsType& rhs, DenseResType& res, const AlphaType& alpha)\n{\n  EIGEN_ONLY_USED_FOR_DEBUG(alpha);\n  \n  typedef typename internal::nested_eval<SparseLhsType,DenseRhsType::MaxColsAtCompileTime>::type SparseLhsTypeNested;\n  typedef typename internal::remove_all<SparseLhsTypeNested>::type SparseLhsTypeNestedCleaned;\n  typedef evaluator<SparseLhsTypeNestedCleaned> LhsEval;\n  typedef typename LhsEval::InnerIterator LhsIterator;\n  typedef typename SparseLhsType::Scalar LhsScalar;\n  \n  enum {\n    LhsIsRowMajor = (LhsEval::Flags&RowMajorBit)==RowMajorBit,\n    ProcessFirstHalf =\n              ((Mode&(Upper|Lower))==(Upper|Lower))\n          || ( (Mode&Upper) && !LhsIsRowMajor)\n          || ( (Mode&Lower) && LhsIsRowMajor),\n    ProcessSecondHalf = !ProcessFirstHalf\n  };\n  \n  SparseLhsTypeNested lhs_nested(lhs);\n  LhsEval lhsEval(lhs_nested);\n\n  // work on one column at once\n  for (Index k=0; k<rhs.cols(); ++k)\n  {\n    for (Index j=0; j<lhs.outerSize(); ++j)\n    {\n      LhsIterator i(lhsEval,j);\n      // handle diagonal coeff\n      if (ProcessSecondHalf)\n      {\n        while (i && i.index()<j) ++i;\n        if(i && i.index()==j)\n        {\n          res.coeffRef(j,k) += alpha * i.value() * rhs.coeff(j,k);\n          ++i;\n        }\n      }\n\n      // premultiplied rhs for scatters\n      typename ScalarBinaryOpTraits<AlphaType, typename DenseRhsType::Scalar>::ReturnType rhs_j(alpha*rhs(j,k));\n      // accumulator for partial scalar product\n      typename DenseResType::Scalar res_j(0);\n      for(; (ProcessFirstHalf ? i && i.index() < j : i) ; ++i)\n      {\n        LhsScalar lhs_ij = i.value();\n        if(!LhsIsRowMajor) lhs_ij = numext::conj(lhs_ij);\n        res_j += lhs_ij * rhs.coeff(i.index(),k);\n        res(i.index(),k) += numext::conj(lhs_ij) * rhs_j;\n      }\n      res.coeffRef(j,k) += alpha * res_j;\n\n      // handle diagonal coeff\n      if (ProcessFirstHalf && i && (i.index()==j))\n        res.coeffRef(j,k) += alpha * i.value() * rhs.coeff(j,k);\n    }\n  }\n}\n\n\ntemplate<typename LhsView, typename Rhs, int ProductType>\nstruct generic_product_impl<LhsView, Rhs, SparseSelfAdjointShape, DenseShape, ProductType>\n: generic_product_impl_base<LhsView, Rhs, generic_product_impl<LhsView, Rhs, SparseSelfAdjointShape, DenseShape, ProductType> >\n{\n  template<typename Dest>\n  static void scaleAndAddTo(Dest& dst, const LhsView& lhsView, const Rhs& rhs, const typename Dest::Scalar& alpha)\n  {\n    typedef typename LhsView::_MatrixTypeNested Lhs;\n    typedef typename nested_eval<Lhs,Dynamic>::type LhsNested;\n    typedef typename nested_eval<Rhs,Dynamic>::type RhsNested;\n    LhsNested lhsNested(lhsView.matrix());\n    RhsNested rhsNested(rhs);\n    \n    internal::sparse_selfadjoint_time_dense_product<LhsView::Mode>(lhsNested, rhsNested, dst, alpha);\n  }\n};\n\ntemplate<typename Lhs, typename RhsView, int ProductType>\nstruct generic_product_impl<Lhs, RhsView, DenseShape, SparseSelfAdjointShape, ProductType>\n: generic_product_impl_base<Lhs, RhsView, generic_product_impl<Lhs, RhsView, DenseShape, SparseSelfAdjointShape, ProductType> >\n{\n  template<typename Dest>\n  static void scaleAndAddTo(Dest& dst, const Lhs& lhs, const RhsView& rhsView, const typename Dest::Scalar& alpha)\n  {\n    typedef typename RhsView::_MatrixTypeNested Rhs;\n    typedef typename nested_eval<Lhs,Dynamic>::type LhsNested;\n    typedef typename nested_eval<Rhs,Dynamic>::type RhsNested;\n    LhsNested lhsNested(lhs);\n    RhsNested rhsNested(rhsView.matrix());\n    \n    // transpose everything\n    Transpose<Dest> dstT(dst);\n    internal::sparse_selfadjoint_time_dense_product<RhsView::TransposeMode>(rhsNested.transpose(), lhsNested.transpose(), dstT, alpha);\n  }\n};\n\n// NOTE: these two overloads are needed to evaluate the sparse selfadjoint view into a full sparse matrix\n// TODO: maybe the copy could be handled by generic_product_impl so that these overloads would not be needed anymore\n\ntemplate<typename LhsView, typename Rhs, int ProductTag>\nstruct product_evaluator<Product<LhsView, Rhs, DefaultProduct>, ProductTag, SparseSelfAdjointShape, SparseShape>\n  : public evaluator<typename Product<typename Rhs::PlainObject, Rhs, DefaultProduct>::PlainObject>\n{\n  typedef Product<LhsView, Rhs, DefaultProduct> XprType;\n  typedef typename XprType::PlainObject PlainObject;\n  typedef evaluator<PlainObject> Base;\n\n  product_evaluator(const XprType& xpr)\n    : m_lhs(xpr.lhs()), m_result(xpr.rows(), xpr.cols())\n  {\n    ::new (static_cast<Base*>(this)) Base(m_result);\n    generic_product_impl<typename Rhs::PlainObject, Rhs, SparseShape, SparseShape, ProductTag>::evalTo(m_result, m_lhs, xpr.rhs());\n  }\n  \nprotected:\n  typename Rhs::PlainObject m_lhs;\n  PlainObject m_result;\n};\n\ntemplate<typename Lhs, typename RhsView, int ProductTag>\nstruct product_evaluator<Product<Lhs, RhsView, DefaultProduct>, ProductTag, SparseShape, SparseSelfAdjointShape>\n  : public evaluator<typename Product<Lhs, typename Lhs::PlainObject, DefaultProduct>::PlainObject>\n{\n  typedef Product<Lhs, RhsView, DefaultProduct> XprType;\n  typedef typename XprType::PlainObject PlainObject;\n  typedef evaluator<PlainObject> Base;\n\n  product_evaluator(const XprType& xpr)\n    : m_rhs(xpr.rhs()), m_result(xpr.rows(), xpr.cols())\n  {\n    ::new (static_cast<Base*>(this)) Base(m_result);\n    generic_product_impl<Lhs, typename Lhs::PlainObject, SparseShape, SparseShape, ProductTag>::evalTo(m_result, xpr.lhs(), m_rhs);\n  }\n  \nprotected:\n  typename Lhs::PlainObject m_rhs;\n  PlainObject m_result;\n};\n\n} // namespace internal\n\n/***************************************************************************\n* Implementation of symmetric copies and permutations\n***************************************************************************/\nnamespace internal {\n\ntemplate<int Mode,typename MatrixType,int DestOrder>\nvoid permute_symm_to_fullsymm(const MatrixType& mat, SparseMatrix<typename MatrixType::Scalar,DestOrder,typename MatrixType::StorageIndex>& _dest, const typename MatrixType::StorageIndex* perm)\n{\n  typedef typename MatrixType::StorageIndex StorageIndex;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef SparseMatrix<Scalar,DestOrder,StorageIndex> Dest;\n  typedef Matrix<StorageIndex,Dynamic,1> VectorI;\n  typedef evaluator<MatrixType> MatEval;\n  typedef typename evaluator<MatrixType>::InnerIterator MatIterator;\n  \n  MatEval matEval(mat);\n  Dest& dest(_dest.derived());\n  enum {\n    StorageOrderMatch = int(Dest::IsRowMajor) == int(MatrixType::IsRowMajor)\n  };\n  \n  Index size = mat.rows();\n  VectorI count;\n  count.resize(size);\n  count.setZero();\n  dest.resize(size,size);\n  for(Index j = 0; j<size; ++j)\n  {\n    Index jp = perm ? perm[j] : j;\n    for(MatIterator it(matEval,j); it; ++it)\n    {\n      Index i = it.index();\n      Index r = it.row();\n      Index c = it.col();\n      Index ip = perm ? perm[i] : i;\n      if(Mode==(Upper|Lower))\n        count[StorageOrderMatch ? jp : ip]++;\n      else if(r==c)\n        count[ip]++;\n      else if(( Mode==Lower && r>c) || ( Mode==Upper && r<c))\n      {\n        count[ip]++;\n        count[jp]++;\n      }\n    }\n  }\n  Index nnz = count.sum();\n  \n  // reserve space\n  dest.resizeNonZeros(nnz);\n  dest.outerIndexPtr()[0] = 0;\n  for(Index j=0; j<size; ++j)\n    dest.outerIndexPtr()[j+1] = dest.outerIndexPtr()[j] + count[j];\n  for(Index j=0; j<size; ++j)\n    count[j] = dest.outerIndexPtr()[j];\n  \n  // copy data\n  for(StorageIndex j = 0; j<size; ++j)\n  {\n    for(MatIterator it(matEval,j); it; ++it)\n    {\n      StorageIndex i = internal::convert_index<StorageIndex>(it.index());\n      Index r = it.row();\n      Index c = it.col();\n      \n      StorageIndex jp = perm ? perm[j] : j;\n      StorageIndex ip = perm ? perm[i] : i;\n      \n      if(Mode==(Upper|Lower))\n      {\n        Index k = count[StorageOrderMatch ? jp : ip]++;\n        dest.innerIndexPtr()[k] = StorageOrderMatch ? ip : jp;\n        dest.valuePtr()[k] = it.value();\n      }\n      else if(r==c)\n      {\n        Index k = count[ip]++;\n        dest.innerIndexPtr()[k] = ip;\n        dest.valuePtr()[k] = it.value();\n      }\n      else if(( (Mode&Lower)==Lower && r>c) || ( (Mode&Upper)==Upper && r<c))\n      {\n        if(!StorageOrderMatch)\n          std::swap(ip,jp);\n        Index k = count[jp]++;\n        dest.innerIndexPtr()[k] = ip;\n        dest.valuePtr()[k] = it.value();\n        k = count[ip]++;\n        dest.innerIndexPtr()[k] = jp;\n        dest.valuePtr()[k] = numext::conj(it.value());\n      }\n    }\n  }\n}\n\ntemplate<int _SrcMode,int _DstMode,typename MatrixType,int DstOrder>\nvoid permute_symm_to_symm(const MatrixType& mat, SparseMatrix<typename MatrixType::Scalar,DstOrder,typename MatrixType::StorageIndex>& _dest, const typename MatrixType::StorageIndex* perm)\n{\n  typedef typename MatrixType::StorageIndex StorageIndex;\n  typedef typename MatrixType::Scalar Scalar;\n  SparseMatrix<Scalar,DstOrder,StorageIndex>& dest(_dest.derived());\n  typedef Matrix<StorageIndex,Dynamic,1> VectorI;\n  typedef evaluator<MatrixType> MatEval;\n  typedef typename evaluator<MatrixType>::InnerIterator MatIterator;\n\n  enum {\n    SrcOrder = MatrixType::IsRowMajor ? RowMajor : ColMajor,\n    StorageOrderMatch = int(SrcOrder) == int(DstOrder),\n    DstMode = DstOrder==RowMajor ? (_DstMode==Upper ? Lower : Upper) : _DstMode,\n    SrcMode = SrcOrder==RowMajor ? (_SrcMode==Upper ? Lower : Upper) : _SrcMode\n  };\n\n  MatEval matEval(mat);\n  \n  Index size = mat.rows();\n  VectorI count(size);\n  count.setZero();\n  dest.resize(size,size);\n  for(StorageIndex j = 0; j<size; ++j)\n  {\n    StorageIndex jp = perm ? perm[j] : j;\n    for(MatIterator it(matEval,j); it; ++it)\n    {\n      StorageIndex i = it.index();\n      if((int(SrcMode)==int(Lower) && i<j) || (int(SrcMode)==int(Upper) && i>j))\n        continue;\n                  \n      StorageIndex ip = perm ? perm[i] : i;\n      count[int(DstMode)==int(Lower) ? (std::min)(ip,jp) : (std::max)(ip,jp)]++;\n    }\n  }\n  dest.outerIndexPtr()[0] = 0;\n  for(Index j=0; j<size; ++j)\n    dest.outerIndexPtr()[j+1] = dest.outerIndexPtr()[j] + count[j];\n  dest.resizeNonZeros(dest.outerIndexPtr()[size]);\n  for(Index j=0; j<size; ++j)\n    count[j] = dest.outerIndexPtr()[j];\n  \n  for(StorageIndex j = 0; j<size; ++j)\n  {\n    \n    for(MatIterator it(matEval,j); it; ++it)\n    {\n      StorageIndex i = it.index();\n      if((int(SrcMode)==int(Lower) && i<j) || (int(SrcMode)==int(Upper) && i>j))\n        continue;\n                  \n      StorageIndex jp = perm ? perm[j] : j;\n      StorageIndex ip = perm? perm[i] : i;\n      \n      Index k = count[int(DstMode)==int(Lower) ? (std::min)(ip,jp) : (std::max)(ip,jp)]++;\n      dest.innerIndexPtr()[k] = int(DstMode)==int(Lower) ? (std::max)(ip,jp) : (std::min)(ip,jp);\n      \n      if(!StorageOrderMatch) std::swap(ip,jp);\n      if( ((int(DstMode)==int(Lower) && ip<jp) || (int(DstMode)==int(Upper) && ip>jp)))\n        dest.valuePtr()[k] = numext::conj(it.value());\n      else\n        dest.valuePtr()[k] = it.value();\n    }\n  }\n}\n\n}\n\n// TODO implement twists in a more evaluator friendly fashion\n\nnamespace internal {\n\ntemplate<typename MatrixType, int Mode>\nstruct traits<SparseSymmetricPermutationProduct<MatrixType,Mode> > : traits<MatrixType> {\n};\n\n}\n\ntemplate<typename MatrixType,int Mode>\nclass SparseSymmetricPermutationProduct\n  : public EigenBase<SparseSymmetricPermutationProduct<MatrixType,Mode> >\n{\n  public:\n    typedef typename MatrixType::Scalar Scalar;\n    typedef typename MatrixType::StorageIndex StorageIndex;\n    enum {\n      RowsAtCompileTime = internal::traits<SparseSymmetricPermutationProduct>::RowsAtCompileTime,\n      ColsAtCompileTime = internal::traits<SparseSymmetricPermutationProduct>::ColsAtCompileTime\n    };\n  protected:\n    typedef PermutationMatrix<Dynamic,Dynamic,StorageIndex> Perm;\n  public:\n    typedef Matrix<StorageIndex,Dynamic,1> VectorI;\n    typedef typename MatrixType::Nested MatrixTypeNested;\n    typedef typename internal::remove_all<MatrixTypeNested>::type NestedExpression;\n    \n    SparseSymmetricPermutationProduct(const MatrixType& mat, const Perm& perm)\n      : m_matrix(mat), m_perm(perm)\n    {}\n    \n    inline Index rows() const { return m_matrix.rows(); }\n    inline Index cols() const { return m_matrix.cols(); }\n        \n    const NestedExpression& matrix() const { return m_matrix; }\n    const Perm& perm() const { return m_perm; }\n    \n  protected:\n    MatrixTypeNested m_matrix;\n    const Perm& m_perm;\n\n};\n\nnamespace internal {\n  \ntemplate<typename DstXprType, typename MatrixType, int Mode, typename Scalar>\nstruct Assignment<DstXprType, SparseSymmetricPermutationProduct<MatrixType,Mode>, internal::assign_op<Scalar,typename MatrixType::Scalar>, Sparse2Sparse>\n{\n  typedef SparseSymmetricPermutationProduct<MatrixType,Mode> SrcXprType;\n  typedef typename DstXprType::StorageIndex DstIndex;\n  template<int Options>\n  static void run(SparseMatrix<Scalar,Options,DstIndex> &dst, const SrcXprType &src, const internal::assign_op<Scalar,typename MatrixType::Scalar> &)\n  {\n    // internal::permute_symm_to_fullsymm<Mode>(m_matrix,_dest,m_perm.indices().data());\n    SparseMatrix<Scalar,(Options&RowMajor)==RowMajor ? ColMajor : RowMajor, DstIndex> tmp;\n    internal::permute_symm_to_fullsymm<Mode>(src.matrix(),tmp,src.perm().indices().data());\n    dst = tmp;\n  }\n  \n  template<typename DestType,unsigned int DestMode>\n  static void run(SparseSelfAdjointView<DestType,DestMode>& dst, const SrcXprType &src, const internal::assign_op<Scalar,typename MatrixType::Scalar> &)\n  {\n    internal::permute_symm_to_symm<Mode,DestMode>(src.matrix(),dst.matrix(),src.perm().indices().data());\n  }\n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_SPARSE_SELFADJOINTVIEW_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseCore/SparseSolverBase.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSESOLVERBASE_H\n#define EIGEN_SPARSESOLVERBASE_H\n\nnamespace Eigen { \n\nnamespace internal {\n\n  /** \\internal\n  * Helper functions to solve with a sparse right-hand-side and result.\n  * The rhs is decomposed into small vertical panels which are solved through dense temporaries.\n  */\ntemplate<typename Decomposition, typename Rhs, typename Dest>\ntypename enable_if<Rhs::ColsAtCompileTime!=1 && Dest::ColsAtCompileTime!=1>::type\nsolve_sparse_through_dense_panels(const Decomposition &dec, const Rhs& rhs, Dest &dest)\n{\n  EIGEN_STATIC_ASSERT((Dest::Flags&RowMajorBit)==0,THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);\n  typedef typename Dest::Scalar DestScalar;\n  // we process the sparse rhs per block of NbColsAtOnce columns temporarily stored into a dense matrix.\n  static const Index NbColsAtOnce = 4;\n  Index rhsCols = rhs.cols();\n  Index size = rhs.rows();\n  // the temporary matrices do not need more columns than NbColsAtOnce:\n  Index tmpCols = (std::min)(rhsCols, NbColsAtOnce); \n  Eigen::Matrix<DestScalar,Dynamic,Dynamic> tmp(size,tmpCols);\n  Eigen::Matrix<DestScalar,Dynamic,Dynamic> tmpX(size,tmpCols);\n  for(Index k=0; k<rhsCols; k+=NbColsAtOnce)\n  {\n    Index actualCols = std::min<Index>(rhsCols-k, NbColsAtOnce);\n    tmp.leftCols(actualCols) = rhs.middleCols(k,actualCols);\n    tmpX.leftCols(actualCols) = dec.solve(tmp.leftCols(actualCols));\n    dest.middleCols(k,actualCols) = tmpX.leftCols(actualCols).sparseView();\n  }\n}\n\n// Overload for vector as rhs\ntemplate<typename Decomposition, typename Rhs, typename Dest>\ntypename enable_if<Rhs::ColsAtCompileTime==1 || Dest::ColsAtCompileTime==1>::type\nsolve_sparse_through_dense_panels(const Decomposition &dec, const Rhs& rhs, Dest &dest)\n{\n  typedef typename Dest::Scalar DestScalar;\n  Index size = rhs.rows();\n  Eigen::Matrix<DestScalar,Dynamic,1> rhs_dense(rhs);\n  Eigen::Matrix<DestScalar,Dynamic,1> dest_dense(size);\n  dest_dense = dec.solve(rhs_dense);\n  dest = dest_dense.sparseView();\n}\n\n} // end namespace internal\n\n/** \\class SparseSolverBase\n  * \\ingroup SparseCore_Module\n  * \\brief A base class for sparse solvers\n  *\n  * \\tparam Derived the actual type of the solver.\n  *\n  */\ntemplate<typename Derived>\nclass SparseSolverBase : internal::noncopyable\n{\n  public:\n\n    /** Default constructor */\n    SparseSolverBase()\n      : m_isInitialized(false)\n    {}\n\n    ~SparseSolverBase()\n    {}\n\n    Derived& derived() { return *static_cast<Derived*>(this); }\n    const Derived& derived() const { return *static_cast<const Derived*>(this); }\n    \n    /** \\returns an expression of the solution x of \\f$ A x = b \\f$ using the current decomposition of A.\n      *\n      * \\sa compute()\n      */\n    template<typename Rhs>\n    inline const Solve<Derived, Rhs>\n    solve(const MatrixBase<Rhs>& b) const\n    {\n      eigen_assert(m_isInitialized && \"Solver is not initialized.\");\n      eigen_assert(derived().rows()==b.rows() && \"solve(): invalid number of rows of the right hand side matrix b\");\n      return Solve<Derived, Rhs>(derived(), b.derived());\n    }\n    \n    /** \\returns an expression of the solution x of \\f$ A x = b \\f$ using the current decomposition of A.\n      *\n      * \\sa compute()\n      */\n    template<typename Rhs>\n    inline const Solve<Derived, Rhs>\n    solve(const SparseMatrixBase<Rhs>& b) const\n    {\n      eigen_assert(m_isInitialized && \"Solver is not initialized.\");\n      eigen_assert(derived().rows()==b.rows() && \"solve(): invalid number of rows of the right hand side matrix b\");\n      return Solve<Derived, Rhs>(derived(), b.derived());\n    }\n    \n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    /** \\internal default implementation of solving with a sparse rhs */\n    template<typename Rhs,typename Dest>\n    void _solve_impl(const SparseMatrixBase<Rhs> &b, SparseMatrixBase<Dest> &dest) const\n    {\n      internal::solve_sparse_through_dense_panels(derived(), b.derived(), dest.derived());\n    }\n    #endif // EIGEN_PARSED_BY_DOXYGEN\n\n  protected:\n    \n    mutable bool m_isInitialized;\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_SPARSESOLVERBASE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseCore/SparseSparseProductWithPruning.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSESPARSEPRODUCTWITHPRUNING_H\n#define EIGEN_SPARSESPARSEPRODUCTWITHPRUNING_H\n\nnamespace Eigen { \n\nnamespace internal {\n\n\n// perform a pseudo in-place sparse * sparse product assuming all matrices are col major\ntemplate<typename Lhs, typename Rhs, typename ResultType>\nstatic void sparse_sparse_product_with_pruning_impl(const Lhs& lhs, const Rhs& rhs, ResultType& res, const typename ResultType::RealScalar& tolerance)\n{\n  // return sparse_sparse_product_with_pruning_impl2(lhs,rhs,res);\n\n  typedef typename remove_all<Rhs>::type::Scalar RhsScalar;\n  typedef typename remove_all<ResultType>::type::Scalar ResScalar;\n  typedef typename remove_all<Lhs>::type::StorageIndex StorageIndex;\n\n  // make sure to call innerSize/outerSize since we fake the storage order.\n  Index rows = lhs.innerSize();\n  Index cols = rhs.outerSize();\n  //Index size = lhs.outerSize();\n  eigen_assert(lhs.outerSize() == rhs.innerSize());\n\n  // allocate a temporary buffer\n  AmbiVector<ResScalar,StorageIndex> tempVector(rows);\n\n  // mimics a resizeByInnerOuter:\n  if(ResultType::IsRowMajor)\n    res.resize(cols, rows);\n  else\n    res.resize(rows, cols);\n  \n  evaluator<Lhs> lhsEval(lhs);\n  evaluator<Rhs> rhsEval(rhs);\n  \n  // estimate the number of non zero entries\n  // given a rhs column containing Y non zeros, we assume that the respective Y columns\n  // of the lhs differs in average of one non zeros, thus the number of non zeros for\n  // the product of a rhs column with the lhs is X+Y where X is the average number of non zero\n  // per column of the lhs.\n  // Therefore, we have nnz(lhs*rhs) = nnz(lhs) + nnz(rhs)\n  Index estimated_nnz_prod = lhsEval.nonZerosEstimate() + rhsEval.nonZerosEstimate();\n\n  res.reserve(estimated_nnz_prod);\n  double ratioColRes = double(estimated_nnz_prod)/(double(lhs.rows())*double(rhs.cols()));\n  for (Index j=0; j<cols; ++j)\n  {\n    // FIXME:\n    //double ratioColRes = (double(rhs.innerVector(j).nonZeros()) + double(lhs.nonZeros())/double(lhs.cols()))/double(lhs.rows());\n    // let's do a more accurate determination of the nnz ratio for the current column j of res\n    tempVector.init(ratioColRes);\n    tempVector.setZero();\n    for (typename evaluator<Rhs>::InnerIterator rhsIt(rhsEval, j); rhsIt; ++rhsIt)\n    {\n      // FIXME should be written like this: tmp += rhsIt.value() * lhs.col(rhsIt.index())\n      tempVector.restart();\n      RhsScalar x = rhsIt.value();\n      for (typename evaluator<Lhs>::InnerIterator lhsIt(lhsEval, rhsIt.index()); lhsIt; ++lhsIt)\n      {\n        tempVector.coeffRef(lhsIt.index()) += lhsIt.value() * x;\n      }\n    }\n    res.startVec(j);\n    for (typename AmbiVector<ResScalar,StorageIndex>::Iterator it(tempVector,tolerance); it; ++it)\n      res.insertBackByOuterInner(j,it.index()) = it.value();\n  }\n  res.finalize();\n}\n\ntemplate<typename Lhs, typename Rhs, typename ResultType,\n  int LhsStorageOrder = traits<Lhs>::Flags&RowMajorBit,\n  int RhsStorageOrder = traits<Rhs>::Flags&RowMajorBit,\n  int ResStorageOrder = traits<ResultType>::Flags&RowMajorBit>\nstruct sparse_sparse_product_with_pruning_selector;\n\ntemplate<typename Lhs, typename Rhs, typename ResultType>\nstruct sparse_sparse_product_with_pruning_selector<Lhs,Rhs,ResultType,ColMajor,ColMajor,ColMajor>\n{\n  typedef typename ResultType::RealScalar RealScalar;\n\n  static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res, const RealScalar& tolerance)\n  {\n    typename remove_all<ResultType>::type _res(res.rows(), res.cols());\n    internal::sparse_sparse_product_with_pruning_impl<Lhs,Rhs,ResultType>(lhs, rhs, _res, tolerance);\n    res.swap(_res);\n  }\n};\n\ntemplate<typename Lhs, typename Rhs, typename ResultType>\nstruct sparse_sparse_product_with_pruning_selector<Lhs,Rhs,ResultType,ColMajor,ColMajor,RowMajor>\n{\n  typedef typename ResultType::RealScalar RealScalar;\n  static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res, const RealScalar& tolerance)\n  {\n    // we need a col-major matrix to hold the result\n    typedef SparseMatrix<typename ResultType::Scalar,ColMajor,typename ResultType::StorageIndex> SparseTemporaryType;\n    SparseTemporaryType _res(res.rows(), res.cols());\n    internal::sparse_sparse_product_with_pruning_impl<Lhs,Rhs,SparseTemporaryType>(lhs, rhs, _res, tolerance);\n    res = _res;\n  }\n};\n\ntemplate<typename Lhs, typename Rhs, typename ResultType>\nstruct sparse_sparse_product_with_pruning_selector<Lhs,Rhs,ResultType,RowMajor,RowMajor,RowMajor>\n{\n  typedef typename ResultType::RealScalar RealScalar;\n  static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res, const RealScalar& tolerance)\n  {\n    // let's transpose the product to get a column x column product\n    typename remove_all<ResultType>::type _res(res.rows(), res.cols());\n    internal::sparse_sparse_product_with_pruning_impl<Rhs,Lhs,ResultType>(rhs, lhs, _res, tolerance);\n    res.swap(_res);\n  }\n};\n\ntemplate<typename Lhs, typename Rhs, typename ResultType>\nstruct sparse_sparse_product_with_pruning_selector<Lhs,Rhs,ResultType,RowMajor,RowMajor,ColMajor>\n{\n  typedef typename ResultType::RealScalar RealScalar;\n  static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res, const RealScalar& tolerance)\n  {\n    typedef SparseMatrix<typename Lhs::Scalar,ColMajor,typename Lhs::StorageIndex> ColMajorMatrixLhs;\n    typedef SparseMatrix<typename Rhs::Scalar,ColMajor,typename Lhs::StorageIndex> ColMajorMatrixRhs;\n    ColMajorMatrixLhs colLhs(lhs);\n    ColMajorMatrixRhs colRhs(rhs);\n    internal::sparse_sparse_product_with_pruning_impl<ColMajorMatrixLhs,ColMajorMatrixRhs,ResultType>(colLhs, colRhs, res, tolerance);\n\n    // let's transpose the product to get a column x column product\n//     typedef SparseMatrix<typename ResultType::Scalar> SparseTemporaryType;\n//     SparseTemporaryType _res(res.cols(), res.rows());\n//     sparse_sparse_product_with_pruning_impl<Rhs,Lhs,SparseTemporaryType>(rhs, lhs, _res);\n//     res = _res.transpose();\n  }\n};\n\ntemplate<typename Lhs, typename Rhs, typename ResultType>\nstruct sparse_sparse_product_with_pruning_selector<Lhs,Rhs,ResultType,ColMajor,RowMajor,RowMajor>\n{\n  typedef typename ResultType::RealScalar RealScalar;\n  static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res, const RealScalar& tolerance)\n  {\n    typedef SparseMatrix<typename Lhs::Scalar,RowMajor,typename Lhs::StorageIndex> RowMajorMatrixLhs;\n    RowMajorMatrixLhs rowLhs(lhs);\n    sparse_sparse_product_with_pruning_selector<RowMajorMatrixLhs,Rhs,ResultType,RowMajor,RowMajor>(rowLhs,rhs,res,tolerance);\n  }\n};\n\ntemplate<typename Lhs, typename Rhs, typename ResultType>\nstruct sparse_sparse_product_with_pruning_selector<Lhs,Rhs,ResultType,RowMajor,ColMajor,RowMajor>\n{\n  typedef typename ResultType::RealScalar RealScalar;\n  static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res, const RealScalar& tolerance)\n  {\n    typedef SparseMatrix<typename Rhs::Scalar,RowMajor,typename Lhs::StorageIndex> RowMajorMatrixRhs;\n    RowMajorMatrixRhs rowRhs(rhs);\n    sparse_sparse_product_with_pruning_selector<Lhs,RowMajorMatrixRhs,ResultType,RowMajor,RowMajor,RowMajor>(lhs,rowRhs,res,tolerance);\n  }\n};\n\ntemplate<typename Lhs, typename Rhs, typename ResultType>\nstruct sparse_sparse_product_with_pruning_selector<Lhs,Rhs,ResultType,ColMajor,RowMajor,ColMajor>\n{\n  typedef typename ResultType::RealScalar RealScalar;\n  static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res, const RealScalar& tolerance)\n  {\n    typedef SparseMatrix<typename Rhs::Scalar,ColMajor,typename Lhs::StorageIndex> ColMajorMatrixRhs;\n    ColMajorMatrixRhs colRhs(rhs);\n    internal::sparse_sparse_product_with_pruning_impl<Lhs,ColMajorMatrixRhs,ResultType>(lhs, colRhs, res, tolerance);\n  }\n};\n\ntemplate<typename Lhs, typename Rhs, typename ResultType>\nstruct sparse_sparse_product_with_pruning_selector<Lhs,Rhs,ResultType,RowMajor,ColMajor,ColMajor>\n{\n  typedef typename ResultType::RealScalar RealScalar;\n  static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res, const RealScalar& tolerance)\n  {\n    typedef SparseMatrix<typename Lhs::Scalar,ColMajor,typename Lhs::StorageIndex> ColMajorMatrixLhs;\n    ColMajorMatrixLhs colLhs(lhs);\n    internal::sparse_sparse_product_with_pruning_impl<ColMajorMatrixLhs,Rhs,ResultType>(colLhs, rhs, res, tolerance);\n  }\n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_SPARSESPARSEPRODUCTWITHPRUNING_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseCore/SparseTranspose.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSETRANSPOSE_H\n#define EIGEN_SPARSETRANSPOSE_H\n\nnamespace Eigen { \n\nnamespace internal {\n  template<typename MatrixType,int CompressedAccess=int(MatrixType::Flags&CompressedAccessBit)>\n  class SparseTransposeImpl\n    : public SparseMatrixBase<Transpose<MatrixType> >\n  {};\n  \n  template<typename MatrixType>\n  class SparseTransposeImpl<MatrixType,CompressedAccessBit>\n    : public SparseCompressedBase<Transpose<MatrixType> >\n  {\n    typedef SparseCompressedBase<Transpose<MatrixType> > Base;\n  public:\n    using Base::derived;\n    typedef typename Base::Scalar Scalar;\n    typedef typename Base::StorageIndex StorageIndex;\n\n    inline Index nonZeros() const { return derived().nestedExpression().nonZeros(); }\n    \n    inline const Scalar* valuePtr() const { return derived().nestedExpression().valuePtr(); }\n    inline const StorageIndex* innerIndexPtr() const { return derived().nestedExpression().innerIndexPtr(); }\n    inline const StorageIndex* outerIndexPtr() const { return derived().nestedExpression().outerIndexPtr(); }\n    inline const StorageIndex* innerNonZeroPtr() const { return derived().nestedExpression().innerNonZeroPtr(); }\n\n    inline Scalar* valuePtr() { return derived().nestedExpression().valuePtr(); }\n    inline StorageIndex* innerIndexPtr() { return derived().nestedExpression().innerIndexPtr(); }\n    inline StorageIndex* outerIndexPtr() { return derived().nestedExpression().outerIndexPtr(); }\n    inline StorageIndex* innerNonZeroPtr() { return derived().nestedExpression().innerNonZeroPtr(); }\n  };\n}\n  \ntemplate<typename MatrixType> class TransposeImpl<MatrixType,Sparse>\n  : public internal::SparseTransposeImpl<MatrixType>\n{\n  protected:\n    typedef internal::SparseTransposeImpl<MatrixType> Base;\n};\n\nnamespace internal {\n  \ntemplate<typename ArgType>\nstruct unary_evaluator<Transpose<ArgType>, IteratorBased>\n  : public evaluator_base<Transpose<ArgType> >\n{\n    typedef typename evaluator<ArgType>::InnerIterator        EvalIterator;\n  public:\n    typedef Transpose<ArgType> XprType;\n    \n    inline Index nonZerosEstimate() const {\n      return m_argImpl.nonZerosEstimate();\n    }\n\n    class InnerIterator : public EvalIterator\n    {\n    public:\n      EIGEN_STRONG_INLINE InnerIterator(const unary_evaluator& unaryOp, Index outer)\n        : EvalIterator(unaryOp.m_argImpl,outer)\n      {}\n      \n      Index row() const { return EvalIterator::col(); }\n      Index col() const { return EvalIterator::row(); }\n    };\n    \n    enum {\n      CoeffReadCost = evaluator<ArgType>::CoeffReadCost,\n      Flags = XprType::Flags\n    };\n    \n    explicit unary_evaluator(const XprType& op) :m_argImpl(op.nestedExpression()) {}\n\n  protected:\n    evaluator<ArgType> m_argImpl;\n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_SPARSETRANSPOSE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseCore/SparseTriangularView.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009-2015 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSE_TRIANGULARVIEW_H\n#define EIGEN_SPARSE_TRIANGULARVIEW_H\n\nnamespace Eigen {\n\n/** \\ingroup SparseCore_Module\n  *\n  * \\brief Base class for a triangular part in a \\b sparse matrix\n  *\n  * This class is an abstract base class of class TriangularView, and objects of type TriangularViewImpl cannot be instantiated.\n  * It extends class TriangularView with additional methods which are available for sparse expressions only.\n  *\n  * \\sa class TriangularView, SparseMatrixBase::triangularView()\n  */\ntemplate<typename MatrixType, unsigned int Mode> class TriangularViewImpl<MatrixType,Mode,Sparse>\n  : public SparseMatrixBase<TriangularView<MatrixType,Mode> >\n{\n    enum { SkipFirst = ((Mode&Lower) && !(MatrixType::Flags&RowMajorBit))\n                    || ((Mode&Upper) &&  (MatrixType::Flags&RowMajorBit)),\n           SkipLast = !SkipFirst,\n           SkipDiag = (Mode&ZeroDiag) ? 1 : 0,\n           HasUnitDiag = (Mode&UnitDiag) ? 1 : 0\n    };\n    \n    typedef TriangularView<MatrixType,Mode> TriangularViewType;\n    \n  protected:\n    // dummy solve function to make TriangularView happy.\n    void solve() const;\n\n    typedef SparseMatrixBase<TriangularViewType> Base;\n  public:\n    \n    EIGEN_SPARSE_PUBLIC_INTERFACE(TriangularViewType)\n    \n    typedef typename MatrixType::Nested MatrixTypeNested;\n    typedef typename internal::remove_reference<MatrixTypeNested>::type MatrixTypeNestedNonRef;\n    typedef typename internal::remove_all<MatrixTypeNested>::type MatrixTypeNestedCleaned;\n\n    template<typename RhsType, typename DstType>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE void _solve_impl(const RhsType &rhs, DstType &dst) const {\n      if(!(internal::is_same<RhsType,DstType>::value && internal::extract_data(dst) == internal::extract_data(rhs)))\n        dst = rhs;\n      this->solveInPlace(dst);\n    }\n\n    /** Applies the inverse of \\c *this to the dense vector or matrix \\a other, \"in-place\" */\n    template<typename OtherDerived> void solveInPlace(MatrixBase<OtherDerived>& other) const;\n\n    /** Applies the inverse of \\c *this to the sparse vector or matrix \\a other, \"in-place\" */\n    template<typename OtherDerived> void solveInPlace(SparseMatrixBase<OtherDerived>& other) const;\n  \n};\n\nnamespace internal {\n\ntemplate<typename ArgType, unsigned int Mode>\nstruct unary_evaluator<TriangularView<ArgType,Mode>, IteratorBased>\n : evaluator_base<TriangularView<ArgType,Mode> >\n{\n  typedef TriangularView<ArgType,Mode> XprType;\n  \nprotected:\n  \n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::StorageIndex StorageIndex;\n  typedef typename evaluator<ArgType>::InnerIterator EvalIterator;\n  \n  enum { SkipFirst = ((Mode&Lower) && !(ArgType::Flags&RowMajorBit))\n                    || ((Mode&Upper) &&  (ArgType::Flags&RowMajorBit)),\n         SkipLast = !SkipFirst,\n         SkipDiag = (Mode&ZeroDiag) ? 1 : 0,\n         HasUnitDiag = (Mode&UnitDiag) ? 1 : 0\n  };\n  \npublic:\n  \n  enum {\n    CoeffReadCost = evaluator<ArgType>::CoeffReadCost,\n    Flags = XprType::Flags\n  };\n    \n  explicit unary_evaluator(const XprType &xpr) : m_argImpl(xpr.nestedExpression()), m_arg(xpr.nestedExpression()) {}\n  \n  inline Index nonZerosEstimate() const {\n    return m_argImpl.nonZerosEstimate();\n  }\n  \n  class InnerIterator : public EvalIterator\n  {\n      typedef EvalIterator Base;\n    public:\n\n      EIGEN_STRONG_INLINE InnerIterator(const unary_evaluator& xprEval, Index outer)\n        : Base(xprEval.m_argImpl,outer), m_returnOne(false), m_containsDiag(Base::outer()<xprEval.m_arg.innerSize())\n      {\n        if(SkipFirst)\n        {\n          while((*this) && ((HasUnitDiag||SkipDiag)  ? this->index()<=outer : this->index()<outer))\n            Base::operator++();\n          if(HasUnitDiag)\n            m_returnOne = m_containsDiag;\n        }\n        else if(HasUnitDiag && ((!Base::operator bool()) || Base::index()>=Base::outer()))\n        {\n          if((!SkipFirst) && Base::operator bool())\n            Base::operator++();\n          m_returnOne = m_containsDiag;\n        }\n      }\n\n      EIGEN_STRONG_INLINE InnerIterator& operator++()\n      {\n        if(HasUnitDiag && m_returnOne)\n          m_returnOne = false;\n        else\n        {\n          Base::operator++();\n          if(HasUnitDiag && (!SkipFirst) && ((!Base::operator bool()) || Base::index()>=Base::outer()))\n          {\n            if((!SkipFirst) && Base::operator bool())\n              Base::operator++();\n            m_returnOne = m_containsDiag;\n          }\n        }\n        return *this;\n      }\n      \n      EIGEN_STRONG_INLINE operator bool() const\n      {\n        if(HasUnitDiag && m_returnOne)\n          return true;\n        if(SkipFirst) return  Base::operator bool();\n        else\n        {\n          if (SkipDiag) return (Base::operator bool() && this->index() < this->outer());\n          else return (Base::operator bool() && this->index() <= this->outer());\n        }\n      }\n\n//       inline Index row() const { return (ArgType::Flags&RowMajorBit ? Base::outer() : this->index()); }\n//       inline Index col() const { return (ArgType::Flags&RowMajorBit ? this->index() : Base::outer()); }\n      inline StorageIndex index() const\n      {\n        if(HasUnitDiag && m_returnOne)  return internal::convert_index<StorageIndex>(Base::outer());\n        else                            return Base::index();\n      }\n      inline Scalar value() const\n      {\n        if(HasUnitDiag && m_returnOne)  return Scalar(1);\n        else                            return Base::value();\n      }\n\n    protected:\n      bool m_returnOne;\n      bool m_containsDiag;\n    private:\n      Scalar& valueRef();\n  };\n  \nprotected:\n  evaluator<ArgType> m_argImpl;\n  const ArgType& m_arg;\n};\n\n} // end namespace internal\n\ntemplate<typename Derived>\ntemplate<int Mode>\ninline const TriangularView<const Derived, Mode>\nSparseMatrixBase<Derived>::triangularView() const\n{\n  return TriangularView<const Derived, Mode>(derived());\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_SPARSE_TRIANGULARVIEW_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseCore/SparseUtil.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSEUTIL_H\n#define EIGEN_SPARSEUTIL_H\n\nnamespace Eigen { \n\n#ifdef NDEBUG\n#define EIGEN_DBG_SPARSE(X)\n#else\n#define EIGEN_DBG_SPARSE(X) X\n#endif\n\n#define EIGEN_SPARSE_INHERIT_ASSIGNMENT_OPERATOR(Derived, Op) \\\ntemplate<typename OtherDerived> \\\nEIGEN_STRONG_INLINE Derived& operator Op(const Eigen::SparseMatrixBase<OtherDerived>& other) \\\n{ \\\n  return Base::operator Op(other.derived()); \\\n} \\\nEIGEN_STRONG_INLINE Derived& operator Op(const Derived& other) \\\n{ \\\n  return Base::operator Op(other); \\\n}\n\n#define EIGEN_SPARSE_INHERIT_SCALAR_ASSIGNMENT_OPERATOR(Derived, Op) \\\ntemplate<typename Other> \\\nEIGEN_STRONG_INLINE Derived& operator Op(const Other& scalar) \\\n{ \\\n  return Base::operator Op(scalar); \\\n}\n\n#define EIGEN_SPARSE_INHERIT_ASSIGNMENT_OPERATORS(Derived) \\\nEIGEN_SPARSE_INHERIT_ASSIGNMENT_OPERATOR(Derived, =)\n\n\n#define EIGEN_SPARSE_PUBLIC_INTERFACE(Derived) \\\n  EIGEN_GENERIC_PUBLIC_INTERFACE(Derived)\n\n  \nconst int CoherentAccessPattern     = 0x1;\nconst int InnerRandomAccessPattern  = 0x2 | CoherentAccessPattern;\nconst int OuterRandomAccessPattern  = 0x4 | CoherentAccessPattern;\nconst int RandomAccessPattern       = 0x8 | OuterRandomAccessPattern | InnerRandomAccessPattern;\n\ntemplate<typename _Scalar, int _Flags = 0, typename _StorageIndex = int>  class SparseMatrix;\ntemplate<typename _Scalar, int _Flags = 0, typename _StorageIndex = int>  class DynamicSparseMatrix;\ntemplate<typename _Scalar, int _Flags = 0, typename _StorageIndex = int>  class SparseVector;\ntemplate<typename _Scalar, int _Flags = 0, typename _StorageIndex = int>  class MappedSparseMatrix;\n\ntemplate<typename MatrixType, unsigned int UpLo>  class SparseSelfAdjointView;\ntemplate<typename Lhs, typename Rhs>              class SparseDiagonalProduct;\ntemplate<typename MatrixType> class SparseView;\n\ntemplate<typename Lhs, typename Rhs>        class SparseSparseProduct;\ntemplate<typename Lhs, typename Rhs>        class SparseTimeDenseProduct;\ntemplate<typename Lhs, typename Rhs>        class DenseTimeSparseProduct;\ntemplate<typename Lhs, typename Rhs, bool Transpose> class SparseDenseOuterProduct;\n\ntemplate<typename Lhs, typename Rhs> struct SparseSparseProductReturnType;\ntemplate<typename Lhs, typename Rhs,\n         int InnerSize = EIGEN_SIZE_MIN_PREFER_FIXED(internal::traits<Lhs>::ColsAtCompileTime,internal::traits<Rhs>::RowsAtCompileTime)> struct DenseSparseProductReturnType;\n         \ntemplate<typename Lhs, typename Rhs,\n         int InnerSize = EIGEN_SIZE_MIN_PREFER_FIXED(internal::traits<Lhs>::ColsAtCompileTime,internal::traits<Rhs>::RowsAtCompileTime)> struct SparseDenseProductReturnType;\ntemplate<typename MatrixType,int UpLo> class SparseSymmetricPermutationProduct;\n\nnamespace internal {\n\ntemplate<typename T,int Rows,int Cols,int Flags> struct sparse_eval;\n\ntemplate<typename T> struct eval<T,Sparse>\n  : sparse_eval<T, traits<T>::RowsAtCompileTime,traits<T>::ColsAtCompileTime,traits<T>::Flags>\n{};\n\ntemplate<typename T,int Cols,int Flags> struct sparse_eval<T,1,Cols,Flags> {\n    typedef typename traits<T>::Scalar _Scalar;\n    typedef typename traits<T>::StorageIndex _StorageIndex;\n  public:\n    typedef SparseVector<_Scalar, RowMajor, _StorageIndex> type;\n};\n\ntemplate<typename T,int Rows,int Flags> struct sparse_eval<T,Rows,1,Flags> {\n    typedef typename traits<T>::Scalar _Scalar;\n    typedef typename traits<T>::StorageIndex _StorageIndex;\n  public:\n    typedef SparseVector<_Scalar, ColMajor, _StorageIndex> type;\n};\n\n// TODO this seems almost identical to plain_matrix_type<T, Sparse>\ntemplate<typename T,int Rows,int Cols,int Flags> struct sparse_eval {\n    typedef typename traits<T>::Scalar _Scalar;\n    typedef typename traits<T>::StorageIndex _StorageIndex;\n    enum { _Options = ((Flags&RowMajorBit)==RowMajorBit) ? RowMajor : ColMajor };\n  public:\n    typedef SparseMatrix<_Scalar, _Options, _StorageIndex> type;\n};\n\ntemplate<typename T,int Flags> struct sparse_eval<T,1,1,Flags> {\n    typedef typename traits<T>::Scalar _Scalar;\n  public:\n    typedef Matrix<_Scalar, 1, 1> type;\n};\n\ntemplate<typename T> struct plain_matrix_type<T,Sparse>\n{\n  typedef typename traits<T>::Scalar _Scalar;\n  typedef typename traits<T>::StorageIndex _StorageIndex;\n  enum { _Options = ((evaluator<T>::Flags&RowMajorBit)==RowMajorBit) ? RowMajor : ColMajor };\n  public:\n    typedef SparseMatrix<_Scalar, _Options, _StorageIndex> type;\n};\n\ntemplate<typename T>\nstruct plain_object_eval<T,Sparse>\n  : sparse_eval<T, traits<T>::RowsAtCompileTime,traits<T>::ColsAtCompileTime, evaluator<T>::Flags>\n{};\n\ntemplate<typename Decomposition, typename RhsType>\nstruct solve_traits<Decomposition,RhsType,Sparse>\n{\n  typedef typename sparse_eval<RhsType, RhsType::RowsAtCompileTime, RhsType::ColsAtCompileTime,traits<RhsType>::Flags>::type PlainObject;\n};\n\ntemplate<typename Derived>\nstruct generic_xpr_base<Derived, MatrixXpr, Sparse>\n{\n  typedef SparseMatrixBase<Derived> type;\n};\n\nstruct SparseTriangularShape  { static std::string debugName() { return \"SparseTriangularShape\"; } };\nstruct SparseSelfAdjointShape { static std::string debugName() { return \"SparseSelfAdjointShape\"; } };\n\ntemplate<> struct glue_shapes<SparseShape,SelfAdjointShape> { typedef SparseSelfAdjointShape type;  };\ntemplate<> struct glue_shapes<SparseShape,TriangularShape > { typedef SparseTriangularShape  type;  };\n\n} // end namespace internal\n\n/** \\ingroup SparseCore_Module\n  *\n  * \\class Triplet\n  *\n  * \\brief A small structure to hold a non zero as a triplet (i,j,value).\n  *\n  * \\sa SparseMatrix::setFromTriplets()\n  */\ntemplate<typename Scalar, typename StorageIndex=typename SparseMatrix<Scalar>::StorageIndex >\nclass Triplet\n{\npublic:\n  Triplet() : m_row(0), m_col(0), m_value(0) {}\n\n  Triplet(const StorageIndex& i, const StorageIndex& j, const Scalar& v = Scalar(0))\n    : m_row(i), m_col(j), m_value(v)\n  {}\n\n  /** \\returns the row index of the element */\n  const StorageIndex& row() const { return m_row; }\n\n  /** \\returns the column index of the element */\n  const StorageIndex& col() const { return m_col; }\n\n  /** \\returns the value of the element */\n  const Scalar& value() const { return m_value; }\nprotected:\n  StorageIndex m_row, m_col;\n  Scalar m_value;\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_SPARSEUTIL_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseCore/SparseVector.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSEVECTOR_H\n#define EIGEN_SPARSEVECTOR_H\n\nnamespace Eigen { \n\n/** \\ingroup SparseCore_Module\n  * \\class SparseVector\n  *\n  * \\brief a sparse vector class\n  *\n  * \\tparam _Scalar the scalar type, i.e. the type of the coefficients\n  *\n  * See http://www.netlib.org/linalg/html_templates/node91.html for details on the storage scheme.\n  *\n  * This class can be extended with the help of the plugin mechanism described on the page\n  * \\ref TopicCustomizing_Plugins by defining the preprocessor symbol \\c EIGEN_SPARSEVECTOR_PLUGIN.\n  */\n\nnamespace internal {\ntemplate<typename _Scalar, int _Options, typename _StorageIndex>\nstruct traits<SparseVector<_Scalar, _Options, _StorageIndex> >\n{\n  typedef _Scalar Scalar;\n  typedef _StorageIndex StorageIndex;\n  typedef Sparse StorageKind;\n  typedef MatrixXpr XprKind;\n  enum {\n    IsColVector = (_Options & RowMajorBit) ? 0 : 1,\n\n    RowsAtCompileTime = IsColVector ? Dynamic : 1,\n    ColsAtCompileTime = IsColVector ? 1 : Dynamic,\n    MaxRowsAtCompileTime = RowsAtCompileTime,\n    MaxColsAtCompileTime = ColsAtCompileTime,\n    Flags = _Options | NestByRefBit | LvalueBit | (IsColVector ? 0 : RowMajorBit) | CompressedAccessBit,\n    SupportedAccessPatterns = InnerRandomAccessPattern\n  };\n};\n\n// Sparse-Vector-Assignment kinds:\nenum {\n  SVA_RuntimeSwitch,\n  SVA_Inner,\n  SVA_Outer\n};\n\ntemplate< typename Dest, typename Src,\n          int AssignmentKind = !bool(Src::IsVectorAtCompileTime) ? SVA_RuntimeSwitch\n                             : Src::InnerSizeAtCompileTime==1 ? SVA_Outer\n                             : SVA_Inner>\nstruct sparse_vector_assign_selector;\n\n}\n\ntemplate<typename _Scalar, int _Options, typename _StorageIndex>\nclass SparseVector\n  : public SparseCompressedBase<SparseVector<_Scalar, _Options, _StorageIndex> >\n{\n    typedef SparseCompressedBase<SparseVector> Base;\n    using Base::convert_index;\n  public:\n    EIGEN_SPARSE_PUBLIC_INTERFACE(SparseVector)\n    EIGEN_SPARSE_INHERIT_ASSIGNMENT_OPERATOR(SparseVector, +=)\n    EIGEN_SPARSE_INHERIT_ASSIGNMENT_OPERATOR(SparseVector, -=)\n    \n    typedef internal::CompressedStorage<Scalar,StorageIndex> Storage;\n    enum { IsColVector = internal::traits<SparseVector>::IsColVector };\n    \n    enum {\n      Options = _Options\n    };\n    \n    EIGEN_STRONG_INLINE Index rows() const { return IsColVector ? m_size : 1; }\n    EIGEN_STRONG_INLINE Index cols() const { return IsColVector ? 1 : m_size; }\n    EIGEN_STRONG_INLINE Index innerSize() const { return m_size; }\n    EIGEN_STRONG_INLINE Index outerSize() const { return 1; }\n\n    EIGEN_STRONG_INLINE const Scalar* valuePtr() const { return m_data.valuePtr(); }\n    EIGEN_STRONG_INLINE Scalar* valuePtr() { return m_data.valuePtr(); }\n\n    EIGEN_STRONG_INLINE const StorageIndex* innerIndexPtr() const { return m_data.indexPtr(); }\n    EIGEN_STRONG_INLINE StorageIndex* innerIndexPtr() { return m_data.indexPtr(); }\n\n    inline const StorageIndex* outerIndexPtr() const { return 0; }\n    inline StorageIndex* outerIndexPtr() { return 0; }\n    inline const StorageIndex* innerNonZeroPtr() const { return 0; }\n    inline StorageIndex* innerNonZeroPtr() { return 0; }\n    \n    /** \\internal */\n    inline Storage& data() { return m_data; }\n    /** \\internal */\n    inline const Storage& data() const { return m_data; }\n\n    inline Scalar coeff(Index row, Index col) const\n    {\n      eigen_assert(IsColVector ? (col==0 && row>=0 && row<m_size) : (row==0 && col>=0 && col<m_size));\n      return coeff(IsColVector ? row : col);\n    }\n    inline Scalar coeff(Index i) const\n    {\n      eigen_assert(i>=0 && i<m_size);\n      return m_data.at(StorageIndex(i));\n    }\n\n    inline Scalar& coeffRef(Index row, Index col)\n    {\n      eigen_assert(IsColVector ? (col==0 && row>=0 && row<m_size) : (row==0 && col>=0 && col<m_size));\n      return coeffRef(IsColVector ? row : col);\n    }\n\n    /** \\returns a reference to the coefficient value at given index \\a i\n      * This operation involes a log(rho*size) binary search. If the coefficient does not\n      * exist yet, then a sorted insertion into a sequential buffer is performed.\n      *\n      * This insertion might be very costly if the number of nonzeros above \\a i is large.\n      */\n    inline Scalar& coeffRef(Index i)\n    {\n      eigen_assert(i>=0 && i<m_size);\n\n      return m_data.atWithInsertion(StorageIndex(i));\n    }\n\n  public:\n\n    typedef typename Base::InnerIterator InnerIterator;\n    typedef typename Base::ReverseInnerIterator ReverseInnerIterator;\n\n    inline void setZero() { m_data.clear(); }\n\n    /** \\returns the number of non zero coefficients */\n    inline Index nonZeros() const  { return m_data.size(); }\n\n    inline void startVec(Index outer)\n    {\n      EIGEN_UNUSED_VARIABLE(outer);\n      eigen_assert(outer==0);\n    }\n\n    inline Scalar& insertBackByOuterInner(Index outer, Index inner)\n    {\n      EIGEN_UNUSED_VARIABLE(outer);\n      eigen_assert(outer==0);\n      return insertBack(inner);\n    }\n    inline Scalar& insertBack(Index i)\n    {\n      m_data.append(0, i);\n      return m_data.value(m_data.size()-1);\n    }\n    \n    Scalar& insertBackByOuterInnerUnordered(Index outer, Index inner)\n    {\n      EIGEN_UNUSED_VARIABLE(outer);\n      eigen_assert(outer==0);\n      return insertBackUnordered(inner);\n    }\n    inline Scalar& insertBackUnordered(Index i)\n    {\n      m_data.append(0, i);\n      return m_data.value(m_data.size()-1);\n    }\n\n    inline Scalar& insert(Index row, Index col)\n    {\n      eigen_assert(IsColVector ? (col==0 && row>=0 && row<m_size) : (row==0 && col>=0 && col<m_size));\n      \n      Index inner = IsColVector ? row : col;\n      Index outer = IsColVector ? col : row;\n      EIGEN_ONLY_USED_FOR_DEBUG(outer);\n      eigen_assert(outer==0);\n      return insert(inner);\n    }\n    Scalar& insert(Index i)\n    {\n      eigen_assert(i>=0 && i<m_size);\n      \n      Index startId = 0;\n      Index p = Index(m_data.size()) - 1;\n      // TODO smart realloc\n      m_data.resize(p+2,1);\n\n      while ( (p >= startId) && (m_data.index(p) > i) )\n      {\n        m_data.index(p+1) = m_data.index(p);\n        m_data.value(p+1) = m_data.value(p);\n        --p;\n      }\n      m_data.index(p+1) = convert_index(i);\n      m_data.value(p+1) = 0;\n      return m_data.value(p+1);\n    }\n\n    /**\n      */\n    inline void reserve(Index reserveSize) { m_data.reserve(reserveSize); }\n\n\n    inline void finalize() {}\n\n    /** \\copydoc SparseMatrix::prune(const Scalar&,const RealScalar&) */\n    void prune(const Scalar& reference, const RealScalar& epsilon = NumTraits<RealScalar>::dummy_precision())\n    {\n      m_data.prune(reference,epsilon);\n    }\n\n    /** Resizes the sparse vector to \\a rows x \\a cols\n      *\n      * This method is provided for compatibility with matrices.\n      * For a column vector, \\a cols must be equal to 1.\n      * For a row vector, \\a rows must be equal to 1.\n      *\n      * \\sa resize(Index)\n      */\n    void resize(Index rows, Index cols)\n    {\n      eigen_assert((IsColVector ? cols : rows)==1 && \"Outer dimension must equal 1\");\n      resize(IsColVector ? rows : cols);\n    }\n\n    /** Resizes the sparse vector to \\a newSize\n      * This method deletes all entries, thus leaving an empty sparse vector\n      *\n      * \\sa  conservativeResize(), setZero() */\n    void resize(Index newSize)\n    {\n      m_size = newSize;\n      m_data.clear();\n    }\n\n    /** Resizes the sparse vector to \\a newSize, while leaving old values untouched.\n      *\n      * If the size of the vector is decreased, then the storage of the out-of bounds coefficients is kept and reserved.\n      * Call .data().squeeze() to free extra memory.\n      *\n      * \\sa reserve(), setZero()\n      */\n    void conservativeResize(Index newSize)\n    {\n      if (newSize < m_size)\n      {\n        Index i = 0;\n        while (i<m_data.size() && m_data.index(i)<newSize) ++i;\n        m_data.resize(i);\n      }\n      m_size = newSize;\n    }\n\n    void resizeNonZeros(Index size) { m_data.resize(size); }\n\n    inline SparseVector() : m_size(0) { check_template_parameters(); resize(0); }\n\n    explicit inline SparseVector(Index size) : m_size(0) { check_template_parameters(); resize(size); }\n\n    inline SparseVector(Index rows, Index cols) : m_size(0) { check_template_parameters(); resize(rows,cols); }\n\n    template<typename OtherDerived>\n    inline SparseVector(const SparseMatrixBase<OtherDerived>& other)\n      : m_size(0)\n    {\n      #ifdef EIGEN_SPARSE_CREATE_TEMPORARY_PLUGIN\n        EIGEN_SPARSE_CREATE_TEMPORARY_PLUGIN\n      #endif\n      check_template_parameters();\n      *this = other.derived();\n    }\n\n    inline SparseVector(const SparseVector& other)\n      : Base(other), m_size(0)\n    {\n      check_template_parameters();\n      *this = other.derived();\n    }\n\n    /** Swaps the values of \\c *this and \\a other.\n      * Overloaded for performance: this version performs a \\em shallow swap by swaping pointers and attributes only.\n      * \\sa SparseMatrixBase::swap()\n      */\n    inline void swap(SparseVector& other)\n    {\n      std::swap(m_size, other.m_size);\n      m_data.swap(other.m_data);\n    }\n\n    template<int OtherOptions>\n    inline void swap(SparseMatrix<Scalar,OtherOptions,StorageIndex>& other)\n    {\n      eigen_assert(other.outerSize()==1);\n      std::swap(m_size, other.m_innerSize);\n      m_data.swap(other.m_data);\n    }\n\n    inline SparseVector& operator=(const SparseVector& other)\n    {\n      if (other.isRValue())\n      {\n        swap(other.const_cast_derived());\n      }\n      else\n      {\n        resize(other.size());\n        m_data = other.m_data;\n      }\n      return *this;\n    }\n\n    template<typename OtherDerived>\n    inline SparseVector& operator=(const SparseMatrixBase<OtherDerived>& other)\n    {\n      SparseVector tmp(other.size());\n      internal::sparse_vector_assign_selector<SparseVector,OtherDerived>::run(tmp,other.derived());\n      this->swap(tmp);\n      return *this;\n    }\n\n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    template<typename Lhs, typename Rhs>\n    inline SparseVector& operator=(const SparseSparseProduct<Lhs,Rhs>& product)\n    {\n      return Base::operator=(product);\n    }\n    #endif\n\n    friend std::ostream & operator << (std::ostream & s, const SparseVector& m)\n    {\n      for (Index i=0; i<m.nonZeros(); ++i)\n        s << \"(\" << m.m_data.value(i) << \",\" << m.m_data.index(i) << \") \";\n      s << std::endl;\n      return s;\n    }\n\n    /** Destructor */\n    inline ~SparseVector() {}\n\n    /** Overloaded for performance */\n    Scalar sum() const;\n\n  public:\n\n    /** \\internal \\deprecated use setZero() and reserve() */\n    EIGEN_DEPRECATED void startFill(Index reserve)\n    {\n      setZero();\n      m_data.reserve(reserve);\n    }\n\n    /** \\internal \\deprecated use insertBack(Index,Index) */\n    EIGEN_DEPRECATED Scalar& fill(Index r, Index c)\n    {\n      eigen_assert(r==0 || c==0);\n      return fill(IsColVector ? r : c);\n    }\n\n    /** \\internal \\deprecated use insertBack(Index) */\n    EIGEN_DEPRECATED Scalar& fill(Index i)\n    {\n      m_data.append(0, i);\n      return m_data.value(m_data.size()-1);\n    }\n\n    /** \\internal \\deprecated use insert(Index,Index) */\n    EIGEN_DEPRECATED Scalar& fillrand(Index r, Index c)\n    {\n      eigen_assert(r==0 || c==0);\n      return fillrand(IsColVector ? r : c);\n    }\n\n    /** \\internal \\deprecated use insert(Index) */\n    EIGEN_DEPRECATED Scalar& fillrand(Index i)\n    {\n      return insert(i);\n    }\n\n    /** \\internal \\deprecated use finalize() */\n    EIGEN_DEPRECATED void endFill() {}\n    \n    // These two functions were here in the 3.1 release, so let's keep them in case some code rely on them.\n    /** \\internal \\deprecated use data() */\n    EIGEN_DEPRECATED Storage& _data() { return m_data; }\n    /** \\internal \\deprecated use data() */\n    EIGEN_DEPRECATED const Storage& _data() const { return m_data; }\n    \n#   ifdef EIGEN_SPARSEVECTOR_PLUGIN\n#     include EIGEN_SPARSEVECTOR_PLUGIN\n#   endif\n\nprotected:\n  \n    static void check_template_parameters()\n    {\n      EIGEN_STATIC_ASSERT(NumTraits<StorageIndex>::IsSigned,THE_INDEX_TYPE_MUST_BE_A_SIGNED_TYPE);\n      EIGEN_STATIC_ASSERT((_Options&(ColMajor|RowMajor))==Options,INVALID_MATRIX_TEMPLATE_PARAMETERS);\n    }\n    \n    Storage m_data;\n    Index m_size;\n};\n\nnamespace internal {\n\ntemplate<typename _Scalar, int _Options, typename _Index>\nstruct evaluator<SparseVector<_Scalar,_Options,_Index> >\n  : evaluator_base<SparseVector<_Scalar,_Options,_Index> >\n{\n  typedef SparseVector<_Scalar,_Options,_Index> SparseVectorType;\n  typedef evaluator_base<SparseVectorType> Base;\n  typedef typename SparseVectorType::InnerIterator InnerIterator;\n  typedef typename SparseVectorType::ReverseInnerIterator ReverseInnerIterator;\n  \n  enum {\n    CoeffReadCost = NumTraits<_Scalar>::ReadCost,\n    Flags = SparseVectorType::Flags\n  };\n\n  evaluator() : Base() {}\n  \n  explicit evaluator(const SparseVectorType &mat) : m_matrix(&mat)\n  {\n    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);\n  }\n  \n  inline Index nonZerosEstimate() const {\n    return m_matrix->nonZeros();\n  }\n  \n  operator SparseVectorType&() { return m_matrix->const_cast_derived(); }\n  operator const SparseVectorType&() const { return *m_matrix; }\n  \n  const SparseVectorType *m_matrix;\n};\n\ntemplate< typename Dest, typename Src>\nstruct sparse_vector_assign_selector<Dest,Src,SVA_Inner> {\n  static void run(Dest& dst, const Src& src) {\n    eigen_internal_assert(src.innerSize()==src.size());\n    typedef internal::evaluator<Src> SrcEvaluatorType;\n    SrcEvaluatorType srcEval(src);\n    for(typename SrcEvaluatorType::InnerIterator it(srcEval, 0); it; ++it)\n      dst.insert(it.index()) = it.value();\n  }\n};\n\ntemplate< typename Dest, typename Src>\nstruct sparse_vector_assign_selector<Dest,Src,SVA_Outer> {\n  static void run(Dest& dst, const Src& src) {\n    eigen_internal_assert(src.outerSize()==src.size());\n    typedef internal::evaluator<Src> SrcEvaluatorType;\n    SrcEvaluatorType srcEval(src);\n    for(Index i=0; i<src.size(); ++i)\n    {\n      typename SrcEvaluatorType::InnerIterator it(srcEval, i);\n      if(it)\n        dst.insert(i) = it.value();\n    }\n  }\n};\n\ntemplate< typename Dest, typename Src>\nstruct sparse_vector_assign_selector<Dest,Src,SVA_RuntimeSwitch> {\n  static void run(Dest& dst, const Src& src) {\n    if(src.outerSize()==1)  sparse_vector_assign_selector<Dest,Src,SVA_Inner>::run(dst, src);\n    else                    sparse_vector_assign_selector<Dest,Src,SVA_Outer>::run(dst, src);\n  }\n};\n\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_SPARSEVECTOR_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseCore/SparseView.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2011-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2010 Daniel Lowengrub <lowdanie@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSEVIEW_H\n#define EIGEN_SPARSEVIEW_H\n\nnamespace Eigen { \n\nnamespace internal {\n\ntemplate<typename MatrixType>\nstruct traits<SparseView<MatrixType> > : traits<MatrixType>\n{\n  typedef typename MatrixType::StorageIndex StorageIndex;\n  typedef Sparse StorageKind;\n  enum {\n    Flags = int(traits<MatrixType>::Flags) & (RowMajorBit)\n  };\n};\n\n} // end namespace internal\n\n/** \\ingroup SparseCore_Module\n  * \\class SparseView\n  *\n  * \\brief Expression of a dense or sparse matrix with zero or too small values removed\n  *\n  * \\tparam MatrixType the type of the object of which we are removing the small entries\n  *\n  * This class represents an expression of a given dense or sparse matrix with\n  * entries smaller than \\c reference * \\c epsilon are removed.\n  * It is the return type of MatrixBase::sparseView() and SparseMatrixBase::pruned()\n  * and most of the time this is the only way it is used.\n  *\n  * \\sa MatrixBase::sparseView(), SparseMatrixBase::pruned()\n  */\ntemplate<typename MatrixType>\nclass SparseView : public SparseMatrixBase<SparseView<MatrixType> >\n{\n  typedef typename MatrixType::Nested MatrixTypeNested;\n  typedef typename internal::remove_all<MatrixTypeNested>::type _MatrixTypeNested;\n  typedef SparseMatrixBase<SparseView > Base;\npublic:\n  EIGEN_SPARSE_PUBLIC_INTERFACE(SparseView)\n  typedef typename internal::remove_all<MatrixType>::type NestedExpression;\n\n  explicit SparseView(const MatrixType& mat, const Scalar& reference = Scalar(0),\n                      const RealScalar &epsilon = NumTraits<Scalar>::dummy_precision())\n    : m_matrix(mat), m_reference(reference), m_epsilon(epsilon) {}\n\n  inline Index rows() const { return m_matrix.rows(); }\n  inline Index cols() const { return m_matrix.cols(); }\n\n  inline Index innerSize() const { return m_matrix.innerSize(); }\n  inline Index outerSize() const { return m_matrix.outerSize(); }\n  \n  /** \\returns the nested expression */\n  const typename internal::remove_all<MatrixTypeNested>::type&\n  nestedExpression() const { return m_matrix; }\n  \n  Scalar reference() const { return m_reference; }\n  RealScalar epsilon() const { return m_epsilon; }\n  \nprotected:\n  MatrixTypeNested m_matrix;\n  Scalar m_reference;\n  RealScalar m_epsilon;\n};\n\nnamespace internal {\n\n// TODO find a way to unify the two following variants\n// This is tricky because implementing an inner iterator on top of an IndexBased evaluator is\n// not easy because the evaluators do not expose the sizes of the underlying expression.\n  \ntemplate<typename ArgType>\nstruct unary_evaluator<SparseView<ArgType>, IteratorBased>\n  : public evaluator_base<SparseView<ArgType> >\n{\n    typedef typename evaluator<ArgType>::InnerIterator EvalIterator;\n  public:\n    typedef SparseView<ArgType> XprType;\n    \n    class InnerIterator : public EvalIterator\n    {\n        typedef typename XprType::Scalar Scalar;\n      public:\n\n        EIGEN_STRONG_INLINE InnerIterator(const unary_evaluator& sve, Index outer)\n          : EvalIterator(sve.m_argImpl,outer), m_view(sve.m_view)\n        {\n          incrementToNonZero();\n        }\n\n        EIGEN_STRONG_INLINE InnerIterator& operator++()\n        {\n          EvalIterator::operator++();\n          incrementToNonZero();\n          return *this;\n        }\n\n        using EvalIterator::value;\n\n      protected:\n        const XprType &m_view;\n\n      private:\n        void incrementToNonZero()\n        {\n          while((bool(*this)) && internal::isMuchSmallerThan(value(), m_view.reference(), m_view.epsilon()))\n          {\n            EvalIterator::operator++();\n          }\n        }\n    };\n    \n    enum {\n      CoeffReadCost = evaluator<ArgType>::CoeffReadCost,\n      Flags = XprType::Flags\n    };\n    \n    explicit unary_evaluator(const XprType& xpr) : m_argImpl(xpr.nestedExpression()), m_view(xpr) {}\n\n  protected:\n    evaluator<ArgType> m_argImpl;\n    const XprType &m_view;\n};\n\ntemplate<typename ArgType>\nstruct unary_evaluator<SparseView<ArgType>, IndexBased>\n  : public evaluator_base<SparseView<ArgType> >\n{\n  public:\n    typedef SparseView<ArgType> XprType;\n  protected:\n    enum { IsRowMajor = (XprType::Flags&RowMajorBit)==RowMajorBit };\n    typedef typename XprType::Scalar Scalar;\n    typedef typename XprType::StorageIndex StorageIndex;\n  public:\n    \n    class InnerIterator\n    {\n      public:\n\n        EIGEN_STRONG_INLINE InnerIterator(const unary_evaluator& sve, Index outer)\n          : m_sve(sve), m_inner(0), m_outer(outer), m_end(sve.m_view.innerSize())\n        {\n          incrementToNonZero();\n        }\n\n        EIGEN_STRONG_INLINE InnerIterator& operator++()\n        {\n          m_inner++;\n          incrementToNonZero();\n          return *this;\n        }\n\n        EIGEN_STRONG_INLINE Scalar value() const\n        {\n          return (IsRowMajor) ? m_sve.m_argImpl.coeff(m_outer, m_inner)\n                              : m_sve.m_argImpl.coeff(m_inner, m_outer);\n        }\n\n        EIGEN_STRONG_INLINE StorageIndex index() const { return m_inner; }\n        inline Index row() const { return IsRowMajor ? m_outer : index(); }\n        inline Index col() const { return IsRowMajor ? index() : m_outer; }\n\n        EIGEN_STRONG_INLINE operator bool() const { return m_inner < m_end && m_inner>=0; }\n\n      protected:\n        const unary_evaluator &m_sve;\n        Index m_inner;\n        const Index m_outer;\n        const Index m_end;\n\n      private:\n        void incrementToNonZero()\n        {\n          while((bool(*this)) && internal::isMuchSmallerThan(value(), m_sve.m_view.reference(), m_sve.m_view.epsilon()))\n          {\n            m_inner++;\n          }\n        }\n    };\n    \n    enum {\n      CoeffReadCost = evaluator<ArgType>::CoeffReadCost,\n      Flags = XprType::Flags\n    };\n    \n    explicit unary_evaluator(const XprType& xpr) : m_argImpl(xpr.nestedExpression()), m_view(xpr) {}\n\n  protected:\n    evaluator<ArgType> m_argImpl;\n    const XprType &m_view;\n};\n\n} // end namespace internal\n\n/** \\ingroup SparseCore_Module\n  *\n  * \\returns a sparse expression of the dense expression \\c *this with values smaller than\n  * \\a reference * \\a epsilon removed.\n  *\n  * This method is typically used when prototyping to convert a quickly assembled dense Matrix \\c D to a SparseMatrix \\c S:\n  * \\code\n  * MatrixXd D(n,m);\n  * SparseMatrix<double> S;\n  * S = D.sparseView();             // suppress numerical zeros (exact)\n  * S = D.sparseView(reference);\n  * S = D.sparseView(reference,epsilon);\n  * \\endcode\n  * where \\a reference is a meaningful non zero reference value,\n  * and \\a epsilon is a tolerance factor defaulting to NumTraits<Scalar>::dummy_precision().\n  *\n  * \\sa SparseMatrixBase::pruned(), class SparseView */\ntemplate<typename Derived>\nconst SparseView<Derived> MatrixBase<Derived>::sparseView(const Scalar& reference,\n                                                          const typename NumTraits<Scalar>::Real& epsilon) const\n{\n  return SparseView<Derived>(derived(), reference, epsilon);\n}\n\n/** \\returns an expression of \\c *this with values smaller than\n  * \\a reference * \\a epsilon removed.\n  *\n  * This method is typically used in conjunction with the product of two sparse matrices\n  * to automatically prune the smallest values as follows:\n  * \\code\n  * C = (A*B).pruned();             // suppress numerical zeros (exact)\n  * C = (A*B).pruned(ref);\n  * C = (A*B).pruned(ref,epsilon);\n  * \\endcode\n  * where \\c ref is a meaningful non zero reference value.\n  * */\ntemplate<typename Derived>\nconst SparseView<Derived>\nSparseMatrixBase<Derived>::pruned(const Scalar& reference,\n                                  const RealScalar& epsilon) const\n{\n  return SparseView<Derived>(derived(), reference, epsilon);\n}\n\n} // end namespace Eigen\n\n#endif\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseCore/TriangularSolver.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSETRIANGULARSOLVER_H\n#define EIGEN_SPARSETRIANGULARSOLVER_H\n\nnamespace Eigen { \n\nnamespace internal {\n\ntemplate<typename Lhs, typename Rhs, int Mode,\n  int UpLo = (Mode & Lower)\n           ? Lower\n           : (Mode & Upper)\n           ? Upper\n           : -1,\n  int StorageOrder = int(traits<Lhs>::Flags) & RowMajorBit>\nstruct sparse_solve_triangular_selector;\n\n// forward substitution, row-major\ntemplate<typename Lhs, typename Rhs, int Mode>\nstruct sparse_solve_triangular_selector<Lhs,Rhs,Mode,Lower,RowMajor>\n{\n  typedef typename Rhs::Scalar Scalar;\n  typedef evaluator<Lhs> LhsEval;\n  typedef typename evaluator<Lhs>::InnerIterator LhsIterator;\n  static void run(const Lhs& lhs, Rhs& other)\n  {\n    LhsEval lhsEval(lhs);\n    for(Index col=0 ; col<other.cols() ; ++col)\n    {\n      for(Index i=0; i<lhs.rows(); ++i)\n      {\n        Scalar tmp = other.coeff(i,col);\n        Scalar lastVal(0);\n        Index lastIndex = 0;\n        for(LhsIterator it(lhsEval, i); it; ++it)\n        {\n          lastVal = it.value();\n          lastIndex = it.index();\n          if(lastIndex==i)\n            break;\n          tmp -= lastVal * other.coeff(lastIndex,col);\n        }\n        if (Mode & UnitDiag)\n          other.coeffRef(i,col) = tmp;\n        else\n        {\n          eigen_assert(lastIndex==i);\n          other.coeffRef(i,col) = tmp/lastVal;\n        }\n      }\n    }\n  }\n};\n\n// backward substitution, row-major\ntemplate<typename Lhs, typename Rhs, int Mode>\nstruct sparse_solve_triangular_selector<Lhs,Rhs,Mode,Upper,RowMajor>\n{\n  typedef typename Rhs::Scalar Scalar;\n  typedef evaluator<Lhs> LhsEval;\n  typedef typename evaluator<Lhs>::InnerIterator LhsIterator;\n  static void run(const Lhs& lhs, Rhs& other)\n  {\n    LhsEval lhsEval(lhs);\n    for(Index col=0 ; col<other.cols() ; ++col)\n    {\n      for(Index i=lhs.rows()-1 ; i>=0 ; --i)\n      {\n        Scalar tmp = other.coeff(i,col);\n        Scalar l_ii(0);\n        LhsIterator it(lhsEval, i);\n        while(it && it.index()<i)\n          ++it;\n        if(!(Mode & UnitDiag))\n        {\n          eigen_assert(it && it.index()==i);\n          l_ii = it.value();\n          ++it;\n        }\n        else if (it && it.index() == i)\n          ++it;\n        for(; it; ++it)\n        {\n          tmp -= it.value() * other.coeff(it.index(),col);\n        }\n\n        if (Mode & UnitDiag)  other.coeffRef(i,col) = tmp;\n        else                  other.coeffRef(i,col) = tmp/l_ii;\n      }\n    }\n  }\n};\n\n// forward substitution, col-major\ntemplate<typename Lhs, typename Rhs, int Mode>\nstruct sparse_solve_triangular_selector<Lhs,Rhs,Mode,Lower,ColMajor>\n{\n  typedef typename Rhs::Scalar Scalar;\n  typedef evaluator<Lhs> LhsEval;\n  typedef typename evaluator<Lhs>::InnerIterator LhsIterator;\n  static void run(const Lhs& lhs, Rhs& other)\n  {\n    LhsEval lhsEval(lhs);\n    for(Index col=0 ; col<other.cols() ; ++col)\n    {\n      for(Index i=0; i<lhs.cols(); ++i)\n      {\n        Scalar& tmp = other.coeffRef(i,col);\n        if (tmp!=Scalar(0)) // optimization when other is actually sparse\n        {\n          LhsIterator it(lhsEval, i);\n          while(it && it.index()<i)\n            ++it;\n          if(!(Mode & UnitDiag))\n          {\n            eigen_assert(it && it.index()==i);\n            tmp /= it.value();\n          }\n          if (it && it.index()==i)\n            ++it;\n          for(; it; ++it)\n            other.coeffRef(it.index(), col) -= tmp * it.value();\n        }\n      }\n    }\n  }\n};\n\n// backward substitution, col-major\ntemplate<typename Lhs, typename Rhs, int Mode>\nstruct sparse_solve_triangular_selector<Lhs,Rhs,Mode,Upper,ColMajor>\n{\n  typedef typename Rhs::Scalar Scalar;\n  typedef evaluator<Lhs> LhsEval;\n  typedef typename evaluator<Lhs>::InnerIterator LhsIterator;\n  static void run(const Lhs& lhs, Rhs& other)\n  {\n    LhsEval lhsEval(lhs);\n    for(Index col=0 ; col<other.cols() ; ++col)\n    {\n      for(Index i=lhs.cols()-1; i>=0; --i)\n      {\n        Scalar& tmp = other.coeffRef(i,col);\n        if (tmp!=Scalar(0)) // optimization when other is actually sparse\n        {\n          if(!(Mode & UnitDiag))\n          {\n            // TODO replace this by a binary search. make sure the binary search is safe for partially sorted elements\n            LhsIterator it(lhsEval, i);\n            while(it && it.index()!=i)\n              ++it;\n            eigen_assert(it && it.index()==i);\n            other.coeffRef(i,col) /= it.value();\n          }\n          LhsIterator it(lhsEval, i);\n          for(; it && it.index()<i; ++it)\n            other.coeffRef(it.index(), col) -= tmp * it.value();\n        }\n      }\n    }\n  }\n};\n\n} // end namespace internal\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\n\ntemplate<typename ExpressionType,unsigned int Mode>\ntemplate<typename OtherDerived>\nvoid TriangularViewImpl<ExpressionType,Mode,Sparse>::solveInPlace(MatrixBase<OtherDerived>& other) const\n{\n  eigen_assert(derived().cols() == derived().rows() && derived().cols() == other.rows());\n  eigen_assert((!(Mode & ZeroDiag)) && bool(Mode & (Upper|Lower)));\n\n  enum { copy = internal::traits<OtherDerived>::Flags & RowMajorBit };\n\n  typedef typename internal::conditional<copy,\n    typename internal::plain_matrix_type_column_major<OtherDerived>::type, OtherDerived&>::type OtherCopy;\n  OtherCopy otherCopy(other.derived());\n\n  internal::sparse_solve_triangular_selector<ExpressionType, typename internal::remove_reference<OtherCopy>::type, Mode>::run(derived().nestedExpression(), otherCopy);\n\n  if (copy)\n    other = otherCopy;\n}\n#endif\n\n// pure sparse path\n\nnamespace internal {\n\ntemplate<typename Lhs, typename Rhs, int Mode,\n  int UpLo = (Mode & Lower)\n           ? Lower\n           : (Mode & Upper)\n           ? Upper\n           : -1,\n  int StorageOrder = int(Lhs::Flags) & (RowMajorBit)>\nstruct sparse_solve_triangular_sparse_selector;\n\n// forward substitution, col-major\ntemplate<typename Lhs, typename Rhs, int Mode, int UpLo>\nstruct sparse_solve_triangular_sparse_selector<Lhs,Rhs,Mode,UpLo,ColMajor>\n{\n  typedef typename Rhs::Scalar Scalar;\n  typedef typename promote_index_type<typename traits<Lhs>::StorageIndex,\n                                      typename traits<Rhs>::StorageIndex>::type StorageIndex;\n  static void run(const Lhs& lhs, Rhs& other)\n  {\n    const bool IsLower = (UpLo==Lower);\n    AmbiVector<Scalar,StorageIndex> tempVector(other.rows()*2);\n    tempVector.setBounds(0,other.rows());\n\n    Rhs res(other.rows(), other.cols());\n    res.reserve(other.nonZeros());\n\n    for(Index col=0 ; col<other.cols() ; ++col)\n    {\n      // FIXME estimate number of non zeros\n      tempVector.init(.99/*float(other.col(col).nonZeros())/float(other.rows())*/);\n      tempVector.setZero();\n      tempVector.restart();\n      for (typename Rhs::InnerIterator rhsIt(other, col); rhsIt; ++rhsIt)\n      {\n        tempVector.coeffRef(rhsIt.index()) = rhsIt.value();\n      }\n\n      for(Index i=IsLower?0:lhs.cols()-1;\n          IsLower?i<lhs.cols():i>=0;\n          i+=IsLower?1:-1)\n      {\n        tempVector.restart();\n        Scalar& ci = tempVector.coeffRef(i);\n        if (ci!=Scalar(0))\n        {\n          // find\n          typename Lhs::InnerIterator it(lhs, i);\n          if(!(Mode & UnitDiag))\n          {\n            if (IsLower)\n            {\n              eigen_assert(it.index()==i);\n              ci /= it.value();\n            }\n            else\n              ci /= lhs.coeff(i,i);\n          }\n          tempVector.restart();\n          if (IsLower)\n          {\n            if (it.index()==i)\n              ++it;\n            for(; it; ++it)\n              tempVector.coeffRef(it.index()) -= ci * it.value();\n          }\n          else\n          {\n            for(; it && it.index()<i; ++it)\n              tempVector.coeffRef(it.index()) -= ci * it.value();\n          }\n        }\n      }\n\n\n      Index count = 0;\n      // FIXME compute a reference value to filter zeros\n      for (typename AmbiVector<Scalar,StorageIndex>::Iterator it(tempVector/*,1e-12*/); it; ++it)\n      {\n        ++ count;\n//         std::cerr << \"fill \" << it.index() << \", \" << col << \"\\n\";\n//         std::cout << it.value() << \"  \";\n        // FIXME use insertBack\n        res.insert(it.index(), col) = it.value();\n      }\n//       std::cout << \"tempVector.nonZeros() == \" << int(count) << \" / \" << (other.rows()) << \"\\n\";\n    }\n    res.finalize();\n    other = res.markAsRValue();\n  }\n};\n\n} // end namespace internal\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\ntemplate<typename ExpressionType,unsigned int Mode>\ntemplate<typename OtherDerived>\nvoid TriangularViewImpl<ExpressionType,Mode,Sparse>::solveInPlace(SparseMatrixBase<OtherDerived>& other) const\n{\n  eigen_assert(derived().cols() == derived().rows() && derived().cols() == other.rows());\n  eigen_assert( (!(Mode & ZeroDiag)) && bool(Mode & (Upper|Lower)));\n\n//   enum { copy = internal::traits<OtherDerived>::Flags & RowMajorBit };\n\n//   typedef typename internal::conditional<copy,\n//     typename internal::plain_matrix_type_column_major<OtherDerived>::type, OtherDerived&>::type OtherCopy;\n//   OtherCopy otherCopy(other.derived());\n\n  internal::sparse_solve_triangular_sparse_selector<ExpressionType, OtherDerived, Mode>::run(derived().nestedExpression(), other.derived());\n\n//   if (copy)\n//     other = otherCopy;\n}\n#endif\n\n} // end namespace Eigen\n\n#endif // EIGEN_SPARSETRIANGULARSOLVER_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseLU/SparseLU.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>\n// Copyright (C) 2012-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n\n#ifndef EIGEN_SPARSE_LU_H\n#define EIGEN_SPARSE_LU_H\n\nnamespace Eigen {\n\ntemplate <typename _MatrixType, typename _OrderingType = COLAMDOrdering<typename _MatrixType::StorageIndex> > class SparseLU;\ntemplate <typename MappedSparseMatrixType> struct SparseLUMatrixLReturnType;\ntemplate <typename MatrixLType, typename MatrixUType> struct SparseLUMatrixUReturnType;\n\n/** \\ingroup SparseLU_Module\n  * \\class SparseLU\n  * \n  * \\brief Sparse supernodal LU factorization for general matrices\n  * \n  * This class implements the supernodal LU factorization for general matrices.\n  * It uses the main techniques from the sequential SuperLU package \n  * (http://crd-legacy.lbl.gov/~xiaoye/SuperLU/). It handles transparently real \n  * and complex arithmetics with single and double precision, depending on the \n  * scalar type of your input matrix. \n  * The code has been optimized to provide BLAS-3 operations during supernode-panel updates. \n  * It benefits directly from the built-in high-performant Eigen BLAS routines. \n  * Moreover, when the size of a supernode is very small, the BLAS calls are avoided to \n  * enable a better optimization from the compiler. For best performance, \n  * you should compile it with NDEBUG flag to avoid the numerous bounds checking on vectors. \n  * \n  * An important parameter of this class is the ordering method. It is used to reorder the columns \n  * (and eventually the rows) of the matrix to reduce the number of new elements that are created during \n  * numerical factorization. The cheapest method available is COLAMD. \n  * See  \\link OrderingMethods_Module the OrderingMethods module \\endlink for the list of \n  * built-in and external ordering methods. \n  *\n  * Simple example with key steps \n  * \\code\n  * VectorXd x(n), b(n);\n  * SparseMatrix<double, ColMajor> A;\n  * SparseLU<SparseMatrix<scalar, ColMajor>, COLAMDOrdering<Index> >   solver;\n  * // fill A and b;\n  * // Compute the ordering permutation vector from the structural pattern of A\n  * solver.analyzePattern(A); \n  * // Compute the numerical factorization \n  * solver.factorize(A); \n  * //Use the factors to solve the linear system \n  * x = solver.solve(b); \n  * \\endcode\n  * \n  * \\warning The input matrix A should be in a \\b compressed and \\b column-major form.\n  * Otherwise an expensive copy will be made. You can call the inexpensive makeCompressed() to get a compressed matrix.\n  * \n  * \\note Unlike the initial SuperLU implementation, there is no step to equilibrate the matrix. \n  * For badly scaled matrices, this step can be useful to reduce the pivoting during factorization. \n  * If this is the case for your matrices, you can try the basic scaling method at\n  *  \"unsupported/Eigen/src/IterativeSolvers/Scaling.h\"\n  * \n  * \\tparam _MatrixType The type of the sparse matrix. It must be a column-major SparseMatrix<>\n  * \\tparam _OrderingType The ordering method to use, either AMD, COLAMD or METIS. Default is COLMAD\n  *\n  * \\implsparsesolverconcept\n  * \n  * \\sa \\ref TutorialSparseSolverConcept\n  * \\sa \\ref OrderingMethods_Module\n  */\ntemplate <typename _MatrixType, typename _OrderingType>\nclass SparseLU : public SparseSolverBase<SparseLU<_MatrixType,_OrderingType> >, public internal::SparseLUImpl<typename _MatrixType::Scalar, typename _MatrixType::StorageIndex>\n{\n  protected:\n    typedef SparseSolverBase<SparseLU<_MatrixType,_OrderingType> > APIBase;\n    using APIBase::m_isInitialized;\n  public:\n    using APIBase::_solve_impl;\n    \n    typedef _MatrixType MatrixType; \n    typedef _OrderingType OrderingType;\n    typedef typename MatrixType::Scalar Scalar; \n    typedef typename MatrixType::RealScalar RealScalar; \n    typedef typename MatrixType::StorageIndex StorageIndex;\n    typedef SparseMatrix<Scalar,ColMajor,StorageIndex> NCMatrix;\n    typedef internal::MappedSuperNodalMatrix<Scalar, StorageIndex> SCMatrix;\n    typedef Matrix<Scalar,Dynamic,1> ScalarVector;\n    typedef Matrix<StorageIndex,Dynamic,1> IndexVector;\n    typedef PermutationMatrix<Dynamic, Dynamic, StorageIndex> PermutationType;\n    typedef internal::SparseLUImpl<Scalar, StorageIndex> Base;\n\n    enum {\n      ColsAtCompileTime = MatrixType::ColsAtCompileTime,\n      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime\n    };\n    \n  public:\n    SparseLU():m_lastError(\"\"),m_Ustore(0,0,0,0,0,0),m_symmetricmode(false),m_diagpivotthresh(1.0),m_detPermR(1)\n    {\n      initperfvalues(); \n    }\n    explicit SparseLU(const MatrixType& matrix)\n      : m_lastError(\"\"),m_Ustore(0,0,0,0,0,0),m_symmetricmode(false),m_diagpivotthresh(1.0),m_detPermR(1)\n    {\n      initperfvalues(); \n      compute(matrix);\n    }\n    \n    ~SparseLU()\n    {\n      // Free all explicit dynamic pointers \n    }\n    \n    void analyzePattern (const MatrixType& matrix);\n    void factorize (const MatrixType& matrix);\n    void simplicialfactorize(const MatrixType& matrix);\n    \n    /**\n      * Compute the symbolic and numeric factorization of the input sparse matrix.\n      * The input matrix should be in column-major storage. \n      */\n    void compute (const MatrixType& matrix)\n    {\n      // Analyze \n      analyzePattern(matrix); \n      //Factorize\n      factorize(matrix);\n    } \n    \n    inline Index rows() const { return m_mat.rows(); }\n    inline Index cols() const { return m_mat.cols(); }\n    /** Indicate that the pattern of the input matrix is symmetric */\n    void isSymmetric(bool sym)\n    {\n      m_symmetricmode = sym;\n    }\n    \n    /** \\returns an expression of the matrix L, internally stored as supernodes\n      * The only operation available with this expression is the triangular solve\n      * \\code\n      * y = b; matrixL().solveInPlace(y);\n      * \\endcode\n      */\n    SparseLUMatrixLReturnType<SCMatrix> matrixL() const\n    {\n      return SparseLUMatrixLReturnType<SCMatrix>(m_Lstore);\n    }\n    /** \\returns an expression of the matrix U,\n      * The only operation available with this expression is the triangular solve\n      * \\code\n      * y = b; matrixU().solveInPlace(y);\n      * \\endcode\n      */\n    SparseLUMatrixUReturnType<SCMatrix,MappedSparseMatrix<Scalar,ColMajor,StorageIndex> > matrixU() const\n    {\n      return SparseLUMatrixUReturnType<SCMatrix, MappedSparseMatrix<Scalar,ColMajor,StorageIndex> >(m_Lstore, m_Ustore);\n    }\n\n    /**\n      * \\returns a reference to the row matrix permutation \\f$ P_r \\f$ such that \\f$P_r A P_c^T = L U\\f$\n      * \\sa colsPermutation()\n      */\n    inline const PermutationType& rowsPermutation() const\n    {\n      return m_perm_r;\n    }\n    /**\n      * \\returns a reference to the column matrix permutation\\f$ P_c^T \\f$ such that \\f$P_r A P_c^T = L U\\f$\n      * \\sa rowsPermutation()\n      */\n    inline const PermutationType& colsPermutation() const\n    {\n      return m_perm_c;\n    }\n    /** Set the threshold used for a diagonal entry to be an acceptable pivot. */\n    void setPivotThreshold(const RealScalar& thresh)\n    {\n      m_diagpivotthresh = thresh; \n    }\n\n#ifdef EIGEN_PARSED_BY_DOXYGEN\n    /** \\returns the solution X of \\f$ A X = B \\f$ using the current decomposition of A.\n      *\n      * \\warning the destination matrix X in X = this->solve(B) must be colmun-major.\n      *\n      * \\sa compute()\n      */\n    template<typename Rhs>\n    inline const Solve<SparseLU, Rhs> solve(const MatrixBase<Rhs>& B) const;\n#endif // EIGEN_PARSED_BY_DOXYGEN\n    \n    /** \\brief Reports whether previous computation was successful.\n      *\n      * \\returns \\c Success if computation was succesful,\n      *          \\c NumericalIssue if the LU factorization reports a problem, zero diagonal for instance\n      *          \\c InvalidInput if the input matrix is invalid\n      *\n      * \\sa iparm()          \n      */\n    ComputationInfo info() const\n    {\n      eigen_assert(m_isInitialized && \"Decomposition is not initialized.\");\n      return m_info;\n    }\n    \n    /**\n      * \\returns A string describing the type of error\n      */\n    std::string lastErrorMessage() const\n    {\n      return m_lastError; \n    }\n\n    template<typename Rhs, typename Dest>\n    bool _solve_impl(const MatrixBase<Rhs> &B, MatrixBase<Dest> &X_base) const\n    {\n      Dest& X(X_base.derived());\n      eigen_assert(m_factorizationIsOk && \"The matrix should be factorized first\");\n      EIGEN_STATIC_ASSERT((Dest::Flags&RowMajorBit)==0,\n                        THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);\n      \n      // Permute the right hand side to form X = Pr*B\n      // on return, X is overwritten by the computed solution\n      X.resize(B.rows(),B.cols());\n\n      // this ugly const_cast_derived() helps to detect aliasing when applying the permutations\n      for(Index j = 0; j < B.cols(); ++j)\n        X.col(j) = rowsPermutation() * B.const_cast_derived().col(j);\n      \n      //Forward substitution with L\n      this->matrixL().solveInPlace(X);\n      this->matrixU().solveInPlace(X);\n      \n      // Permute back the solution \n      for (Index j = 0; j < B.cols(); ++j)\n        X.col(j) = colsPermutation().inverse() * X.col(j);\n      \n      return true; \n    }\n    \n    /**\n      * \\returns the absolute value of the determinant of the matrix of which\n      * *this is the QR decomposition.\n      *\n      * \\warning a determinant can be very big or small, so for matrices\n      * of large enough dimension, there is a risk of overflow/underflow.\n      * One way to work around that is to use logAbsDeterminant() instead.\n      *\n      * \\sa logAbsDeterminant(), signDeterminant()\n      */\n    Scalar absDeterminant()\n    {\n      using std::abs;\n      eigen_assert(m_factorizationIsOk && \"The matrix should be factorized first.\");\n      // Initialize with the determinant of the row matrix\n      Scalar det = Scalar(1.);\n      // Note that the diagonal blocks of U are stored in supernodes,\n      // which are available in the  L part :)\n      for (Index j = 0; j < this->cols(); ++j)\n      {\n        for (typename SCMatrix::InnerIterator it(m_Lstore, j); it; ++it)\n        {\n          if(it.index() == j)\n          {\n            det *= abs(it.value());\n            break;\n          }\n        }\n      }\n      return det;\n    }\n\n    /** \\returns the natural log of the absolute value of the determinant of the matrix\n      * of which **this is the QR decomposition\n      *\n      * \\note This method is useful to work around the risk of overflow/underflow that's\n      * inherent to the determinant computation.\n      *\n      * \\sa absDeterminant(), signDeterminant()\n      */\n    Scalar logAbsDeterminant() const\n    {\n      using std::log;\n      using std::abs;\n\n      eigen_assert(m_factorizationIsOk && \"The matrix should be factorized first.\");\n      Scalar det = Scalar(0.);\n      for (Index j = 0; j < this->cols(); ++j)\n      {\n        for (typename SCMatrix::InnerIterator it(m_Lstore, j); it; ++it)\n        {\n          if(it.row() < j) continue;\n          if(it.row() == j)\n          {\n            det += log(abs(it.value()));\n            break;\n          }\n        }\n      }\n      return det;\n    }\n\n    /** \\returns A number representing the sign of the determinant\n      *\n      * \\sa absDeterminant(), logAbsDeterminant()\n      */\n    Scalar signDeterminant()\n    {\n      eigen_assert(m_factorizationIsOk && \"The matrix should be factorized first.\");\n      // Initialize with the determinant of the row matrix\n      Index det = 1;\n      // Note that the diagonal blocks of U are stored in supernodes,\n      // which are available in the  L part :)\n      for (Index j = 0; j < this->cols(); ++j)\n      {\n        for (typename SCMatrix::InnerIterator it(m_Lstore, j); it; ++it)\n        {\n          if(it.index() == j)\n          {\n            if(it.value()<0)\n              det = -det;\n            else if(it.value()==0)\n              return 0;\n            break;\n          }\n        }\n      }\n      return det * m_detPermR * m_detPermC;\n    }\n    \n    /** \\returns The determinant of the matrix.\n      *\n      * \\sa absDeterminant(), logAbsDeterminant()\n      */\n    Scalar determinant()\n    {\n      eigen_assert(m_factorizationIsOk && \"The matrix should be factorized first.\");\n      // Initialize with the determinant of the row matrix\n      Scalar det = Scalar(1.);\n      // Note that the diagonal blocks of U are stored in supernodes,\n      // which are available in the  L part :)\n      for (Index j = 0; j < this->cols(); ++j)\n      {\n        for (typename SCMatrix::InnerIterator it(m_Lstore, j); it; ++it)\n        {\n          if(it.index() == j)\n          {\n            det *= it.value();\n            break;\n          }\n        }\n      }\n      return (m_detPermR * m_detPermC) > 0 ? det : -det;\n    }\n\n  protected:\n    // Functions \n    void initperfvalues()\n    {\n      m_perfv.panel_size = 16;\n      m_perfv.relax = 1; \n      m_perfv.maxsuper = 128; \n      m_perfv.rowblk = 16; \n      m_perfv.colblk = 8; \n      m_perfv.fillfactor = 20;  \n    }\n      \n    // Variables \n    mutable ComputationInfo m_info;\n    bool m_factorizationIsOk;\n    bool m_analysisIsOk;\n    std::string m_lastError;\n    NCMatrix m_mat; // The input (permuted ) matrix \n    SCMatrix m_Lstore; // The lower triangular matrix (supernodal)\n    MappedSparseMatrix<Scalar,ColMajor,StorageIndex> m_Ustore; // The upper triangular matrix\n    PermutationType m_perm_c; // Column permutation \n    PermutationType m_perm_r ; // Row permutation\n    IndexVector m_etree; // Column elimination tree \n    \n    typename Base::GlobalLU_t m_glu; \n                               \n    // SparseLU options \n    bool m_symmetricmode;\n    // values for performance \n    internal::perfvalues m_perfv;\n    RealScalar m_diagpivotthresh; // Specifies the threshold used for a diagonal entry to be an acceptable pivot\n    Index m_nnzL, m_nnzU; // Nonzeros in L and U factors\n    Index m_detPermR, m_detPermC; // Determinants of the permutation matrices\n  private:\n    // Disable copy constructor \n    SparseLU (const SparseLU& );\n  \n}; // End class SparseLU\n\n\n\n// Functions needed by the anaysis phase\n/** \n  * Compute the column permutation to minimize the fill-in\n  * \n  *  - Apply this permutation to the input matrix - \n  * \n  *  - Compute the column elimination tree on the permuted matrix \n  * \n  *  - Postorder the elimination tree and the column permutation\n  * \n  */\ntemplate <typename MatrixType, typename OrderingType>\nvoid SparseLU<MatrixType, OrderingType>::analyzePattern(const MatrixType& mat)\n{\n  \n  //TODO  It is possible as in SuperLU to compute row and columns scaling vectors to equilibrate the matrix mat.\n  \n  // Firstly, copy the whole input matrix. \n  m_mat = mat;\n  \n  // Compute fill-in ordering\n  OrderingType ord; \n  ord(m_mat,m_perm_c);\n  \n  // Apply the permutation to the column of the input  matrix\n  if (m_perm_c.size())\n  {\n    m_mat.uncompress(); //NOTE: The effect of this command is only to create the InnerNonzeros pointers. FIXME : This vector is filled but not subsequently used.  \n    // Then, permute only the column pointers\n    ei_declare_aligned_stack_constructed_variable(StorageIndex,outerIndexPtr,mat.cols()+1,mat.isCompressed()?const_cast<StorageIndex*>(mat.outerIndexPtr()):0);\n    \n    // If the input matrix 'mat' is uncompressed, then the outer-indices do not match the ones of m_mat, and a copy is thus needed.\n    if(!mat.isCompressed()) \n      IndexVector::Map(outerIndexPtr, mat.cols()+1) = IndexVector::Map(m_mat.outerIndexPtr(),mat.cols()+1);\n    \n    // Apply the permutation and compute the nnz per column.\n    for (Index i = 0; i < mat.cols(); i++)\n    {\n      m_mat.outerIndexPtr()[m_perm_c.indices()(i)] = outerIndexPtr[i];\n      m_mat.innerNonZeroPtr()[m_perm_c.indices()(i)] = outerIndexPtr[i+1] - outerIndexPtr[i];\n    }\n  }\n  \n  // Compute the column elimination tree of the permuted matrix \n  IndexVector firstRowElt;\n  internal::coletree(m_mat, m_etree,firstRowElt); \n     \n  // In symmetric mode, do not do postorder here\n  if (!m_symmetricmode) {\n    IndexVector post, iwork; \n    // Post order etree\n    internal::treePostorder(StorageIndex(m_mat.cols()), m_etree, post); \n      \n   \n    // Renumber etree in postorder \n    Index m = m_mat.cols(); \n    iwork.resize(m+1);\n    for (Index i = 0; i < m; ++i) iwork(post(i)) = post(m_etree(i));\n    m_etree = iwork;\n    \n    // Postmultiply A*Pc by post, i.e reorder the matrix according to the postorder of the etree\n    PermutationType post_perm(m); \n    for (Index i = 0; i < m; i++) \n      post_perm.indices()(i) = post(i); \n        \n    // Combine the two permutations : postorder the permutation for future use\n    if(m_perm_c.size()) {\n      m_perm_c = post_perm * m_perm_c;\n    }\n    \n  } // end postordering \n  \n  m_analysisIsOk = true; \n}\n\n// Functions needed by the numerical factorization phase\n\n\n/** \n  *  - Numerical factorization \n  *  - Interleaved with the symbolic factorization \n  * On exit,  info is \n  * \n  *    = 0: successful factorization\n  * \n  *    > 0: if info = i, and i is\n  * \n  *       <= A->ncol: U(i,i) is exactly zero. The factorization has\n  *          been completed, but the factor U is exactly singular,\n  *          and division by zero will occur if it is used to solve a\n  *          system of equations.\n  * \n  *       > A->ncol: number of bytes allocated when memory allocation\n  *         failure occurred, plus A->ncol. If lwork = -1, it is\n  *         the estimated amount of space needed, plus A->ncol.  \n  */\ntemplate <typename MatrixType, typename OrderingType>\nvoid SparseLU<MatrixType, OrderingType>::factorize(const MatrixType& matrix)\n{\n  using internal::emptyIdxLU;\n  eigen_assert(m_analysisIsOk && \"analyzePattern() should be called first\"); \n  eigen_assert((matrix.rows() == matrix.cols()) && \"Only for squared matrices\");\n  \n  typedef typename IndexVector::Scalar StorageIndex; \n  \n  m_isInitialized = true;\n  \n  \n  // Apply the column permutation computed in analyzepattern()\n  //   m_mat = matrix * m_perm_c.inverse(); \n  m_mat = matrix;\n  if (m_perm_c.size()) \n  {\n    m_mat.uncompress(); //NOTE: The effect of this command is only to create the InnerNonzeros pointers.\n    //Then, permute only the column pointers\n    const StorageIndex * outerIndexPtr;\n    if (matrix.isCompressed()) outerIndexPtr = matrix.outerIndexPtr();\n    else\n    {\n      StorageIndex* outerIndexPtr_t = new StorageIndex[matrix.cols()+1];\n      for(Index i = 0; i <= matrix.cols(); i++) outerIndexPtr_t[i] = m_mat.outerIndexPtr()[i];\n      outerIndexPtr = outerIndexPtr_t;\n    }\n    for (Index i = 0; i < matrix.cols(); i++)\n    {\n      m_mat.outerIndexPtr()[m_perm_c.indices()(i)] = outerIndexPtr[i];\n      m_mat.innerNonZeroPtr()[m_perm_c.indices()(i)] = outerIndexPtr[i+1] - outerIndexPtr[i];\n    }\n    if(!matrix.isCompressed()) delete[] outerIndexPtr;\n  } \n  else \n  { //FIXME This should not be needed if the empty permutation is handled transparently\n    m_perm_c.resize(matrix.cols());\n    for(StorageIndex i = 0; i < matrix.cols(); ++i) m_perm_c.indices()(i) = i;\n  }\n  \n  Index m = m_mat.rows();\n  Index n = m_mat.cols();\n  Index nnz = m_mat.nonZeros();\n  Index maxpanel = m_perfv.panel_size * m;\n  // Allocate working storage common to the factor routines\n  Index lwork = 0;\n  Index info = Base::memInit(m, n, nnz, lwork, m_perfv.fillfactor, m_perfv.panel_size, m_glu); \n  if (info) \n  {\n    m_lastError = \"UNABLE TO ALLOCATE WORKING MEMORY\\n\\n\" ;\n    m_factorizationIsOk = false;\n    return ; \n  }\n  \n  // Set up pointers for integer working arrays \n  IndexVector segrep(m); segrep.setZero();\n  IndexVector parent(m); parent.setZero();\n  IndexVector xplore(m); xplore.setZero();\n  IndexVector repfnz(maxpanel);\n  IndexVector panel_lsub(maxpanel);\n  IndexVector xprune(n); xprune.setZero();\n  IndexVector marker(m*internal::LUNoMarker); marker.setZero();\n  \n  repfnz.setConstant(-1); \n  panel_lsub.setConstant(-1);\n  \n  // Set up pointers for scalar working arrays \n  ScalarVector dense; \n  dense.setZero(maxpanel);\n  ScalarVector tempv; \n  tempv.setZero(internal::LUnumTempV(m, m_perfv.panel_size, m_perfv.maxsuper, /*m_perfv.rowblk*/m) );\n  \n  // Compute the inverse of perm_c\n  PermutationType iperm_c(m_perm_c.inverse()); \n  \n  // Identify initial relaxed snodes\n  IndexVector relax_end(n);\n  if ( m_symmetricmode == true ) \n    Base::heap_relax_snode(n, m_etree, m_perfv.relax, marker, relax_end);\n  else\n    Base::relax_snode(n, m_etree, m_perfv.relax, marker, relax_end);\n  \n  \n  m_perm_r.resize(m); \n  m_perm_r.indices().setConstant(-1);\n  marker.setConstant(-1);\n  m_detPermR = 1; // Record the determinant of the row permutation\n  \n  m_glu.supno(0) = emptyIdxLU; m_glu.xsup.setConstant(0);\n  m_glu.xsup(0) = m_glu.xlsub(0) = m_glu.xusub(0) = m_glu.xlusup(0) = Index(0);\n  \n  // Work on one 'panel' at a time. A panel is one of the following :\n  //  (a) a relaxed supernode at the bottom of the etree, or\n  //  (b) panel_size contiguous columns, <panel_size> defined by the user\n  Index jcol; \n  IndexVector panel_histo(n);\n  Index pivrow; // Pivotal row number in the original row matrix\n  Index nseg1; // Number of segments in U-column above panel row jcol\n  Index nseg; // Number of segments in each U-column \n  Index irep; \n  Index i, k, jj; \n  for (jcol = 0; jcol < n; )\n  {\n    // Adjust panel size so that a panel won't overlap with the next relaxed snode. \n    Index panel_size = m_perfv.panel_size; // upper bound on panel width\n    for (k = jcol + 1; k < (std::min)(jcol+panel_size, n); k++)\n    {\n      if (relax_end(k) != emptyIdxLU) \n      {\n        panel_size = k - jcol; \n        break; \n      }\n    }\n    if (k == n) \n      panel_size = n - jcol; \n      \n    // Symbolic outer factorization on a panel of columns \n    Base::panel_dfs(m, panel_size, jcol, m_mat, m_perm_r.indices(), nseg1, dense, panel_lsub, segrep, repfnz, xprune, marker, parent, xplore, m_glu); \n    \n    // Numeric sup-panel updates in topological order \n    Base::panel_bmod(m, panel_size, jcol, nseg1, dense, tempv, segrep, repfnz, m_glu); \n    \n    // Sparse LU within the panel, and below the panel diagonal \n    for ( jj = jcol; jj< jcol + panel_size; jj++) \n    {\n      k = (jj - jcol) * m; // Column index for w-wide arrays \n      \n      nseg = nseg1; // begin after all the panel segments\n      //Depth-first-search for the current column\n      VectorBlock<IndexVector> panel_lsubk(panel_lsub, k, m);\n      VectorBlock<IndexVector> repfnz_k(repfnz, k, m); \n      info = Base::column_dfs(m, jj, m_perm_r.indices(), m_perfv.maxsuper, nseg, panel_lsubk, segrep, repfnz_k, xprune, marker, parent, xplore, m_glu); \n      if ( info ) \n      {\n        m_lastError =  \"UNABLE TO EXPAND MEMORY IN COLUMN_DFS() \";\n        m_info = NumericalIssue; \n        m_factorizationIsOk = false; \n        return; \n      }\n      // Numeric updates to this column \n      VectorBlock<ScalarVector> dense_k(dense, k, m); \n      VectorBlock<IndexVector> segrep_k(segrep, nseg1, m-nseg1); \n      info = Base::column_bmod(jj, (nseg - nseg1), dense_k, tempv, segrep_k, repfnz_k, jcol, m_glu); \n      if ( info ) \n      {\n        m_lastError = \"UNABLE TO EXPAND MEMORY IN COLUMN_BMOD() \";\n        m_info = NumericalIssue; \n        m_factorizationIsOk = false; \n        return; \n      }\n      \n      // Copy the U-segments to ucol(*)\n      info = Base::copy_to_ucol(jj, nseg, segrep, repfnz_k ,m_perm_r.indices(), dense_k, m_glu); \n      if ( info ) \n      {\n        m_lastError = \"UNABLE TO EXPAND MEMORY IN COPY_TO_UCOL() \";\n        m_info = NumericalIssue; \n        m_factorizationIsOk = false; \n        return; \n      }\n      \n      // Form the L-segment \n      info = Base::pivotL(jj, m_diagpivotthresh, m_perm_r.indices(), iperm_c.indices(), pivrow, m_glu);\n      if ( info ) \n      {\n        m_lastError = \"THE MATRIX IS STRUCTURALLY SINGULAR ... ZERO COLUMN AT \";\n        std::ostringstream returnInfo;\n        returnInfo << info; \n        m_lastError += returnInfo.str();\n        m_info = NumericalIssue; \n        m_factorizationIsOk = false; \n        return; \n      }\n      \n      // Update the determinant of the row permutation matrix\n      // FIXME: the following test is not correct, we should probably take iperm_c into account and pivrow is not directly the row pivot.\n      if (pivrow != jj) m_detPermR = -m_detPermR;\n\n      // Prune columns (0:jj-1) using column jj\n      Base::pruneL(jj, m_perm_r.indices(), pivrow, nseg, segrep, repfnz_k, xprune, m_glu); \n      \n      // Reset repfnz for this column \n      for (i = 0; i < nseg; i++)\n      {\n        irep = segrep(i); \n        repfnz_k(irep) = emptyIdxLU; \n      }\n    } // end SparseLU within the panel  \n    jcol += panel_size;  // Move to the next panel\n  } // end for -- end elimination \n  \n  m_detPermR = m_perm_r.determinant();\n  m_detPermC = m_perm_c.determinant();\n  \n  // Count the number of nonzeros in factors \n  Base::countnz(n, m_nnzL, m_nnzU, m_glu); \n  // Apply permutation  to the L subscripts \n  Base::fixupL(n, m_perm_r.indices(), m_glu);\n  \n  // Create supernode matrix L \n  m_Lstore.setInfos(m, n, m_glu.lusup, m_glu.xlusup, m_glu.lsub, m_glu.xlsub, m_glu.supno, m_glu.xsup); \n  // Create the column major upper sparse matrix  U; \n  new (&m_Ustore) MappedSparseMatrix<Scalar, ColMajor, StorageIndex> ( m, n, m_nnzU, m_glu.xusub.data(), m_glu.usub.data(), m_glu.ucol.data() );\n  \n  m_info = Success;\n  m_factorizationIsOk = true;\n}\n\ntemplate<typename MappedSupernodalType>\nstruct SparseLUMatrixLReturnType : internal::no_assignment_operator\n{\n  typedef typename MappedSupernodalType::Scalar Scalar;\n  explicit SparseLUMatrixLReturnType(const MappedSupernodalType& mapL) : m_mapL(mapL)\n  { }\n  Index rows() { return m_mapL.rows(); }\n  Index cols() { return m_mapL.cols(); }\n  template<typename Dest>\n  void solveInPlace( MatrixBase<Dest> &X) const\n  {\n    m_mapL.solveInPlace(X);\n  }\n  const MappedSupernodalType& m_mapL;\n};\n\ntemplate<typename MatrixLType, typename MatrixUType>\nstruct SparseLUMatrixUReturnType : internal::no_assignment_operator\n{\n  typedef typename MatrixLType::Scalar Scalar;\n  SparseLUMatrixUReturnType(const MatrixLType& mapL, const MatrixUType& mapU)\n  : m_mapL(mapL),m_mapU(mapU)\n  { }\n  Index rows() { return m_mapL.rows(); }\n  Index cols() { return m_mapL.cols(); }\n\n  template<typename Dest>   void solveInPlace(MatrixBase<Dest> &X) const\n  {\n    Index nrhs = X.cols();\n    Index n    = X.rows();\n    // Backward solve with U\n    for (Index k = m_mapL.nsuper(); k >= 0; k--)\n    {\n      Index fsupc = m_mapL.supToCol()[k];\n      Index lda = m_mapL.colIndexPtr()[fsupc+1] - m_mapL.colIndexPtr()[fsupc]; // leading dimension\n      Index nsupc = m_mapL.supToCol()[k+1] - fsupc;\n      Index luptr = m_mapL.colIndexPtr()[fsupc];\n\n      if (nsupc == 1)\n      {\n        for (Index j = 0; j < nrhs; j++)\n        {\n          X(fsupc, j) /= m_mapL.valuePtr()[luptr];\n        }\n      }\n      else\n      {\n        Map<const Matrix<Scalar,Dynamic,Dynamic, ColMajor>, 0, OuterStride<> > A( &(m_mapL.valuePtr()[luptr]), nsupc, nsupc, OuterStride<>(lda) );\n        Map< Matrix<Scalar,Dynamic,Dest::ColsAtCompileTime, ColMajor>, 0, OuterStride<> > U (&(X(fsupc,0)), nsupc, nrhs, OuterStride<>(n) );\n        U = A.template triangularView<Upper>().solve(U);\n      }\n\n      for (Index j = 0; j < nrhs; ++j)\n      {\n        for (Index jcol = fsupc; jcol < fsupc + nsupc; jcol++)\n        {\n          typename MatrixUType::InnerIterator it(m_mapU, jcol);\n          for ( ; it; ++it)\n          {\n            Index irow = it.index();\n            X(irow, j) -= X(jcol, j) * it.value();\n          }\n        }\n      }\n    } // End For U-solve\n  }\n  const MatrixLType& m_mapL;\n  const MatrixUType& m_mapU;\n};\n\n} // End namespace Eigen \n\n#endif\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseLU/SparseLUImpl.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n#ifndef SPARSELU_IMPL_H\n#define SPARSELU_IMPL_H\n\nnamespace Eigen {\nnamespace internal {\n  \n/** \\ingroup SparseLU_Module\n  * \\class SparseLUImpl\n  * Base class for sparseLU\n  */\ntemplate <typename Scalar, typename StorageIndex>\nclass SparseLUImpl\n{\n  public:\n    typedef Matrix<Scalar,Dynamic,1> ScalarVector;\n    typedef Matrix<StorageIndex,Dynamic,1> IndexVector; \n    typedef Matrix<Scalar,Dynamic,Dynamic,ColMajor> ScalarMatrix;\n    typedef Map<ScalarMatrix, 0,  OuterStride<> > MappedMatrixBlock;\n    typedef typename ScalarVector::RealScalar RealScalar; \n    typedef Ref<Matrix<Scalar,Dynamic,1> > BlockScalarVector;\n    typedef Ref<Matrix<StorageIndex,Dynamic,1> > BlockIndexVector;\n    typedef LU_GlobalLU_t<IndexVector, ScalarVector> GlobalLU_t; \n    typedef SparseMatrix<Scalar,ColMajor,StorageIndex> MatrixType; \n    \n  protected:\n     template <typename VectorType>\n     Index expand(VectorType& vec, Index& length, Index nbElts, Index keep_prev, Index& num_expansions);\n     Index memInit(Index m, Index n, Index annz, Index lwork, Index fillratio, Index panel_size,  GlobalLU_t& glu); \n     template <typename VectorType>\n     Index memXpand(VectorType& vec, Index& maxlen, Index nbElts, MemType memtype, Index& num_expansions);\n     void heap_relax_snode (const Index n, IndexVector& et, const Index relax_columns, IndexVector& descendants, IndexVector& relax_end); \n     void relax_snode (const Index n, IndexVector& et, const Index relax_columns, IndexVector& descendants, IndexVector& relax_end); \n     Index snode_dfs(const Index jcol, const Index kcol,const MatrixType& mat,  IndexVector& xprune, IndexVector& marker, GlobalLU_t& glu); \n     Index snode_bmod (const Index jcol, const Index fsupc, ScalarVector& dense, GlobalLU_t& glu);\n     Index pivotL(const Index jcol, const RealScalar& diagpivotthresh, IndexVector& perm_r, IndexVector& iperm_c, Index& pivrow, GlobalLU_t& glu);\n     template <typename Traits>\n     void dfs_kernel(const StorageIndex jj, IndexVector& perm_r,\n                    Index& nseg, IndexVector& panel_lsub, IndexVector& segrep,\n                    Ref<IndexVector> repfnz_col, IndexVector& xprune, Ref<IndexVector> marker, IndexVector& parent,\n                    IndexVector& xplore, GlobalLU_t& glu, Index& nextl_col, Index krow, Traits& traits);\n     void panel_dfs(const Index m, const Index w, const Index jcol, MatrixType& A, IndexVector& perm_r, Index& nseg, ScalarVector& dense, IndexVector& panel_lsub, IndexVector& segrep, IndexVector& repfnz, IndexVector& xprune, IndexVector& marker, IndexVector& parent, IndexVector& xplore, GlobalLU_t& glu);\n    \n     void panel_bmod(const Index m, const Index w, const Index jcol, const Index nseg, ScalarVector& dense, ScalarVector& tempv, IndexVector& segrep, IndexVector& repfnz, GlobalLU_t& glu);\n     Index column_dfs(const Index m, const Index jcol, IndexVector& perm_r, Index maxsuper, Index& nseg,  BlockIndexVector lsub_col, IndexVector& segrep, BlockIndexVector repfnz, IndexVector& xprune, IndexVector& marker, IndexVector& parent, IndexVector& xplore, GlobalLU_t& glu);\n     Index column_bmod(const Index jcol, const Index nseg, BlockScalarVector dense, ScalarVector& tempv, BlockIndexVector segrep, BlockIndexVector repfnz, Index fpanelc, GlobalLU_t& glu); \n     Index copy_to_ucol(const Index jcol, const Index nseg, IndexVector& segrep, BlockIndexVector repfnz ,IndexVector& perm_r, BlockScalarVector dense, GlobalLU_t& glu); \n     void pruneL(const Index jcol, const IndexVector& perm_r, const Index pivrow, const Index nseg, const IndexVector& segrep, BlockIndexVector repfnz, IndexVector& xprune, GlobalLU_t& glu);\n     void countnz(const Index n, Index& nnzL, Index& nnzU, GlobalLU_t& glu); \n     void fixupL(const Index n, const IndexVector& perm_r, GlobalLU_t& glu); \n     \n     template<typename , typename >\n     friend struct column_dfs_traits;\n}; \n\n} // end namespace internal\n} // namespace Eigen\n\n#endif\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseLU/SparseLU_Memory.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n/* \n \n * NOTE: This file is the modified version of [s,d,c,z]memory.c files in SuperLU \n \n * -- SuperLU routine (version 3.1) --\n * Univ. of California Berkeley, Xerox Palo Alto Research Center,\n * and Lawrence Berkeley National Lab.\n * August 1, 2008\n *\n * Copyright (c) 1994 by Xerox Corporation.  All rights reserved.\n *\n * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY\n * EXPRESSED OR IMPLIED.  ANY USE IS AT YOUR OWN RISK.\n *\n * Permission is hereby granted to use or copy this program for any\n * purpose, provided the above notices are retained on all copies.\n * Permission to modify the code and to distribute modified code is\n * granted, provided the above notices are retained, and a notice that\n * the code was modified is included with the above copyright notice.\n */\n\n#ifndef EIGEN_SPARSELU_MEMORY\n#define EIGEN_SPARSELU_MEMORY\n\nnamespace Eigen {\nnamespace internal {\n  \nenum { LUNoMarker = 3 };\nenum {emptyIdxLU = -1};\ninline Index LUnumTempV(Index& m, Index& w, Index& t, Index& b)\n{\n  return (std::max)(m, (t+b)*w);\n}\n\ntemplate< typename Scalar>\ninline Index LUTempSpace(Index&m, Index& w)\n{\n  return (2*w + 4 + LUNoMarker) * m * sizeof(Index) + (w + 1) * m * sizeof(Scalar);\n}\n\n\n\n\n/** \n  * Expand the existing storage to accomodate more fill-ins\n  * \\param vec Valid pointer to the vector to allocate or expand\n  * \\param[in,out] length  At input, contain the current length of the vector that is to be increased. At output, length of the newly allocated vector\n  * \\param[in] nbElts Current number of elements in the factors\n  * \\param keep_prev  1: use length  and do not expand the vector; 0: compute new_len and expand\n  * \\param[in,out] num_expansions Number of times the memory has been expanded\n  */\ntemplate <typename Scalar, typename StorageIndex>\ntemplate <typename VectorType>\nIndex  SparseLUImpl<Scalar,StorageIndex>::expand(VectorType& vec, Index& length, Index nbElts, Index keep_prev, Index& num_expansions) \n{\n  \n  float alpha = 1.5; // Ratio of the memory increase \n  Index new_len; // New size of the allocated memory\n  \n  if(num_expansions == 0 || keep_prev) \n    new_len = length ; // First time allocate requested\n  else \n    new_len = (std::max)(length+1,Index(alpha * length));\n  \n  VectorType old_vec; // Temporary vector to hold the previous values   \n  if (nbElts > 0 )\n    old_vec = vec.segment(0,nbElts); \n  \n  //Allocate or expand the current vector\n#ifdef EIGEN_EXCEPTIONS\n  try\n#endif\n  {\n    vec.resize(new_len); \n  }\n#ifdef EIGEN_EXCEPTIONS\n  catch(std::bad_alloc& )\n#else\n  if(!vec.size())\n#endif\n  {\n    if (!num_expansions)\n    {\n      // First time to allocate from LUMemInit()\n      // Let LUMemInit() deals with it.\n      return -1;\n    }\n    if (keep_prev)\n    {\n      // In this case, the memory length should not not be reduced\n      return new_len;\n    }\n    else \n    {\n      // Reduce the size and increase again \n      Index tries = 0; // Number of attempts\n      do \n      {\n        alpha = (alpha + 1)/2;\n        new_len = (std::max)(length+1,Index(alpha * length));\n#ifdef EIGEN_EXCEPTIONS\n        try\n#endif\n        {\n          vec.resize(new_len); \n        }\n#ifdef EIGEN_EXCEPTIONS\n        catch(std::bad_alloc& )\n#else\n        if (!vec.size())\n#endif\n        {\n          tries += 1; \n          if ( tries > 10) return new_len; \n        }\n      } while (!vec.size());\n    }\n  }\n  //Copy the previous values to the newly allocated space \n  if (nbElts > 0)\n    vec.segment(0, nbElts) = old_vec;   \n   \n  \n  length  = new_len;\n  if(num_expansions) ++num_expansions;\n  return 0; \n}\n\n/**\n * \\brief  Allocate various working space for the numerical factorization phase.\n * \\param m number of rows of the input matrix \n * \\param n number of columns \n * \\param annz number of initial nonzeros in the matrix \n * \\param lwork  if lwork=-1, this routine returns an estimated size of the required memory\n * \\param glu persistent data to facilitate multiple factors : will be deleted later ??\n * \\param fillratio estimated ratio of fill in the factors\n * \\param panel_size Size of a panel\n * \\return an estimated size of the required memory if lwork = -1; otherwise, return the size of actually allocated memory when allocation failed, and 0 on success\n * \\note Unlike SuperLU, this routine does not support successive factorization with the same pattern and the same row permutation\n */\ntemplate <typename Scalar, typename StorageIndex>\nIndex SparseLUImpl<Scalar,StorageIndex>::memInit(Index m, Index n, Index annz, Index lwork, Index fillratio, Index panel_size,  GlobalLU_t& glu)\n{\n  Index& num_expansions = glu.num_expansions; //No memory expansions so far\n  num_expansions = 0;\n  glu.nzumax = glu.nzlumax = (std::min)(fillratio * (annz+1) / n, m) * n; // estimated number of nonzeros in U \n  glu.nzlmax = (std::max)(Index(4), fillratio) * (annz+1) / 4; // estimated  nnz in L factor\n  // Return the estimated size to the user if necessary\n  Index tempSpace;\n  tempSpace = (2*panel_size + 4 + LUNoMarker) * m * sizeof(Index) + (panel_size + 1) * m * sizeof(Scalar);\n  if (lwork == emptyIdxLU) \n  {\n    Index estimated_size;\n    estimated_size = (5 * n + 5) * sizeof(Index)  + tempSpace\n                    + (glu.nzlmax + glu.nzumax) * sizeof(Index) + (glu.nzlumax+glu.nzumax) *  sizeof(Scalar) + n; \n    return estimated_size;\n  }\n  \n  // Setup the required space \n  \n  // First allocate Integer pointers for L\\U factors\n  glu.xsup.resize(n+1);\n  glu.supno.resize(n+1);\n  glu.xlsub.resize(n+1);\n  glu.xlusup.resize(n+1);\n  glu.xusub.resize(n+1);\n\n  // Reserve memory for L/U factors\n  do \n  {\n    if(     (expand<ScalarVector>(glu.lusup, glu.nzlumax, 0, 0, num_expansions)<0)\n        ||  (expand<ScalarVector>(glu.ucol,  glu.nzumax,  0, 0, num_expansions)<0)\n        ||  (expand<IndexVector> (glu.lsub,  glu.nzlmax,  0, 0, num_expansions)<0)\n        ||  (expand<IndexVector> (glu.usub,  glu.nzumax,  0, 1, num_expansions)<0) )\n    {\n      //Reduce the estimated size and retry\n      glu.nzlumax /= 2;\n      glu.nzumax /= 2;\n      glu.nzlmax /= 2;\n      if (glu.nzlumax < annz ) return glu.nzlumax; \n    }\n  } while (!glu.lusup.size() || !glu.ucol.size() || !glu.lsub.size() || !glu.usub.size());\n  \n  ++num_expansions;\n  return 0;\n  \n} // end LuMemInit\n\n/** \n * \\brief Expand the existing storage \n * \\param vec vector to expand \n * \\param[in,out] maxlen On input, previous size of vec (Number of elements to copy ). on output, new size\n * \\param nbElts current number of elements in the vector.\n * \\param memtype Type of the element to expand\n * \\param num_expansions Number of expansions \n * \\return 0 on success, > 0 size of the memory allocated so far\n */\ntemplate <typename Scalar, typename StorageIndex>\ntemplate <typename VectorType>\nIndex SparseLUImpl<Scalar,StorageIndex>::memXpand(VectorType& vec, Index& maxlen, Index nbElts, MemType memtype, Index& num_expansions)\n{\n  Index failed_size; \n  if (memtype == USUB)\n     failed_size = this->expand<VectorType>(vec, maxlen, nbElts, 1, num_expansions);\n  else\n    failed_size = this->expand<VectorType>(vec, maxlen, nbElts, 0, num_expansions);\n\n  if (failed_size)\n    return failed_size; \n  \n  return 0 ;  \n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n#endif // EIGEN_SPARSELU_MEMORY\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseLU/SparseLU_Structs.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n/* \n * NOTE: This file comes from a partly modified version of files slu_[s,d,c,z]defs.h\n * -- SuperLU routine (version 4.1) --\n * Univ. of California Berkeley, Xerox Palo Alto Research Center,\n * and Lawrence Berkeley National Lab.\n * November, 2010\n * \n * Global data structures used in LU factorization -\n * \n *   nsuper: #supernodes = nsuper + 1, numbered [0, nsuper].\n *   (xsup,supno): supno[i] is the supernode no to which i belongs;\n *  xsup(s) points to the beginning of the s-th supernode.\n *  e.g.   supno 0 1 2 2 3 3 3 4 4 4 4 4   (n=12)\n *          xsup 0 1 2 4 7 12\n *  Note: dfs will be performed on supernode rep. relative to the new \n *        row pivoting ordering\n *\n *   (xlsub,lsub): lsub[*] contains the compressed subscript of\n *  rectangular supernodes; xlsub[j] points to the starting\n *  location of the j-th column in lsub[*]. Note that xlsub \n *  is indexed by column.\n *  Storage: original row subscripts\n *\n *      During the course of sparse LU factorization, we also use\n *  (xlsub,lsub) for the purpose of symmetric pruning. For each\n *  supernode {s,s+1,...,t=s+r} with first column s and last\n *  column t, the subscript set\n *    lsub[j], j=xlsub[s], .., xlsub[s+1]-1\n *  is the structure of column s (i.e. structure of this supernode).\n *  It is used for the storage of numerical values.\n *  Furthermore,\n *    lsub[j], j=xlsub[t], .., xlsub[t+1]-1\n *  is the structure of the last column t of this supernode.\n *  It is for the purpose of symmetric pruning. Therefore, the\n *  structural subscripts can be rearranged without making physical\n *  interchanges among the numerical values.\n *\n *  However, if the supernode has only one column, then we\n *  only keep one set of subscripts. For any subscript interchange\n *  performed, similar interchange must be done on the numerical\n *  values.\n *\n *  The last column structures (for pruning) will be removed\n *  after the numercial LU factorization phase.\n *\n *   (xlusup,lusup): lusup[*] contains the numerical values of the\n *  rectangular supernodes; xlusup[j] points to the starting\n *  location of the j-th column in storage vector lusup[*]\n *  Note: xlusup is indexed by column.\n *  Each rectangular supernode is stored by column-major\n *  scheme, consistent with Fortran 2-dim array storage.\n *\n *   (xusub,ucol,usub): ucol[*] stores the numerical values of\n *  U-columns outside the rectangular supernodes. The row\n *  subscript of nonzero ucol[k] is stored in usub[k].\n *  xusub[i] points to the starting location of column i in ucol.\n *  Storage: new row subscripts; that is subscripts of PA.\n */\n\n#ifndef EIGEN_LU_STRUCTS\n#define EIGEN_LU_STRUCTS\nnamespace Eigen {\nnamespace internal {\n  \ntypedef enum {LUSUP, UCOL, LSUB, USUB, LLVL, ULVL} MemType; \n\ntemplate <typename IndexVector, typename ScalarVector>\nstruct LU_GlobalLU_t {\n  typedef typename IndexVector::Scalar StorageIndex; \n  IndexVector xsup; //First supernode column ... xsup(s) points to the beginning of the s-th supernode\n  IndexVector supno; // Supernode number corresponding to this column (column to supernode mapping)\n  ScalarVector  lusup; // nonzero values of L ordered by columns \n  IndexVector lsub; // Compressed row indices of L rectangular supernodes. \n  IndexVector xlusup; // pointers to the beginning of each column in lusup\n  IndexVector xlsub; // pointers to the beginning of each column in lsub\n  Index   nzlmax; // Current max size of lsub\n  Index   nzlumax; // Current max size of lusup\n  ScalarVector  ucol; // nonzero values of U ordered by columns \n  IndexVector usub; // row indices of U columns in ucol\n  IndexVector xusub; // Pointers to the beginning of each column of U in ucol \n  Index   nzumax; // Current max size of ucol\n  Index   n; // Number of columns in the matrix  \n  Index   num_expansions; \n};\n\n// Values to set for performance\nstruct perfvalues {\n  Index panel_size; // a panel consists of at most <panel_size> consecutive columns\n  Index relax; // To control degree of relaxing supernodes. If the number of nodes (columns) \n                // in a subtree of the elimination tree is less than relax, this subtree is considered \n                // as one supernode regardless of the row structures of those columns\n  Index maxsuper; // The maximum size for a supernode in complete LU\n  Index rowblk; // The minimum row dimension for 2-D blocking to be used;\n  Index colblk; // The minimum column dimension for 2-D blocking to be used;\n  Index fillfactor; // The estimated fills factors for L and U, compared with A\n}; \n\n} // end namespace internal\n\n} // end namespace Eigen\n#endif // EIGEN_LU_STRUCTS\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseLU/SparseLU_SupernodalMatrix.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>\n// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSELU_SUPERNODAL_MATRIX_H\n#define EIGEN_SPARSELU_SUPERNODAL_MATRIX_H\n\nnamespace Eigen {\nnamespace internal {\n\n/** \\ingroup SparseLU_Module\n * \\brief a class to manipulate the L supernodal factor from the SparseLU factorization\n * \n * This class  contain the data to easily store \n * and manipulate the supernodes during the factorization and solution phase of Sparse LU. \n * Only the lower triangular matrix has supernodes.\n * \n * NOTE : This class corresponds to the SCformat structure in SuperLU\n * \n */\n/* TODO\n * InnerIterator as for sparsematrix \n * SuperInnerIterator to iterate through all supernodes \n * Function for triangular solve\n */\ntemplate <typename _Scalar, typename _StorageIndex>\nclass MappedSuperNodalMatrix\n{\n  public:\n    typedef _Scalar Scalar; \n    typedef _StorageIndex StorageIndex;\n    typedef Matrix<StorageIndex,Dynamic,1> IndexVector;\n    typedef Matrix<Scalar,Dynamic,1> ScalarVector;\n  public:\n    MappedSuperNodalMatrix()\n    {\n      \n    }\n    MappedSuperNodalMatrix(Index m, Index n,  ScalarVector& nzval, IndexVector& nzval_colptr, IndexVector& rowind,\n             IndexVector& rowind_colptr, IndexVector& col_to_sup, IndexVector& sup_to_col )\n    {\n      setInfos(m, n, nzval, nzval_colptr, rowind, rowind_colptr, col_to_sup, sup_to_col);\n    }\n    \n    ~MappedSuperNodalMatrix()\n    {\n      \n    }\n    /**\n     * Set appropriate pointers for the lower triangular supernodal matrix\n     * These infos are available at the end of the numerical factorization\n     * FIXME This class will be modified such that it can be use in the course \n     * of the factorization.\n     */\n    void setInfos(Index m, Index n, ScalarVector& nzval, IndexVector& nzval_colptr, IndexVector& rowind,\n             IndexVector& rowind_colptr, IndexVector& col_to_sup, IndexVector& sup_to_col )\n    {\n      m_row = m;\n      m_col = n; \n      m_nzval = nzval.data(); \n      m_nzval_colptr = nzval_colptr.data(); \n      m_rowind = rowind.data(); \n      m_rowind_colptr = rowind_colptr.data(); \n      m_nsuper = col_to_sup(n); \n      m_col_to_sup = col_to_sup.data(); \n      m_sup_to_col = sup_to_col.data(); \n    }\n    \n    /**\n     * Number of rows\n     */\n    Index rows() { return m_row; }\n    \n    /**\n     * Number of columns\n     */\n    Index cols() { return m_col; }\n    \n    /**\n     * Return the array of nonzero values packed by column\n     * \n     * The size is nnz\n     */\n    Scalar* valuePtr() {  return m_nzval; }\n    \n    const Scalar* valuePtr() const \n    {\n      return m_nzval; \n    }\n    /**\n     * Return the pointers to the beginning of each column in \\ref valuePtr()\n     */\n    StorageIndex* colIndexPtr()\n    {\n      return m_nzval_colptr; \n    }\n    \n    const StorageIndex* colIndexPtr() const\n    {\n      return m_nzval_colptr; \n    }\n    \n    /**\n     * Return the array of compressed row indices of all supernodes\n     */\n    StorageIndex* rowIndex()  { return m_rowind; }\n    \n    const StorageIndex* rowIndex() const\n    {\n      return m_rowind; \n    }\n    \n    /**\n     * Return the location in \\em rowvaluePtr() which starts each column\n     */\n    StorageIndex* rowIndexPtr() { return m_rowind_colptr; }\n    \n    const StorageIndex* rowIndexPtr() const\n    {\n      return m_rowind_colptr; \n    }\n    \n    /** \n     * Return the array of column-to-supernode mapping \n     */\n    StorageIndex* colToSup()  { return m_col_to_sup; }\n    \n    const StorageIndex* colToSup() const\n    {\n      return m_col_to_sup;       \n    }\n    /**\n     * Return the array of supernode-to-column mapping\n     */\n    StorageIndex* supToCol() { return m_sup_to_col; }\n    \n    const StorageIndex* supToCol() const\n    {\n      return m_sup_to_col;\n    }\n    \n    /**\n     * Return the number of supernodes\n     */\n    Index nsuper() const\n    {\n      return m_nsuper; \n    }\n    \n    class InnerIterator; \n    template<typename Dest>\n    void solveInPlace( MatrixBase<Dest>&X) const;\n    \n      \n      \n    \n  protected:\n    Index m_row; // Number of rows\n    Index m_col; // Number of columns\n    Index m_nsuper; // Number of supernodes\n    Scalar* m_nzval; //array of nonzero values packed by column\n    StorageIndex* m_nzval_colptr; //nzval_colptr[j] Stores the location in nzval[] which starts column j\n    StorageIndex* m_rowind; // Array of compressed row indices of rectangular supernodes\n    StorageIndex* m_rowind_colptr; //rowind_colptr[j] stores the location in rowind[] which starts column j\n    StorageIndex* m_col_to_sup; // col_to_sup[j] is the supernode number to which column j belongs\n    StorageIndex* m_sup_to_col; //sup_to_col[s] points to the starting column of the s-th supernode\n    \n  private :\n};\n\n/**\n  * \\brief InnerIterator class to iterate over nonzero values of the current column in the supernodal matrix L\n  * \n  */\ntemplate<typename Scalar, typename StorageIndex>\nclass MappedSuperNodalMatrix<Scalar,StorageIndex>::InnerIterator\n{\n  public:\n     InnerIterator(const MappedSuperNodalMatrix& mat, Index outer)\n      : m_matrix(mat),\n        m_outer(outer),\n        m_supno(mat.colToSup()[outer]),\n        m_idval(mat.colIndexPtr()[outer]),\n        m_startidval(m_idval),\n        m_endidval(mat.colIndexPtr()[outer+1]),\n        m_idrow(mat.rowIndexPtr()[mat.supToCol()[mat.colToSup()[outer]]]),\n        m_endidrow(mat.rowIndexPtr()[mat.supToCol()[mat.colToSup()[outer]]+1])\n    {}\n    inline InnerIterator& operator++()\n    { \n      m_idval++; \n      m_idrow++;\n      return *this;\n    }\n    inline Scalar value() const { return m_matrix.valuePtr()[m_idval]; }\n    \n    inline Scalar& valueRef() { return const_cast<Scalar&>(m_matrix.valuePtr()[m_idval]); }\n    \n    inline Index index() const { return m_matrix.rowIndex()[m_idrow]; }\n    inline Index row() const { return index(); }\n    inline Index col() const { return m_outer; }\n    \n    inline Index supIndex() const { return m_supno; }\n    \n    inline operator bool() const \n    { \n      return ( (m_idval < m_endidval) && (m_idval >= m_startidval)\n                && (m_idrow < m_endidrow) );\n    }\n    \n  protected:\n    const MappedSuperNodalMatrix& m_matrix; // Supernodal lower triangular matrix \n    const Index m_outer;                    // Current column \n    const Index m_supno;                    // Current SuperNode number\n    Index m_idval;                          // Index to browse the values in the current column\n    const Index m_startidval;               // Start of the column value\n    const Index m_endidval;                 // End of the column value\n    Index m_idrow;                          // Index to browse the row indices \n    Index m_endidrow;                       // End index of row indices of the current column\n};\n\n/**\n * \\brief Solve with the supernode triangular matrix\n * \n */\ntemplate<typename Scalar, typename Index_>\ntemplate<typename Dest>\nvoid MappedSuperNodalMatrix<Scalar,Index_>::solveInPlace( MatrixBase<Dest>&X) const\n{\n    /* Explicit type conversion as the Index type of MatrixBase<Dest> may be wider than Index */\n//    eigen_assert(X.rows() <= NumTraits<Index>::highest());\n//    eigen_assert(X.cols() <= NumTraits<Index>::highest());\n    Index n    = int(X.rows());\n    Index nrhs = Index(X.cols());\n    const Scalar * Lval = valuePtr();                 // Nonzero values \n    Matrix<Scalar,Dynamic,Dest::ColsAtCompileTime, ColMajor> work(n, nrhs);     // working vector\n    work.setZero();\n    for (Index k = 0; k <= nsuper(); k ++)\n    {\n      Index fsupc = supToCol()[k];                    // First column of the current supernode \n      Index istart = rowIndexPtr()[fsupc];            // Pointer index to the subscript of the current column\n      Index nsupr = rowIndexPtr()[fsupc+1] - istart;  // Number of rows in the current supernode\n      Index nsupc = supToCol()[k+1] - fsupc;          // Number of columns in the current supernode\n      Index nrow = nsupr - nsupc;                     // Number of rows in the non-diagonal part of the supernode\n      Index irow;                                     //Current index row\n      \n      if (nsupc == 1 )\n      {\n        for (Index j = 0; j < nrhs; j++)\n        {\n          InnerIterator it(*this, fsupc);\n          ++it; // Skip the diagonal element\n          for (; it; ++it)\n          {\n            irow = it.row();\n            X(irow, j) -= X(fsupc, j) * it.value();\n          }\n        }\n      }\n      else\n      {\n        // The supernode has more than one column \n        Index luptr = colIndexPtr()[fsupc]; \n        Index lda = colIndexPtr()[fsupc+1] - luptr;\n        \n        // Triangular solve \n        Map<const Matrix<Scalar,Dynamic,Dynamic, ColMajor>, 0, OuterStride<> > A( &(Lval[luptr]), nsupc, nsupc, OuterStride<>(lda) );\n        Map< Matrix<Scalar,Dynamic,Dest::ColsAtCompileTime, ColMajor>, 0, OuterStride<> > U (&(X(fsupc,0)), nsupc, nrhs, OuterStride<>(n) );\n        U = A.template triangularView<UnitLower>().solve(U); \n        \n        // Matrix-vector product \n        new (&A) Map<const Matrix<Scalar,Dynamic,Dynamic, ColMajor>, 0, OuterStride<> > ( &(Lval[luptr+nsupc]), nrow, nsupc, OuterStride<>(lda) );\n        work.topRows(nrow).noalias() = A * U;\n        \n        //Begin Scatter \n        for (Index j = 0; j < nrhs; j++)\n        {\n          Index iptr = istart + nsupc; \n          for (Index i = 0; i < nrow; i++)\n          {\n            irow = rowIndex()[iptr]; \n            X(irow, j) -= work(i, j); // Scatter operation\n            work(i, j) = Scalar(0); \n            iptr++;\n          }\n        }\n      }\n    } \n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_SPARSELU_MATRIX_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseLU/SparseLU_Utils.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n\n#ifndef EIGEN_SPARSELU_UTILS_H\n#define EIGEN_SPARSELU_UTILS_H\n\nnamespace Eigen {\nnamespace internal {\n\n/**\n * \\brief Count Nonzero elements in the factors\n */\ntemplate <typename Scalar, typename StorageIndex>\nvoid SparseLUImpl<Scalar,StorageIndex>::countnz(const Index n, Index& nnzL, Index& nnzU, GlobalLU_t& glu)\n{\n nnzL = 0; \n nnzU = (glu.xusub)(n); \n Index nsuper = (glu.supno)(n); \n Index jlen; \n Index i, j, fsupc;\n if (n <= 0 ) return; \n // For each supernode\n for (i = 0; i <= nsuper; i++)\n {\n   fsupc = glu.xsup(i); \n   jlen = glu.xlsub(fsupc+1) - glu.xlsub(fsupc); \n   \n   for (j = fsupc; j < glu.xsup(i+1); j++)\n   {\n     nnzL += jlen; \n     nnzU += j - fsupc + 1; \n     jlen--; \n   }\n }\n}\n\n/**\n * \\brief Fix up the data storage lsub for L-subscripts. \n * \n * It removes the subscripts sets for structural pruning, \n * and applies permutation to the remaining subscripts\n * \n */\ntemplate <typename Scalar, typename StorageIndex>\nvoid SparseLUImpl<Scalar,StorageIndex>::fixupL(const Index n, const IndexVector& perm_r, GlobalLU_t& glu)\n{\n  Index fsupc, i, j, k, jstart; \n  \n  StorageIndex nextl = 0; \n  Index nsuper = (glu.supno)(n); \n  \n  // For each supernode \n  for (i = 0; i <= nsuper; i++)\n  {\n    fsupc = glu.xsup(i); \n    jstart = glu.xlsub(fsupc); \n    glu.xlsub(fsupc) = nextl; \n    for (j = jstart; j < glu.xlsub(fsupc + 1); j++)\n    {\n      glu.lsub(nextl) = perm_r(glu.lsub(j)); // Now indexed into P*A\n      nextl++;\n    }\n    for (k = fsupc+1; k < glu.xsup(i+1); k++)\n      glu.xlsub(k) = nextl; // other columns in supernode i\n  }\n  \n  glu.xlsub(n) = nextl; \n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n#endif // EIGEN_SPARSELU_UTILS_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseLU/SparseLU_column_bmod.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>\n// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n/* \n \n * NOTE: This file is the modified version of xcolumn_bmod.c file in SuperLU \n \n * -- SuperLU routine (version 3.0) --\n * Univ. of California Berkeley, Xerox Palo Alto Research Center,\n * and Lawrence Berkeley National Lab.\n * October 15, 2003\n *\n * Copyright (c) 1994 by Xerox Corporation.  All rights reserved.\n *\n * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY\n * EXPRESSED OR IMPLIED.  ANY USE IS AT YOUR OWN RISK.\n *\n * Permission is hereby granted to use or copy this program for any\n * purpose, provided the above notices are retained on all copies.\n * Permission to modify the code and to distribute modified code is\n * granted, provided the above notices are retained, and a notice that\n * the code was modified is included with the above copyright notice.\n */\n#ifndef SPARSELU_COLUMN_BMOD_H\n#define SPARSELU_COLUMN_BMOD_H\n\nnamespace Eigen {\n\nnamespace internal {\n/**\n * \\brief Performs numeric block updates (sup-col) in topological order\n * \n * \\param jcol current column to update\n * \\param nseg Number of segments in the U part\n * \\param dense Store the full representation of the column\n * \\param tempv working array \n * \\param segrep segment representative ...\n * \\param repfnz ??? First nonzero column in each row ???  ...\n * \\param fpanelc First column in the current panel\n * \\param glu Global LU data. \n * \\return 0 - successful return \n *         > 0 - number of bytes allocated when run out of space\n * \n */\ntemplate <typename Scalar, typename StorageIndex>\nIndex SparseLUImpl<Scalar,StorageIndex>::column_bmod(const Index jcol, const Index nseg, BlockScalarVector dense, ScalarVector& tempv,\n                                                     BlockIndexVector segrep, BlockIndexVector repfnz, Index fpanelc, GlobalLU_t& glu)\n{\n  Index  jsupno, k, ksub, krep, ksupno; \n  Index lptr, nrow, isub, irow, nextlu, new_next, ufirst; \n  Index fsupc, nsupc, nsupr, luptr, kfnz, no_zeros; \n  /* krep = representative of current k-th supernode\n    * fsupc =  first supernodal column\n    * nsupc = number of columns in a supernode\n    * nsupr = number of rows in a supernode\n    * luptr = location of supernodal LU-block in storage\n    * kfnz = first nonz in the k-th supernodal segment\n    * no_zeros = no lf leading zeros in a supernodal U-segment\n    */\n  \n  jsupno = glu.supno(jcol);\n  // For each nonzero supernode segment of U[*,j] in topological order \n  k = nseg - 1; \n  Index d_fsupc; // distance between the first column of the current panel and the \n               // first column of the current snode\n  Index fst_col; // First column within small LU update\n  Index segsize; \n  for (ksub = 0; ksub < nseg; ksub++)\n  {\n    krep = segrep(k); k--; \n    ksupno = glu.supno(krep); \n    if (jsupno != ksupno )\n    {\n      // outside the rectangular supernode \n      fsupc = glu.xsup(ksupno); \n      fst_col = (std::max)(fsupc, fpanelc); \n      \n      // Distance from the current supernode to the current panel; \n      // d_fsupc = 0 if fsupc > fpanelc\n      d_fsupc = fst_col - fsupc; \n      \n      luptr = glu.xlusup(fst_col) + d_fsupc; \n      lptr = glu.xlsub(fsupc) + d_fsupc; \n      \n      kfnz = repfnz(krep); \n      kfnz = (std::max)(kfnz, fpanelc); \n      \n      segsize = krep - kfnz + 1; \n      nsupc = krep - fst_col + 1; \n      nsupr = glu.xlsub(fsupc+1) - glu.xlsub(fsupc); \n      nrow = nsupr - d_fsupc - nsupc;\n      Index lda = glu.xlusup(fst_col+1) - glu.xlusup(fst_col);\n      \n      \n      // Perform a triangular solver and block update, \n      // then scatter the result of sup-col update to dense\n      no_zeros = kfnz - fst_col; \n      if(segsize==1)\n        LU_kernel_bmod<1>::run(segsize, dense, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr, no_zeros);\n      else\n        LU_kernel_bmod<Dynamic>::run(segsize, dense, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr, no_zeros);\n    } // end if jsupno \n  } // end for each segment\n  \n  // Process the supernodal portion of  L\\U[*,j]\n  nextlu = glu.xlusup(jcol); \n  fsupc = glu.xsup(jsupno);\n  \n  // copy the SPA dense into L\\U[*,j]\n  Index mem; \n  new_next = nextlu + glu.xlsub(fsupc + 1) - glu.xlsub(fsupc); \n  Index offset = internal::first_multiple<Index>(new_next, internal::packet_traits<Scalar>::size) - new_next;\n  if(offset)\n    new_next += offset;\n  while (new_next > glu.nzlumax )\n  {\n    mem = memXpand<ScalarVector>(glu.lusup, glu.nzlumax, nextlu, LUSUP, glu.num_expansions);  \n    if (mem) return mem; \n  }\n  \n  for (isub = glu.xlsub(fsupc); isub < glu.xlsub(fsupc+1); isub++)\n  {\n    irow = glu.lsub(isub);\n    glu.lusup(nextlu) = dense(irow);\n    dense(irow) = Scalar(0.0); \n    ++nextlu; \n  }\n  \n  if(offset)\n  {\n    glu.lusup.segment(nextlu,offset).setZero();\n    nextlu += offset;\n  }\n  glu.xlusup(jcol + 1) = StorageIndex(nextlu);  // close L\\U(*,jcol); \n  \n  /* For more updates within the panel (also within the current supernode),\n   * should start from the first column of the panel, or the first column\n   * of the supernode, whichever is bigger. There are two cases:\n   *  1) fsupc < fpanelc, then fst_col <-- fpanelc\n   *  2) fsupc >= fpanelc, then fst_col <-- fsupc\n   */\n  fst_col = (std::max)(fsupc, fpanelc); \n  \n  if (fst_col  < jcol)\n  {\n    // Distance between the current supernode and the current panel\n    // d_fsupc = 0 if fsupc >= fpanelc\n    d_fsupc = fst_col - fsupc; \n    \n    lptr = glu.xlsub(fsupc) + d_fsupc; \n    luptr = glu.xlusup(fst_col) + d_fsupc; \n    nsupr = glu.xlsub(fsupc+1) - glu.xlsub(fsupc); // leading dimension\n    nsupc = jcol - fst_col; // excluding jcol \n    nrow = nsupr - d_fsupc - nsupc; \n    \n    // points to the beginning of jcol in snode L\\U(jsupno) \n    ufirst = glu.xlusup(jcol) + d_fsupc; \n    Index lda = glu.xlusup(jcol+1) - glu.xlusup(jcol);\n    MappedMatrixBlock A( &(glu.lusup.data()[luptr]), nsupc, nsupc, OuterStride<>(lda) );\n    VectorBlock<ScalarVector> u(glu.lusup, ufirst, nsupc); \n    u = A.template triangularView<UnitLower>().solve(u); \n    \n    new (&A) MappedMatrixBlock ( &(glu.lusup.data()[luptr+nsupc]), nrow, nsupc, OuterStride<>(lda) );\n    VectorBlock<ScalarVector> l(glu.lusup, ufirst+nsupc, nrow); \n    l.noalias() -= A * u;\n    \n  } // End if fst_col\n  return 0; \n}\n\n} // end namespace internal\n} // end namespace Eigen\n\n#endif // SPARSELU_COLUMN_BMOD_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseLU/SparseLU_column_dfs.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n/* \n \n * NOTE: This file is the modified version of [s,d,c,z]column_dfs.c file in SuperLU \n \n * -- SuperLU routine (version 2.0) --\n * Univ. of California Berkeley, Xerox Palo Alto Research Center,\n * and Lawrence Berkeley National Lab.\n * November 15, 1997\n *\n * Copyright (c) 1994 by Xerox Corporation.  All rights reserved.\n *\n * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY\n * EXPRESSED OR IMPLIED.  ANY USE IS AT YOUR OWN RISK.\n *\n * Permission is hereby granted to use or copy this program for any\n * purpose, provided the above notices are retained on all copies.\n * Permission to modify the code and to distribute modified code is\n * granted, provided the above notices are retained, and a notice that\n * the code was modified is included with the above copyright notice.\n */\n#ifndef SPARSELU_COLUMN_DFS_H\n#define SPARSELU_COLUMN_DFS_H\n\ntemplate <typename Scalar, typename StorageIndex> class SparseLUImpl;\nnamespace Eigen {\n\nnamespace internal {\n\ntemplate<typename IndexVector, typename ScalarVector>\nstruct column_dfs_traits : no_assignment_operator\n{\n  typedef typename ScalarVector::Scalar Scalar;\n  typedef typename IndexVector::Scalar StorageIndex;\n  column_dfs_traits(Index jcol, Index& jsuper, typename SparseLUImpl<Scalar, StorageIndex>::GlobalLU_t& glu, SparseLUImpl<Scalar, StorageIndex>& luImpl)\n   : m_jcol(jcol), m_jsuper_ref(jsuper), m_glu(glu), m_luImpl(luImpl)\n {}\n  bool update_segrep(Index /*krep*/, Index /*jj*/)\n  {\n    return true;\n  }\n  void mem_expand(IndexVector& lsub, Index& nextl, Index chmark)\n  {\n    if (nextl >= m_glu.nzlmax)\n      m_luImpl.memXpand(lsub, m_glu.nzlmax, nextl, LSUB, m_glu.num_expansions); \n    if (chmark != (m_jcol-1)) m_jsuper_ref = emptyIdxLU;\n  }\n  enum { ExpandMem = true };\n  \n  Index m_jcol;\n  Index& m_jsuper_ref;\n  typename SparseLUImpl<Scalar, StorageIndex>::GlobalLU_t& m_glu;\n  SparseLUImpl<Scalar, StorageIndex>& m_luImpl;\n};\n\n\n/**\n * \\brief Performs a symbolic factorization on column jcol and decide the supernode boundary\n * \n * A supernode representative is the last column of a supernode.\n * The nonzeros in U[*,j] are segments that end at supernodes representatives. \n * The routine returns a list of the supernodal representatives \n * in topological order of the dfs that generates them. \n * The location of the first nonzero in each supernodal segment \n * (supernodal entry location) is also returned. \n * \n * \\param m number of rows in the matrix\n * \\param jcol Current column \n * \\param perm_r Row permutation\n * \\param maxsuper  Maximum number of column allowed in a supernode\n * \\param [in,out] nseg Number of segments in current U[*,j] - new segments appended\n * \\param lsub_col defines the rhs vector to start the dfs\n * \\param [in,out] segrep Segment representatives - new segments appended \n * \\param repfnz  First nonzero location in each row\n * \\param xprune \n * \\param marker  marker[i] == jj, if i was visited during dfs of current column jj;\n * \\param parent\n * \\param xplore working array\n * \\param glu global LU data \n * \\return 0 success\n *         > 0 number of bytes allocated when run out of space\n * \n */\ntemplate <typename Scalar, typename StorageIndex>\nIndex SparseLUImpl<Scalar,StorageIndex>::column_dfs(const Index m, const Index jcol, IndexVector& perm_r, Index maxsuper, Index& nseg,\n                                                    BlockIndexVector lsub_col, IndexVector& segrep, BlockIndexVector repfnz, IndexVector& xprune,\n                                                    IndexVector& marker, IndexVector& parent, IndexVector& xplore, GlobalLU_t& glu)\n{\n  \n  Index jsuper = glu.supno(jcol); \n  Index nextl = glu.xlsub(jcol); \n  VectorBlock<IndexVector> marker2(marker, 2*m, m); \n  \n  \n  column_dfs_traits<IndexVector, ScalarVector> traits(jcol, jsuper, glu, *this);\n  \n  // For each nonzero in A(*,jcol) do dfs \n  for (Index k = 0; ((k < m) ? lsub_col[k] != emptyIdxLU : false) ; k++)\n  {\n    Index krow = lsub_col(k); \n    lsub_col(k) = emptyIdxLU; \n    Index kmark = marker2(krow); \n    \n    // krow was visited before, go to the next nonz; \n    if (kmark == jcol) continue;\n    \n    dfs_kernel(StorageIndex(jcol), perm_r, nseg, glu.lsub, segrep, repfnz, xprune, marker2, parent,\n                   xplore, glu, nextl, krow, traits);\n  } // for each nonzero ... \n  \n  Index fsupc;\n  StorageIndex nsuper = glu.supno(jcol);\n  StorageIndex jcolp1 = StorageIndex(jcol) + 1;\n  Index jcolm1 = jcol - 1;\n  \n  // check to see if j belongs in the same supernode as j-1\n  if ( jcol == 0 )\n  { // Do nothing for column 0 \n    nsuper = glu.supno(0) = 0 ;\n  }\n  else \n  {\n    fsupc = glu.xsup(nsuper); \n    StorageIndex jptr = glu.xlsub(jcol); // Not yet compressed\n    StorageIndex jm1ptr = glu.xlsub(jcolm1); \n    \n    // Use supernodes of type T2 : see SuperLU paper\n    if ( (nextl-jptr != jptr-jm1ptr-1) ) jsuper = emptyIdxLU;\n    \n    // Make sure the number of columns in a supernode doesn't\n    // exceed threshold\n    if ( (jcol - fsupc) >= maxsuper) jsuper = emptyIdxLU; \n    \n    /* If jcol starts a new supernode, reclaim storage space in\n     * glu.lsub from previous supernode. Note we only store \n     * the subscript set of the first and last columns of \n     * a supernode. (first for num values, last for pruning)\n     */\n    if (jsuper == emptyIdxLU)\n    { // starts a new supernode \n      if ( (fsupc < jcolm1-1) ) \n      { // >= 3 columns in nsuper\n        StorageIndex ito = glu.xlsub(fsupc+1);\n        glu.xlsub(jcolm1) = ito; \n        StorageIndex istop = ito + jptr - jm1ptr; \n        xprune(jcolm1) = istop; // intialize xprune(jcol-1)\n        glu.xlsub(jcol) = istop; \n        \n        for (StorageIndex ifrom = jm1ptr; ifrom < nextl; ++ifrom, ++ito)\n          glu.lsub(ito) = glu.lsub(ifrom); \n        nextl = ito;  // = istop + length(jcol)\n      }\n      nsuper++; \n      glu.supno(jcol) = nsuper; \n    } // if a new supernode \n  } // end else:  jcol > 0\n  \n  // Tidy up the pointers before exit\n  glu.xsup(nsuper+1) = jcolp1; \n  glu.supno(jcolp1) = nsuper; \n  xprune(jcol) = StorageIndex(nextl);  // Intialize upper bound for pruning\n  glu.xlsub(jcolp1) = StorageIndex(nextl); \n  \n  return 0; \n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseLU/SparseLU_copy_to_ucol.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n/* \n \n * NOTE: This file is the modified version of [s,d,c,z]copy_to_ucol.c file in SuperLU \n \n * -- SuperLU routine (version 2.0) --\n * Univ. of California Berkeley, Xerox Palo Alto Research Center,\n * and Lawrence Berkeley National Lab.\n * November 15, 1997\n *\n * Copyright (c) 1994 by Xerox Corporation.  All rights reserved.\n *\n * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY\n * EXPRESSED OR IMPLIED.  ANY USE IS AT YOUR OWN RISK.\n *\n * Permission is hereby granted to use or copy this program for any\n * purpose, provided the above notices are retained on all copies.\n * Permission to modify the code and to distribute modified code is\n * granted, provided the above notices are retained, and a notice that\n * the code was modified is included with the above copyright notice.\n */\n#ifndef SPARSELU_COPY_TO_UCOL_H\n#define SPARSELU_COPY_TO_UCOL_H\n\nnamespace Eigen {\nnamespace internal {\n\n/**\n * \\brief Performs numeric block updates (sup-col) in topological order\n * \n * \\param jcol current column to update\n * \\param nseg Number of segments in the U part\n * \\param segrep segment representative ...\n * \\param repfnz First nonzero column in each row  ...\n * \\param perm_r Row permutation \n * \\param dense Store the full representation of the column\n * \\param glu Global LU data. \n * \\return 0 - successful return \n *         > 0 - number of bytes allocated when run out of space\n * \n */\ntemplate <typename Scalar, typename StorageIndex>\nIndex SparseLUImpl<Scalar,StorageIndex>::copy_to_ucol(const Index jcol, const Index nseg, IndexVector& segrep,\n                                                      BlockIndexVector repfnz ,IndexVector& perm_r, BlockScalarVector dense, GlobalLU_t& glu)\n{  \n  Index ksub, krep, ksupno; \n    \n  Index jsupno = glu.supno(jcol);\n  \n  // For each nonzero supernode segment of U[*,j] in topological order \n  Index k = nseg - 1, i; \n  StorageIndex nextu = glu.xusub(jcol); \n  Index kfnz, isub, segsize; \n  Index new_next,irow; \n  Index fsupc, mem; \n  for (ksub = 0; ksub < nseg; ksub++)\n  {\n    krep = segrep(k); k--; \n    ksupno = glu.supno(krep); \n    if (jsupno != ksupno ) // should go into ucol(); \n    {\n      kfnz = repfnz(krep); \n      if (kfnz != emptyIdxLU)\n      { // Nonzero U-segment \n        fsupc = glu.xsup(ksupno); \n        isub = glu.xlsub(fsupc) + kfnz - fsupc; \n        segsize = krep - kfnz + 1; \n        new_next = nextu + segsize; \n        while (new_next > glu.nzumax) \n        {\n          mem = memXpand<ScalarVector>(glu.ucol, glu.nzumax, nextu, UCOL, glu.num_expansions); \n          if (mem) return mem; \n          mem = memXpand<IndexVector>(glu.usub, glu.nzumax, nextu, USUB, glu.num_expansions); \n          if (mem) return mem; \n          \n        }\n        \n        for (i = 0; i < segsize; i++)\n        {\n          irow = glu.lsub(isub); \n          glu.usub(nextu) = perm_r(irow); // Unlike the L part, the U part is stored in its final order\n          glu.ucol(nextu) = dense(irow); \n          dense(irow) = Scalar(0.0); \n          nextu++;\n          isub++;\n        }\n        \n      } // end nonzero U-segment \n      \n    } // end if jsupno \n    \n  } // end for each segment\n  glu.xusub(jcol + 1) = nextu; // close U(*,jcol)\n  return 0; \n}\n\n} // namespace internal\n} // end namespace Eigen\n\n#endif // SPARSELU_COPY_TO_UCOL_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseLU/SparseLU_gemm_kernel.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSELU_GEMM_KERNEL_H\n#define EIGEN_SPARSELU_GEMM_KERNEL_H\n\nnamespace Eigen {\n\nnamespace internal {\n\n\n/** \\internal\n  * A general matrix-matrix product kernel optimized for the SparseLU factorization.\n  *  - A, B, and C must be column major\n  *  - lda and ldc must be multiples of the respective packet size\n  *  - C must have the same alignment as A\n  */\ntemplate<typename Scalar>\nEIGEN_DONT_INLINE\nvoid sparselu_gemm(Index m, Index n, Index d, const Scalar* A, Index lda, const Scalar* B, Index ldb, Scalar* C, Index ldc)\n{\n  using namespace Eigen::internal;\n  \n  typedef typename packet_traits<Scalar>::type Packet;\n  enum {\n    NumberOfRegisters = EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS,\n    PacketSize = packet_traits<Scalar>::size,\n    PM = 8,                             // peeling in M\n    RN = 2,                             // register blocking\n    RK = NumberOfRegisters>=16 ? 4 : 2, // register blocking\n    BM = 4096/sizeof(Scalar),           // number of rows of A-C per chunk\n    SM = PM*PacketSize                  // step along M\n  };\n  Index d_end = (d/RK)*RK;    // number of columns of A (rows of B) suitable for full register blocking\n  Index n_end = (n/RN)*RN;    // number of columns of B-C suitable for processing RN columns at once\n  Index i0 = internal::first_default_aligned(A,m);\n  \n  eigen_internal_assert(((lda%PacketSize)==0) && ((ldc%PacketSize)==0) && (i0==internal::first_default_aligned(C,m)));\n  \n  // handle the non aligned rows of A and C without any optimization:\n  for(Index i=0; i<i0; ++i)\n  {\n    for(Index j=0; j<n; ++j)\n    {\n      Scalar c = C[i+j*ldc];\n      for(Index k=0; k<d; ++k)\n        c += B[k+j*ldb] * A[i+k*lda];\n      C[i+j*ldc] = c;\n    }\n  }\n  // process the remaining rows per chunk of BM rows\n  for(Index ib=i0; ib<m; ib+=BM)\n  {\n    Index actual_b = std::min<Index>(BM, m-ib);                 // actual number of rows\n    Index actual_b_end1 = (actual_b/SM)*SM;                   // actual number of rows suitable for peeling\n    Index actual_b_end2 = (actual_b/PacketSize)*PacketSize;   // actual number of rows suitable for vectorization\n    \n    // Let's process two columns of B-C at once\n    for(Index j=0; j<n_end; j+=RN)\n    {\n      const Scalar* Bc0 = B+(j+0)*ldb;\n      const Scalar* Bc1 = B+(j+1)*ldb;\n      \n      for(Index k=0; k<d_end; k+=RK)\n      {\n        \n        // load and expand a RN x RK block of B\n        Packet b00, b10, b20, b30, b01, b11, b21, b31;\n                  { b00 = pset1<Packet>(Bc0[0]); }\n                  { b10 = pset1<Packet>(Bc0[1]); }\n        if(RK==4) { b20 = pset1<Packet>(Bc0[2]); }\n        if(RK==4) { b30 = pset1<Packet>(Bc0[3]); }\n                  { b01 = pset1<Packet>(Bc1[0]); }\n                  { b11 = pset1<Packet>(Bc1[1]); }\n        if(RK==4) { b21 = pset1<Packet>(Bc1[2]); }\n        if(RK==4) { b31 = pset1<Packet>(Bc1[3]); }\n        \n        Packet a0, a1, a2, a3, c0, c1, t0, t1;\n        \n        const Scalar* A0 = A+ib+(k+0)*lda;\n        const Scalar* A1 = A+ib+(k+1)*lda;\n        const Scalar* A2 = A+ib+(k+2)*lda;\n        const Scalar* A3 = A+ib+(k+3)*lda;\n        \n        Scalar* C0 = C+ib+(j+0)*ldc;\n        Scalar* C1 = C+ib+(j+1)*ldc;\n        \n                  a0 = pload<Packet>(A0);\n                  a1 = pload<Packet>(A1);\n        if(RK==4)\n        {\n          a2 = pload<Packet>(A2);\n          a3 = pload<Packet>(A3);\n        }\n        else\n        {\n          // workaround \"may be used uninitialized in this function\" warning\n          a2 = a3 = a0;\n        }\n        \n#define KMADD(c, a, b, tmp) {tmp = b; tmp = pmul(a,tmp); c = padd(c,tmp);}\n#define WORK(I)  \\\n                     c0 = pload<Packet>(C0+i+(I)*PacketSize);    \\\n                     c1 = pload<Packet>(C1+i+(I)*PacketSize);    \\\n                     KMADD(c0, a0, b00, t0)                      \\\n                     KMADD(c1, a0, b01, t1)                      \\\n                     a0 = pload<Packet>(A0+i+(I+1)*PacketSize);  \\\n                     KMADD(c0, a1, b10, t0)                      \\\n                     KMADD(c1, a1, b11, t1)                      \\\n                     a1 = pload<Packet>(A1+i+(I+1)*PacketSize);  \\\n          if(RK==4){ KMADD(c0, a2, b20, t0)                     }\\\n          if(RK==4){ KMADD(c1, a2, b21, t1)                     }\\\n          if(RK==4){ a2 = pload<Packet>(A2+i+(I+1)*PacketSize); }\\\n          if(RK==4){ KMADD(c0, a3, b30, t0)                     }\\\n          if(RK==4){ KMADD(c1, a3, b31, t1)                     }\\\n          if(RK==4){ a3 = pload<Packet>(A3+i+(I+1)*PacketSize); }\\\n                     pstore(C0+i+(I)*PacketSize, c0);            \\\n                     pstore(C1+i+(I)*PacketSize, c1)\n        \n        // process rows of A' - C' with aggressive vectorization and peeling \n        for(Index i=0; i<actual_b_end1; i+=PacketSize*8)\n        {\n          EIGEN_ASM_COMMENT(\"SPARSELU_GEMML_KERNEL1\");\n                    prefetch((A0+i+(5)*PacketSize));\n                    prefetch((A1+i+(5)*PacketSize));\n          if(RK==4) prefetch((A2+i+(5)*PacketSize));\n          if(RK==4) prefetch((A3+i+(5)*PacketSize));\n\n          WORK(0);\n          WORK(1);\n          WORK(2);\n          WORK(3);\n          WORK(4);\n          WORK(5);\n          WORK(6);\n          WORK(7);\n        }\n        // process the remaining rows with vectorization only\n        for(Index i=actual_b_end1; i<actual_b_end2; i+=PacketSize)\n        {\n          WORK(0);\n        }\n#undef WORK\n        // process the remaining rows without vectorization\n        for(Index i=actual_b_end2; i<actual_b; ++i)\n        {\n          if(RK==4)\n          {\n            C0[i] += A0[i]*Bc0[0]+A1[i]*Bc0[1]+A2[i]*Bc0[2]+A3[i]*Bc0[3];\n            C1[i] += A0[i]*Bc1[0]+A1[i]*Bc1[1]+A2[i]*Bc1[2]+A3[i]*Bc1[3];\n          }\n          else\n          {\n            C0[i] += A0[i]*Bc0[0]+A1[i]*Bc0[1];\n            C1[i] += A0[i]*Bc1[0]+A1[i]*Bc1[1];\n          }\n        }\n        \n        Bc0 += RK;\n        Bc1 += RK;\n      } // peeled loop on k\n    } // peeled loop on the columns j\n    // process the last column (we now perform a matrix-vector product)\n    if((n-n_end)>0)\n    {\n      const Scalar* Bc0 = B+(n-1)*ldb;\n      \n      for(Index k=0; k<d_end; k+=RK)\n      {\n        \n        // load and expand a 1 x RK block of B\n        Packet b00, b10, b20, b30;\n                  b00 = pset1<Packet>(Bc0[0]);\n                  b10 = pset1<Packet>(Bc0[1]);\n        if(RK==4) b20 = pset1<Packet>(Bc0[2]);\n        if(RK==4) b30 = pset1<Packet>(Bc0[3]);\n        \n        Packet a0, a1, a2, a3, c0, t0/*, t1*/;\n        \n        const Scalar* A0 = A+ib+(k+0)*lda;\n        const Scalar* A1 = A+ib+(k+1)*lda;\n        const Scalar* A2 = A+ib+(k+2)*lda;\n        const Scalar* A3 = A+ib+(k+3)*lda;\n        \n        Scalar* C0 = C+ib+(n_end)*ldc;\n        \n                  a0 = pload<Packet>(A0);\n                  a1 = pload<Packet>(A1);\n        if(RK==4)\n        {\n          a2 = pload<Packet>(A2);\n          a3 = pload<Packet>(A3);\n        }\n        else\n        {\n          // workaround \"may be used uninitialized in this function\" warning\n          a2 = a3 = a0;\n        }\n        \n#define WORK(I) \\\n                   c0 = pload<Packet>(C0+i+(I)*PacketSize);     \\\n                   KMADD(c0, a0, b00, t0)                       \\\n                   a0 = pload<Packet>(A0+i+(I+1)*PacketSize);   \\\n                   KMADD(c0, a1, b10, t0)                       \\\n                   a1 = pload<Packet>(A1+i+(I+1)*PacketSize);   \\\n        if(RK==4){ KMADD(c0, a2, b20, t0)                      }\\\n        if(RK==4){ a2 = pload<Packet>(A2+i+(I+1)*PacketSize);  }\\\n        if(RK==4){ KMADD(c0, a3, b30, t0)                      }\\\n        if(RK==4){ a3 = pload<Packet>(A3+i+(I+1)*PacketSize);  }\\\n                   pstore(C0+i+(I)*PacketSize, c0);\n        \n        // agressive vectorization and peeling\n        for(Index i=0; i<actual_b_end1; i+=PacketSize*8)\n        {\n          EIGEN_ASM_COMMENT(\"SPARSELU_GEMML_KERNEL2\");\n          WORK(0);\n          WORK(1);\n          WORK(2);\n          WORK(3);\n          WORK(4);\n          WORK(5);\n          WORK(6);\n          WORK(7);\n        }\n        // vectorization only\n        for(Index i=actual_b_end1; i<actual_b_end2; i+=PacketSize)\n        {\n          WORK(0);\n        }\n        // remaining scalars\n        for(Index i=actual_b_end2; i<actual_b; ++i)\n        {\n          if(RK==4) \n            C0[i] += A0[i]*Bc0[0]+A1[i]*Bc0[1]+A2[i]*Bc0[2]+A3[i]*Bc0[3];\n          else\n            C0[i] += A0[i]*Bc0[0]+A1[i]*Bc0[1];\n        }\n        \n        Bc0 += RK;\n#undef WORK\n      }\n    }\n    \n    // process the last columns of A, corresponding to the last rows of B\n    Index rd = d-d_end;\n    if(rd>0)\n    {\n      for(Index j=0; j<n; ++j)\n      {\n        enum {\n          Alignment = PacketSize>1 ? Aligned : 0\n        };\n        typedef Map<Matrix<Scalar,Dynamic,1>, Alignment > MapVector;\n        typedef Map<const Matrix<Scalar,Dynamic,1>, Alignment > ConstMapVector;\n        if(rd==1)       MapVector(C+j*ldc+ib,actual_b) += B[0+d_end+j*ldb] * ConstMapVector(A+(d_end+0)*lda+ib, actual_b);\n        \n        else if(rd==2)  MapVector(C+j*ldc+ib,actual_b) += B[0+d_end+j*ldb] * ConstMapVector(A+(d_end+0)*lda+ib, actual_b)\n                                                        + B[1+d_end+j*ldb] * ConstMapVector(A+(d_end+1)*lda+ib, actual_b);\n        \n        else            MapVector(C+j*ldc+ib,actual_b) += B[0+d_end+j*ldb] * ConstMapVector(A+(d_end+0)*lda+ib, actual_b)\n                                                        + B[1+d_end+j*ldb] * ConstMapVector(A+(d_end+1)*lda+ib, actual_b)\n                                                        + B[2+d_end+j*ldb] * ConstMapVector(A+(d_end+2)*lda+ib, actual_b);\n      }\n    }\n  \n  } // blocking on the rows of A and C\n}\n#undef KMADD\n\n} // namespace internal\n\n} // namespace Eigen\n\n#endif // EIGEN_SPARSELU_GEMM_KERNEL_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseLU/SparseLU_heap_relax_snode.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n/* This file is a modified version of heap_relax_snode.c file in SuperLU\n * -- SuperLU routine (version 3.0) --\n * Univ. of California Berkeley, Xerox Palo Alto Research Center,\n * and Lawrence Berkeley National Lab.\n * October 15, 2003\n *\n * Copyright (c) 1994 by Xerox Corporation.  All rights reserved.\n *\n * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY\n * EXPRESSED OR IMPLIED.  ANY USE IS AT YOUR OWN RISK.\n *\n * Permission is hereby granted to use or copy this program for any\n * purpose, provided the above notices are retained on all copies.\n * Permission to modify the code and to distribute modified code is\n * granted, provided the above notices are retained, and a notice that\n * the code was modified is included with the above copyright notice.\n */\n\n#ifndef SPARSELU_HEAP_RELAX_SNODE_H\n#define SPARSELU_HEAP_RELAX_SNODE_H\n\nnamespace Eigen {\nnamespace internal {\n\n/** \n * \\brief Identify the initial relaxed supernodes\n * \n * This routine applied to a symmetric elimination tree. \n * It assumes that the matrix has been reordered according to the postorder of the etree\n * \\param n The number of columns\n * \\param et elimination tree \n * \\param relax_columns Maximum number of columns allowed in a relaxed snode \n * \\param descendants Number of descendants of each node in the etree\n * \\param relax_end last column in a supernode\n */\ntemplate <typename Scalar, typename StorageIndex>\nvoid SparseLUImpl<Scalar,StorageIndex>::heap_relax_snode (const Index n, IndexVector& et, const Index relax_columns, IndexVector& descendants, IndexVector& relax_end)\n{\n  \n  // The etree may not be postordered, but its heap ordered  \n  IndexVector post;\n  internal::treePostorder(StorageIndex(n), et, post); // Post order etree\n  IndexVector inv_post(n+1); \n  for (StorageIndex i = 0; i < n+1; ++i) inv_post(post(i)) = i; // inv_post = post.inverse()???\n  \n  // Renumber etree in postorder \n  IndexVector iwork(n);\n  IndexVector et_save(n+1);\n  for (Index i = 0; i < n; ++i)\n  {\n    iwork(post(i)) = post(et(i));\n  }\n  et_save = et; // Save the original etree\n  et = iwork; \n  \n  // compute the number of descendants of each node in the etree\n  relax_end.setConstant(emptyIdxLU);\n  Index j, parent; \n  descendants.setZero();\n  for (j = 0; j < n; j++) \n  {\n    parent = et(j);\n    if (parent != n) // not the dummy root\n      descendants(parent) += descendants(j) + 1;\n  }\n  // Identify the relaxed supernodes by postorder traversal of the etree\n  Index snode_start; // beginning of a snode \n  StorageIndex k;\n  Index nsuper_et_post = 0; // Number of relaxed snodes in postordered etree \n  Index nsuper_et = 0; // Number of relaxed snodes in the original etree \n  StorageIndex l; \n  for (j = 0; j < n; )\n  {\n    parent = et(j);\n    snode_start = j; \n    while ( parent != n && descendants(parent) < relax_columns ) \n    {\n      j = parent; \n      parent = et(j);\n    }\n    // Found a supernode in postordered etree, j is the last column \n    ++nsuper_et_post;\n    k = StorageIndex(n);\n    for (Index i = snode_start; i <= j; ++i)\n      k = (std::min)(k, inv_post(i));\n    l = inv_post(j);\n    if ( (l - k) == (j - snode_start) )  // Same number of columns in the snode\n    {\n      // This is also a supernode in the original etree\n      relax_end(k) = l; // Record last column \n      ++nsuper_et; \n    }\n    else \n    {\n      for (Index i = snode_start; i <= j; ++i) \n      {\n        l = inv_post(i);\n        if (descendants(i) == 0) \n        {\n          relax_end(l) = l;\n          ++nsuper_et;\n        }\n      }\n    }\n    j++;\n    // Search for a new leaf\n    while (descendants(j) != 0 && j < n) j++;\n  } // End postorder traversal of the etree\n  \n  // Recover the original etree\n  et = et_save; \n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n#endif // SPARSELU_HEAP_RELAX_SNODE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseLU/SparseLU_kernel_bmod.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>\n// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef SPARSELU_KERNEL_BMOD_H\n#define SPARSELU_KERNEL_BMOD_H\n\nnamespace Eigen {\nnamespace internal {\n  \ntemplate <int SegSizeAtCompileTime> struct LU_kernel_bmod\n{\n  /** \\internal\n    * \\brief Performs numeric block updates from a given supernode to a single column\n    *\n    * \\param segsize Size of the segment (and blocks ) to use for updates\n    * \\param[in,out] dense Packed values of the original matrix\n    * \\param tempv temporary vector to use for updates\n    * \\param lusup array containing the supernodes\n    * \\param lda Leading dimension in the supernode\n    * \\param nrow Number of rows in the rectangular part of the supernode\n    * \\param lsub compressed row subscripts of supernodes\n    * \\param lptr pointer to the first column of the current supernode in lsub\n    * \\param no_zeros Number of nonzeros elements before the diagonal part of the supernode\n    */\n  template <typename BlockScalarVector, typename ScalarVector, typename IndexVector>\n  static EIGEN_DONT_INLINE void run(const Index segsize, BlockScalarVector& dense, ScalarVector& tempv, ScalarVector& lusup, Index& luptr, const Index lda,\n                                    const Index nrow, IndexVector& lsub, const Index lptr, const Index no_zeros);\n};\n\ntemplate <int SegSizeAtCompileTime>\ntemplate <typename BlockScalarVector, typename ScalarVector, typename IndexVector>\nEIGEN_DONT_INLINE void LU_kernel_bmod<SegSizeAtCompileTime>::run(const Index segsize, BlockScalarVector& dense, ScalarVector& tempv, ScalarVector& lusup, Index& luptr, const Index lda,\n                                                                  const Index nrow, IndexVector& lsub, const Index lptr, const Index no_zeros)\n{\n  typedef typename ScalarVector::Scalar Scalar;\n  // First, copy U[*,j] segment from dense(*) to tempv(*)\n  // The result of triangular solve is in tempv[*]; \n    // The result of matric-vector update is in dense[*]\n  Index isub = lptr + no_zeros; \n  Index i;\n  Index irow;\n  for (i = 0; i < ((SegSizeAtCompileTime==Dynamic)?segsize:SegSizeAtCompileTime); i++)\n  {\n    irow = lsub(isub); \n    tempv(i) = dense(irow); \n    ++isub; \n  }\n  // Dense triangular solve -- start effective triangle\n  luptr += lda * no_zeros + no_zeros; \n  // Form Eigen matrix and vector \n  Map<Matrix<Scalar,SegSizeAtCompileTime,SegSizeAtCompileTime, ColMajor>, 0, OuterStride<> > A( &(lusup.data()[luptr]), segsize, segsize, OuterStride<>(lda) );\n  Map<Matrix<Scalar,SegSizeAtCompileTime,1> > u(tempv.data(), segsize);\n  \n  u = A.template triangularView<UnitLower>().solve(u); \n  \n  // Dense matrix-vector product y <-- B*x \n  luptr += segsize;\n  const Index PacketSize = internal::packet_traits<Scalar>::size;\n  Index ldl = internal::first_multiple(nrow, PacketSize);\n  Map<Matrix<Scalar,Dynamic,SegSizeAtCompileTime, ColMajor>, 0, OuterStride<> > B( &(lusup.data()[luptr]), nrow, segsize, OuterStride<>(lda) );\n  Index aligned_offset = internal::first_default_aligned(tempv.data()+segsize, PacketSize);\n  Index aligned_with_B_offset = (PacketSize-internal::first_default_aligned(B.data(), PacketSize))%PacketSize;\n  Map<Matrix<Scalar,Dynamic,1>, 0, OuterStride<> > l(tempv.data()+segsize+aligned_offset+aligned_with_B_offset, nrow, OuterStride<>(ldl) );\n  \n  l.setZero();\n  internal::sparselu_gemm<Scalar>(l.rows(), l.cols(), B.cols(), B.data(), B.outerStride(), u.data(), u.outerStride(), l.data(), l.outerStride());\n  \n  // Scatter tempv[] into SPA dense[] as a temporary storage \n  isub = lptr + no_zeros;\n  for (i = 0; i < ((SegSizeAtCompileTime==Dynamic)?segsize:SegSizeAtCompileTime); i++)\n  {\n    irow = lsub(isub++); \n    dense(irow) = tempv(i);\n  }\n  \n  // Scatter l into SPA dense[]\n  for (i = 0; i < nrow; i++)\n  {\n    irow = lsub(isub++); \n    dense(irow) -= l(i);\n  } \n}\n\ntemplate <> struct LU_kernel_bmod<1>\n{\n  template <typename BlockScalarVector, typename ScalarVector, typename IndexVector>\n  static EIGEN_DONT_INLINE void run(const Index /*segsize*/, BlockScalarVector& dense, ScalarVector& /*tempv*/, ScalarVector& lusup, Index& luptr,\n                                    const Index lda, const Index nrow, IndexVector& lsub, const Index lptr, const Index no_zeros);\n};\n\n\ntemplate <typename BlockScalarVector, typename ScalarVector, typename IndexVector>\nEIGEN_DONT_INLINE void LU_kernel_bmod<1>::run(const Index /*segsize*/, BlockScalarVector& dense, ScalarVector& /*tempv*/, ScalarVector& lusup, Index& luptr,\n                                              const Index lda, const Index nrow, IndexVector& lsub, const Index lptr, const Index no_zeros)\n{\n  typedef typename ScalarVector::Scalar Scalar;\n  typedef typename IndexVector::Scalar StorageIndex;\n  Scalar f = dense(lsub(lptr + no_zeros));\n  luptr += lda * no_zeros + no_zeros + 1;\n  const Scalar* a(lusup.data() + luptr);\n  const StorageIndex*  irow(lsub.data()+lptr + no_zeros + 1);\n  Index i = 0;\n  for (; i+1 < nrow; i+=2)\n  {\n    Index i0 = *(irow++);\n    Index i1 = *(irow++);\n    Scalar a0 = *(a++);\n    Scalar a1 = *(a++);\n    Scalar d0 = dense.coeff(i0);\n    Scalar d1 = dense.coeff(i1);\n    d0 -= f*a0;\n    d1 -= f*a1;\n    dense.coeffRef(i0) = d0;\n    dense.coeffRef(i1) = d1;\n  }\n  if(i<nrow)\n    dense.coeffRef(*(irow++)) -= f * *(a++);\n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n#endif // SPARSELU_KERNEL_BMOD_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseLU/SparseLU_panel_bmod.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>\n// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n/* \n \n * NOTE: This file is the modified version of [s,d,c,z]panel_bmod.c file in SuperLU \n \n * -- SuperLU routine (version 3.0) --\n * Univ. of California Berkeley, Xerox Palo Alto Research Center,\n * and Lawrence Berkeley National Lab.\n * October 15, 2003\n *\n * Copyright (c) 1994 by Xerox Corporation.  All rights reserved.\n *\n * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY\n * EXPRESSED OR IMPLIED.  ANY USE IS AT YOUR OWN RISK.\n *\n * Permission is hereby granted to use or copy this program for any\n * purpose, provided the above notices are retained on all copies.\n * Permission to modify the code and to distribute modified code is\n * granted, provided the above notices are retained, and a notice that\n * the code was modified is included with the above copyright notice.\n */\n#ifndef SPARSELU_PANEL_BMOD_H\n#define SPARSELU_PANEL_BMOD_H\n\nnamespace Eigen {\nnamespace internal {\n\n/**\n * \\brief Performs numeric block updates (sup-panel) in topological order.\n * \n * Before entering this routine, the original nonzeros in the panel\n * were already copied i nto the spa[m,w]\n * \n * \\param m number of rows in the matrix\n * \\param w Panel size\n * \\param jcol Starting  column of the panel\n * \\param nseg Number of segments in the U part\n * \\param dense Store the full representation of the panel \n * \\param tempv working array \n * \\param segrep segment representative... first row in the segment\n * \\param repfnz First nonzero rows\n * \\param glu Global LU data. \n * \n * \n */\ntemplate <typename Scalar, typename StorageIndex>\nvoid SparseLUImpl<Scalar,StorageIndex>::panel_bmod(const Index m, const Index w, const Index jcol, \n                                            const Index nseg, ScalarVector& dense, ScalarVector& tempv,\n                                            IndexVector& segrep, IndexVector& repfnz, GlobalLU_t& glu)\n{\n  \n  Index ksub,jj,nextl_col; \n  Index fsupc, nsupc, nsupr, nrow; \n  Index krep, kfnz; \n  Index lptr; // points to the row subscripts of a supernode \n  Index luptr; // ...\n  Index segsize,no_zeros ; \n  // For each nonz supernode segment of U[*,j] in topological order\n  Index k = nseg - 1; \n  const Index PacketSize = internal::packet_traits<Scalar>::size;\n  \n  for (ksub = 0; ksub < nseg; ksub++)\n  { // For each updating supernode\n    /* krep = representative of current k-th supernode\n     * fsupc =  first supernodal column\n     * nsupc = number of columns in a supernode\n     * nsupr = number of rows in a supernode\n     */\n    krep = segrep(k); k--; \n    fsupc = glu.xsup(glu.supno(krep)); \n    nsupc = krep - fsupc + 1; \n    nsupr = glu.xlsub(fsupc+1) - glu.xlsub(fsupc); \n    nrow = nsupr - nsupc; \n    lptr = glu.xlsub(fsupc); \n    \n    // loop over the panel columns to detect the actual number of columns and rows\n    Index u_rows = 0;\n    Index u_cols = 0;\n    for (jj = jcol; jj < jcol + w; jj++)\n    {\n      nextl_col = (jj-jcol) * m; \n      VectorBlock<IndexVector> repfnz_col(repfnz, nextl_col, m); // First nonzero column index for each row\n      \n      kfnz = repfnz_col(krep); \n      if ( kfnz == emptyIdxLU ) \n        continue; // skip any zero segment\n      \n      segsize = krep - kfnz + 1;\n      u_cols++;\n      u_rows = (std::max)(segsize,u_rows);\n    }\n    \n    if(nsupc >= 2)\n    { \n      Index ldu = internal::first_multiple<Index>(u_rows, PacketSize);\n      Map<ScalarMatrix, Aligned,  OuterStride<> > U(tempv.data(), u_rows, u_cols, OuterStride<>(ldu));\n      \n      // gather U\n      Index u_col = 0;\n      for (jj = jcol; jj < jcol + w; jj++)\n      {\n        nextl_col = (jj-jcol) * m; \n        VectorBlock<IndexVector> repfnz_col(repfnz, nextl_col, m); // First nonzero column index for each row\n        VectorBlock<ScalarVector> dense_col(dense, nextl_col, m); // Scatter/gather entire matrix column from/to here\n        \n        kfnz = repfnz_col(krep); \n        if ( kfnz == emptyIdxLU ) \n          continue; // skip any zero segment\n        \n        segsize = krep - kfnz + 1;\n        luptr = glu.xlusup(fsupc);    \n        no_zeros = kfnz - fsupc; \n        \n        Index isub = lptr + no_zeros;\n        Index off = u_rows-segsize;\n        for (Index i = 0; i < off; i++) U(i,u_col) = 0;\n        for (Index i = 0; i < segsize; i++)\n        {\n          Index irow = glu.lsub(isub); \n          U(i+off,u_col) = dense_col(irow); \n          ++isub; \n        }\n        u_col++;\n      }\n      // solve U = A^-1 U\n      luptr = glu.xlusup(fsupc);\n      Index lda = glu.xlusup(fsupc+1) - glu.xlusup(fsupc);\n      no_zeros = (krep - u_rows + 1) - fsupc;\n      luptr += lda * no_zeros + no_zeros;\n      MappedMatrixBlock A(glu.lusup.data()+luptr, u_rows, u_rows, OuterStride<>(lda) );\n      U = A.template triangularView<UnitLower>().solve(U);\n      \n      // update\n      luptr += u_rows;\n      MappedMatrixBlock B(glu.lusup.data()+luptr, nrow, u_rows, OuterStride<>(lda) );\n      eigen_assert(tempv.size()>w*ldu + nrow*w + 1);\n      \n      Index ldl = internal::first_multiple<Index>(nrow, PacketSize);\n      Index offset = (PacketSize-internal::first_default_aligned(B.data(), PacketSize)) % PacketSize;\n      MappedMatrixBlock L(tempv.data()+w*ldu+offset, nrow, u_cols, OuterStride<>(ldl));\n      \n      L.setZero();\n      internal::sparselu_gemm<Scalar>(L.rows(), L.cols(), B.cols(), B.data(), B.outerStride(), U.data(), U.outerStride(), L.data(), L.outerStride());\n      \n      // scatter U and L\n      u_col = 0;\n      for (jj = jcol; jj < jcol + w; jj++)\n      {\n        nextl_col = (jj-jcol) * m; \n        VectorBlock<IndexVector> repfnz_col(repfnz, nextl_col, m); // First nonzero column index for each row\n        VectorBlock<ScalarVector> dense_col(dense, nextl_col, m); // Scatter/gather entire matrix column from/to here\n        \n        kfnz = repfnz_col(krep); \n        if ( kfnz == emptyIdxLU ) \n          continue; // skip any zero segment\n        \n        segsize = krep - kfnz + 1;\n        no_zeros = kfnz - fsupc; \n        Index isub = lptr + no_zeros;\n        \n        Index off = u_rows-segsize;\n        for (Index i = 0; i < segsize; i++)\n        {\n          Index irow = glu.lsub(isub++); \n          dense_col(irow) = U.coeff(i+off,u_col);\n          U.coeffRef(i+off,u_col) = 0;\n        }\n        \n        // Scatter l into SPA dense[]\n        for (Index i = 0; i < nrow; i++)\n        {\n          Index irow = glu.lsub(isub++); \n          dense_col(irow) -= L.coeff(i,u_col);\n          L.coeffRef(i,u_col) = 0;\n        }\n        u_col++;\n      }\n    }\n    else // level 2 only\n    {\n      // Sequence through each column in the panel\n      for (jj = jcol; jj < jcol + w; jj++)\n      {\n        nextl_col = (jj-jcol) * m; \n        VectorBlock<IndexVector> repfnz_col(repfnz, nextl_col, m); // First nonzero column index for each row\n        VectorBlock<ScalarVector> dense_col(dense, nextl_col, m); // Scatter/gather entire matrix column from/to here\n        \n        kfnz = repfnz_col(krep); \n        if ( kfnz == emptyIdxLU ) \n          continue; // skip any zero segment\n        \n        segsize = krep - kfnz + 1;\n        luptr = glu.xlusup(fsupc);\n        \n        Index lda = glu.xlusup(fsupc+1)-glu.xlusup(fsupc);// nsupr\n        \n        // Perform a trianglar solve and block update, \n        // then scatter the result of sup-col update to dense[]\n        no_zeros = kfnz - fsupc; \n              if(segsize==1)  LU_kernel_bmod<1>::run(segsize, dense_col, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr, no_zeros);\n        else  if(segsize==2)  LU_kernel_bmod<2>::run(segsize, dense_col, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr, no_zeros);\n        else  if(segsize==3)  LU_kernel_bmod<3>::run(segsize, dense_col, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr, no_zeros);\n        else                  LU_kernel_bmod<Dynamic>::run(segsize, dense_col, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr, no_zeros); \n      } // End for each column in the panel \n    }\n    \n  } // End for each updating supernode\n} // end panel bmod\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // SPARSELU_PANEL_BMOD_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseLU/SparseLU_panel_dfs.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n/* \n \n * NOTE: This file is the modified version of [s,d,c,z]panel_dfs.c file in SuperLU \n \n * -- SuperLU routine (version 2.0) --\n * Univ. of California Berkeley, Xerox Palo Alto Research Center,\n * and Lawrence Berkeley National Lab.\n * November 15, 1997\n *\n * Copyright (c) 1994 by Xerox Corporation.  All rights reserved.\n *\n * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY\n * EXPRESSED OR IMPLIED.  ANY USE IS AT YOUR OWN RISK.\n *\n * Permission is hereby granted to use or copy this program for any\n * purpose, provided the above notices are retained on all copies.\n * Permission to modify the code and to distribute modified code is\n * granted, provided the above notices are retained, and a notice that\n * the code was modified is included with the above copyright notice.\n */\n#ifndef SPARSELU_PANEL_DFS_H\n#define SPARSELU_PANEL_DFS_H\n\nnamespace Eigen {\n\nnamespace internal {\n  \ntemplate<typename IndexVector>\nstruct panel_dfs_traits\n{\n  typedef typename IndexVector::Scalar StorageIndex;\n  panel_dfs_traits(Index jcol, StorageIndex* marker)\n    : m_jcol(jcol), m_marker(marker)\n  {}\n  bool update_segrep(Index krep, StorageIndex jj)\n  {\n    if(m_marker[krep]<m_jcol)\n    {\n      m_marker[krep] = jj; \n      return true;\n    }\n    return false;\n  }\n  void mem_expand(IndexVector& /*glu.lsub*/, Index /*nextl*/, Index /*chmark*/) {}\n  enum { ExpandMem = false };\n  Index m_jcol;\n  StorageIndex* m_marker;\n};\n\n\ntemplate <typename Scalar, typename StorageIndex>\ntemplate <typename Traits>\nvoid SparseLUImpl<Scalar,StorageIndex>::dfs_kernel(const StorageIndex jj, IndexVector& perm_r,\n                   Index& nseg, IndexVector& panel_lsub, IndexVector& segrep,\n                   Ref<IndexVector> repfnz_col, IndexVector& xprune, Ref<IndexVector> marker, IndexVector& parent,\n                   IndexVector& xplore, GlobalLU_t& glu,\n                   Index& nextl_col, Index krow, Traits& traits\n                  )\n{\n  \n  StorageIndex kmark = marker(krow);\n      \n  // For each unmarked krow of jj\n  marker(krow) = jj; \n  StorageIndex kperm = perm_r(krow); \n  if (kperm == emptyIdxLU ) {\n    // krow is in L : place it in structure of L(*, jj)\n    panel_lsub(nextl_col++) = StorageIndex(krow);  // krow is indexed into A\n    \n    traits.mem_expand(panel_lsub, nextl_col, kmark);\n  }\n  else \n  {\n    // krow is in U : if its supernode-representative krep\n    // has been explored, update repfnz(*)\n    // krep = supernode representative of the current row\n    StorageIndex krep = glu.xsup(glu.supno(kperm)+1) - 1; \n    // First nonzero element in the current column:\n    StorageIndex myfnz = repfnz_col(krep); \n    \n    if (myfnz != emptyIdxLU )\n    {\n      // Representative visited before\n      if (myfnz > kperm ) repfnz_col(krep) = kperm; \n      \n    }\n    else \n    {\n      // Otherwise, perform dfs starting at krep\n      StorageIndex oldrep = emptyIdxLU; \n      parent(krep) = oldrep; \n      repfnz_col(krep) = kperm; \n      StorageIndex xdfs =  glu.xlsub(krep); \n      Index maxdfs = xprune(krep); \n      \n      StorageIndex kpar;\n      do \n      {\n        // For each unmarked kchild of krep\n        while (xdfs < maxdfs) \n        {\n          StorageIndex kchild = glu.lsub(xdfs); \n          xdfs++; \n          StorageIndex chmark = marker(kchild); \n          \n          if (chmark != jj ) \n          {\n            marker(kchild) = jj; \n            StorageIndex chperm = perm_r(kchild); \n            \n            if (chperm == emptyIdxLU) \n            {\n              // case kchild is in L: place it in L(*, j)\n              panel_lsub(nextl_col++) = kchild;\n              traits.mem_expand(panel_lsub, nextl_col, chmark);\n            }\n            else\n            {\n              // case kchild is in U :\n              // chrep = its supernode-rep. If its rep has been explored, \n              // update its repfnz(*)\n              StorageIndex chrep = glu.xsup(glu.supno(chperm)+1) - 1; \n              myfnz = repfnz_col(chrep); \n              \n              if (myfnz != emptyIdxLU) \n              { // Visited before \n                if (myfnz > chperm) \n                  repfnz_col(chrep) = chperm; \n              }\n              else \n              { // Cont. dfs at snode-rep of kchild\n                xplore(krep) = xdfs; \n                oldrep = krep; \n                krep = chrep; // Go deeper down G(L)\n                parent(krep) = oldrep; \n                repfnz_col(krep) = chperm; \n                xdfs = glu.xlsub(krep); \n                maxdfs = xprune(krep); \n                \n              } // end if myfnz != -1\n            } // end if chperm == -1 \n                \n          } // end if chmark !=jj\n        } // end while xdfs < maxdfs\n        \n        // krow has no more unexplored nbrs :\n        //    Place snode-rep krep in postorder DFS, if this \n        //    segment is seen for the first time. (Note that \n        //    \"repfnz(krep)\" may change later.)\n        //    Baktrack dfs to its parent\n        if(traits.update_segrep(krep,jj))\n        //if (marker1(krep) < jcol )\n        {\n          segrep(nseg) = krep; \n          ++nseg; \n          //marker1(krep) = jj; \n        }\n        \n        kpar = parent(krep); // Pop recursion, mimic recursion \n        if (kpar == emptyIdxLU) \n          break; // dfs done \n        krep = kpar; \n        xdfs = xplore(krep); \n        maxdfs = xprune(krep); \n\n      } while (kpar != emptyIdxLU); // Do until empty stack \n      \n    } // end if (myfnz = -1)\n\n  } // end if (kperm == -1)   \n}\n\n/**\n * \\brief Performs a symbolic factorization on a panel of columns [jcol, jcol+w)\n * \n * A supernode representative is the last column of a supernode.\n * The nonzeros in U[*,j] are segments that end at supernodes representatives\n * \n * The routine returns a list of the supernodal representatives \n * in topological order of the dfs that generates them. This list is \n * a superset of the topological order of each individual column within \n * the panel.\n * The location of the first nonzero in each supernodal segment \n * (supernodal entry location) is also returned. Each column has \n * a separate list for this purpose. \n * \n * Two markers arrays are used for dfs :\n *    marker[i] == jj, if i was visited during dfs of current column jj;\n *    marker1[i] >= jcol, if i was visited by earlier columns in this panel; \n * \n * \\param[in] m number of rows in the matrix\n * \\param[in] w Panel size\n * \\param[in] jcol Starting  column of the panel\n * \\param[in] A Input matrix in column-major storage\n * \\param[in] perm_r Row permutation\n * \\param[out] nseg Number of U segments\n * \\param[out] dense Accumulate the column vectors of the panel\n * \\param[out] panel_lsub Subscripts of the row in the panel \n * \\param[out] segrep Segment representative i.e first nonzero row of each segment\n * \\param[out] repfnz First nonzero location in each row\n * \\param[out] xprune The pruned elimination tree\n * \\param[out] marker work vector\n * \\param  parent The elimination tree\n * \\param xplore work vector\n * \\param glu The global data structure\n * \n */\n\ntemplate <typename Scalar, typename StorageIndex>\nvoid SparseLUImpl<Scalar,StorageIndex>::panel_dfs(const Index m, const Index w, const Index jcol, MatrixType& A, IndexVector& perm_r, Index& nseg, ScalarVector& dense, IndexVector& panel_lsub, IndexVector& segrep, IndexVector& repfnz, IndexVector& xprune, IndexVector& marker, IndexVector& parent, IndexVector& xplore, GlobalLU_t& glu)\n{\n  Index nextl_col; // Next available position in panel_lsub[*,jj] \n  \n  // Initialize pointers \n  VectorBlock<IndexVector> marker1(marker, m, m); \n  nseg = 0; \n  \n  panel_dfs_traits<IndexVector> traits(jcol, marker1.data());\n  \n  // For each column in the panel \n  for (StorageIndex jj = StorageIndex(jcol); jj < jcol + w; jj++) \n  {\n    nextl_col = (jj - jcol) * m; \n    \n    VectorBlock<IndexVector> repfnz_col(repfnz, nextl_col, m); // First nonzero location in each row\n    VectorBlock<ScalarVector> dense_col(dense,nextl_col, m); // Accumulate a column vector here\n    \n    \n    // For each nnz in A[*, jj] do depth first search\n    for (typename MatrixType::InnerIterator it(A, jj); it; ++it)\n    {\n      Index krow = it.row(); \n      dense_col(krow) = it.value();\n      \n      StorageIndex kmark = marker(krow); \n      if (kmark == jj) \n        continue; // krow visited before, go to the next nonzero\n      \n      dfs_kernel(jj, perm_r, nseg, panel_lsub, segrep, repfnz_col, xprune, marker, parent,\n                   xplore, glu, nextl_col, krow, traits);\n    }// end for nonzeros in column jj\n    \n  } // end for column jj\n}\n\n} // end namespace internal\n} // end namespace Eigen\n\n#endif // SPARSELU_PANEL_DFS_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseLU/SparseLU_pivotL.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n/* \n \n * NOTE: This file is the modified version of xpivotL.c file in SuperLU \n \n * -- SuperLU routine (version 3.0) --\n * Univ. of California Berkeley, Xerox Palo Alto Research Center,\n * and Lawrence Berkeley National Lab.\n * October 15, 2003\n *\n * Copyright (c) 1994 by Xerox Corporation.  All rights reserved.\n *\n * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY\n * EXPRESSED OR IMPLIED.  ANY USE IS AT YOUR OWN RISK.\n *\n * Permission is hereby granted to use or copy this program for any\n * purpose, provided the above notices are retained on all copies.\n * Permission to modify the code and to distribute modified code is\n * granted, provided the above notices are retained, and a notice that\n * the code was modified is included with the above copyright notice.\n */\n#ifndef SPARSELU_PIVOTL_H\n#define SPARSELU_PIVOTL_H\n\nnamespace Eigen {\nnamespace internal {\n  \n/**\n * \\brief Performs the numerical pivotin on the current column of L, and the CDIV operation.\n * \n * Pivot policy :\n * (1) Compute thresh = u * max_(i>=j) abs(A_ij);\n * (2) IF user specifies pivot row k and abs(A_kj) >= thresh THEN\n *           pivot row = k;\n *       ELSE IF abs(A_jj) >= thresh THEN\n *           pivot row = j;\n *       ELSE\n *           pivot row = m;\n * \n *   Note: If you absolutely want to use a given pivot order, then set u=0.0.\n * \n * \\param jcol The current column of L\n * \\param diagpivotthresh diagonal pivoting threshold\n * \\param[in,out] perm_r Row permutation (threshold pivoting)\n * \\param[in] iperm_c column permutation - used to finf diagonal of Pc*A*Pc'\n * \\param[out] pivrow  The pivot row\n * \\param glu Global LU data\n * \\return 0 if success, i > 0 if U(i,i) is exactly zero \n * \n */\ntemplate <typename Scalar, typename StorageIndex>\nIndex SparseLUImpl<Scalar,StorageIndex>::pivotL(const Index jcol, const RealScalar& diagpivotthresh, IndexVector& perm_r, IndexVector& iperm_c, Index& pivrow, GlobalLU_t& glu)\n{\n  \n  Index fsupc = (glu.xsup)((glu.supno)(jcol)); // First column in the supernode containing the column jcol\n  Index nsupc = jcol - fsupc; // Number of columns in the supernode portion, excluding jcol; nsupc >=0\n  Index lptr = glu.xlsub(fsupc); // pointer to the starting location of the row subscripts for this supernode portion\n  Index nsupr = glu.xlsub(fsupc+1) - lptr; // Number of rows in the supernode\n  Index lda = glu.xlusup(fsupc+1) - glu.xlusup(fsupc); // leading dimension\n  Scalar* lu_sup_ptr = &(glu.lusup.data()[glu.xlusup(fsupc)]); // Start of the current supernode\n  Scalar* lu_col_ptr = &(glu.lusup.data()[glu.xlusup(jcol)]); // Start of jcol in the supernode\n  StorageIndex* lsub_ptr = &(glu.lsub.data()[lptr]); // Start of row indices of the supernode\n  \n  // Determine the largest abs numerical value for partial pivoting \n  Index diagind = iperm_c(jcol); // diagonal index \n  RealScalar pivmax(-1.0);\n  Index pivptr = nsupc; \n  Index diag = emptyIdxLU; \n  RealScalar rtemp;\n  Index isub, icol, itemp, k; \n  for (isub = nsupc; isub < nsupr; ++isub) {\n    using std::abs;\n    rtemp = abs(lu_col_ptr[isub]);\n    if (rtemp > pivmax) {\n      pivmax = rtemp; \n      pivptr = isub;\n    } \n    if (lsub_ptr[isub] == diagind) diag = isub;\n  }\n  \n  // Test for singularity\n  if ( pivmax <= RealScalar(0.0) ) {\n    // if pivmax == -1, the column is structurally empty, otherwise it is only numerically zero\n    pivrow = pivmax < RealScalar(0.0) ? diagind : lsub_ptr[pivptr];\n    perm_r(pivrow) = StorageIndex(jcol);\n    return (jcol+1);\n  }\n  \n  RealScalar thresh = diagpivotthresh * pivmax; \n  \n  // Choose appropriate pivotal element \n  \n  {\n    // Test if the diagonal element can be used as a pivot (given the threshold value)\n    if (diag >= 0 ) \n    {\n      // Diagonal element exists\n      using std::abs;\n      rtemp = abs(lu_col_ptr[diag]);\n      if (rtemp != RealScalar(0.0) && rtemp >= thresh) pivptr = diag;\n    }\n    pivrow = lsub_ptr[pivptr];\n  }\n  \n  // Record pivot row\n  perm_r(pivrow) = StorageIndex(jcol);\n  // Interchange row subscripts\n  if (pivptr != nsupc )\n  {\n    std::swap( lsub_ptr[pivptr], lsub_ptr[nsupc] );\n    // Interchange numerical values as well, for the two rows in the whole snode\n    // such that L is indexed the same way as A\n    for (icol = 0; icol <= nsupc; icol++)\n    {\n      itemp = pivptr + icol * lda; \n      std::swap(lu_sup_ptr[itemp], lu_sup_ptr[nsupc + icol * lda]);\n    }\n  }\n  // cdiv operations\n  Scalar temp = Scalar(1.0) / lu_col_ptr[nsupc];\n  for (k = nsupc+1; k < nsupr; k++)\n    lu_col_ptr[k] *= temp; \n  return 0;\n}\n\n} // end namespace internal\n} // end namespace Eigen\n\n#endif // SPARSELU_PIVOTL_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseLU/SparseLU_pruneL.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n/* \n \n * NOTE: This file is the modified version of [s,d,c,z]pruneL.c file in SuperLU \n \n * -- SuperLU routine (version 2.0) --\n * Univ. of California Berkeley, Xerox Palo Alto Research Center,\n * and Lawrence Berkeley National Lab.\n * November 15, 1997\n *\n * Copyright (c) 1994 by Xerox Corporation.  All rights reserved.\n *\n * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY\n * EXPRESSED OR IMPLIED.  ANY USE IS AT YOUR OWN RISK.\n *\n * Permission is hereby granted to use or copy this program for any\n * purpose, provided the above notices are retained on all copies.\n * Permission to modify the code and to distribute modified code is\n * granted, provided the above notices are retained, and a notice that\n * the code was modified is included with the above copyright notice.\n */\n#ifndef SPARSELU_PRUNEL_H\n#define SPARSELU_PRUNEL_H\n\nnamespace Eigen {\nnamespace internal {\n\n/**\n * \\brief Prunes the L-structure.\n *\n * It prunes the L-structure  of supernodes whose L-structure contains the current pivot row \"pivrow\"\n * \n * \n * \\param jcol The current column of L\n * \\param[in] perm_r Row permutation\n * \\param[out] pivrow  The pivot row\n * \\param nseg Number of segments\n * \\param segrep \n * \\param repfnz\n * \\param[out] xprune \n * \\param glu Global LU data\n * \n */\ntemplate <typename Scalar, typename StorageIndex>\nvoid SparseLUImpl<Scalar,StorageIndex>::pruneL(const Index jcol, const IndexVector& perm_r, const Index pivrow, const Index nseg,\n                                               const IndexVector& segrep, BlockIndexVector repfnz, IndexVector& xprune, GlobalLU_t& glu)\n{\n  // For each supernode-rep irep in U(*,j]\n  Index jsupno = glu.supno(jcol); \n  Index i,irep,irep1; \n  bool movnum, do_prune = false; \n  Index kmin = 0, kmax = 0, minloc, maxloc,krow; \n  for (i = 0; i < nseg; i++)\n  {\n    irep = segrep(i); \n    irep1 = irep + 1; \n    do_prune = false; \n    \n    // Don't prune with a zero U-segment \n    if (repfnz(irep) == emptyIdxLU) continue; \n    \n    // If a snode overlaps with the next panel, then the U-segment\n    // is fragmented into two parts -- irep and irep1. We should let \n    // pruning occur at the rep-column in irep1s snode. \n    if (glu.supno(irep) == glu.supno(irep1) ) continue; // don't prune \n    \n    // If it has not been pruned & it has a nonz in row L(pivrow,i)\n    if (glu.supno(irep) != jsupno )\n    {\n      if ( xprune (irep) >= glu.xlsub(irep1) )\n      {\n        kmin = glu.xlsub(irep);\n        kmax = glu.xlsub(irep1) - 1; \n        for (krow = kmin; krow <= kmax; krow++)\n        {\n          if (glu.lsub(krow) == pivrow) \n          {\n            do_prune = true; \n            break; \n          }\n        }\n      }\n      \n      if (do_prune) \n      {\n        // do a quicksort-type partition\n        // movnum=true means that the num values have to be exchanged\n        movnum = false; \n        if (irep == glu.xsup(glu.supno(irep)) ) // Snode of size 1 \n          movnum = true; \n        \n        while (kmin <= kmax)\n        {\n          if (perm_r(glu.lsub(kmax)) == emptyIdxLU)\n            kmax--; \n          else if ( perm_r(glu.lsub(kmin)) != emptyIdxLU)\n            kmin++;\n          else \n          {\n            // kmin below pivrow (not yet pivoted), and kmax\n            // above pivrow: interchange the two suscripts\n            std::swap(glu.lsub(kmin), glu.lsub(kmax)); \n            \n            // If the supernode has only one column, then we \n            // only keep one set of subscripts. For any subscript\n            // intercnahge performed, similar interchange must be \n            // done on the numerical values. \n            if (movnum) \n            {\n              minloc = glu.xlusup(irep) + ( kmin - glu.xlsub(irep) ); \n              maxloc = glu.xlusup(irep) + ( kmax - glu.xlsub(irep) ); \n              std::swap(glu.lusup(minloc), glu.lusup(maxloc)); \n            }\n            kmin++;\n            kmax--;\n          }\n        } // end while \n        \n        xprune(irep) = StorageIndex(kmin);  //Pruning \n      } // end if do_prune \n    } // end pruning \n  } // End for each U-segment\n}\n\n} // end namespace internal\n} // end namespace Eigen\n\n#endif // SPARSELU_PRUNEL_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseLU/SparseLU_relax_snode.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n/* This file is a modified version of heap_relax_snode.c file in SuperLU\n * -- SuperLU routine (version 3.0) --\n * Univ. of California Berkeley, Xerox Palo Alto Research Center,\n * and Lawrence Berkeley National Lab.\n * October 15, 2003\n *\n * Copyright (c) 1994 by Xerox Corporation.  All rights reserved.\n *\n * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY\n * EXPRESSED OR IMPLIED.  ANY USE IS AT YOUR OWN RISK.\n *\n * Permission is hereby granted to use or copy this program for any\n * purpose, provided the above notices are retained on all copies.\n * Permission to modify the code and to distribute modified code is\n * granted, provided the above notices are retained, and a notice that\n * the code was modified is included with the above copyright notice.\n */\n\n#ifndef SPARSELU_RELAX_SNODE_H\n#define SPARSELU_RELAX_SNODE_H\n\nnamespace Eigen {\n\nnamespace internal {\n \n/** \n * \\brief Identify the initial relaxed supernodes\n * \n * This routine is applied to a column elimination tree. \n * It assumes that the matrix has been reordered according to the postorder of the etree\n * \\param n  the number of columns\n * \\param et elimination tree \n * \\param relax_columns Maximum number of columns allowed in a relaxed snode \n * \\param descendants Number of descendants of each node in the etree\n * \\param relax_end last column in a supernode\n */\ntemplate <typename Scalar, typename StorageIndex>\nvoid SparseLUImpl<Scalar,StorageIndex>::relax_snode (const Index n, IndexVector& et, const Index relax_columns, IndexVector& descendants, IndexVector& relax_end)\n{\n  \n  // compute the number of descendants of each node in the etree\n  Index parent; \n  relax_end.setConstant(emptyIdxLU);\n  descendants.setZero();\n  for (Index j = 0; j < n; j++) \n  {\n    parent = et(j);\n    if (parent != n) // not the dummy root\n      descendants(parent) += descendants(j) + 1;\n  }\n  // Identify the relaxed supernodes by postorder traversal of the etree\n  Index snode_start; // beginning of a snode \n  for (Index j = 0; j < n; )\n  {\n    parent = et(j);\n    snode_start = j; \n    while ( parent != n && descendants(parent) < relax_columns ) \n    {\n      j = parent; \n      parent = et(j);\n    }\n    // Found a supernode in postordered etree, j is the last column \n    relax_end(snode_start) = StorageIndex(j); // Record last column\n    j++;\n    // Search for a new leaf\n    while (descendants(j) != 0 && j < n) j++;\n  } // End postorder traversal of the etree\n  \n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n#endif\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SparseQR/SparseQR.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012-2013 Desire Nuentsa <desire.nuentsa_wakam@inria.fr>\n// Copyright (C) 2012-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSE_QR_H\n#define EIGEN_SPARSE_QR_H\n\nnamespace Eigen {\n\ntemplate<typename MatrixType, typename OrderingType> class SparseQR;\ntemplate<typename SparseQRType> struct SparseQRMatrixQReturnType;\ntemplate<typename SparseQRType> struct SparseQRMatrixQTransposeReturnType;\ntemplate<typename SparseQRType, typename Derived> struct SparseQR_QProduct;\nnamespace internal {\n  template <typename SparseQRType> struct traits<SparseQRMatrixQReturnType<SparseQRType> >\n  {\n    typedef typename SparseQRType::MatrixType ReturnType;\n    typedef typename ReturnType::StorageIndex StorageIndex;\n    typedef typename ReturnType::StorageKind StorageKind;\n    enum {\n      RowsAtCompileTime = Dynamic,\n      ColsAtCompileTime = Dynamic\n    };\n  };\n  template <typename SparseQRType> struct traits<SparseQRMatrixQTransposeReturnType<SparseQRType> >\n  {\n    typedef typename SparseQRType::MatrixType ReturnType;\n  };\n  template <typename SparseQRType, typename Derived> struct traits<SparseQR_QProduct<SparseQRType, Derived> >\n  {\n    typedef typename Derived::PlainObject ReturnType;\n  };\n} // End namespace internal\n\n/**\n  * \\ingroup SparseQR_Module\n  * \\class SparseQR\n  * \\brief Sparse left-looking rank-revealing QR factorization\n  * \n  * This class implements a left-looking rank-revealing QR decomposition \n  * of sparse matrices. When a column has a norm less than a given tolerance\n  * it is implicitly permuted to the end. The QR factorization thus obtained is \n  * given by A*P = Q*R where R is upper triangular or trapezoidal. \n  * \n  * P is the column permutation which is the product of the fill-reducing and the\n  * rank-revealing permutations. Use colsPermutation() to get it.\n  * \n  * Q is the orthogonal matrix represented as products of Householder reflectors. \n  * Use matrixQ() to get an expression and matrixQ().adjoint() to get the adjoint.\n  * You can then apply it to a vector.\n  * \n  * R is the sparse triangular or trapezoidal matrix. The later occurs when A is rank-deficient.\n  * matrixR().topLeftCorner(rank(), rank()) always returns a triangular factor of full rank.\n  * \n  * \\tparam _MatrixType The type of the sparse matrix A, must be a column-major SparseMatrix<>\n  * \\tparam _OrderingType The fill-reducing ordering method. See the \\link OrderingMethods_Module \n  *  OrderingMethods \\endlink module for the list of built-in and external ordering methods.\n  * \n  * \\implsparsesolverconcept\n  *\n  * \\warning The input sparse matrix A must be in compressed mode (see SparseMatrix::makeCompressed()).\n  * \\warning For complex matrices matrixQ().transpose() will actually return the adjoint matrix.\n  * \n  */\ntemplate<typename _MatrixType, typename _OrderingType>\nclass SparseQR : public SparseSolverBase<SparseQR<_MatrixType,_OrderingType> >\n{\n  protected:\n    typedef SparseSolverBase<SparseQR<_MatrixType,_OrderingType> > Base;\n    using Base::m_isInitialized;\n  public:\n    using Base::_solve_impl;\n    typedef _MatrixType MatrixType;\n    typedef _OrderingType OrderingType;\n    typedef typename MatrixType::Scalar Scalar;\n    typedef typename MatrixType::RealScalar RealScalar;\n    typedef typename MatrixType::StorageIndex StorageIndex;\n    typedef SparseMatrix<Scalar,ColMajor,StorageIndex> QRMatrixType;\n    typedef Matrix<StorageIndex, Dynamic, 1> IndexVector;\n    typedef Matrix<Scalar, Dynamic, 1> ScalarVector;\n    typedef PermutationMatrix<Dynamic, Dynamic, StorageIndex> PermutationType;\n\n    enum {\n      ColsAtCompileTime = MatrixType::ColsAtCompileTime,\n      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime\n    };\n    \n  public:\n    SparseQR () :  m_analysisIsok(false), m_lastError(\"\"), m_useDefaultThreshold(true),m_isQSorted(false),m_isEtreeOk(false)\n    { }\n    \n    /** Construct a QR factorization of the matrix \\a mat.\n      * \n      * \\warning The matrix \\a mat must be in compressed mode (see SparseMatrix::makeCompressed()).\n      * \n      * \\sa compute()\n      */\n    explicit SparseQR(const MatrixType& mat) : m_analysisIsok(false), m_lastError(\"\"), m_useDefaultThreshold(true),m_isQSorted(false),m_isEtreeOk(false)\n    {\n      compute(mat);\n    }\n    \n    /** Computes the QR factorization of the sparse matrix \\a mat.\n      * \n      * \\warning The matrix \\a mat must be in compressed mode (see SparseMatrix::makeCompressed()).\n      * \n      * \\sa analyzePattern(), factorize()\n      */\n    void compute(const MatrixType& mat)\n    {\n      analyzePattern(mat);\n      factorize(mat);\n    }\n    void analyzePattern(const MatrixType& mat);\n    void factorize(const MatrixType& mat);\n    \n    /** \\returns the number of rows of the represented matrix. \n      */\n    inline Index rows() const { return m_pmat.rows(); }\n    \n    /** \\returns the number of columns of the represented matrix. \n      */\n    inline Index cols() const { return m_pmat.cols();}\n    \n    /** \\returns a const reference to the \\b sparse upper triangular matrix R of the QR factorization.\n      * \\warning The entries of the returned matrix are not sorted. This means that using it in algorithms\n      *          expecting sorted entries will fail. This include random coefficient accesses (SpaseMatrix::coeff()),\n      *          and coefficient-wise operations. Matrix products and triangular solves are fine though.\n      *\n      * To sort the entries, you can assign it to a row-major matrix, and if a column-major matrix\n      * is required, you can copy it again:\n      * \\code\n      * SparseMatrix<double>          R  = qr.matrixR();  // column-major, not sorted!\n      * SparseMatrix<double,RowMajor> Rr = qr.matrixR();  // row-major, sorted\n      * SparseMatrix<double>          Rc = Rr;            // column-major, sorted\n      * \\endcode\n      */\n    const QRMatrixType& matrixR() const { return m_R; }\n    \n    /** \\returns the number of non linearly dependent columns as determined by the pivoting threshold.\n      *\n      * \\sa setPivotThreshold()\n      */\n    Index rank() const\n    {\n      eigen_assert(m_isInitialized && \"The factorization should be called first, use compute()\");\n      return m_nonzeropivots; \n    }\n    \n    /** \\returns an expression of the matrix Q as products of sparse Householder reflectors.\n    * The common usage of this function is to apply it to a dense matrix or vector\n    * \\code\n    * VectorXd B1, B2;\n    * // Initialize B1\n    * B2 = matrixQ() * B1;\n    * \\endcode\n    *\n    * To get a plain SparseMatrix representation of Q:\n    * \\code\n    * SparseMatrix<double> Q;\n    * Q = SparseQR<SparseMatrix<double> >(A).matrixQ();\n    * \\endcode\n    * Internally, this call simply performs a sparse product between the matrix Q\n    * and a sparse identity matrix. However, due to the fact that the sparse\n    * reflectors are stored unsorted, two transpositions are needed to sort\n    * them before performing the product.\n    */\n    SparseQRMatrixQReturnType<SparseQR> matrixQ() const \n    { return SparseQRMatrixQReturnType<SparseQR>(*this); }\n    \n    /** \\returns a const reference to the column permutation P that was applied to A such that A*P = Q*R\n      * It is the combination of the fill-in reducing permutation and numerical column pivoting.\n      */\n    const PermutationType& colsPermutation() const\n    { \n      eigen_assert(m_isInitialized && \"Decomposition is not initialized.\");\n      return m_outputPerm_c;\n    }\n    \n    /** \\returns A string describing the type of error.\n      * This method is provided to ease debugging, not to handle errors.\n      */\n    std::string lastErrorMessage() const { return m_lastError; }\n    \n    /** \\internal */\n    template<typename Rhs, typename Dest>\n    bool _solve_impl(const MatrixBase<Rhs> &B, MatrixBase<Dest> &dest) const\n    {\n      eigen_assert(m_isInitialized && \"The factorization should be called first, use compute()\");\n      eigen_assert(this->rows() == B.rows() && \"SparseQR::solve() : invalid number of rows in the right hand side matrix\");\n\n      Index rank = this->rank();\n      \n      // Compute Q^* * b;\n      typename Dest::PlainObject y, b;\n      y = this->matrixQ().adjoint() * B;\n      b = y;\n      \n      // Solve with the triangular matrix R\n      y.resize((std::max<Index>)(cols(),y.rows()),y.cols());\n      y.topRows(rank) = this->matrixR().topLeftCorner(rank, rank).template triangularView<Upper>().solve(b.topRows(rank));\n      y.bottomRows(y.rows()-rank).setZero();\n      \n      // Apply the column permutation\n      if (m_perm_c.size())  dest = colsPermutation() * y.topRows(cols());\n      else                  dest = y.topRows(cols());\n      \n      m_info = Success;\n      return true;\n    }\n\n    /** Sets the threshold that is used to determine linearly dependent columns during the factorization.\n      *\n      * In practice, if during the factorization the norm of the column that has to be eliminated is below\n      * this threshold, then the entire column is treated as zero, and it is moved at the end.\n      */\n    void setPivotThreshold(const RealScalar& threshold)\n    {\n      m_useDefaultThreshold = false;\n      m_threshold = threshold;\n    }\n    \n    /** \\returns the solution X of \\f$ A X = B \\f$ using the current decomposition of A.\n      *\n      * \\sa compute()\n      */\n    template<typename Rhs>\n    inline const Solve<SparseQR, Rhs> solve(const MatrixBase<Rhs>& B) const \n    {\n      eigen_assert(m_isInitialized && \"The factorization should be called first, use compute()\");\n      eigen_assert(this->rows() == B.rows() && \"SparseQR::solve() : invalid number of rows in the right hand side matrix\");\n      return Solve<SparseQR, Rhs>(*this, B.derived());\n    }\n    template<typename Rhs>\n    inline const Solve<SparseQR, Rhs> solve(const SparseMatrixBase<Rhs>& B) const\n    {\n          eigen_assert(m_isInitialized && \"The factorization should be called first, use compute()\");\n          eigen_assert(this->rows() == B.rows() && \"SparseQR::solve() : invalid number of rows in the right hand side matrix\");\n          return Solve<SparseQR, Rhs>(*this, B.derived());\n    }\n    \n    /** \\brief Reports whether previous computation was successful.\n      *\n      * \\returns \\c Success if computation was successful,\n      *          \\c NumericalIssue if the QR factorization reports a numerical problem\n      *          \\c InvalidInput if the input matrix is invalid\n      *\n      * \\sa iparm()          \n      */\n    ComputationInfo info() const\n    {\n      eigen_assert(m_isInitialized && \"Decomposition is not initialized.\");\n      return m_info;\n    }\n\n\n    /** \\internal */\n    inline void _sort_matrix_Q()\n    {\n      if(this->m_isQSorted) return;\n      // The matrix Q is sorted during the transposition\n      SparseMatrix<Scalar, RowMajor, Index> mQrm(this->m_Q);\n      this->m_Q = mQrm;\n      this->m_isQSorted = true;\n    }\n\n    \n  protected:\n    bool m_analysisIsok;\n    bool m_factorizationIsok;\n    mutable ComputationInfo m_info;\n    std::string m_lastError;\n    QRMatrixType m_pmat;            // Temporary matrix\n    QRMatrixType m_R;               // The triangular factor matrix\n    QRMatrixType m_Q;               // The orthogonal reflectors\n    ScalarVector m_hcoeffs;         // The Householder coefficients\n    PermutationType m_perm_c;       // Fill-reducing  Column  permutation\n    PermutationType m_pivotperm;    // The permutation for rank revealing\n    PermutationType m_outputPerm_c; // The final column permutation\n    RealScalar m_threshold;         // Threshold to determine null Householder reflections\n    bool m_useDefaultThreshold;     // Use default threshold\n    Index m_nonzeropivots;          // Number of non zero pivots found\n    IndexVector m_etree;            // Column elimination tree\n    IndexVector m_firstRowElt;      // First element in each row\n    bool m_isQSorted;               // whether Q is sorted or not\n    bool m_isEtreeOk;               // whether the elimination tree match the initial input matrix\n    \n    template <typename, typename > friend struct SparseQR_QProduct;\n    \n};\n\n/** \\brief Preprocessing step of a QR factorization \n  * \n  * \\warning The matrix \\a mat must be in compressed mode (see SparseMatrix::makeCompressed()).\n  * \n  * In this step, the fill-reducing permutation is computed and applied to the columns of A\n  * and the column elimination tree is computed as well. Only the sparsity pattern of \\a mat is exploited.\n  * \n  * \\note In this step it is assumed that there is no empty row in the matrix \\a mat.\n  */\ntemplate <typename MatrixType, typename OrderingType>\nvoid SparseQR<MatrixType,OrderingType>::analyzePattern(const MatrixType& mat)\n{\n  eigen_assert(mat.isCompressed() && \"SparseQR requires a sparse matrix in compressed mode. Call .makeCompressed() before passing it to SparseQR\");\n  // Copy to a column major matrix if the input is rowmajor\n  typename internal::conditional<MatrixType::IsRowMajor,QRMatrixType,const MatrixType&>::type matCpy(mat);\n  // Compute the column fill reducing ordering\n  OrderingType ord; \n  ord(matCpy, m_perm_c); \n  Index n = mat.cols();\n  Index m = mat.rows();\n  Index diagSize = (std::min)(m,n);\n  \n  if (!m_perm_c.size())\n  {\n    m_perm_c.resize(n);\n    m_perm_c.indices().setLinSpaced(n, 0,StorageIndex(n-1));\n  }\n  \n  // Compute the column elimination tree of the permuted matrix\n  m_outputPerm_c = m_perm_c.inverse();\n  internal::coletree(matCpy, m_etree, m_firstRowElt, m_outputPerm_c.indices().data());\n  m_isEtreeOk = true;\n  \n  m_R.resize(m, n);\n  m_Q.resize(m, diagSize);\n  \n  // Allocate space for nonzero elements : rough estimation\n  m_R.reserve(2*mat.nonZeros()); //FIXME Get a more accurate estimation through symbolic factorization with the etree\n  m_Q.reserve(2*mat.nonZeros());\n  m_hcoeffs.resize(diagSize);\n  m_analysisIsok = true;\n}\n\n/** \\brief Performs the numerical QR factorization of the input matrix\n  * \n  * The function SparseQR::analyzePattern(const MatrixType&) must have been called beforehand with\n  * a matrix having the same sparsity pattern than \\a mat.\n  * \n  * \\param mat The sparse column-major matrix\n  */\ntemplate <typename MatrixType, typename OrderingType>\nvoid SparseQR<MatrixType,OrderingType>::factorize(const MatrixType& mat)\n{\n  using std::abs;\n  \n  eigen_assert(m_analysisIsok && \"analyzePattern() should be called before this step\");\n  StorageIndex m = StorageIndex(mat.rows());\n  StorageIndex n = StorageIndex(mat.cols());\n  StorageIndex diagSize = (std::min)(m,n);\n  IndexVector mark((std::max)(m,n)); mark.setConstant(-1);  // Record the visited nodes\n  IndexVector Ridx(n), Qidx(m);                             // Store temporarily the row indexes for the current column of R and Q\n  Index nzcolR, nzcolQ;                                     // Number of nonzero for the current column of R and Q\n  ScalarVector tval(m);                                     // The dense vector used to compute the current column\n  RealScalar pivotThreshold = m_threshold;\n  \n  m_R.setZero();\n  m_Q.setZero();\n  m_pmat = mat;\n  if(!m_isEtreeOk)\n  {\n    m_outputPerm_c = m_perm_c.inverse();\n    internal::coletree(m_pmat, m_etree, m_firstRowElt, m_outputPerm_c.indices().data());\n    m_isEtreeOk = true;\n  }\n\n  m_pmat.uncompress(); // To have the innerNonZeroPtr allocated\n  \n  // Apply the fill-in reducing permutation lazily:\n  {\n    // If the input is row major, copy the original column indices,\n    // otherwise directly use the input matrix\n    // \n    IndexVector originalOuterIndicesCpy;\n    const StorageIndex *originalOuterIndices = mat.outerIndexPtr();\n    if(MatrixType::IsRowMajor)\n    {\n      originalOuterIndicesCpy = IndexVector::Map(m_pmat.outerIndexPtr(),n+1);\n      originalOuterIndices = originalOuterIndicesCpy.data();\n    }\n    \n    for (int i = 0; i < n; i++)\n    {\n      Index p = m_perm_c.size() ? m_perm_c.indices()(i) : i;\n      m_pmat.outerIndexPtr()[p] = originalOuterIndices[i]; \n      m_pmat.innerNonZeroPtr()[p] = originalOuterIndices[i+1] - originalOuterIndices[i]; \n    }\n  }\n  \n  /* Compute the default threshold as in MatLab, see:\n   * Tim Davis, \"Algorithm 915, SuiteSparseQR: Multifrontal Multithreaded Rank-Revealing\n   * Sparse QR Factorization, ACM Trans. on Math. Soft. 38(1), 2011, Page 8:3 \n   */\n  if(m_useDefaultThreshold) \n  {\n    RealScalar max2Norm = 0.0;\n    for (int j = 0; j < n; j++) max2Norm = numext::maxi(max2Norm, m_pmat.col(j).norm());\n    if(max2Norm==RealScalar(0))\n      max2Norm = RealScalar(1);\n    pivotThreshold = 20 * (m + n) * max2Norm * NumTraits<RealScalar>::epsilon();\n  }\n  \n  // Initialize the numerical permutation\n  m_pivotperm.setIdentity(n);\n  \n  StorageIndex nonzeroCol = 0; // Record the number of valid pivots\n  m_Q.startVec(0);\n\n  // Left looking rank-revealing QR factorization: compute a column of R and Q at a time\n  for (StorageIndex col = 0; col < n; ++col)\n  {\n    mark.setConstant(-1);\n    m_R.startVec(col);\n    mark(nonzeroCol) = col;\n    Qidx(0) = nonzeroCol;\n    nzcolR = 0; nzcolQ = 1;\n    bool found_diag = nonzeroCol>=m;\n    tval.setZero(); \n    \n    // Symbolic factorization: find the nonzero locations of the column k of the factors R and Q, i.e.,\n    // all the nodes (with indexes lower than rank) reachable through the column elimination tree (etree) rooted at node k.\n    // Note: if the diagonal entry does not exist, then its contribution must be explicitly added,\n    // thus the trick with found_diag that permits to do one more iteration on the diagonal element if this one has not been found.\n    for (typename QRMatrixType::InnerIterator itp(m_pmat, col); itp || !found_diag; ++itp)\n    {\n      StorageIndex curIdx = nonzeroCol;\n      if(itp) curIdx = StorageIndex(itp.row());\n      if(curIdx == nonzeroCol) found_diag = true;\n      \n      // Get the nonzeros indexes of the current column of R\n      StorageIndex st = m_firstRowElt(curIdx); // The traversal of the etree starts here\n      if (st < 0 )\n      {\n        m_lastError = \"Empty row found during numerical factorization\";\n        m_info = InvalidInput;\n        return;\n      }\n\n      // Traverse the etree \n      Index bi = nzcolR;\n      for (; mark(st) != col; st = m_etree(st))\n      {\n        Ridx(nzcolR) = st;  // Add this row to the list,\n        mark(st) = col;     // and mark this row as visited\n        nzcolR++;\n      }\n\n      // Reverse the list to get the topological ordering\n      Index nt = nzcolR-bi;\n      for(Index i = 0; i < nt/2; i++) std::swap(Ridx(bi+i), Ridx(nzcolR-i-1));\n       \n      // Copy the current (curIdx,pcol) value of the input matrix\n      if(itp) tval(curIdx) = itp.value();\n      else    tval(curIdx) = Scalar(0);\n      \n      // Compute the pattern of Q(:,k)\n      if(curIdx > nonzeroCol && mark(curIdx) != col ) \n      {\n        Qidx(nzcolQ) = curIdx;  // Add this row to the pattern of Q,\n        mark(curIdx) = col;     // and mark it as visited\n        nzcolQ++;\n      }\n    }\n\n    // Browse all the indexes of R(:,col) in reverse order\n    for (Index i = nzcolR-1; i >= 0; i--)\n    {\n      Index curIdx = Ridx(i);\n      \n      // Apply the curIdx-th householder vector to the current column (temporarily stored into tval)\n      Scalar tdot(0);\n      \n      // First compute q' * tval\n      tdot = m_Q.col(curIdx).dot(tval);\n\n      tdot *= m_hcoeffs(curIdx);\n      \n      // Then update tval = tval - q * tau\n      // FIXME: tval -= tdot * m_Q.col(curIdx) should amount to the same (need to check/add support for efficient \"dense ?= sparse\")\n      for (typename QRMatrixType::InnerIterator itq(m_Q, curIdx); itq; ++itq)\n        tval(itq.row()) -= itq.value() * tdot;\n\n      // Detect fill-in for the current column of Q\n      if(m_etree(Ridx(i)) == nonzeroCol)\n      {\n        for (typename QRMatrixType::InnerIterator itq(m_Q, curIdx); itq; ++itq)\n        {\n          StorageIndex iQ = StorageIndex(itq.row());\n          if (mark(iQ) != col)\n          {\n            Qidx(nzcolQ++) = iQ;  // Add this row to the pattern of Q,\n            mark(iQ) = col;       // and mark it as visited\n          }\n        }\n      }\n    } // End update current column\n    \n    Scalar tau = RealScalar(0);\n    RealScalar beta = 0;\n    \n    if(nonzeroCol < diagSize)\n    {\n      // Compute the Householder reflection that eliminate the current column\n      // FIXME this step should call the Householder module.\n      Scalar c0 = nzcolQ ? tval(Qidx(0)) : Scalar(0);\n      \n      // First, the squared norm of Q((col+1):m, col)\n      RealScalar sqrNorm = 0.;\n      for (Index itq = 1; itq < nzcolQ; ++itq) sqrNorm += numext::abs2(tval(Qidx(itq)));\n      if(sqrNorm == RealScalar(0) && numext::imag(c0) == RealScalar(0))\n      {\n        beta = numext::real(c0);\n        tval(Qidx(0)) = 1;\n      }\n      else\n      {\n        using std::sqrt;\n        beta = sqrt(numext::abs2(c0) + sqrNorm);\n        if(numext::real(c0) >= RealScalar(0))\n          beta = -beta;\n        tval(Qidx(0)) = 1;\n        for (Index itq = 1; itq < nzcolQ; ++itq)\n          tval(Qidx(itq)) /= (c0 - beta);\n        tau = numext::conj((beta-c0) / beta);\n          \n      }\n    }\n\n    // Insert values in R\n    for (Index  i = nzcolR-1; i >= 0; i--)\n    {\n      Index curIdx = Ridx(i);\n      if(curIdx < nonzeroCol) \n      {\n        m_R.insertBackByOuterInnerUnordered(col, curIdx) = tval(curIdx);\n        tval(curIdx) = Scalar(0.);\n      }\n    }\n\n    if(nonzeroCol < diagSize && abs(beta) >= pivotThreshold)\n    {\n      m_R.insertBackByOuterInner(col, nonzeroCol) = beta;\n      // The householder coefficient\n      m_hcoeffs(nonzeroCol) = tau;\n      // Record the householder reflections\n      for (Index itq = 0; itq < nzcolQ; ++itq)\n      {\n        Index iQ = Qidx(itq);\n        m_Q.insertBackByOuterInnerUnordered(nonzeroCol,iQ) = tval(iQ);\n        tval(iQ) = Scalar(0.);\n      }\n      nonzeroCol++;\n      if(nonzeroCol<diagSize)\n        m_Q.startVec(nonzeroCol);\n    }\n    else\n    {\n      // Zero pivot found: move implicitly this column to the end\n      for (Index j = nonzeroCol; j < n-1; j++) \n        std::swap(m_pivotperm.indices()(j), m_pivotperm.indices()[j+1]);\n      \n      // Recompute the column elimination tree\n      internal::coletree(m_pmat, m_etree, m_firstRowElt, m_pivotperm.indices().data());\n      m_isEtreeOk = false;\n    }\n  }\n  \n  m_hcoeffs.tail(diagSize-nonzeroCol).setZero();\n  \n  // Finalize the column pointers of the sparse matrices R and Q\n  m_Q.finalize();\n  m_Q.makeCompressed();\n  m_R.finalize();\n  m_R.makeCompressed();\n  m_isQSorted = false;\n\n  m_nonzeropivots = nonzeroCol;\n  \n  if(nonzeroCol<n)\n  {\n    // Permute the triangular factor to put the 'dead' columns to the end\n    QRMatrixType tempR(m_R);\n    m_R = tempR * m_pivotperm;\n    \n    // Update the column permutation\n    m_outputPerm_c = m_outputPerm_c * m_pivotperm;\n  }\n  \n  m_isInitialized = true; \n  m_factorizationIsok = true;\n  m_info = Success;\n}\n\ntemplate <typename SparseQRType, typename Derived>\nstruct SparseQR_QProduct : ReturnByValue<SparseQR_QProduct<SparseQRType, Derived> >\n{\n  typedef typename SparseQRType::QRMatrixType MatrixType;\n  typedef typename SparseQRType::Scalar Scalar;\n  // Get the references \n  SparseQR_QProduct(const SparseQRType& qr, const Derived& other, bool transpose) : \n  m_qr(qr),m_other(other),m_transpose(transpose) {}\n  inline Index rows() const { return m_qr.matrixQ().rows(); }\n  inline Index cols() const { return m_other.cols(); }\n  \n  // Assign to a vector\n  template<typename DesType>\n  void evalTo(DesType& res) const\n  {\n    Index m = m_qr.rows();\n    Index n = m_qr.cols();\n    Index diagSize = (std::min)(m,n);\n    res = m_other;\n    if (m_transpose)\n    {\n      eigen_assert(m_qr.m_Q.rows() == m_other.rows() && \"Non conforming object sizes\");\n      //Compute res = Q' * other column by column\n      for(Index j = 0; j < res.cols(); j++){\n        for (Index k = 0; k < diagSize; k++)\n        {\n          Scalar tau = Scalar(0);\n          tau = m_qr.m_Q.col(k).dot(res.col(j));\n          if(tau==Scalar(0)) continue;\n          tau = tau * m_qr.m_hcoeffs(k);\n          res.col(j) -= tau * m_qr.m_Q.col(k);\n        }\n      }\n    }\n    else\n    {\n      eigen_assert(m_qr.matrixQ().cols() == m_other.rows() && \"Non conforming object sizes\");\n\n      res.conservativeResize(rows(), cols());\n\n      // Compute res = Q * other column by column\n      for(Index j = 0; j < res.cols(); j++)\n      {\n        for (Index k = diagSize-1; k >=0; k--)\n        {\n          Scalar tau = Scalar(0);\n          tau = m_qr.m_Q.col(k).dot(res.col(j));\n          if(tau==Scalar(0)) continue;\n          tau = tau * numext::conj(m_qr.m_hcoeffs(k));\n          res.col(j) -= tau * m_qr.m_Q.col(k);\n        }\n      }\n    }\n  }\n  \n  const SparseQRType& m_qr;\n  const Derived& m_other;\n  bool m_transpose; // TODO this actually means adjoint\n};\n\ntemplate<typename SparseQRType>\nstruct SparseQRMatrixQReturnType : public EigenBase<SparseQRMatrixQReturnType<SparseQRType> >\n{  \n  typedef typename SparseQRType::Scalar Scalar;\n  typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;\n  enum {\n    RowsAtCompileTime = Dynamic,\n    ColsAtCompileTime = Dynamic\n  };\n  explicit SparseQRMatrixQReturnType(const SparseQRType& qr) : m_qr(qr) {}\n  template<typename Derived>\n  SparseQR_QProduct<SparseQRType, Derived> operator*(const MatrixBase<Derived>& other)\n  {\n    return SparseQR_QProduct<SparseQRType,Derived>(m_qr,other.derived(),false);\n  }\n  // To use for operations with the adjoint of Q\n  SparseQRMatrixQTransposeReturnType<SparseQRType> adjoint() const\n  {\n    return SparseQRMatrixQTransposeReturnType<SparseQRType>(m_qr);\n  }\n  inline Index rows() const { return m_qr.rows(); }\n  inline Index cols() const { return m_qr.rows(); }\n  // To use for operations with the transpose of Q FIXME this is the same as adjoint at the moment\n  SparseQRMatrixQTransposeReturnType<SparseQRType> transpose() const\n  {\n    return SparseQRMatrixQTransposeReturnType<SparseQRType>(m_qr);\n  }\n  const SparseQRType& m_qr;\n};\n\n// TODO this actually represents the adjoint of Q\ntemplate<typename SparseQRType>\nstruct SparseQRMatrixQTransposeReturnType\n{\n  explicit SparseQRMatrixQTransposeReturnType(const SparseQRType& qr) : m_qr(qr) {}\n  template<typename Derived>\n  SparseQR_QProduct<SparseQRType,Derived> operator*(const MatrixBase<Derived>& other)\n  {\n    return SparseQR_QProduct<SparseQRType,Derived>(m_qr,other.derived(), true);\n  }\n  const SparseQRType& m_qr;\n};\n\nnamespace internal {\n  \ntemplate<typename SparseQRType>\nstruct evaluator_traits<SparseQRMatrixQReturnType<SparseQRType> >\n{\n  typedef typename SparseQRType::MatrixType MatrixType;\n  typedef typename storage_kind_to_evaluator_kind<typename MatrixType::StorageKind>::Kind Kind;\n  typedef SparseShape Shape;\n};\n\ntemplate< typename DstXprType, typename SparseQRType>\nstruct Assignment<DstXprType, SparseQRMatrixQReturnType<SparseQRType>, internal::assign_op<typename DstXprType::Scalar,typename DstXprType::Scalar>, Sparse2Sparse>\n{\n  typedef SparseQRMatrixQReturnType<SparseQRType> SrcXprType;\n  typedef typename DstXprType::Scalar Scalar;\n  typedef typename DstXprType::StorageIndex StorageIndex;\n  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &/*func*/)\n  {\n    typename DstXprType::PlainObject idMat(src.rows(), src.cols());\n    idMat.setIdentity();\n    // Sort the sparse householder reflectors if needed\n    const_cast<SparseQRType *>(&src.m_qr)->_sort_matrix_Q();\n    dst = SparseQR_QProduct<SparseQRType, DstXprType>(src.m_qr, idMat, false);\n  }\n};\n\ntemplate< typename DstXprType, typename SparseQRType>\nstruct Assignment<DstXprType, SparseQRMatrixQReturnType<SparseQRType>, internal::assign_op<typename DstXprType::Scalar,typename DstXprType::Scalar>, Sparse2Dense>\n{\n  typedef SparseQRMatrixQReturnType<SparseQRType> SrcXprType;\n  typedef typename DstXprType::Scalar Scalar;\n  typedef typename DstXprType::StorageIndex StorageIndex;\n  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &/*func*/)\n  {\n    dst = src.m_qr.matrixQ() * DstXprType::Identity(src.m_qr.rows(), src.m_qr.rows());\n  }\n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif\n"
  },
  {
    "path": "include/eigen3/Eigen/src/StlSupport/StdDeque.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2009 Hauke Heibel <hauke.heibel@googlemail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_STDDEQUE_H\n#define EIGEN_STDDEQUE_H\n\n#include \"details.h\"\n\n/**\n * This section contains a convenience MACRO which allows an easy specialization of\n * std::deque such that for data types with alignment issues the correct allocator\n * is used automatically.\n */\n#define EIGEN_DEFINE_STL_DEQUE_SPECIALIZATION(...) \\\nnamespace std \\\n{ \\\n  template<> \\\n  class deque<__VA_ARGS__, std::allocator<__VA_ARGS__> >           \\\n    : public deque<__VA_ARGS__, EIGEN_ALIGNED_ALLOCATOR<__VA_ARGS__> > \\\n  { \\\n    typedef deque<__VA_ARGS__, EIGEN_ALIGNED_ALLOCATOR<__VA_ARGS__> > deque_base; \\\n  public: \\\n    typedef __VA_ARGS__ value_type; \\\n    typedef deque_base::allocator_type allocator_type; \\\n    typedef deque_base::size_type size_type;  \\\n    typedef deque_base::iterator iterator;  \\\n    explicit deque(const allocator_type& a = allocator_type()) : deque_base(a) {}  \\\n    template<typename InputIterator> \\\n    deque(InputIterator first, InputIterator last, const allocator_type& a = allocator_type()) : deque_base(first, last, a) {} \\\n    deque(const deque& c) : deque_base(c) {}  \\\n    explicit deque(size_type num, const value_type& val = value_type()) : deque_base(num, val) {} \\\n    deque(iterator start, iterator end) : deque_base(start, end) {}  \\\n    deque& operator=(const deque& x) {  \\\n      deque_base::operator=(x);  \\\n      return *this;  \\\n    } \\\n  }; \\\n}\n\n// check whether we really need the std::deque specialization\n#if !EIGEN_HAS_CXX11_CONTAINERS && !(defined(_GLIBCXX_DEQUE) && (!EIGEN_GNUC_AT_LEAST(4,1))) /* Note that before gcc-4.1 we already have: std::deque::resize(size_type,const T&). */\n\nnamespace std {\n\n#define EIGEN_STD_DEQUE_SPECIALIZATION_BODY \\\n  public:  \\\n    typedef T value_type; \\\n    typedef typename deque_base::allocator_type allocator_type; \\\n    typedef typename deque_base::size_type size_type;  \\\n    typedef typename deque_base::iterator iterator;  \\\n    typedef typename deque_base::const_iterator const_iterator;  \\\n    explicit deque(const allocator_type& a = allocator_type()) : deque_base(a) {}  \\\n    template<typename InputIterator> \\\n    deque(InputIterator first, InputIterator last, const allocator_type& a = allocator_type()) \\\n    : deque_base(first, last, a) {} \\\n    deque(const deque& c) : deque_base(c) {}  \\\n    explicit deque(size_type num, const value_type& val = value_type()) : deque_base(num, val) {} \\\n    deque(iterator start, iterator end) : deque_base(start, end) {}  \\\n    deque& operator=(const deque& x) {  \\\n      deque_base::operator=(x);  \\\n      return *this;  \\\n    }\n\n  template<typename T>\n  class deque<T,EIGEN_ALIGNED_ALLOCATOR<T> >\n    : public deque<EIGEN_WORKAROUND_MSVC_STL_SUPPORT(T),\n                   Eigen::aligned_allocator_indirection<EIGEN_WORKAROUND_MSVC_STL_SUPPORT(T)> >\n{\n  typedef deque<EIGEN_WORKAROUND_MSVC_STL_SUPPORT(T),\n                Eigen::aligned_allocator_indirection<EIGEN_WORKAROUND_MSVC_STL_SUPPORT(T)> > deque_base;\n  EIGEN_STD_DEQUE_SPECIALIZATION_BODY\n\n  void resize(size_type new_size)\n  { resize(new_size, T()); }\n\n#if defined(_DEQUE_)\n  // workaround MSVC std::deque implementation\n  void resize(size_type new_size, const value_type& x)\n  {\n    if (deque_base::size() < new_size)\n      deque_base::_Insert_n(deque_base::end(), new_size - deque_base::size(), x);\n    else if (new_size < deque_base::size())\n      deque_base::erase(deque_base::begin() + new_size, deque_base::end());\n  }\n  void push_back(const value_type& x)\n  { deque_base::push_back(x); } \n  void push_front(const value_type& x)\n  { deque_base::push_front(x); }\n  using deque_base::insert;  \n  iterator insert(const_iterator position, const value_type& x)\n  { return deque_base::insert(position,x); }\n  void insert(const_iterator position, size_type new_size, const value_type& x)\n  { deque_base::insert(position, new_size, x); }\n#elif defined(_GLIBCXX_DEQUE) && EIGEN_GNUC_AT_LEAST(4,2)\n  // workaround GCC std::deque implementation\n  void resize(size_type new_size, const value_type& x)\n  {\n    if (new_size < deque_base::size())\n      deque_base::_M_erase_at_end(this->_M_impl._M_start + new_size);\n    else\n      deque_base::insert(deque_base::end(), new_size - deque_base::size(), x);\n  }\n#else\n  // either GCC 4.1 or non-GCC\n  // default implementation which should always work.\n  void resize(size_type new_size, const value_type& x)\n  {\n    if (new_size < deque_base::size())\n      deque_base::erase(deque_base::begin() + new_size, deque_base::end());\n    else if (new_size > deque_base::size())\n      deque_base::insert(deque_base::end(), new_size - deque_base::size(), x);\n  }\n#endif\n  };\n}\n\n#endif // check whether specialization is actually required\n\n#endif // EIGEN_STDDEQUE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/StlSupport/StdList.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Hauke Heibel <hauke.heibel@googlemail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_STDLIST_H\n#define EIGEN_STDLIST_H\n\n#include \"details.h\"\n\n/**\n * This section contains a convenience MACRO which allows an easy specialization of\n * std::list such that for data types with alignment issues the correct allocator\n * is used automatically.\n */\n#define EIGEN_DEFINE_STL_LIST_SPECIALIZATION(...) \\\nnamespace std \\\n{ \\\n  template<> \\\n  class list<__VA_ARGS__, std::allocator<__VA_ARGS__> >           \\\n    : public list<__VA_ARGS__, EIGEN_ALIGNED_ALLOCATOR<__VA_ARGS__> > \\\n  { \\\n    typedef list<__VA_ARGS__, EIGEN_ALIGNED_ALLOCATOR<__VA_ARGS__> > list_base; \\\n  public: \\\n    typedef __VA_ARGS__ value_type; \\\n    typedef list_base::allocator_type allocator_type; \\\n    typedef list_base::size_type size_type;  \\\n    typedef list_base::iterator iterator;  \\\n    explicit list(const allocator_type& a = allocator_type()) : list_base(a) {}  \\\n    template<typename InputIterator> \\\n    list(InputIterator first, InputIterator last, const allocator_type& a = allocator_type()) : list_base(first, last, a) {} \\\n    list(const list& c) : list_base(c) {}  \\\n    explicit list(size_type num, const value_type& val = value_type()) : list_base(num, val) {} \\\n    list(iterator start, iterator end) : list_base(start, end) {}  \\\n    list& operator=(const list& x) {  \\\n      list_base::operator=(x);  \\\n      return *this;  \\\n    } \\\n  }; \\\n}\n\n// check whether we really need the std::list specialization\n#if !EIGEN_HAS_CXX11_CONTAINERS && !(defined(_GLIBCXX_LIST) && (!EIGEN_GNUC_AT_LEAST(4,1))) /* Note that before gcc-4.1 we already have: std::list::resize(size_type,const T&). */\n\nnamespace std\n{\n\n#define EIGEN_STD_LIST_SPECIALIZATION_BODY \\\n  public:  \\\n    typedef T value_type; \\\n    typedef typename list_base::allocator_type allocator_type; \\\n    typedef typename list_base::size_type size_type;  \\\n    typedef typename list_base::iterator iterator;  \\\n    typedef typename list_base::const_iterator const_iterator;  \\\n    explicit list(const allocator_type& a = allocator_type()) : list_base(a) {}  \\\n    template<typename InputIterator> \\\n    list(InputIterator first, InputIterator last, const allocator_type& a = allocator_type()) \\\n    : list_base(first, last, a) {} \\\n    list(const list& c) : list_base(c) {}  \\\n    explicit list(size_type num, const value_type& val = value_type()) : list_base(num, val) {} \\\n    list(iterator start, iterator end) : list_base(start, end) {}  \\\n    list& operator=(const list& x) {  \\\n    list_base::operator=(x);  \\\n    return *this; \\\n  }\n\n  template<typename T>\n  class list<T,EIGEN_ALIGNED_ALLOCATOR<T> >\n    : public list<EIGEN_WORKAROUND_MSVC_STL_SUPPORT(T),\n                  Eigen::aligned_allocator_indirection<EIGEN_WORKAROUND_MSVC_STL_SUPPORT(T)> >\n  {\n    typedef list<EIGEN_WORKAROUND_MSVC_STL_SUPPORT(T),\n                 Eigen::aligned_allocator_indirection<EIGEN_WORKAROUND_MSVC_STL_SUPPORT(T)> > list_base;\n    EIGEN_STD_LIST_SPECIALIZATION_BODY\n\n    void resize(size_type new_size)\n    { resize(new_size, T()); }\n\n    void resize(size_type new_size, const value_type& x)\n    {\n      if (list_base::size() < new_size)\n        list_base::insert(list_base::end(), new_size - list_base::size(), x);\n      else\n        while (new_size < list_base::size()) list_base::pop_back();\n    }\n\n#if defined(_LIST_)\n    // workaround MSVC std::list implementation\n    void push_back(const value_type& x)\n    { list_base::push_back(x); } \n    using list_base::insert;  \n    iterator insert(const_iterator position, const value_type& x)\n    { return list_base::insert(position,x); }\n    void insert(const_iterator position, size_type new_size, const value_type& x)\n    { list_base::insert(position, new_size, x); }\n#endif\n  };\n}\n\n#endif // check whether specialization is actually required\n\n#endif // EIGEN_STDLIST_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/StlSupport/StdVector.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2009 Hauke Heibel <hauke.heibel@googlemail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_STDVECTOR_H\n#define EIGEN_STDVECTOR_H\n\n#include \"details.h\"\n\n/**\n * This section contains a convenience MACRO which allows an easy specialization of\n * std::vector such that for data types with alignment issues the correct allocator\n * is used automatically.\n */\n#define EIGEN_DEFINE_STL_VECTOR_SPECIALIZATION(...) \\\nnamespace std \\\n{ \\\n  template<> \\\n  class vector<__VA_ARGS__, std::allocator<__VA_ARGS__> >  \\\n    : public vector<__VA_ARGS__, EIGEN_ALIGNED_ALLOCATOR<__VA_ARGS__> > \\\n  { \\\n    typedef vector<__VA_ARGS__, EIGEN_ALIGNED_ALLOCATOR<__VA_ARGS__> > vector_base; \\\n  public: \\\n    typedef __VA_ARGS__ value_type; \\\n    typedef vector_base::allocator_type allocator_type; \\\n    typedef vector_base::size_type size_type;  \\\n    typedef vector_base::iterator iterator;  \\\n    explicit vector(const allocator_type& a = allocator_type()) : vector_base(a) {}  \\\n    template<typename InputIterator> \\\n    vector(InputIterator first, InputIterator last, const allocator_type& a = allocator_type()) : vector_base(first, last, a) {} \\\n    vector(const vector& c) : vector_base(c) {}  \\\n    explicit vector(size_type num, const value_type& val = value_type()) : vector_base(num, val) {} \\\n    vector(iterator start, iterator end) : vector_base(start, end) {}  \\\n    vector& operator=(const vector& x) {  \\\n      vector_base::operator=(x);  \\\n      return *this;  \\\n    } \\\n  }; \\\n}\n\n// Don't specialize if containers are implemented according to C++11\n#if !EIGEN_HAS_CXX11_CONTAINERS\n\nnamespace std {\n\n#define EIGEN_STD_VECTOR_SPECIALIZATION_BODY \\\n  public:  \\\n    typedef T value_type; \\\n    typedef typename vector_base::allocator_type allocator_type; \\\n    typedef typename vector_base::size_type size_type;  \\\n    typedef typename vector_base::iterator iterator;  \\\n    typedef typename vector_base::const_iterator const_iterator;  \\\n    explicit vector(const allocator_type& a = allocator_type()) : vector_base(a) {}  \\\n    template<typename InputIterator> \\\n    vector(InputIterator first, InputIterator last, const allocator_type& a = allocator_type()) \\\n    : vector_base(first, last, a) {} \\\n    vector(const vector& c) : vector_base(c) {}  \\\n    explicit vector(size_type num, const value_type& val = value_type()) : vector_base(num, val) {} \\\n    vector(iterator start, iterator end) : vector_base(start, end) {}  \\\n    vector& operator=(const vector& x) {  \\\n      vector_base::operator=(x);  \\\n      return *this;  \\\n    }\n\n  template<typename T>\n  class vector<T,EIGEN_ALIGNED_ALLOCATOR<T> >\n    : public vector<EIGEN_WORKAROUND_MSVC_STL_SUPPORT(T),\n                    Eigen::aligned_allocator_indirection<EIGEN_WORKAROUND_MSVC_STL_SUPPORT(T)> >\n{\n  typedef vector<EIGEN_WORKAROUND_MSVC_STL_SUPPORT(T),\n                 Eigen::aligned_allocator_indirection<EIGEN_WORKAROUND_MSVC_STL_SUPPORT(T)> > vector_base;\n  EIGEN_STD_VECTOR_SPECIALIZATION_BODY\n\n  void resize(size_type new_size)\n  { resize(new_size, T()); }\n\n#if defined(_VECTOR_)\n  // workaround MSVC std::vector implementation\n  void resize(size_type new_size, const value_type& x)\n  {\n    if (vector_base::size() < new_size)\n      vector_base::_Insert_n(vector_base::end(), new_size - vector_base::size(), x);\n    else if (new_size < vector_base::size())\n      vector_base::erase(vector_base::begin() + new_size, vector_base::end());\n  }\n  void push_back(const value_type& x)\n  { vector_base::push_back(x); } \n  using vector_base::insert;  \n  iterator insert(const_iterator position, const value_type& x)\n  { return vector_base::insert(position,x); }\n  void insert(const_iterator position, size_type new_size, const value_type& x)\n  { vector_base::insert(position, new_size, x); }\n#elif defined(_GLIBCXX_VECTOR) && (!(EIGEN_GNUC_AT_LEAST(4,1)))\n  /* Note that before gcc-4.1 we already have: std::vector::resize(size_type,const T&).\n   * However, this specialization is still needed to make the above EIGEN_DEFINE_STL_VECTOR_SPECIALIZATION trick to work. */\n  void resize(size_type new_size, const value_type& x)\n  {\n    vector_base::resize(new_size,x);\n  }\n#elif defined(_GLIBCXX_VECTOR) && EIGEN_GNUC_AT_LEAST(4,2)\n  // workaround GCC std::vector implementation\n  void resize(size_type new_size, const value_type& x)\n  {\n    if (new_size < vector_base::size())\n      vector_base::_M_erase_at_end(this->_M_impl._M_start + new_size);\n    else\n      vector_base::insert(vector_base::end(), new_size - vector_base::size(), x);\n  }\n#else\n  // either GCC 4.1 or non-GCC\n  // default implementation which should always work.\n  void resize(size_type new_size, const value_type& x)\n  {\n    if (new_size < vector_base::size())\n      vector_base::erase(vector_base::begin() + new_size, vector_base::end());\n    else if (new_size > vector_base::size())\n      vector_base::insert(vector_base::end(), new_size - vector_base::size(), x);\n  }\n#endif\n  };\n}\n#endif // !EIGEN_HAS_CXX11_CONTAINERS\n\n\n#endif // EIGEN_STDVECTOR_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/StlSupport/details.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2009 Hauke Heibel <hauke.heibel@googlemail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_STL_DETAILS_H\n#define EIGEN_STL_DETAILS_H\n\n#ifndef EIGEN_ALIGNED_ALLOCATOR\n  #define EIGEN_ALIGNED_ALLOCATOR Eigen::aligned_allocator\n#endif\n\nnamespace Eigen {\n\n  // This one is needed to prevent reimplementing the whole std::vector.\n  template <class T>\n  class aligned_allocator_indirection : public EIGEN_ALIGNED_ALLOCATOR<T>\n  {\n  public:\n    typedef std::size_t     size_type;\n    typedef std::ptrdiff_t  difference_type;\n    typedef T*              pointer;\n    typedef const T*        const_pointer;\n    typedef T&              reference;\n    typedef const T&        const_reference;\n    typedef T               value_type;\n\n    template<class U>\n    struct rebind\n    {\n      typedef aligned_allocator_indirection<U> other;\n    };\n\n    aligned_allocator_indirection() {}\n    aligned_allocator_indirection(const aligned_allocator_indirection& ) : EIGEN_ALIGNED_ALLOCATOR<T>() {}\n    aligned_allocator_indirection(const EIGEN_ALIGNED_ALLOCATOR<T>& ) {}\n    template<class U>\n    aligned_allocator_indirection(const aligned_allocator_indirection<U>& ) {}\n    template<class U>\n    aligned_allocator_indirection(const EIGEN_ALIGNED_ALLOCATOR<U>& ) {}\n    ~aligned_allocator_indirection() {}\n  };\n\n#if EIGEN_COMP_MSVC\n\n  // sometimes, MSVC detects, at compile time, that the argument x\n  // in std::vector::resize(size_t s,T x) won't be aligned and generate an error\n  // even if this function is never called. Whence this little wrapper.\n#define EIGEN_WORKAROUND_MSVC_STL_SUPPORT(T) \\\n  typename Eigen::internal::conditional< \\\n    Eigen::internal::is_arithmetic<T>::value, \\\n    T, \\\n    Eigen::internal::workaround_msvc_stl_support<T> \\\n  >::type\n\n  namespace internal {\n  template<typename T> struct workaround_msvc_stl_support : public T\n  {\n    inline workaround_msvc_stl_support() : T() {}\n    inline workaround_msvc_stl_support(const T& other) : T(other) {}\n    inline operator T& () { return *static_cast<T*>(this); }\n    inline operator const T& () const { return *static_cast<const T*>(this); }\n    template<typename OtherT>\n    inline T& operator=(const OtherT& other)\n    { T::operator=(other); return *this; }\n    inline workaround_msvc_stl_support& operator=(const workaround_msvc_stl_support& other)\n    { T::operator=(other); return *this; }\n  };\n  }\n\n#else\n\n#define EIGEN_WORKAROUND_MSVC_STL_SUPPORT(T) T\n\n#endif\n\n}\n\n#endif // EIGEN_STL_DETAILS_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/SuperLUSupport/SuperLUSupport.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SUPERLUSUPPORT_H\n#define EIGEN_SUPERLUSUPPORT_H\n\nnamespace Eigen {\n\n#if defined(SUPERLU_MAJOR_VERSION) && (SUPERLU_MAJOR_VERSION >= 5)\n#define DECL_GSSVX(PREFIX,FLOATTYPE,KEYTYPE)\t\t\\\n    extern \"C\" {                                                                                          \\\n      extern void PREFIX##gssvx(superlu_options_t *, SuperMatrix *, int *, int *, int *,                  \\\n                                char *, FLOATTYPE *, FLOATTYPE *, SuperMatrix *, SuperMatrix *,           \\\n                                void *, int, SuperMatrix *, SuperMatrix *,                                \\\n                                FLOATTYPE *, FLOATTYPE *, FLOATTYPE *, FLOATTYPE *,                       \\\n                                GlobalLU_t *, mem_usage_t *, SuperLUStat_t *, int *);                     \\\n    }                                                                                                     \\\n    inline float SuperLU_gssvx(superlu_options_t *options, SuperMatrix *A,                                \\\n         int *perm_c, int *perm_r, int *etree, char *equed,                                               \\\n         FLOATTYPE *R, FLOATTYPE *C, SuperMatrix *L,                                                      \\\n         SuperMatrix *U, void *work, int lwork,                                                           \\\n         SuperMatrix *B, SuperMatrix *X,                                                                  \\\n         FLOATTYPE *recip_pivot_growth,                                                                   \\\n         FLOATTYPE *rcond, FLOATTYPE *ferr, FLOATTYPE *berr,                                              \\\n         SuperLUStat_t *stats, int *info, KEYTYPE) {                                                      \\\n    mem_usage_t mem_usage;                                                                                \\\n    GlobalLU_t gLU;                                                                                       \\\n    PREFIX##gssvx(options, A, perm_c, perm_r, etree, equed, R, C, L,                                      \\\n         U, work, lwork, B, X, recip_pivot_growth, rcond,                                                 \\\n         ferr, berr, &gLU, &mem_usage, stats, info);                                                      \\\n    return mem_usage.for_lu; /* bytes used by the factor storage */                                       \\\n  }\n#else // version < 5.0\n#define DECL_GSSVX(PREFIX,FLOATTYPE,KEYTYPE)\t\t\\\n    extern \"C\" {                                                                                          \\\n      extern void PREFIX##gssvx(superlu_options_t *, SuperMatrix *, int *, int *, int *,                  \\\n                                char *, FLOATTYPE *, FLOATTYPE *, SuperMatrix *, SuperMatrix *,           \\\n                                void *, int, SuperMatrix *, SuperMatrix *,                                \\\n                                FLOATTYPE *, FLOATTYPE *, FLOATTYPE *, FLOATTYPE *,                       \\\n                                mem_usage_t *, SuperLUStat_t *, int *);                                   \\\n    }                                                                                                     \\\n    inline float SuperLU_gssvx(superlu_options_t *options, SuperMatrix *A,                                \\\n         int *perm_c, int *perm_r, int *etree, char *equed,                                               \\\n         FLOATTYPE *R, FLOATTYPE *C, SuperMatrix *L,                                                      \\\n         SuperMatrix *U, void *work, int lwork,                                                           \\\n         SuperMatrix *B, SuperMatrix *X,                                                                  \\\n         FLOATTYPE *recip_pivot_growth,                                                                   \\\n         FLOATTYPE *rcond, FLOATTYPE *ferr, FLOATTYPE *berr,                                              \\\n         SuperLUStat_t *stats, int *info, KEYTYPE) {                                                      \\\n    mem_usage_t mem_usage;                                                                                \\\n    PREFIX##gssvx(options, A, perm_c, perm_r, etree, equed, R, C, L,                                      \\\n         U, work, lwork, B, X, recip_pivot_growth, rcond,                                                 \\\n         ferr, berr, &mem_usage, stats, info);                                                            \\\n    return mem_usage.for_lu; /* bytes used by the factor storage */                                       \\\n  }\n#endif\n\nDECL_GSSVX(s,float,float)\nDECL_GSSVX(c,float,std::complex<float>)\nDECL_GSSVX(d,double,double)\nDECL_GSSVX(z,double,std::complex<double>)\n\n#ifdef MILU_ALPHA\n#define EIGEN_SUPERLU_HAS_ILU\n#endif\n\n#ifdef EIGEN_SUPERLU_HAS_ILU\n\n// similarly for the incomplete factorization using gsisx\n#define DECL_GSISX(PREFIX,FLOATTYPE,KEYTYPE)                                                    \\\n    extern \"C\" {                                                                                \\\n      extern void PREFIX##gsisx(superlu_options_t *, SuperMatrix *, int *, int *, int *,        \\\n                         char *, FLOATTYPE *, FLOATTYPE *, SuperMatrix *, SuperMatrix *,        \\\n                         void *, int, SuperMatrix *, SuperMatrix *, FLOATTYPE *, FLOATTYPE *,   \\\n                         mem_usage_t *, SuperLUStat_t *, int *);                        \\\n    }                                                                                           \\\n    inline float SuperLU_gsisx(superlu_options_t *options, SuperMatrix *A,                      \\\n         int *perm_c, int *perm_r, int *etree, char *equed,                                     \\\n         FLOATTYPE *R, FLOATTYPE *C, SuperMatrix *L,                                            \\\n         SuperMatrix *U, void *work, int lwork,                                                 \\\n         SuperMatrix *B, SuperMatrix *X,                                                        \\\n         FLOATTYPE *recip_pivot_growth,                                                         \\\n         FLOATTYPE *rcond,                                                                      \\\n         SuperLUStat_t *stats, int *info, KEYTYPE) {                                            \\\n    mem_usage_t mem_usage;                                                              \\\n    PREFIX##gsisx(options, A, perm_c, perm_r, etree, equed, R, C, L,                            \\\n         U, work, lwork, B, X, recip_pivot_growth, rcond,                                       \\\n         &mem_usage, stats, info);                                                              \\\n    return mem_usage.for_lu; /* bytes used by the factor storage */                             \\\n  }\n\nDECL_GSISX(s,float,float)\nDECL_GSISX(c,float,std::complex<float>)\nDECL_GSISX(d,double,double)\nDECL_GSISX(z,double,std::complex<double>)\n\n#endif\n\ntemplate<typename MatrixType>\nstruct SluMatrixMapHelper;\n\n/** \\internal\n  *\n  * A wrapper class for SuperLU matrices. It supports only compressed sparse matrices\n  * and dense matrices. Supernodal and other fancy format are not supported by this wrapper.\n  *\n  * This wrapper class mainly aims to avoids the need of dynamic allocation of the storage structure.\n  */\nstruct SluMatrix : SuperMatrix\n{\n  SluMatrix()\n  {\n    Store = &storage;\n  }\n\n  SluMatrix(const SluMatrix& other)\n    : SuperMatrix(other)\n  {\n    Store = &storage;\n    storage = other.storage;\n  }\n\n  SluMatrix& operator=(const SluMatrix& other)\n  {\n    SuperMatrix::operator=(static_cast<const SuperMatrix&>(other));\n    Store = &storage;\n    storage = other.storage;\n    return *this;\n  }\n\n  struct\n  {\n    union {int nnz;int lda;};\n    void *values;\n    int *innerInd;\n    int *outerInd;\n  } storage;\n\n  void setStorageType(Stype_t t)\n  {\n    Stype = t;\n    if (t==SLU_NC || t==SLU_NR || t==SLU_DN)\n      Store = &storage;\n    else\n    {\n      eigen_assert(false && \"storage type not supported\");\n      Store = 0;\n    }\n  }\n\n  template<typename Scalar>\n  void setScalarType()\n  {\n    if (internal::is_same<Scalar,float>::value)\n      Dtype = SLU_S;\n    else if (internal::is_same<Scalar,double>::value)\n      Dtype = SLU_D;\n    else if (internal::is_same<Scalar,std::complex<float> >::value)\n      Dtype = SLU_C;\n    else if (internal::is_same<Scalar,std::complex<double> >::value)\n      Dtype = SLU_Z;\n    else\n    {\n      eigen_assert(false && \"Scalar type not supported by SuperLU\");\n    }\n  }\n\n  template<typename MatrixType>\n  static SluMatrix Map(MatrixBase<MatrixType>& _mat)\n  {\n    MatrixType& mat(_mat.derived());\n    eigen_assert( ((MatrixType::Flags&RowMajorBit)!=RowMajorBit) && \"row-major dense matrices are not supported by SuperLU\");\n    SluMatrix res;\n    res.setStorageType(SLU_DN);\n    res.setScalarType<typename MatrixType::Scalar>();\n    res.Mtype     = SLU_GE;\n\n    res.nrow      = internal::convert_index<int>(mat.rows());\n    res.ncol      = internal::convert_index<int>(mat.cols());\n\n    res.storage.lda       = internal::convert_index<int>(MatrixType::IsVectorAtCompileTime ? mat.size() : mat.outerStride());\n    res.storage.values    = (void*)(mat.data());\n    return res;\n  }\n\n  template<typename MatrixType>\n  static SluMatrix Map(SparseMatrixBase<MatrixType>& a_mat)\n  {\n    MatrixType &mat(a_mat.derived());\n    SluMatrix res;\n    if ((MatrixType::Flags&RowMajorBit)==RowMajorBit)\n    {\n      res.setStorageType(SLU_NR);\n      res.nrow      = internal::convert_index<int>(mat.cols());\n      res.ncol      = internal::convert_index<int>(mat.rows());\n    }\n    else\n    {\n      res.setStorageType(SLU_NC);\n      res.nrow      = internal::convert_index<int>(mat.rows());\n      res.ncol      = internal::convert_index<int>(mat.cols());\n    }\n\n    res.Mtype       = SLU_GE;\n\n    res.storage.nnz       = internal::convert_index<int>(mat.nonZeros());\n    res.storage.values    = mat.valuePtr();\n    res.storage.innerInd  = mat.innerIndexPtr();\n    res.storage.outerInd  = mat.outerIndexPtr();\n\n    res.setScalarType<typename MatrixType::Scalar>();\n\n    // FIXME the following is not very accurate\n    if (MatrixType::Flags & Upper)\n      res.Mtype = SLU_TRU;\n    if (MatrixType::Flags & Lower)\n      res.Mtype = SLU_TRL;\n\n    eigen_assert(((MatrixType::Flags & SelfAdjoint)==0) && \"SelfAdjoint matrix shape not supported by SuperLU\");\n\n    return res;\n  }\n};\n\ntemplate<typename Scalar, int Rows, int Cols, int Options, int MRows, int MCols>\nstruct SluMatrixMapHelper<Matrix<Scalar,Rows,Cols,Options,MRows,MCols> >\n{\n  typedef Matrix<Scalar,Rows,Cols,Options,MRows,MCols> MatrixType;\n  static void run(MatrixType& mat, SluMatrix& res)\n  {\n    eigen_assert( ((Options&RowMajor)!=RowMajor) && \"row-major dense matrices is not supported by SuperLU\");\n    res.setStorageType(SLU_DN);\n    res.setScalarType<Scalar>();\n    res.Mtype     = SLU_GE;\n\n    res.nrow      = mat.rows();\n    res.ncol      = mat.cols();\n\n    res.storage.lda       = mat.outerStride();\n    res.storage.values    = mat.data();\n  }\n};\n\ntemplate<typename Derived>\nstruct SluMatrixMapHelper<SparseMatrixBase<Derived> >\n{\n  typedef Derived MatrixType;\n  static void run(MatrixType& mat, SluMatrix& res)\n  {\n    if ((MatrixType::Flags&RowMajorBit)==RowMajorBit)\n    {\n      res.setStorageType(SLU_NR);\n      res.nrow      = mat.cols();\n      res.ncol      = mat.rows();\n    }\n    else\n    {\n      res.setStorageType(SLU_NC);\n      res.nrow      = mat.rows();\n      res.ncol      = mat.cols();\n    }\n\n    res.Mtype       = SLU_GE;\n\n    res.storage.nnz       = mat.nonZeros();\n    res.storage.values    = mat.valuePtr();\n    res.storage.innerInd  = mat.innerIndexPtr();\n    res.storage.outerInd  = mat.outerIndexPtr();\n\n    res.setScalarType<typename MatrixType::Scalar>();\n\n    // FIXME the following is not very accurate\n    if (MatrixType::Flags & Upper)\n      res.Mtype = SLU_TRU;\n    if (MatrixType::Flags & Lower)\n      res.Mtype = SLU_TRL;\n\n    eigen_assert(((MatrixType::Flags & SelfAdjoint)==0) && \"SelfAdjoint matrix shape not supported by SuperLU\");\n  }\n};\n\nnamespace internal {\n\ntemplate<typename MatrixType>\nSluMatrix asSluMatrix(MatrixType& mat)\n{\n  return SluMatrix::Map(mat);\n}\n\n/** View a Super LU matrix as an Eigen expression */\ntemplate<typename Scalar, int Flags, typename Index>\nMappedSparseMatrix<Scalar,Flags,Index> map_superlu(SluMatrix& sluMat)\n{\n  eigen_assert((Flags&RowMajor)==RowMajor && sluMat.Stype == SLU_NR\n         || (Flags&ColMajor)==ColMajor && sluMat.Stype == SLU_NC);\n\n  Index outerSize = (Flags&RowMajor)==RowMajor ? sluMat.ncol : sluMat.nrow;\n\n  return MappedSparseMatrix<Scalar,Flags,Index>(\n    sluMat.nrow, sluMat.ncol, sluMat.storage.outerInd[outerSize],\n    sluMat.storage.outerInd, sluMat.storage.innerInd, reinterpret_cast<Scalar*>(sluMat.storage.values) );\n}\n\n} // end namespace internal\n\n/** \\ingroup SuperLUSupport_Module\n  * \\class SuperLUBase\n  * \\brief The base class for the direct and incomplete LU factorization of SuperLU\n  */\ntemplate<typename _MatrixType, typename Derived>\nclass SuperLUBase : public SparseSolverBase<Derived>\n{\n  protected:\n    typedef SparseSolverBase<Derived> Base;\n    using Base::derived;\n    using Base::m_isInitialized;\n  public:\n    typedef _MatrixType MatrixType;\n    typedef typename MatrixType::Scalar Scalar;\n    typedef typename MatrixType::RealScalar RealScalar;\n    typedef typename MatrixType::StorageIndex StorageIndex;\n    typedef Matrix<Scalar,Dynamic,1> Vector;\n    typedef Matrix<int, 1, MatrixType::ColsAtCompileTime> IntRowVectorType;\n    typedef Matrix<int, MatrixType::RowsAtCompileTime, 1> IntColVectorType;    \n    typedef Map<PermutationMatrix<Dynamic,Dynamic,int> > PermutationMap;\n    typedef SparseMatrix<Scalar> LUMatrixType;\n    enum {\n      ColsAtCompileTime = MatrixType::ColsAtCompileTime,\n      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime\n    };\n\n  public:\n\n    SuperLUBase() {}\n\n    ~SuperLUBase()\n    {\n      clearFactors();\n    }\n    \n    inline Index rows() const { return m_matrix.rows(); }\n    inline Index cols() const { return m_matrix.cols(); }\n    \n    /** \\returns a reference to the Super LU option object to configure the  Super LU algorithms. */\n    inline superlu_options_t& options() { return m_sluOptions; }\n    \n    /** \\brief Reports whether previous computation was successful.\n      *\n      * \\returns \\c Success if computation was succesful,\n      *          \\c NumericalIssue if the matrix.appears to be negative.\n      */\n    ComputationInfo info() const\n    {\n      eigen_assert(m_isInitialized && \"Decomposition is not initialized.\");\n      return m_info;\n    }\n\n    /** Computes the sparse Cholesky decomposition of \\a matrix */\n    void compute(const MatrixType& matrix)\n    {\n      derived().analyzePattern(matrix);\n      derived().factorize(matrix);\n    }\n\n    /** Performs a symbolic decomposition on the sparcity of \\a matrix.\n      *\n      * This function is particularly useful when solving for several problems having the same structure.\n      * \n      * \\sa factorize()\n      */\n    void analyzePattern(const MatrixType& /*matrix*/)\n    {\n      m_isInitialized = true;\n      m_info = Success;\n      m_analysisIsOk = true;\n      m_factorizationIsOk = false;\n    }\n    \n    template<typename Stream>\n    void dumpMemory(Stream& /*s*/)\n    {}\n    \n  protected:\n    \n    void initFactorization(const MatrixType& a)\n    {\n      set_default_options(&this->m_sluOptions);\n      \n      const Index size = a.rows();\n      m_matrix = a;\n\n      m_sluA = internal::asSluMatrix(m_matrix);\n      clearFactors();\n\n      m_p.resize(size);\n      m_q.resize(size);\n      m_sluRscale.resize(size);\n      m_sluCscale.resize(size);\n      m_sluEtree.resize(size);\n\n      // set empty B and X\n      m_sluB.setStorageType(SLU_DN);\n      m_sluB.setScalarType<Scalar>();\n      m_sluB.Mtype          = SLU_GE;\n      m_sluB.storage.values = 0;\n      m_sluB.nrow           = 0;\n      m_sluB.ncol           = 0;\n      m_sluB.storage.lda    = internal::convert_index<int>(size);\n      m_sluX                = m_sluB;\n      \n      m_extractedDataAreDirty = true;\n    }\n    \n    void init()\n    {\n      m_info = InvalidInput;\n      m_isInitialized = false;\n      m_sluL.Store = 0;\n      m_sluU.Store = 0;\n    }\n    \n    void extractData() const;\n\n    void clearFactors()\n    {\n      if(m_sluL.Store)\n        Destroy_SuperNode_Matrix(&m_sluL);\n      if(m_sluU.Store)\n        Destroy_CompCol_Matrix(&m_sluU);\n\n      m_sluL.Store = 0;\n      m_sluU.Store = 0;\n\n      memset(&m_sluL,0,sizeof m_sluL);\n      memset(&m_sluU,0,sizeof m_sluU);\n    }\n\n    // cached data to reduce reallocation, etc.\n    mutable LUMatrixType m_l;\n    mutable LUMatrixType m_u;\n    mutable IntColVectorType m_p;\n    mutable IntRowVectorType m_q;\n\n    mutable LUMatrixType m_matrix;  // copy of the factorized matrix\n    mutable SluMatrix m_sluA;\n    mutable SuperMatrix m_sluL, m_sluU;\n    mutable SluMatrix m_sluB, m_sluX;\n    mutable SuperLUStat_t m_sluStat;\n    mutable superlu_options_t m_sluOptions;\n    mutable std::vector<int> m_sluEtree;\n    mutable Matrix<RealScalar,Dynamic,1> m_sluRscale, m_sluCscale;\n    mutable Matrix<RealScalar,Dynamic,1> m_sluFerr, m_sluBerr;\n    mutable char m_sluEqued;\n\n    mutable ComputationInfo m_info;\n    int m_factorizationIsOk;\n    int m_analysisIsOk;\n    mutable bool m_extractedDataAreDirty;\n    \n  private:\n    SuperLUBase(SuperLUBase& ) { }\n};\n\n\n/** \\ingroup SuperLUSupport_Module\n  * \\class SuperLU\n  * \\brief A sparse direct LU factorization and solver based on the SuperLU library\n  *\n  * This class allows to solve for A.X = B sparse linear problems via a direct LU factorization\n  * using the SuperLU library. The sparse matrix A must be squared and invertible. The vectors or matrices\n  * X and B can be either dense or sparse.\n  *\n  * \\tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>\n  *\n  * \\warning This class is only for the 4.x versions of SuperLU. The 3.x and 5.x versions are not supported.\n  *\n  * \\implsparsesolverconcept\n  *\n  * \\sa \\ref TutorialSparseSolverConcept, class SparseLU\n  */\ntemplate<typename _MatrixType>\nclass SuperLU : public SuperLUBase<_MatrixType,SuperLU<_MatrixType> >\n{\n  public:\n    typedef SuperLUBase<_MatrixType,SuperLU> Base;\n    typedef _MatrixType MatrixType;\n    typedef typename Base::Scalar Scalar;\n    typedef typename Base::RealScalar RealScalar;\n    typedef typename Base::StorageIndex StorageIndex;\n    typedef typename Base::IntRowVectorType IntRowVectorType;\n    typedef typename Base::IntColVectorType IntColVectorType;   \n    typedef typename Base::PermutationMap PermutationMap;\n    typedef typename Base::LUMatrixType LUMatrixType;\n    typedef TriangularView<LUMatrixType, Lower|UnitDiag>  LMatrixType;\n    typedef TriangularView<LUMatrixType,  Upper>          UMatrixType;\n\n  public:\n    using Base::_solve_impl;\n\n    SuperLU() : Base() { init(); }\n\n    explicit SuperLU(const MatrixType& matrix) : Base()\n    {\n      init();\n      Base::compute(matrix);\n    }\n\n    ~SuperLU()\n    {\n    }\n    \n    /** Performs a symbolic decomposition on the sparcity of \\a matrix.\n      *\n      * This function is particularly useful when solving for several problems having the same structure.\n      * \n      * \\sa factorize()\n      */\n    void analyzePattern(const MatrixType& matrix)\n    {\n      m_info = InvalidInput;\n      m_isInitialized = false;\n      Base::analyzePattern(matrix);\n    }\n    \n    /** Performs a numeric decomposition of \\a matrix\n      *\n      * The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed.\n      *\n      * \\sa analyzePattern()\n      */\n    void factorize(const MatrixType& matrix);\n    \n    /** \\internal */\n    template<typename Rhs,typename Dest>\n    void _solve_impl(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const;\n    \n    inline const LMatrixType& matrixL() const\n    {\n      if (m_extractedDataAreDirty) this->extractData();\n      return m_l;\n    }\n\n    inline const UMatrixType& matrixU() const\n    {\n      if (m_extractedDataAreDirty) this->extractData();\n      return m_u;\n    }\n\n    inline const IntColVectorType& permutationP() const\n    {\n      if (m_extractedDataAreDirty) this->extractData();\n      return m_p;\n    }\n\n    inline const IntRowVectorType& permutationQ() const\n    {\n      if (m_extractedDataAreDirty) this->extractData();\n      return m_q;\n    }\n    \n    Scalar determinant() const;\n    \n  protected:\n    \n    using Base::m_matrix;\n    using Base::m_sluOptions;\n    using Base::m_sluA;\n    using Base::m_sluB;\n    using Base::m_sluX;\n    using Base::m_p;\n    using Base::m_q;\n    using Base::m_sluEtree;\n    using Base::m_sluEqued;\n    using Base::m_sluRscale;\n    using Base::m_sluCscale;\n    using Base::m_sluL;\n    using Base::m_sluU;\n    using Base::m_sluStat;\n    using Base::m_sluFerr;\n    using Base::m_sluBerr;\n    using Base::m_l;\n    using Base::m_u;\n    \n    using Base::m_analysisIsOk;\n    using Base::m_factorizationIsOk;\n    using Base::m_extractedDataAreDirty;\n    using Base::m_isInitialized;\n    using Base::m_info;\n    \n    void init()\n    {\n      Base::init();\n      \n      set_default_options(&this->m_sluOptions);\n      m_sluOptions.PrintStat        = NO;\n      m_sluOptions.ConditionNumber  = NO;\n      m_sluOptions.Trans            = NOTRANS;\n      m_sluOptions.ColPerm          = COLAMD;\n    }\n    \n    \n  private:\n    SuperLU(SuperLU& ) { }\n};\n\ntemplate<typename MatrixType>\nvoid SuperLU<MatrixType>::factorize(const MatrixType& a)\n{\n  eigen_assert(m_analysisIsOk && \"You must first call analyzePattern()\");\n  if(!m_analysisIsOk)\n  {\n    m_info = InvalidInput;\n    return;\n  }\n  \n  this->initFactorization(a);\n  \n  m_sluOptions.ColPerm = COLAMD;\n  int info = 0;\n  RealScalar recip_pivot_growth, rcond;\n  RealScalar ferr, berr;\n\n  StatInit(&m_sluStat);\n  SuperLU_gssvx(&m_sluOptions, &m_sluA, m_q.data(), m_p.data(), &m_sluEtree[0],\n                &m_sluEqued, &m_sluRscale[0], &m_sluCscale[0],\n                &m_sluL, &m_sluU,\n                NULL, 0,\n                &m_sluB, &m_sluX,\n                &recip_pivot_growth, &rcond,\n                &ferr, &berr,\n                &m_sluStat, &info, Scalar());\n  StatFree(&m_sluStat);\n\n  m_extractedDataAreDirty = true;\n\n  // FIXME how to better check for errors ???\n  m_info = info == 0 ? Success : NumericalIssue;\n  m_factorizationIsOk = true;\n}\n\ntemplate<typename MatrixType>\ntemplate<typename Rhs,typename Dest>\nvoid SuperLU<MatrixType>::_solve_impl(const MatrixBase<Rhs> &b, MatrixBase<Dest>& x) const\n{\n  eigen_assert(m_factorizationIsOk && \"The decomposition is not in a valid state for solving, you must first call either compute() or analyzePattern()/factorize()\");\n\n  const Index size = m_matrix.rows();\n  const Index rhsCols = b.cols();\n  eigen_assert(size==b.rows());\n\n  m_sluOptions.Trans = NOTRANS;\n  m_sluOptions.Fact = FACTORED;\n  m_sluOptions.IterRefine = NOREFINE;\n  \n\n  m_sluFerr.resize(rhsCols);\n  m_sluBerr.resize(rhsCols);\n  \n  Ref<const Matrix<typename Rhs::Scalar,Dynamic,Dynamic,ColMajor> > b_ref(b);\n  Ref<const Matrix<typename Dest::Scalar,Dynamic,Dynamic,ColMajor> > x_ref(x);\n  \n  m_sluB = SluMatrix::Map(b_ref.const_cast_derived());\n  m_sluX = SluMatrix::Map(x_ref.const_cast_derived());\n  \n  typename Rhs::PlainObject b_cpy;\n  if(m_sluEqued!='N')\n  {\n    b_cpy = b;\n    m_sluB = SluMatrix::Map(b_cpy.const_cast_derived());  \n  }\n\n  StatInit(&m_sluStat);\n  int info = 0;\n  RealScalar recip_pivot_growth, rcond;\n  SuperLU_gssvx(&m_sluOptions, &m_sluA,\n                m_q.data(), m_p.data(),\n                &m_sluEtree[0], &m_sluEqued,\n                &m_sluRscale[0], &m_sluCscale[0],\n                &m_sluL, &m_sluU,\n                NULL, 0,\n                &m_sluB, &m_sluX,\n                &recip_pivot_growth, &rcond,\n                &m_sluFerr[0], &m_sluBerr[0],\n                &m_sluStat, &info, Scalar());\n  StatFree(&m_sluStat);\n  \n  if(x.derived().data() != x_ref.data())\n    x = x_ref;\n  \n  m_info = info==0 ? Success : NumericalIssue;\n}\n\n// the code of this extractData() function has been adapted from the SuperLU's Matlab support code,\n//\n//  Copyright (c) 1994 by Xerox Corporation.  All rights reserved.\n//\n//  THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY\n//  EXPRESSED OR IMPLIED.  ANY USE IS AT YOUR OWN RISK.\n//\ntemplate<typename MatrixType, typename Derived>\nvoid SuperLUBase<MatrixType,Derived>::extractData() const\n{\n  eigen_assert(m_factorizationIsOk && \"The decomposition is not in a valid state for extracting factors, you must first call either compute() or analyzePattern()/factorize()\");\n  if (m_extractedDataAreDirty)\n  {\n    int         upper;\n    int         fsupc, istart, nsupr;\n    int         lastl = 0, lastu = 0;\n    SCformat    *Lstore = static_cast<SCformat*>(m_sluL.Store);\n    NCformat    *Ustore = static_cast<NCformat*>(m_sluU.Store);\n    Scalar      *SNptr;\n\n    const Index size = m_matrix.rows();\n    m_l.resize(size,size);\n    m_l.resizeNonZeros(Lstore->nnz);\n    m_u.resize(size,size);\n    m_u.resizeNonZeros(Ustore->nnz);\n\n    int* Lcol = m_l.outerIndexPtr();\n    int* Lrow = m_l.innerIndexPtr();\n    Scalar* Lval = m_l.valuePtr();\n\n    int* Ucol = m_u.outerIndexPtr();\n    int* Urow = m_u.innerIndexPtr();\n    Scalar* Uval = m_u.valuePtr();\n\n    Ucol[0] = 0;\n    Ucol[0] = 0;\n\n    /* for each supernode */\n    for (int k = 0; k <= Lstore->nsuper; ++k)\n    {\n      fsupc   = L_FST_SUPC(k);\n      istart  = L_SUB_START(fsupc);\n      nsupr   = L_SUB_START(fsupc+1) - istart;\n      upper   = 1;\n\n      /* for each column in the supernode */\n      for (int j = fsupc; j < L_FST_SUPC(k+1); ++j)\n      {\n        SNptr = &((Scalar*)Lstore->nzval)[L_NZ_START(j)];\n\n        /* Extract U */\n        for (int i = U_NZ_START(j); i < U_NZ_START(j+1); ++i)\n        {\n          Uval[lastu] = ((Scalar*)Ustore->nzval)[i];\n          /* Matlab doesn't like explicit zero. */\n          if (Uval[lastu] != 0.0)\n            Urow[lastu++] = U_SUB(i);\n        }\n        for (int i = 0; i < upper; ++i)\n        {\n          /* upper triangle in the supernode */\n          Uval[lastu] = SNptr[i];\n          /* Matlab doesn't like explicit zero. */\n          if (Uval[lastu] != 0.0)\n            Urow[lastu++] = L_SUB(istart+i);\n        }\n        Ucol[j+1] = lastu;\n\n        /* Extract L */\n        Lval[lastl] = 1.0; /* unit diagonal */\n        Lrow[lastl++] = L_SUB(istart + upper - 1);\n        for (int i = upper; i < nsupr; ++i)\n        {\n          Lval[lastl] = SNptr[i];\n          /* Matlab doesn't like explicit zero. */\n          if (Lval[lastl] != 0.0)\n            Lrow[lastl++] = L_SUB(istart+i);\n        }\n        Lcol[j+1] = lastl;\n\n        ++upper;\n      } /* for j ... */\n\n    } /* for k ... */\n\n    // squeeze the matrices :\n    m_l.resizeNonZeros(lastl);\n    m_u.resizeNonZeros(lastu);\n\n    m_extractedDataAreDirty = false;\n  }\n}\n\ntemplate<typename MatrixType>\ntypename SuperLU<MatrixType>::Scalar SuperLU<MatrixType>::determinant() const\n{\n  eigen_assert(m_factorizationIsOk && \"The decomposition is not in a valid state for computing the determinant, you must first call either compute() or analyzePattern()/factorize()\");\n  \n  if (m_extractedDataAreDirty)\n    this->extractData();\n\n  Scalar det = Scalar(1);\n  for (int j=0; j<m_u.cols(); ++j)\n  {\n    if (m_u.outerIndexPtr()[j+1]-m_u.outerIndexPtr()[j] > 0)\n    {\n      int lastId = m_u.outerIndexPtr()[j+1]-1;\n      eigen_assert(m_u.innerIndexPtr()[lastId]<=j);\n      if (m_u.innerIndexPtr()[lastId]==j)\n        det *= m_u.valuePtr()[lastId];\n    }\n  }\n  if(PermutationMap(m_p.data(),m_p.size()).determinant()*PermutationMap(m_q.data(),m_q.size()).determinant()<0)\n    det = -det;\n  if(m_sluEqued!='N')\n    return det/m_sluRscale.prod()/m_sluCscale.prod();\n  else\n    return det;\n}\n\n#ifdef EIGEN_PARSED_BY_DOXYGEN\n#define EIGEN_SUPERLU_HAS_ILU\n#endif\n\n#ifdef EIGEN_SUPERLU_HAS_ILU\n\n/** \\ingroup SuperLUSupport_Module\n  * \\class SuperILU\n  * \\brief A sparse direct \\b incomplete LU factorization and solver based on the SuperLU library\n  *\n  * This class allows to solve for an approximate solution of A.X = B sparse linear problems via an incomplete LU factorization\n  * using the SuperLU library. This class is aimed to be used as a preconditioner of the iterative linear solvers.\n  *\n  * \\warning This class is only for the 4.x versions of SuperLU. The 3.x and 5.x versions are not supported.\n  *\n  * \\tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>\n  *\n  * \\implsparsesolverconcept\n  *\n  * \\sa \\ref TutorialSparseSolverConcept, class IncompleteLUT, class ConjugateGradient, class BiCGSTAB\n  */\n\ntemplate<typename _MatrixType>\nclass SuperILU : public SuperLUBase<_MatrixType,SuperILU<_MatrixType> >\n{\n  public:\n    typedef SuperLUBase<_MatrixType,SuperILU> Base;\n    typedef _MatrixType MatrixType;\n    typedef typename Base::Scalar Scalar;\n    typedef typename Base::RealScalar RealScalar;\n\n  public:\n    using Base::_solve_impl;\n\n    SuperILU() : Base() { init(); }\n\n    SuperILU(const MatrixType& matrix) : Base()\n    {\n      init();\n      Base::compute(matrix);\n    }\n\n    ~SuperILU()\n    {\n    }\n    \n    /** Performs a symbolic decomposition on the sparcity of \\a matrix.\n      *\n      * This function is particularly useful when solving for several problems having the same structure.\n      * \n      * \\sa factorize()\n      */\n    void analyzePattern(const MatrixType& matrix)\n    {\n      Base::analyzePattern(matrix);\n    }\n    \n    /** Performs a numeric decomposition of \\a matrix\n      *\n      * The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed.\n      *\n      * \\sa analyzePattern()\n      */\n    void factorize(const MatrixType& matrix);\n    \n    #ifndef EIGEN_PARSED_BY_DOXYGEN\n    /** \\internal */\n    template<typename Rhs,typename Dest>\n    void _solve_impl(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const;\n    #endif // EIGEN_PARSED_BY_DOXYGEN\n    \n  protected:\n    \n    using Base::m_matrix;\n    using Base::m_sluOptions;\n    using Base::m_sluA;\n    using Base::m_sluB;\n    using Base::m_sluX;\n    using Base::m_p;\n    using Base::m_q;\n    using Base::m_sluEtree;\n    using Base::m_sluEqued;\n    using Base::m_sluRscale;\n    using Base::m_sluCscale;\n    using Base::m_sluL;\n    using Base::m_sluU;\n    using Base::m_sluStat;\n    using Base::m_sluFerr;\n    using Base::m_sluBerr;\n    using Base::m_l;\n    using Base::m_u;\n    \n    using Base::m_analysisIsOk;\n    using Base::m_factorizationIsOk;\n    using Base::m_extractedDataAreDirty;\n    using Base::m_isInitialized;\n    using Base::m_info;\n\n    void init()\n    {\n      Base::init();\n      \n      ilu_set_default_options(&m_sluOptions);\n      m_sluOptions.PrintStat        = NO;\n      m_sluOptions.ConditionNumber  = NO;\n      m_sluOptions.Trans            = NOTRANS;\n      m_sluOptions.ColPerm          = MMD_AT_PLUS_A;\n      \n      // no attempt to preserve column sum\n      m_sluOptions.ILU_MILU = SILU;\n      // only basic ILU(k) support -- no direct control over memory consumption\n      // better to use ILU_DropRule = DROP_BASIC | DROP_AREA\n      // and set ILU_FillFactor to max memory growth\n      m_sluOptions.ILU_DropRule = DROP_BASIC;\n      m_sluOptions.ILU_DropTol = NumTraits<Scalar>::dummy_precision()*10;\n    }\n    \n  private:\n    SuperILU(SuperILU& ) { }\n};\n\ntemplate<typename MatrixType>\nvoid SuperILU<MatrixType>::factorize(const MatrixType& a)\n{\n  eigen_assert(m_analysisIsOk && \"You must first call analyzePattern()\");\n  if(!m_analysisIsOk)\n  {\n    m_info = InvalidInput;\n    return;\n  }\n  \n  this->initFactorization(a);\n\n  int info = 0;\n  RealScalar recip_pivot_growth, rcond;\n\n  StatInit(&m_sluStat);\n  SuperLU_gsisx(&m_sluOptions, &m_sluA, m_q.data(), m_p.data(), &m_sluEtree[0],\n                &m_sluEqued, &m_sluRscale[0], &m_sluCscale[0],\n                &m_sluL, &m_sluU,\n                NULL, 0,\n                &m_sluB, &m_sluX,\n                &recip_pivot_growth, &rcond,\n                &m_sluStat, &info, Scalar());\n  StatFree(&m_sluStat);\n\n  // FIXME how to better check for errors ???\n  m_info = info == 0 ? Success : NumericalIssue;\n  m_factorizationIsOk = true;\n}\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\ntemplate<typename MatrixType>\ntemplate<typename Rhs,typename Dest>\nvoid SuperILU<MatrixType>::_solve_impl(const MatrixBase<Rhs> &b, MatrixBase<Dest>& x) const\n{\n  eigen_assert(m_factorizationIsOk && \"The decomposition is not in a valid state for solving, you must first call either compute() or analyzePattern()/factorize()\");\n\n  const int size = m_matrix.rows();\n  const int rhsCols = b.cols();\n  eigen_assert(size==b.rows());\n\n  m_sluOptions.Trans = NOTRANS;\n  m_sluOptions.Fact = FACTORED;\n  m_sluOptions.IterRefine = NOREFINE;\n\n  m_sluFerr.resize(rhsCols);\n  m_sluBerr.resize(rhsCols);\n  \n  Ref<const Matrix<typename Rhs::Scalar,Dynamic,Dynamic,ColMajor> > b_ref(b);\n  Ref<const Matrix<typename Dest::Scalar,Dynamic,Dynamic,ColMajor> > x_ref(x);\n  \n  m_sluB = SluMatrix::Map(b_ref.const_cast_derived());\n  m_sluX = SluMatrix::Map(x_ref.const_cast_derived());\n\n  typename Rhs::PlainObject b_cpy;\n  if(m_sluEqued!='N')\n  {\n    b_cpy = b;\n    m_sluB = SluMatrix::Map(b_cpy.const_cast_derived());  \n  }\n  \n  int info = 0;\n  RealScalar recip_pivot_growth, rcond;\n\n  StatInit(&m_sluStat);\n  SuperLU_gsisx(&m_sluOptions, &m_sluA,\n                m_q.data(), m_p.data(),\n                &m_sluEtree[0], &m_sluEqued,\n                &m_sluRscale[0], &m_sluCscale[0],\n                &m_sluL, &m_sluU,\n                NULL, 0,\n                &m_sluB, &m_sluX,\n                &recip_pivot_growth, &rcond,\n                &m_sluStat, &info, Scalar());\n  StatFree(&m_sluStat);\n  \n  if(x.derived().data() != x_ref.data())\n    x = x_ref;\n\n  m_info = info==0 ? Success : NumericalIssue;\n}\n#endif\n\n#endif\n\n} // end namespace Eigen\n\n#endif // EIGEN_SUPERLUSUPPORT_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/UmfPackSupport/UmfPackSupport.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_UMFPACKSUPPORT_H\n#define EIGEN_UMFPACKSUPPORT_H\n\nnamespace Eigen {\n\n/* TODO extract L, extract U, compute det, etc... */\n\n// generic double/complex<double> wrapper functions:\n\n\ninline void umfpack_defaults(double control[UMFPACK_CONTROL], double)\n{ umfpack_di_defaults(control); }\n\ninline void umfpack_defaults(double control[UMFPACK_CONTROL], std::complex<double>)\n{ umfpack_zi_defaults(control); }\n\ninline void umfpack_report_info(double control[UMFPACK_CONTROL], double info[UMFPACK_INFO], double)\n{ umfpack_di_report_info(control, info);}\n\ninline void umfpack_report_info(double control[UMFPACK_CONTROL], double info[UMFPACK_INFO], std::complex<double>)\n{ umfpack_zi_report_info(control, info);}\n\ninline void umfpack_report_status(double control[UMFPACK_CONTROL], int status, double)\n{ umfpack_di_report_status(control, status);}\n\ninline void umfpack_report_status(double control[UMFPACK_CONTROL], int status, std::complex<double>)\n{ umfpack_zi_report_status(control, status);}\n\ninline void umfpack_report_control(double control[UMFPACK_CONTROL], double)\n{ umfpack_di_report_control(control);}\n\ninline void umfpack_report_control(double control[UMFPACK_CONTROL], std::complex<double>)\n{ umfpack_zi_report_control(control);}\n\ninline void umfpack_free_numeric(void **Numeric, double)\n{ umfpack_di_free_numeric(Numeric); *Numeric = 0; }\n\ninline void umfpack_free_numeric(void **Numeric, std::complex<double>)\n{ umfpack_zi_free_numeric(Numeric); *Numeric = 0; }\n\ninline void umfpack_free_symbolic(void **Symbolic, double)\n{ umfpack_di_free_symbolic(Symbolic); *Symbolic = 0; }\n\ninline void umfpack_free_symbolic(void **Symbolic, std::complex<double>)\n{ umfpack_zi_free_symbolic(Symbolic); *Symbolic = 0; }\n\ninline int umfpack_symbolic(int n_row,int n_col,\n                            const int Ap[], const int Ai[], const double Ax[], void **Symbolic,\n                            const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO])\n{\n  return umfpack_di_symbolic(n_row,n_col,Ap,Ai,Ax,Symbolic,Control,Info);\n}\n\ninline int umfpack_symbolic(int n_row,int n_col,\n                            const int Ap[], const int Ai[], const std::complex<double> Ax[], void **Symbolic,\n                            const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO])\n{\n  return umfpack_zi_symbolic(n_row,n_col,Ap,Ai,&numext::real_ref(Ax[0]),0,Symbolic,Control,Info);\n}\n\ninline int umfpack_numeric( const int Ap[], const int Ai[], const double Ax[],\n                            void *Symbolic, void **Numeric,\n                            const double Control[UMFPACK_CONTROL],double Info [UMFPACK_INFO])\n{\n  return umfpack_di_numeric(Ap,Ai,Ax,Symbolic,Numeric,Control,Info);\n}\n\ninline int umfpack_numeric( const int Ap[], const int Ai[], const std::complex<double> Ax[],\n                            void *Symbolic, void **Numeric,\n                            const double Control[UMFPACK_CONTROL],double Info [UMFPACK_INFO])\n{\n  return umfpack_zi_numeric(Ap,Ai,&numext::real_ref(Ax[0]),0,Symbolic,Numeric,Control,Info);\n}\n\ninline int umfpack_solve( int sys, const int Ap[], const int Ai[], const double Ax[],\n                          double X[], const double B[], void *Numeric,\n                          const double Control[UMFPACK_CONTROL], double Info[UMFPACK_INFO])\n{\n  return umfpack_di_solve(sys,Ap,Ai,Ax,X,B,Numeric,Control,Info);\n}\n\ninline int umfpack_solve( int sys, const int Ap[], const int Ai[], const std::complex<double> Ax[],\n                          std::complex<double> X[], const std::complex<double> B[], void *Numeric,\n                          const double Control[UMFPACK_CONTROL], double Info[UMFPACK_INFO])\n{\n  return umfpack_zi_solve(sys,Ap,Ai,&numext::real_ref(Ax[0]),0,&numext::real_ref(X[0]),0,&numext::real_ref(B[0]),0,Numeric,Control,Info);\n}\n\ninline int umfpack_get_lunz(int *lnz, int *unz, int *n_row, int *n_col, int *nz_udiag, void *Numeric, double)\n{\n  return umfpack_di_get_lunz(lnz,unz,n_row,n_col,nz_udiag,Numeric);\n}\n\ninline int umfpack_get_lunz(int *lnz, int *unz, int *n_row, int *n_col, int *nz_udiag, void *Numeric, std::complex<double>)\n{\n  return umfpack_zi_get_lunz(lnz,unz,n_row,n_col,nz_udiag,Numeric);\n}\n\ninline int umfpack_get_numeric(int Lp[], int Lj[], double Lx[], int Up[], int Ui[], double Ux[],\n                               int P[], int Q[], double Dx[], int *do_recip, double Rs[], void *Numeric)\n{\n  return umfpack_di_get_numeric(Lp,Lj,Lx,Up,Ui,Ux,P,Q,Dx,do_recip,Rs,Numeric);\n}\n\ninline int umfpack_get_numeric(int Lp[], int Lj[], std::complex<double> Lx[], int Up[], int Ui[], std::complex<double> Ux[],\n                               int P[], int Q[], std::complex<double> Dx[], int *do_recip, double Rs[], void *Numeric)\n{\n  double& lx0_real = numext::real_ref(Lx[0]);\n  double& ux0_real = numext::real_ref(Ux[0]);\n  double& dx0_real = numext::real_ref(Dx[0]);\n  return umfpack_zi_get_numeric(Lp,Lj,Lx?&lx0_real:0,0,Up,Ui,Ux?&ux0_real:0,0,P,Q,\n                                Dx?&dx0_real:0,0,do_recip,Rs,Numeric);\n}\n\ninline int umfpack_get_determinant(double *Mx, double *Ex, void *NumericHandle, double User_Info [UMFPACK_INFO])\n{\n  return umfpack_di_get_determinant(Mx,Ex,NumericHandle,User_Info);\n}\n\ninline int umfpack_get_determinant(std::complex<double> *Mx, double *Ex, void *NumericHandle, double User_Info [UMFPACK_INFO])\n{\n  double& mx_real = numext::real_ref(*Mx);\n  return umfpack_zi_get_determinant(&mx_real,0,Ex,NumericHandle,User_Info);\n}\n\n\n/** \\ingroup UmfPackSupport_Module\n  * \\brief A sparse LU factorization and solver based on UmfPack\n  *\n  * This class allows to solve for A.X = B sparse linear problems via a LU factorization\n  * using the UmfPack library. The sparse matrix A must be squared and full rank.\n  * The vectors or matrices X and B can be either dense or sparse.\n  *\n  * \\warning The input matrix A should be in a \\b compressed and \\b column-major form.\n  * Otherwise an expensive copy will be made. You can call the inexpensive makeCompressed() to get a compressed matrix.\n  * \\tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>\n  *\n  * \\implsparsesolverconcept\n  *\n  * \\sa \\ref TutorialSparseSolverConcept, class SparseLU\n  */\ntemplate<typename _MatrixType>\nclass UmfPackLU : public SparseSolverBase<UmfPackLU<_MatrixType> >\n{\n  protected:\n    typedef SparseSolverBase<UmfPackLU<_MatrixType> > Base;\n    using Base::m_isInitialized;\n  public:\n    using Base::_solve_impl;\n    typedef _MatrixType MatrixType;\n    typedef typename MatrixType::Scalar Scalar;\n    typedef typename MatrixType::RealScalar RealScalar;\n    typedef typename MatrixType::StorageIndex StorageIndex;\n    typedef Matrix<Scalar,Dynamic,1> Vector;\n    typedef Matrix<int, 1, MatrixType::ColsAtCompileTime> IntRowVectorType;\n    typedef Matrix<int, MatrixType::RowsAtCompileTime, 1> IntColVectorType;\n    typedef SparseMatrix<Scalar> LUMatrixType;\n    typedef SparseMatrix<Scalar,ColMajor,int> UmfpackMatrixType;\n    typedef Ref<const UmfpackMatrixType, StandardCompressedFormat> UmfpackMatrixRef;\n    enum {\n      ColsAtCompileTime = MatrixType::ColsAtCompileTime,\n      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime\n    };\n\n  public:\n\n    typedef Array<double, UMFPACK_CONTROL, 1> UmfpackControl;\n    typedef Array<double, UMFPACK_INFO, 1> UmfpackInfo;\n\n    UmfPackLU()\n      : m_dummy(0,0), mp_matrix(m_dummy)\n    {\n      init();\n    }\n\n    template<typename InputMatrixType>\n    explicit UmfPackLU(const InputMatrixType& matrix)\n      : mp_matrix(matrix)\n    {\n      init();\n      compute(matrix);\n    }\n\n    ~UmfPackLU()\n    {\n      if(m_symbolic) umfpack_free_symbolic(&m_symbolic,Scalar());\n      if(m_numeric)  umfpack_free_numeric(&m_numeric,Scalar());\n    }\n\n    inline Index rows() const { return mp_matrix.rows(); }\n    inline Index cols() const { return mp_matrix.cols(); }\n\n    /** \\brief Reports whether previous computation was successful.\n      *\n      * \\returns \\c Success if computation was succesful,\n      *          \\c NumericalIssue if the matrix.appears to be negative.\n      */\n    ComputationInfo info() const\n    {\n      eigen_assert(m_isInitialized && \"Decomposition is not initialized.\");\n      return m_info;\n    }\n\n    inline const LUMatrixType& matrixL() const\n    {\n      if (m_extractedDataAreDirty) extractData();\n      return m_l;\n    }\n\n    inline const LUMatrixType& matrixU() const\n    {\n      if (m_extractedDataAreDirty) extractData();\n      return m_u;\n    }\n\n    inline const IntColVectorType& permutationP() const\n    {\n      if (m_extractedDataAreDirty) extractData();\n      return m_p;\n    }\n\n    inline const IntRowVectorType& permutationQ() const\n    {\n      if (m_extractedDataAreDirty) extractData();\n      return m_q;\n    }\n\n    /** Computes the sparse Cholesky decomposition of \\a matrix\n     *  Note that the matrix should be column-major, and in compressed format for best performance.\n     *  \\sa SparseMatrix::makeCompressed().\n     */\n    template<typename InputMatrixType>\n    void compute(const InputMatrixType& matrix)\n    {\n      if(m_symbolic) umfpack_free_symbolic(&m_symbolic,Scalar());\n      if(m_numeric)  umfpack_free_numeric(&m_numeric,Scalar());\n      grab(matrix.derived());\n      analyzePattern_impl();\n      factorize_impl();\n    }\n\n    /** Performs a symbolic decomposition on the sparcity of \\a matrix.\n      *\n      * This function is particularly useful when solving for several problems having the same structure.\n      *\n      * \\sa factorize(), compute()\n      */\n    template<typename InputMatrixType>\n    void analyzePattern(const InputMatrixType& matrix)\n    {\n      if(m_symbolic) umfpack_free_symbolic(&m_symbolic,Scalar());\n      if(m_numeric)  umfpack_free_numeric(&m_numeric,Scalar());\n\n      grab(matrix.derived());\n\n      analyzePattern_impl();\n    }\n\n    /** Provides the return status code returned by UmfPack during the numeric\n      * factorization.\n      *\n      * \\sa factorize(), compute()\n      */\n    inline int umfpackFactorizeReturncode() const\n    {\n      eigen_assert(m_numeric && \"UmfPackLU: you must first call factorize()\");\n      return m_fact_errorCode;\n    }\n\n    /** Provides access to the control settings array used by UmfPack.\n      *\n      * If this array contains NaN's, the default values are used.\n      *\n      * See UMFPACK documentation for details.\n      */\n    inline const UmfpackControl& umfpackControl() const\n    {\n      return m_control;\n    }\n\n    /** Provides access to the control settings array used by UmfPack.\n      *\n      * If this array contains NaN's, the default values are used.\n      *\n      * See UMFPACK documentation for details.\n      */\n    inline UmfpackControl& umfpackControl()\n    {\n      return m_control;\n    }\n\n    /** Performs a numeric decomposition of \\a matrix\n      *\n      * The given matrix must has the same sparcity than the matrix on which the pattern anylysis has been performed.\n      *\n      * \\sa analyzePattern(), compute()\n      */\n    template<typename InputMatrixType>\n    void factorize(const InputMatrixType& matrix)\n    {\n      eigen_assert(m_analysisIsOk && \"UmfPackLU: you must first call analyzePattern()\");\n      if(m_numeric)\n        umfpack_free_numeric(&m_numeric,Scalar());\n\n      grab(matrix.derived());\n\n      factorize_impl();\n    }\n\n    /** Prints the current UmfPack control settings.\n      *\n      * \\sa umfpackControl()\n      */\n    void umfpackReportControl()\n    {\n      umfpack_report_control(m_control.data(), Scalar());\n    }\n\n    /** Prints statistics collected by UmfPack.\n      *\n      * \\sa analyzePattern(), compute()\n      */\n    void umfpackReportInfo()\n    {\n      eigen_assert(m_analysisIsOk && \"UmfPackLU: you must first call analyzePattern()\");\n      umfpack_report_info(m_control.data(), m_umfpackInfo.data(), Scalar());\n    }\n\n    /** Prints the status of the previous factorization operation performed by UmfPack (symbolic or numerical factorization).\n      *\n      * \\sa analyzePattern(), compute()\n      */\n    void umfpackReportStatus() {\n      eigen_assert(m_analysisIsOk && \"UmfPackLU: you must first call analyzePattern()\");\n      umfpack_report_status(m_control.data(), m_fact_errorCode, Scalar());\n    }\n\n    /** \\internal */\n    template<typename BDerived,typename XDerived>\n    bool _solve_impl(const MatrixBase<BDerived> &b, MatrixBase<XDerived> &x) const;\n\n    Scalar determinant() const;\n\n    void extractData() const;\n\n  protected:\n\n    void init()\n    {\n      m_info                  = InvalidInput;\n      m_isInitialized         = false;\n      m_numeric               = 0;\n      m_symbolic              = 0;\n      m_extractedDataAreDirty = true;\n\n      umfpack_defaults(m_control.data(), Scalar());\n    }\n\n    void analyzePattern_impl()\n    {\n      m_fact_errorCode = umfpack_symbolic(internal::convert_index<int>(mp_matrix.rows()),\n                                          internal::convert_index<int>(mp_matrix.cols()),\n                                          mp_matrix.outerIndexPtr(), mp_matrix.innerIndexPtr(), mp_matrix.valuePtr(),\n                                          &m_symbolic, m_control.data(), m_umfpackInfo.data());\n\n      m_isInitialized = true;\n      m_info = m_fact_errorCode ? InvalidInput : Success;\n      m_analysisIsOk = true;\n      m_factorizationIsOk = false;\n      m_extractedDataAreDirty = true;\n    }\n\n    void factorize_impl()\n    {\n\n      m_fact_errorCode = umfpack_numeric(mp_matrix.outerIndexPtr(), mp_matrix.innerIndexPtr(), mp_matrix.valuePtr(),\n                                         m_symbolic, &m_numeric, m_control.data(), m_umfpackInfo.data());\n\n      m_info = m_fact_errorCode == UMFPACK_OK ? Success : NumericalIssue;\n      m_factorizationIsOk = true;\n      m_extractedDataAreDirty = true;\n    }\n\n    template<typename MatrixDerived>\n    void grab(const EigenBase<MatrixDerived> &A)\n    {\n      mp_matrix.~UmfpackMatrixRef();\n      ::new (&mp_matrix) UmfpackMatrixRef(A.derived());\n    }\n\n    void grab(const UmfpackMatrixRef &A)\n    {\n      if(&(A.derived()) != &mp_matrix)\n      {\n        mp_matrix.~UmfpackMatrixRef();\n        ::new (&mp_matrix) UmfpackMatrixRef(A);\n      }\n    }\n\n    // cached data to reduce reallocation, etc.\n    mutable LUMatrixType m_l;\n    int m_fact_errorCode;\n    UmfpackControl m_control;\n    mutable UmfpackInfo m_umfpackInfo;\n\n    mutable LUMatrixType m_u;\n    mutable IntColVectorType m_p;\n    mutable IntRowVectorType m_q;\n\n    UmfpackMatrixType m_dummy;\n    UmfpackMatrixRef mp_matrix;\n\n    void* m_numeric;\n    void* m_symbolic;\n\n    mutable ComputationInfo m_info;\n    int m_factorizationIsOk;\n    int m_analysisIsOk;\n    mutable bool m_extractedDataAreDirty;\n\n  private:\n    UmfPackLU(const UmfPackLU& ) { }\n};\n\n\ntemplate<typename MatrixType>\nvoid UmfPackLU<MatrixType>::extractData() const\n{\n  if (m_extractedDataAreDirty)\n  {\n    // get size of the data\n    int lnz, unz, rows, cols, nz_udiag;\n    umfpack_get_lunz(&lnz, &unz, &rows, &cols, &nz_udiag, m_numeric, Scalar());\n\n    // allocate data\n    m_l.resize(rows,(std::min)(rows,cols));\n    m_l.resizeNonZeros(lnz);\n\n    m_u.resize((std::min)(rows,cols),cols);\n    m_u.resizeNonZeros(unz);\n\n    m_p.resize(rows);\n    m_q.resize(cols);\n\n    // extract\n    umfpack_get_numeric(m_l.outerIndexPtr(), m_l.innerIndexPtr(), m_l.valuePtr(),\n                        m_u.outerIndexPtr(), m_u.innerIndexPtr(), m_u.valuePtr(),\n                        m_p.data(), m_q.data(), 0, 0, 0, m_numeric);\n\n    m_extractedDataAreDirty = false;\n  }\n}\n\ntemplate<typename MatrixType>\ntypename UmfPackLU<MatrixType>::Scalar UmfPackLU<MatrixType>::determinant() const\n{\n  Scalar det;\n  umfpack_get_determinant(&det, 0, m_numeric, 0);\n  return det;\n}\n\ntemplate<typename MatrixType>\ntemplate<typename BDerived,typename XDerived>\nbool UmfPackLU<MatrixType>::_solve_impl(const MatrixBase<BDerived> &b, MatrixBase<XDerived> &x) const\n{\n  Index rhsCols = b.cols();\n  eigen_assert((BDerived::Flags&RowMajorBit)==0 && \"UmfPackLU backend does not support non col-major rhs yet\");\n  eigen_assert((XDerived::Flags&RowMajorBit)==0 && \"UmfPackLU backend does not support non col-major result yet\");\n  eigen_assert(b.derived().data() != x.derived().data() && \" Umfpack does not support inplace solve\");\n\n  int errorCode;\n  Scalar* x_ptr = 0;\n  Matrix<Scalar,Dynamic,1> x_tmp;\n  if(x.innerStride()!=1)\n  {\n    x_tmp.resize(x.rows());\n    x_ptr = x_tmp.data();\n  }\n  for (int j=0; j<rhsCols; ++j)\n  {\n    if(x.innerStride()==1)\n      x_ptr = &x.col(j).coeffRef(0);\n    errorCode = umfpack_solve(UMFPACK_A,\n        mp_matrix.outerIndexPtr(), mp_matrix.innerIndexPtr(), mp_matrix.valuePtr(),\n        x_ptr, &b.const_cast_derived().col(j).coeffRef(0), m_numeric, m_control.data(), m_umfpackInfo.data());\n    if(x.innerStride()!=1)\n      x.col(j) = x_tmp;\n    if (errorCode!=0)\n      return false;\n  }\n\n  return true;\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_UMFPACKSUPPORT_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/misc/Image.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_MISC_IMAGE_H\n#define EIGEN_MISC_IMAGE_H\n\nnamespace Eigen { \n\nnamespace internal {\n\n/** \\class image_retval_base\n  *\n  */\ntemplate<typename DecompositionType>\nstruct traits<image_retval_base<DecompositionType> >\n{\n  typedef typename DecompositionType::MatrixType MatrixType;\n  typedef Matrix<\n    typename MatrixType::Scalar,\n    MatrixType::RowsAtCompileTime, // the image is a subspace of the destination space, whose\n                                   // dimension is the number of rows of the original matrix\n    Dynamic,                       // we don't know at compile time the dimension of the image (the rank)\n    MatrixType::Options,\n    MatrixType::MaxRowsAtCompileTime, // the image matrix will consist of columns from the original matrix,\n    MatrixType::MaxColsAtCompileTime  // so it has the same number of rows and at most as many columns.\n  > ReturnType;\n};\n\ntemplate<typename _DecompositionType> struct image_retval_base\n : public ReturnByValue<image_retval_base<_DecompositionType> >\n{\n  typedef _DecompositionType DecompositionType;\n  typedef typename DecompositionType::MatrixType MatrixType;\n  typedef ReturnByValue<image_retval_base> Base;\n\n  image_retval_base(const DecompositionType& dec, const MatrixType& originalMatrix)\n    : m_dec(dec), m_rank(dec.rank()),\n      m_cols(m_rank == 0 ? 1 : m_rank),\n      m_originalMatrix(originalMatrix)\n  {}\n\n  inline Index rows() const { return m_dec.rows(); }\n  inline Index cols() const { return m_cols; }\n  inline Index rank() const { return m_rank; }\n  inline const DecompositionType& dec() const { return m_dec; }\n  inline const MatrixType& originalMatrix() const { return m_originalMatrix; }\n\n  template<typename Dest> inline void evalTo(Dest& dst) const\n  {\n    static_cast<const image_retval<DecompositionType>*>(this)->evalTo(dst);\n  }\n\n  protected:\n    const DecompositionType& m_dec;\n    Index m_rank, m_cols;\n    const MatrixType& m_originalMatrix;\n};\n\n} // end namespace internal\n\n#define EIGEN_MAKE_IMAGE_HELPERS(DecompositionType) \\\n  typedef typename DecompositionType::MatrixType MatrixType; \\\n  typedef typename MatrixType::Scalar Scalar; \\\n  typedef typename MatrixType::RealScalar RealScalar; \\\n  typedef Eigen::internal::image_retval_base<DecompositionType> Base; \\\n  using Base::dec; \\\n  using Base::originalMatrix; \\\n  using Base::rank; \\\n  using Base::rows; \\\n  using Base::cols; \\\n  image_retval(const DecompositionType& dec, const MatrixType& originalMatrix) \\\n    : Base(dec, originalMatrix) {}\n\n} // end namespace Eigen\n\n#endif // EIGEN_MISC_IMAGE_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/misc/Kernel.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_MISC_KERNEL_H\n#define EIGEN_MISC_KERNEL_H\n\nnamespace Eigen { \n\nnamespace internal {\n\n/** \\class kernel_retval_base\n  *\n  */\ntemplate<typename DecompositionType>\nstruct traits<kernel_retval_base<DecompositionType> >\n{\n  typedef typename DecompositionType::MatrixType MatrixType;\n  typedef Matrix<\n    typename MatrixType::Scalar,\n    MatrixType::ColsAtCompileTime, // the number of rows in the \"kernel matrix\"\n                                   // is the number of cols of the original matrix\n                                   // so that the product \"matrix * kernel = zero\" makes sense\n    Dynamic,                       // we don't know at compile-time the dimension of the kernel\n    MatrixType::Options,\n    MatrixType::MaxColsAtCompileTime, // see explanation for 2nd template parameter\n    MatrixType::MaxColsAtCompileTime // the kernel is a subspace of the domain space,\n                                     // whose dimension is the number of columns of the original matrix\n  > ReturnType;\n};\n\ntemplate<typename _DecompositionType> struct kernel_retval_base\n : public ReturnByValue<kernel_retval_base<_DecompositionType> >\n{\n  typedef _DecompositionType DecompositionType;\n  typedef ReturnByValue<kernel_retval_base> Base;\n\n  explicit kernel_retval_base(const DecompositionType& dec)\n    : m_dec(dec),\n      m_rank(dec.rank()),\n      m_cols(m_rank==dec.cols() ? 1 : dec.cols() - m_rank)\n  {}\n\n  inline Index rows() const { return m_dec.cols(); }\n  inline Index cols() const { return m_cols; }\n  inline Index rank() const { return m_rank; }\n  inline const DecompositionType& dec() const { return m_dec; }\n\n  template<typename Dest> inline void evalTo(Dest& dst) const\n  {\n    static_cast<const kernel_retval<DecompositionType>*>(this)->evalTo(dst);\n  }\n\n  protected:\n    const DecompositionType& m_dec;\n    Index m_rank, m_cols;\n};\n\n} // end namespace internal\n\n#define EIGEN_MAKE_KERNEL_HELPERS(DecompositionType) \\\n  typedef typename DecompositionType::MatrixType MatrixType; \\\n  typedef typename MatrixType::Scalar Scalar; \\\n  typedef typename MatrixType::RealScalar RealScalar; \\\n  typedef Eigen::internal::kernel_retval_base<DecompositionType> Base; \\\n  using Base::dec; \\\n  using Base::rank; \\\n  using Base::rows; \\\n  using Base::cols; \\\n  kernel_retval(const DecompositionType& dec) : Base(dec) {}\n\n} // end namespace Eigen\n\n#endif // EIGEN_MISC_KERNEL_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/misc/RealSvd2x2.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2013-2016 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_REALSVD2X2_H\n#define EIGEN_REALSVD2X2_H\n\nnamespace Eigen {\n\nnamespace internal {\n\ntemplate<typename MatrixType, typename RealScalar, typename Index>\nvoid real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q,\n                         JacobiRotation<RealScalar> *j_left,\n                         JacobiRotation<RealScalar> *j_right)\n{\n  using std::sqrt;\n  using std::abs;\n  Matrix<RealScalar,2,2> m;\n  m << numext::real(matrix.coeff(p,p)), numext::real(matrix.coeff(p,q)),\n       numext::real(matrix.coeff(q,p)), numext::real(matrix.coeff(q,q));\n  JacobiRotation<RealScalar> rot1;\n  RealScalar t = m.coeff(0,0) + m.coeff(1,1);\n  RealScalar d = m.coeff(1,0) - m.coeff(0,1);\n\n  if(abs(d) < (std::numeric_limits<RealScalar>::min)())\n  {\n    rot1.s() = RealScalar(0);\n    rot1.c() = RealScalar(1);\n  }\n  else\n  {\n    // If d!=0, then t/d cannot overflow because the magnitude of the\n    // entries forming d are not too small compared to the ones forming t.\n    RealScalar u = t / d;\n    RealScalar tmp = sqrt(RealScalar(1) + numext::abs2(u));\n    rot1.s() = RealScalar(1) / tmp;\n    rot1.c() = u / tmp;\n  }\n  m.applyOnTheLeft(0,1,rot1);\n  j_right->makeJacobi(m,0,1);\n  *j_left = rot1 * j_right->transpose();\n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_REALSVD2X2_H\n"
  },
  {
    "path": "include/eigen3/Eigen/src/misc/blas.h",
    "content": "#ifndef BLAS_H\n#define BLAS_H\n\n#ifdef __cplusplus\nextern \"C\"\n{\n#endif\n\n#define BLASFUNC(FUNC) FUNC##_\n\n#ifdef __WIN64__\ntypedef long long BLASLONG;\ntypedef unsigned long long BLASULONG;\n#else\ntypedef long BLASLONG;\ntypedef unsigned long BLASULONG;\n#endif\n\nint    BLASFUNC(xerbla)(const char *, int *info, int);\n\nfloat  BLASFUNC(sdot)  (int *, float  *, int *, float  *, int *);\nfloat  BLASFUNC(sdsdot)(int *, float  *,        float  *, int *, float  *, int *);\n\ndouble BLASFUNC(dsdot) (int *, float  *, int *, float  *, int *);\ndouble BLASFUNC(ddot)  (int *, double *, int *, double *, int *);\ndouble BLASFUNC(qdot)  (int *, double *, int *, double *, int *);\n\nint  BLASFUNC(cdotuw)  (int *, float  *, int *, float  *, int *, float*);\nint  BLASFUNC(cdotcw)  (int *, float  *, int *, float  *, int *, float*);\nint  BLASFUNC(zdotuw)  (int *, double  *, int *, double  *, int *, double*);\nint  BLASFUNC(zdotcw)  (int *, double  *, int *, double  *, int *, double*);\n\nint    BLASFUNC(saxpy) (const int *, const float  *, const float  *, const int *, float  *, const int *);\nint    BLASFUNC(daxpy) (const int *, const double *, const double *, const int *, double *, const int *);\nint    BLASFUNC(qaxpy) (const int *, const double *, const double *, const int *, double *, const int *);\nint    BLASFUNC(caxpy) (const int *, const float  *, const float  *, const int *, float  *, const int *);\nint    BLASFUNC(zaxpy) (const int *, const double *, const double *, const int *, double *, const int *);\nint    BLASFUNC(xaxpy) (const int *, const double *, const double *, const int *, double *, const int *);\nint    BLASFUNC(caxpyc)(const int *, const float  *, const float  *, const int *, float  *, const int *);\nint    BLASFUNC(zaxpyc)(const int *, const double *, const double *, const int *, double *, const int *);\nint    BLASFUNC(xaxpyc)(const int *, const double *, const double *, const int *, double *, const int *);\n\nint    BLASFUNC(scopy) (int *, float  *, int *, float  *, int *);\nint    BLASFUNC(dcopy) (int *, double *, int *, double *, int *);\nint    BLASFUNC(qcopy) (int *, double *, int *, double *, int *);\nint    BLASFUNC(ccopy) (int *, float  *, int *, float  *, int *);\nint    BLASFUNC(zcopy) (int *, double *, int *, double *, int *);\nint    BLASFUNC(xcopy) (int *, double *, int *, double *, int *);\n\nint    BLASFUNC(sswap) (int *, float  *, int *, float  *, int *);\nint    BLASFUNC(dswap) (int *, double *, int *, double *, int *);\nint    BLASFUNC(qswap) (int *, double *, int *, double *, int *);\nint    BLASFUNC(cswap) (int *, float  *, int *, float  *, int *);\nint    BLASFUNC(zswap) (int *, double *, int *, double *, int *);\nint    BLASFUNC(xswap) (int *, double *, int *, double *, int *);\n\nfloat  BLASFUNC(sasum) (int *, float  *, int *);\nfloat  BLASFUNC(scasum)(int *, float  *, int *);\ndouble BLASFUNC(dasum) (int *, double *, int *);\ndouble BLASFUNC(qasum) (int *, double *, int *);\ndouble BLASFUNC(dzasum)(int *, double *, int *);\ndouble BLASFUNC(qxasum)(int *, double *, int *);\n\nint    BLASFUNC(isamax)(int *, float  *, int *);\nint    BLASFUNC(idamax)(int *, double *, int *);\nint    BLASFUNC(iqamax)(int *, double *, int *);\nint    BLASFUNC(icamax)(int *, float  *, int *);\nint    BLASFUNC(izamax)(int *, double *, int *);\nint    BLASFUNC(ixamax)(int *, double *, int *);\n\nint    BLASFUNC(ismax) (int *, float  *, int *);\nint    BLASFUNC(idmax) (int *, double *, int *);\nint    BLASFUNC(iqmax) (int *, double *, int *);\nint    BLASFUNC(icmax) (int *, float  *, int *);\nint    BLASFUNC(izmax) (int *, double *, int *);\nint    BLASFUNC(ixmax) (int *, double *, int *);\n\nint    BLASFUNC(isamin)(int *, float  *, int *);\nint    BLASFUNC(idamin)(int *, double *, int *);\nint    BLASFUNC(iqamin)(int *, double *, int *);\nint    BLASFUNC(icamin)(int *, float  *, int *);\nint    BLASFUNC(izamin)(int *, double *, int *);\nint    BLASFUNC(ixamin)(int *, double *, int *);\n\nint    BLASFUNC(ismin)(int *, float  *, int *);\nint    BLASFUNC(idmin)(int *, double *, int *);\nint    BLASFUNC(iqmin)(int *, double *, int *);\nint    BLASFUNC(icmin)(int *, float  *, int *);\nint    BLASFUNC(izmin)(int *, double *, int *);\nint    BLASFUNC(ixmin)(int *, double *, int *);\n\nfloat  BLASFUNC(samax) (int *, float  *, int *);\ndouble BLASFUNC(damax) (int *, double *, int *);\ndouble BLASFUNC(qamax) (int *, double *, int *);\nfloat  BLASFUNC(scamax)(int *, float  *, int *);\ndouble BLASFUNC(dzamax)(int *, double *, int *);\ndouble BLASFUNC(qxamax)(int *, double *, int *);\n\nfloat  BLASFUNC(samin) (int *, float  *, int *);\ndouble BLASFUNC(damin) (int *, double *, int *);\ndouble BLASFUNC(qamin) (int *, double *, int *);\nfloat  BLASFUNC(scamin)(int *, float  *, int *);\ndouble BLASFUNC(dzamin)(int *, double *, int *);\ndouble BLASFUNC(qxamin)(int *, double *, int *);\n\nfloat  BLASFUNC(smax)  (int *, float  *, int *);\ndouble BLASFUNC(dmax)  (int *, double *, int *);\ndouble BLASFUNC(qmax)  (int *, double *, int *);\nfloat  BLASFUNC(scmax) (int *, float  *, int *);\ndouble BLASFUNC(dzmax) (int *, double *, int *);\ndouble BLASFUNC(qxmax) (int *, double *, int *);\n\nfloat  BLASFUNC(smin)  (int *, float  *, int *);\ndouble BLASFUNC(dmin)  (int *, double *, int *);\ndouble BLASFUNC(qmin)  (int *, double *, int *);\nfloat  BLASFUNC(scmin) (int *, float  *, int *);\ndouble BLASFUNC(dzmin) (int *, double *, int *);\ndouble BLASFUNC(qxmin) (int *, double *, int *);\n\nint    BLASFUNC(sscal) (int *,  float  *, float  *, int *);\nint    BLASFUNC(dscal) (int *,  double *, double *, int *);\nint    BLASFUNC(qscal) (int *,  double *, double *, int *);\nint    BLASFUNC(cscal) (int *,  float  *, float  *, int *);\nint    BLASFUNC(zscal) (int *,  double *, double *, int *);\nint    BLASFUNC(xscal) (int *,  double *, double *, int *);\nint    BLASFUNC(csscal)(int *,  float  *, float  *, int *);\nint    BLASFUNC(zdscal)(int *,  double *, double *, int *);\nint    BLASFUNC(xqscal)(int *,  double *, double *, int *);\n\nfloat  BLASFUNC(snrm2) (int *, float  *, int *);\nfloat  BLASFUNC(scnrm2)(int *, float  *, int *);\n\ndouble BLASFUNC(dnrm2) (int *, double *, int *);\ndouble BLASFUNC(qnrm2) (int *, double *, int *);\ndouble BLASFUNC(dznrm2)(int *, double *, int *);\ndouble BLASFUNC(qxnrm2)(int *, double *, int *);\n\nint    BLASFUNC(srot)  (int *, float  *, int *, float  *, int *, float  *, float  *);\nint    BLASFUNC(drot)  (int *, double *, int *, double *, int *, double *, double *);\nint    BLASFUNC(qrot)  (int *, double *, int *, double *, int *, double *, double *);\nint    BLASFUNC(csrot) (int *, float  *, int *, float  *, int *, float  *, float  *);\nint    BLASFUNC(zdrot) (int *, double *, int *, double *, int *, double *, double *);\nint    BLASFUNC(xqrot) (int *, double *, int *, double *, int *, double *, double *);\n\nint    BLASFUNC(srotg) (float  *, float  *, float  *, float  *);\nint    BLASFUNC(drotg) (double *, double *, double *, double *);\nint    BLASFUNC(qrotg) (double *, double *, double *, double *);\nint    BLASFUNC(crotg) (float  *, float  *, float  *, float  *);\nint    BLASFUNC(zrotg) (double *, double *, double *, double *);\nint    BLASFUNC(xrotg) (double *, double *, double *, double *);\n\nint    BLASFUNC(srotmg)(float  *, float  *, float  *, float  *, float  *);\nint    BLASFUNC(drotmg)(double *, double *, double *, double *, double *);\n\nint    BLASFUNC(srotm) (int *, float  *, int *, float  *, int *, float  *);\nint    BLASFUNC(drotm) (int *, double *, int *, double *, int *, double *);\nint    BLASFUNC(qrotm) (int *, double *, int *, double *, int *, double *);\n\n/* Level 2 routines */\n\nint BLASFUNC(sger)(int *,    int *, float *,  float *, int *,\n\t\t   float *,  int *, float *,  int *);\nint BLASFUNC(dger)(int *,    int *, double *, double *, int *,\n\t\t   double *, int *, double *, int *);\nint BLASFUNC(qger)(int *,    int *, double *, double *, int *,\n\t\t   double *, int *, double *, int *);\nint BLASFUNC(cgeru)(int *,    int *, float *,  float *, int *,\n\t\t    float *,  int *, float *,  int *);\nint BLASFUNC(cgerc)(int *,    int *, float *,  float *, int *,\n\t\t    float *,  int *, float *,  int *);\nint BLASFUNC(zgeru)(int *,    int *, double *, double *, int *,\n\t\t    double *, int *, double *, int *);\nint BLASFUNC(zgerc)(int *,    int *, double *, double *, int *,\n\t\t    double *, int *, double *, int *);\nint BLASFUNC(xgeru)(int *,    int *, double *, double *, int *,\n\t\t    double *, int *, double *, int *);\nint BLASFUNC(xgerc)(int *,    int *, double *, double *, int *,\n\t\t    double *, int *, double *, int *);\n\nint BLASFUNC(sgemv)(const char *, const int *, const int *, const float  *, const float  *, const int *, const float  *, const int *, const float  *, float  *, const int *);\nint BLASFUNC(dgemv)(const char *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);\nint BLASFUNC(qgemv)(const char *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);\nint BLASFUNC(cgemv)(const char *, const int *, const int *, const float  *, const float  *, const int *, const float  *, const int *, const float  *, float  *, const int *);\nint BLASFUNC(zgemv)(const char *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);\nint BLASFUNC(xgemv)(const char *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);\n\nint BLASFUNC(strsv) (const char *, const char *, const char *, const int *, const float  *, const int *, float  *, const int *);\nint BLASFUNC(dtrsv) (const char *, const char *, const char *, const int *, const double *, const int *, double *, const int *);\nint BLASFUNC(qtrsv) (const char *, const char *, const char *, const int *, const double *, const int *, double *, const int *);\nint BLASFUNC(ctrsv) (const char *, const char *, const char *, const int *, const float  *, const int *, float  *, const int *);\nint BLASFUNC(ztrsv) (const char *, const char *, const char *, const int *, const double *, const int *, double *, const int *);\nint BLASFUNC(xtrsv) (const char *, const char *, const char *, const int *, const double *, const int *, double *, const int *);\n\nint BLASFUNC(stpsv) (char *, char *, char *, int *, float  *, float  *, int *);\nint BLASFUNC(dtpsv) (char *, char *, char *, int *, double *, double *, int *);\nint BLASFUNC(qtpsv) (char *, char *, char *, int *, double *, double *, int *);\nint BLASFUNC(ctpsv) (char *, char *, char *, int *, float  *, float  *, int *);\nint BLASFUNC(ztpsv) (char *, char *, char *, int *, double *, double *, int *);\nint BLASFUNC(xtpsv) (char *, char *, char *, int *, double *, double *, int *);\n\nint BLASFUNC(strmv) (const char *, const char *, const char *, const int *, const float  *, const int *, float  *, const int *);\nint BLASFUNC(dtrmv) (const char *, const char *, const char *, const int *, const double *, const int *, double *, const int *);\nint BLASFUNC(qtrmv) (const char *, const char *, const char *, const int *, const double *, const int *, double *, const int *);\nint BLASFUNC(ctrmv) (const char *, const char *, const char *, const int *, const float  *, const int *, float  *, const int *);\nint BLASFUNC(ztrmv) (const char *, const char *, const char *, const int *, const double *, const int *, double *, const int *);\nint BLASFUNC(xtrmv) (const char *, const char *, const char *, const int *, const double *, const int *, double *, const int *);\n\nint BLASFUNC(stpmv) (char *, char *, char *, int *, float  *, float  *, int *);\nint BLASFUNC(dtpmv) (char *, char *, char *, int *, double *, double *, int *);\nint BLASFUNC(qtpmv) (char *, char *, char *, int *, double *, double *, int *);\nint BLASFUNC(ctpmv) (char *, char *, char *, int *, float  *, float  *, int *);\nint BLASFUNC(ztpmv) (char *, char *, char *, int *, double *, double *, int *);\nint BLASFUNC(xtpmv) (char *, char *, char *, int *, double *, double *, int *);\n\nint BLASFUNC(stbmv) (char *, char *, char *, int *, int *, float  *, int *, float  *, int *);\nint BLASFUNC(dtbmv) (char *, char *, char *, int *, int *, double *, int *, double *, int *);\nint BLASFUNC(qtbmv) (char *, char *, char *, int *, int *, double *, int *, double *, int *);\nint BLASFUNC(ctbmv) (char *, char *, char *, int *, int *, float  *, int *, float  *, int *);\nint BLASFUNC(ztbmv) (char *, char *, char *, int *, int *, double *, int *, double *, int *);\nint BLASFUNC(xtbmv) (char *, char *, char *, int *, int *, double *, int *, double *, int *);\n\nint BLASFUNC(stbsv) (char *, char *, char *, int *, int *, float  *, int *, float  *, int *);\nint BLASFUNC(dtbsv) (char *, char *, char *, int *, int *, double *, int *, double *, int *);\nint BLASFUNC(qtbsv) (char *, char *, char *, int *, int *, double *, int *, double *, int *);\nint BLASFUNC(ctbsv) (char *, char *, char *, int *, int *, float  *, int *, float  *, int *);\nint BLASFUNC(ztbsv) (char *, char *, char *, int *, int *, double *, int *, double *, int *);\nint BLASFUNC(xtbsv) (char *, char *, char *, int *, int *, double *, int *, double *, int *);\n\nint BLASFUNC(ssymv) (const char *, const int *, const float  *, const float  *, const int *, const float  *, const int *, const float  *, float  *, const int *);\nint BLASFUNC(dsymv) (const char *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);\nint BLASFUNC(qsymv) (const char *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);\n\nint BLASFUNC(sspmv) (char *, int *, float  *, float *,\n\t\t     float  *, int *, float *, float *, int *);\nint BLASFUNC(dspmv) (char *, int *, double  *, double *,\n\t\t     double  *, int *, double *, double *, int *);\nint BLASFUNC(qspmv) (char *, int *, double  *, double *,\n\t\t     double  *, int *, double *, double *, int *);\n\nint BLASFUNC(ssyr) (const char *, const int *, const float   *, const float  *, const int *, float  *, const int *);\nint BLASFUNC(dsyr) (const char *, const int *, const double  *, const double *, const int *, double *, const int *);\nint BLASFUNC(qsyr) (const char *, const int *, const double  *, const double *, const int *, double *, const int *);\n\nint BLASFUNC(ssyr2) (const char *, const int *, const float   *, const float  *, const int *, const float  *, const int *, float  *, const int *);\nint BLASFUNC(dsyr2) (const char *, const int *, const double  *, const double *, const int *, const double *, const int *, double *, const int *);\nint BLASFUNC(qsyr2) (const char *, const int *, const double  *, const double *, const int *, const double *, const int *, double *, const int *);\nint BLASFUNC(csyr2) (const char *, const int *, const float   *, const float  *, const int *, const float  *, const int *, float  *, const int *);\nint BLASFUNC(zsyr2) (const char *, const int *, const double  *, const double *, const int *, const double *, const int *, double *, const int *);\nint BLASFUNC(xsyr2) (const char *, const int *, const double  *, const double *, const int *, const double *, const int *, double *, const int *);\n\nint BLASFUNC(sspr) (char *, int *, float   *, float  *, int *,\n\t\t    float  *);\nint BLASFUNC(dspr) (char *, int *, double  *, double *, int *,\n\t\t    double *);\nint BLASFUNC(qspr) (char *, int *, double  *, double *, int *,\n\t\t    double *);\n\nint BLASFUNC(sspr2) (char *, int *, float   *,\n\t\t     float  *, int *, float  *, int *, float  *);\nint BLASFUNC(dspr2) (char *, int *, double  *,\n\t\t     double *, int *, double *, int *, double *);\nint BLASFUNC(qspr2) (char *, int *, double  *,\n\t\t     double *, int *, double *, int *, double *);\nint BLASFUNC(cspr2) (char *, int *, float   *,\n\t\t     float  *, int *, float  *, int *, float  *);\nint BLASFUNC(zspr2) (char *, int *, double  *,\n\t\t     double *, int *, double *, int *, double *);\nint BLASFUNC(xspr2) (char *, int *, double  *,\n\t\t     double *, int *, double *, int *, double *);\n\nint BLASFUNC(cher) (char *, int *, float   *, float  *, int *,\n\t\t    float  *, int *);\nint BLASFUNC(zher) (char *, int *, double  *, double *, int *,\n\t\t    double *, int *);\nint BLASFUNC(xher) (char *, int *, double  *, double *, int *,\n\t\t    double *, int *);\n\nint BLASFUNC(chpr) (char *, int *, float   *, float  *, int *, float  *);\nint BLASFUNC(zhpr) (char *, int *, double  *, double *, int *, double *);\nint BLASFUNC(xhpr) (char *, int *, double  *, double *, int *, double *);\n\nint BLASFUNC(cher2) (char *, int *, float   *,\n\t\t     float  *, int *, float  *, int *, float  *, int *);\nint BLASFUNC(zher2) (char *, int *, double  *,\n\t\t     double *, int *, double *, int *, double *, int *);\nint BLASFUNC(xher2) (char *, int *, double  *,\n\t\t     double *, int *, double *, int *, double *, int *);\n\nint BLASFUNC(chpr2) (char *, int *, float   *,\n\t\t     float  *, int *, float  *, int *, float  *);\nint BLASFUNC(zhpr2) (char *, int *, double  *,\n\t\t     double *, int *, double *, int *, double *);\nint BLASFUNC(xhpr2) (char *, int *, double  *,\n\t\t     double *, int *, double *, int *, double *);\n\nint BLASFUNC(chemv) (const char *, const int *, const float  *, const float  *, const int *, const float  *, const int *, const float  *, float  *, const int *);\nint BLASFUNC(zhemv) (const char *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);\nint BLASFUNC(xhemv) (const char *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);\n\nint BLASFUNC(chpmv) (char *, int *, float  *, float *,\n\t\t     float  *, int *, float *, float *, int *);\nint BLASFUNC(zhpmv) (char *, int *, double  *, double *,\n\t\t     double  *, int *, double *, double *, int *);\nint BLASFUNC(xhpmv) (char *, int *, double  *, double *,\n\t\t     double  *, int *, double *, double *, int *);\n\nint BLASFUNC(snorm)(char *, int *, int *, float  *, int *);\nint BLASFUNC(dnorm)(char *, int *, int *, double *, int *);\nint BLASFUNC(cnorm)(char *, int *, int *, float  *, int *);\nint BLASFUNC(znorm)(char *, int *, int *, double *, int *);\n\nint BLASFUNC(sgbmv)(char *, int *, int *, int *, int *, float  *, float  *, int *,\n\t\t    float  *, int *, float  *, float  *, int *);\nint BLASFUNC(dgbmv)(char *, int *, int *, int *, int *, double *, double *, int *,\n\t\t    double *, int *, double *, double *, int *);\nint BLASFUNC(qgbmv)(char *, int *, int *, int *, int *, double *, double *, int *,\n\t\t    double *, int *, double *, double *, int *);\nint BLASFUNC(cgbmv)(char *, int *, int *, int *, int *, float  *, float  *, int *,\n\t\t    float  *, int *, float  *, float  *, int *);\nint BLASFUNC(zgbmv)(char *, int *, int *, int *, int *, double *, double *, int *,\n\t\t    double *, int *, double *, double *, int *);\nint BLASFUNC(xgbmv)(char *, int *, int *, int *, int *, double *, double *, int *,\n\t\t    double *, int *, double *, double *, int *);\n\nint BLASFUNC(ssbmv)(char *, int *, int *, float  *, float  *, int *,\n\t\t    float  *, int *, float  *, float  *, int *);\nint BLASFUNC(dsbmv)(char *, int *, int *, double *, double *, int *,\n\t\t    double *, int *, double *, double *, int *);\nint BLASFUNC(qsbmv)(char *, int *, int *, double *, double *, int *,\n\t\t    double *, int *, double *, double *, int *);\nint BLASFUNC(csbmv)(char *, int *, int *, float  *, float  *, int *,\n\t\t    float  *, int *, float  *, float  *, int *);\nint BLASFUNC(zsbmv)(char *, int *, int *, double *, double *, int *,\n\t\t    double *, int *, double *, double *, int *);\nint BLASFUNC(xsbmv)(char *, int *, int *, double *, double *, int *,\n\t\t    double *, int *, double *, double *, int *);\n\nint BLASFUNC(chbmv)(char *, int *, int *, float  *, float  *, int *,\n\t\t    float  *, int *, float  *, float  *, int *);\nint BLASFUNC(zhbmv)(char *, int *, int *, double *, double *, int *,\n\t\t    double *, int *, double *, double *, int *);\nint BLASFUNC(xhbmv)(char *, int *, int *, double *, double *, int *,\n\t\t    double *, int *, double *, double *, int *);\n\n/* Level 3 routines */\n\nint BLASFUNC(sgemm)(const char *, const char *, const int *, const int *, const int *, const float  *, const float  *, const int *, const float  *, const int *, const float  *, float  *, const int *);\nint BLASFUNC(dgemm)(const char *, const char *, const int *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);\nint BLASFUNC(qgemm)(const char *, const char *, const int *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);\nint BLASFUNC(cgemm)(const char *, const char *, const int *, const int *, const int *, const float  *, const float  *, const int *, const float  *, const int *, const float  *, float  *, const int *);\nint BLASFUNC(zgemm)(const char *, const char *, const int *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);\nint BLASFUNC(xgemm)(const char *, const char *, const int *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);\n\nint BLASFUNC(cgemm3m)(char *, char *, int *, int *, int *, float *,\n\t   float  *, int *, float  *, int *, float  *, float  *, int *);\nint BLASFUNC(zgemm3m)(char *, char *, int *, int *, int *, double *,\n\t   double *, int *, double *, int *, double *, double *, int *);\nint BLASFUNC(xgemm3m)(char *, char *, int *, int *, int *, double *,\n\t   double *, int *, double *, int *, double *, double *, int *);\n\nint BLASFUNC(sge2mm)(char *, char *, char *, int *, int *,\n\t\t     float *, float  *, int *, float  *, int *,\n\t\t     float *, float  *, int *);\nint BLASFUNC(dge2mm)(char *, char *, char *, int *, int *,\n\t\t     double *, double  *, int *, double  *, int *,\n\t\t     double *, double  *, int *);\nint BLASFUNC(cge2mm)(char *, char *, char *, int *, int *,\n\t\t     float *, float  *, int *, float  *, int *,\n\t\t     float *, float  *, int *);\nint BLASFUNC(zge2mm)(char *, char *, char *, int *, int *,\n\t\t     double *, double  *, int *, double  *, int *,\n\t\t     double *, double  *, int *);\n\nint BLASFUNC(strsm)(const char *, const char *, const char *, const char *, const int *, const int *, const float *,  const float *,  const int *, float *,  const int *);\nint BLASFUNC(dtrsm)(const char *, const char *, const char *, const char *, const int *, const int *, const double *, const double *, const int *, double *, const int *);\nint BLASFUNC(qtrsm)(const char *, const char *, const char *, const char *, const int *, const int *, const double *, const double *, const int *, double *, const int *);\nint BLASFUNC(ctrsm)(const char *, const char *, const char *, const char *, const int *, const int *, const float *,  const float *,  const int *, float *,  const int *);\nint BLASFUNC(ztrsm)(const char *, const char *, const char *, const char *, const int *, const int *, const double *, const double *, const int *, double *, const int *);\nint BLASFUNC(xtrsm)(const char *, const char *, const char *, const char *, const int *, const int *, const double *, const double *, const int *, double *, const int *);\n\nint BLASFUNC(strmm)(const char *, const char *, const char *, const char *, const int *, const int *, const float *,  const float *,  const int *, float *,  const int *);\nint BLASFUNC(dtrmm)(const char *, const char *, const char *, const char *, const int *, const int *, const double *, const double *, const int *, double *, const int *);\nint BLASFUNC(qtrmm)(const char *, const char *, const char *, const char *, const int *, const int *, const double *, const double *, const int *, double *, const int *);\nint BLASFUNC(ctrmm)(const char *, const char *, const char *, const char *, const int *, const int *, const float *,  const float *,  const int *, float *,  const int *);\nint BLASFUNC(ztrmm)(const char *, const char *, const char *, const char *, const int *, const int *, const double *, const double *, const int *, double *, const int *);\nint BLASFUNC(xtrmm)(const char *, const char *, const char *, const char *, const int *, const int *, const double *, const double *, const int *, double *, const int *);\n\nint BLASFUNC(ssymm)(const char *, const char *, const int *, const int *, const float  *, const float  *, const int *, const float  *, const int *, const float  *, float  *, const int *);\nint BLASFUNC(dsymm)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);\nint BLASFUNC(qsymm)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);\nint BLASFUNC(csymm)(const char *, const char *, const int *, const int *, const float  *, const float  *, const int *, const float  *, const int *, const float  *, float  *, const int *);\nint BLASFUNC(zsymm)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);\nint BLASFUNC(xsymm)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);\n\nint BLASFUNC(csymm3m)(char *, char *, int *, int *, float  *, float  *, int *, float  *, int *, float  *, float  *, int *);\nint BLASFUNC(zsymm3m)(char *, char *, int *, int *, double *, double *, int *, double *, int *, double *, double *, int *);\nint BLASFUNC(xsymm3m)(char *, char *, int *, int *, double *, double *, int *, double *, int *, double *, double *, int *);\n\nint BLASFUNC(ssyrk)(const char *, const char *, const int *, const int *, const float  *, const float  *, const int *, const float  *, float  *, const int *);\nint BLASFUNC(dsyrk)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, double *, const int *);\nint BLASFUNC(qsyrk)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, double *, const int *);\nint BLASFUNC(csyrk)(const char *, const char *, const int *, const int *, const float  *, const float  *, const int *, const float  *, float  *, const int *);\nint BLASFUNC(zsyrk)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, double *, const int *);\nint BLASFUNC(xsyrk)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, double *, const int *);\n\nint BLASFUNC(ssyr2k)(const char *, const char *, const int *, const int *, const float  *, const float  *, const int *, const float *, const int *, const float  *, float  *, const int *);\nint BLASFUNC(dsyr2k)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double*, const int *, const double *, double *, const int *);\nint BLASFUNC(qsyr2k)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double*, const int *, const double *, double *, const int *);\nint BLASFUNC(csyr2k)(const char *, const char *, const int *, const int *, const float  *, const float  *, const int *, const float *, const int *, const float  *, float  *, const int *);\nint BLASFUNC(zsyr2k)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double*, const int *, const double *, double *, const int *);\nint BLASFUNC(xsyr2k)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double*, const int *, const double *, double *, const int *);\n\nint BLASFUNC(chemm)(const char *, const char *, const int *, const int *, const float  *, const float  *, const int *, const float  *, const int *, const float  *, float  *, const int *);\nint BLASFUNC(zhemm)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);\nint BLASFUNC(xhemm)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);\n\nint BLASFUNC(chemm3m)(char *, char *, int *, int *, float  *, float  *, int *,\n\t   float  *, int *, float  *, float  *, int *);\nint BLASFUNC(zhemm3m)(char *, char *, int *, int *, double *, double *, int *,\n\t   double *, int *, double *, double *, int *);\nint BLASFUNC(xhemm3m)(char *, char *, int *, int *, double *, double *, int *,\n\t   double *, int *, double *, double *, int *);\n\nint BLASFUNC(cherk)(const char *, const char *, const int *, const int *, const float  *, const float  *, const int *, const float  *, float  *, const int *);\nint BLASFUNC(zherk)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, double *, const int *);\nint BLASFUNC(xherk)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, double *, const int *);\n\nint BLASFUNC(cher2k)(const char *, const char *, const int *, const int *, const float  *, const float  *, const int *, const float  *, const int *, const float  *, float  *, const int *);\nint BLASFUNC(zher2k)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);\nint BLASFUNC(xher2k)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);\nint BLASFUNC(cher2m)(const char *, const char *, const char *, const int *, const int *, const float  *, const float  *, const int *, const float *, const int *, const float  *, float  *, const int *);\nint BLASFUNC(zher2m)(const char *, const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double*, const int *, const double *, double *, const int *);\nint BLASFUNC(xher2m)(const char *, const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double*, const int *, const double *, double *, const int *);\n\n\n#ifdef __cplusplus\n}\n#endif\n\n#endif\n"
  },
  {
    "path": "include/eigen3/Eigen/src/misc/lapack.h",
    "content": "#ifndef LAPACK_H\n#define LAPACK_H\n\n#include \"blas.h\"\n\n#ifdef __cplusplus\nextern \"C\"\n{\n#endif\n\nint BLASFUNC(csymv) (const char *, const int *, const float  *, const float  *, const int *, const float  *, const int *, const float  *, float  *, const int *);\nint BLASFUNC(zsymv) (const char *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);\nint BLASFUNC(xsymv) (const char *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);\n\n\nint BLASFUNC(cspmv) (char *, int *, float  *, float *,\n         float  *, int *, float *, float *, int *);\nint BLASFUNC(zspmv) (char *, int *, double  *, double *,\n         double  *, int *, double *, double *, int *);\nint BLASFUNC(xspmv) (char *, int *, double  *, double *,\n         double  *, int *, double *, double *, int *);\n\nint BLASFUNC(csyr) (char *, int *, float   *, float  *, int *,\n        float  *, int *);\nint BLASFUNC(zsyr) (char *, int *, double  *, double *, int *,\n        double *, int *);\nint BLASFUNC(xsyr) (char *, int *, double  *, double *, int *,\n        double *, int *);\n\nint BLASFUNC(cspr) (char *, int *, float   *, float  *, int *,\n        float  *);\nint BLASFUNC(zspr) (char *, int *, double  *, double *, int *,\n        double *);\nint BLASFUNC(xspr) (char *, int *, double  *, double *, int *,\n        double *);\n\nint BLASFUNC(sgemt)(char *, int *, int *, float  *, float  *, int *,\n        float  *, int *);\nint BLASFUNC(dgemt)(char *, int *, int *, double *, double *, int *,\n        double *, int *);\nint BLASFUNC(cgemt)(char *, int *, int *, float  *, float  *, int *,\n        float  *, int *);\nint BLASFUNC(zgemt)(char *, int *, int *, double *, double *, int *,\n        double *, int *);\n\nint BLASFUNC(sgema)(char *, char *, int *, int *, float  *,\n        float  *, int *, float *, float  *, int *, float *, int *);\nint BLASFUNC(dgema)(char *, char *, int *, int *, double *,\n        double *, int *, double*, double *, int *, double*, int *);\nint BLASFUNC(cgema)(char *, char *, int *, int *, float  *,\n        float  *, int *, float *, float  *, int *, float *, int *);\nint BLASFUNC(zgema)(char *, char *, int *, int *, double *,\n        double *, int *, double*, double *, int *, double*, int *);\n\nint BLASFUNC(sgems)(char *, char *, int *, int *, float  *,\n        float  *, int *, float *, float  *, int *, float *, int *);\nint BLASFUNC(dgems)(char *, char *, int *, int *, double *,\n        double *, int *, double*, double *, int *, double*, int *);\nint BLASFUNC(cgems)(char *, char *, int *, int *, float  *,\n        float  *, int *, float *, float  *, int *, float *, int *);\nint BLASFUNC(zgems)(char *, char *, int *, int *, double *,\n        double *, int *, double*, double *, int *, double*, int *);\n\nint BLASFUNC(sgetf2)(int *, int *, float  *, int *, int *, int *);\nint BLASFUNC(dgetf2)(int *, int *, double *, int *, int *, int *);\nint BLASFUNC(qgetf2)(int *, int *, double *, int *, int *, int *);\nint BLASFUNC(cgetf2)(int *, int *, float  *, int *, int *, int *);\nint BLASFUNC(zgetf2)(int *, int *, double *, int *, int *, int *);\nint BLASFUNC(xgetf2)(int *, int *, double *, int *, int *, int *);\n\nint BLASFUNC(sgetrf)(int *, int *, float  *, int *, int *, int *);\nint BLASFUNC(dgetrf)(int *, int *, double *, int *, int *, int *);\nint BLASFUNC(qgetrf)(int *, int *, double *, int *, int *, int *);\nint BLASFUNC(cgetrf)(int *, int *, float  *, int *, int *, int *);\nint BLASFUNC(zgetrf)(int *, int *, double *, int *, int *, int *);\nint BLASFUNC(xgetrf)(int *, int *, double *, int *, int *, int *);\n\nint BLASFUNC(slaswp)(int *, float  *, int *, int *, int *, int *, int *);\nint BLASFUNC(dlaswp)(int *, double *, int *, int *, int *, int *, int *);\nint BLASFUNC(qlaswp)(int *, double *, int *, int *, int *, int *, int *);\nint BLASFUNC(claswp)(int *, float  *, int *, int *, int *, int *, int *);\nint BLASFUNC(zlaswp)(int *, double *, int *, int *, int *, int *, int *);\nint BLASFUNC(xlaswp)(int *, double *, int *, int *, int *, int *, int *);\n\nint BLASFUNC(sgetrs)(char *, int *, int *, float  *, int *, int *, float  *, int *, int *);\nint BLASFUNC(dgetrs)(char *, int *, int *, double *, int *, int *, double *, int *, int *);\nint BLASFUNC(qgetrs)(char *, int *, int *, double *, int *, int *, double *, int *, int *);\nint BLASFUNC(cgetrs)(char *, int *, int *, float  *, int *, int *, float  *, int *, int *);\nint BLASFUNC(zgetrs)(char *, int *, int *, double *, int *, int *, double *, int *, int *);\nint BLASFUNC(xgetrs)(char *, int *, int *, double *, int *, int *, double *, int *, int *);\n\nint BLASFUNC(sgesv)(int *, int *, float  *, int *, int *, float *, int *, int *);\nint BLASFUNC(dgesv)(int *, int *, double *, int *, int *, double*, int *, int *);\nint BLASFUNC(qgesv)(int *, int *, double *, int *, int *, double*, int *, int *);\nint BLASFUNC(cgesv)(int *, int *, float  *, int *, int *, float *, int *, int *);\nint BLASFUNC(zgesv)(int *, int *, double *, int *, int *, double*, int *, int *);\nint BLASFUNC(xgesv)(int *, int *, double *, int *, int *, double*, int *, int *);\n\nint BLASFUNC(spotf2)(char *, int *, float  *, int *, int *);\nint BLASFUNC(dpotf2)(char *, int *, double *, int *, int *);\nint BLASFUNC(qpotf2)(char *, int *, double *, int *, int *);\nint BLASFUNC(cpotf2)(char *, int *, float  *, int *, int *);\nint BLASFUNC(zpotf2)(char *, int *, double *, int *, int *);\nint BLASFUNC(xpotf2)(char *, int *, double *, int *, int *);\n\nint BLASFUNC(spotrf)(char *, int *, float  *, int *, int *);\nint BLASFUNC(dpotrf)(char *, int *, double *, int *, int *);\nint BLASFUNC(qpotrf)(char *, int *, double *, int *, int *);\nint BLASFUNC(cpotrf)(char *, int *, float  *, int *, int *);\nint BLASFUNC(zpotrf)(char *, int *, double *, int *, int *);\nint BLASFUNC(xpotrf)(char *, int *, double *, int *, int *);\n\nint BLASFUNC(slauu2)(char *, int *, float  *, int *, int *);\nint BLASFUNC(dlauu2)(char *, int *, double *, int *, int *);\nint BLASFUNC(qlauu2)(char *, int *, double *, int *, int *);\nint BLASFUNC(clauu2)(char *, int *, float  *, int *, int *);\nint BLASFUNC(zlauu2)(char *, int *, double *, int *, int *);\nint BLASFUNC(xlauu2)(char *, int *, double *, int *, int *);\n\nint BLASFUNC(slauum)(char *, int *, float  *, int *, int *);\nint BLASFUNC(dlauum)(char *, int *, double *, int *, int *);\nint BLASFUNC(qlauum)(char *, int *, double *, int *, int *);\nint BLASFUNC(clauum)(char *, int *, float  *, int *, int *);\nint BLASFUNC(zlauum)(char *, int *, double *, int *, int *);\nint BLASFUNC(xlauum)(char *, int *, double *, int *, int *);\n\nint BLASFUNC(strti2)(char *, char *, int *, float  *, int *, int *);\nint BLASFUNC(dtrti2)(char *, char *, int *, double *, int *, int *);\nint BLASFUNC(qtrti2)(char *, char *, int *, double *, int *, int *);\nint BLASFUNC(ctrti2)(char *, char *, int *, float  *, int *, int *);\nint BLASFUNC(ztrti2)(char *, char *, int *, double *, int *, int *);\nint BLASFUNC(xtrti2)(char *, char *, int *, double *, int *, int *);\n\nint BLASFUNC(strtri)(char *, char *, int *, float  *, int *, int *);\nint BLASFUNC(dtrtri)(char *, char *, int *, double *, int *, int *);\nint BLASFUNC(qtrtri)(char *, char *, int *, double *, int *, int *);\nint BLASFUNC(ctrtri)(char *, char *, int *, float  *, int *, int *);\nint BLASFUNC(ztrtri)(char *, char *, int *, double *, int *, int *);\nint BLASFUNC(xtrtri)(char *, char *, int *, double *, int *, int *);\n\nint BLASFUNC(spotri)(char *, int *, float  *, int *, int *);\nint BLASFUNC(dpotri)(char *, int *, double *, int *, int *);\nint BLASFUNC(qpotri)(char *, int *, double *, int *, int *);\nint BLASFUNC(cpotri)(char *, int *, float  *, int *, int *);\nint BLASFUNC(zpotri)(char *, int *, double *, int *, int *);\nint BLASFUNC(xpotri)(char *, int *, double *, int *, int *);\n\n#ifdef __cplusplus\n}\n#endif\n\n#endif\n"
  },
  {
    "path": "include/eigen3/Eigen/src/misc/lapacke.h",
    "content": "/*****************************************************************************\n  Copyright (c) 2010, Intel Corp.\n  All rights reserved.\n\n  Redistribution and use in source and binary forms, with or without\n  modification, are permitted provided that the following conditions are met:\n\n    * Redistributions of source code must retain the above copyright notice,\n      this list of conditions and the following disclaimer.\n    * Redistributions in binary form must reproduce the above copyright\n      notice, this list of conditions and the following disclaimer in the\n      documentation and/or other materials provided with the distribution.\n    * Neither the name of Intel Corporation nor the names of its contributors\n      may be used to endorse or promote products derived from this software\n      without specific prior written permission.\n\n  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\"\n  AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE\n  IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE\n  ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE\n  LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR\n  CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF\n  SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS\n  INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN\n  CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)\n  ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF\n  THE POSSIBILITY OF SUCH DAMAGE.\n******************************************************************************\n* Contents: Native C interface to LAPACK\n* Author: Intel Corporation\n* Generated November, 2011\n*****************************************************************************/\n\n#ifndef _MKL_LAPACKE_H_\n\n#ifndef _LAPACKE_H_\n#define _LAPACKE_H_\n\n/*\n*  Turn on HAVE_LAPACK_CONFIG_H to redefine C-LAPACK datatypes\n*/\n#ifdef HAVE_LAPACK_CONFIG_H\n#include \"lapacke_config.h\"\n#endif\n\n#ifdef __cplusplus\nextern \"C\" {\n#endif /* __cplusplus */\n\n#include <stdlib.h>\n\n#ifndef lapack_int\n#define lapack_int     int\n#endif\n\n#ifndef lapack_logical\n#define lapack_logical lapack_int\n#endif\n\n/* Complex types are structures equivalent to the\n* Fortran complex types COMPLEX(4) and COMPLEX(8).\n*\n* One can also redefine the types with his own types\n* for example by including in the code definitions like\n*\n* #define lapack_complex_float std::complex<float>\n* #define lapack_complex_double std::complex<double>\n*\n* or define these types in the command line:\n*\n* -Dlapack_complex_float=\"std::complex<float>\"\n* -Dlapack_complex_double=\"std::complex<double>\"\n*/\n\n#ifndef LAPACK_COMPLEX_CUSTOM\n\n/* Complex type (single precision) */\n#ifndef lapack_complex_float\n#include <complex.h>\n#define lapack_complex_float    float _Complex\n#endif\n\n#ifndef lapack_complex_float_real\n#define lapack_complex_float_real(z)       (creal(z))\n#endif\n\n#ifndef lapack_complex_float_imag\n#define lapack_complex_float_imag(z)       (cimag(z))\n#endif\n\nlapack_complex_float lapack_make_complex_float( float re, float im );\n\n/* Complex type (double precision) */\n#ifndef lapack_complex_double\n#include <complex.h>\n#define lapack_complex_double   double _Complex\n#endif\n\n#ifndef lapack_complex_double_real\n#define lapack_complex_double_real(z)      (creal(z))\n#endif\n\n#ifndef lapack_complex_double_imag\n#define lapack_complex_double_imag(z)       (cimag(z))\n#endif\n\nlapack_complex_double lapack_make_complex_double( double re, double im );\n\n#endif\n\n#ifndef LAPACKE_malloc\n#define LAPACKE_malloc( size ) malloc( size )\n#endif\n#ifndef LAPACKE_free\n#define LAPACKE_free( p )      free( p )\n#endif\n\n#define LAPACK_C2INT( x ) (lapack_int)(*((float*)&x ))\n#define LAPACK_Z2INT( x ) (lapack_int)(*((double*)&x ))\n\n#define LAPACK_ROW_MAJOR               101\n#define LAPACK_COL_MAJOR               102\n\n#define LAPACK_WORK_MEMORY_ERROR       -1010\n#define LAPACK_TRANSPOSE_MEMORY_ERROR  -1011\n\n/* Callback logical functions of one, two, or three arguments are used\n*  to select eigenvalues to sort to the top left of the Schur form.\n*  The value is selected if function returns TRUE (non-zero). */\n\ntypedef lapack_logical (*LAPACK_S_SELECT2) ( const float*, const float* );\ntypedef lapack_logical (*LAPACK_S_SELECT3)\n    ( const float*, const float*, const float* );\ntypedef lapack_logical (*LAPACK_D_SELECT2) ( const double*, const double* );\ntypedef lapack_logical (*LAPACK_D_SELECT3)\n    ( const double*, const double*, const double* );\n\ntypedef lapack_logical (*LAPACK_C_SELECT1) ( const lapack_complex_float* );\ntypedef lapack_logical (*LAPACK_C_SELECT2)\n    ( const lapack_complex_float*, const lapack_complex_float* );\ntypedef lapack_logical (*LAPACK_Z_SELECT1) ( const lapack_complex_double* );\ntypedef lapack_logical (*LAPACK_Z_SELECT2)\n    ( const lapack_complex_double*, const lapack_complex_double* );\n\n#include \"lapacke_mangling.h\"\n\n#define LAPACK_lsame LAPACK_GLOBAL(lsame,LSAME)\nlapack_logical LAPACK_lsame( char* ca,  char* cb,\n                              lapack_int lca, lapack_int lcb );\n\n/* C-LAPACK function prototypes */\n\nlapack_int LAPACKE_sbdsdc( int matrix_order, char uplo, char compq,\n                           lapack_int n, float* d, float* e, float* u,\n                           lapack_int ldu, float* vt, lapack_int ldvt, float* q,\n                           lapack_int* iq );\nlapack_int LAPACKE_dbdsdc( int matrix_order, char uplo, char compq,\n                           lapack_int n, double* d, double* e, double* u,\n                           lapack_int ldu, double* vt, lapack_int ldvt,\n                           double* q, lapack_int* iq );\n\nlapack_int LAPACKE_sbdsqr( int matrix_order, char uplo, lapack_int n,\n                           lapack_int ncvt, lapack_int nru, lapack_int ncc,\n                           float* d, float* e, float* vt, lapack_int ldvt,\n                           float* u, lapack_int ldu, float* c, lapack_int ldc );\nlapack_int LAPACKE_dbdsqr( int matrix_order, char uplo, lapack_int n,\n                           lapack_int ncvt, lapack_int nru, lapack_int ncc,\n                           double* d, double* e, double* vt, lapack_int ldvt,\n                           double* u, lapack_int ldu, double* c,\n                           lapack_int ldc );\nlapack_int LAPACKE_cbdsqr( int matrix_order, char uplo, lapack_int n,\n                           lapack_int ncvt, lapack_int nru, lapack_int ncc,\n                           float* d, float* e, lapack_complex_float* vt,\n                           lapack_int ldvt, lapack_complex_float* u,\n                           lapack_int ldu, lapack_complex_float* c,\n                           lapack_int ldc );\nlapack_int LAPACKE_zbdsqr( int matrix_order, char uplo, lapack_int n,\n                           lapack_int ncvt, lapack_int nru, lapack_int ncc,\n                           double* d, double* e, lapack_complex_double* vt,\n                           lapack_int ldvt, lapack_complex_double* u,\n                           lapack_int ldu, lapack_complex_double* c,\n                           lapack_int ldc );\n\nlapack_int LAPACKE_sdisna( char job, lapack_int m, lapack_int n, const float* d,\n                           float* sep );\nlapack_int LAPACKE_ddisna( char job, lapack_int m, lapack_int n,\n                           const double* d, double* sep );\n\nlapack_int LAPACKE_sgbbrd( int matrix_order, char vect, lapack_int m,\n                           lapack_int n, lapack_int ncc, lapack_int kl,\n                           lapack_int ku, float* ab, lapack_int ldab, float* d,\n                           float* e, float* q, lapack_int ldq, float* pt,\n                           lapack_int ldpt, float* c, lapack_int ldc );\nlapack_int LAPACKE_dgbbrd( int matrix_order, char vect, lapack_int m,\n                           lapack_int n, lapack_int ncc, lapack_int kl,\n                           lapack_int ku, double* ab, lapack_int ldab,\n                           double* d, double* e, double* q, lapack_int ldq,\n                           double* pt, lapack_int ldpt, double* c,\n                           lapack_int ldc );\nlapack_int LAPACKE_cgbbrd( int matrix_order, char vect, lapack_int m,\n                           lapack_int n, lapack_int ncc, lapack_int kl,\n                           lapack_int ku, lapack_complex_float* ab,\n                           lapack_int ldab, float* d, float* e,\n                           lapack_complex_float* q, lapack_int ldq,\n                           lapack_complex_float* pt, lapack_int ldpt,\n                           lapack_complex_float* c, lapack_int ldc );\nlapack_int LAPACKE_zgbbrd( int matrix_order, char vect, lapack_int m,\n                           lapack_int n, lapack_int ncc, lapack_int kl,\n                           lapack_int ku, lapack_complex_double* ab,\n                           lapack_int ldab, double* d, double* e,\n                           lapack_complex_double* q, lapack_int ldq,\n                           lapack_complex_double* pt, lapack_int ldpt,\n                           lapack_complex_double* c, lapack_int ldc );\n\nlapack_int LAPACKE_sgbcon( int matrix_order, char norm, lapack_int n,\n                           lapack_int kl, lapack_int ku, const float* ab,\n                           lapack_int ldab, const lapack_int* ipiv, float anorm,\n                           float* rcond );\nlapack_int LAPACKE_dgbcon( int matrix_order, char norm, lapack_int n,\n                           lapack_int kl, lapack_int ku, const double* ab,\n                           lapack_int ldab, const lapack_int* ipiv,\n                           double anorm, double* rcond );\nlapack_int LAPACKE_cgbcon( int matrix_order, char norm, lapack_int n,\n                           lapack_int kl, lapack_int ku,\n                           const lapack_complex_float* ab, lapack_int ldab,\n                           const lapack_int* ipiv, float anorm, float* rcond );\nlapack_int LAPACKE_zgbcon( int matrix_order, char norm, lapack_int n,\n                           lapack_int kl, lapack_int ku,\n                           const lapack_complex_double* ab, lapack_int ldab,\n                           const lapack_int* ipiv, double anorm,\n                           double* rcond );\n\nlapack_int LAPACKE_sgbequ( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int kl, lapack_int ku, const float* ab,\n                           lapack_int ldab, float* r, float* c, float* rowcnd,\n                           float* colcnd, float* amax );\nlapack_int LAPACKE_dgbequ( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int kl, lapack_int ku, const double* ab,\n                           lapack_int ldab, double* r, double* c,\n                           double* rowcnd, double* colcnd, double* amax );\nlapack_int LAPACKE_cgbequ( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int kl, lapack_int ku,\n                           const lapack_complex_float* ab, lapack_int ldab,\n                           float* r, float* c, float* rowcnd, float* colcnd,\n                           float* amax );\nlapack_int LAPACKE_zgbequ( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int kl, lapack_int ku,\n                           const lapack_complex_double* ab, lapack_int ldab,\n                           double* r, double* c, double* rowcnd, double* colcnd,\n                           double* amax );\n\nlapack_int LAPACKE_sgbequb( int matrix_order, lapack_int m, lapack_int n,\n                            lapack_int kl, lapack_int ku, const float* ab,\n                            lapack_int ldab, float* r, float* c, float* rowcnd,\n                            float* colcnd, float* amax );\nlapack_int LAPACKE_dgbequb( int matrix_order, lapack_int m, lapack_int n,\n                            lapack_int kl, lapack_int ku, const double* ab,\n                            lapack_int ldab, double* r, double* c,\n                            double* rowcnd, double* colcnd, double* amax );\nlapack_int LAPACKE_cgbequb( int matrix_order, lapack_int m, lapack_int n,\n                            lapack_int kl, lapack_int ku,\n                            const lapack_complex_float* ab, lapack_int ldab,\n                            float* r, float* c, float* rowcnd, float* colcnd,\n                            float* amax );\nlapack_int LAPACKE_zgbequb( int matrix_order, lapack_int m, lapack_int n,\n                            lapack_int kl, lapack_int ku,\n                            const lapack_complex_double* ab, lapack_int ldab,\n                            double* r, double* c, double* rowcnd,\n                            double* colcnd, double* amax );\n\nlapack_int LAPACKE_sgbrfs( int matrix_order, char trans, lapack_int n,\n                           lapack_int kl, lapack_int ku, lapack_int nrhs,\n                           const float* ab, lapack_int ldab, const float* afb,\n                           lapack_int ldafb, const lapack_int* ipiv,\n                           const float* b, lapack_int ldb, float* x,\n                           lapack_int ldx, float* ferr, float* berr );\nlapack_int LAPACKE_dgbrfs( int matrix_order, char trans, lapack_int n,\n                           lapack_int kl, lapack_int ku, lapack_int nrhs,\n                           const double* ab, lapack_int ldab, const double* afb,\n                           lapack_int ldafb, const lapack_int* ipiv,\n                           const double* b, lapack_int ldb, double* x,\n                           lapack_int ldx, double* ferr, double* berr );\nlapack_int LAPACKE_cgbrfs( int matrix_order, char trans, lapack_int n,\n                           lapack_int kl, lapack_int ku, lapack_int nrhs,\n                           const lapack_complex_float* ab, lapack_int ldab,\n                           const lapack_complex_float* afb, lapack_int ldafb,\n                           const lapack_int* ipiv,\n                           const lapack_complex_float* b, lapack_int ldb,\n                           lapack_complex_float* x, lapack_int ldx, float* ferr,\n                           float* berr );\nlapack_int LAPACKE_zgbrfs( int matrix_order, char trans, lapack_int n,\n                           lapack_int kl, lapack_int ku, lapack_int nrhs,\n                           const lapack_complex_double* ab, lapack_int ldab,\n                           const lapack_complex_double* afb, lapack_int ldafb,\n                           const lapack_int* ipiv,\n                           const lapack_complex_double* b, lapack_int ldb,\n                           lapack_complex_double* x, lapack_int ldx,\n                           double* ferr, double* berr );\n\nlapack_int LAPACKE_sgbrfsx( int matrix_order, char trans, char equed,\n                            lapack_int n, lapack_int kl, lapack_int ku,\n                            lapack_int nrhs, const float* ab, lapack_int ldab,\n                            const float* afb, lapack_int ldafb,\n                            const lapack_int* ipiv, const float* r,\n                            const float* c, const float* b, lapack_int ldb,\n                            float* x, lapack_int ldx, float* rcond, float* berr,\n                            lapack_int n_err_bnds, float* err_bnds_norm,\n                            float* err_bnds_comp, lapack_int nparams,\n                            float* params );\nlapack_int LAPACKE_dgbrfsx( int matrix_order, char trans, char equed,\n                            lapack_int n, lapack_int kl, lapack_int ku,\n                            lapack_int nrhs, const double* ab, lapack_int ldab,\n                            const double* afb, lapack_int ldafb,\n                            const lapack_int* ipiv, const double* r,\n                            const double* c, const double* b, lapack_int ldb,\n                            double* x, lapack_int ldx, double* rcond,\n                            double* berr, lapack_int n_err_bnds,\n                            double* err_bnds_norm, double* err_bnds_comp,\n                            lapack_int nparams, double* params );\nlapack_int LAPACKE_cgbrfsx( int matrix_order, char trans, char equed,\n                            lapack_int n, lapack_int kl, lapack_int ku,\n                            lapack_int nrhs, const lapack_complex_float* ab,\n                            lapack_int ldab, const lapack_complex_float* afb,\n                            lapack_int ldafb, const lapack_int* ipiv,\n                            const float* r, const float* c,\n                            const lapack_complex_float* b, lapack_int ldb,\n                            lapack_complex_float* x, lapack_int ldx,\n                            float* rcond, float* berr, lapack_int n_err_bnds,\n                            float* err_bnds_norm, float* err_bnds_comp,\n                            lapack_int nparams, float* params );\nlapack_int LAPACKE_zgbrfsx( int matrix_order, char trans, char equed,\n                            lapack_int n, lapack_int kl, lapack_int ku,\n                            lapack_int nrhs, const lapack_complex_double* ab,\n                            lapack_int ldab, const lapack_complex_double* afb,\n                            lapack_int ldafb, const lapack_int* ipiv,\n                            const double* r, const double* c,\n                            const lapack_complex_double* b, lapack_int ldb,\n                            lapack_complex_double* x, lapack_int ldx,\n                            double* rcond, double* berr, lapack_int n_err_bnds,\n                            double* err_bnds_norm, double* err_bnds_comp,\n                            lapack_int nparams, double* params );\n\nlapack_int LAPACKE_sgbsv( int matrix_order, lapack_int n, lapack_int kl,\n                          lapack_int ku, lapack_int nrhs, float* ab,\n                          lapack_int ldab, lapack_int* ipiv, float* b,\n                          lapack_int ldb );\nlapack_int LAPACKE_dgbsv( int matrix_order, lapack_int n, lapack_int kl,\n                          lapack_int ku, lapack_int nrhs, double* ab,\n                          lapack_int ldab, lapack_int* ipiv, double* b,\n                          lapack_int ldb );\nlapack_int LAPACKE_cgbsv( int matrix_order, lapack_int n, lapack_int kl,\n                          lapack_int ku, lapack_int nrhs,\n                          lapack_complex_float* ab, lapack_int ldab,\n                          lapack_int* ipiv, lapack_complex_float* b,\n                          lapack_int ldb );\nlapack_int LAPACKE_zgbsv( int matrix_order, lapack_int n, lapack_int kl,\n                          lapack_int ku, lapack_int nrhs,\n                          lapack_complex_double* ab, lapack_int ldab,\n                          lapack_int* ipiv, lapack_complex_double* b,\n                          lapack_int ldb );\n\nlapack_int LAPACKE_sgbsvx( int matrix_order, char fact, char trans,\n                           lapack_int n, lapack_int kl, lapack_int ku,\n                           lapack_int nrhs, float* ab, lapack_int ldab,\n                           float* afb, lapack_int ldafb, lapack_int* ipiv,\n                           char* equed, float* r, float* c, float* b,\n                           lapack_int ldb, float* x, lapack_int ldx,\n                           float* rcond, float* ferr, float* berr,\n                           float* rpivot );\nlapack_int LAPACKE_dgbsvx( int matrix_order, char fact, char trans,\n                           lapack_int n, lapack_int kl, lapack_int ku,\n                           lapack_int nrhs, double* ab, lapack_int ldab,\n                           double* afb, lapack_int ldafb, lapack_int* ipiv,\n                           char* equed, double* r, double* c, double* b,\n                           lapack_int ldb, double* x, lapack_int ldx,\n                           double* rcond, double* ferr, double* berr,\n                           double* rpivot );\nlapack_int LAPACKE_cgbsvx( int matrix_order, char fact, char trans,\n                           lapack_int n, lapack_int kl, lapack_int ku,\n                           lapack_int nrhs, lapack_complex_float* ab,\n                           lapack_int ldab, lapack_complex_float* afb,\n                           lapack_int ldafb, lapack_int* ipiv, char* equed,\n                           float* r, float* c, lapack_complex_float* b,\n                           lapack_int ldb, lapack_complex_float* x,\n                           lapack_int ldx, float* rcond, float* ferr,\n                           float* berr, float* rpivot );\nlapack_int LAPACKE_zgbsvx( int matrix_order, char fact, char trans,\n                           lapack_int n, lapack_int kl, lapack_int ku,\n                           lapack_int nrhs, lapack_complex_double* ab,\n                           lapack_int ldab, lapack_complex_double* afb,\n                           lapack_int ldafb, lapack_int* ipiv, char* equed,\n                           double* r, double* c, lapack_complex_double* b,\n                           lapack_int ldb, lapack_complex_double* x,\n                           lapack_int ldx, double* rcond, double* ferr,\n                           double* berr, double* rpivot );\n\nlapack_int LAPACKE_sgbsvxx( int matrix_order, char fact, char trans,\n                            lapack_int n, lapack_int kl, lapack_int ku,\n                            lapack_int nrhs, float* ab, lapack_int ldab,\n                            float* afb, lapack_int ldafb, lapack_int* ipiv,\n                            char* equed, float* r, float* c, float* b,\n                            lapack_int ldb, float* x, lapack_int ldx,\n                            float* rcond, float* rpvgrw, float* berr,\n                            lapack_int n_err_bnds, float* err_bnds_norm,\n                            float* err_bnds_comp, lapack_int nparams,\n                            float* params );\nlapack_int LAPACKE_dgbsvxx( int matrix_order, char fact, char trans,\n                            lapack_int n, lapack_int kl, lapack_int ku,\n                            lapack_int nrhs, double* ab, lapack_int ldab,\n                            double* afb, lapack_int ldafb, lapack_int* ipiv,\n                            char* equed, double* r, double* c, double* b,\n                            lapack_int ldb, double* x, lapack_int ldx,\n                            double* rcond, double* rpvgrw, double* berr,\n                            lapack_int n_err_bnds, double* err_bnds_norm,\n                            double* err_bnds_comp, lapack_int nparams,\n                            double* params );\nlapack_int LAPACKE_cgbsvxx( int matrix_order, char fact, char trans,\n                            lapack_int n, lapack_int kl, lapack_int ku,\n                            lapack_int nrhs, lapack_complex_float* ab,\n                            lapack_int ldab, lapack_complex_float* afb,\n                            lapack_int ldafb, lapack_int* ipiv, char* equed,\n                            float* r, float* c, lapack_complex_float* b,\n                            lapack_int ldb, lapack_complex_float* x,\n                            lapack_int ldx, float* rcond, float* rpvgrw,\n                            float* berr, lapack_int n_err_bnds,\n                            float* err_bnds_norm, float* err_bnds_comp,\n                            lapack_int nparams, float* params );\nlapack_int LAPACKE_zgbsvxx( int matrix_order, char fact, char trans,\n                            lapack_int n, lapack_int kl, lapack_int ku,\n                            lapack_int nrhs, lapack_complex_double* ab,\n                            lapack_int ldab, lapack_complex_double* afb,\n                            lapack_int ldafb, lapack_int* ipiv, char* equed,\n                            double* r, double* c, lapack_complex_double* b,\n                            lapack_int ldb, lapack_complex_double* x,\n                            lapack_int ldx, double* rcond, double* rpvgrw,\n                            double* berr, lapack_int n_err_bnds,\n                            double* err_bnds_norm, double* err_bnds_comp,\n                            lapack_int nparams, double* params );\n\nlapack_int LAPACKE_sgbtrf( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int kl, lapack_int ku, float* ab,\n                           lapack_int ldab, lapack_int* ipiv );\nlapack_int LAPACKE_dgbtrf( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int kl, lapack_int ku, double* ab,\n                           lapack_int ldab, lapack_int* ipiv );\nlapack_int LAPACKE_cgbtrf( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int kl, lapack_int ku,\n                           lapack_complex_float* ab, lapack_int ldab,\n                           lapack_int* ipiv );\nlapack_int LAPACKE_zgbtrf( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int kl, lapack_int ku,\n                           lapack_complex_double* ab, lapack_int ldab,\n                           lapack_int* ipiv );\n\nlapack_int LAPACKE_sgbtrs( int matrix_order, char trans, lapack_int n,\n                           lapack_int kl, lapack_int ku, lapack_int nrhs,\n                           const float* ab, lapack_int ldab,\n                           const lapack_int* ipiv, float* b, lapack_int ldb );\nlapack_int LAPACKE_dgbtrs( int matrix_order, char trans, lapack_int n,\n                           lapack_int kl, lapack_int ku, lapack_int nrhs,\n                           const double* ab, lapack_int ldab,\n                           const lapack_int* ipiv, double* b, lapack_int ldb );\nlapack_int LAPACKE_cgbtrs( int matrix_order, char trans, lapack_int n,\n                           lapack_int kl, lapack_int ku, lapack_int nrhs,\n                           const lapack_complex_float* ab, lapack_int ldab,\n                           const lapack_int* ipiv, lapack_complex_float* b,\n                           lapack_int ldb );\nlapack_int LAPACKE_zgbtrs( int matrix_order, char trans, lapack_int n,\n                           lapack_int kl, lapack_int ku, lapack_int nrhs,\n                           const lapack_complex_double* ab, lapack_int ldab,\n                           const lapack_int* ipiv, lapack_complex_double* b,\n                           lapack_int ldb );\n\nlapack_int LAPACKE_sgebak( int matrix_order, char job, char side, lapack_int n,\n                           lapack_int ilo, lapack_int ihi, const float* scale,\n                           lapack_int m, float* v, lapack_int ldv );\nlapack_int LAPACKE_dgebak( int matrix_order, char job, char side, lapack_int n,\n                           lapack_int ilo, lapack_int ihi, const double* scale,\n                           lapack_int m, double* v, lapack_int ldv );\nlapack_int LAPACKE_cgebak( int matrix_order, char job, char side, lapack_int n,\n                           lapack_int ilo, lapack_int ihi, const float* scale,\n                           lapack_int m, lapack_complex_float* v,\n                           lapack_int ldv );\nlapack_int LAPACKE_zgebak( int matrix_order, char job, char side, lapack_int n,\n                           lapack_int ilo, lapack_int ihi, const double* scale,\n                           lapack_int m, lapack_complex_double* v,\n                           lapack_int ldv );\n\nlapack_int LAPACKE_sgebal( int matrix_order, char job, lapack_int n, float* a,\n                           lapack_int lda, lapack_int* ilo, lapack_int* ihi,\n                           float* scale );\nlapack_int LAPACKE_dgebal( int matrix_order, char job, lapack_int n, double* a,\n                           lapack_int lda, lapack_int* ilo, lapack_int* ihi,\n                           double* scale );\nlapack_int LAPACKE_cgebal( int matrix_order, char job, lapack_int n,\n                           lapack_complex_float* a, lapack_int lda,\n                           lapack_int* ilo, lapack_int* ihi, float* scale );\nlapack_int LAPACKE_zgebal( int matrix_order, char job, lapack_int n,\n                           lapack_complex_double* a, lapack_int lda,\n                           lapack_int* ilo, lapack_int* ihi, double* scale );\n\nlapack_int LAPACKE_sgebrd( int matrix_order, lapack_int m, lapack_int n,\n                           float* a, lapack_int lda, float* d, float* e,\n                           float* tauq, float* taup );\nlapack_int LAPACKE_dgebrd( int matrix_order, lapack_int m, lapack_int n,\n                           double* a, lapack_int lda, double* d, double* e,\n                           double* tauq, double* taup );\nlapack_int LAPACKE_cgebrd( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_complex_float* a, lapack_int lda, float* d,\n                           float* e, lapack_complex_float* tauq,\n                           lapack_complex_float* taup );\nlapack_int LAPACKE_zgebrd( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_complex_double* a, lapack_int lda, double* d,\n                           double* e, lapack_complex_double* tauq,\n                           lapack_complex_double* taup );\n\nlapack_int LAPACKE_sgecon( int matrix_order, char norm, lapack_int n,\n                           const float* a, lapack_int lda, float anorm,\n                           float* rcond );\nlapack_int LAPACKE_dgecon( int matrix_order, char norm, lapack_int n,\n                           const double* a, lapack_int lda, double anorm,\n                           double* rcond );\nlapack_int LAPACKE_cgecon( int matrix_order, char norm, lapack_int n,\n                           const lapack_complex_float* a, lapack_int lda,\n                           float anorm, float* rcond );\nlapack_int LAPACKE_zgecon( int matrix_order, char norm, lapack_int n,\n                           const lapack_complex_double* a, lapack_int lda,\n                           double anorm, double* rcond );\n\nlapack_int LAPACKE_sgeequ( int matrix_order, lapack_int m, lapack_int n,\n                           const float* a, lapack_int lda, float* r, float* c,\n                           float* rowcnd, float* colcnd, float* amax );\nlapack_int LAPACKE_dgeequ( int matrix_order, lapack_int m, lapack_int n,\n                           const double* a, lapack_int lda, double* r,\n                           double* c, double* rowcnd, double* colcnd,\n                           double* amax );\nlapack_int LAPACKE_cgeequ( int matrix_order, lapack_int m, lapack_int n,\n                           const lapack_complex_float* a, lapack_int lda,\n                           float* r, float* c, float* rowcnd, float* colcnd,\n                           float* amax );\nlapack_int LAPACKE_zgeequ( int matrix_order, lapack_int m, lapack_int n,\n                           const lapack_complex_double* a, lapack_int lda,\n                           double* r, double* c, double* rowcnd, double* colcnd,\n                           double* amax );\n\nlapack_int LAPACKE_sgeequb( int matrix_order, lapack_int m, lapack_int n,\n                            const float* a, lapack_int lda, float* r, float* c,\n                            float* rowcnd, float* colcnd, float* amax );\nlapack_int LAPACKE_dgeequb( int matrix_order, lapack_int m, lapack_int n,\n                            const double* a, lapack_int lda, double* r,\n                            double* c, double* rowcnd, double* colcnd,\n                            double* amax );\nlapack_int LAPACKE_cgeequb( int matrix_order, lapack_int m, lapack_int n,\n                            const lapack_complex_float* a, lapack_int lda,\n                            float* r, float* c, float* rowcnd, float* colcnd,\n                            float* amax );\nlapack_int LAPACKE_zgeequb( int matrix_order, lapack_int m, lapack_int n,\n                            const lapack_complex_double* a, lapack_int lda,\n                            double* r, double* c, double* rowcnd,\n                            double* colcnd, double* amax );\n\nlapack_int LAPACKE_sgees( int matrix_order, char jobvs, char sort,\n                          LAPACK_S_SELECT2 select, lapack_int n, float* a,\n                          lapack_int lda, lapack_int* sdim, float* wr,\n                          float* wi, float* vs, lapack_int ldvs );\nlapack_int LAPACKE_dgees( int matrix_order, char jobvs, char sort,\n                          LAPACK_D_SELECT2 select, lapack_int n, double* a,\n                          lapack_int lda, lapack_int* sdim, double* wr,\n                          double* wi, double* vs, lapack_int ldvs );\nlapack_int LAPACKE_cgees( int matrix_order, char jobvs, char sort,\n                          LAPACK_C_SELECT1 select, lapack_int n,\n                          lapack_complex_float* a, lapack_int lda,\n                          lapack_int* sdim, lapack_complex_float* w,\n                          lapack_complex_float* vs, lapack_int ldvs );\nlapack_int LAPACKE_zgees( int matrix_order, char jobvs, char sort,\n                          LAPACK_Z_SELECT1 select, lapack_int n,\n                          lapack_complex_double* a, lapack_int lda,\n                          lapack_int* sdim, lapack_complex_double* w,\n                          lapack_complex_double* vs, lapack_int ldvs );\n\nlapack_int LAPACKE_sgeesx( int matrix_order, char jobvs, char sort,\n                           LAPACK_S_SELECT2 select, char sense, lapack_int n,\n                           float* a, lapack_int lda, lapack_int* sdim,\n                           float* wr, float* wi, float* vs, lapack_int ldvs,\n                           float* rconde, float* rcondv );\nlapack_int LAPACKE_dgeesx( int matrix_order, char jobvs, char sort,\n                           LAPACK_D_SELECT2 select, char sense, lapack_int n,\n                           double* a, lapack_int lda, lapack_int* sdim,\n                           double* wr, double* wi, double* vs, lapack_int ldvs,\n                           double* rconde, double* rcondv );\nlapack_int LAPACKE_cgeesx( int matrix_order, char jobvs, char sort,\n                           LAPACK_C_SELECT1 select, char sense, lapack_int n,\n                           lapack_complex_float* a, lapack_int lda,\n                           lapack_int* sdim, lapack_complex_float* w,\n                           lapack_complex_float* vs, lapack_int ldvs,\n                           float* rconde, float* rcondv );\nlapack_int LAPACKE_zgeesx( int matrix_order, char jobvs, char sort,\n                           LAPACK_Z_SELECT1 select, char sense, lapack_int n,\n                           lapack_complex_double* a, lapack_int lda,\n                           lapack_int* sdim, lapack_complex_double* w,\n                           lapack_complex_double* vs, lapack_int ldvs,\n                           double* rconde, double* rcondv );\n\nlapack_int LAPACKE_sgeev( int matrix_order, char jobvl, char jobvr,\n                          lapack_int n, float* a, lapack_int lda, float* wr,\n                          float* wi, float* vl, lapack_int ldvl, float* vr,\n                          lapack_int ldvr );\nlapack_int LAPACKE_dgeev( int matrix_order, char jobvl, char jobvr,\n                          lapack_int n, double* a, lapack_int lda, double* wr,\n                          double* wi, double* vl, lapack_int ldvl, double* vr,\n                          lapack_int ldvr );\nlapack_int LAPACKE_cgeev( int matrix_order, char jobvl, char jobvr,\n                          lapack_int n, lapack_complex_float* a, lapack_int lda,\n                          lapack_complex_float* w, lapack_complex_float* vl,\n                          lapack_int ldvl, lapack_complex_float* vr,\n                          lapack_int ldvr );\nlapack_int LAPACKE_zgeev( int matrix_order, char jobvl, char jobvr,\n                          lapack_int n, lapack_complex_double* a,\n                          lapack_int lda, lapack_complex_double* w,\n                          lapack_complex_double* vl, lapack_int ldvl,\n                          lapack_complex_double* vr, lapack_int ldvr );\n\nlapack_int LAPACKE_sgeevx( int matrix_order, char balanc, char jobvl,\n                           char jobvr, char sense, lapack_int n, float* a,\n                           lapack_int lda, float* wr, float* wi, float* vl,\n                           lapack_int ldvl, float* vr, lapack_int ldvr,\n                           lapack_int* ilo, lapack_int* ihi, float* scale,\n                           float* abnrm, float* rconde, float* rcondv );\nlapack_int LAPACKE_dgeevx( int matrix_order, char balanc, char jobvl,\n                           char jobvr, char sense, lapack_int n, double* a,\n                           lapack_int lda, double* wr, double* wi, double* vl,\n                           lapack_int ldvl, double* vr, lapack_int ldvr,\n                           lapack_int* ilo, lapack_int* ihi, double* scale,\n                           double* abnrm, double* rconde, double* rcondv );\nlapack_int LAPACKE_cgeevx( int matrix_order, char balanc, char jobvl,\n                           char jobvr, char sense, lapack_int n,\n                           lapack_complex_float* a, lapack_int lda,\n                           lapack_complex_float* w, lapack_complex_float* vl,\n                           lapack_int ldvl, lapack_complex_float* vr,\n                           lapack_int ldvr, lapack_int* ilo, lapack_int* ihi,\n                           float* scale, float* abnrm, float* rconde,\n                           float* rcondv );\nlapack_int LAPACKE_zgeevx( int matrix_order, char balanc, char jobvl,\n                           char jobvr, char sense, lapack_int n,\n                           lapack_complex_double* a, lapack_int lda,\n                           lapack_complex_double* w, lapack_complex_double* vl,\n                           lapack_int ldvl, lapack_complex_double* vr,\n                           lapack_int ldvr, lapack_int* ilo, lapack_int* ihi,\n                           double* scale, double* abnrm, double* rconde,\n                           double* rcondv );\n\nlapack_int LAPACKE_sgehrd( int matrix_order, lapack_int n, lapack_int ilo,\n                           lapack_int ihi, float* a, lapack_int lda,\n                           float* tau );\nlapack_int LAPACKE_dgehrd( int matrix_order, lapack_int n, lapack_int ilo,\n                           lapack_int ihi, double* a, lapack_int lda,\n                           double* tau );\nlapack_int LAPACKE_cgehrd( int matrix_order, lapack_int n, lapack_int ilo,\n                           lapack_int ihi, lapack_complex_float* a,\n                           lapack_int lda, lapack_complex_float* tau );\nlapack_int LAPACKE_zgehrd( int matrix_order, lapack_int n, lapack_int ilo,\n                           lapack_int ihi, lapack_complex_double* a,\n                           lapack_int lda, lapack_complex_double* tau );\n\nlapack_int LAPACKE_sgejsv( int matrix_order, char joba, char jobu, char jobv,\n                           char jobr, char jobt, char jobp, lapack_int m,\n                           lapack_int n, float* a, lapack_int lda, float* sva,\n                           float* u, lapack_int ldu, float* v, lapack_int ldv,\n                           float* stat, lapack_int* istat );\nlapack_int LAPACKE_dgejsv( int matrix_order, char joba, char jobu, char jobv,\n                           char jobr, char jobt, char jobp, lapack_int m,\n                           lapack_int n, double* a, lapack_int lda, double* sva,\n                           double* u, lapack_int ldu, double* v, lapack_int ldv,\n                           double* stat, lapack_int* istat );\n\nlapack_int LAPACKE_sgelq2( int matrix_order, lapack_int m, lapack_int n,\n                           float* a, lapack_int lda, float* tau );\nlapack_int LAPACKE_dgelq2( int matrix_order, lapack_int m, lapack_int n,\n                           double* a, lapack_int lda, double* tau );\nlapack_int LAPACKE_cgelq2( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_complex_float* a, lapack_int lda,\n                           lapack_complex_float* tau );\nlapack_int LAPACKE_zgelq2( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_complex_double* a, lapack_int lda,\n                           lapack_complex_double* tau );\n\nlapack_int LAPACKE_sgelqf( int matrix_order, lapack_int m, lapack_int n,\n                           float* a, lapack_int lda, float* tau );\nlapack_int LAPACKE_dgelqf( int matrix_order, lapack_int m, lapack_int n,\n                           double* a, lapack_int lda, double* tau );\nlapack_int LAPACKE_cgelqf( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_complex_float* a, lapack_int lda,\n                           lapack_complex_float* tau );\nlapack_int LAPACKE_zgelqf( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_complex_double* a, lapack_int lda,\n                           lapack_complex_double* tau );\n\nlapack_int LAPACKE_sgels( int matrix_order, char trans, lapack_int m,\n                          lapack_int n, lapack_int nrhs, float* a,\n                          lapack_int lda, float* b, lapack_int ldb );\nlapack_int LAPACKE_dgels( int matrix_order, char trans, lapack_int m,\n                          lapack_int n, lapack_int nrhs, double* a,\n                          lapack_int lda, double* b, lapack_int ldb );\nlapack_int LAPACKE_cgels( int matrix_order, char trans, lapack_int m,\n                          lapack_int n, lapack_int nrhs,\n                          lapack_complex_float* a, lapack_int lda,\n                          lapack_complex_float* b, lapack_int ldb );\nlapack_int LAPACKE_zgels( int matrix_order, char trans, lapack_int m,\n                          lapack_int n, lapack_int nrhs,\n                          lapack_complex_double* a, lapack_int lda,\n                          lapack_complex_double* b, lapack_int ldb );\n\nlapack_int LAPACKE_sgelsd( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int nrhs, float* a, lapack_int lda, float* b,\n                           lapack_int ldb, float* s, float rcond,\n                           lapack_int* rank );\nlapack_int LAPACKE_dgelsd( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int nrhs, double* a, lapack_int lda,\n                           double* b, lapack_int ldb, double* s, double rcond,\n                           lapack_int* rank );\nlapack_int LAPACKE_cgelsd( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int nrhs, lapack_complex_float* a,\n                           lapack_int lda, lapack_complex_float* b,\n                           lapack_int ldb, float* s, float rcond,\n                           lapack_int* rank );\nlapack_int LAPACKE_zgelsd( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int nrhs, lapack_complex_double* a,\n                           lapack_int lda, lapack_complex_double* b,\n                           lapack_int ldb, double* s, double rcond,\n                           lapack_int* rank );\n\nlapack_int LAPACKE_sgelss( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int nrhs, float* a, lapack_int lda, float* b,\n                           lapack_int ldb, float* s, float rcond,\n                           lapack_int* rank );\nlapack_int LAPACKE_dgelss( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int nrhs, double* a, lapack_int lda,\n                           double* b, lapack_int ldb, double* s, double rcond,\n                           lapack_int* rank );\nlapack_int LAPACKE_cgelss( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int nrhs, lapack_complex_float* a,\n                           lapack_int lda, lapack_complex_float* b,\n                           lapack_int ldb, float* s, float rcond,\n                           lapack_int* rank );\nlapack_int LAPACKE_zgelss( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int nrhs, lapack_complex_double* a,\n                           lapack_int lda, lapack_complex_double* b,\n                           lapack_int ldb, double* s, double rcond,\n                           lapack_int* rank );\n\nlapack_int LAPACKE_sgelsy( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int nrhs, float* a, lapack_int lda, float* b,\n                           lapack_int ldb, lapack_int* jpvt, float rcond,\n                           lapack_int* rank );\nlapack_int LAPACKE_dgelsy( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int nrhs, double* a, lapack_int lda,\n                           double* b, lapack_int ldb, lapack_int* jpvt,\n                           double rcond, lapack_int* rank );\nlapack_int LAPACKE_cgelsy( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int nrhs, lapack_complex_float* a,\n                           lapack_int lda, lapack_complex_float* b,\n                           lapack_int ldb, lapack_int* jpvt, float rcond,\n                           lapack_int* rank );\nlapack_int LAPACKE_zgelsy( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int nrhs, lapack_complex_double* a,\n                           lapack_int lda, lapack_complex_double* b,\n                           lapack_int ldb, lapack_int* jpvt, double rcond,\n                           lapack_int* rank );\n\nlapack_int LAPACKE_sgeqlf( int matrix_order, lapack_int m, lapack_int n,\n                           float* a, lapack_int lda, float* tau );\nlapack_int LAPACKE_dgeqlf( int matrix_order, lapack_int m, lapack_int n,\n                           double* a, lapack_int lda, double* tau );\nlapack_int LAPACKE_cgeqlf( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_complex_float* a, lapack_int lda,\n                           lapack_complex_float* tau );\nlapack_int LAPACKE_zgeqlf( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_complex_double* a, lapack_int lda,\n                           lapack_complex_double* tau );\n\nlapack_int LAPACKE_sgeqp3( int matrix_order, lapack_int m, lapack_int n,\n                           float* a, lapack_int lda, lapack_int* jpvt,\n                           float* tau );\nlapack_int LAPACKE_dgeqp3( int matrix_order, lapack_int m, lapack_int n,\n                           double* a, lapack_int lda, lapack_int* jpvt,\n                           double* tau );\nlapack_int LAPACKE_cgeqp3( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_complex_float* a, lapack_int lda,\n                           lapack_int* jpvt, lapack_complex_float* tau );\nlapack_int LAPACKE_zgeqp3( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_complex_double* a, lapack_int lda,\n                           lapack_int* jpvt, lapack_complex_double* tau );\n\nlapack_int LAPACKE_sgeqpf( int matrix_order, lapack_int m, lapack_int n,\n                           float* a, lapack_int lda, lapack_int* jpvt,\n                           float* tau );\nlapack_int LAPACKE_dgeqpf( int matrix_order, lapack_int m, lapack_int n,\n                           double* a, lapack_int lda, lapack_int* jpvt,\n                           double* tau );\nlapack_int LAPACKE_cgeqpf( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_complex_float* a, lapack_int lda,\n                           lapack_int* jpvt, lapack_complex_float* tau );\nlapack_int LAPACKE_zgeqpf( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_complex_double* a, lapack_int lda,\n                           lapack_int* jpvt, lapack_complex_double* tau );\n\nlapack_int LAPACKE_sgeqr2( int matrix_order, lapack_int m, lapack_int n,\n                           float* a, lapack_int lda, float* tau );\nlapack_int LAPACKE_dgeqr2( int matrix_order, lapack_int m, lapack_int n,\n                           double* a, lapack_int lda, double* tau );\nlapack_int LAPACKE_cgeqr2( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_complex_float* a, lapack_int lda,\n                           lapack_complex_float* tau );\nlapack_int LAPACKE_zgeqr2( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_complex_double* a, lapack_int lda,\n                           lapack_complex_double* tau );\n\nlapack_int LAPACKE_sgeqrf( int matrix_order, lapack_int m, lapack_int n,\n                           float* a, lapack_int lda, float* tau );\nlapack_int LAPACKE_dgeqrf( int matrix_order, lapack_int m, lapack_int n,\n                           double* a, lapack_int lda, double* tau );\nlapack_int LAPACKE_cgeqrf( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_complex_float* a, lapack_int lda,\n                           lapack_complex_float* tau );\nlapack_int LAPACKE_zgeqrf( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_complex_double* a, lapack_int lda,\n                           lapack_complex_double* tau );\n\nlapack_int LAPACKE_sgeqrfp( int matrix_order, lapack_int m, lapack_int n,\n                            float* a, lapack_int lda, float* tau );\nlapack_int LAPACKE_dgeqrfp( int matrix_order, lapack_int m, lapack_int n,\n                            double* a, lapack_int lda, double* tau );\nlapack_int LAPACKE_cgeqrfp( int matrix_order, lapack_int m, lapack_int n,\n                            lapack_complex_float* a, lapack_int lda,\n                            lapack_complex_float* tau );\nlapack_int LAPACKE_zgeqrfp( int matrix_order, lapack_int m, lapack_int n,\n                            lapack_complex_double* a, lapack_int lda,\n                            lapack_complex_double* tau );\n\nlapack_int LAPACKE_sgerfs( int matrix_order, char trans, lapack_int n,\n                           lapack_int nrhs, const float* a, lapack_int lda,\n                           const float* af, lapack_int ldaf,\n                           const lapack_int* ipiv, const float* b,\n                           lapack_int ldb, float* x, lapack_int ldx,\n                           float* ferr, float* berr );\nlapack_int LAPACKE_dgerfs( int matrix_order, char trans, lapack_int n,\n                           lapack_int nrhs, const double* a, lapack_int lda,\n                           const double* af, lapack_int ldaf,\n                           const lapack_int* ipiv, const double* b,\n                           lapack_int ldb, double* x, lapack_int ldx,\n                           double* ferr, double* berr );\nlapack_int LAPACKE_cgerfs( int matrix_order, char trans, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_float* a,\n                           lapack_int lda, const lapack_complex_float* af,\n                           lapack_int ldaf, const lapack_int* ipiv,\n                           const lapack_complex_float* b, lapack_int ldb,\n                           lapack_complex_float* x, lapack_int ldx, float* ferr,\n                           float* berr );\nlapack_int LAPACKE_zgerfs( int matrix_order, char trans, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_double* a,\n                           lapack_int lda, const lapack_complex_double* af,\n                           lapack_int ldaf, const lapack_int* ipiv,\n                           const lapack_complex_double* b, lapack_int ldb,\n                           lapack_complex_double* x, lapack_int ldx,\n                           double* ferr, double* berr );\n\nlapack_int LAPACKE_sgerfsx( int matrix_order, char trans, char equed,\n                            lapack_int n, lapack_int nrhs, const float* a,\n                            lapack_int lda, const float* af, lapack_int ldaf,\n                            const lapack_int* ipiv, const float* r,\n                            const float* c, const float* b, lapack_int ldb,\n                            float* x, lapack_int ldx, float* rcond, float* berr,\n                            lapack_int n_err_bnds, float* err_bnds_norm,\n                            float* err_bnds_comp, lapack_int nparams,\n                            float* params );\nlapack_int LAPACKE_dgerfsx( int matrix_order, char trans, char equed,\n                            lapack_int n, lapack_int nrhs, const double* a,\n                            lapack_int lda, const double* af, lapack_int ldaf,\n                            const lapack_int* ipiv, const double* r,\n                            const double* c, const double* b, lapack_int ldb,\n                            double* x, lapack_int ldx, double* rcond,\n                            double* berr, lapack_int n_err_bnds,\n                            double* err_bnds_norm, double* err_bnds_comp,\n                            lapack_int nparams, double* params );\nlapack_int LAPACKE_cgerfsx( int matrix_order, char trans, char equed,\n                            lapack_int n, lapack_int nrhs,\n                            const lapack_complex_float* a, lapack_int lda,\n                            const lapack_complex_float* af, lapack_int ldaf,\n                            const lapack_int* ipiv, const float* r,\n                            const float* c, const lapack_complex_float* b,\n                            lapack_int ldb, lapack_complex_float* x,\n                            lapack_int ldx, float* rcond, float* berr,\n                            lapack_int n_err_bnds, float* err_bnds_norm,\n                            float* err_bnds_comp, lapack_int nparams,\n                            float* params );\nlapack_int LAPACKE_zgerfsx( int matrix_order, char trans, char equed,\n                            lapack_int n, lapack_int nrhs,\n                            const lapack_complex_double* a, lapack_int lda,\n                            const lapack_complex_double* af, lapack_int ldaf,\n                            const lapack_int* ipiv, const double* r,\n                            const double* c, const lapack_complex_double* b,\n                            lapack_int ldb, lapack_complex_double* x,\n                            lapack_int ldx, double* rcond, double* berr,\n                            lapack_int n_err_bnds, double* err_bnds_norm,\n                            double* err_bnds_comp, lapack_int nparams,\n                            double* params );\n\nlapack_int LAPACKE_sgerqf( int matrix_order, lapack_int m, lapack_int n,\n                           float* a, lapack_int lda, float* tau );\nlapack_int LAPACKE_dgerqf( int matrix_order, lapack_int m, lapack_int n,\n                           double* a, lapack_int lda, double* tau );\nlapack_int LAPACKE_cgerqf( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_complex_float* a, lapack_int lda,\n                           lapack_complex_float* tau );\nlapack_int LAPACKE_zgerqf( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_complex_double* a, lapack_int lda,\n                           lapack_complex_double* tau );\n\nlapack_int LAPACKE_sgesdd( int matrix_order, char jobz, lapack_int m,\n                           lapack_int n, float* a, lapack_int lda, float* s,\n                           float* u, lapack_int ldu, float* vt,\n                           lapack_int ldvt );\nlapack_int LAPACKE_dgesdd( int matrix_order, char jobz, lapack_int m,\n                           lapack_int n, double* a, lapack_int lda, double* s,\n                           double* u, lapack_int ldu, double* vt,\n                           lapack_int ldvt );\nlapack_int LAPACKE_cgesdd( int matrix_order, char jobz, lapack_int m,\n                           lapack_int n, lapack_complex_float* a,\n                           lapack_int lda, float* s, lapack_complex_float* u,\n                           lapack_int ldu, lapack_complex_float* vt,\n                           lapack_int ldvt );\nlapack_int LAPACKE_zgesdd( int matrix_order, char jobz, lapack_int m,\n                           lapack_int n, lapack_complex_double* a,\n                           lapack_int lda, double* s, lapack_complex_double* u,\n                           lapack_int ldu, lapack_complex_double* vt,\n                           lapack_int ldvt );\n\nlapack_int LAPACKE_sgesv( int matrix_order, lapack_int n, lapack_int nrhs,\n                          float* a, lapack_int lda, lapack_int* ipiv, float* b,\n                          lapack_int ldb );\nlapack_int LAPACKE_dgesv( int matrix_order, lapack_int n, lapack_int nrhs,\n                          double* a, lapack_int lda, lapack_int* ipiv,\n                          double* b, lapack_int ldb );\nlapack_int LAPACKE_cgesv( int matrix_order, lapack_int n, lapack_int nrhs,\n                          lapack_complex_float* a, lapack_int lda,\n                          lapack_int* ipiv, lapack_complex_float* b,\n                          lapack_int ldb );\nlapack_int LAPACKE_zgesv( int matrix_order, lapack_int n, lapack_int nrhs,\n                          lapack_complex_double* a, lapack_int lda,\n                          lapack_int* ipiv, lapack_complex_double* b,\n                          lapack_int ldb );\nlapack_int LAPACKE_dsgesv( int matrix_order, lapack_int n, lapack_int nrhs,\n                           double* a, lapack_int lda, lapack_int* ipiv,\n                           double* b, lapack_int ldb, double* x, lapack_int ldx,\n                           lapack_int* iter );\nlapack_int LAPACKE_zcgesv( int matrix_order, lapack_int n, lapack_int nrhs,\n                           lapack_complex_double* a, lapack_int lda,\n                           lapack_int* ipiv, lapack_complex_double* b,\n                           lapack_int ldb, lapack_complex_double* x,\n                           lapack_int ldx, lapack_int* iter );\n\nlapack_int LAPACKE_sgesvd( int matrix_order, char jobu, char jobvt,\n                           lapack_int m, lapack_int n, float* a, lapack_int lda,\n                           float* s, float* u, lapack_int ldu, float* vt,\n                           lapack_int ldvt, float* superb );\nlapack_int LAPACKE_dgesvd( int matrix_order, char jobu, char jobvt,\n                           lapack_int m, lapack_int n, double* a,\n                           lapack_int lda, double* s, double* u, lapack_int ldu,\n                           double* vt, lapack_int ldvt, double* superb );\nlapack_int LAPACKE_cgesvd( int matrix_order, char jobu, char jobvt,\n                           lapack_int m, lapack_int n, lapack_complex_float* a,\n                           lapack_int lda, float* s, lapack_complex_float* u,\n                           lapack_int ldu, lapack_complex_float* vt,\n                           lapack_int ldvt, float* superb );\nlapack_int LAPACKE_zgesvd( int matrix_order, char jobu, char jobvt,\n                           lapack_int m, lapack_int n, lapack_complex_double* a,\n                           lapack_int lda, double* s, lapack_complex_double* u,\n                           lapack_int ldu, lapack_complex_double* vt,\n                           lapack_int ldvt, double* superb );\n\nlapack_int LAPACKE_sgesvj( int matrix_order, char joba, char jobu, char jobv,\n                           lapack_int m, lapack_int n, float* a, lapack_int lda,\n                           float* sva, lapack_int mv, float* v, lapack_int ldv,\n                           float* stat );\nlapack_int LAPACKE_dgesvj( int matrix_order, char joba, char jobu, char jobv,\n                           lapack_int m, lapack_int n, double* a,\n                           lapack_int lda, double* sva, lapack_int mv,\n                           double* v, lapack_int ldv, double* stat );\n\nlapack_int LAPACKE_sgesvx( int matrix_order, char fact, char trans,\n                           lapack_int n, lapack_int nrhs, float* a,\n                           lapack_int lda, float* af, lapack_int ldaf,\n                           lapack_int* ipiv, char* equed, float* r, float* c,\n                           float* b, lapack_int ldb, float* x, lapack_int ldx,\n                           float* rcond, float* ferr, float* berr,\n                           float* rpivot );\nlapack_int LAPACKE_dgesvx( int matrix_order, char fact, char trans,\n                           lapack_int n, lapack_int nrhs, double* a,\n                           lapack_int lda, double* af, lapack_int ldaf,\n                           lapack_int* ipiv, char* equed, double* r, double* c,\n                           double* b, lapack_int ldb, double* x, lapack_int ldx,\n                           double* rcond, double* ferr, double* berr,\n                           double* rpivot );\nlapack_int LAPACKE_cgesvx( int matrix_order, char fact, char trans,\n                           lapack_int n, lapack_int nrhs,\n                           lapack_complex_float* a, lapack_int lda,\n                           lapack_complex_float* af, lapack_int ldaf,\n                           lapack_int* ipiv, char* equed, float* r, float* c,\n                           lapack_complex_float* b, lapack_int ldb,\n                           lapack_complex_float* x, lapack_int ldx,\n                           float* rcond, float* ferr, float* berr,\n                           float* rpivot );\nlapack_int LAPACKE_zgesvx( int matrix_order, char fact, char trans,\n                           lapack_int n, lapack_int nrhs,\n                           lapack_complex_double* a, lapack_int lda,\n                           lapack_complex_double* af, lapack_int ldaf,\n                           lapack_int* ipiv, char* equed, double* r, double* c,\n                           lapack_complex_double* b, lapack_int ldb,\n                           lapack_complex_double* x, lapack_int ldx,\n                           double* rcond, double* ferr, double* berr,\n                           double* rpivot );\n\nlapack_int LAPACKE_sgesvxx( int matrix_order, char fact, char trans,\n                            lapack_int n, lapack_int nrhs, float* a,\n                            lapack_int lda, float* af, lapack_int ldaf,\n                            lapack_int* ipiv, char* equed, float* r, float* c,\n                            float* b, lapack_int ldb, float* x, lapack_int ldx,\n                            float* rcond, float* rpvgrw, float* berr,\n                            lapack_int n_err_bnds, float* err_bnds_norm,\n                            float* err_bnds_comp, lapack_int nparams,\n                            float* params );\nlapack_int LAPACKE_dgesvxx( int matrix_order, char fact, char trans,\n                            lapack_int n, lapack_int nrhs, double* a,\n                            lapack_int lda, double* af, lapack_int ldaf,\n                            lapack_int* ipiv, char* equed, double* r, double* c,\n                            double* b, lapack_int ldb, double* x,\n                            lapack_int ldx, double* rcond, double* rpvgrw,\n                            double* berr, lapack_int n_err_bnds,\n                            double* err_bnds_norm, double* err_bnds_comp,\n                            lapack_int nparams, double* params );\nlapack_int LAPACKE_cgesvxx( int matrix_order, char fact, char trans,\n                            lapack_int n, lapack_int nrhs,\n                            lapack_complex_float* a, lapack_int lda,\n                            lapack_complex_float* af, lapack_int ldaf,\n                            lapack_int* ipiv, char* equed, float* r, float* c,\n                            lapack_complex_float* b, lapack_int ldb,\n                            lapack_complex_float* x, lapack_int ldx,\n                            float* rcond, float* rpvgrw, float* berr,\n                            lapack_int n_err_bnds, float* err_bnds_norm,\n                            float* err_bnds_comp, lapack_int nparams,\n                            float* params );\nlapack_int LAPACKE_zgesvxx( int matrix_order, char fact, char trans,\n                            lapack_int n, lapack_int nrhs,\n                            lapack_complex_double* a, lapack_int lda,\n                            lapack_complex_double* af, lapack_int ldaf,\n                            lapack_int* ipiv, char* equed, double* r, double* c,\n                            lapack_complex_double* b, lapack_int ldb,\n                            lapack_complex_double* x, lapack_int ldx,\n                            double* rcond, double* rpvgrw, double* berr,\n                            lapack_int n_err_bnds, double* err_bnds_norm,\n                            double* err_bnds_comp, lapack_int nparams,\n                            double* params );\n\nlapack_int LAPACKE_sgetf2( int matrix_order, lapack_int m, lapack_int n,\n                           float* a, lapack_int lda, lapack_int* ipiv );\nlapack_int LAPACKE_dgetf2( int matrix_order, lapack_int m, lapack_int n,\n                           double* a, lapack_int lda, lapack_int* ipiv );\nlapack_int LAPACKE_cgetf2( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_complex_float* a, lapack_int lda,\n                           lapack_int* ipiv );\nlapack_int LAPACKE_zgetf2( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_complex_double* a, lapack_int lda,\n                           lapack_int* ipiv );\n\nlapack_int LAPACKE_sgetrf( int matrix_order, lapack_int m, lapack_int n,\n                           float* a, lapack_int lda, lapack_int* ipiv );\nlapack_int LAPACKE_dgetrf( int matrix_order, lapack_int m, lapack_int n,\n                           double* a, lapack_int lda, lapack_int* ipiv );\nlapack_int LAPACKE_cgetrf( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_complex_float* a, lapack_int lda,\n                           lapack_int* ipiv );\nlapack_int LAPACKE_zgetrf( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_complex_double* a, lapack_int lda,\n                           lapack_int* ipiv );\n\nlapack_int LAPACKE_sgetri( int matrix_order, lapack_int n, float* a,\n                           lapack_int lda, const lapack_int* ipiv );\nlapack_int LAPACKE_dgetri( int matrix_order, lapack_int n, double* a,\n                           lapack_int lda, const lapack_int* ipiv );\nlapack_int LAPACKE_cgetri( int matrix_order, lapack_int n,\n                           lapack_complex_float* a, lapack_int lda,\n                           const lapack_int* ipiv );\nlapack_int LAPACKE_zgetri( int matrix_order, lapack_int n,\n                           lapack_complex_double* a, lapack_int lda,\n                           const lapack_int* ipiv );\n\nlapack_int LAPACKE_sgetrs( int matrix_order, char trans, lapack_int n,\n                           lapack_int nrhs, const float* a, lapack_int lda,\n                           const lapack_int* ipiv, float* b, lapack_int ldb );\nlapack_int LAPACKE_dgetrs( int matrix_order, char trans, lapack_int n,\n                           lapack_int nrhs, const double* a, lapack_int lda,\n                           const lapack_int* ipiv, double* b, lapack_int ldb );\nlapack_int LAPACKE_cgetrs( int matrix_order, char trans, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_float* a,\n                           lapack_int lda, const lapack_int* ipiv,\n                           lapack_complex_float* b, lapack_int ldb );\nlapack_int LAPACKE_zgetrs( int matrix_order, char trans, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_double* a,\n                           lapack_int lda, const lapack_int* ipiv,\n                           lapack_complex_double* b, lapack_int ldb );\n\nlapack_int LAPACKE_sggbak( int matrix_order, char job, char side, lapack_int n,\n                           lapack_int ilo, lapack_int ihi, const float* lscale,\n                           const float* rscale, lapack_int m, float* v,\n                           lapack_int ldv );\nlapack_int LAPACKE_dggbak( int matrix_order, char job, char side, lapack_int n,\n                           lapack_int ilo, lapack_int ihi, const double* lscale,\n                           const double* rscale, lapack_int m, double* v,\n                           lapack_int ldv );\nlapack_int LAPACKE_cggbak( int matrix_order, char job, char side, lapack_int n,\n                           lapack_int ilo, lapack_int ihi, const float* lscale,\n                           const float* rscale, lapack_int m,\n                           lapack_complex_float* v, lapack_int ldv );\nlapack_int LAPACKE_zggbak( int matrix_order, char job, char side, lapack_int n,\n                           lapack_int ilo, lapack_int ihi, const double* lscale,\n                           const double* rscale, lapack_int m,\n                           lapack_complex_double* v, lapack_int ldv );\n\nlapack_int LAPACKE_sggbal( int matrix_order, char job, lapack_int n, float* a,\n                           lapack_int lda, float* b, lapack_int ldb,\n                           lapack_int* ilo, lapack_int* ihi, float* lscale,\n                           float* rscale );\nlapack_int LAPACKE_dggbal( int matrix_order, char job, lapack_int n, double* a,\n                           lapack_int lda, double* b, lapack_int ldb,\n                           lapack_int* ilo, lapack_int* ihi, double* lscale,\n                           double* rscale );\nlapack_int LAPACKE_cggbal( int matrix_order, char job, lapack_int n,\n                           lapack_complex_float* a, lapack_int lda,\n                           lapack_complex_float* b, lapack_int ldb,\n                           lapack_int* ilo, lapack_int* ihi, float* lscale,\n                           float* rscale );\nlapack_int LAPACKE_zggbal( int matrix_order, char job, lapack_int n,\n                           lapack_complex_double* a, lapack_int lda,\n                           lapack_complex_double* b, lapack_int ldb,\n                           lapack_int* ilo, lapack_int* ihi, double* lscale,\n                           double* rscale );\n\nlapack_int LAPACKE_sgges( int matrix_order, char jobvsl, char jobvsr, char sort,\n                          LAPACK_S_SELECT3 selctg, lapack_int n, float* a,\n                          lapack_int lda, float* b, lapack_int ldb,\n                          lapack_int* sdim, float* alphar, float* alphai,\n                          float* beta, float* vsl, lapack_int ldvsl, float* vsr,\n                          lapack_int ldvsr );\nlapack_int LAPACKE_dgges( int matrix_order, char jobvsl, char jobvsr, char sort,\n                          LAPACK_D_SELECT3 selctg, lapack_int n, double* a,\n                          lapack_int lda, double* b, lapack_int ldb,\n                          lapack_int* sdim, double* alphar, double* alphai,\n                          double* beta, double* vsl, lapack_int ldvsl,\n                          double* vsr, lapack_int ldvsr );\nlapack_int LAPACKE_cgges( int matrix_order, char jobvsl, char jobvsr, char sort,\n                          LAPACK_C_SELECT2 selctg, lapack_int n,\n                          lapack_complex_float* a, lapack_int lda,\n                          lapack_complex_float* b, lapack_int ldb,\n                          lapack_int* sdim, lapack_complex_float* alpha,\n                          lapack_complex_float* beta, lapack_complex_float* vsl,\n                          lapack_int ldvsl, lapack_complex_float* vsr,\n                          lapack_int ldvsr );\nlapack_int LAPACKE_zgges( int matrix_order, char jobvsl, char jobvsr, char sort,\n                          LAPACK_Z_SELECT2 selctg, lapack_int n,\n                          lapack_complex_double* a, lapack_int lda,\n                          lapack_complex_double* b, lapack_int ldb,\n                          lapack_int* sdim, lapack_complex_double* alpha,\n                          lapack_complex_double* beta,\n                          lapack_complex_double* vsl, lapack_int ldvsl,\n                          lapack_complex_double* vsr, lapack_int ldvsr );\n\nlapack_int LAPACKE_sggesx( int matrix_order, char jobvsl, char jobvsr,\n                           char sort, LAPACK_S_SELECT3 selctg, char sense,\n                           lapack_int n, float* a, lapack_int lda, float* b,\n                           lapack_int ldb, lapack_int* sdim, float* alphar,\n                           float* alphai, float* beta, float* vsl,\n                           lapack_int ldvsl, float* vsr, lapack_int ldvsr,\n                           float* rconde, float* rcondv );\nlapack_int LAPACKE_dggesx( int matrix_order, char jobvsl, char jobvsr,\n                           char sort, LAPACK_D_SELECT3 selctg, char sense,\n                           lapack_int n, double* a, lapack_int lda, double* b,\n                           lapack_int ldb, lapack_int* sdim, double* alphar,\n                           double* alphai, double* beta, double* vsl,\n                           lapack_int ldvsl, double* vsr, lapack_int ldvsr,\n                           double* rconde, double* rcondv );\nlapack_int LAPACKE_cggesx( int matrix_order, char jobvsl, char jobvsr,\n                           char sort, LAPACK_C_SELECT2 selctg, char sense,\n                           lapack_int n, lapack_complex_float* a,\n                           lapack_int lda, lapack_complex_float* b,\n                           lapack_int ldb, lapack_int* sdim,\n                           lapack_complex_float* alpha,\n                           lapack_complex_float* beta,\n                           lapack_complex_float* vsl, lapack_int ldvsl,\n                           lapack_complex_float* vsr, lapack_int ldvsr,\n                           float* rconde, float* rcondv );\nlapack_int LAPACKE_zggesx( int matrix_order, char jobvsl, char jobvsr,\n                           char sort, LAPACK_Z_SELECT2 selctg, char sense,\n                           lapack_int n, lapack_complex_double* a,\n                           lapack_int lda, lapack_complex_double* b,\n                           lapack_int ldb, lapack_int* sdim,\n                           lapack_complex_double* alpha,\n                           lapack_complex_double* beta,\n                           lapack_complex_double* vsl, lapack_int ldvsl,\n                           lapack_complex_double* vsr, lapack_int ldvsr,\n                           double* rconde, double* rcondv );\n\nlapack_int LAPACKE_sggev( int matrix_order, char jobvl, char jobvr,\n                          lapack_int n, float* a, lapack_int lda, float* b,\n                          lapack_int ldb, float* alphar, float* alphai,\n                          float* beta, float* vl, lapack_int ldvl, float* vr,\n                          lapack_int ldvr );\nlapack_int LAPACKE_dggev( int matrix_order, char jobvl, char jobvr,\n                          lapack_int n, double* a, lapack_int lda, double* b,\n                          lapack_int ldb, double* alphar, double* alphai,\n                          double* beta, double* vl, lapack_int ldvl, double* vr,\n                          lapack_int ldvr );\nlapack_int LAPACKE_cggev( int matrix_order, char jobvl, char jobvr,\n                          lapack_int n, lapack_complex_float* a, lapack_int lda,\n                          lapack_complex_float* b, lapack_int ldb,\n                          lapack_complex_float* alpha,\n                          lapack_complex_float* beta, lapack_complex_float* vl,\n                          lapack_int ldvl, lapack_complex_float* vr,\n                          lapack_int ldvr );\nlapack_int LAPACKE_zggev( int matrix_order, char jobvl, char jobvr,\n                          lapack_int n, lapack_complex_double* a,\n                          lapack_int lda, lapack_complex_double* b,\n                          lapack_int ldb, lapack_complex_double* alpha,\n                          lapack_complex_double* beta,\n                          lapack_complex_double* vl, lapack_int ldvl,\n                          lapack_complex_double* vr, lapack_int ldvr );\n\nlapack_int LAPACKE_sggevx( int matrix_order, char balanc, char jobvl,\n                           char jobvr, char sense, lapack_int n, float* a,\n                           lapack_int lda, float* b, lapack_int ldb,\n                           float* alphar, float* alphai, float* beta, float* vl,\n                           lapack_int ldvl, float* vr, lapack_int ldvr,\n                           lapack_int* ilo, lapack_int* ihi, float* lscale,\n                           float* rscale, float* abnrm, float* bbnrm,\n                           float* rconde, float* rcondv );\nlapack_int LAPACKE_dggevx( int matrix_order, char balanc, char jobvl,\n                           char jobvr, char sense, lapack_int n, double* a,\n                           lapack_int lda, double* b, lapack_int ldb,\n                           double* alphar, double* alphai, double* beta,\n                           double* vl, lapack_int ldvl, double* vr,\n                           lapack_int ldvr, lapack_int* ilo, lapack_int* ihi,\n                           double* lscale, double* rscale, double* abnrm,\n                           double* bbnrm, double* rconde, double* rcondv );\nlapack_int LAPACKE_cggevx( int matrix_order, char balanc, char jobvl,\n                           char jobvr, char sense, lapack_int n,\n                           lapack_complex_float* a, lapack_int lda,\n                           lapack_complex_float* b, lapack_int ldb,\n                           lapack_complex_float* alpha,\n                           lapack_complex_float* beta, lapack_complex_float* vl,\n                           lapack_int ldvl, lapack_complex_float* vr,\n                           lapack_int ldvr, lapack_int* ilo, lapack_int* ihi,\n                           float* lscale, float* rscale, float* abnrm,\n                           float* bbnrm, float* rconde, float* rcondv );\nlapack_int LAPACKE_zggevx( int matrix_order, char balanc, char jobvl,\n                           char jobvr, char sense, lapack_int n,\n                           lapack_complex_double* a, lapack_int lda,\n                           lapack_complex_double* b, lapack_int ldb,\n                           lapack_complex_double* alpha,\n                           lapack_complex_double* beta,\n                           lapack_complex_double* vl, lapack_int ldvl,\n                           lapack_complex_double* vr, lapack_int ldvr,\n                           lapack_int* ilo, lapack_int* ihi, double* lscale,\n                           double* rscale, double* abnrm, double* bbnrm,\n                           double* rconde, double* rcondv );\n\nlapack_int LAPACKE_sggglm( int matrix_order, lapack_int n, lapack_int m,\n                           lapack_int p, float* a, lapack_int lda, float* b,\n                           lapack_int ldb, float* d, float* x, float* y );\nlapack_int LAPACKE_dggglm( int matrix_order, lapack_int n, lapack_int m,\n                           lapack_int p, double* a, lapack_int lda, double* b,\n                           lapack_int ldb, double* d, double* x, double* y );\nlapack_int LAPACKE_cggglm( int matrix_order, lapack_int n, lapack_int m,\n                           lapack_int p, lapack_complex_float* a,\n                           lapack_int lda, lapack_complex_float* b,\n                           lapack_int ldb, lapack_complex_float* d,\n                           lapack_complex_float* x, lapack_complex_float* y );\nlapack_int LAPACKE_zggglm( int matrix_order, lapack_int n, lapack_int m,\n                           lapack_int p, lapack_complex_double* a,\n                           lapack_int lda, lapack_complex_double* b,\n                           lapack_int ldb, lapack_complex_double* d,\n                           lapack_complex_double* x, lapack_complex_double* y );\n\nlapack_int LAPACKE_sgghrd( int matrix_order, char compq, char compz,\n                           lapack_int n, lapack_int ilo, lapack_int ihi,\n                           float* a, lapack_int lda, float* b, lapack_int ldb,\n                           float* q, lapack_int ldq, float* z, lapack_int ldz );\nlapack_int LAPACKE_dgghrd( int matrix_order, char compq, char compz,\n                           lapack_int n, lapack_int ilo, lapack_int ihi,\n                           double* a, lapack_int lda, double* b, lapack_int ldb,\n                           double* q, lapack_int ldq, double* z,\n                           lapack_int ldz );\nlapack_int LAPACKE_cgghrd( int matrix_order, char compq, char compz,\n                           lapack_int n, lapack_int ilo, lapack_int ihi,\n                           lapack_complex_float* a, lapack_int lda,\n                           lapack_complex_float* b, lapack_int ldb,\n                           lapack_complex_float* q, lapack_int ldq,\n                           lapack_complex_float* z, lapack_int ldz );\nlapack_int LAPACKE_zgghrd( int matrix_order, char compq, char compz,\n                           lapack_int n, lapack_int ilo, lapack_int ihi,\n                           lapack_complex_double* a, lapack_int lda,\n                           lapack_complex_double* b, lapack_int ldb,\n                           lapack_complex_double* q, lapack_int ldq,\n                           lapack_complex_double* z, lapack_int ldz );\n\nlapack_int LAPACKE_sgglse( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int p, float* a, lapack_int lda, float* b,\n                           lapack_int ldb, float* c, float* d, float* x );\nlapack_int LAPACKE_dgglse( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int p, double* a, lapack_int lda, double* b,\n                           lapack_int ldb, double* c, double* d, double* x );\nlapack_int LAPACKE_cgglse( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int p, lapack_complex_float* a,\n                           lapack_int lda, lapack_complex_float* b,\n                           lapack_int ldb, lapack_complex_float* c,\n                           lapack_complex_float* d, lapack_complex_float* x );\nlapack_int LAPACKE_zgglse( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int p, lapack_complex_double* a,\n                           lapack_int lda, lapack_complex_double* b,\n                           lapack_int ldb, lapack_complex_double* c,\n                           lapack_complex_double* d, lapack_complex_double* x );\n\nlapack_int LAPACKE_sggqrf( int matrix_order, lapack_int n, lapack_int m,\n                           lapack_int p, float* a, lapack_int lda, float* taua,\n                           float* b, lapack_int ldb, float* taub );\nlapack_int LAPACKE_dggqrf( int matrix_order, lapack_int n, lapack_int m,\n                           lapack_int p, double* a, lapack_int lda,\n                           double* taua, double* b, lapack_int ldb,\n                           double* taub );\nlapack_int LAPACKE_cggqrf( int matrix_order, lapack_int n, lapack_int m,\n                           lapack_int p, lapack_complex_float* a,\n                           lapack_int lda, lapack_complex_float* taua,\n                           lapack_complex_float* b, lapack_int ldb,\n                           lapack_complex_float* taub );\nlapack_int LAPACKE_zggqrf( int matrix_order, lapack_int n, lapack_int m,\n                           lapack_int p, lapack_complex_double* a,\n                           lapack_int lda, lapack_complex_double* taua,\n                           lapack_complex_double* b, lapack_int ldb,\n                           lapack_complex_double* taub );\n\nlapack_int LAPACKE_sggrqf( int matrix_order, lapack_int m, lapack_int p,\n                           lapack_int n, float* a, lapack_int lda, float* taua,\n                           float* b, lapack_int ldb, float* taub );\nlapack_int LAPACKE_dggrqf( int matrix_order, lapack_int m, lapack_int p,\n                           lapack_int n, double* a, lapack_int lda,\n                           double* taua, double* b, lapack_int ldb,\n                           double* taub );\nlapack_int LAPACKE_cggrqf( int matrix_order, lapack_int m, lapack_int p,\n                           lapack_int n, lapack_complex_float* a,\n                           lapack_int lda, lapack_complex_float* taua,\n                           lapack_complex_float* b, lapack_int ldb,\n                           lapack_complex_float* taub );\nlapack_int LAPACKE_zggrqf( int matrix_order, lapack_int m, lapack_int p,\n                           lapack_int n, lapack_complex_double* a,\n                           lapack_int lda, lapack_complex_double* taua,\n                           lapack_complex_double* b, lapack_int ldb,\n                           lapack_complex_double* taub );\n\nlapack_int LAPACKE_sggsvd( int matrix_order, char jobu, char jobv, char jobq,\n                           lapack_int m, lapack_int n, lapack_int p,\n                           lapack_int* k, lapack_int* l, float* a,\n                           lapack_int lda, float* b, lapack_int ldb,\n                           float* alpha, float* beta, float* u, lapack_int ldu,\n                           float* v, lapack_int ldv, float* q, lapack_int ldq,\n                           lapack_int* iwork );\nlapack_int LAPACKE_dggsvd( int matrix_order, char jobu, char jobv, char jobq,\n                           lapack_int m, lapack_int n, lapack_int p,\n                           lapack_int* k, lapack_int* l, double* a,\n                           lapack_int lda, double* b, lapack_int ldb,\n                           double* alpha, double* beta, double* u,\n                           lapack_int ldu, double* v, lapack_int ldv, double* q,\n                           lapack_int ldq, lapack_int* iwork );\nlapack_int LAPACKE_cggsvd( int matrix_order, char jobu, char jobv, char jobq,\n                           lapack_int m, lapack_int n, lapack_int p,\n                           lapack_int* k, lapack_int* l,\n                           lapack_complex_float* a, lapack_int lda,\n                           lapack_complex_float* b, lapack_int ldb,\n                           float* alpha, float* beta, lapack_complex_float* u,\n                           lapack_int ldu, lapack_complex_float* v,\n                           lapack_int ldv, lapack_complex_float* q,\n                           lapack_int ldq, lapack_int* iwork );\nlapack_int LAPACKE_zggsvd( int matrix_order, char jobu, char jobv, char jobq,\n                           lapack_int m, lapack_int n, lapack_int p,\n                           lapack_int* k, lapack_int* l,\n                           lapack_complex_double* a, lapack_int lda,\n                           lapack_complex_double* b, lapack_int ldb,\n                           double* alpha, double* beta,\n                           lapack_complex_double* u, lapack_int ldu,\n                           lapack_complex_double* v, lapack_int ldv,\n                           lapack_complex_double* q, lapack_int ldq,\n                           lapack_int* iwork );\n\nlapack_int LAPACKE_sggsvp( int matrix_order, char jobu, char jobv, char jobq,\n                           lapack_int m, lapack_int p, lapack_int n, float* a,\n                           lapack_int lda, float* b, lapack_int ldb, float tola,\n                           float tolb, lapack_int* k, lapack_int* l, float* u,\n                           lapack_int ldu, float* v, lapack_int ldv, float* q,\n                           lapack_int ldq );\nlapack_int LAPACKE_dggsvp( int matrix_order, char jobu, char jobv, char jobq,\n                           lapack_int m, lapack_int p, lapack_int n, double* a,\n                           lapack_int lda, double* b, lapack_int ldb,\n                           double tola, double tolb, lapack_int* k,\n                           lapack_int* l, double* u, lapack_int ldu, double* v,\n                           lapack_int ldv, double* q, lapack_int ldq );\nlapack_int LAPACKE_cggsvp( int matrix_order, char jobu, char jobv, char jobq,\n                           lapack_int m, lapack_int p, lapack_int n,\n                           lapack_complex_float* a, lapack_int lda,\n                           lapack_complex_float* b, lapack_int ldb, float tola,\n                           float tolb, lapack_int* k, lapack_int* l,\n                           lapack_complex_float* u, lapack_int ldu,\n                           lapack_complex_float* v, lapack_int ldv,\n                           lapack_complex_float* q, lapack_int ldq );\nlapack_int LAPACKE_zggsvp( int matrix_order, char jobu, char jobv, char jobq,\n                           lapack_int m, lapack_int p, lapack_int n,\n                           lapack_complex_double* a, lapack_int lda,\n                           lapack_complex_double* b, lapack_int ldb,\n                           double tola, double tolb, lapack_int* k,\n                           lapack_int* l, lapack_complex_double* u,\n                           lapack_int ldu, lapack_complex_double* v,\n                           lapack_int ldv, lapack_complex_double* q,\n                           lapack_int ldq );\n\nlapack_int LAPACKE_sgtcon( char norm, lapack_int n, const float* dl,\n                           const float* d, const float* du, const float* du2,\n                           const lapack_int* ipiv, float anorm, float* rcond );\nlapack_int LAPACKE_dgtcon( char norm, lapack_int n, const double* dl,\n                           const double* d, const double* du, const double* du2,\n                           const lapack_int* ipiv, double anorm,\n                           double* rcond );\nlapack_int LAPACKE_cgtcon( char norm, lapack_int n,\n                           const lapack_complex_float* dl,\n                           const lapack_complex_float* d,\n                           const lapack_complex_float* du,\n                           const lapack_complex_float* du2,\n                           const lapack_int* ipiv, float anorm, float* rcond );\nlapack_int LAPACKE_zgtcon( char norm, lapack_int n,\n                           const lapack_complex_double* dl,\n                           const lapack_complex_double* d,\n                           const lapack_complex_double* du,\n                           const lapack_complex_double* du2,\n                           const lapack_int* ipiv, double anorm,\n                           double* rcond );\n\nlapack_int LAPACKE_sgtrfs( int matrix_order, char trans, lapack_int n,\n                           lapack_int nrhs, const float* dl, const float* d,\n                           const float* du, const float* dlf, const float* df,\n                           const float* duf, const float* du2,\n                           const lapack_int* ipiv, const float* b,\n                           lapack_int ldb, float* x, lapack_int ldx,\n                           float* ferr, float* berr );\nlapack_int LAPACKE_dgtrfs( int matrix_order, char trans, lapack_int n,\n                           lapack_int nrhs, const double* dl, const double* d,\n                           const double* du, const double* dlf,\n                           const double* df, const double* duf,\n                           const double* du2, const lapack_int* ipiv,\n                           const double* b, lapack_int ldb, double* x,\n                           lapack_int ldx, double* ferr, double* berr );\nlapack_int LAPACKE_cgtrfs( int matrix_order, char trans, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_float* dl,\n                           const lapack_complex_float* d,\n                           const lapack_complex_float* du,\n                           const lapack_complex_float* dlf,\n                           const lapack_complex_float* df,\n                           const lapack_complex_float* duf,\n                           const lapack_complex_float* du2,\n                           const lapack_int* ipiv,\n                           const lapack_complex_float* b, lapack_int ldb,\n                           lapack_complex_float* x, lapack_int ldx, float* ferr,\n                           float* berr );\nlapack_int LAPACKE_zgtrfs( int matrix_order, char trans, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_double* dl,\n                           const lapack_complex_double* d,\n                           const lapack_complex_double* du,\n                           const lapack_complex_double* dlf,\n                           const lapack_complex_double* df,\n                           const lapack_complex_double* duf,\n                           const lapack_complex_double* du2,\n                           const lapack_int* ipiv,\n                           const lapack_complex_double* b, lapack_int ldb,\n                           lapack_complex_double* x, lapack_int ldx,\n                           double* ferr, double* berr );\n\nlapack_int LAPACKE_sgtsv( int matrix_order, lapack_int n, lapack_int nrhs,\n                          float* dl, float* d, float* du, float* b,\n                          lapack_int ldb );\nlapack_int LAPACKE_dgtsv( int matrix_order, lapack_int n, lapack_int nrhs,\n                          double* dl, double* d, double* du, double* b,\n                          lapack_int ldb );\nlapack_int LAPACKE_cgtsv( int matrix_order, lapack_int n, lapack_int nrhs,\n                          lapack_complex_float* dl, lapack_complex_float* d,\n                          lapack_complex_float* du, lapack_complex_float* b,\n                          lapack_int ldb );\nlapack_int LAPACKE_zgtsv( int matrix_order, lapack_int n, lapack_int nrhs,\n                          lapack_complex_double* dl, lapack_complex_double* d,\n                          lapack_complex_double* du, lapack_complex_double* b,\n                          lapack_int ldb );\n\nlapack_int LAPACKE_sgtsvx( int matrix_order, char fact, char trans,\n                           lapack_int n, lapack_int nrhs, const float* dl,\n                           const float* d, const float* du, float* dlf,\n                           float* df, float* duf, float* du2, lapack_int* ipiv,\n                           const float* b, lapack_int ldb, float* x,\n                           lapack_int ldx, float* rcond, float* ferr,\n                           float* berr );\nlapack_int LAPACKE_dgtsvx( int matrix_order, char fact, char trans,\n                           lapack_int n, lapack_int nrhs, const double* dl,\n                           const double* d, const double* du, double* dlf,\n                           double* df, double* duf, double* du2,\n                           lapack_int* ipiv, const double* b, lapack_int ldb,\n                           double* x, lapack_int ldx, double* rcond,\n                           double* ferr, double* berr );\nlapack_int LAPACKE_cgtsvx( int matrix_order, char fact, char trans,\n                           lapack_int n, lapack_int nrhs,\n                           const lapack_complex_float* dl,\n                           const lapack_complex_float* d,\n                           const lapack_complex_float* du,\n                           lapack_complex_float* dlf, lapack_complex_float* df,\n                           lapack_complex_float* duf, lapack_complex_float* du2,\n                           lapack_int* ipiv, const lapack_complex_float* b,\n                           lapack_int ldb, lapack_complex_float* x,\n                           lapack_int ldx, float* rcond, float* ferr,\n                           float* berr );\nlapack_int LAPACKE_zgtsvx( int matrix_order, char fact, char trans,\n                           lapack_int n, lapack_int nrhs,\n                           const lapack_complex_double* dl,\n                           const lapack_complex_double* d,\n                           const lapack_complex_double* du,\n                           lapack_complex_double* dlf,\n                           lapack_complex_double* df,\n                           lapack_complex_double* duf,\n                           lapack_complex_double* du2, lapack_int* ipiv,\n                           const lapack_complex_double* b, lapack_int ldb,\n                           lapack_complex_double* x, lapack_int ldx,\n                           double* rcond, double* ferr, double* berr );\n\nlapack_int LAPACKE_sgttrf( lapack_int n, float* dl, float* d, float* du,\n                           float* du2, lapack_int* ipiv );\nlapack_int LAPACKE_dgttrf( lapack_int n, double* dl, double* d, double* du,\n                           double* du2, lapack_int* ipiv );\nlapack_int LAPACKE_cgttrf( lapack_int n, lapack_complex_float* dl,\n                           lapack_complex_float* d, lapack_complex_float* du,\n                           lapack_complex_float* du2, lapack_int* ipiv );\nlapack_int LAPACKE_zgttrf( lapack_int n, lapack_complex_double* dl,\n                           lapack_complex_double* d, lapack_complex_double* du,\n                           lapack_complex_double* du2, lapack_int* ipiv );\n\nlapack_int LAPACKE_sgttrs( int matrix_order, char trans, lapack_int n,\n                           lapack_int nrhs, const float* dl, const float* d,\n                           const float* du, const float* du2,\n                           const lapack_int* ipiv, float* b, lapack_int ldb );\nlapack_int LAPACKE_dgttrs( int matrix_order, char trans, lapack_int n,\n                           lapack_int nrhs, const double* dl, const double* d,\n                           const double* du, const double* du2,\n                           const lapack_int* ipiv, double* b, lapack_int ldb );\nlapack_int LAPACKE_cgttrs( int matrix_order, char trans, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_float* dl,\n                           const lapack_complex_float* d,\n                           const lapack_complex_float* du,\n                           const lapack_complex_float* du2,\n                           const lapack_int* ipiv, lapack_complex_float* b,\n                           lapack_int ldb );\nlapack_int LAPACKE_zgttrs( int matrix_order, char trans, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_double* dl,\n                           const lapack_complex_double* d,\n                           const lapack_complex_double* du,\n                           const lapack_complex_double* du2,\n                           const lapack_int* ipiv, lapack_complex_double* b,\n                           lapack_int ldb );\n\nlapack_int LAPACKE_chbev( int matrix_order, char jobz, char uplo, lapack_int n,\n                          lapack_int kd, lapack_complex_float* ab,\n                          lapack_int ldab, float* w, lapack_complex_float* z,\n                          lapack_int ldz );\nlapack_int LAPACKE_zhbev( int matrix_order, char jobz, char uplo, lapack_int n,\n                          lapack_int kd, lapack_complex_double* ab,\n                          lapack_int ldab, double* w, lapack_complex_double* z,\n                          lapack_int ldz );\n\nlapack_int LAPACKE_chbevd( int matrix_order, char jobz, char uplo, lapack_int n,\n                           lapack_int kd, lapack_complex_float* ab,\n                           lapack_int ldab, float* w, lapack_complex_float* z,\n                           lapack_int ldz );\nlapack_int LAPACKE_zhbevd( int matrix_order, char jobz, char uplo, lapack_int n,\n                           lapack_int kd, lapack_complex_double* ab,\n                           lapack_int ldab, double* w, lapack_complex_double* z,\n                           lapack_int ldz );\n\nlapack_int LAPACKE_chbevx( int matrix_order, char jobz, char range, char uplo,\n                           lapack_int n, lapack_int kd,\n                           lapack_complex_float* ab, lapack_int ldab,\n                           lapack_complex_float* q, lapack_int ldq, float vl,\n                           float vu, lapack_int il, lapack_int iu, float abstol,\n                           lapack_int* m, float* w, lapack_complex_float* z,\n                           lapack_int ldz, lapack_int* ifail );\nlapack_int LAPACKE_zhbevx( int matrix_order, char jobz, char range, char uplo,\n                           lapack_int n, lapack_int kd,\n                           lapack_complex_double* ab, lapack_int ldab,\n                           lapack_complex_double* q, lapack_int ldq, double vl,\n                           double vu, lapack_int il, lapack_int iu,\n                           double abstol, lapack_int* m, double* w,\n                           lapack_complex_double* z, lapack_int ldz,\n                           lapack_int* ifail );\n\nlapack_int LAPACKE_chbgst( int matrix_order, char vect, char uplo, lapack_int n,\n                           lapack_int ka, lapack_int kb,\n                           lapack_complex_float* ab, lapack_int ldab,\n                           const lapack_complex_float* bb, lapack_int ldbb,\n                           lapack_complex_float* x, lapack_int ldx );\nlapack_int LAPACKE_zhbgst( int matrix_order, char vect, char uplo, lapack_int n,\n                           lapack_int ka, lapack_int kb,\n                           lapack_complex_double* ab, lapack_int ldab,\n                           const lapack_complex_double* bb, lapack_int ldbb,\n                           lapack_complex_double* x, lapack_int ldx );\n\nlapack_int LAPACKE_chbgv( int matrix_order, char jobz, char uplo, lapack_int n,\n                          lapack_int ka, lapack_int kb,\n                          lapack_complex_float* ab, lapack_int ldab,\n                          lapack_complex_float* bb, lapack_int ldbb, float* w,\n                          lapack_complex_float* z, lapack_int ldz );\nlapack_int LAPACKE_zhbgv( int matrix_order, char jobz, char uplo, lapack_int n,\n                          lapack_int ka, lapack_int kb,\n                          lapack_complex_double* ab, lapack_int ldab,\n                          lapack_complex_double* bb, lapack_int ldbb, double* w,\n                          lapack_complex_double* z, lapack_int ldz );\n\nlapack_int LAPACKE_chbgvd( int matrix_order, char jobz, char uplo, lapack_int n,\n                           lapack_int ka, lapack_int kb,\n                           lapack_complex_float* ab, lapack_int ldab,\n                           lapack_complex_float* bb, lapack_int ldbb, float* w,\n                           lapack_complex_float* z, lapack_int ldz );\nlapack_int LAPACKE_zhbgvd( int matrix_order, char jobz, char uplo, lapack_int n,\n                           lapack_int ka, lapack_int kb,\n                           lapack_complex_double* ab, lapack_int ldab,\n                           lapack_complex_double* bb, lapack_int ldbb,\n                           double* w, lapack_complex_double* z,\n                           lapack_int ldz );\n\nlapack_int LAPACKE_chbgvx( int matrix_order, char jobz, char range, char uplo,\n                           lapack_int n, lapack_int ka, lapack_int kb,\n                           lapack_complex_float* ab, lapack_int ldab,\n                           lapack_complex_float* bb, lapack_int ldbb,\n                           lapack_complex_float* q, lapack_int ldq, float vl,\n                           float vu, lapack_int il, lapack_int iu, float abstol,\n                           lapack_int* m, float* w, lapack_complex_float* z,\n                           lapack_int ldz, lapack_int* ifail );\nlapack_int LAPACKE_zhbgvx( int matrix_order, char jobz, char range, char uplo,\n                           lapack_int n, lapack_int ka, lapack_int kb,\n                           lapack_complex_double* ab, lapack_int ldab,\n                           lapack_complex_double* bb, lapack_int ldbb,\n                           lapack_complex_double* q, lapack_int ldq, double vl,\n                           double vu, lapack_int il, lapack_int iu,\n                           double abstol, lapack_int* m, double* w,\n                           lapack_complex_double* z, lapack_int ldz,\n                           lapack_int* ifail );\n\nlapack_int LAPACKE_chbtrd( int matrix_order, char vect, char uplo, lapack_int n,\n                           lapack_int kd, lapack_complex_float* ab,\n                           lapack_int ldab, float* d, float* e,\n                           lapack_complex_float* q, lapack_int ldq );\nlapack_int LAPACKE_zhbtrd( int matrix_order, char vect, char uplo, lapack_int n,\n                           lapack_int kd, lapack_complex_double* ab,\n                           lapack_int ldab, double* d, double* e,\n                           lapack_complex_double* q, lapack_int ldq );\n\nlapack_int LAPACKE_checon( int matrix_order, char uplo, lapack_int n,\n                           const lapack_complex_float* a, lapack_int lda,\n                           const lapack_int* ipiv, float anorm, float* rcond );\nlapack_int LAPACKE_zhecon( int matrix_order, char uplo, lapack_int n,\n                           const lapack_complex_double* a, lapack_int lda,\n                           const lapack_int* ipiv, double anorm,\n                           double* rcond );\n\nlapack_int LAPACKE_cheequb( int matrix_order, char uplo, lapack_int n,\n                            const lapack_complex_float* a, lapack_int lda,\n                            float* s, float* scond, float* amax );\nlapack_int LAPACKE_zheequb( int matrix_order, char uplo, lapack_int n,\n                            const lapack_complex_double* a, lapack_int lda,\n                            double* s, double* scond, double* amax );\n\nlapack_int LAPACKE_cheev( int matrix_order, char jobz, char uplo, lapack_int n,\n                          lapack_complex_float* a, lapack_int lda, float* w );\nlapack_int LAPACKE_zheev( int matrix_order, char jobz, char uplo, lapack_int n,\n                          lapack_complex_double* a, lapack_int lda, double* w );\n\nlapack_int LAPACKE_cheevd( int matrix_order, char jobz, char uplo, lapack_int n,\n                           lapack_complex_float* a, lapack_int lda, float* w );\nlapack_int LAPACKE_zheevd( int matrix_order, char jobz, char uplo, lapack_int n,\n                           lapack_complex_double* a, lapack_int lda,\n                           double* w );\n\nlapack_int LAPACKE_cheevr( int matrix_order, char jobz, char range, char uplo,\n                           lapack_int n, lapack_complex_float* a,\n                           lapack_int lda, float vl, float vu, lapack_int il,\n                           lapack_int iu, float abstol, lapack_int* m, float* w,\n                           lapack_complex_float* z, lapack_int ldz,\n                           lapack_int* isuppz );\nlapack_int LAPACKE_zheevr( int matrix_order, char jobz, char range, char uplo,\n                           lapack_int n, lapack_complex_double* a,\n                           lapack_int lda, double vl, double vu, lapack_int il,\n                           lapack_int iu, double abstol, lapack_int* m,\n                           double* w, lapack_complex_double* z, lapack_int ldz,\n                           lapack_int* isuppz );\n\nlapack_int LAPACKE_cheevx( int matrix_order, char jobz, char range, char uplo,\n                           lapack_int n, lapack_complex_float* a,\n                           lapack_int lda, float vl, float vu, lapack_int il,\n                           lapack_int iu, float abstol, lapack_int* m, float* w,\n                           lapack_complex_float* z, lapack_int ldz,\n                           lapack_int* ifail );\nlapack_int LAPACKE_zheevx( int matrix_order, char jobz, char range, char uplo,\n                           lapack_int n, lapack_complex_double* a,\n                           lapack_int lda, double vl, double vu, lapack_int il,\n                           lapack_int iu, double abstol, lapack_int* m,\n                           double* w, lapack_complex_double* z, lapack_int ldz,\n                           lapack_int* ifail );\n\nlapack_int LAPACKE_chegst( int matrix_order, lapack_int itype, char uplo,\n                           lapack_int n, lapack_complex_float* a,\n                           lapack_int lda, const lapack_complex_float* b,\n                           lapack_int ldb );\nlapack_int LAPACKE_zhegst( int matrix_order, lapack_int itype, char uplo,\n                           lapack_int n, lapack_complex_double* a,\n                           lapack_int lda, const lapack_complex_double* b,\n                           lapack_int ldb );\n\nlapack_int LAPACKE_chegv( int matrix_order, lapack_int itype, char jobz,\n                          char uplo, lapack_int n, lapack_complex_float* a,\n                          lapack_int lda, lapack_complex_float* b,\n                          lapack_int ldb, float* w );\nlapack_int LAPACKE_zhegv( int matrix_order, lapack_int itype, char jobz,\n                          char uplo, lapack_int n, lapack_complex_double* a,\n                          lapack_int lda, lapack_complex_double* b,\n                          lapack_int ldb, double* w );\n\nlapack_int LAPACKE_chegvd( int matrix_order, lapack_int itype, char jobz,\n                           char uplo, lapack_int n, lapack_complex_float* a,\n                           lapack_int lda, lapack_complex_float* b,\n                           lapack_int ldb, float* w );\nlapack_int LAPACKE_zhegvd( int matrix_order, lapack_int itype, char jobz,\n                           char uplo, lapack_int n, lapack_complex_double* a,\n                           lapack_int lda, lapack_complex_double* b,\n                           lapack_int ldb, double* w );\n\nlapack_int LAPACKE_chegvx( int matrix_order, lapack_int itype, char jobz,\n                           char range, char uplo, lapack_int n,\n                           lapack_complex_float* a, lapack_int lda,\n                           lapack_complex_float* b, lapack_int ldb, float vl,\n                           float vu, lapack_int il, lapack_int iu, float abstol,\n                           lapack_int* m, float* w, lapack_complex_float* z,\n                           lapack_int ldz, lapack_int* ifail );\nlapack_int LAPACKE_zhegvx( int matrix_order, lapack_int itype, char jobz,\n                           char range, char uplo, lapack_int n,\n                           lapack_complex_double* a, lapack_int lda,\n                           lapack_complex_double* b, lapack_int ldb, double vl,\n                           double vu, lapack_int il, lapack_int iu,\n                           double abstol, lapack_int* m, double* w,\n                           lapack_complex_double* z, lapack_int ldz,\n                           lapack_int* ifail );\n\nlapack_int LAPACKE_cherfs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_float* a,\n                           lapack_int lda, const lapack_complex_float* af,\n                           lapack_int ldaf, const lapack_int* ipiv,\n                           const lapack_complex_float* b, lapack_int ldb,\n                           lapack_complex_float* x, lapack_int ldx, float* ferr,\n                           float* berr );\nlapack_int LAPACKE_zherfs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_double* a,\n                           lapack_int lda, const lapack_complex_double* af,\n                           lapack_int ldaf, const lapack_int* ipiv,\n                           const lapack_complex_double* b, lapack_int ldb,\n                           lapack_complex_double* x, lapack_int ldx,\n                           double* ferr, double* berr );\n\nlapack_int LAPACKE_cherfsx( int matrix_order, char uplo, char equed,\n                            lapack_int n, lapack_int nrhs,\n                            const lapack_complex_float* a, lapack_int lda,\n                            const lapack_complex_float* af, lapack_int ldaf,\n                            const lapack_int* ipiv, const float* s,\n                            const lapack_complex_float* b, lapack_int ldb,\n                            lapack_complex_float* x, lapack_int ldx,\n                            float* rcond, float* berr, lapack_int n_err_bnds,\n                            float* err_bnds_norm, float* err_bnds_comp,\n                            lapack_int nparams, float* params );\nlapack_int LAPACKE_zherfsx( int matrix_order, char uplo, char equed,\n                            lapack_int n, lapack_int nrhs,\n                            const lapack_complex_double* a, lapack_int lda,\n                            const lapack_complex_double* af, lapack_int ldaf,\n                            const lapack_int* ipiv, const double* s,\n                            const lapack_complex_double* b, lapack_int ldb,\n                            lapack_complex_double* x, lapack_int ldx,\n                            double* rcond, double* berr, lapack_int n_err_bnds,\n                            double* err_bnds_norm, double* err_bnds_comp,\n                            lapack_int nparams, double* params );\n\nlapack_int LAPACKE_chesv( int matrix_order, char uplo, lapack_int n,\n                          lapack_int nrhs, lapack_complex_float* a,\n                          lapack_int lda, lapack_int* ipiv,\n                          lapack_complex_float* b, lapack_int ldb );\nlapack_int LAPACKE_zhesv( int matrix_order, char uplo, lapack_int n,\n                          lapack_int nrhs, lapack_complex_double* a,\n                          lapack_int lda, lapack_int* ipiv,\n                          lapack_complex_double* b, lapack_int ldb );\n\nlapack_int LAPACKE_chesvx( int matrix_order, char fact, char uplo, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_float* a,\n                           lapack_int lda, lapack_complex_float* af,\n                           lapack_int ldaf, lapack_int* ipiv,\n                           const lapack_complex_float* b, lapack_int ldb,\n                           lapack_complex_float* x, lapack_int ldx,\n                           float* rcond, float* ferr, float* berr );\nlapack_int LAPACKE_zhesvx( int matrix_order, char fact, char uplo, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_double* a,\n                           lapack_int lda, lapack_complex_double* af,\n                           lapack_int ldaf, lapack_int* ipiv,\n                           const lapack_complex_double* b, lapack_int ldb,\n                           lapack_complex_double* x, lapack_int ldx,\n                           double* rcond, double* ferr, double* berr );\n\nlapack_int LAPACKE_chesvxx( int matrix_order, char fact, char uplo,\n                            lapack_int n, lapack_int nrhs,\n                            lapack_complex_float* a, lapack_int lda,\n                            lapack_complex_float* af, lapack_int ldaf,\n                            lapack_int* ipiv, char* equed, float* s,\n                            lapack_complex_float* b, lapack_int ldb,\n                            lapack_complex_float* x, lapack_int ldx,\n                            float* rcond, float* rpvgrw, float* berr,\n                            lapack_int n_err_bnds, float* err_bnds_norm,\n                            float* err_bnds_comp, lapack_int nparams,\n                            float* params );\nlapack_int LAPACKE_zhesvxx( int matrix_order, char fact, char uplo,\n                            lapack_int n, lapack_int nrhs,\n                            lapack_complex_double* a, lapack_int lda,\n                            lapack_complex_double* af, lapack_int ldaf,\n                            lapack_int* ipiv, char* equed, double* s,\n                            lapack_complex_double* b, lapack_int ldb,\n                            lapack_complex_double* x, lapack_int ldx,\n                            double* rcond, double* rpvgrw, double* berr,\n                            lapack_int n_err_bnds, double* err_bnds_norm,\n                            double* err_bnds_comp, lapack_int nparams,\n                            double* params );\n\nlapack_int LAPACKE_chetrd( int matrix_order, char uplo, lapack_int n,\n                           lapack_complex_float* a, lapack_int lda, float* d,\n                           float* e, lapack_complex_float* tau );\nlapack_int LAPACKE_zhetrd( int matrix_order, char uplo, lapack_int n,\n                           lapack_complex_double* a, lapack_int lda, double* d,\n                           double* e, lapack_complex_double* tau );\n\nlapack_int LAPACKE_chetrf( int matrix_order, char uplo, lapack_int n,\n                           lapack_complex_float* a, lapack_int lda,\n                           lapack_int* ipiv );\nlapack_int LAPACKE_zhetrf( int matrix_order, char uplo, lapack_int n,\n                           lapack_complex_double* a, lapack_int lda,\n                           lapack_int* ipiv );\n\nlapack_int LAPACKE_chetri( int matrix_order, char uplo, lapack_int n,\n                           lapack_complex_float* a, lapack_int lda,\n                           const lapack_int* ipiv );\nlapack_int LAPACKE_zhetri( int matrix_order, char uplo, lapack_int n,\n                           lapack_complex_double* a, lapack_int lda,\n                           const lapack_int* ipiv );\n\nlapack_int LAPACKE_chetrs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_float* a,\n                           lapack_int lda, const lapack_int* ipiv,\n                           lapack_complex_float* b, lapack_int ldb );\nlapack_int LAPACKE_zhetrs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_double* a,\n                           lapack_int lda, const lapack_int* ipiv,\n                           lapack_complex_double* b, lapack_int ldb );\n\nlapack_int LAPACKE_chfrk( int matrix_order, char transr, char uplo, char trans,\n                          lapack_int n, lapack_int k, float alpha,\n                          const lapack_complex_float* a, lapack_int lda,\n                          float beta, lapack_complex_float* c );\nlapack_int LAPACKE_zhfrk( int matrix_order, char transr, char uplo, char trans,\n                          lapack_int n, lapack_int k, double alpha,\n                          const lapack_complex_double* a, lapack_int lda,\n                          double beta, lapack_complex_double* c );\n\nlapack_int LAPACKE_shgeqz( int matrix_order, char job, char compq, char compz,\n                           lapack_int n, lapack_int ilo, lapack_int ihi,\n                           float* h, lapack_int ldh, float* t, lapack_int ldt,\n                           float* alphar, float* alphai, float* beta, float* q,\n                           lapack_int ldq, float* z, lapack_int ldz );\nlapack_int LAPACKE_dhgeqz( int matrix_order, char job, char compq, char compz,\n                           lapack_int n, lapack_int ilo, lapack_int ihi,\n                           double* h, lapack_int ldh, double* t, lapack_int ldt,\n                           double* alphar, double* alphai, double* beta,\n                           double* q, lapack_int ldq, double* z,\n                           lapack_int ldz );\nlapack_int LAPACKE_chgeqz( int matrix_order, char job, char compq, char compz,\n                           lapack_int n, lapack_int ilo, lapack_int ihi,\n                           lapack_complex_float* h, lapack_int ldh,\n                           lapack_complex_float* t, lapack_int ldt,\n                           lapack_complex_float* alpha,\n                           lapack_complex_float* beta, lapack_complex_float* q,\n                           lapack_int ldq, lapack_complex_float* z,\n                           lapack_int ldz );\nlapack_int LAPACKE_zhgeqz( int matrix_order, char job, char compq, char compz,\n                           lapack_int n, lapack_int ilo, lapack_int ihi,\n                           lapack_complex_double* h, lapack_int ldh,\n                           lapack_complex_double* t, lapack_int ldt,\n                           lapack_complex_double* alpha,\n                           lapack_complex_double* beta,\n                           lapack_complex_double* q, lapack_int ldq,\n                           lapack_complex_double* z, lapack_int ldz );\n\nlapack_int LAPACKE_chpcon( int matrix_order, char uplo, lapack_int n,\n                           const lapack_complex_float* ap,\n                           const lapack_int* ipiv, float anorm, float* rcond );\nlapack_int LAPACKE_zhpcon( int matrix_order, char uplo, lapack_int n,\n                           const lapack_complex_double* ap,\n                           const lapack_int* ipiv, double anorm,\n                           double* rcond );\n\nlapack_int LAPACKE_chpev( int matrix_order, char jobz, char uplo, lapack_int n,\n                          lapack_complex_float* ap, float* w,\n                          lapack_complex_float* z, lapack_int ldz );\nlapack_int LAPACKE_zhpev( int matrix_order, char jobz, char uplo, lapack_int n,\n                          lapack_complex_double* ap, double* w,\n                          lapack_complex_double* z, lapack_int ldz );\n\nlapack_int LAPACKE_chpevd( int matrix_order, char jobz, char uplo, lapack_int n,\n                           lapack_complex_float* ap, float* w,\n                           lapack_complex_float* z, lapack_int ldz );\nlapack_int LAPACKE_zhpevd( int matrix_order, char jobz, char uplo, lapack_int n,\n                           lapack_complex_double* ap, double* w,\n                           lapack_complex_double* z, lapack_int ldz );\n\nlapack_int LAPACKE_chpevx( int matrix_order, char jobz, char range, char uplo,\n                           lapack_int n, lapack_complex_float* ap, float vl,\n                           float vu, lapack_int il, lapack_int iu, float abstol,\n                           lapack_int* m, float* w, lapack_complex_float* z,\n                           lapack_int ldz, lapack_int* ifail );\nlapack_int LAPACKE_zhpevx( int matrix_order, char jobz, char range, char uplo,\n                           lapack_int n, lapack_complex_double* ap, double vl,\n                           double vu, lapack_int il, lapack_int iu,\n                           double abstol, lapack_int* m, double* w,\n                           lapack_complex_double* z, lapack_int ldz,\n                           lapack_int* ifail );\n\nlapack_int LAPACKE_chpgst( int matrix_order, lapack_int itype, char uplo,\n                           lapack_int n, lapack_complex_float* ap,\n                           const lapack_complex_float* bp );\nlapack_int LAPACKE_zhpgst( int matrix_order, lapack_int itype, char uplo,\n                           lapack_int n, lapack_complex_double* ap,\n                           const lapack_complex_double* bp );\n\nlapack_int LAPACKE_chpgv( int matrix_order, lapack_int itype, char jobz,\n                          char uplo, lapack_int n, lapack_complex_float* ap,\n                          lapack_complex_float* bp, float* w,\n                          lapack_complex_float* z, lapack_int ldz );\nlapack_int LAPACKE_zhpgv( int matrix_order, lapack_int itype, char jobz,\n                          char uplo, lapack_int n, lapack_complex_double* ap,\n                          lapack_complex_double* bp, double* w,\n                          lapack_complex_double* z, lapack_int ldz );\n\nlapack_int LAPACKE_chpgvd( int matrix_order, lapack_int itype, char jobz,\n                           char uplo, lapack_int n, lapack_complex_float* ap,\n                           lapack_complex_float* bp, float* w,\n                           lapack_complex_float* z, lapack_int ldz );\nlapack_int LAPACKE_zhpgvd( int matrix_order, lapack_int itype, char jobz,\n                           char uplo, lapack_int n, lapack_complex_double* ap,\n                           lapack_complex_double* bp, double* w,\n                           lapack_complex_double* z, lapack_int ldz );\n\nlapack_int LAPACKE_chpgvx( int matrix_order, lapack_int itype, char jobz,\n                           char range, char uplo, lapack_int n,\n                           lapack_complex_float* ap, lapack_complex_float* bp,\n                           float vl, float vu, lapack_int il, lapack_int iu,\n                           float abstol, lapack_int* m, float* w,\n                           lapack_complex_float* z, lapack_int ldz,\n                           lapack_int* ifail );\nlapack_int LAPACKE_zhpgvx( int matrix_order, lapack_int itype, char jobz,\n                           char range, char uplo, lapack_int n,\n                           lapack_complex_double* ap, lapack_complex_double* bp,\n                           double vl, double vu, lapack_int il, lapack_int iu,\n                           double abstol, lapack_int* m, double* w,\n                           lapack_complex_double* z, lapack_int ldz,\n                           lapack_int* ifail );\n\nlapack_int LAPACKE_chprfs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_float* ap,\n                           const lapack_complex_float* afp,\n                           const lapack_int* ipiv,\n                           const lapack_complex_float* b, lapack_int ldb,\n                           lapack_complex_float* x, lapack_int ldx, float* ferr,\n                           float* berr );\nlapack_int LAPACKE_zhprfs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_double* ap,\n                           const lapack_complex_double* afp,\n                           const lapack_int* ipiv,\n                           const lapack_complex_double* b, lapack_int ldb,\n                           lapack_complex_double* x, lapack_int ldx,\n                           double* ferr, double* berr );\n\nlapack_int LAPACKE_chpsv( int matrix_order, char uplo, lapack_int n,\n                          lapack_int nrhs, lapack_complex_float* ap,\n                          lapack_int* ipiv, lapack_complex_float* b,\n                          lapack_int ldb );\nlapack_int LAPACKE_zhpsv( int matrix_order, char uplo, lapack_int n,\n                          lapack_int nrhs, lapack_complex_double* ap,\n                          lapack_int* ipiv, lapack_complex_double* b,\n                          lapack_int ldb );\n\nlapack_int LAPACKE_chpsvx( int matrix_order, char fact, char uplo, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_float* ap,\n                           lapack_complex_float* afp, lapack_int* ipiv,\n                           const lapack_complex_float* b, lapack_int ldb,\n                           lapack_complex_float* x, lapack_int ldx,\n                           float* rcond, float* ferr, float* berr );\nlapack_int LAPACKE_zhpsvx( int matrix_order, char fact, char uplo, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_double* ap,\n                           lapack_complex_double* afp, lapack_int* ipiv,\n                           const lapack_complex_double* b, lapack_int ldb,\n                           lapack_complex_double* x, lapack_int ldx,\n                           double* rcond, double* ferr, double* berr );\n\nlapack_int LAPACKE_chptrd( int matrix_order, char uplo, lapack_int n,\n                           lapack_complex_float* ap, float* d, float* e,\n                           lapack_complex_float* tau );\nlapack_int LAPACKE_zhptrd( int matrix_order, char uplo, lapack_int n,\n                           lapack_complex_double* ap, double* d, double* e,\n                           lapack_complex_double* tau );\n\nlapack_int LAPACKE_chptrf( int matrix_order, char uplo, lapack_int n,\n                           lapack_complex_float* ap, lapack_int* ipiv );\nlapack_int LAPACKE_zhptrf( int matrix_order, char uplo, lapack_int n,\n                           lapack_complex_double* ap, lapack_int* ipiv );\n\nlapack_int LAPACKE_chptri( int matrix_order, char uplo, lapack_int n,\n                           lapack_complex_float* ap, const lapack_int* ipiv );\nlapack_int LAPACKE_zhptri( int matrix_order, char uplo, lapack_int n,\n                           lapack_complex_double* ap, const lapack_int* ipiv );\n\nlapack_int LAPACKE_chptrs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_float* ap,\n                           const lapack_int* ipiv, lapack_complex_float* b,\n                           lapack_int ldb );\nlapack_int LAPACKE_zhptrs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_double* ap,\n                           const lapack_int* ipiv, lapack_complex_double* b,\n                           lapack_int ldb );\n\nlapack_int LAPACKE_shsein( int matrix_order, char job, char eigsrc, char initv,\n                           lapack_logical* select, lapack_int n, const float* h,\n                           lapack_int ldh, float* wr, const float* wi,\n                           float* vl, lapack_int ldvl, float* vr,\n                           lapack_int ldvr, lapack_int mm, lapack_int* m,\n                           lapack_int* ifaill, lapack_int* ifailr );\nlapack_int LAPACKE_dhsein( int matrix_order, char job, char eigsrc, char initv,\n                           lapack_logical* select, lapack_int n,\n                           const double* h, lapack_int ldh, double* wr,\n                           const double* wi, double* vl, lapack_int ldvl,\n                           double* vr, lapack_int ldvr, lapack_int mm,\n                           lapack_int* m, lapack_int* ifaill,\n                           lapack_int* ifailr );\nlapack_int LAPACKE_chsein( int matrix_order, char job, char eigsrc, char initv,\n                           const lapack_logical* select, lapack_int n,\n                           const lapack_complex_float* h, lapack_int ldh,\n                           lapack_complex_float* w, lapack_complex_float* vl,\n                           lapack_int ldvl, lapack_complex_float* vr,\n                           lapack_int ldvr, lapack_int mm, lapack_int* m,\n                           lapack_int* ifaill, lapack_int* ifailr );\nlapack_int LAPACKE_zhsein( int matrix_order, char job, char eigsrc, char initv,\n                           const lapack_logical* select, lapack_int n,\n                           const lapack_complex_double* h, lapack_int ldh,\n                           lapack_complex_double* w, lapack_complex_double* vl,\n                           lapack_int ldvl, lapack_complex_double* vr,\n                           lapack_int ldvr, lapack_int mm, lapack_int* m,\n                           lapack_int* ifaill, lapack_int* ifailr );\n\nlapack_int LAPACKE_shseqr( int matrix_order, char job, char compz, lapack_int n,\n                           lapack_int ilo, lapack_int ihi, float* h,\n                           lapack_int ldh, float* wr, float* wi, float* z,\n                           lapack_int ldz );\nlapack_int LAPACKE_dhseqr( int matrix_order, char job, char compz, lapack_int n,\n                           lapack_int ilo, lapack_int ihi, double* h,\n                           lapack_int ldh, double* wr, double* wi, double* z,\n                           lapack_int ldz );\nlapack_int LAPACKE_chseqr( int matrix_order, char job, char compz, lapack_int n,\n                           lapack_int ilo, lapack_int ihi,\n                           lapack_complex_float* h, lapack_int ldh,\n                           lapack_complex_float* w, lapack_complex_float* z,\n                           lapack_int ldz );\nlapack_int LAPACKE_zhseqr( int matrix_order, char job, char compz, lapack_int n,\n                           lapack_int ilo, lapack_int ihi,\n                           lapack_complex_double* h, lapack_int ldh,\n                           lapack_complex_double* w, lapack_complex_double* z,\n                           lapack_int ldz );\n\nlapack_int LAPACKE_clacgv( lapack_int n, lapack_complex_float* x,\n                           lapack_int incx );\nlapack_int LAPACKE_zlacgv( lapack_int n, lapack_complex_double* x,\n                           lapack_int incx );\n\nlapack_int LAPACKE_slacpy( int matrix_order, char uplo, lapack_int m,\n                           lapack_int n, const float* a, lapack_int lda, float* b,\n                           lapack_int ldb );\nlapack_int LAPACKE_dlacpy( int matrix_order, char uplo, lapack_int m,\n                           lapack_int n, const double* a, lapack_int lda, double* b,\n                           lapack_int ldb );\nlapack_int LAPACKE_clacpy( int matrix_order, char uplo, lapack_int m,\n                           lapack_int n, const lapack_complex_float* a,\n                           lapack_int lda, lapack_complex_float* b,\n                           lapack_int ldb );\nlapack_int LAPACKE_zlacpy( int matrix_order, char uplo, lapack_int m,\n                           lapack_int n, const lapack_complex_double* a,\n                           lapack_int lda, lapack_complex_double* b,\n                           lapack_int ldb );\n\nlapack_int LAPACKE_zlag2c( int matrix_order, lapack_int m, lapack_int n,\n                           const lapack_complex_double* a, lapack_int lda,\n                           lapack_complex_float* sa, lapack_int ldsa );\n\nlapack_int LAPACKE_slag2d( int matrix_order, lapack_int m, lapack_int n,\n                           const float* sa, lapack_int ldsa, double* a,\n                           lapack_int lda );\n\nlapack_int LAPACKE_dlag2s( int matrix_order, lapack_int m, lapack_int n,\n                           const double* a, lapack_int lda, float* sa,\n                           lapack_int ldsa );\n\nlapack_int LAPACKE_clag2z( int matrix_order, lapack_int m, lapack_int n,\n                           const lapack_complex_float* sa, lapack_int ldsa,\n                           lapack_complex_double* a, lapack_int lda );\n\nlapack_int LAPACKE_slagge( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int kl, lapack_int ku, const float* d,\n                           float* a, lapack_int lda, lapack_int* iseed );\nlapack_int LAPACKE_dlagge( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int kl, lapack_int ku, const double* d,\n                           double* a, lapack_int lda, lapack_int* iseed );\nlapack_int LAPACKE_clagge( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int kl, lapack_int ku, const float* d,\n                           lapack_complex_float* a, lapack_int lda,\n                           lapack_int* iseed );\nlapack_int LAPACKE_zlagge( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int kl, lapack_int ku, const double* d,\n                           lapack_complex_double* a, lapack_int lda,\n                           lapack_int* iseed );\n\nfloat LAPACKE_slamch( char cmach );\ndouble LAPACKE_dlamch( char cmach );\n\nfloat LAPACKE_slange( int matrix_order, char norm, lapack_int m,\n                           lapack_int n, const float* a, lapack_int lda );\ndouble LAPACKE_dlange( int matrix_order, char norm, lapack_int m,\n                           lapack_int n, const double* a, lapack_int lda );\nfloat LAPACKE_clange( int matrix_order, char norm, lapack_int m,\n                           lapack_int n, const lapack_complex_float* a,\n                           lapack_int lda );\ndouble LAPACKE_zlange( int matrix_order, char norm, lapack_int m,\n                           lapack_int n, const lapack_complex_double* a,\n                           lapack_int lda );\n\nfloat LAPACKE_clanhe( int matrix_order, char norm, char uplo, lapack_int n,\n                           const lapack_complex_float* a, lapack_int lda );\ndouble LAPACKE_zlanhe( int matrix_order, char norm, char uplo, lapack_int n,\n                           const lapack_complex_double* a, lapack_int lda );\n\nfloat LAPACKE_slansy( int matrix_order, char norm, char uplo, lapack_int n,\n                           const float* a, lapack_int lda );\ndouble LAPACKE_dlansy( int matrix_order, char norm, char uplo, lapack_int n,\n                           const double* a, lapack_int lda );\nfloat LAPACKE_clansy( int matrix_order, char norm, char uplo, lapack_int n,\n                           const lapack_complex_float* a, lapack_int lda );\ndouble LAPACKE_zlansy( int matrix_order, char norm, char uplo, lapack_int n,\n                           const lapack_complex_double* a, lapack_int lda );\n\nfloat LAPACKE_slantr( int matrix_order, char norm, char uplo, char diag,\n                           lapack_int m, lapack_int n, const float* a,\n                           lapack_int lda );\ndouble LAPACKE_dlantr( int matrix_order, char norm, char uplo, char diag,\n                           lapack_int m, lapack_int n, const double* a,\n                           lapack_int lda );\nfloat LAPACKE_clantr( int matrix_order, char norm, char uplo, char diag,\n                           lapack_int m, lapack_int n, const lapack_complex_float* a,\n                           lapack_int lda );\ndouble LAPACKE_zlantr( int matrix_order, char norm, char uplo, char diag,\n                           lapack_int m, lapack_int n, const lapack_complex_double* a,\n                           lapack_int lda );\n\n\nlapack_int LAPACKE_slarfb( int matrix_order, char side, char trans, char direct,\n                           char storev, lapack_int m, lapack_int n,\n                           lapack_int k, const float* v, lapack_int ldv,\n                           const float* t, lapack_int ldt, float* c,\n                           lapack_int ldc );\nlapack_int LAPACKE_dlarfb( int matrix_order, char side, char trans, char direct,\n                           char storev, lapack_int m, lapack_int n,\n                           lapack_int k, const double* v, lapack_int ldv,\n                           const double* t, lapack_int ldt, double* c,\n                           lapack_int ldc );\nlapack_int LAPACKE_clarfb( int matrix_order, char side, char trans, char direct,\n                           char storev, lapack_int m, lapack_int n,\n                           lapack_int k, const lapack_complex_float* v,\n                           lapack_int ldv, const lapack_complex_float* t,\n                           lapack_int ldt, lapack_complex_float* c,\n                           lapack_int ldc );\nlapack_int LAPACKE_zlarfb( int matrix_order, char side, char trans, char direct,\n                           char storev, lapack_int m, lapack_int n,\n                           lapack_int k, const lapack_complex_double* v,\n                           lapack_int ldv, const lapack_complex_double* t,\n                           lapack_int ldt, lapack_complex_double* c,\n                           lapack_int ldc );\n\nlapack_int LAPACKE_slarfg( lapack_int n, float* alpha, float* x,\n                           lapack_int incx, float* tau );\nlapack_int LAPACKE_dlarfg( lapack_int n, double* alpha, double* x,\n                           lapack_int incx, double* tau );\nlapack_int LAPACKE_clarfg( lapack_int n, lapack_complex_float* alpha,\n                           lapack_complex_float* x, lapack_int incx,\n                           lapack_complex_float* tau );\nlapack_int LAPACKE_zlarfg( lapack_int n, lapack_complex_double* alpha,\n                           lapack_complex_double* x, lapack_int incx,\n                           lapack_complex_double* tau );\n\nlapack_int LAPACKE_slarft( int matrix_order, char direct, char storev,\n                           lapack_int n, lapack_int k, const float* v,\n                           lapack_int ldv, const float* tau, float* t,\n                           lapack_int ldt );\nlapack_int LAPACKE_dlarft( int matrix_order, char direct, char storev,\n                           lapack_int n, lapack_int k, const double* v,\n                           lapack_int ldv, const double* tau, double* t,\n                           lapack_int ldt );\nlapack_int LAPACKE_clarft( int matrix_order, char direct, char storev,\n                           lapack_int n, lapack_int k,\n                           const lapack_complex_float* v, lapack_int ldv,\n                           const lapack_complex_float* tau,\n                           lapack_complex_float* t, lapack_int ldt );\nlapack_int LAPACKE_zlarft( int matrix_order, char direct, char storev,\n                           lapack_int n, lapack_int k,\n                           const lapack_complex_double* v, lapack_int ldv,\n                           const lapack_complex_double* tau,\n                           lapack_complex_double* t, lapack_int ldt );\n\nlapack_int LAPACKE_slarfx( int matrix_order, char side, lapack_int m,\n                           lapack_int n, const float* v, float tau, float* c,\n                           lapack_int ldc, float* work );\nlapack_int LAPACKE_dlarfx( int matrix_order, char side, lapack_int m,\n                           lapack_int n, const double* v, double tau, double* c,\n                           lapack_int ldc, double* work );\nlapack_int LAPACKE_clarfx( int matrix_order, char side, lapack_int m,\n                           lapack_int n, const lapack_complex_float* v,\n                           lapack_complex_float tau, lapack_complex_float* c,\n                           lapack_int ldc, lapack_complex_float* work );\nlapack_int LAPACKE_zlarfx( int matrix_order, char side, lapack_int m,\n                           lapack_int n, const lapack_complex_double* v,\n                           lapack_complex_double tau, lapack_complex_double* c,\n                           lapack_int ldc, lapack_complex_double* work );\n\nlapack_int LAPACKE_slarnv( lapack_int idist, lapack_int* iseed, lapack_int n,\n                           float* x );\nlapack_int LAPACKE_dlarnv( lapack_int idist, lapack_int* iseed, lapack_int n,\n                           double* x );\nlapack_int LAPACKE_clarnv( lapack_int idist, lapack_int* iseed, lapack_int n,\n                           lapack_complex_float* x );\nlapack_int LAPACKE_zlarnv( lapack_int idist, lapack_int* iseed, lapack_int n,\n                           lapack_complex_double* x );\n\nlapack_int LAPACKE_slaset( int matrix_order, char uplo, lapack_int m,\n                           lapack_int n, float alpha, float beta, float* a,\n                           lapack_int lda );\nlapack_int LAPACKE_dlaset( int matrix_order, char uplo, lapack_int m,\n                           lapack_int n, double alpha, double beta, double* a,\n                           lapack_int lda );\nlapack_int LAPACKE_claset( int matrix_order, char uplo, lapack_int m,\n                           lapack_int n, lapack_complex_float alpha,\n                           lapack_complex_float beta, lapack_complex_float* a,\n                           lapack_int lda );\nlapack_int LAPACKE_zlaset( int matrix_order, char uplo, lapack_int m,\n                           lapack_int n, lapack_complex_double alpha,\n                           lapack_complex_double beta, lapack_complex_double* a,\n                           lapack_int lda );\n\nlapack_int LAPACKE_slasrt( char id, lapack_int n, float* d );\nlapack_int LAPACKE_dlasrt( char id, lapack_int n, double* d );\n\nlapack_int LAPACKE_slaswp( int matrix_order, lapack_int n, float* a,\n                           lapack_int lda, lapack_int k1, lapack_int k2,\n                           const lapack_int* ipiv, lapack_int incx );\nlapack_int LAPACKE_dlaswp( int matrix_order, lapack_int n, double* a,\n                           lapack_int lda, lapack_int k1, lapack_int k2,\n                           const lapack_int* ipiv, lapack_int incx );\nlapack_int LAPACKE_claswp( int matrix_order, lapack_int n,\n                           lapack_complex_float* a, lapack_int lda,\n                           lapack_int k1, lapack_int k2, const lapack_int* ipiv,\n                           lapack_int incx );\nlapack_int LAPACKE_zlaswp( int matrix_order, lapack_int n,\n                           lapack_complex_double* a, lapack_int lda,\n                           lapack_int k1, lapack_int k2, const lapack_int* ipiv,\n                           lapack_int incx );\n\nlapack_int LAPACKE_slatms( int matrix_order, lapack_int m, lapack_int n,\n                           char dist, lapack_int* iseed, char sym, float* d,\n                           lapack_int mode, float cond, float dmax,\n                           lapack_int kl, lapack_int ku, char pack, float* a,\n                           lapack_int lda );\nlapack_int LAPACKE_dlatms( int matrix_order, lapack_int m, lapack_int n,\n                           char dist, lapack_int* iseed, char sym, double* d,\n                           lapack_int mode, double cond, double dmax,\n                           lapack_int kl, lapack_int ku, char pack, double* a,\n                           lapack_int lda );\nlapack_int LAPACKE_clatms( int matrix_order, lapack_int m, lapack_int n,\n                           char dist, lapack_int* iseed, char sym, float* d,\n                           lapack_int mode, float cond, float dmax,\n                           lapack_int kl, lapack_int ku, char pack,\n                           lapack_complex_float* a, lapack_int lda );\nlapack_int LAPACKE_zlatms( int matrix_order, lapack_int m, lapack_int n,\n                           char dist, lapack_int* iseed, char sym, double* d,\n                           lapack_int mode, double cond, double dmax,\n                           lapack_int kl, lapack_int ku, char pack,\n                           lapack_complex_double* a, lapack_int lda );\n\nlapack_int LAPACKE_slauum( int matrix_order, char uplo, lapack_int n, float* a,\n                           lapack_int lda );\nlapack_int LAPACKE_dlauum( int matrix_order, char uplo, lapack_int n, double* a,\n                           lapack_int lda );\nlapack_int LAPACKE_clauum( int matrix_order, char uplo, lapack_int n,\n                           lapack_complex_float* a, lapack_int lda );\nlapack_int LAPACKE_zlauum( int matrix_order, char uplo, lapack_int n,\n                           lapack_complex_double* a, lapack_int lda );\n\nlapack_int LAPACKE_sopgtr( int matrix_order, char uplo, lapack_int n,\n                           const float* ap, const float* tau, float* q,\n                           lapack_int ldq );\nlapack_int LAPACKE_dopgtr( int matrix_order, char uplo, lapack_int n,\n                           const double* ap, const double* tau, double* q,\n                           lapack_int ldq );\n\nlapack_int LAPACKE_sopmtr( int matrix_order, char side, char uplo, char trans,\n                           lapack_int m, lapack_int n, const float* ap,\n                           const float* tau, float* c, lapack_int ldc );\nlapack_int LAPACKE_dopmtr( int matrix_order, char side, char uplo, char trans,\n                           lapack_int m, lapack_int n, const double* ap,\n                           const double* tau, double* c, lapack_int ldc );\n\nlapack_int LAPACKE_sorgbr( int matrix_order, char vect, lapack_int m,\n                           lapack_int n, lapack_int k, float* a, lapack_int lda,\n                           const float* tau );\nlapack_int LAPACKE_dorgbr( int matrix_order, char vect, lapack_int m,\n                           lapack_int n, lapack_int k, double* a,\n                           lapack_int lda, const double* tau );\n\nlapack_int LAPACKE_sorghr( int matrix_order, lapack_int n, lapack_int ilo,\n                           lapack_int ihi, float* a, lapack_int lda,\n                           const float* tau );\nlapack_int LAPACKE_dorghr( int matrix_order, lapack_int n, lapack_int ilo,\n                           lapack_int ihi, double* a, lapack_int lda,\n                           const double* tau );\n\nlapack_int LAPACKE_sorglq( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int k, float* a, lapack_int lda,\n                           const float* tau );\nlapack_int LAPACKE_dorglq( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int k, double* a, lapack_int lda,\n                           const double* tau );\n\nlapack_int LAPACKE_sorgql( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int k, float* a, lapack_int lda,\n                           const float* tau );\nlapack_int LAPACKE_dorgql( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int k, double* a, lapack_int lda,\n                           const double* tau );\n\nlapack_int LAPACKE_sorgqr( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int k, float* a, lapack_int lda,\n                           const float* tau );\nlapack_int LAPACKE_dorgqr( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int k, double* a, lapack_int lda,\n                           const double* tau );\n\nlapack_int LAPACKE_sorgrq( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int k, float* a, lapack_int lda,\n                           const float* tau );\nlapack_int LAPACKE_dorgrq( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int k, double* a, lapack_int lda,\n                           const double* tau );\n\nlapack_int LAPACKE_sorgtr( int matrix_order, char uplo, lapack_int n, float* a,\n                           lapack_int lda, const float* tau );\nlapack_int LAPACKE_dorgtr( int matrix_order, char uplo, lapack_int n, double* a,\n                           lapack_int lda, const double* tau );\n\nlapack_int LAPACKE_sormbr( int matrix_order, char vect, char side, char trans,\n                           lapack_int m, lapack_int n, lapack_int k,\n                           const float* a, lapack_int lda, const float* tau,\n                           float* c, lapack_int ldc );\nlapack_int LAPACKE_dormbr( int matrix_order, char vect, char side, char trans,\n                           lapack_int m, lapack_int n, lapack_int k,\n                           const double* a, lapack_int lda, const double* tau,\n                           double* c, lapack_int ldc );\n\nlapack_int LAPACKE_sormhr( int matrix_order, char side, char trans,\n                           lapack_int m, lapack_int n, lapack_int ilo,\n                           lapack_int ihi, const float* a, lapack_int lda,\n                           const float* tau, float* c, lapack_int ldc );\nlapack_int LAPACKE_dormhr( int matrix_order, char side, char trans,\n                           lapack_int m, lapack_int n, lapack_int ilo,\n                           lapack_int ihi, const double* a, lapack_int lda,\n                           const double* tau, double* c, lapack_int ldc );\n\nlapack_int LAPACKE_sormlq( int matrix_order, char side, char trans,\n                           lapack_int m, lapack_int n, lapack_int k,\n                           const float* a, lapack_int lda, const float* tau,\n                           float* c, lapack_int ldc );\nlapack_int LAPACKE_dormlq( int matrix_order, char side, char trans,\n                           lapack_int m, lapack_int n, lapack_int k,\n                           const double* a, lapack_int lda, const double* tau,\n                           double* c, lapack_int ldc );\n\nlapack_int LAPACKE_sormql( int matrix_order, char side, char trans,\n                           lapack_int m, lapack_int n, lapack_int k,\n                           const float* a, lapack_int lda, const float* tau,\n                           float* c, lapack_int ldc );\nlapack_int LAPACKE_dormql( int matrix_order, char side, char trans,\n                           lapack_int m, lapack_int n, lapack_int k,\n                           const double* a, lapack_int lda, const double* tau,\n                           double* c, lapack_int ldc );\n\nlapack_int LAPACKE_sormqr( int matrix_order, char side, char trans,\n                           lapack_int m, lapack_int n, lapack_int k,\n                           const float* a, lapack_int lda, const float* tau,\n                           float* c, lapack_int ldc );\nlapack_int LAPACKE_dormqr( int matrix_order, char side, char trans,\n                           lapack_int m, lapack_int n, lapack_int k,\n                           const double* a, lapack_int lda, const double* tau,\n                           double* c, lapack_int ldc );\n\nlapack_int LAPACKE_sormrq( int matrix_order, char side, char trans,\n                           lapack_int m, lapack_int n, lapack_int k,\n                           const float* a, lapack_int lda, const float* tau,\n                           float* c, lapack_int ldc );\nlapack_int LAPACKE_dormrq( int matrix_order, char side, char trans,\n                           lapack_int m, lapack_int n, lapack_int k,\n                           const double* a, lapack_int lda, const double* tau,\n                           double* c, lapack_int ldc );\n\nlapack_int LAPACKE_sormrz( int matrix_order, char side, char trans,\n                           lapack_int m, lapack_int n, lapack_int k,\n                           lapack_int l, const float* a, lapack_int lda,\n                           const float* tau, float* c, lapack_int ldc );\nlapack_int LAPACKE_dormrz( int matrix_order, char side, char trans,\n                           lapack_int m, lapack_int n, lapack_int k,\n                           lapack_int l, const double* a, lapack_int lda,\n                           const double* tau, double* c, lapack_int ldc );\n\nlapack_int LAPACKE_sormtr( int matrix_order, char side, char uplo, char trans,\n                           lapack_int m, lapack_int n, const float* a,\n                           lapack_int lda, const float* tau, float* c,\n                           lapack_int ldc );\nlapack_int LAPACKE_dormtr( int matrix_order, char side, char uplo, char trans,\n                           lapack_int m, lapack_int n, const double* a,\n                           lapack_int lda, const double* tau, double* c,\n                           lapack_int ldc );\n\nlapack_int LAPACKE_spbcon( int matrix_order, char uplo, lapack_int n,\n                           lapack_int kd, const float* ab, lapack_int ldab,\n                           float anorm, float* rcond );\nlapack_int LAPACKE_dpbcon( int matrix_order, char uplo, lapack_int n,\n                           lapack_int kd, const double* ab, lapack_int ldab,\n                           double anorm, double* rcond );\nlapack_int LAPACKE_cpbcon( int matrix_order, char uplo, lapack_int n,\n                           lapack_int kd, const lapack_complex_float* ab,\n                           lapack_int ldab, float anorm, float* rcond );\nlapack_int LAPACKE_zpbcon( int matrix_order, char uplo, lapack_int n,\n                           lapack_int kd, const lapack_complex_double* ab,\n                           lapack_int ldab, double anorm, double* rcond );\n\nlapack_int LAPACKE_spbequ( int matrix_order, char uplo, lapack_int n,\n                           lapack_int kd, const float* ab, lapack_int ldab,\n                           float* s, float* scond, float* amax );\nlapack_int LAPACKE_dpbequ( int matrix_order, char uplo, lapack_int n,\n                           lapack_int kd, const double* ab, lapack_int ldab,\n                           double* s, double* scond, double* amax );\nlapack_int LAPACKE_cpbequ( int matrix_order, char uplo, lapack_int n,\n                           lapack_int kd, const lapack_complex_float* ab,\n                           lapack_int ldab, float* s, float* scond,\n                           float* amax );\nlapack_int LAPACKE_zpbequ( int matrix_order, char uplo, lapack_int n,\n                           lapack_int kd, const lapack_complex_double* ab,\n                           lapack_int ldab, double* s, double* scond,\n                           double* amax );\n\nlapack_int LAPACKE_spbrfs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int kd, lapack_int nrhs, const float* ab,\n                           lapack_int ldab, const float* afb, lapack_int ldafb,\n                           const float* b, lapack_int ldb, float* x,\n                           lapack_int ldx, float* ferr, float* berr );\nlapack_int LAPACKE_dpbrfs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int kd, lapack_int nrhs, const double* ab,\n                           lapack_int ldab, const double* afb, lapack_int ldafb,\n                           const double* b, lapack_int ldb, double* x,\n                           lapack_int ldx, double* ferr, double* berr );\nlapack_int LAPACKE_cpbrfs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int kd, lapack_int nrhs,\n                           const lapack_complex_float* ab, lapack_int ldab,\n                           const lapack_complex_float* afb, lapack_int ldafb,\n                           const lapack_complex_float* b, lapack_int ldb,\n                           lapack_complex_float* x, lapack_int ldx, float* ferr,\n                           float* berr );\nlapack_int LAPACKE_zpbrfs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int kd, lapack_int nrhs,\n                           const lapack_complex_double* ab, lapack_int ldab,\n                           const lapack_complex_double* afb, lapack_int ldafb,\n                           const lapack_complex_double* b, lapack_int ldb,\n                           lapack_complex_double* x, lapack_int ldx,\n                           double* ferr, double* berr );\n\nlapack_int LAPACKE_spbstf( int matrix_order, char uplo, lapack_int n,\n                           lapack_int kb, float* bb, lapack_int ldbb );\nlapack_int LAPACKE_dpbstf( int matrix_order, char uplo, lapack_int n,\n                           lapack_int kb, double* bb, lapack_int ldbb );\nlapack_int LAPACKE_cpbstf( int matrix_order, char uplo, lapack_int n,\n                           lapack_int kb, lapack_complex_float* bb,\n                           lapack_int ldbb );\nlapack_int LAPACKE_zpbstf( int matrix_order, char uplo, lapack_int n,\n                           lapack_int kb, lapack_complex_double* bb,\n                           lapack_int ldbb );\n\nlapack_int LAPACKE_spbsv( int matrix_order, char uplo, lapack_int n,\n                          lapack_int kd, lapack_int nrhs, float* ab,\n                          lapack_int ldab, float* b, lapack_int ldb );\nlapack_int LAPACKE_dpbsv( int matrix_order, char uplo, lapack_int n,\n                          lapack_int kd, lapack_int nrhs, double* ab,\n                          lapack_int ldab, double* b, lapack_int ldb );\nlapack_int LAPACKE_cpbsv( int matrix_order, char uplo, lapack_int n,\n                          lapack_int kd, lapack_int nrhs,\n                          lapack_complex_float* ab, lapack_int ldab,\n                          lapack_complex_float* b, lapack_int ldb );\nlapack_int LAPACKE_zpbsv( int matrix_order, char uplo, lapack_int n,\n                          lapack_int kd, lapack_int nrhs,\n                          lapack_complex_double* ab, lapack_int ldab,\n                          lapack_complex_double* b, lapack_int ldb );\n\nlapack_int LAPACKE_spbsvx( int matrix_order, char fact, char uplo, lapack_int n,\n                           lapack_int kd, lapack_int nrhs, float* ab,\n                           lapack_int ldab, float* afb, lapack_int ldafb,\n                           char* equed, float* s, float* b, lapack_int ldb,\n                           float* x, lapack_int ldx, float* rcond, float* ferr,\n                           float* berr );\nlapack_int LAPACKE_dpbsvx( int matrix_order, char fact, char uplo, lapack_int n,\n                           lapack_int kd, lapack_int nrhs, double* ab,\n                           lapack_int ldab, double* afb, lapack_int ldafb,\n                           char* equed, double* s, double* b, lapack_int ldb,\n                           double* x, lapack_int ldx, double* rcond,\n                           double* ferr, double* berr );\nlapack_int LAPACKE_cpbsvx( int matrix_order, char fact, char uplo, lapack_int n,\n                           lapack_int kd, lapack_int nrhs,\n                           lapack_complex_float* ab, lapack_int ldab,\n                           lapack_complex_float* afb, lapack_int ldafb,\n                           char* equed, float* s, lapack_complex_float* b,\n                           lapack_int ldb, lapack_complex_float* x,\n                           lapack_int ldx, float* rcond, float* ferr,\n                           float* berr );\nlapack_int LAPACKE_zpbsvx( int matrix_order, char fact, char uplo, lapack_int n,\n                           lapack_int kd, lapack_int nrhs,\n                           lapack_complex_double* ab, lapack_int ldab,\n                           lapack_complex_double* afb, lapack_int ldafb,\n                           char* equed, double* s, lapack_complex_double* b,\n                           lapack_int ldb, lapack_complex_double* x,\n                           lapack_int ldx, double* rcond, double* ferr,\n                           double* berr );\n\nlapack_int LAPACKE_spbtrf( int matrix_order, char uplo, lapack_int n,\n                           lapack_int kd, float* ab, lapack_int ldab );\nlapack_int LAPACKE_dpbtrf( int matrix_order, char uplo, lapack_int n,\n                           lapack_int kd, double* ab, lapack_int ldab );\nlapack_int LAPACKE_cpbtrf( int matrix_order, char uplo, lapack_int n,\n                           lapack_int kd, lapack_complex_float* ab,\n                           lapack_int ldab );\nlapack_int LAPACKE_zpbtrf( int matrix_order, char uplo, lapack_int n,\n                           lapack_int kd, lapack_complex_double* ab,\n                           lapack_int ldab );\n\nlapack_int LAPACKE_spbtrs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int kd, lapack_int nrhs, const float* ab,\n                           lapack_int ldab, float* b, lapack_int ldb );\nlapack_int LAPACKE_dpbtrs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int kd, lapack_int nrhs, const double* ab,\n                           lapack_int ldab, double* b, lapack_int ldb );\nlapack_int LAPACKE_cpbtrs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int kd, lapack_int nrhs,\n                           const lapack_complex_float* ab, lapack_int ldab,\n                           lapack_complex_float* b, lapack_int ldb );\nlapack_int LAPACKE_zpbtrs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int kd, lapack_int nrhs,\n                           const lapack_complex_double* ab, lapack_int ldab,\n                           lapack_complex_double* b, lapack_int ldb );\n\nlapack_int LAPACKE_spftrf( int matrix_order, char transr, char uplo,\n                           lapack_int n, float* a );\nlapack_int LAPACKE_dpftrf( int matrix_order, char transr, char uplo,\n                           lapack_int n, double* a );\nlapack_int LAPACKE_cpftrf( int matrix_order, char transr, char uplo,\n                           lapack_int n, lapack_complex_float* a );\nlapack_int LAPACKE_zpftrf( int matrix_order, char transr, char uplo,\n                           lapack_int n, lapack_complex_double* a );\n\nlapack_int LAPACKE_spftri( int matrix_order, char transr, char uplo,\n                           lapack_int n, float* a );\nlapack_int LAPACKE_dpftri( int matrix_order, char transr, char uplo,\n                           lapack_int n, double* a );\nlapack_int LAPACKE_cpftri( int matrix_order, char transr, char uplo,\n                           lapack_int n, lapack_complex_float* a );\nlapack_int LAPACKE_zpftri( int matrix_order, char transr, char uplo,\n                           lapack_int n, lapack_complex_double* a );\n\nlapack_int LAPACKE_spftrs( int matrix_order, char transr, char uplo,\n                           lapack_int n, lapack_int nrhs, const float* a,\n                           float* b, lapack_int ldb );\nlapack_int LAPACKE_dpftrs( int matrix_order, char transr, char uplo,\n                           lapack_int n, lapack_int nrhs, const double* a,\n                           double* b, lapack_int ldb );\nlapack_int LAPACKE_cpftrs( int matrix_order, char transr, char uplo,\n                           lapack_int n, lapack_int nrhs,\n                           const lapack_complex_float* a,\n                           lapack_complex_float* b, lapack_int ldb );\nlapack_int LAPACKE_zpftrs( int matrix_order, char transr, char uplo,\n                           lapack_int n, lapack_int nrhs,\n                           const lapack_complex_double* a,\n                           lapack_complex_double* b, lapack_int ldb );\n\nlapack_int LAPACKE_spocon( int matrix_order, char uplo, lapack_int n,\n                           const float* a, lapack_int lda, float anorm,\n                           float* rcond );\nlapack_int LAPACKE_dpocon( int matrix_order, char uplo, lapack_int n,\n                           const double* a, lapack_int lda, double anorm,\n                           double* rcond );\nlapack_int LAPACKE_cpocon( int matrix_order, char uplo, lapack_int n,\n                           const lapack_complex_float* a, lapack_int lda,\n                           float anorm, float* rcond );\nlapack_int LAPACKE_zpocon( int matrix_order, char uplo, lapack_int n,\n                           const lapack_complex_double* a, lapack_int lda,\n                           double anorm, double* rcond );\n\nlapack_int LAPACKE_spoequ( int matrix_order, lapack_int n, const float* a,\n                           lapack_int lda, float* s, float* scond,\n                           float* amax );\nlapack_int LAPACKE_dpoequ( int matrix_order, lapack_int n, const double* a,\n                           lapack_int lda, double* s, double* scond,\n                           double* amax );\nlapack_int LAPACKE_cpoequ( int matrix_order, lapack_int n,\n                           const lapack_complex_float* a, lapack_int lda,\n                           float* s, float* scond, float* amax );\nlapack_int LAPACKE_zpoequ( int matrix_order, lapack_int n,\n                           const lapack_complex_double* a, lapack_int lda,\n                           double* s, double* scond, double* amax );\n\nlapack_int LAPACKE_spoequb( int matrix_order, lapack_int n, const float* a,\n                            lapack_int lda, float* s, float* scond,\n                            float* amax );\nlapack_int LAPACKE_dpoequb( int matrix_order, lapack_int n, const double* a,\n                            lapack_int lda, double* s, double* scond,\n                            double* amax );\nlapack_int LAPACKE_cpoequb( int matrix_order, lapack_int n,\n                            const lapack_complex_float* a, lapack_int lda,\n                            float* s, float* scond, float* amax );\nlapack_int LAPACKE_zpoequb( int matrix_order, lapack_int n,\n                            const lapack_complex_double* a, lapack_int lda,\n                            double* s, double* scond, double* amax );\n\nlapack_int LAPACKE_sporfs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const float* a, lapack_int lda,\n                           const float* af, lapack_int ldaf, const float* b,\n                           lapack_int ldb, float* x, lapack_int ldx,\n                           float* ferr, float* berr );\nlapack_int LAPACKE_dporfs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const double* a, lapack_int lda,\n                           const double* af, lapack_int ldaf, const double* b,\n                           lapack_int ldb, double* x, lapack_int ldx,\n                           double* ferr, double* berr );\nlapack_int LAPACKE_cporfs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_float* a,\n                           lapack_int lda, const lapack_complex_float* af,\n                           lapack_int ldaf, const lapack_complex_float* b,\n                           lapack_int ldb, lapack_complex_float* x,\n                           lapack_int ldx, float* ferr, float* berr );\nlapack_int LAPACKE_zporfs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_double* a,\n                           lapack_int lda, const lapack_complex_double* af,\n                           lapack_int ldaf, const lapack_complex_double* b,\n                           lapack_int ldb, lapack_complex_double* x,\n                           lapack_int ldx, double* ferr, double* berr );\n\nlapack_int LAPACKE_sporfsx( int matrix_order, char uplo, char equed,\n                            lapack_int n, lapack_int nrhs, const float* a,\n                            lapack_int lda, const float* af, lapack_int ldaf,\n                            const float* s, const float* b, lapack_int ldb,\n                            float* x, lapack_int ldx, float* rcond, float* berr,\n                            lapack_int n_err_bnds, float* err_bnds_norm,\n                            float* err_bnds_comp, lapack_int nparams,\n                            float* params );\nlapack_int LAPACKE_dporfsx( int matrix_order, char uplo, char equed,\n                            lapack_int n, lapack_int nrhs, const double* a,\n                            lapack_int lda, const double* af, lapack_int ldaf,\n                            const double* s, const double* b, lapack_int ldb,\n                            double* x, lapack_int ldx, double* rcond,\n                            double* berr, lapack_int n_err_bnds,\n                            double* err_bnds_norm, double* err_bnds_comp,\n                            lapack_int nparams, double* params );\nlapack_int LAPACKE_cporfsx( int matrix_order, char uplo, char equed,\n                            lapack_int n, lapack_int nrhs,\n                            const lapack_complex_float* a, lapack_int lda,\n                            const lapack_complex_float* af, lapack_int ldaf,\n                            const float* s, const lapack_complex_float* b,\n                            lapack_int ldb, lapack_complex_float* x,\n                            lapack_int ldx, float* rcond, float* berr,\n                            lapack_int n_err_bnds, float* err_bnds_norm,\n                            float* err_bnds_comp, lapack_int nparams,\n                            float* params );\nlapack_int LAPACKE_zporfsx( int matrix_order, char uplo, char equed,\n                            lapack_int n, lapack_int nrhs,\n                            const lapack_complex_double* a, lapack_int lda,\n                            const lapack_complex_double* af, lapack_int ldaf,\n                            const double* s, const lapack_complex_double* b,\n                            lapack_int ldb, lapack_complex_double* x,\n                            lapack_int ldx, double* rcond, double* berr,\n                            lapack_int n_err_bnds, double* err_bnds_norm,\n                            double* err_bnds_comp, lapack_int nparams,\n                            double* params );\n\nlapack_int LAPACKE_sposv( int matrix_order, char uplo, lapack_int n,\n                          lapack_int nrhs, float* a, lapack_int lda, float* b,\n                          lapack_int ldb );\nlapack_int LAPACKE_dposv( int matrix_order, char uplo, lapack_int n,\n                          lapack_int nrhs, double* a, lapack_int lda, double* b,\n                          lapack_int ldb );\nlapack_int LAPACKE_cposv( int matrix_order, char uplo, lapack_int n,\n                          lapack_int nrhs, lapack_complex_float* a,\n                          lapack_int lda, lapack_complex_float* b,\n                          lapack_int ldb );\nlapack_int LAPACKE_zposv( int matrix_order, char uplo, lapack_int n,\n                          lapack_int nrhs, lapack_complex_double* a,\n                          lapack_int lda, lapack_complex_double* b,\n                          lapack_int ldb );\nlapack_int LAPACKE_dsposv( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, double* a, lapack_int lda,\n                           double* b, lapack_int ldb, double* x, lapack_int ldx,\n                           lapack_int* iter );\nlapack_int LAPACKE_zcposv( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, lapack_complex_double* a,\n                           lapack_int lda, lapack_complex_double* b,\n                           lapack_int ldb, lapack_complex_double* x,\n                           lapack_int ldx, lapack_int* iter );\n\nlapack_int LAPACKE_sposvx( int matrix_order, char fact, char uplo, lapack_int n,\n                           lapack_int nrhs, float* a, lapack_int lda, float* af,\n                           lapack_int ldaf, char* equed, float* s, float* b,\n                           lapack_int ldb, float* x, lapack_int ldx,\n                           float* rcond, float* ferr, float* berr );\nlapack_int LAPACKE_dposvx( int matrix_order, char fact, char uplo, lapack_int n,\n                           lapack_int nrhs, double* a, lapack_int lda,\n                           double* af, lapack_int ldaf, char* equed, double* s,\n                           double* b, lapack_int ldb, double* x, lapack_int ldx,\n                           double* rcond, double* ferr, double* berr );\nlapack_int LAPACKE_cposvx( int matrix_order, char fact, char uplo, lapack_int n,\n                           lapack_int nrhs, lapack_complex_float* a,\n                           lapack_int lda, lapack_complex_float* af,\n                           lapack_int ldaf, char* equed, float* s,\n                           lapack_complex_float* b, lapack_int ldb,\n                           lapack_complex_float* x, lapack_int ldx,\n                           float* rcond, float* ferr, float* berr );\nlapack_int LAPACKE_zposvx( int matrix_order, char fact, char uplo, lapack_int n,\n                           lapack_int nrhs, lapack_complex_double* a,\n                           lapack_int lda, lapack_complex_double* af,\n                           lapack_int ldaf, char* equed, double* s,\n                           lapack_complex_double* b, lapack_int ldb,\n                           lapack_complex_double* x, lapack_int ldx,\n                           double* rcond, double* ferr, double* berr );\n\nlapack_int LAPACKE_sposvxx( int matrix_order, char fact, char uplo,\n                            lapack_int n, lapack_int nrhs, float* a,\n                            lapack_int lda, float* af, lapack_int ldaf,\n                            char* equed, float* s, float* b, lapack_int ldb,\n                            float* x, lapack_int ldx, float* rcond,\n                            float* rpvgrw, float* berr, lapack_int n_err_bnds,\n                            float* err_bnds_norm, float* err_bnds_comp,\n                            lapack_int nparams, float* params );\nlapack_int LAPACKE_dposvxx( int matrix_order, char fact, char uplo,\n                            lapack_int n, lapack_int nrhs, double* a,\n                            lapack_int lda, double* af, lapack_int ldaf,\n                            char* equed, double* s, double* b, lapack_int ldb,\n                            double* x, lapack_int ldx, double* rcond,\n                            double* rpvgrw, double* berr, lapack_int n_err_bnds,\n                            double* err_bnds_norm, double* err_bnds_comp,\n                            lapack_int nparams, double* params );\nlapack_int LAPACKE_cposvxx( int matrix_order, char fact, char uplo,\n                            lapack_int n, lapack_int nrhs,\n                            lapack_complex_float* a, lapack_int lda,\n                            lapack_complex_float* af, lapack_int ldaf,\n                            char* equed, float* s, lapack_complex_float* b,\n                            lapack_int ldb, lapack_complex_float* x,\n                            lapack_int ldx, float* rcond, float* rpvgrw,\n                            float* berr, lapack_int n_err_bnds,\n                            float* err_bnds_norm, float* err_bnds_comp,\n                            lapack_int nparams, float* params );\nlapack_int LAPACKE_zposvxx( int matrix_order, char fact, char uplo,\n                            lapack_int n, lapack_int nrhs,\n                            lapack_complex_double* a, lapack_int lda,\n                            lapack_complex_double* af, lapack_int ldaf,\n                            char* equed, double* s, lapack_complex_double* b,\n                            lapack_int ldb, lapack_complex_double* x,\n                            lapack_int ldx, double* rcond, double* rpvgrw,\n                            double* berr, lapack_int n_err_bnds,\n                            double* err_bnds_norm, double* err_bnds_comp,\n                            lapack_int nparams, double* params );\n\nlapack_int LAPACKE_spotrf( int matrix_order, char uplo, lapack_int n, float* a,\n                           lapack_int lda );\nlapack_int LAPACKE_dpotrf( int matrix_order, char uplo, lapack_int n, double* a,\n                           lapack_int lda );\nlapack_int LAPACKE_cpotrf( int matrix_order, char uplo, lapack_int n,\n                           lapack_complex_float* a, lapack_int lda );\nlapack_int LAPACKE_zpotrf( int matrix_order, char uplo, lapack_int n,\n                           lapack_complex_double* a, lapack_int lda );\n\nlapack_int LAPACKE_spotri( int matrix_order, char uplo, lapack_int n, float* a,\n                           lapack_int lda );\nlapack_int LAPACKE_dpotri( int matrix_order, char uplo, lapack_int n, double* a,\n                           lapack_int lda );\nlapack_int LAPACKE_cpotri( int matrix_order, char uplo, lapack_int n,\n                           lapack_complex_float* a, lapack_int lda );\nlapack_int LAPACKE_zpotri( int matrix_order, char uplo, lapack_int n,\n                           lapack_complex_double* a, lapack_int lda );\n\nlapack_int LAPACKE_spotrs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const float* a, lapack_int lda,\n                           float* b, lapack_int ldb );\nlapack_int LAPACKE_dpotrs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const double* a, lapack_int lda,\n                           double* b, lapack_int ldb );\nlapack_int LAPACKE_cpotrs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_float* a,\n                           lapack_int lda, lapack_complex_float* b,\n                           lapack_int ldb );\nlapack_int LAPACKE_zpotrs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_double* a,\n                           lapack_int lda, lapack_complex_double* b,\n                           lapack_int ldb );\n\nlapack_int LAPACKE_sppcon( int matrix_order, char uplo, lapack_int n,\n                           const float* ap, float anorm, float* rcond );\nlapack_int LAPACKE_dppcon( int matrix_order, char uplo, lapack_int n,\n                           const double* ap, double anorm, double* rcond );\nlapack_int LAPACKE_cppcon( int matrix_order, char uplo, lapack_int n,\n                           const lapack_complex_float* ap, float anorm,\n                           float* rcond );\nlapack_int LAPACKE_zppcon( int matrix_order, char uplo, lapack_int n,\n                           const lapack_complex_double* ap, double anorm,\n                           double* rcond );\n\nlapack_int LAPACKE_sppequ( int matrix_order, char uplo, lapack_int n,\n                           const float* ap, float* s, float* scond,\n                           float* amax );\nlapack_int LAPACKE_dppequ( int matrix_order, char uplo, lapack_int n,\n                           const double* ap, double* s, double* scond,\n                           double* amax );\nlapack_int LAPACKE_cppequ( int matrix_order, char uplo, lapack_int n,\n                           const lapack_complex_float* ap, float* s,\n                           float* scond, float* amax );\nlapack_int LAPACKE_zppequ( int matrix_order, char uplo, lapack_int n,\n                           const lapack_complex_double* ap, double* s,\n                           double* scond, double* amax );\n\nlapack_int LAPACKE_spprfs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const float* ap, const float* afp,\n                           const float* b, lapack_int ldb, float* x,\n                           lapack_int ldx, float* ferr, float* berr );\nlapack_int LAPACKE_dpprfs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const double* ap, const double* afp,\n                           const double* b, lapack_int ldb, double* x,\n                           lapack_int ldx, double* ferr, double* berr );\nlapack_int LAPACKE_cpprfs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_float* ap,\n                           const lapack_complex_float* afp,\n                           const lapack_complex_float* b, lapack_int ldb,\n                           lapack_complex_float* x, lapack_int ldx, float* ferr,\n                           float* berr );\nlapack_int LAPACKE_zpprfs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_double* ap,\n                           const lapack_complex_double* afp,\n                           const lapack_complex_double* b, lapack_int ldb,\n                           lapack_complex_double* x, lapack_int ldx,\n                           double* ferr, double* berr );\n\nlapack_int LAPACKE_sppsv( int matrix_order, char uplo, lapack_int n,\n                          lapack_int nrhs, float* ap, float* b,\n                          lapack_int ldb );\nlapack_int LAPACKE_dppsv( int matrix_order, char uplo, lapack_int n,\n                          lapack_int nrhs, double* ap, double* b,\n                          lapack_int ldb );\nlapack_int LAPACKE_cppsv( int matrix_order, char uplo, lapack_int n,\n                          lapack_int nrhs, lapack_complex_float* ap,\n                          lapack_complex_float* b, lapack_int ldb );\nlapack_int LAPACKE_zppsv( int matrix_order, char uplo, lapack_int n,\n                          lapack_int nrhs, lapack_complex_double* ap,\n                          lapack_complex_double* b, lapack_int ldb );\n\nlapack_int LAPACKE_sppsvx( int matrix_order, char fact, char uplo, lapack_int n,\n                           lapack_int nrhs, float* ap, float* afp, char* equed,\n                           float* s, float* b, lapack_int ldb, float* x,\n                           lapack_int ldx, float* rcond, float* ferr,\n                           float* berr );\nlapack_int LAPACKE_dppsvx( int matrix_order, char fact, char uplo, lapack_int n,\n                           lapack_int nrhs, double* ap, double* afp,\n                           char* equed, double* s, double* b, lapack_int ldb,\n                           double* x, lapack_int ldx, double* rcond,\n                           double* ferr, double* berr );\nlapack_int LAPACKE_cppsvx( int matrix_order, char fact, char uplo, lapack_int n,\n                           lapack_int nrhs, lapack_complex_float* ap,\n                           lapack_complex_float* afp, char* equed, float* s,\n                           lapack_complex_float* b, lapack_int ldb,\n                           lapack_complex_float* x, lapack_int ldx,\n                           float* rcond, float* ferr, float* berr );\nlapack_int LAPACKE_zppsvx( int matrix_order, char fact, char uplo, lapack_int n,\n                           lapack_int nrhs, lapack_complex_double* ap,\n                           lapack_complex_double* afp, char* equed, double* s,\n                           lapack_complex_double* b, lapack_int ldb,\n                           lapack_complex_double* x, lapack_int ldx,\n                           double* rcond, double* ferr, double* berr );\n\nlapack_int LAPACKE_spptrf( int matrix_order, char uplo, lapack_int n,\n                           float* ap );\nlapack_int LAPACKE_dpptrf( int matrix_order, char uplo, lapack_int n,\n                           double* ap );\nlapack_int LAPACKE_cpptrf( int matrix_order, char uplo, lapack_int n,\n                           lapack_complex_float* ap );\nlapack_int LAPACKE_zpptrf( int matrix_order, char uplo, lapack_int n,\n                           lapack_complex_double* ap );\n\nlapack_int LAPACKE_spptri( int matrix_order, char uplo, lapack_int n,\n                           float* ap );\nlapack_int LAPACKE_dpptri( int matrix_order, char uplo, lapack_int n,\n                           double* ap );\nlapack_int LAPACKE_cpptri( int matrix_order, char uplo, lapack_int n,\n                           lapack_complex_float* ap );\nlapack_int LAPACKE_zpptri( int matrix_order, char uplo, lapack_int n,\n                           lapack_complex_double* ap );\n\nlapack_int LAPACKE_spptrs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const float* ap, float* b,\n                           lapack_int ldb );\nlapack_int LAPACKE_dpptrs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const double* ap, double* b,\n                           lapack_int ldb );\nlapack_int LAPACKE_cpptrs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_float* ap,\n                           lapack_complex_float* b, lapack_int ldb );\nlapack_int LAPACKE_zpptrs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_double* ap,\n                           lapack_complex_double* b, lapack_int ldb );\n\nlapack_int LAPACKE_spstrf( int matrix_order, char uplo, lapack_int n, float* a,\n                           lapack_int lda, lapack_int* piv, lapack_int* rank,\n                           float tol );\nlapack_int LAPACKE_dpstrf( int matrix_order, char uplo, lapack_int n, double* a,\n                           lapack_int lda, lapack_int* piv, lapack_int* rank,\n                           double tol );\nlapack_int LAPACKE_cpstrf( int matrix_order, char uplo, lapack_int n,\n                           lapack_complex_float* a, lapack_int lda,\n                           lapack_int* piv, lapack_int* rank, float tol );\nlapack_int LAPACKE_zpstrf( int matrix_order, char uplo, lapack_int n,\n                           lapack_complex_double* a, lapack_int lda,\n                           lapack_int* piv, lapack_int* rank, double tol );\n\nlapack_int LAPACKE_sptcon( lapack_int n, const float* d, const float* e,\n                           float anorm, float* rcond );\nlapack_int LAPACKE_dptcon( lapack_int n, const double* d, const double* e,\n                           double anorm, double* rcond );\nlapack_int LAPACKE_cptcon( lapack_int n, const float* d,\n                           const lapack_complex_float* e, float anorm,\n                           float* rcond );\nlapack_int LAPACKE_zptcon( lapack_int n, const double* d,\n                           const lapack_complex_double* e, double anorm,\n                           double* rcond );\n\nlapack_int LAPACKE_spteqr( int matrix_order, char compz, lapack_int n, float* d,\n                           float* e, float* z, lapack_int ldz );\nlapack_int LAPACKE_dpteqr( int matrix_order, char compz, lapack_int n,\n                           double* d, double* e, double* z, lapack_int ldz );\nlapack_int LAPACKE_cpteqr( int matrix_order, char compz, lapack_int n, float* d,\n                           float* e, lapack_complex_float* z, lapack_int ldz );\nlapack_int LAPACKE_zpteqr( int matrix_order, char compz, lapack_int n,\n                           double* d, double* e, lapack_complex_double* z,\n                           lapack_int ldz );\n\nlapack_int LAPACKE_sptrfs( int matrix_order, lapack_int n, lapack_int nrhs,\n                           const float* d, const float* e, const float* df,\n                           const float* ef, const float* b, lapack_int ldb,\n                           float* x, lapack_int ldx, float* ferr, float* berr );\nlapack_int LAPACKE_dptrfs( int matrix_order, lapack_int n, lapack_int nrhs,\n                           const double* d, const double* e, const double* df,\n                           const double* ef, const double* b, lapack_int ldb,\n                           double* x, lapack_int ldx, double* ferr,\n                           double* berr );\nlapack_int LAPACKE_cptrfs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const float* d,\n                           const lapack_complex_float* e, const float* df,\n                           const lapack_complex_float* ef,\n                           const lapack_complex_float* b, lapack_int ldb,\n                           lapack_complex_float* x, lapack_int ldx, float* ferr,\n                           float* berr );\nlapack_int LAPACKE_zptrfs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const double* d,\n                           const lapack_complex_double* e, const double* df,\n                           const lapack_complex_double* ef,\n                           const lapack_complex_double* b, lapack_int ldb,\n                           lapack_complex_double* x, lapack_int ldx,\n                           double* ferr, double* berr );\n\nlapack_int LAPACKE_sptsv( int matrix_order, lapack_int n, lapack_int nrhs,\n                          float* d, float* e, float* b, lapack_int ldb );\nlapack_int LAPACKE_dptsv( int matrix_order, lapack_int n, lapack_int nrhs,\n                          double* d, double* e, double* b, lapack_int ldb );\nlapack_int LAPACKE_cptsv( int matrix_order, lapack_int n, lapack_int nrhs,\n                          float* d, lapack_complex_float* e,\n                          lapack_complex_float* b, lapack_int ldb );\nlapack_int LAPACKE_zptsv( int matrix_order, lapack_int n, lapack_int nrhs,\n                          double* d, lapack_complex_double* e,\n                          lapack_complex_double* b, lapack_int ldb );\n\nlapack_int LAPACKE_sptsvx( int matrix_order, char fact, lapack_int n,\n                           lapack_int nrhs, const float* d, const float* e,\n                           float* df, float* ef, const float* b, lapack_int ldb,\n                           float* x, lapack_int ldx, float* rcond, float* ferr,\n                           float* berr );\nlapack_int LAPACKE_dptsvx( int matrix_order, char fact, lapack_int n,\n                           lapack_int nrhs, const double* d, const double* e,\n                           double* df, double* ef, const double* b,\n                           lapack_int ldb, double* x, lapack_int ldx,\n                           double* rcond, double* ferr, double* berr );\nlapack_int LAPACKE_cptsvx( int matrix_order, char fact, lapack_int n,\n                           lapack_int nrhs, const float* d,\n                           const lapack_complex_float* e, float* df,\n                           lapack_complex_float* ef,\n                           const lapack_complex_float* b, lapack_int ldb,\n                           lapack_complex_float* x, lapack_int ldx,\n                           float* rcond, float* ferr, float* berr );\nlapack_int LAPACKE_zptsvx( int matrix_order, char fact, lapack_int n,\n                           lapack_int nrhs, const double* d,\n                           const lapack_complex_double* e, double* df,\n                           lapack_complex_double* ef,\n                           const lapack_complex_double* b, lapack_int ldb,\n                           lapack_complex_double* x, lapack_int ldx,\n                           double* rcond, double* ferr, double* berr );\n\nlapack_int LAPACKE_spttrf( lapack_int n, float* d, float* e );\nlapack_int LAPACKE_dpttrf( lapack_int n, double* d, double* e );\nlapack_int LAPACKE_cpttrf( lapack_int n, float* d, lapack_complex_float* e );\nlapack_int LAPACKE_zpttrf( lapack_int n, double* d, lapack_complex_double* e );\n\nlapack_int LAPACKE_spttrs( int matrix_order, lapack_int n, lapack_int nrhs,\n                           const float* d, const float* e, float* b,\n                           lapack_int ldb );\nlapack_int LAPACKE_dpttrs( int matrix_order, lapack_int n, lapack_int nrhs,\n                           const double* d, const double* e, double* b,\n                           lapack_int ldb );\nlapack_int LAPACKE_cpttrs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const float* d,\n                           const lapack_complex_float* e,\n                           lapack_complex_float* b, lapack_int ldb );\nlapack_int LAPACKE_zpttrs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const double* d,\n                           const lapack_complex_double* e,\n                           lapack_complex_double* b, lapack_int ldb );\n\nlapack_int LAPACKE_ssbev( int matrix_order, char jobz, char uplo, lapack_int n,\n                          lapack_int kd, float* ab, lapack_int ldab, float* w,\n                          float* z, lapack_int ldz );\nlapack_int LAPACKE_dsbev( int matrix_order, char jobz, char uplo, lapack_int n,\n                          lapack_int kd, double* ab, lapack_int ldab, double* w,\n                          double* z, lapack_int ldz );\n\nlapack_int LAPACKE_ssbevd( int matrix_order, char jobz, char uplo, lapack_int n,\n                           lapack_int kd, float* ab, lapack_int ldab, float* w,\n                           float* z, lapack_int ldz );\nlapack_int LAPACKE_dsbevd( int matrix_order, char jobz, char uplo, lapack_int n,\n                           lapack_int kd, double* ab, lapack_int ldab,\n                           double* w, double* z, lapack_int ldz );\n\nlapack_int LAPACKE_ssbevx( int matrix_order, char jobz, char range, char uplo,\n                           lapack_int n, lapack_int kd, float* ab,\n                           lapack_int ldab, float* q, lapack_int ldq, float vl,\n                           float vu, lapack_int il, lapack_int iu, float abstol,\n                           lapack_int* m, float* w, float* z, lapack_int ldz,\n                           lapack_int* ifail );\nlapack_int LAPACKE_dsbevx( int matrix_order, char jobz, char range, char uplo,\n                           lapack_int n, lapack_int kd, double* ab,\n                           lapack_int ldab, double* q, lapack_int ldq,\n                           double vl, double vu, lapack_int il, lapack_int iu,\n                           double abstol, lapack_int* m, double* w, double* z,\n                           lapack_int ldz, lapack_int* ifail );\n\nlapack_int LAPACKE_ssbgst( int matrix_order, char vect, char uplo, lapack_int n,\n                           lapack_int ka, lapack_int kb, float* ab,\n                           lapack_int ldab, const float* bb, lapack_int ldbb,\n                           float* x, lapack_int ldx );\nlapack_int LAPACKE_dsbgst( int matrix_order, char vect, char uplo, lapack_int n,\n                           lapack_int ka, lapack_int kb, double* ab,\n                           lapack_int ldab, const double* bb, lapack_int ldbb,\n                           double* x, lapack_int ldx );\n\nlapack_int LAPACKE_ssbgv( int matrix_order, char jobz, char uplo, lapack_int n,\n                          lapack_int ka, lapack_int kb, float* ab,\n                          lapack_int ldab, float* bb, lapack_int ldbb, float* w,\n                          float* z, lapack_int ldz );\nlapack_int LAPACKE_dsbgv( int matrix_order, char jobz, char uplo, lapack_int n,\n                          lapack_int ka, lapack_int kb, double* ab,\n                          lapack_int ldab, double* bb, lapack_int ldbb,\n                          double* w, double* z, lapack_int ldz );\n\nlapack_int LAPACKE_ssbgvd( int matrix_order, char jobz, char uplo, lapack_int n,\n                           lapack_int ka, lapack_int kb, float* ab,\n                           lapack_int ldab, float* bb, lapack_int ldbb,\n                           float* w, float* z, lapack_int ldz );\nlapack_int LAPACKE_dsbgvd( int matrix_order, char jobz, char uplo, lapack_int n,\n                           lapack_int ka, lapack_int kb, double* ab,\n                           lapack_int ldab, double* bb, lapack_int ldbb,\n                           double* w, double* z, lapack_int ldz );\n\nlapack_int LAPACKE_ssbgvx( int matrix_order, char jobz, char range, char uplo,\n                           lapack_int n, lapack_int ka, lapack_int kb,\n                           float* ab, lapack_int ldab, float* bb,\n                           lapack_int ldbb, float* q, lapack_int ldq, float vl,\n                           float vu, lapack_int il, lapack_int iu, float abstol,\n                           lapack_int* m, float* w, float* z, lapack_int ldz,\n                           lapack_int* ifail );\nlapack_int LAPACKE_dsbgvx( int matrix_order, char jobz, char range, char uplo,\n                           lapack_int n, lapack_int ka, lapack_int kb,\n                           double* ab, lapack_int ldab, double* bb,\n                           lapack_int ldbb, double* q, lapack_int ldq,\n                           double vl, double vu, lapack_int il, lapack_int iu,\n                           double abstol, lapack_int* m, double* w, double* z,\n                           lapack_int ldz, lapack_int* ifail );\n\nlapack_int LAPACKE_ssbtrd( int matrix_order, char vect, char uplo, lapack_int n,\n                           lapack_int kd, float* ab, lapack_int ldab, float* d,\n                           float* e, float* q, lapack_int ldq );\nlapack_int LAPACKE_dsbtrd( int matrix_order, char vect, char uplo, lapack_int n,\n                           lapack_int kd, double* ab, lapack_int ldab,\n                           double* d, double* e, double* q, lapack_int ldq );\n\nlapack_int LAPACKE_ssfrk( int matrix_order, char transr, char uplo, char trans,\n                          lapack_int n, lapack_int k, float alpha,\n                          const float* a, lapack_int lda, float beta,\n                          float* c );\nlapack_int LAPACKE_dsfrk( int matrix_order, char transr, char uplo, char trans,\n                          lapack_int n, lapack_int k, double alpha,\n                          const double* a, lapack_int lda, double beta,\n                          double* c );\n\nlapack_int LAPACKE_sspcon( int matrix_order, char uplo, lapack_int n,\n                           const float* ap, const lapack_int* ipiv, float anorm,\n                           float* rcond );\nlapack_int LAPACKE_dspcon( int matrix_order, char uplo, lapack_int n,\n                           const double* ap, const lapack_int* ipiv,\n                           double anorm, double* rcond );\nlapack_int LAPACKE_cspcon( int matrix_order, char uplo, lapack_int n,\n                           const lapack_complex_float* ap,\n                           const lapack_int* ipiv, float anorm, float* rcond );\nlapack_int LAPACKE_zspcon( int matrix_order, char uplo, lapack_int n,\n                           const lapack_complex_double* ap,\n                           const lapack_int* ipiv, double anorm,\n                           double* rcond );\n\nlapack_int LAPACKE_sspev( int matrix_order, char jobz, char uplo, lapack_int n,\n                          float* ap, float* w, float* z, lapack_int ldz );\nlapack_int LAPACKE_dspev( int matrix_order, char jobz, char uplo, lapack_int n,\n                          double* ap, double* w, double* z, lapack_int ldz );\n\nlapack_int LAPACKE_sspevd( int matrix_order, char jobz, char uplo, lapack_int n,\n                           float* ap, float* w, float* z, lapack_int ldz );\nlapack_int LAPACKE_dspevd( int matrix_order, char jobz, char uplo, lapack_int n,\n                           double* ap, double* w, double* z, lapack_int ldz );\n\nlapack_int LAPACKE_sspevx( int matrix_order, char jobz, char range, char uplo,\n                           lapack_int n, float* ap, float vl, float vu,\n                           lapack_int il, lapack_int iu, float abstol,\n                           lapack_int* m, float* w, float* z, lapack_int ldz,\n                           lapack_int* ifail );\nlapack_int LAPACKE_dspevx( int matrix_order, char jobz, char range, char uplo,\n                           lapack_int n, double* ap, double vl, double vu,\n                           lapack_int il, lapack_int iu, double abstol,\n                           lapack_int* m, double* w, double* z, lapack_int ldz,\n                           lapack_int* ifail );\n\nlapack_int LAPACKE_sspgst( int matrix_order, lapack_int itype, char uplo,\n                           lapack_int n, float* ap, const float* bp );\nlapack_int LAPACKE_dspgst( int matrix_order, lapack_int itype, char uplo,\n                           lapack_int n, double* ap, const double* bp );\n\nlapack_int LAPACKE_sspgv( int matrix_order, lapack_int itype, char jobz,\n                          char uplo, lapack_int n, float* ap, float* bp,\n                          float* w, float* z, lapack_int ldz );\nlapack_int LAPACKE_dspgv( int matrix_order, lapack_int itype, char jobz,\n                          char uplo, lapack_int n, double* ap, double* bp,\n                          double* w, double* z, lapack_int ldz );\n\nlapack_int LAPACKE_sspgvd( int matrix_order, lapack_int itype, char jobz,\n                           char uplo, lapack_int n, float* ap, float* bp,\n                           float* w, float* z, lapack_int ldz );\nlapack_int LAPACKE_dspgvd( int matrix_order, lapack_int itype, char jobz,\n                           char uplo, lapack_int n, double* ap, double* bp,\n                           double* w, double* z, lapack_int ldz );\n\nlapack_int LAPACKE_sspgvx( int matrix_order, lapack_int itype, char jobz,\n                           char range, char uplo, lapack_int n, float* ap,\n                           float* bp, float vl, float vu, lapack_int il,\n                           lapack_int iu, float abstol, lapack_int* m, float* w,\n                           float* z, lapack_int ldz, lapack_int* ifail );\nlapack_int LAPACKE_dspgvx( int matrix_order, lapack_int itype, char jobz,\n                           char range, char uplo, lapack_int n, double* ap,\n                           double* bp, double vl, double vu, lapack_int il,\n                           lapack_int iu, double abstol, lapack_int* m,\n                           double* w, double* z, lapack_int ldz,\n                           lapack_int* ifail );\n\nlapack_int LAPACKE_ssprfs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const float* ap, const float* afp,\n                           const lapack_int* ipiv, const float* b,\n                           lapack_int ldb, float* x, lapack_int ldx,\n                           float* ferr, float* berr );\nlapack_int LAPACKE_dsprfs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const double* ap, const double* afp,\n                           const lapack_int* ipiv, const double* b,\n                           lapack_int ldb, double* x, lapack_int ldx,\n                           double* ferr, double* berr );\nlapack_int LAPACKE_csprfs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_float* ap,\n                           const lapack_complex_float* afp,\n                           const lapack_int* ipiv,\n                           const lapack_complex_float* b, lapack_int ldb,\n                           lapack_complex_float* x, lapack_int ldx, float* ferr,\n                           float* berr );\nlapack_int LAPACKE_zsprfs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_double* ap,\n                           const lapack_complex_double* afp,\n                           const lapack_int* ipiv,\n                           const lapack_complex_double* b, lapack_int ldb,\n                           lapack_complex_double* x, lapack_int ldx,\n                           double* ferr, double* berr );\n\nlapack_int LAPACKE_sspsv( int matrix_order, char uplo, lapack_int n,\n                          lapack_int nrhs, float* ap, lapack_int* ipiv,\n                          float* b, lapack_int ldb );\nlapack_int LAPACKE_dspsv( int matrix_order, char uplo, lapack_int n,\n                          lapack_int nrhs, double* ap, lapack_int* ipiv,\n                          double* b, lapack_int ldb );\nlapack_int LAPACKE_cspsv( int matrix_order, char uplo, lapack_int n,\n                          lapack_int nrhs, lapack_complex_float* ap,\n                          lapack_int* ipiv, lapack_complex_float* b,\n                          lapack_int ldb );\nlapack_int LAPACKE_zspsv( int matrix_order, char uplo, lapack_int n,\n                          lapack_int nrhs, lapack_complex_double* ap,\n                          lapack_int* ipiv, lapack_complex_double* b,\n                          lapack_int ldb );\n\nlapack_int LAPACKE_sspsvx( int matrix_order, char fact, char uplo, lapack_int n,\n                           lapack_int nrhs, const float* ap, float* afp,\n                           lapack_int* ipiv, const float* b, lapack_int ldb,\n                           float* x, lapack_int ldx, float* rcond, float* ferr,\n                           float* berr );\nlapack_int LAPACKE_dspsvx( int matrix_order, char fact, char uplo, lapack_int n,\n                           lapack_int nrhs, const double* ap, double* afp,\n                           lapack_int* ipiv, const double* b, lapack_int ldb,\n                           double* x, lapack_int ldx, double* rcond,\n                           double* ferr, double* berr );\nlapack_int LAPACKE_cspsvx( int matrix_order, char fact, char uplo, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_float* ap,\n                           lapack_complex_float* afp, lapack_int* ipiv,\n                           const lapack_complex_float* b, lapack_int ldb,\n                           lapack_complex_float* x, lapack_int ldx,\n                           float* rcond, float* ferr, float* berr );\nlapack_int LAPACKE_zspsvx( int matrix_order, char fact, char uplo, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_double* ap,\n                           lapack_complex_double* afp, lapack_int* ipiv,\n                           const lapack_complex_double* b, lapack_int ldb,\n                           lapack_complex_double* x, lapack_int ldx,\n                           double* rcond, double* ferr, double* berr );\n\nlapack_int LAPACKE_ssptrd( int matrix_order, char uplo, lapack_int n, float* ap,\n                           float* d, float* e, float* tau );\nlapack_int LAPACKE_dsptrd( int matrix_order, char uplo, lapack_int n,\n                           double* ap, double* d, double* e, double* tau );\n\nlapack_int LAPACKE_ssptrf( int matrix_order, char uplo, lapack_int n, float* ap,\n                           lapack_int* ipiv );\nlapack_int LAPACKE_dsptrf( int matrix_order, char uplo, lapack_int n,\n                           double* ap, lapack_int* ipiv );\nlapack_int LAPACKE_csptrf( int matrix_order, char uplo, lapack_int n,\n                           lapack_complex_float* ap, lapack_int* ipiv );\nlapack_int LAPACKE_zsptrf( int matrix_order, char uplo, lapack_int n,\n                           lapack_complex_double* ap, lapack_int* ipiv );\n\nlapack_int LAPACKE_ssptri( int matrix_order, char uplo, lapack_int n, float* ap,\n                           const lapack_int* ipiv );\nlapack_int LAPACKE_dsptri( int matrix_order, char uplo, lapack_int n,\n                           double* ap, const lapack_int* ipiv );\nlapack_int LAPACKE_csptri( int matrix_order, char uplo, lapack_int n,\n                           lapack_complex_float* ap, const lapack_int* ipiv );\nlapack_int LAPACKE_zsptri( int matrix_order, char uplo, lapack_int n,\n                           lapack_complex_double* ap, const lapack_int* ipiv );\n\nlapack_int LAPACKE_ssptrs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const float* ap,\n                           const lapack_int* ipiv, float* b, lapack_int ldb );\nlapack_int LAPACKE_dsptrs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const double* ap,\n                           const lapack_int* ipiv, double* b, lapack_int ldb );\nlapack_int LAPACKE_csptrs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_float* ap,\n                           const lapack_int* ipiv, lapack_complex_float* b,\n                           lapack_int ldb );\nlapack_int LAPACKE_zsptrs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_double* ap,\n                           const lapack_int* ipiv, lapack_complex_double* b,\n                           lapack_int ldb );\n\nlapack_int LAPACKE_sstebz( char range, char order, lapack_int n, float vl,\n                           float vu, lapack_int il, lapack_int iu, float abstol,\n                           const float* d, const float* e, lapack_int* m,\n                           lapack_int* nsplit, float* w, lapack_int* iblock,\n                           lapack_int* isplit );\nlapack_int LAPACKE_dstebz( char range, char order, lapack_int n, double vl,\n                           double vu, lapack_int il, lapack_int iu,\n                           double abstol, const double* d, const double* e,\n                           lapack_int* m, lapack_int* nsplit, double* w,\n                           lapack_int* iblock, lapack_int* isplit );\n\nlapack_int LAPACKE_sstedc( int matrix_order, char compz, lapack_int n, float* d,\n                           float* e, float* z, lapack_int ldz );\nlapack_int LAPACKE_dstedc( int matrix_order, char compz, lapack_int n,\n                           double* d, double* e, double* z, lapack_int ldz );\nlapack_int LAPACKE_cstedc( int matrix_order, char compz, lapack_int n, float* d,\n                           float* e, lapack_complex_float* z, lapack_int ldz );\nlapack_int LAPACKE_zstedc( int matrix_order, char compz, lapack_int n,\n                           double* d, double* e, lapack_complex_double* z,\n                           lapack_int ldz );\n\nlapack_int LAPACKE_sstegr( int matrix_order, char jobz, char range,\n                           lapack_int n, float* d, float* e, float vl, float vu,\n                           lapack_int il, lapack_int iu, float abstol,\n                           lapack_int* m, float* w, float* z, lapack_int ldz,\n                           lapack_int* isuppz );\nlapack_int LAPACKE_dstegr( int matrix_order, char jobz, char range,\n                           lapack_int n, double* d, double* e, double vl,\n                           double vu, lapack_int il, lapack_int iu,\n                           double abstol, lapack_int* m, double* w, double* z,\n                           lapack_int ldz, lapack_int* isuppz );\nlapack_int LAPACKE_cstegr( int matrix_order, char jobz, char range,\n                           lapack_int n, float* d, float* e, float vl, float vu,\n                           lapack_int il, lapack_int iu, float abstol,\n                           lapack_int* m, float* w, lapack_complex_float* z,\n                           lapack_int ldz, lapack_int* isuppz );\nlapack_int LAPACKE_zstegr( int matrix_order, char jobz, char range,\n                           lapack_int n, double* d, double* e, double vl,\n                           double vu, lapack_int il, lapack_int iu,\n                           double abstol, lapack_int* m, double* w,\n                           lapack_complex_double* z, lapack_int ldz,\n                           lapack_int* isuppz );\n\nlapack_int LAPACKE_sstein( int matrix_order, lapack_int n, const float* d,\n                           const float* e, lapack_int m, const float* w,\n                           const lapack_int* iblock, const lapack_int* isplit,\n                           float* z, lapack_int ldz, lapack_int* ifailv );\nlapack_int LAPACKE_dstein( int matrix_order, lapack_int n, const double* d,\n                           const double* e, lapack_int m, const double* w,\n                           const lapack_int* iblock, const lapack_int* isplit,\n                           double* z, lapack_int ldz, lapack_int* ifailv );\nlapack_int LAPACKE_cstein( int matrix_order, lapack_int n, const float* d,\n                           const float* e, lapack_int m, const float* w,\n                           const lapack_int* iblock, const lapack_int* isplit,\n                           lapack_complex_float* z, lapack_int ldz,\n                           lapack_int* ifailv );\nlapack_int LAPACKE_zstein( int matrix_order, lapack_int n, const double* d,\n                           const double* e, lapack_int m, const double* w,\n                           const lapack_int* iblock, const lapack_int* isplit,\n                           lapack_complex_double* z, lapack_int ldz,\n                           lapack_int* ifailv );\n\nlapack_int LAPACKE_sstemr( int matrix_order, char jobz, char range,\n                           lapack_int n, float* d, float* e, float vl, float vu,\n                           lapack_int il, lapack_int iu, lapack_int* m,\n                           float* w, float* z, lapack_int ldz, lapack_int nzc,\n                           lapack_int* isuppz, lapack_logical* tryrac );\nlapack_int LAPACKE_dstemr( int matrix_order, char jobz, char range,\n                           lapack_int n, double* d, double* e, double vl,\n                           double vu, lapack_int il, lapack_int iu,\n                           lapack_int* m, double* w, double* z, lapack_int ldz,\n                           lapack_int nzc, lapack_int* isuppz,\n                           lapack_logical* tryrac );\nlapack_int LAPACKE_cstemr( int matrix_order, char jobz, char range,\n                           lapack_int n, float* d, float* e, float vl, float vu,\n                           lapack_int il, lapack_int iu, lapack_int* m,\n                           float* w, lapack_complex_float* z, lapack_int ldz,\n                           lapack_int nzc, lapack_int* isuppz,\n                           lapack_logical* tryrac );\nlapack_int LAPACKE_zstemr( int matrix_order, char jobz, char range,\n                           lapack_int n, double* d, double* e, double vl,\n                           double vu, lapack_int il, lapack_int iu,\n                           lapack_int* m, double* w, lapack_complex_double* z,\n                           lapack_int ldz, lapack_int nzc, lapack_int* isuppz,\n                           lapack_logical* tryrac );\n\nlapack_int LAPACKE_ssteqr( int matrix_order, char compz, lapack_int n, float* d,\n                           float* e, float* z, lapack_int ldz );\nlapack_int LAPACKE_dsteqr( int matrix_order, char compz, lapack_int n,\n                           double* d, double* e, double* z, lapack_int ldz );\nlapack_int LAPACKE_csteqr( int matrix_order, char compz, lapack_int n, float* d,\n                           float* e, lapack_complex_float* z, lapack_int ldz );\nlapack_int LAPACKE_zsteqr( int matrix_order, char compz, lapack_int n,\n                           double* d, double* e, lapack_complex_double* z,\n                           lapack_int ldz );\n\nlapack_int LAPACKE_ssterf( lapack_int n, float* d, float* e );\nlapack_int LAPACKE_dsterf( lapack_int n, double* d, double* e );\n\nlapack_int LAPACKE_sstev( int matrix_order, char jobz, lapack_int n, float* d,\n                          float* e, float* z, lapack_int ldz );\nlapack_int LAPACKE_dstev( int matrix_order, char jobz, lapack_int n, double* d,\n                          double* e, double* z, lapack_int ldz );\n\nlapack_int LAPACKE_sstevd( int matrix_order, char jobz, lapack_int n, float* d,\n                           float* e, float* z, lapack_int ldz );\nlapack_int LAPACKE_dstevd( int matrix_order, char jobz, lapack_int n, double* d,\n                           double* e, double* z, lapack_int ldz );\n\nlapack_int LAPACKE_sstevr( int matrix_order, char jobz, char range,\n                           lapack_int n, float* d, float* e, float vl, float vu,\n                           lapack_int il, lapack_int iu, float abstol,\n                           lapack_int* m, float* w, float* z, lapack_int ldz,\n                           lapack_int* isuppz );\nlapack_int LAPACKE_dstevr( int matrix_order, char jobz, char range,\n                           lapack_int n, double* d, double* e, double vl,\n                           double vu, lapack_int il, lapack_int iu,\n                           double abstol, lapack_int* m, double* w, double* z,\n                           lapack_int ldz, lapack_int* isuppz );\n\nlapack_int LAPACKE_sstevx( int matrix_order, char jobz, char range,\n                           lapack_int n, float* d, float* e, float vl, float vu,\n                           lapack_int il, lapack_int iu, float abstol,\n                           lapack_int* m, float* w, float* z, lapack_int ldz,\n                           lapack_int* ifail );\nlapack_int LAPACKE_dstevx( int matrix_order, char jobz, char range,\n                           lapack_int n, double* d, double* e, double vl,\n                           double vu, lapack_int il, lapack_int iu,\n                           double abstol, lapack_int* m, double* w, double* z,\n                           lapack_int ldz, lapack_int* ifail );\n\nlapack_int LAPACKE_ssycon( int matrix_order, char uplo, lapack_int n,\n                           const float* a, lapack_int lda,\n                           const lapack_int* ipiv, float anorm, float* rcond );\nlapack_int LAPACKE_dsycon( int matrix_order, char uplo, lapack_int n,\n                           const double* a, lapack_int lda,\n                           const lapack_int* ipiv, double anorm,\n                           double* rcond );\nlapack_int LAPACKE_csycon( int matrix_order, char uplo, lapack_int n,\n                           const lapack_complex_float* a, lapack_int lda,\n                           const lapack_int* ipiv, float anorm, float* rcond );\nlapack_int LAPACKE_zsycon( int matrix_order, char uplo, lapack_int n,\n                           const lapack_complex_double* a, lapack_int lda,\n                           const lapack_int* ipiv, double anorm,\n                           double* rcond );\n\nlapack_int LAPACKE_ssyequb( int matrix_order, char uplo, lapack_int n,\n                            const float* a, lapack_int lda, float* s,\n                            float* scond, float* amax );\nlapack_int LAPACKE_dsyequb( int matrix_order, char uplo, lapack_int n,\n                            const double* a, lapack_int lda, double* s,\n                            double* scond, double* amax );\nlapack_int LAPACKE_csyequb( int matrix_order, char uplo, lapack_int n,\n                            const lapack_complex_float* a, lapack_int lda,\n                            float* s, float* scond, float* amax );\nlapack_int LAPACKE_zsyequb( int matrix_order, char uplo, lapack_int n,\n                            const lapack_complex_double* a, lapack_int lda,\n                            double* s, double* scond, double* amax );\n\nlapack_int LAPACKE_ssyev( int matrix_order, char jobz, char uplo, lapack_int n,\n                          float* a, lapack_int lda, float* w );\nlapack_int LAPACKE_dsyev( int matrix_order, char jobz, char uplo, lapack_int n,\n                          double* a, lapack_int lda, double* w );\n\nlapack_int LAPACKE_ssyevd( int matrix_order, char jobz, char uplo, lapack_int n,\n                           float* a, lapack_int lda, float* w );\nlapack_int LAPACKE_dsyevd( int matrix_order, char jobz, char uplo, lapack_int n,\n                           double* a, lapack_int lda, double* w );\n\nlapack_int LAPACKE_ssyevr( int matrix_order, char jobz, char range, char uplo,\n                           lapack_int n, float* a, lapack_int lda, float vl,\n                           float vu, lapack_int il, lapack_int iu, float abstol,\n                           lapack_int* m, float* w, float* z, lapack_int ldz,\n                           lapack_int* isuppz );\nlapack_int LAPACKE_dsyevr( int matrix_order, char jobz, char range, char uplo,\n                           lapack_int n, double* a, lapack_int lda, double vl,\n                           double vu, lapack_int il, lapack_int iu,\n                           double abstol, lapack_int* m, double* w, double* z,\n                           lapack_int ldz, lapack_int* isuppz );\n\nlapack_int LAPACKE_ssyevx( int matrix_order, char jobz, char range, char uplo,\n                           lapack_int n, float* a, lapack_int lda, float vl,\n                           float vu, lapack_int il, lapack_int iu, float abstol,\n                           lapack_int* m, float* w, float* z, lapack_int ldz,\n                           lapack_int* ifail );\nlapack_int LAPACKE_dsyevx( int matrix_order, char jobz, char range, char uplo,\n                           lapack_int n, double* a, lapack_int lda, double vl,\n                           double vu, lapack_int il, lapack_int iu,\n                           double abstol, lapack_int* m, double* w, double* z,\n                           lapack_int ldz, lapack_int* ifail );\n\nlapack_int LAPACKE_ssygst( int matrix_order, lapack_int itype, char uplo,\n                           lapack_int n, float* a, lapack_int lda,\n                           const float* b, lapack_int ldb );\nlapack_int LAPACKE_dsygst( int matrix_order, lapack_int itype, char uplo,\n                           lapack_int n, double* a, lapack_int lda,\n                           const double* b, lapack_int ldb );\n\nlapack_int LAPACKE_ssygv( int matrix_order, lapack_int itype, char jobz,\n                          char uplo, lapack_int n, float* a, lapack_int lda,\n                          float* b, lapack_int ldb, float* w );\nlapack_int LAPACKE_dsygv( int matrix_order, lapack_int itype, char jobz,\n                          char uplo, lapack_int n, double* a, lapack_int lda,\n                          double* b, lapack_int ldb, double* w );\n\nlapack_int LAPACKE_ssygvd( int matrix_order, lapack_int itype, char jobz,\n                           char uplo, lapack_int n, float* a, lapack_int lda,\n                           float* b, lapack_int ldb, float* w );\nlapack_int LAPACKE_dsygvd( int matrix_order, lapack_int itype, char jobz,\n                           char uplo, lapack_int n, double* a, lapack_int lda,\n                           double* b, lapack_int ldb, double* w );\n\nlapack_int LAPACKE_ssygvx( int matrix_order, lapack_int itype, char jobz,\n                           char range, char uplo, lapack_int n, float* a,\n                           lapack_int lda, float* b, lapack_int ldb, float vl,\n                           float vu, lapack_int il, lapack_int iu, float abstol,\n                           lapack_int* m, float* w, float* z, lapack_int ldz,\n                           lapack_int* ifail );\nlapack_int LAPACKE_dsygvx( int matrix_order, lapack_int itype, char jobz,\n                           char range, char uplo, lapack_int n, double* a,\n                           lapack_int lda, double* b, lapack_int ldb, double vl,\n                           double vu, lapack_int il, lapack_int iu,\n                           double abstol, lapack_int* m, double* w, double* z,\n                           lapack_int ldz, lapack_int* ifail );\n\nlapack_int LAPACKE_ssyrfs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const float* a, lapack_int lda,\n                           const float* af, lapack_int ldaf,\n                           const lapack_int* ipiv, const float* b,\n                           lapack_int ldb, float* x, lapack_int ldx,\n                           float* ferr, float* berr );\nlapack_int LAPACKE_dsyrfs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const double* a, lapack_int lda,\n                           const double* af, lapack_int ldaf,\n                           const lapack_int* ipiv, const double* b,\n                           lapack_int ldb, double* x, lapack_int ldx,\n                           double* ferr, double* berr );\nlapack_int LAPACKE_csyrfs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_float* a,\n                           lapack_int lda, const lapack_complex_float* af,\n                           lapack_int ldaf, const lapack_int* ipiv,\n                           const lapack_complex_float* b, lapack_int ldb,\n                           lapack_complex_float* x, lapack_int ldx, float* ferr,\n                           float* berr );\nlapack_int LAPACKE_zsyrfs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_double* a,\n                           lapack_int lda, const lapack_complex_double* af,\n                           lapack_int ldaf, const lapack_int* ipiv,\n                           const lapack_complex_double* b, lapack_int ldb,\n                           lapack_complex_double* x, lapack_int ldx,\n                           double* ferr, double* berr );\n\nlapack_int LAPACKE_ssyrfsx( int matrix_order, char uplo, char equed,\n                            lapack_int n, lapack_int nrhs, const float* a,\n                            lapack_int lda, const float* af, lapack_int ldaf,\n                            const lapack_int* ipiv, const float* s,\n                            const float* b, lapack_int ldb, float* x,\n                            lapack_int ldx, float* rcond, float* berr,\n                            lapack_int n_err_bnds, float* err_bnds_norm,\n                            float* err_bnds_comp, lapack_int nparams,\n                            float* params );\nlapack_int LAPACKE_dsyrfsx( int matrix_order, char uplo, char equed,\n                            lapack_int n, lapack_int nrhs, const double* a,\n                            lapack_int lda, const double* af, lapack_int ldaf,\n                            const lapack_int* ipiv, const double* s,\n                            const double* b, lapack_int ldb, double* x,\n                            lapack_int ldx, double* rcond, double* berr,\n                            lapack_int n_err_bnds, double* err_bnds_norm,\n                            double* err_bnds_comp, lapack_int nparams,\n                            double* params );\nlapack_int LAPACKE_csyrfsx( int matrix_order, char uplo, char equed,\n                            lapack_int n, lapack_int nrhs,\n                            const lapack_complex_float* a, lapack_int lda,\n                            const lapack_complex_float* af, lapack_int ldaf,\n                            const lapack_int* ipiv, const float* s,\n                            const lapack_complex_float* b, lapack_int ldb,\n                            lapack_complex_float* x, lapack_int ldx,\n                            float* rcond, float* berr, lapack_int n_err_bnds,\n                            float* err_bnds_norm, float* err_bnds_comp,\n                            lapack_int nparams, float* params );\nlapack_int LAPACKE_zsyrfsx( int matrix_order, char uplo, char equed,\n                            lapack_int n, lapack_int nrhs,\n                            const lapack_complex_double* a, lapack_int lda,\n                            const lapack_complex_double* af, lapack_int ldaf,\n                            const lapack_int* ipiv, const double* s,\n                            const lapack_complex_double* b, lapack_int ldb,\n                            lapack_complex_double* x, lapack_int ldx,\n                            double* rcond, double* berr, lapack_int n_err_bnds,\n                            double* err_bnds_norm, double* err_bnds_comp,\n                            lapack_int nparams, double* params );\n\nlapack_int LAPACKE_ssysv( int matrix_order, char uplo, lapack_int n,\n                          lapack_int nrhs, float* a, lapack_int lda,\n                          lapack_int* ipiv, float* b, lapack_int ldb );\nlapack_int LAPACKE_dsysv( int matrix_order, char uplo, lapack_int n,\n                          lapack_int nrhs, double* a, lapack_int lda,\n                          lapack_int* ipiv, double* b, lapack_int ldb );\nlapack_int LAPACKE_csysv( int matrix_order, char uplo, lapack_int n,\n                          lapack_int nrhs, lapack_complex_float* a,\n                          lapack_int lda, lapack_int* ipiv,\n                          lapack_complex_float* b, lapack_int ldb );\nlapack_int LAPACKE_zsysv( int matrix_order, char uplo, lapack_int n,\n                          lapack_int nrhs, lapack_complex_double* a,\n                          lapack_int lda, lapack_int* ipiv,\n                          lapack_complex_double* b, lapack_int ldb );\n\nlapack_int LAPACKE_ssysvx( int matrix_order, char fact, char uplo, lapack_int n,\n                           lapack_int nrhs, const float* a, lapack_int lda,\n                           float* af, lapack_int ldaf, lapack_int* ipiv,\n                           const float* b, lapack_int ldb, float* x,\n                           lapack_int ldx, float* rcond, float* ferr,\n                           float* berr );\nlapack_int LAPACKE_dsysvx( int matrix_order, char fact, char uplo, lapack_int n,\n                           lapack_int nrhs, const double* a, lapack_int lda,\n                           double* af, lapack_int ldaf, lapack_int* ipiv,\n                           const double* b, lapack_int ldb, double* x,\n                           lapack_int ldx, double* rcond, double* ferr,\n                           double* berr );\nlapack_int LAPACKE_csysvx( int matrix_order, char fact, char uplo, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_float* a,\n                           lapack_int lda, lapack_complex_float* af,\n                           lapack_int ldaf, lapack_int* ipiv,\n                           const lapack_complex_float* b, lapack_int ldb,\n                           lapack_complex_float* x, lapack_int ldx,\n                           float* rcond, float* ferr, float* berr );\nlapack_int LAPACKE_zsysvx( int matrix_order, char fact, char uplo, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_double* a,\n                           lapack_int lda, lapack_complex_double* af,\n                           lapack_int ldaf, lapack_int* ipiv,\n                           const lapack_complex_double* b, lapack_int ldb,\n                           lapack_complex_double* x, lapack_int ldx,\n                           double* rcond, double* ferr, double* berr );\n\nlapack_int LAPACKE_ssysvxx( int matrix_order, char fact, char uplo,\n                            lapack_int n, lapack_int nrhs, float* a,\n                            lapack_int lda, float* af, lapack_int ldaf,\n                            lapack_int* ipiv, char* equed, float* s, float* b,\n                            lapack_int ldb, float* x, lapack_int ldx,\n                            float* rcond, float* rpvgrw, float* berr,\n                            lapack_int n_err_bnds, float* err_bnds_norm,\n                            float* err_bnds_comp, lapack_int nparams,\n                            float* params );\nlapack_int LAPACKE_dsysvxx( int matrix_order, char fact, char uplo,\n                            lapack_int n, lapack_int nrhs, double* a,\n                            lapack_int lda, double* af, lapack_int ldaf,\n                            lapack_int* ipiv, char* equed, double* s, double* b,\n                            lapack_int ldb, double* x, lapack_int ldx,\n                            double* rcond, double* rpvgrw, double* berr,\n                            lapack_int n_err_bnds, double* err_bnds_norm,\n                            double* err_bnds_comp, lapack_int nparams,\n                            double* params );\nlapack_int LAPACKE_csysvxx( int matrix_order, char fact, char uplo,\n                            lapack_int n, lapack_int nrhs,\n                            lapack_complex_float* a, lapack_int lda,\n                            lapack_complex_float* af, lapack_int ldaf,\n                            lapack_int* ipiv, char* equed, float* s,\n                            lapack_complex_float* b, lapack_int ldb,\n                            lapack_complex_float* x, lapack_int ldx,\n                            float* rcond, float* rpvgrw, float* berr,\n                            lapack_int n_err_bnds, float* err_bnds_norm,\n                            float* err_bnds_comp, lapack_int nparams,\n                            float* params );\nlapack_int LAPACKE_zsysvxx( int matrix_order, char fact, char uplo,\n                            lapack_int n, lapack_int nrhs,\n                            lapack_complex_double* a, lapack_int lda,\n                            lapack_complex_double* af, lapack_int ldaf,\n                            lapack_int* ipiv, char* equed, double* s,\n                            lapack_complex_double* b, lapack_int ldb,\n                            lapack_complex_double* x, lapack_int ldx,\n                            double* rcond, double* rpvgrw, double* berr,\n                            lapack_int n_err_bnds, double* err_bnds_norm,\n                            double* err_bnds_comp, lapack_int nparams,\n                            double* params );\n\nlapack_int LAPACKE_ssytrd( int matrix_order, char uplo, lapack_int n, float* a,\n                           lapack_int lda, float* d, float* e, float* tau );\nlapack_int LAPACKE_dsytrd( int matrix_order, char uplo, lapack_int n, double* a,\n                           lapack_int lda, double* d, double* e, double* tau );\n\nlapack_int LAPACKE_ssytrf( int matrix_order, char uplo, lapack_int n, float* a,\n                           lapack_int lda, lapack_int* ipiv );\nlapack_int LAPACKE_dsytrf( int matrix_order, char uplo, lapack_int n, double* a,\n                           lapack_int lda, lapack_int* ipiv );\nlapack_int LAPACKE_csytrf( int matrix_order, char uplo, lapack_int n,\n                           lapack_complex_float* a, lapack_int lda,\n                           lapack_int* ipiv );\nlapack_int LAPACKE_zsytrf( int matrix_order, char uplo, lapack_int n,\n                           lapack_complex_double* a, lapack_int lda,\n                           lapack_int* ipiv );\n\nlapack_int LAPACKE_ssytri( int matrix_order, char uplo, lapack_int n, float* a,\n                           lapack_int lda, const lapack_int* ipiv );\nlapack_int LAPACKE_dsytri( int matrix_order, char uplo, lapack_int n, double* a,\n                           lapack_int lda, const lapack_int* ipiv );\nlapack_int LAPACKE_csytri( int matrix_order, char uplo, lapack_int n,\n                           lapack_complex_float* a, lapack_int lda,\n                           const lapack_int* ipiv );\nlapack_int LAPACKE_zsytri( int matrix_order, char uplo, lapack_int n,\n                           lapack_complex_double* a, lapack_int lda,\n                           const lapack_int* ipiv );\n\nlapack_int LAPACKE_ssytrs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const float* a, lapack_int lda,\n                           const lapack_int* ipiv, float* b, lapack_int ldb );\nlapack_int LAPACKE_dsytrs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const double* a, lapack_int lda,\n                           const lapack_int* ipiv, double* b, lapack_int ldb );\nlapack_int LAPACKE_csytrs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_float* a,\n                           lapack_int lda, const lapack_int* ipiv,\n                           lapack_complex_float* b, lapack_int ldb );\nlapack_int LAPACKE_zsytrs( int matrix_order, char uplo, lapack_int n,\n                           lapack_int nrhs, const lapack_complex_double* a,\n                           lapack_int lda, const lapack_int* ipiv,\n                           lapack_complex_double* b, lapack_int ldb );\n\nlapack_int LAPACKE_stbcon( int matrix_order, char norm, char uplo, char diag,\n                           lapack_int n, lapack_int kd, const float* ab,\n                           lapack_int ldab, float* rcond );\nlapack_int LAPACKE_dtbcon( int matrix_order, char norm, char uplo, char diag,\n                           lapack_int n, lapack_int kd, const double* ab,\n                           lapack_int ldab, double* rcond );\nlapack_int LAPACKE_ctbcon( int matrix_order, char norm, char uplo, char diag,\n                           lapack_int n, lapack_int kd,\n                           const lapack_complex_float* ab, lapack_int ldab,\n                           float* rcond );\nlapack_int LAPACKE_ztbcon( int matrix_order, char norm, char uplo, char diag,\n                           lapack_int n, lapack_int kd,\n                           const lapack_complex_double* ab, lapack_int ldab,\n                           double* rcond );\n\nlapack_int LAPACKE_stbrfs( int matrix_order, char uplo, char trans, char diag,\n                           lapack_int n, lapack_int kd, lapack_int nrhs,\n                           const float* ab, lapack_int ldab, const float* b,\n                           lapack_int ldb, const float* x, lapack_int ldx,\n                           float* ferr, float* berr );\nlapack_int LAPACKE_dtbrfs( int matrix_order, char uplo, char trans, char diag,\n                           lapack_int n, lapack_int kd, lapack_int nrhs,\n                           const double* ab, lapack_int ldab, const double* b,\n                           lapack_int ldb, const double* x, lapack_int ldx,\n                           double* ferr, double* berr );\nlapack_int LAPACKE_ctbrfs( int matrix_order, char uplo, char trans, char diag,\n                           lapack_int n, lapack_int kd, lapack_int nrhs,\n                           const lapack_complex_float* ab, lapack_int ldab,\n                           const lapack_complex_float* b, lapack_int ldb,\n                           const lapack_complex_float* x, lapack_int ldx,\n                           float* ferr, float* berr );\nlapack_int LAPACKE_ztbrfs( int matrix_order, char uplo, char trans, char diag,\n                           lapack_int n, lapack_int kd, lapack_int nrhs,\n                           const lapack_complex_double* ab, lapack_int ldab,\n                           const lapack_complex_double* b, lapack_int ldb,\n                           const lapack_complex_double* x, lapack_int ldx,\n                           double* ferr, double* berr );\n\nlapack_int LAPACKE_stbtrs( int matrix_order, char uplo, char trans, char diag,\n                           lapack_int n, lapack_int kd, lapack_int nrhs,\n                           const float* ab, lapack_int ldab, float* b,\n                           lapack_int ldb );\nlapack_int LAPACKE_dtbtrs( int matrix_order, char uplo, char trans, char diag,\n                           lapack_int n, lapack_int kd, lapack_int nrhs,\n                           const double* ab, lapack_int ldab, double* b,\n                           lapack_int ldb );\nlapack_int LAPACKE_ctbtrs( int matrix_order, char uplo, char trans, char diag,\n                           lapack_int n, lapack_int kd, lapack_int nrhs,\n                           const lapack_complex_float* ab, lapack_int ldab,\n                           lapack_complex_float* b, lapack_int ldb );\nlapack_int LAPACKE_ztbtrs( int matrix_order, char uplo, char trans, char diag,\n                           lapack_int n, lapack_int kd, lapack_int nrhs,\n                           const lapack_complex_double* ab, lapack_int ldab,\n                           lapack_complex_double* b, lapack_int ldb );\n\nlapack_int LAPACKE_stfsm( int matrix_order, char transr, char side, char uplo,\n                          char trans, char diag, lapack_int m, lapack_int n,\n                          float alpha, const float* a, float* b,\n                          lapack_int ldb );\nlapack_int LAPACKE_dtfsm( int matrix_order, char transr, char side, char uplo,\n                          char trans, char diag, lapack_int m, lapack_int n,\n                          double alpha, const double* a, double* b,\n                          lapack_int ldb );\nlapack_int LAPACKE_ctfsm( int matrix_order, char transr, char side, char uplo,\n                          char trans, char diag, lapack_int m, lapack_int n,\n                          lapack_complex_float alpha,\n                          const lapack_complex_float* a,\n                          lapack_complex_float* b, lapack_int ldb );\nlapack_int LAPACKE_ztfsm( int matrix_order, char transr, char side, char uplo,\n                          char trans, char diag, lapack_int m, lapack_int n,\n                          lapack_complex_double alpha,\n                          const lapack_complex_double* a,\n                          lapack_complex_double* b, lapack_int ldb );\n\nlapack_int LAPACKE_stftri( int matrix_order, char transr, char uplo, char diag,\n                           lapack_int n, float* a );\nlapack_int LAPACKE_dtftri( int matrix_order, char transr, char uplo, char diag,\n                           lapack_int n, double* a );\nlapack_int LAPACKE_ctftri( int matrix_order, char transr, char uplo, char diag,\n                           lapack_int n, lapack_complex_float* a );\nlapack_int LAPACKE_ztftri( int matrix_order, char transr, char uplo, char diag,\n                           lapack_int n, lapack_complex_double* a );\n\nlapack_int LAPACKE_stfttp( int matrix_order, char transr, char uplo,\n                           lapack_int n, const float* arf, float* ap );\nlapack_int LAPACKE_dtfttp( int matrix_order, char transr, char uplo,\n                           lapack_int n, const double* arf, double* ap );\nlapack_int LAPACKE_ctfttp( int matrix_order, char transr, char uplo,\n                           lapack_int n, const lapack_complex_float* arf,\n                           lapack_complex_float* ap );\nlapack_int LAPACKE_ztfttp( int matrix_order, char transr, char uplo,\n                           lapack_int n, const lapack_complex_double* arf,\n                           lapack_complex_double* ap );\n\nlapack_int LAPACKE_stfttr( int matrix_order, char transr, char uplo,\n                           lapack_int n, const float* arf, float* a,\n                           lapack_int lda );\nlapack_int LAPACKE_dtfttr( int matrix_order, char transr, char uplo,\n                           lapack_int n, const double* arf, double* a,\n                           lapack_int lda );\nlapack_int LAPACKE_ctfttr( int matrix_order, char transr, char uplo,\n                           lapack_int n, const lapack_complex_float* arf,\n                           lapack_complex_float* a, lapack_int lda );\nlapack_int LAPACKE_ztfttr( int matrix_order, char transr, char uplo,\n                           lapack_int n, const lapack_complex_double* arf,\n                           lapack_complex_double* a, lapack_int lda );\n\nlapack_int LAPACKE_stgevc( int matrix_order, char side, char howmny,\n                           const lapack_logical* select, lapack_int n,\n                           const float* s, lapack_int lds, const float* p,\n                           lapack_int ldp, float* vl, lapack_int ldvl,\n                           float* vr, lapack_int ldvr, lapack_int mm,\n                           lapack_int* m );\nlapack_int LAPACKE_dtgevc( int matrix_order, char side, char howmny,\n                           const lapack_logical* select, lapack_int n,\n                           const double* s, lapack_int lds, const double* p,\n                           lapack_int ldp, double* vl, lapack_int ldvl,\n                           double* vr, lapack_int ldvr, lapack_int mm,\n                           lapack_int* m );\nlapack_int LAPACKE_ctgevc( int matrix_order, char side, char howmny,\n                           const lapack_logical* select, lapack_int n,\n                           const lapack_complex_float* s, lapack_int lds,\n                           const lapack_complex_float* p, lapack_int ldp,\n                           lapack_complex_float* vl, lapack_int ldvl,\n                           lapack_complex_float* vr, lapack_int ldvr,\n                           lapack_int mm, lapack_int* m );\nlapack_int LAPACKE_ztgevc( int matrix_order, char side, char howmny,\n                           const lapack_logical* select, lapack_int n,\n                           const lapack_complex_double* s, lapack_int lds,\n                           const lapack_complex_double* p, lapack_int ldp,\n                           lapack_complex_double* vl, lapack_int ldvl,\n                           lapack_complex_double* vr, lapack_int ldvr,\n                           lapack_int mm, lapack_int* m );\n\nlapack_int LAPACKE_stgexc( int matrix_order, lapack_logical wantq,\n                           lapack_logical wantz, lapack_int n, float* a,\n                           lapack_int lda, float* b, lapack_int ldb, float* q,\n                           lapack_int ldq, float* z, lapack_int ldz,\n                           lapack_int* ifst, lapack_int* ilst );\nlapack_int LAPACKE_dtgexc( int matrix_order, lapack_logical wantq,\n                           lapack_logical wantz, lapack_int n, double* a,\n                           lapack_int lda, double* b, lapack_int ldb, double* q,\n                           lapack_int ldq, double* z, lapack_int ldz,\n                           lapack_int* ifst, lapack_int* ilst );\nlapack_int LAPACKE_ctgexc( int matrix_order, lapack_logical wantq,\n                           lapack_logical wantz, lapack_int n,\n                           lapack_complex_float* a, lapack_int lda,\n                           lapack_complex_float* b, lapack_int ldb,\n                           lapack_complex_float* q, lapack_int ldq,\n                           lapack_complex_float* z, lapack_int ldz,\n                           lapack_int ifst, lapack_int ilst );\nlapack_int LAPACKE_ztgexc( int matrix_order, lapack_logical wantq,\n                           lapack_logical wantz, lapack_int n,\n                           lapack_complex_double* a, lapack_int lda,\n                           lapack_complex_double* b, lapack_int ldb,\n                           lapack_complex_double* q, lapack_int ldq,\n                           lapack_complex_double* z, lapack_int ldz,\n                           lapack_int ifst, lapack_int ilst );\n\nlapack_int LAPACKE_stgsen( int matrix_order, lapack_int ijob,\n                           lapack_logical wantq, lapack_logical wantz,\n                           const lapack_logical* select, lapack_int n, float* a,\n                           lapack_int lda, float* b, lapack_int ldb,\n                           float* alphar, float* alphai, float* beta, float* q,\n                           lapack_int ldq, float* z, lapack_int ldz,\n                           lapack_int* m, float* pl, float* pr, float* dif );\nlapack_int LAPACKE_dtgsen( int matrix_order, lapack_int ijob,\n                           lapack_logical wantq, lapack_logical wantz,\n                           const lapack_logical* select, lapack_int n,\n                           double* a, lapack_int lda, double* b, lapack_int ldb,\n                           double* alphar, double* alphai, double* beta,\n                           double* q, lapack_int ldq, double* z, lapack_int ldz,\n                           lapack_int* m, double* pl, double* pr, double* dif );\nlapack_int LAPACKE_ctgsen( int matrix_order, lapack_int ijob,\n                           lapack_logical wantq, lapack_logical wantz,\n                           const lapack_logical* select, lapack_int n,\n                           lapack_complex_float* a, lapack_int lda,\n                           lapack_complex_float* b, lapack_int ldb,\n                           lapack_complex_float* alpha,\n                           lapack_complex_float* beta, lapack_complex_float* q,\n                           lapack_int ldq, lapack_complex_float* z,\n                           lapack_int ldz, lapack_int* m, float* pl, float* pr,\n                           float* dif );\nlapack_int LAPACKE_ztgsen( int matrix_order, lapack_int ijob,\n                           lapack_logical wantq, lapack_logical wantz,\n                           const lapack_logical* select, lapack_int n,\n                           lapack_complex_double* a, lapack_int lda,\n                           lapack_complex_double* b, lapack_int ldb,\n                           lapack_complex_double* alpha,\n                           lapack_complex_double* beta,\n                           lapack_complex_double* q, lapack_int ldq,\n                           lapack_complex_double* z, lapack_int ldz,\n                           lapack_int* m, double* pl, double* pr, double* dif );\n\nlapack_int LAPACKE_stgsja( int matrix_order, char jobu, char jobv, char jobq,\n                           lapack_int m, lapack_int p, lapack_int n,\n                           lapack_int k, lapack_int l, float* a, lapack_int lda,\n                           float* b, lapack_int ldb, float tola, float tolb,\n                           float* alpha, float* beta, float* u, lapack_int ldu,\n                           float* v, lapack_int ldv, float* q, lapack_int ldq,\n                           lapack_int* ncycle );\nlapack_int LAPACKE_dtgsja( int matrix_order, char jobu, char jobv, char jobq,\n                           lapack_int m, lapack_int p, lapack_int n,\n                           lapack_int k, lapack_int l, double* a,\n                           lapack_int lda, double* b, lapack_int ldb,\n                           double tola, double tolb, double* alpha,\n                           double* beta, double* u, lapack_int ldu, double* v,\n                           lapack_int ldv, double* q, lapack_int ldq,\n                           lapack_int* ncycle );\nlapack_int LAPACKE_ctgsja( int matrix_order, char jobu, char jobv, char jobq,\n                           lapack_int m, lapack_int p, lapack_int n,\n                           lapack_int k, lapack_int l, lapack_complex_float* a,\n                           lapack_int lda, lapack_complex_float* b,\n                           lapack_int ldb, float tola, float tolb, float* alpha,\n                           float* beta, lapack_complex_float* u, lapack_int ldu,\n                           lapack_complex_float* v, lapack_int ldv,\n                           lapack_complex_float* q, lapack_int ldq,\n                           lapack_int* ncycle );\nlapack_int LAPACKE_ztgsja( int matrix_order, char jobu, char jobv, char jobq,\n                           lapack_int m, lapack_int p, lapack_int n,\n                           lapack_int k, lapack_int l, lapack_complex_double* a,\n                           lapack_int lda, lapack_complex_double* b,\n                           lapack_int ldb, double tola, double tolb,\n                           double* alpha, double* beta,\n                           lapack_complex_double* u, lapack_int ldu,\n                           lapack_complex_double* v, lapack_int ldv,\n                           lapack_complex_double* q, lapack_int ldq,\n                           lapack_int* ncycle );\n\nlapack_int LAPACKE_stgsna( int matrix_order, char job, char howmny,\n                           const lapack_logical* select, lapack_int n,\n                           const float* a, lapack_int lda, const float* b,\n                           lapack_int ldb, const float* vl, lapack_int ldvl,\n                           const float* vr, lapack_int ldvr, float* s,\n                           float* dif, lapack_int mm, lapack_int* m );\nlapack_int LAPACKE_dtgsna( int matrix_order, char job, char howmny,\n                           const lapack_logical* select, lapack_int n,\n                           const double* a, lapack_int lda, const double* b,\n                           lapack_int ldb, const double* vl, lapack_int ldvl,\n                           const double* vr, lapack_int ldvr, double* s,\n                           double* dif, lapack_int mm, lapack_int* m );\nlapack_int LAPACKE_ctgsna( int matrix_order, char job, char howmny,\n                           const lapack_logical* select, lapack_int n,\n                           const lapack_complex_float* a, lapack_int lda,\n                           const lapack_complex_float* b, lapack_int ldb,\n                           const lapack_complex_float* vl, lapack_int ldvl,\n                           const lapack_complex_float* vr, lapack_int ldvr,\n                           float* s, float* dif, lapack_int mm, lapack_int* m );\nlapack_int LAPACKE_ztgsna( int matrix_order, char job, char howmny,\n                           const lapack_logical* select, lapack_int n,\n                           const lapack_complex_double* a, lapack_int lda,\n                           const lapack_complex_double* b, lapack_int ldb,\n                           const lapack_complex_double* vl, lapack_int ldvl,\n                           const lapack_complex_double* vr, lapack_int ldvr,\n                           double* s, double* dif, lapack_int mm,\n                           lapack_int* m );\n\nlapack_int LAPACKE_stgsyl( int matrix_order, char trans, lapack_int ijob,\n                           lapack_int m, lapack_int n, const float* a,\n                           lapack_int lda, const float* b, lapack_int ldb,\n                           float* c, lapack_int ldc, const float* d,\n                           lapack_int ldd, const float* e, lapack_int lde,\n                           float* f, lapack_int ldf, float* scale, float* dif );\nlapack_int LAPACKE_dtgsyl( int matrix_order, char trans, lapack_int ijob,\n                           lapack_int m, lapack_int n, const double* a,\n                           lapack_int lda, const double* b, lapack_int ldb,\n                           double* c, lapack_int ldc, const double* d,\n                           lapack_int ldd, const double* e, lapack_int lde,\n                           double* f, lapack_int ldf, double* scale,\n                           double* dif );\nlapack_int LAPACKE_ctgsyl( int matrix_order, char trans, lapack_int ijob,\n                           lapack_int m, lapack_int n,\n                           const lapack_complex_float* a, lapack_int lda,\n                           const lapack_complex_float* b, lapack_int ldb,\n                           lapack_complex_float* c, lapack_int ldc,\n                           const lapack_complex_float* d, lapack_int ldd,\n                           const lapack_complex_float* e, lapack_int lde,\n                           lapack_complex_float* f, lapack_int ldf,\n                           float* scale, float* dif );\nlapack_int LAPACKE_ztgsyl( int matrix_order, char trans, lapack_int ijob,\n                           lapack_int m, lapack_int n,\n                           const lapack_complex_double* a, lapack_int lda,\n                           const lapack_complex_double* b, lapack_int ldb,\n                           lapack_complex_double* c, lapack_int ldc,\n                           const lapack_complex_double* d, lapack_int ldd,\n                           const lapack_complex_double* e, lapack_int lde,\n                           lapack_complex_double* f, lapack_int ldf,\n                           double* scale, double* dif );\n\nlapack_int LAPACKE_stpcon( int matrix_order, char norm, char uplo, char diag,\n                           lapack_int n, const float* ap, float* rcond );\nlapack_int LAPACKE_dtpcon( int matrix_order, char norm, char uplo, char diag,\n                           lapack_int n, const double* ap, double* rcond );\nlapack_int LAPACKE_ctpcon( int matrix_order, char norm, char uplo, char diag,\n                           lapack_int n, const lapack_complex_float* ap,\n                           float* rcond );\nlapack_int LAPACKE_ztpcon( int matrix_order, char norm, char uplo, char diag,\n                           lapack_int n, const lapack_complex_double* ap,\n                           double* rcond );\n\nlapack_int LAPACKE_stprfs( int matrix_order, char uplo, char trans, char diag,\n                           lapack_int n, lapack_int nrhs, const float* ap,\n                           const float* b, lapack_int ldb, const float* x,\n                           lapack_int ldx, float* ferr, float* berr );\nlapack_int LAPACKE_dtprfs( int matrix_order, char uplo, char trans, char diag,\n                           lapack_int n, lapack_int nrhs, const double* ap,\n                           const double* b, lapack_int ldb, const double* x,\n                           lapack_int ldx, double* ferr, double* berr );\nlapack_int LAPACKE_ctprfs( int matrix_order, char uplo, char trans, char diag,\n                           lapack_int n, lapack_int nrhs,\n                           const lapack_complex_float* ap,\n                           const lapack_complex_float* b, lapack_int ldb,\n                           const lapack_complex_float* x, lapack_int ldx,\n                           float* ferr, float* berr );\nlapack_int LAPACKE_ztprfs( int matrix_order, char uplo, char trans, char diag,\n                           lapack_int n, lapack_int nrhs,\n                           const lapack_complex_double* ap,\n                           const lapack_complex_double* b, lapack_int ldb,\n                           const lapack_complex_double* x, lapack_int ldx,\n                           double* ferr, double* berr );\n\nlapack_int LAPACKE_stptri( int matrix_order, char uplo, char diag, lapack_int n,\n                           float* ap );\nlapack_int LAPACKE_dtptri( int matrix_order, char uplo, char diag, lapack_int n,\n                           double* ap );\nlapack_int LAPACKE_ctptri( int matrix_order, char uplo, char diag, lapack_int n,\n                           lapack_complex_float* ap );\nlapack_int LAPACKE_ztptri( int matrix_order, char uplo, char diag, lapack_int n,\n                           lapack_complex_double* ap );\n\nlapack_int LAPACKE_stptrs( int matrix_order, char uplo, char trans, char diag,\n                           lapack_int n, lapack_int nrhs, const float* ap,\n                           float* b, lapack_int ldb );\nlapack_int LAPACKE_dtptrs( int matrix_order, char uplo, char trans, char diag,\n                           lapack_int n, lapack_int nrhs, const double* ap,\n                           double* b, lapack_int ldb );\nlapack_int LAPACKE_ctptrs( int matrix_order, char uplo, char trans, char diag,\n                           lapack_int n, lapack_int nrhs,\n                           const lapack_complex_float* ap,\n                           lapack_complex_float* b, lapack_int ldb );\nlapack_int LAPACKE_ztptrs( int matrix_order, char uplo, char trans, char diag,\n                           lapack_int n, lapack_int nrhs,\n                           const lapack_complex_double* ap,\n                           lapack_complex_double* b, lapack_int ldb );\n\nlapack_int LAPACKE_stpttf( int matrix_order, char transr, char uplo,\n                           lapack_int n, const float* ap, float* arf );\nlapack_int LAPACKE_dtpttf( int matrix_order, char transr, char uplo,\n                           lapack_int n, const double* ap, double* arf );\nlapack_int LAPACKE_ctpttf( int matrix_order, char transr, char uplo,\n                           lapack_int n, const lapack_complex_float* ap,\n                           lapack_complex_float* arf );\nlapack_int LAPACKE_ztpttf( int matrix_order, char transr, char uplo,\n                           lapack_int n, const lapack_complex_double* ap,\n                           lapack_complex_double* arf );\n\nlapack_int LAPACKE_stpttr( int matrix_order, char uplo, lapack_int n,\n                           const float* ap, float* a, lapack_int lda );\nlapack_int LAPACKE_dtpttr( int matrix_order, char uplo, lapack_int n,\n                           const double* ap, double* a, lapack_int lda );\nlapack_int LAPACKE_ctpttr( int matrix_order, char uplo, lapack_int n,\n                           const lapack_complex_float* ap,\n                           lapack_complex_float* a, lapack_int lda );\nlapack_int LAPACKE_ztpttr( int matrix_order, char uplo, lapack_int n,\n                           const lapack_complex_double* ap,\n                           lapack_complex_double* a, lapack_int lda );\n\nlapack_int LAPACKE_strcon( int matrix_order, char norm, char uplo, char diag,\n                           lapack_int n, const float* a, lapack_int lda,\n                           float* rcond );\nlapack_int LAPACKE_dtrcon( int matrix_order, char norm, char uplo, char diag,\n                           lapack_int n, const double* a, lapack_int lda,\n                           double* rcond );\nlapack_int LAPACKE_ctrcon( int matrix_order, char norm, char uplo, char diag,\n                           lapack_int n, const lapack_complex_float* a,\n                           lapack_int lda, float* rcond );\nlapack_int LAPACKE_ztrcon( int matrix_order, char norm, char uplo, char diag,\n                           lapack_int n, const lapack_complex_double* a,\n                           lapack_int lda, double* rcond );\n\nlapack_int LAPACKE_strevc( int matrix_order, char side, char howmny,\n                           lapack_logical* select, lapack_int n, const float* t,\n                           lapack_int ldt, float* vl, lapack_int ldvl,\n                           float* vr, lapack_int ldvr, lapack_int mm,\n                           lapack_int* m );\nlapack_int LAPACKE_dtrevc( int matrix_order, char side, char howmny,\n                           lapack_logical* select, lapack_int n,\n                           const double* t, lapack_int ldt, double* vl,\n                           lapack_int ldvl, double* vr, lapack_int ldvr,\n                           lapack_int mm, lapack_int* m );\nlapack_int LAPACKE_ctrevc( int matrix_order, char side, char howmny,\n                           const lapack_logical* select, lapack_int n,\n                           lapack_complex_float* t, lapack_int ldt,\n                           lapack_complex_float* vl, lapack_int ldvl,\n                           lapack_complex_float* vr, lapack_int ldvr,\n                           lapack_int mm, lapack_int* m );\nlapack_int LAPACKE_ztrevc( int matrix_order, char side, char howmny,\n                           const lapack_logical* select, lapack_int n,\n                           lapack_complex_double* t, lapack_int ldt,\n                           lapack_complex_double* vl, lapack_int ldvl,\n                           lapack_complex_double* vr, lapack_int ldvr,\n                           lapack_int mm, lapack_int* m );\n\nlapack_int LAPACKE_strexc( int matrix_order, char compq, lapack_int n, float* t,\n                           lapack_int ldt, float* q, lapack_int ldq,\n                           lapack_int* ifst, lapack_int* ilst );\nlapack_int LAPACKE_dtrexc( int matrix_order, char compq, lapack_int n,\n                           double* t, lapack_int ldt, double* q, lapack_int ldq,\n                           lapack_int* ifst, lapack_int* ilst );\nlapack_int LAPACKE_ctrexc( int matrix_order, char compq, lapack_int n,\n                           lapack_complex_float* t, lapack_int ldt,\n                           lapack_complex_float* q, lapack_int ldq,\n                           lapack_int ifst, lapack_int ilst );\nlapack_int LAPACKE_ztrexc( int matrix_order, char compq, lapack_int n,\n                           lapack_complex_double* t, lapack_int ldt,\n                           lapack_complex_double* q, lapack_int ldq,\n                           lapack_int ifst, lapack_int ilst );\n\nlapack_int LAPACKE_strrfs( int matrix_order, char uplo, char trans, char diag,\n                           lapack_int n, lapack_int nrhs, const float* a,\n                           lapack_int lda, const float* b, lapack_int ldb,\n                           const float* x, lapack_int ldx, float* ferr,\n                           float* berr );\nlapack_int LAPACKE_dtrrfs( int matrix_order, char uplo, char trans, char diag,\n                           lapack_int n, lapack_int nrhs, const double* a,\n                           lapack_int lda, const double* b, lapack_int ldb,\n                           const double* x, lapack_int ldx, double* ferr,\n                           double* berr );\nlapack_int LAPACKE_ctrrfs( int matrix_order, char uplo, char trans, char diag,\n                           lapack_int n, lapack_int nrhs,\n                           const lapack_complex_float* a, lapack_int lda,\n                           const lapack_complex_float* b, lapack_int ldb,\n                           const lapack_complex_float* x, lapack_int ldx,\n                           float* ferr, float* berr );\nlapack_int LAPACKE_ztrrfs( int matrix_order, char uplo, char trans, char diag,\n                           lapack_int n, lapack_int nrhs,\n                           const lapack_complex_double* a, lapack_int lda,\n                           const lapack_complex_double* b, lapack_int ldb,\n                           const lapack_complex_double* x, lapack_int ldx,\n                           double* ferr, double* berr );\n\nlapack_int LAPACKE_strsen( int matrix_order, char job, char compq,\n                           const lapack_logical* select, lapack_int n, float* t,\n                           lapack_int ldt, float* q, lapack_int ldq, float* wr,\n                           float* wi, lapack_int* m, float* s, float* sep );\nlapack_int LAPACKE_dtrsen( int matrix_order, char job, char compq,\n                           const lapack_logical* select, lapack_int n,\n                           double* t, lapack_int ldt, double* q, lapack_int ldq,\n                           double* wr, double* wi, lapack_int* m, double* s,\n                           double* sep );\nlapack_int LAPACKE_ctrsen( int matrix_order, char job, char compq,\n                           const lapack_logical* select, lapack_int n,\n                           lapack_complex_float* t, lapack_int ldt,\n                           lapack_complex_float* q, lapack_int ldq,\n                           lapack_complex_float* w, lapack_int* m, float* s,\n                           float* sep );\nlapack_int LAPACKE_ztrsen( int matrix_order, char job, char compq,\n                           const lapack_logical* select, lapack_int n,\n                           lapack_complex_double* t, lapack_int ldt,\n                           lapack_complex_double* q, lapack_int ldq,\n                           lapack_complex_double* w, lapack_int* m, double* s,\n                           double* sep );\n\nlapack_int LAPACKE_strsna( int matrix_order, char job, char howmny,\n                           const lapack_logical* select, lapack_int n,\n                           const float* t, lapack_int ldt, const float* vl,\n                           lapack_int ldvl, const float* vr, lapack_int ldvr,\n                           float* s, float* sep, lapack_int mm, lapack_int* m );\nlapack_int LAPACKE_dtrsna( int matrix_order, char job, char howmny,\n                           const lapack_logical* select, lapack_int n,\n                           const double* t, lapack_int ldt, const double* vl,\n                           lapack_int ldvl, const double* vr, lapack_int ldvr,\n                           double* s, double* sep, lapack_int mm,\n                           lapack_int* m );\nlapack_int LAPACKE_ctrsna( int matrix_order, char job, char howmny,\n                           const lapack_logical* select, lapack_int n,\n                           const lapack_complex_float* t, lapack_int ldt,\n                           const lapack_complex_float* vl, lapack_int ldvl,\n                           const lapack_complex_float* vr, lapack_int ldvr,\n                           float* s, float* sep, lapack_int mm, lapack_int* m );\nlapack_int LAPACKE_ztrsna( int matrix_order, char job, char howmny,\n                           const lapack_logical* select, lapack_int n,\n                           const lapack_complex_double* t, lapack_int ldt,\n                           const lapack_complex_double* vl, lapack_int ldvl,\n                           const lapack_complex_double* vr, lapack_int ldvr,\n                           double* s, double* sep, lapack_int mm,\n                           lapack_int* m );\n\nlapack_int LAPACKE_strsyl( int matrix_order, char trana, char tranb,\n                           lapack_int isgn, lapack_int m, lapack_int n,\n                           const float* a, lapack_int lda, const float* b,\n                           lapack_int ldb, float* c, lapack_int ldc,\n                           float* scale );\nlapack_int LAPACKE_dtrsyl( int matrix_order, char trana, char tranb,\n                           lapack_int isgn, lapack_int m, lapack_int n,\n                           const double* a, lapack_int lda, const double* b,\n                           lapack_int ldb, double* c, lapack_int ldc,\n                           double* scale );\nlapack_int LAPACKE_ctrsyl( int matrix_order, char trana, char tranb,\n                           lapack_int isgn, lapack_int m, lapack_int n,\n                           const lapack_complex_float* a, lapack_int lda,\n                           const lapack_complex_float* b, lapack_int ldb,\n                           lapack_complex_float* c, lapack_int ldc,\n                           float* scale );\nlapack_int LAPACKE_ztrsyl( int matrix_order, char trana, char tranb,\n                           lapack_int isgn, lapack_int m, lapack_int n,\n                           const lapack_complex_double* a, lapack_int lda,\n                           const lapack_complex_double* b, lapack_int ldb,\n                           lapack_complex_double* c, lapack_int ldc,\n                           double* scale );\n\nlapack_int LAPACKE_strtri( int matrix_order, char uplo, char diag, lapack_int n,\n                           float* a, lapack_int lda );\nlapack_int LAPACKE_dtrtri( int matrix_order, char uplo, char diag, lapack_int n,\n                           double* a, lapack_int lda );\nlapack_int LAPACKE_ctrtri( int matrix_order, char uplo, char diag, lapack_int n,\n                           lapack_complex_float* a, lapack_int lda );\nlapack_int LAPACKE_ztrtri( int matrix_order, char uplo, char diag, lapack_int n,\n                           lapack_complex_double* a, lapack_int lda );\n\nlapack_int LAPACKE_strtrs( int matrix_order, char uplo, char trans, char diag,\n                           lapack_int n, lapack_int nrhs, const float* a,\n                           lapack_int lda, float* b, lapack_int ldb );\nlapack_int LAPACKE_dtrtrs( int matrix_order, char uplo, char trans, char diag,\n                           lapack_int n, lapack_int nrhs, const double* a,\n                           lapack_int lda, double* b, lapack_int ldb );\nlapack_int LAPACKE_ctrtrs( int matrix_order, char uplo, char trans, char diag,\n                           lapack_int n, lapack_int nrhs,\n                           const lapack_complex_float* a, lapack_int lda,\n                           lapack_complex_float* b, lapack_int ldb );\nlapack_int LAPACKE_ztrtrs( int matrix_order, char uplo, char trans, char diag,\n                           lapack_int n, lapack_int nrhs,\n                           const lapack_complex_double* a, lapack_int lda,\n                           lapack_complex_double* b, lapack_int ldb );\n\nlapack_int LAPACKE_strttf( int matrix_order, char transr, char uplo,\n                           lapack_int n, const float* a, lapack_int lda,\n                           float* arf );\nlapack_int LAPACKE_dtrttf( int matrix_order, char transr, char uplo,\n                           lapack_int n, const double* a, lapack_int lda,\n                           double* arf );\nlapack_int LAPACKE_ctrttf( int matrix_order, char transr, char uplo,\n                           lapack_int n, const lapack_complex_float* a,\n                           lapack_int lda, lapack_complex_float* arf );\nlapack_int LAPACKE_ztrttf( int matrix_order, char transr, char uplo,\n                           lapack_int n, const lapack_complex_double* a,\n                           lapack_int lda, lapack_complex_double* arf );\n\nlapack_int LAPACKE_strttp( int matrix_order, char uplo, lapack_int n,\n                           const float* a, lapack_int lda, float* ap );\nlapack_int LAPACKE_dtrttp( int matrix_order, char uplo, lapack_int n,\n                           const double* a, lapack_int lda, double* ap );\nlapack_int LAPACKE_ctrttp( int matrix_order, char uplo, lapack_int n,\n                           const lapack_complex_float* a, lapack_int lda,\n                           lapack_complex_float* ap );\nlapack_int LAPACKE_ztrttp( int matrix_order, char uplo, lapack_int n,\n                           const lapack_complex_double* a, lapack_int lda,\n                           lapack_complex_double* ap );\n\nlapack_int LAPACKE_stzrzf( int matrix_order, lapack_int m, lapack_int n,\n                           float* a, lapack_int lda, float* tau );\nlapack_int LAPACKE_dtzrzf( int matrix_order, lapack_int m, lapack_int n,\n                           double* a, lapack_int lda, double* tau );\nlapack_int LAPACKE_ctzrzf( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_complex_float* a, lapack_int lda,\n                           lapack_complex_float* tau );\nlapack_int LAPACKE_ztzrzf( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_complex_double* a, lapack_int lda,\n                           lapack_complex_double* tau );\n\nlapack_int LAPACKE_cungbr( int matrix_order, char vect, lapack_int m,\n                           lapack_int n, lapack_int k, lapack_complex_float* a,\n                           lapack_int lda, const lapack_complex_float* tau );\nlapack_int LAPACKE_zungbr( int matrix_order, char vect, lapack_int m,\n                           lapack_int n, lapack_int k, lapack_complex_double* a,\n                           lapack_int lda, const lapack_complex_double* tau );\n\nlapack_int LAPACKE_cunghr( int matrix_order, lapack_int n, lapack_int ilo,\n                           lapack_int ihi, lapack_complex_float* a,\n                           lapack_int lda, const lapack_complex_float* tau );\nlapack_int LAPACKE_zunghr( int matrix_order, lapack_int n, lapack_int ilo,\n                           lapack_int ihi, lapack_complex_double* a,\n                           lapack_int lda, const lapack_complex_double* tau );\n\nlapack_int LAPACKE_cunglq( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int k, lapack_complex_float* a,\n                           lapack_int lda, const lapack_complex_float* tau );\nlapack_int LAPACKE_zunglq( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int k, lapack_complex_double* a,\n                           lapack_int lda, const lapack_complex_double* tau );\n\nlapack_int LAPACKE_cungql( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int k, lapack_complex_float* a,\n                           lapack_int lda, const lapack_complex_float* tau );\nlapack_int LAPACKE_zungql( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int k, lapack_complex_double* a,\n                           lapack_int lda, const lapack_complex_double* tau );\n\nlapack_int LAPACKE_cungqr( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int k, lapack_complex_float* a,\n                           lapack_int lda, const lapack_complex_float* tau );\nlapack_int LAPACKE_zungqr( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int k, lapack_complex_double* a,\n                           lapack_int lda, const lapack_complex_double* tau );\n\nlapack_int LAPACKE_cungrq( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int k, lapack_complex_float* a,\n                           lapack_int lda, const lapack_complex_float* tau );\nlapack_int LAPACKE_zungrq( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int k, lapack_complex_double* a,\n                           lapack_int lda, const lapack_complex_double* tau );\n\nlapack_int LAPACKE_cungtr( int matrix_order, char uplo, lapack_int n,\n                           lapack_complex_float* a, lapack_int lda,\n                           const lapack_complex_float* tau );\nlapack_int LAPACKE_zungtr( int matrix_order, char uplo, lapack_int n,\n                           lapack_complex_double* a, lapack_int lda,\n                           const lapack_complex_double* tau );\n\nlapack_int LAPACKE_cunmbr( int matrix_order, char vect, char side, char trans,\n                           lapack_int m, lapack_int n, lapack_int k,\n                           const lapack_complex_float* a, lapack_int lda,\n                           const lapack_complex_float* tau,\n                           lapack_complex_float* c, lapack_int ldc );\nlapack_int LAPACKE_zunmbr( int matrix_order, char vect, char side, char trans,\n                           lapack_int m, lapack_int n, lapack_int k,\n                           const lapack_complex_double* a, lapack_int lda,\n                           const lapack_complex_double* tau,\n                           lapack_complex_double* c, lapack_int ldc );\n\nlapack_int LAPACKE_cunmhr( int matrix_order, char side, char trans,\n                           lapack_int m, lapack_int n, lapack_int ilo,\n                           lapack_int ihi, const lapack_complex_float* a,\n                           lapack_int lda, const lapack_complex_float* tau,\n                           lapack_complex_float* c, lapack_int ldc );\nlapack_int LAPACKE_zunmhr( int matrix_order, char side, char trans,\n                           lapack_int m, lapack_int n, lapack_int ilo,\n                           lapack_int ihi, const lapack_complex_double* a,\n                           lapack_int lda, const lapack_complex_double* tau,\n                           lapack_complex_double* c, lapack_int ldc );\n\nlapack_int LAPACKE_cunmlq( int matrix_order, char side, char trans,\n                           lapack_int m, lapack_int n, lapack_int k,\n                           const lapack_complex_float* a, lapack_int lda,\n                           const lapack_complex_float* tau,\n                           lapack_complex_float* c, lapack_int ldc );\nlapack_int LAPACKE_zunmlq( int matrix_order, char side, char trans,\n                           lapack_int m, lapack_int n, lapack_int k,\n                           const lapack_complex_double* a, lapack_int lda,\n                           const lapack_complex_double* tau,\n                           lapack_complex_double* c, lapack_int ldc );\n\nlapack_int LAPACKE_cunmql( int matrix_order, char side, char trans,\n                           lapack_int m, lapack_int n, lapack_int k,\n                           const lapack_complex_float* a, lapack_int lda,\n                           const lapack_complex_float* tau,\n                           lapack_complex_float* c, lapack_int ldc );\nlapack_int LAPACKE_zunmql( int matrix_order, char side, char trans,\n                           lapack_int m, lapack_int n, lapack_int k,\n                           const lapack_complex_double* a, lapack_int lda,\n                           const lapack_complex_double* tau,\n                           lapack_complex_double* c, lapack_int ldc );\n\nlapack_int LAPACKE_cunmqr( int matrix_order, char side, char trans,\n                           lapack_int m, lapack_int n, lapack_int k,\n                           const lapack_complex_float* a, lapack_int lda,\n                           const lapack_complex_float* tau,\n                           lapack_complex_float* c, lapack_int ldc );\nlapack_int LAPACKE_zunmqr( int matrix_order, char side, char trans,\n                           lapack_int m, lapack_int n, lapack_int k,\n                           const lapack_complex_double* a, lapack_int lda,\n                           const lapack_complex_double* tau,\n                           lapack_complex_double* c, lapack_int ldc );\n\nlapack_int LAPACKE_cunmrq( int matrix_order, char side, char trans,\n                           lapack_int m, lapack_int n, lapack_int k,\n                           const lapack_complex_float* a, lapack_int lda,\n                           const lapack_complex_float* tau,\n                           lapack_complex_float* c, lapack_int ldc );\nlapack_int LAPACKE_zunmrq( int matrix_order, char side, char trans,\n                           lapack_int m, lapack_int n, lapack_int k,\n                           const lapack_complex_double* a, lapack_int lda,\n                           const lapack_complex_double* tau,\n                           lapack_complex_double* c, lapack_int ldc );\n\nlapack_int LAPACKE_cunmrz( int matrix_order, char side, char trans,\n                           lapack_int m, lapack_int n, lapack_int k,\n                           lapack_int l, const lapack_complex_float* a,\n                           lapack_int lda, const lapack_complex_float* tau,\n                           lapack_complex_float* c, lapack_int ldc );\nlapack_int LAPACKE_zunmrz( int matrix_order, char side, char trans,\n                           lapack_int m, lapack_int n, lapack_int k,\n                           lapack_int l, const lapack_complex_double* a,\n                           lapack_int lda, const lapack_complex_double* tau,\n                           lapack_complex_double* c, lapack_int ldc );\n\nlapack_int LAPACKE_cunmtr( int matrix_order, char side, char uplo, char trans,\n                           lapack_int m, lapack_int n,\n                           const lapack_complex_float* a, lapack_int lda,\n                           const lapack_complex_float* tau,\n                           lapack_complex_float* c, lapack_int ldc );\nlapack_int LAPACKE_zunmtr( int matrix_order, char side, char uplo, char trans,\n                           lapack_int m, lapack_int n,\n                           const lapack_complex_double* a, lapack_int lda,\n                           const lapack_complex_double* tau,\n                           lapack_complex_double* c, lapack_int ldc );\n\nlapack_int LAPACKE_cupgtr( int matrix_order, char uplo, lapack_int n,\n                           const lapack_complex_float* ap,\n                           const lapack_complex_float* tau,\n                           lapack_complex_float* q, lapack_int ldq );\nlapack_int LAPACKE_zupgtr( int matrix_order, char uplo, lapack_int n,\n                           const lapack_complex_double* ap,\n                           const lapack_complex_double* tau,\n                           lapack_complex_double* q, lapack_int ldq );\n\nlapack_int LAPACKE_cupmtr( int matrix_order, char side, char uplo, char trans,\n                           lapack_int m, lapack_int n,\n                           const lapack_complex_float* ap,\n                           const lapack_complex_float* tau,\n                           lapack_complex_float* c, lapack_int ldc );\nlapack_int LAPACKE_zupmtr( int matrix_order, char side, char uplo, char trans,\n                           lapack_int m, lapack_int n,\n                           const lapack_complex_double* ap,\n                           const lapack_complex_double* tau,\n                           lapack_complex_double* c, lapack_int ldc );\n\nlapack_int LAPACKE_sbdsdc_work( int matrix_order, char uplo, char compq,\n                                lapack_int n, float* d, float* e, float* u,\n                                lapack_int ldu, float* vt, lapack_int ldvt,\n                                float* q, lapack_int* iq, float* work,\n                                lapack_int* iwork );\nlapack_int LAPACKE_dbdsdc_work( int matrix_order, char uplo, char compq,\n                                lapack_int n, double* d, double* e, double* u,\n                                lapack_int ldu, double* vt, lapack_int ldvt,\n                                double* q, lapack_int* iq, double* work,\n                                lapack_int* iwork );\n\nlapack_int LAPACKE_sbdsqr_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int ncvt, lapack_int nru, lapack_int ncc,\n                                float* d, float* e, float* vt, lapack_int ldvt,\n                                float* u, lapack_int ldu, float* c,\n                                lapack_int ldc, float* work );\nlapack_int LAPACKE_dbdsqr_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int ncvt, lapack_int nru, lapack_int ncc,\n                                double* d, double* e, double* vt,\n                                lapack_int ldvt, double* u, lapack_int ldu,\n                                double* c, lapack_int ldc, double* work );\nlapack_int LAPACKE_cbdsqr_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int ncvt, lapack_int nru, lapack_int ncc,\n                                float* d, float* e, lapack_complex_float* vt,\n                                lapack_int ldvt, lapack_complex_float* u,\n                                lapack_int ldu, lapack_complex_float* c,\n                                lapack_int ldc, float* work );\nlapack_int LAPACKE_zbdsqr_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int ncvt, lapack_int nru, lapack_int ncc,\n                                double* d, double* e, lapack_complex_double* vt,\n                                lapack_int ldvt, lapack_complex_double* u,\n                                lapack_int ldu, lapack_complex_double* c,\n                                lapack_int ldc, double* work );\n\nlapack_int LAPACKE_sdisna_work( char job, lapack_int m, lapack_int n,\n                                const float* d, float* sep );\nlapack_int LAPACKE_ddisna_work( char job, lapack_int m, lapack_int n,\n                                const double* d, double* sep );\n\nlapack_int LAPACKE_sgbbrd_work( int matrix_order, char vect, lapack_int m,\n                                lapack_int n, lapack_int ncc, lapack_int kl,\n                                lapack_int ku, float* ab, lapack_int ldab,\n                                float* d, float* e, float* q, lapack_int ldq,\n                                float* pt, lapack_int ldpt, float* c,\n                                lapack_int ldc, float* work );\nlapack_int LAPACKE_dgbbrd_work( int matrix_order, char vect, lapack_int m,\n                                lapack_int n, lapack_int ncc, lapack_int kl,\n                                lapack_int ku, double* ab, lapack_int ldab,\n                                double* d, double* e, double* q, lapack_int ldq,\n                                double* pt, lapack_int ldpt, double* c,\n                                lapack_int ldc, double* work );\nlapack_int LAPACKE_cgbbrd_work( int matrix_order, char vect, lapack_int m,\n                                lapack_int n, lapack_int ncc, lapack_int kl,\n                                lapack_int ku, lapack_complex_float* ab,\n                                lapack_int ldab, float* d, float* e,\n                                lapack_complex_float* q, lapack_int ldq,\n                                lapack_complex_float* pt, lapack_int ldpt,\n                                lapack_complex_float* c, lapack_int ldc,\n                                lapack_complex_float* work, float* rwork );\nlapack_int LAPACKE_zgbbrd_work( int matrix_order, char vect, lapack_int m,\n                                lapack_int n, lapack_int ncc, lapack_int kl,\n                                lapack_int ku, lapack_complex_double* ab,\n                                lapack_int ldab, double* d, double* e,\n                                lapack_complex_double* q, lapack_int ldq,\n                                lapack_complex_double* pt, lapack_int ldpt,\n                                lapack_complex_double* c, lapack_int ldc,\n                                lapack_complex_double* work, double* rwork );\n\nlapack_int LAPACKE_sgbcon_work( int matrix_order, char norm, lapack_int n,\n                                lapack_int kl, lapack_int ku, const float* ab,\n                                lapack_int ldab, const lapack_int* ipiv,\n                                float anorm, float* rcond, float* work,\n                                lapack_int* iwork );\nlapack_int LAPACKE_dgbcon_work( int matrix_order, char norm, lapack_int n,\n                                lapack_int kl, lapack_int ku, const double* ab,\n                                lapack_int ldab, const lapack_int* ipiv,\n                                double anorm, double* rcond, double* work,\n                                lapack_int* iwork );\nlapack_int LAPACKE_cgbcon_work( int matrix_order, char norm, lapack_int n,\n                                lapack_int kl, lapack_int ku,\n                                const lapack_complex_float* ab, lapack_int ldab,\n                                const lapack_int* ipiv, float anorm,\n                                float* rcond, lapack_complex_float* work,\n                                float* rwork );\nlapack_int LAPACKE_zgbcon_work( int matrix_order, char norm, lapack_int n,\n                                lapack_int kl, lapack_int ku,\n                                const lapack_complex_double* ab,\n                                lapack_int ldab, const lapack_int* ipiv,\n                                double anorm, double* rcond,\n                                lapack_complex_double* work, double* rwork );\n\nlapack_int LAPACKE_sgbequ_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int kl, lapack_int ku, const float* ab,\n                                lapack_int ldab, float* r, float* c,\n                                float* rowcnd, float* colcnd, float* amax );\nlapack_int LAPACKE_dgbequ_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int kl, lapack_int ku, const double* ab,\n                                lapack_int ldab, double* r, double* c,\n                                double* rowcnd, double* colcnd, double* amax );\nlapack_int LAPACKE_cgbequ_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int kl, lapack_int ku,\n                                const lapack_complex_float* ab, lapack_int ldab,\n                                float* r, float* c, float* rowcnd,\n                                float* colcnd, float* amax );\nlapack_int LAPACKE_zgbequ_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int kl, lapack_int ku,\n                                const lapack_complex_double* ab,\n                                lapack_int ldab, double* r, double* c,\n                                double* rowcnd, double* colcnd, double* amax );\n\nlapack_int LAPACKE_sgbequb_work( int matrix_order, lapack_int m, lapack_int n,\n                                 lapack_int kl, lapack_int ku, const float* ab,\n                                 lapack_int ldab, float* r, float* c,\n                                 float* rowcnd, float* colcnd, float* amax );\nlapack_int LAPACKE_dgbequb_work( int matrix_order, lapack_int m, lapack_int n,\n                                 lapack_int kl, lapack_int ku, const double* ab,\n                                 lapack_int ldab, double* r, double* c,\n                                 double* rowcnd, double* colcnd, double* amax );\nlapack_int LAPACKE_cgbequb_work( int matrix_order, lapack_int m, lapack_int n,\n                                 lapack_int kl, lapack_int ku,\n                                 const lapack_complex_float* ab,\n                                 lapack_int ldab, float* r, float* c,\n                                 float* rowcnd, float* colcnd, float* amax );\nlapack_int LAPACKE_zgbequb_work( int matrix_order, lapack_int m, lapack_int n,\n                                 lapack_int kl, lapack_int ku,\n                                 const lapack_complex_double* ab,\n                                 lapack_int ldab, double* r, double* c,\n                                 double* rowcnd, double* colcnd, double* amax );\n\nlapack_int LAPACKE_sgbrfs_work( int matrix_order, char trans, lapack_int n,\n                                lapack_int kl, lapack_int ku, lapack_int nrhs,\n                                const float* ab, lapack_int ldab,\n                                const float* afb, lapack_int ldafb,\n                                const lapack_int* ipiv, const float* b,\n                                lapack_int ldb, float* x, lapack_int ldx,\n                                float* ferr, float* berr, float* work,\n                                lapack_int* iwork );\nlapack_int LAPACKE_dgbrfs_work( int matrix_order, char trans, lapack_int n,\n                                lapack_int kl, lapack_int ku, lapack_int nrhs,\n                                const double* ab, lapack_int ldab,\n                                const double* afb, lapack_int ldafb,\n                                const lapack_int* ipiv, const double* b,\n                                lapack_int ldb, double* x, lapack_int ldx,\n                                double* ferr, double* berr, double* work,\n                                lapack_int* iwork );\nlapack_int LAPACKE_cgbrfs_work( int matrix_order, char trans, lapack_int n,\n                                lapack_int kl, lapack_int ku, lapack_int nrhs,\n                                const lapack_complex_float* ab, lapack_int ldab,\n                                const lapack_complex_float* afb,\n                                lapack_int ldafb, const lapack_int* ipiv,\n                                const lapack_complex_float* b, lapack_int ldb,\n                                lapack_complex_float* x, lapack_int ldx,\n                                float* ferr, float* berr,\n                                lapack_complex_float* work, float* rwork );\nlapack_int LAPACKE_zgbrfs_work( int matrix_order, char trans, lapack_int n,\n                                lapack_int kl, lapack_int ku, lapack_int nrhs,\n                                const lapack_complex_double* ab,\n                                lapack_int ldab,\n                                const lapack_complex_double* afb,\n                                lapack_int ldafb, const lapack_int* ipiv,\n                                const lapack_complex_double* b, lapack_int ldb,\n                                lapack_complex_double* x, lapack_int ldx,\n                                double* ferr, double* berr,\n                                lapack_complex_double* work, double* rwork );\n\nlapack_int LAPACKE_sgbrfsx_work( int matrix_order, char trans, char equed,\n                                 lapack_int n, lapack_int kl, lapack_int ku,\n                                 lapack_int nrhs, const float* ab,\n                                 lapack_int ldab, const float* afb,\n                                 lapack_int ldafb, const lapack_int* ipiv,\n                                 const float* r, const float* c, const float* b,\n                                 lapack_int ldb, float* x, lapack_int ldx,\n                                 float* rcond, float* berr,\n                                 lapack_int n_err_bnds, float* err_bnds_norm,\n                                 float* err_bnds_comp, lapack_int nparams,\n                                 float* params, float* work,\n                                 lapack_int* iwork );\nlapack_int LAPACKE_dgbrfsx_work( int matrix_order, char trans, char equed,\n                                 lapack_int n, lapack_int kl, lapack_int ku,\n                                 lapack_int nrhs, const double* ab,\n                                 lapack_int ldab, const double* afb,\n                                 lapack_int ldafb, const lapack_int* ipiv,\n                                 const double* r, const double* c,\n                                 const double* b, lapack_int ldb, double* x,\n                                 lapack_int ldx, double* rcond, double* berr,\n                                 lapack_int n_err_bnds, double* err_bnds_norm,\n                                 double* err_bnds_comp, lapack_int nparams,\n                                 double* params, double* work,\n                                 lapack_int* iwork );\nlapack_int LAPACKE_cgbrfsx_work( int matrix_order, char trans, char equed,\n                                 lapack_int n, lapack_int kl, lapack_int ku,\n                                 lapack_int nrhs,\n                                 const lapack_complex_float* ab,\n                                 lapack_int ldab,\n                                 const lapack_complex_float* afb,\n                                 lapack_int ldafb, const lapack_int* ipiv,\n                                 const float* r, const float* c,\n                                 const lapack_complex_float* b, lapack_int ldb,\n                                 lapack_complex_float* x, lapack_int ldx,\n                                 float* rcond, float* berr,\n                                 lapack_int n_err_bnds, float* err_bnds_norm,\n                                 float* err_bnds_comp, lapack_int nparams,\n                                 float* params, lapack_complex_float* work,\n                                 float* rwork );\nlapack_int LAPACKE_zgbrfsx_work( int matrix_order, char trans, char equed,\n                                 lapack_int n, lapack_int kl, lapack_int ku,\n                                 lapack_int nrhs,\n                                 const lapack_complex_double* ab,\n                                 lapack_int ldab,\n                                 const lapack_complex_double* afb,\n                                 lapack_int ldafb, const lapack_int* ipiv,\n                                 const double* r, const double* c,\n                                 const lapack_complex_double* b, lapack_int ldb,\n                                 lapack_complex_double* x, lapack_int ldx,\n                                 double* rcond, double* berr,\n                                 lapack_int n_err_bnds, double* err_bnds_norm,\n                                 double* err_bnds_comp, lapack_int nparams,\n                                 double* params, lapack_complex_double* work,\n                                 double* rwork );\n\nlapack_int LAPACKE_sgbsv_work( int matrix_order, lapack_int n, lapack_int kl,\n                               lapack_int ku, lapack_int nrhs, float* ab,\n                               lapack_int ldab, lapack_int* ipiv, float* b,\n                               lapack_int ldb );\nlapack_int LAPACKE_dgbsv_work( int matrix_order, lapack_int n, lapack_int kl,\n                               lapack_int ku, lapack_int nrhs, double* ab,\n                               lapack_int ldab, lapack_int* ipiv, double* b,\n                               lapack_int ldb );\nlapack_int LAPACKE_cgbsv_work( int matrix_order, lapack_int n, lapack_int kl,\n                               lapack_int ku, lapack_int nrhs,\n                               lapack_complex_float* ab, lapack_int ldab,\n                               lapack_int* ipiv, lapack_complex_float* b,\n                               lapack_int ldb );\nlapack_int LAPACKE_zgbsv_work( int matrix_order, lapack_int n, lapack_int kl,\n                               lapack_int ku, lapack_int nrhs,\n                               lapack_complex_double* ab, lapack_int ldab,\n                               lapack_int* ipiv, lapack_complex_double* b,\n                               lapack_int ldb );\n\nlapack_int LAPACKE_sgbsvx_work( int matrix_order, char fact, char trans,\n                                lapack_int n, lapack_int kl, lapack_int ku,\n                                lapack_int nrhs, float* ab, lapack_int ldab,\n                                float* afb, lapack_int ldafb, lapack_int* ipiv,\n                                char* equed, float* r, float* c, float* b,\n                                lapack_int ldb, float* x, lapack_int ldx,\n                                float* rcond, float* ferr, float* berr,\n                                float* work, lapack_int* iwork );\nlapack_int LAPACKE_dgbsvx_work( int matrix_order, char fact, char trans,\n                                lapack_int n, lapack_int kl, lapack_int ku,\n                                lapack_int nrhs, double* ab, lapack_int ldab,\n                                double* afb, lapack_int ldafb, lapack_int* ipiv,\n                                char* equed, double* r, double* c, double* b,\n                                lapack_int ldb, double* x, lapack_int ldx,\n                                double* rcond, double* ferr, double* berr,\n                                double* work, lapack_int* iwork );\nlapack_int LAPACKE_cgbsvx_work( int matrix_order, char fact, char trans,\n                                lapack_int n, lapack_int kl, lapack_int ku,\n                                lapack_int nrhs, lapack_complex_float* ab,\n                                lapack_int ldab, lapack_complex_float* afb,\n                                lapack_int ldafb, lapack_int* ipiv, char* equed,\n                                float* r, float* c, lapack_complex_float* b,\n                                lapack_int ldb, lapack_complex_float* x,\n                                lapack_int ldx, float* rcond, float* ferr,\n                                float* berr, lapack_complex_float* work,\n                                float* rwork );\nlapack_int LAPACKE_zgbsvx_work( int matrix_order, char fact, char trans,\n                                lapack_int n, lapack_int kl, lapack_int ku,\n                                lapack_int nrhs, lapack_complex_double* ab,\n                                lapack_int ldab, lapack_complex_double* afb,\n                                lapack_int ldafb, lapack_int* ipiv, char* equed,\n                                double* r, double* c, lapack_complex_double* b,\n                                lapack_int ldb, lapack_complex_double* x,\n                                lapack_int ldx, double* rcond, double* ferr,\n                                double* berr, lapack_complex_double* work,\n                                double* rwork );\n\nlapack_int LAPACKE_sgbsvxx_work( int matrix_order, char fact, char trans,\n                                 lapack_int n, lapack_int kl, lapack_int ku,\n                                 lapack_int nrhs, float* ab, lapack_int ldab,\n                                 float* afb, lapack_int ldafb, lapack_int* ipiv,\n                                 char* equed, float* r, float* c, float* b,\n                                 lapack_int ldb, float* x, lapack_int ldx,\n                                 float* rcond, float* rpvgrw, float* berr,\n                                 lapack_int n_err_bnds, float* err_bnds_norm,\n                                 float* err_bnds_comp, lapack_int nparams,\n                                 float* params, float* work,\n                                 lapack_int* iwork );\nlapack_int LAPACKE_dgbsvxx_work( int matrix_order, char fact, char trans,\n                                 lapack_int n, lapack_int kl, lapack_int ku,\n                                 lapack_int nrhs, double* ab, lapack_int ldab,\n                                 double* afb, lapack_int ldafb,\n                                 lapack_int* ipiv, char* equed, double* r,\n                                 double* c, double* b, lapack_int ldb,\n                                 double* x, lapack_int ldx, double* rcond,\n                                 double* rpvgrw, double* berr,\n                                 lapack_int n_err_bnds, double* err_bnds_norm,\n                                 double* err_bnds_comp, lapack_int nparams,\n                                 double* params, double* work,\n                                 lapack_int* iwork );\nlapack_int LAPACKE_cgbsvxx_work( int matrix_order, char fact, char trans,\n                                 lapack_int n, lapack_int kl, lapack_int ku,\n                                 lapack_int nrhs, lapack_complex_float* ab,\n                                 lapack_int ldab, lapack_complex_float* afb,\n                                 lapack_int ldafb, lapack_int* ipiv,\n                                 char* equed, float* r, float* c,\n                                 lapack_complex_float* b, lapack_int ldb,\n                                 lapack_complex_float* x, lapack_int ldx,\n                                 float* rcond, float* rpvgrw, float* berr,\n                                 lapack_int n_err_bnds, float* err_bnds_norm,\n                                 float* err_bnds_comp, lapack_int nparams,\n                                 float* params, lapack_complex_float* work,\n                                 float* rwork );\nlapack_int LAPACKE_zgbsvxx_work( int matrix_order, char fact, char trans,\n                                 lapack_int n, lapack_int kl, lapack_int ku,\n                                 lapack_int nrhs, lapack_complex_double* ab,\n                                 lapack_int ldab, lapack_complex_double* afb,\n                                 lapack_int ldafb, lapack_int* ipiv,\n                                 char* equed, double* r, double* c,\n                                 lapack_complex_double* b, lapack_int ldb,\n                                 lapack_complex_double* x, lapack_int ldx,\n                                 double* rcond, double* rpvgrw, double* berr,\n                                 lapack_int n_err_bnds, double* err_bnds_norm,\n                                 double* err_bnds_comp, lapack_int nparams,\n                                 double* params, lapack_complex_double* work,\n                                 double* rwork );\n\nlapack_int LAPACKE_sgbtrf_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int kl, lapack_int ku, float* ab,\n                                lapack_int ldab, lapack_int* ipiv );\nlapack_int LAPACKE_dgbtrf_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int kl, lapack_int ku, double* ab,\n                                lapack_int ldab, lapack_int* ipiv );\nlapack_int LAPACKE_cgbtrf_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int kl, lapack_int ku,\n                                lapack_complex_float* ab, lapack_int ldab,\n                                lapack_int* ipiv );\nlapack_int LAPACKE_zgbtrf_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int kl, lapack_int ku,\n                                lapack_complex_double* ab, lapack_int ldab,\n                                lapack_int* ipiv );\n\nlapack_int LAPACKE_sgbtrs_work( int matrix_order, char trans, lapack_int n,\n                                lapack_int kl, lapack_int ku, lapack_int nrhs,\n                                const float* ab, lapack_int ldab,\n                                const lapack_int* ipiv, float* b,\n                                lapack_int ldb );\nlapack_int LAPACKE_dgbtrs_work( int matrix_order, char trans, lapack_int n,\n                                lapack_int kl, lapack_int ku, lapack_int nrhs,\n                                const double* ab, lapack_int ldab,\n                                const lapack_int* ipiv, double* b,\n                                lapack_int ldb );\nlapack_int LAPACKE_cgbtrs_work( int matrix_order, char trans, lapack_int n,\n                                lapack_int kl, lapack_int ku, lapack_int nrhs,\n                                const lapack_complex_float* ab, lapack_int ldab,\n                                const lapack_int* ipiv, lapack_complex_float* b,\n                                lapack_int ldb );\nlapack_int LAPACKE_zgbtrs_work( int matrix_order, char trans, lapack_int n,\n                                lapack_int kl, lapack_int ku, lapack_int nrhs,\n                                const lapack_complex_double* ab,\n                                lapack_int ldab, const lapack_int* ipiv,\n                                lapack_complex_double* b, lapack_int ldb );\n\nlapack_int LAPACKE_sgebak_work( int matrix_order, char job, char side,\n                                lapack_int n, lapack_int ilo, lapack_int ihi,\n                                const float* scale, lapack_int m, float* v,\n                                lapack_int ldv );\nlapack_int LAPACKE_dgebak_work( int matrix_order, char job, char side,\n                                lapack_int n, lapack_int ilo, lapack_int ihi,\n                                const double* scale, lapack_int m, double* v,\n                                lapack_int ldv );\nlapack_int LAPACKE_cgebak_work( int matrix_order, char job, char side,\n                                lapack_int n, lapack_int ilo, lapack_int ihi,\n                                const float* scale, lapack_int m,\n                                lapack_complex_float* v, lapack_int ldv );\nlapack_int LAPACKE_zgebak_work( int matrix_order, char job, char side,\n                                lapack_int n, lapack_int ilo, lapack_int ihi,\n                                const double* scale, lapack_int m,\n                                lapack_complex_double* v, lapack_int ldv );\n\nlapack_int LAPACKE_sgebal_work( int matrix_order, char job, lapack_int n,\n                                float* a, lapack_int lda, lapack_int* ilo,\n                                lapack_int* ihi, float* scale );\nlapack_int LAPACKE_dgebal_work( int matrix_order, char job, lapack_int n,\n                                double* a, lapack_int lda, lapack_int* ilo,\n                                lapack_int* ihi, double* scale );\nlapack_int LAPACKE_cgebal_work( int matrix_order, char job, lapack_int n,\n                                lapack_complex_float* a, lapack_int lda,\n                                lapack_int* ilo, lapack_int* ihi,\n                                float* scale );\nlapack_int LAPACKE_zgebal_work( int matrix_order, char job, lapack_int n,\n                                lapack_complex_double* a, lapack_int lda,\n                                lapack_int* ilo, lapack_int* ihi,\n                                double* scale );\n\nlapack_int LAPACKE_sgebrd_work( int matrix_order, lapack_int m, lapack_int n,\n                                float* a, lapack_int lda, float* d, float* e,\n                                float* tauq, float* taup, float* work,\n                                lapack_int lwork );\nlapack_int LAPACKE_dgebrd_work( int matrix_order, lapack_int m, lapack_int n,\n                                double* a, lapack_int lda, double* d, double* e,\n                                double* tauq, double* taup, double* work,\n                                lapack_int lwork );\nlapack_int LAPACKE_cgebrd_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_complex_float* a, lapack_int lda,\n                                float* d, float* e, lapack_complex_float* tauq,\n                                lapack_complex_float* taup,\n                                lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_zgebrd_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_complex_double* a, lapack_int lda,\n                                double* d, double* e,\n                                lapack_complex_double* tauq,\n                                lapack_complex_double* taup,\n                                lapack_complex_double* work, lapack_int lwork );\n\nlapack_int LAPACKE_sgecon_work( int matrix_order, char norm, lapack_int n,\n                                const float* a, lapack_int lda, float anorm,\n                                float* rcond, float* work, lapack_int* iwork );\nlapack_int LAPACKE_dgecon_work( int matrix_order, char norm, lapack_int n,\n                                const double* a, lapack_int lda, double anorm,\n                                double* rcond, double* work,\n                                lapack_int* iwork );\nlapack_int LAPACKE_cgecon_work( int matrix_order, char norm, lapack_int n,\n                                const lapack_complex_float* a, lapack_int lda,\n                                float anorm, float* rcond,\n                                lapack_complex_float* work, float* rwork );\nlapack_int LAPACKE_zgecon_work( int matrix_order, char norm, lapack_int n,\n                                const lapack_complex_double* a, lapack_int lda,\n                                double anorm, double* rcond,\n                                lapack_complex_double* work, double* rwork );\n\nlapack_int LAPACKE_sgeequ_work( int matrix_order, lapack_int m, lapack_int n,\n                                const float* a, lapack_int lda, float* r,\n                                float* c, float* rowcnd, float* colcnd,\n                                float* amax );\nlapack_int LAPACKE_dgeequ_work( int matrix_order, lapack_int m, lapack_int n,\n                                const double* a, lapack_int lda, double* r,\n                                double* c, double* rowcnd, double* colcnd,\n                                double* amax );\nlapack_int LAPACKE_cgeequ_work( int matrix_order, lapack_int m, lapack_int n,\n                                const lapack_complex_float* a, lapack_int lda,\n                                float* r, float* c, float* rowcnd,\n                                float* colcnd, float* amax );\nlapack_int LAPACKE_zgeequ_work( int matrix_order, lapack_int m, lapack_int n,\n                                const lapack_complex_double* a, lapack_int lda,\n                                double* r, double* c, double* rowcnd,\n                                double* colcnd, double* amax );\n\nlapack_int LAPACKE_sgeequb_work( int matrix_order, lapack_int m, lapack_int n,\n                                 const float* a, lapack_int lda, float* r,\n                                 float* c, float* rowcnd, float* colcnd,\n                                 float* amax );\nlapack_int LAPACKE_dgeequb_work( int matrix_order, lapack_int m, lapack_int n,\n                                 const double* a, lapack_int lda, double* r,\n                                 double* c, double* rowcnd, double* colcnd,\n                                 double* amax );\nlapack_int LAPACKE_cgeequb_work( int matrix_order, lapack_int m, lapack_int n,\n                                 const lapack_complex_float* a, lapack_int lda,\n                                 float* r, float* c, float* rowcnd,\n                                 float* colcnd, float* amax );\nlapack_int LAPACKE_zgeequb_work( int matrix_order, lapack_int m, lapack_int n,\n                                 const lapack_complex_double* a, lapack_int lda,\n                                 double* r, double* c, double* rowcnd,\n                                 double* colcnd, double* amax );\n\nlapack_int LAPACKE_sgees_work( int matrix_order, char jobvs, char sort,\n                               LAPACK_S_SELECT2 select, lapack_int n, float* a,\n                               lapack_int lda, lapack_int* sdim, float* wr,\n                               float* wi, float* vs, lapack_int ldvs,\n                               float* work, lapack_int lwork,\n                               lapack_logical* bwork );\nlapack_int LAPACKE_dgees_work( int matrix_order, char jobvs, char sort,\n                               LAPACK_D_SELECT2 select, lapack_int n, double* a,\n                               lapack_int lda, lapack_int* sdim, double* wr,\n                               double* wi, double* vs, lapack_int ldvs,\n                               double* work, lapack_int lwork,\n                               lapack_logical* bwork );\nlapack_int LAPACKE_cgees_work( int matrix_order, char jobvs, char sort,\n                               LAPACK_C_SELECT1 select, lapack_int n,\n                               lapack_complex_float* a, lapack_int lda,\n                               lapack_int* sdim, lapack_complex_float* w,\n                               lapack_complex_float* vs, lapack_int ldvs,\n                               lapack_complex_float* work, lapack_int lwork,\n                               float* rwork, lapack_logical* bwork );\nlapack_int LAPACKE_zgees_work( int matrix_order, char jobvs, char sort,\n                               LAPACK_Z_SELECT1 select, lapack_int n,\n                               lapack_complex_double* a, lapack_int lda,\n                               lapack_int* sdim, lapack_complex_double* w,\n                               lapack_complex_double* vs, lapack_int ldvs,\n                               lapack_complex_double* work, lapack_int lwork,\n                               double* rwork, lapack_logical* bwork );\n\nlapack_int LAPACKE_sgeesx_work( int matrix_order, char jobvs, char sort,\n                                LAPACK_S_SELECT2 select, char sense,\n                                lapack_int n, float* a, lapack_int lda,\n                                lapack_int* sdim, float* wr, float* wi,\n                                float* vs, lapack_int ldvs, float* rconde,\n                                float* rcondv, float* work, lapack_int lwork,\n                                lapack_int* iwork, lapack_int liwork,\n                                lapack_logical* bwork );\nlapack_int LAPACKE_dgeesx_work( int matrix_order, char jobvs, char sort,\n                                LAPACK_D_SELECT2 select, char sense,\n                                lapack_int n, double* a, lapack_int lda,\n                                lapack_int* sdim, double* wr, double* wi,\n                                double* vs, lapack_int ldvs, double* rconde,\n                                double* rcondv, double* work, lapack_int lwork,\n                                lapack_int* iwork, lapack_int liwork,\n                                lapack_logical* bwork );\nlapack_int LAPACKE_cgeesx_work( int matrix_order, char jobvs, char sort,\n                                LAPACK_C_SELECT1 select, char sense,\n                                lapack_int n, lapack_complex_float* a,\n                                lapack_int lda, lapack_int* sdim,\n                                lapack_complex_float* w,\n                                lapack_complex_float* vs, lapack_int ldvs,\n                                float* rconde, float* rcondv,\n                                lapack_complex_float* work, lapack_int lwork,\n                                float* rwork, lapack_logical* bwork );\nlapack_int LAPACKE_zgeesx_work( int matrix_order, char jobvs, char sort,\n                                LAPACK_Z_SELECT1 select, char sense,\n                                lapack_int n, lapack_complex_double* a,\n                                lapack_int lda, lapack_int* sdim,\n                                lapack_complex_double* w,\n                                lapack_complex_double* vs, lapack_int ldvs,\n                                double* rconde, double* rcondv,\n                                lapack_complex_double* work, lapack_int lwork,\n                                double* rwork, lapack_logical* bwork );\n\nlapack_int LAPACKE_sgeev_work( int matrix_order, char jobvl, char jobvr,\n                               lapack_int n, float* a, lapack_int lda,\n                               float* wr, float* wi, float* vl, lapack_int ldvl,\n                               float* vr, lapack_int ldvr, float* work,\n                               lapack_int lwork );\nlapack_int LAPACKE_dgeev_work( int matrix_order, char jobvl, char jobvr,\n                               lapack_int n, double* a, lapack_int lda,\n                               double* wr, double* wi, double* vl,\n                               lapack_int ldvl, double* vr, lapack_int ldvr,\n                               double* work, lapack_int lwork );\nlapack_int LAPACKE_cgeev_work( int matrix_order, char jobvl, char jobvr,\n                               lapack_int n, lapack_complex_float* a,\n                               lapack_int lda, lapack_complex_float* w,\n                               lapack_complex_float* vl, lapack_int ldvl,\n                               lapack_complex_float* vr, lapack_int ldvr,\n                               lapack_complex_float* work, lapack_int lwork,\n                               float* rwork );\nlapack_int LAPACKE_zgeev_work( int matrix_order, char jobvl, char jobvr,\n                               lapack_int n, lapack_complex_double* a,\n                               lapack_int lda, lapack_complex_double* w,\n                               lapack_complex_double* vl, lapack_int ldvl,\n                               lapack_complex_double* vr, lapack_int ldvr,\n                               lapack_complex_double* work, lapack_int lwork,\n                               double* rwork );\n\nlapack_int LAPACKE_sgeevx_work( int matrix_order, char balanc, char jobvl,\n                                char jobvr, char sense, lapack_int n, float* a,\n                                lapack_int lda, float* wr, float* wi, float* vl,\n                                lapack_int ldvl, float* vr, lapack_int ldvr,\n                                lapack_int* ilo, lapack_int* ihi, float* scale,\n                                float* abnrm, float* rconde, float* rcondv,\n                                float* work, lapack_int lwork,\n                                lapack_int* iwork );\nlapack_int LAPACKE_dgeevx_work( int matrix_order, char balanc, char jobvl,\n                                char jobvr, char sense, lapack_int n, double* a,\n                                lapack_int lda, double* wr, double* wi,\n                                double* vl, lapack_int ldvl, double* vr,\n                                lapack_int ldvr, lapack_int* ilo,\n                                lapack_int* ihi, double* scale, double* abnrm,\n                                double* rconde, double* rcondv, double* work,\n                                lapack_int lwork, lapack_int* iwork );\nlapack_int LAPACKE_cgeevx_work( int matrix_order, char balanc, char jobvl,\n                                char jobvr, char sense, lapack_int n,\n                                lapack_complex_float* a, lapack_int lda,\n                                lapack_complex_float* w,\n                                lapack_complex_float* vl, lapack_int ldvl,\n                                lapack_complex_float* vr, lapack_int ldvr,\n                                lapack_int* ilo, lapack_int* ihi, float* scale,\n                                float* abnrm, float* rconde, float* rcondv,\n                                lapack_complex_float* work, lapack_int lwork,\n                                float* rwork );\nlapack_int LAPACKE_zgeevx_work( int matrix_order, char balanc, char jobvl,\n                                char jobvr, char sense, lapack_int n,\n                                lapack_complex_double* a, lapack_int lda,\n                                lapack_complex_double* w,\n                                lapack_complex_double* vl, lapack_int ldvl,\n                                lapack_complex_double* vr, lapack_int ldvr,\n                                lapack_int* ilo, lapack_int* ihi, double* scale,\n                                double* abnrm, double* rconde, double* rcondv,\n                                lapack_complex_double* work, lapack_int lwork,\n                                double* rwork );\n\nlapack_int LAPACKE_sgehrd_work( int matrix_order, lapack_int n, lapack_int ilo,\n                                lapack_int ihi, float* a, lapack_int lda,\n                                float* tau, float* work, lapack_int lwork );\nlapack_int LAPACKE_dgehrd_work( int matrix_order, lapack_int n, lapack_int ilo,\n                                lapack_int ihi, double* a, lapack_int lda,\n                                double* tau, double* work, lapack_int lwork );\nlapack_int LAPACKE_cgehrd_work( int matrix_order, lapack_int n, lapack_int ilo,\n                                lapack_int ihi, lapack_complex_float* a,\n                                lapack_int lda, lapack_complex_float* tau,\n                                lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_zgehrd_work( int matrix_order, lapack_int n, lapack_int ilo,\n                                lapack_int ihi, lapack_complex_double* a,\n                                lapack_int lda, lapack_complex_double* tau,\n                                lapack_complex_double* work, lapack_int lwork );\n\nlapack_int LAPACKE_sgejsv_work( int matrix_order, char joba, char jobu,\n                                char jobv, char jobr, char jobt, char jobp,\n                                lapack_int m, lapack_int n, float* a,\n                                lapack_int lda, float* sva, float* u,\n                                lapack_int ldu, float* v, lapack_int ldv,\n                                float* work, lapack_int lwork,\n                                lapack_int* iwork );\nlapack_int LAPACKE_dgejsv_work( int matrix_order, char joba, char jobu,\n                                char jobv, char jobr, char jobt, char jobp,\n                                lapack_int m, lapack_int n, double* a,\n                                lapack_int lda, double* sva, double* u,\n                                lapack_int ldu, double* v, lapack_int ldv,\n                                double* work, lapack_int lwork,\n                                lapack_int* iwork );\n\nlapack_int LAPACKE_sgelq2_work( int matrix_order, lapack_int m, lapack_int n,\n                                float* a, lapack_int lda, float* tau,\n                                float* work );\nlapack_int LAPACKE_dgelq2_work( int matrix_order, lapack_int m, lapack_int n,\n                                double* a, lapack_int lda, double* tau,\n                                double* work );\nlapack_int LAPACKE_cgelq2_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_complex_float* a, lapack_int lda,\n                                lapack_complex_float* tau,\n                                lapack_complex_float* work );\nlapack_int LAPACKE_zgelq2_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_complex_double* a, lapack_int lda,\n                                lapack_complex_double* tau,\n                                lapack_complex_double* work );\n\nlapack_int LAPACKE_sgelqf_work( int matrix_order, lapack_int m, lapack_int n,\n                                float* a, lapack_int lda, float* tau,\n                                float* work, lapack_int lwork );\nlapack_int LAPACKE_dgelqf_work( int matrix_order, lapack_int m, lapack_int n,\n                                double* a, lapack_int lda, double* tau,\n                                double* work, lapack_int lwork );\nlapack_int LAPACKE_cgelqf_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_complex_float* a, lapack_int lda,\n                                lapack_complex_float* tau,\n                                lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_zgelqf_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_complex_double* a, lapack_int lda,\n                                lapack_complex_double* tau,\n                                lapack_complex_double* work, lapack_int lwork );\n\nlapack_int LAPACKE_sgels_work( int matrix_order, char trans, lapack_int m,\n                               lapack_int n, lapack_int nrhs, float* a,\n                               lapack_int lda, float* b, lapack_int ldb,\n                               float* work, lapack_int lwork );\nlapack_int LAPACKE_dgels_work( int matrix_order, char trans, lapack_int m,\n                               lapack_int n, lapack_int nrhs, double* a,\n                               lapack_int lda, double* b, lapack_int ldb,\n                               double* work, lapack_int lwork );\nlapack_int LAPACKE_cgels_work( int matrix_order, char trans, lapack_int m,\n                               lapack_int n, lapack_int nrhs,\n                               lapack_complex_float* a, lapack_int lda,\n                               lapack_complex_float* b, lapack_int ldb,\n                               lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_zgels_work( int matrix_order, char trans, lapack_int m,\n                               lapack_int n, lapack_int nrhs,\n                               lapack_complex_double* a, lapack_int lda,\n                               lapack_complex_double* b, lapack_int ldb,\n                               lapack_complex_double* work, lapack_int lwork );\n\nlapack_int LAPACKE_sgelsd_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int nrhs, float* a, lapack_int lda,\n                                float* b, lapack_int ldb, float* s, float rcond,\n                                lapack_int* rank, float* work, lapack_int lwork,\n                                lapack_int* iwork );\nlapack_int LAPACKE_dgelsd_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int nrhs, double* a, lapack_int lda,\n                                double* b, lapack_int ldb, double* s,\n                                double rcond, lapack_int* rank, double* work,\n                                lapack_int lwork, lapack_int* iwork );\nlapack_int LAPACKE_cgelsd_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int nrhs, lapack_complex_float* a,\n                                lapack_int lda, lapack_complex_float* b,\n                                lapack_int ldb, float* s, float rcond,\n                                lapack_int* rank, lapack_complex_float* work,\n                                lapack_int lwork, float* rwork,\n                                lapack_int* iwork );\nlapack_int LAPACKE_zgelsd_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int nrhs, lapack_complex_double* a,\n                                lapack_int lda, lapack_complex_double* b,\n                                lapack_int ldb, double* s, double rcond,\n                                lapack_int* rank, lapack_complex_double* work,\n                                lapack_int lwork, double* rwork,\n                                lapack_int* iwork );\n\nlapack_int LAPACKE_sgelss_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int nrhs, float* a, lapack_int lda,\n                                float* b, lapack_int ldb, float* s, float rcond,\n                                lapack_int* rank, float* work,\n                                lapack_int lwork );\nlapack_int LAPACKE_dgelss_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int nrhs, double* a, lapack_int lda,\n                                double* b, lapack_int ldb, double* s,\n                                double rcond, lapack_int* rank, double* work,\n                                lapack_int lwork );\nlapack_int LAPACKE_cgelss_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int nrhs, lapack_complex_float* a,\n                                lapack_int lda, lapack_complex_float* b,\n                                lapack_int ldb, float* s, float rcond,\n                                lapack_int* rank, lapack_complex_float* work,\n                                lapack_int lwork, float* rwork );\nlapack_int LAPACKE_zgelss_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int nrhs, lapack_complex_double* a,\n                                lapack_int lda, lapack_complex_double* b,\n                                lapack_int ldb, double* s, double rcond,\n                                lapack_int* rank, lapack_complex_double* work,\n                                lapack_int lwork, double* rwork );\n\nlapack_int LAPACKE_sgelsy_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int nrhs, float* a, lapack_int lda,\n                                float* b, lapack_int ldb, lapack_int* jpvt,\n                                float rcond, lapack_int* rank, float* work,\n                                lapack_int lwork );\nlapack_int LAPACKE_dgelsy_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int nrhs, double* a, lapack_int lda,\n                                double* b, lapack_int ldb, lapack_int* jpvt,\n                                double rcond, lapack_int* rank, double* work,\n                                lapack_int lwork );\nlapack_int LAPACKE_cgelsy_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int nrhs, lapack_complex_float* a,\n                                lapack_int lda, lapack_complex_float* b,\n                                lapack_int ldb, lapack_int* jpvt, float rcond,\n                                lapack_int* rank, lapack_complex_float* work,\n                                lapack_int lwork, float* rwork );\nlapack_int LAPACKE_zgelsy_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int nrhs, lapack_complex_double* a,\n                                lapack_int lda, lapack_complex_double* b,\n                                lapack_int ldb, lapack_int* jpvt, double rcond,\n                                lapack_int* rank, lapack_complex_double* work,\n                                lapack_int lwork, double* rwork );\n\nlapack_int LAPACKE_sgeqlf_work( int matrix_order, lapack_int m, lapack_int n,\n                                float* a, lapack_int lda, float* tau,\n                                float* work, lapack_int lwork );\nlapack_int LAPACKE_dgeqlf_work( int matrix_order, lapack_int m, lapack_int n,\n                                double* a, lapack_int lda, double* tau,\n                                double* work, lapack_int lwork );\nlapack_int LAPACKE_cgeqlf_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_complex_float* a, lapack_int lda,\n                                lapack_complex_float* tau,\n                                lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_zgeqlf_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_complex_double* a, lapack_int lda,\n                                lapack_complex_double* tau,\n                                lapack_complex_double* work, lapack_int lwork );\n\nlapack_int LAPACKE_sgeqp3_work( int matrix_order, lapack_int m, lapack_int n,\n                                float* a, lapack_int lda, lapack_int* jpvt,\n                                float* tau, float* work, lapack_int lwork );\nlapack_int LAPACKE_dgeqp3_work( int matrix_order, lapack_int m, lapack_int n,\n                                double* a, lapack_int lda, lapack_int* jpvt,\n                                double* tau, double* work, lapack_int lwork );\nlapack_int LAPACKE_cgeqp3_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_complex_float* a, lapack_int lda,\n                                lapack_int* jpvt, lapack_complex_float* tau,\n                                lapack_complex_float* work, lapack_int lwork,\n                                float* rwork );\nlapack_int LAPACKE_zgeqp3_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_complex_double* a, lapack_int lda,\n                                lapack_int* jpvt, lapack_complex_double* tau,\n                                lapack_complex_double* work, lapack_int lwork,\n                                double* rwork );\n\nlapack_int LAPACKE_sgeqpf_work( int matrix_order, lapack_int m, lapack_int n,\n                                float* a, lapack_int lda, lapack_int* jpvt,\n                                float* tau, float* work );\nlapack_int LAPACKE_dgeqpf_work( int matrix_order, lapack_int m, lapack_int n,\n                                double* a, lapack_int lda, lapack_int* jpvt,\n                                double* tau, double* work );\nlapack_int LAPACKE_cgeqpf_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_complex_float* a, lapack_int lda,\n                                lapack_int* jpvt, lapack_complex_float* tau,\n                                lapack_complex_float* work, float* rwork );\nlapack_int LAPACKE_zgeqpf_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_complex_double* a, lapack_int lda,\n                                lapack_int* jpvt, lapack_complex_double* tau,\n                                lapack_complex_double* work, double* rwork );\n\nlapack_int LAPACKE_sgeqr2_work( int matrix_order, lapack_int m, lapack_int n,\n                                float* a, lapack_int lda, float* tau,\n                                float* work );\nlapack_int LAPACKE_dgeqr2_work( int matrix_order, lapack_int m, lapack_int n,\n                                double* a, lapack_int lda, double* tau,\n                                double* work );\nlapack_int LAPACKE_cgeqr2_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_complex_float* a, lapack_int lda,\n                                lapack_complex_float* tau,\n                                lapack_complex_float* work );\nlapack_int LAPACKE_zgeqr2_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_complex_double* a, lapack_int lda,\n                                lapack_complex_double* tau,\n                                lapack_complex_double* work );\n\nlapack_int LAPACKE_sgeqrf_work( int matrix_order, lapack_int m, lapack_int n,\n                                float* a, lapack_int lda, float* tau,\n                                float* work, lapack_int lwork );\nlapack_int LAPACKE_dgeqrf_work( int matrix_order, lapack_int m, lapack_int n,\n                                double* a, lapack_int lda, double* tau,\n                                double* work, lapack_int lwork );\nlapack_int LAPACKE_cgeqrf_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_complex_float* a, lapack_int lda,\n                                lapack_complex_float* tau,\n                                lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_zgeqrf_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_complex_double* a, lapack_int lda,\n                                lapack_complex_double* tau,\n                                lapack_complex_double* work, lapack_int lwork );\n\nlapack_int LAPACKE_sgeqrfp_work( int matrix_order, lapack_int m, lapack_int n,\n                                 float* a, lapack_int lda, float* tau,\n                                 float* work, lapack_int lwork );\nlapack_int LAPACKE_dgeqrfp_work( int matrix_order, lapack_int m, lapack_int n,\n                                 double* a, lapack_int lda, double* tau,\n                                 double* work, lapack_int lwork );\nlapack_int LAPACKE_cgeqrfp_work( int matrix_order, lapack_int m, lapack_int n,\n                                 lapack_complex_float* a, lapack_int lda,\n                                 lapack_complex_float* tau,\n                                 lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_zgeqrfp_work( int matrix_order, lapack_int m, lapack_int n,\n                                 lapack_complex_double* a, lapack_int lda,\n                                 lapack_complex_double* tau,\n                                 lapack_complex_double* work,\n                                 lapack_int lwork );\n\nlapack_int LAPACKE_sgerfs_work( int matrix_order, char trans, lapack_int n,\n                                lapack_int nrhs, const float* a, lapack_int lda,\n                                const float* af, lapack_int ldaf,\n                                const lapack_int* ipiv, const float* b,\n                                lapack_int ldb, float* x, lapack_int ldx,\n                                float* ferr, float* berr, float* work,\n                                lapack_int* iwork );\nlapack_int LAPACKE_dgerfs_work( int matrix_order, char trans, lapack_int n,\n                                lapack_int nrhs, const double* a,\n                                lapack_int lda, const double* af,\n                                lapack_int ldaf, const lapack_int* ipiv,\n                                const double* b, lapack_int ldb, double* x,\n                                lapack_int ldx, double* ferr, double* berr,\n                                double* work, lapack_int* iwork );\nlapack_int LAPACKE_cgerfs_work( int matrix_order, char trans, lapack_int n,\n                                lapack_int nrhs, const lapack_complex_float* a,\n                                lapack_int lda, const lapack_complex_float* af,\n                                lapack_int ldaf, const lapack_int* ipiv,\n                                const lapack_complex_float* b, lapack_int ldb,\n                                lapack_complex_float* x, lapack_int ldx,\n                                float* ferr, float* berr,\n                                lapack_complex_float* work, float* rwork );\nlapack_int LAPACKE_zgerfs_work( int matrix_order, char trans, lapack_int n,\n                                lapack_int nrhs, const lapack_complex_double* a,\n                                lapack_int lda, const lapack_complex_double* af,\n                                lapack_int ldaf, const lapack_int* ipiv,\n                                const lapack_complex_double* b, lapack_int ldb,\n                                lapack_complex_double* x, lapack_int ldx,\n                                double* ferr, double* berr,\n                                lapack_complex_double* work, double* rwork );\n\nlapack_int LAPACKE_sgerfsx_work( int matrix_order, char trans, char equed,\n                                 lapack_int n, lapack_int nrhs, const float* a,\n                                 lapack_int lda, const float* af,\n                                 lapack_int ldaf, const lapack_int* ipiv,\n                                 const float* r, const float* c, const float* b,\n                                 lapack_int ldb, float* x, lapack_int ldx,\n                                 float* rcond, float* berr,\n                                 lapack_int n_err_bnds, float* err_bnds_norm,\n                                 float* err_bnds_comp, lapack_int nparams,\n                                 float* params, float* work,\n                                 lapack_int* iwork );\nlapack_int LAPACKE_dgerfsx_work( int matrix_order, char trans, char equed,\n                                 lapack_int n, lapack_int nrhs, const double* a,\n                                 lapack_int lda, const double* af,\n                                 lapack_int ldaf, const lapack_int* ipiv,\n                                 const double* r, const double* c,\n                                 const double* b, lapack_int ldb, double* x,\n                                 lapack_int ldx, double* rcond, double* berr,\n                                 lapack_int n_err_bnds, double* err_bnds_norm,\n                                 double* err_bnds_comp, lapack_int nparams,\n                                 double* params, double* work,\n                                 lapack_int* iwork );\nlapack_int LAPACKE_cgerfsx_work( int matrix_order, char trans, char equed,\n                                 lapack_int n, lapack_int nrhs,\n                                 const lapack_complex_float* a, lapack_int lda,\n                                 const lapack_complex_float* af,\n                                 lapack_int ldaf, const lapack_int* ipiv,\n                                 const float* r, const float* c,\n                                 const lapack_complex_float* b, lapack_int ldb,\n                                 lapack_complex_float* x, lapack_int ldx,\n                                 float* rcond, float* berr,\n                                 lapack_int n_err_bnds, float* err_bnds_norm,\n                                 float* err_bnds_comp, lapack_int nparams,\n                                 float* params, lapack_complex_float* work,\n                                 float* rwork );\nlapack_int LAPACKE_zgerfsx_work( int matrix_order, char trans, char equed,\n                                 lapack_int n, lapack_int nrhs,\n                                 const lapack_complex_double* a, lapack_int lda,\n                                 const lapack_complex_double* af,\n                                 lapack_int ldaf, const lapack_int* ipiv,\n                                 const double* r, const double* c,\n                                 const lapack_complex_double* b, lapack_int ldb,\n                                 lapack_complex_double* x, lapack_int ldx,\n                                 double* rcond, double* berr,\n                                 lapack_int n_err_bnds, double* err_bnds_norm,\n                                 double* err_bnds_comp, lapack_int nparams,\n                                 double* params, lapack_complex_double* work,\n                                 double* rwork );\n\nlapack_int LAPACKE_sgerqf_work( int matrix_order, lapack_int m, lapack_int n,\n                                float* a, lapack_int lda, float* tau,\n                                float* work, lapack_int lwork );\nlapack_int LAPACKE_dgerqf_work( int matrix_order, lapack_int m, lapack_int n,\n                                double* a, lapack_int lda, double* tau,\n                                double* work, lapack_int lwork );\nlapack_int LAPACKE_cgerqf_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_complex_float* a, lapack_int lda,\n                                lapack_complex_float* tau,\n                                lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_zgerqf_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_complex_double* a, lapack_int lda,\n                                lapack_complex_double* tau,\n                                lapack_complex_double* work, lapack_int lwork );\n\nlapack_int LAPACKE_sgesdd_work( int matrix_order, char jobz, lapack_int m,\n                                lapack_int n, float* a, lapack_int lda,\n                                float* s, float* u, lapack_int ldu, float* vt,\n                                lapack_int ldvt, float* work, lapack_int lwork,\n                                lapack_int* iwork );\nlapack_int LAPACKE_dgesdd_work( int matrix_order, char jobz, lapack_int m,\n                                lapack_int n, double* a, lapack_int lda,\n                                double* s, double* u, lapack_int ldu,\n                                double* vt, lapack_int ldvt, double* work,\n                                lapack_int lwork, lapack_int* iwork );\nlapack_int LAPACKE_cgesdd_work( int matrix_order, char jobz, lapack_int m,\n                                lapack_int n, lapack_complex_float* a,\n                                lapack_int lda, float* s,\n                                lapack_complex_float* u, lapack_int ldu,\n                                lapack_complex_float* vt, lapack_int ldvt,\n                                lapack_complex_float* work, lapack_int lwork,\n                                float* rwork, lapack_int* iwork );\nlapack_int LAPACKE_zgesdd_work( int matrix_order, char jobz, lapack_int m,\n                                lapack_int n, lapack_complex_double* a,\n                                lapack_int lda, double* s,\n                                lapack_complex_double* u, lapack_int ldu,\n                                lapack_complex_double* vt, lapack_int ldvt,\n                                lapack_complex_double* work, lapack_int lwork,\n                                double* rwork, lapack_int* iwork );\n\nlapack_int LAPACKE_sgesv_work( int matrix_order, lapack_int n, lapack_int nrhs,\n                               float* a, lapack_int lda, lapack_int* ipiv,\n                               float* b, lapack_int ldb );\nlapack_int LAPACKE_dgesv_work( int matrix_order, lapack_int n, lapack_int nrhs,\n                               double* a, lapack_int lda, lapack_int* ipiv,\n                               double* b, lapack_int ldb );\nlapack_int LAPACKE_cgesv_work( int matrix_order, lapack_int n, lapack_int nrhs,\n                               lapack_complex_float* a, lapack_int lda,\n                               lapack_int* ipiv, lapack_complex_float* b,\n                               lapack_int ldb );\nlapack_int LAPACKE_zgesv_work( int matrix_order, lapack_int n, lapack_int nrhs,\n                               lapack_complex_double* a, lapack_int lda,\n                               lapack_int* ipiv, lapack_complex_double* b,\n                               lapack_int ldb );\nlapack_int LAPACKE_dsgesv_work( int matrix_order, lapack_int n, lapack_int nrhs,\n                                double* a, lapack_int lda, lapack_int* ipiv,\n                                double* b, lapack_int ldb, double* x,\n                                lapack_int ldx, double* work, float* swork,\n                                lapack_int* iter );\nlapack_int LAPACKE_zcgesv_work( int matrix_order, lapack_int n, lapack_int nrhs,\n                                lapack_complex_double* a, lapack_int lda,\n                                lapack_int* ipiv, lapack_complex_double* b,\n                                lapack_int ldb, lapack_complex_double* x,\n                                lapack_int ldx, lapack_complex_double* work,\n                                lapack_complex_float* swork, double* rwork,\n                                lapack_int* iter );\n\nlapack_int LAPACKE_sgesvd_work( int matrix_order, char jobu, char jobvt,\n                                lapack_int m, lapack_int n, float* a,\n                                lapack_int lda, float* s, float* u,\n                                lapack_int ldu, float* vt, lapack_int ldvt,\n                                float* work, lapack_int lwork );\nlapack_int LAPACKE_dgesvd_work( int matrix_order, char jobu, char jobvt,\n                                lapack_int m, lapack_int n, double* a,\n                                lapack_int lda, double* s, double* u,\n                                lapack_int ldu, double* vt, lapack_int ldvt,\n                                double* work, lapack_int lwork );\nlapack_int LAPACKE_cgesvd_work( int matrix_order, char jobu, char jobvt,\n                                lapack_int m, lapack_int n,\n                                lapack_complex_float* a, lapack_int lda,\n                                float* s, lapack_complex_float* u,\n                                lapack_int ldu, lapack_complex_float* vt,\n                                lapack_int ldvt, lapack_complex_float* work,\n                                lapack_int lwork, float* rwork );\nlapack_int LAPACKE_zgesvd_work( int matrix_order, char jobu, char jobvt,\n                                lapack_int m, lapack_int n,\n                                lapack_complex_double* a, lapack_int lda,\n                                double* s, lapack_complex_double* u,\n                                lapack_int ldu, lapack_complex_double* vt,\n                                lapack_int ldvt, lapack_complex_double* work,\n                                lapack_int lwork, double* rwork );\n\nlapack_int LAPACKE_sgesvj_work( int matrix_order, char joba, char jobu,\n                                char jobv, lapack_int m, lapack_int n, float* a,\n                                lapack_int lda, float* sva, lapack_int mv,\n                                float* v, lapack_int ldv, float* work,\n                                lapack_int lwork );\nlapack_int LAPACKE_dgesvj_work( int matrix_order, char joba, char jobu,\n                                char jobv, lapack_int m, lapack_int n,\n                                double* a, lapack_int lda, double* sva,\n                                lapack_int mv, double* v, lapack_int ldv,\n                                double* work, lapack_int lwork );\n\nlapack_int LAPACKE_sgesvx_work( int matrix_order, char fact, char trans,\n                                lapack_int n, lapack_int nrhs, float* a,\n                                lapack_int lda, float* af, lapack_int ldaf,\n                                lapack_int* ipiv, char* equed, float* r,\n                                float* c, float* b, lapack_int ldb, float* x,\n                                lapack_int ldx, float* rcond, float* ferr,\n                                float* berr, float* work, lapack_int* iwork );\nlapack_int LAPACKE_dgesvx_work( int matrix_order, char fact, char trans,\n                                lapack_int n, lapack_int nrhs, double* a,\n                                lapack_int lda, double* af, lapack_int ldaf,\n                                lapack_int* ipiv, char* equed, double* r,\n                                double* c, double* b, lapack_int ldb, double* x,\n                                lapack_int ldx, double* rcond, double* ferr,\n                                double* berr, double* work, lapack_int* iwork );\nlapack_int LAPACKE_cgesvx_work( int matrix_order, char fact, char trans,\n                                lapack_int n, lapack_int nrhs,\n                                lapack_complex_float* a, lapack_int lda,\n                                lapack_complex_float* af, lapack_int ldaf,\n                                lapack_int* ipiv, char* equed, float* r,\n                                float* c, lapack_complex_float* b,\n                                lapack_int ldb, lapack_complex_float* x,\n                                lapack_int ldx, float* rcond, float* ferr,\n                                float* berr, lapack_complex_float* work,\n                                float* rwork );\nlapack_int LAPACKE_zgesvx_work( int matrix_order, char fact, char trans,\n                                lapack_int n, lapack_int nrhs,\n                                lapack_complex_double* a, lapack_int lda,\n                                lapack_complex_double* af, lapack_int ldaf,\n                                lapack_int* ipiv, char* equed, double* r,\n                                double* c, lapack_complex_double* b,\n                                lapack_int ldb, lapack_complex_double* x,\n                                lapack_int ldx, double* rcond, double* ferr,\n                                double* berr, lapack_complex_double* work,\n                                double* rwork );\n\nlapack_int LAPACKE_sgesvxx_work( int matrix_order, char fact, char trans,\n                                 lapack_int n, lapack_int nrhs, float* a,\n                                 lapack_int lda, float* af, lapack_int ldaf,\n                                 lapack_int* ipiv, char* equed, float* r,\n                                 float* c, float* b, lapack_int ldb, float* x,\n                                 lapack_int ldx, float* rcond, float* rpvgrw,\n                                 float* berr, lapack_int n_err_bnds,\n                                 float* err_bnds_norm, float* err_bnds_comp,\n                                 lapack_int nparams, float* params, float* work,\n                                 lapack_int* iwork );\nlapack_int LAPACKE_dgesvxx_work( int matrix_order, char fact, char trans,\n                                 lapack_int n, lapack_int nrhs, double* a,\n                                 lapack_int lda, double* af, lapack_int ldaf,\n                                 lapack_int* ipiv, char* equed, double* r,\n                                 double* c, double* b, lapack_int ldb,\n                                 double* x, lapack_int ldx, double* rcond,\n                                 double* rpvgrw, double* berr,\n                                 lapack_int n_err_bnds, double* err_bnds_norm,\n                                 double* err_bnds_comp, lapack_int nparams,\n                                 double* params, double* work,\n                                 lapack_int* iwork );\nlapack_int LAPACKE_cgesvxx_work( int matrix_order, char fact, char trans,\n                                 lapack_int n, lapack_int nrhs,\n                                 lapack_complex_float* a, lapack_int lda,\n                                 lapack_complex_float* af, lapack_int ldaf,\n                                 lapack_int* ipiv, char* equed, float* r,\n                                 float* c, lapack_complex_float* b,\n                                 lapack_int ldb, lapack_complex_float* x,\n                                 lapack_int ldx, float* rcond, float* rpvgrw,\n                                 float* berr, lapack_int n_err_bnds,\n                                 float* err_bnds_norm, float* err_bnds_comp,\n                                 lapack_int nparams, float* params,\n                                 lapack_complex_float* work, float* rwork );\nlapack_int LAPACKE_zgesvxx_work( int matrix_order, char fact, char trans,\n                                 lapack_int n, lapack_int nrhs,\n                                 lapack_complex_double* a, lapack_int lda,\n                                 lapack_complex_double* af, lapack_int ldaf,\n                                 lapack_int* ipiv, char* equed, double* r,\n                                 double* c, lapack_complex_double* b,\n                                 lapack_int ldb, lapack_complex_double* x,\n                                 lapack_int ldx, double* rcond, double* rpvgrw,\n                                 double* berr, lapack_int n_err_bnds,\n                                 double* err_bnds_norm, double* err_bnds_comp,\n                                 lapack_int nparams, double* params,\n                                 lapack_complex_double* work, double* rwork );\n\nlapack_int LAPACKE_sgetf2_work( int matrix_order, lapack_int m, lapack_int n,\n                                float* a, lapack_int lda, lapack_int* ipiv );\nlapack_int LAPACKE_dgetf2_work( int matrix_order, lapack_int m, lapack_int n,\n                                double* a, lapack_int lda, lapack_int* ipiv );\nlapack_int LAPACKE_cgetf2_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_complex_float* a, lapack_int lda,\n                                lapack_int* ipiv );\nlapack_int LAPACKE_zgetf2_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_complex_double* a, lapack_int lda,\n                                lapack_int* ipiv );\n\nlapack_int LAPACKE_sgetrf_work( int matrix_order, lapack_int m, lapack_int n,\n                                float* a, lapack_int lda, lapack_int* ipiv );\nlapack_int LAPACKE_dgetrf_work( int matrix_order, lapack_int m, lapack_int n,\n                                double* a, lapack_int lda, lapack_int* ipiv );\nlapack_int LAPACKE_cgetrf_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_complex_float* a, lapack_int lda,\n                                lapack_int* ipiv );\nlapack_int LAPACKE_zgetrf_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_complex_double* a, lapack_int lda,\n                                lapack_int* ipiv );\n\nlapack_int LAPACKE_sgetri_work( int matrix_order, lapack_int n, float* a,\n                                lapack_int lda, const lapack_int* ipiv,\n                                float* work, lapack_int lwork );\nlapack_int LAPACKE_dgetri_work( int matrix_order, lapack_int n, double* a,\n                                lapack_int lda, const lapack_int* ipiv,\n                                double* work, lapack_int lwork );\nlapack_int LAPACKE_cgetri_work( int matrix_order, lapack_int n,\n                                lapack_complex_float* a, lapack_int lda,\n                                const lapack_int* ipiv,\n                                lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_zgetri_work( int matrix_order, lapack_int n,\n                                lapack_complex_double* a, lapack_int lda,\n                                const lapack_int* ipiv,\n                                lapack_complex_double* work, lapack_int lwork );\n\nlapack_int LAPACKE_sgetrs_work( int matrix_order, char trans, lapack_int n,\n                                lapack_int nrhs, const float* a, lapack_int lda,\n                                const lapack_int* ipiv, float* b,\n                                lapack_int ldb );\nlapack_int LAPACKE_dgetrs_work( int matrix_order, char trans, lapack_int n,\n                                lapack_int nrhs, const double* a,\n                                lapack_int lda, const lapack_int* ipiv,\n                                double* b, lapack_int ldb );\nlapack_int LAPACKE_cgetrs_work( int matrix_order, char trans, lapack_int n,\n                                lapack_int nrhs, const lapack_complex_float* a,\n                                lapack_int lda, const lapack_int* ipiv,\n                                lapack_complex_float* b, lapack_int ldb );\nlapack_int LAPACKE_zgetrs_work( int matrix_order, char trans, lapack_int n,\n                                lapack_int nrhs, const lapack_complex_double* a,\n                                lapack_int lda, const lapack_int* ipiv,\n                                lapack_complex_double* b, lapack_int ldb );\n\nlapack_int LAPACKE_sggbak_work( int matrix_order, char job, char side,\n                                lapack_int n, lapack_int ilo, lapack_int ihi,\n                                const float* lscale, const float* rscale,\n                                lapack_int m, float* v, lapack_int ldv );\nlapack_int LAPACKE_dggbak_work( int matrix_order, char job, char side,\n                                lapack_int n, lapack_int ilo, lapack_int ihi,\n                                const double* lscale, const double* rscale,\n                                lapack_int m, double* v, lapack_int ldv );\nlapack_int LAPACKE_cggbak_work( int matrix_order, char job, char side,\n                                lapack_int n, lapack_int ilo, lapack_int ihi,\n                                const float* lscale, const float* rscale,\n                                lapack_int m, lapack_complex_float* v,\n                                lapack_int ldv );\nlapack_int LAPACKE_zggbak_work( int matrix_order, char job, char side,\n                                lapack_int n, lapack_int ilo, lapack_int ihi,\n                                const double* lscale, const double* rscale,\n                                lapack_int m, lapack_complex_double* v,\n                                lapack_int ldv );\n\nlapack_int LAPACKE_sggbal_work( int matrix_order, char job, lapack_int n,\n                                float* a, lapack_int lda, float* b,\n                                lapack_int ldb, lapack_int* ilo,\n                                lapack_int* ihi, float* lscale, float* rscale,\n                                float* work );\nlapack_int LAPACKE_dggbal_work( int matrix_order, char job, lapack_int n,\n                                double* a, lapack_int lda, double* b,\n                                lapack_int ldb, lapack_int* ilo,\n                                lapack_int* ihi, double* lscale, double* rscale,\n                                double* work );\nlapack_int LAPACKE_cggbal_work( int matrix_order, char job, lapack_int n,\n                                lapack_complex_float* a, lapack_int lda,\n                                lapack_complex_float* b, lapack_int ldb,\n                                lapack_int* ilo, lapack_int* ihi, float* lscale,\n                                float* rscale, float* work );\nlapack_int LAPACKE_zggbal_work( int matrix_order, char job, lapack_int n,\n                                lapack_complex_double* a, lapack_int lda,\n                                lapack_complex_double* b, lapack_int ldb,\n                                lapack_int* ilo, lapack_int* ihi,\n                                double* lscale, double* rscale, double* work );\n\nlapack_int LAPACKE_sgges_work( int matrix_order, char jobvsl, char jobvsr,\n                               char sort, LAPACK_S_SELECT3 selctg, lapack_int n,\n                               float* a, lapack_int lda, float* b,\n                               lapack_int ldb, lapack_int* sdim, float* alphar,\n                               float* alphai, float* beta, float* vsl,\n                               lapack_int ldvsl, float* vsr, lapack_int ldvsr,\n                               float* work, lapack_int lwork,\n                               lapack_logical* bwork );\nlapack_int LAPACKE_dgges_work( int matrix_order, char jobvsl, char jobvsr,\n                               char sort, LAPACK_D_SELECT3 selctg, lapack_int n,\n                               double* a, lapack_int lda, double* b,\n                               lapack_int ldb, lapack_int* sdim, double* alphar,\n                               double* alphai, double* beta, double* vsl,\n                               lapack_int ldvsl, double* vsr, lapack_int ldvsr,\n                               double* work, lapack_int lwork,\n                               lapack_logical* bwork );\nlapack_int LAPACKE_cgges_work( int matrix_order, char jobvsl, char jobvsr,\n                               char sort, LAPACK_C_SELECT2 selctg, lapack_int n,\n                               lapack_complex_float* a, lapack_int lda,\n                               lapack_complex_float* b, lapack_int ldb,\n                               lapack_int* sdim, lapack_complex_float* alpha,\n                               lapack_complex_float* beta,\n                               lapack_complex_float* vsl, lapack_int ldvsl,\n                               lapack_complex_float* vsr, lapack_int ldvsr,\n                               lapack_complex_float* work, lapack_int lwork,\n                               float* rwork, lapack_logical* bwork );\nlapack_int LAPACKE_zgges_work( int matrix_order, char jobvsl, char jobvsr,\n                               char sort, LAPACK_Z_SELECT2 selctg, lapack_int n,\n                               lapack_complex_double* a, lapack_int lda,\n                               lapack_complex_double* b, lapack_int ldb,\n                               lapack_int* sdim, lapack_complex_double* alpha,\n                               lapack_complex_double* beta,\n                               lapack_complex_double* vsl, lapack_int ldvsl,\n                               lapack_complex_double* vsr, lapack_int ldvsr,\n                               lapack_complex_double* work, lapack_int lwork,\n                               double* rwork, lapack_logical* bwork );\n\nlapack_int LAPACKE_sggesx_work( int matrix_order, char jobvsl, char jobvsr,\n                                char sort, LAPACK_S_SELECT3 selctg, char sense,\n                                lapack_int n, float* a, lapack_int lda,\n                                float* b, lapack_int ldb, lapack_int* sdim,\n                                float* alphar, float* alphai, float* beta,\n                                float* vsl, lapack_int ldvsl, float* vsr,\n                                lapack_int ldvsr, float* rconde, float* rcondv,\n                                float* work, lapack_int lwork,\n                                lapack_int* iwork, lapack_int liwork,\n                                lapack_logical* bwork );\nlapack_int LAPACKE_dggesx_work( int matrix_order, char jobvsl, char jobvsr,\n                                char sort, LAPACK_D_SELECT3 selctg, char sense,\n                                lapack_int n, double* a, lapack_int lda,\n                                double* b, lapack_int ldb, lapack_int* sdim,\n                                double* alphar, double* alphai, double* beta,\n                                double* vsl, lapack_int ldvsl, double* vsr,\n                                lapack_int ldvsr, double* rconde,\n                                double* rcondv, double* work, lapack_int lwork,\n                                lapack_int* iwork, lapack_int liwork,\n                                lapack_logical* bwork );\nlapack_int LAPACKE_cggesx_work( int matrix_order, char jobvsl, char jobvsr,\n                                char sort, LAPACK_C_SELECT2 selctg, char sense,\n                                lapack_int n, lapack_complex_float* a,\n                                lapack_int lda, lapack_complex_float* b,\n                                lapack_int ldb, lapack_int* sdim,\n                                lapack_complex_float* alpha,\n                                lapack_complex_float* beta,\n                                lapack_complex_float* vsl, lapack_int ldvsl,\n                                lapack_complex_float* vsr, lapack_int ldvsr,\n                                float* rconde, float* rcondv,\n                                lapack_complex_float* work, lapack_int lwork,\n                                float* rwork, lapack_int* iwork,\n                                lapack_int liwork, lapack_logical* bwork );\nlapack_int LAPACKE_zggesx_work( int matrix_order, char jobvsl, char jobvsr,\n                                char sort, LAPACK_Z_SELECT2 selctg, char sense,\n                                lapack_int n, lapack_complex_double* a,\n                                lapack_int lda, lapack_complex_double* b,\n                                lapack_int ldb, lapack_int* sdim,\n                                lapack_complex_double* alpha,\n                                lapack_complex_double* beta,\n                                lapack_complex_double* vsl, lapack_int ldvsl,\n                                lapack_complex_double* vsr, lapack_int ldvsr,\n                                double* rconde, double* rcondv,\n                                lapack_complex_double* work, lapack_int lwork,\n                                double* rwork, lapack_int* iwork,\n                                lapack_int liwork, lapack_logical* bwork );\n\nlapack_int LAPACKE_sggev_work( int matrix_order, char jobvl, char jobvr,\n                               lapack_int n, float* a, lapack_int lda, float* b,\n                               lapack_int ldb, float* alphar, float* alphai,\n                               float* beta, float* vl, lapack_int ldvl,\n                               float* vr, lapack_int ldvr, float* work,\n                               lapack_int lwork );\nlapack_int LAPACKE_dggev_work( int matrix_order, char jobvl, char jobvr,\n                               lapack_int n, double* a, lapack_int lda,\n                               double* b, lapack_int ldb, double* alphar,\n                               double* alphai, double* beta, double* vl,\n                               lapack_int ldvl, double* vr, lapack_int ldvr,\n                               double* work, lapack_int lwork );\nlapack_int LAPACKE_cggev_work( int matrix_order, char jobvl, char jobvr,\n                               lapack_int n, lapack_complex_float* a,\n                               lapack_int lda, lapack_complex_float* b,\n                               lapack_int ldb, lapack_complex_float* alpha,\n                               lapack_complex_float* beta,\n                               lapack_complex_float* vl, lapack_int ldvl,\n                               lapack_complex_float* vr, lapack_int ldvr,\n                               lapack_complex_float* work, lapack_int lwork,\n                               float* rwork );\nlapack_int LAPACKE_zggev_work( int matrix_order, char jobvl, char jobvr,\n                               lapack_int n, lapack_complex_double* a,\n                               lapack_int lda, lapack_complex_double* b,\n                               lapack_int ldb, lapack_complex_double* alpha,\n                               lapack_complex_double* beta,\n                               lapack_complex_double* vl, lapack_int ldvl,\n                               lapack_complex_double* vr, lapack_int ldvr,\n                               lapack_complex_double* work, lapack_int lwork,\n                               double* rwork );\n\nlapack_int LAPACKE_sggevx_work( int matrix_order, char balanc, char jobvl,\n                                char jobvr, char sense, lapack_int n, float* a,\n                                lapack_int lda, float* b, lapack_int ldb,\n                                float* alphar, float* alphai, float* beta,\n                                float* vl, lapack_int ldvl, float* vr,\n                                lapack_int ldvr, lapack_int* ilo,\n                                lapack_int* ihi, float* lscale, float* rscale,\n                                float* abnrm, float* bbnrm, float* rconde,\n                                float* rcondv, float* work, lapack_int lwork,\n                                lapack_int* iwork, lapack_logical* bwork );\nlapack_int LAPACKE_dggevx_work( int matrix_order, char balanc, char jobvl,\n                                char jobvr, char sense, lapack_int n, double* a,\n                                lapack_int lda, double* b, lapack_int ldb,\n                                double* alphar, double* alphai, double* beta,\n                                double* vl, lapack_int ldvl, double* vr,\n                                lapack_int ldvr, lapack_int* ilo,\n                                lapack_int* ihi, double* lscale, double* rscale,\n                                double* abnrm, double* bbnrm, double* rconde,\n                                double* rcondv, double* work, lapack_int lwork,\n                                lapack_int* iwork, lapack_logical* bwork );\nlapack_int LAPACKE_cggevx_work( int matrix_order, char balanc, char jobvl,\n                                char jobvr, char sense, lapack_int n,\n                                lapack_complex_float* a, lapack_int lda,\n                                lapack_complex_float* b, lapack_int ldb,\n                                lapack_complex_float* alpha,\n                                lapack_complex_float* beta,\n                                lapack_complex_float* vl, lapack_int ldvl,\n                                lapack_complex_float* vr, lapack_int ldvr,\n                                lapack_int* ilo, lapack_int* ihi, float* lscale,\n                                float* rscale, float* abnrm, float* bbnrm,\n                                float* rconde, float* rcondv,\n                                lapack_complex_float* work, lapack_int lwork,\n                                float* rwork, lapack_int* iwork,\n                                lapack_logical* bwork );\nlapack_int LAPACKE_zggevx_work( int matrix_order, char balanc, char jobvl,\n                                char jobvr, char sense, lapack_int n,\n                                lapack_complex_double* a, lapack_int lda,\n                                lapack_complex_double* b, lapack_int ldb,\n                                lapack_complex_double* alpha,\n                                lapack_complex_double* beta,\n                                lapack_complex_double* vl, lapack_int ldvl,\n                                lapack_complex_double* vr, lapack_int ldvr,\n                                lapack_int* ilo, lapack_int* ihi,\n                                double* lscale, double* rscale, double* abnrm,\n                                double* bbnrm, double* rconde, double* rcondv,\n                                lapack_complex_double* work, lapack_int lwork,\n                                double* rwork, lapack_int* iwork,\n                                lapack_logical* bwork );\n\nlapack_int LAPACKE_sggglm_work( int matrix_order, lapack_int n, lapack_int m,\n                                lapack_int p, float* a, lapack_int lda,\n                                float* b, lapack_int ldb, float* d, float* x,\n                                float* y, float* work, lapack_int lwork );\nlapack_int LAPACKE_dggglm_work( int matrix_order, lapack_int n, lapack_int m,\n                                lapack_int p, double* a, lapack_int lda,\n                                double* b, lapack_int ldb, double* d, double* x,\n                                double* y, double* work, lapack_int lwork );\nlapack_int LAPACKE_cggglm_work( int matrix_order, lapack_int n, lapack_int m,\n                                lapack_int p, lapack_complex_float* a,\n                                lapack_int lda, lapack_complex_float* b,\n                                lapack_int ldb, lapack_complex_float* d,\n                                lapack_complex_float* x,\n                                lapack_complex_float* y,\n                                lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_zggglm_work( int matrix_order, lapack_int n, lapack_int m,\n                                lapack_int p, lapack_complex_double* a,\n                                lapack_int lda, lapack_complex_double* b,\n                                lapack_int ldb, lapack_complex_double* d,\n                                lapack_complex_double* x,\n                                lapack_complex_double* y,\n                                lapack_complex_double* work, lapack_int lwork );\n\nlapack_int LAPACKE_sgghrd_work( int matrix_order, char compq, char compz,\n                                lapack_int n, lapack_int ilo, lapack_int ihi,\n                                float* a, lapack_int lda, float* b,\n                                lapack_int ldb, float* q, lapack_int ldq,\n                                float* z, lapack_int ldz );\nlapack_int LAPACKE_dgghrd_work( int matrix_order, char compq, char compz,\n                                lapack_int n, lapack_int ilo, lapack_int ihi,\n                                double* a, lapack_int lda, double* b,\n                                lapack_int ldb, double* q, lapack_int ldq,\n                                double* z, lapack_int ldz );\nlapack_int LAPACKE_cgghrd_work( int matrix_order, char compq, char compz,\n                                lapack_int n, lapack_int ilo, lapack_int ihi,\n                                lapack_complex_float* a, lapack_int lda,\n                                lapack_complex_float* b, lapack_int ldb,\n                                lapack_complex_float* q, lapack_int ldq,\n                                lapack_complex_float* z, lapack_int ldz );\nlapack_int LAPACKE_zgghrd_work( int matrix_order, char compq, char compz,\n                                lapack_int n, lapack_int ilo, lapack_int ihi,\n                                lapack_complex_double* a, lapack_int lda,\n                                lapack_complex_double* b, lapack_int ldb,\n                                lapack_complex_double* q, lapack_int ldq,\n                                lapack_complex_double* z, lapack_int ldz );\n\nlapack_int LAPACKE_sgglse_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int p, float* a, lapack_int lda,\n                                float* b, lapack_int ldb, float* c, float* d,\n                                float* x, float* work, lapack_int lwork );\nlapack_int LAPACKE_dgglse_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int p, double* a, lapack_int lda,\n                                double* b, lapack_int ldb, double* c, double* d,\n                                double* x, double* work, lapack_int lwork );\nlapack_int LAPACKE_cgglse_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int p, lapack_complex_float* a,\n                                lapack_int lda, lapack_complex_float* b,\n                                lapack_int ldb, lapack_complex_float* c,\n                                lapack_complex_float* d,\n                                lapack_complex_float* x,\n                                lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_zgglse_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int p, lapack_complex_double* a,\n                                lapack_int lda, lapack_complex_double* b,\n                                lapack_int ldb, lapack_complex_double* c,\n                                lapack_complex_double* d,\n                                lapack_complex_double* x,\n                                lapack_complex_double* work, lapack_int lwork );\n\nlapack_int LAPACKE_sggqrf_work( int matrix_order, lapack_int n, lapack_int m,\n                                lapack_int p, float* a, lapack_int lda,\n                                float* taua, float* b, lapack_int ldb,\n                                float* taub, float* work, lapack_int lwork );\nlapack_int LAPACKE_dggqrf_work( int matrix_order, lapack_int n, lapack_int m,\n                                lapack_int p, double* a, lapack_int lda,\n                                double* taua, double* b, lapack_int ldb,\n                                double* taub, double* work, lapack_int lwork );\nlapack_int LAPACKE_cggqrf_work( int matrix_order, lapack_int n, lapack_int m,\n                                lapack_int p, lapack_complex_float* a,\n                                lapack_int lda, lapack_complex_float* taua,\n                                lapack_complex_float* b, lapack_int ldb,\n                                lapack_complex_float* taub,\n                                lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_zggqrf_work( int matrix_order, lapack_int n, lapack_int m,\n                                lapack_int p, lapack_complex_double* a,\n                                lapack_int lda, lapack_complex_double* taua,\n                                lapack_complex_double* b, lapack_int ldb,\n                                lapack_complex_double* taub,\n                                lapack_complex_double* work, lapack_int lwork );\n\nlapack_int LAPACKE_sggrqf_work( int matrix_order, lapack_int m, lapack_int p,\n                                lapack_int n, float* a, lapack_int lda,\n                                float* taua, float* b, lapack_int ldb,\n                                float* taub, float* work, lapack_int lwork );\nlapack_int LAPACKE_dggrqf_work( int matrix_order, lapack_int m, lapack_int p,\n                                lapack_int n, double* a, lapack_int lda,\n                                double* taua, double* b, lapack_int ldb,\n                                double* taub, double* work, lapack_int lwork );\nlapack_int LAPACKE_cggrqf_work( int matrix_order, lapack_int m, lapack_int p,\n                                lapack_int n, lapack_complex_float* a,\n                                lapack_int lda, lapack_complex_float* taua,\n                                lapack_complex_float* b, lapack_int ldb,\n                                lapack_complex_float* taub,\n                                lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_zggrqf_work( int matrix_order, lapack_int m, lapack_int p,\n                                lapack_int n, lapack_complex_double* a,\n                                lapack_int lda, lapack_complex_double* taua,\n                                lapack_complex_double* b, lapack_int ldb,\n                                lapack_complex_double* taub,\n                                lapack_complex_double* work, lapack_int lwork );\n\nlapack_int LAPACKE_sggsvd_work( int matrix_order, char jobu, char jobv,\n                                char jobq, lapack_int m, lapack_int n,\n                                lapack_int p, lapack_int* k, lapack_int* l,\n                                float* a, lapack_int lda, float* b,\n                                lapack_int ldb, float* alpha, float* beta,\n                                float* u, lapack_int ldu, float* v,\n                                lapack_int ldv, float* q, lapack_int ldq,\n                                float* work, lapack_int* iwork );\nlapack_int LAPACKE_dggsvd_work( int matrix_order, char jobu, char jobv,\n                                char jobq, lapack_int m, lapack_int n,\n                                lapack_int p, lapack_int* k, lapack_int* l,\n                                double* a, lapack_int lda, double* b,\n                                lapack_int ldb, double* alpha, double* beta,\n                                double* u, lapack_int ldu, double* v,\n                                lapack_int ldv, double* q, lapack_int ldq,\n                                double* work, lapack_int* iwork );\nlapack_int LAPACKE_cggsvd_work( int matrix_order, char jobu, char jobv,\n                                char jobq, lapack_int m, lapack_int n,\n                                lapack_int p, lapack_int* k, lapack_int* l,\n                                lapack_complex_float* a, lapack_int lda,\n                                lapack_complex_float* b, lapack_int ldb,\n                                float* alpha, float* beta,\n                                lapack_complex_float* u, lapack_int ldu,\n                                lapack_complex_float* v, lapack_int ldv,\n                                lapack_complex_float* q, lapack_int ldq,\n                                lapack_complex_float* work, float* rwork,\n                                lapack_int* iwork );\nlapack_int LAPACKE_zggsvd_work( int matrix_order, char jobu, char jobv,\n                                char jobq, lapack_int m, lapack_int n,\n                                lapack_int p, lapack_int* k, lapack_int* l,\n                                lapack_complex_double* a, lapack_int lda,\n                                lapack_complex_double* b, lapack_int ldb,\n                                double* alpha, double* beta,\n                                lapack_complex_double* u, lapack_int ldu,\n                                lapack_complex_double* v, lapack_int ldv,\n                                lapack_complex_double* q, lapack_int ldq,\n                                lapack_complex_double* work, double* rwork,\n                                lapack_int* iwork );\n\nlapack_int LAPACKE_sggsvp_work( int matrix_order, char jobu, char jobv,\n                                char jobq, lapack_int m, lapack_int p,\n                                lapack_int n, float* a, lapack_int lda,\n                                float* b, lapack_int ldb, float tola,\n                                float tolb, lapack_int* k, lapack_int* l,\n                                float* u, lapack_int ldu, float* v,\n                                lapack_int ldv, float* q, lapack_int ldq,\n                                lapack_int* iwork, float* tau, float* work );\nlapack_int LAPACKE_dggsvp_work( int matrix_order, char jobu, char jobv,\n                                char jobq, lapack_int m, lapack_int p,\n                                lapack_int n, double* a, lapack_int lda,\n                                double* b, lapack_int ldb, double tola,\n                                double tolb, lapack_int* k, lapack_int* l,\n                                double* u, lapack_int ldu, double* v,\n                                lapack_int ldv, double* q, lapack_int ldq,\n                                lapack_int* iwork, double* tau, double* work );\nlapack_int LAPACKE_cggsvp_work( int matrix_order, char jobu, char jobv,\n                                char jobq, lapack_int m, lapack_int p,\n                                lapack_int n, lapack_complex_float* a,\n                                lapack_int lda, lapack_complex_float* b,\n                                lapack_int ldb, float tola, float tolb,\n                                lapack_int* k, lapack_int* l,\n                                lapack_complex_float* u, lapack_int ldu,\n                                lapack_complex_float* v, lapack_int ldv,\n                                lapack_complex_float* q, lapack_int ldq,\n                                lapack_int* iwork, float* rwork,\n                                lapack_complex_float* tau,\n                                lapack_complex_float* work );\nlapack_int LAPACKE_zggsvp_work( int matrix_order, char jobu, char jobv,\n                                char jobq, lapack_int m, lapack_int p,\n                                lapack_int n, lapack_complex_double* a,\n                                lapack_int lda, lapack_complex_double* b,\n                                lapack_int ldb, double tola, double tolb,\n                                lapack_int* k, lapack_int* l,\n                                lapack_complex_double* u, lapack_int ldu,\n                                lapack_complex_double* v, lapack_int ldv,\n                                lapack_complex_double* q, lapack_int ldq,\n                                lapack_int* iwork, double* rwork,\n                                lapack_complex_double* tau,\n                                lapack_complex_double* work );\n\nlapack_int LAPACKE_sgtcon_work( char norm, lapack_int n, const float* dl,\n                                const float* d, const float* du,\n                                const float* du2, const lapack_int* ipiv,\n                                float anorm, float* rcond, float* work,\n                                lapack_int* iwork );\nlapack_int LAPACKE_dgtcon_work( char norm, lapack_int n, const double* dl,\n                                const double* d, const double* du,\n                                const double* du2, const lapack_int* ipiv,\n                                double anorm, double* rcond, double* work,\n                                lapack_int* iwork );\nlapack_int LAPACKE_cgtcon_work( char norm, lapack_int n,\n                                const lapack_complex_float* dl,\n                                const lapack_complex_float* d,\n                                const lapack_complex_float* du,\n                                const lapack_complex_float* du2,\n                                const lapack_int* ipiv, float anorm,\n                                float* rcond, lapack_complex_float* work );\nlapack_int LAPACKE_zgtcon_work( char norm, lapack_int n,\n                                const lapack_complex_double* dl,\n                                const lapack_complex_double* d,\n                                const lapack_complex_double* du,\n                                const lapack_complex_double* du2,\n                                const lapack_int* ipiv, double anorm,\n                                double* rcond, lapack_complex_double* work );\n\nlapack_int LAPACKE_sgtrfs_work( int matrix_order, char trans, lapack_int n,\n                                lapack_int nrhs, const float* dl,\n                                const float* d, const float* du,\n                                const float* dlf, const float* df,\n                                const float* duf, const float* du2,\n                                const lapack_int* ipiv, const float* b,\n                                lapack_int ldb, float* x, lapack_int ldx,\n                                float* ferr, float* berr, float* work,\n                                lapack_int* iwork );\nlapack_int LAPACKE_dgtrfs_work( int matrix_order, char trans, lapack_int n,\n                                lapack_int nrhs, const double* dl,\n                                const double* d, const double* du,\n                                const double* dlf, const double* df,\n                                const double* duf, const double* du2,\n                                const lapack_int* ipiv, const double* b,\n                                lapack_int ldb, double* x, lapack_int ldx,\n                                double* ferr, double* berr, double* work,\n                                lapack_int* iwork );\nlapack_int LAPACKE_cgtrfs_work( int matrix_order, char trans, lapack_int n,\n                                lapack_int nrhs, const lapack_complex_float* dl,\n                                const lapack_complex_float* d,\n                                const lapack_complex_float* du,\n                                const lapack_complex_float* dlf,\n                                const lapack_complex_float* df,\n                                const lapack_complex_float* duf,\n                                const lapack_complex_float* du2,\n                                const lapack_int* ipiv,\n                                const lapack_complex_float* b, lapack_int ldb,\n                                lapack_complex_float* x, lapack_int ldx,\n                                float* ferr, float* berr,\n                                lapack_complex_float* work, float* rwork );\nlapack_int LAPACKE_zgtrfs_work( int matrix_order, char trans, lapack_int n,\n                                lapack_int nrhs,\n                                const lapack_complex_double* dl,\n                                const lapack_complex_double* d,\n                                const lapack_complex_double* du,\n                                const lapack_complex_double* dlf,\n                                const lapack_complex_double* df,\n                                const lapack_complex_double* duf,\n                                const lapack_complex_double* du2,\n                                const lapack_int* ipiv,\n                                const lapack_complex_double* b, lapack_int ldb,\n                                lapack_complex_double* x, lapack_int ldx,\n                                double* ferr, double* berr,\n                                lapack_complex_double* work, double* rwork );\n\nlapack_int LAPACKE_sgtsv_work( int matrix_order, lapack_int n, lapack_int nrhs,\n                               float* dl, float* d, float* du, float* b,\n                               lapack_int ldb );\nlapack_int LAPACKE_dgtsv_work( int matrix_order, lapack_int n, lapack_int nrhs,\n                               double* dl, double* d, double* du, double* b,\n                               lapack_int ldb );\nlapack_int LAPACKE_cgtsv_work( int matrix_order, lapack_int n, lapack_int nrhs,\n                               lapack_complex_float* dl,\n                               lapack_complex_float* d,\n                               lapack_complex_float* du,\n                               lapack_complex_float* b, lapack_int ldb );\nlapack_int LAPACKE_zgtsv_work( int matrix_order, lapack_int n, lapack_int nrhs,\n                               lapack_complex_double* dl,\n                               lapack_complex_double* d,\n                               lapack_complex_double* du,\n                               lapack_complex_double* b, lapack_int ldb );\n\nlapack_int LAPACKE_sgtsvx_work( int matrix_order, char fact, char trans,\n                                lapack_int n, lapack_int nrhs, const float* dl,\n                                const float* d, const float* du, float* dlf,\n                                float* df, float* duf, float* du2,\n                                lapack_int* ipiv, const float* b,\n                                lapack_int ldb, float* x, lapack_int ldx,\n                                float* rcond, float* ferr, float* berr,\n                                float* work, lapack_int* iwork );\nlapack_int LAPACKE_dgtsvx_work( int matrix_order, char fact, char trans,\n                                lapack_int n, lapack_int nrhs, const double* dl,\n                                const double* d, const double* du, double* dlf,\n                                double* df, double* duf, double* du2,\n                                lapack_int* ipiv, const double* b,\n                                lapack_int ldb, double* x, lapack_int ldx,\n                                double* rcond, double* ferr, double* berr,\n                                double* work, lapack_int* iwork );\nlapack_int LAPACKE_cgtsvx_work( int matrix_order, char fact, char trans,\n                                lapack_int n, lapack_int nrhs,\n                                const lapack_complex_float* dl,\n                                const lapack_complex_float* d,\n                                const lapack_complex_float* du,\n                                lapack_complex_float* dlf,\n                                lapack_complex_float* df,\n                                lapack_complex_float* duf,\n                                lapack_complex_float* du2, lapack_int* ipiv,\n                                const lapack_complex_float* b, lapack_int ldb,\n                                lapack_complex_float* x, lapack_int ldx,\n                                float* rcond, float* ferr, float* berr,\n                                lapack_complex_float* work, float* rwork );\nlapack_int LAPACKE_zgtsvx_work( int matrix_order, char fact, char trans,\n                                lapack_int n, lapack_int nrhs,\n                                const lapack_complex_double* dl,\n                                const lapack_complex_double* d,\n                                const lapack_complex_double* du,\n                                lapack_complex_double* dlf,\n                                lapack_complex_double* df,\n                                lapack_complex_double* duf,\n                                lapack_complex_double* du2, lapack_int* ipiv,\n                                const lapack_complex_double* b, lapack_int ldb,\n                                lapack_complex_double* x, lapack_int ldx,\n                                double* rcond, double* ferr, double* berr,\n                                lapack_complex_double* work, double* rwork );\n\nlapack_int LAPACKE_sgttrf_work( lapack_int n, float* dl, float* d, float* du,\n                                float* du2, lapack_int* ipiv );\nlapack_int LAPACKE_dgttrf_work( lapack_int n, double* dl, double* d, double* du,\n                                double* du2, lapack_int* ipiv );\nlapack_int LAPACKE_cgttrf_work( lapack_int n, lapack_complex_float* dl,\n                                lapack_complex_float* d,\n                                lapack_complex_float* du,\n                                lapack_complex_float* du2, lapack_int* ipiv );\nlapack_int LAPACKE_zgttrf_work( lapack_int n, lapack_complex_double* dl,\n                                lapack_complex_double* d,\n                                lapack_complex_double* du,\n                                lapack_complex_double* du2, lapack_int* ipiv );\n\nlapack_int LAPACKE_sgttrs_work( int matrix_order, char trans, lapack_int n,\n                                lapack_int nrhs, const float* dl,\n                                const float* d, const float* du,\n                                const float* du2, const lapack_int* ipiv,\n                                float* b, lapack_int ldb );\nlapack_int LAPACKE_dgttrs_work( int matrix_order, char trans, lapack_int n,\n                                lapack_int nrhs, const double* dl,\n                                const double* d, const double* du,\n                                const double* du2, const lapack_int* ipiv,\n                                double* b, lapack_int ldb );\nlapack_int LAPACKE_cgttrs_work( int matrix_order, char trans, lapack_int n,\n                                lapack_int nrhs, const lapack_complex_float* dl,\n                                const lapack_complex_float* d,\n                                const lapack_complex_float* du,\n                                const lapack_complex_float* du2,\n                                const lapack_int* ipiv, lapack_complex_float* b,\n                                lapack_int ldb );\nlapack_int LAPACKE_zgttrs_work( int matrix_order, char trans, lapack_int n,\n                                lapack_int nrhs,\n                                const lapack_complex_double* dl,\n                                const lapack_complex_double* d,\n                                const lapack_complex_double* du,\n                                const lapack_complex_double* du2,\n                                const lapack_int* ipiv,\n                                lapack_complex_double* b, lapack_int ldb );\n\nlapack_int LAPACKE_chbev_work( int matrix_order, char jobz, char uplo,\n                               lapack_int n, lapack_int kd,\n                               lapack_complex_float* ab, lapack_int ldab,\n                               float* w, lapack_complex_float* z,\n                               lapack_int ldz, lapack_complex_float* work,\n                               float* rwork );\nlapack_int LAPACKE_zhbev_work( int matrix_order, char jobz, char uplo,\n                               lapack_int n, lapack_int kd,\n                               lapack_complex_double* ab, lapack_int ldab,\n                               double* w, lapack_complex_double* z,\n                               lapack_int ldz, lapack_complex_double* work,\n                               double* rwork );\n\nlapack_int LAPACKE_chbevd_work( int matrix_order, char jobz, char uplo,\n                                lapack_int n, lapack_int kd,\n                                lapack_complex_float* ab, lapack_int ldab,\n                                float* w, lapack_complex_float* z,\n                                lapack_int ldz, lapack_complex_float* work,\n                                lapack_int lwork, float* rwork,\n                                lapack_int lrwork, lapack_int* iwork,\n                                lapack_int liwork );\nlapack_int LAPACKE_zhbevd_work( int matrix_order, char jobz, char uplo,\n                                lapack_int n, lapack_int kd,\n                                lapack_complex_double* ab, lapack_int ldab,\n                                double* w, lapack_complex_double* z,\n                                lapack_int ldz, lapack_complex_double* work,\n                                lapack_int lwork, double* rwork,\n                                lapack_int lrwork, lapack_int* iwork,\n                                lapack_int liwork );\n\nlapack_int LAPACKE_chbevx_work( int matrix_order, char jobz, char range,\n                                char uplo, lapack_int n, lapack_int kd,\n                                lapack_complex_float* ab, lapack_int ldab,\n                                lapack_complex_float* q, lapack_int ldq,\n                                float vl, float vu, lapack_int il,\n                                lapack_int iu, float abstol, lapack_int* m,\n                                float* w, lapack_complex_float* z,\n                                lapack_int ldz, lapack_complex_float* work,\n                                float* rwork, lapack_int* iwork,\n                                lapack_int* ifail );\nlapack_int LAPACKE_zhbevx_work( int matrix_order, char jobz, char range,\n                                char uplo, lapack_int n, lapack_int kd,\n                                lapack_complex_double* ab, lapack_int ldab,\n                                lapack_complex_double* q, lapack_int ldq,\n                                double vl, double vu, lapack_int il,\n                                lapack_int iu, double abstol, lapack_int* m,\n                                double* w, lapack_complex_double* z,\n                                lapack_int ldz, lapack_complex_double* work,\n                                double* rwork, lapack_int* iwork,\n                                lapack_int* ifail );\n\nlapack_int LAPACKE_chbgst_work( int matrix_order, char vect, char uplo,\n                                lapack_int n, lapack_int ka, lapack_int kb,\n                                lapack_complex_float* ab, lapack_int ldab,\n                                const lapack_complex_float* bb, lapack_int ldbb,\n                                lapack_complex_float* x, lapack_int ldx,\n                                lapack_complex_float* work, float* rwork );\nlapack_int LAPACKE_zhbgst_work( int matrix_order, char vect, char uplo,\n                                lapack_int n, lapack_int ka, lapack_int kb,\n                                lapack_complex_double* ab, lapack_int ldab,\n                                const lapack_complex_double* bb,\n                                lapack_int ldbb, lapack_complex_double* x,\n                                lapack_int ldx, lapack_complex_double* work,\n                                double* rwork );\n\nlapack_int LAPACKE_chbgv_work( int matrix_order, char jobz, char uplo,\n                               lapack_int n, lapack_int ka, lapack_int kb,\n                               lapack_complex_float* ab, lapack_int ldab,\n                               lapack_complex_float* bb, lapack_int ldbb,\n                               float* w, lapack_complex_float* z,\n                               lapack_int ldz, lapack_complex_float* work,\n                               float* rwork );\nlapack_int LAPACKE_zhbgv_work( int matrix_order, char jobz, char uplo,\n                               lapack_int n, lapack_int ka, lapack_int kb,\n                               lapack_complex_double* ab, lapack_int ldab,\n                               lapack_complex_double* bb, lapack_int ldbb,\n                               double* w, lapack_complex_double* z,\n                               lapack_int ldz, lapack_complex_double* work,\n                               double* rwork );\n\nlapack_int LAPACKE_chbgvd_work( int matrix_order, char jobz, char uplo,\n                                lapack_int n, lapack_int ka, lapack_int kb,\n                                lapack_complex_float* ab, lapack_int ldab,\n                                lapack_complex_float* bb, lapack_int ldbb,\n                                float* w, lapack_complex_float* z,\n                                lapack_int ldz, lapack_complex_float* work,\n                                lapack_int lwork, float* rwork,\n                                lapack_int lrwork, lapack_int* iwork,\n                                lapack_int liwork );\nlapack_int LAPACKE_zhbgvd_work( int matrix_order, char jobz, char uplo,\n                                lapack_int n, lapack_int ka, lapack_int kb,\n                                lapack_complex_double* ab, lapack_int ldab,\n                                lapack_complex_double* bb, lapack_int ldbb,\n                                double* w, lapack_complex_double* z,\n                                lapack_int ldz, lapack_complex_double* work,\n                                lapack_int lwork, double* rwork,\n                                lapack_int lrwork, lapack_int* iwork,\n                                lapack_int liwork );\n\nlapack_int LAPACKE_chbgvx_work( int matrix_order, char jobz, char range,\n                                char uplo, lapack_int n, lapack_int ka,\n                                lapack_int kb, lapack_complex_float* ab,\n                                lapack_int ldab, lapack_complex_float* bb,\n                                lapack_int ldbb, lapack_complex_float* q,\n                                lapack_int ldq, float vl, float vu,\n                                lapack_int il, lapack_int iu, float abstol,\n                                lapack_int* m, float* w,\n                                lapack_complex_float* z, lapack_int ldz,\n                                lapack_complex_float* work, float* rwork,\n                                lapack_int* iwork, lapack_int* ifail );\nlapack_int LAPACKE_zhbgvx_work( int matrix_order, char jobz, char range,\n                                char uplo, lapack_int n, lapack_int ka,\n                                lapack_int kb, lapack_complex_double* ab,\n                                lapack_int ldab, lapack_complex_double* bb,\n                                lapack_int ldbb, lapack_complex_double* q,\n                                lapack_int ldq, double vl, double vu,\n                                lapack_int il, lapack_int iu, double abstol,\n                                lapack_int* m, double* w,\n                                lapack_complex_double* z, lapack_int ldz,\n                                lapack_complex_double* work, double* rwork,\n                                lapack_int* iwork, lapack_int* ifail );\n\nlapack_int LAPACKE_chbtrd_work( int matrix_order, char vect, char uplo,\n                                lapack_int n, lapack_int kd,\n                                lapack_complex_float* ab, lapack_int ldab,\n                                float* d, float* e, lapack_complex_float* q,\n                                lapack_int ldq, lapack_complex_float* work );\nlapack_int LAPACKE_zhbtrd_work( int matrix_order, char vect, char uplo,\n                                lapack_int n, lapack_int kd,\n                                lapack_complex_double* ab, lapack_int ldab,\n                                double* d, double* e, lapack_complex_double* q,\n                                lapack_int ldq, lapack_complex_double* work );\n\nlapack_int LAPACKE_checon_work( int matrix_order, char uplo, lapack_int n,\n                                const lapack_complex_float* a, lapack_int lda,\n                                const lapack_int* ipiv, float anorm,\n                                float* rcond, lapack_complex_float* work );\nlapack_int LAPACKE_zhecon_work( int matrix_order, char uplo, lapack_int n,\n                                const lapack_complex_double* a, lapack_int lda,\n                                const lapack_int* ipiv, double anorm,\n                                double* rcond, lapack_complex_double* work );\n\nlapack_int LAPACKE_cheequb_work( int matrix_order, char uplo, lapack_int n,\n                                 const lapack_complex_float* a, lapack_int lda,\n                                 float* s, float* scond, float* amax,\n                                 lapack_complex_float* work );\nlapack_int LAPACKE_zheequb_work( int matrix_order, char uplo, lapack_int n,\n                                 const lapack_complex_double* a, lapack_int lda,\n                                 double* s, double* scond, double* amax,\n                                 lapack_complex_double* work );\n\nlapack_int LAPACKE_cheev_work( int matrix_order, char jobz, char uplo,\n                               lapack_int n, lapack_complex_float* a,\n                               lapack_int lda, float* w,\n                               lapack_complex_float* work, lapack_int lwork,\n                               float* rwork );\nlapack_int LAPACKE_zheev_work( int matrix_order, char jobz, char uplo,\n                               lapack_int n, lapack_complex_double* a,\n                               lapack_int lda, double* w,\n                               lapack_complex_double* work, lapack_int lwork,\n                               double* rwork );\n\nlapack_int LAPACKE_cheevd_work( int matrix_order, char jobz, char uplo,\n                                lapack_int n, lapack_complex_float* a,\n                                lapack_int lda, float* w,\n                                lapack_complex_float* work, lapack_int lwork,\n                                float* rwork, lapack_int lrwork,\n                                lapack_int* iwork, lapack_int liwork );\nlapack_int LAPACKE_zheevd_work( int matrix_order, char jobz, char uplo,\n                                lapack_int n, lapack_complex_double* a,\n                                lapack_int lda, double* w,\n                                lapack_complex_double* work, lapack_int lwork,\n                                double* rwork, lapack_int lrwork,\n                                lapack_int* iwork, lapack_int liwork );\n\nlapack_int LAPACKE_cheevr_work( int matrix_order, char jobz, char range,\n                                char uplo, lapack_int n,\n                                lapack_complex_float* a, lapack_int lda,\n                                float vl, float vu, lapack_int il,\n                                lapack_int iu, float abstol, lapack_int* m,\n                                float* w, lapack_complex_float* z,\n                                lapack_int ldz, lapack_int* isuppz,\n                                lapack_complex_float* work, lapack_int lwork,\n                                float* rwork, lapack_int lrwork,\n                                lapack_int* iwork, lapack_int liwork );\nlapack_int LAPACKE_zheevr_work( int matrix_order, char jobz, char range,\n                                char uplo, lapack_int n,\n                                lapack_complex_double* a, lapack_int lda,\n                                double vl, double vu, lapack_int il,\n                                lapack_int iu, double abstol, lapack_int* m,\n                                double* w, lapack_complex_double* z,\n                                lapack_int ldz, lapack_int* isuppz,\n                                lapack_complex_double* work, lapack_int lwork,\n                                double* rwork, lapack_int lrwork,\n                                lapack_int* iwork, lapack_int liwork );\n\nlapack_int LAPACKE_cheevx_work( int matrix_order, char jobz, char range,\n                                char uplo, lapack_int n,\n                                lapack_complex_float* a, lapack_int lda,\n                                float vl, float vu, lapack_int il,\n                                lapack_int iu, float abstol, lapack_int* m,\n                                float* w, lapack_complex_float* z,\n                                lapack_int ldz, lapack_complex_float* work,\n                                lapack_int lwork, float* rwork,\n                                lapack_int* iwork, lapack_int* ifail );\nlapack_int LAPACKE_zheevx_work( int matrix_order, char jobz, char range,\n                                char uplo, lapack_int n,\n                                lapack_complex_double* a, lapack_int lda,\n                                double vl, double vu, lapack_int il,\n                                lapack_int iu, double abstol, lapack_int* m,\n                                double* w, lapack_complex_double* z,\n                                lapack_int ldz, lapack_complex_double* work,\n                                lapack_int lwork, double* rwork,\n                                lapack_int* iwork, lapack_int* ifail );\n\nlapack_int LAPACKE_chegst_work( int matrix_order, lapack_int itype, char uplo,\n                                lapack_int n, lapack_complex_float* a,\n                                lapack_int lda, const lapack_complex_float* b,\n                                lapack_int ldb );\nlapack_int LAPACKE_zhegst_work( int matrix_order, lapack_int itype, char uplo,\n                                lapack_int n, lapack_complex_double* a,\n                                lapack_int lda, const lapack_complex_double* b,\n                                lapack_int ldb );\n\nlapack_int LAPACKE_chegv_work( int matrix_order, lapack_int itype, char jobz,\n                               char uplo, lapack_int n, lapack_complex_float* a,\n                               lapack_int lda, lapack_complex_float* b,\n                               lapack_int ldb, float* w,\n                               lapack_complex_float* work, lapack_int lwork,\n                               float* rwork );\nlapack_int LAPACKE_zhegv_work( int matrix_order, lapack_int itype, char jobz,\n                               char uplo, lapack_int n,\n                               lapack_complex_double* a, lapack_int lda,\n                               lapack_complex_double* b, lapack_int ldb,\n                               double* w, lapack_complex_double* work,\n                               lapack_int lwork, double* rwork );\n\nlapack_int LAPACKE_chegvd_work( int matrix_order, lapack_int itype, char jobz,\n                                char uplo, lapack_int n,\n                                lapack_complex_float* a, lapack_int lda,\n                                lapack_complex_float* b, lapack_int ldb,\n                                float* w, lapack_complex_float* work,\n                                lapack_int lwork, float* rwork,\n                                lapack_int lrwork, lapack_int* iwork,\n                                lapack_int liwork );\nlapack_int LAPACKE_zhegvd_work( int matrix_order, lapack_int itype, char jobz,\n                                char uplo, lapack_int n,\n                                lapack_complex_double* a, lapack_int lda,\n                                lapack_complex_double* b, lapack_int ldb,\n                                double* w, lapack_complex_double* work,\n                                lapack_int lwork, double* rwork,\n                                lapack_int lrwork, lapack_int* iwork,\n                                lapack_int liwork );\n\nlapack_int LAPACKE_chegvx_work( int matrix_order, lapack_int itype, char jobz,\n                                char range, char uplo, lapack_int n,\n                                lapack_complex_float* a, lapack_int lda,\n                                lapack_complex_float* b, lapack_int ldb,\n                                float vl, float vu, lapack_int il,\n                                lapack_int iu, float abstol, lapack_int* m,\n                                float* w, lapack_complex_float* z,\n                                lapack_int ldz, lapack_complex_float* work,\n                                lapack_int lwork, float* rwork,\n                                lapack_int* iwork, lapack_int* ifail );\nlapack_int LAPACKE_zhegvx_work( int matrix_order, lapack_int itype, char jobz,\n                                char range, char uplo, lapack_int n,\n                                lapack_complex_double* a, lapack_int lda,\n                                lapack_complex_double* b, lapack_int ldb,\n                                double vl, double vu, lapack_int il,\n                                lapack_int iu, double abstol, lapack_int* m,\n                                double* w, lapack_complex_double* z,\n                                lapack_int ldz, lapack_complex_double* work,\n                                lapack_int lwork, double* rwork,\n                                lapack_int* iwork, lapack_int* ifail );\n\nlapack_int LAPACKE_cherfs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const lapack_complex_float* a,\n                                lapack_int lda, const lapack_complex_float* af,\n                                lapack_int ldaf, const lapack_int* ipiv,\n                                const lapack_complex_float* b, lapack_int ldb,\n                                lapack_complex_float* x, lapack_int ldx,\n                                float* ferr, float* berr,\n                                lapack_complex_float* work, float* rwork );\nlapack_int LAPACKE_zherfs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const lapack_complex_double* a,\n                                lapack_int lda, const lapack_complex_double* af,\n                                lapack_int ldaf, const lapack_int* ipiv,\n                                const lapack_complex_double* b, lapack_int ldb,\n                                lapack_complex_double* x, lapack_int ldx,\n                                double* ferr, double* berr,\n                                lapack_complex_double* work, double* rwork );\n\nlapack_int LAPACKE_cherfsx_work( int matrix_order, char uplo, char equed,\n                                 lapack_int n, lapack_int nrhs,\n                                 const lapack_complex_float* a, lapack_int lda,\n                                 const lapack_complex_float* af,\n                                 lapack_int ldaf, const lapack_int* ipiv,\n                                 const float* s, const lapack_complex_float* b,\n                                 lapack_int ldb, lapack_complex_float* x,\n                                 lapack_int ldx, float* rcond, float* berr,\n                                 lapack_int n_err_bnds, float* err_bnds_norm,\n                                 float* err_bnds_comp, lapack_int nparams,\n                                 float* params, lapack_complex_float* work,\n                                 float* rwork );\nlapack_int LAPACKE_zherfsx_work( int matrix_order, char uplo, char equed,\n                                 lapack_int n, lapack_int nrhs,\n                                 const lapack_complex_double* a, lapack_int lda,\n                                 const lapack_complex_double* af,\n                                 lapack_int ldaf, const lapack_int* ipiv,\n                                 const double* s,\n                                 const lapack_complex_double* b, lapack_int ldb,\n                                 lapack_complex_double* x, lapack_int ldx,\n                                 double* rcond, double* berr,\n                                 lapack_int n_err_bnds, double* err_bnds_norm,\n                                 double* err_bnds_comp, lapack_int nparams,\n                                 double* params, lapack_complex_double* work,\n                                 double* rwork );\n\nlapack_int LAPACKE_chesv_work( int matrix_order, char uplo, lapack_int n,\n                               lapack_int nrhs, lapack_complex_float* a,\n                               lapack_int lda, lapack_int* ipiv,\n                               lapack_complex_float* b, lapack_int ldb,\n                               lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_zhesv_work( int matrix_order, char uplo, lapack_int n,\n                               lapack_int nrhs, lapack_complex_double* a,\n                               lapack_int lda, lapack_int* ipiv,\n                               lapack_complex_double* b, lapack_int ldb,\n                               lapack_complex_double* work, lapack_int lwork );\n\nlapack_int LAPACKE_chesvx_work( int matrix_order, char fact, char uplo,\n                                lapack_int n, lapack_int nrhs,\n                                const lapack_complex_float* a, lapack_int lda,\n                                lapack_complex_float* af, lapack_int ldaf,\n                                lapack_int* ipiv, const lapack_complex_float* b,\n                                lapack_int ldb, lapack_complex_float* x,\n                                lapack_int ldx, float* rcond, float* ferr,\n                                float* berr, lapack_complex_float* work,\n                                lapack_int lwork, float* rwork );\nlapack_int LAPACKE_zhesvx_work( int matrix_order, char fact, char uplo,\n                                lapack_int n, lapack_int nrhs,\n                                const lapack_complex_double* a, lapack_int lda,\n                                lapack_complex_double* af, lapack_int ldaf,\n                                lapack_int* ipiv,\n                                const lapack_complex_double* b, lapack_int ldb,\n                                lapack_complex_double* x, lapack_int ldx,\n                                double* rcond, double* ferr, double* berr,\n                                lapack_complex_double* work, lapack_int lwork,\n                                double* rwork );\n\nlapack_int LAPACKE_chesvxx_work( int matrix_order, char fact, char uplo,\n                                 lapack_int n, lapack_int nrhs,\n                                 lapack_complex_float* a, lapack_int lda,\n                                 lapack_complex_float* af, lapack_int ldaf,\n                                 lapack_int* ipiv, char* equed, float* s,\n                                 lapack_complex_float* b, lapack_int ldb,\n                                 lapack_complex_float* x, lapack_int ldx,\n                                 float* rcond, float* rpvgrw, float* berr,\n                                 lapack_int n_err_bnds, float* err_bnds_norm,\n                                 float* err_bnds_comp, lapack_int nparams,\n                                 float* params, lapack_complex_float* work,\n                                 float* rwork );\nlapack_int LAPACKE_zhesvxx_work( int matrix_order, char fact, char uplo,\n                                 lapack_int n, lapack_int nrhs,\n                                 lapack_complex_double* a, lapack_int lda,\n                                 lapack_complex_double* af, lapack_int ldaf,\n                                 lapack_int* ipiv, char* equed, double* s,\n                                 lapack_complex_double* b, lapack_int ldb,\n                                 lapack_complex_double* x, lapack_int ldx,\n                                 double* rcond, double* rpvgrw, double* berr,\n                                 lapack_int n_err_bnds, double* err_bnds_norm,\n                                 double* err_bnds_comp, lapack_int nparams,\n                                 double* params, lapack_complex_double* work,\n                                 double* rwork );\n\nlapack_int LAPACKE_chetrd_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_complex_float* a, lapack_int lda,\n                                float* d, float* e, lapack_complex_float* tau,\n                                lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_zhetrd_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_complex_double* a, lapack_int lda,\n                                double* d, double* e,\n                                lapack_complex_double* tau,\n                                lapack_complex_double* work, lapack_int lwork );\n\nlapack_int LAPACKE_chetrf_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_complex_float* a, lapack_int lda,\n                                lapack_int* ipiv, lapack_complex_float* work,\n                                lapack_int lwork );\nlapack_int LAPACKE_zhetrf_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_complex_double* a, lapack_int lda,\n                                lapack_int* ipiv, lapack_complex_double* work,\n                                lapack_int lwork );\n\nlapack_int LAPACKE_chetri_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_complex_float* a, lapack_int lda,\n                                const lapack_int* ipiv,\n                                lapack_complex_float* work );\nlapack_int LAPACKE_zhetri_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_complex_double* a, lapack_int lda,\n                                const lapack_int* ipiv,\n                                lapack_complex_double* work );\n\nlapack_int LAPACKE_chetrs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const lapack_complex_float* a,\n                                lapack_int lda, const lapack_int* ipiv,\n                                lapack_complex_float* b, lapack_int ldb );\nlapack_int LAPACKE_zhetrs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const lapack_complex_double* a,\n                                lapack_int lda, const lapack_int* ipiv,\n                                lapack_complex_double* b, lapack_int ldb );\n\nlapack_int LAPACKE_chfrk_work( int matrix_order, char transr, char uplo,\n                               char trans, lapack_int n, lapack_int k,\n                               float alpha, const lapack_complex_float* a,\n                               lapack_int lda, float beta,\n                               lapack_complex_float* c );\nlapack_int LAPACKE_zhfrk_work( int matrix_order, char transr, char uplo,\n                               char trans, lapack_int n, lapack_int k,\n                               double alpha, const lapack_complex_double* a,\n                               lapack_int lda, double beta,\n                               lapack_complex_double* c );\n\nlapack_int LAPACKE_shgeqz_work( int matrix_order, char job, char compq,\n                                char compz, lapack_int n, lapack_int ilo,\n                                lapack_int ihi, float* h, lapack_int ldh,\n                                float* t, lapack_int ldt, float* alphar,\n                                float* alphai, float* beta, float* q,\n                                lapack_int ldq, float* z, lapack_int ldz,\n                                float* work, lapack_int lwork );\nlapack_int LAPACKE_dhgeqz_work( int matrix_order, char job, char compq,\n                                char compz, lapack_int n, lapack_int ilo,\n                                lapack_int ihi, double* h, lapack_int ldh,\n                                double* t, lapack_int ldt, double* alphar,\n                                double* alphai, double* beta, double* q,\n                                lapack_int ldq, double* z, lapack_int ldz,\n                                double* work, lapack_int lwork );\nlapack_int LAPACKE_chgeqz_work( int matrix_order, char job, char compq,\n                                char compz, lapack_int n, lapack_int ilo,\n                                lapack_int ihi, lapack_complex_float* h,\n                                lapack_int ldh, lapack_complex_float* t,\n                                lapack_int ldt, lapack_complex_float* alpha,\n                                lapack_complex_float* beta,\n                                lapack_complex_float* q, lapack_int ldq,\n                                lapack_complex_float* z, lapack_int ldz,\n                                lapack_complex_float* work, lapack_int lwork,\n                                float* rwork );\nlapack_int LAPACKE_zhgeqz_work( int matrix_order, char job, char compq,\n                                char compz, lapack_int n, lapack_int ilo,\n                                lapack_int ihi, lapack_complex_double* h,\n                                lapack_int ldh, lapack_complex_double* t,\n                                lapack_int ldt, lapack_complex_double* alpha,\n                                lapack_complex_double* beta,\n                                lapack_complex_double* q, lapack_int ldq,\n                                lapack_complex_double* z, lapack_int ldz,\n                                lapack_complex_double* work, lapack_int lwork,\n                                double* rwork );\n\nlapack_int LAPACKE_chpcon_work( int matrix_order, char uplo, lapack_int n,\n                                const lapack_complex_float* ap,\n                                const lapack_int* ipiv, float anorm,\n                                float* rcond, lapack_complex_float* work );\nlapack_int LAPACKE_zhpcon_work( int matrix_order, char uplo, lapack_int n,\n                                const lapack_complex_double* ap,\n                                const lapack_int* ipiv, double anorm,\n                                double* rcond, lapack_complex_double* work );\n\nlapack_int LAPACKE_chpev_work( int matrix_order, char jobz, char uplo,\n                               lapack_int n, lapack_complex_float* ap, float* w,\n                               lapack_complex_float* z, lapack_int ldz,\n                               lapack_complex_float* work, float* rwork );\nlapack_int LAPACKE_zhpev_work( int matrix_order, char jobz, char uplo,\n                               lapack_int n, lapack_complex_double* ap,\n                               double* w, lapack_complex_double* z,\n                               lapack_int ldz, lapack_complex_double* work,\n                               double* rwork );\n\nlapack_int LAPACKE_chpevd_work( int matrix_order, char jobz, char uplo,\n                                lapack_int n, lapack_complex_float* ap,\n                                float* w, lapack_complex_float* z,\n                                lapack_int ldz, lapack_complex_float* work,\n                                lapack_int lwork, float* rwork,\n                                lapack_int lrwork, lapack_int* iwork,\n                                lapack_int liwork );\nlapack_int LAPACKE_zhpevd_work( int matrix_order, char jobz, char uplo,\n                                lapack_int n, lapack_complex_double* ap,\n                                double* w, lapack_complex_double* z,\n                                lapack_int ldz, lapack_complex_double* work,\n                                lapack_int lwork, double* rwork,\n                                lapack_int lrwork, lapack_int* iwork,\n                                lapack_int liwork );\n\nlapack_int LAPACKE_chpevx_work( int matrix_order, char jobz, char range,\n                                char uplo, lapack_int n,\n                                lapack_complex_float* ap, float vl, float vu,\n                                lapack_int il, lapack_int iu, float abstol,\n                                lapack_int* m, float* w,\n                                lapack_complex_float* z, lapack_int ldz,\n                                lapack_complex_float* work, float* rwork,\n                                lapack_int* iwork, lapack_int* ifail );\nlapack_int LAPACKE_zhpevx_work( int matrix_order, char jobz, char range,\n                                char uplo, lapack_int n,\n                                lapack_complex_double* ap, double vl, double vu,\n                                lapack_int il, lapack_int iu, double abstol,\n                                lapack_int* m, double* w,\n                                lapack_complex_double* z, lapack_int ldz,\n                                lapack_complex_double* work, double* rwork,\n                                lapack_int* iwork, lapack_int* ifail );\n\nlapack_int LAPACKE_chpgst_work( int matrix_order, lapack_int itype, char uplo,\n                                lapack_int n, lapack_complex_float* ap,\n                                const lapack_complex_float* bp );\nlapack_int LAPACKE_zhpgst_work( int matrix_order, lapack_int itype, char uplo,\n                                lapack_int n, lapack_complex_double* ap,\n                                const lapack_complex_double* bp );\n\nlapack_int LAPACKE_chpgv_work( int matrix_order, lapack_int itype, char jobz,\n                               char uplo, lapack_int n,\n                               lapack_complex_float* ap,\n                               lapack_complex_float* bp, float* w,\n                               lapack_complex_float* z, lapack_int ldz,\n                               lapack_complex_float* work, float* rwork );\nlapack_int LAPACKE_zhpgv_work( int matrix_order, lapack_int itype, char jobz,\n                               char uplo, lapack_int n,\n                               lapack_complex_double* ap,\n                               lapack_complex_double* bp, double* w,\n                               lapack_complex_double* z, lapack_int ldz,\n                               lapack_complex_double* work, double* rwork );\n\nlapack_int LAPACKE_chpgvd_work( int matrix_order, lapack_int itype, char jobz,\n                                char uplo, lapack_int n,\n                                lapack_complex_float* ap,\n                                lapack_complex_float* bp, float* w,\n                                lapack_complex_float* z, lapack_int ldz,\n                                lapack_complex_float* work, lapack_int lwork,\n                                float* rwork, lapack_int lrwork,\n                                lapack_int* iwork, lapack_int liwork );\nlapack_int LAPACKE_zhpgvd_work( int matrix_order, lapack_int itype, char jobz,\n                                char uplo, lapack_int n,\n                                lapack_complex_double* ap,\n                                lapack_complex_double* bp, double* w,\n                                lapack_complex_double* z, lapack_int ldz,\n                                lapack_complex_double* work, lapack_int lwork,\n                                double* rwork, lapack_int lrwork,\n                                lapack_int* iwork, lapack_int liwork );\n\nlapack_int LAPACKE_chpgvx_work( int matrix_order, lapack_int itype, char jobz,\n                                char range, char uplo, lapack_int n,\n                                lapack_complex_float* ap,\n                                lapack_complex_float* bp, float vl, float vu,\n                                lapack_int il, lapack_int iu, float abstol,\n                                lapack_int* m, float* w,\n                                lapack_complex_float* z, lapack_int ldz,\n                                lapack_complex_float* work, float* rwork,\n                                lapack_int* iwork, lapack_int* ifail );\nlapack_int LAPACKE_zhpgvx_work( int matrix_order, lapack_int itype, char jobz,\n                                char range, char uplo, lapack_int n,\n                                lapack_complex_double* ap,\n                                lapack_complex_double* bp, double vl, double vu,\n                                lapack_int il, lapack_int iu, double abstol,\n                                lapack_int* m, double* w,\n                                lapack_complex_double* z, lapack_int ldz,\n                                lapack_complex_double* work, double* rwork,\n                                lapack_int* iwork, lapack_int* ifail );\n\nlapack_int LAPACKE_chprfs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const lapack_complex_float* ap,\n                                const lapack_complex_float* afp,\n                                const lapack_int* ipiv,\n                                const lapack_complex_float* b, lapack_int ldb,\n                                lapack_complex_float* x, lapack_int ldx,\n                                float* ferr, float* berr,\n                                lapack_complex_float* work, float* rwork );\nlapack_int LAPACKE_zhprfs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs,\n                                const lapack_complex_double* ap,\n                                const lapack_complex_double* afp,\n                                const lapack_int* ipiv,\n                                const lapack_complex_double* b, lapack_int ldb,\n                                lapack_complex_double* x, lapack_int ldx,\n                                double* ferr, double* berr,\n                                lapack_complex_double* work, double* rwork );\n\nlapack_int LAPACKE_chpsv_work( int matrix_order, char uplo, lapack_int n,\n                               lapack_int nrhs, lapack_complex_float* ap,\n                               lapack_int* ipiv, lapack_complex_float* b,\n                               lapack_int ldb );\nlapack_int LAPACKE_zhpsv_work( int matrix_order, char uplo, lapack_int n,\n                               lapack_int nrhs, lapack_complex_double* ap,\n                               lapack_int* ipiv, lapack_complex_double* b,\n                               lapack_int ldb );\n\nlapack_int LAPACKE_chpsvx_work( int matrix_order, char fact, char uplo,\n                                lapack_int n, lapack_int nrhs,\n                                const lapack_complex_float* ap,\n                                lapack_complex_float* afp, lapack_int* ipiv,\n                                const lapack_complex_float* b, lapack_int ldb,\n                                lapack_complex_float* x, lapack_int ldx,\n                                float* rcond, float* ferr, float* berr,\n                                lapack_complex_float* work, float* rwork );\nlapack_int LAPACKE_zhpsvx_work( int matrix_order, char fact, char uplo,\n                                lapack_int n, lapack_int nrhs,\n                                const lapack_complex_double* ap,\n                                lapack_complex_double* afp, lapack_int* ipiv,\n                                const lapack_complex_double* b, lapack_int ldb,\n                                lapack_complex_double* x, lapack_int ldx,\n                                double* rcond, double* ferr, double* berr,\n                                lapack_complex_double* work, double* rwork );\n\nlapack_int LAPACKE_chptrd_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_complex_float* ap, float* d, float* e,\n                                lapack_complex_float* tau );\nlapack_int LAPACKE_zhptrd_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_complex_double* ap, double* d, double* e,\n                                lapack_complex_double* tau );\n\nlapack_int LAPACKE_chptrf_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_complex_float* ap, lapack_int* ipiv );\nlapack_int LAPACKE_zhptrf_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_complex_double* ap, lapack_int* ipiv );\n\nlapack_int LAPACKE_chptri_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_complex_float* ap,\n                                const lapack_int* ipiv,\n                                lapack_complex_float* work );\nlapack_int LAPACKE_zhptri_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_complex_double* ap,\n                                const lapack_int* ipiv,\n                                lapack_complex_double* work );\n\nlapack_int LAPACKE_chptrs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const lapack_complex_float* ap,\n                                const lapack_int* ipiv, lapack_complex_float* b,\n                                lapack_int ldb );\nlapack_int LAPACKE_zhptrs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs,\n                                const lapack_complex_double* ap,\n                                const lapack_int* ipiv,\n                                lapack_complex_double* b, lapack_int ldb );\n\nlapack_int LAPACKE_shsein_work( int matrix_order, char job, char eigsrc,\n                                char initv, lapack_logical* select,\n                                lapack_int n, const float* h, lapack_int ldh,\n                                float* wr, const float* wi, float* vl,\n                                lapack_int ldvl, float* vr, lapack_int ldvr,\n                                lapack_int mm, lapack_int* m, float* work,\n                                lapack_int* ifaill, lapack_int* ifailr );\nlapack_int LAPACKE_dhsein_work( int matrix_order, char job, char eigsrc,\n                                char initv, lapack_logical* select,\n                                lapack_int n, const double* h, lapack_int ldh,\n                                double* wr, const double* wi, double* vl,\n                                lapack_int ldvl, double* vr, lapack_int ldvr,\n                                lapack_int mm, lapack_int* m, double* work,\n                                lapack_int* ifaill, lapack_int* ifailr );\nlapack_int LAPACKE_chsein_work( int matrix_order, char job, char eigsrc,\n                                char initv, const lapack_logical* select,\n                                lapack_int n, const lapack_complex_float* h,\n                                lapack_int ldh, lapack_complex_float* w,\n                                lapack_complex_float* vl, lapack_int ldvl,\n                                lapack_complex_float* vr, lapack_int ldvr,\n                                lapack_int mm, lapack_int* m,\n                                lapack_complex_float* work, float* rwork,\n                                lapack_int* ifaill, lapack_int* ifailr );\nlapack_int LAPACKE_zhsein_work( int matrix_order, char job, char eigsrc,\n                                char initv, const lapack_logical* select,\n                                lapack_int n, const lapack_complex_double* h,\n                                lapack_int ldh, lapack_complex_double* w,\n                                lapack_complex_double* vl, lapack_int ldvl,\n                                lapack_complex_double* vr, lapack_int ldvr,\n                                lapack_int mm, lapack_int* m,\n                                lapack_complex_double* work, double* rwork,\n                                lapack_int* ifaill, lapack_int* ifailr );\n\nlapack_int LAPACKE_shseqr_work( int matrix_order, char job, char compz,\n                                lapack_int n, lapack_int ilo, lapack_int ihi,\n                                float* h, lapack_int ldh, float* wr, float* wi,\n                                float* z, lapack_int ldz, float* work,\n                                lapack_int lwork );\nlapack_int LAPACKE_dhseqr_work( int matrix_order, char job, char compz,\n                                lapack_int n, lapack_int ilo, lapack_int ihi,\n                                double* h, lapack_int ldh, double* wr,\n                                double* wi, double* z, lapack_int ldz,\n                                double* work, lapack_int lwork );\nlapack_int LAPACKE_chseqr_work( int matrix_order, char job, char compz,\n                                lapack_int n, lapack_int ilo, lapack_int ihi,\n                                lapack_complex_float* h, lapack_int ldh,\n                                lapack_complex_float* w,\n                                lapack_complex_float* z, lapack_int ldz,\n                                lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_zhseqr_work( int matrix_order, char job, char compz,\n                                lapack_int n, lapack_int ilo, lapack_int ihi,\n                                lapack_complex_double* h, lapack_int ldh,\n                                lapack_complex_double* w,\n                                lapack_complex_double* z, lapack_int ldz,\n                                lapack_complex_double* work, lapack_int lwork );\n\nlapack_int LAPACKE_clacgv_work( lapack_int n, lapack_complex_float* x,\n                                lapack_int incx );\nlapack_int LAPACKE_zlacgv_work( lapack_int n, lapack_complex_double* x,\n                                lapack_int incx );\n\nlapack_int LAPACKE_slacpy_work( int matrix_order, char uplo, lapack_int m,\n                                lapack_int n, const float* a, lapack_int lda,\n                                float* b, lapack_int ldb );\nlapack_int LAPACKE_dlacpy_work( int matrix_order, char uplo, lapack_int m,\n                                lapack_int n, const double* a, lapack_int lda,\n                                double* b, lapack_int ldb );\nlapack_int LAPACKE_clacpy_work( int matrix_order, char uplo, lapack_int m,\n                                lapack_int n, const lapack_complex_float* a,\n                                lapack_int lda, lapack_complex_float* b,\n                                lapack_int ldb );\nlapack_int LAPACKE_zlacpy_work( int matrix_order, char uplo, lapack_int m,\n                                lapack_int n, const lapack_complex_double* a,\n                                lapack_int lda, lapack_complex_double* b,\n                                lapack_int ldb );\n\nlapack_int LAPACKE_zlag2c_work( int matrix_order, lapack_int m, lapack_int n,\n                                const lapack_complex_double* a, lapack_int lda,\n                                lapack_complex_float* sa, lapack_int ldsa );\n\nlapack_int LAPACKE_slag2d_work( int matrix_order, lapack_int m, lapack_int n,\n                                const float* sa, lapack_int ldsa, double* a,\n                                lapack_int lda );\n\nlapack_int LAPACKE_dlag2s_work( int matrix_order, lapack_int m, lapack_int n,\n                                const double* a, lapack_int lda, float* sa,\n                                lapack_int ldsa );\n\nlapack_int LAPACKE_clag2z_work( int matrix_order, lapack_int m, lapack_int n,\n                                const lapack_complex_float* sa, lapack_int ldsa,\n                                lapack_complex_double* a, lapack_int lda );\n\nlapack_int LAPACKE_slagge_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int kl, lapack_int ku, const float* d,\n                                float* a, lapack_int lda, lapack_int* iseed,\n                                float* work );\nlapack_int LAPACKE_dlagge_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int kl, lapack_int ku, const double* d,\n                                double* a, lapack_int lda, lapack_int* iseed,\n                                double* work );\nlapack_int LAPACKE_clagge_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int kl, lapack_int ku, const float* d,\n                                lapack_complex_float* a, lapack_int lda,\n                                lapack_int* iseed, lapack_complex_float* work );\nlapack_int LAPACKE_zlagge_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int kl, lapack_int ku, const double* d,\n                                lapack_complex_double* a, lapack_int lda,\n                                lapack_int* iseed,\n                                lapack_complex_double* work );\n                                \nlapack_int LAPACKE_claghe_work( int matrix_order, lapack_int n, lapack_int k,\n                                const float* d, lapack_complex_float* a,\n                                lapack_int lda, lapack_int* iseed,\n                                lapack_complex_float* work );\nlapack_int LAPACKE_zlaghe_work( int matrix_order, lapack_int n, lapack_int k,\n                                const double* d, lapack_complex_double* a,\n                                lapack_int lda, lapack_int* iseed,\n                                lapack_complex_double* work );\n\nlapack_int LAPACKE_slagsy_work( int matrix_order, lapack_int n, lapack_int k,\n                                const float* d, float* a, lapack_int lda,\n                                lapack_int* iseed, float* work );\nlapack_int LAPACKE_dlagsy_work( int matrix_order, lapack_int n, lapack_int k,\n                                const double* d, double* a, lapack_int lda,\n                                lapack_int* iseed, double* work );\nlapack_int LAPACKE_clagsy_work( int matrix_order, lapack_int n, lapack_int k,\n                                const float* d, lapack_complex_float* a,\n                                lapack_int lda, lapack_int* iseed,\n                                lapack_complex_float* work );\nlapack_int LAPACKE_zlagsy_work( int matrix_order, lapack_int n, lapack_int k,\n                                const double* d, lapack_complex_double* a,\n                                lapack_int lda, lapack_int* iseed,\n                                lapack_complex_double* work );\n\nlapack_int LAPACKE_slapmr_work( int matrix_order, lapack_logical forwrd,\n                                lapack_int m, lapack_int n, float* x,\n                                lapack_int ldx, lapack_int* k );\nlapack_int LAPACKE_dlapmr_work( int matrix_order, lapack_logical forwrd,\n                                lapack_int m, lapack_int n, double* x,\n                                lapack_int ldx, lapack_int* k );\nlapack_int LAPACKE_clapmr_work( int matrix_order, lapack_logical forwrd,\n                                lapack_int m, lapack_int n,\n                                lapack_complex_float* x, lapack_int ldx,\n                                lapack_int* k );\nlapack_int LAPACKE_zlapmr_work( int matrix_order, lapack_logical forwrd,\n                                lapack_int m, lapack_int n,\n                                lapack_complex_double* x, lapack_int ldx,\n                                lapack_int* k );\n\nlapack_int LAPACKE_slartgp_work( float f, float g, float* cs, float* sn,\n                                 float* r );\nlapack_int LAPACKE_dlartgp_work( double f, double g, double* cs, double* sn,\n                                 double* r );\n\nlapack_int LAPACKE_slartgs_work( float x, float y, float sigma, float* cs,\n                                 float* sn );\nlapack_int LAPACKE_dlartgs_work( double x, double y, double sigma, double* cs,\n                                 double* sn );\n                                \nfloat LAPACKE_slapy2_work( float x, float y );\ndouble LAPACKE_dlapy2_work( double x, double y );\n\nfloat LAPACKE_slapy3_work( float x, float y, float z );\ndouble LAPACKE_dlapy3_work( double x, double y, double z );\n\nfloat LAPACKE_slamch_work( char cmach );\ndouble LAPACKE_dlamch_work( char cmach );\n\nfloat LAPACKE_slange_work( int matrix_order, char norm, lapack_int m,\n                                lapack_int n, const float* a, lapack_int lda,\n                                float* work );\ndouble LAPACKE_dlange_work( int matrix_order, char norm, lapack_int m,\n                                lapack_int n, const double* a, lapack_int lda,\n                                double* work );\nfloat LAPACKE_clange_work( int matrix_order, char norm, lapack_int m,\n                                lapack_int n, const lapack_complex_float* a,\n                                lapack_int lda, float* work );\ndouble LAPACKE_zlange_work( int matrix_order, char norm, lapack_int m,\n                                lapack_int n, const lapack_complex_double* a,\n                                lapack_int lda, double* work );\n\nfloat LAPACKE_clanhe_work( int matrix_order, char norm, char uplo,\n                                lapack_int n, const lapack_complex_float* a,\n                                lapack_int lda, float* work );\ndouble LAPACKE_zlanhe_work( int matrix_order, char norm, char uplo,\n                                lapack_int n, const lapack_complex_double* a,\n                                lapack_int lda, double* work );\n\nfloat LAPACKE_slansy_work( int matrix_order, char norm, char uplo,\n                                lapack_int n, const float* a, lapack_int lda,\n                                float* work );\ndouble LAPACKE_dlansy_work( int matrix_order, char norm, char uplo,\n                                lapack_int n, const double* a, lapack_int lda,\n                                double* work );\nfloat LAPACKE_clansy_work( int matrix_order, char norm, char uplo,\n                                lapack_int n, const lapack_complex_float* a,\n                                lapack_int lda, float* work );\ndouble LAPACKE_zlansy_work( int matrix_order, char norm, char uplo,\n                                lapack_int n, const lapack_complex_double* a,\n                                lapack_int lda, double* work );\n\nfloat LAPACKE_slantr_work( int matrix_order, char norm, char uplo,\n                                char diag, lapack_int m, lapack_int n, const float* a,\n                                lapack_int lda, float* work );\ndouble LAPACKE_dlantr_work( int matrix_order, char norm, char uplo,\n                                char diag, lapack_int m, lapack_int n,\n                                const double* a, lapack_int lda, double* work );\nfloat LAPACKE_clantr_work( int matrix_order, char norm, char uplo,\n                                char diag, lapack_int m, lapack_int n,\n                                const lapack_complex_float* a, lapack_int lda,\n                                float* work );\ndouble LAPACKE_zlantr_work( int matrix_order, char norm, char uplo,\n                                char diag, lapack_int m, lapack_int n,\n                                const lapack_complex_double* a, lapack_int lda,\n                                double* work );\n\nlapack_int LAPACKE_slarfb_work( int matrix_order, char side, char trans,\n                                char direct, char storev, lapack_int m,\n                                lapack_int n, lapack_int k, const float* v,\n                                lapack_int ldv, const float* t, lapack_int ldt,\n                                float* c, lapack_int ldc, float* work,\n                                lapack_int ldwork );\nlapack_int LAPACKE_dlarfb_work( int matrix_order, char side, char trans,\n                                char direct, char storev, lapack_int m,\n                                lapack_int n, lapack_int k, const double* v,\n                                lapack_int ldv, const double* t, lapack_int ldt,\n                                double* c, lapack_int ldc, double* work,\n                                lapack_int ldwork );\nlapack_int LAPACKE_clarfb_work( int matrix_order, char side, char trans,\n                                char direct, char storev, lapack_int m,\n                                lapack_int n, lapack_int k,\n                                const lapack_complex_float* v, lapack_int ldv,\n                                const lapack_complex_float* t, lapack_int ldt,\n                                lapack_complex_float* c, lapack_int ldc,\n                                lapack_complex_float* work, lapack_int ldwork );\nlapack_int LAPACKE_zlarfb_work( int matrix_order, char side, char trans,\n                                char direct, char storev, lapack_int m,\n                                lapack_int n, lapack_int k,\n                                const lapack_complex_double* v, lapack_int ldv,\n                                const lapack_complex_double* t, lapack_int ldt,\n                                lapack_complex_double* c, lapack_int ldc,\n                                lapack_complex_double* work,\n                                lapack_int ldwork );\n\nlapack_int LAPACKE_slarfg_work( lapack_int n, float* alpha, float* x,\n                                lapack_int incx, float* tau );\nlapack_int LAPACKE_dlarfg_work( lapack_int n, double* alpha, double* x,\n                                lapack_int incx, double* tau );\nlapack_int LAPACKE_clarfg_work( lapack_int n, lapack_complex_float* alpha,\n                                lapack_complex_float* x, lapack_int incx,\n                                lapack_complex_float* tau );\nlapack_int LAPACKE_zlarfg_work( lapack_int n, lapack_complex_double* alpha,\n                                lapack_complex_double* x, lapack_int incx,\n                                lapack_complex_double* tau );\n\nlapack_int LAPACKE_slarft_work( int matrix_order, char direct, char storev,\n                                lapack_int n, lapack_int k, const float* v,\n                                lapack_int ldv, const float* tau, float* t,\n                                lapack_int ldt );\nlapack_int LAPACKE_dlarft_work( int matrix_order, char direct, char storev,\n                                lapack_int n, lapack_int k, const double* v,\n                                lapack_int ldv, const double* tau, double* t,\n                                lapack_int ldt );\nlapack_int LAPACKE_clarft_work( int matrix_order, char direct, char storev,\n                                lapack_int n, lapack_int k,\n                                const lapack_complex_float* v, lapack_int ldv,\n                                const lapack_complex_float* tau,\n                                lapack_complex_float* t, lapack_int ldt );\nlapack_int LAPACKE_zlarft_work( int matrix_order, char direct, char storev,\n                                lapack_int n, lapack_int k,\n                                const lapack_complex_double* v, lapack_int ldv,\n                                const lapack_complex_double* tau,\n                                lapack_complex_double* t, lapack_int ldt );\n\nlapack_int LAPACKE_slarfx_work( int matrix_order, char side, lapack_int m,\n                                lapack_int n, const float* v, float tau,\n                                float* c, lapack_int ldc, float* work );\nlapack_int LAPACKE_dlarfx_work( int matrix_order, char side, lapack_int m,\n                                lapack_int n, const double* v, double tau,\n                                double* c, lapack_int ldc, double* work );\nlapack_int LAPACKE_clarfx_work( int matrix_order, char side, lapack_int m,\n                                lapack_int n, const lapack_complex_float* v,\n                                lapack_complex_float tau,\n                                lapack_complex_float* c, lapack_int ldc,\n                                lapack_complex_float* work );\nlapack_int LAPACKE_zlarfx_work( int matrix_order, char side, lapack_int m,\n                                lapack_int n, const lapack_complex_double* v,\n                                lapack_complex_double tau,\n                                lapack_complex_double* c, lapack_int ldc,\n                                lapack_complex_double* work );\n\nlapack_int LAPACKE_slarnv_work( lapack_int idist, lapack_int* iseed,\n                                lapack_int n, float* x );\nlapack_int LAPACKE_dlarnv_work( lapack_int idist, lapack_int* iseed,\n                                lapack_int n, double* x );\nlapack_int LAPACKE_clarnv_work( lapack_int idist, lapack_int* iseed,\n                                lapack_int n, lapack_complex_float* x );\nlapack_int LAPACKE_zlarnv_work( lapack_int idist, lapack_int* iseed,\n                                lapack_int n, lapack_complex_double* x );\n\nlapack_int LAPACKE_slaset_work( int matrix_order, char uplo, lapack_int m,\n                                lapack_int n, float alpha, float beta, float* a,\n                                lapack_int lda );\nlapack_int LAPACKE_dlaset_work( int matrix_order, char uplo, lapack_int m,\n                                lapack_int n, double alpha, double beta,\n                                double* a, lapack_int lda );\nlapack_int LAPACKE_claset_work( int matrix_order, char uplo, lapack_int m,\n                                lapack_int n, lapack_complex_float alpha,\n                                lapack_complex_float beta,\n                                lapack_complex_float* a, lapack_int lda );\nlapack_int LAPACKE_zlaset_work( int matrix_order, char uplo, lapack_int m,\n                                lapack_int n, lapack_complex_double alpha,\n                                lapack_complex_double beta,\n                                lapack_complex_double* a, lapack_int lda );\n\nlapack_int LAPACKE_slasrt_work( char id, lapack_int n, float* d );\nlapack_int LAPACKE_dlasrt_work( char id, lapack_int n, double* d );\n\nlapack_int LAPACKE_slaswp_work( int matrix_order, lapack_int n, float* a,\n                                lapack_int lda, lapack_int k1, lapack_int k2,\n                                const lapack_int* ipiv, lapack_int incx );\nlapack_int LAPACKE_dlaswp_work( int matrix_order, lapack_int n, double* a,\n                                lapack_int lda, lapack_int k1, lapack_int k2,\n                                const lapack_int* ipiv, lapack_int incx );\nlapack_int LAPACKE_claswp_work( int matrix_order, lapack_int n,\n                                lapack_complex_float* a, lapack_int lda,\n                                lapack_int k1, lapack_int k2,\n                                const lapack_int* ipiv, lapack_int incx );\nlapack_int LAPACKE_zlaswp_work( int matrix_order, lapack_int n,\n                                lapack_complex_double* a, lapack_int lda,\n                                lapack_int k1, lapack_int k2,\n                                const lapack_int* ipiv, lapack_int incx );\n\nlapack_int LAPACKE_slatms_work( int matrix_order, lapack_int m, lapack_int n,\n                                char dist, lapack_int* iseed, char sym,\n                                float* d, lapack_int mode, float cond,\n                                float dmax, lapack_int kl, lapack_int ku,\n                                char pack, float* a, lapack_int lda,\n                                float* work );\nlapack_int LAPACKE_dlatms_work( int matrix_order, lapack_int m, lapack_int n,\n                                char dist, lapack_int* iseed, char sym,\n                                double* d, lapack_int mode, double cond,\n                                double dmax, lapack_int kl, lapack_int ku,\n                                char pack, double* a, lapack_int lda,\n                                double* work );\nlapack_int LAPACKE_clatms_work( int matrix_order, lapack_int m, lapack_int n,\n                                char dist, lapack_int* iseed, char sym,\n                                float* d, lapack_int mode, float cond,\n                                float dmax, lapack_int kl, lapack_int ku,\n                                char pack, lapack_complex_float* a,\n                                lapack_int lda, lapack_complex_float* work );\nlapack_int LAPACKE_zlatms_work( int matrix_order, lapack_int m, lapack_int n,\n                                char dist, lapack_int* iseed, char sym,\n                                double* d, lapack_int mode, double cond,\n                                double dmax, lapack_int kl, lapack_int ku,\n                                char pack, lapack_complex_double* a,\n                                lapack_int lda, lapack_complex_double* work );\n\nlapack_int LAPACKE_slauum_work( int matrix_order, char uplo, lapack_int n,\n                                float* a, lapack_int lda );\nlapack_int LAPACKE_dlauum_work( int matrix_order, char uplo, lapack_int n,\n                                double* a, lapack_int lda );\nlapack_int LAPACKE_clauum_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_complex_float* a, lapack_int lda );\nlapack_int LAPACKE_zlauum_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_complex_double* a, lapack_int lda );\n\nlapack_int LAPACKE_sopgtr_work( int matrix_order, char uplo, lapack_int n,\n                                const float* ap, const float* tau, float* q,\n                                lapack_int ldq, float* work );\nlapack_int LAPACKE_dopgtr_work( int matrix_order, char uplo, lapack_int n,\n                                const double* ap, const double* tau, double* q,\n                                lapack_int ldq, double* work );\n\nlapack_int LAPACKE_sopmtr_work( int matrix_order, char side, char uplo,\n                                char trans, lapack_int m, lapack_int n,\n                                const float* ap, const float* tau, float* c,\n                                lapack_int ldc, float* work );\nlapack_int LAPACKE_dopmtr_work( int matrix_order, char side, char uplo,\n                                char trans, lapack_int m, lapack_int n,\n                                const double* ap, const double* tau, double* c,\n                                lapack_int ldc, double* work );\n\nlapack_int LAPACKE_sorgbr_work( int matrix_order, char vect, lapack_int m,\n                                lapack_int n, lapack_int k, float* a,\n                                lapack_int lda, const float* tau, float* work,\n                                lapack_int lwork );\nlapack_int LAPACKE_dorgbr_work( int matrix_order, char vect, lapack_int m,\n                                lapack_int n, lapack_int k, double* a,\n                                lapack_int lda, const double* tau, double* work,\n                                lapack_int lwork );\n\nlapack_int LAPACKE_sorghr_work( int matrix_order, lapack_int n, lapack_int ilo,\n                                lapack_int ihi, float* a, lapack_int lda,\n                                const float* tau, float* work,\n                                lapack_int lwork );\nlapack_int LAPACKE_dorghr_work( int matrix_order, lapack_int n, lapack_int ilo,\n                                lapack_int ihi, double* a, lapack_int lda,\n                                const double* tau, double* work,\n                                lapack_int lwork );\n\nlapack_int LAPACKE_sorglq_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int k, float* a, lapack_int lda,\n                                const float* tau, float* work,\n                                lapack_int lwork );\nlapack_int LAPACKE_dorglq_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int k, double* a, lapack_int lda,\n                                const double* tau, double* work,\n                                lapack_int lwork );\n\nlapack_int LAPACKE_sorgql_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int k, float* a, lapack_int lda,\n                                const float* tau, float* work,\n                                lapack_int lwork );\nlapack_int LAPACKE_dorgql_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int k, double* a, lapack_int lda,\n                                const double* tau, double* work,\n                                lapack_int lwork );\n\nlapack_int LAPACKE_sorgqr_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int k, float* a, lapack_int lda,\n                                const float* tau, float* work,\n                                lapack_int lwork );\nlapack_int LAPACKE_dorgqr_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int k, double* a, lapack_int lda,\n                                const double* tau, double* work,\n                                lapack_int lwork );\n\nlapack_int LAPACKE_sorgrq_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int k, float* a, lapack_int lda,\n                                const float* tau, float* work,\n                                lapack_int lwork );\nlapack_int LAPACKE_dorgrq_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int k, double* a, lapack_int lda,\n                                const double* tau, double* work,\n                                lapack_int lwork );\n\nlapack_int LAPACKE_sorgtr_work( int matrix_order, char uplo, lapack_int n,\n                                float* a, lapack_int lda, const float* tau,\n                                float* work, lapack_int lwork );\nlapack_int LAPACKE_dorgtr_work( int matrix_order, char uplo, lapack_int n,\n                                double* a, lapack_int lda, const double* tau,\n                                double* work, lapack_int lwork );\n\nlapack_int LAPACKE_sormbr_work( int matrix_order, char vect, char side,\n                                char trans, lapack_int m, lapack_int n,\n                                lapack_int k, const float* a, lapack_int lda,\n                                const float* tau, float* c, lapack_int ldc,\n                                float* work, lapack_int lwork );\nlapack_int LAPACKE_dormbr_work( int matrix_order, char vect, char side,\n                                char trans, lapack_int m, lapack_int n,\n                                lapack_int k, const double* a, lapack_int lda,\n                                const double* tau, double* c, lapack_int ldc,\n                                double* work, lapack_int lwork );\n\nlapack_int LAPACKE_sormhr_work( int matrix_order, char side, char trans,\n                                lapack_int m, lapack_int n, lapack_int ilo,\n                                lapack_int ihi, const float* a, lapack_int lda,\n                                const float* tau, float* c, lapack_int ldc,\n                                float* work, lapack_int lwork );\nlapack_int LAPACKE_dormhr_work( int matrix_order, char side, char trans,\n                                lapack_int m, lapack_int n, lapack_int ilo,\n                                lapack_int ihi, const double* a, lapack_int lda,\n                                const double* tau, double* c, lapack_int ldc,\n                                double* work, lapack_int lwork );\n\nlapack_int LAPACKE_sormlq_work( int matrix_order, char side, char trans,\n                                lapack_int m, lapack_int n, lapack_int k,\n                                const float* a, lapack_int lda,\n                                const float* tau, float* c, lapack_int ldc,\n                                float* work, lapack_int lwork );\nlapack_int LAPACKE_dormlq_work( int matrix_order, char side, char trans,\n                                lapack_int m, lapack_int n, lapack_int k,\n                                const double* a, lapack_int lda,\n                                const double* tau, double* c, lapack_int ldc,\n                                double* work, lapack_int lwork );\n\nlapack_int LAPACKE_sormql_work( int matrix_order, char side, char trans,\n                                lapack_int m, lapack_int n, lapack_int k,\n                                const float* a, lapack_int lda,\n                                const float* tau, float* c, lapack_int ldc,\n                                float* work, lapack_int lwork );\nlapack_int LAPACKE_dormql_work( int matrix_order, char side, char trans,\n                                lapack_int m, lapack_int n, lapack_int k,\n                                const double* a, lapack_int lda,\n                                const double* tau, double* c, lapack_int ldc,\n                                double* work, lapack_int lwork );\n\nlapack_int LAPACKE_sormqr_work( int matrix_order, char side, char trans,\n                                lapack_int m, lapack_int n, lapack_int k,\n                                const float* a, lapack_int lda,\n                                const float* tau, float* c, lapack_int ldc,\n                                float* work, lapack_int lwork );\nlapack_int LAPACKE_dormqr_work( int matrix_order, char side, char trans,\n                                lapack_int m, lapack_int n, lapack_int k,\n                                const double* a, lapack_int lda,\n                                const double* tau, double* c, lapack_int ldc,\n                                double* work, lapack_int lwork );\n\nlapack_int LAPACKE_sormrq_work( int matrix_order, char side, char trans,\n                                lapack_int m, lapack_int n, lapack_int k,\n                                const float* a, lapack_int lda,\n                                const float* tau, float* c, lapack_int ldc,\n                                float* work, lapack_int lwork );\nlapack_int LAPACKE_dormrq_work( int matrix_order, char side, char trans,\n                                lapack_int m, lapack_int n, lapack_int k,\n                                const double* a, lapack_int lda,\n                                const double* tau, double* c, lapack_int ldc,\n                                double* work, lapack_int lwork );\n\nlapack_int LAPACKE_sormrz_work( int matrix_order, char side, char trans,\n                                lapack_int m, lapack_int n, lapack_int k,\n                                lapack_int l, const float* a, lapack_int lda,\n                                const float* tau, float* c, lapack_int ldc,\n                                float* work, lapack_int lwork );\nlapack_int LAPACKE_dormrz_work( int matrix_order, char side, char trans,\n                                lapack_int m, lapack_int n, lapack_int k,\n                                lapack_int l, const double* a, lapack_int lda,\n                                const double* tau, double* c, lapack_int ldc,\n                                double* work, lapack_int lwork );\n\nlapack_int LAPACKE_sormtr_work( int matrix_order, char side, char uplo,\n                                char trans, lapack_int m, lapack_int n,\n                                const float* a, lapack_int lda,\n                                const float* tau, float* c, lapack_int ldc,\n                                float* work, lapack_int lwork );\nlapack_int LAPACKE_dormtr_work( int matrix_order, char side, char uplo,\n                                char trans, lapack_int m, lapack_int n,\n                                const double* a, lapack_int lda,\n                                const double* tau, double* c, lapack_int ldc,\n                                double* work, lapack_int lwork );\n\nlapack_int LAPACKE_spbcon_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int kd, const float* ab, lapack_int ldab,\n                                float anorm, float* rcond, float* work,\n                                lapack_int* iwork );\nlapack_int LAPACKE_dpbcon_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int kd, const double* ab,\n                                lapack_int ldab, double anorm, double* rcond,\n                                double* work, lapack_int* iwork );\nlapack_int LAPACKE_cpbcon_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int kd, const lapack_complex_float* ab,\n                                lapack_int ldab, float anorm, float* rcond,\n                                lapack_complex_float* work, float* rwork );\nlapack_int LAPACKE_zpbcon_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int kd, const lapack_complex_double* ab,\n                                lapack_int ldab, double anorm, double* rcond,\n                                lapack_complex_double* work, double* rwork );\n\nlapack_int LAPACKE_spbequ_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int kd, const float* ab, lapack_int ldab,\n                                float* s, float* scond, float* amax );\nlapack_int LAPACKE_dpbequ_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int kd, const double* ab,\n                                lapack_int ldab, double* s, double* scond,\n                                double* amax );\nlapack_int LAPACKE_cpbequ_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int kd, const lapack_complex_float* ab,\n                                lapack_int ldab, float* s, float* scond,\n                                float* amax );\nlapack_int LAPACKE_zpbequ_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int kd, const lapack_complex_double* ab,\n                                lapack_int ldab, double* s, double* scond,\n                                double* amax );\n\nlapack_int LAPACKE_spbrfs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int kd, lapack_int nrhs, const float* ab,\n                                lapack_int ldab, const float* afb,\n                                lapack_int ldafb, const float* b,\n                                lapack_int ldb, float* x, lapack_int ldx,\n                                float* ferr, float* berr, float* work,\n                                lapack_int* iwork );\nlapack_int LAPACKE_dpbrfs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int kd, lapack_int nrhs,\n                                const double* ab, lapack_int ldab,\n                                const double* afb, lapack_int ldafb,\n                                const double* b, lapack_int ldb, double* x,\n                                lapack_int ldx, double* ferr, double* berr,\n                                double* work, lapack_int* iwork );\nlapack_int LAPACKE_cpbrfs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int kd, lapack_int nrhs,\n                                const lapack_complex_float* ab, lapack_int ldab,\n                                const lapack_complex_float* afb,\n                                lapack_int ldafb, const lapack_complex_float* b,\n                                lapack_int ldb, lapack_complex_float* x,\n                                lapack_int ldx, float* ferr, float* berr,\n                                lapack_complex_float* work, float* rwork );\nlapack_int LAPACKE_zpbrfs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int kd, lapack_int nrhs,\n                                const lapack_complex_double* ab,\n                                lapack_int ldab,\n                                const lapack_complex_double* afb,\n                                lapack_int ldafb,\n                                const lapack_complex_double* b, lapack_int ldb,\n                                lapack_complex_double* x, lapack_int ldx,\n                                double* ferr, double* berr,\n                                lapack_complex_double* work, double* rwork );\n\nlapack_int LAPACKE_spbstf_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int kb, float* bb, lapack_int ldbb );\nlapack_int LAPACKE_dpbstf_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int kb, double* bb, lapack_int ldbb );\nlapack_int LAPACKE_cpbstf_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int kb, lapack_complex_float* bb,\n                                lapack_int ldbb );\nlapack_int LAPACKE_zpbstf_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int kb, lapack_complex_double* bb,\n                                lapack_int ldbb );\n\nlapack_int LAPACKE_spbsv_work( int matrix_order, char uplo, lapack_int n,\n                               lapack_int kd, lapack_int nrhs, float* ab,\n                               lapack_int ldab, float* b, lapack_int ldb );\nlapack_int LAPACKE_dpbsv_work( int matrix_order, char uplo, lapack_int n,\n                               lapack_int kd, lapack_int nrhs, double* ab,\n                               lapack_int ldab, double* b, lapack_int ldb );\nlapack_int LAPACKE_cpbsv_work( int matrix_order, char uplo, lapack_int n,\n                               lapack_int kd, lapack_int nrhs,\n                               lapack_complex_float* ab, lapack_int ldab,\n                               lapack_complex_float* b, lapack_int ldb );\nlapack_int LAPACKE_zpbsv_work( int matrix_order, char uplo, lapack_int n,\n                               lapack_int kd, lapack_int nrhs,\n                               lapack_complex_double* ab, lapack_int ldab,\n                               lapack_complex_double* b, lapack_int ldb );\n\nlapack_int LAPACKE_spbsvx_work( int matrix_order, char fact, char uplo,\n                                lapack_int n, lapack_int kd, lapack_int nrhs,\n                                float* ab, lapack_int ldab, float* afb,\n                                lapack_int ldafb, char* equed, float* s,\n                                float* b, lapack_int ldb, float* x,\n                                lapack_int ldx, float* rcond, float* ferr,\n                                float* berr, float* work, lapack_int* iwork );\nlapack_int LAPACKE_dpbsvx_work( int matrix_order, char fact, char uplo,\n                                lapack_int n, lapack_int kd, lapack_int nrhs,\n                                double* ab, lapack_int ldab, double* afb,\n                                lapack_int ldafb, char* equed, double* s,\n                                double* b, lapack_int ldb, double* x,\n                                lapack_int ldx, double* rcond, double* ferr,\n                                double* berr, double* work, lapack_int* iwork );\nlapack_int LAPACKE_cpbsvx_work( int matrix_order, char fact, char uplo,\n                                lapack_int n, lapack_int kd, lapack_int nrhs,\n                                lapack_complex_float* ab, lapack_int ldab,\n                                lapack_complex_float* afb, lapack_int ldafb,\n                                char* equed, float* s, lapack_complex_float* b,\n                                lapack_int ldb, lapack_complex_float* x,\n                                lapack_int ldx, float* rcond, float* ferr,\n                                float* berr, lapack_complex_float* work,\n                                float* rwork );\nlapack_int LAPACKE_zpbsvx_work( int matrix_order, char fact, char uplo,\n                                lapack_int n, lapack_int kd, lapack_int nrhs,\n                                lapack_complex_double* ab, lapack_int ldab,\n                                lapack_complex_double* afb, lapack_int ldafb,\n                                char* equed, double* s,\n                                lapack_complex_double* b, lapack_int ldb,\n                                lapack_complex_double* x, lapack_int ldx,\n                                double* rcond, double* ferr, double* berr,\n                                lapack_complex_double* work, double* rwork );\n\nlapack_int LAPACKE_spbtrf_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int kd, float* ab, lapack_int ldab );\nlapack_int LAPACKE_dpbtrf_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int kd, double* ab, lapack_int ldab );\nlapack_int LAPACKE_cpbtrf_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int kd, lapack_complex_float* ab,\n                                lapack_int ldab );\nlapack_int LAPACKE_zpbtrf_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int kd, lapack_complex_double* ab,\n                                lapack_int ldab );\n\nlapack_int LAPACKE_spbtrs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int kd, lapack_int nrhs, const float* ab,\n                                lapack_int ldab, float* b, lapack_int ldb );\nlapack_int LAPACKE_dpbtrs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int kd, lapack_int nrhs,\n                                const double* ab, lapack_int ldab, double* b,\n                                lapack_int ldb );\nlapack_int LAPACKE_cpbtrs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int kd, lapack_int nrhs,\n                                const lapack_complex_float* ab, lapack_int ldab,\n                                lapack_complex_float* b, lapack_int ldb );\nlapack_int LAPACKE_zpbtrs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int kd, lapack_int nrhs,\n                                const lapack_complex_double* ab,\n                                lapack_int ldab, lapack_complex_double* b,\n                                lapack_int ldb );\n\nlapack_int LAPACKE_spftrf_work( int matrix_order, char transr, char uplo,\n                                lapack_int n, float* a );\nlapack_int LAPACKE_dpftrf_work( int matrix_order, char transr, char uplo,\n                                lapack_int n, double* a );\nlapack_int LAPACKE_cpftrf_work( int matrix_order, char transr, char uplo,\n                                lapack_int n, lapack_complex_float* a );\nlapack_int LAPACKE_zpftrf_work( int matrix_order, char transr, char uplo,\n                                lapack_int n, lapack_complex_double* a );\n\nlapack_int LAPACKE_spftri_work( int matrix_order, char transr, char uplo,\n                                lapack_int n, float* a );\nlapack_int LAPACKE_dpftri_work( int matrix_order, char transr, char uplo,\n                                lapack_int n, double* a );\nlapack_int LAPACKE_cpftri_work( int matrix_order, char transr, char uplo,\n                                lapack_int n, lapack_complex_float* a );\nlapack_int LAPACKE_zpftri_work( int matrix_order, char transr, char uplo,\n                                lapack_int n, lapack_complex_double* a );\n\nlapack_int LAPACKE_spftrs_work( int matrix_order, char transr, char uplo,\n                                lapack_int n, lapack_int nrhs, const float* a,\n                                float* b, lapack_int ldb );\nlapack_int LAPACKE_dpftrs_work( int matrix_order, char transr, char uplo,\n                                lapack_int n, lapack_int nrhs, const double* a,\n                                double* b, lapack_int ldb );\nlapack_int LAPACKE_cpftrs_work( int matrix_order, char transr, char uplo,\n                                lapack_int n, lapack_int nrhs,\n                                const lapack_complex_float* a,\n                                lapack_complex_float* b, lapack_int ldb );\nlapack_int LAPACKE_zpftrs_work( int matrix_order, char transr, char uplo,\n                                lapack_int n, lapack_int nrhs,\n                                const lapack_complex_double* a,\n                                lapack_complex_double* b, lapack_int ldb );\n\nlapack_int LAPACKE_spocon_work( int matrix_order, char uplo, lapack_int n,\n                                const float* a, lapack_int lda, float anorm,\n                                float* rcond, float* work, lapack_int* iwork );\nlapack_int LAPACKE_dpocon_work( int matrix_order, char uplo, lapack_int n,\n                                const double* a, lapack_int lda, double anorm,\n                                double* rcond, double* work,\n                                lapack_int* iwork );\nlapack_int LAPACKE_cpocon_work( int matrix_order, char uplo, lapack_int n,\n                                const lapack_complex_float* a, lapack_int lda,\n                                float anorm, float* rcond,\n                                lapack_complex_float* work, float* rwork );\nlapack_int LAPACKE_zpocon_work( int matrix_order, char uplo, lapack_int n,\n                                const lapack_complex_double* a, lapack_int lda,\n                                double anorm, double* rcond,\n                                lapack_complex_double* work, double* rwork );\n\nlapack_int LAPACKE_spoequ_work( int matrix_order, lapack_int n, const float* a,\n                                lapack_int lda, float* s, float* scond,\n                                float* amax );\nlapack_int LAPACKE_dpoequ_work( int matrix_order, lapack_int n, const double* a,\n                                lapack_int lda, double* s, double* scond,\n                                double* amax );\nlapack_int LAPACKE_cpoequ_work( int matrix_order, lapack_int n,\n                                const lapack_complex_float* a, lapack_int lda,\n                                float* s, float* scond, float* amax );\nlapack_int LAPACKE_zpoequ_work( int matrix_order, lapack_int n,\n                                const lapack_complex_double* a, lapack_int lda,\n                                double* s, double* scond, double* amax );\n\nlapack_int LAPACKE_spoequb_work( int matrix_order, lapack_int n, const float* a,\n                                 lapack_int lda, float* s, float* scond,\n                                 float* amax );\nlapack_int LAPACKE_dpoequb_work( int matrix_order, lapack_int n,\n                                 const double* a, lapack_int lda, double* s,\n                                 double* scond, double* amax );\nlapack_int LAPACKE_cpoequb_work( int matrix_order, lapack_int n,\n                                 const lapack_complex_float* a, lapack_int lda,\n                                 float* s, float* scond, float* amax );\nlapack_int LAPACKE_zpoequb_work( int matrix_order, lapack_int n,\n                                 const lapack_complex_double* a, lapack_int lda,\n                                 double* s, double* scond, double* amax );\n\nlapack_int LAPACKE_sporfs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const float* a, lapack_int lda,\n                                const float* af, lapack_int ldaf,\n                                const float* b, lapack_int ldb, float* x,\n                                lapack_int ldx, float* ferr, float* berr,\n                                float* work, lapack_int* iwork );\nlapack_int LAPACKE_dporfs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const double* a,\n                                lapack_int lda, const double* af,\n                                lapack_int ldaf, const double* b,\n                                lapack_int ldb, double* x, lapack_int ldx,\n                                double* ferr, double* berr, double* work,\n                                lapack_int* iwork );\nlapack_int LAPACKE_cporfs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const lapack_complex_float* a,\n                                lapack_int lda, const lapack_complex_float* af,\n                                lapack_int ldaf, const lapack_complex_float* b,\n                                lapack_int ldb, lapack_complex_float* x,\n                                lapack_int ldx, float* ferr, float* berr,\n                                lapack_complex_float* work, float* rwork );\nlapack_int LAPACKE_zporfs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const lapack_complex_double* a,\n                                lapack_int lda, const lapack_complex_double* af,\n                                lapack_int ldaf, const lapack_complex_double* b,\n                                lapack_int ldb, lapack_complex_double* x,\n                                lapack_int ldx, double* ferr, double* berr,\n                                lapack_complex_double* work, double* rwork );\n\nlapack_int LAPACKE_sporfsx_work( int matrix_order, char uplo, char equed,\n                                 lapack_int n, lapack_int nrhs, const float* a,\n                                 lapack_int lda, const float* af,\n                                 lapack_int ldaf, const float* s,\n                                 const float* b, lapack_int ldb, float* x,\n                                 lapack_int ldx, float* rcond, float* berr,\n                                 lapack_int n_err_bnds, float* err_bnds_norm,\n                                 float* err_bnds_comp, lapack_int nparams,\n                                 float* params, float* work,\n                                 lapack_int* iwork );\nlapack_int LAPACKE_dporfsx_work( int matrix_order, char uplo, char equed,\n                                 lapack_int n, lapack_int nrhs, const double* a,\n                                 lapack_int lda, const double* af,\n                                 lapack_int ldaf, const double* s,\n                                 const double* b, lapack_int ldb, double* x,\n                                 lapack_int ldx, double* rcond, double* berr,\n                                 lapack_int n_err_bnds, double* err_bnds_norm,\n                                 double* err_bnds_comp, lapack_int nparams,\n                                 double* params, double* work,\n                                 lapack_int* iwork );\nlapack_int LAPACKE_cporfsx_work( int matrix_order, char uplo, char equed,\n                                 lapack_int n, lapack_int nrhs,\n                                 const lapack_complex_float* a, lapack_int lda,\n                                 const lapack_complex_float* af,\n                                 lapack_int ldaf, const float* s,\n                                 const lapack_complex_float* b, lapack_int ldb,\n                                 lapack_complex_float* x, lapack_int ldx,\n                                 float* rcond, float* berr,\n                                 lapack_int n_err_bnds, float* err_bnds_norm,\n                                 float* err_bnds_comp, lapack_int nparams,\n                                 float* params, lapack_complex_float* work,\n                                 float* rwork );\nlapack_int LAPACKE_zporfsx_work( int matrix_order, char uplo, char equed,\n                                 lapack_int n, lapack_int nrhs,\n                                 const lapack_complex_double* a, lapack_int lda,\n                                 const lapack_complex_double* af,\n                                 lapack_int ldaf, const double* s,\n                                 const lapack_complex_double* b, lapack_int ldb,\n                                 lapack_complex_double* x, lapack_int ldx,\n                                 double* rcond, double* berr,\n                                 lapack_int n_err_bnds, double* err_bnds_norm,\n                                 double* err_bnds_comp, lapack_int nparams,\n                                 double* params, lapack_complex_double* work,\n                                 double* rwork );\n\nlapack_int LAPACKE_sposv_work( int matrix_order, char uplo, lapack_int n,\n                               lapack_int nrhs, float* a, lapack_int lda,\n                               float* b, lapack_int ldb );\nlapack_int LAPACKE_dposv_work( int matrix_order, char uplo, lapack_int n,\n                               lapack_int nrhs, double* a, lapack_int lda,\n                               double* b, lapack_int ldb );\nlapack_int LAPACKE_cposv_work( int matrix_order, char uplo, lapack_int n,\n                               lapack_int nrhs, lapack_complex_float* a,\n                               lapack_int lda, lapack_complex_float* b,\n                               lapack_int ldb );\nlapack_int LAPACKE_zposv_work( int matrix_order, char uplo, lapack_int n,\n                               lapack_int nrhs, lapack_complex_double* a,\n                               lapack_int lda, lapack_complex_double* b,\n                               lapack_int ldb );\nlapack_int LAPACKE_dsposv_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, double* a, lapack_int lda,\n                                double* b, lapack_int ldb, double* x,\n                                lapack_int ldx, double* work, float* swork,\n                                lapack_int* iter );\nlapack_int LAPACKE_zcposv_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, lapack_complex_double* a,\n                                lapack_int lda, lapack_complex_double* b,\n                                lapack_int ldb, lapack_complex_double* x,\n                                lapack_int ldx, lapack_complex_double* work,\n                                lapack_complex_float* swork, double* rwork,\n                                lapack_int* iter );\n\nlapack_int LAPACKE_sposvx_work( int matrix_order, char fact, char uplo,\n                                lapack_int n, lapack_int nrhs, float* a,\n                                lapack_int lda, float* af, lapack_int ldaf,\n                                char* equed, float* s, float* b, lapack_int ldb,\n                                float* x, lapack_int ldx, float* rcond,\n                                float* ferr, float* berr, float* work,\n                                lapack_int* iwork );\nlapack_int LAPACKE_dposvx_work( int matrix_order, char fact, char uplo,\n                                lapack_int n, lapack_int nrhs, double* a,\n                                lapack_int lda, double* af, lapack_int ldaf,\n                                char* equed, double* s, double* b,\n                                lapack_int ldb, double* x, lapack_int ldx,\n                                double* rcond, double* ferr, double* berr,\n                                double* work, lapack_int* iwork );\nlapack_int LAPACKE_cposvx_work( int matrix_order, char fact, char uplo,\n                                lapack_int n, lapack_int nrhs,\n                                lapack_complex_float* a, lapack_int lda,\n                                lapack_complex_float* af, lapack_int ldaf,\n                                char* equed, float* s, lapack_complex_float* b,\n                                lapack_int ldb, lapack_complex_float* x,\n                                lapack_int ldx, float* rcond, float* ferr,\n                                float* berr, lapack_complex_float* work,\n                                float* rwork );\nlapack_int LAPACKE_zposvx_work( int matrix_order, char fact, char uplo,\n                                lapack_int n, lapack_int nrhs,\n                                lapack_complex_double* a, lapack_int lda,\n                                lapack_complex_double* af, lapack_int ldaf,\n                                char* equed, double* s,\n                                lapack_complex_double* b, lapack_int ldb,\n                                lapack_complex_double* x, lapack_int ldx,\n                                double* rcond, double* ferr, double* berr,\n                                lapack_complex_double* work, double* rwork );\n\nlapack_int LAPACKE_sposvxx_work( int matrix_order, char fact, char uplo,\n                                 lapack_int n, lapack_int nrhs, float* a,\n                                 lapack_int lda, float* af, lapack_int ldaf,\n                                 char* equed, float* s, float* b,\n                                 lapack_int ldb, float* x, lapack_int ldx,\n                                 float* rcond, float* rpvgrw, float* berr,\n                                 lapack_int n_err_bnds, float* err_bnds_norm,\n                                 float* err_bnds_comp, lapack_int nparams,\n                                 float* params, float* work,\n                                 lapack_int* iwork );\nlapack_int LAPACKE_dposvxx_work( int matrix_order, char fact, char uplo,\n                                 lapack_int n, lapack_int nrhs, double* a,\n                                 lapack_int lda, double* af, lapack_int ldaf,\n                                 char* equed, double* s, double* b,\n                                 lapack_int ldb, double* x, lapack_int ldx,\n                                 double* rcond, double* rpvgrw, double* berr,\n                                 lapack_int n_err_bnds, double* err_bnds_norm,\n                                 double* err_bnds_comp, lapack_int nparams,\n                                 double* params, double* work,\n                                 lapack_int* iwork );\nlapack_int LAPACKE_cposvxx_work( int matrix_order, char fact, char uplo,\n                                 lapack_int n, lapack_int nrhs,\n                                 lapack_complex_float* a, lapack_int lda,\n                                 lapack_complex_float* af, lapack_int ldaf,\n                                 char* equed, float* s, lapack_complex_float* b,\n                                 lapack_int ldb, lapack_complex_float* x,\n                                 lapack_int ldx, float* rcond, float* rpvgrw,\n                                 float* berr, lapack_int n_err_bnds,\n                                 float* err_bnds_norm, float* err_bnds_comp,\n                                 lapack_int nparams, float* params,\n                                 lapack_complex_float* work, float* rwork );\nlapack_int LAPACKE_zposvxx_work( int matrix_order, char fact, char uplo,\n                                 lapack_int n, lapack_int nrhs,\n                                 lapack_complex_double* a, lapack_int lda,\n                                 lapack_complex_double* af, lapack_int ldaf,\n                                 char* equed, double* s,\n                                 lapack_complex_double* b, lapack_int ldb,\n                                 lapack_complex_double* x, lapack_int ldx,\n                                 double* rcond, double* rpvgrw, double* berr,\n                                 lapack_int n_err_bnds, double* err_bnds_norm,\n                                 double* err_bnds_comp, lapack_int nparams,\n                                 double* params, lapack_complex_double* work,\n                                 double* rwork );\n\nlapack_int LAPACKE_spotrf_work( int matrix_order, char uplo, lapack_int n,\n                                float* a, lapack_int lda );\nlapack_int LAPACKE_dpotrf_work( int matrix_order, char uplo, lapack_int n,\n                                double* a, lapack_int lda );\nlapack_int LAPACKE_cpotrf_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_complex_float* a, lapack_int lda );\nlapack_int LAPACKE_zpotrf_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_complex_double* a, lapack_int lda );\n\nlapack_int LAPACKE_spotri_work( int matrix_order, char uplo, lapack_int n,\n                                float* a, lapack_int lda );\nlapack_int LAPACKE_dpotri_work( int matrix_order, char uplo, lapack_int n,\n                                double* a, lapack_int lda );\nlapack_int LAPACKE_cpotri_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_complex_float* a, lapack_int lda );\nlapack_int LAPACKE_zpotri_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_complex_double* a, lapack_int lda );\n\nlapack_int LAPACKE_spotrs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const float* a, lapack_int lda,\n                                float* b, lapack_int ldb );\nlapack_int LAPACKE_dpotrs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const double* a,\n                                lapack_int lda, double* b, lapack_int ldb );\nlapack_int LAPACKE_cpotrs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const lapack_complex_float* a,\n                                lapack_int lda, lapack_complex_float* b,\n                                lapack_int ldb );\nlapack_int LAPACKE_zpotrs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const lapack_complex_double* a,\n                                lapack_int lda, lapack_complex_double* b,\n                                lapack_int ldb );\n\nlapack_int LAPACKE_sppcon_work( int matrix_order, char uplo, lapack_int n,\n                                const float* ap, float anorm, float* rcond,\n                                float* work, lapack_int* iwork );\nlapack_int LAPACKE_dppcon_work( int matrix_order, char uplo, lapack_int n,\n                                const double* ap, double anorm, double* rcond,\n                                double* work, lapack_int* iwork );\nlapack_int LAPACKE_cppcon_work( int matrix_order, char uplo, lapack_int n,\n                                const lapack_complex_float* ap, float anorm,\n                                float* rcond, lapack_complex_float* work,\n                                float* rwork );\nlapack_int LAPACKE_zppcon_work( int matrix_order, char uplo, lapack_int n,\n                                const lapack_complex_double* ap, double anorm,\n                                double* rcond, lapack_complex_double* work,\n                                double* rwork );\n\nlapack_int LAPACKE_sppequ_work( int matrix_order, char uplo, lapack_int n,\n                                const float* ap, float* s, float* scond,\n                                float* amax );\nlapack_int LAPACKE_dppequ_work( int matrix_order, char uplo, lapack_int n,\n                                const double* ap, double* s, double* scond,\n                                double* amax );\nlapack_int LAPACKE_cppequ_work( int matrix_order, char uplo, lapack_int n,\n                                const lapack_complex_float* ap, float* s,\n                                float* scond, float* amax );\nlapack_int LAPACKE_zppequ_work( int matrix_order, char uplo, lapack_int n,\n                                const lapack_complex_double* ap, double* s,\n                                double* scond, double* amax );\n\nlapack_int LAPACKE_spprfs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const float* ap,\n                                const float* afp, const float* b,\n                                lapack_int ldb, float* x, lapack_int ldx,\n                                float* ferr, float* berr, float* work,\n                                lapack_int* iwork );\nlapack_int LAPACKE_dpprfs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const double* ap,\n                                const double* afp, const double* b,\n                                lapack_int ldb, double* x, lapack_int ldx,\n                                double* ferr, double* berr, double* work,\n                                lapack_int* iwork );\nlapack_int LAPACKE_cpprfs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const lapack_complex_float* ap,\n                                const lapack_complex_float* afp,\n                                const lapack_complex_float* b, lapack_int ldb,\n                                lapack_complex_float* x, lapack_int ldx,\n                                float* ferr, float* berr,\n                                lapack_complex_float* work, float* rwork );\nlapack_int LAPACKE_zpprfs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs,\n                                const lapack_complex_double* ap,\n                                const lapack_complex_double* afp,\n                                const lapack_complex_double* b, lapack_int ldb,\n                                lapack_complex_double* x, lapack_int ldx,\n                                double* ferr, double* berr,\n                                lapack_complex_double* work, double* rwork );\n\nlapack_int LAPACKE_sppsv_work( int matrix_order, char uplo, lapack_int n,\n                               lapack_int nrhs, float* ap, float* b,\n                               lapack_int ldb );\nlapack_int LAPACKE_dppsv_work( int matrix_order, char uplo, lapack_int n,\n                               lapack_int nrhs, double* ap, double* b,\n                               lapack_int ldb );\nlapack_int LAPACKE_cppsv_work( int matrix_order, char uplo, lapack_int n,\n                               lapack_int nrhs, lapack_complex_float* ap,\n                               lapack_complex_float* b, lapack_int ldb );\nlapack_int LAPACKE_zppsv_work( int matrix_order, char uplo, lapack_int n,\n                               lapack_int nrhs, lapack_complex_double* ap,\n                               lapack_complex_double* b, lapack_int ldb );\n\nlapack_int LAPACKE_sppsvx_work( int matrix_order, char fact, char uplo,\n                                lapack_int n, lapack_int nrhs, float* ap,\n                                float* afp, char* equed, float* s, float* b,\n                                lapack_int ldb, float* x, lapack_int ldx,\n                                float* rcond, float* ferr, float* berr,\n                                float* work, lapack_int* iwork );\nlapack_int LAPACKE_dppsvx_work( int matrix_order, char fact, char uplo,\n                                lapack_int n, lapack_int nrhs, double* ap,\n                                double* afp, char* equed, double* s, double* b,\n                                lapack_int ldb, double* x, lapack_int ldx,\n                                double* rcond, double* ferr, double* berr,\n                                double* work, lapack_int* iwork );\nlapack_int LAPACKE_cppsvx_work( int matrix_order, char fact, char uplo,\n                                lapack_int n, lapack_int nrhs,\n                                lapack_complex_float* ap,\n                                lapack_complex_float* afp, char* equed,\n                                float* s, lapack_complex_float* b,\n                                lapack_int ldb, lapack_complex_float* x,\n                                lapack_int ldx, float* rcond, float* ferr,\n                                float* berr, lapack_complex_float* work,\n                                float* rwork );\nlapack_int LAPACKE_zppsvx_work( int matrix_order, char fact, char uplo,\n                                lapack_int n, lapack_int nrhs,\n                                lapack_complex_double* ap,\n                                lapack_complex_double* afp, char* equed,\n                                double* s, lapack_complex_double* b,\n                                lapack_int ldb, lapack_complex_double* x,\n                                lapack_int ldx, double* rcond, double* ferr,\n                                double* berr, lapack_complex_double* work,\n                                double* rwork );\n\nlapack_int LAPACKE_spptrf_work( int matrix_order, char uplo, lapack_int n,\n                                float* ap );\nlapack_int LAPACKE_dpptrf_work( int matrix_order, char uplo, lapack_int n,\n                                double* ap );\nlapack_int LAPACKE_cpptrf_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_complex_float* ap );\nlapack_int LAPACKE_zpptrf_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_complex_double* ap );\n\nlapack_int LAPACKE_spptri_work( int matrix_order, char uplo, lapack_int n,\n                                float* ap );\nlapack_int LAPACKE_dpptri_work( int matrix_order, char uplo, lapack_int n,\n                                double* ap );\nlapack_int LAPACKE_cpptri_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_complex_float* ap );\nlapack_int LAPACKE_zpptri_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_complex_double* ap );\n\nlapack_int LAPACKE_spptrs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const float* ap, float* b,\n                                lapack_int ldb );\nlapack_int LAPACKE_dpptrs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const double* ap, double* b,\n                                lapack_int ldb );\nlapack_int LAPACKE_cpptrs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const lapack_complex_float* ap,\n                                lapack_complex_float* b, lapack_int ldb );\nlapack_int LAPACKE_zpptrs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs,\n                                const lapack_complex_double* ap,\n                                lapack_complex_double* b, lapack_int ldb );\n\nlapack_int LAPACKE_spstrf_work( int matrix_order, char uplo, lapack_int n,\n                                float* a, lapack_int lda, lapack_int* piv,\n                                lapack_int* rank, float tol, float* work );\nlapack_int LAPACKE_dpstrf_work( int matrix_order, char uplo, lapack_int n,\n                                double* a, lapack_int lda, lapack_int* piv,\n                                lapack_int* rank, double tol, double* work );\nlapack_int LAPACKE_cpstrf_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_complex_float* a, lapack_int lda,\n                                lapack_int* piv, lapack_int* rank, float tol,\n                                float* work );\nlapack_int LAPACKE_zpstrf_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_complex_double* a, lapack_int lda,\n                                lapack_int* piv, lapack_int* rank, double tol,\n                                double* work );\n\nlapack_int LAPACKE_sptcon_work( lapack_int n, const float* d, const float* e,\n                                float anorm, float* rcond, float* work );\nlapack_int LAPACKE_dptcon_work( lapack_int n, const double* d, const double* e,\n                                double anorm, double* rcond, double* work );\nlapack_int LAPACKE_cptcon_work( lapack_int n, const float* d,\n                                const lapack_complex_float* e, float anorm,\n                                float* rcond, float* work );\nlapack_int LAPACKE_zptcon_work( lapack_int n, const double* d,\n                                const lapack_complex_double* e, double anorm,\n                                double* rcond, double* work );\n\nlapack_int LAPACKE_spteqr_work( int matrix_order, char compz, lapack_int n,\n                                float* d, float* e, float* z, lapack_int ldz,\n                                float* work );\nlapack_int LAPACKE_dpteqr_work( int matrix_order, char compz, lapack_int n,\n                                double* d, double* e, double* z, lapack_int ldz,\n                                double* work );\nlapack_int LAPACKE_cpteqr_work( int matrix_order, char compz, lapack_int n,\n                                float* d, float* e, lapack_complex_float* z,\n                                lapack_int ldz, float* work );\nlapack_int LAPACKE_zpteqr_work( int matrix_order, char compz, lapack_int n,\n                                double* d, double* e, lapack_complex_double* z,\n                                lapack_int ldz, double* work );\n\nlapack_int LAPACKE_sptrfs_work( int matrix_order, lapack_int n, lapack_int nrhs,\n                                const float* d, const float* e, const float* df,\n                                const float* ef, const float* b, lapack_int ldb,\n                                float* x, lapack_int ldx, float* ferr,\n                                float* berr, float* work );\nlapack_int LAPACKE_dptrfs_work( int matrix_order, lapack_int n, lapack_int nrhs,\n                                const double* d, const double* e,\n                                const double* df, const double* ef,\n                                const double* b, lapack_int ldb, double* x,\n                                lapack_int ldx, double* ferr, double* berr,\n                                double* work );\nlapack_int LAPACKE_cptrfs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const float* d,\n                                const lapack_complex_float* e, const float* df,\n                                const lapack_complex_float* ef,\n                                const lapack_complex_float* b, lapack_int ldb,\n                                lapack_complex_float* x, lapack_int ldx,\n                                float* ferr, float* berr,\n                                lapack_complex_float* work, float* rwork );\nlapack_int LAPACKE_zptrfs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const double* d,\n                                const lapack_complex_double* e,\n                                const double* df,\n                                const lapack_complex_double* ef,\n                                const lapack_complex_double* b, lapack_int ldb,\n                                lapack_complex_double* x, lapack_int ldx,\n                                double* ferr, double* berr,\n                                lapack_complex_double* work, double* rwork );\n\nlapack_int LAPACKE_sptsv_work( int matrix_order, lapack_int n, lapack_int nrhs,\n                               float* d, float* e, float* b, lapack_int ldb );\nlapack_int LAPACKE_dptsv_work( int matrix_order, lapack_int n, lapack_int nrhs,\n                               double* d, double* e, double* b,\n                               lapack_int ldb );\nlapack_int LAPACKE_cptsv_work( int matrix_order, lapack_int n, lapack_int nrhs,\n                               float* d, lapack_complex_float* e,\n                               lapack_complex_float* b, lapack_int ldb );\nlapack_int LAPACKE_zptsv_work( int matrix_order, lapack_int n, lapack_int nrhs,\n                               double* d, lapack_complex_double* e,\n                               lapack_complex_double* b, lapack_int ldb );\n\nlapack_int LAPACKE_sptsvx_work( int matrix_order, char fact, lapack_int n,\n                                lapack_int nrhs, const float* d, const float* e,\n                                float* df, float* ef, const float* b,\n                                lapack_int ldb, float* x, lapack_int ldx,\n                                float* rcond, float* ferr, float* berr,\n                                float* work );\nlapack_int LAPACKE_dptsvx_work( int matrix_order, char fact, lapack_int n,\n                                lapack_int nrhs, const double* d,\n                                const double* e, double* df, double* ef,\n                                const double* b, lapack_int ldb, double* x,\n                                lapack_int ldx, double* rcond, double* ferr,\n                                double* berr, double* work );\nlapack_int LAPACKE_cptsvx_work( int matrix_order, char fact, lapack_int n,\n                                lapack_int nrhs, const float* d,\n                                const lapack_complex_float* e, float* df,\n                                lapack_complex_float* ef,\n                                const lapack_complex_float* b, lapack_int ldb,\n                                lapack_complex_float* x, lapack_int ldx,\n                                float* rcond, float* ferr, float* berr,\n                                lapack_complex_float* work, float* rwork );\nlapack_int LAPACKE_zptsvx_work( int matrix_order, char fact, lapack_int n,\n                                lapack_int nrhs, const double* d,\n                                const lapack_complex_double* e, double* df,\n                                lapack_complex_double* ef,\n                                const lapack_complex_double* b, lapack_int ldb,\n                                lapack_complex_double* x, lapack_int ldx,\n                                double* rcond, double* ferr, double* berr,\n                                lapack_complex_double* work, double* rwork );\n\nlapack_int LAPACKE_spttrf_work( lapack_int n, float* d, float* e );\nlapack_int LAPACKE_dpttrf_work( lapack_int n, double* d, double* e );\nlapack_int LAPACKE_cpttrf_work( lapack_int n, float* d,\n                                lapack_complex_float* e );\nlapack_int LAPACKE_zpttrf_work( lapack_int n, double* d,\n                                lapack_complex_double* e );\n\nlapack_int LAPACKE_spttrs_work( int matrix_order, lapack_int n, lapack_int nrhs,\n                                const float* d, const float* e, float* b,\n                                lapack_int ldb );\nlapack_int LAPACKE_dpttrs_work( int matrix_order, lapack_int n, lapack_int nrhs,\n                                const double* d, const double* e, double* b,\n                                lapack_int ldb );\nlapack_int LAPACKE_cpttrs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const float* d,\n                                const lapack_complex_float* e,\n                                lapack_complex_float* b, lapack_int ldb );\nlapack_int LAPACKE_zpttrs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const double* d,\n                                const lapack_complex_double* e,\n                                lapack_complex_double* b, lapack_int ldb );\n\nlapack_int LAPACKE_ssbev_work( int matrix_order, char jobz, char uplo,\n                               lapack_int n, lapack_int kd, float* ab,\n                               lapack_int ldab, float* w, float* z,\n                               lapack_int ldz, float* work );\nlapack_int LAPACKE_dsbev_work( int matrix_order, char jobz, char uplo,\n                               lapack_int n, lapack_int kd, double* ab,\n                               lapack_int ldab, double* w, double* z,\n                               lapack_int ldz, double* work );\n\nlapack_int LAPACKE_ssbevd_work( int matrix_order, char jobz, char uplo,\n                                lapack_int n, lapack_int kd, float* ab,\n                                lapack_int ldab, float* w, float* z,\n                                lapack_int ldz, float* work, lapack_int lwork,\n                                lapack_int* iwork, lapack_int liwork );\nlapack_int LAPACKE_dsbevd_work( int matrix_order, char jobz, char uplo,\n                                lapack_int n, lapack_int kd, double* ab,\n                                lapack_int ldab, double* w, double* z,\n                                lapack_int ldz, double* work, lapack_int lwork,\n                                lapack_int* iwork, lapack_int liwork );\n\nlapack_int LAPACKE_ssbevx_work( int matrix_order, char jobz, char range,\n                                char uplo, lapack_int n, lapack_int kd,\n                                float* ab, lapack_int ldab, float* q,\n                                lapack_int ldq, float vl, float vu,\n                                lapack_int il, lapack_int iu, float abstol,\n                                lapack_int* m, float* w, float* z,\n                                lapack_int ldz, float* work, lapack_int* iwork,\n                                lapack_int* ifail );\nlapack_int LAPACKE_dsbevx_work( int matrix_order, char jobz, char range,\n                                char uplo, lapack_int n, lapack_int kd,\n                                double* ab, lapack_int ldab, double* q,\n                                lapack_int ldq, double vl, double vu,\n                                lapack_int il, lapack_int iu, double abstol,\n                                lapack_int* m, double* w, double* z,\n                                lapack_int ldz, double* work, lapack_int* iwork,\n                                lapack_int* ifail );\n\nlapack_int LAPACKE_ssbgst_work( int matrix_order, char vect, char uplo,\n                                lapack_int n, lapack_int ka, lapack_int kb,\n                                float* ab, lapack_int ldab, const float* bb,\n                                lapack_int ldbb, float* x, lapack_int ldx,\n                                float* work );\nlapack_int LAPACKE_dsbgst_work( int matrix_order, char vect, char uplo,\n                                lapack_int n, lapack_int ka, lapack_int kb,\n                                double* ab, lapack_int ldab, const double* bb,\n                                lapack_int ldbb, double* x, lapack_int ldx,\n                                double* work );\n\nlapack_int LAPACKE_ssbgv_work( int matrix_order, char jobz, char uplo,\n                               lapack_int n, lapack_int ka, lapack_int kb,\n                               float* ab, lapack_int ldab, float* bb,\n                               lapack_int ldbb, float* w, float* z,\n                               lapack_int ldz, float* work );\nlapack_int LAPACKE_dsbgv_work( int matrix_order, char jobz, char uplo,\n                               lapack_int n, lapack_int ka, lapack_int kb,\n                               double* ab, lapack_int ldab, double* bb,\n                               lapack_int ldbb, double* w, double* z,\n                               lapack_int ldz, double* work );\n\nlapack_int LAPACKE_ssbgvd_work( int matrix_order, char jobz, char uplo,\n                                lapack_int n, lapack_int ka, lapack_int kb,\n                                float* ab, lapack_int ldab, float* bb,\n                                lapack_int ldbb, float* w, float* z,\n                                lapack_int ldz, float* work, lapack_int lwork,\n                                lapack_int* iwork, lapack_int liwork );\nlapack_int LAPACKE_dsbgvd_work( int matrix_order, char jobz, char uplo,\n                                lapack_int n, lapack_int ka, lapack_int kb,\n                                double* ab, lapack_int ldab, double* bb,\n                                lapack_int ldbb, double* w, double* z,\n                                lapack_int ldz, double* work, lapack_int lwork,\n                                lapack_int* iwork, lapack_int liwork );\n\nlapack_int LAPACKE_ssbgvx_work( int matrix_order, char jobz, char range,\n                                char uplo, lapack_int n, lapack_int ka,\n                                lapack_int kb, float* ab, lapack_int ldab,\n                                float* bb, lapack_int ldbb, float* q,\n                                lapack_int ldq, float vl, float vu,\n                                lapack_int il, lapack_int iu, float abstol,\n                                lapack_int* m, float* w, float* z,\n                                lapack_int ldz, float* work, lapack_int* iwork,\n                                lapack_int* ifail );\nlapack_int LAPACKE_dsbgvx_work( int matrix_order, char jobz, char range,\n                                char uplo, lapack_int n, lapack_int ka,\n                                lapack_int kb, double* ab, lapack_int ldab,\n                                double* bb, lapack_int ldbb, double* q,\n                                lapack_int ldq, double vl, double vu,\n                                lapack_int il, lapack_int iu, double abstol,\n                                lapack_int* m, double* w, double* z,\n                                lapack_int ldz, double* work, lapack_int* iwork,\n                                lapack_int* ifail );\n\nlapack_int LAPACKE_ssbtrd_work( int matrix_order, char vect, char uplo,\n                                lapack_int n, lapack_int kd, float* ab,\n                                lapack_int ldab, float* d, float* e, float* q,\n                                lapack_int ldq, float* work );\nlapack_int LAPACKE_dsbtrd_work( int matrix_order, char vect, char uplo,\n                                lapack_int n, lapack_int kd, double* ab,\n                                lapack_int ldab, double* d, double* e,\n                                double* q, lapack_int ldq, double* work );\n\nlapack_int LAPACKE_ssfrk_work( int matrix_order, char transr, char uplo,\n                               char trans, lapack_int n, lapack_int k,\n                               float alpha, const float* a, lapack_int lda,\n                               float beta, float* c );\nlapack_int LAPACKE_dsfrk_work( int matrix_order, char transr, char uplo,\n                               char trans, lapack_int n, lapack_int k,\n                               double alpha, const double* a, lapack_int lda,\n                               double beta, double* c );\n\nlapack_int LAPACKE_sspcon_work( int matrix_order, char uplo, lapack_int n,\n                                const float* ap, const lapack_int* ipiv,\n                                float anorm, float* rcond, float* work,\n                                lapack_int* iwork );\nlapack_int LAPACKE_dspcon_work( int matrix_order, char uplo, lapack_int n,\n                                const double* ap, const lapack_int* ipiv,\n                                double anorm, double* rcond, double* work,\n                                lapack_int* iwork );\nlapack_int LAPACKE_cspcon_work( int matrix_order, char uplo, lapack_int n,\n                                const lapack_complex_float* ap,\n                                const lapack_int* ipiv, float anorm,\n                                float* rcond, lapack_complex_float* work );\nlapack_int LAPACKE_zspcon_work( int matrix_order, char uplo, lapack_int n,\n                                const lapack_complex_double* ap,\n                                const lapack_int* ipiv, double anorm,\n                                double* rcond, lapack_complex_double* work );\n\nlapack_int LAPACKE_sspev_work( int matrix_order, char jobz, char uplo,\n                               lapack_int n, float* ap, float* w, float* z,\n                               lapack_int ldz, float* work );\nlapack_int LAPACKE_dspev_work( int matrix_order, char jobz, char uplo,\n                               lapack_int n, double* ap, double* w, double* z,\n                               lapack_int ldz, double* work );\n\nlapack_int LAPACKE_sspevd_work( int matrix_order, char jobz, char uplo,\n                                lapack_int n, float* ap, float* w, float* z,\n                                lapack_int ldz, float* work, lapack_int lwork,\n                                lapack_int* iwork, lapack_int liwork );\nlapack_int LAPACKE_dspevd_work( int matrix_order, char jobz, char uplo,\n                                lapack_int n, double* ap, double* w, double* z,\n                                lapack_int ldz, double* work, lapack_int lwork,\n                                lapack_int* iwork, lapack_int liwork );\n\nlapack_int LAPACKE_sspevx_work( int matrix_order, char jobz, char range,\n                                char uplo, lapack_int n, float* ap, float vl,\n                                float vu, lapack_int il, lapack_int iu,\n                                float abstol, lapack_int* m, float* w, float* z,\n                                lapack_int ldz, float* work, lapack_int* iwork,\n                                lapack_int* ifail );\nlapack_int LAPACKE_dspevx_work( int matrix_order, char jobz, char range,\n                                char uplo, lapack_int n, double* ap, double vl,\n                                double vu, lapack_int il, lapack_int iu,\n                                double abstol, lapack_int* m, double* w,\n                                double* z, lapack_int ldz, double* work,\n                                lapack_int* iwork, lapack_int* ifail );\n\nlapack_int LAPACKE_sspgst_work( int matrix_order, lapack_int itype, char uplo,\n                                lapack_int n, float* ap, const float* bp );\nlapack_int LAPACKE_dspgst_work( int matrix_order, lapack_int itype, char uplo,\n                                lapack_int n, double* ap, const double* bp );\n\nlapack_int LAPACKE_sspgv_work( int matrix_order, lapack_int itype, char jobz,\n                               char uplo, lapack_int n, float* ap, float* bp,\n                               float* w, float* z, lapack_int ldz,\n                               float* work );\nlapack_int LAPACKE_dspgv_work( int matrix_order, lapack_int itype, char jobz,\n                               char uplo, lapack_int n, double* ap, double* bp,\n                               double* w, double* z, lapack_int ldz,\n                               double* work );\n\nlapack_int LAPACKE_sspgvd_work( int matrix_order, lapack_int itype, char jobz,\n                                char uplo, lapack_int n, float* ap, float* bp,\n                                float* w, float* z, lapack_int ldz, float* work,\n                                lapack_int lwork, lapack_int* iwork,\n                                lapack_int liwork );\nlapack_int LAPACKE_dspgvd_work( int matrix_order, lapack_int itype, char jobz,\n                                char uplo, lapack_int n, double* ap, double* bp,\n                                double* w, double* z, lapack_int ldz,\n                                double* work, lapack_int lwork,\n                                lapack_int* iwork, lapack_int liwork );\n\nlapack_int LAPACKE_sspgvx_work( int matrix_order, lapack_int itype, char jobz,\n                                char range, char uplo, lapack_int n, float* ap,\n                                float* bp, float vl, float vu, lapack_int il,\n                                lapack_int iu, float abstol, lapack_int* m,\n                                float* w, float* z, lapack_int ldz, float* work,\n                                lapack_int* iwork, lapack_int* ifail );\nlapack_int LAPACKE_dspgvx_work( int matrix_order, lapack_int itype, char jobz,\n                                char range, char uplo, lapack_int n, double* ap,\n                                double* bp, double vl, double vu, lapack_int il,\n                                lapack_int iu, double abstol, lapack_int* m,\n                                double* w, double* z, lapack_int ldz,\n                                double* work, lapack_int* iwork,\n                                lapack_int* ifail );\n\nlapack_int LAPACKE_ssprfs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const float* ap,\n                                const float* afp, const lapack_int* ipiv,\n                                const float* b, lapack_int ldb, float* x,\n                                lapack_int ldx, float* ferr, float* berr,\n                                float* work, lapack_int* iwork );\nlapack_int LAPACKE_dsprfs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const double* ap,\n                                const double* afp, const lapack_int* ipiv,\n                                const double* b, lapack_int ldb, double* x,\n                                lapack_int ldx, double* ferr, double* berr,\n                                double* work, lapack_int* iwork );\nlapack_int LAPACKE_csprfs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const lapack_complex_float* ap,\n                                const lapack_complex_float* afp,\n                                const lapack_int* ipiv,\n                                const lapack_complex_float* b, lapack_int ldb,\n                                lapack_complex_float* x, lapack_int ldx,\n                                float* ferr, float* berr,\n                                lapack_complex_float* work, float* rwork );\nlapack_int LAPACKE_zsprfs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs,\n                                const lapack_complex_double* ap,\n                                const lapack_complex_double* afp,\n                                const lapack_int* ipiv,\n                                const lapack_complex_double* b, lapack_int ldb,\n                                lapack_complex_double* x, lapack_int ldx,\n                                double* ferr, double* berr,\n                                lapack_complex_double* work, double* rwork );\n\nlapack_int LAPACKE_sspsv_work( int matrix_order, char uplo, lapack_int n,\n                               lapack_int nrhs, float* ap, lapack_int* ipiv,\n                               float* b, lapack_int ldb );\nlapack_int LAPACKE_dspsv_work( int matrix_order, char uplo, lapack_int n,\n                               lapack_int nrhs, double* ap, lapack_int* ipiv,\n                               double* b, lapack_int ldb );\nlapack_int LAPACKE_cspsv_work( int matrix_order, char uplo, lapack_int n,\n                               lapack_int nrhs, lapack_complex_float* ap,\n                               lapack_int* ipiv, lapack_complex_float* b,\n                               lapack_int ldb );\nlapack_int LAPACKE_zspsv_work( int matrix_order, char uplo, lapack_int n,\n                               lapack_int nrhs, lapack_complex_double* ap,\n                               lapack_int* ipiv, lapack_complex_double* b,\n                               lapack_int ldb );\n\nlapack_int LAPACKE_sspsvx_work( int matrix_order, char fact, char uplo,\n                                lapack_int n, lapack_int nrhs, const float* ap,\n                                float* afp, lapack_int* ipiv, const float* b,\n                                lapack_int ldb, float* x, lapack_int ldx,\n                                float* rcond, float* ferr, float* berr,\n                                float* work, lapack_int* iwork );\nlapack_int LAPACKE_dspsvx_work( int matrix_order, char fact, char uplo,\n                                lapack_int n, lapack_int nrhs, const double* ap,\n                                double* afp, lapack_int* ipiv, const double* b,\n                                lapack_int ldb, double* x, lapack_int ldx,\n                                double* rcond, double* ferr, double* berr,\n                                double* work, lapack_int* iwork );\nlapack_int LAPACKE_cspsvx_work( int matrix_order, char fact, char uplo,\n                                lapack_int n, lapack_int nrhs,\n                                const lapack_complex_float* ap,\n                                lapack_complex_float* afp, lapack_int* ipiv,\n                                const lapack_complex_float* b, lapack_int ldb,\n                                lapack_complex_float* x, lapack_int ldx,\n                                float* rcond, float* ferr, float* berr,\n                                lapack_complex_float* work, float* rwork );\nlapack_int LAPACKE_zspsvx_work( int matrix_order, char fact, char uplo,\n                                lapack_int n, lapack_int nrhs,\n                                const lapack_complex_double* ap,\n                                lapack_complex_double* afp, lapack_int* ipiv,\n                                const lapack_complex_double* b, lapack_int ldb,\n                                lapack_complex_double* x, lapack_int ldx,\n                                double* rcond, double* ferr, double* berr,\n                                lapack_complex_double* work, double* rwork );\n\nlapack_int LAPACKE_ssptrd_work( int matrix_order, char uplo, lapack_int n,\n                                float* ap, float* d, float* e, float* tau );\nlapack_int LAPACKE_dsptrd_work( int matrix_order, char uplo, lapack_int n,\n                                double* ap, double* d, double* e, double* tau );\n\nlapack_int LAPACKE_ssptrf_work( int matrix_order, char uplo, lapack_int n,\n                                float* ap, lapack_int* ipiv );\nlapack_int LAPACKE_dsptrf_work( int matrix_order, char uplo, lapack_int n,\n                                double* ap, lapack_int* ipiv );\nlapack_int LAPACKE_csptrf_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_complex_float* ap, lapack_int* ipiv );\nlapack_int LAPACKE_zsptrf_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_complex_double* ap, lapack_int* ipiv );\n\nlapack_int LAPACKE_ssptri_work( int matrix_order, char uplo, lapack_int n,\n                                float* ap, const lapack_int* ipiv,\n                                float* work );\nlapack_int LAPACKE_dsptri_work( int matrix_order, char uplo, lapack_int n,\n                                double* ap, const lapack_int* ipiv,\n                                double* work );\nlapack_int LAPACKE_csptri_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_complex_float* ap,\n                                const lapack_int* ipiv,\n                                lapack_complex_float* work );\nlapack_int LAPACKE_zsptri_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_complex_double* ap,\n                                const lapack_int* ipiv,\n                                lapack_complex_double* work );\n\nlapack_int LAPACKE_ssptrs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const float* ap,\n                                const lapack_int* ipiv, float* b,\n                                lapack_int ldb );\nlapack_int LAPACKE_dsptrs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const double* ap,\n                                const lapack_int* ipiv, double* b,\n                                lapack_int ldb );\nlapack_int LAPACKE_csptrs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const lapack_complex_float* ap,\n                                const lapack_int* ipiv, lapack_complex_float* b,\n                                lapack_int ldb );\nlapack_int LAPACKE_zsptrs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs,\n                                const lapack_complex_double* ap,\n                                const lapack_int* ipiv,\n                                lapack_complex_double* b, lapack_int ldb );\n\nlapack_int LAPACKE_sstebz_work( char range, char order, lapack_int n, float vl,\n                                float vu, lapack_int il, lapack_int iu,\n                                float abstol, const float* d, const float* e,\n                                lapack_int* m, lapack_int* nsplit, float* w,\n                                lapack_int* iblock, lapack_int* isplit,\n                                float* work, lapack_int* iwork );\nlapack_int LAPACKE_dstebz_work( char range, char order, lapack_int n, double vl,\n                                double vu, lapack_int il, lapack_int iu,\n                                double abstol, const double* d, const double* e,\n                                lapack_int* m, lapack_int* nsplit, double* w,\n                                lapack_int* iblock, lapack_int* isplit,\n                                double* work, lapack_int* iwork );\n\nlapack_int LAPACKE_sstedc_work( int matrix_order, char compz, lapack_int n,\n                                float* d, float* e, float* z, lapack_int ldz,\n                                float* work, lapack_int lwork,\n                                lapack_int* iwork, lapack_int liwork );\nlapack_int LAPACKE_dstedc_work( int matrix_order, char compz, lapack_int n,\n                                double* d, double* e, double* z, lapack_int ldz,\n                                double* work, lapack_int lwork,\n                                lapack_int* iwork, lapack_int liwork );\nlapack_int LAPACKE_cstedc_work( int matrix_order, char compz, lapack_int n,\n                                float* d, float* e, lapack_complex_float* z,\n                                lapack_int ldz, lapack_complex_float* work,\n                                lapack_int lwork, float* rwork,\n                                lapack_int lrwork, lapack_int* iwork,\n                                lapack_int liwork );\nlapack_int LAPACKE_zstedc_work( int matrix_order, char compz, lapack_int n,\n                                double* d, double* e, lapack_complex_double* z,\n                                lapack_int ldz, lapack_complex_double* work,\n                                lapack_int lwork, double* rwork,\n                                lapack_int lrwork, lapack_int* iwork,\n                                lapack_int liwork );\n\nlapack_int LAPACKE_sstegr_work( int matrix_order, char jobz, char range,\n                                lapack_int n, float* d, float* e, float vl,\n                                float vu, lapack_int il, lapack_int iu,\n                                float abstol, lapack_int* m, float* w, float* z,\n                                lapack_int ldz, lapack_int* isuppz, float* work,\n                                lapack_int lwork, lapack_int* iwork,\n                                lapack_int liwork );\nlapack_int LAPACKE_dstegr_work( int matrix_order, char jobz, char range,\n                                lapack_int n, double* d, double* e, double vl,\n                                double vu, lapack_int il, lapack_int iu,\n                                double abstol, lapack_int* m, double* w,\n                                double* z, lapack_int ldz, lapack_int* isuppz,\n                                double* work, lapack_int lwork,\n                                lapack_int* iwork, lapack_int liwork );\nlapack_int LAPACKE_cstegr_work( int matrix_order, char jobz, char range,\n                                lapack_int n, float* d, float* e, float vl,\n                                float vu, lapack_int il, lapack_int iu,\n                                float abstol, lapack_int* m, float* w,\n                                lapack_complex_float* z, lapack_int ldz,\n                                lapack_int* isuppz, float* work,\n                                lapack_int lwork, lapack_int* iwork,\n                                lapack_int liwork );\nlapack_int LAPACKE_zstegr_work( int matrix_order, char jobz, char range,\n                                lapack_int n, double* d, double* e, double vl,\n                                double vu, lapack_int il, lapack_int iu,\n                                double abstol, lapack_int* m, double* w,\n                                lapack_complex_double* z, lapack_int ldz,\n                                lapack_int* isuppz, double* work,\n                                lapack_int lwork, lapack_int* iwork,\n                                lapack_int liwork );\n\nlapack_int LAPACKE_sstein_work( int matrix_order, lapack_int n, const float* d,\n                                const float* e, lapack_int m, const float* w,\n                                const lapack_int* iblock,\n                                const lapack_int* isplit, float* z,\n                                lapack_int ldz, float* work, lapack_int* iwork,\n                                lapack_int* ifailv );\nlapack_int LAPACKE_dstein_work( int matrix_order, lapack_int n, const double* d,\n                                const double* e, lapack_int m, const double* w,\n                                const lapack_int* iblock,\n                                const lapack_int* isplit, double* z,\n                                lapack_int ldz, double* work, lapack_int* iwork,\n                                lapack_int* ifailv );\nlapack_int LAPACKE_cstein_work( int matrix_order, lapack_int n, const float* d,\n                                const float* e, lapack_int m, const float* w,\n                                const lapack_int* iblock,\n                                const lapack_int* isplit,\n                                lapack_complex_float* z, lapack_int ldz,\n                                float* work, lapack_int* iwork,\n                                lapack_int* ifailv );\nlapack_int LAPACKE_zstein_work( int matrix_order, lapack_int n, const double* d,\n                                const double* e, lapack_int m, const double* w,\n                                const lapack_int* iblock,\n                                const lapack_int* isplit,\n                                lapack_complex_double* z, lapack_int ldz,\n                                double* work, lapack_int* iwork,\n                                lapack_int* ifailv );\n\nlapack_int LAPACKE_sstemr_work( int matrix_order, char jobz, char range,\n                                lapack_int n, float* d, float* e, float vl,\n                                float vu, lapack_int il, lapack_int iu,\n                                lapack_int* m, float* w, float* z,\n                                lapack_int ldz, lapack_int nzc,\n                                lapack_int* isuppz, lapack_logical* tryrac,\n                                float* work, lapack_int lwork,\n                                lapack_int* iwork, lapack_int liwork );\nlapack_int LAPACKE_dstemr_work( int matrix_order, char jobz, char range,\n                                lapack_int n, double* d, double* e, double vl,\n                                double vu, lapack_int il, lapack_int iu,\n                                lapack_int* m, double* w, double* z,\n                                lapack_int ldz, lapack_int nzc,\n                                lapack_int* isuppz, lapack_logical* tryrac,\n                                double* work, lapack_int lwork,\n                                lapack_int* iwork, lapack_int liwork );\nlapack_int LAPACKE_cstemr_work( int matrix_order, char jobz, char range,\n                                lapack_int n, float* d, float* e, float vl,\n                                float vu, lapack_int il, lapack_int iu,\n                                lapack_int* m, float* w,\n                                lapack_complex_float* z, lapack_int ldz,\n                                lapack_int nzc, lapack_int* isuppz,\n                                lapack_logical* tryrac, float* work,\n                                lapack_int lwork, lapack_int* iwork,\n                                lapack_int liwork );\nlapack_int LAPACKE_zstemr_work( int matrix_order, char jobz, char range,\n                                lapack_int n, double* d, double* e, double vl,\n                                double vu, lapack_int il, lapack_int iu,\n                                lapack_int* m, double* w,\n                                lapack_complex_double* z, lapack_int ldz,\n                                lapack_int nzc, lapack_int* isuppz,\n                                lapack_logical* tryrac, double* work,\n                                lapack_int lwork, lapack_int* iwork,\n                                lapack_int liwork );\n\nlapack_int LAPACKE_ssteqr_work( int matrix_order, char compz, lapack_int n,\n                                float* d, float* e, float* z, lapack_int ldz,\n                                float* work );\nlapack_int LAPACKE_dsteqr_work( int matrix_order, char compz, lapack_int n,\n                                double* d, double* e, double* z, lapack_int ldz,\n                                double* work );\nlapack_int LAPACKE_csteqr_work( int matrix_order, char compz, lapack_int n,\n                                float* d, float* e, lapack_complex_float* z,\n                                lapack_int ldz, float* work );\nlapack_int LAPACKE_zsteqr_work( int matrix_order, char compz, lapack_int n,\n                                double* d, double* e, lapack_complex_double* z,\n                                lapack_int ldz, double* work );\n\nlapack_int LAPACKE_ssterf_work( lapack_int n, float* d, float* e );\nlapack_int LAPACKE_dsterf_work( lapack_int n, double* d, double* e );\n\nlapack_int LAPACKE_sstev_work( int matrix_order, char jobz, lapack_int n,\n                               float* d, float* e, float* z, lapack_int ldz,\n                               float* work );\nlapack_int LAPACKE_dstev_work( int matrix_order, char jobz, lapack_int n,\n                               double* d, double* e, double* z, lapack_int ldz,\n                               double* work );\n\nlapack_int LAPACKE_sstevd_work( int matrix_order, char jobz, lapack_int n,\n                                float* d, float* e, float* z, lapack_int ldz,\n                                float* work, lapack_int lwork,\n                                lapack_int* iwork, lapack_int liwork );\nlapack_int LAPACKE_dstevd_work( int matrix_order, char jobz, lapack_int n,\n                                double* d, double* e, double* z, lapack_int ldz,\n                                double* work, lapack_int lwork,\n                                lapack_int* iwork, lapack_int liwork );\n\nlapack_int LAPACKE_sstevr_work( int matrix_order, char jobz, char range,\n                                lapack_int n, float* d, float* e, float vl,\n                                float vu, lapack_int il, lapack_int iu,\n                                float abstol, lapack_int* m, float* w, float* z,\n                                lapack_int ldz, lapack_int* isuppz, float* work,\n                                lapack_int lwork, lapack_int* iwork,\n                                lapack_int liwork );\nlapack_int LAPACKE_dstevr_work( int matrix_order, char jobz, char range,\n                                lapack_int n, double* d, double* e, double vl,\n                                double vu, lapack_int il, lapack_int iu,\n                                double abstol, lapack_int* m, double* w,\n                                double* z, lapack_int ldz, lapack_int* isuppz,\n                                double* work, lapack_int lwork,\n                                lapack_int* iwork, lapack_int liwork );\n\nlapack_int LAPACKE_sstevx_work( int matrix_order, char jobz, char range,\n                                lapack_int n, float* d, float* e, float vl,\n                                float vu, lapack_int il, lapack_int iu,\n                                float abstol, lapack_int* m, float* w, float* z,\n                                lapack_int ldz, float* work, lapack_int* iwork,\n                                lapack_int* ifail );\nlapack_int LAPACKE_dstevx_work( int matrix_order, char jobz, char range,\n                                lapack_int n, double* d, double* e, double vl,\n                                double vu, lapack_int il, lapack_int iu,\n                                double abstol, lapack_int* m, double* w,\n                                double* z, lapack_int ldz, double* work,\n                                lapack_int* iwork, lapack_int* ifail );\n\nlapack_int LAPACKE_ssycon_work( int matrix_order, char uplo, lapack_int n,\n                                const float* a, lapack_int lda,\n                                const lapack_int* ipiv, float anorm,\n                                float* rcond, float* work, lapack_int* iwork );\nlapack_int LAPACKE_dsycon_work( int matrix_order, char uplo, lapack_int n,\n                                const double* a, lapack_int lda,\n                                const lapack_int* ipiv, double anorm,\n                                double* rcond, double* work,\n                                lapack_int* iwork );\nlapack_int LAPACKE_csycon_work( int matrix_order, char uplo, lapack_int n,\n                                const lapack_complex_float* a, lapack_int lda,\n                                const lapack_int* ipiv, float anorm,\n                                float* rcond, lapack_complex_float* work );\nlapack_int LAPACKE_zsycon_work( int matrix_order, char uplo, lapack_int n,\n                                const lapack_complex_double* a, lapack_int lda,\n                                const lapack_int* ipiv, double anorm,\n                                double* rcond, lapack_complex_double* work );\n\nlapack_int LAPACKE_ssyequb_work( int matrix_order, char uplo, lapack_int n,\n                                 const float* a, lapack_int lda, float* s,\n                                 float* scond, float* amax, float* work );\nlapack_int LAPACKE_dsyequb_work( int matrix_order, char uplo, lapack_int n,\n                                 const double* a, lapack_int lda, double* s,\n                                 double* scond, double* amax, double* work );\nlapack_int LAPACKE_csyequb_work( int matrix_order, char uplo, lapack_int n,\n                                 const lapack_complex_float* a, lapack_int lda,\n                                 float* s, float* scond, float* amax,\n                                 lapack_complex_float* work );\nlapack_int LAPACKE_zsyequb_work( int matrix_order, char uplo, lapack_int n,\n                                 const lapack_complex_double* a, lapack_int lda,\n                                 double* s, double* scond, double* amax,\n                                 lapack_complex_double* work );\n\nlapack_int LAPACKE_ssyev_work( int matrix_order, char jobz, char uplo,\n                               lapack_int n, float* a, lapack_int lda, float* w,\n                               float* work, lapack_int lwork );\nlapack_int LAPACKE_dsyev_work( int matrix_order, char jobz, char uplo,\n                               lapack_int n, double* a, lapack_int lda,\n                               double* w, double* work, lapack_int lwork );\n\nlapack_int LAPACKE_ssyevd_work( int matrix_order, char jobz, char uplo,\n                                lapack_int n, float* a, lapack_int lda,\n                                float* w, float* work, lapack_int lwork,\n                                lapack_int* iwork, lapack_int liwork );\nlapack_int LAPACKE_dsyevd_work( int matrix_order, char jobz, char uplo,\n                                lapack_int n, double* a, lapack_int lda,\n                                double* w, double* work, lapack_int lwork,\n                                lapack_int* iwork, lapack_int liwork );\n\nlapack_int LAPACKE_ssyevr_work( int matrix_order, char jobz, char range,\n                                char uplo, lapack_int n, float* a,\n                                lapack_int lda, float vl, float vu,\n                                lapack_int il, lapack_int iu, float abstol,\n                                lapack_int* m, float* w, float* z,\n                                lapack_int ldz, lapack_int* isuppz, float* work,\n                                lapack_int lwork, lapack_int* iwork,\n                                lapack_int liwork );\nlapack_int LAPACKE_dsyevr_work( int matrix_order, char jobz, char range,\n                                char uplo, lapack_int n, double* a,\n                                lapack_int lda, double vl, double vu,\n                                lapack_int il, lapack_int iu, double abstol,\n                                lapack_int* m, double* w, double* z,\n                                lapack_int ldz, lapack_int* isuppz,\n                                double* work, lapack_int lwork,\n                                lapack_int* iwork, lapack_int liwork );\n\nlapack_int LAPACKE_ssyevx_work( int matrix_order, char jobz, char range,\n                                char uplo, lapack_int n, float* a,\n                                lapack_int lda, float vl, float vu,\n                                lapack_int il, lapack_int iu, float abstol,\n                                lapack_int* m, float* w, float* z,\n                                lapack_int ldz, float* work, lapack_int lwork,\n                                lapack_int* iwork, lapack_int* ifail );\nlapack_int LAPACKE_dsyevx_work( int matrix_order, char jobz, char range,\n                                char uplo, lapack_int n, double* a,\n                                lapack_int lda, double vl, double vu,\n                                lapack_int il, lapack_int iu, double abstol,\n                                lapack_int* m, double* w, double* z,\n                                lapack_int ldz, double* work, lapack_int lwork,\n                                lapack_int* iwork, lapack_int* ifail );\n\nlapack_int LAPACKE_ssygst_work( int matrix_order, lapack_int itype, char uplo,\n                                lapack_int n, float* a, lapack_int lda,\n                                const float* b, lapack_int ldb );\nlapack_int LAPACKE_dsygst_work( int matrix_order, lapack_int itype, char uplo,\n                                lapack_int n, double* a, lapack_int lda,\n                                const double* b, lapack_int ldb );\n\nlapack_int LAPACKE_ssygv_work( int matrix_order, lapack_int itype, char jobz,\n                               char uplo, lapack_int n, float* a,\n                               lapack_int lda, float* b, lapack_int ldb,\n                               float* w, float* work, lapack_int lwork );\nlapack_int LAPACKE_dsygv_work( int matrix_order, lapack_int itype, char jobz,\n                               char uplo, lapack_int n, double* a,\n                               lapack_int lda, double* b, lapack_int ldb,\n                               double* w, double* work, lapack_int lwork );\n\nlapack_int LAPACKE_ssygvd_work( int matrix_order, lapack_int itype, char jobz,\n                                char uplo, lapack_int n, float* a,\n                                lapack_int lda, float* b, lapack_int ldb,\n                                float* w, float* work, lapack_int lwork,\n                                lapack_int* iwork, lapack_int liwork );\nlapack_int LAPACKE_dsygvd_work( int matrix_order, lapack_int itype, char jobz,\n                                char uplo, lapack_int n, double* a,\n                                lapack_int lda, double* b, lapack_int ldb,\n                                double* w, double* work, lapack_int lwork,\n                                lapack_int* iwork, lapack_int liwork );\n\nlapack_int LAPACKE_ssygvx_work( int matrix_order, lapack_int itype, char jobz,\n                                char range, char uplo, lapack_int n, float* a,\n                                lapack_int lda, float* b, lapack_int ldb,\n                                float vl, float vu, lapack_int il,\n                                lapack_int iu, float abstol, lapack_int* m,\n                                float* w, float* z, lapack_int ldz, float* work,\n                                lapack_int lwork, lapack_int* iwork,\n                                lapack_int* ifail );\nlapack_int LAPACKE_dsygvx_work( int matrix_order, lapack_int itype, char jobz,\n                                char range, char uplo, lapack_int n, double* a,\n                                lapack_int lda, double* b, lapack_int ldb,\n                                double vl, double vu, lapack_int il,\n                                lapack_int iu, double abstol, lapack_int* m,\n                                double* w, double* z, lapack_int ldz,\n                                double* work, lapack_int lwork,\n                                lapack_int* iwork, lapack_int* ifail );\n\nlapack_int LAPACKE_ssyrfs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const float* a, lapack_int lda,\n                                const float* af, lapack_int ldaf,\n                                const lapack_int* ipiv, const float* b,\n                                lapack_int ldb, float* x, lapack_int ldx,\n                                float* ferr, float* berr, float* work,\n                                lapack_int* iwork );\nlapack_int LAPACKE_dsyrfs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const double* a,\n                                lapack_int lda, const double* af,\n                                lapack_int ldaf, const lapack_int* ipiv,\n                                const double* b, lapack_int ldb, double* x,\n                                lapack_int ldx, double* ferr, double* berr,\n                                double* work, lapack_int* iwork );\nlapack_int LAPACKE_csyrfs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const lapack_complex_float* a,\n                                lapack_int lda, const lapack_complex_float* af,\n                                lapack_int ldaf, const lapack_int* ipiv,\n                                const lapack_complex_float* b, lapack_int ldb,\n                                lapack_complex_float* x, lapack_int ldx,\n                                float* ferr, float* berr,\n                                lapack_complex_float* work, float* rwork );\nlapack_int LAPACKE_zsyrfs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const lapack_complex_double* a,\n                                lapack_int lda, const lapack_complex_double* af,\n                                lapack_int ldaf, const lapack_int* ipiv,\n                                const lapack_complex_double* b, lapack_int ldb,\n                                lapack_complex_double* x, lapack_int ldx,\n                                double* ferr, double* berr,\n                                lapack_complex_double* work, double* rwork );\n\nlapack_int LAPACKE_ssyrfsx_work( int matrix_order, char uplo, char equed,\n                                 lapack_int n, lapack_int nrhs, const float* a,\n                                 lapack_int lda, const float* af,\n                                 lapack_int ldaf, const lapack_int* ipiv,\n                                 const float* s, const float* b, lapack_int ldb,\n                                 float* x, lapack_int ldx, float* rcond,\n                                 float* berr, lapack_int n_err_bnds,\n                                 float* err_bnds_norm, float* err_bnds_comp,\n                                 lapack_int nparams, float* params, float* work,\n                                 lapack_int* iwork );\nlapack_int LAPACKE_dsyrfsx_work( int matrix_order, char uplo, char equed,\n                                 lapack_int n, lapack_int nrhs, const double* a,\n                                 lapack_int lda, const double* af,\n                                 lapack_int ldaf, const lapack_int* ipiv,\n                                 const double* s, const double* b,\n                                 lapack_int ldb, double* x, lapack_int ldx,\n                                 double* rcond, double* berr,\n                                 lapack_int n_err_bnds, double* err_bnds_norm,\n                                 double* err_bnds_comp, lapack_int nparams,\n                                 double* params, double* work,\n                                 lapack_int* iwork );\nlapack_int LAPACKE_csyrfsx_work( int matrix_order, char uplo, char equed,\n                                 lapack_int n, lapack_int nrhs,\n                                 const lapack_complex_float* a, lapack_int lda,\n                                 const lapack_complex_float* af,\n                                 lapack_int ldaf, const lapack_int* ipiv,\n                                 const float* s, const lapack_complex_float* b,\n                                 lapack_int ldb, lapack_complex_float* x,\n                                 lapack_int ldx, float* rcond, float* berr,\n                                 lapack_int n_err_bnds, float* err_bnds_norm,\n                                 float* err_bnds_comp, lapack_int nparams,\n                                 float* params, lapack_complex_float* work,\n                                 float* rwork );\nlapack_int LAPACKE_zsyrfsx_work( int matrix_order, char uplo, char equed,\n                                 lapack_int n, lapack_int nrhs,\n                                 const lapack_complex_double* a, lapack_int lda,\n                                 const lapack_complex_double* af,\n                                 lapack_int ldaf, const lapack_int* ipiv,\n                                 const double* s,\n                                 const lapack_complex_double* b, lapack_int ldb,\n                                 lapack_complex_double* x, lapack_int ldx,\n                                 double* rcond, double* berr,\n                                 lapack_int n_err_bnds, double* err_bnds_norm,\n                                 double* err_bnds_comp, lapack_int nparams,\n                                 double* params, lapack_complex_double* work,\n                                 double* rwork );\n\nlapack_int LAPACKE_ssysv_work( int matrix_order, char uplo, lapack_int n,\n                               lapack_int nrhs, float* a, lapack_int lda,\n                               lapack_int* ipiv, float* b, lapack_int ldb,\n                               float* work, lapack_int lwork );\nlapack_int LAPACKE_dsysv_work( int matrix_order, char uplo, lapack_int n,\n                               lapack_int nrhs, double* a, lapack_int lda,\n                               lapack_int* ipiv, double* b, lapack_int ldb,\n                               double* work, lapack_int lwork );\nlapack_int LAPACKE_csysv_work( int matrix_order, char uplo, lapack_int n,\n                               lapack_int nrhs, lapack_complex_float* a,\n                               lapack_int lda, lapack_int* ipiv,\n                               lapack_complex_float* b, lapack_int ldb,\n                               lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_zsysv_work( int matrix_order, char uplo, lapack_int n,\n                               lapack_int nrhs, lapack_complex_double* a,\n                               lapack_int lda, lapack_int* ipiv,\n                               lapack_complex_double* b, lapack_int ldb,\n                               lapack_complex_double* work, lapack_int lwork );\n\nlapack_int LAPACKE_ssysvx_work( int matrix_order, char fact, char uplo,\n                                lapack_int n, lapack_int nrhs, const float* a,\n                                lapack_int lda, float* af, lapack_int ldaf,\n                                lapack_int* ipiv, const float* b,\n                                lapack_int ldb, float* x, lapack_int ldx,\n                                float* rcond, float* ferr, float* berr,\n                                float* work, lapack_int lwork,\n                                lapack_int* iwork );\nlapack_int LAPACKE_dsysvx_work( int matrix_order, char fact, char uplo,\n                                lapack_int n, lapack_int nrhs, const double* a,\n                                lapack_int lda, double* af, lapack_int ldaf,\n                                lapack_int* ipiv, const double* b,\n                                lapack_int ldb, double* x, lapack_int ldx,\n                                double* rcond, double* ferr, double* berr,\n                                double* work, lapack_int lwork,\n                                lapack_int* iwork );\nlapack_int LAPACKE_csysvx_work( int matrix_order, char fact, char uplo,\n                                lapack_int n, lapack_int nrhs,\n                                const lapack_complex_float* a, lapack_int lda,\n                                lapack_complex_float* af, lapack_int ldaf,\n                                lapack_int* ipiv, const lapack_complex_float* b,\n                                lapack_int ldb, lapack_complex_float* x,\n                                lapack_int ldx, float* rcond, float* ferr,\n                                float* berr, lapack_complex_float* work,\n                                lapack_int lwork, float* rwork );\nlapack_int LAPACKE_zsysvx_work( int matrix_order, char fact, char uplo,\n                                lapack_int n, lapack_int nrhs,\n                                const lapack_complex_double* a, lapack_int lda,\n                                lapack_complex_double* af, lapack_int ldaf,\n                                lapack_int* ipiv,\n                                const lapack_complex_double* b, lapack_int ldb,\n                                lapack_complex_double* x, lapack_int ldx,\n                                double* rcond, double* ferr, double* berr,\n                                lapack_complex_double* work, lapack_int lwork,\n                                double* rwork );\n\nlapack_int LAPACKE_ssysvxx_work( int matrix_order, char fact, char uplo,\n                                 lapack_int n, lapack_int nrhs, float* a,\n                                 lapack_int lda, float* af, lapack_int ldaf,\n                                 lapack_int* ipiv, char* equed, float* s,\n                                 float* b, lapack_int ldb, float* x,\n                                 lapack_int ldx, float* rcond, float* rpvgrw,\n                                 float* berr, lapack_int n_err_bnds,\n                                 float* err_bnds_norm, float* err_bnds_comp,\n                                 lapack_int nparams, float* params, float* work,\n                                 lapack_int* iwork );\nlapack_int LAPACKE_dsysvxx_work( int matrix_order, char fact, char uplo,\n                                 lapack_int n, lapack_int nrhs, double* a,\n                                 lapack_int lda, double* af, lapack_int ldaf,\n                                 lapack_int* ipiv, char* equed, double* s,\n                                 double* b, lapack_int ldb, double* x,\n                                 lapack_int ldx, double* rcond, double* rpvgrw,\n                                 double* berr, lapack_int n_err_bnds,\n                                 double* err_bnds_norm, double* err_bnds_comp,\n                                 lapack_int nparams, double* params,\n                                 double* work, lapack_int* iwork );\nlapack_int LAPACKE_csysvxx_work( int matrix_order, char fact, char uplo,\n                                 lapack_int n, lapack_int nrhs,\n                                 lapack_complex_float* a, lapack_int lda,\n                                 lapack_complex_float* af, lapack_int ldaf,\n                                 lapack_int* ipiv, char* equed, float* s,\n                                 lapack_complex_float* b, lapack_int ldb,\n                                 lapack_complex_float* x, lapack_int ldx,\n                                 float* rcond, float* rpvgrw, float* berr,\n                                 lapack_int n_err_bnds, float* err_bnds_norm,\n                                 float* err_bnds_comp, lapack_int nparams,\n                                 float* params, lapack_complex_float* work,\n                                 float* rwork );\nlapack_int LAPACKE_zsysvxx_work( int matrix_order, char fact, char uplo,\n                                 lapack_int n, lapack_int nrhs,\n                                 lapack_complex_double* a, lapack_int lda,\n                                 lapack_complex_double* af, lapack_int ldaf,\n                                 lapack_int* ipiv, char* equed, double* s,\n                                 lapack_complex_double* b, lapack_int ldb,\n                                 lapack_complex_double* x, lapack_int ldx,\n                                 double* rcond, double* rpvgrw, double* berr,\n                                 lapack_int n_err_bnds, double* err_bnds_norm,\n                                 double* err_bnds_comp, lapack_int nparams,\n                                 double* params, lapack_complex_double* work,\n                                 double* rwork );\n\nlapack_int LAPACKE_ssytrd_work( int matrix_order, char uplo, lapack_int n,\n                                float* a, lapack_int lda, float* d, float* e,\n                                float* tau, float* work, lapack_int lwork );\nlapack_int LAPACKE_dsytrd_work( int matrix_order, char uplo, lapack_int n,\n                                double* a, lapack_int lda, double* d, double* e,\n                                double* tau, double* work, lapack_int lwork );\n\nlapack_int LAPACKE_ssytrf_work( int matrix_order, char uplo, lapack_int n,\n                                float* a, lapack_int lda, lapack_int* ipiv,\n                                float* work, lapack_int lwork );\nlapack_int LAPACKE_dsytrf_work( int matrix_order, char uplo, lapack_int n,\n                                double* a, lapack_int lda, lapack_int* ipiv,\n                                double* work, lapack_int lwork );\nlapack_int LAPACKE_csytrf_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_complex_float* a, lapack_int lda,\n                                lapack_int* ipiv, lapack_complex_float* work,\n                                lapack_int lwork );\nlapack_int LAPACKE_zsytrf_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_complex_double* a, lapack_int lda,\n                                lapack_int* ipiv, lapack_complex_double* work,\n                                lapack_int lwork );\n\nlapack_int LAPACKE_ssytri_work( int matrix_order, char uplo, lapack_int n,\n                                float* a, lapack_int lda,\n                                const lapack_int* ipiv, float* work );\nlapack_int LAPACKE_dsytri_work( int matrix_order, char uplo, lapack_int n,\n                                double* a, lapack_int lda,\n                                const lapack_int* ipiv, double* work );\nlapack_int LAPACKE_csytri_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_complex_float* a, lapack_int lda,\n                                const lapack_int* ipiv,\n                                lapack_complex_float* work );\nlapack_int LAPACKE_zsytri_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_complex_double* a, lapack_int lda,\n                                const lapack_int* ipiv,\n                                lapack_complex_double* work );\n\nlapack_int LAPACKE_ssytrs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const float* a, lapack_int lda,\n                                const lapack_int* ipiv, float* b,\n                                lapack_int ldb );\nlapack_int LAPACKE_dsytrs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const double* a,\n                                lapack_int lda, const lapack_int* ipiv,\n                                double* b, lapack_int ldb );\nlapack_int LAPACKE_csytrs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const lapack_complex_float* a,\n                                lapack_int lda, const lapack_int* ipiv,\n                                lapack_complex_float* b, lapack_int ldb );\nlapack_int LAPACKE_zsytrs_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_int nrhs, const lapack_complex_double* a,\n                                lapack_int lda, const lapack_int* ipiv,\n                                lapack_complex_double* b, lapack_int ldb );\n\nlapack_int LAPACKE_stbcon_work( int matrix_order, char norm, char uplo,\n                                char diag, lapack_int n, lapack_int kd,\n                                const float* ab, lapack_int ldab, float* rcond,\n                                float* work, lapack_int* iwork );\nlapack_int LAPACKE_dtbcon_work( int matrix_order, char norm, char uplo,\n                                char diag, lapack_int n, lapack_int kd,\n                                const double* ab, lapack_int ldab,\n                                double* rcond, double* work,\n                                lapack_int* iwork );\nlapack_int LAPACKE_ctbcon_work( int matrix_order, char norm, char uplo,\n                                char diag, lapack_int n, lapack_int kd,\n                                const lapack_complex_float* ab, lapack_int ldab,\n                                float* rcond, lapack_complex_float* work,\n                                float* rwork );\nlapack_int LAPACKE_ztbcon_work( int matrix_order, char norm, char uplo,\n                                char diag, lapack_int n, lapack_int kd,\n                                const lapack_complex_double* ab,\n                                lapack_int ldab, double* rcond,\n                                lapack_complex_double* work, double* rwork );\n\nlapack_int LAPACKE_stbrfs_work( int matrix_order, char uplo, char trans,\n                                char diag, lapack_int n, lapack_int kd,\n                                lapack_int nrhs, const float* ab,\n                                lapack_int ldab, const float* b, lapack_int ldb,\n                                const float* x, lapack_int ldx, float* ferr,\n                                float* berr, float* work, lapack_int* iwork );\nlapack_int LAPACKE_dtbrfs_work( int matrix_order, char uplo, char trans,\n                                char diag, lapack_int n, lapack_int kd,\n                                lapack_int nrhs, const double* ab,\n                                lapack_int ldab, const double* b,\n                                lapack_int ldb, const double* x, lapack_int ldx,\n                                double* ferr, double* berr, double* work,\n                                lapack_int* iwork );\nlapack_int LAPACKE_ctbrfs_work( int matrix_order, char uplo, char trans,\n                                char diag, lapack_int n, lapack_int kd,\n                                lapack_int nrhs, const lapack_complex_float* ab,\n                                lapack_int ldab, const lapack_complex_float* b,\n                                lapack_int ldb, const lapack_complex_float* x,\n                                lapack_int ldx, float* ferr, float* berr,\n                                lapack_complex_float* work, float* rwork );\nlapack_int LAPACKE_ztbrfs_work( int matrix_order, char uplo, char trans,\n                                char diag, lapack_int n, lapack_int kd,\n                                lapack_int nrhs,\n                                const lapack_complex_double* ab,\n                                lapack_int ldab, const lapack_complex_double* b,\n                                lapack_int ldb, const lapack_complex_double* x,\n                                lapack_int ldx, double* ferr, double* berr,\n                                lapack_complex_double* work, double* rwork );\n\nlapack_int LAPACKE_stbtrs_work( int matrix_order, char uplo, char trans,\n                                char diag, lapack_int n, lapack_int kd,\n                                lapack_int nrhs, const float* ab,\n                                lapack_int ldab, float* b, lapack_int ldb );\nlapack_int LAPACKE_dtbtrs_work( int matrix_order, char uplo, char trans,\n                                char diag, lapack_int n, lapack_int kd,\n                                lapack_int nrhs, const double* ab,\n                                lapack_int ldab, double* b, lapack_int ldb );\nlapack_int LAPACKE_ctbtrs_work( int matrix_order, char uplo, char trans,\n                                char diag, lapack_int n, lapack_int kd,\n                                lapack_int nrhs, const lapack_complex_float* ab,\n                                lapack_int ldab, lapack_complex_float* b,\n                                lapack_int ldb );\nlapack_int LAPACKE_ztbtrs_work( int matrix_order, char uplo, char trans,\n                                char diag, lapack_int n, lapack_int kd,\n                                lapack_int nrhs,\n                                const lapack_complex_double* ab,\n                                lapack_int ldab, lapack_complex_double* b,\n                                lapack_int ldb );\n\nlapack_int LAPACKE_stfsm_work( int matrix_order, char transr, char side,\n                               char uplo, char trans, char diag, lapack_int m,\n                               lapack_int n, float alpha, const float* a,\n                               float* b, lapack_int ldb );\nlapack_int LAPACKE_dtfsm_work( int matrix_order, char transr, char side,\n                               char uplo, char trans, char diag, lapack_int m,\n                               lapack_int n, double alpha, const double* a,\n                               double* b, lapack_int ldb );\nlapack_int LAPACKE_ctfsm_work( int matrix_order, char transr, char side,\n                               char uplo, char trans, char diag, lapack_int m,\n                               lapack_int n, lapack_complex_float alpha,\n                               const lapack_complex_float* a,\n                               lapack_complex_float* b, lapack_int ldb );\nlapack_int LAPACKE_ztfsm_work( int matrix_order, char transr, char side,\n                               char uplo, char trans, char diag, lapack_int m,\n                               lapack_int n, lapack_complex_double alpha,\n                               const lapack_complex_double* a,\n                               lapack_complex_double* b, lapack_int ldb );\n\nlapack_int LAPACKE_stftri_work( int matrix_order, char transr, char uplo,\n                                char diag, lapack_int n, float* a );\nlapack_int LAPACKE_dtftri_work( int matrix_order, char transr, char uplo,\n                                char diag, lapack_int n, double* a );\nlapack_int LAPACKE_ctftri_work( int matrix_order, char transr, char uplo,\n                                char diag, lapack_int n,\n                                lapack_complex_float* a );\nlapack_int LAPACKE_ztftri_work( int matrix_order, char transr, char uplo,\n                                char diag, lapack_int n,\n                                lapack_complex_double* a );\n\nlapack_int LAPACKE_stfttp_work( int matrix_order, char transr, char uplo,\n                                lapack_int n, const float* arf, float* ap );\nlapack_int LAPACKE_dtfttp_work( int matrix_order, char transr, char uplo,\n                                lapack_int n, const double* arf, double* ap );\nlapack_int LAPACKE_ctfttp_work( int matrix_order, char transr, char uplo,\n                                lapack_int n, const lapack_complex_float* arf,\n                                lapack_complex_float* ap );\nlapack_int LAPACKE_ztfttp_work( int matrix_order, char transr, char uplo,\n                                lapack_int n, const lapack_complex_double* arf,\n                                lapack_complex_double* ap );\n\nlapack_int LAPACKE_stfttr_work( int matrix_order, char transr, char uplo,\n                                lapack_int n, const float* arf, float* a,\n                                lapack_int lda );\nlapack_int LAPACKE_dtfttr_work( int matrix_order, char transr, char uplo,\n                                lapack_int n, const double* arf, double* a,\n                                lapack_int lda );\nlapack_int LAPACKE_ctfttr_work( int matrix_order, char transr, char uplo,\n                                lapack_int n, const lapack_complex_float* arf,\n                                lapack_complex_float* a, lapack_int lda );\nlapack_int LAPACKE_ztfttr_work( int matrix_order, char transr, char uplo,\n                                lapack_int n, const lapack_complex_double* arf,\n                                lapack_complex_double* a, lapack_int lda );\n\nlapack_int LAPACKE_stgevc_work( int matrix_order, char side, char howmny,\n                                const lapack_logical* select, lapack_int n,\n                                const float* s, lapack_int lds, const float* p,\n                                lapack_int ldp, float* vl, lapack_int ldvl,\n                                float* vr, lapack_int ldvr, lapack_int mm,\n                                lapack_int* m, float* work );\nlapack_int LAPACKE_dtgevc_work( int matrix_order, char side, char howmny,\n                                const lapack_logical* select, lapack_int n,\n                                const double* s, lapack_int lds,\n                                const double* p, lapack_int ldp, double* vl,\n                                lapack_int ldvl, double* vr, lapack_int ldvr,\n                                lapack_int mm, lapack_int* m, double* work );\nlapack_int LAPACKE_ctgevc_work( int matrix_order, char side, char howmny,\n                                const lapack_logical* select, lapack_int n,\n                                const lapack_complex_float* s, lapack_int lds,\n                                const lapack_complex_float* p, lapack_int ldp,\n                                lapack_complex_float* vl, lapack_int ldvl,\n                                lapack_complex_float* vr, lapack_int ldvr,\n                                lapack_int mm, lapack_int* m,\n                                lapack_complex_float* work, float* rwork );\nlapack_int LAPACKE_ztgevc_work( int matrix_order, char side, char howmny,\n                                const lapack_logical* select, lapack_int n,\n                                const lapack_complex_double* s, lapack_int lds,\n                                const lapack_complex_double* p, lapack_int ldp,\n                                lapack_complex_double* vl, lapack_int ldvl,\n                                lapack_complex_double* vr, lapack_int ldvr,\n                                lapack_int mm, lapack_int* m,\n                                lapack_complex_double* work, double* rwork );\n\nlapack_int LAPACKE_stgexc_work( int matrix_order, lapack_logical wantq,\n                                lapack_logical wantz, lapack_int n, float* a,\n                                lapack_int lda, float* b, lapack_int ldb,\n                                float* q, lapack_int ldq, float* z,\n                                lapack_int ldz, lapack_int* ifst,\n                                lapack_int* ilst, float* work,\n                                lapack_int lwork );\nlapack_int LAPACKE_dtgexc_work( int matrix_order, lapack_logical wantq,\n                                lapack_logical wantz, lapack_int n, double* a,\n                                lapack_int lda, double* b, lapack_int ldb,\n                                double* q, lapack_int ldq, double* z,\n                                lapack_int ldz, lapack_int* ifst,\n                                lapack_int* ilst, double* work,\n                                lapack_int lwork );\nlapack_int LAPACKE_ctgexc_work( int matrix_order, lapack_logical wantq,\n                                lapack_logical wantz, lapack_int n,\n                                lapack_complex_float* a, lapack_int lda,\n                                lapack_complex_float* b, lapack_int ldb,\n                                lapack_complex_float* q, lapack_int ldq,\n                                lapack_complex_float* z, lapack_int ldz,\n                                lapack_int ifst, lapack_int ilst );\nlapack_int LAPACKE_ztgexc_work( int matrix_order, lapack_logical wantq,\n                                lapack_logical wantz, lapack_int n,\n                                lapack_complex_double* a, lapack_int lda,\n                                lapack_complex_double* b, lapack_int ldb,\n                                lapack_complex_double* q, lapack_int ldq,\n                                lapack_complex_double* z, lapack_int ldz,\n                                lapack_int ifst, lapack_int ilst );\n\nlapack_int LAPACKE_stgsen_work( int matrix_order, lapack_int ijob,\n                                lapack_logical wantq, lapack_logical wantz,\n                                const lapack_logical* select, lapack_int n,\n                                float* a, lapack_int lda, float* b,\n                                lapack_int ldb, float* alphar, float* alphai,\n                                float* beta, float* q, lapack_int ldq, float* z,\n                                lapack_int ldz, lapack_int* m, float* pl,\n                                float* pr, float* dif, float* work,\n                                lapack_int lwork, lapack_int* iwork,\n                                lapack_int liwork );\nlapack_int LAPACKE_dtgsen_work( int matrix_order, lapack_int ijob,\n                                lapack_logical wantq, lapack_logical wantz,\n                                const lapack_logical* select, lapack_int n,\n                                double* a, lapack_int lda, double* b,\n                                lapack_int ldb, double* alphar, double* alphai,\n                                double* beta, double* q, lapack_int ldq,\n                                double* z, lapack_int ldz, lapack_int* m,\n                                double* pl, double* pr, double* dif,\n                                double* work, lapack_int lwork,\n                                lapack_int* iwork, lapack_int liwork );\nlapack_int LAPACKE_ctgsen_work( int matrix_order, lapack_int ijob,\n                                lapack_logical wantq, lapack_logical wantz,\n                                const lapack_logical* select, lapack_int n,\n                                lapack_complex_float* a, lapack_int lda,\n                                lapack_complex_float* b, lapack_int ldb,\n                                lapack_complex_float* alpha,\n                                lapack_complex_float* beta,\n                                lapack_complex_float* q, lapack_int ldq,\n                                lapack_complex_float* z, lapack_int ldz,\n                                lapack_int* m, float* pl, float* pr, float* dif,\n                                lapack_complex_float* work, lapack_int lwork,\n                                lapack_int* iwork, lapack_int liwork );\nlapack_int LAPACKE_ztgsen_work( int matrix_order, lapack_int ijob,\n                                lapack_logical wantq, lapack_logical wantz,\n                                const lapack_logical* select, lapack_int n,\n                                lapack_complex_double* a, lapack_int lda,\n                                lapack_complex_double* b, lapack_int ldb,\n                                lapack_complex_double* alpha,\n                                lapack_complex_double* beta,\n                                lapack_complex_double* q, lapack_int ldq,\n                                lapack_complex_double* z, lapack_int ldz,\n                                lapack_int* m, double* pl, double* pr,\n                                double* dif, lapack_complex_double* work,\n                                lapack_int lwork, lapack_int* iwork,\n                                lapack_int liwork );\n\nlapack_int LAPACKE_stgsja_work( int matrix_order, char jobu, char jobv,\n                                char jobq, lapack_int m, lapack_int p,\n                                lapack_int n, lapack_int k, lapack_int l,\n                                float* a, lapack_int lda, float* b,\n                                lapack_int ldb, float tola, float tolb,\n                                float* alpha, float* beta, float* u,\n                                lapack_int ldu, float* v, lapack_int ldv,\n                                float* q, lapack_int ldq, float* work,\n                                lapack_int* ncycle );\nlapack_int LAPACKE_dtgsja_work( int matrix_order, char jobu, char jobv,\n                                char jobq, lapack_int m, lapack_int p,\n                                lapack_int n, lapack_int k, lapack_int l,\n                                double* a, lapack_int lda, double* b,\n                                lapack_int ldb, double tola, double tolb,\n                                double* alpha, double* beta, double* u,\n                                lapack_int ldu, double* v, lapack_int ldv,\n                                double* q, lapack_int ldq, double* work,\n                                lapack_int* ncycle );\nlapack_int LAPACKE_ctgsja_work( int matrix_order, char jobu, char jobv,\n                                char jobq, lapack_int m, lapack_int p,\n                                lapack_int n, lapack_int k, lapack_int l,\n                                lapack_complex_float* a, lapack_int lda,\n                                lapack_complex_float* b, lapack_int ldb,\n                                float tola, float tolb, float* alpha,\n                                float* beta, lapack_complex_float* u,\n                                lapack_int ldu, lapack_complex_float* v,\n                                lapack_int ldv, lapack_complex_float* q,\n                                lapack_int ldq, lapack_complex_float* work,\n                                lapack_int* ncycle );\nlapack_int LAPACKE_ztgsja_work( int matrix_order, char jobu, char jobv,\n                                char jobq, lapack_int m, lapack_int p,\n                                lapack_int n, lapack_int k, lapack_int l,\n                                lapack_complex_double* a, lapack_int lda,\n                                lapack_complex_double* b, lapack_int ldb,\n                                double tola, double tolb, double* alpha,\n                                double* beta, lapack_complex_double* u,\n                                lapack_int ldu, lapack_complex_double* v,\n                                lapack_int ldv, lapack_complex_double* q,\n                                lapack_int ldq, lapack_complex_double* work,\n                                lapack_int* ncycle );\n\nlapack_int LAPACKE_stgsna_work( int matrix_order, char job, char howmny,\n                                const lapack_logical* select, lapack_int n,\n                                const float* a, lapack_int lda, const float* b,\n                                lapack_int ldb, const float* vl,\n                                lapack_int ldvl, const float* vr,\n                                lapack_int ldvr, float* s, float* dif,\n                                lapack_int mm, lapack_int* m, float* work,\n                                lapack_int lwork, lapack_int* iwork );\nlapack_int LAPACKE_dtgsna_work( int matrix_order, char job, char howmny,\n                                const lapack_logical* select, lapack_int n,\n                                const double* a, lapack_int lda,\n                                const double* b, lapack_int ldb,\n                                const double* vl, lapack_int ldvl,\n                                const double* vr, lapack_int ldvr, double* s,\n                                double* dif, lapack_int mm, lapack_int* m,\n                                double* work, lapack_int lwork,\n                                lapack_int* iwork );\nlapack_int LAPACKE_ctgsna_work( int matrix_order, char job, char howmny,\n                                const lapack_logical* select, lapack_int n,\n                                const lapack_complex_float* a, lapack_int lda,\n                                const lapack_complex_float* b, lapack_int ldb,\n                                const lapack_complex_float* vl, lapack_int ldvl,\n                                const lapack_complex_float* vr, lapack_int ldvr,\n                                float* s, float* dif, lapack_int mm,\n                                lapack_int* m, lapack_complex_float* work,\n                                lapack_int lwork, lapack_int* iwork );\nlapack_int LAPACKE_ztgsna_work( int matrix_order, char job, char howmny,\n                                const lapack_logical* select, lapack_int n,\n                                const lapack_complex_double* a, lapack_int lda,\n                                const lapack_complex_double* b, lapack_int ldb,\n                                const lapack_complex_double* vl,\n                                lapack_int ldvl,\n                                const lapack_complex_double* vr,\n                                lapack_int ldvr, double* s, double* dif,\n                                lapack_int mm, lapack_int* m,\n                                lapack_complex_double* work, lapack_int lwork,\n                                lapack_int* iwork );\n\nlapack_int LAPACKE_stgsyl_work( int matrix_order, char trans, lapack_int ijob,\n                                lapack_int m, lapack_int n, const float* a,\n                                lapack_int lda, const float* b, lapack_int ldb,\n                                float* c, lapack_int ldc, const float* d,\n                                lapack_int ldd, const float* e, lapack_int lde,\n                                float* f, lapack_int ldf, float* scale,\n                                float* dif, float* work, lapack_int lwork,\n                                lapack_int* iwork );\nlapack_int LAPACKE_dtgsyl_work( int matrix_order, char trans, lapack_int ijob,\n                                lapack_int m, lapack_int n, const double* a,\n                                lapack_int lda, const double* b, lapack_int ldb,\n                                double* c, lapack_int ldc, const double* d,\n                                lapack_int ldd, const double* e, lapack_int lde,\n                                double* f, lapack_int ldf, double* scale,\n                                double* dif, double* work, lapack_int lwork,\n                                lapack_int* iwork );\nlapack_int LAPACKE_ctgsyl_work( int matrix_order, char trans, lapack_int ijob,\n                                lapack_int m, lapack_int n,\n                                const lapack_complex_float* a, lapack_int lda,\n                                const lapack_complex_float* b, lapack_int ldb,\n                                lapack_complex_float* c, lapack_int ldc,\n                                const lapack_complex_float* d, lapack_int ldd,\n                                const lapack_complex_float* e, lapack_int lde,\n                                lapack_complex_float* f, lapack_int ldf,\n                                float* scale, float* dif,\n                                lapack_complex_float* work, lapack_int lwork,\n                                lapack_int* iwork );\nlapack_int LAPACKE_ztgsyl_work( int matrix_order, char trans, lapack_int ijob,\n                                lapack_int m, lapack_int n,\n                                const lapack_complex_double* a, lapack_int lda,\n                                const lapack_complex_double* b, lapack_int ldb,\n                                lapack_complex_double* c, lapack_int ldc,\n                                const lapack_complex_double* d, lapack_int ldd,\n                                const lapack_complex_double* e, lapack_int lde,\n                                lapack_complex_double* f, lapack_int ldf,\n                                double* scale, double* dif,\n                                lapack_complex_double* work, lapack_int lwork,\n                                lapack_int* iwork );\n\nlapack_int LAPACKE_stpcon_work( int matrix_order, char norm, char uplo,\n                                char diag, lapack_int n, const float* ap,\n                                float* rcond, float* work, lapack_int* iwork );\nlapack_int LAPACKE_dtpcon_work( int matrix_order, char norm, char uplo,\n                                char diag, lapack_int n, const double* ap,\n                                double* rcond, double* work,\n                                lapack_int* iwork );\nlapack_int LAPACKE_ctpcon_work( int matrix_order, char norm, char uplo,\n                                char diag, lapack_int n,\n                                const lapack_complex_float* ap, float* rcond,\n                                lapack_complex_float* work, float* rwork );\nlapack_int LAPACKE_ztpcon_work( int matrix_order, char norm, char uplo,\n                                char diag, lapack_int n,\n                                const lapack_complex_double* ap, double* rcond,\n                                lapack_complex_double* work, double* rwork );\n\nlapack_int LAPACKE_stprfs_work( int matrix_order, char uplo, char trans,\n                                char diag, lapack_int n, lapack_int nrhs,\n                                const float* ap, const float* b, lapack_int ldb,\n                                const float* x, lapack_int ldx, float* ferr,\n                                float* berr, float* work, lapack_int* iwork );\nlapack_int LAPACKE_dtprfs_work( int matrix_order, char uplo, char trans,\n                                char diag, lapack_int n, lapack_int nrhs,\n                                const double* ap, const double* b,\n                                lapack_int ldb, const double* x, lapack_int ldx,\n                                double* ferr, double* berr, double* work,\n                                lapack_int* iwork );\nlapack_int LAPACKE_ctprfs_work( int matrix_order, char uplo, char trans,\n                                char diag, lapack_int n, lapack_int nrhs,\n                                const lapack_complex_float* ap,\n                                const lapack_complex_float* b, lapack_int ldb,\n                                const lapack_complex_float* x, lapack_int ldx,\n                                float* ferr, float* berr,\n                                lapack_complex_float* work, float* rwork );\nlapack_int LAPACKE_ztprfs_work( int matrix_order, char uplo, char trans,\n                                char diag, lapack_int n, lapack_int nrhs,\n                                const lapack_complex_double* ap,\n                                const lapack_complex_double* b, lapack_int ldb,\n                                const lapack_complex_double* x, lapack_int ldx,\n                                double* ferr, double* berr,\n                                lapack_complex_double* work, double* rwork );\n\nlapack_int LAPACKE_stptri_work( int matrix_order, char uplo, char diag,\n                                lapack_int n, float* ap );\nlapack_int LAPACKE_dtptri_work( int matrix_order, char uplo, char diag,\n                                lapack_int n, double* ap );\nlapack_int LAPACKE_ctptri_work( int matrix_order, char uplo, char diag,\n                                lapack_int n, lapack_complex_float* ap );\nlapack_int LAPACKE_ztptri_work( int matrix_order, char uplo, char diag,\n                                lapack_int n, lapack_complex_double* ap );\n\nlapack_int LAPACKE_stptrs_work( int matrix_order, char uplo, char trans,\n                                char diag, lapack_int n, lapack_int nrhs,\n                                const float* ap, float* b, lapack_int ldb );\nlapack_int LAPACKE_dtptrs_work( int matrix_order, char uplo, char trans,\n                                char diag, lapack_int n, lapack_int nrhs,\n                                const double* ap, double* b, lapack_int ldb );\nlapack_int LAPACKE_ctptrs_work( int matrix_order, char uplo, char trans,\n                                char diag, lapack_int n, lapack_int nrhs,\n                                const lapack_complex_float* ap,\n                                lapack_complex_float* b, lapack_int ldb );\nlapack_int LAPACKE_ztptrs_work( int matrix_order, char uplo, char trans,\n                                char diag, lapack_int n, lapack_int nrhs,\n                                const lapack_complex_double* ap,\n                                lapack_complex_double* b, lapack_int ldb );\n\nlapack_int LAPACKE_stpttf_work( int matrix_order, char transr, char uplo,\n                                lapack_int n, const float* ap, float* arf );\nlapack_int LAPACKE_dtpttf_work( int matrix_order, char transr, char uplo,\n                                lapack_int n, const double* ap, double* arf );\nlapack_int LAPACKE_ctpttf_work( int matrix_order, char transr, char uplo,\n                                lapack_int n, const lapack_complex_float* ap,\n                                lapack_complex_float* arf );\nlapack_int LAPACKE_ztpttf_work( int matrix_order, char transr, char uplo,\n                                lapack_int n, const lapack_complex_double* ap,\n                                lapack_complex_double* arf );\n\nlapack_int LAPACKE_stpttr_work( int matrix_order, char uplo, lapack_int n,\n                                const float* ap, float* a, lapack_int lda );\nlapack_int LAPACKE_dtpttr_work( int matrix_order, char uplo, lapack_int n,\n                                const double* ap, double* a, lapack_int lda );\nlapack_int LAPACKE_ctpttr_work( int matrix_order, char uplo, lapack_int n,\n                                const lapack_complex_float* ap,\n                                lapack_complex_float* a, lapack_int lda );\nlapack_int LAPACKE_ztpttr_work( int matrix_order, char uplo, lapack_int n,\n                                const lapack_complex_double* ap,\n                                lapack_complex_double* a, lapack_int lda );\n\nlapack_int LAPACKE_strcon_work( int matrix_order, char norm, char uplo,\n                                char diag, lapack_int n, const float* a,\n                                lapack_int lda, float* rcond, float* work,\n                                lapack_int* iwork );\nlapack_int LAPACKE_dtrcon_work( int matrix_order, char norm, char uplo,\n                                char diag, lapack_int n, const double* a,\n                                lapack_int lda, double* rcond, double* work,\n                                lapack_int* iwork );\nlapack_int LAPACKE_ctrcon_work( int matrix_order, char norm, char uplo,\n                                char diag, lapack_int n,\n                                const lapack_complex_float* a, lapack_int lda,\n                                float* rcond, lapack_complex_float* work,\n                                float* rwork );\nlapack_int LAPACKE_ztrcon_work( int matrix_order, char norm, char uplo,\n                                char diag, lapack_int n,\n                                const lapack_complex_double* a, lapack_int lda,\n                                double* rcond, lapack_complex_double* work,\n                                double* rwork );\n\nlapack_int LAPACKE_strevc_work( int matrix_order, char side, char howmny,\n                                lapack_logical* select, lapack_int n,\n                                const float* t, lapack_int ldt, float* vl,\n                                lapack_int ldvl, float* vr, lapack_int ldvr,\n                                lapack_int mm, lapack_int* m, float* work );\nlapack_int LAPACKE_dtrevc_work( int matrix_order, char side, char howmny,\n                                lapack_logical* select, lapack_int n,\n                                const double* t, lapack_int ldt, double* vl,\n                                lapack_int ldvl, double* vr, lapack_int ldvr,\n                                lapack_int mm, lapack_int* m, double* work );\nlapack_int LAPACKE_ctrevc_work( int matrix_order, char side, char howmny,\n                                const lapack_logical* select, lapack_int n,\n                                lapack_complex_float* t, lapack_int ldt,\n                                lapack_complex_float* vl, lapack_int ldvl,\n                                lapack_complex_float* vr, lapack_int ldvr,\n                                lapack_int mm, lapack_int* m,\n                                lapack_complex_float* work, float* rwork );\nlapack_int LAPACKE_ztrevc_work( int matrix_order, char side, char howmny,\n                                const lapack_logical* select, lapack_int n,\n                                lapack_complex_double* t, lapack_int ldt,\n                                lapack_complex_double* vl, lapack_int ldvl,\n                                lapack_complex_double* vr, lapack_int ldvr,\n                                lapack_int mm, lapack_int* m,\n                                lapack_complex_double* work, double* rwork );\n\nlapack_int LAPACKE_strexc_work( int matrix_order, char compq, lapack_int n,\n                                float* t, lapack_int ldt, float* q,\n                                lapack_int ldq, lapack_int* ifst,\n                                lapack_int* ilst, float* work );\nlapack_int LAPACKE_dtrexc_work( int matrix_order, char compq, lapack_int n,\n                                double* t, lapack_int ldt, double* q,\n                                lapack_int ldq, lapack_int* ifst,\n                                lapack_int* ilst, double* work );\nlapack_int LAPACKE_ctrexc_work( int matrix_order, char compq, lapack_int n,\n                                lapack_complex_float* t, lapack_int ldt,\n                                lapack_complex_float* q, lapack_int ldq,\n                                lapack_int ifst, lapack_int ilst );\nlapack_int LAPACKE_ztrexc_work( int matrix_order, char compq, lapack_int n,\n                                lapack_complex_double* t, lapack_int ldt,\n                                lapack_complex_double* q, lapack_int ldq,\n                                lapack_int ifst, lapack_int ilst );\n\nlapack_int LAPACKE_strrfs_work( int matrix_order, char uplo, char trans,\n                                char diag, lapack_int n, lapack_int nrhs,\n                                const float* a, lapack_int lda, const float* b,\n                                lapack_int ldb, const float* x, lapack_int ldx,\n                                float* ferr, float* berr, float* work,\n                                lapack_int* iwork );\nlapack_int LAPACKE_dtrrfs_work( int matrix_order, char uplo, char trans,\n                                char diag, lapack_int n, lapack_int nrhs,\n                                const double* a, lapack_int lda,\n                                const double* b, lapack_int ldb,\n                                const double* x, lapack_int ldx, double* ferr,\n                                double* berr, double* work, lapack_int* iwork );\nlapack_int LAPACKE_ctrrfs_work( int matrix_order, char uplo, char trans,\n                                char diag, lapack_int n, lapack_int nrhs,\n                                const lapack_complex_float* a, lapack_int lda,\n                                const lapack_complex_float* b, lapack_int ldb,\n                                const lapack_complex_float* x, lapack_int ldx,\n                                float* ferr, float* berr,\n                                lapack_complex_float* work, float* rwork );\nlapack_int LAPACKE_ztrrfs_work( int matrix_order, char uplo, char trans,\n                                char diag, lapack_int n, lapack_int nrhs,\n                                const lapack_complex_double* a, lapack_int lda,\n                                const lapack_complex_double* b, lapack_int ldb,\n                                const lapack_complex_double* x, lapack_int ldx,\n                                double* ferr, double* berr,\n                                lapack_complex_double* work, double* rwork );\n\nlapack_int LAPACKE_strsen_work( int matrix_order, char job, char compq,\n                                const lapack_logical* select, lapack_int n,\n                                float* t, lapack_int ldt, float* q,\n                                lapack_int ldq, float* wr, float* wi,\n                                lapack_int* m, float* s, float* sep,\n                                float* work, lapack_int lwork,\n                                lapack_int* iwork, lapack_int liwork );\nlapack_int LAPACKE_dtrsen_work( int matrix_order, char job, char compq,\n                                const lapack_logical* select, lapack_int n,\n                                double* t, lapack_int ldt, double* q,\n                                lapack_int ldq, double* wr, double* wi,\n                                lapack_int* m, double* s, double* sep,\n                                double* work, lapack_int lwork,\n                                lapack_int* iwork, lapack_int liwork );\nlapack_int LAPACKE_ctrsen_work( int matrix_order, char job, char compq,\n                                const lapack_logical* select, lapack_int n,\n                                lapack_complex_float* t, lapack_int ldt,\n                                lapack_complex_float* q, lapack_int ldq,\n                                lapack_complex_float* w, lapack_int* m,\n                                float* s, float* sep,\n                                lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_ztrsen_work( int matrix_order, char job, char compq,\n                                const lapack_logical* select, lapack_int n,\n                                lapack_complex_double* t, lapack_int ldt,\n                                lapack_complex_double* q, lapack_int ldq,\n                                lapack_complex_double* w, lapack_int* m,\n                                double* s, double* sep,\n                                lapack_complex_double* work, lapack_int lwork );\n\nlapack_int LAPACKE_strsna_work( int matrix_order, char job, char howmny,\n                                const lapack_logical* select, lapack_int n,\n                                const float* t, lapack_int ldt, const float* vl,\n                                lapack_int ldvl, const float* vr,\n                                lapack_int ldvr, float* s, float* sep,\n                                lapack_int mm, lapack_int* m, float* work,\n                                lapack_int ldwork, lapack_int* iwork );\nlapack_int LAPACKE_dtrsna_work( int matrix_order, char job, char howmny,\n                                const lapack_logical* select, lapack_int n,\n                                const double* t, lapack_int ldt,\n                                const double* vl, lapack_int ldvl,\n                                const double* vr, lapack_int ldvr, double* s,\n                                double* sep, lapack_int mm, lapack_int* m,\n                                double* work, lapack_int ldwork,\n                                lapack_int* iwork );\nlapack_int LAPACKE_ctrsna_work( int matrix_order, char job, char howmny,\n                                const lapack_logical* select, lapack_int n,\n                                const lapack_complex_float* t, lapack_int ldt,\n                                const lapack_complex_float* vl, lapack_int ldvl,\n                                const lapack_complex_float* vr, lapack_int ldvr,\n                                float* s, float* sep, lapack_int mm,\n                                lapack_int* m, lapack_complex_float* work,\n                                lapack_int ldwork, float* rwork );\nlapack_int LAPACKE_ztrsna_work( int matrix_order, char job, char howmny,\n                                const lapack_logical* select, lapack_int n,\n                                const lapack_complex_double* t, lapack_int ldt,\n                                const lapack_complex_double* vl,\n                                lapack_int ldvl,\n                                const lapack_complex_double* vr,\n                                lapack_int ldvr, double* s, double* sep,\n                                lapack_int mm, lapack_int* m,\n                                lapack_complex_double* work, lapack_int ldwork,\n                                double* rwork );\n\nlapack_int LAPACKE_strsyl_work( int matrix_order, char trana, char tranb,\n                                lapack_int isgn, lapack_int m, lapack_int n,\n                                const float* a, lapack_int lda, const float* b,\n                                lapack_int ldb, float* c, lapack_int ldc,\n                                float* scale );\nlapack_int LAPACKE_dtrsyl_work( int matrix_order, char trana, char tranb,\n                                lapack_int isgn, lapack_int m, lapack_int n,\n                                const double* a, lapack_int lda,\n                                const double* b, lapack_int ldb, double* c,\n                                lapack_int ldc, double* scale );\nlapack_int LAPACKE_ctrsyl_work( int matrix_order, char trana, char tranb,\n                                lapack_int isgn, lapack_int m, lapack_int n,\n                                const lapack_complex_float* a, lapack_int lda,\n                                const lapack_complex_float* b, lapack_int ldb,\n                                lapack_complex_float* c, lapack_int ldc,\n                                float* scale );\nlapack_int LAPACKE_ztrsyl_work( int matrix_order, char trana, char tranb,\n                                lapack_int isgn, lapack_int m, lapack_int n,\n                                const lapack_complex_double* a, lapack_int lda,\n                                const lapack_complex_double* b, lapack_int ldb,\n                                lapack_complex_double* c, lapack_int ldc,\n                                double* scale );\n\nlapack_int LAPACKE_strtri_work( int matrix_order, char uplo, char diag,\n                                lapack_int n, float* a, lapack_int lda );\nlapack_int LAPACKE_dtrtri_work( int matrix_order, char uplo, char diag,\n                                lapack_int n, double* a, lapack_int lda );\nlapack_int LAPACKE_ctrtri_work( int matrix_order, char uplo, char diag,\n                                lapack_int n, lapack_complex_float* a,\n                                lapack_int lda );\nlapack_int LAPACKE_ztrtri_work( int matrix_order, char uplo, char diag,\n                                lapack_int n, lapack_complex_double* a,\n                                lapack_int lda );\n\nlapack_int LAPACKE_strtrs_work( int matrix_order, char uplo, char trans,\n                                char diag, lapack_int n, lapack_int nrhs,\n                                const float* a, lapack_int lda, float* b,\n                                lapack_int ldb );\nlapack_int LAPACKE_dtrtrs_work( int matrix_order, char uplo, char trans,\n                                char diag, lapack_int n, lapack_int nrhs,\n                                const double* a, lapack_int lda, double* b,\n                                lapack_int ldb );\nlapack_int LAPACKE_ctrtrs_work( int matrix_order, char uplo, char trans,\n                                char diag, lapack_int n, lapack_int nrhs,\n                                const lapack_complex_float* a, lapack_int lda,\n                                lapack_complex_float* b, lapack_int ldb );\nlapack_int LAPACKE_ztrtrs_work( int matrix_order, char uplo, char trans,\n                                char diag, lapack_int n, lapack_int nrhs,\n                                const lapack_complex_double* a, lapack_int lda,\n                                lapack_complex_double* b, lapack_int ldb );\n\nlapack_int LAPACKE_strttf_work( int matrix_order, char transr, char uplo,\n                                lapack_int n, const float* a, lapack_int lda,\n                                float* arf );\nlapack_int LAPACKE_dtrttf_work( int matrix_order, char transr, char uplo,\n                                lapack_int n, const double* a, lapack_int lda,\n                                double* arf );\nlapack_int LAPACKE_ctrttf_work( int matrix_order, char transr, char uplo,\n                                lapack_int n, const lapack_complex_float* a,\n                                lapack_int lda, lapack_complex_float* arf );\nlapack_int LAPACKE_ztrttf_work( int matrix_order, char transr, char uplo,\n                                lapack_int n, const lapack_complex_double* a,\n                                lapack_int lda, lapack_complex_double* arf );\n\nlapack_int LAPACKE_strttp_work( int matrix_order, char uplo, lapack_int n,\n                                const float* a, lapack_int lda, float* ap );\nlapack_int LAPACKE_dtrttp_work( int matrix_order, char uplo, lapack_int n,\n                                const double* a, lapack_int lda, double* ap );\nlapack_int LAPACKE_ctrttp_work( int matrix_order, char uplo, lapack_int n,\n                                const lapack_complex_float* a, lapack_int lda,\n                                lapack_complex_float* ap );\nlapack_int LAPACKE_ztrttp_work( int matrix_order, char uplo, lapack_int n,\n                                const lapack_complex_double* a, lapack_int lda,\n                                lapack_complex_double* ap );\n\nlapack_int LAPACKE_stzrzf_work( int matrix_order, lapack_int m, lapack_int n,\n                                float* a, lapack_int lda, float* tau,\n                                float* work, lapack_int lwork );\nlapack_int LAPACKE_dtzrzf_work( int matrix_order, lapack_int m, lapack_int n,\n                                double* a, lapack_int lda, double* tau,\n                                double* work, lapack_int lwork );\nlapack_int LAPACKE_ctzrzf_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_complex_float* a, lapack_int lda,\n                                lapack_complex_float* tau,\n                                lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_ztzrzf_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_complex_double* a, lapack_int lda,\n                                lapack_complex_double* tau,\n                                lapack_complex_double* work, lapack_int lwork );\n\nlapack_int LAPACKE_cungbr_work( int matrix_order, char vect, lapack_int m,\n                                lapack_int n, lapack_int k,\n                                lapack_complex_float* a, lapack_int lda,\n                                const lapack_complex_float* tau,\n                                lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_zungbr_work( int matrix_order, char vect, lapack_int m,\n                                lapack_int n, lapack_int k,\n                                lapack_complex_double* a, lapack_int lda,\n                                const lapack_complex_double* tau,\n                                lapack_complex_double* work, lapack_int lwork );\n\nlapack_int LAPACKE_cunghr_work( int matrix_order, lapack_int n, lapack_int ilo,\n                                lapack_int ihi, lapack_complex_float* a,\n                                lapack_int lda, const lapack_complex_float* tau,\n                                lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_zunghr_work( int matrix_order, lapack_int n, lapack_int ilo,\n                                lapack_int ihi, lapack_complex_double* a,\n                                lapack_int lda,\n                                const lapack_complex_double* tau,\n                                lapack_complex_double* work, lapack_int lwork );\n\nlapack_int LAPACKE_cunglq_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int k, lapack_complex_float* a,\n                                lapack_int lda, const lapack_complex_float* tau,\n                                lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_zunglq_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int k, lapack_complex_double* a,\n                                lapack_int lda,\n                                const lapack_complex_double* tau,\n                                lapack_complex_double* work, lapack_int lwork );\n\nlapack_int LAPACKE_cungql_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int k, lapack_complex_float* a,\n                                lapack_int lda, const lapack_complex_float* tau,\n                                lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_zungql_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int k, lapack_complex_double* a,\n                                lapack_int lda,\n                                const lapack_complex_double* tau,\n                                lapack_complex_double* work, lapack_int lwork );\n\nlapack_int LAPACKE_cungqr_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int k, lapack_complex_float* a,\n                                lapack_int lda, const lapack_complex_float* tau,\n                                lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_zungqr_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int k, lapack_complex_double* a,\n                                lapack_int lda,\n                                const lapack_complex_double* tau,\n                                lapack_complex_double* work, lapack_int lwork );\n\nlapack_int LAPACKE_cungrq_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int k, lapack_complex_float* a,\n                                lapack_int lda, const lapack_complex_float* tau,\n                                lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_zungrq_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int k, lapack_complex_double* a,\n                                lapack_int lda,\n                                const lapack_complex_double* tau,\n                                lapack_complex_double* work, lapack_int lwork );\n\nlapack_int LAPACKE_cungtr_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_complex_float* a, lapack_int lda,\n                                const lapack_complex_float* tau,\n                                lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_zungtr_work( int matrix_order, char uplo, lapack_int n,\n                                lapack_complex_double* a, lapack_int lda,\n                                const lapack_complex_double* tau,\n                                lapack_complex_double* work, lapack_int lwork );\n\nlapack_int LAPACKE_cunmbr_work( int matrix_order, char vect, char side,\n                                char trans, lapack_int m, lapack_int n,\n                                lapack_int k, const lapack_complex_float* a,\n                                lapack_int lda, const lapack_complex_float* tau,\n                                lapack_complex_float* c, lapack_int ldc,\n                                lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_zunmbr_work( int matrix_order, char vect, char side,\n                                char trans, lapack_int m, lapack_int n,\n                                lapack_int k, const lapack_complex_double* a,\n                                lapack_int lda,\n                                const lapack_complex_double* tau,\n                                lapack_complex_double* c, lapack_int ldc,\n                                lapack_complex_double* work, lapack_int lwork );\n\nlapack_int LAPACKE_cunmhr_work( int matrix_order, char side, char trans,\n                                lapack_int m, lapack_int n, lapack_int ilo,\n                                lapack_int ihi, const lapack_complex_float* a,\n                                lapack_int lda, const lapack_complex_float* tau,\n                                lapack_complex_float* c, lapack_int ldc,\n                                lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_zunmhr_work( int matrix_order, char side, char trans,\n                                lapack_int m, lapack_int n, lapack_int ilo,\n                                lapack_int ihi, const lapack_complex_double* a,\n                                lapack_int lda,\n                                const lapack_complex_double* tau,\n                                lapack_complex_double* c, lapack_int ldc,\n                                lapack_complex_double* work, lapack_int lwork );\n\nlapack_int LAPACKE_cunmlq_work( int matrix_order, char side, char trans,\n                                lapack_int m, lapack_int n, lapack_int k,\n                                const lapack_complex_float* a, lapack_int lda,\n                                const lapack_complex_float* tau,\n                                lapack_complex_float* c, lapack_int ldc,\n                                lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_zunmlq_work( int matrix_order, char side, char trans,\n                                lapack_int m, lapack_int n, lapack_int k,\n                                const lapack_complex_double* a, lapack_int lda,\n                                const lapack_complex_double* tau,\n                                lapack_complex_double* c, lapack_int ldc,\n                                lapack_complex_double* work, lapack_int lwork );\n\nlapack_int LAPACKE_cunmql_work( int matrix_order, char side, char trans,\n                                lapack_int m, lapack_int n, lapack_int k,\n                                const lapack_complex_float* a, lapack_int lda,\n                                const lapack_complex_float* tau,\n                                lapack_complex_float* c, lapack_int ldc,\n                                lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_zunmql_work( int matrix_order, char side, char trans,\n                                lapack_int m, lapack_int n, lapack_int k,\n                                const lapack_complex_double* a, lapack_int lda,\n                                const lapack_complex_double* tau,\n                                lapack_complex_double* c, lapack_int ldc,\n                                lapack_complex_double* work, lapack_int lwork );\n\nlapack_int LAPACKE_cunmqr_work( int matrix_order, char side, char trans,\n                                lapack_int m, lapack_int n, lapack_int k,\n                                const lapack_complex_float* a, lapack_int lda,\n                                const lapack_complex_float* tau,\n                                lapack_complex_float* c, lapack_int ldc,\n                                lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_zunmqr_work( int matrix_order, char side, char trans,\n                                lapack_int m, lapack_int n, lapack_int k,\n                                const lapack_complex_double* a, lapack_int lda,\n                                const lapack_complex_double* tau,\n                                lapack_complex_double* c, lapack_int ldc,\n                                lapack_complex_double* work, lapack_int lwork );\n\nlapack_int LAPACKE_cunmrq_work( int matrix_order, char side, char trans,\n                                lapack_int m, lapack_int n, lapack_int k,\n                                const lapack_complex_float* a, lapack_int lda,\n                                const lapack_complex_float* tau,\n                                lapack_complex_float* c, lapack_int ldc,\n                                lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_zunmrq_work( int matrix_order, char side, char trans,\n                                lapack_int m, lapack_int n, lapack_int k,\n                                const lapack_complex_double* a, lapack_int lda,\n                                const lapack_complex_double* tau,\n                                lapack_complex_double* c, lapack_int ldc,\n                                lapack_complex_double* work, lapack_int lwork );\n\nlapack_int LAPACKE_cunmrz_work( int matrix_order, char side, char trans,\n                                lapack_int m, lapack_int n, lapack_int k,\n                                lapack_int l, const lapack_complex_float* a,\n                                lapack_int lda, const lapack_complex_float* tau,\n                                lapack_complex_float* c, lapack_int ldc,\n                                lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_zunmrz_work( int matrix_order, char side, char trans,\n                                lapack_int m, lapack_int n, lapack_int k,\n                                lapack_int l, const lapack_complex_double* a,\n                                lapack_int lda,\n                                const lapack_complex_double* tau,\n                                lapack_complex_double* c, lapack_int ldc,\n                                lapack_complex_double* work, lapack_int lwork );\n\nlapack_int LAPACKE_cunmtr_work( int matrix_order, char side, char uplo,\n                                char trans, lapack_int m, lapack_int n,\n                                const lapack_complex_float* a, lapack_int lda,\n                                const lapack_complex_float* tau,\n                                lapack_complex_float* c, lapack_int ldc,\n                                lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_zunmtr_work( int matrix_order, char side, char uplo,\n                                char trans, lapack_int m, lapack_int n,\n                                const lapack_complex_double* a, lapack_int lda,\n                                const lapack_complex_double* tau,\n                                lapack_complex_double* c, lapack_int ldc,\n                                lapack_complex_double* work, lapack_int lwork );\n\nlapack_int LAPACKE_cupgtr_work( int matrix_order, char uplo, lapack_int n,\n                                const lapack_complex_float* ap,\n                                const lapack_complex_float* tau,\n                                lapack_complex_float* q, lapack_int ldq,\n                                lapack_complex_float* work );\nlapack_int LAPACKE_zupgtr_work( int matrix_order, char uplo, lapack_int n,\n                                const lapack_complex_double* ap,\n                                const lapack_complex_double* tau,\n                                lapack_complex_double* q, lapack_int ldq,\n                                lapack_complex_double* work );\n\nlapack_int LAPACKE_cupmtr_work( int matrix_order, char side, char uplo,\n                                char trans, lapack_int m, lapack_int n,\n                                const lapack_complex_float* ap,\n                                const lapack_complex_float* tau,\n                                lapack_complex_float* c, lapack_int ldc,\n                                lapack_complex_float* work );\nlapack_int LAPACKE_zupmtr_work( int matrix_order, char side, char uplo,\n                                char trans, lapack_int m, lapack_int n,\n                                const lapack_complex_double* ap,\n                                const lapack_complex_double* tau,\n                                lapack_complex_double* c, lapack_int ldc,\n                                lapack_complex_double* work );\n\nlapack_int LAPACKE_claghe( int matrix_order, lapack_int n, lapack_int k,\n                           const float* d, lapack_complex_float* a,\n                           lapack_int lda, lapack_int* iseed );\nlapack_int LAPACKE_zlaghe( int matrix_order, lapack_int n, lapack_int k,\n                           const double* d, lapack_complex_double* a,\n                           lapack_int lda, lapack_int* iseed );\n\nlapack_int LAPACKE_slagsy( int matrix_order, lapack_int n, lapack_int k,\n                           const float* d, float* a, lapack_int lda,\n                           lapack_int* iseed );\nlapack_int LAPACKE_dlagsy( int matrix_order, lapack_int n, lapack_int k,\n                           const double* d, double* a, lapack_int lda,\n                           lapack_int* iseed );\nlapack_int LAPACKE_clagsy( int matrix_order, lapack_int n, lapack_int k,\n                           const float* d, lapack_complex_float* a,\n                           lapack_int lda, lapack_int* iseed );\nlapack_int LAPACKE_zlagsy( int matrix_order, lapack_int n, lapack_int k,\n                           const double* d, lapack_complex_double* a,\n                           lapack_int lda, lapack_int* iseed );\n\nlapack_int LAPACKE_slapmr( int matrix_order, lapack_logical forwrd,\n                           lapack_int m, lapack_int n, float* x, lapack_int ldx,\n                           lapack_int* k );\nlapack_int LAPACKE_dlapmr( int matrix_order, lapack_logical forwrd,\n                           lapack_int m, lapack_int n, double* x,\n                           lapack_int ldx, lapack_int* k );\nlapack_int LAPACKE_clapmr( int matrix_order, lapack_logical forwrd,\n                           lapack_int m, lapack_int n, lapack_complex_float* x,\n                           lapack_int ldx, lapack_int* k );\nlapack_int LAPACKE_zlapmr( int matrix_order, lapack_logical forwrd,\n                           lapack_int m, lapack_int n, lapack_complex_double* x,\n                           lapack_int ldx, lapack_int* k );\n\n\nfloat LAPACKE_slapy2( float x, float y );\ndouble LAPACKE_dlapy2( double x, double y );\n\nfloat LAPACKE_slapy3( float x, float y, float z );\ndouble LAPACKE_dlapy3( double x, double y, double z );\n\nlapack_int LAPACKE_slartgp( float f, float g, float* cs, float* sn, float* r );\nlapack_int LAPACKE_dlartgp( double f, double g, double* cs, double* sn,\n                            double* r );\n\nlapack_int LAPACKE_slartgs( float x, float y, float sigma, float* cs,\n                            float* sn );\nlapack_int LAPACKE_dlartgs( double x, double y, double sigma, double* cs,\n                            double* sn );\n\n\n//LAPACK 3.3.0\nlapack_int LAPACKE_cbbcsd( int matrix_order, char jobu1, char jobu2,\n                           char jobv1t, char jobv2t, char trans, lapack_int m,\n                           lapack_int p, lapack_int q, float* theta, float* phi,\n                           lapack_complex_float* u1, lapack_int ldu1,\n                           lapack_complex_float* u2, lapack_int ldu2,\n                           lapack_complex_float* v1t, lapack_int ldv1t,\n                           lapack_complex_float* v2t, lapack_int ldv2t,\n                           float* b11d, float* b11e, float* b12d, float* b12e,\n                           float* b21d, float* b21e, float* b22d, float* b22e );\nlapack_int LAPACKE_cbbcsd_work( int matrix_order, char jobu1, char jobu2,\n                                char jobv1t, char jobv2t, char trans,\n                                lapack_int m, lapack_int p, lapack_int q,\n                                float* theta, float* phi,\n                                lapack_complex_float* u1, lapack_int ldu1,\n                                lapack_complex_float* u2, lapack_int ldu2,\n                                lapack_complex_float* v1t, lapack_int ldv1t,\n                                lapack_complex_float* v2t, lapack_int ldv2t,\n                                float* b11d, float* b11e, float* b12d,\n                                float* b12e, float* b21d, float* b21e,\n                                float* b22d, float* b22e, float* rwork,\n                                lapack_int lrwork );\nlapack_int LAPACKE_cheswapr( int matrix_order, char uplo, lapack_int n,\n                             lapack_complex_float* a, lapack_int i1,\n                             lapack_int i2 );\nlapack_int LAPACKE_cheswapr_work( int matrix_order, char uplo, lapack_int n,\n                                  lapack_complex_float* a, lapack_int i1,\n                                  lapack_int i2 );\nlapack_int LAPACKE_chetri2( int matrix_order, char uplo, lapack_int n,\n                            lapack_complex_float* a, lapack_int lda,\n                            const lapack_int* ipiv );\nlapack_int LAPACKE_chetri2_work( int matrix_order, char uplo, lapack_int n,\n                                 lapack_complex_float* a, lapack_int lda,\n                                 const lapack_int* ipiv,\n                                 lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_chetri2x( int matrix_order, char uplo, lapack_int n,\n                             lapack_complex_float* a, lapack_int lda,\n                             const lapack_int* ipiv, lapack_int nb );\nlapack_int LAPACKE_chetri2x_work( int matrix_order, char uplo, lapack_int n,\n                                  lapack_complex_float* a, lapack_int lda,\n                                  const lapack_int* ipiv,\n                                  lapack_complex_float* work, lapack_int nb );\nlapack_int LAPACKE_chetrs2( int matrix_order, char uplo, lapack_int n,\n                            lapack_int nrhs, const lapack_complex_float* a,\n                            lapack_int lda, const lapack_int* ipiv,\n                            lapack_complex_float* b, lapack_int ldb );\nlapack_int LAPACKE_chetrs2_work( int matrix_order, char uplo, lapack_int n,\n                                 lapack_int nrhs, const lapack_complex_float* a,\n                                 lapack_int lda, const lapack_int* ipiv,\n                                 lapack_complex_float* b, lapack_int ldb,\n                                 lapack_complex_float* work );\nlapack_int LAPACKE_csyconv( int matrix_order, char uplo, char way, lapack_int n,\n                            lapack_complex_float* a, lapack_int lda,\n                            const lapack_int* ipiv );\nlapack_int LAPACKE_csyconv_work( int matrix_order, char uplo, char way,\n                                 lapack_int n, lapack_complex_float* a,\n                                 lapack_int lda, const lapack_int* ipiv,\n                                 lapack_complex_float* work );\nlapack_int LAPACKE_csyswapr( int matrix_order, char uplo, lapack_int n,\n                             lapack_complex_float* a, lapack_int i1,\n                             lapack_int i2 );\nlapack_int LAPACKE_csyswapr_work( int matrix_order, char uplo, lapack_int n,\n                                  lapack_complex_float* a, lapack_int i1,\n                                  lapack_int i2 );\nlapack_int LAPACKE_csytri2( int matrix_order, char uplo, lapack_int n,\n                            lapack_complex_float* a, lapack_int lda,\n                            const lapack_int* ipiv );\nlapack_int LAPACKE_csytri2_work( int matrix_order, char uplo, lapack_int n,\n                                 lapack_complex_float* a, lapack_int lda,\n                                 const lapack_int* ipiv,\n                                 lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_csytri2x( int matrix_order, char uplo, lapack_int n,\n                             lapack_complex_float* a, lapack_int lda,\n                             const lapack_int* ipiv, lapack_int nb );\nlapack_int LAPACKE_csytri2x_work( int matrix_order, char uplo, lapack_int n,\n                                  lapack_complex_float* a, lapack_int lda,\n                                  const lapack_int* ipiv,\n                                  lapack_complex_float* work, lapack_int nb );\nlapack_int LAPACKE_csytrs2( int matrix_order, char uplo, lapack_int n,\n                            lapack_int nrhs, const lapack_complex_float* a,\n                            lapack_int lda, const lapack_int* ipiv,\n                            lapack_complex_float* b, lapack_int ldb );\nlapack_int LAPACKE_csytrs2_work( int matrix_order, char uplo, lapack_int n,\n                                 lapack_int nrhs, const lapack_complex_float* a,\n                                 lapack_int lda, const lapack_int* ipiv,\n                                 lapack_complex_float* b, lapack_int ldb,\n                                 lapack_complex_float* work );\nlapack_int LAPACKE_cunbdb( int matrix_order, char trans, char signs,\n                           lapack_int m, lapack_int p, lapack_int q,\n                           lapack_complex_float* x11, lapack_int ldx11,\n                           lapack_complex_float* x12, lapack_int ldx12,\n                           lapack_complex_float* x21, lapack_int ldx21,\n                           lapack_complex_float* x22, lapack_int ldx22,\n                           float* theta, float* phi,\n                           lapack_complex_float* taup1,\n                           lapack_complex_float* taup2,\n                           lapack_complex_float* tauq1,\n                           lapack_complex_float* tauq2 );\nlapack_int LAPACKE_cunbdb_work( int matrix_order, char trans, char signs,\n                                lapack_int m, lapack_int p, lapack_int q,\n                                lapack_complex_float* x11, lapack_int ldx11,\n                                lapack_complex_float* x12, lapack_int ldx12,\n                                lapack_complex_float* x21, lapack_int ldx21,\n                                lapack_complex_float* x22, lapack_int ldx22,\n                                float* theta, float* phi,\n                                lapack_complex_float* taup1,\n                                lapack_complex_float* taup2,\n                                lapack_complex_float* tauq1,\n                                lapack_complex_float* tauq2,\n                                lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_cuncsd( int matrix_order, char jobu1, char jobu2,\n                           char jobv1t, char jobv2t, char trans, char signs,\n                           lapack_int m, lapack_int p, lapack_int q,\n                           lapack_complex_float* x11, lapack_int ldx11,\n                           lapack_complex_float* x12, lapack_int ldx12,\n                           lapack_complex_float* x21, lapack_int ldx21,\n                           lapack_complex_float* x22, lapack_int ldx22,\n                           float* theta, lapack_complex_float* u1,\n                           lapack_int ldu1, lapack_complex_float* u2,\n                           lapack_int ldu2, lapack_complex_float* v1t,\n                           lapack_int ldv1t, lapack_complex_float* v2t,\n                           lapack_int ldv2t );\nlapack_int LAPACKE_cuncsd_work( int matrix_order, char jobu1, char jobu2,\n                                char jobv1t, char jobv2t, char trans,\n                                char signs, lapack_int m, lapack_int p,\n                                lapack_int q, lapack_complex_float* x11,\n                                lapack_int ldx11, lapack_complex_float* x12,\n                                lapack_int ldx12, lapack_complex_float* x21,\n                                lapack_int ldx21, lapack_complex_float* x22,\n                                lapack_int ldx22, float* theta,\n                                lapack_complex_float* u1, lapack_int ldu1,\n                                lapack_complex_float* u2, lapack_int ldu2,\n                                lapack_complex_float* v1t, lapack_int ldv1t,\n                                lapack_complex_float* v2t, lapack_int ldv2t,\n                                lapack_complex_float* work, lapack_int lwork,\n                                float* rwork, lapack_int lrwork,\n                                lapack_int* iwork );\nlapack_int LAPACKE_dbbcsd( int matrix_order, char jobu1, char jobu2,\n                           char jobv1t, char jobv2t, char trans, lapack_int m,\n                           lapack_int p, lapack_int q, double* theta,\n                           double* phi, double* u1, lapack_int ldu1, double* u2,\n                           lapack_int ldu2, double* v1t, lapack_int ldv1t,\n                           double* v2t, lapack_int ldv2t, double* b11d,\n                           double* b11e, double* b12d, double* b12e,\n                           double* b21d, double* b21e, double* b22d,\n                           double* b22e );\nlapack_int LAPACKE_dbbcsd_work( int matrix_order, char jobu1, char jobu2,\n                                char jobv1t, char jobv2t, char trans,\n                                lapack_int m, lapack_int p, lapack_int q,\n                                double* theta, double* phi, double* u1,\n                                lapack_int ldu1, double* u2, lapack_int ldu2,\n                                double* v1t, lapack_int ldv1t, double* v2t,\n                                lapack_int ldv2t, double* b11d, double* b11e,\n                                double* b12d, double* b12e, double* b21d,\n                                double* b21e, double* b22d, double* b22e,\n                                double* work, lapack_int lwork );\nlapack_int LAPACKE_dorbdb( int matrix_order, char trans, char signs,\n                           lapack_int m, lapack_int p, lapack_int q,\n                           double* x11, lapack_int ldx11, double* x12,\n                           lapack_int ldx12, double* x21, lapack_int ldx21,\n                           double* x22, lapack_int ldx22, double* theta,\n                           double* phi, double* taup1, double* taup2,\n                           double* tauq1, double* tauq2 );\nlapack_int LAPACKE_dorbdb_work( int matrix_order, char trans, char signs,\n                                lapack_int m, lapack_int p, lapack_int q,\n                                double* x11, lapack_int ldx11, double* x12,\n                                lapack_int ldx12, double* x21, lapack_int ldx21,\n                                double* x22, lapack_int ldx22, double* theta,\n                                double* phi, double* taup1, double* taup2,\n                                double* tauq1, double* tauq2, double* work,\n                                lapack_int lwork );\nlapack_int LAPACKE_dorcsd( int matrix_order, char jobu1, char jobu2,\n                           char jobv1t, char jobv2t, char trans, char signs,\n                           lapack_int m, lapack_int p, lapack_int q,\n                           double* x11, lapack_int ldx11, double* x12,\n                           lapack_int ldx12, double* x21, lapack_int ldx21,\n                           double* x22, lapack_int ldx22, double* theta,\n                           double* u1, lapack_int ldu1, double* u2,\n                           lapack_int ldu2, double* v1t, lapack_int ldv1t,\n                           double* v2t, lapack_int ldv2t );\nlapack_int LAPACKE_dorcsd_work( int matrix_order, char jobu1, char jobu2,\n                                char jobv1t, char jobv2t, char trans,\n                                char signs, lapack_int m, lapack_int p,\n                                lapack_int q, double* x11, lapack_int ldx11,\n                                double* x12, lapack_int ldx12, double* x21,\n                                lapack_int ldx21, double* x22, lapack_int ldx22,\n                                double* theta, double* u1, lapack_int ldu1,\n                                double* u2, lapack_int ldu2, double* v1t,\n                                lapack_int ldv1t, double* v2t, lapack_int ldv2t,\n                                double* work, lapack_int lwork,\n                                lapack_int* iwork );\nlapack_int LAPACKE_dsyconv( int matrix_order, char uplo, char way, lapack_int n,\n                            double* a, lapack_int lda, const lapack_int* ipiv );\nlapack_int LAPACKE_dsyconv_work( int matrix_order, char uplo, char way,\n                                 lapack_int n, double* a, lapack_int lda,\n                                 const lapack_int* ipiv, double* work );\nlapack_int LAPACKE_dsyswapr( int matrix_order, char uplo, lapack_int n,\n                             double* a, lapack_int i1, lapack_int i2 );\nlapack_int LAPACKE_dsyswapr_work( int matrix_order, char uplo, lapack_int n,\n                                  double* a, lapack_int i1, lapack_int i2 );\nlapack_int LAPACKE_dsytri2( int matrix_order, char uplo, lapack_int n,\n                            double* a, lapack_int lda, const lapack_int* ipiv );\nlapack_int LAPACKE_dsytri2_work( int matrix_order, char uplo, lapack_int n,\n                                 double* a, lapack_int lda,\n                                 const lapack_int* ipiv,\n                                 lapack_complex_double* work, lapack_int lwork );\nlapack_int LAPACKE_dsytri2x( int matrix_order, char uplo, lapack_int n,\n                             double* a, lapack_int lda, const lapack_int* ipiv,\n                             lapack_int nb );\nlapack_int LAPACKE_dsytri2x_work( int matrix_order, char uplo, lapack_int n,\n                                  double* a, lapack_int lda,\n                                  const lapack_int* ipiv, double* work,\n                                  lapack_int nb );\nlapack_int LAPACKE_dsytrs2( int matrix_order, char uplo, lapack_int n,\n                            lapack_int nrhs, const double* a, lapack_int lda,\n                            const lapack_int* ipiv, double* b, lapack_int ldb );\nlapack_int LAPACKE_dsytrs2_work( int matrix_order, char uplo, lapack_int n,\n                                 lapack_int nrhs, const double* a,\n                                 lapack_int lda, const lapack_int* ipiv,\n                                 double* b, lapack_int ldb, double* work );\nlapack_int LAPACKE_sbbcsd( int matrix_order, char jobu1, char jobu2,\n                           char jobv1t, char jobv2t, char trans, lapack_int m,\n                           lapack_int p, lapack_int q, float* theta, float* phi,\n                           float* u1, lapack_int ldu1, float* u2,\n                           lapack_int ldu2, float* v1t, lapack_int ldv1t,\n                           float* v2t, lapack_int ldv2t, float* b11d,\n                           float* b11e, float* b12d, float* b12e, float* b21d,\n                           float* b21e, float* b22d, float* b22e );\nlapack_int LAPACKE_sbbcsd_work( int matrix_order, char jobu1, char jobu2,\n                                char jobv1t, char jobv2t, char trans,\n                                lapack_int m, lapack_int p, lapack_int q,\n                                float* theta, float* phi, float* u1,\n                                lapack_int ldu1, float* u2, lapack_int ldu2,\n                                float* v1t, lapack_int ldv1t, float* v2t,\n                                lapack_int ldv2t, float* b11d, float* b11e,\n                                float* b12d, float* b12e, float* b21d,\n                                float* b21e, float* b22d, float* b22e,\n                                float* work, lapack_int lwork );\nlapack_int LAPACKE_sorbdb( int matrix_order, char trans, char signs,\n                           lapack_int m, lapack_int p, lapack_int q, float* x11,\n                           lapack_int ldx11, float* x12, lapack_int ldx12,\n                           float* x21, lapack_int ldx21, float* x22,\n                           lapack_int ldx22, float* theta, float* phi,\n                           float* taup1, float* taup2, float* tauq1,\n                           float* tauq2 );\nlapack_int LAPACKE_sorbdb_work( int matrix_order, char trans, char signs,\n                                lapack_int m, lapack_int p, lapack_int q,\n                                float* x11, lapack_int ldx11, float* x12,\n                                lapack_int ldx12, float* x21, lapack_int ldx21,\n                                float* x22, lapack_int ldx22, float* theta,\n                                float* phi, float* taup1, float* taup2,\n                                float* tauq1, float* tauq2, float* work,\n                                lapack_int lwork );\nlapack_int LAPACKE_sorcsd( int matrix_order, char jobu1, char jobu2,\n                           char jobv1t, char jobv2t, char trans, char signs,\n                           lapack_int m, lapack_int p, lapack_int q, float* x11,\n                           lapack_int ldx11, float* x12, lapack_int ldx12,\n                           float* x21, lapack_int ldx21, float* x22,\n                           lapack_int ldx22, float* theta, float* u1,\n                           lapack_int ldu1, float* u2, lapack_int ldu2,\n                           float* v1t, lapack_int ldv1t, float* v2t,\n                           lapack_int ldv2t );\nlapack_int LAPACKE_sorcsd_work( int matrix_order, char jobu1, char jobu2,\n                                char jobv1t, char jobv2t, char trans,\n                                char signs, lapack_int m, lapack_int p,\n                                lapack_int q, float* x11, lapack_int ldx11,\n                                float* x12, lapack_int ldx12, float* x21,\n                                lapack_int ldx21, float* x22, lapack_int ldx22,\n                                float* theta, float* u1, lapack_int ldu1,\n                                float* u2, lapack_int ldu2, float* v1t,\n                                lapack_int ldv1t, float* v2t, lapack_int ldv2t,\n                                float* work, lapack_int lwork,\n                                lapack_int* iwork );\nlapack_int LAPACKE_ssyconv( int matrix_order, char uplo, char way, lapack_int n,\n                            float* a, lapack_int lda, const lapack_int* ipiv );\nlapack_int LAPACKE_ssyconv_work( int matrix_order, char uplo, char way,\n                                 lapack_int n, float* a, lapack_int lda,\n                                 const lapack_int* ipiv, float* work );\nlapack_int LAPACKE_ssyswapr( int matrix_order, char uplo, lapack_int n,\n                             float* a, lapack_int i1, lapack_int i2 );\nlapack_int LAPACKE_ssyswapr_work( int matrix_order, char uplo, lapack_int n,\n                                  float* a, lapack_int i1, lapack_int i2 );\nlapack_int LAPACKE_ssytri2( int matrix_order, char uplo, lapack_int n, float* a,\n                            lapack_int lda, const lapack_int* ipiv );\nlapack_int LAPACKE_ssytri2_work( int matrix_order, char uplo, lapack_int n,\n                                 float* a, lapack_int lda,\n                                 const lapack_int* ipiv,\n                                 lapack_complex_float* work, lapack_int lwork );\nlapack_int LAPACKE_ssytri2x( int matrix_order, char uplo, lapack_int n,\n                             float* a, lapack_int lda, const lapack_int* ipiv,\n                             lapack_int nb );\nlapack_int LAPACKE_ssytri2x_work( int matrix_order, char uplo, lapack_int n,\n                                  float* a, lapack_int lda,\n                                  const lapack_int* ipiv, float* work,\n                                  lapack_int nb );\nlapack_int LAPACKE_ssytrs2( int matrix_order, char uplo, lapack_int n,\n                            lapack_int nrhs, const float* a, lapack_int lda,\n                            const lapack_int* ipiv, float* b, lapack_int ldb );\nlapack_int LAPACKE_ssytrs2_work( int matrix_order, char uplo, lapack_int n,\n                                 lapack_int nrhs, const float* a,\n                                 lapack_int lda, const lapack_int* ipiv,\n                                 float* b, lapack_int ldb, float* work );\nlapack_int LAPACKE_zbbcsd( int matrix_order, char jobu1, char jobu2,\n                           char jobv1t, char jobv2t, char trans, lapack_int m,\n                           lapack_int p, lapack_int q, double* theta,\n                           double* phi, lapack_complex_double* u1,\n                           lapack_int ldu1, lapack_complex_double* u2,\n                           lapack_int ldu2, lapack_complex_double* v1t,\n                           lapack_int ldv1t, lapack_complex_double* v2t,\n                           lapack_int ldv2t, double* b11d, double* b11e,\n                           double* b12d, double* b12e, double* b21d,\n                           double* b21e, double* b22d, double* b22e );\nlapack_int LAPACKE_zbbcsd_work( int matrix_order, char jobu1, char jobu2,\n                                char jobv1t, char jobv2t, char trans,\n                                lapack_int m, lapack_int p, lapack_int q,\n                                double* theta, double* phi,\n                                lapack_complex_double* u1, lapack_int ldu1,\n                                lapack_complex_double* u2, lapack_int ldu2,\n                                lapack_complex_double* v1t, lapack_int ldv1t,\n                                lapack_complex_double* v2t, lapack_int ldv2t,\n                                double* b11d, double* b11e, double* b12d,\n                                double* b12e, double* b21d, double* b21e,\n                                double* b22d, double* b22e, double* rwork,\n                                lapack_int lrwork );\nlapack_int LAPACKE_zheswapr( int matrix_order, char uplo, lapack_int n,\n                             lapack_complex_double* a, lapack_int i1,\n                             lapack_int i2 );\nlapack_int LAPACKE_zheswapr_work( int matrix_order, char uplo, lapack_int n,\n                                  lapack_complex_double* a, lapack_int i1,\n                                  lapack_int i2 );\nlapack_int LAPACKE_zhetri2( int matrix_order, char uplo, lapack_int n,\n                            lapack_complex_double* a, lapack_int lda,\n                            const lapack_int* ipiv );\nlapack_int LAPACKE_zhetri2_work( int matrix_order, char uplo, lapack_int n,\n                                 lapack_complex_double* a, lapack_int lda,\n                                 const lapack_int* ipiv,\n                                 lapack_complex_double* work, lapack_int lwork );\nlapack_int LAPACKE_zhetri2x( int matrix_order, char uplo, lapack_int n,\n                             lapack_complex_double* a, lapack_int lda,\n                             const lapack_int* ipiv, lapack_int nb );\nlapack_int LAPACKE_zhetri2x_work( int matrix_order, char uplo, lapack_int n,\n                                  lapack_complex_double* a, lapack_int lda,\n                                  const lapack_int* ipiv,\n                                  lapack_complex_double* work, lapack_int nb );\nlapack_int LAPACKE_zhetrs2( int matrix_order, char uplo, lapack_int n,\n                            lapack_int nrhs, const lapack_complex_double* a,\n                            lapack_int lda, const lapack_int* ipiv,\n                            lapack_complex_double* b, lapack_int ldb );\nlapack_int LAPACKE_zhetrs2_work( int matrix_order, char uplo, lapack_int n,\n                                 lapack_int nrhs, const lapack_complex_double* a,\n                                 lapack_int lda, const lapack_int* ipiv,\n                                 lapack_complex_double* b, lapack_int ldb,\n                                 lapack_complex_double* work );\nlapack_int LAPACKE_zsyconv( int matrix_order, char uplo, char way, lapack_int n,\n                            lapack_complex_double* a, lapack_int lda,\n                            const lapack_int* ipiv );\nlapack_int LAPACKE_zsyconv_work( int matrix_order, char uplo, char way,\n                                 lapack_int n, lapack_complex_double* a,\n                                 lapack_int lda, const lapack_int* ipiv,\n                                 lapack_complex_double* work );\nlapack_int LAPACKE_zsyswapr( int matrix_order, char uplo, lapack_int n,\n                             lapack_complex_double* a, lapack_int i1,\n                             lapack_int i2 );\nlapack_int LAPACKE_zsyswapr_work( int matrix_order, char uplo, lapack_int n,\n                                  lapack_complex_double* a, lapack_int i1,\n                                  lapack_int i2 );\nlapack_int LAPACKE_zsytri2( int matrix_order, char uplo, lapack_int n,\n                            lapack_complex_double* a, lapack_int lda,\n                            const lapack_int* ipiv );\nlapack_int LAPACKE_zsytri2_work( int matrix_order, char uplo, lapack_int n,\n                                 lapack_complex_double* a, lapack_int lda,\n                                 const lapack_int* ipiv,\n                                 lapack_complex_double* work, lapack_int lwork );\nlapack_int LAPACKE_zsytri2x( int matrix_order, char uplo, lapack_int n,\n                             lapack_complex_double* a, lapack_int lda,\n                             const lapack_int* ipiv, lapack_int nb );\nlapack_int LAPACKE_zsytri2x_work( int matrix_order, char uplo, lapack_int n,\n                                  lapack_complex_double* a, lapack_int lda,\n                                  const lapack_int* ipiv,\n                                  lapack_complex_double* work, lapack_int nb );\nlapack_int LAPACKE_zsytrs2( int matrix_order, char uplo, lapack_int n,\n                            lapack_int nrhs, const lapack_complex_double* a,\n                            lapack_int lda, const lapack_int* ipiv,\n                            lapack_complex_double* b, lapack_int ldb );\nlapack_int LAPACKE_zsytrs2_work( int matrix_order, char uplo, lapack_int n,\n                                 lapack_int nrhs, const lapack_complex_double* a,\n                                 lapack_int lda, const lapack_int* ipiv,\n                                 lapack_complex_double* b, lapack_int ldb,\n                                 lapack_complex_double* work );\nlapack_int LAPACKE_zunbdb( int matrix_order, char trans, char signs,\n                           lapack_int m, lapack_int p, lapack_int q,\n                           lapack_complex_double* x11, lapack_int ldx11,\n                           lapack_complex_double* x12, lapack_int ldx12,\n                           lapack_complex_double* x21, lapack_int ldx21,\n                           lapack_complex_double* x22, lapack_int ldx22,\n                           double* theta, double* phi,\n                           lapack_complex_double* taup1,\n                           lapack_complex_double* taup2,\n                           lapack_complex_double* tauq1,\n                           lapack_complex_double* tauq2 );\nlapack_int LAPACKE_zunbdb_work( int matrix_order, char trans, char signs,\n                                lapack_int m, lapack_int p, lapack_int q,\n                                lapack_complex_double* x11, lapack_int ldx11,\n                                lapack_complex_double* x12, lapack_int ldx12,\n                                lapack_complex_double* x21, lapack_int ldx21,\n                                lapack_complex_double* x22, lapack_int ldx22,\n                                double* theta, double* phi,\n                                lapack_complex_double* taup1,\n                                lapack_complex_double* taup2,\n                                lapack_complex_double* tauq1,\n                                lapack_complex_double* tauq2,\n                                lapack_complex_double* work, lapack_int lwork );\nlapack_int LAPACKE_zuncsd( int matrix_order, char jobu1, char jobu2,\n                           char jobv1t, char jobv2t, char trans, char signs,\n                           lapack_int m, lapack_int p, lapack_int q,\n                           lapack_complex_double* x11, lapack_int ldx11,\n                           lapack_complex_double* x12, lapack_int ldx12,\n                           lapack_complex_double* x21, lapack_int ldx21,\n                           lapack_complex_double* x22, lapack_int ldx22,\n                           double* theta, lapack_complex_double* u1,\n                           lapack_int ldu1, lapack_complex_double* u2,\n                           lapack_int ldu2, lapack_complex_double* v1t,\n                           lapack_int ldv1t, lapack_complex_double* v2t,\n                           lapack_int ldv2t );\nlapack_int LAPACKE_zuncsd_work( int matrix_order, char jobu1, char jobu2,\n                                char jobv1t, char jobv2t, char trans,\n                                char signs, lapack_int m, lapack_int p,\n                                lapack_int q, lapack_complex_double* x11,\n                                lapack_int ldx11, lapack_complex_double* x12,\n                                lapack_int ldx12, lapack_complex_double* x21,\n                                lapack_int ldx21, lapack_complex_double* x22,\n                                lapack_int ldx22, double* theta,\n                                lapack_complex_double* u1, lapack_int ldu1,\n                                lapack_complex_double* u2, lapack_int ldu2,\n                                lapack_complex_double* v1t, lapack_int ldv1t,\n                                lapack_complex_double* v2t, lapack_int ldv2t,\n                                lapack_complex_double* work, lapack_int lwork,\n                                double* rwork, lapack_int lrwork,\n                                lapack_int* iwork );\n//LAPACK 3.4.0\nlapack_int LAPACKE_sgemqrt( int matrix_order, char side, char trans,\n                            lapack_int m, lapack_int n, lapack_int k,\n                            lapack_int nb, const float* v, lapack_int ldv,\n                            const float* t, lapack_int ldt, float* c,\n                            lapack_int ldc );\nlapack_int LAPACKE_dgemqrt( int matrix_order, char side, char trans,\n                            lapack_int m, lapack_int n, lapack_int k,\n                            lapack_int nb, const double* v, lapack_int ldv,\n                            const double* t, lapack_int ldt, double* c,\n                            lapack_int ldc );\nlapack_int LAPACKE_cgemqrt( int matrix_order, char side, char trans,\n                            lapack_int m, lapack_int n, lapack_int k,\n                            lapack_int nb, const lapack_complex_float* v,\n                            lapack_int ldv, const lapack_complex_float* t,\n                            lapack_int ldt, lapack_complex_float* c,\n                            lapack_int ldc );\nlapack_int LAPACKE_zgemqrt( int matrix_order, char side, char trans,\n                            lapack_int m, lapack_int n, lapack_int k,\n                            lapack_int nb, const lapack_complex_double* v,\n                            lapack_int ldv, const lapack_complex_double* t,\n                            lapack_int ldt, lapack_complex_double* c,\n                            lapack_int ldc );\n\nlapack_int LAPACKE_sgeqrt( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int nb, float* a, lapack_int lda, float* t,\n                           lapack_int ldt );\nlapack_int LAPACKE_dgeqrt( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int nb, double* a, lapack_int lda, double* t,\n                           lapack_int ldt );\nlapack_int LAPACKE_cgeqrt( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int nb, lapack_complex_float* a,\n                           lapack_int lda, lapack_complex_float* t,\n                           lapack_int ldt );\nlapack_int LAPACKE_zgeqrt( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int nb, lapack_complex_double* a,\n                           lapack_int lda, lapack_complex_double* t,\n                           lapack_int ldt );\n\nlapack_int LAPACKE_sgeqrt2( int matrix_order, lapack_int m, lapack_int n,\n                            float* a, lapack_int lda, float* t,\n                            lapack_int ldt );\nlapack_int LAPACKE_dgeqrt2( int matrix_order, lapack_int m, lapack_int n,\n                            double* a, lapack_int lda, double* t,\n                            lapack_int ldt );\nlapack_int LAPACKE_cgeqrt2( int matrix_order, lapack_int m, lapack_int n,\n                            lapack_complex_float* a, lapack_int lda,\n                            lapack_complex_float* t, lapack_int ldt );\nlapack_int LAPACKE_zgeqrt2( int matrix_order, lapack_int m, lapack_int n,\n                            lapack_complex_double* a, lapack_int lda,\n                            lapack_complex_double* t, lapack_int ldt );\n\nlapack_int LAPACKE_sgeqrt3( int matrix_order, lapack_int m, lapack_int n,\n                            float* a, lapack_int lda, float* t,\n                            lapack_int ldt );\nlapack_int LAPACKE_dgeqrt3( int matrix_order, lapack_int m, lapack_int n,\n                            double* a, lapack_int lda, double* t,\n                            lapack_int ldt );\nlapack_int LAPACKE_cgeqrt3( int matrix_order, lapack_int m, lapack_int n,\n                            lapack_complex_float* a, lapack_int lda,\n                            lapack_complex_float* t, lapack_int ldt );\nlapack_int LAPACKE_zgeqrt3( int matrix_order, lapack_int m, lapack_int n,\n                            lapack_complex_double* a, lapack_int lda,\n                            lapack_complex_double* t, lapack_int ldt );\n\nlapack_int LAPACKE_stpmqrt( int matrix_order, char side, char trans,\n                            lapack_int m, lapack_int n, lapack_int k,\n                            lapack_int l, lapack_int nb, const float* v,\n                            lapack_int ldv, const float* t, lapack_int ldt,\n                            float* a, lapack_int lda, float* b,\n                            lapack_int ldb );\nlapack_int LAPACKE_dtpmqrt( int matrix_order, char side, char trans,\n                            lapack_int m, lapack_int n, lapack_int k,\n                            lapack_int l, lapack_int nb, const double* v,\n                            lapack_int ldv, const double* t, lapack_int ldt,\n                            double* a, lapack_int lda, double* b,\n                            lapack_int ldb );\nlapack_int LAPACKE_ctpmqrt( int matrix_order, char side, char trans,\n                            lapack_int m, lapack_int n, lapack_int k,\n                            lapack_int l, lapack_int nb,\n                            const lapack_complex_float* v, lapack_int ldv,\n                            const lapack_complex_float* t, lapack_int ldt,\n                            lapack_complex_float* a, lapack_int lda,\n                            lapack_complex_float* b, lapack_int ldb );\nlapack_int LAPACKE_ztpmqrt( int matrix_order, char side, char trans,\n                            lapack_int m, lapack_int n, lapack_int k,\n                            lapack_int l, lapack_int nb,\n                            const lapack_complex_double* v, lapack_int ldv,\n                            const lapack_complex_double* t, lapack_int ldt,\n                            lapack_complex_double* a, lapack_int lda,\n                            lapack_complex_double* b, lapack_int ldb );\n\nlapack_int LAPACKE_dtpqrt( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int l, lapack_int nb, double* a,\n                           lapack_int lda, double* b, lapack_int ldb, double* t,\n                           lapack_int ldt );\nlapack_int LAPACKE_ctpqrt( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int l, lapack_int nb, lapack_complex_float* a,\n                           lapack_int lda, lapack_complex_float* t,\n                           lapack_complex_float* b, lapack_int ldb,\n                           lapack_int ldt );\nlapack_int LAPACKE_ztpqrt( int matrix_order, lapack_int m, lapack_int n,\n                           lapack_int l, lapack_int nb,\n                           lapack_complex_double* a, lapack_int lda,\n                           lapack_complex_double* b, lapack_int ldb,\n                           lapack_complex_double* t, lapack_int ldt );\n\nlapack_int LAPACKE_stpqrt2( int matrix_order, lapack_int m, lapack_int n,\n                            float* a, lapack_int lda, float* b, lapack_int ldb,\n                            float* t, lapack_int ldt );\nlapack_int LAPACKE_dtpqrt2( int matrix_order, lapack_int m, lapack_int n,\n                            double* a, lapack_int lda, double* b,\n                            lapack_int ldb, double* t, lapack_int ldt );\nlapack_int LAPACKE_ctpqrt2( int matrix_order, lapack_int m, lapack_int n,\n                            lapack_complex_float* a, lapack_int lda,\n                            lapack_complex_float* b, lapack_int ldb,\n                            lapack_complex_float* t, lapack_int ldt );\nlapack_int LAPACKE_ztpqrt2( int matrix_order, lapack_int m, lapack_int n,\n                            lapack_complex_double* a, lapack_int lda,\n                            lapack_complex_double* b, lapack_int ldb,\n                            lapack_complex_double* t, lapack_int ldt );\n\nlapack_int LAPACKE_stprfb( int matrix_order, char side, char trans, char direct,\n                           char storev, lapack_int m, lapack_int n,\n                           lapack_int k, lapack_int l, const float* v,\n                           lapack_int ldv, const float* t, lapack_int ldt,\n                           float* a, lapack_int lda, float* b, lapack_int ldb,\n                           lapack_int myldwork );\nlapack_int LAPACKE_dtprfb( int matrix_order, char side, char trans, char direct,\n                           char storev, lapack_int m, lapack_int n,\n                           lapack_int k, lapack_int l, const double* v,\n                           lapack_int ldv, const double* t, lapack_int ldt,\n                           double* a, lapack_int lda, double* b, lapack_int ldb,\n                           lapack_int myldwork );\nlapack_int LAPACKE_ctprfb( int matrix_order, char side, char trans, char direct,\n                           char storev, lapack_int m, lapack_int n,\n                           lapack_int k, lapack_int l,\n                           const lapack_complex_float* v, lapack_int ldv,\n                           const lapack_complex_float* t, lapack_int ldt,\n                           lapack_complex_float* a, lapack_int lda,\n                           lapack_complex_float* b, lapack_int ldb,\n                           lapack_int myldwork );\nlapack_int LAPACKE_ztprfb( int matrix_order, char side, char trans, char direct,\n                           char storev, lapack_int m, lapack_int n,\n                           lapack_int k, lapack_int l,\n                           const lapack_complex_double* v, lapack_int ldv,\n                           const lapack_complex_double* t, lapack_int ldt,\n                           lapack_complex_double* a, lapack_int lda,\n                           lapack_complex_double* b, lapack_int ldb,\n                           lapack_int myldwork );\n\nlapack_int LAPACKE_sgemqrt_work( int matrix_order, char side, char trans,\n                                 lapack_int m, lapack_int n, lapack_int k,\n                                 lapack_int nb, const float* v, lapack_int ldv,\n                                 const float* t, lapack_int ldt, float* c,\n                                 lapack_int ldc, float* work );\nlapack_int LAPACKE_dgemqrt_work( int matrix_order, char side, char trans,\n                                 lapack_int m, lapack_int n, lapack_int k,\n                                 lapack_int nb, const double* v, lapack_int ldv,\n                                 const double* t, lapack_int ldt, double* c,\n                                 lapack_int ldc, double* work );\nlapack_int LAPACKE_cgemqrt_work( int matrix_order, char side, char trans,\n                                 lapack_int m, lapack_int n, lapack_int k,\n                                 lapack_int nb, const lapack_complex_float* v,\n                                 lapack_int ldv, const lapack_complex_float* t,\n                                 lapack_int ldt, lapack_complex_float* c,\n                                 lapack_int ldc, lapack_complex_float* work );\nlapack_int LAPACKE_zgemqrt_work( int matrix_order, char side, char trans,\n                                 lapack_int m, lapack_int n, lapack_int k,\n                                 lapack_int nb, const lapack_complex_double* v,\n                                 lapack_int ldv, const lapack_complex_double* t,\n                                 lapack_int ldt, lapack_complex_double* c,\n                                 lapack_int ldc, lapack_complex_double* work );\n\nlapack_int LAPACKE_sgeqrt_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int nb, float* a, lapack_int lda,\n                                float* t, lapack_int ldt, float* work );\nlapack_int LAPACKE_dgeqrt_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int nb, double* a, lapack_int lda,\n                                double* t, lapack_int ldt, double* work );\nlapack_int LAPACKE_cgeqrt_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int nb, lapack_complex_float* a,\n                                lapack_int lda, lapack_complex_float* t,\n                                lapack_int ldt, lapack_complex_float* work );\nlapack_int LAPACKE_zgeqrt_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int nb, lapack_complex_double* a,\n                                lapack_int lda, lapack_complex_double* t,\n                                lapack_int ldt, lapack_complex_double* work );\n\nlapack_int LAPACKE_sgeqrt2_work( int matrix_order, lapack_int m, lapack_int n,\n                                 float* a, lapack_int lda, float* t,\n                                 lapack_int ldt );\nlapack_int LAPACKE_dgeqrt2_work( int matrix_order, lapack_int m, lapack_int n,\n                                 double* a, lapack_int lda, double* t,\n                                 lapack_int ldt );\nlapack_int LAPACKE_cgeqrt2_work( int matrix_order, lapack_int m, lapack_int n,\n                                 lapack_complex_float* a, lapack_int lda,\n                                 lapack_complex_float* t, lapack_int ldt );\nlapack_int LAPACKE_zgeqrt2_work( int matrix_order, lapack_int m, lapack_int n,\n                                 lapack_complex_double* a, lapack_int lda,\n                                 lapack_complex_double* t, lapack_int ldt );\n\nlapack_int LAPACKE_sgeqrt3_work( int matrix_order, lapack_int m, lapack_int n,\n                                 float* a, lapack_int lda, float* t,\n                                 lapack_int ldt );\nlapack_int LAPACKE_dgeqrt3_work( int matrix_order, lapack_int m, lapack_int n,\n                                 double* a, lapack_int lda, double* t,\n                                 lapack_int ldt );\nlapack_int LAPACKE_cgeqrt3_work( int matrix_order, lapack_int m, lapack_int n,\n                                 lapack_complex_float* a, lapack_int lda,\n                                 lapack_complex_float* t, lapack_int ldt );\nlapack_int LAPACKE_zgeqrt3_work( int matrix_order, lapack_int m, lapack_int n,\n                                 lapack_complex_double* a, lapack_int lda,\n                                 lapack_complex_double* t, lapack_int ldt );\n\nlapack_int LAPACKE_stpmqrt_work( int matrix_order, char side, char trans,\n                                 lapack_int m, lapack_int n, lapack_int k,\n                                 lapack_int l, lapack_int nb, const float* v,\n                                 lapack_int ldv, const float* t, lapack_int ldt,\n                                 float* a, lapack_int lda, float* b,\n                                 lapack_int ldb, float* work );\nlapack_int LAPACKE_dtpmqrt_work( int matrix_order, char side, char trans,\n                                 lapack_int m, lapack_int n, lapack_int k,\n                                 lapack_int l, lapack_int nb, const double* v,\n                                 lapack_int ldv, const double* t,\n                                 lapack_int ldt, double* a, lapack_int lda,\n                                 double* b, lapack_int ldb, double* work );\nlapack_int LAPACKE_ctpmqrt_work( int matrix_order, char side, char trans,\n                                 lapack_int m, lapack_int n, lapack_int k,\n                                 lapack_int l, lapack_int nb,\n                                 const lapack_complex_float* v, lapack_int ldv,\n                                 const lapack_complex_float* t, lapack_int ldt,\n                                 lapack_complex_float* a, lapack_int lda,\n                                 lapack_complex_float* b, lapack_int ldb,\n                                 lapack_complex_float* work );\nlapack_int LAPACKE_ztpmqrt_work( int matrix_order, char side, char trans,\n                                 lapack_int m, lapack_int n, lapack_int k,\n                                 lapack_int l, lapack_int nb,\n                                 const lapack_complex_double* v, lapack_int ldv,\n                                 const lapack_complex_double* t, lapack_int ldt,\n                                 lapack_complex_double* a, lapack_int lda,\n                                 lapack_complex_double* b, lapack_int ldb,\n                                 lapack_complex_double* work );\n\nlapack_int LAPACKE_dtpqrt_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int l, lapack_int nb, double* a,\n                                lapack_int lda, double* b, lapack_int ldb,\n                                double* t, lapack_int ldt, double* work );\nlapack_int LAPACKE_ctpqrt_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int l, lapack_int nb,\n                                lapack_complex_float* a, lapack_int lda,\n                                lapack_complex_float* t,\n                                lapack_complex_float* b, lapack_int ldb,\n                                lapack_int ldt, lapack_complex_float* work );\nlapack_int LAPACKE_ztpqrt_work( int matrix_order, lapack_int m, lapack_int n,\n                                lapack_int l, lapack_int nb,\n                                lapack_complex_double* a, lapack_int lda,\n                                lapack_complex_double* b, lapack_int ldb,\n                                lapack_complex_double* t, lapack_int ldt,\n                                lapack_complex_double* work );\n\nlapack_int LAPACKE_stpqrt2_work( int matrix_order, lapack_int m, lapack_int n,\n                                 float* a, lapack_int lda, float* b,\n                                 lapack_int ldb, float* t, lapack_int ldt );\nlapack_int LAPACKE_dtpqrt2_work( int matrix_order, lapack_int m, lapack_int n,\n                                 double* a, lapack_int lda, double* b,\n                                 lapack_int ldb, double* t, lapack_int ldt );\nlapack_int LAPACKE_ctpqrt2_work( int matrix_order, lapack_int m, lapack_int n,\n                                 lapack_complex_float* a, lapack_int lda,\n                                 lapack_complex_float* b, lapack_int ldb,\n                                 lapack_complex_float* t, lapack_int ldt );\nlapack_int LAPACKE_ztpqrt2_work( int matrix_order, lapack_int m, lapack_int n,\n                                 lapack_complex_double* a, lapack_int lda,\n                                 lapack_complex_double* b, lapack_int ldb,\n                                 lapack_complex_double* t, lapack_int ldt );\n\nlapack_int LAPACKE_stprfb_work( int matrix_order, char side, char trans,\n                                char direct, char storev, lapack_int m,\n                                lapack_int n, lapack_int k, lapack_int l,\n                                const float* v, lapack_int ldv, const float* t,\n                                lapack_int ldt, float* a, lapack_int lda,\n                                float* b, lapack_int ldb, const float* mywork,\n                                lapack_int myldwork );\nlapack_int LAPACKE_dtprfb_work( int matrix_order, char side, char trans,\n                                char direct, char storev, lapack_int m,\n                                lapack_int n, lapack_int k, lapack_int l,\n                                const double* v, lapack_int ldv,\n                                const double* t, lapack_int ldt, double* a,\n                                lapack_int lda, double* b, lapack_int ldb,\n                                const double* mywork, lapack_int myldwork );\nlapack_int LAPACKE_ctprfb_work( int matrix_order, char side, char trans,\n                                char direct, char storev, lapack_int m,\n                                lapack_int n, lapack_int k, lapack_int l,\n                                const lapack_complex_float* v, lapack_int ldv,\n                                const lapack_complex_float* t, lapack_int ldt,\n                                lapack_complex_float* a, lapack_int lda,\n                                lapack_complex_float* b, lapack_int ldb,\n                                const float* mywork, lapack_int myldwork );\nlapack_int LAPACKE_ztprfb_work( int matrix_order, char side, char trans,\n                                char direct, char storev, lapack_int m,\n                                lapack_int n, lapack_int k, lapack_int l,\n                                const lapack_complex_double* v, lapack_int ldv,\n                                const lapack_complex_double* t, lapack_int ldt,\n                                lapack_complex_double* a, lapack_int lda,\n                                lapack_complex_double* b, lapack_int ldb,\n                                const double* mywork, lapack_int myldwork );\n//LAPACK 3.X.X\nlapack_int LAPACKE_csyr( int matrix_order, char uplo, lapack_int n,\n                             lapack_complex_float alpha,\n                             const lapack_complex_float* x, lapack_int incx,\n                             lapack_complex_float* a, lapack_int lda );\nlapack_int LAPACKE_zsyr( int matrix_order, char uplo, lapack_int n,\n                             lapack_complex_double alpha,\n                             const lapack_complex_double* x, lapack_int incx,\n                             lapack_complex_double* a, lapack_int lda );\n\nlapack_int LAPACKE_csyr_work( int matrix_order, char uplo, lapack_int n,\n                                  lapack_complex_float alpha,\n                                  const lapack_complex_float* x,\n                                  lapack_int incx, lapack_complex_float* a,\n                                  lapack_int lda );\nlapack_int LAPACKE_zsyr_work( int matrix_order, char uplo, lapack_int n,\n                                  lapack_complex_double alpha,\n                                  const lapack_complex_double* x,\n                                  lapack_int incx, lapack_complex_double* a,\n                                  lapack_int lda );\n\n\n\n#define LAPACK_sgetrf LAPACK_GLOBAL(sgetrf,SGETRF)\n#define LAPACK_dgetrf LAPACK_GLOBAL(dgetrf,DGETRF)\n#define LAPACK_cgetrf LAPACK_GLOBAL(cgetrf,CGETRF)\n#define LAPACK_zgetrf LAPACK_GLOBAL(zgetrf,ZGETRF)\n#define LAPACK_sgbtrf LAPACK_GLOBAL(sgbtrf,SGBTRF)\n#define LAPACK_dgbtrf LAPACK_GLOBAL(dgbtrf,DGBTRF)\n#define LAPACK_cgbtrf LAPACK_GLOBAL(cgbtrf,CGBTRF)\n#define LAPACK_zgbtrf LAPACK_GLOBAL(zgbtrf,ZGBTRF)\n#define LAPACK_sgttrf LAPACK_GLOBAL(sgttrf,SGTTRF)\n#define LAPACK_dgttrf LAPACK_GLOBAL(dgttrf,DGTTRF)\n#define LAPACK_cgttrf LAPACK_GLOBAL(cgttrf,CGTTRF)\n#define LAPACK_zgttrf LAPACK_GLOBAL(zgttrf,ZGTTRF)\n#define LAPACK_spotrf LAPACK_GLOBAL(spotrf,SPOTRF)\n#define LAPACK_dpotrf LAPACK_GLOBAL(dpotrf,DPOTRF)\n#define LAPACK_cpotrf LAPACK_GLOBAL(cpotrf,CPOTRF)\n#define LAPACK_zpotrf LAPACK_GLOBAL(zpotrf,ZPOTRF)\n#define LAPACK_dpstrf LAPACK_GLOBAL(dpstrf,DPSTRF)\n#define LAPACK_spstrf LAPACK_GLOBAL(spstrf,SPSTRF)\n#define LAPACK_zpstrf LAPACK_GLOBAL(zpstrf,ZPSTRF)\n#define LAPACK_cpstrf LAPACK_GLOBAL(cpstrf,CPSTRF)\n#define LAPACK_dpftrf LAPACK_GLOBAL(dpftrf,DPFTRF)\n#define LAPACK_spftrf LAPACK_GLOBAL(spftrf,SPFTRF)\n#define LAPACK_zpftrf LAPACK_GLOBAL(zpftrf,ZPFTRF)\n#define LAPACK_cpftrf LAPACK_GLOBAL(cpftrf,CPFTRF)\n#define LAPACK_spptrf LAPACK_GLOBAL(spptrf,SPPTRF)\n#define LAPACK_dpptrf LAPACK_GLOBAL(dpptrf,DPPTRF)\n#define LAPACK_cpptrf LAPACK_GLOBAL(cpptrf,CPPTRF)\n#define LAPACK_zpptrf LAPACK_GLOBAL(zpptrf,ZPPTRF)\n#define LAPACK_spbtrf LAPACK_GLOBAL(spbtrf,SPBTRF)\n#define LAPACK_dpbtrf LAPACK_GLOBAL(dpbtrf,DPBTRF)\n#define LAPACK_cpbtrf LAPACK_GLOBAL(cpbtrf,CPBTRF)\n#define LAPACK_zpbtrf LAPACK_GLOBAL(zpbtrf,ZPBTRF)\n#define LAPACK_spttrf LAPACK_GLOBAL(spttrf,SPTTRF)\n#define LAPACK_dpttrf LAPACK_GLOBAL(dpttrf,DPTTRF)\n#define LAPACK_cpttrf LAPACK_GLOBAL(cpttrf,CPTTRF)\n#define LAPACK_zpttrf LAPACK_GLOBAL(zpttrf,ZPTTRF)\n#define LAPACK_ssytrf LAPACK_GLOBAL(ssytrf,SSYTRF)\n#define LAPACK_dsytrf LAPACK_GLOBAL(dsytrf,DSYTRF)\n#define LAPACK_csytrf LAPACK_GLOBAL(csytrf,CSYTRF)\n#define LAPACK_zsytrf LAPACK_GLOBAL(zsytrf,ZSYTRF)\n#define LAPACK_chetrf LAPACK_GLOBAL(chetrf,CHETRF)\n#define LAPACK_zhetrf LAPACK_GLOBAL(zhetrf,ZHETRF)\n#define LAPACK_ssptrf LAPACK_GLOBAL(ssptrf,SSPTRF)\n#define LAPACK_dsptrf LAPACK_GLOBAL(dsptrf,DSPTRF)\n#define LAPACK_csptrf LAPACK_GLOBAL(csptrf,CSPTRF)\n#define LAPACK_zsptrf LAPACK_GLOBAL(zsptrf,ZSPTRF)\n#define LAPACK_chptrf LAPACK_GLOBAL(chptrf,CHPTRF)\n#define LAPACK_zhptrf LAPACK_GLOBAL(zhptrf,ZHPTRF)\n#define LAPACK_sgetrs LAPACK_GLOBAL(sgetrs,SGETRS)\n#define LAPACK_dgetrs LAPACK_GLOBAL(dgetrs,DGETRS)\n#define LAPACK_cgetrs LAPACK_GLOBAL(cgetrs,CGETRS)\n#define LAPACK_zgetrs LAPACK_GLOBAL(zgetrs,ZGETRS)\n#define LAPACK_sgbtrs LAPACK_GLOBAL(sgbtrs,SGBTRS)\n#define LAPACK_dgbtrs LAPACK_GLOBAL(dgbtrs,DGBTRS)\n#define LAPACK_cgbtrs LAPACK_GLOBAL(cgbtrs,CGBTRS)\n#define LAPACK_zgbtrs LAPACK_GLOBAL(zgbtrs,ZGBTRS)\n#define LAPACK_sgttrs LAPACK_GLOBAL(sgttrs,SGTTRS)\n#define LAPACK_dgttrs LAPACK_GLOBAL(dgttrs,DGTTRS)\n#define LAPACK_cgttrs LAPACK_GLOBAL(cgttrs,CGTTRS)\n#define LAPACK_zgttrs LAPACK_GLOBAL(zgttrs,ZGTTRS)\n#define LAPACK_spotrs LAPACK_GLOBAL(spotrs,SPOTRS)\n#define LAPACK_dpotrs LAPACK_GLOBAL(dpotrs,DPOTRS)\n#define LAPACK_cpotrs LAPACK_GLOBAL(cpotrs,CPOTRS)\n#define LAPACK_zpotrs LAPACK_GLOBAL(zpotrs,ZPOTRS)\n#define LAPACK_dpftrs LAPACK_GLOBAL(dpftrs,DPFTRS)\n#define LAPACK_spftrs LAPACK_GLOBAL(spftrs,SPFTRS)\n#define LAPACK_zpftrs LAPACK_GLOBAL(zpftrs,ZPFTRS)\n#define LAPACK_cpftrs LAPACK_GLOBAL(cpftrs,CPFTRS)\n#define LAPACK_spptrs LAPACK_GLOBAL(spptrs,SPPTRS)\n#define LAPACK_dpptrs LAPACK_GLOBAL(dpptrs,DPPTRS)\n#define LAPACK_cpptrs LAPACK_GLOBAL(cpptrs,CPPTRS)\n#define LAPACK_zpptrs LAPACK_GLOBAL(zpptrs,ZPPTRS)\n#define LAPACK_spbtrs LAPACK_GLOBAL(spbtrs,SPBTRS)\n#define LAPACK_dpbtrs LAPACK_GLOBAL(dpbtrs,DPBTRS)\n#define LAPACK_cpbtrs LAPACK_GLOBAL(cpbtrs,CPBTRS)\n#define LAPACK_zpbtrs LAPACK_GLOBAL(zpbtrs,ZPBTRS)\n#define LAPACK_spttrs LAPACK_GLOBAL(spttrs,SPTTRS)\n#define LAPACK_dpttrs LAPACK_GLOBAL(dpttrs,DPTTRS)\n#define LAPACK_cpttrs LAPACK_GLOBAL(cpttrs,CPTTRS)\n#define LAPACK_zpttrs LAPACK_GLOBAL(zpttrs,ZPTTRS)\n#define LAPACK_ssytrs LAPACK_GLOBAL(ssytrs,SSYTRS)\n#define LAPACK_dsytrs LAPACK_GLOBAL(dsytrs,DSYTRS)\n#define LAPACK_csytrs LAPACK_GLOBAL(csytrs,CSYTRS)\n#define LAPACK_zsytrs LAPACK_GLOBAL(zsytrs,ZSYTRS)\n#define LAPACK_chetrs LAPACK_GLOBAL(chetrs,CHETRS)\n#define LAPACK_zhetrs LAPACK_GLOBAL(zhetrs,ZHETRS)\n#define LAPACK_ssptrs LAPACK_GLOBAL(ssptrs,SSPTRS)\n#define LAPACK_dsptrs LAPACK_GLOBAL(dsptrs,DSPTRS)\n#define LAPACK_csptrs LAPACK_GLOBAL(csptrs,CSPTRS)\n#define LAPACK_zsptrs LAPACK_GLOBAL(zsptrs,ZSPTRS)\n#define LAPACK_chptrs LAPACK_GLOBAL(chptrs,CHPTRS)\n#define LAPACK_zhptrs LAPACK_GLOBAL(zhptrs,ZHPTRS)\n#define LAPACK_strtrs LAPACK_GLOBAL(strtrs,STRTRS)\n#define LAPACK_dtrtrs LAPACK_GLOBAL(dtrtrs,DTRTRS)\n#define LAPACK_ctrtrs LAPACK_GLOBAL(ctrtrs,CTRTRS)\n#define LAPACK_ztrtrs LAPACK_GLOBAL(ztrtrs,ZTRTRS)\n#define LAPACK_stptrs LAPACK_GLOBAL(stptrs,STPTRS)\n#define LAPACK_dtptrs LAPACK_GLOBAL(dtptrs,DTPTRS)\n#define LAPACK_ctptrs LAPACK_GLOBAL(ctptrs,CTPTRS)\n#define LAPACK_ztptrs LAPACK_GLOBAL(ztptrs,ZTPTRS)\n#define LAPACK_stbtrs LAPACK_GLOBAL(stbtrs,STBTRS)\n#define LAPACK_dtbtrs LAPACK_GLOBAL(dtbtrs,DTBTRS)\n#define LAPACK_ctbtrs LAPACK_GLOBAL(ctbtrs,CTBTRS)\n#define LAPACK_ztbtrs LAPACK_GLOBAL(ztbtrs,ZTBTRS)\n#define LAPACK_sgecon LAPACK_GLOBAL(sgecon,SGECON)\n#define LAPACK_dgecon LAPACK_GLOBAL(dgecon,DGECON)\n#define LAPACK_cgecon LAPACK_GLOBAL(cgecon,CGECON)\n#define LAPACK_zgecon LAPACK_GLOBAL(zgecon,ZGECON)\n#define LAPACK_sgbcon LAPACK_GLOBAL(sgbcon,SGBCON)\n#define LAPACK_dgbcon LAPACK_GLOBAL(dgbcon,DGBCON)\n#define LAPACK_cgbcon LAPACK_GLOBAL(cgbcon,CGBCON)\n#define LAPACK_zgbcon LAPACK_GLOBAL(zgbcon,ZGBCON)\n#define LAPACK_sgtcon LAPACK_GLOBAL(sgtcon,SGTCON)\n#define LAPACK_dgtcon LAPACK_GLOBAL(dgtcon,DGTCON)\n#define LAPACK_cgtcon LAPACK_GLOBAL(cgtcon,CGTCON)\n#define LAPACK_zgtcon LAPACK_GLOBAL(zgtcon,ZGTCON)\n#define LAPACK_spocon LAPACK_GLOBAL(spocon,SPOCON)\n#define LAPACK_dpocon LAPACK_GLOBAL(dpocon,DPOCON)\n#define LAPACK_cpocon LAPACK_GLOBAL(cpocon,CPOCON)\n#define LAPACK_zpocon LAPACK_GLOBAL(zpocon,ZPOCON)\n#define LAPACK_sppcon LAPACK_GLOBAL(sppcon,SPPCON)\n#define LAPACK_dppcon LAPACK_GLOBAL(dppcon,DPPCON)\n#define LAPACK_cppcon LAPACK_GLOBAL(cppcon,CPPCON)\n#define LAPACK_zppcon LAPACK_GLOBAL(zppcon,ZPPCON)\n#define LAPACK_spbcon LAPACK_GLOBAL(spbcon,SPBCON)\n#define LAPACK_dpbcon LAPACK_GLOBAL(dpbcon,DPBCON)\n#define LAPACK_cpbcon LAPACK_GLOBAL(cpbcon,CPBCON)\n#define LAPACK_zpbcon LAPACK_GLOBAL(zpbcon,ZPBCON)\n#define LAPACK_sptcon LAPACK_GLOBAL(sptcon,SPTCON)\n#define LAPACK_dptcon LAPACK_GLOBAL(dptcon,DPTCON)\n#define LAPACK_cptcon LAPACK_GLOBAL(cptcon,CPTCON)\n#define LAPACK_zptcon LAPACK_GLOBAL(zptcon,ZPTCON)\n#define LAPACK_ssycon LAPACK_GLOBAL(ssycon,SSYCON)\n#define LAPACK_dsycon LAPACK_GLOBAL(dsycon,DSYCON)\n#define LAPACK_csycon LAPACK_GLOBAL(csycon,CSYCON)\n#define LAPACK_zsycon LAPACK_GLOBAL(zsycon,ZSYCON)\n#define LAPACK_checon LAPACK_GLOBAL(checon,CHECON)\n#define LAPACK_zhecon LAPACK_GLOBAL(zhecon,ZHECON)\n#define LAPACK_sspcon LAPACK_GLOBAL(sspcon,SSPCON)\n#define LAPACK_dspcon LAPACK_GLOBAL(dspcon,DSPCON)\n#define LAPACK_cspcon LAPACK_GLOBAL(cspcon,CSPCON)\n#define LAPACK_zspcon LAPACK_GLOBAL(zspcon,ZSPCON)\n#define LAPACK_chpcon LAPACK_GLOBAL(chpcon,CHPCON)\n#define LAPACK_zhpcon LAPACK_GLOBAL(zhpcon,ZHPCON)\n#define LAPACK_strcon LAPACK_GLOBAL(strcon,STRCON)\n#define LAPACK_dtrcon LAPACK_GLOBAL(dtrcon,DTRCON)\n#define LAPACK_ctrcon LAPACK_GLOBAL(ctrcon,CTRCON)\n#define LAPACK_ztrcon LAPACK_GLOBAL(ztrcon,ZTRCON)\n#define LAPACK_stpcon LAPACK_GLOBAL(stpcon,STPCON)\n#define LAPACK_dtpcon LAPACK_GLOBAL(dtpcon,DTPCON)\n#define LAPACK_ctpcon LAPACK_GLOBAL(ctpcon,CTPCON)\n#define LAPACK_ztpcon LAPACK_GLOBAL(ztpcon,ZTPCON)\n#define LAPACK_stbcon LAPACK_GLOBAL(stbcon,STBCON)\n#define LAPACK_dtbcon LAPACK_GLOBAL(dtbcon,DTBCON)\n#define LAPACK_ctbcon LAPACK_GLOBAL(ctbcon,CTBCON)\n#define LAPACK_ztbcon LAPACK_GLOBAL(ztbcon,ZTBCON)\n#define LAPACK_sgerfs LAPACK_GLOBAL(sgerfs,SGERFS)\n#define LAPACK_dgerfs LAPACK_GLOBAL(dgerfs,DGERFS)\n#define LAPACK_cgerfs LAPACK_GLOBAL(cgerfs,CGERFS)\n#define LAPACK_zgerfs LAPACK_GLOBAL(zgerfs,ZGERFS)\n#define LAPACK_dgerfsx LAPACK_GLOBAL(dgerfsx,DGERFSX)\n#define LAPACK_sgerfsx LAPACK_GLOBAL(sgerfsx,SGERFSX)\n#define LAPACK_zgerfsx LAPACK_GLOBAL(zgerfsx,ZGERFSX)\n#define LAPACK_cgerfsx LAPACK_GLOBAL(cgerfsx,CGERFSX)\n#define LAPACK_sgbrfs LAPACK_GLOBAL(sgbrfs,SGBRFS)\n#define LAPACK_dgbrfs LAPACK_GLOBAL(dgbrfs,DGBRFS)\n#define LAPACK_cgbrfs LAPACK_GLOBAL(cgbrfs,CGBRFS)\n#define LAPACK_zgbrfs LAPACK_GLOBAL(zgbrfs,ZGBRFS)\n#define LAPACK_dgbrfsx LAPACK_GLOBAL(dgbrfsx,DGBRFSX)\n#define LAPACK_sgbrfsx LAPACK_GLOBAL(sgbrfsx,SGBRFSX)\n#define LAPACK_zgbrfsx LAPACK_GLOBAL(zgbrfsx,ZGBRFSX)\n#define LAPACK_cgbrfsx LAPACK_GLOBAL(cgbrfsx,CGBRFSX)\n#define LAPACK_sgtrfs LAPACK_GLOBAL(sgtrfs,SGTRFS)\n#define LAPACK_dgtrfs LAPACK_GLOBAL(dgtrfs,DGTRFS)\n#define LAPACK_cgtrfs LAPACK_GLOBAL(cgtrfs,CGTRFS)\n#define LAPACK_zgtrfs LAPACK_GLOBAL(zgtrfs,ZGTRFS)\n#define LAPACK_sporfs LAPACK_GLOBAL(sporfs,SPORFS)\n#define LAPACK_dporfs LAPACK_GLOBAL(dporfs,DPORFS)\n#define LAPACK_cporfs LAPACK_GLOBAL(cporfs,CPORFS)\n#define LAPACK_zporfs LAPACK_GLOBAL(zporfs,ZPORFS)\n#define LAPACK_dporfsx LAPACK_GLOBAL(dporfsx,DPORFSX)\n#define LAPACK_sporfsx LAPACK_GLOBAL(sporfsx,SPORFSX)\n#define LAPACK_zporfsx LAPACK_GLOBAL(zporfsx,ZPORFSX)\n#define LAPACK_cporfsx LAPACK_GLOBAL(cporfsx,CPORFSX)\n#define LAPACK_spprfs LAPACK_GLOBAL(spprfs,SPPRFS)\n#define LAPACK_dpprfs LAPACK_GLOBAL(dpprfs,DPPRFS)\n#define LAPACK_cpprfs LAPACK_GLOBAL(cpprfs,CPPRFS)\n#define LAPACK_zpprfs LAPACK_GLOBAL(zpprfs,ZPPRFS)\n#define LAPACK_spbrfs LAPACK_GLOBAL(spbrfs,SPBRFS)\n#define LAPACK_dpbrfs LAPACK_GLOBAL(dpbrfs,DPBRFS)\n#define LAPACK_cpbrfs LAPACK_GLOBAL(cpbrfs,CPBRFS)\n#define LAPACK_zpbrfs LAPACK_GLOBAL(zpbrfs,ZPBRFS)\n#define LAPACK_sptrfs LAPACK_GLOBAL(sptrfs,SPTRFS)\n#define LAPACK_dptrfs LAPACK_GLOBAL(dptrfs,DPTRFS)\n#define LAPACK_cptrfs LAPACK_GLOBAL(cptrfs,CPTRFS)\n#define LAPACK_zptrfs LAPACK_GLOBAL(zptrfs,ZPTRFS)\n#define LAPACK_ssyrfs LAPACK_GLOBAL(ssyrfs,SSYRFS)\n#define LAPACK_dsyrfs LAPACK_GLOBAL(dsyrfs,DSYRFS)\n#define LAPACK_csyrfs LAPACK_GLOBAL(csyrfs,CSYRFS)\n#define LAPACK_zsyrfs LAPACK_GLOBAL(zsyrfs,ZSYRFS)\n#define LAPACK_dsyrfsx LAPACK_GLOBAL(dsyrfsx,DSYRFSX)\n#define LAPACK_ssyrfsx LAPACK_GLOBAL(ssyrfsx,SSYRFSX)\n#define LAPACK_zsyrfsx LAPACK_GLOBAL(zsyrfsx,ZSYRFSX)\n#define LAPACK_csyrfsx LAPACK_GLOBAL(csyrfsx,CSYRFSX)\n#define LAPACK_cherfs LAPACK_GLOBAL(cherfs,CHERFS)\n#define LAPACK_zherfs LAPACK_GLOBAL(zherfs,ZHERFS)\n#define LAPACK_zherfsx LAPACK_GLOBAL(zherfsx,ZHERFSX)\n#define LAPACK_cherfsx LAPACK_GLOBAL(cherfsx,CHERFSX)\n#define LAPACK_ssprfs LAPACK_GLOBAL(ssprfs,SSPRFS)\n#define LAPACK_dsprfs LAPACK_GLOBAL(dsprfs,DSPRFS)\n#define LAPACK_csprfs LAPACK_GLOBAL(csprfs,CSPRFS)\n#define LAPACK_zsprfs LAPACK_GLOBAL(zsprfs,ZSPRFS)\n#define LAPACK_chprfs LAPACK_GLOBAL(chprfs,CHPRFS)\n#define LAPACK_zhprfs LAPACK_GLOBAL(zhprfs,ZHPRFS)\n#define LAPACK_strrfs LAPACK_GLOBAL(strrfs,STRRFS)\n#define LAPACK_dtrrfs LAPACK_GLOBAL(dtrrfs,DTRRFS)\n#define LAPACK_ctrrfs LAPACK_GLOBAL(ctrrfs,CTRRFS)\n#define LAPACK_ztrrfs LAPACK_GLOBAL(ztrrfs,ZTRRFS)\n#define LAPACK_stprfs LAPACK_GLOBAL(stprfs,STPRFS)\n#define LAPACK_dtprfs LAPACK_GLOBAL(dtprfs,DTPRFS)\n#define LAPACK_ctprfs LAPACK_GLOBAL(ctprfs,CTPRFS)\n#define LAPACK_ztprfs LAPACK_GLOBAL(ztprfs,ZTPRFS)\n#define LAPACK_stbrfs LAPACK_GLOBAL(stbrfs,STBRFS)\n#define LAPACK_dtbrfs LAPACK_GLOBAL(dtbrfs,DTBRFS)\n#define LAPACK_ctbrfs LAPACK_GLOBAL(ctbrfs,CTBRFS)\n#define LAPACK_ztbrfs LAPACK_GLOBAL(ztbrfs,ZTBRFS)\n#define LAPACK_sgetri LAPACK_GLOBAL(sgetri,SGETRI)\n#define LAPACK_dgetri LAPACK_GLOBAL(dgetri,DGETRI)\n#define LAPACK_cgetri LAPACK_GLOBAL(cgetri,CGETRI)\n#define LAPACK_zgetri LAPACK_GLOBAL(zgetri,ZGETRI)\n#define LAPACK_spotri LAPACK_GLOBAL(spotri,SPOTRI)\n#define LAPACK_dpotri LAPACK_GLOBAL(dpotri,DPOTRI)\n#define LAPACK_cpotri LAPACK_GLOBAL(cpotri,CPOTRI)\n#define LAPACK_zpotri LAPACK_GLOBAL(zpotri,ZPOTRI)\n#define LAPACK_dpftri LAPACK_GLOBAL(dpftri,DPFTRI)\n#define LAPACK_spftri LAPACK_GLOBAL(spftri,SPFTRI)\n#define LAPACK_zpftri LAPACK_GLOBAL(zpftri,ZPFTRI)\n#define LAPACK_cpftri LAPACK_GLOBAL(cpftri,CPFTRI)\n#define LAPACK_spptri LAPACK_GLOBAL(spptri,SPPTRI)\n#define LAPACK_dpptri LAPACK_GLOBAL(dpptri,DPPTRI)\n#define LAPACK_cpptri LAPACK_GLOBAL(cpptri,CPPTRI)\n#define LAPACK_zpptri LAPACK_GLOBAL(zpptri,ZPPTRI)\n#define LAPACK_ssytri LAPACK_GLOBAL(ssytri,SSYTRI)\n#define LAPACK_dsytri LAPACK_GLOBAL(dsytri,DSYTRI)\n#define LAPACK_csytri LAPACK_GLOBAL(csytri,CSYTRI)\n#define LAPACK_zsytri LAPACK_GLOBAL(zsytri,ZSYTRI)\n#define LAPACK_chetri LAPACK_GLOBAL(chetri,CHETRI)\n#define LAPACK_zhetri LAPACK_GLOBAL(zhetri,ZHETRI)\n#define LAPACK_ssptri LAPACK_GLOBAL(ssptri,SSPTRI)\n#define LAPACK_dsptri LAPACK_GLOBAL(dsptri,DSPTRI)\n#define LAPACK_csptri LAPACK_GLOBAL(csptri,CSPTRI)\n#define LAPACK_zsptri LAPACK_GLOBAL(zsptri,ZSPTRI)\n#define LAPACK_chptri LAPACK_GLOBAL(chptri,CHPTRI)\n#define LAPACK_zhptri LAPACK_GLOBAL(zhptri,ZHPTRI)\n#define LAPACK_strtri LAPACK_GLOBAL(strtri,STRTRI)\n#define LAPACK_dtrtri LAPACK_GLOBAL(dtrtri,DTRTRI)\n#define LAPACK_ctrtri LAPACK_GLOBAL(ctrtri,CTRTRI)\n#define LAPACK_ztrtri LAPACK_GLOBAL(ztrtri,ZTRTRI)\n#define LAPACK_dtftri LAPACK_GLOBAL(dtftri,DTFTRI)\n#define LAPACK_stftri LAPACK_GLOBAL(stftri,STFTRI)\n#define LAPACK_ztftri LAPACK_GLOBAL(ztftri,ZTFTRI)\n#define LAPACK_ctftri LAPACK_GLOBAL(ctftri,CTFTRI)\n#define LAPACK_stptri LAPACK_GLOBAL(stptri,STPTRI)\n#define LAPACK_dtptri LAPACK_GLOBAL(dtptri,DTPTRI)\n#define LAPACK_ctptri LAPACK_GLOBAL(ctptri,CTPTRI)\n#define LAPACK_ztptri LAPACK_GLOBAL(ztptri,ZTPTRI)\n#define LAPACK_sgeequ LAPACK_GLOBAL(sgeequ,SGEEQU)\n#define LAPACK_dgeequ LAPACK_GLOBAL(dgeequ,DGEEQU)\n#define LAPACK_cgeequ LAPACK_GLOBAL(cgeequ,CGEEQU)\n#define LAPACK_zgeequ LAPACK_GLOBAL(zgeequ,ZGEEQU)\n#define LAPACK_dgeequb LAPACK_GLOBAL(dgeequb,DGEEQUB)\n#define LAPACK_sgeequb LAPACK_GLOBAL(sgeequb,SGEEQUB)\n#define LAPACK_zgeequb LAPACK_GLOBAL(zgeequb,ZGEEQUB)\n#define LAPACK_cgeequb LAPACK_GLOBAL(cgeequb,CGEEQUB)\n#define LAPACK_sgbequ LAPACK_GLOBAL(sgbequ,SGBEQU)\n#define LAPACK_dgbequ LAPACK_GLOBAL(dgbequ,DGBEQU)\n#define LAPACK_cgbequ LAPACK_GLOBAL(cgbequ,CGBEQU)\n#define LAPACK_zgbequ LAPACK_GLOBAL(zgbequ,ZGBEQU)\n#define LAPACK_dgbequb LAPACK_GLOBAL(dgbequb,DGBEQUB)\n#define LAPACK_sgbequb LAPACK_GLOBAL(sgbequb,SGBEQUB)\n#define LAPACK_zgbequb LAPACK_GLOBAL(zgbequb,ZGBEQUB)\n#define LAPACK_cgbequb LAPACK_GLOBAL(cgbequb,CGBEQUB)\n#define LAPACK_spoequ LAPACK_GLOBAL(spoequ,SPOEQU)\n#define LAPACK_dpoequ LAPACK_GLOBAL(dpoequ,DPOEQU)\n#define LAPACK_cpoequ LAPACK_GLOBAL(cpoequ,CPOEQU)\n#define LAPACK_zpoequ LAPACK_GLOBAL(zpoequ,ZPOEQU)\n#define LAPACK_dpoequb LAPACK_GLOBAL(dpoequb,DPOEQUB)\n#define LAPACK_spoequb LAPACK_GLOBAL(spoequb,SPOEQUB)\n#define LAPACK_zpoequb LAPACK_GLOBAL(zpoequb,ZPOEQUB)\n#define LAPACK_cpoequb LAPACK_GLOBAL(cpoequb,CPOEQUB)\n#define LAPACK_sppequ LAPACK_GLOBAL(sppequ,SPPEQU)\n#define LAPACK_dppequ LAPACK_GLOBAL(dppequ,DPPEQU)\n#define LAPACK_cppequ LAPACK_GLOBAL(cppequ,CPPEQU)\n#define LAPACK_zppequ LAPACK_GLOBAL(zppequ,ZPPEQU)\n#define LAPACK_spbequ LAPACK_GLOBAL(spbequ,SPBEQU)\n#define LAPACK_dpbequ LAPACK_GLOBAL(dpbequ,DPBEQU)\n#define LAPACK_cpbequ LAPACK_GLOBAL(cpbequ,CPBEQU)\n#define LAPACK_zpbequ LAPACK_GLOBAL(zpbequ,ZPBEQU)\n#define LAPACK_dsyequb LAPACK_GLOBAL(dsyequb,DSYEQUB)\n#define LAPACK_ssyequb LAPACK_GLOBAL(ssyequb,SSYEQUB)\n#define LAPACK_zsyequb LAPACK_GLOBAL(zsyequb,ZSYEQUB)\n#define LAPACK_csyequb LAPACK_GLOBAL(csyequb,CSYEQUB)\n#define LAPACK_zheequb LAPACK_GLOBAL(zheequb,ZHEEQUB)\n#define LAPACK_cheequb LAPACK_GLOBAL(cheequb,CHEEQUB)\n#define LAPACK_sgesv LAPACK_GLOBAL(sgesv,SGESV)\n#define LAPACK_dgesv LAPACK_GLOBAL(dgesv,DGESV)\n#define LAPACK_cgesv LAPACK_GLOBAL(cgesv,CGESV)\n#define LAPACK_zgesv LAPACK_GLOBAL(zgesv,ZGESV)\n#define LAPACK_dsgesv LAPACK_GLOBAL(dsgesv,DSGESV)\n#define LAPACK_zcgesv LAPACK_GLOBAL(zcgesv,ZCGESV)\n#define LAPACK_sgesvx LAPACK_GLOBAL(sgesvx,SGESVX)\n#define LAPACK_dgesvx LAPACK_GLOBAL(dgesvx,DGESVX)\n#define LAPACK_cgesvx LAPACK_GLOBAL(cgesvx,CGESVX)\n#define LAPACK_zgesvx LAPACK_GLOBAL(zgesvx,ZGESVX)\n#define LAPACK_dgesvxx LAPACK_GLOBAL(dgesvxx,DGESVXX)\n#define LAPACK_sgesvxx LAPACK_GLOBAL(sgesvxx,SGESVXX)\n#define LAPACK_zgesvxx LAPACK_GLOBAL(zgesvxx,ZGESVXX)\n#define LAPACK_cgesvxx LAPACK_GLOBAL(cgesvxx,CGESVXX)\n#define LAPACK_sgbsv LAPACK_GLOBAL(sgbsv,SGBSV)\n#define LAPACK_dgbsv LAPACK_GLOBAL(dgbsv,DGBSV)\n#define LAPACK_cgbsv LAPACK_GLOBAL(cgbsv,CGBSV)\n#define LAPACK_zgbsv LAPACK_GLOBAL(zgbsv,ZGBSV)\n#define LAPACK_sgbsvx LAPACK_GLOBAL(sgbsvx,SGBSVX)\n#define LAPACK_dgbsvx LAPACK_GLOBAL(dgbsvx,DGBSVX)\n#define LAPACK_cgbsvx LAPACK_GLOBAL(cgbsvx,CGBSVX)\n#define LAPACK_zgbsvx LAPACK_GLOBAL(zgbsvx,ZGBSVX)\n#define LAPACK_dgbsvxx LAPACK_GLOBAL(dgbsvxx,DGBSVXX)\n#define LAPACK_sgbsvxx LAPACK_GLOBAL(sgbsvxx,SGBSVXX)\n#define LAPACK_zgbsvxx LAPACK_GLOBAL(zgbsvxx,ZGBSVXX)\n#define LAPACK_cgbsvxx LAPACK_GLOBAL(cgbsvxx,CGBSVXX)\n#define LAPACK_sgtsv LAPACK_GLOBAL(sgtsv,SGTSV)\n#define LAPACK_dgtsv LAPACK_GLOBAL(dgtsv,DGTSV)\n#define LAPACK_cgtsv LAPACK_GLOBAL(cgtsv,CGTSV)\n#define LAPACK_zgtsv LAPACK_GLOBAL(zgtsv,ZGTSV)\n#define LAPACK_sgtsvx LAPACK_GLOBAL(sgtsvx,SGTSVX)\n#define LAPACK_dgtsvx LAPACK_GLOBAL(dgtsvx,DGTSVX)\n#define LAPACK_cgtsvx LAPACK_GLOBAL(cgtsvx,CGTSVX)\n#define LAPACK_zgtsvx LAPACK_GLOBAL(zgtsvx,ZGTSVX)\n#define LAPACK_sposv LAPACK_GLOBAL(sposv,SPOSV)\n#define LAPACK_dposv LAPACK_GLOBAL(dposv,DPOSV)\n#define LAPACK_cposv LAPACK_GLOBAL(cposv,CPOSV)\n#define LAPACK_zposv LAPACK_GLOBAL(zposv,ZPOSV)\n#define LAPACK_dsposv LAPACK_GLOBAL(dsposv,DSPOSV)\n#define LAPACK_zcposv LAPACK_GLOBAL(zcposv,ZCPOSV)\n#define LAPACK_sposvx LAPACK_GLOBAL(sposvx,SPOSVX)\n#define LAPACK_dposvx LAPACK_GLOBAL(dposvx,DPOSVX)\n#define LAPACK_cposvx LAPACK_GLOBAL(cposvx,CPOSVX)\n#define LAPACK_zposvx LAPACK_GLOBAL(zposvx,ZPOSVX)\n#define LAPACK_dposvxx LAPACK_GLOBAL(dposvxx,DPOSVXX)\n#define LAPACK_sposvxx LAPACK_GLOBAL(sposvxx,SPOSVXX)\n#define LAPACK_zposvxx LAPACK_GLOBAL(zposvxx,ZPOSVXX)\n#define LAPACK_cposvxx LAPACK_GLOBAL(cposvxx,CPOSVXX)\n#define LAPACK_sppsv LAPACK_GLOBAL(sppsv,SPPSV)\n#define LAPACK_dppsv LAPACK_GLOBAL(dppsv,DPPSV)\n#define LAPACK_cppsv LAPACK_GLOBAL(cppsv,CPPSV)\n#define LAPACK_zppsv LAPACK_GLOBAL(zppsv,ZPPSV)\n#define LAPACK_sppsvx LAPACK_GLOBAL(sppsvx,SPPSVX)\n#define LAPACK_dppsvx LAPACK_GLOBAL(dppsvx,DPPSVX)\n#define LAPACK_cppsvx LAPACK_GLOBAL(cppsvx,CPPSVX)\n#define LAPACK_zppsvx LAPACK_GLOBAL(zppsvx,ZPPSVX)\n#define LAPACK_spbsv LAPACK_GLOBAL(spbsv,SPBSV)\n#define LAPACK_dpbsv LAPACK_GLOBAL(dpbsv,DPBSV)\n#define LAPACK_cpbsv LAPACK_GLOBAL(cpbsv,CPBSV)\n#define LAPACK_zpbsv LAPACK_GLOBAL(zpbsv,ZPBSV)\n#define LAPACK_spbsvx LAPACK_GLOBAL(spbsvx,SPBSVX)\n#define LAPACK_dpbsvx LAPACK_GLOBAL(dpbsvx,DPBSVX)\n#define LAPACK_cpbsvx LAPACK_GLOBAL(cpbsvx,CPBSVX)\n#define LAPACK_zpbsvx LAPACK_GLOBAL(zpbsvx,ZPBSVX)\n#define LAPACK_sptsv LAPACK_GLOBAL(sptsv,SPTSV)\n#define LAPACK_dptsv LAPACK_GLOBAL(dptsv,DPTSV)\n#define LAPACK_cptsv LAPACK_GLOBAL(cptsv,CPTSV)\n#define LAPACK_zptsv LAPACK_GLOBAL(zptsv,ZPTSV)\n#define LAPACK_sptsvx LAPACK_GLOBAL(sptsvx,SPTSVX)\n#define LAPACK_dptsvx LAPACK_GLOBAL(dptsvx,DPTSVX)\n#define LAPACK_cptsvx LAPACK_GLOBAL(cptsvx,CPTSVX)\n#define LAPACK_zptsvx LAPACK_GLOBAL(zptsvx,ZPTSVX)\n#define LAPACK_ssysv LAPACK_GLOBAL(ssysv,SSYSV)\n#define LAPACK_dsysv LAPACK_GLOBAL(dsysv,DSYSV)\n#define LAPACK_csysv LAPACK_GLOBAL(csysv,CSYSV)\n#define LAPACK_zsysv LAPACK_GLOBAL(zsysv,ZSYSV)\n#define LAPACK_ssysvx LAPACK_GLOBAL(ssysvx,SSYSVX)\n#define LAPACK_dsysvx LAPACK_GLOBAL(dsysvx,DSYSVX)\n#define LAPACK_csysvx LAPACK_GLOBAL(csysvx,CSYSVX)\n#define LAPACK_zsysvx LAPACK_GLOBAL(zsysvx,ZSYSVX)\n#define LAPACK_dsysvxx LAPACK_GLOBAL(dsysvxx,DSYSVXX)\n#define LAPACK_ssysvxx LAPACK_GLOBAL(ssysvxx,SSYSVXX)\n#define LAPACK_zsysvxx LAPACK_GLOBAL(zsysvxx,ZSYSVXX)\n#define LAPACK_csysvxx LAPACK_GLOBAL(csysvxx,CSYSVXX)\n#define LAPACK_chesv LAPACK_GLOBAL(chesv,CHESV)\n#define LAPACK_zhesv LAPACK_GLOBAL(zhesv,ZHESV)\n#define LAPACK_chesvx LAPACK_GLOBAL(chesvx,CHESVX)\n#define LAPACK_zhesvx LAPACK_GLOBAL(zhesvx,ZHESVX)\n#define LAPACK_zhesvxx LAPACK_GLOBAL(zhesvxx,ZHESVXX)\n#define LAPACK_chesvxx LAPACK_GLOBAL(chesvxx,CHESVXX)\n#define LAPACK_sspsv LAPACK_GLOBAL(sspsv,SSPSV)\n#define LAPACK_dspsv LAPACK_GLOBAL(dspsv,DSPSV)\n#define LAPACK_cspsv LAPACK_GLOBAL(cspsv,CSPSV)\n#define LAPACK_zspsv LAPACK_GLOBAL(zspsv,ZSPSV)\n#define LAPACK_sspsvx LAPACK_GLOBAL(sspsvx,SSPSVX)\n#define LAPACK_dspsvx LAPACK_GLOBAL(dspsvx,DSPSVX)\n#define LAPACK_cspsvx LAPACK_GLOBAL(cspsvx,CSPSVX)\n#define LAPACK_zspsvx LAPACK_GLOBAL(zspsvx,ZSPSVX)\n#define LAPACK_chpsv LAPACK_GLOBAL(chpsv,CHPSV)\n#define LAPACK_zhpsv LAPACK_GLOBAL(zhpsv,ZHPSV)\n#define LAPACK_chpsvx LAPACK_GLOBAL(chpsvx,CHPSVX)\n#define LAPACK_zhpsvx LAPACK_GLOBAL(zhpsvx,ZHPSVX)\n#define LAPACK_sgeqrf LAPACK_GLOBAL(sgeqrf,SGEQRF)\n#define LAPACK_dgeqrf LAPACK_GLOBAL(dgeqrf,DGEQRF)\n#define LAPACK_cgeqrf LAPACK_GLOBAL(cgeqrf,CGEQRF)\n#define LAPACK_zgeqrf LAPACK_GLOBAL(zgeqrf,ZGEQRF)\n#define LAPACK_sgeqpf LAPACK_GLOBAL(sgeqpf,SGEQPF)\n#define LAPACK_dgeqpf LAPACK_GLOBAL(dgeqpf,DGEQPF)\n#define LAPACK_cgeqpf LAPACK_GLOBAL(cgeqpf,CGEQPF)\n#define LAPACK_zgeqpf LAPACK_GLOBAL(zgeqpf,ZGEQPF)\n#define LAPACK_sgeqp3 LAPACK_GLOBAL(sgeqp3,SGEQP3)\n#define LAPACK_dgeqp3 LAPACK_GLOBAL(dgeqp3,DGEQP3)\n#define LAPACK_cgeqp3 LAPACK_GLOBAL(cgeqp3,CGEQP3)\n#define LAPACK_zgeqp3 LAPACK_GLOBAL(zgeqp3,ZGEQP3)\n#define LAPACK_sorgqr LAPACK_GLOBAL(sorgqr,SORGQR)\n#define LAPACK_dorgqr LAPACK_GLOBAL(dorgqr,DORGQR)\n#define LAPACK_sormqr LAPACK_GLOBAL(sormqr,SORMQR)\n#define LAPACK_dormqr LAPACK_GLOBAL(dormqr,DORMQR)\n#define LAPACK_cungqr LAPACK_GLOBAL(cungqr,CUNGQR)\n#define LAPACK_zungqr LAPACK_GLOBAL(zungqr,ZUNGQR)\n#define LAPACK_cunmqr LAPACK_GLOBAL(cunmqr,CUNMQR)\n#define LAPACK_zunmqr LAPACK_GLOBAL(zunmqr,ZUNMQR)\n#define LAPACK_sgelqf LAPACK_GLOBAL(sgelqf,SGELQF)\n#define LAPACK_dgelqf LAPACK_GLOBAL(dgelqf,DGELQF)\n#define LAPACK_cgelqf LAPACK_GLOBAL(cgelqf,CGELQF)\n#define LAPACK_zgelqf LAPACK_GLOBAL(zgelqf,ZGELQF)\n#define LAPACK_sorglq LAPACK_GLOBAL(sorglq,SORGLQ)\n#define LAPACK_dorglq LAPACK_GLOBAL(dorglq,DORGLQ)\n#define LAPACK_sormlq LAPACK_GLOBAL(sormlq,SORMLQ)\n#define LAPACK_dormlq LAPACK_GLOBAL(dormlq,DORMLQ)\n#define LAPACK_cunglq LAPACK_GLOBAL(cunglq,CUNGLQ)\n#define LAPACK_zunglq LAPACK_GLOBAL(zunglq,ZUNGLQ)\n#define LAPACK_cunmlq LAPACK_GLOBAL(cunmlq,CUNMLQ)\n#define LAPACK_zunmlq LAPACK_GLOBAL(zunmlq,ZUNMLQ)\n#define LAPACK_sgeqlf LAPACK_GLOBAL(sgeqlf,SGEQLF)\n#define LAPACK_dgeqlf LAPACK_GLOBAL(dgeqlf,DGEQLF)\n#define LAPACK_cgeqlf LAPACK_GLOBAL(cgeqlf,CGEQLF)\n#define LAPACK_zgeqlf LAPACK_GLOBAL(zgeqlf,ZGEQLF)\n#define LAPACK_sorgql LAPACK_GLOBAL(sorgql,SORGQL)\n#define LAPACK_dorgql LAPACK_GLOBAL(dorgql,DORGQL)\n#define LAPACK_cungql LAPACK_GLOBAL(cungql,CUNGQL)\n#define LAPACK_zungql LAPACK_GLOBAL(zungql,ZUNGQL)\n#define LAPACK_sormql LAPACK_GLOBAL(sormql,SORMQL)\n#define LAPACK_dormql LAPACK_GLOBAL(dormql,DORMQL)\n#define LAPACK_cunmql LAPACK_GLOBAL(cunmql,CUNMQL)\n#define LAPACK_zunmql LAPACK_GLOBAL(zunmql,ZUNMQL)\n#define LAPACK_sgerqf LAPACK_GLOBAL(sgerqf,SGERQF)\n#define LAPACK_dgerqf LAPACK_GLOBAL(dgerqf,DGERQF)\n#define LAPACK_cgerqf LAPACK_GLOBAL(cgerqf,CGERQF)\n#define LAPACK_zgerqf LAPACK_GLOBAL(zgerqf,ZGERQF)\n#define LAPACK_sorgrq LAPACK_GLOBAL(sorgrq,SORGRQ)\n#define LAPACK_dorgrq LAPACK_GLOBAL(dorgrq,DORGRQ)\n#define LAPACK_cungrq LAPACK_GLOBAL(cungrq,CUNGRQ)\n#define LAPACK_zungrq LAPACK_GLOBAL(zungrq,ZUNGRQ)\n#define LAPACK_sormrq LAPACK_GLOBAL(sormrq,SORMRQ)\n#define LAPACK_dormrq LAPACK_GLOBAL(dormrq,DORMRQ)\n#define LAPACK_cunmrq LAPACK_GLOBAL(cunmrq,CUNMRQ)\n#define LAPACK_zunmrq LAPACK_GLOBAL(zunmrq,ZUNMRQ)\n#define LAPACK_stzrzf LAPACK_GLOBAL(stzrzf,STZRZF)\n#define LAPACK_dtzrzf LAPACK_GLOBAL(dtzrzf,DTZRZF)\n#define LAPACK_ctzrzf LAPACK_GLOBAL(ctzrzf,CTZRZF)\n#define LAPACK_ztzrzf LAPACK_GLOBAL(ztzrzf,ZTZRZF)\n#define LAPACK_sormrz LAPACK_GLOBAL(sormrz,SORMRZ)\n#define LAPACK_dormrz LAPACK_GLOBAL(dormrz,DORMRZ)\n#define LAPACK_cunmrz LAPACK_GLOBAL(cunmrz,CUNMRZ)\n#define LAPACK_zunmrz LAPACK_GLOBAL(zunmrz,ZUNMRZ)\n#define LAPACK_sggqrf LAPACK_GLOBAL(sggqrf,SGGQRF)\n#define LAPACK_dggqrf LAPACK_GLOBAL(dggqrf,DGGQRF)\n#define LAPACK_cggqrf LAPACK_GLOBAL(cggqrf,CGGQRF)\n#define LAPACK_zggqrf LAPACK_GLOBAL(zggqrf,ZGGQRF)\n#define LAPACK_sggrqf LAPACK_GLOBAL(sggrqf,SGGRQF)\n#define LAPACK_dggrqf LAPACK_GLOBAL(dggrqf,DGGRQF)\n#define LAPACK_cggrqf LAPACK_GLOBAL(cggrqf,CGGRQF)\n#define LAPACK_zggrqf LAPACK_GLOBAL(zggrqf,ZGGRQF)\n#define LAPACK_sgebrd LAPACK_GLOBAL(sgebrd,SGEBRD)\n#define LAPACK_dgebrd LAPACK_GLOBAL(dgebrd,DGEBRD)\n#define LAPACK_cgebrd LAPACK_GLOBAL(cgebrd,CGEBRD)\n#define LAPACK_zgebrd LAPACK_GLOBAL(zgebrd,ZGEBRD)\n#define LAPACK_sgbbrd LAPACK_GLOBAL(sgbbrd,SGBBRD)\n#define LAPACK_dgbbrd LAPACK_GLOBAL(dgbbrd,DGBBRD)\n#define LAPACK_cgbbrd LAPACK_GLOBAL(cgbbrd,CGBBRD)\n#define LAPACK_zgbbrd LAPACK_GLOBAL(zgbbrd,ZGBBRD)\n#define LAPACK_sorgbr LAPACK_GLOBAL(sorgbr,SORGBR)\n#define LAPACK_dorgbr LAPACK_GLOBAL(dorgbr,DORGBR)\n#define LAPACK_sormbr LAPACK_GLOBAL(sormbr,SORMBR)\n#define LAPACK_dormbr LAPACK_GLOBAL(dormbr,DORMBR)\n#define LAPACK_cungbr LAPACK_GLOBAL(cungbr,CUNGBR)\n#define LAPACK_zungbr LAPACK_GLOBAL(zungbr,ZUNGBR)\n#define LAPACK_cunmbr LAPACK_GLOBAL(cunmbr,CUNMBR)\n#define LAPACK_zunmbr LAPACK_GLOBAL(zunmbr,ZUNMBR)\n#define LAPACK_sbdsqr LAPACK_GLOBAL(sbdsqr,SBDSQR)\n#define LAPACK_dbdsqr LAPACK_GLOBAL(dbdsqr,DBDSQR)\n#define LAPACK_cbdsqr LAPACK_GLOBAL(cbdsqr,CBDSQR)\n#define LAPACK_zbdsqr LAPACK_GLOBAL(zbdsqr,ZBDSQR)\n#define LAPACK_sbdsdc LAPACK_GLOBAL(sbdsdc,SBDSDC)\n#define LAPACK_dbdsdc LAPACK_GLOBAL(dbdsdc,DBDSDC)\n#define LAPACK_ssytrd LAPACK_GLOBAL(ssytrd,SSYTRD)\n#define LAPACK_dsytrd LAPACK_GLOBAL(dsytrd,DSYTRD)\n#define LAPACK_sorgtr LAPACK_GLOBAL(sorgtr,SORGTR)\n#define LAPACK_dorgtr LAPACK_GLOBAL(dorgtr,DORGTR)\n#define LAPACK_sormtr LAPACK_GLOBAL(sormtr,SORMTR)\n#define LAPACK_dormtr LAPACK_GLOBAL(dormtr,DORMTR)\n#define LAPACK_chetrd LAPACK_GLOBAL(chetrd,CHETRD)\n#define LAPACK_zhetrd LAPACK_GLOBAL(zhetrd,ZHETRD)\n#define LAPACK_cungtr LAPACK_GLOBAL(cungtr,CUNGTR)\n#define LAPACK_zungtr LAPACK_GLOBAL(zungtr,ZUNGTR)\n#define LAPACK_cunmtr LAPACK_GLOBAL(cunmtr,CUNMTR)\n#define LAPACK_zunmtr LAPACK_GLOBAL(zunmtr,ZUNMTR)\n#define LAPACK_ssptrd LAPACK_GLOBAL(ssptrd,SSPTRD)\n#define LAPACK_dsptrd LAPACK_GLOBAL(dsptrd,DSPTRD)\n#define LAPACK_sopgtr LAPACK_GLOBAL(sopgtr,SOPGTR)\n#define LAPACK_dopgtr LAPACK_GLOBAL(dopgtr,DOPGTR)\n#define LAPACK_sopmtr LAPACK_GLOBAL(sopmtr,SOPMTR)\n#define LAPACK_dopmtr LAPACK_GLOBAL(dopmtr,DOPMTR)\n#define LAPACK_chptrd LAPACK_GLOBAL(chptrd,CHPTRD)\n#define LAPACK_zhptrd LAPACK_GLOBAL(zhptrd,ZHPTRD)\n#define LAPACK_cupgtr LAPACK_GLOBAL(cupgtr,CUPGTR)\n#define LAPACK_zupgtr LAPACK_GLOBAL(zupgtr,ZUPGTR)\n#define LAPACK_cupmtr LAPACK_GLOBAL(cupmtr,CUPMTR)\n#define LAPACK_zupmtr LAPACK_GLOBAL(zupmtr,ZUPMTR)\n#define LAPACK_ssbtrd LAPACK_GLOBAL(ssbtrd,SSBTRD)\n#define LAPACK_dsbtrd LAPACK_GLOBAL(dsbtrd,DSBTRD)\n#define LAPACK_chbtrd LAPACK_GLOBAL(chbtrd,CHBTRD)\n#define LAPACK_zhbtrd LAPACK_GLOBAL(zhbtrd,ZHBTRD)\n#define LAPACK_ssterf LAPACK_GLOBAL(ssterf,SSTERF)\n#define LAPACK_dsterf LAPACK_GLOBAL(dsterf,DSTERF)\n#define LAPACK_ssteqr LAPACK_GLOBAL(ssteqr,SSTEQR)\n#define LAPACK_dsteqr LAPACK_GLOBAL(dsteqr,DSTEQR)\n#define LAPACK_csteqr LAPACK_GLOBAL(csteqr,CSTEQR)\n#define LAPACK_zsteqr LAPACK_GLOBAL(zsteqr,ZSTEQR)\n#define LAPACK_sstemr LAPACK_GLOBAL(sstemr,SSTEMR)\n#define LAPACK_dstemr LAPACK_GLOBAL(dstemr,DSTEMR)\n#define LAPACK_cstemr LAPACK_GLOBAL(cstemr,CSTEMR)\n#define LAPACK_zstemr LAPACK_GLOBAL(zstemr,ZSTEMR)\n#define LAPACK_sstedc LAPACK_GLOBAL(sstedc,SSTEDC)\n#define LAPACK_dstedc LAPACK_GLOBAL(dstedc,DSTEDC)\n#define LAPACK_cstedc LAPACK_GLOBAL(cstedc,CSTEDC)\n#define LAPACK_zstedc LAPACK_GLOBAL(zstedc,ZSTEDC)\n#define LAPACK_sstegr LAPACK_GLOBAL(sstegr,SSTEGR)\n#define LAPACK_dstegr LAPACK_GLOBAL(dstegr,DSTEGR)\n#define LAPACK_cstegr LAPACK_GLOBAL(cstegr,CSTEGR)\n#define LAPACK_zstegr LAPACK_GLOBAL(zstegr,ZSTEGR)\n#define LAPACK_spteqr LAPACK_GLOBAL(spteqr,SPTEQR)\n#define LAPACK_dpteqr LAPACK_GLOBAL(dpteqr,DPTEQR)\n#define LAPACK_cpteqr LAPACK_GLOBAL(cpteqr,CPTEQR)\n#define LAPACK_zpteqr LAPACK_GLOBAL(zpteqr,ZPTEQR)\n#define LAPACK_sstebz LAPACK_GLOBAL(sstebz,SSTEBZ)\n#define LAPACK_dstebz LAPACK_GLOBAL(dstebz,DSTEBZ)\n#define LAPACK_sstein LAPACK_GLOBAL(sstein,SSTEIN)\n#define LAPACK_dstein LAPACK_GLOBAL(dstein,DSTEIN)\n#define LAPACK_cstein LAPACK_GLOBAL(cstein,CSTEIN)\n#define LAPACK_zstein LAPACK_GLOBAL(zstein,ZSTEIN)\n#define LAPACK_sdisna LAPACK_GLOBAL(sdisna,SDISNA)\n#define LAPACK_ddisna LAPACK_GLOBAL(ddisna,DDISNA)\n#define LAPACK_ssygst LAPACK_GLOBAL(ssygst,SSYGST)\n#define LAPACK_dsygst LAPACK_GLOBAL(dsygst,DSYGST)\n#define LAPACK_chegst LAPACK_GLOBAL(chegst,CHEGST)\n#define LAPACK_zhegst LAPACK_GLOBAL(zhegst,ZHEGST)\n#define LAPACK_sspgst LAPACK_GLOBAL(sspgst,SSPGST)\n#define LAPACK_dspgst LAPACK_GLOBAL(dspgst,DSPGST)\n#define LAPACK_chpgst LAPACK_GLOBAL(chpgst,CHPGST)\n#define LAPACK_zhpgst LAPACK_GLOBAL(zhpgst,ZHPGST)\n#define LAPACK_ssbgst LAPACK_GLOBAL(ssbgst,SSBGST)\n#define LAPACK_dsbgst LAPACK_GLOBAL(dsbgst,DSBGST)\n#define LAPACK_chbgst LAPACK_GLOBAL(chbgst,CHBGST)\n#define LAPACK_zhbgst LAPACK_GLOBAL(zhbgst,ZHBGST)\n#define LAPACK_spbstf LAPACK_GLOBAL(spbstf,SPBSTF)\n#define LAPACK_dpbstf LAPACK_GLOBAL(dpbstf,DPBSTF)\n#define LAPACK_cpbstf LAPACK_GLOBAL(cpbstf,CPBSTF)\n#define LAPACK_zpbstf LAPACK_GLOBAL(zpbstf,ZPBSTF)\n#define LAPACK_sgehrd LAPACK_GLOBAL(sgehrd,SGEHRD)\n#define LAPACK_dgehrd LAPACK_GLOBAL(dgehrd,DGEHRD)\n#define LAPACK_cgehrd LAPACK_GLOBAL(cgehrd,CGEHRD)\n#define LAPACK_zgehrd LAPACK_GLOBAL(zgehrd,ZGEHRD)\n#define LAPACK_sorghr LAPACK_GLOBAL(sorghr,SORGHR)\n#define LAPACK_dorghr LAPACK_GLOBAL(dorghr,DORGHR)\n#define LAPACK_sormhr LAPACK_GLOBAL(sormhr,SORMHR)\n#define LAPACK_dormhr LAPACK_GLOBAL(dormhr,DORMHR)\n#define LAPACK_cunghr LAPACK_GLOBAL(cunghr,CUNGHR)\n#define LAPACK_zunghr LAPACK_GLOBAL(zunghr,ZUNGHR)\n#define LAPACK_cunmhr LAPACK_GLOBAL(cunmhr,CUNMHR)\n#define LAPACK_zunmhr LAPACK_GLOBAL(zunmhr,ZUNMHR)\n#define LAPACK_sgebal LAPACK_GLOBAL(sgebal,SGEBAL)\n#define LAPACK_dgebal LAPACK_GLOBAL(dgebal,DGEBAL)\n#define LAPACK_cgebal LAPACK_GLOBAL(cgebal,CGEBAL)\n#define LAPACK_zgebal LAPACK_GLOBAL(zgebal,ZGEBAL)\n#define LAPACK_sgebak LAPACK_GLOBAL(sgebak,SGEBAK)\n#define LAPACK_dgebak LAPACK_GLOBAL(dgebak,DGEBAK)\n#define LAPACK_cgebak LAPACK_GLOBAL(cgebak,CGEBAK)\n#define LAPACK_zgebak LAPACK_GLOBAL(zgebak,ZGEBAK)\n#define LAPACK_shseqr LAPACK_GLOBAL(shseqr,SHSEQR)\n#define LAPACK_dhseqr LAPACK_GLOBAL(dhseqr,DHSEQR)\n#define LAPACK_chseqr LAPACK_GLOBAL(chseqr,CHSEQR)\n#define LAPACK_zhseqr LAPACK_GLOBAL(zhseqr,ZHSEQR)\n#define LAPACK_shsein LAPACK_GLOBAL(shsein,SHSEIN)\n#define LAPACK_dhsein LAPACK_GLOBAL(dhsein,DHSEIN)\n#define LAPACK_chsein LAPACK_GLOBAL(chsein,CHSEIN)\n#define LAPACK_zhsein LAPACK_GLOBAL(zhsein,ZHSEIN)\n#define LAPACK_strevc LAPACK_GLOBAL(strevc,STREVC)\n#define LAPACK_dtrevc LAPACK_GLOBAL(dtrevc,DTREVC)\n#define LAPACK_ctrevc LAPACK_GLOBAL(ctrevc,CTREVC)\n#define LAPACK_ztrevc LAPACK_GLOBAL(ztrevc,ZTREVC)\n#define LAPACK_strsna LAPACK_GLOBAL(strsna,STRSNA)\n#define LAPACK_dtrsna LAPACK_GLOBAL(dtrsna,DTRSNA)\n#define LAPACK_ctrsna LAPACK_GLOBAL(ctrsna,CTRSNA)\n#define LAPACK_ztrsna LAPACK_GLOBAL(ztrsna,ZTRSNA)\n#define LAPACK_strexc LAPACK_GLOBAL(strexc,STREXC)\n#define LAPACK_dtrexc LAPACK_GLOBAL(dtrexc,DTREXC)\n#define LAPACK_ctrexc LAPACK_GLOBAL(ctrexc,CTREXC)\n#define LAPACK_ztrexc LAPACK_GLOBAL(ztrexc,ZTREXC)\n#define LAPACK_strsen LAPACK_GLOBAL(strsen,STRSEN)\n#define LAPACK_dtrsen LAPACK_GLOBAL(dtrsen,DTRSEN)\n#define LAPACK_ctrsen LAPACK_GLOBAL(ctrsen,CTRSEN)\n#define LAPACK_ztrsen LAPACK_GLOBAL(ztrsen,ZTRSEN)\n#define LAPACK_strsyl LAPACK_GLOBAL(strsyl,STRSYL)\n#define LAPACK_dtrsyl LAPACK_GLOBAL(dtrsyl,DTRSYL)\n#define LAPACK_ctrsyl LAPACK_GLOBAL(ctrsyl,CTRSYL)\n#define LAPACK_ztrsyl LAPACK_GLOBAL(ztrsyl,ZTRSYL)\n#define LAPACK_sgghrd LAPACK_GLOBAL(sgghrd,SGGHRD)\n#define LAPACK_dgghrd LAPACK_GLOBAL(dgghrd,DGGHRD)\n#define LAPACK_cgghrd LAPACK_GLOBAL(cgghrd,CGGHRD)\n#define LAPACK_zgghrd LAPACK_GLOBAL(zgghrd,ZGGHRD)\n#define LAPACK_sggbal LAPACK_GLOBAL(sggbal,SGGBAL)\n#define LAPACK_dggbal LAPACK_GLOBAL(dggbal,DGGBAL)\n#define LAPACK_cggbal LAPACK_GLOBAL(cggbal,CGGBAL)\n#define LAPACK_zggbal LAPACK_GLOBAL(zggbal,ZGGBAL)\n#define LAPACK_sggbak LAPACK_GLOBAL(sggbak,SGGBAK)\n#define LAPACK_dggbak LAPACK_GLOBAL(dggbak,DGGBAK)\n#define LAPACK_cggbak LAPACK_GLOBAL(cggbak,CGGBAK)\n#define LAPACK_zggbak LAPACK_GLOBAL(zggbak,ZGGBAK)\n#define LAPACK_shgeqz LAPACK_GLOBAL(shgeqz,SHGEQZ)\n#define LAPACK_dhgeqz LAPACK_GLOBAL(dhgeqz,DHGEQZ)\n#define LAPACK_chgeqz LAPACK_GLOBAL(chgeqz,CHGEQZ)\n#define LAPACK_zhgeqz LAPACK_GLOBAL(zhgeqz,ZHGEQZ)\n#define LAPACK_stgevc LAPACK_GLOBAL(stgevc,STGEVC)\n#define LAPACK_dtgevc LAPACK_GLOBAL(dtgevc,DTGEVC)\n#define LAPACK_ctgevc LAPACK_GLOBAL(ctgevc,CTGEVC)\n#define LAPACK_ztgevc LAPACK_GLOBAL(ztgevc,ZTGEVC)\n#define LAPACK_stgexc LAPACK_GLOBAL(stgexc,STGEXC)\n#define LAPACK_dtgexc LAPACK_GLOBAL(dtgexc,DTGEXC)\n#define LAPACK_ctgexc LAPACK_GLOBAL(ctgexc,CTGEXC)\n#define LAPACK_ztgexc LAPACK_GLOBAL(ztgexc,ZTGEXC)\n#define LAPACK_stgsen LAPACK_GLOBAL(stgsen,STGSEN)\n#define LAPACK_dtgsen LAPACK_GLOBAL(dtgsen,DTGSEN)\n#define LAPACK_ctgsen LAPACK_GLOBAL(ctgsen,CTGSEN)\n#define LAPACK_ztgsen LAPACK_GLOBAL(ztgsen,ZTGSEN)\n#define LAPACK_stgsyl LAPACK_GLOBAL(stgsyl,STGSYL)\n#define LAPACK_dtgsyl LAPACK_GLOBAL(dtgsyl,DTGSYL)\n#define LAPACK_ctgsyl LAPACK_GLOBAL(ctgsyl,CTGSYL)\n#define LAPACK_ztgsyl LAPACK_GLOBAL(ztgsyl,ZTGSYL)\n#define LAPACK_stgsna LAPACK_GLOBAL(stgsna,STGSNA)\n#define LAPACK_dtgsna LAPACK_GLOBAL(dtgsna,DTGSNA)\n#define LAPACK_ctgsna LAPACK_GLOBAL(ctgsna,CTGSNA)\n#define LAPACK_ztgsna LAPACK_GLOBAL(ztgsna,ZTGSNA)\n#define LAPACK_sggsvp LAPACK_GLOBAL(sggsvp,SGGSVP)\n#define LAPACK_dggsvp LAPACK_GLOBAL(dggsvp,DGGSVP)\n#define LAPACK_cggsvp LAPACK_GLOBAL(cggsvp,CGGSVP)\n#define LAPACK_zggsvp LAPACK_GLOBAL(zggsvp,ZGGSVP)\n#define LAPACK_stgsja LAPACK_GLOBAL(stgsja,STGSJA)\n#define LAPACK_dtgsja LAPACK_GLOBAL(dtgsja,DTGSJA)\n#define LAPACK_ctgsja LAPACK_GLOBAL(ctgsja,CTGSJA)\n#define LAPACK_ztgsja LAPACK_GLOBAL(ztgsja,ZTGSJA)\n#define LAPACK_sgels LAPACK_GLOBAL(sgels,SGELS)\n#define LAPACK_dgels LAPACK_GLOBAL(dgels,DGELS)\n#define LAPACK_cgels LAPACK_GLOBAL(cgels,CGELS)\n#define LAPACK_zgels LAPACK_GLOBAL(zgels,ZGELS)\n#define LAPACK_sgelsy LAPACK_GLOBAL(sgelsy,SGELSY)\n#define LAPACK_dgelsy LAPACK_GLOBAL(dgelsy,DGELSY)\n#define LAPACK_cgelsy LAPACK_GLOBAL(cgelsy,CGELSY)\n#define LAPACK_zgelsy LAPACK_GLOBAL(zgelsy,ZGELSY)\n#define LAPACK_sgelss LAPACK_GLOBAL(sgelss,SGELSS)\n#define LAPACK_dgelss LAPACK_GLOBAL(dgelss,DGELSS)\n#define LAPACK_cgelss LAPACK_GLOBAL(cgelss,CGELSS)\n#define LAPACK_zgelss LAPACK_GLOBAL(zgelss,ZGELSS)\n#define LAPACK_sgelsd LAPACK_GLOBAL(sgelsd,SGELSD)\n#define LAPACK_dgelsd LAPACK_GLOBAL(dgelsd,DGELSD)\n#define LAPACK_cgelsd LAPACK_GLOBAL(cgelsd,CGELSD)\n#define LAPACK_zgelsd LAPACK_GLOBAL(zgelsd,ZGELSD)\n#define LAPACK_sgglse LAPACK_GLOBAL(sgglse,SGGLSE)\n#define LAPACK_dgglse LAPACK_GLOBAL(dgglse,DGGLSE)\n#define LAPACK_cgglse LAPACK_GLOBAL(cgglse,CGGLSE)\n#define LAPACK_zgglse LAPACK_GLOBAL(zgglse,ZGGLSE)\n#define LAPACK_sggglm LAPACK_GLOBAL(sggglm,SGGGLM)\n#define LAPACK_dggglm LAPACK_GLOBAL(dggglm,DGGGLM)\n#define LAPACK_cggglm LAPACK_GLOBAL(cggglm,CGGGLM)\n#define LAPACK_zggglm LAPACK_GLOBAL(zggglm,ZGGGLM)\n#define LAPACK_ssyev LAPACK_GLOBAL(ssyev,SSYEV)\n#define LAPACK_dsyev LAPACK_GLOBAL(dsyev,DSYEV)\n#define LAPACK_cheev LAPACK_GLOBAL(cheev,CHEEV)\n#define LAPACK_zheev LAPACK_GLOBAL(zheev,ZHEEV)\n#define LAPACK_ssyevd LAPACK_GLOBAL(ssyevd,SSYEVD)\n#define LAPACK_dsyevd LAPACK_GLOBAL(dsyevd,DSYEVD)\n#define LAPACK_cheevd LAPACK_GLOBAL(cheevd,CHEEVD)\n#define LAPACK_zheevd LAPACK_GLOBAL(zheevd,ZHEEVD)\n#define LAPACK_ssyevx LAPACK_GLOBAL(ssyevx,SSYEVX)\n#define LAPACK_dsyevx LAPACK_GLOBAL(dsyevx,DSYEVX)\n#define LAPACK_cheevx LAPACK_GLOBAL(cheevx,CHEEVX)\n#define LAPACK_zheevx LAPACK_GLOBAL(zheevx,ZHEEVX)\n#define LAPACK_ssyevr LAPACK_GLOBAL(ssyevr,SSYEVR)\n#define LAPACK_dsyevr LAPACK_GLOBAL(dsyevr,DSYEVR)\n#define LAPACK_cheevr LAPACK_GLOBAL(cheevr,CHEEVR)\n#define LAPACK_zheevr LAPACK_GLOBAL(zheevr,ZHEEVR)\n#define LAPACK_sspev LAPACK_GLOBAL(sspev,SSPEV)\n#define LAPACK_dspev LAPACK_GLOBAL(dspev,DSPEV)\n#define LAPACK_chpev LAPACK_GLOBAL(chpev,CHPEV)\n#define LAPACK_zhpev LAPACK_GLOBAL(zhpev,ZHPEV)\n#define LAPACK_sspevd LAPACK_GLOBAL(sspevd,SSPEVD)\n#define LAPACK_dspevd LAPACK_GLOBAL(dspevd,DSPEVD)\n#define LAPACK_chpevd LAPACK_GLOBAL(chpevd,CHPEVD)\n#define LAPACK_zhpevd LAPACK_GLOBAL(zhpevd,ZHPEVD)\n#define LAPACK_sspevx LAPACK_GLOBAL(sspevx,SSPEVX)\n#define LAPACK_dspevx LAPACK_GLOBAL(dspevx,DSPEVX)\n#define LAPACK_chpevx LAPACK_GLOBAL(chpevx,CHPEVX)\n#define LAPACK_zhpevx LAPACK_GLOBAL(zhpevx,ZHPEVX)\n#define LAPACK_ssbev LAPACK_GLOBAL(ssbev,SSBEV)\n#define LAPACK_dsbev LAPACK_GLOBAL(dsbev,DSBEV)\n#define LAPACK_chbev LAPACK_GLOBAL(chbev,CHBEV)\n#define LAPACK_zhbev LAPACK_GLOBAL(zhbev,ZHBEV)\n#define LAPACK_ssbevd LAPACK_GLOBAL(ssbevd,SSBEVD)\n#define LAPACK_dsbevd LAPACK_GLOBAL(dsbevd,DSBEVD)\n#define LAPACK_chbevd LAPACK_GLOBAL(chbevd,CHBEVD)\n#define LAPACK_zhbevd LAPACK_GLOBAL(zhbevd,ZHBEVD)\n#define LAPACK_ssbevx LAPACK_GLOBAL(ssbevx,SSBEVX)\n#define LAPACK_dsbevx LAPACK_GLOBAL(dsbevx,DSBEVX)\n#define LAPACK_chbevx LAPACK_GLOBAL(chbevx,CHBEVX)\n#define LAPACK_zhbevx LAPACK_GLOBAL(zhbevx,ZHBEVX)\n#define LAPACK_sstev LAPACK_GLOBAL(sstev,SSTEV)\n#define LAPACK_dstev LAPACK_GLOBAL(dstev,DSTEV)\n#define LAPACK_sstevd LAPACK_GLOBAL(sstevd,SSTEVD)\n#define LAPACK_dstevd LAPACK_GLOBAL(dstevd,DSTEVD)\n#define LAPACK_sstevx LAPACK_GLOBAL(sstevx,SSTEVX)\n#define LAPACK_dstevx LAPACK_GLOBAL(dstevx,DSTEVX)\n#define LAPACK_sstevr LAPACK_GLOBAL(sstevr,SSTEVR)\n#define LAPACK_dstevr LAPACK_GLOBAL(dstevr,DSTEVR)\n#define LAPACK_sgees LAPACK_GLOBAL(sgees,SGEES)\n#define LAPACK_dgees LAPACK_GLOBAL(dgees,DGEES)\n#define LAPACK_cgees LAPACK_GLOBAL(cgees,CGEES)\n#define LAPACK_zgees LAPACK_GLOBAL(zgees,ZGEES)\n#define LAPACK_sgeesx LAPACK_GLOBAL(sgeesx,SGEESX)\n#define LAPACK_dgeesx LAPACK_GLOBAL(dgeesx,DGEESX)\n#define LAPACK_cgeesx LAPACK_GLOBAL(cgeesx,CGEESX)\n#define LAPACK_zgeesx LAPACK_GLOBAL(zgeesx,ZGEESX)\n#define LAPACK_sgeev LAPACK_GLOBAL(sgeev,SGEEV)\n#define LAPACK_dgeev LAPACK_GLOBAL(dgeev,DGEEV)\n#define LAPACK_cgeev LAPACK_GLOBAL(cgeev,CGEEV)\n#define LAPACK_zgeev LAPACK_GLOBAL(zgeev,ZGEEV)\n#define LAPACK_sgeevx LAPACK_GLOBAL(sgeevx,SGEEVX)\n#define LAPACK_dgeevx LAPACK_GLOBAL(dgeevx,DGEEVX)\n#define LAPACK_cgeevx LAPACK_GLOBAL(cgeevx,CGEEVX)\n#define LAPACK_zgeevx LAPACK_GLOBAL(zgeevx,ZGEEVX)\n#define LAPACK_sgesvd LAPACK_GLOBAL(sgesvd,SGESVD)\n#define LAPACK_dgesvd LAPACK_GLOBAL(dgesvd,DGESVD)\n#define LAPACK_cgesvd LAPACK_GLOBAL(cgesvd,CGESVD)\n#define LAPACK_zgesvd LAPACK_GLOBAL(zgesvd,ZGESVD)\n#define LAPACK_sgesdd LAPACK_GLOBAL(sgesdd,SGESDD)\n#define LAPACK_dgesdd LAPACK_GLOBAL(dgesdd,DGESDD)\n#define LAPACK_cgesdd LAPACK_GLOBAL(cgesdd,CGESDD)\n#define LAPACK_zgesdd LAPACK_GLOBAL(zgesdd,ZGESDD)\n#define LAPACK_dgejsv LAPACK_GLOBAL(dgejsv,DGEJSV)\n#define LAPACK_sgejsv LAPACK_GLOBAL(sgejsv,SGEJSV)\n#define LAPACK_dgesvj LAPACK_GLOBAL(dgesvj,DGESVJ)\n#define LAPACK_sgesvj LAPACK_GLOBAL(sgesvj,SGESVJ)\n#define LAPACK_sggsvd LAPACK_GLOBAL(sggsvd,SGGSVD)\n#define LAPACK_dggsvd LAPACK_GLOBAL(dggsvd,DGGSVD)\n#define LAPACK_cggsvd LAPACK_GLOBAL(cggsvd,CGGSVD)\n#define LAPACK_zggsvd LAPACK_GLOBAL(zggsvd,ZGGSVD)\n#define LAPACK_ssygv LAPACK_GLOBAL(ssygv,SSYGV)\n#define LAPACK_dsygv LAPACK_GLOBAL(dsygv,DSYGV)\n#define LAPACK_chegv LAPACK_GLOBAL(chegv,CHEGV)\n#define LAPACK_zhegv LAPACK_GLOBAL(zhegv,ZHEGV)\n#define LAPACK_ssygvd LAPACK_GLOBAL(ssygvd,SSYGVD)\n#define LAPACK_dsygvd LAPACK_GLOBAL(dsygvd,DSYGVD)\n#define LAPACK_chegvd LAPACK_GLOBAL(chegvd,CHEGVD)\n#define LAPACK_zhegvd LAPACK_GLOBAL(zhegvd,ZHEGVD)\n#define LAPACK_ssygvx LAPACK_GLOBAL(ssygvx,SSYGVX)\n#define LAPACK_dsygvx LAPACK_GLOBAL(dsygvx,DSYGVX)\n#define LAPACK_chegvx LAPACK_GLOBAL(chegvx,CHEGVX)\n#define LAPACK_zhegvx LAPACK_GLOBAL(zhegvx,ZHEGVX)\n#define LAPACK_sspgv LAPACK_GLOBAL(sspgv,SSPGV)\n#define LAPACK_dspgv LAPACK_GLOBAL(dspgv,DSPGV)\n#define LAPACK_chpgv LAPACK_GLOBAL(chpgv,CHPGV)\n#define LAPACK_zhpgv LAPACK_GLOBAL(zhpgv,ZHPGV)\n#define LAPACK_sspgvd LAPACK_GLOBAL(sspgvd,SSPGVD)\n#define LAPACK_dspgvd LAPACK_GLOBAL(dspgvd,DSPGVD)\n#define LAPACK_chpgvd LAPACK_GLOBAL(chpgvd,CHPGVD)\n#define LAPACK_zhpgvd LAPACK_GLOBAL(zhpgvd,ZHPGVD)\n#define LAPACK_sspgvx LAPACK_GLOBAL(sspgvx,SSPGVX)\n#define LAPACK_dspgvx LAPACK_GLOBAL(dspgvx,DSPGVX)\n#define LAPACK_chpgvx LAPACK_GLOBAL(chpgvx,CHPGVX)\n#define LAPACK_zhpgvx LAPACK_GLOBAL(zhpgvx,ZHPGVX)\n#define LAPACK_ssbgv LAPACK_GLOBAL(ssbgv,SSBGV)\n#define LAPACK_dsbgv LAPACK_GLOBAL(dsbgv,DSBGV)\n#define LAPACK_chbgv LAPACK_GLOBAL(chbgv,CHBGV)\n#define LAPACK_zhbgv LAPACK_GLOBAL(zhbgv,ZHBGV)\n#define LAPACK_ssbgvd LAPACK_GLOBAL(ssbgvd,SSBGVD)\n#define LAPACK_dsbgvd LAPACK_GLOBAL(dsbgvd,DSBGVD)\n#define LAPACK_chbgvd LAPACK_GLOBAL(chbgvd,CHBGVD)\n#define LAPACK_zhbgvd LAPACK_GLOBAL(zhbgvd,ZHBGVD)\n#define LAPACK_ssbgvx LAPACK_GLOBAL(ssbgvx,SSBGVX)\n#define LAPACK_dsbgvx LAPACK_GLOBAL(dsbgvx,DSBGVX)\n#define LAPACK_chbgvx LAPACK_GLOBAL(chbgvx,CHBGVX)\n#define LAPACK_zhbgvx LAPACK_GLOBAL(zhbgvx,ZHBGVX)\n#define LAPACK_sgges LAPACK_GLOBAL(sgges,SGGES)\n#define LAPACK_dgges LAPACK_GLOBAL(dgges,DGGES)\n#define LAPACK_cgges LAPACK_GLOBAL(cgges,CGGES)\n#define LAPACK_zgges LAPACK_GLOBAL(zgges,ZGGES)\n#define LAPACK_sggesx LAPACK_GLOBAL(sggesx,SGGESX)\n#define LAPACK_dggesx LAPACK_GLOBAL(dggesx,DGGESX)\n#define LAPACK_cggesx LAPACK_GLOBAL(cggesx,CGGESX)\n#define LAPACK_zggesx LAPACK_GLOBAL(zggesx,ZGGESX)\n#define LAPACK_sggev LAPACK_GLOBAL(sggev,SGGEV)\n#define LAPACK_dggev LAPACK_GLOBAL(dggev,DGGEV)\n#define LAPACK_cggev LAPACK_GLOBAL(cggev,CGGEV)\n#define LAPACK_zggev LAPACK_GLOBAL(zggev,ZGGEV)\n#define LAPACK_sggevx LAPACK_GLOBAL(sggevx,SGGEVX)\n#define LAPACK_dggevx LAPACK_GLOBAL(dggevx,DGGEVX)\n#define LAPACK_cggevx LAPACK_GLOBAL(cggevx,CGGEVX)\n#define LAPACK_zggevx LAPACK_GLOBAL(zggevx,ZGGEVX)\n#define LAPACK_dsfrk LAPACK_GLOBAL(dsfrk,DSFRK)\n#define LAPACK_ssfrk LAPACK_GLOBAL(ssfrk,SSFRK)\n#define LAPACK_zhfrk LAPACK_GLOBAL(zhfrk,ZHFRK)\n#define LAPACK_chfrk LAPACK_GLOBAL(chfrk,CHFRK)\n#define LAPACK_dtfsm LAPACK_GLOBAL(dtfsm,DTFSM)\n#define LAPACK_stfsm LAPACK_GLOBAL(stfsm,STFSM)\n#define LAPACK_ztfsm LAPACK_GLOBAL(ztfsm,ZTFSM)\n#define LAPACK_ctfsm LAPACK_GLOBAL(ctfsm,CTFSM)\n#define LAPACK_dtfttp LAPACK_GLOBAL(dtfttp,DTFTTP)\n#define LAPACK_stfttp LAPACK_GLOBAL(stfttp,STFTTP)\n#define LAPACK_ztfttp LAPACK_GLOBAL(ztfttp,ZTFTTP)\n#define LAPACK_ctfttp LAPACK_GLOBAL(ctfttp,CTFTTP)\n#define LAPACK_dtfttr LAPACK_GLOBAL(dtfttr,DTFTTR)\n#define LAPACK_stfttr LAPACK_GLOBAL(stfttr,STFTTR)\n#define LAPACK_ztfttr LAPACK_GLOBAL(ztfttr,ZTFTTR)\n#define LAPACK_ctfttr LAPACK_GLOBAL(ctfttr,CTFTTR)\n#define LAPACK_dtpttf LAPACK_GLOBAL(dtpttf,DTPTTF)\n#define LAPACK_stpttf LAPACK_GLOBAL(stpttf,STPTTF)\n#define LAPACK_ztpttf LAPACK_GLOBAL(ztpttf,ZTPTTF)\n#define LAPACK_ctpttf LAPACK_GLOBAL(ctpttf,CTPTTF)\n#define LAPACK_dtpttr LAPACK_GLOBAL(dtpttr,DTPTTR)\n#define LAPACK_stpttr LAPACK_GLOBAL(stpttr,STPTTR)\n#define LAPACK_ztpttr LAPACK_GLOBAL(ztpttr,ZTPTTR)\n#define LAPACK_ctpttr LAPACK_GLOBAL(ctpttr,CTPTTR)\n#define LAPACK_dtrttf LAPACK_GLOBAL(dtrttf,DTRTTF)\n#define LAPACK_strttf LAPACK_GLOBAL(strttf,STRTTF)\n#define LAPACK_ztrttf LAPACK_GLOBAL(ztrttf,ZTRTTF)\n#define LAPACK_ctrttf LAPACK_GLOBAL(ctrttf,CTRTTF)\n#define LAPACK_dtrttp LAPACK_GLOBAL(dtrttp,DTRTTP)\n#define LAPACK_strttp LAPACK_GLOBAL(strttp,STRTTP)\n#define LAPACK_ztrttp LAPACK_GLOBAL(ztrttp,ZTRTTP)\n#define LAPACK_ctrttp LAPACK_GLOBAL(ctrttp,CTRTTP)\n#define LAPACK_sgeqrfp LAPACK_GLOBAL(sgeqrfp,SGEQRFP)\n#define LAPACK_dgeqrfp LAPACK_GLOBAL(dgeqrfp,DGEQRFP)\n#define LAPACK_cgeqrfp LAPACK_GLOBAL(cgeqrfp,CGEQRFP)\n#define LAPACK_zgeqrfp LAPACK_GLOBAL(zgeqrfp,ZGEQRFP)\n#define LAPACK_clacgv LAPACK_GLOBAL(clacgv,CLACGV)\n#define LAPACK_zlacgv LAPACK_GLOBAL(zlacgv,ZLACGV)\n#define LAPACK_slarnv LAPACK_GLOBAL(slarnv,SLARNV)\n#define LAPACK_dlarnv LAPACK_GLOBAL(dlarnv,DLARNV)\n#define LAPACK_clarnv LAPACK_GLOBAL(clarnv,CLARNV)\n#define LAPACK_zlarnv LAPACK_GLOBAL(zlarnv,ZLARNV)\n#define LAPACK_sgeqr2 LAPACK_GLOBAL(sgeqr2,SGEQR2)\n#define LAPACK_dgeqr2 LAPACK_GLOBAL(dgeqr2,DGEQR2)\n#define LAPACK_cgeqr2 LAPACK_GLOBAL(cgeqr2,CGEQR2)\n#define LAPACK_zgeqr2 LAPACK_GLOBAL(zgeqr2,ZGEQR2)\n#define LAPACK_slacpy LAPACK_GLOBAL(slacpy,SLACPY)\n#define LAPACK_dlacpy LAPACK_GLOBAL(dlacpy,DLACPY)\n#define LAPACK_clacpy LAPACK_GLOBAL(clacpy,CLACPY)\n#define LAPACK_zlacpy LAPACK_GLOBAL(zlacpy,ZLACPY)\n#define LAPACK_sgetf2 LAPACK_GLOBAL(sgetf2,SGETF2)\n#define LAPACK_dgetf2 LAPACK_GLOBAL(dgetf2,DGETF2)\n#define LAPACK_cgetf2 LAPACK_GLOBAL(cgetf2,CGETF2)\n#define LAPACK_zgetf2 LAPACK_GLOBAL(zgetf2,ZGETF2)\n#define LAPACK_slaswp LAPACK_GLOBAL(slaswp,SLASWP)\n#define LAPACK_dlaswp LAPACK_GLOBAL(dlaswp,DLASWP)\n#define LAPACK_claswp LAPACK_GLOBAL(claswp,CLASWP)\n#define LAPACK_zlaswp LAPACK_GLOBAL(zlaswp,ZLASWP)\n#define LAPACK_slange LAPACK_GLOBAL(slange,SLANGE)\n#define LAPACK_dlange LAPACK_GLOBAL(dlange,DLANGE)\n#define LAPACK_clange LAPACK_GLOBAL(clange,CLANGE)\n#define LAPACK_zlange LAPACK_GLOBAL(zlange,ZLANGE)\n#define LAPACK_clanhe LAPACK_GLOBAL(clanhe,CLANHE)\n#define LAPACK_zlanhe LAPACK_GLOBAL(zlanhe,ZLANHE)\n#define LAPACK_slansy LAPACK_GLOBAL(slansy,SLANSY)\n#define LAPACK_dlansy LAPACK_GLOBAL(dlansy,DLANSY)\n#define LAPACK_clansy LAPACK_GLOBAL(clansy,CLANSY)\n#define LAPACK_zlansy LAPACK_GLOBAL(zlansy,ZLANSY)\n#define LAPACK_slantr LAPACK_GLOBAL(slantr,SLANTR)\n#define LAPACK_dlantr LAPACK_GLOBAL(dlantr,DLANTR)\n#define LAPACK_clantr LAPACK_GLOBAL(clantr,CLANTR)\n#define LAPACK_zlantr LAPACK_GLOBAL(zlantr,ZLANTR)\n#define LAPACK_slamch LAPACK_GLOBAL(slamch,SLAMCH)\n#define LAPACK_dlamch LAPACK_GLOBAL(dlamch,DLAMCH)\n#define LAPACK_sgelq2 LAPACK_GLOBAL(sgelq2,SGELQ2)\n#define LAPACK_dgelq2 LAPACK_GLOBAL(dgelq2,DGELQ2)\n#define LAPACK_cgelq2 LAPACK_GLOBAL(cgelq2,CGELQ2)\n#define LAPACK_zgelq2 LAPACK_GLOBAL(zgelq2,ZGELQ2)\n#define LAPACK_slarfb LAPACK_GLOBAL(slarfb,SLARFB)\n#define LAPACK_dlarfb LAPACK_GLOBAL(dlarfb,DLARFB)\n#define LAPACK_clarfb LAPACK_GLOBAL(clarfb,CLARFB)\n#define LAPACK_zlarfb LAPACK_GLOBAL(zlarfb,ZLARFB)\n#define LAPACK_slarfg LAPACK_GLOBAL(slarfg,SLARFG)\n#define LAPACK_dlarfg LAPACK_GLOBAL(dlarfg,DLARFG)\n#define LAPACK_clarfg LAPACK_GLOBAL(clarfg,CLARFG)\n#define LAPACK_zlarfg LAPACK_GLOBAL(zlarfg,ZLARFG)\n#define LAPACK_slarft LAPACK_GLOBAL(slarft,SLARFT)\n#define LAPACK_dlarft LAPACK_GLOBAL(dlarft,DLARFT)\n#define LAPACK_clarft LAPACK_GLOBAL(clarft,CLARFT)\n#define LAPACK_zlarft LAPACK_GLOBAL(zlarft,ZLARFT)\n#define LAPACK_slarfx LAPACK_GLOBAL(slarfx,SLARFX)\n#define LAPACK_dlarfx LAPACK_GLOBAL(dlarfx,DLARFX)\n#define LAPACK_clarfx LAPACK_GLOBAL(clarfx,CLARFX)\n#define LAPACK_zlarfx LAPACK_GLOBAL(zlarfx,ZLARFX)\n#define LAPACK_slatms LAPACK_GLOBAL(slatms,SLATMS)\n#define LAPACK_dlatms LAPACK_GLOBAL(dlatms,DLATMS)\n#define LAPACK_clatms LAPACK_GLOBAL(clatms,CLATMS)\n#define LAPACK_zlatms LAPACK_GLOBAL(zlatms,ZLATMS)\n#define LAPACK_slag2d LAPACK_GLOBAL(slag2d,SLAG2D)\n#define LAPACK_dlag2s LAPACK_GLOBAL(dlag2s,DLAG2S)\n#define LAPACK_clag2z LAPACK_GLOBAL(clag2z,CLAG2Z)\n#define LAPACK_zlag2c LAPACK_GLOBAL(zlag2c,ZLAG2C)\n#define LAPACK_slauum LAPACK_GLOBAL(slauum,SLAUUM)\n#define LAPACK_dlauum LAPACK_GLOBAL(dlauum,DLAUUM)\n#define LAPACK_clauum LAPACK_GLOBAL(clauum,CLAUUM)\n#define LAPACK_zlauum LAPACK_GLOBAL(zlauum,ZLAUUM)\n#define LAPACK_slagge LAPACK_GLOBAL(slagge,SLAGGE)\n#define LAPACK_dlagge LAPACK_GLOBAL(dlagge,DLAGGE)\n#define LAPACK_clagge LAPACK_GLOBAL(clagge,CLAGGE)\n#define LAPACK_zlagge LAPACK_GLOBAL(zlagge,ZLAGGE)\n#define LAPACK_slaset LAPACK_GLOBAL(slaset,SLASET)\n#define LAPACK_dlaset LAPACK_GLOBAL(dlaset,DLASET)\n#define LAPACK_claset LAPACK_GLOBAL(claset,CLASET)\n#define LAPACK_zlaset LAPACK_GLOBAL(zlaset,ZLASET)\n#define LAPACK_slasrt LAPACK_GLOBAL(slasrt,SLASRT)\n#define LAPACK_dlasrt LAPACK_GLOBAL(dlasrt,DLASRT)\n#define LAPACK_slagsy LAPACK_GLOBAL(slagsy,SLAGSY)\n#define LAPACK_dlagsy LAPACK_GLOBAL(dlagsy,DLAGSY)\n#define LAPACK_clagsy LAPACK_GLOBAL(clagsy,CLAGSY)\n#define LAPACK_zlagsy LAPACK_GLOBAL(zlagsy,ZLAGSY)\n#define LAPACK_claghe LAPACK_GLOBAL(claghe,CLAGHE)\n#define LAPACK_zlaghe LAPACK_GLOBAL(zlaghe,ZLAGHE)\n#define LAPACK_slapmr LAPACK_GLOBAL(slapmr,SLAPMR)\n#define LAPACK_dlapmr LAPACK_GLOBAL(dlapmr,DLAPMR)\n#define LAPACK_clapmr LAPACK_GLOBAL(clapmr,CLAPMR)\n#define LAPACK_zlapmr LAPACK_GLOBAL(zlapmr,ZLAPMR)\n#define LAPACK_slapy2 LAPACK_GLOBAL(slapy2,SLAPY2)\n#define LAPACK_dlapy2 LAPACK_GLOBAL(dlapy2,DLAPY2)\n#define LAPACK_slapy3 LAPACK_GLOBAL(slapy3,SLAPY3)\n#define LAPACK_dlapy3 LAPACK_GLOBAL(dlapy3,DLAPY3)\n#define LAPACK_slartgp LAPACK_GLOBAL(slartgp,SLARTGP)\n#define LAPACK_dlartgp LAPACK_GLOBAL(dlartgp,DLARTGP)\n#define LAPACK_slartgs LAPACK_GLOBAL(slartgs,SLARTGS)\n#define LAPACK_dlartgs LAPACK_GLOBAL(dlartgs,DLARTGS)\n// LAPACK 3.3.0\n#define LAPACK_cbbcsd LAPACK_GLOBAL(cbbcsd,CBBCSD)\n#define LAPACK_cheswapr LAPACK_GLOBAL(cheswapr,CHESWAPR)\n#define LAPACK_chetri2 LAPACK_GLOBAL(chetri2,CHETRI2)\n#define LAPACK_chetri2x LAPACK_GLOBAL(chetri2x,CHETRI2X)\n#define LAPACK_chetrs2 LAPACK_GLOBAL(chetrs2,CHETRS2)\n#define LAPACK_csyconv LAPACK_GLOBAL(csyconv,CSYCONV)\n#define LAPACK_csyswapr LAPACK_GLOBAL(csyswapr,CSYSWAPR)\n#define LAPACK_csytri2 LAPACK_GLOBAL(csytri2,CSYTRI2)\n#define LAPACK_csytri2x LAPACK_GLOBAL(csytri2x,CSYTRI2X)\n#define LAPACK_csytrs2 LAPACK_GLOBAL(csytrs2,CSYTRS2)\n#define LAPACK_cunbdb LAPACK_GLOBAL(cunbdb,CUNBDB)\n#define LAPACK_cuncsd LAPACK_GLOBAL(cuncsd,CUNCSD)\n#define LAPACK_dbbcsd LAPACK_GLOBAL(dbbcsd,DBBCSD)\n#define LAPACK_dorbdb LAPACK_GLOBAL(dorbdb,DORBDB)\n#define LAPACK_dorcsd LAPACK_GLOBAL(dorcsd,DORCSD)\n#define LAPACK_dsyconv LAPACK_GLOBAL(dsyconv,DSYCONV)\n#define LAPACK_dsyswapr LAPACK_GLOBAL(dsyswapr,DSYSWAPR)\n#define LAPACK_dsytri2 LAPACK_GLOBAL(dsytri2,DSYTRI2)\n#define LAPACK_dsytri2x LAPACK_GLOBAL(dsytri2x,DSYTRI2X)\n#define LAPACK_dsytrs2 LAPACK_GLOBAL(dsytrs2,DSYTRS2)\n#define LAPACK_sbbcsd LAPACK_GLOBAL(sbbcsd,SBBCSD)\n#define LAPACK_sorbdb LAPACK_GLOBAL(sorbdb,SORBDB)\n#define LAPACK_sorcsd LAPACK_GLOBAL(sorcsd,SORCSD)\n#define LAPACK_ssyconv LAPACK_GLOBAL(ssyconv,SSYCONV)\n#define LAPACK_ssyswapr LAPACK_GLOBAL(ssyswapr,SSYSWAPR)\n#define LAPACK_ssytri2 LAPACK_GLOBAL(ssytri2,SSYTRI2)\n#define LAPACK_ssytri2x LAPACK_GLOBAL(ssytri2x,SSYTRI2X)\n#define LAPACK_ssytrs2 LAPACK_GLOBAL(ssytrs2,SSYTRS2)\n#define LAPACK_zbbcsd LAPACK_GLOBAL(zbbcsd,ZBBCSD)\n#define LAPACK_zheswapr LAPACK_GLOBAL(zheswapr,ZHESWAPR)\n#define LAPACK_zhetri2 LAPACK_GLOBAL(zhetri2,ZHETRI2)\n#define LAPACK_zhetri2x LAPACK_GLOBAL(zhetri2x,ZHETRI2X)\n#define LAPACK_zhetrs2 LAPACK_GLOBAL(zhetrs2,ZHETRS2)\n#define LAPACK_zsyconv LAPACK_GLOBAL(zsyconv,ZSYCONV)\n#define LAPACK_zsyswapr LAPACK_GLOBAL(zsyswapr,ZSYSWAPR)\n#define LAPACK_zsytri2 LAPACK_GLOBAL(zsytri2,ZSYTRI2)\n#define LAPACK_zsytri2x LAPACK_GLOBAL(zsytri2x,ZSYTRI2X)\n#define LAPACK_zsytrs2 LAPACK_GLOBAL(zsytrs2,ZSYTRS2)\n#define LAPACK_zunbdb LAPACK_GLOBAL(zunbdb,ZUNBDB)\n#define LAPACK_zuncsd LAPACK_GLOBAL(zuncsd,ZUNCSD)\n// LAPACK 3.4.0\n#define LAPACK_sgemqrt LAPACK_GLOBAL(sgemqrt,SGEMQRT)\n#define LAPACK_dgemqrt LAPACK_GLOBAL(dgemqrt,DGEMQRT)\n#define LAPACK_cgemqrt LAPACK_GLOBAL(cgemqrt,CGEMQRT)\n#define LAPACK_zgemqrt LAPACK_GLOBAL(zgemqrt,ZGEMQRT)\n#define LAPACK_sgeqrt LAPACK_GLOBAL(sgeqrt,SGEQRT)\n#define LAPACK_dgeqrt LAPACK_GLOBAL(dgeqrt,DGEQRT)\n#define LAPACK_cgeqrt LAPACK_GLOBAL(cgeqrt,CGEQRT)\n#define LAPACK_zgeqrt LAPACK_GLOBAL(zgeqrt,ZGEQRT)\n#define LAPACK_sgeqrt2 LAPACK_GLOBAL(sgeqrt2,SGEQRT2)\n#define LAPACK_dgeqrt2 LAPACK_GLOBAL(dgeqrt2,DGEQRT2)\n#define LAPACK_cgeqrt2 LAPACK_GLOBAL(cgeqrt2,CGEQRT2)\n#define LAPACK_zgeqrt2 LAPACK_GLOBAL(zgeqrt2,ZGEQRT2)\n#define LAPACK_sgeqrt3 LAPACK_GLOBAL(sgeqrt3,SGEQRT3)\n#define LAPACK_dgeqrt3 LAPACK_GLOBAL(dgeqrt3,DGEQRT3)\n#define LAPACK_cgeqrt3 LAPACK_GLOBAL(cgeqrt3,CGEQRT3)\n#define LAPACK_zgeqrt3 LAPACK_GLOBAL(zgeqrt3,ZGEQRT3)\n#define LAPACK_stpmqrt LAPACK_GLOBAL(stpmqrt,STPMQRT)\n#define LAPACK_dtpmqrt LAPACK_GLOBAL(dtpmqrt,DTPMQRT)\n#define LAPACK_ctpmqrt LAPACK_GLOBAL(ctpmqrt,CTPMQRT)\n#define LAPACK_ztpmqrt LAPACK_GLOBAL(ztpmqrt,ZTPMQRT)\n#define LAPACK_dtpqrt LAPACK_GLOBAL(dtpqrt,DTPQRT)\n#define LAPACK_ctpqrt LAPACK_GLOBAL(ctpqrt,CTPQRT)\n#define LAPACK_ztpqrt LAPACK_GLOBAL(ztpqrt,ZTPQRT)\n#define LAPACK_stpqrt2 LAPACK_GLOBAL(stpqrt2,STPQRT2)\n#define LAPACK_dtpqrt2 LAPACK_GLOBAL(dtpqrt2,DTPQRT2)\n#define LAPACK_ctpqrt2 LAPACK_GLOBAL(ctpqrt2,CTPQRT2)\n#define LAPACK_ztpqrt2 LAPACK_GLOBAL(ztpqrt2,ZTPQRT2)\n#define LAPACK_stprfb LAPACK_GLOBAL(stprfb,STPRFB)\n#define LAPACK_dtprfb LAPACK_GLOBAL(dtprfb,DTPRFB)\n#define LAPACK_ctprfb LAPACK_GLOBAL(ctprfb,CTPRFB)\n#define LAPACK_ztprfb LAPACK_GLOBAL(ztprfb,ZTPRFB)\n// LAPACK 3.X.X\n#define LAPACK_csyr LAPACK_GLOBAL(csyr,CSYR)\n#define LAPACK_zsyr LAPACK_GLOBAL(zsyr,ZSYR)\n\n\nvoid LAPACK_sgetrf( lapack_int* m, lapack_int* n, float* a, lapack_int* lda,\n                    lapack_int* ipiv, lapack_int *info );\nvoid LAPACK_dgetrf( lapack_int* m, lapack_int* n, double* a, lapack_int* lda,\n                    lapack_int* ipiv, lapack_int *info );\nvoid LAPACK_cgetrf( lapack_int* m, lapack_int* n, lapack_complex_float* a,\n                    lapack_int* lda, lapack_int* ipiv, lapack_int *info );\nvoid LAPACK_zgetrf( lapack_int* m, lapack_int* n, lapack_complex_double* a,\n                    lapack_int* lda, lapack_int* ipiv, lapack_int *info );\nvoid LAPACK_sgbtrf( lapack_int* m, lapack_int* n, lapack_int* kl,\n                    lapack_int* ku, float* ab, lapack_int* ldab,\n                    lapack_int* ipiv, lapack_int *info );\nvoid LAPACK_dgbtrf( lapack_int* m, lapack_int* n, lapack_int* kl,\n                    lapack_int* ku, double* ab, lapack_int* ldab,\n                    lapack_int* ipiv, lapack_int *info );\nvoid LAPACK_cgbtrf( lapack_int* m, lapack_int* n, lapack_int* kl,\n                    lapack_int* ku, lapack_complex_float* ab, lapack_int* ldab,\n                    lapack_int* ipiv, lapack_int *info );\nvoid LAPACK_zgbtrf( lapack_int* m, lapack_int* n, lapack_int* kl,\n                    lapack_int* ku, lapack_complex_double* ab, lapack_int* ldab,\n                    lapack_int* ipiv, lapack_int *info );\nvoid LAPACK_sgttrf( lapack_int* n, float* dl, float* d, float* du, float* du2,\n                    lapack_int* ipiv, lapack_int *info );\nvoid LAPACK_dgttrf( lapack_int* n, double* dl, double* d, double* du,\n                    double* du2, lapack_int* ipiv, lapack_int *info );\nvoid LAPACK_cgttrf( lapack_int* n, lapack_complex_float* dl,\n                    lapack_complex_float* d, lapack_complex_float* du,\n                    lapack_complex_float* du2, lapack_int* ipiv,\n                    lapack_int *info );\nvoid LAPACK_zgttrf( lapack_int* n, lapack_complex_double* dl,\n                    lapack_complex_double* d, lapack_complex_double* du,\n                    lapack_complex_double* du2, lapack_int* ipiv,\n                    lapack_int *info );\nvoid LAPACK_spotrf( char* uplo, lapack_int* n, float* a, lapack_int* lda,\n                    lapack_int *info );\nvoid LAPACK_dpotrf( char* uplo, lapack_int* n, double* a, lapack_int* lda,\n                    lapack_int *info );\nvoid LAPACK_cpotrf( char* uplo, lapack_int* n, lapack_complex_float* a,\n                    lapack_int* lda, lapack_int *info );\nvoid LAPACK_zpotrf( char* uplo, lapack_int* n, lapack_complex_double* a,\n                    lapack_int* lda, lapack_int *info );\nvoid LAPACK_dpstrf( char* uplo, lapack_int* n, double* a, lapack_int* lda,\n                    lapack_int* piv, lapack_int* rank, double* tol,\n                    double* work, lapack_int *info );\nvoid LAPACK_spstrf( char* uplo, lapack_int* n, float* a, lapack_int* lda,\n                    lapack_int* piv, lapack_int* rank, float* tol, float* work,\n                    lapack_int *info );\nvoid LAPACK_zpstrf( char* uplo, lapack_int* n, lapack_complex_double* a,\n                    lapack_int* lda, lapack_int* piv, lapack_int* rank,\n                    double* tol, double* work, lapack_int *info );\nvoid LAPACK_cpstrf( char* uplo, lapack_int* n, lapack_complex_float* a,\n                    lapack_int* lda, lapack_int* piv, lapack_int* rank,\n                    float* tol, float* work, lapack_int *info );\nvoid LAPACK_dpftrf( char* transr, char* uplo, lapack_int* n, double* a,\n                    lapack_int *info );\nvoid LAPACK_spftrf( char* transr, char* uplo, lapack_int* n, float* a,\n                    lapack_int *info );\nvoid LAPACK_zpftrf( char* transr, char* uplo, lapack_int* n,\n                    lapack_complex_double* a, lapack_int *info );\nvoid LAPACK_cpftrf( char* transr, char* uplo, lapack_int* n,\n                    lapack_complex_float* a, lapack_int *info );\nvoid LAPACK_spptrf( char* uplo, lapack_int* n, float* ap, lapack_int *info );\nvoid LAPACK_dpptrf( char* uplo, lapack_int* n, double* ap, lapack_int *info );\nvoid LAPACK_cpptrf( char* uplo, lapack_int* n, lapack_complex_float* ap,\n                    lapack_int *info );\nvoid LAPACK_zpptrf( char* uplo, lapack_int* n, lapack_complex_double* ap,\n                    lapack_int *info );\nvoid LAPACK_spbtrf( char* uplo, lapack_int* n, lapack_int* kd, float* ab,\n                    lapack_int* ldab, lapack_int *info );\nvoid LAPACK_dpbtrf( char* uplo, lapack_int* n, lapack_int* kd, double* ab,\n                    lapack_int* ldab, lapack_int *info );\nvoid LAPACK_cpbtrf( char* uplo, lapack_int* n, lapack_int* kd,\n                    lapack_complex_float* ab, lapack_int* ldab,\n                    lapack_int *info );\nvoid LAPACK_zpbtrf( char* uplo, lapack_int* n, lapack_int* kd,\n                    lapack_complex_double* ab, lapack_int* ldab,\n                    lapack_int *info );\nvoid LAPACK_spttrf( lapack_int* n, float* d, float* e, lapack_int *info );\nvoid LAPACK_dpttrf( lapack_int* n, double* d, double* e, lapack_int *info );\nvoid LAPACK_cpttrf( lapack_int* n, float* d, lapack_complex_float* e,\n                    lapack_int *info );\nvoid LAPACK_zpttrf( lapack_int* n, double* d, lapack_complex_double* e,\n                    lapack_int *info );\nvoid LAPACK_ssytrf( char* uplo, lapack_int* n, float* a, lapack_int* lda,\n                    lapack_int* ipiv, float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_dsytrf( char* uplo, lapack_int* n, double* a, lapack_int* lda,\n                    lapack_int* ipiv, double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_csytrf( char* uplo, lapack_int* n, lapack_complex_float* a,\n                    lapack_int* lda, lapack_int* ipiv,\n                    lapack_complex_float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_zsytrf( char* uplo, lapack_int* n, lapack_complex_double* a,\n                    lapack_int* lda, lapack_int* ipiv,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_chetrf( char* uplo, lapack_int* n, lapack_complex_float* a,\n                    lapack_int* lda, lapack_int* ipiv,\n                    lapack_complex_float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_zhetrf( char* uplo, lapack_int* n, lapack_complex_double* a,\n                    lapack_int* lda, lapack_int* ipiv,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_ssptrf( char* uplo, lapack_int* n, float* ap, lapack_int* ipiv,\n                    lapack_int *info );\nvoid LAPACK_dsptrf( char* uplo, lapack_int* n, double* ap, lapack_int* ipiv,\n                    lapack_int *info );\nvoid LAPACK_csptrf( char* uplo, lapack_int* n, lapack_complex_float* ap,\n                    lapack_int* ipiv, lapack_int *info );\nvoid LAPACK_zsptrf( char* uplo, lapack_int* n, lapack_complex_double* ap,\n                    lapack_int* ipiv, lapack_int *info );\nvoid LAPACK_chptrf( char* uplo, lapack_int* n, lapack_complex_float* ap,\n                    lapack_int* ipiv, lapack_int *info );\nvoid LAPACK_zhptrf( char* uplo, lapack_int* n, lapack_complex_double* ap,\n                    lapack_int* ipiv, lapack_int *info );\nvoid LAPACK_sgetrs( char* trans, lapack_int* n, lapack_int* nrhs,\n                    const float* a, lapack_int* lda, const lapack_int* ipiv,\n                    float* b, lapack_int* ldb, lapack_int *info );\nvoid LAPACK_dgetrs( char* trans, lapack_int* n, lapack_int* nrhs,\n                    const double* a, lapack_int* lda, const lapack_int* ipiv,\n                    double* b, lapack_int* ldb, lapack_int *info );\nvoid LAPACK_cgetrs( char* trans, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_float* a, lapack_int* lda,\n                    const lapack_int* ipiv, lapack_complex_float* b,\n                    lapack_int* ldb, lapack_int *info );\nvoid LAPACK_zgetrs( char* trans, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_double* a, lapack_int* lda,\n                    const lapack_int* ipiv, lapack_complex_double* b,\n                    lapack_int* ldb, lapack_int *info );\nvoid LAPACK_sgbtrs( char* trans, lapack_int* n, lapack_int* kl, lapack_int* ku,\n                    lapack_int* nrhs, const float* ab, lapack_int* ldab,\n                    const lapack_int* ipiv, float* b, lapack_int* ldb,\n                    lapack_int *info );\nvoid LAPACK_dgbtrs( char* trans, lapack_int* n, lapack_int* kl, lapack_int* ku,\n                    lapack_int* nrhs, const double* ab, lapack_int* ldab,\n                    const lapack_int* ipiv, double* b, lapack_int* ldb,\n                    lapack_int *info );\nvoid LAPACK_cgbtrs( char* trans, lapack_int* n, lapack_int* kl, lapack_int* ku,\n                    lapack_int* nrhs, const lapack_complex_float* ab,\n                    lapack_int* ldab, const lapack_int* ipiv,\n                    lapack_complex_float* b, lapack_int* ldb,\n                    lapack_int *info );\nvoid LAPACK_zgbtrs( char* trans, lapack_int* n, lapack_int* kl, lapack_int* ku,\n                    lapack_int* nrhs, const lapack_complex_double* ab,\n                    lapack_int* ldab, const lapack_int* ipiv,\n                    lapack_complex_double* b, lapack_int* ldb,\n                    lapack_int *info );\nvoid LAPACK_sgttrs( char* trans, lapack_int* n, lapack_int* nrhs,\n                    const float* dl, const float* d, const float* du,\n                    const float* du2, const lapack_int* ipiv, float* b,\n                    lapack_int* ldb, lapack_int *info );\nvoid LAPACK_dgttrs( char* trans, lapack_int* n, lapack_int* nrhs,\n                    const double* dl, const double* d, const double* du,\n                    const double* du2, const lapack_int* ipiv, double* b,\n                    lapack_int* ldb, lapack_int *info );\nvoid LAPACK_cgttrs( char* trans, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_float* dl,\n                    const lapack_complex_float* d,\n                    const lapack_complex_float* du,\n                    const lapack_complex_float* du2, const lapack_int* ipiv,\n                    lapack_complex_float* b, lapack_int* ldb,\n                    lapack_int *info );\nvoid LAPACK_zgttrs( char* trans, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_double* dl,\n                    const lapack_complex_double* d,\n                    const lapack_complex_double* du,\n                    const lapack_complex_double* du2, const lapack_int* ipiv,\n                    lapack_complex_double* b, lapack_int* ldb,\n                    lapack_int *info );\nvoid LAPACK_spotrs( char* uplo, lapack_int* n, lapack_int* nrhs, const float* a,\n                    lapack_int* lda, float* b, lapack_int* ldb,\n                    lapack_int *info );\nvoid LAPACK_dpotrs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const double* a, lapack_int* lda, double* b,\n                    lapack_int* ldb, lapack_int *info );\nvoid LAPACK_cpotrs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_float* a, lapack_int* lda,\n                    lapack_complex_float* b, lapack_int* ldb,\n                    lapack_int *info );\nvoid LAPACK_zpotrs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_double* a, lapack_int* lda,\n                    lapack_complex_double* b, lapack_int* ldb,\n                    lapack_int *info );\nvoid LAPACK_dpftrs( char* transr, char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const double* a, double* b, lapack_int* ldb,\n                    lapack_int *info );\nvoid LAPACK_spftrs( char* transr, char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const float* a, float* b, lapack_int* ldb,\n                    lapack_int *info );\nvoid LAPACK_zpftrs( char* transr, char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_double* a, lapack_complex_double* b,\n                    lapack_int* ldb, lapack_int *info );\nvoid LAPACK_cpftrs( char* transr, char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_float* a, lapack_complex_float* b,\n                    lapack_int* ldb, lapack_int *info );\nvoid LAPACK_spptrs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const float* ap, float* b, lapack_int* ldb,\n                    lapack_int *info );\nvoid LAPACK_dpptrs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const double* ap, double* b, lapack_int* ldb,\n                    lapack_int *info );\nvoid LAPACK_cpptrs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_float* ap, lapack_complex_float* b,\n                    lapack_int* ldb, lapack_int *info );\nvoid LAPACK_zpptrs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_double* ap, lapack_complex_double* b,\n                    lapack_int* ldb, lapack_int *info );\nvoid LAPACK_spbtrs( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs,\n                    const float* ab, lapack_int* ldab, float* b,\n                    lapack_int* ldb, lapack_int *info );\nvoid LAPACK_dpbtrs( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs,\n                    const double* ab, lapack_int* ldab, double* b,\n                    lapack_int* ldb, lapack_int *info );\nvoid LAPACK_cpbtrs( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs,\n                    const lapack_complex_float* ab, lapack_int* ldab,\n                    lapack_complex_float* b, lapack_int* ldb,\n                    lapack_int *info );\nvoid LAPACK_zpbtrs( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs,\n                    const lapack_complex_double* ab, lapack_int* ldab,\n                    lapack_complex_double* b, lapack_int* ldb,\n                    lapack_int *info );\nvoid LAPACK_spttrs( lapack_int* n, lapack_int* nrhs, const float* d,\n                    const float* e, float* b, lapack_int* ldb,\n                    lapack_int *info );\nvoid LAPACK_dpttrs( lapack_int* n, lapack_int* nrhs, const double* d,\n                    const double* e, double* b, lapack_int* ldb,\n                    lapack_int *info );\nvoid LAPACK_cpttrs( char* uplo, lapack_int* n, lapack_int* nrhs, const float* d,\n                    const lapack_complex_float* e, lapack_complex_float* b,\n                    lapack_int* ldb, lapack_int *info );\nvoid LAPACK_zpttrs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const double* d, const lapack_complex_double* e,\n                    lapack_complex_double* b, lapack_int* ldb,\n                    lapack_int *info );\nvoid LAPACK_ssytrs( char* uplo, lapack_int* n, lapack_int* nrhs, const float* a,\n                    lapack_int* lda, const lapack_int* ipiv, float* b,\n                    lapack_int* ldb, lapack_int *info );\nvoid LAPACK_dsytrs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const double* a, lapack_int* lda, const lapack_int* ipiv,\n                    double* b, lapack_int* ldb, lapack_int *info );\nvoid LAPACK_csytrs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_float* a, lapack_int* lda,\n                    const lapack_int* ipiv, lapack_complex_float* b,\n                    lapack_int* ldb, lapack_int *info );\nvoid LAPACK_zsytrs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_double* a, lapack_int* lda,\n                    const lapack_int* ipiv, lapack_complex_double* b,\n                    lapack_int* ldb, lapack_int *info );\nvoid LAPACK_chetrs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_float* a, lapack_int* lda,\n                    const lapack_int* ipiv, lapack_complex_float* b,\n                    lapack_int* ldb, lapack_int *info );\nvoid LAPACK_zhetrs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_double* a, lapack_int* lda,\n                    const lapack_int* ipiv, lapack_complex_double* b,\n                    lapack_int* ldb, lapack_int *info );\nvoid LAPACK_ssptrs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const float* ap, const lapack_int* ipiv, float* b,\n                    lapack_int* ldb, lapack_int *info );\nvoid LAPACK_dsptrs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const double* ap, const lapack_int* ipiv, double* b,\n                    lapack_int* ldb, lapack_int *info );\nvoid LAPACK_csptrs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_float* ap, const lapack_int* ipiv,\n                    lapack_complex_float* b, lapack_int* ldb,\n                    lapack_int *info );\nvoid LAPACK_zsptrs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_double* ap, const lapack_int* ipiv,\n                    lapack_complex_double* b, lapack_int* ldb,\n                    lapack_int *info );\nvoid LAPACK_chptrs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_float* ap, const lapack_int* ipiv,\n                    lapack_complex_float* b, lapack_int* ldb,\n                    lapack_int *info );\nvoid LAPACK_zhptrs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_double* ap, const lapack_int* ipiv,\n                    lapack_complex_double* b, lapack_int* ldb,\n                    lapack_int *info );\nvoid LAPACK_strtrs( char* uplo, char* trans, char* diag, lapack_int* n,\n                    lapack_int* nrhs, const float* a, lapack_int* lda, float* b,\n                    lapack_int* ldb, lapack_int *info );\nvoid LAPACK_dtrtrs( char* uplo, char* trans, char* diag, lapack_int* n,\n                    lapack_int* nrhs, const double* a, lapack_int* lda,\n                    double* b, lapack_int* ldb, lapack_int *info );\nvoid LAPACK_ctrtrs( char* uplo, char* trans, char* diag, lapack_int* n,\n                    lapack_int* nrhs, const lapack_complex_float* a,\n                    lapack_int* lda, lapack_complex_float* b, lapack_int* ldb,\n                    lapack_int *info );\nvoid LAPACK_ztrtrs( char* uplo, char* trans, char* diag, lapack_int* n,\n                    lapack_int* nrhs, const lapack_complex_double* a,\n                    lapack_int* lda, lapack_complex_double* b, lapack_int* ldb,\n                    lapack_int *info );\nvoid LAPACK_stptrs( char* uplo, char* trans, char* diag, lapack_int* n,\n                    lapack_int* nrhs, const float* ap, float* b,\n                    lapack_int* ldb, lapack_int *info );\nvoid LAPACK_dtptrs( char* uplo, char* trans, char* diag, lapack_int* n,\n                    lapack_int* nrhs, const double* ap, double* b,\n                    lapack_int* ldb, lapack_int *info );\nvoid LAPACK_ctptrs( char* uplo, char* trans, char* diag, lapack_int* n,\n                    lapack_int* nrhs, const lapack_complex_float* ap,\n                    lapack_complex_float* b, lapack_int* ldb,\n                    lapack_int *info );\nvoid LAPACK_ztptrs( char* uplo, char* trans, char* diag, lapack_int* n,\n                    lapack_int* nrhs, const lapack_complex_double* ap,\n                    lapack_complex_double* b, lapack_int* ldb,\n                    lapack_int *info );\nvoid LAPACK_stbtrs( char* uplo, char* trans, char* diag, lapack_int* n,\n                    lapack_int* kd, lapack_int* nrhs, const float* ab,\n                    lapack_int* ldab, float* b, lapack_int* ldb,\n                    lapack_int *info );\nvoid LAPACK_dtbtrs( char* uplo, char* trans, char* diag, lapack_int* n,\n                    lapack_int* kd, lapack_int* nrhs, const double* ab,\n                    lapack_int* ldab, double* b, lapack_int* ldb,\n                    lapack_int *info );\nvoid LAPACK_ctbtrs( char* uplo, char* trans, char* diag, lapack_int* n,\n                    lapack_int* kd, lapack_int* nrhs,\n                    const lapack_complex_float* ab, lapack_int* ldab,\n                    lapack_complex_float* b, lapack_int* ldb,\n                    lapack_int *info );\nvoid LAPACK_ztbtrs( char* uplo, char* trans, char* diag, lapack_int* n,\n                    lapack_int* kd, lapack_int* nrhs,\n                    const lapack_complex_double* ab, lapack_int* ldab,\n                    lapack_complex_double* b, lapack_int* ldb,\n                    lapack_int *info );\nvoid LAPACK_sgecon( char* norm, lapack_int* n, const float* a, lapack_int* lda,\n                    float* anorm, float* rcond, float* work, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_dgecon( char* norm, lapack_int* n, const double* a, lapack_int* lda,\n                    double* anorm, double* rcond, double* work,\n                    lapack_int* iwork, lapack_int *info );\nvoid LAPACK_cgecon( char* norm, lapack_int* n, const lapack_complex_float* a,\n                    lapack_int* lda, float* anorm, float* rcond,\n                    lapack_complex_float* work, float* rwork,\n                    lapack_int *info );\nvoid LAPACK_zgecon( char* norm, lapack_int* n, const lapack_complex_double* a,\n                    lapack_int* lda, double* anorm, double* rcond,\n                    lapack_complex_double* work, double* rwork,\n                    lapack_int *info );\nvoid LAPACK_sgbcon( char* norm, lapack_int* n, lapack_int* kl, lapack_int* ku,\n                    const float* ab, lapack_int* ldab, const lapack_int* ipiv,\n                    float* anorm, float* rcond, float* work, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_dgbcon( char* norm, lapack_int* n, lapack_int* kl, lapack_int* ku,\n                    const double* ab, lapack_int* ldab, const lapack_int* ipiv,\n                    double* anorm, double* rcond, double* work,\n                    lapack_int* iwork, lapack_int *info );\nvoid LAPACK_cgbcon( char* norm, lapack_int* n, lapack_int* kl, lapack_int* ku,\n                    const lapack_complex_float* ab, lapack_int* ldab,\n                    const lapack_int* ipiv, float* anorm, float* rcond,\n                    lapack_complex_float* work, float* rwork,\n                    lapack_int *info );\nvoid LAPACK_zgbcon( char* norm, lapack_int* n, lapack_int* kl, lapack_int* ku,\n                    const lapack_complex_double* ab, lapack_int* ldab,\n                    const lapack_int* ipiv, double* anorm, double* rcond,\n                    lapack_complex_double* work, double* rwork,\n                    lapack_int *info );\nvoid LAPACK_sgtcon( char* norm, lapack_int* n, const float* dl, const float* d,\n                    const float* du, const float* du2, const lapack_int* ipiv,\n                    float* anorm, float* rcond, float* work, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_dgtcon( char* norm, lapack_int* n, const double* dl,\n                    const double* d, const double* du, const double* du2,\n                    const lapack_int* ipiv, double* anorm, double* rcond,\n                    double* work, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_cgtcon( char* norm, lapack_int* n, const lapack_complex_float* dl,\n                    const lapack_complex_float* d,\n                    const lapack_complex_float* du,\n                    const lapack_complex_float* du2, const lapack_int* ipiv,\n                    float* anorm, float* rcond, lapack_complex_float* work,\n                    lapack_int *info );\nvoid LAPACK_zgtcon( char* norm, lapack_int* n, const lapack_complex_double* dl,\n                    const lapack_complex_double* d,\n                    const lapack_complex_double* du,\n                    const lapack_complex_double* du2, const lapack_int* ipiv,\n                    double* anorm, double* rcond, lapack_complex_double* work,\n                    lapack_int *info );\nvoid LAPACK_spocon( char* uplo, lapack_int* n, const float* a, lapack_int* lda,\n                    float* anorm, float* rcond, float* work, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_dpocon( char* uplo, lapack_int* n, const double* a, lapack_int* lda,\n                    double* anorm, double* rcond, double* work,\n                    lapack_int* iwork, lapack_int *info );\nvoid LAPACK_cpocon( char* uplo, lapack_int* n, const lapack_complex_float* a,\n                    lapack_int* lda, float* anorm, float* rcond,\n                    lapack_complex_float* work, float* rwork,\n                    lapack_int *info );\nvoid LAPACK_zpocon( char* uplo, lapack_int* n, const lapack_complex_double* a,\n                    lapack_int* lda, double* anorm, double* rcond,\n                    lapack_complex_double* work, double* rwork,\n                    lapack_int *info );\nvoid LAPACK_sppcon( char* uplo, lapack_int* n, const float* ap, float* anorm,\n                    float* rcond, float* work, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_dppcon( char* uplo, lapack_int* n, const double* ap, double* anorm,\n                    double* rcond, double* work, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_cppcon( char* uplo, lapack_int* n, const lapack_complex_float* ap,\n                    float* anorm, float* rcond, lapack_complex_float* work,\n                    float* rwork, lapack_int *info );\nvoid LAPACK_zppcon( char* uplo, lapack_int* n, const lapack_complex_double* ap,\n                    double* anorm, double* rcond, lapack_complex_double* work,\n                    double* rwork, lapack_int *info );\nvoid LAPACK_spbcon( char* uplo, lapack_int* n, lapack_int* kd, const float* ab,\n                    lapack_int* ldab, float* anorm, float* rcond, float* work,\n                    lapack_int* iwork, lapack_int *info );\nvoid LAPACK_dpbcon( char* uplo, lapack_int* n, lapack_int* kd, const double* ab,\n                    lapack_int* ldab, double* anorm, double* rcond,\n                    double* work, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_cpbcon( char* uplo, lapack_int* n, lapack_int* kd,\n                    const lapack_complex_float* ab, lapack_int* ldab,\n                    float* anorm, float* rcond, lapack_complex_float* work,\n                    float* rwork, lapack_int *info );\nvoid LAPACK_zpbcon( char* uplo, lapack_int* n, lapack_int* kd,\n                    const lapack_complex_double* ab, lapack_int* ldab,\n                    double* anorm, double* rcond, lapack_complex_double* work,\n                    double* rwork, lapack_int *info );\nvoid LAPACK_sptcon( lapack_int* n, const float* d, const float* e, float* anorm,\n                    float* rcond, float* work, lapack_int *info );\nvoid LAPACK_dptcon( lapack_int* n, const double* d, const double* e,\n                    double* anorm, double* rcond, double* work,\n                    lapack_int *info );\nvoid LAPACK_cptcon( lapack_int* n, const float* d,\n                    const lapack_complex_float* e, float* anorm, float* rcond,\n                    float* work, lapack_int *info );\nvoid LAPACK_zptcon( lapack_int* n, const double* d,\n                    const lapack_complex_double* e, double* anorm,\n                    double* rcond, double* work, lapack_int *info );\nvoid LAPACK_ssycon( char* uplo, lapack_int* n, const float* a, lapack_int* lda,\n                    const lapack_int* ipiv, float* anorm, float* rcond,\n                    float* work, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_dsycon( char* uplo, lapack_int* n, const double* a, lapack_int* lda,\n                    const lapack_int* ipiv, double* anorm, double* rcond,\n                    double* work, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_csycon( char* uplo, lapack_int* n, const lapack_complex_float* a,\n                    lapack_int* lda, const lapack_int* ipiv, float* anorm,\n                    float* rcond, lapack_complex_float* work,\n                    lapack_int *info );\nvoid LAPACK_zsycon( char* uplo, lapack_int* n, const lapack_complex_double* a,\n                    lapack_int* lda, const lapack_int* ipiv, double* anorm,\n                    double* rcond, lapack_complex_double* work,\n                    lapack_int *info );\nvoid LAPACK_checon( char* uplo, lapack_int* n, const lapack_complex_float* a,\n                    lapack_int* lda, const lapack_int* ipiv, float* anorm,\n                    float* rcond, lapack_complex_float* work,\n                    lapack_int *info );\nvoid LAPACK_zhecon( char* uplo, lapack_int* n, const lapack_complex_double* a,\n                    lapack_int* lda, const lapack_int* ipiv, double* anorm,\n                    double* rcond, lapack_complex_double* work,\n                    lapack_int *info );\nvoid LAPACK_sspcon( char* uplo, lapack_int* n, const float* ap,\n                    const lapack_int* ipiv, float* anorm, float* rcond,\n                    float* work, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_dspcon( char* uplo, lapack_int* n, const double* ap,\n                    const lapack_int* ipiv, double* anorm, double* rcond,\n                    double* work, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_cspcon( char* uplo, lapack_int* n, const lapack_complex_float* ap,\n                    const lapack_int* ipiv, float* anorm, float* rcond,\n                    lapack_complex_float* work, lapack_int *info );\nvoid LAPACK_zspcon( char* uplo, lapack_int* n, const lapack_complex_double* ap,\n                    const lapack_int* ipiv, double* anorm, double* rcond,\n                    lapack_complex_double* work, lapack_int *info );\nvoid LAPACK_chpcon( char* uplo, lapack_int* n, const lapack_complex_float* ap,\n                    const lapack_int* ipiv, float* anorm, float* rcond,\n                    lapack_complex_float* work, lapack_int *info );\nvoid LAPACK_zhpcon( char* uplo, lapack_int* n, const lapack_complex_double* ap,\n                    const lapack_int* ipiv, double* anorm, double* rcond,\n                    lapack_complex_double* work, lapack_int *info );\nvoid LAPACK_strcon( char* norm, char* uplo, char* diag, lapack_int* n,\n                    const float* a, lapack_int* lda, float* rcond, float* work,\n                    lapack_int* iwork, lapack_int *info );\nvoid LAPACK_dtrcon( char* norm, char* uplo, char* diag, lapack_int* n,\n                    const double* a, lapack_int* lda, double* rcond,\n                    double* work, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_ctrcon( char* norm, char* uplo, char* diag, lapack_int* n,\n                    const lapack_complex_float* a, lapack_int* lda,\n                    float* rcond, lapack_complex_float* work, float* rwork,\n                    lapack_int *info );\nvoid LAPACK_ztrcon( char* norm, char* uplo, char* diag, lapack_int* n,\n                    const lapack_complex_double* a, lapack_int* lda,\n                    double* rcond, lapack_complex_double* work, double* rwork,\n                    lapack_int *info );\nvoid LAPACK_stpcon( char* norm, char* uplo, char* diag, lapack_int* n,\n                    const float* ap, float* rcond, float* work,\n                    lapack_int* iwork, lapack_int *info );\nvoid LAPACK_dtpcon( char* norm, char* uplo, char* diag, lapack_int* n,\n                    const double* ap, double* rcond, double* work,\n                    lapack_int* iwork, lapack_int *info );\nvoid LAPACK_ctpcon( char* norm, char* uplo, char* diag, lapack_int* n,\n                    const lapack_complex_float* ap, float* rcond,\n                    lapack_complex_float* work, float* rwork,\n                    lapack_int *info );\nvoid LAPACK_ztpcon( char* norm, char* uplo, char* diag, lapack_int* n,\n                    const lapack_complex_double* ap, double* rcond,\n                    lapack_complex_double* work, double* rwork,\n                    lapack_int *info );\nvoid LAPACK_stbcon( char* norm, char* uplo, char* diag, lapack_int* n,\n                    lapack_int* kd, const float* ab, lapack_int* ldab,\n                    float* rcond, float* work, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_dtbcon( char* norm, char* uplo, char* diag, lapack_int* n,\n                    lapack_int* kd, const double* ab, lapack_int* ldab,\n                    double* rcond, double* work, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_ctbcon( char* norm, char* uplo, char* diag, lapack_int* n,\n                    lapack_int* kd, const lapack_complex_float* ab,\n                    lapack_int* ldab, float* rcond, lapack_complex_float* work,\n                    float* rwork, lapack_int *info );\nvoid LAPACK_ztbcon( char* norm, char* uplo, char* diag, lapack_int* n,\n                    lapack_int* kd, const lapack_complex_double* ab,\n                    lapack_int* ldab, double* rcond,\n                    lapack_complex_double* work, double* rwork,\n                    lapack_int *info );\nvoid LAPACK_sgerfs( char* trans, lapack_int* n, lapack_int* nrhs,\n                    const float* a, lapack_int* lda, const float* af,\n                    lapack_int* ldaf, const lapack_int* ipiv, const float* b,\n                    lapack_int* ldb, float* x, lapack_int* ldx, float* ferr,\n                    float* berr, float* work, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_dgerfs( char* trans, lapack_int* n, lapack_int* nrhs,\n                    const double* a, lapack_int* lda, const double* af,\n                    lapack_int* ldaf, const lapack_int* ipiv, const double* b,\n                    lapack_int* ldb, double* x, lapack_int* ldx, double* ferr,\n                    double* berr, double* work, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_cgerfs( char* trans, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_float* a, lapack_int* lda,\n                    const lapack_complex_float* af, lapack_int* ldaf,\n                    const lapack_int* ipiv, const lapack_complex_float* b,\n                    lapack_int* ldb, lapack_complex_float* x, lapack_int* ldx,\n                    float* ferr, float* berr, lapack_complex_float* work,\n                    float* rwork, lapack_int *info );\nvoid LAPACK_zgerfs( char* trans, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_double* a, lapack_int* lda,\n                    const lapack_complex_double* af, lapack_int* ldaf,\n                    const lapack_int* ipiv, const lapack_complex_double* b,\n                    lapack_int* ldb, lapack_complex_double* x, lapack_int* ldx,\n                    double* ferr, double* berr, lapack_complex_double* work,\n                    double* rwork, lapack_int *info );\nvoid LAPACK_dgerfsx( char* trans, char* equed, lapack_int* n, lapack_int* nrhs,\n                     const double* a, lapack_int* lda, const double* af,\n                     lapack_int* ldaf, const lapack_int* ipiv, const double* r,\n                     const double* c, const double* b, lapack_int* ldb,\n                     double* x, lapack_int* ldx, double* rcond, double* berr,\n                     lapack_int* n_err_bnds, double* err_bnds_norm,\n                     double* err_bnds_comp, lapack_int* nparams, double* params,\n                     double* work, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_sgerfsx( char* trans, char* equed, lapack_int* n, lapack_int* nrhs,\n                     const float* a, lapack_int* lda, const float* af,\n                     lapack_int* ldaf, const lapack_int* ipiv, const float* r,\n                     const float* c, const float* b, lapack_int* ldb, float* x,\n                     lapack_int* ldx, float* rcond, float* berr,\n                     lapack_int* n_err_bnds, float* err_bnds_norm,\n                     float* err_bnds_comp, lapack_int* nparams, float* params,\n                     float* work, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_zgerfsx( char* trans, char* equed, lapack_int* n, lapack_int* nrhs,\n                     const lapack_complex_double* a, lapack_int* lda,\n                     const lapack_complex_double* af, lapack_int* ldaf,\n                     const lapack_int* ipiv, const double* r, const double* c,\n                     const lapack_complex_double* b, lapack_int* ldb,\n                     lapack_complex_double* x, lapack_int* ldx, double* rcond,\n                     double* berr, lapack_int* n_err_bnds,\n                     double* err_bnds_norm, double* err_bnds_comp,\n                     lapack_int* nparams, double* params,\n                     lapack_complex_double* work, double* rwork,\n                     lapack_int *info );\nvoid LAPACK_cgerfsx( char* trans, char* equed, lapack_int* n, lapack_int* nrhs,\n                     const lapack_complex_float* a, lapack_int* lda,\n                     const lapack_complex_float* af, lapack_int* ldaf,\n                     const lapack_int* ipiv, const float* r, const float* c,\n                     const lapack_complex_float* b, lapack_int* ldb,\n                     lapack_complex_float* x, lapack_int* ldx, float* rcond,\n                     float* berr, lapack_int* n_err_bnds, float* err_bnds_norm,\n                     float* err_bnds_comp, lapack_int* nparams, float* params,\n                     lapack_complex_float* work, float* rwork,\n                     lapack_int *info );\nvoid LAPACK_sgbrfs( char* trans, lapack_int* n, lapack_int* kl, lapack_int* ku,\n                    lapack_int* nrhs, const float* ab, lapack_int* ldab,\n                    const float* afb, lapack_int* ldafb, const lapack_int* ipiv,\n                    const float* b, lapack_int* ldb, float* x, lapack_int* ldx,\n                    float* ferr, float* berr, float* work, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_dgbrfs( char* trans, lapack_int* n, lapack_int* kl, lapack_int* ku,\n                    lapack_int* nrhs, const double* ab, lapack_int* ldab,\n                    const double* afb, lapack_int* ldafb,\n                    const lapack_int* ipiv, const double* b, lapack_int* ldb,\n                    double* x, lapack_int* ldx, double* ferr, double* berr,\n                    double* work, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_cgbrfs( char* trans, lapack_int* n, lapack_int* kl, lapack_int* ku,\n                    lapack_int* nrhs, const lapack_complex_float* ab,\n                    lapack_int* ldab, const lapack_complex_float* afb,\n                    lapack_int* ldafb, const lapack_int* ipiv,\n                    const lapack_complex_float* b, lapack_int* ldb,\n                    lapack_complex_float* x, lapack_int* ldx, float* ferr,\n                    float* berr, lapack_complex_float* work, float* rwork,\n                    lapack_int *info );\nvoid LAPACK_zgbrfs( char* trans, lapack_int* n, lapack_int* kl, lapack_int* ku,\n                    lapack_int* nrhs, const lapack_complex_double* ab,\n                    lapack_int* ldab, const lapack_complex_double* afb,\n                    lapack_int* ldafb, const lapack_int* ipiv,\n                    const lapack_complex_double* b, lapack_int* ldb,\n                    lapack_complex_double* x, lapack_int* ldx, double* ferr,\n                    double* berr, lapack_complex_double* work, double* rwork,\n                    lapack_int *info );\nvoid LAPACK_dgbrfsx( char* trans, char* equed, lapack_int* n, lapack_int* kl,\n                     lapack_int* ku, lapack_int* nrhs, const double* ab,\n                     lapack_int* ldab, const double* afb, lapack_int* ldafb,\n                     const lapack_int* ipiv, const double* r, const double* c,\n                     const double* b, lapack_int* ldb, double* x,\n                     lapack_int* ldx, double* rcond, double* berr,\n                     lapack_int* n_err_bnds, double* err_bnds_norm,\n                     double* err_bnds_comp, lapack_int* nparams, double* params,\n                     double* work, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_sgbrfsx( char* trans, char* equed, lapack_int* n, lapack_int* kl,\n                     lapack_int* ku, lapack_int* nrhs, const float* ab,\n                     lapack_int* ldab, const float* afb, lapack_int* ldafb,\n                     const lapack_int* ipiv, const float* r, const float* c,\n                     const float* b, lapack_int* ldb, float* x, lapack_int* ldx,\n                     float* rcond, float* berr, lapack_int* n_err_bnds,\n                     float* err_bnds_norm, float* err_bnds_comp,\n                     lapack_int* nparams, float* params, float* work,\n                     lapack_int* iwork, lapack_int *info );\nvoid LAPACK_zgbrfsx( char* trans, char* equed, lapack_int* n, lapack_int* kl,\n                     lapack_int* ku, lapack_int* nrhs,\n                     const lapack_complex_double* ab, lapack_int* ldab,\n                     const lapack_complex_double* afb, lapack_int* ldafb,\n                     const lapack_int* ipiv, const double* r, const double* c,\n                     const lapack_complex_double* b, lapack_int* ldb,\n                     lapack_complex_double* x, lapack_int* ldx, double* rcond,\n                     double* berr, lapack_int* n_err_bnds,\n                     double* err_bnds_norm, double* err_bnds_comp,\n                     lapack_int* nparams, double* params,\n                     lapack_complex_double* work, double* rwork,\n                     lapack_int *info );\nvoid LAPACK_cgbrfsx( char* trans, char* equed, lapack_int* n, lapack_int* kl,\n                     lapack_int* ku, lapack_int* nrhs,\n                     const lapack_complex_float* ab, lapack_int* ldab,\n                     const lapack_complex_float* afb, lapack_int* ldafb,\n                     const lapack_int* ipiv, const float* r, const float* c,\n                     const lapack_complex_float* b, lapack_int* ldb,\n                     lapack_complex_float* x, lapack_int* ldx, float* rcond,\n                     float* berr, lapack_int* n_err_bnds, float* err_bnds_norm,\n                     float* err_bnds_comp, lapack_int* nparams, float* params,\n                     lapack_complex_float* work, float* rwork,\n                     lapack_int *info );\nvoid LAPACK_sgtrfs( char* trans, lapack_int* n, lapack_int* nrhs,\n                    const float* dl, const float* d, const float* du,\n                    const float* dlf, const float* df, const float* duf,\n                    const float* du2, const lapack_int* ipiv, const float* b,\n                    lapack_int* ldb, float* x, lapack_int* ldx, float* ferr,\n                    float* berr, float* work, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_dgtrfs( char* trans, lapack_int* n, lapack_int* nrhs,\n                    const double* dl, const double* d, const double* du,\n                    const double* dlf, const double* df, const double* duf,\n                    const double* du2, const lapack_int* ipiv, const double* b,\n                    lapack_int* ldb, double* x, lapack_int* ldx, double* ferr,\n                    double* berr, double* work, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_cgtrfs( char* trans, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_float* dl,\n                    const lapack_complex_float* d,\n                    const lapack_complex_float* du,\n                    const lapack_complex_float* dlf,\n                    const lapack_complex_float* df,\n                    const lapack_complex_float* duf,\n                    const lapack_complex_float* du2, const lapack_int* ipiv,\n                    const lapack_complex_float* b, lapack_int* ldb,\n                    lapack_complex_float* x, lapack_int* ldx, float* ferr,\n                    float* berr, lapack_complex_float* work, float* rwork,\n                    lapack_int *info );\nvoid LAPACK_zgtrfs( char* trans, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_double* dl,\n                    const lapack_complex_double* d,\n                    const lapack_complex_double* du,\n                    const lapack_complex_double* dlf,\n                    const lapack_complex_double* df,\n                    const lapack_complex_double* duf,\n                    const lapack_complex_double* du2, const lapack_int* ipiv,\n                    const lapack_complex_double* b, lapack_int* ldb,\n                    lapack_complex_double* x, lapack_int* ldx, double* ferr,\n                    double* berr, lapack_complex_double* work, double* rwork,\n                    lapack_int *info );\nvoid LAPACK_sporfs( char* uplo, lapack_int* n, lapack_int* nrhs, const float* a,\n                    lapack_int* lda, const float* af, lapack_int* ldaf,\n                    const float* b, lapack_int* ldb, float* x, lapack_int* ldx,\n                    float* ferr, float* berr, float* work, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_dporfs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const double* a, lapack_int* lda, const double* af,\n                    lapack_int* ldaf, const double* b, lapack_int* ldb,\n                    double* x, lapack_int* ldx, double* ferr, double* berr,\n                    double* work, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_cporfs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_float* a, lapack_int* lda,\n                    const lapack_complex_float* af, lapack_int* ldaf,\n                    const lapack_complex_float* b, lapack_int* ldb,\n                    lapack_complex_float* x, lapack_int* ldx, float* ferr,\n                    float* berr, lapack_complex_float* work, float* rwork,\n                    lapack_int *info );\nvoid LAPACK_zporfs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_double* a, lapack_int* lda,\n                    const lapack_complex_double* af, lapack_int* ldaf,\n                    const lapack_complex_double* b, lapack_int* ldb,\n                    lapack_complex_double* x, lapack_int* ldx, double* ferr,\n                    double* berr, lapack_complex_double* work, double* rwork,\n                    lapack_int *info );\nvoid LAPACK_dporfsx( char* uplo, char* equed, lapack_int* n, lapack_int* nrhs,\n                     const double* a, lapack_int* lda, const double* af,\n                     lapack_int* ldaf, const double* s, const double* b,\n                     lapack_int* ldb, double* x, lapack_int* ldx, double* rcond,\n                     double* berr, lapack_int* n_err_bnds,\n                     double* err_bnds_norm, double* err_bnds_comp,\n                     lapack_int* nparams, double* params, double* work,\n                     lapack_int* iwork, lapack_int *info );\nvoid LAPACK_sporfsx( char* uplo, char* equed, lapack_int* n, lapack_int* nrhs,\n                     const float* a, lapack_int* lda, const float* af,\n                     lapack_int* ldaf, const float* s, const float* b,\n                     lapack_int* ldb, float* x, lapack_int* ldx, float* rcond,\n                     float* berr, lapack_int* n_err_bnds, float* err_bnds_norm,\n                     float* err_bnds_comp, lapack_int* nparams, float* params,\n                     float* work, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_zporfsx( char* uplo, char* equed, lapack_int* n, lapack_int* nrhs,\n                     const lapack_complex_double* a, lapack_int* lda,\n                     const lapack_complex_double* af, lapack_int* ldaf,\n                     const double* s, const lapack_complex_double* b,\n                     lapack_int* ldb, lapack_complex_double* x, lapack_int* ldx,\n                     double* rcond, double* berr, lapack_int* n_err_bnds,\n                     double* err_bnds_norm, double* err_bnds_comp,\n                     lapack_int* nparams, double* params,\n                     lapack_complex_double* work, double* rwork,\n                     lapack_int *info );\nvoid LAPACK_cporfsx( char* uplo, char* equed, lapack_int* n, lapack_int* nrhs,\n                     const lapack_complex_float* a, lapack_int* lda,\n                     const lapack_complex_float* af, lapack_int* ldaf,\n                     const float* s, const lapack_complex_float* b,\n                     lapack_int* ldb, lapack_complex_float* x, lapack_int* ldx,\n                     float* rcond, float* berr, lapack_int* n_err_bnds,\n                     float* err_bnds_norm, float* err_bnds_comp,\n                     lapack_int* nparams, float* params,\n                     lapack_complex_float* work, float* rwork,\n                     lapack_int *info );\nvoid LAPACK_spprfs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const float* ap, const float* afp, const float* b,\n                    lapack_int* ldb, float* x, lapack_int* ldx, float* ferr,\n                    float* berr, float* work, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_dpprfs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const double* ap, const double* afp, const double* b,\n                    lapack_int* ldb, double* x, lapack_int* ldx, double* ferr,\n                    double* berr, double* work, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_cpprfs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_float* ap,\n                    const lapack_complex_float* afp,\n                    const lapack_complex_float* b, lapack_int* ldb,\n                    lapack_complex_float* x, lapack_int* ldx, float* ferr,\n                    float* berr, lapack_complex_float* work, float* rwork,\n                    lapack_int *info );\nvoid LAPACK_zpprfs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_double* ap,\n                    const lapack_complex_double* afp,\n                    const lapack_complex_double* b, lapack_int* ldb,\n                    lapack_complex_double* x, lapack_int* ldx, double* ferr,\n                    double* berr, lapack_complex_double* work, double* rwork,\n                    lapack_int *info );\nvoid LAPACK_spbrfs( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs,\n                    const float* ab, lapack_int* ldab, const float* afb,\n                    lapack_int* ldafb, const float* b, lapack_int* ldb,\n                    float* x, lapack_int* ldx, float* ferr, float* berr,\n                    float* work, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_dpbrfs( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs,\n                    const double* ab, lapack_int* ldab, const double* afb,\n                    lapack_int* ldafb, const double* b, lapack_int* ldb,\n                    double* x, lapack_int* ldx, double* ferr, double* berr,\n                    double* work, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_cpbrfs( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs,\n                    const lapack_complex_float* ab, lapack_int* ldab,\n                    const lapack_complex_float* afb, lapack_int* ldafb,\n                    const lapack_complex_float* b, lapack_int* ldb,\n                    lapack_complex_float* x, lapack_int* ldx, float* ferr,\n                    float* berr, lapack_complex_float* work, float* rwork,\n                    lapack_int *info );\nvoid LAPACK_zpbrfs( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs,\n                    const lapack_complex_double* ab, lapack_int* ldab,\n                    const lapack_complex_double* afb, lapack_int* ldafb,\n                    const lapack_complex_double* b, lapack_int* ldb,\n                    lapack_complex_double* x, lapack_int* ldx, double* ferr,\n                    double* berr, lapack_complex_double* work, double* rwork,\n                    lapack_int *info );\nvoid LAPACK_sptrfs( lapack_int* n, lapack_int* nrhs, const float* d,\n                    const float* e, const float* df, const float* ef,\n                    const float* b, lapack_int* ldb, float* x, lapack_int* ldx,\n                    float* ferr, float* berr, float* work, lapack_int *info );\nvoid LAPACK_dptrfs( lapack_int* n, lapack_int* nrhs, const double* d,\n                    const double* e, const double* df, const double* ef,\n                    const double* b, lapack_int* ldb, double* x,\n                    lapack_int* ldx, double* ferr, double* berr, double* work,\n                    lapack_int *info );\nvoid LAPACK_cptrfs( char* uplo, lapack_int* n, lapack_int* nrhs, const float* d,\n                    const lapack_complex_float* e, const float* df,\n                    const lapack_complex_float* ef,\n                    const lapack_complex_float* b, lapack_int* ldb,\n                    lapack_complex_float* x, lapack_int* ldx, float* ferr,\n                    float* berr, lapack_complex_float* work, float* rwork,\n                    lapack_int *info );\nvoid LAPACK_zptrfs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const double* d, const lapack_complex_double* e,\n                    const double* df, const lapack_complex_double* ef,\n                    const lapack_complex_double* b, lapack_int* ldb,\n                    lapack_complex_double* x, lapack_int* ldx, double* ferr,\n                    double* berr, lapack_complex_double* work, double* rwork,\n                    lapack_int *info );\nvoid LAPACK_ssyrfs( char* uplo, lapack_int* n, lapack_int* nrhs, const float* a,\n                    lapack_int* lda, const float* af, lapack_int* ldaf,\n                    const lapack_int* ipiv, const float* b, lapack_int* ldb,\n                    float* x, lapack_int* ldx, float* ferr, float* berr,\n                    float* work, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_dsyrfs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const double* a, lapack_int* lda, const double* af,\n                    lapack_int* ldaf, const lapack_int* ipiv, const double* b,\n                    lapack_int* ldb, double* x, lapack_int* ldx, double* ferr,\n                    double* berr, double* work, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_csyrfs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_float* a, lapack_int* lda,\n                    const lapack_complex_float* af, lapack_int* ldaf,\n                    const lapack_int* ipiv, const lapack_complex_float* b,\n                    lapack_int* ldb, lapack_complex_float* x, lapack_int* ldx,\n                    float* ferr, float* berr, lapack_complex_float* work,\n                    float* rwork, lapack_int *info );\nvoid LAPACK_zsyrfs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_double* a, lapack_int* lda,\n                    const lapack_complex_double* af, lapack_int* ldaf,\n                    const lapack_int* ipiv, const lapack_complex_double* b,\n                    lapack_int* ldb, lapack_complex_double* x, lapack_int* ldx,\n                    double* ferr, double* berr, lapack_complex_double* work,\n                    double* rwork, lapack_int *info );\nvoid LAPACK_dsyrfsx( char* uplo, char* equed, lapack_int* n, lapack_int* nrhs,\n                     const double* a, lapack_int* lda, const double* af,\n                     lapack_int* ldaf, const lapack_int* ipiv, const double* s,\n                     const double* b, lapack_int* ldb, double* x,\n                     lapack_int* ldx, double* rcond, double* berr,\n                     lapack_int* n_err_bnds, double* err_bnds_norm,\n                     double* err_bnds_comp, lapack_int* nparams, double* params,\n                     double* work, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_ssyrfsx( char* uplo, char* equed, lapack_int* n, lapack_int* nrhs,\n                     const float* a, lapack_int* lda, const float* af,\n                     lapack_int* ldaf, const lapack_int* ipiv, const float* s,\n                     const float* b, lapack_int* ldb, float* x, lapack_int* ldx,\n                     float* rcond, float* berr, lapack_int* n_err_bnds,\n                     float* err_bnds_norm, float* err_bnds_comp,\n                     lapack_int* nparams, float* params, float* work,\n                     lapack_int* iwork, lapack_int *info );\nvoid LAPACK_zsyrfsx( char* uplo, char* equed, lapack_int* n, lapack_int* nrhs,\n                     const lapack_complex_double* a, lapack_int* lda,\n                     const lapack_complex_double* af, lapack_int* ldaf,\n                     const lapack_int* ipiv, const double* s,\n                     const lapack_complex_double* b, lapack_int* ldb,\n                     lapack_complex_double* x, lapack_int* ldx, double* rcond,\n                     double* berr, lapack_int* n_err_bnds,\n                     double* err_bnds_norm, double* err_bnds_comp,\n                     lapack_int* nparams, double* params,\n                     lapack_complex_double* work, double* rwork,\n                     lapack_int *info );\nvoid LAPACK_csyrfsx( char* uplo, char* equed, lapack_int* n, lapack_int* nrhs,\n                     const lapack_complex_float* a, lapack_int* lda,\n                     const lapack_complex_float* af, lapack_int* ldaf,\n                     const lapack_int* ipiv, const float* s,\n                     const lapack_complex_float* b, lapack_int* ldb,\n                     lapack_complex_float* x, lapack_int* ldx, float* rcond,\n                     float* berr, lapack_int* n_err_bnds, float* err_bnds_norm,\n                     float* err_bnds_comp, lapack_int* nparams, float* params,\n                     lapack_complex_float* work, float* rwork,\n                     lapack_int *info );\nvoid LAPACK_cherfs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_float* a, lapack_int* lda,\n                    const lapack_complex_float* af, lapack_int* ldaf,\n                    const lapack_int* ipiv, const lapack_complex_float* b,\n                    lapack_int* ldb, lapack_complex_float* x, lapack_int* ldx,\n                    float* ferr, float* berr, lapack_complex_float* work,\n                    float* rwork, lapack_int *info );\nvoid LAPACK_zherfs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_double* a, lapack_int* lda,\n                    const lapack_complex_double* af, lapack_int* ldaf,\n                    const lapack_int* ipiv, const lapack_complex_double* b,\n                    lapack_int* ldb, lapack_complex_double* x, lapack_int* ldx,\n                    double* ferr, double* berr, lapack_complex_double* work,\n                    double* rwork, lapack_int *info );\nvoid LAPACK_zherfsx( char* uplo, char* equed, lapack_int* n, lapack_int* nrhs,\n                     const lapack_complex_double* a, lapack_int* lda,\n                     const lapack_complex_double* af, lapack_int* ldaf,\n                     const lapack_int* ipiv, const double* s,\n                     const lapack_complex_double* b, lapack_int* ldb,\n                     lapack_complex_double* x, lapack_int* ldx, double* rcond,\n                     double* berr, lapack_int* n_err_bnds,\n                     double* err_bnds_norm, double* err_bnds_comp,\n                     lapack_int* nparams, double* params,\n                     lapack_complex_double* work, double* rwork,\n                     lapack_int *info );\nvoid LAPACK_cherfsx( char* uplo, char* equed, lapack_int* n, lapack_int* nrhs,\n                     const lapack_complex_float* a, lapack_int* lda,\n                     const lapack_complex_float* af, lapack_int* ldaf,\n                     const lapack_int* ipiv, const float* s,\n                     const lapack_complex_float* b, lapack_int* ldb,\n                     lapack_complex_float* x, lapack_int* ldx, float* rcond,\n                     float* berr, lapack_int* n_err_bnds, float* err_bnds_norm,\n                     float* err_bnds_comp, lapack_int* nparams, float* params,\n                     lapack_complex_float* work, float* rwork,\n                     lapack_int *info );\nvoid LAPACK_ssprfs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const float* ap, const float* afp, const lapack_int* ipiv,\n                    const float* b, lapack_int* ldb, float* x, lapack_int* ldx,\n                    float* ferr, float* berr, float* work, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_dsprfs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const double* ap, const double* afp, const lapack_int* ipiv,\n                    const double* b, lapack_int* ldb, double* x,\n                    lapack_int* ldx, double* ferr, double* berr, double* work,\n                    lapack_int* iwork, lapack_int *info );\nvoid LAPACK_csprfs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_float* ap,\n                    const lapack_complex_float* afp, const lapack_int* ipiv,\n                    const lapack_complex_float* b, lapack_int* ldb,\n                    lapack_complex_float* x, lapack_int* ldx, float* ferr,\n                    float* berr, lapack_complex_float* work, float* rwork,\n                    lapack_int *info );\nvoid LAPACK_zsprfs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_double* ap,\n                    const lapack_complex_double* afp, const lapack_int* ipiv,\n                    const lapack_complex_double* b, lapack_int* ldb,\n                    lapack_complex_double* x, lapack_int* ldx, double* ferr,\n                    double* berr, lapack_complex_double* work, double* rwork,\n                    lapack_int *info );\nvoid LAPACK_chprfs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_float* ap,\n                    const lapack_complex_float* afp, const lapack_int* ipiv,\n                    const lapack_complex_float* b, lapack_int* ldb,\n                    lapack_complex_float* x, lapack_int* ldx, float* ferr,\n                    float* berr, lapack_complex_float* work, float* rwork,\n                    lapack_int *info );\nvoid LAPACK_zhprfs( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_double* ap,\n                    const lapack_complex_double* afp, const lapack_int* ipiv,\n                    const lapack_complex_double* b, lapack_int* ldb,\n                    lapack_complex_double* x, lapack_int* ldx, double* ferr,\n                    double* berr, lapack_complex_double* work, double* rwork,\n                    lapack_int *info );\nvoid LAPACK_strrfs( char* uplo, char* trans, char* diag, lapack_int* n,\n                    lapack_int* nrhs, const float* a, lapack_int* lda,\n                    const float* b, lapack_int* ldb, const float* x,\n                    lapack_int* ldx, float* ferr, float* berr, float* work,\n                    lapack_int* iwork, lapack_int *info );\nvoid LAPACK_dtrrfs( char* uplo, char* trans, char* diag, lapack_int* n,\n                    lapack_int* nrhs, const double* a, lapack_int* lda,\n                    const double* b, lapack_int* ldb, const double* x,\n                    lapack_int* ldx, double* ferr, double* berr, double* work,\n                    lapack_int* iwork, lapack_int *info );\nvoid LAPACK_ctrrfs( char* uplo, char* trans, char* diag, lapack_int* n,\n                    lapack_int* nrhs, const lapack_complex_float* a,\n                    lapack_int* lda, const lapack_complex_float* b,\n                    lapack_int* ldb, const lapack_complex_float* x,\n                    lapack_int* ldx, float* ferr, float* berr,\n                    lapack_complex_float* work, float* rwork,\n                    lapack_int *info );\nvoid LAPACK_ztrrfs( char* uplo, char* trans, char* diag, lapack_int* n,\n                    lapack_int* nrhs, const lapack_complex_double* a,\n                    lapack_int* lda, const lapack_complex_double* b,\n                    lapack_int* ldb, const lapack_complex_double* x,\n                    lapack_int* ldx, double* ferr, double* berr,\n                    lapack_complex_double* work, double* rwork,\n                    lapack_int *info );\nvoid LAPACK_stprfs( char* uplo, char* trans, char* diag, lapack_int* n,\n                    lapack_int* nrhs, const float* ap, const float* b,\n                    lapack_int* ldb, const float* x, lapack_int* ldx,\n                    float* ferr, float* berr, float* work, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_dtprfs( char* uplo, char* trans, char* diag, lapack_int* n,\n                    lapack_int* nrhs, const double* ap, const double* b,\n                    lapack_int* ldb, const double* x, lapack_int* ldx,\n                    double* ferr, double* berr, double* work, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_ctprfs( char* uplo, char* trans, char* diag, lapack_int* n,\n                    lapack_int* nrhs, const lapack_complex_float* ap,\n                    const lapack_complex_float* b, lapack_int* ldb,\n                    const lapack_complex_float* x, lapack_int* ldx, float* ferr,\n                    float* berr, lapack_complex_float* work, float* rwork,\n                    lapack_int *info );\nvoid LAPACK_ztprfs( char* uplo, char* trans, char* diag, lapack_int* n,\n                    lapack_int* nrhs, const lapack_complex_double* ap,\n                    const lapack_complex_double* b, lapack_int* ldb,\n                    const lapack_complex_double* x, lapack_int* ldx,\n                    double* ferr, double* berr, lapack_complex_double* work,\n                    double* rwork, lapack_int *info );\nvoid LAPACK_stbrfs( char* uplo, char* trans, char* diag, lapack_int* n,\n                    lapack_int* kd, lapack_int* nrhs, const float* ab,\n                    lapack_int* ldab, const float* b, lapack_int* ldb,\n                    const float* x, lapack_int* ldx, float* ferr, float* berr,\n                    float* work, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_dtbrfs( char* uplo, char* trans, char* diag, lapack_int* n,\n                    lapack_int* kd, lapack_int* nrhs, const double* ab,\n                    lapack_int* ldab, const double* b, lapack_int* ldb,\n                    const double* x, lapack_int* ldx, double* ferr,\n                    double* berr, double* work, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_ctbrfs( char* uplo, char* trans, char* diag, lapack_int* n,\n                    lapack_int* kd, lapack_int* nrhs,\n                    const lapack_complex_float* ab, lapack_int* ldab,\n                    const lapack_complex_float* b, lapack_int* ldb,\n                    const lapack_complex_float* x, lapack_int* ldx, float* ferr,\n                    float* berr, lapack_complex_float* work, float* rwork,\n                    lapack_int *info );\nvoid LAPACK_ztbrfs( char* uplo, char* trans, char* diag, lapack_int* n,\n                    lapack_int* kd, lapack_int* nrhs,\n                    const lapack_complex_double* ab, lapack_int* ldab,\n                    const lapack_complex_double* b, lapack_int* ldb,\n                    const lapack_complex_double* x, lapack_int* ldx,\n                    double* ferr, double* berr, lapack_complex_double* work,\n                    double* rwork, lapack_int *info );\nvoid LAPACK_sgetri( lapack_int* n, float* a, lapack_int* lda,\n                    const lapack_int* ipiv, float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_dgetri( lapack_int* n, double* a, lapack_int* lda,\n                    const lapack_int* ipiv, double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_cgetri( lapack_int* n, lapack_complex_float* a, lapack_int* lda,\n                    const lapack_int* ipiv, lapack_complex_float* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_zgetri( lapack_int* n, lapack_complex_double* a, lapack_int* lda,\n                    const lapack_int* ipiv, lapack_complex_double* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_spotri( char* uplo, lapack_int* n, float* a, lapack_int* lda,\n                    lapack_int *info );\nvoid LAPACK_dpotri( char* uplo, lapack_int* n, double* a, lapack_int* lda,\n                    lapack_int *info );\nvoid LAPACK_cpotri( char* uplo, lapack_int* n, lapack_complex_float* a,\n                    lapack_int* lda, lapack_int *info );\nvoid LAPACK_zpotri( char* uplo, lapack_int* n, lapack_complex_double* a,\n                    lapack_int* lda, lapack_int *info );\nvoid LAPACK_dpftri( char* transr, char* uplo, lapack_int* n, double* a,\n                    lapack_int *info );\nvoid LAPACK_spftri( char* transr, char* uplo, lapack_int* n, float* a,\n                    lapack_int *info );\nvoid LAPACK_zpftri( char* transr, char* uplo, lapack_int* n,\n                    lapack_complex_double* a, lapack_int *info );\nvoid LAPACK_cpftri( char* transr, char* uplo, lapack_int* n,\n                    lapack_complex_float* a, lapack_int *info );\nvoid LAPACK_spptri( char* uplo, lapack_int* n, float* ap, lapack_int *info );\nvoid LAPACK_dpptri( char* uplo, lapack_int* n, double* ap, lapack_int *info );\nvoid LAPACK_cpptri( char* uplo, lapack_int* n, lapack_complex_float* ap,\n                    lapack_int *info );\nvoid LAPACK_zpptri( char* uplo, lapack_int* n, lapack_complex_double* ap,\n                    lapack_int *info );\nvoid LAPACK_ssytri( char* uplo, lapack_int* n, float* a, lapack_int* lda,\n                    const lapack_int* ipiv, float* work, lapack_int *info );\nvoid LAPACK_dsytri( char* uplo, lapack_int* n, double* a, lapack_int* lda,\n                    const lapack_int* ipiv, double* work, lapack_int *info );\nvoid LAPACK_csytri( char* uplo, lapack_int* n, lapack_complex_float* a,\n                    lapack_int* lda, const lapack_int* ipiv,\n                    lapack_complex_float* work, lapack_int *info );\nvoid LAPACK_zsytri( char* uplo, lapack_int* n, lapack_complex_double* a,\n                    lapack_int* lda, const lapack_int* ipiv,\n                    lapack_complex_double* work, lapack_int *info );\nvoid LAPACK_chetri( char* uplo, lapack_int* n, lapack_complex_float* a,\n                    lapack_int* lda, const lapack_int* ipiv,\n                    lapack_complex_float* work, lapack_int *info );\nvoid LAPACK_zhetri( char* uplo, lapack_int* n, lapack_complex_double* a,\n                    lapack_int* lda, const lapack_int* ipiv,\n                    lapack_complex_double* work, lapack_int *info );\nvoid LAPACK_ssptri( char* uplo, lapack_int* n, float* ap,\n                    const lapack_int* ipiv, float* work, lapack_int *info );\nvoid LAPACK_dsptri( char* uplo, lapack_int* n, double* ap,\n                    const lapack_int* ipiv, double* work, lapack_int *info );\nvoid LAPACK_csptri( char* uplo, lapack_int* n, lapack_complex_float* ap,\n                    const lapack_int* ipiv, lapack_complex_float* work,\n                    lapack_int *info );\nvoid LAPACK_zsptri( char* uplo, lapack_int* n, lapack_complex_double* ap,\n                    const lapack_int* ipiv, lapack_complex_double* work,\n                    lapack_int *info );\nvoid LAPACK_chptri( char* uplo, lapack_int* n, lapack_complex_float* ap,\n                    const lapack_int* ipiv, lapack_complex_float* work,\n                    lapack_int *info );\nvoid LAPACK_zhptri( char* uplo, lapack_int* n, lapack_complex_double* ap,\n                    const lapack_int* ipiv, lapack_complex_double* work,\n                    lapack_int *info );\nvoid LAPACK_strtri( char* uplo, char* diag, lapack_int* n, float* a,\n                    lapack_int* lda, lapack_int *info );\nvoid LAPACK_dtrtri( char* uplo, char* diag, lapack_int* n, double* a,\n                    lapack_int* lda, lapack_int *info );\nvoid LAPACK_ctrtri( char* uplo, char* diag, lapack_int* n,\n                    lapack_complex_float* a, lapack_int* lda,\n                    lapack_int *info );\nvoid LAPACK_ztrtri( char* uplo, char* diag, lapack_int* n,\n                    lapack_complex_double* a, lapack_int* lda,\n                    lapack_int *info );\nvoid LAPACK_dtftri( char* transr, char* uplo, char* diag, lapack_int* n,\n                    double* a, lapack_int *info );\nvoid LAPACK_stftri( char* transr, char* uplo, char* diag, lapack_int* n,\n                    float* a, lapack_int *info );\nvoid LAPACK_ztftri( char* transr, char* uplo, char* diag, lapack_int* n,\n                    lapack_complex_double* a, lapack_int *info );\nvoid LAPACK_ctftri( char* transr, char* uplo, char* diag, lapack_int* n,\n                    lapack_complex_float* a, lapack_int *info );\nvoid LAPACK_stptri( char* uplo, char* diag, lapack_int* n, float* ap,\n                    lapack_int *info );\nvoid LAPACK_dtptri( char* uplo, char* diag, lapack_int* n, double* ap,\n                    lapack_int *info );\nvoid LAPACK_ctptri( char* uplo, char* diag, lapack_int* n,\n                    lapack_complex_float* ap, lapack_int *info );\nvoid LAPACK_ztptri( char* uplo, char* diag, lapack_int* n,\n                    lapack_complex_double* ap, lapack_int *info );\nvoid LAPACK_sgeequ( lapack_int* m, lapack_int* n, const float* a,\n                    lapack_int* lda, float* r, float* c, float* rowcnd,\n                    float* colcnd, float* amax, lapack_int *info );\nvoid LAPACK_dgeequ( lapack_int* m, lapack_int* n, const double* a,\n                    lapack_int* lda, double* r, double* c, double* rowcnd,\n                    double* colcnd, double* amax, lapack_int *info );\nvoid LAPACK_cgeequ( lapack_int* m, lapack_int* n, const lapack_complex_float* a,\n                    lapack_int* lda, float* r, float* c, float* rowcnd,\n                    float* colcnd, float* amax, lapack_int *info );\nvoid LAPACK_zgeequ( lapack_int* m, lapack_int* n,\n                    const lapack_complex_double* a, lapack_int* lda, double* r,\n                    double* c, double* rowcnd, double* colcnd, double* amax,\n                    lapack_int *info );\nvoid LAPACK_dgeequb( lapack_int* m, lapack_int* n, const double* a,\n                     lapack_int* lda, double* r, double* c, double* rowcnd,\n                     double* colcnd, double* amax, lapack_int *info );\nvoid LAPACK_sgeequb( lapack_int* m, lapack_int* n, const float* a,\n                     lapack_int* lda, float* r, float* c, float* rowcnd,\n                     float* colcnd, float* amax, lapack_int *info );\nvoid LAPACK_zgeequb( lapack_int* m, lapack_int* n,\n                     const lapack_complex_double* a, lapack_int* lda, double* r,\n                     double* c, double* rowcnd, double* colcnd, double* amax,\n                     lapack_int *info );\nvoid LAPACK_cgeequb( lapack_int* m, lapack_int* n,\n                     const lapack_complex_float* a, lapack_int* lda, float* r,\n                     float* c, float* rowcnd, float* colcnd, float* amax,\n                     lapack_int *info );\nvoid LAPACK_sgbequ( lapack_int* m, lapack_int* n, lapack_int* kl,\n                    lapack_int* ku, const float* ab, lapack_int* ldab, float* r,\n                    float* c, float* rowcnd, float* colcnd, float* amax,\n                    lapack_int *info );\nvoid LAPACK_dgbequ( lapack_int* m, lapack_int* n, lapack_int* kl,\n                    lapack_int* ku, const double* ab, lapack_int* ldab,\n                    double* r, double* c, double* rowcnd, double* colcnd,\n                    double* amax, lapack_int *info );\nvoid LAPACK_cgbequ( lapack_int* m, lapack_int* n, lapack_int* kl,\n                    lapack_int* ku, const lapack_complex_float* ab,\n                    lapack_int* ldab, float* r, float* c, float* rowcnd,\n                    float* colcnd, float* amax, lapack_int *info );\nvoid LAPACK_zgbequ( lapack_int* m, lapack_int* n, lapack_int* kl,\n                    lapack_int* ku, const lapack_complex_double* ab,\n                    lapack_int* ldab, double* r, double* c, double* rowcnd,\n                    double* colcnd, double* amax, lapack_int *info );\nvoid LAPACK_dgbequb( lapack_int* m, lapack_int* n, lapack_int* kl,\n                     lapack_int* ku, const double* ab, lapack_int* ldab,\n                     double* r, double* c, double* rowcnd, double* colcnd,\n                     double* amax, lapack_int *info );\nvoid LAPACK_sgbequb( lapack_int* m, lapack_int* n, lapack_int* kl,\n                     lapack_int* ku, const float* ab, lapack_int* ldab,\n                     float* r, float* c, float* rowcnd, float* colcnd,\n                     float* amax, lapack_int *info );\nvoid LAPACK_zgbequb( lapack_int* m, lapack_int* n, lapack_int* kl,\n                     lapack_int* ku, const lapack_complex_double* ab,\n                     lapack_int* ldab, double* r, double* c, double* rowcnd,\n                     double* colcnd, double* amax, lapack_int *info );\nvoid LAPACK_cgbequb( lapack_int* m, lapack_int* n, lapack_int* kl,\n                     lapack_int* ku, const lapack_complex_float* ab,\n                     lapack_int* ldab, float* r, float* c, float* rowcnd,\n                     float* colcnd, float* amax, lapack_int *info );\nvoid LAPACK_spoequ( lapack_int* n, const float* a, lapack_int* lda, float* s,\n                    float* scond, float* amax, lapack_int *info );\nvoid LAPACK_dpoequ( lapack_int* n, const double* a, lapack_int* lda, double* s,\n                    double* scond, double* amax, lapack_int *info );\nvoid LAPACK_cpoequ( lapack_int* n, const lapack_complex_float* a,\n                    lapack_int* lda, float* s, float* scond, float* amax,\n                    lapack_int *info );\nvoid LAPACK_zpoequ( lapack_int* n, const lapack_complex_double* a,\n                    lapack_int* lda, double* s, double* scond, double* amax,\n                    lapack_int *info );\nvoid LAPACK_dpoequb( lapack_int* n, const double* a, lapack_int* lda, double* s,\n                     double* scond, double* amax, lapack_int *info );\nvoid LAPACK_spoequb( lapack_int* n, const float* a, lapack_int* lda, float* s,\n                     float* scond, float* amax, lapack_int *info );\nvoid LAPACK_zpoequb( lapack_int* n, const lapack_complex_double* a,\n                     lapack_int* lda, double* s, double* scond, double* amax,\n                     lapack_int *info );\nvoid LAPACK_cpoequb( lapack_int* n, const lapack_complex_float* a,\n                     lapack_int* lda, float* s, float* scond, float* amax,\n                     lapack_int *info );\nvoid LAPACK_sppequ( char* uplo, lapack_int* n, const float* ap, float* s,\n                    float* scond, float* amax, lapack_int *info );\nvoid LAPACK_dppequ( char* uplo, lapack_int* n, const double* ap, double* s,\n                    double* scond, double* amax, lapack_int *info );\nvoid LAPACK_cppequ( char* uplo, lapack_int* n, const lapack_complex_float* ap,\n                    float* s, float* scond, float* amax, lapack_int *info );\nvoid LAPACK_zppequ( char* uplo, lapack_int* n, const lapack_complex_double* ap,\n                    double* s, double* scond, double* amax, lapack_int *info );\nvoid LAPACK_spbequ( char* uplo, lapack_int* n, lapack_int* kd, const float* ab,\n                    lapack_int* ldab, float* s, float* scond, float* amax,\n                    lapack_int *info );\nvoid LAPACK_dpbequ( char* uplo, lapack_int* n, lapack_int* kd, const double* ab,\n                    lapack_int* ldab, double* s, double* scond, double* amax,\n                    lapack_int *info );\nvoid LAPACK_cpbequ( char* uplo, lapack_int* n, lapack_int* kd,\n                    const lapack_complex_float* ab, lapack_int* ldab, float* s,\n                    float* scond, float* amax, lapack_int *info );\nvoid LAPACK_zpbequ( char* uplo, lapack_int* n, lapack_int* kd,\n                    const lapack_complex_double* ab, lapack_int* ldab,\n                    double* s, double* scond, double* amax, lapack_int *info );\nvoid LAPACK_dsyequb( char* uplo, lapack_int* n, const double* a,\n                     lapack_int* lda, double* s, double* scond, double* amax,\n                     double* work, lapack_int *info );\nvoid LAPACK_ssyequb( char* uplo, lapack_int* n, const float* a, lapack_int* lda,\n                     float* s, float* scond, float* amax, float* work,\n                     lapack_int *info );\nvoid LAPACK_zsyequb( char* uplo, lapack_int* n, const lapack_complex_double* a,\n                     lapack_int* lda, double* s, double* scond, double* amax,\n                     lapack_complex_double* work, lapack_int *info );\nvoid LAPACK_csyequb( char* uplo, lapack_int* n, const lapack_complex_float* a,\n                     lapack_int* lda, float* s, float* scond, float* amax,\n                     lapack_complex_float* work, lapack_int *info );\nvoid LAPACK_zheequb( char* uplo, lapack_int* n, const lapack_complex_double* a,\n                     lapack_int* lda, double* s, double* scond, double* amax,\n                     lapack_complex_double* work, lapack_int *info );\nvoid LAPACK_cheequb( char* uplo, lapack_int* n, const lapack_complex_float* a,\n                     lapack_int* lda, float* s, float* scond, float* amax,\n                     lapack_complex_float* work, lapack_int *info );\nvoid LAPACK_sgesv( lapack_int* n, lapack_int* nrhs, float* a, lapack_int* lda,\n                   lapack_int* ipiv, float* b, lapack_int* ldb,\n                   lapack_int *info );\nvoid LAPACK_dgesv( lapack_int* n, lapack_int* nrhs, double* a, lapack_int* lda,\n                   lapack_int* ipiv, double* b, lapack_int* ldb,\n                   lapack_int *info );\nvoid LAPACK_cgesv( lapack_int* n, lapack_int* nrhs, lapack_complex_float* a,\n                   lapack_int* lda, lapack_int* ipiv, lapack_complex_float* b,\n                   lapack_int* ldb, lapack_int *info );\nvoid LAPACK_zgesv( lapack_int* n, lapack_int* nrhs, lapack_complex_double* a,\n                   lapack_int* lda, lapack_int* ipiv, lapack_complex_double* b,\n                   lapack_int* ldb, lapack_int *info );\nvoid LAPACK_dsgesv( lapack_int* n, lapack_int* nrhs, double* a, lapack_int* lda,\n                    lapack_int* ipiv, double* b, lapack_int* ldb, double* x,\n                    lapack_int* ldx, double* work, float* swork,\n                    lapack_int* iter, lapack_int *info );\nvoid LAPACK_zcgesv( lapack_int* n, lapack_int* nrhs, lapack_complex_double* a,\n                    lapack_int* lda, lapack_int* ipiv, lapack_complex_double* b,\n                    lapack_int* ldb, lapack_complex_double* x, lapack_int* ldx,\n                    lapack_complex_double* work, lapack_complex_float* swork,\n                    double* rwork, lapack_int* iter, lapack_int *info );\nvoid LAPACK_sgesvx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs,\n                    float* a, lapack_int* lda, float* af, lapack_int* ldaf,\n                    lapack_int* ipiv, char* equed, float* r, float* c, float* b,\n                    lapack_int* ldb, float* x, lapack_int* ldx, float* rcond,\n                    float* ferr, float* berr, float* work, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_dgesvx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs,\n                    double* a, lapack_int* lda, double* af, lapack_int* ldaf,\n                    lapack_int* ipiv, char* equed, double* r, double* c,\n                    double* b, lapack_int* ldb, double* x, lapack_int* ldx,\n                    double* rcond, double* ferr, double* berr, double* work,\n                    lapack_int* iwork, lapack_int *info );\nvoid LAPACK_cgesvx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs,\n                    lapack_complex_float* a, lapack_int* lda,\n                    lapack_complex_float* af, lapack_int* ldaf,\n                    lapack_int* ipiv, char* equed, float* r, float* c,\n                    lapack_complex_float* b, lapack_int* ldb,\n                    lapack_complex_float* x, lapack_int* ldx, float* rcond,\n                    float* ferr, float* berr, lapack_complex_float* work,\n                    float* rwork, lapack_int *info );\nvoid LAPACK_zgesvx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs,\n                    lapack_complex_double* a, lapack_int* lda,\n                    lapack_complex_double* af, lapack_int* ldaf,\n                    lapack_int* ipiv, char* equed, double* r, double* c,\n                    lapack_complex_double* b, lapack_int* ldb,\n                    lapack_complex_double* x, lapack_int* ldx, double* rcond,\n                    double* ferr, double* berr, lapack_complex_double* work,\n                    double* rwork, lapack_int *info );\nvoid LAPACK_dgesvxx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs,\n                     double* a, lapack_int* lda, double* af, lapack_int* ldaf,\n                     lapack_int* ipiv, char* equed, double* r, double* c,\n                     double* b, lapack_int* ldb, double* x, lapack_int* ldx,\n                     double* rcond, double* rpvgrw, double* berr,\n                     lapack_int* n_err_bnds, double* err_bnds_norm,\n                     double* err_bnds_comp, lapack_int* nparams, double* params,\n                     double* work, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_sgesvxx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs,\n                     float* a, lapack_int* lda, float* af, lapack_int* ldaf,\n                     lapack_int* ipiv, char* equed, float* r, float* c,\n                     float* b, lapack_int* ldb, float* x, lapack_int* ldx,\n                     float* rcond, float* rpvgrw, float* berr,\n                     lapack_int* n_err_bnds, float* err_bnds_norm,\n                     float* err_bnds_comp, lapack_int* nparams, float* params,\n                     float* work, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_zgesvxx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs,\n                     lapack_complex_double* a, lapack_int* lda,\n                     lapack_complex_double* af, lapack_int* ldaf,\n                     lapack_int* ipiv, char* equed, double* r, double* c,\n                     lapack_complex_double* b, lapack_int* ldb,\n                     lapack_complex_double* x, lapack_int* ldx, double* rcond,\n                     double* rpvgrw, double* berr, lapack_int* n_err_bnds,\n                     double* err_bnds_norm, double* err_bnds_comp,\n                     lapack_int* nparams, double* params,\n                     lapack_complex_double* work, double* rwork,\n                     lapack_int *info );\nvoid LAPACK_cgesvxx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs,\n                     lapack_complex_float* a, lapack_int* lda,\n                     lapack_complex_float* af, lapack_int* ldaf,\n                     lapack_int* ipiv, char* equed, float* r, float* c,\n                     lapack_complex_float* b, lapack_int* ldb,\n                     lapack_complex_float* x, lapack_int* ldx, float* rcond,\n                     float* rpvgrw, float* berr, lapack_int* n_err_bnds,\n                     float* err_bnds_norm, float* err_bnds_comp,\n                     lapack_int* nparams, float* params,\n                     lapack_complex_float* work, float* rwork,\n                     lapack_int *info );\nvoid LAPACK_sgbsv( lapack_int* n, lapack_int* kl, lapack_int* ku,\n                   lapack_int* nrhs, float* ab, lapack_int* ldab,\n                   lapack_int* ipiv, float* b, lapack_int* ldb,\n                   lapack_int *info );\nvoid LAPACK_dgbsv( lapack_int* n, lapack_int* kl, lapack_int* ku,\n                   lapack_int* nrhs, double* ab, lapack_int* ldab,\n                   lapack_int* ipiv, double* b, lapack_int* ldb,\n                   lapack_int *info );\nvoid LAPACK_cgbsv( lapack_int* n, lapack_int* kl, lapack_int* ku,\n                   lapack_int* nrhs, lapack_complex_float* ab, lapack_int* ldab,\n                   lapack_int* ipiv, lapack_complex_float* b, lapack_int* ldb,\n                   lapack_int *info );\nvoid LAPACK_zgbsv( lapack_int* n, lapack_int* kl, lapack_int* ku,\n                   lapack_int* nrhs, lapack_complex_double* ab,\n                   lapack_int* ldab, lapack_int* ipiv, lapack_complex_double* b,\n                   lapack_int* ldb, lapack_int *info );\nvoid LAPACK_sgbsvx( char* fact, char* trans, lapack_int* n, lapack_int* kl,\n                    lapack_int* ku, lapack_int* nrhs, float* ab,\n                    lapack_int* ldab, float* afb, lapack_int* ldafb,\n                    lapack_int* ipiv, char* equed, float* r, float* c, float* b,\n                    lapack_int* ldb, float* x, lapack_int* ldx, float* rcond,\n                    float* ferr, float* berr, float* work, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_dgbsvx( char* fact, char* trans, lapack_int* n, lapack_int* kl,\n                    lapack_int* ku, lapack_int* nrhs, double* ab,\n                    lapack_int* ldab, double* afb, lapack_int* ldafb,\n                    lapack_int* ipiv, char* equed, double* r, double* c,\n                    double* b, lapack_int* ldb, double* x, lapack_int* ldx,\n                    double* rcond, double* ferr, double* berr, double* work,\n                    lapack_int* iwork, lapack_int *info );\nvoid LAPACK_cgbsvx( char* fact, char* trans, lapack_int* n, lapack_int* kl,\n                    lapack_int* ku, lapack_int* nrhs, lapack_complex_float* ab,\n                    lapack_int* ldab, lapack_complex_float* afb,\n                    lapack_int* ldafb, lapack_int* ipiv, char* equed, float* r,\n                    float* c, lapack_complex_float* b, lapack_int* ldb,\n                    lapack_complex_float* x, lapack_int* ldx, float* rcond,\n                    float* ferr, float* berr, lapack_complex_float* work,\n                    float* rwork, lapack_int *info );\nvoid LAPACK_zgbsvx( char* fact, char* trans, lapack_int* n, lapack_int* kl,\n                    lapack_int* ku, lapack_int* nrhs, lapack_complex_double* ab,\n                    lapack_int* ldab, lapack_complex_double* afb,\n                    lapack_int* ldafb, lapack_int* ipiv, char* equed, double* r,\n                    double* c, lapack_complex_double* b, lapack_int* ldb,\n                    lapack_complex_double* x, lapack_int* ldx, double* rcond,\n                    double* ferr, double* berr, lapack_complex_double* work,\n                    double* rwork, lapack_int *info );\nvoid LAPACK_dgbsvxx( char* fact, char* trans, lapack_int* n, lapack_int* kl,\n                     lapack_int* ku, lapack_int* nrhs, double* ab,\n                     lapack_int* ldab, double* afb, lapack_int* ldafb,\n                     lapack_int* ipiv, char* equed, double* r, double* c,\n                     double* b, lapack_int* ldb, double* x, lapack_int* ldx,\n                     double* rcond, double* rpvgrw, double* berr,\n                     lapack_int* n_err_bnds, double* err_bnds_norm,\n                     double* err_bnds_comp, lapack_int* nparams, double* params,\n                     double* work, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_sgbsvxx( char* fact, char* trans, lapack_int* n, lapack_int* kl,\n                     lapack_int* ku, lapack_int* nrhs, float* ab,\n                     lapack_int* ldab, float* afb, lapack_int* ldafb,\n                     lapack_int* ipiv, char* equed, float* r, float* c,\n                     float* b, lapack_int* ldb, float* x, lapack_int* ldx,\n                     float* rcond, float* rpvgrw, float* berr,\n                     lapack_int* n_err_bnds, float* err_bnds_norm,\n                     float* err_bnds_comp, lapack_int* nparams, float* params,\n                     float* work, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_zgbsvxx( char* fact, char* trans, lapack_int* n, lapack_int* kl,\n                     lapack_int* ku, lapack_int* nrhs,\n                     lapack_complex_double* ab, lapack_int* ldab,\n                     lapack_complex_double* afb, lapack_int* ldafb,\n                     lapack_int* ipiv, char* equed, double* r, double* c,\n                     lapack_complex_double* b, lapack_int* ldb,\n                     lapack_complex_double* x, lapack_int* ldx, double* rcond,\n                     double* rpvgrw, double* berr, lapack_int* n_err_bnds,\n                     double* err_bnds_norm, double* err_bnds_comp,\n                     lapack_int* nparams, double* params,\n                     lapack_complex_double* work, double* rwork,\n                     lapack_int *info );\nvoid LAPACK_cgbsvxx( char* fact, char* trans, lapack_int* n, lapack_int* kl,\n                     lapack_int* ku, lapack_int* nrhs, lapack_complex_float* ab,\n                     lapack_int* ldab, lapack_complex_float* afb,\n                     lapack_int* ldafb, lapack_int* ipiv, char* equed, float* r,\n                     float* c, lapack_complex_float* b, lapack_int* ldb,\n                     lapack_complex_float* x, lapack_int* ldx, float* rcond,\n                     float* rpvgrw, float* berr, lapack_int* n_err_bnds,\n                     float* err_bnds_norm, float* err_bnds_comp,\n                     lapack_int* nparams, float* params,\n                     lapack_complex_float* work, float* rwork,\n                     lapack_int *info );\nvoid LAPACK_sgtsv( lapack_int* n, lapack_int* nrhs, float* dl, float* d,\n                   float* du, float* b, lapack_int* ldb, lapack_int *info );\nvoid LAPACK_dgtsv( lapack_int* n, lapack_int* nrhs, double* dl, double* d,\n                   double* du, double* b, lapack_int* ldb, lapack_int *info );\nvoid LAPACK_cgtsv( lapack_int* n, lapack_int* nrhs, lapack_complex_float* dl,\n                   lapack_complex_float* d, lapack_complex_float* du,\n                   lapack_complex_float* b, lapack_int* ldb, lapack_int *info );\nvoid LAPACK_zgtsv( lapack_int* n, lapack_int* nrhs, lapack_complex_double* dl,\n                   lapack_complex_double* d, lapack_complex_double* du,\n                   lapack_complex_double* b, lapack_int* ldb,\n                   lapack_int *info );\nvoid LAPACK_sgtsvx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs,\n                    const float* dl, const float* d, const float* du,\n                    float* dlf, float* df, float* duf, float* du2,\n                    lapack_int* ipiv, const float* b, lapack_int* ldb, float* x,\n                    lapack_int* ldx, float* rcond, float* ferr, float* berr,\n                    float* work, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_dgtsvx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs,\n                    const double* dl, const double* d, const double* du,\n                    double* dlf, double* df, double* duf, double* du2,\n                    lapack_int* ipiv, const double* b, lapack_int* ldb,\n                    double* x, lapack_int* ldx, double* rcond, double* ferr,\n                    double* berr, double* work, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_cgtsvx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_float* dl,\n                    const lapack_complex_float* d,\n                    const lapack_complex_float* du, lapack_complex_float* dlf,\n                    lapack_complex_float* df, lapack_complex_float* duf,\n                    lapack_complex_float* du2, lapack_int* ipiv,\n                    const lapack_complex_float* b, lapack_int* ldb,\n                    lapack_complex_float* x, lapack_int* ldx, float* rcond,\n                    float* ferr, float* berr, lapack_complex_float* work,\n                    float* rwork, lapack_int *info );\nvoid LAPACK_zgtsvx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_double* dl,\n                    const lapack_complex_double* d,\n                    const lapack_complex_double* du, lapack_complex_double* dlf,\n                    lapack_complex_double* df, lapack_complex_double* duf,\n                    lapack_complex_double* du2, lapack_int* ipiv,\n                    const lapack_complex_double* b, lapack_int* ldb,\n                    lapack_complex_double* x, lapack_int* ldx, double* rcond,\n                    double* ferr, double* berr, lapack_complex_double* work,\n                    double* rwork, lapack_int *info );\nvoid LAPACK_sposv( char* uplo, lapack_int* n, lapack_int* nrhs, float* a,\n                   lapack_int* lda, float* b, lapack_int* ldb,\n                   lapack_int *info );\nvoid LAPACK_dposv( char* uplo, lapack_int* n, lapack_int* nrhs, double* a,\n                   lapack_int* lda, double* b, lapack_int* ldb,\n                   lapack_int *info );\nvoid LAPACK_cposv( char* uplo, lapack_int* n, lapack_int* nrhs,\n                   lapack_complex_float* a, lapack_int* lda,\n                   lapack_complex_float* b, lapack_int* ldb, lapack_int *info );\nvoid LAPACK_zposv( char* uplo, lapack_int* n, lapack_int* nrhs,\n                   lapack_complex_double* a, lapack_int* lda,\n                   lapack_complex_double* b, lapack_int* ldb,\n                   lapack_int *info );\nvoid LAPACK_dsposv( char* uplo, lapack_int* n, lapack_int* nrhs, double* a,\n                    lapack_int* lda, double* b, lapack_int* ldb, double* x,\n                    lapack_int* ldx, double* work, float* swork,\n                    lapack_int* iter, lapack_int *info );\nvoid LAPACK_zcposv( char* uplo, lapack_int* n, lapack_int* nrhs,\n                    lapack_complex_double* a, lapack_int* lda,\n                    lapack_complex_double* b, lapack_int* ldb,\n                    lapack_complex_double* x, lapack_int* ldx,\n                    lapack_complex_double* work, lapack_complex_float* swork,\n                    double* rwork, lapack_int* iter, lapack_int *info );\nvoid LAPACK_sposvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,\n                    float* a, lapack_int* lda, float* af, lapack_int* ldaf,\n                    char* equed, float* s, float* b, lapack_int* ldb, float* x,\n                    lapack_int* ldx, float* rcond, float* ferr, float* berr,\n                    float* work, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_dposvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,\n                    double* a, lapack_int* lda, double* af, lapack_int* ldaf,\n                    char* equed, double* s, double* b, lapack_int* ldb,\n                    double* x, lapack_int* ldx, double* rcond, double* ferr,\n                    double* berr, double* work, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_cposvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,\n                    lapack_complex_float* a, lapack_int* lda,\n                    lapack_complex_float* af, lapack_int* ldaf, char* equed,\n                    float* s, lapack_complex_float* b, lapack_int* ldb,\n                    lapack_complex_float* x, lapack_int* ldx, float* rcond,\n                    float* ferr, float* berr, lapack_complex_float* work,\n                    float* rwork, lapack_int *info );\nvoid LAPACK_zposvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,\n                    lapack_complex_double* a, lapack_int* lda,\n                    lapack_complex_double* af, lapack_int* ldaf, char* equed,\n                    double* s, lapack_complex_double* b, lapack_int* ldb,\n                    lapack_complex_double* x, lapack_int* ldx, double* rcond,\n                    double* ferr, double* berr, lapack_complex_double* work,\n                    double* rwork, lapack_int *info );\nvoid LAPACK_dposvxx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,\n                     double* a, lapack_int* lda, double* af, lapack_int* ldaf,\n                     char* equed, double* s, double* b, lapack_int* ldb,\n                     double* x, lapack_int* ldx, double* rcond, double* rpvgrw,\n                     double* berr, lapack_int* n_err_bnds,\n                     double* err_bnds_norm, double* err_bnds_comp,\n                     lapack_int* nparams, double* params, double* work,\n                     lapack_int* iwork, lapack_int *info );\nvoid LAPACK_sposvxx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,\n                     float* a, lapack_int* lda, float* af, lapack_int* ldaf,\n                     char* equed, float* s, float* b, lapack_int* ldb, float* x,\n                     lapack_int* ldx, float* rcond, float* rpvgrw, float* berr,\n                     lapack_int* n_err_bnds, float* err_bnds_norm,\n                     float* err_bnds_comp, lapack_int* nparams, float* params,\n                     float* work, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_zposvxx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,\n                     lapack_complex_double* a, lapack_int* lda,\n                     lapack_complex_double* af, lapack_int* ldaf, char* equed,\n                     double* s, lapack_complex_double* b, lapack_int* ldb,\n                     lapack_complex_double* x, lapack_int* ldx, double* rcond,\n                     double* rpvgrw, double* berr, lapack_int* n_err_bnds,\n                     double* err_bnds_norm, double* err_bnds_comp,\n                     lapack_int* nparams, double* params,\n                     lapack_complex_double* work, double* rwork,\n                     lapack_int *info );\nvoid LAPACK_cposvxx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,\n                     lapack_complex_float* a, lapack_int* lda,\n                     lapack_complex_float* af, lapack_int* ldaf, char* equed,\n                     float* s, lapack_complex_float* b, lapack_int* ldb,\n                     lapack_complex_float* x, lapack_int* ldx, float* rcond,\n                     float* rpvgrw, float* berr, lapack_int* n_err_bnds,\n                     float* err_bnds_norm, float* err_bnds_comp,\n                     lapack_int* nparams, float* params,\n                     lapack_complex_float* work, float* rwork,\n                     lapack_int *info );\nvoid LAPACK_sppsv( char* uplo, lapack_int* n, lapack_int* nrhs, float* ap,\n                   float* b, lapack_int* ldb, lapack_int *info );\nvoid LAPACK_dppsv( char* uplo, lapack_int* n, lapack_int* nrhs, double* ap,\n                   double* b, lapack_int* ldb, lapack_int *info );\nvoid LAPACK_cppsv( char* uplo, lapack_int* n, lapack_int* nrhs,\n                   lapack_complex_float* ap, lapack_complex_float* b,\n                   lapack_int* ldb, lapack_int *info );\nvoid LAPACK_zppsv( char* uplo, lapack_int* n, lapack_int* nrhs,\n                   lapack_complex_double* ap, lapack_complex_double* b,\n                   lapack_int* ldb, lapack_int *info );\nvoid LAPACK_sppsvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,\n                    float* ap, float* afp, char* equed, float* s, float* b,\n                    lapack_int* ldb, float* x, lapack_int* ldx, float* rcond,\n                    float* ferr, float* berr, float* work, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_dppsvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,\n                    double* ap, double* afp, char* equed, double* s, double* b,\n                    lapack_int* ldb, double* x, lapack_int* ldx, double* rcond,\n                    double* ferr, double* berr, double* work, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_cppsvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,\n                    lapack_complex_float* ap, lapack_complex_float* afp,\n                    char* equed, float* s, lapack_complex_float* b,\n                    lapack_int* ldb, lapack_complex_float* x, lapack_int* ldx,\n                    float* rcond, float* ferr, float* berr,\n                    lapack_complex_float* work, float* rwork,\n                    lapack_int *info );\nvoid LAPACK_zppsvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,\n                    lapack_complex_double* ap, lapack_complex_double* afp,\n                    char* equed, double* s, lapack_complex_double* b,\n                    lapack_int* ldb, lapack_complex_double* x, lapack_int* ldx,\n                    double* rcond, double* ferr, double* berr,\n                    lapack_complex_double* work, double* rwork,\n                    lapack_int *info );\nvoid LAPACK_spbsv( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs,\n                   float* ab, lapack_int* ldab, float* b, lapack_int* ldb,\n                   lapack_int *info );\nvoid LAPACK_dpbsv( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs,\n                   double* ab, lapack_int* ldab, double* b, lapack_int* ldb,\n                   lapack_int *info );\nvoid LAPACK_cpbsv( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs,\n                   lapack_complex_float* ab, lapack_int* ldab,\n                   lapack_complex_float* b, lapack_int* ldb, lapack_int *info );\nvoid LAPACK_zpbsv( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs,\n                   lapack_complex_double* ab, lapack_int* ldab,\n                   lapack_complex_double* b, lapack_int* ldb,\n                   lapack_int *info );\nvoid LAPACK_spbsvx( char* fact, char* uplo, lapack_int* n, lapack_int* kd,\n                    lapack_int* nrhs, float* ab, lapack_int* ldab, float* afb,\n                    lapack_int* ldafb, char* equed, float* s, float* b,\n                    lapack_int* ldb, float* x, lapack_int* ldx, float* rcond,\n                    float* ferr, float* berr, float* work, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_dpbsvx( char* fact, char* uplo, lapack_int* n, lapack_int* kd,\n                    lapack_int* nrhs, double* ab, lapack_int* ldab, double* afb,\n                    lapack_int* ldafb, char* equed, double* s, double* b,\n                    lapack_int* ldb, double* x, lapack_int* ldx, double* rcond,\n                    double* ferr, double* berr, double* work, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_cpbsvx( char* fact, char* uplo, lapack_int* n, lapack_int* kd,\n                    lapack_int* nrhs, lapack_complex_float* ab,\n                    lapack_int* ldab, lapack_complex_float* afb,\n                    lapack_int* ldafb, char* equed, float* s,\n                    lapack_complex_float* b, lapack_int* ldb,\n                    lapack_complex_float* x, lapack_int* ldx, float* rcond,\n                    float* ferr, float* berr, lapack_complex_float* work,\n                    float* rwork, lapack_int *info );\nvoid LAPACK_zpbsvx( char* fact, char* uplo, lapack_int* n, lapack_int* kd,\n                    lapack_int* nrhs, lapack_complex_double* ab,\n                    lapack_int* ldab, lapack_complex_double* afb,\n                    lapack_int* ldafb, char* equed, double* s,\n                    lapack_complex_double* b, lapack_int* ldb,\n                    lapack_complex_double* x, lapack_int* ldx, double* rcond,\n                    double* ferr, double* berr, lapack_complex_double* work,\n                    double* rwork, lapack_int *info );\nvoid LAPACK_sptsv( lapack_int* n, lapack_int* nrhs, float* d, float* e,\n                   float* b, lapack_int* ldb, lapack_int *info );\nvoid LAPACK_dptsv( lapack_int* n, lapack_int* nrhs, double* d, double* e,\n                   double* b, lapack_int* ldb, lapack_int *info );\nvoid LAPACK_cptsv( lapack_int* n, lapack_int* nrhs, float* d,\n                   lapack_complex_float* e, lapack_complex_float* b,\n                   lapack_int* ldb, lapack_int *info );\nvoid LAPACK_zptsv( lapack_int* n, lapack_int* nrhs, double* d,\n                   lapack_complex_double* e, lapack_complex_double* b,\n                   lapack_int* ldb, lapack_int *info );\nvoid LAPACK_sptsvx( char* fact, lapack_int* n, lapack_int* nrhs, const float* d,\n                    const float* e, float* df, float* ef, const float* b,\n                    lapack_int* ldb, float* x, lapack_int* ldx, float* rcond,\n                    float* ferr, float* berr, float* work, lapack_int *info );\nvoid LAPACK_dptsvx( char* fact, lapack_int* n, lapack_int* nrhs,\n                    const double* d, const double* e, double* df, double* ef,\n                    const double* b, lapack_int* ldb, double* x,\n                    lapack_int* ldx, double* rcond, double* ferr, double* berr,\n                    double* work, lapack_int *info );\nvoid LAPACK_cptsvx( char* fact, lapack_int* n, lapack_int* nrhs, const float* d,\n                    const lapack_complex_float* e, float* df,\n                    lapack_complex_float* ef, const lapack_complex_float* b,\n                    lapack_int* ldb, lapack_complex_float* x, lapack_int* ldx,\n                    float* rcond, float* ferr, float* berr,\n                    lapack_complex_float* work, float* rwork,\n                    lapack_int *info );\nvoid LAPACK_zptsvx( char* fact, lapack_int* n, lapack_int* nrhs,\n                    const double* d, const lapack_complex_double* e, double* df,\n                    lapack_complex_double* ef, const lapack_complex_double* b,\n                    lapack_int* ldb, lapack_complex_double* x, lapack_int* ldx,\n                    double* rcond, double* ferr, double* berr,\n                    lapack_complex_double* work, double* rwork,\n                    lapack_int *info );\nvoid LAPACK_ssysv( char* uplo, lapack_int* n, lapack_int* nrhs, float* a,\n                   lapack_int* lda, lapack_int* ipiv, float* b, lapack_int* ldb,\n                   float* work, lapack_int* lwork, lapack_int *info );\nvoid LAPACK_dsysv( char* uplo, lapack_int* n, lapack_int* nrhs, double* a,\n                   lapack_int* lda, lapack_int* ipiv, double* b,\n                   lapack_int* ldb, double* work, lapack_int* lwork,\n                   lapack_int *info );\nvoid LAPACK_csysv( char* uplo, lapack_int* n, lapack_int* nrhs,\n                   lapack_complex_float* a, lapack_int* lda, lapack_int* ipiv,\n                   lapack_complex_float* b, lapack_int* ldb,\n                   lapack_complex_float* work, lapack_int* lwork,\n                   lapack_int *info );\nvoid LAPACK_zsysv( char* uplo, lapack_int* n, lapack_int* nrhs,\n                   lapack_complex_double* a, lapack_int* lda, lapack_int* ipiv,\n                   lapack_complex_double* b, lapack_int* ldb,\n                   lapack_complex_double* work, lapack_int* lwork,\n                   lapack_int *info );\nvoid LAPACK_ssysvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const float* a, lapack_int* lda, float* af,\n                    lapack_int* ldaf, lapack_int* ipiv, const float* b,\n                    lapack_int* ldb, float* x, lapack_int* ldx, float* rcond,\n                    float* ferr, float* berr, float* work, lapack_int* lwork,\n                    lapack_int* iwork, lapack_int *info );\nvoid LAPACK_dsysvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const double* a, lapack_int* lda, double* af,\n                    lapack_int* ldaf, lapack_int* ipiv, const double* b,\n                    lapack_int* ldb, double* x, lapack_int* ldx, double* rcond,\n                    double* ferr, double* berr, double* work, lapack_int* lwork,\n                    lapack_int* iwork, lapack_int *info );\nvoid LAPACK_csysvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_float* a, lapack_int* lda,\n                    lapack_complex_float* af, lapack_int* ldaf,\n                    lapack_int* ipiv, const lapack_complex_float* b,\n                    lapack_int* ldb, lapack_complex_float* x, lapack_int* ldx,\n                    float* rcond, float* ferr, float* berr,\n                    lapack_complex_float* work, lapack_int* lwork, float* rwork,\n                    lapack_int *info );\nvoid LAPACK_zsysvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_double* a, lapack_int* lda,\n                    lapack_complex_double* af, lapack_int* ldaf,\n                    lapack_int* ipiv, const lapack_complex_double* b,\n                    lapack_int* ldb, lapack_complex_double* x, lapack_int* ldx,\n                    double* rcond, double* ferr, double* berr,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    double* rwork, lapack_int *info );\nvoid LAPACK_dsysvxx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,\n                     double* a, lapack_int* lda, double* af, lapack_int* ldaf,\n                     lapack_int* ipiv, char* equed, double* s, double* b,\n                     lapack_int* ldb, double* x, lapack_int* ldx, double* rcond,\n                     double* rpvgrw, double* berr, lapack_int* n_err_bnds,\n                     double* err_bnds_norm, double* err_bnds_comp,\n                     lapack_int* nparams, double* params, double* work,\n                     lapack_int* iwork, lapack_int *info );\nvoid LAPACK_ssysvxx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,\n                     float* a, lapack_int* lda, float* af, lapack_int* ldaf,\n                     lapack_int* ipiv, char* equed, float* s, float* b,\n                     lapack_int* ldb, float* x, lapack_int* ldx, float* rcond,\n                     float* rpvgrw, float* berr, lapack_int* n_err_bnds,\n                     float* err_bnds_norm, float* err_bnds_comp,\n                     lapack_int* nparams, float* params, float* work,\n                     lapack_int* iwork, lapack_int *info );\nvoid LAPACK_zsysvxx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,\n                     lapack_complex_double* a, lapack_int* lda,\n                     lapack_complex_double* af, lapack_int* ldaf,\n                     lapack_int* ipiv, char* equed, double* s,\n                     lapack_complex_double* b, lapack_int* ldb,\n                     lapack_complex_double* x, lapack_int* ldx, double* rcond,\n                     double* rpvgrw, double* berr, lapack_int* n_err_bnds,\n                     double* err_bnds_norm, double* err_bnds_comp,\n                     lapack_int* nparams, double* params,\n                     lapack_complex_double* work, double* rwork,\n                     lapack_int *info );\nvoid LAPACK_csysvxx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,\n                     lapack_complex_float* a, lapack_int* lda,\n                     lapack_complex_float* af, lapack_int* ldaf,\n                     lapack_int* ipiv, char* equed, float* s,\n                     lapack_complex_float* b, lapack_int* ldb,\n                     lapack_complex_float* x, lapack_int* ldx, float* rcond,\n                     float* rpvgrw, float* berr, lapack_int* n_err_bnds,\n                     float* err_bnds_norm, float* err_bnds_comp,\n                     lapack_int* nparams, float* params,\n                     lapack_complex_float* work, float* rwork,\n                     lapack_int *info );\nvoid LAPACK_chesv( char* uplo, lapack_int* n, lapack_int* nrhs,\n                   lapack_complex_float* a, lapack_int* lda, lapack_int* ipiv,\n                   lapack_complex_float* b, lapack_int* ldb,\n                   lapack_complex_float* work, lapack_int* lwork,\n                   lapack_int *info );\nvoid LAPACK_zhesv( char* uplo, lapack_int* n, lapack_int* nrhs,\n                   lapack_complex_double* a, lapack_int* lda, lapack_int* ipiv,\n                   lapack_complex_double* b, lapack_int* ldb,\n                   lapack_complex_double* work, lapack_int* lwork,\n                   lapack_int *info );\nvoid LAPACK_chesvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_float* a, lapack_int* lda,\n                    lapack_complex_float* af, lapack_int* ldaf,\n                    lapack_int* ipiv, const lapack_complex_float* b,\n                    lapack_int* ldb, lapack_complex_float* x, lapack_int* ldx,\n                    float* rcond, float* ferr, float* berr,\n                    lapack_complex_float* work, lapack_int* lwork, float* rwork,\n                    lapack_int *info );\nvoid LAPACK_zhesvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_double* a, lapack_int* lda,\n                    lapack_complex_double* af, lapack_int* ldaf,\n                    lapack_int* ipiv, const lapack_complex_double* b,\n                    lapack_int* ldb, lapack_complex_double* x, lapack_int* ldx,\n                    double* rcond, double* ferr, double* berr,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    double* rwork, lapack_int *info );\nvoid LAPACK_zhesvxx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,\n                     lapack_complex_double* a, lapack_int* lda,\n                     lapack_complex_double* af, lapack_int* ldaf,\n                     lapack_int* ipiv, char* equed, double* s,\n                     lapack_complex_double* b, lapack_int* ldb,\n                     lapack_complex_double* x, lapack_int* ldx, double* rcond,\n                     double* rpvgrw, double* berr, lapack_int* n_err_bnds,\n                     double* err_bnds_norm, double* err_bnds_comp,\n                     lapack_int* nparams, double* params,\n                     lapack_complex_double* work, double* rwork,\n                     lapack_int *info );\nvoid LAPACK_chesvxx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,\n                     lapack_complex_float* a, lapack_int* lda,\n                     lapack_complex_float* af, lapack_int* ldaf,\n                     lapack_int* ipiv, char* equed, float* s,\n                     lapack_complex_float* b, lapack_int* ldb,\n                     lapack_complex_float* x, lapack_int* ldx, float* rcond,\n                     float* rpvgrw, float* berr, lapack_int* n_err_bnds,\n                     float* err_bnds_norm, float* err_bnds_comp,\n                     lapack_int* nparams, float* params,\n                     lapack_complex_float* work, float* rwork,\n                     lapack_int *info );\nvoid LAPACK_sspsv( char* uplo, lapack_int* n, lapack_int* nrhs, float* ap,\n                   lapack_int* ipiv, float* b, lapack_int* ldb,\n                   lapack_int *info );\nvoid LAPACK_dspsv( char* uplo, lapack_int* n, lapack_int* nrhs, double* ap,\n                   lapack_int* ipiv, double* b, lapack_int* ldb,\n                   lapack_int *info );\nvoid LAPACK_cspsv( char* uplo, lapack_int* n, lapack_int* nrhs,\n                   lapack_complex_float* ap, lapack_int* ipiv,\n                   lapack_complex_float* b, lapack_int* ldb, lapack_int *info );\nvoid LAPACK_zspsv( char* uplo, lapack_int* n, lapack_int* nrhs,\n                   lapack_complex_double* ap, lapack_int* ipiv,\n                   lapack_complex_double* b, lapack_int* ldb,\n                   lapack_int *info );\nvoid LAPACK_sspsvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const float* ap, float* afp, lapack_int* ipiv,\n                    const float* b, lapack_int* ldb, float* x, lapack_int* ldx,\n                    float* rcond, float* ferr, float* berr, float* work,\n                    lapack_int* iwork, lapack_int *info );\nvoid LAPACK_dspsvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const double* ap, double* afp, lapack_int* ipiv,\n                    const double* b, lapack_int* ldb, double* x,\n                    lapack_int* ldx, double* rcond, double* ferr, double* berr,\n                    double* work, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_cspsvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_float* ap, lapack_complex_float* afp,\n                    lapack_int* ipiv, const lapack_complex_float* b,\n                    lapack_int* ldb, lapack_complex_float* x, lapack_int* ldx,\n                    float* rcond, float* ferr, float* berr,\n                    lapack_complex_float* work, float* rwork,\n                    lapack_int *info );\nvoid LAPACK_zspsvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_double* ap, lapack_complex_double* afp,\n                    lapack_int* ipiv, const lapack_complex_double* b,\n                    lapack_int* ldb, lapack_complex_double* x, lapack_int* ldx,\n                    double* rcond, double* ferr, double* berr,\n                    lapack_complex_double* work, double* rwork,\n                    lapack_int *info );\nvoid LAPACK_chpsv( char* uplo, lapack_int* n, lapack_int* nrhs,\n                   lapack_complex_float* ap, lapack_int* ipiv,\n                   lapack_complex_float* b, lapack_int* ldb, lapack_int *info );\nvoid LAPACK_zhpsv( char* uplo, lapack_int* n, lapack_int* nrhs,\n                   lapack_complex_double* ap, lapack_int* ipiv,\n                   lapack_complex_double* b, lapack_int* ldb,\n                   lapack_int *info );\nvoid LAPACK_chpsvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_float* ap, lapack_complex_float* afp,\n                    lapack_int* ipiv, const lapack_complex_float* b,\n                    lapack_int* ldb, lapack_complex_float* x, lapack_int* ldx,\n                    float* rcond, float* ferr, float* berr,\n                    lapack_complex_float* work, float* rwork,\n                    lapack_int *info );\nvoid LAPACK_zhpsvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,\n                    const lapack_complex_double* ap, lapack_complex_double* afp,\n                    lapack_int* ipiv, const lapack_complex_double* b,\n                    lapack_int* ldb, lapack_complex_double* x, lapack_int* ldx,\n                    double* rcond, double* ferr, double* berr,\n                    lapack_complex_double* work, double* rwork,\n                    lapack_int *info );\nvoid LAPACK_sgeqrf( lapack_int* m, lapack_int* n, float* a, lapack_int* lda,\n                    float* tau, float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_dgeqrf( lapack_int* m, lapack_int* n, double* a, lapack_int* lda,\n                    double* tau, double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_cgeqrf( lapack_int* m, lapack_int* n, lapack_complex_float* a,\n                    lapack_int* lda, lapack_complex_float* tau,\n                    lapack_complex_float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_zgeqrf( lapack_int* m, lapack_int* n, lapack_complex_double* a,\n                    lapack_int* lda, lapack_complex_double* tau,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_sgeqpf( lapack_int* m, lapack_int* n, float* a, lapack_int* lda,\n                    lapack_int* jpvt, float* tau, float* work,\n                    lapack_int *info );\nvoid LAPACK_dgeqpf( lapack_int* m, lapack_int* n, double* a, lapack_int* lda,\n                    lapack_int* jpvt, double* tau, double* work,\n                    lapack_int *info );\nvoid LAPACK_cgeqpf( lapack_int* m, lapack_int* n, lapack_complex_float* a,\n                    lapack_int* lda, lapack_int* jpvt,\n                    lapack_complex_float* tau, lapack_complex_float* work,\n                    float* rwork, lapack_int *info );\nvoid LAPACK_zgeqpf( lapack_int* m, lapack_int* n, lapack_complex_double* a,\n                    lapack_int* lda, lapack_int* jpvt,\n                    lapack_complex_double* tau, lapack_complex_double* work,\n                    double* rwork, lapack_int *info );\nvoid LAPACK_sgeqp3( lapack_int* m, lapack_int* n, float* a, lapack_int* lda,\n                    lapack_int* jpvt, float* tau, float* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_dgeqp3( lapack_int* m, lapack_int* n, double* a, lapack_int* lda,\n                    lapack_int* jpvt, double* tau, double* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_cgeqp3( lapack_int* m, lapack_int* n, lapack_complex_float* a,\n                    lapack_int* lda, lapack_int* jpvt,\n                    lapack_complex_float* tau, lapack_complex_float* work,\n                    lapack_int* lwork, float* rwork, lapack_int *info );\nvoid LAPACK_zgeqp3( lapack_int* m, lapack_int* n, lapack_complex_double* a,\n                    lapack_int* lda, lapack_int* jpvt,\n                    lapack_complex_double* tau, lapack_complex_double* work,\n                    lapack_int* lwork, double* rwork, lapack_int *info );\nvoid LAPACK_sorgqr( lapack_int* m, lapack_int* n, lapack_int* k, float* a,\n                    lapack_int* lda, const float* tau, float* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_dorgqr( lapack_int* m, lapack_int* n, lapack_int* k, double* a,\n                    lapack_int* lda, const double* tau, double* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_sormqr( char* side, char* trans, lapack_int* m, lapack_int* n,\n                    lapack_int* k, const float* a, lapack_int* lda,\n                    const float* tau, float* c, lapack_int* ldc, float* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_dormqr( char* side, char* trans, lapack_int* m, lapack_int* n,\n                    lapack_int* k, const double* a, lapack_int* lda,\n                    const double* tau, double* c, lapack_int* ldc, double* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_cungqr( lapack_int* m, lapack_int* n, lapack_int* k,\n                    lapack_complex_float* a, lapack_int* lda,\n                    const lapack_complex_float* tau, lapack_complex_float* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_zungqr( lapack_int* m, lapack_int* n, lapack_int* k,\n                    lapack_complex_double* a, lapack_int* lda,\n                    const lapack_complex_double* tau,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_cunmqr( char* side, char* trans, lapack_int* m, lapack_int* n,\n                    lapack_int* k, const lapack_complex_float* a,\n                    lapack_int* lda, const lapack_complex_float* tau,\n                    lapack_complex_float* c, lapack_int* ldc,\n                    lapack_complex_float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_zunmqr( char* side, char* trans, lapack_int* m, lapack_int* n,\n                    lapack_int* k, const lapack_complex_double* a,\n                    lapack_int* lda, const lapack_complex_double* tau,\n                    lapack_complex_double* c, lapack_int* ldc,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_sgelqf( lapack_int* m, lapack_int* n, float* a, lapack_int* lda,\n                    float* tau, float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_dgelqf( lapack_int* m, lapack_int* n, double* a, lapack_int* lda,\n                    double* tau, double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_cgelqf( lapack_int* m, lapack_int* n, lapack_complex_float* a,\n                    lapack_int* lda, lapack_complex_float* tau,\n                    lapack_complex_float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_zgelqf( lapack_int* m, lapack_int* n, lapack_complex_double* a,\n                    lapack_int* lda, lapack_complex_double* tau,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_sorglq( lapack_int* m, lapack_int* n, lapack_int* k, float* a,\n                    lapack_int* lda, const float* tau, float* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_dorglq( lapack_int* m, lapack_int* n, lapack_int* k, double* a,\n                    lapack_int* lda, const double* tau, double* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_sormlq( char* side, char* trans, lapack_int* m, lapack_int* n,\n                    lapack_int* k, const float* a, lapack_int* lda,\n                    const float* tau, float* c, lapack_int* ldc, float* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_dormlq( char* side, char* trans, lapack_int* m, lapack_int* n,\n                    lapack_int* k, const double* a, lapack_int* lda,\n                    const double* tau, double* c, lapack_int* ldc, double* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_cunglq( lapack_int* m, lapack_int* n, lapack_int* k,\n                    lapack_complex_float* a, lapack_int* lda,\n                    const lapack_complex_float* tau, lapack_complex_float* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_zunglq( lapack_int* m, lapack_int* n, lapack_int* k,\n                    lapack_complex_double* a, lapack_int* lda,\n                    const lapack_complex_double* tau,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_cunmlq( char* side, char* trans, lapack_int* m, lapack_int* n,\n                    lapack_int* k, const lapack_complex_float* a,\n                    lapack_int* lda, const lapack_complex_float* tau,\n                    lapack_complex_float* c, lapack_int* ldc,\n                    lapack_complex_float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_zunmlq( char* side, char* trans, lapack_int* m, lapack_int* n,\n                    lapack_int* k, const lapack_complex_double* a,\n                    lapack_int* lda, const lapack_complex_double* tau,\n                    lapack_complex_double* c, lapack_int* ldc,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_sgeqlf( lapack_int* m, lapack_int* n, float* a, lapack_int* lda,\n                    float* tau, float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_dgeqlf( lapack_int* m, lapack_int* n, double* a, lapack_int* lda,\n                    double* tau, double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_cgeqlf( lapack_int* m, lapack_int* n, lapack_complex_float* a,\n                    lapack_int* lda, lapack_complex_float* tau,\n                    lapack_complex_float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_zgeqlf( lapack_int* m, lapack_int* n, lapack_complex_double* a,\n                    lapack_int* lda, lapack_complex_double* tau,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_sorgql( lapack_int* m, lapack_int* n, lapack_int* k, float* a,\n                    lapack_int* lda, const float* tau, float* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_dorgql( lapack_int* m, lapack_int* n, lapack_int* k, double* a,\n                    lapack_int* lda, const double* tau, double* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_cungql( lapack_int* m, lapack_int* n, lapack_int* k,\n                    lapack_complex_float* a, lapack_int* lda,\n                    const lapack_complex_float* tau, lapack_complex_float* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_zungql( lapack_int* m, lapack_int* n, lapack_int* k,\n                    lapack_complex_double* a, lapack_int* lda,\n                    const lapack_complex_double* tau,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_sormql( char* side, char* trans, lapack_int* m, lapack_int* n,\n                    lapack_int* k, const float* a, lapack_int* lda,\n                    const float* tau, float* c, lapack_int* ldc, float* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_dormql( char* side, char* trans, lapack_int* m, lapack_int* n,\n                    lapack_int* k, const double* a, lapack_int* lda,\n                    const double* tau, double* c, lapack_int* ldc, double* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_cunmql( char* side, char* trans, lapack_int* m, lapack_int* n,\n                    lapack_int* k, const lapack_complex_float* a,\n                    lapack_int* lda, const lapack_complex_float* tau,\n                    lapack_complex_float* c, lapack_int* ldc,\n                    lapack_complex_float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_zunmql( char* side, char* trans, lapack_int* m, lapack_int* n,\n                    lapack_int* k, const lapack_complex_double* a,\n                    lapack_int* lda, const lapack_complex_double* tau,\n                    lapack_complex_double* c, lapack_int* ldc,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_sgerqf( lapack_int* m, lapack_int* n, float* a, lapack_int* lda,\n                    float* tau, float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_dgerqf( lapack_int* m, lapack_int* n, double* a, lapack_int* lda,\n                    double* tau, double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_cgerqf( lapack_int* m, lapack_int* n, lapack_complex_float* a,\n                    lapack_int* lda, lapack_complex_float* tau,\n                    lapack_complex_float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_zgerqf( lapack_int* m, lapack_int* n, lapack_complex_double* a,\n                    lapack_int* lda, lapack_complex_double* tau,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_sorgrq( lapack_int* m, lapack_int* n, lapack_int* k, float* a,\n                    lapack_int* lda, const float* tau, float* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_dorgrq( lapack_int* m, lapack_int* n, lapack_int* k, double* a,\n                    lapack_int* lda, const double* tau, double* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_cungrq( lapack_int* m, lapack_int* n, lapack_int* k,\n                    lapack_complex_float* a, lapack_int* lda,\n                    const lapack_complex_float* tau, lapack_complex_float* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_zungrq( lapack_int* m, lapack_int* n, lapack_int* k,\n                    lapack_complex_double* a, lapack_int* lda,\n                    const lapack_complex_double* tau,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_sormrq( char* side, char* trans, lapack_int* m, lapack_int* n,\n                    lapack_int* k, const float* a, lapack_int* lda,\n                    const float* tau, float* c, lapack_int* ldc, float* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_dormrq( char* side, char* trans, lapack_int* m, lapack_int* n,\n                    lapack_int* k, const double* a, lapack_int* lda,\n                    const double* tau, double* c, lapack_int* ldc, double* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_cunmrq( char* side, char* trans, lapack_int* m, lapack_int* n,\n                    lapack_int* k, const lapack_complex_float* a,\n                    lapack_int* lda, const lapack_complex_float* tau,\n                    lapack_complex_float* c, lapack_int* ldc,\n                    lapack_complex_float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_zunmrq( char* side, char* trans, lapack_int* m, lapack_int* n,\n                    lapack_int* k, const lapack_complex_double* a,\n                    lapack_int* lda, const lapack_complex_double* tau,\n                    lapack_complex_double* c, lapack_int* ldc,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_stzrzf( lapack_int* m, lapack_int* n, float* a, lapack_int* lda,\n                    float* tau, float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_dtzrzf( lapack_int* m, lapack_int* n, double* a, lapack_int* lda,\n                    double* tau, double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_ctzrzf( lapack_int* m, lapack_int* n, lapack_complex_float* a,\n                    lapack_int* lda, lapack_complex_float* tau,\n                    lapack_complex_float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_ztzrzf( lapack_int* m, lapack_int* n, lapack_complex_double* a,\n                    lapack_int* lda, lapack_complex_double* tau,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_sormrz( char* side, char* trans, lapack_int* m, lapack_int* n,\n                    lapack_int* k, lapack_int* l, const float* a,\n                    lapack_int* lda, const float* tau, float* c,\n                    lapack_int* ldc, float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_dormrz( char* side, char* trans, lapack_int* m, lapack_int* n,\n                    lapack_int* k, lapack_int* l, const double* a,\n                    lapack_int* lda, const double* tau, double* c,\n                    lapack_int* ldc, double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_cunmrz( char* side, char* trans, lapack_int* m, lapack_int* n,\n                    lapack_int* k, lapack_int* l, const lapack_complex_float* a,\n                    lapack_int* lda, const lapack_complex_float* tau,\n                    lapack_complex_float* c, lapack_int* ldc,\n                    lapack_complex_float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_zunmrz( char* side, char* trans, lapack_int* m, lapack_int* n,\n                    lapack_int* k, lapack_int* l,\n                    const lapack_complex_double* a, lapack_int* lda,\n                    const lapack_complex_double* tau, lapack_complex_double* c,\n                    lapack_int* ldc, lapack_complex_double* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_sggqrf( lapack_int* n, lapack_int* m, lapack_int* p, float* a,\n                    lapack_int* lda, float* taua, float* b, lapack_int* ldb,\n                    float* taub, float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_dggqrf( lapack_int* n, lapack_int* m, lapack_int* p, double* a,\n                    lapack_int* lda, double* taua, double* b, lapack_int* ldb,\n                    double* taub, double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_cggqrf( lapack_int* n, lapack_int* m, lapack_int* p,\n                    lapack_complex_float* a, lapack_int* lda,\n                    lapack_complex_float* taua, lapack_complex_float* b,\n                    lapack_int* ldb, lapack_complex_float* taub,\n                    lapack_complex_float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_zggqrf( lapack_int* n, lapack_int* m, lapack_int* p,\n                    lapack_complex_double* a, lapack_int* lda,\n                    lapack_complex_double* taua, lapack_complex_double* b,\n                    lapack_int* ldb, lapack_complex_double* taub,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_sggrqf( lapack_int* m, lapack_int* p, lapack_int* n, float* a,\n                    lapack_int* lda, float* taua, float* b, lapack_int* ldb,\n                    float* taub, float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_dggrqf( lapack_int* m, lapack_int* p, lapack_int* n, double* a,\n                    lapack_int* lda, double* taua, double* b, lapack_int* ldb,\n                    double* taub, double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_cggrqf( lapack_int* m, lapack_int* p, lapack_int* n,\n                    lapack_complex_float* a, lapack_int* lda,\n                    lapack_complex_float* taua, lapack_complex_float* b,\n                    lapack_int* ldb, lapack_complex_float* taub,\n                    lapack_complex_float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_zggrqf( lapack_int* m, lapack_int* p, lapack_int* n,\n                    lapack_complex_double* a, lapack_int* lda,\n                    lapack_complex_double* taua, lapack_complex_double* b,\n                    lapack_int* ldb, lapack_complex_double* taub,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_sgebrd( lapack_int* m, lapack_int* n, float* a, lapack_int* lda,\n                    float* d, float* e, float* tauq, float* taup, float* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_dgebrd( lapack_int* m, lapack_int* n, double* a, lapack_int* lda,\n                    double* d, double* e, double* tauq, double* taup,\n                    double* work, lapack_int* lwork, lapack_int *info );\nvoid LAPACK_cgebrd( lapack_int* m, lapack_int* n, lapack_complex_float* a,\n                    lapack_int* lda, float* d, float* e,\n                    lapack_complex_float* tauq, lapack_complex_float* taup,\n                    lapack_complex_float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_zgebrd( lapack_int* m, lapack_int* n, lapack_complex_double* a,\n                    lapack_int* lda, double* d, double* e,\n                    lapack_complex_double* tauq, lapack_complex_double* taup,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_sgbbrd( char* vect, lapack_int* m, lapack_int* n, lapack_int* ncc,\n                    lapack_int* kl, lapack_int* ku, float* ab, lapack_int* ldab,\n                    float* d, float* e, float* q, lapack_int* ldq, float* pt,\n                    lapack_int* ldpt, float* c, lapack_int* ldc, float* work,\n                    lapack_int *info );\nvoid LAPACK_dgbbrd( char* vect, lapack_int* m, lapack_int* n, lapack_int* ncc,\n                    lapack_int* kl, lapack_int* ku, double* ab,\n                    lapack_int* ldab, double* d, double* e, double* q,\n                    lapack_int* ldq, double* pt, lapack_int* ldpt, double* c,\n                    lapack_int* ldc, double* work, lapack_int *info );\nvoid LAPACK_cgbbrd( char* vect, lapack_int* m, lapack_int* n, lapack_int* ncc,\n                    lapack_int* kl, lapack_int* ku, lapack_complex_float* ab,\n                    lapack_int* ldab, float* d, float* e,\n                    lapack_complex_float* q, lapack_int* ldq,\n                    lapack_complex_float* pt, lapack_int* ldpt,\n                    lapack_complex_float* c, lapack_int* ldc,\n                    lapack_complex_float* work, float* rwork,\n                    lapack_int *info );\nvoid LAPACK_zgbbrd( char* vect, lapack_int* m, lapack_int* n, lapack_int* ncc,\n                    lapack_int* kl, lapack_int* ku, lapack_complex_double* ab,\n                    lapack_int* ldab, double* d, double* e,\n                    lapack_complex_double* q, lapack_int* ldq,\n                    lapack_complex_double* pt, lapack_int* ldpt,\n                    lapack_complex_double* c, lapack_int* ldc,\n                    lapack_complex_double* work, double* rwork,\n                    lapack_int *info );\nvoid LAPACK_sorgbr( char* vect, lapack_int* m, lapack_int* n, lapack_int* k,\n                    float* a, lapack_int* lda, const float* tau, float* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_dorgbr( char* vect, lapack_int* m, lapack_int* n, lapack_int* k,\n                    double* a, lapack_int* lda, const double* tau, double* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_sormbr( char* vect, char* side, char* trans, lapack_int* m,\n                    lapack_int* n, lapack_int* k, const float* a,\n                    lapack_int* lda, const float* tau, float* c,\n                    lapack_int* ldc, float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_dormbr( char* vect, char* side, char* trans, lapack_int* m,\n                    lapack_int* n, lapack_int* k, const double* a,\n                    lapack_int* lda, const double* tau, double* c,\n                    lapack_int* ldc, double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_cungbr( char* vect, lapack_int* m, lapack_int* n, lapack_int* k,\n                    lapack_complex_float* a, lapack_int* lda,\n                    const lapack_complex_float* tau, lapack_complex_float* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_zungbr( char* vect, lapack_int* m, lapack_int* n, lapack_int* k,\n                    lapack_complex_double* a, lapack_int* lda,\n                    const lapack_complex_double* tau,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_cunmbr( char* vect, char* side, char* trans, lapack_int* m,\n                    lapack_int* n, lapack_int* k, const lapack_complex_float* a,\n                    lapack_int* lda, const lapack_complex_float* tau,\n                    lapack_complex_float* c, lapack_int* ldc,\n                    lapack_complex_float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_zunmbr( char* vect, char* side, char* trans, lapack_int* m,\n                    lapack_int* n, lapack_int* k,\n                    const lapack_complex_double* a, lapack_int* lda,\n                    const lapack_complex_double* tau, lapack_complex_double* c,\n                    lapack_int* ldc, lapack_complex_double* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_sbdsqr( char* uplo, lapack_int* n, lapack_int* ncvt,\n                    lapack_int* nru, lapack_int* ncc, float* d, float* e,\n                    float* vt, lapack_int* ldvt, float* u, lapack_int* ldu,\n                    float* c, lapack_int* ldc, float* work, lapack_int *info );\nvoid LAPACK_dbdsqr( char* uplo, lapack_int* n, lapack_int* ncvt,\n                    lapack_int* nru, lapack_int* ncc, double* d, double* e,\n                    double* vt, lapack_int* ldvt, double* u, lapack_int* ldu,\n                    double* c, lapack_int* ldc, double* work,\n                    lapack_int *info );\nvoid LAPACK_cbdsqr( char* uplo, lapack_int* n, lapack_int* ncvt,\n                    lapack_int* nru, lapack_int* ncc, float* d, float* e,\n                    lapack_complex_float* vt, lapack_int* ldvt,\n                    lapack_complex_float* u, lapack_int* ldu,\n                    lapack_complex_float* c, lapack_int* ldc, float* work,\n                    lapack_int *info );\nvoid LAPACK_zbdsqr( char* uplo, lapack_int* n, lapack_int* ncvt,\n                    lapack_int* nru, lapack_int* ncc, double* d, double* e,\n                    lapack_complex_double* vt, lapack_int* ldvt,\n                    lapack_complex_double* u, lapack_int* ldu,\n                    lapack_complex_double* c, lapack_int* ldc, double* work,\n                    lapack_int *info );\nvoid LAPACK_sbdsdc( char* uplo, char* compq, lapack_int* n, float* d, float* e,\n                    float* u, lapack_int* ldu, float* vt, lapack_int* ldvt,\n                    float* q, lapack_int* iq, float* work, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_dbdsdc( char* uplo, char* compq, lapack_int* n, double* d,\n                    double* e, double* u, lapack_int* ldu, double* vt,\n                    lapack_int* ldvt, double* q, lapack_int* iq, double* work,\n                    lapack_int* iwork, lapack_int *info );\nvoid LAPACK_ssytrd( char* uplo, lapack_int* n, float* a, lapack_int* lda,\n                    float* d, float* e, float* tau, float* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_dsytrd( char* uplo, lapack_int* n, double* a, lapack_int* lda,\n                    double* d, double* e, double* tau, double* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_sorgtr( char* uplo, lapack_int* n, float* a, lapack_int* lda,\n                    const float* tau, float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_dorgtr( char* uplo, lapack_int* n, double* a, lapack_int* lda,\n                    const double* tau, double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_sormtr( char* side, char* uplo, char* trans, lapack_int* m,\n                    lapack_int* n, const float* a, lapack_int* lda,\n                    const float* tau, float* c, lapack_int* ldc, float* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_dormtr( char* side, char* uplo, char* trans, lapack_int* m,\n                    lapack_int* n, const double* a, lapack_int* lda,\n                    const double* tau, double* c, lapack_int* ldc, double* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_chetrd( char* uplo, lapack_int* n, lapack_complex_float* a,\n                    lapack_int* lda, float* d, float* e,\n                    lapack_complex_float* tau, lapack_complex_float* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_zhetrd( char* uplo, lapack_int* n, lapack_complex_double* a,\n                    lapack_int* lda, double* d, double* e,\n                    lapack_complex_double* tau, lapack_complex_double* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_cungtr( char* uplo, lapack_int* n, lapack_complex_float* a,\n                    lapack_int* lda, const lapack_complex_float* tau,\n                    lapack_complex_float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_zungtr( char* uplo, lapack_int* n, lapack_complex_double* a,\n                    lapack_int* lda, const lapack_complex_double* tau,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_cunmtr( char* side, char* uplo, char* trans, lapack_int* m,\n                    lapack_int* n, const lapack_complex_float* a,\n                    lapack_int* lda, const lapack_complex_float* tau,\n                    lapack_complex_float* c, lapack_int* ldc,\n                    lapack_complex_float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_zunmtr( char* side, char* uplo, char* trans, lapack_int* m,\n                    lapack_int* n, const lapack_complex_double* a,\n                    lapack_int* lda, const lapack_complex_double* tau,\n                    lapack_complex_double* c, lapack_int* ldc,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_ssptrd( char* uplo, lapack_int* n, float* ap, float* d, float* e,\n                    float* tau, lapack_int *info );\nvoid LAPACK_dsptrd( char* uplo, lapack_int* n, double* ap, double* d, double* e,\n                    double* tau, lapack_int *info );\nvoid LAPACK_sopgtr( char* uplo, lapack_int* n, const float* ap,\n                    const float* tau, float* q, lapack_int* ldq, float* work,\n                    lapack_int *info );\nvoid LAPACK_dopgtr( char* uplo, lapack_int* n, const double* ap,\n                    const double* tau, double* q, lapack_int* ldq, double* work,\n                    lapack_int *info );\nvoid LAPACK_sopmtr( char* side, char* uplo, char* trans, lapack_int* m,\n                    lapack_int* n, const float* ap, const float* tau, float* c,\n                    lapack_int* ldc, float* work, lapack_int *info );\nvoid LAPACK_dopmtr( char* side, char* uplo, char* trans, lapack_int* m,\n                    lapack_int* n, const double* ap, const double* tau,\n                    double* c, lapack_int* ldc, double* work,\n                    lapack_int *info );\nvoid LAPACK_chptrd( char* uplo, lapack_int* n, lapack_complex_float* ap,\n                    float* d, float* e, lapack_complex_float* tau,\n                    lapack_int *info );\nvoid LAPACK_zhptrd( char* uplo, lapack_int* n, lapack_complex_double* ap,\n                    double* d, double* e, lapack_complex_double* tau,\n                    lapack_int *info );\nvoid LAPACK_cupgtr( char* uplo, lapack_int* n, const lapack_complex_float* ap,\n                    const lapack_complex_float* tau, lapack_complex_float* q,\n                    lapack_int* ldq, lapack_complex_float* work,\n                    lapack_int *info );\nvoid LAPACK_zupgtr( char* uplo, lapack_int* n, const lapack_complex_double* ap,\n                    const lapack_complex_double* tau, lapack_complex_double* q,\n                    lapack_int* ldq, lapack_complex_double* work,\n                    lapack_int *info );\nvoid LAPACK_cupmtr( char* side, char* uplo, char* trans, lapack_int* m,\n                    lapack_int* n, const lapack_complex_float* ap,\n                    const lapack_complex_float* tau, lapack_complex_float* c,\n                    lapack_int* ldc, lapack_complex_float* work,\n                    lapack_int *info );\nvoid LAPACK_zupmtr( char* side, char* uplo, char* trans, lapack_int* m,\n                    lapack_int* n, const lapack_complex_double* ap,\n                    const lapack_complex_double* tau, lapack_complex_double* c,\n                    lapack_int* ldc, lapack_complex_double* work,\n                    lapack_int *info );\nvoid LAPACK_ssbtrd( char* vect, char* uplo, lapack_int* n, lapack_int* kd,\n                    float* ab, lapack_int* ldab, float* d, float* e, float* q,\n                    lapack_int* ldq, float* work, lapack_int *info );\nvoid LAPACK_dsbtrd( char* vect, char* uplo, lapack_int* n, lapack_int* kd,\n                    double* ab, lapack_int* ldab, double* d, double* e,\n                    double* q, lapack_int* ldq, double* work,\n                    lapack_int *info );\nvoid LAPACK_chbtrd( char* vect, char* uplo, lapack_int* n, lapack_int* kd,\n                    lapack_complex_float* ab, lapack_int* ldab, float* d,\n                    float* e, lapack_complex_float* q, lapack_int* ldq,\n                    lapack_complex_float* work, lapack_int *info );\nvoid LAPACK_zhbtrd( char* vect, char* uplo, lapack_int* n, lapack_int* kd,\n                    lapack_complex_double* ab, lapack_int* ldab, double* d,\n                    double* e, lapack_complex_double* q, lapack_int* ldq,\n                    lapack_complex_double* work, lapack_int *info );\nvoid LAPACK_ssterf( lapack_int* n, float* d, float* e, lapack_int *info );\nvoid LAPACK_dsterf( lapack_int* n, double* d, double* e, lapack_int *info );\nvoid LAPACK_ssteqr( char* compz, lapack_int* n, float* d, float* e, float* z,\n                    lapack_int* ldz, float* work, lapack_int *info );\nvoid LAPACK_dsteqr( char* compz, lapack_int* n, double* d, double* e, double* z,\n                    lapack_int* ldz, double* work, lapack_int *info );\nvoid LAPACK_csteqr( char* compz, lapack_int* n, float* d, float* e,\n                    lapack_complex_float* z, lapack_int* ldz, float* work,\n                    lapack_int *info );\nvoid LAPACK_zsteqr( char* compz, lapack_int* n, double* d, double* e,\n                    lapack_complex_double* z, lapack_int* ldz, double* work,\n                    lapack_int *info );\nvoid LAPACK_sstemr( char* jobz, char* range, lapack_int* n, float* d, float* e,\n                    float* vl, float* vu, lapack_int* il, lapack_int* iu,\n                    lapack_int* m, float* w, float* z, lapack_int* ldz,\n                    lapack_int* nzc, lapack_int* isuppz, lapack_logical* tryrac,\n                    float* work, lapack_int* lwork, lapack_int* iwork,\n                    lapack_int* liwork, lapack_int *info );\nvoid LAPACK_dstemr( char* jobz, char* range, lapack_int* n, double* d,\n                    double* e, double* vl, double* vu, lapack_int* il,\n                    lapack_int* iu, lapack_int* m, double* w, double* z,\n                    lapack_int* ldz, lapack_int* nzc, lapack_int* isuppz,\n                    lapack_logical* tryrac, double* work, lapack_int* lwork,\n                    lapack_int* iwork, lapack_int* liwork, lapack_int *info );\nvoid LAPACK_cstemr( char* jobz, char* range, lapack_int* n, float* d, float* e,\n                    float* vl, float* vu, lapack_int* il, lapack_int* iu,\n                    lapack_int* m, float* w, lapack_complex_float* z,\n                    lapack_int* ldz, lapack_int* nzc, lapack_int* isuppz,\n                    lapack_logical* tryrac, float* work, lapack_int* lwork,\n                    lapack_int* iwork, lapack_int* liwork, lapack_int *info );\nvoid LAPACK_zstemr( char* jobz, char* range, lapack_int* n, double* d,\n                    double* e, double* vl, double* vu, lapack_int* il,\n                    lapack_int* iu, lapack_int* m, double* w,\n                    lapack_complex_double* z, lapack_int* ldz, lapack_int* nzc,\n                    lapack_int* isuppz, lapack_logical* tryrac, double* work,\n                    lapack_int* lwork, lapack_int* iwork, lapack_int* liwork,\n                    lapack_int *info );\nvoid LAPACK_sstedc( char* compz, lapack_int* n, float* d, float* e, float* z,\n                    lapack_int* ldz, float* work, lapack_int* lwork,\n                    lapack_int* iwork, lapack_int* liwork, lapack_int *info );\nvoid LAPACK_dstedc( char* compz, lapack_int* n, double* d, double* e, double* z,\n                    lapack_int* ldz, double* work, lapack_int* lwork,\n                    lapack_int* iwork, lapack_int* liwork, lapack_int *info );\nvoid LAPACK_cstedc( char* compz, lapack_int* n, float* d, float* e,\n                    lapack_complex_float* z, lapack_int* ldz,\n                    lapack_complex_float* work, lapack_int* lwork, float* rwork,\n                    lapack_int* lrwork, lapack_int* iwork, lapack_int* liwork,\n                    lapack_int *info );\nvoid LAPACK_zstedc( char* compz, lapack_int* n, double* d, double* e,\n                    lapack_complex_double* z, lapack_int* ldz,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    double* rwork, lapack_int* lrwork, lapack_int* iwork,\n                    lapack_int* liwork, lapack_int *info );\nvoid LAPACK_sstegr( char* jobz, char* range, lapack_int* n, float* d, float* e,\n                    float* vl, float* vu, lapack_int* il, lapack_int* iu,\n                    float* abstol, lapack_int* m, float* w, float* z,\n                    lapack_int* ldz, lapack_int* isuppz, float* work,\n                    lapack_int* lwork, lapack_int* iwork, lapack_int* liwork,\n                    lapack_int *info );\nvoid LAPACK_dstegr( char* jobz, char* range, lapack_int* n, double* d,\n                    double* e, double* vl, double* vu, lapack_int* il,\n                    lapack_int* iu, double* abstol, lapack_int* m, double* w,\n                    double* z, lapack_int* ldz, lapack_int* isuppz,\n                    double* work, lapack_int* lwork, lapack_int* iwork,\n                    lapack_int* liwork, lapack_int *info );\nvoid LAPACK_cstegr( char* jobz, char* range, lapack_int* n, float* d, float* e,\n                    float* vl, float* vu, lapack_int* il, lapack_int* iu,\n                    float* abstol, lapack_int* m, float* w,\n                    lapack_complex_float* z, lapack_int* ldz,\n                    lapack_int* isuppz, float* work, lapack_int* lwork,\n                    lapack_int* iwork, lapack_int* liwork, lapack_int *info );\nvoid LAPACK_zstegr( char* jobz, char* range, lapack_int* n, double* d,\n                    double* e, double* vl, double* vu, lapack_int* il,\n                    lapack_int* iu, double* abstol, lapack_int* m, double* w,\n                    lapack_complex_double* z, lapack_int* ldz,\n                    lapack_int* isuppz, double* work, lapack_int* lwork,\n                    lapack_int* iwork, lapack_int* liwork, lapack_int *info );\nvoid LAPACK_spteqr( char* compz, lapack_int* n, float* d, float* e, float* z,\n                    lapack_int* ldz, float* work, lapack_int *info );\nvoid LAPACK_dpteqr( char* compz, lapack_int* n, double* d, double* e, double* z,\n                    lapack_int* ldz, double* work, lapack_int *info );\nvoid LAPACK_cpteqr( char* compz, lapack_int* n, float* d, float* e,\n                    lapack_complex_float* z, lapack_int* ldz, float* work,\n                    lapack_int *info );\nvoid LAPACK_zpteqr( char* compz, lapack_int* n, double* d, double* e,\n                    lapack_complex_double* z, lapack_int* ldz, double* work,\n                    lapack_int *info );\nvoid LAPACK_sstebz( char* range, char* order, lapack_int* n, float* vl,\n                    float* vu, lapack_int* il, lapack_int* iu, float* abstol,\n                    const float* d, const float* e, lapack_int* m,\n                    lapack_int* nsplit, float* w, lapack_int* iblock,\n                    lapack_int* isplit, float* work, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_dstebz( char* range, char* order, lapack_int* n, double* vl,\n                    double* vu, lapack_int* il, lapack_int* iu, double* abstol,\n                    const double* d, const double* e, lapack_int* m,\n                    lapack_int* nsplit, double* w, lapack_int* iblock,\n                    lapack_int* isplit, double* work, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_sstein( lapack_int* n, const float* d, const float* e,\n                    lapack_int* m, const float* w, const lapack_int* iblock,\n                    const lapack_int* isplit, float* z, lapack_int* ldz,\n                    float* work, lapack_int* iwork, lapack_int* ifailv,\n                    lapack_int *info );\nvoid LAPACK_dstein( lapack_int* n, const double* d, const double* e,\n                    lapack_int* m, const double* w, const lapack_int* iblock,\n                    const lapack_int* isplit, double* z, lapack_int* ldz,\n                    double* work, lapack_int* iwork, lapack_int* ifailv,\n                    lapack_int *info );\nvoid LAPACK_cstein( lapack_int* n, const float* d, const float* e,\n                    lapack_int* m, const float* w, const lapack_int* iblock,\n                    const lapack_int* isplit, lapack_complex_float* z,\n                    lapack_int* ldz, float* work, lapack_int* iwork,\n                    lapack_int* ifailv, lapack_int *info );\nvoid LAPACK_zstein( lapack_int* n, const double* d, const double* e,\n                    lapack_int* m, const double* w, const lapack_int* iblock,\n                    const lapack_int* isplit, lapack_complex_double* z,\n                    lapack_int* ldz, double* work, lapack_int* iwork,\n                    lapack_int* ifailv, lapack_int *info );\nvoid LAPACK_sdisna( char* job, lapack_int* m, lapack_int* n, const float* d,\n                    float* sep, lapack_int *info );\nvoid LAPACK_ddisna( char* job, lapack_int* m, lapack_int* n, const double* d,\n                    double* sep, lapack_int *info );\nvoid LAPACK_ssygst( lapack_int* itype, char* uplo, lapack_int* n, float* a,\n                    lapack_int* lda, const float* b, lapack_int* ldb,\n                    lapack_int *info );\nvoid LAPACK_dsygst( lapack_int* itype, char* uplo, lapack_int* n, double* a,\n                    lapack_int* lda, const double* b, lapack_int* ldb,\n                    lapack_int *info );\nvoid LAPACK_chegst( lapack_int* itype, char* uplo, lapack_int* n,\n                    lapack_complex_float* a, lapack_int* lda,\n                    const lapack_complex_float* b, lapack_int* ldb,\n                    lapack_int *info );\nvoid LAPACK_zhegst( lapack_int* itype, char* uplo, lapack_int* n,\n                    lapack_complex_double* a, lapack_int* lda,\n                    const lapack_complex_double* b, lapack_int* ldb,\n                    lapack_int *info );\nvoid LAPACK_sspgst( lapack_int* itype, char* uplo, lapack_int* n, float* ap,\n                    const float* bp, lapack_int *info );\nvoid LAPACK_dspgst( lapack_int* itype, char* uplo, lapack_int* n, double* ap,\n                    const double* bp, lapack_int *info );\nvoid LAPACK_chpgst( lapack_int* itype, char* uplo, lapack_int* n,\n                    lapack_complex_float* ap, const lapack_complex_float* bp,\n                    lapack_int *info );\nvoid LAPACK_zhpgst( lapack_int* itype, char* uplo, lapack_int* n,\n                    lapack_complex_double* ap, const lapack_complex_double* bp,\n                    lapack_int *info );\nvoid LAPACK_ssbgst( char* vect, char* uplo, lapack_int* n, lapack_int* ka,\n                    lapack_int* kb, float* ab, lapack_int* ldab,\n                    const float* bb, lapack_int* ldbb, float* x,\n                    lapack_int* ldx, float* work, lapack_int *info );\nvoid LAPACK_dsbgst( char* vect, char* uplo, lapack_int* n, lapack_int* ka,\n                    lapack_int* kb, double* ab, lapack_int* ldab,\n                    const double* bb, lapack_int* ldbb, double* x,\n                    lapack_int* ldx, double* work, lapack_int *info );\nvoid LAPACK_chbgst( char* vect, char* uplo, lapack_int* n, lapack_int* ka,\n                    lapack_int* kb, lapack_complex_float* ab, lapack_int* ldab,\n                    const lapack_complex_float* bb, lapack_int* ldbb,\n                    lapack_complex_float* x, lapack_int* ldx,\n                    lapack_complex_float* work, float* rwork,\n                    lapack_int *info );\nvoid LAPACK_zhbgst( char* vect, char* uplo, lapack_int* n, lapack_int* ka,\n                    lapack_int* kb, lapack_complex_double* ab, lapack_int* ldab,\n                    const lapack_complex_double* bb, lapack_int* ldbb,\n                    lapack_complex_double* x, lapack_int* ldx,\n                    lapack_complex_double* work, double* rwork,\n                    lapack_int *info );\nvoid LAPACK_spbstf( char* uplo, lapack_int* n, lapack_int* kb, float* bb,\n                    lapack_int* ldbb, lapack_int *info );\nvoid LAPACK_dpbstf( char* uplo, lapack_int* n, lapack_int* kb, double* bb,\n                    lapack_int* ldbb, lapack_int *info );\nvoid LAPACK_cpbstf( char* uplo, lapack_int* n, lapack_int* kb,\n                    lapack_complex_float* bb, lapack_int* ldbb,\n                    lapack_int *info );\nvoid LAPACK_zpbstf( char* uplo, lapack_int* n, lapack_int* kb,\n                    lapack_complex_double* bb, lapack_int* ldbb,\n                    lapack_int *info );\nvoid LAPACK_sgehrd( lapack_int* n, lapack_int* ilo, lapack_int* ihi, float* a,\n                    lapack_int* lda, float* tau, float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_dgehrd( lapack_int* n, lapack_int* ilo, lapack_int* ihi, double* a,\n                    lapack_int* lda, double* tau, double* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_cgehrd( lapack_int* n, lapack_int* ilo, lapack_int* ihi,\n                    lapack_complex_float* a, lapack_int* lda,\n                    lapack_complex_float* tau, lapack_complex_float* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_zgehrd( lapack_int* n, lapack_int* ilo, lapack_int* ihi,\n                    lapack_complex_double* a, lapack_int* lda,\n                    lapack_complex_double* tau, lapack_complex_double* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_sorghr( lapack_int* n, lapack_int* ilo, lapack_int* ihi, float* a,\n                    lapack_int* lda, const float* tau, float* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_dorghr( lapack_int* n, lapack_int* ilo, lapack_int* ihi, double* a,\n                    lapack_int* lda, const double* tau, double* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_sormhr( char* side, char* trans, lapack_int* m, lapack_int* n,\n                    lapack_int* ilo, lapack_int* ihi, const float* a,\n                    lapack_int* lda, const float* tau, float* c,\n                    lapack_int* ldc, float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_dormhr( char* side, char* trans, lapack_int* m, lapack_int* n,\n                    lapack_int* ilo, lapack_int* ihi, const double* a,\n                    lapack_int* lda, const double* tau, double* c,\n                    lapack_int* ldc, double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_cunghr( lapack_int* n, lapack_int* ilo, lapack_int* ihi,\n                    lapack_complex_float* a, lapack_int* lda,\n                    const lapack_complex_float* tau, lapack_complex_float* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_zunghr( lapack_int* n, lapack_int* ilo, lapack_int* ihi,\n                    lapack_complex_double* a, lapack_int* lda,\n                    const lapack_complex_double* tau,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_cunmhr( char* side, char* trans, lapack_int* m, lapack_int* n,\n                    lapack_int* ilo, lapack_int* ihi,\n                    const lapack_complex_float* a, lapack_int* lda,\n                    const lapack_complex_float* tau, lapack_complex_float* c,\n                    lapack_int* ldc, lapack_complex_float* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_zunmhr( char* side, char* trans, lapack_int* m, lapack_int* n,\n                    lapack_int* ilo, lapack_int* ihi,\n                    const lapack_complex_double* a, lapack_int* lda,\n                    const lapack_complex_double* tau, lapack_complex_double* c,\n                    lapack_int* ldc, lapack_complex_double* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_sgebal( char* job, lapack_int* n, float* a, lapack_int* lda,\n                    lapack_int* ilo, lapack_int* ihi, float* scale,\n                    lapack_int *info );\nvoid LAPACK_dgebal( char* job, lapack_int* n, double* a, lapack_int* lda,\n                    lapack_int* ilo, lapack_int* ihi, double* scale,\n                    lapack_int *info );\nvoid LAPACK_cgebal( char* job, lapack_int* n, lapack_complex_float* a,\n                    lapack_int* lda, lapack_int* ilo, lapack_int* ihi,\n                    float* scale, lapack_int *info );\nvoid LAPACK_zgebal( char* job, lapack_int* n, lapack_complex_double* a,\n                    lapack_int* lda, lapack_int* ilo, lapack_int* ihi,\n                    double* scale, lapack_int *info );\nvoid LAPACK_sgebak( char* job, char* side, lapack_int* n, lapack_int* ilo,\n                    lapack_int* ihi, const float* scale, lapack_int* m,\n                    float* v, lapack_int* ldv, lapack_int *info );\nvoid LAPACK_dgebak( char* job, char* side, lapack_int* n, lapack_int* ilo,\n                    lapack_int* ihi, const double* scale, lapack_int* m,\n                    double* v, lapack_int* ldv, lapack_int *info );\nvoid LAPACK_cgebak( char* job, char* side, lapack_int* n, lapack_int* ilo,\n                    lapack_int* ihi, const float* scale, lapack_int* m,\n                    lapack_complex_float* v, lapack_int* ldv,\n                    lapack_int *info );\nvoid LAPACK_zgebak( char* job, char* side, lapack_int* n, lapack_int* ilo,\n                    lapack_int* ihi, const double* scale, lapack_int* m,\n                    lapack_complex_double* v, lapack_int* ldv,\n                    lapack_int *info );\nvoid LAPACK_shseqr( char* job, char* compz, lapack_int* n, lapack_int* ilo,\n                    lapack_int* ihi, float* h, lapack_int* ldh, float* wr,\n                    float* wi, float* z, lapack_int* ldz, float* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_dhseqr( char* job, char* compz, lapack_int* n, lapack_int* ilo,\n                    lapack_int* ihi, double* h, lapack_int* ldh, double* wr,\n                    double* wi, double* z, lapack_int* ldz, double* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_chseqr( char* job, char* compz, lapack_int* n, lapack_int* ilo,\n                    lapack_int* ihi, lapack_complex_float* h, lapack_int* ldh,\n                    lapack_complex_float* w, lapack_complex_float* z,\n                    lapack_int* ldz, lapack_complex_float* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_zhseqr( char* job, char* compz, lapack_int* n, lapack_int* ilo,\n                    lapack_int* ihi, lapack_complex_double* h, lapack_int* ldh,\n                    lapack_complex_double* w, lapack_complex_double* z,\n                    lapack_int* ldz, lapack_complex_double* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_shsein( char* job, char* eigsrc, char* initv,\n                    lapack_logical* select, lapack_int* n, const float* h,\n                    lapack_int* ldh, float* wr, const float* wi, float* vl,\n                    lapack_int* ldvl, float* vr, lapack_int* ldvr,\n                    lapack_int* mm, lapack_int* m, float* work,\n                    lapack_int* ifaill, lapack_int* ifailr, lapack_int *info );\nvoid LAPACK_dhsein( char* job, char* eigsrc, char* initv,\n                    lapack_logical* select, lapack_int* n, const double* h,\n                    lapack_int* ldh, double* wr, const double* wi, double* vl,\n                    lapack_int* ldvl, double* vr, lapack_int* ldvr,\n                    lapack_int* mm, lapack_int* m, double* work,\n                    lapack_int* ifaill, lapack_int* ifailr, lapack_int *info );\nvoid LAPACK_chsein( char* job, char* eigsrc, char* initv,\n                    const lapack_logical* select, lapack_int* n,\n                    const lapack_complex_float* h, lapack_int* ldh,\n                    lapack_complex_float* w, lapack_complex_float* vl,\n                    lapack_int* ldvl, lapack_complex_float* vr,\n                    lapack_int* ldvr, lapack_int* mm, lapack_int* m,\n                    lapack_complex_float* work, float* rwork,\n                    lapack_int* ifaill, lapack_int* ifailr, lapack_int *info );\nvoid LAPACK_zhsein( char* job, char* eigsrc, char* initv,\n                    const lapack_logical* select, lapack_int* n,\n                    const lapack_complex_double* h, lapack_int* ldh,\n                    lapack_complex_double* w, lapack_complex_double* vl,\n                    lapack_int* ldvl, lapack_complex_double* vr,\n                    lapack_int* ldvr, lapack_int* mm, lapack_int* m,\n                    lapack_complex_double* work, double* rwork,\n                    lapack_int* ifaill, lapack_int* ifailr, lapack_int *info );\nvoid LAPACK_strevc( char* side, char* howmny, lapack_logical* select,\n                    lapack_int* n, const float* t, lapack_int* ldt, float* vl,\n                    lapack_int* ldvl, float* vr, lapack_int* ldvr,\n                    lapack_int* mm, lapack_int* m, float* work,\n                    lapack_int *info );\nvoid LAPACK_dtrevc( char* side, char* howmny, lapack_logical* select,\n                    lapack_int* n, const double* t, lapack_int* ldt, double* vl,\n                    lapack_int* ldvl, double* vr, lapack_int* ldvr,\n                    lapack_int* mm, lapack_int* m, double* work,\n                    lapack_int *info );\nvoid LAPACK_ctrevc( char* side, char* howmny, const lapack_logical* select,\n                    lapack_int* n, lapack_complex_float* t, lapack_int* ldt,\n                    lapack_complex_float* vl, lapack_int* ldvl,\n                    lapack_complex_float* vr, lapack_int* ldvr, lapack_int* mm,\n                    lapack_int* m, lapack_complex_float* work, float* rwork,\n                    lapack_int *info );\nvoid LAPACK_ztrevc( char* side, char* howmny, const lapack_logical* select,\n                    lapack_int* n, lapack_complex_double* t, lapack_int* ldt,\n                    lapack_complex_double* vl, lapack_int* ldvl,\n                    lapack_complex_double* vr, lapack_int* ldvr, lapack_int* mm,\n                    lapack_int* m, lapack_complex_double* work, double* rwork,\n                    lapack_int *info );\nvoid LAPACK_strsna( char* job, char* howmny, const lapack_logical* select,\n                    lapack_int* n, const float* t, lapack_int* ldt,\n                    const float* vl, lapack_int* ldvl, const float* vr,\n                    lapack_int* ldvr, float* s, float* sep, lapack_int* mm,\n                    lapack_int* m, float* work, lapack_int* ldwork,\n                    lapack_int* iwork, lapack_int *info );\nvoid LAPACK_dtrsna( char* job, char* howmny, const lapack_logical* select,\n                    lapack_int* n, const double* t, lapack_int* ldt,\n                    const double* vl, lapack_int* ldvl, const double* vr,\n                    lapack_int* ldvr, double* s, double* sep, lapack_int* mm,\n                    lapack_int* m, double* work, lapack_int* ldwork,\n                    lapack_int* iwork, lapack_int *info );\nvoid LAPACK_ctrsna( char* job, char* howmny, const lapack_logical* select,\n                    lapack_int* n, const lapack_complex_float* t,\n                    lapack_int* ldt, const lapack_complex_float* vl,\n                    lapack_int* ldvl, const lapack_complex_float* vr,\n                    lapack_int* ldvr, float* s, float* sep, lapack_int* mm,\n                    lapack_int* m, lapack_complex_float* work,\n                    lapack_int* ldwork, float* rwork, lapack_int *info );\nvoid LAPACK_ztrsna( char* job, char* howmny, const lapack_logical* select,\n                    lapack_int* n, const lapack_complex_double* t,\n                    lapack_int* ldt, const lapack_complex_double* vl,\n                    lapack_int* ldvl, const lapack_complex_double* vr,\n                    lapack_int* ldvr, double* s, double* sep, lapack_int* mm,\n                    lapack_int* m, lapack_complex_double* work,\n                    lapack_int* ldwork, double* rwork, lapack_int *info );\nvoid LAPACK_strexc( char* compq, lapack_int* n, float* t, lapack_int* ldt,\n                    float* q, lapack_int* ldq, lapack_int* ifst,\n                    lapack_int* ilst, float* work, lapack_int *info );\nvoid LAPACK_dtrexc( char* compq, lapack_int* n, double* t, lapack_int* ldt,\n                    double* q, lapack_int* ldq, lapack_int* ifst,\n                    lapack_int* ilst, double* work, lapack_int *info );\nvoid LAPACK_ctrexc( char* compq, lapack_int* n, lapack_complex_float* t,\n                    lapack_int* ldt, lapack_complex_float* q, lapack_int* ldq,\n                    lapack_int* ifst, lapack_int* ilst, lapack_int *info );\nvoid LAPACK_ztrexc( char* compq, lapack_int* n, lapack_complex_double* t,\n                    lapack_int* ldt, lapack_complex_double* q, lapack_int* ldq,\n                    lapack_int* ifst, lapack_int* ilst, lapack_int *info );\nvoid LAPACK_strsen( char* job, char* compq, const lapack_logical* select,\n                    lapack_int* n, float* t, lapack_int* ldt, float* q,\n                    lapack_int* ldq, float* wr, float* wi, lapack_int* m,\n                    float* s, float* sep, float* work, lapack_int* lwork,\n                    lapack_int* iwork, lapack_int* liwork, lapack_int *info );\nvoid LAPACK_dtrsen( char* job, char* compq, const lapack_logical* select,\n                    lapack_int* n, double* t, lapack_int* ldt, double* q,\n                    lapack_int* ldq, double* wr, double* wi, lapack_int* m,\n                    double* s, double* sep, double* work, lapack_int* lwork,\n                    lapack_int* iwork, lapack_int* liwork, lapack_int *info );\nvoid LAPACK_ctrsen( char* job, char* compq, const lapack_logical* select,\n                    lapack_int* n, lapack_complex_float* t, lapack_int* ldt,\n                    lapack_complex_float* q, lapack_int* ldq,\n                    lapack_complex_float* w, lapack_int* m, float* s,\n                    float* sep, lapack_complex_float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_ztrsen( char* job, char* compq, const lapack_logical* select,\n                    lapack_int* n, lapack_complex_double* t, lapack_int* ldt,\n                    lapack_complex_double* q, lapack_int* ldq,\n                    lapack_complex_double* w, lapack_int* m, double* s,\n                    double* sep, lapack_complex_double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_strsyl( char* trana, char* tranb, lapack_int* isgn, lapack_int* m,\n                    lapack_int* n, const float* a, lapack_int* lda,\n                    const float* b, lapack_int* ldb, float* c, lapack_int* ldc,\n                    float* scale, lapack_int *info );\nvoid LAPACK_dtrsyl( char* trana, char* tranb, lapack_int* isgn, lapack_int* m,\n                    lapack_int* n, const double* a, lapack_int* lda,\n                    const double* b, lapack_int* ldb, double* c,\n                    lapack_int* ldc, double* scale, lapack_int *info );\nvoid LAPACK_ctrsyl( char* trana, char* tranb, lapack_int* isgn, lapack_int* m,\n                    lapack_int* n, const lapack_complex_float* a,\n                    lapack_int* lda, const lapack_complex_float* b,\n                    lapack_int* ldb, lapack_complex_float* c, lapack_int* ldc,\n                    float* scale, lapack_int *info );\nvoid LAPACK_ztrsyl( char* trana, char* tranb, lapack_int* isgn, lapack_int* m,\n                    lapack_int* n, const lapack_complex_double* a,\n                    lapack_int* lda, const lapack_complex_double* b,\n                    lapack_int* ldb, lapack_complex_double* c, lapack_int* ldc,\n                    double* scale, lapack_int *info );\nvoid LAPACK_sgghrd( char* compq, char* compz, lapack_int* n, lapack_int* ilo,\n                    lapack_int* ihi, float* a, lapack_int* lda, float* b,\n                    lapack_int* ldb, float* q, lapack_int* ldq, float* z,\n                    lapack_int* ldz, lapack_int *info );\nvoid LAPACK_dgghrd( char* compq, char* compz, lapack_int* n, lapack_int* ilo,\n                    lapack_int* ihi, double* a, lapack_int* lda, double* b,\n                    lapack_int* ldb, double* q, lapack_int* ldq, double* z,\n                    lapack_int* ldz, lapack_int *info );\nvoid LAPACK_cgghrd( char* compq, char* compz, lapack_int* n, lapack_int* ilo,\n                    lapack_int* ihi, lapack_complex_float* a, lapack_int* lda,\n                    lapack_complex_float* b, lapack_int* ldb,\n                    lapack_complex_float* q, lapack_int* ldq,\n                    lapack_complex_float* z, lapack_int* ldz,\n                    lapack_int *info );\nvoid LAPACK_zgghrd( char* compq, char* compz, lapack_int* n, lapack_int* ilo,\n                    lapack_int* ihi, lapack_complex_double* a, lapack_int* lda,\n                    lapack_complex_double* b, lapack_int* ldb,\n                    lapack_complex_double* q, lapack_int* ldq,\n                    lapack_complex_double* z, lapack_int* ldz,\n                    lapack_int *info );\nvoid LAPACK_sggbal( char* job, lapack_int* n, float* a, lapack_int* lda,\n                    float* b, lapack_int* ldb, lapack_int* ilo, lapack_int* ihi,\n                    float* lscale, float* rscale, float* work,\n                    lapack_int *info );\nvoid LAPACK_dggbal( char* job, lapack_int* n, double* a, lapack_int* lda,\n                    double* b, lapack_int* ldb, lapack_int* ilo,\n                    lapack_int* ihi, double* lscale, double* rscale,\n                    double* work, lapack_int *info );\nvoid LAPACK_cggbal( char* job, lapack_int* n, lapack_complex_float* a,\n                    lapack_int* lda, lapack_complex_float* b, lapack_int* ldb,\n                    lapack_int* ilo, lapack_int* ihi, float* lscale,\n                    float* rscale, float* work, lapack_int *info );\nvoid LAPACK_zggbal( char* job, lapack_int* n, lapack_complex_double* a,\n                    lapack_int* lda, lapack_complex_double* b, lapack_int* ldb,\n                    lapack_int* ilo, lapack_int* ihi, double* lscale,\n                    double* rscale, double* work, lapack_int *info );\nvoid LAPACK_sggbak( char* job, char* side, lapack_int* n, lapack_int* ilo,\n                    lapack_int* ihi, const float* lscale, const float* rscale,\n                    lapack_int* m, float* v, lapack_int* ldv,\n                    lapack_int *info );\nvoid LAPACK_dggbak( char* job, char* side, lapack_int* n, lapack_int* ilo,\n                    lapack_int* ihi, const double* lscale, const double* rscale,\n                    lapack_int* m, double* v, lapack_int* ldv,\n                    lapack_int *info );\nvoid LAPACK_cggbak( char* job, char* side, lapack_int* n, lapack_int* ilo,\n                    lapack_int* ihi, const float* lscale, const float* rscale,\n                    lapack_int* m, lapack_complex_float* v, lapack_int* ldv,\n                    lapack_int *info );\nvoid LAPACK_zggbak( char* job, char* side, lapack_int* n, lapack_int* ilo,\n                    lapack_int* ihi, const double* lscale, const double* rscale,\n                    lapack_int* m, lapack_complex_double* v, lapack_int* ldv,\n                    lapack_int *info );\nvoid LAPACK_shgeqz( char* job, char* compq, char* compz, lapack_int* n,\n                    lapack_int* ilo, lapack_int* ihi, float* h, lapack_int* ldh,\n                    float* t, lapack_int* ldt, float* alphar, float* alphai,\n                    float* beta, float* q, lapack_int* ldq, float* z,\n                    lapack_int* ldz, float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_dhgeqz( char* job, char* compq, char* compz, lapack_int* n,\n                    lapack_int* ilo, lapack_int* ihi, double* h,\n                    lapack_int* ldh, double* t, lapack_int* ldt, double* alphar,\n                    double* alphai, double* beta, double* q, lapack_int* ldq,\n                    double* z, lapack_int* ldz, double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_chgeqz( char* job, char* compq, char* compz, lapack_int* n,\n                    lapack_int* ilo, lapack_int* ihi, lapack_complex_float* h,\n                    lapack_int* ldh, lapack_complex_float* t, lapack_int* ldt,\n                    lapack_complex_float* alpha, lapack_complex_float* beta,\n                    lapack_complex_float* q, lapack_int* ldq,\n                    lapack_complex_float* z, lapack_int* ldz,\n                    lapack_complex_float* work, lapack_int* lwork, float* rwork,\n                    lapack_int *info );\nvoid LAPACK_zhgeqz( char* job, char* compq, char* compz, lapack_int* n,\n                    lapack_int* ilo, lapack_int* ihi, lapack_complex_double* h,\n                    lapack_int* ldh, lapack_complex_double* t, lapack_int* ldt,\n                    lapack_complex_double* alpha, lapack_complex_double* beta,\n                    lapack_complex_double* q, lapack_int* ldq,\n                    lapack_complex_double* z, lapack_int* ldz,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    double* rwork, lapack_int *info );\nvoid LAPACK_stgevc( char* side, char* howmny, const lapack_logical* select,\n                    lapack_int* n, const float* s, lapack_int* lds,\n                    const float* p, lapack_int* ldp, float* vl,\n                    lapack_int* ldvl, float* vr, lapack_int* ldvr,\n                    lapack_int* mm, lapack_int* m, float* work,\n                    lapack_int *info );\nvoid LAPACK_dtgevc( char* side, char* howmny, const lapack_logical* select,\n                    lapack_int* n, const double* s, lapack_int* lds,\n                    const double* p, lapack_int* ldp, double* vl,\n                    lapack_int* ldvl, double* vr, lapack_int* ldvr,\n                    lapack_int* mm, lapack_int* m, double* work,\n                    lapack_int *info );\nvoid LAPACK_ctgevc( char* side, char* howmny, const lapack_logical* select,\n                    lapack_int* n, const lapack_complex_float* s,\n                    lapack_int* lds, const lapack_complex_float* p,\n                    lapack_int* ldp, lapack_complex_float* vl, lapack_int* ldvl,\n                    lapack_complex_float* vr, lapack_int* ldvr, lapack_int* mm,\n                    lapack_int* m, lapack_complex_float* work, float* rwork,\n                    lapack_int *info );\nvoid LAPACK_ztgevc( char* side, char* howmny, const lapack_logical* select,\n                    lapack_int* n, const lapack_complex_double* s,\n                    lapack_int* lds, const lapack_complex_double* p,\n                    lapack_int* ldp, lapack_complex_double* vl,\n                    lapack_int* ldvl, lapack_complex_double* vr,\n                    lapack_int* ldvr, lapack_int* mm, lapack_int* m,\n                    lapack_complex_double* work, double* rwork,\n                    lapack_int *info );\nvoid LAPACK_stgexc( lapack_logical* wantq, lapack_logical* wantz, lapack_int* n,\n                    float* a, lapack_int* lda, float* b, lapack_int* ldb,\n                    float* q, lapack_int* ldq, float* z, lapack_int* ldz,\n                    lapack_int* ifst, lapack_int* ilst, float* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_dtgexc( lapack_logical* wantq, lapack_logical* wantz, lapack_int* n,\n                    double* a, lapack_int* lda, double* b, lapack_int* ldb,\n                    double* q, lapack_int* ldq, double* z, lapack_int* ldz,\n                    lapack_int* ifst, lapack_int* ilst, double* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_ctgexc( lapack_logical* wantq, lapack_logical* wantz, lapack_int* n,\n                    lapack_complex_float* a, lapack_int* lda,\n                    lapack_complex_float* b, lapack_int* ldb,\n                    lapack_complex_float* q, lapack_int* ldq,\n                    lapack_complex_float* z, lapack_int* ldz, lapack_int* ifst,\n                    lapack_int* ilst, lapack_int *info );\nvoid LAPACK_ztgexc( lapack_logical* wantq, lapack_logical* wantz, lapack_int* n,\n                    lapack_complex_double* a, lapack_int* lda,\n                    lapack_complex_double* b, lapack_int* ldb,\n                    lapack_complex_double* q, lapack_int* ldq,\n                    lapack_complex_double* z, lapack_int* ldz, lapack_int* ifst,\n                    lapack_int* ilst, lapack_int *info );\nvoid LAPACK_stgsen( lapack_int* ijob, lapack_logical* wantq,\n                    lapack_logical* wantz, const lapack_logical* select,\n                    lapack_int* n, float* a, lapack_int* lda, float* b,\n                    lapack_int* ldb, float* alphar, float* alphai, float* beta,\n                    float* q, lapack_int* ldq, float* z, lapack_int* ldz,\n                    lapack_int* m, float* pl, float* pr, float* dif,\n                    float* work, lapack_int* lwork, lapack_int* iwork,\n                    lapack_int* liwork, lapack_int *info );\nvoid LAPACK_dtgsen( lapack_int* ijob, lapack_logical* wantq,\n                    lapack_logical* wantz, const lapack_logical* select,\n                    lapack_int* n, double* a, lapack_int* lda, double* b,\n                    lapack_int* ldb, double* alphar, double* alphai,\n                    double* beta, double* q, lapack_int* ldq, double* z,\n                    lapack_int* ldz, lapack_int* m, double* pl, double* pr,\n                    double* dif, double* work, lapack_int* lwork,\n                    lapack_int* iwork, lapack_int* liwork, lapack_int *info );\nvoid LAPACK_ctgsen( lapack_int* ijob, lapack_logical* wantq,\n                    lapack_logical* wantz, const lapack_logical* select,\n                    lapack_int* n, lapack_complex_float* a, lapack_int* lda,\n                    lapack_complex_float* b, lapack_int* ldb,\n                    lapack_complex_float* alpha, lapack_complex_float* beta,\n                    lapack_complex_float* q, lapack_int* ldq,\n                    lapack_complex_float* z, lapack_int* ldz, lapack_int* m,\n                    float* pl, float* pr, float* dif,\n                    lapack_complex_float* work, lapack_int* lwork,\n                    lapack_int* iwork, lapack_int* liwork, lapack_int *info );\nvoid LAPACK_ztgsen( lapack_int* ijob, lapack_logical* wantq,\n                    lapack_logical* wantz, const lapack_logical* select,\n                    lapack_int* n, lapack_complex_double* a, lapack_int* lda,\n                    lapack_complex_double* b, lapack_int* ldb,\n                    lapack_complex_double* alpha, lapack_complex_double* beta,\n                    lapack_complex_double* q, lapack_int* ldq,\n                    lapack_complex_double* z, lapack_int* ldz, lapack_int* m,\n                    double* pl, double* pr, double* dif,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    lapack_int* iwork, lapack_int* liwork, lapack_int *info );\nvoid LAPACK_stgsyl( char* trans, lapack_int* ijob, lapack_int* m, lapack_int* n,\n                    const float* a, lapack_int* lda, const float* b,\n                    lapack_int* ldb, float* c, lapack_int* ldc, const float* d,\n                    lapack_int* ldd, const float* e, lapack_int* lde, float* f,\n                    lapack_int* ldf, float* scale, float* dif, float* work,\n                    lapack_int* lwork, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_dtgsyl( char* trans, lapack_int* ijob, lapack_int* m, lapack_int* n,\n                    const double* a, lapack_int* lda, const double* b,\n                    lapack_int* ldb, double* c, lapack_int* ldc,\n                    const double* d, lapack_int* ldd, const double* e,\n                    lapack_int* lde, double* f, lapack_int* ldf, double* scale,\n                    double* dif, double* work, lapack_int* lwork,\n                    lapack_int* iwork, lapack_int *info );\nvoid LAPACK_ctgsyl( char* trans, lapack_int* ijob, lapack_int* m, lapack_int* n,\n                    const lapack_complex_float* a, lapack_int* lda,\n                    const lapack_complex_float* b, lapack_int* ldb,\n                    lapack_complex_float* c, lapack_int* ldc,\n                    const lapack_complex_float* d, lapack_int* ldd,\n                    const lapack_complex_float* e, lapack_int* lde,\n                    lapack_complex_float* f, lapack_int* ldf, float* scale,\n                    float* dif, lapack_complex_float* work, lapack_int* lwork,\n                    lapack_int* iwork, lapack_int *info );\nvoid LAPACK_ztgsyl( char* trans, lapack_int* ijob, lapack_int* m, lapack_int* n,\n                    const lapack_complex_double* a, lapack_int* lda,\n                    const lapack_complex_double* b, lapack_int* ldb,\n                    lapack_complex_double* c, lapack_int* ldc,\n                    const lapack_complex_double* d, lapack_int* ldd,\n                    const lapack_complex_double* e, lapack_int* lde,\n                    lapack_complex_double* f, lapack_int* ldf, double* scale,\n                    double* dif, lapack_complex_double* work, lapack_int* lwork,\n                    lapack_int* iwork, lapack_int *info );\nvoid LAPACK_stgsna( char* job, char* howmny, const lapack_logical* select,\n                    lapack_int* n, const float* a, lapack_int* lda,\n                    const float* b, lapack_int* ldb, const float* vl,\n                    lapack_int* ldvl, const float* vr, lapack_int* ldvr,\n                    float* s, float* dif, lapack_int* mm, lapack_int* m,\n                    float* work, lapack_int* lwork, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_dtgsna( char* job, char* howmny, const lapack_logical* select,\n                    lapack_int* n, const double* a, lapack_int* lda,\n                    const double* b, lapack_int* ldb, const double* vl,\n                    lapack_int* ldvl, const double* vr, lapack_int* ldvr,\n                    double* s, double* dif, lapack_int* mm, lapack_int* m,\n                    double* work, lapack_int* lwork, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_ctgsna( char* job, char* howmny, const lapack_logical* select,\n                    lapack_int* n, const lapack_complex_float* a,\n                    lapack_int* lda, const lapack_complex_float* b,\n                    lapack_int* ldb, const lapack_complex_float* vl,\n                    lapack_int* ldvl, const lapack_complex_float* vr,\n                    lapack_int* ldvr, float* s, float* dif, lapack_int* mm,\n                    lapack_int* m, lapack_complex_float* work,\n                    lapack_int* lwork, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_ztgsna( char* job, char* howmny, const lapack_logical* select,\n                    lapack_int* n, const lapack_complex_double* a,\n                    lapack_int* lda, const lapack_complex_double* b,\n                    lapack_int* ldb, const lapack_complex_double* vl,\n                    lapack_int* ldvl, const lapack_complex_double* vr,\n                    lapack_int* ldvr, double* s, double* dif, lapack_int* mm,\n                    lapack_int* m, lapack_complex_double* work,\n                    lapack_int* lwork, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_sggsvp( char* jobu, char* jobv, char* jobq, lapack_int* m,\n                    lapack_int* p, lapack_int* n, float* a, lapack_int* lda,\n                    float* b, lapack_int* ldb, float* tola, float* tolb,\n                    lapack_int* k, lapack_int* l, float* u, lapack_int* ldu,\n                    float* v, lapack_int* ldv, float* q, lapack_int* ldq,\n                    lapack_int* iwork, float* tau, float* work,\n                    lapack_int *info );\nvoid LAPACK_dggsvp( char* jobu, char* jobv, char* jobq, lapack_int* m,\n                    lapack_int* p, lapack_int* n, double* a, lapack_int* lda,\n                    double* b, lapack_int* ldb, double* tola, double* tolb,\n                    lapack_int* k, lapack_int* l, double* u, lapack_int* ldu,\n                    double* v, lapack_int* ldv, double* q, lapack_int* ldq,\n                    lapack_int* iwork, double* tau, double* work,\n                    lapack_int *info );\nvoid LAPACK_cggsvp( char* jobu, char* jobv, char* jobq, lapack_int* m,\n                    lapack_int* p, lapack_int* n, lapack_complex_float* a,\n                    lapack_int* lda, lapack_complex_float* b, lapack_int* ldb,\n                    float* tola, float* tolb, lapack_int* k, lapack_int* l,\n                    lapack_complex_float* u, lapack_int* ldu,\n                    lapack_complex_float* v, lapack_int* ldv,\n                    lapack_complex_float* q, lapack_int* ldq, lapack_int* iwork,\n                    float* rwork, lapack_complex_float* tau,\n                    lapack_complex_float* work, lapack_int *info );\nvoid LAPACK_zggsvp( char* jobu, char* jobv, char* jobq, lapack_int* m,\n                    lapack_int* p, lapack_int* n, lapack_complex_double* a,\n                    lapack_int* lda, lapack_complex_double* b, lapack_int* ldb,\n                    double* tola, double* tolb, lapack_int* k, lapack_int* l,\n                    lapack_complex_double* u, lapack_int* ldu,\n                    lapack_complex_double* v, lapack_int* ldv,\n                    lapack_complex_double* q, lapack_int* ldq,\n                    lapack_int* iwork, double* rwork,\n                    lapack_complex_double* tau, lapack_complex_double* work,\n                    lapack_int *info );\nvoid LAPACK_stgsja( char* jobu, char* jobv, char* jobq, lapack_int* m,\n                    lapack_int* p, lapack_int* n, lapack_int* k, lapack_int* l,\n                    float* a, lapack_int* lda, float* b, lapack_int* ldb,\n                    float* tola, float* tolb, float* alpha, float* beta,\n                    float* u, lapack_int* ldu, float* v, lapack_int* ldv,\n                    float* q, lapack_int* ldq, float* work, lapack_int* ncycle,\n                    lapack_int *info );\nvoid LAPACK_dtgsja( char* jobu, char* jobv, char* jobq, lapack_int* m,\n                    lapack_int* p, lapack_int* n, lapack_int* k, lapack_int* l,\n                    double* a, lapack_int* lda, double* b, lapack_int* ldb,\n                    double* tola, double* tolb, double* alpha, double* beta,\n                    double* u, lapack_int* ldu, double* v, lapack_int* ldv,\n                    double* q, lapack_int* ldq, double* work,\n                    lapack_int* ncycle, lapack_int *info );\nvoid LAPACK_ctgsja( char* jobu, char* jobv, char* jobq, lapack_int* m,\n                    lapack_int* p, lapack_int* n, lapack_int* k, lapack_int* l,\n                    lapack_complex_float* a, lapack_int* lda,\n                    lapack_complex_float* b, lapack_int* ldb, float* tola,\n                    float* tolb, float* alpha, float* beta,\n                    lapack_complex_float* u, lapack_int* ldu,\n                    lapack_complex_float* v, lapack_int* ldv,\n                    lapack_complex_float* q, lapack_int* ldq,\n                    lapack_complex_float* work, lapack_int* ncycle,\n                    lapack_int *info );\nvoid LAPACK_ztgsja( char* jobu, char* jobv, char* jobq, lapack_int* m,\n                    lapack_int* p, lapack_int* n, lapack_int* k, lapack_int* l,\n                    lapack_complex_double* a, lapack_int* lda,\n                    lapack_complex_double* b, lapack_int* ldb, double* tola,\n                    double* tolb, double* alpha, double* beta,\n                    lapack_complex_double* u, lapack_int* ldu,\n                    lapack_complex_double* v, lapack_int* ldv,\n                    lapack_complex_double* q, lapack_int* ldq,\n                    lapack_complex_double* work, lapack_int* ncycle,\n                    lapack_int *info );\nvoid LAPACK_sgels( char* trans, lapack_int* m, lapack_int* n, lapack_int* nrhs,\n                   float* a, lapack_int* lda, float* b, lapack_int* ldb,\n                   float* work, lapack_int* lwork, lapack_int *info );\nvoid LAPACK_dgels( char* trans, lapack_int* m, lapack_int* n, lapack_int* nrhs,\n                   double* a, lapack_int* lda, double* b, lapack_int* ldb,\n                   double* work, lapack_int* lwork, lapack_int *info );\nvoid LAPACK_cgels( char* trans, lapack_int* m, lapack_int* n, lapack_int* nrhs,\n                   lapack_complex_float* a, lapack_int* lda,\n                   lapack_complex_float* b, lapack_int* ldb,\n                   lapack_complex_float* work, lapack_int* lwork,\n                   lapack_int *info );\nvoid LAPACK_zgels( char* trans, lapack_int* m, lapack_int* n, lapack_int* nrhs,\n                   lapack_complex_double* a, lapack_int* lda,\n                   lapack_complex_double* b, lapack_int* ldb,\n                   lapack_complex_double* work, lapack_int* lwork,\n                   lapack_int *info );\nvoid LAPACK_sgelsy( lapack_int* m, lapack_int* n, lapack_int* nrhs, float* a,\n                    lapack_int* lda, float* b, lapack_int* ldb,\n                    lapack_int* jpvt, float* rcond, lapack_int* rank,\n                    float* work, lapack_int* lwork, lapack_int *info );\nvoid LAPACK_dgelsy( lapack_int* m, lapack_int* n, lapack_int* nrhs, double* a,\n                    lapack_int* lda, double* b, lapack_int* ldb,\n                    lapack_int* jpvt, double* rcond, lapack_int* rank,\n                    double* work, lapack_int* lwork, lapack_int *info );\nvoid LAPACK_cgelsy( lapack_int* m, lapack_int* n, lapack_int* nrhs,\n                    lapack_complex_float* a, lapack_int* lda,\n                    lapack_complex_float* b, lapack_int* ldb, lapack_int* jpvt,\n                    float* rcond, lapack_int* rank, lapack_complex_float* work,\n                    lapack_int* lwork, float* rwork, lapack_int *info );\nvoid LAPACK_zgelsy( lapack_int* m, lapack_int* n, lapack_int* nrhs,\n                    lapack_complex_double* a, lapack_int* lda,\n                    lapack_complex_double* b, lapack_int* ldb, lapack_int* jpvt,\n                    double* rcond, lapack_int* rank,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    double* rwork, lapack_int *info );\nvoid LAPACK_sgelss( lapack_int* m, lapack_int* n, lapack_int* nrhs, float* a,\n                    lapack_int* lda, float* b, lapack_int* ldb, float* s,\n                    float* rcond, lapack_int* rank, float* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_dgelss( lapack_int* m, lapack_int* n, lapack_int* nrhs, double* a,\n                    lapack_int* lda, double* b, lapack_int* ldb, double* s,\n                    double* rcond, lapack_int* rank, double* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_cgelss( lapack_int* m, lapack_int* n, lapack_int* nrhs,\n                    lapack_complex_float* a, lapack_int* lda,\n                    lapack_complex_float* b, lapack_int* ldb, float* s,\n                    float* rcond, lapack_int* rank, lapack_complex_float* work,\n                    lapack_int* lwork, float* rwork, lapack_int *info );\nvoid LAPACK_zgelss( lapack_int* m, lapack_int* n, lapack_int* nrhs,\n                    lapack_complex_double* a, lapack_int* lda,\n                    lapack_complex_double* b, lapack_int* ldb, double* s,\n                    double* rcond, lapack_int* rank,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    double* rwork, lapack_int *info );\nvoid LAPACK_sgelsd( lapack_int* m, lapack_int* n, lapack_int* nrhs, float* a,\n                    lapack_int* lda, float* b, lapack_int* ldb, float* s,\n                    float* rcond, lapack_int* rank, float* work,\n                    lapack_int* lwork, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_dgelsd( lapack_int* m, lapack_int* n, lapack_int* nrhs, double* a,\n                    lapack_int* lda, double* b, lapack_int* ldb, double* s,\n                    double* rcond, lapack_int* rank, double* work,\n                    lapack_int* lwork, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_cgelsd( lapack_int* m, lapack_int* n, lapack_int* nrhs,\n                    lapack_complex_float* a, lapack_int* lda,\n                    lapack_complex_float* b, lapack_int* ldb, float* s,\n                    float* rcond, lapack_int* rank, lapack_complex_float* work,\n                    lapack_int* lwork, float* rwork, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_zgelsd( lapack_int* m, lapack_int* n, lapack_int* nrhs,\n                    lapack_complex_double* a, lapack_int* lda,\n                    lapack_complex_double* b, lapack_int* ldb, double* s,\n                    double* rcond, lapack_int* rank,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    double* rwork, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_sgglse( lapack_int* m, lapack_int* n, lapack_int* p, float* a,\n                    lapack_int* lda, float* b, lapack_int* ldb, float* c,\n                    float* d, float* x, float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_dgglse( lapack_int* m, lapack_int* n, lapack_int* p, double* a,\n                    lapack_int* lda, double* b, lapack_int* ldb, double* c,\n                    double* d, double* x, double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_cgglse( lapack_int* m, lapack_int* n, lapack_int* p,\n                    lapack_complex_float* a, lapack_int* lda,\n                    lapack_complex_float* b, lapack_int* ldb,\n                    lapack_complex_float* c, lapack_complex_float* d,\n                    lapack_complex_float* x, lapack_complex_float* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_zgglse( lapack_int* m, lapack_int* n, lapack_int* p,\n                    lapack_complex_double* a, lapack_int* lda,\n                    lapack_complex_double* b, lapack_int* ldb,\n                    lapack_complex_double* c, lapack_complex_double* d,\n                    lapack_complex_double* x, lapack_complex_double* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_sggglm( lapack_int* n, lapack_int* m, lapack_int* p, float* a,\n                    lapack_int* lda, float* b, lapack_int* ldb, float* d,\n                    float* x, float* y, float* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_dggglm( lapack_int* n, lapack_int* m, lapack_int* p, double* a,\n                    lapack_int* lda, double* b, lapack_int* ldb, double* d,\n                    double* x, double* y, double* work, lapack_int* lwork,\n                    lapack_int *info );\nvoid LAPACK_cggglm( lapack_int* n, lapack_int* m, lapack_int* p,\n                    lapack_complex_float* a, lapack_int* lda,\n                    lapack_complex_float* b, lapack_int* ldb,\n                    lapack_complex_float* d, lapack_complex_float* x,\n                    lapack_complex_float* y, lapack_complex_float* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_zggglm( lapack_int* n, lapack_int* m, lapack_int* p,\n                    lapack_complex_double* a, lapack_int* lda,\n                    lapack_complex_double* b, lapack_int* ldb,\n                    lapack_complex_double* d, lapack_complex_double* x,\n                    lapack_complex_double* y, lapack_complex_double* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_ssyev( char* jobz, char* uplo, lapack_int* n, float* a,\n                   lapack_int* lda, float* w, float* work, lapack_int* lwork,\n                   lapack_int *info );\nvoid LAPACK_dsyev( char* jobz, char* uplo, lapack_int* n, double* a,\n                   lapack_int* lda, double* w, double* work, lapack_int* lwork,\n                   lapack_int *info );\nvoid LAPACK_cheev( char* jobz, char* uplo, lapack_int* n,\n                   lapack_complex_float* a, lapack_int* lda, float* w,\n                   lapack_complex_float* work, lapack_int* lwork, float* rwork,\n                   lapack_int *info );\nvoid LAPACK_zheev( char* jobz, char* uplo, lapack_int* n,\n                   lapack_complex_double* a, lapack_int* lda, double* w,\n                   lapack_complex_double* work, lapack_int* lwork,\n                   double* rwork, lapack_int *info );\nvoid LAPACK_ssyevd( char* jobz, char* uplo, lapack_int* n, float* a,\n                    lapack_int* lda, float* w, float* work, lapack_int* lwork,\n                    lapack_int* iwork, lapack_int* liwork, lapack_int *info );\nvoid LAPACK_dsyevd( char* jobz, char* uplo, lapack_int* n, double* a,\n                    lapack_int* lda, double* w, double* work, lapack_int* lwork,\n                    lapack_int* iwork, lapack_int* liwork, lapack_int *info );\nvoid LAPACK_cheevd( char* jobz, char* uplo, lapack_int* n,\n                    lapack_complex_float* a, lapack_int* lda, float* w,\n                    lapack_complex_float* work, lapack_int* lwork, float* rwork,\n                    lapack_int* lrwork, lapack_int* iwork, lapack_int* liwork,\n                    lapack_int *info );\nvoid LAPACK_zheevd( char* jobz, char* uplo, lapack_int* n,\n                    lapack_complex_double* a, lapack_int* lda, double* w,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    double* rwork, lapack_int* lrwork, lapack_int* iwork,\n                    lapack_int* liwork, lapack_int *info );\nvoid LAPACK_ssyevx( char* jobz, char* range, char* uplo, lapack_int* n,\n                    float* a, lapack_int* lda, float* vl, float* vu,\n                    lapack_int* il, lapack_int* iu, float* abstol,\n                    lapack_int* m, float* w, float* z, lapack_int* ldz,\n                    float* work, lapack_int* lwork, lapack_int* iwork,\n                    lapack_int* ifail, lapack_int *info );\nvoid LAPACK_dsyevx( char* jobz, char* range, char* uplo, lapack_int* n,\n                    double* a, lapack_int* lda, double* vl, double* vu,\n                    lapack_int* il, lapack_int* iu, double* abstol,\n                    lapack_int* m, double* w, double* z, lapack_int* ldz,\n                    double* work, lapack_int* lwork, lapack_int* iwork,\n                    lapack_int* ifail, lapack_int *info );\nvoid LAPACK_cheevx( char* jobz, char* range, char* uplo, lapack_int* n,\n                    lapack_complex_float* a, lapack_int* lda, float* vl,\n                    float* vu, lapack_int* il, lapack_int* iu, float* abstol,\n                    lapack_int* m, float* w, lapack_complex_float* z,\n                    lapack_int* ldz, lapack_complex_float* work,\n                    lapack_int* lwork, float* rwork, lapack_int* iwork,\n                    lapack_int* ifail, lapack_int *info );\nvoid LAPACK_zheevx( char* jobz, char* range, char* uplo, lapack_int* n,\n                    lapack_complex_double* a, lapack_int* lda, double* vl,\n                    double* vu, lapack_int* il, lapack_int* iu, double* abstol,\n                    lapack_int* m, double* w, lapack_complex_double* z,\n                    lapack_int* ldz, lapack_complex_double* work,\n                    lapack_int* lwork, double* rwork, lapack_int* iwork,\n                    lapack_int* ifail, lapack_int *info );\nvoid LAPACK_ssyevr( char* jobz, char* range, char* uplo, lapack_int* n,\n                    float* a, lapack_int* lda, float* vl, float* vu,\n                    lapack_int* il, lapack_int* iu, float* abstol,\n                    lapack_int* m, float* w, float* z, lapack_int* ldz,\n                    lapack_int* isuppz, float* work, lapack_int* lwork,\n                    lapack_int* iwork, lapack_int* liwork, lapack_int *info );\nvoid LAPACK_dsyevr( char* jobz, char* range, char* uplo, lapack_int* n,\n                    double* a, lapack_int* lda, double* vl, double* vu,\n                    lapack_int* il, lapack_int* iu, double* abstol,\n                    lapack_int* m, double* w, double* z, lapack_int* ldz,\n                    lapack_int* isuppz, double* work, lapack_int* lwork,\n                    lapack_int* iwork, lapack_int* liwork, lapack_int *info );\nvoid LAPACK_cheevr( char* jobz, char* range, char* uplo, lapack_int* n,\n                    lapack_complex_float* a, lapack_int* lda, float* vl,\n                    float* vu, lapack_int* il, lapack_int* iu, float* abstol,\n                    lapack_int* m, float* w, lapack_complex_float* z,\n                    lapack_int* ldz, lapack_int* isuppz,\n                    lapack_complex_float* work, lapack_int* lwork, float* rwork,\n                    lapack_int* lrwork, lapack_int* iwork, lapack_int* liwork,\n                    lapack_int *info );\nvoid LAPACK_zheevr( char* jobz, char* range, char* uplo, lapack_int* n,\n                    lapack_complex_double* a, lapack_int* lda, double* vl,\n                    double* vu, lapack_int* il, lapack_int* iu, double* abstol,\n                    lapack_int* m, double* w, lapack_complex_double* z,\n                    lapack_int* ldz, lapack_int* isuppz,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    double* rwork, lapack_int* lrwork, lapack_int* iwork,\n                    lapack_int* liwork, lapack_int *info );\nvoid LAPACK_sspev( char* jobz, char* uplo, lapack_int* n, float* ap, float* w,\n                   float* z, lapack_int* ldz, float* work, lapack_int *info );\nvoid LAPACK_dspev( char* jobz, char* uplo, lapack_int* n, double* ap, double* w,\n                   double* z, lapack_int* ldz, double* work, lapack_int *info );\nvoid LAPACK_chpev( char* jobz, char* uplo, lapack_int* n,\n                   lapack_complex_float* ap, float* w, lapack_complex_float* z,\n                   lapack_int* ldz, lapack_complex_float* work, float* rwork,\n                   lapack_int *info );\nvoid LAPACK_zhpev( char* jobz, char* uplo, lapack_int* n,\n                   lapack_complex_double* ap, double* w,\n                   lapack_complex_double* z, lapack_int* ldz,\n                   lapack_complex_double* work, double* rwork,\n                   lapack_int *info );\nvoid LAPACK_sspevd( char* jobz, char* uplo, lapack_int* n, float* ap, float* w,\n                    float* z, lapack_int* ldz, float* work, lapack_int* lwork,\n                    lapack_int* iwork, lapack_int* liwork, lapack_int *info );\nvoid LAPACK_dspevd( char* jobz, char* uplo, lapack_int* n, double* ap,\n                    double* w, double* z, lapack_int* ldz, double* work,\n                    lapack_int* lwork, lapack_int* iwork, lapack_int* liwork,\n                    lapack_int *info );\nvoid LAPACK_chpevd( char* jobz, char* uplo, lapack_int* n,\n                    lapack_complex_float* ap, float* w, lapack_complex_float* z,\n                    lapack_int* ldz, lapack_complex_float* work,\n                    lapack_int* lwork, float* rwork, lapack_int* lrwork,\n                    lapack_int* iwork, lapack_int* liwork, lapack_int *info );\nvoid LAPACK_zhpevd( char* jobz, char* uplo, lapack_int* n,\n                    lapack_complex_double* ap, double* w,\n                    lapack_complex_double* z, lapack_int* ldz,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    double* rwork, lapack_int* lrwork, lapack_int* iwork,\n                    lapack_int* liwork, lapack_int *info );\nvoid LAPACK_sspevx( char* jobz, char* range, char* uplo, lapack_int* n,\n                    float* ap, float* vl, float* vu, lapack_int* il,\n                    lapack_int* iu, float* abstol, lapack_int* m, float* w,\n                    float* z, lapack_int* ldz, float* work, lapack_int* iwork,\n                    lapack_int* ifail, lapack_int *info );\nvoid LAPACK_dspevx( char* jobz, char* range, char* uplo, lapack_int* n,\n                    double* ap, double* vl, double* vu, lapack_int* il,\n                    lapack_int* iu, double* abstol, lapack_int* m, double* w,\n                    double* z, lapack_int* ldz, double* work, lapack_int* iwork,\n                    lapack_int* ifail, lapack_int *info );\nvoid LAPACK_chpevx( char* jobz, char* range, char* uplo, lapack_int* n,\n                    lapack_complex_float* ap, float* vl, float* vu,\n                    lapack_int* il, lapack_int* iu, float* abstol,\n                    lapack_int* m, float* w, lapack_complex_float* z,\n                    lapack_int* ldz, lapack_complex_float* work, float* rwork,\n                    lapack_int* iwork, lapack_int* ifail, lapack_int *info );\nvoid LAPACK_zhpevx( char* jobz, char* range, char* uplo, lapack_int* n,\n                    lapack_complex_double* ap, double* vl, double* vu,\n                    lapack_int* il, lapack_int* iu, double* abstol,\n                    lapack_int* m, double* w, lapack_complex_double* z,\n                    lapack_int* ldz, lapack_complex_double* work, double* rwork,\n                    lapack_int* iwork, lapack_int* ifail, lapack_int *info );\nvoid LAPACK_ssbev( char* jobz, char* uplo, lapack_int* n, lapack_int* kd,\n                   float* ab, lapack_int* ldab, float* w, float* z,\n                   lapack_int* ldz, float* work, lapack_int *info );\nvoid LAPACK_dsbev( char* jobz, char* uplo, lapack_int* n, lapack_int* kd,\n                   double* ab, lapack_int* ldab, double* w, double* z,\n                   lapack_int* ldz, double* work, lapack_int *info );\nvoid LAPACK_chbev( char* jobz, char* uplo, lapack_int* n, lapack_int* kd,\n                   lapack_complex_float* ab, lapack_int* ldab, float* w,\n                   lapack_complex_float* z, lapack_int* ldz,\n                   lapack_complex_float* work, float* rwork, lapack_int *info );\nvoid LAPACK_zhbev( char* jobz, char* uplo, lapack_int* n, lapack_int* kd,\n                   lapack_complex_double* ab, lapack_int* ldab, double* w,\n                   lapack_complex_double* z, lapack_int* ldz,\n                   lapack_complex_double* work, double* rwork,\n                   lapack_int *info );\nvoid LAPACK_ssbevd( char* jobz, char* uplo, lapack_int* n, lapack_int* kd,\n                    float* ab, lapack_int* ldab, float* w, float* z,\n                    lapack_int* ldz, float* work, lapack_int* lwork,\n                    lapack_int* iwork, lapack_int* liwork, lapack_int *info );\nvoid LAPACK_dsbevd( char* jobz, char* uplo, lapack_int* n, lapack_int* kd,\n                    double* ab, lapack_int* ldab, double* w, double* z,\n                    lapack_int* ldz, double* work, lapack_int* lwork,\n                    lapack_int* iwork, lapack_int* liwork, lapack_int *info );\nvoid LAPACK_chbevd( char* jobz, char* uplo, lapack_int* n, lapack_int* kd,\n                    lapack_complex_float* ab, lapack_int* ldab, float* w,\n                    lapack_complex_float* z, lapack_int* ldz,\n                    lapack_complex_float* work, lapack_int* lwork, float* rwork,\n                    lapack_int* lrwork, lapack_int* iwork, lapack_int* liwork,\n                    lapack_int *info );\nvoid LAPACK_zhbevd( char* jobz, char* uplo, lapack_int* n, lapack_int* kd,\n                    lapack_complex_double* ab, lapack_int* ldab, double* w,\n                    lapack_complex_double* z, lapack_int* ldz,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    double* rwork, lapack_int* lrwork, lapack_int* iwork,\n                    lapack_int* liwork, lapack_int *info );\nvoid LAPACK_ssbevx( char* jobz, char* range, char* uplo, lapack_int* n,\n                    lapack_int* kd, float* ab, lapack_int* ldab, float* q,\n                    lapack_int* ldq, float* vl, float* vu, lapack_int* il,\n                    lapack_int* iu, float* abstol, lapack_int* m, float* w,\n                    float* z, lapack_int* ldz, float* work, lapack_int* iwork,\n                    lapack_int* ifail, lapack_int *info );\nvoid LAPACK_dsbevx( char* jobz, char* range, char* uplo, lapack_int* n,\n                    lapack_int* kd, double* ab, lapack_int* ldab, double* q,\n                    lapack_int* ldq, double* vl, double* vu, lapack_int* il,\n                    lapack_int* iu, double* abstol, lapack_int* m, double* w,\n                    double* z, lapack_int* ldz, double* work, lapack_int* iwork,\n                    lapack_int* ifail, lapack_int *info );\nvoid LAPACK_chbevx( char* jobz, char* range, char* uplo, lapack_int* n,\n                    lapack_int* kd, lapack_complex_float* ab, lapack_int* ldab,\n                    lapack_complex_float* q, lapack_int* ldq, float* vl,\n                    float* vu, lapack_int* il, lapack_int* iu, float* abstol,\n                    lapack_int* m, float* w, lapack_complex_float* z,\n                    lapack_int* ldz, lapack_complex_float* work, float* rwork,\n                    lapack_int* iwork, lapack_int* ifail, lapack_int *info );\nvoid LAPACK_zhbevx( char* jobz, char* range, char* uplo, lapack_int* n,\n                    lapack_int* kd, lapack_complex_double* ab, lapack_int* ldab,\n                    lapack_complex_double* q, lapack_int* ldq, double* vl,\n                    double* vu, lapack_int* il, lapack_int* iu, double* abstol,\n                    lapack_int* m, double* w, lapack_complex_double* z,\n                    lapack_int* ldz, lapack_complex_double* work, double* rwork,\n                    lapack_int* iwork, lapack_int* ifail, lapack_int *info );\nvoid LAPACK_sstev( char* jobz, lapack_int* n, float* d, float* e, float* z,\n                   lapack_int* ldz, float* work, lapack_int *info );\nvoid LAPACK_dstev( char* jobz, lapack_int* n, double* d, double* e, double* z,\n                   lapack_int* ldz, double* work, lapack_int *info );\nvoid LAPACK_sstevd( char* jobz, lapack_int* n, float* d, float* e, float* z,\n                    lapack_int* ldz, float* work, lapack_int* lwork,\n                    lapack_int* iwork, lapack_int* liwork, lapack_int *info );\nvoid LAPACK_dstevd( char* jobz, lapack_int* n, double* d, double* e, double* z,\n                    lapack_int* ldz, double* work, lapack_int* lwork,\n                    lapack_int* iwork, lapack_int* liwork, lapack_int *info );\nvoid LAPACK_sstevx( char* jobz, char* range, lapack_int* n, float* d, float* e,\n                    float* vl, float* vu, lapack_int* il, lapack_int* iu,\n                    float* abstol, lapack_int* m, float* w, float* z,\n                    lapack_int* ldz, float* work, lapack_int* iwork,\n                    lapack_int* ifail, lapack_int *info );\nvoid LAPACK_dstevx( char* jobz, char* range, lapack_int* n, double* d,\n                    double* e, double* vl, double* vu, lapack_int* il,\n                    lapack_int* iu, double* abstol, lapack_int* m, double* w,\n                    double* z, lapack_int* ldz, double* work, lapack_int* iwork,\n                    lapack_int* ifail, lapack_int *info );\nvoid LAPACK_sstevr( char* jobz, char* range, lapack_int* n, float* d, float* e,\n                    float* vl, float* vu, lapack_int* il, lapack_int* iu,\n                    float* abstol, lapack_int* m, float* w, float* z,\n                    lapack_int* ldz, lapack_int* isuppz, float* work,\n                    lapack_int* lwork, lapack_int* iwork, lapack_int* liwork,\n                    lapack_int *info );\nvoid LAPACK_dstevr( char* jobz, char* range, lapack_int* n, double* d,\n                    double* e, double* vl, double* vu, lapack_int* il,\n                    lapack_int* iu, double* abstol, lapack_int* m, double* w,\n                    double* z, lapack_int* ldz, lapack_int* isuppz,\n                    double* work, lapack_int* lwork, lapack_int* iwork,\n                    lapack_int* liwork, lapack_int *info );\nvoid LAPACK_sgees( char* jobvs, char* sort, LAPACK_S_SELECT2 select,\n                   lapack_int* n, float* a, lapack_int* lda, lapack_int* sdim,\n                   float* wr, float* wi, float* vs, lapack_int* ldvs,\n                   float* work, lapack_int* lwork, lapack_logical* bwork,\n                   lapack_int *info );\nvoid LAPACK_dgees( char* jobvs, char* sort, LAPACK_D_SELECT2 select,\n                   lapack_int* n, double* a, lapack_int* lda, lapack_int* sdim,\n                   double* wr, double* wi, double* vs, lapack_int* ldvs,\n                   double* work, lapack_int* lwork, lapack_logical* bwork,\n                   lapack_int *info );\nvoid LAPACK_cgees( char* jobvs, char* sort, LAPACK_C_SELECT1 select,\n                   lapack_int* n, lapack_complex_float* a, lapack_int* lda,\n                   lapack_int* sdim, lapack_complex_float* w,\n                   lapack_complex_float* vs, lapack_int* ldvs,\n                   lapack_complex_float* work, lapack_int* lwork, float* rwork,\n                   lapack_logical* bwork, lapack_int *info );\nvoid LAPACK_zgees( char* jobvs, char* sort, LAPACK_Z_SELECT1 select,\n                   lapack_int* n, lapack_complex_double* a, lapack_int* lda,\n                   lapack_int* sdim, lapack_complex_double* w,\n                   lapack_complex_double* vs, lapack_int* ldvs,\n                   lapack_complex_double* work, lapack_int* lwork,\n                   double* rwork, lapack_logical* bwork, lapack_int *info );\nvoid LAPACK_sgeesx( char* jobvs, char* sort, LAPACK_S_SELECT2 select,\n                    char* sense, lapack_int* n, float* a, lapack_int* lda,\n                    lapack_int* sdim, float* wr, float* wi, float* vs,\n                    lapack_int* ldvs, float* rconde, float* rcondv, float* work,\n                    lapack_int* lwork, lapack_int* iwork, lapack_int* liwork,\n                    lapack_logical* bwork, lapack_int *info );\nvoid LAPACK_dgeesx( char* jobvs, char* sort, LAPACK_D_SELECT2 select,\n                    char* sense, lapack_int* n, double* a, lapack_int* lda,\n                    lapack_int* sdim, double* wr, double* wi, double* vs,\n                    lapack_int* ldvs, double* rconde, double* rcondv,\n                    double* work, lapack_int* lwork, lapack_int* iwork,\n                    lapack_int* liwork, lapack_logical* bwork,\n                    lapack_int *info );\nvoid LAPACK_cgeesx( char* jobvs, char* sort, LAPACK_C_SELECT1 select,\n                    char* sense, lapack_int* n, lapack_complex_float* a,\n                    lapack_int* lda, lapack_int* sdim, lapack_complex_float* w,\n                    lapack_complex_float* vs, lapack_int* ldvs, float* rconde,\n                    float* rcondv, lapack_complex_float* work,\n                    lapack_int* lwork, float* rwork, lapack_logical* bwork,\n                    lapack_int *info );\nvoid LAPACK_zgeesx( char* jobvs, char* sort, LAPACK_Z_SELECT1 select,\n                    char* sense, lapack_int* n, lapack_complex_double* a,\n                    lapack_int* lda, lapack_int* sdim, lapack_complex_double* w,\n                    lapack_complex_double* vs, lapack_int* ldvs, double* rconde,\n                    double* rcondv, lapack_complex_double* work,\n                    lapack_int* lwork, double* rwork, lapack_logical* bwork,\n                    lapack_int *info );\nvoid LAPACK_sgeev( char* jobvl, char* jobvr, lapack_int* n, float* a,\n                   lapack_int* lda, float* wr, float* wi, float* vl,\n                   lapack_int* ldvl, float* vr, lapack_int* ldvr, float* work,\n                   lapack_int* lwork, lapack_int *info );\nvoid LAPACK_dgeev( char* jobvl, char* jobvr, lapack_int* n, double* a,\n                   lapack_int* lda, double* wr, double* wi, double* vl,\n                   lapack_int* ldvl, double* vr, lapack_int* ldvr, double* work,\n                   lapack_int* lwork, lapack_int *info );\nvoid LAPACK_cgeev( char* jobvl, char* jobvr, lapack_int* n,\n                   lapack_complex_float* a, lapack_int* lda,\n                   lapack_complex_float* w, lapack_complex_float* vl,\n                   lapack_int* ldvl, lapack_complex_float* vr, lapack_int* ldvr,\n                   lapack_complex_float* work, lapack_int* lwork, float* rwork,\n                   lapack_int *info );\nvoid LAPACK_zgeev( char* jobvl, char* jobvr, lapack_int* n,\n                   lapack_complex_double* a, lapack_int* lda,\n                   lapack_complex_double* w, lapack_complex_double* vl,\n                   lapack_int* ldvl, lapack_complex_double* vr,\n                   lapack_int* ldvr, lapack_complex_double* work,\n                   lapack_int* lwork, double* rwork, lapack_int *info );\nvoid LAPACK_sgeevx( char* balanc, char* jobvl, char* jobvr, char* sense,\n                    lapack_int* n, float* a, lapack_int* lda, float* wr,\n                    float* wi, float* vl, lapack_int* ldvl, float* vr,\n                    lapack_int* ldvr, lapack_int* ilo, lapack_int* ihi,\n                    float* scale, float* abnrm, float* rconde, float* rcondv,\n                    float* work, lapack_int* lwork, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_dgeevx( char* balanc, char* jobvl, char* jobvr, char* sense,\n                    lapack_int* n, double* a, lapack_int* lda, double* wr,\n                    double* wi, double* vl, lapack_int* ldvl, double* vr,\n                    lapack_int* ldvr, lapack_int* ilo, lapack_int* ihi,\n                    double* scale, double* abnrm, double* rconde,\n                    double* rcondv, double* work, lapack_int* lwork,\n                    lapack_int* iwork, lapack_int *info );\nvoid LAPACK_cgeevx( char* balanc, char* jobvl, char* jobvr, char* sense,\n                    lapack_int* n, lapack_complex_float* a, lapack_int* lda,\n                    lapack_complex_float* w, lapack_complex_float* vl,\n                    lapack_int* ldvl, lapack_complex_float* vr,\n                    lapack_int* ldvr, lapack_int* ilo, lapack_int* ihi,\n                    float* scale, float* abnrm, float* rconde, float* rcondv,\n                    lapack_complex_float* work, lapack_int* lwork, float* rwork,\n                    lapack_int *info );\nvoid LAPACK_zgeevx( char* balanc, char* jobvl, char* jobvr, char* sense,\n                    lapack_int* n, lapack_complex_double* a, lapack_int* lda,\n                    lapack_complex_double* w, lapack_complex_double* vl,\n                    lapack_int* ldvl, lapack_complex_double* vr,\n                    lapack_int* ldvr, lapack_int* ilo, lapack_int* ihi,\n                    double* scale, double* abnrm, double* rconde,\n                    double* rcondv, lapack_complex_double* work,\n                    lapack_int* lwork, double* rwork, lapack_int *info );\nvoid LAPACK_sgesvd( char* jobu, char* jobvt, lapack_int* m, lapack_int* n,\n                    float* a, lapack_int* lda, float* s, float* u,\n                    lapack_int* ldu, float* vt, lapack_int* ldvt, float* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_dgesvd( char* jobu, char* jobvt, lapack_int* m, lapack_int* n,\n                    double* a, lapack_int* lda, double* s, double* u,\n                    lapack_int* ldu, double* vt, lapack_int* ldvt, double* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_cgesvd( char* jobu, char* jobvt, lapack_int* m, lapack_int* n,\n                    lapack_complex_float* a, lapack_int* lda, float* s,\n                    lapack_complex_float* u, lapack_int* ldu,\n                    lapack_complex_float* vt, lapack_int* ldvt,\n                    lapack_complex_float* work, lapack_int* lwork, float* rwork,\n                    lapack_int *info );\nvoid LAPACK_zgesvd( char* jobu, char* jobvt, lapack_int* m, lapack_int* n,\n                    lapack_complex_double* a, lapack_int* lda, double* s,\n                    lapack_complex_double* u, lapack_int* ldu,\n                    lapack_complex_double* vt, lapack_int* ldvt,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    double* rwork, lapack_int *info );\nvoid LAPACK_sgesdd( char* jobz, lapack_int* m, lapack_int* n, float* a,\n                    lapack_int* lda, float* s, float* u, lapack_int* ldu,\n                    float* vt, lapack_int* ldvt, float* work, lapack_int* lwork,\n                    lapack_int* iwork, lapack_int *info );\nvoid LAPACK_dgesdd( char* jobz, lapack_int* m, lapack_int* n, double* a,\n                    lapack_int* lda, double* s, double* u, lapack_int* ldu,\n                    double* vt, lapack_int* ldvt, double* work,\n                    lapack_int* lwork, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_cgesdd( char* jobz, lapack_int* m, lapack_int* n,\n                    lapack_complex_float* a, lapack_int* lda, float* s,\n                    lapack_complex_float* u, lapack_int* ldu,\n                    lapack_complex_float* vt, lapack_int* ldvt,\n                    lapack_complex_float* work, lapack_int* lwork, float* rwork,\n                    lapack_int* iwork, lapack_int *info );\nvoid LAPACK_zgesdd( char* jobz, lapack_int* m, lapack_int* n,\n                    lapack_complex_double* a, lapack_int* lda, double* s,\n                    lapack_complex_double* u, lapack_int* ldu,\n                    lapack_complex_double* vt, lapack_int* ldvt,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    double* rwork, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_dgejsv( char* joba, char* jobu, char* jobv, char* jobr, char* jobt,\n                    char* jobp, lapack_int* m, lapack_int* n, double* a,\n                    lapack_int* lda, double* sva, double* u, lapack_int* ldu,\n                    double* v, lapack_int* ldv, double* work, lapack_int* lwork,\n                    lapack_int* iwork, lapack_int *info );\nvoid LAPACK_sgejsv( char* joba, char* jobu, char* jobv, char* jobr, char* jobt,\n                    char* jobp, lapack_int* m, lapack_int* n, float* a,\n                    lapack_int* lda, float* sva, float* u, lapack_int* ldu,\n                    float* v, lapack_int* ldv, float* work, lapack_int* lwork,\n                    lapack_int* iwork, lapack_int *info );\nvoid LAPACK_dgesvj( char* joba, char* jobu, char* jobv, lapack_int* m,\n                    lapack_int* n, double* a, lapack_int* lda, double* sva,\n                    lapack_int* mv, double* v, lapack_int* ldv, double* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_sgesvj( char* joba, char* jobu, char* jobv, lapack_int* m,\n                    lapack_int* n, float* a, lapack_int* lda, float* sva,\n                    lapack_int* mv, float* v, lapack_int* ldv, float* work,\n                    lapack_int* lwork, lapack_int *info );\nvoid LAPACK_sggsvd( char* jobu, char* jobv, char* jobq, lapack_int* m,\n                    lapack_int* n, lapack_int* p, lapack_int* k, lapack_int* l,\n                    float* a, lapack_int* lda, float* b, lapack_int* ldb,\n                    float* alpha, float* beta, float* u, lapack_int* ldu,\n                    float* v, lapack_int* ldv, float* q, lapack_int* ldq,\n                    float* work, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_dggsvd( char* jobu, char* jobv, char* jobq, lapack_int* m,\n                    lapack_int* n, lapack_int* p, lapack_int* k, lapack_int* l,\n                    double* a, lapack_int* lda, double* b, lapack_int* ldb,\n                    double* alpha, double* beta, double* u, lapack_int* ldu,\n                    double* v, lapack_int* ldv, double* q, lapack_int* ldq,\n                    double* work, lapack_int* iwork, lapack_int *info );\nvoid LAPACK_cggsvd( char* jobu, char* jobv, char* jobq, lapack_int* m,\n                    lapack_int* n, lapack_int* p, lapack_int* k, lapack_int* l,\n                    lapack_complex_float* a, lapack_int* lda,\n                    lapack_complex_float* b, lapack_int* ldb, float* alpha,\n                    float* beta, lapack_complex_float* u, lapack_int* ldu,\n                    lapack_complex_float* v, lapack_int* ldv,\n                    lapack_complex_float* q, lapack_int* ldq,\n                    lapack_complex_float* work, float* rwork, lapack_int* iwork,\n                    lapack_int *info );\nvoid LAPACK_zggsvd( char* jobu, char* jobv, char* jobq, lapack_int* m,\n                    lapack_int* n, lapack_int* p, lapack_int* k, lapack_int* l,\n                    lapack_complex_double* a, lapack_int* lda,\n                    lapack_complex_double* b, lapack_int* ldb, double* alpha,\n                    double* beta, lapack_complex_double* u, lapack_int* ldu,\n                    lapack_complex_double* v, lapack_int* ldv,\n                    lapack_complex_double* q, lapack_int* ldq,\n                    lapack_complex_double* work, double* rwork,\n                    lapack_int* iwork, lapack_int *info );\nvoid LAPACK_ssygv( lapack_int* itype, char* jobz, char* uplo, lapack_int* n,\n                   float* a, lapack_int* lda, float* b, lapack_int* ldb,\n                   float* w, float* work, lapack_int* lwork, lapack_int *info );\nvoid LAPACK_dsygv( lapack_int* itype, char* jobz, char* uplo, lapack_int* n,\n                   double* a, lapack_int* lda, double* b, lapack_int* ldb,\n                   double* w, double* work, lapack_int* lwork,\n                   lapack_int *info );\nvoid LAPACK_chegv( lapack_int* itype, char* jobz, char* uplo, lapack_int* n,\n                   lapack_complex_float* a, lapack_int* lda,\n                   lapack_complex_float* b, lapack_int* ldb, float* w,\n                   lapack_complex_float* work, lapack_int* lwork, float* rwork,\n                   lapack_int *info );\nvoid LAPACK_zhegv( lapack_int* itype, char* jobz, char* uplo, lapack_int* n,\n                   lapack_complex_double* a, lapack_int* lda,\n                   lapack_complex_double* b, lapack_int* ldb, double* w,\n                   lapack_complex_double* work, lapack_int* lwork,\n                   double* rwork, lapack_int *info );\nvoid LAPACK_ssygvd( lapack_int* itype, char* jobz, char* uplo, lapack_int* n,\n                    float* a, lapack_int* lda, float* b, lapack_int* ldb,\n                    float* w, float* work, lapack_int* lwork, lapack_int* iwork,\n                    lapack_int* liwork, lapack_int *info );\nvoid LAPACK_dsygvd( lapack_int* itype, char* jobz, char* uplo, lapack_int* n,\n                    double* a, lapack_int* lda, double* b, lapack_int* ldb,\n                    double* w, double* work, lapack_int* lwork,\n                    lapack_int* iwork, lapack_int* liwork, lapack_int *info );\nvoid LAPACK_chegvd( lapack_int* itype, char* jobz, char* uplo, lapack_int* n,\n                    lapack_complex_float* a, lapack_int* lda,\n                    lapack_complex_float* b, lapack_int* ldb, float* w,\n                    lapack_complex_float* work, lapack_int* lwork, float* rwork,\n                    lapack_int* lrwork, lapack_int* iwork, lapack_int* liwork,\n                    lapack_int *info );\nvoid LAPACK_zhegvd( lapack_int* itype, char* jobz, char* uplo, lapack_int* n,\n                    lapack_complex_double* a, lapack_int* lda,\n                    lapack_complex_double* b, lapack_int* ldb, double* w,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    double* rwork, lapack_int* lrwork, lapack_int* iwork,\n                    lapack_int* liwork, lapack_int *info );\nvoid LAPACK_ssygvx( lapack_int* itype, char* jobz, char* range, char* uplo,\n                    lapack_int* n, float* a, lapack_int* lda, float* b,\n                    lapack_int* ldb, float* vl, float* vu, lapack_int* il,\n                    lapack_int* iu, float* abstol, lapack_int* m, float* w,\n                    float* z, lapack_int* ldz, float* work, lapack_int* lwork,\n                    lapack_int* iwork, lapack_int* ifail, lapack_int *info );\nvoid LAPACK_dsygvx( lapack_int* itype, char* jobz, char* range, char* uplo,\n                    lapack_int* n, double* a, lapack_int* lda, double* b,\n                    lapack_int* ldb, double* vl, double* vu, lapack_int* il,\n                    lapack_int* iu, double* abstol, lapack_int* m, double* w,\n                    double* z, lapack_int* ldz, double* work, lapack_int* lwork,\n                    lapack_int* iwork, lapack_int* ifail, lapack_int *info );\nvoid LAPACK_chegvx( lapack_int* itype, char* jobz, char* range, char* uplo,\n                    lapack_int* n, lapack_complex_float* a, lapack_int* lda,\n                    lapack_complex_float* b, lapack_int* ldb, float* vl,\n                    float* vu, lapack_int* il, lapack_int* iu, float* abstol,\n                    lapack_int* m, float* w, lapack_complex_float* z,\n                    lapack_int* ldz, lapack_complex_float* work,\n                    lapack_int* lwork, float* rwork, lapack_int* iwork,\n                    lapack_int* ifail, lapack_int *info );\nvoid LAPACK_zhegvx( lapack_int* itype, char* jobz, char* range, char* uplo,\n                    lapack_int* n, lapack_complex_double* a, lapack_int* lda,\n                    lapack_complex_double* b, lapack_int* ldb, double* vl,\n                    double* vu, lapack_int* il, lapack_int* iu, double* abstol,\n                    lapack_int* m, double* w, lapack_complex_double* z,\n                    lapack_int* ldz, lapack_complex_double* work,\n                    lapack_int* lwork, double* rwork, lapack_int* iwork,\n                    lapack_int* ifail, lapack_int *info );\nvoid LAPACK_sspgv( lapack_int* itype, char* jobz, char* uplo, lapack_int* n,\n                   float* ap, float* bp, float* w, float* z, lapack_int* ldz,\n                   float* work, lapack_int *info );\nvoid LAPACK_dspgv( lapack_int* itype, char* jobz, char* uplo, lapack_int* n,\n                   double* ap, double* bp, double* w, double* z,\n                   lapack_int* ldz, double* work, lapack_int *info );\nvoid LAPACK_chpgv( lapack_int* itype, char* jobz, char* uplo, lapack_int* n,\n                   lapack_complex_float* ap, lapack_complex_float* bp, float* w,\n                   lapack_complex_float* z, lapack_int* ldz,\n                   lapack_complex_float* work, float* rwork, lapack_int *info );\nvoid LAPACK_zhpgv( lapack_int* itype, char* jobz, char* uplo, lapack_int* n,\n                   lapack_complex_double* ap, lapack_complex_double* bp,\n                   double* w, lapack_complex_double* z, lapack_int* ldz,\n                   lapack_complex_double* work, double* rwork,\n                   lapack_int *info );\nvoid LAPACK_sspgvd( lapack_int* itype, char* jobz, char* uplo, lapack_int* n,\n                    float* ap, float* bp, float* w, float* z, lapack_int* ldz,\n                    float* work, lapack_int* lwork, lapack_int* iwork,\n                    lapack_int* liwork, lapack_int *info );\nvoid LAPACK_dspgvd( lapack_int* itype, char* jobz, char* uplo, lapack_int* n,\n                    double* ap, double* bp, double* w, double* z,\n                    lapack_int* ldz, double* work, lapack_int* lwork,\n                    lapack_int* iwork, lapack_int* liwork, lapack_int *info );\nvoid LAPACK_chpgvd( lapack_int* itype, char* jobz, char* uplo, lapack_int* n,\n                    lapack_complex_float* ap, lapack_complex_float* bp,\n                    float* w, lapack_complex_float* z, lapack_int* ldz,\n                    lapack_complex_float* work, lapack_int* lwork, float* rwork,\n                    lapack_int* lrwork, lapack_int* iwork, lapack_int* liwork,\n                    lapack_int *info );\nvoid LAPACK_zhpgvd( lapack_int* itype, char* jobz, char* uplo, lapack_int* n,\n                    lapack_complex_double* ap, lapack_complex_double* bp,\n                    double* w, lapack_complex_double* z, lapack_int* ldz,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    double* rwork, lapack_int* lrwork, lapack_int* iwork,\n                    lapack_int* liwork, lapack_int *info );\nvoid LAPACK_sspgvx( lapack_int* itype, char* jobz, char* range, char* uplo,\n                    lapack_int* n, float* ap, float* bp, float* vl, float* vu,\n                    lapack_int* il, lapack_int* iu, float* abstol,\n                    lapack_int* m, float* w, float* z, lapack_int* ldz,\n                    float* work, lapack_int* iwork, lapack_int* ifail,\n                    lapack_int *info );\nvoid LAPACK_dspgvx( lapack_int* itype, char* jobz, char* range, char* uplo,\n                    lapack_int* n, double* ap, double* bp, double* vl,\n                    double* vu, lapack_int* il, lapack_int* iu, double* abstol,\n                    lapack_int* m, double* w, double* z, lapack_int* ldz,\n                    double* work, lapack_int* iwork, lapack_int* ifail,\n                    lapack_int *info );\nvoid LAPACK_chpgvx( lapack_int* itype, char* jobz, char* range, char* uplo,\n                    lapack_int* n, lapack_complex_float* ap,\n                    lapack_complex_float* bp, float* vl, float* vu,\n                    lapack_int* il, lapack_int* iu, float* abstol,\n                    lapack_int* m, float* w, lapack_complex_float* z,\n                    lapack_int* ldz, lapack_complex_float* work, float* rwork,\n                    lapack_int* iwork, lapack_int* ifail, lapack_int *info );\nvoid LAPACK_zhpgvx( lapack_int* itype, char* jobz, char* range, char* uplo,\n                    lapack_int* n, lapack_complex_double* ap,\n                    lapack_complex_double* bp, double* vl, double* vu,\n                    lapack_int* il, lapack_int* iu, double* abstol,\n                    lapack_int* m, double* w, lapack_complex_double* z,\n                    lapack_int* ldz, lapack_complex_double* work, double* rwork,\n                    lapack_int* iwork, lapack_int* ifail, lapack_int *info );\nvoid LAPACK_ssbgv( char* jobz, char* uplo, lapack_int* n, lapack_int* ka,\n                   lapack_int* kb, float* ab, lapack_int* ldab, float* bb,\n                   lapack_int* ldbb, float* w, float* z, lapack_int* ldz,\n                   float* work, lapack_int *info );\nvoid LAPACK_dsbgv( char* jobz, char* uplo, lapack_int* n, lapack_int* ka,\n                   lapack_int* kb, double* ab, lapack_int* ldab, double* bb,\n                   lapack_int* ldbb, double* w, double* z, lapack_int* ldz,\n                   double* work, lapack_int *info );\nvoid LAPACK_chbgv( char* jobz, char* uplo, lapack_int* n, lapack_int* ka,\n                   lapack_int* kb, lapack_complex_float* ab, lapack_int* ldab,\n                   lapack_complex_float* bb, lapack_int* ldbb, float* w,\n                   lapack_complex_float* z, lapack_int* ldz,\n                   lapack_complex_float* work, float* rwork, lapack_int *info );\nvoid LAPACK_zhbgv( char* jobz, char* uplo, lapack_int* n, lapack_int* ka,\n                   lapack_int* kb, lapack_complex_double* ab, lapack_int* ldab,\n                   lapack_complex_double* bb, lapack_int* ldbb, double* w,\n                   lapack_complex_double* z, lapack_int* ldz,\n                   lapack_complex_double* work, double* rwork,\n                   lapack_int *info );\nvoid LAPACK_ssbgvd( char* jobz, char* uplo, lapack_int* n, lapack_int* ka,\n                    lapack_int* kb, float* ab, lapack_int* ldab, float* bb,\n                    lapack_int* ldbb, float* w, float* z, lapack_int* ldz,\n                    float* work, lapack_int* lwork, lapack_int* iwork,\n                    lapack_int* liwork, lapack_int *info );\nvoid LAPACK_dsbgvd( char* jobz, char* uplo, lapack_int* n, lapack_int* ka,\n                    lapack_int* kb, double* ab, lapack_int* ldab, double* bb,\n                    lapack_int* ldbb, double* w, double* z, lapack_int* ldz,\n                    double* work, lapack_int* lwork, lapack_int* iwork,\n                    lapack_int* liwork, lapack_int *info );\nvoid LAPACK_chbgvd( char* jobz, char* uplo, lapack_int* n, lapack_int* ka,\n                    lapack_int* kb, lapack_complex_float* ab, lapack_int* ldab,\n                    lapack_complex_float* bb, lapack_int* ldbb, float* w,\n                    lapack_complex_float* z, lapack_int* ldz,\n                    lapack_complex_float* work, lapack_int* lwork, float* rwork,\n                    lapack_int* lrwork, lapack_int* iwork, lapack_int* liwork,\n                    lapack_int *info );\nvoid LAPACK_zhbgvd( char* jobz, char* uplo, lapack_int* n, lapack_int* ka,\n                    lapack_int* kb, lapack_complex_double* ab, lapack_int* ldab,\n                    lapack_complex_double* bb, lapack_int* ldbb, double* w,\n                    lapack_complex_double* z, lapack_int* ldz,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    double* rwork, lapack_int* lrwork, lapack_int* iwork,\n                    lapack_int* liwork, lapack_int *info );\nvoid LAPACK_ssbgvx( char* jobz, char* range, char* uplo, lapack_int* n,\n                    lapack_int* ka, lapack_int* kb, float* ab, lapack_int* ldab,\n                    float* bb, lapack_int* ldbb, float* q, lapack_int* ldq,\n                    float* vl, float* vu, lapack_int* il, lapack_int* iu,\n                    float* abstol, lapack_int* m, float* w, float* z,\n                    lapack_int* ldz, float* work, lapack_int* iwork,\n                    lapack_int* ifail, lapack_int *info );\nvoid LAPACK_dsbgvx( char* jobz, char* range, char* uplo, lapack_int* n,\n                    lapack_int* ka, lapack_int* kb, double* ab,\n                    lapack_int* ldab, double* bb, lapack_int* ldbb, double* q,\n                    lapack_int* ldq, double* vl, double* vu, lapack_int* il,\n                    lapack_int* iu, double* abstol, lapack_int* m, double* w,\n                    double* z, lapack_int* ldz, double* work, lapack_int* iwork,\n                    lapack_int* ifail, lapack_int *info );\nvoid LAPACK_chbgvx( char* jobz, char* range, char* uplo, lapack_int* n,\n                    lapack_int* ka, lapack_int* kb, lapack_complex_float* ab,\n                    lapack_int* ldab, lapack_complex_float* bb,\n                    lapack_int* ldbb, lapack_complex_float* q, lapack_int* ldq,\n                    float* vl, float* vu, lapack_int* il, lapack_int* iu,\n                    float* abstol, lapack_int* m, float* w,\n                    lapack_complex_float* z, lapack_int* ldz,\n                    lapack_complex_float* work, float* rwork, lapack_int* iwork,\n                    lapack_int* ifail, lapack_int *info );\nvoid LAPACK_zhbgvx( char* jobz, char* range, char* uplo, lapack_int* n,\n                    lapack_int* ka, lapack_int* kb, lapack_complex_double* ab,\n                    lapack_int* ldab, lapack_complex_double* bb,\n                    lapack_int* ldbb, lapack_complex_double* q, lapack_int* ldq,\n                    double* vl, double* vu, lapack_int* il, lapack_int* iu,\n                    double* abstol, lapack_int* m, double* w,\n                    lapack_complex_double* z, lapack_int* ldz,\n                    lapack_complex_double* work, double* rwork,\n                    lapack_int* iwork, lapack_int* ifail, lapack_int *info );\nvoid LAPACK_sgges( char* jobvsl, char* jobvsr, char* sort,\n                   LAPACK_S_SELECT3 selctg, lapack_int* n, float* a,\n                   lapack_int* lda, float* b, lapack_int* ldb, lapack_int* sdim,\n                   float* alphar, float* alphai, float* beta, float* vsl,\n                   lapack_int* ldvsl, float* vsr, lapack_int* ldvsr,\n                   float* work, lapack_int* lwork, lapack_logical* bwork,\n                   lapack_int *info );\nvoid LAPACK_dgges( char* jobvsl, char* jobvsr, char* sort,\n                   LAPACK_D_SELECT3 selctg, lapack_int* n, double* a,\n                   lapack_int* lda, double* b, lapack_int* ldb,\n                   lapack_int* sdim, double* alphar, double* alphai,\n                   double* beta, double* vsl, lapack_int* ldvsl, double* vsr,\n                   lapack_int* ldvsr, double* work, lapack_int* lwork,\n                   lapack_logical* bwork, lapack_int *info );\nvoid LAPACK_cgges( char* jobvsl, char* jobvsr, char* sort,\n                   LAPACK_C_SELECT2 selctg, lapack_int* n,\n                   lapack_complex_float* a, lapack_int* lda,\n                   lapack_complex_float* b, lapack_int* ldb, lapack_int* sdim,\n                   lapack_complex_float* alpha, lapack_complex_float* beta,\n                   lapack_complex_float* vsl, lapack_int* ldvsl,\n                   lapack_complex_float* vsr, lapack_int* ldvsr,\n                   lapack_complex_float* work, lapack_int* lwork, float* rwork,\n                   lapack_logical* bwork, lapack_int *info );\nvoid LAPACK_zgges( char* jobvsl, char* jobvsr, char* sort,\n                   LAPACK_Z_SELECT2 selctg, lapack_int* n,\n                   lapack_complex_double* a, lapack_int* lda,\n                   lapack_complex_double* b, lapack_int* ldb, lapack_int* sdim,\n                   lapack_complex_double* alpha, lapack_complex_double* beta,\n                   lapack_complex_double* vsl, lapack_int* ldvsl,\n                   lapack_complex_double* vsr, lapack_int* ldvsr,\n                   lapack_complex_double* work, lapack_int* lwork,\n                   double* rwork, lapack_logical* bwork, lapack_int *info );\nvoid LAPACK_sggesx( char* jobvsl, char* jobvsr, char* sort,\n                    LAPACK_S_SELECT3 selctg, char* sense, lapack_int* n,\n                    float* a, lapack_int* lda, float* b, lapack_int* ldb,\n                    lapack_int* sdim, float* alphar, float* alphai, float* beta,\n                    float* vsl, lapack_int* ldvsl, float* vsr,\n                    lapack_int* ldvsr, float* rconde, float* rcondv,\n                    float* work, lapack_int* lwork, lapack_int* iwork,\n                    lapack_int* liwork, lapack_logical* bwork,\n                    lapack_int *info );\nvoid LAPACK_dggesx( char* jobvsl, char* jobvsr, char* sort,\n                    LAPACK_D_SELECT3 selctg, char* sense, lapack_int* n,\n                    double* a, lapack_int* lda, double* b, lapack_int* ldb,\n                    lapack_int* sdim, double* alphar, double* alphai,\n                    double* beta, double* vsl, lapack_int* ldvsl, double* vsr,\n                    lapack_int* ldvsr, double* rconde, double* rcondv,\n                    double* work, lapack_int* lwork, lapack_int* iwork,\n                    lapack_int* liwork, lapack_logical* bwork,\n                    lapack_int *info );\nvoid LAPACK_cggesx( char* jobvsl, char* jobvsr, char* sort,\n                    LAPACK_C_SELECT2 selctg, char* sense, lapack_int* n,\n                    lapack_complex_float* a, lapack_int* lda,\n                    lapack_complex_float* b, lapack_int* ldb, lapack_int* sdim,\n                    lapack_complex_float* alpha, lapack_complex_float* beta,\n                    lapack_complex_float* vsl, lapack_int* ldvsl,\n                    lapack_complex_float* vsr, lapack_int* ldvsr, float* rconde,\n                    float* rcondv, lapack_complex_float* work,\n                    lapack_int* lwork, float* rwork, lapack_int* iwork,\n                    lapack_int* liwork, lapack_logical* bwork,\n                    lapack_int *info );\nvoid LAPACK_zggesx( char* jobvsl, char* jobvsr, char* sort,\n                    LAPACK_Z_SELECT2 selctg, char* sense, lapack_int* n,\n                    lapack_complex_double* a, lapack_int* lda,\n                    lapack_complex_double* b, lapack_int* ldb, lapack_int* sdim,\n                    lapack_complex_double* alpha, lapack_complex_double* beta,\n                    lapack_complex_double* vsl, lapack_int* ldvsl,\n                    lapack_complex_double* vsr, lapack_int* ldvsr,\n                    double* rconde, double* rcondv, lapack_complex_double* work,\n                    lapack_int* lwork, double* rwork, lapack_int* iwork,\n                    lapack_int* liwork, lapack_logical* bwork,\n                    lapack_int *info );\nvoid LAPACK_sggev( char* jobvl, char* jobvr, lapack_int* n, float* a,\n                   lapack_int* lda, float* b, lapack_int* ldb, float* alphar,\n                   float* alphai, float* beta, float* vl, lapack_int* ldvl,\n                   float* vr, lapack_int* ldvr, float* work, lapack_int* lwork,\n                   lapack_int *info );\nvoid LAPACK_dggev( char* jobvl, char* jobvr, lapack_int* n, double* a,\n                   lapack_int* lda, double* b, lapack_int* ldb, double* alphar,\n                   double* alphai, double* beta, double* vl, lapack_int* ldvl,\n                   double* vr, lapack_int* ldvr, double* work,\n                   lapack_int* lwork, lapack_int *info );\nvoid LAPACK_cggev( char* jobvl, char* jobvr, lapack_int* n,\n                   lapack_complex_float* a, lapack_int* lda,\n                   lapack_complex_float* b, lapack_int* ldb,\n                   lapack_complex_float* alpha, lapack_complex_float* beta,\n                   lapack_complex_float* vl, lapack_int* ldvl,\n                   lapack_complex_float* vr, lapack_int* ldvr,\n                   lapack_complex_float* work, lapack_int* lwork, float* rwork,\n                   lapack_int *info );\nvoid LAPACK_zggev( char* jobvl, char* jobvr, lapack_int* n,\n                   lapack_complex_double* a, lapack_int* lda,\n                   lapack_complex_double* b, lapack_int* ldb,\n                   lapack_complex_double* alpha, lapack_complex_double* beta,\n                   lapack_complex_double* vl, lapack_int* ldvl,\n                   lapack_complex_double* vr, lapack_int* ldvr,\n                   lapack_complex_double* work, lapack_int* lwork,\n                   double* rwork, lapack_int *info );\nvoid LAPACK_sggevx( char* balanc, char* jobvl, char* jobvr, char* sense,\n                    lapack_int* n, float* a, lapack_int* lda, float* b,\n                    lapack_int* ldb, float* alphar, float* alphai, float* beta,\n                    float* vl, lapack_int* ldvl, float* vr, lapack_int* ldvr,\n                    lapack_int* ilo, lapack_int* ihi, float* lscale,\n                    float* rscale, float* abnrm, float* bbnrm, float* rconde,\n                    float* rcondv, float* work, lapack_int* lwork,\n                    lapack_int* iwork, lapack_logical* bwork,\n                    lapack_int *info );\nvoid LAPACK_dggevx( char* balanc, char* jobvl, char* jobvr, char* sense,\n                    lapack_int* n, double* a, lapack_int* lda, double* b,\n                    lapack_int* ldb, double* alphar, double* alphai,\n                    double* beta, double* vl, lapack_int* ldvl, double* vr,\n                    lapack_int* ldvr, lapack_int* ilo, lapack_int* ihi,\n                    double* lscale, double* rscale, double* abnrm,\n                    double* bbnrm, double* rconde, double* rcondv, double* work,\n                    lapack_int* lwork, lapack_int* iwork, lapack_logical* bwork,\n                    lapack_int *info );\nvoid LAPACK_cggevx( char* balanc, char* jobvl, char* jobvr, char* sense,\n                    lapack_int* n, lapack_complex_float* a, lapack_int* lda,\n                    lapack_complex_float* b, lapack_int* ldb,\n                    lapack_complex_float* alpha, lapack_complex_float* beta,\n                    lapack_complex_float* vl, lapack_int* ldvl,\n                    lapack_complex_float* vr, lapack_int* ldvr, lapack_int* ilo,\n                    lapack_int* ihi, float* lscale, float* rscale, float* abnrm,\n                    float* bbnrm, float* rconde, float* rcondv,\n                    lapack_complex_float* work, lapack_int* lwork, float* rwork,\n                    lapack_int* iwork, lapack_logical* bwork,\n                    lapack_int *info );\nvoid LAPACK_zggevx( char* balanc, char* jobvl, char* jobvr, char* sense,\n                    lapack_int* n, lapack_complex_double* a, lapack_int* lda,\n                    lapack_complex_double* b, lapack_int* ldb,\n                    lapack_complex_double* alpha, lapack_complex_double* beta,\n                    lapack_complex_double* vl, lapack_int* ldvl,\n                    lapack_complex_double* vr, lapack_int* ldvr,\n                    lapack_int* ilo, lapack_int* ihi, double* lscale,\n                    double* rscale, double* abnrm, double* bbnrm,\n                    double* rconde, double* rcondv, lapack_complex_double* work,\n                    lapack_int* lwork, double* rwork, lapack_int* iwork,\n                    lapack_logical* bwork, lapack_int *info );\nvoid LAPACK_dsfrk( char* transr, char* uplo, char* trans, lapack_int* n,\n                   lapack_int* k, double* alpha, const double* a,\n                   lapack_int* lda, double* beta, double* c );\nvoid LAPACK_ssfrk( char* transr, char* uplo, char* trans, lapack_int* n,\n                   lapack_int* k, float* alpha, const float* a, lapack_int* lda,\n                   float* beta, float* c );\nvoid LAPACK_zhfrk( char* transr, char* uplo, char* trans, lapack_int* n,\n                   lapack_int* k, double* alpha, const lapack_complex_double* a,\n                   lapack_int* lda, double* beta, lapack_complex_double* c );\nvoid LAPACK_chfrk( char* transr, char* uplo, char* trans, lapack_int* n,\n                   lapack_int* k, float* alpha, const lapack_complex_float* a,\n                   lapack_int* lda, float* beta, lapack_complex_float* c );\nvoid LAPACK_dtfsm( char* transr, char* side, char* uplo, char* trans,\n                   char* diag, lapack_int* m, lapack_int* n, double* alpha,\n                   const double* a, double* b, lapack_int* ldb );\nvoid LAPACK_stfsm( char* transr, char* side, char* uplo, char* trans,\n                   char* diag, lapack_int* m, lapack_int* n, float* alpha,\n                   const float* a, float* b, lapack_int* ldb );\nvoid LAPACK_ztfsm( char* transr, char* side, char* uplo, char* trans,\n                   char* diag, lapack_int* m, lapack_int* n,\n                   lapack_complex_double* alpha, const lapack_complex_double* a,\n                   lapack_complex_double* b, lapack_int* ldb );\nvoid LAPACK_ctfsm( char* transr, char* side, char* uplo, char* trans,\n                   char* diag, lapack_int* m, lapack_int* n,\n                   lapack_complex_float* alpha, const lapack_complex_float* a,\n                   lapack_complex_float* b, lapack_int* ldb );\nvoid LAPACK_dtfttp( char* transr, char* uplo, lapack_int* n, const double* arf,\n                    double* ap, lapack_int *info );\nvoid LAPACK_stfttp( char* transr, char* uplo, lapack_int* n, const float* arf,\n                    float* ap, lapack_int *info );\nvoid LAPACK_ztfttp( char* transr, char* uplo, lapack_int* n,\n                    const lapack_complex_double* arf, lapack_complex_double* ap,\n                    lapack_int *info );\nvoid LAPACK_ctfttp( char* transr, char* uplo, lapack_int* n,\n                    const lapack_complex_float* arf, lapack_complex_float* ap,\n                    lapack_int *info );\nvoid LAPACK_dtfttr( char* transr, char* uplo, lapack_int* n, const double* arf,\n                    double* a, lapack_int* lda, lapack_int *info );\nvoid LAPACK_stfttr( char* transr, char* uplo, lapack_int* n, const float* arf,\n                    float* a, lapack_int* lda, lapack_int *info );\nvoid LAPACK_ztfttr( char* transr, char* uplo, lapack_int* n,\n                    const lapack_complex_double* arf, lapack_complex_double* a,\n                    lapack_int* lda, lapack_int *info );\nvoid LAPACK_ctfttr( char* transr, char* uplo, lapack_int* n,\n                    const lapack_complex_float* arf, lapack_complex_float* a,\n                    lapack_int* lda, lapack_int *info );\nvoid LAPACK_dtpttf( char* transr, char* uplo, lapack_int* n, const double* ap,\n                    double* arf, lapack_int *info );\nvoid LAPACK_stpttf( char* transr, char* uplo, lapack_int* n, const float* ap,\n                    float* arf, lapack_int *info );\nvoid LAPACK_ztpttf( char* transr, char* uplo, lapack_int* n,\n                    const lapack_complex_double* ap, lapack_complex_double* arf,\n                    lapack_int *info );\nvoid LAPACK_ctpttf( char* transr, char* uplo, lapack_int* n,\n                    const lapack_complex_float* ap, lapack_complex_float* arf,\n                    lapack_int *info );\nvoid LAPACK_dtpttr( char* uplo, lapack_int* n, const double* ap, double* a,\n                    lapack_int* lda, lapack_int *info );\nvoid LAPACK_stpttr( char* uplo, lapack_int* n, const float* ap, float* a,\n                    lapack_int* lda, lapack_int *info );\nvoid LAPACK_ztpttr( char* uplo, lapack_int* n, const lapack_complex_double* ap,\n                    lapack_complex_double* a, lapack_int* lda,\n                    lapack_int *info );\nvoid LAPACK_ctpttr( char* uplo, lapack_int* n, const lapack_complex_float* ap,\n                    lapack_complex_float* a, lapack_int* lda,\n                    lapack_int *info );\nvoid LAPACK_dtrttf( char* transr, char* uplo, lapack_int* n, const double* a,\n                    lapack_int* lda, double* arf, lapack_int *info );\nvoid LAPACK_strttf( char* transr, char* uplo, lapack_int* n, const float* a,\n                    lapack_int* lda, float* arf, lapack_int *info );\nvoid LAPACK_ztrttf( char* transr, char* uplo, lapack_int* n,\n                    const lapack_complex_double* a, lapack_int* lda,\n                    lapack_complex_double* arf, lapack_int *info );\nvoid LAPACK_ctrttf( char* transr, char* uplo, lapack_int* n,\n                    const lapack_complex_float* a, lapack_int* lda,\n                    lapack_complex_float* arf, lapack_int *info );\nvoid LAPACK_dtrttp( char* uplo, lapack_int* n, const double* a, lapack_int* lda,\n                    double* ap, lapack_int *info );\nvoid LAPACK_strttp( char* uplo, lapack_int* n, const float* a, lapack_int* lda,\n                    float* ap, lapack_int *info );\nvoid LAPACK_ztrttp( char* uplo, lapack_int* n, const lapack_complex_double* a,\n                    lapack_int* lda, lapack_complex_double* ap,\n                    lapack_int *info );\nvoid LAPACK_ctrttp( char* uplo, lapack_int* n, const lapack_complex_float* a,\n                    lapack_int* lda, lapack_complex_float* ap,\n                    lapack_int *info );\nvoid LAPACK_sgeqrfp( lapack_int* m, lapack_int* n, float* a, lapack_int* lda,\n                     float* tau, float* work, lapack_int* lwork,\n                     lapack_int *info );\nvoid LAPACK_dgeqrfp( lapack_int* m, lapack_int* n, double* a, lapack_int* lda,\n                     double* tau, double* work, lapack_int* lwork,\n                     lapack_int *info );\nvoid LAPACK_cgeqrfp( lapack_int* m, lapack_int* n, lapack_complex_float* a,\n                     lapack_int* lda, lapack_complex_float* tau,\n                     lapack_complex_float* work, lapack_int* lwork,\n                     lapack_int *info );\nvoid LAPACK_zgeqrfp( lapack_int* m, lapack_int* n, lapack_complex_double* a,\n                     lapack_int* lda, lapack_complex_double* tau,\n                     lapack_complex_double* work, lapack_int* lwork,\n                     lapack_int *info );\nvoid LAPACK_clacgv( lapack_int* n, lapack_complex_float* x, lapack_int* incx );\nvoid LAPACK_zlacgv( lapack_int* n, lapack_complex_double* x, lapack_int* incx );\nvoid LAPACK_slarnv( lapack_int* idist, lapack_int* iseed, lapack_int* n,\n                    float* x );\nvoid LAPACK_dlarnv( lapack_int* idist, lapack_int* iseed, lapack_int* n,\n                    double* x );\nvoid LAPACK_clarnv( lapack_int* idist, lapack_int* iseed, lapack_int* n,\n                    lapack_complex_float* x );\nvoid LAPACK_zlarnv( lapack_int* idist, lapack_int* iseed, lapack_int* n,\n                    lapack_complex_double* x );\nvoid LAPACK_sgeqr2( lapack_int* m, lapack_int* n, float* a, lapack_int* lda,\n                    float* tau, float* work, lapack_int *info );\nvoid LAPACK_dgeqr2( lapack_int* m, lapack_int* n, double* a, lapack_int* lda,\n                    double* tau, double* work, lapack_int *info );\nvoid LAPACK_cgeqr2( lapack_int* m, lapack_int* n, lapack_complex_float* a,\n                    lapack_int* lda, lapack_complex_float* tau,\n                    lapack_complex_float* work, lapack_int *info );\nvoid LAPACK_zgeqr2( lapack_int* m, lapack_int* n, lapack_complex_double* a,\n                    lapack_int* lda, lapack_complex_double* tau,\n                    lapack_complex_double* work, lapack_int *info );\nvoid LAPACK_slacpy( char* uplo, lapack_int* m, lapack_int* n, const float* a,\n                    lapack_int* lda, float* b, lapack_int* ldb );\nvoid LAPACK_dlacpy( char* uplo, lapack_int* m, lapack_int* n, const double* a,\n                    lapack_int* lda, double* b, lapack_int* ldb );\nvoid LAPACK_clacpy( char* uplo, lapack_int* m, lapack_int* n,\n                    const lapack_complex_float* a, lapack_int* lda,\n                    lapack_complex_float* b, lapack_int* ldb );\nvoid LAPACK_zlacpy( char* uplo, lapack_int* m, lapack_int* n,\n                    const lapack_complex_double* a, lapack_int* lda,\n                    lapack_complex_double* b, lapack_int* ldb );\nvoid LAPACK_sgetf2( lapack_int* m, lapack_int* n, float* a, lapack_int* lda,\n                    lapack_int* ipiv, lapack_int *info );\nvoid LAPACK_dgetf2( lapack_int* m, lapack_int* n, double* a, lapack_int* lda,\n                    lapack_int* ipiv, lapack_int *info );\nvoid LAPACK_cgetf2( lapack_int* m, lapack_int* n, lapack_complex_float* a,\n                    lapack_int* lda, lapack_int* ipiv, lapack_int *info );\nvoid LAPACK_zgetf2( lapack_int* m, lapack_int* n, lapack_complex_double* a,\n                    lapack_int* lda, lapack_int* ipiv, lapack_int *info );\nvoid LAPACK_slaswp( lapack_int* n, float* a, lapack_int* lda, lapack_int* k1,\n                    lapack_int* k2, const lapack_int* ipiv, lapack_int* incx );\nvoid LAPACK_dlaswp( lapack_int* n, double* a, lapack_int* lda, lapack_int* k1,\n                    lapack_int* k2, const lapack_int* ipiv, lapack_int* incx );\nvoid LAPACK_claswp( lapack_int* n, lapack_complex_float* a, lapack_int* lda,\n                    lapack_int* k1, lapack_int* k2, const lapack_int* ipiv,\n                    lapack_int* incx );\nvoid LAPACK_zlaswp( lapack_int* n, lapack_complex_double* a, lapack_int* lda,\n                    lapack_int* k1, lapack_int* k2, const lapack_int* ipiv,\n                    lapack_int* incx );\nfloat LAPACK_slange( char* norm, lapack_int* m, lapack_int* n, const float* a,\n                    lapack_int* lda, float* work );\ndouble LAPACK_dlange( char* norm, lapack_int* m, lapack_int* n, const double* a,\n                    lapack_int* lda, double* work );\nfloat LAPACK_clange( char* norm, lapack_int* m, lapack_int* n,\n                    const lapack_complex_float* a, lapack_int* lda, float* work );\ndouble LAPACK_zlange( char* norm, lapack_int* m, lapack_int* n,\n                    const lapack_complex_double* a, lapack_int* lda, double* work );\nfloat LAPACK_clanhe( char* norm, char* uplo, lapack_int* n,\n                    const lapack_complex_float* a, lapack_int* lda, float* work );\ndouble LAPACK_zlanhe( char* norm, char* uplo, lapack_int* n,\n                    const lapack_complex_double* a, lapack_int* lda, double* work );\nfloat LAPACK_slansy( char* norm, char* uplo, lapack_int* n, const float* a,\n                    lapack_int* lda, float* work );\ndouble LAPACK_dlansy( char* norm, char* uplo, lapack_int* n, const double* a,\n                    lapack_int* lda, double* work );\nfloat LAPACK_clansy( char* norm, char* uplo, lapack_int* n,\n                    const lapack_complex_float* a, lapack_int* lda, float* work );\ndouble LAPACK_zlansy( char* norm, char* uplo, lapack_int* n,\n                    const lapack_complex_double* a, lapack_int* lda, double* work );\nfloat LAPACK_slantr( char* norm, char* uplo, char* diag, lapack_int* m,\n                    lapack_int* n, const float* a, lapack_int* lda, float* work );\ndouble LAPACK_dlantr( char* norm, char* uplo, char* diag, lapack_int* m,\n                    lapack_int* n, const double* a, lapack_int* lda, double* work );\nfloat LAPACK_clantr( char* norm, char* uplo, char* diag, lapack_int* m,\n                    lapack_int* n, const lapack_complex_float* a, lapack_int* lda,\n                    float* work );\ndouble LAPACK_zlantr( char* norm, char* uplo, char* diag, lapack_int* m,\n                    lapack_int* n, const lapack_complex_double* a, lapack_int* lda,\n                    double* work );\nfloat LAPACK_slamch( char* cmach );\ndouble LAPACK_dlamch( char* cmach );\nvoid LAPACK_sgelq2( lapack_int* m, lapack_int* n, float* a, lapack_int* lda,\n                    float* tau, float* work, lapack_int *info );\nvoid LAPACK_dgelq2( lapack_int* m, lapack_int* n, double* a, lapack_int* lda,\n                    double* tau, double* work, lapack_int *info );\nvoid LAPACK_cgelq2( lapack_int* m, lapack_int* n, lapack_complex_float* a,\n                    lapack_int* lda, lapack_complex_float* tau,\n                    lapack_complex_float* work, lapack_int *info );\nvoid LAPACK_zgelq2( lapack_int* m, lapack_int* n, lapack_complex_double* a,\n                    lapack_int* lda, lapack_complex_double* tau,\n                    lapack_complex_double* work, lapack_int *info );\nvoid LAPACK_slarfb( char* side, char* trans, char* direct, char* storev,\n                    lapack_int* m, lapack_int* n, lapack_int* k, const float* v,\n                    lapack_int* ldv, const float* t, lapack_int* ldt, float* c,\n                    lapack_int* ldc, float* work, lapack_int* ldwork );\nvoid LAPACK_dlarfb( char* side, char* trans, char* direct, char* storev,\n                    lapack_int* m, lapack_int* n, lapack_int* k,\n                    const double* v, lapack_int* ldv, const double* t,\n                    lapack_int* ldt, double* c, lapack_int* ldc, double* work,\n                    lapack_int* ldwork );\nvoid LAPACK_clarfb( char* side, char* trans, char* direct, char* storev,\n                    lapack_int* m, lapack_int* n, lapack_int* k,\n                    const lapack_complex_float* v, lapack_int* ldv,\n                    const lapack_complex_float* t, lapack_int* ldt,\n                    lapack_complex_float* c, lapack_int* ldc,\n                    lapack_complex_float* work, lapack_int* ldwork );\nvoid LAPACK_zlarfb( char* side, char* trans, char* direct, char* storev,\n                    lapack_int* m, lapack_int* n, lapack_int* k,\n                    const lapack_complex_double* v, lapack_int* ldv,\n                    const lapack_complex_double* t, lapack_int* ldt,\n                    lapack_complex_double* c, lapack_int* ldc,\n                    lapack_complex_double* work, lapack_int* ldwork );\nvoid LAPACK_slarfg( lapack_int* n, float* alpha, float* x, lapack_int* incx,\n                    float* tau );\nvoid LAPACK_dlarfg( lapack_int* n, double* alpha, double* x, lapack_int* incx,\n                    double* tau );\nvoid LAPACK_clarfg( lapack_int* n, lapack_complex_float* alpha,\n                    lapack_complex_float* x, lapack_int* incx,\n                    lapack_complex_float* tau );\nvoid LAPACK_zlarfg( lapack_int* n, lapack_complex_double* alpha,\n                    lapack_complex_double* x, lapack_int* incx,\n                    lapack_complex_double* tau );\nvoid LAPACK_slarft( char* direct, char* storev, lapack_int* n, lapack_int* k,\n                    const float* v, lapack_int* ldv, const float* tau, float* t,\n                    lapack_int* ldt );\nvoid LAPACK_dlarft( char* direct, char* storev, lapack_int* n, lapack_int* k,\n                    const double* v, lapack_int* ldv, const double* tau,\n                    double* t, lapack_int* ldt );\nvoid LAPACK_clarft( char* direct, char* storev, lapack_int* n, lapack_int* k,\n                    const lapack_complex_float* v, lapack_int* ldv,\n                    const lapack_complex_float* tau, lapack_complex_float* t,\n                    lapack_int* ldt );\nvoid LAPACK_zlarft( char* direct, char* storev, lapack_int* n, lapack_int* k,\n                    const lapack_complex_double* v, lapack_int* ldv,\n                    const lapack_complex_double* tau, lapack_complex_double* t,\n                    lapack_int* ldt );\nvoid LAPACK_slarfx( char* side, lapack_int* m, lapack_int* n, const float* v,\n                    float* tau, float* c, lapack_int* ldc, float* work );\nvoid LAPACK_dlarfx( char* side, lapack_int* m, lapack_int* n, const double* v,\n                    double* tau, double* c, lapack_int* ldc, double* work );\nvoid LAPACK_clarfx( char* side, lapack_int* m, lapack_int* n,\n                    const lapack_complex_float* v, lapack_complex_float* tau,\n                    lapack_complex_float* c, lapack_int* ldc,\n                    lapack_complex_float* work );\nvoid LAPACK_zlarfx( char* side, lapack_int* m, lapack_int* n,\n                    const lapack_complex_double* v, lapack_complex_double* tau,\n                    lapack_complex_double* c, lapack_int* ldc,\n                    lapack_complex_double* work );\nvoid LAPACK_slatms( lapack_int* m, lapack_int* n, char* dist, lapack_int* iseed,\n                    char* sym, float* d, lapack_int* mode, float* cond,\n                    float* dmax, lapack_int* kl, lapack_int* ku, char* pack,\n                    float* a, lapack_int* lda, float* work, lapack_int *info );\nvoid LAPACK_dlatms( lapack_int* m, lapack_int* n, char* dist, lapack_int* iseed,\n                    char* sym, double* d, lapack_int* mode, double* cond,\n                    double* dmax, lapack_int* kl, lapack_int* ku, char* pack,\n                    double* a, lapack_int* lda, double* work,\n                    lapack_int *info );\nvoid LAPACK_clatms( lapack_int* m, lapack_int* n, char* dist, lapack_int* iseed,\n                    char* sym, float* d, lapack_int* mode, float* cond,\n                    float* dmax, lapack_int* kl, lapack_int* ku, char* pack,\n                    lapack_complex_float* a, lapack_int* lda,\n                    lapack_complex_float* work, lapack_int *info );\nvoid LAPACK_zlatms( lapack_int* m, lapack_int* n, char* dist, lapack_int* iseed,\n                    char* sym, double* d, lapack_int* mode, double* cond,\n                    double* dmax, lapack_int* kl, lapack_int* ku, char* pack,\n                    lapack_complex_double* a, lapack_int* lda,\n                    lapack_complex_double* work, lapack_int *info );\nvoid LAPACK_slag2d( lapack_int* m, lapack_int* n, const float* sa,\n                    lapack_int* ldsa, double* a, lapack_int* lda,\n                    lapack_int *info );\nvoid LAPACK_dlag2s( lapack_int* m, lapack_int* n, const double* a,\n                    lapack_int* lda, float* sa, lapack_int* ldsa,\n                    lapack_int *info );\nvoid LAPACK_clag2z( lapack_int* m, lapack_int* n,\n                    const lapack_complex_float* sa, lapack_int* ldsa,\n                    lapack_complex_double* a, lapack_int* lda,\n                    lapack_int *info );\nvoid LAPACK_zlag2c( lapack_int* m, lapack_int* n,\n                    const lapack_complex_double* a, lapack_int* lda,\n                    lapack_complex_float* sa, lapack_int* ldsa,\n                    lapack_int *info );\nvoid LAPACK_slauum( char* uplo, lapack_int* n, float* a, lapack_int* lda,\n                    lapack_int *info );\nvoid LAPACK_dlauum( char* uplo, lapack_int* n, double* a, lapack_int* lda,\n                    lapack_int *info );\nvoid LAPACK_clauum( char* uplo, lapack_int* n, lapack_complex_float* a,\n                    lapack_int* lda, lapack_int *info );\nvoid LAPACK_zlauum( char* uplo, lapack_int* n, lapack_complex_double* a,\n                    lapack_int* lda, lapack_int *info );\nvoid LAPACK_slagge( lapack_int* m, lapack_int* n, lapack_int* kl,\n                    lapack_int* ku, const float* d, float* a, lapack_int* lda,\n                    lapack_int* iseed, float* work, lapack_int *info );\nvoid LAPACK_dlagge( lapack_int* m, lapack_int* n, lapack_int* kl,\n                    lapack_int* ku, const double* d, double* a, lapack_int* lda,\n                    lapack_int* iseed, double* work, lapack_int *info );\nvoid LAPACK_clagge( lapack_int* m, lapack_int* n, lapack_int* kl,\n                    lapack_int* ku, const float* d, lapack_complex_float* a,\n                    lapack_int* lda, lapack_int* iseed,\n                    lapack_complex_float* work, lapack_int *info );\nvoid LAPACK_zlagge( lapack_int* m, lapack_int* n, lapack_int* kl,\n                    lapack_int* ku, const double* d, lapack_complex_double* a,\n                    lapack_int* lda, lapack_int* iseed,\n                    lapack_complex_double* work, lapack_int *info );\nvoid LAPACK_slaset( char* uplo, lapack_int* m, lapack_int* n, float* alpha,\n                    float* beta, float* a, lapack_int* lda );\nvoid LAPACK_dlaset( char* uplo, lapack_int* m, lapack_int* n, double* alpha,\n                    double* beta, double* a, lapack_int* lda );\nvoid LAPACK_claset( char* uplo, lapack_int* m, lapack_int* n,\n                    lapack_complex_float* alpha, lapack_complex_float* beta,\n                    lapack_complex_float* a, lapack_int* lda );\nvoid LAPACK_zlaset( char* uplo, lapack_int* m, lapack_int* n,\n                    lapack_complex_double* alpha, lapack_complex_double* beta,\n                    lapack_complex_double* a, lapack_int* lda );\nvoid LAPACK_slasrt( char* id, lapack_int* n, float* d, lapack_int *info );\nvoid LAPACK_dlasrt( char* id, lapack_int* n, double* d, lapack_int *info );\nvoid LAPACK_claghe( lapack_int* n, lapack_int* k, const float* d,\n                    lapack_complex_float* a, lapack_int* lda, lapack_int* iseed,\n                    lapack_complex_float* work, lapack_int *info );\nvoid LAPACK_zlaghe( lapack_int* n, lapack_int* k, const double* d,\n                    lapack_complex_double* a, lapack_int* lda,\n                    lapack_int* iseed, lapack_complex_double* work,\n                    lapack_int *info );\nvoid LAPACK_slagsy( lapack_int* n, lapack_int* k, const float* d, float* a,\n                    lapack_int* lda, lapack_int* iseed, float* work,\n                    lapack_int *info );\nvoid LAPACK_dlagsy( lapack_int* n, lapack_int* k, const double* d, double* a,\n                    lapack_int* lda, lapack_int* iseed, double* work,\n                    lapack_int *info );\nvoid LAPACK_clagsy( lapack_int* n, lapack_int* k, const float* d,\n                    lapack_complex_float* a, lapack_int* lda, lapack_int* iseed,\n                    lapack_complex_float* work, lapack_int *info );\nvoid LAPACK_zlagsy( lapack_int* n, lapack_int* k, const double* d,\n                    lapack_complex_double* a, lapack_int* lda,\n                    lapack_int* iseed, lapack_complex_double* work,\n                    lapack_int *info );\nvoid LAPACK_slapmr( lapack_logical* forwrd, lapack_int* m, lapack_int* n,\n                    float* x, lapack_int* ldx, lapack_int* k );\nvoid LAPACK_dlapmr( lapack_logical* forwrd, lapack_int* m, lapack_int* n,\n                    double* x, lapack_int* ldx, lapack_int* k );\nvoid LAPACK_clapmr( lapack_logical* forwrd, lapack_int* m, lapack_int* n,\n                    lapack_complex_float* x, lapack_int* ldx, lapack_int* k );\nvoid LAPACK_zlapmr( lapack_logical* forwrd, lapack_int* m, lapack_int* n,\n                    lapack_complex_double* x, lapack_int* ldx, lapack_int* k );\nfloat LAPACK_slapy2( float* x, float* y );\ndouble LAPACK_dlapy2( double* x, double* y );\nfloat LAPACK_slapy3( float* x, float* y, float* z );\ndouble LAPACK_dlapy3( double* x, double* y, double* z );\nvoid LAPACK_slartgp( float* f, float* g, float* cs, float* sn, float* r );\nvoid LAPACK_dlartgp( double* f, double* g, double* cs, double* sn, double* r );\nvoid LAPACK_slartgs( float* x, float* y, float* sigma, float* cs, float* sn );\nvoid LAPACK_dlartgs( double* x, double* y, double* sigma, double* cs,\n                     double* sn );\n// LAPACK 3.3.0\nvoid LAPACK_cbbcsd( char* jobu1, char* jobu2,\n                    char* jobv1t, char* jobv2t, char* trans,\n                    lapack_int* m, lapack_int* p, lapack_int* q,\n                    float* theta, float* phi,\n                    lapack_complex_float* u1, lapack_int* ldu1,\n                    lapack_complex_float* u2, lapack_int* ldu2,\n                    lapack_complex_float* v1t, lapack_int* ldv1t,\n                    lapack_complex_float* v2t, lapack_int* ldv2t,\n                    float* b11d, float* b11e, float* b12d,\n                    float* b12e, float* b21d, float* b21e,\n                    float* b22d, float* b22e, float* rwork,\n                    lapack_int* lrwork , lapack_int *info );\nvoid LAPACK_cheswapr( char* uplo, lapack_int* n,\n                      lapack_complex_float* a, lapack_int* i1,\n                      lapack_int* i2 );\nvoid LAPACK_chetri2( char* uplo, lapack_int* n,\n                     lapack_complex_float* a, lapack_int* lda,\n                     const lapack_int* ipiv,\n                     lapack_complex_float* work, lapack_int* lwork , lapack_int *info );\nvoid LAPACK_chetri2x( char* uplo, lapack_int* n,\n                      lapack_complex_float* a, lapack_int* lda,\n                      const lapack_int* ipiv,\n                      lapack_complex_float* work, lapack_int* nb , lapack_int *info );\nvoid LAPACK_chetrs2( char* uplo, lapack_int* n,\n                     lapack_int* nrhs, const lapack_complex_float* a,\n                     lapack_int* lda, const lapack_int* ipiv,\n                     lapack_complex_float* b, lapack_int* ldb,\n                     lapack_complex_float* work , lapack_int *info );\nvoid LAPACK_csyconv( char* uplo, char* way,\n                     lapack_int* n, lapack_complex_float* a,\n                     lapack_int* lda, const lapack_int* ipiv,\n                     lapack_complex_float* work , lapack_int *info );\nvoid LAPACK_csyswapr( char* uplo, lapack_int* n,\n                      lapack_complex_float* a, lapack_int* i1,\n                      lapack_int* i2 );\nvoid LAPACK_csytri2( char* uplo, lapack_int* n,\n                     lapack_complex_float* a, lapack_int* lda,\n                     const lapack_int* ipiv,\n                     lapack_complex_float* work, lapack_int* lwork , lapack_int *info );\nvoid LAPACK_csytri2x( char* uplo, lapack_int* n,\n                      lapack_complex_float* a, lapack_int* lda,\n                      const lapack_int* ipiv,\n                      lapack_complex_float* work, lapack_int* nb , lapack_int *info );\nvoid LAPACK_csytrs2( char* uplo, lapack_int* n,\n                     lapack_int* nrhs, const lapack_complex_float* a,\n                     lapack_int* lda, const lapack_int* ipiv,\n                     lapack_complex_float* b, lapack_int* ldb,\n                     lapack_complex_float* work , lapack_int *info );\nvoid LAPACK_cunbdb( char* trans, char* signs,\n                    lapack_int* m, lapack_int* p, lapack_int* q,\n                    lapack_complex_float* x11, lapack_int* ldx11,\n                    lapack_complex_float* x12, lapack_int* ldx12,\n                    lapack_complex_float* x21, lapack_int* ldx21,\n                    lapack_complex_float* x22, lapack_int* ldx22,\n                    float* theta, float* phi,\n                    lapack_complex_float* taup1,\n                    lapack_complex_float* taup2,\n                    lapack_complex_float* tauq1,\n                    lapack_complex_float* tauq2,\n                    lapack_complex_float* work, lapack_int* lwork , lapack_int *info );\nvoid LAPACK_cuncsd( char* jobu1, char* jobu2,\n                    char* jobv1t, char* jobv2t, char* trans,\n                    char* signs, lapack_int* m, lapack_int* p,\n                    lapack_int* q, lapack_complex_float* x11,\n                    lapack_int* ldx11, lapack_complex_float* x12,\n                    lapack_int* ldx12, lapack_complex_float* x21,\n                    lapack_int* ldx21, lapack_complex_float* x22,\n                    lapack_int* ldx22, float* theta,\n                    lapack_complex_float* u1, lapack_int* ldu1,\n                    lapack_complex_float* u2, lapack_int* ldu2,\n                    lapack_complex_float* v1t, lapack_int* ldv1t,\n                    lapack_complex_float* v2t, lapack_int* ldv2t,\n                    lapack_complex_float* work, lapack_int* lwork,\n                    float* rwork, lapack_int* lrwork,\n                    lapack_int* iwork , lapack_int *info );\nvoid LAPACK_dbbcsd( char* jobu1, char* jobu2,\n                    char* jobv1t, char* jobv2t, char* trans,\n                    lapack_int* m, lapack_int* p, lapack_int* q,\n                    double* theta, double* phi, double* u1,\n                    lapack_int* ldu1, double* u2, lapack_int* ldu2,\n                    double* v1t, lapack_int* ldv1t, double* v2t,\n                    lapack_int* ldv2t, double* b11d, double* b11e,\n                    double* b12d, double* b12e, double* b21d,\n                    double* b21e, double* b22d, double* b22e,\n                    double* work, lapack_int* lwork , lapack_int *info );\nvoid LAPACK_dorbdb( char* trans, char* signs,\n                    lapack_int* m, lapack_int* p, lapack_int* q,\n                    double* x11, lapack_int* ldx11, double* x12,\n                    lapack_int* ldx12, double* x21, lapack_int* ldx21,\n                    double* x22, lapack_int* ldx22, double* theta,\n                    double* phi, double* taup1, double* taup2,\n                    double* tauq1, double* tauq2, double* work,\n                    lapack_int* lwork , lapack_int *info );\nvoid LAPACK_dorcsd( char* jobu1, char* jobu2,\n                    char* jobv1t, char* jobv2t, char* trans,\n                    char* signs, lapack_int* m, lapack_int* p,\n                    lapack_int* q, double* x11, lapack_int* ldx11,\n                    double* x12, lapack_int* ldx12, double* x21,\n                    lapack_int* ldx21, double* x22, lapack_int* ldx22,\n                    double* theta, double* u1, lapack_int* ldu1,\n                    double* u2, lapack_int* ldu2, double* v1t,\n                    lapack_int* ldv1t, double* v2t, lapack_int* ldv2t,\n                    double* work, lapack_int* lwork,\n                    lapack_int* iwork , lapack_int *info );\nvoid LAPACK_dsyconv( char* uplo, char* way,\n                     lapack_int* n, double* a, lapack_int* lda,\n                     const lapack_int* ipiv, double* work , lapack_int *info );\nvoid LAPACK_dsyswapr( char* uplo, lapack_int* n,\n                      double* a, lapack_int* i1, lapack_int* i2 );\nvoid LAPACK_dsytri2( char* uplo, lapack_int* n,\n                     double* a, lapack_int* lda,\n                     const lapack_int* ipiv,\n                     lapack_complex_double* work, lapack_int* lwork , lapack_int *info );\nvoid LAPACK_dsytri2x( char* uplo, lapack_int* n,\n                      double* a, lapack_int* lda,\n                      const lapack_int* ipiv, double* work,\n                      lapack_int* nb , lapack_int *info );\nvoid LAPACK_dsytrs2( char* uplo, lapack_int* n,\n                     lapack_int* nrhs, const double* a,\n                     lapack_int* lda, const lapack_int* ipiv,\n                     double* b, lapack_int* ldb, double* work , lapack_int *info );\nvoid LAPACK_sbbcsd( char* jobu1, char* jobu2,\n                    char* jobv1t, char* jobv2t, char* trans,\n                    lapack_int* m, lapack_int* p, lapack_int* q,\n                    float* theta, float* phi, float* u1,\n                    lapack_int* ldu1, float* u2, lapack_int* ldu2,\n                    float* v1t, lapack_int* ldv1t, float* v2t,\n                    lapack_int* ldv2t, float* b11d, float* b11e,\n                    float* b12d, float* b12e, float* b21d,\n                    float* b21e, float* b22d, float* b22e,\n                    float* work, lapack_int* lwork , lapack_int *info );\nvoid LAPACK_sorbdb( char* trans, char* signs,\n                    lapack_int* m, lapack_int* p, lapack_int* q,\n                    float* x11, lapack_int* ldx11, float* x12,\n                    lapack_int* ldx12, float* x21, lapack_int* ldx21,\n                    float* x22, lapack_int* ldx22, float* theta,\n                    float* phi, float* taup1, float* taup2,\n                    float* tauq1, float* tauq2, float* work,\n                    lapack_int* lwork , lapack_int *info );\nvoid LAPACK_sorcsd( char* jobu1, char* jobu2,\n                    char* jobv1t, char* jobv2t, char* trans,\n                    char* signs, lapack_int* m, lapack_int* p,\n                    lapack_int* q, float* x11, lapack_int* ldx11,\n                    float* x12, lapack_int* ldx12, float* x21,\n                    lapack_int* ldx21, float* x22, lapack_int* ldx22,\n                    float* theta, float* u1, lapack_int* ldu1,\n                    float* u2, lapack_int* ldu2, float* v1t,\n                    lapack_int* ldv1t, float* v2t, lapack_int* ldv2t,\n                    float* work, lapack_int* lwork,\n                    lapack_int* iwork , lapack_int *info );\nvoid LAPACK_ssyconv( char* uplo, char* way,\n                     lapack_int* n, float* a, lapack_int* lda,\n                     const lapack_int* ipiv, float* work , lapack_int *info );\nvoid LAPACK_ssyswapr( char* uplo, lapack_int* n,\n                      float* a, lapack_int* i1, lapack_int* i2 );\nvoid LAPACK_ssytri2( char* uplo, lapack_int* n,\n                     float* a, lapack_int* lda,\n                     const lapack_int* ipiv,\n                     lapack_complex_float* work, lapack_int* lwork , lapack_int *info );\nvoid LAPACK_ssytri2x( char* uplo, lapack_int* n,\n                      float* a, lapack_int* lda,\n                      const lapack_int* ipiv, float* work,\n                      lapack_int* nb , lapack_int *info );\nvoid LAPACK_ssytrs2( char* uplo, lapack_int* n,\n                     lapack_int* nrhs, const float* a,\n                     lapack_int* lda, const lapack_int* ipiv,\n                     float* b, lapack_int* ldb, float* work , lapack_int *info );\nvoid LAPACK_zbbcsd( char* jobu1, char* jobu2,\n                    char* jobv1t, char* jobv2t, char* trans,\n                    lapack_int* m, lapack_int* p, lapack_int* q,\n                    double* theta, double* phi,\n                    lapack_complex_double* u1, lapack_int* ldu1,\n                    lapack_complex_double* u2, lapack_int* ldu2,\n                    lapack_complex_double* v1t, lapack_int* ldv1t,\n                    lapack_complex_double* v2t, lapack_int* ldv2t,\n                    double* b11d, double* b11e, double* b12d,\n                    double* b12e, double* b21d, double* b21e,\n                    double* b22d, double* b22e, double* rwork,\n                    lapack_int* lrwork , lapack_int *info );\nvoid LAPACK_zheswapr( char* uplo, lapack_int* n,\n                      lapack_complex_double* a, lapack_int* i1,\n                      lapack_int* i2 );\nvoid LAPACK_zhetri2( char* uplo, lapack_int* n,\n                     lapack_complex_double* a, lapack_int* lda,\n                     const lapack_int* ipiv,\n                     lapack_complex_double* work, lapack_int* lwork , lapack_int *info );\nvoid LAPACK_zhetri2x( char* uplo, lapack_int* n,\n                      lapack_complex_double* a, lapack_int* lda,\n                      const lapack_int* ipiv,\n                      lapack_complex_double* work, lapack_int* nb , lapack_int *info );\nvoid LAPACK_zhetrs2( char* uplo, lapack_int* n,\n                     lapack_int* nrhs,\n                     const lapack_complex_double* a, lapack_int* lda,\n                     const lapack_int* ipiv,\n                     lapack_complex_double* b, lapack_int* ldb,\n                     lapack_complex_double* work , lapack_int *info );\nvoid LAPACK_zsyconv( char* uplo, char* way,\n                     lapack_int* n, lapack_complex_double* a,\n                     lapack_int* lda, const lapack_int* ipiv,\n                     lapack_complex_double* work , lapack_int *info );\nvoid LAPACK_zsyswapr( char* uplo, lapack_int* n,\n                      lapack_complex_double* a, lapack_int* i1,\n                      lapack_int* i2 );\nvoid LAPACK_zsytri2( char* uplo, lapack_int* n,\n                     lapack_complex_double* a, lapack_int* lda,\n                     const lapack_int* ipiv,\n                     lapack_complex_double* work, lapack_int* lwork , lapack_int *info );\nvoid LAPACK_zsytri2x( char* uplo, lapack_int* n,\n                      lapack_complex_double* a, lapack_int* lda,\n                      const lapack_int* ipiv,\n                      lapack_complex_double* work, lapack_int* nb , lapack_int *info );\nvoid LAPACK_zsytrs2( char* uplo, lapack_int* n,\n                     lapack_int* nrhs,\n                     const lapack_complex_double* a, lapack_int* lda,\n                     const lapack_int* ipiv,\n                     lapack_complex_double* b, lapack_int* ldb,\n                     lapack_complex_double* work , lapack_int *info );\nvoid LAPACK_zunbdb( char* trans, char* signs,\n                    lapack_int* m, lapack_int* p, lapack_int* q,\n                    lapack_complex_double* x11, lapack_int* ldx11,\n                    lapack_complex_double* x12, lapack_int* ldx12,\n                    lapack_complex_double* x21, lapack_int* ldx21,\n                    lapack_complex_double* x22, lapack_int* ldx22,\n                    double* theta, double* phi,\n                    lapack_complex_double* taup1,\n                    lapack_complex_double* taup2,\n                    lapack_complex_double* tauq1,\n                    lapack_complex_double* tauq2,\n                    lapack_complex_double* work, lapack_int* lwork , lapack_int *info );\nvoid LAPACK_zuncsd( char* jobu1, char* jobu2,\n                    char* jobv1t, char* jobv2t, char* trans,\n                    char* signs, lapack_int* m, lapack_int* p,\n                    lapack_int* q, lapack_complex_double* x11,\n                    lapack_int* ldx11, lapack_complex_double* x12,\n                    lapack_int* ldx12, lapack_complex_double* x21,\n                    lapack_int* ldx21, lapack_complex_double* x22,\n                    lapack_int* ldx22, double* theta,\n                    lapack_complex_double* u1, lapack_int* ldu1,\n                    lapack_complex_double* u2, lapack_int* ldu2,\n                    lapack_complex_double* v1t, lapack_int* ldv1t,\n                    lapack_complex_double* v2t, lapack_int* ldv2t,\n                    lapack_complex_double* work, lapack_int* lwork,\n                    double* rwork, lapack_int* lrwork,\n                    lapack_int* iwork , lapack_int *info );\n// LAPACK 3.4.0\nvoid LAPACK_sgemqrt( char* side, char* trans, lapack_int* m, lapack_int* n,\n                     lapack_int* k, lapack_int* nb, const float* v,\n                     lapack_int* ldv, const float* t, lapack_int* ldt, float* c,\n                     lapack_int* ldc, float* work, lapack_int *info );\nvoid LAPACK_dgemqrt( char* side, char* trans, lapack_int* m, lapack_int* n,\n                     lapack_int* k, lapack_int* nb, const double* v,\n                     lapack_int* ldv, const double* t, lapack_int* ldt,\n                     double* c, lapack_int* ldc, double* work,\n                     lapack_int *info );\nvoid LAPACK_cgemqrt( char* side, char* trans, lapack_int* m, lapack_int* n,\n                     lapack_int* k, lapack_int* nb,\n                     const lapack_complex_float* v, lapack_int* ldv,\n                     const lapack_complex_float* t, lapack_int* ldt,\n                     lapack_complex_float* c, lapack_int* ldc,\n                     lapack_complex_float* work, lapack_int *info );\nvoid LAPACK_zgemqrt( char* side, char* trans, lapack_int* m, lapack_int* n,\n                     lapack_int* k, lapack_int* nb,\n                     const lapack_complex_double* v, lapack_int* ldv,\n                     const lapack_complex_double* t, lapack_int* ldt,\n                     lapack_complex_double* c, lapack_int* ldc,\n                     lapack_complex_double* work, lapack_int *info );\nvoid LAPACK_sgeqrt( lapack_int* m, lapack_int* n, lapack_int* nb, float* a,\n                    lapack_int* lda, float* t, lapack_int* ldt, float* work,\n                    lapack_int *info );\nvoid LAPACK_dgeqrt( lapack_int* m, lapack_int* n, lapack_int* nb, double* a,\n                    lapack_int* lda, double* t, lapack_int* ldt, double* work,\n                    lapack_int *info );\nvoid LAPACK_cgeqrt( lapack_int* m, lapack_int* n, lapack_int* nb,\n                    lapack_complex_float* a, lapack_int* lda,\n                    lapack_complex_float* t, lapack_int* ldt,\n                    lapack_complex_float* work, lapack_int *info );\nvoid LAPACK_zgeqrt( lapack_int* m, lapack_int* n, lapack_int* nb,\n                    lapack_complex_double* a, lapack_int* lda,\n                    lapack_complex_double* t, lapack_int* ldt,\n                    lapack_complex_double* work, lapack_int *info );\nvoid LAPACK_sgeqrt2( lapack_int* m, lapack_int* n, float* a, lapack_int* lda,\n                     float* t, lapack_int* ldt, lapack_int *info );\nvoid LAPACK_dgeqrt2( lapack_int* m, lapack_int* n, double* a, lapack_int* lda,\n                     double* t, lapack_int* ldt, lapack_int *info );\nvoid LAPACK_cgeqrt2( lapack_int* m, lapack_int* n, lapack_complex_float* a,\n                     lapack_int* lda, lapack_complex_float* t, lapack_int* ldt,\n                     lapack_int *info );\nvoid LAPACK_zgeqrt2( lapack_int* m, lapack_int* n, lapack_complex_double* a,\n                     lapack_int* lda, lapack_complex_double* t, lapack_int* ldt,\n                     lapack_int *info );\nvoid LAPACK_sgeqrt3( lapack_int* m, lapack_int* n, float* a, lapack_int* lda,\n                     float* t, lapack_int* ldt, lapack_int *info );\nvoid LAPACK_dgeqrt3( lapack_int* m, lapack_int* n, double* a, lapack_int* lda,\n                     double* t, lapack_int* ldt, lapack_int *info );\nvoid LAPACK_cgeqrt3( lapack_int* m, lapack_int* n, lapack_complex_float* a,\n                     lapack_int* lda, lapack_complex_float* t, lapack_int* ldt,\n                     lapack_int *info );\nvoid LAPACK_zgeqrt3( lapack_int* m, lapack_int* n, lapack_complex_double* a,\n                     lapack_int* lda, lapack_complex_double* t, lapack_int* ldt,\n                     lapack_int *info );\nvoid LAPACK_stpmqrt( char* side, char* trans, lapack_int* m, lapack_int* n,\n                     lapack_int* k, lapack_int* l, lapack_int* nb,\n                     const float* v, lapack_int* ldv, const float* t,\n                     lapack_int* ldt, float* a, lapack_int* lda, float* b,\n                     lapack_int* ldb, float* work, lapack_int *info );\nvoid LAPACK_dtpmqrt( char* side, char* trans, lapack_int* m, lapack_int* n,\n                     lapack_int* k, lapack_int* l, lapack_int* nb,\n                     const double* v, lapack_int* ldv, const double* t,\n                     lapack_int* ldt, double* a, lapack_int* lda, double* b,\n                     lapack_int* ldb, double* work, lapack_int *info );\nvoid LAPACK_ctpmqrt( char* side, char* trans, lapack_int* m, lapack_int* n,\n                     lapack_int* k, lapack_int* l, lapack_int* nb,\n                     const lapack_complex_float* v, lapack_int* ldv,\n                     const lapack_complex_float* t, lapack_int* ldt,\n                     lapack_complex_float* a, lapack_int* lda,\n                     lapack_complex_float* b, lapack_int* ldb,\n                     lapack_complex_float* work, lapack_int *info );\nvoid LAPACK_ztpmqrt( char* side, char* trans, lapack_int* m, lapack_int* n,\n                     lapack_int* k, lapack_int* l, lapack_int* nb,\n                     const lapack_complex_double* v, lapack_int* ldv,\n                     const lapack_complex_double* t, lapack_int* ldt,\n                     lapack_complex_double* a, lapack_int* lda,\n                     lapack_complex_double* b, lapack_int* ldb,\n                     lapack_complex_double* work, lapack_int *info );\nvoid LAPACK_dtpqrt( lapack_int* m, lapack_int* n, lapack_int* l, lapack_int* nb,\n                    double* a, lapack_int* lda, double* b, lapack_int* ldb,\n                    double* t, lapack_int* ldt, double* work,\n                    lapack_int *info );\nvoid LAPACK_ctpqrt( lapack_int* m, lapack_int* n, lapack_int* l, lapack_int* nb,\n                    lapack_complex_float* a, lapack_int* lda,\n                    lapack_complex_float* t, lapack_complex_float* b,\n                    lapack_int* ldb, lapack_int* ldt,\n                    lapack_complex_float* work, lapack_int *info );\nvoid LAPACK_ztpqrt( lapack_int* m, lapack_int* n, lapack_int* l, lapack_int* nb,\n                    lapack_complex_double* a, lapack_int* lda,\n                    lapack_complex_double* b, lapack_int* ldb,\n                    lapack_complex_double* t, lapack_int* ldt,\n                    lapack_complex_double* work, lapack_int *info );\nvoid LAPACK_stpqrt2( lapack_int* m, lapack_int* n, float* a, lapack_int* lda,\n                     float* b, lapack_int* ldb, float* t, lapack_int* ldt,\n                     lapack_int *info );\nvoid LAPACK_dtpqrt2( lapack_int* m, lapack_int* n, double* a, lapack_int* lda,\n                     double* b, lapack_int* ldb, double* t, lapack_int* ldt,\n                     lapack_int *info );\nvoid LAPACK_ctpqrt2( lapack_int* m, lapack_int* n, lapack_complex_float* a,\n                     lapack_int* lda, lapack_complex_float* b, lapack_int* ldb,\n                     lapack_complex_float* t, lapack_int* ldt,\n                     lapack_int *info );\nvoid LAPACK_ztpqrt2( lapack_int* m, lapack_int* n, lapack_complex_double* a,\n                     lapack_int* lda, lapack_complex_double* b, lapack_int* ldb,\n                     lapack_complex_double* t, lapack_int* ldt,\n                     lapack_int *info );\nvoid LAPACK_stprfb( char* side, char* trans, char* direct, char* storev,\n                    lapack_int* m, lapack_int* n, lapack_int* k, lapack_int* l,\n                    const float* v, lapack_int* ldv, const float* t,\n                    lapack_int* ldt, float* a, lapack_int* lda, float* b,\n                    lapack_int* ldb, const float* mywork,\n                    lapack_int* myldwork );\nvoid LAPACK_dtprfb( char* side, char* trans, char* direct, char* storev,\n                    lapack_int* m, lapack_int* n, lapack_int* k, lapack_int* l,\n                    const double* v, lapack_int* ldv, const double* t,\n                    lapack_int* ldt, double* a, lapack_int* lda, double* b,\n                    lapack_int* ldb, const double* mywork,\n                    lapack_int* myldwork );\nvoid LAPACK_ctprfb( char* side, char* trans, char* direct, char* storev,\n                    lapack_int* m, lapack_int* n, lapack_int* k, lapack_int* l,\n                    const lapack_complex_float* v, lapack_int* ldv,\n                    const lapack_complex_float* t, lapack_int* ldt,\n                    lapack_complex_float* a, lapack_int* lda,\n                    lapack_complex_float* b, lapack_int* ldb,\n                    const float* mywork, lapack_int* myldwork );\nvoid LAPACK_ztprfb( char* side, char* trans, char* direct, char* storev,\n                    lapack_int* m, lapack_int* n, lapack_int* k, lapack_int* l,\n                    const lapack_complex_double* v, lapack_int* ldv,\n                    const lapack_complex_double* t, lapack_int* ldt,\n                    lapack_complex_double* a, lapack_int* lda,\n                    lapack_complex_double* b, lapack_int* ldb,\n                    const double* mywork, lapack_int* myldwork );\n// LAPACK 3.X.X\nvoid LAPACK_csyr( char* uplo, lapack_int* n, lapack_complex_float* alpha,\n                      const lapack_complex_float* x, lapack_int* incx,\n                      lapack_complex_float* a, lapack_int* lda );\nvoid LAPACK_zsyr( char* uplo, lapack_int* n, lapack_complex_double* alpha,\n                      const lapack_complex_double* x, lapack_int* incx,\n                      lapack_complex_double* a, lapack_int* lda );\n\n#ifdef __cplusplus\n}\n#endif /* __cplusplus */\n\n#endif /* _LAPACKE_H_ */\n\n#endif /* _MKL_LAPACKE_H_ */\n"
  },
  {
    "path": "include/eigen3/Eigen/src/misc/lapacke_mangling.h",
    "content": "#ifndef LAPACK_HEADER_INCLUDED\n#define LAPACK_HEADER_INCLUDED\n\n#ifndef LAPACK_GLOBAL\n#if defined(LAPACK_GLOBAL_PATTERN_LC) || defined(ADD_)\n#define LAPACK_GLOBAL(lcname,UCNAME)  lcname##_\n#elif defined(LAPACK_GLOBAL_PATTERN_UC) || defined(UPPER)\n#define LAPACK_GLOBAL(lcname,UCNAME)  UCNAME\n#elif defined(LAPACK_GLOBAL_PATTERN_MC) || defined(NOCHANGE)\n#define LAPACK_GLOBAL(lcname,UCNAME)  lcname\n#else\n#define LAPACK_GLOBAL(lcname,UCNAME)  lcname##_\n#endif\n#endif\n\n#endif\n\n"
  },
  {
    "path": "include/eigen3/Eigen/src/plugins/ArrayCwiseBinaryOps.h",
    "content": "\n/** \\returns an expression of the coefficient wise product of \\c *this and \\a other\n  *\n  * \\sa MatrixBase::cwiseProduct\n  */\ntemplate<typename OtherDerived>\nEIGEN_DEVICE_FUNC\nEIGEN_STRONG_INLINE const EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,product)\noperator*(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const\n{\n  return EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,product)(derived(), other.derived());\n}\n\n/** \\returns an expression of the coefficient wise quotient of \\c *this and \\a other\n  *\n  * \\sa MatrixBase::cwiseQuotient\n  */\ntemplate<typename OtherDerived>\nEIGEN_DEVICE_FUNC\nEIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_quotient_op<Scalar,typename OtherDerived::Scalar>, const Derived, const OtherDerived>\noperator/(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const\n{\n  return CwiseBinaryOp<internal::scalar_quotient_op<Scalar,typename OtherDerived::Scalar>, const Derived, const OtherDerived>(derived(), other.derived());\n}\n\n/** \\returns an expression of the coefficient-wise min of \\c *this and \\a other\n  *\n  * Example: \\include Cwise_min.cpp\n  * Output: \\verbinclude Cwise_min.out\n  *\n  * \\sa max()\n  */\nEIGEN_MAKE_CWISE_BINARY_OP(min,min)\n\n/** \\returns an expression of the coefficient-wise min of \\c *this and scalar \\a other\n  *\n  * \\sa max()\n  */\nEIGEN_DEVICE_FUNC\nEIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_min_op<Scalar,Scalar>, const Derived,\n                                        const CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject> >\n#ifdef EIGEN_PARSED_BY_DOXYGEN\nmin\n#else\n(min)\n#endif\n(const Scalar &other) const\n{\n  return (min)(Derived::PlainObject::Constant(rows(), cols(), other));\n}\n\n/** \\returns an expression of the coefficient-wise max of \\c *this and \\a other\n  *\n  * Example: \\include Cwise_max.cpp\n  * Output: \\verbinclude Cwise_max.out\n  *\n  * \\sa min()\n  */\nEIGEN_MAKE_CWISE_BINARY_OP(max,max)\n\n/** \\returns an expression of the coefficient-wise max of \\c *this and scalar \\a other\n  *\n  * \\sa min()\n  */\nEIGEN_DEVICE_FUNC\nEIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_max_op<Scalar,Scalar>, const Derived,\n                                        const CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject> >\n#ifdef EIGEN_PARSED_BY_DOXYGEN\nmax\n#else\n(max)\n#endif\n(const Scalar &other) const\n{\n  return (max)(Derived::PlainObject::Constant(rows(), cols(), other));\n}\n\n/** \\returns an expression of the coefficient-wise power of \\c *this to the given array of \\a exponents.\n  *\n  * This function computes the coefficient-wise power.\n  *\n  * Example: \\include Cwise_array_power_array.cpp\n  * Output: \\verbinclude Cwise_array_power_array.out\n  */\nEIGEN_MAKE_CWISE_BINARY_OP(pow,pow)\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\nEIGEN_MAKE_SCALAR_BINARY_OP_ONTHERIGHT(pow,pow)\n#else\n/** \\returns an expression of the coefficients of \\c *this rasied to the constant power \\a exponent\n  *\n  * \\tparam T is the scalar type of \\a exponent. It must be compatible with the scalar type of the given expression.\n  *\n  * This function computes the coefficient-wise power. The function MatrixBase::pow() in the\n  * unsupported module MatrixFunctions computes the matrix power.\n  *\n  * Example: \\include Cwise_pow.cpp\n  * Output: \\verbinclude Cwise_pow.out\n  *\n  * \\sa ArrayBase::pow(ArrayBase), square(), cube(), exp(), log()\n  */\ntemplate<typename T>\nconst CwiseBinaryOp<internal::scalar_pow_op<Scalar,T>,Derived,Constant<T> > pow(const T& exponent) const;\n#endif\n\n\n// TODO code generating macros could be moved to Macros.h and could include generation of documentation\n#define EIGEN_MAKE_CWISE_COMP_OP(OP, COMPARATOR) \\\ntemplate<typename OtherDerived> \\\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_cmp_op<Scalar, typename OtherDerived::Scalar, internal::cmp_ ## COMPARATOR>, const Derived, const OtherDerived> \\\nOP(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const \\\n{ \\\n  return CwiseBinaryOp<internal::scalar_cmp_op<Scalar, typename OtherDerived::Scalar, internal::cmp_ ## COMPARATOR>, const Derived, const OtherDerived>(derived(), other.derived()); \\\n}\\\ntypedef CwiseBinaryOp<internal::scalar_cmp_op<Scalar,Scalar, internal::cmp_ ## COMPARATOR>, const Derived, const CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject> > Cmp ## COMPARATOR ## ReturnType; \\\ntypedef CwiseBinaryOp<internal::scalar_cmp_op<Scalar,Scalar, internal::cmp_ ## COMPARATOR>, const CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject>, const Derived > RCmp ## COMPARATOR ## ReturnType; \\\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Cmp ## COMPARATOR ## ReturnType \\\nOP(const Scalar& s) const { \\\n  return this->OP(Derived::PlainObject::Constant(rows(), cols(), s)); \\\n} \\\nEIGEN_DEVICE_FUNC friend EIGEN_STRONG_INLINE const RCmp ## COMPARATOR ## ReturnType \\\nOP(const Scalar& s, const Derived& d) { \\\n  return Derived::PlainObject::Constant(d.rows(), d.cols(), s).OP(d); \\\n}\n\n#define EIGEN_MAKE_CWISE_COMP_R_OP(OP, R_OP, RCOMPARATOR) \\\ntemplate<typename OtherDerived> \\\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_cmp_op<typename OtherDerived::Scalar, Scalar, internal::cmp_##RCOMPARATOR>, const OtherDerived, const Derived> \\\nOP(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const \\\n{ \\\n  return CwiseBinaryOp<internal::scalar_cmp_op<typename OtherDerived::Scalar, Scalar, internal::cmp_##RCOMPARATOR>, const OtherDerived, const Derived>(other.derived(), derived()); \\\n} \\\nEIGEN_DEVICE_FUNC \\\ninline const RCmp ## RCOMPARATOR ## ReturnType \\\nOP(const Scalar& s) const { \\\n  return Derived::PlainObject::Constant(rows(), cols(), s).R_OP(*this); \\\n} \\\nfriend inline const Cmp ## RCOMPARATOR ## ReturnType \\\nOP(const Scalar& s, const Derived& d) { \\\n  return d.R_OP(Derived::PlainObject::Constant(d.rows(), d.cols(), s)); \\\n}\n\n\n\n/** \\returns an expression of the coefficient-wise \\< operator of *this and \\a other\n  *\n  * Example: \\include Cwise_less.cpp\n  * Output: \\verbinclude Cwise_less.out\n  *\n  * \\sa all(), any(), operator>(), operator<=()\n  */\nEIGEN_MAKE_CWISE_COMP_OP(operator<, LT)\n\n/** \\returns an expression of the coefficient-wise \\<= operator of *this and \\a other\n  *\n  * Example: \\include Cwise_less_equal.cpp\n  * Output: \\verbinclude Cwise_less_equal.out\n  *\n  * \\sa all(), any(), operator>=(), operator<()\n  */\nEIGEN_MAKE_CWISE_COMP_OP(operator<=, LE)\n\n/** \\returns an expression of the coefficient-wise \\> operator of *this and \\a other\n  *\n  * Example: \\include Cwise_greater.cpp\n  * Output: \\verbinclude Cwise_greater.out\n  *\n  * \\sa all(), any(), operator>=(), operator<()\n  */\nEIGEN_MAKE_CWISE_COMP_R_OP(operator>, operator<, LT)\n\n/** \\returns an expression of the coefficient-wise \\>= operator of *this and \\a other\n  *\n  * Example: \\include Cwise_greater_equal.cpp\n  * Output: \\verbinclude Cwise_greater_equal.out\n  *\n  * \\sa all(), any(), operator>(), operator<=()\n  */\nEIGEN_MAKE_CWISE_COMP_R_OP(operator>=, operator<=, LE)\n\n/** \\returns an expression of the coefficient-wise == operator of *this and \\a other\n  *\n  * \\warning this performs an exact comparison, which is generally a bad idea with floating-point types.\n  * In order to check for equality between two vectors or matrices with floating-point coefficients, it is\n  * generally a far better idea to use a fuzzy comparison as provided by isApprox() and\n  * isMuchSmallerThan().\n  *\n  * Example: \\include Cwise_equal_equal.cpp\n  * Output: \\verbinclude Cwise_equal_equal.out\n  *\n  * \\sa all(), any(), isApprox(), isMuchSmallerThan()\n  */\nEIGEN_MAKE_CWISE_COMP_OP(operator==, EQ)\n\n/** \\returns an expression of the coefficient-wise != operator of *this and \\a other\n  *\n  * \\warning this performs an exact comparison, which is generally a bad idea with floating-point types.\n  * In order to check for equality between two vectors or matrices with floating-point coefficients, it is\n  * generally a far better idea to use a fuzzy comparison as provided by isApprox() and\n  * isMuchSmallerThan().\n  *\n  * Example: \\include Cwise_not_equal.cpp\n  * Output: \\verbinclude Cwise_not_equal.out\n  *\n  * \\sa all(), any(), isApprox(), isMuchSmallerThan()\n  */\nEIGEN_MAKE_CWISE_COMP_OP(operator!=, NEQ)\n\n\n#undef EIGEN_MAKE_CWISE_COMP_OP\n#undef EIGEN_MAKE_CWISE_COMP_R_OP\n\n// scalar addition\n#ifndef EIGEN_PARSED_BY_DOXYGEN\nEIGEN_MAKE_SCALAR_BINARY_OP(operator+,sum)\n#else\n/** \\returns an expression of \\c *this with each coeff incremented by the constant \\a scalar\n  *\n  * \\tparam T is the scalar type of \\a scalar. It must be compatible with the scalar type of the given expression.\n  *\n  * Example: \\include Cwise_plus.cpp\n  * Output: \\verbinclude Cwise_plus.out\n  *\n  * \\sa operator+=(), operator-()\n  */\ntemplate<typename T>\nconst CwiseBinaryOp<internal::scalar_sum_op<Scalar,T>,Derived,Constant<T> > operator+(const T& scalar) const;\n/** \\returns an expression of \\a expr with each coeff incremented by the constant \\a scalar\n  *\n  * \\tparam T is the scalar type of \\a scalar. It must be compatible with the scalar type of the given expression.\n  */\ntemplate<typename T> friend\nconst CwiseBinaryOp<internal::scalar_sum_op<T,Scalar>,Constant<T>,Derived> operator+(const T& scalar, const StorageBaseType& expr);\n#endif\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\nEIGEN_MAKE_SCALAR_BINARY_OP(operator-,difference)\n#else\n/** \\returns an expression of \\c *this with each coeff decremented by the constant \\a scalar\n  *\n  * \\tparam T is the scalar type of \\a scalar. It must be compatible with the scalar type of the given expression.\n  *\n  * Example: \\include Cwise_minus.cpp\n  * Output: \\verbinclude Cwise_minus.out\n  *\n  * \\sa operator+=(), operator-()\n  */\ntemplate<typename T>\nconst CwiseBinaryOp<internal::scalar_difference_op<Scalar,T>,Derived,Constant<T> > operator-(const T& scalar) const;\n/** \\returns an expression of the constant matrix of value \\a scalar decremented by the coefficients of \\a expr\n  *\n  * \\tparam T is the scalar type of \\a scalar. It must be compatible with the scalar type of the given expression.\n  */\ntemplate<typename T> friend\nconst CwiseBinaryOp<internal::scalar_difference_op<T,Scalar>,Constant<T>,Derived> operator-(const T& scalar, const StorageBaseType& expr);\n#endif\n\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\n  EIGEN_MAKE_SCALAR_BINARY_OP_ONTHELEFT(operator/,quotient)\n#else\n  /**\n    * \\brief Component-wise division of the scalar \\a s by array elements of \\a a.\n    *\n    * \\tparam Scalar is the scalar type of \\a x. It must be compatible with the scalar type of the given array expression (\\c Derived::Scalar).\n    */\n  template<typename T> friend\n  inline const CwiseBinaryOp<internal::scalar_quotient_op<T,Scalar>,Constant<T>,Derived>\n  operator/(const T& s,const StorageBaseType& a);\n#endif\n\n/** \\returns an expression of the coefficient-wise ^ operator of *this and \\a other\n *\n * \\warning this operator is for expression of bool only.\n *\n * Example: \\include Cwise_boolean_xor.cpp\n * Output: \\verbinclude Cwise_boolean_xor.out\n *\n * \\sa operator&&(), select()\n */\ntemplate<typename OtherDerived>\nEIGEN_DEVICE_FUNC\ninline const CwiseBinaryOp<internal::scalar_boolean_xor_op, const Derived, const OtherDerived>\noperator^(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const\n{\n  EIGEN_STATIC_ASSERT((internal::is_same<bool,Scalar>::value && internal::is_same<bool,typename OtherDerived::Scalar>::value),\n                      THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_OF_BOOL);\n  return CwiseBinaryOp<internal::scalar_boolean_xor_op, const Derived, const OtherDerived>(derived(),other.derived());\n}\n\n// NOTE disabled until we agree on argument order\n#if 0\n/** \\cpp11 \\returns an expression of the coefficient-wise polygamma function.\n  *\n  * \\specialfunctions_module\n  *\n  * It returns the \\a n -th derivative of the digamma(psi) evaluated at \\c *this.\n  *\n  * \\warning Be careful with the order of the parameters: x.polygamma(n) is equivalent to polygamma(n,x)\n  *\n  * \\sa Eigen::polygamma()\n  */\ntemplate<typename DerivedN>\ninline const CwiseBinaryOp<internal::scalar_polygamma_op<Scalar>, const DerivedN, const Derived>\npolygamma(const EIGEN_CURRENT_STORAGE_BASE_CLASS<DerivedN> &n) const\n{\n  return CwiseBinaryOp<internal::scalar_polygamma_op<Scalar>, const DerivedN, const Derived>(n.derived(), this->derived());\n}\n#endif\n\n/** \\returns an expression of the coefficient-wise zeta function.\n  *\n  * \\specialfunctions_module\n  *\n  * It returns the Riemann zeta function of two arguments \\c *this and \\a q:\n  *\n  * \\param *this is the exposent, it must be > 1\n  * \\param q is the shift, it must be > 0\n  *\n  * \\note This function supports only float and double scalar types. To support other scalar types, the user has\n  * to provide implementations of zeta(T,T) for any scalar type T to be supported.\n  *\n  * This method is an alias for zeta(*this,q);\n  *\n  * \\sa Eigen::zeta()\n  */\ntemplate<typename DerivedQ>\ninline const CwiseBinaryOp<internal::scalar_zeta_op<Scalar>, const Derived, const DerivedQ>\nzeta(const EIGEN_CURRENT_STORAGE_BASE_CLASS<DerivedQ> &q) const\n{\n  return CwiseBinaryOp<internal::scalar_zeta_op<Scalar>, const Derived, const DerivedQ>(this->derived(), q.derived());\n}\n"
  },
  {
    "path": "include/eigen3/Eigen/src/plugins/ArrayCwiseUnaryOps.h",
    "content": "\n\ntypedef CwiseUnaryOp<internal::scalar_abs_op<Scalar>, const Derived> AbsReturnType;\ntypedef CwiseUnaryOp<internal::scalar_arg_op<Scalar>, const Derived> ArgReturnType;\ntypedef CwiseUnaryOp<internal::scalar_abs2_op<Scalar>, const Derived> Abs2ReturnType;\ntypedef CwiseUnaryOp<internal::scalar_sqrt_op<Scalar>, const Derived> SqrtReturnType;\ntypedef CwiseUnaryOp<internal::scalar_rsqrt_op<Scalar>, const Derived> RsqrtReturnType;\ntypedef CwiseUnaryOp<internal::scalar_sign_op<Scalar>, const Derived> SignReturnType;\ntypedef CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const Derived> InverseReturnType;\ntypedef CwiseUnaryOp<internal::scalar_boolean_not_op<Scalar>, const Derived> BooleanNotReturnType;\n\ntypedef CwiseUnaryOp<internal::scalar_exp_op<Scalar>, const Derived> ExpReturnType;\ntypedef CwiseUnaryOp<internal::scalar_log_op<Scalar>, const Derived> LogReturnType;\ntypedef CwiseUnaryOp<internal::scalar_log1p_op<Scalar>, const Derived> Log1pReturnType;\ntypedef CwiseUnaryOp<internal::scalar_log10_op<Scalar>, const Derived> Log10ReturnType;\ntypedef CwiseUnaryOp<internal::scalar_cos_op<Scalar>, const Derived> CosReturnType;\ntypedef CwiseUnaryOp<internal::scalar_sin_op<Scalar>, const Derived> SinReturnType;\ntypedef CwiseUnaryOp<internal::scalar_tan_op<Scalar>, const Derived> TanReturnType;\ntypedef CwiseUnaryOp<internal::scalar_acos_op<Scalar>, const Derived> AcosReturnType;\ntypedef CwiseUnaryOp<internal::scalar_asin_op<Scalar>, const Derived> AsinReturnType;\ntypedef CwiseUnaryOp<internal::scalar_atan_op<Scalar>, const Derived> AtanReturnType;\ntypedef CwiseUnaryOp<internal::scalar_tanh_op<Scalar>, const Derived> TanhReturnType;\ntypedef CwiseUnaryOp<internal::scalar_sinh_op<Scalar>, const Derived> SinhReturnType;\ntypedef CwiseUnaryOp<internal::scalar_cosh_op<Scalar>, const Derived> CoshReturnType;\ntypedef CwiseUnaryOp<internal::scalar_square_op<Scalar>, const Derived> SquareReturnType;\ntypedef CwiseUnaryOp<internal::scalar_cube_op<Scalar>, const Derived> CubeReturnType;\ntypedef CwiseUnaryOp<internal::scalar_round_op<Scalar>, const Derived> RoundReturnType;\ntypedef CwiseUnaryOp<internal::scalar_floor_op<Scalar>, const Derived> FloorReturnType;\ntypedef CwiseUnaryOp<internal::scalar_ceil_op<Scalar>, const Derived> CeilReturnType;\ntypedef CwiseUnaryOp<internal::scalar_isnan_op<Scalar>, const Derived> IsNaNReturnType;\ntypedef CwiseUnaryOp<internal::scalar_isinf_op<Scalar>, const Derived> IsInfReturnType;\ntypedef CwiseUnaryOp<internal::scalar_isfinite_op<Scalar>, const Derived> IsFiniteReturnType;\n\n/** \\returns an expression of the coefficient-wise absolute value of \\c *this\n  *\n  * Example: \\include Cwise_abs.cpp\n  * Output: \\verbinclude Cwise_abs.out\n  *\n  * \\sa <a href=\"group__CoeffwiseMathFunctions.html#cwisetable_abs\">Math functions</a>, abs2()\n  */\nEIGEN_DEVICE_FUNC\nEIGEN_STRONG_INLINE const AbsReturnType\nabs() const\n{\n  return AbsReturnType(derived());\n}\n\n/** \\returns an expression of the coefficient-wise phase angle of \\c *this\n  *\n  * Example: \\include Cwise_arg.cpp\n  * Output: \\verbinclude Cwise_arg.out\n  *\n  * \\sa abs()\n  */\nEIGEN_DEVICE_FUNC\nEIGEN_STRONG_INLINE const ArgReturnType\narg() const\n{\n  return ArgReturnType(derived());\n}\n\n/** \\returns an expression of the coefficient-wise squared absolute value of \\c *this\n  *\n  * Example: \\include Cwise_abs2.cpp\n  * Output: \\verbinclude Cwise_abs2.out\n  *\n  * \\sa <a href=\"group__CoeffwiseMathFunctions.html#cwisetable_abs2\">Math functions</a>, abs(), square()\n  */\nEIGEN_DEVICE_FUNC\nEIGEN_STRONG_INLINE const Abs2ReturnType\nabs2() const\n{\n  return Abs2ReturnType(derived());\n}\n\n/** \\returns an expression of the coefficient-wise exponential of *this.\n  *\n  * This function computes the coefficient-wise exponential. The function MatrixBase::exp() in the\n  * unsupported module MatrixFunctions computes the matrix exponential.\n  *\n  * Example: \\include Cwise_exp.cpp\n  * Output: \\verbinclude Cwise_exp.out\n  *\n  * \\sa <a href=\"group__CoeffwiseMathFunctions.html#cwisetable_exp\">Math functions</a>, pow(), log(), sin(), cos()\n  */\nEIGEN_DEVICE_FUNC\ninline const ExpReturnType\nexp() const\n{\n  return ExpReturnType(derived());\n}\n\n/** \\returns an expression of the coefficient-wise logarithm of *this.\n  *\n  * This function computes the coefficient-wise logarithm. The function MatrixBase::log() in the\n  * unsupported module MatrixFunctions computes the matrix logarithm.\n  *\n  * Example: \\include Cwise_log.cpp\n  * Output: \\verbinclude Cwise_log.out\n  *\n  * \\sa <a href=\"group__CoeffwiseMathFunctions.html#cwisetable_log\">Math functions</a>, exp()\n  */\nEIGEN_DEVICE_FUNC\ninline const LogReturnType\nlog() const\n{\n  return LogReturnType(derived());\n}\n\n/** \\returns an expression of the coefficient-wise logarithm of 1 plus \\c *this.\n  *\n  * In exact arithmetic, \\c x.log() is equivalent to \\c (x+1).log(),\n  * however, with finite precision, this function is much more accurate when \\c x is close to zero.\n  *\n  * \\sa <a href=\"group__CoeffwiseMathFunctions.html#cwisetable_log1p\">Math functions</a>, log()\n  */\nEIGEN_DEVICE_FUNC\ninline const Log1pReturnType\nlog1p() const\n{\n  return Log1pReturnType(derived());\n}\n\n/** \\returns an expression of the coefficient-wise base-10 logarithm of *this.\n  *\n  * This function computes the coefficient-wise base-10 logarithm.\n  *\n  * Example: \\include Cwise_log10.cpp\n  * Output: \\verbinclude Cwise_log10.out\n  *\n  * \\sa <a href=\"group__CoeffwiseMathFunctions.html#cwisetable_log10\">Math functions</a>, log()\n  */\nEIGEN_DEVICE_FUNC\ninline const Log10ReturnType\nlog10() const\n{\n  return Log10ReturnType(derived());\n}\n\n/** \\returns an expression of the coefficient-wise square root of *this.\n  *\n  * This function computes the coefficient-wise square root. The function MatrixBase::sqrt() in the\n  * unsupported module MatrixFunctions computes the matrix square root.\n  *\n  * Example: \\include Cwise_sqrt.cpp\n  * Output: \\verbinclude Cwise_sqrt.out\n  *\n  * \\sa <a href=\"group__CoeffwiseMathFunctions.html#cwisetable_sqrt\">Math functions</a>, pow(), square()\n  */\nEIGEN_DEVICE_FUNC\ninline const SqrtReturnType\nsqrt() const\n{\n  return SqrtReturnType(derived());\n}\n\n/** \\returns an expression of the coefficient-wise inverse square root of *this.\n  *\n  * This function computes the coefficient-wise inverse square root.\n  *\n  * Example: \\include Cwise_sqrt.cpp\n  * Output: \\verbinclude Cwise_sqrt.out\n  *\n  * \\sa pow(), square()\n  */\nEIGEN_DEVICE_FUNC\ninline const RsqrtReturnType\nrsqrt() const\n{\n  return RsqrtReturnType(derived());\n}\n\n/** \\returns an expression of the coefficient-wise signum of *this.\n  *\n  * This function computes the coefficient-wise signum.\n  *\n  * Example: \\include Cwise_sign.cpp\n  * Output: \\verbinclude Cwise_sign.out\n  *\n  * \\sa pow(), square()\n  */\nEIGEN_DEVICE_FUNC\ninline const SignReturnType\nsign() const\n{\n  return SignReturnType(derived());\n}\n\n\n/** \\returns an expression of the coefficient-wise cosine of *this.\n  *\n  * This function computes the coefficient-wise cosine. The function MatrixBase::cos() in the\n  * unsupported module MatrixFunctions computes the matrix cosine.\n  *\n  * Example: \\include Cwise_cos.cpp\n  * Output: \\verbinclude Cwise_cos.out\n  *\n  * \\sa <a href=\"group__CoeffwiseMathFunctions.html#cwisetable_cos\">Math functions</a>, sin(), acos()\n  */\nEIGEN_DEVICE_FUNC\ninline const CosReturnType\ncos() const\n{\n  return CosReturnType(derived());\n}\n\n\n/** \\returns an expression of the coefficient-wise sine of *this.\n  *\n  * This function computes the coefficient-wise sine. The function MatrixBase::sin() in the\n  * unsupported module MatrixFunctions computes the matrix sine.\n  *\n  * Example: \\include Cwise_sin.cpp\n  * Output: \\verbinclude Cwise_sin.out\n  *\n  * \\sa <a href=\"group__CoeffwiseMathFunctions.html#cwisetable_sin\">Math functions</a>, cos(), asin()\n  */\nEIGEN_DEVICE_FUNC\ninline const SinReturnType\nsin() const\n{\n  return SinReturnType(derived());\n}\n\n/** \\returns an expression of the coefficient-wise tan of *this.\n  *\n  * Example: \\include Cwise_tan.cpp\n  * Output: \\verbinclude Cwise_tan.out\n  *\n  * \\sa <a href=\"group__CoeffwiseMathFunctions.html#cwisetable_tan\">Math functions</a>, cos(), sin()\n  */\nEIGEN_DEVICE_FUNC\ninline const TanReturnType\ntan() const\n{\n  return TanReturnType(derived());\n}\n\n/** \\returns an expression of the coefficient-wise arc tan of *this.\n  *\n  * Example: \\include Cwise_atan.cpp\n  * Output: \\verbinclude Cwise_atan.out\n  *\n  * \\sa <a href=\"group__CoeffwiseMathFunctions.html#cwisetable_atan\">Math functions</a>, tan(), asin(), acos()\n  */\nEIGEN_DEVICE_FUNC\ninline const AtanReturnType\natan() const\n{\n  return AtanReturnType(derived());\n}\n\n/** \\returns an expression of the coefficient-wise arc cosine of *this.\n  *\n  * Example: \\include Cwise_acos.cpp\n  * Output: \\verbinclude Cwise_acos.out\n  *\n  * \\sa <a href=\"group__CoeffwiseMathFunctions.html#cwisetable_acos\">Math functions</a>, cos(), asin()\n  */\nEIGEN_DEVICE_FUNC\ninline const AcosReturnType\nacos() const\n{\n  return AcosReturnType(derived());\n}\n\n/** \\returns an expression of the coefficient-wise arc sine of *this.\n  *\n  * Example: \\include Cwise_asin.cpp\n  * Output: \\verbinclude Cwise_asin.out\n  *\n  * \\sa <a href=\"group__CoeffwiseMathFunctions.html#cwisetable_asin\">Math functions</a>, sin(), acos()\n  */\nEIGEN_DEVICE_FUNC\ninline const AsinReturnType\nasin() const\n{\n  return AsinReturnType(derived());\n}\n\n/** \\returns an expression of the coefficient-wise hyperbolic tan of *this.\n  *\n  * Example: \\include Cwise_tanh.cpp\n  * Output: \\verbinclude Cwise_tanh.out\n  *\n  * \\sa <a href=\"group__CoeffwiseMathFunctions.html#cwisetable_tanh\">Math functions</a>, tan(), sinh(), cosh()\n  */\nEIGEN_DEVICE_FUNC\ninline const TanhReturnType\ntanh() const\n{\n  return TanhReturnType(derived());\n}\n\n/** \\returns an expression of the coefficient-wise hyperbolic sin of *this.\n  *\n  * Example: \\include Cwise_sinh.cpp\n  * Output: \\verbinclude Cwise_sinh.out\n  *\n  * \\sa <a href=\"group__CoeffwiseMathFunctions.html#cwisetable_sinh\">Math functions</a>, sin(), tanh(), cosh()\n  */\nEIGEN_DEVICE_FUNC\ninline const SinhReturnType\nsinh() const\n{\n  return SinhReturnType(derived());\n}\n\n/** \\returns an expression of the coefficient-wise hyperbolic cos of *this.\n  *\n  * Example: \\include Cwise_cosh.cpp\n  * Output: \\verbinclude Cwise_cosh.out\n  *\n  * \\sa <a href=\"group__CoeffwiseMathFunctions.html#cwisetable_cosh\">Math functions</a>, tan(), sinh(), cosh()\n  */\nEIGEN_DEVICE_FUNC\ninline const CoshReturnType\ncosh() const\n{\n  return CoshReturnType(derived());\n}\n\n/** \\returns an expression of the coefficient-wise inverse of *this.\n  *\n  * Example: \\include Cwise_inverse.cpp\n  * Output: \\verbinclude Cwise_inverse.out\n  *\n  * \\sa operator/(), operator*()\n  */\nEIGEN_DEVICE_FUNC\ninline const InverseReturnType\ninverse() const\n{\n  return InverseReturnType(derived());\n}\n\n/** \\returns an expression of the coefficient-wise square of *this.\n  *\n  * Example: \\include Cwise_square.cpp\n  * Output: \\verbinclude Cwise_square.out\n  *\n  * \\sa <a href=\"group__CoeffwiseMathFunctions.html#cwisetable_squareE\">Math functions</a>, abs2(), cube(), pow()\n  */\nEIGEN_DEVICE_FUNC\ninline const SquareReturnType\nsquare() const\n{\n  return SquareReturnType(derived());\n}\n\n/** \\returns an expression of the coefficient-wise cube of *this.\n  *\n  * Example: \\include Cwise_cube.cpp\n  * Output: \\verbinclude Cwise_cube.out\n  *\n  * \\sa <a href=\"group__CoeffwiseMathFunctions.html#cwisetable_cube\">Math functions</a>, square(), pow()\n  */\nEIGEN_DEVICE_FUNC\ninline const CubeReturnType\ncube() const\n{\n  return CubeReturnType(derived());\n}\n\n/** \\returns an expression of the coefficient-wise round of *this.\n  *\n  * Example: \\include Cwise_round.cpp\n  * Output: \\verbinclude Cwise_round.out\n  *\n  * \\sa <a href=\"group__CoeffwiseMathFunctions.html#cwisetable_round\">Math functions</a>, ceil(), floor()\n  */\nEIGEN_DEVICE_FUNC\ninline const RoundReturnType\nround() const\n{\n  return RoundReturnType(derived());\n}\n\n/** \\returns an expression of the coefficient-wise floor of *this.\n  *\n  * Example: \\include Cwise_floor.cpp\n  * Output: \\verbinclude Cwise_floor.out\n  *\n  * \\sa <a href=\"group__CoeffwiseMathFunctions.html#cwisetable_floor\">Math functions</a>, ceil(), round()\n  */\nEIGEN_DEVICE_FUNC\ninline const FloorReturnType\nfloor() const\n{\n  return FloorReturnType(derived());\n}\n\n/** \\returns an expression of the coefficient-wise ceil of *this.\n  *\n  * Example: \\include Cwise_ceil.cpp\n  * Output: \\verbinclude Cwise_ceil.out\n  *\n  * \\sa <a href=\"group__CoeffwiseMathFunctions.html#cwisetable_ceil\">Math functions</a>, floor(), round()\n  */\nEIGEN_DEVICE_FUNC\ninline const CeilReturnType\nceil() const\n{\n  return CeilReturnType(derived());\n}\n\n/** \\returns an expression of the coefficient-wise isnan of *this.\n  *\n  * Example: \\include Cwise_isNaN.cpp\n  * Output: \\verbinclude Cwise_isNaN.out\n  *\n  * \\sa isfinite(), isinf()\n  */\nEIGEN_DEVICE_FUNC\ninline const IsNaNReturnType\nisNaN() const\n{\n  return IsNaNReturnType(derived());\n}\n\n/** \\returns an expression of the coefficient-wise isinf of *this.\n  *\n  * Example: \\include Cwise_isInf.cpp\n  * Output: \\verbinclude Cwise_isInf.out\n  *\n  * \\sa isnan(), isfinite()\n  */\nEIGEN_DEVICE_FUNC\ninline const IsInfReturnType\nisInf() const\n{\n  return IsInfReturnType(derived());\n}\n\n/** \\returns an expression of the coefficient-wise isfinite of *this.\n  *\n  * Example: \\include Cwise_isFinite.cpp\n  * Output: \\verbinclude Cwise_isFinite.out\n  *\n  * \\sa isnan(), isinf()\n  */\nEIGEN_DEVICE_FUNC\ninline const IsFiniteReturnType\nisFinite() const\n{\n  return IsFiniteReturnType(derived());\n}\n\n/** \\returns an expression of the coefficient-wise ! operator of *this\n  *\n  * \\warning this operator is for expression of bool only.\n  *\n  * Example: \\include Cwise_boolean_not.cpp\n  * Output: \\verbinclude Cwise_boolean_not.out\n  *\n  * \\sa operator!=()\n  */\nEIGEN_DEVICE_FUNC\ninline const BooleanNotReturnType\noperator!() const\n{\n  EIGEN_STATIC_ASSERT((internal::is_same<bool,Scalar>::value),\n                      THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_OF_BOOL);\n  return BooleanNotReturnType(derived());\n}\n\n\n// --- SpecialFunctions module ---\n\ntypedef CwiseUnaryOp<internal::scalar_lgamma_op<Scalar>, const Derived> LgammaReturnType;\ntypedef CwiseUnaryOp<internal::scalar_digamma_op<Scalar>, const Derived> DigammaReturnType;\ntypedef CwiseUnaryOp<internal::scalar_erf_op<Scalar>, const Derived> ErfReturnType;\ntypedef CwiseUnaryOp<internal::scalar_erfc_op<Scalar>, const Derived> ErfcReturnType;\n\n/** \\cpp11 \\returns an expression of the coefficient-wise ln(|gamma(*this)|).\n  *\n  * \\specialfunctions_module\n  *\n  * Example: \\include Cwise_lgamma.cpp\n  * Output: \\verbinclude Cwise_lgamma.out\n  *\n  * \\note This function supports only float and double scalar types in c++11 mode. To support other scalar types,\n  * or float/double in non c++11 mode, the user has to provide implementations of lgamma(T) for any scalar\n  * type T to be supported.\n  *\n  * \\sa <a href=\"group__CoeffwiseMathFunctions.html#cwisetable_lgamma\">Math functions</a>, digamma()\n  */\nEIGEN_DEVICE_FUNC\ninline const LgammaReturnType\nlgamma() const\n{\n  return LgammaReturnType(derived());\n}\n\n/** \\returns an expression of the coefficient-wise digamma (psi, derivative of lgamma).\n  *\n  * \\specialfunctions_module\n  *\n  * \\note This function supports only float and double scalar types. To support other scalar types,\n  * the user has to provide implementations of digamma(T) for any scalar\n  * type T to be supported.\n  *\n  * \\sa <a href=\"group__CoeffwiseMathFunctions.html#cwisetable_digamma\">Math functions</a>, Eigen::digamma(), Eigen::polygamma(), lgamma()\n  */\nEIGEN_DEVICE_FUNC\ninline const DigammaReturnType\ndigamma() const\n{\n  return DigammaReturnType(derived());\n}\n\n/** \\cpp11 \\returns an expression of the coefficient-wise Gauss error\n  * function of *this.\n  *\n  * \\specialfunctions_module\n  *\n  * Example: \\include Cwise_erf.cpp\n  * Output: \\verbinclude Cwise_erf.out\n  *\n  * \\note This function supports only float and double scalar types in c++11 mode. To support other scalar types,\n  * or float/double in non c++11 mode, the user has to provide implementations of erf(T) for any scalar\n  * type T to be supported.\n  *\n  * \\sa <a href=\"group__CoeffwiseMathFunctions.html#cwisetable_erf\">Math functions</a>, erfc()\n  */\nEIGEN_DEVICE_FUNC\ninline const ErfReturnType\nerf() const\n{\n  return ErfReturnType(derived());\n}\n\n/** \\cpp11 \\returns an expression of the coefficient-wise Complementary error\n  * function of *this.\n  *\n  * \\specialfunctions_module\n  *\n  * Example: \\include Cwise_erfc.cpp\n  * Output: \\verbinclude Cwise_erfc.out\n  *\n  * \\note This function supports only float and double scalar types in c++11 mode. To support other scalar types,\n  * or float/double in non c++11 mode, the user has to provide implementations of erfc(T) for any scalar\n  * type T to be supported.\n  *\n  * \\sa <a href=\"group__CoeffwiseMathFunctions.html#cwisetable_erfc\">Math functions</a>, erf()\n  */\nEIGEN_DEVICE_FUNC\ninline const ErfcReturnType\nerfc() const\n{\n  return ErfcReturnType(derived());\n}\n"
  },
  {
    "path": "include/eigen3/Eigen/src/plugins/BlockMethods.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\n\n/// \\internal expression type of a column */\ntypedef Block<Derived, internal::traits<Derived>::RowsAtCompileTime, 1, !IsRowMajor> ColXpr;\ntypedef const Block<const Derived, internal::traits<Derived>::RowsAtCompileTime, 1, !IsRowMajor> ConstColXpr;\n/// \\internal expression type of a row */\ntypedef Block<Derived, 1, internal::traits<Derived>::ColsAtCompileTime, IsRowMajor> RowXpr;\ntypedef const Block<const Derived, 1, internal::traits<Derived>::ColsAtCompileTime, IsRowMajor> ConstRowXpr;\n/// \\internal expression type of a block of whole columns */\ntypedef Block<Derived, internal::traits<Derived>::RowsAtCompileTime, Dynamic, !IsRowMajor> ColsBlockXpr;\ntypedef const Block<const Derived, internal::traits<Derived>::RowsAtCompileTime, Dynamic, !IsRowMajor> ConstColsBlockXpr;\n/// \\internal expression type of a block of whole rows */\ntypedef Block<Derived, Dynamic, internal::traits<Derived>::ColsAtCompileTime, IsRowMajor> RowsBlockXpr;\ntypedef const Block<const Derived, Dynamic, internal::traits<Derived>::ColsAtCompileTime, IsRowMajor> ConstRowsBlockXpr;\n/// \\internal expression type of a block of whole columns */\ntemplate<int N> struct NColsBlockXpr { typedef Block<Derived, internal::traits<Derived>::RowsAtCompileTime, N, !IsRowMajor> Type; };\ntemplate<int N> struct ConstNColsBlockXpr { typedef const Block<const Derived, internal::traits<Derived>::RowsAtCompileTime, N, !IsRowMajor> Type; };\n/// \\internal expression type of a block of whole rows */\ntemplate<int N> struct NRowsBlockXpr { typedef Block<Derived, N, internal::traits<Derived>::ColsAtCompileTime, IsRowMajor> Type; };\ntemplate<int N> struct ConstNRowsBlockXpr { typedef const Block<const Derived, N, internal::traits<Derived>::ColsAtCompileTime, IsRowMajor> Type; };\n/// \\internal expression of a block */\ntypedef Block<Derived> BlockXpr;\ntypedef const Block<const Derived> ConstBlockXpr;\n/// \\internal expression of a block of fixed sizes */\ntemplate<int Rows, int Cols> struct FixedBlockXpr { typedef Block<Derived,Rows,Cols> Type; };\ntemplate<int Rows, int Cols> struct ConstFixedBlockXpr { typedef Block<const Derived,Rows,Cols> Type; };\n\ntypedef VectorBlock<Derived> SegmentReturnType;\ntypedef const VectorBlock<const Derived> ConstSegmentReturnType;\ntemplate<int Size> struct FixedSegmentReturnType { typedef VectorBlock<Derived, Size> Type; };\ntemplate<int Size> struct ConstFixedSegmentReturnType { typedef const VectorBlock<const Derived, Size> Type; };\n\n#endif // not EIGEN_PARSED_BY_DOXYGEN\n\n/// \\returns a dynamic-size expression of a block in *this.\n///\n/// \\param startRow the first row in the block\n/// \\param startCol the first column in the block\n/// \\param blockRows the number of rows in the block\n/// \\param blockCols the number of columns in the block\n///\n/// Example: \\include MatrixBase_block_int_int_int_int.cpp\n/// Output: \\verbinclude MatrixBase_block_int_int_int_int.out\n///\n/// \\note Even though the returned expression has dynamic size, in the case\n/// when it is applied to a fixed-size matrix, it inherits a fixed maximal size,\n/// which means that evaluating it does not cause a dynamic memory allocation.\n///\nEIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL\n///\n/// \\sa class Block, block(Index,Index)\n///\nEIGEN_DEVICE_FUNC\ninline BlockXpr block(Index startRow, Index startCol, Index blockRows, Index blockCols)\n{\n  return BlockXpr(derived(), startRow, startCol, blockRows, blockCols);\n}\n\n/// This is the const version of block(Index,Index,Index,Index). */\nEIGEN_DEVICE_FUNC\ninline const ConstBlockXpr block(Index startRow, Index startCol, Index blockRows, Index blockCols) const\n{\n  return ConstBlockXpr(derived(), startRow, startCol, blockRows, blockCols);\n}\n\n\n\n\n/// \\returns a dynamic-size expression of a top-right corner of *this.\n///\n/// \\param cRows the number of rows in the corner\n/// \\param cCols the number of columns in the corner\n///\n/// Example: \\include MatrixBase_topRightCorner_int_int.cpp\n/// Output: \\verbinclude MatrixBase_topRightCorner_int_int.out\n///\nEIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL\n///\n/// \\sa class Block, block(Index,Index,Index,Index)\n///\nEIGEN_DEVICE_FUNC\ninline BlockXpr topRightCorner(Index cRows, Index cCols)\n{\n  return BlockXpr(derived(), 0, cols() - cCols, cRows, cCols);\n}\n\n/// This is the const version of topRightCorner(Index, Index).\nEIGEN_DEVICE_FUNC\ninline const ConstBlockXpr topRightCorner(Index cRows, Index cCols) const\n{\n  return ConstBlockXpr(derived(), 0, cols() - cCols, cRows, cCols);\n}\n\n/// \\returns an expression of a fixed-size top-right corner of *this.\n///\n/// \\tparam CRows the number of rows in the corner\n/// \\tparam CCols the number of columns in the corner\n///\n/// Example: \\include MatrixBase_template_int_int_topRightCorner.cpp\n/// Output: \\verbinclude MatrixBase_template_int_int_topRightCorner.out\n///\nEIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL\n///\n/// \\sa class Block, block<int,int>(Index,Index)\n///\ntemplate<int CRows, int CCols>\nEIGEN_DEVICE_FUNC\ninline typename FixedBlockXpr<CRows,CCols>::Type topRightCorner()\n{\n  return typename FixedBlockXpr<CRows,CCols>::Type(derived(), 0, cols() - CCols);\n}\n\n/// This is the const version of topRightCorner<int, int>().\ntemplate<int CRows, int CCols>\nEIGEN_DEVICE_FUNC\ninline const typename ConstFixedBlockXpr<CRows,CCols>::Type topRightCorner() const\n{\n  return typename ConstFixedBlockXpr<CRows,CCols>::Type(derived(), 0, cols() - CCols);\n}\n\n/// \\returns an expression of a top-right corner of *this.\n///\n/// \\tparam CRows number of rows in corner as specified at compile-time\n/// \\tparam CCols number of columns in corner as specified at compile-time\n/// \\param  cRows number of rows in corner as specified at run-time\n/// \\param  cCols number of columns in corner as specified at run-time\n///\n/// This function is mainly useful for corners where the number of rows is specified at compile-time\n/// and the number of columns is specified at run-time, or vice versa. The compile-time and run-time\n/// information should not contradict. In other words, \\a cRows should equal \\a CRows unless\n/// \\a CRows is \\a Dynamic, and the same for the number of columns.\n///\n/// Example: \\include MatrixBase_template_int_int_topRightCorner_int_int.cpp\n/// Output: \\verbinclude MatrixBase_template_int_int_topRightCorner_int_int.out\n///\nEIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL\n///\n/// \\sa class Block\n///\ntemplate<int CRows, int CCols>\ninline typename FixedBlockXpr<CRows,CCols>::Type topRightCorner(Index cRows, Index cCols)\n{\n  return typename FixedBlockXpr<CRows,CCols>::Type(derived(), 0, cols() - cCols, cRows, cCols);\n}\n\n/// This is the const version of topRightCorner<int, int>(Index, Index).\ntemplate<int CRows, int CCols>\ninline const typename ConstFixedBlockXpr<CRows,CCols>::Type topRightCorner(Index cRows, Index cCols) const\n{\n  return typename ConstFixedBlockXpr<CRows,CCols>::Type(derived(), 0, cols() - cCols, cRows, cCols);\n}\n\n\n\n/// \\returns a dynamic-size expression of a top-left corner of *this.\n///\n/// \\param cRows the number of rows in the corner\n/// \\param cCols the number of columns in the corner\n///\n/// Example: \\include MatrixBase_topLeftCorner_int_int.cpp\n/// Output: \\verbinclude MatrixBase_topLeftCorner_int_int.out\n///\nEIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL\n///\n/// \\sa class Block, block(Index,Index,Index,Index)\n///\nEIGEN_DEVICE_FUNC\ninline BlockXpr topLeftCorner(Index cRows, Index cCols)\n{\n  return BlockXpr(derived(), 0, 0, cRows, cCols);\n}\n\n/// This is the const version of topLeftCorner(Index, Index).\nEIGEN_DEVICE_FUNC\ninline const ConstBlockXpr topLeftCorner(Index cRows, Index cCols) const\n{\n  return ConstBlockXpr(derived(), 0, 0, cRows, cCols);\n}\n\n/// \\returns an expression of a fixed-size top-left corner of *this.\n///\n/// The template parameters CRows and CCols are the number of rows and columns in the corner.\n///\n/// Example: \\include MatrixBase_template_int_int_topLeftCorner.cpp\n/// Output: \\verbinclude MatrixBase_template_int_int_topLeftCorner.out\n///\nEIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL\n///\n/// \\sa class Block, block(Index,Index,Index,Index)\n///\ntemplate<int CRows, int CCols>\nEIGEN_DEVICE_FUNC\ninline typename FixedBlockXpr<CRows,CCols>::Type topLeftCorner()\n{\n  return typename FixedBlockXpr<CRows,CCols>::Type(derived(), 0, 0);\n}\n\n/// This is the const version of topLeftCorner<int, int>().\ntemplate<int CRows, int CCols>\nEIGEN_DEVICE_FUNC\ninline const typename ConstFixedBlockXpr<CRows,CCols>::Type topLeftCorner() const\n{\n  return typename ConstFixedBlockXpr<CRows,CCols>::Type(derived(), 0, 0);\n}\n\n/// \\returns an expression of a top-left corner of *this.\n///\n/// \\tparam CRows number of rows in corner as specified at compile-time\n/// \\tparam CCols number of columns in corner as specified at compile-time\n/// \\param  cRows number of rows in corner as specified at run-time\n/// \\param  cCols number of columns in corner as specified at run-time\n///\n/// This function is mainly useful for corners where the number of rows is specified at compile-time\n/// and the number of columns is specified at run-time, or vice versa. The compile-time and run-time\n/// information should not contradict. In other words, \\a cRows should equal \\a CRows unless\n/// \\a CRows is \\a Dynamic, and the same for the number of columns.\n///\n/// Example: \\include MatrixBase_template_int_int_topLeftCorner_int_int.cpp\n/// Output: \\verbinclude MatrixBase_template_int_int_topLeftCorner_int_int.out\n///\nEIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL\n///\n/// \\sa class Block\n///\ntemplate<int CRows, int CCols>\ninline typename FixedBlockXpr<CRows,CCols>::Type topLeftCorner(Index cRows, Index cCols)\n{\n  return typename FixedBlockXpr<CRows,CCols>::Type(derived(), 0, 0, cRows, cCols);\n}\n\n/// This is the const version of topLeftCorner<int, int>(Index, Index).\ntemplate<int CRows, int CCols>\ninline const typename ConstFixedBlockXpr<CRows,CCols>::Type topLeftCorner(Index cRows, Index cCols) const\n{\n  return typename ConstFixedBlockXpr<CRows,CCols>::Type(derived(), 0, 0, cRows, cCols);\n}\n\n\n\n/// \\returns a dynamic-size expression of a bottom-right corner of *this.\n///\n/// \\param cRows the number of rows in the corner\n/// \\param cCols the number of columns in the corner\n///\n/// Example: \\include MatrixBase_bottomRightCorner_int_int.cpp\n/// Output: \\verbinclude MatrixBase_bottomRightCorner_int_int.out\n///\nEIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL\n///\n/// \\sa class Block, block(Index,Index,Index,Index)\n///\nEIGEN_DEVICE_FUNC\ninline BlockXpr bottomRightCorner(Index cRows, Index cCols)\n{\n  return BlockXpr(derived(), rows() - cRows, cols() - cCols, cRows, cCols);\n}\n\n/// This is the const version of bottomRightCorner(Index, Index).\nEIGEN_DEVICE_FUNC\ninline const ConstBlockXpr bottomRightCorner(Index cRows, Index cCols) const\n{\n  return ConstBlockXpr(derived(), rows() - cRows, cols() - cCols, cRows, cCols);\n}\n\n/// \\returns an expression of a fixed-size bottom-right corner of *this.\n///\n/// The template parameters CRows and CCols are the number of rows and columns in the corner.\n///\n/// Example: \\include MatrixBase_template_int_int_bottomRightCorner.cpp\n/// Output: \\verbinclude MatrixBase_template_int_int_bottomRightCorner.out\n///\nEIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL\n///\n/// \\sa class Block, block(Index,Index,Index,Index)\n///\ntemplate<int CRows, int CCols>\nEIGEN_DEVICE_FUNC\ninline typename FixedBlockXpr<CRows,CCols>::Type bottomRightCorner()\n{\n  return typename FixedBlockXpr<CRows,CCols>::Type(derived(), rows() - CRows, cols() - CCols);\n}\n\n/// This is the const version of bottomRightCorner<int, int>().\ntemplate<int CRows, int CCols>\nEIGEN_DEVICE_FUNC\ninline const typename ConstFixedBlockXpr<CRows,CCols>::Type bottomRightCorner() const\n{\n  return typename ConstFixedBlockXpr<CRows,CCols>::Type(derived(), rows() - CRows, cols() - CCols);\n}\n\n/// \\returns an expression of a bottom-right corner of *this.\n///\n/// \\tparam CRows number of rows in corner as specified at compile-time\n/// \\tparam CCols number of columns in corner as specified at compile-time\n/// \\param  cRows number of rows in corner as specified at run-time\n/// \\param  cCols number of columns in corner as specified at run-time\n///\n/// This function is mainly useful for corners where the number of rows is specified at compile-time\n/// and the number of columns is specified at run-time, or vice versa. The compile-time and run-time\n/// information should not contradict. In other words, \\a cRows should equal \\a CRows unless\n/// \\a CRows is \\a Dynamic, and the same for the number of columns.\n///\n/// Example: \\include MatrixBase_template_int_int_bottomRightCorner_int_int.cpp\n/// Output: \\verbinclude MatrixBase_template_int_int_bottomRightCorner_int_int.out\n///\nEIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL\n///\n/// \\sa class Block\n///\ntemplate<int CRows, int CCols>\ninline typename FixedBlockXpr<CRows,CCols>::Type bottomRightCorner(Index cRows, Index cCols)\n{\n  return typename FixedBlockXpr<CRows,CCols>::Type(derived(), rows() - cRows, cols() - cCols, cRows, cCols);\n}\n\n/// This is the const version of bottomRightCorner<int, int>(Index, Index).\ntemplate<int CRows, int CCols>\ninline const typename ConstFixedBlockXpr<CRows,CCols>::Type bottomRightCorner(Index cRows, Index cCols) const\n{\n  return typename ConstFixedBlockXpr<CRows,CCols>::Type(derived(), rows() - cRows, cols() - cCols, cRows, cCols);\n}\n\n\n\n/// \\returns a dynamic-size expression of a bottom-left corner of *this.\n///\n/// \\param cRows the number of rows in the corner\n/// \\param cCols the number of columns in the corner\n///\n/// Example: \\include MatrixBase_bottomLeftCorner_int_int.cpp\n/// Output: \\verbinclude MatrixBase_bottomLeftCorner_int_int.out\n///\nEIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL\n///\n/// \\sa class Block, block(Index,Index,Index,Index)\n///\nEIGEN_DEVICE_FUNC\ninline BlockXpr bottomLeftCorner(Index cRows, Index cCols)\n{\n  return BlockXpr(derived(), rows() - cRows, 0, cRows, cCols);\n}\n\n/// This is the const version of bottomLeftCorner(Index, Index).\nEIGEN_DEVICE_FUNC\ninline const ConstBlockXpr bottomLeftCorner(Index cRows, Index cCols) const\n{\n  return ConstBlockXpr(derived(), rows() - cRows, 0, cRows, cCols);\n}\n\n/// \\returns an expression of a fixed-size bottom-left corner of *this.\n///\n/// The template parameters CRows and CCols are the number of rows and columns in the corner.\n///\n/// Example: \\include MatrixBase_template_int_int_bottomLeftCorner.cpp\n/// Output: \\verbinclude MatrixBase_template_int_int_bottomLeftCorner.out\n///\nEIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL\n///\n/// \\sa class Block, block(Index,Index,Index,Index)\n///\ntemplate<int CRows, int CCols>\nEIGEN_DEVICE_FUNC\ninline typename FixedBlockXpr<CRows,CCols>::Type bottomLeftCorner()\n{\n  return typename FixedBlockXpr<CRows,CCols>::Type(derived(), rows() - CRows, 0);\n}\n\n/// This is the const version of bottomLeftCorner<int, int>().\ntemplate<int CRows, int CCols>\nEIGEN_DEVICE_FUNC\ninline const typename ConstFixedBlockXpr<CRows,CCols>::Type bottomLeftCorner() const\n{\n  return typename ConstFixedBlockXpr<CRows,CCols>::Type(derived(), rows() - CRows, 0);\n}\n\n/// \\returns an expression of a bottom-left corner of *this.\n///\n/// \\tparam CRows number of rows in corner as specified at compile-time\n/// \\tparam CCols number of columns in corner as specified at compile-time\n/// \\param  cRows number of rows in corner as specified at run-time\n/// \\param  cCols number of columns in corner as specified at run-time\n///\n/// This function is mainly useful for corners where the number of rows is specified at compile-time\n/// and the number of columns is specified at run-time, or vice versa. The compile-time and run-time\n/// information should not contradict. In other words, \\a cRows should equal \\a CRows unless\n/// \\a CRows is \\a Dynamic, and the same for the number of columns.\n///\n/// Example: \\include MatrixBase_template_int_int_bottomLeftCorner_int_int.cpp\n/// Output: \\verbinclude MatrixBase_template_int_int_bottomLeftCorner_int_int.out\n///\nEIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL\n///\n/// \\sa class Block\n///\ntemplate<int CRows, int CCols>\ninline typename FixedBlockXpr<CRows,CCols>::Type bottomLeftCorner(Index cRows, Index cCols)\n{\n  return typename FixedBlockXpr<CRows,CCols>::Type(derived(), rows() - cRows, 0, cRows, cCols);\n}\n\n/// This is the const version of bottomLeftCorner<int, int>(Index, Index).\ntemplate<int CRows, int CCols>\ninline const typename ConstFixedBlockXpr<CRows,CCols>::Type bottomLeftCorner(Index cRows, Index cCols) const\n{\n  return typename ConstFixedBlockXpr<CRows,CCols>::Type(derived(), rows() - cRows, 0, cRows, cCols);\n}\n\n\n\n/// \\returns a block consisting of the top rows of *this.\n///\n/// \\param n the number of rows in the block\n///\n/// Example: \\include MatrixBase_topRows_int.cpp\n/// Output: \\verbinclude MatrixBase_topRows_int.out\n///\nEIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(row-major)\n///\n/// \\sa class Block, block(Index,Index,Index,Index)\n///\nEIGEN_DEVICE_FUNC\ninline RowsBlockXpr topRows(Index n)\n{\n  return RowsBlockXpr(derived(), 0, 0, n, cols());\n}\n\n/// This is the const version of topRows(Index).\nEIGEN_DEVICE_FUNC\ninline ConstRowsBlockXpr topRows(Index n) const\n{\n  return ConstRowsBlockXpr(derived(), 0, 0, n, cols());\n}\n\n/// \\returns a block consisting of the top rows of *this.\n///\n/// \\tparam N the number of rows in the block as specified at compile-time\n/// \\param n the number of rows in the block as specified at run-time\n///\n/// The compile-time and run-time information should not contradict. In other words,\n/// \\a n should equal \\a N unless \\a N is \\a Dynamic.\n///\n/// Example: \\include MatrixBase_template_int_topRows.cpp\n/// Output: \\verbinclude MatrixBase_template_int_topRows.out\n///\nEIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(row-major)\n///\n/// \\sa class Block, block(Index,Index,Index,Index)\n///\ntemplate<int N>\nEIGEN_DEVICE_FUNC\ninline typename NRowsBlockXpr<N>::Type topRows(Index n = N)\n{\n  return typename NRowsBlockXpr<N>::Type(derived(), 0, 0, n, cols());\n}\n\n/// This is the const version of topRows<int>().\ntemplate<int N>\nEIGEN_DEVICE_FUNC\ninline typename ConstNRowsBlockXpr<N>::Type topRows(Index n = N) const\n{\n  return typename ConstNRowsBlockXpr<N>::Type(derived(), 0, 0, n, cols());\n}\n\n\n\n/// \\returns a block consisting of the bottom rows of *this.\n///\n/// \\param n the number of rows in the block\n///\n/// Example: \\include MatrixBase_bottomRows_int.cpp\n/// Output: \\verbinclude MatrixBase_bottomRows_int.out\n///\nEIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(row-major)\n///\n/// \\sa class Block, block(Index,Index,Index,Index)\n///\nEIGEN_DEVICE_FUNC\ninline RowsBlockXpr bottomRows(Index n)\n{\n  return RowsBlockXpr(derived(), rows() - n, 0, n, cols());\n}\n\n/// This is the const version of bottomRows(Index).\nEIGEN_DEVICE_FUNC\ninline ConstRowsBlockXpr bottomRows(Index n) const\n{\n  return ConstRowsBlockXpr(derived(), rows() - n, 0, n, cols());\n}\n\n/// \\returns a block consisting of the bottom rows of *this.\n///\n/// \\tparam N the number of rows in the block as specified at compile-time\n/// \\param n the number of rows in the block as specified at run-time\n///\n/// The compile-time and run-time information should not contradict. In other words,\n/// \\a n should equal \\a N unless \\a N is \\a Dynamic.\n///\n/// Example: \\include MatrixBase_template_int_bottomRows.cpp\n/// Output: \\verbinclude MatrixBase_template_int_bottomRows.out\n///\nEIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(row-major)\n///\n/// \\sa class Block, block(Index,Index,Index,Index)\n///\ntemplate<int N>\nEIGEN_DEVICE_FUNC\ninline typename NRowsBlockXpr<N>::Type bottomRows(Index n = N)\n{\n  return typename NRowsBlockXpr<N>::Type(derived(), rows() - n, 0, n, cols());\n}\n\n/// This is the const version of bottomRows<int>().\ntemplate<int N>\nEIGEN_DEVICE_FUNC\ninline typename ConstNRowsBlockXpr<N>::Type bottomRows(Index n = N) const\n{\n  return typename ConstNRowsBlockXpr<N>::Type(derived(), rows() - n, 0, n, cols());\n}\n\n\n\n/// \\returns a block consisting of a range of rows of *this.\n///\n/// \\param startRow the index of the first row in the block\n/// \\param n the number of rows in the block\n///\n/// Example: \\include DenseBase_middleRows_int.cpp\n/// Output: \\verbinclude DenseBase_middleRows_int.out\n///\nEIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(row-major)\n///\n/// \\sa class Block, block(Index,Index,Index,Index)\n///\nEIGEN_DEVICE_FUNC\ninline RowsBlockXpr middleRows(Index startRow, Index n)\n{\n  return RowsBlockXpr(derived(), startRow, 0, n, cols());\n}\n\n/// This is the const version of middleRows(Index,Index).\nEIGEN_DEVICE_FUNC\ninline ConstRowsBlockXpr middleRows(Index startRow, Index n) const\n{\n  return ConstRowsBlockXpr(derived(), startRow, 0, n, cols());\n}\n\n/// \\returns a block consisting of a range of rows of *this.\n///\n/// \\tparam N the number of rows in the block as specified at compile-time\n/// \\param startRow the index of the first row in the block\n/// \\param n the number of rows in the block as specified at run-time\n///\n/// The compile-time and run-time information should not contradict. In other words,\n/// \\a n should equal \\a N unless \\a N is \\a Dynamic.\n///\n/// Example: \\include DenseBase_template_int_middleRows.cpp\n/// Output: \\verbinclude DenseBase_template_int_middleRows.out\n///\nEIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(row-major)\n///\n/// \\sa class Block, block(Index,Index,Index,Index)\n///\ntemplate<int N>\nEIGEN_DEVICE_FUNC\ninline typename NRowsBlockXpr<N>::Type middleRows(Index startRow, Index n = N)\n{\n  return typename NRowsBlockXpr<N>::Type(derived(), startRow, 0, n, cols());\n}\n\n/// This is the const version of middleRows<int>().\ntemplate<int N>\nEIGEN_DEVICE_FUNC\ninline typename ConstNRowsBlockXpr<N>::Type middleRows(Index startRow, Index n = N) const\n{\n  return typename ConstNRowsBlockXpr<N>::Type(derived(), startRow, 0, n, cols());\n}\n\n\n\n/// \\returns a block consisting of the left columns of *this.\n///\n/// \\param n the number of columns in the block\n///\n/// Example: \\include MatrixBase_leftCols_int.cpp\n/// Output: \\verbinclude MatrixBase_leftCols_int.out\n///\nEIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(column-major)\n///\n/// \\sa class Block, block(Index,Index,Index,Index)\n///\nEIGEN_DEVICE_FUNC\ninline ColsBlockXpr leftCols(Index n)\n{\n  return ColsBlockXpr(derived(), 0, 0, rows(), n);\n}\n\n/// This is the const version of leftCols(Index).\nEIGEN_DEVICE_FUNC\ninline ConstColsBlockXpr leftCols(Index n) const\n{\n  return ConstColsBlockXpr(derived(), 0, 0, rows(), n);\n}\n\n/// \\returns a block consisting of the left columns of *this.\n///\n/// \\tparam N the number of columns in the block as specified at compile-time\n/// \\param n the number of columns in the block as specified at run-time\n///\n/// The compile-time and run-time information should not contradict. In other words,\n/// \\a n should equal \\a N unless \\a N is \\a Dynamic.\n///\n/// Example: \\include MatrixBase_template_int_leftCols.cpp\n/// Output: \\verbinclude MatrixBase_template_int_leftCols.out\n///\nEIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(column-major)\n///\n/// \\sa class Block, block(Index,Index,Index,Index)\n///\ntemplate<int N>\nEIGEN_DEVICE_FUNC\ninline typename NColsBlockXpr<N>::Type leftCols(Index n = N)\n{\n  return typename NColsBlockXpr<N>::Type(derived(), 0, 0, rows(), n);\n}\n\n/// This is the const version of leftCols<int>().\ntemplate<int N>\nEIGEN_DEVICE_FUNC\ninline typename ConstNColsBlockXpr<N>::Type leftCols(Index n = N) const\n{\n  return typename ConstNColsBlockXpr<N>::Type(derived(), 0, 0, rows(), n);\n}\n\n\n\n/// \\returns a block consisting of the right columns of *this.\n///\n/// \\param n the number of columns in the block\n///\n/// Example: \\include MatrixBase_rightCols_int.cpp\n/// Output: \\verbinclude MatrixBase_rightCols_int.out\n///\nEIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(column-major)\n///\n/// \\sa class Block, block(Index,Index,Index,Index)\n///\nEIGEN_DEVICE_FUNC\ninline ColsBlockXpr rightCols(Index n)\n{\n  return ColsBlockXpr(derived(), 0, cols() - n, rows(), n);\n}\n\n/// This is the const version of rightCols(Index).\nEIGEN_DEVICE_FUNC\ninline ConstColsBlockXpr rightCols(Index n) const\n{\n  return ConstColsBlockXpr(derived(), 0, cols() - n, rows(), n);\n}\n\n/// \\returns a block consisting of the right columns of *this.\n///\n/// \\tparam N the number of columns in the block as specified at compile-time\n/// \\param n the number of columns in the block as specified at run-time\n///\n/// The compile-time and run-time information should not contradict. In other words,\n/// \\a n should equal \\a N unless \\a N is \\a Dynamic.\n///\n/// Example: \\include MatrixBase_template_int_rightCols.cpp\n/// Output: \\verbinclude MatrixBase_template_int_rightCols.out\n///\nEIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(column-major)\n///\n/// \\sa class Block, block(Index,Index,Index,Index)\n///\ntemplate<int N>\nEIGEN_DEVICE_FUNC\ninline typename NColsBlockXpr<N>::Type rightCols(Index n = N)\n{\n  return typename NColsBlockXpr<N>::Type(derived(), 0, cols() - n, rows(), n);\n}\n\n/// This is the const version of rightCols<int>().\ntemplate<int N>\nEIGEN_DEVICE_FUNC\ninline typename ConstNColsBlockXpr<N>::Type rightCols(Index n = N) const\n{\n  return typename ConstNColsBlockXpr<N>::Type(derived(), 0, cols() - n, rows(), n);\n}\n\n\n\n/// \\returns a block consisting of a range of columns of *this.\n///\n/// \\param startCol the index of the first column in the block\n/// \\param numCols the number of columns in the block\n///\n/// Example: \\include DenseBase_middleCols_int.cpp\n/// Output: \\verbinclude DenseBase_middleCols_int.out\n///\nEIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(column-major)\n///\n/// \\sa class Block, block(Index,Index,Index,Index)\n///\nEIGEN_DEVICE_FUNC\ninline ColsBlockXpr middleCols(Index startCol, Index numCols)\n{\n  return ColsBlockXpr(derived(), 0, startCol, rows(), numCols);\n}\n\n/// This is the const version of middleCols(Index,Index).\nEIGEN_DEVICE_FUNC\ninline ConstColsBlockXpr middleCols(Index startCol, Index numCols) const\n{\n  return ConstColsBlockXpr(derived(), 0, startCol, rows(), numCols);\n}\n\n/// \\returns a block consisting of a range of columns of *this.\n///\n/// \\tparam N the number of columns in the block as specified at compile-time\n/// \\param startCol the index of the first column in the block\n/// \\param n the number of columns in the block as specified at run-time\n///\n/// The compile-time and run-time information should not contradict. In other words,\n/// \\a n should equal \\a N unless \\a N is \\a Dynamic.\n///\n/// Example: \\include DenseBase_template_int_middleCols.cpp\n/// Output: \\verbinclude DenseBase_template_int_middleCols.out\n///\nEIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(column-major)\n///\n/// \\sa class Block, block(Index,Index,Index,Index)\n///\ntemplate<int N>\nEIGEN_DEVICE_FUNC\ninline typename NColsBlockXpr<N>::Type middleCols(Index startCol, Index n = N)\n{\n  return typename NColsBlockXpr<N>::Type(derived(), 0, startCol, rows(), n);\n}\n\n/// This is the const version of middleCols<int>().\ntemplate<int N>\nEIGEN_DEVICE_FUNC\ninline typename ConstNColsBlockXpr<N>::Type middleCols(Index startCol, Index n = N) const\n{\n  return typename ConstNColsBlockXpr<N>::Type(derived(), 0, startCol, rows(), n);\n}\n\n\n\n/// \\returns a fixed-size expression of a block in *this.\n///\n/// The template parameters \\a NRows and \\a NCols are the number of\n/// rows and columns in the block.\n///\n/// \\param startRow the first row in the block\n/// \\param startCol the first column in the block\n///\n/// Example: \\include MatrixBase_block_int_int.cpp\n/// Output: \\verbinclude MatrixBase_block_int_int.out\n///\n/// \\note since block is a templated member, the keyword template has to be used\n/// if the matrix type is also a template parameter: \\code m.template block<3,3>(1,1); \\endcode\n///\nEIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL\n///\n/// \\sa class Block, block(Index,Index,Index,Index)\n///\ntemplate<int NRows, int NCols>\nEIGEN_DEVICE_FUNC\ninline typename FixedBlockXpr<NRows,NCols>::Type block(Index startRow, Index startCol)\n{\n  return typename FixedBlockXpr<NRows,NCols>::Type(derived(), startRow, startCol);\n}\n\n/// This is the const version of block<>(Index, Index). */\ntemplate<int NRows, int NCols>\nEIGEN_DEVICE_FUNC\ninline const typename ConstFixedBlockXpr<NRows,NCols>::Type block(Index startRow, Index startCol) const\n{\n  return typename ConstFixedBlockXpr<NRows,NCols>::Type(derived(), startRow, startCol);\n}\n\n/// \\returns an expression of a block in *this.\n///\n/// \\tparam NRows number of rows in block as specified at compile-time\n/// \\tparam NCols number of columns in block as specified at compile-time\n/// \\param  startRow  the first row in the block\n/// \\param  startCol  the first column in the block\n/// \\param  blockRows number of rows in block as specified at run-time\n/// \\param  blockCols number of columns in block as specified at run-time\n///\n/// This function is mainly useful for blocks where the number of rows is specified at compile-time\n/// and the number of columns is specified at run-time, or vice versa. The compile-time and run-time\n/// information should not contradict. In other words, \\a blockRows should equal \\a NRows unless\n/// \\a NRows is \\a Dynamic, and the same for the number of columns.\n///\n/// Example: \\include MatrixBase_template_int_int_block_int_int_int_int.cpp\n/// Output: \\verbinclude MatrixBase_template_int_int_block_int_int_int_int.cpp\n///\nEIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL\n///\n/// \\sa class Block, block(Index,Index,Index,Index)\n///\ntemplate<int NRows, int NCols>\ninline typename FixedBlockXpr<NRows,NCols>::Type block(Index startRow, Index startCol,\n                                                  Index blockRows, Index blockCols)\n{\n  return typename FixedBlockXpr<NRows,NCols>::Type(derived(), startRow, startCol, blockRows, blockCols);\n}\n\n/// This is the const version of block<>(Index, Index, Index, Index).\ntemplate<int NRows, int NCols>\ninline const typename ConstFixedBlockXpr<NRows,NCols>::Type block(Index startRow, Index startCol,\n                                                              Index blockRows, Index blockCols) const\n{\n  return typename ConstFixedBlockXpr<NRows,NCols>::Type(derived(), startRow, startCol, blockRows, blockCols);\n}\n\n/// \\returns an expression of the \\a i-th column of *this. Note that the numbering starts at 0.\n///\n/// Example: \\include MatrixBase_col.cpp\n/// Output: \\verbinclude MatrixBase_col.out\n///\nEIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(column-major)\n/**\n  * \\sa row(), class Block */\nEIGEN_DEVICE_FUNC\ninline ColXpr col(Index i)\n{\n  return ColXpr(derived(), i);\n}\n\n/// This is the const version of col().\nEIGEN_DEVICE_FUNC\ninline ConstColXpr col(Index i) const\n{\n  return ConstColXpr(derived(), i);\n}\n\n/// \\returns an expression of the \\a i-th row of *this. Note that the numbering starts at 0.\n///\n/// Example: \\include MatrixBase_row.cpp\n/// Output: \\verbinclude MatrixBase_row.out\n///\nEIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(row-major)\n/**\n  * \\sa col(), class Block */\nEIGEN_DEVICE_FUNC\ninline RowXpr row(Index i)\n{\n  return RowXpr(derived(), i);\n}\n\n/// This is the const version of row(). */\nEIGEN_DEVICE_FUNC\ninline ConstRowXpr row(Index i) const\n{\n  return ConstRowXpr(derived(), i);\n}\n\n/// \\returns a dynamic-size expression of a segment (i.e. a vector block) in *this.\n///\n/// \\only_for_vectors\n///\n/// \\param start the first coefficient in the segment\n/// \\param n the number of coefficients in the segment\n///\n/// Example: \\include MatrixBase_segment_int_int.cpp\n/// Output: \\verbinclude MatrixBase_segment_int_int.out\n///\n/// \\note Even though the returned expression has dynamic size, in the case\n/// when it is applied to a fixed-size vector, it inherits a fixed maximal size,\n/// which means that evaluating it does not cause a dynamic memory allocation.\n///\n/// \\sa class Block, segment(Index)\n///\nEIGEN_DEVICE_FUNC\ninline SegmentReturnType segment(Index start, Index n)\n{\n  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)\n  return SegmentReturnType(derived(), start, n);\n}\n\n\n/// This is the const version of segment(Index,Index).\nEIGEN_DEVICE_FUNC\ninline ConstSegmentReturnType segment(Index start, Index n) const\n{\n  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)\n  return ConstSegmentReturnType(derived(), start, n);\n}\n\n/// \\returns a dynamic-size expression of the first coefficients of *this.\n///\n/// \\only_for_vectors\n///\n/// \\param n the number of coefficients in the segment\n///\n/// Example: \\include MatrixBase_start_int.cpp\n/// Output: \\verbinclude MatrixBase_start_int.out\n///\n/// \\note Even though the returned expression has dynamic size, in the case\n/// when it is applied to a fixed-size vector, it inherits a fixed maximal size,\n/// which means that evaluating it does not cause a dynamic memory allocation.\n///\n/// \\sa class Block, block(Index,Index)\n///\nEIGEN_DEVICE_FUNC\ninline SegmentReturnType head(Index n)\n{\n  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)\n  return SegmentReturnType(derived(), 0, n);\n}\n\n/// This is the const version of head(Index).\nEIGEN_DEVICE_FUNC\ninline ConstSegmentReturnType head(Index n) const\n{\n  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)\n  return ConstSegmentReturnType(derived(), 0, n);\n}\n\n/// \\returns a dynamic-size expression of the last coefficients of *this.\n///\n/// \\only_for_vectors\n///\n/// \\param n the number of coefficients in the segment\n///\n/// Example: \\include MatrixBase_end_int.cpp\n/// Output: \\verbinclude MatrixBase_end_int.out\n///\n/// \\note Even though the returned expression has dynamic size, in the case\n/// when it is applied to a fixed-size vector, it inherits a fixed maximal size,\n/// which means that evaluating it does not cause a dynamic memory allocation.\n///\n/// \\sa class Block, block(Index,Index)\n///\nEIGEN_DEVICE_FUNC\ninline SegmentReturnType tail(Index n)\n{\n  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)\n  return SegmentReturnType(derived(), this->size() - n, n);\n}\n\n/// This is the const version of tail(Index).\nEIGEN_DEVICE_FUNC\ninline ConstSegmentReturnType tail(Index n) const\n{\n  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)\n  return ConstSegmentReturnType(derived(), this->size() - n, n);\n}\n\n/// \\returns a fixed-size expression of a segment (i.e. a vector block) in \\c *this\n///\n/// \\only_for_vectors\n///\n/// \\tparam N the number of coefficients in the segment as specified at compile-time\n/// \\param start the index of the first element in the segment\n/// \\param n the number of coefficients in the segment as specified at compile-time\n///\n/// The compile-time and run-time information should not contradict. In other words,\n/// \\a n should equal \\a N unless \\a N is \\a Dynamic.\n///\n/// Example: \\include MatrixBase_template_int_segment.cpp\n/// Output: \\verbinclude MatrixBase_template_int_segment.out\n///\n/// \\sa class Block\n///\ntemplate<int N>\nEIGEN_DEVICE_FUNC\ninline typename FixedSegmentReturnType<N>::Type segment(Index start, Index n = N)\n{\n  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)\n  return typename FixedSegmentReturnType<N>::Type(derived(), start, n);\n}\n\n/// This is the const version of segment<int>(Index).\ntemplate<int N>\nEIGEN_DEVICE_FUNC\ninline typename ConstFixedSegmentReturnType<N>::Type segment(Index start, Index n = N) const\n{\n  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)\n  return typename ConstFixedSegmentReturnType<N>::Type(derived(), start, n);\n}\n\n/// \\returns a fixed-size expression of the first coefficients of *this.\n///\n/// \\only_for_vectors\n///\n/// \\tparam N the number of coefficients in the segment as specified at compile-time\n/// \\param  n the number of coefficients in the segment as specified at run-time\n///\n/// The compile-time and run-time information should not contradict. In other words,\n/// \\a n should equal \\a N unless \\a N is \\a Dynamic.\n///\n/// Example: \\include MatrixBase_template_int_start.cpp\n/// Output: \\verbinclude MatrixBase_template_int_start.out\n///\n/// \\sa class Block\n///\ntemplate<int N>\nEIGEN_DEVICE_FUNC\ninline typename FixedSegmentReturnType<N>::Type head(Index n = N)\n{\n  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)\n  return typename FixedSegmentReturnType<N>::Type(derived(), 0, n);\n}\n\n/// This is the const version of head<int>().\ntemplate<int N>\nEIGEN_DEVICE_FUNC\ninline typename ConstFixedSegmentReturnType<N>::Type head(Index n = N) const\n{\n  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)\n  return typename ConstFixedSegmentReturnType<N>::Type(derived(), 0, n);\n}\n\n/// \\returns a fixed-size expression of the last coefficients of *this.\n///\n/// \\only_for_vectors\n///\n/// \\tparam N the number of coefficients in the segment as specified at compile-time\n/// \\param  n the number of coefficients in the segment as specified at run-time\n///\n/// The compile-time and run-time information should not contradict. In other words,\n/// \\a n should equal \\a N unless \\a N is \\a Dynamic.\n///\n/// Example: \\include MatrixBase_template_int_end.cpp\n/// Output: \\verbinclude MatrixBase_template_int_end.out\n///\n/// \\sa class Block\n///\ntemplate<int N>\nEIGEN_DEVICE_FUNC\ninline typename FixedSegmentReturnType<N>::Type tail(Index n = N)\n{\n  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)\n  return typename FixedSegmentReturnType<N>::Type(derived(), size() - n);\n}\n\n/// This is the const version of tail<int>.\ntemplate<int N>\nEIGEN_DEVICE_FUNC\ninline typename ConstFixedSegmentReturnType<N>::Type tail(Index n = N) const\n{\n  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)\n  return typename ConstFixedSegmentReturnType<N>::Type(derived(), size() - n);\n}\n"
  },
  {
    "path": "include/eigen3/Eigen/src/plugins/CommonCwiseBinaryOps.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2016 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n// This file is a base class plugin containing common coefficient wise functions.\n\n/** \\returns an expression of the difference of \\c *this and \\a other\n  *\n  * \\note If you want to substract a given scalar from all coefficients, see Cwise::operator-().\n  *\n  * \\sa class CwiseBinaryOp, operator-=()\n  */\nEIGEN_MAKE_CWISE_BINARY_OP(operator-,difference)\n\n/** \\returns an expression of the sum of \\c *this and \\a other\n  *\n  * \\note If you want to add a given scalar to all coefficients, see Cwise::operator+().\n  *\n  * \\sa class CwiseBinaryOp, operator+=()\n  */\nEIGEN_MAKE_CWISE_BINARY_OP(operator+,sum)\n\n/** \\returns an expression of a custom coefficient-wise operator \\a func of *this and \\a other\n  *\n  * The template parameter \\a CustomBinaryOp is the type of the functor\n  * of the custom operator (see class CwiseBinaryOp for an example)\n  *\n  * Here is an example illustrating the use of custom functors:\n  * \\include class_CwiseBinaryOp.cpp\n  * Output: \\verbinclude class_CwiseBinaryOp.out\n  *\n  * \\sa class CwiseBinaryOp, operator+(), operator-(), cwiseProduct()\n  */\ntemplate<typename CustomBinaryOp, typename OtherDerived>\nEIGEN_DEVICE_FUNC\nEIGEN_STRONG_INLINE const CwiseBinaryOp<CustomBinaryOp, const Derived, const OtherDerived>\nbinaryExpr(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other, const CustomBinaryOp& func = CustomBinaryOp()) const\n{\n  return CwiseBinaryOp<CustomBinaryOp, const Derived, const OtherDerived>(derived(), other.derived(), func);\n}\n\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\nEIGEN_MAKE_SCALAR_BINARY_OP(operator*,product)\n#else\n/** \\returns an expression of \\c *this scaled by the scalar factor \\a scalar\n  *\n  * \\tparam T is the scalar type of \\a scalar. It must be compatible with the scalar type of the given expression.\n  */\ntemplate<typename T>\nconst CwiseBinaryOp<internal::scalar_product_op<Scalar,T>,Derived,Constant<T> > operator*(const T& scalar) const;\n/** \\returns an expression of \\a expr scaled by the scalar factor \\a scalar\n  *\n  * \\tparam T is the scalar type of \\a scalar. It must be compatible with the scalar type of the given expression.\n  */\ntemplate<typename T> friend\nconst CwiseBinaryOp<internal::scalar_product_op<T,Scalar>,Constant<T>,Derived> operator*(const T& scalar, const StorageBaseType& expr);\n#endif\n\n\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\nEIGEN_MAKE_SCALAR_BINARY_OP_ONTHERIGHT(operator/,quotient)\n#else\n/** \\returns an expression of \\c *this divided by the scalar value \\a scalar\n  *\n  * \\tparam T is the scalar type of \\a scalar. It must be compatible with the scalar type of the given expression.\n  */\ntemplate<typename T>\nconst CwiseBinaryOp<internal::scalar_quotient_op<Scalar,T>,Derived,Constant<T> > operator/(const T& scalar) const;\n#endif\n\n/** \\returns an expression of the coefficient-wise boolean \\b and operator of \\c *this and \\a other\n  *\n  * \\warning this operator is for expression of bool only.\n  *\n  * Example: \\include Cwise_boolean_and.cpp\n  * Output: \\verbinclude Cwise_boolean_and.out\n  *\n  * \\sa operator||(), select()\n  */\ntemplate<typename OtherDerived>\nEIGEN_DEVICE_FUNC\ninline const CwiseBinaryOp<internal::scalar_boolean_and_op, const Derived, const OtherDerived>\noperator&&(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const\n{\n  EIGEN_STATIC_ASSERT((internal::is_same<bool,Scalar>::value && internal::is_same<bool,typename OtherDerived::Scalar>::value),\n                      THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_OF_BOOL);\n  return CwiseBinaryOp<internal::scalar_boolean_and_op, const Derived, const OtherDerived>(derived(),other.derived());\n}\n\n/** \\returns an expression of the coefficient-wise boolean \\b or operator of \\c *this and \\a other\n  *\n  * \\warning this operator is for expression of bool only.\n  *\n  * Example: \\include Cwise_boolean_or.cpp\n  * Output: \\verbinclude Cwise_boolean_or.out\n  *\n  * \\sa operator&&(), select()\n  */\ntemplate<typename OtherDerived>\nEIGEN_DEVICE_FUNC\ninline const CwiseBinaryOp<internal::scalar_boolean_or_op, const Derived, const OtherDerived>\noperator||(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const\n{\n  EIGEN_STATIC_ASSERT((internal::is_same<bool,Scalar>::value && internal::is_same<bool,typename OtherDerived::Scalar>::value),\n                      THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_OF_BOOL);\n  return CwiseBinaryOp<internal::scalar_boolean_or_op, const Derived, const OtherDerived>(derived(),other.derived());\n}\n"
  },
  {
    "path": "include/eigen3/Eigen/src/plugins/CommonCwiseUnaryOps.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n// This file is a base class plugin containing common coefficient wise functions.\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\n\n/** \\internal the return type of conjugate() */\ntypedef typename internal::conditional<NumTraits<Scalar>::IsComplex,\n                    const CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>, const Derived>,\n                    const Derived&\n                  >::type ConjugateReturnType;\n/** \\internal the return type of real() const */\ntypedef typename internal::conditional<NumTraits<Scalar>::IsComplex,\n                    const CwiseUnaryOp<internal::scalar_real_op<Scalar>, const Derived>,\n                    const Derived&\n                  >::type RealReturnType;\n/** \\internal the return type of real() */\ntypedef typename internal::conditional<NumTraits<Scalar>::IsComplex,\n                    CwiseUnaryView<internal::scalar_real_ref_op<Scalar>, Derived>,\n                    Derived&\n                  >::type NonConstRealReturnType;\n/** \\internal the return type of imag() const */\ntypedef CwiseUnaryOp<internal::scalar_imag_op<Scalar>, const Derived> ImagReturnType;\n/** \\internal the return type of imag() */\ntypedef CwiseUnaryView<internal::scalar_imag_ref_op<Scalar>, Derived> NonConstImagReturnType;\n\ntypedef CwiseUnaryOp<internal::scalar_opposite_op<Scalar>, const Derived> NegativeReturnType;\n\n#endif // not EIGEN_PARSED_BY_DOXYGEN\n\n/// \\returns an expression of the opposite of \\c *this\n///\nEIGEN_DOC_UNARY_ADDONS(operator-,opposite)\n///\nEIGEN_DEVICE_FUNC\ninline const NegativeReturnType\noperator-() const { return NegativeReturnType(derived()); }\n\n\ntemplate<class NewType> struct CastXpr { typedef typename internal::cast_return_type<Derived,const CwiseUnaryOp<internal::scalar_cast_op<Scalar, NewType>, const Derived> >::type Type; };\n\n/// \\returns an expression of \\c *this with the \\a Scalar type casted to\n/// \\a NewScalar.\n///\n/// The template parameter \\a NewScalar is the type we are casting the scalars to.\n///\nEIGEN_DOC_UNARY_ADDONS(cast,conversion function)\n///\n/// \\sa class CwiseUnaryOp\n///\ntemplate<typename NewType>\nEIGEN_DEVICE_FUNC\ntypename CastXpr<NewType>::Type\ncast() const\n{\n  return typename CastXpr<NewType>::Type(derived());\n}\n\n/// \\returns an expression of the complex conjugate of \\c *this.\n///\nEIGEN_DOC_UNARY_ADDONS(conjugate,complex conjugate)\n///\n/// \\sa <a href=\"group__CoeffwiseMathFunctions.html#cwisetable_conj\">Math functions</a>, MatrixBase::adjoint()\nEIGEN_DEVICE_FUNC\ninline ConjugateReturnType\nconjugate() const\n{\n  return ConjugateReturnType(derived());\n}\n\n/// \\returns a read-only expression of the real part of \\c *this.\n///\nEIGEN_DOC_UNARY_ADDONS(real,real part function)\n///\n/// \\sa imag()\nEIGEN_DEVICE_FUNC\ninline RealReturnType\nreal() const { return RealReturnType(derived()); }\n\n/// \\returns an read-only expression of the imaginary part of \\c *this.\n///\nEIGEN_DOC_UNARY_ADDONS(imag,imaginary part function)\n///\n/// \\sa real()\nEIGEN_DEVICE_FUNC\ninline const ImagReturnType\nimag() const { return ImagReturnType(derived()); }\n\n/// \\brief Apply a unary operator coefficient-wise\n/// \\param[in]  func  Functor implementing the unary operator\n/// \\tparam  CustomUnaryOp Type of \\a func\n/// \\returns An expression of a custom coefficient-wise unary operator \\a func of *this\n///\n/// The function \\c ptr_fun() from the C++ standard library can be used to make functors out of normal functions.\n///\n/// Example:\n/// \\include class_CwiseUnaryOp_ptrfun.cpp\n/// Output: \\verbinclude class_CwiseUnaryOp_ptrfun.out\n///\n/// Genuine functors allow for more possibilities, for instance it may contain a state.\n///\n/// Example:\n/// \\include class_CwiseUnaryOp.cpp\n/// Output: \\verbinclude class_CwiseUnaryOp.out\n///\nEIGEN_DOC_UNARY_ADDONS(unaryExpr,unary function)\n///\n/// \\sa unaryViewExpr, binaryExpr, class CwiseUnaryOp\n///\ntemplate<typename CustomUnaryOp>\nEIGEN_DEVICE_FUNC\ninline const CwiseUnaryOp<CustomUnaryOp, const Derived>\nunaryExpr(const CustomUnaryOp& func = CustomUnaryOp()) const\n{\n  return CwiseUnaryOp<CustomUnaryOp, const Derived>(derived(), func);\n}\n\n/// \\returns an expression of a custom coefficient-wise unary operator \\a func of *this\n///\n/// The template parameter \\a CustomUnaryOp is the type of the functor\n/// of the custom unary operator.\n///\n/// Example:\n/// \\include class_CwiseUnaryOp.cpp\n/// Output: \\verbinclude class_CwiseUnaryOp.out\n///\nEIGEN_DOC_UNARY_ADDONS(unaryViewExpr,unary function)\n///\n/// \\sa unaryExpr, binaryExpr class CwiseUnaryOp\n///\ntemplate<typename CustomViewOp>\nEIGEN_DEVICE_FUNC\ninline const CwiseUnaryView<CustomViewOp, const Derived>\nunaryViewExpr(const CustomViewOp& func = CustomViewOp()) const\n{\n  return CwiseUnaryView<CustomViewOp, const Derived>(derived(), func);\n}\n\n/// \\returns a non const expression of the real part of \\c *this.\n///\nEIGEN_DOC_UNARY_ADDONS(real,real part function)\n///\n/// \\sa imag()\nEIGEN_DEVICE_FUNC\ninline NonConstRealReturnType\nreal() { return NonConstRealReturnType(derived()); }\n\n/// \\returns a non const expression of the imaginary part of \\c *this.\n///\nEIGEN_DOC_UNARY_ADDONS(imag,imaginary part function)\n///\n/// \\sa real()\nEIGEN_DEVICE_FUNC\ninline NonConstImagReturnType\nimag() { return NonConstImagReturnType(derived()); }\n"
  },
  {
    "path": "include/eigen3/Eigen/src/plugins/MatrixCwiseBinaryOps.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n// This file is a base class plugin containing matrix specifics coefficient wise functions.\n\n/** \\returns an expression of the Schur product (coefficient wise product) of *this and \\a other\n  *\n  * Example: \\include MatrixBase_cwiseProduct.cpp\n  * Output: \\verbinclude MatrixBase_cwiseProduct.out\n  *\n  * \\sa class CwiseBinaryOp, cwiseAbs2\n  */\ntemplate<typename OtherDerived>\nEIGEN_DEVICE_FUNC\nEIGEN_STRONG_INLINE const EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,product)\ncwiseProduct(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const\n{\n  return EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,product)(derived(), other.derived());\n}\n\n/** \\returns an expression of the coefficient-wise == operator of *this and \\a other\n  *\n  * \\warning this performs an exact comparison, which is generally a bad idea with floating-point types.\n  * In order to check for equality between two vectors or matrices with floating-point coefficients, it is\n  * generally a far better idea to use a fuzzy comparison as provided by isApprox() and\n  * isMuchSmallerThan().\n  *\n  * Example: \\include MatrixBase_cwiseEqual.cpp\n  * Output: \\verbinclude MatrixBase_cwiseEqual.out\n  *\n  * \\sa cwiseNotEqual(), isApprox(), isMuchSmallerThan()\n  */\ntemplate<typename OtherDerived>\nEIGEN_DEVICE_FUNC\ninline const CwiseBinaryOp<std::equal_to<Scalar>, const Derived, const OtherDerived>\ncwiseEqual(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const\n{\n  return CwiseBinaryOp<std::equal_to<Scalar>, const Derived, const OtherDerived>(derived(), other.derived());\n}\n\n/** \\returns an expression of the coefficient-wise != operator of *this and \\a other\n  *\n  * \\warning this performs an exact comparison, which is generally a bad idea with floating-point types.\n  * In order to check for equality between two vectors or matrices with floating-point coefficients, it is\n  * generally a far better idea to use a fuzzy comparison as provided by isApprox() and\n  * isMuchSmallerThan().\n  *\n  * Example: \\include MatrixBase_cwiseNotEqual.cpp\n  * Output: \\verbinclude MatrixBase_cwiseNotEqual.out\n  *\n  * \\sa cwiseEqual(), isApprox(), isMuchSmallerThan()\n  */\ntemplate<typename OtherDerived>\nEIGEN_DEVICE_FUNC\ninline const CwiseBinaryOp<std::not_equal_to<Scalar>, const Derived, const OtherDerived>\ncwiseNotEqual(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const\n{\n  return CwiseBinaryOp<std::not_equal_to<Scalar>, const Derived, const OtherDerived>(derived(), other.derived());\n}\n\n/** \\returns an expression of the coefficient-wise min of *this and \\a other\n  *\n  * Example: \\include MatrixBase_cwiseMin.cpp\n  * Output: \\verbinclude MatrixBase_cwiseMin.out\n  *\n  * \\sa class CwiseBinaryOp, max()\n  */\ntemplate<typename OtherDerived>\nEIGEN_DEVICE_FUNC\nEIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_min_op<Scalar,Scalar>, const Derived, const OtherDerived>\ncwiseMin(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const\n{\n  return CwiseBinaryOp<internal::scalar_min_op<Scalar,Scalar>, const Derived, const OtherDerived>(derived(), other.derived());\n}\n\n/** \\returns an expression of the coefficient-wise min of *this and scalar \\a other\n  *\n  * \\sa class CwiseBinaryOp, min()\n  */\nEIGEN_DEVICE_FUNC\nEIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_min_op<Scalar,Scalar>, const Derived, const ConstantReturnType>\ncwiseMin(const Scalar &other) const\n{\n  return cwiseMin(Derived::Constant(rows(), cols(), other));\n}\n\n/** \\returns an expression of the coefficient-wise max of *this and \\a other\n  *\n  * Example: \\include MatrixBase_cwiseMax.cpp\n  * Output: \\verbinclude MatrixBase_cwiseMax.out\n  *\n  * \\sa class CwiseBinaryOp, min()\n  */\ntemplate<typename OtherDerived>\nEIGEN_DEVICE_FUNC\nEIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_max_op<Scalar,Scalar>, const Derived, const OtherDerived>\ncwiseMax(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const\n{\n  return CwiseBinaryOp<internal::scalar_max_op<Scalar,Scalar>, const Derived, const OtherDerived>(derived(), other.derived());\n}\n\n/** \\returns an expression of the coefficient-wise max of *this and scalar \\a other\n  *\n  * \\sa class CwiseBinaryOp, min()\n  */\nEIGEN_DEVICE_FUNC\nEIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_max_op<Scalar,Scalar>, const Derived, const ConstantReturnType>\ncwiseMax(const Scalar &other) const\n{\n  return cwiseMax(Derived::Constant(rows(), cols(), other));\n}\n\n\n/** \\returns an expression of the coefficient-wise quotient of *this and \\a other\n  *\n  * Example: \\include MatrixBase_cwiseQuotient.cpp\n  * Output: \\verbinclude MatrixBase_cwiseQuotient.out\n  *\n  * \\sa class CwiseBinaryOp, cwiseProduct(), cwiseInverse()\n  */\ntemplate<typename OtherDerived>\nEIGEN_DEVICE_FUNC\nEIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const Derived, const OtherDerived>\ncwiseQuotient(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const\n{\n  return CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const Derived, const OtherDerived>(derived(), other.derived());\n}\n\ntypedef CwiseBinaryOp<internal::scalar_cmp_op<Scalar,Scalar,internal::cmp_EQ>, const Derived, const ConstantReturnType> CwiseScalarEqualReturnType;\n\n/** \\returns an expression of the coefficient-wise == operator of \\c *this and a scalar \\a s\n  *\n  * \\warning this performs an exact comparison, which is generally a bad idea with floating-point types.\n  * In order to check for equality between two vectors or matrices with floating-point coefficients, it is\n  * generally a far better idea to use a fuzzy comparison as provided by isApprox() and\n  * isMuchSmallerThan().\n  *\n  * \\sa cwiseEqual(const MatrixBase<OtherDerived> &) const\n  */\nEIGEN_DEVICE_FUNC\ninline const CwiseScalarEqualReturnType\ncwiseEqual(const Scalar& s) const\n{\n  return CwiseScalarEqualReturnType(derived(), Derived::Constant(rows(), cols(), s), internal::scalar_cmp_op<Scalar,Scalar,internal::cmp_EQ>());\n}\n"
  },
  {
    "path": "include/eigen3/Eigen/src/plugins/MatrixCwiseUnaryOps.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n// This file is included into the body of the base classes supporting matrix specific coefficient-wise functions.\n// This include MatrixBase and SparseMatrixBase.\n\n\ntypedef CwiseUnaryOp<internal::scalar_abs_op<Scalar>, const Derived> CwiseAbsReturnType;\ntypedef CwiseUnaryOp<internal::scalar_abs2_op<Scalar>, const Derived> CwiseAbs2ReturnType;\ntypedef CwiseUnaryOp<internal::scalar_sqrt_op<Scalar>, const Derived> CwiseSqrtReturnType;\ntypedef CwiseUnaryOp<internal::scalar_sign_op<Scalar>, const Derived> CwiseSignReturnType;\ntypedef CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const Derived> CwiseInverseReturnType;\n\n/// \\returns an expression of the coefficient-wise absolute value of \\c *this\n///\n/// Example: \\include MatrixBase_cwiseAbs.cpp\n/// Output: \\verbinclude MatrixBase_cwiseAbs.out\n///\nEIGEN_DOC_UNARY_ADDONS(cwiseAbs,absolute value)\n///\n/// \\sa cwiseAbs2()\n///\nEIGEN_DEVICE_FUNC\nEIGEN_STRONG_INLINE const CwiseAbsReturnType\ncwiseAbs() const { return CwiseAbsReturnType(derived()); }\n\n/// \\returns an expression of the coefficient-wise squared absolute value of \\c *this\n///\n/// Example: \\include MatrixBase_cwiseAbs2.cpp\n/// Output: \\verbinclude MatrixBase_cwiseAbs2.out\n///\nEIGEN_DOC_UNARY_ADDONS(cwiseAbs2,squared absolute value)\n///\n/// \\sa cwiseAbs()\n///\nEIGEN_DEVICE_FUNC\nEIGEN_STRONG_INLINE const CwiseAbs2ReturnType\ncwiseAbs2() const { return CwiseAbs2ReturnType(derived()); }\n\n/// \\returns an expression of the coefficient-wise square root of *this.\n///\n/// Example: \\include MatrixBase_cwiseSqrt.cpp\n/// Output: \\verbinclude MatrixBase_cwiseSqrt.out\n///\nEIGEN_DOC_UNARY_ADDONS(cwiseSqrt,square-root)\n///\n/// \\sa cwisePow(), cwiseSquare()\n///\nEIGEN_DEVICE_FUNC\ninline const CwiseSqrtReturnType\ncwiseSqrt() const { return CwiseSqrtReturnType(derived()); }\n\n/// \\returns an expression of the coefficient-wise signum of *this.\n///\n/// Example: \\include MatrixBase_cwiseSign.cpp\n/// Output: \\verbinclude MatrixBase_cwiseSign.out\n///\nEIGEN_DOC_UNARY_ADDONS(cwiseSign,sign function)\n///\nEIGEN_DEVICE_FUNC\ninline const CwiseSignReturnType\ncwiseSign() const { return CwiseSignReturnType(derived()); }\n\n\n/// \\returns an expression of the coefficient-wise inverse of *this.\n///\n/// Example: \\include MatrixBase_cwiseInverse.cpp\n/// Output: \\verbinclude MatrixBase_cwiseInverse.out\n///\nEIGEN_DOC_UNARY_ADDONS(cwiseInverse,inverse)\n///\n/// \\sa cwiseProduct()\n///\nEIGEN_DEVICE_FUNC\ninline const CwiseInverseReturnType\ncwiseInverse() const { return CwiseInverseReturnType(derived()); }\n\n\n"
  },
  {
    "path": "include/eigen3/INSTALL",
    "content": "Installation instructions for Eigen\n***********************************\n\nExplanation before starting\n***************************\n\nEigen consists only of header files, hence there is nothing to compile\nbefore you can use it. Moreover, these header files do not depend on your\nplatform, they are the same for everybody.\n\nMethod 1. Installing without using CMake\n****************************************\n\nYou can use right away the headers in the Eigen/ subdirectory. In order\nto install, just copy this Eigen/ subdirectory to your favorite location.\nIf you also want the unsupported features, copy the unsupported/\nsubdirectory too.\n\nMethod 2. Installing using CMake\n********************************\n\nLet's call this directory 'source_dir' (where this INSTALL file is).\nBefore starting, create another directory which we will call 'build_dir'.\n\nDo:\n\n  cd build_dir\n  cmake source_dir\n  make install\n\nThe \"make install\" step may require administrator privileges.\n\nYou can adjust the installation destination (the \"prefix\")\nby passing the -DCMAKE_INSTALL_PREFIX=myprefix option to cmake, as is\nexplained in the message that cmake prints at the end.\n"
  },
  {
    "path": "include/eigen3/README.md",
    "content": "**Eigen is a C++ template library for linear algebra: matrices, vectors, numerical solvers, and related algorithms.**\n\nFor more information go to http://eigen.tuxfamily.org/.\n"
  },
  {
    "path": "include/eigen3/bench/BenchSparseUtil.h",
    "content": "\n#include <Eigen/Sparse>\n#include <bench/BenchTimer.h>\n#include <set>\n\nusing namespace std;\nusing namespace Eigen;\nusing namespace Eigen;\n\n#ifndef SIZE\n#define SIZE 1024\n#endif\n\n#ifndef DENSITY\n#define DENSITY 0.01\n#endif\n\n#ifndef SCALAR\n#define SCALAR double\n#endif\n\ntypedef SCALAR Scalar;\ntypedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;\ntypedef Matrix<Scalar,Dynamic,1> DenseVector;\ntypedef SparseMatrix<Scalar> EigenSparseMatrix;\n\nvoid fillMatrix(float density, int rows, int cols,  EigenSparseMatrix& dst)\n{\n  dst.reserve(double(rows)*cols*density);\n  for(int j = 0; j < cols; j++)\n  {\n    for(int i = 0; i < rows; i++)\n    {\n      Scalar v = (internal::random<float>(0,1) < density) ? internal::random<Scalar>() : 0;\n      if (v!=0)\n        dst.insert(i,j) = v;\n    }\n  }\n  dst.finalize();\n}\n\nvoid fillMatrix2(int nnzPerCol, int rows, int cols,  EigenSparseMatrix& dst)\n{\n//   std::cout << \"alloc \" << nnzPerCol*cols << \"\\n\";\n  dst.reserve(nnzPerCol*cols);\n  for(int j = 0; j < cols; j++)\n  {\n    std::set<int> aux;\n    for(int i = 0; i < nnzPerCol; i++)\n    {\n      int k = internal::random<int>(0,rows-1);\n      while (aux.find(k)!=aux.end())\n        k = internal::random<int>(0,rows-1);\n      aux.insert(k);\n\n      dst.insert(k,j) = internal::random<Scalar>();\n    }\n  }\n  dst.finalize();\n}\n\nvoid eiToDense(const EigenSparseMatrix& src, DenseMatrix& dst)\n{\n  dst.setZero();\n  for (int j=0; j<src.cols(); ++j)\n    for (EigenSparseMatrix::InnerIterator it(src.derived(), j); it; ++it)\n      dst(it.index(),j) = it.value();\n}\n\n#ifndef NOGMM\n#include \"gmm/gmm.h\"\ntypedef gmm::csc_matrix<Scalar> GmmSparse;\ntypedef gmm::col_matrix< gmm::wsvector<Scalar> > GmmDynSparse;\nvoid eiToGmm(const EigenSparseMatrix& src, GmmSparse& dst)\n{\n  GmmDynSparse tmp(src.rows(), src.cols());\n  for (int j=0; j<src.cols(); ++j)\n    for (EigenSparseMatrix::InnerIterator it(src.derived(), j); it; ++it)\n      tmp(it.index(),j) = it.value();\n  gmm::copy(tmp, dst);\n}\n#endif\n\n#ifndef NOMTL\n#include <boost/numeric/mtl/mtl.hpp>\ntypedef mtl::compressed2D<Scalar, mtl::matrix::parameters<mtl::tag::col_major> > MtlSparse;\ntypedef mtl::compressed2D<Scalar, mtl::matrix::parameters<mtl::tag::row_major> > MtlSparseRowMajor;\nvoid eiToMtl(const EigenSparseMatrix& src, MtlSparse& dst)\n{\n  mtl::matrix::inserter<MtlSparse> ins(dst);\n  for (int j=0; j<src.cols(); ++j)\n    for (EigenSparseMatrix::InnerIterator it(src.derived(), j); it; ++it)\n      ins[it.index()][j] = it.value();\n}\n#endif\n\n#ifdef CSPARSE\nextern \"C\" {\n#include \"cs.h\"\n}\nvoid eiToCSparse(const EigenSparseMatrix& src, cs* &dst)\n{\n  cs* aux = cs_spalloc (0, 0, 1, 1, 1);\n  for (int j=0; j<src.cols(); ++j)\n    for (EigenSparseMatrix::InnerIterator it(src.derived(), j); it; ++it)\n      if (!cs_entry(aux, it.index(), j, it.value()))\n      {\n        std::cout << \"cs_entry error\\n\";\n        exit(2);\n      }\n   dst = cs_compress(aux);\n//    cs_spfree(aux);\n}\n#endif // CSPARSE\n\n#ifndef NOUBLAS\n#include <boost/numeric/ublas/vector.hpp>\n#include <boost/numeric/ublas/matrix.hpp>\n#include <boost/numeric/ublas/io.hpp>\n#include <boost/numeric/ublas/triangular.hpp>\n#include <boost/numeric/ublas/vector_sparse.hpp>\n#include <boost/numeric/ublas/matrix_sparse.hpp>\n#include <boost/numeric/ublas/vector_of_vector.hpp>\n#include <boost/numeric/ublas/operation.hpp>\n\ntypedef boost::numeric::ublas::compressed_matrix<Scalar,boost::numeric::ublas::column_major> UBlasSparse;\n\nvoid eiToUblas(const EigenSparseMatrix& src, UBlasSparse& dst)\n{\n  dst.resize(src.rows(), src.cols(), false);\n  for (int j=0; j<src.cols(); ++j)\n    for (EigenSparseMatrix::InnerIterator it(src.derived(), j); it; ++it)\n      dst(it.index(),j) = it.value();\n}\n\ntemplate <typename EigenType, typename UblasType>\nvoid eiToUblasVec(const EigenType& src, UblasType& dst)\n{\n  dst.resize(src.size());\n  for (int j=0; j<src.size(); ++j)\n      dst[j] = src.coeff(j);\n}\n#endif\n\n#ifdef OSKI\nextern \"C\" {\n#include <oski/oski.h>\n}\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/BenchTimer.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_BENCH_TIMERR_H\n#define EIGEN_BENCH_TIMERR_H\n\n#if defined(_WIN32) || defined(__CYGWIN__)\n# ifndef NOMINMAX\n#   define NOMINMAX\n#   define EIGEN_BT_UNDEF_NOMINMAX\n# endif\n# ifndef WIN32_LEAN_AND_MEAN\n#   define WIN32_LEAN_AND_MEAN\n#   define EIGEN_BT_UNDEF_WIN32_LEAN_AND_MEAN\n# endif\n# include <windows.h>\n#elif defined(__APPLE__)\n#include <mach/mach_time.h>\n#else\n# include <unistd.h>\n#endif\n\nstatic void escape(void *p) {\n  asm volatile(\"\" : : \"g\"(p) : \"memory\");\n}\n\nstatic void clobber() {\n  asm volatile(\"\" : : : \"memory\");\n}\n\n#include <Eigen/Core>\n\nnamespace Eigen\n{\n\nenum {\n  CPU_TIMER = 0,\n  REAL_TIMER = 1\n};\n\n/** Elapsed time timer keeping the best try.\n  *\n  * On POSIX platforms we use clock_gettime with CLOCK_PROCESS_CPUTIME_ID.\n  * On Windows we use QueryPerformanceCounter\n  *\n  * Important: on linux, you must link with -lrt\n  */\nclass BenchTimer\n{\npublic:\n\n  BenchTimer()\n  {\n#if defined(_WIN32) || defined(__CYGWIN__)\n    LARGE_INTEGER freq;\n    QueryPerformanceFrequency(&freq);\n    m_frequency = (double)freq.QuadPart;\n#endif\n    reset();\n  }\n\n  ~BenchTimer() {}\n\n  inline void reset()\n  {\n    m_bests.fill(1e9);\n    m_worsts.fill(0);\n    m_totals.setZero();\n  }\n  inline void start()\n  {\n    m_starts[CPU_TIMER]  = getCpuTime();\n    m_starts[REAL_TIMER] = getRealTime();\n  }\n  inline void stop()\n  {\n    m_times[CPU_TIMER] = getCpuTime() - m_starts[CPU_TIMER];\n    m_times[REAL_TIMER] = getRealTime() - m_starts[REAL_TIMER];\n    #if EIGEN_VERSION_AT_LEAST(2,90,0)\n    m_bests = m_bests.cwiseMin(m_times);\n    m_worsts = m_worsts.cwiseMax(m_times);\n    #else\n    m_bests(0) = std::min(m_bests(0),m_times(0));\n    m_bests(1) = std::min(m_bests(1),m_times(1));\n    m_worsts(0) = std::max(m_worsts(0),m_times(0));\n    m_worsts(1) = std::max(m_worsts(1),m_times(1));\n    #endif\n    m_totals += m_times;\n  }\n\n  /** Return the elapsed time in seconds between the last start/stop pair\n    */\n  inline double value(int TIMER = CPU_TIMER) const\n  {\n    return m_times[TIMER];\n  }\n\n  /** Return the best elapsed time in seconds\n    */\n  inline double best(int TIMER = CPU_TIMER) const\n  {\n    return m_bests[TIMER];\n  }\n\n  /** Return the worst elapsed time in seconds\n    */\n  inline double worst(int TIMER = CPU_TIMER) const\n  {\n    return m_worsts[TIMER];\n  }\n\n  /** Return the total elapsed time in seconds.\n    */\n  inline double total(int TIMER = CPU_TIMER) const\n  {\n    return m_totals[TIMER];\n  }\n\n  inline double getCpuTime() const\n  {\n#ifdef _WIN32\n    LARGE_INTEGER query_ticks;\n    QueryPerformanceCounter(&query_ticks);\n    return query_ticks.QuadPart/m_frequency;\n#elif __APPLE__\n    return double(mach_absolute_time())*1e-9;\n#else\n    timespec ts;\n    clock_gettime(CLOCK_PROCESS_CPUTIME_ID, &ts);\n    return double(ts.tv_sec) + 1e-9 * double(ts.tv_nsec);\n#endif\n  }\n\n  inline double getRealTime() const\n  {\n#ifdef _WIN32\n    SYSTEMTIME st;\n    GetSystemTime(&st);\n    return (double)st.wSecond + 1.e-3 * (double)st.wMilliseconds;\n#elif __APPLE__\n    return double(mach_absolute_time())*1e-9;\n#else\n    timespec ts;\n    clock_gettime(CLOCK_REALTIME, &ts);\n    return double(ts.tv_sec) + 1e-9 * double(ts.tv_nsec);\n#endif\n  }\n\nprotected:\n#if defined(_WIN32) || defined(__CYGWIN__)\n  double m_frequency;\n#endif\n  Vector2d m_starts;\n  Vector2d m_times;\n  Vector2d m_bests;\n  Vector2d m_worsts;\n  Vector2d m_totals;\n\npublic:\n  EIGEN_MAKE_ALIGNED_OPERATOR_NEW\n};\n\n#define BENCH(TIMER,TRIES,REP,CODE) { \\\n    TIMER.reset(); \\\n    for(int uglyvarname1=0; uglyvarname1<TRIES; ++uglyvarname1){ \\\n      TIMER.start(); \\\n      for(int uglyvarname2=0; uglyvarname2<REP; ++uglyvarname2){ \\\n        CODE; \\\n      } \\\n      TIMER.stop(); \\\n      clobber(); \\\n    } \\\n  }\n\n}\n\n// clean #defined tokens\n#ifdef EIGEN_BT_UNDEF_NOMINMAX\n# undef EIGEN_BT_UNDEF_NOMINMAX\n# undef NOMINMAX\n#endif\n\n#ifdef EIGEN_BT_UNDEF_WIN32_LEAN_AND_MEAN\n# undef EIGEN_BT_UNDEF_WIN32_LEAN_AND_MEAN\n# undef WIN32_LEAN_AND_MEAN\n#endif\n\n#endif // EIGEN_BENCH_TIMERR_H\n"
  },
  {
    "path": "include/eigen3/bench/BenchUtil.h",
    "content": "\n#ifndef EIGEN_BENCH_UTIL_H\n#define EIGEN_BENCH_UTIL_H\n\n#include <Eigen/Core>\n#include \"BenchTimer.h\"\n\nusing namespace std;\nusing namespace Eigen;\n\n#include <boost/preprocessor/repetition/enum_params.hpp>\n#include <boost/preprocessor/repetition.hpp>\n#include <boost/preprocessor/seq.hpp>\n#include <boost/preprocessor/array.hpp>\n#include <boost/preprocessor/arithmetic.hpp>\n#include <boost/preprocessor/comparison.hpp>\n#include <boost/preprocessor/punctuation.hpp>\n#include <boost/preprocessor/punctuation/comma.hpp>\n#include <boost/preprocessor/stringize.hpp>\n\ntemplate<typename MatrixType> void initMatrix_random(MatrixType& mat) __attribute__((noinline));\ntemplate<typename MatrixType> void initMatrix_random(MatrixType& mat)\n{\n  mat.setRandom();// = MatrixType::random(mat.rows(), mat.cols());\n}\n\ntemplate<typename MatrixType> void initMatrix_identity(MatrixType& mat) __attribute__((noinline));\ntemplate<typename MatrixType> void initMatrix_identity(MatrixType& mat)\n{\n  mat.setIdentity();\n}\n\n#ifndef __INTEL_COMPILER\n#define DISABLE_SSE_EXCEPTIONS()  { \\\n  int aux; \\\n  asm( \\\n  \"stmxcsr   %[aux]           \\n\\t\" \\\n  \"orl       $32832, %[aux]   \\n\\t\" \\\n  \"ldmxcsr   %[aux]           \\n\\t\" \\\n  : : [aux] \"m\" (aux)); \\\n}\n#else\n#define DISABLE_SSE_EXCEPTIONS()  \n#endif\n\n#ifdef BENCH_GMM\n#include <gmm/gmm.h>\ntemplate <typename EigenMatrixType, typename GmmMatrixType>\nvoid eiToGmm(const EigenMatrixType& src, GmmMatrixType& dst)\n{\n  dst.resize(src.rows(),src.cols());\n  for (int j=0; j<src.cols(); ++j)\n    for (int i=0; i<src.rows(); ++i)\n      dst(i,j) = src.coeff(i,j);\n}\n#endif\n\n\n#ifdef BENCH_GSL\n#include <gsl/gsl_matrix.h>\n#include <gsl/gsl_linalg.h>\n#include <gsl/gsl_eigen.h>\ntemplate <typename EigenMatrixType>\nvoid eiToGsl(const EigenMatrixType& src, gsl_matrix** dst)\n{\n  for (int j=0; j<src.cols(); ++j)\n    for (int i=0; i<src.rows(); ++i)\n      gsl_matrix_set(*dst, i, j, src.coeff(i,j));\n}\n#endif\n\n#ifdef BENCH_UBLAS\n#include <boost/numeric/ublas/matrix.hpp>\n#include <boost/numeric/ublas/vector.hpp>\ntemplate <typename EigenMatrixType, typename UblasMatrixType>\nvoid eiToUblas(const EigenMatrixType& src, UblasMatrixType& dst)\n{\n  dst.resize(src.rows(),src.cols());\n  for (int j=0; j<src.cols(); ++j)\n    for (int i=0; i<src.rows(); ++i)\n      dst(i,j) = src.coeff(i,j);\n}\ntemplate <typename EigenType, typename UblasType>\nvoid eiToUblasVec(const EigenType& src, UblasType& dst)\n{\n  dst.resize(src.size());\n  for (int j=0; j<src.size(); ++j)\n      dst[j] = src.coeff(j);\n}\n#endif\n\n#endif // EIGEN_BENCH_UTIL_H\n"
  },
  {
    "path": "include/eigen3/bench/README.txt",
    "content": "\nThis folder contains a couple of benchmark utities and Eigen benchmarks.\n\n****************************\n* bench_multi_compilers.sh *\n****************************\n\nThis script allows to run a benchmark on a set of different compilers/compiler options.\nIt takes two arguments:\n - a file defining the list of the compilers with their options\n - the .cpp file of the benchmark\n\nExamples:\n\n$ ./bench_multi_compilers.sh basicbench.cxxlist basicbenchmark.cpp\n\n    g++-4.1 -O3 -DNDEBUG -finline-limit=10000\n    3d-3x3   /   4d-4x4   /   Xd-4x4   /   Xd-20x20   /\n    0.271102   0.131416   0.422322   0.198633\n    0.201658   0.102436   0.397566   0.207282\n\n    g++-4.2 -O3 -DNDEBUG -finline-limit=10000\n    3d-3x3   /   4d-4x4   /   Xd-4x4   /   Xd-20x20   /\n    0.107805   0.0890579   0.30265   0.161843\n    0.127157   0.0712581   0.278341   0.191029\n\n    g++-4.3 -O3 -DNDEBUG -finline-limit=10000\n    3d-3x3   /   4d-4x4   /   Xd-4x4   /   Xd-20x20   /\n    0.134318   0.105291   0.3704   0.180966\n    0.137703   0.0732472   0.31225   0.202204\n\n    icpc -fast -DNDEBUG -fno-exceptions -no-inline-max-size\n    3d-3x3   /   4d-4x4   /   Xd-4x4   /   Xd-20x20   /\n    0.226145   0.0941319   0.371873   0.159433\n    0.109302   0.0837538   0.328102   0.173891\n\n\n$ ./bench_multi_compilers.sh ompbench.cxxlist ompbenchmark.cpp\n\n    g++-4.2 -O3 -DNDEBUG -finline-limit=10000 -fopenmp\n    double, fixed-size 4x4: 0.00165105s  0.0778739s\n    double, 32x32: 0.0654769s 0.075289s  => x0.869674 (2)\n    double, 128x128: 0.054148s 0.0419669s  => x1.29025 (2)\n    double, 512x512: 0.913799s 0.428533s  => x2.13239 (2)\n    double, 1024x1024: 14.5972s 9.3542s  => x1.5605 (2)\n\n    icpc -fast -DNDEBUG -fno-exceptions -no-inline-max-size -openmp\n    double, fixed-size 4x4: 0.000589848s  0.019949s\n    double, 32x32: 0.0682781s 0.0449722s  => x1.51823 (2)\n    double, 128x128: 0.0547509s 0.0435519s  => x1.25714 (2)\n    double, 512x512: 0.829436s 0.424438s  => x1.9542 (2)\n    double, 1024x1024: 14.5243s 10.7735s  => x1.34815 (2)\n\n\n\n"
  },
  {
    "path": "include/eigen3/bench/analyze-blocking-sizes.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Benoit Jacob <benoitjacob@google.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include <iostream>\n#include <cstdint>\n#include <cstdlib>\n#include <vector>\n#include <algorithm>\n#include <fstream>\n#include <string>\n#include <cmath>\n#include <cassert>\n#include <cstring>\n#include <memory>\n\n#include <Eigen/Core>\n\nusing namespace std;\n\nconst int default_precision = 4;\n\n// see --only-cubic-sizes\nbool only_cubic_sizes = false;\n\n// see --dump-tables\nbool dump_tables = false;\n\nuint8_t log2_pot(size_t x) {\n  size_t l = 0;\n  while (x >>= 1) l++;\n  return l;\n}\n\nuint16_t compact_size_triple(size_t k, size_t m, size_t n)\n{\n  return (log2_pot(k) << 8) | (log2_pot(m) << 4) | log2_pot(n);\n}\n\n// just a helper to store a triple of K,M,N sizes for matrix product\nstruct size_triple_t\n{\n  uint16_t k, m, n;\n  size_triple_t() : k(0), m(0), n(0) {}\n  size_triple_t(size_t _k, size_t _m, size_t _n) : k(_k), m(_m), n(_n) {}\n  size_triple_t(const size_triple_t& o) : k(o.k), m(o.m), n(o.n) {}\n  size_triple_t(uint16_t compact)\n  {\n    k = 1 << ((compact & 0xf00) >> 8);\n    m = 1 << ((compact & 0x0f0) >> 4);\n    n = 1 << ((compact & 0x00f) >> 0);\n  }\n  bool is_cubic() const { return k == m && m == n; }\n};\n\nostream& operator<<(ostream& s, const size_triple_t& t)\n{\n  return s << \"(\" << t.k << \", \" << t.m << \", \" << t.n << \")\";\n}\n\nstruct inputfile_entry_t\n{\n  uint16_t product_size;\n  uint16_t pot_block_size;\n  size_triple_t nonpot_block_size;\n  float gflops;\n};\n\nstruct inputfile_t\n{\n  enum class type_t {\n    unknown,\n    all_pot_sizes,\n    default_sizes\n  };\n\n  string filename;\n  vector<inputfile_entry_t> entries;\n  type_t type;\n\n  inputfile_t(const string& fname)\n    : filename(fname)\n    , type(type_t::unknown)\n  {\n    ifstream stream(filename);\n    if (!stream.is_open()) {\n      cerr << \"couldn't open input file: \" << filename << endl;\n      exit(1);\n    }\n    string line;\n    while (getline(stream, line)) {\n      if (line.empty()) continue;\n      if (line.find(\"BEGIN MEASUREMENTS ALL POT SIZES\") == 0) {\n        if (type != type_t::unknown) {\n          cerr << \"Input file \" << filename << \" contains redundant BEGIN MEASUREMENTS lines\";\n          exit(1);\n        }\n        type = type_t::all_pot_sizes;\n        continue;\n      }\n      if (line.find(\"BEGIN MEASUREMENTS DEFAULT SIZES\") == 0) {\n        if (type != type_t::unknown) {\n          cerr << \"Input file \" << filename << \" contains redundant BEGIN MEASUREMENTS lines\";\n          exit(1);\n        }\n        type = type_t::default_sizes;\n        continue;\n      }\n      \n\n      if (type == type_t::unknown) {\n        continue;\n      }\n      switch(type) {\n        case type_t::all_pot_sizes: {\n          unsigned int product_size, block_size;\n          float gflops;\n          int sscanf_result =\n            sscanf(line.c_str(), \"%x %x %f\",\n                   &product_size,\n                   &block_size,\n                   &gflops);\n          if (3 != sscanf_result ||\n              !product_size ||\n              product_size > 0xfff ||\n              !block_size ||\n              block_size > 0xfff ||\n              !isfinite(gflops))\n          {\n            cerr << \"ill-formed input file: \" << filename << endl;\n            cerr << \"offending line:\" << endl << line << endl;\n            exit(1);\n          }\n          if (only_cubic_sizes && !size_triple_t(product_size).is_cubic()) {\n            continue;\n          }\n          inputfile_entry_t entry;\n          entry.product_size = uint16_t(product_size);\n          entry.pot_block_size = uint16_t(block_size);\n          entry.gflops = gflops;\n          entries.push_back(entry);\n          break;\n        }\n        case type_t::default_sizes: {\n          unsigned int product_size;\n          float gflops;\n          int bk, bm, bn;\n          int sscanf_result =\n            sscanf(line.c_str(), \"%x default(%d, %d, %d) %f\",\n                   &product_size,\n                   &bk, &bm, &bn,\n                   &gflops);\n          if (5 != sscanf_result ||\n              !product_size ||\n              product_size > 0xfff ||\n              !isfinite(gflops))\n          {\n            cerr << \"ill-formed input file: \" << filename << endl;\n            cerr << \"offending line:\" << endl << line << endl;\n            exit(1);\n          }\n          if (only_cubic_sizes && !size_triple_t(product_size).is_cubic()) {\n            continue;\n          }\n          inputfile_entry_t entry;\n          entry.product_size = uint16_t(product_size);\n          entry.pot_block_size = 0;\n          entry.nonpot_block_size = size_triple_t(bk, bm, bn);\n          entry.gflops = gflops;\n          entries.push_back(entry);\n          break;\n        }\n        \n        default:\n          break;\n      }\n    }\n    stream.close();\n    if (type == type_t::unknown) {\n      cerr << \"Unrecognized input file \" << filename << endl;\n      exit(1);\n    }\n    if (entries.empty()) {\n      cerr << \"didn't find any measurements in input file: \" << filename << endl;\n      exit(1);\n    }\n  }\n};\n\nstruct preprocessed_inputfile_entry_t\n{\n  uint16_t product_size;\n  uint16_t block_size;\n\n  float efficiency;\n};\n\nbool lower_efficiency(const preprocessed_inputfile_entry_t& e1, const preprocessed_inputfile_entry_t& e2)\n{\n  return e1.efficiency < e2.efficiency;\n}\n\nstruct preprocessed_inputfile_t\n{\n  string filename;\n  vector<preprocessed_inputfile_entry_t> entries;\n\n  preprocessed_inputfile_t(const inputfile_t& inputfile)\n    : filename(inputfile.filename)\n  {\n    if (inputfile.type != inputfile_t::type_t::all_pot_sizes) {\n      abort();\n    }\n    auto it = inputfile.entries.begin();\n    auto it_first_with_given_product_size = it;\n    while (it != inputfile.entries.end()) {\n      ++it;\n      if (it == inputfile.entries.end() ||\n        it->product_size != it_first_with_given_product_size->product_size)\n      {\n        import_input_file_range_one_product_size(it_first_with_given_product_size, it);\n        it_first_with_given_product_size = it;\n      }\n    }\n  }\n\nprivate:\n  void import_input_file_range_one_product_size(\n    const vector<inputfile_entry_t>::const_iterator& begin,\n    const vector<inputfile_entry_t>::const_iterator& end)\n  {\n    uint16_t product_size = begin->product_size;\n    float max_gflops = 0.0f;\n    for (auto it = begin; it != end; ++it) {\n      if (it->product_size != product_size) {\n        cerr << \"Unexpected ordering of entries in \" << filename << endl;\n        cerr << \"(Expected all entries for product size \" << hex << product_size << dec << \" to be grouped)\" << endl;\n        exit(1);\n      }\n      max_gflops = max(max_gflops, it->gflops);\n    }\n    for (auto it = begin; it != end; ++it) {\n      preprocessed_inputfile_entry_t entry;\n      entry.product_size = it->product_size;\n      entry.block_size = it->pot_block_size;\n      entry.efficiency = it->gflops / max_gflops;\n      entries.push_back(entry);\n    }\n  }\n};\n\nvoid check_all_files_in_same_exact_order(\n       const vector<preprocessed_inputfile_t>& preprocessed_inputfiles)\n{\n  if (preprocessed_inputfiles.empty()) {\n    return;\n  }\n\n  const preprocessed_inputfile_t& first_file = preprocessed_inputfiles[0];\n  const size_t num_entries = first_file.entries.size();\n\n  for (size_t i = 0; i < preprocessed_inputfiles.size(); i++) {\n    if (preprocessed_inputfiles[i].entries.size() != num_entries) {\n      cerr << \"these files have different number of entries: \"\n           << preprocessed_inputfiles[i].filename\n           << \" and \"\n           << first_file.filename\n           << endl;\n      exit(1);\n    }\n  }\n\n  for (size_t entry_index = 0; entry_index < num_entries; entry_index++) {\n    const uint16_t entry_product_size = first_file.entries[entry_index].product_size;\n    const uint16_t entry_block_size = first_file.entries[entry_index].block_size;\n    for (size_t file_index = 0; file_index < preprocessed_inputfiles.size(); file_index++) {\n      const preprocessed_inputfile_t& cur_file = preprocessed_inputfiles[file_index];\n      if (cur_file.entries[entry_index].product_size != entry_product_size ||\n          cur_file.entries[entry_index].block_size != entry_block_size)\n      {\n        cerr << \"entries not in same order between these files: \"\n             << first_file.filename\n             << \" and \"\n             << cur_file.filename\n             << endl;\n        exit(1);\n      }\n    }\n  }\n}\n\nfloat efficiency_of_subset(\n        const vector<preprocessed_inputfile_t>& preprocessed_inputfiles,\n        const vector<size_t>& subset)\n{\n  if (subset.size() <= 1) {\n    return 1.0f;\n  }\n  const preprocessed_inputfile_t& first_file = preprocessed_inputfiles[subset[0]];\n  const size_t num_entries = first_file.entries.size();\n  float efficiency = 1.0f;\n  size_t entry_index = 0;\n  size_t first_entry_index_with_this_product_size = 0;\n  uint16_t product_size = first_file.entries[0].product_size;\n  while (entry_index < num_entries) {\n    ++entry_index;\n    if (entry_index == num_entries ||\n        first_file.entries[entry_index].product_size != product_size)\n    {\n      float efficiency_this_product_size = 0.0f;\n      for (size_t e = first_entry_index_with_this_product_size; e < entry_index; e++) {\n        float efficiency_this_entry = 1.0f;\n        for (auto i = subset.begin(); i != subset.end(); ++i) {\n          efficiency_this_entry = min(efficiency_this_entry, preprocessed_inputfiles[*i].entries[e].efficiency);\n        }\n        efficiency_this_product_size = max(efficiency_this_product_size, efficiency_this_entry);\n      }\n      efficiency = min(efficiency, efficiency_this_product_size);\n      if (entry_index < num_entries) {\n        first_entry_index_with_this_product_size = entry_index;\n        product_size = first_file.entries[entry_index].product_size;\n      }\n    }\n  }\n\n  return efficiency;\n}\n\nvoid dump_table_for_subset(\n        const vector<preprocessed_inputfile_t>& preprocessed_inputfiles,\n        const vector<size_t>& subset)\n{\n  const preprocessed_inputfile_t& first_file = preprocessed_inputfiles[subset[0]];\n  const size_t num_entries = first_file.entries.size();\n  size_t entry_index = 0;\n  size_t first_entry_index_with_this_product_size = 0;\n  uint16_t product_size = first_file.entries[0].product_size;\n  size_t i = 0;\n  size_triple_t min_product_size(first_file.entries.front().product_size);\n  size_triple_t max_product_size(first_file.entries.back().product_size);\n  if (!min_product_size.is_cubic() || !max_product_size.is_cubic()) {\n    abort();\n  }\n  if (only_cubic_sizes) {\n    cerr << \"Can't generate tables with --only-cubic-sizes.\" << endl;\n    abort();\n  }\n  cout << \"struct LookupTable {\" << endl;\n  cout << \"  static const size_t BaseSize = \" << min_product_size.k << \";\" << endl;\n  const size_t NumSizes = log2_pot(max_product_size.k / min_product_size.k) + 1;\n  const size_t TableSize = NumSizes * NumSizes * NumSizes;\n  cout << \"  static const size_t NumSizes = \" << NumSizes << \";\" << endl;\n  cout << \"  static const unsigned short* Data() {\" << endl;\n  cout << \"    static const unsigned short data[\" << TableSize << \"] = {\";\n  while (entry_index < num_entries) {\n    ++entry_index;\n    if (entry_index == num_entries ||\n        first_file.entries[entry_index].product_size != product_size)\n    {\n      float best_efficiency_this_product_size = 0.0f;\n      uint16_t best_block_size_this_product_size = 0;\n      for (size_t e = first_entry_index_with_this_product_size; e < entry_index; e++) {\n        float efficiency_this_entry = 1.0f;\n        for (auto i = subset.begin(); i != subset.end(); ++i) {\n          efficiency_this_entry = min(efficiency_this_entry, preprocessed_inputfiles[*i].entries[e].efficiency);\n        }\n        if (efficiency_this_entry > best_efficiency_this_product_size) {\n          best_efficiency_this_product_size = efficiency_this_entry;\n          best_block_size_this_product_size = first_file.entries[e].block_size;\n        }\n      }\n      if ((i++) % NumSizes) {\n        cout << \" \";\n      } else {\n        cout << endl << \"      \";\n      }\n      cout << \"0x\" << hex << best_block_size_this_product_size << dec;\n      if (entry_index < num_entries) {\n        cout << \",\";\n        first_entry_index_with_this_product_size = entry_index;\n        product_size = first_file.entries[entry_index].product_size;\n      }\n    }\n  }\n  if (i != TableSize) {\n    cerr << endl << \"Wrote \" << i << \" table entries, expected \" << TableSize << endl;\n    abort();\n  }\n  cout << endl << \"    };\" << endl;\n  cout << \"    return data;\" << endl;\n  cout << \"  }\" << endl;\n  cout << \"};\" << endl;\n}\n\nfloat efficiency_of_partition(\n        const vector<preprocessed_inputfile_t>& preprocessed_inputfiles,\n        const vector<vector<size_t>>& partition)\n{\n  float efficiency = 1.0f;\n  for (auto s = partition.begin(); s != partition.end(); ++s) {\n    efficiency = min(efficiency, efficiency_of_subset(preprocessed_inputfiles, *s));\n  }\n  return efficiency;\n}\n\nvoid make_first_subset(size_t subset_size, vector<size_t>& out_subset, size_t set_size)\n{\n  assert(subset_size >= 1 && subset_size <= set_size);\n  out_subset.resize(subset_size);\n  for (size_t i = 0; i < subset_size; i++) {\n    out_subset[i] = i;\n  }\n}\n\nbool is_last_subset(const vector<size_t>& subset, size_t set_size)\n{\n  return subset[0] == set_size - subset.size();\n}\n\nvoid next_subset(vector<size_t>& inout_subset, size_t set_size)\n{\n  if (is_last_subset(inout_subset, set_size)) {\n    cerr << \"iterating past the last subset\" << endl;\n    abort();\n  }\n  size_t i = 1;\n  while (inout_subset[inout_subset.size() - i] == set_size - i) {\n    i++;\n    assert(i <= inout_subset.size());\n  }\n  size_t first_index_to_change = inout_subset.size() - i;\n  inout_subset[first_index_to_change]++;\n  size_t p = inout_subset[first_index_to_change];\n  for (size_t j = first_index_to_change + 1; j < inout_subset.size(); j++) {\n    inout_subset[j] = ++p;\n  }\n}\n\nconst size_t number_of_subsets_limit = 100;\nconst size_t always_search_subsets_of_size_at_least = 2;\n\nbool is_number_of_subsets_feasible(size_t n, size_t p)\n{ \n  assert(n>0 && p>0 && p<=n);\n  uint64_t numerator = 1, denominator = 1;\n  for (size_t i = 0; i < p; i++) {\n    numerator *= n - i;\n    denominator *= i + 1;\n    if (numerator > denominator * number_of_subsets_limit) {\n      return false;\n    }\n  }\n  return true;\n}\n\nsize_t max_feasible_subset_size(size_t n)\n{\n  assert(n > 0);\n  const size_t minresult = min<size_t>(n-1, always_search_subsets_of_size_at_least);\n  for (size_t p = 1; p <= n - 1; p++) {\n    if (!is_number_of_subsets_feasible(n, p+1)) {\n      return max(p, minresult);\n    }\n  }\n  return n - 1;\n}\n\nvoid find_subset_with_efficiency_higher_than(\n       const vector<preprocessed_inputfile_t>& preprocessed_inputfiles,\n       float required_efficiency_to_beat,\n       vector<size_t>& inout_remainder,\n       vector<size_t>& out_subset)\n{\n  out_subset.resize(0);\n\n  if (required_efficiency_to_beat >= 1.0f) {\n    cerr << \"can't beat efficiency 1.\" << endl;\n    abort();\n  }\n\n  while (!inout_remainder.empty()) {\n\n    vector<size_t> candidate_indices(inout_remainder.size());\n    for (size_t i = 0; i < candidate_indices.size(); i++) {\n      candidate_indices[i] = i;\n    }\n\n    size_t candidate_indices_subset_size = max_feasible_subset_size(candidate_indices.size());\n    while (candidate_indices_subset_size >= 1) {\n      vector<size_t> candidate_indices_subset;\n      make_first_subset(candidate_indices_subset_size,\n                        candidate_indices_subset,\n                        candidate_indices.size());\n\n      vector<size_t> best_candidate_indices_subset;\n      float best_efficiency = 0.0f;\n      vector<size_t> trial_subset = out_subset;\n      trial_subset.resize(out_subset.size() + candidate_indices_subset_size);\n      while (true)\n      {\n        for (size_t i = 0; i < candidate_indices_subset_size; i++) {\n          trial_subset[out_subset.size() + i] = inout_remainder[candidate_indices_subset[i]];\n        }\n        \n        float trial_efficiency = efficiency_of_subset(preprocessed_inputfiles, trial_subset);\n        if (trial_efficiency > best_efficiency) {\n          best_efficiency = trial_efficiency;\n          best_candidate_indices_subset = candidate_indices_subset;\n        }\n        if (is_last_subset(candidate_indices_subset, candidate_indices.size())) {\n          break;\n        }\n        next_subset(candidate_indices_subset, candidate_indices.size());\n      }\n       \n      if (best_efficiency > required_efficiency_to_beat) {\n        for (size_t i = 0; i < best_candidate_indices_subset.size(); i++) {\n          candidate_indices[i] = candidate_indices[best_candidate_indices_subset[i]];\n        }\n        candidate_indices.resize(best_candidate_indices_subset.size());\n      }\n      candidate_indices_subset_size--;\n    }\n      \n    size_t candidate_index = candidate_indices[0];\n    auto candidate_iterator = inout_remainder.begin() + candidate_index;\n    vector<size_t> trial_subset = out_subset;\n\n    trial_subset.push_back(*candidate_iterator);\n    float trial_efficiency = efficiency_of_subset(preprocessed_inputfiles, trial_subset);\n    if (trial_efficiency > required_efficiency_to_beat) {\n      out_subset.push_back(*candidate_iterator);\n      inout_remainder.erase(candidate_iterator);\n    } else {\n      break;\n    }\n  }\n}\n\nvoid find_partition_with_efficiency_higher_than(\n       const vector<preprocessed_inputfile_t>& preprocessed_inputfiles,\n       float required_efficiency_to_beat,\n       vector<vector<size_t>>& out_partition)\n{\n  out_partition.resize(0);\n\n  vector<size_t> remainder;\n  for (size_t i = 0; i < preprocessed_inputfiles.size(); i++) {\n    remainder.push_back(i);\n  }\n\n  while (!remainder.empty()) {\n    vector<size_t> new_subset;\n    find_subset_with_efficiency_higher_than(\n      preprocessed_inputfiles,\n      required_efficiency_to_beat,\n      remainder,\n      new_subset);\n    out_partition.push_back(new_subset);\n  }\n}\n\nvoid print_partition(\n       const vector<preprocessed_inputfile_t>& preprocessed_inputfiles,\n       const vector<vector<size_t>>& partition)\n{\n  float efficiency = efficiency_of_partition(preprocessed_inputfiles, partition);\n  cout << \"Partition into \" << partition.size() << \" subsets for \" << efficiency * 100.0f << \"% efficiency\"  << endl;\n  for (auto subset = partition.begin(); subset != partition.end(); ++subset) {\n    cout << \"  Subset \" << (subset - partition.begin())\n         << \", efficiency \" << efficiency_of_subset(preprocessed_inputfiles, *subset) * 100.0f << \"%:\"\n         << endl;\n    for (auto file = subset->begin(); file != subset->end(); ++file) {\n      cout << \"    \" << preprocessed_inputfiles[*file].filename << endl;\n    }\n    if (dump_tables) {\n      cout << \"  Table:\" << endl;\n      dump_table_for_subset(preprocessed_inputfiles, *subset);\n    }\n  }\n  cout << endl;\n}\n\nstruct action_t\n{\n  virtual const char* invokation_name() const { abort(); return nullptr; }\n  virtual void run(const vector<string>&) const { abort(); }\n  virtual ~action_t() {}\n};\n\nstruct partition_action_t : action_t\n{\n  virtual const char* invokation_name() const override { return \"partition\"; }\n  virtual void run(const vector<string>& input_filenames) const override\n  {\n    vector<preprocessed_inputfile_t> preprocessed_inputfiles;\n\n    if (input_filenames.empty()) {\n      cerr << \"The \" << invokation_name() << \" action needs a list of input files.\" << endl;\n      exit(1);\n    }\n\n    for (auto it = input_filenames.begin(); it != input_filenames.end(); ++it) {\n      inputfile_t inputfile(*it);\n      switch (inputfile.type) {\n        case inputfile_t::type_t::all_pot_sizes:\n          preprocessed_inputfiles.emplace_back(inputfile);\n          break;\n        case inputfile_t::type_t::default_sizes:\n          cerr << \"The \" << invokation_name() << \" action only uses measurements for all pot sizes, and \"\n               << \"has no use for \" << *it << \" which contains measurements for default sizes.\" << endl;\n          exit(1);\n          break;\n        default:\n          cerr << \"Unrecognized input file: \" << *it << endl;\n          exit(1);\n      }\n    }\n\n    check_all_files_in_same_exact_order(preprocessed_inputfiles);\n\n    float required_efficiency_to_beat = 0.0f;\n    vector<vector<vector<size_t>>> partitions;\n    cerr << \"searching for partitions...\\r\" << flush;\n    while (true)\n    {\n      vector<vector<size_t>> partition;\n      find_partition_with_efficiency_higher_than(\n        preprocessed_inputfiles,\n        required_efficiency_to_beat,\n        partition);\n      float actual_efficiency = efficiency_of_partition(preprocessed_inputfiles, partition);\n      cerr << \"partition \" << preprocessed_inputfiles.size() << \" files into \" << partition.size()\n           << \" subsets for \" << 100.0f * actual_efficiency\n           << \" % efficiency\"\n           << \"                  \\r\" << flush;\n      partitions.push_back(partition);\n      if (partition.size() == preprocessed_inputfiles.size() || actual_efficiency == 1.0f) {\n        break;\n      }\n      required_efficiency_to_beat = actual_efficiency;\n    }\n    cerr << \"                                                                  \" << endl;\n    while (true) {\n      bool repeat = false;\n      for (size_t i = 0; i < partitions.size() - 1; i++) {\n        if (partitions[i].size() >= partitions[i+1].size()) {\n          partitions.erase(partitions.begin() + i);\n          repeat = true;\n          break;\n        }\n      }\n      if (!repeat) {\n        break;\n      }\n    }\n    for (auto it = partitions.begin(); it != partitions.end(); ++it) {\n      print_partition(preprocessed_inputfiles, *it);\n    }\n  }\n};\n\nstruct evaluate_defaults_action_t : action_t\n{\n  struct results_entry_t {\n    uint16_t product_size;\n    size_triple_t default_block_size;\n    uint16_t best_pot_block_size;\n    float default_gflops;\n    float best_pot_gflops;\n    float default_efficiency;\n  };\n  friend ostream& operator<<(ostream& s, const results_entry_t& entry)\n  {\n    return s\n      << \"Product size \" << size_triple_t(entry.product_size)\n      << \": default block size \" << entry.default_block_size\n      << \" -> \" << entry.default_gflops\n      << \" GFlop/s = \" << entry.default_efficiency * 100.0f << \" %\"\n      << \" of best POT block size \" << size_triple_t(entry.best_pot_block_size)\n      << \" -> \" << entry.best_pot_gflops\n      << \" GFlop/s\" << dec;\n  }\n  static bool lower_efficiency(const results_entry_t& e1, const results_entry_t& e2) {\n    return e1.default_efficiency < e2.default_efficiency;\n  }\n  virtual const char* invokation_name() const override { return \"evaluate-defaults\"; }\n  void show_usage_and_exit() const\n  {\n    cerr << \"usage: \" << invokation_name() << \" default-sizes-data all-pot-sizes-data\" << endl;\n    cerr << \"checks how well the performance with default sizes compares to the best \"\n         << \"performance measured over all POT sizes.\" << endl;\n    exit(1);\n  }\n  virtual void run(const vector<string>& input_filenames) const override\n  {\n    if (input_filenames.size() != 2) {\n      show_usage_and_exit();\n    }\n    inputfile_t inputfile_default_sizes(input_filenames[0]);\n    inputfile_t inputfile_all_pot_sizes(input_filenames[1]);\n    if (inputfile_default_sizes.type != inputfile_t::type_t::default_sizes) {\n      cerr << inputfile_default_sizes.filename << \" is not an input file with default sizes.\" << endl;\n      show_usage_and_exit();\n    }\n    if (inputfile_all_pot_sizes.type != inputfile_t::type_t::all_pot_sizes) {\n      cerr << inputfile_all_pot_sizes.filename << \" is not an input file with all POT sizes.\" << endl;\n      show_usage_and_exit();\n    }\n    vector<results_entry_t> results;\n    vector<results_entry_t> cubic_results;\n    \n    uint16_t product_size = 0;\n    auto it_all_pot_sizes = inputfile_all_pot_sizes.entries.begin();\n    for (auto it_default_sizes = inputfile_default_sizes.entries.begin();\n         it_default_sizes != inputfile_default_sizes.entries.end();\n         ++it_default_sizes)\n    {\n      if (it_default_sizes->product_size == product_size) {\n        continue;\n      }\n      product_size = it_default_sizes->product_size;\n      while (it_all_pot_sizes != inputfile_all_pot_sizes.entries.end() &&\n             it_all_pot_sizes->product_size != product_size)\n      {\n        ++it_all_pot_sizes;\n      }\n      if (it_all_pot_sizes == inputfile_all_pot_sizes.entries.end()) {\n        break;\n      }\n      uint16_t best_pot_block_size = 0;\n      float best_pot_gflops = 0;\n      for (auto it = it_all_pot_sizes;\n           it != inputfile_all_pot_sizes.entries.end() && it->product_size == product_size;\n           ++it)\n      {\n        if (it->gflops > best_pot_gflops) {\n          best_pot_gflops = it->gflops;\n          best_pot_block_size = it->pot_block_size;\n        }\n      }\n      results_entry_t entry;\n      entry.product_size = product_size;\n      entry.default_block_size = it_default_sizes->nonpot_block_size;\n      entry.best_pot_block_size = best_pot_block_size;\n      entry.default_gflops = it_default_sizes->gflops;\n      entry.best_pot_gflops = best_pot_gflops;\n      entry.default_efficiency = entry.default_gflops / entry.best_pot_gflops;\n      results.push_back(entry);\n\n      size_triple_t t(product_size);\n      if (t.k == t.m && t.m == t.n) {\n        cubic_results.push_back(entry);\n      }\n    }\n\n    cout << \"All results:\" << endl;\n    for (auto it = results.begin(); it != results.end(); ++it) {\n      cout << *it << endl;\n    }\n    cout << endl;\n\n    sort(results.begin(), results.end(), lower_efficiency);\n    \n    const size_t n = min<size_t>(20, results.size());\n    cout << n << \" worst results:\" << endl;\n    for (size_t i = 0; i < n; i++) {\n      cout << results[i] << endl;\n    }\n    cout << endl;\n\n    cout << \"cubic results:\" << endl;\n    for (auto it = cubic_results.begin(); it != cubic_results.end(); ++it) {\n      cout << *it << endl;\n    }\n    cout << endl;\n\n    sort(cubic_results.begin(), cubic_results.end(), lower_efficiency);\n    \n    cout.precision(2);\n    vector<float> a = {0.5f, 0.20f, 0.10f, 0.05f, 0.02f, 0.01f};\n    for (auto it = a.begin(); it != a.end(); ++it) {\n      size_t n = min(results.size() - 1, size_t(*it * results.size()));\n      cout << (100.0f * n / (results.size() - 1))\n           << \" % of product sizes have default efficiency <= \"\n           << 100.0f * results[n].default_efficiency << \" %\" << endl;\n    }\n    cout.precision(default_precision);\n  }\n};\n\n\nvoid show_usage_and_exit(int argc, char* argv[],\n                         const vector<unique_ptr<action_t>>& available_actions)\n{\n  cerr << \"usage: \" << argv[0] << \" <action> [options...] <input files...>\" << endl;\n  cerr << \"available actions:\" << endl;\n  for (auto it = available_actions.begin(); it != available_actions.end(); ++it) {\n    cerr << \"  \" << (*it)->invokation_name() << endl;\n  } \n  cerr << \"the input files should each contain an output of benchmark-blocking-sizes\" << endl;\n  exit(1);\n}\n\nint main(int argc, char* argv[])\n{\n  cout.precision(default_precision);\n  cerr.precision(default_precision);\n\n  vector<unique_ptr<action_t>> available_actions;\n  available_actions.emplace_back(new partition_action_t);\n  available_actions.emplace_back(new evaluate_defaults_action_t);\n\n  vector<string> input_filenames;\n\n  action_t* action = nullptr;\n\n  if (argc < 2) {\n    show_usage_and_exit(argc, argv, available_actions);\n  }\n  for (int i = 1; i < argc; i++) {\n    bool arg_handled = false;\n    // Step 1. Try to match action invokation names.\n    for (auto it = available_actions.begin(); it != available_actions.end(); ++it) {\n      if (!strcmp(argv[i], (*it)->invokation_name())) {\n        if (!action) {\n          action = it->get();\n          arg_handled = true;\n          break;\n        } else {\n          cerr << \"can't specify more than one action!\" << endl;\n          show_usage_and_exit(argc, argv, available_actions);\n        }\n      }\n    }\n    if (arg_handled) {\n      continue;\n    }\n    // Step 2. Try to match option names.\n    if (argv[i][0] == '-') {\n      if (!strcmp(argv[i], \"--only-cubic-sizes\")) {\n        only_cubic_sizes = true;\n        arg_handled = true;\n      }\n      if (!strcmp(argv[i], \"--dump-tables\")) {\n        dump_tables = true;\n        arg_handled = true;\n      }\n      if (!arg_handled) {\n        cerr << \"Unrecognized option: \" << argv[i] << endl;\n        show_usage_and_exit(argc, argv, available_actions);\n      }\n    }\n    if (arg_handled) {\n      continue;\n    }\n    // Step 3. Default to interpreting args as input filenames.\n    input_filenames.emplace_back(argv[i]);\n  }\n\n  if (dump_tables && only_cubic_sizes) {\n    cerr << \"Incompatible options: --only-cubic-sizes and --dump-tables.\" << endl;\n    show_usage_and_exit(argc, argv, available_actions);\n  }\n\n  if (!action) {\n    show_usage_and_exit(argc, argv, available_actions);\n  }\n\n  action->run(input_filenames);\n}\n"
  },
  {
    "path": "include/eigen3/bench/basicbench.cxxlist",
    "content": "#!/bin/bash\n\n# CLIST[((g++))]=\"g++-3.4 -O3 -DNDEBUG\"\n# CLIST[((g++))]=\"g++-3.4 -O3 -DNDEBUG -finline-limit=20000\"\n\n# CLIST[((g++))]=\"g++-4.1 -O3 -DNDEBUG\"\n#CLIST[((g++))]=\"g++-4.1 -O3 -DNDEBUG -finline-limit=20000\"\n\n# CLIST[((g++))]=\"g++-4.2 -O3 -DNDEBUG\"\n#CLIST[((g++))]=\"g++-4.2 -O3 -DNDEBUG -finline-limit=20000\"\n# CLIST[((g++))]=\"g++-4.2 -O3 -DNDEBUG -finline-limit=20000 -fprofile-generate\"\n# CLIST[((g++))]=\"g++-4.2 -O3 -DNDEBUG -finline-limit=20000 -fprofile-use\"\n\n# CLIST[((g++))]=\"g++-4.3 -O3 -DNDEBUG\"\n#CLIST[((g++))]=\"g++-4.3 -O3 -DNDEBUG -finline-limit=20000\"\n# CLIST[((g++))]=\"g++-4.3 -O3 -DNDEBUG -finline-limit=20000 -fprofile-generate\"\n# CLIST[((g++))]=\"g++-4.3 -O3 -DNDEBUG -finline-limit=20000 -fprofile-use\"\n\n# CLIST[((g++))]=\"icpc -fast -DNDEBUG -fno-exceptions -no-inline-max-size -prof-genx\"\n# CLIST[((g++))]=\"icpc -fast -DNDEBUG -fno-exceptions -no-inline-max-size -prof-use\"\n\n#CLIST[((g++))]=\"/opt/intel/Compiler/11.1/072/bin/intel64/icpc -fast -DNDEBUG -fno-exceptions -no-inline-max-size -lrt\"\nCLIST[((g++))]=\"/home/orzel/svn/llvm/Release/bin/clang++ -O3 -DNDEBUG -DEIGEN_DONT_VECTORIZE -lrt\"\nCLIST[((g++))]=\"/home/orzel/svn/llvm/Release/bin/clang++ -O3 -DNDEBUG -lrt\"\nCLIST[((g++))]=\"g++-4.4.4 -O3 -DNDEBUG -DEIGEN_DONT_VECTORIZE -lrt\"\nCLIST[((g++))]=\"g++-4.4.4 -O3 -DNDEBUG -lrt\"\nCLIST[((g++))]=\"g++-4.5.0 -O3 -DNDEBUG -DEIGEN_DONT_VECTORIZE -lrt\"\nCLIST[((g++))]=\"g++-4.5.0 -O3 -DNDEBUG -lrt\"\n"
  },
  {
    "path": "include/eigen3/bench/basicbenchmark.cpp",
    "content": "\n#include <iostream>\n#include \"BenchUtil.h\"\n#include \"basicbenchmark.h\"\n\nint main(int argc, char *argv[])\n{\n  DISABLE_SSE_EXCEPTIONS();\n\n  // this is the list of matrix type and size we want to bench:\n  // ((suffix) (matrix size) (number of iterations))\n  #define MODES ((3d)(3)(4000000)) ((4d)(4)(1000000)) ((Xd)(4)(1000000)) ((Xd)(20)(10000))\n//   #define MODES ((Xd)(20)(10000))\n\n  #define _GENERATE_HEADER(R,ARG,EL) << BOOST_PP_STRINGIZE(BOOST_PP_SEQ_HEAD(EL)) << \"-\" \\\n    << BOOST_PP_STRINGIZE(BOOST_PP_SEQ_ELEM(1,EL)) << \"x\" \\\n    << BOOST_PP_STRINGIZE(BOOST_PP_SEQ_ELEM(1,EL)) << \"   /   \"\n\n  std::cout BOOST_PP_SEQ_FOR_EACH(_GENERATE_HEADER, ~, MODES ) << endl;\n\n  const int tries = 10;\n\n  #define _RUN_BENCH(R,ARG,EL) \\\n    std::cout << ARG( \\\n      BOOST_PP_CAT(Matrix, BOOST_PP_SEQ_HEAD(EL)) (\\\n         BOOST_PP_SEQ_ELEM(1,EL),BOOST_PP_SEQ_ELEM(1,EL)), BOOST_PP_SEQ_ELEM(2,EL), tries) \\\n    << \"   \";\n\n  BOOST_PP_SEQ_FOR_EACH(_RUN_BENCH, benchBasic<LazyEval>, MODES );\n  std::cout << endl;\n  BOOST_PP_SEQ_FOR_EACH(_RUN_BENCH, benchBasic<EarlyEval>, MODES );\n  std::cout << endl;\n\n  return 0;\n}\n"
  },
  {
    "path": "include/eigen3/bench/basicbenchmark.h",
    "content": "\n#ifndef EIGEN_BENCH_BASICBENCH_H\n#define EIGEN_BENCH_BASICBENCH_H\n\nenum {LazyEval, EarlyEval, OmpEval};\n\ntemplate<int Mode, typename MatrixType>\nvoid benchBasic_loop(const MatrixType& I, MatrixType& m, int iterations) __attribute__((noinline));\n\ntemplate<int Mode, typename MatrixType>\nvoid benchBasic_loop(const MatrixType& I, MatrixType& m, int iterations)\n{\n  for(int a = 0; a < iterations; a++)\n  {\n    if (Mode==LazyEval)\n    {\n      asm(\"#begin_bench_loop LazyEval\");\n      if (MatrixType::SizeAtCompileTime!=Eigen::Dynamic) asm(\"#fixedsize\");\n      m = (I + 0.00005 * (m + m.lazy() * m)).eval();\n    }\n    else if (Mode==OmpEval)\n    {\n      asm(\"#begin_bench_loop OmpEval\");\n      if (MatrixType::SizeAtCompileTime!=Eigen::Dynamic) asm(\"#fixedsize\");\n      m = (I + 0.00005 * (m + m.lazy() * m)).evalOMP();\n    }\n    else\n    {\n      asm(\"#begin_bench_loop EarlyEval\");\n      if (MatrixType::SizeAtCompileTime!=Eigen::Dynamic) asm(\"#fixedsize\");\n      m = I + 0.00005 * (m + m * m);\n    }\n    asm(\"#end_bench_loop\");\n  }\n}\n\ntemplate<int Mode, typename MatrixType>\ndouble benchBasic(const MatrixType& mat, int size, int tries) __attribute__((noinline));\n\ntemplate<int Mode, typename MatrixType>\ndouble benchBasic(const MatrixType& mat, int iterations, int tries)\n{\n  const int rows = mat.rows();\n  const int cols = mat.cols();\n\n  MatrixType I(rows,cols);\n  MatrixType m(rows,cols);\n\n  initMatrix_identity(I);\n\n  Eigen::BenchTimer timer;\n  for(uint t=0; t<tries; ++t)\n  {\n    initMatrix_random(m);\n    timer.start();\n    benchBasic_loop<Mode>(I, m, iterations);\n    timer.stop();\n    cerr << m;\n  }\n  return timer.value();\n};\n\n#endif // EIGEN_BENCH_BASICBENCH_H\n"
  },
  {
    "path": "include/eigen3/bench/benchBlasGemm.cpp",
    "content": "// g++ -O3 -DNDEBUG -I.. -L /usr/lib64/atlas/ benchBlasGemm.cpp -o benchBlasGemm -lrt -lcblas\n// possible options:\n//    -DEIGEN_DONT_VECTORIZE\n//    -msse2\n\n// #define EIGEN_DEFAULT_TO_ROW_MAJOR\n#define _FLOAT\n\n#include <iostream>\n\n#include <Eigen/Core>\n#include \"BenchTimer.h\"\n\n// include the BLAS headers\nextern \"C\" {\n#include <cblas.h>\n}\n#include <string>\n\n#ifdef _FLOAT\ntypedef float Scalar;\n#define CBLAS_GEMM cblas_sgemm\n#else\ntypedef double Scalar;\n#define CBLAS_GEMM cblas_dgemm\n#endif\n\n\ntypedef Eigen::Matrix<Scalar,Eigen::Dynamic,Eigen::Dynamic> MyMatrix;\nvoid bench_eigengemm(MyMatrix& mc, const MyMatrix& ma, const MyMatrix& mb, int nbloops);\nvoid check_product(int M, int N, int K);\nvoid check_product(void);\n\nint main(int argc, char *argv[])\n{\n  // disable SSE exceptions\n  #ifdef __GNUC__\n  {\n    int aux;\n    asm(\n    \"stmxcsr   %[aux]           \\n\\t\"\n    \"orl       $32832, %[aux]   \\n\\t\"\n    \"ldmxcsr   %[aux]           \\n\\t\"\n    : : [aux] \"m\" (aux));\n  }\n  #endif\n\n  int nbtries=1, nbloops=1, M, N, K;\n\n  if (argc==2)\n  {\n    if (std::string(argv[1])==\"check\")\n      check_product();\n    else\n      M = N = K = atoi(argv[1]);\n  }\n  else if ((argc==3) && (std::string(argv[1])==\"auto\"))\n  {\n    M = N = K = atoi(argv[2]);\n    nbloops = 1000000000/(M*M*M);\n    if (nbloops<1)\n      nbloops = 1;\n    nbtries = 6;\n  }\n  else if (argc==4)\n  {\n    M = N = K = atoi(argv[1]);\n    nbloops = atoi(argv[2]);\n    nbtries = atoi(argv[3]);\n  }\n  else if (argc==6)\n  {\n    M = atoi(argv[1]);\n    N = atoi(argv[2]);\n    K = atoi(argv[3]);\n    nbloops = atoi(argv[4]);\n    nbtries = atoi(argv[5]);\n  }\n  else\n  {\n    std::cout << \"Usage: \" << argv[0] << \" size  \\n\";\n    std::cout << \"Usage: \" << argv[0] << \" auto size\\n\";\n    std::cout << \"Usage: \" << argv[0] << \" size nbloops nbtries\\n\";\n    std::cout << \"Usage: \" << argv[0] << \" M N K nbloops nbtries\\n\";\n    std::cout << \"Usage: \" << argv[0] << \" check\\n\";\n    std::cout << \"Options:\\n\";\n    std::cout << \"    size       unique size of the 2 matrices (integer)\\n\";\n    std::cout << \"    auto       automatically set the number of repetitions and tries\\n\";\n    std::cout << \"    nbloops    number of times the GEMM routines is executed\\n\";\n    std::cout << \"    nbtries    number of times the loop is benched (return the best try)\\n\";\n    std::cout << \"    M N K      sizes of the matrices: MxN  =  MxK * KxN (integers)\\n\";\n    std::cout << \"    check      check eigen product using cblas as a reference\\n\";\n    exit(1);\n  }\n\n  double nbmad = double(M) * double(N) * double(K) * double(nbloops);\n\n  if (!(std::string(argv[1])==\"auto\"))\n    std::cout << M << \" x \" << N << \" x \" << K << \"\\n\";\n\n  Scalar alpha, beta;\n  MyMatrix ma(M,K), mb(K,N), mc(M,N);\n  ma = MyMatrix::Random(M,K);\n  mb = MyMatrix::Random(K,N);\n  mc = MyMatrix::Random(M,N);\n\n  Eigen::BenchTimer timer;\n\n  // we simply compute c += a*b, so:\n  alpha = 1;\n  beta = 1;\n\n  // bench cblas\n  // ROWS_A, COLS_B, COLS_A, 1.0,  A, COLS_A, B, COLS_B, 0.0, C, COLS_B);\n  if (!(std::string(argv[1])==\"auto\"))\n  {\n    timer.reset();\n    for (uint k=0 ; k<nbtries ; ++k)\n    {\n        timer.start();\n        for (uint j=0 ; j<nbloops ; ++j)\n              #ifdef EIGEN_DEFAULT_TO_ROW_MAJOR\n              CBLAS_GEMM(CblasRowMajor, CblasNoTrans, CblasNoTrans, M, N, K, alpha, ma.data(), K, mb.data(), N, beta, mc.data(), N);\n              #else\n              CBLAS_GEMM(CblasColMajor, CblasNoTrans, CblasNoTrans, M, N, K, alpha, ma.data(), M, mb.data(), K, beta, mc.data(), M);\n              #endif\n        timer.stop();\n    }\n    if (!(std::string(argv[1])==\"auto\"))\n      std::cout << \"cblas: \" << timer.value() << \" (\" << 1e-3*floor(1e-6*nbmad/timer.value()) << \" GFlops/s)\\n\";\n    else\n        std::cout << M << \" : \" << timer.value() << \" ; \" << 1e-3*floor(1e-6*nbmad/timer.value()) << \"\\n\";\n  }\n\n  // clear\n  ma = MyMatrix::Random(M,K);\n  mb = MyMatrix::Random(K,N);\n  mc = MyMatrix::Random(M,N);\n\n  // eigen\n//   if (!(std::string(argv[1])==\"auto\"))\n  {\n      timer.reset();\n      for (uint k=0 ; k<nbtries ; ++k)\n      {\n          timer.start();\n          bench_eigengemm(mc, ma, mb, nbloops);\n          timer.stop();\n      }\n      if (!(std::string(argv[1])==\"auto\"))\n        std::cout << \"eigen : \" << timer.value() << \" (\" << 1e-3*floor(1e-6*nbmad/timer.value()) << \" GFlops/s)\\n\";\n      else\n        std::cout << M << \" : \" << timer.value() << \" ; \" << 1e-3*floor(1e-6*nbmad/timer.value()) << \"\\n\";\n  }\n\n  std::cout << \"l1: \" << Eigen::l1CacheSize() << std::endl;\n  std::cout << \"l2: \" << Eigen::l2CacheSize() << std::endl;\n  \n\n  return 0;\n}\n\nusing namespace Eigen;\n\nvoid bench_eigengemm(MyMatrix& mc, const MyMatrix& ma, const MyMatrix& mb, int nbloops)\n{\n  for (uint j=0 ; j<nbloops ; ++j)\n      mc.noalias() += ma * mb;\n}\n\n#define MYVERIFY(A,M) if (!(A)) { \\\n    std::cout << \"FAIL: \" << M << \"\\n\"; \\\n  }\nvoid check_product(int M, int N, int K)\n{\n  MyMatrix ma(M,K), mb(K,N), mc(M,N), maT(K,M), mbT(N,K), meigen(M,N), mref(M,N);\n  ma = MyMatrix::Random(M,K);\n  mb = MyMatrix::Random(K,N);\n  maT = ma.transpose();\n  mbT = mb.transpose();\n  mc = MyMatrix::Random(M,N);\n\n  MyMatrix::Scalar eps = 1e-4;\n\n  meigen = mref = mc;\n  CBLAS_GEMM(CblasColMajor, CblasNoTrans, CblasNoTrans, M, N, K, 1, ma.data(), M, mb.data(), K, 1, mref.data(), M);\n  meigen += ma * mb;\n  MYVERIFY(meigen.isApprox(mref, eps),\". * .\");\n\n  meigen = mref = mc;\n  CBLAS_GEMM(CblasColMajor, CblasTrans, CblasNoTrans, M, N, K, 1, maT.data(), K, mb.data(), K, 1, mref.data(), M);\n  meigen += maT.transpose() * mb;\n  MYVERIFY(meigen.isApprox(mref, eps),\"T * .\");\n\n  meigen = mref = mc;\n  CBLAS_GEMM(CblasColMajor, CblasTrans, CblasTrans, M, N, K, 1, maT.data(), K, mbT.data(), N, 1, mref.data(), M);\n  meigen += (maT.transpose()) * (mbT.transpose());\n  MYVERIFY(meigen.isApprox(mref, eps),\"T * T\");\n\n  meigen = mref = mc;\n  CBLAS_GEMM(CblasColMajor, CblasNoTrans, CblasTrans, M, N, K, 1, ma.data(), M, mbT.data(), N, 1, mref.data(), M);\n  meigen += ma * mbT.transpose();\n  MYVERIFY(meigen.isApprox(mref, eps),\". * T\");\n}\n\nvoid check_product(void)\n{\n  int M, N, K;\n  for (uint i=0; i<1000; ++i)\n  {\n    M = internal::random<int>(1,64);\n    N = internal::random<int>(1,768);\n    K = internal::random<int>(1,768);\n    M = (0 + M) * 1;\n    std::cout << M << \" x \" << N << \" x \" << K << \"\\n\";\n    check_product(M, N, K);\n  }\n}\n\n"
  },
  {
    "path": "include/eigen3/bench/benchCholesky.cpp",
    "content": "\n// g++ -DNDEBUG -O3 -I.. benchLLT.cpp  -o benchLLT && ./benchLLT\n// options:\n//  -DBENCH_GSL -lgsl /usr/lib/libcblas.so.3\n//  -DEIGEN_DONT_VECTORIZE\n//  -msse2\n//  -DREPEAT=100\n//  -DTRIES=10\n//  -DSCALAR=double\n\n#include <iostream>\n\n#include <Eigen/Core>\n#include <Eigen/Cholesky>\n#include <bench/BenchUtil.h>\nusing namespace Eigen;\n\n#ifndef REPEAT\n#define REPEAT 10000\n#endif\n\n#ifndef TRIES\n#define TRIES 10\n#endif\n\ntypedef float Scalar;\n\ntemplate <typename MatrixType>\n__attribute__ ((noinline)) void benchLLT(const MatrixType& m)\n{\n  int rows = m.rows();\n  int cols = m.cols();\n\n  double cost = 0;\n  for (int j=0; j<rows; ++j)\n  {\n    int r = std::max(rows - j -1,0);\n    cost += 2*(r*j+r+j);\n  }\n\n  int repeats = (REPEAT*1000)/(rows*rows);\n\n  typedef typename MatrixType::Scalar Scalar;\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;\n\n  MatrixType a = MatrixType::Random(rows,cols);\n  SquareMatrixType covMat =  a * a.adjoint();\n\n  BenchTimer timerNoSqrt, timerSqrt;\n\n  Scalar acc = 0;\n  int r = internal::random<int>(0,covMat.rows()-1);\n  int c = internal::random<int>(0,covMat.cols()-1);\n  for (int t=0; t<TRIES; ++t)\n  {\n    timerNoSqrt.start();\n    for (int k=0; k<repeats; ++k)\n    {\n      LDLT<SquareMatrixType> cholnosqrt(covMat);\n      acc += cholnosqrt.matrixL().coeff(r,c);\n    }\n    timerNoSqrt.stop();\n  }\n\n  for (int t=0; t<TRIES; ++t)\n  {\n    timerSqrt.start();\n    for (int k=0; k<repeats; ++k)\n    {\n      LLT<SquareMatrixType> chol(covMat);\n      acc += chol.matrixL().coeff(r,c);\n    }\n    timerSqrt.stop();\n  }\n\n  if (MatrixType::RowsAtCompileTime==Dynamic)\n    std::cout << \"dyn   \";\n  else\n    std::cout << \"fixed \";\n  std::cout << covMat.rows() << \" \\t\"\n            << (timerNoSqrt.best()) / repeats << \"s \"\n            << \"(\" << 1e-9 * cost*repeats/timerNoSqrt.best() << \" GFLOPS)\\t\"\n            << (timerSqrt.best()) / repeats << \"s \"\n            << \"(\" << 1e-9 * cost*repeats/timerSqrt.best() << \" GFLOPS)\\n\";\n\n\n  #ifdef BENCH_GSL\n  if (MatrixType::RowsAtCompileTime==Dynamic)\n  {\n    timerSqrt.reset();\n\n    gsl_matrix* gslCovMat = gsl_matrix_alloc(covMat.rows(),covMat.cols());\n    gsl_matrix* gslCopy = gsl_matrix_alloc(covMat.rows(),covMat.cols());\n\n    eiToGsl(covMat, &gslCovMat);\n    for (int t=0; t<TRIES; ++t)\n    {\n      timerSqrt.start();\n      for (int k=0; k<repeats; ++k)\n      {\n        gsl_matrix_memcpy(gslCopy,gslCovMat);\n        gsl_linalg_cholesky_decomp(gslCopy);\n        acc += gsl_matrix_get(gslCopy,r,c);\n      }\n      timerSqrt.stop();\n    }\n\n    std::cout << \" | \\t\"\n              << timerSqrt.value() * REPEAT / repeats << \"s\";\n\n    gsl_matrix_free(gslCovMat);\n  }\n  #endif\n  std::cout << \"\\n\";\n  // make sure the compiler does not optimize too much\n  if (acc==123)\n    std::cout << acc;\n}\n\nint main(int argc, char* argv[])\n{\n  const int dynsizes[] = {4,6,8,16,24,32,49,64,128,256,512,900,1500,0};\n  std::cout << \"size            LDLT                            LLT\";\n//   #ifdef BENCH_GSL\n//   std::cout << \"       GSL (standard + double + ATLAS)  \";\n//   #endif\n  std::cout << \"\\n\";\n  for (int i=0; dynsizes[i]>0; ++i)\n    benchLLT(Matrix<Scalar,Dynamic,Dynamic>(dynsizes[i],dynsizes[i]));\n\n  benchLLT(Matrix<Scalar,2,2>());\n  benchLLT(Matrix<Scalar,3,3>());\n  benchLLT(Matrix<Scalar,4,4>());\n  benchLLT(Matrix<Scalar,5,5>());\n  benchLLT(Matrix<Scalar,6,6>());\n  benchLLT(Matrix<Scalar,7,7>());\n  benchLLT(Matrix<Scalar,8,8>());\n  benchLLT(Matrix<Scalar,12,12>());\n  benchLLT(Matrix<Scalar,16,16>());\n  return 0;\n}\n\n"
  },
  {
    "path": "include/eigen3/bench/benchEigenSolver.cpp",
    "content": "\n// g++ -DNDEBUG -O3 -I.. benchEigenSolver.cpp  -o benchEigenSolver && ./benchEigenSolver\n// options:\n//  -DBENCH_GMM\n//  -DBENCH_GSL -lgsl /usr/lib/libcblas.so.3\n//  -DEIGEN_DONT_VECTORIZE\n//  -msse2\n//  -DREPEAT=100\n//  -DTRIES=10\n//  -DSCALAR=double\n\n#include <iostream>\n\n#include <Eigen/Core>\n#include <Eigen/QR>\n#include <bench/BenchUtil.h>\nusing namespace Eigen;\n\n#ifndef REPEAT\n#define REPEAT 1000\n#endif\n\n#ifndef TRIES\n#define TRIES 4\n#endif\n\n#ifndef SCALAR\n#define SCALAR float\n#endif\n\ntypedef SCALAR Scalar;\n\ntemplate <typename MatrixType>\n__attribute__ ((noinline)) void benchEigenSolver(const MatrixType& m)\n{\n  int rows = m.rows();\n  int cols = m.cols();\n\n  int stdRepeats = std::max(1,int((REPEAT*1000)/(rows*rows*sqrt(rows))));\n  int saRepeats = stdRepeats * 4;\n\n  typedef typename MatrixType::Scalar Scalar;\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;\n\n  MatrixType a = MatrixType::Random(rows,cols);\n  SquareMatrixType covMat =  a * a.adjoint();\n\n  BenchTimer timerSa, timerStd;\n\n  Scalar acc = 0;\n  int r = internal::random<int>(0,covMat.rows()-1);\n  int c = internal::random<int>(0,covMat.cols()-1);\n  {\n    SelfAdjointEigenSolver<SquareMatrixType> ei(covMat);\n    for (int t=0; t<TRIES; ++t)\n    {\n      timerSa.start();\n      for (int k=0; k<saRepeats; ++k)\n      {\n        ei.compute(covMat);\n        acc += ei.eigenvectors().coeff(r,c);\n      }\n      timerSa.stop();\n    }\n  }\n\n  {\n    EigenSolver<SquareMatrixType> ei(covMat);\n    for (int t=0; t<TRIES; ++t)\n    {\n      timerStd.start();\n      for (int k=0; k<stdRepeats; ++k)\n      {\n        ei.compute(covMat);\n        acc += ei.eigenvectors().coeff(r,c);\n      }\n      timerStd.stop();\n    }\n  }\n\n  if (MatrixType::RowsAtCompileTime==Dynamic)\n    std::cout << \"dyn   \";\n  else\n    std::cout << \"fixed \";\n  std::cout << covMat.rows() << \" \\t\"\n            << timerSa.value() * REPEAT / saRepeats << \"s \\t\"\n            << timerStd.value() * REPEAT / stdRepeats << \"s\";\n\n  #ifdef BENCH_GMM\n  if (MatrixType::RowsAtCompileTime==Dynamic)\n  {\n    timerSa.reset();\n    timerStd.reset();\n\n    gmm::dense_matrix<Scalar> gmmCovMat(covMat.rows(),covMat.cols());\n    gmm::dense_matrix<Scalar> eigvect(covMat.rows(),covMat.cols());\n    std::vector<Scalar> eigval(covMat.rows());\n    eiToGmm(covMat, gmmCovMat);\n    for (int t=0; t<TRIES; ++t)\n    {\n      timerSa.start();\n      for (int k=0; k<saRepeats; ++k)\n      {\n        gmm::symmetric_qr_algorithm(gmmCovMat, eigval, eigvect);\n        acc += eigvect(r,c);\n      }\n      timerSa.stop();\n    }\n    // the non-selfadjoint solver does not compute the eigen vectors\n//     for (int t=0; t<TRIES; ++t)\n//     {\n//       timerStd.start();\n//       for (int k=0; k<stdRepeats; ++k)\n//       {\n//         gmm::implicit_qr_algorithm(gmmCovMat, eigval, eigvect);\n//         acc += eigvect(r,c);\n//       }\n//       timerStd.stop();\n//     }\n\n    std::cout << \" | \\t\"\n              << timerSa.value() * REPEAT / saRepeats << \"s\"\n              << /*timerStd.value() * REPEAT / stdRepeats << \"s\"*/ \"   na   \";\n  }\n  #endif\n\n  #ifdef BENCH_GSL\n  if (MatrixType::RowsAtCompileTime==Dynamic)\n  {\n    timerSa.reset();\n    timerStd.reset();\n\n    gsl_matrix* gslCovMat = gsl_matrix_alloc(covMat.rows(),covMat.cols());\n    gsl_matrix* gslCopy = gsl_matrix_alloc(covMat.rows(),covMat.cols());\n    gsl_matrix* eigvect = gsl_matrix_alloc(covMat.rows(),covMat.cols());\n    gsl_vector* eigval  = gsl_vector_alloc(covMat.rows());\n    gsl_eigen_symmv_workspace* eisymm = gsl_eigen_symmv_alloc(covMat.rows());\n    \n    gsl_matrix_complex* eigvectz = gsl_matrix_complex_alloc(covMat.rows(),covMat.cols());\n    gsl_vector_complex* eigvalz  = gsl_vector_complex_alloc(covMat.rows());\n    gsl_eigen_nonsymmv_workspace* einonsymm = gsl_eigen_nonsymmv_alloc(covMat.rows());\n    \n    eiToGsl(covMat, &gslCovMat);\n    for (int t=0; t<TRIES; ++t)\n    {\n      timerSa.start();\n      for (int k=0; k<saRepeats; ++k)\n      {\n        gsl_matrix_memcpy(gslCopy,gslCovMat);\n        gsl_eigen_symmv(gslCopy, eigval, eigvect, eisymm);\n        acc += gsl_matrix_get(eigvect,r,c);\n      }\n      timerSa.stop();\n    }\n    for (int t=0; t<TRIES; ++t)\n    {\n      timerStd.start();\n      for (int k=0; k<stdRepeats; ++k)\n      {\n        gsl_matrix_memcpy(gslCopy,gslCovMat);\n        gsl_eigen_nonsymmv(gslCopy, eigvalz, eigvectz, einonsymm);\n        acc += GSL_REAL(gsl_matrix_complex_get(eigvectz,r,c));\n      }\n      timerStd.stop();\n    }\n\n    std::cout << \" | \\t\"\n              << timerSa.value() * REPEAT / saRepeats << \"s \\t\"\n              << timerStd.value() * REPEAT / stdRepeats << \"s\";\n\n    gsl_matrix_free(gslCovMat);\n    gsl_vector_free(gslCopy);\n    gsl_matrix_free(eigvect);\n    gsl_vector_free(eigval);\n    gsl_matrix_complex_free(eigvectz);\n    gsl_vector_complex_free(eigvalz);\n    gsl_eigen_symmv_free(eisymm);\n    gsl_eigen_nonsymmv_free(einonsymm);\n  }\n  #endif\n\n  std::cout << \"\\n\";\n  \n  // make sure the compiler does not optimize too much\n  if (acc==123)\n    std::cout << acc;\n}\n\nint main(int argc, char* argv[])\n{\n  const int dynsizes[] = {4,6,8,12,16,24,32,64,128,256,512,0};\n  std::cout << \"size            selfadjoint       generic\";\n  #ifdef BENCH_GMM\n  std::cout << \"        GMM++          \";\n  #endif\n  #ifdef BENCH_GSL\n  std::cout << \"       GSL (double + ATLAS)  \";\n  #endif\n  std::cout << \"\\n\";\n  for (uint i=0; dynsizes[i]>0; ++i)\n    benchEigenSolver(Matrix<Scalar,Dynamic,Dynamic>(dynsizes[i],dynsizes[i]));\n\n  benchEigenSolver(Matrix<Scalar,2,2>());\n  benchEigenSolver(Matrix<Scalar,3,3>());\n  benchEigenSolver(Matrix<Scalar,4,4>());\n  benchEigenSolver(Matrix<Scalar,6,6>());\n  benchEigenSolver(Matrix<Scalar,8,8>());\n  benchEigenSolver(Matrix<Scalar,12,12>());\n  benchEigenSolver(Matrix<Scalar,16,16>());\n  return 0;\n}\n\n"
  },
  {
    "path": "include/eigen3/bench/benchFFT.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Mark Borgerding mark a borgerding net\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include <iostream>\n\n#include <bench/BenchUtil.h>\n#include <complex>\n#include <vector>\n#include <Eigen/Core>\n\n#include <unsupported/Eigen/FFT>\n\nusing namespace Eigen;\nusing namespace std;\n\n\ntemplate <typename T>\nstring nameof();\n\ntemplate <> string nameof<float>() {return \"float\";}\ntemplate <> string nameof<double>() {return \"double\";}\ntemplate <> string nameof<long double>() {return \"long double\";}\n\n#ifndef TYPE\n#define TYPE float\n#endif\n\n#ifndef NFFT\n#define NFFT 1024\n#endif\n#ifndef NDATA\n#define NDATA 1000000\n#endif\n\nusing namespace Eigen;\n\ntemplate <typename T>\nvoid bench(int nfft,bool fwd,bool unscaled=false, bool halfspec=false)\n{\n    typedef typename NumTraits<T>::Real Scalar;\n    typedef typename std::complex<Scalar> Complex;\n    int nits = NDATA/nfft;\n    vector<T> inbuf(nfft);\n    vector<Complex > outbuf(nfft);\n    FFT< Scalar > fft;\n\n    if (unscaled) {\n        fft.SetFlag(fft.Unscaled);\n        cout << \"unscaled \";\n    }\n    if (halfspec) {\n        fft.SetFlag(fft.HalfSpectrum);\n        cout << \"halfspec \";\n    }\n\n\n    std::fill(inbuf.begin(),inbuf.end(),0);\n    fft.fwd( outbuf , inbuf);\n\n    BenchTimer timer;\n    timer.reset();\n    for (int k=0;k<8;++k) {\n        timer.start();\n        if (fwd)\n            for(int i = 0; i < nits; i++)\n                fft.fwd( outbuf , inbuf);\n        else\n            for(int i = 0; i < nits; i++)\n                fft.inv(inbuf,outbuf);\n        timer.stop();\n    }\n\n    cout << nameof<Scalar>() << \" \";\n    double mflops = 5.*nfft*log2((double)nfft) / (1e6 * timer.value() / (double)nits );\n    if ( NumTraits<T>::IsComplex ) {\n        cout << \"complex\";\n    }else{\n        cout << \"real   \";\n        mflops /= 2;\n    }\n\n\n    if (fwd)\n        cout << \" fwd\";\n    else\n        cout << \" inv\";\n\n    cout << \" NFFT=\" << nfft << \"  \" << (double(1e-6*nfft*nits)/timer.value()) << \" MS/s  \" << mflops << \"MFLOPS\\n\";\n}\n\nint main(int argc,char ** argv)\n{\n    bench<complex<float> >(NFFT,true);\n    bench<complex<float> >(NFFT,false);\n    bench<float>(NFFT,true);\n    bench<float>(NFFT,false);\n    bench<float>(NFFT,false,true);\n    bench<float>(NFFT,false,true,true);\n\n    bench<complex<double> >(NFFT,true);\n    bench<complex<double> >(NFFT,false);\n    bench<double>(NFFT,true);\n    bench<double>(NFFT,false);\n    bench<complex<long double> >(NFFT,true);\n    bench<complex<long double> >(NFFT,false);\n    bench<long double>(NFFT,true);\n    bench<long double>(NFFT,false);\n    return 0;\n}\n"
  },
  {
    "path": "include/eigen3/bench/benchGeometry.cpp",
    "content": "#include <iostream>\n#include <iomanip>\n#include <Eigen/Core>\n#include <Eigen/Geometry>\n#include <bench/BenchTimer.h>\n\nusing namespace Eigen;\nusing namespace std;\n\n#ifndef REPEAT\n#define REPEAT 1000000\n#endif\n\nenum func_opt\n{\n    TV,\n    TMATV,\n    TMATVMAT,\n};\n\n\ntemplate <class res, class arg1, class arg2, int opt>\nstruct func;\n\ntemplate <class res, class arg1, class arg2>\nstruct func<res, arg1, arg2, TV>\n{\n    static EIGEN_DONT_INLINE res run( arg1& a1, arg2& a2 )\n    {\n\tasm (\"\");\n\treturn a1 * a2;\n    }\n};\n\ntemplate <class res, class arg1, class arg2>\nstruct func<res, arg1, arg2, TMATV>\n{\n    static EIGEN_DONT_INLINE res run( arg1& a1, arg2& a2 )\n    {\n\tasm (\"\");\n\treturn a1.matrix() * a2;\n    }\n};\n\ntemplate <class res, class arg1, class arg2>\nstruct func<res, arg1, arg2, TMATVMAT>\n{\n    static EIGEN_DONT_INLINE res run( arg1& a1, arg2& a2 )\n    {\n\tasm (\"\");\n\treturn res(a1.matrix() * a2.matrix());\n    }\n};\n\ntemplate <class func, class arg1, class arg2>\nstruct test_transform\n{\n    static void run()\n    {\n\targ1 a1;\n\ta1.setIdentity();\n\targ2 a2;\n\ta2.setIdentity();\n\n\tBenchTimer timer;\n\ttimer.reset();\n\tfor (int k=0; k<10; ++k)\n\t{\n\t    timer.start();\n\t    for (int k=0; k<REPEAT; ++k)\n\t\ta2 = func::run( a1, a2 );\n\t    timer.stop();\n\t}\n\tcout << setprecision(4) << fixed << timer.value() << \"s  \" << endl;;\n    }\n};\n\n\n#define run_vec( op, scalar, mode, option, vsize ) \\\n    std::cout << #scalar << \"\\t \" << #mode << \"\\t \" << #option << \" \" << #vsize \" \"; \\\n    {\\\n\ttypedef Transform<scalar, 3, mode, option> Trans;\\\n\ttypedef Matrix<scalar, vsize, 1, option> Vec;\\\n\ttypedef func<Vec,Trans,Vec,op> Func;\\\n\ttest_transform< Func, Trans, Vec >::run();\\\n    }\n\n#define run_trans( op, scalar, mode, option ) \\\n    std::cout << #scalar << \"\\t \" << #mode << \"\\t \" << #option << \"   \"; \\\n    {\\\n\ttypedef Transform<scalar, 3, mode, option> Trans;\\\n\ttypedef func<Trans,Trans,Trans,op> Func;\\\n\ttest_transform< Func, Trans, Trans >::run();\\\n    }\n\nint main(int argc, char* argv[])\n{\n    cout << \"vec = trans * vec\" << endl;\n    run_vec(TV, float,  Isometry, AutoAlign, 3);\n    run_vec(TV, float,  Isometry, DontAlign, 3);\n    run_vec(TV, float,  Isometry, AutoAlign, 4);\n    run_vec(TV, float,  Isometry, DontAlign, 4);\n    run_vec(TV, float,  Projective, AutoAlign, 4);\n    run_vec(TV, float,  Projective, DontAlign, 4);\n    run_vec(TV, double, Isometry, AutoAlign, 3);\n    run_vec(TV, double, Isometry, DontAlign, 3);\n    run_vec(TV, double, Isometry, AutoAlign, 4);\n    run_vec(TV, double, Isometry, DontAlign, 4);\n    run_vec(TV, double, Projective, AutoAlign, 4);\n    run_vec(TV, double, Projective, DontAlign, 4);\n\n    cout << \"vec = trans.matrix() * vec\" << endl;\n    run_vec(TMATV, float,  Isometry, AutoAlign, 4);\n    run_vec(TMATV, float,  Isometry, DontAlign, 4);\n    run_vec(TMATV, double, Isometry, AutoAlign, 4);\n    run_vec(TMATV, double, Isometry, DontAlign, 4);\n\n    cout << \"trans = trans1 * trans\" << endl;\n    run_trans(TV, float,  Isometry, AutoAlign);\n    run_trans(TV, float,  Isometry, DontAlign);\n    run_trans(TV, double, Isometry, AutoAlign);\n    run_trans(TV, double, Isometry, DontAlign);\n    run_trans(TV, float,  Projective, AutoAlign);\n    run_trans(TV, float,  Projective, DontAlign);\n    run_trans(TV, double, Projective, AutoAlign);\n    run_trans(TV, double, Projective, DontAlign);\n\n    cout << \"trans = trans1.matrix() * trans.matrix()\" << endl;\n    run_trans(TMATVMAT, float,  Isometry, AutoAlign);\n    run_trans(TMATVMAT, float,  Isometry, DontAlign);\n    run_trans(TMATVMAT, double, Isometry, AutoAlign);\n    run_trans(TMATVMAT, double, Isometry, DontAlign);\n}\n\n"
  },
  {
    "path": "include/eigen3/bench/benchVecAdd.cpp",
    "content": "\n#include <iostream>\n#include <Eigen/Core>\n#include <bench/BenchTimer.h>\nusing namespace Eigen;\n\n#ifndef SIZE\n#define SIZE 50\n#endif\n\n#ifndef REPEAT\n#define REPEAT 10000\n#endif\n\ntypedef float Scalar;\n\n__attribute__ ((noinline)) void benchVec(Scalar* a, Scalar* b, Scalar* c, int size);\n__attribute__ ((noinline)) void benchVec(MatrixXf& a, MatrixXf& b, MatrixXf& c);\n__attribute__ ((noinline)) void benchVec(VectorXf& a, VectorXf& b, VectorXf& c);\n\nint main(int argc, char* argv[])\n{\n    int size = SIZE * 8;\n    int size2 = size * size;\n    Scalar* a = internal::aligned_new<Scalar>(size2);\n    Scalar* b = internal::aligned_new<Scalar>(size2+4)+1;\n    Scalar* c = internal::aligned_new<Scalar>(size2); \n    \n    for (int i=0; i<size; ++i)\n    {\n        a[i] = b[i] = c[i] = 0;\n    }\n    \n    BenchTimer timer;\n    \n    timer.reset();\n    for (int k=0; k<10; ++k)\n    {\n        timer.start();\n        benchVec(a, b, c, size2);\n        timer.stop();\n    }\n    std::cout << timer.value() << \"s  \" << (double(size2*REPEAT)/timer.value())/(1024.*1024.*1024.) << \" GFlops\\n\";\n    return 0;\n    for (int innersize = size; innersize>2 ; --innersize)\n    {\n        if (size2%innersize==0)\n        {\n            int outersize = size2/innersize;\n            MatrixXf ma = Map<MatrixXf>(a, innersize, outersize );\n            MatrixXf mb = Map<MatrixXf>(b, innersize, outersize );\n            MatrixXf mc = Map<MatrixXf>(c, innersize, outersize );\n            timer.reset();\n            for (int k=0; k<3; ++k)\n            {\n                timer.start();\n                benchVec(ma, mb, mc);\n                timer.stop();\n            }\n            std::cout << innersize << \" x \" << outersize << \"  \" << timer.value() << \"s   \" << (double(size2*REPEAT)/timer.value())/(1024.*1024.*1024.) << \" GFlops\\n\";\n        }\n    }\n    \n    VectorXf va = Map<VectorXf>(a, size2);\n    VectorXf vb = Map<VectorXf>(b, size2);\n    VectorXf vc = Map<VectorXf>(c, size2);\n    timer.reset();\n    for (int k=0; k<3; ++k)\n    {\n        timer.start();\n        benchVec(va, vb, vc);\n        timer.stop();\n    }\n    std::cout << timer.value() << \"s   \" << (double(size2*REPEAT)/timer.value())/(1024.*1024.*1024.) << \" GFlops\\n\";\n\n    return 0;\n}\n\nvoid benchVec(MatrixXf& a, MatrixXf& b, MatrixXf& c)\n{\n    for (int k=0; k<REPEAT; ++k)\n        a = a + b;\n}\n\nvoid benchVec(VectorXf& a, VectorXf& b, VectorXf& c)\n{\n    for (int k=0; k<REPEAT; ++k)\n        a = a + b;\n}\n\nvoid benchVec(Scalar* a, Scalar* b, Scalar* c, int size)\n{\n    typedef internal::packet_traits<Scalar>::type PacketScalar;\n    const int PacketSize = internal::packet_traits<Scalar>::size;\n    PacketScalar a0, a1, a2, a3, b0, b1, b2, b3;\n    for (int k=0; k<REPEAT; ++k)\n        for (int i=0; i<size; i+=PacketSize*8)\n        {\n//             a0 = internal::pload(&a[i]);\n//             b0 = internal::pload(&b[i]);\n//             a1 = internal::pload(&a[i+1*PacketSize]);\n//             b1 = internal::pload(&b[i+1*PacketSize]);\n//             a2 = internal::pload(&a[i+2*PacketSize]);\n//             b2 = internal::pload(&b[i+2*PacketSize]);\n//             a3 = internal::pload(&a[i+3*PacketSize]);\n//             b3 = internal::pload(&b[i+3*PacketSize]);\n//             internal::pstore(&a[i], internal::padd(a0, b0));\n//             a0 = internal::pload(&a[i+4*PacketSize]);\n//             b0 = internal::pload(&b[i+4*PacketSize]);\n//             \n//             internal::pstore(&a[i+1*PacketSize], internal::padd(a1, b1));\n//             a1 = internal::pload(&a[i+5*PacketSize]);\n//             b1 = internal::pload(&b[i+5*PacketSize]);\n//             \n//             internal::pstore(&a[i+2*PacketSize], internal::padd(a2, b2));\n//             a2 = internal::pload(&a[i+6*PacketSize]);\n//             b2 = internal::pload(&b[i+6*PacketSize]);\n//             \n//             internal::pstore(&a[i+3*PacketSize], internal::padd(a3, b3));\n//             a3 = internal::pload(&a[i+7*PacketSize]);\n//             b3 = internal::pload(&b[i+7*PacketSize]);\n//             \n//             internal::pstore(&a[i+4*PacketSize], internal::padd(a0, b0));\n//             internal::pstore(&a[i+5*PacketSize], internal::padd(a1, b1));\n//             internal::pstore(&a[i+6*PacketSize], internal::padd(a2, b2));\n//             internal::pstore(&a[i+7*PacketSize], internal::padd(a3, b3));\n            \n            internal::pstore(&a[i+2*PacketSize], internal::padd(internal::ploadu(&a[i+2*PacketSize]), internal::ploadu(&b[i+2*PacketSize])));\n            internal::pstore(&a[i+3*PacketSize], internal::padd(internal::ploadu(&a[i+3*PacketSize]), internal::ploadu(&b[i+3*PacketSize])));\n            internal::pstore(&a[i+4*PacketSize], internal::padd(internal::ploadu(&a[i+4*PacketSize]), internal::ploadu(&b[i+4*PacketSize])));\n            internal::pstore(&a[i+5*PacketSize], internal::padd(internal::ploadu(&a[i+5*PacketSize]), internal::ploadu(&b[i+5*PacketSize])));\n            internal::pstore(&a[i+6*PacketSize], internal::padd(internal::ploadu(&a[i+6*PacketSize]), internal::ploadu(&b[i+6*PacketSize])));\n            internal::pstore(&a[i+7*PacketSize], internal::padd(internal::ploadu(&a[i+7*PacketSize]), internal::ploadu(&b[i+7*PacketSize])));\n        }\n}\n"
  },
  {
    "path": "include/eigen3/bench/bench_gemm.cpp",
    "content": "\n// g++-4.4 bench_gemm.cpp -I .. -O2 -DNDEBUG -lrt -fopenmp && OMP_NUM_THREADS=2  ./a.out\n// icpc bench_gemm.cpp -I .. -O3 -DNDEBUG -lrt -openmp  && OMP_NUM_THREADS=2  ./a.out\n\n// Compilation options:\n// \n// -DSCALAR=std::complex<double>\n// -DSCALARA=double or -DSCALARB=double\n// -DHAVE_BLAS\n// -DDECOUPLED\n//\n\n#include <iostream>\n#include <Eigen/Core>\n#include <bench/BenchTimer.h>\n\nusing namespace std;\nusing namespace Eigen;\n\n#ifndef SCALAR\n// #define SCALAR std::complex<float>\n#define SCALAR float\n#endif\n\n#ifndef SCALARA\n#define SCALARA SCALAR\n#endif\n\n#ifndef SCALARB\n#define SCALARB SCALAR\n#endif\n\ntypedef SCALAR Scalar;\ntypedef NumTraits<Scalar>::Real RealScalar;\ntypedef Matrix<SCALARA,Dynamic,Dynamic> A;\ntypedef Matrix<SCALARB,Dynamic,Dynamic> B;\ntypedef Matrix<Scalar,Dynamic,Dynamic> C;\ntypedef Matrix<RealScalar,Dynamic,Dynamic> M;\n\n#ifdef HAVE_BLAS\n\nextern \"C\" {\n  #include <Eigen/src/misc/blas.h>\n}\n\nstatic float fone = 1;\nstatic float fzero = 0;\nstatic double done = 1;\nstatic double szero = 0;\nstatic std::complex<float> cfone = 1;\nstatic std::complex<float> cfzero = 0;\nstatic std::complex<double> cdone = 1;\nstatic std::complex<double> cdzero = 0;\nstatic char notrans = 'N';\nstatic char trans = 'T';  \nstatic char nonunit = 'N';\nstatic char lower = 'L';\nstatic char right = 'R';\nstatic int intone = 1;\n\nvoid blas_gemm(const MatrixXf& a, const MatrixXf& b, MatrixXf& c)\n{\n  int M = c.rows(); int N = c.cols(); int K = a.cols();\n  int lda = a.rows(); int ldb = b.rows(); int ldc = c.rows();\n\n  sgemm_(&notrans,&notrans,&M,&N,&K,&fone,\n         const_cast<float*>(a.data()),&lda,\n         const_cast<float*>(b.data()),&ldb,&fone,\n         c.data(),&ldc);\n}\n\nEIGEN_DONT_INLINE void blas_gemm(const MatrixXd& a, const MatrixXd& b, MatrixXd& c)\n{\n  int M = c.rows(); int N = c.cols(); int K = a.cols();\n  int lda = a.rows(); int ldb = b.rows(); int ldc = c.rows();\n\n  dgemm_(&notrans,&notrans,&M,&N,&K,&done,\n         const_cast<double*>(a.data()),&lda,\n         const_cast<double*>(b.data()),&ldb,&done,\n         c.data(),&ldc);\n}\n\nvoid blas_gemm(const MatrixXcf& a, const MatrixXcf& b, MatrixXcf& c)\n{\n  int M = c.rows(); int N = c.cols(); int K = a.cols();\n  int lda = a.rows(); int ldb = b.rows(); int ldc = c.rows();\n\n  cgemm_(&notrans,&notrans,&M,&N,&K,(float*)&cfone,\n         const_cast<float*>((const float*)a.data()),&lda,\n         const_cast<float*>((const float*)b.data()),&ldb,(float*)&cfone,\n         (float*)c.data(),&ldc);\n}\n\nvoid blas_gemm(const MatrixXcd& a, const MatrixXcd& b, MatrixXcd& c)\n{\n  int M = c.rows(); int N = c.cols(); int K = a.cols();\n  int lda = a.rows(); int ldb = b.rows(); int ldc = c.rows();\n\n  zgemm_(&notrans,&notrans,&M,&N,&K,(double*)&cdone,\n         const_cast<double*>((const double*)a.data()),&lda,\n         const_cast<double*>((const double*)b.data()),&ldb,(double*)&cdone,\n         (double*)c.data(),&ldc);\n}\n\n\n\n#endif\n\nvoid matlab_cplx_cplx(const M& ar, const M& ai, const M& br, const M& bi, M& cr, M& ci)\n{\n  cr.noalias() += ar * br;\n  cr.noalias() -= ai * bi;\n  ci.noalias() += ar * bi;\n  ci.noalias() += ai * br;\n}\n\nvoid matlab_real_cplx(const M& a, const M& br, const M& bi, M& cr, M& ci)\n{\n  cr.noalias() += a * br;\n  ci.noalias() += a * bi;\n}\n\nvoid matlab_cplx_real(const M& ar, const M& ai, const M& b, M& cr, M& ci)\n{\n  cr.noalias() += ar * b;\n  ci.noalias() += ai * b;\n}\n\ntemplate<typename A, typename B, typename C>\nEIGEN_DONT_INLINE void gemm(const A& a, const B& b, C& c)\n{\n c.noalias() += a * b;\n}\n\nint main(int argc, char ** argv)\n{\n  std::ptrdiff_t l1 = internal::queryL1CacheSize();\n  std::ptrdiff_t l2 = internal::queryTopLevelCacheSize();\n  std::cout << \"L1 cache size     = \" << (l1>0 ? l1/1024 : -1) << \" KB\\n\";\n  std::cout << \"L2/L3 cache size  = \" << (l2>0 ? l2/1024 : -1) << \" KB\\n\";\n  typedef internal::gebp_traits<Scalar,Scalar> Traits;\n  std::cout << \"Register blocking = \" << Traits::mr << \" x \" << Traits::nr << \"\\n\";\n\n  int rep = 1;    // number of repetitions per try\n  int tries = 2;  // number of tries, we keep the best\n\n  int s = 2048;\n  int m = s;\n  int n = s;\n  int p = s;\n  int cache_size1=-1, cache_size2=l2, cache_size3 = 0;\n\n  bool need_help = false;\n  for (int i=1; i<argc;)\n  {\n    if(argv[i][0]=='-')\n    {\n      if(argv[i][1]=='s')\n      {\n        ++i;\n        s = atoi(argv[i++]);\n        m = n = p = s;\n        if(argv[i][0]!='-')\n        {\n          n = atoi(argv[i++]);\n          p = atoi(argv[i++]);\n        }\n      }\n      else if(argv[i][1]=='c')\n      {\n        ++i;\n        cache_size1 = atoi(argv[i++]);\n        if(argv[i][0]!='-')\n        {\n          cache_size2 = atoi(argv[i++]);\n          if(argv[i][0]!='-')\n            cache_size3 = atoi(argv[i++]);\n        }\n      }\n      else if(argv[i][1]=='t')\n      {\n        ++i;\n        tries = atoi(argv[i++]);\n      }\n      else if(argv[i][1]=='p')\n      {\n        ++i;\n        rep = atoi(argv[i++]);\n      }\n    }\n    else\n    {\n      need_help = true;\n      break;\n    }\n  }\n\n  if(need_help)\n  {\n    std::cout << argv[0] << \" -s <matrix sizes> -c <cache sizes> -t <nb tries> -p <nb repeats>\\n\";\n    std::cout << \"   <matrix sizes> : size\\n\";\n    std::cout << \"   <matrix sizes> : rows columns depth\\n\";\n    return 1;\n  }\n\n#if EIGEN_VERSION_AT_LEAST(3,2,90)\n  if(cache_size1>0)\n    setCpuCacheSizes(cache_size1,cache_size2,cache_size3);\n#endif\n  \n  A a(m,p); a.setRandom();\n  B b(p,n); b.setRandom();\n  C c(m,n); c.setOnes();\n  C rc = c;\n\n  std::cout << \"Matrix sizes = \" << m << \"x\" << p << \" * \" << p << \"x\" << n << \"\\n\";\n  std::ptrdiff_t mc(m), nc(n), kc(p);\n  internal::computeProductBlockingSizes<Scalar,Scalar>(kc, mc, nc);\n  std::cout << \"blocking size (mc x kc) = \" << mc << \" x \" << kc << \"\\n\";\n\n  C r = c;\n\n  // check the parallel product is correct\n  #if defined EIGEN_HAS_OPENMP\n  Eigen::initParallel();\n  int procs = omp_get_max_threads();\n  if(procs>1)\n  {\n    #ifdef HAVE_BLAS\n    blas_gemm(a,b,r);\n    #else\n    omp_set_num_threads(1);\n    r.noalias() += a * b;\n    omp_set_num_threads(procs);\n    #endif\n    c.noalias() += a * b;\n    if(!r.isApprox(c)) std::cerr << \"Warning, your parallel product is crap!\\n\\n\";\n  }\n  #elif defined HAVE_BLAS\n    blas_gemm(a,b,r);\n    c.noalias() += a * b;\n    if(!r.isApprox(c)) {\n      std::cout << r  - c << \"\\n\";\n      std::cerr << \"Warning, your product is crap!\\n\\n\";\n    }\n  #else\n    if(1.*m*n*p<2000.*2000*2000)\n    {\n      gemm(a,b,c);\n      r.noalias() += a.cast<Scalar>() .lazyProduct( b.cast<Scalar>() );\n      if(!r.isApprox(c)) {\n        std::cout << r - c << \"\\n\";\n        std::cerr << \"Warning, your product is crap!\\n\\n\";\n      }\n    }\n  #endif\n\n  #ifdef HAVE_BLAS\n  BenchTimer tblas;\n  c = rc;\n  BENCH(tblas, tries, rep, blas_gemm(a,b,c));\n  std::cout << \"blas  cpu         \" << tblas.best(CPU_TIMER)/rep  << \"s  \\t\" << (double(m)*n*p*rep*2/tblas.best(CPU_TIMER))*1e-9  <<  \" GFLOPS \\t(\" << tblas.total(CPU_TIMER)  << \"s)\\n\";\n  std::cout << \"blas  real        \" << tblas.best(REAL_TIMER)/rep << \"s  \\t\" << (double(m)*n*p*rep*2/tblas.best(REAL_TIMER))*1e-9 <<  \" GFLOPS \\t(\" << tblas.total(REAL_TIMER) << \"s)\\n\";\n  #endif\n\n  BenchTimer tmt;\n  c = rc;\n  BENCH(tmt, tries, rep, gemm(a,b,c));\n  std::cout << \"eigen cpu         \" << tmt.best(CPU_TIMER)/rep  << \"s  \\t\" << (double(m)*n*p*rep*2/tmt.best(CPU_TIMER))*1e-9  <<  \" GFLOPS \\t(\" << tmt.total(CPU_TIMER)  << \"s)\\n\";\n  std::cout << \"eigen real        \" << tmt.best(REAL_TIMER)/rep << \"s  \\t\" << (double(m)*n*p*rep*2/tmt.best(REAL_TIMER))*1e-9 <<  \" GFLOPS \\t(\" << tmt.total(REAL_TIMER) << \"s)\\n\";\n\n  #ifdef EIGEN_HAS_OPENMP\n  if(procs>1)\n  {\n    BenchTimer tmono;\n    omp_set_num_threads(1);\n    Eigen::setNbThreads(1);\n    c = rc;\n    BENCH(tmono, tries, rep, gemm(a,b,c));\n    std::cout << \"eigen mono cpu    \" << tmono.best(CPU_TIMER)/rep  << \"s  \\t\" << (double(m)*n*p*rep*2/tmono.best(CPU_TIMER))*1e-9  <<  \" GFLOPS \\t(\" << tmono.total(CPU_TIMER)  << \"s)\\n\";\n    std::cout << \"eigen mono real   \" << tmono.best(REAL_TIMER)/rep << \"s  \\t\" << (double(m)*n*p*rep*2/tmono.best(REAL_TIMER))*1e-9 <<  \" GFLOPS \\t(\" << tmono.total(REAL_TIMER) << \"s)\\n\";\n    std::cout << \"mt speed up x\" << tmono.best(CPU_TIMER) / tmt.best(REAL_TIMER)  << \" => \" << (100.0*tmono.best(CPU_TIMER) / tmt.best(REAL_TIMER))/procs << \"%\\n\";\n  }\n  #endif\n  \n  if(1.*m*n*p<30*30*30)\n  {\n      BenchTimer tmt;\n      c = rc;\n      BENCH(tmt, tries, rep, c.noalias()+=a.lazyProduct(b));\n      std::cout << \"lazy cpu         \" << tmt.best(CPU_TIMER)/rep  << \"s  \\t\" << (double(m)*n*p*rep*2/tmt.best(CPU_TIMER))*1e-9  <<  \" GFLOPS \\t(\" << tmt.total(CPU_TIMER)  << \"s)\\n\";\n      std::cout << \"lazy real        \" << tmt.best(REAL_TIMER)/rep << \"s  \\t\" << (double(m)*n*p*rep*2/tmt.best(REAL_TIMER))*1e-9 <<  \" GFLOPS \\t(\" << tmt.total(REAL_TIMER) << \"s)\\n\";\n  }\n  \n  #ifdef DECOUPLED\n  if((NumTraits<A::Scalar>::IsComplex) && (NumTraits<B::Scalar>::IsComplex))\n  {\n    M ar(m,p); ar.setRandom();\n    M ai(m,p); ai.setRandom();\n    M br(p,n); br.setRandom();\n    M bi(p,n); bi.setRandom();\n    M cr(m,n); cr.setRandom();\n    M ci(m,n); ci.setRandom();\n    \n    BenchTimer t;\n    BENCH(t, tries, rep, matlab_cplx_cplx(ar,ai,br,bi,cr,ci));\n    std::cout << \"\\\"matlab\\\" cpu    \" << t.best(CPU_TIMER)/rep  << \"s  \\t\" << (double(m)*n*p*rep*2/t.best(CPU_TIMER))*1e-9  <<  \" GFLOPS \\t(\" << t.total(CPU_TIMER)  << \"s)\\n\";\n    std::cout << \"\\\"matlab\\\" real   \" << t.best(REAL_TIMER)/rep << \"s  \\t\" << (double(m)*n*p*rep*2/t.best(REAL_TIMER))*1e-9 <<  \" GFLOPS \\t(\" << t.total(REAL_TIMER) << \"s)\\n\";\n  }\n  if((!NumTraits<A::Scalar>::IsComplex) && (NumTraits<B::Scalar>::IsComplex))\n  {\n    M a(m,p);  a.setRandom();\n    M br(p,n); br.setRandom();\n    M bi(p,n); bi.setRandom();\n    M cr(m,n); cr.setRandom();\n    M ci(m,n); ci.setRandom();\n    \n    BenchTimer t;\n    BENCH(t, tries, rep, matlab_real_cplx(a,br,bi,cr,ci));\n    std::cout << \"\\\"matlab\\\" cpu    \" << t.best(CPU_TIMER)/rep  << \"s  \\t\" << (double(m)*n*p*rep*2/t.best(CPU_TIMER))*1e-9  <<  \" GFLOPS \\t(\" << t.total(CPU_TIMER)  << \"s)\\n\";\n    std::cout << \"\\\"matlab\\\" real   \" << t.best(REAL_TIMER)/rep << \"s  \\t\" << (double(m)*n*p*rep*2/t.best(REAL_TIMER))*1e-9 <<  \" GFLOPS \\t(\" << t.total(REAL_TIMER) << \"s)\\n\";\n  }\n  if((NumTraits<A::Scalar>::IsComplex) && (!NumTraits<B::Scalar>::IsComplex))\n  {\n    M ar(m,p); ar.setRandom();\n    M ai(m,p); ai.setRandom();\n    M b(p,n);  b.setRandom();\n    M cr(m,n); cr.setRandom();\n    M ci(m,n); ci.setRandom();\n    \n    BenchTimer t;\n    BENCH(t, tries, rep, matlab_cplx_real(ar,ai,b,cr,ci));\n    std::cout << \"\\\"matlab\\\" cpu    \" << t.best(CPU_TIMER)/rep  << \"s  \\t\" << (double(m)*n*p*rep*2/t.best(CPU_TIMER))*1e-9  <<  \" GFLOPS \\t(\" << t.total(CPU_TIMER)  << \"s)\\n\";\n    std::cout << \"\\\"matlab\\\" real   \" << t.best(REAL_TIMER)/rep << \"s  \\t\" << (double(m)*n*p*rep*2/t.best(REAL_TIMER))*1e-9 <<  \" GFLOPS \\t(\" << t.total(REAL_TIMER) << \"s)\\n\";\n  }\n  #endif\n\n  return 0;\n}\n\n"
  },
  {
    "path": "include/eigen3/bench/bench_multi_compilers.sh",
    "content": "#!/bin/bash\n\nif (($# < 2)); then\n    echo \"Usage: $0 compilerlist.txt benchfile.cpp\"\nelse\n\ncompilerlist=$1\nbenchfile=$2\n\ng=0\nsource $compilerlist\n\n# for each compiler, compile benchfile and run the benchmark\nfor (( i=0 ; i<g ; ++i )) ; do\n  # check the compiler exists\n  compiler=`echo ${CLIST[$i]} | cut -d \" \" -f 1`\n  if [ -e `which $compiler` ]; then\n    echo \"${CLIST[$i]}\"\n#     echo \"${CLIST[$i]} $benchfile -I.. -o bench~\"\n#     if [ -e ./.bench ] ; then rm .bench; fi\n    ${CLIST[$i]} $benchfile -I.. -o .bench && ./.bench 2> /dev/null\n    echo \"\"\n  else\n    echo \"compiler not found: $compiler\"\n  fi\ndone\n\nfi\n"
  },
  {
    "path": "include/eigen3/bench/bench_norm.cpp",
    "content": "#include <typeinfo>\n#include <iostream>\n#include <Eigen/Core>\n#include \"BenchTimer.h\"\nusing namespace Eigen;\nusing namespace std;\n\ntemplate<typename T>\nEIGEN_DONT_INLINE typename T::Scalar sqsumNorm(T& v)\n{\n  return v.norm();\n}\n\ntemplate<typename T>\nEIGEN_DONT_INLINE typename T::Scalar stableNorm(T& v)\n{\n  return v.stableNorm();\n}\n\ntemplate<typename T>\nEIGEN_DONT_INLINE typename T::Scalar hypotNorm(T& v)\n{\n  return v.hypotNorm();\n}\n\ntemplate<typename T>\nEIGEN_DONT_INLINE typename T::Scalar blueNorm(T& v)\n{\n  return v.blueNorm();\n}\n\ntemplate<typename T>\nEIGEN_DONT_INLINE typename T::Scalar lapackNorm(T& v)\n{\n  typedef typename T::Scalar Scalar;\n  int n = v.size();\n  Scalar scale = 0;\n  Scalar ssq = 1;\n  for (int i=0;i<n;++i)\n  {\n    Scalar ax = std::abs(v.coeff(i));\n    if (scale >= ax)\n    {\n      ssq += numext::abs2(ax/scale);\n    }\n    else\n    {\n      ssq = Scalar(1) + ssq * numext::abs2(scale/ax);\n      scale = ax;\n    }\n  }\n  return scale * std::sqrt(ssq);\n}\n\ntemplate<typename T>\nEIGEN_DONT_INLINE typename T::Scalar twopassNorm(T& v)\n{\n  typedef typename T::Scalar Scalar;\n  Scalar s = v.array().abs().maxCoeff();\n  return s*(v/s).norm();\n}\n\ntemplate<typename T>\nEIGEN_DONT_INLINE typename T::Scalar bl2passNorm(T& v)\n{\n  return v.stableNorm();\n}\n\ntemplate<typename T>\nEIGEN_DONT_INLINE typename T::Scalar divacNorm(T& v)\n{\n  int n =v.size() / 2;\n  for (int i=0;i<n;++i)\n    v(i) = v(2*i)*v(2*i) + v(2*i+1)*v(2*i+1);\n  n = n/2;\n  while (n>0)\n  {\n    for (int i=0;i<n;++i)\n      v(i) = v(2*i) + v(2*i+1);\n    n = n/2;\n  }\n  return std::sqrt(v(0));\n}\n\nnamespace Eigen {\nnamespace internal {\n#ifdef EIGEN_VECTORIZE\nPacket4f plt(const Packet4f& a, Packet4f& b) { return _mm_cmplt_ps(a,b); }\nPacket2d plt(const Packet2d& a, Packet2d& b) { return _mm_cmplt_pd(a,b); }\n\nPacket4f pandnot(const Packet4f& a, Packet4f& b) { return _mm_andnot_ps(a,b); }\nPacket2d pandnot(const Packet2d& a, Packet2d& b) { return _mm_andnot_pd(a,b); }\n#endif\n}\n}\n\ntemplate<typename T>\nEIGEN_DONT_INLINE typename T::Scalar pblueNorm(const T& v)\n{\n  #ifndef EIGEN_VECTORIZE\n  return v.blueNorm();\n  #else\n  typedef typename T::Scalar Scalar;\n\n  static int nmax = 0;\n  static Scalar b1, b2, s1m, s2m, overfl, rbig, relerr;\n  int n;\n\n  if(nmax <= 0)\n  {\n    int nbig, ibeta, it, iemin, iemax, iexp;\n    Scalar abig, eps;\n\n    nbig  = std::numeric_limits<int>::max();            // largest integer\n    ibeta = std::numeric_limits<Scalar>::radix; //NumTraits<Scalar>::Base;                    // base for floating-point numbers\n    it    = std::numeric_limits<Scalar>::digits; //NumTraits<Scalar>::Mantissa;                // number of base-beta digits in mantissa\n    iemin = std::numeric_limits<Scalar>::min_exponent;  // minimum exponent\n    iemax = std::numeric_limits<Scalar>::max_exponent;  // maximum exponent\n    rbig  = std::numeric_limits<Scalar>::max();         // largest floating-point number\n\n    // Check the basic machine-dependent constants.\n    if(iemin > 1 - 2*it || 1+it>iemax || (it==2 && ibeta<5)\n      || (it<=4 && ibeta <= 3 ) || it<2)\n    {\n      eigen_assert(false && \"the algorithm cannot be guaranteed on this computer\");\n    }\n    iexp  = -((1-iemin)/2);\n    b1    = std::pow(ibeta, iexp);  // lower boundary of midrange\n    iexp  = (iemax + 1 - it)/2;\n    b2    = std::pow(ibeta,iexp);   // upper boundary of midrange\n\n    iexp  = (2-iemin)/2;\n    s1m   = std::pow(ibeta,iexp);   // scaling factor for lower range\n    iexp  = - ((iemax+it)/2);\n    s2m   = std::pow(ibeta,iexp);   // scaling factor for upper range\n\n    overfl  = rbig*s2m;          // overfow boundary for abig\n    eps     = std::pow(ibeta, 1-it);\n    relerr  = std::sqrt(eps);      // tolerance for neglecting asml\n    abig    = 1.0/eps - 1.0;\n    if (Scalar(nbig)>abig)  nmax = abig;  // largest safe n\n    else                    nmax = nbig;\n  }\n\n  typedef typename internal::packet_traits<Scalar>::type Packet;\n  const int ps = internal::packet_traits<Scalar>::size;\n  Packet pasml = internal::pset1<Packet>(Scalar(0));\n  Packet pamed = internal::pset1<Packet>(Scalar(0));\n  Packet pabig = internal::pset1<Packet>(Scalar(0));\n  Packet ps2m = internal::pset1<Packet>(s2m);\n  Packet ps1m = internal::pset1<Packet>(s1m);\n  Packet pb2  = internal::pset1<Packet>(b2);\n  Packet pb1  = internal::pset1<Packet>(b1);\n  for(int j=0; j<v.size(); j+=ps)\n  {\n    Packet ax = internal::pabs(v.template packet<Aligned>(j));\n    Packet ax_s2m = internal::pmul(ax,ps2m);\n    Packet ax_s1m = internal::pmul(ax,ps1m);\n    Packet maskBig = internal::plt(pb2,ax);\n    Packet maskSml = internal::plt(ax,pb1);\n\n//     Packet maskMed = internal::pand(maskSml,maskBig);\n//     Packet scale = internal::pset1(Scalar(0));\n//     scale = internal::por(scale, internal::pand(maskBig,ps2m));\n//     scale = internal::por(scale, internal::pand(maskSml,ps1m));\n//     scale = internal::por(scale, internal::pandnot(internal::pset1(Scalar(1)),maskMed));\n//     ax = internal::pmul(ax,scale);\n//     ax = internal::pmul(ax,ax);\n//     pabig = internal::padd(pabig, internal::pand(maskBig, ax));\n//     pasml = internal::padd(pasml, internal::pand(maskSml, ax));\n//     pamed = internal::padd(pamed, internal::pandnot(ax,maskMed));\n\n\n    pabig = internal::padd(pabig, internal::pand(maskBig, internal::pmul(ax_s2m,ax_s2m)));\n    pasml = internal::padd(pasml, internal::pand(maskSml, internal::pmul(ax_s1m,ax_s1m)));\n    pamed = internal::padd(pamed, internal::pandnot(internal::pmul(ax,ax),internal::pand(maskSml,maskBig)));\n  }\n  Scalar abig = internal::predux(pabig);\n  Scalar asml = internal::predux(pasml);\n  Scalar amed = internal::predux(pamed);\n  if(abig > Scalar(0))\n  {\n    abig = std::sqrt(abig);\n    if(abig > overfl)\n    {\n      eigen_assert(false && \"overflow\");\n      return rbig;\n    }\n    if(amed > Scalar(0))\n    {\n      abig = abig/s2m;\n      amed = std::sqrt(amed);\n    }\n    else\n    {\n      return abig/s2m;\n    }\n\n  }\n  else if(asml > Scalar(0))\n  {\n    if (amed > Scalar(0))\n    {\n      abig = std::sqrt(amed);\n      amed = std::sqrt(asml) / s1m;\n    }\n    else\n    {\n      return std::sqrt(asml)/s1m;\n    }\n  }\n  else\n  {\n    return std::sqrt(amed);\n  }\n  asml = std::min(abig, amed);\n  abig = std::max(abig, amed);\n  if(asml <= abig*relerr)\n    return abig;\n  else\n    return abig * std::sqrt(Scalar(1) + numext::abs2(asml/abig));\n  #endif\n}\n\n#define BENCH_PERF(NRM) { \\\n  float af = 0; double ad = 0; std::complex<float> ac = 0; \\\n  Eigen::BenchTimer tf, td, tcf; tf.reset(); td.reset(); tcf.reset();\\\n  for (int k=0; k<tries; ++k) { \\\n    tf.start(); \\\n    for (int i=0; i<iters; ++i) { af += NRM(vf); } \\\n    tf.stop(); \\\n  } \\\n  for (int k=0; k<tries; ++k) { \\\n    td.start(); \\\n    for (int i=0; i<iters; ++i) { ad += NRM(vd); } \\\n    td.stop(); \\\n  } \\\n  /*for (int k=0; k<std::max(1,tries/3); ++k) { \\\n    tcf.start(); \\\n    for (int i=0; i<iters; ++i) { ac += NRM(vcf); } \\\n    tcf.stop(); \\\n  } */\\\n  std::cout << #NRM << \"\\t\" << tf.value() << \"   \" << td.value() <<  \"    \" << tcf.value() << \"\\n\"; \\\n}\n\nvoid check_accuracy(double basef, double based, int s)\n{\n  double yf = basef * std::abs(internal::random<double>());\n  double yd = based * std::abs(internal::random<double>());\n  VectorXf vf = VectorXf::Ones(s) * yf;\n  VectorXd vd = VectorXd::Ones(s) * yd;\n\n  std::cout << \"reference\\t\" << std::sqrt(double(s))*yf << \"\\t\" << std::sqrt(double(s))*yd << \"\\n\";\n  std::cout << \"sqsumNorm\\t\" << sqsumNorm(vf) << \"\\t\" << sqsumNorm(vd) << \"\\n\";\n  std::cout << \"hypotNorm\\t\" << hypotNorm(vf) << \"\\t\" << hypotNorm(vd) << \"\\n\";\n  std::cout << \"blueNorm\\t\" << blueNorm(vf) << \"\\t\" << blueNorm(vd) << \"\\n\";\n  std::cout << \"pblueNorm\\t\" << pblueNorm(vf) << \"\\t\" << pblueNorm(vd) << \"\\n\";\n  std::cout << \"lapackNorm\\t\" << lapackNorm(vf) << \"\\t\" << lapackNorm(vd) << \"\\n\";\n  std::cout << \"twopassNorm\\t\" << twopassNorm(vf) << \"\\t\" << twopassNorm(vd) << \"\\n\";\n  std::cout << \"bl2passNorm\\t\" << bl2passNorm(vf) << \"\\t\" << bl2passNorm(vd) << \"\\n\";\n}\n\nvoid check_accuracy_var(int ef0, int ef1, int ed0, int ed1, int s)\n{\n  VectorXf vf(s);\n  VectorXd vd(s);\n  for (int i=0; i<s; ++i)\n  {\n    vf[i] = std::abs(internal::random<double>()) * std::pow(double(10), internal::random<int>(ef0,ef1));\n    vd[i] = std::abs(internal::random<double>()) * std::pow(double(10), internal::random<int>(ed0,ed1));\n  }\n\n  //std::cout << \"reference\\t\" << internal::sqrt(double(s))*yf << \"\\t\" << internal::sqrt(double(s))*yd << \"\\n\";\n  std::cout << \"sqsumNorm\\t\"  << sqsumNorm(vf)  << \"\\t\" << sqsumNorm(vd)  << \"\\t\" << sqsumNorm(vf.cast<long double>()) << \"\\t\" << sqsumNorm(vd.cast<long double>()) << \"\\n\";\n  std::cout << \"hypotNorm\\t\"  << hypotNorm(vf)  << \"\\t\" << hypotNorm(vd)  << \"\\t\" << hypotNorm(vf.cast<long double>()) << \"\\t\" << hypotNorm(vd.cast<long double>()) << \"\\n\";\n  std::cout << \"blueNorm\\t\"   << blueNorm(vf)   << \"\\t\" << blueNorm(vd)   << \"\\t\" << blueNorm(vf.cast<long double>()) << \"\\t\" << blueNorm(vd.cast<long double>()) << \"\\n\";\n  std::cout << \"pblueNorm\\t\"  << pblueNorm(vf)  << \"\\t\" << pblueNorm(vd)  << \"\\t\" << blueNorm(vf.cast<long double>()) << \"\\t\" << blueNorm(vd.cast<long double>()) << \"\\n\";\n  std::cout << \"lapackNorm\\t\" << lapackNorm(vf) << \"\\t\" << lapackNorm(vd) << \"\\t\" << lapackNorm(vf.cast<long double>()) << \"\\t\" << lapackNorm(vd.cast<long double>()) << \"\\n\";\n  std::cout << \"twopassNorm\\t\" << twopassNorm(vf) << \"\\t\" << twopassNorm(vd) << \"\\t\" << twopassNorm(vf.cast<long double>()) << \"\\t\" << twopassNorm(vd.cast<long double>()) << \"\\n\";\n//   std::cout << \"bl2passNorm\\t\" << bl2passNorm(vf) << \"\\t\" << bl2passNorm(vd) << \"\\t\" << bl2passNorm(vf.cast<long double>()) << \"\\t\" << bl2passNorm(vd.cast<long double>()) << \"\\n\";\n}\n\nint main(int argc, char** argv)\n{\n  int tries = 10;\n  int iters = 100000;\n  double y = 1.1345743233455785456788e12 * internal::random<double>();\n  VectorXf v = VectorXf::Ones(1024) * y;\n\n// return 0;\n  int s = 10000;\n  double basef_ok = 1.1345743233455785456788e15;\n  double based_ok = 1.1345743233455785456788e95;\n\n  double basef_under = 1.1345743233455785456788e-27;\n  double based_under = 1.1345743233455785456788e-303;\n\n  double basef_over = 1.1345743233455785456788e+27;\n  double based_over = 1.1345743233455785456788e+302;\n\n  std::cout.precision(20);\n\n  std::cerr << \"\\nNo under/overflow:\\n\";\n  check_accuracy(basef_ok, based_ok, s);\n\n  std::cerr << \"\\nUnderflow:\\n\";\n  check_accuracy(basef_under, based_under, s);\n\n  std::cerr << \"\\nOverflow:\\n\";\n  check_accuracy(basef_over, based_over, s);\n\n  std::cerr << \"\\nVarying (over):\\n\";\n  for (int k=0; k<1; ++k)\n  {\n    check_accuracy_var(20,27,190,302,s);\n    std::cout << \"\\n\";\n  }\n\n  std::cerr << \"\\nVarying (under):\\n\";\n  for (int k=0; k<1; ++k)\n  {\n    check_accuracy_var(-27,20,-302,-190,s);\n    std::cout << \"\\n\";\n  }\n\n  y = 1;\n  std::cout.precision(4);\n  int s1 = 1024*1024*32;\n  std::cerr << \"Performance (out of cache, \" << s1 << \"):\\n\";\n  {\n    int iters = 1;\n    VectorXf vf = VectorXf::Random(s1) * y;\n    VectorXd vd = VectorXd::Random(s1) * y;\n    VectorXcf vcf = VectorXcf::Random(s1) * y;\n    BENCH_PERF(sqsumNorm);\n    BENCH_PERF(stableNorm);\n    BENCH_PERF(blueNorm);\n    BENCH_PERF(pblueNorm);\n    BENCH_PERF(lapackNorm);\n    BENCH_PERF(hypotNorm);\n    BENCH_PERF(twopassNorm);\n    BENCH_PERF(bl2passNorm);\n  }\n\n  std::cerr << \"\\nPerformance (in cache, \" << 512 << \"):\\n\";\n  {\n    int iters = 100000;\n    VectorXf vf = VectorXf::Random(512) * y;\n    VectorXd vd = VectorXd::Random(512) * y;\n    VectorXcf vcf = VectorXcf::Random(512) * y;\n    BENCH_PERF(sqsumNorm);\n    BENCH_PERF(stableNorm);\n    BENCH_PERF(blueNorm);\n    BENCH_PERF(pblueNorm);\n    BENCH_PERF(lapackNorm);\n    BENCH_PERF(hypotNorm);\n    BENCH_PERF(twopassNorm);\n    BENCH_PERF(bl2passNorm);\n  }\n}\n"
  },
  {
    "path": "include/eigen3/bench/bench_reverse.cpp",
    "content": "\n#include <iostream>\n#include <Eigen/Core>\n#include <bench/BenchUtil.h>\nusing namespace Eigen;\n\n#ifndef REPEAT\n#define REPEAT 100000\n#endif\n\n#ifndef TRIES\n#define TRIES 20\n#endif\n\ntypedef double Scalar;\n\ntemplate <typename MatrixType>\n__attribute__ ((noinline)) void bench_reverse(const MatrixType& m)\n{\n  int rows = m.rows();\n  int cols = m.cols();\n  int size = m.size();\n\n  int repeats = (REPEAT*1000)/size;\n  MatrixType a = MatrixType::Random(rows,cols);\n  MatrixType b = MatrixType::Random(rows,cols);\n\n  BenchTimer timerB, timerH, timerV;\n\n  Scalar acc = 0;\n  int r = internal::random<int>(0,rows-1);\n  int c = internal::random<int>(0,cols-1);\n  for (int t=0; t<TRIES; ++t)\n  {\n    timerB.start();\n    for (int k=0; k<repeats; ++k)\n    {\n      asm(\"#begin foo\");\n      b = a.reverse();\n      asm(\"#end foo\");\n      acc += b.coeff(r,c);\n    }\n    timerB.stop();\n  }\n\n  if (MatrixType::RowsAtCompileTime==Dynamic)\n    std::cout << \"dyn   \";\n  else\n    std::cout << \"fixed \";\n  std::cout << rows << \" x \" << cols << \" \\t\"\n            << (timerB.value() * REPEAT) / repeats << \"s \"\n            << \"(\" << 1e-6 * size*repeats/timerB.value() << \" MFLOPS)\\t\";\n\n  std::cout << \"\\n\";\n  // make sure the compiler does not optimize too much\n  if (acc==123)\n    std::cout << acc;\n}\n\nint main(int argc, char* argv[])\n{\n  const int dynsizes[] = {4,6,8,16,24,32,49,64,128,256,512,900,0};\n  std::cout << \"size            no sqrt                           standard\";\n//   #ifdef BENCH_GSL\n//   std::cout << \"       GSL (standard + double + ATLAS)  \";\n//   #endif\n  std::cout << \"\\n\";\n  for (uint i=0; dynsizes[i]>0; ++i)\n  {\n    bench_reverse(Matrix<Scalar,Dynamic,Dynamic>(dynsizes[i],dynsizes[i]));\n    bench_reverse(Matrix<Scalar,Dynamic,1>(dynsizes[i]*dynsizes[i]));\n  }\n//   bench_reverse(Matrix<Scalar,2,2>());\n//   bench_reverse(Matrix<Scalar,3,3>());\n//   bench_reverse(Matrix<Scalar,4,4>());\n//   bench_reverse(Matrix<Scalar,5,5>());\n//   bench_reverse(Matrix<Scalar,6,6>());\n//   bench_reverse(Matrix<Scalar,7,7>());\n//   bench_reverse(Matrix<Scalar,8,8>());\n//   bench_reverse(Matrix<Scalar,12,12>());\n//   bench_reverse(Matrix<Scalar,16,16>());\n  return 0;\n}\n\n"
  },
  {
    "path": "include/eigen3/bench/bench_sum.cpp",
    "content": "#include <iostream>\n#include <Eigen/Core>\nusing namespace Eigen;\nusing namespace std;\n\nint main() \n{\n  typedef Matrix<SCALAR,Eigen::Dynamic,1> Vec;\n  Vec v(SIZE);\n  v.setZero();\n  v[0] = 1;\n  v[1] = 2;\n  for(int i = 0; i < 1000000; i++)\n  {\n    v.coeffRef(0) += v.sum() * SCALAR(1e-20);\n  }\n  cout << v.sum() << endl;\n}\n"
  },
  {
    "path": "include/eigen3/bench/bench_unrolling",
    "content": "#!/bin/bash\n\n# gcc : CXX=\"g++  -finline-limit=10000 -ftemplate-depth-2000 --param max-inline-recursive-depth=2000\"\n# icc : CXX=\"icpc -fast -no-inline-max-size -fno-exceptions\"\nCXX=${CXX-g++  -finline-limit=10000 -ftemplate-depth-2000 --param max-inline-recursive-depth=2000} # default value\n\nfor ((i=1; i<16; ++i)); do\n    echo \"Matrix size: $i x $i :\"\n    $CXX -O3 -I.. -DNDEBUG  benchmark.cpp -DMATSIZE=$i -DEIGEN_UNROLLING_LIMIT=400 -o benchmark && time ./benchmark >/dev/null\n    $CXX -O3 -I.. -DNDEBUG -finline-limit=10000 benchmark.cpp -DMATSIZE=$i -DEIGEN_DONT_USE_UNROLLED_LOOPS=1 -o benchmark && time ./benchmark >/dev/null\n    echo \" \"\ndone\n"
  },
  {
    "path": "include/eigen3/bench/benchmark-blocking-sizes.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Benoit Jacob <benoitjacob@google.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include <iostream>\n#include <cstdint>\n#include <cstdlib>\n#include <vector>\n#include <fstream>\n#include <memory>\n#include <cstdio>\n\nbool eigen_use_specific_block_size;\nint eigen_block_size_k, eigen_block_size_m, eigen_block_size_n;\n#define EIGEN_TEST_SPECIFIC_BLOCKING_SIZES eigen_use_specific_block_size\n#define EIGEN_TEST_SPECIFIC_BLOCKING_SIZE_K eigen_block_size_k\n#define EIGEN_TEST_SPECIFIC_BLOCKING_SIZE_M eigen_block_size_m\n#define EIGEN_TEST_SPECIFIC_BLOCKING_SIZE_N eigen_block_size_n\n#include <Eigen/Core>\n\n#include <bench/BenchTimer.h>\n\nusing namespace Eigen;\nusing namespace std;\n\nstatic BenchTimer timer;\n\n// how many times we repeat each measurement.\n// measurements are randomly shuffled - we're not doing\n// all N identical measurements in a row.\nconst int measurement_repetitions = 3;\n\n// Timings below this value are too short to be accurate,\n// we'll repeat measurements with more iterations until\n// we get a timing above that threshold.\nconst float min_accurate_time = 1e-2f;\n\n// See --min-working-set-size command line parameter.\nsize_t min_working_set_size = 0;\n\nfloat max_clock_speed = 0.0f;\n\n// range of sizes that we will benchmark (in all 3 K,M,N dimensions)\nconst size_t maxsize = 2048;\nconst size_t minsize = 16;\n\ntypedef MatrixXf MatrixType;\ntypedef MatrixType::Scalar Scalar;\ntypedef internal::packet_traits<Scalar>::type Packet;\n\nstatic_assert((maxsize & (maxsize - 1)) == 0, \"maxsize must be a power of two\");\nstatic_assert((minsize & (minsize - 1)) == 0, \"minsize must be a power of two\");\nstatic_assert(maxsize > minsize, \"maxsize must be larger than minsize\");\nstatic_assert(maxsize < (minsize << 16), \"maxsize must be less than (minsize<<16)\");\n\n// just a helper to store a triple of K,M,N sizes for matrix product\nstruct size_triple_t\n{\n  size_t k, m, n;\n  size_triple_t() : k(0), m(0), n(0) {}\n  size_triple_t(size_t _k, size_t _m, size_t _n) : k(_k), m(_m), n(_n) {}\n  size_triple_t(const size_triple_t& o) : k(o.k), m(o.m), n(o.n) {}\n  size_triple_t(uint16_t compact)\n  {\n    k = 1 << ((compact & 0xf00) >> 8);\n    m = 1 << ((compact & 0x0f0) >> 4);\n    n = 1 << ((compact & 0x00f) >> 0);\n  }\n};\n\nuint8_t log2_pot(size_t x) {\n  size_t l = 0;\n  while (x >>= 1) l++;\n  return l;\n}\n\n// Convert between size tripes and a compact form fitting in 12 bits\n// where each size, which must be a POT, is encoded as its log2, on 4 bits\n// so the largest representable size is 2^15 == 32k  ... big enough.\nuint16_t compact_size_triple(size_t k, size_t m, size_t n)\n{\n  return (log2_pot(k) << 8) | (log2_pot(m) << 4) | log2_pot(n);\n}\n\nuint16_t compact_size_triple(const size_triple_t& t)\n{\n  return compact_size_triple(t.k, t.m, t.n);\n}\n\n// A single benchmark. Initially only contains benchmark params.\n// Then call run(), which stores the result in the gflops field.\nstruct benchmark_t\n{\n  uint16_t compact_product_size;\n  uint16_t compact_block_size;\n  bool use_default_block_size;\n  float gflops;\n  benchmark_t()\n    : compact_product_size(0)\n    , compact_block_size(0)\n    , use_default_block_size(false)\n    , gflops(0)\n  {\n  }\n  benchmark_t(size_t pk, size_t pm, size_t pn,\n              size_t bk, size_t bm, size_t bn)\n    : compact_product_size(compact_size_triple(pk, pm, pn))\n    , compact_block_size(compact_size_triple(bk, bm, bn))\n    , use_default_block_size(false)\n    , gflops(0)\n  {}\n  benchmark_t(size_t pk, size_t pm, size_t pn)\n    : compact_product_size(compact_size_triple(pk, pm, pn))\n    , compact_block_size(0)\n    , use_default_block_size(true)\n    , gflops(0)\n  {}\n\n  void run();\n};\n\nostream& operator<<(ostream& s, const benchmark_t& b)\n{\n  s << hex << b.compact_product_size << dec;\n  if (b.use_default_block_size) {\n    size_triple_t t(b.compact_product_size);\n    Index k = t.k, m = t.m, n = t.n;\n    internal::computeProductBlockingSizes<Scalar, Scalar>(k, m, n);\n    s << \" default(\" << k << \", \" << m << \", \" << n << \")\";\n  } else {\n    s << \" \" << hex << b.compact_block_size << dec;\n  }\n  s << \" \" << b.gflops;\n  return s;\n}\n\n// We sort first by increasing benchmark parameters,\n// then by decreasing performance.\nbool operator<(const benchmark_t& b1, const benchmark_t& b2)\n{ \n  return b1.compact_product_size < b2.compact_product_size ||\n           (b1.compact_product_size == b2.compact_product_size && (\n             (b1.compact_block_size < b2.compact_block_size || (\n               b1.compact_block_size == b2.compact_block_size &&\n                 b1.gflops > b2.gflops))));\n}\n\nvoid benchmark_t::run()\n{\n  size_triple_t productsizes(compact_product_size);\n\n  if (use_default_block_size) {\n    eigen_use_specific_block_size = false;\n  } else {\n    // feed eigen with our custom blocking params\n    eigen_use_specific_block_size = true;\n    size_triple_t blocksizes(compact_block_size);\n    eigen_block_size_k = blocksizes.k;\n    eigen_block_size_m = blocksizes.m;\n    eigen_block_size_n = blocksizes.n;\n  }\n\n  // set up the matrix pool\n\n  const size_t combined_three_matrices_sizes =\n    sizeof(Scalar) *\n      (productsizes.k * productsizes.m +\n       productsizes.k * productsizes.n +\n       productsizes.m * productsizes.n);\n\n  // 64 M is large enough that nobody has a cache bigger than that,\n  // while still being small enough that everybody has this much RAM,\n  // so conveniently we don't need to special-case platforms here.\n  const size_t unlikely_large_cache_size = 64 << 20;\n\n  const size_t working_set_size =\n    min_working_set_size ? min_working_set_size : unlikely_large_cache_size;\n\n  const size_t matrix_pool_size =\n    1 + working_set_size / combined_three_matrices_sizes;\n\n  MatrixType *lhs = new MatrixType[matrix_pool_size];\n  MatrixType *rhs = new MatrixType[matrix_pool_size];\n  MatrixType *dst = new MatrixType[matrix_pool_size];\n  \n  for (size_t i = 0; i < matrix_pool_size; i++) {\n    lhs[i] = MatrixType::Zero(productsizes.m, productsizes.k);\n    rhs[i] = MatrixType::Zero(productsizes.k, productsizes.n);\n    dst[i] = MatrixType::Zero(productsizes.m, productsizes.n);\n  }\n\n  // main benchmark loop\n\n  int iters_at_a_time = 1;\n  float time_per_iter = 0.0f;\n  size_t matrix_index = 0;\n  while (true) {\n\n    double starttime = timer.getCpuTime();\n    for (int i = 0; i < iters_at_a_time; i++) {\n      dst[matrix_index].noalias() = lhs[matrix_index] * rhs[matrix_index];\n      matrix_index++;\n      if (matrix_index == matrix_pool_size) {\n        matrix_index = 0;\n      }\n    }\n    double endtime = timer.getCpuTime();\n\n    const float timing = float(endtime - starttime);\n\n    if (timing >= min_accurate_time) {\n      time_per_iter = timing / iters_at_a_time;\n      break;\n    }\n\n    iters_at_a_time *= 2;\n  }\n\n  delete[] lhs;\n  delete[] rhs;\n  delete[] dst;\n\n  gflops = 2e-9 * productsizes.k * productsizes.m * productsizes.n / time_per_iter;\n}\n\nvoid print_cpuinfo()\n{\n#ifdef __linux__\n  cout << \"contents of /proc/cpuinfo:\" << endl;\n  string line;\n  ifstream cpuinfo(\"/proc/cpuinfo\");\n  if (cpuinfo.is_open()) {\n    while (getline(cpuinfo, line)) {\n      cout << line << endl;\n    }\n    cpuinfo.close();\n  }\n  cout << endl;\n#elif defined __APPLE__\n  cout << \"output of sysctl hw:\" << endl;\n  system(\"sysctl hw\");\n  cout << endl;\n#endif\n}\n\ntemplate <typename T>\nstring type_name()\n{\n  return \"unknown\";\n}\n\ntemplate<>\nstring type_name<float>()\n{\n  return \"float\";\n}\n\ntemplate<>\nstring type_name<double>()\n{\n  return \"double\";\n}\n\nstruct action_t\n{\n  virtual const char* invokation_name() const { abort(); return nullptr; }\n  virtual void run() const { abort(); }\n  virtual ~action_t() {}\n};\n\nvoid show_usage_and_exit(int /*argc*/, char* argv[],\n                         const vector<unique_ptr<action_t>>& available_actions)\n{\n  cerr << \"usage: \" << argv[0] << \" <action> [options...]\" << endl << endl;\n  cerr << \"available actions:\" << endl << endl;\n  for (auto it = available_actions.begin(); it != available_actions.end(); ++it) {\n    cerr << \"  \" << (*it)->invokation_name() << endl;\n  }\n  cerr << endl;\n  cerr << \"options:\" << endl << endl;\n  cerr << \"  --min-working-set-size=N:\" << endl;\n  cerr << \"       Set the minimum working set size to N bytes.\" << endl;\n  cerr << \"       This is rounded up as needed to a multiple of matrix size.\" << endl;\n  cerr << \"       A larger working set lowers the chance of a warm cache.\" << endl;\n  cerr << \"       The default value 0 means use a large enough working\" << endl;\n  cerr << \"       set to likely outsize caches.\" << endl;\n  cerr << \"       A value of 1 (that is, 1 byte) would mean don't do anything to\" << endl;\n  cerr << \"       avoid warm caches.\" << endl;\n  exit(1);\n}\n     \nfloat measure_clock_speed()\n{\n  cerr << \"Measuring clock speed...                              \\r\" << flush;\n          \n  vector<float> all_gflops;\n  for (int i = 0; i < 8; i++) {\n    benchmark_t b(1024, 1024, 1024);\n    b.run();\n    all_gflops.push_back(b.gflops);\n  }\n\n  sort(all_gflops.begin(), all_gflops.end());\n  float stable_estimate = all_gflops[2] + all_gflops[3] + all_gflops[4] + all_gflops[5];\n\n  // multiply by an arbitrary constant to discourage trying doing anything with the\n  // returned values besides just comparing them with each other.\n  float result = stable_estimate * 123.456f;\n\n  return result;\n}\n\nstruct human_duration_t\n{\n  int seconds;\n  human_duration_t(int s) : seconds(s) {}\n};\n\nostream& operator<<(ostream& s, const human_duration_t& d)\n{\n  int remainder = d.seconds;\n  if (remainder > 3600) {\n    int hours = remainder / 3600;\n    s << hours << \" h \";\n    remainder -= hours * 3600;\n  }\n  if (remainder > 60) {\n    int minutes = remainder / 60;\n    s << minutes << \" min \";\n    remainder -= minutes * 60;\n  }\n  if (d.seconds < 600) {\n    s << remainder << \" s\";\n  }\n  return s;\n}\n\nconst char session_filename[] = \"/data/local/tmp/benchmark-blocking-sizes-session.data\";\n\nvoid serialize_benchmarks(const char* filename, const vector<benchmark_t>& benchmarks, size_t first_benchmark_to_run)\n{\n  FILE* file = fopen(filename, \"w\");\n  if (!file) {\n    cerr << \"Could not open file \" << filename << \" for writing.\" << endl;\n    cerr << \"Do you have write permissions on the current working directory?\" << endl;\n    exit(1);\n  }\n  size_t benchmarks_vector_size = benchmarks.size();\n  fwrite(&max_clock_speed, sizeof(max_clock_speed), 1, file);\n  fwrite(&benchmarks_vector_size, sizeof(benchmarks_vector_size), 1, file);\n  fwrite(&first_benchmark_to_run, sizeof(first_benchmark_to_run), 1, file);\n  fwrite(benchmarks.data(), sizeof(benchmark_t), benchmarks.size(), file);\n  fclose(file);\n}\n\nbool deserialize_benchmarks(const char* filename, vector<benchmark_t>& benchmarks, size_t& first_benchmark_to_run)\n{\n  FILE* file = fopen(filename, \"r\");\n  if (!file) {\n    return false;\n  }\n  if (1 != fread(&max_clock_speed, sizeof(max_clock_speed), 1, file)) {\n    return false;\n  }\n  size_t benchmarks_vector_size = 0;\n  if (1 != fread(&benchmarks_vector_size, sizeof(benchmarks_vector_size), 1, file)) {\n    return false;\n  }\n  if (1 != fread(&first_benchmark_to_run, sizeof(first_benchmark_to_run), 1, file)) {\n    return false;\n  }\n  benchmarks.resize(benchmarks_vector_size);\n  if (benchmarks.size() != fread(benchmarks.data(), sizeof(benchmark_t), benchmarks.size(), file)) {\n    return false;\n  }\n  unlink(filename);\n  return true;\n}\n\nvoid try_run_some_benchmarks(\n  vector<benchmark_t>& benchmarks,\n  double time_start,\n  size_t& first_benchmark_to_run)\n{\n  if (first_benchmark_to_run == benchmarks.size()) {\n    return;\n  }\n\n  double time_last_progress_update = 0;\n  double time_last_clock_speed_measurement = 0;\n  double time_now = 0;\n\n  size_t benchmark_index = first_benchmark_to_run;\n\n  while (true) {\n    float ratio_done = float(benchmark_index) / benchmarks.size();\n    time_now = timer.getRealTime();\n\n    // We check clock speed every minute and at the end.\n    if (benchmark_index == benchmarks.size() ||\n        time_now > time_last_clock_speed_measurement + 60.0f)\n    {\n      time_last_clock_speed_measurement = time_now;\n\n      // Ensure that clock speed is as expected\n      float current_clock_speed = measure_clock_speed();\n\n      // The tolerance needs to be smaller than the relative difference between\n      // clock speeds that a device could operate under.\n      // It seems unlikely that a device would be throttling clock speeds by\n      // amounts smaller than 2%.\n      // With a value of 1%, I was getting within noise on a Sandy Bridge.\n      const float clock_speed_tolerance = 0.02f;\n\n      if (current_clock_speed > (1 + clock_speed_tolerance) * max_clock_speed) {\n        // Clock speed is now higher than we previously measured.\n        // Either our initial measurement was inaccurate, which won't happen\n        // too many times as we are keeping the best clock speed value and\n        // and allowing some tolerance; or something really weird happened,\n        // which invalidates all benchmark results collected so far.\n        // Either way, we better restart all over again now.\n        if (benchmark_index) {\n          cerr << \"Restarting at \" << 100.0f * ratio_done\n               << \" % because clock speed increased.          \" << endl;\n        }\n        max_clock_speed = current_clock_speed;\n        first_benchmark_to_run = 0;\n        return;\n      }\n\n      bool rerun_last_tests = false;\n\n      if (current_clock_speed < (1 - clock_speed_tolerance) * max_clock_speed) {\n        cerr << \"Measurements completed so far: \"\n             << 100.0f * ratio_done\n             << \" %                             \" << endl;\n        cerr << \"Clock speed seems to be only \"\n             << current_clock_speed/max_clock_speed\n             << \" times what it used to be.\" << endl;\n\n        unsigned int seconds_to_sleep_if_lower_clock_speed = 1;\n\n        while (current_clock_speed < (1 - clock_speed_tolerance) * max_clock_speed) {\n          if (seconds_to_sleep_if_lower_clock_speed > 32) {\n            cerr << \"Sleeping longer probably won't make a difference.\" << endl;\n            cerr << \"Serializing benchmarks to \" << session_filename << endl;\n            serialize_benchmarks(session_filename, benchmarks, first_benchmark_to_run);\n            cerr << \"Now restart this benchmark, and it should pick up where we left.\" << endl;\n            exit(2);\n          }\n          rerun_last_tests = true;\n          cerr << \"Sleeping \"\n               << seconds_to_sleep_if_lower_clock_speed\n               << \" s...                                   \\r\" << endl;\n          sleep(seconds_to_sleep_if_lower_clock_speed);\n          current_clock_speed = measure_clock_speed();\n          seconds_to_sleep_if_lower_clock_speed *= 2;\n        }\n      }\n\n      if (rerun_last_tests) {\n        cerr << \"Redoing the last \"\n             << 100.0f * float(benchmark_index - first_benchmark_to_run) / benchmarks.size()\n             << \" % because clock speed had been low.   \" << endl;\n        return;\n      }\n\n      // nothing wrong with the clock speed so far, so there won't be a need to rerun\n      // benchmarks run so far in case we later encounter a lower clock speed.\n      first_benchmark_to_run = benchmark_index;\n    }\n\n    if (benchmark_index == benchmarks.size()) {\n      // We're done!\n      first_benchmark_to_run = benchmarks.size();\n      // Erase progress info\n      cerr << \"                                                            \" << endl;\n      return;\n    }\n\n    // Display progress info on stderr\n    if (time_now > time_last_progress_update + 1.0f) {\n      time_last_progress_update = time_now;\n      cerr << \"Measurements... \" << 100.0f * ratio_done\n           << \" %, ETA \"\n           << human_duration_t(float(time_now - time_start) * (1.0f - ratio_done) / ratio_done)\n           << \"                          \\r\" << flush;\n    }\n\n    // This is where we actually run a benchmark!\n    benchmarks[benchmark_index].run();\n    benchmark_index++;\n  }\n}\n\nvoid run_benchmarks(vector<benchmark_t>& benchmarks)\n{\n  size_t first_benchmark_to_run;\n  vector<benchmark_t> deserialized_benchmarks;\n  bool use_deserialized_benchmarks = false;\n  if (deserialize_benchmarks(session_filename, deserialized_benchmarks, first_benchmark_to_run)) {\n    cerr << \"Found serialized session with \"\n         << 100.0f * first_benchmark_to_run / deserialized_benchmarks.size()\n         << \" % already done\" << endl;\n    if (deserialized_benchmarks.size() == benchmarks.size() &&\n        first_benchmark_to_run > 0 &&\n        first_benchmark_to_run < benchmarks.size())\n    {\n      use_deserialized_benchmarks = true;\n    }\n  }\n\n  if (use_deserialized_benchmarks) {\n    benchmarks = deserialized_benchmarks;\n  } else {\n    // not using deserialized benchmarks, starting from scratch\n    first_benchmark_to_run = 0;\n\n    // Randomly shuffling benchmarks allows us to get accurate enough progress info,\n    // as now the cheap/expensive benchmarks are randomly mixed so they average out.\n    // It also means that if data is corrupted for some time span, the odds are that\n    // not all repetitions of a given benchmark will be corrupted.\n    random_shuffle(benchmarks.begin(), benchmarks.end());\n  }\n\n  for (int i = 0; i < 4; i++) {\n    max_clock_speed = max(max_clock_speed, measure_clock_speed());\n  }\n  \n  double time_start = 0.0;\n  while (first_benchmark_to_run < benchmarks.size()) {\n    if (first_benchmark_to_run == 0) {\n      time_start = timer.getRealTime();\n    }\n    try_run_some_benchmarks(benchmarks,\n                            time_start,\n                            first_benchmark_to_run);\n  }\n\n  // Sort timings by increasing benchmark parameters, and decreasing gflops.\n  // The latter is very important. It means that we can ignore all but the first\n  // benchmark with given parameters.\n  sort(benchmarks.begin(), benchmarks.end());\n\n  // Collect best (i.e. now first) results for each parameter values.\n  vector<benchmark_t> best_benchmarks;\n  for (auto it = benchmarks.begin(); it != benchmarks.end(); ++it) {\n    if (best_benchmarks.empty() ||\n        best_benchmarks.back().compact_product_size != it->compact_product_size ||\n        best_benchmarks.back().compact_block_size != it->compact_block_size)\n    {\n      best_benchmarks.push_back(*it);\n    }\n  }\n\n  // keep and return only the best benchmarks\n  benchmarks = best_benchmarks;\n}\n\nstruct measure_all_pot_sizes_action_t : action_t\n{\n  virtual const char* invokation_name() const { return \"all-pot-sizes\"; }\n  virtual void run() const\n  {\n    vector<benchmark_t> benchmarks;\n    for (int repetition = 0; repetition < measurement_repetitions; repetition++) {\n      for (size_t ksize = minsize; ksize <= maxsize; ksize *= 2) {\n        for (size_t msize = minsize; msize <= maxsize; msize *= 2) {\n          for (size_t nsize = minsize; nsize <= maxsize; nsize *= 2) {\n            for (size_t kblock = minsize; kblock <= ksize; kblock *= 2) {\n              for (size_t mblock = minsize; mblock <= msize; mblock *= 2) {\n                for (size_t nblock = minsize; nblock <= nsize; nblock *= 2) {\n                  benchmarks.emplace_back(ksize, msize, nsize, kblock, mblock, nblock);\n                }\n              }\n            }\n          }\n        }\n      }\n    }\n\n    run_benchmarks(benchmarks);\n\n    cout << \"BEGIN MEASUREMENTS ALL POT SIZES\" << endl;\n    for (auto it = benchmarks.begin(); it != benchmarks.end(); ++it) {\n      cout << *it << endl;\n    }\n  }\n};\n\nstruct measure_default_sizes_action_t : action_t\n{\n  virtual const char* invokation_name() const { return \"default-sizes\"; }\n  virtual void run() const\n  {\n    vector<benchmark_t> benchmarks;\n    for (int repetition = 0; repetition < measurement_repetitions; repetition++) {\n      for (size_t ksize = minsize; ksize <= maxsize; ksize *= 2) {\n        for (size_t msize = minsize; msize <= maxsize; msize *= 2) {\n          for (size_t nsize = minsize; nsize <= maxsize; nsize *= 2) {\n            benchmarks.emplace_back(ksize, msize, nsize);\n          }\n        }\n      }\n    }\n\n    run_benchmarks(benchmarks);\n\n    cout << \"BEGIN MEASUREMENTS DEFAULT SIZES\" << endl;\n    for (auto it = benchmarks.begin(); it != benchmarks.end(); ++it) {\n      cout << *it << endl;\n    }\n  }\n};\n\nint main(int argc, char* argv[])\n{\n  double time_start = timer.getRealTime();\n  cout.precision(4);\n  cerr.precision(4);\n\n  vector<unique_ptr<action_t>> available_actions;\n  available_actions.emplace_back(new measure_all_pot_sizes_action_t);\n  available_actions.emplace_back(new measure_default_sizes_action_t);\n\n  auto action = available_actions.end();\n\n  if (argc <= 1) {\n    show_usage_and_exit(argc, argv, available_actions);\n  }\n  for (auto it = available_actions.begin(); it != available_actions.end(); ++it) {\n    if (!strcmp(argv[1], (*it)->invokation_name())) {\n      action = it;\n      break;\n    }\n  }\n\n  if (action == available_actions.end()) {\n    show_usage_and_exit(argc, argv, available_actions);\n  }\n\n  for (int i = 2; i < argc; i++) {\n    if (argv[i] == strstr(argv[i], \"--min-working-set-size=\")) {\n      const char* equals_sign = strchr(argv[i], '=');\n      min_working_set_size = strtoul(equals_sign+1, nullptr, 10);\n    } else {\n      cerr << \"unrecognized option: \" << argv[i] << endl << endl;\n      show_usage_and_exit(argc, argv, available_actions);\n    }\n  }\n\n  print_cpuinfo();\n\n  cout << \"benchmark parameters:\" << endl;\n  cout << \"pointer size: \" << 8*sizeof(void*) << \" bits\" << endl;\n  cout << \"scalar type: \" << type_name<Scalar>() << endl;\n  cout << \"packet size: \" << internal::packet_traits<MatrixType::Scalar>::size << endl;\n  cout << \"minsize = \" << minsize << endl;\n  cout << \"maxsize = \" << maxsize << endl;\n  cout << \"measurement_repetitions = \" << measurement_repetitions << endl;\n  cout << \"min_accurate_time = \" << min_accurate_time << endl;\n  cout << \"min_working_set_size = \" << min_working_set_size;\n  if (min_working_set_size == 0) {\n    cout << \" (try to outsize caches)\";\n  }\n  cout << endl << endl;\n\n  (*action)->run();\n\n  double time_end = timer.getRealTime();\n  cerr << \"Finished in \" << human_duration_t(time_end - time_start) << endl;\n}\n"
  },
  {
    "path": "include/eigen3/bench/benchmark.cpp",
    "content": "// g++ -O3 -DNDEBUG -DMATSIZE=<x> benchmark.cpp -o benchmark && time ./benchmark\n\n#include <iostream>\n\n#include <Eigen/Core>\n\n#ifndef MATSIZE\n#define MATSIZE 3\n#endif\n\nusing namespace std;\nusing namespace Eigen;\n\n#ifndef REPEAT\n#define REPEAT 40000000\n#endif\n\n#ifndef SCALAR\n#define SCALAR double\n#endif\n\nint main(int argc, char *argv[])\n{\n    Matrix<SCALAR,MATSIZE,MATSIZE> I = Matrix<SCALAR,MATSIZE,MATSIZE>::Ones();\n    Matrix<SCALAR,MATSIZE,MATSIZE> m;\n    for(int i = 0; i < MATSIZE; i++)\n        for(int j = 0; j < MATSIZE; j++)\n        {\n            m(i,j) = (i+MATSIZE*j);\n        }\n    asm(\"#begin\");\n    for(int a = 0; a < REPEAT; a++)\n    {\n        m = Matrix<SCALAR,MATSIZE,MATSIZE>::Ones() + 0.00005 * (m + (m*m));\n    }\n    asm(\"#end\");\n    cout << m << endl;\n    return 0;\n}\n"
  },
  {
    "path": "include/eigen3/bench/benchmarkSlice.cpp",
    "content": "// g++ -O3 -DNDEBUG benchmarkX.cpp -o benchmarkX && time ./benchmarkX\n\n#include <iostream>\n\n#include <Eigen/Core>\n\nusing namespace std;\nusing namespace Eigen;\n\n#ifndef REPEAT\n#define REPEAT 10000\n#endif\n\n#ifndef SCALAR\n#define SCALAR float\n#endif\n\nint main(int argc, char *argv[])\n{\n  typedef Matrix<SCALAR, Eigen::Dynamic, Eigen::Dynamic> Mat;\n  Mat m(100, 100);\n  m.setRandom();\n\n  for(int a = 0; a < REPEAT; a++)\n  {\n    int r, c, nr, nc;\n    r = Eigen::internal::random<int>(0,10);\n    c = Eigen::internal::random<int>(0,10);\n    nr = Eigen::internal::random<int>(50,80);\n    nc = Eigen::internal::random<int>(50,80);\n    m.block(r,c,nr,nc) += Mat::Ones(nr,nc);\n    m.block(r,c,nr,nc) *= SCALAR(10);\n    m.block(r,c,nr,nc) -= Mat::constant(nr,nc,10);\n    m.block(r,c,nr,nc) /= SCALAR(10);\n  }\n  cout << m[0] << endl;\n  return 0;\n}\n"
  },
  {
    "path": "include/eigen3/bench/benchmarkX.cpp",
    "content": "// g++ -fopenmp -I .. -O3 -DNDEBUG -finline-limit=1000 benchmarkX.cpp -o b && time ./b\n\n#include <iostream>\n\n#include <Eigen/Core>\n\nusing namespace std;\nusing namespace Eigen;\n\n#ifndef MATTYPE\n#define MATTYPE MatrixXLd\n#endif\n\n#ifndef MATSIZE\n#define MATSIZE 400\n#endif\n\n#ifndef REPEAT\n#define REPEAT 100\n#endif\n\nint main(int argc, char *argv[])\n{\n\tMATTYPE I = MATTYPE::Ones(MATSIZE,MATSIZE);\n\tMATTYPE m(MATSIZE,MATSIZE);\n\tfor(int i = 0; i < MATSIZE; i++) for(int j = 0; j < MATSIZE; j++)\n\t{\n\t\tm(i,j) = (i+j+1)/(MATSIZE*MATSIZE);\n\t}\n\tfor(int a = 0; a < REPEAT; a++)\n\t{\n\t\tm = I + 0.0001 * (m + m*m);\n\t}\n\tcout << m(0,0) << endl;\n\treturn 0;\n}\n"
  },
  {
    "path": "include/eigen3/bench/benchmarkXcwise.cpp",
    "content": "// g++ -O3 -DNDEBUG benchmarkX.cpp -o benchmarkX && time ./benchmarkX\n\n#include <iostream>\n#include <Eigen/Core>\n\nusing namespace std;\nusing namespace Eigen;\n\n#ifndef VECTYPE\n#define VECTYPE VectorXLd\n#endif\n\n#ifndef VECSIZE\n#define VECSIZE 1000000\n#endif\n\n#ifndef REPEAT\n#define REPEAT 1000\n#endif\n\nint main(int argc, char *argv[])\n{\n\tVECTYPE I = VECTYPE::Ones(VECSIZE);\n\tVECTYPE m(VECSIZE,1);\n\tfor(int i = 0; i < VECSIZE; i++)\n\t{\n\t\tm[i] = 0.1 * i/VECSIZE;\n\t}\n\tfor(int a = 0; a < REPEAT; a++)\n\t{\n\t\tm = VECTYPE::Ones(VECSIZE) + 0.00005 * (m.cwise().square() + m/4);\n\t}\n\tcout << m[0] << endl;\n\treturn 0;\n}\n"
  },
  {
    "path": "include/eigen3/bench/benchmark_suite",
    "content": "#!/bin/bash\nCXX=${CXX-g++} # default value unless caller has defined CXX\necho \"Fixed size 3x3, column-major, -DNDEBUG\"\n$CXX -O3 -I .. -DNDEBUG benchmark.cpp -o benchmark && time ./benchmark >/dev/null\necho \"Fixed size 3x3, column-major, with asserts\"\n$CXX -O3 -I .. benchmark.cpp -o benchmark && time ./benchmark >/dev/null\necho \"Fixed size 3x3, row-major, -DNDEBUG\"\n$CXX -O3 -I .. -DEIGEN_DEFAULT_TO_ROW_MAJOR -DNDEBUG benchmark.cpp -o benchmark && time ./benchmark >/dev/null\necho \"Fixed size 3x3, row-major, with asserts\"\n$CXX -O3 -I .. -DEIGEN_DEFAULT_TO_ROW_MAJOR benchmark.cpp -o benchmark && time ./benchmark >/dev/null\necho \"Dynamic size 20x20, column-major, -DNDEBUG\"\n$CXX -O3 -I .. -DNDEBUG benchmarkX.cpp -o benchmarkX && time ./benchmarkX >/dev/null\necho \"Dynamic size 20x20, column-major, with asserts\"\n$CXX -O3 -I .. benchmarkX.cpp -o benchmarkX && time ./benchmarkX >/dev/null\necho \"Dynamic size 20x20, row-major, -DNDEBUG\"\n$CXX -O3 -I .. -DEIGEN_DEFAULT_TO_ROW_MAJOR -DNDEBUG benchmarkX.cpp -o benchmarkX && time ./benchmarkX >/dev/null\necho \"Dynamic size 20x20, row-major, with asserts\"\n$CXX -O3 -I .. -DEIGEN_DEFAULT_TO_ROW_MAJOR benchmarkX.cpp -o benchmarkX && time ./benchmarkX >/dev/null\n"
  },
  {
    "path": "include/eigen3/bench/btl/CMakeLists.txt",
    "content": "PROJECT(BTL)\n\nCMAKE_MINIMUM_REQUIRED(VERSION 2.6.2)\n\nset(CMAKE_MODULE_PATH ${PROJECT_SOURCE_DIR}/cmake ${Eigen_SOURCE_DIR}/cmake)\ninclude(MacroOptionalAddSubdirectory)\n\nOPTION(BTL_NOVEC \"Disable SSE/Altivec optimizations when possible\" OFF)\n\nSET(CMAKE_INCLUDE_CURRENT_DIR ON)\n\nstring(REGEX MATCH icpc IS_ICPC ${CMAKE_CXX_COMPILER})\nIF(CMAKE_COMPILER_IS_GNUCXX OR IS_ICPC)\n  SET(CMAKE_CXX_FLAGS \"-g0 -O3 -DNDEBUG ${CMAKE_CXX_FLAGS}\")\n  SET(CMAKE_Fortran_FLAGS \"-g0 -O3 -DNDEBUG ${CMAKE_Fortran_FLAGS}\")\n  IF(BTL_NOVEC)\n    SET(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} -DEIGEN_DONT_VECTORIZE\")\n  ENDIF(BTL_NOVEC)\nENDIF(CMAKE_COMPILER_IS_GNUCXX OR IS_ICPC)\n\nIF(MSVC)\n  SET(CMAKE_CXX_FLAGS \" /O2 /Ot /GL /fp:fast -DNDEBUG\")\n#   SET(CMAKE_Fortran_FLAGS \"-g0 -O3 -DNDEBUG\")\n  IF(BTL_NOVEC)\n    SET(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} -DEIGEN_DONT_VECTORIZE\")\n  ENDIF(BTL_NOVEC)\nENDIF(MSVC)\n\nif(IS_ICPC)\n  set(CMAKE_CXX_FLAGS \"-fast ${CMAKE_CXX_FLAGS}\")\n  set(CMAKE_Fortran_FLAGS \"-fast ${CMAKE_Fortran_FLAGS}\")\nendif(IS_ICPC)\n\ninclude_directories(\n  ${PROJECT_SOURCE_DIR}/actions\n  ${PROJECT_SOURCE_DIR}/generic_bench\n  ${PROJECT_SOURCE_DIR}/generic_bench/utils\n  ${PROJECT_SOURCE_DIR}/libs/STL)\n\n# find_package(MKL)\n# if (MKL_FOUND)\n#   add_definitions(-DHAVE_MKL)\n#   set(DEFAULT_LIBRARIES ${MKL_LIBRARIES})\n# endif (MKL_FOUND)\n\nfind_library(EIGEN_BTL_RT_LIBRARY rt)\n# if we cannot find it easily, then we don't need it!\nif(NOT EIGEN_BTL_RT_LIBRARY)\n  set(EIGEN_BTL_RT_LIBRARY \"\")\nendif()\n\nMACRO(BTL_ADD_BENCH targetname)\n\n  foreach(_current_var ${ARGN})\n    set(_last_var ${_current_var})\n  endforeach(_current_var)\n\n  set(_sources ${ARGN})\n  list(LENGTH _sources _argn_length)\n\n  list(REMOVE_ITEM _sources ON OFF TRUE FALSE)\n\n  list(LENGTH _sources _src_length)\n\n  if (${_argn_length} EQUAL ${_src_length})\n    set(_last_var ON)\n  endif (${_argn_length} EQUAL ${_src_length})\n\n  OPTION(BUILD_${targetname} \"Build benchmark ${targetname}\" ${_last_var})\n\n  IF(BUILD_${targetname})\n    ADD_EXECUTABLE(${targetname} ${_sources})\n    ADD_TEST(${targetname} \"${targetname}\")\n    target_link_libraries(${targetname} ${DEFAULT_LIBRARIES} ${EIGEN_BTL_RT_LIBRARY})\n  ENDIF(BUILD_${targetname})\n\nENDMACRO(BTL_ADD_BENCH)\n\nmacro(btl_add_target_property target prop value)\n\n  if(BUILD_${target})\n    get_target_property(previous ${target} ${prop})\n    if(NOT previous)\n      set(previous \"\")\n    endif()\n    set_target_properties(${target} PROPERTIES ${prop} \"${previous} ${value}\")\n  endif()\n\nendmacro(btl_add_target_property)\n\nENABLE_TESTING()\n\nadd_subdirectory(libs/eigen3)\nadd_subdirectory(libs/eigen2)\nadd_subdirectory(libs/tensors)\nadd_subdirectory(libs/BLAS)\nadd_subdirectory(libs/ublas)\nadd_subdirectory(libs/gmm)\nadd_subdirectory(libs/mtl4)\nadd_subdirectory(libs/blitz)\nadd_subdirectory(libs/tvmet)\nadd_subdirectory(libs/STL)\nadd_subdirectory(libs/blaze)\n\nadd_subdirectory(data)\n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/COPYING",
    "content": "                    GNU GENERAL PUBLIC LICENSE\n                       Version 2, June 1991\n\n Copyright (C) 1989, 1991 Free Software Foundation, Inc.\n                       59 Temple Place, Suite 330, Boston, MA  02111-1307  USA\n Everyone is permitted to copy and distribute verbatim copies\n of this license document, but changing it is not allowed.\n\n                            Preamble\n\n  The licenses for most software are designed to take away your\nfreedom to share and change it.  By contrast, the GNU General Public\nLicense is intended to guarantee your freedom to share and change free\nsoftware--to make sure the software is free for all its users.  This\nGeneral Public License applies to most of the Free Software\nFoundation's software and to any other program whose authors commit to\nusing it.  (Some other Free Software Foundation software is covered by\nthe GNU Library General Public License instead.)  You can apply it to\nyour programs, too.\n\n  When we speak of free software, we are referring to freedom, not\nprice.  Our General Public Licenses are designed to make sure that you\nhave the freedom to distribute copies of free software (and charge for\nthis service if you wish), that you receive source code or can get it\nif you want it, that you can change the software or use pieces of it\nin new free programs; and that you know you can do these things.\n\n  To protect your rights, we need to make restrictions that forbid\nanyone to deny you these rights or to ask you to surrender the rights.\nThese restrictions translate to certain responsibilities for you if you\ndistribute copies of the software, or if you modify it.\n\n  For example, if you distribute copies of such a program, whether\ngratis or for a fee, you must give the recipients all the rights that\nyou have.  You must make sure that they, too, receive or can get the\nsource code.  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  },
  {
    "path": "include/eigen3/bench/btl/README",
    "content": "Bench Template Library\n\n****************************************\nIntroduction :\n\nThe aim of this project is to compare the performance\nof available numerical libraries. The code is designed\nas generic and modular as possible. Thus, adding new\nnumerical libraries or new numerical tests should\nrequire minimal effort.\n\n\n*****************************************\n\nInstallation :\n\nBTL uses cmake / ctest:\n\n1 - create a build directory:\n\n  $ mkdir build\n  $ cd build\n\n2 - configure:\n\n  $ ccmake ..\n\n3 - run the bench using ctest:\n\n  $ ctest -V\n\nYou can run the benchmarks only on libraries matching a given regular expression:\n  ctest -V -R <regexp>\nFor instance:\n  ctest -V -R eigen2\n\nYou can also select a given set of actions defining the environment variable BTL_CONFIG this way:\n  BTL_CONFIG=\"-a action1{:action2}*\" ctest -V\nAn exemple:\n  BTL_CONFIG=\"-a axpy:vector_matrix:trisolve:ata\" ctest -V -R eigen2\n\nFinally, if bench results already exist (the bench*.dat files) then they merges by keeping the best for each matrix size. If you want to overwrite the previous ones you can simply add the \"--overwrite\" option:\n  BTL_CONFIG=\"-a axpy:vector_matrix:trisolve:ata --overwrite\" ctest -V -R eigen2\n\n4 : Analyze the result. different data files (.dat) are produced in each libs directories.\n If gnuplot is available, choose a directory name in the data directory to store the results and type:\n        $ cd data\n        $ mkdir my_directory\n        $ cp ../libs/*/*.dat my_directory\n Build the data utilities in this (data) directory\n        make\n Then you can look the raw data,\n        go_mean my_directory\n or smooth the data first :\n\tsmooth_all.sh my_directory\n\tgo_mean my_directory_smooth\n\n\n*************************************************\n\nFiles and directories :\n\n generic_bench : all the bench sources common to all libraries\n\n actions : sources for different action wrappers (axpy, matrix-matrix product) to be tested.\n\n libs/* : bench sources specific to each tested libraries.\n\n machine_dep : directory used to store machine specific Makefile.in\n\n data : directory used to store gnuplot scripts and data analysis utilities\n\n**************************************************\n\nPrinciples : the code modularity is achieved by defining two concepts :\n\n ****** Action concept : This is a class defining which kind\n  of test must be performed (e.g. a matrix_vector_product).\n\tAn Action should define the following methods :\n\n        *** Ctor using the size of the problem (matrix or vector size) as an argument\n\t    Action action(size);\n        *** initialize : this method initialize the calculation (e.g. initialize the matrices and vectors arguments)\n\t    action.initialize();\n\t*** calculate : this method actually launch the calculation to be benchmarked\n\t    action.calculate;\n\t*** nb_op_base() : this method returns the complexity of the calculate method (allowing the mflops evaluation)\n        *** name() : this method returns the name of the action (std::string)\n\n ****** Interface concept : This is a class or namespace defining how to use a given library and\n  its specific containers (matrix and vector). Up to now an interface should following types\n\n\t*** real_type : kind of float to be used (float or double)\n\t*** stl_vector : must correspond to std::vector<real_type>\n\t*** stl_matrix : must correspond to std::vector<stl_vector>\n\t*** gene_vector : the vector type for this interface        --> e.g. (real_type *) for the C_interface\n\t*** gene_matrix : the matrix type for this interface        --> e.g. (gene_vector *) for the C_interface\n\n\t+ the following common methods\n\n        *** free_matrix(gene_matrix & A, int N)  dealocation of a N sized gene_matrix A\n        *** free_vector(gene_vector & B)  dealocation of a N sized gene_vector B\n        *** matrix_from_stl(gene_matrix & A, stl_matrix & A_stl) copy the content of an stl_matrix A_stl into a gene_matrix A.\n\t     The allocation of A is done in this function.\n\t*** vector_to_stl(gene_vector & B, stl_vector & B_stl)  copy the content of an stl_vector B_stl into a gene_vector B.\n\t     The allocation of B is done in this function.\n        *** matrix_to_stl(gene_matrix & A, stl_matrix & A_stl) copy the content of an gene_matrix A into an stl_matrix A_stl.\n             The size of A_STL must corresponds to the size of A.\n        *** vector_to_stl(gene_vector & A, stl_vector & A_stl) copy the content of an gene_vector A into an stl_vector A_stl.\n             The size of B_STL must corresponds to the size of B.\n\t*** copy_matrix(gene_matrix & source, gene_matrix & cible, int N) : copy the content of source in cible. Both source\n\t\tand cible must be sized NxN.\n\t*** copy_vector(gene_vector & source, gene_vector & cible, int N) : copy the content of source in cible. Both source\n \t\tand cible must be sized N.\n\n\tand the following method corresponding to the action one wants to be benchmarked :\n\n\t***  matrix_vector_product(const gene_matrix & A, const gene_vector & B, gene_vector & X, int N)\n\t***  matrix_matrix_product(const gene_matrix & A, const gene_matrix & B, gene_matrix & X, int N)\n        ***  ata_product(const gene_matrix & A, gene_matrix & X, int N)\n\t***  aat_product(const gene_matrix & A, gene_matrix & X, int N)\n        ***  axpy(real coef, const gene_vector & X, gene_vector & Y, int N)\n\n The bench algorithm (generic_bench/bench.hh) is templated with an action itself templated with\n an interface. A typical main.cpp source stored in a given library directory libs/A_LIB\n looks like :\n\n bench< AN_ACTION < AN_INTERFACE > >( 10 , 1000 , 50 ) ;\n\n this function will produce XY data file containing measured  mflops as a function of the size for 50\n sizes between 10 and 10000.\n\n This algorithm can be adapted by providing a given Perf_Analyzer object which determines how the time\n measurements must be done. For example, the X86_Perf_Analyzer use the asm rdtsc function and provides\n a very fast and accurate (but less portable) timing method. The default is the Portable_Perf_Analyzer\n so\n\n bench< AN_ACTION < AN_INTERFACE > >( 10 , 1000 , 50 ) ;\n\n is equivalent to\n\n bench< Portable_Perf_Analyzer,AN_ACTION < AN_INTERFACE > >( 10 , 1000 , 50 ) ;\n\n If your system supports it we suggest to use a mixed implementation (X86_perf_Analyzer+Portable_Perf_Analyzer).\n replace\n     bench<Portable_Perf_Analyzer,Action>(size_min,size_max,nb_point);\n with\n     bench<Mixed_Perf_Analyzer,Action>(size_min,size_max,nb_point);\n in generic/bench.hh\n\n.\n\n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/actions/action_aat_product.hh",
    "content": "//=====================================================\n// File   :  action_aat_product.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>\n// Copyright (C) EDF R&D,  lun sep 30 14:23:19 CEST 2002\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef ACTION_AAT_PRODUCT\n#define ACTION_AAT_PRODUCT\n#include \"utilities.h\"\n#include \"STL_interface.hh\"\n#include <string>\n#include \"init/init_function.hh\"\n#include \"init/init_vector.hh\"\n#include \"init/init_matrix.hh\"\n\nusing namespace std;\n\ntemplate<class Interface>\nclass Action_aat_product {\n\npublic :\n\n  // Ctor\n\n  Action_aat_product( int size ):_size(size)\n  {\n    MESSAGE(\"Action_aat_product Ctor\");\n\n    // STL matrix and vector initialization\n\n    init_matrix<pseudo_random>(A_stl,_size);\n    init_matrix<null_function>(X_stl,_size);\n    init_matrix<null_function>(resu_stl,_size);\n\n    // generic matrix and vector initialization\n\n    Interface::matrix_from_stl(A_ref,A_stl);\n    Interface::matrix_from_stl(X_ref,X_stl);\n\n    Interface::matrix_from_stl(A,A_stl);\n    Interface::matrix_from_stl(X,X_stl);\n\n  }\n\n  // invalidate copy ctor\n\n  Action_aat_product( const  Action_aat_product & )\n  {\n    INFOS(\"illegal call to Action_aat_product Copy Ctor\");\n    exit(0);\n  }\n\n  // Dtor\n\n  ~Action_aat_product( void ){\n\n    MESSAGE(\"Action_aat_product Dtor\");\n\n    // deallocation\n\n    Interface::free_matrix(A,_size);\n    Interface::free_matrix(X,_size);\n\n    Interface::free_matrix(A_ref,_size);\n    Interface::free_matrix(X_ref,_size);\n\n  }\n\n  // action name\n\n  static inline std::string name( void )\n  {\n    return \"aat_\"+Interface::name();\n  }\n\n  double nb_op_base( void ){\n    return double(_size)*double(_size)*double(_size);\n  }\n\n  inline void initialize( void ){\n\n    Interface::copy_matrix(A_ref,A,_size);\n    Interface::copy_matrix(X_ref,X,_size);\n\n  }\n\n  inline void calculate( void ) {\n\n      Interface::aat_product(A,X,_size);\n\n  }\n\n  void check_result( void ){\n    if (_size>128) return;\n    // calculation check\n\n    Interface::matrix_to_stl(X,resu_stl);\n\n    STL_interface<typename Interface::real_type>::aat_product(A_stl,X_stl,_size);\n\n    typename Interface::real_type error=\n      STL_interface<typename Interface::real_type>::norm_diff(X_stl,resu_stl);\n\n    if (error>1.e-6){\n      INFOS(\"WRONG CALCULATION...residual=\" << error);\n      exit(1);\n    }\n\n  }\n\nprivate :\n\n  typename Interface::stl_matrix A_stl;\n  typename Interface::stl_matrix X_stl;\n  typename Interface::stl_matrix resu_stl;\n\n  typename Interface::gene_matrix A_ref;\n  typename Interface::gene_matrix X_ref;\n\n  typename Interface::gene_matrix A;\n  typename Interface::gene_matrix X;\n\n\n  int _size;\n\n};\n\n\n#endif\n\n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/actions/action_ata_product.hh",
    "content": "//=====================================================\n// File   :  action_ata_product.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>\n// Copyright (C) EDF R&D,  lun sep 30 14:23:19 CEST 2002\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef ACTION_ATA_PRODUCT\n#define ACTION_ATA_PRODUCT\n#include \"utilities.h\"\n#include \"STL_interface.hh\"\n#include <string>\n#include \"init/init_function.hh\"\n#include \"init/init_vector.hh\"\n#include \"init/init_matrix.hh\"\n\nusing namespace std;\n\ntemplate<class Interface>\nclass Action_ata_product {\n\npublic :\n\n  // Ctor\n\n  Action_ata_product( int size ):_size(size)\n  {\n    MESSAGE(\"Action_ata_product Ctor\");\n\n    // STL matrix and vector initialization\n\n    init_matrix<pseudo_random>(A_stl,_size);\n    init_matrix<null_function>(X_stl,_size);\n    init_matrix<null_function>(resu_stl,_size);\n\n    // generic matrix and vector initialization\n\n    Interface::matrix_from_stl(A_ref,A_stl);\n    Interface::matrix_from_stl(X_ref,X_stl);\n\n    Interface::matrix_from_stl(A,A_stl);\n    Interface::matrix_from_stl(X,X_stl);\n\n  }\n\n  // invalidate copy ctor\n\n  Action_ata_product( const  Action_ata_product & )\n  {\n    INFOS(\"illegal call to Action_ata_product Copy Ctor\");\n    exit(0);\n  }\n\n  // Dtor\n\n  ~Action_ata_product( void ){\n\n    MESSAGE(\"Action_ata_product Dtor\");\n\n    // deallocation\n\n    Interface::free_matrix(A,_size);\n    Interface::free_matrix(X,_size);\n\n    Interface::free_matrix(A_ref,_size);\n    Interface::free_matrix(X_ref,_size);\n\n  }\n\n  // action name\n\n  static inline std::string name( void )\n  {\n    return \"ata_\"+Interface::name();\n  }\n\n  double nb_op_base( void ){\n    return 2.0*_size*_size*_size;\n  }\n\n  inline void initialize( void ){\n\n    Interface::copy_matrix(A_ref,A,_size);\n    Interface::copy_matrix(X_ref,X,_size);\n\n  }\n\n  inline void calculate( void ) {\n\n      Interface::ata_product(A,X,_size);\n\n  }\n\n  void check_result( void ){\n    if (_size>128) return;\n    // calculation check\n\n    Interface::matrix_to_stl(X,resu_stl);\n\n    STL_interface<typename Interface::real_type>::ata_product(A_stl,X_stl,_size);\n\n    typename Interface::real_type error=\n      STL_interface<typename Interface::real_type>::norm_diff(X_stl,resu_stl);\n\n    if (error>1.e-6){\n      INFOS(\"WRONG CALCULATION...residual=\" << error);\n      exit(1);\n    }\n\n  }\n\nprivate :\n\n  typename Interface::stl_matrix A_stl;\n  typename Interface::stl_matrix X_stl;\n  typename Interface::stl_matrix resu_stl;\n\n  typename Interface::gene_matrix A_ref;\n  typename Interface::gene_matrix X_ref;\n\n  typename Interface::gene_matrix A;\n  typename Interface::gene_matrix X;\n\n\n  int _size;\n\n};\n\n\n#endif\n\n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/actions/action_atv_product.hh",
    "content": "//=====================================================\n// File   :  action_atv_product.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>\n// Copyright (C) EDF R&D,  lun sep 30 14:23:19 CEST 2002\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef ACTION_ATV_PRODUCT\n#define ACTION_ATV_PRODUCT\n#include \"utilities.h\"\n#include \"STL_interface.hh\"\n#include <string>\n#include \"init/init_function.hh\"\n#include \"init/init_vector.hh\"\n#include \"init/init_matrix.hh\"\n\nusing namespace std;\n\ntemplate<class Interface>\nclass Action_atv_product {\n\npublic :\n\n  Action_atv_product( int size ) : _size(size)\n  {\n    MESSAGE(\"Action_atv_product Ctor\");\n\n    // STL matrix and vector initialization\n\n    init_matrix<pseudo_random>(A_stl,_size);\n    init_vector<pseudo_random>(B_stl,_size);\n    init_vector<null_function>(X_stl,_size);\n    init_vector<null_function>(resu_stl,_size);\n\n    // generic matrix and vector initialization\n\n    Interface::matrix_from_stl(A_ref,A_stl);\n    Interface::vector_from_stl(B_ref,B_stl);\n    Interface::vector_from_stl(X_ref,X_stl);\n\n    Interface::matrix_from_stl(A,A_stl);\n    Interface::vector_from_stl(B,B_stl);\n    Interface::vector_from_stl(X,X_stl);\n  }\n\n  // invalidate copy ctor\n  Action_atv_product( const  Action_atv_product & )\n  {\n    INFOS(\"illegal call to Action_atv_product Copy Ctor\");\n    exit(1);\n  }\n\n  ~Action_atv_product( void )\n  {\n    MESSAGE(\"Action_atv_product Dtor\");\n\n    Interface::free_matrix(A,_size);\n    Interface::free_vector(B);\n    Interface::free_vector(X);\n\n    Interface::free_matrix(A_ref,_size);\n    Interface::free_vector(B_ref);\n    Interface::free_vector(X_ref);\n  }\n\n  static inline std::string name() { return \"atv_\" + Interface::name(); }\n\n  double nb_op_base( void ) { return 2.0*_size*_size; }\n\n  inline void initialize( void ){\n    Interface::copy_matrix(A_ref,A,_size);\n    Interface::copy_vector(B_ref,B,_size);\n    Interface::copy_vector(X_ref,X,_size);\n  }\n\n  BTL_DONT_INLINE void calculate( void ) {\n    BTL_ASM_COMMENT(\"begin atv\");\n    Interface::atv_product(A,B,X,_size);\n    BTL_ASM_COMMENT(\"end atv\");\n  }\n\n  void check_result( void )\n  {\n    if (_size>128) return;\n    Interface::vector_to_stl(X,resu_stl);\n\n    STL_interface<typename Interface::real_type>::atv_product(A_stl,B_stl,X_stl,_size);\n\n    typename Interface::real_type error=\n      STL_interface<typename Interface::real_type>::norm_diff(X_stl,resu_stl);\n\n    if (error>1.e-6){\n      INFOS(\"WRONG CALCULATION...residual=\" << error);\n      exit(1);\n    }\n  }\n\nprivate :\n\n  typename Interface::stl_matrix A_stl;\n  typename Interface::stl_vector B_stl;\n  typename Interface::stl_vector X_stl;\n  typename Interface::stl_vector resu_stl;\n\n  typename Interface::gene_matrix A_ref;\n  typename Interface::gene_vector B_ref;\n  typename Interface::gene_vector X_ref;\n\n  typename Interface::gene_matrix A;\n  typename Interface::gene_vector B;\n  typename Interface::gene_vector X;\n\n\n  int _size;\n\n};\n\n\n#endif\n\n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/actions/action_axpby.hh",
    "content": "//=====================================================\n// File   :  action_axpby.hh\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef ACTION_AXPBY\n#define ACTION_AXPBY\n#include \"utilities.h\"\n#include \"STL_interface.hh\"\n#include <string>\n#include \"init/init_function.hh\"\n#include \"init/init_vector.hh\"\n#include \"init/init_matrix.hh\"\n\nusing namespace std;\n\ntemplate<class Interface>\nclass Action_axpby {\n\npublic :\n\n  // Ctor\n  Action_axpby( int size ):_alpha(0.5),_beta(0.95),_size(size)\n  {\n    MESSAGE(\"Action_axpby Ctor\");\n\n    // STL vector initialization\n    init_vector<pseudo_random>(X_stl,_size);\n    init_vector<pseudo_random>(Y_stl,_size);\n    init_vector<null_function>(resu_stl,_size);\n\n    // generic matrix and vector initialization\n    Interface::vector_from_stl(X_ref,X_stl);\n    Interface::vector_from_stl(Y_ref,Y_stl);\n\n    Interface::vector_from_stl(X,X_stl);\n    Interface::vector_from_stl(Y,Y_stl);\n  }\n\n  // invalidate copy ctor\n  Action_axpby( const  Action_axpby & )\n  {\n    INFOS(\"illegal call to Action_axpby Copy Ctor\");\n    exit(1);\n  }\n\n  // Dtor\n  ~Action_axpby( void ){\n    MESSAGE(\"Action_axpby Dtor\");\n\n    // deallocation\n    Interface::free_vector(X_ref);\n    Interface::free_vector(Y_ref);\n\n    Interface::free_vector(X);\n    Interface::free_vector(Y);\n  }\n\n  // action name\n  static inline std::string name( void )\n  {\n    return \"axpby_\"+Interface::name();\n  }\n\n  double nb_op_base( void ){\n    return 3.0*_size;\n  }\n\n  inline void initialize( void ){\n    Interface::copy_vector(X_ref,X,_size);\n    Interface::copy_vector(Y_ref,Y,_size);\n  }\n\n  inline void calculate( void ) {\n    BTL_ASM_COMMENT(\"mybegin axpby\");\n    Interface::axpby(_alpha,X,_beta,Y,_size);\n    BTL_ASM_COMMENT(\"myend axpby\");\n  }\n\n  void check_result( void ){\n    if (_size>128) return;\n    // calculation check\n    Interface::vector_to_stl(Y,resu_stl);\n\n    STL_interface<typename Interface::real_type>::axpby(_alpha,X_stl,_beta,Y_stl,_size);\n\n    typename Interface::real_type error=\n      STL_interface<typename Interface::real_type>::norm_diff(Y_stl,resu_stl);\n\n    if (error>1.e-6){\n      INFOS(\"WRONG CALCULATION...residual=\" << error);\n      exit(2);\n    }\n  }\n\nprivate :\n\n  typename Interface::stl_vector X_stl;\n  typename Interface::stl_vector Y_stl;\n  typename Interface::stl_vector resu_stl;\n\n  typename Interface::gene_vector X_ref;\n  typename Interface::gene_vector Y_ref;\n\n  typename Interface::gene_vector X;\n  typename Interface::gene_vector Y;\n\n  typename Interface::real_type _alpha;\n  typename Interface::real_type _beta;\n\n  int _size;\n};\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/actions/action_axpy.hh",
    "content": "//=====================================================\n// File   :  action_axpy.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>\n// Copyright (C) EDF R&D,  lun sep 30 14:23:19 CEST 2002\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef ACTION_AXPY\n#define ACTION_AXPY\n#include \"utilities.h\"\n#include \"STL_interface.hh\"\n#include <string>\n#include \"init/init_function.hh\"\n#include \"init/init_vector.hh\"\n#include \"init/init_matrix.hh\"\n\nusing namespace std;\n\ntemplate<class Interface>\nclass Action_axpy {\n\npublic :\n\n  // Ctor\n\n  Action_axpy( int size ):_coef(1.0),_size(size)\n  {\n    MESSAGE(\"Action_axpy Ctor\");\n\n    // STL vector initialization\n\n    init_vector<pseudo_random>(X_stl,_size);\n    init_vector<pseudo_random>(Y_stl,_size);\n    init_vector<null_function>(resu_stl,_size);\n\n    // generic matrix and vector initialization\n\n    Interface::vector_from_stl(X_ref,X_stl);\n    Interface::vector_from_stl(Y_ref,Y_stl);\n\n    Interface::vector_from_stl(X,X_stl);\n    Interface::vector_from_stl(Y,Y_stl);\n\n\n  }\n\n  // invalidate copy ctor\n\n  Action_axpy( const  Action_axpy & )\n  {\n    INFOS(\"illegal call to Action_axpy Copy Ctor\");\n    exit(1);\n  }\n\n  // Dtor\n\n  ~Action_axpy( void ){\n\n    MESSAGE(\"Action_axpy Dtor\");\n\n    // deallocation\n\n    Interface::free_vector(X_ref);\n    Interface::free_vector(Y_ref);\n\n    Interface::free_vector(X);\n    Interface::free_vector(Y);\n  }\n\n  // action name\n\n  static inline std::string name( void )\n  {\n    return \"axpy_\"+Interface::name();\n  }\n\n  double nb_op_base( void ){\n    return 2.0*_size;\n  }\n\n  inline void initialize( void ){\n    Interface::copy_vector(X_ref,X,_size);\n    Interface::copy_vector(Y_ref,Y,_size);\n  }\n\n  inline void calculate( void ) {\n    BTL_ASM_COMMENT(\"mybegin axpy\");\n    Interface::axpy(_coef,X,Y,_size);\n    BTL_ASM_COMMENT(\"myend axpy\");\n  }\n\n  void check_result( void ){\n    if (_size>128) return;\n    // calculation check\n\n    Interface::vector_to_stl(Y,resu_stl);\n\n    STL_interface<typename Interface::real_type>::axpy(_coef,X_stl,Y_stl,_size);\n\n    typename Interface::real_type error=\n      STL_interface<typename Interface::real_type>::norm_diff(Y_stl,resu_stl);\n\n    if (error>1.e-6){\n      INFOS(\"WRONG CALCULATION...residual=\" << error);\n      exit(0);\n    }\n\n  }\n\nprivate :\n\n  typename Interface::stl_vector X_stl;\n  typename Interface::stl_vector Y_stl;\n  typename Interface::stl_vector resu_stl;\n\n  typename Interface::gene_vector X_ref;\n  typename Interface::gene_vector Y_ref;\n\n  typename Interface::gene_vector X;\n  typename Interface::gene_vector Y;\n\n  typename Interface::real_type _coef;\n\n  int _size;\n};\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/actions/action_cholesky.hh",
    "content": "//=====================================================\n// File   :  action_cholesky.hh\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef ACTION_CHOLESKY\n#define ACTION_CHOLESKY\n#include \"utilities.h\"\n#include \"STL_interface.hh\"\n#include <string>\n#include \"init/init_function.hh\"\n#include \"init/init_vector.hh\"\n#include \"init/init_matrix.hh\"\n\nusing namespace std;\n\ntemplate<class Interface>\nclass Action_cholesky {\n\npublic :\n\n  // Ctor\n\n  Action_cholesky( int size ):_size(size)\n  {\n    MESSAGE(\"Action_cholesky Ctor\");\n\n    // STL mat/vec initialization\n    init_matrix_symm<pseudo_random>(X_stl,_size);\n    init_matrix<null_function>(C_stl,_size);\n\n    // make sure X is invertible\n    for (int i=0; i<_size; ++i)\n      X_stl[i][i] = std::abs(X_stl[i][i]) * 1e2 + 100;\n\n    // generic matrix and vector initialization\n    Interface::matrix_from_stl(X_ref,X_stl);\n    Interface::matrix_from_stl(X,X_stl);\n    Interface::matrix_from_stl(C,C_stl);\n\n    _cost = 0;\n    for (int j=0; j<_size; ++j)\n    {\n      double r = std::max(_size - j -1,0);\n      _cost += 2*(r*j+r+j);\n    }\n  }\n\n  // invalidate copy ctor\n\n  Action_cholesky( const  Action_cholesky & )\n  {\n    INFOS(\"illegal call to Action_cholesky Copy Ctor\");\n    exit(1);\n  }\n\n  // Dtor\n\n  ~Action_cholesky( void ){\n\n    MESSAGE(\"Action_cholesky Dtor\");\n\n    // deallocation\n    Interface::free_matrix(X_ref,_size);\n    Interface::free_matrix(X,_size);\n    Interface::free_matrix(C,_size);\n  }\n\n  // action name\n\n  static inline std::string name( void )\n  {\n    return \"cholesky_\"+Interface::name();\n  }\n\n  double nb_op_base( void ){\n    return _cost;\n  }\n\n  inline void initialize( void ){\n    Interface::copy_matrix(X_ref,X,_size);\n  }\n\n  inline void calculate( void ) {\n      Interface::cholesky(X,C,_size);\n  }\n\n  void check_result( void ){\n    // calculation check\n//     STL_interface<typename Interface::real_type>::cholesky(X_stl,C_stl,_size);\n//\n//     typename Interface::real_type error=\n//       STL_interface<typename Interface::real_type>::norm_diff(C_stl,resu_stl);\n//\n//     if (error>1.e-6){\n//       INFOS(\"WRONG CALCULATION...residual=\" << error);\n//       exit(0);\n//     }\n\n  }\n\nprivate :\n\n  typename Interface::stl_matrix X_stl;\n  typename Interface::stl_matrix C_stl;\n\n  typename Interface::gene_matrix X_ref;\n  typename Interface::gene_matrix X;\n  typename Interface::gene_matrix C;\n\n  int _size;\n  double _cost;\n};\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/actions/action_ger.hh",
    "content": "\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef ACTION_GER\n#define ACTION_GER\n#include \"utilities.h\"\n#include \"STL_interface.hh\"\n#include <string>\n#include \"init/init_function.hh\"\n#include \"init/init_vector.hh\"\n#include \"init/init_matrix.hh\"\n\nusing namespace std;\n\ntemplate<class Interface>\nclass Action_ger {\n\npublic :\n\n  // Ctor\n  BTL_DONT_INLINE Action_ger( int size ):_size(size)\n  {\n    MESSAGE(\"Action_ger Ctor\");\n\n    // STL matrix and vector initialization\n    typename Interface::stl_matrix tmp;\n    init_matrix<pseudo_random>(A_stl,_size);\n    init_vector<pseudo_random>(B_stl,_size);\n    init_vector<pseudo_random>(X_stl,_size);\n    init_vector<null_function>(resu_stl,_size);\n\n    // generic matrix and vector initialization\n    Interface::matrix_from_stl(A_ref,A_stl);\n    Interface::matrix_from_stl(A,A_stl);\n    Interface::vector_from_stl(B_ref,B_stl);\n    Interface::vector_from_stl(B,B_stl);\n    Interface::vector_from_stl(X_ref,X_stl);\n    Interface::vector_from_stl(X,X_stl);\n  }\n\n  // invalidate copy ctor\n  Action_ger( const  Action_ger & )\n  {\n    INFOS(\"illegal call to Action_ger Copy Ctor\");\n    exit(1);\n  }\n\n  // Dtor\n  BTL_DONT_INLINE ~Action_ger( void ){\n    MESSAGE(\"Action_ger Dtor\");\n    Interface::free_matrix(A,_size);\n    Interface::free_vector(B);\n    Interface::free_vector(X);\n    Interface::free_matrix(A_ref,_size);\n    Interface::free_vector(B_ref);\n    Interface::free_vector(X_ref);\n\n  }\n\n  // action name\n  static inline std::string name( void )\n  {\n    return \"ger_\" + Interface::name();\n  }\n\n  double nb_op_base( void ){\n    return 2.0*_size*_size;\n  }\n\n  BTL_DONT_INLINE  void initialize( void ){\n    Interface::copy_matrix(A_ref,A,_size);\n    Interface::copy_vector(B_ref,B,_size);\n    Interface::copy_vector(X_ref,X,_size);\n  }\n\n  BTL_DONT_INLINE void calculate( void ) {\n    BTL_ASM_COMMENT(\"#begin ger\");\n    Interface::ger(A,B,X,_size);\n    BTL_ASM_COMMENT(\"end ger\");\n  }\n\n  BTL_DONT_INLINE void check_result( void ){\n    // calculation check\n    Interface::vector_to_stl(X,resu_stl);\n\n    STL_interface<typename Interface::real_type>::ger(A_stl,B_stl,X_stl,_size);\n\n    typename Interface::real_type error=\n      STL_interface<typename Interface::real_type>::norm_diff(X_stl,resu_stl);\n\n    if (error>1.e-3){\n      INFOS(\"WRONG CALCULATION...residual=\" << error);\n//       exit(0);\n    }\n\n  }\n\nprivate :\n\n  typename Interface::stl_matrix A_stl;\n  typename Interface::stl_vector B_stl;\n  typename Interface::stl_vector X_stl;\n  typename Interface::stl_vector resu_stl;\n\n  typename Interface::gene_matrix A_ref;\n  typename Interface::gene_vector B_ref;\n  typename Interface::gene_vector X_ref;\n\n  typename Interface::gene_matrix A;\n  typename Interface::gene_vector B;\n  typename Interface::gene_vector X;\n\n  int _size;\n};\n\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/actions/action_hessenberg.hh",
    "content": "//=====================================================\n// File   :  action_hessenberg.hh\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef ACTION_HESSENBERG\n#define ACTION_HESSENBERG\n#include \"utilities.h\"\n#include \"STL_interface.hh\"\n#include <string>\n#include \"init/init_function.hh\"\n#include \"init/init_vector.hh\"\n#include \"init/init_matrix.hh\"\n\nusing namespace std;\n\ntemplate<class Interface>\nclass Action_hessenberg {\n\npublic :\n\n  // Ctor\n\n  Action_hessenberg( int size ):_size(size)\n  {\n    MESSAGE(\"Action_hessenberg Ctor\");\n\n    // STL vector initialization\n    init_matrix<pseudo_random>(X_stl,_size);\n\n    init_matrix<null_function>(C_stl,_size);\n    init_matrix<null_function>(resu_stl,_size);\n\n    // generic matrix and vector initialization\n    Interface::matrix_from_stl(X_ref,X_stl);\n    Interface::matrix_from_stl(X,X_stl);\n    Interface::matrix_from_stl(C,C_stl);\n\n    _cost = 0;\n    for (int j=0; j<_size-2; ++j)\n    {\n      double r = std::max(0,_size-j-1);\n      double b = std::max(0,_size-j-2);\n      _cost += 6 + 3*b + r*r*4 + r*_size*4;\n    }\n  }\n\n  // invalidate copy ctor\n\n  Action_hessenberg( const  Action_hessenberg & )\n  {\n    INFOS(\"illegal call to Action_hessenberg Copy Ctor\");\n    exit(1);\n  }\n\n  // Dtor\n\n  ~Action_hessenberg( void ){\n\n    MESSAGE(\"Action_hessenberg Dtor\");\n\n    // deallocation\n    Interface::free_matrix(X_ref,_size);\n    Interface::free_matrix(X,_size);\n    Interface::free_matrix(C,_size);\n  }\n\n  // action name\n\n  static inline std::string name( void )\n  {\n    return \"hessenberg_\"+Interface::name();\n  }\n\n  double nb_op_base( void ){\n    return _cost;\n  }\n\n  inline void initialize( void ){\n    Interface::copy_matrix(X_ref,X,_size);\n  }\n\n  inline void calculate( void ) {\n      Interface::hessenberg(X,C,_size);\n  }\n\n  void check_result( void ){\n    // calculation check\n    Interface::matrix_to_stl(C,resu_stl);\n\n//     STL_interface<typename Interface::real_type>::hessenberg(X_stl,C_stl,_size);\n//\n//     typename Interface::real_type error=\n//       STL_interface<typename Interface::real_type>::norm_diff(C_stl,resu_stl);\n//\n//     if (error>1.e-6){\n//       INFOS(\"WRONG CALCULATION...residual=\" << error);\n//       exit(0);\n//     }\n\n  }\n\nprivate :\n\n  typename Interface::stl_matrix X_stl;\n  typename Interface::stl_matrix C_stl;\n  typename Interface::stl_matrix resu_stl;\n\n  typename Interface::gene_matrix X_ref;\n  typename Interface::gene_matrix X;\n  typename Interface::gene_matrix C;\n\n  int _size;\n  double _cost;\n};\n\ntemplate<class Interface>\nclass Action_tridiagonalization {\n\npublic :\n\n  // Ctor\n\n  Action_tridiagonalization( int size ):_size(size)\n  {\n    MESSAGE(\"Action_tridiagonalization Ctor\");\n\n    // STL vector initialization\n    init_matrix<pseudo_random>(X_stl,_size);\n    \n    for(int i=0; i<_size; ++i)\n    {\n      for(int j=0; j<i; ++j)\n        X_stl[i][j] = X_stl[j][i];\n    }\n    \n    init_matrix<null_function>(C_stl,_size);\n    init_matrix<null_function>(resu_stl,_size);\n\n    // generic matrix and vector initialization\n    Interface::matrix_from_stl(X_ref,X_stl);\n    Interface::matrix_from_stl(X,X_stl);\n    Interface::matrix_from_stl(C,C_stl);\n\n    _cost = 0;\n    for (int j=0; j<_size-2; ++j)\n    {\n      double r = std::max(0,_size-j-1);\n      double b = std::max(0,_size-j-2);\n      _cost += 6. + 3.*b + r*r*8.;\n    }\n  }\n\n  // invalidate copy ctor\n\n  Action_tridiagonalization( const  Action_tridiagonalization & )\n  {\n    INFOS(\"illegal call to Action_tridiagonalization Copy Ctor\");\n    exit(1);\n  }\n\n  // Dtor\n\n  ~Action_tridiagonalization( void ){\n\n    MESSAGE(\"Action_tridiagonalization Dtor\");\n\n    // deallocation\n    Interface::free_matrix(X_ref,_size);\n    Interface::free_matrix(X,_size);\n    Interface::free_matrix(C,_size);\n  }\n\n  // action name\n\n  static inline std::string name( void ) { return \"tridiagonalization_\"+Interface::name(); }\n\n  double nb_op_base( void ){\n    return _cost;\n  }\n\n  inline void initialize( void ){\n    Interface::copy_matrix(X_ref,X,_size);\n  }\n\n  inline void calculate( void ) {\n      Interface::tridiagonalization(X,C,_size);\n  }\n\n  void check_result( void ){\n    // calculation check\n    Interface::matrix_to_stl(C,resu_stl);\n\n//     STL_interface<typename Interface::real_type>::tridiagonalization(X_stl,C_stl,_size);\n//\n//     typename Interface::real_type error=\n//       STL_interface<typename Interface::real_type>::norm_diff(C_stl,resu_stl);\n//\n//     if (error>1.e-6){\n//       INFOS(\"WRONG CALCULATION...residual=\" << error);\n//       exit(0);\n//     }\n\n  }\n\nprivate :\n\n  typename Interface::stl_matrix X_stl;\n  typename Interface::stl_matrix C_stl;\n  typename Interface::stl_matrix resu_stl;\n\n  typename Interface::gene_matrix X_ref;\n  typename Interface::gene_matrix X;\n  typename Interface::gene_matrix C;\n\n  int _size;\n  double _cost;\n};\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/actions/action_lu_decomp.hh",
    "content": "//=====================================================\n// File   :  action_lu_decomp.hh\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef ACTION_LU_DECOMP\n#define ACTION_LU_DECOMP\n#include \"utilities.h\"\n#include \"STL_interface.hh\"\n#include <string>\n#include \"init/init_function.hh\"\n#include \"init/init_vector.hh\"\n#include \"init/init_matrix.hh\"\n\nusing namespace std;\n\ntemplate<class Interface>\nclass Action_lu_decomp {\n\npublic :\n\n  // Ctor\n\n  Action_lu_decomp( int size ):_size(size)\n  {\n    MESSAGE(\"Action_lu_decomp Ctor\");\n\n    // STL vector initialization\n    init_matrix<pseudo_random>(X_stl,_size);\n\n    init_matrix<null_function>(C_stl,_size);\n    init_matrix<null_function>(resu_stl,_size);\n\n    // generic matrix and vector initialization\n    Interface::matrix_from_stl(X_ref,X_stl);\n    Interface::matrix_from_stl(X,X_stl);\n    Interface::matrix_from_stl(C,C_stl);\n\n    _cost = 2.0*size*size*size/3.0 + size*size;\n  }\n\n  // invalidate copy ctor\n\n  Action_lu_decomp( const  Action_lu_decomp & )\n  {\n    INFOS(\"illegal call to Action_lu_decomp Copy Ctor\");\n    exit(1);\n  }\n\n  // Dtor\n\n  ~Action_lu_decomp( void ){\n\n    MESSAGE(\"Action_lu_decomp Dtor\");\n\n    // deallocation\n    Interface::free_matrix(X_ref,_size);\n    Interface::free_matrix(X,_size);\n    Interface::free_matrix(C,_size);\n  }\n\n  // action name\n\n  static inline std::string name( void )\n  {\n    return \"complete_lu_decomp_\"+Interface::name();\n  }\n\n  double nb_op_base( void ){\n    return _cost;\n  }\n\n  inline void initialize( void ){\n    Interface::copy_matrix(X_ref,X,_size);\n  }\n\n  inline void calculate( void ) {\n      Interface::lu_decomp(X,C,_size);\n  }\n\n  void check_result( void ){\n    // calculation check\n    Interface::matrix_to_stl(C,resu_stl);\n\n//     STL_interface<typename Interface::real_type>::lu_decomp(X_stl,C_stl,_size);\n//\n//     typename Interface::real_type error=\n//       STL_interface<typename Interface::real_type>::norm_diff(C_stl,resu_stl);\n//\n//     if (error>1.e-6){\n//       INFOS(\"WRONG CALCULATION...residual=\" << error);\n//       exit(0);\n//     }\n\n  }\n\nprivate :\n\n  typename Interface::stl_matrix X_stl;\n  typename Interface::stl_matrix C_stl;\n  typename Interface::stl_matrix resu_stl;\n\n  typename Interface::gene_matrix X_ref;\n  typename Interface::gene_matrix X;\n  typename Interface::gene_matrix C;\n\n  int _size;\n  double _cost;\n};\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/actions/action_lu_solve.hh",
    "content": "//=====================================================\n// File   :  action_lu_solve.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>        \n// Copyright (C) EDF R&D,  lun sep 30 14:23:19 CEST 2002\n//=====================================================\n// \n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n// \n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n// \n#ifndef ACTION_LU_SOLVE\n#define ACTION_LU_SOLVE\n#include \"utilities.h\"\n#include \"STL_interface.hh\"\n#include <string>\n#include \"init/init_function.hh\"\n#include \"init/init_vector.hh\"\n#include \"init/init_matrix.hh\"\n\nusing namespace std;\n\ntemplate<class Interface>\nclass Action_lu_solve \n{\n\npublic :\n\n  static inline std::string name( void )\n  {\n    return \"lu_solve_\"+Interface::name();\n  }\n  \n  static double nb_op_base(int size){\n    return 2.0*size*size*size/3.0;  // questionable but not really important\n  }\n\n\n  static double calculate( int nb_calc, int size ) {\n\n    // STL matrix and vector initialization\n    \n    typename Interface::stl_matrix A_stl;\n    typename Interface::stl_vector B_stl;\n    typename Interface::stl_vector X_stl;\n\n    init_matrix<pseudo_random>(A_stl,size);\n    init_vector<pseudo_random>(B_stl,size);\n    init_vector<null_function>(X_stl,size);\n\n    // generic matrix and vector initialization\n\n    typename Interface::gene_matrix A;\n    typename Interface::gene_vector B;\n    typename Interface::gene_vector X;\n\n    typename Interface::gene_matrix LU; \n\n    Interface::matrix_from_stl(A,A_stl);\n    Interface::vector_from_stl(B,B_stl);\n    Interface::vector_from_stl(X,X_stl);\n    Interface::matrix_from_stl(LU,A_stl);\n  \n    // local variable :\n\n    typename Interface::Pivot_Vector pivot; // pivot vector\n    Interface::new_Pivot_Vector(pivot,size);\n    \n    // timer utilities\n\n    Portable_Timer chronos;\n\n    // time measurement\n\n    chronos.start();\n    \n    for (int ii=0;ii<nb_calc;ii++){\n\n      // LU factorization\n      Interface::copy_matrix(A,LU,size);\n      Interface::LU_factor(LU,pivot,size);\n      \n      // LU solve\n\n      Interface::LU_solve(LU,pivot,B,X,size);\n\n    }\n\n    // Time stop\n\n    chronos.stop();\n\n    double time=chronos.user_time();\n  \n    // check result :\n\n    typename Interface::stl_vector B_new_stl(size);\n    Interface::vector_to_stl(X,X_stl);\n\n    STL_interface<typename Interface::real_type>::matrix_vector_product(A_stl,X_stl,B_new_stl,size); \n  \n    typename Interface::real_type error=\n      STL_interface<typename Interface::real_type>::norm_diff(B_stl,B_new_stl);\n    \n    if (error>1.e-5){\n      INFOS(\"WRONG CALCULATION...residual=\" << error);\n      STL_interface<typename Interface::real_type>::display_vector(B_stl);\n      STL_interface<typename Interface::real_type>::display_vector(B_new_stl);\n      exit(0);\n    }\n    \n    // deallocation and return time\n    \n    Interface::free_matrix(A,size);\n    Interface::free_vector(B);\n    Interface::free_vector(X);\n    Interface::free_Pivot_Vector(pivot);\n\n    return time;\n  }\n\n};\n  \n\n#endif\n\n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/actions/action_matrix_matrix_product.hh",
    "content": "//=====================================================\n// File   :  action_matrix_matrix_product.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>\n// Copyright (C) EDF R&D,  lun sep 30 14:23:19 CEST 2002\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef ACTION_MATRIX_MATRIX_PRODUCT\n#define ACTION_MATRIX_MATRIX_PRODUCT\n#include \"utilities.h\"\n#include \"STL_interface.hh\"\n#include <string>\n#include \"init/init_function.hh\"\n#include \"init/init_vector.hh\"\n#include \"init/init_matrix.hh\"\n\nusing namespace std;\n\ntemplate<class Interface>\nclass Action_matrix_matrix_product {\n\npublic :\n\n  // Ctor\n\n  Action_matrix_matrix_product( int size ):_size(size)\n  {\n    MESSAGE(\"Action_matrix_matrix_product Ctor\");\n\n    // STL matrix and vector initialization\n\n    init_matrix<pseudo_random>(A_stl,_size);\n    init_matrix<pseudo_random>(B_stl,_size);\n    init_matrix<null_function>(X_stl,_size);\n    init_matrix<null_function>(resu_stl,_size);\n\n    // generic matrix and vector initialization\n\n    Interface::matrix_from_stl(A_ref,A_stl);\n    Interface::matrix_from_stl(B_ref,B_stl);\n    Interface::matrix_from_stl(X_ref,X_stl);\n\n    Interface::matrix_from_stl(A,A_stl);\n    Interface::matrix_from_stl(B,B_stl);\n    Interface::matrix_from_stl(X,X_stl);\n\n  }\n\n  // invalidate copy ctor\n\n  Action_matrix_matrix_product( const  Action_matrix_matrix_product & )\n  {\n    INFOS(\"illegal call to Action_matrix_matrix_product Copy Ctor\");\n    exit(0);\n  }\n\n  // Dtor\n\n  ~Action_matrix_matrix_product( void ){\n\n    MESSAGE(\"Action_matrix_matrix_product Dtor\");\n\n    // deallocation\n\n    Interface::free_matrix(A,_size);\n    Interface::free_matrix(B,_size);\n    Interface::free_matrix(X,_size);\n\n    Interface::free_matrix(A_ref,_size);\n    Interface::free_matrix(B_ref,_size);\n    Interface::free_matrix(X_ref,_size);\n\n  }\n\n  // action name\n\n  static inline std::string name( void )\n  {\n    return \"matrix_matrix_\"+Interface::name();\n  }\n\n  double nb_op_base( void ){\n    return 2.0*_size*_size*_size;\n  }\n\n  inline void initialize( void ){\n\n    Interface::copy_matrix(A_ref,A,_size);\n    Interface::copy_matrix(B_ref,B,_size);\n    Interface::copy_matrix(X_ref,X,_size);\n\n  }\n\n  inline void calculate( void ) {\n      Interface::matrix_matrix_product(A,B,X,_size);\n  }\n\n  void check_result( void ){\n\n    // calculation check\n    if (_size<200)\n    {\n      Interface::matrix_to_stl(X,resu_stl);\n      STL_interface<typename Interface::real_type>::matrix_matrix_product(A_stl,B_stl,X_stl,_size);\n      typename Interface::real_type error=\n        STL_interface<typename Interface::real_type>::norm_diff(X_stl,resu_stl);\n      if (error>1.e-6){\n        INFOS(\"WRONG CALCULATION...residual=\" << error);\n        exit(1);\n      }\n    }\n  }\n\nprivate :\n\n  typename Interface::stl_matrix A_stl;\n  typename Interface::stl_matrix B_stl;\n  typename Interface::stl_matrix X_stl;\n  typename Interface::stl_matrix resu_stl;\n\n  typename Interface::gene_matrix A_ref;\n  typename Interface::gene_matrix B_ref;\n  typename Interface::gene_matrix X_ref;\n\n  typename Interface::gene_matrix A;\n  typename Interface::gene_matrix B;\n  typename Interface::gene_matrix X;\n\n\n  int _size;\n\n};\n\n\n#endif\n\n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/actions/action_matrix_matrix_product_bis.hh",
    "content": "//=====================================================\n// File   :  action_matrix_matrix_product_bis.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>\n// Copyright (C) EDF R&D,  lun sep 30 14:23:19 CEST 2002\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef ACTION_MATRIX_MATRIX_PRODUCT_BIS\n#define ACTION_MATRIX_MATRIX_PRODUCT_BIS\n#include \"utilities.h\"\n#include \"STL_interface.hh\"\n#include \"STL_timer.hh\"\n#include <string>\n#include \"init_function.hh\"\n#include \"init_vector.hh\"\n#include \"init_matrix.hh\"\n\nusing namespace std;\n\ntemplate<class Interface>\nclass Action_matrix_matrix_product_bis {\n\npublic :\n\n  static inline std::string name( void )\n  {\n    return \"matrix_matrix_\"+Interface::name();\n  }\n\n  static double nb_op_base(int size){\n    return 2.0*size*size*size;\n  }\n\n  static double calculate( int nb_calc, int size ) {\n\n    // STL matrix and vector initialization\n\n    typename Interface::stl_matrix A_stl;\n    typename Interface::stl_matrix B_stl;\n    typename Interface::stl_matrix X_stl;\n\n    init_matrix<pseudo_random>(A_stl,size);\n    init_matrix<pseudo_random>(B_stl,size);\n    init_matrix<null_function>(X_stl,size);\n\n    // generic matrix and vector initialization\n\n    typename Interface::gene_matrix A_ref;\n    typename Interface::gene_matrix B_ref;\n    typename Interface::gene_matrix X_ref;\n\n    typename Interface::gene_matrix A;\n    typename Interface::gene_matrix B;\n    typename Interface::gene_matrix X;\n\n\n    Interface::matrix_from_stl(A_ref,A_stl);\n    Interface::matrix_from_stl(B_ref,B_stl);\n    Interface::matrix_from_stl(X_ref,X_stl);\n\n    Interface::matrix_from_stl(A,A_stl);\n    Interface::matrix_from_stl(B,B_stl);\n    Interface::matrix_from_stl(X,X_stl);\n\n\n    // STL_timer utilities\n\n    STL_timer chronos;\n\n    // Baseline evaluation\n\n    chronos.start_baseline(nb_calc);\n\n    do {\n\n      Interface::copy_matrix(A_ref,A,size);\n      Interface::copy_matrix(B_ref,B,size);\n      Interface::copy_matrix(X_ref,X,size);\n\n\n      //      Interface::matrix_matrix_product(A,B,X,size); This line must be commented !!!!\n    }\n    while(chronos.check());\n\n    chronos.report(true);\n\n    // Time measurement\n\n    chronos.start(nb_calc);\n\n    do {\n\n      Interface::copy_matrix(A_ref,A,size);\n      Interface::copy_matrix(B_ref,B,size);\n      Interface::copy_matrix(X_ref,X,size);\n\n      Interface::matrix_matrix_product(A,B,X,size); // here it is not commented !!!!\n    }\n    while(chronos.check());\n\n    chronos.report(true);\n\n    double time=chronos.calculated_time/2000.0;\n\n    // calculation check\n\n    typename Interface::stl_matrix resu_stl(size);\n\n    Interface::matrix_to_stl(X,resu_stl);\n\n    STL_interface<typename Interface::real_type>::matrix_matrix_product(A_stl,B_stl,X_stl,size);\n\n    typename Interface::real_type error=\n      STL_interface<typename Interface::real_type>::norm_diff(X_stl,resu_stl);\n\n    if (error>1.e-6){\n      INFOS(\"WRONG CALCULATION...residual=\" << error);\n      exit(1);\n    }\n\n    // deallocation and return time\n\n    Interface::free_matrix(A,size);\n    Interface::free_matrix(B,size);\n    Interface::free_matrix(X,size);\n\n    Interface::free_matrix(A_ref,size);\n    Interface::free_matrix(B_ref,size);\n    Interface::free_matrix(X_ref,size);\n\n    return time;\n  }\n\n};\n\n\n#endif\n\n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/actions/action_matrix_vector_product.hh",
    "content": "//=====================================================\n// File   :  action_matrix_vector_product.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>\n// Copyright (C) EDF R&D,  lun sep 30 14:23:19 CEST 2002\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef ACTION_MATRIX_VECTOR_PRODUCT\n#define ACTION_MATRIX_VECTOR_PRODUCT\n#include \"utilities.h\"\n#include \"STL_interface.hh\"\n#include <string>\n#include \"init/init_function.hh\"\n#include \"init/init_vector.hh\"\n#include \"init/init_matrix.hh\"\n\nusing namespace std;\n\ntemplate<class Interface>\nclass Action_matrix_vector_product {\n\npublic :\n\n  // Ctor\n\n  BTL_DONT_INLINE Action_matrix_vector_product( int size ):_size(size)\n  {\n    MESSAGE(\"Action_matrix_vector_product Ctor\");\n\n    // STL matrix and vector initialization\n\n    init_matrix<pseudo_random>(A_stl,_size);\n    init_vector<pseudo_random>(B_stl,_size);\n    init_vector<null_function>(X_stl,_size);\n    init_vector<null_function>(resu_stl,_size);\n\n    // generic matrix and vector initialization\n\n    Interface::matrix_from_stl(A_ref,A_stl);\n    Interface::matrix_from_stl(A,A_stl);\n    Interface::vector_from_stl(B_ref,B_stl);\n    Interface::vector_from_stl(B,B_stl);\n    Interface::vector_from_stl(X_ref,X_stl);\n    Interface::vector_from_stl(X,X_stl);\n\n  }\n\n  // invalidate copy ctor\n\n  Action_matrix_vector_product( const  Action_matrix_vector_product & )\n  {\n    INFOS(\"illegal call to Action_matrix_vector_product Copy Ctor\");\n    exit(1);\n  }\n\n  // Dtor\n\n  BTL_DONT_INLINE ~Action_matrix_vector_product( void ){\n\n    MESSAGE(\"Action_matrix_vector_product Dtor\");\n\n    // deallocation\n\n    Interface::free_matrix(A,_size);\n    Interface::free_vector(B);\n    Interface::free_vector(X);\n\n    Interface::free_matrix(A_ref,_size);\n    Interface::free_vector(B_ref);\n    Interface::free_vector(X_ref);\n\n  }\n\n  // action name\n\n  static inline std::string name( void )\n  {\n    return \"matrix_vector_\" + Interface::name();\n  }\n\n  double nb_op_base( void ){\n    return 2.0*_size*_size;\n  }\n\n  BTL_DONT_INLINE  void initialize( void ){\n\n    Interface::copy_matrix(A_ref,A,_size);\n    Interface::copy_vector(B_ref,B,_size);\n    Interface::copy_vector(X_ref,X,_size);\n\n  }\n\n  BTL_DONT_INLINE void calculate( void ) {\n      BTL_ASM_COMMENT(\"#begin matrix_vector_product\");\n      Interface::matrix_vector_product(A,B,X,_size);\n      BTL_ASM_COMMENT(\"end matrix_vector_product\");\n  }\n\n  BTL_DONT_INLINE void check_result( void ){\n\n    // calculation check\n\n    Interface::vector_to_stl(X,resu_stl);\n\n    STL_interface<typename Interface::real_type>::matrix_vector_product(A_stl,B_stl,X_stl,_size);\n\n    typename Interface::real_type error=\n      STL_interface<typename Interface::real_type>::norm_diff(X_stl,resu_stl);\n\n    if (error>1.e-5){\n      INFOS(\"WRONG CALCULATION...residual=\" << error);\n      exit(0);\n    }\n\n  }\n\nprivate :\n\n  typename Interface::stl_matrix A_stl;\n  typename Interface::stl_vector B_stl;\n  typename Interface::stl_vector X_stl;\n  typename Interface::stl_vector resu_stl;\n\n  typename Interface::gene_matrix A_ref;\n  typename Interface::gene_vector B_ref;\n  typename Interface::gene_vector X_ref;\n\n  typename Interface::gene_matrix A;\n  typename Interface::gene_vector B;\n  typename Interface::gene_vector X;\n\n\n  int _size;\n\n};\n\n\n#endif\n\n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/actions/action_partial_lu.hh",
    "content": "//=====================================================\n// File   :  action_lu_decomp.hh\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef ACTION_PARTIAL_LU\n#define ACTION_PARTIAL_LU\n#include \"utilities.h\"\n#include \"STL_interface.hh\"\n#include <string>\n#include \"init/init_function.hh\"\n#include \"init/init_vector.hh\"\n#include \"init/init_matrix.hh\"\n\nusing namespace std;\n\ntemplate<class Interface>\nclass Action_partial_lu {\n\npublic :\n\n  // Ctor\n\n  Action_partial_lu( int size ):_size(size)\n  {\n    MESSAGE(\"Action_partial_lu Ctor\");\n\n    // STL vector initialization\n    init_matrix<pseudo_random>(X_stl,_size);\n    init_matrix<null_function>(C_stl,_size);\n\n    // make sure X is invertible\n    for (int i=0; i<_size; ++i)\n      X_stl[i][i] = X_stl[i][i] * 1e2 + 1;\n\n    // generic matrix and vector initialization\n    Interface::matrix_from_stl(X_ref,X_stl);\n    Interface::matrix_from_stl(X,X_stl);\n    Interface::matrix_from_stl(C,C_stl);\n\n    _cost = 2.0*size*size*size/3.0 + size*size;\n  }\n\n  // invalidate copy ctor\n\n  Action_partial_lu( const  Action_partial_lu & )\n  {\n    INFOS(\"illegal call to Action_partial_lu Copy Ctor\");\n    exit(1);\n  }\n\n  // Dtor\n\n  ~Action_partial_lu( void ){\n\n    MESSAGE(\"Action_partial_lu Dtor\");\n\n    // deallocation\n    Interface::free_matrix(X_ref,_size);\n    Interface::free_matrix(X,_size);\n    Interface::free_matrix(C,_size);\n  }\n\n  // action name\n\n  static inline std::string name( void )\n  {\n    return \"partial_lu_decomp_\"+Interface::name();\n  }\n\n  double nb_op_base( void ){\n    return _cost;\n  }\n\n  inline void initialize( void ){\n    Interface::copy_matrix(X_ref,X,_size);\n  }\n\n  inline void calculate( void ) {\n      Interface::partial_lu_decomp(X,C,_size);\n  }\n\n  void check_result( void ){\n    // calculation check\n//     Interface::matrix_to_stl(C,resu_stl);\n\n//     STL_interface<typename Interface::real_type>::lu_decomp(X_stl,C_stl,_size);\n//\n//     typename Interface::real_type error=\n//       STL_interface<typename Interface::real_type>::norm_diff(C_stl,resu_stl);\n//\n//     if (error>1.e-6){\n//       INFOS(\"WRONG CALCULATION...residual=\" << error);\n//       exit(0);\n//     }\n\n  }\n\nprivate :\n\n  typename Interface::stl_matrix X_stl;\n  typename Interface::stl_matrix C_stl;\n\n  typename Interface::gene_matrix X_ref;\n  typename Interface::gene_matrix X;\n  typename Interface::gene_matrix C;\n\n  int _size;\n  double _cost;\n};\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/actions/action_rot.hh",
    "content": "\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef ACTION_ROT\n#define ACTION_ROT\n#include \"utilities.h\"\n#include \"STL_interface.hh\"\n#include <string>\n#include \"init/init_function.hh\"\n#include \"init/init_vector.hh\"\n#include \"init/init_matrix.hh\"\n\nusing namespace std;\n\ntemplate<class Interface>\nclass Action_rot {\n\npublic :\n\n  // Ctor\n  BTL_DONT_INLINE Action_rot( int size ):_size(size)\n  {\n    MESSAGE(\"Action_rot Ctor\");\n\n    // STL matrix and vector initialization\n    typename Interface::stl_matrix tmp;\n    init_vector<pseudo_random>(A_stl,_size);\n    init_vector<pseudo_random>(B_stl,_size);\n\n    // generic matrix and vector initialization\n    Interface::vector_from_stl(A_ref,A_stl);\n    Interface::vector_from_stl(A,A_stl);\n    Interface::vector_from_stl(B_ref,B_stl);\n    Interface::vector_from_stl(B,B_stl);\n  }\n\n  // invalidate copy ctor\n  Action_rot( const  Action_rot & )\n  {\n    INFOS(\"illegal call to Action_rot Copy Ctor\");\n    exit(1);\n  }\n\n  // Dtor\n  BTL_DONT_INLINE ~Action_rot( void ){\n    MESSAGE(\"Action_rot Dtor\");\n    Interface::free_vector(A);\n    Interface::free_vector(B);\n    Interface::free_vector(A_ref);\n    Interface::free_vector(B_ref);\n  }\n\n  // action name\n  static inline std::string name( void )\n  {\n    return \"rot_\" + Interface::name();\n  }\n\n  double nb_op_base( void ){\n    return 6.0*_size;\n  }\n\n  BTL_DONT_INLINE  void initialize( void ){\n    Interface::copy_vector(A_ref,A,_size);\n    Interface::copy_vector(B_ref,B,_size);\n  }\n\n  BTL_DONT_INLINE void calculate( void ) {\n    BTL_ASM_COMMENT(\"#begin rot\");\n    Interface::rot(A,B,0.5,0.6,_size);\n    BTL_ASM_COMMENT(\"end rot\");\n  }\n\n  BTL_DONT_INLINE void check_result( void ){\n    // calculation check\n//     Interface::vector_to_stl(X,resu_stl);\n\n//     STL_interface<typename Interface::real_type>::rot(A_stl,B_stl,X_stl,_size);\n\n//     typename Interface::real_type error=\n//       STL_interface<typename Interface::real_type>::norm_diff(X_stl,resu_stl);\n\n//     if (error>1.e-3){\n//       INFOS(\"WRONG CALCULATION...residual=\" << error);\n//       exit(0);\n//     }\n\n  }\n\nprivate :\n\n  typename Interface::stl_vector A_stl;\n  typename Interface::stl_vector B_stl;\n\n  typename Interface::gene_vector A_ref;\n  typename Interface::gene_vector B_ref;\n\n  typename Interface::gene_vector A;\n  typename Interface::gene_vector B;\n\n  int _size;\n};\n\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/actions/action_symv.hh",
    "content": "//=====================================================\n// File   :  action_symv.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>\n// Copyright (C) EDF R&D,  lun sep 30 14:23:19 CEST 2002\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef ACTION_SYMV\n#define ACTION_SYMV\n#include \"utilities.h\"\n#include \"STL_interface.hh\"\n#include <string>\n#include \"init/init_function.hh\"\n#include \"init/init_vector.hh\"\n#include \"init/init_matrix.hh\"\n\nusing namespace std;\n\ntemplate<class Interface>\nclass Action_symv {\n\npublic :\n\n  // Ctor\n\n  BTL_DONT_INLINE Action_symv( int size ):_size(size)\n  {\n    MESSAGE(\"Action_symv Ctor\");\n\n    // STL matrix and vector initialization\n    init_matrix_symm<pseudo_random>(A_stl,_size);\n    init_vector<pseudo_random>(B_stl,_size);\n    init_vector<null_function>(X_stl,_size);\n    init_vector<null_function>(resu_stl,_size);\n\n    // generic matrix and vector initialization\n    Interface::matrix_from_stl(A_ref,A_stl);\n    Interface::matrix_from_stl(A,A_stl);\n    Interface::vector_from_stl(B_ref,B_stl);\n    Interface::vector_from_stl(B,B_stl);\n    Interface::vector_from_stl(X_ref,X_stl);\n    Interface::vector_from_stl(X,X_stl);\n\n  }\n\n  // invalidate copy ctor\n\n  Action_symv( const  Action_symv & )\n  {\n    INFOS(\"illegal call to Action_symv Copy Ctor\");\n    exit(1);\n  }\n\n  // Dtor\n  BTL_DONT_INLINE ~Action_symv( void ){\n    Interface::free_matrix(A,_size);\n    Interface::free_vector(B);\n    Interface::free_vector(X);\n    Interface::free_matrix(A_ref,_size);\n    Interface::free_vector(B_ref);\n    Interface::free_vector(X_ref);\n  }\n\n  // action name\n\n  static inline std::string name( void )\n  {\n    return \"symv_\" + Interface::name();\n  }\n\n  double nb_op_base( void ){\n    return 2.0*_size*_size;\n  }\n\n  BTL_DONT_INLINE  void initialize( void ){\n\n    Interface::copy_matrix(A_ref,A,_size);\n    Interface::copy_vector(B_ref,B,_size);\n    Interface::copy_vector(X_ref,X,_size);\n\n  }\n\n  BTL_DONT_INLINE void calculate( void ) {\n      BTL_ASM_COMMENT(\"#begin symv\");\n      Interface::symv(A,B,X,_size);\n      BTL_ASM_COMMENT(\"end symv\");\n  }\n\n  BTL_DONT_INLINE void check_result( void ){\n    if (_size>128) return;\n    // calculation check\n    Interface::vector_to_stl(X,resu_stl);\n\n    STL_interface<typename Interface::real_type>::symv(A_stl,B_stl,X_stl,_size);\n\n    typename Interface::real_type error=\n      STL_interface<typename Interface::real_type>::norm_diff(X_stl,resu_stl);\n\n    if (error>1.e-5){\n      INFOS(\"WRONG CALCULATION...residual=\" << error);\n      exit(0);\n    }\n\n  }\n\nprivate :\n\n  typename Interface::stl_matrix A_stl;\n  typename Interface::stl_vector B_stl;\n  typename Interface::stl_vector X_stl;\n  typename Interface::stl_vector resu_stl;\n\n  typename Interface::gene_matrix A_ref;\n  typename Interface::gene_vector B_ref;\n  typename Interface::gene_vector X_ref;\n\n  typename Interface::gene_matrix A;\n  typename Interface::gene_vector B;\n  typename Interface::gene_vector X;\n\n\n  int _size;\n\n};\n\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/actions/action_syr2.hh",
    "content": "//=====================================================\n// File   :  action_syr2.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>\n// Copyright (C) EDF R&D,  lun sep 30 14:23:19 CEST 2002\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef ACTION_SYR2\n#define ACTION_SYR2\n#include \"utilities.h\"\n#include \"STL_interface.hh\"\n#include <string>\n#include \"init/init_function.hh\"\n#include \"init/init_vector.hh\"\n#include \"init/init_matrix.hh\"\n\nusing namespace std;\n\ntemplate<class Interface>\nclass Action_syr2 {\n\npublic :\n\n  // Ctor\n\n  BTL_DONT_INLINE Action_syr2( int size ):_size(size)\n  {\n    // STL matrix and vector initialization\n    typename Interface::stl_matrix tmp;\n    init_matrix<pseudo_random>(A_stl,_size);\n    init_vector<pseudo_random>(B_stl,_size);\n    init_vector<pseudo_random>(X_stl,_size);\n    init_vector<null_function>(resu_stl,_size);\n\n    // generic matrix and vector initialization\n    Interface::matrix_from_stl(A_ref,A_stl);\n    Interface::matrix_from_stl(A,A_stl);\n    Interface::vector_from_stl(B_ref,B_stl);\n    Interface::vector_from_stl(B,B_stl);\n    Interface::vector_from_stl(X_ref,X_stl);\n    Interface::vector_from_stl(X,X_stl);\n  }\n\n  // invalidate copy ctor\n  Action_syr2( const  Action_syr2 & )\n  {\n    INFOS(\"illegal call to Action_syr2 Copy Ctor\");\n    exit(1);\n  }\n\n  // Dtor\n  BTL_DONT_INLINE ~Action_syr2( void ){\n    Interface::free_matrix(A,_size);\n    Interface::free_vector(B);\n    Interface::free_vector(X);\n    Interface::free_matrix(A_ref,_size);\n    Interface::free_vector(B_ref);\n    Interface::free_vector(X_ref);\n  }\n\n  // action name\n\n  static inline std::string name( void )\n  {\n    return \"syr2_\" + Interface::name();\n  }\n\n  double nb_op_base( void ){\n    return 2.0*_size*_size;\n  }\n\n  BTL_DONT_INLINE  void initialize( void ){\n    Interface::copy_matrix(A_ref,A,_size);\n    Interface::copy_vector(B_ref,B,_size);\n    Interface::copy_vector(X_ref,X,_size);\n  }\n\n  BTL_DONT_INLINE void calculate( void ) {\n      BTL_ASM_COMMENT(\"#begin syr2\");\n      Interface::syr2(A,B,X,_size);\n      BTL_ASM_COMMENT(\"end syr2\");\n  }\n\n  BTL_DONT_INLINE void check_result( void ){\n    // calculation check\n    Interface::vector_to_stl(X,resu_stl);\n\n    STL_interface<typename Interface::real_type>::syr2(A_stl,B_stl,X_stl,_size);\n\n    typename Interface::real_type error=\n      STL_interface<typename Interface::real_type>::norm_diff(X_stl,resu_stl);\n\n    if (error>1.e-3){\n      INFOS(\"WRONG CALCULATION...residual=\" << error);\n//       exit(0);\n    }\n\n  }\n\nprivate :\n\n  typename Interface::stl_matrix A_stl;\n  typename Interface::stl_vector B_stl;\n  typename Interface::stl_vector X_stl;\n  typename Interface::stl_vector resu_stl;\n\n  typename Interface::gene_matrix A_ref;\n  typename Interface::gene_vector B_ref;\n  typename Interface::gene_vector X_ref;\n\n  typename Interface::gene_matrix A;\n  typename Interface::gene_vector B;\n  typename Interface::gene_vector X;\n\n\n  int _size;\n\n};\n\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/actions/action_trisolve.hh",
    "content": "//=====================================================\n// File   :  action_trisolve.hh\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef ACTION_TRISOLVE\n#define ACTION_TRISOLVE\n#include \"utilities.h\"\n#include \"STL_interface.hh\"\n#include <string>\n#include \"init/init_function.hh\"\n#include \"init/init_vector.hh\"\n#include \"init/init_matrix.hh\"\n\nusing namespace std;\n\ntemplate<class Interface>\nclass Action_trisolve {\n\npublic :\n\n  // Ctor\n\n  Action_trisolve( int size ):_size(size)\n  {\n    MESSAGE(\"Action_trisolve Ctor\");\n\n    // STL vector initialization\n    init_matrix<pseudo_random>(L_stl,_size);\n    init_vector<pseudo_random>(B_stl,_size);\n    init_vector<null_function>(X_stl,_size);\n    for (int j=0; j<_size; ++j)\n    {\n      for (int i=0; i<j; ++i)\n        L_stl[j][i] = 0;\n      L_stl[j][j] += 3;\n    }\n\n    init_vector<null_function>(resu_stl,_size);\n\n    // generic matrix and vector initialization\n    Interface::matrix_from_stl(L,L_stl);\n    Interface::vector_from_stl(X,X_stl);\n    Interface::vector_from_stl(B,B_stl);\n\n    _cost = 0;\n    for (int j=0; j<_size; ++j)\n    {\n      _cost += 2*j + 1;\n    }\n  }\n\n  // invalidate copy ctor\n\n  Action_trisolve( const  Action_trisolve & )\n  {\n    INFOS(\"illegal call to Action_trisolve Copy Ctor\");\n    exit(1);\n  }\n\n  // Dtor\n\n  ~Action_trisolve( void ){\n\n    MESSAGE(\"Action_trisolve Dtor\");\n\n    // deallocation\n    Interface::free_matrix(L,_size);\n    Interface::free_vector(B);\n    Interface::free_vector(X);\n  }\n\n  // action name\n\n  static inline std::string name( void )\n  {\n    return \"trisolve_vector_\"+Interface::name();\n  }\n\n  double nb_op_base( void ){\n    return _cost;\n  }\n\n  inline void initialize( void ){\n    //Interface::copy_vector(X_ref,X,_size);\n  }\n\n  inline void calculate( void ) {\n      Interface::trisolve_lower(L,B,X,_size);\n  }\n\n  void check_result(){\n    if (_size>128) return;\n    // calculation check\n    Interface::vector_to_stl(X,resu_stl);\n\n    STL_interface<typename Interface::real_type>::trisolve_lower(L_stl,B_stl,X_stl,_size);\n\n    typename Interface::real_type error=\n      STL_interface<typename Interface::real_type>::norm_diff(X_stl,resu_stl);\n\n    if (error>1.e-4){\n      INFOS(\"WRONG CALCULATION...residual=\" << error);\n      exit(2);\n    } //else INFOS(\"CALCULATION OK...residual=\" << error);\n\n  }\n\nprivate :\n\n  typename Interface::stl_matrix L_stl;\n  typename Interface::stl_vector X_stl;\n  typename Interface::stl_vector B_stl;\n  typename Interface::stl_vector resu_stl;\n\n  typename Interface::gene_matrix L;\n  typename Interface::gene_vector X;\n  typename Interface::gene_vector B;\n\n  int _size;\n  double _cost;\n};\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/actions/action_trisolve_matrix.hh",
    "content": "//=====================================================\n// File   :  action_matrix_matrix_product.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>\n// Copyright (C) EDF R&D,  lun sep 30 14:23:19 CEST 2002\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef ACTION_TRISOLVE_MATRIX_PRODUCT\n#define ACTION_TRISOLVE_MATRIX_PRODUCT\n#include \"utilities.h\"\n#include \"STL_interface.hh\"\n#include <string>\n#include \"init/init_function.hh\"\n#include \"init/init_vector.hh\"\n#include \"init/init_matrix.hh\"\n\nusing namespace std;\n\ntemplate<class Interface>\nclass Action_trisolve_matrix {\n\npublic :\n\n  // Ctor\n\n  Action_trisolve_matrix( int size ):_size(size)\n  {\n    MESSAGE(\"Action_trisolve_matrix Ctor\");\n\n    // STL matrix and vector initialization\n\n    init_matrix<pseudo_random>(A_stl,_size);\n    init_matrix<pseudo_random>(B_stl,_size);\n    init_matrix<null_function>(X_stl,_size);\n    init_matrix<null_function>(resu_stl,_size);\n\n    for (int j=0; j<_size; ++j)\n    {\n      for (int i=0; i<j; ++i)\n        A_stl[j][i] = 0;\n      A_stl[j][j] += 3;\n    }\n\n    // generic matrix and vector initialization\n\n    Interface::matrix_from_stl(A_ref,A_stl);\n    Interface::matrix_from_stl(B_ref,B_stl);\n    Interface::matrix_from_stl(X_ref,X_stl);\n\n    Interface::matrix_from_stl(A,A_stl);\n    Interface::matrix_from_stl(B,B_stl);\n    Interface::matrix_from_stl(X,X_stl);\n\n    _cost = 0;\n    for (int j=0; j<_size; ++j)\n    {\n      _cost += 2*j + 1;\n    }\n    _cost *= _size;\n  }\n\n  // invalidate copy ctor\n\n  Action_trisolve_matrix( const  Action_trisolve_matrix & )\n  {\n    INFOS(\"illegal call to Action_trisolve_matrix Copy Ctor\");\n    exit(0);\n  }\n\n  // Dtor\n\n  ~Action_trisolve_matrix( void ){\n\n    MESSAGE(\"Action_trisolve_matrix Dtor\");\n\n    // deallocation\n\n    Interface::free_matrix(A,_size);\n    Interface::free_matrix(B,_size);\n    Interface::free_matrix(X,_size);\n\n    Interface::free_matrix(A_ref,_size);\n    Interface::free_matrix(B_ref,_size);\n    Interface::free_matrix(X_ref,_size);\n\n  }\n\n  // action name\n\n  static inline std::string name( void )\n  {\n    return \"trisolve_matrix_\"+Interface::name();\n  }\n\n  double nb_op_base( void ){\n    return _cost;\n  }\n\n  inline void initialize( void ){\n\n    Interface::copy_matrix(A_ref,A,_size);\n    Interface::copy_matrix(B_ref,B,_size);\n    Interface::copy_matrix(X_ref,X,_size);\n\n  }\n\n  inline void calculate( void ) {\n      Interface::trisolve_lower_matrix(A,B,X,_size);\n  }\n\n  void check_result( void ){\n\n    // calculation check\n\n//     Interface::matrix_to_stl(X,resu_stl);\n//\n//     STL_interface<typename Interface::real_type>::matrix_matrix_product(A_stl,B_stl,X_stl,_size);\n//\n//     typename Interface::real_type error=\n//       STL_interface<typename Interface::real_type>::norm_diff(X_stl,resu_stl);\n//\n//     if (error>1.e-6){\n//       INFOS(\"WRONG CALCULATION...residual=\" << error);\n// //       exit(1);\n//     }\n\n  }\n\nprivate :\n\n  typename Interface::stl_matrix A_stl;\n  typename Interface::stl_matrix B_stl;\n  typename Interface::stl_matrix X_stl;\n  typename Interface::stl_matrix resu_stl;\n\n  typename Interface::gene_matrix A_ref;\n  typename Interface::gene_matrix B_ref;\n  typename Interface::gene_matrix X_ref;\n\n  typename Interface::gene_matrix A;\n  typename Interface::gene_matrix B;\n  typename Interface::gene_matrix X;\n\n  int _size;\n  double _cost;\n\n};\n\n\n#endif\n\n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/actions/action_trmm.hh",
    "content": "//=====================================================\n// File   :  action_matrix_matrix_product.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>\n// Copyright (C) EDF R&D,  lun sep 30 14:23:19 CEST 2002\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef ACTION_TRMM\n#define ACTION_TRMM\n#include \"utilities.h\"\n#include \"STL_interface.hh\"\n#include <string>\n#include \"init/init_function.hh\"\n#include \"init/init_vector.hh\"\n#include \"init/init_matrix.hh\"\n\nusing namespace std;\n\ntemplate<class Interface>\nclass Action_trmm {\n\npublic :\n\n  // Ctor\n\n  Action_trmm( int size ):_size(size)\n  {\n    MESSAGE(\"Action_trmm Ctor\");\n\n    // STL matrix and vector initialization\n\n    init_matrix<pseudo_random>(A_stl,_size);\n    init_matrix<pseudo_random>(B_stl,_size);\n    init_matrix<null_function>(X_stl,_size);\n    init_matrix<null_function>(resu_stl,_size);\n\n    for (int j=0; j<_size; ++j)\n    {\n      for (int i=0; i<j; ++i)\n        A_stl[j][i] = 0;\n      A_stl[j][j] += 3;\n    }\n\n    // generic matrix and vector initialization\n\n    Interface::matrix_from_stl(A_ref,A_stl);\n    Interface::matrix_from_stl(B_ref,B_stl);\n    Interface::matrix_from_stl(X_ref,X_stl);\n\n    Interface::matrix_from_stl(A,A_stl);\n    Interface::matrix_from_stl(B,B_stl);\n    Interface::matrix_from_stl(X,X_stl);\n\n    _cost = 0;\n    for (int j=0; j<_size; ++j)\n    {\n      _cost += 2*j + 1;\n    }\n    _cost *= _size;\n  }\n\n  // invalidate copy ctor\n\n  Action_trmm( const  Action_trmm & )\n  {\n    INFOS(\"illegal call to Action_trmm Copy Ctor\");\n    exit(0);\n  }\n\n  // Dtor\n\n  ~Action_trmm( void ){\n\n    MESSAGE(\"Action_trmm Dtor\");\n\n    // deallocation\n\n    Interface::free_matrix(A,_size);\n    Interface::free_matrix(B,_size);\n    Interface::free_matrix(X,_size);\n\n    Interface::free_matrix(A_ref,_size);\n    Interface::free_matrix(B_ref,_size);\n    Interface::free_matrix(X_ref,_size);\n\n  }\n\n  // action name\n\n  static inline std::string name( void )\n  {\n    return \"trmm_\"+Interface::name();\n  }\n\n  double nb_op_base( void ){\n    return _cost;\n  }\n\n  inline void initialize( void ){\n\n    Interface::copy_matrix(A_ref,A,_size);\n    Interface::copy_matrix(B_ref,B,_size);\n    Interface::copy_matrix(X_ref,X,_size);\n\n  }\n\n  inline void calculate( void ) {\n      Interface::trmm(A,B,X,_size);\n  }\n\n  void check_result( void ){\n\n    // calculation check\n\n//     Interface::matrix_to_stl(X,resu_stl);\n//\n//     STL_interface<typename Interface::real_type>::matrix_matrix_product(A_stl,B_stl,X_stl,_size);\n//\n//     typename Interface::real_type error=\n//       STL_interface<typename Interface::real_type>::norm_diff(X_stl,resu_stl);\n//\n//     if (error>1.e-6){\n//       INFOS(\"WRONG CALCULATION...residual=\" << error);\n// //       exit(1);\n//     }\n\n  }\n\nprivate :\n\n  typename Interface::stl_matrix A_stl;\n  typename Interface::stl_matrix B_stl;\n  typename Interface::stl_matrix X_stl;\n  typename Interface::stl_matrix resu_stl;\n\n  typename Interface::gene_matrix A_ref;\n  typename Interface::gene_matrix B_ref;\n  typename Interface::gene_matrix X_ref;\n\n  typename Interface::gene_matrix A;\n  typename Interface::gene_matrix B;\n  typename Interface::gene_matrix X;\n\n  int _size;\n  double _cost;\n\n};\n\n\n#endif\n\n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/actions/basic_actions.hh",
    "content": "\n#include \"action_axpy.hh\"\n#include \"action_axpby.hh\"\n\n#include \"action_matrix_vector_product.hh\"\n#include \"action_atv_product.hh\"\n\n#include \"action_matrix_matrix_product.hh\"\n// #include \"action_ata_product.hh\"\n#include \"action_aat_product.hh\"\n\n#include \"action_trisolve.hh\"\n#include \"action_trmm.hh\"\n#include \"action_symv.hh\"\n// #include \"action_symm.hh\"\n#include \"action_syr2.hh\"\n#include \"action_ger.hh\"\n#include \"action_rot.hh\"\n\n// #include \"action_lu_solve.hh\"\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/cmake/FindACML.cmake",
    "content": "\nif (ACML_LIBRARIES)\n  set(ACML_FIND_QUIETLY TRUE)\nendif (ACML_LIBRARIES)\n\nfind_library(ACML_LIBRARIES\n  NAMES\n  acml_mp acml_mv\n  PATHS\n  $ENV{ACMLDIR}/lib\n  $ENV{ACML_DIR}/lib\n  ${LIB_INSTALL_DIR}\n)\n\nfind_file(ACML_LIBRARIES\n  NAMES\n  libacml_mp.so\n  PATHS\n  /usr/lib\n  /usr/lib64\n  $ENV{ACMLDIR}/lib\n  ${LIB_INSTALL_DIR}\n)\n\nif(NOT ACML_LIBRARIES)\n    message(STATUS \"Multi-threaded library not found, looking for single-threaded\")\n    find_library(ACML_LIBRARIES\n        NAMES\n        acml acml_mv\n        PATHS\n        $ENV{ACMLDIR}/lib\n        $ENV{ACML_DIR}/lib\n        ${LIB_INSTALL_DIR}\n        )\n    find_file(ACML_LIBRARIES\n        libacml.so libacml_mv.so\n        PATHS\n        /usr/lib\n        /usr/lib64\n        $ENV{ACMLDIR}/lib\n        ${LIB_INSTALL_DIR}\n        )\nendif()\n\n\n\n\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(ACML DEFAULT_MSG ACML_LIBRARIES)\n\nmark_as_advanced(ACML_LIBRARIES)\n"
  },
  {
    "path": "include/eigen3/bench/btl/cmake/FindATLAS.cmake",
    "content": "\nif (ATLAS_LIBRARIES)\n  set(ATLAS_FIND_QUIETLY TRUE)\nendif (ATLAS_LIBRARIES)\n\nfind_file(ATLAS_LIB libatlas.so.3 PATHS /usr/lib /usr/lib/atlas /usr/lib64 /usr/lib64/atlas $ENV{ATLASDIR} ${LIB_INSTALL_DIR})\nfind_library(ATLAS_LIB satlas PATHS $ENV{ATLASDIR} ${LIB_INSTALL_DIR})\n\nfind_file(ATLAS_LAPACK NAMES liblapack_atlas.so.3 liblapack.so.3 PATHS /usr/lib /usr/lib/atlas /usr/lib64 /usr/lib64/atlas $ENV{ATLASDIR} ${LIB_INSTALL_DIR})\nfind_library(ATLAS_LAPACK NAMES lapack_atlas lapack PATHS $ENV{ATLASDIR} ${LIB_INSTALL_DIR})\n\nfind_file(ATLAS_F77BLAS libf77blas.so.3 PATHS /usr/lib /usr/lib/atlas /usr/lib64 /usr/lib64/atlas $ENV{ATLASDIR} ${LIB_INSTALL_DIR})\nfind_library(ATLAS_F77BLAS f77blas PATHS $ENV{ATLASDIR} ${LIB_INSTALL_DIR})\n\nif(ATLAS_LIB AND ATLAS_CBLAS AND ATLAS_LAPACK AND ATLAS_F77BLAS)\n\n  set(ATLAS_LIBRARIES ${ATLAS_LAPACK}  ${ATLAS_LIB})\n  \n  # search the default lapack lib link to it\n  find_file(ATLAS_REFERENCE_LAPACK liblapack.so.3 PATHS /usr/lib /usr/lib64)\n  find_library(ATLAS_REFERENCE_LAPACK NAMES lapack)\n#   if(ATLAS_REFERENCE_LAPACK)\n#     set(ATLAS_LIBRARIES ${ATLAS_LIBRARIES} ${ATLAS_REFERENCE_LAPACK})\n#   endif()\n  \nendif(ATLAS_LIB AND ATLAS_CBLAS AND ATLAS_LAPACK AND ATLAS_F77BLAS)\n\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(ATLAS DEFAULT_MSG ATLAS_LIBRARIES)\n\nmark_as_advanced(ATLAS_LIBRARIES)\n"
  },
  {
    "path": "include/eigen3/bench/btl/cmake/FindBLAZE.cmake",
    "content": "# - Try to find eigen2 headers\n# Once done this will define\n#\n#  BLAZE_FOUND - system has blaze lib\n#  BLAZE_INCLUDE_DIR - the blaze include directory\n#\n# Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n# Adapted from FindEigen.cmake:\n# Copyright (c) 2006, 2007 Montel Laurent, <montel@kde.org>\n# Redistribution and use is allowed according to the terms of the BSD license.\n# For details see the accompanying COPYING-CMAKE-SCRIPTS file.\n\nif (BLAZE_INCLUDE_DIR)\n\n  # in cache already\n  set(BLAZE_FOUND TRUE)\n\nelse (BLAZE_INCLUDE_DIR)\n\nfind_path(BLAZE_INCLUDE_DIR NAMES blaze/Blaze.h\n     PATHS\n     ${INCLUDE_INSTALL_DIR}\n   )\n\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(BLAZE DEFAULT_MSG BLAZE_INCLUDE_DIR)\n\nmark_as_advanced(BLAZE_INCLUDE_DIR)\n\nendif(BLAZE_INCLUDE_DIR)\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/cmake/FindBlitz.cmake",
    "content": "# - Try to find blitz lib\n# Once done this will define\n#\n#  BLITZ_FOUND - system has blitz lib\n#  BLITZ_INCLUDES - the blitz include directory\n#  BLITZ_LIBRARIES - The libraries needed to use blitz\n\n# Copyright (c) 2006, Montel Laurent, <montel@kde.org>\n# Copyright (c) 2007, Allen Winter, <winter@kde.org>\n# Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n# Redistribution and use is allowed according to the terms of the BSD license.\n# For details see the accompanying COPYING-CMAKE-SCRIPTS file.\n\n# include(FindLibraryWithDebug)\n\nif (BLITZ_INCLUDES AND BLITZ_LIBRARIES)\n  set(Blitz_FIND_QUIETLY TRUE)\nendif (BLITZ_INCLUDES AND BLITZ_LIBRARIES)\n\nfind_path(BLITZ_INCLUDES\n  NAMES\n  blitz/array.h\n  PATH_SUFFIXES blitz*\n  PATHS\n  $ENV{BLITZDIR}/include\n  ${INCLUDE_INSTALL_DIR}\n)\n\nfind_library(BLITZ_LIBRARIES\n  blitz\n  PATHS\n  $ENV{BLITZDIR}/lib\n  ${LIB_INSTALL_DIR}\n)\n\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(Blitz DEFAULT_MSG\n                                  BLITZ_INCLUDES BLITZ_LIBRARIES)\n\nmark_as_advanced(BLITZ_INCLUDES BLITZ_LIBRARIES)\n"
  },
  {
    "path": "include/eigen3/bench/btl/cmake/FindCBLAS.cmake",
    "content": "# include(FindLibraryWithDebug)\n\nif (CBLAS_INCLUDES AND CBLAS_LIBRARIES)\n  set(CBLAS_FIND_QUIETLY TRUE)\nendif (CBLAS_INCLUDES AND CBLAS_LIBRARIES)\n\nfind_path(CBLAS_INCLUDES\n  NAMES\n  cblas.h\n  PATHS\n  $ENV{CBLASDIR}/include\n  ${INCLUDE_INSTALL_DIR}\n)\n\nfind_library(CBLAS_LIBRARIES\n  cblas\n  PATHS\n  $ENV{CBLASDIR}/lib\n  ${LIB_INSTALL_DIR}\n)\n\nfind_file(CBLAS_LIBRARIES\n  libcblas.so.3\n  PATHS\n  /usr/lib\n  /usr/lib64\n  $ENV{CBLASDIR}/lib\n  ${LIB_INSTALL_DIR}\n)\n\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(CBLAS DEFAULT_MSG\n                                  CBLAS_INCLUDES CBLAS_LIBRARIES)\n\nmark_as_advanced(CBLAS_INCLUDES CBLAS_LIBRARIES)\n"
  },
  {
    "path": "include/eigen3/bench/btl/cmake/FindGMM.cmake",
    "content": "if (GMM_INCLUDE_DIR)\n  # in cache already\n  set(GMM_FOUND TRUE)\nelse (GMM_INCLUDE_DIR)\n\nfind_path(GMM_INCLUDE_DIR NAMES gmm/gmm.h\n     PATHS\n     ${INCLUDE_INSTALL_DIR}\n     ${GMM_INCLUDE_PATH}\n   )\n\ninclude(FindPackageHandleStandardArgs)\nFIND_PACKAGE_HANDLE_STANDARD_ARGS(GMM DEFAULT_MSG GMM_INCLUDE_DIR )\n\nmark_as_advanced(GMM_INCLUDE_DIR)\n\nendif(GMM_INCLUDE_DIR)\n"
  },
  {
    "path": "include/eigen3/bench/btl/cmake/FindMKL.cmake",
    "content": "\nif (MKL_LIBRARIES)\n  set(MKL_FIND_QUIETLY TRUE)\nendif (MKL_LIBRARIES)\n\nif(CMAKE_MINOR_VERSION GREATER 4)\n\nif(${CMAKE_HOST_SYSTEM_PROCESSOR} STREQUAL \"x86_64\")\n\nfind_library(MKL_LIBRARIES\n  mkl_core\n  PATHS\n  $ENV{MKLLIB}\n  /opt/intel/mkl/*/lib/em64t\n  /opt/intel/Compiler/*/*/mkl/lib/em64t\n  ${LIB_INSTALL_DIR}\n)\n\nfind_library(MKL_GUIDE\n  guide\n  PATHS\n  $ENV{MKLLIB}\n  /opt/intel/mkl/*/lib/em64t\n  /opt/intel/Compiler/*/*/mkl/lib/em64t\n  /opt/intel/Compiler/*/*/lib/intel64\n  ${LIB_INSTALL_DIR}\n)\n\nif(MKL_LIBRARIES AND MKL_GUIDE)\n  set(MKL_LIBRARIES ${MKL_LIBRARIES} mkl_intel_lp64 mkl_sequential ${MKL_GUIDE} pthread)\nendif()\n\nelse(${CMAKE_HOST_SYSTEM_PROCESSOR} STREQUAL \"x86_64\")\n\nfind_library(MKL_LIBRARIES\n  mkl_core\n  PATHS\n  $ENV{MKLLIB}\n  /opt/intel/mkl/*/lib/32\n  /opt/intel/Compiler/*/*/mkl/lib/32\n  ${LIB_INSTALL_DIR}\n)\n\nfind_library(MKL_GUIDE\n  guide\n  PATHS\n  $ENV{MKLLIB}\n  /opt/intel/mkl/*/lib/32\n  /opt/intel/Compiler/*/*/mkl/lib/32\n  /opt/intel/Compiler/*/*/lib/intel32\n  ${LIB_INSTALL_DIR}\n)\n\nif(MKL_LIBRARIES AND MKL_GUIDE)\n  set(MKL_LIBRARIES ${MKL_LIBRARIES} mkl_intel mkl_sequential ${MKL_GUIDE} pthread)\nendif()\n\nendif(${CMAKE_HOST_SYSTEM_PROCESSOR} STREQUAL \"x86_64\")\n\nendif(CMAKE_MINOR_VERSION GREATER 4)\n\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(MKL DEFAULT_MSG MKL_LIBRARIES)\n\nmark_as_advanced(MKL_LIBRARIES)\n"
  },
  {
    "path": "include/eigen3/bench/btl/cmake/FindMTL4.cmake",
    "content": "# - Try to find eigen2 headers\n# Once done this will define\n#\n#  MTL4_FOUND - system has eigen2 lib\n#  MTL4_INCLUDE_DIR - the eigen2 include directory\n#\n# Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n# Adapted from FindEigen.cmake:\n# Copyright (c) 2006, 2007 Montel Laurent, <montel@kde.org>\n# Redistribution and use is allowed according to the terms of the BSD license.\n# For details see the accompanying COPYING-CMAKE-SCRIPTS file.\n\nif (MTL4_INCLUDE_DIR)\n\n  # in cache already\n  set(MTL4_FOUND TRUE)\n\nelse (MTL4_INCLUDE_DIR)\n\nfind_path(MTL4_INCLUDE_DIR NAMES boost/numeric/mtl/mtl.hpp\n     PATHS\n     ${INCLUDE_INSTALL_DIR}\n   )\n\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(MTL4 DEFAULT_MSG MTL4_INCLUDE_DIR)\n\nmark_as_advanced(MTL4_INCLUDE_DIR)\n\nendif(MTL4_INCLUDE_DIR)\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/cmake/FindOPENBLAS.cmake",
    "content": "\nif (OPENBLAS_LIBRARIES)\n  set(OPENBLAS_FIND_QUIETLY TRUE)\nendif (OPENBLAS_LIBRARIES)\n\nfind_file(OPENBLAS_LIBRARIES NAMES libopenblas.so libopenblas.so.0 PATHS /usr/lib /usr/lib64 $ENV{OPENBLASDIR} ${LIB_INSTALL_DIR})\nfind_library(OPENBLAS_LIBRARIES openblas PATHS $ENV{OPENBLASDIR} ${LIB_INSTALL_DIR})\n\nif(OPENBLAS_LIBRARIES AND CMAKE_COMPILER_IS_GNUCXX)\n  set(OPENBLAS_LIBRARIES ${OPENBLAS_LIBRARIES} \"-lpthread -lgfortran\")\nendif()\n\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(OPENBLAS DEFAULT_MSG\n                                  OPENBLAS_LIBRARIES)\n\nmark_as_advanced(OPENBLAS_LIBRARIES)\n"
  },
  {
    "path": "include/eigen3/bench/btl/cmake/FindPackageHandleStandardArgs.cmake",
    "content": "# FIND_PACKAGE_HANDLE_STANDARD_ARGS(NAME (DEFAULT_MSG|\"Custom failure message\") VAR1 ... )\n#\n# This macro is intended to be used in FindXXX.cmake modules files.\n# It handles the REQUIRED and QUIET argument to FIND_PACKAGE() and\n# it also sets the <UPPERCASED_NAME>_FOUND variable.\n# The package is found if all variables listed are TRUE.\n# Example:\n#\n#    FIND_PACKAGE_HANDLE_STANDARD_ARGS(LibXml2 DEFAULT_MSG LIBXML2_LIBRARIES LIBXML2_INCLUDE_DIR)\n#\n# LibXml2 is considered to be found, if both LIBXML2_LIBRARIES and \n# LIBXML2_INCLUDE_DIR are valid. Then also LIBXML2_FOUND is set to TRUE.\n# If it is not found and REQUIRED was used, it fails with FATAL_ERROR, \n# independent whether QUIET was used or not.\n#\n# If it is found, the location is reported using the VAR1 argument, so \n# here a message \"Found LibXml2: /usr/lib/libxml2.so\" will be printed out.\n# If the second argument is DEFAULT_MSG, the message in the failure case will \n# be \"Could NOT find LibXml2\", if you don't like this message you can specify\n# your own custom failure message there.\n\nMACRO(FIND_PACKAGE_HANDLE_STANDARD_ARGS _NAME _FAIL_MSG _VAR1 )\n\n  IF(\"${_FAIL_MSG}\" STREQUAL \"DEFAULT_MSG\")\n    IF (${_NAME}_FIND_REQUIRED)\n      SET(_FAIL_MESSAGE \"Could not find REQUIRED package ${_NAME}\")\n    ELSE (${_NAME}_FIND_REQUIRED)\n      SET(_FAIL_MESSAGE \"Could not find OPTIONAL package ${_NAME}\")\n    ENDIF (${_NAME}_FIND_REQUIRED)\n  ELSE(\"${_FAIL_MSG}\" STREQUAL \"DEFAULT_MSG\")\n    SET(_FAIL_MESSAGE \"${_FAIL_MSG}\")\n  ENDIF(\"${_FAIL_MSG}\" STREQUAL \"DEFAULT_MSG\")\n\n  STRING(TOUPPER ${_NAME} _NAME_UPPER)\n\n  SET(${_NAME_UPPER}_FOUND TRUE)\n  IF(NOT ${_VAR1})\n    SET(${_NAME_UPPER}_FOUND FALSE)\n  ENDIF(NOT ${_VAR1})\n\n  FOREACH(_CURRENT_VAR ${ARGN})\n    IF(NOT ${_CURRENT_VAR})\n      SET(${_NAME_UPPER}_FOUND FALSE)\n    ENDIF(NOT ${_CURRENT_VAR})\n  ENDFOREACH(_CURRENT_VAR)\n\n  IF (${_NAME_UPPER}_FOUND)\n    IF (NOT ${_NAME}_FIND_QUIETLY)\n        MESSAGE(STATUS \"Found ${_NAME}: ${${_VAR1}}\")\n    ENDIF (NOT ${_NAME}_FIND_QUIETLY)\n  ELSE (${_NAME_UPPER}_FOUND)\n    IF (${_NAME}_FIND_REQUIRED)\n        MESSAGE(FATAL_ERROR \"${_FAIL_MESSAGE}\")\n    ELSE (${_NAME}_FIND_REQUIRED)\n      IF (NOT ${_NAME}_FIND_QUIETLY)\n        MESSAGE(STATUS \"${_FAIL_MESSAGE}\")\n      ENDIF (NOT ${_NAME}_FIND_QUIETLY)\n    ENDIF (${_NAME}_FIND_REQUIRED)\n  ENDIF (${_NAME_UPPER}_FOUND)\nENDMACRO(FIND_PACKAGE_HANDLE_STANDARD_ARGS)\n"
  },
  {
    "path": "include/eigen3/bench/btl/cmake/FindTvmet.cmake",
    "content": "# - Try to find tvmet headers\n# Once done this will define\n#\n#  TVMET_FOUND - system has tvmet lib\n#  TVMET_INCLUDE_DIR - the tvmet include directory\n#\n# Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n# Adapted from FindEigen.cmake:\n# Copyright (c) 2006, 2007 Montel Laurent, <montel@kde.org>\n# Redistribution and use is allowed according to the terms of the BSD license.\n# For details see the accompanying COPYING-CMAKE-SCRIPTS file.\n\nif (TVMET_INCLUDE_DIR)\n\n  # in cache already\n  set(TVMET_FOUND TRUE)\n\nelse (TVMET_INCLUDE_DIR)\n\nfind_path(TVMET_INCLUDE_DIR NAMES tvmet/tvmet.h\n     PATHS\n     ${TVMETDIR}/\n     ${INCLUDE_INSTALL_DIR}\n   )\n\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(Tvmet DEFAULT_MSG TVMET_INCLUDE_DIR)\n\nmark_as_advanced(TVMET_INCLUDE_DIR)\n\nendif(TVMET_INCLUDE_DIR)\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/cmake/MacroOptionalAddSubdirectory.cmake",
    "content": "# - MACRO_OPTIONAL_ADD_SUBDIRECTORY() combines ADD_SUBDIRECTORY() with an OPTION()\n# MACRO_OPTIONAL_ADD_SUBDIRECTORY( <dir> )\n# If you use MACRO_OPTIONAL_ADD_SUBDIRECTORY() instead of ADD_SUBDIRECTORY(),\n# this will have two effects\n# 1 - CMake will not complain if the directory doesn't exist\n#     This makes sense if you want to distribute just one of the subdirs\n#     in a source package, e.g. just one of the subdirs in kdeextragear.\n# 2 - If the directory exists, it will offer an option to skip the \n#     subdirectory.\n#     This is useful if you want to compile only a subset of all\n#     directories.\n\n# Copyright (c) 2007, Alexander Neundorf, <neundorf@kde.org>\n#\n# Redistribution and use is allowed according to the terms of the BSD license.\n# For details see the accompanying COPYING-CMAKE-SCRIPTS file.\n\n\nMACRO (MACRO_OPTIONAL_ADD_SUBDIRECTORY _dir )\n   GET_FILENAME_COMPONENT(_fullPath ${_dir} ABSOLUTE)\n   IF(EXISTS ${_fullPath})\n      IF(${ARGC} EQUAL 2)\n        OPTION(BUILD_${_dir} \"Build directory ${_dir}\" ${ARGV1})\n      ELSE(${ARGC} EQUAL 2)\n        OPTION(BUILD_${_dir} \"Build directory ${_dir}\" TRUE)\n      ENDIF(${ARGC} EQUAL 2)\n      IF(BUILD_${_dir})\n         ADD_SUBDIRECTORY(${_dir})\n      ENDIF(BUILD_${_dir})\n   ENDIF(EXISTS ${_fullPath})\nENDMACRO (MACRO_OPTIONAL_ADD_SUBDIRECTORY)\n"
  },
  {
    "path": "include/eigen3/bench/btl/data/CMakeLists.txt",
    "content": "\nADD_CUSTOM_TARGET(copy_scripts)\n\nSET(script_files go_mean mk_mean_script.sh mk_new_gnuplot.sh\n    perlib_plot_settings.txt action_settings.txt gnuplot_common_settings.hh )\n\nFOREACH(script_file ${script_files})\nADD_CUSTOM_COMMAND(\n  TARGET copy_scripts\n  POST_BUILD\n  COMMAND ${CMAKE_COMMAND} -E copy ${CMAKE_CURRENT_SOURCE_DIR}/${script_file} ${CMAKE_CURRENT_BINARY_DIR}/\n  ARGS\n)\nENDFOREACH(script_file)\n\nADD_CUSTOM_COMMAND(\n  TARGET copy_scripts\n  POST_BUILD\n  COMMAND ${CMAKE_CXX_COMPILER} --version | head -n 1 > ${CMAKE_CURRENT_BINARY_DIR}/compiler_version.txt\n  ARGS\n)\nADD_CUSTOM_COMMAND(\n  TARGET copy_scripts\n  POST_BUILD\n  COMMAND echo \"${Eigen_SOURCE_DIR}\" > ${CMAKE_CURRENT_BINARY_DIR}/eigen_root_dir.txt\n  ARGS\n)\n\nadd_executable(smooth smooth.cxx)\nadd_executable(regularize regularize.cxx)\nadd_executable(main mean.cxx)\nadd_dependencies(main copy_scripts)\n"
  },
  {
    "path": "include/eigen3/bench/btl/data/action_settings.txt",
    "content": "aat ; \"{/*1.5 A x A^T}\" ; \"matrix size\" ; 4:5000\nata ; \"{/*1.5 A^T x A}\" ; \"matrix size\" ; 4:5000\natv ; \"{/*1.5 matrix^T x vector}\" ; \"matrix size\" ; 4:5000\naxpby ; \"{/*1.5 Y = alpha X + beta Y}\" ; \"vector size\" ; 5:1000000\naxpy ; \"{/*1.5 Y += alpha X}\" ; \"vector size\" ; 5:1000000\nmatrix_matrix ; \"{/*1.5 matrix matrix product}\" ; \"matrix size\" ; 4:5000\nmatrix_vector ; \"{/*1.5 matrix vector product}\" ; \"matrix size\" ; 4:5000\ntrmm ; \"{/*1.5 triangular matrix matrix product}\" ; \"matrix size\" ; 4:5000\ntrisolve_vector ; \"{/*1.5 triangular solver - vector (X = inv(L) X)}\" ; \"size\" ; 4:5000\ntrisolve_matrix ; \"{/*1.5 triangular solver - matrix (M = inv(L) M)}\" ; \"size\" ; 4:5000\ncholesky ; \"{/*1.5 Cholesky decomposition}\" ; \"matrix size\" ; 4:5000\ncomplete_lu_decomp ; \"{/*1.5 Complete LU decomposition}\" ; \"matrix size\" ; 4:5000\npartial_lu_decomp ; \"{/*1.5 Partial LU decomposition}\" ; \"matrix size\" ; 4:5000\ntridiagonalization ; \"{/*1.5 Tridiagonalization}\" ; \"matrix size\" ; 4:5000\nhessenberg ; \"{/*1.5 Hessenberg decomposition}\" ; \"matrix size\" ; 4:5000\nsymv ; \"{/*1.5 symmetric matrix vector product}\" ; \"matrix size\" ; 4:5000\nsyr2 ; \"{/*1.5 symmretric rank-2 update (A += u^T v + u v^T)}\" ; \"matrix size\" ; 4:5000\nger ; \"{/*1.5 general rank-1 update (A += u v^T)}\" ; \"matrix size\" ; 4:5000\nrot ; \"{/*1.5 apply rotation in the plane}\" ; \"vector size\" ; 4:1000000\n"
  },
  {
    "path": "include/eigen3/bench/btl/data/gnuplot_common_settings.hh",
    "content": "set noclip points\nset clip one\nset noclip two\nset bar 1.000000\nset border 31 lt -1 lw 1.000\nset xdata\nset ydata\nset zdata\nset x2data\nset y2data\nset boxwidth\nset dummy x,y\nset format x \"%g\"\nset format y \"%g\"\nset format x2 \"%g\"\nset format y2 \"%g\"\nset format z \"%g\"\nset angles radians\nset nogrid\nset key title \"\"\nset key left top Right noreverse box linetype -2 linewidth 1.000 samplen 4 spacing 1 width 0\nset nolabel\nset noarrow\n# set nolinestyle # deprecated\nset nologscale\nset logscale x 10\nset offsets 0, 0, 0, 0\nset pointsize 1\nset encoding default\nset nopolar\nset noparametric\nset view 60, 30, 1, 1\nset samples 100, 100\nset isosamples 10, 10\nset surface\nset nocontour\nset clabel '%8.3g'\nset mapping cartesian\nset nohidden3d\nset cntrparam order 4\nset cntrparam linear\nset cntrparam levels auto 5\nset cntrparam points 5\nset size ratio 0 1,1\nset origin 0,0\n# set data style lines\n# set function style lines\nset xzeroaxis lt -2 lw 1.000\nset x2zeroaxis lt -2 lw 1.000\nset yzeroaxis lt -2 lw 1.000\nset y2zeroaxis lt -2 lw 1.000\nset tics in\nset ticslevel 0.5\nset tics scale 1, 0.5\nset mxtics default\nset mytics default\nset mx2tics default\nset my2tics default\nset xtics border mirror norotate autofreq\nset ytics border mirror norotate autofreq\nset ztics border nomirror norotate autofreq\nset nox2tics\nset noy2tics\nset timestamp \"\" bottom norotate offset 0,0\nset rrange [ * : * ] noreverse nowriteback  # (currently [-0:10] )\nset trange [ * : * ] noreverse nowriteback  # (currently [-5:5] )\nset urange [ * : * ] noreverse nowriteback  # (currently [-5:5] )\nset vrange [ * : * ] noreverse nowriteback  # (currently [-5:5] )\nset xlabel \"matrix size\" offset 0,0\nset x2label \"\" offset 0,0\nset timefmt \"%d/%m/%y\\n%H:%M\"\nset xrange [ 10 : 1000 ] noreverse nowriteback\nset x2range [ * : * ] noreverse nowriteback  # (currently [-10:10] )\nset ylabel \"MFLOPS\" offset 0,0\nset y2label \"\" offset 0,0\nset yrange [ * : * ] noreverse nowriteback  # (currently [-10:10] )\nset y2range [ * : * ] noreverse nowriteback  # (currently [-10:10] )\nset zlabel \"\" offset 0,0\nset zrange [ * : * ] noreverse nowriteback  # (currently [-10:10] )\nset zero 1e-08\nset lmargin -1\nset bmargin -1\nset rmargin -1\nset tmargin -1\nset locale \"C\"\nset xrange [4:1024]\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/data/go_mean",
    "content": "#!/bin/bash\n\nif [ $# < 1 ]; then\n  echo \"Usage: $0 working_directory [tiny|large [prefix]]\"\nelse\n\nmkdir -p $1\n##cp ../libs/*/*.dat $1\n\nmode=large\nif [ $# > 2 ]; then\n  mode=$2\nfi\nif [ $# > 3 ]; then\n  prefix=$3\nfi\n\nEIGENDIR=`cat eigen_root_dir.txt`\n\nwebpagefilename=$1/index.html\nmeanstatsfilename=$1/mean.html\n\necho ''  > $meanstatsfilename\necho ''  > $webpagefilename\necho '<p><strong>Configuration</strong>'  >> $webpagefilename\necho '<ul>'\\\n  '<li>' `cat /proc/cpuinfo | grep \"model name\" | head -n 1`\\\n  '  (' `uname -m` ')</li>'\\\n  '<li> compiler: ' `cat compiler_version.txt` '</li>'\\\n  '<li> eigen3: ' `hg identify -i $EIGENDIR` '</li>'\\\n  '</ul>' \\\n  '</p>'  >> $webpagefilename\n\nsource mk_mean_script.sh axpy $1 11 2500 100000 250000  $mode $prefix\nsource mk_mean_script.sh axpby $1 11 2500 100000 250000 $mode $prefix\nsource mk_mean_script.sh matrix_vector $1 11 50 300 1000 $mode $prefix\nsource mk_mean_script.sh atv $1 11 50 300 1000 $mode $prefix\nsource mk_mean_script.sh matrix_matrix $1 11 100 300 1000 $mode $prefix\nsource mk_mean_script.sh aat $1 11 100 300 1000 $mode $prefix\n# source mk_mean_script.sh ata $1 11 100 300 1000 $mode $prefix\nsource mk_mean_script.sh trmm $1 11 100 300 1000 $mode $prefix\nsource mk_mean_script.sh trisolve_vector $1 11 100 300 1000 $mode $prefix\nsource mk_mean_script.sh trisolve_matrix $1 11 100 300 1000 $mode $prefix\nsource mk_mean_script.sh cholesky $1 11 100 300 1000 $mode $prefix\nsource mk_mean_script.sh partial_lu_decomp $1 11 100 300 1000 $mode $prefix\nsource mk_mean_script.sh tridiagonalization $1 11 100 300 1000 $mode $prefix\nsource mk_mean_script.sh hessenberg $1 11 100 300 1000 $mode $prefix\nsource mk_mean_script.sh symv $1 11 50 300 1000 $mode $prefix\nsource mk_mean_script.sh syr2 $1 11 50 300 1000 $mode $prefix\nsource mk_mean_script.sh ger $1 11 50 300 1000 $mode $prefix\nsource mk_mean_script.sh rot $1 11 2500 100000 250000 $mode $prefix\nsource mk_mean_script.sh complete_lu_decomp $1 11 100 300 1000 $mode $prefix\n\nfi\n\n## compile the web page ##\n\n#echo `cat footer.html` >> $webpagefilename"
  },
  {
    "path": "include/eigen3/bench/btl/data/mean.cxx",
    "content": "//=====================================================\n// File   :  mean.cxx\n// Author :  L. Plagne <laurent.plagne@edf.fr)>        \n// Copyright (C) EDF R&D,  lun sep 30 14:23:15 CEST 2002\n//=====================================================\n// \n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n// \n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n// \n#include \"utilities.h\"\n#include <vector>\n#include <string>\n#include <iostream>\n#include <fstream>\n#include \"bench_parameter.hh\"\n#include \"utils/xy_file.hh\"\n#include <set>\n\nusing namespace std;\n\ndouble mean_calc(const vector<int> & tab_sizes, const vector<double> & tab_mflops, const int size_min, const int size_max);\n\nclass Lib_Mean{\n\npublic:\n  Lib_Mean( void ):_lib_name(),_mean_in_cache(),_mean_out_of_cache(){\n    MESSAGE(\"Lib_mean Default Ctor\");\n    MESSAGE(\"!!! should not be used\");\n    exit(0);\n  }\n  Lib_Mean(const string & name, const double & mic, const double & moc):_lib_name(name),_mean_in_cache(mic),_mean_out_of_cache(moc){\n    MESSAGE(\"Lib_mean Ctor\");\n  }\n  Lib_Mean(const Lib_Mean & lm):_lib_name(lm._lib_name),_mean_in_cache(lm._mean_in_cache),_mean_out_of_cache(lm._mean_out_of_cache){\n    MESSAGE(\"Lib_mean Copy Ctor\");\n  }\n  ~Lib_Mean( void ){\n    MESSAGE(\"Lib_mean Dtor\");\n  }\n    \n  double _mean_in_cache;\n  double _mean_out_of_cache;\n  string _lib_name;\n\n  bool operator < ( const Lib_Mean &right) const \n  {\n    //return ( this->_mean_out_of_cache > right._mean_out_of_cache) ;\n    return ( this->_mean_in_cache > right._mean_in_cache) ;\n  }\n\n}; \n\n\nint main( int argc , char *argv[] )\n{\n\n  if (argc<6){\n    INFOS(\"!!! Error ... usage : main what mic Mic moc Moc filename1 finename2...\");\n    exit(0);\n  }\n  INFOS(argc);\n\n  int min_in_cache=atoi(argv[2]);\n  int max_in_cache=atoi(argv[3]);\n  int min_out_of_cache=atoi(argv[4]);\n  int max_out_of_cache=atoi(argv[5]);\n\n\n  multiset<Lib_Mean> s_lib_mean ;\n\n  for (int i=6;i<argc;i++){\n    \n    string filename=argv[i];\n    \n    INFOS(filename);\n\n    double mic=0;\n    double moc=0;\n\n    {\n      \n      vector<int> tab_sizes;\n      vector<double> tab_mflops;\n\n      read_xy_file(filename,tab_sizes,tab_mflops);\n\n      mic=mean_calc(tab_sizes,tab_mflops,min_in_cache,max_in_cache);\n      moc=mean_calc(tab_sizes,tab_mflops,min_out_of_cache,max_out_of_cache);\n\n      Lib_Mean cur_lib_mean(filename,mic,moc);\n      \n      s_lib_mean.insert(cur_lib_mean);\t\n\n    }   \n           \n  }\n\n\n  cout << \"<TABLE BORDER CELLPADDING=2>\" << endl ;\n  cout << \"  <TR>\" << endl ;\n  cout << \"    <TH ALIGN=CENTER> \" << argv[1] << \" </TH>\" << endl ;\n  cout << \"    <TH ALIGN=CENTER> <a href=\"\"#mean_marker\"\"> in cache <BR> mean perf <BR> Mflops </a></TH>\" << endl ;\n  cout << \"    <TH ALIGN=CENTER> in cache <BR> % best </TH>\" << endl ;\n  cout << \"    <TH ALIGN=CENTER> <a href=\"\"#mean_marker\"\"> out of cache <BR> mean perf <BR> Mflops </a></TH>\" << endl ;\n  cout << \"    <TH ALIGN=CENTER> out of cache <BR> % best </TH>\" << endl ;\n  cout << \"    <TH ALIGN=CENTER> details </TH>\" << endl ;\n  cout << \"    <TH ALIGN=CENTER> comments </TH>\" << endl ;\n  cout << \"  </TR>\" << endl ;\n\n  multiset<Lib_Mean>::iterator is = s_lib_mean.begin();\n  Lib_Mean best(*is);  \n  \n\n  for (is=s_lib_mean.begin(); is!=s_lib_mean.end() ; is++){\n\n    cout << \"  <TR>\" << endl ;\n    cout << \"     <TD> \" << is->_lib_name << \" </TD>\" << endl ;\n    cout << \"     <TD> \" << is->_mean_in_cache << \" </TD>\" << endl ;\n    cout << \"     <TD> \" << 100*(is->_mean_in_cache/best._mean_in_cache) << \" </TD>\" << endl ;\n    cout << \"     <TD> \" << is->_mean_out_of_cache << \" </TD>\" << endl ;\n    cout << \"     <TD> \" << 100*(is->_mean_out_of_cache/best._mean_out_of_cache) << \" </TD>\" << endl ;\n    cout << \"     <TD> \" << \n      \"<a href=\\\"#\"<<is->_lib_name<<\"_\"<<argv[1]<<\"\\\">snippet</a>/\" \n      \"<a href=\\\"#\"<<is->_lib_name<<\"_flags\\\">flags</a>  </TD>\" << endl ;\n    cout << \"     <TD> \" << \n      \"<a href=\\\"#\"<<is->_lib_name<<\"_comments\\\">click here</a>  </TD>\" << endl ;\n    cout << \"  </TR>\" << endl ;\n  \n  }\n\n  cout << \"</TABLE>\" << endl ;\n\n  ofstream output_file (\"../order_lib\",ios::out) ;\n  \n  for (is=s_lib_mean.begin(); is!=s_lib_mean.end() ; is++){\n    output_file << is->_lib_name << endl ;\n  }\n\n  output_file.close();\n\n}\n\ndouble mean_calc(const vector<int> & tab_sizes, const vector<double> & tab_mflops, const int size_min, const int size_max){\n  \n  int size=tab_sizes.size();\n  int nb_sample=0;\n  double mean=0.0;\n\n  for (int i=0;i<size;i++){\n    \n    \n    if ((tab_sizes[i]>=size_min)&&(tab_sizes[i]<=size_max)){\n      \n      nb_sample++;\n      mean+=tab_mflops[i];\n\n    }\n\n    \n  }\n\n  if (nb_sample==0){\n    INFOS(\"no data for mean calculation\");\n    return 0.0;\n  }\n\n  return mean/nb_sample;\n}\n\n  \n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/data/mk_gnuplot_script.sh",
    "content": "#! /bin/bash\nWHAT=$1\nDIR=$2\necho $WHAT script generation\ncat $WHAT.hh > $WHAT.gnuplot\n\nDATA_FILE=`find $DIR -name \"*.dat\" | grep $WHAT`\n\necho plot \\\\ >> $WHAT.gnuplot\n\nfor FILE in $DATA_FILE\ndo\n    LAST=$FILE\ndone\n\necho LAST=$LAST\n\nfor FILE in $DATA_FILE\ndo\n     if [ $FILE != $LAST ]\n     then\n\tBASE=${FILE##*/} ; BASE=${FILE##*/} ; AVANT=bench_${WHAT}_ ; REDUC=${BASE##*$AVANT} ; TITLE=${REDUC%.dat}\n\techo \"'\"$FILE\"'\" title \"'\"$TITLE\"'\" \",\\\\\" >>  $WHAT.gnuplot\n     fi\ndone\nBASE=${LAST##*/} ; BASE=${FILE##*/} ; AVANT=bench_${WHAT}_ ; REDUC=${BASE##*$AVANT} ; TITLE=${REDUC%.dat}\necho \"'\"$LAST\"'\" title \"'\"$TITLE\"'\" >>  $WHAT.gnuplot\n\n#echo set term postscript color >> $WHAT.gnuplot\n#echo set output \"'\"$WHAT.ps\"'\" >> $WHAT.gnuplot\necho set term pbm small color >> $WHAT.gnuplot\necho set output \"'\"$WHAT.ppm\"'\" >> $WHAT.gnuplot\necho plot \\\\ >> $WHAT.gnuplot\n\nfor FILE in $DATA_FILE\ndo\n     if [ $FILE != $LAST ]\n     then\n\tBASE=${FILE##*/} ; BASE=${FILE##*/} ; AVANT=bench_${WHAT}_ ; REDUC=${BASE##*$AVANT} ; TITLE=${REDUC%.dat}\n\techo \"'\"$FILE\"'\" title \"'\"$TITLE\"'\" \",\\\\\" >>  $WHAT.gnuplot\n     fi\ndone\nBASE=${LAST##*/} ; BASE=${FILE##*/} ; AVANT=bench_${WHAT}_ ; REDUC=${BASE##*$AVANT} ; TITLE=${REDUC%.dat}\necho \"'\"$LAST\"'\" title \"'\"$TITLE\"'\" >>  $WHAT.gnuplot\n\necho set term jpeg large >> $WHAT.gnuplot\necho set output \"'\"$WHAT.jpg\"'\" >> $WHAT.gnuplot\necho plot \\\\ >> $WHAT.gnuplot\n\nfor FILE in $DATA_FILE\ndo\n     if [ $FILE != $LAST ]\n     then\n\tBASE=${FILE##*/} ; BASE=${FILE##*/} ; AVANT=bench_${WHAT}_ ; REDUC=${BASE##*$AVANT} ; TITLE=${REDUC%.dat}\n\techo \"'\"$FILE\"'\" title \"'\"$TITLE\"'\" \",\\\\\" >>  $WHAT.gnuplot\n     fi\ndone\nBASE=${LAST##*/} ; BASE=${FILE##*/} ; AVANT=bench_${WHAT}_ ; REDUC=${BASE##*$AVANT} ; TITLE=${REDUC%.dat}\necho \"'\"$LAST\"'\" title \"'\"$TITLE\"'\" >>  $WHAT.gnuplot\n\n\ngnuplot -persist < $WHAT.gnuplot\n\nrm $WHAT.gnuplot\n\n\n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/data/mk_mean_script.sh",
    "content": "#! /bin/bash\nWHAT=$1\nDIR=$2\nMINIC=$3\nMAXIC=$4\nMINOC=$5\nMAXOC=$6\nprefix=$8\n\nmeanstatsfilename=$2/mean.html\n\nWORK_DIR=tmp\nmkdir $WORK_DIR\n\nDATA_FILE=`find $DIR -name \"*.dat\" | grep _${WHAT}`\n\nif [ -n \"$DATA_FILE\" ]; then\n\n  echo \"\"\n  echo \"$1...\"\n  for FILE in $DATA_FILE\n  do\n          ##echo hello world\n          ##echo \"mk_mean_script1\" ${FILE}\n    BASE=${FILE##*/} ; BASE=${FILE##*/} ; AVANT=bench_${WHAT}_ ; REDUC=${BASE##*$AVANT} ; TITLE=${REDUC%.dat}\n\n    ##echo \"mk_mean_script1\" ${TITLE}\n    cp $FILE ${WORK_DIR}/${TITLE}\n\n  done\n\n  cd $WORK_DIR\n  ../main $1 $3 $4 $5 $6 * >> ../$meanstatsfilename\n  ../mk_new_gnuplot.sh $1 $2 $7\n  rm -f *.gnuplot\n  cd ..\n\n  echo '<br/>' >> $meanstatsfilename\n\n  webpagefilename=$2/index.html\n  # echo '<h3>'${WHAT}'</h3>'  >> $webpagefilename\n  echo '<hr/><a href=\"'$prefix$1'.pdf\"><img src=\"'$prefix$1'.png\" alt=\"'${WHAT}'\" /></a><br/>'  >> $webpagefilename\n\nfi\n\nrm -R $WORK_DIR\n\n\n\n\n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/data/mk_new_gnuplot.sh",
    "content": "#!/bin/bash\nWHAT=$1\nDIR=$2\n\ncat ../gnuplot_common_settings.hh > ${WHAT}.gnuplot\n\necho \"set title \" `grep ${WHAT} ../action_settings.txt | head -n 1 | cut -d \";\" -f 2` >> $WHAT.gnuplot\necho \"set xlabel \" `grep ${WHAT} ../action_settings.txt | head -n 1 | cut -d \";\" -f 3` \" offset 0,0\" >> $WHAT.gnuplot\necho \"set xrange [\" `grep ${WHAT} ../action_settings.txt | head -n 1 | cut -d \";\" -f 4` \"]\" >> $WHAT.gnuplot\n\nif [ $# > 3 ]; then\n  if [ \"$3\" == \"tiny\" ]; then\n    echo \"set xrange [2:16]\" >> $WHAT.gnuplot\n    echo \"set nologscale\" >> $WHAT.gnuplot\n  fi\nfi\n\n\n\nDATA_FILE=`cat ../order_lib`\necho set term postscript color rounded enhanced >> $WHAT.gnuplot\necho set output \"'\"../${DIR}/$WHAT.ps\"'\" >> $WHAT.gnuplot\n\n# echo set term svg color rounded enhanced >> $WHAT.gnuplot\n# echo \"set terminal svg enhanced size 1000 1000 fname \\\"Times\\\" fsize 36\" >> $WHAT.gnuplot\n# echo set output \"'\"../${DIR}/$WHAT.svg\"'\" >> $WHAT.gnuplot\n\necho plot \\\\ >> $WHAT.gnuplot\n\nfor FILE in $DATA_FILE\ndo\n    LAST=$FILE\ndone\n\nfor FILE in $DATA_FILE\ndo\n    BASE=${FILE##*/} ; BASE=${FILE##*/} ; AVANT=bench_${WHAT}_ ; REDUC=${BASE##*$AVANT} ; TITLE=${REDUC%.dat}\n\n    echo \"'\"$FILE\"'\" `grep $TITLE ../perlib_plot_settings.txt | head -n 1 | cut -d \";\" -f 2` \"\\\\\" >>  $WHAT.gnuplot\n    if [ $FILE != $LAST ]\n    then\n      echo \", \\\\\" >>  $WHAT.gnuplot\n    fi\ndone\necho \" \" >>  $WHAT.gnuplot\n\ngnuplot -persist < $WHAT.gnuplot\n\nrm $WHAT.gnuplot\n\nps2pdf ../${DIR}/$WHAT.ps ../${DIR}/$WHAT.pdf\nconvert -background white -density 120 -rotate 90 -resize 800 +dither -colors 256 -quality 0 ../${DIR}/$WHAT.ps -background white -flatten  ../${DIR}/$WHAT.png\n\n# pstoedit -rotate -90 -xscale 0.8 -yscale 0.8 -centered -yshift -50 -xshift -100  -f plot-svg aat.ps  aat2.svg\n"
  },
  {
    "path": "include/eigen3/bench/btl/data/perlib_plot_settings.txt",
    "content": "eigen3 ;          with lines lw 4 lt 1 lc rgbcolor \"black\"\neigen2 ;          with lines lw 3 lt 1 lc rgbcolor \"#999999\"\nEigenBLAS ;       with lines lw 3 lt 3 lc rgbcolor \"#999999\"\neigen3_novec ;    with lines lw 2 lt 1 lc rgbcolor \"#999999\"\neigen3_nogccvec ; with lines lw 2 lt 2 lc rgbcolor \"#991010\"\nINTEL_MKL ;       with lines lw 3 lt 1 lc rgbcolor \"#ff0000\"\nATLAS ;           with lines lw 3 lt 1 lc rgbcolor \"#008000\"\ngmm ;             with lines lw 3 lt 1 lc rgbcolor \"#0000ff\"\nublas ;           with lines lw 3 lt 1 lc rgbcolor \"#00b7ff\"\nmtl4 ;            with lines lw 3 lt 1 lc rgbcolor \"#d18847\"\nblitz ;           with lines lw 3 lt 1 lc rgbcolor \"#ff00ff\"\nF77 ;             with lines lw 3 lt 3 lc rgbcolor \"#e6e64c\"\nOPENBLAS ;        with lines lw 3 lt 1 lc rgbcolor \"#C05600\"\nC ;               with lines lw 3 lt 3 lc rgbcolor \"#e6bd96\"\nACML ;            with lines lw 2 lt 3 lc rgbcolor \"#e6e64c\"\nblaze ;           with lines lw 3 lt 1 lc rgbcolor \"#ff00ff\"\n"
  },
  {
    "path": "include/eigen3/bench/btl/data/regularize.cxx",
    "content": "//=====================================================\n// File   :  regularize.cxx\n// Author :  L. Plagne <laurent.plagne@edf.fr)>        \n// Copyright (C) EDF R&D,  lun sep 30 14:23:15 CEST 2002\n//=====================================================\n// \n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n// \n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n// \n#include \"utilities.h\"\n#include <vector>\n#include <string>\n#include <iostream>\n#include <fstream>\n#include \"bench_parameter.hh\"\n#include <set>\n\nusing namespace std;\n\nvoid read_xy_file(const string & filename, vector<int> & tab_sizes, vector<double> & tab_mflops);\nvoid regularize_curve(const string & filename,\n\t\t      const vector<double> & tab_mflops, \n\t\t      const vector<int> & tab_sizes, \n\t\t      int start_cut_size, int stop_cut_size);\n/////////////////////////////////////////////////////////////////////////////////////////////////\n\nint main( int argc , char *argv[] )\n{\n\n  // input data\n\n  if (argc<4){\n    INFOS(\"!!! Error ... usage : main filename start_cut_size stop_cut_size regularize_filename\");\n    exit(0);\n  }\n  INFOS(argc);\n\n  int start_cut_size=atoi(argv[2]);\n  int stop_cut_size=atoi(argv[3]);\n\n  string filename=argv[1];\n  string regularize_filename=argv[4];\n  \n  INFOS(filename);\n  INFOS(\"start_cut_size=\"<<start_cut_size);\n\n  vector<int> tab_sizes;\n  vector<double> tab_mflops;\n\n  read_xy_file(filename,tab_sizes,tab_mflops);\n\n  // regularizeing\n\n  regularize_curve(regularize_filename,tab_mflops,tab_sizes,start_cut_size,stop_cut_size);\n  \n\n}\n\n//////////////////////////////////////////////////////////////////////////////////////\n\nvoid regularize_curve(const string & filename,\n\t\t      const vector<double> & tab_mflops, \n\t\t      const vector<int> & tab_sizes, \n\t\t      int start_cut_size, int stop_cut_size)\n{\n  int size=tab_mflops.size();\n  ofstream output_file (filename.c_str(),ios::out) ;\n\n  int i=0;\n\n  while(tab_sizes[i]<start_cut_size){\n    \n    output_file << tab_sizes[i] << \" \" <<  tab_mflops[i] << endl ;\n    i++;\n\n  }\n    \n  output_file << endl ;\n\n  while(tab_sizes[i]<stop_cut_size){\n    \n    i++;\n\n  }\n\n  while(i<size){\n    \n    output_file << tab_sizes[i] << \" \" <<  tab_mflops[i] << endl ;\n    i++;\n\n  }\n\n  output_file.close();\n\n}\n\n///////////////////////////////////////////////////////////////////////////////////////////////////////////////////\n\nvoid read_xy_file(const string & filename, vector<int> & tab_sizes, vector<double> & tab_mflops){\n\n  ifstream input_file (filename.c_str(),ios::in) ;\n\n  if (!input_file){\n    INFOS(\"!!! Error opening \"<<filename);\n    exit(0);\n  }\n  \n  int nb_point=0;\n  int size=0;\n  double mflops=0;\n\n  while (input_file >> size >> mflops ){\n    nb_point++;\n    tab_sizes.push_back(size);\n    tab_mflops.push_back(mflops);\n  }\n  SCRUTE(nb_point);\n\n  input_file.close();\n}\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/data/smooth.cxx",
    "content": "//=====================================================\n// File   :  smooth.cxx\n// Author :  L. Plagne <laurent.plagne@edf.fr)>        \n// Copyright (C) EDF R&D,  lun sep 30 14:23:15 CEST 2002\n//=====================================================\n// \n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n// \n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n// \n#include \"utilities.h\"\n#include <vector>\n#include <deque>\n#include <string>\n#include <iostream>\n#include <fstream>\n#include \"bench_parameter.hh\"\n#include <set>\n\nusing namespace std;\n\nvoid read_xy_file(const string & filename, vector<int> & tab_sizes, vector<double> & tab_mflops);\nvoid write_xy_file(const string & filename, vector<int> & tab_sizes, vector<double> & tab_mflops);\nvoid smooth_curve(const vector<double> & tab_mflops, vector<double> & smooth_tab_mflops,int window_half_width);\nvoid centered_smooth_curve(const vector<double> & tab_mflops, vector<double> & smooth_tab_mflops,int window_half_width);\n\n/////////////////////////////////////////////////////////////////////////////////////////////////\n\nint main( int argc , char *argv[] )\n{\n\n  // input data\n\n  if (argc<3){\n    INFOS(\"!!! Error ... usage : main filename window_half_width smooth_filename\");\n    exit(0);\n  }\n  INFOS(argc);\n\n  int window_half_width=atoi(argv[2]);\n\n  string filename=argv[1];\n  string smooth_filename=argv[3];\n  \n  INFOS(filename);\n  INFOS(\"window_half_width=\"<<window_half_width);\n\n  vector<int> tab_sizes;\n  vector<double> tab_mflops;\n\n  read_xy_file(filename,tab_sizes,tab_mflops);\n\n  // smoothing\n\n  vector<double> smooth_tab_mflops;\n\n  //smooth_curve(tab_mflops,smooth_tab_mflops,window_half_width);\n  centered_smooth_curve(tab_mflops,smooth_tab_mflops,window_half_width);\n\n  // output result\n\n  write_xy_file(smooth_filename,tab_sizes,smooth_tab_mflops);\n  \n\n}\n\n///////////////////////////////////////////////////////////////////////////////////////////////////////////////////\n\ntemplate<class VECTOR>\ndouble weighted_mean(const VECTOR & data)\n{\n\n  double mean=0.0;\n  \n  for (int i=0 ; i<data.size() ; i++){\n\n    mean+=data[i];\n\n  }\n\n  return mean/double(data.size()) ;\n\n}    \n\n\n\n\n///////////////////////////////////////////////////////////////////////////////////////////////////////////////////\n\n\nvoid smooth_curve(const vector<double> & tab_mflops, vector<double> & smooth_tab_mflops,int window_half_width){\n  \n  int window_width=2*window_half_width+1;\n\n  int size=tab_mflops.size();\n\n  vector<double> sample(window_width);\n  \n  for (int i=0 ; i < size ; i++){\n    \n    for ( int j=0 ; j < window_width ; j++ ){\n      \n      int shifted_index=i+j-window_half_width;\n      if (shifted_index<0) shifted_index=0;\n      if (shifted_index>size-1) shifted_index=size-1;\n      sample[j]=tab_mflops[shifted_index];\n      \n    }\n\n    smooth_tab_mflops.push_back(weighted_mean(sample));\n\n  }\n\n}\n\nvoid centered_smooth_curve(const vector<double> & tab_mflops, vector<double> & smooth_tab_mflops,int window_half_width){\n  \n  int max_window_width=2*window_half_width+1;\n\n  int size=tab_mflops.size();\n\n  \n  for (int i=0 ; i < size ; i++){\n\n    deque<double> sample;\n\n    \n    sample.push_back(tab_mflops[i]);\n\n    for ( int j=1 ; j <= window_half_width ; j++ ){\n      \n      int before=i-j;\n      int after=i+j;\n      \n      if ((before>=0)&&(after<size)) // inside of the vector\n\t{ \n\t  sample.push_front(tab_mflops[before]);\n\t  sample.push_back(tab_mflops[after]);\n\t}\n    }\n    \n    smooth_tab_mflops.push_back(weighted_mean(sample));\n    \n  }\n\n}\n\n\n///////////////////////////////////////////////////////////////////////////////////////////////////////////////////\n\nvoid write_xy_file(const string & filename, vector<int> & tab_sizes, vector<double> & tab_mflops){\n\n  ofstream output_file (filename.c_str(),ios::out) ;\n  \n  for (int i=0 ; i < tab_sizes.size() ; i++)\n    {\n      output_file << tab_sizes[i] << \" \" <<  tab_mflops[i] << endl ;\n    }\n  \n  output_file.close();\n\n}\n\n\n///////////////////////////////////////////////////////////////////////////////////////////////////////////////////\n\nvoid read_xy_file(const string & filename, vector<int> & tab_sizes, vector<double> & tab_mflops){\n\n  ifstream input_file (filename.c_str(),ios::in) ;\n\n  if (!input_file){\n    INFOS(\"!!! Error opening \"<<filename);\n    exit(0);\n  }\n  \n  int nb_point=0;\n  int size=0;\n  double mflops=0;\n\n  while (input_file >> size >> mflops ){\n    nb_point++;\n    tab_sizes.push_back(size);\n    tab_mflops.push_back(mflops);\n  }\n  SCRUTE(nb_point);\n\n  input_file.close();\n}\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/data/smooth_all.sh",
    "content": "#! /bin/bash\nORIG_DIR=$1\nSMOOTH_DIR=${ORIG_DIR}_smooth\nmkdir ${SMOOTH_DIR}\n\nAXPY_FILE=`find ${ORIG_DIR} -name \"*.dat\" | grep axpy`\nfor FILE in ${AXPY_FILE}\ndo\n    echo $FILE\n    BASE=${FILE##*/}\n    ./smooth ${ORIG_DIR}/${BASE} 4 ${SMOOTH_DIR}/${BASE}_tmp\n    ./regularize ${SMOOTH_DIR}/${BASE}_tmp 2500 15000 ${SMOOTH_DIR}/${BASE}\n    rm -f  ${SMOOTH_DIR}/${BASE}_tmp\ndone\n\n\nMATRIX_VECTOR_FILE=`find ${ORIG_DIR} -name \"*.dat\" | grep matrix_vector`\nfor FILE in ${MATRIX_VECTOR_FILE}\ndo\n    echo $FILE\n    BASE=${FILE##*/}\n    ./smooth ${ORIG_DIR}/${BASE} 4 ${SMOOTH_DIR}/${BASE}_tmp\n    ./regularize ${SMOOTH_DIR}/${BASE}_tmp 50 180 ${SMOOTH_DIR}/${BASE}\n    rm -f  ${SMOOTH_DIR}/${BASE}_tmp\ndone\n\nMATRIX_MATRIX_FILE=`find ${ORIG_DIR} -name \"*.dat\" | grep matrix_matrix`\nfor FILE in ${MATRIX_MATRIX_FILE}\ndo\n    echo $FILE\n    BASE=${FILE##*/}\n    ./smooth ${ORIG_DIR}/${BASE} 4 ${SMOOTH_DIR}/${BASE}\ndone\n\nAAT_FILE=`find ${ORIG_DIR} -name \"*.dat\" | grep _aat`\nfor FILE in ${AAT_FILE}\ndo\n    echo $FILE\n    BASE=${FILE##*/}\n    ./smooth ${ORIG_DIR}/${BASE} 4 ${SMOOTH_DIR}/${BASE}\ndone\n\n\nATA_FILE=`find ${ORIG_DIR} -name \"*.dat\" | grep _ata`\nfor FILE in ${ATA_FILE}\ndo\n    echo $FILE\n    BASE=${FILE##*/}\n    ./smooth ${ORIG_DIR}/${BASE} 4 ${SMOOTH_DIR}/${BASE}\ndone\n\n### no smoothing for tinyvector and matrices libs\n\nTINY_BLITZ_FILE=`find ${ORIG_DIR} -name \"*.dat\" | grep tiny_blitz`\nfor FILE in ${TINY_BLITZ_FILE}\ndo\n    echo $FILE\n    BASE=${FILE##*/}\n    cp ${ORIG_DIR}/${BASE} ${SMOOTH_DIR}/${BASE}\ndone\n\nTVMET_FILE=`find ${ORIG_DIR} -name \"*.dat\" | grep tvmet`\nfor FILE in ${TVMET_FILE}\ndo\n    echo $FILE\n    BASE=${FILE##*/}\n    cp ${ORIG_DIR}/${BASE} ${SMOOTH_DIR}/${BASE}\ndone\n"
  },
  {
    "path": "include/eigen3/bench/btl/generic_bench/bench.hh",
    "content": "//=====================================================\n// File   :  bench.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>\n// Copyright (C) EDF R&D,  lun sep 30 14:23:16 CEST 2002\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef BENCH_HH\n#define BENCH_HH\n\n#include \"btl.hh\"\n#include \"bench_parameter.hh\"\n#include <iostream>\n#include \"utilities.h\"\n#include \"size_lin_log.hh\"\n#include \"xy_file.hh\"\n#include <vector>\n#include <string>\n#include \"timers/portable_perf_analyzer.hh\"\n// #include \"timers/mixed_perf_analyzer.hh\"\n// #include \"timers/x86_perf_analyzer.hh\"\n// #include \"timers/STL_perf_analyzer.hh\"\n#ifdef HAVE_MKL\nextern \"C\" void cblas_saxpy(const int, const float, const float*, const int, float *, const int);\n#endif\nusing namespace std;\n\ntemplate <template<class> class Perf_Analyzer, class Action>\nBTL_DONT_INLINE void bench( int size_min, int size_max, int nb_point )\n{\n  if (BtlConfig::skipAction(Action::name()))\n    return;\n\n  string filename=\"bench_\"+Action::name()+\".dat\";\n\n  INFOS(\"starting \" <<filename);\n\n  // utilities\n\n  std::vector<double> tab_mflops(nb_point);\n  std::vector<int> tab_sizes(nb_point);\n\n  // matrices and vector size calculations\n  size_lin_log(nb_point,size_min,size_max,tab_sizes);\n\n  std::vector<int> oldSizes;\n  std::vector<double> oldFlops;\n  bool hasOldResults = read_xy_file(filename, oldSizes, oldFlops, true);\n  int oldi = oldSizes.size() - 1;\n\n  // loop on matrix size\n  Perf_Analyzer<Action> perf_action;\n  for (int i=nb_point-1;i>=0;i--)\n  {\n    //INFOS(\"size=\" <<tab_sizes[i]<<\"   (\"<<nb_point-i<<\"/\"<<nb_point<<\")\");\n    std::cout << \" \" << \"size = \" << tab_sizes[i] << \"  \" << std::flush;\n\n    BTL_DISABLE_SSE_EXCEPTIONS();\n    #ifdef HAVE_MKL\n    {\n      float dummy;\n      cblas_saxpy(1,0,&dummy,1,&dummy,1);\n    }\n    #endif\n\n    tab_mflops[i] = perf_action.eval_mflops(tab_sizes[i]);\n    std::cout << tab_mflops[i];\n    \n    if (hasOldResults)\n    {\n      while (oldi>=0 && oldSizes[oldi]>tab_sizes[i])\n        --oldi;\n      if (oldi>=0 && oldSizes[oldi]==tab_sizes[i])\n      {\n        if (oldFlops[oldi]<tab_mflops[i])\n          std::cout << \"\\t > \";\n        else\n          std::cout << \"\\t < \";\n        std::cout << oldFlops[oldi];\n      }\n      --oldi;\n    }\n    std::cout << \" MFlops    (\" << nb_point-i << \"/\" << nb_point << \")\" << std::endl;\n  }\n\n  if (!BtlConfig::Instance.overwriteResults)\n  {\n    if (hasOldResults)\n    {\n      // merge the two data\n      std::vector<int> newSizes;\n      std::vector<double> newFlops;\n      unsigned int i=0;\n      unsigned int j=0;\n      while (i<tab_sizes.size() && j<oldSizes.size())\n      {\n        if (tab_sizes[i] == oldSizes[j])\n        {\n          newSizes.push_back(tab_sizes[i]);\n          newFlops.push_back(std::max(tab_mflops[i], oldFlops[j]));\n          ++i;\n          ++j;\n        }\n        else if (tab_sizes[i] < oldSizes[j])\n        {\n          newSizes.push_back(tab_sizes[i]);\n          newFlops.push_back(tab_mflops[i]);\n          ++i;\n        }\n        else\n        {\n          newSizes.push_back(oldSizes[j]);\n          newFlops.push_back(oldFlops[j]);\n          ++j;\n        }\n      }\n      while (i<tab_sizes.size())\n      {\n        newSizes.push_back(tab_sizes[i]);\n        newFlops.push_back(tab_mflops[i]);\n        ++i;\n      }\n      while (j<oldSizes.size())\n      {\n        newSizes.push_back(oldSizes[j]);\n        newFlops.push_back(oldFlops[j]);\n        ++j;\n      }\n      tab_mflops = newFlops;\n      tab_sizes = newSizes;\n    }\n  }\n\n  // dump the result in a file  :\n  dump_xy_file(tab_sizes,tab_mflops,filename);\n\n}\n\n// default Perf Analyzer\n\ntemplate <class Action>\nBTL_DONT_INLINE void bench( int size_min, int size_max, int nb_point ){\n\n  // if the rdtsc is not available :\n  bench<Portable_Perf_Analyzer,Action>(size_min,size_max,nb_point);\n  // if the rdtsc is available :\n//    bench<Mixed_Perf_Analyzer,Action>(size_min,size_max,nb_point);\n\n\n  // Only for small problem size. Otherwize it will be too long\n//   bench<X86_Perf_Analyzer,Action>(size_min,size_max,nb_point);\n//   bench<STL_Perf_Analyzer,Action>(size_min,size_max,nb_point);\n\n}\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/generic_bench/bench_parameter.hh",
    "content": "//=====================================================\n// File   :  bench_parameter.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>\n// Copyright (C) EDF R&D,  lun sep 30 14:23:16 CEST 2002\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef BENCH_PARAMETER_HH\n#define BENCH_PARAMETER_HH\n\n// minimal time for each measurement\n#define REAL_TYPE float\n// minimal time for each measurement\n#define MIN_TIME 0.2\n// nb of point on bench curves\n#define NB_POINT 100\n// min vector size for axpy bench\n#define MIN_AXPY 5\n// max vector size for axpy bench\n#define MAX_AXPY 3000000\n// min matrix size for matrix vector product bench\n#define MIN_MV 5\n// max matrix size for matrix vector product bench\n#define MAX_MV 5000\n// min matrix size for matrix matrix product bench\n#define MIN_MM 5\n// max matrix size for matrix matrix product bench\n#define MAX_MM MAX_MV\n// min matrix size for LU bench\n#define MIN_LU 5\n// max matrix size for LU bench\n#define MAX_LU 3000\n// max size for tiny vector and matrix\n#define TINY_MV_MAX_SIZE 16\n// default nb_sample for x86 timer\n#define DEFAULT_NB_SAMPLE 1000\n\n// how many times we run a single bench (keep the best perf)\n#define DEFAULT_NB_TRIES 3\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/generic_bench/btl.hh",
    "content": "//=====================================================\n// File   :  btl.hh\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef BTL_HH\n#define BTL_HH\n\n#include \"bench_parameter.hh\"\n#include <iostream>\n#include <algorithm>\n#include <vector>\n#include <string>\n#include \"utilities.h\"\n\n#if (defined __GNUC__)\n#define BTL_ALWAYS_INLINE __attribute__((always_inline)) inline\n#else\n#define BTL_ALWAYS_INLINE inline\n#endif\n\n#if (defined __GNUC__)\n#define BTL_DONT_INLINE __attribute__((noinline))\n#else\n#define BTL_DONT_INLINE\n#endif\n\n#if (defined __GNUC__)\n#define BTL_ASM_COMMENT(X)  asm(\"#\" X)\n#else\n#define BTL_ASM_COMMENT(X)\n#endif\n\n#ifdef __SSE__\n#include \"xmmintrin.h\"\n// This enables flush to zero (FTZ) and denormals are zero (DAZ) modes:\n#define BTL_DISABLE_SSE_EXCEPTIONS()  { _mm_setcsr(_mm_getcsr() | 0x8040); }\n#else\n#define BTL_DISABLE_SSE_EXCEPTIONS()\n#endif\n\n/** Enhanced std::string\n*/\nclass BtlString : public std::string\n{\npublic:\n    BtlString() : std::string() {}\n    BtlString(const BtlString& str) : std::string(static_cast<const std::string&>(str)) {}\n    BtlString(const std::string& str) : std::string(str) {}\n    BtlString(const char* str) : std::string(str) {}\n\n    operator const char* () const { return c_str(); }\n\n    void trim( bool left = true, bool right = true )\n    {\n        int lspaces, rspaces, len = length(), i;\n        lspaces = rspaces = 0;\n\n        if ( left )\n            for (i=0; i<len && (at(i)==' '||at(i)=='\\t'||at(i)=='\\r'||at(i)=='\\n'); ++lspaces,++i);\n\n        if ( right && lspaces < len )\n            for(i=len-1; i>=0 && (at(i)==' '||at(i)=='\\t'||at(i)=='\\r'||at(i)=='\\n'); rspaces++,i--);\n\n        *this = substr(lspaces, len-lspaces-rspaces);\n    }\n\n    std::vector<BtlString> split( const BtlString& delims = \"\\t\\n \") const\n    {\n        std::vector<BtlString> ret;\n        unsigned int numSplits = 0;\n        size_t start, pos;\n        start = 0;\n        do\n        {\n            pos = find_first_of(delims, start);\n            if (pos == start)\n            {\n                ret.push_back(\"\");\n                start = pos + 1;\n            }\n            else if (pos == npos)\n                ret.push_back( substr(start) );\n            else\n            {\n                ret.push_back( substr(start, pos - start) );\n                start = pos + 1;\n            }\n            //start = find_first_not_of(delims, start);\n            ++numSplits;\n        } while (pos != npos);\n        return ret;\n    }\n\n    bool endsWith(const BtlString& str) const\n    {\n        if(str.size()>this->size())\n            return false;\n        return this->substr(this->size()-str.size(),str.size()) == str;\n    }\n    bool contains(const BtlString& str) const\n    {\n        return this->find(str)<this->size();\n    }\n    bool beginsWith(const BtlString& str) const\n    {\n        if(str.size()>this->size())\n            return false;\n        return this->substr(0,str.size()) == str;\n    }\n\n    BtlString toLowerCase( void )\n    {\n        std::transform(begin(), end(), begin(), static_cast<int(*)(int)>(::tolower) );\n        return *this;\n    }\n    BtlString toUpperCase( void )\n    {\n        std::transform(begin(), end(), begin(), static_cast<int(*)(int)>(::toupper) );\n        return *this;\n    }\n\n    /** Case insensitive comparison.\n    */\n    bool isEquiv(const BtlString& str) const\n    {\n        BtlString str0 = *this;\n        str0.toLowerCase();\n        BtlString str1 = str;\n        str1.toLowerCase();\n        return str0 == str1;\n    }\n\n    /** Decompose the current string as a path and a file.\n        For instance: \"dir1/dir2/file.ext\" leads to path=\"dir1/dir2/\" and filename=\"file.ext\"\n    */\n    void decomposePathAndFile(BtlString& path, BtlString& filename) const\n    {\n        std::vector<BtlString> elements = this->split(\"/\\\\\");\n        path = \"\";\n        filename = elements.back();\n        elements.pop_back();\n        if (this->at(0)=='/')\n            path = \"/\";\n        for (unsigned int i=0 ; i<elements.size() ; ++i)\n            path += elements[i] + \"/\";\n    }\n};\n\nclass BtlConfig\n{\npublic:\n  BtlConfig()\n    : overwriteResults(false), checkResults(true), realclock(false), tries(DEFAULT_NB_TRIES)\n  {\n    char * _config;\n    _config = getenv (\"BTL_CONFIG\");\n    if (_config!=NULL)\n    {\n      std::vector<BtlString> config = BtlString(_config).split(\" \\t\\n\");\n      for (unsigned int i = 0; i<config.size(); i++)\n      {\n        if (config[i].beginsWith(\"-a\"))\n        {\n          if (i+1==config.size())\n          {\n            std::cerr << \"error processing option: \" << config[i] << \"\\n\";\n            exit(2);\n          }\n          Instance.m_selectedActionNames = config[i+1].split(\":\");\n\n          i += 1;\n        }\n        else if (config[i].beginsWith(\"-t\"))\n        {\n          if (i+1==config.size())\n          {\n            std::cerr << \"error processing option: \" << config[i] << \"\\n\";\n            exit(2);\n          }\n          Instance.tries = atoi(config[i+1].c_str());\n\n          i += 1;\n        }\n        else if (config[i].beginsWith(\"--overwrite\"))\n        {\n          Instance.overwriteResults = true;\n        }\n        else if (config[i].beginsWith(\"--nocheck\"))\n        {\n          Instance.checkResults = false;\n        }\n        else if (config[i].beginsWith(\"--real\"))\n        {\n          Instance.realclock = true;\n        }\n      }\n    }\n\n    BTL_DISABLE_SSE_EXCEPTIONS();\n  }\n\n  BTL_DONT_INLINE static bool skipAction(const std::string& _name)\n  {\n    if (Instance.m_selectedActionNames.empty())\n      return false;\n\n    BtlString name(_name);\n    for (unsigned int i=0; i<Instance.m_selectedActionNames.size(); ++i)\n      if (name.contains(Instance.m_selectedActionNames[i]))\n        return false;\n\n    return true;\n  }\n\n  static BtlConfig Instance;\n  bool overwriteResults;\n  bool checkResults;\n  bool realclock;\n  int tries;\n\nprotected:\n  std::vector<BtlString> m_selectedActionNames;\n};\n\n#define BTL_MAIN \\\n  BtlConfig BtlConfig::Instance\n\n#endif // BTL_HH\n"
  },
  {
    "path": "include/eigen3/bench/btl/generic_bench/init/init_function.hh",
    "content": "//=====================================================\n// File   :  init_function.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>        \n// Copyright (C) EDF R&D,  lun sep 30 14:23:18 CEST 2002\n//=====================================================\n// \n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n// \n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n// \n#ifndef INIT_FUNCTION_HH\n#define INIT_FUNCTION_HH\n\ndouble simple_function(int index)\n{\n  return index;\n}\n\ndouble simple_function(int index_i, int index_j)\n{\n  return index_i+index_j;\n}\n\ndouble pseudo_random(int /*index*/)\n{\n  return std::rand()/double(RAND_MAX);\n}\n\ndouble pseudo_random(int /*index_i*/, int /*index_j*/)\n{\n  return std::rand()/double(RAND_MAX);\n}\n\n\ndouble null_function(int /*index*/)\n{\n  return 0.0;\n}\n\ndouble null_function(int /*index_i*/, int /*index_j*/)\n{\n  return 0.0;\n}\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/generic_bench/init/init_matrix.hh",
    "content": "//=====================================================\n// File   :  init_matrix.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>\n// Copyright (C) EDF R&D,  lun sep 30 14:23:19 CEST 2002\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef INIT_MATRIX_HH\n#define INIT_MATRIX_HH\n\n// The Vector class must satisfy the following part of STL vector concept :\n//            resize() method\n//            [] operator for setting element\n//            value_type defined\ntemplate<double init_function(int,int), class Vector>\nBTL_DONT_INLINE void init_row(Vector & X, int size, int row){\n\n  X.resize(size);\n\n  for (unsigned int j=0;j<X.size();j++){\n    X[j]=typename Vector::value_type(init_function(row,j));\n  }\n}\n\n\n// Matrix is a Vector of Vector\n// The Matrix class must satisfy the following part of STL vector concept :\n//            resize() method\n//            [] operator for setting rows\ntemplate<double init_function(int,int),class Vector>\nBTL_DONT_INLINE void init_matrix(Vector &  A, int size){\n  A.resize(size);\n  for (unsigned int row=0; row<A.size() ; row++){\n    init_row<init_function>(A[row],size,row);\n  }\n}\n\ntemplate<double init_function(int,int),class Matrix>\nBTL_DONT_INLINE void init_matrix_symm(Matrix&  A, int size){\n  A.resize(size);\n  for (unsigned int row=0; row<A.size() ; row++)\n    A[row].resize(size);\n  for (unsigned int row=0; row<A.size() ; row++){\n    A[row][row] = init_function(row,row);\n    for (unsigned int col=0; col<row ; col++){\n      double x = init_function(row,col);\n      A[row][col] = A[col][row] = x;\n    }\n  }\n}\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/generic_bench/init/init_vector.hh",
    "content": "//=====================================================\n// File   :  init_vector.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>\n// Copyright (C) EDF R&D,  lun sep 30 14:23:18 CEST 2002\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef INIT_VECTOR_HH\n#define INIT_VECTOR_HH\n\n// The Vector class must satisfy the following part of STL vector concept :\n//            resize() method\n//            [] operator for setting element\n//            value_type defined\ntemplate<double init_function(int), class Vector>\nvoid init_vector(Vector & X, int size){\n\n  X.resize(size);\n\n  for (unsigned int i=0;i<X.size();i++){\n    X[i]=typename Vector::value_type(init_function(i));\n  }\n}\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/generic_bench/static/bench_static.hh",
    "content": "//=====================================================\n// File   :  bench_static.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>\n// Copyright (C) EDF R&D,  lun sep 30 14:23:16 CEST 2002\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef BENCH_STATIC_HH\n#define BENCH_STATIC_HH\n\n#include \"btl.hh\"\n#include \"bench_parameter.hh\"\n#include <iostream>\n#include \"utilities.h\"\n#include \"xy_file.hh\"\n#include \"static/static_size_generator.hh\"\n#include \"timers/portable_perf_analyzer.hh\"\n// #include \"timers/mixed_perf_analyzer.hh\"\n// #include \"timers/x86_perf_analyzer.hh\"\n\nusing namespace std;\n\n\ntemplate <template<class> class Perf_Analyzer, template<class> class Action, template<class,int> class Interface>\nBTL_DONT_INLINE  void bench_static(void)\n{\n  if (BtlConfig::skipAction(Action<Interface<REAL_TYPE,10> >::name()))\n    return;\n\n  string filename = \"bench_\" + Action<Interface<REAL_TYPE,10> >::name() + \".dat\";\n\n  INFOS(\"starting \" << filename);\n\n  const int max_size = TINY_MV_MAX_SIZE;\n\n  std::vector<double> tab_mflops;\n  std::vector<double> tab_sizes;\n\n  static_size_generator<max_size,Perf_Analyzer,Action,Interface>::go(tab_sizes,tab_mflops);\n\n  dump_xy_file(tab_sizes,tab_mflops,filename);\n}\n\n// default Perf Analyzer\ntemplate <template<class> class Action, template<class,int> class Interface>\nBTL_DONT_INLINE  void bench_static(void)\n{\n  bench_static<Portable_Perf_Analyzer,Action,Interface>();\n  //bench_static<Mixed_Perf_Analyzer,Action,Interface>();\n  //bench_static<X86_Perf_Analyzer,Action,Interface>();\n}\n\n#endif\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/generic_bench/static/intel_bench_fixed_size.hh",
    "content": "//=====================================================\n// File   :  intel_bench_fixed_size.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>        \n// Copyright (C) EDF R&D,  mar dc 3 18:59:37 CET 2002\n//=====================================================\n// \n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n// \n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n// \n#ifndef _BENCH_FIXED_SIZE_HH_\n#define _BENCH_FIXED_SIZE_HH_\n\n#include \"utilities.h\"\n#include \"function_time.hh\"\n\ntemplate <class Action>\ndouble bench_fixed_size(int size, unsigned long long  & nb_calc,unsigned long long & nb_init)\n{\n  \n  Action action(size);\n  \n  double time_baseline=time_init(nb_init,action);\n\n  while (time_baseline < MIN_TIME) {\n\n    //INFOS(\"nb_init=\"<<nb_init);\n    //INFOS(\"time_baseline=\"<<time_baseline);\n    nb_init*=2;\n    time_baseline=time_init(nb_init,action);\n  }\n  \n  time_baseline=time_baseline/(double(nb_init));\n  \n  double time_action=time_calculate(nb_calc,action);\n  \n  while (time_action < MIN_TIME) {\n    \n    nb_calc*=2;\n    time_action=time_calculate(nb_calc,action);\n  }\n\n  INFOS(\"nb_init=\"<<nb_init);\n  INFOS(\"nb_calc=\"<<nb_calc);\n  \n  \n  time_action=time_action/(double(nb_calc));\n  \n  action.check_result();\n  \n  time_action=time_action-time_baseline;\n\n  return action.nb_op_base()/(time_action*1000000.0);\n\n}\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/generic_bench/static/static_size_generator.hh",
    "content": "//=====================================================\n// File   :  static_size_generator.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>        \n// Copyright (C) EDF R&D,  mar dc 3 18:59:36 CET 2002\n//=====================================================\n// \n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n// \n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n// \n#ifndef _STATIC_SIZE_GENERATOR_HH\n#define _STATIC_SIZE_GENERATOR_HH\n#include <vector>\n\nusing namespace std;\n\n//recursive generation of statically defined matrix and vector sizes\n\ntemplate <int SIZE,template<class> class Perf_Analyzer, template<class> class Action, template<class,int> class Interface> \nstruct static_size_generator{\n  static void go(vector<double> & tab_sizes, vector<double> & tab_mflops)\n  {\n    tab_sizes.push_back(SIZE);\n    std::cout << tab_sizes.back() << \" \\t\" << std::flush;\n    Perf_Analyzer<Action<Interface<REAL_TYPE,SIZE> > > perf_action;\n    tab_mflops.push_back(perf_action.eval_mflops(SIZE));\n    std::cout << tab_mflops.back() << \" MFlops\" << std::endl;\n    static_size_generator<SIZE-1,Perf_Analyzer,Action,Interface>::go(tab_sizes,tab_mflops);\n  };\n};\n\n//recursion end\n\ntemplate <template<class> class Perf_Analyzer, template<class> class Action, template<class,int> class Interface> \nstruct static_size_generator<1,Perf_Analyzer,Action,Interface>{  \n  static  void go(vector<double> & tab_sizes, vector<double> & tab_mflops)\n  {\n    tab_sizes.push_back(1);\n    Perf_Analyzer<Action<Interface<REAL_TYPE,1> > > perf_action;\n    tab_mflops.push_back(perf_action.eval_mflops(1));\n  };\n};\n\n#endif\n  \n  \n  \n  \n"
  },
  {
    "path": "include/eigen3/bench/btl/generic_bench/timers/STL_perf_analyzer.hh",
    "content": "//=====================================================\n// File   :  STL_perf_analyzer.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>        \n// Copyright (C) EDF R&D,  mar dc 3 18:59:35 CET 2002\n//=====================================================\n// \n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n// \n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n// \n#ifndef _STL_PERF_ANALYSER_HH\n#define _STL_PERF_ANALYSER_HH\n\n#include \"STL_timer.hh\"\n#include \"bench_parameter.hh\"\n\ntemplate<class ACTION>\nclass STL_Perf_Analyzer{\npublic:  \n  STL_Perf_Analyzer(unsigned long long nb_sample=DEFAULT_NB_SAMPLE):_nb_sample(nb_sample),_chronos()\n  {\n    MESSAGE(\"STL_Perf_Analyzer Ctor\");\n  }; \n  STL_Perf_Analyzer( const STL_Perf_Analyzer & ){\n    INFOS(\"Copy Ctor not implemented\");\n    exit(0);\n  };\n  ~STL_Perf_Analyzer( void ){\n    MESSAGE(\"STL_Perf_Analyzer Dtor\");\n  };\n  \n  \n  inline double eval_mflops(int size)\n  {\n\n    ACTION action(size);\n\n    _chronos.start_baseline(_nb_sample);\n      \n    do {\n\n      action.initialize();\n    } while (_chronos.check());\n\n    double baseline_time=_chronos.get_time();\n\n    _chronos.start(_nb_sample);\n    do {\n      action.initialize();\n      action.calculate();\n    } while (_chronos.check());\n\n    double calculate_time=_chronos.get_time();\n\n    double corrected_time=calculate_time-baseline_time;\n    \n    //    cout << size <<\" \"<<baseline_time<<\" \"<<calculate_time<<\" \"<<corrected_time<<\" \"<<action.nb_op_base() << endl;    \n    \n    return action.nb_op_base()/(corrected_time*1000000.0);\n    //return action.nb_op_base()/(calculate_time*1000000.0);\n    \n  }\nprivate:\n\n  STL_Timer _chronos;\n  unsigned long long _nb_sample;\n\n  \n};\n\n  \n  \n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/generic_bench/timers/STL_timer.hh",
    "content": "//=====================================================\n// File   :  STL_Timer.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>        \n// Copyright (C) EDF R&D,  mar dc 3 18:59:35 CET 2002\n//=====================================================\n// \n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n// \n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n// \n// STL Timer Class. Adapted (L.P.) from the timer class by Musser et Al\n// described int the Book : STL Tutorial and reference guide.\n// Define a timer class for analyzing algorithm performance.\n#include <iostream>\n#include <iomanip>\n#include <vector>\n#include <map>\n#include <algorithm>\nusing namespace std;\n\nclass STL_Timer {\npublic:\n  STL_Timer(){ baseline = false; };  // Default constructor\n  // Start a series of r trials:\n  void start(unsigned int r){\n    reps = r;\n    count = 0;\n    iterations.clear();\n    iterations.reserve(reps);\n    initial = time(0);\n  };\n  // Start a series of r trials to determine baseline time:\n  void start_baseline(unsigned int r)\n  {\n    baseline = true;\n    start(r);\n  }\n  // Returns true if the trials have been completed, else false\n  bool check()\n  {\n    ++count;\n    final = time(0);\n    if (initial < final) {\n      iterations.push_back(count);  \n      initial = final;\n      count = 0;\n    }\n    return (iterations.size() < reps);\n  };\n  // Returns the results for external use\n  double get_time( void )\n  {\n    sort(iterations.begin(), iterations.end());\n    return 1.0/iterations[reps/2];\n  };\nprivate:\n  unsigned int reps;  // Number of trials\n  // For storing loop iterations of a trial\n  vector<long> iterations;\n  // For saving initial and final times of a trial\n  time_t initial, final;\n  // For counting loop iterations of a trial\n  unsigned long count;\n  // true if this is a baseline computation, false otherwise\n  bool baseline;\n  // For recording the baseline time \n  double baseline_time;\n};\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/generic_bench/timers/mixed_perf_analyzer.hh",
    "content": "//=====================================================\n// File   :  mixed_perf_analyzer.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>        \n// Copyright (C) EDF R&D,  mar dc 3 18:59:36 CET 2002\n//=====================================================\n// \n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n// \n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n// \n#ifndef _MIXED_PERF_ANALYSER_HH\n#define _MIXED_PERF_ANALYSER_HH\n\n#include \"x86_perf_analyzer.hh\"\n#include \"portable_perf_analyzer.hh\"\n\n// choose portable perf analyzer for long calculations and x86 analyser for short ones\n\n\ntemplate<class Action>\nclass Mixed_Perf_Analyzer{\n  \npublic:  \n  Mixed_Perf_Analyzer( void ):_x86pa(),_ppa(),_use_ppa(true)\n  {\n    MESSAGE(\"Mixed_Perf_Analyzer Ctor\");\n  }; \n  Mixed_Perf_Analyzer( const Mixed_Perf_Analyzer & ){\n    INFOS(\"Copy Ctor not implemented\");\n    exit(0);\n  };\n  ~Mixed_Perf_Analyzer( void ){\n    MESSAGE(\"Mixed_Perf_Analyzer Dtor\");\n  };\n    \n  \n  inline double eval_mflops(int size)\n  {\n\n    double result=0.0;\n    if (_use_ppa){      \n      result=_ppa.eval_mflops(size);\n      if (_ppa.get_nb_calc()>DEFAULT_NB_SAMPLE){_use_ppa=false;}      \n    }\n    else{      \n      result=_x86pa.eval_mflops(size);\n    }\n\n    return result;\n  }\n\nprivate:\n\n  Portable_Perf_Analyzer<Action> _ppa;\n  X86_Perf_Analyzer<Action> _x86pa;\n  bool _use_ppa;\n\n};\n\n#endif\n\n  \n    \n  \n"
  },
  {
    "path": "include/eigen3/bench/btl/generic_bench/timers/portable_perf_analyzer.hh",
    "content": "//=====================================================\n// File   :  portable_perf_analyzer.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>\n// Copyright (C) EDF R&D,  mar d�c 3 18:59:35 CET 2002\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef _PORTABLE_PERF_ANALYZER_HH\n#define _PORTABLE_PERF_ANALYZER_HH\n\n#include \"utilities.h\"\n#include \"timers/portable_timer.hh\"\n\ntemplate <class Action>\nclass Portable_Perf_Analyzer{\npublic:\n  Portable_Perf_Analyzer( ):_nb_calc(0), m_time_action(0), _chronos(){\n    MESSAGE(\"Portable_Perf_Analyzer Ctor\");\n  };\n  Portable_Perf_Analyzer( const Portable_Perf_Analyzer & ){\n    INFOS(\"Copy Ctor not implemented\");\n    exit(0);\n  };\n  ~Portable_Perf_Analyzer(){\n    MESSAGE(\"Portable_Perf_Analyzer Dtor\");\n  };\n\n  BTL_DONT_INLINE double eval_mflops(int size)\n  {\n    Action action(size);\n\n//     action.initialize();\n//     time_action = time_calculate(action);\n    while (m_time_action < MIN_TIME)\n    {\n      if(_nb_calc==0) _nb_calc = 1;\n      else            _nb_calc *= 2;\n      action.initialize();\n      m_time_action = time_calculate(action);\n    }\n\n    // optimize\n    for (int i=1; i<BtlConfig::Instance.tries; ++i)\n    {\n      Action _action(size);\n      std::cout << \" \" << _action.nb_op_base()*_nb_calc/(m_time_action*1e6) << \" \";\n      _action.initialize();\n      m_time_action = std::min(m_time_action, time_calculate(_action));\n    }\n\n    double time_action = m_time_action / (double(_nb_calc));\n\n    // check\n    if (BtlConfig::Instance.checkResults && size<128)\n    {\n      action.initialize();\n      action.calculate();\n      action.check_result();\n    }\n    return action.nb_op_base()/(time_action*1e6);\n  }\n\n  BTL_DONT_INLINE double time_calculate(Action & action)\n  {\n    // time measurement\n    action.calculate();\n    _chronos.start();\n    for (unsigned int ii=0;ii<_nb_calc;ii++)\n    {\n      action.calculate();\n    }\n    _chronos.stop();\n    return _chronos.user_time();\n  }\n\n  unsigned long long get_nb_calc()\n  {\n    return _nb_calc;\n  }\n\n\nprivate:\n  unsigned long long _nb_calc;\n  double m_time_action;\n  Portable_Timer _chronos;\n\n};\n\n#endif //_PORTABLE_PERF_ANALYZER_HH\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/generic_bench/timers/portable_perf_analyzer_old.hh",
    "content": "//=====================================================\n// File   :  portable_perf_analyzer.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>\n// Copyright (C) EDF R&D,  mar d�c 3 18:59:35 CET 2002\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef _PORTABLE_PERF_ANALYZER_HH\n#define _PORTABLE_PERF_ANALYZER_HH\n\n#include \"utilities.h\"\n#include \"timers/portable_timer.hh\"\n\ntemplate <class Action>\nclass Portable_Perf_Analyzer{\npublic:\n  Portable_Perf_Analyzer( void ):_nb_calc(1),_nb_init(1),_chronos(){\n    MESSAGE(\"Portable_Perf_Analyzer Ctor\");\n  };\n  Portable_Perf_Analyzer( const Portable_Perf_Analyzer & ){\n    INFOS(\"Copy Ctor not implemented\");\n    exit(0);\n  };\n  ~Portable_Perf_Analyzer( void ){\n    MESSAGE(\"Portable_Perf_Analyzer Dtor\");\n  };\n\n\n\n  inline double eval_mflops(int size)\n  {\n\n    Action action(size);\n\n//     double time_baseline = time_init(action);\n//     while (time_baseline < MIN_TIME_INIT)\n//     {\n//       _nb_init *= 2;\n//       time_baseline = time_init(action);\n//     }\n//\n//     // optimize\n//     for (int i=1; i<NB_TRIES; ++i)\n//       time_baseline = std::min(time_baseline, time_init(action));\n//\n//     time_baseline = time_baseline/(double(_nb_init));\n\n    double time_action = time_calculate(action);\n    while (time_action < MIN_TIME)\n    {\n      _nb_calc *= 2;\n      time_action = time_calculate(action);\n    }\n\n    // optimize\n    for (int i=1; i<NB_TRIES; ++i)\n      time_action = std::min(time_action, time_calculate(action));\n\n//     INFOS(\"size=\"<<size);\n//     INFOS(\"_nb_init=\"<<_nb_init);\n//     INFOS(\"_nb_calc=\"<<_nb_calc);\n\n    time_action = time_action / (double(_nb_calc));\n\n    action.check_result();\n\n\n    double time_baseline = time_init(action);\n    for (int i=1; i<NB_TRIES; ++i)\n      time_baseline = std::min(time_baseline, time_init(action));\n    time_baseline = time_baseline/(double(_nb_init));\n\n\n\n//     INFOS(\"time_baseline=\"<<time_baseline);\n//     INFOS(\"time_action=\"<<time_action);\n\n    time_action = time_action - time_baseline;\n\n//     INFOS(\"time_corrected=\"<<time_action);\n\n    return action.nb_op_base()/(time_action*1000000.0);\n  }\n\n  inline double time_init(Action & action)\n  {\n    // time measurement\n    _chronos.start();\n    for (int ii=0; ii<_nb_init; ii++)\n      action.initialize();\n    _chronos.stop();\n    return _chronos.user_time();\n  }\n\n\n  inline double time_calculate(Action & action)\n  {\n    // time measurement\n    _chronos.start();\n    for (int ii=0;ii<_nb_calc;ii++)\n    {\n      action.initialize();\n      action.calculate();\n    }\n    _chronos.stop();\n    return _chronos.user_time();\n  }\n\n  unsigned long long get_nb_calc( void )\n  {\n    return _nb_calc;\n  }\n\n\nprivate:\n  unsigned long long _nb_calc;\n  unsigned long long _nb_init;\n  Portable_Timer _chronos;\n\n};\n\n#endif //_PORTABLE_PERF_ANALYZER_HH\n"
  },
  {
    "path": "include/eigen3/bench/btl/generic_bench/timers/portable_timer.hh",
    "content": "//=====================================================\n// File   :  portable_timer.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)> from boost lib\n// Copyright (C) EDF R&D,  lun sep 30 14:23:17 CEST 2002\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n//  simple_time extracted from the boost library\n//\n#ifndef _PORTABLE_TIMER_HH\n#define _PORTABLE_TIMER_HH\n\n#include <ctime>\n#include <cstdlib>\n\n#include <time.h>\n\n\n#define USEC_IN_SEC 1000000\n\n\n//  timer  -------------------------------------------------------------------//\n\n//  A timer object measures CPU time.\n#if defined(_MSC_VER)\n\n#define NOMINMAX\n#include <windows.h>\n\n/*#ifndef hr_timer\n#include \"hr_time.h\"\n#define hr_timer\n#endif*/\n\n class Portable_Timer\n {\n  public:\n\n   typedef struct {\n    LARGE_INTEGER start;\n    LARGE_INTEGER stop;\n   } stopWatch;\n\n\n   Portable_Timer()\n   {\n\t startVal.QuadPart = 0;\n\t stopVal.QuadPart = 0;\n\t QueryPerformanceFrequency(&frequency);\n   }\n\n   void start() { QueryPerformanceCounter(&startVal); }\n\n   void stop() { QueryPerformanceCounter(&stopVal); }\n\n   double elapsed() {\n\t LARGE_INTEGER time;\n     time.QuadPart = stopVal.QuadPart - startVal.QuadPart;\n     return LIToSecs(time);\n   }\n\n   double user_time() { return elapsed(); }\n\n\n private:\n\n   double LIToSecs(LARGE_INTEGER& L) {\n     return ((double)L.QuadPart /(double)frequency.QuadPart) ;\n   }\n\n   LARGE_INTEGER startVal;\n   LARGE_INTEGER stopVal;\n   LARGE_INTEGER frequency;\n\n\n }; // Portable_Timer\n\n#elif defined(__APPLE__)\n#include <CoreServices/CoreServices.h>\n#include <mach/mach_time.h>\n\n\nclass Portable_Timer\n{\n public:\n\n  Portable_Timer()\n  {\n  }\n\n  void start()\n  {\n    m_start_time = double(mach_absolute_time())*1e-9;;\n\n  }\n\n  void stop()\n  {\n    m_stop_time = double(mach_absolute_time())*1e-9;;\n\n  }\n\n  double elapsed()\n  {\n    return  user_time();\n  }\n\n  double user_time()\n  {\n    return m_stop_time - m_start_time;\n  }\n\n\nprivate:\n\n  double m_stop_time, m_start_time;\n\n}; // Portable_Timer (Apple)\n\n#else\n\n#include <sys/time.h>\n#include <sys/resource.h>\n#include <unistd.h>\n#include <sys/times.h>\n\nclass Portable_Timer\n{\n public:\n\n  Portable_Timer()\n  {\n    m_clkid = BtlConfig::Instance.realclock ? CLOCK_REALTIME : CLOCK_PROCESS_CPUTIME_ID;\n  }\n\n  Portable_Timer(int clkid) : m_clkid(clkid)\n  {}\n\n  void start()\n  {\n    timespec ts;\n    clock_gettime(m_clkid, &ts);\n    m_start_time = double(ts.tv_sec) + 1e-9 * double(ts.tv_nsec);\n\n  }\n\n  void stop()\n  {\n    timespec ts;\n    clock_gettime(m_clkid, &ts);\n    m_stop_time = double(ts.tv_sec) + 1e-9 * double(ts.tv_nsec);\n\n  }\n\n  double elapsed()\n  {\n    return  user_time();\n  }\n\n  double user_time()\n  {\n    return m_stop_time - m_start_time;\n  }\n\n\nprivate:\n\n  int m_clkid;\n  double m_stop_time, m_start_time;\n\n}; // Portable_Timer (Linux)\n\n#endif\n\n#endif  // PORTABLE_TIMER_HPP\n"
  },
  {
    "path": "include/eigen3/bench/btl/generic_bench/timers/x86_perf_analyzer.hh",
    "content": "//=====================================================\n// File   :  x86_perf_analyzer.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>\n// Copyright (C) EDF R&D,  mar d�c 3 18:59:35 CET 2002\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef _X86_PERF_ANALYSER_HH\n#define _X86_PERF_ANALYSER_HH\n\n#include \"x86_timer.hh\"\n#include \"bench_parameter.hh\"\n\ntemplate<class ACTION>\nclass X86_Perf_Analyzer{\npublic:\n  X86_Perf_Analyzer( unsigned long long nb_sample=DEFAULT_NB_SAMPLE):_nb_sample(nb_sample),_chronos()\n  {\n    MESSAGE(\"X86_Perf_Analyzer Ctor\");\n    _chronos.find_frequency();\n  };\n  X86_Perf_Analyzer( const X86_Perf_Analyzer & ){\n    INFOS(\"Copy Ctor not implemented\");\n    exit(0);\n  };\n  ~X86_Perf_Analyzer( void ){\n    MESSAGE(\"X86_Perf_Analyzer Dtor\");\n  };\n\n\n  inline double eval_mflops(int size)\n  {\n\n    ACTION action(size);\n\n    int nb_loop=5;\n    double calculate_time=0.0;\n    double baseline_time=0.0;\n\n    for (int j=0 ; j < nb_loop ; j++){\n\n      _chronos.clear();\n\n      for(int i=0 ; i < _nb_sample  ; i++)\n      {\n        _chronos.start();\n        action.initialize();\n        action.calculate();\n        _chronos.stop();\n        _chronos.add_get_click();\n      }\n\n      calculate_time += double(_chronos.get_shortest_clicks())/_chronos.frequency();\n\n      if (j==0) action.check_result();\n\n      _chronos.clear();\n\n      for(int i=0 ; i < _nb_sample  ; i++)\n      {\n        _chronos.start();\n        action.initialize();\n        _chronos.stop();\n        _chronos.add_get_click();\n\n      }\n\n      baseline_time+=double(_chronos.get_shortest_clicks())/_chronos.frequency();\n\n    }\n\n    double corrected_time = (calculate_time-baseline_time)/double(nb_loop);\n\n\n//     INFOS(\"_nb_sample=\"<<_nb_sample);\n//     INFOS(\"baseline_time=\"<<baseline_time);\n//     INFOS(\"calculate_time=\"<<calculate_time);\n//     INFOS(\"corrected_time=\"<<corrected_time);\n\n//    cout << size <<\" \"<<baseline_time<<\" \"<<calculate_time<<\" \"<<corrected_time<<\" \"<<action.nb_op_base() << endl;\n\n    return action.nb_op_base()/(corrected_time*1000000.0);\n    //return action.nb_op_base()/(calculate_time*1000000.0);\n  }\n\nprivate:\n\n  X86_Timer _chronos;\n  unsigned long long _nb_sample;\n\n\n};\n\n\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/generic_bench/timers/x86_timer.hh",
    "content": "//=====================================================\n// File   :  x86_timer.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>        \n// Copyright (C) EDF R&D,  mar d�c 3 18:59:35 CET 2002\n//=====================================================\n// \n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n// \n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n// \n#ifndef _X86_TIMER_HH\n#define _X86_TIMER_HH\n\n#include <sys/time.h>\n#include <sys/resource.h>\n#include <unistd.h>\n#include <sys/times.h>\n//#include \"system_time.h\"\n#define u32 unsigned int\n#include <asm/msr.h>\n#include \"utilities.h\"\n#include <map>\n#include <fstream>\n#include <string>\n#include <iostream>\n\n// frequence de la becanne en Hz\n//#define FREQUENCY 648000000\n//#define FREQUENCY 1400000000\n#define FREQUENCY 1695000000\n\nusing namespace std;\n\n\nclass X86_Timer {\n\npublic :\n\n  X86_Timer( void ):_frequency(FREQUENCY),_nb_sample(0)\n  {\n    MESSAGE(\"X86_Timer Default Ctor\");    \n  }\n\n  inline void start( void ){\n\n    rdtsc(_click_start.n32[0],_click_start.n32[1]);\n\n  }\n\n\n  inline void stop( void ){\n\n    rdtsc(_click_stop.n32[0],_click_stop.n32[1]);\n\n  }\n  \n\n  inline double frequency( void ){\n    return _frequency;\n  }\n\n  double get_elapsed_time_in_second( void ){\n\n    return (_click_stop.n64-_click_start.n64)/double(FREQUENCY);\n\n\n  }    \n\n  unsigned long long  get_click( void ){\n    \n    return (_click_stop.n64-_click_start.n64);\n\n  }    \n\n  inline void find_frequency( void ){\n\n    time_t initial, final;\n    int dummy=2;\n\n    initial = time(0);\n    start();\n    do {\n      dummy+=2;\n    }\n    while(time(0)==initial);\n    // On est au debut d'un cycle d'une seconde !!!\n    initial = time(0);\n    start();\n    do {\n      dummy+=2;\n    }\n    while(time(0)==initial);\n    final=time(0);\n    stop();\n    //    INFOS(\"fine grained time : \"<<  get_elapsed_time_in_second());\n    //  INFOS(\"coarse grained time : \"<<  final-initial);\n    _frequency=_frequency*get_elapsed_time_in_second()/double(final-initial);\n    ///  INFOS(\"CPU frequency : \"<<  _frequency);        \n\n  }\n\n  void  add_get_click( void ){\n       \n    _nb_sample++;\n    _counted_clicks[get_click()]++;\n    fill_history_clicks();\n\n  }    \n\n  void dump_statistics(string filemane){\n    \n    ofstream outfile (filemane.c_str(),ios::out) ;\n\n    std::map<unsigned long long , unsigned long long>::iterator itr;\n    for(itr=_counted_clicks.begin() ; itr!=_counted_clicks.end()  ; itr++)\n      {      \n      outfile  << (*itr).first << \"  \" << (*itr).second << endl ;       \n      }      \n    \n    outfile.close();\n\n  }\n\n  void dump_history(string filemane){\n    \n    ofstream outfile (filemane.c_str(),ios::out) ;\n\n\n\n    for(int i=0 ; i<_history_mean_clicks.size() ; i++)\n      {      \n\toutfile  << i << \" \" \n\t\t << _history_mean_clicks[i] << \" \" \n\t\t << _history_shortest_clicks[i] << \" \" \n\t\t << _history_most_occured_clicks[i] << endl ;\n      }      \n    \n    outfile.close();\n\n  }\n     \n\n\n  double get_mean_clicks( void ){\n    \n    std::map<unsigned long long,unsigned long long>::iterator itr;\n    \n    unsigned long long mean_clicks=0;\n\n    for(itr=_counted_clicks.begin() ; itr!=_counted_clicks.end()  ; itr++)\n      {      \n\t\n\tmean_clicks+=(*itr).second*(*itr).first;\n      }      \n\n    return mean_clicks/double(_nb_sample);\n\n  }\n\n  double get_shortest_clicks( void ){\n    \n    return double((*_counted_clicks.begin()).first);\n\n  }\n\n  void fill_history_clicks( void ){\n\n    _history_mean_clicks.push_back(get_mean_clicks());\n    _history_shortest_clicks.push_back(get_shortest_clicks());\n    _history_most_occured_clicks.push_back(get_most_occured_clicks());\n\n  }\n\n\n  double get_most_occured_clicks( void ){\n\n    unsigned long long moc=0;\n    unsigned long long max_occurence=0;\n\n    std::map<unsigned long long,unsigned long long>::iterator itr;\n\n    for(itr=_counted_clicks.begin() ; itr!=_counted_clicks.end()  ; itr++)\n      {      \n\t\n\tif (max_occurence<=(*itr).second){\n\t  max_occurence=(*itr).second;\n\t  moc=(*itr).first;\n\t}\n      }      \n    \n    return double(moc);    \n\n  }\n  \n  void clear( void )\n  {\n    _counted_clicks.clear();\n\n    _history_mean_clicks.clear();\n    _history_shortest_clicks.clear();\n    _history_most_occured_clicks.clear();\n\n    _nb_sample=0;\n  }\n\n\n    \nprivate :\n  \n  union\n  {\n    unsigned long int n32[2] ;\n    unsigned long long n64 ;\n  } _click_start;\n\n  union\n  {\n    unsigned long int n32[2] ;\n    unsigned long long n64 ;\n  } _click_stop;\n\n  double _frequency ;\n\n  map<unsigned long long,unsigned long long> _counted_clicks;\n\n  vector<double> _history_mean_clicks;\n  vector<double> _history_shortest_clicks;\n  vector<double> _history_most_occured_clicks;\n\n  unsigned long long _nb_sample;\n\n  \n\n};\n\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/generic_bench/utils/size_lin_log.hh",
    "content": "//=====================================================\n// File   :  size_lin_log.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>        \n// Copyright (C) EDF R&D,  mar dc 3 18:59:37 CET 2002\n//=====================================================\n// \n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n// \n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n// \n#ifndef SIZE_LIN_LOG\n#define SIZE_LIN_LOG\n\n#include \"size_log.hh\"\n\ntemplate<class Vector>\nvoid size_lin_log(const int nb_point, const int /*size_min*/, const int size_max, Vector & X)\n{\n  int ten=10;\n  int nine=9;\n\n  X.resize(nb_point);\n\n  if (nb_point>ten){\n\n    for (int i=0;i<nine;i++){\n      \n      X[i]=i+1;\n\n    }\n\n    Vector log_size;\n    size_log(nb_point-nine,ten,size_max,log_size);\n\n    for (int i=0;i<nb_point-nine;i++){\n      \n      X[i+nine]=log_size[i];\n\n    }\n  }\n  else{\n\n    for (int i=0;i<nb_point;i++){\n      \n      X[i]=i+1;\n\n    }\n  }\n\n //  for (int i=0;i<nb_point;i++){\n    \n//        INFOS(\"computed sizes : X[\"<<i<<\"]=\"<<X[i]);\n    \n//   }\n\n}\n  \n#endif\n    \n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/generic_bench/utils/size_log.hh",
    "content": "//=====================================================\n// File   :  size_log.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>        \n// Copyright (C) EDF R&D,  lun sep 30 14:23:17 CEST 2002\n//=====================================================\n// \n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n// \n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n// \n#ifndef SIZE_LOG\n#define SIZE_LOG\n\n#include \"math.h\"\n// The Vector class must satisfy the following part of STL vector concept :\n//            resize() method\n//            [] operator for seting element\n// the vector element are int compatible.\ntemplate<class Vector>\nvoid size_log(const int nb_point, const int size_min, const int size_max, Vector & X)\n{\n  X.resize(nb_point);\n\n  float ls_min=log(float(size_min));\n  float ls_max=log(float(size_max));\n\n  float ls=0.0;\n\n  float delta_ls=(ls_max-ls_min)/(float(nb_point-1));\n\n  int size=0;\n\n  for (int i=0;i<nb_point;i++){\n\n    ls = ls_min + float(i)*delta_ls ;\n    \n    size=int(exp(ls)); \n\n    X[i]=size;\n  }\n\n}\n\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/generic_bench/utils/utilities.h",
    "content": "//=============================================================================\n// File      : utilities.h\n// Created   : mar jun 19 13:18:14 CEST 2001\n// Author    : Antoine YESSAYAN, Paul RASCLE, EDF\n// Project   : SALOME\n// Copyright : EDF 2001\n// $Header$\n//=============================================================================\n\n/* ---  Definition macros file to print information if _DEBUG_ is defined --- */\n\n# ifndef UTILITIES_H\n# define UTILITIES_H\n\n# include <stdlib.h>\n//# include <iostream> ok for gcc3.01\n# include <iostream>\n\n/* ---  INFOS is always defined (without _DEBUG_): to be used for warnings, with release version --- */\n\n# define HEREWEARE cout<<flush ; cerr << __FILE__ << \" [\" << __LINE__ << \"] : \" << flush ;\n# define INFOS(chain) {HEREWEARE ; cerr << chain << endl ;}\n# define PYSCRIPT(chain) {cout<<flush ; cerr << \"---PYSCRIPT--- \" << chain << endl ;}\n\n/* --- To print date and time of compilation of current source on stdout --- */\n\n# if defined ( __GNUC__ )\n# define COMPILER\t\t\"g++\" ;\n# elif defined ( __sun )\n# define COMPILER\t\t\"CC\" ;\n# elif defined ( __KCC )\n# define COMPILER\t\t\"KCC\" ;\n# elif defined ( __PGI )\n# define COMPILER\t\t\"pgCC\" ;\n# else\n# define COMPILER\t\t\"undefined\" ;\n# endif\n\n# ifdef INFOS_COMPILATION\n# error INFOS_COMPILATION already defined\n# endif\n# define INFOS_COMPILATION\t{\\\n\t\t\t\t\tcerr << flush;\\\n\t\t\t\t\tcout << __FILE__ ;\\\n\t\t\t\t\tcout << \" [\" << __LINE__ << \"] : \" ;\\\n\t\t\t\t\tcout << \"COMPILED with \" << COMPILER ;\\\n\t\t\t\t\tcout << \", \" << __DATE__ ; \\\n\t\t\t\t\tcout << \" at \" << __TIME__ << endl ;\\\n\t\t\t\t\tcout << \"\\n\\n\" ;\\\n\t\t\t\t\tcout << flush ;\\\n\t\t\t\t}\n\n# ifdef _DEBUG_\n\n/* --- the following MACROS are useful at debug time --- */\n\n# define HERE cout<<flush ; cerr << \"- Trace \" << __FILE__ << \" [\" << __LINE__ << \"] : \" << flush ;\n# define SCRUTE(var) HERE ; cerr << #var << \"=\" << var << endl ;\n# define MESSAGE(chain) {HERE ; cerr << chain << endl ;}\n# define INTERRUPTION(code) HERE ; cerr << \"INTERRUPTION return code= \" << code << endl ; exit(code) ;\n\n# ifndef ASSERT\n# define ASSERT(condition) if (!(condition)){ HERE ; cerr << \"CONDITION \" << #condition << \" NOT VERIFIED\"<< endl ; INTERRUPTION(1) ;}\n# endif /* ASSERT */\n\n#define REPERE cout<<flush ; cerr << \"   --------------\" << endl << flush ;\n#define BEGIN_OF(chain) {REPERE ; HERE ; cerr << \"Begin of: \" << chain << endl ; REPERE ; }\n#define END_OF(chain) {REPERE ; HERE ; cerr << \"Normal end of: \" << chain << endl ; REPERE ; }\n\n\n\n# else /* ifdef _DEBUG_*/\n\n# define HERE\n# define SCRUTE(var)\n# define MESSAGE(chain)\n# define INTERRUPTION(code)\n\n# ifndef ASSERT\n# define ASSERT(condition)\n# endif /* ASSERT */\n\n#define REPERE\n#define BEGIN_OF(chain)\n#define END_OF(chain)\n\n\n# endif /* ifdef _DEBUG_*/\n\n# endif /* ifndef UTILITIES_H */\n"
  },
  {
    "path": "include/eigen3/bench/btl/generic_bench/utils/xy_file.hh",
    "content": "//=====================================================\n// File   :  dump_file_x_y.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>        \n// Copyright (C) EDF R&D,  lun sep 30 14:23:20 CEST 2002\n//=====================================================\n// \n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n// \n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n// \n#ifndef XY_FILE_HH\n#define XY_FILE_HH\n#include <fstream>\n#include <iostream>\n#include <string>\n#include <vector>\nusing namespace std;\n\nbool read_xy_file(const std::string & filename, std::vector<int> & tab_sizes,\n                  std::vector<double> & tab_mflops, bool quiet = false)\n{\n\n  std::ifstream input_file (filename.c_str(),std::ios::in);\n\n  if (!input_file){\n    if (!quiet) {\n      INFOS(\"!!! Error opening \"<<filename);\n    }\n    return false;\n  }\n\n  int nb_point=0;\n  int size=0;\n  double mflops=0;\n\n  while (input_file >> size >> mflops ){\n    nb_point++;\n    tab_sizes.push_back(size);\n    tab_mflops.push_back(mflops);\n  }\n  SCRUTE(nb_point);\n\n  input_file.close();\n  return true;\n}\n\n// The Vector class must satisfy the following part of STL vector concept :\n//            resize() method\n//            [] operator for seting element\n// the vector element must have the << operator define\n\nusing namespace std;\n\ntemplate<class Vector_A, class Vector_B>\nvoid dump_xy_file(const Vector_A & X, const Vector_B & Y, const std::string & filename){\n  \n  ofstream outfile (filename.c_str(),ios::out) ;\n  int size=X.size();\n  \n  for (int i=0;i<size;i++)\n    outfile << X[i] << \" \" << Y[i] << endl;\n\n  outfile.close();\n} \n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/BLAS/CMakeLists.txt",
    "content": "\nfind_package(ATLAS)\nif (ATLAS_FOUND)\n  btl_add_bench(btl_atlas main.cpp)\n  if(BUILD_btl_atlas)\n    target_link_libraries(btl_atlas ${ATLAS_LIBRARIES})\n    set_target_properties(btl_atlas PROPERTIES COMPILE_FLAGS \"-DCBLASNAME=ATLAS -DHAS_LAPACK=1\")\n  endif(BUILD_btl_atlas)\nendif (ATLAS_FOUND)\n\nfind_package(MKL)\nif (MKL_FOUND)\n  btl_add_bench(btl_mkl main.cpp)\n  if(BUILD_btl_mkl)\n    target_link_libraries(btl_mkl ${MKL_LIBRARIES})\n    set_target_properties(btl_mkl PROPERTIES COMPILE_FLAGS \"-DCBLASNAME=INTEL_MKL -DHAS_LAPACK=1\")\n  endif(BUILD_btl_mkl)\nendif (MKL_FOUND)\n\n\nfind_package(OPENBLAS)\nif (OPENBLAS_FOUND)\n  btl_add_bench(btl_openblas main.cpp)\n  if(BUILD_btl_openblas)\n    target_link_libraries(btl_openblas ${OPENBLAS_LIBRARIES} )\n    set_target_properties(btl_openblas PROPERTIES COMPILE_FLAGS \"-DCBLASNAME=OPENBLAS\")\n  endif(BUILD_btl_openblas)\nendif (OPENBLAS_FOUND)\n\nfind_package(ACML)\nif (ACML_FOUND)\n  btl_add_bench(btl_acml main.cpp)\n  if(BUILD_btl_acml)\n    target_link_libraries(btl_acml ${ACML_LIBRARIES} )\n    set_target_properties(btl_acml PROPERTIES COMPILE_FLAGS \"-DCBLASNAME=ACML -DHAS_LAPACK=1\")\n  endif(BUILD_btl_acml)\nendif (ACML_FOUND)\n\nif(Eigen_SOURCE_DIR AND CMAKE_Fortran_COMPILER_WORKS)\n  # we are inside Eigen and blas/lapack interface is compilable\n  include_directories(${Eigen_SOURCE_DIR})\n  btl_add_bench(btl_eigenblas main.cpp)\n  if(BUILD_btl_eigenblas)\n    target_link_libraries(btl_eigenblas eigen_blas eigen_lapack )\n    set_target_properties(btl_eigenblas PROPERTIES COMPILE_FLAGS \"-DCBLASNAME=EigenBLAS\")\n  endif()\nendif()\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/BLAS/blas.h",
    "content": "#ifndef BLAS_H\n#define BLAS_H\n\n#define BLASFUNC(FUNC) FUNC##_\n\n#ifdef __WIN64__\ntypedef long long BLASLONG;\ntypedef unsigned long long BLASULONG;\n#else\ntypedef long BLASLONG;\ntypedef unsigned long BLASULONG;\n#endif\n\nint    BLASFUNC(xerbla)(const char *, int *info, int);\n\nfloat  BLASFUNC(sdot)  (int *, float  *, int *, float  *, int *);\nfloat  BLASFUNC(sdsdot)(int *, float  *,        float  *, int *, float  *, int *);\n\ndouble BLASFUNC(dsdot) (int *, float  *, int *, float  *, int *);\ndouble BLASFUNC(ddot)  (int *, double *, int *, double *, int *);\ndouble BLASFUNC(qdot)  (int *, double *, int *, double *, int *);\n\n#if defined(F_INTERFACE_GFORT) && !defined(__64BIT__)\nint   BLASFUNC(cdotu)  (int *, float  * , int *, float  *,  int *);\nint   BLASFUNC(cdotc)  (int *, float  *,  int *, float  *,  int *);\nvoid  BLASFUNC(zdotu)  (double *, int *, double  *, int *, double  *, int *);\nvoid  BLASFUNC(zdotc)  (double *, int *, double  *, int *, double  *, int *);\nvoid  BLASFUNC(xdotu)  (double *, int *, double  *, int *, double  *, int *);\nvoid  BLASFUNC(xdotc)  (double *, int *, double  *, int *, double  *, int *);\n#elif  defined(F_INTERFACE_F2C) || \\\n     defined(F_INTERFACE_PGI) || \\\n     defined(F_INTERFACE_GFORT) || \\\n    (defined(F_INTERFACE_PATHSCALE) && defined(__64BIT__))\nvoid  BLASFUNC(cdotu)  (float *,  int *, float  * , int *, float  *,  int *);\nvoid  BLASFUNC(cdotc)  (float *,  int *, float  *,  int *, float  *,  int *);\nvoid  BLASFUNC(zdotu)  (double *, int *, double  *, int *, double  *, int *);\nvoid  BLASFUNC(zdotc)  (double *, int *, double  *, int *, double  *, int *);\nvoid  BLASFUNC(xdotu)  (double *, int *, double  *, int *, double  *, int *);\nvoid  BLASFUNC(xdotc)  (double *, int *, double  *, int *, double  *, int *);\n#else\nstd::complex<float>   BLASFUNC(cdotu)  (int *, float  *, int *, float  *, int *);\nstd::complex<float>   BLASFUNC(cdotc)  (int *, float  *, int *, float  *, int *);\nstd::complex<double>  BLASFUNC(zdotu)  (int *, double  *, int *, double  *, int *);\nstd::complex<double>  BLASFUNC(zdotc)  (int *, double  *, int *, double  *, int *);\ndouble  BLASFUNC(xdotu)  (int *, double  *, int *, double  *, int *);\ndouble  BLASFUNC(xdotc)  (int *, double  *, int *, double  *, int *);\n#endif\n\nint  BLASFUNC(cdotuw)  (int *, float  *, int *, float  *, int *, float*);\nint  BLASFUNC(cdotcw)  (int *, float  *, int *, float  *, int *, float*);\nint  BLASFUNC(zdotuw)  (int *, double  *, int *, double  *, int *, double*);\nint  BLASFUNC(zdotcw)  (int *, double  *, int *, double  *, int *, double*);\n\nint    BLASFUNC(saxpy) (int *, float  *, float  *, int *, float  *, int *);\nint    BLASFUNC(daxpy) (int *, double *, double *, int *, double *, int *);\nint    BLASFUNC(qaxpy) (int *, double *, double *, int *, double *, int *);\nint    BLASFUNC(caxpy) (int *, float  *, float  *, int *, float  *, int *);\nint    BLASFUNC(zaxpy) (int *, double *, double *, int *, double *, int *);\nint    BLASFUNC(xaxpy) (int *, double *, double *, int *, double *, int *);\nint    BLASFUNC(caxpyc)(int *, float  *, float  *, int *, float  *, int *);\nint    BLASFUNC(zaxpyc)(int *, double *, double *, int *, double *, int *);\nint    BLASFUNC(xaxpyc)(int *, double *, double *, int *, double *, int *);\n\nint    BLASFUNC(scopy) (int *, float  *, int *, float  *, int *);\nint    BLASFUNC(dcopy) (int *, double *, int *, double *, int *);\nint    BLASFUNC(qcopy) (int *, double *, int *, double *, int *);\nint    BLASFUNC(ccopy) (int *, float  *, int *, float  *, int *);\nint    BLASFUNC(zcopy) (int *, double *, int *, double *, int *);\nint    BLASFUNC(xcopy) (int *, double *, int *, double *, int *);\n\nint    BLASFUNC(sswap) (int *, float  *, int *, float  *, int *);\nint    BLASFUNC(dswap) (int *, double *, int *, double *, int *);\nint    BLASFUNC(qswap) (int *, double *, int *, double *, int *);\nint    BLASFUNC(cswap) (int *, float  *, int *, float  *, int *);\nint    BLASFUNC(zswap) (int *, double *, int *, double *, int *);\nint    BLASFUNC(xswap) (int *, double *, int *, double *, int *);\n\nfloat  BLASFUNC(sasum) (int *, float  *, int *);\nfloat  BLASFUNC(scasum)(int *, float  *, int *);\ndouble BLASFUNC(dasum) (int *, double *, int *);\ndouble BLASFUNC(qasum) (int *, double *, int *);\ndouble BLASFUNC(dzasum)(int *, double *, int *);\ndouble BLASFUNC(qxasum)(int *, double *, int *);\n\nint    BLASFUNC(isamax)(int *, float  *, int *);\nint    BLASFUNC(idamax)(int *, double *, int *);\nint    BLASFUNC(iqamax)(int *, double *, int *);\nint    BLASFUNC(icamax)(int *, float  *, int *);\nint    BLASFUNC(izamax)(int *, double *, int *);\nint    BLASFUNC(ixamax)(int *, double *, int *);\n\nint    BLASFUNC(ismax) (int *, float  *, int *);\nint    BLASFUNC(idmax) (int *, double *, int *);\nint    BLASFUNC(iqmax) (int *, double *, int *);\nint    BLASFUNC(icmax) (int *, float  *, int *);\nint    BLASFUNC(izmax) (int *, double *, int *);\nint    BLASFUNC(ixmax) (int *, double *, int *);\n\nint    BLASFUNC(isamin)(int *, float  *, int *);\nint    BLASFUNC(idamin)(int *, double *, int *);\nint    BLASFUNC(iqamin)(int *, double *, int *);\nint    BLASFUNC(icamin)(int *, float  *, int *);\nint    BLASFUNC(izamin)(int *, double *, int *);\nint    BLASFUNC(ixamin)(int *, double *, int *);\n\nint    BLASFUNC(ismin)(int *, float  *, int *);\nint    BLASFUNC(idmin)(int *, double *, int *);\nint    BLASFUNC(iqmin)(int *, double *, int *);\nint    BLASFUNC(icmin)(int *, float  *, int *);\nint    BLASFUNC(izmin)(int *, double *, int *);\nint    BLASFUNC(ixmin)(int *, double *, int *);\n\nfloat  BLASFUNC(samax) (int *, float  *, int *);\ndouble BLASFUNC(damax) (int *, double *, int *);\ndouble BLASFUNC(qamax) (int *, double *, int *);\nfloat  BLASFUNC(scamax)(int *, float  *, int *);\ndouble BLASFUNC(dzamax)(int *, double *, int *);\ndouble BLASFUNC(qxamax)(int *, double *, int *);\n\nfloat  BLASFUNC(samin) (int *, float  *, int *);\ndouble BLASFUNC(damin) (int *, double *, int *);\ndouble BLASFUNC(qamin) (int *, double *, int *);\nfloat  BLASFUNC(scamin)(int *, float  *, int *);\ndouble BLASFUNC(dzamin)(int *, double *, int *);\ndouble BLASFUNC(qxamin)(int *, double *, int *);\n\nfloat  BLASFUNC(smax)  (int *, float  *, int *);\ndouble BLASFUNC(dmax)  (int *, double *, int *);\ndouble BLASFUNC(qmax)  (int *, double *, int *);\nfloat  BLASFUNC(scmax) (int *, float  *, int *);\ndouble BLASFUNC(dzmax) (int *, double *, int *);\ndouble BLASFUNC(qxmax) (int *, double *, int *);\n\nfloat  BLASFUNC(smin)  (int *, float  *, int *);\ndouble BLASFUNC(dmin)  (int *, double *, int *);\ndouble BLASFUNC(qmin)  (int *, double *, int *);\nfloat  BLASFUNC(scmin) (int *, float  *, int *);\ndouble BLASFUNC(dzmin) (int *, double *, int *);\ndouble BLASFUNC(qxmin) (int *, double *, int *);\n\nint    BLASFUNC(sscal) (int *,  float  *, float  *, int *);\nint    BLASFUNC(dscal) (int *,  double *, double *, int *);\nint    BLASFUNC(qscal) (int *,  double *, double *, int *);\nint    BLASFUNC(cscal) (int *,  float  *, float  *, int *);\nint    BLASFUNC(zscal) (int *,  double *, double *, int *);\nint    BLASFUNC(xscal) (int *,  double *, double *, int *);\nint    BLASFUNC(csscal)(int *,  float  *, float  *, int *);\nint    BLASFUNC(zdscal)(int *,  double *, double *, int *);\nint    BLASFUNC(xqscal)(int *,  double *, double *, int *);\n\nfloat  BLASFUNC(snrm2) (int *, float  *, int *);\nfloat  BLASFUNC(scnrm2)(int *, float  *, int *);\n\ndouble BLASFUNC(dnrm2) (int *, double *, int *);\ndouble BLASFUNC(qnrm2) (int *, double *, int *);\ndouble BLASFUNC(dznrm2)(int *, double *, int *);\ndouble BLASFUNC(qxnrm2)(int *, double *, int *);\n\nint    BLASFUNC(srot)  (int *, float  *, int *, float  *, int *, float  *, float  *);\nint    BLASFUNC(drot)  (int *, double *, int *, double *, int *, double *, double *);\nint    BLASFUNC(qrot)  (int *, double *, int *, double *, int *, double *, double *);\nint    BLASFUNC(csrot) (int *, float  *, int *, float  *, int *, float  *, float  *);\nint    BLASFUNC(zdrot) (int *, double *, int *, double *, int *, double *, double *);\nint    BLASFUNC(xqrot) (int *, double *, int *, double *, int *, double *, double *);\n\nint    BLASFUNC(srotg) (float  *, float  *, float  *, float  *);\nint    BLASFUNC(drotg) (double *, double *, double *, double *);\nint    BLASFUNC(qrotg) (double *, double *, double *, double *);\nint    BLASFUNC(crotg) (float  *, float  *, float  *, float  *);\nint    BLASFUNC(zrotg) (double *, double *, double *, double *);\nint    BLASFUNC(xrotg) (double *, double *, double *, double *);\n\nint    BLASFUNC(srotmg)(float  *, float  *, float  *, float  *, float  *);\nint    BLASFUNC(drotmg)(double *, double *, double *, double *, double *);\n\nint    BLASFUNC(srotm) (int *, float  *, int *, float  *, int *, float  *);\nint    BLASFUNC(drotm) (int *, double *, int *, double *, int *, double *);\nint    BLASFUNC(qrotm) (int *, double *, int *, double *, int *, double *);\n\n/* Level 2 routines */\n\nint BLASFUNC(sger)(int *,    int *, float *,  float *, int *,\n\t\t   float *,  int *, float *,  int *);\nint BLASFUNC(dger)(int *,    int *, double *, double *, int *,\n\t\t   double *, int *, double *, int *);\nint BLASFUNC(qger)(int *,    int *, double *, double *, int *,\n\t\t   double *, int *, double *, int *);\nint BLASFUNC(cgeru)(int *,    int *, float *,  float *, int *,\n\t\t    float *,  int *, float *,  int *);\nint BLASFUNC(cgerc)(int *,    int *, float *,  float *, int *,\n\t\t    float *,  int *, float *,  int *);\nint BLASFUNC(zgeru)(int *,    int *, double *, double *, int *,\n\t\t    double *, int *, double *, int *);\nint BLASFUNC(zgerc)(int *,    int *, double *, double *, int *,\n\t\t    double *, int *, double *, int *);\nint BLASFUNC(xgeru)(int *,    int *, double *, double *, int *,\n\t\t    double *, int *, double *, int *);\nint BLASFUNC(xgerc)(int *,    int *, double *, double *, int *,\n\t\t    double *, int *, double *, int *);\n\nint BLASFUNC(sgemv)(char *, int *, int *, float  *, float  *, int *,\n\t\t    float  *, int *, float  *, float  *, int *);\nint BLASFUNC(dgemv)(char *, int *, int *, double *, double *, int *,\n\t\t    double *, int *, double *, double *, int *);\nint BLASFUNC(qgemv)(char *, int *, int *, double *, double *, int *,\n\t\t    double *, int *, double *, double *, int *);\nint BLASFUNC(cgemv)(char *, int *, int *, float  *, float  *, int *,\n\t\t    float  *, int *, float  *, float  *, int *);\nint BLASFUNC(zgemv)(char *, int *, int *, double *, double *, int *,\n\t\t    double *, int *, double *, double *, int *);\nint BLASFUNC(xgemv)(char *, int *, int *, double *, double *, int *,\n\t\t    double *, int *, double *, double *, int *);\n\nint BLASFUNC(strsv) (char *, char *, char *, int *, float  *, int *,\n\t\t     float  *, int *);\nint BLASFUNC(dtrsv) (char *, char *, char *, int *, double *, int *,\n\t\t     double *, int *);\nint BLASFUNC(qtrsv) (char *, char *, char *, int *, double *, int *,\n\t\t     double *, int *);\nint BLASFUNC(ctrsv) (char *, char *, char *, int *, float  *, int *,\n\t\t     float  *, int *);\nint BLASFUNC(ztrsv) (char *, char *, char *, int *, double *, int *,\n\t\t     double *, int *);\nint BLASFUNC(xtrsv) (char *, char *, char *, int *, double *, int *,\n\t\t     double *, int *);\n\nint BLASFUNC(stpsv) (char *, char *, char *, int *, float  *, float  *, int *);\nint BLASFUNC(dtpsv) (char *, char *, char *, int *, double *, double *, int *);\nint BLASFUNC(qtpsv) (char *, char *, char *, int *, double *, double *, int *);\nint BLASFUNC(ctpsv) (char *, char *, char *, int *, float  *, float  *, int *);\nint BLASFUNC(ztpsv) (char *, char *, char *, int *, double *, double *, int *);\nint BLASFUNC(xtpsv) (char *, char *, char *, int *, double *, double *, int *);\n\nint BLASFUNC(strmv) (char *, char *, char *, int *, float  *, int *,\n\t\t     float  *, int *);\nint BLASFUNC(dtrmv) (char *, char *, char *, int *, double *, int *,\n\t\t     double *, int *);\nint BLASFUNC(qtrmv) (char *, char *, char *, int *, double *, int *,\n\t\t     double *, int *);\nint BLASFUNC(ctrmv) (char *, char *, char *, int *, float  *, int *,\n\t\t     float  *, int *);\nint BLASFUNC(ztrmv) (char *, char *, char *, int *, double *, int *,\n\t\t     double *, int *);\nint BLASFUNC(xtrmv) (char *, char *, char *, int *, double *, int *,\n\t\t     double *, int *);\n\nint BLASFUNC(stpmv) (char *, char *, char *, int *, float  *, float  *, int *);\nint BLASFUNC(dtpmv) (char *, char *, char *, int *, double *, double *, int *);\nint BLASFUNC(qtpmv) (char *, char *, char *, int *, double *, double *, int *);\nint BLASFUNC(ctpmv) (char *, char *, char *, int *, float  *, float  *, int *);\nint BLASFUNC(ztpmv) (char *, char *, char *, int *, double *, double *, int *);\nint BLASFUNC(xtpmv) (char *, char *, char *, int *, double *, double *, int *);\n\nint BLASFUNC(stbmv) (char *, char *, char *, int *, int *, float  *, int *, float  *, int *);\nint BLASFUNC(dtbmv) (char *, char *, char *, int *, int *, double *, int *, double *, int *);\nint BLASFUNC(qtbmv) (char *, char *, char *, int *, int *, double *, int *, double *, int *);\nint BLASFUNC(ctbmv) (char *, char *, char *, int *, int *, float  *, int *, float  *, int *);\nint BLASFUNC(ztbmv) (char *, char *, char *, int *, int *, double *, int *, double *, int *);\nint BLASFUNC(xtbmv) (char *, char *, char *, int *, int *, double *, int *, double *, int *);\n\nint BLASFUNC(stbsv) (char *, char *, char *, int *, int *, float  *, int *, float  *, int *);\nint BLASFUNC(dtbsv) (char *, char *, char *, int *, int *, double *, int *, double *, int *);\nint BLASFUNC(qtbsv) (char *, char *, char *, int *, int *, double *, int *, double *, int *);\nint BLASFUNC(ctbsv) (char *, char *, char *, int *, int *, float  *, int *, float  *, int *);\nint BLASFUNC(ztbsv) (char *, char *, char *, int *, int *, double *, int *, double *, int *);\nint BLASFUNC(xtbsv) (char *, char *, char *, int *, int *, double *, int *, double *, int *);\n\nint BLASFUNC(ssymv) (char *, int *, float  *, float *, int *,\n\t\t     float  *, int *, float *, float *, int *);\nint BLASFUNC(dsymv) (char *, int *, double  *, double *, int *,\n\t\t     double  *, int *, double *, double *, int *);\nint BLASFUNC(qsymv) (char *, int *, double  *, double *, int *,\n\t\t     double  *, int *, double *, double *, int *);\nint BLASFUNC(csymv) (char *, int *, float  *, float *, int *,\n\t\t     float  *, int *, float *, float *, int *);\nint BLASFUNC(zsymv) (char *, int *, double  *, double *, int *,\n\t\t     double  *, int *, double *, double *, int *);\nint BLASFUNC(xsymv) (char *, int *, double  *, double *, int *,\n\t\t     double  *, int *, double *, double *, int *);\n\nint BLASFUNC(sspmv) (char *, int *, float  *, float *,\n\t\t     float  *, int *, float *, float *, int *);\nint BLASFUNC(dspmv) (char *, int *, double  *, double *,\n\t\t     double  *, int *, double *, double *, int *);\nint BLASFUNC(qspmv) (char *, int *, double  *, double *,\n\t\t     double  *, int *, double *, double *, int *);\nint BLASFUNC(cspmv) (char *, int *, float  *, float *,\n\t\t     float  *, int *, float *, float *, int *);\nint BLASFUNC(zspmv) (char *, int *, double  *, double *,\n\t\t     double  *, int *, double *, double *, int *);\nint BLASFUNC(xspmv) (char *, int *, double  *, double *,\n\t\t     double  *, int *, double *, double *, int *);\n\nint BLASFUNC(ssyr) (char *, int *, float   *, float  *, int *,\n\t\t    float  *, int *);\nint BLASFUNC(dsyr) (char *, int *, double  *, double *, int *,\n\t\t    double *, int *);\nint BLASFUNC(qsyr) (char *, int *, double  *, double *, int *,\n\t\t    double *, int *);\nint BLASFUNC(csyr) (char *, int *, float   *, float  *, int *,\n\t\t    float  *, int *);\nint BLASFUNC(zsyr) (char *, int *, double  *, double *, int *,\n\t\t    double *, int *);\nint BLASFUNC(xsyr) (char *, int *, double  *, double *, int *,\n\t\t    double *, int *);\n\nint BLASFUNC(ssyr2) (char *, int *, float   *,\n\t\t     float  *, int *, float  *, int *, float  *, int *);\nint BLASFUNC(dsyr2) (char *, int *, double  *,\n\t\t     double *, int *, double *, int *, double *, int *);\nint BLASFUNC(qsyr2) (char *, int *, double  *,\n\t\t     double *, int *, double *, int *, double *, int *);\nint BLASFUNC(csyr2) (char *, int *, float   *,\n\t\t     float  *, int *, float  *, int *, float  *, int *);\nint BLASFUNC(zsyr2) (char *, int *, double  *,\n\t\t     double *, int *, double *, int *, double *, int *);\nint BLASFUNC(xsyr2) (char *, int *, double  *,\n\t\t     double *, int *, double *, int *, double *, int *);\n\nint BLASFUNC(sspr) (char *, int *, float   *, float  *, int *,\n\t\t    float  *);\nint BLASFUNC(dspr) (char *, int *, double  *, double *, int *,\n\t\t    double *);\nint BLASFUNC(qspr) (char *, int *, double  *, double *, int *,\n\t\t    double *);\nint BLASFUNC(cspr) (char *, int *, float   *, float  *, int *,\n\t\t    float  *);\nint BLASFUNC(zspr) (char *, int *, double  *, double *, int *,\n\t\t    double *);\nint BLASFUNC(xspr) (char *, int *, double  *, double *, int *,\n\t\t    double *);\n\nint BLASFUNC(sspr2) (char *, int *, float   *,\n\t\t     float  *, int *, float  *, int *, float  *);\nint BLASFUNC(dspr2) (char *, int *, double  *,\n\t\t     double *, int *, double *, int *, double *);\nint BLASFUNC(qspr2) (char *, int *, double  *,\n\t\t     double *, int *, double *, int *, double *);\nint BLASFUNC(cspr2) (char *, int *, float   *,\n\t\t     float  *, int *, float  *, int *, float  *);\nint BLASFUNC(zspr2) (char *, int *, double  *,\n\t\t     double *, int *, double *, int *, double *);\nint BLASFUNC(xspr2) (char *, int *, double  *,\n\t\t     double *, int *, double *, int *, double *);\n\nint BLASFUNC(cher) (char *, int *, float   *, float  *, int *,\n\t\t    float  *, int *);\nint BLASFUNC(zher) (char *, int *, double  *, double *, int *,\n\t\t    double *, int *);\nint BLASFUNC(xher) (char *, int *, double  *, double *, int *,\n\t\t    double *, int *);\n\nint BLASFUNC(chpr) (char *, int *, float   *, float  *, int *, float  *);\nint BLASFUNC(zhpr) (char *, int *, double  *, double *, int *, double *);\nint BLASFUNC(xhpr) (char *, int *, double  *, double *, int *, double *);\n\nint BLASFUNC(cher2) (char *, int *, float   *,\n\t\t     float  *, int *, float  *, int *, float  *, int *);\nint BLASFUNC(zher2) (char *, int *, double  *,\n\t\t     double *, int *, double *, int *, double *, int *);\nint BLASFUNC(xher2) (char *, int *, double  *,\n\t\t     double *, int *, double *, int *, double *, int *);\n\nint BLASFUNC(chpr2) (char *, int *, float   *,\n\t\t     float  *, int *, float  *, int *, float  *);\nint BLASFUNC(zhpr2) (char *, int *, double  *,\n\t\t     double *, int *, double *, int *, double *);\nint BLASFUNC(xhpr2) (char *, int *, double  *,\n\t\t     double *, int *, double *, int *, double *);\n\nint BLASFUNC(chemv) (char *, int *, float  *, float *, int *,\n\t\t     float  *, int *, float *, float *, int *);\nint BLASFUNC(zhemv) (char *, int *, double  *, double *, int *,\n\t\t     double  *, int *, double *, double *, int *);\nint BLASFUNC(xhemv) (char *, int *, double  *, double *, int *,\n\t\t     double  *, int *, double *, double *, int *);\n\nint BLASFUNC(chpmv) (char *, int *, float  *, float *,\n\t\t     float  *, int *, float *, float *, int *);\nint BLASFUNC(zhpmv) (char *, int *, double  *, double *,\n\t\t     double  *, int *, double *, double *, int *);\nint BLASFUNC(xhpmv) (char *, int *, double  *, double *,\n\t\t     double  *, int *, double *, double *, int *);\n\nint BLASFUNC(snorm)(char *, int *, int *, float  *, int *);\nint BLASFUNC(dnorm)(char *, int *, int *, double *, int *);\nint BLASFUNC(cnorm)(char *, int *, int *, float  *, int *);\nint BLASFUNC(znorm)(char *, int *, int *, double *, int *);\n\nint BLASFUNC(sgbmv)(char *, int *, int *, int *, int *, float  *, float  *, int *,\n\t\t    float  *, int *, float  *, float  *, int *);\nint BLASFUNC(dgbmv)(char *, int *, int *, int *, int *, double *, double *, int *,\n\t\t    double *, int *, double *, double *, int *);\nint BLASFUNC(qgbmv)(char *, int *, int *, int *, int *, double *, double *, int *,\n\t\t    double *, int *, double *, double *, int *);\nint BLASFUNC(cgbmv)(char *, int *, int *, int *, int *, float  *, float  *, int *,\n\t\t    float  *, int *, float  *, float  *, int *);\nint BLASFUNC(zgbmv)(char *, int *, int *, int *, int *, double *, double *, int *,\n\t\t    double *, int *, double *, double *, int *);\nint BLASFUNC(xgbmv)(char *, int *, int *, int *, int *, double *, double *, int *,\n\t\t    double *, int *, double *, double *, int *);\n\nint BLASFUNC(ssbmv)(char *, int *, int *, float  *, float  *, int *,\n\t\t    float  *, int *, float  *, float  *, int *);\nint BLASFUNC(dsbmv)(char *, int *, int *, double *, double *, int *,\n\t\t    double *, int *, double *, double *, int *);\nint BLASFUNC(qsbmv)(char *, int *, int *, double *, double *, int *,\n\t\t    double *, int *, double *, double *, int *);\nint BLASFUNC(csbmv)(char *, int *, int *, float  *, float  *, int *,\n\t\t    float  *, int *, float  *, float  *, int *);\nint BLASFUNC(zsbmv)(char *, int *, int *, double *, double *, int *,\n\t\t    double *, int *, double *, double *, int *);\nint BLASFUNC(xsbmv)(char *, int *, int *, double *, double *, int *,\n\t\t    double *, int *, double *, double *, int *);\n\nint BLASFUNC(chbmv)(char *, int *, int *, float  *, float  *, int *,\n\t\t    float  *, int *, float  *, float  *, int *);\nint BLASFUNC(zhbmv)(char *, int *, int *, double *, double *, int *,\n\t\t    double *, int *, double *, double *, int *);\nint BLASFUNC(xhbmv)(char *, int *, int *, double *, double *, int *,\n\t\t    double *, int *, double *, double *, int *);\n\n/* Level 3 routines */\n\nint BLASFUNC(sgemm)(char *, char *, int *, int *, int *, float *,\n\t   float  *, int *, float  *, int *, float  *, float  *, int *);\nint BLASFUNC(dgemm)(char *, char *, int *, int *, int *, double *,\n\t   double *, int *, double *, int *, double *, double *, int *);\nint BLASFUNC(qgemm)(char *, char *, int *, int *, int *, double *,\n\t   double *, int *, double *, int *, double *, double *, int *);\nint BLASFUNC(cgemm)(char *, char *, int *, int *, int *, float *,\n\t   float  *, int *, float  *, int *, float  *, float  *, int *);\nint BLASFUNC(zgemm)(char *, char *, int *, int *, int *, double *,\n\t   double *, int *, double *, int *, double *, double *, int *);\nint BLASFUNC(xgemm)(char *, char *, int *, int *, int *, double *,\n\t   double *, int *, double *, int *, double *, double *, int *);\n\nint BLASFUNC(cgemm3m)(char *, char *, int *, int *, int *, float *,\n\t   float  *, int *, float  *, int *, float  *, float  *, int *);\nint BLASFUNC(zgemm3m)(char *, char *, int *, int *, int *, double *,\n\t   double *, int *, double *, int *, double *, double *, int *);\nint BLASFUNC(xgemm3m)(char *, char *, int *, int *, int *, double *,\n\t   double *, int *, double *, int *, double *, double *, int *);\n\nint BLASFUNC(sge2mm)(char *, char *, char *, int *, int *,\n\t\t     float *, float  *, int *, float  *, int *,\n\t\t     float *, float  *, int *);\nint BLASFUNC(dge2mm)(char *, char *, char *, int *, int *,\n\t\t     double *, double  *, int *, double  *, int *,\n\t\t     double *, double  *, int *);\nint BLASFUNC(cge2mm)(char *, char *, char *, int *, int *,\n\t\t     float *, float  *, int *, float  *, int *,\n\t\t     float *, float  *, int *);\nint BLASFUNC(zge2mm)(char *, char *, char *, int *, int *,\n\t\t     double *, double  *, int *, double  *, int *,\n\t\t     double *, double  *, int *);\n\nint BLASFUNC(strsm)(char *, char *, char *, char *, int *, int *,\n\t   float *,  float *, int *, float *, int *);\nint BLASFUNC(dtrsm)(char *, char *, char *, char *, int *, int *,\n\t   double *,  double *, int *, double *, int *);\nint BLASFUNC(qtrsm)(char *, char *, char *, char *, int *, int *,\n\t   double *,  double *, int *, double *, int *);\nint BLASFUNC(ctrsm)(char *, char *, char *, char *, int *, int *,\n\t   float *,  float *, int *, float *, int *);\nint BLASFUNC(ztrsm)(char *, char *, char *, char *, int *, int *,\n\t   double *,  double *, int *, double *, int *);\nint BLASFUNC(xtrsm)(char *, char *, char *, char *, int *, int *,\n\t   double *,  double *, int *, double *, int *);\n\nint BLASFUNC(strmm)(char *, char *, char *, char *, int *, int *,\n\t   float *,  float *, int *, float *, int *);\nint BLASFUNC(dtrmm)(char *, char *, char *, char *, int *, int *,\n\t   double *,  double *, int *, double *, int *);\nint BLASFUNC(qtrmm)(char *, char *, char *, char *, int *, int *,\n\t   double *,  double *, int *, double *, int *);\nint BLASFUNC(ctrmm)(char *, char *, char *, char *, int *, int *,\n\t   float *,  float *, int *, float *, int *);\nint BLASFUNC(ztrmm)(char *, char *, char *, char *, int *, int *,\n\t   double *,  double *, int *, double *, int *);\nint BLASFUNC(xtrmm)(char *, char *, char *, char *, int *, int *,\n\t   double *,  double *, int *, double *, int *);\n\nint BLASFUNC(ssymm)(char *, char *, int *, int *, float  *, float  *, int *,\n\t   float  *, int *, float  *, float  *, int *);\nint BLASFUNC(dsymm)(char *, char *, int *, int *, double *, double *, int *,\n\t   double *, int *, double *, double *, int *);\nint BLASFUNC(qsymm)(char *, char *, int *, int *, double *, double *, int *,\n\t   double *, int *, double *, double *, int *);\nint BLASFUNC(csymm)(char *, char *, int *, int *, float  *, float  *, int *,\n\t   float  *, int *, float  *, float  *, int *);\nint BLASFUNC(zsymm)(char *, char *, int *, int *, double *, double *, int *,\n\t   double *, int *, double *, double *, int *);\nint BLASFUNC(xsymm)(char *, char *, int *, int *, double *, double *, int *,\n\t   double *, int *, double *, double *, int *);\n\nint BLASFUNC(csymm3m)(char *, char *, int *, int *, float  *, float  *, int *,\n\t   float  *, int *, float  *, float  *, int *);\nint BLASFUNC(zsymm3m)(char *, char *, int *, int *, double *, double *, int *,\n\t   double *, int *, double *, double *, int *);\nint BLASFUNC(xsymm3m)(char *, char *, int *, int *, double *, double *, int *,\n\t   double *, int *, double *, double *, int *);\n\nint BLASFUNC(ssyrk)(char *, char *, int *, int *, float  *, float  *, int *,\n\t   float  *, float  *, int *);\nint BLASFUNC(dsyrk)(char *, char *, int *, int *, double *, double *, int *,\n\t   double *, double *, int *);\nint BLASFUNC(qsyrk)(char *, char *, int *, int *, double *, double *, int *,\n\t   double *, double *, int *);\nint BLASFUNC(csyrk)(char *, char *, int *, int *, float  *, float  *, int *,\n\t   float  *, float  *, int *);\nint BLASFUNC(zsyrk)(char *, char *, int *, int *, double *, double *, int *,\n\t   double *, double *, int *);\nint BLASFUNC(xsyrk)(char *, char *, int *, int *, double *, double *, int *,\n\t   double *, double *, int *);\n\nint BLASFUNC(ssyr2k)(char *, char *, int *, int *, float  *, float  *, int *,\n\t   float *, int *, float  *, float  *, int *);\nint BLASFUNC(dsyr2k)(char *, char *, int *, int *, double *, double *, int *,\n\t   double*, int *, double *, double *, int *);\nint BLASFUNC(qsyr2k)(char *, char *, int *, int *, double *, double *, int *,\n\t   double*, int *, double *, double *, int *);\nint BLASFUNC(csyr2k)(char *, char *, int *, int *, float  *, float  *, int *,\n\t   float *, int *, float  *, float  *, int *);\nint BLASFUNC(zsyr2k)(char *, char *, int *, int *, double *, double *, int *,\n\t   double*, int *, double *, double *, int *);\nint BLASFUNC(xsyr2k)(char *, char *, int *, int *, double *, double *, int *,\n\t   double*, int *, double *, double *, int *);\n\nint BLASFUNC(chemm)(char *, char *, int *, int *, float  *, float  *, int *,\n\t   float  *, int *, float  *, float  *, int *);\nint BLASFUNC(zhemm)(char *, char *, int *, int *, double *, double *, int *,\n\t   double *, int *, double *, double *, int *);\nint BLASFUNC(xhemm)(char *, char *, int *, int *, double *, double *, int *,\n\t   double *, int *, double *, double *, int *);\n\nint BLASFUNC(chemm3m)(char *, char *, int *, int *, float  *, float  *, int *,\n\t   float  *, int *, float  *, float  *, int *);\nint BLASFUNC(zhemm3m)(char *, char *, int *, int *, double *, double *, int *,\n\t   double *, int *, double *, double *, int *);\nint BLASFUNC(xhemm3m)(char *, char *, int *, int *, double *, double *, int *,\n\t   double *, int *, double *, double *, int *);\n\nint BLASFUNC(cherk)(char *, char *, int *, int *, float  *, float  *, int *,\n\t   float  *, float  *, int *);\nint BLASFUNC(zherk)(char *, char *, int *, int *, double *, double *, int *,\n\t   double *, double *, int *);\nint BLASFUNC(xherk)(char *, char *, int *, int *, double *, double *, int *,\n\t   double *, double *, int *);\n\nint BLASFUNC(cher2k)(char *, char *, int *, int *, float  *, float  *, int *,\n\t   float *, int *, float  *, float  *, int *);\nint BLASFUNC(zher2k)(char *, char *, int *, int *, double *, double *, int *,\n\t   double*, int *, double *, double *, int *);\nint BLASFUNC(xher2k)(char *, char *, int *, int *, double *, double *, int *,\n\t   double*, int *, double *, double *, int *);\nint BLASFUNC(cher2m)(char *, char *, char *, int *, int *, float  *, float  *, int *,\n\t   float *, int *, float  *, float  *, int *);\nint BLASFUNC(zher2m)(char *, char *, char *, int *, int *, double *, double *, int *,\n\t   double*, int *, double *, double *, int *);\nint BLASFUNC(xher2m)(char *, char *, char *, int *, int *, double *, double *, int *,\n\t   double*, int *, double *, double *, int *);\n\nint BLASFUNC(sgemt)(char *, int *, int *, float  *, float  *, int *,\n\t\t    float  *, int *);\nint BLASFUNC(dgemt)(char *, int *, int *, double *, double *, int *,\n\t\t    double *, int *);\nint BLASFUNC(cgemt)(char *, int *, int *, float  *, float  *, int *,\n\t\t    float  *, int *);\nint BLASFUNC(zgemt)(char *, int *, int *, double *, double *, int *,\n\t\t    double *, int *);\n\nint BLASFUNC(sgema)(char *, char *, int *, int *, float  *,\n\t\t    float  *, int *, float *, float  *, int *, float *, int *);\nint BLASFUNC(dgema)(char *, char *, int *, int *, double *,\n\t\t    double *, int *, double*, double *, int *, double*, int *);\nint BLASFUNC(cgema)(char *, char *, int *, int *, float  *,\n\t\t    float  *, int *, float *, float  *, int *, float *, int *);\nint BLASFUNC(zgema)(char *, char *, int *, int *, double *,\n\t\t    double *, int *, double*, double *, int *, double*, int *);\n\nint BLASFUNC(sgems)(char *, char *, int *, int *, float  *,\n\t\t    float  *, int *, float *, float  *, int *, float *, int *);\nint BLASFUNC(dgems)(char *, char *, int *, int *, double *,\n\t\t    double *, int *, double*, double *, int *, double*, int *);\nint BLASFUNC(cgems)(char *, char *, int *, int *, float  *,\n\t\t    float  *, int *, float *, float  *, int *, float *, int *);\nint BLASFUNC(zgems)(char *, char *, int *, int *, double *,\n\t\t    double *, int *, double*, double *, int *, double*, int *);\n\nint BLASFUNC(sgetf2)(int *, int *, float  *, int *, int *, int *);\nint BLASFUNC(dgetf2)(int *, int *, double *, int *, int *, int *);\nint BLASFUNC(qgetf2)(int *, int *, double *, int *, int *, int *);\nint BLASFUNC(cgetf2)(int *, int *, float  *, int *, int *, int *);\nint BLASFUNC(zgetf2)(int *, int *, double *, int *, int *, int *);\nint BLASFUNC(xgetf2)(int *, int *, double *, int *, int *, int *);\n\nint BLASFUNC(sgetrf)(int *, int *, float  *, int *, int *, int *);\nint BLASFUNC(dgetrf)(int *, int *, double *, int *, int *, int *);\nint BLASFUNC(qgetrf)(int *, int *, double *, int *, int *, int *);\nint BLASFUNC(cgetrf)(int *, int *, float  *, int *, int *, int *);\nint BLASFUNC(zgetrf)(int *, int *, double *, int *, int *, int *);\nint BLASFUNC(xgetrf)(int *, int *, double *, int *, int *, int *);\n\nint BLASFUNC(slaswp)(int *, float  *, int *, int *, int *, int *, int *);\nint BLASFUNC(dlaswp)(int *, double *, int *, int *, int *, int *, int *);\nint BLASFUNC(qlaswp)(int *, double *, int *, int *, int *, int *, int *);\nint BLASFUNC(claswp)(int *, float  *, int *, int *, int *, int *, int *);\nint BLASFUNC(zlaswp)(int *, double *, int *, int *, int *, int *, int *);\nint BLASFUNC(xlaswp)(int *, double *, int *, int *, int *, int *, int *);\n\nint BLASFUNC(sgetrs)(char *, int *, int *, float  *, int *, int *, float  *, int *, int *);\nint BLASFUNC(dgetrs)(char *, int *, int *, double *, int *, int *, double *, int *, int *);\nint BLASFUNC(qgetrs)(char *, int *, int *, double *, int *, int *, double *, int *, int *);\nint BLASFUNC(cgetrs)(char *, int *, int *, float  *, int *, int *, float  *, int *, int *);\nint BLASFUNC(zgetrs)(char *, int *, int *, double *, int *, int *, double *, int *, int *);\nint BLASFUNC(xgetrs)(char *, int *, int *, double *, int *, int *, double *, int *, int *);\n\nint BLASFUNC(sgesv)(int *, int *, float  *, int *, int *, float *, int *, int *);\nint BLASFUNC(dgesv)(int *, int *, double *, int *, int *, double*, int *, int *);\nint BLASFUNC(qgesv)(int *, int *, double *, int *, int *, double*, int *, int *);\nint BLASFUNC(cgesv)(int *, int *, float  *, int *, int *, float *, int *, int *);\nint BLASFUNC(zgesv)(int *, int *, double *, int *, int *, double*, int *, int *);\nint BLASFUNC(xgesv)(int *, int *, double *, int *, int *, double*, int *, int *);\n\nint BLASFUNC(spotf2)(char *, int *, float  *, int *, int *);\nint BLASFUNC(dpotf2)(char *, int *, double *, int *, int *);\nint BLASFUNC(qpotf2)(char *, int *, double *, int *, int *);\nint BLASFUNC(cpotf2)(char *, int *, float  *, int *, int *);\nint BLASFUNC(zpotf2)(char *, int *, double *, int *, int *);\nint BLASFUNC(xpotf2)(char *, int *, double *, int *, int *);\n\nint BLASFUNC(spotrf)(char *, int *, float  *, int *, int *);\nint BLASFUNC(dpotrf)(char *, int *, double *, int *, int *);\nint BLASFUNC(qpotrf)(char *, int *, double *, int *, int *);\nint BLASFUNC(cpotrf)(char *, int *, float  *, int *, int *);\nint BLASFUNC(zpotrf)(char *, int *, double *, int *, int *);\nint BLASFUNC(xpotrf)(char *, int *, double *, int *, int *);\n\nint BLASFUNC(slauu2)(char *, int *, float  *, int *, int *);\nint BLASFUNC(dlauu2)(char *, int *, double *, int *, int *);\nint BLASFUNC(qlauu2)(char *, int *, double *, int *, int *);\nint BLASFUNC(clauu2)(char *, int *, float  *, int *, int *);\nint BLASFUNC(zlauu2)(char *, int *, double *, int *, int *);\nint BLASFUNC(xlauu2)(char *, int *, double *, int *, int *);\n\nint BLASFUNC(slauum)(char *, int *, float  *, int *, int *);\nint BLASFUNC(dlauum)(char *, int *, double *, int *, int *);\nint BLASFUNC(qlauum)(char *, int *, double *, int *, int *);\nint BLASFUNC(clauum)(char *, int *, float  *, int *, int *);\nint BLASFUNC(zlauum)(char *, int *, double *, int *, int *);\nint BLASFUNC(xlauum)(char *, int *, double *, int *, int *);\n\nint BLASFUNC(strti2)(char *, char *, int *, float  *, int *, int *);\nint BLASFUNC(dtrti2)(char *, char *, int *, double *, int *, int *);\nint BLASFUNC(qtrti2)(char *, char *, int *, double *, int *, int *);\nint BLASFUNC(ctrti2)(char *, char *, int *, float  *, int *, int *);\nint BLASFUNC(ztrti2)(char *, char *, int *, double *, int *, int *);\nint BLASFUNC(xtrti2)(char *, char *, int *, double *, int *, int *);\n\nint BLASFUNC(strtri)(char *, char *, int *, float  *, int *, int *);\nint BLASFUNC(dtrtri)(char *, char *, int *, double *, int *, int *);\nint BLASFUNC(qtrtri)(char *, char *, int *, double *, int *, int *);\nint BLASFUNC(ctrtri)(char *, char *, int *, float  *, int *, int *);\nint BLASFUNC(ztrtri)(char *, char *, int *, double *, int *, int *);\nint BLASFUNC(xtrtri)(char *, char *, int *, double *, int *, int *);\n\nint BLASFUNC(spotri)(char *, int *, float  *, int *, int *);\nint BLASFUNC(dpotri)(char *, int *, double *, int *, int *);\nint BLASFUNC(qpotri)(char *, int *, double *, int *, int *);\nint BLASFUNC(cpotri)(char *, int *, float  *, int *, int *);\nint BLASFUNC(zpotri)(char *, int *, double *, int *, int *);\nint BLASFUNC(xpotri)(char *, int *, double *, int *, int *);\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/BLAS/blas_interface.hh",
    "content": "//=====================================================\n// File   :  blas_interface.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>\n// Copyright (C) EDF R&D,  lun sep 30 14:23:28 CEST 2002\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef blas_PRODUIT_MATRICE_VECTEUR_HH\n#define blas_PRODUIT_MATRICE_VECTEUR_HH\n\n#include <c_interface_base.h>\n#include <complex>\nextern \"C\"\n{\n#include \"blas.h\"\n\n  // Cholesky Factorization\n//   void spotrf_(const char* uplo, const int* n, float *a, const int* ld, int* info);\n//   void dpotrf_(const char* uplo, const int* n, double *a, const int* ld, int* info);\n  void ssytrd_(char *uplo, const int *n, float *a, const int *lda, float *d, float *e, float *tau, float *work, int *lwork, int *info );\n  void dsytrd_(char *uplo, const int *n, double *a, const int *lda, double *d, double *e, double *tau, double *work, int *lwork, int *info );\n  void sgehrd_( const int *n, int *ilo, int *ihi, float *a, const int *lda, float *tau, float *work, int *lwork, int *info );\n  void dgehrd_( const int *n, int *ilo, int *ihi, double *a, const int *lda, double *tau, double *work, int *lwork, int *info );\n\n  // LU row pivoting\n//   void dgetrf_( int *m, int *n, double *a, int *lda, int *ipiv, int *info );\n//   void sgetrf_(const int* m, const int* n, float *a, const int* ld, int* ipivot, int* info);\n  // LU full pivoting\n  void sgetc2_(const int* n, float *a, const int *lda, int *ipiv, int *jpiv, int*info );\n  void dgetc2_(const int* n, double *a, const int *lda, int *ipiv, int *jpiv, int*info );\n#ifdef HAS_LAPACK\n#endif\n}\n\n#define MAKE_STRING2(S) #S\n#define MAKE_STRING(S) MAKE_STRING2(S)\n\n#define CAT2(A,B) A##B\n#define CAT(A,B) CAT2(A,B)\n\n\ntemplate<class real> class blas_interface;\n\n\nstatic char notrans = 'N';\nstatic char trans = 'T';\nstatic char nonunit = 'N';\nstatic char lower = 'L';\nstatic char right = 'R';\nstatic char left = 'L';\nstatic int intone = 1;\n\n\n\n#define SCALAR        float\n#define SCALAR_PREFIX s\n#include \"blas_interface_impl.hh\"\n#undef SCALAR\n#undef SCALAR_PREFIX\n\n\n#define SCALAR        double\n#define SCALAR_PREFIX d\n#include \"blas_interface_impl.hh\"\n#undef SCALAR\n#undef SCALAR_PREFIX\n\n#endif\n\n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/BLAS/blas_interface_impl.hh",
    "content": "\n#define BLAS_FUNC(NAME) CAT(CAT(SCALAR_PREFIX,NAME),_)\n\ntemplate<> class blas_interface<SCALAR> : public c_interface_base<SCALAR>\n{\n\npublic :\n  \n  static SCALAR fone;\n  static SCALAR fzero;\n\n  static inline std::string name()\n  {\n    return MAKE_STRING(CBLASNAME);\n  }\n\n  static inline void matrix_vector_product(gene_matrix & A, gene_vector & B, gene_vector & X, int N){\n    BLAS_FUNC(gemv)(&notrans,&N,&N,&fone,A,&N,B,&intone,&fzero,X,&intone);\n  }\n\n  static inline void symv(gene_matrix & A, gene_vector & B, gene_vector & X, int N){\n    BLAS_FUNC(symv)(&lower, &N,&fone,A,&N,B,&intone,&fzero,X,&intone);\n  }\n\n  static inline void syr2(gene_matrix & A, gene_vector & B, gene_vector & X, int N){\n    BLAS_FUNC(syr2)(&lower,&N,&fone,B,&intone,X,&intone,A,&N);\n  }\n\n  static inline void ger(gene_matrix & A, gene_vector & X, gene_vector & Y, int N){\n    BLAS_FUNC(ger)(&N,&N,&fone,X,&intone,Y,&intone,A,&N);\n  }\n\n  static inline void rot(gene_vector & A,  gene_vector & B, SCALAR c, SCALAR s, int N){\n    BLAS_FUNC(rot)(&N,A,&intone,B,&intone,&c,&s);\n  }\n\n  static inline void atv_product(gene_matrix & A, gene_vector & B, gene_vector & X, int N){\n    BLAS_FUNC(gemv)(&trans,&N,&N,&fone,A,&N,B,&intone,&fzero,X,&intone);\n  }\n\n  static inline void matrix_matrix_product(gene_matrix & A, gene_matrix & B, gene_matrix & X, int N){\n    BLAS_FUNC(gemm)(&notrans,&notrans,&N,&N,&N,&fone,A,&N,B,&N,&fzero,X,&N);\n  }\n\n  static inline void transposed_matrix_matrix_product(gene_matrix & A, gene_matrix & B, gene_matrix & X, int N){\n    BLAS_FUNC(gemm)(&notrans,&notrans,&N,&N,&N,&fone,A,&N,B,&N,&fzero,X,&N);\n  }\n\n//   static inline void ata_product(gene_matrix & A, gene_matrix & X, int N){\n//     ssyrk_(&lower,&trans,&N,&N,&fone,A,&N,&fzero,X,&N);\n//   }\n\n  static inline void aat_product(gene_matrix & A, gene_matrix & X, int N){\n    BLAS_FUNC(syrk)(&lower,&notrans,&N,&N,&fone,A,&N,&fzero,X,&N);\n  }\n\n  static inline void axpy(SCALAR coef, const gene_vector & X, gene_vector & Y, int N){\n    BLAS_FUNC(axpy)(&N,&coef,X,&intone,Y,&intone);\n  }\n\n  static inline void axpby(SCALAR a, const gene_vector & X, SCALAR b, gene_vector & Y, int N){\n    BLAS_FUNC(scal)(&N,&b,Y,&intone);\n    BLAS_FUNC(axpy)(&N,&a,X,&intone,Y,&intone);\n  }\n\n  static inline void cholesky(const gene_matrix & X, gene_matrix & C, int N){\n    int N2 = N*N;\n    BLAS_FUNC(copy)(&N2, X, &intone, C, &intone);\n    char uplo = 'L';\n    int info = 0;\n    BLAS_FUNC(potrf)(&uplo, &N, C, &N, &info);\n    if(info!=0) std::cerr << \"potrf_ error \" << info << \"\\n\";\n  }\n\n  static inline void partial_lu_decomp(const gene_matrix & X, gene_matrix & C, int N){\n    int N2 = N*N;\n    BLAS_FUNC(copy)(&N2, X, &intone, C, &intone);\n    int info = 0;\n    int * ipiv = (int*)alloca(sizeof(int)*N);\n    BLAS_FUNC(getrf)(&N, &N, C, &N, ipiv, &info);\n    if(info!=0) std::cerr << \"getrf_ error \" << info << \"\\n\";\n  }\n  \n  static inline void trisolve_lower(const gene_matrix & L, const gene_vector& B, gene_vector & X, int N){\n    BLAS_FUNC(copy)(&N, B, &intone, X, &intone);\n    BLAS_FUNC(trsv)(&lower, &notrans, &nonunit, &N, L, &N, X, &intone);\n  }\n\n  static inline void trisolve_lower_matrix(const gene_matrix & L, const gene_matrix& B, gene_matrix & X, int N){\n    BLAS_FUNC(copy)(&N, B, &intone, X, &intone);\n    BLAS_FUNC(trsm)(&right, &lower, &notrans, &nonunit, &N, &N, &fone, L, &N, X, &N);\n  }\n\n  static inline void trmm(gene_matrix & A, gene_matrix & B, gene_matrix & /*X*/, int N){\n    BLAS_FUNC(trmm)(&left, &lower, &notrans,&nonunit, &N,&N,&fone,A,&N,B,&N);\n  }\n\n  #ifdef HAS_LAPACK\n\n  static inline void lu_decomp(const gene_matrix & X, gene_matrix & C, int N){\n    int N2 = N*N;\n    BLAS_FUNC(copy)(&N2, X, &intone, C, &intone);\n    int info = 0;\n    int * ipiv = (int*)alloca(sizeof(int)*N);\n    int * jpiv = (int*)alloca(sizeof(int)*N);\n    BLAS_FUNC(getc2)(&N, C, &N, ipiv, jpiv, &info);\n  }\n\n\n\n  static inline void hessenberg(const gene_matrix & X, gene_matrix & C, int N){\n    {\n      int N2 = N*N;\n      int inc = 1;\n      BLAS_FUNC(copy)(&N2, X, &inc, C, &inc);\n    }\n    int info = 0;\n    int ilo = 1;\n    int ihi = N;\n    int bsize = 64;\n    int worksize = N*bsize;\n    SCALAR* d = new SCALAR[N+worksize];\n    BLAS_FUNC(gehrd)(&N, &ilo, &ihi, C, &N, d, d+N, &worksize, &info);\n    delete[] d;\n  }\n\n  static inline void tridiagonalization(const gene_matrix & X, gene_matrix & C, int N){\n    {\n      int N2 = N*N;\n      int inc = 1;\n      BLAS_FUNC(copy)(&N2, X, &inc, C, &inc);\n    }\n    char uplo = 'U';\n    int info = 0;\n    int bsize = 64;\n    int worksize = N*bsize;\n    SCALAR* d = new SCALAR[3*N+worksize];\n    BLAS_FUNC(sytrd)(&uplo, &N, C, &N, d, d+N, d+2*N, d+3*N, &worksize, &info);\n    delete[] d;\n  }\n  \n  #endif // HAS_LAPACK\n\n};\n\nSCALAR blas_interface<SCALAR>::fone = SCALAR(1);\nSCALAR blas_interface<SCALAR>::fzero = SCALAR(0);\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/BLAS/c_interface_base.h",
    "content": "\n#ifndef BTL_C_INTERFACE_BASE_H\n#define BTL_C_INTERFACE_BASE_H\n\n#include \"utilities.h\"\n#include <vector>\n\ntemplate<class real> class c_interface_base\n{\n\npublic:\n\n  typedef real                      real_type;\n  typedef std::vector<real>         stl_vector;\n  typedef std::vector<stl_vector >  stl_matrix;\n\n  typedef real* gene_matrix;\n  typedef real* gene_vector;\n\n  static void free_matrix(gene_matrix & A, int /*N*/){\n    delete[] A;\n  }\n\n  static void free_vector(gene_vector & B){\n    delete[] B;\n  }\n\n  static inline void matrix_from_stl(gene_matrix & A, stl_matrix & A_stl){\n    int N = A_stl.size();\n    A = new real[N*N];\n    for (int j=0;j<N;j++)\n      for (int i=0;i<N;i++)\n        A[i+N*j] = A_stl[j][i];\n  }\n\n  static inline void vector_from_stl(gene_vector & B, stl_vector & B_stl){\n    int N = B_stl.size();\n    B = new real[N];\n    for (int i=0;i<N;i++)\n      B[i] = B_stl[i];\n  }\n\n  static inline void vector_to_stl(gene_vector & B, stl_vector & B_stl){\n    int N = B_stl.size();\n    for (int i=0;i<N;i++)\n      B_stl[i] = B[i];\n  }\n\n  static inline void matrix_to_stl(gene_matrix & A, stl_matrix & A_stl){\n    int N = A_stl.size();\n    for (int j=0;j<N;j++){\n      A_stl[j].resize(N);\n      for (int i=0;i<N;i++)\n        A_stl[j][i] = A[i+N*j];\n    }\n  }\n\n  static inline void copy_vector(const gene_vector & source, gene_vector & cible, int N){\n    for (int i=0;i<N;i++)\n      cible[i]=source[i];\n  }\n\n  static inline void copy_matrix(const gene_matrix & source, gene_matrix & cible, int N){\n    for (int j=0;j<N;j++){\n      for (int i=0;i<N;i++){\n        cible[i+N*j] = source[i+N*j];\n      }\n    }\n  }\n\n};\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/BLAS/main.cpp",
    "content": "//=====================================================\n// File   :  main.cpp\n// Author :  L. Plagne <laurent.plagne@edf.fr)>\n// Copyright (C) EDF R&D,  lun sep 30 14:23:28 CEST 2002\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#include \"utilities.h\"\n#include \"blas_interface.hh\"\n#include \"bench.hh\"\n#include \"basic_actions.hh\"\n\n#include \"action_cholesky.hh\"\n#include \"action_lu_decomp.hh\"\n#include \"action_partial_lu.hh\"\n#include \"action_trisolve_matrix.hh\"\n\n#ifdef HAS_LAPACK\n#include \"action_hessenberg.hh\"\n#endif\n\nBTL_MAIN;\n\nint main()\n{\n\n  bench<Action_axpy<blas_interface<REAL_TYPE> > >(MIN_AXPY,MAX_AXPY,NB_POINT);\n  bench<Action_axpby<blas_interface<REAL_TYPE> > >(MIN_AXPY,MAX_AXPY,NB_POINT);\n\n  bench<Action_matrix_vector_product<blas_interface<REAL_TYPE> > >(MIN_MV,MAX_MV,NB_POINT);\n  bench<Action_atv_product<blas_interface<REAL_TYPE> > >(MIN_MV,MAX_MV,NB_POINT);\n  bench<Action_symv<blas_interface<REAL_TYPE> > >(MIN_MV,MAX_MV,NB_POINT);\n  bench<Action_syr2<blas_interface<REAL_TYPE> > >(MIN_MV,MAX_MV,NB_POINT);\n\n  bench<Action_ger<blas_interface<REAL_TYPE> > >(MIN_MV,MAX_MV,NB_POINT);\n  bench<Action_rot<blas_interface<REAL_TYPE> > >(MIN_AXPY,MAX_AXPY,NB_POINT);\n\n  bench<Action_matrix_matrix_product<blas_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n//   bench<Action_ata_product<blas_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n  bench<Action_aat_product<blas_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n\n  bench<Action_trisolve<blas_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n  bench<Action_trisolve_matrix<blas_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n\n  bench<Action_trmm<blas_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n\n  bench<Action_cholesky<blas_interface<REAL_TYPE> > >(MIN_LU,MAX_LU,NB_POINT);\n  bench<Action_partial_lu<blas_interface<REAL_TYPE> > >(MIN_LU,MAX_LU,NB_POINT);\n\n  #ifdef HAS_LAPACK\n//   bench<Action_lu_decomp<blas_interface<REAL_TYPE> > >(MIN_LU,MAX_LU,NB_POINT);\n  bench<Action_hessenberg<blas_interface<REAL_TYPE> > >(MIN_LU,MAX_LU,NB_POINT);\n  bench<Action_tridiagonalization<blas_interface<REAL_TYPE> > >(MIN_LU,MAX_LU,NB_POINT);\n  #endif\n\n  //bench<Action_lu_solve<blas_LU_solve_interface<REAL_TYPE> > >(MIN_LU,MAX_LU,NB_POINT);\n\n  return 0;\n}\n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/STL/CMakeLists.txt",
    "content": "\nbtl_add_bench(btl_STL main.cpp OFF)\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/STL/STL_interface.hh",
    "content": "//=====================================================\n// File   :  STL_interface.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>\n// Copyright (C) EDF R&D,  lun sep 30 14:23:24 CEST 2002\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef STL_INTERFACE_HH\n#define STL_INTERFACE_HH\n#include <string>\n#include <vector>\n#include \"utilities.h\"\n\nusing namespace std;\n\ntemplate<class real>\nclass STL_interface{\n\npublic :\n\n  typedef real real_type ;\n\n  typedef std::vector<real>  stl_vector;\n  typedef std::vector<stl_vector > stl_matrix;\n\n  typedef stl_matrix gene_matrix;\n\n  typedef stl_vector gene_vector;\n\n  static inline std::string name( void )\n  {\n    return \"STL\";\n  }\n\n  static void free_matrix(gene_matrix & /*A*/, int /*N*/){}\n\n  static void free_vector(gene_vector & /*B*/){}\n\n  static inline void matrix_from_stl(gene_matrix & A, stl_matrix & A_stl){\n    A = A_stl;\n  }\n\n  static inline void vector_from_stl(gene_vector & B, stl_vector & B_stl){\n    B = B_stl;\n  }\n\n  static inline void vector_to_stl(gene_vector & B, stl_vector & B_stl){\n    B_stl = B ;\n  }\n\n\n  static inline void matrix_to_stl(gene_matrix & A, stl_matrix & A_stl){\n    A_stl = A ;\n  }\n\n  static inline void copy_vector(const gene_vector & source, gene_vector & cible, int N){\n    for (int i=0;i<N;i++){\n      cible[i]=source[i];\n    }\n  }\n\n\n  static inline void copy_matrix(const gene_matrix & source, gene_matrix & cible, int N){\n    for (int i=0;i<N;i++)\n      for (int j=0;j<N;j++)\n        cible[i][j]=source[i][j];\n  }\n\n//   static inline void ata_product(const gene_matrix & A, gene_matrix & X, int N)\n//   {\n//     real somme;\n//     for (int j=0;j<N;j++){\n//       for (int i=0;i<N;i++){\n//         somme=0.0;\n//         for (int k=0;k<N;k++)\n//           somme += A[i][k]*A[j][k];\n//         X[j][i]=somme;\n//       }\n//     }\n//   }\n\n  static inline void aat_product(const gene_matrix & A, gene_matrix & X, int N)\n  {\n    real somme;\n    for (int j=0;j<N;j++){\n      for (int i=0;i<N;i++){\n        somme=0.0;\n        if(i>=j)\n        {\n          for (int k=0;k<N;k++){\n            somme+=A[k][i]*A[k][j];\n          }\n          X[j][i]=somme;\n        }\n      }\n    }\n  }\n\n\n  static inline void matrix_matrix_product(const gene_matrix & A, const gene_matrix & B, gene_matrix & X, int N)\n  {\n    real somme;\n    for (int j=0;j<N;j++){\n      for (int i=0;i<N;i++){\n        somme=0.0;\n        for (int k=0;k<N;k++)\n          somme+=A[k][i]*B[j][k];\n        X[j][i]=somme;\n      }\n    }\n  }\n\n  static inline void matrix_vector_product(gene_matrix & A, gene_vector & B, gene_vector & X, int N)\n  {\n    real somme;\n    for (int i=0;i<N;i++){\n      somme=0.0;\n      for (int j=0;j<N;j++)\n        somme+=A[j][i]*B[j];\n      X[i]=somme;\n    }\n  }\n\n  static inline void symv(gene_matrix & A, gene_vector & B, gene_vector & X, int N)\n  {\n    for (int j=0; j<N; ++j)\n      X[j] = 0;\n    for (int j=0; j<N; ++j)\n    {\n      real t1 = B[j];\n      real t2 = 0;\n      X[j] += t1 * A[j][j];\n      for (int i=j+1; i<N; ++i) {\n        X[i] += t1 * A[j][i];\n        t2 += A[j][i] * B[i];\n      }\n      X[j] += t2;\n    }\n  }\n  \n  static inline void syr2(gene_matrix & A, gene_vector & B, gene_vector & X, int N)\n  {\n    for (int j=0; j<N; ++j)\n    {\n      for (int i=j; i<N; ++i)\n        A[j][i] += B[i]*X[j] + B[j]*X[i];\n    }\n  }\n\n  static inline void ger(gene_matrix & A, gene_vector & X, gene_vector & Y, int N)\n  {\n    for (int j=0; j<N; ++j)\n    {\n      for (int i=j; i<N; ++i)\n        A[j][i] += X[i]*Y[j];\n    }\n  }\n\n  static inline void atv_product(gene_matrix & A, gene_vector & B, gene_vector & X, int N)\n  {\n    real somme;\n    for (int i=0;i<N;i++){\n      somme = 0.0;\n      for (int j=0;j<N;j++)\n        somme += A[i][j]*B[j];\n      X[i] = somme;\n    }\n  }\n\n  static inline void axpy(real coef, const gene_vector & X, gene_vector & Y, int N){\n    for (int i=0;i<N;i++)\n      Y[i]+=coef*X[i];\n  }\n\n  static inline void axpby(real a, const gene_vector & X, real b, gene_vector & Y, int N){\n    for (int i=0;i<N;i++)\n      Y[i] = a*X[i] + b*Y[i];\n  }\n\n  static inline void trisolve_lower(const gene_matrix & L, const gene_vector & B, gene_vector & X, int N){\n    copy_vector(B,X,N);\n    for(int i=0; i<N; ++i)\n    {\n      X[i] /= L[i][i];\n      real tmp = X[i];\n      for (int j=i+1; j<N; ++j)\n        X[j] -= tmp * L[i][j];\n    }\n  }\n\n  static inline real norm_diff(const stl_vector & A, const stl_vector & B)\n  {\n    int N=A.size();\n    real somme=0.0;\n    real somme2=0.0;\n\n    for (int i=0;i<N;i++){\n      real diff=A[i]-B[i];\n      somme+=diff*diff;\n      somme2+=A[i]*A[i];\n    }\n    return somme/somme2;\n  }\n\n  static inline real norm_diff(const stl_matrix & A, const stl_matrix & B)\n  {\n    int N=A[0].size();\n    real somme=0.0;\n    real somme2=0.0;\n\n    for (int i=0;i<N;i++){\n      for (int j=0;j<N;j++){\n        real diff=A[i][j] - B[i][j];\n        somme += diff*diff;\n        somme2 += A[i][j]*A[i][j];\n      }\n    }\n\n    return somme/somme2;\n  }\n\n  static inline void display_vector(const stl_vector & A)\n  {\n    int N=A.size();\n    for (int i=0;i<N;i++){\n      INFOS(\"A[\"<<i<<\"]=\"<<A[i]<<endl);\n    }\n  }\n\n};\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/STL/main.cpp",
    "content": "//=====================================================\n// File   :  main.cpp\n// Author :  L. Plagne <laurent.plagne@edf.fr)>\n// Copyright (C) EDF R&D,  lun sep 30 14:23:23 CEST 2002\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#include \"utilities.h\"\n#include \"STL_interface.hh\"\n#include \"bench.hh\"\n#include \"basic_actions.hh\"\n\nBTL_MAIN;\n\nint main()\n{\n  bench<Action_axpy<STL_interface<REAL_TYPE> > >(MIN_AXPY,MAX_AXPY,NB_POINT);\n  bench<Action_axpby<STL_interface<REAL_TYPE> > >(MIN_AXPY,MAX_AXPY,NB_POINT);\n  bench<Action_matrix_vector_product<STL_interface<REAL_TYPE> > >(MIN_MV,MAX_MV,NB_POINT);\n  bench<Action_atv_product<STL_interface<REAL_TYPE> > >(MIN_MV,MAX_MV,NB_POINT);\n  bench<Action_symv<STL_interface<REAL_TYPE> > >(MIN_MV,MAX_MV,NB_POINT);\n  bench<Action_syr2<STL_interface<REAL_TYPE> > >(MIN_MV,MAX_MV,NB_POINT);\n  bench<Action_matrix_matrix_product<STL_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n  bench<Action_ata_product<STL_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n  bench<Action_aat_product<STL_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n\n  return 0;\n}\n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/blaze/CMakeLists.txt",
    "content": "\nfind_package(BLAZE)\nfind_package(Boost COMPONENTS system)\nif (BLAZE_FOUND AND Boost_FOUND)\n  include_directories(${BLAZE_INCLUDE_DIR} ${Boost_INCLUDE_DIRS})\n  btl_add_bench(btl_blaze main.cpp)\n  # Note: The newest blaze version requires C++14.\n  # Ideally, we should set this depending on the version of Blaze we found\n  set_property(TARGET btl_blaze PROPERTY CXX_STANDARD 14)\n  if(BUILD_btl_blaze)\n    target_link_libraries(btl_blaze ${Boost_LIBRARIES})\n  endif()\nendif ()\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/blaze/blaze_interface.hh",
    "content": "//=====================================================\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef BLAZE_INTERFACE_HH\n#define BLAZE_INTERFACE_HH\n\n#include <blaze/Math.h>\n#include <blaze/Blaze.h>\n// using namespace blaze;\n\n#include <vector>\n\ntemplate<class real>\nclass blaze_interface {\n\npublic :\n\n  typedef real real_type ;\n\n  typedef std::vector<real>        stl_vector;\n  typedef std::vector<stl_vector > stl_matrix;\n\n  typedef blaze::DynamicMatrix<real,blaze::columnMajor>  gene_matrix;\n  typedef blaze::DynamicVector<real>  gene_vector;\n\n  static inline std::string name() { return \"blaze\"; }\n\n  static void free_matrix(gene_matrix & A, int N){\n    return ;\n  }\n\n  static void free_vector(gene_vector & B){\n    return ;\n  }\n\n  static inline void matrix_from_stl(gene_matrix & A, stl_matrix & A_stl){\n    A.resize(A_stl[0].size(), A_stl.size());\n\n    for (int j=0; j<A_stl.size() ; j++){\n      for (int i=0; i<A_stl[j].size() ; i++){\n        A(i,j) = A_stl[j][i];\n      }\n    }\n  }\n\n  static inline void vector_from_stl(gene_vector & B, stl_vector & B_stl){\n    B.resize(B_stl.size());\n    for (int i=0; i<B_stl.size() ; i++){\n      B[i] = B_stl[i];\n    }\n  }\n\n  static inline void vector_to_stl(gene_vector & B, stl_vector & B_stl){\n    for (int i=0; i<B_stl.size() ; i++){\n      B_stl[i] = B[i];\n    }\n  }\n\n  static inline void matrix_to_stl(gene_matrix & A, stl_matrix & A_stl){\n    int N=A_stl.size();\n    for (int j=0;j<N;j++){\n      A_stl[j].resize(N);\n      for (int i=0;i<N;i++){\n        A_stl[j][i] = A(i,j);\n      }\n    }\n  }\n\n  static inline void matrix_matrix_product(const gene_matrix & A, const gene_matrix & B, gene_matrix & X, int N){\n    X = (A*B);\n  }\n\n  static inline void transposed_matrix_matrix_product(const gene_matrix & A, const gene_matrix & B, gene_matrix & X, int N){\n    X = (trans(A)*trans(B));\n  }\n\n  static inline void ata_product(const gene_matrix & A, gene_matrix & X, int N){\n    X = (trans(A)*A);\n  }\n\n  static inline void aat_product(const gene_matrix & A, gene_matrix & X, int N){\n    X = (A*trans(A));\n  }\n\n  static inline void matrix_vector_product(gene_matrix & A, gene_vector & B, gene_vector & X, int N){\n    X = (A*B);\n  }\n\n  static inline void atv_product(gene_matrix & A, gene_vector & B, gene_vector & X, int N){\n    X = (trans(A)*B);\n  }\n\n  static inline void axpy(const real coef, const gene_vector & X, gene_vector & Y, int N){\n    Y += coef * X;\n  }\n\n  static inline void axpby(real a, const gene_vector & X, real b, gene_vector & Y, int N){\n    Y = a*X + b*Y;\n  }\n\n//   static inline void cholesky(const gene_matrix & X, gene_matrix & C, int N){\n//     C = X;\n//     recursive_cholesky(C);\n//   }\n\n//   static inline void lu_decomp(const gene_matrix & X, gene_matrix & R, int N){\n//     R = X;\n//     std::vector<int> ipvt(N);\n//     lu_factor(R, ipvt);\n//   }\n\n//   static inline void trisolve_lower(const gene_matrix & L, const gene_vector& B, gene_vector & X, int N){\n//     X = lower_trisolve(L, B);\n//   }\n\n  static inline void copy_matrix(const gene_matrix & source, gene_matrix & cible, int N){\n    cible = source;\n  }\n\n  static inline void copy_vector(const gene_vector & source, gene_vector & cible, int N){\n    cible = source;\n  }\n\n};\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/blaze/main.cpp",
    "content": "//=====================================================\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#include \"utilities.h\"\n#include \"blaze_interface.hh\"\n#include \"bench.hh\"\n#include \"basic_actions.hh\"\n\nBTL_MAIN;\n\nint main()\n{\n\n  bench<Action_axpy<blaze_interface<REAL_TYPE> > >(MIN_AXPY,MAX_AXPY,NB_POINT);\n  bench<Action_axpby<blaze_interface<REAL_TYPE> > >(MIN_AXPY,MAX_AXPY,NB_POINT);\n\n  bench<Action_matrix_vector_product<blaze_interface<REAL_TYPE> > >(MIN_MV,MAX_MV,NB_POINT);\n  bench<Action_atv_product<blaze_interface<REAL_TYPE> > >(MIN_MV,MAX_MV,NB_POINT);\n//   bench<Action_matrix_matrix_product<blaze_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n//   bench<Action_ata_product<blaze_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n//   bench<Action_aat_product<blaze_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n\n  return 0;\n}\n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/blitz/CMakeLists.txt",
    "content": "\nfind_package(Blitz)\n\nif (BLITZ_FOUND)\n  include_directories(${BLITZ_INCLUDES})\n\n  btl_add_bench(btl_blitz btl_blitz.cpp)\n  if (BUILD_btl_blitz)\n    target_link_libraries(btl_blitz ${BLITZ_LIBRARIES})\n  endif (BUILD_btl_blitz)\n\n  btl_add_bench(btl_tiny_blitz btl_tiny_blitz.cpp OFF)\n  if (BUILD_btl_tiny_blitz)\n    target_link_libraries(btl_tiny_blitz ${BLITZ_LIBRARIES})\n  endif (BUILD_btl_tiny_blitz)\n\nendif (BLITZ_FOUND)\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/blitz/blitz_LU_solve_interface.hh",
    "content": "//=====================================================\n// File   :  blitz_LU_solve_interface.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>        \n// Copyright (C) EDF R&D,  lun sep 30 14:23:31 CEST 2002\n//=====================================================\n// \n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n// \n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n// \n#ifndef BLITZ_LU_SOLVE_INTERFACE_HH\n#define BLITZ_LU_SOLVE_INTERFACE_HH\n\n#include \"blitz/array.h\"\n#include <vector>\n\nBZ_USING_NAMESPACE(blitz)\n\ntemplate<class real>\nclass blitz_LU_solve_interface : public blitz_interface<real>\n{\n\npublic :\n\n  typedef typename blitz_interface<real>::gene_matrix gene_matrix;\n  typedef typename blitz_interface<real>::gene_vector gene_vector;\n\n  typedef blitz::Array<int,1> Pivot_Vector;\n\n  inline static void new_Pivot_Vector(Pivot_Vector & pivot,int N)\n  {\n\n    pivot.resize(N);\n\n  }\n\n  inline static void free_Pivot_Vector(Pivot_Vector & pivot)\n  {\n    \n    return;\n\n  }\n\n\n  static inline real matrix_vector_product_sliced(const gene_matrix & A, gene_vector B, int row, int col_start, int col_end)\n  {\n    \n    real somme=0.;\n    \n    for (int j=col_start ; j<col_end+1 ; j++){\n\t\n\tsomme+=A(row,j)*B(j);\n\t\n    }\n\n    return somme;\n\n  }\n\n\n\n\n  static inline real matrix_matrix_product_sliced(gene_matrix & A, int row, int col_start, int col_end, gene_matrix & B, int row_shift, int col )\n  {\n    \n    real somme=0.;\n    \n    for (int j=col_start ; j<col_end+1 ; j++){\n\t\n\tsomme+=A(row,j)*B(j+row_shift,col);\n\t\n    }\n\n    return somme;\n\n  }\n\n  inline static void LU_factor(gene_matrix & LU, Pivot_Vector & pivot, int N)\n  {\n\n    ASSERT( LU.rows()==LU.cols() ) ;\n    int index_max = 0 ;\n    real big = 0. ;\n    real theSum = 0. ;\n    real dum = 0. ;\n    // Get the implicit scaling information :\n    gene_vector ImplicitScaling( N ) ;\n    for( int i=0; i<N; i++ ) {\n      big = 0. ;\n      for( int j=0; j<N; j++ ) {\n\tif( abs( LU( i, j ) )>=big ) big = abs( LU( i, j ) ) ;\n      }\n      if( big==0. ) {\n\tINFOS( \"blitz_LU_factor::Singular matrix\" ) ;\n\texit( 0 ) ;\n      }\n      ImplicitScaling( i ) = 1./big ;\n    }\n    // Loop over columns of Crout's method :\n    for( int j=0; j<N; j++ ) {\n      for( int i=0; i<j; i++ ) {\n\ttheSum = LU( i, j ) ;\n\ttheSum -= matrix_matrix_product_sliced(LU, i, 0, i-1, LU, 0, j) ;\n\t//\ttheSum -= sum( LU( i, Range( fromStart, i-1 ) )*LU( Range( fromStart, i-1 ), j ) ) ;\n\tLU( i, j ) = theSum ;\n      }\n      \n      // Search for the largest pivot element :\n      big = 0. ;\n      for( int i=j; i<N; i++ ) {\n\ttheSum = LU( i, j ) ;\n\ttheSum -= matrix_matrix_product_sliced(LU, i, 0, j-1, LU, 0, j) ;\n\t//\ttheSum -= sum( LU( i, Range( fromStart, j-1 ) )*LU( Range( fromStart, j-1 ), j ) ) ;\n\tLU( i, j ) = theSum ;\n\tif( (ImplicitScaling( i )*abs( theSum ))>=big ) {\n\t  dum = ImplicitScaling( i )*abs( theSum ) ;\n\t  big = dum ;\n\t  index_max = i ;\n\t}\n      }\n      // Interchanging rows and the scale factor :\n      if( j!=index_max ) {\n\tfor( int k=0; k<N; k++ ) {\n\t  dum = LU( index_max, k ) ;\n\t  LU( index_max, k ) = LU( j, k ) ;\n\t  LU( j, k ) = dum ;\n\t}\n\tImplicitScaling( index_max ) = ImplicitScaling( j ) ;\n      }\n      pivot( j ) = index_max ;\n      if ( LU( j, j )==0. ) LU( j, j ) = 1.e-20 ;\n      // Divide by the pivot element :\n      if( j<N ) {\n\tdum = 1./LU( j, j ) ;\n\tfor( int i=j+1; i<N; i++ ) LU( i, j ) *= dum ;\n      }\n    }\n\n  }\n\n  inline static void LU_solve(const gene_matrix & LU, const Pivot_Vector pivot, gene_vector &B, gene_vector X, int N)\n  {\n\n    // Pour conserver le meme header, on travaille sur X, copie du second-membre B\n    X = B.copy() ;\n    ASSERT( LU.rows()==LU.cols() ) ;\n    firstIndex indI ;\n    // Forward substitution :\n    int ii = 0 ;\n    real theSum = 0. ;\n    for( int i=0; i<N; i++ ) {\n      int ip = pivot( i ) ;\n      theSum = X( ip ) ;\n      //      theSum = B( ip ) ;\n      X( ip ) = X( i ) ;\n      //      B( ip ) = B( i ) ;\n      if( ii ) {\n\ttheSum -= matrix_vector_product_sliced(LU, X, i, ii-1, i-1) ;\n\t//\ttheSum -= sum( LU( i, Range( ii-1, i-1 ) )*X( Range( ii-1, i-1 ) ) ) ;\n\t//\ttheSum -= sum( LU( i, Range( ii-1, i-1 ) )*B( Range( ii-1, i-1 ) ) ) ;\n      } else if( theSum ) {\n\tii = i+1 ;\n      }\n      X( i ) = theSum ;\n      //      B( i ) = theSum ;\n    }\n    // Backsubstitution :\n    for( int i=N-1; i>=0; i-- ) {\n      theSum = X( i ) ;\n      //      theSum = B( i ) ;\n      theSum -= matrix_vector_product_sliced(LU, X, i, i+1, N) ;\n      //      theSum -= sum( LU( i, Range( i+1, toEnd ) )*X( Range( i+1, toEnd ) ) ) ;\n      //      theSum -= sum( LU( i, Range( i+1, toEnd ) )*B( Range( i+1, toEnd ) ) ) ;\n      // Store a component of the solution vector :\n      X( i ) = theSum/LU( i, i ) ;\n      //      B( i ) = theSum/LU( i, i ) ;\n    }\n\n  }\n\n};\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/blitz/blitz_interface.hh",
    "content": "//=====================================================\n// File   :  blitz_interface.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>\n// Copyright (C) EDF R&D,  lun sep 30 14:23:30 CEST 2002\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef BLITZ_INTERFACE_HH\n#define BLITZ_INTERFACE_HH\n\n#include <blitz/blitz.h>\n#include <blitz/array.h>\n#include <blitz/vector-et.h>\n#include <blitz/vecwhere.h>\n#include <blitz/matrix.h>\n#include <vector>\n\nBZ_USING_NAMESPACE(blitz)\n\ntemplate<class real>\nclass blitz_interface{\n\npublic :\n\n  typedef real real_type ;\n\n  typedef std::vector<real>  stl_vector;\n  typedef std::vector<stl_vector > stl_matrix;\n\n  typedef blitz::Array<real, 2>  gene_matrix;\n  typedef blitz::Array<real, 1>  gene_vector;\n//   typedef blitz::Matrix<real, blitz::ColumnMajor>  gene_matrix;\n//   typedef blitz::Vector<real> gene_vector;\n\n  static inline std::string name() { return \"blitz\"; }\n\n  static void free_matrix(gene_matrix & A, int N){}\n\n  static void free_vector(gene_vector & B){}\n\n  static inline void matrix_from_stl(gene_matrix & A, stl_matrix & A_stl){\n    A.resize(A_stl[0].size(),A_stl.size());\n    for (int j=0; j<A_stl.size() ; j++){\n      for (int i=0; i<A_stl[j].size() ; i++){\n        A(i,j)=A_stl[j][i];\n      }\n    }\n  }\n\n  static inline void vector_from_stl(gene_vector & B, stl_vector & B_stl){\n    B.resize(B_stl.size());\n    for (int i=0; i<B_stl.size() ; i++){\n      B(i)=B_stl[i];\n    }\n  }\n\n  static inline void vector_to_stl(gene_vector & B, stl_vector & B_stl){\n    for (int i=0; i<B_stl.size() ; i++){\n      B_stl[i]=B(i);\n    }\n  }\n\n  static inline void matrix_to_stl(gene_matrix & A, stl_matrix & A_stl){\n    int N=A_stl.size();\n    for (int j=0;j<N;j++){\n      A_stl[j].resize(N);\n      for (int i=0;i<N;i++)\n        A_stl[j][i] = A(i,j);\n    }\n  }\n\n  static inline void matrix_matrix_product(const gene_matrix & A, const gene_matrix & B, gene_matrix & X, int N)\n  {\n    firstIndex i;\n    secondIndex j;\n    thirdIndex k;\n    X = sum(A(i,k) * B(k,j), k);\n  }\n\n  static inline void ata_product(const gene_matrix & A, gene_matrix & X, int N)\n  {\n    firstIndex i;\n    secondIndex j;\n    thirdIndex k;\n    X = sum(A(k,i) * A(k,j), k);\n  }\n\n  static inline void aat_product(const gene_matrix & A, gene_matrix & X, int N)\n  {\n    firstIndex i;\n    secondIndex j;\n    thirdIndex k;\n    X = sum(A(i,k) * A(j,k), k);\n  }\n\n  static inline void matrix_vector_product(gene_matrix & A, gene_vector & B, gene_vector & X, int N)\n  {\n    firstIndex i;\n    secondIndex j;\n    X = sum(A(i,j)*B(j),j);\n  }\n\n  static inline void atv_product(gene_matrix & A, gene_vector & B, gene_vector & X, int N)\n  {\n    firstIndex i;\n    secondIndex j;\n    X = sum(A(j,i) * B(j),j);\n  }\n\n  static inline void axpy(const real coef, const gene_vector & X, gene_vector & Y, int N)\n  {\n    firstIndex i;\n    Y = Y(i) + coef * X(i);\n    //Y += coef * X;\n  }\n\n  static inline void copy_matrix(const gene_matrix & source, gene_matrix & cible, int N){\n    cible = source;\n    //cible.template operator=<gene_matrix>(source);\n//     for (int i=0;i<N;i++){\n//       for (int j=0;j<N;j++){\n//         cible(i,j)=source(i,j);\n//       }\n//     }\n  }\n\n  static inline void copy_vector(const gene_vector & source, gene_vector & cible, int N){\n    //cible.template operator=<gene_vector>(source);\n    cible = source;\n  }\n\n};\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/blitz/btl_blitz.cpp",
    "content": "//=====================================================\n// File   :  main.cpp\n// Author :  L. Plagne <laurent.plagne@edf.fr)>\n// Copyright (C) EDF R&D,  lun sep 30 14:23:30 CEST 2002\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#include \"utilities.h\"\n#include \"blitz_interface.hh\"\n#include \"blitz_LU_solve_interface.hh\"\n#include \"bench.hh\"\n#include \"action_matrix_vector_product.hh\"\n#include \"action_matrix_matrix_product.hh\"\n#include \"action_axpy.hh\"\n#include \"action_lu_solve.hh\"\n#include \"action_ata_product.hh\"\n#include \"action_aat_product.hh\"\n#include \"action_atv_product.hh\"\n\nBTL_MAIN;\n\nint main()\n{\n\n  bench<Action_matrix_vector_product<blitz_interface<REAL_TYPE> > >(MIN_MV,MAX_MV,NB_POINT);\n  bench<Action_atv_product<blitz_interface<REAL_TYPE> > >(MIN_MV,MAX_MV,NB_POINT);\n\n  bench<Action_matrix_matrix_product<blitz_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n  bench<Action_ata_product<blitz_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n  bench<Action_aat_product<blitz_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n\n  bench<Action_axpy<blitz_interface<REAL_TYPE> > >(MIN_AXPY,MAX_AXPY,NB_POINT);\n\n  //bench<Action_lu_solve<blitz_LU_solve_interface<REAL_TYPE> > >(MIN_LU,MAX_LU,NB_POINT);\n\n  return 0;\n}\n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/blitz/btl_tiny_blitz.cpp",
    "content": "//=====================================================\n// File   :  main.cpp\n// Author :  L. Plagne <laurent.plagne@edf.fr)>\n// Copyright (C) EDF R&D,  lun sep 30 14:23:30 CEST 2002\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#include \"utilities.h\"\n#include \"tiny_blitz_interface.hh\"\n#include \"static/bench_static.hh\"\n#include \"action_matrix_vector_product.hh\"\n#include \"action_matrix_matrix_product.hh\"\n#include \"action_axpy.hh\"\n\nBTL_MAIN;\n\nint main()\n{\n  bench_static<Action_axpy,tiny_blitz_interface>();\n  bench_static<Action_matrix_matrix_product,tiny_blitz_interface>();\n  bench_static<Action_matrix_vector_product,tiny_blitz_interface>();\n\n  return 0;\n}\n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/blitz/tiny_blitz_interface.hh",
    "content": "//=====================================================\n// File   :  tiny_blitz_interface.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>\n// Copyright (C) EDF R&D,  lun sep 30 14:23:30 CEST 2002\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef TINY_BLITZ_INTERFACE_HH\n#define TINY_BLITZ_INTERFACE_HH\n\n#include \"blitz/array.h\"\n#include \"blitz/tiny.h\"\n#include \"blitz/tinymat.h\"\n#include \"blitz/tinyvec.h\"\n#include <blitz/tinyvec-et.h>\n\n#include <vector>\n\nBZ_USING_NAMESPACE(blitz)\n\ntemplate<class real, int SIZE>\nclass tiny_blitz_interface\n{\n\npublic :\n\n  typedef real real_type ;\n\n  typedef std::vector<real>  stl_vector;\n  typedef std::vector<stl_vector > stl_matrix;\n\n  typedef TinyVector<real,SIZE> gene_vector;\n  typedef TinyMatrix<real,SIZE,SIZE> gene_matrix;\n\n  static inline std::string name() { return \"tiny_blitz\"; }\n\n  static void free_matrix(gene_matrix & A, int N){}\n\n  static void free_vector(gene_vector & B){}\n\n  static inline void matrix_from_stl(gene_matrix & A, stl_matrix & A_stl){\n    for (int j=0; j<A_stl.size() ; j++)\n      for (int i=0; i<A_stl[j].size() ; i++)\n        A(i,j)=A_stl[j][i];\n  }\n\n  static inline void vector_from_stl(gene_vector & B, stl_vector & B_stl){\n    for (int i=0; i<B_stl.size() ; i++)\n      B(i) = B_stl[i];\n  }\n\n  static inline void vector_to_stl(gene_vector & B, stl_vector & B_stl){\n    for (int i=0; i<B_stl.size() ; i++)\n      B_stl[i] = B(i);\n  }\n\n  static inline void matrix_to_stl(gene_matrix & A, stl_matrix & A_stl){\n    int N = A_stl.size();\n    for (int j=0;j<N;j++)\n    {\n      A_stl[j].resize(N);\n      for (int i=0;i<N;i++)\n        A_stl[j][i] = A(i,j);\n    }\n  }\n\n  static inline void copy_matrix(const gene_matrix & source, gene_matrix & cible, int N){\n    for (int j=0;j<N;j++)\n      for (int i=0;i<N;i++)\n        cible(i,j) = source(i,j);\n  }\n\n  static inline void copy_vector(const gene_vector & source, gene_vector & cible, int N){\n    for (int i=0;i<N;i++){\n      cible(i) = source(i);\n    }\n  }\n\n  static inline void matrix_matrix_product(const gene_matrix & A, const gene_matrix & B, gene_matrix & X, int N){\n    X = product(A,B);\n  }\n\n  static inline void matrix_vector_product(gene_matrix & A, gene_vector & B, gene_vector & X, int N){\n    X = product(A,B);\n  }\n\n  static inline void axpy(const real coef, const gene_vector & X, gene_vector & Y, int N){\n    Y += coef * X;\n  }\n\n};\n\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/eigen2/CMakeLists.txt",
    "content": "\nfind_package(Eigen2)\n\nif(EIGEN2_FOUND)\n\n  include_directories(BEFORE ${EIGEN2_INCLUDE_DIR})\n  btl_add_bench(btl_eigen2_linear main_linear.cpp)\n  btl_add_bench(btl_eigen2_vecmat main_vecmat.cpp)\n  btl_add_bench(btl_eigen2_matmat main_matmat.cpp)\n  btl_add_bench(btl_eigen2_adv main_adv.cpp      )\n\n  btl_add_target_property(btl_eigen2_linear COMPILE_FLAGS \"-fno-exceptions -DBTL_PREFIX=eigen2\")\n  btl_add_target_property(btl_eigen2_vecmat COMPILE_FLAGS \"-fno-exceptions -DBTL_PREFIX=eigen2\")\n  btl_add_target_property(btl_eigen2_matmat COMPILE_FLAGS \"-fno-exceptions -DBTL_PREFIX=eigen2\")\n  btl_add_target_property(btl_eigen2_adv    COMPILE_FLAGS \"-fno-exceptions -DBTL_PREFIX=eigen2\")\n\n  btl_add_bench(btl_tiny_eigen2 btl_tiny_eigen2.cpp OFF)\n\nendif() # EIGEN2_FOUND\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/eigen2/btl_tiny_eigen2.cpp",
    "content": "//=====================================================\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#include \"utilities.h\"\n#include \"eigen3_interface.hh\"\n#include \"static/bench_static.hh\"\n#include \"action_matrix_vector_product.hh\"\n#include \"action_matrix_matrix_product.hh\"\n#include \"action_axpy.hh\"\n#include \"action_lu_solve.hh\"\n#include \"action_ata_product.hh\"\n#include \"action_aat_product.hh\"\n#include \"action_atv_product.hh\"\n#include \"action_cholesky.hh\"\n#include \"action_trisolve.hh\"\n\nBTL_MAIN;\n\nint main()\n{\n\n  bench_static<Action_axpy,eigen2_interface>();\n  bench_static<Action_matrix_matrix_product,eigen2_interface>();\n  bench_static<Action_matrix_vector_product,eigen2_interface>();\n  bench_static<Action_atv_product,eigen2_interface>();\n  bench_static<Action_cholesky,eigen2_interface>();\n  bench_static<Action_trisolve,eigen2_interface>();\n\n  return 0;\n}\n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/eigen2/eigen2_interface.hh",
    "content": "//=====================================================\n// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef EIGEN2_INTERFACE_HH\n#define EIGEN2_INTERFACE_HH\n// #include <cblas.h>\n#include <Eigen/Core>\n#include <Eigen/Cholesky>\n#include <Eigen/LU>\n#include <Eigen/QR>\n#include <vector>\n#include \"btl.hh\"\n\nusing namespace Eigen;\n\ntemplate<class real, int SIZE=Dynamic>\nclass eigen2_interface\n{\n\npublic :\n\n  enum {IsFixedSize = (SIZE!=Dynamic)};\n\n  typedef real real_type;\n\n  typedef std::vector<real> stl_vector;\n  typedef std::vector<stl_vector> stl_matrix;\n\n  typedef Eigen::Matrix<real,SIZE,SIZE> gene_matrix;\n  typedef Eigen::Matrix<real,SIZE,1> gene_vector;\n\n  static inline std::string name( void )\n  {\n    #if defined(EIGEN_VECTORIZE_SSE)\n    if (SIZE==Dynamic) return \"eigen2\"; else return \"tiny_eigen2\";\n    #elif defined(EIGEN_VECTORIZE_ALTIVEC) || defined(EIGEN_VECTORIZE_VSX)\n    if (SIZE==Dynamic) return \"eigen2\"; else return \"tiny_eigen2\";\n    #else\n    if (SIZE==Dynamic) return \"eigen2_novec\"; else return \"tiny_eigen2_novec\";\n    #endif\n  }\n\n  static void free_matrix(gene_matrix & A, int N) {}\n\n  static void free_vector(gene_vector & B) {}\n\n  static BTL_DONT_INLINE void matrix_from_stl(gene_matrix & A, stl_matrix & A_stl){\n    A.resize(A_stl[0].size(), A_stl.size());\n\n    for (int j=0; j<A_stl.size() ; j++){\n      for (int i=0; i<A_stl[j].size() ; i++){\n        A.coeffRef(i,j) = A_stl[j][i];\n      }\n    }\n  }\n\n  static BTL_DONT_INLINE  void vector_from_stl(gene_vector & B, stl_vector & B_stl){\n    B.resize(B_stl.size(),1);\n\n    for (int i=0; i<B_stl.size() ; i++){\n      B.coeffRef(i) = B_stl[i];\n    }\n  }\n\n  static BTL_DONT_INLINE  void vector_to_stl(gene_vector & B, stl_vector & B_stl){\n    for (int i=0; i<B_stl.size() ; i++){\n      B_stl[i] = B.coeff(i);\n    }\n  }\n\n  static BTL_DONT_INLINE  void matrix_to_stl(gene_matrix & A, stl_matrix & A_stl){\n    int N=A_stl.size();\n\n    for (int j=0;j<N;j++){\n      A_stl[j].resize(N);\n      for (int i=0;i<N;i++){\n        A_stl[j][i] = A.coeff(i,j);\n      }\n    }\n  }\n\n  static inline void matrix_matrix_product(const gene_matrix & A, const gene_matrix & B, gene_matrix & X, int N){\n    X = (A*B).lazy();\n  }\n\n  static inline void transposed_matrix_matrix_product(const gene_matrix & A, const gene_matrix & B, gene_matrix & X, int N){\n    X = (A.transpose()*B.transpose()).lazy();\n  }\n\n  static inline void ata_product(const gene_matrix & A, gene_matrix & X, int N){\n    X = (A.transpose()*A).lazy();\n  }\n\n  static inline void aat_product(const gene_matrix & A, gene_matrix & X, int N){\n    X = (A*A.transpose()).lazy();\n  }\n\n  static inline void matrix_vector_product(const gene_matrix & A, const gene_vector & B, gene_vector & X, int N){\n    X = (A*B)/*.lazy()*/;\n  }\n\n  static inline void atv_product(gene_matrix & A, gene_vector & B, gene_vector & X, int N){\n    X = (A.transpose()*B)/*.lazy()*/;\n  }\n\n  static inline void axpy(real coef, const gene_vector & X, gene_vector & Y, int N){\n    Y += coef * X;\n  }\n\n  static inline void axpby(real a, const gene_vector & X, real b, gene_vector & Y, int N){\n    Y = a*X + b*Y;\n  }\n\n  static inline void copy_matrix(const gene_matrix & source, gene_matrix & cible, int N){\n    cible = source;\n  }\n\n  static inline void copy_vector(const gene_vector & source, gene_vector & cible, int N){\n    cible = source;\n  }\n\n  static inline void trisolve_lower(const gene_matrix & L, const gene_vector& B, gene_vector& X, int N){\n    X = L.template marked<LowerTriangular>().solveTriangular(B);\n  }\n\n  static inline void trisolve_lower_matrix(const gene_matrix & L, const gene_matrix& B, gene_matrix& X, int N){\n    X = L.template marked<LowerTriangular>().solveTriangular(B);\n  }\n\n  static inline void cholesky(const gene_matrix & X, gene_matrix & C, int N){\n    C = X.llt().matrixL();\n//     C = X;\n//     Cholesky<gene_matrix>::computeInPlace(C);\n//     Cholesky<gene_matrix>::computeInPlaceBlock(C);\n  }\n\n  static inline void lu_decomp(const gene_matrix & X, gene_matrix & C, int N){\n    C = X.lu().matrixLU();\n//     C = X.inverse();\n  }\n\n  static inline void tridiagonalization(const gene_matrix & X, gene_matrix & C, int N){\n    C = Tridiagonalization<gene_matrix>(X).packedMatrix();\n  }\n\n  static inline void hessenberg(const gene_matrix & X, gene_matrix & C, int N){\n    C = HessenbergDecomposition<gene_matrix>(X).packedMatrix();\n  }\n\n\n\n};\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/eigen2/main_adv.cpp",
    "content": "//=====================================================\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#include \"utilities.h\"\n#include \"eigen2_interface.hh\"\n#include \"bench.hh\"\n#include \"action_trisolve.hh\"\n#include \"action_trisolve_matrix.hh\"\n#include \"action_cholesky.hh\"\n#include \"action_hessenberg.hh\"\n#include \"action_lu_decomp.hh\"\n// #include \"action_partial_lu.hh\"\n\nBTL_MAIN;\n\nint main()\n{\n  bench<Action_trisolve<eigen2_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n  bench<Action_trisolve_matrix<eigen2_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n  bench<Action_cholesky<eigen2_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n  bench<Action_lu_decomp<eigen2_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n//   bench<Action_partial_lu<eigen2_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n\n  bench<Action_hessenberg<eigen2_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n  bench<Action_tridiagonalization<eigen2_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n\n  return 0;\n}\n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/eigen2/main_linear.cpp",
    "content": "//=====================================================\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#include \"utilities.h\"\n#include \"eigen2_interface.hh\"\n#include \"bench.hh\"\n#include \"basic_actions.hh\"\n\nBTL_MAIN;\n\nint main()\n{\n\n  bench<Action_axpy<eigen2_interface<REAL_TYPE> > >(MIN_AXPY,MAX_AXPY,NB_POINT);\n  bench<Action_axpby<eigen2_interface<REAL_TYPE> > >(MIN_AXPY,MAX_AXPY,NB_POINT);\n  \n  return 0;\n}\n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/eigen2/main_matmat.cpp",
    "content": "//=====================================================\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#include \"utilities.h\"\n#include \"eigen2_interface.hh\"\n#include \"bench.hh\"\n#include \"basic_actions.hh\"\n\nBTL_MAIN;\n\nint main()\n{\n  bench<Action_matrix_matrix_product<eigen2_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n//   bench<Action_ata_product<eigen2_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n  bench<Action_aat_product<eigen2_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n//   bench<Action_trmm<eigen2_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n\n  return 0;\n}\n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/eigen2/main_vecmat.cpp",
    "content": "//=====================================================\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#include \"utilities.h\"\n#include \"eigen2_interface.hh\"\n#include \"bench.hh\"\n#include \"basic_actions.hh\"\n\nBTL_MAIN;\n\nint main()\n{\n  bench<Action_matrix_vector_product<eigen2_interface<REAL_TYPE> > >(MIN_MV,MAX_MV,NB_POINT);\n  bench<Action_atv_product<eigen2_interface<REAL_TYPE> > >(MIN_MV,MAX_MV,NB_POINT);\n//   bench<Action_symv<eigen2_interface<REAL_TYPE> > >(MIN_MV,MAX_MV,NB_POINT);\n//   bench<Action_syr2<eigen2_interface<REAL_TYPE> > >(MIN_MV,MAX_MV,NB_POINT);\n//   bench<Action_ger<eigen2_interface<REAL_TYPE> > >(MIN_MV,MAX_MV,NB_POINT);\n\n  return 0;\n}\n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/eigen3/CMakeLists.txt",
    "content": "\n\nif((NOT EIGEN3_INCLUDE_DIR) AND Eigen_SOURCE_DIR)\n  # unless EIGEN3_INCLUDE_DIR is defined, let's use current Eigen version\n  set(EIGEN3_INCLUDE_DIR ${Eigen_SOURCE_DIR})\n  set(EIGEN3_FOUND TRUE)\nelse()\n  find_package(Eigen3)\nendif()\n\nif (EIGEN3_FOUND)\n\n  include_directories(${EIGEN3_INCLUDE_DIR})\n  btl_add_bench(btl_eigen3_linear main_linear.cpp)\n  btl_add_bench(btl_eigen3_vecmat main_vecmat.cpp)\n  btl_add_bench(btl_eigen3_matmat main_matmat.cpp)\n  btl_add_bench(btl_eigen3_adv main_adv.cpp      )\n\n  btl_add_target_property(btl_eigen3_linear COMPILE_FLAGS \"-fno-exceptions -DBTL_PREFIX=eigen3\")\n  btl_add_target_property(btl_eigen3_vecmat COMPILE_FLAGS \"-fno-exceptions -DBTL_PREFIX=eigen3\")\n  btl_add_target_property(btl_eigen3_matmat COMPILE_FLAGS \"-fno-exceptions -DBTL_PREFIX=eigen3\")\n  btl_add_target_property(btl_eigen3_adv    COMPILE_FLAGS \"-fno-exceptions -DBTL_PREFIX=eigen3\")\n\n  option(BTL_BENCH_NOGCCVEC \"also bench Eigen explicit vec without GCC's auto vec\" OFF)\n  if(CMAKE_COMPILER_IS_GNUCXX AND BTL_BENCH_NOGCCVEC)\n    btl_add_bench(btl_eigen3_nogccvec_linear main_linear.cpp)\n    btl_add_bench(btl_eigen3_nogccvec_vecmat main_vecmat.cpp)\n    btl_add_bench(btl_eigen3_nogccvec_matmat main_matmat.cpp)\n    btl_add_bench(btl_eigen3_nogccvec_adv    main_adv.cpp   )\n\n    btl_add_target_property(btl_eigen3_nogccvec_linear COMPILE_FLAGS \"-fno-exceptions -fno-tree-vectorize -DBTL_PREFIX=eigen3_nogccvec\")\n    btl_add_target_property(btl_eigen3_nogccvec_vecmat COMPILE_FLAGS \"-fno-exceptions -fno-tree-vectorize -DBTL_PREFIX=eigen3_nogccvec\")\n    btl_add_target_property(btl_eigen3_nogccvec_matmat COMPILE_FLAGS \"-fno-exceptions -fno-tree-vectorize -DBTL_PREFIX=eigen3_nogccvec\")\n    btl_add_target_property(btl_eigen3_nogccvec_adv    COMPILE_FLAGS \"-fno-exceptions -fno-tree-vectorize -DBTL_PREFIX=eigen3_nogccvec\")\n  endif()\n\n\n  if(NOT BTL_NOVEC)\n    btl_add_bench(btl_eigen3_novec_linear main_linear.cpp OFF)\n    btl_add_bench(btl_eigen3_novec_vecmat main_vecmat.cpp OFF)\n    btl_add_bench(btl_eigen3_novec_matmat main_matmat.cpp OFF)\n    btl_add_bench(btl_eigen3_novec_adv main_adv.cpp       OFF)\n    btl_add_target_property(btl_eigen3_novec_linear COMPILE_FLAGS \"-fno-exceptions -DEIGEN_DONT_VECTORIZE -DBTL_PREFIX=eigen3_novec\")\n    btl_add_target_property(btl_eigen3_novec_vecmat COMPILE_FLAGS \"-fno-exceptions -DEIGEN_DONT_VECTORIZE -DBTL_PREFIX=eigen3_novec\")\n    btl_add_target_property(btl_eigen3_novec_matmat COMPILE_FLAGS \"-fno-exceptions -DEIGEN_DONT_VECTORIZE -DBTL_PREFIX=eigen3_novec\")\n    btl_add_target_property(btl_eigen3_novec_adv    COMPILE_FLAGS \"-fno-exceptions -DEIGEN_DONT_VECTORIZE -DBTL_PREFIX=eigen3_novec\")\n\n#     if(BUILD_btl_eigen3_adv)\n#       target_link_libraries(btl_eigen3_adv ${MKL_LIBRARIES})\n#     endif(BUILD_btl_eigen3_adv)\n\n  endif(NOT BTL_NOVEC)\n\n  btl_add_bench(btl_tiny_eigen3 btl_tiny_eigen3.cpp OFF)\n\n  if(NOT BTL_NOVEC)\n    btl_add_bench(btl_tiny_eigen3_novec btl_tiny_eigen3.cpp OFF)\n    btl_add_target_property(btl_tiny_eigen3_novec    COMPILE_FLAGS \"-DBTL_PREFIX=eigen3_tiny\")\n\n    if(BUILD_btl_tiny_eigen3_novec)\n      btl_add_target_property(btl_tiny_eigen3_novec    COMPILE_FLAGS \"-DEIGEN_DONT_VECTORIZE -DBTL_PREFIX=eigen3_tiny_novec\")\n    endif(BUILD_btl_tiny_eigen3_novec)\n  endif(NOT BTL_NOVEC)\n\nendif (EIGEN3_FOUND)\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/eigen3/btl_tiny_eigen3.cpp",
    "content": "//=====================================================\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#include \"utilities.h\"\n#include \"eigen3_interface.hh\"\n#include \"static/bench_static.hh\"\n#include \"action_matrix_vector_product.hh\"\n#include \"action_matrix_matrix_product.hh\"\n#include \"action_axpy.hh\"\n#include \"action_lu_solve.hh\"\n#include \"action_ata_product.hh\"\n#include \"action_aat_product.hh\"\n#include \"action_atv_product.hh\"\n#include \"action_cholesky.hh\"\n#include \"action_trisolve.hh\"\n\nBTL_MAIN;\n\nint main()\n{\n\n  bench_static<Action_axpy,eigen2_interface>();\n  bench_static<Action_matrix_matrix_product,eigen2_interface>();\n  bench_static<Action_matrix_vector_product,eigen2_interface>();\n  bench_static<Action_atv_product,eigen2_interface>();\n  bench_static<Action_cholesky,eigen2_interface>();\n  bench_static<Action_trisolve,eigen2_interface>();\n\n  return 0;\n}\n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/eigen3/eigen3_interface.hh",
    "content": "//=====================================================\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef EIGEN3_INTERFACE_HH\n#define EIGEN3_INTERFACE_HH\n\n#include <Eigen/Eigen>\n#include <vector>\n#include \"btl.hh\"\n\nusing namespace Eigen;\n\ntemplate<class real, int SIZE=Dynamic>\nclass eigen3_interface\n{\n\npublic :\n\n  enum {IsFixedSize = (SIZE!=Dynamic)};\n\n  typedef real real_type;\n\n  typedef std::vector<real> stl_vector;\n  typedef std::vector<stl_vector> stl_matrix;\n\n  typedef Eigen::Matrix<real,SIZE,SIZE> gene_matrix;\n  typedef Eigen::Matrix<real,SIZE,1> gene_vector;\n\n  static inline std::string name( void )\n  {\n    return EIGEN_MAKESTRING(BTL_PREFIX);\n  }\n\n  static void free_matrix(gene_matrix & /*A*/, int /*N*/) {}\n\n  static void free_vector(gene_vector & /*B*/) {}\n\n  static BTL_DONT_INLINE void matrix_from_stl(gene_matrix & A, stl_matrix & A_stl){\n    A.resize(A_stl[0].size(), A_stl.size());\n\n    for (unsigned int j=0; j<A_stl.size() ; j++){\n      for (unsigned int i=0; i<A_stl[j].size() ; i++){\n        A.coeffRef(i,j) = A_stl[j][i];\n      }\n    }\n  }\n\n  static BTL_DONT_INLINE  void vector_from_stl(gene_vector & B, stl_vector & B_stl){\n    B.resize(B_stl.size(),1);\n\n    for (unsigned int i=0; i<B_stl.size() ; i++){\n      B.coeffRef(i) = B_stl[i];\n    }\n  }\n\n  static BTL_DONT_INLINE  void vector_to_stl(gene_vector & B, stl_vector & B_stl){\n    for (unsigned int i=0; i<B_stl.size() ; i++){\n      B_stl[i] = B.coeff(i);\n    }\n  }\n\n  static BTL_DONT_INLINE  void matrix_to_stl(gene_matrix & A, stl_matrix & A_stl){\n    int  N=A_stl.size();\n\n    for (int j=0;j<N;j++){\n      A_stl[j].resize(N);\n      for (int i=0;i<N;i++){\n        A_stl[j][i] = A.coeff(i,j);\n      }\n    }\n  }\n\n  static inline void matrix_matrix_product(const gene_matrix & A, const gene_matrix & B, gene_matrix & X, int  /*N*/){\n    X.noalias() = A*B;\n  }\n\n  static inline void transposed_matrix_matrix_product(const gene_matrix & A, const gene_matrix & B, gene_matrix & X, int  /*N*/){\n    X.noalias() = A.transpose()*B.transpose();\n  }\n\n//   static inline void ata_product(const gene_matrix & A, gene_matrix & X, int  /*N*/){\n//     X.noalias() = A.transpose()*A;\n//   }\n\n  static inline void aat_product(const gene_matrix & A, gene_matrix & X, int  /*N*/){\n    X.template triangularView<Lower>().setZero();\n    X.template selfadjointView<Lower>().rankUpdate(A);\n  }\n\n  static inline void matrix_vector_product(const gene_matrix & A, const gene_vector & B, gene_vector & X, int  /*N*/){\n    X.noalias() = A*B;\n  }\n\n  static inline void symv(const gene_matrix & A, const gene_vector & B, gene_vector & X, int  /*N*/){\n    X.noalias() = (A.template selfadjointView<Lower>() * B);\n//     internal::product_selfadjoint_vector<real,0,LowerTriangularBit,false,false>(N,A.data(),N, B.data(), 1, X.data(), 1);\n  }\n\n  template<typename Dest, typename Src> static void triassign(Dest& dst, const Src& src)\n  {\n    typedef typename Dest::Scalar Scalar;\n    typedef typename internal::packet_traits<Scalar>::type Packet;\n    const int PacketSize = sizeof(Packet)/sizeof(Scalar);\n    int size = dst.cols();\n    for(int j=0; j<size; j+=1)\n    {\n//       const int alignedEnd = alignedStart + ((innerSize-alignedStart) & ~packetAlignedMask);\n      Scalar* A0 = dst.data() + j*dst.stride();\n      int starti = j;\n      int alignedEnd = starti;\n      int alignedStart = (starti) + internal::first_aligned(&A0[starti], size-starti);\n      alignedEnd = alignedStart + ((size-alignedStart)/(2*PacketSize))*(PacketSize*2);\n\n      // do the non-vectorizable part of the assignment\n      for (int index = starti; index<alignedStart ; ++index)\n      {\n        if(Dest::Flags&RowMajorBit)\n          dst.copyCoeff(j, index, src);\n        else\n          dst.copyCoeff(index, j, src);\n      }\n\n      // do the vectorizable part of the assignment\n      for (int index = alignedStart; index<alignedEnd; index+=PacketSize)\n      {\n        if(Dest::Flags&RowMajorBit)\n          dst.template copyPacket<Src, Aligned, Unaligned>(j, index, src);\n        else\n          dst.template copyPacket<Src, Aligned, Unaligned>(index, j, src);\n      }\n\n      // do the non-vectorizable part of the assignment\n      for (int index = alignedEnd; index<size; ++index)\n      {\n        if(Dest::Flags&RowMajorBit)\n          dst.copyCoeff(j, index, src);\n        else\n          dst.copyCoeff(index, j, src);\n      }\n      //dst.col(j).tail(N-j) = src.col(j).tail(N-j);\n    }\n  }\n\n  static EIGEN_DONT_INLINE void syr2(gene_matrix & A,  gene_vector & X, gene_vector & Y, int  N){\n    // internal::product_selfadjoint_rank2_update<real,0,LowerTriangularBit>(N,A.data(),N, X.data(), 1, Y.data(), 1, -1);\n    for(int j=0; j<N; ++j)\n      A.col(j).tail(N-j) += X[j] * Y.tail(N-j) + Y[j] * X.tail(N-j);\n  }\n\n  static EIGEN_DONT_INLINE void ger(gene_matrix & A,  gene_vector & X, gene_vector & Y, int  N){\n    for(int j=0; j<N; ++j)\n      A.col(j) += X * Y[j];\n  }\n\n  static EIGEN_DONT_INLINE void rot(gene_vector & A,  gene_vector & B, real c, real s, int  /*N*/){\n    internal::apply_rotation_in_the_plane(A, B, JacobiRotation<real>(c,s));\n  }\n\n  static inline void atv_product(gene_matrix & A, gene_vector & B, gene_vector & X, int  /*N*/){\n    X.noalias() = (A.transpose()*B);\n  }\n\n  static inline void axpy(real coef, const gene_vector & X, gene_vector & Y, int  /*N*/){\n    Y += coef * X;\n  }\n\n  static inline void axpby(real a, const gene_vector & X, real b, gene_vector & Y, int  /*N*/){\n    Y = a*X + b*Y;\n  }\n\n  static EIGEN_DONT_INLINE void copy_matrix(const gene_matrix & source, gene_matrix & cible, int  /*N*/){\n    cible = source;\n  }\n\n  static EIGEN_DONT_INLINE void copy_vector(const gene_vector & source, gene_vector & cible, int  /*N*/){\n    cible = source;\n  }\n\n  static inline void trisolve_lower(const gene_matrix & L, const gene_vector& B, gene_vector& X, int  /*N*/){\n    X = L.template triangularView<Lower>().solve(B);\n  }\n\n  static inline void trisolve_lower_matrix(const gene_matrix & L, const gene_matrix& B, gene_matrix& X, int  /*N*/){\n    X = L.template triangularView<Upper>().solve(B);\n  }\n\n  static inline void trmm(const gene_matrix & L, const gene_matrix& B, gene_matrix& X, int  /*N*/){\n    X.noalias() = L.template triangularView<Lower>() * B;\n  }\n\n  static inline void cholesky(const gene_matrix & X, gene_matrix & C, int  /*N*/){\n    C = X;\n    internal::llt_inplace<real,Lower>::blocked(C);\n    //C = X.llt().matrixL();\n//     C = X;\n//     Cholesky<gene_matrix>::computeInPlace(C);\n//     Cholesky<gene_matrix>::computeInPlaceBlock(C);\n  }\n\n  static inline void lu_decomp(const gene_matrix & X, gene_matrix & C, int  /*N*/){\n    C = X.fullPivLu().matrixLU();\n  }\n\n  static inline void partial_lu_decomp(const gene_matrix & X, gene_matrix & C, int  N){\n    Matrix<DenseIndex,1,Dynamic> piv(N);\n    DenseIndex nb;\n    C = X;\n    internal::partial_lu_inplace(C,piv,nb);\n//     C = X.partialPivLu().matrixLU();\n  }\n\n  static inline void tridiagonalization(const gene_matrix & X, gene_matrix & C, int  N){\n    typename Tridiagonalization<gene_matrix>::CoeffVectorType aux(N-1);\n    C = X;\n    internal::tridiagonalization_inplace(C, aux);\n  }\n\n  static inline void hessenberg(const gene_matrix & X, gene_matrix & C, int  /*N*/){\n    C = HessenbergDecomposition<gene_matrix>(X).packedMatrix();\n  }\n\n\n\n};\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/eigen3/main_adv.cpp",
    "content": "//=====================================================\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#include \"utilities.h\"\n#include \"eigen3_interface.hh\"\n#include \"bench.hh\"\n#include \"action_trisolve.hh\"\n#include \"action_trisolve_matrix.hh\"\n#include \"action_cholesky.hh\"\n#include \"action_hessenberg.hh\"\n#include \"action_lu_decomp.hh\"\n#include \"action_partial_lu.hh\"\n\nBTL_MAIN;\n\nint main()\n{\n  bench<Action_trisolve<eigen3_interface<REAL_TYPE> > >(MIN_LU,MAX_LU,NB_POINT);\n  bench<Action_trisolve_matrix<eigen3_interface<REAL_TYPE> > >(MIN_LU,MAX_LU,NB_POINT);\n  bench<Action_cholesky<eigen3_interface<REAL_TYPE> > >(MIN_LU,MAX_LU,NB_POINT);\n//   bench<Action_lu_decomp<eigen3_interface<REAL_TYPE> > >(MIN_LU,MAX_LU,NB_POINT);\n  bench<Action_partial_lu<eigen3_interface<REAL_TYPE> > >(MIN_LU,MAX_LU,NB_POINT);\n\n//   bench<Action_hessenberg<eigen3_interface<REAL_TYPE> > >(MIN_LU,MAX_LU,NB_POINT);\n  bench<Action_tridiagonalization<eigen3_interface<REAL_TYPE> > >(MIN_LU,MAX_LU,NB_POINT);\n\n  return 0;\n}\n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/eigen3/main_linear.cpp",
    "content": "//=====================================================\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#include \"utilities.h\"\n#include \"eigen3_interface.hh\"\n#include \"bench.hh\"\n#include \"basic_actions.hh\"\n\nBTL_MAIN;\n\nint main()\n{\n\n  bench<Action_axpy<eigen3_interface<REAL_TYPE> > >(MIN_AXPY,MAX_AXPY,NB_POINT);\n  bench<Action_axpby<eigen3_interface<REAL_TYPE> > >(MIN_AXPY,MAX_AXPY,NB_POINT);\n  bench<Action_rot<eigen3_interface<REAL_TYPE> > >(MIN_AXPY,MAX_AXPY,NB_POINT);\n  \n  return 0;\n}\n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/eigen3/main_matmat.cpp",
    "content": "//=====================================================\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#include \"utilities.h\"\n#include \"eigen3_interface.hh\"\n#include \"bench.hh\"\n#include \"basic_actions.hh\"\n\nBTL_MAIN;\n\nint main()\n{\n  bench<Action_matrix_matrix_product<eigen3_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n//   bench<Action_ata_product<eigen3_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n  bench<Action_aat_product<eigen3_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n  bench<Action_trmm<eigen3_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n\n  return 0;\n}\n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/eigen3/main_vecmat.cpp",
    "content": "//=====================================================\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#include \"utilities.h\"\n#include \"eigen3_interface.hh\"\n#include \"bench.hh\"\n#include \"basic_actions.hh\"\n\nBTL_MAIN;\n\nint main()\n{\n  bench<Action_matrix_vector_product<eigen3_interface<REAL_TYPE> > >(MIN_MV,MAX_MV,NB_POINT);\n  bench<Action_atv_product<eigen3_interface<REAL_TYPE> > >(MIN_MV,MAX_MV,NB_POINT);\n  bench<Action_symv<eigen3_interface<REAL_TYPE> > >(MIN_MV,MAX_MV,NB_POINT);\n  bench<Action_syr2<eigen3_interface<REAL_TYPE> > >(MIN_MV,MAX_MV,NB_POINT);\n  bench<Action_ger<eigen3_interface<REAL_TYPE> > >(MIN_MV,MAX_MV,NB_POINT);\n\n  return 0;\n}\n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/gmm/CMakeLists.txt",
    "content": "\nfind_package(GMM)\nif (GMM_FOUND)\n  include_directories(${GMM_INCLUDES})\n  btl_add_bench(btl_gmm main.cpp)\nendif (GMM_FOUND)\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/gmm/gmm_LU_solve_interface.hh",
    "content": "//=====================================================\n// File   :  blitz_LU_solve_interface.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>        \n// Copyright (C) EDF R&D,  lun sep 30 14:23:31 CEST 2002\n//=====================================================\n// \n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n// \n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n// \n#ifndef BLITZ_LU_SOLVE_INTERFACE_HH\n#define BLITZ_LU_SOLVE_INTERFACE_HH\n\n#include \"blitz/array.h\"\n#include <vector>\n\nBZ_USING_NAMESPACE(blitz)\n\ntemplate<class real>\nclass blitz_LU_solve_interface : public blitz_interface<real>\n{\n\npublic :\n\n  typedef typename blitz_interface<real>::gene_matrix gene_matrix;\n  typedef typename blitz_interface<real>::gene_vector gene_vector;\n\n  typedef blitz::Array<int,1> Pivot_Vector;\n\n  inline static void new_Pivot_Vector(Pivot_Vector & pivot,int N)\n  {\n\n    pivot.resize(N);\n\n  }\n\n  inline static void free_Pivot_Vector(Pivot_Vector & pivot)\n  {\n    \n    return;\n\n  }\n\n\n  static inline real matrix_vector_product_sliced(const gene_matrix & A, gene_vector B, int row, int col_start, int col_end)\n  {\n    \n    real somme=0.;\n    \n    for (int j=col_start ; j<col_end+1 ; j++){\n\t\n\tsomme+=A(row,j)*B(j);\n\t\n    }\n\n    return somme;\n\n  }\n\n\n\n\n  static inline real matrix_matrix_product_sliced(gene_matrix & A, int row, int col_start, int col_end, gene_matrix & B, int row_shift, int col )\n  {\n    \n    real somme=0.;\n    \n    for (int j=col_start ; j<col_end+1 ; j++){\n\t\n\tsomme+=A(row,j)*B(j+row_shift,col);\n\t\n    }\n\n    return somme;\n\n  }\n\n  inline static void LU_factor(gene_matrix & LU, Pivot_Vector & pivot, int N)\n  {\n\n    ASSERT( LU.rows()==LU.cols() ) ;\n    int index_max = 0 ;\n    real big = 0. ;\n    real theSum = 0. ;\n    real dum = 0. ;\n    // Get the implicit scaling information :\n    gene_vector ImplicitScaling( N ) ;\n    for( int i=0; i<N; i++ ) {\n      big = 0. ;\n      for( int j=0; j<N; j++ ) {\n\tif( abs( LU( i, j ) )>=big ) big = abs( LU( i, j ) ) ;\n      }\n      if( big==0. ) {\n\tINFOS( \"blitz_LU_factor::Singular matrix\" ) ;\n\texit( 0 ) ;\n      }\n      ImplicitScaling( i ) = 1./big ;\n    }\n    // Loop over columns of Crout's method :\n    for( int j=0; j<N; j++ ) {\n      for( int i=0; i<j; i++ ) {\n\ttheSum = LU( i, j ) ;\n\ttheSum -= matrix_matrix_product_sliced(LU, i, 0, i-1, LU, 0, j) ;\n\t//\ttheSum -= sum( LU( i, Range( fromStart, i-1 ) )*LU( Range( fromStart, i-1 ), j ) ) ;\n\tLU( i, j ) = theSum ;\n      }\n      \n      // Search for the largest pivot element :\n      big = 0. ;\n      for( int i=j; i<N; i++ ) {\n\ttheSum = LU( i, j ) ;\n\ttheSum -= matrix_matrix_product_sliced(LU, i, 0, j-1, LU, 0, j) ;\n\t//\ttheSum -= sum( LU( i, Range( fromStart, j-1 ) )*LU( Range( fromStart, j-1 ), j ) ) ;\n\tLU( i, j ) = theSum ;\n\tif( (ImplicitScaling( i )*abs( theSum ))>=big ) {\n\t  dum = ImplicitScaling( i )*abs( theSum ) ;\n\t  big = dum ;\n\t  index_max = i ;\n\t}\n      }\n      // Interchanging rows and the scale factor :\n      if( j!=index_max ) {\n\tfor( int k=0; k<N; k++ ) {\n\t  dum = LU( index_max, k ) ;\n\t  LU( index_max, k ) = LU( j, k ) ;\n\t  LU( j, k ) = dum ;\n\t}\n\tImplicitScaling( index_max ) = ImplicitScaling( j ) ;\n      }\n      pivot( j ) = index_max ;\n      if ( LU( j, j )==0. ) LU( j, j ) = 1.e-20 ;\n      // Divide by the pivot element :\n      if( j<N ) {\n\tdum = 1./LU( j, j ) ;\n\tfor( int i=j+1; i<N; i++ ) LU( i, j ) *= dum ;\n      }\n    }\n\n  }\n\n  inline static void LU_solve(const gene_matrix & LU, const Pivot_Vector pivot, gene_vector &B, gene_vector X, int N)\n  {\n\n    // Pour conserver le meme header, on travaille sur X, copie du second-membre B\n    X = B.copy() ;\n    ASSERT( LU.rows()==LU.cols() ) ;\n    firstIndex indI ;\n    // Forward substitution :\n    int ii = 0 ;\n    real theSum = 0. ;\n    for( int i=0; i<N; i++ ) {\n      int ip = pivot( i ) ;\n      theSum = X( ip ) ;\n      //      theSum = B( ip ) ;\n      X( ip ) = X( i ) ;\n      //      B( ip ) = B( i ) ;\n      if( ii ) {\n\ttheSum -= matrix_vector_product_sliced(LU, X, i, ii-1, i-1) ;\n\t//\ttheSum -= sum( LU( i, Range( ii-1, i-1 ) )*X( Range( ii-1, i-1 ) ) ) ;\n\t//\ttheSum -= sum( LU( i, Range( ii-1, i-1 ) )*B( Range( ii-1, i-1 ) ) ) ;\n      } else if( theSum ) {\n\tii = i+1 ;\n      }\n      X( i ) = theSum ;\n      //      B( i ) = theSum ;\n    }\n    // Backsubstitution :\n    for( int i=N-1; i>=0; i-- ) {\n      theSum = X( i ) ;\n      //      theSum = B( i ) ;\n      theSum -= matrix_vector_product_sliced(LU, X, i, i+1, N) ;\n      //      theSum -= sum( LU( i, Range( i+1, toEnd ) )*X( Range( i+1, toEnd ) ) ) ;\n      //      theSum -= sum( LU( i, Range( i+1, toEnd ) )*B( Range( i+1, toEnd ) ) ) ;\n      // Store a component of the solution vector :\n      X( i ) = theSum/LU( i, i ) ;\n      //      B( i ) = theSum/LU( i, i ) ;\n    }\n\n  }\n\n};\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/gmm/gmm_interface.hh",
    "content": "//=====================================================\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef GMM_INTERFACE_HH\n#define GMM_INTERFACE_HH\n\n#include <gmm/gmm.h>\n#include <vector>\n\nusing namespace gmm;\n\ntemplate<class real>\nclass gmm_interface {\n\npublic :\n\n  typedef real real_type ;\n\n  typedef std::vector<real>  stl_vector;\n  typedef std::vector<stl_vector > stl_matrix;\n\n  typedef gmm::dense_matrix<real> gene_matrix;\n  typedef stl_vector gene_vector;\n\n  static inline std::string name( void )\n  {\n    return \"gmm\";\n  }\n\n  static void free_matrix(gene_matrix & A, int N){\n    return ;\n  }\n\n  static void free_vector(gene_vector & B){\n    return ;\n  }\n\n  static inline void matrix_from_stl(gene_matrix & A, stl_matrix & A_stl){\n    A.resize(A_stl[0].size(),A_stl.size());\n\n    for (int j=0; j<A_stl.size() ; j++){\n      for (int i=0; i<A_stl[j].size() ; i++){\n        A(i,j) = A_stl[j][i];\n      }\n    }\n  }\n\n  static inline void vector_from_stl(gene_vector & B, stl_vector & B_stl){\n    B = B_stl;\n  }\n\n  static inline void vector_to_stl(gene_vector & B, stl_vector & B_stl){\n    B_stl = B;\n  }\n\n  static inline void matrix_to_stl(gene_matrix & A, stl_matrix & A_stl){\n    int N=A_stl.size();\n\n    for (int j=0;j<N;j++){\n      A_stl[j].resize(N);\n      for (int i=0;i<N;i++){\n        A_stl[j][i] = A(i,j);\n      }\n    }\n  }\n\n  static inline void matrix_matrix_product(const gene_matrix & A, const gene_matrix & B, gene_matrix & X, int N){\n    gmm::mult(A,B, X);\n  }\n\n  static inline void transposed_matrix_matrix_product(const gene_matrix & A, const gene_matrix & B, gene_matrix & X, int N){\n    gmm::mult(gmm::transposed(A),gmm::transposed(B), X);\n  }\n\n  static inline void ata_product(const gene_matrix & A, gene_matrix & X, int N){\n    gmm::mult(gmm::transposed(A),A, X);\n  }\n\n  static inline void aat_product(const gene_matrix & A, gene_matrix & X, int N){\n    gmm::mult(A,gmm::transposed(A), X);\n  }\n\n  static inline void matrix_vector_product(gene_matrix & A, gene_vector & B, gene_vector & X, int N){\n    gmm::mult(A,B,X);\n  }\n\n  static inline void atv_product(gene_matrix & A, gene_vector & B, gene_vector & X, int N){\n    gmm::mult(gmm::transposed(A),B,X);\n  }\n\n  static inline void axpy(const real coef, const gene_vector & X, gene_vector & Y, int N){\n    gmm::add(gmm::scaled(X,coef), Y);\n  }\n\n  static inline void axpby(real a, const gene_vector & X, real b, gene_vector & Y, int N){\n    gmm::add(gmm::scaled(X,a), gmm::scaled(Y,b), Y);\n  }\n\n  static inline void copy_matrix(const gene_matrix & source, gene_matrix & cible, int N){\n    gmm::copy(source,cible);\n  }\n\n  static inline void copy_vector(const gene_vector & source, gene_vector & cible, int N){\n    gmm::copy(source,cible);\n  }\n\n  static inline void trisolve_lower(const gene_matrix & L, const gene_vector& B, gene_vector & X, int N){\n    gmm::copy(B,X);\n    gmm::lower_tri_solve(L, X, false);\n  }\n\n  static inline void partial_lu_decomp(const gene_matrix & X, gene_matrix & R, int N){\n    gmm::copy(X,R);\n    std::vector<int> ipvt(N);\n    gmm::lu_factor(R, ipvt);\n  }\n\n  static inline void hessenberg(const gene_matrix & X, gene_matrix & R, int N){\n    gmm::copy(X,R);\n    gmm::Hessenberg_reduction(R,X,false);\n  }\n\n  static inline void tridiagonalization(const gene_matrix & X, gene_matrix & R, int N){\n    gmm::copy(X,R);\n    gmm::Householder_tridiagonalization(R,X,false);\n  }\n\n};\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/gmm/main.cpp",
    "content": "//=====================================================\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#include \"utilities.h\"\n#include \"gmm_interface.hh\"\n#include \"bench.hh\"\n#include \"basic_actions.hh\"\n#include \"action_hessenberg.hh\"\n#include \"action_partial_lu.hh\"\n\nBTL_MAIN;\n\nint main()\n{\n\n  bench<Action_axpy<gmm_interface<REAL_TYPE> > >(MIN_AXPY,MAX_AXPY,NB_POINT);\n  bench<Action_axpby<gmm_interface<REAL_TYPE> > >(MIN_AXPY,MAX_AXPY,NB_POINT);\n\n  bench<Action_matrix_vector_product<gmm_interface<REAL_TYPE> > >(MIN_MV,MAX_MV,NB_POINT);\n  bench<Action_atv_product<gmm_interface<REAL_TYPE> > >(MIN_MV,MAX_MV,NB_POINT);\n\n  bench<Action_matrix_matrix_product<gmm_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n//   bench<Action_ata_product<gmm_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n//   bench<Action_aat_product<gmm_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n\n  bench<Action_trisolve<gmm_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n  //bench<Action_lu_solve<blitz_LU_solve_interface<REAL_TYPE> > >(MIN_LU,MAX_LU,NB_POINT);\n\n  bench<Action_partial_lu<gmm_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n  \n  bench<Action_hessenberg<gmm_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n  bench<Action_tridiagonalization<gmm_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n\n  return 0;\n}\n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/mtl4/.kdbgrc.main",
    "content": "[General]\nDebuggerCmdStr=\nDriverName=GDB\nFileVersion=1\nOptionsSelected=\nProgramArgs=\nTTYLevel=7\nWorkingDirectory=\n\n[Memory]\nColumnWidths=80,0\nNumExprs=0\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/mtl4/CMakeLists.txt",
    "content": "\nfind_package(MTL4)\nif (MTL4_FOUND)\n  include_directories(${MTL4_INCLUDE_DIR})\n  btl_add_bench(btl_mtl4 main.cpp)\nendif (MTL4_FOUND)\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/mtl4/main.cpp",
    "content": "//=====================================================\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#include \"utilities.h\"\n#include \"mtl4_interface.hh\"\n#include \"bench.hh\"\n#include \"basic_actions.hh\"\n#include \"action_cholesky.hh\"\n// #include \"action_lu_decomp.hh\"\n\nBTL_MAIN;\n\nint main()\n{\n\n  bench<Action_axpy<mtl4_interface<REAL_TYPE> > >(MIN_AXPY,MAX_AXPY,NB_POINT);\n  bench<Action_axpby<mtl4_interface<REAL_TYPE> > >(MIN_AXPY,MAX_AXPY,NB_POINT);\n\n  bench<Action_matrix_vector_product<mtl4_interface<REAL_TYPE> > >(MIN_MV,MAX_MV,NB_POINT);\n  bench<Action_atv_product<mtl4_interface<REAL_TYPE> > >(MIN_MV,MAX_MV,NB_POINT);\n  bench<Action_matrix_matrix_product<mtl4_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n//   bench<Action_ata_product<mtl4_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n//   bench<Action_aat_product<mtl4_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n\n  bench<Action_trisolve<mtl4_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n//   bench<Action_cholesky<mtl4_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n//   bench<Action_lu_decomp<mtl4_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n\n  return 0;\n}\n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/mtl4/mtl4_LU_solve_interface.hh",
    "content": "//=====================================================\n// File   :  blitz_LU_solve_interface.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>        \n// Copyright (C) EDF R&D,  lun sep 30 14:23:31 CEST 2002\n//=====================================================\n// \n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n// \n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n// \n#ifndef BLITZ_LU_SOLVE_INTERFACE_HH\n#define BLITZ_LU_SOLVE_INTERFACE_HH\n\n#include \"blitz/array.h\"\n#include <vector>\n\nBZ_USING_NAMESPACE(blitz)\n\ntemplate<class real>\nclass blitz_LU_solve_interface : public blitz_interface<real>\n{\n\npublic :\n\n  typedef typename blitz_interface<real>::gene_matrix gene_matrix;\n  typedef typename blitz_interface<real>::gene_vector gene_vector;\n\n  typedef blitz::Array<int,1> Pivot_Vector;\n\n  inline static void new_Pivot_Vector(Pivot_Vector & pivot,int N)\n  {\n\n    pivot.resize(N);\n\n  }\n\n  inline static void free_Pivot_Vector(Pivot_Vector & pivot)\n  {\n    \n    return;\n\n  }\n\n\n  static inline real matrix_vector_product_sliced(const gene_matrix & A, gene_vector B, int row, int col_start, int col_end)\n  {\n    \n    real somme=0.;\n    \n    for (int j=col_start ; j<col_end+1 ; j++){\n\t\n\tsomme+=A(row,j)*B(j);\n\t\n    }\n\n    return somme;\n\n  }\n\n\n\n\n  static inline real matrix_matrix_product_sliced(gene_matrix & A, int row, int col_start, int col_end, gene_matrix & B, int row_shift, int col )\n  {\n    \n    real somme=0.;\n    \n    for (int j=col_start ; j<col_end+1 ; j++){\n\t\n\tsomme+=A(row,j)*B(j+row_shift,col);\n\t\n    }\n\n    return somme;\n\n  }\n\n  inline static void LU_factor(gene_matrix & LU, Pivot_Vector & pivot, int N)\n  {\n\n    ASSERT( LU.rows()==LU.cols() ) ;\n    int index_max = 0 ;\n    real big = 0. ;\n    real theSum = 0. ;\n    real dum = 0. ;\n    // Get the implicit scaling information :\n    gene_vector ImplicitScaling( N ) ;\n    for( int i=0; i<N; i++ ) {\n      big = 0. ;\n      for( int j=0; j<N; j++ ) {\n\tif( abs( LU( i, j ) )>=big ) big = abs( LU( i, j ) ) ;\n      }\n      if( big==0. ) {\n\tINFOS( \"blitz_LU_factor::Singular matrix\" ) ;\n\texit( 0 ) ;\n      }\n      ImplicitScaling( i ) = 1./big ;\n    }\n    // Loop over columns of Crout's method :\n    for( int j=0; j<N; j++ ) {\n      for( int i=0; i<j; i++ ) {\n\ttheSum = LU( i, j ) ;\n\ttheSum -= matrix_matrix_product_sliced(LU, i, 0, i-1, LU, 0, j) ;\n\t//\ttheSum -= sum( LU( i, Range( fromStart, i-1 ) )*LU( Range( fromStart, i-1 ), j ) ) ;\n\tLU( i, j ) = theSum ;\n      }\n      \n      // Search for the largest pivot element :\n      big = 0. ;\n      for( int i=j; i<N; i++ ) {\n\ttheSum = LU( i, j ) ;\n\ttheSum -= matrix_matrix_product_sliced(LU, i, 0, j-1, LU, 0, j) ;\n\t//\ttheSum -= sum( LU( i, Range( fromStart, j-1 ) )*LU( Range( fromStart, j-1 ), j ) ) ;\n\tLU( i, j ) = theSum ;\n\tif( (ImplicitScaling( i )*abs( theSum ))>=big ) {\n\t  dum = ImplicitScaling( i )*abs( theSum ) ;\n\t  big = dum ;\n\t  index_max = i ;\n\t}\n      }\n      // Interchanging rows and the scale factor :\n      if( j!=index_max ) {\n\tfor( int k=0; k<N; k++ ) {\n\t  dum = LU( index_max, k ) ;\n\t  LU( index_max, k ) = LU( j, k ) ;\n\t  LU( j, k ) = dum ;\n\t}\n\tImplicitScaling( index_max ) = ImplicitScaling( j ) ;\n      }\n      pivot( j ) = index_max ;\n      if ( LU( j, j )==0. ) LU( j, j ) = 1.e-20 ;\n      // Divide by the pivot element :\n      if( j<N ) {\n\tdum = 1./LU( j, j ) ;\n\tfor( int i=j+1; i<N; i++ ) LU( i, j ) *= dum ;\n      }\n    }\n\n  }\n\n  inline static void LU_solve(const gene_matrix & LU, const Pivot_Vector pivot, gene_vector &B, gene_vector X, int N)\n  {\n\n    // Pour conserver le meme header, on travaille sur X, copie du second-membre B\n    X = B.copy() ;\n    ASSERT( LU.rows()==LU.cols() ) ;\n    firstIndex indI ;\n    // Forward substitution :\n    int ii = 0 ;\n    real theSum = 0. ;\n    for( int i=0; i<N; i++ ) {\n      int ip = pivot( i ) ;\n      theSum = X( ip ) ;\n      //      theSum = B( ip ) ;\n      X( ip ) = X( i ) ;\n      //      B( ip ) = B( i ) ;\n      if( ii ) {\n\ttheSum -= matrix_vector_product_sliced(LU, X, i, ii-1, i-1) ;\n\t//\ttheSum -= sum( LU( i, Range( ii-1, i-1 ) )*X( Range( ii-1, i-1 ) ) ) ;\n\t//\ttheSum -= sum( LU( i, Range( ii-1, i-1 ) )*B( Range( ii-1, i-1 ) ) ) ;\n      } else if( theSum ) {\n\tii = i+1 ;\n      }\n      X( i ) = theSum ;\n      //      B( i ) = theSum ;\n    }\n    // Backsubstitution :\n    for( int i=N-1; i>=0; i-- ) {\n      theSum = X( i ) ;\n      //      theSum = B( i ) ;\n      theSum -= matrix_vector_product_sliced(LU, X, i, i+1, N) ;\n      //      theSum -= sum( LU( i, Range( i+1, toEnd ) )*X( Range( i+1, toEnd ) ) ) ;\n      //      theSum -= sum( LU( i, Range( i+1, toEnd ) )*B( Range( i+1, toEnd ) ) ) ;\n      // Store a component of the solution vector :\n      X( i ) = theSum/LU( i, i ) ;\n      //      B( i ) = theSum/LU( i, i ) ;\n    }\n\n  }\n\n};\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/mtl4/mtl4_interface.hh",
    "content": "//=====================================================\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef MTL4_INTERFACE_HH\n#define MTL4_INTERFACE_HH\n\n#include <boost/numeric/mtl/mtl.hpp>\n#include <boost/numeric/mtl/utility/range_generator.hpp>\n// #include <boost/numeric/mtl/operation/cholesky.hpp>\n#include <vector>\n\nusing namespace mtl;\n\ntemplate<class real>\nclass mtl4_interface {\n\npublic :\n\n  typedef real real_type ;\n\n  typedef std::vector<real>  stl_vector;\n  typedef std::vector<stl_vector > stl_matrix;\n\n  typedef mtl::dense2D<real, mtl::matrix::parameters<mtl::tag::col_major> > gene_matrix;\n  typedef mtl::dense_vector<real>  gene_vector;\n\n  static inline std::string name() { return \"mtl4\"; }\n\n  static void free_matrix(gene_matrix & A, int N){\n    return ;\n  }\n\n  static void free_vector(gene_vector & B){\n    return ;\n  }\n\n  static inline void matrix_from_stl(gene_matrix & A, stl_matrix & A_stl){\n    A.change_dim(A_stl[0].size(), A_stl.size());\n\n    for (int j=0; j<A_stl.size() ; j++){\n      for (int i=0; i<A_stl[j].size() ; i++){\n        A(i,j) = A_stl[j][i];\n      }\n    }\n  }\n\n  static inline void vector_from_stl(gene_vector & B, stl_vector & B_stl){\n    B.change_dim(B_stl.size());\n    for (int i=0; i<B_stl.size() ; i++){\n      B[i] = B_stl[i];\n    }\n  }\n\n  static inline void vector_to_stl(gene_vector & B, stl_vector & B_stl){\n    for (int i=0; i<B_stl.size() ; i++){\n      B_stl[i] = B[i];\n    }\n  }\n\n  static inline void matrix_to_stl(gene_matrix & A, stl_matrix & A_stl){\n    int N=A_stl.size();\n    for (int j=0;j<N;j++){\n      A_stl[j].resize(N);\n      for (int i=0;i<N;i++){\n        A_stl[j][i] = A(i,j);\n      }\n    }\n  }\n\n  static inline void matrix_matrix_product(const gene_matrix & A, const gene_matrix & B, gene_matrix & X, int N){\n    X = (A*B);\n//     morton_dense<double, doppled_64_row_mask> C(N,N);\n//     C = B;\n//     X = (A*C);\n  }\n\n  static inline void transposed_matrix_matrix_product(const gene_matrix & A, const gene_matrix & B, gene_matrix & X, int N){\n    X = (trans(A)*trans(B));\n  }\n\n//   static inline void ata_product(const gene_matrix & A, gene_matrix & X, int N){\n//     X = (trans(A)*A);\n//   }\n\n  static inline void aat_product(const gene_matrix & A, gene_matrix & X, int N){\n    X = (A*trans(A));\n  }\n\n  static inline void matrix_vector_product(gene_matrix & A, gene_vector & B, gene_vector & X, int N){\n    X = (A*B);\n  }\n\n  static inline void atv_product(gene_matrix & A, gene_vector & B, gene_vector & X, int N){\n    X = (trans(A)*B);\n  }\n\n  static inline void axpy(const real coef, const gene_vector & X, gene_vector & Y, int N){\n    Y += coef * X;\n  }\n\n  static inline void axpby(real a, const gene_vector & X, real b, gene_vector & Y, int N){\n    Y = a*X + b*Y;\n  }\n\n//   static inline void cholesky(const gene_matrix & X, gene_matrix & C, int N){\n//     C = X;\n//     recursive_cholesky(C);\n//   }\n\n//   static inline void lu_decomp(const gene_matrix & X, gene_matrix & R, int N){\n//     R = X;\n//     std::vector<int> ipvt(N);\n//     lu_factor(R, ipvt);\n//   }\n\n  static inline void trisolve_lower(const gene_matrix & L, const gene_vector& B, gene_vector & X, int N){\n    X = lower_trisolve(L, B);\n  }\n\n  static inline void copy_matrix(const gene_matrix & source, gene_matrix & cible, int N){\n    cible = source;\n  }\n\n  static inline void copy_vector(const gene_vector & source, gene_vector & cible, int N){\n    cible = source;\n  }\n\n};\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/tensors/CMakeLists.txt",
    "content": "\n\nif((NOT TENSOR_INCLUDE_DIR) AND Eigen_SOURCE_DIR)\n  # unless TENSOR_INCLUDE_DIR is defined, let's use current Eigen version\n  set(TENSOR_INCLUDE_DIR ${Eigen_SOURCE_DIR})\n  set(TENSOR_FOUND TRUE)\nelse()\n  find_package(Tensor)\nendif()\n\nif (TENSOR_FOUND)\n\n  include_directories(${TENSOR_INCLUDE_DIR})\n  btl_add_bench(btl_tensor_linear main_linear.cpp)\n  btl_add_bench(btl_tensor_vecmat main_vecmat.cpp)\n  btl_add_bench(btl_tensor_matmat main_matmat.cpp)\n\n  btl_add_target_property(btl_tensor_linear COMPILE_FLAGS \"-fno-exceptions -DBTL_PREFIX=tensor\")\n  btl_add_target_property(btl_tensor_vecmat COMPILE_FLAGS \"-fno-exceptions -DBTL_PREFIX=tensor\")\n  btl_add_target_property(btl_tensor_matmat COMPILE_FLAGS \"-fno-exceptions -DBTL_PREFIX=tensor\")\n\n  option(BTL_BENCH_NOGCCVEC \"also bench Eigen explicit vec without GCC's auto vec\" OFF)\n  if(CMAKE_COMPILER_IS_GNUCXX AND BTL_BENCH_NOGCCVEC)\n    btl_add_bench(btl_tensor_nogccvec_linear main_linear.cpp)\n    btl_add_bench(btl_tensor_nogccvec_vecmat main_vecmat.cpp)\n    btl_add_bench(btl_tensor_nogccvec_matmat main_matmat.cpp)\n\n    btl_add_target_property(btl_tensor_nogccvec_linear COMPILE_FLAGS \"-fno-exceptions -fno-tree-vectorize -DBTL_PREFIX=tensor_nogccvec\")\n    btl_add_target_property(btl_tensor_nogccvec_vecmat COMPILE_FLAGS \"-fno-exceptions -fno-tree-vectorize -DBTL_PREFIX=tensor_nogccvec\")\n    btl_add_target_property(btl_tensor_nogccvec_matmat COMPILE_FLAGS \"-fno-exceptions -fno-tree-vectorize -DBTL_PREFIX=tensor_nogccvec\")\n  endif()\n\n\n  if(NOT BTL_NOVEC)\n    btl_add_bench(btl_tensor_novec_linear main_linear.cpp OFF)\n    btl_add_bench(btl_tensor_novec_vecmat main_vecmat.cpp OFF)\n    btl_add_bench(btl_tensor_novec_matmat main_matmat.cpp OFF)\n    btl_add_target_property(btl_tensor_novec_linear COMPILE_FLAGS \"-fno-exceptions -DEIGEN_DONT_VECTORIZE -DBTL_PREFIX=tensor_novec\")\n    btl_add_target_property(btl_tensor_novec_vecmat COMPILE_FLAGS \"-fno-exceptions -DEIGEN_DONT_VECTORIZE -DBTL_PREFIX=tensor_novec\")\n    btl_add_target_property(btl_tensor_novec_matmat COMPILE_FLAGS \"-fno-exceptions -DEIGEN_DONT_VECTORIZE -DBTL_PREFIX=tensor_novec\")\n\n  endif(NOT BTL_NOVEC)\n\nendif (TENSOR_FOUND)\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/tensors/main_linear.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"utilities.h\"\n#include \"tensor_interface.hh\"\n#include \"bench.hh\"\n#include \"basic_actions.hh\"\n\nBTL_MAIN;\n\nint main()\n{\n  bench<Action_axpy<tensor_interface<REAL_TYPE> > >(MIN_AXPY,MAX_AXPY,NB_POINT);\n  bench<Action_axpby<tensor_interface<REAL_TYPE> > >(MIN_AXPY,MAX_AXPY,NB_POINT);\n\n  return 0;\n}\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/tensors/main_matmat.cpp",
    "content": "//=====================================================\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//=====================================================\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n//\n#include \"utilities.h\"\n#include \"tensor_interface.hh\"\n#include \"bench.hh\"\n#include \"basic_actions.hh\"\n\nBTL_MAIN;\n\nint main()\n{\n  bench<Action_matrix_matrix_product<tensor_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n\n  return 0;\n}\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/tensors/main_vecmat.cpp",
    "content": "//=====================================================\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//=====================================================\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n//\n#include \"utilities.h\"\n#include \"tensor_interface.hh\"\n#include \"bench.hh\"\n#include \"basic_actions.hh\"\n\nBTL_MAIN;\n\nint main()\n{\n  bench<Action_matrix_vector_product<tensor_interface<REAL_TYPE> > >(MIN_MV,MAX_MV,NB_POINT);\n\n  return 0;\n}\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/tensors/tensor_interface.hh",
    "content": "//=====================================================\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//=====================================================\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n//\n#ifndef TENSOR_INTERFACE_HH\n#define TENSOR_INTERFACE_HH\n\n#include <unsupported/Eigen/CXX11/Tensor>\n#include <vector>\n#include \"btl.hh\"\n\nusing namespace Eigen;\n\ntemplate<class real>\nclass tensor_interface\n{\npublic :\n  typedef real real_type;\n  typedef typename Eigen::Tensor<real,2>::Index Index;\n\n  typedef std::vector<real> stl_vector;\n  typedef std::vector<stl_vector> stl_matrix;\n\n  typedef Eigen::Tensor<real,2> gene_matrix;\n  typedef Eigen::Tensor<real,1> gene_vector;\n\n\n  static inline std::string name( void )\n  {\n    return EIGEN_MAKESTRING(BTL_PREFIX);\n  }\n\n  static void free_matrix(gene_matrix & /*A*/, int /*N*/) {}\n\n  static void free_vector(gene_vector & /*B*/) {}\n\n  static BTL_DONT_INLINE void matrix_from_stl(gene_matrix & A, stl_matrix & A_stl){\n    A.resize(Eigen::array<Index,2>(A_stl[0].size(), A_stl.size()));\n\n    for (unsigned int j=0; j<A_stl.size() ; j++){\n      for (unsigned int i=0; i<A_stl[j].size() ; i++){\n        A.coeffRef(Eigen::array<Index,2>(i,j)) = A_stl[j][i];\n      }\n    }\n  }\n\n  static BTL_DONT_INLINE  void vector_from_stl(gene_vector & B, stl_vector & B_stl){\n    B.resize(B_stl.size());\n\n    for (unsigned int i=0; i<B_stl.size() ; i++){\n      B.coeffRef(i) = B_stl[i];\n    }\n  }\n\n  static BTL_DONT_INLINE  void vector_to_stl(gene_vector & B, stl_vector & B_stl){\n    for (unsigned int i=0; i<B_stl.size() ; i++){\n      B_stl[i] = B.coeff(i);\n    }\n  }\n\n  static BTL_DONT_INLINE  void matrix_to_stl(gene_matrix & A, stl_matrix & A_stl){\n    int  N=A_stl.size();\n\n    for (int j=0;j<N;j++){\n      A_stl[j].resize(N);\n      for (int i=0;i<N;i++){\n        A_stl[j][i] = A.coeff(Eigen::array<Index,2>(i,j));\n      }\n    }\n  }\n\n  static inline void matrix_matrix_product(const gene_matrix & A, const gene_matrix & B, gene_matrix & X, int  /*N*/){\n    typedef typename Eigen::Tensor<real_type, 1>::DimensionPair DimPair;\n    const Eigen::array<DimPair, 1> dims(DimPair(1, 0));\n    X/*.noalias()*/ = A.contract(B, dims);\n  }\n\n  static inline void matrix_vector_product(const gene_matrix & A, const gene_vector & B, gene_vector & X, int  /*N*/){\n    typedef typename Eigen::Tensor<real_type, 1>::DimensionPair DimPair;\n    const Eigen::array<DimPair, 1> dims(DimPair(1, 0));\n    X/*.noalias()*/ = A.contract(B, dims);\n  }\n\n  static inline void axpy(real coef, const gene_vector & X, gene_vector & Y, int  /*N*/){\n    Y += X.constant(coef) * X;\n  }\n\n  static inline void axpby(real a, const gene_vector & X, real b, gene_vector & Y, int  /*N*/){\n    Y = X.constant(a)*X + Y.constant(b)*Y;\n  }\n\n  static EIGEN_DONT_INLINE void copy_matrix(const gene_matrix & source, gene_matrix & cible, int  /*N*/){\n    cible = source;\n  }\n\n  static EIGEN_DONT_INLINE void copy_vector(const gene_vector & source, gene_vector & cible, int  /*N*/){\n    cible = source;\n  }\n};\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/tvmet/CMakeLists.txt",
    "content": "\nfind_package(Tvmet)\nif (TVMET_FOUND)\n  include_directories(${TVMET_INCLUDE_DIR})\n  btl_add_bench(btl_tvmet main.cpp OFF)\nendif (TVMET_FOUND)\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/tvmet/main.cpp",
    "content": "//=====================================================\n// File   :  main.cpp\n// Author :  L. Plagne <laurent.plagne@edf.fr)>\n// Copyright (C) EDF R&D,  lun sep 30 14:23:30 CEST 2002\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#include \"utilities.h\"\n#include \"tvmet_interface.hh\"\n#include \"static/bench_static.hh\"\n#include \"action_matrix_vector_product.hh\"\n#include \"action_matrix_matrix_product.hh\"\n#include \"action_atv_product.hh\"\n#include \"action_axpy.hh\"\n\nBTL_MAIN;\n\nint main()\n{\n  bench_static<Action_axpy,tvmet_interface>();\n  bench_static<Action_matrix_matrix_product,tvmet_interface>();\n  bench_static<Action_matrix_vector_product,tvmet_interface>();\n  bench_static<Action_atv_product,tvmet_interface>();\n\n  return 0;\n}\n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/tvmet/tvmet_interface.hh",
    "content": "//=====================================================\n// File   :  tvmet_interface.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>\n// Copyright (C) EDF R&D,  lun sep 30 14:23:30 CEST 2002\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef TVMET_INTERFACE_HH\n#define TVMET_INTERFACE_HH\n\n#include <tvmet/tvmet.h>\n#include <tvmet/Vector.h>\n#include <tvmet/Matrix.h>\n\n#include <vector>\n\nusing namespace tvmet;\n\ntemplate<class real, int SIZE>\nclass tvmet_interface{\n\npublic :\n\n  typedef real real_type ;\n\n  typedef std::vector<real>  stl_vector;\n  typedef std::vector<stl_vector > stl_matrix;\n\n  typedef Vector<real,SIZE> gene_vector;\n  typedef Matrix<real,SIZE,SIZE> gene_matrix;\n\n  static inline std::string name() { return \"tiny_tvmet\"; }\n\n  static void free_matrix(gene_matrix & A, int N){}\n\n  static void free_vector(gene_vector & B){}\n\n  static inline void matrix_from_stl(gene_matrix & A, stl_matrix & A_stl){\n    for (int j=0; j<A_stl.size() ; j++)\n      for (int i=0; i<A_stl[j].size() ; i++)\n        A(i,j) = A_stl[j][i];\n  }\n\n  static inline void vector_from_stl(gene_vector & B, stl_vector & B_stl){\n    for (int i=0; i<B_stl.size() ; i++)\n      B[i]=B_stl[i];\n  }\n\n  static inline void vector_to_stl(gene_vector & B, stl_vector & B_stl){\n    for (int i=0; i<B_stl.size() ; i++){\n      B_stl[i]=B[i];\n    }\n  }\n\n  static inline void matrix_to_stl(gene_matrix & A, stl_matrix & A_stl){\n    int N = A_stl.size();\n    for (int j=0;j<N;j++){\n      A_stl[j].resize(N);\n      for (int i=0;i<N;i++)\n        A_stl[j][i] = A(i,j);\n    }\n  }\n\n\n  static inline void copy_matrix(const gene_matrix & source, gene_matrix & cible, int N){\n    cible = source;\n  }\n\n  static inline void copy_vector(const gene_vector & source, gene_vector & cible, int N){\n    cible = source;\n  }\n\n  static inline void matrix_matrix_product(const gene_matrix & A, const gene_matrix & B, gene_matrix & X, int N){\n    X = prod(A,B);\n  }\n\n  static inline void matrix_vector_product(gene_matrix & A, gene_vector & B, gene_vector & X, int N){\n    X = prod(A,B);\n  }\n\n  static inline void atv_product(gene_matrix & A, gene_vector & B, gene_vector & X, int N){\n    X = prod(trans(A),B);\n  }\n\n  static inline void axpy(const real coef, const gene_vector & X, gene_vector & Y, int N){\n    Y+=coef*X;\n  }\n\n};\n\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/ublas/CMakeLists.txt",
    "content": "\nfind_package(Boost)\nif (Boost_FOUND)\n  include_directories(${Boost_INCLUDE_DIRS})\n  include_directories(${Boost_INCLUDES})\n  btl_add_bench(btl_ublas main.cpp)\nendif (Boost_FOUND)\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/ublas/main.cpp",
    "content": "//=====================================================\n// File   :  main.cpp\n// Author :  L. Plagne <laurent.plagne@edf.fr)>\n// Copyright (C) EDF R&D,  lun sep 30 14:23:27 CEST 2002\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#include \"utilities.h\"\n#include \"ublas_interface.hh\"\n#include \"bench.hh\"\n#include \"basic_actions.hh\"\n\nBTL_MAIN;\n\nint main()\n{\n  bench<Action_axpy<ublas_interface<REAL_TYPE> > >(MIN_AXPY,MAX_AXPY,NB_POINT);\n  bench<Action_axpby<ublas_interface<REAL_TYPE> > >(MIN_AXPY,MAX_AXPY,NB_POINT);\n\n  bench<Action_matrix_vector_product<ublas_interface<REAL_TYPE> > >(MIN_MV,MAX_MV,NB_POINT);\n  bench<Action_atv_product<ublas_interface<REAL_TYPE> > >(MIN_MV,MAX_MV,NB_POINT);\n\n  bench<Action_matrix_matrix_product<ublas_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n//   bench<Action_ata_product<ublas_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n//   bench<Action_aat_product<ublas_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n\n  bench<Action_trisolve<ublas_interface<REAL_TYPE> > >(MIN_MM,MAX_MM,NB_POINT);\n\n  return 0;\n}\n\n\n"
  },
  {
    "path": "include/eigen3/bench/btl/libs/ublas/ublas_interface.hh",
    "content": "//=====================================================\n// File   :  ublas_interface.hh\n// Author :  L. Plagne <laurent.plagne@edf.fr)>\n// Copyright (C) EDF R&D,  lun sep 30 14:23:27 CEST 2002\n//=====================================================\n//\n// This program is free software; you can redistribute it and/or\n// modify it under the terms of the GNU General Public License\n// as published by the Free Software Foundation; either version 2\n// of the License, or (at your option) any later version.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU General Public License for more details.\n// You should have received a copy of the GNU General Public License\n// along with this program; if not, write to the Free Software\n// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.\n//\n#ifndef UBLAS_INTERFACE_HH\n#define UBLAS_INTERFACE_HH\n\n#include <boost/numeric/ublas/vector.hpp>\n#include <boost/numeric/ublas/matrix.hpp>\n#include <boost/numeric/ublas/io.hpp>\n#include <boost/numeric/ublas/triangular.hpp>\n\nusing namespace boost::numeric;\n\ntemplate <class real>\nclass ublas_interface{\n\npublic :\n\n  typedef real real_type ;\n\n  typedef std::vector<real> stl_vector;\n  typedef std::vector<stl_vector> stl_matrix;\n\n  typedef typename boost::numeric::ublas::matrix<real,boost::numeric::ublas::column_major> gene_matrix;\n  typedef typename boost::numeric::ublas::vector<real> gene_vector;\n\n  static inline std::string name( void ) { return \"ublas\"; }\n\n  static void free_matrix(gene_matrix & A, int N) {}\n\n  static void free_vector(gene_vector & B) {}\n\n  static inline void matrix_from_stl(gene_matrix & A, stl_matrix & A_stl){\n    A.resize(A_stl.size(),A_stl[0].size());\n    for (int j=0; j<A_stl.size() ; j++)\n      for (int i=0; i<A_stl[j].size() ; i++)\n        A(i,j)=A_stl[j][i];\n  }\n\n  static inline void vector_from_stl(gene_vector & B, stl_vector & B_stl){\n    B.resize(B_stl.size());\n    for (int i=0; i<B_stl.size() ; i++)\n      B(i)=B_stl[i];\n  }\n\n  static inline void vector_to_stl(gene_vector & B, stl_vector & B_stl){\n    for (int i=0; i<B_stl.size() ; i++)\n      B_stl[i]=B(i);\n  }\n\n  static inline void matrix_to_stl(gene_matrix & A, stl_matrix & A_stl){\n    int N=A_stl.size();\n    for (int j=0;j<N;j++)\n    {\n      A_stl[j].resize(N);\n      for (int i=0;i<N;i++)\n        A_stl[j][i]=A(i,j);\n    }\n  }\n\n  static inline void copy_vector(const gene_vector & source, gene_vector & cible, int N){\n    for (int i=0;i<N;i++){\n      cible(i) = source(i);\n    }\n  }\n\n  static inline void copy_matrix(const gene_matrix & source, gene_matrix & cible, int N){\n    for (int i=0;i<N;i++){\n      for (int j=0;j<N;j++){\n        cible(i,j) = source(i,j);\n      }\n    }\n  }\n\n  static inline void matrix_vector_product_slow(gene_matrix & A, gene_vector & B, gene_vector & X, int N){\n    X =  prod(A,B);\n  }\n\n  static inline void matrix_matrix_product_slow(gene_matrix & A, gene_matrix & B, gene_matrix & X, int N){\n    X =  prod(A,B);\n  }\n\n  static inline void axpy_slow(const real coef, const gene_vector & X, gene_vector & Y, int N){\n    Y+=coef*X;\n  }\n\n  // alias free assignements\n\n  static inline void matrix_vector_product(gene_matrix & A, gene_vector & B, gene_vector & X, int N){\n    X.assign(prod(A,B));\n  }\n\n  static inline void atv_product(gene_matrix & A, gene_vector & B, gene_vector & X, int N){\n    X.assign(prod(trans(A),B));\n  }\n\n  static inline void matrix_matrix_product(gene_matrix & A, gene_matrix & B, gene_matrix & X, int N){\n    X.assign(prod(A,B));\n  }\n\n  static inline void axpy(const real coef, const gene_vector & X, gene_vector & Y, int N){\n    Y.plus_assign(coef*X);\n  }\n\n  static inline void axpby(real a, const gene_vector & X, real b, gene_vector & Y, int N){\n    Y = a*X + b*Y;\n  }\n\n  static inline void ata_product(gene_matrix & A, gene_matrix & X, int N){\n    // X =  prod(trans(A),A);\n    X.assign(prod(trans(A),A));\n  }\n\n  static inline void aat_product(gene_matrix & A, gene_matrix & X, int N){\n    // X =  prod(A,trans(A));\n    X.assign(prod(A,trans(A)));\n  }\n\n  static inline void trisolve_lower(const gene_matrix & L, const gene_vector& B, gene_vector & X, int N){\n    X = solve(L, B, ublas::lower_tag ());\n  }\n\n};\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/check_cache_queries.cpp",
    "content": "\n#define EIGEN_INTERNAL_DEBUG_CACHE_QUERY\n#include <iostream>\n#include \"../Eigen/Core\"\n\nusing namespace Eigen;\nusing namespace std;\n\n#define DUMP_CPUID(CODE) {\\\n  int abcd[4]; \\\n  abcd[0] = abcd[1] = abcd[2] = abcd[3] = 0;\\\n  EIGEN_CPUID(abcd, CODE, 0); \\\n  std::cout << \"The code \" << CODE << \" gives \" \\\n              << (int*)(abcd[0]) << \" \" << (int*)(abcd[1]) << \" \" \\\n              << (int*)(abcd[2]) << \" \" << (int*)(abcd[3]) << \" \" << std::endl; \\\n  }\n  \nint main()\n{\n  cout << \"Eigen's L1    = \" << internal::queryL1CacheSize() << endl;\n  cout << \"Eigen's L2/L3 = \" << internal::queryTopLevelCacheSize() << endl;\n  int l1, l2, l3;\n  internal::queryCacheSizes(l1, l2, l3);\n  cout << \"Eigen's L1, L2, L3       = \" << l1 << \" \" << l2 << \" \" << l3 << endl;\n  \n  #ifdef EIGEN_CPUID\n\n  int abcd[4];\n  int string[8];\n  char* string_char = (char*)(string);\n\n  // vendor ID\n  EIGEN_CPUID(abcd,0x0,0);\n  string[0] = abcd[1];\n  string[1] = abcd[3];\n  string[2] = abcd[2];\n  string[3] = 0;\n  cout << endl;\n  cout << \"vendor id = \" << string_char << endl;\n  cout << endl;\n  int max_funcs = abcd[0];\n\n  internal::queryCacheSizes_intel_codes(l1, l2, l3);\n  cout << \"Eigen's intel codes L1, L2, L3 = \" << l1 << \" \" << l2 << \" \" << l3 << endl;\n  if(max_funcs>=4)\n  {\n    internal::queryCacheSizes_intel_direct(l1, l2, l3);\n    cout << \"Eigen's intel direct L1, L2, L3 = \" << l1 << \" \" << l2 << \" \" << l3 << endl;\n  }\n  internal::queryCacheSizes_amd(l1, l2, l3);\n  cout << \"Eigen's amd L1, L2, L3         = \" << l1 << \" \" << l2 << \" \" << l3 << endl;\n  cout << endl;\n  \n  // dump Intel direct method\n  if(max_funcs>=4)\n  {\n    l1 = l2 = l3 = 0;\n    int cache_id = 0;\n    int cache_type = 0;\n    do {\n      abcd[0] = abcd[1] = abcd[2] = abcd[3] = 0;\n      EIGEN_CPUID(abcd,0x4,cache_id);\n      cache_type  = (abcd[0] & 0x0F) >> 0;\n      int cache_level = (abcd[0] & 0xE0) >> 5;  // A[7:5]\n      int ways        = (abcd[1] & 0xFFC00000) >> 22; // B[31:22]\n      int partitions  = (abcd[1] & 0x003FF000) >> 12; // B[21:12]\n      int line_size   = (abcd[1] & 0x00000FFF) >>  0; // B[11:0]\n      int sets        = (abcd[2]);                    // C[31:0]\n      int cache_size = (ways+1) * (partitions+1) * (line_size+1) * (sets+1);\n      \n      cout << \"cache[\" << cache_id << \"].type       = \" << cache_type << \"\\n\";\n      cout << \"cache[\" << cache_id << \"].level      = \" << cache_level << \"\\n\";\n      cout << \"cache[\" << cache_id << \"].ways       = \" << ways << \"\\n\";\n      cout << \"cache[\" << cache_id << \"].partitions = \" << partitions << \"\\n\";\n      cout << \"cache[\" << cache_id << \"].line_size  = \" << line_size << \"\\n\";\n      cout << \"cache[\" << cache_id << \"].sets       = \" << sets << \"\\n\";\n      cout << \"cache[\" << cache_id << \"].size       = \" << cache_size << \"\\n\";\n      \n      cache_id++;\n    } while(cache_type>0 && cache_id<16);\n  }\n  \n  // dump everything\n  std::cout << endl <<\"Raw dump:\" << endl;\n  for(int i=0; i<max_funcs; ++i)\n    DUMP_CPUID(i);\n\n  DUMP_CPUID(0x80000000);\n  DUMP_CPUID(0x80000001);\n  DUMP_CPUID(0x80000002);\n  DUMP_CPUID(0x80000003);\n  DUMP_CPUID(0x80000004);\n  DUMP_CPUID(0x80000005);\n  DUMP_CPUID(0x80000006);\n  DUMP_CPUID(0x80000007);\n  DUMP_CPUID(0x80000008);\n  #else\n  cout << \"EIGEN_CPUID is not defined\" << endl;\n  #endif\n  return 0;\n}\n"
  },
  {
    "path": "include/eigen3/bench/dense_solvers.cpp",
    "content": "#include <iostream>\n#include \"BenchTimer.h\"\n#include <Eigen/Dense>\n#include <map>\n#include <vector>\n#include <string>\n#include <sstream>\nusing namespace Eigen;\n\nstd::map<std::string,Array<float,1,8,DontAlign|RowMajor> > results;\nstd::vector<std::string> labels;\nstd::vector<Array2i> sizes;\n\ntemplate<typename Solver,typename MatrixType>\nEIGEN_DONT_INLINE\nvoid compute_norm_equation(Solver &solver, const MatrixType &A) {\n  if(A.rows()!=A.cols())\n    solver.compute(A.transpose()*A);\n  else\n    solver.compute(A);\n}\n\ntemplate<typename Solver,typename MatrixType>\nEIGEN_DONT_INLINE\nvoid compute(Solver &solver, const MatrixType &A) {\n  solver.compute(A);\n}\n\ntemplate<typename Scalar,int Size>\nvoid bench(int id, int rows, int size = Size)\n{\n  typedef Matrix<Scalar,Dynamic,Size> Mat;\n  typedef Matrix<Scalar,Dynamic,Dynamic> MatDyn;\n  typedef Matrix<Scalar,Size,Size> MatSquare;\n  Mat A(rows,size);\n  A.setRandom();\n  if(rows==size)\n    A = A*A.adjoint();\n  BenchTimer t_llt, t_ldlt, t_lu, t_fplu, t_qr, t_cpqr, t_cod, t_fpqr, t_jsvd, t_bdcsvd;\n\n  int svd_opt = ComputeThinU|ComputeThinV;\n  \n  int tries = 5;\n  int rep = 1000/size;\n  if(rep==0) rep = 1;\n//   rep = rep*rep;\n  \n  LLT<MatSquare> llt(size);\n  LDLT<MatSquare> ldlt(size);\n  PartialPivLU<MatSquare> lu(size);\n  FullPivLU<MatSquare> fplu(size,size);\n  HouseholderQR<Mat> qr(A.rows(),A.cols());\n  ColPivHouseholderQR<Mat> cpqr(A.rows(),A.cols());\n  CompleteOrthogonalDecomposition<Mat> cod(A.rows(),A.cols());\n  FullPivHouseholderQR<Mat> fpqr(A.rows(),A.cols());\n  JacobiSVD<MatDyn> jsvd(A.rows(),A.cols());\n  BDCSVD<MatDyn> bdcsvd(A.rows(),A.cols());\n  \n  BENCH(t_llt, tries, rep, compute_norm_equation(llt,A));\n  BENCH(t_ldlt, tries, rep, compute_norm_equation(ldlt,A));\n  BENCH(t_lu, tries, rep, compute_norm_equation(lu,A));\n  if(size<=1000)\n    BENCH(t_fplu, tries, rep, compute_norm_equation(fplu,A));\n  BENCH(t_qr, tries, rep, compute(qr,A));\n  BENCH(t_cpqr, tries, rep, compute(cpqr,A));\n  BENCH(t_cod, tries, rep, compute(cod,A));\n  if(size*rows<=10000000)\n    BENCH(t_fpqr, tries, rep, compute(fpqr,A));\n  if(size<500) // JacobiSVD is really too slow for too large matrices\n    BENCH(t_jsvd, tries, rep, jsvd.compute(A,svd_opt));\n//   if(size*rows<=20000000)\n    BENCH(t_bdcsvd, tries, rep, bdcsvd.compute(A,svd_opt));\n  \n  results[\"LLT\"][id] = t_llt.best();\n  results[\"LDLT\"][id] = t_ldlt.best();\n  results[\"PartialPivLU\"][id] = t_lu.best();\n  results[\"FullPivLU\"][id] = t_fplu.best();\n  results[\"HouseholderQR\"][id] = t_qr.best();\n  results[\"ColPivHouseholderQR\"][id] = t_cpqr.best();\n  results[\"CompleteOrthogonalDecomposition\"][id] = t_cod.best();\n  results[\"FullPivHouseholderQR\"][id] = t_fpqr.best();\n  results[\"JacobiSVD\"][id] = t_jsvd.best();\n  results[\"BDCSVD\"][id] = t_bdcsvd.best();\n}\n\n\nint main()\n{\n  labels.push_back(\"LLT\");\n  labels.push_back(\"LDLT\");\n  labels.push_back(\"PartialPivLU\");\n  labels.push_back(\"FullPivLU\");\n  labels.push_back(\"HouseholderQR\");\n  labels.push_back(\"ColPivHouseholderQR\");\n  labels.push_back(\"CompleteOrthogonalDecomposition\");\n  labels.push_back(\"FullPivHouseholderQR\");\n  labels.push_back(\"JacobiSVD\");\n  labels.push_back(\"BDCSVD\");\n\n  for(int i=0; i<labels.size(); ++i)\n    results[labels[i]].fill(-1);\n\n  const int small = 8;\n  sizes.push_back(Array2i(small,small));\n  sizes.push_back(Array2i(100,100));\n  sizes.push_back(Array2i(1000,1000));\n  sizes.push_back(Array2i(4000,4000));\n  sizes.push_back(Array2i(10000,small));\n  sizes.push_back(Array2i(10000,100));\n  sizes.push_back(Array2i(10000,1000));\n  sizes.push_back(Array2i(10000,4000));\n\n  using namespace std;\n\n  for(int k=0; k<sizes.size(); ++k)\n  {\n    cout << sizes[k](0) << \"x\" << sizes[k](1) << \"...\\n\";\n    bench<float,Dynamic>(k,sizes[k](0),sizes[k](1));\n  }\n\n  cout.width(32);\n  cout << \"solver/size\";\n  cout << \"  \";\n  for(int k=0; k<sizes.size(); ++k)\n  {\n    std::stringstream ss;\n    ss << sizes[k](0) << \"x\" << sizes[k](1);\n    cout.width(10); cout << ss.str(); cout << \" \";\n  }\n  cout << endl;\n\n\n  for(int i=0; i<labels.size(); ++i)\n  {\n    cout.width(32); cout << labels[i]; cout << \"  \";\n    ArrayXf r = (results[labels[i]]*100000.f).floor()/100.f;\n    for(int k=0; k<sizes.size(); ++k)\n    {\n      cout.width(10);\n      if(r(k)>=1e6)  cout << \"-\";\n      else           cout << r(k);\n      cout << \" \";\n    }\n    cout << endl;\n  }\n\n  // HTML output\n  cout << \"<table class=\\\"manual\\\">\" << endl;\n  cout << \"<tr><th>solver/size</th>\" << endl;\n  for(int k=0; k<sizes.size(); ++k)\n    cout << \"  <th>\" << sizes[k](0) << \"x\" << sizes[k](1) << \"</th>\";\n  cout << \"</tr>\" << endl;\n  for(int i=0; i<labels.size(); ++i)\n  {\n    cout << \"<tr\";\n    if(i%2==1) cout << \" class=\\\"alt\\\"\";\n    cout << \"><td>\" << labels[i] << \"</td>\";\n    ArrayXf r = (results[labels[i]]*100000.f).floor()/100.f;\n    for(int k=0; k<sizes.size(); ++k)\n    {\n      if(r(k)>=1e6) cout << \"<td>-</td>\";\n      else\n      {\n        cout << \"<td>\" << r(k);\n        if(i>0)\n          cout << \" (x\" << numext::round(10.f*results[labels[i]](k)/results[\"LLT\"](k))/10.f << \")\";\n        if(i<4 && sizes[k](0)!=sizes[k](1))\n          cout << \" <sup><a href=\\\"#note_ls\\\">*</a></sup>\";\n        cout << \"</td>\";\n      }\n    }\n    cout << \"</tr>\" << endl;\n  }\n  cout << \"</table>\" << endl;\n\n//   cout << \"LLT                             (ms)  \" << (results[\"LLT\"]*1000.).format(fmt) << \"\\n\";\n//   cout << \"LDLT                             (%)  \" << (results[\"LDLT\"]/results[\"LLT\"]).format(fmt) << \"\\n\";\n//   cout << \"PartialPivLU                     (%)  \" << (results[\"PartialPivLU\"]/results[\"LLT\"]).format(fmt) << \"\\n\";\n//   cout << \"FullPivLU                        (%)  \" << (results[\"FullPivLU\"]/results[\"LLT\"]).format(fmt) << \"\\n\";\n//   cout << \"HouseholderQR                    (%)  \" << (results[\"HouseholderQR\"]/results[\"LLT\"]).format(fmt) << \"\\n\";\n//   cout << \"ColPivHouseholderQR              (%)  \" << (results[\"ColPivHouseholderQR\"]/results[\"LLT\"]).format(fmt) << \"\\n\";\n//   cout << \"CompleteOrthogonalDecomposition  (%)  \" << (results[\"CompleteOrthogonalDecomposition\"]/results[\"LLT\"]).format(fmt) << \"\\n\";\n//   cout << \"FullPivHouseholderQR             (%)  \" << (results[\"FullPivHouseholderQR\"]/results[\"LLT\"]).format(fmt) << \"\\n\";\n//   cout << \"JacobiSVD                        (%)  \" << (results[\"JacobiSVD\"]/results[\"LLT\"]).format(fmt) << \"\\n\";\n//   cout << \"BDCSVD                           (%)  \" << (results[\"BDCSVD\"]/results[\"LLT\"]).format(fmt) << \"\\n\";\n}\n"
  },
  {
    "path": "include/eigen3/bench/eig33.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n// The computeRoots function included in this is based on materials\n// covered by the following copyright and license:\n// \n// Geometric Tools, LLC\n// Copyright (c) 1998-2010\n// Distributed under the Boost Software License, Version 1.0.\n// \n// Permission is hereby granted, free of charge, to any person or organization\n// obtaining a copy of the software and accompanying documentation covered by\n// this license (the \"Software\") to use, reproduce, display, distribute,\n// execute, and transmit the Software, and to prepare derivative works of the\n// Software, and to permit third-parties to whom the Software is furnished to\n// do so, all subject to the following:\n// \n// The copyright notices in the Software and this entire statement, including\n// the above license grant, this restriction and the following disclaimer,\n// must be included in all copies of the Software, in whole or in part, and\n// all derivative works of the Software, unless such copies or derivative\n// works are solely in the form of machine-executable object code generated by\n// a source language processor.\n// \n// THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n// FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT\n// SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE\n// FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,\n// ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n// DEALINGS IN THE SOFTWARE.\n\n#include <iostream>\n#include <Eigen/Core>\n#include <Eigen/Eigenvalues>\n#include <Eigen/Geometry>\n#include <bench/BenchTimer.h>\n\nusing namespace Eigen;\nusing namespace std;\n\ntemplate<typename Matrix, typename Roots>\ninline void computeRoots(const Matrix& m, Roots& roots)\n{\n  typedef typename Matrix::Scalar Scalar;\n  const Scalar s_inv3 = 1.0/3.0;\n  const Scalar s_sqrt3 = std::sqrt(Scalar(3.0));\n\n  // The characteristic equation is x^3 - c2*x^2 + c1*x - c0 = 0.  The\n  // eigenvalues are the roots to this equation, all guaranteed to be\n  // real-valued, because the matrix is symmetric.\n  Scalar c0 = m(0,0)*m(1,1)*m(2,2) + Scalar(2)*m(0,1)*m(0,2)*m(1,2) - m(0,0)*m(1,2)*m(1,2) - m(1,1)*m(0,2)*m(0,2) - m(2,2)*m(0,1)*m(0,1);\n  Scalar c1 = m(0,0)*m(1,1) - m(0,1)*m(0,1) + m(0,0)*m(2,2) - m(0,2)*m(0,2) + m(1,1)*m(2,2) - m(1,2)*m(1,2);\n  Scalar c2 = m(0,0) + m(1,1) + m(2,2);\n\n  // Construct the parameters used in classifying the roots of the equation\n  // and in solving the equation for the roots in closed form.\n  Scalar c2_over_3 = c2*s_inv3;\n  Scalar a_over_3 = (c1 - c2*c2_over_3)*s_inv3;\n  if (a_over_3 > Scalar(0))\n    a_over_3 = Scalar(0);\n\n  Scalar half_b = Scalar(0.5)*(c0 + c2_over_3*(Scalar(2)*c2_over_3*c2_over_3 - c1));\n\n  Scalar q = half_b*half_b + a_over_3*a_over_3*a_over_3;\n  if (q > Scalar(0))\n    q = Scalar(0);\n\n  // Compute the eigenvalues by solving for the roots of the polynomial.\n  Scalar rho = std::sqrt(-a_over_3);\n  Scalar theta = std::atan2(std::sqrt(-q),half_b)*s_inv3;\n  Scalar cos_theta = std::cos(theta);\n  Scalar sin_theta = std::sin(theta);\n  roots(2) = c2_over_3 + Scalar(2)*rho*cos_theta;\n  roots(0) = c2_over_3 - rho*(cos_theta + s_sqrt3*sin_theta);\n  roots(1) = c2_over_3 - rho*(cos_theta - s_sqrt3*sin_theta);\n}\n\ntemplate<typename Matrix, typename Vector>\nvoid eigen33(const Matrix& mat, Matrix& evecs, Vector& evals)\n{\n  typedef typename Matrix::Scalar Scalar;\n  // Scale the matrix so its entries are in [-1,1].  The scaling is applied\n  // only when at least one matrix entry has magnitude larger than 1.\n\n  Scalar shift = mat.trace()/3;\n  Matrix scaledMat = mat;\n  scaledMat.diagonal().array() -= shift;\n  Scalar scale = scaledMat.cwiseAbs()/*.template triangularView<Lower>()*/.maxCoeff();\n  scale = std::max(scale,Scalar(1));\n  scaledMat/=scale;\n\n  // Compute the eigenvalues\n//   scaledMat.setZero();\n  computeRoots(scaledMat,evals);\n\n  // compute the eigen vectors\n  // **here we assume 3 differents eigenvalues**\n\n  // \"optimized version\" which appears to be slower with gcc!\n//     Vector base;\n//     Scalar alpha, beta;\n//     base <<   scaledMat(1,0) * scaledMat(2,1),\n//               scaledMat(1,0) * scaledMat(2,0),\n//              -scaledMat(1,0) * scaledMat(1,0);\n//     for(int k=0; k<2; ++k)\n//     {\n//       alpha = scaledMat(0,0) - evals(k);\n//       beta  = scaledMat(1,1) - evals(k);\n//       evecs.col(k) = (base + Vector(-beta*scaledMat(2,0), -alpha*scaledMat(2,1), alpha*beta)).normalized();\n//     }\n//     evecs.col(2) = evecs.col(0).cross(evecs.col(1)).normalized();\n\n//   // naive version\n//   Matrix tmp;\n//   tmp = scaledMat;\n//   tmp.diagonal().array() -= evals(0);\n//   evecs.col(0) = tmp.row(0).cross(tmp.row(1)).normalized();\n// \n//   tmp = scaledMat;\n//   tmp.diagonal().array() -= evals(1);\n//   evecs.col(1) = tmp.row(0).cross(tmp.row(1)).normalized();\n// \n//   tmp = scaledMat;\n//   tmp.diagonal().array() -= evals(2);\n//   evecs.col(2) = tmp.row(0).cross(tmp.row(1)).normalized();\n  \n  // a more stable version:\n  if((evals(2)-evals(0))<=Eigen::NumTraits<Scalar>::epsilon())\n  {\n    evecs.setIdentity();\n  }\n  else\n  {\n    Matrix tmp;\n    tmp = scaledMat;\n    tmp.diagonal ().array () -= evals (2);\n    evecs.col (2) = tmp.row (0).cross (tmp.row (1)).normalized ();\n    \n    tmp = scaledMat;\n    tmp.diagonal ().array () -= evals (1);\n    evecs.col(1) = tmp.row (0).cross(tmp.row (1));\n    Scalar n1 = evecs.col(1).norm();\n    if(n1<=Eigen::NumTraits<Scalar>::epsilon())\n      evecs.col(1) = evecs.col(2).unitOrthogonal();\n    else\n      evecs.col(1) /= n1;\n    \n    // make sure that evecs[1] is orthogonal to evecs[2]\n    evecs.col(1) = evecs.col(2).cross(evecs.col(1).cross(evecs.col(2))).normalized();\n    evecs.col(0) = evecs.col(2).cross(evecs.col(1));\n  }\n  \n  // Rescale back to the original size.\n  evals *= scale;\n  evals.array()+=shift;\n}\n\nint main()\n{\n  BenchTimer t;\n  int tries = 10;\n  int rep = 400000;\n  typedef Matrix3d Mat;\n  typedef Vector3d Vec;\n  Mat A = Mat::Random(3,3);\n  A = A.adjoint() * A;\n//   Mat Q = A.householderQr().householderQ();\n//   A = Q * Vec(2.2424567,2.2424566,7.454353).asDiagonal() * Q.transpose();\n\n  SelfAdjointEigenSolver<Mat> eig(A);\n  BENCH(t, tries, rep, eig.compute(A));\n  std::cout << \"Eigen iterative:  \" << t.best() << \"s\\n\";\n  \n  BENCH(t, tries, rep, eig.computeDirect(A));\n  std::cout << \"Eigen direct   :  \" << t.best() << \"s\\n\";\n\n  Mat evecs;\n  Vec evals;\n  BENCH(t, tries, rep, eigen33(A,evecs,evals));\n  std::cout << \"Direct: \" << t.best() << \"s\\n\\n\";\n\n//   std::cerr << \"Eigenvalue/eigenvector diffs:\\n\";\n//   std::cerr << (evals - eig.eigenvalues()).transpose() << \"\\n\";\n//   for(int k=0;k<3;++k)\n//     if(evecs.col(k).dot(eig.eigenvectors().col(k))<0)\n//       evecs.col(k) = -evecs.col(k);\n//   std::cerr << evecs - eig.eigenvectors() << \"\\n\\n\";\n}\n"
  },
  {
    "path": "include/eigen3/bench/geometry.cpp",
    "content": "\n#include <iostream>\n#include <Eigen/Geometry>\n#include <bench/BenchTimer.h>\n\nusing namespace std;\nusing namespace Eigen;\n\n#ifndef SCALAR\n#define SCALAR float\n#endif\n\n#ifndef SIZE\n#define SIZE 8\n#endif\n\ntypedef SCALAR Scalar;\ntypedef NumTraits<Scalar>::Real RealScalar;\ntypedef Matrix<RealScalar,Dynamic,Dynamic> A;\ntypedef Matrix</*Real*/Scalar,Dynamic,Dynamic> B;\ntypedef Matrix<Scalar,Dynamic,Dynamic> C;\ntypedef Matrix<RealScalar,Dynamic,Dynamic> M;\n\ntemplate<typename Transformation, typename Data>\nEIGEN_DONT_INLINE void transform(const Transformation& t, Data& data)\n{\n  EIGEN_ASM_COMMENT(\"begin\");\n  data = t * data;\n  EIGEN_ASM_COMMENT(\"end\");\n}\n\ntemplate<typename Scalar, typename Data>\nEIGEN_DONT_INLINE void transform(const Quaternion<Scalar>& t, Data& data)\n{\n  EIGEN_ASM_COMMENT(\"begin quat\");\n  for(int i=0;i<data.cols();++i)\n    data.col(i) = t * data.col(i);\n  EIGEN_ASM_COMMENT(\"end quat\");\n}\n\ntemplate<typename T> struct ToRotationMatrixWrapper\n{\n  enum {Dim = T::Dim};\n  typedef typename T::Scalar Scalar;\n  ToRotationMatrixWrapper(const T& o) : object(o) {}\n  T object;\n};\n\ntemplate<typename QType, typename Data>\nEIGEN_DONT_INLINE void transform(const ToRotationMatrixWrapper<QType>& t, Data& data)\n{\n  EIGEN_ASM_COMMENT(\"begin quat via mat\");\n  data = t.object.toRotationMatrix() * data;\n  EIGEN_ASM_COMMENT(\"end quat via mat\");\n}\n\ntemplate<typename Scalar, int Dim, typename Data>\nEIGEN_DONT_INLINE void transform(const Transform<Scalar,Dim,Projective>& t, Data& data)\n{\n  data = (t * data.colwise().homogeneous()).template block<Dim,Data::ColsAtCompileTime>(0,0);\n}\n\ntemplate<typename T> struct get_dim { enum { Dim = T::Dim }; };\ntemplate<typename S, int R, int C, int O, int MR, int MC>\nstruct get_dim<Matrix<S,R,C,O,MR,MC> > { enum { Dim = R }; };\n\ntemplate<typename Transformation, int N>\nstruct bench_impl\n{\n  static EIGEN_DONT_INLINE void run(const Transformation& t)\n  {\n    Matrix<typename Transformation::Scalar,get_dim<Transformation>::Dim,N> data;\n    data.setRandom();\n    bench_impl<Transformation,N-1>::run(t);\n    BenchTimer timer;\n    BENCH(timer,10,100000,transform(t,data));\n    cout.width(9);\n    cout << timer.best() << \" \";\n  }\n};\n\n\ntemplate<typename Transformation>\nstruct bench_impl<Transformation,0>\n{\n  static EIGEN_DONT_INLINE void run(const Transformation&) {}\n};\n\ntemplate<typename Transformation>\nEIGEN_DONT_INLINE void bench(const std::string& msg, const Transformation& t)\n{\n  cout << msg << \" \";\n  bench_impl<Transformation,SIZE>::run(t);\n  std::cout << \"\\n\";\n}\n\nint main(int argc, char ** argv)\n{\n  Matrix<Scalar,3,4> mat34; mat34.setRandom();\n  Transform<Scalar,3,Isometry> iso3(mat34);\n  Transform<Scalar,3,Affine> aff3(mat34);\n  Transform<Scalar,3,AffineCompact> caff3(mat34);\n  Transform<Scalar,3,Projective> proj3(mat34);\n  Quaternion<Scalar> quat;quat.setIdentity();\n  ToRotationMatrixWrapper<Quaternion<Scalar> > quatmat(quat);\n  Matrix<Scalar,3,3> mat33; mat33.setRandom();\n  \n  cout.precision(4);\n  std::cout\n     << \"N          \";\n  for(int i=0;i<SIZE;++i)\n  {\n    cout.width(9);\n    cout << i+1 << \" \";\n  }\n  cout << \"\\n\";\n  \n  bench(\"matrix 3x3\", mat33);\n  bench(\"quaternion\", quat);\n  bench(\"quat-mat  \", quatmat);\n  bench(\"isometry3 \", iso3);\n  bench(\"affine3   \", aff3);\n  bench(\"c affine3 \", caff3);\n  bench(\"proj3     \", proj3);\n}\n\n"
  },
  {
    "path": "include/eigen3/bench/perf_monitoring/gemm/changesets.txt",
    "content": "#3.0.1\n#3.1.1\n#3.2.0\n3.2.4\n#5745:37f59e65eb6c\n5891:d8652709345d  # introduce AVX\n#5893:24b4dc92c6d3  # merge\n5895:997c2ef9fc8b  # introduce FMA\n#5904:e1eafd14eaa1  # complex and AVX\n5908:f8ee3c721251  # improve packing with ptranspose\n#5921:ca808bb456b0  # merge\n#5927:8b1001f9e3ac\n5937:5a4ca1ad8c53  # New gebp kernel handling up to 3 packets x 4 register-level blocks\n#5949:f3488f4e45b2  # merge\n#5969:e09031dccfd9  # Disable 3pX4 kernel on Altivec\n#5992:4a429f5e0483  # merge\nbefore-evaluators\n#6334:f6a45e5b8b7c  # Implement evaluator for sparse outer products\n#6639:c9121c60b5c7\n#6655:06f163b5221f  # Properly detect FMA support on ARM\n#6677:700e023044e7   # FMA has been wrongly disabled\n#6681:11d31dafb0e3\n#6699:5e6e8e10aad1   # merge default to tensors\n#6726:ff2d2388e7b9   # merge default to tensors\n#6742:0cbd6195e829   # merge default to tensors\n#6747:853d2bafeb8f   # Generalized the gebp apis\n6765:71584fd55762   # Made the blocking computation aware of the l3 cache; Also optimized the blocking parameters to take into account the number of threads used for a computation\n#6781:9cc5a931b2c6   # generalized gemv\n#6792:f6e1daab600a   # ensured that contractions that can be reduced to a matrix vector product\n#6844:039efd86b75c   # merge tensor\n6845:7333ed40c6ef   # change prefetching in gebp\n#6856:b5be5e10eb7f   # merge index conversion\n#6893:c3a64aba7c70   # clean blocking size computation\n#6898:6fb31ebe6492   # rotating kernel for ARM\n6899:877facace746   # rotating kernel for ARM only\n#6904:c250623ae9fa   # result_of\n6921:915f1b1fc158   # fix prefetching change for ARM\n6923:9ff25f6dacc6   # prefetching\n6933:52572e60b5d3   # blocking size strategy\n6937:c8c042f286b2   # avoid redundant pack_rhs\n6981:7e5d6f78da59   # dynamic loop swapping\n6984:45f26866c091   # rm dynamic loop swapping, adjust lhs's micro panel height to fully exploit L1 cache\n6986:a675d05b6f8f   # blocking heuristic: block on the rhs in L1 if the lhs fit in L1.\n7013:f875e75f07e5   # organize a little our default cache sizes, and use a saner default L1 outside of x86 (10% faster on Nexus 5)\n7015:8aad8f35c955   # Refactor computeProductBlockingSizes to make room for the possibility of using lookup tables\n7016:a58d253e8c91   # Polish lookup tables generation\n7018:9b27294a8186   # actual_panel_rows computation should always be resilient to parameters not consistent with the known L1 cache size, see comment\n7019:c758b1e2c073   # Provide a empirical lookup table for blocking sizes measured on a Nexus 5. Only for float, only for Android on ARM 32bit for now.\n7085:627e039fba68   # Bug 986: add support for coefficient-based product with 0 depth.\n7098:b6f1db9cf9ec   # Bug 992: don't select a 3p GEMM path with non-vectorizable scalar types, this hits unsupported paths in symm/triangular products code\n7591:09a8e2186610   # 3.3-alpha1\n7650:b0f3c8f43025   # help clang inlining\n#8744:74b789ada92a   # Improved the matrix multiplication blocking in the case where mr is not a power of 2 (e.g on Haswell CPUs)\n8789:efcb912e4356   # Made the index type a template parameter to evaluateProductBlockingSizes. Use numext::mini and numext::maxi instead of std::min/std::max to compute blocking sizes\n8972:81d53c711775   # Don't optimize the processing of the last rows of a matrix matrix product in cases that violate the assumptions made by the optimized code path\n8985:d935df21a082   # Remove the rotating kernel.\n8988:6c2dc56e73b3   # Bug 256: enable vectorization with unaligned loads/stores.\n9148:b8b8c421e36c   # Relax mixing-type constraints for binary coefficient-wise operators\n9174:d228bc282ac9   # merge\n9212:c90098affa7b   # Fix performance regression introduced in changeset 8aad8f35c955\n9213:9f1c14e4694b   # Fix performance regression in dgemm introduced by changeset 81d53c711775\n"
  },
  {
    "path": "include/eigen3/bench/perf_monitoring/gemm/gemm.cpp",
    "content": "#include <iostream>\n#include <fstream>\n#include <vector>\n#include <Eigen/Core>\n#include \"../../BenchTimer.h\"\nusing namespace Eigen;\n\n#ifndef SCALAR\n#error SCALAR must be defined\n#endif\n\ntypedef SCALAR Scalar;\n\ntypedef Matrix<Scalar,Dynamic,Dynamic> Mat;\n\nEIGEN_DONT_INLINE\nvoid gemm(const Mat &A, const Mat &B, Mat &C)\n{\n  C.noalias() += A * B;\n}\n\nEIGEN_DONT_INLINE\ndouble bench(long m, long n, long k)\n{\n  Mat A(m,k);\n  Mat B(k,n);\n  Mat C(m,n);\n  A.setRandom();\n  B.setRandom();\n  C.setZero();\n  \n  BenchTimer t;\n  \n  double up = 1e8*4/sizeof(Scalar);\n  double tm0 = 4, tm1 = 10;\n  if(NumTraits<Scalar>::IsComplex)\n  {\n    up /= 4;\n    tm0 = 2;\n    tm1 = 4;\n  }\n  \n  double flops = 2. * m * n * k;\n  long rep = std::max(1., std::min(100., up/flops) );\n  long tries = std::max(tm0, std::min(tm1, up/flops) );\n  \n  BENCH(t, tries, rep, gemm(A,B,C));\n  \n  return 1e-9 * rep * flops / t.best();\n}\n\nint main(int argc, char **argv)\n{\n  std::vector<double> results;\n  \n  std::ifstream settings(\"gemm_settings.txt\");\n  long m, n, k;\n  while(settings >> m >> n >> k)\n  {\n    //std::cerr << \"  Testing \" << m << \" \" << n << \" \" << k << std::endl;\n    results.push_back( bench(m, n, k) );\n  }\n  \n  std::cout << RowVectorXd::Map(results.data(), results.size());\n  \n  return 0;\n}\n"
  },
  {
    "path": "include/eigen3/bench/perf_monitoring/gemm/gemm_settings.txt",
    "content": "8 8 8\n9 9 9\n24 24 24\n239 239 239\n240 240 240\n2400 24 24\n24 2400 24\n24 24 2400\n24 2400 2400\n2400 24 2400\n2400 2400 24\n2400 2400 64\n4800 23 160\n23 4800 160\n2400 2400 2400\n"
  },
  {
    "path": "include/eigen3/bench/perf_monitoring/gemm/lazy_gemm.cpp",
    "content": "#include <iostream>\n#include <fstream>\n#include <vector>\n#include <Eigen/Core>\n#include \"../../BenchTimer.h\"\nusing namespace Eigen;\n\n#ifndef SCALAR\n#error SCALAR must be defined\n#endif\n\ntypedef SCALAR Scalar;\n\ntemplate<typename MatA, typename MatB, typename MatC>\nEIGEN_DONT_INLINE\nvoid lazy_gemm(const MatA &A, const MatB &B, MatC &C)\n{\n//   escape((void*)A.data());\n//   escape((void*)B.data());\n  C.noalias() += A.lazyProduct(B);\n//   escape((void*)C.data());\n}\n\ntemplate<int m, int n, int k, int TA>\nEIGEN_DONT_INLINE\ndouble bench()\n{\n  typedef Matrix<Scalar,m,k,TA> MatA;\n  typedef Matrix<Scalar,k,n> MatB;\n  typedef Matrix<Scalar,m,n> MatC;\n\n  MatA A(m,k);\n  MatB B(k,n);\n  MatC C(m,n);\n  A.setRandom();\n  B.setRandom();\n  C.setZero();\n\n  BenchTimer t;\n\n  double up = 1e7*4/sizeof(Scalar);\n  double tm0 = 10, tm1 = 20;\n\n  double flops = 2. * m * n * k;\n  long rep = std::max(10., std::min(10000., up/flops) );\n  long tries = std::max(tm0, std::min(tm1, up/flops) );\n\n  BENCH(t, tries, rep, lazy_gemm(A,B,C));\n\n  return 1e-9 * rep * flops / t.best();\n}\n\ntemplate<int m, int n, int k>\ndouble bench_t(int t)\n{\n  if(t)\n    return bench<m,n,k,RowMajor>();\n  else\n    return bench<m,n,k,0>();\n}\n\nEIGEN_DONT_INLINE\ndouble bench_mnk(int m, int n, int k, int t)\n{\n  int id = m*10000 + n*100 + k;\n  switch(id) {\n    case  10101 : return bench_t< 1, 1, 1>(t); break;\n    case  20202 : return bench_t< 2, 2, 2>(t); break;\n    case  30303 : return bench_t< 3, 3, 3>(t); break;\n    case  40404 : return bench_t< 4, 4, 4>(t); break;\n    case  50505 : return bench_t< 5, 5, 5>(t); break;\n    case  60606 : return bench_t< 6, 6, 6>(t); break;\n    case  70707 : return bench_t< 7, 7, 7>(t); break;\n    case  80808 : return bench_t< 8, 8, 8>(t); break;\n    case  90909 : return bench_t< 9, 9, 9>(t); break;\n    case 101010 : return bench_t<10,10,10>(t); break;\n    case 111111 : return bench_t<11,11,11>(t); break;\n    case 121212 : return bench_t<12,12,12>(t); break;\n  }\n  return 0;\n}\n\nint main(int argc, char **argv)\n{\n  std::vector<double> results;\n  \n  std::ifstream settings(\"lazy_gemm_settings.txt\");\n  long m, n, k, t;\n  while(settings >> m >> n >> k >> t)\n  {\n    //std::cerr << \"  Testing \" << m << \" \" << n << \" \" << k << std::endl;\n    results.push_back( bench_mnk(m, n, k, t) );\n  }\n  \n  std::cout << RowVectorXd::Map(results.data(), results.size());\n  \n  return 0;\n}\n"
  },
  {
    "path": "include/eigen3/bench/perf_monitoring/gemm/lazy_gemm_settings.txt",
    "content": "1 1 1 0\n2 2 2 0\n3 3 3 0\n4 4 4 0\n4 4 4 1\n5 5 5 0\n6 6 6 0\n7 7 7 0\n7 7 7 1\n8 8 8 0\n9 9 9 0\n10 10 10 0\n11 11 11 0\n12 12 12 0\n12 12 12 1\n"
  },
  {
    "path": "include/eigen3/bench/perf_monitoring/gemm/make_plot.sh",
    "content": "#!/bin/bash\n\n# base name of the bench\n# it reads $1.out\n# and generates $1.pdf\nWHAT=$1\nbench=$2\n\nheader=\"rev \"\nwhile read line\ndo\n  if [ ! -z '$line' ]; then\n    header=\"$header  \\\"$line\\\"\"\n  fi\ndone < $bench\"_settings.txt\"\n\necho $header > $WHAT.out.header\ncat $WHAT.out >> $WHAT.out.header\n\n\necho \"set title '$WHAT'\" > $WHAT.gnuplot\necho \"set key autotitle columnhead outside \" >> $WHAT.gnuplot\necho \"set xtics rotate 1\" >> $WHAT.gnuplot\n\necho \"set term pdf color rounded enhanced fontscale 0.35 size 7in,5in\" >> $WHAT.gnuplot\necho set output \"'\"$WHAT.pdf\"'\" >> $WHAT.gnuplot\n\ncol=`cat $bench\"_settings.txt\" | wc -l`\necho \"plot for [col=2:$col+1] '$WHAT.out.header' using 0:col:xticlabels(1) with lines\" >> $WHAT.gnuplot\necho \" \" >>  $WHAT.gnuplot\n\ngnuplot -persist < $WHAT.gnuplot\n\n# generate a png file\n# convert -background white -density 120 -rotate 90 -resize 800 +dither -colors 256 -quality 0 $WHAT.ps -background white -flatten  .$WHAT.png\n\n# clean\nrm $WHAT.out.header $WHAT.gnuplot"
  },
  {
    "path": "include/eigen3/bench/perf_monitoring/gemm/run.sh",
    "content": "#!/bin/bash\n\n# ./run.sh gemm\n# ./run.sh lazy_gemm\n\n# Examples of environment variables to be set:\n#   PREFIX=\"haswell-fma-\"\n#   CXX_FLAGS=\"-mfma\"\n\n# Options:\n#   -up : enforce the recomputation of existing data, and keep best results as a merging strategy\n#   -s  : recompute selected changesets only and keep bests\n\nbench=$1\n\nif echo \"$*\" | grep '\\-up' > /dev/null; then\n  update=true\nelse\n  update=false\nfi\n\nif echo \"$*\" | grep '\\-s' > /dev/null; then\n  selected=true\nelse\n  selected=false\nfi\n\nglobal_args=\"$*\"\n\nif [ $selected == true ]; then\n echo \"Recompute selected changesets only and keep bests\"\nelif [ $update == true ]; then\n echo \"(Re-)Compute all changesets and keep bests\"\nelse\n echo \"Skip previously computed changesets\"\nfi\n\n\n\nif [ ! -d \"eigen_src\" ]; then\n  hg clone https://bitbucket.org/eigen/eigen eigen_src\nelse\n  cd eigen_src\n  hg pull -u\n  cd ..\nfi\n\nif [ ! -z '$CXX' ]; then\n  CXX=g++\nfi\n\nfunction make_backup\n{\n  if [ -f \"$1.out\" ]; then\n    mv \"$1.out\" \"$1.backup\"\n  fi\n}\n\nfunction merge\n{\n  count1=`echo $1 |  wc -w`\n  count2=`echo $2 |  wc -w`\n  \n  if [ $count1 == $count2 ]; then\n    a=( $1 ); b=( $2 )\n    res=\"\"\n    for (( i=0 ; i<$count1 ; i++ )); do\n      ai=${a[$i]}; bi=${b[$i]}\n      tmp=`echo \"if ($ai > $bi) $ai else $bi \" | bc -l`\n      res=\"$res $tmp\"\n    done\n    echo $res\n\n  else\n    echo $1\n  fi\n}\n\nfunction test_current \n{\n  rev=$1\n  scalar=$2\n  name=$3\n  \n  prev=\"\"\n  if [ -e \"$name.backup\" ]; then\n    prev=`grep $rev \"$name.backup\" | cut -c 14-`\n  fi\n  res=$prev\n  count_rev=`echo $prev |  wc -w`\n  count_ref=`cat $bench\"_settings.txt\" |  wc -l`\n  if echo \"$global_args\" | grep \"$rev\" > /dev/null; then\n    rev_found=true\n  else\n    rev_found=false\n  fi\n#  echo $update et $selected et $rev_found because $rev et \"$global_args\"\n#  echo $count_rev et $count_ref\n  if [ $update == true ] || [ $count_rev != $count_ref ] || ([ $selected == true ] &&  [ $rev_found == true ]); then\n    if $CXX -O2 -DNDEBUG -march=native $CXX_FLAGS -I eigen_src $bench.cpp -DSCALAR=$scalar -o $name; then\n      curr=`./$name`\n      if [ $count_rev == $count_ref ]; then\n        echo \"merge previous $prev\"\n        echo \"with new       $curr\"\n      else\n        echo \"got            $curr\"\n      fi\n      res=`merge \"$curr\" \"$prev\"`\n#       echo $res\n      echo \"$rev $res\" >> $name.out\n    else\n      echo \"Compilation failed, skip rev $rev\"\n    fi\n  else\n    echo \"Skip existing results for $rev / $name\"\n    echo \"$rev $res\" >> $name.out\n  fi\n}\n\nmake_backup $PREFIX\"s\"$bench\nmake_backup $PREFIX\"d\"$bench\nmake_backup $PREFIX\"c\"$bench\n\ncut -f1 -d\"#\" < changesets.txt | grep -E '[[:alnum:]]' | while read rev\ndo\n  if [ ! -z '$rev' ]; then\n    echo \"Testing rev $rev\"\n    cd eigen_src\n    hg up -C $rev > /dev/null\n    actual_rev=`hg identify | cut -f1 -d' '`\n    cd ..\n    \n    test_current $actual_rev float                  $PREFIX\"s\"$bench\n    test_current $actual_rev double                 $PREFIX\"d\"$bench\n    test_current $actual_rev \"std::complex<double>\" $PREFIX\"c\"$bench\n  fi\n  \ndone\n\necho \"Float:\"\ncat $PREFIX\"s\"\"$bench.out\"\necho \" \"\n\necho \"Double:\"\ncat $PREFIX\"d\"\"$bench.out\"\necho \"\"\n\necho \"Complex:\"\ncat $PREFIX\"c\"\"$bench.out\"\necho \"\"\n\n./make_plot.sh $PREFIX\"s\"$bench $bench\n./make_plot.sh $PREFIX\"d\"$bench $bench\n./make_plot.sh $PREFIX\"c\"$bench $bench\n\n\n"
  },
  {
    "path": "include/eigen3/bench/product_threshold.cpp",
    "content": "\n#include <iostream>\n#include <Eigen/Core>\n#include <bench/BenchTimer.h>\n\nusing namespace Eigen;\nusing namespace std;\n\n#define END 9\n\ntemplate<int S> struct map_size { enum { ret = S }; };\ntemplate<>  struct map_size<10> { enum { ret = 20 }; };\ntemplate<>  struct map_size<11> { enum { ret = 50 }; };\ntemplate<>  struct map_size<12> { enum { ret = 100 }; };\ntemplate<>  struct map_size<13> { enum { ret = 300 }; };\n\ntemplate<int M, int N,int K> struct alt_prod\n{\n  enum {\n    ret = M==1 && N==1 ? InnerProduct\n        : K==1 ? OuterProduct\n        : M==1 ? GemvProduct\n        : N==1 ? GemvProduct\n        : GemmProduct\n  };\n};\n        \nvoid print_mode(int mode)\n{\n  if(mode==InnerProduct) std::cout << \"i\";\n  if(mode==OuterProduct) std::cout << \"o\";\n  if(mode==CoeffBasedProductMode) std::cout << \"c\";\n  if(mode==LazyCoeffBasedProductMode) std::cout << \"l\";\n  if(mode==GemvProduct) std::cout << \"v\";\n  if(mode==GemmProduct) std::cout << \"m\";\n}\n\ntemplate<int Mode, typename Lhs, typename Rhs, typename Res>\nEIGEN_DONT_INLINE void prod(const Lhs& a, const Rhs& b, Res& c)\n{\n  c.noalias() += typename ProductReturnType<Lhs,Rhs,Mode>::Type(a,b);\n}\n\ntemplate<int M, int N, int K, typename Scalar, int Mode>\nEIGEN_DONT_INLINE void bench_prod()\n{\n  typedef Matrix<Scalar,M,K> Lhs; Lhs a; a.setRandom();\n  typedef Matrix<Scalar,K,N> Rhs; Rhs b; b.setRandom();\n  typedef Matrix<Scalar,M,N> Res; Res c; c.setRandom();\n\n  BenchTimer t;\n  double n = 2.*double(M)*double(N)*double(K);\n  int rep = 100000./n;\n  rep /= 2;\n  if(rep<1) rep = 1;\n  do {\n    rep *= 2;\n    t.reset();\n    BENCH(t,1,rep,prod<CoeffBasedProductMode>(a,b,c));\n  } while(t.best()<0.1);\n  \n  t.reset();\n  BENCH(t,5,rep,prod<Mode>(a,b,c));\n\n  print_mode(Mode);\n  std::cout << int(1e-6*n*rep/t.best()) << \"\\t\";\n}\n\ntemplate<int N> struct print_n;\ntemplate<int M, int N, int K> struct loop_on_m;\ntemplate<int M, int N, int K, typename Scalar, int Mode> struct loop_on_n;\n\ntemplate<int M, int N, int K>\nstruct loop_on_k\n{\n  static void run()\n  {\n    std::cout << \"K=\" << K << \"\\t\";\n    print_n<N>::run();\n    std::cout << \"\\n\";\n\n    loop_on_m<M,N,K>::run();\n    std::cout << \"\\n\\n\";\n\n    loop_on_k<M,N,K+1>::run();\n  }\n};\n\ntemplate<int M, int N>\nstruct loop_on_k<M,N,END> { static void run(){} };\n\n\ntemplate<int M, int N, int K>\nstruct loop_on_m\n{\n  static void run()\n  {\n    std::cout << M << \"f\\t\";\n    loop_on_n<M,N,K,float,CoeffBasedProductMode>::run();\n    std::cout << \"\\n\";\n    \n    std::cout << M << \"f\\t\";\n    loop_on_n<M,N,K,float,-1>::run();\n    std::cout << \"\\n\";\n\n    loop_on_m<M+1,N,K>::run();\n  }\n};\n\ntemplate<int N, int K>\nstruct loop_on_m<END,N,K> { static void run(){} };\n\ntemplate<int M, int N, int K, typename Scalar, int Mode>\nstruct loop_on_n\n{\n  static void run()\n  {\n    bench_prod<M,N,K,Scalar,Mode==-1? alt_prod<M,N,K>::ret : Mode>();\n    \n    loop_on_n<M,N+1,K,Scalar,Mode>::run();\n  }\n};\n\ntemplate<int M, int K, typename Scalar, int Mode>\nstruct loop_on_n<M,END,K,Scalar,Mode> { static void run(){} };\n\ntemplate<int N> struct print_n\n{\n  static void run()\n  {\n    std::cout << map_size<N>::ret << \"\\t\";\n    print_n<N+1>::run();\n  }\n};\n\ntemplate<> struct print_n<END> { static void run(){} };\n\nint main()\n{\n  loop_on_k<1,1,1>::run();\n  \n  return 0; \n}\n"
  },
  {
    "path": "include/eigen3/bench/quat_slerp.cpp",
    "content": "\n#include <iostream>\n#include <Eigen/Geometry>\n#include <bench/BenchTimer.h>\nusing namespace Eigen;\nusing namespace std;\n\n\n\ntemplate<typename Q>\nEIGEN_DONT_INLINE Q nlerp(const Q& a, const Q& b, typename Q::Scalar t)\n{\n  return Q((a.coeffs() * (1.0-t) + b.coeffs() * t).normalized());\n}\n\ntemplate<typename Q>\nEIGEN_DONT_INLINE Q slerp_eigen(const Q& a, const Q& b, typename Q::Scalar t)\n{\n  return a.slerp(t,b);\n}\n\ntemplate<typename Q>\nEIGEN_DONT_INLINE Q slerp_legacy(const Q& a, const Q& b, typename Q::Scalar t)\n{\n  typedef typename Q::Scalar Scalar;\n  static const Scalar one = Scalar(1) - dummy_precision<Scalar>();\n  Scalar d = a.dot(b);\n  Scalar absD = internal::abs(d);\n  if (absD>=one)\n    return a;\n\n  // theta is the angle between the 2 quaternions\n  Scalar theta = std::acos(absD);\n  Scalar sinTheta = internal::sin(theta);\n\n  Scalar scale0 = internal::sin( ( Scalar(1) - t ) * theta) / sinTheta;\n  Scalar scale1 = internal::sin( ( t * theta) ) / sinTheta;\n  if (d<0)\n    scale1 = -scale1;\n\n  return Q(scale0 * a.coeffs() + scale1 * b.coeffs());\n}\n\ntemplate<typename Q>\nEIGEN_DONT_INLINE Q slerp_legacy_nlerp(const Q& a, const Q& b, typename Q::Scalar t)\n{\n  typedef typename Q::Scalar Scalar;\n  static const Scalar one = Scalar(1) - epsilon<Scalar>();\n  Scalar d = a.dot(b);\n  Scalar absD = internal::abs(d);\n  \n  Scalar scale0;\n  Scalar scale1;\n  \n  if (absD>=one)\n  {\n    scale0 = Scalar(1) - t;\n    scale1 = t;\n  }\n  else\n  {\n    // theta is the angle between the 2 quaternions\n    Scalar theta = std::acos(absD);\n    Scalar sinTheta = internal::sin(theta);\n\n    scale0 = internal::sin( ( Scalar(1) - t ) * theta) / sinTheta;\n    scale1 = internal::sin( ( t * theta) ) / sinTheta;\n    if (d<0)\n      scale1 = -scale1;\n  }\n\n  return Q(scale0 * a.coeffs() + scale1 * b.coeffs());\n}\n\ntemplate<typename T>\ninline T sin_over_x(T x)\n{\n  if (T(1) + x*x == T(1))\n    return T(1);\n  else\n    return std::sin(x)/x;\n}\n\ntemplate<typename Q>\nEIGEN_DONT_INLINE Q slerp_rw(const Q& a, const Q& b, typename Q::Scalar t)\n{\n  typedef typename Q::Scalar Scalar;\n  \n  Scalar d = a.dot(b);\n  Scalar theta;\n  if (d<0.0)\n    theta = /*M_PI -*/ Scalar(2)*std::asin( (a.coeffs()+b.coeffs()).norm()/2 );\n  else\n    theta = Scalar(2)*std::asin( (a.coeffs()-b.coeffs()).norm()/2 );\n  \n  // theta is the angle between the 2 quaternions\n//   Scalar theta = std::acos(absD);\n  Scalar sinOverTheta = sin_over_x(theta);\n\n  Scalar scale0 = (Scalar(1)-t)*sin_over_x( ( Scalar(1) - t ) * theta) / sinOverTheta;\n  Scalar scale1 = t * sin_over_x( ( t * theta) ) / sinOverTheta;\n  if (d<0)\n    scale1 = -scale1;\n\n  return Quaternion<Scalar>(scale0 * a.coeffs() + scale1 * b.coeffs());\n}\n\ntemplate<typename Q>\nEIGEN_DONT_INLINE Q slerp_gael(const Q& a, const Q& b, typename Q::Scalar t)\n{\n  typedef typename Q::Scalar Scalar;\n  \n  Scalar d = a.dot(b);\n  Scalar theta;\n//   theta = Scalar(2) * atan2((a.coeffs()-b.coeffs()).norm(),(a.coeffs()+b.coeffs()).norm());\n//   if (d<0.0)\n//     theta = M_PI-theta;\n  \n  if (d<0.0)\n    theta = /*M_PI -*/ Scalar(2)*std::asin( (-a.coeffs()-b.coeffs()).norm()/2 );\n  else\n    theta = Scalar(2)*std::asin( (a.coeffs()-b.coeffs()).norm()/2 );\n  \n  \n  Scalar scale0;\n  Scalar scale1;\n  if(theta*theta-Scalar(6)==-Scalar(6))\n  {\n    scale0 = Scalar(1) - t;\n    scale1 = t;\n  }\n  else\n  {\n    Scalar sinTheta = std::sin(theta);\n    scale0 = internal::sin( ( Scalar(1) - t ) * theta) / sinTheta;\n    scale1 = internal::sin( ( t * theta) ) / sinTheta;\n    if (d<0)\n      scale1 = -scale1;\n  }\n\n  return Quaternion<Scalar>(scale0 * a.coeffs() + scale1 * b.coeffs());\n}\n\nint main()\n{\n  typedef double RefScalar;\n  typedef float TestScalar;\n  \n  typedef Quaternion<RefScalar>  Qd;\n  typedef Quaternion<TestScalar> Qf;\n  \n  unsigned int g_seed = (unsigned int) time(NULL);\n  std::cout << g_seed << \"\\n\";\n//   g_seed = 1259932496;\n  srand(g_seed);\n  \n  Matrix<RefScalar,Dynamic,1> maxerr(7);\n  maxerr.setZero();\n  \n  Matrix<RefScalar,Dynamic,1> avgerr(7);\n  avgerr.setZero();\n  \n  cout << \"double=>float=>double       nlerp        eigen        legacy(snap)         legacy(nlerp)        rightway         gael's criteria\\n\";\n  \n  int rep = 100;\n  int iters = 40;\n  for (int w=0; w<rep; ++w)\n  {\n    Qf a, b;\n    a.coeffs().setRandom();\n    a.normalize();\n    b.coeffs().setRandom();\n    b.normalize();\n    \n    Qf c[6];\n    \n    Qd ar(a.cast<RefScalar>());\n    Qd br(b.cast<RefScalar>());\n    Qd cr;\n    \n    \n    \n    cout.precision(8);\n    cout << std::scientific;\n    for (int i=0; i<iters; ++i)\n    {\n      RefScalar t = 0.65;\n      cr = slerp_rw(ar,br,t);\n      \n      Qf refc = cr.cast<TestScalar>();\n      c[0] = nlerp(a,b,t);\n      c[1] = slerp_eigen(a,b,t);\n      c[2] = slerp_legacy(a,b,t);\n      c[3] = slerp_legacy_nlerp(a,b,t);\n      c[4] = slerp_rw(a,b,t);\n      c[5] = slerp_gael(a,b,t);\n      \n      VectorXd err(7);\n      err[0] = (cr.coeffs()-refc.cast<RefScalar>().coeffs()).norm();\n//       std::cout << err[0] << \"    \";\n      for (int k=0; k<6; ++k)\n      {\n        err[k+1] = (c[k].coeffs()-refc.coeffs()).norm();\n//         std::cout << err[k+1] << \"    \";\n      }\n      maxerr = maxerr.cwise().max(err);\n      avgerr += err;\n//       std::cout << \"\\n\";\n      b = cr.cast<TestScalar>();\n      br = cr;\n    }\n//     std::cout << \"\\n\";\n  }\n  avgerr /= RefScalar(rep*iters);\n  cout << \"\\n\\nAccuracy:\\n\"\n       << \"  max: \" << maxerr.transpose() << \"\\n\";\n  cout << \"  avg: \" << avgerr.transpose() << \"\\n\";\n  \n  // perf bench\n  Quaternionf a,b;\n  a.coeffs().setRandom();\n  a.normalize();\n  b.coeffs().setRandom();\n  b.normalize();\n  //b = a;\n  float s = 0.65;\n    \n  #define BENCH(FUNC) {\\\n    BenchTimer t; \\\n    for(int k=0; k<2; ++k) {\\\n      t.start(); \\\n      for(int i=0; i<1000000; ++i) \\\n        FUNC(a,b,s); \\\n      t.stop(); \\\n    } \\\n    cout << \"  \" << #FUNC << \" => \\t \" << t.value() << \"s\\n\"; \\\n  }\n  \n  cout << \"\\nSpeed:\\n\" << std::fixed;\n  BENCH(nlerp);\n  BENCH(slerp_eigen);\n  BENCH(slerp_legacy);\n  BENCH(slerp_legacy_nlerp);\n  BENCH(slerp_rw);\n  BENCH(slerp_gael);\n}\n\n"
  },
  {
    "path": "include/eigen3/bench/quatmul.cpp",
    "content": "#include <iostream>\n#include <Eigen/Core>\n#include <Eigen/Geometry>\n#include <bench/BenchTimer.h>\n\nusing namespace Eigen; \n\ntemplate<typename Quat>\nEIGEN_DONT_INLINE void quatmul_default(const Quat& a, const Quat& b, Quat& c)\n{\n  c = a * b;\n}\n\ntemplate<typename Quat>\nEIGEN_DONT_INLINE void quatmul_novec(const Quat& a, const Quat& b, Quat& c)\n{\n  c = internal::quat_product<0, Quat, Quat, typename Quat::Scalar, Aligned>::run(a,b);\n}\n\ntemplate<typename Quat> void bench(const std::string& label)\n{\n  int tries = 10;\n  int rep = 1000000;\n  BenchTimer t;\n  \n  Quat a(4, 1, 2, 3);\n  Quat b(2, 3, 4, 5);\n  Quat c;\n  \n  std::cout.precision(3);\n  \n  BENCH(t, tries, rep, quatmul_default(a,b,c));\n  std::cout << label << \" default \" << 1e3*t.best(CPU_TIMER) << \"ms  \\t\" << 1e-6*double(rep)/(t.best(CPU_TIMER)) << \" M mul/s\\n\";\n  \n  BENCH(t, tries, rep, quatmul_novec(a,b,c));\n  std::cout << label << \" novec   \" << 1e3*t.best(CPU_TIMER) << \"ms  \\t\" << 1e-6*double(rep)/(t.best(CPU_TIMER)) << \" M mul/s\\n\";\n}\n\nint main()\n{\n  bench<Quaternionf>(\"float \");\n  bench<Quaterniond>(\"double\");\n\n  return 0;\n\n}\n\n"
  },
  {
    "path": "include/eigen3/bench/sparse_cholesky.cpp",
    "content": "// #define EIGEN_TAUCS_SUPPORT\n// #define EIGEN_CHOLMOD_SUPPORT\n#include <iostream>\n#include <Eigen/Sparse>\n\n// g++ -DSIZE=10000 -DDENSITY=0.001  sparse_cholesky.cpp -I.. -DDENSEMATRI -O3 -g0 -DNDEBUG   -DNBTRIES=1 -I /home/gael/Coding/LinearAlgebra/taucs_full/src/ -I/home/gael/Coding/LinearAlgebra/taucs_full/build/linux/  -L/home/gael/Coding/LinearAlgebra/taucs_full/lib/linux/ -ltaucs /home/gael/Coding/LinearAlgebra/GotoBLAS/libgoto.a -lpthread -I /home/gael/Coding/LinearAlgebra/SuiteSparse/CHOLMOD/Include/ $CHOLLIB -I /home/gael/Coding/LinearAlgebra/SuiteSparse/UFconfig/ /home/gael/Coding/LinearAlgebra/SuiteSparse/CCOLAMD/Lib/libccolamd.a   /home/gael/Coding/LinearAlgebra/SuiteSparse/CHOLMOD/Lib/libcholmod.a -lmetis /home/gael/Coding/LinearAlgebra/SuiteSparse/AMD/Lib/libamd.a  /home/gael/Coding/LinearAlgebra/SuiteSparse/CAMD/Lib/libcamd.a   /home/gael/Coding/LinearAlgebra/SuiteSparse/CCOLAMD/Lib/libccolamd.a  /home/gael/Coding/LinearAlgebra/SuiteSparse/COLAMD/Lib/libcolamd.a -llapack && ./a.out\n\n#define NOGMM\n#define NOMTL\n\n#ifndef SIZE\n#define SIZE 10\n#endif\n\n#ifndef DENSITY\n#define DENSITY 0.01\n#endif\n\n#ifndef REPEAT\n#define REPEAT 1\n#endif\n\n#include \"BenchSparseUtil.h\"\n\n#ifndef MINDENSITY\n#define MINDENSITY 0.0004\n#endif\n\n#ifndef NBTRIES\n#define NBTRIES 10\n#endif\n\n#define BENCH(X) \\\n  timer.reset(); \\\n  for (int _j=0; _j<NBTRIES; ++_j) { \\\n    timer.start(); \\\n    for (int _k=0; _k<REPEAT; ++_k) { \\\n        X  \\\n  } timer.stop(); }\n\n// typedef SparseMatrix<Scalar,UpperTriangular> EigenSparseTriMatrix;\ntypedef SparseMatrix<Scalar,SelfAdjoint|LowerTriangular> EigenSparseSelfAdjointMatrix;\n\nvoid fillSpdMatrix(float density, int rows, int cols,  EigenSparseSelfAdjointMatrix& dst)\n{\n  dst.startFill(rows*cols*density);\n  for(int j = 0; j < cols; j++)\n  {\n    dst.fill(j,j) = internal::random<Scalar>(10,20);\n    for(int i = j+1; i < rows; i++)\n    {\n      Scalar v = (internal::random<float>(0,1) < density) ? internal::random<Scalar>() : 0;\n      if (v!=0)\n        dst.fill(i,j) = v;\n    }\n\n  }\n  dst.endFill();\n}\n\n#include <Eigen/Cholesky>\n\ntemplate<int Backend>\nvoid doEigen(const char* name, const EigenSparseSelfAdjointMatrix& sm1, int flags = 0)\n{\n  std::cout << name << \"...\" << std::flush;\n  BenchTimer timer;\n  timer.start();\n  SparseLLT<EigenSparseSelfAdjointMatrix,Backend> chol(sm1, flags);\n  timer.stop();\n  std::cout << \":\\t\" << timer.value() << endl;\n\n  std::cout << \"  nnz: \" << sm1.nonZeros() << \" => \" << chol.matrixL().nonZeros() << \"\\n\";\n//   std::cout << \"sparse\\n\" << chol.matrixL() << \"%\\n\";\n}\n\nint main(int argc, char *argv[])\n{\n  int rows = SIZE;\n  int cols = SIZE;\n  float density = DENSITY;\n  BenchTimer timer;\n\n  VectorXf b = VectorXf::Random(cols);\n  VectorXf x = VectorXf::Random(cols);\n\n  bool densedone = false;\n\n  //for (float density = DENSITY; density>=MINDENSITY; density*=0.5)\n//   float density = 0.5;\n  {\n    EigenSparseSelfAdjointMatrix sm1(rows, cols);\n    std::cout << \"Generate sparse matrix (might take a while)...\\n\";\n    fillSpdMatrix(density, rows, cols, sm1);\n    std::cout << \"DONE\\n\\n\";\n\n    // dense matrices\n    #ifdef DENSEMATRIX\n    if (!densedone)\n    {\n      densedone = true;\n      std::cout << \"Eigen Dense\\t\" << density*100 << \"%\\n\";\n      DenseMatrix m1(rows,cols);\n      eiToDense(sm1, m1);\n      m1 = (m1 + m1.transpose()).eval();\n      m1.diagonal() *= 0.5;\n\n//       BENCH(LLT<DenseMatrix> chol(m1);)\n//       std::cout << \"dense:\\t\" << timer.value() << endl;\n\n      BenchTimer timer;\n      timer.start();\n      LLT<DenseMatrix> chol(m1);\n      timer.stop();\n      std::cout << \"dense:\\t\" << timer.value() << endl;\n      int count = 0;\n      for (int j=0; j<cols; ++j)\n        for (int i=j; i<rows; ++i)\n          if (!internal::isMuchSmallerThan(internal::abs(chol.matrixL()(i,j)), 0.1))\n            count++;\n      std::cout << \"dense: \" << \"nnz = \" << count << \"\\n\";\n//       std::cout << \"dense:\\n\" << m1 << \"\\n\\n\" << chol.matrixL() << endl;\n    }\n    #endif\n\n    // eigen sparse matrices\n    doEigen<Eigen::DefaultBackend>(\"Eigen/Sparse\", sm1, Eigen::IncompleteFactorization);\n\n    #ifdef EIGEN_CHOLMOD_SUPPORT\n    doEigen<Eigen::Cholmod>(\"Eigen/Cholmod\", sm1, Eigen::IncompleteFactorization);\n    #endif\n\n    #ifdef EIGEN_TAUCS_SUPPORT\n    doEigen<Eigen::Taucs>(\"Eigen/Taucs\", sm1, Eigen::IncompleteFactorization);\n    #endif\n\n    #if 0\n    // TAUCS\n    {\n      taucs_ccs_matrix A = sm1.asTaucsMatrix();\n\n      //BENCH(taucs_ccs_matrix* chol = taucs_ccs_factor_llt(&A, 0, 0);)\n//       BENCH(taucs_supernodal_factor_to_ccs(taucs_ccs_factor_llt_ll(&A));)\n//       std::cout << \"taucs:\\t\" << timer.value() << endl;\n\n      taucs_ccs_matrix* chol = taucs_ccs_factor_llt(&A, 0, 0);\n\n      for (int j=0; j<cols; ++j)\n      {\n        for (int i=chol->colptr[j]; i<chol->colptr[j+1]; ++i)\n          std::cout << chol->values.d[i] << \" \";\n      }\n    }\n\n    // CHOLMOD\n    #ifdef EIGEN_CHOLMOD_SUPPORT\n    {\n      cholmod_common c;\n      cholmod_start (&c);\n      cholmod_sparse A;\n      cholmod_factor *L;\n\n      A = sm1.asCholmodMatrix();\n      BenchTimer timer;\n//       timer.reset();\n      timer.start();\n      std::vector<int> perm(cols);\n//       std::vector<int> set(ncols);\n      for (int i=0; i<cols; ++i)\n        perm[i] = i;\n//       c.nmethods = 1;\n//       c.method[0] = 1;\n\n      c.nmethods = 1;\n      c.method [0].ordering = CHOLMOD_NATURAL;\n      c.postorder = 0;\n      c.final_ll = 1;\n\n      L = cholmod_analyze_p(&A, &perm[0], &perm[0], cols, &c);\n      timer.stop();\n      std::cout << \"cholmod/analyze:\\t\" << timer.value() << endl;\n      timer.reset();\n      timer.start();\n      cholmod_factorize(&A, L, &c);\n      timer.stop();\n      std::cout << \"cholmod/factorize:\\t\" << timer.value() << endl;\n\n      cholmod_sparse* cholmat = cholmod_factor_to_sparse(L, &c);\n\n      cholmod_print_factor(L, \"Factors\", &c);\n\n      cholmod_print_sparse(cholmat, \"Chol\", &c);\n      cholmod_write_sparse(stdout, cholmat, 0, 0, &c);\n//\n//       cholmod_print_sparse(&A, \"A\", &c);\n//       cholmod_write_sparse(stdout, &A, 0, 0, &c);\n\n\n//       for (int j=0; j<cols; ++j)\n//       {\n//           for (int i=chol->colptr[j]; i<chol->colptr[j+1]; ++i)\n//             std::cout << chol->values.s[i] << \" \";\n//       }\n    }\n    #endif\n\n    #endif\n\n\n\n  }\n\n\n  return 0;\n}\n\n"
  },
  {
    "path": "include/eigen3/bench/sparse_dense_product.cpp",
    "content": "\n//g++ -O3 -g0 -DNDEBUG  sparse_product.cpp -I.. -I/home/gael/Coding/LinearAlgebra/mtl4/ -DDENSITY=0.005 -DSIZE=10000 && ./a.out\n//g++ -O3 -g0 -DNDEBUG  sparse_product.cpp -I.. -I/home/gael/Coding/LinearAlgebra/mtl4/ -DDENSITY=0.05 -DSIZE=2000 && ./a.out\n// -DNOGMM -DNOMTL -DCSPARSE\n// -I /home/gael/Coding/LinearAlgebra/CSparse/Include/ /home/gael/Coding/LinearAlgebra/CSparse/Lib/libcsparse.a\n#ifndef SIZE\n#define SIZE 650000\n#endif\n\n#ifndef DENSITY\n#define DENSITY 0.01\n#endif\n\n#ifndef REPEAT\n#define REPEAT 1\n#endif\n\n#include \"BenchSparseUtil.h\"\n\n#ifndef MINDENSITY\n#define MINDENSITY 0.0004\n#endif\n\n#ifndef NBTRIES\n#define NBTRIES 10\n#endif\n\n#define BENCH(X) \\\n  timer.reset(); \\\n  for (int _j=0; _j<NBTRIES; ++_j) { \\\n    timer.start(); \\\n    for (int _k=0; _k<REPEAT; ++_k) { \\\n        X  \\\n  } timer.stop(); }\n\n\n#ifdef CSPARSE\ncs* cs_sorted_multiply(const cs* a, const cs* b)\n{\n  cs* A = cs_transpose (a, 1) ;\n  cs* B = cs_transpose (b, 1) ;\n  cs* D = cs_multiply (B,A) ;   /* D = B'*A' */\n  cs_spfree (A) ;\n  cs_spfree (B) ;\n  cs_dropzeros (D) ;      /* drop zeros from D */\n  cs* C = cs_transpose (D, 1) ;   /* C = D', so that C is sorted */\n  cs_spfree (D) ;\n  return C;\n}\n#endif\n\nint main(int argc, char *argv[])\n{\n  int rows = SIZE;\n  int cols = SIZE;\n  float density = DENSITY;\n\n  EigenSparseMatrix sm1(rows,cols);\n  DenseVector v1(cols), v2(cols);\n  v1.setRandom();\n\n  BenchTimer timer;\n  for (float density = DENSITY; density>=MINDENSITY; density*=0.5)\n  {\n    //fillMatrix(density, rows, cols, sm1);\n    fillMatrix2(7, rows, cols, sm1);\n\n    // dense matrices\n    #ifdef DENSEMATRIX\n    {\n      std::cout << \"Eigen Dense\\t\" << density*100 << \"%\\n\";\n      DenseMatrix m1(rows,cols);\n      eiToDense(sm1, m1);\n\n      timer.reset();\n      timer.start();\n      for (int k=0; k<REPEAT; ++k)\n        v2 = m1 * v1;\n      timer.stop();\n      std::cout << \"   a * v:\\t\" << timer.best() << \"  \" << double(REPEAT)/timer.best() << \" * / sec \" << endl;\n\n      timer.reset();\n      timer.start();\n      for (int k=0; k<REPEAT; ++k)\n        v2 = m1.transpose() * v1;\n      timer.stop();\n      std::cout << \"   a' * v:\\t\" << timer.best() << endl;\n    }\n    #endif\n\n    // eigen sparse matrices\n    {\n      std::cout << \"Eigen sparse\\t\" << sm1.nonZeros()/float(sm1.rows()*sm1.cols())*100 << \"%\\n\";\n\n      BENCH(asm(\"#myc\"); v2 = sm1 * v1; asm(\"#myd\");)\n      std::cout << \"   a * v:\\t\" << timer.best()/REPEAT << \"  \" << double(REPEAT)/timer.best(REAL_TIMER) << \" * / sec \" << endl;\n\n\n      BENCH( { asm(\"#mya\"); v2 = sm1.transpose() * v1; asm(\"#myb\"); })\n\n      std::cout << \"   a' * v:\\t\" << timer.best()/REPEAT << endl;\n    }\n\n//     {\n//       DynamicSparseMatrix<Scalar> m1(sm1);\n//       std::cout << \"Eigen dyn-sparse\\t\" << m1.nonZeros()/float(m1.rows()*m1.cols())*100 << \"%\\n\";\n//\n//       BENCH(for (int k=0; k<REPEAT; ++k) v2 = m1 * v1;)\n//       std::cout << \"   a * v:\\t\" << timer.value() << endl;\n//\n//       BENCH(for (int k=0; k<REPEAT; ++k) v2 = m1.transpose() * v1;)\n//       std::cout << \"   a' * v:\\t\" << timer.value() << endl;\n//     }\n\n    // GMM++\n    #ifndef NOGMM\n    {\n      std::cout << \"GMM++ sparse\\t\" << density*100 << \"%\\n\";\n      //GmmDynSparse  gmmT3(rows,cols);\n      GmmSparse m1(rows,cols);\n      eiToGmm(sm1, m1);\n\n      std::vector<Scalar> gmmV1(cols), gmmV2(cols);\n      Map<Matrix<Scalar,Dynamic,1> >(&gmmV1[0], cols) = v1;\n      Map<Matrix<Scalar,Dynamic,1> >(&gmmV2[0], cols) = v2;\n\n      BENCH( asm(\"#myx\"); gmm::mult(m1, gmmV1, gmmV2); asm(\"#myy\"); )\n      std::cout << \"   a * v:\\t\" << timer.value() << endl;\n\n      BENCH( gmm::mult(gmm::transposed(m1), gmmV1, gmmV2); )\n      std::cout << \"   a' * v:\\t\" << timer.value() << endl;\n    }\n    #endif\n    \n    #ifndef NOUBLAS\n    {\n      std::cout << \"ublas sparse\\t\" << density*100 << \"%\\n\";\n      UBlasSparse m1(rows,cols);\n      eiToUblas(sm1, m1);\n      \n      boost::numeric::ublas::vector<Scalar> uv1, uv2;\n      eiToUblasVec(v1,uv1);\n      eiToUblasVec(v2,uv2);\n\n//       std::vector<Scalar> gmmV1(cols), gmmV2(cols);\n//       Map<Matrix<Scalar,Dynamic,1> >(&gmmV1[0], cols) = v1;\n//       Map<Matrix<Scalar,Dynamic,1> >(&gmmV2[0], cols) = v2;\n\n      BENCH( uv2 = boost::numeric::ublas::prod(m1, uv1); )\n      std::cout << \"   a * v:\\t\" << timer.value() << endl;\n\n//       BENCH( boost::ublas::prod(gmm::transposed(m1), gmmV1, gmmV2); )\n//       std::cout << \"   a' * v:\\t\" << timer.value() << endl;\n    }\n    #endif\n\n    // MTL4\n    #ifndef NOMTL\n    {\n      std::cout << \"MTL4\\t\" << density*100 << \"%\\n\";\n      MtlSparse m1(rows,cols);\n      eiToMtl(sm1, m1);\n      mtl::dense_vector<Scalar> mtlV1(cols, 1.0);\n      mtl::dense_vector<Scalar> mtlV2(cols, 1.0);\n\n      timer.reset();\n      timer.start();\n      for (int k=0; k<REPEAT; ++k)\n        mtlV2 = m1 * mtlV1;\n      timer.stop();\n      std::cout << \"   a * v:\\t\" << timer.value() << endl;\n\n      timer.reset();\n      timer.start();\n      for (int k=0; k<REPEAT; ++k)\n        mtlV2 = trans(m1) * mtlV1;\n      timer.stop();\n      std::cout << \"   a' * v:\\t\" << timer.value() << endl;\n    }\n    #endif\n\n    std::cout << \"\\n\\n\";\n  }\n\n  return 0;\n}\n\n"
  },
  {
    "path": "include/eigen3/bench/sparse_lu.cpp",
    "content": "\n// g++ -I.. sparse_lu.cpp -O3 -g0 -I /usr/include/superlu/ -lsuperlu -lgfortran -DSIZE=1000 -DDENSITY=.05 && ./a.out\n\n#define EIGEN_SUPERLU_SUPPORT\n#define EIGEN_UMFPACK_SUPPORT\n#include <Eigen/Sparse>\n\n#define NOGMM\n#define NOMTL\n\n#ifndef SIZE\n#define SIZE 10\n#endif\n\n#ifndef DENSITY\n#define DENSITY 0.01\n#endif\n\n#ifndef REPEAT\n#define REPEAT 1\n#endif\n\n#include \"BenchSparseUtil.h\"\n\n#ifndef MINDENSITY\n#define MINDENSITY 0.0004\n#endif\n\n#ifndef NBTRIES\n#define NBTRIES 10\n#endif\n\n#define BENCH(X) \\\n  timer.reset(); \\\n  for (int _j=0; _j<NBTRIES; ++_j) { \\\n    timer.start(); \\\n    for (int _k=0; _k<REPEAT; ++_k) { \\\n        X  \\\n  } timer.stop(); }\n\ntypedef Matrix<Scalar,Dynamic,1> VectorX;\n\n#include <Eigen/LU>\n\ntemplate<int Backend>\nvoid doEigen(const char* name, const EigenSparseMatrix& sm1, const VectorX& b, VectorX& x, int flags = 0)\n{\n  std::cout << name << \"...\" << std::flush;\n  BenchTimer timer; timer.start();\n  SparseLU<EigenSparseMatrix,Backend> lu(sm1, flags);\n  timer.stop();\n  if (lu.succeeded())\n    std::cout << \":\\t\" << timer.value() << endl;\n  else\n  {\n    std::cout << \":\\t FAILED\" << endl;\n    return;\n  }\n\n  bool ok;\n  timer.reset(); timer.start();\n  ok = lu.solve(b,&x);\n  timer.stop();\n  if (ok)\n    std::cout << \"  solve:\\t\" << timer.value() << endl;\n  else\n    std::cout << \"  solve:\\t\" << \" FAILED\" << endl;\n\n  //std::cout << x.transpose() << \"\\n\";\n}\n\nint main(int argc, char *argv[])\n{\n  int rows = SIZE;\n  int cols = SIZE;\n  float density = DENSITY;\n  BenchTimer timer;\n\n  VectorX b = VectorX::Random(cols);\n  VectorX x = VectorX::Random(cols);\n\n  bool densedone = false;\n\n  //for (float density = DENSITY; density>=MINDENSITY; density*=0.5)\n//   float density = 0.5;\n  {\n    EigenSparseMatrix sm1(rows, cols);\n    fillMatrix(density, rows, cols, sm1);\n\n    // dense matrices\n    #ifdef DENSEMATRIX\n    if (!densedone)\n    {\n      densedone = true;\n      std::cout << \"Eigen Dense\\t\" << density*100 << \"%\\n\";\n      DenseMatrix m1(rows,cols);\n      eiToDense(sm1, m1);\n\n      BenchTimer timer;\n      timer.start();\n      FullPivLU<DenseMatrix> lu(m1);\n      timer.stop();\n      std::cout << \"Eigen/dense:\\t\" << timer.value() << endl;\n\n      timer.reset();\n      timer.start();\n      lu.solve(b,&x);\n      timer.stop();\n      std::cout << \"  solve:\\t\" << timer.value() << endl;\n//       std::cout << b.transpose() << \"\\n\";\n//       std::cout << x.transpose() << \"\\n\";\n    }\n    #endif\n\n    #ifdef EIGEN_UMFPACK_SUPPORT\n    x.setZero();\n    doEigen<Eigen::UmfPack>(\"Eigen/UmfPack (auto)\", sm1, b, x, 0);\n    #endif\n\n    #ifdef EIGEN_SUPERLU_SUPPORT\n    x.setZero();\n    doEigen<Eigen::SuperLU>(\"Eigen/SuperLU (nat)\", sm1, b, x, Eigen::NaturalOrdering);\n//     doEigen<Eigen::SuperLU>(\"Eigen/SuperLU (MD AT+A)\", sm1, b, x, Eigen::MinimumDegree_AT_PLUS_A);\n//     doEigen<Eigen::SuperLU>(\"Eigen/SuperLU (MD ATA)\", sm1, b, x, Eigen::MinimumDegree_ATA);\n    doEigen<Eigen::SuperLU>(\"Eigen/SuperLU (COLAMD)\", sm1, b, x, Eigen::ColApproxMinimumDegree);\n    #endif\n\n  }\n\n  return 0;\n}\n\n"
  },
  {
    "path": "include/eigen3/bench/sparse_product.cpp",
    "content": "\n//g++ -O3 -g0 -DNDEBUG  sparse_product.cpp -I.. -I/home/gael/Coding/LinearAlgebra/mtl4/ -DDENSITY=0.005 -DSIZE=10000 && ./a.out\n//g++ -O3 -g0 -DNDEBUG  sparse_product.cpp -I.. -I/home/gael/Coding/LinearAlgebra/mtl4/ -DDENSITY=0.05 -DSIZE=2000 && ./a.out\n// -DNOGMM -DNOMTL -DCSPARSE\n// -I /home/gael/Coding/LinearAlgebra/CSparse/Include/ /home/gael/Coding/LinearAlgebra/CSparse/Lib/libcsparse.a\n\n#include <typeinfo>\n\n#ifndef SIZE\n#define SIZE 1000000\n#endif\n\n#ifndef NNZPERCOL\n#define NNZPERCOL 6\n#endif\n\n#ifndef REPEAT\n#define REPEAT 1\n#endif\n\n#include <algorithm>\n#include \"BenchTimer.h\"\n#include \"BenchUtil.h\"\n#include \"BenchSparseUtil.h\"\n\n#ifndef NBTRIES\n#define NBTRIES 1\n#endif\n\n#define BENCH(X) \\\n  timer.reset(); \\\n  for (int _j=0; _j<NBTRIES; ++_j) { \\\n    timer.start(); \\\n    for (int _k=0; _k<REPEAT; ++_k) { \\\n        X  \\\n  } timer.stop(); }\n\n// #ifdef MKL\n//\n// #include \"mkl_types.h\"\n// #include \"mkl_spblas.h\"\n//\n// template<typename Lhs,typename Rhs,typename Res>\n// void mkl_multiply(const Lhs& lhs, const Rhs& rhs, Res& res)\n// {\n//   char n = 'N';\n//   float alpha = 1;\n//   char matdescra[6];\n//   matdescra[0] = 'G';\n//   matdescra[1] = 0;\n//   matdescra[2] = 0;\n//   matdescra[3] = 'C';\n//   mkl_scscmm(&n, lhs.rows(), rhs.cols(), lhs.cols(), &alpha, matdescra,\n//              lhs._valuePtr(), lhs._innerIndexPtr(), lhs.outerIndexPtr(),\n//              pntre, b, &ldb, &beta, c, &ldc);\n// //   mkl_somatcopy('C', 'T', lhs.rows(), lhs.cols(), 1,\n// //                 lhs._valuePtr(), lhs.rows(), DST, dst_stride);\n// }\n//\n// #endif\n\n\n#ifdef CSPARSE\ncs* cs_sorted_multiply(const cs* a, const cs* b)\n{\n//   return cs_multiply(a,b);\n\n  cs* A = cs_transpose(a, 1);\n  cs* B = cs_transpose(b, 1);\n  cs* D = cs_multiply(B,A);   /* D = B'*A' */\n  cs_spfree (A) ;\n  cs_spfree (B) ;\n  cs_dropzeros (D) ;      /* drop zeros from D */\n  cs* C = cs_transpose (D, 1) ;   /* C = D', so that C is sorted */\n  cs_spfree (D) ;\n  return C;\n\n//   cs* A = cs_transpose(a, 1);\n//   cs* C = cs_transpose(A, 1);\n//   return C;\n}\n\ncs* cs_sorted_multiply2(const cs* a, const cs* b)\n{\n  cs* D = cs_multiply(a,b);\n  cs* E = cs_transpose(D,1);\n  cs_spfree(D);\n  cs* C = cs_transpose(E,1);\n  cs_spfree(E);\n  return C;\n}\n#endif\n\nvoid bench_sort();\n\nint main(int argc, char *argv[])\n{\n//   bench_sort();\n\n  int rows = SIZE;\n  int cols = SIZE;\n  float density = DENSITY;\n\n  EigenSparseMatrix sm1(rows,cols), sm2(rows,cols), sm3(rows,cols), sm4(rows,cols);\n\n  BenchTimer timer;\n  for (int nnzPerCol = NNZPERCOL; nnzPerCol>1; nnzPerCol/=1.1)\n  {\n    sm1.setZero();\n    sm2.setZero();\n    fillMatrix2(nnzPerCol, rows, cols, sm1);\n    fillMatrix2(nnzPerCol, rows, cols, sm2);\n//     std::cerr << \"filling OK\\n\";\n\n    // dense matrices\n    #ifdef DENSEMATRIX\n    {\n      std::cout << \"Eigen Dense\\t\" << nnzPerCol << \"%\\n\";\n      DenseMatrix m1(rows,cols), m2(rows,cols), m3(rows,cols);\n      eiToDense(sm1, m1);\n      eiToDense(sm2, m2);\n\n      timer.reset();\n      timer.start();\n      for (int k=0; k<REPEAT; ++k)\n        m3 = m1 * m2;\n      timer.stop();\n      std::cout << \"   a * b:\\t\" << timer.value() << endl;\n\n      timer.reset();\n      timer.start();\n      for (int k=0; k<REPEAT; ++k)\n        m3 = m1.transpose() * m2;\n      timer.stop();\n      std::cout << \"   a' * b:\\t\" << timer.value() << endl;\n\n      timer.reset();\n      timer.start();\n      for (int k=0; k<REPEAT; ++k)\n        m3 = m1.transpose() * m2.transpose();\n      timer.stop();\n      std::cout << \"   a' * b':\\t\" << timer.value() << endl;\n\n      timer.reset();\n      timer.start();\n      for (int k=0; k<REPEAT; ++k)\n        m3 = m1 * m2.transpose();\n      timer.stop();\n      std::cout << \"   a * b':\\t\" << timer.value() << endl;\n    }\n    #endif\n\n    // eigen sparse matrices\n    {\n      std::cout << \"Eigen sparse\\t\" << sm1.nonZeros()/(float(sm1.rows())*float(sm1.cols()))*100 << \"% * \"\n                << sm2.nonZeros()/(float(sm2.rows())*float(sm2.cols()))*100 << \"%\\n\";\n\n      BENCH(sm3 = sm1 * sm2; )\n      std::cout << \"   a * b:\\t\" << timer.value() << endl;\n\n//       BENCH(sm3 = sm1.transpose() * sm2; )\n//       std::cout << \"   a' * b:\\t\" << timer.value() << endl;\n// //\n//       BENCH(sm3 = sm1.transpose() * sm2.transpose(); )\n//       std::cout << \"   a' * b':\\t\" << timer.value() << endl;\n// //\n//       BENCH(sm3 = sm1 * sm2.transpose(); )\n//       std::cout << \"   a * b' :\\t\" << timer.value() << endl;\n\n\n//       std::cout << \"\\n\";\n//\n//       BENCH( sm3._experimentalNewProduct(sm1, sm2); )\n//       std::cout << \"   a * b:\\t\" << timer.value() << endl;\n//\n//       BENCH(sm3._experimentalNewProduct(sm1.transpose(),sm2); )\n//       std::cout << \"   a' * b:\\t\" << timer.value() << endl;\n// //\n//       BENCH(sm3._experimentalNewProduct(sm1.transpose(),sm2.transpose()); )\n//       std::cout << \"   a' * b':\\t\" << timer.value() << endl;\n// //\n//       BENCH(sm3._experimentalNewProduct(sm1, sm2.transpose());)\n//       std::cout << \"   a * b' :\\t\" << timer.value() << endl;\n    }\n\n    // eigen dyn-sparse matrices\n    /*{\n      DynamicSparseMatrix<Scalar> m1(sm1), m2(sm2), m3(sm3);\n      std::cout << \"Eigen dyn-sparse\\t\" << m1.nonZeros()/(float(m1.rows())*float(m1.cols()))*100 << \"% * \"\n                << m2.nonZeros()/(float(m2.rows())*float(m2.cols()))*100 << \"%\\n\";\n\n//       timer.reset();\n//       timer.start();\n      BENCH(for (int k=0; k<REPEAT; ++k) m3 = m1 * m2;)\n//       timer.stop();\n      std::cout << \"   a * b:\\t\" << timer.value() << endl;\n//       std::cout << sm3 << \"\\n\";\n\n      timer.reset();\n      timer.start();\n//       std::cerr << \"transpose...\\n\";\n//       EigenSparseMatrix sm4 = sm1.transpose();\n//       std::cout << sm4.nonZeros() << \" == \" << sm1.nonZeros() << \"\\n\";\n//       exit(1);\n//       std::cerr << \"transpose OK\\n\";\n//       std::cout << sm1 << \"\\n\\n\" << sm1.transpose() << \"\\n\\n\" << sm4.transpose() << \"\\n\\n\";\n      BENCH(for (int k=0; k<REPEAT; ++k) m3 = m1.transpose() * m2;)\n//       timer.stop();\n      std::cout << \"   a' * b:\\t\" << timer.value() << endl;\n\n//       timer.reset();\n//       timer.start();\n      BENCH( for (int k=0; k<REPEAT; ++k) m3 = m1.transpose() * m2.transpose(); )\n//       timer.stop();\n      std::cout << \"   a' * b':\\t\" << timer.value() << endl;\n\n//       timer.reset();\n//       timer.start();\n      BENCH( for (int k=0; k<REPEAT; ++k) m3 = m1 * m2.transpose(); )\n//       timer.stop();\n      std::cout << \"   a * b' :\\t\" << timer.value() << endl;\n    }*/\n\n    // CSparse\n    #ifdef CSPARSE\n    {\n      std::cout << \"CSparse \\t\" << nnzPerCol << \"%\\n\";\n      cs *m1, *m2, *m3;\n      eiToCSparse(sm1, m1);\n      eiToCSparse(sm2, m2);\n\n      BENCH(\n      {\n        m3 = cs_sorted_multiply(m1, m2);\n        if (!m3)\n        {\n          std::cerr << \"cs_multiply failed\\n\";\n        }\n//         cs_print(m3, 0);\n        cs_spfree(m3);\n      }\n      );\n//       timer.stop();\n      std::cout << \"   a * b:\\t\" << timer.value() << endl;\n\n//       BENCH( { m3 = cs_sorted_multiply2(m1, m2); cs_spfree(m3); } );\n//       std::cout << \"   a * b:\\t\" << timer.value() << endl;\n    }\n    #endif\n\n    #ifndef NOUBLAS\n    {\n      std::cout << \"ublas\\t\" << nnzPerCol << \"%\\n\";\n      UBlasSparse m1(rows,cols), m2(rows,cols), m3(rows,cols);\n      eiToUblas(sm1, m1);\n      eiToUblas(sm2, m2);\n\n      BENCH(boost::numeric::ublas::prod(m1, m2, m3););\n      std::cout << \"   a * b:\\t\" << timer.value() << endl;\n    }\n    #endif\n\n    // GMM++\n    #ifndef NOGMM\n    {\n      std::cout << \"GMM++ sparse\\t\" << nnzPerCol << \"%\\n\";\n      GmmDynSparse  gmmT3(rows,cols);\n      GmmSparse m1(rows,cols), m2(rows,cols), m3(rows,cols);\n      eiToGmm(sm1, m1);\n      eiToGmm(sm2, m2);\n\n      BENCH(gmm::mult(m1, m2, gmmT3););\n      std::cout << \"   a * b:\\t\" << timer.value() << endl;\n\n//       BENCH(gmm::mult(gmm::transposed(m1), m2, gmmT3););\n//       std::cout << \"   a' * b:\\t\" << timer.value() << endl;\n//\n//       if (rows<500)\n//       {\n//         BENCH(gmm::mult(gmm::transposed(m1), gmm::transposed(m2), gmmT3););\n//         std::cout << \"   a' * b':\\t\" << timer.value() << endl;\n//\n//         BENCH(gmm::mult(m1, gmm::transposed(m2), gmmT3););\n//         std::cout << \"   a * b':\\t\" << timer.value() << endl;\n//       }\n//       else\n//       {\n//         std::cout << \"   a' * b':\\t\" << \"forever\" << endl;\n//         std::cout << \"   a * b':\\t\" << \"forever\" << endl;\n//       }\n    }\n    #endif\n\n    // MTL4\n    #ifndef NOMTL\n    {\n      std::cout << \"MTL4\\t\" << nnzPerCol << \"%\\n\";\n      MtlSparse m1(rows,cols), m2(rows,cols), m3(rows,cols);\n      eiToMtl(sm1, m1);\n      eiToMtl(sm2, m2);\n\n      BENCH(m3 = m1 * m2;);\n      std::cout << \"   a * b:\\t\" << timer.value() << endl;\n\n//       BENCH(m3 = trans(m1) * m2;);\n//       std::cout << \"   a' * b:\\t\" << timer.value() << endl;\n//\n//       BENCH(m3 = trans(m1) * trans(m2););\n//       std::cout << \"  a' * b':\\t\" << timer.value() << endl;\n//\n//       BENCH(m3 = m1 * trans(m2););\n//       std::cout << \"   a * b' :\\t\" << timer.value() << endl;\n    }\n    #endif\n\n    std::cout << \"\\n\\n\";\n  }\n\n  return 0;\n}\n\n\n\n"
  },
  {
    "path": "include/eigen3/bench/sparse_randomsetter.cpp",
    "content": "\n#define NOGMM\n#define NOMTL\n\n#include <map>\n#include <ext/hash_map>\n#include <google/dense_hash_map>\n#include <google/sparse_hash_map>\n\n#ifndef SIZE\n#define SIZE 10000\n#endif\n\n#ifndef DENSITY\n#define DENSITY 0.01\n#endif\n\n#ifndef REPEAT\n#define REPEAT 1\n#endif\n\n#include \"BenchSparseUtil.h\"\n\n#ifndef MINDENSITY\n#define MINDENSITY 0.0004\n#endif\n\n#ifndef NBTRIES\n#define NBTRIES 10\n#endif\n\n#define BENCH(X) \\\n  timer.reset(); \\\n  for (int _j=0; _j<NBTRIES; ++_j) { \\\n    timer.start(); \\\n    for (int _k=0; _k<REPEAT; ++_k) { \\\n        X  \\\n  } timer.stop(); }\n\n\nstatic double rtime;\nstatic double nentries;\n\ntemplate<typename SetterType>\nvoid dostuff(const char* name, EigenSparseMatrix& sm1)\n{\n  int rows = sm1.rows();\n  int cols = sm1.cols();\n  sm1.setZero();\n  BenchTimer t;\n  SetterType* set1 = new SetterType(sm1);\n  t.reset(); t.start();\n  for (int k=0; k<nentries; ++k)\n    (*set1)(internal::random<int>(0,rows-1),internal::random<int>(0,cols-1)) += 1;\n  t.stop();\n  std::cout << \"std::map =>      \\t\" << t.value()-rtime\n            << \" nnz=\" << set1->nonZeros() << std::flush;\n\n  // getchar();\n\n  t.reset(); t.start(); delete set1; t.stop();\n  std::cout << \"  back: \\t\" << t.value() << \"\\n\";\n}\n    \nint main(int argc, char *argv[])\n{\n  int rows = SIZE;\n  int cols = SIZE;\n  float density = DENSITY;\n\n  EigenSparseMatrix sm1(rows,cols), sm2(rows,cols);\n\n\n  nentries = rows*cols*density;\n  std::cout << \"n = \" << nentries << \"\\n\";\n  int dummy;\n  BenchTimer t;\n\n  t.reset(); t.start();\n  for (int k=0; k<nentries; ++k)\n    dummy = internal::random<int>(0,rows-1) + internal::random<int>(0,cols-1);\n  t.stop();\n  rtime = t.value();\n  std::cout << \"rtime = \" << rtime << \" (\" << dummy << \")\\n\\n\";\n  const int Bits = 6;\n  for (;;)\n  {\n    dostuff<RandomSetter<EigenSparseMatrix,StdMapTraits,Bits> >(\"std::map     \", sm1);\n    dostuff<RandomSetter<EigenSparseMatrix,GnuHashMapTraits,Bits> >(\"gnu::hash_map\", sm1);\n    dostuff<RandomSetter<EigenSparseMatrix,GoogleDenseHashMapTraits,Bits> >(\"google::dense\", sm1);\n    dostuff<RandomSetter<EigenSparseMatrix,GoogleSparseHashMapTraits,Bits> >(\"google::sparse\", sm1);\n\n//     {\n//       RandomSetter<EigenSparseMatrix,GnuHashMapTraits,Bits> set1(sm1);\n//       t.reset(); t.start();\n//       for (int k=0; k<n; ++k)\n//         set1(internal::random<int>(0,rows-1),internal::random<int>(0,cols-1)) += 1;\n//       t.stop();\n//       std::cout << \"gnu::hash_map => \\t\" << t.value()-rtime\n//                 << \" nnz=\" << set1.nonZeros() << \"\\n\";getchar();\n//     }\n//     {\n//       RandomSetter<EigenSparseMatrix,GoogleDenseHashMapTraits,Bits> set1(sm1);\n//       t.reset(); t.start();\n//       for (int k=0; k<n; ++k)\n//         set1(internal::random<int>(0,rows-1),internal::random<int>(0,cols-1)) += 1;\n//       t.stop();\n//       std::cout << \"google::dense => \\t\" << t.value()-rtime\n//                 << \" nnz=\" << set1.nonZeros() << \"\\n\";getchar();\n//     }\n//     {\n//       RandomSetter<EigenSparseMatrix,GoogleSparseHashMapTraits,Bits> set1(sm1);\n//       t.reset(); t.start();\n//       for (int k=0; k<n; ++k)\n//         set1(internal::random<int>(0,rows-1),internal::random<int>(0,cols-1)) += 1;\n//       t.stop();\n//       std::cout << \"google::sparse => \\t\" << t.value()-rtime\n//                 << \" nnz=\" << set1.nonZeros() << \"\\n\";getchar();\n//     }\n    std::cout << \"\\n\\n\";\n  }\n\n  return 0;\n}\n\n"
  },
  {
    "path": "include/eigen3/bench/sparse_setter.cpp",
    "content": "\n//g++ -O3 -g0 -DNDEBUG  sparse_product.cpp -I.. -I/home/gael/Coding/LinearAlgebra/mtl4/ -DDENSITY=0.005 -DSIZE=10000 && ./a.out\n//g++ -O3 -g0 -DNDEBUG  sparse_product.cpp -I.. -I/home/gael/Coding/LinearAlgebra/mtl4/ -DDENSITY=0.05 -DSIZE=2000 && ./a.out\n// -DNOGMM -DNOMTL -DCSPARSE\n// -I /home/gael/Coding/LinearAlgebra/CSparse/Include/ /home/gael/Coding/LinearAlgebra/CSparse/Lib/libcsparse.a\n#ifndef SIZE\n#define SIZE 100000\n#endif\n\n#ifndef NBPERROW\n#define NBPERROW 24\n#endif\n\n#ifndef REPEAT\n#define REPEAT 2\n#endif\n\n#ifndef NBTRIES\n#define NBTRIES 2\n#endif\n\n#ifndef KK\n#define KK 10\n#endif\n\n#ifndef NOGOOGLE\n#define EIGEN_GOOGLEHASH_SUPPORT\n#include <google/sparse_hash_map>\n#endif\n\n#include \"BenchSparseUtil.h\"\n\n#define CHECK_MEM\n// #define CHECK_MEM  std/**/::cout << \"check mem\\n\"; getchar();\n\n#define BENCH(X) \\\n  timer.reset(); \\\n  for (int _j=0; _j<NBTRIES; ++_j) { \\\n    timer.start(); \\\n    for (int _k=0; _k<REPEAT; ++_k) { \\\n        X  \\\n  } timer.stop(); }\n\ntypedef std::vector<Vector2i> Coordinates;\ntypedef std::vector<float> Values;\n\nEIGEN_DONT_INLINE Scalar* setinnerrand_eigen(const Coordinates& coords, const Values& vals);\nEIGEN_DONT_INLINE Scalar* setrand_eigen_dynamic(const Coordinates& coords, const Values& vals);\nEIGEN_DONT_INLINE Scalar* setrand_eigen_compact(const Coordinates& coords, const Values& vals);\nEIGEN_DONT_INLINE Scalar* setrand_eigen_sumeq(const Coordinates& coords, const Values& vals);\nEIGEN_DONT_INLINE Scalar* setrand_eigen_gnu_hash(const Coordinates& coords, const Values& vals);\nEIGEN_DONT_INLINE Scalar* setrand_eigen_google_dense(const Coordinates& coords, const Values& vals);\nEIGEN_DONT_INLINE Scalar* setrand_eigen_google_sparse(const Coordinates& coords, const Values& vals);\nEIGEN_DONT_INLINE Scalar* setrand_scipy(const Coordinates& coords, const Values& vals);\nEIGEN_DONT_INLINE Scalar* setrand_ublas_mapped(const Coordinates& coords, const Values& vals);\nEIGEN_DONT_INLINE Scalar* setrand_ublas_coord(const Coordinates& coords, const Values& vals);\nEIGEN_DONT_INLINE Scalar* setrand_ublas_compressed(const Coordinates& coords, const Values& vals);\nEIGEN_DONT_INLINE Scalar* setrand_ublas_genvec(const Coordinates& coords, const Values& vals);\nEIGEN_DONT_INLINE Scalar* setrand_mtl(const Coordinates& coords, const Values& vals);\n\nint main(int argc, char *argv[])\n{\n  int rows = SIZE;\n  int cols = SIZE;\n  bool fullyrand = true;\n\n  BenchTimer timer;\n  Coordinates coords;\n  Values values;\n  if(fullyrand)\n  {\n    Coordinates pool;\n    pool.reserve(cols*NBPERROW);\n    std::cerr << \"fill pool\" << \"\\n\";\n    for (int i=0; i<cols*NBPERROW; )\n    {\n//       DynamicSparseMatrix<int> stencil(SIZE,SIZE);\n      Vector2i ij(internal::random<int>(0,rows-1),internal::random<int>(0,cols-1));\n//       if(stencil.coeffRef(ij.x(), ij.y())==0)\n      {\n//         stencil.coeffRef(ij.x(), ij.y()) = 1;\n        pool.push_back(ij);\n\n      }\n      ++i;\n    }\n    std::cerr << \"pool ok\" << \"\\n\";\n    int n = cols*NBPERROW*KK;\n    coords.reserve(n);\n    values.reserve(n);\n    for (int i=0; i<n; ++i)\n    {\n      int i = internal::random<int>(0,pool.size());\n      coords.push_back(pool[i]);\n      values.push_back(internal::random<Scalar>());\n    }\n  }\n  else\n  {\n    for (int j=0; j<cols; ++j)\n    for (int i=0; i<NBPERROW; ++i)\n    {\n      coords.push_back(Vector2i(internal::random<int>(0,rows-1),j));\n      values.push_back(internal::random<Scalar>());\n    }\n  }\n  std::cout << \"nnz = \" << coords.size()  << \"\\n\";\n  CHECK_MEM\n\n    // dense matrices\n    #ifdef DENSEMATRIX\n    {\n      BENCH(setrand_eigen_dense(coords,values);)\n      std::cout << \"Eigen Dense\\t\" << timer.value() << \"\\n\";\n    }\n    #endif\n\n    // eigen sparse matrices\n//     if (!fullyrand)\n//     {\n//       BENCH(setinnerrand_eigen(coords,values);)\n//       std::cout << \"Eigen fillrand\\t\" << timer.value() << \"\\n\";\n//     }\n    {\n      BENCH(setrand_eigen_dynamic(coords,values);)\n      std::cout << \"Eigen dynamic\\t\" << timer.value() << \"\\n\";\n    }\n//     {\n//       BENCH(setrand_eigen_compact(coords,values);)\n//       std::cout << \"Eigen compact\\t\" << timer.value() << \"\\n\";\n//     }\n    {\n      BENCH(setrand_eigen_sumeq(coords,values);)\n      std::cout << \"Eigen sumeq\\t\" << timer.value() << \"\\n\";\n    }\n    {\n//       BENCH(setrand_eigen_gnu_hash(coords,values);)\n//       std::cout << \"Eigen std::map\\t\" << timer.value() << \"\\n\";\n    }\n    {\n      BENCH(setrand_scipy(coords,values);)\n      std::cout << \"scipy\\t\" << timer.value() << \"\\n\";\n    }\n    #ifndef NOGOOGLE\n    {\n      BENCH(setrand_eigen_google_dense(coords,values);)\n      std::cout << \"Eigen google dense\\t\" << timer.value() << \"\\n\";\n    }\n    {\n      BENCH(setrand_eigen_google_sparse(coords,values);)\n      std::cout << \"Eigen google sparse\\t\" << timer.value() << \"\\n\";\n    }\n    #endif\n\n    #ifndef NOUBLAS\n    {\n//       BENCH(setrand_ublas_mapped(coords,values);)\n//       std::cout << \"ublas mapped\\t\" << timer.value() << \"\\n\";\n    }\n    {\n      BENCH(setrand_ublas_genvec(coords,values);)\n      std::cout << \"ublas vecofvec\\t\" << timer.value() << \"\\n\";\n    }\n    /*{\n      timer.reset();\n      timer.start();\n      for (int k=0; k<REPEAT; ++k)\n        setrand_ublas_compressed(coords,values);\n      timer.stop();\n      std::cout << \"ublas comp\\t\" << timer.value() << \"\\n\";\n    }\n    {\n      timer.reset();\n      timer.start();\n      for (int k=0; k<REPEAT; ++k)\n        setrand_ublas_coord(coords,values);\n      timer.stop();\n      std::cout << \"ublas coord\\t\" << timer.value() << \"\\n\";\n    }*/\n    #endif\n\n\n    // MTL4\n    #ifndef NOMTL\n    {\n      BENCH(setrand_mtl(coords,values));\n      std::cout << \"MTL\\t\" << timer.value() << \"\\n\";\n    }\n    #endif\n\n  return 0;\n}\n\nEIGEN_DONT_INLINE Scalar* setinnerrand_eigen(const Coordinates& coords, const Values& vals)\n{\n  using namespace Eigen;\n  SparseMatrix<Scalar> mat(SIZE,SIZE);\n  //mat.startFill(2000000/*coords.size()*/);\n  for (int i=0; i<coords.size(); ++i)\n  {\n    mat.insert(coords[i].x(), coords[i].y()) = vals[i];\n  }\n  mat.finalize();\n  CHECK_MEM;\n  return 0;\n}\n\nEIGEN_DONT_INLINE Scalar* setrand_eigen_dynamic(const Coordinates& coords, const Values& vals)\n{\n  using namespace Eigen;\n  DynamicSparseMatrix<Scalar> mat(SIZE,SIZE);\n  mat.reserve(coords.size()/10);\n  for (int i=0; i<coords.size(); ++i)\n  {\n    mat.coeffRef(coords[i].x(), coords[i].y()) += vals[i];\n  }\n  mat.finalize();\n  CHECK_MEM;\n  return &mat.coeffRef(coords[0].x(), coords[0].y());\n}\n\nEIGEN_DONT_INLINE Scalar* setrand_eigen_sumeq(const Coordinates& coords, const Values& vals)\n{\n  using namespace Eigen;\n  int n = coords.size()/KK;\n  DynamicSparseMatrix<Scalar> mat(SIZE,SIZE);\n  for (int j=0; j<KK; ++j)\n  {\n    DynamicSparseMatrix<Scalar> aux(SIZE,SIZE);\n    mat.reserve(n);\n    for (int i=j*n; i<(j+1)*n; ++i)\n    {\n      aux.insert(coords[i].x(), coords[i].y()) += vals[i];\n    }\n    aux.finalize();\n    mat += aux;\n  }\n  return &mat.coeffRef(coords[0].x(), coords[0].y());\n}\n\nEIGEN_DONT_INLINE Scalar* setrand_eigen_compact(const Coordinates& coords, const Values& vals)\n{\n  using namespace Eigen;\n  DynamicSparseMatrix<Scalar> setter(SIZE,SIZE);\n  setter.reserve(coords.size()/10);\n  for (int i=0; i<coords.size(); ++i)\n  {\n    setter.coeffRef(coords[i].x(), coords[i].y()) += vals[i];\n  }\n  SparseMatrix<Scalar> mat = setter;\n  CHECK_MEM;\n  return &mat.coeffRef(coords[0].x(), coords[0].y());\n}\n\nEIGEN_DONT_INLINE Scalar* setrand_eigen_gnu_hash(const Coordinates& coords, const Values& vals)\n{\n  using namespace Eigen;\n  SparseMatrix<Scalar> mat(SIZE,SIZE);\n  {\n    RandomSetter<SparseMatrix<Scalar>, StdMapTraits > setter(mat);\n    for (int i=0; i<coords.size(); ++i)\n    {\n      setter(coords[i].x(), coords[i].y()) += vals[i];\n    }\n    CHECK_MEM;\n  }\n  return &mat.coeffRef(coords[0].x(), coords[0].y());\n}\n\n#ifndef NOGOOGLE\nEIGEN_DONT_INLINE Scalar* setrand_eigen_google_dense(const Coordinates& coords, const Values& vals)\n{\n  using namespace Eigen;\n  SparseMatrix<Scalar> mat(SIZE,SIZE);\n  {\n    RandomSetter<SparseMatrix<Scalar>, GoogleDenseHashMapTraits> setter(mat);\n    for (int i=0; i<coords.size(); ++i)\n      setter(coords[i].x(), coords[i].y()) += vals[i];\n    CHECK_MEM;\n  }\n  return &mat.coeffRef(coords[0].x(), coords[0].y());\n}\n\nEIGEN_DONT_INLINE Scalar* setrand_eigen_google_sparse(const Coordinates& coords, const Values& vals)\n{\n  using namespace Eigen;\n  SparseMatrix<Scalar> mat(SIZE,SIZE);\n  {\n    RandomSetter<SparseMatrix<Scalar>, GoogleSparseHashMapTraits> setter(mat);\n    for (int i=0; i<coords.size(); ++i)\n      setter(coords[i].x(), coords[i].y()) += vals[i];\n    CHECK_MEM;\n  }\n  return &mat.coeffRef(coords[0].x(), coords[0].y());\n}\n#endif\n\n\ntemplate <class T>\nvoid coo_tocsr(const int n_row,\n               const int n_col,\n               const int nnz,\n               const Coordinates Aij,\n               const Values Ax,\n                     int Bp[],\n                     int Bj[],\n                     T Bx[])\n{\n    //compute number of non-zero entries per row of A coo_tocsr\n    std::fill(Bp, Bp + n_row, 0);\n\n    for (int n = 0; n < nnz; n++){\n        Bp[Aij[n].x()]++;\n    }\n\n    //cumsum the nnz per row to get Bp[]\n    for(int i = 0, cumsum = 0; i < n_row; i++){\n        int temp = Bp[i];\n        Bp[i] = cumsum;\n        cumsum += temp;\n    }\n    Bp[n_row] = nnz;\n\n    //write Aj,Ax into Bj,Bx\n    for(int n = 0; n < nnz; n++){\n        int row  = Aij[n].x();\n        int dest = Bp[row];\n\n        Bj[dest] = Aij[n].y();\n        Bx[dest] = Ax[n];\n\n        Bp[row]++;\n    }\n\n    for(int i = 0, last = 0; i <= n_row; i++){\n        int temp = Bp[i];\n        Bp[i]  = last;\n        last   = temp;\n    }\n\n    //now Bp,Bj,Bx form a CSR representation (with possible duplicates)\n}\n\ntemplate< class T1, class T2 >\nbool kv_pair_less(const std::pair<T1,T2>& x, const std::pair<T1,T2>& y){\n    return x.first < y.first;\n}\n\n\ntemplate<class I, class T>\nvoid csr_sort_indices(const I n_row,\n                      const I Ap[],\n                            I Aj[],\n                            T Ax[])\n{\n    std::vector< std::pair<I,T> > temp;\n\n    for(I i = 0; i < n_row; i++){\n        I row_start = Ap[i];\n        I row_end   = Ap[i+1];\n\n        temp.clear();\n\n        for(I jj = row_start; jj < row_end; jj++){\n            temp.push_back(std::make_pair(Aj[jj],Ax[jj]));\n        }\n\n        std::sort(temp.begin(),temp.end(),kv_pair_less<I,T>);\n\n        for(I jj = row_start, n = 0; jj < row_end; jj++, n++){\n            Aj[jj] = temp[n].first;\n            Ax[jj] = temp[n].second;\n        }\n    }\n}\n\ntemplate <class I, class T>\nvoid csr_sum_duplicates(const I n_row,\n                        const I n_col,\n                              I Ap[],\n                              I Aj[],\n                              T Ax[])\n{\n    I nnz = 0;\n    I row_end = 0;\n    for(I i = 0; i < n_row; i++){\n        I jj = row_end;\n        row_end = Ap[i+1];\n        while( jj < row_end ){\n            I j = Aj[jj];\n            T x = Ax[jj];\n            jj++;\n            while( jj < row_end && Aj[jj] == j ){\n                x += Ax[jj];\n                jj++;\n            }\n            Aj[nnz] = j;\n            Ax[nnz] = x;\n            nnz++;\n        }\n        Ap[i+1] = nnz;\n    }\n}\n\nEIGEN_DONT_INLINE Scalar* setrand_scipy(const Coordinates& coords, const Values& vals)\n{\n  using namespace Eigen;\n  SparseMatrix<Scalar> mat(SIZE,SIZE);\n  mat.resizeNonZeros(coords.size());\n//   std::cerr << \"setrand_scipy...\\n\";\n  coo_tocsr<Scalar>(SIZE,SIZE, coords.size(), coords, vals, mat._outerIndexPtr(), mat._innerIndexPtr(), mat._valuePtr());\n//   std::cerr << \"coo_tocsr ok\\n\";\n\n  csr_sort_indices(SIZE, mat._outerIndexPtr(), mat._innerIndexPtr(), mat._valuePtr());\n\n  csr_sum_duplicates(SIZE, SIZE, mat._outerIndexPtr(), mat._innerIndexPtr(), mat._valuePtr());\n\n  mat.resizeNonZeros(mat._outerIndexPtr()[SIZE]);\n\n  return &mat.coeffRef(coords[0].x(), coords[0].y());\n}\n\n\n#ifndef NOUBLAS\nEIGEN_DONT_INLINE Scalar* setrand_ublas_mapped(const Coordinates& coords, const Values& vals)\n{\n  using namespace boost;\n  using namespace boost::numeric;\n  using namespace boost::numeric::ublas;\n  mapped_matrix<Scalar> aux(SIZE,SIZE);\n  for (int i=0; i<coords.size(); ++i)\n  {\n    aux(coords[i].x(), coords[i].y()) += vals[i];\n  }\n  CHECK_MEM;\n  compressed_matrix<Scalar> mat(aux);\n  return 0;// &mat(coords[0].x(), coords[0].y());\n}\n/*EIGEN_DONT_INLINE Scalar* setrand_ublas_coord(const Coordinates& coords, const Values& vals)\n{\n  using namespace boost;\n  using namespace boost::numeric;\n  using namespace boost::numeric::ublas;\n  coordinate_matrix<Scalar> aux(SIZE,SIZE);\n  for (int i=0; i<coords.size(); ++i)\n  {\n    aux(coords[i].x(), coords[i].y()) = vals[i];\n  }\n  compressed_matrix<Scalar> mat(aux);\n  return 0;//&mat(coords[0].x(), coords[0].y());\n}\nEIGEN_DONT_INLINE Scalar* setrand_ublas_compressed(const Coordinates& coords, const Values& vals)\n{\n  using namespace boost;\n  using namespace boost::numeric;\n  using namespace boost::numeric::ublas;\n  compressed_matrix<Scalar> mat(SIZE,SIZE);\n  for (int i=0; i<coords.size(); ++i)\n  {\n    mat(coords[i].x(), coords[i].y()) = vals[i];\n  }\n  return 0;//&mat(coords[0].x(), coords[0].y());\n}*/\nEIGEN_DONT_INLINE Scalar* setrand_ublas_genvec(const Coordinates& coords, const Values& vals)\n{\n  using namespace boost;\n  using namespace boost::numeric;\n  using namespace boost::numeric::ublas;\n\n//   ublas::vector<coordinate_vector<Scalar> > foo;\n  generalized_vector_of_vector<Scalar, row_major, ublas::vector<coordinate_vector<Scalar> > > aux(SIZE,SIZE);\n  for (int i=0; i<coords.size(); ++i)\n  {\n    aux(coords[i].x(), coords[i].y()) += vals[i];\n  }\n  CHECK_MEM;\n  compressed_matrix<Scalar,row_major> mat(aux);\n  return 0;//&mat(coords[0].x(), coords[0].y());\n}\n#endif\n\n#ifndef NOMTL\nEIGEN_DONT_INLINE void setrand_mtl(const Coordinates& coords, const Values& vals);\n#endif\n\n"
  },
  {
    "path": "include/eigen3/bench/sparse_transpose.cpp",
    "content": "\n//g++ -O3 -g0 -DNDEBUG  sparse_transpose.cpp -I.. -I/home/gael/Coding/LinearAlgebra/mtl4/ -DDENSITY=0.005 -DSIZE=10000 && ./a.out\n// -DNOGMM -DNOMTL\n// -DCSPARSE -I /home/gael/Coding/LinearAlgebra/CSparse/Include/ /home/gael/Coding/LinearAlgebra/CSparse/Lib/libcsparse.a\n\n#ifndef SIZE\n#define SIZE 10000\n#endif\n\n#ifndef DENSITY\n#define DENSITY 0.01\n#endif\n\n#ifndef REPEAT\n#define REPEAT 1\n#endif\n\n#include \"BenchSparseUtil.h\"\n\n#ifndef MINDENSITY\n#define MINDENSITY 0.0004\n#endif\n\n#ifndef NBTRIES\n#define NBTRIES 10\n#endif\n\n#define BENCH(X) \\\n  timer.reset(); \\\n  for (int _j=0; _j<NBTRIES; ++_j) { \\\n    timer.start(); \\\n    for (int _k=0; _k<REPEAT; ++_k) { \\\n        X  \\\n  } timer.stop(); }\n\nint main(int argc, char *argv[])\n{\n  int rows = SIZE;\n  int cols = SIZE;\n  float density = DENSITY;\n\n  EigenSparseMatrix sm1(rows,cols), sm3(rows,cols);\n\n  BenchTimer timer;\n  for (float density = DENSITY; density>=MINDENSITY; density*=0.5)\n  {\n    fillMatrix(density, rows, cols, sm1);\n\n    // dense matrices\n    #ifdef DENSEMATRIX\n    {\n      DenseMatrix m1(rows,cols), m3(rows,cols);\n      eiToDense(sm1, m1);\n      BENCH(for (int k=0; k<REPEAT; ++k) m3 = m1.transpose();)\n      std::cout << \"  Eigen dense:\\t\" << timer.value() << endl;\n    }\n    #endif\n\n    std::cout << \"Non zeros: \" << sm1.nonZeros()/float(sm1.rows()*sm1.cols())*100 << \"%\\n\";\n\n    // eigen sparse matrices\n    {\n      BENCH(for (int k=0; k<REPEAT; ++k) sm3 = sm1.transpose();)\n      std::cout << \"  Eigen:\\t\" << timer.value() << endl;\n    }\n\n    // CSparse\n    #ifdef CSPARSE\n    {\n      cs *m1, *m3;\n      eiToCSparse(sm1, m1);\n\n      BENCH(for (int k=0; k<REPEAT; ++k) { m3 = cs_transpose(m1,1); cs_spfree(m3);})\n      std::cout << \"  CSparse:\\t\" << timer.value() << endl;\n    }\n    #endif\n\n    // GMM++\n    #ifndef NOGMM\n    {\n      GmmDynSparse  gmmT3(rows,cols);\n      GmmSparse m1(rows,cols), m3(rows,cols);\n      eiToGmm(sm1, m1);\n      BENCH(for (int k=0; k<REPEAT; ++k) gmm::copy(gmm::transposed(m1),m3);)\n      std::cout << \"  GMM:\\t\\t\" << timer.value() << endl;\n    }\n    #endif\n\n    // MTL4\n    #ifndef NOMTL\n    {\n      MtlSparse m1(rows,cols), m3(rows,cols);\n      eiToMtl(sm1, m1);\n      BENCH(for (int k=0; k<REPEAT; ++k) m3 = trans(m1);)\n      std::cout << \"  MTL4:\\t\\t\" << timer.value() << endl;\n    }\n    #endif\n\n    std::cout << \"\\n\\n\";\n  }\n\n  return 0;\n}\n\n"
  },
  {
    "path": "include/eigen3/bench/sparse_trisolver.cpp",
    "content": "\n//g++ -O3 -g0 -DNDEBUG  sparse_product.cpp -I.. -I/home/gael/Coding/LinearAlgebra/mtl4/ -DDENSITY=0.005 -DSIZE=10000 && ./a.out\n//g++ -O3 -g0 -DNDEBUG  sparse_product.cpp -I.. -I/home/gael/Coding/LinearAlgebra/mtl4/ -DDENSITY=0.05 -DSIZE=2000 && ./a.out\n// -DNOGMM -DNOMTL\n// -I /home/gael/Coding/LinearAlgebra/CSparse/Include/ /home/gael/Coding/LinearAlgebra/CSparse/Lib/libcsparse.a\n\n#ifndef SIZE\n#define SIZE 10000\n#endif\n\n#ifndef DENSITY\n#define DENSITY 0.01\n#endif\n\n#ifndef REPEAT\n#define REPEAT 1\n#endif\n\n#include \"BenchSparseUtil.h\"\n\n#ifndef MINDENSITY\n#define MINDENSITY 0.0004\n#endif\n\n#ifndef NBTRIES\n#define NBTRIES 10\n#endif\n\n#define BENCH(X) \\\n  timer.reset(); \\\n  for (int _j=0; _j<NBTRIES; ++_j) { \\\n    timer.start(); \\\n    for (int _k=0; _k<REPEAT; ++_k) { \\\n        X  \\\n  } timer.stop(); }\n\ntypedef SparseMatrix<Scalar,UpperTriangular> EigenSparseTriMatrix;\ntypedef SparseMatrix<Scalar,RowMajorBit|UpperTriangular> EigenSparseTriMatrixRow;\n\nvoid fillMatrix(float density, int rows, int cols,  EigenSparseTriMatrix& dst)\n{\n  dst.startFill(rows*cols*density);\n  for(int j = 0; j < cols; j++)\n  {\n    for(int i = 0; i < j; i++)\n    {\n      Scalar v = (internal::random<float>(0,1) < density) ? internal::random<Scalar>() : 0;\n      if (v!=0)\n        dst.fill(i,j) = v;\n    }\n    dst.fill(j,j) = internal::random<Scalar>();\n  }\n  dst.endFill();\n}\n\nint main(int argc, char *argv[])\n{\n  int rows = SIZE;\n  int cols = SIZE;\n  float density = DENSITY;\n  BenchTimer timer;\n  #if 1\n  EigenSparseTriMatrix sm1(rows,cols);\n  typedef Matrix<Scalar,Dynamic,1> DenseVector;\n  DenseVector b = DenseVector::Random(cols);\n  DenseVector x = DenseVector::Random(cols);\n\n  bool densedone = false;\n\n  for (float density = DENSITY; density>=MINDENSITY; density*=0.5)\n  {\n    EigenSparseTriMatrix sm1(rows, cols);\n    fillMatrix(density, rows, cols, sm1);\n\n    // dense matrices\n    #ifdef DENSEMATRIX\n    if (!densedone)\n    {\n      densedone = true;\n      std::cout << \"Eigen Dense\\t\" << density*100 << \"%\\n\";\n      DenseMatrix m1(rows,cols);\n      Matrix<Scalar,Dynamic,Dynamic,Dynamic,Dynamic,RowMajorBit> m2(rows,cols);\n      eiToDense(sm1, m1);\n      m2 = m1;\n\n      BENCH(x = m1.marked<UpperTriangular>().solveTriangular(b);)\n      std::cout << \"   colmajor^-1 * b:\\t\" << timer.value() << endl;\n//       std::cerr << x.transpose() << \"\\n\";\n\n      BENCH(x = m2.marked<UpperTriangular>().solveTriangular(b);)\n      std::cout << \"   rowmajor^-1 * b:\\t\" << timer.value() << endl;\n//       std::cerr << x.transpose() << \"\\n\";\n    }\n    #endif\n\n    // eigen sparse matrices\n    {\n      std::cout << \"Eigen sparse\\t\" << density*100 << \"%\\n\";\n      EigenSparseTriMatrixRow sm2 = sm1;\n\n      BENCH(x = sm1.solveTriangular(b);)\n      std::cout << \"   colmajor^-1 * b:\\t\" << timer.value() << endl;\n//       std::cerr << x.transpose() << \"\\n\";\n\n      BENCH(x = sm2.solveTriangular(b);)\n      std::cout << \"   rowmajor^-1 * b:\\t\" << timer.value() << endl;\n//       std::cerr << x.transpose() << \"\\n\";\n\n//       x = b;\n//       BENCH(sm1.inverseProductInPlace(x);)\n//       std::cout << \"   colmajor^-1 * b:\\t\" << timer.value() << \" (inplace)\" << endl;\n//       std::cerr << x.transpose() << \"\\n\";\n//\n//       x = b;\n//       BENCH(sm2.inverseProductInPlace(x);)\n//       std::cout << \"   rowmajor^-1 * b:\\t\" << timer.value() << \" (inplace)\" << endl;\n//       std::cerr << x.transpose() << \"\\n\";\n    }\n\n\n\n    // CSparse\n    #ifdef CSPARSE\n    {\n      std::cout << \"CSparse \\t\" << density*100 << \"%\\n\";\n      cs *m1;\n      eiToCSparse(sm1, m1);\n\n      BENCH(x = b; if (!cs_lsolve (m1, x.data())){std::cerr << \"cs_lsolve failed\\n\"; break;}; )\n      std::cout << \"   colmajor^-1 * b:\\t\" << timer.value() << endl;\n    }\n    #endif\n\n    // GMM++\n    #ifndef NOGMM\n    {\n      std::cout << \"GMM++ sparse\\t\" << density*100 << \"%\\n\";\n      GmmSparse m1(rows,cols);\n      gmm::csr_matrix<Scalar> m2;\n      eiToGmm(sm1, m1);\n      gmm::copy(m1,m2);\n      std::vector<Scalar> gmmX(cols), gmmB(cols);\n      Map<Matrix<Scalar,Dynamic,1> >(&gmmX[0], cols) = x;\n      Map<Matrix<Scalar,Dynamic,1> >(&gmmB[0], cols) = b;\n\n      gmmX = gmmB;\n      BENCH(gmm::upper_tri_solve(m1, gmmX, false);)\n      std::cout << \"   colmajor^-1 * b:\\t\" << timer.value() << endl;\n//       std::cerr << Map<Matrix<Scalar,Dynamic,1> >(&gmmX[0], cols).transpose() << \"\\n\";\n\n      gmmX = gmmB;\n      BENCH(gmm::upper_tri_solve(m2, gmmX, false);)\n      timer.stop();\n      std::cout << \"   rowmajor^-1 * b:\\t\" << timer.value() << endl;\n//       std::cerr << Map<Matrix<Scalar,Dynamic,1> >(&gmmX[0], cols).transpose() << \"\\n\";\n    }\n    #endif\n\n    // MTL4\n    #ifndef NOMTL\n    {\n      std::cout << \"MTL4\\t\" << density*100 << \"%\\n\";\n      MtlSparse m1(rows,cols);\n      MtlSparseRowMajor m2(rows,cols);\n      eiToMtl(sm1, m1);\n      m2 = m1;\n      mtl::dense_vector<Scalar> x(rows, 1.0);\n      mtl::dense_vector<Scalar> b(rows, 1.0);\n\n      BENCH(x = mtl::upper_trisolve(m1,b);)\n      std::cout << \"   colmajor^-1 * b:\\t\" << timer.value() << endl;\n//       std::cerr << x << \"\\n\";\n\n      BENCH(x = mtl::upper_trisolve(m2,b);)\n      std::cout << \"   rowmajor^-1 * b:\\t\" << timer.value() << endl;\n//       std::cerr << x << \"\\n\";\n    }\n    #endif\n\n\n    std::cout << \"\\n\\n\";\n  }\n  #endif\n\n  #if 0\n    // bench small matrices (in-place versus return bye value)\n    {\n      timer.reset();\n      for (int _j=0; _j<10; ++_j) {\n        Matrix4f m = Matrix4f::Random();\n        Vector4f b = Vector4f::Random();\n        Vector4f x = Vector4f::Random();\n        timer.start();\n        for (int _k=0; _k<1000000; ++_k) {\n          b = m.inverseProduct(b);\n        }\n        timer.stop();\n      }\n      std::cout << \"4x4 :\\t\" << timer.value() << endl;\n    }\n\n    {\n      timer.reset();\n      for (int _j=0; _j<10; ++_j) {\n        Matrix4f m = Matrix4f::Random();\n        Vector4f b = Vector4f::Random();\n        Vector4f x = Vector4f::Random();\n        timer.start();\n        for (int _k=0; _k<1000000; ++_k) {\n          m.inverseProductInPlace(x);\n        }\n        timer.stop();\n      }\n      std::cout << \"4x4 IP :\\t\" << timer.value() << endl;\n    }\n  #endif\n\n  return 0;\n}\n\n"
  },
  {
    "path": "include/eigen3/bench/spbench/CMakeLists.txt",
    "content": "\n\nset(BLAS_FOUND TRUE)\nset(LAPACK_FOUND TRUE)\nset(BLAS_LIBRARIES eigen_blas_static)\nset(LAPACK_LIBRARIES eigen_lapack_static)\n\nset(SPARSE_LIBS \"\")\n\n# find_library(PARDISO_LIBRARIES pardiso412-GNU450-X86-64)\n# if(PARDISO_LIBRARIES)\n#   add_definitions(\"-DEIGEN_PARDISO_SUPPORT\")\n#   set(SPARSE_LIBS ${SPARSE_LIBS} ${PARDISO_LIBRARIES})\n# endif(PARDISO_LIBRARIES)\n\nfind_package(Cholmod)\nif(CHOLMOD_FOUND AND BLAS_FOUND AND LAPACK_FOUND)\n  add_definitions(\"-DEIGEN_CHOLMOD_SUPPORT\")\n  include_directories(${CHOLMOD_INCLUDES})\n  set(SPARSE_LIBS ${SPARSE_LIBS} ${CHOLMOD_LIBRARIES} ${BLAS_LIBRARIES} ${LAPACK_LIBRARIES})\n  set(CHOLMOD_ALL_LIBS  ${CHOLMOD_LIBRARIES} ${BLAS_LIBRARIES} ${LAPACK_LIBRARIES})\nendif()\n\nfind_package(Umfpack)\nif(UMFPACK_FOUND AND BLAS_FOUND)\n  add_definitions(\"-DEIGEN_UMFPACK_SUPPORT\")\n  include_directories(${UMFPACK_INCLUDES})\n  set(SPARSE_LIBS ${SPARSE_LIBS} ${UMFPACK_LIBRARIES} ${BLAS_LIBRARIES})\n  set(UMFPACK_ALL_LIBS ${UMFPACK_LIBRARIES} ${BLAS_LIBRARIES})\nendif()\n\nfind_package(SuperLU 4.0)\nif(SUPERLU_FOUND AND BLAS_FOUND)\n  add_definitions(\"-DEIGEN_SUPERLU_SUPPORT\")\n  include_directories(${SUPERLU_INCLUDES})\n  set(SPARSE_LIBS ${SPARSE_LIBS} ${SUPERLU_LIBRARIES} ${BLAS_LIBRARIES})\n  set(SUPERLU_ALL_LIBS ${SUPERLU_LIBRARIES} ${BLAS_LIBRARIES})\nendif()\n\n\nfind_package(PASTIX QUIET COMPONENTS METIS SCOTCH)\n# check that the PASTIX found is a version without MPI\nfind_path(PASTIX_pastix_nompi.h_INCLUDE_DIRS\n  NAMES pastix_nompi.h\n  HINTS ${PASTIX_INCLUDE_DIRS}\n)\nif (NOT PASTIX_pastix_nompi.h_INCLUDE_DIRS)\n  message(STATUS \"A version of Pastix has been found but pastix_nompi.h does not exist in the include directory.\"\n                 \" Because Eigen tests require a version without MPI, we disable the Pastix backend.\")\nendif()\nif(PASTIX_FOUND AND PASTIX_pastix_nompi.h_INCLUDE_DIRS AND BLAS_FOUND)\n  add_definitions(\"-DEIGEN_PASTIX_SUPPORT\")\n  include_directories(${PASTIX_INCLUDE_DIRS_DEP})\n  if(SCOTCH_FOUND)\n    include_directories(${SCOTCH_INCLUDE_DIRS})\n    set(PASTIX_LIBRARIES ${PASTIX_LIBRARIES} ${SCOTCH_LIBRARIES})\n  elseif(METIS_FOUND)\n    include_directories(${METIS_INCLUDE_DIRS})\n    set(PASTIX_LIBRARIES ${PASTIX_LIBRARIES} ${METIS_LIBRARIES})  \n  endif(SCOTCH_FOUND)\n  set(SPARSE_LIBS ${SPARSE_LIBS} ${PASTIX_LIBRARIES_DEP} ${ORDERING_LIBRARIES})\n  set(PASTIX_ALL_LIBS ${PASTIX_LIBRARIES_DEP})\nendif()\n\nif(METIS_FOUND)\n  include_directories(${METIS_INCLUDE_DIRS})\n  set (SPARSE_LIBS ${SPARSE_LIBS} ${METIS_LIBRARIES})\n  add_definitions(\"-DEIGEN_METIS_SUPPORT\")\nendif(METIS_FOUND)\n\nfind_library(RT_LIBRARY rt)\nif(RT_LIBRARY)\n  set(SPARSE_LIBS ${SPARSE_LIBS} ${RT_LIBRARY})\nendif(RT_LIBRARY)\n\nadd_executable(spbenchsolver spbenchsolver.cpp)\ntarget_link_libraries (spbenchsolver ${SPARSE_LIBS})\n\nadd_executable(spsolver sp_solver.cpp)\ntarget_link_libraries (spsolver ${SPARSE_LIBS})\n\n\nadd_executable(test_sparseLU test_sparseLU.cpp)\ntarget_link_libraries (test_sparseLU ${SPARSE_LIBS})\n\n"
  },
  {
    "path": "include/eigen3/bench/spbench/sp_solver.cpp",
    "content": "// Small bench routine for Eigen available in Eigen\n// (C) Desire NUENTSA WAKAM, INRIA\n\n#include <iostream>\n#include <fstream>\n#include <iomanip>\n#include <Eigen/Jacobi>\n#include <Eigen/Householder>\n#include <Eigen/IterativeLinearSolvers>\n#include <Eigen/LU>\n#include <unsupported/Eigen/SparseExtra>\n//#include <Eigen/SparseLU>\n#include <Eigen/SuperLUSupport>\n// #include <unsupported/Eigen/src/IterativeSolvers/Scaling.h>\n#include <bench/BenchTimer.h>\n#include <unsupported/Eigen/IterativeSolvers>\nusing namespace std;\nusing namespace Eigen;\n\nint main(int argc, char **args)\n{\n  SparseMatrix<double, ColMajor> A; \n  typedef SparseMatrix<double, ColMajor>::Index Index;\n  typedef Matrix<double, Dynamic, Dynamic> DenseMatrix;\n  typedef Matrix<double, Dynamic, 1> DenseRhs;\n  VectorXd b, x, tmp;\n  BenchTimer timer,totaltime; \n  //SparseLU<SparseMatrix<double, ColMajor> >   solver;\n//   SuperLU<SparseMatrix<double, ColMajor> >   solver;\n  ConjugateGradient<SparseMatrix<double, ColMajor>, Lower,IncompleteCholesky<double,Lower> > solver; \n  ifstream matrix_file; \n  string line;\n  int  n;\n  // Set parameters\n//   solver.iparm(IPARM_THREAD_NBR) = 4;\n  /* Fill the matrix with sparse matrix stored in Matrix-Market coordinate column-oriented format */\n  if (argc < 2) assert(false && \"please, give the matrix market file \");\n  \n  timer.start();\n  totaltime.start();\n  loadMarket(A, args[1]);\n  cout << \"End charging matrix \" << endl;\n  bool iscomplex=false, isvector=false;\n  int sym;\n  getMarketHeader(args[1], sym, iscomplex, isvector);\n  if (iscomplex) { cout<< \" Not for complex matrices \\n\"; return -1; }\n  if (isvector) { cout << \"The provided file is not a matrix file\\n\"; return -1;}\n  if (sym != 0) { // symmetric matrices, only the lower part is stored\n    SparseMatrix<double, ColMajor> temp; \n    temp = A;\n    A = temp.selfadjointView<Lower>();\n  }\n  timer.stop();\n  \n  n = A.cols();\n  // ====== TESTS FOR SPARSE TUTORIAL ======\n//   cout<< \"OuterSize \" << A.outerSize() << \" inner \" << A.innerSize() << endl; \n//   SparseMatrix<double, RowMajor> mat1(A); \n//   SparseMatrix<double, RowMajor> mat2;\n//   cout << \" norm of A \" << mat1.norm() << endl; ;\n//   PermutationMatrix<Dynamic, Dynamic, int> perm(n);\n//   perm.resize(n,1);\n//   perm.indices().setLinSpaced(n, 0, n-1);\n//   mat2 = perm * mat1;\n//   mat.subrows();\n//   mat2.resize(n,n); \n//   mat2.reserve(10);\n//   mat2.setConstant();\n//   std::cout<< \"NORM \" << mat1.squaredNorm()<< endl;  \n\n  cout<< \"Time to load the matrix \" << timer.value() <<endl;\n  /* Fill the right hand side */\n\n//   solver.set_restart(374);\n  if (argc > 2)\n    loadMarketVector(b, args[2]);\n  else \n  {\n    b.resize(n);\n    tmp.resize(n);\n//       tmp.setRandom();\n    for (int i = 0; i < n; i++) tmp(i) = i; \n    b = A * tmp ;\n  }\n//   Scaling<SparseMatrix<double> > scal; \n//   scal.computeRef(A);\n//   b = scal.LeftScaling().cwiseProduct(b);\n\n  /* Compute the factorization */\n  cout<< \"Starting the factorization \"<< endl; \n  timer.reset();\n  timer.start(); \n  cout<< \"Size of Input Matrix \"<< b.size()<<\"\\n\\n\";\n  cout<< \"Rows and columns \"<< A.rows() <<\" \" <<A.cols() <<\"\\n\";\n  solver.compute(A);\n//   solver.analyzePattern(A);\n//   solver.factorize(A);\n  if (solver.info() != Success) {\n    std::cout<< \"The solver failed \\n\";\n    return -1; \n  }\n  timer.stop(); \n  float time_comp = timer.value(); \n  cout <<\" Compute Time \" << time_comp<< endl; \n  \n  timer.reset();\n  timer.start();\n  x = solver.solve(b);\n//   x = scal.RightScaling().cwiseProduct(x);\n  timer.stop();\n  float time_solve = timer.value(); \n  cout<< \" Time to solve \" << time_solve << endl; \n \n  /* Check the accuracy */\n  VectorXd tmp2 = b - A*x;\n  double tempNorm = tmp2.norm()/b.norm();\n  cout << \"Relative norm of the computed solution : \" << tempNorm <<\"\\n\";\n//   cout << \"Iterations : \" << solver.iterations() << \"\\n\"; \n  \n  totaltime.stop();\n  cout << \"Total time \" << totaltime.value() << \"\\n\";\n//  std::cout<<x.transpose()<<\"\\n\";\n  \n  return 0;\n}"
  },
  {
    "path": "include/eigen3/bench/spbench/spbench.dtd",
    "content": "<!ELEMENT BENCH (AVAILSOLVER+,LINEARSYSTEM+)>\n  <!ELEMENT AVAILSOLVER (SOLVER+)>\n    <!ELEMENT SOLVER (TYPE,PACKAGE)>\n      <!ELEMENT TYPE (#PCDATA)>  <!-- One of LU, LLT, LDLT, ITER -->\n      <!ELEMENT PACKAGE (#PCDATA)>  <!-- Derived from a library -->\n  <!ELEMENT LINEARSYSTEM (MATRIX,SOLVER_STAT+,BEST_SOLVER,GLOBAL_PARAMS*)>\n    <!ELEMENT MATRIX (NAME,SIZE,ENTRIES,PATTERN?,SYMMETRY,POSDEF?,ARITHMETIC,RHS*)>\n      <!ELEMENT NAME (#PCDATA)>\n      <!ELEMENT SIZE (#PCDATA)>\n      <!ELEMENT ENTRIES (#PCDATA)> <!-- The number of nonzeros elements -->\n      <!ELEMENT PATTERN (#PCDATA)>  <!-- Is structural pattern symmetric or not -->\n      <!ELEMENT SYMMETRY (#PCDATA)> <!-- symmmetry with numerical values -->\n      <!ELEMENT POSDEF (#PCDATA)> <!-- Is the matrix positive definite or not -->\n      <!ELEMENT ARITHMETIC (#PCDATA)> \n      <!ELEMENT RHS (SOURCE)>  <!-- A matrix can have one or more right hand side associated. -->\n        <!ELEMENT SOURCE (#PCDATA)> <!-- Source of the right hand side, either generated or provided -->\n    <!ELEMENT SOLVER_STAT (PARAMS*,TIME,ERROR,ITER?)>\n      <!ELEMENT PARAMS (#PCDATA)>\n      <!ELEMENT TIME (COMPUTE,SOLVE,TOTAL)>\n        <!ELEMENT COMPUTE (#PCDATA)> <!-- Time to analyze,to factorize, or to setup the preconditioner-->\n        <!ELEMENT SOLVE (#PCDATA)> <!-- Time to solve with all the available rhs -->\n        <!ELEMENT TOTAL (#PCDATA)>\n      <!ELEMENT ERROR (#PCDATA)> <!-- Either the relative error or the relative residual norm -->\n      <!ELEMENT ITER (#PCDATA)> <!-- Number of iterations -->\n    <!ELEMENT BEST_SOLVER CDATA> <!-- Id of the best solver -->\n    <!ELEMENT GLOBAL_PARAMS (#PCDATA)> <!-- Parameters shared by all solvers -->\n\n<!ATTLIST SOLVER ID CDATA #REQUIRED>\n<!ATTLIST SOLVER_STAT ID CDATA #REQUIRED>\n<!ATTLIST BEST_SOLVER ID CDATA #REQUIRED>\n<!ATTLIST RHS ID CDATA #IMPLIED>"
  },
  {
    "path": "include/eigen3/bench/spbench/spbenchsolver.cpp",
    "content": "#include <bench/spbench/spbenchsolver.h>\n\nvoid bench_printhelp()\n{\n    cout<< \" \\nbenchsolver : performs a benchmark of all the solvers available in Eigen \\n\\n\";\n    cout<< \" MATRIX FOLDER : \\n\";\n    cout<< \" The matrices for the benchmark should be collected in a folder specified with an environment variable EIGEN_MATRIXDIR \\n\";\n    cout<< \" The matrices are stored using the matrix market coordinate format \\n\";\n    cout<< \" The matrix and associated right-hand side (rhs) files are named respectively \\n\";\n    cout<< \" as MatrixName.mtx and MatrixName_b.mtx. If the rhs does not exist, a random one is generated. \\n\";\n    cout<< \" If a matrix is SPD, the matrix should be named as MatrixName_SPD.mtx \\n\";\n    cout<< \" If a true solution exists, it should be named as MatrixName_x.mtx; \\n\"     ;\n    cout<< \" it will be used to compute the norm of the error relative to the computed solutions\\n\\n\";\n    cout<< \" OPTIONS : \\n\"; \n    cout<< \" -h or --help \\n    print this help and return\\n\\n\";\n    cout<< \" -d matrixdir \\n    Use matrixdir as the matrix folder instead of the one specified in the environment variable EIGEN_MATRIXDIR\\n\\n\"; \n    cout<< \" -o outputfile.xml \\n    Output the statistics to a xml file \\n\\n\";\n    cout<< \" --eps <RelErr> Sets the relative tolerance for iterative solvers (default 1e-08) \\n\\n\";\n    cout<< \" --maxits <MaxIts> Sets the maximum number of iterations (default 1000) \\n\\n\";\n    \n}\nint main(int argc, char ** args)\n{\n  \n  bool help = ( get_options(argc, args, \"-h\") || get_options(argc, args, \"--help\") );\n  if(help) {\n    bench_printhelp();\n    return 0;\n  }\n\n  // Get the location of the test matrices\n  string matrix_dir;\n  if (!get_options(argc, args, \"-d\", &matrix_dir))\n  {\n    if(getenv(\"EIGEN_MATRIXDIR\") == NULL){\n      std::cerr << \"Please, specify the location of the matrices with -d mat_folder or the environment variable EIGEN_MATRIXDIR \\n\";\n      std::cerr << \" Run with --help to see the list of all the available options \\n\";\n      return -1;\n    }\n    matrix_dir = getenv(\"EIGEN_MATRIXDIR\");\n  }\n     \n  std::ofstream statbuf;\n  string statFile ;\n  \n  // Get the file to write the statistics\n  bool statFileExists = get_options(argc, args, \"-o\", &statFile);\n  if(statFileExists)\n  {\n    statbuf.open(statFile.c_str(), std::ios::out);\n    if(statbuf.good()){\n      statFileExists = true; \n      printStatheader(statbuf);\n      statbuf.close();\n    }\n    else\n      std::cerr << \"Unable to open the provided file for writting... \\n\";\n  }       \n  \n  // Get the maximum number of iterations and the tolerance\n  int maxiters = 1000; \n  double tol = 1e-08; \n  string inval; \n  if (get_options(argc, args, \"--eps\", &inval))\n    tol = atof(inval.c_str()); \n  if(get_options(argc, args, \"--maxits\", &inval))\n    maxiters = atoi(inval.c_str()); \n  \n  string current_dir; \n  // Test the real-arithmetics matrices\n  Browse_Matrices<double>(matrix_dir, statFileExists, statFile,maxiters, tol);\n  \n  // Test the complex-arithmetics matrices\n  Browse_Matrices<std::complex<double> >(matrix_dir, statFileExists, statFile, maxiters, tol); \n  \n  if(statFileExists)\n  {\n    statbuf.open(statFile.c_str(), std::ios::app); \n    statbuf << \"</BENCH> \\n\";\n    cout << \"\\n Output written in \" << statFile << \" ...\\n\";\n    statbuf.close();\n  }\n\n  return 0;\n}\n\n      \n"
  },
  {
    "path": "include/eigen3/bench/spbench/spbenchsolver.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n\n#include <iostream>\n#include <fstream>\n#include <Eigen/SparseCore>\n#include <bench/BenchTimer.h>\n#include <cstdlib>\n#include <string>\n#include <Eigen/Cholesky>\n#include <Eigen/Jacobi>\n#include <Eigen/Householder>\n#include <Eigen/IterativeLinearSolvers>\n#include <unsupported/Eigen/IterativeSolvers>\n#include <Eigen/LU>\n#include <unsupported/Eigen/SparseExtra>\n#include <Eigen/SparseLU>\n\n#include \"spbenchstyle.h\"\n\n#ifdef EIGEN_METIS_SUPPORT\n#include <Eigen/MetisSupport>\n#endif\n\n#ifdef EIGEN_CHOLMOD_SUPPORT\n#include <Eigen/CholmodSupport>\n#endif\n\n#ifdef EIGEN_UMFPACK_SUPPORT\n#include <Eigen/UmfPackSupport>\n#endif\n\n#ifdef EIGEN_PARDISO_SUPPORT\n#include <Eigen/PardisoSupport>\n#endif\n\n#ifdef EIGEN_SUPERLU_SUPPORT\n#include <Eigen/SuperLUSupport>\n#endif\n\n#ifdef EIGEN_PASTIX_SUPPORT\n#include <Eigen/PaStiXSupport>\n#endif\n\n// CONSTANTS\n#define EIGEN_UMFPACK  10\n#define EIGEN_SUPERLU  20\n#define EIGEN_PASTIX  30\n#define EIGEN_PARDISO  40\n#define EIGEN_SPARSELU_COLAMD 50\n#define EIGEN_SPARSELU_METIS 51\n#define EIGEN_BICGSTAB  60\n#define EIGEN_BICGSTAB_ILUT  61\n#define EIGEN_GMRES 70\n#define EIGEN_GMRES_ILUT 71\n#define EIGEN_SIMPLICIAL_LDLT  80\n#define EIGEN_CHOLMOD_LDLT  90\n#define EIGEN_PASTIX_LDLT  100\n#define EIGEN_PARDISO_LDLT  110\n#define EIGEN_SIMPLICIAL_LLT  120\n#define EIGEN_CHOLMOD_SUPERNODAL_LLT  130\n#define EIGEN_CHOLMOD_SIMPLICIAL_LLT  140\n#define EIGEN_PASTIX_LLT  150\n#define EIGEN_PARDISO_LLT  160\n#define EIGEN_CG  170\n#define EIGEN_CG_PRECOND  180\n\nusing namespace Eigen;\nusing namespace std; \n\n\n// Global variables for input parameters\nint MaximumIters; // Maximum number of iterations\ndouble RelErr; // Relative error of the computed solution\ndouble best_time_val; // Current best time overall solvers \nint best_time_id; //  id of the best solver for the current system \n\ntemplate<typename T> inline typename NumTraits<T>::Real test_precision() { return NumTraits<T>::dummy_precision(); }\ntemplate<> inline float test_precision<float>() { return 1e-3f; }                                                             \ntemplate<> inline double test_precision<double>() { return 1e-6; }                                                            \ntemplate<> inline float test_precision<std::complex<float> >() { return test_precision<float>(); }\ntemplate<> inline double test_precision<std::complex<double> >() { return test_precision<double>(); }\n\nvoid printStatheader(std::ofstream& out)\n{\n  // Print XML header\n  // NOTE It would have been much easier to write these XML documents using external libraries like tinyXML or Xerces-C++.\n  \n  out << \"<?xml version='1.0' encoding='UTF-8'?> \\n\";\n  out << \"<?xml-stylesheet type='text/xsl' href='#stylesheet' ?> \\n\"; \n  out << \"<!DOCTYPE BENCH  [\\n<!ATTLIST xsl:stylesheet\\n id\\t ID  #REQUIRED>\\n]>\";\n  out << \"\\n\\n<!-- Generated by the Eigen library -->\\n\"; \n  \n  out << \"\\n<BENCH> \\n\" ; //root XML element \n  // Print the xsl style section\n  printBenchStyle(out); \n  // List all available solvers \n  out << \" <AVAILSOLVER> \\n\";\n#ifdef EIGEN_UMFPACK_SUPPORT\n  out <<\"  <SOLVER ID='\" << EIGEN_UMFPACK << \"'>\\n\"; \n  out << \"   <TYPE> LU </TYPE> \\n\";\n  out << \"   <PACKAGE> UMFPACK </PACKAGE> \\n\"; \n  out << \"  </SOLVER> \\n\"; \n#endif\n#ifdef EIGEN_SUPERLU_SUPPORT\n  out <<\"  <SOLVER ID='\" << EIGEN_SUPERLU << \"'>\\n\"; \n  out << \"   <TYPE> LU </TYPE> \\n\";\n  out << \"   <PACKAGE> SUPERLU </PACKAGE> \\n\"; \n  out << \"  </SOLVER> \\n\"; \n#endif\n#ifdef EIGEN_CHOLMOD_SUPPORT\n  out <<\"  <SOLVER ID='\" << EIGEN_CHOLMOD_SIMPLICIAL_LLT << \"'>\\n\"; \n  out << \"   <TYPE> LLT SP</TYPE> \\n\";\n  out << \"   <PACKAGE> CHOLMOD </PACKAGE> \\n\";\n  out << \"  </SOLVER> \\n\"; \n  \n  out <<\"  <SOLVER ID='\" << EIGEN_CHOLMOD_SUPERNODAL_LLT << \"'>\\n\"; \n  out << \"   <TYPE> LLT</TYPE> \\n\";\n  out << \"   <PACKAGE> CHOLMOD </PACKAGE> \\n\";\n  out << \"  </SOLVER> \\n\";\n  \n  out <<\"  <SOLVER ID='\" << EIGEN_CHOLMOD_LDLT << \"'>\\n\"; \n  out << \"   <TYPE> LDLT </TYPE> \\n\";\n  out << \"   <PACKAGE> CHOLMOD </PACKAGE> \\n\";  \n  out << \"  </SOLVER> \\n\"; \n#endif\n#ifdef EIGEN_PARDISO_SUPPORT\n  out <<\"  <SOLVER ID='\" << EIGEN_PARDISO << \"'>\\n\"; \n  out << \"   <TYPE> LU </TYPE> \\n\";\n  out << \"   <PACKAGE> PARDISO </PACKAGE> \\n\"; \n  out << \"  </SOLVER> \\n\"; \n  \n  out <<\"  <SOLVER ID='\" << EIGEN_PARDISO_LLT << \"'>\\n\"; \n  out << \"   <TYPE> LLT </TYPE> \\n\";\n  out << \"   <PACKAGE> PARDISO </PACKAGE> \\n\"; \n  out << \"  </SOLVER> \\n\"; \n  \n  out <<\"  <SOLVER ID='\" << EIGEN_PARDISO_LDLT << \"'>\\n\"; \n  out << \"   <TYPE> LDLT </TYPE> \\n\";\n  out << \"   <PACKAGE> PARDISO </PACKAGE> \\n\"; \n  out << \"  </SOLVER> \\n\"; \n#endif\n#ifdef EIGEN_PASTIX_SUPPORT\n  out <<\"  <SOLVER ID='\" << EIGEN_PASTIX << \"'>\\n\"; \n  out << \"   <TYPE> LU </TYPE> \\n\";\n  out << \"   <PACKAGE> PASTIX </PACKAGE> \\n\"; \n  out << \"  </SOLVER> \\n\"; \n  \n  out <<\"  <SOLVER ID='\" << EIGEN_PASTIX_LLT << \"'>\\n\"; \n  out << \"   <TYPE> LLT </TYPE> \\n\";\n  out << \"   <PACKAGE> PASTIX </PACKAGE> \\n\"; \n  out << \"  </SOLVER> \\n\"; \n  \n  out <<\"  <SOLVER ID='\" << EIGEN_PASTIX_LDLT << \"'>\\n\"; \n  out << \"   <TYPE> LDLT </TYPE> \\n\";\n  out << \"   <PACKAGE> PASTIX </PACKAGE> \\n\"; \n  out << \"  </SOLVER> \\n\"; \n#endif\n  \n  out <<\"  <SOLVER ID='\" << EIGEN_BICGSTAB << \"'>\\n\"; \n  out << \"   <TYPE> BICGSTAB </TYPE> \\n\";\n  out << \"   <PACKAGE> EIGEN </PACKAGE> \\n\"; \n  out << \"  </SOLVER> \\n\"; \n  \n  out <<\"  <SOLVER ID='\" << EIGEN_BICGSTAB_ILUT << \"'>\\n\"; \n  out << \"   <TYPE> BICGSTAB_ILUT </TYPE> \\n\";\n  out << \"   <PACKAGE> EIGEN </PACKAGE> \\n\"; \n  out << \"  </SOLVER> \\n\"; \n  \n  out <<\"  <SOLVER ID='\" << EIGEN_GMRES_ILUT << \"'>\\n\"; \n  out << \"   <TYPE> GMRES_ILUT </TYPE> \\n\";\n  out << \"   <PACKAGE> EIGEN </PACKAGE> \\n\"; \n  out << \"  </SOLVER> \\n\"; \n  \n  out <<\"  <SOLVER ID='\" << EIGEN_SIMPLICIAL_LDLT << \"'>\\n\"; \n  out << \"   <TYPE> LDLT </TYPE> \\n\";\n  out << \"   <PACKAGE> EIGEN </PACKAGE> \\n\"; \n  out << \"  </SOLVER> \\n\"; \n  \n  out <<\"  <SOLVER ID='\" << EIGEN_SIMPLICIAL_LLT << \"'>\\n\"; \n  out << \"   <TYPE> LLT </TYPE> \\n\";\n  out << \"   <PACKAGE> EIGEN </PACKAGE> \\n\"; \n  out << \"  </SOLVER> \\n\"; \n  \n  out <<\"  <SOLVER ID='\" << EIGEN_CG << \"'>\\n\"; \n  out << \"   <TYPE> CG </TYPE> \\n\";\n  out << \"   <PACKAGE> EIGEN </PACKAGE> \\n\"; \n  out << \"  </SOLVER> \\n\"; \n  \n  out <<\"  <SOLVER ID='\" << EIGEN_SPARSELU_COLAMD << \"'>\\n\"; \n  out << \"   <TYPE> LU_COLAMD </TYPE> \\n\";\n  out << \"   <PACKAGE> EIGEN </PACKAGE> \\n\"; \n  out << \"  </SOLVER> \\n\"; \n  \n#ifdef EIGEN_METIS_SUPPORT\n  out <<\"  <SOLVER ID='\" << EIGEN_SPARSELU_METIS << \"'>\\n\"; \n  out << \"   <TYPE> LU_METIS </TYPE> \\n\";\n  out << \"   <PACKAGE> EIGEN </PACKAGE> \\n\"; \n  out << \"  </SOLVER> \\n\"; \n#endif\n  out << \" </AVAILSOLVER> \\n\"; \n  \n}\n\n\ntemplate<typename Solver, typename Scalar>\nvoid call_solver(Solver &solver, const int solver_id, const typename Solver::MatrixType& A, const Matrix<Scalar, Dynamic, 1>& b, const Matrix<Scalar, Dynamic, 1>& refX,std::ofstream& statbuf)\n{\n  \n  double total_time;\n  double compute_time;\n  double solve_time; \n  double rel_error;\n  Matrix<Scalar, Dynamic, 1> x; \n  BenchTimer timer; \n  timer.reset();\n  timer.start();\n  solver.compute(A); \n  if (solver.info() != Success)\n  {\n    std::cerr << \"Solver failed ... \\n\";\n    return;\n  }\n  timer.stop();\n  compute_time = timer.value();\n  statbuf << \"    <TIME>\\n\"; \n  statbuf << \"     <COMPUTE> \" << timer.value() << \"</COMPUTE>\\n\";\n  std::cout<< \"COMPUTE TIME : \" << timer.value() <<std::endl; \n    \n  timer.reset();\n  timer.start();\n  x = solver.solve(b); \n  if (solver.info() == NumericalIssue)\n  {\n    std::cerr << \"Solver failed ... \\n\";\n    return;\n  }\n  timer.stop();\n  solve_time = timer.value();\n  statbuf << \"     <SOLVE> \" << timer.value() << \"</SOLVE>\\n\"; \n  std::cout<< \"SOLVE TIME : \" << timer.value() <<std::endl; \n  \n  total_time = solve_time + compute_time;\n  statbuf << \"     <TOTAL> \" << total_time << \"</TOTAL>\\n\"; \n  std::cout<< \"TOTAL TIME : \" << total_time <<std::endl; \n  statbuf << \"    </TIME>\\n\"; \n  \n  // Verify the relative error\n  if(refX.size() != 0)\n    rel_error = (refX - x).norm()/refX.norm();\n  else \n  {\n    // Compute the relative residual norm\n    Matrix<Scalar, Dynamic, 1> temp; \n    temp = A * x; \n    rel_error = (b-temp).norm()/b.norm();\n  }\n  statbuf << \"    <ERROR> \" << rel_error << \"</ERROR>\\n\"; \n  std::cout<< \"REL. ERROR : \" << rel_error << \"\\n\\n\" ;\n  if ( rel_error <= RelErr )\n  {\n    // check the best time if convergence\n    if(!best_time_val || (best_time_val > total_time))\n    {\n      best_time_val = total_time;\n      best_time_id = solver_id;\n    }\n  }\n}\n\ntemplate<typename Solver, typename Scalar>\nvoid call_directsolver(Solver& solver, const int solver_id, const typename Solver::MatrixType& A, const Matrix<Scalar, Dynamic, 1>& b, const Matrix<Scalar, Dynamic, 1>& refX, std::string& statFile)\n{\n    std::ofstream statbuf(statFile.c_str(), std::ios::app);\n    statbuf << \"   <SOLVER_STAT ID='\" << solver_id <<\"'>\\n\"; \n    call_solver(solver, solver_id, A, b, refX,statbuf);\n    statbuf << \"   </SOLVER_STAT>\\n\";\n    statbuf.close();\n}\n\ntemplate<typename Solver, typename Scalar>\nvoid call_itersolver(Solver &solver, const int solver_id, const typename Solver::MatrixType& A, const Matrix<Scalar, Dynamic, 1>& b, const Matrix<Scalar, Dynamic, 1>& refX, std::string& statFile)\n{\n  solver.setTolerance(RelErr); \n  solver.setMaxIterations(MaximumIters);\n  \n  std::ofstream statbuf(statFile.c_str(), std::ios::app);\n  statbuf << \" <SOLVER_STAT ID='\" << solver_id <<\"'>\\n\"; \n  call_solver(solver, solver_id, A, b, refX,statbuf); \n  statbuf << \"   <ITER> \"<< solver.iterations() << \"</ITER>\\n\";\n  statbuf << \" </SOLVER_STAT>\\n\";\n  std::cout << \"ITERATIONS : \" << solver.iterations() <<\"\\n\\n\\n\"; \n  \n}\n\n\ntemplate <typename Scalar>\nvoid SelectSolvers(const SparseMatrix<Scalar>&A, unsigned int sym, Matrix<Scalar, Dynamic, 1>& b, const Matrix<Scalar, Dynamic, 1>& refX, std::string& statFile)\n{\n  typedef SparseMatrix<Scalar, ColMajor> SpMat; \n  // First, deal with Nonsymmetric and symmetric matrices\n  best_time_id = 0; \n  best_time_val = 0.0;\n  //UMFPACK\n  #ifdef EIGEN_UMFPACK_SUPPORT\n  {\n    cout << \"Solving with UMFPACK LU ... \\n\"; \n    UmfPackLU<SpMat> solver; \n    call_directsolver(solver, EIGEN_UMFPACK, A, b, refX,statFile); \n  }\n  #endif\n    //SuperLU\n  #ifdef EIGEN_SUPERLU_SUPPORT\n  {\n    cout << \"\\nSolving with SUPERLU ... \\n\"; \n    SuperLU<SpMat> solver;\n    call_directsolver(solver, EIGEN_SUPERLU, A, b, refX,statFile); \n  }\n  #endif\n    \n   // PaStix LU\n  #ifdef EIGEN_PASTIX_SUPPORT\n  {\n    cout << \"\\nSolving with PASTIX LU ... \\n\"; \n    PastixLU<SpMat> solver; \n    call_directsolver(solver, EIGEN_PASTIX, A, b, refX,statFile) ;\n  }\n  #endif\n\n   //PARDISO LU\n  #ifdef EIGEN_PARDISO_SUPPORT\n  {\n    cout << \"\\nSolving with PARDISO LU ... \\n\"; \n    PardisoLU<SpMat>  solver; \n    call_directsolver(solver, EIGEN_PARDISO, A, b, refX,statFile);\n  }\n  #endif\n  \n  // Eigen SparseLU METIS\n  cout << \"\\n Solving with Sparse LU AND COLAMD ... \\n\";\n  SparseLU<SpMat, COLAMDOrdering<int> >   solver;\n  call_directsolver(solver, EIGEN_SPARSELU_COLAMD, A, b, refX, statFile); \n  // Eigen SparseLU METIS\n  #ifdef EIGEN_METIS_SUPPORT\n  {\n    cout << \"\\n Solving with Sparse LU AND METIS ... \\n\";\n    SparseLU<SpMat, MetisOrdering<int> >   solver;\n    call_directsolver(solver, EIGEN_SPARSELU_METIS, A, b, refX, statFile); \n  }\n  #endif\n  \n  //BiCGSTAB\n  {\n    cout << \"\\nSolving with BiCGSTAB ... \\n\"; \n    BiCGSTAB<SpMat> solver; \n    call_itersolver(solver, EIGEN_BICGSTAB, A, b, refX,statFile);\n  }\n  //BiCGSTAB+ILUT\n  {\n    cout << \"\\nSolving with BiCGSTAB and ILUT ... \\n\"; \n    BiCGSTAB<SpMat, IncompleteLUT<Scalar> > solver; \n    call_itersolver(solver, EIGEN_BICGSTAB_ILUT, A, b, refX,statFile); \n  }\n  \n   \n  //GMRES\n//   {\n//     cout << \"\\nSolving with GMRES ... \\n\"; \n//     GMRES<SpMat> solver; \n//     call_itersolver(solver, EIGEN_GMRES, A, b, refX,statFile); \n//   }\n  //GMRES+ILUT\n  {\n    cout << \"\\nSolving with GMRES and ILUT ... \\n\"; \n    GMRES<SpMat, IncompleteLUT<Scalar> > solver; \n    call_itersolver(solver, EIGEN_GMRES_ILUT, A, b, refX,statFile);\n  }\n  \n  // Hermitian and not necessarily positive-definites\n  if (sym != NonSymmetric)\n  {\n    // Internal Cholesky\n    {\n      cout << \"\\nSolving with Simplicial LDLT ... \\n\"; \n      SimplicialLDLT<SpMat, Lower> solver;\n      call_directsolver(solver, EIGEN_SIMPLICIAL_LDLT, A, b, refX,statFile); \n    }\n    \n    // CHOLMOD\n    #ifdef EIGEN_CHOLMOD_SUPPORT\n    {\n      cout << \"\\nSolving with CHOLMOD LDLT ... \\n\"; \n      CholmodDecomposition<SpMat, Lower> solver;\n      solver.setMode(CholmodLDLt);\n       call_directsolver(solver,EIGEN_CHOLMOD_LDLT, A, b, refX,statFile);\n    }\n    #endif\n    \n    //PASTIX LLT\n    #ifdef EIGEN_PASTIX_SUPPORT\n    {\n      cout << \"\\nSolving with PASTIX LDLT ... \\n\"; \n      PastixLDLT<SpMat, Lower> solver; \n      call_directsolver(solver,EIGEN_PASTIX_LDLT, A, b, refX,statFile); \n    }\n    #endif\n    \n    //PARDISO LLT\n    #ifdef EIGEN_PARDISO_SUPPORT\n    {\n      cout << \"\\nSolving with PARDISO LDLT ... \\n\"; \n      PardisoLDLT<SpMat, Lower> solver; \n      call_directsolver(solver,EIGEN_PARDISO_LDLT, A, b, refX,statFile); \n    }\n    #endif\n  }\n\n   // Now, symmetric POSITIVE DEFINITE matrices\n  if (sym == SPD)\n  {\n    \n    //Internal Sparse Cholesky\n    {\n      cout << \"\\nSolving with SIMPLICIAL LLT ... \\n\"; \n      SimplicialLLT<SpMat, Lower> solver; \n      call_directsolver(solver,EIGEN_SIMPLICIAL_LLT, A, b, refX,statFile); \n    }\n    \n    // CHOLMOD\n    #ifdef EIGEN_CHOLMOD_SUPPORT\n    {\n      // CholMOD SuperNodal LLT\n      cout << \"\\nSolving with CHOLMOD LLT (Supernodal)... \\n\"; \n      CholmodDecomposition<SpMat, Lower> solver;\n      solver.setMode(CholmodSupernodalLLt);\n       call_directsolver(solver,EIGEN_CHOLMOD_SUPERNODAL_LLT, A, b, refX,statFile);\n      // CholMod Simplicial LLT\n      cout << \"\\nSolving with CHOLMOD LLT (Simplicial) ... \\n\"; \n      solver.setMode(CholmodSimplicialLLt);\n      call_directsolver(solver,EIGEN_CHOLMOD_SIMPLICIAL_LLT, A, b, refX,statFile);\n    }\n    #endif\n    \n    //PASTIX LLT\n    #ifdef EIGEN_PASTIX_SUPPORT\n    {\n      cout << \"\\nSolving with PASTIX LLT ... \\n\"; \n      PastixLLT<SpMat, Lower> solver; \n      call_directsolver(solver,EIGEN_PASTIX_LLT, A, b, refX,statFile);\n    }\n    #endif\n    \n    //PARDISO LLT\n    #ifdef EIGEN_PARDISO_SUPPORT\n    {\n      cout << \"\\nSolving with PARDISO LLT ... \\n\"; \n      PardisoLLT<SpMat, Lower> solver; \n      call_directsolver(solver,EIGEN_PARDISO_LLT, A, b, refX,statFile); \n    }\n    #endif\n    \n    // Internal CG\n    {\n      cout << \"\\nSolving with CG ... \\n\"; \n      ConjugateGradient<SpMat, Lower> solver; \n      call_itersolver(solver,EIGEN_CG, A, b, refX,statFile);\n    }\n    //CG+IdentityPreconditioner\n//     {\n//       cout << \"\\nSolving with CG and IdentityPreconditioner ... \\n\"; \n//       ConjugateGradient<SpMat, Lower, IdentityPreconditioner> solver; \n//       call_itersolver(solver,EIGEN_CG_PRECOND, A, b, refX,statFile);\n//     }\n  } // End SPD matrices \n}\n\n/* Browse all the matrices available in the specified folder \n * and solve the associated linear system.\n * The results of each solve are printed in the standard output\n * and optionally in the provided html file\n */\ntemplate <typename Scalar>\nvoid Browse_Matrices(const string folder, bool statFileExists, std::string& statFile, int maxiters, double tol)\n{\n  MaximumIters = maxiters; // Maximum number of iterations, global variable \n  RelErr = tol;  //Relative residual error  as stopping criterion for iterative solvers\n  MatrixMarketIterator<Scalar> it(folder);\n  for ( ; it; ++it)\n  {\n    //print the infos for this linear system \n    if(statFileExists)\n    {\n      std::ofstream statbuf(statFile.c_str(), std::ios::app);\n      statbuf << \"<LINEARSYSTEM> \\n\";\n      statbuf << \"   <MATRIX> \\n\";\n      statbuf << \"     <NAME> \" << it.matname() << \" </NAME>\\n\"; \n      statbuf << \"     <SIZE> \" << it.matrix().rows() << \" </SIZE>\\n\"; \n      statbuf << \"     <ENTRIES> \" << it.matrix().nonZeros() << \"</ENTRIES>\\n\";\n      if (it.sym()!=NonSymmetric)\n      {\n        statbuf << \"     <SYMMETRY> Symmetric </SYMMETRY>\\n\" ; \n        if (it.sym() == SPD) \n          statbuf << \"     <POSDEF> YES </POSDEF>\\n\"; \n        else \n          statbuf << \"     <POSDEF> NO </POSDEF>\\n\"; \n          \n      }\n      else\n      {\n        statbuf << \"     <SYMMETRY> NonSymmetric </SYMMETRY>\\n\" ; \n        statbuf << \"     <POSDEF> NO </POSDEF>\\n\"; \n      }\n      statbuf << \"   </MATRIX> \\n\";\n      statbuf.close();\n    }\n    \n    cout<< \"\\n\\n===================================================== \\n\";\n    cout<< \" ======  SOLVING WITH MATRIX \" << it.matname() << \" ====\\n\";\n    cout<< \" =================================================== \\n\\n\";\n    Matrix<Scalar, Dynamic, 1> refX;\n    if(it.hasrefX()) refX = it.refX();\n    // Call all suitable solvers for this linear system \n    SelectSolvers<Scalar>(it.matrix(), it.sym(), it.rhs(), refX, statFile);\n    \n    if(statFileExists)\n    {\n      std::ofstream statbuf(statFile.c_str(), std::ios::app);\n      statbuf << \"  <BEST_SOLVER ID='\"<< best_time_id\n              << \"'></BEST_SOLVER>\\n\"; \n      statbuf << \" </LINEARSYSTEM> \\n\"; \n      statbuf.close();\n    }\n  } \n} \n\nbool get_options(int argc, char **args, string option, string* value=0)\n{\n  int idx = 1, found=false; \n  while (idx<argc && !found){\n    if (option.compare(args[idx]) == 0){\n      found = true; \n      if(value) *value = args[idx+1];\n    }\n    idx+=2;\n  }\n  return found; \n}\n"
  },
  {
    "path": "include/eigen3/bench/spbench/spbenchstyle.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef SPBENCHSTYLE_H\n#define SPBENCHSTYLE_H\n\nvoid printBenchStyle(std::ofstream& out)\n{\n  out << \"<xsl:stylesheet id='stylesheet' version='1.0' \\\n      xmlns:xsl='http://www.w3.org/1999/XSL/Transform' >\\n \\\n      <xsl:template match='xsl:stylesheet' />\\n \\\n      <xsl:template match='/'> <!-- Root of the document -->\\n \\\n      <html>\\n \\\n        <head> \\n \\\n          <style type='text/css'> \\n \\\n            td { white-space: nowrap;}\\n \\\n          </style>\\n \\\n        </head>\\n \\\n        <body>\";\n  out<<\"<table border='1' width='100%' height='100%'>\\n \\\n        <TR> <!-- Write the table header -->\\n \\\n        <TH>Matrix</TH> <TH>N</TH> <TH> NNZ</TH>  <TH> Sym</TH>  <TH> SPD</TH> <TH> </TH>\\n \\\n          <xsl:for-each select='BENCH/AVAILSOLVER/SOLVER'>\\n \\\n            <xsl:sort select='@ID' data-type='number'/>\\n \\\n            <TH>\\n \\\n              <xsl:value-of select='TYPE' />\\n \\\n              <xsl:text></xsl:text>\\n \\\n              <xsl:value-of select='PACKAGE' />\\n \\\n              <xsl:text></xsl:text>\\n \\\n            </TH>\\n \\\n          </xsl:for-each>\\n \\\n        </TR>\";\n        \n  out<<\"  <xsl:for-each select='BENCH/LINEARSYSTEM'>\\n \\\n          <TR> <!-- print statistics for one linear system-->\\n \\\n            <TH rowspan='4'> <xsl:value-of select='MATRIX/NAME' /> </TH>\\n \\\n            <TD rowspan='4'> <xsl:value-of select='MATRIX/SIZE' /> </TD>\\n \\\n            <TD rowspan='4'> <xsl:value-of select='MATRIX/ENTRIES' /> </TD>\\n \\\n            <TD rowspan='4'> <xsl:value-of select='MATRIX/SYMMETRY' /> </TD>\\n \\\n            <TD rowspan='4'> <xsl:value-of select='MATRIX/POSDEF' /> </TD>\\n \\\n            <TH> Compute Time </TH>\\n \\\n            <xsl:for-each select='SOLVER_STAT'>\\n \\\n              <xsl:sort select='@ID' data-type='number'/>\\n \\\n              <TD> <xsl:value-of select='TIME/COMPUTE' /> </TD>\\n \\\n            </xsl:for-each>\\n \\\n          </TR>\";\n  out<<\"  <TR>\\n \\\n            <TH> Solve Time </TH>\\n \\\n            <xsl:for-each select='SOLVER_STAT'>\\n \\\n              <xsl:sort select='@ID' data-type='number'/>\\n \\\n              <TD> <xsl:value-of select='TIME/SOLVE' /> </TD>\\n \\\n            </xsl:for-each>\\n \\\n          </TR>\\n \\\n          <TR>\\n \\\n            <TH> Total Time </TH>\\n \\\n            <xsl:for-each select='SOLVER_STAT'>\\n \\\n              <xsl:sort select='@ID' data-type='number'/>\\n \\\n              <xsl:choose>\\n \\\n                <xsl:when test='@ID=../BEST_SOLVER/@ID'>\\n \\\n                  <TD style='background-color:red'> <xsl:value-of select='TIME/TOTAL' />  </TD>\\n \\\n                </xsl:when>\\n \\\n                <xsl:otherwise>\\n \\\n                  <TD>  <xsl:value-of select='TIME/TOTAL' /></TD>\\n \\\n                </xsl:otherwise>\\n \\\n              </xsl:choose>\\n \\\n            </xsl:for-each>\\n \\\n          </TR>\";\n  out<<\"  <TR>\\n \\\n              <TH> Error </TH>\\n \\\n              <xsl:for-each select='SOLVER_STAT'>\\n \\\n                <xsl:sort select='@ID' data-type='number'/>\\n \\\n                <TD> <xsl:value-of select='ERROR' />\\n \\\n                <xsl:if test='ITER'>\\n \\\n                  <xsl:text>(</xsl:text>\\n \\\n                  <xsl:value-of select='ITER' />\\n \\\n                  <xsl:text>)</xsl:text>\\n \\\n                </xsl:if> </TD>\\n \\\n              </xsl:for-each>\\n \\\n            </TR>\\n \\\n          </xsl:for-each>\\n \\\n      </table>\\n \\\n    </body>\\n \\\n    </html>\\n \\\n  </xsl:template>\\n \\\n  </xsl:stylesheet>\\n\\n\";\n  \n}\n\n#endif\n"
  },
  {
    "path": "include/eigen3/bench/spbench/test_sparseLU.cpp",
    "content": "// Small bench routine for Eigen available in Eigen\n// (C) Desire NUENTSA WAKAM, INRIA\n\n#include <iostream>\n#include <fstream>\n#include <iomanip>\n#include <unsupported/Eigen/SparseExtra>\n#include <Eigen/SparseLU>\n#include <bench/BenchTimer.h>\n#ifdef EIGEN_METIS_SUPPORT\n#include <Eigen/MetisSupport>\n#endif\n\nusing namespace std;\nusing namespace Eigen;\n\nint main(int argc, char **args)\n{\n//   typedef complex<double> scalar; \n  typedef double scalar; \n  SparseMatrix<scalar, ColMajor> A; \n  typedef SparseMatrix<scalar, ColMajor>::Index Index;\n  typedef Matrix<scalar, Dynamic, Dynamic> DenseMatrix;\n  typedef Matrix<scalar, Dynamic, 1> DenseRhs;\n  Matrix<scalar, Dynamic, 1> b, x, tmp;\n//   SparseLU<SparseMatrix<scalar, ColMajor>, AMDOrdering<int> >   solver;\n// #ifdef EIGEN_METIS_SUPPORT\n//   SparseLU<SparseMatrix<scalar, ColMajor>, MetisOrdering<int> > solver; \n//   std::cout<< \"ORDERING : METIS\\n\"; \n// #else\n  SparseLU<SparseMatrix<scalar, ColMajor>, COLAMDOrdering<int> >  solver;\n  std::cout<< \"ORDERING : COLAMD\\n\"; \n// #endif\n  \n  ifstream matrix_file; \n  string line;\n  int  n;\n  BenchTimer timer; \n  \n  // Set parameters\n  /* Fill the matrix with sparse matrix stored in Matrix-Market coordinate column-oriented format */\n  if (argc < 2) assert(false && \"please, give the matrix market file \");\n  loadMarket(A, args[1]);\n  cout << \"End charging matrix \" << endl;\n  bool iscomplex=false, isvector=false;\n  int sym;\n  getMarketHeader(args[1], sym, iscomplex, isvector);\n//   if (iscomplex) { cout<< \" Not for complex matrices \\n\"; return -1; }\n  if (isvector) { cout << \"The provided file is not a matrix file\\n\"; return -1;}\n  if (sym != 0) { // symmetric matrices, only the lower part is stored\n    SparseMatrix<scalar, ColMajor> temp; \n    temp = A;\n    A = temp.selfadjointView<Lower>();\n  }\n  n = A.cols();\n  /* Fill the right hand side */\n\n  if (argc > 2)\n    loadMarketVector(b, args[2]);\n  else \n  {\n    b.resize(n);\n    tmp.resize(n);\n//       tmp.setRandom();\n    for (int i = 0; i < n; i++) tmp(i) = i; \n    b = A * tmp ;\n  }\n\n  /* Compute the factorization */\n//   solver.isSymmetric(true);\n  timer.start(); \n//   solver.compute(A);\n  solver.analyzePattern(A); \n  timer.stop(); \n  cout << \"Time to analyze \" << timer.value() << std::endl;\n  timer.reset(); \n  timer.start(); \n  solver.factorize(A); \n  timer.stop(); \n  cout << \"Factorize Time \" << timer.value() << std::endl;\n  timer.reset(); \n  timer.start(); \n  x = solver.solve(b);\n  timer.stop();\n  cout << \"solve time \" << timer.value() << std::endl; \n  /* Check the accuracy */\n  Matrix<scalar, Dynamic, 1> tmp2 = b - A*x;\n  scalar tempNorm = tmp2.norm()/b.norm();\n  cout << \"Relative norm of the computed solution : \" << tempNorm <<\"\\n\";\n  cout << \"Number of nonzeros in the factor : \" << solver.nnzL() + solver.nnzU() << std::endl; \n  \n  return 0;\n}"
  },
  {
    "path": "include/eigen3/bench/spmv.cpp",
    "content": "\n//g++-4.4 -DNOMTL  -Wl,-rpath /usr/local/lib/oski -L /usr/local/lib/oski/ -l oski -l oski_util -l oski_util_Tid  -DOSKI -I ~/Coding/LinearAlgebra/mtl4/  spmv.cpp  -I .. -O2 -DNDEBUG -lrt  -lm -l oski_mat_CSC_Tid  -loskilt && ./a.out r200000 c200000 n100 t1 p1\n\n#define SCALAR double\n\n#include <iostream>\n#include <algorithm>\n#include \"BenchTimer.h\"\n#include \"BenchSparseUtil.h\"\n\n#define SPMV_BENCH(CODE) BENCH(t,tries,repeats,CODE);\n\n// #ifdef MKL\n//\n// #include \"mkl_types.h\"\n// #include \"mkl_spblas.h\"\n//\n// template<typename Lhs,typename Rhs,typename Res>\n// void mkl_multiply(const Lhs& lhs, const Rhs& rhs, Res& res)\n// {\n//   char n = 'N';\n//   float alpha = 1;\n//   char matdescra[6];\n//   matdescra[0] = 'G';\n//   matdescra[1] = 0;\n//   matdescra[2] = 0;\n//   matdescra[3] = 'C';\n//   mkl_scscmm(&n, lhs.rows(), rhs.cols(), lhs.cols(), &alpha, matdescra,\n//              lhs._valuePtr(), lhs._innerIndexPtr(), lhs.outerIndexPtr(),\n//              pntre, b, &ldb, &beta, c, &ldc);\n// //   mkl_somatcopy('C', 'T', lhs.rows(), lhs.cols(), 1,\n// //                 lhs._valuePtr(), lhs.rows(), DST, dst_stride);\n// }\n//\n// #endif\n\nint main(int argc, char *argv[])\n{\n  int size = 10000;\n  int rows = size;\n  int cols = size;\n  int nnzPerCol = 40;\n  int tries = 2;\n  int repeats = 2;\n\n  bool need_help = false;\n  for(int i = 1; i < argc; i++)\n  {\n    if(argv[i][0] == 'r')\n    {\n      rows = atoi(argv[i]+1);\n    }\n    else if(argv[i][0] == 'c')\n    {\n      cols = atoi(argv[i]+1);\n    }\n    else if(argv[i][0] == 'n')\n    {\n      nnzPerCol = atoi(argv[i]+1);\n    }\n    else if(argv[i][0] == 't')\n    {\n      tries = atoi(argv[i]+1);\n    }\n    else if(argv[i][0] == 'p')\n    {\n      repeats = atoi(argv[i]+1);\n    }\n    else\n    {\n      need_help = true;\n    }\n  }\n  if(need_help)\n  {\n    std::cout << argv[0] << \" r<nb rows> c<nb columns> n<non zeros per column> t<nb tries> p<nb repeats>\\n\";\n    return 1;\n  }\n\n  std::cout << \"SpMV \" << rows << \" x \" << cols << \" with \" << nnzPerCol << \" non zeros per column. (\" << repeats << \" repeats, and \" << tries << \" tries)\\n\\n\";\n\n  EigenSparseMatrix sm(rows,cols);\n  DenseVector dv(cols), res(rows);\n  dv.setRandom();\n\n  BenchTimer t;\n  while (nnzPerCol>=4)\n  {\n    std::cout << \"nnz: \" << nnzPerCol << \"\\n\";\n    sm.setZero();\n    fillMatrix2(nnzPerCol, rows, cols, sm);\n\n    // dense matrices\n    #ifdef DENSEMATRIX\n    {\n      DenseMatrix dm(rows,cols), (rows,cols);\n      eiToDense(sm, dm);\n\n      SPMV_BENCH(res = dm * sm);\n      std::cout << \"Dense       \" << t.value()/repeats << \"\\t\";\n\n      SPMV_BENCH(res = dm.transpose() * sm);\n      std::cout << t.value()/repeats << endl;\n    }\n    #endif\n\n    // eigen sparse matrices\n    {\n      SPMV_BENCH(res.noalias() += sm * dv; )\n      std::cout << \"Eigen       \" << t.value()/repeats << \"\\t\";\n\n      SPMV_BENCH(res.noalias() += sm.transpose() * dv; )\n      std::cout << t.value()/repeats << endl;\n    }\n\n    // CSparse\n    #ifdef CSPARSE\n    {\n      std::cout << \"CSparse \\n\";\n      cs *csm;\n      eiToCSparse(sm, csm);\n\n//       BENCH();\n//       timer.stop();\n//       std::cout << \"   a * b:\\t\" << timer.value() << endl;\n\n//       BENCH( { m3 = cs_sorted_multiply2(m1, m2); cs_spfree(m3); } );\n//       std::cout << \"   a * b:\\t\" << timer.value() << endl;\n    }\n    #endif\n\n    #ifdef OSKI\n    {\n      oski_matrix_t om;\n      oski_vecview_t ov, ores;\n      oski_Init();\n      om = oski_CreateMatCSC(sm._outerIndexPtr(), sm._innerIndexPtr(), sm._valuePtr(), rows, cols,\n                             SHARE_INPUTMAT, 1, INDEX_ZERO_BASED);\n      ov = oski_CreateVecView(dv.data(), cols, STRIDE_UNIT);\n      ores = oski_CreateVecView(res.data(), rows, STRIDE_UNIT);\n\n      SPMV_BENCH( oski_MatMult(om, OP_NORMAL, 1, ov, 0, ores) );\n      std::cout << \"OSKI        \" << t.value()/repeats << \"\\t\";\n\n      SPMV_BENCH( oski_MatMult(om, OP_TRANS, 1, ov, 0, ores) );\n      std::cout << t.value()/repeats << \"\\n\";\n\n      // tune\n      t.reset();\n      t.start();\n      oski_SetHintMatMult(om, OP_NORMAL, 1.0, SYMBOLIC_VEC, 0.0, SYMBOLIC_VEC, ALWAYS_TUNE_AGGRESSIVELY);\n      oski_TuneMat(om);\n      t.stop();\n      double tuning = t.value();\n\n      SPMV_BENCH( oski_MatMult(om, OP_NORMAL, 1, ov, 0, ores) );\n      std::cout << \"OSKI tuned  \" << t.value()/repeats << \"\\t\";\n\n      SPMV_BENCH( oski_MatMult(om, OP_TRANS, 1, ov, 0, ores) );\n      std::cout << t.value()/repeats << \"\\t(\" << tuning <<  \")\\n\";\n\n\n      oski_DestroyMat(om);\n      oski_DestroyVecView(ov);\n      oski_DestroyVecView(ores);\n      oski_Close();\n    }\n    #endif\n\n    #ifndef NOUBLAS\n    {\n      using namespace boost::numeric;\n      UblasMatrix um(rows,cols);\n      eiToUblas(sm, um);\n\n      boost::numeric::ublas::vector<Scalar> uv(cols), ures(rows);\n      Map<Matrix<Scalar,Dynamic,1> >(&uv[0], cols) = dv;\n      Map<Matrix<Scalar,Dynamic,1> >(&ures[0], rows) = res;\n\n      SPMV_BENCH(ublas::axpy_prod(um, uv, ures, true));\n      std::cout << \"ublas       \" << t.value()/repeats << \"\\t\";\n\n      SPMV_BENCH(ublas::axpy_prod(boost::numeric::ublas::trans(um), uv, ures, true));\n      std::cout << t.value()/repeats << endl;\n    }\n    #endif\n\n    // GMM++\n    #ifndef NOGMM\n    {\n      GmmSparse gm(rows,cols);\n      eiToGmm(sm, gm);\n\n      std::vector<Scalar> gv(cols), gres(rows);\n      Map<Matrix<Scalar,Dynamic,1> >(&gv[0], cols) = dv;\n      Map<Matrix<Scalar,Dynamic,1> >(&gres[0], rows) = res;\n\n      SPMV_BENCH(gmm::mult(gm, gv, gres));\n      std::cout << \"GMM++       \" << t.value()/repeats << \"\\t\";\n\n      SPMV_BENCH(gmm::mult(gmm::transposed(gm), gv, gres));\n      std::cout << t.value()/repeats << endl;\n    }\n    #endif\n\n    // MTL4\n    #ifndef NOMTL\n    {\n      MtlSparse mm(rows,cols);\n      eiToMtl(sm, mm);\n      mtl::dense_vector<Scalar> mv(cols, 1.0);\n      mtl::dense_vector<Scalar> mres(rows, 1.0);\n\n      SPMV_BENCH(mres = mm * mv);\n      std::cout << \"MTL4        \" << t.value()/repeats << \"\\t\";\n\n      SPMV_BENCH(mres = trans(mm) * mv);\n      std::cout << t.value()/repeats << endl;\n    }\n    #endif\n\n    std::cout << \"\\n\";\n\n    if(nnzPerCol==1)\n      break;\n    nnzPerCol -= nnzPerCol/2;\n  }\n\n  return 0;\n}\n\n\n\n"
  },
  {
    "path": "include/eigen3/bench/tensors/README",
    "content": "The tensor benchmark suite is made of several parts.\n\nThe first part is a generic suite, in which each benchmark comes in 2 flavors: one that runs on CPU, and one that runs on GPU.\n\nTo compile the floating point CPU benchmarks, simply call:\ng++ tensor_benchmarks_cpu.cc benchmark_main.cc -I ../../ -std=c++11 -O3 -DNDEBUG -pthread -mavx -o benchmarks_cpu\n\nTo compile the floating point GPU benchmarks, simply call:\nnvcc tensor_benchmarks_gpu.cu benchmark_main.cc -I ../../ -std=c++11 -O2 -DNDEBUG -use_fast_math -ftz=true -arch compute_35 -o benchmarks_gpu\n\nWe also provide a version of the generic GPU tensor benchmarks that uses half floats (aka fp16) instead of regular floats. To compile these benchmarks, simply call the command line below. You'll need a recent GPU that supports compute capability 5.3 or higher to run them and nvcc 7.5 or higher to compile the code.\nnvcc tensor_benchmarks_fp16_gpu.cu benchmark_main.cc -I ../../ -std=c++11 -O2 -DNDEBUG -use_fast_math -ftz=true -arch compute_53 -o benchmarks_fp16_gpu\n\nlast but not least, we also provide a suite of benchmarks to measure the scalability of the contraction code on CPU. To compile these benchmarks, call\ng++ contraction_benchmarks_cpu.cc benchmark_main.cc -I ../../ -std=c++11 -O3 -DNDEBUG -pthread -mavx -o benchmarks_cpu\n\nTo compile the benchmark for SYCL, using ComputeCpp you currently need 2 passes (only for translation units containing device code):\n1. The device compilation pass that generates the device code (SYCL kernels and referenced device functions) and glue code needed by the host compiler to reference the device code from host code.\n{ComputeCpp_ROOT}/bin/compute++ -I ../../ -I {ComputeCpp_ROOT}/include/ -std=c++11 -mllvm -inline-threshold=1000 -Wno-ignored-attributes -sycl -intelspirmetadata -emit-llvm -no-serial-memop -sycl-compress-name -DBUILD_PLATFORM_SPIR -DNDBUG -O3 -c tensor_benchmarks_sycl.cc\n2. The host compilation pass that generates the final host binary.\nclang++-3.7 -include tensor_benchmarks_sycl.sycl benchmark_main.cc tensor_benchmarks_sycl.cc -pthread -I ../../ -I {ComputeCpp_ROOT}/include/ -L {ComputeCpp_ROOT}/lib/ -lComputeCpp -lOpenCL -D_GLIBCXX_USE_CXX11_ABI=0 -std=c++11 -o tensor_benchmark_sycl\n"
  },
  {
    "path": "include/eigen3/bench/tensors/benchmark.h",
    "content": "/*\n * Copyright (C) 2012 The Android Open Source Project\n *\n * Licensed under the Apache License, Version 2.0 (the \"License\");\n * you may not use this file except in compliance with the License.\n * You may obtain a copy of the License at\n *\n *      http://www.apache.org/licenses/LICENSE-2.0\n *\n * Unless required by applicable law or agreed to in writing, software\n * distributed under the License is distributed on an \"AS IS\" BASIS,\n * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n * See the License for the specific language governing permissions and\n * limitations under the License.\n */\n#include <stddef.h>\n#include <stdint.h>\n#include <vector>\n\nnamespace testing {\nclass Benchmark {\n public:\n  Benchmark(const char* name, void (*fn)(int)) {\n    Register(name, fn, NULL);\n  }\n  Benchmark(const char* name, void (*fn_range)(int, int)) {\n    Register(name, NULL, fn_range);\n  }\n  Benchmark* Arg(int x);\n  Benchmark* Range(int lo, int hi);\n  const char* Name();\n  bool ShouldRun(int argc, char* argv[]);\n  void Run();\n private:\n  const char* name_;\n  void (*fn_)(int);\n  void (*fn_range_)(int, int);\n  std::vector<int> args_;\n  void Register(const char* name, void (*fn)(int), void (*fn_range)(int, int));\n  void RunRepeatedlyWithArg(int iterations, int arg);\n  void RunWithArg(int arg);\n};\n}  // namespace testing\nvoid SetBenchmarkFlopsProcessed(int64_t);\nvoid StopBenchmarkTiming();\nvoid StartBenchmarkTiming();\n#define BENCHMARK(f) \\\n    static ::testing::Benchmark* _benchmark_##f __attribute__((unused)) = \\\n        (new ::testing::Benchmark(#f, f))\n"
  },
  {
    "path": "include/eigen3/bench/tensors/benchmark_main.cc",
    "content": "/*\n * Copyright (C) 2012 The Android Open Source Project\n *\n * Licensed under the Apache License, Version 2.0 (the \"License\");\n * you may not use this file except in compliance with the License.\n * You may obtain a copy of the License at\n *\n *      http://www.apache.org/licenses/LICENSE-2.0\n *\n * Unless required by applicable law or agreed to in writing, software\n * distributed under the License is distributed on an \"AS IS\" BASIS,\n * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n * See the License for the specific language governing permissions and\n * limitations under the License.\n */\n#include \"benchmark.h\"\n#include <regex.h>\n#include <stdio.h>\n#include <stdlib.h>\n#include <string.h>\n#include <string>\n#include <inttypes.h>\n#include <time.h>\n#include <map>\n\nstatic int64_t g_flops_processed;\nstatic int64_t g_benchmark_total_time_ns;\nstatic int64_t g_benchmark_start_time_ns;\ntypedef std::map<std::string, ::testing::Benchmark*> BenchmarkMap;\ntypedef BenchmarkMap::iterator BenchmarkMapIt;\n\nBenchmarkMap& gBenchmarks() {\n  static BenchmarkMap g_benchmarks;\n  return g_benchmarks;\n}\n\nstatic int g_name_column_width = 20;\n\nstatic int Round(int n) {\n  int base = 1;\n  while (base*10 < n) {\n    base *= 10;\n  }\n  if (n < 2*base) {\n    return 2*base;\n  }\n  if (n < 5*base) {\n    return 5*base;\n  }\n  return 10*base;\n}\n\n#ifdef __APPLE__\n  #include <mach/mach_time.h>\n  static mach_timebase_info_data_t g_time_info;\n  static void __attribute__((constructor)) init_info() {\n    mach_timebase_info(&g_time_info);\n  }\n#endif\n\nstatic int64_t NanoTime() {\n#if defined(__APPLE__)\n  uint64_t t = mach_absolute_time();\n  return t * g_time_info.numer / g_time_info.denom;\n#else\n  struct timespec t;\n  t.tv_sec = t.tv_nsec = 0;\n  clock_gettime(CLOCK_MONOTONIC, &t);\n  return static_cast<int64_t>(t.tv_sec) * 1000000000LL + t.tv_nsec;\n#endif\n}\n\nnamespace testing {\nBenchmark* Benchmark::Arg(int arg) {\n  args_.push_back(arg);\n  return this;\n}\n\nBenchmark* Benchmark::Range(int lo, int hi) {\n  const int kRangeMultiplier = 8;\n  if (hi < lo) {\n    int temp = hi;\n    hi = lo;\n    lo = temp;\n  }\n  while (lo < hi) {\n    args_.push_back(lo);\n    lo *= kRangeMultiplier;\n  }\n  // We always run the hi number.\n  args_.push_back(hi);\n  return this;\n}\n\nconst char* Benchmark::Name() {\n  return name_;\n}\nbool Benchmark::ShouldRun(int argc, char* argv[]) {\n  if (argc == 1) {\n    return true;  // With no arguments, we run all benchmarks.\n  }\n  // Otherwise, we interpret each argument as a regular expression and\n  // see if any of our benchmarks match.\n  for (int i = 1; i < argc; i++) {\n    regex_t re;\n    if (regcomp(&re, argv[i], 0) != 0) {\n      fprintf(stderr, \"couldn't compile \\\"%s\\\" as a regular expression!\\n\", argv[i]);\n      exit(EXIT_FAILURE);\n    }\n    int match = regexec(&re, name_, 0, NULL, 0);\n    regfree(&re);\n    if (match != REG_NOMATCH) {\n      return true;\n    }\n  }\n  return false;\n}\nvoid Benchmark::Register(const char* name, void (*fn)(int), void (*fn_range)(int, int)) {\n  name_ = name;\n  fn_ = fn;\n  fn_range_ = fn_range;\n  if (fn_ == NULL && fn_range_ == NULL) {\n    fprintf(stderr, \"%s: missing function\\n\", name_);\n    exit(EXIT_FAILURE);\n  }\n  gBenchmarks().insert(std::make_pair(name, this));\n}\nvoid Benchmark::Run() {\n  if (fn_ != NULL) {\n    RunWithArg(0);\n  } else {\n    if (args_.empty()) {\n      fprintf(stderr, \"%s: no args!\\n\", name_);\n      exit(EXIT_FAILURE);\n    }\n    for (size_t i = 0; i < args_.size(); ++i) {\n      RunWithArg(args_[i]);\n    }\n  }\n}\nvoid Benchmark::RunRepeatedlyWithArg(int iterations, int arg) {\n  g_flops_processed = 0;\n  g_benchmark_total_time_ns = 0;\n  g_benchmark_start_time_ns = NanoTime();\n  if (fn_ != NULL) {\n    fn_(iterations);\n  } else {\n    fn_range_(iterations, arg);\n  }\n  if (g_benchmark_start_time_ns != 0) {\n    g_benchmark_total_time_ns += NanoTime() - g_benchmark_start_time_ns;\n  }\n}\nvoid Benchmark::RunWithArg(int arg) {\n  // run once in case it's expensive\n  int iterations = 1;\n  RunRepeatedlyWithArg(iterations, arg);\n  while (g_benchmark_total_time_ns < 1e9 && iterations < 1e9) {\n    int last = iterations;\n    if (g_benchmark_total_time_ns/iterations == 0) {\n      iterations = 1e9;\n    } else {\n      iterations = 1e9 / (g_benchmark_total_time_ns/iterations);\n    }\n    iterations = std::max(last + 1, std::min(iterations + iterations/2, 100*last));\n    iterations = Round(iterations);\n    RunRepeatedlyWithArg(iterations, arg);\n  }\n  char throughput[100];\n  throughput[0] = '\\0';\n  if (g_benchmark_total_time_ns > 0 && g_flops_processed > 0) {\n    double mflops_processed = static_cast<double>(g_flops_processed)/1e6;\n    double seconds = static_cast<double>(g_benchmark_total_time_ns)/1e9;\n    snprintf(throughput, sizeof(throughput), \" %8.2f MFlops/s\", mflops_processed/seconds);\n  }\n  char full_name[100];\n  if (fn_range_ != NULL) {\n    if (arg >= (1<<20)) {\n      snprintf(full_name, sizeof(full_name), \"%s/%dM\", name_, arg/(1<<20));\n    } else if (arg >= (1<<10)) {\n      snprintf(full_name, sizeof(full_name), \"%s/%dK\", name_, arg/(1<<10));\n    } else {\n      snprintf(full_name, sizeof(full_name), \"%s/%d\", name_, arg);\n    }\n  } else {\n    snprintf(full_name, sizeof(full_name), \"%s\", name_);\n  }\n  printf(\"%-*s %10d %10\" PRId64 \"%s\\n\", g_name_column_width, full_name,\n         iterations, g_benchmark_total_time_ns/iterations, throughput);\n  fflush(stdout);\n}\n}  // namespace testing\nvoid SetBenchmarkFlopsProcessed(int64_t x) {\n  g_flops_processed = x;\n}\nvoid StopBenchmarkTiming() {\n  if (g_benchmark_start_time_ns != 0) {\n    g_benchmark_total_time_ns += NanoTime() - g_benchmark_start_time_ns;\n  }\n  g_benchmark_start_time_ns = 0;\n}\nvoid StartBenchmarkTiming() {\n  if (g_benchmark_start_time_ns == 0) {\n    g_benchmark_start_time_ns = NanoTime();\n  }\n}\nint main(int argc, char* argv[]) {\n  if (gBenchmarks().empty()) {\n    fprintf(stderr, \"No benchmarks registered!\\n\");\n    exit(EXIT_FAILURE);\n  }\n  for (BenchmarkMapIt it = gBenchmarks().begin(); it != gBenchmarks().end(); ++it) {\n    int name_width = static_cast<int>(strlen(it->second->Name()));\n    g_name_column_width = std::max(g_name_column_width, name_width);\n  }\n  bool need_header = true;\n  for (BenchmarkMapIt it = gBenchmarks().begin(); it != gBenchmarks().end(); ++it) {\n    ::testing::Benchmark* b = it->second;\n    if (b->ShouldRun(argc, argv)) {\n      if (need_header) {\n        printf(\"%-*s %10s %10s\\n\", g_name_column_width, \"\", \"iterations\", \"ns/op\");\n        fflush(stdout);\n        need_header = false;\n      }\n      b->Run();\n    }\n  }\n  if (need_header) {\n    fprintf(stderr, \"No matching benchmarks!\\n\");\n    fprintf(stderr, \"Available benchmarks:\\n\");\n    for (BenchmarkMapIt it = gBenchmarks().begin(); it != gBenchmarks().end(); ++it) {\n      fprintf(stderr, \"  %s\\n\", it->second->Name());\n    }\n    exit(EXIT_FAILURE);\n  }\n  return 0;\n}\n"
  },
  {
    "path": "include/eigen3/bench/tensors/contraction_benchmarks_cpu.cc",
    "content": "#define EIGEN_USE_THREADS\n\n#include <string>\n\n#include \"tensor_benchmarks.h\"\n\n#define CREATE_THREAD_POOL(threads)             \\\nEigen::ThreadPool pool(threads);                \\\nEigen::ThreadPoolDevice device(&pool, threads);\n\n\n// Contractions for number of threads ranging from 1 to 32\n// Dimensions are Rows, Cols, Depth\n#define BM_ContractionCPU(D1, D2, D3)                                         \\\n  static void BM_##Contraction##_##D1##x##D2##x##D3(int iters, int Threads) { \\\n    StopBenchmarkTiming();                                                    \\\n    CREATE_THREAD_POOL(Threads);                                              \\\n    BenchmarkSuite<Eigen::ThreadPoolDevice, float> suite(device, D1, D2, D3); \\\n    suite.contraction(iters);                                                 \\\n  }                                                                           \\\n  BENCHMARK_RANGE(BM_##Contraction##_##D1##x##D2##x##D3, 1, 32);\n\n\n// Vector Matrix and Matrix Vector products\nBM_ContractionCPU(1, 2000, 500);\nBM_ContractionCPU(2000, 1, 500);\n\n// Various skinny matrices\nBM_ContractionCPU(250, 3, 512);\nBM_ContractionCPU(1500, 3, 512);\n\nBM_ContractionCPU(512, 800, 4);\nBM_ContractionCPU(512, 80, 800);\nBM_ContractionCPU(512, 80, 13522);\nBM_ContractionCPU(1, 80, 13522);\n\nBM_ContractionCPU(3200, 512, 4);\nBM_ContractionCPU(3200, 512, 80);\nBM_ContractionCPU(3200, 80, 512);\n"
  },
  {
    "path": "include/eigen3/bench/tensors/tensor_benchmarks.h",
    "content": "#ifndef THIRD_PARTY_EIGEN3_TENSOR_BENCHMARKS_H_\n#define THIRD_PARTY_EIGEN3_TENSOR_BENCHMARKS_H_\n\ntypedef int TensorIndex;\n#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int\n\n#include \"unsupported/Eigen/CXX11/Tensor\"\n#include \"benchmark.h\"\n\n#define BENCHMARK_RANGE(bench, lo, hi) \\\n  BENCHMARK(bench)->Range(lo, hi)\n\nusing Eigen::Tensor;\nusing Eigen::TensorMap;\n\n// TODO(bsteiner): also templatize on the input type since we have users\n// for int8 as well as floats.\ntemplate <typename Device, typename T> class BenchmarkSuite {\n public:\n  BenchmarkSuite(const Device& device, size_t m, size_t k, size_t n)\n      : m_(m), k_(k), n_(n), device_(device) {\n    initialize();\n  }\n\n  BenchmarkSuite(const Device& device, size_t m)\n      : m_(m), k_(m), n_(m), device_(device) {\n    initialize();\n  }\n\n  ~BenchmarkSuite() {\n    device_.deallocate(a_);\n    device_.deallocate(b_);\n    device_.deallocate(c_);\n  }\n\n  void memcpy(int num_iters) {\n    eigen_assert(m_ == k_ && k_ == n_);\n    StartBenchmarkTiming();\n    for (int iter = 0; iter < num_iters; ++iter) {\n      device_.memcpy(c_, a_, m_ * m_ * sizeof(T));\n    }\n    // Record the number of values copied per second\n    finalizeBenchmark(static_cast<int64_t>(m_) * m_ * num_iters);\n  }\n\n  void typeCasting(int num_iters) {\n    eigen_assert(m_ == n_);\n    Eigen::array<TensorIndex, 2> sizes;\n    if (sizeof(T) >= sizeof(int)) {\n      sizes[0] = m_;\n      sizes[1] = k_;\n    } else {\n      sizes[0] = m_ * sizeof(T) / sizeof(int);\n      sizes[1] = k_ * sizeof(T) / sizeof(int);\n    }\n    const TensorMap<Tensor<int, 2, 0, TensorIndex>, Eigen::Aligned> A((int*)a_, sizes);\n    TensorMap<Tensor<T, 2, 0, TensorIndex>, Eigen::Aligned> B(b_, sizes);\n\n    StartBenchmarkTiming();\n    for (int iter = 0; iter < num_iters; ++iter) {\n      B.device(device_) = A.template cast<T>();\n    }\n    // Record the number of values copied per second\n    finalizeBenchmark(static_cast<int64_t>(m_) * k_ * num_iters);\n  }\n\n  void random(int num_iters) {\n    eigen_assert(m_ == k_ && k_ == n_);\n    Eigen::array<TensorIndex, 2> sizes;\n    sizes[0] = m_;\n    sizes[1] = m_;\n    TensorMap<Tensor<T, 2>, Eigen::Aligned> C(c_, sizes);\n\n    StartBenchmarkTiming();\n    for (int iter = 0; iter < num_iters; ++iter) {\n      C.device(device_) = C.random();\n    }\n    // Record the number of random numbers generated per second\n    finalizeBenchmark(static_cast<int64_t>(m_) * m_ * num_iters);\n  }\n\n  void slicing(int num_iters) {\n    eigen_assert(m_ == k_ && k_ == n_);\n    Eigen::array<TensorIndex, 2> sizes;\n    sizes[0] = m_;\n    sizes[1] = m_;\n    const TensorMap<Tensor<T, 2>, Eigen::Aligned> A(a_, sizes);\n    const TensorMap<Tensor<T, 2>, Eigen::Aligned> B(b_, sizes);\n    TensorMap<Tensor<T, 2>, Eigen::Aligned> C(c_, sizes);\n\n    const Eigen::DSizes<TensorIndex, 2> quarter_sizes(m_/2, m_/2);\n    const Eigen::DSizes<TensorIndex, 2> first_quadrant(0, 0);\n    const Eigen::DSizes<TensorIndex, 2> second_quadrant(0, m_/2);\n    const Eigen::DSizes<TensorIndex, 2> third_quadrant(m_/2, 0);\n    const Eigen::DSizes<TensorIndex, 2> fourth_quadrant(m_/2, m_/2);\n\n    StartBenchmarkTiming();\n    for (int iter = 0; iter < num_iters; ++iter) {\n      C.slice(first_quadrant, quarter_sizes).device(device_) =\n          A.slice(first_quadrant, quarter_sizes);\n      C.slice(second_quadrant, quarter_sizes).device(device_) =\n          B.slice(second_quadrant, quarter_sizes);\n      C.slice(third_quadrant, quarter_sizes).device(device_) =\n          A.slice(third_quadrant, quarter_sizes);\n      C.slice(fourth_quadrant, quarter_sizes).device(device_) =\n          B.slice(fourth_quadrant, quarter_sizes);\n    }\n    // Record the number of values copied from the rhs slice to the lhs slice\n    // each second\n    finalizeBenchmark(static_cast<int64_t>(m_) * m_ * num_iters);\n  }\n\n  void rowChip(int num_iters) {\n    Eigen::array<TensorIndex, 2> input_size;\n    input_size[0] = k_;\n    input_size[1] = n_;\n    const TensorMap<Tensor<T, 2, 0, TensorIndex>, Eigen::Aligned> B(b_, input_size);\n    Eigen::array<TensorIndex, 1> output_size;\n    output_size[0] = n_;\n    TensorMap<Tensor<T, 1, 0, TensorIndex>, Eigen::Aligned> C(c_, output_size);\n\n    StartBenchmarkTiming();\n    for (int iter = 0; iter < num_iters; ++iter) {\n      C.device(device_) = B.chip(iter % k_, 0);\n    }\n    // Record the number of values copied from the rhs chip to the lhs.\n    finalizeBenchmark(static_cast<int64_t>(n_) * num_iters);\n  }\n\n  void colChip(int num_iters) {\n    Eigen::array<TensorIndex, 2> input_size;\n    input_size[0] = k_;\n    input_size[1] = n_;\n    const TensorMap<Tensor<T, 2, 0, TensorIndex>, Eigen::Aligned> B(b_, input_size);\n    Eigen::array<TensorIndex, 1> output_size;\n    output_size[0] = n_;\n    TensorMap<Tensor<T, 1, 0, TensorIndex>, Eigen::Aligned> C(c_, output_size);\n\n    StartBenchmarkTiming();\n    for (int iter = 0; iter < num_iters; ++iter) {\n      C.device(device_) = B.chip(iter % n_, 1);\n    }\n    // Record the number of values copied from the rhs chip to the lhs.\n    finalizeBenchmark(static_cast<int64_t>(n_) * num_iters);\n  }\n\n  void shuffling(int num_iters) {\n    eigen_assert(m_ == n_);\n    Eigen::array<TensorIndex, 2> size_a;\n    size_a[0] = m_;\n    size_a[1] = k_;\n    const TensorMap<Tensor<T, 2>, Eigen::Aligned> A(a_, size_a);\n    Eigen::array<TensorIndex, 2> size_b;\n    size_b[0] = k_;\n    size_b[1] = m_;\n    TensorMap<Tensor<T, 2>, Eigen::Aligned> B(b_, size_b);\n\n    Eigen::array<int, 2> shuffle;\n    shuffle[0] = 1;\n    shuffle[1] = 0;\n\n    StartBenchmarkTiming();\n    for (int iter = 0; iter < num_iters; ++iter) {\n      B.device(device_) = A.shuffle(shuffle);\n    }\n    // Record the number of values shuffled from A and copied to B each second\n    finalizeBenchmark(static_cast<int64_t>(m_) * k_ * num_iters);\n  }\n\n void padding(int num_iters) {\n    eigen_assert(m_ == k_);\n    Eigen::array<TensorIndex, 2> size_a;\n    size_a[0] = m_;\n    size_a[1] = k_-3;\n    const TensorMap<Tensor<T, 2>, Eigen::Aligned> A(a_, size_a);\n    Eigen::array<TensorIndex, 2> size_b;\n    size_b[0] = k_;\n    size_b[1] = m_;\n    TensorMap<Tensor<T, 2>, Eigen::Aligned> B(b_, size_b);\n\n#if defined(EIGEN_HAS_INDEX_LIST)\n    Eigen::IndexPairList<Eigen::type2indexpair<0, 0>,\n                         Eigen::type2indexpair<2, 1> > paddings;\n#else\n    Eigen::array<Eigen::IndexPair<TensorIndex>, 2> paddings;\n    paddings[0] = Eigen::IndexPair<TensorIndex>(0, 0);\n    paddings[1] = Eigen::IndexPair<TensorIndex>(2, 1);\n#endif\n\n    StartBenchmarkTiming();\n    for (int iter = 0; iter < num_iters; ++iter) {\n      B.device(device_) = A.pad(paddings);\n    }\n    // Record the number of values copied from the padded tensor A each second\n    finalizeBenchmark(static_cast<int64_t>(m_) * k_ * num_iters);\n  }\n\n void striding(int num_iters) {\n    eigen_assert(m_ == k_);\n    Eigen::array<TensorIndex, 2> size_a;\n    size_a[0] = m_;\n    size_a[1] = k_;\n    const TensorMap<Tensor<T, 2>, Eigen::Aligned> A(a_, size_a);\n    Eigen::array<TensorIndex, 2> size_b;\n    size_b[0] = m_;\n    size_b[1] = k_/2;\n    TensorMap<Tensor<T, 2>, Eigen::Aligned> B(b_, size_b);\n\n#ifndef EIGEN_HAS_INDEX_LIST\n    Eigen::array<TensorIndex, 2> strides;\n    strides[0] = 1;\n    strides[1] = 2;\n#else\n    // Take advantage of cxx11 to give the compiler information it can use to\n    // optimize the code.\n    Eigen::IndexList<Eigen::type2index<1>, Eigen::type2index<2> > strides;\n#endif\n\n    StartBenchmarkTiming();\n    for (int iter = 0; iter < num_iters; ++iter) {\n      B.device(device_) = A.stride(strides);\n    }\n    // Record the number of values copied from the padded tensor A each second\n    finalizeBenchmark(static_cast<int64_t>(m_) * k_ * num_iters);\n  }\n\n  void broadcasting(int num_iters) {\n    Eigen::array<TensorIndex, 2> size_a;\n    size_a[0] = m_;\n    size_a[1] = 1;\n    const TensorMap<Tensor<T, 2>, Eigen::Aligned> A(a_, size_a);\n    Eigen::array<TensorIndex, 2> size_c;\n    size_c[0] = m_;\n    size_c[1] = n_;\n    TensorMap<Tensor<T, 2>, Eigen::Aligned> C(c_, size_c);\n\n#ifndef EIGEN_HAS_INDEX_LIST\n    Eigen::array<int, 2> broadcast;\n    broadcast[0] = 1;\n    broadcast[1] = n_;\n#else\n    // Take advantage of cxx11 to give the compiler information it can use to\n    // optimize the code.\n    Eigen::IndexList<Eigen::type2index<1>, int> broadcast;\n    broadcast.set(1, n_);\n#endif\n\n    StartBenchmarkTiming();\n    for (int iter = 0; iter < num_iters; ++iter) {\n      C.device(device_) = A.broadcast(broadcast);\n    }\n    // Record the number of values broadcasted from A and copied to C each second\n    finalizeBenchmark(static_cast<int64_t>(m_) * n_ * num_iters);\n  }\n\n  void coeffWiseOp(int num_iters) {\n    eigen_assert(m_ == k_ && k_ == n_);\n    Eigen::array<TensorIndex, 2> sizes;\n    sizes[0] = m_;\n    sizes[1] = m_;\n    const TensorMap<Tensor<T, 2>, Eigen::Aligned> A(a_, sizes);\n    const TensorMap<Tensor<T, 2>, Eigen::Aligned> B(b_, sizes);\n    TensorMap<Tensor<T, 2>, Eigen::Aligned> C(c_, sizes);\n\n    StartBenchmarkTiming();\n    for (int iter = 0; iter < num_iters; ++iter) {\n      C.device(device_) = A * A.constant(static_cast<T>(3.14)) + B * B.constant(static_cast<T>(2.7));\n    }\n    // Record the number of FLOP executed per second (2 multiplications and\n    // 1 addition per value)\n    finalizeBenchmark(static_cast<int64_t>(3) * m_ * m_ * num_iters);\n  }\n\n  void algebraicFunc(int num_iters) {\n    eigen_assert(m_ == k_ && k_ == n_);\n    Eigen::array<TensorIndex, 2> sizes;\n    sizes[0] = m_;\n    sizes[1] = m_;\n    const TensorMap<Tensor<T, 2>, Eigen::Aligned> A(a_, sizes);\n    const TensorMap<Tensor<T, 2>, Eigen::Aligned> B(b_, sizes);\n    TensorMap<Tensor<T, 2>, Eigen::Aligned> C(c_, sizes);\n\n    StartBenchmarkTiming();\n    for (int iter = 0; iter < num_iters; ++iter) {\n      C.device(device_) = A.rsqrt() + B.sqrt() * B.square();\n    }\n    // Record the number of FLOP executed per second (assuming one operation\n    // per value)\n    finalizeBenchmark(static_cast<int64_t>(m_) * m_ * num_iters);\n  }\n\n  void transcendentalFunc(int num_iters) {\n    eigen_assert(m_ == k_ && k_ == n_);\n    Eigen::array<TensorIndex, 2> sizes;\n    sizes[0] = m_;\n    sizes[1] = m_;\n    const TensorMap<Tensor<T, 2>, Eigen::Aligned> A(a_, sizes);\n    const TensorMap<Tensor<T, 2>, Eigen::Aligned> B(b_, sizes);\n    TensorMap<Tensor<T, 2>, Eigen::Aligned> C(c_, sizes);\n\n    StartBenchmarkTiming();\n    for (int iter = 0; iter < num_iters; ++iter) {\n      C.device(device_) = A.exp() + B.log();\n    }\n    // Record the number of FLOP executed per second (assuming one operation\n    // per value)\n    finalizeBenchmark(static_cast<int64_t>(m_) * m_ * num_iters);\n  }\n\n // Row reduction\n  void rowReduction(int num_iters) {\n    Eigen::array<TensorIndex, 2> input_size;\n    input_size[0] = k_;\n    input_size[1] = n_;\n    const TensorMap<Tensor<T, 2, 0, TensorIndex>, Eigen::Aligned> B(b_, input_size);\n    Eigen::array<TensorIndex, 1> output_size;\n    output_size[0] = n_;\n    TensorMap<Tensor<T, 1, 0, TensorIndex>, Eigen::Aligned> C(c_, output_size);\n\n#ifndef EIGEN_HAS_INDEX_LIST\n    Eigen::array<TensorIndex, 1> sum_along_dim;\n    sum_along_dim[0] = 0;\n#else\n    // Take advantage of cxx11 to give the compiler information it can use to\n    // optimize the code.\n    Eigen::IndexList<Eigen::type2index<0>> sum_along_dim;\n#endif\n\n    StartBenchmarkTiming();\n    for (int iter = 0; iter < num_iters; ++iter) {\n      C.device(device_) = B.sum(sum_along_dim);\n    }\n    // Record the number of FLOP executed per second (assuming one operation\n    // per value)\n    finalizeBenchmark(static_cast<int64_t>(k_) * n_ * num_iters);\n  }\n\n  // Column reduction\n  void colReduction(int num_iters) {\n    Eigen::array<TensorIndex, 2> input_size;\n    input_size[0] = k_;\n    input_size[1] = n_;\n    const TensorMap<Tensor<T, 2, 0, TensorIndex>, Eigen::Aligned> B(\n        b_, input_size);\n    Eigen::array<TensorIndex, 1> output_size;\n    output_size[0] = k_;\n    TensorMap<Tensor<T, 1, 0, TensorIndex>, Eigen::Aligned> C(\n        c_, output_size);\n\n#ifndef EIGEN_HAS_INDEX_LIST\n    Eigen::array<TensorIndex, 1> sum_along_dim;\n    sum_along_dim[0] = 1;\n#else\n    // Take advantage of cxx11 to give the compiler information it can use to\n    // optimize the code.\n    Eigen::IndexList<Eigen::type2index<1>> sum_along_dim;\n#endif\n\n    StartBenchmarkTiming();\n    for (int iter = 0; iter < num_iters; ++iter) {\n      C.device(device_) = B.sum(sum_along_dim);\n    }\n    // Record the number of FLOP executed per second (assuming one operation\n    // per value)\n    finalizeBenchmark(static_cast<int64_t>(k_) * n_ * num_iters);\n  }\n\n  // Full reduction\n  void fullReduction(int num_iters) {\n    Eigen::array<TensorIndex, 2> input_size;\n    input_size[0] = k_;\n    input_size[1] = n_;\n    const TensorMap<Tensor<T, 2, 0, TensorIndex>, Eigen::Aligned> B(\n        b_, input_size);\n    Eigen::array<TensorIndex, 0> output_size;\n    TensorMap<Tensor<T, 0, 0, TensorIndex>, Eigen::Aligned> C(\n        c_, output_size);\n\n    StartBenchmarkTiming();\n    for (int iter = 0; iter < num_iters; ++iter) {\n      C.device(device_) = B.sum();\n    }\n    // Record the number of FLOP executed per second (assuming one operation\n    // per value)\n    finalizeBenchmark(static_cast<int64_t>(k_) * n_ * num_iters);\n  }\n\n  // do a contraction which is equivalent to a matrix multiplication\n  void contraction(int num_iters) {\n    Eigen::array<TensorIndex, 2> sizeA;\n    sizeA[0] = m_;\n    sizeA[1] = k_;\n    Eigen::array<TensorIndex, 2> sizeB;\n    sizeB[0] = k_;\n    sizeB[1] = n_;\n    Eigen::array<TensorIndex, 2> sizeC;\n    sizeC[0] = m_;\n    sizeC[1] = n_;\n\n    const TensorMap<Tensor<T, 2>, Eigen::Aligned> A(a_, sizeA);\n    const TensorMap<Tensor<T, 2>, Eigen::Aligned> B(b_, sizeB);\n    TensorMap<Tensor<T, 2>, Eigen::Aligned> C(c_, sizeC);\n\n    typedef typename Tensor<T, 2>::DimensionPair DimPair;\n    Eigen::array<DimPair, 1> dims;\n    dims[0] = DimPair(1, 0);\n\n    StartBenchmarkTiming();\n    for (int iter = 0; iter < num_iters; ++iter) {\n      C.device(device_) = A.contract(B, dims);\n    }\n    // Record the number of FLOP executed per second (size_ multiplications and\n    // additions for each value in the resulting tensor)\n    finalizeBenchmark(static_cast<int64_t>(2) * m_ * n_ * k_ * num_iters);\n  }\n\n  void convolution(int num_iters, int kernel_x, int kernel_y) {\n    Eigen::array<TensorIndex, 2> input_sizes;\n    input_sizes[0] = m_;\n    input_sizes[1] = n_;\n    TensorMap<Tensor<T, 2>, Eigen::Aligned> A(a_, input_sizes);\n    Eigen::array<TensorIndex, 2> kernel_sizes;\n    kernel_sizes[0] = kernel_x;\n    kernel_sizes[1] = kernel_y;\n    TensorMap<Tensor<T, 2>, Eigen::Aligned> B(b_, kernel_sizes);\n    Eigen::array<TensorIndex, 2> result_sizes;\n    result_sizes[0] = m_ - kernel_x + 1;\n    result_sizes[1] = n_ - kernel_y + 1;\n    TensorMap<Tensor<T, 2>, Eigen::Aligned> C(c_, result_sizes);\n    Eigen::array<TensorIndex, 2> dims;\n    dims[0] = 0;\n    dims[1] = 1;\n\n    StartBenchmarkTiming();\n    for (int iter = 0; iter < num_iters; ++iter) {\n      C.device(device_) = A.convolve(B, dims);\n    }\n    // Record the number of FLOP executed per second (kernel_size\n    // multiplications and additions for each value in the resulting tensor)\n    finalizeBenchmark(static_cast<int64_t>(2) *\n        (m_ - kernel_x + 1) * (n_ - kernel_y + 1) * kernel_x * kernel_y * num_iters);\n  }\n\n private:\n  void initialize() {\n    a_ = (T *) device_.allocate(m_ * k_ * sizeof(T));\n    b_ = (T *) device_.allocate(k_ * n_ * sizeof(T));\n    c_ = (T *) device_.allocate(m_ * n_ * sizeof(T));\n\n    // Initialize the content of the memory pools to prevent asan from\n    // complaining.\n    device_.memset(a_, 12, m_ * k_ * sizeof(T));\n    device_.memset(b_, 23, k_ * n_ * sizeof(T));\n    device_.memset(c_, 31, m_ * n_ * sizeof(T));\n\n    //BenchmarkUseRealTime();\n  }\n\n  inline void finalizeBenchmark(int64_t num_items) {\n#if defined(EIGEN_USE_GPU) && defined(__CUDACC__)\n    if (Eigen::internal::is_same<Device, Eigen::GpuDevice>::value) {\n      device_.synchronize();\n    }\n#endif\n    StopBenchmarkTiming();\n    SetBenchmarkFlopsProcessed(num_items);\n  }\n\n\n  TensorIndex m_;\n  TensorIndex k_;\n  TensorIndex n_;\n  T* a_;\n  T* b_;\n  T* c_;\n  Device device_;\n};\n#endif  // THIRD_PARTY_EIGEN3_TENSOR_BENCHMARKS_H_\n"
  },
  {
    "path": "include/eigen3/bench/tensors/tensor_benchmarks_cpu.cc",
    "content": "#define EIGEN_USE_THREADS\n\n#include <string>\n\n#include \"tensor_benchmarks.h\"\n\n#define CREATE_THREAD_POOL(threads)             \\\nEigen::ThreadPool pool(threads);                \\\nEigen::ThreadPoolDevice device(&pool, threads);\n\n// Simple functions\n#define BM_FuncCPU(FUNC, THREADS)                                    \\\n  static void BM_##FUNC##_##THREADS##T(int iters, int N) {           \\\n    StopBenchmarkTiming();                                           \\\n    CREATE_THREAD_POOL(THREADS);                                     \\\n    BenchmarkSuite<Eigen::ThreadPoolDevice, float> suite(device, N); \\\n    suite.FUNC(iters);                                               \\\n  }                                                                  \\\n  BENCHMARK_RANGE(BM_##FUNC##_##THREADS##T, 10, 5000);\n\nBM_FuncCPU(memcpy, 4);\nBM_FuncCPU(memcpy, 8);\nBM_FuncCPU(memcpy, 12);\n\nBM_FuncCPU(typeCasting, 4);\nBM_FuncCPU(typeCasting, 8);\nBM_FuncCPU(typeCasting, 12);\n\nBM_FuncCPU(random, 4);\nBM_FuncCPU(random, 8);\nBM_FuncCPU(random, 12);\n\nBM_FuncCPU(slicing, 4);\nBM_FuncCPU(slicing, 8);\nBM_FuncCPU(slicing, 12);\n\nBM_FuncCPU(rowChip, 4);\nBM_FuncCPU(rowChip, 8);\nBM_FuncCPU(rowChip, 12);\n\nBM_FuncCPU(colChip, 4);\nBM_FuncCPU(colChip, 8);\nBM_FuncCPU(colChip, 12);\n\nBM_FuncCPU(shuffling, 4);\nBM_FuncCPU(shuffling, 8);\nBM_FuncCPU(shuffling, 12);\n\nBM_FuncCPU(padding, 4);\nBM_FuncCPU(padding, 8);\nBM_FuncCPU(padding, 12);\n\nBM_FuncCPU(striding, 4);\nBM_FuncCPU(striding, 8);\nBM_FuncCPU(striding, 12);\n\nBM_FuncCPU(broadcasting, 4);\nBM_FuncCPU(broadcasting, 8);\nBM_FuncCPU(broadcasting, 12);\n\nBM_FuncCPU(coeffWiseOp, 4);\nBM_FuncCPU(coeffWiseOp, 8);\nBM_FuncCPU(coeffWiseOp, 12);\n\nBM_FuncCPU(algebraicFunc, 4);\nBM_FuncCPU(algebraicFunc, 8);\nBM_FuncCPU(algebraicFunc, 12);\n\nBM_FuncCPU(transcendentalFunc, 4);\nBM_FuncCPU(transcendentalFunc, 8);\nBM_FuncCPU(transcendentalFunc, 12);\n\nBM_FuncCPU(rowReduction, 4);\nBM_FuncCPU(rowReduction, 8);\nBM_FuncCPU(rowReduction, 12);\n\nBM_FuncCPU(colReduction, 4);\nBM_FuncCPU(colReduction, 8);\nBM_FuncCPU(colReduction, 12);\n\n\n// Contractions\n#define BM_FuncWithInputDimsCPU(FUNC, D1, D2, D3, THREADS)                      \\\n  static void BM_##FUNC##_##D1##x##D2##x##D3##_##THREADS##T(int iters, int N) { \\\n    StopBenchmarkTiming();                                                      \\\n    if (THREADS == 1) {                                                         \\\n      Eigen::DefaultDevice device;                                              \\\n      BenchmarkSuite<Eigen::DefaultDevice, float> suite(device, D1, D2, D3);    \\\n      suite.FUNC(iters);                                                        \\\n    } else {                                                                    \\\n      CREATE_THREAD_POOL(THREADS);                                              \\\n      BenchmarkSuite<Eigen::ThreadPoolDevice, float> suite(device, D1, D2, D3); \\\n      suite.FUNC(iters);                                                        \\\n    }                                                                           \\\n  }                                                                             \\\n  BENCHMARK_RANGE(BM_##FUNC##_##D1##x##D2##x##D3##_##THREADS##T, 10, 5000);\n\n\nBM_FuncWithInputDimsCPU(contraction, N, N, N, 1);\nBM_FuncWithInputDimsCPU(contraction, N, N, N, 4);\nBM_FuncWithInputDimsCPU(contraction, N, N, N, 8);\nBM_FuncWithInputDimsCPU(contraction, N, N, N, 12);\nBM_FuncWithInputDimsCPU(contraction, N, N, N, 16);\n\nBM_FuncWithInputDimsCPU(contraction, 64, N, N, 1);\nBM_FuncWithInputDimsCPU(contraction, 64, N, N, 4);\nBM_FuncWithInputDimsCPU(contraction, 64, N, N, 8);\nBM_FuncWithInputDimsCPU(contraction, 64, N, N, 12);\nBM_FuncWithInputDimsCPU(contraction, 64, N, N, 16);\n\nBM_FuncWithInputDimsCPU(contraction, N, 64, N, 1);\nBM_FuncWithInputDimsCPU(contraction, N, 64, N, 4);\nBM_FuncWithInputDimsCPU(contraction, N, 64, N, 8);\nBM_FuncWithInputDimsCPU(contraction, N, 64, N, 12);\nBM_FuncWithInputDimsCPU(contraction, N, 64, N, 16);\n\nBM_FuncWithInputDimsCPU(contraction, N, N, 64, 1);\nBM_FuncWithInputDimsCPU(contraction, N, N, 64, 4);\nBM_FuncWithInputDimsCPU(contraction, N, N, 64, 8);\nBM_FuncWithInputDimsCPU(contraction, N, N, 64, 12);\nBM_FuncWithInputDimsCPU(contraction, N, N, 64, 16);\n\nBM_FuncWithInputDimsCPU(contraction, 1, N, N, 1);\nBM_FuncWithInputDimsCPU(contraction, 1, N, N, 4);\nBM_FuncWithInputDimsCPU(contraction, 1, N, N, 8);\nBM_FuncWithInputDimsCPU(contraction, 1, N, N, 12);\nBM_FuncWithInputDimsCPU(contraction, 1, N, N, 16);\n\nBM_FuncWithInputDimsCPU(contraction, N, N, 1, 1);\nBM_FuncWithInputDimsCPU(contraction, N, N, 1, 4);\nBM_FuncWithInputDimsCPU(contraction, N, N, 1, 8);\nBM_FuncWithInputDimsCPU(contraction, N, N, 1, 12);\nBM_FuncWithInputDimsCPU(contraction, N, N, 1, 16);\n\n\n// Convolutions\n#define BM_FuncWithKernelDimsCPU(FUNC, DIM1, DIM2, THREADS)                    \\\n  static void BM_##FUNC##_##DIM1##x##DIM2##_##THREADS##T(int iters, int N) {   \\\n    StopBenchmarkTiming();                                                     \\\n    CREATE_THREAD_POOL(THREADS);                                               \\\n    BenchmarkSuite<Eigen::ThreadPoolDevice, float> suite(device, N);\t       \\\n    suite.FUNC(iters, DIM1, DIM2);                                             \\\n  }                                                                            \\\n  BENCHMARK_RANGE(BM_##FUNC##_##DIM1##x##DIM2##_##THREADS##T, 128, 5000);\n\nBM_FuncWithKernelDimsCPU(convolution, 7, 1, 4);\nBM_FuncWithKernelDimsCPU(convolution, 7, 1, 8);\nBM_FuncWithKernelDimsCPU(convolution, 7, 1, 12);\n\nBM_FuncWithKernelDimsCPU(convolution, 1, 7, 4);\nBM_FuncWithKernelDimsCPU(convolution, 1, 7, 8);\nBM_FuncWithKernelDimsCPU(convolution, 1, 7, 12);\n\nBM_FuncWithKernelDimsCPU(convolution, 7, 4, 4);\nBM_FuncWithKernelDimsCPU(convolution, 7, 4, 8);\nBM_FuncWithKernelDimsCPU(convolution, 7, 4, 12);\n\nBM_FuncWithKernelDimsCPU(convolution, 4, 7, 4);\nBM_FuncWithKernelDimsCPU(convolution, 4, 7, 8);\nBM_FuncWithKernelDimsCPU(convolution, 4, 7, 12);\n\nBM_FuncWithKernelDimsCPU(convolution, 7, 64, 4);\nBM_FuncWithKernelDimsCPU(convolution, 7, 64, 8);\nBM_FuncWithKernelDimsCPU(convolution, 7, 64, 12);\n\nBM_FuncWithKernelDimsCPU(convolution, 64, 7, 4);\nBM_FuncWithKernelDimsCPU(convolution, 64, 7, 8);\nBM_FuncWithKernelDimsCPU(convolution, 64, 7, 12);\n"
  },
  {
    "path": "include/eigen3/bench/tensors/tensor_benchmarks_fp16_gpu.cu",
    "content": "#define EIGEN_USE_GPU\n\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <iostream>\n\n#include \"tensor_benchmarks.h\"\n\n// Simple functions\n#define BM_FuncGPU(FUNC)                                                       \\\n  static void BM_##FUNC(int iters, int N) {                                    \\\n    StopBenchmarkTiming();                                                     \\\n    Eigen::CudaStreamDevice stream;                                            \\\n    Eigen::GpuDevice device(&stream);                                          \\\n    BenchmarkSuite<Eigen::GpuDevice, Eigen::half> suite(device, N);            \\\n    cudaDeviceSynchronize();                                                   \\\n    suite.FUNC(iters);                                                         \\\n  }                                                                            \\\n  BENCHMARK_RANGE(BM_##FUNC, 10, 5000);\n\nBM_FuncGPU(memcpy);\nBM_FuncGPU(typeCasting);\n//BM_FuncGPU(random);\nBM_FuncGPU(slicing);\nBM_FuncGPU(rowChip);\nBM_FuncGPU(colChip);\nBM_FuncGPU(shuffling);\nBM_FuncGPU(padding);\nBM_FuncGPU(striding);\nBM_FuncGPU(broadcasting);\nBM_FuncGPU(coeffWiseOp);\nBM_FuncGPU(algebraicFunc);\nBM_FuncGPU(transcendentalFunc);\nBM_FuncGPU(rowReduction);\nBM_FuncGPU(colReduction);\nBM_FuncGPU(fullReduction);\n\n\n// Contractions\n#define BM_FuncWithInputDimsGPU(FUNC, D1, D2, D3)                              \\\n  static void BM_##FUNC##_##D1##x##D2##x##D3(int iters, int N) {               \\\n    StopBenchmarkTiming();                                                     \\\n    Eigen::CudaStreamDevice stream;                                            \\\n    Eigen::GpuDevice device(&stream);                                          \\\n    BenchmarkSuite<Eigen::GpuDevice, Eigen::half> suite(device, D1, D2, D3);   \\\n    cudaDeviceSynchronize();                                                   \\\n    suite.FUNC(iters);                                                         \\\n  }                                                                            \\\n  BENCHMARK_RANGE(BM_##FUNC##_##D1##x##D2##x##D3, 10, 5000);\n\n\nBM_FuncWithInputDimsGPU(contraction, N, N, N);\nBM_FuncWithInputDimsGPU(contraction, 64, N, N);\nBM_FuncWithInputDimsGPU(contraction, N, 64, N);\nBM_FuncWithInputDimsGPU(contraction, N, N, 64);\n\n\n// Convolutions\n#define BM_FuncWithKernelDimsGPU(FUNC, DIM1, DIM2)                             \\\n  static void BM_##FUNC##_##DIM1##x##DIM2(int iters, int N) {                  \\\n    StopBenchmarkTiming();                                                     \\\n    Eigen::CudaStreamDevice stream;                                            \\\n    Eigen::GpuDevice device(&stream);                                          \\\n    BenchmarkSuite<Eigen::GpuDevice, Eigen::half> suite(device, N);            \\\n    cudaDeviceSynchronize();                                                   \\\n    suite.FUNC(iters, DIM1, DIM2);                                             \\\n  }                                                                            \\\n  BENCHMARK_RANGE(BM_##FUNC##_##DIM1##x##DIM2, 128, 5000);\n\n/*\nBM_FuncWithKernelDimsGPU(convolution, 7, 1);\nBM_FuncWithKernelDimsGPU(convolution, 1, 7);\nBM_FuncWithKernelDimsGPU(convolution, 7, 4);\nBM_FuncWithKernelDimsGPU(convolution, 4, 7);\nBM_FuncWithKernelDimsGPU(convolution, 7, 64);\nBM_FuncWithKernelDimsGPU(convolution, 64, 7);\n*/\n"
  },
  {
    "path": "include/eigen3/bench/tensors/tensor_benchmarks_gpu.cu",
    "content": "#define EIGEN_USE_GPU\n\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <iostream>\n\n#include \"tensor_benchmarks.h\"\n\n// Simple functions\n#define BM_FuncGPU(FUNC)                                                       \\\n  static void BM_##FUNC(int iters, int N) {                                    \\\n    StopBenchmarkTiming();                                                     \\\n    Eigen::CudaStreamDevice stream;                                            \\\n    Eigen::GpuDevice device(&stream);                                          \\\n    BenchmarkSuite<Eigen::GpuDevice, float> suite(device, N);                  \\\n    cudaDeviceSynchronize();                                                   \\\n    suite.FUNC(iters);                                                         \\\n  }                                                                            \\\n  BENCHMARK_RANGE(BM_##FUNC, 10, 5000);\n\nBM_FuncGPU(memcpy);\nBM_FuncGPU(typeCasting);\nBM_FuncGPU(random);\nBM_FuncGPU(slicing);\nBM_FuncGPU(rowChip);\nBM_FuncGPU(colChip);\nBM_FuncGPU(shuffling);\nBM_FuncGPU(padding);\nBM_FuncGPU(striding);\nBM_FuncGPU(broadcasting);\nBM_FuncGPU(coeffWiseOp);\nBM_FuncGPU(algebraicFunc);\nBM_FuncGPU(transcendentalFunc);\nBM_FuncGPU(rowReduction);\nBM_FuncGPU(colReduction);\nBM_FuncGPU(fullReduction);\n\n\n// Contractions\n#define BM_FuncWithInputDimsGPU(FUNC, D1, D2, D3)                              \\\n  static void BM_##FUNC##_##D1##x##D2##x##D3(int iters, int N) {               \\\n    StopBenchmarkTiming();                                                     \\\n    Eigen::CudaStreamDevice stream;                                            \\\n    Eigen::GpuDevice device(&stream);                                          \\\n    BenchmarkSuite<Eigen::GpuDevice, float> suite(device, D1, D2, D3);         \\\n    cudaDeviceSynchronize();                                                   \\\n    suite.FUNC(iters);                                                         \\\n  }                                                                            \\\n  BENCHMARK_RANGE(BM_##FUNC##_##D1##x##D2##x##D3, 10, 5000);\n\n\nBM_FuncWithInputDimsGPU(contraction, N, N, N);\nBM_FuncWithInputDimsGPU(contraction, 64, N, N);\nBM_FuncWithInputDimsGPU(contraction, N, 64, N);\nBM_FuncWithInputDimsGPU(contraction, N, N, 64);\n\n\n// Convolutions\n#define BM_FuncWithKernelDimsGPU(FUNC, DIM1, DIM2)                             \\\n  static void BM_##FUNC##_##DIM1##x##DIM2(int iters, int N) {                  \\\n    StopBenchmarkTiming();                                                     \\\n    Eigen::CudaStreamDevice stream;                                            \\\n    Eigen::GpuDevice device(&stream);                                          \\\n    BenchmarkSuite<Eigen::GpuDevice, float> suite(device, N);                  \\\n    cudaDeviceSynchronize();                                                   \\\n    suite.FUNC(iters, DIM1, DIM2);                                             \\\n  }                                                                            \\\n  BENCHMARK_RANGE(BM_##FUNC##_##DIM1##x##DIM2, 128, 5000);\n\nBM_FuncWithKernelDimsGPU(convolution, 7, 1);\nBM_FuncWithKernelDimsGPU(convolution, 1, 7);\nBM_FuncWithKernelDimsGPU(convolution, 7, 4);\nBM_FuncWithKernelDimsGPU(convolution, 4, 7);\nBM_FuncWithKernelDimsGPU(convolution, 7, 64);\nBM_FuncWithKernelDimsGPU(convolution, 64, 7);\n"
  },
  {
    "path": "include/eigen3/bench/tensors/tensor_benchmarks_sycl.cc",
    "content": "#define EIGEN_USE_SYCL\n\n#include <SYCL/sycl.hpp>\n#include <iostream>\n\n#include \"tensor_benchmarks.h\"\n\nusing Eigen::array;\nusing Eigen::SyclDevice;\nusing Eigen::Tensor;\nusing Eigen::TensorMap;\n// Simple functions\ntemplate <typename device_selector>\ncl::sycl::queue sycl_queue() {\n  return cl::sycl::queue(device_selector(), [=](cl::sycl::exception_list l) {\n    for (const auto& e : l) {\n      try {\n        std::rethrow_exception(e);\n      } catch (cl::sycl::exception e) {\n        std::cout << e.what() << std::endl;\n      }\n    }\n  });\n}\n\n#define BM_FuncGPU(FUNC)                                       \\\n  static void BM_##FUNC(int iters, int N) {                    \\\n    StopBenchmarkTiming();                                     \\\n    cl::sycl::queue q = sycl_queue<cl::sycl::gpu_selector>();  \\\n    Eigen::SyclDevice device(q);                               \\\n    BenchmarkSuite<Eigen::SyclDevice, float> suite(device, N); \\\n    suite.FUNC(iters);                                         \\\n  }                                                            \\\n  BENCHMARK_RANGE(BM_##FUNC, 10, 5000);\n\nBM_FuncGPU(broadcasting);\nBM_FuncGPU(coeffWiseOp);\n"
  },
  {
    "path": "include/eigen3/bench/vdw_new.cpp",
    "content": "#include <iostream>\n#include <Eigen/Core>\n\nusing namespace Eigen;\n\n#ifndef SCALAR\n#define SCALAR float\n#endif\n\n#ifndef SIZE\n#define SIZE 10000\n#endif\n\n#ifndef REPEAT\n#define REPEAT 10000\n#endif\n\ntypedef Matrix<SCALAR, Eigen::Dynamic, 1> Vec;\n\nusing namespace std;\n\nSCALAR E_VDW(const Vec &interactions1, const Vec &interactions2)\n{\n  return (interactions2.cwise()/interactions1)\n         .cwise().cube()\n         .cwise().square()\n         .cwise().square()\n         .sum();\n}\n\nint main() \n{\n  //\n  //          1   2   3   4  ... (interactions)\n  // ka       .   .   .   .  ...\n  // rab      .   .   .   .  ...\n  // energy   .   .   .   .  ...\n  // ...     ... ... ... ... ...\n  // (variables\n  //    for\n  // interaction)\n  //\n  Vec interactions1(SIZE), interactions2(SIZE); // SIZE is the number of vdw interactions in our system\n  // SetupCalculations()\n  SCALAR rab = 1.0;  \n  interactions1.setConstant(2.4);\n  interactions2.setConstant(rab);\n  \n  // Energy()\n  SCALAR energy = 0.0;\n  for (unsigned int i = 0; i<REPEAT; ++i) {\n    energy += E_VDW(interactions1, interactions2);\n    energy *= 1 + 1e-20 * i; // prevent compiler from optimizing the loop\n  }\n  cout << \"energy = \" << energy << endl;\n}\n"
  },
  {
    "path": "include/eigen3/blas/BandTriangularSolver.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2011 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_BAND_TRIANGULARSOLVER_H\n#define EIGEN_BAND_TRIANGULARSOLVER_H\n\nnamespace internal {\n\n /* \\internal\n  * Solve Ax=b with A a band triangular matrix\n  * TODO: extend it to matrices for x abd b */\ntemplate<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, int StorageOrder>\nstruct band_solve_triangular_selector;\n\n\ntemplate<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar>\nstruct band_solve_triangular_selector<Index,Mode,LhsScalar,ConjLhs,RhsScalar,RowMajor>\n{\n  typedef Map<const Matrix<LhsScalar,Dynamic,Dynamic,RowMajor>, 0, OuterStride<> > LhsMap;\n  typedef Map<Matrix<RhsScalar,Dynamic,1> > RhsMap;\n  enum { IsLower = (Mode&Lower) ? 1 : 0 };\n  static void run(Index size, Index k, const LhsScalar* _lhs, Index lhsStride, RhsScalar* _other)\n  {\n    const LhsMap lhs(_lhs,size,k+1,OuterStride<>(lhsStride));\n    RhsMap other(_other,size,1);\n    typename internal::conditional<\n                          ConjLhs,\n                          const CwiseUnaryOp<typename internal::scalar_conjugate_op<LhsScalar>,LhsMap>,\n                          const LhsMap&>\n                        ::type cjLhs(lhs);\n                        \n    for(int col=0 ; col<other.cols() ; ++col)\n    {\n      for(int ii=0; ii<size; ++ii)\n      {\n        int i = IsLower ? ii : size-ii-1;\n        int actual_k = (std::min)(k,ii);\n        int actual_start = IsLower ? k-actual_k : 1;\n        \n        if(actual_k>0)\n          other.coeffRef(i,col) -= cjLhs.row(i).segment(actual_start,actual_k).transpose()\n                                  .cwiseProduct(other.col(col).segment(IsLower ? i-actual_k : i+1,actual_k)).sum();\n\n        if((Mode&UnitDiag)==0)\n          other.coeffRef(i,col) /= cjLhs(i,IsLower ? k : 0);\n      }\n    }\n  }\n  \n};\n\ntemplate<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar>\nstruct band_solve_triangular_selector<Index,Mode,LhsScalar,ConjLhs,RhsScalar,ColMajor>\n{\n  typedef Map<const Matrix<LhsScalar,Dynamic,Dynamic,ColMajor>, 0, OuterStride<> > LhsMap;\n  typedef Map<Matrix<RhsScalar,Dynamic,1> > RhsMap;\n  enum { IsLower = (Mode&Lower) ? 1 : 0 };\n  static void run(Index size, Index k, const LhsScalar* _lhs, Index lhsStride, RhsScalar* _other)\n  {\n    const LhsMap lhs(_lhs,k+1,size,OuterStride<>(lhsStride));\n    RhsMap other(_other,size,1);\n    typename internal::conditional<\n                          ConjLhs,\n                          const CwiseUnaryOp<typename internal::scalar_conjugate_op<LhsScalar>,LhsMap>,\n                          const LhsMap&>\n                        ::type cjLhs(lhs);\n                        \n    for(int col=0 ; col<other.cols() ; ++col)\n    {\n      for(int ii=0; ii<size; ++ii)\n      {\n        int i = IsLower ? ii : size-ii-1;\n        int actual_k = (std::min)(k,size-ii-1);\n        int actual_start = IsLower ? 1 : k-actual_k;\n        \n        if((Mode&UnitDiag)==0)\n          other.coeffRef(i,col) /= cjLhs(IsLower ? 0 : k, i);\n\n        if(actual_k>0)\n          other.col(col).segment(IsLower ? i+1 : i-actual_k, actual_k)\n              -= other.coeff(i,col) * cjLhs.col(i).segment(actual_start,actual_k);\n        \n      }\n    }\n  }\n};\n\n\n} // end namespace internal\n\n#endif // EIGEN_BAND_TRIANGULARSOLVER_H\n"
  },
  {
    "path": "include/eigen3/blas/CMakeLists.txt",
    "content": "\nproject(EigenBlas CXX)\n\ninclude(\"../cmake/language_support.cmake\")\n\nworkaround_9220(Fortran EIGEN_Fortran_COMPILER_WORKS)\n\nif(EIGEN_Fortran_COMPILER_WORKS)\n  enable_language(Fortran OPTIONAL)\n  if(NOT CMAKE_Fortran_COMPILER)\n    set(EIGEN_Fortran_COMPILER_WORKS OFF)\n  endif()\nendif()\n\nadd_custom_target(blas)\n\nset(EigenBlas_SRCS  single.cpp double.cpp complex_single.cpp complex_double.cpp xerbla.cpp\n                    f2c/srotm.c   f2c/srotmg.c  f2c/drotm.c f2c/drotmg.c\n                    f2c/lsame.c   f2c/dspmv.c   f2c/ssbmv.c f2c/chbmv.c\n                    f2c/sspmv.c   f2c/zhbmv.c   f2c/chpmv.c f2c/dsbmv.c\n                    f2c/zhpmv.c   f2c/dtbmv.c   f2c/stbmv.c f2c/ctbmv.c\n                    f2c/ztbmv.c   f2c/d_cnjg.c  f2c/r_cnjg.c\n   )\n\nif (EIGEN_Fortran_COMPILER_WORKS)\n  set(EigenBlas_SRCS ${EigenBlas_SRCS} fortran/complexdots.f)\nelse()\n  set(EigenBlas_SRCS ${EigenBlas_SRCS} f2c/complexdots.c)\nendif()\n\nadd_library(eigen_blas_static ${EigenBlas_SRCS})\nadd_library(eigen_blas SHARED ${EigenBlas_SRCS})\n\nif(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO)\n  target_link_libraries(eigen_blas_static ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO})\n  target_link_libraries(eigen_blas        ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO})\nendif()\n\nadd_dependencies(blas eigen_blas eigen_blas_static)\n\ninstall(TARGETS eigen_blas eigen_blas_static\n        RUNTIME DESTINATION bin\n        LIBRARY DESTINATION lib\n        ARCHIVE DESTINATION lib)\n\nif(EIGEN_Fortran_COMPILER_WORKS)\n\nif(BUILD_TESTING)\n  if(EIGEN_LEAVE_TEST_IN_ALL_TARGET)\n    add_subdirectory(testing) # can't do EXCLUDE_FROM_ALL here, breaks CTest\n  else()\n    add_subdirectory(testing EXCLUDE_FROM_ALL)\n  endif()\nendif()\n\nendif()\n\n"
  },
  {
    "path": "include/eigen3/blas/GeneralRank1Update.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Chen-Pang He <jdh8@ms63.hinet.net>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_GENERAL_RANK1UPDATE_H\n#define EIGEN_GENERAL_RANK1UPDATE_H\n\nnamespace internal {\n\n/* Optimized matrix += alpha * uv' */\ntemplate<typename Scalar, typename Index, int StorageOrder, bool ConjLhs, bool ConjRhs>\nstruct general_rank1_update;\n\ntemplate<typename Scalar, typename Index, bool ConjLhs, bool ConjRhs>\nstruct general_rank1_update<Scalar,Index,ColMajor,ConjLhs,ConjRhs>\n{\n  static void run(Index rows, Index cols, Scalar* mat, Index stride, const Scalar* u, const Scalar* v, Scalar alpha)\n  {\n    typedef Map<const Matrix<Scalar,Dynamic,1> > OtherMap;\n    typedef typename conj_expr_if<ConjLhs,OtherMap>::type ConjRhsType;\n    conj_if<ConjRhs> cj;\n\n    for (Index i=0; i<cols; ++i)\n      Map<Matrix<Scalar,Dynamic,1> >(mat+stride*i,rows) += alpha * cj(v[i]) * ConjRhsType(OtherMap(u,rows));\n  }\n};\n\ntemplate<typename Scalar, typename Index, bool ConjLhs, bool ConjRhs>\nstruct general_rank1_update<Scalar,Index,RowMajor,ConjLhs,ConjRhs>\n{\n  static void run(Index rows, Index cols, Scalar* mat, Index stride, const Scalar* u, const Scalar* v, Scalar alpha)\n  {\n    general_rank1_update<Scalar,Index,ColMajor,ConjRhs,ConjRhs>::run(rows,cols,mat,stride,u,v,alpha);\n  }\n};\n\n} // end namespace internal\n\n#endif // EIGEN_GENERAL_RANK1UPDATE_H\n"
  },
  {
    "path": "include/eigen3/blas/PackedSelfadjointProduct.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Chen-Pang He <jdh8@ms63.hinet.net>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SELFADJOINT_PACKED_PRODUCT_H\n#define EIGEN_SELFADJOINT_PACKED_PRODUCT_H\n\nnamespace internal {\n\n/* Optimized matrix += alpha * uv'\n * The matrix is in packed form.\n */\ntemplate<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjLhs, bool ConjRhs>\nstruct selfadjoint_packed_rank1_update;\n\ntemplate<typename Scalar, typename Index, int UpLo, bool ConjLhs, bool ConjRhs>\nstruct selfadjoint_packed_rank1_update<Scalar,Index,ColMajor,UpLo,ConjLhs,ConjRhs>\n{\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  static void run(Index size, Scalar* mat, const Scalar* vec, RealScalar alpha)\n  {\n    typedef Map<const Matrix<Scalar,Dynamic,1> > OtherMap;\n    typedef typename conj_expr_if<ConjLhs,OtherMap>::type ConjRhsType;\n    conj_if<ConjRhs> cj;\n\n    for (Index i=0; i<size; ++i)\n    {\n      Map<Matrix<Scalar,Dynamic,1> >(mat, UpLo==Lower ? size-i : (i+1)) += alpha * cj(vec[i]) * ConjRhsType(OtherMap(vec+(UpLo==Lower ? i : 0), UpLo==Lower ? size-i : (i+1)));\n      //FIXME This should be handled outside.\n      mat[UpLo==Lower ? 0 : i] = numext::real(mat[UpLo==Lower ? 0 : i]);\n      mat += UpLo==Lower ? size-i : (i+1);\n    }\n  }\n};\n\ntemplate<typename Scalar, typename Index, int UpLo, bool ConjLhs, bool ConjRhs>\nstruct selfadjoint_packed_rank1_update<Scalar,Index,RowMajor,UpLo,ConjLhs,ConjRhs>\n{\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  static void run(Index size, Scalar* mat, const Scalar* vec, RealScalar alpha)\n  {\n    selfadjoint_packed_rank1_update<Scalar,Index,ColMajor,UpLo==Lower?Upper:Lower,ConjRhs,ConjLhs>::run(size,mat,vec,alpha);\n  }\n};\n\n} // end namespace internal\n\n#endif // EIGEN_SELFADJOINT_PACKED_PRODUCT_H\n"
  },
  {
    "path": "include/eigen3/blas/PackedTriangularMatrixVector.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Chen-Pang He <jdh8@ms63.hinet.net>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_PACKED_TRIANGULAR_MATRIX_VECTOR_H\n#define EIGEN_PACKED_TRIANGULAR_MATRIX_VECTOR_H\n\nnamespace internal {\n\ntemplate<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, bool ConjRhs, int StorageOrder>\nstruct packed_triangular_matrix_vector_product;\n\ntemplate<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, bool ConjRhs>\nstruct packed_triangular_matrix_vector_product<Index,Mode,LhsScalar,ConjLhs,RhsScalar,ConjRhs,ColMajor>\n{\n  typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;\n  enum {\n    IsLower     = (Mode & Lower)   ==Lower,\n    HasUnitDiag = (Mode & UnitDiag)==UnitDiag,\n    HasZeroDiag = (Mode & ZeroDiag)==ZeroDiag\n  };\n  static void run(Index size, const LhsScalar* lhs, const RhsScalar* rhs, ResScalar* res, ResScalar alpha)\n  {\n    internal::conj_if<ConjRhs> cj;\n    typedef Map<const Matrix<LhsScalar,Dynamic,1> > LhsMap;\n    typedef typename conj_expr_if<ConjLhs,LhsMap>::type ConjLhsType;\n    typedef Map<Matrix<ResScalar,Dynamic,1> > ResMap;\n\n    for (Index i=0; i<size; ++i)\n    {\n      Index s = IsLower&&(HasUnitDiag||HasZeroDiag) ? 1 : 0;\n      Index r = IsLower ? size-i: i+1;\n      if (EIGEN_IMPLIES(HasUnitDiag||HasZeroDiag, (--r)>0))\n\tResMap(res+(IsLower ? s+i : 0),r) += alpha * cj(rhs[i]) * ConjLhsType(LhsMap(lhs+s,r));\n      if (HasUnitDiag)\n\tres[i] += alpha * cj(rhs[i]);\n      lhs += IsLower ? size-i: i+1;\n    }\n  };\n};\n\ntemplate<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, bool ConjRhs>\nstruct packed_triangular_matrix_vector_product<Index,Mode,LhsScalar,ConjLhs,RhsScalar,ConjRhs,RowMajor>\n{\n  typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;\n  enum {\n    IsLower     = (Mode & Lower)   ==Lower,\n    HasUnitDiag = (Mode & UnitDiag)==UnitDiag,\n    HasZeroDiag = (Mode & ZeroDiag)==ZeroDiag\n  };\n  static void run(Index size, const LhsScalar* lhs, const RhsScalar* rhs, ResScalar* res, ResScalar alpha)\n  {\n    internal::conj_if<ConjRhs> cj;\n    typedef Map<const Matrix<LhsScalar,Dynamic,1> > LhsMap;\n    typedef typename conj_expr_if<ConjLhs,LhsMap>::type ConjLhsType;\n    typedef Map<const Matrix<RhsScalar,Dynamic,1> > RhsMap;\n    typedef typename conj_expr_if<ConjRhs,RhsMap>::type ConjRhsType;\n\n    for (Index i=0; i<size; ++i)\n    {\n      Index s = !IsLower&&(HasUnitDiag||HasZeroDiag) ? 1 : 0;\n      Index r = IsLower ? i+1 : size-i;\n      if (EIGEN_IMPLIES(HasUnitDiag||HasZeroDiag, (--r)>0))\n\tres[i] += alpha * (ConjLhsType(LhsMap(lhs+s,r)).cwiseProduct(ConjRhsType(RhsMap(rhs+(IsLower ? 0 : s+i),r)))).sum();\n      if (HasUnitDiag)\n\tres[i] += alpha * cj(rhs[i]);\n      lhs += IsLower ? i+1 : size-i;\n    }\n  };\n};\n\n} // end namespace internal\n\n#endif // EIGEN_PACKED_TRIANGULAR_MATRIX_VECTOR_H\n"
  },
  {
    "path": "include/eigen3/blas/PackedTriangularSolverVector.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Chen-Pang He <jdh8@ms63.hinet.net>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_PACKED_TRIANGULAR_SOLVER_VECTOR_H\n#define EIGEN_PACKED_TRIANGULAR_SOLVER_VECTOR_H\n\nnamespace internal {\n\ntemplate<typename LhsScalar, typename RhsScalar, typename Index, int Side, int Mode, bool Conjugate, int StorageOrder>\nstruct packed_triangular_solve_vector;\n\n// forward and backward substitution, row-major, rhs is a vector\ntemplate<typename LhsScalar, typename RhsScalar, typename Index, int Mode, bool Conjugate>\nstruct packed_triangular_solve_vector<LhsScalar, RhsScalar, Index, OnTheLeft, Mode, Conjugate, RowMajor>\n{\n  enum {\n    IsLower = (Mode&Lower)==Lower\n  };\n  static void run(Index size, const LhsScalar* lhs, RhsScalar* rhs)\n  {\n    internal::conj_if<Conjugate> cj;\n    typedef Map<const Matrix<LhsScalar,Dynamic,1> > LhsMap;\n    typedef typename conj_expr_if<Conjugate,LhsMap>::type ConjLhsType;\n\n    lhs += IsLower ? 0 : (size*(size+1)>>1)-1;\n    for(Index pi=0; pi<size; ++pi)\n    {\n      Index i = IsLower ? pi : size-pi-1;\n      Index s = IsLower ? 0 : 1;\n      if (pi>0)\n\trhs[i] -= (ConjLhsType(LhsMap(lhs+s,pi))\n\t    .cwiseProduct(Map<const Matrix<RhsScalar,Dynamic,1> >(rhs+(IsLower ? 0 : i+1),pi))).sum();\n      if (!(Mode & UnitDiag))\n\trhs[i] /= cj(lhs[IsLower ? i : 0]);\n      IsLower ? lhs += pi+1 : lhs -= pi+2;\n    }\n  }\n};\n\n// forward and backward substitution, column-major, rhs is a vector\ntemplate<typename LhsScalar, typename RhsScalar, typename Index, int Mode, bool Conjugate>\nstruct packed_triangular_solve_vector<LhsScalar, RhsScalar, Index, OnTheLeft, Mode, Conjugate, ColMajor>\n{\n  enum {\n    IsLower = (Mode&Lower)==Lower\n  };\n  static void run(Index size, const LhsScalar* lhs, RhsScalar* rhs)\n  {\n    internal::conj_if<Conjugate> cj;\n    typedef Map<const Matrix<LhsScalar,Dynamic,1> > LhsMap;\n    typedef typename conj_expr_if<Conjugate,LhsMap>::type ConjLhsType;\n\n    lhs += IsLower ? 0 : size*(size-1)>>1;\n    for(Index pi=0; pi<size; ++pi)\n    {\n      Index i = IsLower ? pi : size-pi-1;\n      Index r = size - pi - 1;\n      if (!(Mode & UnitDiag))\n\trhs[i] /= cj(lhs[IsLower ? 0 : i]);\n      if (r>0)\n\tMap<Matrix<RhsScalar,Dynamic,1> >(rhs+(IsLower? i+1 : 0),r) -=\n\t    rhs[i] * ConjLhsType(LhsMap(lhs+(IsLower? 1 : 0),r));\n      IsLower ? lhs += size-pi : lhs -= r;\n    }\n  }\n};\n\ntemplate<typename LhsScalar, typename RhsScalar, typename Index, int Mode, bool Conjugate, int StorageOrder>\nstruct packed_triangular_solve_vector<LhsScalar, RhsScalar, Index, OnTheRight, Mode, Conjugate, StorageOrder>\n{\n  static void run(Index size, const LhsScalar* lhs, RhsScalar* rhs)\n  {\n    packed_triangular_solve_vector<LhsScalar,RhsScalar,Index,OnTheLeft,\n\t((Mode&Upper)==Upper ? Lower : Upper) | (Mode&UnitDiag),\n\tConjugate,StorageOrder==RowMajor?ColMajor:RowMajor\n      >::run(size, lhs, rhs);\n  }\n};\n\n} // end namespace internal\n\n#endif // EIGEN_PACKED_TRIANGULAR_SOLVER_VECTOR_H\n"
  },
  {
    "path": "include/eigen3/blas/README.txt",
    "content": "\nThis directory contains a BLAS library built on top of Eigen.\n\nThis module is not built by default. In order to compile it, you need to\ntype 'make blas' from within your build dir.\n\n"
  },
  {
    "path": "include/eigen3/blas/Rank2Update.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Chen-Pang He <jdh8@ms63.hinet.net>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_RANK2UPDATE_H\n#define EIGEN_RANK2UPDATE_H\n\nnamespace internal {\n\n/* Optimized selfadjoint matrix += alpha * uv' + conj(alpha)*vu'\n * This is the low-level version of SelfadjointRank2Update.h\n */\ntemplate<typename Scalar, typename Index, int UpLo>\nstruct rank2_update_selector\n{\n  static void run(Index size, Scalar* mat, Index stride, const Scalar* u, const Scalar* v, Scalar alpha)\n  {\n    typedef Map<const Matrix<Scalar,Dynamic,1> > OtherMap;\n    for (Index i=0; i<size; ++i)\n    {\n      Map<Matrix<Scalar,Dynamic,1> >(mat+stride*i+(UpLo==Lower ? i : 0), UpLo==Lower ? size-i : (i+1)) +=\n      numext::conj(alpha) * numext::conj(u[i]) * OtherMap(v+(UpLo==Lower ? i : 0), UpLo==Lower ? size-i : (i+1))\n                + alpha * numext::conj(v[i]) * OtherMap(u+(UpLo==Lower ? i : 0), UpLo==Lower ? size-i : (i+1));\n    }\n  }\n};\n\n/* Optimized selfadjoint matrix += alpha * uv' + conj(alpha)*vu'\n * The matrix is in packed form.\n */\ntemplate<typename Scalar, typename Index, int UpLo>\nstruct packed_rank2_update_selector\n{\n  static void run(Index size, Scalar* mat, const Scalar* u, const Scalar* v, Scalar alpha)\n  {\n    typedef Map<const Matrix<Scalar,Dynamic,1> > OtherMap;\n    Index offset = 0;\n    for (Index i=0; i<size; ++i)\n    {\n      Map<Matrix<Scalar,Dynamic,1> >(mat+offset, UpLo==Lower ? size-i : (i+1)) +=\n      numext::conj(alpha) * numext::conj(u[i]) * OtherMap(v+(UpLo==Lower ? i : 0), UpLo==Lower ? size-i : (i+1))\n                + alpha * numext::conj(v[i]) * OtherMap(u+(UpLo==Lower ? i : 0), UpLo==Lower ? size-i : (i+1));\n      //FIXME This should be handled outside.\n      mat[offset+(UpLo==Lower ? 0 : i)] = numext::real(mat[offset+(UpLo==Lower ? 0 : i)]);\n      offset += UpLo==Lower ? size-i : (i+1);\n    }\n  }\n};\n\n} // end namespace internal\n\n#endif // EIGEN_RANK2UPDATE_H\n"
  },
  {
    "path": "include/eigen3/blas/common.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009-2015 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_BLAS_COMMON_H\n#define EIGEN_BLAS_COMMON_H\n\n#include \"../Eigen/Core\"\n#include \"../Eigen/Jacobi\"\n\n#include <complex>\n\n#ifndef SCALAR\n#error the token SCALAR must be defined to compile this file\n#endif\n\n#include \"../Eigen/src/misc/blas.h\"\n\n#define NOTR    0\n#define TR      1\n#define ADJ     2\n\n#define LEFT    0\n#define RIGHT   1\n\n#define UP      0\n#define LO      1\n\n#define NUNIT   0\n#define UNIT    1\n\n#define INVALID 0xff\n\n#define OP(X)   (   ((X)=='N' || (X)=='n') ? NOTR   \\\n                  : ((X)=='T' || (X)=='t') ? TR     \\\n                  : ((X)=='C' || (X)=='c') ? ADJ    \\\n                  : INVALID)\n\n#define SIDE(X) (   ((X)=='L' || (X)=='l') ? LEFT   \\\n                  : ((X)=='R' || (X)=='r') ? RIGHT  \\\n                  : INVALID)\n\n#define UPLO(X) (   ((X)=='U' || (X)=='u') ? UP     \\\n                  : ((X)=='L' || (X)=='l') ? LO     \\\n                  : INVALID)\n\n#define DIAG(X) (   ((X)=='N' || (X)=='n') ? NUNIT  \\\n                  : ((X)=='U' || (X)=='u') ? UNIT   \\\n                  : INVALID)\n\n\ninline bool check_op(const char* op)\n{\n  return OP(*op)!=0xff;\n}\n\ninline bool check_side(const char* side)\n{\n  return SIDE(*side)!=0xff;\n}\n\ninline bool check_uplo(const char* uplo)\n{\n  return UPLO(*uplo)!=0xff;\n}\n\n\nnamespace Eigen {\n#include \"BandTriangularSolver.h\"\n#include \"GeneralRank1Update.h\"\n#include \"PackedSelfadjointProduct.h\"\n#include \"PackedTriangularMatrixVector.h\"\n#include \"PackedTriangularSolverVector.h\"\n#include \"Rank2Update.h\"\n}\n\nusing namespace Eigen;\n\ntypedef SCALAR Scalar;\ntypedef NumTraits<Scalar>::Real RealScalar;\ntypedef std::complex<RealScalar> Complex;\n\nenum\n{\n  IsComplex = Eigen::NumTraits<SCALAR>::IsComplex,\n  Conj = IsComplex\n};\n\ntypedef Matrix<Scalar,Dynamic,Dynamic,ColMajor> PlainMatrixType;\ntypedef Map<Matrix<Scalar,Dynamic,Dynamic,ColMajor>, 0, OuterStride<> > MatrixType;\ntypedef Map<const Matrix<Scalar,Dynamic,Dynamic,ColMajor>, 0, OuterStride<> > ConstMatrixType;\ntypedef Map<Matrix<Scalar,Dynamic,1>, 0, InnerStride<Dynamic> > StridedVectorType;\ntypedef Map<Matrix<Scalar,Dynamic,1> > CompactVectorType;\n\ntemplate<typename T>\nMap<Matrix<T,Dynamic,Dynamic,ColMajor>, 0, OuterStride<> >\nmatrix(T* data, int rows, int cols, int stride)\n{\n  return Map<Matrix<T,Dynamic,Dynamic,ColMajor>, 0, OuterStride<> >(data, rows, cols, OuterStride<>(stride));\n}\n\ntemplate<typename T>\nMap<const Matrix<T,Dynamic,Dynamic,ColMajor>, 0, OuterStride<> >\nmatrix(const T* data, int rows, int cols, int stride)\n{\n  return Map<const Matrix<T,Dynamic,Dynamic,ColMajor>, 0, OuterStride<> >(data, rows, cols, OuterStride<>(stride));\n}\n\ntemplate<typename T>\nMap<Matrix<T,Dynamic,1>, 0, InnerStride<Dynamic> > make_vector(T* data, int size, int incr)\n{\n  return Map<Matrix<T,Dynamic,1>, 0, InnerStride<Dynamic> >(data, size, InnerStride<Dynamic>(incr));\n}\n\ntemplate<typename T>\nMap<const Matrix<T,Dynamic,1>, 0, InnerStride<Dynamic> > make_vector(const T* data, int size, int incr)\n{\n  return Map<const Matrix<T,Dynamic,1>, 0, InnerStride<Dynamic> >(data, size, InnerStride<Dynamic>(incr));\n}\n\ntemplate<typename T>\nMap<Matrix<T,Dynamic,1> > make_vector(T* data, int size)\n{\n  return Map<Matrix<T,Dynamic,1> >(data, size);\n}\n\ntemplate<typename T>\nMap<const Matrix<T,Dynamic,1> > make_vector(const T* data, int size)\n{\n  return Map<const Matrix<T,Dynamic,1> >(data, size);\n}\n\ntemplate<typename T>\nT* get_compact_vector(T* x, int n, int incx)\n{\n  if(incx==1)\n    return x;\n\n  typename Eigen::internal::remove_const<T>::type* ret = new Scalar[n];\n  if(incx<0) make_vector(ret,n) = make_vector(x,n,-incx).reverse();\n  else       make_vector(ret,n) = make_vector(x,n, incx);\n  return ret;\n}\n\ntemplate<typename T>\nT* copy_back(T* x_cpy, T* x, int n, int incx)\n{\n  if(x_cpy==x)\n    return 0;\n\n  if(incx<0) make_vector(x,n,-incx).reverse() = make_vector(x_cpy,n);\n  else       make_vector(x,n, incx)           = make_vector(x_cpy,n);\n  return x_cpy;\n}\n\n#define EIGEN_BLAS_FUNC(X) EIGEN_CAT(SCALAR_SUFFIX,X##_)\n\n#endif // EIGEN_BLAS_COMMON_H\n"
  },
  {
    "path": "include/eigen3/blas/complex_double.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define SCALAR        std::complex<double>\n#define SCALAR_SUFFIX z\n#define SCALAR_SUFFIX_UP \"Z\"\n#define REAL_SCALAR_SUFFIX d\n#define ISCOMPLEX     1\n\n#include \"level1_impl.h\"\n#include \"level1_cplx_impl.h\"\n#include \"level2_impl.h\"\n#include \"level2_cplx_impl.h\"\n#include \"level3_impl.h\"\n"
  },
  {
    "path": "include/eigen3/blas/complex_single.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define SCALAR        std::complex<float>\n#define SCALAR_SUFFIX c\n#define SCALAR_SUFFIX_UP \"C\"\n#define REAL_SCALAR_SUFFIX s\n#define ISCOMPLEX     1\n\n#include \"level1_impl.h\"\n#include \"level1_cplx_impl.h\"\n#include \"level2_impl.h\"\n#include \"level2_cplx_impl.h\"\n#include \"level3_impl.h\"\n"
  },
  {
    "path": "include/eigen3/blas/double.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2012 Chen-Pang He <jdh8@ms63.hinet.net>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define SCALAR        double\n#define SCALAR_SUFFIX d\n#define SCALAR_SUFFIX_UP \"D\"\n#define ISCOMPLEX     0\n\n#include \"level1_impl.h\"\n#include \"level1_real_impl.h\"\n#include \"level2_impl.h\"\n#include \"level2_real_impl.h\"\n#include \"level3_impl.h\"\n\ndouble BLASFUNC(dsdot)(int* n, float* x, int* incx, float* y, int* incy)\n{\n  if(*n<=0) return 0;\n\n  if(*incx==1 && *incy==1)    return (make_vector(x,*n).cast<double>().cwiseProduct(make_vector(y,*n).cast<double>())).sum();\n  else if(*incx>0 && *incy>0) return (make_vector(x,*n,*incx).cast<double>().cwiseProduct(make_vector(y,*n,*incy).cast<double>())).sum();\n  else if(*incx<0 && *incy>0) return (make_vector(x,*n,-*incx).reverse().cast<double>().cwiseProduct(make_vector(y,*n,*incy).cast<double>())).sum();\n  else if(*incx>0 && *incy<0) return (make_vector(x,*n,*incx).cast<double>().cwiseProduct(make_vector(y,*n,-*incy).reverse().cast<double>())).sum();\n  else if(*incx<0 && *incy<0) return (make_vector(x,*n,-*incx).reverse().cast<double>().cwiseProduct(make_vector(y,*n,-*incy).reverse().cast<double>())).sum();\n  else return 0;\n}\n"
  },
  {
    "path": "include/eigen3/blas/f2c/chbmv.c",
    "content": "/* chbmv.f -- translated by f2c (version 20100827).\n   You must link the resulting object file with libf2c:\n\ton Microsoft Windows system, link with libf2c.lib;\n\ton Linux or Unix systems, link with .../path/to/libf2c.a -lm\n\tor, if you install libf2c.a in a standard place, with -lf2c -lm\n\t-- in that order, at the end of the command line, as in\n\t\tcc *.o -lf2c -lm\n\tSource for libf2c is in /netlib/f2c/libf2c.zip, e.g.,\n\n\t\thttp://www.netlib.org/f2c/libf2c.zip\n*/\n\n#include \"datatypes.h\"\n\n/* Subroutine */ int chbmv_(char *uplo, integer *n, integer *k, complex *\n\talpha, complex *a, integer *lda, complex *x, integer *incx, complex *\n\tbeta, complex *y, integer *incy, ftnlen uplo_len)\n{\n    /* System generated locals */\n    integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;\n    real r__1;\n    complex q__1, q__2, q__3, q__4;\n\n    /* Builtin functions */\n    void r_cnjg(complex *, complex *);\n\n    /* Local variables */\n    integer i__, j, l, ix, iy, jx, jy, kx, ky, info;\n    complex temp1, temp2;\n    extern logical lsame_(char *, char *, ftnlen, ftnlen);\n    integer kplus1;\n    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);\n\n/*     .. Scalar Arguments .. */\n/*     .. */\n/*     .. Array Arguments .. */\n/*     .. */\n\n/*  Purpose */\n/*  ======= */\n\n/*  CHBMV  performs the matrix-vector  operation */\n\n/*     y := alpha*A*x + beta*y, */\n\n/*  where alpha and beta are scalars, x and y are n element vectors and */\n/*  A is an n by n hermitian band matrix, with k super-diagonals. */\n\n/*  Arguments */\n/*  ========== */\n\n/*  UPLO   - CHARACTER*1. */\n/*           On entry, UPLO specifies whether the upper or lower */\n/*           triangular part of the band matrix A is being supplied as */\n/*           follows: */\n\n/*              UPLO = 'U' or 'u'   The upper triangular part of A is */\n/*                                  being supplied. */\n\n/*              UPLO = 'L' or 'l'   The lower triangular part of A is */\n/*                                  being supplied. */\n\n/*           Unchanged on exit. */\n\n/*  N      - INTEGER. */\n/*           On entry, N specifies the order of the matrix A. */\n/*           N must be at least zero. */\n/*           Unchanged on exit. */\n\n/*  K      - INTEGER. */\n/*           On entry, K specifies the number of super-diagonals of the */\n/*           matrix A. K must satisfy  0 .le. K. */\n/*           Unchanged on exit. */\n\n/*  ALPHA  - COMPLEX         . */\n/*           On entry, ALPHA specifies the scalar alpha. */\n/*           Unchanged on exit. */\n\n/*  A      - COMPLEX          array of DIMENSION ( LDA, n ). */\n/*           Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) */\n/*           by n part of the array A must contain the upper triangular */\n/*           band part of the hermitian matrix, supplied column by */\n/*           column, with the leading diagonal of the matrix in row */\n/*           ( k + 1 ) of the array, the first super-diagonal starting at */\n/*           position 2 in row k, and so on. The top left k by k triangle */\n/*           of the array A is not referenced. */\n/*           The following program segment will transfer the upper */\n/*           triangular part of a hermitian band matrix from conventional */\n/*           full matrix storage to band storage: */\n\n/*                 DO 20, J = 1, N */\n/*                    M = K + 1 - J */\n/*                    DO 10, I = MAX( 1, J - K ), J */\n/*                       A( M + I, J ) = matrix( I, J ) */\n/*              10    CONTINUE */\n/*              20 CONTINUE */\n\n/*           Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) */\n/*           by n part of the array A must contain the lower triangular */\n/*           band part of the hermitian matrix, supplied column by */\n/*           column, with the leading diagonal of the matrix in row 1 of */\n/*           the array, the first sub-diagonal starting at position 1 in */\n/*           row 2, and so on. The bottom right k by k triangle of the */\n/*           array A is not referenced. */\n/*           The following program segment will transfer the lower */\n/*           triangular part of a hermitian band matrix from conventional */\n/*           full matrix storage to band storage: */\n\n/*                 DO 20, J = 1, N */\n/*                    M = 1 - J */\n/*                    DO 10, I = J, MIN( N, J + K ) */\n/*                       A( M + I, J ) = matrix( I, J ) */\n/*              10    CONTINUE */\n/*              20 CONTINUE */\n\n/*           Note that the imaginary parts of the diagonal elements need */\n/*           not be set and are assumed to be zero. */\n/*           Unchanged on exit. */\n\n/*  LDA    - INTEGER. */\n/*           On entry, LDA specifies the first dimension of A as declared */\n/*           in the calling (sub) program. LDA must be at least */\n/*           ( k + 1 ). */\n/*           Unchanged on exit. */\n\n/*  X      - COMPLEX          array of DIMENSION at least */\n/*           ( 1 + ( n - 1 )*abs( INCX ) ). */\n/*           Before entry, the incremented array X must contain the */\n/*           vector x. */\n/*           Unchanged on exit. */\n\n/*  INCX   - INTEGER. */\n/*           On entry, INCX specifies the increment for the elements of */\n/*           X. INCX must not be zero. */\n/*           Unchanged on exit. */\n\n/*  BETA   - COMPLEX         . */\n/*           On entry, BETA specifies the scalar beta. */\n/*           Unchanged on exit. */\n\n/*  Y      - COMPLEX          array of DIMENSION at least */\n/*           ( 1 + ( n - 1 )*abs( INCY ) ). */\n/*           Before entry, the incremented array Y must contain the */\n/*           vector y. On exit, Y is overwritten by the updated vector y. */\n\n/*  INCY   - INTEGER. */\n/*           On entry, INCY specifies the increment for the elements of */\n/*           Y. INCY must not be zero. */\n/*           Unchanged on exit. */\n\n/*  Further Details */\n/*  =============== */\n\n/*  Level 2 Blas routine. */\n\n/*  -- Written on 22-October-1986. */\n/*     Jack Dongarra, Argonne National Lab. */\n/*     Jeremy Du Croz, Nag Central Office. */\n/*     Sven Hammarling, Nag Central Office. */\n/*     Richard Hanson, Sandia National Labs. */\n\n/*  ===================================================================== */\n\n/*     .. Parameters .. */\n/*     .. */\n/*     .. Local Scalars .. */\n/*     .. */\n/*     .. External Functions .. */\n/*     .. */\n/*     .. External Subroutines .. */\n/*     .. */\n/*     .. Intrinsic Functions .. */\n/*     .. */\n\n/*     Test the input parameters. */\n\n    /* Parameter adjustments */\n    a_dim1 = *lda;\n    a_offset = 1 + a_dim1;\n    a -= a_offset;\n    --x;\n    --y;\n\n    /* Function Body */\n    info = 0;\n    if (! lsame_(uplo, \"U\", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, \"L\", (\n\t    ftnlen)1, (ftnlen)1)) {\n\tinfo = 1;\n    } else if (*n < 0) {\n\tinfo = 2;\n    } else if (*k < 0) {\n\tinfo = 3;\n    } else if (*lda < *k + 1) {\n\tinfo = 6;\n    } else if (*incx == 0) {\n\tinfo = 8;\n    } else if (*incy == 0) {\n\tinfo = 11;\n    }\n    if (info != 0) {\n\txerbla_(\"CHBMV \", &info, (ftnlen)6);\n\treturn 0;\n    }\n\n/*     Quick return if possible. */\n\n    if (*n == 0 || (alpha->r == 0.f && alpha->i == 0.f && (beta->r == 1.f && \n                                                           beta->i == 0.f))) {\n\treturn 0;\n    }\n\n/*     Set up the start points in  X  and  Y. */\n\n    if (*incx > 0) {\n\tkx = 1;\n    } else {\n\tkx = 1 - (*n - 1) * *incx;\n    }\n    if (*incy > 0) {\n\tky = 1;\n    } else {\n\tky = 1 - (*n - 1) * *incy;\n    }\n\n/*     Start the operations. In this version the elements of the array A */\n/*     are accessed sequentially with one pass through A. */\n\n/*     First form  y := beta*y. */\n\n    if (beta->r != 1.f || beta->i != 0.f) {\n\tif (*incy == 1) {\n\t    if (beta->r == 0.f && beta->i == 0.f) {\n\t\ti__1 = *n;\n\t\tfor (i__ = 1; i__ <= i__1; ++i__) {\n\t\t    i__2 = i__;\n\t\t    y[i__2].r = 0.f, y[i__2].i = 0.f;\n/* L10: */\n\t\t}\n\t    } else {\n\t\ti__1 = *n;\n\t\tfor (i__ = 1; i__ <= i__1; ++i__) {\n\t\t    i__2 = i__;\n\t\t    i__3 = i__;\n\t\t    q__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i, \n\t\t\t    q__1.i = beta->r * y[i__3].i + beta->i * y[i__3]\n\t\t\t    .r;\n\t\t    y[i__2].r = q__1.r, y[i__2].i = q__1.i;\n/* L20: */\n\t\t}\n\t    }\n\t} else {\n\t    iy = ky;\n\t    if (beta->r == 0.f && beta->i == 0.f) {\n\t\ti__1 = *n;\n\t\tfor (i__ = 1; i__ <= i__1; ++i__) {\n\t\t    i__2 = iy;\n\t\t    y[i__2].r = 0.f, y[i__2].i = 0.f;\n\t\t    iy += *incy;\n/* L30: */\n\t\t}\n\t    } else {\n\t\ti__1 = *n;\n\t\tfor (i__ = 1; i__ <= i__1; ++i__) {\n\t\t    i__2 = iy;\n\t\t    i__3 = iy;\n\t\t    q__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i, \n\t\t\t    q__1.i = beta->r * y[i__3].i + beta->i * y[i__3]\n\t\t\t    .r;\n\t\t    y[i__2].r = q__1.r, y[i__2].i = q__1.i;\n\t\t    iy += *incy;\n/* L40: */\n\t\t}\n\t    }\n\t}\n    }\n    if (alpha->r == 0.f && alpha->i == 0.f) {\n\treturn 0;\n    }\n    if (lsame_(uplo, \"U\", (ftnlen)1, (ftnlen)1)) {\n\n/*        Form  y  when upper triangle of A is stored. */\n\n\tkplus1 = *k + 1;\n\tif (*incx == 1 && *incy == 1) {\n\t    i__1 = *n;\n\t    for (j = 1; j <= i__1; ++j) {\n\t\ti__2 = j;\n\t\tq__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, q__1.i =\n\t\t\t alpha->r * x[i__2].i + alpha->i * x[i__2].r;\n\t\ttemp1.r = q__1.r, temp1.i = q__1.i;\n\t\ttemp2.r = 0.f, temp2.i = 0.f;\n\t\tl = kplus1 - j;\n/* Computing MAX */\n\t\ti__2 = 1, i__3 = j - *k;\n\t\ti__4 = j - 1;\n\t\tfor (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {\n\t\t    i__2 = i__;\n\t\t    i__3 = i__;\n\t\t    i__5 = l + i__ + j * a_dim1;\n\t\t    q__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, \n\t\t\t    q__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5]\n\t\t\t    .r;\n\t\t    q__1.r = y[i__3].r + q__2.r, q__1.i = y[i__3].i + q__2.i;\n\t\t    y[i__2].r = q__1.r, y[i__2].i = q__1.i;\n\t\t    r_cnjg(&q__3, &a[l + i__ + j * a_dim1]);\n\t\t    i__2 = i__;\n\t\t    q__2.r = q__3.r * x[i__2].r - q__3.i * x[i__2].i, q__2.i =\n\t\t\t     q__3.r * x[i__2].i + q__3.i * x[i__2].r;\n\t\t    q__1.r = temp2.r + q__2.r, q__1.i = temp2.i + q__2.i;\n\t\t    temp2.r = q__1.r, temp2.i = q__1.i;\n/* L50: */\n\t\t}\n\t\ti__4 = j;\n\t\ti__2 = j;\n\t\ti__3 = kplus1 + j * a_dim1;\n\t\tr__1 = a[i__3].r;\n\t\tq__3.r = r__1 * temp1.r, q__3.i = r__1 * temp1.i;\n\t\tq__2.r = y[i__2].r + q__3.r, q__2.i = y[i__2].i + q__3.i;\n\t\tq__4.r = alpha->r * temp2.r - alpha->i * temp2.i, q__4.i = \n\t\t\talpha->r * temp2.i + alpha->i * temp2.r;\n\t\tq__1.r = q__2.r + q__4.r, q__1.i = q__2.i + q__4.i;\n\t\ty[i__4].r = q__1.r, y[i__4].i = q__1.i;\n/* L60: */\n\t    }\n\t} else {\n\t    jx = kx;\n\t    jy = ky;\n\t    i__1 = *n;\n\t    for (j = 1; j <= i__1; ++j) {\n\t\ti__4 = jx;\n\t\tq__1.r = alpha->r * x[i__4].r - alpha->i * x[i__4].i, q__1.i =\n\t\t\t alpha->r * x[i__4].i + alpha->i * x[i__4].r;\n\t\ttemp1.r = q__1.r, temp1.i = q__1.i;\n\t\ttemp2.r = 0.f, temp2.i = 0.f;\n\t\tix = kx;\n\t\tiy = ky;\n\t\tl = kplus1 - j;\n/* Computing MAX */\n\t\ti__4 = 1, i__2 = j - *k;\n\t\ti__3 = j - 1;\n\t\tfor (i__ = max(i__4,i__2); i__ <= i__3; ++i__) {\n\t\t    i__4 = iy;\n\t\t    i__2 = iy;\n\t\t    i__5 = l + i__ + j * a_dim1;\n\t\t    q__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, \n\t\t\t    q__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5]\n\t\t\t    .r;\n\t\t    q__1.r = y[i__2].r + q__2.r, q__1.i = y[i__2].i + q__2.i;\n\t\t    y[i__4].r = q__1.r, y[i__4].i = q__1.i;\n\t\t    r_cnjg(&q__3, &a[l + i__ + j * a_dim1]);\n\t\t    i__4 = ix;\n\t\t    q__2.r = q__3.r * x[i__4].r - q__3.i * x[i__4].i, q__2.i =\n\t\t\t     q__3.r * x[i__4].i + q__3.i * x[i__4].r;\n\t\t    q__1.r = temp2.r + q__2.r, q__1.i = temp2.i + q__2.i;\n\t\t    temp2.r = q__1.r, temp2.i = q__1.i;\n\t\t    ix += *incx;\n\t\t    iy += *incy;\n/* L70: */\n\t\t}\n\t\ti__3 = jy;\n\t\ti__4 = jy;\n\t\ti__2 = kplus1 + j * a_dim1;\n\t\tr__1 = a[i__2].r;\n\t\tq__3.r = r__1 * temp1.r, q__3.i = r__1 * temp1.i;\n\t\tq__2.r = y[i__4].r + q__3.r, q__2.i = y[i__4].i + q__3.i;\n\t\tq__4.r = alpha->r * temp2.r - alpha->i * temp2.i, q__4.i = \n\t\t\talpha->r * temp2.i + alpha->i * temp2.r;\n\t\tq__1.r = q__2.r + q__4.r, q__1.i = q__2.i + q__4.i;\n\t\ty[i__3].r = q__1.r, y[i__3].i = q__1.i;\n\t\tjx += *incx;\n\t\tjy += *incy;\n\t\tif (j > *k) {\n\t\t    kx += *incx;\n\t\t    ky += *incy;\n\t\t}\n/* L80: */\n\t    }\n\t}\n    } else {\n\n/*        Form  y  when lower triangle of A is stored. */\n\n\tif (*incx == 1 && *incy == 1) {\n\t    i__1 = *n;\n\t    for (j = 1; j <= i__1; ++j) {\n\t\ti__3 = j;\n\t\tq__1.r = alpha->r * x[i__3].r - alpha->i * x[i__3].i, q__1.i =\n\t\t\t alpha->r * x[i__3].i + alpha->i * x[i__3].r;\n\t\ttemp1.r = q__1.r, temp1.i = q__1.i;\n\t\ttemp2.r = 0.f, temp2.i = 0.f;\n\t\ti__3 = j;\n\t\ti__4 = j;\n\t\ti__2 = j * a_dim1 + 1;\n\t\tr__1 = a[i__2].r;\n\t\tq__2.r = r__1 * temp1.r, q__2.i = r__1 * temp1.i;\n\t\tq__1.r = y[i__4].r + q__2.r, q__1.i = y[i__4].i + q__2.i;\n\t\ty[i__3].r = q__1.r, y[i__3].i = q__1.i;\n\t\tl = 1 - j;\n/* Computing MIN */\n\t\ti__4 = *n, i__2 = j + *k;\n\t\ti__3 = min(i__4,i__2);\n\t\tfor (i__ = j + 1; i__ <= i__3; ++i__) {\n\t\t    i__4 = i__;\n\t\t    i__2 = i__;\n\t\t    i__5 = l + i__ + j * a_dim1;\n\t\t    q__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, \n\t\t\t    q__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5]\n\t\t\t    .r;\n\t\t    q__1.r = y[i__2].r + q__2.r, q__1.i = y[i__2].i + q__2.i;\n\t\t    y[i__4].r = q__1.r, y[i__4].i = q__1.i;\n\t\t    r_cnjg(&q__3, &a[l + i__ + j * a_dim1]);\n\t\t    i__4 = i__;\n\t\t    q__2.r = q__3.r * x[i__4].r - q__3.i * x[i__4].i, q__2.i =\n\t\t\t     q__3.r * x[i__4].i + q__3.i * x[i__4].r;\n\t\t    q__1.r = temp2.r + q__2.r, q__1.i = temp2.i + q__2.i;\n\t\t    temp2.r = q__1.r, temp2.i = q__1.i;\n/* L90: */\n\t\t}\n\t\ti__3 = j;\n\t\ti__4 = j;\n\t\tq__2.r = alpha->r * temp2.r - alpha->i * temp2.i, q__2.i = \n\t\t\talpha->r * temp2.i + alpha->i * temp2.r;\n\t\tq__1.r = y[i__4].r + q__2.r, q__1.i = y[i__4].i + q__2.i;\n\t\ty[i__3].r = q__1.r, y[i__3].i = q__1.i;\n/* L100: */\n\t    }\n\t} else {\n\t    jx = kx;\n\t    jy = ky;\n\t    i__1 = *n;\n\t    for (j = 1; j <= i__1; ++j) {\n\t\ti__3 = jx;\n\t\tq__1.r = alpha->r * x[i__3].r - alpha->i * x[i__3].i, q__1.i =\n\t\t\t alpha->r * x[i__3].i + alpha->i * x[i__3].r;\n\t\ttemp1.r = q__1.r, temp1.i = q__1.i;\n\t\ttemp2.r = 0.f, temp2.i = 0.f;\n\t\ti__3 = jy;\n\t\ti__4 = jy;\n\t\ti__2 = j * a_dim1 + 1;\n\t\tr__1 = a[i__2].r;\n\t\tq__2.r = r__1 * temp1.r, q__2.i = r__1 * temp1.i;\n\t\tq__1.r = y[i__4].r + q__2.r, q__1.i = y[i__4].i + q__2.i;\n\t\ty[i__3].r = q__1.r, y[i__3].i = q__1.i;\n\t\tl = 1 - j;\n\t\tix = jx;\n\t\tiy = jy;\n/* Computing MIN */\n\t\ti__4 = *n, i__2 = j + *k;\n\t\ti__3 = min(i__4,i__2);\n\t\tfor (i__ = j + 1; i__ <= i__3; ++i__) {\n\t\t    ix += *incx;\n\t\t    iy += *incy;\n\t\t    i__4 = iy;\n\t\t    i__2 = iy;\n\t\t    i__5 = l + i__ + j * a_dim1;\n\t\t    q__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, \n\t\t\t    q__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5]\n\t\t\t    .r;\n\t\t    q__1.r = y[i__2].r + q__2.r, q__1.i = y[i__2].i + q__2.i;\n\t\t    y[i__4].r = q__1.r, y[i__4].i = q__1.i;\n\t\t    r_cnjg(&q__3, &a[l + i__ + j * a_dim1]);\n\t\t    i__4 = ix;\n\t\t    q__2.r = q__3.r * x[i__4].r - q__3.i * x[i__4].i, q__2.i =\n\t\t\t     q__3.r * x[i__4].i + q__3.i * x[i__4].r;\n\t\t    q__1.r = temp2.r + q__2.r, q__1.i = temp2.i + q__2.i;\n\t\t    temp2.r = q__1.r, temp2.i = q__1.i;\n/* L110: */\n\t\t}\n\t\ti__3 = jy;\n\t\ti__4 = jy;\n\t\tq__2.r = alpha->r * temp2.r - alpha->i * temp2.i, q__2.i = \n\t\t\talpha->r * temp2.i + alpha->i * temp2.r;\n\t\tq__1.r = y[i__4].r + q__2.r, q__1.i = y[i__4].i + q__2.i;\n\t\ty[i__3].r = q__1.r, y[i__3].i = q__1.i;\n\t\tjx += *incx;\n\t\tjy += *incy;\n/* L120: */\n\t    }\n\t}\n    }\n\n    return 0;\n\n/*     End of CHBMV . */\n\n} /* chbmv_ */\n\n"
  },
  {
    "path": "include/eigen3/blas/f2c/chpmv.c",
    "content": "/* chpmv.f -- translated by f2c (version 20100827).\n   You must link the resulting object file with libf2c:\n\ton Microsoft Windows system, link with libf2c.lib;\n\ton Linux or Unix systems, link with .../path/to/libf2c.a -lm\n\tor, if you install libf2c.a in a standard place, with -lf2c -lm\n\t-- in that order, at the end of the command line, as in\n\t\tcc *.o -lf2c -lm\n\tSource for libf2c is in /netlib/f2c/libf2c.zip, e.g.,\n\n\t\thttp://www.netlib.org/f2c/libf2c.zip\n*/\n\n#include \"datatypes.h\"\n\n/* Subroutine */ int chpmv_(char *uplo, integer *n, complex *alpha, complex *\n\tap, complex *x, integer *incx, complex *beta, complex *y, integer *\n\tincy, ftnlen uplo_len)\n{\n    /* System generated locals */\n    integer i__1, i__2, i__3, i__4, i__5;\n    real r__1;\n    complex q__1, q__2, q__3, q__4;\n\n    /* Builtin functions */\n    void r_cnjg(complex *, complex *);\n\n    /* Local variables */\n    integer i__, j, k, kk, ix, iy, jx, jy, kx, ky, info;\n    complex temp1, temp2;\n    extern logical lsame_(char *, char *, ftnlen, ftnlen);\n    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);\n\n/*     .. Scalar Arguments .. */\n/*     .. */\n/*     .. Array Arguments .. */\n/*     .. */\n\n/*  Purpose */\n/*  ======= */\n\n/*  CHPMV  performs the matrix-vector operation */\n\n/*     y := alpha*A*x + beta*y, */\n\n/*  where alpha and beta are scalars, x and y are n element vectors and */\n/*  A is an n by n hermitian matrix, supplied in packed form. */\n\n/*  Arguments */\n/*  ========== */\n\n/*  UPLO   - CHARACTER*1. */\n/*           On entry, UPLO specifies whether the upper or lower */\n/*           triangular part of the matrix A is supplied in the packed */\n/*           array AP as follows: */\n\n/*              UPLO = 'U' or 'u'   The upper triangular part of A is */\n/*                                  supplied in AP. */\n\n/*              UPLO = 'L' or 'l'   The lower triangular part of A is */\n/*                                  supplied in AP. */\n\n/*           Unchanged on exit. */\n\n/*  N      - INTEGER. */\n/*           On entry, N specifies the order of the matrix A. */\n/*           N must be at least zero. */\n/*           Unchanged on exit. */\n\n/*  ALPHA  - COMPLEX         . */\n/*           On entry, ALPHA specifies the scalar alpha. */\n/*           Unchanged on exit. */\n\n/*  AP     - COMPLEX          array of DIMENSION at least */\n/*           ( ( n*( n + 1 ) )/2 ). */\n/*           Before entry with UPLO = 'U' or 'u', the array AP must */\n/*           contain the upper triangular part of the hermitian matrix */\n/*           packed sequentially, column by column, so that AP( 1 ) */\n/*           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) */\n/*           and a( 2, 2 ) respectively, and so on. */\n/*           Before entry with UPLO = 'L' or 'l', the array AP must */\n/*           contain the lower triangular part of the hermitian matrix */\n/*           packed sequentially, column by column, so that AP( 1 ) */\n/*           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) */\n/*           and a( 3, 1 ) respectively, and so on. */\n/*           Note that the imaginary parts of the diagonal elements need */\n/*           not be set and are assumed to be zero. */\n/*           Unchanged on exit. */\n\n/*  X      - COMPLEX          array of dimension at least */\n/*           ( 1 + ( n - 1 )*abs( INCX ) ). */\n/*           Before entry, the incremented array X must contain the n */\n/*           element vector x. */\n/*           Unchanged on exit. */\n\n/*  INCX   - INTEGER. */\n/*           On entry, INCX specifies the increment for the elements of */\n/*           X. INCX must not be zero. */\n/*           Unchanged on exit. */\n\n/*  BETA   - COMPLEX         . */\n/*           On entry, BETA specifies the scalar beta. When BETA is */\n/*           supplied as zero then Y need not be set on input. */\n/*           Unchanged on exit. */\n\n/*  Y      - COMPLEX          array of dimension at least */\n/*           ( 1 + ( n - 1 )*abs( INCY ) ). */\n/*           Before entry, the incremented array Y must contain the n */\n/*           element vector y. On exit, Y is overwritten by the updated */\n/*           vector y. */\n\n/*  INCY   - INTEGER. */\n/*           On entry, INCY specifies the increment for the elements of */\n/*           Y. INCY must not be zero. */\n/*           Unchanged on exit. */\n\n/*  Further Details */\n/*  =============== */\n\n/*  Level 2 Blas routine. */\n\n/*  -- Written on 22-October-1986. */\n/*     Jack Dongarra, Argonne National Lab. */\n/*     Jeremy Du Croz, Nag Central Office. */\n/*     Sven Hammarling, Nag Central Office. */\n/*     Richard Hanson, Sandia National Labs. */\n\n/*  ===================================================================== */\n\n/*     .. Parameters .. */\n/*     .. */\n/*     .. Local Scalars .. */\n/*     .. */\n/*     .. External Functions .. */\n/*     .. */\n/*     .. External Subroutines .. */\n/*     .. */\n/*     .. Intrinsic Functions .. */\n/*     .. */\n\n/*     Test the input parameters. */\n\n    /* Parameter adjustments */\n    --y;\n    --x;\n    --ap;\n\n    /* Function Body */\n    info = 0;\n    if (! lsame_(uplo, \"U\", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, \"L\", (\n\t    ftnlen)1, (ftnlen)1)) {\n\tinfo = 1;\n    } else if (*n < 0) {\n\tinfo = 2;\n    } else if (*incx == 0) {\n\tinfo = 6;\n    } else if (*incy == 0) {\n\tinfo = 9;\n    }\n    if (info != 0) {\n\txerbla_(\"CHPMV \", &info, (ftnlen)6);\n\treturn 0;\n    }\n\n/*     Quick return if possible. */\n\n    if (*n == 0 || (alpha->r == 0.f && alpha->i == 0.f && (beta->r == 1.f && \n                                                           beta->i == 0.f))) {\n\treturn 0;\n    }\n\n/*     Set up the start points in  X  and  Y. */\n\n    if (*incx > 0) {\n\tkx = 1;\n    } else {\n\tkx = 1 - (*n - 1) * *incx;\n    }\n    if (*incy > 0) {\n\tky = 1;\n    } else {\n\tky = 1 - (*n - 1) * *incy;\n    }\n\n/*     Start the operations. In this version the elements of the array AP */\n/*     are accessed sequentially with one pass through AP. */\n\n/*     First form  y := beta*y. */\n\n    if (beta->r != 1.f || beta->i != 0.f) {\n\tif (*incy == 1) {\n\t    if (beta->r == 0.f && beta->i == 0.f) {\n\t\ti__1 = *n;\n\t\tfor (i__ = 1; i__ <= i__1; ++i__) {\n\t\t    i__2 = i__;\n\t\t    y[i__2].r = 0.f, y[i__2].i = 0.f;\n/* L10: */\n\t\t}\n\t    } else {\n\t\ti__1 = *n;\n\t\tfor (i__ = 1; i__ <= i__1; ++i__) {\n\t\t    i__2 = i__;\n\t\t    i__3 = i__;\n\t\t    q__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i, \n\t\t\t    q__1.i = beta->r * y[i__3].i + beta->i * y[i__3]\n\t\t\t    .r;\n\t\t    y[i__2].r = q__1.r, y[i__2].i = q__1.i;\n/* L20: */\n\t\t}\n\t    }\n\t} else {\n\t    iy = ky;\n\t    if (beta->r == 0.f && beta->i == 0.f) {\n\t\ti__1 = *n;\n\t\tfor (i__ = 1; i__ <= i__1; ++i__) {\n\t\t    i__2 = iy;\n\t\t    y[i__2].r = 0.f, y[i__2].i = 0.f;\n\t\t    iy += *incy;\n/* L30: */\n\t\t}\n\t    } else {\n\t\ti__1 = *n;\n\t\tfor (i__ = 1; i__ <= i__1; ++i__) {\n\t\t    i__2 = iy;\n\t\t    i__3 = iy;\n\t\t    q__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i, \n\t\t\t    q__1.i = beta->r * y[i__3].i + beta->i * y[i__3]\n\t\t\t    .r;\n\t\t    y[i__2].r = q__1.r, y[i__2].i = q__1.i;\n\t\t    iy += *incy;\n/* L40: */\n\t\t}\n\t    }\n\t}\n    }\n    if (alpha->r == 0.f && alpha->i == 0.f) {\n\treturn 0;\n    }\n    kk = 1;\n    if (lsame_(uplo, \"U\", (ftnlen)1, (ftnlen)1)) {\n\n/*        Form  y  when AP contains the upper triangle. */\n\n\tif (*incx == 1 && *incy == 1) {\n\t    i__1 = *n;\n\t    for (j = 1; j <= i__1; ++j) {\n\t\ti__2 = j;\n\t\tq__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, q__1.i =\n\t\t\t alpha->r * x[i__2].i + alpha->i * x[i__2].r;\n\t\ttemp1.r = q__1.r, temp1.i = q__1.i;\n\t\ttemp2.r = 0.f, temp2.i = 0.f;\n\t\tk = kk;\n\t\ti__2 = j - 1;\n\t\tfor (i__ = 1; i__ <= i__2; ++i__) {\n\t\t    i__3 = i__;\n\t\t    i__4 = i__;\n\t\t    i__5 = k;\n\t\t    q__2.r = temp1.r * ap[i__5].r - temp1.i * ap[i__5].i, \n\t\t\t    q__2.i = temp1.r * ap[i__5].i + temp1.i * ap[i__5]\n\t\t\t    .r;\n\t\t    q__1.r = y[i__4].r + q__2.r, q__1.i = y[i__4].i + q__2.i;\n\t\t    y[i__3].r = q__1.r, y[i__3].i = q__1.i;\n\t\t    r_cnjg(&q__3, &ap[k]);\n\t\t    i__3 = i__;\n\t\t    q__2.r = q__3.r * x[i__3].r - q__3.i * x[i__3].i, q__2.i =\n\t\t\t     q__3.r * x[i__3].i + q__3.i * x[i__3].r;\n\t\t    q__1.r = temp2.r + q__2.r, q__1.i = temp2.i + q__2.i;\n\t\t    temp2.r = q__1.r, temp2.i = q__1.i;\n\t\t    ++k;\n/* L50: */\n\t\t}\n\t\ti__2 = j;\n\t\ti__3 = j;\n\t\ti__4 = kk + j - 1;\n\t\tr__1 = ap[i__4].r;\n\t\tq__3.r = r__1 * temp1.r, q__3.i = r__1 * temp1.i;\n\t\tq__2.r = y[i__3].r + q__3.r, q__2.i = y[i__3].i + q__3.i;\n\t\tq__4.r = alpha->r * temp2.r - alpha->i * temp2.i, q__4.i = \n\t\t\talpha->r * temp2.i + alpha->i * temp2.r;\n\t\tq__1.r = q__2.r + q__4.r, q__1.i = q__2.i + q__4.i;\n\t\ty[i__2].r = q__1.r, y[i__2].i = q__1.i;\n\t\tkk += j;\n/* L60: */\n\t    }\n\t} else {\n\t    jx = kx;\n\t    jy = ky;\n\t    i__1 = *n;\n\t    for (j = 1; j <= i__1; ++j) {\n\t\ti__2 = jx;\n\t\tq__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, q__1.i =\n\t\t\t alpha->r * x[i__2].i + alpha->i * x[i__2].r;\n\t\ttemp1.r = q__1.r, temp1.i = q__1.i;\n\t\ttemp2.r = 0.f, temp2.i = 0.f;\n\t\tix = kx;\n\t\tiy = ky;\n\t\ti__2 = kk + j - 2;\n\t\tfor (k = kk; k <= i__2; ++k) {\n\t\t    i__3 = iy;\n\t\t    i__4 = iy;\n\t\t    i__5 = k;\n\t\t    q__2.r = temp1.r * ap[i__5].r - temp1.i * ap[i__5].i, \n\t\t\t    q__2.i = temp1.r * ap[i__5].i + temp1.i * ap[i__5]\n\t\t\t    .r;\n\t\t    q__1.r = y[i__4].r + q__2.r, q__1.i = y[i__4].i + q__2.i;\n\t\t    y[i__3].r = q__1.r, y[i__3].i = q__1.i;\n\t\t    r_cnjg(&q__3, &ap[k]);\n\t\t    i__3 = ix;\n\t\t    q__2.r = q__3.r * x[i__3].r - q__3.i * x[i__3].i, q__2.i =\n\t\t\t     q__3.r * x[i__3].i + q__3.i * x[i__3].r;\n\t\t    q__1.r = temp2.r + q__2.r, q__1.i = temp2.i + q__2.i;\n\t\t    temp2.r = q__1.r, temp2.i = q__1.i;\n\t\t    ix += *incx;\n\t\t    iy += *incy;\n/* L70: */\n\t\t}\n\t\ti__2 = jy;\n\t\ti__3 = jy;\n\t\ti__4 = kk + j - 1;\n\t\tr__1 = ap[i__4].r;\n\t\tq__3.r = r__1 * temp1.r, q__3.i = r__1 * temp1.i;\n\t\tq__2.r = y[i__3].r + q__3.r, q__2.i = y[i__3].i + q__3.i;\n\t\tq__4.r = alpha->r * temp2.r - alpha->i * temp2.i, q__4.i = \n\t\t\talpha->r * temp2.i + alpha->i * temp2.r;\n\t\tq__1.r = q__2.r + q__4.r, q__1.i = q__2.i + q__4.i;\n\t\ty[i__2].r = q__1.r, y[i__2].i = q__1.i;\n\t\tjx += *incx;\n\t\tjy += *incy;\n\t\tkk += j;\n/* L80: */\n\t    }\n\t}\n    } else {\n\n/*        Form  y  when AP contains the lower triangle. */\n\n\tif (*incx == 1 && *incy == 1) {\n\t    i__1 = *n;\n\t    for (j = 1; j <= i__1; ++j) {\n\t\ti__2 = j;\n\t\tq__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, q__1.i =\n\t\t\t alpha->r * x[i__2].i + alpha->i * x[i__2].r;\n\t\ttemp1.r = q__1.r, temp1.i = q__1.i;\n\t\ttemp2.r = 0.f, temp2.i = 0.f;\n\t\ti__2 = j;\n\t\ti__3 = j;\n\t\ti__4 = kk;\n\t\tr__1 = ap[i__4].r;\n\t\tq__2.r = r__1 * temp1.r, q__2.i = r__1 * temp1.i;\n\t\tq__1.r = y[i__3].r + q__2.r, q__1.i = y[i__3].i + q__2.i;\n\t\ty[i__2].r = q__1.r, y[i__2].i = q__1.i;\n\t\tk = kk + 1;\n\t\ti__2 = *n;\n\t\tfor (i__ = j + 1; i__ <= i__2; ++i__) {\n\t\t    i__3 = i__;\n\t\t    i__4 = i__;\n\t\t    i__5 = k;\n\t\t    q__2.r = temp1.r * ap[i__5].r - temp1.i * ap[i__5].i, \n\t\t\t    q__2.i = temp1.r * ap[i__5].i + temp1.i * ap[i__5]\n\t\t\t    .r;\n\t\t    q__1.r = y[i__4].r + q__2.r, q__1.i = y[i__4].i + q__2.i;\n\t\t    y[i__3].r = q__1.r, y[i__3].i = q__1.i;\n\t\t    r_cnjg(&q__3, &ap[k]);\n\t\t    i__3 = i__;\n\t\t    q__2.r = q__3.r * x[i__3].r - q__3.i * x[i__3].i, q__2.i =\n\t\t\t     q__3.r * x[i__3].i + q__3.i * x[i__3].r;\n\t\t    q__1.r = temp2.r + q__2.r, q__1.i = temp2.i + q__2.i;\n\t\t    temp2.r = q__1.r, temp2.i = q__1.i;\n\t\t    ++k;\n/* L90: */\n\t\t}\n\t\ti__2 = j;\n\t\ti__3 = j;\n\t\tq__2.r = alpha->r * temp2.r - alpha->i * temp2.i, q__2.i = \n\t\t\talpha->r * temp2.i + alpha->i * temp2.r;\n\t\tq__1.r = y[i__3].r + q__2.r, q__1.i = y[i__3].i + q__2.i;\n\t\ty[i__2].r = q__1.r, y[i__2].i = q__1.i;\n\t\tkk += *n - j + 1;\n/* L100: */\n\t    }\n\t} else {\n\t    jx = kx;\n\t    jy = ky;\n\t    i__1 = *n;\n\t    for (j = 1; j <= i__1; ++j) {\n\t\ti__2 = jx;\n\t\tq__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, q__1.i =\n\t\t\t alpha->r * x[i__2].i + alpha->i * x[i__2].r;\n\t\ttemp1.r = q__1.r, temp1.i = q__1.i;\n\t\ttemp2.r = 0.f, temp2.i = 0.f;\n\t\ti__2 = jy;\n\t\ti__3 = jy;\n\t\ti__4 = kk;\n\t\tr__1 = ap[i__4].r;\n\t\tq__2.r = r__1 * temp1.r, q__2.i = r__1 * temp1.i;\n\t\tq__1.r = y[i__3].r + q__2.r, q__1.i = y[i__3].i + q__2.i;\n\t\ty[i__2].r = q__1.r, y[i__2].i = q__1.i;\n\t\tix = jx;\n\t\tiy = jy;\n\t\ti__2 = kk + *n - j;\n\t\tfor (k = kk + 1; k <= i__2; ++k) {\n\t\t    ix += *incx;\n\t\t    iy += *incy;\n\t\t    i__3 = iy;\n\t\t    i__4 = iy;\n\t\t    i__5 = k;\n\t\t    q__2.r = temp1.r * ap[i__5].r - temp1.i * ap[i__5].i, \n\t\t\t    q__2.i = temp1.r * ap[i__5].i + temp1.i * ap[i__5]\n\t\t\t    .r;\n\t\t    q__1.r = y[i__4].r + q__2.r, q__1.i = y[i__4].i + q__2.i;\n\t\t    y[i__3].r = q__1.r, y[i__3].i = q__1.i;\n\t\t    r_cnjg(&q__3, &ap[k]);\n\t\t    i__3 = ix;\n\t\t    q__2.r = q__3.r * x[i__3].r - q__3.i * x[i__3].i, q__2.i =\n\t\t\t     q__3.r * x[i__3].i + q__3.i * x[i__3].r;\n\t\t    q__1.r = temp2.r + q__2.r, q__1.i = temp2.i + q__2.i;\n\t\t    temp2.r = q__1.r, temp2.i = q__1.i;\n/* L110: */\n\t\t}\n\t\ti__2 = jy;\n\t\ti__3 = jy;\n\t\tq__2.r = alpha->r * temp2.r - alpha->i * temp2.i, q__2.i = \n\t\t\talpha->r * temp2.i + alpha->i * temp2.r;\n\t\tq__1.r = y[i__3].r + q__2.r, q__1.i = y[i__3].i + q__2.i;\n\t\ty[i__2].r = q__1.r, y[i__2].i = q__1.i;\n\t\tjx += *incx;\n\t\tjy += *incy;\n\t\tkk += *n - j + 1;\n/* L120: */\n\t    }\n\t}\n    }\n\n    return 0;\n\n/*     End of CHPMV . */\n\n} /* chpmv_ */\n\n"
  },
  {
    "path": "include/eigen3/blas/f2c/complexdots.c",
    "content": "/* This file has been modified to use the standard gfortran calling\n   convention, rather than the f2c calling convention.\n\n   It does not require -ff2c when compiled with gfortran.\n*/\n\n/* complexdots.f -- translated by f2c (version 20100827).\n   You must link the resulting object file with libf2c:\n\ton Microsoft Windows system, link with libf2c.lib;\n\ton Linux or Unix systems, link with .../path/to/libf2c.a -lm\n\tor, if you install libf2c.a in a standard place, with -lf2c -lm\n\t-- in that order, at the end of the command line, as in\n\t\tcc *.o -lf2c -lm\n\tSource for libf2c is in /netlib/f2c/libf2c.zip, e.g.,\n\n\t\thttp://www.netlib.org/f2c/libf2c.zip\n*/\n\n#include \"datatypes.h\"\n\ncomplex cdotc_(integer *n, complex *cx, integer \n\t*incx, complex *cy, integer *incy)\n{\n    complex res;\n    extern /* Subroutine */ int cdotcw_(integer *, complex *, integer *, \n\t    complex *, integer *, complex *);\n\n    /* Parameter adjustments */\n    --cy;\n    --cx;\n\n    /* Function Body */\n    cdotcw_(n, &cx[1], incx, &cy[1], incy, &res);\n    return res;\n} /* cdotc_ */\n\ncomplex cdotu_(integer *n, complex *cx, integer \n\t*incx, complex *cy, integer *incy)\n{\n    complex res;\n    extern /* Subroutine */ int cdotuw_(integer *, complex *, integer *, \n\t    complex *, integer *, complex *);\n\n    /* Parameter adjustments */\n    --cy;\n    --cx;\n\n    /* Function Body */\n    cdotuw_(n, &cx[1], incx, &cy[1], incy, &res);\n    return res;\n} /* cdotu_ */\n\ndoublecomplex zdotc_(integer *n, doublecomplex *cx, integer *incx, \n                     doublecomplex *cy, integer *incy)\n{\n    doublecomplex res;\n    extern /* Subroutine */ int zdotcw_(integer *, doublecomplex *, integer *,\n\t     doublecomplex *, integer *, doublecomplex *);\n\n    /* Parameter adjustments */\n    --cy;\n    --cx;\n\n    /* Function Body */\n    zdotcw_(n, &cx[1], incx, &cy[1], incy, &res);\n    return res;\n} /* zdotc_ */\n\ndoublecomplex zdotu_(integer *n, doublecomplex *cx, integer *incx, \n                     doublecomplex *cy, integer *incy)\n{\n    doublecomplex res;\n    extern /* Subroutine */ int zdotuw_(integer *, doublecomplex *, integer *,\n\t     doublecomplex *, integer *, doublecomplex *);\n\n    /* Parameter adjustments */\n    --cy;\n    --cx;\n\n    /* Function Body */\n    zdotuw_(n, &cx[1], incx, &cy[1], incy, &res);\n    return res;\n} /* zdotu_ */\n\n"
  },
  {
    "path": "include/eigen3/blas/f2c/ctbmv.c",
    "content": "/* ctbmv.f -- translated by f2c (version 20100827).\n   You must link the resulting object file with libf2c:\n\ton Microsoft Windows system, link with libf2c.lib;\n\ton Linux or Unix systems, link with .../path/to/libf2c.a -lm\n\tor, if you install libf2c.a in a standard place, with -lf2c -lm\n\t-- in that order, at the end of the command line, as in\n\t\tcc *.o -lf2c -lm\n\tSource for libf2c is in /netlib/f2c/libf2c.zip, e.g.,\n\n\t\thttp://www.netlib.org/f2c/libf2c.zip\n*/\n\n#include \"datatypes.h\"\n\n/* Subroutine */ int ctbmv_(char *uplo, char *trans, char *diag, integer *n, \n\tinteger *k, complex *a, integer *lda, complex *x, integer *incx, \n\tftnlen uplo_len, ftnlen trans_len, ftnlen diag_len)\n{\n    /* System generated locals */\n    integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;\n    complex q__1, q__2, q__3;\n\n    /* Builtin functions */\n    void r_cnjg(complex *, complex *);\n\n    /* Local variables */\n    integer i__, j, l, ix, jx, kx, info;\n    complex temp;\n    extern logical lsame_(char *, char *, ftnlen, ftnlen);\n    integer kplus1;\n    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);\n    logical noconj, nounit;\n\n/*     .. Scalar Arguments .. */\n/*     .. */\n/*     .. Array Arguments .. */\n/*     .. */\n\n/*  Purpose */\n/*  ======= */\n\n/*  CTBMV  performs one of the matrix-vector operations */\n\n/*     x := A*x,   or   x := A'*x,   or   x := conjg( A' )*x, */\n\n/*  where x is an n element vector and  A is an n by n unit, or non-unit, */\n/*  upper or lower triangular band matrix, with ( k + 1 ) diagonals. */\n\n/*  Arguments */\n/*  ========== */\n\n/*  UPLO   - CHARACTER*1. */\n/*           On entry, UPLO specifies whether the matrix is an upper or */\n/*           lower triangular matrix as follows: */\n\n/*              UPLO = 'U' or 'u'   A is an upper triangular matrix. */\n\n/*              UPLO = 'L' or 'l'   A is a lower triangular matrix. */\n\n/*           Unchanged on exit. */\n\n/*  TRANS  - CHARACTER*1. */\n/*           On entry, TRANS specifies the operation to be performed as */\n/*           follows: */\n\n/*              TRANS = 'N' or 'n'   x := A*x. */\n\n/*              TRANS = 'T' or 't'   x := A'*x. */\n\n/*              TRANS = 'C' or 'c'   x := conjg( A' )*x. */\n\n/*           Unchanged on exit. */\n\n/*  DIAG   - CHARACTER*1. */\n/*           On entry, DIAG specifies whether or not A is unit */\n/*           triangular as follows: */\n\n/*              DIAG = 'U' or 'u'   A is assumed to be unit triangular. */\n\n/*              DIAG = 'N' or 'n'   A is not assumed to be unit */\n/*                                  triangular. */\n\n/*           Unchanged on exit. */\n\n/*  N      - INTEGER. */\n/*           On entry, N specifies the order of the matrix A. */\n/*           N must be at least zero. */\n/*           Unchanged on exit. */\n\n/*  K      - INTEGER. */\n/*           On entry with UPLO = 'U' or 'u', K specifies the number of */\n/*           super-diagonals of the matrix A. */\n/*           On entry with UPLO = 'L' or 'l', K specifies the number of */\n/*           sub-diagonals of the matrix A. */\n/*           K must satisfy  0 .le. K. */\n/*           Unchanged on exit. */\n\n/*  A      - COMPLEX          array of DIMENSION ( LDA, n ). */\n/*           Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) */\n/*           by n part of the array A must contain the upper triangular */\n/*           band part of the matrix of coefficients, supplied column by */\n/*           column, with the leading diagonal of the matrix in row */\n/*           ( k + 1 ) of the array, the first super-diagonal starting at */\n/*           position 2 in row k, and so on. The top left k by k triangle */\n/*           of the array A is not referenced. */\n/*           The following program segment will transfer an upper */\n/*           triangular band matrix from conventional full matrix storage */\n/*           to band storage: */\n\n/*                 DO 20, J = 1, N */\n/*                    M = K + 1 - J */\n/*                    DO 10, I = MAX( 1, J - K ), J */\n/*                       A( M + I, J ) = matrix( I, J ) */\n/*              10    CONTINUE */\n/*              20 CONTINUE */\n\n/*           Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) */\n/*           by n part of the array A must contain the lower triangular */\n/*           band part of the matrix of coefficients, supplied column by */\n/*           column, with the leading diagonal of the matrix in row 1 of */\n/*           the array, the first sub-diagonal starting at position 1 in */\n/*           row 2, and so on. The bottom right k by k triangle of the */\n/*           array A is not referenced. */\n/*           The following program segment will transfer a lower */\n/*           triangular band matrix from conventional full matrix storage */\n/*           to band storage: */\n\n/*                 DO 20, J = 1, N */\n/*                    M = 1 - J */\n/*                    DO 10, I = J, MIN( N, J + K ) */\n/*                       A( M + I, J ) = matrix( I, J ) */\n/*              10    CONTINUE */\n/*              20 CONTINUE */\n\n/*           Note that when DIAG = 'U' or 'u' the elements of the array A */\n/*           corresponding to the diagonal elements of the matrix are not */\n/*           referenced, but are assumed to be unity. */\n/*           Unchanged on exit. */\n\n/*  LDA    - INTEGER. */\n/*           On entry, LDA specifies the first dimension of A as declared */\n/*           in the calling (sub) program. LDA must be at least */\n/*           ( k + 1 ). */\n/*           Unchanged on exit. */\n\n/*  X      - COMPLEX          array of dimension at least */\n/*           ( 1 + ( n - 1 )*abs( INCX ) ). */\n/*           Before entry, the incremented array X must contain the n */\n/*           element vector x. On exit, X is overwritten with the */\n/*           tranformed vector x. */\n\n/*  INCX   - INTEGER. */\n/*           On entry, INCX specifies the increment for the elements of */\n/*           X. INCX must not be zero. */\n/*           Unchanged on exit. */\n\n/*  Further Details */\n/*  =============== */\n\n/*  Level 2 Blas routine. */\n\n/*  -- Written on 22-October-1986. */\n/*     Jack Dongarra, Argonne National Lab. */\n/*     Jeremy Du Croz, Nag Central Office. */\n/*     Sven Hammarling, Nag Central Office. */\n/*     Richard Hanson, Sandia National Labs. */\n\n/*  ===================================================================== */\n\n/*     .. Parameters .. */\n/*     .. */\n/*     .. Local Scalars .. */\n/*     .. */\n/*     .. External Functions .. */\n/*     .. */\n/*     .. External Subroutines .. */\n/*     .. */\n/*     .. Intrinsic Functions .. */\n/*     .. */\n\n/*     Test the input parameters. */\n\n    /* Parameter adjustments */\n    a_dim1 = *lda;\n    a_offset = 1 + a_dim1;\n    a -= a_offset;\n    --x;\n\n    /* Function Body */\n    info = 0;\n    if (! lsame_(uplo, \"U\", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, \"L\", (\n\t    ftnlen)1, (ftnlen)1)) {\n\tinfo = 1;\n    } else if (! lsame_(trans, \"N\", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, \n\t    \"T\", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, \"C\", (ftnlen)1, (\n\t    ftnlen)1)) {\n\tinfo = 2;\n    } else if (! lsame_(diag, \"U\", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, \n\t    \"N\", (ftnlen)1, (ftnlen)1)) {\n\tinfo = 3;\n    } else if (*n < 0) {\n\tinfo = 4;\n    } else if (*k < 0) {\n\tinfo = 5;\n    } else if (*lda < *k + 1) {\n\tinfo = 7;\n    } else if (*incx == 0) {\n\tinfo = 9;\n    }\n    if (info != 0) {\n\txerbla_(\"CTBMV \", &info, (ftnlen)6);\n\treturn 0;\n    }\n\n/*     Quick return if possible. */\n\n    if (*n == 0) {\n\treturn 0;\n    }\n\n    noconj = lsame_(trans, \"T\", (ftnlen)1, (ftnlen)1);\n    nounit = lsame_(diag, \"N\", (ftnlen)1, (ftnlen)1);\n\n/*     Set up the start point in X if the increment is not unity. This */\n/*     will be  ( N - 1 )*INCX   too small for descending loops. */\n\n    if (*incx <= 0) {\n\tkx = 1 - (*n - 1) * *incx;\n    } else if (*incx != 1) {\n\tkx = 1;\n    }\n\n/*     Start the operations. In this version the elements of A are */\n/*     accessed sequentially with one pass through A. */\n\n    if (lsame_(trans, \"N\", (ftnlen)1, (ftnlen)1)) {\n\n/*         Form  x := A*x. */\n\n\tif (lsame_(uplo, \"U\", (ftnlen)1, (ftnlen)1)) {\n\t    kplus1 = *k + 1;\n\t    if (*incx == 1) {\n\t\ti__1 = *n;\n\t\tfor (j = 1; j <= i__1; ++j) {\n\t\t    i__2 = j;\n\t\t    if (x[i__2].r != 0.f || x[i__2].i != 0.f) {\n\t\t\ti__2 = j;\n\t\t\ttemp.r = x[i__2].r, temp.i = x[i__2].i;\n\t\t\tl = kplus1 - j;\n/* Computing MAX */\n\t\t\ti__2 = 1, i__3 = j - *k;\n\t\t\ti__4 = j - 1;\n\t\t\tfor (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {\n\t\t\t    i__2 = i__;\n\t\t\t    i__3 = i__;\n\t\t\t    i__5 = l + i__ + j * a_dim1;\n\t\t\t    q__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, \n\t\t\t\t    q__2.i = temp.r * a[i__5].i + temp.i * a[\n\t\t\t\t    i__5].r;\n\t\t\t    q__1.r = x[i__3].r + q__2.r, q__1.i = x[i__3].i + \n\t\t\t\t    q__2.i;\n\t\t\t    x[i__2].r = q__1.r, x[i__2].i = q__1.i;\n/* L10: */\n\t\t\t}\n\t\t\tif (nounit) {\n\t\t\t    i__4 = j;\n\t\t\t    i__2 = j;\n\t\t\t    i__3 = kplus1 + j * a_dim1;\n\t\t\t    q__1.r = x[i__2].r * a[i__3].r - x[i__2].i * a[\n\t\t\t\t    i__3].i, q__1.i = x[i__2].r * a[i__3].i + \n\t\t\t\t    x[i__2].i * a[i__3].r;\n\t\t\t    x[i__4].r = q__1.r, x[i__4].i = q__1.i;\n\t\t\t}\n\t\t    }\n/* L20: */\n\t\t}\n\t    } else {\n\t\tjx = kx;\n\t\ti__1 = *n;\n\t\tfor (j = 1; j <= i__1; ++j) {\n\t\t    i__4 = jx;\n\t\t    if (x[i__4].r != 0.f || x[i__4].i != 0.f) {\n\t\t\ti__4 = jx;\n\t\t\ttemp.r = x[i__4].r, temp.i = x[i__4].i;\n\t\t\tix = kx;\n\t\t\tl = kplus1 - j;\n/* Computing MAX */\n\t\t\ti__4 = 1, i__2 = j - *k;\n\t\t\ti__3 = j - 1;\n\t\t\tfor (i__ = max(i__4,i__2); i__ <= i__3; ++i__) {\n\t\t\t    i__4 = ix;\n\t\t\t    i__2 = ix;\n\t\t\t    i__5 = l + i__ + j * a_dim1;\n\t\t\t    q__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, \n\t\t\t\t    q__2.i = temp.r * a[i__5].i + temp.i * a[\n\t\t\t\t    i__5].r;\n\t\t\t    q__1.r = x[i__2].r + q__2.r, q__1.i = x[i__2].i + \n\t\t\t\t    q__2.i;\n\t\t\t    x[i__4].r = q__1.r, x[i__4].i = q__1.i;\n\t\t\t    ix += *incx;\n/* L30: */\n\t\t\t}\n\t\t\tif (nounit) {\n\t\t\t    i__3 = jx;\n\t\t\t    i__4 = jx;\n\t\t\t    i__2 = kplus1 + j * a_dim1;\n\t\t\t    q__1.r = x[i__4].r * a[i__2].r - x[i__4].i * a[\n\t\t\t\t    i__2].i, q__1.i = x[i__4].r * a[i__2].i + \n\t\t\t\t    x[i__4].i * a[i__2].r;\n\t\t\t    x[i__3].r = q__1.r, x[i__3].i = q__1.i;\n\t\t\t}\n\t\t    }\n\t\t    jx += *incx;\n\t\t    if (j > *k) {\n\t\t\tkx += *incx;\n\t\t    }\n/* L40: */\n\t\t}\n\t    }\n\t} else {\n\t    if (*incx == 1) {\n\t\tfor (j = *n; j >= 1; --j) {\n\t\t    i__1 = j;\n\t\t    if (x[i__1].r != 0.f || x[i__1].i != 0.f) {\n\t\t\ti__1 = j;\n\t\t\ttemp.r = x[i__1].r, temp.i = x[i__1].i;\n\t\t\tl = 1 - j;\n/* Computing MIN */\n\t\t\ti__1 = *n, i__3 = j + *k;\n\t\t\ti__4 = j + 1;\n\t\t\tfor (i__ = min(i__1,i__3); i__ >= i__4; --i__) {\n\t\t\t    i__1 = i__;\n\t\t\t    i__3 = i__;\n\t\t\t    i__2 = l + i__ + j * a_dim1;\n\t\t\t    q__2.r = temp.r * a[i__2].r - temp.i * a[i__2].i, \n\t\t\t\t    q__2.i = temp.r * a[i__2].i + temp.i * a[\n\t\t\t\t    i__2].r;\n\t\t\t    q__1.r = x[i__3].r + q__2.r, q__1.i = x[i__3].i + \n\t\t\t\t    q__2.i;\n\t\t\t    x[i__1].r = q__1.r, x[i__1].i = q__1.i;\n/* L50: */\n\t\t\t}\n\t\t\tif (nounit) {\n\t\t\t    i__4 = j;\n\t\t\t    i__1 = j;\n\t\t\t    i__3 = j * a_dim1 + 1;\n\t\t\t    q__1.r = x[i__1].r * a[i__3].r - x[i__1].i * a[\n\t\t\t\t    i__3].i, q__1.i = x[i__1].r * a[i__3].i + \n\t\t\t\t    x[i__1].i * a[i__3].r;\n\t\t\t    x[i__4].r = q__1.r, x[i__4].i = q__1.i;\n\t\t\t}\n\t\t    }\n/* L60: */\n\t\t}\n\t    } else {\n\t\tkx += (*n - 1) * *incx;\n\t\tjx = kx;\n\t\tfor (j = *n; j >= 1; --j) {\n\t\t    i__4 = jx;\n\t\t    if (x[i__4].r != 0.f || x[i__4].i != 0.f) {\n\t\t\ti__4 = jx;\n\t\t\ttemp.r = x[i__4].r, temp.i = x[i__4].i;\n\t\t\tix = kx;\n\t\t\tl = 1 - j;\n/* Computing MIN */\n\t\t\ti__4 = *n, i__1 = j + *k;\n\t\t\ti__3 = j + 1;\n\t\t\tfor (i__ = min(i__4,i__1); i__ >= i__3; --i__) {\n\t\t\t    i__4 = ix;\n\t\t\t    i__1 = ix;\n\t\t\t    i__2 = l + i__ + j * a_dim1;\n\t\t\t    q__2.r = temp.r * a[i__2].r - temp.i * a[i__2].i, \n\t\t\t\t    q__2.i = temp.r * a[i__2].i + temp.i * a[\n\t\t\t\t    i__2].r;\n\t\t\t    q__1.r = x[i__1].r + q__2.r, q__1.i = x[i__1].i + \n\t\t\t\t    q__2.i;\n\t\t\t    x[i__4].r = q__1.r, x[i__4].i = q__1.i;\n\t\t\t    ix -= *incx;\n/* L70: */\n\t\t\t}\n\t\t\tif (nounit) {\n\t\t\t    i__3 = jx;\n\t\t\t    i__4 = jx;\n\t\t\t    i__1 = j * a_dim1 + 1;\n\t\t\t    q__1.r = x[i__4].r * a[i__1].r - x[i__4].i * a[\n\t\t\t\t    i__1].i, q__1.i = x[i__4].r * a[i__1].i + \n\t\t\t\t    x[i__4].i * a[i__1].r;\n\t\t\t    x[i__3].r = q__1.r, x[i__3].i = q__1.i;\n\t\t\t}\n\t\t    }\n\t\t    jx -= *incx;\n\t\t    if (*n - j >= *k) {\n\t\t\tkx -= *incx;\n\t\t    }\n/* L80: */\n\t\t}\n\t    }\n\t}\n    } else {\n\n/*        Form  x := A'*x  or  x := conjg( A' )*x. */\n\n\tif (lsame_(uplo, \"U\", (ftnlen)1, (ftnlen)1)) {\n\t    kplus1 = *k + 1;\n\t    if (*incx == 1) {\n\t\tfor (j = *n; j >= 1; --j) {\n\t\t    i__3 = j;\n\t\t    temp.r = x[i__3].r, temp.i = x[i__3].i;\n\t\t    l = kplus1 - j;\n\t\t    if (noconj) {\n\t\t\tif (nounit) {\n\t\t\t    i__3 = kplus1 + j * a_dim1;\n\t\t\t    q__1.r = temp.r * a[i__3].r - temp.i * a[i__3].i, \n\t\t\t\t    q__1.i = temp.r * a[i__3].i + temp.i * a[\n\t\t\t\t    i__3].r;\n\t\t\t    temp.r = q__1.r, temp.i = q__1.i;\n\t\t\t}\n/* Computing MAX */\n\t\t\ti__4 = 1, i__1 = j - *k;\n\t\t\ti__3 = max(i__4,i__1);\n\t\t\tfor (i__ = j - 1; i__ >= i__3; --i__) {\n\t\t\t    i__4 = l + i__ + j * a_dim1;\n\t\t\t    i__1 = i__;\n\t\t\t    q__2.r = a[i__4].r * x[i__1].r - a[i__4].i * x[\n\t\t\t\t    i__1].i, q__2.i = a[i__4].r * x[i__1].i + \n\t\t\t\t    a[i__4].i * x[i__1].r;\n\t\t\t    q__1.r = temp.r + q__2.r, q__1.i = temp.i + \n\t\t\t\t    q__2.i;\n\t\t\t    temp.r = q__1.r, temp.i = q__1.i;\n/* L90: */\n\t\t\t}\n\t\t    } else {\n\t\t\tif (nounit) {\n\t\t\t    r_cnjg(&q__2, &a[kplus1 + j * a_dim1]);\n\t\t\t    q__1.r = temp.r * q__2.r - temp.i * q__2.i, \n\t\t\t\t    q__1.i = temp.r * q__2.i + temp.i * \n\t\t\t\t    q__2.r;\n\t\t\t    temp.r = q__1.r, temp.i = q__1.i;\n\t\t\t}\n/* Computing MAX */\n\t\t\ti__4 = 1, i__1 = j - *k;\n\t\t\ti__3 = max(i__4,i__1);\n\t\t\tfor (i__ = j - 1; i__ >= i__3; --i__) {\n\t\t\t    r_cnjg(&q__3, &a[l + i__ + j * a_dim1]);\n\t\t\t    i__4 = i__;\n\t\t\t    q__2.r = q__3.r * x[i__4].r - q__3.i * x[i__4].i, \n\t\t\t\t    q__2.i = q__3.r * x[i__4].i + q__3.i * x[\n\t\t\t\t    i__4].r;\n\t\t\t    q__1.r = temp.r + q__2.r, q__1.i = temp.i + \n\t\t\t\t    q__2.i;\n\t\t\t    temp.r = q__1.r, temp.i = q__1.i;\n/* L100: */\n\t\t\t}\n\t\t    }\n\t\t    i__3 = j;\n\t\t    x[i__3].r = temp.r, x[i__3].i = temp.i;\n/* L110: */\n\t\t}\n\t    } else {\n\t\tkx += (*n - 1) * *incx;\n\t\tjx = kx;\n\t\tfor (j = *n; j >= 1; --j) {\n\t\t    i__3 = jx;\n\t\t    temp.r = x[i__3].r, temp.i = x[i__3].i;\n\t\t    kx -= *incx;\n\t\t    ix = kx;\n\t\t    l = kplus1 - j;\n\t\t    if (noconj) {\n\t\t\tif (nounit) {\n\t\t\t    i__3 = kplus1 + j * a_dim1;\n\t\t\t    q__1.r = temp.r * a[i__3].r - temp.i * a[i__3].i, \n\t\t\t\t    q__1.i = temp.r * a[i__3].i + temp.i * a[\n\t\t\t\t    i__3].r;\n\t\t\t    temp.r = q__1.r, temp.i = q__1.i;\n\t\t\t}\n/* Computing MAX */\n\t\t\ti__4 = 1, i__1 = j - *k;\n\t\t\ti__3 = max(i__4,i__1);\n\t\t\tfor (i__ = j - 1; i__ >= i__3; --i__) {\n\t\t\t    i__4 = l + i__ + j * a_dim1;\n\t\t\t    i__1 = ix;\n\t\t\t    q__2.r = a[i__4].r * x[i__1].r - a[i__4].i * x[\n\t\t\t\t    i__1].i, q__2.i = a[i__4].r * x[i__1].i + \n\t\t\t\t    a[i__4].i * x[i__1].r;\n\t\t\t    q__1.r = temp.r + q__2.r, q__1.i = temp.i + \n\t\t\t\t    q__2.i;\n\t\t\t    temp.r = q__1.r, temp.i = q__1.i;\n\t\t\t    ix -= *incx;\n/* L120: */\n\t\t\t}\n\t\t    } else {\n\t\t\tif (nounit) {\n\t\t\t    r_cnjg(&q__2, &a[kplus1 + j * a_dim1]);\n\t\t\t    q__1.r = temp.r * q__2.r - temp.i * q__2.i, \n\t\t\t\t    q__1.i = temp.r * q__2.i + temp.i * \n\t\t\t\t    q__2.r;\n\t\t\t    temp.r = q__1.r, temp.i = q__1.i;\n\t\t\t}\n/* Computing MAX */\n\t\t\ti__4 = 1, i__1 = j - *k;\n\t\t\ti__3 = max(i__4,i__1);\n\t\t\tfor (i__ = j - 1; i__ >= i__3; --i__) {\n\t\t\t    r_cnjg(&q__3, &a[l + i__ + j * a_dim1]);\n\t\t\t    i__4 = ix;\n\t\t\t    q__2.r = q__3.r * x[i__4].r - q__3.i * x[i__4].i, \n\t\t\t\t    q__2.i = q__3.r * x[i__4].i + q__3.i * x[\n\t\t\t\t    i__4].r;\n\t\t\t    q__1.r = temp.r + q__2.r, q__1.i = temp.i + \n\t\t\t\t    q__2.i;\n\t\t\t    temp.r = q__1.r, temp.i = q__1.i;\n\t\t\t    ix -= *incx;\n/* L130: */\n\t\t\t}\n\t\t    }\n\t\t    i__3 = jx;\n\t\t    x[i__3].r = temp.r, x[i__3].i = temp.i;\n\t\t    jx -= *incx;\n/* L140: */\n\t\t}\n\t    }\n\t} else {\n\t    if (*incx == 1) {\n\t\ti__3 = *n;\n\t\tfor (j = 1; j <= i__3; ++j) {\n\t\t    i__4 = j;\n\t\t    temp.r = x[i__4].r, temp.i = x[i__4].i;\n\t\t    l = 1 - j;\n\t\t    if (noconj) {\n\t\t\tif (nounit) {\n\t\t\t    i__4 = j * a_dim1 + 1;\n\t\t\t    q__1.r = temp.r * a[i__4].r - temp.i * a[i__4].i, \n\t\t\t\t    q__1.i = temp.r * a[i__4].i + temp.i * a[\n\t\t\t\t    i__4].r;\n\t\t\t    temp.r = q__1.r, temp.i = q__1.i;\n\t\t\t}\n/* Computing MIN */\n\t\t\ti__1 = *n, i__2 = j + *k;\n\t\t\ti__4 = min(i__1,i__2);\n\t\t\tfor (i__ = j + 1; i__ <= i__4; ++i__) {\n\t\t\t    i__1 = l + i__ + j * a_dim1;\n\t\t\t    i__2 = i__;\n\t\t\t    q__2.r = a[i__1].r * x[i__2].r - a[i__1].i * x[\n\t\t\t\t    i__2].i, q__2.i = a[i__1].r * x[i__2].i + \n\t\t\t\t    a[i__1].i * x[i__2].r;\n\t\t\t    q__1.r = temp.r + q__2.r, q__1.i = temp.i + \n\t\t\t\t    q__2.i;\n\t\t\t    temp.r = q__1.r, temp.i = q__1.i;\n/* L150: */\n\t\t\t}\n\t\t    } else {\n\t\t\tif (nounit) {\n\t\t\t    r_cnjg(&q__2, &a[j * a_dim1 + 1]);\n\t\t\t    q__1.r = temp.r * q__2.r - temp.i * q__2.i, \n\t\t\t\t    q__1.i = temp.r * q__2.i + temp.i * \n\t\t\t\t    q__2.r;\n\t\t\t    temp.r = q__1.r, temp.i = q__1.i;\n\t\t\t}\n/* Computing MIN */\n\t\t\ti__1 = *n, i__2 = j + *k;\n\t\t\ti__4 = min(i__1,i__2);\n\t\t\tfor (i__ = j + 1; i__ <= i__4; ++i__) {\n\t\t\t    r_cnjg(&q__3, &a[l + i__ + j * a_dim1]);\n\t\t\t    i__1 = i__;\n\t\t\t    q__2.r = q__3.r * x[i__1].r - q__3.i * x[i__1].i, \n\t\t\t\t    q__2.i = q__3.r * x[i__1].i + q__3.i * x[\n\t\t\t\t    i__1].r;\n\t\t\t    q__1.r = temp.r + q__2.r, q__1.i = temp.i + \n\t\t\t\t    q__2.i;\n\t\t\t    temp.r = q__1.r, temp.i = q__1.i;\n/* L160: */\n\t\t\t}\n\t\t    }\n\t\t    i__4 = j;\n\t\t    x[i__4].r = temp.r, x[i__4].i = temp.i;\n/* L170: */\n\t\t}\n\t    } else {\n\t\tjx = kx;\n\t\ti__3 = *n;\n\t\tfor (j = 1; j <= i__3; ++j) {\n\t\t    i__4 = jx;\n\t\t    temp.r = x[i__4].r, temp.i = x[i__4].i;\n\t\t    kx += *incx;\n\t\t    ix = kx;\n\t\t    l = 1 - j;\n\t\t    if (noconj) {\n\t\t\tif (nounit) {\n\t\t\t    i__4 = j * a_dim1 + 1;\n\t\t\t    q__1.r = temp.r * a[i__4].r - temp.i * a[i__4].i, \n\t\t\t\t    q__1.i = temp.r * a[i__4].i + temp.i * a[\n\t\t\t\t    i__4].r;\n\t\t\t    temp.r = q__1.r, temp.i = q__1.i;\n\t\t\t}\n/* Computing MIN */\n\t\t\ti__1 = *n, i__2 = j + *k;\n\t\t\ti__4 = min(i__1,i__2);\n\t\t\tfor (i__ = j + 1; i__ <= i__4; ++i__) {\n\t\t\t    i__1 = l + i__ + j * a_dim1;\n\t\t\t    i__2 = ix;\n\t\t\t    q__2.r = a[i__1].r * x[i__2].r - a[i__1].i * x[\n\t\t\t\t    i__2].i, q__2.i = a[i__1].r * x[i__2].i + \n\t\t\t\t    a[i__1].i * x[i__2].r;\n\t\t\t    q__1.r = temp.r + q__2.r, q__1.i = temp.i + \n\t\t\t\t    q__2.i;\n\t\t\t    temp.r = q__1.r, temp.i = q__1.i;\n\t\t\t    ix += *incx;\n/* L180: */\n\t\t\t}\n\t\t    } else {\n\t\t\tif (nounit) {\n\t\t\t    r_cnjg(&q__2, &a[j * a_dim1 + 1]);\n\t\t\t    q__1.r = temp.r * q__2.r - temp.i * q__2.i, \n\t\t\t\t    q__1.i = temp.r * q__2.i + temp.i * \n\t\t\t\t    q__2.r;\n\t\t\t    temp.r = q__1.r, temp.i = q__1.i;\n\t\t\t}\n/* Computing MIN */\n\t\t\ti__1 = *n, i__2 = j + *k;\n\t\t\ti__4 = min(i__1,i__2);\n\t\t\tfor (i__ = j + 1; i__ <= i__4; ++i__) {\n\t\t\t    r_cnjg(&q__3, &a[l + i__ + j * a_dim1]);\n\t\t\t    i__1 = ix;\n\t\t\t    q__2.r = q__3.r * x[i__1].r - q__3.i * x[i__1].i, \n\t\t\t\t    q__2.i = q__3.r * x[i__1].i + q__3.i * x[\n\t\t\t\t    i__1].r;\n\t\t\t    q__1.r = temp.r + q__2.r, q__1.i = temp.i + \n\t\t\t\t    q__2.i;\n\t\t\t    temp.r = q__1.r, temp.i = q__1.i;\n\t\t\t    ix += *incx;\n/* L190: */\n\t\t\t}\n\t\t    }\n\t\t    i__4 = jx;\n\t\t    x[i__4].r = temp.r, x[i__4].i = temp.i;\n\t\t    jx += *incx;\n/* L200: */\n\t\t}\n\t    }\n\t}\n    }\n\n    return 0;\n\n/*     End of CTBMV . */\n\n} /* ctbmv_ */\n\n"
  },
  {
    "path": "include/eigen3/blas/f2c/d_cnjg.c",
    "content": "#include \"datatypes.h\"    \n\nvoid d_cnjg(doublecomplex *r, doublecomplex *z) {\n    r->r = z->r;\n    r->i = -(z->i);\n}\n"
  },
  {
    "path": "include/eigen3/blas/f2c/datatypes.h",
    "content": "/* This contains a limited subset of the typedefs exposed by f2c\n   for use by the Eigen BLAS C-only implementation.\n*/\n\n#ifndef __EIGEN_DATATYPES_H__\n#define __EIGEN_DATATYPES_H__\n\ntypedef int integer;\ntypedef unsigned int uinteger;\ntypedef float real;\ntypedef double doublereal;\ntypedef struct { real r, i; } complex;\ntypedef struct { doublereal r, i; } doublecomplex;\ntypedef int ftnlen;\ntypedef int logical;\n\n#define abs(x) ((x) >= 0 ? (x) : -(x))\n#define dabs(x) (doublereal)abs(x)\n#define min(a,b) ((a) <= (b) ? (a) : (b))\n#define max(a,b) ((a) >= (b) ? (a) : (b))\n#define dmin(a,b) (doublereal)min(a,b)\n#define dmax(a,b) (doublereal)max(a,b)\n\n#endif\n"
  },
  {
    "path": "include/eigen3/blas/f2c/drotm.c",
    "content": "/* drotm.f -- translated by f2c (version 20100827).\n   You must link the resulting object file with libf2c:\n\ton Microsoft Windows system, link with libf2c.lib;\n\ton Linux or Unix systems, link with .../path/to/libf2c.a -lm\n\tor, if you install libf2c.a in a standard place, with -lf2c -lm\n\t-- in that order, at the end of the command line, as in\n\t\tcc *.o -lf2c -lm\n\tSource for libf2c is in /netlib/f2c/libf2c.zip, e.g.,\n\n\t\thttp://www.netlib.org/f2c/libf2c.zip\n*/\n\n#include \"datatypes.h\"\n\n/* Subroutine */ int drotm_(integer *n, doublereal *dx, integer *incx, \n\tdoublereal *dy, integer *incy, doublereal *dparam)\n{\n    /* Initialized data */\n\n    static doublereal zero = 0.;\n    static doublereal two = 2.;\n\n    /* System generated locals */\n    integer i__1, i__2;\n\n    /* Local variables */\n    integer i__;\n    doublereal w, z__;\n    integer kx, ky;\n    doublereal dh11, dh12, dh21, dh22, dflag;\n    integer nsteps;\n\n/*     .. Scalar Arguments .. */\n/*     .. */\n/*     .. Array Arguments .. */\n/*     .. */\n\n/*  Purpose */\n/*  ======= */\n\n/*     APPLY THE MODIFIED GIVENS TRANSFORMATION, H, TO THE 2 BY N MATRIX */\n\n/*     (DX**T) , WHERE **T INDICATES TRANSPOSE. THE ELEMENTS OF DX ARE IN */\n/*     (DY**T) */\n\n/*     DX(LX+I*INCX), I = 0 TO N-1, WHERE LX = 1 IF INCX .GE. 0, ELSE */\n/*     LX = (-INCX)*N, AND SIMILARLY FOR SY USING LY AND INCY. */\n/*     WITH DPARAM(1)=DFLAG, H HAS ONE OF THE FOLLOWING FORMS.. */\n\n/*     DFLAG=-1.D0     DFLAG=0.D0        DFLAG=1.D0     DFLAG=-2.D0 */\n\n/*       (DH11  DH12)    (1.D0  DH12)    (DH11  1.D0)    (1.D0  0.D0) */\n/*     H=(          )    (          )    (          )    (          ) */\n/*       (DH21  DH22),   (DH21  1.D0),   (-1.D0 DH22),   (0.D0  1.D0). */\n/*     SEE DROTMG FOR A DESCRIPTION OF DATA STORAGE IN DPARAM. */\n\n/*  Arguments */\n/*  ========= */\n\n/*  N      (input) INTEGER */\n/*         number of elements in input vector(s) */\n\n/*  DX     (input/output) DOUBLE PRECISION array, dimension N */\n/*         double precision vector with N elements */\n\n/*  INCX   (input) INTEGER */\n/*         storage spacing between elements of DX */\n\n/*  DY     (input/output) DOUBLE PRECISION array, dimension N */\n/*         double precision vector with N elements */\n\n/*  INCY   (input) INTEGER */\n/*         storage spacing between elements of DY */\n\n/*  DPARAM (input/output)  DOUBLE PRECISION array, dimension 5 */\n/*     DPARAM(1)=DFLAG */\n/*     DPARAM(2)=DH11 */\n/*     DPARAM(3)=DH21 */\n/*     DPARAM(4)=DH12 */\n/*     DPARAM(5)=DH22 */\n\n/*  ===================================================================== */\n\n/*     .. Local Scalars .. */\n/*     .. */\n/*     .. Data statements .. */\n    /* Parameter adjustments */\n    --dparam;\n    --dy;\n    --dx;\n\n    /* Function Body */\n/*     .. */\n\n    dflag = dparam[1];\n    if (*n <= 0 || dflag + two == zero) {\n\tgoto L140;\n    }\n    if (! (*incx == *incy && *incx > 0)) {\n\tgoto L70;\n    }\n\n    nsteps = *n * *incx;\n    if (dflag < 0.) {\n\tgoto L50;\n    } else if (dflag == 0) {\n\tgoto L10;\n    } else {\n\tgoto L30;\n    }\nL10:\n    dh12 = dparam[4];\n    dh21 = dparam[3];\n    i__1 = nsteps;\n    i__2 = *incx;\n    for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {\n\tw = dx[i__];\n\tz__ = dy[i__];\n\tdx[i__] = w + z__ * dh12;\n\tdy[i__] = w * dh21 + z__;\n/* L20: */\n    }\n    goto L140;\nL30:\n    dh11 = dparam[2];\n    dh22 = dparam[5];\n    i__2 = nsteps;\n    i__1 = *incx;\n    for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) {\n\tw = dx[i__];\n\tz__ = dy[i__];\n\tdx[i__] = w * dh11 + z__;\n\tdy[i__] = -w + dh22 * z__;\n/* L40: */\n    }\n    goto L140;\nL50:\n    dh11 = dparam[2];\n    dh12 = dparam[4];\n    dh21 = dparam[3];\n    dh22 = dparam[5];\n    i__1 = nsteps;\n    i__2 = *incx;\n    for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {\n\tw = dx[i__];\n\tz__ = dy[i__];\n\tdx[i__] = w * dh11 + z__ * dh12;\n\tdy[i__] = w * dh21 + z__ * dh22;\n/* L60: */\n    }\n    goto L140;\nL70:\n    kx = 1;\n    ky = 1;\n    if (*incx < 0) {\n\tkx = (1 - *n) * *incx + 1;\n    }\n    if (*incy < 0) {\n\tky = (1 - *n) * *incy + 1;\n    }\n\n    if (dflag < 0.) {\n\tgoto L120;\n    } else if (dflag == 0) {\n\tgoto L80;\n    } else {\n\tgoto L100;\n    }\nL80:\n    dh12 = dparam[4];\n    dh21 = dparam[3];\n    i__2 = *n;\n    for (i__ = 1; i__ <= i__2; ++i__) {\n\tw = dx[kx];\n\tz__ = dy[ky];\n\tdx[kx] = w + z__ * dh12;\n\tdy[ky] = w * dh21 + z__;\n\tkx += *incx;\n\tky += *incy;\n/* L90: */\n    }\n    goto L140;\nL100:\n    dh11 = dparam[2];\n    dh22 = dparam[5];\n    i__2 = *n;\n    for (i__ = 1; i__ <= i__2; ++i__) {\n\tw = dx[kx];\n\tz__ = dy[ky];\n\tdx[kx] = w * dh11 + z__;\n\tdy[ky] = -w + dh22 * z__;\n\tkx += *incx;\n\tky += *incy;\n/* L110: */\n    }\n    goto L140;\nL120:\n    dh11 = dparam[2];\n    dh12 = dparam[4];\n    dh21 = dparam[3];\n    dh22 = dparam[5];\n    i__2 = *n;\n    for (i__ = 1; i__ <= i__2; ++i__) {\n\tw = dx[kx];\n\tz__ = dy[ky];\n\tdx[kx] = w * dh11 + z__ * dh12;\n\tdy[ky] = w * dh21 + z__ * dh22;\n\tkx += *incx;\n\tky += *incy;\n/* L130: */\n    }\nL140:\n    return 0;\n} /* drotm_ */\n\n"
  },
  {
    "path": "include/eigen3/blas/f2c/drotmg.c",
    "content": "/* drotmg.f -- translated by f2c (version 20100827).\n   You must link the resulting object file with libf2c:\n\ton Microsoft Windows system, link with libf2c.lib;\n\ton Linux or Unix systems, link with .../path/to/libf2c.a -lm\n\tor, if you install libf2c.a in a standard place, with -lf2c -lm\n\t-- in that order, at the end of the command line, as in\n\t\tcc *.o -lf2c -lm\n\tSource for libf2c is in /netlib/f2c/libf2c.zip, e.g.,\n\n\t\thttp://www.netlib.org/f2c/libf2c.zip\n*/\n\n#include \"datatypes.h\"\n\n/* Subroutine */ int drotmg_(doublereal *dd1, doublereal *dd2, doublereal *\n\tdx1, doublereal *dy1, doublereal *dparam)\n{\n    /* Initialized data */\n\n    static doublereal zero = 0.;\n    static doublereal one = 1.;\n    static doublereal two = 2.;\n    static doublereal gam = 4096.;\n    static doublereal gamsq = 16777216.;\n    static doublereal rgamsq = 5.9604645e-8;\n\n    /* Format strings */\n    static char fmt_120[] = \"\";\n    static char fmt_150[] = \"\";\n    static char fmt_180[] = \"\";\n    static char fmt_210[] = \"\";\n\n    /* System generated locals */\n    doublereal d__1;\n\n    /* Local variables */\n    doublereal du, dp1, dp2, dq1, dq2, dh11, dh12, dh21, dh22;\n    integer igo;\n    doublereal dflag, dtemp;\n\n    /* Assigned format variables */\n    static char *igo_fmt;\n\n/*     .. Scalar Arguments .. */\n/*     .. */\n/*     .. Array Arguments .. */\n/*     .. */\n\n/*  Purpose */\n/*  ======= */\n\n/*     CONSTRUCT THE MODIFIED GIVENS TRANSFORMATION MATRIX H WHICH ZEROS */\n/*     THE SECOND COMPONENT OF THE 2-VECTOR  (DSQRT(DD1)*DX1,DSQRT(DD2)* */\n/*     DY2)**T. */\n/*     WITH DPARAM(1)=DFLAG, H HAS ONE OF THE FOLLOWING FORMS.. */\n\n/*     DFLAG=-1.D0     DFLAG=0.D0        DFLAG=1.D0     DFLAG=-2.D0 */\n\n/*       (DH11  DH12)    (1.D0  DH12)    (DH11  1.D0)    (1.D0  0.D0) */\n/*     H=(          )    (          )    (          )    (          ) */\n/*       (DH21  DH22),   (DH21  1.D0),   (-1.D0 DH22),   (0.D0  1.D0). */\n/*     LOCATIONS 2-4 OF DPARAM CONTAIN DH11, DH21, DH12, AND DH22 */\n/*     RESPECTIVELY. (VALUES OF 1.D0, -1.D0, OR 0.D0 IMPLIED BY THE */\n/*     VALUE OF DPARAM(1) ARE NOT STORED IN DPARAM.) */\n\n/*     THE VALUES OF GAMSQ AND RGAMSQ SET IN THE DATA STATEMENT MAY BE */\n/*     INEXACT.  THIS IS OK AS THEY ARE ONLY USED FOR TESTING THE SIZE */\n/*     OF DD1 AND DD2.  ALL ACTUAL SCALING OF DATA IS DONE USING GAM. */\n\n\n/*  Arguments */\n/*  ========= */\n\n/*  DD1    (input/output) DOUBLE PRECISION */\n\n/*  DD2    (input/output) DOUBLE PRECISION */\n\n/*  DX1    (input/output) DOUBLE PRECISION */\n\n/*  DY1    (input) DOUBLE PRECISION */\n\n/*  DPARAM (input/output)  DOUBLE PRECISION array, dimension 5 */\n/*     DPARAM(1)=DFLAG */\n/*     DPARAM(2)=DH11 */\n/*     DPARAM(3)=DH21 */\n/*     DPARAM(4)=DH12 */\n/*     DPARAM(5)=DH22 */\n\n/*  ===================================================================== */\n\n/*     .. Local Scalars .. */\n/*     .. */\n/*     .. Intrinsic Functions .. */\n/*     .. */\n/*     .. Data statements .. */\n\n    /* Parameter adjustments */\n    --dparam;\n\n    /* Function Body */\n/*     .. */\n    if (! (*dd1 < zero)) {\n\tgoto L10;\n    }\n/*       GO ZERO-H-D-AND-DX1.. */\n    goto L60;\nL10:\n/*     CASE-DD1-NONNEGATIVE */\n    dp2 = *dd2 * *dy1;\n    if (! (dp2 == zero)) {\n\tgoto L20;\n    }\n    dflag = -two;\n    goto L260;\n/*     REGULAR-CASE.. */\nL20:\n    dp1 = *dd1 * *dx1;\n    dq2 = dp2 * *dy1;\n    dq1 = dp1 * *dx1;\n\n    if (! (abs(dq1) > abs(dq2))) {\n\tgoto L40;\n    }\n    dh21 = -(*dy1) / *dx1;\n    dh12 = dp2 / dp1;\n\n    du = one - dh12 * dh21;\n\n    if (! (du <= zero)) {\n\tgoto L30;\n    }\n/*         GO ZERO-H-D-AND-DX1.. */\n    goto L60;\nL30:\n    dflag = zero;\n    *dd1 /= du;\n    *dd2 /= du;\n    *dx1 *= du;\n/*         GO SCALE-CHECK.. */\n    goto L100;\nL40:\n    if (! (dq2 < zero)) {\n\tgoto L50;\n    }\n/*         GO ZERO-H-D-AND-DX1.. */\n    goto L60;\nL50:\n    dflag = one;\n    dh11 = dp1 / dp2;\n    dh22 = *dx1 / *dy1;\n    du = one + dh11 * dh22;\n    dtemp = *dd2 / du;\n    *dd2 = *dd1 / du;\n    *dd1 = dtemp;\n    *dx1 = *dy1 * du;\n/*         GO SCALE-CHECK */\n    goto L100;\n/*     PROCEDURE..ZERO-H-D-AND-DX1.. */\nL60:\n    dflag = -one;\n    dh11 = zero;\n    dh12 = zero;\n    dh21 = zero;\n    dh22 = zero;\n\n    *dd1 = zero;\n    *dd2 = zero;\n    *dx1 = zero;\n/*         RETURN.. */\n    goto L220;\n/*     PROCEDURE..FIX-H.. */\nL70:\n    if (! (dflag >= zero)) {\n\tgoto L90;\n    }\n\n    if (! (dflag == zero)) {\n\tgoto L80;\n    }\n    dh11 = one;\n    dh22 = one;\n    dflag = -one;\n    goto L90;\nL80:\n    dh21 = -one;\n    dh12 = one;\n    dflag = -one;\nL90:\n    switch (igo) {\n\tcase 0: goto L120;\n\tcase 1: goto L150;\n\tcase 2: goto L180;\n\tcase 3: goto L210;\n    }\n/*     PROCEDURE..SCALE-CHECK */\nL100:\nL110:\n    if (! (*dd1 <= rgamsq)) {\n\tgoto L130;\n    }\n    if (*dd1 == zero) {\n\tgoto L160;\n    }\n    igo = 0;\n    igo_fmt = fmt_120;\n/*              FIX-H.. */\n    goto L70;\nL120:\n/* Computing 2nd power */\n    d__1 = gam;\n    *dd1 *= d__1 * d__1;\n    *dx1 /= gam;\n    dh11 /= gam;\n    dh12 /= gam;\n    goto L110;\nL130:\nL140:\n    if (! (*dd1 >= gamsq)) {\n\tgoto L160;\n    }\n    igo = 1;\n    igo_fmt = fmt_150;\n/*              FIX-H.. */\n    goto L70;\nL150:\n/* Computing 2nd power */\n    d__1 = gam;\n    *dd1 /= d__1 * d__1;\n    *dx1 *= gam;\n    dh11 *= gam;\n    dh12 *= gam;\n    goto L140;\nL160:\nL170:\n    if (! (abs(*dd2) <= rgamsq)) {\n\tgoto L190;\n    }\n    if (*dd2 == zero) {\n\tgoto L220;\n    }\n    igo = 2;\n    igo_fmt = fmt_180;\n/*              FIX-H.. */\n    goto L70;\nL180:\n/* Computing 2nd power */\n    d__1 = gam;\n    *dd2 *= d__1 * d__1;\n    dh21 /= gam;\n    dh22 /= gam;\n    goto L170;\nL190:\nL200:\n    if (! (abs(*dd2) >= gamsq)) {\n\tgoto L220;\n    }\n    igo = 3;\n    igo_fmt = fmt_210;\n/*              FIX-H.. */\n    goto L70;\nL210:\n/* Computing 2nd power */\n    d__1 = gam;\n    *dd2 /= d__1 * d__1;\n    dh21 *= gam;\n    dh22 *= gam;\n    goto L200;\nL220:\n    if (dflag < 0.) {\n\tgoto L250;\n    } else if (dflag == 0) {\n\tgoto L230;\n    } else {\n\tgoto L240;\n    }\nL230:\n    dparam[3] = dh21;\n    dparam[4] = dh12;\n    goto L260;\nL240:\n    dparam[2] = dh11;\n    dparam[5] = dh22;\n    goto L260;\nL250:\n    dparam[2] = dh11;\n    dparam[3] = dh21;\n    dparam[4] = dh12;\n    dparam[5] = dh22;\nL260:\n    dparam[1] = dflag;\n    return 0;\n} /* drotmg_ */\n\n"
  },
  {
    "path": "include/eigen3/blas/f2c/dsbmv.c",
    "content": "/* dsbmv.f -- translated by f2c (version 20100827).\n   You must link the resulting object file with libf2c:\n\ton Microsoft Windows system, link with libf2c.lib;\n\ton Linux or Unix systems, link with .../path/to/libf2c.a -lm\n\tor, if you install libf2c.a in a standard place, with -lf2c -lm\n\t-- in that order, at the end of the command line, as in\n\t\tcc *.o -lf2c -lm\n\tSource for libf2c is in /netlib/f2c/libf2c.zip, e.g.,\n\n\t\thttp://www.netlib.org/f2c/libf2c.zip\n*/\n\n#include \"datatypes.h\"\n\n/* Subroutine */ int dsbmv_(char *uplo, integer *n, integer *k, doublereal *\n\talpha, doublereal *a, integer *lda, doublereal *x, integer *incx, \n\tdoublereal *beta, doublereal *y, integer *incy, ftnlen uplo_len)\n{\n    /* System generated locals */\n    integer a_dim1, a_offset, i__1, i__2, i__3, i__4;\n\n    /* Local variables */\n    integer i__, j, l, ix, iy, jx, jy, kx, ky, info;\n    doublereal temp1, temp2;\n    extern logical lsame_(char *, char *, ftnlen, ftnlen);\n    integer kplus1;\n    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);\n\n/*     .. Scalar Arguments .. */\n/*     .. */\n/*     .. Array Arguments .. */\n/*     .. */\n\n/*  Purpose */\n/*  ======= */\n\n/*  DSBMV  performs the matrix-vector  operation */\n\n/*     y := alpha*A*x + beta*y, */\n\n/*  where alpha and beta are scalars, x and y are n element vectors and */\n/*  A is an n by n symmetric band matrix, with k super-diagonals. */\n\n/*  Arguments */\n/*  ========== */\n\n/*  UPLO   - CHARACTER*1. */\n/*           On entry, UPLO specifies whether the upper or lower */\n/*           triangular part of the band matrix A is being supplied as */\n/*           follows: */\n\n/*              UPLO = 'U' or 'u'   The upper triangular part of A is */\n/*                                  being supplied. */\n\n/*              UPLO = 'L' or 'l'   The lower triangular part of A is */\n/*                                  being supplied. */\n\n/*           Unchanged on exit. */\n\n/*  N      - INTEGER. */\n/*           On entry, N specifies the order of the matrix A. */\n/*           N must be at least zero. */\n/*           Unchanged on exit. */\n\n/*  K      - INTEGER. */\n/*           On entry, K specifies the number of super-diagonals of the */\n/*           matrix A. K must satisfy  0 .le. K. */\n/*           Unchanged on exit. */\n\n/*  ALPHA  - DOUBLE PRECISION. */\n/*           On entry, ALPHA specifies the scalar alpha. */\n/*           Unchanged on exit. */\n\n/*  A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ). */\n/*           Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) */\n/*           by n part of the array A must contain the upper triangular */\n/*           band part of the symmetric matrix, supplied column by */\n/*           column, with the leading diagonal of the matrix in row */\n/*           ( k + 1 ) of the array, the first super-diagonal starting at */\n/*           position 2 in row k, and so on. The top left k by k triangle */\n/*           of the array A is not referenced. */\n/*           The following program segment will transfer the upper */\n/*           triangular part of a symmetric band matrix from conventional */\n/*           full matrix storage to band storage: */\n\n/*                 DO 20, J = 1, N */\n/*                    M = K + 1 - J */\n/*                    DO 10, I = MAX( 1, J - K ), J */\n/*                       A( M + I, J ) = matrix( I, J ) */\n/*              10    CONTINUE */\n/*              20 CONTINUE */\n\n/*           Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) */\n/*           by n part of the array A must contain the lower triangular */\n/*           band part of the symmetric matrix, supplied column by */\n/*           column, with the leading diagonal of the matrix in row 1 of */\n/*           the array, the first sub-diagonal starting at position 1 in */\n/*           row 2, and so on. The bottom right k by k triangle of the */\n/*           array A is not referenced. */\n/*           The following program segment will transfer the lower */\n/*           triangular part of a symmetric band matrix from conventional */\n/*           full matrix storage to band storage: */\n\n/*                 DO 20, J = 1, N */\n/*                    M = 1 - J */\n/*                    DO 10, I = J, MIN( N, J + K ) */\n/*                       A( M + I, J ) = matrix( I, J ) */\n/*              10    CONTINUE */\n/*              20 CONTINUE */\n\n/*           Unchanged on exit. */\n\n/*  LDA    - INTEGER. */\n/*           On entry, LDA specifies the first dimension of A as declared */\n/*           in the calling (sub) program. LDA must be at least */\n/*           ( k + 1 ). */\n/*           Unchanged on exit. */\n\n/*  X      - DOUBLE PRECISION array of DIMENSION at least */\n/*           ( 1 + ( n - 1 )*abs( INCX ) ). */\n/*           Before entry, the incremented array X must contain the */\n/*           vector x. */\n/*           Unchanged on exit. */\n\n/*  INCX   - INTEGER. */\n/*           On entry, INCX specifies the increment for the elements of */\n/*           X. INCX must not be zero. */\n/*           Unchanged on exit. */\n\n/*  BETA   - DOUBLE PRECISION. */\n/*           On entry, BETA specifies the scalar beta. */\n/*           Unchanged on exit. */\n\n/*  Y      - DOUBLE PRECISION array of DIMENSION at least */\n/*           ( 1 + ( n - 1 )*abs( INCY ) ). */\n/*           Before entry, the incremented array Y must contain the */\n/*           vector y. On exit, Y is overwritten by the updated vector y. */\n\n/*  INCY   - INTEGER. */\n/*           On entry, INCY specifies the increment for the elements of */\n/*           Y. INCY must not be zero. */\n/*           Unchanged on exit. */\n\n\n/*  Level 2 Blas routine. */\n\n/*  -- Written on 22-October-1986. */\n/*     Jack Dongarra, Argonne National Lab. */\n/*     Jeremy Du Croz, Nag Central Office. */\n/*     Sven Hammarling, Nag Central Office. */\n/*     Richard Hanson, Sandia National Labs. */\n\n/*  ===================================================================== */\n\n/*     .. Parameters .. */\n/*     .. */\n/*     .. Local Scalars .. */\n/*     .. */\n/*     .. External Functions .. */\n/*     .. */\n/*     .. External Subroutines .. */\n/*     .. */\n/*     .. Intrinsic Functions .. */\n/*     .. */\n\n/*     Test the input parameters. */\n\n    /* Parameter adjustments */\n    a_dim1 = *lda;\n    a_offset = 1 + a_dim1;\n    a -= a_offset;\n    --x;\n    --y;\n\n    /* Function Body */\n    info = 0;\n    if (! lsame_(uplo, \"U\", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, \"L\", (\n\t    ftnlen)1, (ftnlen)1)) {\n\tinfo = 1;\n    } else if (*n < 0) {\n\tinfo = 2;\n    } else if (*k < 0) {\n\tinfo = 3;\n    } else if (*lda < *k + 1) {\n\tinfo = 6;\n    } else if (*incx == 0) {\n\tinfo = 8;\n    } else if (*incy == 0) {\n\tinfo = 11;\n    }\n    if (info != 0) {\n\txerbla_(\"DSBMV \", &info, (ftnlen)6);\n\treturn 0;\n    }\n\n/*     Quick return if possible. */\n\n    if (*n == 0 || (*alpha == 0. && *beta == 1.)) {\n\treturn 0;\n    }\n\n/*     Set up the start points in  X  and  Y. */\n\n    if (*incx > 0) {\n\tkx = 1;\n    } else {\n\tkx = 1 - (*n - 1) * *incx;\n    }\n    if (*incy > 0) {\n\tky = 1;\n    } else {\n\tky = 1 - (*n - 1) * *incy;\n    }\n\n/*     Start the operations. In this version the elements of the array A */\n/*     are accessed sequentially with one pass through A. */\n\n/*     First form  y := beta*y. */\n\n    if (*beta != 1.) {\n\tif (*incy == 1) {\n\t    if (*beta == 0.) {\n\t\ti__1 = *n;\n\t\tfor (i__ = 1; i__ <= i__1; ++i__) {\n\t\t    y[i__] = 0.;\n/* L10: */\n\t\t}\n\t    } else {\n\t\ti__1 = *n;\n\t\tfor (i__ = 1; i__ <= i__1; ++i__) {\n\t\t    y[i__] = *beta * y[i__];\n/* L20: */\n\t\t}\n\t    }\n\t} else {\n\t    iy = ky;\n\t    if (*beta == 0.) {\n\t\ti__1 = *n;\n\t\tfor (i__ = 1; i__ <= i__1; ++i__) {\n\t\t    y[iy] = 0.;\n\t\t    iy += *incy;\n/* L30: */\n\t\t}\n\t    } else {\n\t\ti__1 = *n;\n\t\tfor (i__ = 1; i__ <= i__1; ++i__) {\n\t\t    y[iy] = *beta * y[iy];\n\t\t    iy += *incy;\n/* L40: */\n\t\t}\n\t    }\n\t}\n    }\n    if (*alpha == 0.) {\n\treturn 0;\n    }\n    if (lsame_(uplo, \"U\", (ftnlen)1, (ftnlen)1)) {\n\n/*        Form  y  when upper triangle of A is stored. */\n\n\tkplus1 = *k + 1;\n\tif (*incx == 1 && *incy == 1) {\n\t    i__1 = *n;\n\t    for (j = 1; j <= i__1; ++j) {\n\t\ttemp1 = *alpha * x[j];\n\t\ttemp2 = 0.;\n\t\tl = kplus1 - j;\n/* Computing MAX */\n\t\ti__2 = 1, i__3 = j - *k;\n\t\ti__4 = j - 1;\n\t\tfor (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {\n\t\t    y[i__] += temp1 * a[l + i__ + j * a_dim1];\n\t\t    temp2 += a[l + i__ + j * a_dim1] * x[i__];\n/* L50: */\n\t\t}\n\t\ty[j] = y[j] + temp1 * a[kplus1 + j * a_dim1] + *alpha * temp2;\n/* L60: */\n\t    }\n\t} else {\n\t    jx = kx;\n\t    jy = ky;\n\t    i__1 = *n;\n\t    for (j = 1; j <= i__1; ++j) {\n\t\ttemp1 = *alpha * x[jx];\n\t\ttemp2 = 0.;\n\t\tix = kx;\n\t\tiy = ky;\n\t\tl = kplus1 - j;\n/* Computing MAX */\n\t\ti__4 = 1, i__2 = j - *k;\n\t\ti__3 = j - 1;\n\t\tfor (i__ = max(i__4,i__2); i__ <= i__3; ++i__) {\n\t\t    y[iy] += temp1 * a[l + i__ + j * a_dim1];\n\t\t    temp2 += a[l + i__ + j * a_dim1] * x[ix];\n\t\t    ix += *incx;\n\t\t    iy += *incy;\n/* L70: */\n\t\t}\n\t\ty[jy] = y[jy] + temp1 * a[kplus1 + j * a_dim1] + *alpha * \n\t\t\ttemp2;\n\t\tjx += *incx;\n\t\tjy += *incy;\n\t\tif (j > *k) {\n\t\t    kx += *incx;\n\t\t    ky += *incy;\n\t\t}\n/* L80: */\n\t    }\n\t}\n    } else {\n\n/*        Form  y  when lower triangle of A is stored. */\n\n\tif (*incx == 1 && *incy == 1) {\n\t    i__1 = *n;\n\t    for (j = 1; j <= i__1; ++j) {\n\t\ttemp1 = *alpha * x[j];\n\t\ttemp2 = 0.;\n\t\ty[j] += temp1 * a[j * a_dim1 + 1];\n\t\tl = 1 - j;\n/* Computing MIN */\n\t\ti__4 = *n, i__2 = j + *k;\n\t\ti__3 = min(i__4,i__2);\n\t\tfor (i__ = j + 1; i__ <= i__3; ++i__) {\n\t\t    y[i__] += temp1 * a[l + i__ + j * a_dim1];\n\t\t    temp2 += a[l + i__ + j * a_dim1] * x[i__];\n/* L90: */\n\t\t}\n\t\ty[j] += *alpha * temp2;\n/* L100: */\n\t    }\n\t} else {\n\t    jx = kx;\n\t    jy = ky;\n\t    i__1 = *n;\n\t    for (j = 1; j <= i__1; ++j) {\n\t\ttemp1 = *alpha * x[jx];\n\t\ttemp2 = 0.;\n\t\ty[jy] += temp1 * a[j * a_dim1 + 1];\n\t\tl = 1 - j;\n\t\tix = jx;\n\t\tiy = jy;\n/* Computing MIN */\n\t\ti__4 = *n, i__2 = j + *k;\n\t\ti__3 = min(i__4,i__2);\n\t\tfor (i__ = j + 1; i__ <= i__3; ++i__) {\n\t\t    ix += *incx;\n\t\t    iy += *incy;\n\t\t    y[iy] += temp1 * a[l + i__ + j * a_dim1];\n\t\t    temp2 += a[l + i__ + j * a_dim1] * x[ix];\n/* L110: */\n\t\t}\n\t\ty[jy] += *alpha * temp2;\n\t\tjx += *incx;\n\t\tjy += *incy;\n/* L120: */\n\t    }\n\t}\n    }\n\n    return 0;\n\n/*     End of DSBMV . */\n\n} /* dsbmv_ */\n\n"
  },
  {
    "path": "include/eigen3/blas/f2c/dspmv.c",
    "content": "/* dspmv.f -- translated by f2c (version 20100827).\n   You must link the resulting object file with libf2c:\n\ton Microsoft Windows system, link with libf2c.lib;\n\ton Linux or Unix systems, link with .../path/to/libf2c.a -lm\n\tor, if you install libf2c.a in a standard place, with -lf2c -lm\n\t-- in that order, at the end of the command line, as in\n\t\tcc *.o -lf2c -lm\n\tSource for libf2c is in /netlib/f2c/libf2c.zip, e.g.,\n\n\t\thttp://www.netlib.org/f2c/libf2c.zip\n*/\n\n#include \"datatypes.h\"\n\n/* Subroutine */ int dspmv_(char *uplo, integer *n, doublereal *alpha, \n\tdoublereal *ap, doublereal *x, integer *incx, doublereal *beta, \n\tdoublereal *y, integer *incy, ftnlen uplo_len)\n{\n    /* System generated locals */\n    integer i__1, i__2;\n\n    /* Local variables */\n    integer i__, j, k, kk, ix, iy, jx, jy, kx, ky, info;\n    doublereal temp1, temp2;\n    extern logical lsame_(char *, char *, ftnlen, ftnlen);\n    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);\n\n/*     .. Scalar Arguments .. */\n/*     .. */\n/*     .. Array Arguments .. */\n/*     .. */\n\n/*  Purpose */\n/*  ======= */\n\n/*  DSPMV  performs the matrix-vector operation */\n\n/*     y := alpha*A*x + beta*y, */\n\n/*  where alpha and beta are scalars, x and y are n element vectors and */\n/*  A is an n by n symmetric matrix, supplied in packed form. */\n\n/*  Arguments */\n/*  ========== */\n\n/*  UPLO   - CHARACTER*1. */\n/*           On entry, UPLO specifies whether the upper or lower */\n/*           triangular part of the matrix A is supplied in the packed */\n/*           array AP as follows: */\n\n/*              UPLO = 'U' or 'u'   The upper triangular part of A is */\n/*                                  supplied in AP. */\n\n/*              UPLO = 'L' or 'l'   The lower triangular part of A is */\n/*                                  supplied in AP. */\n\n/*           Unchanged on exit. */\n\n/*  N      - INTEGER. */\n/*           On entry, N specifies the order of the matrix A. */\n/*           N must be at least zero. */\n/*           Unchanged on exit. */\n\n/*  ALPHA  - DOUBLE PRECISION. */\n/*           On entry, ALPHA specifies the scalar alpha. */\n/*           Unchanged on exit. */\n\n/*  AP     - DOUBLE PRECISION array of DIMENSION at least */\n/*           ( ( n*( n + 1 ) )/2 ). */\n/*           Before entry with UPLO = 'U' or 'u', the array AP must */\n/*           contain the upper triangular part of the symmetric matrix */\n/*           packed sequentially, column by column, so that AP( 1 ) */\n/*           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) */\n/*           and a( 2, 2 ) respectively, and so on. */\n/*           Before entry with UPLO = 'L' or 'l', the array AP must */\n/*           contain the lower triangular part of the symmetric matrix */\n/*           packed sequentially, column by column, so that AP( 1 ) */\n/*           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) */\n/*           and a( 3, 1 ) respectively, and so on. */\n/*           Unchanged on exit. */\n\n/*  X      - DOUBLE PRECISION array of dimension at least */\n/*           ( 1 + ( n - 1 )*abs( INCX ) ). */\n/*           Before entry, the incremented array X must contain the n */\n/*           element vector x. */\n/*           Unchanged on exit. */\n\n/*  INCX   - INTEGER. */\n/*           On entry, INCX specifies the increment for the elements of */\n/*           X. INCX must not be zero. */\n/*           Unchanged on exit. */\n\n/*  BETA   - DOUBLE PRECISION. */\n/*           On entry, BETA specifies the scalar beta. When BETA is */\n/*           supplied as zero then Y need not be set on input. */\n/*           Unchanged on exit. */\n\n/*  Y      - DOUBLE PRECISION array of dimension at least */\n/*           ( 1 + ( n - 1 )*abs( INCY ) ). */\n/*           Before entry, the incremented array Y must contain the n */\n/*           element vector y. On exit, Y is overwritten by the updated */\n/*           vector y. */\n\n/*  INCY   - INTEGER. */\n/*           On entry, INCY specifies the increment for the elements of */\n/*           Y. INCY must not be zero. */\n/*           Unchanged on exit. */\n\n/*  Further Details */\n/*  =============== */\n\n/*  Level 2 Blas routine. */\n\n/*  -- Written on 22-October-1986. */\n/*     Jack Dongarra, Argonne National Lab. */\n/*     Jeremy Du Croz, Nag Central Office. */\n/*     Sven Hammarling, Nag Central Office. */\n/*     Richard Hanson, Sandia National Labs. */\n\n/*  ===================================================================== */\n\n/*     .. Parameters .. */\n/*     .. */\n/*     .. Local Scalars .. */\n/*     .. */\n/*     .. External Functions .. */\n/*     .. */\n/*     .. External Subroutines .. */\n/*     .. */\n\n/*     Test the input parameters. */\n\n    /* Parameter adjustments */\n    --y;\n    --x;\n    --ap;\n\n    /* Function Body */\n    info = 0;\n    if (! lsame_(uplo, \"U\", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, \"L\", (\n\t    ftnlen)1, (ftnlen)1)) {\n\tinfo = 1;\n    } else if (*n < 0) {\n\tinfo = 2;\n    } else if (*incx == 0) {\n\tinfo = 6;\n    } else if (*incy == 0) {\n\tinfo = 9;\n    }\n    if (info != 0) {\n\txerbla_(\"DSPMV \", &info, (ftnlen)6);\n\treturn 0;\n    }\n\n/*     Quick return if possible. */\n\n    if (*n == 0 || (*alpha == 0. && *beta == 1.)) {\n\treturn 0;\n    }\n\n/*     Set up the start points in  X  and  Y. */\n\n    if (*incx > 0) {\n\tkx = 1;\n    } else {\n\tkx = 1 - (*n - 1) * *incx;\n    }\n    if (*incy > 0) {\n\tky = 1;\n    } else {\n\tky = 1 - (*n - 1) * *incy;\n    }\n\n/*     Start the operations. In this version the elements of the array AP */\n/*     are accessed sequentially with one pass through AP. */\n\n/*     First form  y := beta*y. */\n\n    if (*beta != 1.) {\n\tif (*incy == 1) {\n\t    if (*beta == 0.) {\n\t\ti__1 = *n;\n\t\tfor (i__ = 1; i__ <= i__1; ++i__) {\n\t\t    y[i__] = 0.;\n/* L10: */\n\t\t}\n\t    } else {\n\t\ti__1 = *n;\n\t\tfor (i__ = 1; i__ <= i__1; ++i__) {\n\t\t    y[i__] = *beta * y[i__];\n/* L20: */\n\t\t}\n\t    }\n\t} else {\n\t    iy = ky;\n\t    if (*beta == 0.) {\n\t\ti__1 = *n;\n\t\tfor (i__ = 1; i__ <= i__1; ++i__) {\n\t\t    y[iy] = 0.;\n\t\t    iy += *incy;\n/* L30: */\n\t\t}\n\t    } else {\n\t\ti__1 = *n;\n\t\tfor (i__ = 1; i__ <= i__1; ++i__) {\n\t\t    y[iy] = *beta * y[iy];\n\t\t    iy += *incy;\n/* L40: */\n\t\t}\n\t    }\n\t}\n    }\n    if (*alpha == 0.) {\n\treturn 0;\n    }\n    kk = 1;\n    if (lsame_(uplo, \"U\", (ftnlen)1, (ftnlen)1)) {\n\n/*        Form  y  when AP contains the upper triangle. */\n\n\tif (*incx == 1 && *incy == 1) {\n\t    i__1 = *n;\n\t    for (j = 1; j <= i__1; ++j) {\n\t\ttemp1 = *alpha * x[j];\n\t\ttemp2 = 0.;\n\t\tk = kk;\n\t\ti__2 = j - 1;\n\t\tfor (i__ = 1; i__ <= i__2; ++i__) {\n\t\t    y[i__] += temp1 * ap[k];\n\t\t    temp2 += ap[k] * x[i__];\n\t\t    ++k;\n/* L50: */\n\t\t}\n\t\ty[j] = y[j] + temp1 * ap[kk + j - 1] + *alpha * temp2;\n\t\tkk += j;\n/* L60: */\n\t    }\n\t} else {\n\t    jx = kx;\n\t    jy = ky;\n\t    i__1 = *n;\n\t    for (j = 1; j <= i__1; ++j) {\n\t\ttemp1 = *alpha * x[jx];\n\t\ttemp2 = 0.;\n\t\tix = kx;\n\t\tiy = ky;\n\t\ti__2 = kk + j - 2;\n\t\tfor (k = kk; k <= i__2; ++k) {\n\t\t    y[iy] += temp1 * ap[k];\n\t\t    temp2 += ap[k] * x[ix];\n\t\t    ix += *incx;\n\t\t    iy += *incy;\n/* L70: */\n\t\t}\n\t\ty[jy] = y[jy] + temp1 * ap[kk + j - 1] + *alpha * temp2;\n\t\tjx += *incx;\n\t\tjy += *incy;\n\t\tkk += j;\n/* L80: */\n\t    }\n\t}\n    } else {\n\n/*        Form  y  when AP contains the lower triangle. */\n\n\tif (*incx == 1 && *incy == 1) {\n\t    i__1 = *n;\n\t    for (j = 1; j <= i__1; ++j) {\n\t\ttemp1 = *alpha * x[j];\n\t\ttemp2 = 0.;\n\t\ty[j] += temp1 * ap[kk];\n\t\tk = kk + 1;\n\t\ti__2 = *n;\n\t\tfor (i__ = j + 1; i__ <= i__2; ++i__) {\n\t\t    y[i__] += temp1 * ap[k];\n\t\t    temp2 += ap[k] * x[i__];\n\t\t    ++k;\n/* L90: */\n\t\t}\n\t\ty[j] += *alpha * temp2;\n\t\tkk += *n - j + 1;\n/* L100: */\n\t    }\n\t} else {\n\t    jx = kx;\n\t    jy = ky;\n\t    i__1 = *n;\n\t    for (j = 1; j <= i__1; ++j) {\n\t\ttemp1 = *alpha * x[jx];\n\t\ttemp2 = 0.;\n\t\ty[jy] += temp1 * ap[kk];\n\t\tix = jx;\n\t\tiy = jy;\n\t\ti__2 = kk + *n - j;\n\t\tfor (k = kk + 1; k <= i__2; ++k) {\n\t\t    ix += *incx;\n\t\t    iy += *incy;\n\t\t    y[iy] += temp1 * ap[k];\n\t\t    temp2 += ap[k] * x[ix];\n/* L110: */\n\t\t}\n\t\ty[jy] += *alpha * temp2;\n\t\tjx += *incx;\n\t\tjy += *incy;\n\t\tkk += *n - j + 1;\n/* L120: */\n\t    }\n\t}\n    }\n\n    return 0;\n\n/*     End of DSPMV . */\n\n} /* dspmv_ */\n\n"
  },
  {
    "path": "include/eigen3/blas/f2c/dtbmv.c",
    "content": "/* dtbmv.f -- translated by f2c (version 20100827).\n   You must link the resulting object file with libf2c:\n\ton Microsoft Windows system, link with libf2c.lib;\n\ton Linux or Unix systems, link with .../path/to/libf2c.a -lm\n\tor, if you install libf2c.a in a standard place, with -lf2c -lm\n\t-- in that order, at the end of the command line, as in\n\t\tcc *.o -lf2c -lm\n\tSource for libf2c is in /netlib/f2c/libf2c.zip, e.g.,\n\n\t\thttp://www.netlib.org/f2c/libf2c.zip\n*/\n\n#include \"datatypes.h\"\n\n/* Subroutine */ int dtbmv_(char *uplo, char *trans, char *diag, integer *n, \n\tinteger *k, doublereal *a, integer *lda, doublereal *x, integer *incx,\n\t ftnlen uplo_len, ftnlen trans_len, ftnlen diag_len)\n{\n    /* System generated locals */\n    integer a_dim1, a_offset, i__1, i__2, i__3, i__4;\n\n    /* Local variables */\n    integer i__, j, l, ix, jx, kx, info;\n    doublereal temp;\n    extern logical lsame_(char *, char *, ftnlen, ftnlen);\n    integer kplus1;\n    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);\n    logical nounit;\n\n/*     .. Scalar Arguments .. */\n/*     .. */\n/*     .. Array Arguments .. */\n/*     .. */\n\n/*  Purpose */\n/*  ======= */\n\n/*  DTBMV  performs one of the matrix-vector operations */\n\n/*     x := A*x,   or   x := A'*x, */\n\n/*  where x is an n element vector and  A is an n by n unit, or non-unit, */\n/*  upper or lower triangular band matrix, with ( k + 1 ) diagonals. */\n\n/*  Arguments */\n/*  ========== */\n\n/*  UPLO   - CHARACTER*1. */\n/*           On entry, UPLO specifies whether the matrix is an upper or */\n/*           lower triangular matrix as follows: */\n\n/*              UPLO = 'U' or 'u'   A is an upper triangular matrix. */\n\n/*              UPLO = 'L' or 'l'   A is a lower triangular matrix. */\n\n/*           Unchanged on exit. */\n\n/*  TRANS  - CHARACTER*1. */\n/*           On entry, TRANS specifies the operation to be performed as */\n/*           follows: */\n\n/*              TRANS = 'N' or 'n'   x := A*x. */\n\n/*              TRANS = 'T' or 't'   x := A'*x. */\n\n/*              TRANS = 'C' or 'c'   x := A'*x. */\n\n/*           Unchanged on exit. */\n\n/*  DIAG   - CHARACTER*1. */\n/*           On entry, DIAG specifies whether or not A is unit */\n/*           triangular as follows: */\n\n/*              DIAG = 'U' or 'u'   A is assumed to be unit triangular. */\n\n/*              DIAG = 'N' or 'n'   A is not assumed to be unit */\n/*                                  triangular. */\n\n/*           Unchanged on exit. */\n\n/*  N      - INTEGER. */\n/*           On entry, N specifies the order of the matrix A. */\n/*           N must be at least zero. */\n/*           Unchanged on exit. */\n\n/*  K      - INTEGER. */\n/*           On entry with UPLO = 'U' or 'u', K specifies the number of */\n/*           super-diagonals of the matrix A. */\n/*           On entry with UPLO = 'L' or 'l', K specifies the number of */\n/*           sub-diagonals of the matrix A. */\n/*           K must satisfy  0 .le. K. */\n/*           Unchanged on exit. */\n\n/*  A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ). */\n/*           Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) */\n/*           by n part of the array A must contain the upper triangular */\n/*           band part of the matrix of coefficients, supplied column by */\n/*           column, with the leading diagonal of the matrix in row */\n/*           ( k + 1 ) of the array, the first super-diagonal starting at */\n/*           position 2 in row k, and so on. The top left k by k triangle */\n/*           of the array A is not referenced. */\n/*           The following program segment will transfer an upper */\n/*           triangular band matrix from conventional full matrix storage */\n/*           to band storage: */\n\n/*                 DO 20, J = 1, N */\n/*                    M = K + 1 - J */\n/*                    DO 10, I = MAX( 1, J - K ), J */\n/*                       A( M + I, J ) = matrix( I, J ) */\n/*              10    CONTINUE */\n/*              20 CONTINUE */\n\n/*           Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) */\n/*           by n part of the array A must contain the lower triangular */\n/*           band part of the matrix of coefficients, supplied column by */\n/*           column, with the leading diagonal of the matrix in row 1 of */\n/*           the array, the first sub-diagonal starting at position 1 in */\n/*           row 2, and so on. The bottom right k by k triangle of the */\n/*           array A is not referenced. */\n/*           The following program segment will transfer a lower */\n/*           triangular band matrix from conventional full matrix storage */\n/*           to band storage: */\n\n/*                 DO 20, J = 1, N */\n/*                    M = 1 - J */\n/*                    DO 10, I = J, MIN( N, J + K ) */\n/*                       A( M + I, J ) = matrix( I, J ) */\n/*              10    CONTINUE */\n/*              20 CONTINUE */\n\n/*           Note that when DIAG = 'U' or 'u' the elements of the array A */\n/*           corresponding to the diagonal elements of the matrix are not */\n/*           referenced, but are assumed to be unity. */\n/*           Unchanged on exit. */\n\n/*  LDA    - INTEGER. */\n/*           On entry, LDA specifies the first dimension of A as declared */\n/*           in the calling (sub) program. LDA must be at least */\n/*           ( k + 1 ). */\n/*           Unchanged on exit. */\n\n/*  X      - DOUBLE PRECISION array of dimension at least */\n/*           ( 1 + ( n - 1 )*abs( INCX ) ). */\n/*           Before entry, the incremented array X must contain the n */\n/*           element vector x. On exit, X is overwritten with the */\n/*           tranformed vector x. */\n\n/*  INCX   - INTEGER. */\n/*           On entry, INCX specifies the increment for the elements of */\n/*           X. INCX must not be zero. */\n/*           Unchanged on exit. */\n\n/*  Further Details */\n/*  =============== */\n\n/*  Level 2 Blas routine. */\n\n/*  -- Written on 22-October-1986. */\n/*     Jack Dongarra, Argonne National Lab. */\n/*     Jeremy Du Croz, Nag Central Office. */\n/*     Sven Hammarling, Nag Central Office. */\n/*     Richard Hanson, Sandia National Labs. */\n\n/*  ===================================================================== */\n\n/*     .. Parameters .. */\n/*     .. */\n/*     .. Local Scalars .. */\n/*     .. */\n/*     .. External Functions .. */\n/*     .. */\n/*     .. External Subroutines .. */\n/*     .. */\n/*     .. Intrinsic Functions .. */\n/*     .. */\n\n/*     Test the input parameters. */\n\n    /* Parameter adjustments */\n    a_dim1 = *lda;\n    a_offset = 1 + a_dim1;\n    a -= a_offset;\n    --x;\n\n    /* Function Body */\n    info = 0;\n    if (! lsame_(uplo, \"U\", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, \"L\", (\n\t    ftnlen)1, (ftnlen)1)) {\n\tinfo = 1;\n    } else if (! lsame_(trans, \"N\", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, \n\t    \"T\", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, \"C\", (ftnlen)1, (\n\t    ftnlen)1)) {\n\tinfo = 2;\n    } else if (! lsame_(diag, \"U\", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, \n\t    \"N\", (ftnlen)1, (ftnlen)1)) {\n\tinfo = 3;\n    } else if (*n < 0) {\n\tinfo = 4;\n    } else if (*k < 0) {\n\tinfo = 5;\n    } else if (*lda < *k + 1) {\n\tinfo = 7;\n    } else if (*incx == 0) {\n\tinfo = 9;\n    }\n    if (info != 0) {\n\txerbla_(\"DTBMV \", &info, (ftnlen)6);\n\treturn 0;\n    }\n\n/*     Quick return if possible. */\n\n    if (*n == 0) {\n\treturn 0;\n    }\n\n    nounit = lsame_(diag, \"N\", (ftnlen)1, (ftnlen)1);\n\n/*     Set up the start point in X if the increment is not unity. This */\n/*     will be  ( N - 1 )*INCX   too small for descending loops. */\n\n    if (*incx <= 0) {\n\tkx = 1 - (*n - 1) * *incx;\n    } else if (*incx != 1) {\n\tkx = 1;\n    }\n\n/*     Start the operations. In this version the elements of A are */\n/*     accessed sequentially with one pass through A. */\n\n    if (lsame_(trans, \"N\", (ftnlen)1, (ftnlen)1)) {\n\n/*         Form  x := A*x. */\n\n\tif (lsame_(uplo, \"U\", (ftnlen)1, (ftnlen)1)) {\n\t    kplus1 = *k + 1;\n\t    if (*incx == 1) {\n\t\ti__1 = *n;\n\t\tfor (j = 1; j <= i__1; ++j) {\n\t\t    if (x[j] != 0.) {\n\t\t\ttemp = x[j];\n\t\t\tl = kplus1 - j;\n/* Computing MAX */\n\t\t\ti__2 = 1, i__3 = j - *k;\n\t\t\ti__4 = j - 1;\n\t\t\tfor (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {\n\t\t\t    x[i__] += temp * a[l + i__ + j * a_dim1];\n/* L10: */\n\t\t\t}\n\t\t\tif (nounit) {\n\t\t\t    x[j] *= a[kplus1 + j * a_dim1];\n\t\t\t}\n\t\t    }\n/* L20: */\n\t\t}\n\t    } else {\n\t\tjx = kx;\n\t\ti__1 = *n;\n\t\tfor (j = 1; j <= i__1; ++j) {\n\t\t    if (x[jx] != 0.) {\n\t\t\ttemp = x[jx];\n\t\t\tix = kx;\n\t\t\tl = kplus1 - j;\n/* Computing MAX */\n\t\t\ti__4 = 1, i__2 = j - *k;\n\t\t\ti__3 = j - 1;\n\t\t\tfor (i__ = max(i__4,i__2); i__ <= i__3; ++i__) {\n\t\t\t    x[ix] += temp * a[l + i__ + j * a_dim1];\n\t\t\t    ix += *incx;\n/* L30: */\n\t\t\t}\n\t\t\tif (nounit) {\n\t\t\t    x[jx] *= a[kplus1 + j * a_dim1];\n\t\t\t}\n\t\t    }\n\t\t    jx += *incx;\n\t\t    if (j > *k) {\n\t\t\tkx += *incx;\n\t\t    }\n/* L40: */\n\t\t}\n\t    }\n\t} else {\n\t    if (*incx == 1) {\n\t\tfor (j = *n; j >= 1; --j) {\n\t\t    if (x[j] != 0.) {\n\t\t\ttemp = x[j];\n\t\t\tl = 1 - j;\n/* Computing MIN */\n\t\t\ti__1 = *n, i__3 = j + *k;\n\t\t\ti__4 = j + 1;\n\t\t\tfor (i__ = min(i__1,i__3); i__ >= i__4; --i__) {\n\t\t\t    x[i__] += temp * a[l + i__ + j * a_dim1];\n/* L50: */\n\t\t\t}\n\t\t\tif (nounit) {\n\t\t\t    x[j] *= a[j * a_dim1 + 1];\n\t\t\t}\n\t\t    }\n/* L60: */\n\t\t}\n\t    } else {\n\t\tkx += (*n - 1) * *incx;\n\t\tjx = kx;\n\t\tfor (j = *n; j >= 1; --j) {\n\t\t    if (x[jx] != 0.) {\n\t\t\ttemp = x[jx];\n\t\t\tix = kx;\n\t\t\tl = 1 - j;\n/* Computing MIN */\n\t\t\ti__4 = *n, i__1 = j + *k;\n\t\t\ti__3 = j + 1;\n\t\t\tfor (i__ = min(i__4,i__1); i__ >= i__3; --i__) {\n\t\t\t    x[ix] += temp * a[l + i__ + j * a_dim1];\n\t\t\t    ix -= *incx;\n/* L70: */\n\t\t\t}\n\t\t\tif (nounit) {\n\t\t\t    x[jx] *= a[j * a_dim1 + 1];\n\t\t\t}\n\t\t    }\n\t\t    jx -= *incx;\n\t\t    if (*n - j >= *k) {\n\t\t\tkx -= *incx;\n\t\t    }\n/* L80: */\n\t\t}\n\t    }\n\t}\n    } else {\n\n/*        Form  x := A'*x. */\n\n\tif (lsame_(uplo, \"U\", (ftnlen)1, (ftnlen)1)) {\n\t    kplus1 = *k + 1;\n\t    if (*incx == 1) {\n\t\tfor (j = *n; j >= 1; --j) {\n\t\t    temp = x[j];\n\t\t    l = kplus1 - j;\n\t\t    if (nounit) {\n\t\t\ttemp *= a[kplus1 + j * a_dim1];\n\t\t    }\n/* Computing MAX */\n\t\t    i__4 = 1, i__1 = j - *k;\n\t\t    i__3 = max(i__4,i__1);\n\t\t    for (i__ = j - 1; i__ >= i__3; --i__) {\n\t\t\ttemp += a[l + i__ + j * a_dim1] * x[i__];\n/* L90: */\n\t\t    }\n\t\t    x[j] = temp;\n/* L100: */\n\t\t}\n\t    } else {\n\t\tkx += (*n - 1) * *incx;\n\t\tjx = kx;\n\t\tfor (j = *n; j >= 1; --j) {\n\t\t    temp = x[jx];\n\t\t    kx -= *incx;\n\t\t    ix = kx;\n\t\t    l = kplus1 - j;\n\t\t    if (nounit) {\n\t\t\ttemp *= a[kplus1 + j * a_dim1];\n\t\t    }\n/* Computing MAX */\n\t\t    i__4 = 1, i__1 = j - *k;\n\t\t    i__3 = max(i__4,i__1);\n\t\t    for (i__ = j - 1; i__ >= i__3; --i__) {\n\t\t\ttemp += a[l + i__ + j * a_dim1] * x[ix];\n\t\t\tix -= *incx;\n/* L110: */\n\t\t    }\n\t\t    x[jx] = temp;\n\t\t    jx -= *incx;\n/* L120: */\n\t\t}\n\t    }\n\t} else {\n\t    if (*incx == 1) {\n\t\ti__3 = *n;\n\t\tfor (j = 1; j <= i__3; ++j) {\n\t\t    temp = x[j];\n\t\t    l = 1 - j;\n\t\t    if (nounit) {\n\t\t\ttemp *= a[j * a_dim1 + 1];\n\t\t    }\n/* Computing MIN */\n\t\t    i__1 = *n, i__2 = j + *k;\n\t\t    i__4 = min(i__1,i__2);\n\t\t    for (i__ = j + 1; i__ <= i__4; ++i__) {\n\t\t\ttemp += a[l + i__ + j * a_dim1] * x[i__];\n/* L130: */\n\t\t    }\n\t\t    x[j] = temp;\n/* L140: */\n\t\t}\n\t    } else {\n\t\tjx = kx;\n\t\ti__3 = *n;\n\t\tfor (j = 1; j <= i__3; ++j) {\n\t\t    temp = x[jx];\n\t\t    kx += *incx;\n\t\t    ix = kx;\n\t\t    l = 1 - j;\n\t\t    if (nounit) {\n\t\t\ttemp *= a[j * a_dim1 + 1];\n\t\t    }\n/* Computing MIN */\n\t\t    i__1 = *n, i__2 = j + *k;\n\t\t    i__4 = min(i__1,i__2);\n\t\t    for (i__ = j + 1; i__ <= i__4; ++i__) {\n\t\t\ttemp += a[l + i__ + j * a_dim1] * x[ix];\n\t\t\tix += *incx;\n/* L150: */\n\t\t    }\n\t\t    x[jx] = temp;\n\t\t    jx += *incx;\n/* L160: */\n\t\t}\n\t    }\n\t}\n    }\n\n    return 0;\n\n/*     End of DTBMV . */\n\n} /* dtbmv_ */\n\n"
  },
  {
    "path": "include/eigen3/blas/f2c/lsame.c",
    "content": "/* lsame.f -- translated by f2c (version 20100827).\n   You must link the resulting object file with libf2c:\n\ton Microsoft Windows system, link with libf2c.lib;\n\ton Linux or Unix systems, link with .../path/to/libf2c.a -lm\n\tor, if you install libf2c.a in a standard place, with -lf2c -lm\n\t-- in that order, at the end of the command line, as in\n\t\tcc *.o -lf2c -lm\n\tSource for libf2c is in /netlib/f2c/libf2c.zip, e.g.,\n\n\t\thttp://www.netlib.org/f2c/libf2c.zip\n*/\n\n#include \"datatypes.h\"\n\nlogical lsame_(char *ca, char *cb, ftnlen ca_len, ftnlen cb_len)\n{\n    /* System generated locals */\n    logical ret_val;\n\n    /* Local variables */\n    integer inta, intb, zcode;\n\n\n/*  -- LAPACK auxiliary routine (version 3.1) -- */\n/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */\n/*     November 2006 */\n\n/*     .. Scalar Arguments .. */\n/*     .. */\n\n/*  Purpose */\n/*  ======= */\n\n/*  LSAME returns .TRUE. if CA is the same letter as CB regardless of */\n/*  case. */\n\n/*  Arguments */\n/*  ========= */\n\n/*  CA      (input) CHARACTER*1 */\n\n/*  CB      (input) CHARACTER*1 */\n/*          CA and CB specify the single characters to be compared. */\n\n/* ===================================================================== */\n\n/*     .. Intrinsic Functions .. */\n/*     .. */\n/*     .. Local Scalars .. */\n/*     .. */\n\n/*     Test if the characters are equal */\n\n    ret_val = *(unsigned char *)ca == *(unsigned char *)cb;\n    if (ret_val) {\n\treturn ret_val;\n    }\n\n/*     Now test for equivalence if both characters are alphabetic. */\n\n    zcode = 'Z';\n\n/*     Use 'Z' rather than 'A' so that ASCII can be detected on Prime */\n/*     machines, on which ICHAR returns a value with bit 8 set. */\n/*     ICHAR('A') on Prime machines returns 193 which is the same as */\n/*     ICHAR('A') on an EBCDIC machine. */\n\n    inta = *(unsigned char *)ca;\n    intb = *(unsigned char *)cb;\n\n    if (zcode == 90 || zcode == 122) {\n\n/*        ASCII is assumed - ZCODE is the ASCII code of either lower or */\n/*        upper case 'Z'. */\n\n\tif (inta >= 97 && inta <= 122) {\n\t    inta += -32;\n\t}\n\tif (intb >= 97 && intb <= 122) {\n\t    intb += -32;\n\t}\n\n    } else if (zcode == 233 || zcode == 169) {\n\n/*        EBCDIC is assumed - ZCODE is the EBCDIC code of either lower or */\n/*        upper case 'Z'. */\n\n\tif ((inta >= 129 && inta <= 137) || (inta >= 145 && inta <= 153) || \n            (inta >= 162 && inta <= 169)) {\n\t    inta += 64;\n\t}\n\tif ((intb >= 129 && intb <= 137) || (intb >= 145 && intb <= 153) || \n            (intb >= 162 && intb <= 169)) {\n\t    intb += 64;\n\t}\n\n    } else if (zcode == 218 || zcode == 250) {\n\n/*        ASCII is assumed, on Prime machines - ZCODE is the ASCII code */\n/*        plus 128 of either lower or upper case 'Z'. */\n\n\tif (inta >= 225 && inta <= 250) {\n\t    inta += -32;\n\t}\n\tif (intb >= 225 && intb <= 250) {\n\t    intb += -32;\n\t}\n    }\n    ret_val = inta == intb;\n\n/*     RETURN */\n\n/*     End of LSAME */\n\n    return ret_val;\n} /* lsame_ */\n\n"
  },
  {
    "path": "include/eigen3/blas/f2c/r_cnjg.c",
    "content": "#include \"datatypes.h\"    \n\nvoid r_cnjg(complex *r, complex *z) {\n    r->r = z->r;\n    r->i = -(z->i);\n}\n"
  },
  {
    "path": "include/eigen3/blas/f2c/srotm.c",
    "content": "/* srotm.f -- translated by f2c (version 20100827).\n   You must link the resulting object file with libf2c:\n\ton Microsoft Windows system, link with libf2c.lib;\n\ton Linux or Unix systems, link with .../path/to/libf2c.a -lm\n\tor, if you install libf2c.a in a standard place, with -lf2c -lm\n\t-- in that order, at the end of the command line, as in\n\t\tcc *.o -lf2c -lm\n\tSource for libf2c is in /netlib/f2c/libf2c.zip, e.g.,\n\n\t\thttp://www.netlib.org/f2c/libf2c.zip\n*/\n\n#include \"datatypes.h\"\n\n/* Subroutine */ int srotm_(integer *n, real *sx, integer *incx, real *sy, \n\tinteger *incy, real *sparam)\n{\n    /* Initialized data */\n\n    static real zero = 0.f;\n    static real two = 2.f;\n\n    /* System generated locals */\n    integer i__1, i__2;\n\n    /* Local variables */\n    integer i__;\n    real w, z__;\n    integer kx, ky;\n    real sh11, sh12, sh21, sh22, sflag;\n    integer nsteps;\n\n/*     .. Scalar Arguments .. */\n/*     .. */\n/*     .. Array Arguments .. */\n/*     .. */\n\n/*  Purpose */\n/*  ======= */\n\n/*     APPLY THE MODIFIED GIVENS TRANSFORMATION, H, TO THE 2 BY N MATRIX */\n\n/*     (SX**T) , WHERE **T INDICATES TRANSPOSE. THE ELEMENTS OF SX ARE IN */\n/*     (DX**T) */\n\n/*     SX(LX+I*INCX), I = 0 TO N-1, WHERE LX = 1 IF INCX .GE. 0, ELSE */\n/*     LX = (-INCX)*N, AND SIMILARLY FOR SY USING USING LY AND INCY. */\n/*     WITH SPARAM(1)=SFLAG, H HAS ONE OF THE FOLLOWING FORMS.. */\n\n/*     SFLAG=-1.E0     SFLAG=0.E0        SFLAG=1.E0     SFLAG=-2.E0 */\n\n/*       (SH11  SH12)    (1.E0  SH12)    (SH11  1.E0)    (1.E0  0.E0) */\n/*     H=(          )    (          )    (          )    (          ) */\n/*       (SH21  SH22),   (SH21  1.E0),   (-1.E0 SH22),   (0.E0  1.E0). */\n/*     SEE  SROTMG FOR A DESCRIPTION OF DATA STORAGE IN SPARAM. */\n\n\n/*  Arguments */\n/*  ========= */\n\n/*  N      (input) INTEGER */\n/*         number of elements in input vector(s) */\n\n/*  SX     (input/output) REAL array, dimension N */\n/*         double precision vector with N elements */\n\n/*  INCX   (input) INTEGER */\n/*         storage spacing between elements of SX */\n\n/*  SY     (input/output) REAL array, dimension N */\n/*         double precision vector with N elements */\n\n/*  INCY   (input) INTEGER */\n/*         storage spacing between elements of SY */\n\n/*  SPARAM (input/output)  REAL array, dimension 5 */\n/*     SPARAM(1)=SFLAG */\n/*     SPARAM(2)=SH11 */\n/*     SPARAM(3)=SH21 */\n/*     SPARAM(4)=SH12 */\n/*     SPARAM(5)=SH22 */\n\n/*  ===================================================================== */\n\n/*     .. Local Scalars .. */\n/*     .. */\n/*     .. Data statements .. */\n    /* Parameter adjustments */\n    --sparam;\n    --sy;\n    --sx;\n\n    /* Function Body */\n/*     .. */\n\n    sflag = sparam[1];\n    if (*n <= 0 || sflag + two == zero) {\n\tgoto L140;\n    }\n    if (! (*incx == *incy && *incx > 0)) {\n\tgoto L70;\n    }\n\n    nsteps = *n * *incx;\n    if (sflag < 0.f) {\n\tgoto L50;\n    } else if (sflag == 0) {\n\tgoto L10;\n    } else {\n\tgoto L30;\n    }\nL10:\n    sh12 = sparam[4];\n    sh21 = sparam[3];\n    i__1 = nsteps;\n    i__2 = *incx;\n    for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {\n\tw = sx[i__];\n\tz__ = sy[i__];\n\tsx[i__] = w + z__ * sh12;\n\tsy[i__] = w * sh21 + z__;\n/* L20: */\n    }\n    goto L140;\nL30:\n    sh11 = sparam[2];\n    sh22 = sparam[5];\n    i__2 = nsteps;\n    i__1 = *incx;\n    for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) {\n\tw = sx[i__];\n\tz__ = sy[i__];\n\tsx[i__] = w * sh11 + z__;\n\tsy[i__] = -w + sh22 * z__;\n/* L40: */\n    }\n    goto L140;\nL50:\n    sh11 = sparam[2];\n    sh12 = sparam[4];\n    sh21 = sparam[3];\n    sh22 = sparam[5];\n    i__1 = nsteps;\n    i__2 = *incx;\n    for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {\n\tw = sx[i__];\n\tz__ = sy[i__];\n\tsx[i__] = w * sh11 + z__ * sh12;\n\tsy[i__] = w * sh21 + z__ * sh22;\n/* L60: */\n    }\n    goto L140;\nL70:\n    kx = 1;\n    ky = 1;\n    if (*incx < 0) {\n\tkx = (1 - *n) * *incx + 1;\n    }\n    if (*incy < 0) {\n\tky = (1 - *n) * *incy + 1;\n    }\n\n    if (sflag < 0.f) {\n\tgoto L120;\n    } else if (sflag == 0) {\n\tgoto L80;\n    } else {\n\tgoto L100;\n    }\nL80:\n    sh12 = sparam[4];\n    sh21 = sparam[3];\n    i__2 = *n;\n    for (i__ = 1; i__ <= i__2; ++i__) {\n\tw = sx[kx];\n\tz__ = sy[ky];\n\tsx[kx] = w + z__ * sh12;\n\tsy[ky] = w * sh21 + z__;\n\tkx += *incx;\n\tky += *incy;\n/* L90: */\n    }\n    goto L140;\nL100:\n    sh11 = sparam[2];\n    sh22 = sparam[5];\n    i__2 = *n;\n    for (i__ = 1; i__ <= i__2; ++i__) {\n\tw = sx[kx];\n\tz__ = sy[ky];\n\tsx[kx] = w * sh11 + z__;\n\tsy[ky] = -w + sh22 * z__;\n\tkx += *incx;\n\tky += *incy;\n/* L110: */\n    }\n    goto L140;\nL120:\n    sh11 = sparam[2];\n    sh12 = sparam[4];\n    sh21 = sparam[3];\n    sh22 = sparam[5];\n    i__2 = *n;\n    for (i__ = 1; i__ <= i__2; ++i__) {\n\tw = sx[kx];\n\tz__ = sy[ky];\n\tsx[kx] = w * sh11 + z__ * sh12;\n\tsy[ky] = w * sh21 + z__ * sh22;\n\tkx += *incx;\n\tky += *incy;\n/* L130: */\n    }\nL140:\n    return 0;\n} /* srotm_ */\n\n"
  },
  {
    "path": "include/eigen3/blas/f2c/srotmg.c",
    "content": "/* srotmg.f -- translated by f2c (version 20100827).\n   You must link the resulting object file with libf2c:\n\ton Microsoft Windows system, link with libf2c.lib;\n\ton Linux or Unix systems, link with .../path/to/libf2c.a -lm\n\tor, if you install libf2c.a in a standard place, with -lf2c -lm\n\t-- in that order, at the end of the command line, as in\n\t\tcc *.o -lf2c -lm\n\tSource for libf2c is in /netlib/f2c/libf2c.zip, e.g.,\n\n\t\thttp://www.netlib.org/f2c/libf2c.zip\n*/\n\n#include \"datatypes.h\"\n\n/* Subroutine */ int srotmg_(real *sd1, real *sd2, real *sx1, real *sy1, real \n\t*sparam)\n{\n    /* Initialized data */\n\n    static real zero = 0.f;\n    static real one = 1.f;\n    static real two = 2.f;\n    static real gam = 4096.f;\n    static real gamsq = 16777200.f;\n    static real rgamsq = 5.96046e-8f;\n\n    /* Format strings */\n    static char fmt_120[] = \"\";\n    static char fmt_150[] = \"\";\n    static char fmt_180[] = \"\";\n    static char fmt_210[] = \"\";\n\n    /* System generated locals */\n    real r__1;\n\n    /* Local variables */\n    real su, sp1, sp2, sq1, sq2, sh11, sh12, sh21, sh22;\n    integer igo;\n    real sflag, stemp;\n\n    /* Assigned format variables */\n    static char *igo_fmt;\n\n/*     .. Scalar Arguments .. */\n/*     .. */\n/*     .. Array Arguments .. */\n/*     .. */\n\n/*  Purpose */\n/*  ======= */\n\n/*     CONSTRUCT THE MODIFIED GIVENS TRANSFORMATION MATRIX H WHICH ZEROS */\n/*     THE SECOND COMPONENT OF THE 2-VECTOR  (SQRT(SD1)*SX1,SQRT(SD2)* */\n/*     SY2)**T. */\n/*     WITH SPARAM(1)=SFLAG, H HAS ONE OF THE FOLLOWING FORMS.. */\n\n/*     SFLAG=-1.E0     SFLAG=0.E0        SFLAG=1.E0     SFLAG=-2.E0 */\n\n/*       (SH11  SH12)    (1.E0  SH12)    (SH11  1.E0)    (1.E0  0.E0) */\n/*     H=(          )    (          )    (          )    (          ) */\n/*       (SH21  SH22),   (SH21  1.E0),   (-1.E0 SH22),   (0.E0  1.E0). */\n/*     LOCATIONS 2-4 OF SPARAM CONTAIN SH11,SH21,SH12, AND SH22 */\n/*     RESPECTIVELY. (VALUES OF 1.E0, -1.E0, OR 0.E0 IMPLIED BY THE */\n/*     VALUE OF SPARAM(1) ARE NOT STORED IN SPARAM.) */\n\n/*     THE VALUES OF GAMSQ AND RGAMSQ SET IN THE DATA STATEMENT MAY BE */\n/*     INEXACT.  THIS IS OK AS THEY ARE ONLY USED FOR TESTING THE SIZE */\n/*     OF SD1 AND SD2.  ALL ACTUAL SCALING OF DATA IS DONE USING GAM. */\n\n\n/*  Arguments */\n/*  ========= */\n\n\n/*  SD1    (input/output) REAL */\n\n/*  SD2    (input/output) REAL */\n\n/*  SX1    (input/output) REAL */\n\n/*  SY1    (input) REAL */\n\n\n/*  SPARAM (input/output)  REAL array, dimension 5 */\n/*     SPARAM(1)=SFLAG */\n/*     SPARAM(2)=SH11 */\n/*     SPARAM(3)=SH21 */\n/*     SPARAM(4)=SH12 */\n/*     SPARAM(5)=SH22 */\n\n/*  ===================================================================== */\n\n/*     .. Local Scalars .. */\n/*     .. */\n/*     .. Intrinsic Functions .. */\n/*     .. */\n/*     .. Data statements .. */\n\n    /* Parameter adjustments */\n    --sparam;\n\n    /* Function Body */\n/*     .. */\n    if (! (*sd1 < zero)) {\n\tgoto L10;\n    }\n/*       GO ZERO-H-D-AND-SX1.. */\n    goto L60;\nL10:\n/*     CASE-SD1-NONNEGATIVE */\n    sp2 = *sd2 * *sy1;\n    if (! (sp2 == zero)) {\n\tgoto L20;\n    }\n    sflag = -two;\n    goto L260;\n/*     REGULAR-CASE.. */\nL20:\n    sp1 = *sd1 * *sx1;\n    sq2 = sp2 * *sy1;\n    sq1 = sp1 * *sx1;\n\n    if (! (dabs(sq1) > dabs(sq2))) {\n\tgoto L40;\n    }\n    sh21 = -(*sy1) / *sx1;\n    sh12 = sp2 / sp1;\n\n    su = one - sh12 * sh21;\n\n    if (! (su <= zero)) {\n\tgoto L30;\n    }\n/*         GO ZERO-H-D-AND-SX1.. */\n    goto L60;\nL30:\n    sflag = zero;\n    *sd1 /= su;\n    *sd2 /= su;\n    *sx1 *= su;\n/*         GO SCALE-CHECK.. */\n    goto L100;\nL40:\n    if (! (sq2 < zero)) {\n\tgoto L50;\n    }\n/*         GO ZERO-H-D-AND-SX1.. */\n    goto L60;\nL50:\n    sflag = one;\n    sh11 = sp1 / sp2;\n    sh22 = *sx1 / *sy1;\n    su = one + sh11 * sh22;\n    stemp = *sd2 / su;\n    *sd2 = *sd1 / su;\n    *sd1 = stemp;\n    *sx1 = *sy1 * su;\n/*         GO SCALE-CHECK */\n    goto L100;\n/*     PROCEDURE..ZERO-H-D-AND-SX1.. */\nL60:\n    sflag = -one;\n    sh11 = zero;\n    sh12 = zero;\n    sh21 = zero;\n    sh22 = zero;\n\n    *sd1 = zero;\n    *sd2 = zero;\n    *sx1 = zero;\n/*         RETURN.. */\n    goto L220;\n/*     PROCEDURE..FIX-H.. */\nL70:\n    if (! (sflag >= zero)) {\n\tgoto L90;\n    }\n\n    if (! (sflag == zero)) {\n\tgoto L80;\n    }\n    sh11 = one;\n    sh22 = one;\n    sflag = -one;\n    goto L90;\nL80:\n    sh21 = -one;\n    sh12 = one;\n    sflag = -one;\nL90:\n    switch (igo) {\n\tcase 0: goto L120;\n\tcase 1: goto L150;\n\tcase 2: goto L180;\n\tcase 3: goto L210;\n    }\n/*     PROCEDURE..SCALE-CHECK */\nL100:\nL110:\n    if (! (*sd1 <= rgamsq)) {\n\tgoto L130;\n    }\n    if (*sd1 == zero) {\n\tgoto L160;\n    }\n    igo = 0;\n    igo_fmt = fmt_120;\n/*              FIX-H.. */\n    goto L70;\nL120:\n/* Computing 2nd power */\n    r__1 = gam;\n    *sd1 *= r__1 * r__1;\n    *sx1 /= gam;\n    sh11 /= gam;\n    sh12 /= gam;\n    goto L110;\nL130:\nL140:\n    if (! (*sd1 >= gamsq)) {\n\tgoto L160;\n    }\n    igo = 1;\n    igo_fmt = fmt_150;\n/*              FIX-H.. */\n    goto L70;\nL150:\n/* Computing 2nd power */\n    r__1 = gam;\n    *sd1 /= r__1 * r__1;\n    *sx1 *= gam;\n    sh11 *= gam;\n    sh12 *= gam;\n    goto L140;\nL160:\nL170:\n    if (! (dabs(*sd2) <= rgamsq)) {\n\tgoto L190;\n    }\n    if (*sd2 == zero) {\n\tgoto L220;\n    }\n    igo = 2;\n    igo_fmt = fmt_180;\n/*              FIX-H.. */\n    goto L70;\nL180:\n/* Computing 2nd power */\n    r__1 = gam;\n    *sd2 *= r__1 * r__1;\n    sh21 /= gam;\n    sh22 /= gam;\n    goto L170;\nL190:\nL200:\n    if (! (dabs(*sd2) >= gamsq)) {\n\tgoto L220;\n    }\n    igo = 3;\n    igo_fmt = fmt_210;\n/*              FIX-H.. */\n    goto L70;\nL210:\n/* Computing 2nd power */\n    r__1 = gam;\n    *sd2 /= r__1 * r__1;\n    sh21 *= gam;\n    sh22 *= gam;\n    goto L200;\nL220:\n    if (sflag < 0.f) {\n\tgoto L250;\n    } else if (sflag == 0) {\n\tgoto L230;\n    } else {\n\tgoto L240;\n    }\nL230:\n    sparam[3] = sh21;\n    sparam[4] = sh12;\n    goto L260;\nL240:\n    sparam[2] = sh11;\n    sparam[5] = sh22;\n    goto L260;\nL250:\n    sparam[2] = sh11;\n    sparam[3] = sh21;\n    sparam[4] = sh12;\n    sparam[5] = sh22;\nL260:\n    sparam[1] = sflag;\n    return 0;\n} /* srotmg_ */\n\n"
  },
  {
    "path": "include/eigen3/blas/f2c/ssbmv.c",
    "content": "/* ssbmv.f -- translated by f2c (version 20100827).\n   You must link the resulting object file with libf2c:\n\ton Microsoft Windows system, link with libf2c.lib;\n\ton Linux or Unix systems, link with .../path/to/libf2c.a -lm\n\tor, if you install libf2c.a in a standard place, with -lf2c -lm\n\t-- in that order, at the end of the command line, as in\n\t\tcc *.o -lf2c -lm\n\tSource for libf2c is in /netlib/f2c/libf2c.zip, e.g.,\n\n\t\thttp://www.netlib.org/f2c/libf2c.zip\n*/\n\n#include \"datatypes.h\"\n\n/* Subroutine */ int ssbmv_(char *uplo, integer *n, integer *k, real *alpha, \n\treal *a, integer *lda, real *x, integer *incx, real *beta, real *y, \n\tinteger *incy, ftnlen uplo_len)\n{\n    /* System generated locals */\n    integer a_dim1, a_offset, i__1, i__2, i__3, i__4;\n\n    /* Local variables */\n    integer i__, j, l, ix, iy, jx, jy, kx, ky, info;\n    real temp1, temp2;\n    extern logical lsame_(char *, char *, ftnlen, ftnlen);\n    integer kplus1;\n    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);\n\n/*     .. Scalar Arguments .. */\n/*     .. */\n/*     .. Array Arguments .. */\n/*     .. */\n\n/*  Purpose */\n/*  ======= */\n\n/*  SSBMV  performs the matrix-vector  operation */\n\n/*     y := alpha*A*x + beta*y, */\n\n/*  where alpha and beta are scalars, x and y are n element vectors and */\n/*  A is an n by n symmetric band matrix, with k super-diagonals. */\n\n/*  Arguments */\n/*  ========== */\n\n/*  UPLO   - CHARACTER*1. */\n/*           On entry, UPLO specifies whether the upper or lower */\n/*           triangular part of the band matrix A is being supplied as */\n/*           follows: */\n\n/*              UPLO = 'U' or 'u'   The upper triangular part of A is */\n/*                                  being supplied. */\n\n/*              UPLO = 'L' or 'l'   The lower triangular part of A is */\n/*                                  being supplied. */\n\n/*           Unchanged on exit. */\n\n/*  N      - INTEGER. */\n/*           On entry, N specifies the order of the matrix A. */\n/*           N must be at least zero. */\n/*           Unchanged on exit. */\n\n/*  K      - INTEGER. */\n/*           On entry, K specifies the number of super-diagonals of the */\n/*           matrix A. K must satisfy  0 .le. K. */\n/*           Unchanged on exit. */\n\n/*  ALPHA  - REAL            . */\n/*           On entry, ALPHA specifies the scalar alpha. */\n/*           Unchanged on exit. */\n\n/*  A      - REAL             array of DIMENSION ( LDA, n ). */\n/*           Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) */\n/*           by n part of the array A must contain the upper triangular */\n/*           band part of the symmetric matrix, supplied column by */\n/*           column, with the leading diagonal of the matrix in row */\n/*           ( k + 1 ) of the array, the first super-diagonal starting at */\n/*           position 2 in row k, and so on. The top left k by k triangle */\n/*           of the array A is not referenced. */\n/*           The following program segment will transfer the upper */\n/*           triangular part of a symmetric band matrix from conventional */\n/*           full matrix storage to band storage: */\n\n/*                 DO 20, J = 1, N */\n/*                    M = K + 1 - J */\n/*                    DO 10, I = MAX( 1, J - K ), J */\n/*                       A( M + I, J ) = matrix( I, J ) */\n/*              10    CONTINUE */\n/*              20 CONTINUE */\n\n/*           Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) */\n/*           by n part of the array A must contain the lower triangular */\n/*           band part of the symmetric matrix, supplied column by */\n/*           column, with the leading diagonal of the matrix in row 1 of */\n/*           the array, the first sub-diagonal starting at position 1 in */\n/*           row 2, and so on. The bottom right k by k triangle of the */\n/*           array A is not referenced. */\n/*           The following program segment will transfer the lower */\n/*           triangular part of a symmetric band matrix from conventional */\n/*           full matrix storage to band storage: */\n\n/*                 DO 20, J = 1, N */\n/*                    M = 1 - J */\n/*                    DO 10, I = J, MIN( N, J + K ) */\n/*                       A( M + I, J ) = matrix( I, J ) */\n/*              10    CONTINUE */\n/*              20 CONTINUE */\n\n/*           Unchanged on exit. */\n\n/*  LDA    - INTEGER. */\n/*           On entry, LDA specifies the first dimension of A as declared */\n/*           in the calling (sub) program. LDA must be at least */\n/*           ( k + 1 ). */\n/*           Unchanged on exit. */\n\n/*  X      - REAL             array of DIMENSION at least */\n/*           ( 1 + ( n - 1 )*abs( INCX ) ). */\n/*           Before entry, the incremented array X must contain the */\n/*           vector x. */\n/*           Unchanged on exit. */\n\n/*  INCX   - INTEGER. */\n/*           On entry, INCX specifies the increment for the elements of */\n/*           X. INCX must not be zero. */\n/*           Unchanged on exit. */\n\n/*  BETA   - REAL            . */\n/*           On entry, BETA specifies the scalar beta. */\n/*           Unchanged on exit. */\n\n/*  Y      - REAL             array of DIMENSION at least */\n/*           ( 1 + ( n - 1 )*abs( INCY ) ). */\n/*           Before entry, the incremented array Y must contain the */\n/*           vector y. On exit, Y is overwritten by the updated vector y. */\n\n/*  INCY   - INTEGER. */\n/*           On entry, INCY specifies the increment for the elements of */\n/*           Y. INCY must not be zero. */\n/*           Unchanged on exit. */\n\n/*  Further Details */\n/*  =============== */\n\n/*  Level 2 Blas routine. */\n\n/*  -- Written on 22-October-1986. */\n/*     Jack Dongarra, Argonne National Lab. */\n/*     Jeremy Du Croz, Nag Central Office. */\n/*     Sven Hammarling, Nag Central Office. */\n/*     Richard Hanson, Sandia National Labs. */\n\n/*  ===================================================================== */\n\n/*     .. Parameters .. */\n/*     .. */\n/*     .. Local Scalars .. */\n/*     .. */\n/*     .. External Functions .. */\n/*     .. */\n/*     .. External Subroutines .. */\n/*     .. */\n/*     .. Intrinsic Functions .. */\n/*     .. */\n\n/*     Test the input parameters. */\n\n    /* Parameter adjustments */\n    a_dim1 = *lda;\n    a_offset = 1 + a_dim1;\n    a -= a_offset;\n    --x;\n    --y;\n\n    /* Function Body */\n    info = 0;\n    if (! lsame_(uplo, \"U\", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, \"L\", (\n\t    ftnlen)1, (ftnlen)1)) {\n\tinfo = 1;\n    } else if (*n < 0) {\n\tinfo = 2;\n    } else if (*k < 0) {\n\tinfo = 3;\n    } else if (*lda < *k + 1) {\n\tinfo = 6;\n    } else if (*incx == 0) {\n\tinfo = 8;\n    } else if (*incy == 0) {\n\tinfo = 11;\n    }\n    if (info != 0) {\n\txerbla_(\"SSBMV \", &info, (ftnlen)6);\n\treturn 0;\n    }\n\n/*     Quick return if possible. */\n\n    if (*n == 0 || (*alpha == 0.f && *beta == 1.f)) {\n\treturn 0;\n    }\n\n/*     Set up the start points in  X  and  Y. */\n\n    if (*incx > 0) {\n\tkx = 1;\n    } else {\n\tkx = 1 - (*n - 1) * *incx;\n    }\n    if (*incy > 0) {\n\tky = 1;\n    } else {\n\tky = 1 - (*n - 1) * *incy;\n    }\n\n/*     Start the operations. In this version the elements of the array A */\n/*     are accessed sequentially with one pass through A. */\n\n/*     First form  y := beta*y. */\n\n    if (*beta != 1.f) {\n\tif (*incy == 1) {\n\t    if (*beta == 0.f) {\n\t\ti__1 = *n;\n\t\tfor (i__ = 1; i__ <= i__1; ++i__) {\n\t\t    y[i__] = 0.f;\n/* L10: */\n\t\t}\n\t    } else {\n\t\ti__1 = *n;\n\t\tfor (i__ = 1; i__ <= i__1; ++i__) {\n\t\t    y[i__] = *beta * y[i__];\n/* L20: */\n\t\t}\n\t    }\n\t} else {\n\t    iy = ky;\n\t    if (*beta == 0.f) {\n\t\ti__1 = *n;\n\t\tfor (i__ = 1; i__ <= i__1; ++i__) {\n\t\t    y[iy] = 0.f;\n\t\t    iy += *incy;\n/* L30: */\n\t\t}\n\t    } else {\n\t\ti__1 = *n;\n\t\tfor (i__ = 1; i__ <= i__1; ++i__) {\n\t\t    y[iy] = *beta * y[iy];\n\t\t    iy += *incy;\n/* L40: */\n\t\t}\n\t    }\n\t}\n    }\n    if (*alpha == 0.f) {\n\treturn 0;\n    }\n    if (lsame_(uplo, \"U\", (ftnlen)1, (ftnlen)1)) {\n\n/*        Form  y  when upper triangle of A is stored. */\n\n\tkplus1 = *k + 1;\n\tif (*incx == 1 && *incy == 1) {\n\t    i__1 = *n;\n\t    for (j = 1; j <= i__1; ++j) {\n\t\ttemp1 = *alpha * x[j];\n\t\ttemp2 = 0.f;\n\t\tl = kplus1 - j;\n/* Computing MAX */\n\t\ti__2 = 1, i__3 = j - *k;\n\t\ti__4 = j - 1;\n\t\tfor (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {\n\t\t    y[i__] += temp1 * a[l + i__ + j * a_dim1];\n\t\t    temp2 += a[l + i__ + j * a_dim1] * x[i__];\n/* L50: */\n\t\t}\n\t\ty[j] = y[j] + temp1 * a[kplus1 + j * a_dim1] + *alpha * temp2;\n/* L60: */\n\t    }\n\t} else {\n\t    jx = kx;\n\t    jy = ky;\n\t    i__1 = *n;\n\t    for (j = 1; j <= i__1; ++j) {\n\t\ttemp1 = *alpha * x[jx];\n\t\ttemp2 = 0.f;\n\t\tix = kx;\n\t\tiy = ky;\n\t\tl = kplus1 - j;\n/* Computing MAX */\n\t\ti__4 = 1, i__2 = j - *k;\n\t\ti__3 = j - 1;\n\t\tfor (i__ = max(i__4,i__2); i__ <= i__3; ++i__) {\n\t\t    y[iy] += temp1 * a[l + i__ + j * a_dim1];\n\t\t    temp2 += a[l + i__ + j * a_dim1] * x[ix];\n\t\t    ix += *incx;\n\t\t    iy += *incy;\n/* L70: */\n\t\t}\n\t\ty[jy] = y[jy] + temp1 * a[kplus1 + j * a_dim1] + *alpha * \n\t\t\ttemp2;\n\t\tjx += *incx;\n\t\tjy += *incy;\n\t\tif (j > *k) {\n\t\t    kx += *incx;\n\t\t    ky += *incy;\n\t\t}\n/* L80: */\n\t    }\n\t}\n    } else {\n\n/*        Form  y  when lower triangle of A is stored. */\n\n\tif (*incx == 1 && *incy == 1) {\n\t    i__1 = *n;\n\t    for (j = 1; j <= i__1; ++j) {\n\t\ttemp1 = *alpha * x[j];\n\t\ttemp2 = 0.f;\n\t\ty[j] += temp1 * a[j * a_dim1 + 1];\n\t\tl = 1 - j;\n/* Computing MIN */\n\t\ti__4 = *n, i__2 = j + *k;\n\t\ti__3 = min(i__4,i__2);\n\t\tfor (i__ = j + 1; i__ <= i__3; ++i__) {\n\t\t    y[i__] += temp1 * a[l + i__ + j * a_dim1];\n\t\t    temp2 += a[l + i__ + j * a_dim1] * x[i__];\n/* L90: */\n\t\t}\n\t\ty[j] += *alpha * temp2;\n/* L100: */\n\t    }\n\t} else {\n\t    jx = kx;\n\t    jy = ky;\n\t    i__1 = *n;\n\t    for (j = 1; j <= i__1; ++j) {\n\t\ttemp1 = *alpha * x[jx];\n\t\ttemp2 = 0.f;\n\t\ty[jy] += temp1 * a[j * a_dim1 + 1];\n\t\tl = 1 - j;\n\t\tix = jx;\n\t\tiy = jy;\n/* Computing MIN */\n\t\ti__4 = *n, i__2 = j + *k;\n\t\ti__3 = min(i__4,i__2);\n\t\tfor (i__ = j + 1; i__ <= i__3; ++i__) {\n\t\t    ix += *incx;\n\t\t    iy += *incy;\n\t\t    y[iy] += temp1 * a[l + i__ + j * a_dim1];\n\t\t    temp2 += a[l + i__ + j * a_dim1] * x[ix];\n/* L110: */\n\t\t}\n\t\ty[jy] += *alpha * temp2;\n\t\tjx += *incx;\n\t\tjy += *incy;\n/* L120: */\n\t    }\n\t}\n    }\n\n    return 0;\n\n/*     End of SSBMV . */\n\n} /* ssbmv_ */\n\n"
  },
  {
    "path": "include/eigen3/blas/f2c/sspmv.c",
    "content": "/* sspmv.f -- translated by f2c (version 20100827).\n   You must link the resulting object file with libf2c:\n\ton Microsoft Windows system, link with libf2c.lib;\n\ton Linux or Unix systems, link with .../path/to/libf2c.a -lm\n\tor, if you install libf2c.a in a standard place, with -lf2c -lm\n\t-- in that order, at the end of the command line, as in\n\t\tcc *.o -lf2c -lm\n\tSource for libf2c is in /netlib/f2c/libf2c.zip, e.g.,\n\n\t\thttp://www.netlib.org/f2c/libf2c.zip\n*/\n\n#include \"datatypes.h\"\n\n/* Subroutine */ int sspmv_(char *uplo, integer *n, real *alpha, real *ap, \n\treal *x, integer *incx, real *beta, real *y, integer *incy, ftnlen \n\tuplo_len)\n{\n    /* System generated locals */\n    integer i__1, i__2;\n\n    /* Local variables */\n    integer i__, j, k, kk, ix, iy, jx, jy, kx, ky, info;\n    real temp1, temp2;\n    extern logical lsame_(char *, char *, ftnlen, ftnlen);\n    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);\n\n/*     .. Scalar Arguments .. */\n/*     .. */\n/*     .. Array Arguments .. */\n/*     .. */\n\n/*  Purpose */\n/*  ======= */\n\n/*  SSPMV  performs the matrix-vector operation */\n\n/*     y := alpha*A*x + beta*y, */\n\n/*  where alpha and beta are scalars, x and y are n element vectors and */\n/*  A is an n by n symmetric matrix, supplied in packed form. */\n\n/*  Arguments */\n/*  ========== */\n\n/*  UPLO   - CHARACTER*1. */\n/*           On entry, UPLO specifies whether the upper or lower */\n/*           triangular part of the matrix A is supplied in the packed */\n/*           array AP as follows: */\n\n/*              UPLO = 'U' or 'u'   The upper triangular part of A is */\n/*                                  supplied in AP. */\n\n/*              UPLO = 'L' or 'l'   The lower triangular part of A is */\n/*                                  supplied in AP. */\n\n/*           Unchanged on exit. */\n\n/*  N      - INTEGER. */\n/*           On entry, N specifies the order of the matrix A. */\n/*           N must be at least zero. */\n/*           Unchanged on exit. */\n\n/*  ALPHA  - REAL            . */\n/*           On entry, ALPHA specifies the scalar alpha. */\n/*           Unchanged on exit. */\n\n/*  AP     - REAL             array of DIMENSION at least */\n/*           ( ( n*( n + 1 ) )/2 ). */\n/*           Before entry with UPLO = 'U' or 'u', the array AP must */\n/*           contain the upper triangular part of the symmetric matrix */\n/*           packed sequentially, column by column, so that AP( 1 ) */\n/*           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) */\n/*           and a( 2, 2 ) respectively, and so on. */\n/*           Before entry with UPLO = 'L' or 'l', the array AP must */\n/*           contain the lower triangular part of the symmetric matrix */\n/*           packed sequentially, column by column, so that AP( 1 ) */\n/*           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) */\n/*           and a( 3, 1 ) respectively, and so on. */\n/*           Unchanged on exit. */\n\n/*  X      - REAL             array of dimension at least */\n/*           ( 1 + ( n - 1 )*abs( INCX ) ). */\n/*           Before entry, the incremented array X must contain the n */\n/*           element vector x. */\n/*           Unchanged on exit. */\n\n/*  INCX   - INTEGER. */\n/*           On entry, INCX specifies the increment for the elements of */\n/*           X. INCX must not be zero. */\n/*           Unchanged on exit. */\n\n/*  BETA   - REAL            . */\n/*           On entry, BETA specifies the scalar beta. When BETA is */\n/*           supplied as zero then Y need not be set on input. */\n/*           Unchanged on exit. */\n\n/*  Y      - REAL             array of dimension at least */\n/*           ( 1 + ( n - 1 )*abs( INCY ) ). */\n/*           Before entry, the incremented array Y must contain the n */\n/*           element vector y. On exit, Y is overwritten by the updated */\n/*           vector y. */\n\n/*  INCY   - INTEGER. */\n/*           On entry, INCY specifies the increment for the elements of */\n/*           Y. INCY must not be zero. */\n/*           Unchanged on exit. */\n\n/*  Further Details */\n/*  =============== */\n\n/*  Level 2 Blas routine. */\n\n/*  -- Written on 22-October-1986. */\n/*     Jack Dongarra, Argonne National Lab. */\n/*     Jeremy Du Croz, Nag Central Office. */\n/*     Sven Hammarling, Nag Central Office. */\n/*     Richard Hanson, Sandia National Labs. */\n\n/*  ===================================================================== */\n\n/*     .. Parameters .. */\n/*     .. */\n/*     .. Local Scalars .. */\n/*     .. */\n/*     .. External Functions .. */\n/*     .. */\n/*     .. External Subroutines .. */\n/*     .. */\n\n/*     Test the input parameters. */\n\n    /* Parameter adjustments */\n    --y;\n    --x;\n    --ap;\n\n    /* Function Body */\n    info = 0;\n    if (! lsame_(uplo, \"U\", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, \"L\", (\n\t    ftnlen)1, (ftnlen)1)) {\n\tinfo = 1;\n    } else if (*n < 0) {\n\tinfo = 2;\n    } else if (*incx == 0) {\n\tinfo = 6;\n    } else if (*incy == 0) {\n\tinfo = 9;\n    }\n    if (info != 0) {\n\txerbla_(\"SSPMV \", &info, (ftnlen)6);\n\treturn 0;\n    }\n\n/*     Quick return if possible. */\n\n    if (*n == 0 || (*alpha == 0.f && *beta == 1.f)) {\n\treturn 0;\n    }\n\n/*     Set up the start points in  X  and  Y. */\n\n    if (*incx > 0) {\n\tkx = 1;\n    } else {\n\tkx = 1 - (*n - 1) * *incx;\n    }\n    if (*incy > 0) {\n\tky = 1;\n    } else {\n\tky = 1 - (*n - 1) * *incy;\n    }\n\n/*     Start the operations. In this version the elements of the array AP */\n/*     are accessed sequentially with one pass through AP. */\n\n/*     First form  y := beta*y. */\n\n    if (*beta != 1.f) {\n\tif (*incy == 1) {\n\t    if (*beta == 0.f) {\n\t\ti__1 = *n;\n\t\tfor (i__ = 1; i__ <= i__1; ++i__) {\n\t\t    y[i__] = 0.f;\n/* L10: */\n\t\t}\n\t    } else {\n\t\ti__1 = *n;\n\t\tfor (i__ = 1; i__ <= i__1; ++i__) {\n\t\t    y[i__] = *beta * y[i__];\n/* L20: */\n\t\t}\n\t    }\n\t} else {\n\t    iy = ky;\n\t    if (*beta == 0.f) {\n\t\ti__1 = *n;\n\t\tfor (i__ = 1; i__ <= i__1; ++i__) {\n\t\t    y[iy] = 0.f;\n\t\t    iy += *incy;\n/* L30: */\n\t\t}\n\t    } else {\n\t\ti__1 = *n;\n\t\tfor (i__ = 1; i__ <= i__1; ++i__) {\n\t\t    y[iy] = *beta * y[iy];\n\t\t    iy += *incy;\n/* L40: */\n\t\t}\n\t    }\n\t}\n    }\n    if (*alpha == 0.f) {\n\treturn 0;\n    }\n    kk = 1;\n    if (lsame_(uplo, \"U\", (ftnlen)1, (ftnlen)1)) {\n\n/*        Form  y  when AP contains the upper triangle. */\n\n\tif (*incx == 1 && *incy == 1) {\n\t    i__1 = *n;\n\t    for (j = 1; j <= i__1; ++j) {\n\t\ttemp1 = *alpha * x[j];\n\t\ttemp2 = 0.f;\n\t\tk = kk;\n\t\ti__2 = j - 1;\n\t\tfor (i__ = 1; i__ <= i__2; ++i__) {\n\t\t    y[i__] += temp1 * ap[k];\n\t\t    temp2 += ap[k] * x[i__];\n\t\t    ++k;\n/* L50: */\n\t\t}\n\t\ty[j] = y[j] + temp1 * ap[kk + j - 1] + *alpha * temp2;\n\t\tkk += j;\n/* L60: */\n\t    }\n\t} else {\n\t    jx = kx;\n\t    jy = ky;\n\t    i__1 = *n;\n\t    for (j = 1; j <= i__1; ++j) {\n\t\ttemp1 = *alpha * x[jx];\n\t\ttemp2 = 0.f;\n\t\tix = kx;\n\t\tiy = ky;\n\t\ti__2 = kk + j - 2;\n\t\tfor (k = kk; k <= i__2; ++k) {\n\t\t    y[iy] += temp1 * ap[k];\n\t\t    temp2 += ap[k] * x[ix];\n\t\t    ix += *incx;\n\t\t    iy += *incy;\n/* L70: */\n\t\t}\n\t\ty[jy] = y[jy] + temp1 * ap[kk + j - 1] + *alpha * temp2;\n\t\tjx += *incx;\n\t\tjy += *incy;\n\t\tkk += j;\n/* L80: */\n\t    }\n\t}\n    } else {\n\n/*        Form  y  when AP contains the lower triangle. */\n\n\tif (*incx == 1 && *incy == 1) {\n\t    i__1 = *n;\n\t    for (j = 1; j <= i__1; ++j) {\n\t\ttemp1 = *alpha * x[j];\n\t\ttemp2 = 0.f;\n\t\ty[j] += temp1 * ap[kk];\n\t\tk = kk + 1;\n\t\ti__2 = *n;\n\t\tfor (i__ = j + 1; i__ <= i__2; ++i__) {\n\t\t    y[i__] += temp1 * ap[k];\n\t\t    temp2 += ap[k] * x[i__];\n\t\t    ++k;\n/* L90: */\n\t\t}\n\t\ty[j] += *alpha * temp2;\n\t\tkk += *n - j + 1;\n/* L100: */\n\t    }\n\t} else {\n\t    jx = kx;\n\t    jy = ky;\n\t    i__1 = *n;\n\t    for (j = 1; j <= i__1; ++j) {\n\t\ttemp1 = *alpha * x[jx];\n\t\ttemp2 = 0.f;\n\t\ty[jy] += temp1 * ap[kk];\n\t\tix = jx;\n\t\tiy = jy;\n\t\ti__2 = kk + *n - j;\n\t\tfor (k = kk + 1; k <= i__2; ++k) {\n\t\t    ix += *incx;\n\t\t    iy += *incy;\n\t\t    y[iy] += temp1 * ap[k];\n\t\t    temp2 += ap[k] * x[ix];\n/* L110: */\n\t\t}\n\t\ty[jy] += *alpha * temp2;\n\t\tjx += *incx;\n\t\tjy += *incy;\n\t\tkk += *n - j + 1;\n/* L120: */\n\t    }\n\t}\n    }\n\n    return 0;\n\n/*     End of SSPMV . */\n\n} /* sspmv_ */\n\n"
  },
  {
    "path": "include/eigen3/blas/f2c/stbmv.c",
    "content": "/* stbmv.f -- translated by f2c (version 20100827).\n   You must link the resulting object file with libf2c:\n\ton Microsoft Windows system, link with libf2c.lib;\n\ton Linux or Unix systems, link with .../path/to/libf2c.a -lm\n\tor, if you install libf2c.a in a standard place, with -lf2c -lm\n\t-- in that order, at the end of the command line, as in\n\t\tcc *.o -lf2c -lm\n\tSource for libf2c is in /netlib/f2c/libf2c.zip, e.g.,\n\n\t\thttp://www.netlib.org/f2c/libf2c.zip\n*/\n\n#include \"datatypes.h\"\n\n/* Subroutine */ int stbmv_(char *uplo, char *trans, char *diag, integer *n, \n\tinteger *k, real *a, integer *lda, real *x, integer *incx, ftnlen \n\tuplo_len, ftnlen trans_len, ftnlen diag_len)\n{\n    /* System generated locals */\n    integer a_dim1, a_offset, i__1, i__2, i__3, i__4;\n\n    /* Local variables */\n    integer i__, j, l, ix, jx, kx, info;\n    real temp;\n    extern logical lsame_(char *, char *, ftnlen, ftnlen);\n    integer kplus1;\n    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);\n    logical nounit;\n\n/*     .. Scalar Arguments .. */\n/*     .. */\n/*     .. Array Arguments .. */\n/*     .. */\n\n/*  Purpose */\n/*  ======= */\n\n/*  STBMV  performs one of the matrix-vector operations */\n\n/*     x := A*x,   or   x := A'*x, */\n\n/*  where x is an n element vector and  A is an n by n unit, or non-unit, */\n/*  upper or lower triangular band matrix, with ( k + 1 ) diagonals. */\n\n/*  Arguments */\n/*  ========== */\n\n/*  UPLO   - CHARACTER*1. */\n/*           On entry, UPLO specifies whether the matrix is an upper or */\n/*           lower triangular matrix as follows: */\n\n/*              UPLO = 'U' or 'u'   A is an upper triangular matrix. */\n\n/*              UPLO = 'L' or 'l'   A is a lower triangular matrix. */\n\n/*           Unchanged on exit. */\n\n/*  TRANS  - CHARACTER*1. */\n/*           On entry, TRANS specifies the operation to be performed as */\n/*           follows: */\n\n/*              TRANS = 'N' or 'n'   x := A*x. */\n\n/*              TRANS = 'T' or 't'   x := A'*x. */\n\n/*              TRANS = 'C' or 'c'   x := A'*x. */\n\n/*           Unchanged on exit. */\n\n/*  DIAG   - CHARACTER*1. */\n/*           On entry, DIAG specifies whether or not A is unit */\n/*           triangular as follows: */\n\n/*              DIAG = 'U' or 'u'   A is assumed to be unit triangular. */\n\n/*              DIAG = 'N' or 'n'   A is not assumed to be unit */\n/*                                  triangular. */\n\n/*           Unchanged on exit. */\n\n/*  N      - INTEGER. */\n/*           On entry, N specifies the order of the matrix A. */\n/*           N must be at least zero. */\n/*           Unchanged on exit. */\n\n/*  K      - INTEGER. */\n/*           On entry with UPLO = 'U' or 'u', K specifies the number of */\n/*           super-diagonals of the matrix A. */\n/*           On entry with UPLO = 'L' or 'l', K specifies the number of */\n/*           sub-diagonals of the matrix A. */\n/*           K must satisfy  0 .le. K. */\n/*           Unchanged on exit. */\n\n/*  A      - REAL             array of DIMENSION ( LDA, n ). */\n/*           Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) */\n/*           by n part of the array A must contain the upper triangular */\n/*           band part of the matrix of coefficients, supplied column by */\n/*           column, with the leading diagonal of the matrix in row */\n/*           ( k + 1 ) of the array, the first super-diagonal starting at */\n/*           position 2 in row k, and so on. The top left k by k triangle */\n/*           of the array A is not referenced. */\n/*           The following program segment will transfer an upper */\n/*           triangular band matrix from conventional full matrix storage */\n/*           to band storage: */\n\n/*                 DO 20, J = 1, N */\n/*                    M = K + 1 - J */\n/*                    DO 10, I = MAX( 1, J - K ), J */\n/*                       A( M + I, J ) = matrix( I, J ) */\n/*              10    CONTINUE */\n/*              20 CONTINUE */\n\n/*           Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) */\n/*           by n part of the array A must contain the lower triangular */\n/*           band part of the matrix of coefficients, supplied column by */\n/*           column, with the leading diagonal of the matrix in row 1 of */\n/*           the array, the first sub-diagonal starting at position 1 in */\n/*           row 2, and so on. The bottom right k by k triangle of the */\n/*           array A is not referenced. */\n/*           The following program segment will transfer a lower */\n/*           triangular band matrix from conventional full matrix storage */\n/*           to band storage: */\n\n/*                 DO 20, J = 1, N */\n/*                    M = 1 - J */\n/*                    DO 10, I = J, MIN( N, J + K ) */\n/*                       A( M + I, J ) = matrix( I, J ) */\n/*              10    CONTINUE */\n/*              20 CONTINUE */\n\n/*           Note that when DIAG = 'U' or 'u' the elements of the array A */\n/*           corresponding to the diagonal elements of the matrix are not */\n/*           referenced, but are assumed to be unity. */\n/*           Unchanged on exit. */\n\n/*  LDA    - INTEGER. */\n/*           On entry, LDA specifies the first dimension of A as declared */\n/*           in the calling (sub) program. LDA must be at least */\n/*           ( k + 1 ). */\n/*           Unchanged on exit. */\n\n/*  X      - REAL             array of dimension at least */\n/*           ( 1 + ( n - 1 )*abs( INCX ) ). */\n/*           Before entry, the incremented array X must contain the n */\n/*           element vector x. On exit, X is overwritten with the */\n/*           tranformed vector x. */\n\n/*  INCX   - INTEGER. */\n/*           On entry, INCX specifies the increment for the elements of */\n/*           X. INCX must not be zero. */\n/*           Unchanged on exit. */\n\n/*  Further Details */\n/*  =============== */\n\n/*  Level 2 Blas routine. */\n\n/*  -- Written on 22-October-1986. */\n/*     Jack Dongarra, Argonne National Lab. */\n/*     Jeremy Du Croz, Nag Central Office. */\n/*     Sven Hammarling, Nag Central Office. */\n/*     Richard Hanson, Sandia National Labs. */\n\n/*  ===================================================================== */\n\n/*     .. Parameters .. */\n/*     .. */\n/*     .. Local Scalars .. */\n/*     .. */\n/*     .. External Functions .. */\n/*     .. */\n/*     .. External Subroutines .. */\n/*     .. */\n/*     .. Intrinsic Functions .. */\n/*     .. */\n\n/*     Test the input parameters. */\n\n    /* Parameter adjustments */\n    a_dim1 = *lda;\n    a_offset = 1 + a_dim1;\n    a -= a_offset;\n    --x;\n\n    /* Function Body */\n    info = 0;\n    if (! lsame_(uplo, \"U\", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, \"L\", (\n\t    ftnlen)1, (ftnlen)1)) {\n\tinfo = 1;\n    } else if (! lsame_(trans, \"N\", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, \n\t    \"T\", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, \"C\", (ftnlen)1, (\n\t    ftnlen)1)) {\n\tinfo = 2;\n    } else if (! lsame_(diag, \"U\", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, \n\t    \"N\", (ftnlen)1, (ftnlen)1)) {\n\tinfo = 3;\n    } else if (*n < 0) {\n\tinfo = 4;\n    } else if (*k < 0) {\n\tinfo = 5;\n    } else if (*lda < *k + 1) {\n\tinfo = 7;\n    } else if (*incx == 0) {\n\tinfo = 9;\n    }\n    if (info != 0) {\n\txerbla_(\"STBMV \", &info, (ftnlen)6);\n\treturn 0;\n    }\n\n/*     Quick return if possible. */\n\n    if (*n == 0) {\n\treturn 0;\n    }\n\n    nounit = lsame_(diag, \"N\", (ftnlen)1, (ftnlen)1);\n\n/*     Set up the start point in X if the increment is not unity. This */\n/*     will be  ( N - 1 )*INCX   too small for descending loops. */\n\n    if (*incx <= 0) {\n\tkx = 1 - (*n - 1) * *incx;\n    } else if (*incx != 1) {\n\tkx = 1;\n    }\n\n/*     Start the operations. In this version the elements of A are */\n/*     accessed sequentially with one pass through A. */\n\n    if (lsame_(trans, \"N\", (ftnlen)1, (ftnlen)1)) {\n\n/*         Form  x := A*x. */\n\n\tif (lsame_(uplo, \"U\", (ftnlen)1, (ftnlen)1)) {\n\t    kplus1 = *k + 1;\n\t    if (*incx == 1) {\n\t\ti__1 = *n;\n\t\tfor (j = 1; j <= i__1; ++j) {\n\t\t    if (x[j] != 0.f) {\n\t\t\ttemp = x[j];\n\t\t\tl = kplus1 - j;\n/* Computing MAX */\n\t\t\ti__2 = 1, i__3 = j - *k;\n\t\t\ti__4 = j - 1;\n\t\t\tfor (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {\n\t\t\t    x[i__] += temp * a[l + i__ + j * a_dim1];\n/* L10: */\n\t\t\t}\n\t\t\tif (nounit) {\n\t\t\t    x[j] *= a[kplus1 + j * a_dim1];\n\t\t\t}\n\t\t    }\n/* L20: */\n\t\t}\n\t    } else {\n\t\tjx = kx;\n\t\ti__1 = *n;\n\t\tfor (j = 1; j <= i__1; ++j) {\n\t\t    if (x[jx] != 0.f) {\n\t\t\ttemp = x[jx];\n\t\t\tix = kx;\n\t\t\tl = kplus1 - j;\n/* Computing MAX */\n\t\t\ti__4 = 1, i__2 = j - *k;\n\t\t\ti__3 = j - 1;\n\t\t\tfor (i__ = max(i__4,i__2); i__ <= i__3; ++i__) {\n\t\t\t    x[ix] += temp * a[l + i__ + j * a_dim1];\n\t\t\t    ix += *incx;\n/* L30: */\n\t\t\t}\n\t\t\tif (nounit) {\n\t\t\t    x[jx] *= a[kplus1 + j * a_dim1];\n\t\t\t}\n\t\t    }\n\t\t    jx += *incx;\n\t\t    if (j > *k) {\n\t\t\tkx += *incx;\n\t\t    }\n/* L40: */\n\t\t}\n\t    }\n\t} else {\n\t    if (*incx == 1) {\n\t\tfor (j = *n; j >= 1; --j) {\n\t\t    if (x[j] != 0.f) {\n\t\t\ttemp = x[j];\n\t\t\tl = 1 - j;\n/* Computing MIN */\n\t\t\ti__1 = *n, i__3 = j + *k;\n\t\t\ti__4 = j + 1;\n\t\t\tfor (i__ = min(i__1,i__3); i__ >= i__4; --i__) {\n\t\t\t    x[i__] += temp * a[l + i__ + j * a_dim1];\n/* L50: */\n\t\t\t}\n\t\t\tif (nounit) {\n\t\t\t    x[j] *= a[j * a_dim1 + 1];\n\t\t\t}\n\t\t    }\n/* L60: */\n\t\t}\n\t    } else {\n\t\tkx += (*n - 1) * *incx;\n\t\tjx = kx;\n\t\tfor (j = *n; j >= 1; --j) {\n\t\t    if (x[jx] != 0.f) {\n\t\t\ttemp = x[jx];\n\t\t\tix = kx;\n\t\t\tl = 1 - j;\n/* Computing MIN */\n\t\t\ti__4 = *n, i__1 = j + *k;\n\t\t\ti__3 = j + 1;\n\t\t\tfor (i__ = min(i__4,i__1); i__ >= i__3; --i__) {\n\t\t\t    x[ix] += temp * a[l + i__ + j * a_dim1];\n\t\t\t    ix -= *incx;\n/* L70: */\n\t\t\t}\n\t\t\tif (nounit) {\n\t\t\t    x[jx] *= a[j * a_dim1 + 1];\n\t\t\t}\n\t\t    }\n\t\t    jx -= *incx;\n\t\t    if (*n - j >= *k) {\n\t\t\tkx -= *incx;\n\t\t    }\n/* L80: */\n\t\t}\n\t    }\n\t}\n    } else {\n\n/*        Form  x := A'*x. */\n\n\tif (lsame_(uplo, \"U\", (ftnlen)1, (ftnlen)1)) {\n\t    kplus1 = *k + 1;\n\t    if (*incx == 1) {\n\t\tfor (j = *n; j >= 1; --j) {\n\t\t    temp = x[j];\n\t\t    l = kplus1 - j;\n\t\t    if (nounit) {\n\t\t\ttemp *= a[kplus1 + j * a_dim1];\n\t\t    }\n/* Computing MAX */\n\t\t    i__4 = 1, i__1 = j - *k;\n\t\t    i__3 = max(i__4,i__1);\n\t\t    for (i__ = j - 1; i__ >= i__3; --i__) {\n\t\t\ttemp += a[l + i__ + j * a_dim1] * x[i__];\n/* L90: */\n\t\t    }\n\t\t    x[j] = temp;\n/* L100: */\n\t\t}\n\t    } else {\n\t\tkx += (*n - 1) * *incx;\n\t\tjx = kx;\n\t\tfor (j = *n; j >= 1; --j) {\n\t\t    temp = x[jx];\n\t\t    kx -= *incx;\n\t\t    ix = kx;\n\t\t    l = kplus1 - j;\n\t\t    if (nounit) {\n\t\t\ttemp *= a[kplus1 + j * a_dim1];\n\t\t    }\n/* Computing MAX */\n\t\t    i__4 = 1, i__1 = j - *k;\n\t\t    i__3 = max(i__4,i__1);\n\t\t    for (i__ = j - 1; i__ >= i__3; --i__) {\n\t\t\ttemp += a[l + i__ + j * a_dim1] * x[ix];\n\t\t\tix -= *incx;\n/* L110: */\n\t\t    }\n\t\t    x[jx] = temp;\n\t\t    jx -= *incx;\n/* L120: */\n\t\t}\n\t    }\n\t} else {\n\t    if (*incx == 1) {\n\t\ti__3 = *n;\n\t\tfor (j = 1; j <= i__3; ++j) {\n\t\t    temp = x[j];\n\t\t    l = 1 - j;\n\t\t    if (nounit) {\n\t\t\ttemp *= a[j * a_dim1 + 1];\n\t\t    }\n/* Computing MIN */\n\t\t    i__1 = *n, i__2 = j + *k;\n\t\t    i__4 = min(i__1,i__2);\n\t\t    for (i__ = j + 1; i__ <= i__4; ++i__) {\n\t\t\ttemp += a[l + i__ + j * a_dim1] * x[i__];\n/* L130: */\n\t\t    }\n\t\t    x[j] = temp;\n/* L140: */\n\t\t}\n\t    } else {\n\t\tjx = kx;\n\t\ti__3 = *n;\n\t\tfor (j = 1; j <= i__3; ++j) {\n\t\t    temp = x[jx];\n\t\t    kx += *incx;\n\t\t    ix = kx;\n\t\t    l = 1 - j;\n\t\t    if (nounit) {\n\t\t\ttemp *= a[j * a_dim1 + 1];\n\t\t    }\n/* Computing MIN */\n\t\t    i__1 = *n, i__2 = j + *k;\n\t\t    i__4 = min(i__1,i__2);\n\t\t    for (i__ = j + 1; i__ <= i__4; ++i__) {\n\t\t\ttemp += a[l + i__ + j * a_dim1] * x[ix];\n\t\t\tix += *incx;\n/* L150: */\n\t\t    }\n\t\t    x[jx] = temp;\n\t\t    jx += *incx;\n/* L160: */\n\t\t}\n\t    }\n\t}\n    }\n\n    return 0;\n\n/*     End of STBMV . */\n\n} /* stbmv_ */\n\n"
  },
  {
    "path": "include/eigen3/blas/f2c/zhbmv.c",
    "content": "/* zhbmv.f -- translated by f2c (version 20100827).\n   You must link the resulting object file with libf2c:\n\ton Microsoft Windows system, link with libf2c.lib;\n\ton Linux or Unix systems, link with .../path/to/libf2c.a -lm\n\tor, if you install libf2c.a in a standard place, with -lf2c -lm\n\t-- in that order, at the end of the command line, as in\n\t\tcc *.o -lf2c -lm\n\tSource for libf2c is in /netlib/f2c/libf2c.zip, e.g.,\n\n\t\thttp://www.netlib.org/f2c/libf2c.zip\n*/\n\n#include \"datatypes.h\"\n\n/* Subroutine */ int zhbmv_(char *uplo, integer *n, integer *k, doublecomplex \n\t*alpha, doublecomplex *a, integer *lda, doublecomplex *x, integer *\n\tincx, doublecomplex *beta, doublecomplex *y, integer *incy, ftnlen \n\tuplo_len)\n{\n    /* System generated locals */\n    integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;\n    doublereal d__1;\n    doublecomplex z__1, z__2, z__3, z__4;\n\n    /* Builtin functions */\n    void d_cnjg(doublecomplex *, doublecomplex *);\n\n    /* Local variables */\n    integer i__, j, l, ix, iy, jx, jy, kx, ky, info;\n    doublecomplex temp1, temp2;\n    extern logical lsame_(char *, char *, ftnlen, ftnlen);\n    integer kplus1;\n    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);\n\n/*     .. Scalar Arguments .. */\n/*     .. */\n/*     .. Array Arguments .. */\n/*     .. */\n\n/*  Purpose */\n/*  ======= */\n\n/*  ZHBMV  performs the matrix-vector  operation */\n\n/*     y := alpha*A*x + beta*y, */\n\n/*  where alpha and beta are scalars, x and y are n element vectors and */\n/*  A is an n by n hermitian band matrix, with k super-diagonals. */\n\n/*  Arguments */\n/*  ========== */\n\n/*  UPLO   - CHARACTER*1. */\n/*           On entry, UPLO specifies whether the upper or lower */\n/*           triangular part of the band matrix A is being supplied as */\n/*           follows: */\n\n/*              UPLO = 'U' or 'u'   The upper triangular part of A is */\n/*                                  being supplied. */\n\n/*              UPLO = 'L' or 'l'   The lower triangular part of A is */\n/*                                  being supplied. */\n\n/*           Unchanged on exit. */\n\n/*  N      - INTEGER. */\n/*           On entry, N specifies the order of the matrix A. */\n/*           N must be at least zero. */\n/*           Unchanged on exit. */\n\n/*  K      - INTEGER. */\n/*           On entry, K specifies the number of super-diagonals of the */\n/*           matrix A. K must satisfy  0 .le. K. */\n/*           Unchanged on exit. */\n\n/*  ALPHA  - COMPLEX*16      . */\n/*           On entry, ALPHA specifies the scalar alpha. */\n/*           Unchanged on exit. */\n\n/*  A      - COMPLEX*16       array of DIMENSION ( LDA, n ). */\n/*           Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) */\n/*           by n part of the array A must contain the upper triangular */\n/*           band part of the hermitian matrix, supplied column by */\n/*           column, with the leading diagonal of the matrix in row */\n/*           ( k + 1 ) of the array, the first super-diagonal starting at */\n/*           position 2 in row k, and so on. The top left k by k triangle */\n/*           of the array A is not referenced. */\n/*           The following program segment will transfer the upper */\n/*           triangular part of a hermitian band matrix from conventional */\n/*           full matrix storage to band storage: */\n\n/*                 DO 20, J = 1, N */\n/*                    M = K + 1 - J */\n/*                    DO 10, I = MAX( 1, J - K ), J */\n/*                       A( M + I, J ) = matrix( I, J ) */\n/*              10    CONTINUE */\n/*              20 CONTINUE */\n\n/*           Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) */\n/*           by n part of the array A must contain the lower triangular */\n/*           band part of the hermitian matrix, supplied column by */\n/*           column, with the leading diagonal of the matrix in row 1 of */\n/*           the array, the first sub-diagonal starting at position 1 in */\n/*           row 2, and so on. The bottom right k by k triangle of the */\n/*           array A is not referenced. */\n/*           The following program segment will transfer the lower */\n/*           triangular part of a hermitian band matrix from conventional */\n/*           full matrix storage to band storage: */\n\n/*                 DO 20, J = 1, N */\n/*                    M = 1 - J */\n/*                    DO 10, I = J, MIN( N, J + K ) */\n/*                       A( M + I, J ) = matrix( I, J ) */\n/*              10    CONTINUE */\n/*              20 CONTINUE */\n\n/*           Note that the imaginary parts of the diagonal elements need */\n/*           not be set and are assumed to be zero. */\n/*           Unchanged on exit. */\n\n/*  LDA    - INTEGER. */\n/*           On entry, LDA specifies the first dimension of A as declared */\n/*           in the calling (sub) program. LDA must be at least */\n/*           ( k + 1 ). */\n/*           Unchanged on exit. */\n\n/*  X      - COMPLEX*16       array of DIMENSION at least */\n/*           ( 1 + ( n - 1 )*abs( INCX ) ). */\n/*           Before entry, the incremented array X must contain the */\n/*           vector x. */\n/*           Unchanged on exit. */\n\n/*  INCX   - INTEGER. */\n/*           On entry, INCX specifies the increment for the elements of */\n/*           X. INCX must not be zero. */\n/*           Unchanged on exit. */\n\n/*  BETA   - COMPLEX*16      . */\n/*           On entry, BETA specifies the scalar beta. */\n/*           Unchanged on exit. */\n\n/*  Y      - COMPLEX*16       array of DIMENSION at least */\n/*           ( 1 + ( n - 1 )*abs( INCY ) ). */\n/*           Before entry, the incremented array Y must contain the */\n/*           vector y. On exit, Y is overwritten by the updated vector y. */\n\n/*  INCY   - INTEGER. */\n/*           On entry, INCY specifies the increment for the elements of */\n/*           Y. INCY must not be zero. */\n/*           Unchanged on exit. */\n\n/*  Further Details */\n/*  =============== */\n\n/*  Level 2 Blas routine. */\n\n/*  -- Written on 22-October-1986. */\n/*     Jack Dongarra, Argonne National Lab. */\n/*     Jeremy Du Croz, Nag Central Office. */\n/*     Sven Hammarling, Nag Central Office. */\n/*     Richard Hanson, Sandia National Labs. */\n\n/*  ===================================================================== */\n\n/*     .. Parameters .. */\n/*     .. */\n/*     .. Local Scalars .. */\n/*     .. */\n/*     .. External Functions .. */\n/*     .. */\n/*     .. External Subroutines .. */\n/*     .. */\n/*     .. Intrinsic Functions .. */\n/*     .. */\n\n/*     Test the input parameters. */\n\n    /* Parameter adjustments */\n    a_dim1 = *lda;\n    a_offset = 1 + a_dim1;\n    a -= a_offset;\n    --x;\n    --y;\n\n    /* Function Body */\n    info = 0;\n    if (! lsame_(uplo, \"U\", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, \"L\", (\n\t    ftnlen)1, (ftnlen)1)) {\n\tinfo = 1;\n    } else if (*n < 0) {\n\tinfo = 2;\n    } else if (*k < 0) {\n\tinfo = 3;\n    } else if (*lda < *k + 1) {\n\tinfo = 6;\n    } else if (*incx == 0) {\n\tinfo = 8;\n    } else if (*incy == 0) {\n\tinfo = 11;\n    }\n    if (info != 0) {\n\txerbla_(\"ZHBMV \", &info, (ftnlen)6);\n\treturn 0;\n    }\n\n/*     Quick return if possible. */\n\n    if (*n == 0 || (alpha->r == 0. && alpha->i == 0. && (beta->r == 1. && \n                                                         beta->i == 0.))) {\n\treturn 0;\n    }\n\n/*     Set up the start points in  X  and  Y. */\n\n    if (*incx > 0) {\n\tkx = 1;\n    } else {\n\tkx = 1 - (*n - 1) * *incx;\n    }\n    if (*incy > 0) {\n\tky = 1;\n    } else {\n\tky = 1 - (*n - 1) * *incy;\n    }\n\n/*     Start the operations. In this version the elements of the array A */\n/*     are accessed sequentially with one pass through A. */\n\n/*     First form  y := beta*y. */\n\n    if (beta->r != 1. || beta->i != 0.) {\n\tif (*incy == 1) {\n\t    if (beta->r == 0. && beta->i == 0.) {\n\t\ti__1 = *n;\n\t\tfor (i__ = 1; i__ <= i__1; ++i__) {\n\t\t    i__2 = i__;\n\t\t    y[i__2].r = 0., y[i__2].i = 0.;\n/* L10: */\n\t\t}\n\t    } else {\n\t\ti__1 = *n;\n\t\tfor (i__ = 1; i__ <= i__1; ++i__) {\n\t\t    i__2 = i__;\n\t\t    i__3 = i__;\n\t\t    z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i, \n\t\t\t    z__1.i = beta->r * y[i__3].i + beta->i * y[i__3]\n\t\t\t    .r;\n\t\t    y[i__2].r = z__1.r, y[i__2].i = z__1.i;\n/* L20: */\n\t\t}\n\t    }\n\t} else {\n\t    iy = ky;\n\t    if (beta->r == 0. && beta->i == 0.) {\n\t\ti__1 = *n;\n\t\tfor (i__ = 1; i__ <= i__1; ++i__) {\n\t\t    i__2 = iy;\n\t\t    y[i__2].r = 0., y[i__2].i = 0.;\n\t\t    iy += *incy;\n/* L30: */\n\t\t}\n\t    } else {\n\t\ti__1 = *n;\n\t\tfor (i__ = 1; i__ <= i__1; ++i__) {\n\t\t    i__2 = iy;\n\t\t    i__3 = iy;\n\t\t    z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i, \n\t\t\t    z__1.i = beta->r * y[i__3].i + beta->i * y[i__3]\n\t\t\t    .r;\n\t\t    y[i__2].r = z__1.r, y[i__2].i = z__1.i;\n\t\t    iy += *incy;\n/* L40: */\n\t\t}\n\t    }\n\t}\n    }\n    if (alpha->r == 0. && alpha->i == 0.) {\n\treturn 0;\n    }\n    if (lsame_(uplo, \"U\", (ftnlen)1, (ftnlen)1)) {\n\n/*        Form  y  when upper triangle of A is stored. */\n\n\tkplus1 = *k + 1;\n\tif (*incx == 1 && *incy == 1) {\n\t    i__1 = *n;\n\t    for (j = 1; j <= i__1; ++j) {\n\t\ti__2 = j;\n\t\tz__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i =\n\t\t\t alpha->r * x[i__2].i + alpha->i * x[i__2].r;\n\t\ttemp1.r = z__1.r, temp1.i = z__1.i;\n\t\ttemp2.r = 0., temp2.i = 0.;\n\t\tl = kplus1 - j;\n/* Computing MAX */\n\t\ti__2 = 1, i__3 = j - *k;\n\t\ti__4 = j - 1;\n\t\tfor (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {\n\t\t    i__2 = i__;\n\t\t    i__3 = i__;\n\t\t    i__5 = l + i__ + j * a_dim1;\n\t\t    z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, \n\t\t\t    z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5]\n\t\t\t    .r;\n\t\t    z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i;\n\t\t    y[i__2].r = z__1.r, y[i__2].i = z__1.i;\n\t\t    d_cnjg(&z__3, &a[l + i__ + j * a_dim1]);\n\t\t    i__2 = i__;\n\t\t    z__2.r = z__3.r * x[i__2].r - z__3.i * x[i__2].i, z__2.i =\n\t\t\t     z__3.r * x[i__2].i + z__3.i * x[i__2].r;\n\t\t    z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;\n\t\t    temp2.r = z__1.r, temp2.i = z__1.i;\n/* L50: */\n\t\t}\n\t\ti__4 = j;\n\t\ti__2 = j;\n\t\ti__3 = kplus1 + j * a_dim1;\n\t\td__1 = a[i__3].r;\n\t\tz__3.r = d__1 * temp1.r, z__3.i = d__1 * temp1.i;\n\t\tz__2.r = y[i__2].r + z__3.r, z__2.i = y[i__2].i + z__3.i;\n\t\tz__4.r = alpha->r * temp2.r - alpha->i * temp2.i, z__4.i = \n\t\t\talpha->r * temp2.i + alpha->i * temp2.r;\n\t\tz__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i;\n\t\ty[i__4].r = z__1.r, y[i__4].i = z__1.i;\n/* L60: */\n\t    }\n\t} else {\n\t    jx = kx;\n\t    jy = ky;\n\t    i__1 = *n;\n\t    for (j = 1; j <= i__1; ++j) {\n\t\ti__4 = jx;\n\t\tz__1.r = alpha->r * x[i__4].r - alpha->i * x[i__4].i, z__1.i =\n\t\t\t alpha->r * x[i__4].i + alpha->i * x[i__4].r;\n\t\ttemp1.r = z__1.r, temp1.i = z__1.i;\n\t\ttemp2.r = 0., temp2.i = 0.;\n\t\tix = kx;\n\t\tiy = ky;\n\t\tl = kplus1 - j;\n/* Computing MAX */\n\t\ti__4 = 1, i__2 = j - *k;\n\t\ti__3 = j - 1;\n\t\tfor (i__ = max(i__4,i__2); i__ <= i__3; ++i__) {\n\t\t    i__4 = iy;\n\t\t    i__2 = iy;\n\t\t    i__5 = l + i__ + j * a_dim1;\n\t\t    z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, \n\t\t\t    z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5]\n\t\t\t    .r;\n\t\t    z__1.r = y[i__2].r + z__2.r, z__1.i = y[i__2].i + z__2.i;\n\t\t    y[i__4].r = z__1.r, y[i__4].i = z__1.i;\n\t\t    d_cnjg(&z__3, &a[l + i__ + j * a_dim1]);\n\t\t    i__4 = ix;\n\t\t    z__2.r = z__3.r * x[i__4].r - z__3.i * x[i__4].i, z__2.i =\n\t\t\t     z__3.r * x[i__4].i + z__3.i * x[i__4].r;\n\t\t    z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;\n\t\t    temp2.r = z__1.r, temp2.i = z__1.i;\n\t\t    ix += *incx;\n\t\t    iy += *incy;\n/* L70: */\n\t\t}\n\t\ti__3 = jy;\n\t\ti__4 = jy;\n\t\ti__2 = kplus1 + j * a_dim1;\n\t\td__1 = a[i__2].r;\n\t\tz__3.r = d__1 * temp1.r, z__3.i = d__1 * temp1.i;\n\t\tz__2.r = y[i__4].r + z__3.r, z__2.i = y[i__4].i + z__3.i;\n\t\tz__4.r = alpha->r * temp2.r - alpha->i * temp2.i, z__4.i = \n\t\t\talpha->r * temp2.i + alpha->i * temp2.r;\n\t\tz__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i;\n\t\ty[i__3].r = z__1.r, y[i__3].i = z__1.i;\n\t\tjx += *incx;\n\t\tjy += *incy;\n\t\tif (j > *k) {\n\t\t    kx += *incx;\n\t\t    ky += *incy;\n\t\t}\n/* L80: */\n\t    }\n\t}\n    } else {\n\n/*        Form  y  when lower triangle of A is stored. */\n\n\tif (*incx == 1 && *incy == 1) {\n\t    i__1 = *n;\n\t    for (j = 1; j <= i__1; ++j) {\n\t\ti__3 = j;\n\t\tz__1.r = alpha->r * x[i__3].r - alpha->i * x[i__3].i, z__1.i =\n\t\t\t alpha->r * x[i__3].i + alpha->i * x[i__3].r;\n\t\ttemp1.r = z__1.r, temp1.i = z__1.i;\n\t\ttemp2.r = 0., temp2.i = 0.;\n\t\ti__3 = j;\n\t\ti__4 = j;\n\t\ti__2 = j * a_dim1 + 1;\n\t\td__1 = a[i__2].r;\n\t\tz__2.r = d__1 * temp1.r, z__2.i = d__1 * temp1.i;\n\t\tz__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i;\n\t\ty[i__3].r = z__1.r, y[i__3].i = z__1.i;\n\t\tl = 1 - j;\n/* Computing MIN */\n\t\ti__4 = *n, i__2 = j + *k;\n\t\ti__3 = min(i__4,i__2);\n\t\tfor (i__ = j + 1; i__ <= i__3; ++i__) {\n\t\t    i__4 = i__;\n\t\t    i__2 = i__;\n\t\t    i__5 = l + i__ + j * a_dim1;\n\t\t    z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, \n\t\t\t    z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5]\n\t\t\t    .r;\n\t\t    z__1.r = y[i__2].r + z__2.r, z__1.i = y[i__2].i + z__2.i;\n\t\t    y[i__4].r = z__1.r, y[i__4].i = z__1.i;\n\t\t    d_cnjg(&z__3, &a[l + i__ + j * a_dim1]);\n\t\t    i__4 = i__;\n\t\t    z__2.r = z__3.r * x[i__4].r - z__3.i * x[i__4].i, z__2.i =\n\t\t\t     z__3.r * x[i__4].i + z__3.i * x[i__4].r;\n\t\t    z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;\n\t\t    temp2.r = z__1.r, temp2.i = z__1.i;\n/* L90: */\n\t\t}\n\t\ti__3 = j;\n\t\ti__4 = j;\n\t\tz__2.r = alpha->r * temp2.r - alpha->i * temp2.i, z__2.i = \n\t\t\talpha->r * temp2.i + alpha->i * temp2.r;\n\t\tz__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i;\n\t\ty[i__3].r = z__1.r, y[i__3].i = z__1.i;\n/* L100: */\n\t    }\n\t} else {\n\t    jx = kx;\n\t    jy = ky;\n\t    i__1 = *n;\n\t    for (j = 1; j <= i__1; ++j) {\n\t\ti__3 = jx;\n\t\tz__1.r = alpha->r * x[i__3].r - alpha->i * x[i__3].i, z__1.i =\n\t\t\t alpha->r * x[i__3].i + alpha->i * x[i__3].r;\n\t\ttemp1.r = z__1.r, temp1.i = z__1.i;\n\t\ttemp2.r = 0., temp2.i = 0.;\n\t\ti__3 = jy;\n\t\ti__4 = jy;\n\t\ti__2 = j * a_dim1 + 1;\n\t\td__1 = a[i__2].r;\n\t\tz__2.r = d__1 * temp1.r, z__2.i = d__1 * temp1.i;\n\t\tz__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i;\n\t\ty[i__3].r = z__1.r, y[i__3].i = z__1.i;\n\t\tl = 1 - j;\n\t\tix = jx;\n\t\tiy = jy;\n/* Computing MIN */\n\t\ti__4 = *n, i__2 = j + *k;\n\t\ti__3 = min(i__4,i__2);\n\t\tfor (i__ = j + 1; i__ <= i__3; ++i__) {\n\t\t    ix += *incx;\n\t\t    iy += *incy;\n\t\t    i__4 = iy;\n\t\t    i__2 = iy;\n\t\t    i__5 = l + i__ + j * a_dim1;\n\t\t    z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, \n\t\t\t    z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5]\n\t\t\t    .r;\n\t\t    z__1.r = y[i__2].r + z__2.r, z__1.i = y[i__2].i + z__2.i;\n\t\t    y[i__4].r = z__1.r, y[i__4].i = z__1.i;\n\t\t    d_cnjg(&z__3, &a[l + i__ + j * a_dim1]);\n\t\t    i__4 = ix;\n\t\t    z__2.r = z__3.r * x[i__4].r - z__3.i * x[i__4].i, z__2.i =\n\t\t\t     z__3.r * x[i__4].i + z__3.i * x[i__4].r;\n\t\t    z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;\n\t\t    temp2.r = z__1.r, temp2.i = z__1.i;\n/* L110: */\n\t\t}\n\t\ti__3 = jy;\n\t\ti__4 = jy;\n\t\tz__2.r = alpha->r * temp2.r - alpha->i * temp2.i, z__2.i = \n\t\t\talpha->r * temp2.i + alpha->i * temp2.r;\n\t\tz__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i;\n\t\ty[i__3].r = z__1.r, y[i__3].i = z__1.i;\n\t\tjx += *incx;\n\t\tjy += *incy;\n/* L120: */\n\t    }\n\t}\n    }\n\n    return 0;\n\n/*     End of ZHBMV . */\n\n} /* zhbmv_ */\n\n"
  },
  {
    "path": "include/eigen3/blas/f2c/zhpmv.c",
    "content": "/* zhpmv.f -- translated by f2c (version 20100827).\n   You must link the resulting object file with libf2c:\n\ton Microsoft Windows system, link with libf2c.lib;\n\ton Linux or Unix systems, link with .../path/to/libf2c.a -lm\n\tor, if you install libf2c.a in a standard place, with -lf2c -lm\n\t-- in that order, at the end of the command line, as in\n\t\tcc *.o -lf2c -lm\n\tSource for libf2c is in /netlib/f2c/libf2c.zip, e.g.,\n\n\t\thttp://www.netlib.org/f2c/libf2c.zip\n*/\n\n#include \"datatypes.h\"\n\n/* Subroutine */ int zhpmv_(char *uplo, integer *n, doublecomplex *alpha, \n\tdoublecomplex *ap, doublecomplex *x, integer *incx, doublecomplex *\n\tbeta, doublecomplex *y, integer *incy, ftnlen uplo_len)\n{\n    /* System generated locals */\n    integer i__1, i__2, i__3, i__4, i__5;\n    doublereal d__1;\n    doublecomplex z__1, z__2, z__3, z__4;\n\n    /* Builtin functions */\n    void d_cnjg(doublecomplex *, doublecomplex *);\n\n    /* Local variables */\n    integer i__, j, k, kk, ix, iy, jx, jy, kx, ky, info;\n    doublecomplex temp1, temp2;\n    extern logical lsame_(char *, char *, ftnlen, ftnlen);\n    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);\n\n/*     .. Scalar Arguments .. */\n/*     .. */\n/*     .. Array Arguments .. */\n/*     .. */\n\n/*  Purpose */\n/*  ======= */\n\n/*  ZHPMV  performs the matrix-vector operation */\n\n/*     y := alpha*A*x + beta*y, */\n\n/*  where alpha and beta are scalars, x and y are n element vectors and */\n/*  A is an n by n hermitian matrix, supplied in packed form. */\n\n/*  Arguments */\n/*  ========== */\n\n/*  UPLO   - CHARACTER*1. */\n/*           On entry, UPLO specifies whether the upper or lower */\n/*           triangular part of the matrix A is supplied in the packed */\n/*           array AP as follows: */\n\n/*              UPLO = 'U' or 'u'   The upper triangular part of A is */\n/*                                  supplied in AP. */\n\n/*              UPLO = 'L' or 'l'   The lower triangular part of A is */\n/*                                  supplied in AP. */\n\n/*           Unchanged on exit. */\n\n/*  N      - INTEGER. */\n/*           On entry, N specifies the order of the matrix A. */\n/*           N must be at least zero. */\n/*           Unchanged on exit. */\n\n/*  ALPHA  - COMPLEX*16      . */\n/*           On entry, ALPHA specifies the scalar alpha. */\n/*           Unchanged on exit. */\n\n/*  AP     - COMPLEX*16       array of DIMENSION at least */\n/*           ( ( n*( n + 1 ) )/2 ). */\n/*           Before entry with UPLO = 'U' or 'u', the array AP must */\n/*           contain the upper triangular part of the hermitian matrix */\n/*           packed sequentially, column by column, so that AP( 1 ) */\n/*           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) */\n/*           and a( 2, 2 ) respectively, and so on. */\n/*           Before entry with UPLO = 'L' or 'l', the array AP must */\n/*           contain the lower triangular part of the hermitian matrix */\n/*           packed sequentially, column by column, so that AP( 1 ) */\n/*           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) */\n/*           and a( 3, 1 ) respectively, and so on. */\n/*           Note that the imaginary parts of the diagonal elements need */\n/*           not be set and are assumed to be zero. */\n/*           Unchanged on exit. */\n\n/*  X      - COMPLEX*16       array of dimension at least */\n/*           ( 1 + ( n - 1 )*abs( INCX ) ). */\n/*           Before entry, the incremented array X must contain the n */\n/*           element vector x. */\n/*           Unchanged on exit. */\n\n/*  INCX   - INTEGER. */\n/*           On entry, INCX specifies the increment for the elements of */\n/*           X. INCX must not be zero. */\n/*           Unchanged on exit. */\n\n/*  BETA   - COMPLEX*16      . */\n/*           On entry, BETA specifies the scalar beta. When BETA is */\n/*           supplied as zero then Y need not be set on input. */\n/*           Unchanged on exit. */\n\n/*  Y      - COMPLEX*16       array of dimension at least */\n/*           ( 1 + ( n - 1 )*abs( INCY ) ). */\n/*           Before entry, the incremented array Y must contain the n */\n/*           element vector y. On exit, Y is overwritten by the updated */\n/*           vector y. */\n\n/*  INCY   - INTEGER. */\n/*           On entry, INCY specifies the increment for the elements of */\n/*           Y. INCY must not be zero. */\n/*           Unchanged on exit. */\n\n/*  Further Details */\n/*  =============== */\n\n/*  Level 2 Blas routine. */\n\n/*  -- Written on 22-October-1986. */\n/*     Jack Dongarra, Argonne National Lab. */\n/*     Jeremy Du Croz, Nag Central Office. */\n/*     Sven Hammarling, Nag Central Office. */\n/*     Richard Hanson, Sandia National Labs. */\n\n/*  ===================================================================== */\n\n/*     .. Parameters .. */\n/*     .. */\n/*     .. Local Scalars .. */\n/*     .. */\n/*     .. External Functions .. */\n/*     .. */\n/*     .. External Subroutines .. */\n/*     .. */\n/*     .. Intrinsic Functions .. */\n/*     .. */\n\n/*     Test the input parameters. */\n\n    /* Parameter adjustments */\n    --y;\n    --x;\n    --ap;\n\n    /* Function Body */\n    info = 0;\n    if (! lsame_(uplo, \"U\", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, \"L\", (\n\t    ftnlen)1, (ftnlen)1)) {\n\tinfo = 1;\n    } else if (*n < 0) {\n\tinfo = 2;\n    } else if (*incx == 0) {\n\tinfo = 6;\n    } else if (*incy == 0) {\n\tinfo = 9;\n    }\n    if (info != 0) {\n\txerbla_(\"ZHPMV \", &info, (ftnlen)6);\n\treturn 0;\n    }\n\n/*     Quick return if possible. */\n\n    if (*n == 0 || (alpha->r == 0. && alpha->i == 0. && (beta->r == 1. && \n                                                         beta->i == 0.))) {\n\treturn 0;\n    }\n\n/*     Set up the start points in  X  and  Y. */\n\n    if (*incx > 0) {\n\tkx = 1;\n    } else {\n\tkx = 1 - (*n - 1) * *incx;\n    }\n    if (*incy > 0) {\n\tky = 1;\n    } else {\n\tky = 1 - (*n - 1) * *incy;\n    }\n\n/*     Start the operations. In this version the elements of the array AP */\n/*     are accessed sequentially with one pass through AP. */\n\n/*     First form  y := beta*y. */\n\n    if (beta->r != 1. || beta->i != 0.) {\n\tif (*incy == 1) {\n\t    if (beta->r == 0. && beta->i == 0.) {\n\t\ti__1 = *n;\n\t\tfor (i__ = 1; i__ <= i__1; ++i__) {\n\t\t    i__2 = i__;\n\t\t    y[i__2].r = 0., y[i__2].i = 0.;\n/* L10: */\n\t\t}\n\t    } else {\n\t\ti__1 = *n;\n\t\tfor (i__ = 1; i__ <= i__1; ++i__) {\n\t\t    i__2 = i__;\n\t\t    i__3 = i__;\n\t\t    z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i, \n\t\t\t    z__1.i = beta->r * y[i__3].i + beta->i * y[i__3]\n\t\t\t    .r;\n\t\t    y[i__2].r = z__1.r, y[i__2].i = z__1.i;\n/* L20: */\n\t\t}\n\t    }\n\t} else {\n\t    iy = ky;\n\t    if (beta->r == 0. && beta->i == 0.) {\n\t\ti__1 = *n;\n\t\tfor (i__ = 1; i__ <= i__1; ++i__) {\n\t\t    i__2 = iy;\n\t\t    y[i__2].r = 0., y[i__2].i = 0.;\n\t\t    iy += *incy;\n/* L30: */\n\t\t}\n\t    } else {\n\t\ti__1 = *n;\n\t\tfor (i__ = 1; i__ <= i__1; ++i__) {\n\t\t    i__2 = iy;\n\t\t    i__3 = iy;\n\t\t    z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i, \n\t\t\t    z__1.i = beta->r * y[i__3].i + beta->i * y[i__3]\n\t\t\t    .r;\n\t\t    y[i__2].r = z__1.r, y[i__2].i = z__1.i;\n\t\t    iy += *incy;\n/* L40: */\n\t\t}\n\t    }\n\t}\n    }\n    if (alpha->r == 0. && alpha->i == 0.) {\n\treturn 0;\n    }\n    kk = 1;\n    if (lsame_(uplo, \"U\", (ftnlen)1, (ftnlen)1)) {\n\n/*        Form  y  when AP contains the upper triangle. */\n\n\tif (*incx == 1 && *incy == 1) {\n\t    i__1 = *n;\n\t    for (j = 1; j <= i__1; ++j) {\n\t\ti__2 = j;\n\t\tz__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i =\n\t\t\t alpha->r * x[i__2].i + alpha->i * x[i__2].r;\n\t\ttemp1.r = z__1.r, temp1.i = z__1.i;\n\t\ttemp2.r = 0., temp2.i = 0.;\n\t\tk = kk;\n\t\ti__2 = j - 1;\n\t\tfor (i__ = 1; i__ <= i__2; ++i__) {\n\t\t    i__3 = i__;\n\t\t    i__4 = i__;\n\t\t    i__5 = k;\n\t\t    z__2.r = temp1.r * ap[i__5].r - temp1.i * ap[i__5].i, \n\t\t\t    z__2.i = temp1.r * ap[i__5].i + temp1.i * ap[i__5]\n\t\t\t    .r;\n\t\t    z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i;\n\t\t    y[i__3].r = z__1.r, y[i__3].i = z__1.i;\n\t\t    d_cnjg(&z__3, &ap[k]);\n\t\t    i__3 = i__;\n\t\t    z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i =\n\t\t\t     z__3.r * x[i__3].i + z__3.i * x[i__3].r;\n\t\t    z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;\n\t\t    temp2.r = z__1.r, temp2.i = z__1.i;\n\t\t    ++k;\n/* L50: */\n\t\t}\n\t\ti__2 = j;\n\t\ti__3 = j;\n\t\ti__4 = kk + j - 1;\n\t\td__1 = ap[i__4].r;\n\t\tz__3.r = d__1 * temp1.r, z__3.i = d__1 * temp1.i;\n\t\tz__2.r = y[i__3].r + z__3.r, z__2.i = y[i__3].i + z__3.i;\n\t\tz__4.r = alpha->r * temp2.r - alpha->i * temp2.i, z__4.i = \n\t\t\talpha->r * temp2.i + alpha->i * temp2.r;\n\t\tz__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i;\n\t\ty[i__2].r = z__1.r, y[i__2].i = z__1.i;\n\t\tkk += j;\n/* L60: */\n\t    }\n\t} else {\n\t    jx = kx;\n\t    jy = ky;\n\t    i__1 = *n;\n\t    for (j = 1; j <= i__1; ++j) {\n\t\ti__2 = jx;\n\t\tz__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i =\n\t\t\t alpha->r * x[i__2].i + alpha->i * x[i__2].r;\n\t\ttemp1.r = z__1.r, temp1.i = z__1.i;\n\t\ttemp2.r = 0., temp2.i = 0.;\n\t\tix = kx;\n\t\tiy = ky;\n\t\ti__2 = kk + j - 2;\n\t\tfor (k = kk; k <= i__2; ++k) {\n\t\t    i__3 = iy;\n\t\t    i__4 = iy;\n\t\t    i__5 = k;\n\t\t    z__2.r = temp1.r * ap[i__5].r - temp1.i * ap[i__5].i, \n\t\t\t    z__2.i = temp1.r * ap[i__5].i + temp1.i * ap[i__5]\n\t\t\t    .r;\n\t\t    z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i;\n\t\t    y[i__3].r = z__1.r, y[i__3].i = z__1.i;\n\t\t    d_cnjg(&z__3, &ap[k]);\n\t\t    i__3 = ix;\n\t\t    z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i =\n\t\t\t     z__3.r * x[i__3].i + z__3.i * x[i__3].r;\n\t\t    z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;\n\t\t    temp2.r = z__1.r, temp2.i = z__1.i;\n\t\t    ix += *incx;\n\t\t    iy += *incy;\n/* L70: */\n\t\t}\n\t\ti__2 = jy;\n\t\ti__3 = jy;\n\t\ti__4 = kk + j - 1;\n\t\td__1 = ap[i__4].r;\n\t\tz__3.r = d__1 * temp1.r, z__3.i = d__1 * temp1.i;\n\t\tz__2.r = y[i__3].r + z__3.r, z__2.i = y[i__3].i + z__3.i;\n\t\tz__4.r = alpha->r * temp2.r - alpha->i * temp2.i, z__4.i = \n\t\t\talpha->r * temp2.i + alpha->i * temp2.r;\n\t\tz__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i;\n\t\ty[i__2].r = z__1.r, y[i__2].i = z__1.i;\n\t\tjx += *incx;\n\t\tjy += *incy;\n\t\tkk += j;\n/* L80: */\n\t    }\n\t}\n    } else {\n\n/*        Form  y  when AP contains the lower triangle. */\n\n\tif (*incx == 1 && *incy == 1) {\n\t    i__1 = *n;\n\t    for (j = 1; j <= i__1; ++j) {\n\t\ti__2 = j;\n\t\tz__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i =\n\t\t\t alpha->r * x[i__2].i + alpha->i * x[i__2].r;\n\t\ttemp1.r = z__1.r, temp1.i = z__1.i;\n\t\ttemp2.r = 0., temp2.i = 0.;\n\t\ti__2 = j;\n\t\ti__3 = j;\n\t\ti__4 = kk;\n\t\td__1 = ap[i__4].r;\n\t\tz__2.r = d__1 * temp1.r, z__2.i = d__1 * temp1.i;\n\t\tz__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i;\n\t\ty[i__2].r = z__1.r, y[i__2].i = z__1.i;\n\t\tk = kk + 1;\n\t\ti__2 = *n;\n\t\tfor (i__ = j + 1; i__ <= i__2; ++i__) {\n\t\t    i__3 = i__;\n\t\t    i__4 = i__;\n\t\t    i__5 = k;\n\t\t    z__2.r = temp1.r * ap[i__5].r - temp1.i * ap[i__5].i, \n\t\t\t    z__2.i = temp1.r * ap[i__5].i + temp1.i * ap[i__5]\n\t\t\t    .r;\n\t\t    z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i;\n\t\t    y[i__3].r = z__1.r, y[i__3].i = z__1.i;\n\t\t    d_cnjg(&z__3, &ap[k]);\n\t\t    i__3 = i__;\n\t\t    z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i =\n\t\t\t     z__3.r * x[i__3].i + z__3.i * x[i__3].r;\n\t\t    z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;\n\t\t    temp2.r = z__1.r, temp2.i = z__1.i;\n\t\t    ++k;\n/* L90: */\n\t\t}\n\t\ti__2 = j;\n\t\ti__3 = j;\n\t\tz__2.r = alpha->r * temp2.r - alpha->i * temp2.i, z__2.i = \n\t\t\talpha->r * temp2.i + alpha->i * temp2.r;\n\t\tz__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i;\n\t\ty[i__2].r = z__1.r, y[i__2].i = z__1.i;\n\t\tkk += *n - j + 1;\n/* L100: */\n\t    }\n\t} else {\n\t    jx = kx;\n\t    jy = ky;\n\t    i__1 = *n;\n\t    for (j = 1; j <= i__1; ++j) {\n\t\ti__2 = jx;\n\t\tz__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i =\n\t\t\t alpha->r * x[i__2].i + alpha->i * x[i__2].r;\n\t\ttemp1.r = z__1.r, temp1.i = z__1.i;\n\t\ttemp2.r = 0., temp2.i = 0.;\n\t\ti__2 = jy;\n\t\ti__3 = jy;\n\t\ti__4 = kk;\n\t\td__1 = ap[i__4].r;\n\t\tz__2.r = d__1 * temp1.r, z__2.i = d__1 * temp1.i;\n\t\tz__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i;\n\t\ty[i__2].r = z__1.r, y[i__2].i = z__1.i;\n\t\tix = jx;\n\t\tiy = jy;\n\t\ti__2 = kk + *n - j;\n\t\tfor (k = kk + 1; k <= i__2; ++k) {\n\t\t    ix += *incx;\n\t\t    iy += *incy;\n\t\t    i__3 = iy;\n\t\t    i__4 = iy;\n\t\t    i__5 = k;\n\t\t    z__2.r = temp1.r * ap[i__5].r - temp1.i * ap[i__5].i, \n\t\t\t    z__2.i = temp1.r * ap[i__5].i + temp1.i * ap[i__5]\n\t\t\t    .r;\n\t\t    z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i;\n\t\t    y[i__3].r = z__1.r, y[i__3].i = z__1.i;\n\t\t    d_cnjg(&z__3, &ap[k]);\n\t\t    i__3 = ix;\n\t\t    z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i =\n\t\t\t     z__3.r * x[i__3].i + z__3.i * x[i__3].r;\n\t\t    z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;\n\t\t    temp2.r = z__1.r, temp2.i = z__1.i;\n/* L110: */\n\t\t}\n\t\ti__2 = jy;\n\t\ti__3 = jy;\n\t\tz__2.r = alpha->r * temp2.r - alpha->i * temp2.i, z__2.i = \n\t\t\talpha->r * temp2.i + alpha->i * temp2.r;\n\t\tz__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i;\n\t\ty[i__2].r = z__1.r, y[i__2].i = z__1.i;\n\t\tjx += *incx;\n\t\tjy += *incy;\n\t\tkk += *n - j + 1;\n/* L120: */\n\t    }\n\t}\n    }\n\n    return 0;\n\n/*     End of ZHPMV . */\n\n} /* zhpmv_ */\n\n"
  },
  {
    "path": "include/eigen3/blas/f2c/ztbmv.c",
    "content": "/* ztbmv.f -- translated by f2c (version 20100827).\n   You must link the resulting object file with libf2c:\n\ton Microsoft Windows system, link with libf2c.lib;\n\ton Linux or Unix systems, link with .../path/to/libf2c.a -lm\n\tor, if you install libf2c.a in a standard place, with -lf2c -lm\n\t-- in that order, at the end of the command line, as in\n\t\tcc *.o -lf2c -lm\n\tSource for libf2c is in /netlib/f2c/libf2c.zip, e.g.,\n\n\t\thttp://www.netlib.org/f2c/libf2c.zip\n*/\n\n#include \"datatypes.h\"\n\n/* Subroutine */ int ztbmv_(char *uplo, char *trans, char *diag, integer *n, \n\tinteger *k, doublecomplex *a, integer *lda, doublecomplex *x, integer \n\t*incx, ftnlen uplo_len, ftnlen trans_len, ftnlen diag_len)\n{\n    /* System generated locals */\n    integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;\n    doublecomplex z__1, z__2, z__3;\n\n    /* Builtin functions */\n    void d_cnjg(doublecomplex *, doublecomplex *);\n\n    /* Local variables */\n    integer i__, j, l, ix, jx, kx, info;\n    doublecomplex temp;\n    extern logical lsame_(char *, char *, ftnlen, ftnlen);\n    integer kplus1;\n    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);\n    logical noconj, nounit;\n\n/*     .. Scalar Arguments .. */\n/*     .. */\n/*     .. Array Arguments .. */\n/*     .. */\n\n/*  Purpose */\n/*  ======= */\n\n/*  ZTBMV  performs one of the matrix-vector operations */\n\n/*     x := A*x,   or   x := A'*x,   or   x := conjg( A' )*x, */\n\n/*  where x is an n element vector and  A is an n by n unit, or non-unit, */\n/*  upper or lower triangular band matrix, with ( k + 1 ) diagonals. */\n\n/*  Arguments */\n/*  ========== */\n\n/*  UPLO   - CHARACTER*1. */\n/*           On entry, UPLO specifies whether the matrix is an upper or */\n/*           lower triangular matrix as follows: */\n\n/*              UPLO = 'U' or 'u'   A is an upper triangular matrix. */\n\n/*              UPLO = 'L' or 'l'   A is a lower triangular matrix. */\n\n/*           Unchanged on exit. */\n\n/*  TRANS  - CHARACTER*1. */\n/*           On entry, TRANS specifies the operation to be performed as */\n/*           follows: */\n\n/*              TRANS = 'N' or 'n'   x := A*x. */\n\n/*              TRANS = 'T' or 't'   x := A'*x. */\n\n/*              TRANS = 'C' or 'c'   x := conjg( A' )*x. */\n\n/*           Unchanged on exit. */\n\n/*  DIAG   - CHARACTER*1. */\n/*           On entry, DIAG specifies whether or not A is unit */\n/*           triangular as follows: */\n\n/*              DIAG = 'U' or 'u'   A is assumed to be unit triangular. */\n\n/*              DIAG = 'N' or 'n'   A is not assumed to be unit */\n/*                                  triangular. */\n\n/*           Unchanged on exit. */\n\n/*  N      - INTEGER. */\n/*           On entry, N specifies the order of the matrix A. */\n/*           N must be at least zero. */\n/*           Unchanged on exit. */\n\n/*  K      - INTEGER. */\n/*           On entry with UPLO = 'U' or 'u', K specifies the number of */\n/*           super-diagonals of the matrix A. */\n/*           On entry with UPLO = 'L' or 'l', K specifies the number of */\n/*           sub-diagonals of the matrix A. */\n/*           K must satisfy  0 .le. K. */\n/*           Unchanged on exit. */\n\n/*  A      - COMPLEX*16       array of DIMENSION ( LDA, n ). */\n/*           Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) */\n/*           by n part of the array A must contain the upper triangular */\n/*           band part of the matrix of coefficients, supplied column by */\n/*           column, with the leading diagonal of the matrix in row */\n/*           ( k + 1 ) of the array, the first super-diagonal starting at */\n/*           position 2 in row k, and so on. The top left k by k triangle */\n/*           of the array A is not referenced. */\n/*           The following program segment will transfer an upper */\n/*           triangular band matrix from conventional full matrix storage */\n/*           to band storage: */\n\n/*                 DO 20, J = 1, N */\n/*                    M = K + 1 - J */\n/*                    DO 10, I = MAX( 1, J - K ), J */\n/*                       A( M + I, J ) = matrix( I, J ) */\n/*              10    CONTINUE */\n/*              20 CONTINUE */\n\n/*           Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) */\n/*           by n part of the array A must contain the lower triangular */\n/*           band part of the matrix of coefficients, supplied column by */\n/*           column, with the leading diagonal of the matrix in row 1 of */\n/*           the array, the first sub-diagonal starting at position 1 in */\n/*           row 2, and so on. The bottom right k by k triangle of the */\n/*           array A is not referenced. */\n/*           The following program segment will transfer a lower */\n/*           triangular band matrix from conventional full matrix storage */\n/*           to band storage: */\n\n/*                 DO 20, J = 1, N */\n/*                    M = 1 - J */\n/*                    DO 10, I = J, MIN( N, J + K ) */\n/*                       A( M + I, J ) = matrix( I, J ) */\n/*              10    CONTINUE */\n/*              20 CONTINUE */\n\n/*           Note that when DIAG = 'U' or 'u' the elements of the array A */\n/*           corresponding to the diagonal elements of the matrix are not */\n/*           referenced, but are assumed to be unity. */\n/*           Unchanged on exit. */\n\n/*  LDA    - INTEGER. */\n/*           On entry, LDA specifies the first dimension of A as declared */\n/*           in the calling (sub) program. LDA must be at least */\n/*           ( k + 1 ). */\n/*           Unchanged on exit. */\n\n/*  X      - COMPLEX*16       array of dimension at least */\n/*           ( 1 + ( n - 1 )*abs( INCX ) ). */\n/*           Before entry, the incremented array X must contain the n */\n/*           element vector x. On exit, X is overwritten with the */\n/*           tranformed vector x. */\n\n/*  INCX   - INTEGER. */\n/*           On entry, INCX specifies the increment for the elements of */\n/*           X. INCX must not be zero. */\n/*           Unchanged on exit. */\n\n/*  Further Details */\n/*  =============== */\n\n/*  Level 2 Blas routine. */\n\n/*  -- Written on 22-October-1986. */\n/*     Jack Dongarra, Argonne National Lab. */\n/*     Jeremy Du Croz, Nag Central Office. */\n/*     Sven Hammarling, Nag Central Office. */\n/*     Richard Hanson, Sandia National Labs. */\n\n/*  ===================================================================== */\n\n/*     .. Parameters .. */\n/*     .. */\n/*     .. Local Scalars .. */\n/*     .. */\n/*     .. External Functions .. */\n/*     .. */\n/*     .. External Subroutines .. */\n/*     .. */\n/*     .. Intrinsic Functions .. */\n/*     .. */\n\n/*     Test the input parameters. */\n\n    /* Parameter adjustments */\n    a_dim1 = *lda;\n    a_offset = 1 + a_dim1;\n    a -= a_offset;\n    --x;\n\n    /* Function Body */\n    info = 0;\n    if (! lsame_(uplo, \"U\", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, \"L\", (\n\t    ftnlen)1, (ftnlen)1)) {\n\tinfo = 1;\n    } else if (! lsame_(trans, \"N\", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, \n\t    \"T\", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, \"C\", (ftnlen)1, (\n\t    ftnlen)1)) {\n\tinfo = 2;\n    } else if (! lsame_(diag, \"U\", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, \n\t    \"N\", (ftnlen)1, (ftnlen)1)) {\n\tinfo = 3;\n    } else if (*n < 0) {\n\tinfo = 4;\n    } else if (*k < 0) {\n\tinfo = 5;\n    } else if (*lda < *k + 1) {\n\tinfo = 7;\n    } else if (*incx == 0) {\n\tinfo = 9;\n    }\n    if (info != 0) {\n\txerbla_(\"ZTBMV \", &info, (ftnlen)6);\n\treturn 0;\n    }\n\n/*     Quick return if possible. */\n\n    if (*n == 0) {\n\treturn 0;\n    }\n\n    noconj = lsame_(trans, \"T\", (ftnlen)1, (ftnlen)1);\n    nounit = lsame_(diag, \"N\", (ftnlen)1, (ftnlen)1);\n\n/*     Set up the start point in X if the increment is not unity. This */\n/*     will be  ( N - 1 )*INCX   too small for descending loops. */\n\n    if (*incx <= 0) {\n\tkx = 1 - (*n - 1) * *incx;\n    } else if (*incx != 1) {\n\tkx = 1;\n    }\n\n/*     Start the operations. In this version the elements of A are */\n/*     accessed sequentially with one pass through A. */\n\n    if (lsame_(trans, \"N\", (ftnlen)1, (ftnlen)1)) {\n\n/*         Form  x := A*x. */\n\n\tif (lsame_(uplo, \"U\", (ftnlen)1, (ftnlen)1)) {\n\t    kplus1 = *k + 1;\n\t    if (*incx == 1) {\n\t\ti__1 = *n;\n\t\tfor (j = 1; j <= i__1; ++j) {\n\t\t    i__2 = j;\n\t\t    if (x[i__2].r != 0. || x[i__2].i != 0.) {\n\t\t\ti__2 = j;\n\t\t\ttemp.r = x[i__2].r, temp.i = x[i__2].i;\n\t\t\tl = kplus1 - j;\n/* Computing MAX */\n\t\t\ti__2 = 1, i__3 = j - *k;\n\t\t\ti__4 = j - 1;\n\t\t\tfor (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {\n\t\t\t    i__2 = i__;\n\t\t\t    i__3 = i__;\n\t\t\t    i__5 = l + i__ + j * a_dim1;\n\t\t\t    z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, \n\t\t\t\t    z__2.i = temp.r * a[i__5].i + temp.i * a[\n\t\t\t\t    i__5].r;\n\t\t\t    z__1.r = x[i__3].r + z__2.r, z__1.i = x[i__3].i + \n\t\t\t\t    z__2.i;\n\t\t\t    x[i__2].r = z__1.r, x[i__2].i = z__1.i;\n/* L10: */\n\t\t\t}\n\t\t\tif (nounit) {\n\t\t\t    i__4 = j;\n\t\t\t    i__2 = j;\n\t\t\t    i__3 = kplus1 + j * a_dim1;\n\t\t\t    z__1.r = x[i__2].r * a[i__3].r - x[i__2].i * a[\n\t\t\t\t    i__3].i, z__1.i = x[i__2].r * a[i__3].i + \n\t\t\t\t    x[i__2].i * a[i__3].r;\n\t\t\t    x[i__4].r = z__1.r, x[i__4].i = z__1.i;\n\t\t\t}\n\t\t    }\n/* L20: */\n\t\t}\n\t    } else {\n\t\tjx = kx;\n\t\ti__1 = *n;\n\t\tfor (j = 1; j <= i__1; ++j) {\n\t\t    i__4 = jx;\n\t\t    if (x[i__4].r != 0. || x[i__4].i != 0.) {\n\t\t\ti__4 = jx;\n\t\t\ttemp.r = x[i__4].r, temp.i = x[i__4].i;\n\t\t\tix = kx;\n\t\t\tl = kplus1 - j;\n/* Computing MAX */\n\t\t\ti__4 = 1, i__2 = j - *k;\n\t\t\ti__3 = j - 1;\n\t\t\tfor (i__ = max(i__4,i__2); i__ <= i__3; ++i__) {\n\t\t\t    i__4 = ix;\n\t\t\t    i__2 = ix;\n\t\t\t    i__5 = l + i__ + j * a_dim1;\n\t\t\t    z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, \n\t\t\t\t    z__2.i = temp.r * a[i__5].i + temp.i * a[\n\t\t\t\t    i__5].r;\n\t\t\t    z__1.r = x[i__2].r + z__2.r, z__1.i = x[i__2].i + \n\t\t\t\t    z__2.i;\n\t\t\t    x[i__4].r = z__1.r, x[i__4].i = z__1.i;\n\t\t\t    ix += *incx;\n/* L30: */\n\t\t\t}\n\t\t\tif (nounit) {\n\t\t\t    i__3 = jx;\n\t\t\t    i__4 = jx;\n\t\t\t    i__2 = kplus1 + j * a_dim1;\n\t\t\t    z__1.r = x[i__4].r * a[i__2].r - x[i__4].i * a[\n\t\t\t\t    i__2].i, z__1.i = x[i__4].r * a[i__2].i + \n\t\t\t\t    x[i__4].i * a[i__2].r;\n\t\t\t    x[i__3].r = z__1.r, x[i__3].i = z__1.i;\n\t\t\t}\n\t\t    }\n\t\t    jx += *incx;\n\t\t    if (j > *k) {\n\t\t\tkx += *incx;\n\t\t    }\n/* L40: */\n\t\t}\n\t    }\n\t} else {\n\t    if (*incx == 1) {\n\t\tfor (j = *n; j >= 1; --j) {\n\t\t    i__1 = j;\n\t\t    if (x[i__1].r != 0. || x[i__1].i != 0.) {\n\t\t\ti__1 = j;\n\t\t\ttemp.r = x[i__1].r, temp.i = x[i__1].i;\n\t\t\tl = 1 - j;\n/* Computing MIN */\n\t\t\ti__1 = *n, i__3 = j + *k;\n\t\t\ti__4 = j + 1;\n\t\t\tfor (i__ = min(i__1,i__3); i__ >= i__4; --i__) {\n\t\t\t    i__1 = i__;\n\t\t\t    i__3 = i__;\n\t\t\t    i__2 = l + i__ + j * a_dim1;\n\t\t\t    z__2.r = temp.r * a[i__2].r - temp.i * a[i__2].i, \n\t\t\t\t    z__2.i = temp.r * a[i__2].i + temp.i * a[\n\t\t\t\t    i__2].r;\n\t\t\t    z__1.r = x[i__3].r + z__2.r, z__1.i = x[i__3].i + \n\t\t\t\t    z__2.i;\n\t\t\t    x[i__1].r = z__1.r, x[i__1].i = z__1.i;\n/* L50: */\n\t\t\t}\n\t\t\tif (nounit) {\n\t\t\t    i__4 = j;\n\t\t\t    i__1 = j;\n\t\t\t    i__3 = j * a_dim1 + 1;\n\t\t\t    z__1.r = x[i__1].r * a[i__3].r - x[i__1].i * a[\n\t\t\t\t    i__3].i, z__1.i = x[i__1].r * a[i__3].i + \n\t\t\t\t    x[i__1].i * a[i__3].r;\n\t\t\t    x[i__4].r = z__1.r, x[i__4].i = z__1.i;\n\t\t\t}\n\t\t    }\n/* L60: */\n\t\t}\n\t    } else {\n\t\tkx += (*n - 1) * *incx;\n\t\tjx = kx;\n\t\tfor (j = *n; j >= 1; --j) {\n\t\t    i__4 = jx;\n\t\t    if (x[i__4].r != 0. || x[i__4].i != 0.) {\n\t\t\ti__4 = jx;\n\t\t\ttemp.r = x[i__4].r, temp.i = x[i__4].i;\n\t\t\tix = kx;\n\t\t\tl = 1 - j;\n/* Computing MIN */\n\t\t\ti__4 = *n, i__1 = j + *k;\n\t\t\ti__3 = j + 1;\n\t\t\tfor (i__ = min(i__4,i__1); i__ >= i__3; --i__) {\n\t\t\t    i__4 = ix;\n\t\t\t    i__1 = ix;\n\t\t\t    i__2 = l + i__ + j * a_dim1;\n\t\t\t    z__2.r = temp.r * a[i__2].r - temp.i * a[i__2].i, \n\t\t\t\t    z__2.i = temp.r * a[i__2].i + temp.i * a[\n\t\t\t\t    i__2].r;\n\t\t\t    z__1.r = x[i__1].r + z__2.r, z__1.i = x[i__1].i + \n\t\t\t\t    z__2.i;\n\t\t\t    x[i__4].r = z__1.r, x[i__4].i = z__1.i;\n\t\t\t    ix -= *incx;\n/* L70: */\n\t\t\t}\n\t\t\tif (nounit) {\n\t\t\t    i__3 = jx;\n\t\t\t    i__4 = jx;\n\t\t\t    i__1 = j * a_dim1 + 1;\n\t\t\t    z__1.r = x[i__4].r * a[i__1].r - x[i__4].i * a[\n\t\t\t\t    i__1].i, z__1.i = x[i__4].r * a[i__1].i + \n\t\t\t\t    x[i__4].i * a[i__1].r;\n\t\t\t    x[i__3].r = z__1.r, x[i__3].i = z__1.i;\n\t\t\t}\n\t\t    }\n\t\t    jx -= *incx;\n\t\t    if (*n - j >= *k) {\n\t\t\tkx -= *incx;\n\t\t    }\n/* L80: */\n\t\t}\n\t    }\n\t}\n    } else {\n\n/*        Form  x := A'*x  or  x := conjg( A' )*x. */\n\n\tif (lsame_(uplo, \"U\", (ftnlen)1, (ftnlen)1)) {\n\t    kplus1 = *k + 1;\n\t    if (*incx == 1) {\n\t\tfor (j = *n; j >= 1; --j) {\n\t\t    i__3 = j;\n\t\t    temp.r = x[i__3].r, temp.i = x[i__3].i;\n\t\t    l = kplus1 - j;\n\t\t    if (noconj) {\n\t\t\tif (nounit) {\n\t\t\t    i__3 = kplus1 + j * a_dim1;\n\t\t\t    z__1.r = temp.r * a[i__3].r - temp.i * a[i__3].i, \n\t\t\t\t    z__1.i = temp.r * a[i__3].i + temp.i * a[\n\t\t\t\t    i__3].r;\n\t\t\t    temp.r = z__1.r, temp.i = z__1.i;\n\t\t\t}\n/* Computing MAX */\n\t\t\ti__4 = 1, i__1 = j - *k;\n\t\t\ti__3 = max(i__4,i__1);\n\t\t\tfor (i__ = j - 1; i__ >= i__3; --i__) {\n\t\t\t    i__4 = l + i__ + j * a_dim1;\n\t\t\t    i__1 = i__;\n\t\t\t    z__2.r = a[i__4].r * x[i__1].r - a[i__4].i * x[\n\t\t\t\t    i__1].i, z__2.i = a[i__4].r * x[i__1].i + \n\t\t\t\t    a[i__4].i * x[i__1].r;\n\t\t\t    z__1.r = temp.r + z__2.r, z__1.i = temp.i + \n\t\t\t\t    z__2.i;\n\t\t\t    temp.r = z__1.r, temp.i = z__1.i;\n/* L90: */\n\t\t\t}\n\t\t    } else {\n\t\t\tif (nounit) {\n\t\t\t    d_cnjg(&z__2, &a[kplus1 + j * a_dim1]);\n\t\t\t    z__1.r = temp.r * z__2.r - temp.i * z__2.i, \n\t\t\t\t    z__1.i = temp.r * z__2.i + temp.i * \n\t\t\t\t    z__2.r;\n\t\t\t    temp.r = z__1.r, temp.i = z__1.i;\n\t\t\t}\n/* Computing MAX */\n\t\t\ti__4 = 1, i__1 = j - *k;\n\t\t\ti__3 = max(i__4,i__1);\n\t\t\tfor (i__ = j - 1; i__ >= i__3; --i__) {\n\t\t\t    d_cnjg(&z__3, &a[l + i__ + j * a_dim1]);\n\t\t\t    i__4 = i__;\n\t\t\t    z__2.r = z__3.r * x[i__4].r - z__3.i * x[i__4].i, \n\t\t\t\t    z__2.i = z__3.r * x[i__4].i + z__3.i * x[\n\t\t\t\t    i__4].r;\n\t\t\t    z__1.r = temp.r + z__2.r, z__1.i = temp.i + \n\t\t\t\t    z__2.i;\n\t\t\t    temp.r = z__1.r, temp.i = z__1.i;\n/* L100: */\n\t\t\t}\n\t\t    }\n\t\t    i__3 = j;\n\t\t    x[i__3].r = temp.r, x[i__3].i = temp.i;\n/* L110: */\n\t\t}\n\t    } else {\n\t\tkx += (*n - 1) * *incx;\n\t\tjx = kx;\n\t\tfor (j = *n; j >= 1; --j) {\n\t\t    i__3 = jx;\n\t\t    temp.r = x[i__3].r, temp.i = x[i__3].i;\n\t\t    kx -= *incx;\n\t\t    ix = kx;\n\t\t    l = kplus1 - j;\n\t\t    if (noconj) {\n\t\t\tif (nounit) {\n\t\t\t    i__3 = kplus1 + j * a_dim1;\n\t\t\t    z__1.r = temp.r * a[i__3].r - temp.i * a[i__3].i, \n\t\t\t\t    z__1.i = temp.r * a[i__3].i + temp.i * a[\n\t\t\t\t    i__3].r;\n\t\t\t    temp.r = z__1.r, temp.i = z__1.i;\n\t\t\t}\n/* Computing MAX */\n\t\t\ti__4 = 1, i__1 = j - *k;\n\t\t\ti__3 = max(i__4,i__1);\n\t\t\tfor (i__ = j - 1; i__ >= i__3; --i__) {\n\t\t\t    i__4 = l + i__ + j * a_dim1;\n\t\t\t    i__1 = ix;\n\t\t\t    z__2.r = a[i__4].r * x[i__1].r - a[i__4].i * x[\n\t\t\t\t    i__1].i, z__2.i = a[i__4].r * x[i__1].i + \n\t\t\t\t    a[i__4].i * x[i__1].r;\n\t\t\t    z__1.r = temp.r + z__2.r, z__1.i = temp.i + \n\t\t\t\t    z__2.i;\n\t\t\t    temp.r = z__1.r, temp.i = z__1.i;\n\t\t\t    ix -= *incx;\n/* L120: */\n\t\t\t}\n\t\t    } else {\n\t\t\tif (nounit) {\n\t\t\t    d_cnjg(&z__2, &a[kplus1 + j * a_dim1]);\n\t\t\t    z__1.r = temp.r * z__2.r - temp.i * z__2.i, \n\t\t\t\t    z__1.i = temp.r * z__2.i + temp.i * \n\t\t\t\t    z__2.r;\n\t\t\t    temp.r = z__1.r, temp.i = z__1.i;\n\t\t\t}\n/* Computing MAX */\n\t\t\ti__4 = 1, i__1 = j - *k;\n\t\t\ti__3 = max(i__4,i__1);\n\t\t\tfor (i__ = j - 1; i__ >= i__3; --i__) {\n\t\t\t    d_cnjg(&z__3, &a[l + i__ + j * a_dim1]);\n\t\t\t    i__4 = ix;\n\t\t\t    z__2.r = z__3.r * x[i__4].r - z__3.i * x[i__4].i, \n\t\t\t\t    z__2.i = z__3.r * x[i__4].i + z__3.i * x[\n\t\t\t\t    i__4].r;\n\t\t\t    z__1.r = temp.r + z__2.r, z__1.i = temp.i + \n\t\t\t\t    z__2.i;\n\t\t\t    temp.r = z__1.r, temp.i = z__1.i;\n\t\t\t    ix -= *incx;\n/* L130: */\n\t\t\t}\n\t\t    }\n\t\t    i__3 = jx;\n\t\t    x[i__3].r = temp.r, x[i__3].i = temp.i;\n\t\t    jx -= *incx;\n/* L140: */\n\t\t}\n\t    }\n\t} else {\n\t    if (*incx == 1) {\n\t\ti__3 = *n;\n\t\tfor (j = 1; j <= i__3; ++j) {\n\t\t    i__4 = j;\n\t\t    temp.r = x[i__4].r, temp.i = x[i__4].i;\n\t\t    l = 1 - j;\n\t\t    if (noconj) {\n\t\t\tif (nounit) {\n\t\t\t    i__4 = j * a_dim1 + 1;\n\t\t\t    z__1.r = temp.r * a[i__4].r - temp.i * a[i__4].i, \n\t\t\t\t    z__1.i = temp.r * a[i__4].i + temp.i * a[\n\t\t\t\t    i__4].r;\n\t\t\t    temp.r = z__1.r, temp.i = z__1.i;\n\t\t\t}\n/* Computing MIN */\n\t\t\ti__1 = *n, i__2 = j + *k;\n\t\t\ti__4 = min(i__1,i__2);\n\t\t\tfor (i__ = j + 1; i__ <= i__4; ++i__) {\n\t\t\t    i__1 = l + i__ + j * a_dim1;\n\t\t\t    i__2 = i__;\n\t\t\t    z__2.r = a[i__1].r * x[i__2].r - a[i__1].i * x[\n\t\t\t\t    i__2].i, z__2.i = a[i__1].r * x[i__2].i + \n\t\t\t\t    a[i__1].i * x[i__2].r;\n\t\t\t    z__1.r = temp.r + z__2.r, z__1.i = temp.i + \n\t\t\t\t    z__2.i;\n\t\t\t    temp.r = z__1.r, temp.i = z__1.i;\n/* L150: */\n\t\t\t}\n\t\t    } else {\n\t\t\tif (nounit) {\n\t\t\t    d_cnjg(&z__2, &a[j * a_dim1 + 1]);\n\t\t\t    z__1.r = temp.r * z__2.r - temp.i * z__2.i, \n\t\t\t\t    z__1.i = temp.r * z__2.i + temp.i * \n\t\t\t\t    z__2.r;\n\t\t\t    temp.r = z__1.r, temp.i = z__1.i;\n\t\t\t}\n/* Computing MIN */\n\t\t\ti__1 = *n, i__2 = j + *k;\n\t\t\ti__4 = min(i__1,i__2);\n\t\t\tfor (i__ = j + 1; i__ <= i__4; ++i__) {\n\t\t\t    d_cnjg(&z__3, &a[l + i__ + j * a_dim1]);\n\t\t\t    i__1 = i__;\n\t\t\t    z__2.r = z__3.r * x[i__1].r - z__3.i * x[i__1].i, \n\t\t\t\t    z__2.i = z__3.r * x[i__1].i + z__3.i * x[\n\t\t\t\t    i__1].r;\n\t\t\t    z__1.r = temp.r + z__2.r, z__1.i = temp.i + \n\t\t\t\t    z__2.i;\n\t\t\t    temp.r = z__1.r, temp.i = z__1.i;\n/* L160: */\n\t\t\t}\n\t\t    }\n\t\t    i__4 = j;\n\t\t    x[i__4].r = temp.r, x[i__4].i = temp.i;\n/* L170: */\n\t\t}\n\t    } else {\n\t\tjx = kx;\n\t\ti__3 = *n;\n\t\tfor (j = 1; j <= i__3; ++j) {\n\t\t    i__4 = jx;\n\t\t    temp.r = x[i__4].r, temp.i = x[i__4].i;\n\t\t    kx += *incx;\n\t\t    ix = kx;\n\t\t    l = 1 - j;\n\t\t    if (noconj) {\n\t\t\tif (nounit) {\n\t\t\t    i__4 = j * a_dim1 + 1;\n\t\t\t    z__1.r = temp.r * a[i__4].r - temp.i * a[i__4].i, \n\t\t\t\t    z__1.i = temp.r * a[i__4].i + temp.i * a[\n\t\t\t\t    i__4].r;\n\t\t\t    temp.r = z__1.r, temp.i = z__1.i;\n\t\t\t}\n/* Computing MIN */\n\t\t\ti__1 = *n, i__2 = j + *k;\n\t\t\ti__4 = min(i__1,i__2);\n\t\t\tfor (i__ = j + 1; i__ <= i__4; ++i__) {\n\t\t\t    i__1 = l + i__ + j * a_dim1;\n\t\t\t    i__2 = ix;\n\t\t\t    z__2.r = a[i__1].r * x[i__2].r - a[i__1].i * x[\n\t\t\t\t    i__2].i, z__2.i = a[i__1].r * x[i__2].i + \n\t\t\t\t    a[i__1].i * x[i__2].r;\n\t\t\t    z__1.r = temp.r + z__2.r, z__1.i = temp.i + \n\t\t\t\t    z__2.i;\n\t\t\t    temp.r = z__1.r, temp.i = z__1.i;\n\t\t\t    ix += *incx;\n/* L180: */\n\t\t\t}\n\t\t    } else {\n\t\t\tif (nounit) {\n\t\t\t    d_cnjg(&z__2, &a[j * a_dim1 + 1]);\n\t\t\t    z__1.r = temp.r * z__2.r - temp.i * z__2.i, \n\t\t\t\t    z__1.i = temp.r * z__2.i + temp.i * \n\t\t\t\t    z__2.r;\n\t\t\t    temp.r = z__1.r, temp.i = z__1.i;\n\t\t\t}\n/* Computing MIN */\n\t\t\ti__1 = *n, i__2 = j + *k;\n\t\t\ti__4 = min(i__1,i__2);\n\t\t\tfor (i__ = j + 1; i__ <= i__4; ++i__) {\n\t\t\t    d_cnjg(&z__3, &a[l + i__ + j * a_dim1]);\n\t\t\t    i__1 = ix;\n\t\t\t    z__2.r = z__3.r * x[i__1].r - z__3.i * x[i__1].i, \n\t\t\t\t    z__2.i = z__3.r * x[i__1].i + z__3.i * x[\n\t\t\t\t    i__1].r;\n\t\t\t    z__1.r = temp.r + z__2.r, z__1.i = temp.i + \n\t\t\t\t    z__2.i;\n\t\t\t    temp.r = z__1.r, temp.i = z__1.i;\n\t\t\t    ix += *incx;\n/* L190: */\n\t\t\t}\n\t\t    }\n\t\t    i__4 = jx;\n\t\t    x[i__4].r = temp.r, x[i__4].i = temp.i;\n\t\t    jx += *incx;\n/* L200: */\n\t\t}\n\t    }\n\t}\n    }\n\n    return 0;\n\n/*     End of ZTBMV . */\n\n} /* ztbmv_ */\n\n"
  },
  {
    "path": "include/eigen3/blas/fortran/complexdots.f",
    "content": "      COMPLEX FUNCTION CDOTC(N,CX,INCX,CY,INCY)\n      INTEGER INCX,INCY,N\n      COMPLEX CX(*),CY(*)\n      COMPLEX RES\n      EXTERNAL CDOTCW\n      \n      CALL CDOTCW(N,CX,INCX,CY,INCY,RES)\n      CDOTC = RES\n      RETURN\n      END\n      \n      COMPLEX FUNCTION CDOTU(N,CX,INCX,CY,INCY)\n      INTEGER INCX,INCY,N\n      COMPLEX CX(*),CY(*)\n      COMPLEX RES\n      EXTERNAL CDOTUW\n      \n      CALL CDOTUW(N,CX,INCX,CY,INCY,RES)\n      CDOTU = RES\n      RETURN\n      END\n      \n      DOUBLE COMPLEX FUNCTION ZDOTC(N,CX,INCX,CY,INCY)\n      INTEGER INCX,INCY,N\n      DOUBLE COMPLEX CX(*),CY(*)\n      DOUBLE COMPLEX RES\n      EXTERNAL ZDOTCW\n      \n      CALL ZDOTCW(N,CX,INCX,CY,INCY,RES)\n      ZDOTC = RES\n      RETURN\n      END\n      \n      DOUBLE COMPLEX FUNCTION ZDOTU(N,CX,INCX,CY,INCY)\n      INTEGER INCX,INCY,N\n      DOUBLE COMPLEX CX(*),CY(*)\n      DOUBLE COMPLEX RES\n      EXTERNAL ZDOTUW\n      \n      CALL ZDOTUW(N,CX,INCX,CY,INCY,RES)\n      ZDOTU = RES\n      RETURN\n      END\n"
  },
  {
    "path": "include/eigen3/blas/level1_cplx_impl.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"common.h\"\n\nstruct scalar_norm1_op {\n  typedef RealScalar result_type;\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_norm1_op)\n  inline RealScalar operator() (const Scalar& a) const { return numext::norm1(a); }\n};\nnamespace Eigen {\n  namespace internal {\n    template<> struct functor_traits<scalar_norm1_op >\n    {\n      enum { Cost = 3 * NumTraits<Scalar>::AddCost, PacketAccess = 0 };\n    };\n  }\n}\n\n// computes the sum of magnitudes of all vector elements or, for a complex vector x, the sum\n// res = |Rex1| + |Imx1| + |Rex2| + |Imx2| + ... + |Rexn| + |Imxn|, where x is a vector of order n\nRealScalar EIGEN_CAT(EIGEN_CAT(REAL_SCALAR_SUFFIX,SCALAR_SUFFIX),asum_)(int *n, RealScalar *px, int *incx)\n{\n//   std::cerr << \"__asum \" << *n << \" \" << *incx << \"\\n\";\n  Complex* x = reinterpret_cast<Complex*>(px);\n\n  if(*n<=0) return 0;\n\n  if(*incx==1)  return make_vector(x,*n).unaryExpr<scalar_norm1_op>().sum();\n  else          return make_vector(x,*n,std::abs(*incx)).unaryExpr<scalar_norm1_op>().sum();\n}\n\n// computes a dot product of a conjugated vector with another vector.\nint EIGEN_BLAS_FUNC(dotcw)(int *n, RealScalar *px, int *incx, RealScalar *py, int *incy, RealScalar* pres)\n{\n//   std::cerr << \"_dotc \" << *n << \" \" << *incx << \" \" << *incy << \"\\n\";\n  Scalar* res = reinterpret_cast<Scalar*>(pres);\n\n  if(*n<=0)\n  {\n    *res = Scalar(0);\n    return 0;\n  }\n\n  Scalar* x = reinterpret_cast<Scalar*>(px);\n  Scalar* y = reinterpret_cast<Scalar*>(py);\n\n  if(*incx==1 && *incy==1)    *res = (make_vector(x,*n).dot(make_vector(y,*n)));\n  else if(*incx>0 && *incy>0) *res = (make_vector(x,*n,*incx).dot(make_vector(y,*n,*incy)));\n  else if(*incx<0 && *incy>0) *res = (make_vector(x,*n,-*incx).reverse().dot(make_vector(y,*n,*incy)));\n  else if(*incx>0 && *incy<0) *res = (make_vector(x,*n,*incx).dot(make_vector(y,*n,-*incy).reverse()));\n  else if(*incx<0 && *incy<0) *res = (make_vector(x,*n,-*incx).reverse().dot(make_vector(y,*n,-*incy).reverse()));\n  return 0;\n}\n\n// computes a vector-vector dot product without complex conjugation.\nint EIGEN_BLAS_FUNC(dotuw)(int *n, RealScalar *px, int *incx, RealScalar *py, int *incy, RealScalar* pres)\n{\n  Scalar* res = reinterpret_cast<Scalar*>(pres);\n\n  if(*n<=0)\n  {\n    *res = Scalar(0);\n    return 0;\n  }\n\n  Scalar* x = reinterpret_cast<Scalar*>(px);\n  Scalar* y = reinterpret_cast<Scalar*>(py);\n\n  if(*incx==1 && *incy==1)    *res = (make_vector(x,*n).cwiseProduct(make_vector(y,*n))).sum();\n  else if(*incx>0 && *incy>0) *res = (make_vector(x,*n,*incx).cwiseProduct(make_vector(y,*n,*incy))).sum();\n  else if(*incx<0 && *incy>0) *res = (make_vector(x,*n,-*incx).reverse().cwiseProduct(make_vector(y,*n,*incy))).sum();\n  else if(*incx>0 && *incy<0) *res = (make_vector(x,*n,*incx).cwiseProduct(make_vector(y,*n,-*incy).reverse())).sum();\n  else if(*incx<0 && *incy<0) *res = (make_vector(x,*n,-*incx).reverse().cwiseProduct(make_vector(y,*n,-*incy).reverse())).sum();\n  return 0;\n}\n\nRealScalar EIGEN_CAT(EIGEN_CAT(REAL_SCALAR_SUFFIX,SCALAR_SUFFIX),nrm2_)(int *n, RealScalar *px, int *incx)\n{\n//   std::cerr << \"__nrm2 \" << *n << \" \" << *incx << \"\\n\";\n  if(*n<=0) return 0;\n\n  Scalar* x = reinterpret_cast<Scalar*>(px);\n\n  if(*incx==1)\n    return make_vector(x,*n).stableNorm();\n\n  return make_vector(x,*n,*incx).stableNorm();\n}\n\nint EIGEN_CAT(EIGEN_CAT(SCALAR_SUFFIX,REAL_SCALAR_SUFFIX),rot_)(int *n, RealScalar *px, int *incx, RealScalar *py, int *incy, RealScalar *pc, RealScalar *ps)\n{\n  if(*n<=0) return 0;\n\n  Scalar* x = reinterpret_cast<Scalar*>(px);\n  Scalar* y = reinterpret_cast<Scalar*>(py);\n  RealScalar c = *pc;\n  RealScalar s = *ps;\n\n  StridedVectorType vx(make_vector(x,*n,std::abs(*incx)));\n  StridedVectorType vy(make_vector(y,*n,std::abs(*incy)));\n\n  Reverse<StridedVectorType> rvx(vx);\n  Reverse<StridedVectorType> rvy(vy);\n\n  // TODO implement mixed real-scalar rotations\n       if(*incx<0 && *incy>0) internal::apply_rotation_in_the_plane(rvx, vy, JacobiRotation<Scalar>(c,s));\n  else if(*incx>0 && *incy<0) internal::apply_rotation_in_the_plane(vx, rvy, JacobiRotation<Scalar>(c,s));\n  else                        internal::apply_rotation_in_the_plane(vx, vy,  JacobiRotation<Scalar>(c,s));\n\n  return 0;\n}\n\nint EIGEN_CAT(EIGEN_CAT(SCALAR_SUFFIX,REAL_SCALAR_SUFFIX),scal_)(int *n, RealScalar *palpha, RealScalar *px, int *incx)\n{\n  if(*n<=0) return 0;\n\n  Scalar* x = reinterpret_cast<Scalar*>(px);\n  RealScalar alpha = *palpha;\n\n//   std::cerr << \"__scal \" << *n << \" \" << alpha << \" \" << *incx << \"\\n\";\n\n  if(*incx==1)  make_vector(x,*n) *= alpha;\n  else          make_vector(x,*n,std::abs(*incx)) *= alpha;\n\n  return 0;\n}\n"
  },
  {
    "path": "include/eigen3/blas/level1_impl.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"common.h\"\n\nint EIGEN_BLAS_FUNC(axpy)(const int *n, const RealScalar *palpha, const RealScalar *px, const int *incx, RealScalar *py, const int *incy)\n{\n  const Scalar* x = reinterpret_cast<const Scalar*>(px);\n  Scalar* y = reinterpret_cast<Scalar*>(py);\n  Scalar alpha  = *reinterpret_cast<const Scalar*>(palpha);\n\n  if(*n<=0) return 0;\n\n  if(*incx==1 && *incy==1)    make_vector(y,*n) += alpha * make_vector(x,*n);\n  else if(*incx>0 && *incy>0) make_vector(y,*n,*incy) += alpha * make_vector(x,*n,*incx);\n  else if(*incx>0 && *incy<0) make_vector(y,*n,-*incy).reverse() += alpha * make_vector(x,*n,*incx);\n  else if(*incx<0 && *incy>0) make_vector(y,*n,*incy) += alpha * make_vector(x,*n,-*incx).reverse();\n  else if(*incx<0 && *incy<0) make_vector(y,*n,-*incy).reverse() += alpha * make_vector(x,*n,-*incx).reverse();\n\n  return 0;\n}\n\nint EIGEN_BLAS_FUNC(copy)(int *n, RealScalar *px, int *incx, RealScalar *py, int *incy)\n{\n  if(*n<=0) return 0;\n\n  Scalar* x = reinterpret_cast<Scalar*>(px);\n  Scalar* y = reinterpret_cast<Scalar*>(py);\n\n  // be carefull, *incx==0 is allowed !!\n  if(*incx==1 && *incy==1)\n    make_vector(y,*n) = make_vector(x,*n);\n  else\n  {\n    if(*incx<0) x = x - (*n-1)*(*incx);\n    if(*incy<0) y = y - (*n-1)*(*incy);\n    for(int i=0;i<*n;++i)\n    {\n      *y = *x;\n      x += *incx;\n      y += *incy;\n    }\n  }\n\n  return 0;\n}\n\nint EIGEN_CAT(EIGEN_CAT(i,SCALAR_SUFFIX),amax_)(int *n, RealScalar *px, int *incx)\n{\n  if(*n<=0) return 0;\n  Scalar* x = reinterpret_cast<Scalar*>(px);\n\n  DenseIndex ret;\n  if(*incx==1)  make_vector(x,*n).cwiseAbs().maxCoeff(&ret);\n  else          make_vector(x,*n,std::abs(*incx)).cwiseAbs().maxCoeff(&ret);\n  return int(ret)+1;\n}\n\nint EIGEN_CAT(EIGEN_CAT(i,SCALAR_SUFFIX),amin_)(int *n, RealScalar *px, int *incx)\n{\n  if(*n<=0) return 0;\n  Scalar* x = reinterpret_cast<Scalar*>(px);\n\n  DenseIndex ret;\n  if(*incx==1)  make_vector(x,*n).cwiseAbs().minCoeff(&ret);\n  else          make_vector(x,*n,std::abs(*incx)).cwiseAbs().minCoeff(&ret);\n  return int(ret)+1;\n}\n\nint EIGEN_BLAS_FUNC(rotg)(RealScalar *pa, RealScalar *pb, RealScalar *pc, RealScalar *ps)\n{\n  using std::sqrt;\n  using std::abs;\n\n  Scalar& a = *reinterpret_cast<Scalar*>(pa);\n  Scalar& b = *reinterpret_cast<Scalar*>(pb);\n  RealScalar* c = pc;\n  Scalar* s = reinterpret_cast<Scalar*>(ps);\n\n  #if !ISCOMPLEX\n  Scalar r,z;\n  Scalar aa = abs(a);\n  Scalar ab = abs(b);\n  if((aa+ab)==Scalar(0))\n  {\n    *c = 1;\n    *s = 0;\n    r = 0;\n    z = 0;\n  }\n  else\n  {\n    r = sqrt(a*a + b*b);\n    Scalar amax = aa>ab ? a : b;\n    r = amax>0 ? r : -r;\n    *c = a/r;\n    *s = b/r;\n    z = 1;\n    if (aa > ab) z = *s;\n    if (ab > aa && *c!=RealScalar(0))\n      z = Scalar(1)/ *c;\n  }\n  *pa = r;\n  *pb = z;\n  #else\n  Scalar alpha;\n  RealScalar norm,scale;\n  if(abs(a)==RealScalar(0))\n  {\n    *c = RealScalar(0);\n    *s = Scalar(1);\n    a = b;\n  }\n  else\n  {\n    scale = abs(a) + abs(b);\n    norm = scale*sqrt((numext::abs2(a/scale)) + (numext::abs2(b/scale)));\n    alpha = a/abs(a);\n    *c = abs(a)/norm;\n    *s = alpha*numext::conj(b)/norm;\n    a = alpha*norm;\n  }\n  #endif\n\n//   JacobiRotation<Scalar> r;\n//   r.makeGivens(a,b);\n//   *c = r.c();\n//   *s = r.s();\n\n  return 0;\n}\n\nint EIGEN_BLAS_FUNC(scal)(int *n, RealScalar *palpha, RealScalar *px, int *incx)\n{\n  if(*n<=0) return 0;\n\n  Scalar* x = reinterpret_cast<Scalar*>(px);\n  Scalar alpha = *reinterpret_cast<Scalar*>(palpha);\n\n  if(*incx==1)  make_vector(x,*n) *= alpha;\n  else          make_vector(x,*n,std::abs(*incx)) *= alpha;\n\n  return 0;\n}\n\nint EIGEN_BLAS_FUNC(swap)(int *n, RealScalar *px, int *incx, RealScalar *py, int *incy)\n{\n  if(*n<=0) return 0;\n\n  Scalar* x = reinterpret_cast<Scalar*>(px);\n  Scalar* y = reinterpret_cast<Scalar*>(py);\n\n  if(*incx==1 && *incy==1)    make_vector(y,*n).swap(make_vector(x,*n));\n  else if(*incx>0 && *incy>0) make_vector(y,*n,*incy).swap(make_vector(x,*n,*incx));\n  else if(*incx>0 && *incy<0) make_vector(y,*n,-*incy).reverse().swap(make_vector(x,*n,*incx));\n  else if(*incx<0 && *incy>0) make_vector(y,*n,*incy).swap(make_vector(x,*n,-*incx).reverse());\n  else if(*incx<0 && *incy<0) make_vector(y,*n,-*incy).reverse().swap(make_vector(x,*n,-*incx).reverse());\n\n  return 1;\n}\n"
  },
  {
    "path": "include/eigen3/blas/level1_real_impl.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"common.h\"\n\n// computes the sum of magnitudes of all vector elements or, for a complex vector x, the sum\n// res = |Rex1| + |Imx1| + |Rex2| + |Imx2| + ... + |Rexn| + |Imxn|, where x is a vector of order n\nRealScalar EIGEN_BLAS_FUNC(asum)(int *n, RealScalar *px, int *incx)\n{\n//   std::cerr << \"_asum \" << *n << \" \" << *incx << \"\\n\";\n\n  Scalar* x = reinterpret_cast<Scalar*>(px);\n\n  if(*n<=0) return 0;\n\n  if(*incx==1)  return make_vector(x,*n).cwiseAbs().sum();\n  else          return make_vector(x,*n,std::abs(*incx)).cwiseAbs().sum();\n}\n\n// computes a vector-vector dot product.\nScalar EIGEN_BLAS_FUNC(dot)(int *n, RealScalar *px, int *incx, RealScalar *py, int *incy)\n{\n//   std::cerr << \"_dot \" << *n << \" \" << *incx << \" \" << *incy << \"\\n\";\n\n  if(*n<=0) return 0;\n\n  Scalar* x = reinterpret_cast<Scalar*>(px);\n  Scalar* y = reinterpret_cast<Scalar*>(py);\n\n  if(*incx==1 && *incy==1)    return (make_vector(x,*n).cwiseProduct(make_vector(y,*n))).sum();\n  else if(*incx>0 && *incy>0) return (make_vector(x,*n,*incx).cwiseProduct(make_vector(y,*n,*incy))).sum();\n  else if(*incx<0 && *incy>0) return (make_vector(x,*n,-*incx).reverse().cwiseProduct(make_vector(y,*n,*incy))).sum();\n  else if(*incx>0 && *incy<0) return (make_vector(x,*n,*incx).cwiseProduct(make_vector(y,*n,-*incy).reverse())).sum();\n  else if(*incx<0 && *incy<0) return (make_vector(x,*n,-*incx).reverse().cwiseProduct(make_vector(y,*n,-*incy).reverse())).sum();\n  else return 0;\n}\n\n// computes the Euclidean norm of a vector.\n// FIXME\nScalar EIGEN_BLAS_FUNC(nrm2)(int *n, RealScalar *px, int *incx)\n{\n//   std::cerr << \"_nrm2 \" << *n << \" \" << *incx << \"\\n\";\n  if(*n<=0) return 0;\n\n  Scalar* x = reinterpret_cast<Scalar*>(px);\n\n  if(*incx==1)  return make_vector(x,*n).stableNorm();\n  else          return make_vector(x,*n,std::abs(*incx)).stableNorm();\n}\n\nint EIGEN_BLAS_FUNC(rot)(int *n, RealScalar *px, int *incx, RealScalar *py, int *incy, RealScalar *pc, RealScalar *ps)\n{\n//   std::cerr << \"_rot \" << *n << \" \" << *incx << \" \" << *incy << \"\\n\";\n  if(*n<=0) return 0;\n\n  Scalar* x = reinterpret_cast<Scalar*>(px);\n  Scalar* y = reinterpret_cast<Scalar*>(py);\n  Scalar c = *reinterpret_cast<Scalar*>(pc);\n  Scalar s = *reinterpret_cast<Scalar*>(ps);\n\n  StridedVectorType vx(make_vector(x,*n,std::abs(*incx)));\n  StridedVectorType vy(make_vector(y,*n,std::abs(*incy)));\n\n  Reverse<StridedVectorType> rvx(vx);\n  Reverse<StridedVectorType> rvy(vy);\n\n       if(*incx<0 && *incy>0) internal::apply_rotation_in_the_plane(rvx, vy, JacobiRotation<Scalar>(c,s));\n  else if(*incx>0 && *incy<0) internal::apply_rotation_in_the_plane(vx, rvy, JacobiRotation<Scalar>(c,s));\n  else                        internal::apply_rotation_in_the_plane(vx, vy,  JacobiRotation<Scalar>(c,s));\n\n\n  return 0;\n}\n\n/*\n// performs rotation of points in the modified plane.\nint EIGEN_BLAS_FUNC(rotm)(int *n, RealScalar *px, int *incx, RealScalar *py, int *incy, RealScalar *param)\n{\n  Scalar* x = reinterpret_cast<Scalar*>(px);\n  Scalar* y = reinterpret_cast<Scalar*>(py);\n\n  // TODO\n\n  return 0;\n}\n\n// computes the modified parameters for a Givens rotation.\nint EIGEN_BLAS_FUNC(rotmg)(RealScalar *d1, RealScalar *d2, RealScalar *x1, RealScalar *x2, RealScalar *param)\n{\n  // TODO\n\n  return 0;\n}\n*/\n"
  },
  {
    "path": "include/eigen3/blas/level2_cplx_impl.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"common.h\"\n\n/**  ZHEMV  performs the matrix-vector  operation\n  *\n  *     y := alpha*A*x + beta*y,\n  *\n  *  where alpha and beta are scalars, x and y are n element vectors and\n  *  A is an n by n hermitian matrix.\n  */\nint EIGEN_BLAS_FUNC(hemv)(const char *uplo, const int *n, const RealScalar *palpha, const RealScalar *pa, const int *lda,\n                          const RealScalar *px, const int *incx, const RealScalar *pbeta, RealScalar *py, const int *incy)\n{\n  typedef void (*functype)(int, const Scalar*, int, const Scalar*, Scalar*, Scalar);\n  static const functype func[2] = {\n    // array index: UP\n    (internal::selfadjoint_matrix_vector_product<Scalar,int,ColMajor,Upper,false,false>::run),\n    // array index: LO\n    (internal::selfadjoint_matrix_vector_product<Scalar,int,ColMajor,Lower,false,false>::run),\n  };\n\n  const Scalar* a = reinterpret_cast<const Scalar*>(pa);\n  const Scalar* x = reinterpret_cast<const Scalar*>(px);\n  Scalar* y = reinterpret_cast<Scalar*>(py);\n  Scalar alpha  = *reinterpret_cast<const Scalar*>(palpha);\n  Scalar beta   = *reinterpret_cast<const Scalar*>(pbeta);\n\n  // check arguments\n  int info = 0;\n  if(UPLO(*uplo)==INVALID)        info = 1;\n  else if(*n<0)                   info = 2;\n  else if(*lda<std::max(1,*n))    info = 5;\n  else if(*incx==0)               info = 7;\n  else if(*incy==0)               info = 10;\n  if(info)\n    return xerbla_(SCALAR_SUFFIX_UP\"HEMV \",&info,6);\n\n  if(*n==0)\n    return 1;\n\n  const Scalar* actual_x = get_compact_vector(x,*n,*incx);\n  Scalar* actual_y = get_compact_vector(y,*n,*incy);\n\n  if(beta!=Scalar(1))\n  {\n    if(beta==Scalar(0)) make_vector(actual_y, *n).setZero();\n    else                make_vector(actual_y, *n) *= beta;\n  }\n\n  if(alpha!=Scalar(0))\n  {\n    int code = UPLO(*uplo);\n    if(code>=2 || func[code]==0)\n      return 0;\n\n    func[code](*n, a, *lda, actual_x, actual_y, alpha);\n  }\n\n  if(actual_x!=x) delete[] actual_x;\n  if(actual_y!=y) delete[] copy_back(actual_y,y,*n,*incy);\n\n  return 1;\n}\n\n/**  ZHBMV  performs the matrix-vector  operation\n  *\n  *     y := alpha*A*x + beta*y,\n  *\n  *  where alpha and beta are scalars, x and y are n element vectors and\n  *  A is an n by n hermitian band matrix, with k super-diagonals.\n  */\n// int EIGEN_BLAS_FUNC(hbmv)(char *uplo, int *n, int *k, RealScalar *alpha, RealScalar *a, int *lda,\n//                           RealScalar *x, int *incx, RealScalar *beta, RealScalar *y, int *incy)\n// {\n//   return 1;\n// }\n\n/**  ZHPMV  performs the matrix-vector operation\n  *\n  *     y := alpha*A*x + beta*y,\n  *\n  *  where alpha and beta are scalars, x and y are n element vectors and\n  *  A is an n by n hermitian matrix, supplied in packed form.\n  */\n// int EIGEN_BLAS_FUNC(hpmv)(char *uplo, int *n, RealScalar *alpha, RealScalar *ap, RealScalar *x, int *incx, RealScalar *beta, RealScalar *y, int *incy)\n// {\n//   return 1;\n// }\n\n/**  ZHPR    performs the hermitian rank 1 operation\n  *\n  *     A := alpha*x*conjg( x' ) + A,\n  *\n  *  where alpha is a real scalar, x is an n element vector and A is an\n  *  n by n hermitian matrix, supplied in packed form.\n  */\nint EIGEN_BLAS_FUNC(hpr)(char *uplo, int *n, RealScalar *palpha, RealScalar *px, int *incx, RealScalar *pap)\n{\n  typedef void (*functype)(int, Scalar*, const Scalar*, RealScalar);\n  static const functype func[2] = {\n    // array index: UP\n    (internal::selfadjoint_packed_rank1_update<Scalar,int,ColMajor,Upper,false,Conj>::run),\n    // array index: LO\n    (internal::selfadjoint_packed_rank1_update<Scalar,int,ColMajor,Lower,false,Conj>::run),\n  };\n\n  Scalar* x = reinterpret_cast<Scalar*>(px);\n  Scalar* ap = reinterpret_cast<Scalar*>(pap);\n  RealScalar alpha = *palpha;\n\n  int info = 0;\n  if(UPLO(*uplo)==INVALID)                                            info = 1;\n  else if(*n<0)                                                       info = 2;\n  else if(*incx==0)                                                   info = 5;\n  if(info)\n    return xerbla_(SCALAR_SUFFIX_UP\"HPR  \",&info,6);\n\n  if(alpha==Scalar(0))\n    return 1;\n\n  Scalar* x_cpy = get_compact_vector(x, *n, *incx);\n\n  int code = UPLO(*uplo);\n  if(code>=2 || func[code]==0)\n    return 0;\n\n  func[code](*n, ap, x_cpy, alpha);\n\n  if(x_cpy!=x)  delete[] x_cpy;\n\n  return 1;\n}\n\n/**  ZHPR2  performs the hermitian rank 2 operation\n  *\n  *     A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A,\n  *\n  *  where alpha is a scalar, x and y are n element vectors and A is an\n  *  n by n hermitian matrix, supplied in packed form.\n  */\nint EIGEN_BLAS_FUNC(hpr2)(char *uplo, int *n, RealScalar *palpha, RealScalar *px, int *incx, RealScalar *py, int *incy, RealScalar *pap)\n{\n  typedef void (*functype)(int, Scalar*, const Scalar*, const Scalar*, Scalar);\n  static const functype func[2] = {\n    // array index: UP\n    (internal::packed_rank2_update_selector<Scalar,int,Upper>::run),\n    // array index: LO\n    (internal::packed_rank2_update_selector<Scalar,int,Lower>::run),\n  };\n\n  Scalar* x = reinterpret_cast<Scalar*>(px);\n  Scalar* y = reinterpret_cast<Scalar*>(py);\n  Scalar* ap = reinterpret_cast<Scalar*>(pap);\n  Scalar alpha = *reinterpret_cast<Scalar*>(palpha);\n\n  int info = 0;\n  if(UPLO(*uplo)==INVALID)                                            info = 1;\n  else if(*n<0)                                                       info = 2;\n  else if(*incx==0)                                                   info = 5;\n  else if(*incy==0)                                                   info = 7;\n  if(info)\n    return xerbla_(SCALAR_SUFFIX_UP\"HPR2 \",&info,6);\n\n  if(alpha==Scalar(0))\n    return 1;\n\n  Scalar* x_cpy = get_compact_vector(x, *n, *incx);\n  Scalar* y_cpy = get_compact_vector(y, *n, *incy);\n\n  int code = UPLO(*uplo);\n  if(code>=2 || func[code]==0)\n    return 0;\n\n  func[code](*n, ap, x_cpy, y_cpy, alpha);\n\n  if(x_cpy!=x)  delete[] x_cpy;\n  if(y_cpy!=y)  delete[] y_cpy;\n\n  return 1;\n}\n\n/**  ZHER   performs the hermitian rank 1 operation\n  *\n  *     A := alpha*x*conjg( x' ) + A,\n  *\n  *  where alpha is a real scalar, x is an n element vector and A is an\n  *  n by n hermitian matrix.\n  */\nint EIGEN_BLAS_FUNC(her)(char *uplo, int *n, RealScalar *palpha, RealScalar *px, int *incx, RealScalar *pa, int *lda)\n{\n  typedef void (*functype)(int, Scalar*, int, const Scalar*, const Scalar*, const Scalar&);\n  static const functype func[2] = {\n    // array index: UP\n    (selfadjoint_rank1_update<Scalar,int,ColMajor,Upper,false,Conj>::run),\n    // array index: LO\n    (selfadjoint_rank1_update<Scalar,int,ColMajor,Lower,false,Conj>::run),\n  };\n\n  Scalar* x = reinterpret_cast<Scalar*>(px);\n  Scalar* a = reinterpret_cast<Scalar*>(pa);\n  RealScalar alpha = *reinterpret_cast<RealScalar*>(palpha);\n\n  int info = 0;\n  if(UPLO(*uplo)==INVALID)                                            info = 1;\n  else if(*n<0)                                                       info = 2;\n  else if(*incx==0)                                                   info = 5;\n  else if(*lda<std::max(1,*n))                                        info = 7;\n  if(info)\n    return xerbla_(SCALAR_SUFFIX_UP\"HER  \",&info,6);\n\n  if(alpha==RealScalar(0))\n    return 1;\n\n  Scalar* x_cpy = get_compact_vector(x, *n, *incx);\n\n  int code = UPLO(*uplo);\n  if(code>=2 || func[code]==0)\n    return 0;\n\n  func[code](*n, a, *lda, x_cpy, x_cpy, alpha);\n\n  matrix(a,*n,*n,*lda).diagonal().imag().setZero();\n\n  if(x_cpy!=x)  delete[] x_cpy;\n\n  return 1;\n}\n\n/**  ZHER2  performs the hermitian rank 2 operation\n  *\n  *     A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A,\n  *\n  *  where alpha is a scalar, x and y are n element vectors and A is an n\n  *  by n hermitian matrix.\n  */\nint EIGEN_BLAS_FUNC(her2)(char *uplo, int *n, RealScalar *palpha, RealScalar *px, int *incx, RealScalar *py, int *incy, RealScalar *pa, int *lda)\n{\n  typedef void (*functype)(int, Scalar*, int, const Scalar*, const Scalar*, Scalar);\n  static const functype func[2] = {\n    // array index: UP\n    (internal::rank2_update_selector<Scalar,int,Upper>::run),\n    // array index: LO\n    (internal::rank2_update_selector<Scalar,int,Lower>::run),\n  };\n\n  Scalar* x = reinterpret_cast<Scalar*>(px);\n  Scalar* y = reinterpret_cast<Scalar*>(py);\n  Scalar* a = reinterpret_cast<Scalar*>(pa);\n  Scalar alpha = *reinterpret_cast<Scalar*>(palpha);\n\n  int info = 0;\n  if(UPLO(*uplo)==INVALID)                                            info = 1;\n  else if(*n<0)                                                       info = 2;\n  else if(*incx==0)                                                   info = 5;\n  else if(*incy==0)                                                   info = 7;\n  else if(*lda<std::max(1,*n))                                        info = 9;\n  if(info)\n    return xerbla_(SCALAR_SUFFIX_UP\"HER2 \",&info,6);\n\n  if(alpha==Scalar(0))\n    return 1;\n\n  Scalar* x_cpy = get_compact_vector(x, *n, *incx);\n  Scalar* y_cpy = get_compact_vector(y, *n, *incy);\n\n  int code = UPLO(*uplo);\n  if(code>=2 || func[code]==0)\n    return 0;\n\n  func[code](*n, a, *lda, x_cpy, y_cpy, alpha);\n\n  matrix(a,*n,*n,*lda).diagonal().imag().setZero();\n\n  if(x_cpy!=x)  delete[] x_cpy;\n  if(y_cpy!=y)  delete[] y_cpy;\n\n  return 1;\n}\n\n/**  ZGERU  performs the rank 1 operation\n  *\n  *     A := alpha*x*y' + A,\n  *\n  *  where alpha is a scalar, x is an m element vector, y is an n element\n  *  vector and A is an m by n matrix.\n  */\nint EIGEN_BLAS_FUNC(geru)(int *m, int *n, RealScalar *palpha, RealScalar *px, int *incx, RealScalar *py, int *incy, RealScalar *pa, int *lda)\n{\n  Scalar* x = reinterpret_cast<Scalar*>(px);\n  Scalar* y = reinterpret_cast<Scalar*>(py);\n  Scalar* a = reinterpret_cast<Scalar*>(pa);\n  Scalar alpha = *reinterpret_cast<Scalar*>(palpha);\n\n  int info = 0;\n       if(*m<0)                                                       info = 1;\n  else if(*n<0)                                                       info = 2;\n  else if(*incx==0)                                                   info = 5;\n  else if(*incy==0)                                                   info = 7;\n  else if(*lda<std::max(1,*m))                                        info = 9;\n  if(info)\n    return xerbla_(SCALAR_SUFFIX_UP\"GERU \",&info,6);\n\n  if(alpha==Scalar(0))\n    return 1;\n\n  Scalar* x_cpy = get_compact_vector(x,*m,*incx);\n  Scalar* y_cpy = get_compact_vector(y,*n,*incy);\n\n  internal::general_rank1_update<Scalar,int,ColMajor,false,false>::run(*m, *n, a, *lda, x_cpy, y_cpy, alpha);\n\n  if(x_cpy!=x)  delete[] x_cpy;\n  if(y_cpy!=y)  delete[] y_cpy;\n\n  return 1;\n}\n\n/**  ZGERC  performs the rank 1 operation\n  *\n  *     A := alpha*x*conjg( y' ) + A,\n  *\n  *  where alpha is a scalar, x is an m element vector, y is an n element\n  *  vector and A is an m by n matrix.\n  */\nint EIGEN_BLAS_FUNC(gerc)(int *m, int *n, RealScalar *palpha, RealScalar *px, int *incx, RealScalar *py, int *incy, RealScalar *pa, int *lda)\n{\n  Scalar* x = reinterpret_cast<Scalar*>(px);\n  Scalar* y = reinterpret_cast<Scalar*>(py);\n  Scalar* a = reinterpret_cast<Scalar*>(pa);\n  Scalar alpha = *reinterpret_cast<Scalar*>(palpha);\n\n  int info = 0;\n       if(*m<0)                                                       info = 1;\n  else if(*n<0)                                                       info = 2;\n  else if(*incx==0)                                                   info = 5;\n  else if(*incy==0)                                                   info = 7;\n  else if(*lda<std::max(1,*m))                                        info = 9;\n  if(info)\n    return xerbla_(SCALAR_SUFFIX_UP\"GERC \",&info,6);\n\n  if(alpha==Scalar(0))\n    return 1;\n\n  Scalar* x_cpy = get_compact_vector(x,*m,*incx);\n  Scalar* y_cpy = get_compact_vector(y,*n,*incy);\n\n  internal::general_rank1_update<Scalar,int,ColMajor,false,Conj>::run(*m, *n, a, *lda, x_cpy, y_cpy, alpha);\n\n  if(x_cpy!=x)  delete[] x_cpy;\n  if(y_cpy!=y)  delete[] y_cpy;\n\n  return 1;\n}\n"
  },
  {
    "path": "include/eigen3/blas/level2_impl.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"common.h\"\n\ntemplate<typename Index, typename Scalar, int StorageOrder, bool ConjugateLhs, bool ConjugateRhs>\nstruct general_matrix_vector_product_wrapper\n{\n  static void run(Index rows, Index cols,const Scalar *lhs, Index lhsStride, const Scalar *rhs, Index rhsIncr, Scalar* res, Index resIncr, Scalar alpha)\n  {\n    typedef internal::const_blas_data_mapper<Scalar,Index,StorageOrder> LhsMapper;\n    typedef internal::const_blas_data_mapper<Scalar,Index,RowMajor> RhsMapper;\n    \n    internal::general_matrix_vector_product\n        <Index,Scalar,LhsMapper,StorageOrder,ConjugateLhs,Scalar,RhsMapper,ConjugateRhs>::run(\n        rows, cols, LhsMapper(lhs, lhsStride), RhsMapper(rhs, rhsIncr), res, resIncr, alpha);\n  }\n};\n\nint EIGEN_BLAS_FUNC(gemv)(const char *opa, const int *m, const int *n, const RealScalar *palpha,\n                          const RealScalar *pa, const int *lda, const RealScalar *pb, const int *incb, const RealScalar *pbeta, RealScalar *pc, const int *incc)\n{\n  typedef void (*functype)(int, int, const Scalar *, int, const Scalar *, int , Scalar *, int, Scalar);\n  static const functype func[4] = {\n    // array index: NOTR\n    (general_matrix_vector_product_wrapper<int,Scalar,ColMajor,false,false>::run),\n    // array index: TR  \n    (general_matrix_vector_product_wrapper<int,Scalar,RowMajor,false,false>::run),\n    // array index: ADJ \n    (general_matrix_vector_product_wrapper<int,Scalar,RowMajor,Conj ,false>::run),\n    0\n  };\n\n  const Scalar* a = reinterpret_cast<const Scalar*>(pa);\n  const Scalar* b = reinterpret_cast<const Scalar*>(pb);\n  Scalar* c = reinterpret_cast<Scalar*>(pc);\n  Scalar alpha  = *reinterpret_cast<const Scalar*>(palpha);\n  Scalar beta   = *reinterpret_cast<const Scalar*>(pbeta);\n\n  // check arguments\n  int info = 0;\n  if(OP(*opa)==INVALID)           info = 1;\n  else if(*m<0)                   info = 2;\n  else if(*n<0)                   info = 3;\n  else if(*lda<std::max(1,*m))    info = 6;\n  else if(*incb==0)               info = 8;\n  else if(*incc==0)               info = 11;\n  if(info)\n    return xerbla_(SCALAR_SUFFIX_UP\"GEMV \",&info,6);\n\n  if(*m==0 || *n==0 || (alpha==Scalar(0) && beta==Scalar(1)))\n    return 0;\n\n  int actual_m = *m;\n  int actual_n = *n;\n  int code = OP(*opa);\n  if(code!=NOTR)\n    std::swap(actual_m,actual_n);\n\n  const Scalar* actual_b = get_compact_vector(b,actual_n,*incb);\n  Scalar* actual_c = get_compact_vector(c,actual_m,*incc);\n\n  if(beta!=Scalar(1))\n  {\n    if(beta==Scalar(0)) make_vector(actual_c, actual_m).setZero();\n    else                make_vector(actual_c, actual_m) *= beta;\n  }\n\n  if(code>=4 || func[code]==0)\n    return 0;\n\n  func[code](actual_m, actual_n, a, *lda, actual_b, 1, actual_c, 1, alpha);\n\n  if(actual_b!=b) delete[] actual_b;\n  if(actual_c!=c) delete[] copy_back(actual_c,c,actual_m,*incc);\n\n  return 1;\n}\n\nint EIGEN_BLAS_FUNC(trsv)(const char *uplo, const char *opa, const char *diag, const int *n, const RealScalar *pa, const int *lda, RealScalar *pb, const int *incb)\n{\n  typedef void (*functype)(int, const Scalar *, int, Scalar *);\n  static const functype func[16] = {\n    // array index: NOTR  | (UP << 2) | (NUNIT << 3)\n    (internal::triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Upper|0,       false,ColMajor>::run),\n    // array index: TR    | (UP << 2) | (NUNIT << 3)\n    (internal::triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Lower|0,       false,RowMajor>::run),\n    // array index: ADJ   | (UP << 2) | (NUNIT << 3)\n    (internal::triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Lower|0,       Conj, RowMajor>::run),\n    0,\n    // array index: NOTR  | (LO << 2) | (NUNIT << 3)\n    (internal::triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Lower|0,       false,ColMajor>::run),\n    // array index: TR    | (LO << 2) | (NUNIT << 3)\n    (internal::triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Upper|0,       false,RowMajor>::run),\n    // array index: ADJ   | (LO << 2) | (NUNIT << 3)\n    (internal::triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Upper|0,       Conj, RowMajor>::run),\n    0,\n    // array index: NOTR  | (UP << 2) | (UNIT  << 3)\n    (internal::triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Upper|UnitDiag,false,ColMajor>::run),\n    // array index: TR    | (UP << 2) | (UNIT  << 3)\n    (internal::triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Lower|UnitDiag,false,RowMajor>::run),\n    // array index: ADJ   | (UP << 2) | (UNIT  << 3)\n    (internal::triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Lower|UnitDiag,Conj, RowMajor>::run),\n    0,\n    // array index: NOTR  | (LO << 2) | (UNIT  << 3)\n    (internal::triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Lower|UnitDiag,false,ColMajor>::run),\n    // array index: TR    | (LO << 2) | (UNIT  << 3)\n    (internal::triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Upper|UnitDiag,false,RowMajor>::run),\n    // array index: ADJ   | (LO << 2) | (UNIT  << 3)\n    (internal::triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Upper|UnitDiag,Conj, RowMajor>::run),\n    0\n  };\n\n  const Scalar* a = reinterpret_cast<const Scalar*>(pa);\n  Scalar* b = reinterpret_cast<Scalar*>(pb);\n\n  int info = 0;\n  if(UPLO(*uplo)==INVALID)                                            info = 1;\n  else if(OP(*opa)==INVALID)                                          info = 2;\n  else if(DIAG(*diag)==INVALID)                                       info = 3;\n  else if(*n<0)                                                       info = 4;\n  else if(*lda<std::max(1,*n))                                        info = 6;\n  else if(*incb==0)                                                   info = 8;\n  if(info)\n    return xerbla_(SCALAR_SUFFIX_UP\"TRSV \",&info,6);\n\n  Scalar* actual_b = get_compact_vector(b,*n,*incb);\n\n  int code = OP(*opa) | (UPLO(*uplo) << 2) | (DIAG(*diag) << 3);\n  func[code](*n, a, *lda, actual_b);\n\n  if(actual_b!=b) delete[] copy_back(actual_b,b,*n,*incb);\n\n  return 0;\n}\n\n\n\nint EIGEN_BLAS_FUNC(trmv)(const char *uplo, const char *opa, const char *diag, const int *n, const RealScalar *pa, const int *lda, RealScalar *pb, const int *incb)\n{\n  typedef void (*functype)(int, int, const Scalar *, int, const Scalar *, int, Scalar *, int, const Scalar&);\n  static const functype func[16] = {\n    // array index: NOTR  | (UP << 2) | (NUNIT << 3)\n    (internal::triangular_matrix_vector_product<int,Upper|0,       Scalar,false,Scalar,false,ColMajor>::run),\n    // array index: TR    | (UP << 2) | (NUNIT << 3)\n    (internal::triangular_matrix_vector_product<int,Lower|0,       Scalar,false,Scalar,false,RowMajor>::run),\n    // array index: ADJ   | (UP << 2) | (NUNIT << 3)\n    (internal::triangular_matrix_vector_product<int,Lower|0,       Scalar,Conj, Scalar,false,RowMajor>::run),\n    0,\n    // array index: NOTR  | (LO << 2) | (NUNIT << 3)\n    (internal::triangular_matrix_vector_product<int,Lower|0,       Scalar,false,Scalar,false,ColMajor>::run),\n    // array index: TR    | (LO << 2) | (NUNIT << 3)\n    (internal::triangular_matrix_vector_product<int,Upper|0,       Scalar,false,Scalar,false,RowMajor>::run),\n    // array index: ADJ   | (LO << 2) | (NUNIT << 3)\n    (internal::triangular_matrix_vector_product<int,Upper|0,       Scalar,Conj, Scalar,false,RowMajor>::run),\n    0,\n    // array index: NOTR  | (UP << 2) | (UNIT  << 3)\n    (internal::triangular_matrix_vector_product<int,Upper|UnitDiag,Scalar,false,Scalar,false,ColMajor>::run),\n    // array index: TR    | (UP << 2) | (UNIT  << 3)\n    (internal::triangular_matrix_vector_product<int,Lower|UnitDiag,Scalar,false,Scalar,false,RowMajor>::run),\n    // array index: ADJ   | (UP << 2) | (UNIT  << 3)\n    (internal::triangular_matrix_vector_product<int,Lower|UnitDiag,Scalar,Conj, Scalar,false,RowMajor>::run),\n    0,\n    // array index: NOTR  | (LO << 2) | (UNIT  << 3)\n    (internal::triangular_matrix_vector_product<int,Lower|UnitDiag,Scalar,false,Scalar,false,ColMajor>::run),\n    // array index: TR    | (LO << 2) | (UNIT  << 3)\n    (internal::triangular_matrix_vector_product<int,Upper|UnitDiag,Scalar,false,Scalar,false,RowMajor>::run),\n    // array index: ADJ   | (LO << 2) | (UNIT  << 3)\n    (internal::triangular_matrix_vector_product<int,Upper|UnitDiag,Scalar,Conj, Scalar,false,RowMajor>::run),\n    0\n  };\n\n  const Scalar* a = reinterpret_cast<const Scalar*>(pa);\n  Scalar* b = reinterpret_cast<Scalar*>(pb);\n\n  int info = 0;\n  if(UPLO(*uplo)==INVALID)                                            info = 1;\n  else if(OP(*opa)==INVALID)                                          info = 2;\n  else if(DIAG(*diag)==INVALID)                                       info = 3;\n  else if(*n<0)                                                       info = 4;\n  else if(*lda<std::max(1,*n))                                        info = 6;\n  else if(*incb==0)                                                   info = 8;\n  if(info)\n    return xerbla_(SCALAR_SUFFIX_UP\"TRMV \",&info,6);\n\n  if(*n==0)\n    return 1;\n\n  Scalar* actual_b = get_compact_vector(b,*n,*incb);\n  Matrix<Scalar,Dynamic,1> res(*n);\n  res.setZero();\n\n  int code = OP(*opa) | (UPLO(*uplo) << 2) | (DIAG(*diag) << 3);\n  if(code>=16 || func[code]==0)\n    return 0;\n\n  func[code](*n, *n, a, *lda, actual_b, 1, res.data(), 1, Scalar(1));\n\n  copy_back(res.data(),b,*n,*incb);\n  if(actual_b!=b) delete[] actual_b;\n\n  return 1;\n}\n\n/**  GBMV  performs one of the matrix-vector operations\n  *\n  *     y := alpha*A*x + beta*y,   or   y := alpha*A'*x + beta*y,\n  *\n  *  where alpha and beta are scalars, x and y are vectors and A is an\n  *  m by n band matrix, with kl sub-diagonals and ku super-diagonals.\n  */\nint EIGEN_BLAS_FUNC(gbmv)(char *trans, int *m, int *n, int *kl, int *ku, RealScalar *palpha, RealScalar *pa, int *lda,\n                          RealScalar *px, int *incx, RealScalar *pbeta, RealScalar *py, int *incy)\n{\n  const Scalar* a = reinterpret_cast<const Scalar*>(pa);\n  const Scalar* x = reinterpret_cast<const Scalar*>(px);\n  Scalar* y = reinterpret_cast<Scalar*>(py);\n  Scalar alpha = *reinterpret_cast<const Scalar*>(palpha);\n  Scalar beta = *reinterpret_cast<const Scalar*>(pbeta);\n  int coeff_rows = *kl+*ku+1;\n\n  int info = 0;\n       if(OP(*trans)==INVALID)                                        info = 1;\n  else if(*m<0)                                                       info = 2;\n  else if(*n<0)                                                       info = 3;\n  else if(*kl<0)                                                      info = 4;\n  else if(*ku<0)                                                      info = 5;\n  else if(*lda<coeff_rows)                                            info = 8;\n  else if(*incx==0)                                                   info = 10;\n  else if(*incy==0)                                                   info = 13;\n  if(info)\n    return xerbla_(SCALAR_SUFFIX_UP\"GBMV \",&info,6);\n\n  if(*m==0 || *n==0 || (alpha==Scalar(0) && beta==Scalar(1)))\n    return 0;\n\n  int actual_m = *m;\n  int actual_n = *n;\n  if(OP(*trans)!=NOTR)\n    std::swap(actual_m,actual_n);\n\n  const Scalar* actual_x = get_compact_vector(x,actual_n,*incx);\n  Scalar* actual_y = get_compact_vector(y,actual_m,*incy);\n\n  if(beta!=Scalar(1))\n  {\n    if(beta==Scalar(0)) make_vector(actual_y, actual_m).setZero();\n    else                make_vector(actual_y, actual_m) *= beta;\n  }\n\n  ConstMatrixType mat_coeffs(a,coeff_rows,*n,*lda);\n\n  int nb = std::min(*n,(*m)+(*ku));\n  for(int j=0; j<nb; ++j)\n  {\n    int start = std::max(0,j - *ku);\n    int end = std::min((*m)-1,j + *kl);\n    int len = end - start + 1;\n    int offset = (*ku) - j + start;\n    if(OP(*trans)==NOTR)\n      make_vector(actual_y+start,len) += (alpha*actual_x[j]) * mat_coeffs.col(j).segment(offset,len);\n    else if(OP(*trans)==TR)\n      actual_y[j] += alpha * ( mat_coeffs.col(j).segment(offset,len).transpose() * make_vector(actual_x+start,len) ).value();\n    else\n      actual_y[j] += alpha * ( mat_coeffs.col(j).segment(offset,len).adjoint()   * make_vector(actual_x+start,len) ).value();\n  }\n\n  if(actual_x!=x) delete[] actual_x;\n  if(actual_y!=y) delete[] copy_back(actual_y,y,actual_m,*incy);\n\n  return 0;\n}\n\n#if 0\n/**  TBMV  performs one of the matrix-vector operations\n  *\n  *     x := A*x,   or   x := A'*x,\n  *\n  *  where x is an n element vector and  A is an n by n unit, or non-unit,\n  *  upper or lower triangular band matrix, with ( k + 1 ) diagonals.\n  */\nint EIGEN_BLAS_FUNC(tbmv)(char *uplo, char *opa, char *diag, int *n, int *k, RealScalar *pa, int *lda, RealScalar *px, int *incx)\n{\n  Scalar* a = reinterpret_cast<Scalar*>(pa);\n  Scalar* x = reinterpret_cast<Scalar*>(px);\n  int coeff_rows = *k + 1;\n\n  int info = 0;\n       if(UPLO(*uplo)==INVALID)                                       info = 1;\n  else if(OP(*opa)==INVALID)                                          info = 2;\n  else if(DIAG(*diag)==INVALID)                                       info = 3;\n  else if(*n<0)                                                       info = 4;\n  else if(*k<0)                                                       info = 5;\n  else if(*lda<coeff_rows)                                            info = 7;\n  else if(*incx==0)                                                   info = 9;\n  if(info)\n    return xerbla_(SCALAR_SUFFIX_UP\"TBMV \",&info,6);\n\n  if(*n==0)\n    return 0;\n\n  int actual_n = *n;\n\n  Scalar* actual_x = get_compact_vector(x,actual_n,*incx);\n\n  MatrixType mat_coeffs(a,coeff_rows,*n,*lda);\n\n  int ku = UPLO(*uplo)==UPPER ? *k : 0;\n  int kl = UPLO(*uplo)==LOWER ? *k : 0;\n\n  for(int j=0; j<*n; ++j)\n  {\n    int start = std::max(0,j - ku);\n    int end = std::min((*m)-1,j + kl);\n    int len = end - start + 1;\n    int offset = (ku) - j + start;\n\n    if(OP(*trans)==NOTR)\n      make_vector(actual_y+start,len) += (alpha*actual_x[j]) * mat_coeffs.col(j).segment(offset,len);\n    else if(OP(*trans)==TR)\n      actual_y[j] += alpha * ( mat_coeffs.col(j).segment(offset,len).transpose() * make_vector(actual_x+start,len) ).value();\n    else\n      actual_y[j] += alpha * ( mat_coeffs.col(j).segment(offset,len).adjoint()   * make_vector(actual_x+start,len) ).value();\n  }\n\n  if(actual_x!=x) delete[] actual_x;\n  if(actual_y!=y) delete[] copy_back(actual_y,y,actual_m,*incy);\n\n  return 0;\n}\n#endif\n\n/**  DTBSV  solves one of the systems of equations\n  *\n  *     A*x = b,   or   A'*x = b,\n  *\n  *  where b and x are n element vectors and A is an n by n unit, or\n  *  non-unit, upper or lower triangular band matrix, with ( k + 1 )\n  *  diagonals.\n  *\n  *  No test for singularity or near-singularity is included in this\n  *  routine. Such tests must be performed before calling this routine.\n  */\nint EIGEN_BLAS_FUNC(tbsv)(char *uplo, char *op, char *diag, int *n, int *k, RealScalar *pa, int *lda, RealScalar *px, int *incx)\n{\n  typedef void (*functype)(int, int, const Scalar *, int, Scalar *);\n  static const functype func[16] = {\n    // array index: NOTR  | (UP << 2) | (NUNIT << 3)\n    (internal::band_solve_triangular_selector<int,Upper|0,       Scalar,false,Scalar,ColMajor>::run),\n    // array index: TR    | (UP << 2) | (NUNIT << 3)\n    (internal::band_solve_triangular_selector<int,Lower|0,       Scalar,false,Scalar,RowMajor>::run),\n    // array index: ADJ   | (UP << 2) | (NUNIT << 3)\n    (internal::band_solve_triangular_selector<int,Lower|0,       Scalar,Conj, Scalar,RowMajor>::run),\n    0,\n    // array index: NOTR  | (LO << 2) | (NUNIT << 3)\n    (internal::band_solve_triangular_selector<int,Lower|0,       Scalar,false,Scalar,ColMajor>::run),\n    // array index: TR    | (LO << 2) | (NUNIT << 3)\n    (internal::band_solve_triangular_selector<int,Upper|0,       Scalar,false,Scalar,RowMajor>::run),\n    // array index: ADJ   | (LO << 2) | (NUNIT << 3)\n    (internal::band_solve_triangular_selector<int,Upper|0,       Scalar,Conj, Scalar,RowMajor>::run),\n    0,\n    // array index: NOTR  | (UP << 2) | (UNIT  << 3)\n    (internal::band_solve_triangular_selector<int,Upper|UnitDiag,Scalar,false,Scalar,ColMajor>::run),\n    // array index: TR    | (UP << 2) | (UNIT  << 3)\n    (internal::band_solve_triangular_selector<int,Lower|UnitDiag,Scalar,false,Scalar,RowMajor>::run),\n    // array index: ADJ   | (UP << 2) | (UNIT  << 3)\n    (internal::band_solve_triangular_selector<int,Lower|UnitDiag,Scalar,Conj, Scalar,RowMajor>::run),\n    0,\n    // array index: NOTR  | (LO << 2) | (UNIT  << 3)\n    (internal::band_solve_triangular_selector<int,Lower|UnitDiag,Scalar,false,Scalar,ColMajor>::run),\n    // array index: TR    | (LO << 2) | (UNIT  << 3)\n    (internal::band_solve_triangular_selector<int,Upper|UnitDiag,Scalar,false,Scalar,RowMajor>::run),\n    // array index: ADJ   | (LO << 2) | (UNIT  << 3)\n    (internal::band_solve_triangular_selector<int,Upper|UnitDiag,Scalar,Conj, Scalar,RowMajor>::run),\n    0,\n  };\n\n  Scalar* a = reinterpret_cast<Scalar*>(pa);\n  Scalar* x = reinterpret_cast<Scalar*>(px);\n  int coeff_rows = *k+1;\n\n  int info = 0;\n       if(UPLO(*uplo)==INVALID)                                       info = 1;\n  else if(OP(*op)==INVALID)                                           info = 2;\n  else if(DIAG(*diag)==INVALID)                                       info = 3;\n  else if(*n<0)                                                       info = 4;\n  else if(*k<0)                                                       info = 5;\n  else if(*lda<coeff_rows)                                            info = 7;\n  else if(*incx==0)                                                   info = 9;\n  if(info)\n    return xerbla_(SCALAR_SUFFIX_UP\"TBSV \",&info,6);\n\n  if(*n==0 || (*k==0 && DIAG(*diag)==UNIT))\n    return 0;\n\n  int actual_n = *n;\n\n  Scalar* actual_x = get_compact_vector(x,actual_n,*incx);\n\n  int code = OP(*op) | (UPLO(*uplo) << 2) | (DIAG(*diag) << 3);\n  if(code>=16 || func[code]==0)\n    return 0;\n\n  func[code](*n, *k, a, *lda, actual_x);\n\n  if(actual_x!=x) delete[] copy_back(actual_x,x,actual_n,*incx);\n\n  return 0;\n}\n\n/**  DTPMV  performs one of the matrix-vector operations\n  *\n  *     x := A*x,   or   x := A'*x,\n  *\n  *  where x is an n element vector and  A is an n by n unit, or non-unit,\n  *  upper or lower triangular matrix, supplied in packed form.\n  */\nint EIGEN_BLAS_FUNC(tpmv)(char *uplo, char *opa, char *diag, int *n, RealScalar *pap, RealScalar *px, int *incx)\n{\n  typedef void (*functype)(int, const Scalar*, const Scalar*, Scalar*, Scalar);\n  static const functype func[16] = {\n    // array index: NOTR  | (UP << 2) | (NUNIT << 3)\n    (internal::packed_triangular_matrix_vector_product<int,Upper|0,       Scalar,false,Scalar,false,ColMajor>::run),\n    // array index: TR    | (UP << 2) | (NUNIT << 3)\n    (internal::packed_triangular_matrix_vector_product<int,Lower|0,       Scalar,false,Scalar,false,RowMajor>::run),\n    // array index: ADJ   | (UP << 2) | (NUNIT << 3)\n    (internal::packed_triangular_matrix_vector_product<int,Lower|0,       Scalar,Conj, Scalar,false,RowMajor>::run),\n    0,\n    // array index: NOTR  | (LO << 2) | (NUNIT << 3)\n    (internal::packed_triangular_matrix_vector_product<int,Lower|0,       Scalar,false,Scalar,false,ColMajor>::run),\n    // array index: TR    | (LO << 2) | (NUNIT << 3)\n    (internal::packed_triangular_matrix_vector_product<int,Upper|0,       Scalar,false,Scalar,false,RowMajor>::run),\n    // array index: ADJ   | (LO << 2) | (NUNIT << 3)\n    (internal::packed_triangular_matrix_vector_product<int,Upper|0,       Scalar,Conj, Scalar,false,RowMajor>::run),\n    0,\n    // array index: NOTR  | (UP << 2) | (UNIT  << 3)\n    (internal::packed_triangular_matrix_vector_product<int,Upper|UnitDiag,Scalar,false,Scalar,false,ColMajor>::run),\n    // array index: TR    | (UP << 2) | (UNIT  << 3)\n    (internal::packed_triangular_matrix_vector_product<int,Lower|UnitDiag,Scalar,false,Scalar,false,RowMajor>::run),\n    // array index: ADJ   | (UP << 2) | (UNIT  << 3)\n    (internal::packed_triangular_matrix_vector_product<int,Lower|UnitDiag,Scalar,Conj, Scalar,false,RowMajor>::run),\n    0,\n    // array index: NOTR  | (LO << 2) | (UNIT  << 3)\n    (internal::packed_triangular_matrix_vector_product<int,Lower|UnitDiag,Scalar,false,Scalar,false,ColMajor>::run),\n    // array index: TR    | (LO << 2) | (UNIT  << 3)\n    (internal::packed_triangular_matrix_vector_product<int,Upper|UnitDiag,Scalar,false,Scalar,false,RowMajor>::run),\n    // array index: ADJ   | (LO << 2) | (UNIT  << 3)\n    (internal::packed_triangular_matrix_vector_product<int,Upper|UnitDiag,Scalar,Conj, Scalar,false,RowMajor>::run),\n    0\n  };\n\n  Scalar* ap = reinterpret_cast<Scalar*>(pap);\n  Scalar* x = reinterpret_cast<Scalar*>(px);\n\n  int info = 0;\n  if(UPLO(*uplo)==INVALID)                                            info = 1;\n  else if(OP(*opa)==INVALID)                                          info = 2;\n  else if(DIAG(*diag)==INVALID)                                       info = 3;\n  else if(*n<0)                                                       info = 4;\n  else if(*incx==0)                                                   info = 7;\n  if(info)\n    return xerbla_(SCALAR_SUFFIX_UP\"TPMV \",&info,6);\n\n  if(*n==0)\n    return 1;\n\n  Scalar* actual_x = get_compact_vector(x,*n,*incx);\n  Matrix<Scalar,Dynamic,1> res(*n);\n  res.setZero();\n\n  int code = OP(*opa) | (UPLO(*uplo) << 2) | (DIAG(*diag) << 3);\n  if(code>=16 || func[code]==0)\n    return 0;\n\n  func[code](*n, ap, actual_x, res.data(), Scalar(1));\n\n  copy_back(res.data(),x,*n,*incx);\n  if(actual_x!=x) delete[] actual_x;\n\n  return 1;\n}\n\n/**  DTPSV  solves one of the systems of equations\n  *\n  *     A*x = b,   or   A'*x = b,\n  *\n  *  where b and x are n element vectors and A is an n by n unit, or\n  *  non-unit, upper or lower triangular matrix, supplied in packed form.\n  *\n  *  No test for singularity or near-singularity is included in this\n  *  routine. Such tests must be performed before calling this routine.\n  */\nint EIGEN_BLAS_FUNC(tpsv)(char *uplo, char *opa, char *diag, int *n, RealScalar *pap, RealScalar *px, int *incx)\n{\n  typedef void (*functype)(int, const Scalar*, Scalar*);\n  static const functype func[16] = {\n    // array index: NOTR  | (UP << 2) | (NUNIT << 3)\n    (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Upper|0,       false,ColMajor>::run),\n    // array index: TR    | (UP << 2) | (NUNIT << 3)\n    (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Lower|0,       false,RowMajor>::run),\n    // array index: ADJ   | (UP << 2) | (NUNIT << 3)\n    (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Lower|0,       Conj, RowMajor>::run),\n    0,\n    // array index: NOTR  | (LO << 2) | (NUNIT << 3)\n    (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Lower|0,       false,ColMajor>::run),\n    // array index: TR    | (LO << 2) | (NUNIT << 3)\n    (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Upper|0,       false,RowMajor>::run),\n    // array index: ADJ   | (LO << 2) | (NUNIT << 3)\n    (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Upper|0,       Conj, RowMajor>::run),\n    0,\n    // array index: NOTR  | (UP << 2) | (UNIT  << 3)\n    (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Upper|UnitDiag,false,ColMajor>::run),\n    // array index: TR    | (UP << 2) | (UNIT  << 3)\n    (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Lower|UnitDiag,false,RowMajor>::run),\n    // array index: ADJ   | (UP << 2) | (UNIT  << 3)\n    (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Lower|UnitDiag,Conj, RowMajor>::run),\n    0,\n    // array index: NOTR  | (LO << 2) | (UNIT  << 3)\n    (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Lower|UnitDiag,false,ColMajor>::run),\n    // array index: TR    | (LO << 2) | (UNIT  << 3)\n    (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Upper|UnitDiag,false,RowMajor>::run),\n    // array index: ADJ   | (LO << 2) | (UNIT  << 3)\n    (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Upper|UnitDiag,Conj, RowMajor>::run),\n    0\n  };\n\n  Scalar* ap = reinterpret_cast<Scalar*>(pap);\n  Scalar* x = reinterpret_cast<Scalar*>(px);\n\n  int info = 0;\n  if(UPLO(*uplo)==INVALID)                                            info = 1;\n  else if(OP(*opa)==INVALID)                                          info = 2;\n  else if(DIAG(*diag)==INVALID)                                       info = 3;\n  else if(*n<0)                                                       info = 4;\n  else if(*incx==0)                                                   info = 7;\n  if(info)\n    return xerbla_(SCALAR_SUFFIX_UP\"TPSV \",&info,6);\n\n  Scalar* actual_x = get_compact_vector(x,*n,*incx);\n\n  int code = OP(*opa) | (UPLO(*uplo) << 2) | (DIAG(*diag) << 3);\n  func[code](*n, ap, actual_x);\n\n  if(actual_x!=x) delete[] copy_back(actual_x,x,*n,*incx);\n\n  return 1;\n}\n"
  },
  {
    "path": "include/eigen3/blas/level2_real_impl.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"common.h\"\n\n// y = alpha*A*x + beta*y\nint EIGEN_BLAS_FUNC(symv) (const char *uplo, const int *n, const RealScalar *palpha, const RealScalar *pa, const int *lda,\n                           const RealScalar *px, const int *incx, const RealScalar *pbeta, RealScalar *py, const int *incy)\n{\n  typedef void (*functype)(int, const Scalar*, int, const Scalar*, Scalar*, Scalar);\n  static const functype func[2] = {\n    // array index: UP\n    (internal::selfadjoint_matrix_vector_product<Scalar,int,ColMajor,Upper,false,false>::run),\n    // array index: LO\n    (internal::selfadjoint_matrix_vector_product<Scalar,int,ColMajor,Lower,false,false>::run),\n  };\n\n  const Scalar* a = reinterpret_cast<const Scalar*>(pa);\n  const Scalar* x = reinterpret_cast<const Scalar*>(px);\n  Scalar* y = reinterpret_cast<Scalar*>(py);\n  Scalar alpha  = *reinterpret_cast<const Scalar*>(palpha);\n  Scalar beta   = *reinterpret_cast<const Scalar*>(pbeta);\n\n  // check arguments\n  int info = 0;\n  if(UPLO(*uplo)==INVALID)        info = 1;\n  else if(*n<0)                   info = 2;\n  else if(*lda<std::max(1,*n))    info = 5;\n  else if(*incx==0)               info = 7;\n  else if(*incy==0)               info = 10;\n  if(info)\n    return xerbla_(SCALAR_SUFFIX_UP\"SYMV \",&info,6);\n\n  if(*n==0)\n    return 0;\n\n  const Scalar* actual_x = get_compact_vector(x,*n,*incx);\n  Scalar* actual_y = get_compact_vector(y,*n,*incy);\n\n  if(beta!=Scalar(1))\n  {\n    if(beta==Scalar(0)) make_vector(actual_y, *n).setZero();\n    else                make_vector(actual_y, *n) *= beta;\n  }\n\n  int code = UPLO(*uplo);\n  if(code>=2 || func[code]==0)\n    return 0;\n\n  func[code](*n, a, *lda, actual_x, actual_y, alpha);\n\n  if(actual_x!=x) delete[] actual_x;\n  if(actual_y!=y) delete[] copy_back(actual_y,y,*n,*incy);\n\n  return 1;\n}\n\n// C := alpha*x*x' + C\nint EIGEN_BLAS_FUNC(syr)(const char *uplo, const int *n, const RealScalar *palpha, const RealScalar *px, const int *incx, RealScalar *pc, const int *ldc)\n{\n\n  typedef void (*functype)(int, Scalar*, int, const Scalar*, const Scalar*, const Scalar&);\n  static const functype func[2] = {\n    // array index: UP\n    (selfadjoint_rank1_update<Scalar,int,ColMajor,Upper,false,Conj>::run),\n    // array index: LO\n    (selfadjoint_rank1_update<Scalar,int,ColMajor,Lower,false,Conj>::run),\n  };\n\n  const Scalar* x = reinterpret_cast<const Scalar*>(px);\n  Scalar* c = reinterpret_cast<Scalar*>(pc);\n  Scalar alpha = *reinterpret_cast<const Scalar*>(palpha);\n\n  int info = 0;\n  if(UPLO(*uplo)==INVALID)                                            info = 1;\n  else if(*n<0)                                                       info = 2;\n  else if(*incx==0)                                                   info = 5;\n  else if(*ldc<std::max(1,*n))                                        info = 7;\n  if(info)\n    return xerbla_(SCALAR_SUFFIX_UP\"SYR  \",&info,6);\n\n  if(*n==0 || alpha==Scalar(0)) return 1;\n\n  // if the increment is not 1, let's copy it to a temporary vector to enable vectorization\n  const Scalar* x_cpy = get_compact_vector(x,*n,*incx);\n\n  int code = UPLO(*uplo);\n  if(code>=2 || func[code]==0)\n    return 0;\n\n  func[code](*n, c, *ldc, x_cpy, x_cpy, alpha);\n\n  if(x_cpy!=x)  delete[] x_cpy;\n\n  return 1;\n}\n\n// C := alpha*x*y' + alpha*y*x' + C\nint EIGEN_BLAS_FUNC(syr2)(const char *uplo, const int *n, const RealScalar *palpha, const RealScalar *px, const int *incx, const RealScalar *py, const int *incy, RealScalar *pc, const int *ldc)\n{\n  typedef void (*functype)(int, Scalar*, int, const Scalar*, const Scalar*, Scalar);\n  static const functype func[2] = {\n    // array index: UP\n    (internal::rank2_update_selector<Scalar,int,Upper>::run),\n    // array index: LO\n    (internal::rank2_update_selector<Scalar,int,Lower>::run),\n  };\n\n  const Scalar* x = reinterpret_cast<const Scalar*>(px);\n  const Scalar* y = reinterpret_cast<const Scalar*>(py);\n  Scalar* c = reinterpret_cast<Scalar*>(pc);\n  Scalar alpha = *reinterpret_cast<const Scalar*>(palpha);\n\n  int info = 0;\n  if(UPLO(*uplo)==INVALID)                                            info = 1;\n  else if(*n<0)                                                       info = 2;\n  else if(*incx==0)                                                   info = 5;\n  else if(*incy==0)                                                   info = 7;\n  else if(*ldc<std::max(1,*n))                                        info = 9;\n  if(info)\n    return xerbla_(SCALAR_SUFFIX_UP\"SYR2 \",&info,6);\n\n  if(alpha==Scalar(0))\n    return 1;\n\n  const Scalar* x_cpy = get_compact_vector(x,*n,*incx);\n  const Scalar* y_cpy = get_compact_vector(y,*n,*incy);\n\n  int code = UPLO(*uplo);\n  if(code>=2 || func[code]==0)\n    return 0;\n\n  func[code](*n, c, *ldc, x_cpy, y_cpy, alpha);\n\n  if(x_cpy!=x)  delete[] x_cpy;\n  if(y_cpy!=y)  delete[] y_cpy;\n\n//   int code = UPLO(*uplo);\n//   if(code>=2 || func[code]==0)\n//     return 0;\n\n//   func[code](*n, a, *inca, b, *incb, c, *ldc, alpha);\n  return 1;\n}\n\n/**  DSBMV  performs the matrix-vector  operation\n  *\n  *     y := alpha*A*x + beta*y,\n  *\n  *  where alpha and beta are scalars, x and y are n element vectors and\n  *  A is an n by n symmetric band matrix, with k super-diagonals.\n  */\n// int EIGEN_BLAS_FUNC(sbmv)( char *uplo, int *n, int *k, RealScalar *alpha, RealScalar *a, int *lda,\n//                            RealScalar *x, int *incx, RealScalar *beta, RealScalar *y, int *incy)\n// {\n//   return 1;\n// }\n\n\n/**  DSPMV  performs the matrix-vector operation\n  *\n  *     y := alpha*A*x + beta*y,\n  *\n  *  where alpha and beta are scalars, x and y are n element vectors and\n  *  A is an n by n symmetric matrix, supplied in packed form.\n  *\n  */\n// int EIGEN_BLAS_FUNC(spmv)(char *uplo, int *n, RealScalar *alpha, RealScalar *ap, RealScalar *x, int *incx, RealScalar *beta, RealScalar *y, int *incy)\n// {\n//   return 1;\n// }\n\n/**  DSPR    performs the symmetric rank 1 operation\n  *\n  *     A := alpha*x*x' + A,\n  *\n  *  where alpha is a real scalar, x is an n element vector and A is an\n  *  n by n symmetric matrix, supplied in packed form.\n  */\nint EIGEN_BLAS_FUNC(spr)(char *uplo, int *n, Scalar *palpha, Scalar *px, int *incx, Scalar *pap)\n{\n  typedef void (*functype)(int, Scalar*, const Scalar*, Scalar);\n  static const functype func[2] = {\n    // array index: UP\n    (internal::selfadjoint_packed_rank1_update<Scalar,int,ColMajor,Upper,false,false>::run),\n    // array index: LO\n    (internal::selfadjoint_packed_rank1_update<Scalar,int,ColMajor,Lower,false,false>::run),\n  };\n\n  Scalar* x = reinterpret_cast<Scalar*>(px);\n  Scalar* ap = reinterpret_cast<Scalar*>(pap);\n  Scalar alpha = *reinterpret_cast<Scalar*>(palpha);\n\n  int info = 0;\n  if(UPLO(*uplo)==INVALID)                                            info = 1;\n  else if(*n<0)                                                       info = 2;\n  else if(*incx==0)                                                   info = 5;\n  if(info)\n    return xerbla_(SCALAR_SUFFIX_UP\"SPR  \",&info,6);\n\n  if(alpha==Scalar(0))\n    return 1;\n\n  Scalar* x_cpy = get_compact_vector(x, *n, *incx);\n\n  int code = UPLO(*uplo);\n  if(code>=2 || func[code]==0)\n    return 0;\n\n  func[code](*n, ap, x_cpy, alpha);\n\n  if(x_cpy!=x)  delete[] x_cpy;\n\n  return 1;\n}\n\n/**  DSPR2  performs the symmetric rank 2 operation\n  *\n  *     A := alpha*x*y' + alpha*y*x' + A,\n  *\n  *  where alpha is a scalar, x and y are n element vectors and A is an\n  *  n by n symmetric matrix, supplied in packed form.\n  */\nint EIGEN_BLAS_FUNC(spr2)(char *uplo, int *n, RealScalar *palpha, RealScalar *px, int *incx, RealScalar *py, int *incy, RealScalar *pap)\n{\n  typedef void (*functype)(int, Scalar*, const Scalar*, const Scalar*, Scalar);\n  static const functype func[2] = {\n    // array index: UP\n    (internal::packed_rank2_update_selector<Scalar,int,Upper>::run),\n    // array index: LO\n    (internal::packed_rank2_update_selector<Scalar,int,Lower>::run),\n  };\n\n  Scalar* x = reinterpret_cast<Scalar*>(px);\n  Scalar* y = reinterpret_cast<Scalar*>(py);\n  Scalar* ap = reinterpret_cast<Scalar*>(pap);\n  Scalar alpha = *reinterpret_cast<Scalar*>(palpha);\n\n  int info = 0;\n  if(UPLO(*uplo)==INVALID)                                            info = 1;\n  else if(*n<0)                                                       info = 2;\n  else if(*incx==0)                                                   info = 5;\n  else if(*incy==0)                                                   info = 7;\n  if(info)\n    return xerbla_(SCALAR_SUFFIX_UP\"SPR2 \",&info,6);\n\n  if(alpha==Scalar(0))\n    return 1;\n\n  Scalar* x_cpy = get_compact_vector(x, *n, *incx);\n  Scalar* y_cpy = get_compact_vector(y, *n, *incy);\n\n  int code = UPLO(*uplo);\n  if(code>=2 || func[code]==0)\n    return 0;\n\n  func[code](*n, ap, x_cpy, y_cpy, alpha);\n\n  if(x_cpy!=x)  delete[] x_cpy;\n  if(y_cpy!=y)  delete[] y_cpy;\n\n  return 1;\n}\n\n/**  DGER   performs the rank 1 operation\n  *\n  *     A := alpha*x*y' + A,\n  *\n  *  where alpha is a scalar, x is an m element vector, y is an n element\n  *  vector and A is an m by n matrix.\n  */\nint EIGEN_BLAS_FUNC(ger)(int *m, int *n, Scalar *palpha, Scalar *px, int *incx, Scalar *py, int *incy, Scalar *pa, int *lda)\n{\n  Scalar* x = reinterpret_cast<Scalar*>(px);\n  Scalar* y = reinterpret_cast<Scalar*>(py);\n  Scalar* a = reinterpret_cast<Scalar*>(pa);\n  Scalar alpha = *reinterpret_cast<Scalar*>(palpha);\n\n  int info = 0;\n       if(*m<0)                                                       info = 1;\n  else if(*n<0)                                                       info = 2;\n  else if(*incx==0)                                                   info = 5;\n  else if(*incy==0)                                                   info = 7;\n  else if(*lda<std::max(1,*m))                                        info = 9;\n  if(info)\n    return xerbla_(SCALAR_SUFFIX_UP\"GER  \",&info,6);\n\n  if(alpha==Scalar(0))\n    return 1;\n\n  Scalar* x_cpy = get_compact_vector(x,*m,*incx);\n  Scalar* y_cpy = get_compact_vector(y,*n,*incy);\n\n  internal::general_rank1_update<Scalar,int,ColMajor,false,false>::run(*m, *n, a, *lda, x_cpy, y_cpy, alpha);\n\n  if(x_cpy!=x)  delete[] x_cpy;\n  if(y_cpy!=y)  delete[] y_cpy;\n\n  return 1;\n}\n"
  },
  {
    "path": "include/eigen3/blas/level3_impl.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n#include <iostream>\n#include \"common.h\"\n\nint EIGEN_BLAS_FUNC(gemm)(const char *opa, const char *opb, const int *m, const int *n, const int *k, const RealScalar *palpha,\n                          const RealScalar *pa, const int *lda, const RealScalar *pb, const int *ldb, const RealScalar *pbeta, RealScalar *pc, const int *ldc)\n{\n//   std::cerr << \"in gemm \" << *opa << \" \" << *opb << \" \" << *m << \" \" << *n << \" \" << *k << \" \" << *lda << \" \" << *ldb << \" \" << *ldc << \" \" << *palpha << \" \" << *pbeta << \"\\n\";\n  typedef void (*functype)(DenseIndex, DenseIndex, DenseIndex, const Scalar *, DenseIndex, const Scalar *, DenseIndex, Scalar *, DenseIndex, Scalar, internal::level3_blocking<Scalar,Scalar>&, Eigen::internal::GemmParallelInfo<DenseIndex>*);\n  static const functype func[12] = {\n    // array index: NOTR  | (NOTR << 2)\n    (internal::general_matrix_matrix_product<DenseIndex,Scalar,ColMajor,false,Scalar,ColMajor,false,ColMajor>::run),\n    // array index: TR    | (NOTR << 2)\n    (internal::general_matrix_matrix_product<DenseIndex,Scalar,RowMajor,false,Scalar,ColMajor,false,ColMajor>::run),\n    // array index: ADJ   | (NOTR << 2)\n    (internal::general_matrix_matrix_product<DenseIndex,Scalar,RowMajor,Conj, Scalar,ColMajor,false,ColMajor>::run),\n    0,\n    // array index: NOTR  | (TR   << 2)\n    (internal::general_matrix_matrix_product<DenseIndex,Scalar,ColMajor,false,Scalar,RowMajor,false,ColMajor>::run),\n    // array index: TR    | (TR   << 2)\n    (internal::general_matrix_matrix_product<DenseIndex,Scalar,RowMajor,false,Scalar,RowMajor,false,ColMajor>::run),\n    // array index: ADJ   | (TR   << 2)\n    (internal::general_matrix_matrix_product<DenseIndex,Scalar,RowMajor,Conj, Scalar,RowMajor,false,ColMajor>::run),\n    0,\n    // array index: NOTR  | (ADJ  << 2)\n    (internal::general_matrix_matrix_product<DenseIndex,Scalar,ColMajor,false,Scalar,RowMajor,Conj, ColMajor>::run),\n    // array index: TR    | (ADJ  << 2)\n    (internal::general_matrix_matrix_product<DenseIndex,Scalar,RowMajor,false,Scalar,RowMajor,Conj, ColMajor>::run),\n    // array index: ADJ   | (ADJ  << 2)\n    (internal::general_matrix_matrix_product<DenseIndex,Scalar,RowMajor,Conj, Scalar,RowMajor,Conj, ColMajor>::run),\n    0\n  };\n\n  const Scalar* a = reinterpret_cast<const Scalar*>(pa);\n  const Scalar* b = reinterpret_cast<const Scalar*>(pb);\n  Scalar* c = reinterpret_cast<Scalar*>(pc);\n  Scalar alpha  = *reinterpret_cast<const Scalar*>(palpha);\n  Scalar beta   = *reinterpret_cast<const Scalar*>(pbeta);\n\n  int info = 0;\n  if(OP(*opa)==INVALID)                                               info = 1;\n  else if(OP(*opb)==INVALID)                                          info = 2;\n  else if(*m<0)                                                       info = 3;\n  else if(*n<0)                                                       info = 4;\n  else if(*k<0)                                                       info = 5;\n  else if(*lda<std::max(1,(OP(*opa)==NOTR)?*m:*k))                    info = 8;\n  else if(*ldb<std::max(1,(OP(*opb)==NOTR)?*k:*n))                    info = 10;\n  else if(*ldc<std::max(1,*m))                                        info = 13;\n  if(info)\n    return xerbla_(SCALAR_SUFFIX_UP\"GEMM \",&info,6);\n\n  if (*m == 0 || *n == 0)\n    return 0;\n\n  if(beta!=Scalar(1))\n  {\n    if(beta==Scalar(0)) matrix(c, *m, *n, *ldc).setZero();\n    else                matrix(c, *m, *n, *ldc) *= beta;\n  }\n\n  if(*k == 0)\n    return 0;\n\n  internal::gemm_blocking_space<ColMajor,Scalar,Scalar,Dynamic,Dynamic,Dynamic> blocking(*m,*n,*k,1,true);\n\n  int code = OP(*opa) | (OP(*opb) << 2);\n  func[code](*m, *n, *k, a, *lda, b, *ldb, c, *ldc, alpha, blocking, 0);\n  return 0;\n}\n\nint EIGEN_BLAS_FUNC(trsm)(const char *side, const char *uplo, const char *opa, const char *diag, const int *m, const int *n,\n                          const RealScalar *palpha,  const RealScalar *pa, const int *lda, RealScalar *pb, const int *ldb)\n{\n//   std::cerr << \"in trsm \" << *side << \" \" << *uplo << \" \" << *opa << \" \" << *diag << \" \" << *m << \",\" << *n << \" \" << *palpha << \" \" << *lda << \" \" << *ldb<< \"\\n\";\n  typedef void (*functype)(DenseIndex, DenseIndex, const Scalar *, DenseIndex, Scalar *, DenseIndex, internal::level3_blocking<Scalar,Scalar>&);\n  static const functype func[32] = {\n    // array index: NOTR  | (LEFT  << 2) | (UP << 3) | (NUNIT << 4)\n    (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheLeft, Upper|0,          false,ColMajor,ColMajor>::run),\n    // array index: TR    | (LEFT  << 2) | (UP << 3) | (NUNIT << 4)\n    (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheLeft, Lower|0,          false,RowMajor,ColMajor>::run),\n    // array index: ADJ   | (LEFT  << 2) | (UP << 3) | (NUNIT << 4)\n    (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheLeft, Lower|0,          Conj, RowMajor,ColMajor>::run),\\\n    0,\n    // array index: NOTR  | (RIGHT << 2) | (UP << 3) | (NUNIT << 4)\n    (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheRight,Upper|0,          false,ColMajor,ColMajor>::run),\n    // array index: TR    | (RIGHT << 2) | (UP << 3) | (NUNIT << 4)\n    (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheRight,Lower|0,          false,RowMajor,ColMajor>::run),\n    // array index: ADJ   | (RIGHT << 2) | (UP << 3) | (NUNIT << 4)\n    (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheRight,Lower|0,          Conj, RowMajor,ColMajor>::run),\n    0,\n    // array index: NOTR  | (LEFT  << 2) | (LO << 3) | (NUNIT << 4)\n    (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheLeft, Lower|0,          false,ColMajor,ColMajor>::run),\n    // array index: TR    | (LEFT  << 2) | (LO << 3) | (NUNIT << 4)\n    (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheLeft, Upper|0,          false,RowMajor,ColMajor>::run),\n    // array index: ADJ   | (LEFT  << 2) | (LO << 3) | (NUNIT << 4)\n    (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheLeft, Upper|0,          Conj, RowMajor,ColMajor>::run),\n    0,\n    // array index: NOTR  | (RIGHT << 2) | (LO << 3) | (NUNIT << 4)\n    (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheRight,Lower|0,          false,ColMajor,ColMajor>::run),\n    // array index: TR    | (RIGHT << 2) | (LO << 3) | (NUNIT << 4)\n    (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheRight,Upper|0,          false,RowMajor,ColMajor>::run),\n    // array index: ADJ   | (RIGHT << 2) | (LO << 3) | (NUNIT << 4)\n    (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheRight,Upper|0,          Conj, RowMajor,ColMajor>::run),\n    0,\n    // array index: NOTR  | (LEFT  << 2) | (UP << 3) | (UNIT  << 4)\n    (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheLeft, Upper|UnitDiag,false,ColMajor,ColMajor>::run),\n    // array index: TR    | (LEFT  << 2) | (UP << 3) | (UNIT  << 4)\n    (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheLeft, Lower|UnitDiag,false,RowMajor,ColMajor>::run),\n    // array index: ADJ   | (LEFT  << 2) | (UP << 3) | (UNIT  << 4)\n    (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheLeft, Lower|UnitDiag,Conj, RowMajor,ColMajor>::run),\n    0,\n    // array index: NOTR  | (RIGHT << 2) | (UP << 3) | (UNIT  << 4)\n    (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheRight,Upper|UnitDiag,false,ColMajor,ColMajor>::run),\n    // array index: TR    | (RIGHT << 2) | (UP << 3) | (UNIT  << 4)\n    (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheRight,Lower|UnitDiag,false,RowMajor,ColMajor>::run),\n    // array index: ADJ   | (RIGHT << 2) | (UP << 3) | (UNIT  << 4)\n    (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheRight,Lower|UnitDiag,Conj, RowMajor,ColMajor>::run),\n    0,\n    // array index: NOTR  | (LEFT  << 2) | (LO << 3) | (UNIT  << 4)\n    (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheLeft, Lower|UnitDiag,false,ColMajor,ColMajor>::run),\n    // array index: TR    | (LEFT  << 2) | (LO << 3) | (UNIT  << 4)\n    (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheLeft, Upper|UnitDiag,false,RowMajor,ColMajor>::run),\n    // array index: ADJ   | (LEFT  << 2) | (LO << 3) | (UNIT  << 4)\n    (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheLeft, Upper|UnitDiag,Conj, RowMajor,ColMajor>::run),\n    0,\n    // array index: NOTR  | (RIGHT << 2) | (LO << 3) | (UNIT  << 4)\n    (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheRight,Lower|UnitDiag,false,ColMajor,ColMajor>::run),\n    // array index: TR    | (RIGHT << 2) | (LO << 3) | (UNIT  << 4)\n    (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheRight,Upper|UnitDiag,false,RowMajor,ColMajor>::run),\n    // array index: ADJ   | (RIGHT << 2) | (LO << 3) | (UNIT  << 4)\n    (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheRight,Upper|UnitDiag,Conj, RowMajor,ColMajor>::run),\n    0\n  };\n\n  const Scalar* a = reinterpret_cast<const Scalar*>(pa);\n  Scalar* b = reinterpret_cast<Scalar*>(pb);\n  Scalar  alpha = *reinterpret_cast<const Scalar*>(palpha);\n\n  int info = 0;\n  if(SIDE(*side)==INVALID)                                            info = 1;\n  else if(UPLO(*uplo)==INVALID)                                       info = 2;\n  else if(OP(*opa)==INVALID)                                          info = 3;\n  else if(DIAG(*diag)==INVALID)                                       info = 4;\n  else if(*m<0)                                                       info = 5;\n  else if(*n<0)                                                       info = 6;\n  else if(*lda<std::max(1,(SIDE(*side)==LEFT)?*m:*n))                 info = 9;\n  else if(*ldb<std::max(1,*m))                                        info = 11;\n  if(info)\n    return xerbla_(SCALAR_SUFFIX_UP\"TRSM \",&info,6);\n\n  if(*m==0 || *n==0)\n    return 0;\n\n  int code = OP(*opa) | (SIDE(*side) << 2) | (UPLO(*uplo) << 3) | (DIAG(*diag) << 4);\n\n  if(SIDE(*side)==LEFT)\n  {\n    internal::gemm_blocking_space<ColMajor,Scalar,Scalar,Dynamic,Dynamic,Dynamic,4> blocking(*m,*n,*m,1,false);\n    func[code](*m, *n, a, *lda, b, *ldb, blocking);\n  }\n  else\n  {\n    internal::gemm_blocking_space<ColMajor,Scalar,Scalar,Dynamic,Dynamic,Dynamic,4> blocking(*m,*n,*n,1,false);\n    func[code](*n, *m, a, *lda, b, *ldb, blocking);\n  }\n\n  if(alpha!=Scalar(1))\n    matrix(b,*m,*n,*ldb) *= alpha;\n\n  return 0;\n}\n\n\n// b = alpha*op(a)*b  for side = 'L'or'l'\n// b = alpha*b*op(a)  for side = 'R'or'r'\nint EIGEN_BLAS_FUNC(trmm)(const char *side, const char *uplo, const char *opa, const char *diag, const int *m, const int *n,\n                          const RealScalar *palpha, const RealScalar *pa, const int *lda, RealScalar *pb, const int *ldb)\n{\n//   std::cerr << \"in trmm \" << *side << \" \" << *uplo << \" \" << *opa << \" \" << *diag << \" \" << *m << \" \" << *n << \" \" << *lda << \" \" << *ldb << \" \" << *palpha << \"\\n\";\n  typedef void (*functype)(DenseIndex, DenseIndex, DenseIndex, const Scalar *, DenseIndex, const Scalar *, DenseIndex, Scalar *, DenseIndex, const Scalar&, internal::level3_blocking<Scalar,Scalar>&);\n  static const functype func[32] = {\n    // array index: NOTR  | (LEFT  << 2) | (UP << 3) | (NUNIT << 4)\n    (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Upper|0,          true, ColMajor,false,ColMajor,false,ColMajor>::run),\n    // array index: TR    | (LEFT  << 2) | (UP << 3) | (NUNIT << 4)\n    (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Lower|0,          true, RowMajor,false,ColMajor,false,ColMajor>::run),\n    // array index: ADJ   | (LEFT  << 2) | (UP << 3) | (NUNIT << 4)\n    (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Lower|0,          true, RowMajor,Conj, ColMajor,false,ColMajor>::run),\n    0,\n    // array index: NOTR  | (RIGHT << 2) | (UP << 3) | (NUNIT << 4)\n    (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Upper|0,          false,ColMajor,false,ColMajor,false,ColMajor>::run),\n    // array index: TR    | (RIGHT << 2) | (UP << 3) | (NUNIT << 4)\n    (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Lower|0,          false,ColMajor,false,RowMajor,false,ColMajor>::run),\n    // array index: ADJ   | (RIGHT << 2) | (UP << 3) | (NUNIT << 4)\n    (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Lower|0,          false,ColMajor,false,RowMajor,Conj, ColMajor>::run),\n    0,\n    // array index: NOTR  | (LEFT  << 2) | (LO << 3) | (NUNIT << 4)\n    (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Lower|0,          true, ColMajor,false,ColMajor,false,ColMajor>::run),\n    // array index: TR    | (LEFT  << 2) | (LO << 3) | (NUNIT << 4)\n    (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Upper|0,          true, RowMajor,false,ColMajor,false,ColMajor>::run),\n    // array index: ADJ   | (LEFT  << 2) | (LO << 3) | (NUNIT << 4)\n    (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Upper|0,          true, RowMajor,Conj, ColMajor,false,ColMajor>::run),\n    0,\n    // array index: NOTR  | (RIGHT << 2) | (LO << 3) | (NUNIT << 4)\n    (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Lower|0,          false,ColMajor,false,ColMajor,false,ColMajor>::run),\n    // array index: TR    | (RIGHT << 2) | (LO << 3) | (NUNIT << 4)\n    (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Upper|0,          false,ColMajor,false,RowMajor,false,ColMajor>::run),\n    // array index: ADJ   | (RIGHT << 2) | (LO << 3) | (NUNIT << 4)\n    (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Upper|0,          false,ColMajor,false,RowMajor,Conj, ColMajor>::run),\n    0,\n    // array index: NOTR  | (LEFT  << 2) | (UP << 3) | (UNIT  << 4)\n    (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Upper|UnitDiag,true, ColMajor,false,ColMajor,false,ColMajor>::run),\n    // array index: TR    | (LEFT  << 2) | (UP << 3) | (UNIT  << 4)\n    (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Lower|UnitDiag,true, RowMajor,false,ColMajor,false,ColMajor>::run),\n    // array index: ADJ   | (LEFT  << 2) | (UP << 3) | (UNIT  << 4)\n    (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Lower|UnitDiag,true, RowMajor,Conj, ColMajor,false,ColMajor>::run),\n    0,\n    // array index: NOTR  | (RIGHT << 2) | (UP << 3) | (UNIT  << 4)\n    (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Upper|UnitDiag,false,ColMajor,false,ColMajor,false,ColMajor>::run),\n    // array index: TR    | (RIGHT << 2) | (UP << 3) | (UNIT  << 4)\n    (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Lower|UnitDiag,false,ColMajor,false,RowMajor,false,ColMajor>::run),\n    // array index: ADJ   | (RIGHT << 2) | (UP << 3) | (UNIT  << 4)\n    (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Lower|UnitDiag,false,ColMajor,false,RowMajor,Conj, ColMajor>::run),\n    0,\n    // array index: NOTR  | (LEFT  << 2) | (LO << 3) | (UNIT  << 4)\n    (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Lower|UnitDiag,true, ColMajor,false,ColMajor,false,ColMajor>::run),\n    // array index: TR    | (LEFT  << 2) | (LO << 3) | (UNIT  << 4)\n    (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Upper|UnitDiag,true, RowMajor,false,ColMajor,false,ColMajor>::run),\n    // array index: ADJ   | (LEFT  << 2) | (LO << 3) | (UNIT  << 4)\n    (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Upper|UnitDiag,true, RowMajor,Conj, ColMajor,false,ColMajor>::run),\n    0,\n    // array index: NOTR  | (RIGHT << 2) | (LO << 3) | (UNIT  << 4)\n    (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Lower|UnitDiag,false,ColMajor,false,ColMajor,false,ColMajor>::run),\n    // array index: TR    | (RIGHT << 2) | (LO << 3) | (UNIT  << 4)\n    (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Upper|UnitDiag,false,ColMajor,false,RowMajor,false,ColMajor>::run),\n    // array index: ADJ   | (RIGHT << 2) | (LO << 3) | (UNIT  << 4)\n    (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Upper|UnitDiag,false,ColMajor,false,RowMajor,Conj, ColMajor>::run),\n    0\n  };\n\n  const Scalar* a = reinterpret_cast<const Scalar*>(pa);\n  Scalar* b = reinterpret_cast<Scalar*>(pb);\n  Scalar  alpha = *reinterpret_cast<const Scalar*>(palpha);\n\n  int info = 0;\n  if(SIDE(*side)==INVALID)                                            info = 1;\n  else if(UPLO(*uplo)==INVALID)                                       info = 2;\n  else if(OP(*opa)==INVALID)                                          info = 3;\n  else if(DIAG(*diag)==INVALID)                                       info = 4;\n  else if(*m<0)                                                       info = 5;\n  else if(*n<0)                                                       info = 6;\n  else if(*lda<std::max(1,(SIDE(*side)==LEFT)?*m:*n))                 info = 9;\n  else if(*ldb<std::max(1,*m))                                        info = 11;\n  if(info)\n    return xerbla_(SCALAR_SUFFIX_UP\"TRMM \",&info,6);\n\n  int code = OP(*opa) | (SIDE(*side) << 2) | (UPLO(*uplo) << 3) | (DIAG(*diag) << 4);\n\n  if(*m==0 || *n==0)\n    return 1;\n\n  // FIXME find a way to avoid this copy\n  Matrix<Scalar,Dynamic,Dynamic,ColMajor> tmp = matrix(b,*m,*n,*ldb);\n  matrix(b,*m,*n,*ldb).setZero();\n\n  if(SIDE(*side)==LEFT)\n  {\n    internal::gemm_blocking_space<ColMajor,Scalar,Scalar,Dynamic,Dynamic,Dynamic,4> blocking(*m,*n,*m,1,false);\n    func[code](*m, *n, *m, a, *lda, tmp.data(), tmp.outerStride(), b, *ldb, alpha, blocking);\n  }\n  else\n  {\n    internal::gemm_blocking_space<ColMajor,Scalar,Scalar,Dynamic,Dynamic,Dynamic,4> blocking(*m,*n,*n,1,false);\n    func[code](*m, *n, *n, tmp.data(), tmp.outerStride(), a, *lda, b, *ldb, alpha, blocking);\n  }\n  return 1;\n}\n\n// c = alpha*a*b + beta*c  for side = 'L'or'l'\n// c = alpha*b*a + beta*c  for side = 'R'or'r\nint EIGEN_BLAS_FUNC(symm)(const char *side, const char *uplo, const int *m, const int *n, const RealScalar *palpha,\n                          const RealScalar *pa, const int *lda, const RealScalar *pb, const int *ldb, const RealScalar *pbeta, RealScalar *pc, const int *ldc)\n{\n//   std::cerr << \"in symm \" << *side << \" \" << *uplo << \" \" << *m << \"x\" << *n << \" lda:\" << *lda << \" ldb:\" << *ldb << \" ldc:\" << *ldc << \" alpha:\" << *palpha << \" beta:\" << *pbeta << \"\\n\";\n  const Scalar* a = reinterpret_cast<const Scalar*>(pa);\n  const Scalar* b = reinterpret_cast<const Scalar*>(pb);\n  Scalar* c = reinterpret_cast<Scalar*>(pc);\n  Scalar alpha = *reinterpret_cast<const Scalar*>(palpha);\n  Scalar beta  = *reinterpret_cast<const Scalar*>(pbeta);\n\n  int info = 0;\n  if(SIDE(*side)==INVALID)                                            info = 1;\n  else if(UPLO(*uplo)==INVALID)                                       info = 2;\n  else if(*m<0)                                                       info = 3;\n  else if(*n<0)                                                       info = 4;\n  else if(*lda<std::max(1,(SIDE(*side)==LEFT)?*m:*n))                 info = 7;\n  else if(*ldb<std::max(1,*m))                                        info = 9;\n  else if(*ldc<std::max(1,*m))                                        info = 12;\n  if(info)\n    return xerbla_(SCALAR_SUFFIX_UP\"SYMM \",&info,6);\n\n  if(beta!=Scalar(1))\n  {\n    if(beta==Scalar(0)) matrix(c, *m, *n, *ldc).setZero();\n    else                matrix(c, *m, *n, *ldc) *= beta;\n  }\n\n  if(*m==0 || *n==0)\n  {\n    return 1;\n  }\n\n  int size = (SIDE(*side)==LEFT) ? (*m) : (*n);\n  #if ISCOMPLEX\n  // FIXME add support for symmetric complex matrix\n  Matrix<Scalar,Dynamic,Dynamic,ColMajor> matA(size,size);\n  if(UPLO(*uplo)==UP)\n  {\n    matA.triangularView<Upper>() = matrix(a,size,size,*lda);\n    matA.triangularView<Lower>() = matrix(a,size,size,*lda).transpose();\n  }\n  else if(UPLO(*uplo)==LO)\n  {\n    matA.triangularView<Lower>() = matrix(a,size,size,*lda);\n    matA.triangularView<Upper>() = matrix(a,size,size,*lda).transpose();\n  }\n  if(SIDE(*side)==LEFT)\n    matrix(c, *m, *n, *ldc) += alpha * matA * matrix(b, *m, *n, *ldb);\n  else if(SIDE(*side)==RIGHT)\n    matrix(c, *m, *n, *ldc) += alpha * matrix(b, *m, *n, *ldb) * matA;\n  #else\n  internal::gemm_blocking_space<ColMajor,Scalar,Scalar,Dynamic,Dynamic,Dynamic> blocking(*m,*n,size,1,false);\n\n  if(SIDE(*side)==LEFT)\n    if(UPLO(*uplo)==UP)       internal::product_selfadjoint_matrix<Scalar, DenseIndex, RowMajor,true,false, ColMajor,false,false, ColMajor>::run(*m, *n, a, *lda, b, *ldb, c, *ldc, alpha, blocking);\n    else if(UPLO(*uplo)==LO)  internal::product_selfadjoint_matrix<Scalar, DenseIndex, ColMajor,true,false, ColMajor,false,false, ColMajor>::run(*m, *n, a, *lda, b, *ldb, c, *ldc, alpha, blocking);\n    else                      return 0;\n  else if(SIDE(*side)==RIGHT)\n    if(UPLO(*uplo)==UP)       internal::product_selfadjoint_matrix<Scalar, DenseIndex, ColMajor,false,false, RowMajor,true,false, ColMajor>::run(*m, *n, b, *ldb, a, *lda, c, *ldc, alpha, blocking);\n    else if(UPLO(*uplo)==LO)  internal::product_selfadjoint_matrix<Scalar, DenseIndex, ColMajor,false,false, ColMajor,true,false, ColMajor>::run(*m, *n, b, *ldb, a, *lda, c, *ldc, alpha, blocking);\n    else                      return 0;\n  else\n    return 0;\n  #endif\n\n  return 0;\n}\n\n// c = alpha*a*a' + beta*c  for op = 'N'or'n'\n// c = alpha*a'*a + beta*c  for op = 'T'or't','C'or'c'\nint EIGEN_BLAS_FUNC(syrk)(const char *uplo, const char *op, const int *n, const int *k,\n                          const RealScalar *palpha, const RealScalar *pa, const int *lda, const RealScalar *pbeta, RealScalar *pc, const int *ldc)\n{\n//   std::cerr << \"in syrk \" << *uplo << \" \" << *op << \" \" << *n << \" \" << *k << \" \" << *palpha << \" \" << *lda << \" \" << *pbeta << \" \" << *ldc << \"\\n\";\n  #if !ISCOMPLEX\n  typedef void (*functype)(DenseIndex, DenseIndex, const Scalar *, DenseIndex, const Scalar *, DenseIndex, Scalar *, DenseIndex, const Scalar&, internal::level3_blocking<Scalar,Scalar>&);\n  static const functype func[8] = {\n    // array index: NOTR  | (UP << 2)\n    (internal::general_matrix_matrix_triangular_product<DenseIndex,Scalar,ColMajor,false,Scalar,RowMajor,ColMajor,Conj, Upper>::run),\n    // array index: TR    | (UP << 2)\n    (internal::general_matrix_matrix_triangular_product<DenseIndex,Scalar,RowMajor,false,Scalar,ColMajor,ColMajor,Conj, Upper>::run),\n    // array index: ADJ   | (UP << 2)\n    (internal::general_matrix_matrix_triangular_product<DenseIndex,Scalar,RowMajor,Conj, Scalar,ColMajor,ColMajor,false,Upper>::run),\n    0,\n    // array index: NOTR  | (LO << 2)\n    (internal::general_matrix_matrix_triangular_product<DenseIndex,Scalar,ColMajor,false,Scalar,RowMajor,ColMajor,Conj, Lower>::run),\n    // array index: TR    | (LO << 2)\n    (internal::general_matrix_matrix_triangular_product<DenseIndex,Scalar,RowMajor,false,Scalar,ColMajor,ColMajor,Conj, Lower>::run),\n    // array index: ADJ   | (LO << 2)\n    (internal::general_matrix_matrix_triangular_product<DenseIndex,Scalar,RowMajor,Conj, Scalar,ColMajor,ColMajor,false,Lower>::run),\n    0\n  };\n  #endif\n\n  const Scalar* a = reinterpret_cast<const Scalar*>(pa);\n  Scalar* c = reinterpret_cast<Scalar*>(pc);\n  Scalar alpha = *reinterpret_cast<const Scalar*>(palpha);\n  Scalar beta  = *reinterpret_cast<const Scalar*>(pbeta);\n\n  int info = 0;\n  if(UPLO(*uplo)==INVALID)                                            info = 1;\n  else if(OP(*op)==INVALID || (ISCOMPLEX && OP(*op)==ADJ) )           info = 2;\n  else if(*n<0)                                                       info = 3;\n  else if(*k<0)                                                       info = 4;\n  else if(*lda<std::max(1,(OP(*op)==NOTR)?*n:*k))                     info = 7;\n  else if(*ldc<std::max(1,*n))                                        info = 10;\n  if(info)\n    return xerbla_(SCALAR_SUFFIX_UP\"SYRK \",&info,6);\n\n  if(beta!=Scalar(1))\n  {\n    if(UPLO(*uplo)==UP)\n      if(beta==Scalar(0)) matrix(c, *n, *n, *ldc).triangularView<Upper>().setZero();\n      else                matrix(c, *n, *n, *ldc).triangularView<Upper>() *= beta;\n    else\n      if(beta==Scalar(0)) matrix(c, *n, *n, *ldc).triangularView<Lower>().setZero();\n      else                matrix(c, *n, *n, *ldc).triangularView<Lower>() *= beta;\n  }\n\n  if(*n==0 || *k==0)\n    return 0;\n\n  #if ISCOMPLEX\n  // FIXME add support for symmetric complex matrix\n  if(UPLO(*uplo)==UP)\n  {\n    if(OP(*op)==NOTR)\n      matrix(c, *n, *n, *ldc).triangularView<Upper>() += alpha * matrix(a,*n,*k,*lda) * matrix(a,*n,*k,*lda).transpose();\n    else\n      matrix(c, *n, *n, *ldc).triangularView<Upper>() += alpha * matrix(a,*k,*n,*lda).transpose() * matrix(a,*k,*n,*lda);\n  }\n  else\n  {\n    if(OP(*op)==NOTR)\n      matrix(c, *n, *n, *ldc).triangularView<Lower>() += alpha * matrix(a,*n,*k,*lda) * matrix(a,*n,*k,*lda).transpose();\n    else\n      matrix(c, *n, *n, *ldc).triangularView<Lower>() += alpha * matrix(a,*k,*n,*lda).transpose() * matrix(a,*k,*n,*lda);\n  }\n  #else\n  internal::gemm_blocking_space<ColMajor,Scalar,Scalar,Dynamic,Dynamic,Dynamic> blocking(*n,*n,*k,1,false);\n\n  int code = OP(*op) | (UPLO(*uplo) << 2);\n  func[code](*n, *k, a, *lda, a, *lda, c, *ldc, alpha, blocking);\n  #endif\n\n  return 0;\n}\n\n// c = alpha*a*b' + alpha*b*a' + beta*c  for op = 'N'or'n'\n// c = alpha*a'*b + alpha*b'*a + beta*c  for op = 'T'or't'\nint EIGEN_BLAS_FUNC(syr2k)(const char *uplo, const char *op, const int *n, const int *k, const RealScalar *palpha,\n                           const RealScalar *pa, const int *lda, const RealScalar *pb, const int *ldb, const RealScalar *pbeta, RealScalar *pc, const int *ldc)\n{\n  const Scalar* a = reinterpret_cast<const Scalar*>(pa);\n  const Scalar* b = reinterpret_cast<const Scalar*>(pb);\n  Scalar* c = reinterpret_cast<Scalar*>(pc);\n  Scalar alpha = *reinterpret_cast<const Scalar*>(palpha);\n  Scalar beta  = *reinterpret_cast<const Scalar*>(pbeta);\n\n//   std::cerr << \"in syr2k \" << *uplo << \" \" << *op << \" \" << *n << \" \" << *k << \" \" << alpha << \" \" << *lda << \" \" << *ldb << \" \" << beta << \" \" << *ldc << \"\\n\";\n\n  int info = 0;\n  if(UPLO(*uplo)==INVALID)                                            info = 1;\n  else if(OP(*op)==INVALID || (ISCOMPLEX && OP(*op)==ADJ) )           info = 2;\n  else if(*n<0)                                                       info = 3;\n  else if(*k<0)                                                       info = 4;\n  else if(*lda<std::max(1,(OP(*op)==NOTR)?*n:*k))                     info = 7;\n  else if(*ldb<std::max(1,(OP(*op)==NOTR)?*n:*k))                     info = 9;\n  else if(*ldc<std::max(1,*n))                                        info = 12;\n  if(info)\n    return xerbla_(SCALAR_SUFFIX_UP\"SYR2K\",&info,6);\n\n  if(beta!=Scalar(1))\n  {\n    if(UPLO(*uplo)==UP)\n      if(beta==Scalar(0)) matrix(c, *n, *n, *ldc).triangularView<Upper>().setZero();\n      else                matrix(c, *n, *n, *ldc).triangularView<Upper>() *= beta;\n    else\n      if(beta==Scalar(0)) matrix(c, *n, *n, *ldc).triangularView<Lower>().setZero();\n      else                matrix(c, *n, *n, *ldc).triangularView<Lower>() *= beta;\n  }\n\n  if(*k==0)\n    return 1;\n\n  if(OP(*op)==NOTR)\n  {\n    if(UPLO(*uplo)==UP)\n    {\n      matrix(c, *n, *n, *ldc).triangularView<Upper>()\n        += alpha *matrix(a, *n, *k, *lda)*matrix(b, *n, *k, *ldb).transpose()\n        +  alpha*matrix(b, *n, *k, *ldb)*matrix(a, *n, *k, *lda).transpose();\n    }\n    else if(UPLO(*uplo)==LO)\n      matrix(c, *n, *n, *ldc).triangularView<Lower>()\n        += alpha*matrix(a, *n, *k, *lda)*matrix(b, *n, *k, *ldb).transpose()\n        +  alpha*matrix(b, *n, *k, *ldb)*matrix(a, *n, *k, *lda).transpose();\n  }\n  else if(OP(*op)==TR || OP(*op)==ADJ)\n  {\n    if(UPLO(*uplo)==UP)\n      matrix(c, *n, *n, *ldc).triangularView<Upper>()\n        += alpha*matrix(a, *k, *n, *lda).transpose()*matrix(b, *k, *n, *ldb)\n        +  alpha*matrix(b, *k, *n, *ldb).transpose()*matrix(a, *k, *n, *lda);\n    else if(UPLO(*uplo)==LO)\n      matrix(c, *n, *n, *ldc).triangularView<Lower>()\n        += alpha*matrix(a, *k, *n, *lda).transpose()*matrix(b, *k, *n, *ldb)\n        +  alpha*matrix(b, *k, *n, *ldb).transpose()*matrix(a, *k, *n, *lda);\n  }\n\n  return 0;\n}\n\n\n#if ISCOMPLEX\n\n// c = alpha*a*b + beta*c  for side = 'L'or'l'\n// c = alpha*b*a + beta*c  for side = 'R'or'r\nint EIGEN_BLAS_FUNC(hemm)(const char *side, const char *uplo, const int *m, const int *n, const RealScalar *palpha,\n                          const RealScalar *pa, const int *lda, const RealScalar *pb, const int *ldb, const RealScalar *pbeta, RealScalar *pc, const int *ldc)\n{\n  const Scalar* a = reinterpret_cast<const Scalar*>(pa);\n  const Scalar* b = reinterpret_cast<const Scalar*>(pb);\n  Scalar* c = reinterpret_cast<Scalar*>(pc);\n  Scalar alpha = *reinterpret_cast<const Scalar*>(palpha);\n  Scalar beta  = *reinterpret_cast<const Scalar*>(pbeta);\n\n//   std::cerr << \"in hemm \" << *side << \" \" << *uplo << \" \" << *m << \" \" << *n << \" \" << alpha << \" \" << *lda << \" \" << beta << \" \" << *ldc << \"\\n\";\n\n  int info = 0;\n  if(SIDE(*side)==INVALID)                                            info = 1;\n  else if(UPLO(*uplo)==INVALID)                                       info = 2;\n  else if(*m<0)                                                       info = 3;\n  else if(*n<0)                                                       info = 4;\n  else if(*lda<std::max(1,(SIDE(*side)==LEFT)?*m:*n))                 info = 7;\n  else if(*ldb<std::max(1,*m))                                        info = 9;\n  else if(*ldc<std::max(1,*m))                                        info = 12;\n  if(info)\n    return xerbla_(SCALAR_SUFFIX_UP\"HEMM \",&info,6);\n\n  if(beta==Scalar(0))       matrix(c, *m, *n, *ldc).setZero();\n  else if(beta!=Scalar(1))  matrix(c, *m, *n, *ldc) *= beta;\n\n  if(*m==0 || *n==0)\n  {\n    return 1;\n  }\n\n  int size = (SIDE(*side)==LEFT) ? (*m) : (*n);\n  internal::gemm_blocking_space<ColMajor,Scalar,Scalar,Dynamic,Dynamic,Dynamic> blocking(*m,*n,size,1,false);\n\n  if(SIDE(*side)==LEFT)\n  {\n    if(UPLO(*uplo)==UP)       internal::product_selfadjoint_matrix<Scalar,DenseIndex,RowMajor,true,Conj,  ColMajor,false,false, ColMajor>\n                                ::run(*m, *n, a, *lda, b, *ldb, c, *ldc, alpha, blocking);\n    else if(UPLO(*uplo)==LO)  internal::product_selfadjoint_matrix<Scalar,DenseIndex,ColMajor,true,false, ColMajor,false,false, ColMajor>\n                                ::run(*m, *n, a, *lda, b, *ldb, c, *ldc, alpha, blocking);\n    else                      return 0;\n  }\n  else if(SIDE(*side)==RIGHT)\n  {\n    if(UPLO(*uplo)==UP)       matrix(c,*m,*n,*ldc) += alpha * matrix(b,*m,*n,*ldb) * matrix(a,*n,*n,*lda).selfadjointView<Upper>();/*internal::product_selfadjoint_matrix<Scalar,DenseIndex,ColMajor,false,false, RowMajor,true,Conj,  ColMajor>\n                                ::run(*m, *n, b, *ldb, a, *lda, c, *ldc, alpha, blocking);*/\n    else if(UPLO(*uplo)==LO)  internal::product_selfadjoint_matrix<Scalar,DenseIndex,ColMajor,false,false, ColMajor,true,false, ColMajor>\n                                ::run(*m, *n, b, *ldb, a, *lda, c, *ldc, alpha, blocking);\n    else                      return 0;\n  }\n  else\n  {\n    return 0;\n  }\n\n  return 0;\n}\n\n// c = alpha*a*conj(a') + beta*c  for op = 'N'or'n'\n// c = alpha*conj(a')*a + beta*c  for op  = 'C'or'c'\nint EIGEN_BLAS_FUNC(herk)(const char *uplo, const char *op, const int *n, const int *k,\n                          const RealScalar *palpha, const RealScalar *pa, const int *lda, const RealScalar *pbeta, RealScalar *pc, const int *ldc)\n{\n//   std::cerr << \"in herk \" << *uplo << \" \" << *op << \" \" << *n << \" \" << *k << \" \" << *palpha << \" \" << *lda << \" \" << *pbeta << \" \" << *ldc << \"\\n\";\n\n  typedef void (*functype)(DenseIndex, DenseIndex, const Scalar *, DenseIndex, const Scalar *, DenseIndex, Scalar *, DenseIndex, const Scalar&, internal::level3_blocking<Scalar,Scalar>&);\n  static const functype func[8] = {\n    // array index: NOTR  | (UP << 2)\n    (internal::general_matrix_matrix_triangular_product<DenseIndex,Scalar,ColMajor,false,Scalar,RowMajor,Conj, ColMajor,Upper>::run),\n    0,\n    // array index: ADJ   | (UP << 2)\n    (internal::general_matrix_matrix_triangular_product<DenseIndex,Scalar,RowMajor,Conj, Scalar,ColMajor,false,ColMajor,Upper>::run),\n    0,\n    // array index: NOTR  | (LO << 2)\n    (internal::general_matrix_matrix_triangular_product<DenseIndex,Scalar,ColMajor,false,Scalar,RowMajor,Conj, ColMajor,Lower>::run),\n    0,\n    // array index: ADJ   | (LO << 2)\n    (internal::general_matrix_matrix_triangular_product<DenseIndex,Scalar,RowMajor,Conj, Scalar,ColMajor,false,ColMajor,Lower>::run),\n    0\n  };\n\n  const Scalar* a = reinterpret_cast<const Scalar*>(pa);\n  Scalar* c = reinterpret_cast<Scalar*>(pc);\n  RealScalar alpha = *palpha;\n  RealScalar beta  = *pbeta;\n\n//   std::cerr << \"in herk \" << *uplo << \" \" << *op << \" \" << *n << \" \" << *k << \" \" << alpha << \" \" << *lda << \" \" << beta << \" \" << *ldc << \"\\n\";\n\n  int info = 0;\n  if(UPLO(*uplo)==INVALID)                                            info = 1;\n  else if((OP(*op)==INVALID) || (OP(*op)==TR))                        info = 2;\n  else if(*n<0)                                                       info = 3;\n  else if(*k<0)                                                       info = 4;\n  else if(*lda<std::max(1,(OP(*op)==NOTR)?*n:*k))                     info = 7;\n  else if(*ldc<std::max(1,*n))                                        info = 10;\n  if(info)\n    return xerbla_(SCALAR_SUFFIX_UP\"HERK \",&info,6);\n\n  int code = OP(*op) | (UPLO(*uplo) << 2);\n\n  if(beta!=RealScalar(1))\n  {\n    if(UPLO(*uplo)==UP)\n      if(beta==Scalar(0)) matrix(c, *n, *n, *ldc).triangularView<Upper>().setZero();\n      else                matrix(c, *n, *n, *ldc).triangularView<StrictlyUpper>() *= beta;\n    else\n      if(beta==Scalar(0)) matrix(c, *n, *n, *ldc).triangularView<Lower>().setZero();\n      else                matrix(c, *n, *n, *ldc).triangularView<StrictlyLower>() *= beta;\n\n    if(beta!=Scalar(0))\n    {\n      matrix(c, *n, *n, *ldc).diagonal().real() *= beta;\n      matrix(c, *n, *n, *ldc).diagonal().imag().setZero();\n    }\n  }\n\n  if(*k>0 && alpha!=RealScalar(0))\n  {\n    internal::gemm_blocking_space<ColMajor,Scalar,Scalar,Dynamic,Dynamic,Dynamic> blocking(*n,*n,*k,1,false);\n    func[code](*n, *k, a, *lda, a, *lda, c, *ldc, alpha, blocking);\n    matrix(c, *n, *n, *ldc).diagonal().imag().setZero();\n  }\n  return 0;\n}\n\n// c = alpha*a*conj(b') + conj(alpha)*b*conj(a') + beta*c,  for op = 'N'or'n'\n// c = alpha*conj(a')*b + conj(alpha)*conj(b')*a + beta*c,  for op = 'C'or'c'\nint EIGEN_BLAS_FUNC(her2k)(const char *uplo, const char *op, const int *n, const int *k,\n                           const RealScalar *palpha, const RealScalar *pa, const int *lda, const RealScalar *pb, const int *ldb, const RealScalar *pbeta, RealScalar *pc, const int *ldc)\n{\n  const Scalar* a = reinterpret_cast<const Scalar*>(pa);\n  const Scalar* b = reinterpret_cast<const Scalar*>(pb);\n  Scalar* c = reinterpret_cast<Scalar*>(pc);\n  Scalar alpha = *reinterpret_cast<const Scalar*>(palpha);\n  RealScalar beta  = *pbeta;\n\n//   std::cerr << \"in her2k \" << *uplo << \" \" << *op << \" \" << *n << \" \" << *k << \" \" << alpha << \" \" << *lda << \" \" << *ldb << \" \" << beta << \" \" << *ldc << \"\\n\";\n\n  int info = 0;\n  if(UPLO(*uplo)==INVALID)                                            info = 1;\n  else if((OP(*op)==INVALID) || (OP(*op)==TR))                        info = 2;\n  else if(*n<0)                                                       info = 3;\n  else if(*k<0)                                                       info = 4;\n  else if(*lda<std::max(1,(OP(*op)==NOTR)?*n:*k))                     info = 7;\n  else if(*ldb<std::max(1,(OP(*op)==NOTR)?*n:*k))                     info = 9;\n  else if(*ldc<std::max(1,*n))                                        info = 12;\n  if(info)\n    return xerbla_(SCALAR_SUFFIX_UP\"HER2K\",&info,6);\n\n  if(beta!=RealScalar(1))\n  {\n    if(UPLO(*uplo)==UP)\n      if(beta==Scalar(0)) matrix(c, *n, *n, *ldc).triangularView<Upper>().setZero();\n      else                matrix(c, *n, *n, *ldc).triangularView<StrictlyUpper>() *= beta;\n    else\n      if(beta==Scalar(0)) matrix(c, *n, *n, *ldc).triangularView<Lower>().setZero();\n      else                matrix(c, *n, *n, *ldc).triangularView<StrictlyLower>() *= beta;\n\n    if(beta!=Scalar(0))\n    {\n      matrix(c, *n, *n, *ldc).diagonal().real() *= beta;\n      matrix(c, *n, *n, *ldc).diagonal().imag().setZero();\n    }\n  }\n  else if(*k>0 && alpha!=Scalar(0))\n    matrix(c, *n, *n, *ldc).diagonal().imag().setZero();\n\n  if(*k==0)\n    return 1;\n\n  if(OP(*op)==NOTR)\n  {\n    if(UPLO(*uplo)==UP)\n    {\n      matrix(c, *n, *n, *ldc).triangularView<Upper>()\n        +=            alpha *matrix(a, *n, *k, *lda)*matrix(b, *n, *k, *ldb).adjoint()\n        +  numext::conj(alpha)*matrix(b, *n, *k, *ldb)*matrix(a, *n, *k, *lda).adjoint();\n    }\n    else if(UPLO(*uplo)==LO)\n      matrix(c, *n, *n, *ldc).triangularView<Lower>()\n        += alpha*matrix(a, *n, *k, *lda)*matrix(b, *n, *k, *ldb).adjoint()\n        +  numext::conj(alpha)*matrix(b, *n, *k, *ldb)*matrix(a, *n, *k, *lda).adjoint();\n  }\n  else if(OP(*op)==ADJ)\n  {\n    if(UPLO(*uplo)==UP)\n      matrix(c, *n, *n, *ldc).triangularView<Upper>()\n        +=             alpha*matrix(a, *k, *n, *lda).adjoint()*matrix(b, *k, *n, *ldb)\n        +  numext::conj(alpha)*matrix(b, *k, *n, *ldb).adjoint()*matrix(a, *k, *n, *lda);\n    else if(UPLO(*uplo)==LO)\n      matrix(c, *n, *n, *ldc).triangularView<Lower>()\n        +=             alpha*matrix(a, *k, *n, *lda).adjoint()*matrix(b, *k, *n, *ldb)\n        +  numext::conj(alpha)*matrix(b, *k, *n, *ldb).adjoint()*matrix(a, *k, *n, *lda);\n  }\n\n  return 1;\n}\n\n#endif // ISCOMPLEX\n"
  },
  {
    "path": "include/eigen3/blas/single.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define SCALAR        float\n#define SCALAR_SUFFIX s\n#define SCALAR_SUFFIX_UP \"S\"\n#define ISCOMPLEX     0\n\n#include \"level1_impl.h\"\n#include \"level1_real_impl.h\"\n#include \"level2_impl.h\"\n#include \"level2_real_impl.h\"\n#include \"level3_impl.h\"\n\nfloat BLASFUNC(sdsdot)(int* n, float* alpha, float* x, int* incx, float* y, int* incy)\n{ return double(*alpha) + BLASFUNC(dsdot)(n, x, incx, y, incy); }\n"
  },
  {
    "path": "include/eigen3/blas/testing/CMakeLists.txt",
    "content": "\nmacro(ei_add_blas_test testname)\n\n  set(targetname ${testname})\n\n  set(filename ${testname}.f)\n  add_executable(${targetname} ${filename})\n\n  target_link_libraries(${targetname} eigen_blas)\n\n  if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO)\n    target_link_libraries(${targetname} ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO})\n  endif()\n\n  target_link_libraries(${targetname} ${EXTERNAL_LIBS})\n\n  add_test(${testname} \"${Eigen_SOURCE_DIR}/blas/testing/runblastest.sh\" \"${testname}\" \"${Eigen_SOURCE_DIR}/blas/testing/${testname}.dat\")\n  add_dependencies(buildtests ${targetname})\n  \nendmacro(ei_add_blas_test)\n\nei_add_blas_test(sblat1)\nei_add_blas_test(sblat2)\nei_add_blas_test(sblat3)\n\nei_add_blas_test(dblat1)\nei_add_blas_test(dblat2)\nei_add_blas_test(dblat3)\n\nei_add_blas_test(cblat1)\nei_add_blas_test(cblat2)\nei_add_blas_test(cblat3)\n\nei_add_blas_test(zblat1)\nei_add_blas_test(zblat2)\nei_add_blas_test(zblat3)\n\n# add_custom_target(level1)\n# add_dependencies(level1 sblat1)\n\n"
  },
  {
    "path": "include/eigen3/blas/testing/cblat1.f",
    "content": "*> \\brief \\b CBLAT1\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*  Definition:\n*  ===========\n*\n*       PROGRAM CBLAT1\n* \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*>    Test program for the COMPLEX Level 1 BLAS.\n*>    Based upon the original BLAS test routine together with:\n*>\n*>    F06GAF Example Program Text\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date April 2012\n*\n*> \\ingroup complex_blas_testing\n*\n*  =====================================================================\n      PROGRAM CBLAT1\n*\n*  -- Reference BLAS test routine (version 3.4.1) --\n*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     April 2012\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      INTEGER          NOUT\n      PARAMETER        (NOUT=6)\n*     .. Scalars in Common ..\n      INTEGER          ICASE, INCX, INCY, MODE, N\n      LOGICAL          PASS\n*     .. Local Scalars ..\n      REAL             SFAC\n      INTEGER          IC\n*     .. External Subroutines ..\n      EXTERNAL         CHECK1, CHECK2, HEADER\n*     .. Common blocks ..\n      COMMON           /COMBLA/ICASE, N, INCX, INCY, MODE, PASS\n*     .. Data statements ..\n      DATA             SFAC/9.765625E-4/\n*     .. Executable Statements ..\n      WRITE (NOUT,99999)\n      DO 20 IC = 1, 10\n         ICASE = IC\n         CALL HEADER\n*\n*        Initialize PASS, INCX, INCY, and MODE for a new case.\n*        The value 9999 for INCX, INCY or MODE will appear in the\n*        detailed  output, if any, for cases that do not involve\n*        these parameters.\n*\n         PASS = .TRUE.\n         INCX = 9999\n         INCY = 9999\n         MODE = 9999\n         IF (ICASE.LE.5) THEN\n            CALL CHECK2(SFAC)\n         ELSE IF (ICASE.GE.6) THEN\n            CALL CHECK1(SFAC)\n         END IF\n*        -- Print\n         IF (PASS) WRITE (NOUT,99998)\n   20 CONTINUE\n      STOP\n*\n99999 FORMAT (' Complex BLAS Test Program Results',/1X)\n99998 FORMAT ('                                    ----- PASS -----')\n      END\n      SUBROUTINE HEADER\n*     .. Parameters ..\n      INTEGER          NOUT\n      PARAMETER        (NOUT=6)\n*     .. Scalars in Common ..\n      INTEGER          ICASE, INCX, INCY, MODE, N\n      LOGICAL          PASS\n*     .. Local Arrays ..\n      CHARACTER*6      L(10)\n*     .. Common blocks ..\n      COMMON           /COMBLA/ICASE, N, INCX, INCY, MODE, PASS\n*     .. Data statements ..\n      DATA             L(1)/'CDOTC '/\n      DATA             L(2)/'CDOTU '/\n      DATA             L(3)/'CAXPY '/\n      DATA             L(4)/'CCOPY '/\n      DATA             L(5)/'CSWAP '/\n      DATA             L(6)/'SCNRM2'/\n      DATA             L(7)/'SCASUM'/\n      DATA             L(8)/'CSCAL '/\n      DATA             L(9)/'CSSCAL'/\n      DATA             L(10)/'ICAMAX'/\n*     .. Executable Statements ..\n      WRITE (NOUT,99999) ICASE, L(ICASE)\n      RETURN\n*\n99999 FORMAT (/' Test of subprogram number',I3,12X,A6)\n      END\n      SUBROUTINE CHECK1(SFAC)\n*     .. Parameters ..\n      INTEGER           NOUT\n      PARAMETER         (NOUT=6)\n*     .. Scalar Arguments ..\n      REAL              SFAC\n*     .. Scalars in Common ..\n      INTEGER           ICASE, INCX, INCY, MODE, N\n      LOGICAL           PASS\n*     .. Local Scalars ..\n      COMPLEX           CA\n      REAL              SA\n      INTEGER           I, J, LEN, NP1\n*     .. Local Arrays ..\n      COMPLEX           CTRUE5(8,5,2), CTRUE6(8,5,2), CV(8,5,2), CX(8),\n     +                  MWPCS(5), MWPCT(5)\n      REAL              STRUE2(5), STRUE4(5)\n      INTEGER           ITRUE3(5)\n*     .. External Functions ..\n      REAL              SCASUM, SCNRM2\n      INTEGER           ICAMAX\n      EXTERNAL          SCASUM, SCNRM2, ICAMAX\n*     .. External Subroutines ..\n      EXTERNAL          CSCAL, CSSCAL, CTEST, ITEST1, STEST1\n*     .. Intrinsic Functions ..\n      INTRINSIC         MAX\n*     .. Common blocks ..\n      COMMON            /COMBLA/ICASE, N, INCX, INCY, MODE, PASS\n*     .. Data statements ..\n      DATA              SA, CA/0.3E0, (0.4E0,-0.7E0)/\n      DATA              ((CV(I,J,1),I=1,8),J=1,5)/(0.1E0,0.1E0),\n     +                  (1.0E0,2.0E0), (1.0E0,2.0E0), (1.0E0,2.0E0),\n     +                  (1.0E0,2.0E0), (1.0E0,2.0E0), (1.0E0,2.0E0),\n     +                  (1.0E0,2.0E0), (0.3E0,-0.4E0), (3.0E0,4.0E0),\n     +                  (3.0E0,4.0E0), (3.0E0,4.0E0), (3.0E0,4.0E0),\n     +                  (3.0E0,4.0E0), (3.0E0,4.0E0), (3.0E0,4.0E0),\n     +                  (0.1E0,-0.3E0), (0.5E0,-0.1E0), (5.0E0,6.0E0),\n     +                  (5.0E0,6.0E0), (5.0E0,6.0E0), (5.0E0,6.0E0),\n     +                  (5.0E0,6.0E0), (5.0E0,6.0E0), (0.1E0,0.1E0),\n     +                  (-0.6E0,0.1E0), (0.1E0,-0.3E0), (7.0E0,8.0E0),\n     +                  (7.0E0,8.0E0), (7.0E0,8.0E0), (7.0E0,8.0E0),\n     +                  (7.0E0,8.0E0), (0.3E0,0.1E0), (0.5E0,0.0E0),\n     +                  (0.0E0,0.5E0), (0.0E0,0.2E0), (2.0E0,3.0E0),\n     +                  (2.0E0,3.0E0), (2.0E0,3.0E0), (2.0E0,3.0E0)/\n      DATA              ((CV(I,J,2),I=1,8),J=1,5)/(0.1E0,0.1E0),\n     +                  (4.0E0,5.0E0), (4.0E0,5.0E0), (4.0E0,5.0E0),\n     +                  (4.0E0,5.0E0), (4.0E0,5.0E0), (4.0E0,5.0E0),\n     +                  (4.0E0,5.0E0), (0.3E0,-0.4E0), (6.0E0,7.0E0),\n     +                  (6.0E0,7.0E0), (6.0E0,7.0E0), (6.0E0,7.0E0),\n     +                  (6.0E0,7.0E0), (6.0E0,7.0E0), (6.0E0,7.0E0),\n     +                  (0.1E0,-0.3E0), (8.0E0,9.0E0), (0.5E0,-0.1E0),\n     +                  (2.0E0,5.0E0), (2.0E0,5.0E0), (2.0E0,5.0E0),\n     +                  (2.0E0,5.0E0), (2.0E0,5.0E0), (0.1E0,0.1E0),\n     +                  (3.0E0,6.0E0), (-0.6E0,0.1E0), (4.0E0,7.0E0),\n     +                  (0.1E0,-0.3E0), (7.0E0,2.0E0), (7.0E0,2.0E0),\n     +                  (7.0E0,2.0E0), (0.3E0,0.1E0), (5.0E0,8.0E0),\n     +                  (0.5E0,0.0E0), (6.0E0,9.0E0), (0.0E0,0.5E0),\n     +                  (8.0E0,3.0E0), (0.0E0,0.2E0), (9.0E0,4.0E0)/\n      DATA              STRUE2/0.0E0, 0.5E0, 0.6E0, 0.7E0, 0.8E0/\n      DATA              STRUE4/0.0E0, 0.7E0, 1.0E0, 1.3E0, 1.6E0/\n      DATA              ((CTRUE5(I,J,1),I=1,8),J=1,5)/(0.1E0,0.1E0),\n     +                  (1.0E0,2.0E0), (1.0E0,2.0E0), (1.0E0,2.0E0),\n     +                  (1.0E0,2.0E0), (1.0E0,2.0E0), (1.0E0,2.0E0),\n     +                  (1.0E0,2.0E0), (-0.16E0,-0.37E0), (3.0E0,4.0E0),\n     +                  (3.0E0,4.0E0), (3.0E0,4.0E0), (3.0E0,4.0E0),\n     +                  (3.0E0,4.0E0), (3.0E0,4.0E0), (3.0E0,4.0E0),\n     +                  (-0.17E0,-0.19E0), (0.13E0,-0.39E0),\n     +                  (5.0E0,6.0E0), (5.0E0,6.0E0), (5.0E0,6.0E0),\n     +                  (5.0E0,6.0E0), (5.0E0,6.0E0), (5.0E0,6.0E0),\n     +                  (0.11E0,-0.03E0), (-0.17E0,0.46E0),\n     +                  (-0.17E0,-0.19E0), (7.0E0,8.0E0), (7.0E0,8.0E0),\n     +                  (7.0E0,8.0E0), (7.0E0,8.0E0), (7.0E0,8.0E0),\n     +                  (0.19E0,-0.17E0), (0.20E0,-0.35E0),\n     +                  (0.35E0,0.20E0), (0.14E0,0.08E0),\n     +                  (2.0E0,3.0E0), (2.0E0,3.0E0), (2.0E0,3.0E0),\n     +                  (2.0E0,3.0E0)/\n      DATA              ((CTRUE5(I,J,2),I=1,8),J=1,5)/(0.1E0,0.1E0),\n     +                  (4.0E0,5.0E0), (4.0E0,5.0E0), (4.0E0,5.0E0),\n     +                  (4.0E0,5.0E0), (4.0E0,5.0E0), (4.0E0,5.0E0),\n     +                  (4.0E0,5.0E0), (-0.16E0,-0.37E0), (6.0E0,7.0E0),\n     +                  (6.0E0,7.0E0), (6.0E0,7.0E0), (6.0E0,7.0E0),\n     +                  (6.0E0,7.0E0), (6.0E0,7.0E0), (6.0E0,7.0E0),\n     +                  (-0.17E0,-0.19E0), (8.0E0,9.0E0),\n     +                  (0.13E0,-0.39E0), (2.0E0,5.0E0), (2.0E0,5.0E0),\n     +                  (2.0E0,5.0E0), (2.0E0,5.0E0), (2.0E0,5.0E0),\n     +                  (0.11E0,-0.03E0), (3.0E0,6.0E0),\n     +                  (-0.17E0,0.46E0), (4.0E0,7.0E0),\n     +                  (-0.17E0,-0.19E0), (7.0E0,2.0E0), (7.0E0,2.0E0),\n     +                  (7.0E0,2.0E0), (0.19E0,-0.17E0), (5.0E0,8.0E0),\n     +                  (0.20E0,-0.35E0), (6.0E0,9.0E0),\n     +                  (0.35E0,0.20E0), (8.0E0,3.0E0),\n     +                  (0.14E0,0.08E0), (9.0E0,4.0E0)/\n      DATA              ((CTRUE6(I,J,1),I=1,8),J=1,5)/(0.1E0,0.1E0),\n     +                  (1.0E0,2.0E0), (1.0E0,2.0E0), (1.0E0,2.0E0),\n     +                  (1.0E0,2.0E0), (1.0E0,2.0E0), (1.0E0,2.0E0),\n     +                  (1.0E0,2.0E0), (0.09E0,-0.12E0), (3.0E0,4.0E0),\n     +                  (3.0E0,4.0E0), (3.0E0,4.0E0), (3.0E0,4.0E0),\n     +                  (3.0E0,4.0E0), (3.0E0,4.0E0), (3.0E0,4.0E0),\n     +                  (0.03E0,-0.09E0), (0.15E0,-0.03E0),\n     +                  (5.0E0,6.0E0), (5.0E0,6.0E0), (5.0E0,6.0E0),\n     +                  (5.0E0,6.0E0), (5.0E0,6.0E0), (5.0E0,6.0E0),\n     +                  (0.03E0,0.03E0), (-0.18E0,0.03E0),\n     +                  (0.03E0,-0.09E0), (7.0E0,8.0E0), (7.0E0,8.0E0),\n     +                  (7.0E0,8.0E0), (7.0E0,8.0E0), (7.0E0,8.0E0),\n     +                  (0.09E0,0.03E0), (0.15E0,0.00E0),\n     +                  (0.00E0,0.15E0), (0.00E0,0.06E0), (2.0E0,3.0E0),\n     +                  (2.0E0,3.0E0), (2.0E0,3.0E0), (2.0E0,3.0E0)/\n      DATA              ((CTRUE6(I,J,2),I=1,8),J=1,5)/(0.1E0,0.1E0),\n     +                  (4.0E0,5.0E0), (4.0E0,5.0E0), (4.0E0,5.0E0),\n     +                  (4.0E0,5.0E0), (4.0E0,5.0E0), (4.0E0,5.0E0),\n     +                  (4.0E0,5.0E0), (0.09E0,-0.12E0), (6.0E0,7.0E0),\n     +                  (6.0E0,7.0E0), (6.0E0,7.0E0), (6.0E0,7.0E0),\n     +                  (6.0E0,7.0E0), (6.0E0,7.0E0), (6.0E0,7.0E0),\n     +                  (0.03E0,-0.09E0), (8.0E0,9.0E0),\n     +                  (0.15E0,-0.03E0), (2.0E0,5.0E0), (2.0E0,5.0E0),\n     +                  (2.0E0,5.0E0), (2.0E0,5.0E0), (2.0E0,5.0E0),\n     +                  (0.03E0,0.03E0), (3.0E0,6.0E0),\n     +                  (-0.18E0,0.03E0), (4.0E0,7.0E0),\n     +                  (0.03E0,-0.09E0), (7.0E0,2.0E0), (7.0E0,2.0E0),\n     +                  (7.0E0,2.0E0), (0.09E0,0.03E0), (5.0E0,8.0E0),\n     +                  (0.15E0,0.00E0), (6.0E0,9.0E0), (0.00E0,0.15E0),\n     +                  (8.0E0,3.0E0), (0.00E0,0.06E0), (9.0E0,4.0E0)/\n      DATA              ITRUE3/0, 1, 2, 2, 2/\n*     .. Executable Statements ..\n      DO 60 INCX = 1, 2\n         DO 40 NP1 = 1, 5\n            N = NP1 - 1\n            LEN = 2*MAX(N,1)\n*           .. Set vector arguments ..\n            DO 20 I = 1, LEN\n               CX(I) = CV(I,NP1,INCX)\n   20       CONTINUE\n            IF (ICASE.EQ.6) THEN\n*              .. SCNRM2 ..\n               CALL STEST1(SCNRM2(N,CX,INCX),STRUE2(NP1),STRUE2(NP1),\n     +                     SFAC)\n            ELSE IF (ICASE.EQ.7) THEN\n*              .. SCASUM ..\n               CALL STEST1(SCASUM(N,CX,INCX),STRUE4(NP1),STRUE4(NP1),\n     +                     SFAC)\n            ELSE IF (ICASE.EQ.8) THEN\n*              .. CSCAL ..\n               CALL CSCAL(N,CA,CX,INCX)\n               CALL CTEST(LEN,CX,CTRUE5(1,NP1,INCX),CTRUE5(1,NP1,INCX),\n     +                    SFAC)\n            ELSE IF (ICASE.EQ.9) THEN\n*              .. CSSCAL ..\n               CALL CSSCAL(N,SA,CX,INCX)\n               CALL CTEST(LEN,CX,CTRUE6(1,NP1,INCX),CTRUE6(1,NP1,INCX),\n     +                    SFAC)\n            ELSE IF (ICASE.EQ.10) THEN\n*              .. ICAMAX ..\n               CALL ITEST1(ICAMAX(N,CX,INCX),ITRUE3(NP1))\n            ELSE\n               WRITE (NOUT,*) ' Shouldn''t be here in CHECK1'\n               STOP\n            END IF\n*\n   40    CONTINUE\n   60 CONTINUE\n*\n      INCX = 1\n      IF (ICASE.EQ.8) THEN\n*        CSCAL\n*        Add a test for alpha equal to zero.\n         CA = (0.0E0,0.0E0)\n         DO 80 I = 1, 5\n            MWPCT(I) = (0.0E0,0.0E0)\n            MWPCS(I) = (1.0E0,1.0E0)\n   80    CONTINUE\n         CALL CSCAL(5,CA,CX,INCX)\n         CALL CTEST(5,CX,MWPCT,MWPCS,SFAC)\n      ELSE IF (ICASE.EQ.9) THEN\n*        CSSCAL\n*        Add a test for alpha equal to zero.\n         SA = 0.0E0\n         DO 100 I = 1, 5\n            MWPCT(I) = (0.0E0,0.0E0)\n            MWPCS(I) = (1.0E0,1.0E0)\n  100    CONTINUE\n         CALL CSSCAL(5,SA,CX,INCX)\n         CALL CTEST(5,CX,MWPCT,MWPCS,SFAC)\n*        Add a test for alpha equal to one.\n         SA = 1.0E0\n         DO 120 I = 1, 5\n            MWPCT(I) = CX(I)\n            MWPCS(I) = CX(I)\n  120    CONTINUE\n         CALL CSSCAL(5,SA,CX,INCX)\n         CALL CTEST(5,CX,MWPCT,MWPCS,SFAC)\n*        Add a test for alpha equal to minus one.\n         SA = -1.0E0\n         DO 140 I = 1, 5\n            MWPCT(I) = -CX(I)\n            MWPCS(I) = -CX(I)\n  140    CONTINUE\n         CALL CSSCAL(5,SA,CX,INCX)\n         CALL CTEST(5,CX,MWPCT,MWPCS,SFAC)\n      END IF\n      RETURN\n      END\n      SUBROUTINE CHECK2(SFAC)\n*     .. Parameters ..\n      INTEGER           NOUT\n      PARAMETER         (NOUT=6)\n*     .. Scalar Arguments ..\n      REAL              SFAC\n*     .. Scalars in Common ..\n      INTEGER           ICASE, INCX, INCY, MODE, N\n      LOGICAL           PASS\n*     .. Local Scalars ..\n      COMPLEX           CA\n      INTEGER           I, J, KI, KN, KSIZE, LENX, LENY, MX, MY\n*     .. Local Arrays ..\n      COMPLEX           CDOT(1), CSIZE1(4), CSIZE2(7,2), CSIZE3(14),\n     +                  CT10X(7,4,4), CT10Y(7,4,4), CT6(4,4), CT7(4,4),\n     +                  CT8(7,4,4), CX(7), CX1(7), CY(7), CY1(7)\n      INTEGER           INCXS(4), INCYS(4), LENS(4,2), NS(4)\n*     .. External Functions ..\n      COMPLEX           CDOTC, CDOTU\n      EXTERNAL          CDOTC, CDOTU\n*     .. External Subroutines ..\n      EXTERNAL          CAXPY, CCOPY, CSWAP, CTEST\n*     .. Intrinsic Functions ..\n      INTRINSIC         ABS, MIN\n*     .. Common blocks ..\n      COMMON            /COMBLA/ICASE, N, INCX, INCY, MODE, PASS\n*     .. Data statements ..\n      DATA              CA/(0.4E0,-0.7E0)/\n      DATA              INCXS/1, 2, -2, -1/\n      DATA              INCYS/1, -2, 1, -2/\n      DATA              LENS/1, 1, 2, 4, 1, 1, 3, 7/\n      DATA              NS/0, 1, 2, 4/\n      DATA              CX1/(0.7E0,-0.8E0), (-0.4E0,-0.7E0),\n     +                  (-0.1E0,-0.9E0), (0.2E0,-0.8E0),\n     +                  (-0.9E0,-0.4E0), (0.1E0,0.4E0), (-0.6E0,0.6E0)/\n      DATA              CY1/(0.6E0,-0.6E0), (-0.9E0,0.5E0),\n     +                  (0.7E0,-0.6E0), (0.1E0,-0.5E0), (-0.1E0,-0.2E0),\n     +                  (-0.5E0,-0.3E0), (0.8E0,-0.7E0)/\n      DATA              ((CT8(I,J,1),I=1,7),J=1,4)/(0.6E0,-0.6E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.32E0,-1.41E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.32E0,-1.41E0),\n     +                  (-1.55E0,0.5E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.32E0,-1.41E0), (-1.55E0,0.5E0),\n     +                  (0.03E0,-0.89E0), (-0.38E0,-0.96E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0)/\n      DATA              ((CT8(I,J,2),I=1,7),J=1,4)/(0.6E0,-0.6E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.32E0,-1.41E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (-0.07E0,-0.89E0),\n     +                  (-0.9E0,0.5E0), (0.42E0,-1.41E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.78E0,0.06E0), (-0.9E0,0.5E0),\n     +                  (0.06E0,-0.13E0), (0.1E0,-0.5E0),\n     +                  (-0.77E0,-0.49E0), (-0.5E0,-0.3E0),\n     +                  (0.52E0,-1.51E0)/\n      DATA              ((CT8(I,J,3),I=1,7),J=1,4)/(0.6E0,-0.6E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.32E0,-1.41E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (-0.07E0,-0.89E0),\n     +                  (-1.18E0,-0.31E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.78E0,0.06E0), (-1.54E0,0.97E0),\n     +                  (0.03E0,-0.89E0), (-0.18E0,-1.31E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0)/\n      DATA              ((CT8(I,J,4),I=1,7),J=1,4)/(0.6E0,-0.6E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.32E0,-1.41E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.32E0,-1.41E0), (-0.9E0,0.5E0),\n     +                  (0.05E0,-0.6E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.32E0,-1.41E0),\n     +                  (-0.9E0,0.5E0), (0.05E0,-0.6E0), (0.1E0,-0.5E0),\n     +                  (-0.77E0,-0.49E0), (-0.5E0,-0.3E0),\n     +                  (0.32E0,-1.16E0)/\n      DATA              CT7/(0.0E0,0.0E0), (-0.06E0,-0.90E0),\n     +                  (0.65E0,-0.47E0), (-0.34E0,-1.22E0),\n     +                  (0.0E0,0.0E0), (-0.06E0,-0.90E0),\n     +                  (-0.59E0,-1.46E0), (-1.04E0,-0.04E0),\n     +                  (0.0E0,0.0E0), (-0.06E0,-0.90E0),\n     +                  (-0.83E0,0.59E0), (0.07E0,-0.37E0),\n     +                  (0.0E0,0.0E0), (-0.06E0,-0.90E0),\n     +                  (-0.76E0,-1.15E0), (-1.33E0,-1.82E0)/\n      DATA              CT6/(0.0E0,0.0E0), (0.90E0,0.06E0),\n     +                  (0.91E0,-0.77E0), (1.80E0,-0.10E0),\n     +                  (0.0E0,0.0E0), (0.90E0,0.06E0), (1.45E0,0.74E0),\n     +                  (0.20E0,0.90E0), (0.0E0,0.0E0), (0.90E0,0.06E0),\n     +                  (-0.55E0,0.23E0), (0.83E0,-0.39E0),\n     +                  (0.0E0,0.0E0), (0.90E0,0.06E0), (1.04E0,0.79E0),\n     +                  (1.95E0,1.22E0)/\n      DATA              ((CT10X(I,J,1),I=1,7),J=1,4)/(0.7E0,-0.8E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.6E0,-0.6E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.6E0,-0.6E0), (-0.9E0,0.5E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.6E0,-0.6E0),\n     +                  (-0.9E0,0.5E0), (0.7E0,-0.6E0), (0.1E0,-0.5E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0)/\n      DATA              ((CT10X(I,J,2),I=1,7),J=1,4)/(0.7E0,-0.8E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.6E0,-0.6E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.7E0,-0.6E0), (-0.4E0,-0.7E0),\n     +                  (0.6E0,-0.6E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.8E0,-0.7E0),\n     +                  (-0.4E0,-0.7E0), (-0.1E0,-0.2E0),\n     +                  (0.2E0,-0.8E0), (0.7E0,-0.6E0), (0.1E0,0.4E0),\n     +                  (0.6E0,-0.6E0)/\n      DATA              ((CT10X(I,J,3),I=1,7),J=1,4)/(0.7E0,-0.8E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.6E0,-0.6E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (-0.9E0,0.5E0), (-0.4E0,-0.7E0),\n     +                  (0.6E0,-0.6E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.1E0,-0.5E0),\n     +                  (-0.4E0,-0.7E0), (0.7E0,-0.6E0), (0.2E0,-0.8E0),\n     +                  (-0.9E0,0.5E0), (0.1E0,0.4E0), (0.6E0,-0.6E0)/\n      DATA              ((CT10X(I,J,4),I=1,7),J=1,4)/(0.7E0,-0.8E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.6E0,-0.6E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.6E0,-0.6E0), (0.7E0,-0.6E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.6E0,-0.6E0),\n     +                  (0.7E0,-0.6E0), (-0.1E0,-0.2E0), (0.8E0,-0.7E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0)/\n      DATA              ((CT10Y(I,J,1),I=1,7),J=1,4)/(0.6E0,-0.6E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.7E0,-0.8E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.7E0,-0.8E0), (-0.4E0,-0.7E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.7E0,-0.8E0),\n     +                  (-0.4E0,-0.7E0), (-0.1E0,-0.9E0),\n     +                  (0.2E0,-0.8E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0)/\n      DATA              ((CT10Y(I,J,2),I=1,7),J=1,4)/(0.6E0,-0.6E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.7E0,-0.8E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (-0.1E0,-0.9E0), (-0.9E0,0.5E0),\n     +                  (0.7E0,-0.8E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (-0.6E0,0.6E0),\n     +                  (-0.9E0,0.5E0), (-0.9E0,-0.4E0), (0.1E0,-0.5E0),\n     +                  (-0.1E0,-0.9E0), (-0.5E0,-0.3E0),\n     +                  (0.7E0,-0.8E0)/\n      DATA              ((CT10Y(I,J,3),I=1,7),J=1,4)/(0.6E0,-0.6E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.7E0,-0.8E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (-0.1E0,-0.9E0), (0.7E0,-0.8E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (-0.6E0,0.6E0),\n     +                  (-0.9E0,-0.4E0), (-0.1E0,-0.9E0),\n     +                  (0.7E0,-0.8E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0)/\n      DATA              ((CT10Y(I,J,4),I=1,7),J=1,4)/(0.6E0,-0.6E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.7E0,-0.8E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.7E0,-0.8E0), (-0.9E0,0.5E0),\n     +                  (-0.4E0,-0.7E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.7E0,-0.8E0),\n     +                  (-0.9E0,0.5E0), (-0.4E0,-0.7E0), (0.1E0,-0.5E0),\n     +                  (-0.1E0,-0.9E0), (-0.5E0,-0.3E0),\n     +                  (0.2E0,-0.8E0)/\n      DATA              CSIZE1/(0.0E0,0.0E0), (0.9E0,0.9E0),\n     +                  (1.63E0,1.73E0), (2.90E0,2.78E0)/\n      DATA              CSIZE3/(0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (1.17E0,1.17E0),\n     +                  (1.17E0,1.17E0), (1.17E0,1.17E0),\n     +                  (1.17E0,1.17E0), (1.17E0,1.17E0),\n     +                  (1.17E0,1.17E0), (1.17E0,1.17E0)/\n      DATA              CSIZE2/(0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),\n     +                  (0.0E0,0.0E0), (0.0E0,0.0E0), (1.54E0,1.54E0),\n     +                  (1.54E0,1.54E0), (1.54E0,1.54E0),\n     +                  (1.54E0,1.54E0), (1.54E0,1.54E0),\n     +                  (1.54E0,1.54E0), (1.54E0,1.54E0)/\n*     .. Executable Statements ..\n      DO 60 KI = 1, 4\n         INCX = INCXS(KI)\n         INCY = INCYS(KI)\n         MX = ABS(INCX)\n         MY = ABS(INCY)\n*\n         DO 40 KN = 1, 4\n            N = NS(KN)\n            KSIZE = MIN(2,KN)\n            LENX = LENS(KN,MX)\n            LENY = LENS(KN,MY)\n*           .. initialize all argument arrays ..\n            DO 20 I = 1, 7\n               CX(I) = CX1(I)\n               CY(I) = CY1(I)\n   20       CONTINUE\n            IF (ICASE.EQ.1) THEN\n*              .. CDOTC ..\n               CDOT(1) = CDOTC(N,CX,INCX,CY,INCY)\n               CALL CTEST(1,CDOT,CT6(KN,KI),CSIZE1(KN),SFAC)\n            ELSE IF (ICASE.EQ.2) THEN\n*              .. CDOTU ..\n               CDOT(1) = CDOTU(N,CX,INCX,CY,INCY)\n               CALL CTEST(1,CDOT,CT7(KN,KI),CSIZE1(KN),SFAC)\n            ELSE IF (ICASE.EQ.3) THEN\n*              .. CAXPY ..\n               CALL CAXPY(N,CA,CX,INCX,CY,INCY)\n               CALL CTEST(LENY,CY,CT8(1,KN,KI),CSIZE2(1,KSIZE),SFAC)\n            ELSE IF (ICASE.EQ.4) THEN\n*              .. CCOPY ..\n               CALL CCOPY(N,CX,INCX,CY,INCY)\n               CALL CTEST(LENY,CY,CT10Y(1,KN,KI),CSIZE3,1.0E0)\n            ELSE IF (ICASE.EQ.5) THEN\n*              .. CSWAP ..\n               CALL CSWAP(N,CX,INCX,CY,INCY)\n               CALL CTEST(LENX,CX,CT10X(1,KN,KI),CSIZE3,1.0E0)\n               CALL CTEST(LENY,CY,CT10Y(1,KN,KI),CSIZE3,1.0E0)\n            ELSE\n               WRITE (NOUT,*) ' Shouldn''t be here in CHECK2'\n               STOP\n            END IF\n*\n   40    CONTINUE\n   60 CONTINUE\n      RETURN\n      END\n      SUBROUTINE STEST(LEN,SCOMP,STRUE,SSIZE,SFAC)\n*     ********************************* STEST **************************\n*\n*     THIS SUBR COMPARES ARRAYS  SCOMP() AND STRUE() OF LENGTH LEN TO\n*     SEE IF THE TERM BY TERM DIFFERENCES, MULTIPLIED BY SFAC, ARE\n*     NEGLIGIBLE.\n*\n*     C. L. LAWSON, JPL, 1974 DEC 10\n*\n*     .. Parameters ..\n      INTEGER          NOUT\n      REAL             ZERO\n      PARAMETER        (NOUT=6, ZERO=0.0E0)\n*     .. Scalar Arguments ..\n      REAL             SFAC\n      INTEGER          LEN\n*     .. Array Arguments ..\n      REAL             SCOMP(LEN), SSIZE(LEN), STRUE(LEN)\n*     .. Scalars in Common ..\n      INTEGER          ICASE, INCX, INCY, MODE, N\n      LOGICAL          PASS\n*     .. Local Scalars ..\n      REAL             SD\n      INTEGER          I\n*     .. External Functions ..\n      REAL             SDIFF\n      EXTERNAL         SDIFF\n*     .. Intrinsic Functions ..\n      INTRINSIC        ABS\n*     .. Common blocks ..\n      COMMON           /COMBLA/ICASE, N, INCX, INCY, MODE, PASS\n*     .. Executable Statements ..\n*\n      DO 40 I = 1, LEN\n         SD = SCOMP(I) - STRUE(I)\n         IF (ABS(SFAC*SD) .LE. ABS(SSIZE(I))*EPSILON(ZERO))\n     +       GO TO 40\n*\n*                             HERE    SCOMP(I) IS NOT CLOSE TO STRUE(I).\n*\n         IF ( .NOT. PASS) GO TO 20\n*                             PRINT FAIL MESSAGE AND HEADER.\n         PASS = .FALSE.\n         WRITE (NOUT,99999)\n         WRITE (NOUT,99998)\n   20    WRITE (NOUT,99997) ICASE, N, INCX, INCY, MODE, I, SCOMP(I),\n     +     STRUE(I), SD, SSIZE(I)\n   40 CONTINUE\n      RETURN\n*\n99999 FORMAT ('                                       FAIL')\n99998 FORMAT (/' CASE  N INCX INCY MODE  I                            ',\n     +       ' COMP(I)                             TRUE(I)  DIFFERENCE',\n     +       '     SIZE(I)',/1X)\n99997 FORMAT (1X,I4,I3,3I5,I3,2E36.8,2E12.4)\n      END\n      SUBROUTINE STEST1(SCOMP1,STRUE1,SSIZE,SFAC)\n*     ************************* STEST1 *****************************\n*\n*     THIS IS AN INTERFACE SUBROUTINE TO ACCOMODATE THE FORTRAN\n*     REQUIREMENT THAT WHEN A DUMMY ARGUMENT IS AN ARRAY, THE\n*     ACTUAL ARGUMENT MUST ALSO BE AN ARRAY OR AN ARRAY ELEMENT.\n*\n*     C.L. LAWSON, JPL, 1978 DEC 6\n*\n*     .. Scalar Arguments ..\n      REAL              SCOMP1, SFAC, STRUE1\n*     .. Array Arguments ..\n      REAL              SSIZE(*)\n*     .. Local Arrays ..\n      REAL              SCOMP(1), STRUE(1)\n*     .. External Subroutines ..\n      EXTERNAL          STEST\n*     .. Executable Statements ..\n*\n      SCOMP(1) = SCOMP1\n      STRUE(1) = STRUE1\n      CALL STEST(1,SCOMP,STRUE,SSIZE,SFAC)\n*\n      RETURN\n      END\n      REAL             FUNCTION SDIFF(SA,SB)\n*     ********************************* SDIFF **************************\n*     COMPUTES DIFFERENCE OF TWO NUMBERS.  C. L. LAWSON, JPL 1974 FEB 15\n*\n*     .. Scalar Arguments ..\n      REAL                            SA, SB\n*     .. Executable Statements ..\n      SDIFF = SA - SB\n      RETURN\n      END\n      SUBROUTINE CTEST(LEN,CCOMP,CTRUE,CSIZE,SFAC)\n*     **************************** CTEST *****************************\n*\n*     C.L. LAWSON, JPL, 1978 DEC 6\n*\n*     .. Scalar Arguments ..\n      REAL             SFAC\n      INTEGER          LEN\n*     .. Array Arguments ..\n      COMPLEX          CCOMP(LEN), CSIZE(LEN), CTRUE(LEN)\n*     .. Local Scalars ..\n      INTEGER          I\n*     .. Local Arrays ..\n      REAL             SCOMP(20), SSIZE(20), STRUE(20)\n*     .. External Subroutines ..\n      EXTERNAL         STEST\n*     .. Intrinsic Functions ..\n      INTRINSIC        AIMAG, REAL\n*     .. Executable Statements ..\n      DO 20 I = 1, LEN\n         SCOMP(2*I-1) = REAL(CCOMP(I))\n         SCOMP(2*I) = AIMAG(CCOMP(I))\n         STRUE(2*I-1) = REAL(CTRUE(I))\n         STRUE(2*I) = AIMAG(CTRUE(I))\n         SSIZE(2*I-1) = REAL(CSIZE(I))\n         SSIZE(2*I) = AIMAG(CSIZE(I))\n   20 CONTINUE\n*\n      CALL STEST(2*LEN,SCOMP,STRUE,SSIZE,SFAC)\n      RETURN\n      END\n      SUBROUTINE ITEST1(ICOMP,ITRUE)\n*     ********************************* ITEST1 *************************\n*\n*     THIS SUBROUTINE COMPARES THE VARIABLES ICOMP AND ITRUE FOR\n*     EQUALITY.\n*     C. L. LAWSON, JPL, 1974 DEC 10\n*\n*     .. Parameters ..\n      INTEGER           NOUT\n      PARAMETER         (NOUT=6)\n*     .. Scalar Arguments ..\n      INTEGER           ICOMP, ITRUE\n*     .. Scalars in Common ..\n      INTEGER           ICASE, INCX, INCY, MODE, N\n      LOGICAL           PASS\n*     .. Local Scalars ..\n      INTEGER           ID\n*     .. Common blocks ..\n      COMMON            /COMBLA/ICASE, N, INCX, INCY, MODE, PASS\n*     .. Executable Statements ..\n      IF (ICOMP.EQ.ITRUE) GO TO 40\n*\n*                            HERE ICOMP IS NOT EQUAL TO ITRUE.\n*\n      IF ( .NOT. PASS) GO TO 20\n*                             PRINT FAIL MESSAGE AND HEADER.\n      PASS = .FALSE.\n      WRITE (NOUT,99999)\n      WRITE (NOUT,99998)\n   20 ID = ICOMP - ITRUE\n      WRITE (NOUT,99997) ICASE, N, INCX, INCY, MODE, ICOMP, ITRUE, ID\n   40 CONTINUE\n      RETURN\n*\n99999 FORMAT ('                                       FAIL')\n99998 FORMAT (/' CASE  N INCX INCY MODE                               ',\n     +       ' COMP                                TRUE     DIFFERENCE',\n     +       /1X)\n99997 FORMAT (1X,I4,I3,3I5,2I36,I12)\n      END\n"
  },
  {
    "path": "include/eigen3/blas/testing/cblat2.f",
    "content": "*> \\brief \\b CBLAT2\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*  Definition:\n*  ===========\n*\n*       PROGRAM CBLAT2\n* \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> Test program for the COMPLEX          Level 2 Blas.\n*>\n*> The program must be driven by a short data file. The first 18 records\n*> of the file are read using list-directed input, the last 17 records\n*> are read using the format ( A6, L2 ). An annotated example of a data\n*> file can be obtained by deleting the first 3 characters from the\n*> following 35 lines:\n*> 'cblat2.out'      NAME OF SUMMARY OUTPUT FILE\n*> 6                 UNIT NUMBER OF SUMMARY FILE\n*> 'CBLA2T.SNAP'     NAME OF SNAPSHOT OUTPUT FILE\n*> -1                UNIT NUMBER OF SNAPSHOT FILE (NOT USED IF .LT. 0)\n*> F        LOGICAL FLAG, T TO REWIND SNAPSHOT FILE AFTER EACH RECORD.\n*> F        LOGICAL FLAG, T TO STOP ON FAILURES.\n*> T        LOGICAL FLAG, T TO TEST ERROR EXITS.\n*> 16.0     THRESHOLD VALUE OF TEST RATIO\n*> 6                 NUMBER OF VALUES OF N\n*> 0 1 2 3 5 9       VALUES OF N\n*> 4                 NUMBER OF VALUES OF K\n*> 0 1 2 4           VALUES OF K\n*> 4                 NUMBER OF VALUES OF INCX AND INCY\n*> 1 2 -1 -2         VALUES OF INCX AND INCY\n*> 3                 NUMBER OF VALUES OF ALPHA\n*> (0.0,0.0) (1.0,0.0) (0.7,-0.9)       VALUES OF ALPHA\n*> 3                 NUMBER OF VALUES OF BETA\n*> (0.0,0.0) (1.0,0.0) (1.3,-1.1)       VALUES OF BETA\n*> CGEMV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> CGBMV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> CHEMV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> CHBMV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> CHPMV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> CTRMV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> CTBMV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> CTPMV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> CTRSV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> CTBSV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> CTPSV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> CGERC  T PUT F FOR NO TEST. SAME COLUMNS.\n*> CGERU  T PUT F FOR NO TEST. SAME COLUMNS.\n*> CHER   T PUT F FOR NO TEST. SAME COLUMNS.\n*> CHPR   T PUT F FOR NO TEST. SAME COLUMNS.\n*> CHER2  T PUT F FOR NO TEST. SAME COLUMNS.\n*> CHPR2  T PUT F FOR NO TEST. SAME COLUMNS.\n*>\n*> Further Details\n*> ===============\n*>\n*>    See:\n*>\n*>       Dongarra J. J., Du Croz J. J., Hammarling S.  and Hanson R. J..\n*>       An  extended  set of Fortran  Basic Linear Algebra Subprograms.\n*>\n*>       Technical  Memoranda  Nos. 41 (revision 3) and 81,  Mathematics\n*>       and  Computer Science  Division,  Argonne  National Laboratory,\n*>       9700 South Cass Avenue, Argonne, Illinois 60439, US.\n*>\n*>       Or\n*>\n*>       NAG  Technical Reports TR3/87 and TR4/87,  Numerical Algorithms\n*>       Group  Ltd.,  NAG  Central  Office,  256  Banbury  Road, Oxford\n*>       OX2 7DE, UK,  and  Numerical Algorithms Group Inc.,  1101  31st\n*>       Street,  Suite 100,  Downers Grove,  Illinois 60515-1263,  USA.\n*>\n*>\n*> -- Written on 10-August-1987.\n*>    Richard Hanson, Sandia National Labs.\n*>    Jeremy Du Croz, NAG Central Office.\n*>\n*>    10-9-00:  Change STATUS='NEW' to 'UNKNOWN' so that the testers\n*>              can be run multiple times without deleting generated\n*>              output files (susan)\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date April 2012\n*\n*> \\ingroup complex_blas_testing\n*\n*  =====================================================================\n      PROGRAM CBLAT2\n*\n*  -- Reference BLAS test routine (version 3.4.1) --\n*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     April 2012\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      INTEGER            NIN\n      PARAMETER          ( NIN = 5 )\n      INTEGER            NSUBS\n      PARAMETER          ( NSUBS = 17 )\n      COMPLEX            ZERO, ONE\n      PARAMETER          ( ZERO = ( 0.0, 0.0 ), ONE = ( 1.0, 0.0 ) )\n      REAL               RZERO\n      PARAMETER          ( RZERO = 0.0 )\n      INTEGER            NMAX, INCMAX\n      PARAMETER          ( NMAX = 65, INCMAX = 2 )\n      INTEGER            NINMAX, NIDMAX, NKBMAX, NALMAX, NBEMAX\n      PARAMETER          ( NINMAX = 7, NIDMAX = 9, NKBMAX = 7,\n     $                   NALMAX = 7, NBEMAX = 7 )\n*     .. Local Scalars ..\n      REAL               EPS, ERR, THRESH\n      INTEGER            I, ISNUM, J, N, NALF, NBET, NIDIM, NINC, NKB,\n     $                   NOUT, NTRA\n      LOGICAL            FATAL, LTESTT, REWI, SAME, SFATAL, TRACE,\n     $                   TSTERR\n      CHARACTER*1        TRANS\n      CHARACTER*6        SNAMET\n      CHARACTER*32       SNAPS, SUMMRY\n*     .. Local Arrays ..\n      COMPLEX            A( NMAX, NMAX ), AA( NMAX*NMAX ),\n     $                   ALF( NALMAX ), AS( NMAX*NMAX ), BET( NBEMAX ),\n     $                   X( NMAX ), XS( NMAX*INCMAX ),\n     $                   XX( NMAX*INCMAX ), Y( NMAX ),\n     $                   YS( NMAX*INCMAX ), YT( NMAX ),\n     $                   YY( NMAX*INCMAX ), Z( 2*NMAX )\n      REAL               G( NMAX )\n      INTEGER            IDIM( NIDMAX ), INC( NINMAX ), KB( NKBMAX )\n      LOGICAL            LTEST( NSUBS )\n      CHARACTER*6        SNAMES( NSUBS )\n*     .. External Functions ..\n      REAL               SDIFF\n      LOGICAL            LCE\n      EXTERNAL           SDIFF, LCE\n*     .. External Subroutines ..\n      EXTERNAL           CCHK1, CCHK2, CCHK3, CCHK4, CCHK5, CCHK6,\n     $                   CCHKE, CMVCH\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, MAX, MIN\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n      CHARACTER*6        SRNAMT\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n      COMMON             /SRNAMC/SRNAMT\n*     .. Data statements ..\n      DATA               SNAMES/'CGEMV ', 'CGBMV ', 'CHEMV ', 'CHBMV ',\n     $                   'CHPMV ', 'CTRMV ', 'CTBMV ', 'CTPMV ',\n     $                   'CTRSV ', 'CTBSV ', 'CTPSV ', 'CGERC ',\n     $                   'CGERU ', 'CHER  ', 'CHPR  ', 'CHER2 ',\n     $                   'CHPR2 '/\n*     .. Executable Statements ..\n*\n*     Read name and unit number for summary output file and open file.\n*\n      READ( NIN, FMT = * )SUMMRY\n      READ( NIN, FMT = * )NOUT\n      OPEN( NOUT, FILE = SUMMRY, STATUS = 'UNKNOWN' )\n      NOUTC = NOUT\n*\n*     Read name and unit number for snapshot output file and open file.\n*\n      READ( NIN, FMT = * )SNAPS\n      READ( NIN, FMT = * )NTRA\n      TRACE = NTRA.GE.0\n      IF( TRACE )THEN\n         OPEN( NTRA, FILE = SNAPS, STATUS = 'UNKNOWN' )\n      END IF\n*     Read the flag that directs rewinding of the snapshot file.\n      READ( NIN, FMT = * )REWI\n      REWI = REWI.AND.TRACE\n*     Read the flag that directs stopping on any failure.\n      READ( NIN, FMT = * )SFATAL\n*     Read the flag that indicates whether error exits are to be tested.\n      READ( NIN, FMT = * )TSTERR\n*     Read the threshold value of the test ratio\n      READ( NIN, FMT = * )THRESH\n*\n*     Read and check the parameter values for the tests.\n*\n*     Values of N\n      READ( NIN, FMT = * )NIDIM\n      IF( NIDIM.LT.1.OR.NIDIM.GT.NIDMAX )THEN\n         WRITE( NOUT, FMT = 9997 )'N', NIDMAX\n         GO TO 230\n      END IF\n      READ( NIN, FMT = * )( IDIM( I ), I = 1, NIDIM )\n      DO 10 I = 1, NIDIM\n         IF( IDIM( I ).LT.0.OR.IDIM( I ).GT.NMAX )THEN\n            WRITE( NOUT, FMT = 9996 )NMAX\n            GO TO 230\n         END IF\n   10 CONTINUE\n*     Values of K\n      READ( NIN, FMT = * )NKB\n      IF( NKB.LT.1.OR.NKB.GT.NKBMAX )THEN\n         WRITE( NOUT, FMT = 9997 )'K', NKBMAX\n         GO TO 230\n      END IF\n      READ( NIN, FMT = * )( KB( I ), I = 1, NKB )\n      DO 20 I = 1, NKB\n         IF( KB( I ).LT.0 )THEN\n            WRITE( NOUT, FMT = 9995 )\n            GO TO 230\n         END IF\n   20 CONTINUE\n*     Values of INCX and INCY\n      READ( NIN, FMT = * )NINC\n      IF( NINC.LT.1.OR.NINC.GT.NINMAX )THEN\n         WRITE( NOUT, FMT = 9997 )'INCX AND INCY', NINMAX\n         GO TO 230\n      END IF\n      READ( NIN, FMT = * )( INC( I ), I = 1, NINC )\n      DO 30 I = 1, NINC\n         IF( INC( I ).EQ.0.OR.ABS( INC( I ) ).GT.INCMAX )THEN\n            WRITE( NOUT, FMT = 9994 )INCMAX\n            GO TO 230\n         END IF\n   30 CONTINUE\n*     Values of ALPHA\n      READ( NIN, FMT = * )NALF\n      IF( NALF.LT.1.OR.NALF.GT.NALMAX )THEN\n         WRITE( NOUT, FMT = 9997 )'ALPHA', NALMAX\n         GO TO 230\n      END IF\n      READ( NIN, FMT = * )( ALF( I ), I = 1, NALF )\n*     Values of BETA\n      READ( NIN, FMT = * )NBET\n      IF( NBET.LT.1.OR.NBET.GT.NBEMAX )THEN\n         WRITE( NOUT, FMT = 9997 )'BETA', NBEMAX\n         GO TO 230\n      END IF\n      READ( NIN, FMT = * )( BET( I ), I = 1, NBET )\n*\n*     Report values of parameters.\n*\n      WRITE( NOUT, FMT = 9993 )\n      WRITE( NOUT, FMT = 9992 )( IDIM( I ), I = 1, NIDIM )\n      WRITE( NOUT, FMT = 9991 )( KB( I ), I = 1, NKB )\n      WRITE( NOUT, FMT = 9990 )( INC( I ), I = 1, NINC )\n      WRITE( NOUT, FMT = 9989 )( ALF( I ), I = 1, NALF )\n      WRITE( NOUT, FMT = 9988 )( BET( I ), I = 1, NBET )\n      IF( .NOT.TSTERR )THEN\n         WRITE( NOUT, FMT = * )\n         WRITE( NOUT, FMT = 9980 )\n      END IF\n      WRITE( NOUT, FMT = * )\n      WRITE( NOUT, FMT = 9999 )THRESH\n      WRITE( NOUT, FMT = * )\n*\n*     Read names of subroutines and flags which indicate\n*     whether they are to be tested.\n*\n      DO 40 I = 1, NSUBS\n         LTEST( I ) = .FALSE.\n   40 CONTINUE\n   50 READ( NIN, FMT = 9984, END = 80 )SNAMET, LTESTT\n      DO 60 I = 1, NSUBS\n         IF( SNAMET.EQ.SNAMES( I ) )\n     $      GO TO 70\n   60 CONTINUE\n      WRITE( NOUT, FMT = 9986 )SNAMET\n      STOP\n   70 LTEST( I ) = LTESTT\n      GO TO 50\n*\n   80 CONTINUE\n      CLOSE ( NIN )\n*\n*     Compute EPS (the machine precision).\n*\n      EPS = EPSILON(RZERO)\n      WRITE( NOUT, FMT = 9998 )EPS\n*\n*     Check the reliability of CMVCH using exact data.\n*\n      N = MIN( 32, NMAX )\n      DO 120 J = 1, N\n         DO 110 I = 1, N\n            A( I, J ) = MAX( I - J + 1, 0 )\n  110    CONTINUE\n         X( J ) = J\n         Y( J ) = ZERO\n  120 CONTINUE\n      DO 130 J = 1, N\n         YY( J ) = J*( ( J + 1 )*J )/2 - ( ( J + 1 )*J*( J - 1 ) )/3\n  130 CONTINUE\n*     YY holds the exact result. On exit from CMVCH YT holds\n*     the result computed by CMVCH.\n      TRANS = 'N'\n      CALL CMVCH( TRANS, N, N, ONE, A, NMAX, X, 1, ZERO, Y, 1, YT, G,\n     $            YY, EPS, ERR, FATAL, NOUT, .TRUE. )\n      SAME = LCE( YY, YT, N )\n      IF( .NOT.SAME.OR.ERR.NE.RZERO )THEN\n         WRITE( NOUT, FMT = 9985 )TRANS, SAME, ERR\n         STOP\n      END IF\n      TRANS = 'T'\n      CALL CMVCH( TRANS, N, N, ONE, A, NMAX, X, -1, ZERO, Y, -1, YT, G,\n     $            YY, EPS, ERR, FATAL, NOUT, .TRUE. )\n      SAME = LCE( YY, YT, N )\n      IF( .NOT.SAME.OR.ERR.NE.RZERO )THEN\n         WRITE( NOUT, FMT = 9985 )TRANS, SAME, ERR\n         STOP\n      END IF\n*\n*     Test each subroutine in turn.\n*\n      DO 210 ISNUM = 1, NSUBS\n         WRITE( NOUT, FMT = * )\n         IF( .NOT.LTEST( ISNUM ) )THEN\n*           Subprogram is not to be tested.\n            WRITE( NOUT, FMT = 9983 )SNAMES( ISNUM )\n         ELSE\n            SRNAMT = SNAMES( ISNUM )\n*           Test error exits.\n            IF( TSTERR )THEN\n               CALL CCHKE( ISNUM, SNAMES( ISNUM ), NOUT )\n               WRITE( NOUT, FMT = * )\n            END IF\n*           Test computations.\n            INFOT = 0\n            OK = .TRUE.\n            FATAL = .FALSE.\n            GO TO ( 140, 140, 150, 150, 150, 160, 160,\n     $              160, 160, 160, 160, 170, 170, 180,\n     $              180, 190, 190 )ISNUM\n*           Test CGEMV, 01, and CGBMV, 02.\n  140       CALL CCHK1( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF,\n     $                  NBET, BET, NINC, INC, NMAX, INCMAX, A, AA, AS,\n     $                  X, XX, XS, Y, YY, YS, YT, G )\n            GO TO 200\n*           Test CHEMV, 03, CHBMV, 04, and CHPMV, 05.\n  150       CALL CCHK2( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF,\n     $                  NBET, BET, NINC, INC, NMAX, INCMAX, A, AA, AS,\n     $                  X, XX, XS, Y, YY, YS, YT, G )\n            GO TO 200\n*           Test CTRMV, 06, CTBMV, 07, CTPMV, 08,\n*           CTRSV, 09, CTBSV, 10, and CTPSV, 11.\n  160       CALL CCHK3( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NKB, KB, NINC, INC,\n     $                  NMAX, INCMAX, A, AA, AS, Y, YY, YS, YT, G, Z )\n            GO TO 200\n*           Test CGERC, 12, CGERU, 13.\n  170       CALL CCHK4( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC,\n     $                  NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS,\n     $                  YT, G, Z )\n            GO TO 200\n*           Test CHER, 14, and CHPR, 15.\n  180       CALL CCHK5( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC,\n     $                  NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS,\n     $                  YT, G, Z )\n            GO TO 200\n*           Test CHER2, 16, and CHPR2, 17.\n  190       CALL CCHK6( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC,\n     $                  NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS,\n     $                  YT, G, Z )\n*\n  200       IF( FATAL.AND.SFATAL )\n     $         GO TO 220\n         END IF\n  210 CONTINUE\n      WRITE( NOUT, FMT = 9982 )\n      GO TO 240\n*\n  220 CONTINUE\n      WRITE( NOUT, FMT = 9981 )\n      GO TO 240\n*\n  230 CONTINUE\n      WRITE( NOUT, FMT = 9987 )\n*\n  240 CONTINUE\n      IF( TRACE )\n     $   CLOSE ( NTRA )\n      CLOSE ( NOUT )\n      STOP\n*\n 9999 FORMAT( ' ROUTINES PASS COMPUTATIONAL TESTS IF TEST RATIO IS LES',\n     $      'S THAN', F8.2 )\n 9998 FORMAT( ' RELATIVE MACHINE PRECISION IS TAKEN TO BE', 1P, E9.1 )\n 9997 FORMAT( ' NUMBER OF VALUES OF ', A, ' IS LESS THAN 1 OR GREATER ',\n     $      'THAN ', I2 )\n 9996 FORMAT( ' VALUE OF N IS LESS THAN 0 OR GREATER THAN ', I2 )\n 9995 FORMAT( ' VALUE OF K IS LESS THAN 0' )\n 9994 FORMAT( ' ABSOLUTE VALUE OF INCX OR INCY IS 0 OR GREATER THAN ',\n     $      I2 )\n 9993 FORMAT( ' TESTS OF THE COMPLEX          LEVEL 2 BLAS', //' THE F',\n     $      'OLLOWING PARAMETER VALUES WILL BE USED:' )\n 9992 FORMAT( '   FOR N              ', 9I6 )\n 9991 FORMAT( '   FOR K              ', 7I6 )\n 9990 FORMAT( '   FOR INCX AND INCY  ', 7I6 )\n 9989 FORMAT( '   FOR ALPHA          ',\n     $      7( '(', F4.1, ',', F4.1, ')  ', : ) )\n 9988 FORMAT( '   FOR BETA           ',\n     $      7( '(', F4.1, ',', F4.1, ')  ', : ) )\n 9987 FORMAT( ' AMEND DATA FILE OR INCREASE ARRAY SIZES IN PROGRAM',\n     $      /' ******* TESTS ABANDONED *******' )\n 9986 FORMAT( ' SUBPROGRAM NAME ', A6, ' NOT RECOGNIZED', /' ******* T',\n     $      'ESTS ABANDONED *******' )\n 9985 FORMAT( ' ERROR IN CMVCH -  IN-LINE DOT PRODUCTS ARE BEING EVALU',\n     $      'ATED WRONGLY.', /' CMVCH WAS CALLED WITH TRANS = ', A1,\n     $      ' AND RETURNED SAME = ', L1, ' AND ERR = ', F12.3, '.', /\n     $   ' THIS MAY BE DUE TO FAULTS IN THE ARITHMETIC OR THE COMPILER.'\n     $      , /' ******* TESTS ABANDONED *******' )\n 9984 FORMAT( A6, L2 )\n 9983 FORMAT( 1X, A6, ' WAS NOT TESTED' )\n 9982 FORMAT( /' END OF TESTS' )\n 9981 FORMAT( /' ******* FATAL ERROR - TESTS ABANDONED *******' )\n 9980 FORMAT( ' ERROR-EXITS WILL NOT BE TESTED' )\n*\n*     End of CBLAT2.\n*\n      END\n      SUBROUTINE CCHK1( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF, NBET,\n     $                  BET, NINC, INC, NMAX, INCMAX, A, AA, AS, X, XX,\n     $                  XS, Y, YY, YS, YT, G )\n*\n*  Tests CGEMV and CGBMV.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Parameters ..\n      COMPLEX            ZERO, HALF\n      PARAMETER          ( ZERO = ( 0.0, 0.0 ), HALF = ( 0.5, 0.0 ) )\n      REAL               RZERO\n      PARAMETER          ( RZERO = 0.0 )\n*     .. Scalar Arguments ..\n      REAL               EPS, THRESH\n      INTEGER            INCMAX, NALF, NBET, NIDIM, NINC, NKB, NMAX,\n     $                   NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      COMPLEX            A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), BET( NBET ), X( NMAX ),\n     $                   XS( NMAX*INCMAX ), XX( NMAX*INCMAX ),\n     $                   Y( NMAX ), YS( NMAX*INCMAX ), YT( NMAX ),\n     $                   YY( NMAX*INCMAX )\n      REAL               G( NMAX )\n      INTEGER            IDIM( NIDIM ), INC( NINC ), KB( NKB )\n*     .. Local Scalars ..\n      COMPLEX            ALPHA, ALS, BETA, BLS, TRANSL\n      REAL               ERR, ERRMAX\n      INTEGER            I, IA, IB, IC, IKU, IM, IN, INCX, INCXS, INCY,\n     $                   INCYS, IX, IY, KL, KLS, KU, KUS, LAA, LDA,\n     $                   LDAS, LX, LY, M, ML, MS, N, NARGS, NC, ND, NK,\n     $                   NL, NS\n      LOGICAL            BANDED, FULL, NULL, RESET, SAME, TRAN\n      CHARACTER*1        TRANS, TRANSS\n      CHARACTER*3        ICH\n*     .. Local Arrays ..\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LCE, LCERES\n      EXTERNAL           LCE, LCERES\n*     .. External Subroutines ..\n      EXTERNAL           CGBMV, CGEMV, CMAKE, CMVCH\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, MAX, MIN\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICH/'NTC'/\n*     .. Executable Statements ..\n      FULL = SNAME( 3: 3 ).EQ.'E'\n      BANDED = SNAME( 3: 3 ).EQ.'B'\n*     Define the number of arguments.\n      IF( FULL )THEN\n         NARGS = 11\n      ELSE IF( BANDED )THEN\n         NARGS = 13\n      END IF\n*\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = RZERO\n*\n      DO 120 IN = 1, NIDIM\n         N = IDIM( IN )\n         ND = N/2 + 1\n*\n         DO 110 IM = 1, 2\n            IF( IM.EQ.1 )\n     $         M = MAX( N - ND, 0 )\n            IF( IM.EQ.2 )\n     $         M = MIN( N + ND, NMAX )\n*\n            IF( BANDED )THEN\n               NK = NKB\n            ELSE\n               NK = 1\n            END IF\n            DO 100 IKU = 1, NK\n               IF( BANDED )THEN\n                  KU = KB( IKU )\n                  KL = MAX( KU - 1, 0 )\n               ELSE\n                  KU = N - 1\n                  KL = M - 1\n               END IF\n*              Set LDA to 1 more than minimum value if room.\n               IF( BANDED )THEN\n                  LDA = KL + KU + 1\n               ELSE\n                  LDA = M\n               END IF\n               IF( LDA.LT.NMAX )\n     $            LDA = LDA + 1\n*              Skip tests if not enough room.\n               IF( LDA.GT.NMAX )\n     $            GO TO 100\n               LAA = LDA*N\n               NULL = N.LE.0.OR.M.LE.0\n*\n*              Generate the matrix A.\n*\n               TRANSL = ZERO\n               CALL CMAKE( SNAME( 2: 3 ), ' ', ' ', M, N, A, NMAX, AA,\n     $                     LDA, KL, KU, RESET, TRANSL )\n*\n               DO 90 IC = 1, 3\n                  TRANS = ICH( IC: IC )\n                  TRAN = TRANS.EQ.'T'.OR.TRANS.EQ.'C'\n*\n                  IF( TRAN )THEN\n                     ML = N\n                     NL = M\n                  ELSE\n                     ML = M\n                     NL = N\n                  END IF\n*\n                  DO 80 IX = 1, NINC\n                     INCX = INC( IX )\n                     LX = ABS( INCX )*NL\n*\n*                    Generate the vector X.\n*\n                     TRANSL = HALF\n                     CALL CMAKE( 'GE', ' ', ' ', 1, NL, X, 1, XX,\n     $                           ABS( INCX ), 0, NL - 1, RESET, TRANSL )\n                     IF( NL.GT.1 )THEN\n                        X( NL/2 ) = ZERO\n                        XX( 1 + ABS( INCX )*( NL/2 - 1 ) ) = ZERO\n                     END IF\n*\n                     DO 70 IY = 1, NINC\n                        INCY = INC( IY )\n                        LY = ABS( INCY )*ML\n*\n                        DO 60 IA = 1, NALF\n                           ALPHA = ALF( IA )\n*\n                           DO 50 IB = 1, NBET\n                              BETA = BET( IB )\n*\n*                             Generate the vector Y.\n*\n                              TRANSL = ZERO\n                              CALL CMAKE( 'GE', ' ', ' ', 1, ML, Y, 1,\n     $                                    YY, ABS( INCY ), 0, ML - 1,\n     $                                    RESET, TRANSL )\n*\n                              NC = NC + 1\n*\n*                             Save every datum before calling the\n*                             subroutine.\n*\n                              TRANSS = TRANS\n                              MS = M\n                              NS = N\n                              KLS = KL\n                              KUS = KU\n                              ALS = ALPHA\n                              DO 10 I = 1, LAA\n                                 AS( I ) = AA( I )\n   10                         CONTINUE\n                              LDAS = LDA\n                              DO 20 I = 1, LX\n                                 XS( I ) = XX( I )\n   20                         CONTINUE\n                              INCXS = INCX\n                              BLS = BETA\n                              DO 30 I = 1, LY\n                                 YS( I ) = YY( I )\n   30                         CONTINUE\n                              INCYS = INCY\n*\n*                             Call the subroutine.\n*\n                              IF( FULL )THEN\n                                 IF( TRACE )\n     $                              WRITE( NTRA, FMT = 9994 )NC, SNAME,\n     $                              TRANS, M, N, ALPHA, LDA, INCX, BETA,\n     $                              INCY\n                                 IF( REWI )\n     $                              REWIND NTRA\n                                 CALL CGEMV( TRANS, M, N, ALPHA, AA,\n     $                                       LDA, XX, INCX, BETA, YY,\n     $                                       INCY )\n                              ELSE IF( BANDED )THEN\n                                 IF( TRACE )\n     $                              WRITE( NTRA, FMT = 9995 )NC, SNAME,\n     $                              TRANS, M, N, KL, KU, ALPHA, LDA,\n     $                              INCX, BETA, INCY\n                                 IF( REWI )\n     $                              REWIND NTRA\n                                 CALL CGBMV( TRANS, M, N, KL, KU, ALPHA,\n     $                                       AA, LDA, XX, INCX, BETA,\n     $                                       YY, INCY )\n                              END IF\n*\n*                             Check if error-exit was taken incorrectly.\n*\n                              IF( .NOT.OK )THEN\n                                 WRITE( NOUT, FMT = 9993 )\n                                 FATAL = .TRUE.\n                                 GO TO 130\n                              END IF\n*\n*                             See what data changed inside subroutines.\n*\n                              ISAME( 1 ) = TRANS.EQ.TRANSS\n                              ISAME( 2 ) = MS.EQ.M\n                              ISAME( 3 ) = NS.EQ.N\n                              IF( FULL )THEN\n                                 ISAME( 4 ) = ALS.EQ.ALPHA\n                                 ISAME( 5 ) = LCE( AS, AA, LAA )\n                                 ISAME( 6 ) = LDAS.EQ.LDA\n                                 ISAME( 7 ) = LCE( XS, XX, LX )\n                                 ISAME( 8 ) = INCXS.EQ.INCX\n                                 ISAME( 9 ) = BLS.EQ.BETA\n                                 IF( NULL )THEN\n                                    ISAME( 10 ) = LCE( YS, YY, LY )\n                                 ELSE\n                                    ISAME( 10 ) = LCERES( 'GE', ' ', 1,\n     $                                            ML, YS, YY,\n     $                                            ABS( INCY ) )\n                                 END IF\n                                 ISAME( 11 ) = INCYS.EQ.INCY\n                              ELSE IF( BANDED )THEN\n                                 ISAME( 4 ) = KLS.EQ.KL\n                                 ISAME( 5 ) = KUS.EQ.KU\n                                 ISAME( 6 ) = ALS.EQ.ALPHA\n                                 ISAME( 7 ) = LCE( AS, AA, LAA )\n                                 ISAME( 8 ) = LDAS.EQ.LDA\n                                 ISAME( 9 ) = LCE( XS, XX, LX )\n                                 ISAME( 10 ) = INCXS.EQ.INCX\n                                 ISAME( 11 ) = BLS.EQ.BETA\n                                 IF( NULL )THEN\n                                    ISAME( 12 ) = LCE( YS, YY, LY )\n                                 ELSE\n                                    ISAME( 12 ) = LCERES( 'GE', ' ', 1,\n     $                                            ML, YS, YY,\n     $                                            ABS( INCY ) )\n                                 END IF\n                                 ISAME( 13 ) = INCYS.EQ.INCY\n                              END IF\n*\n*                             If data was incorrectly changed, report\n*                             and return.\n*\n                              SAME = .TRUE.\n                              DO 40 I = 1, NARGS\n                                 SAME = SAME.AND.ISAME( I )\n                                 IF( .NOT.ISAME( I ) )\n     $                              WRITE( NOUT, FMT = 9998 )I\n   40                         CONTINUE\n                              IF( .NOT.SAME )THEN\n                                 FATAL = .TRUE.\n                                 GO TO 130\n                              END IF\n*\n                              IF( .NOT.NULL )THEN\n*\n*                                Check the result.\n*\n                                 CALL CMVCH( TRANS, M, N, ALPHA, A,\n     $                                       NMAX, X, INCX, BETA, Y,\n     $                                       INCY, YT, G, YY, EPS, ERR,\n     $                                       FATAL, NOUT, .TRUE. )\n                                 ERRMAX = MAX( ERRMAX, ERR )\n*                                If got really bad answer, report and\n*                                return.\n                                 IF( FATAL )\n     $                              GO TO 130\n                              ELSE\n*                                Avoid repeating tests with M.le.0 or\n*                                N.le.0.\n                                 GO TO 110\n                              END IF\n*\n   50                      CONTINUE\n*\n   60                   CONTINUE\n*\n   70                CONTINUE\n*\n   80             CONTINUE\n*\n   90          CONTINUE\n*\n  100       CONTINUE\n*\n  110    CONTINUE\n*\n  120 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 140\n*\n  130 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      IF( FULL )THEN\n         WRITE( NOUT, FMT = 9994 )NC, SNAME, TRANS, M, N, ALPHA, LDA,\n     $      INCX, BETA, INCY\n      ELSE IF( BANDED )THEN\n         WRITE( NOUT, FMT = 9995 )NC, SNAME, TRANS, M, N, KL, KU,\n     $      ALPHA, LDA, INCX, BETA, INCY\n      END IF\n*\n  140 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 4( I3, ',' ), '(',\n     $      F4.1, ',', F4.1, '), A,', I3, ', X,', I2, ',(', F4.1, ',',\n     $      F4.1, '), Y,', I2, ') .' )\n 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 2( I3, ',' ), '(',\n     $      F4.1, ',', F4.1, '), A,', I3, ', X,', I2, ',(', F4.1, ',',\n     $      F4.1, '), Y,', I2, ')         .' )\n 9993 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of CCHK1.\n*\n      END\n      SUBROUTINE CCHK2( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF, NBET,\n     $                  BET, NINC, INC, NMAX, INCMAX, A, AA, AS, X, XX,\n     $                  XS, Y, YY, YS, YT, G )\n*\n*  Tests CHEMV, CHBMV and CHPMV.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Parameters ..\n      COMPLEX            ZERO, HALF\n      PARAMETER          ( ZERO = ( 0.0, 0.0 ), HALF = ( 0.5, 0.0 ) )\n      REAL               RZERO\n      PARAMETER          ( RZERO = 0.0 )\n*     .. Scalar Arguments ..\n      REAL               EPS, THRESH\n      INTEGER            INCMAX, NALF, NBET, NIDIM, NINC, NKB, NMAX,\n     $                   NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      COMPLEX            A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), BET( NBET ), X( NMAX ),\n     $                   XS( NMAX*INCMAX ), XX( NMAX*INCMAX ),\n     $                   Y( NMAX ), YS( NMAX*INCMAX ), YT( NMAX ),\n     $                   YY( NMAX*INCMAX )\n      REAL               G( NMAX )\n      INTEGER            IDIM( NIDIM ), INC( NINC ), KB( NKB )\n*     .. Local Scalars ..\n      COMPLEX            ALPHA, ALS, BETA, BLS, TRANSL\n      REAL               ERR, ERRMAX\n      INTEGER            I, IA, IB, IC, IK, IN, INCX, INCXS, INCY,\n     $                   INCYS, IX, IY, K, KS, LAA, LDA, LDAS, LX, LY,\n     $                   N, NARGS, NC, NK, NS\n      LOGICAL            BANDED, FULL, NULL, PACKED, RESET, SAME\n      CHARACTER*1        UPLO, UPLOS\n      CHARACTER*2        ICH\n*     .. Local Arrays ..\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LCE, LCERES\n      EXTERNAL           LCE, LCERES\n*     .. External Subroutines ..\n      EXTERNAL           CHBMV, CHEMV, CHPMV, CMAKE, CMVCH\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, MAX\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICH/'UL'/\n*     .. Executable Statements ..\n      FULL = SNAME( 3: 3 ).EQ.'E'\n      BANDED = SNAME( 3: 3 ).EQ.'B'\n      PACKED = SNAME( 3: 3 ).EQ.'P'\n*     Define the number of arguments.\n      IF( FULL )THEN\n         NARGS = 10\n      ELSE IF( BANDED )THEN\n         NARGS = 11\n      ELSE IF( PACKED )THEN\n         NARGS = 9\n      END IF\n*\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = RZERO\n*\n      DO 110 IN = 1, NIDIM\n         N = IDIM( IN )\n*\n         IF( BANDED )THEN\n            NK = NKB\n         ELSE\n            NK = 1\n         END IF\n         DO 100 IK = 1, NK\n            IF( BANDED )THEN\n               K = KB( IK )\n            ELSE\n               K = N - 1\n            END IF\n*           Set LDA to 1 more than minimum value if room.\n            IF( BANDED )THEN\n               LDA = K + 1\n            ELSE\n               LDA = N\n            END IF\n            IF( LDA.LT.NMAX )\n     $         LDA = LDA + 1\n*           Skip tests if not enough room.\n            IF( LDA.GT.NMAX )\n     $         GO TO 100\n            IF( PACKED )THEN\n               LAA = ( N*( N + 1 ) )/2\n            ELSE\n               LAA = LDA*N\n            END IF\n            NULL = N.LE.0\n*\n            DO 90 IC = 1, 2\n               UPLO = ICH( IC: IC )\n*\n*              Generate the matrix A.\n*\n               TRANSL = ZERO\n               CALL CMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A, NMAX, AA,\n     $                     LDA, K, K, RESET, TRANSL )\n*\n               DO 80 IX = 1, NINC\n                  INCX = INC( IX )\n                  LX = ABS( INCX )*N\n*\n*                 Generate the vector X.\n*\n                  TRANSL = HALF\n                  CALL CMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX,\n     $                        ABS( INCX ), 0, N - 1, RESET, TRANSL )\n                  IF( N.GT.1 )THEN\n                     X( N/2 ) = ZERO\n                     XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO\n                  END IF\n*\n                  DO 70 IY = 1, NINC\n                     INCY = INC( IY )\n                     LY = ABS( INCY )*N\n*\n                     DO 60 IA = 1, NALF\n                        ALPHA = ALF( IA )\n*\n                        DO 50 IB = 1, NBET\n                           BETA = BET( IB )\n*\n*                          Generate the vector Y.\n*\n                           TRANSL = ZERO\n                           CALL CMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY,\n     $                                 ABS( INCY ), 0, N - 1, RESET,\n     $                                 TRANSL )\n*\n                           NC = NC + 1\n*\n*                          Save every datum before calling the\n*                          subroutine.\n*\n                           UPLOS = UPLO\n                           NS = N\n                           KS = K\n                           ALS = ALPHA\n                           DO 10 I = 1, LAA\n                              AS( I ) = AA( I )\n   10                      CONTINUE\n                           LDAS = LDA\n                           DO 20 I = 1, LX\n                              XS( I ) = XX( I )\n   20                      CONTINUE\n                           INCXS = INCX\n                           BLS = BETA\n                           DO 30 I = 1, LY\n                              YS( I ) = YY( I )\n   30                      CONTINUE\n                           INCYS = INCY\n*\n*                          Call the subroutine.\n*\n                           IF( FULL )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9993 )NC, SNAME,\n     $                           UPLO, N, ALPHA, LDA, INCX, BETA, INCY\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL CHEMV( UPLO, N, ALPHA, AA, LDA, XX,\n     $                                    INCX, BETA, YY, INCY )\n                           ELSE IF( BANDED )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9994 )NC, SNAME,\n     $                           UPLO, N, K, ALPHA, LDA, INCX, BETA,\n     $                           INCY\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL CHBMV( UPLO, N, K, ALPHA, AA, LDA,\n     $                                    XX, INCX, BETA, YY, INCY )\n                           ELSE IF( PACKED )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9995 )NC, SNAME,\n     $                           UPLO, N, ALPHA, INCX, BETA, INCY\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL CHPMV( UPLO, N, ALPHA, AA, XX, INCX,\n     $                                    BETA, YY, INCY )\n                           END IF\n*\n*                          Check if error-exit was taken incorrectly.\n*\n                           IF( .NOT.OK )THEN\n                              WRITE( NOUT, FMT = 9992 )\n                              FATAL = .TRUE.\n                              GO TO 120\n                           END IF\n*\n*                          See what data changed inside subroutines.\n*\n                           ISAME( 1 ) = UPLO.EQ.UPLOS\n                           ISAME( 2 ) = NS.EQ.N\n                           IF( FULL )THEN\n                              ISAME( 3 ) = ALS.EQ.ALPHA\n                              ISAME( 4 ) = LCE( AS, AA, LAA )\n                              ISAME( 5 ) = LDAS.EQ.LDA\n                              ISAME( 6 ) = LCE( XS, XX, LX )\n                              ISAME( 7 ) = INCXS.EQ.INCX\n                              ISAME( 8 ) = BLS.EQ.BETA\n                              IF( NULL )THEN\n                                 ISAME( 9 ) = LCE( YS, YY, LY )\n                              ELSE\n                                 ISAME( 9 ) = LCERES( 'GE', ' ', 1, N,\n     $                                        YS, YY, ABS( INCY ) )\n                              END IF\n                              ISAME( 10 ) = INCYS.EQ.INCY\n                           ELSE IF( BANDED )THEN\n                              ISAME( 3 ) = KS.EQ.K\n                              ISAME( 4 ) = ALS.EQ.ALPHA\n                              ISAME( 5 ) = LCE( AS, AA, LAA )\n                              ISAME( 6 ) = LDAS.EQ.LDA\n                              ISAME( 7 ) = LCE( XS, XX, LX )\n                              ISAME( 8 ) = INCXS.EQ.INCX\n                              ISAME( 9 ) = BLS.EQ.BETA\n                              IF( NULL )THEN\n                                 ISAME( 10 ) = LCE( YS, YY, LY )\n                              ELSE\n                                 ISAME( 10 ) = LCERES( 'GE', ' ', 1, N,\n     $                                         YS, YY, ABS( INCY ) )\n                              END IF\n                              ISAME( 11 ) = INCYS.EQ.INCY\n                           ELSE IF( PACKED )THEN\n                              ISAME( 3 ) = ALS.EQ.ALPHA\n                              ISAME( 4 ) = LCE( AS, AA, LAA )\n                              ISAME( 5 ) = LCE( XS, XX, LX )\n                              ISAME( 6 ) = INCXS.EQ.INCX\n                              ISAME( 7 ) = BLS.EQ.BETA\n                              IF( NULL )THEN\n                                 ISAME( 8 ) = LCE( YS, YY, LY )\n                              ELSE\n                                 ISAME( 8 ) = LCERES( 'GE', ' ', 1, N,\n     $                                        YS, YY, ABS( INCY ) )\n                              END IF\n                              ISAME( 9 ) = INCYS.EQ.INCY\n                           END IF\n*\n*                          If data was incorrectly changed, report and\n*                          return.\n*\n                           SAME = .TRUE.\n                           DO 40 I = 1, NARGS\n                              SAME = SAME.AND.ISAME( I )\n                              IF( .NOT.ISAME( I ) )\n     $                           WRITE( NOUT, FMT = 9998 )I\n   40                      CONTINUE\n                           IF( .NOT.SAME )THEN\n                              FATAL = .TRUE.\n                              GO TO 120\n                           END IF\n*\n                           IF( .NOT.NULL )THEN\n*\n*                             Check the result.\n*\n                              CALL CMVCH( 'N', N, N, ALPHA, A, NMAX, X,\n     $                                    INCX, BETA, Y, INCY, YT, G,\n     $                                    YY, EPS, ERR, FATAL, NOUT,\n     $                                    .TRUE. )\n                              ERRMAX = MAX( ERRMAX, ERR )\n*                             If got really bad answer, report and\n*                             return.\n                              IF( FATAL )\n     $                           GO TO 120\n                           ELSE\n*                             Avoid repeating tests with N.le.0\n                              GO TO 110\n                           END IF\n*\n   50                   CONTINUE\n*\n   60                CONTINUE\n*\n   70             CONTINUE\n*\n   80          CONTINUE\n*\n   90       CONTINUE\n*\n  100    CONTINUE\n*\n  110 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 130\n*\n  120 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      IF( FULL )THEN\n         WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, ALPHA, LDA, INCX,\n     $      BETA, INCY\n      ELSE IF( BANDED )THEN\n         WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, K, ALPHA, LDA,\n     $      INCX, BETA, INCY\n      ELSE IF( PACKED )THEN\n         WRITE( NOUT, FMT = 9995 )NC, SNAME, UPLO, N, ALPHA, INCX,\n     $      BETA, INCY\n      END IF\n*\n  130 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',(', F4.1, ',',\n     $      F4.1, '), AP, X,', I2, ',(', F4.1, ',', F4.1, '), Y,', I2,\n     $      ')                .' )\n 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 2( I3, ',' ), '(',\n     $      F4.1, ',', F4.1, '), A,', I3, ', X,', I2, ',(', F4.1, ',',\n     $      F4.1, '), Y,', I2, ')         .' )\n 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',(', F4.1, ',',\n     $      F4.1, '), A,', I3, ', X,', I2, ',(', F4.1, ',', F4.1, '), ',\n     $      'Y,', I2, ')             .' )\n 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of CCHK2.\n*\n      END\n      SUBROUTINE CCHK3( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NKB, KB, NINC, INC, NMAX,\n     $                  INCMAX, A, AA, AS, X, XX, XS, XT, G, Z )\n*\n*  Tests CTRMV, CTBMV, CTPMV, CTRSV, CTBSV and CTPSV.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Parameters ..\n      COMPLEX            ZERO, HALF, ONE\n      PARAMETER          ( ZERO = ( 0.0, 0.0 ), HALF = ( 0.5, 0.0 ),\n     $                   ONE = ( 1.0, 0.0 ) )\n      REAL               RZERO\n      PARAMETER          ( RZERO = 0.0 )\n*     .. Scalar Arguments ..\n      REAL               EPS, THRESH\n      INTEGER            INCMAX, NIDIM, NINC, NKB, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      COMPLEX            A( NMAX, NMAX ), AA( NMAX*NMAX ),\n     $                   AS( NMAX*NMAX ), X( NMAX ), XS( NMAX*INCMAX ),\n     $                   XT( NMAX ), XX( NMAX*INCMAX ), Z( NMAX )\n      REAL               G( NMAX )\n      INTEGER            IDIM( NIDIM ), INC( NINC ), KB( NKB )\n*     .. Local Scalars ..\n      COMPLEX            TRANSL\n      REAL               ERR, ERRMAX\n      INTEGER            I, ICD, ICT, ICU, IK, IN, INCX, INCXS, IX, K,\n     $                   KS, LAA, LDA, LDAS, LX, N, NARGS, NC, NK, NS\n      LOGICAL            BANDED, FULL, NULL, PACKED, RESET, SAME\n      CHARACTER*1        DIAG, DIAGS, TRANS, TRANSS, UPLO, UPLOS\n      CHARACTER*2        ICHD, ICHU\n      CHARACTER*3        ICHT\n*     .. Local Arrays ..\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LCE, LCERES\n      EXTERNAL           LCE, LCERES\n*     .. External Subroutines ..\n      EXTERNAL           CMAKE, CMVCH, CTBMV, CTBSV, CTPMV, CTPSV,\n     $                   CTRMV, CTRSV\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, MAX\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICHU/'UL'/, ICHT/'NTC'/, ICHD/'UN'/\n*     .. Executable Statements ..\n      FULL = SNAME( 3: 3 ).EQ.'R'\n      BANDED = SNAME( 3: 3 ).EQ.'B'\n      PACKED = SNAME( 3: 3 ).EQ.'P'\n*     Define the number of arguments.\n      IF( FULL )THEN\n         NARGS = 8\n      ELSE IF( BANDED )THEN\n         NARGS = 9\n      ELSE IF( PACKED )THEN\n         NARGS = 7\n      END IF\n*\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = RZERO\n*     Set up zero vector for CMVCH.\n      DO 10 I = 1, NMAX\n         Z( I ) = ZERO\n   10 CONTINUE\n*\n      DO 110 IN = 1, NIDIM\n         N = IDIM( IN )\n*\n         IF( BANDED )THEN\n            NK = NKB\n         ELSE\n            NK = 1\n         END IF\n         DO 100 IK = 1, NK\n            IF( BANDED )THEN\n               K = KB( IK )\n            ELSE\n               K = N - 1\n            END IF\n*           Set LDA to 1 more than minimum value if room.\n            IF( BANDED )THEN\n               LDA = K + 1\n            ELSE\n               LDA = N\n            END IF\n            IF( LDA.LT.NMAX )\n     $         LDA = LDA + 1\n*           Skip tests if not enough room.\n            IF( LDA.GT.NMAX )\n     $         GO TO 100\n            IF( PACKED )THEN\n               LAA = ( N*( N + 1 ) )/2\n            ELSE\n               LAA = LDA*N\n            END IF\n            NULL = N.LE.0\n*\n            DO 90 ICU = 1, 2\n               UPLO = ICHU( ICU: ICU )\n*\n               DO 80 ICT = 1, 3\n                  TRANS = ICHT( ICT: ICT )\n*\n                  DO 70 ICD = 1, 2\n                     DIAG = ICHD( ICD: ICD )\n*\n*                    Generate the matrix A.\n*\n                     TRANSL = ZERO\n                     CALL CMAKE( SNAME( 2: 3 ), UPLO, DIAG, N, N, A,\n     $                           NMAX, AA, LDA, K, K, RESET, TRANSL )\n*\n                     DO 60 IX = 1, NINC\n                        INCX = INC( IX )\n                        LX = ABS( INCX )*N\n*\n*                       Generate the vector X.\n*\n                        TRANSL = HALF\n                        CALL CMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX,\n     $                              ABS( INCX ), 0, N - 1, RESET,\n     $                              TRANSL )\n                        IF( N.GT.1 )THEN\n                           X( N/2 ) = ZERO\n                           XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO\n                        END IF\n*\n                        NC = NC + 1\n*\n*                       Save every datum before calling the subroutine.\n*\n                        UPLOS = UPLO\n                        TRANSS = TRANS\n                        DIAGS = DIAG\n                        NS = N\n                        KS = K\n                        DO 20 I = 1, LAA\n                           AS( I ) = AA( I )\n   20                   CONTINUE\n                        LDAS = LDA\n                        DO 30 I = 1, LX\n                           XS( I ) = XX( I )\n   30                   CONTINUE\n                        INCXS = INCX\n*\n*                       Call the subroutine.\n*\n                        IF( SNAME( 4: 5 ).EQ.'MV' )THEN\n                           IF( FULL )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9993 )NC, SNAME,\n     $                           UPLO, TRANS, DIAG, N, LDA, INCX\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL CTRMV( UPLO, TRANS, DIAG, N, AA, LDA,\n     $                                    XX, INCX )\n                           ELSE IF( BANDED )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9994 )NC, SNAME,\n     $                           UPLO, TRANS, DIAG, N, K, LDA, INCX\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL CTBMV( UPLO, TRANS, DIAG, N, K, AA,\n     $                                    LDA, XX, INCX )\n                           ELSE IF( PACKED )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9995 )NC, SNAME,\n     $                           UPLO, TRANS, DIAG, N, INCX\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL CTPMV( UPLO, TRANS, DIAG, N, AA, XX,\n     $                                    INCX )\n                           END IF\n                        ELSE IF( SNAME( 4: 5 ).EQ.'SV' )THEN\n                           IF( FULL )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9993 )NC, SNAME,\n     $                           UPLO, TRANS, DIAG, N, LDA, INCX\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL CTRSV( UPLO, TRANS, DIAG, N, AA, LDA,\n     $                                    XX, INCX )\n                           ELSE IF( BANDED )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9994 )NC, SNAME,\n     $                           UPLO, TRANS, DIAG, N, K, LDA, INCX\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL CTBSV( UPLO, TRANS, DIAG, N, K, AA,\n     $                                    LDA, XX, INCX )\n                           ELSE IF( PACKED )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9995 )NC, SNAME,\n     $                           UPLO, TRANS, DIAG, N, INCX\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL CTPSV( UPLO, TRANS, DIAG, N, AA, XX,\n     $                                    INCX )\n                           END IF\n                        END IF\n*\n*                       Check if error-exit was taken incorrectly.\n*\n                        IF( .NOT.OK )THEN\n                           WRITE( NOUT, FMT = 9992 )\n                           FATAL = .TRUE.\n                           GO TO 120\n                        END IF\n*\n*                       See what data changed inside subroutines.\n*\n                        ISAME( 1 ) = UPLO.EQ.UPLOS\n                        ISAME( 2 ) = TRANS.EQ.TRANSS\n                        ISAME( 3 ) = DIAG.EQ.DIAGS\n                        ISAME( 4 ) = NS.EQ.N\n                        IF( FULL )THEN\n                           ISAME( 5 ) = LCE( AS, AA, LAA )\n                           ISAME( 6 ) = LDAS.EQ.LDA\n                           IF( NULL )THEN\n                              ISAME( 7 ) = LCE( XS, XX, LX )\n                           ELSE\n                              ISAME( 7 ) = LCERES( 'GE', ' ', 1, N, XS,\n     $                                     XX, ABS( INCX ) )\n                           END IF\n                           ISAME( 8 ) = INCXS.EQ.INCX\n                        ELSE IF( BANDED )THEN\n                           ISAME( 5 ) = KS.EQ.K\n                           ISAME( 6 ) = LCE( AS, AA, LAA )\n                           ISAME( 7 ) = LDAS.EQ.LDA\n                           IF( NULL )THEN\n                              ISAME( 8 ) = LCE( XS, XX, LX )\n                           ELSE\n                              ISAME( 8 ) = LCERES( 'GE', ' ', 1, N, XS,\n     $                                     XX, ABS( INCX ) )\n                           END IF\n                           ISAME( 9 ) = INCXS.EQ.INCX\n                        ELSE IF( PACKED )THEN\n                           ISAME( 5 ) = LCE( AS, AA, LAA )\n                           IF( NULL )THEN\n                              ISAME( 6 ) = LCE( XS, XX, LX )\n                           ELSE\n                              ISAME( 6 ) = LCERES( 'GE', ' ', 1, N, XS,\n     $                                     XX, ABS( INCX ) )\n                           END IF\n                           ISAME( 7 ) = INCXS.EQ.INCX\n                        END IF\n*\n*                       If data was incorrectly changed, report and\n*                       return.\n*\n                        SAME = .TRUE.\n                        DO 40 I = 1, NARGS\n                           SAME = SAME.AND.ISAME( I )\n                           IF( .NOT.ISAME( I ) )\n     $                        WRITE( NOUT, FMT = 9998 )I\n   40                   CONTINUE\n                        IF( .NOT.SAME )THEN\n                           FATAL = .TRUE.\n                           GO TO 120\n                        END IF\n*\n                        IF( .NOT.NULL )THEN\n                           IF( SNAME( 4: 5 ).EQ.'MV' )THEN\n*\n*                             Check the result.\n*\n                              CALL CMVCH( TRANS, N, N, ONE, A, NMAX, X,\n     $                                    INCX, ZERO, Z, INCX, XT, G,\n     $                                    XX, EPS, ERR, FATAL, NOUT,\n     $                                    .TRUE. )\n                           ELSE IF( SNAME( 4: 5 ).EQ.'SV' )THEN\n*\n*                             Compute approximation to original vector.\n*\n                              DO 50 I = 1, N\n                                 Z( I ) = XX( 1 + ( I - 1 )*\n     $                                    ABS( INCX ) )\n                                 XX( 1 + ( I - 1 )*ABS( INCX ) )\n     $                              = X( I )\n   50                         CONTINUE\n                              CALL CMVCH( TRANS, N, N, ONE, A, NMAX, Z,\n     $                                    INCX, ZERO, X, INCX, XT, G,\n     $                                    XX, EPS, ERR, FATAL, NOUT,\n     $                                    .FALSE. )\n                           END IF\n                           ERRMAX = MAX( ERRMAX, ERR )\n*                          If got really bad answer, report and return.\n                           IF( FATAL )\n     $                        GO TO 120\n                        ELSE\n*                          Avoid repeating tests with N.le.0.\n                           GO TO 110\n                        END IF\n*\n   60                CONTINUE\n*\n   70             CONTINUE\n*\n   80          CONTINUE\n*\n   90       CONTINUE\n*\n  100    CONTINUE\n*\n  110 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 130\n*\n  120 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      IF( FULL )THEN\n         WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, TRANS, DIAG, N, LDA,\n     $      INCX\n      ELSE IF( BANDED )THEN\n         WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, TRANS, DIAG, N, K,\n     $      LDA, INCX\n      ELSE IF( PACKED )THEN\n         WRITE( NOUT, FMT = 9995 )NC, SNAME, UPLO, TRANS, DIAG, N, INCX\n      END IF\n*\n  130 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), I3, ', AP, ',\n     $      'X,', I2, ')                                      .' )\n 9994 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), 2( I3, ',' ),\n     $      ' A,', I3, ', X,', I2, ')                               .' )\n 9993 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), I3, ', A,',\n     $      I3, ', X,', I2, ')                                   .' )\n 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of CCHK3.\n*\n      END\n      SUBROUTINE CCHK4( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX,\n     $                  INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G,\n     $                  Z )\n*\n*  Tests CGERC and CGERU.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Parameters ..\n      COMPLEX            ZERO, HALF, ONE\n      PARAMETER          ( ZERO = ( 0.0, 0.0 ), HALF = ( 0.5, 0.0 ),\n     $                   ONE = ( 1.0, 0.0 ) )\n      REAL               RZERO\n      PARAMETER          ( RZERO = 0.0 )\n*     .. Scalar Arguments ..\n      REAL               EPS, THRESH\n      INTEGER            INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      COMPLEX            A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), X( NMAX ), XS( NMAX*INCMAX ),\n     $                   XX( NMAX*INCMAX ), Y( NMAX ),\n     $                   YS( NMAX*INCMAX ), YT( NMAX ),\n     $                   YY( NMAX*INCMAX ), Z( NMAX )\n      REAL               G( NMAX )\n      INTEGER            IDIM( NIDIM ), INC( NINC )\n*     .. Local Scalars ..\n      COMPLEX            ALPHA, ALS, TRANSL\n      REAL               ERR, ERRMAX\n      INTEGER            I, IA, IM, IN, INCX, INCXS, INCY, INCYS, IX,\n     $                   IY, J, LAA, LDA, LDAS, LX, LY, M, MS, N, NARGS,\n     $                   NC, ND, NS\n      LOGICAL            CONJ, NULL, RESET, SAME\n*     .. Local Arrays ..\n      COMPLEX            W( 1 )\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LCE, LCERES\n      EXTERNAL           LCE, LCERES\n*     .. External Subroutines ..\n      EXTERNAL           CGERC, CGERU, CMAKE, CMVCH\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, CONJG, MAX, MIN\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Executable Statements ..\n      CONJ = SNAME( 5: 5 ).EQ.'C'\n*     Define the number of arguments.\n      NARGS = 9\n*\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = RZERO\n*\n      DO 120 IN = 1, NIDIM\n         N = IDIM( IN )\n         ND = N/2 + 1\n*\n         DO 110 IM = 1, 2\n            IF( IM.EQ.1 )\n     $         M = MAX( N - ND, 0 )\n            IF( IM.EQ.2 )\n     $         M = MIN( N + ND, NMAX )\n*\n*           Set LDA to 1 more than minimum value if room.\n            LDA = M\n            IF( LDA.LT.NMAX )\n     $         LDA = LDA + 1\n*           Skip tests if not enough room.\n            IF( LDA.GT.NMAX )\n     $         GO TO 110\n            LAA = LDA*N\n            NULL = N.LE.0.OR.M.LE.0\n*\n            DO 100 IX = 1, NINC\n               INCX = INC( IX )\n               LX = ABS( INCX )*M\n*\n*              Generate the vector X.\n*\n               TRANSL = HALF\n               CALL CMAKE( 'GE', ' ', ' ', 1, M, X, 1, XX, ABS( INCX ),\n     $                     0, M - 1, RESET, TRANSL )\n               IF( M.GT.1 )THEN\n                  X( M/2 ) = ZERO\n                  XX( 1 + ABS( INCX )*( M/2 - 1 ) ) = ZERO\n               END IF\n*\n               DO 90 IY = 1, NINC\n                  INCY = INC( IY )\n                  LY = ABS( INCY )*N\n*\n*                 Generate the vector Y.\n*\n                  TRANSL = ZERO\n                  CALL CMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY,\n     $                        ABS( INCY ), 0, N - 1, RESET, TRANSL )\n                  IF( N.GT.1 )THEN\n                     Y( N/2 ) = ZERO\n                     YY( 1 + ABS( INCY )*( N/2 - 1 ) ) = ZERO\n                  END IF\n*\n                  DO 80 IA = 1, NALF\n                     ALPHA = ALF( IA )\n*\n*                    Generate the matrix A.\n*\n                     TRANSL = ZERO\n                     CALL CMAKE( SNAME( 2: 3 ), ' ', ' ', M, N, A, NMAX,\n     $                           AA, LDA, M - 1, N - 1, RESET, TRANSL )\n*\n                     NC = NC + 1\n*\n*                    Save every datum before calling the subroutine.\n*\n                     MS = M\n                     NS = N\n                     ALS = ALPHA\n                     DO 10 I = 1, LAA\n                        AS( I ) = AA( I )\n   10                CONTINUE\n                     LDAS = LDA\n                     DO 20 I = 1, LX\n                        XS( I ) = XX( I )\n   20                CONTINUE\n                     INCXS = INCX\n                     DO 30 I = 1, LY\n                        YS( I ) = YY( I )\n   30                CONTINUE\n                     INCYS = INCY\n*\n*                    Call the subroutine.\n*\n                     IF( TRACE )\n     $                  WRITE( NTRA, FMT = 9994 )NC, SNAME, M, N,\n     $                  ALPHA, INCX, INCY, LDA\n                     IF( CONJ )THEN\n                        IF( REWI )\n     $                     REWIND NTRA\n                        CALL CGERC( M, N, ALPHA, XX, INCX, YY, INCY, AA,\n     $                              LDA )\n                     ELSE\n                        IF( REWI )\n     $                     REWIND NTRA\n                        CALL CGERU( M, N, ALPHA, XX, INCX, YY, INCY, AA,\n     $                              LDA )\n                     END IF\n*\n*                    Check if error-exit was taken incorrectly.\n*\n                     IF( .NOT.OK )THEN\n                        WRITE( NOUT, FMT = 9993 )\n                        FATAL = .TRUE.\n                        GO TO 140\n                     END IF\n*\n*                    See what data changed inside subroutine.\n*\n                     ISAME( 1 ) = MS.EQ.M\n                     ISAME( 2 ) = NS.EQ.N\n                     ISAME( 3 ) = ALS.EQ.ALPHA\n                     ISAME( 4 ) = LCE( XS, XX, LX )\n                     ISAME( 5 ) = INCXS.EQ.INCX\n                     ISAME( 6 ) = LCE( YS, YY, LY )\n                     ISAME( 7 ) = INCYS.EQ.INCY\n                     IF( NULL )THEN\n                        ISAME( 8 ) = LCE( AS, AA, LAA )\n                     ELSE\n                        ISAME( 8 ) = LCERES( 'GE', ' ', M, N, AS, AA,\n     $                               LDA )\n                     END IF\n                     ISAME( 9 ) = LDAS.EQ.LDA\n*\n*                    If data was incorrectly changed, report and return.\n*\n                     SAME = .TRUE.\n                     DO 40 I = 1, NARGS\n                        SAME = SAME.AND.ISAME( I )\n                        IF( .NOT.ISAME( I ) )\n     $                     WRITE( NOUT, FMT = 9998 )I\n   40                CONTINUE\n                     IF( .NOT.SAME )THEN\n                        FATAL = .TRUE.\n                        GO TO 140\n                     END IF\n*\n                     IF( .NOT.NULL )THEN\n*\n*                       Check the result column by column.\n*\n                        IF( INCX.GT.0 )THEN\n                           DO 50 I = 1, M\n                              Z( I ) = X( I )\n   50                      CONTINUE\n                        ELSE\n                           DO 60 I = 1, M\n                              Z( I ) = X( M - I + 1 )\n   60                      CONTINUE\n                        END IF\n                        DO 70 J = 1, N\n                           IF( INCY.GT.0 )THEN\n                              W( 1 ) = Y( J )\n                           ELSE\n                              W( 1 ) = Y( N - J + 1 )\n                           END IF\n                           IF( CONJ )\n     $                        W( 1 ) = CONJG( W( 1 ) )\n                           CALL CMVCH( 'N', M, 1, ALPHA, Z, NMAX, W, 1,\n     $                                 ONE, A( 1, J ), 1, YT, G,\n     $                                 AA( 1 + ( J - 1 )*LDA ), EPS,\n     $                                 ERR, FATAL, NOUT, .TRUE. )\n                           ERRMAX = MAX( ERRMAX, ERR )\n*                          If got really bad answer, report and return.\n                           IF( FATAL )\n     $                        GO TO 130\n   70                   CONTINUE\n                     ELSE\n*                       Avoid repeating tests with M.le.0 or N.le.0.\n                        GO TO 110\n                     END IF\n*\n   80             CONTINUE\n*\n   90          CONTINUE\n*\n  100       CONTINUE\n*\n  110    CONTINUE\n*\n  120 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 150\n*\n  130 CONTINUE\n      WRITE( NOUT, FMT = 9995 )J\n*\n  140 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      WRITE( NOUT, FMT = 9994 )NC, SNAME, M, N, ALPHA, INCX, INCY, LDA\n*\n  150 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( '      THESE ARE THE RESULTS FOR COLUMN ', I3 )\n 9994 FORMAT( 1X, I6, ': ', A6, '(', 2( I3, ',' ), '(', F4.1, ',', F4.1,\n     $      '), X,', I2, ', Y,', I2, ', A,', I3, ')                   ',\n     $      '      .' )\n 9993 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of CCHK4.\n*\n      END\n      SUBROUTINE CCHK5( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX,\n     $                  INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G,\n     $                  Z )\n*\n*  Tests CHER and CHPR.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Parameters ..\n      COMPLEX            ZERO, HALF, ONE\n      PARAMETER          ( ZERO = ( 0.0, 0.0 ), HALF = ( 0.5, 0.0 ),\n     $                   ONE = ( 1.0, 0.0 ) )\n      REAL               RZERO\n      PARAMETER          ( RZERO = 0.0 )\n*     .. Scalar Arguments ..\n      REAL               EPS, THRESH\n      INTEGER            INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      COMPLEX            A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), X( NMAX ), XS( NMAX*INCMAX ),\n     $                   XX( NMAX*INCMAX ), Y( NMAX ),\n     $                   YS( NMAX*INCMAX ), YT( NMAX ),\n     $                   YY( NMAX*INCMAX ), Z( NMAX )\n      REAL               G( NMAX )\n      INTEGER            IDIM( NIDIM ), INC( NINC )\n*     .. Local Scalars ..\n      COMPLEX            ALPHA, TRANSL\n      REAL               ERR, ERRMAX, RALPHA, RALS\n      INTEGER            I, IA, IC, IN, INCX, INCXS, IX, J, JA, JJ, LAA,\n     $                   LDA, LDAS, LJ, LX, N, NARGS, NC, NS\n      LOGICAL            FULL, NULL, PACKED, RESET, SAME, UPPER\n      CHARACTER*1        UPLO, UPLOS\n      CHARACTER*2        ICH\n*     .. Local Arrays ..\n      COMPLEX            W( 1 )\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LCE, LCERES\n      EXTERNAL           LCE, LCERES\n*     .. External Subroutines ..\n      EXTERNAL           CHER, CHPR, CMAKE, CMVCH\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, CMPLX, CONJG, MAX, REAL\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICH/'UL'/\n*     .. Executable Statements ..\n      FULL = SNAME( 3: 3 ).EQ.'E'\n      PACKED = SNAME( 3: 3 ).EQ.'P'\n*     Define the number of arguments.\n      IF( FULL )THEN\n         NARGS = 7\n      ELSE IF( PACKED )THEN\n         NARGS = 6\n      END IF\n*\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = RZERO\n*\n      DO 100 IN = 1, NIDIM\n         N = IDIM( IN )\n*        Set LDA to 1 more than minimum value if room.\n         LDA = N\n         IF( LDA.LT.NMAX )\n     $      LDA = LDA + 1\n*        Skip tests if not enough room.\n         IF( LDA.GT.NMAX )\n     $      GO TO 100\n         IF( PACKED )THEN\n            LAA = ( N*( N + 1 ) )/2\n         ELSE\n            LAA = LDA*N\n         END IF\n*\n         DO 90 IC = 1, 2\n            UPLO = ICH( IC: IC )\n            UPPER = UPLO.EQ.'U'\n*\n            DO 80 IX = 1, NINC\n               INCX = INC( IX )\n               LX = ABS( INCX )*N\n*\n*              Generate the vector X.\n*\n               TRANSL = HALF\n               CALL CMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX, ABS( INCX ),\n     $                     0, N - 1, RESET, TRANSL )\n               IF( N.GT.1 )THEN\n                  X( N/2 ) = ZERO\n                  XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO\n               END IF\n*\n               DO 70 IA = 1, NALF\n                  RALPHA = REAL( ALF( IA ) )\n                  ALPHA = CMPLX( RALPHA, RZERO )\n                  NULL = N.LE.0.OR.RALPHA.EQ.RZERO\n*\n*                 Generate the matrix A.\n*\n                  TRANSL = ZERO\n                  CALL CMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A, NMAX,\n     $                        AA, LDA, N - 1, N - 1, RESET, TRANSL )\n*\n                  NC = NC + 1\n*\n*                 Save every datum before calling the subroutine.\n*\n                  UPLOS = UPLO\n                  NS = N\n                  RALS = RALPHA\n                  DO 10 I = 1, LAA\n                     AS( I ) = AA( I )\n   10             CONTINUE\n                  LDAS = LDA\n                  DO 20 I = 1, LX\n                     XS( I ) = XX( I )\n   20             CONTINUE\n                  INCXS = INCX\n*\n*                 Call the subroutine.\n*\n                  IF( FULL )THEN\n                     IF( TRACE )\n     $                  WRITE( NTRA, FMT = 9993 )NC, SNAME, UPLO, N,\n     $                  RALPHA, INCX, LDA\n                     IF( REWI )\n     $                  REWIND NTRA\n                     CALL CHER( UPLO, N, RALPHA, XX, INCX, AA, LDA )\n                  ELSE IF( PACKED )THEN\n                     IF( TRACE )\n     $                  WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO, N,\n     $                  RALPHA, INCX\n                     IF( REWI )\n     $                  REWIND NTRA\n                     CALL CHPR( UPLO, N, RALPHA, XX, INCX, AA )\n                  END IF\n*\n*                 Check if error-exit was taken incorrectly.\n*\n                  IF( .NOT.OK )THEN\n                     WRITE( NOUT, FMT = 9992 )\n                     FATAL = .TRUE.\n                     GO TO 120\n                  END IF\n*\n*                 See what data changed inside subroutines.\n*\n                  ISAME( 1 ) = UPLO.EQ.UPLOS\n                  ISAME( 2 ) = NS.EQ.N\n                  ISAME( 3 ) = RALS.EQ.RALPHA\n                  ISAME( 4 ) = LCE( XS, XX, LX )\n                  ISAME( 5 ) = INCXS.EQ.INCX\n                  IF( NULL )THEN\n                     ISAME( 6 ) = LCE( AS, AA, LAA )\n                  ELSE\n                     ISAME( 6 ) = LCERES( SNAME( 2: 3 ), UPLO, N, N, AS,\n     $                            AA, LDA )\n                  END IF\n                  IF( .NOT.PACKED )THEN\n                     ISAME( 7 ) = LDAS.EQ.LDA\n                  END IF\n*\n*                 If data was incorrectly changed, report and return.\n*\n                  SAME = .TRUE.\n                  DO 30 I = 1, NARGS\n                     SAME = SAME.AND.ISAME( I )\n                     IF( .NOT.ISAME( I ) )\n     $                  WRITE( NOUT, FMT = 9998 )I\n   30             CONTINUE\n                  IF( .NOT.SAME )THEN\n                     FATAL = .TRUE.\n                     GO TO 120\n                  END IF\n*\n                  IF( .NOT.NULL )THEN\n*\n*                    Check the result column by column.\n*\n                     IF( INCX.GT.0 )THEN\n                        DO 40 I = 1, N\n                           Z( I ) = X( I )\n   40                   CONTINUE\n                     ELSE\n                        DO 50 I = 1, N\n                           Z( I ) = X( N - I + 1 )\n   50                   CONTINUE\n                     END IF\n                     JA = 1\n                     DO 60 J = 1, N\n                        W( 1 ) = CONJG( Z( J ) )\n                        IF( UPPER )THEN\n                           JJ = 1\n                           LJ = J\n                        ELSE\n                           JJ = J\n                           LJ = N - J + 1\n                        END IF\n                        CALL CMVCH( 'N', LJ, 1, ALPHA, Z( JJ ), LJ, W,\n     $                              1, ONE, A( JJ, J ), 1, YT, G,\n     $                              AA( JA ), EPS, ERR, FATAL, NOUT,\n     $                              .TRUE. )\n                        IF( FULL )THEN\n                           IF( UPPER )THEN\n                              JA = JA + LDA\n                           ELSE\n                              JA = JA + LDA + 1\n                           END IF\n                        ELSE\n                           JA = JA + LJ\n                        END IF\n                        ERRMAX = MAX( ERRMAX, ERR )\n*                       If got really bad answer, report and return.\n                        IF( FATAL )\n     $                     GO TO 110\n   60                CONTINUE\n                  ELSE\n*                    Avoid repeating tests if N.le.0.\n                     IF( N.LE.0 )\n     $                  GO TO 100\n                  END IF\n*\n   70          CONTINUE\n*\n   80       CONTINUE\n*\n   90    CONTINUE\n*\n  100 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 130\n*\n  110 CONTINUE\n      WRITE( NOUT, FMT = 9995 )J\n*\n  120 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      IF( FULL )THEN\n         WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, RALPHA, INCX, LDA\n      ELSE IF( PACKED )THEN\n         WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, RALPHA, INCX\n      END IF\n*\n  130 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( '      THESE ARE THE RESULTS FOR COLUMN ', I3 )\n 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,',\n     $      I2, ', AP)                                         .' )\n 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,',\n     $      I2, ', A,', I3, ')                                      .' )\n 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of CCHK5.\n*\n      END\n      SUBROUTINE CCHK6( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX,\n     $                  INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G,\n     $                  Z )\n*\n*  Tests CHER2 and CHPR2.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Parameters ..\n      COMPLEX            ZERO, HALF, ONE\n      PARAMETER          ( ZERO = ( 0.0, 0.0 ), HALF = ( 0.5, 0.0 ),\n     $                   ONE = ( 1.0, 0.0 ) )\n      REAL               RZERO\n      PARAMETER          ( RZERO = 0.0 )\n*     .. Scalar Arguments ..\n      REAL               EPS, THRESH\n      INTEGER            INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      COMPLEX            A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), X( NMAX ), XS( NMAX*INCMAX ),\n     $                   XX( NMAX*INCMAX ), Y( NMAX ),\n     $                   YS( NMAX*INCMAX ), YT( NMAX ),\n     $                   YY( NMAX*INCMAX ), Z( NMAX, 2 )\n      REAL               G( NMAX )\n      INTEGER            IDIM( NIDIM ), INC( NINC )\n*     .. Local Scalars ..\n      COMPLEX            ALPHA, ALS, TRANSL\n      REAL               ERR, ERRMAX\n      INTEGER            I, IA, IC, IN, INCX, INCXS, INCY, INCYS, IX,\n     $                   IY, J, JA, JJ, LAA, LDA, LDAS, LJ, LX, LY, N,\n     $                   NARGS, NC, NS\n      LOGICAL            FULL, NULL, PACKED, RESET, SAME, UPPER\n      CHARACTER*1        UPLO, UPLOS\n      CHARACTER*2        ICH\n*     .. Local Arrays ..\n      COMPLEX            W( 2 )\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LCE, LCERES\n      EXTERNAL           LCE, LCERES\n*     .. External Subroutines ..\n      EXTERNAL           CHER2, CHPR2, CMAKE, CMVCH\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, CONJG, MAX\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICH/'UL'/\n*     .. Executable Statements ..\n      FULL = SNAME( 3: 3 ).EQ.'E'\n      PACKED = SNAME( 3: 3 ).EQ.'P'\n*     Define the number of arguments.\n      IF( FULL )THEN\n         NARGS = 9\n      ELSE IF( PACKED )THEN\n         NARGS = 8\n      END IF\n*\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = RZERO\n*\n      DO 140 IN = 1, NIDIM\n         N = IDIM( IN )\n*        Set LDA to 1 more than minimum value if room.\n         LDA = N\n         IF( LDA.LT.NMAX )\n     $      LDA = LDA + 1\n*        Skip tests if not enough room.\n         IF( LDA.GT.NMAX )\n     $      GO TO 140\n         IF( PACKED )THEN\n            LAA = ( N*( N + 1 ) )/2\n         ELSE\n            LAA = LDA*N\n         END IF\n*\n         DO 130 IC = 1, 2\n            UPLO = ICH( IC: IC )\n            UPPER = UPLO.EQ.'U'\n*\n            DO 120 IX = 1, NINC\n               INCX = INC( IX )\n               LX = ABS( INCX )*N\n*\n*              Generate the vector X.\n*\n               TRANSL = HALF\n               CALL CMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX, ABS( INCX ),\n     $                     0, N - 1, RESET, TRANSL )\n               IF( N.GT.1 )THEN\n                  X( N/2 ) = ZERO\n                  XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO\n               END IF\n*\n               DO 110 IY = 1, NINC\n                  INCY = INC( IY )\n                  LY = ABS( INCY )*N\n*\n*                 Generate the vector Y.\n*\n                  TRANSL = ZERO\n                  CALL CMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY,\n     $                        ABS( INCY ), 0, N - 1, RESET, TRANSL )\n                  IF( N.GT.1 )THEN\n                     Y( N/2 ) = ZERO\n                     YY( 1 + ABS( INCY )*( N/2 - 1 ) ) = ZERO\n                  END IF\n*\n                  DO 100 IA = 1, NALF\n                     ALPHA = ALF( IA )\n                     NULL = N.LE.0.OR.ALPHA.EQ.ZERO\n*\n*                    Generate the matrix A.\n*\n                     TRANSL = ZERO\n                     CALL CMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A,\n     $                           NMAX, AA, LDA, N - 1, N - 1, RESET,\n     $                           TRANSL )\n*\n                     NC = NC + 1\n*\n*                    Save every datum before calling the subroutine.\n*\n                     UPLOS = UPLO\n                     NS = N\n                     ALS = ALPHA\n                     DO 10 I = 1, LAA\n                        AS( I ) = AA( I )\n   10                CONTINUE\n                     LDAS = LDA\n                     DO 20 I = 1, LX\n                        XS( I ) = XX( I )\n   20                CONTINUE\n                     INCXS = INCX\n                     DO 30 I = 1, LY\n                        YS( I ) = YY( I )\n   30                CONTINUE\n                     INCYS = INCY\n*\n*                    Call the subroutine.\n*\n                     IF( FULL )THEN\n                        IF( TRACE )\n     $                     WRITE( NTRA, FMT = 9993 )NC, SNAME, UPLO, N,\n     $                     ALPHA, INCX, INCY, LDA\n                        IF( REWI )\n     $                     REWIND NTRA\n                        CALL CHER2( UPLO, N, ALPHA, XX, INCX, YY, INCY,\n     $                              AA, LDA )\n                     ELSE IF( PACKED )THEN\n                        IF( TRACE )\n     $                     WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO, N,\n     $                     ALPHA, INCX, INCY\n                        IF( REWI )\n     $                     REWIND NTRA\n                        CALL CHPR2( UPLO, N, ALPHA, XX, INCX, YY, INCY,\n     $                              AA )\n                     END IF\n*\n*                    Check if error-exit was taken incorrectly.\n*\n                     IF( .NOT.OK )THEN\n                        WRITE( NOUT, FMT = 9992 )\n                        FATAL = .TRUE.\n                        GO TO 160\n                     END IF\n*\n*                    See what data changed inside subroutines.\n*\n                     ISAME( 1 ) = UPLO.EQ.UPLOS\n                     ISAME( 2 ) = NS.EQ.N\n                     ISAME( 3 ) = ALS.EQ.ALPHA\n                     ISAME( 4 ) = LCE( XS, XX, LX )\n                     ISAME( 5 ) = INCXS.EQ.INCX\n                     ISAME( 6 ) = LCE( YS, YY, LY )\n                     ISAME( 7 ) = INCYS.EQ.INCY\n                     IF( NULL )THEN\n                        ISAME( 8 ) = LCE( AS, AA, LAA )\n                     ELSE\n                        ISAME( 8 ) = LCERES( SNAME( 2: 3 ), UPLO, N, N,\n     $                               AS, AA, LDA )\n                     END IF\n                     IF( .NOT.PACKED )THEN\n                        ISAME( 9 ) = LDAS.EQ.LDA\n                     END IF\n*\n*                    If data was incorrectly changed, report and return.\n*\n                     SAME = .TRUE.\n                     DO 40 I = 1, NARGS\n                        SAME = SAME.AND.ISAME( I )\n                        IF( .NOT.ISAME( I ) )\n     $                     WRITE( NOUT, FMT = 9998 )I\n   40                CONTINUE\n                     IF( .NOT.SAME )THEN\n                        FATAL = .TRUE.\n                        GO TO 160\n                     END IF\n*\n                     IF( .NOT.NULL )THEN\n*\n*                       Check the result column by column.\n*\n                        IF( INCX.GT.0 )THEN\n                           DO 50 I = 1, N\n                              Z( I, 1 ) = X( I )\n   50                      CONTINUE\n                        ELSE\n                           DO 60 I = 1, N\n                              Z( I, 1 ) = X( N - I + 1 )\n   60                      CONTINUE\n                        END IF\n                        IF( INCY.GT.0 )THEN\n                           DO 70 I = 1, N\n                              Z( I, 2 ) = Y( I )\n   70                      CONTINUE\n                        ELSE\n                           DO 80 I = 1, N\n                              Z( I, 2 ) = Y( N - I + 1 )\n   80                      CONTINUE\n                        END IF\n                        JA = 1\n                        DO 90 J = 1, N\n                           W( 1 ) = ALPHA*CONJG( Z( J, 2 ) )\n                           W( 2 ) = CONJG( ALPHA )*CONJG( Z( J, 1 ) )\n                           IF( UPPER )THEN\n                              JJ = 1\n                              LJ = J\n                           ELSE\n                              JJ = J\n                              LJ = N - J + 1\n                           END IF\n                           CALL CMVCH( 'N', LJ, 2, ONE, Z( JJ, 1 ),\n     $                                 NMAX, W, 1, ONE, A( JJ, J ), 1,\n     $                                 YT, G, AA( JA ), EPS, ERR, FATAL,\n     $                                 NOUT, .TRUE. )\n                           IF( FULL )THEN\n                              IF( UPPER )THEN\n                                 JA = JA + LDA\n                              ELSE\n                                 JA = JA + LDA + 1\n                              END IF\n                           ELSE\n                              JA = JA + LJ\n                           END IF\n                           ERRMAX = MAX( ERRMAX, ERR )\n*                          If got really bad answer, report and return.\n                           IF( FATAL )\n     $                        GO TO 150\n   90                   CONTINUE\n                     ELSE\n*                       Avoid repeating tests with N.le.0.\n                        IF( N.LE.0 )\n     $                     GO TO 140\n                     END IF\n*\n  100             CONTINUE\n*\n  110          CONTINUE\n*\n  120       CONTINUE\n*\n  130    CONTINUE\n*\n  140 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 170\n*\n  150 CONTINUE\n      WRITE( NOUT, FMT = 9995 )J\n*\n  160 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      IF( FULL )THEN\n         WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, ALPHA, INCX,\n     $      INCY, LDA\n      ELSE IF( PACKED )THEN\n         WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, ALPHA, INCX, INCY\n      END IF\n*\n  170 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( '      THESE ARE THE RESULTS FOR COLUMN ', I3 )\n 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',(', F4.1, ',',\n     $      F4.1, '), X,', I2, ', Y,', I2, ', AP)                     ',\n     $      '       .' )\n 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',(', F4.1, ',',\n     $      F4.1, '), X,', I2, ', Y,', I2, ', A,', I3, ')             ',\n     $      '            .' )\n 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of CCHK6.\n*\n      END\n      SUBROUTINE CCHKE( ISNUM, SRNAMT, NOUT )\n*\n*  Tests the error exits from the Level 2 Blas.\n*  Requires a special version of the error-handling routine XERBLA.\n*  ALPHA, RALPHA, BETA, A, X and Y should not need to be defined.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Scalar Arguments ..\n      INTEGER            ISNUM, NOUT\n      CHARACTER*6        SRNAMT\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Local Scalars ..\n      COMPLEX            ALPHA, BETA\n      REAL               RALPHA\n*     .. Local Arrays ..\n      COMPLEX            A( 1, 1 ), X( 1 ), Y( 1 )\n*     .. External Subroutines ..\n      EXTERNAL           CGBMV, CGEMV, CGERC, CGERU, CHBMV, CHEMV, CHER,\n     $                   CHER2, CHKXER, CHPMV, CHPR, CHPR2, CTBMV,\n     $                   CTBSV, CTPMV, CTPSV, CTRMV, CTRSV\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Executable Statements ..\n*     OK is set to .FALSE. by the special version of XERBLA or by CHKXER\n*     if anything is wrong.\n      OK = .TRUE.\n*     LERR is set to .TRUE. by the special version of XERBLA each time\n*     it is called, and is then tested and re-set by CHKXER.\n      LERR = .FALSE.\n      GO TO ( 10, 20, 30, 40, 50, 60, 70, 80,\n     $        90, 100, 110, 120, 130, 140, 150, 160,\n     $        170 )ISNUM\n   10 INFOT = 1\n      CALL CGEMV( '/', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL CGEMV( 'N', -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CGEMV( 'N', 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL CGEMV( 'N', 2, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL CGEMV( 'N', 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL CGEMV( 'N', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 180\n   20 INFOT = 1\n      CALL CGBMV( '/', 0, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL CGBMV( 'N', -1, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CGBMV( 'N', 0, -1, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CGBMV( 'N', 0, 0, -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CGBMV( 'N', 2, 0, 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL CGBMV( 'N', 0, 0, 1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL CGBMV( 'N', 0, 0, 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 13\n      CALL CGBMV( 'N', 0, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 180\n   30 INFOT = 1\n      CALL CHEMV( '/', 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL CHEMV( 'U', -1, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CHEMV( 'U', 2, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL CHEMV( 'U', 0, ALPHA, A, 1, X, 0, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL CHEMV( 'U', 0, ALPHA, A, 1, X, 1, BETA, Y, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 180\n   40 INFOT = 1\n      CALL CHBMV( '/', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL CHBMV( 'U', -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CHBMV( 'U', 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL CHBMV( 'U', 0, 1, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL CHBMV( 'U', 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL CHBMV( 'U', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 180\n   50 INFOT = 1\n      CALL CHPMV( '/', 0, ALPHA, A, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL CHPMV( 'U', -1, ALPHA, A, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL CHPMV( 'U', 0, ALPHA, A, X, 0, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CHPMV( 'U', 0, ALPHA, A, X, 1, BETA, Y, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 180\n   60 INFOT = 1\n      CALL CTRMV( '/', 'N', 'N', 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL CTRMV( 'U', '/', 'N', 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CTRMV( 'U', 'N', '/', 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CTRMV( 'U', 'N', 'N', -1, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL CTRMV( 'U', 'N', 'N', 2, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL CTRMV( 'U', 'N', 'N', 0, A, 1, X, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 180\n   70 INFOT = 1\n      CALL CTBMV( '/', 'N', 'N', 0, 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL CTBMV( 'U', '/', 'N', 0, 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CTBMV( 'U', 'N', '/', 0, 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CTBMV( 'U', 'N', 'N', -1, 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CTBMV( 'U', 'N', 'N', 0, -1, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL CTBMV( 'U', 'N', 'N', 0, 1, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CTBMV( 'U', 'N', 'N', 0, 0, A, 1, X, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 180\n   80 INFOT = 1\n      CALL CTPMV( '/', 'N', 'N', 0, A, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL CTPMV( 'U', '/', 'N', 0, A, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CTPMV( 'U', 'N', '/', 0, A, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CTPMV( 'U', 'N', 'N', -1, A, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL CTPMV( 'U', 'N', 'N', 0, A, X, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 180\n   90 INFOT = 1\n      CALL CTRSV( '/', 'N', 'N', 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL CTRSV( 'U', '/', 'N', 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CTRSV( 'U', 'N', '/', 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CTRSV( 'U', 'N', 'N', -1, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL CTRSV( 'U', 'N', 'N', 2, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL CTRSV( 'U', 'N', 'N', 0, A, 1, X, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 180\n  100 INFOT = 1\n      CALL CTBSV( '/', 'N', 'N', 0, 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL CTBSV( 'U', '/', 'N', 0, 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CTBSV( 'U', 'N', '/', 0, 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CTBSV( 'U', 'N', 'N', -1, 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CTBSV( 'U', 'N', 'N', 0, -1, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL CTBSV( 'U', 'N', 'N', 0, 1, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CTBSV( 'U', 'N', 'N', 0, 0, A, 1, X, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 180\n  110 INFOT = 1\n      CALL CTPSV( '/', 'N', 'N', 0, A, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL CTPSV( 'U', '/', 'N', 0, A, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CTPSV( 'U', 'N', '/', 0, A, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CTPSV( 'U', 'N', 'N', -1, A, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL CTPSV( 'U', 'N', 'N', 0, A, X, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 180\n  120 INFOT = 1\n      CALL CGERC( -1, 0, ALPHA, X, 1, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL CGERC( 0, -1, ALPHA, X, 1, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CGERC( 0, 0, ALPHA, X, 0, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL CGERC( 0, 0, ALPHA, X, 1, Y, 0, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CGERC( 2, 0, ALPHA, X, 1, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 180\n  130 INFOT = 1\n      CALL CGERU( -1, 0, ALPHA, X, 1, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL CGERU( 0, -1, ALPHA, X, 1, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CGERU( 0, 0, ALPHA, X, 0, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL CGERU( 0, 0, ALPHA, X, 1, Y, 0, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CGERU( 2, 0, ALPHA, X, 1, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 180\n  140 INFOT = 1\n      CALL CHER( '/', 0, RALPHA, X, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL CHER( 'U', -1, RALPHA, X, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CHER( 'U', 0, RALPHA, X, 0, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL CHER( 'U', 2, RALPHA, X, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 180\n  150 INFOT = 1\n      CALL CHPR( '/', 0, RALPHA, X, 1, A )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL CHPR( 'U', -1, RALPHA, X, 1, A )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CHPR( 'U', 0, RALPHA, X, 0, A )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 180\n  160 INFOT = 1\n      CALL CHER2( '/', 0, ALPHA, X, 1, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL CHER2( 'U', -1, ALPHA, X, 1, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CHER2( 'U', 0, ALPHA, X, 0, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL CHER2( 'U', 0, ALPHA, X, 1, Y, 0, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CHER2( 'U', 2, ALPHA, X, 1, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 180\n  170 INFOT = 1\n      CALL CHPR2( '/', 0, ALPHA, X, 1, Y, 1, A )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL CHPR2( 'U', -1, ALPHA, X, 1, Y, 1, A )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CHPR2( 'U', 0, ALPHA, X, 0, Y, 1, A )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL CHPR2( 'U', 0, ALPHA, X, 1, Y, 0, A )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n*\n  180 IF( OK )THEN\n         WRITE( NOUT, FMT = 9999 )SRNAMT\n      ELSE\n         WRITE( NOUT, FMT = 9998 )SRNAMT\n      END IF\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE TESTS OF ERROR-EXITS' )\n 9998 FORMAT( ' ******* ', A6, ' FAILED THE TESTS OF ERROR-EXITS *****',\n     $      '**' )\n*\n*     End of CCHKE.\n*\n      END\n      SUBROUTINE CMAKE( TYPE, UPLO, DIAG, M, N, A, NMAX, AA, LDA, KL,\n     $                  KU, RESET, TRANSL )\n*\n*  Generates values for an M by N matrix A within the bandwidth\n*  defined by KL and KU.\n*  Stores the values in the array AA in the data structure required\n*  by the routine, with unwanted elements set to rogue value.\n*\n*  TYPE is 'GE', 'GB', 'HE', 'HB', 'HP', 'TR', 'TB' OR 'TP'.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Parameters ..\n      COMPLEX            ZERO, ONE\n      PARAMETER          ( ZERO = ( 0.0, 0.0 ), ONE = ( 1.0, 0.0 ) )\n      COMPLEX            ROGUE\n      PARAMETER          ( ROGUE = ( -1.0E10, 1.0E10 ) )\n      REAL               RZERO\n      PARAMETER          ( RZERO = 0.0 )\n      REAL               RROGUE\n      PARAMETER          ( RROGUE = -1.0E10 )\n*     .. Scalar Arguments ..\n      COMPLEX            TRANSL\n      INTEGER            KL, KU, LDA, M, N, NMAX\n      LOGICAL            RESET\n      CHARACTER*1        DIAG, UPLO\n      CHARACTER*2        TYPE\n*     .. Array Arguments ..\n      COMPLEX            A( NMAX, * ), AA( * )\n*     .. Local Scalars ..\n      INTEGER            I, I1, I2, I3, IBEG, IEND, IOFF, J, JJ, KK\n      LOGICAL            GEN, LOWER, SYM, TRI, UNIT, UPPER\n*     .. External Functions ..\n      COMPLEX            CBEG\n      EXTERNAL           CBEG\n*     .. Intrinsic Functions ..\n      INTRINSIC          CMPLX, CONJG, MAX, MIN, REAL\n*     .. Executable Statements ..\n      GEN = TYPE( 1: 1 ).EQ.'G'\n      SYM = TYPE( 1: 1 ).EQ.'H'\n      TRI = TYPE( 1: 1 ).EQ.'T'\n      UPPER = ( SYM.OR.TRI ).AND.UPLO.EQ.'U'\n      LOWER = ( SYM.OR.TRI ).AND.UPLO.EQ.'L'\n      UNIT = TRI.AND.DIAG.EQ.'U'\n*\n*     Generate data in array A.\n*\n      DO 20 J = 1, N\n         DO 10 I = 1, M\n            IF( GEN.OR.( UPPER.AND.I.LE.J ).OR.( LOWER.AND.I.GE.J ) )\n     $          THEN\n               IF( ( I.LE.J.AND.J - I.LE.KU ).OR.\n     $             ( I.GE.J.AND.I - J.LE.KL ) )THEN\n                  A( I, J ) = CBEG( RESET ) + TRANSL\n               ELSE\n                  A( I, J ) = ZERO\n               END IF\n               IF( I.NE.J )THEN\n                  IF( SYM )THEN\n                     A( J, I ) = CONJG( A( I, J ) )\n                  ELSE IF( TRI )THEN\n                     A( J, I ) = ZERO\n                  END IF\n               END IF\n            END IF\n   10    CONTINUE\n         IF( SYM )\n     $      A( J, J ) = CMPLX( REAL( A( J, J ) ), RZERO )\n         IF( TRI )\n     $      A( J, J ) = A( J, J ) + ONE\n         IF( UNIT )\n     $      A( J, J ) = ONE\n   20 CONTINUE\n*\n*     Store elements in array AS in data structure required by routine.\n*\n      IF( TYPE.EQ.'GE' )THEN\n         DO 50 J = 1, N\n            DO 30 I = 1, M\n               AA( I + ( J - 1 )*LDA ) = A( I, J )\n   30       CONTINUE\n            DO 40 I = M + 1, LDA\n               AA( I + ( J - 1 )*LDA ) = ROGUE\n   40       CONTINUE\n   50    CONTINUE\n      ELSE IF( TYPE.EQ.'GB' )THEN\n         DO 90 J = 1, N\n            DO 60 I1 = 1, KU + 1 - J\n               AA( I1 + ( J - 1 )*LDA ) = ROGUE\n   60       CONTINUE\n            DO 70 I2 = I1, MIN( KL + KU + 1, KU + 1 + M - J )\n               AA( I2 + ( J - 1 )*LDA ) = A( I2 + J - KU - 1, J )\n   70       CONTINUE\n            DO 80 I3 = I2, LDA\n               AA( I3 + ( J - 1 )*LDA ) = ROGUE\n   80       CONTINUE\n   90    CONTINUE\n      ELSE IF( TYPE.EQ.'HE'.OR.TYPE.EQ.'TR' )THEN\n         DO 130 J = 1, N\n            IF( UPPER )THEN\n               IBEG = 1\n               IF( UNIT )THEN\n                  IEND = J - 1\n               ELSE\n                  IEND = J\n               END IF\n            ELSE\n               IF( UNIT )THEN\n                  IBEG = J + 1\n               ELSE\n                  IBEG = J\n               END IF\n               IEND = N\n            END IF\n            DO 100 I = 1, IBEG - 1\n               AA( I + ( J - 1 )*LDA ) = ROGUE\n  100       CONTINUE\n            DO 110 I = IBEG, IEND\n               AA( I + ( J - 1 )*LDA ) = A( I, J )\n  110       CONTINUE\n            DO 120 I = IEND + 1, LDA\n               AA( I + ( J - 1 )*LDA ) = ROGUE\n  120       CONTINUE\n            IF( SYM )THEN\n               JJ = J + ( J - 1 )*LDA\n               AA( JJ ) = CMPLX( REAL( AA( JJ ) ), RROGUE )\n            END IF\n  130    CONTINUE\n      ELSE IF( TYPE.EQ.'HB'.OR.TYPE.EQ.'TB' )THEN\n         DO 170 J = 1, N\n            IF( UPPER )THEN\n               KK = KL + 1\n               IBEG = MAX( 1, KL + 2 - J )\n               IF( UNIT )THEN\n                  IEND = KL\n               ELSE\n                  IEND = KL + 1\n               END IF\n            ELSE\n               KK = 1\n               IF( UNIT )THEN\n                  IBEG = 2\n               ELSE\n                  IBEG = 1\n               END IF\n               IEND = MIN( KL + 1, 1 + M - J )\n            END IF\n            DO 140 I = 1, IBEG - 1\n               AA( I + ( J - 1 )*LDA ) = ROGUE\n  140       CONTINUE\n            DO 150 I = IBEG, IEND\n               AA( I + ( J - 1 )*LDA ) = A( I + J - KK, J )\n  150       CONTINUE\n            DO 160 I = IEND + 1, LDA\n               AA( I + ( J - 1 )*LDA ) = ROGUE\n  160       CONTINUE\n            IF( SYM )THEN\n               JJ = KK + ( J - 1 )*LDA\n               AA( JJ ) = CMPLX( REAL( AA( JJ ) ), RROGUE )\n            END IF\n  170    CONTINUE\n      ELSE IF( TYPE.EQ.'HP'.OR.TYPE.EQ.'TP' )THEN\n         IOFF = 0\n         DO 190 J = 1, N\n            IF( UPPER )THEN\n               IBEG = 1\n               IEND = J\n            ELSE\n               IBEG = J\n               IEND = N\n            END IF\n            DO 180 I = IBEG, IEND\n               IOFF = IOFF + 1\n               AA( IOFF ) = A( I, J )\n               IF( I.EQ.J )THEN\n                  IF( UNIT )\n     $               AA( IOFF ) = ROGUE\n                  IF( SYM )\n     $               AA( IOFF ) = CMPLX( REAL( AA( IOFF ) ), RROGUE )\n               END IF\n  180       CONTINUE\n  190    CONTINUE\n      END IF\n      RETURN\n*\n*     End of CMAKE.\n*\n      END\n      SUBROUTINE CMVCH( TRANS, M, N, ALPHA, A, NMAX, X, INCX, BETA, Y,\n     $                  INCY, YT, G, YY, EPS, ERR, FATAL, NOUT, MV )\n*\n*  Checks the results of the computational tests.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Parameters ..\n      COMPLEX            ZERO\n      PARAMETER          ( ZERO = ( 0.0, 0.0 ) )\n      REAL               RZERO, RONE\n      PARAMETER          ( RZERO = 0.0, RONE = 1.0 )\n*     .. Scalar Arguments ..\n      COMPLEX            ALPHA, BETA\n      REAL               EPS, ERR\n      INTEGER            INCX, INCY, M, N, NMAX, NOUT\n      LOGICAL            FATAL, MV\n      CHARACTER*1        TRANS\n*     .. Array Arguments ..\n      COMPLEX            A( NMAX, * ), X( * ), Y( * ), YT( * ), YY( * )\n      REAL               G( * )\n*     .. Local Scalars ..\n      COMPLEX            C\n      REAL               ERRI\n      INTEGER            I, INCXL, INCYL, IY, J, JX, KX, KY, ML, NL\n      LOGICAL            CTRAN, TRAN\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, AIMAG, CONJG, MAX, REAL, SQRT\n*     .. Statement Functions ..\n      REAL               ABS1\n*     .. Statement Function definitions ..\n      ABS1( C ) = ABS( REAL( C ) ) + ABS( AIMAG( C ) )\n*     .. Executable Statements ..\n      TRAN = TRANS.EQ.'T'\n      CTRAN = TRANS.EQ.'C'\n      IF( TRAN.OR.CTRAN )THEN\n         ML = N\n         NL = M\n      ELSE\n         ML = M\n         NL = N\n      END IF\n      IF( INCX.LT.0 )THEN\n         KX = NL\n         INCXL = -1\n      ELSE\n         KX = 1\n         INCXL = 1\n      END IF\n      IF( INCY.LT.0 )THEN\n         KY = ML\n         INCYL = -1\n      ELSE\n         KY = 1\n         INCYL = 1\n      END IF\n*\n*     Compute expected result in YT using data in A, X and Y.\n*     Compute gauges in G.\n*\n      IY = KY\n      DO 40 I = 1, ML\n         YT( IY ) = ZERO\n         G( IY ) = RZERO\n         JX = KX\n         IF( TRAN )THEN\n            DO 10 J = 1, NL\n               YT( IY ) = YT( IY ) + A( J, I )*X( JX )\n               G( IY ) = G( IY ) + ABS1( A( J, I ) )*ABS1( X( JX ) )\n               JX = JX + INCXL\n   10       CONTINUE\n         ELSE IF( CTRAN )THEN\n            DO 20 J = 1, NL\n               YT( IY ) = YT( IY ) + CONJG( A( J, I ) )*X( JX )\n               G( IY ) = G( IY ) + ABS1( A( J, I ) )*ABS1( X( JX ) )\n               JX = JX + INCXL\n   20       CONTINUE\n         ELSE\n            DO 30 J = 1, NL\n               YT( IY ) = YT( IY ) + A( I, J )*X( JX )\n               G( IY ) = G( IY ) + ABS1( A( I, J ) )*ABS1( X( JX ) )\n               JX = JX + INCXL\n   30       CONTINUE\n         END IF\n         YT( IY ) = ALPHA*YT( IY ) + BETA*Y( IY )\n         G( IY ) = ABS1( ALPHA )*G( IY ) + ABS1( BETA )*ABS1( Y( IY ) )\n         IY = IY + INCYL\n   40 CONTINUE\n*\n*     Compute the error ratio for this result.\n*\n      ERR = ZERO\n      DO 50 I = 1, ML\n         ERRI = ABS( YT( I ) - YY( 1 + ( I - 1 )*ABS( INCY ) ) )/EPS\n         IF( G( I ).NE.RZERO )\n     $      ERRI = ERRI/G( I )\n         ERR = MAX( ERR, ERRI )\n         IF( ERR*SQRT( EPS ).GE.RONE )\n     $      GO TO 60\n   50 CONTINUE\n*     If the loop completes, all results are at least half accurate.\n      GO TO 80\n*\n*     Report fatal error.\n*\n   60 FATAL = .TRUE.\n      WRITE( NOUT, FMT = 9999 )\n      DO 70 I = 1, ML\n         IF( MV )THEN\n            WRITE( NOUT, FMT = 9998 )I, YT( I ),\n     $         YY( 1 + ( I - 1 )*ABS( INCY ) )\n         ELSE\n            WRITE( NOUT, FMT = 9998 )I,\n     $         YY( 1 + ( I - 1 )*ABS( INCY ) ), YT( I )\n         END IF\n   70 CONTINUE\n*\n   80 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ******* FATAL ERROR - COMPUTED RESULT IS LESS THAN HAL',\n     $      'F ACCURATE *******', /'                       EXPECTED RE',\n     $      'SULT                    COMPUTED RESULT' )\n 9998 FORMAT( 1X, I7, 2( '  (', G15.6, ',', G15.6, ')' ) )\n*\n*     End of CMVCH.\n*\n      END\n      LOGICAL FUNCTION LCE( RI, RJ, LR )\n*\n*  Tests if two arrays are identical.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Scalar Arguments ..\n      INTEGER            LR\n*     .. Array Arguments ..\n      COMPLEX            RI( * ), RJ( * )\n*     .. Local Scalars ..\n      INTEGER            I\n*     .. Executable Statements ..\n      DO 10 I = 1, LR\n         IF( RI( I ).NE.RJ( I ) )\n     $      GO TO 20\n   10 CONTINUE\n      LCE = .TRUE.\n      GO TO 30\n   20 CONTINUE\n      LCE = .FALSE.\n   30 RETURN\n*\n*     End of LCE.\n*\n      END\n      LOGICAL FUNCTION LCERES( TYPE, UPLO, M, N, AA, AS, LDA )\n*\n*  Tests if selected elements in two arrays are equal.\n*\n*  TYPE is 'GE', 'HE' or 'HP'.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Scalar Arguments ..\n      INTEGER            LDA, M, N\n      CHARACTER*1        UPLO\n      CHARACTER*2        TYPE\n*     .. Array Arguments ..\n      COMPLEX            AA( LDA, * ), AS( LDA, * )\n*     .. Local Scalars ..\n      INTEGER            I, IBEG, IEND, J\n      LOGICAL            UPPER\n*     .. Executable Statements ..\n      UPPER = UPLO.EQ.'U'\n      IF( TYPE.EQ.'GE' )THEN\n         DO 20 J = 1, N\n            DO 10 I = M + 1, LDA\n               IF( AA( I, J ).NE.AS( I, J ) )\n     $            GO TO 70\n   10       CONTINUE\n   20    CONTINUE\n      ELSE IF( TYPE.EQ.'HE' )THEN\n         DO 50 J = 1, N\n            IF( UPPER )THEN\n               IBEG = 1\n               IEND = J\n            ELSE\n               IBEG = J\n               IEND = N\n            END IF\n            DO 30 I = 1, IBEG - 1\n               IF( AA( I, J ).NE.AS( I, J ) )\n     $            GO TO 70\n   30       CONTINUE\n            DO 40 I = IEND + 1, LDA\n               IF( AA( I, J ).NE.AS( I, J ) )\n     $            GO TO 70\n   40       CONTINUE\n   50    CONTINUE\n      END IF\n*\n      LCERES = .TRUE.\n      GO TO 80\n   70 CONTINUE\n      LCERES = .FALSE.\n   80 RETURN\n*\n*     End of LCERES.\n*\n      END\n      COMPLEX FUNCTION CBEG( RESET )\n*\n*  Generates complex numbers as pairs of random numbers uniformly\n*  distributed between -0.5 and 0.5.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Scalar Arguments ..\n      LOGICAL            RESET\n*     .. Local Scalars ..\n      INTEGER            I, IC, J, MI, MJ\n*     .. Save statement ..\n      SAVE               I, IC, J, MI, MJ\n*     .. Intrinsic Functions ..\n      INTRINSIC          CMPLX\n*     .. Executable Statements ..\n      IF( RESET )THEN\n*        Initialize local variables.\n         MI = 891\n         MJ = 457\n         I = 7\n         J = 7\n         IC = 0\n         RESET = .FALSE.\n      END IF\n*\n*     The sequence of values of I or J is bounded between 1 and 999.\n*     If initial I or J = 1,2,3,6,7 or 9, the period will be 50.\n*     If initial I or J = 4 or 8, the period will be 25.\n*     If initial I or J = 5, the period will be 10.\n*     IC is used to break up the period by skipping 1 value of I or J\n*     in 6.\n*\n      IC = IC + 1\n   10 I = I*MI\n      J = J*MJ\n      I = I - 1000*( I/1000 )\n      J = J - 1000*( J/1000 )\n      IF( IC.GE.5 )THEN\n         IC = 0\n         GO TO 10\n      END IF\n      CBEG = CMPLX( ( I - 500 )/1001.0, ( J - 500 )/1001.0 )\n      RETURN\n*\n*     End of CBEG.\n*\n      END\n      REAL FUNCTION SDIFF( X, Y )\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*\n*     .. Scalar Arguments ..\n      REAL               X, Y\n*     .. Executable Statements ..\n      SDIFF = X - Y\n      RETURN\n*\n*     End of SDIFF.\n*\n      END\n      SUBROUTINE CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n*\n*  Tests whether XERBLA has detected an error when it should.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Scalar Arguments ..\n      INTEGER            INFOT, NOUT\n      LOGICAL            LERR, OK\n      CHARACTER*6        SRNAMT\n*     .. Executable Statements ..\n      IF( .NOT.LERR )THEN\n         WRITE( NOUT, FMT = 9999 )INFOT, SRNAMT\n         OK = .FALSE.\n      END IF\n      LERR = .FALSE.\n      RETURN\n*\n 9999 FORMAT( ' ***** ILLEGAL VALUE OF PARAMETER NUMBER ', I2, ' NOT D',\n     $      'ETECTED BY ', A6, ' *****' )\n*\n*     End of CHKXER.\n*\n      END\n      SUBROUTINE XERBLA( SRNAME, INFO )\n*\n*  This is a special version of XERBLA to be used only as part of\n*  the test program for testing error exits from the Level 2 BLAS\n*  routines.\n*\n*  XERBLA  is an error handler for the Level 2 BLAS routines.\n*\n*  It is called by the Level 2 BLAS routines if an input parameter is\n*  invalid.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Scalar Arguments ..\n      INTEGER            INFO\n      CHARACTER*6        SRNAME\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUT\n      LOGICAL            LERR, OK\n      CHARACTER*6        SRNAMT\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUT, OK, LERR\n      COMMON             /SRNAMC/SRNAMT\n*     .. Executable Statements ..\n      LERR = .TRUE.\n      IF( INFO.NE.INFOT )THEN\n         IF( INFOT.NE.0 )THEN\n            WRITE( NOUT, FMT = 9999 )INFO, INFOT\n         ELSE\n            WRITE( NOUT, FMT = 9997 )INFO\n         END IF\n         OK = .FALSE.\n      END IF\n      IF( SRNAME.NE.SRNAMT )THEN\n         WRITE( NOUT, FMT = 9998 )SRNAME, SRNAMT\n         OK = .FALSE.\n      END IF\n      RETURN\n*\n 9999 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6, ' INSTEAD',\n     $      ' OF ', I2, ' *******' )\n 9998 FORMAT( ' ******* XERBLA WAS CALLED WITH SRNAME = ', A6, ' INSTE',\n     $      'AD OF ', A6, ' *******' )\n 9997 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6,\n     $      ' *******' )\n*\n*     End of XERBLA\n*\n      END\n\n"
  },
  {
    "path": "include/eigen3/blas/testing/cblat3.f",
    "content": "*> \\brief \\b CBLAT3\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*  Definition:\n*  ===========\n*\n*       PROGRAM CBLAT3\n* \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> Test program for the COMPLEX          Level 3 Blas.\n*>\n*> The program must be driven by a short data file. The first 14 records\n*> of the file are read using list-directed input, the last 9 records\n*> are read using the format ( A6, L2 ). An annotated example of a data\n*> file can be obtained by deleting the first 3 characters from the\n*> following 23 lines:\n*> 'cblat3.out'      NAME OF SUMMARY OUTPUT FILE\n*> 6                 UNIT NUMBER OF SUMMARY FILE\n*> 'CBLAT3.SNAP'     NAME OF SNAPSHOT OUTPUT FILE\n*> -1                UNIT NUMBER OF SNAPSHOT FILE (NOT USED IF .LT. 0)\n*> F        LOGICAL FLAG, T TO REWIND SNAPSHOT FILE AFTER EACH RECORD.\n*> F        LOGICAL FLAG, T TO STOP ON FAILURES.\n*> T        LOGICAL FLAG, T TO TEST ERROR EXITS.\n*> 16.0     THRESHOLD VALUE OF TEST RATIO\n*> 6                 NUMBER OF VALUES OF N\n*> 0 1 2 3 5 9       VALUES OF N\n*> 3                 NUMBER OF VALUES OF ALPHA\n*> (0.0,0.0) (1.0,0.0) (0.7,-0.9)       VALUES OF ALPHA\n*> 3                 NUMBER OF VALUES OF BETA\n*> (0.0,0.0) (1.0,0.0) (1.3,-1.1)       VALUES OF BETA\n*> CGEMM  T PUT F FOR NO TEST. SAME COLUMNS.\n*> CHEMM  T PUT F FOR NO TEST. SAME COLUMNS.\n*> CSYMM  T PUT F FOR NO TEST. SAME COLUMNS.\n*> CTRMM  T PUT F FOR NO TEST. SAME COLUMNS.\n*> CTRSM  T PUT F FOR NO TEST. SAME COLUMNS.\n*> CHERK  T PUT F FOR NO TEST. SAME COLUMNS.\n*> CSYRK  T PUT F FOR NO TEST. SAME COLUMNS.\n*> CHER2K T PUT F FOR NO TEST. SAME COLUMNS.\n*> CSYR2K T PUT F FOR NO TEST. SAME COLUMNS.\n*>\n*> Further Details\n*> ===============\n*>\n*> See:\n*>\n*>    Dongarra J. J., Du Croz J. J., Duff I. S. and Hammarling S.\n*>    A Set of Level 3 Basic Linear Algebra Subprograms.\n*>\n*>    Technical Memorandum No.88 (Revision 1), Mathematics and\n*>    Computer Science Division, Argonne National Laboratory, 9700\n*>    South Cass Avenue, Argonne, Illinois 60439, US.\n*>\n*> -- Written on 8-February-1989.\n*>    Jack Dongarra, Argonne National Laboratory.\n*>    Iain Duff, AERE Harwell.\n*>    Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*>    Sven Hammarling, Numerical Algorithms Group Ltd.\n*>\n*>    10-9-00:  Change STATUS='NEW' to 'UNKNOWN' so that the testers\n*>              can be run multiple times without deleting generated\n*>              output files (susan)\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date April 2012\n*\n*> \\ingroup complex_blas_testing\n*\n*  =====================================================================\n      PROGRAM CBLAT3\n*\n*  -- Reference BLAS test routine (version 3.4.1) --\n*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     April 2012\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      INTEGER            NIN\n      PARAMETER          ( NIN = 5 )\n      INTEGER            NSUBS\n      PARAMETER          ( NSUBS = 9 )\n      COMPLEX            ZERO, ONE\n      PARAMETER          ( ZERO = ( 0.0, 0.0 ), ONE = ( 1.0, 0.0 ) )\n      REAL               RZERO\n      PARAMETER          ( RZERO = 0.0 )\n      INTEGER            NMAX\n      PARAMETER          ( NMAX = 65 )\n      INTEGER            NIDMAX, NALMAX, NBEMAX\n      PARAMETER          ( NIDMAX = 9, NALMAX = 7, NBEMAX = 7 )\n*     .. Local Scalars ..\n      REAL               EPS, ERR, THRESH\n      INTEGER            I, ISNUM, J, N, NALF, NBET, NIDIM, NOUT, NTRA\n      LOGICAL            FATAL, LTESTT, REWI, SAME, SFATAL, TRACE,\n     $                   TSTERR\n      CHARACTER*1        TRANSA, TRANSB\n      CHARACTER*6        SNAMET\n      CHARACTER*32       SNAPS, SUMMRY\n*     .. Local Arrays ..\n      COMPLEX            AA( NMAX*NMAX ), AB( NMAX, 2*NMAX ),\n     $                   ALF( NALMAX ), AS( NMAX*NMAX ),\n     $                   BB( NMAX*NMAX ), BET( NBEMAX ),\n     $                   BS( NMAX*NMAX ), C( NMAX, NMAX ),\n     $                   CC( NMAX*NMAX ), CS( NMAX*NMAX ), CT( NMAX ),\n     $                   W( 2*NMAX )\n      REAL               G( NMAX )\n      INTEGER            IDIM( NIDMAX )\n      LOGICAL            LTEST( NSUBS )\n      CHARACTER*6        SNAMES( NSUBS )\n*     .. External Functions ..\n      REAL               SDIFF\n      LOGICAL            LCE\n      EXTERNAL           SDIFF, LCE\n*     .. External Subroutines ..\n      EXTERNAL           CCHK1, CCHK2, CCHK3, CCHK4, CCHK5, CCHKE, CMMCH\n*     .. Intrinsic Functions ..\n      INTRINSIC          MAX, MIN\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n      CHARACTER*6        SRNAMT\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n      COMMON             /SRNAMC/SRNAMT\n*     .. Data statements ..\n      DATA               SNAMES/'CGEMM ', 'CHEMM ', 'CSYMM ', 'CTRMM ',\n     $                   'CTRSM ', 'CHERK ', 'CSYRK ', 'CHER2K',\n     $                   'CSYR2K'/\n*     .. Executable Statements ..\n*\n*     Read name and unit number for summary output file and open file.\n*\n      READ( NIN, FMT = * )SUMMRY\n      READ( NIN, FMT = * )NOUT\n      OPEN( NOUT, FILE = SUMMRY )\n      NOUTC = NOUT\n*\n*     Read name and unit number for snapshot output file and open file.\n*\n      READ( NIN, FMT = * )SNAPS\n      READ( NIN, FMT = * )NTRA\n      TRACE = NTRA.GE.0\n      IF( TRACE )THEN\n         OPEN( NTRA, FILE = SNAPS )\n      END IF\n*     Read the flag that directs rewinding of the snapshot file.\n      READ( NIN, FMT = * )REWI\n      REWI = REWI.AND.TRACE\n*     Read the flag that directs stopping on any failure.\n      READ( NIN, FMT = * )SFATAL\n*     Read the flag that indicates whether error exits are to be tested.\n      READ( NIN, FMT = * )TSTERR\n*     Read the threshold value of the test ratio\n      READ( NIN, FMT = * )THRESH\n*\n*     Read and check the parameter values for the tests.\n*\n*     Values of N\n      READ( NIN, FMT = * )NIDIM\n      IF( NIDIM.LT.1.OR.NIDIM.GT.NIDMAX )THEN\n         WRITE( NOUT, FMT = 9997 )'N', NIDMAX\n         GO TO 220\n      END IF\n      READ( NIN, FMT = * )( IDIM( I ), I = 1, NIDIM )\n      DO 10 I = 1, NIDIM\n         IF( IDIM( I ).LT.0.OR.IDIM( I ).GT.NMAX )THEN\n            WRITE( NOUT, FMT = 9996 )NMAX\n            GO TO 220\n         END IF\n   10 CONTINUE\n*     Values of ALPHA\n      READ( NIN, FMT = * )NALF\n      IF( NALF.LT.1.OR.NALF.GT.NALMAX )THEN\n         WRITE( NOUT, FMT = 9997 )'ALPHA', NALMAX\n         GO TO 220\n      END IF\n      READ( NIN, FMT = * )( ALF( I ), I = 1, NALF )\n*     Values of BETA\n      READ( NIN, FMT = * )NBET\n      IF( NBET.LT.1.OR.NBET.GT.NBEMAX )THEN\n         WRITE( NOUT, FMT = 9997 )'BETA', NBEMAX\n         GO TO 220\n      END IF\n      READ( NIN, FMT = * )( BET( I ), I = 1, NBET )\n*\n*     Report values of parameters.\n*\n      WRITE( NOUT, FMT = 9995 )\n      WRITE( NOUT, FMT = 9994 )( IDIM( I ), I = 1, NIDIM )\n      WRITE( NOUT, FMT = 9993 )( ALF( I ), I = 1, NALF )\n      WRITE( NOUT, FMT = 9992 )( BET( I ), I = 1, NBET )\n      IF( .NOT.TSTERR )THEN\n         WRITE( NOUT, FMT = * )\n         WRITE( NOUT, FMT = 9984 )\n      END IF\n      WRITE( NOUT, FMT = * )\n      WRITE( NOUT, FMT = 9999 )THRESH\n      WRITE( NOUT, FMT = * )\n*\n*     Read names of subroutines and flags which indicate\n*     whether they are to be tested.\n*\n      DO 20 I = 1, NSUBS\n         LTEST( I ) = .FALSE.\n   20 CONTINUE\n   30 READ( NIN, FMT = 9988, END = 60 )SNAMET, LTESTT\n      DO 40 I = 1, NSUBS\n         IF( SNAMET.EQ.SNAMES( I ) )\n     $      GO TO 50\n   40 CONTINUE\n      WRITE( NOUT, FMT = 9990 )SNAMET\n      STOP\n   50 LTEST( I ) = LTESTT\n      GO TO 30\n*\n   60 CONTINUE\n      CLOSE ( NIN )\n*\n*     Compute EPS (the machine precision).\n*\n      EPS = EPSILON(RZERO)\n      WRITE( NOUT, FMT = 9998 )EPS\n*\n*     Check the reliability of CMMCH using exact data.\n*\n      N = MIN( 32, NMAX )\n      DO 100 J = 1, N\n         DO 90 I = 1, N\n            AB( I, J ) = MAX( I - J + 1, 0 )\n   90    CONTINUE\n         AB( J, NMAX + 1 ) = J\n         AB( 1, NMAX + J ) = J\n         C( J, 1 ) = ZERO\n  100 CONTINUE\n      DO 110 J = 1, N\n         CC( J ) = J*( ( J + 1 )*J )/2 - ( ( J + 1 )*J*( J - 1 ) )/3\n  110 CONTINUE\n*     CC holds the exact result. On exit from CMMCH CT holds\n*     the result computed by CMMCH.\n      TRANSA = 'N'\n      TRANSB = 'N'\n      CALL CMMCH( TRANSA, TRANSB, N, 1, N, ONE, AB, NMAX,\n     $            AB( 1, NMAX + 1 ), NMAX, ZERO, C, NMAX, CT, G, CC,\n     $            NMAX, EPS, ERR, FATAL, NOUT, .TRUE. )\n      SAME = LCE( CC, CT, N )\n      IF( .NOT.SAME.OR.ERR.NE.RZERO )THEN\n         WRITE( NOUT, FMT = 9989 )TRANSA, TRANSB, SAME, ERR\n         STOP\n      END IF\n      TRANSB = 'C'\n      CALL CMMCH( TRANSA, TRANSB, N, 1, N, ONE, AB, NMAX,\n     $            AB( 1, NMAX + 1 ), NMAX, ZERO, C, NMAX, CT, G, CC,\n     $            NMAX, EPS, ERR, FATAL, NOUT, .TRUE. )\n      SAME = LCE( CC, CT, N )\n      IF( .NOT.SAME.OR.ERR.NE.RZERO )THEN\n         WRITE( NOUT, FMT = 9989 )TRANSA, TRANSB, SAME, ERR\n         STOP\n      END IF\n      DO 120 J = 1, N\n         AB( J, NMAX + 1 ) = N - J + 1\n         AB( 1, NMAX + J ) = N - J + 1\n  120 CONTINUE\n      DO 130 J = 1, N\n         CC( N - J + 1 ) = J*( ( J + 1 )*J )/2 -\n     $                     ( ( J + 1 )*J*( J - 1 ) )/3\n  130 CONTINUE\n      TRANSA = 'C'\n      TRANSB = 'N'\n      CALL CMMCH( TRANSA, TRANSB, N, 1, N, ONE, AB, NMAX,\n     $            AB( 1, NMAX + 1 ), NMAX, ZERO, C, NMAX, CT, G, CC,\n     $            NMAX, EPS, ERR, FATAL, NOUT, .TRUE. )\n      SAME = LCE( CC, CT, N )\n      IF( .NOT.SAME.OR.ERR.NE.RZERO )THEN\n         WRITE( NOUT, FMT = 9989 )TRANSA, TRANSB, SAME, ERR\n         STOP\n      END IF\n      TRANSB = 'C'\n      CALL CMMCH( TRANSA, TRANSB, N, 1, N, ONE, AB, NMAX,\n     $            AB( 1, NMAX + 1 ), NMAX, ZERO, C, NMAX, CT, G, CC,\n     $            NMAX, EPS, ERR, FATAL, NOUT, .TRUE. )\n      SAME = LCE( CC, CT, N )\n      IF( .NOT.SAME.OR.ERR.NE.RZERO )THEN\n         WRITE( NOUT, FMT = 9989 )TRANSA, TRANSB, SAME, ERR\n         STOP\n      END IF\n*\n*     Test each subroutine in turn.\n*\n      DO 200 ISNUM = 1, NSUBS\n         WRITE( NOUT, FMT = * )\n         IF( .NOT.LTEST( ISNUM ) )THEN\n*           Subprogram is not to be tested.\n            WRITE( NOUT, FMT = 9987 )SNAMES( ISNUM )\n         ELSE\n            SRNAMT = SNAMES( ISNUM )\n*           Test error exits.\n            IF( TSTERR )THEN\n               CALL CCHKE( ISNUM, SNAMES( ISNUM ), NOUT )\n               WRITE( NOUT, FMT = * )\n            END IF\n*           Test computations.\n            INFOT = 0\n            OK = .TRUE.\n            FATAL = .FALSE.\n            GO TO ( 140, 150, 150, 160, 160, 170, 170,\n     $              180, 180 )ISNUM\n*           Test CGEMM, 01.\n  140       CALL CCHK1( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET,\n     $                  NMAX, AB, AA, AS, AB( 1, NMAX + 1 ), BB, BS, C,\n     $                  CC, CS, CT, G )\n            GO TO 190\n*           Test CHEMM, 02, CSYMM, 03.\n  150       CALL CCHK2( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET,\n     $                  NMAX, AB, AA, AS, AB( 1, NMAX + 1 ), BB, BS, C,\n     $                  CC, CS, CT, G )\n            GO TO 190\n*           Test CTRMM, 04, CTRSM, 05.\n  160       CALL CCHK3( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NALF, ALF, NMAX, AB,\n     $                  AA, AS, AB( 1, NMAX + 1 ), BB, BS, CT, G, C )\n            GO TO 190\n*           Test CHERK, 06, CSYRK, 07.\n  170       CALL CCHK4( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET,\n     $                  NMAX, AB, AA, AS, AB( 1, NMAX + 1 ), BB, BS, C,\n     $                  CC, CS, CT, G )\n            GO TO 190\n*           Test CHER2K, 08, CSYR2K, 09.\n  180       CALL CCHK5( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET,\n     $                  NMAX, AB, AA, AS, BB, BS, C, CC, CS, CT, G, W )\n            GO TO 190\n*\n  190       IF( FATAL.AND.SFATAL )\n     $         GO TO 210\n         END IF\n  200 CONTINUE\n      WRITE( NOUT, FMT = 9986 )\n      GO TO 230\n*\n  210 CONTINUE\n      WRITE( NOUT, FMT = 9985 )\n      GO TO 230\n*\n  220 CONTINUE\n      WRITE( NOUT, FMT = 9991 )\n*\n  230 CONTINUE\n      IF( TRACE )\n     $   CLOSE ( NTRA )\n      CLOSE ( NOUT )\n      STOP\n*\n 9999 FORMAT( ' ROUTINES PASS COMPUTATIONAL TESTS IF TEST RATIO IS LES',\n     $      'S THAN', F8.2 )\n 9998 FORMAT( ' RELATIVE MACHINE PRECISION IS TAKEN TO BE', 1P, E9.1 )\n 9997 FORMAT( ' NUMBER OF VALUES OF ', A, ' IS LESS THAN 1 OR GREATER ',\n     $      'THAN ', I2 )\n 9996 FORMAT( ' VALUE OF N IS LESS THAN 0 OR GREATER THAN ', I2 )\n 9995 FORMAT( ' TESTS OF THE COMPLEX          LEVEL 3 BLAS', //' THE F',\n     $      'OLLOWING PARAMETER VALUES WILL BE USED:' )\n 9994 FORMAT( '   FOR N              ', 9I6 )\n 9993 FORMAT( '   FOR ALPHA          ',\n     $      7( '(', F4.1, ',', F4.1, ')  ', : ) )\n 9992 FORMAT( '   FOR BETA           ',\n     $      7( '(', F4.1, ',', F4.1, ')  ', : ) )\n 9991 FORMAT( ' AMEND DATA FILE OR INCREASE ARRAY SIZES IN PROGRAM',\n     $      /' ******* TESTS ABANDONED *******' )\n 9990 FORMAT( ' SUBPROGRAM NAME ', A6, ' NOT RECOGNIZED', /' ******* T',\n     $      'ESTS ABANDONED *******' )\n 9989 FORMAT( ' ERROR IN CMMCH -  IN-LINE DOT PRODUCTS ARE BEING EVALU',\n     $      'ATED WRONGLY.', /' CMMCH WAS CALLED WITH TRANSA = ', A1,\n     $      ' AND TRANSB = ', A1, /' AND RETURNED SAME = ', L1, ' AND ',\n     $      'ERR = ', F12.3, '.', /' THIS MAY BE DUE TO FAULTS IN THE ',\n     $      'ARITHMETIC OR THE COMPILER.', /' ******* TESTS ABANDONED ',\n     $      '*******' )\n 9988 FORMAT( A6, L2 )\n 9987 FORMAT( 1X, A6, ' WAS NOT TESTED' )\n 9986 FORMAT( /' END OF TESTS' )\n 9985 FORMAT( /' ******* FATAL ERROR - TESTS ABANDONED *******' )\n 9984 FORMAT( ' ERROR-EXITS WILL NOT BE TESTED' )\n*\n*     End of CBLAT3.\n*\n      END\n      SUBROUTINE CCHK1( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET, NMAX,\n     $                  A, AA, AS, B, BB, BS, C, CC, CS, CT, G )\n*\n*  Tests CGEMM.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Parameters ..\n      COMPLEX            ZERO\n      PARAMETER          ( ZERO = ( 0.0, 0.0 ) )\n      REAL               RZERO\n      PARAMETER          ( RZERO = 0.0 )\n*     .. Scalar Arguments ..\n      REAL               EPS, THRESH\n      INTEGER            NALF, NBET, NIDIM, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      COMPLEX            A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), B( NMAX, NMAX ),\n     $                   BB( NMAX*NMAX ), BET( NBET ), BS( NMAX*NMAX ),\n     $                   C( NMAX, NMAX ), CC( NMAX*NMAX ),\n     $                   CS( NMAX*NMAX ), CT( NMAX )\n      REAL               G( NMAX )\n      INTEGER            IDIM( NIDIM )\n*     .. Local Scalars ..\n      COMPLEX            ALPHA, ALS, BETA, BLS\n      REAL               ERR, ERRMAX\n      INTEGER            I, IA, IB, ICA, ICB, IK, IM, IN, K, KS, LAA,\n     $                   LBB, LCC, LDA, LDAS, LDB, LDBS, LDC, LDCS, M,\n     $                   MA, MB, MS, N, NA, NARGS, NB, NC, NS\n      LOGICAL            NULL, RESET, SAME, TRANA, TRANB\n      CHARACTER*1        TRANAS, TRANBS, TRANSA, TRANSB\n      CHARACTER*3        ICH\n*     .. Local Arrays ..\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LCE, LCERES\n      EXTERNAL           LCE, LCERES\n*     .. External Subroutines ..\n      EXTERNAL           CGEMM, CMAKE, CMMCH\n*     .. Intrinsic Functions ..\n      INTRINSIC          MAX\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICH/'NTC'/\n*     .. Executable Statements ..\n*\n      NARGS = 13\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = RZERO\n*\n      DO 110 IM = 1, NIDIM\n         M = IDIM( IM )\n*\n         DO 100 IN = 1, NIDIM\n            N = IDIM( IN )\n*           Set LDC to 1 more than minimum value if room.\n            LDC = M\n            IF( LDC.LT.NMAX )\n     $         LDC = LDC + 1\n*           Skip tests if not enough room.\n            IF( LDC.GT.NMAX )\n     $         GO TO 100\n            LCC = LDC*N\n            NULL = N.LE.0.OR.M.LE.0\n*\n            DO 90 IK = 1, NIDIM\n               K = IDIM( IK )\n*\n               DO 80 ICA = 1, 3\n                  TRANSA = ICH( ICA: ICA )\n                  TRANA = TRANSA.EQ.'T'.OR.TRANSA.EQ.'C'\n*\n                  IF( TRANA )THEN\n                     MA = K\n                     NA = M\n                  ELSE\n                     MA = M\n                     NA = K\n                  END IF\n*                 Set LDA to 1 more than minimum value if room.\n                  LDA = MA\n                  IF( LDA.LT.NMAX )\n     $               LDA = LDA + 1\n*                 Skip tests if not enough room.\n                  IF( LDA.GT.NMAX )\n     $               GO TO 80\n                  LAA = LDA*NA\n*\n*                 Generate the matrix A.\n*\n                  CALL CMAKE( 'GE', ' ', ' ', MA, NA, A, NMAX, AA, LDA,\n     $                        RESET, ZERO )\n*\n                  DO 70 ICB = 1, 3\n                     TRANSB = ICH( ICB: ICB )\n                     TRANB = TRANSB.EQ.'T'.OR.TRANSB.EQ.'C'\n*\n                     IF( TRANB )THEN\n                        MB = N\n                        NB = K\n                     ELSE\n                        MB = K\n                        NB = N\n                     END IF\n*                    Set LDB to 1 more than minimum value if room.\n                     LDB = MB\n                     IF( LDB.LT.NMAX )\n     $                  LDB = LDB + 1\n*                    Skip tests if not enough room.\n                     IF( LDB.GT.NMAX )\n     $                  GO TO 70\n                     LBB = LDB*NB\n*\n*                    Generate the matrix B.\n*\n                     CALL CMAKE( 'GE', ' ', ' ', MB, NB, B, NMAX, BB,\n     $                           LDB, RESET, ZERO )\n*\n                     DO 60 IA = 1, NALF\n                        ALPHA = ALF( IA )\n*\n                        DO 50 IB = 1, NBET\n                           BETA = BET( IB )\n*\n*                          Generate the matrix C.\n*\n                           CALL CMAKE( 'GE', ' ', ' ', M, N, C, NMAX,\n     $                                 CC, LDC, RESET, ZERO )\n*\n                           NC = NC + 1\n*\n*                          Save every datum before calling the\n*                          subroutine.\n*\n                           TRANAS = TRANSA\n                           TRANBS = TRANSB\n                           MS = M\n                           NS = N\n                           KS = K\n                           ALS = ALPHA\n                           DO 10 I = 1, LAA\n                              AS( I ) = AA( I )\n   10                      CONTINUE\n                           LDAS = LDA\n                           DO 20 I = 1, LBB\n                              BS( I ) = BB( I )\n   20                      CONTINUE\n                           LDBS = LDB\n                           BLS = BETA\n                           DO 30 I = 1, LCC\n                              CS( I ) = CC( I )\n   30                      CONTINUE\n                           LDCS = LDC\n*\n*                          Call the subroutine.\n*\n                           IF( TRACE )\n     $                        WRITE( NTRA, FMT = 9995 )NC, SNAME,\n     $                        TRANSA, TRANSB, M, N, K, ALPHA, LDA, LDB,\n     $                        BETA, LDC\n                           IF( REWI )\n     $                        REWIND NTRA\n                           CALL CGEMM( TRANSA, TRANSB, M, N, K, ALPHA,\n     $                                 AA, LDA, BB, LDB, BETA, CC, LDC )\n*\n*                          Check if error-exit was taken incorrectly.\n*\n                           IF( .NOT.OK )THEN\n                              WRITE( NOUT, FMT = 9994 )\n                              FATAL = .TRUE.\n                              GO TO 120\n                           END IF\n*\n*                          See what data changed inside subroutines.\n*\n                           ISAME( 1 ) = TRANSA.EQ.TRANAS\n                           ISAME( 2 ) = TRANSB.EQ.TRANBS\n                           ISAME( 3 ) = MS.EQ.M\n                           ISAME( 4 ) = NS.EQ.N\n                           ISAME( 5 ) = KS.EQ.K\n                           ISAME( 6 ) = ALS.EQ.ALPHA\n                           ISAME( 7 ) = LCE( AS, AA, LAA )\n                           ISAME( 8 ) = LDAS.EQ.LDA\n                           ISAME( 9 ) = LCE( BS, BB, LBB )\n                           ISAME( 10 ) = LDBS.EQ.LDB\n                           ISAME( 11 ) = BLS.EQ.BETA\n                           IF( NULL )THEN\n                              ISAME( 12 ) = LCE( CS, CC, LCC )\n                           ELSE\n                              ISAME( 12 ) = LCERES( 'GE', ' ', M, N, CS,\n     $                                      CC, LDC )\n                           END IF\n                           ISAME( 13 ) = LDCS.EQ.LDC\n*\n*                          If data was incorrectly changed, report\n*                          and return.\n*\n                           SAME = .TRUE.\n                           DO 40 I = 1, NARGS\n                              SAME = SAME.AND.ISAME( I )\n                              IF( .NOT.ISAME( I ) )\n     $                           WRITE( NOUT, FMT = 9998 )I\n   40                      CONTINUE\n                           IF( .NOT.SAME )THEN\n                              FATAL = .TRUE.\n                              GO TO 120\n                           END IF\n*\n                           IF( .NOT.NULL )THEN\n*\n*                             Check the result.\n*\n                              CALL CMMCH( TRANSA, TRANSB, M, N, K,\n     $                                    ALPHA, A, NMAX, B, NMAX, BETA,\n     $                                    C, NMAX, CT, G, CC, LDC, EPS,\n     $                                    ERR, FATAL, NOUT, .TRUE. )\n                              ERRMAX = MAX( ERRMAX, ERR )\n*                             If got really bad answer, report and\n*                             return.\n                              IF( FATAL )\n     $                           GO TO 120\n                           END IF\n*\n   50                   CONTINUE\n*\n   60                CONTINUE\n*\n   70             CONTINUE\n*\n   80          CONTINUE\n*\n   90       CONTINUE\n*\n  100    CONTINUE\n*\n  110 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 130\n*\n  120 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      WRITE( NOUT, FMT = 9995 )NC, SNAME, TRANSA, TRANSB, M, N, K,\n     $   ALPHA, LDA, LDB, BETA, LDC\n*\n  130 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',''', A1, ''',',\n     $      3( I3, ',' ), '(', F4.1, ',', F4.1, '), A,', I3, ', B,', I3,\n     $      ',(', F4.1, ',', F4.1, '), C,', I3, ').' )\n 9994 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of CCHK1.\n*\n      END\n      SUBROUTINE CCHK2( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET, NMAX,\n     $                  A, AA, AS, B, BB, BS, C, CC, CS, CT, G )\n*\n*  Tests CHEMM and CSYMM.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Parameters ..\n      COMPLEX            ZERO\n      PARAMETER          ( ZERO = ( 0.0, 0.0 ) )\n      REAL               RZERO\n      PARAMETER          ( RZERO = 0.0 )\n*     .. Scalar Arguments ..\n      REAL               EPS, THRESH\n      INTEGER            NALF, NBET, NIDIM, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      COMPLEX            A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), B( NMAX, NMAX ),\n     $                   BB( NMAX*NMAX ), BET( NBET ), BS( NMAX*NMAX ),\n     $                   C( NMAX, NMAX ), CC( NMAX*NMAX ),\n     $                   CS( NMAX*NMAX ), CT( NMAX )\n      REAL               G( NMAX )\n      INTEGER            IDIM( NIDIM )\n*     .. Local Scalars ..\n      COMPLEX            ALPHA, ALS, BETA, BLS\n      REAL               ERR, ERRMAX\n      INTEGER            I, IA, IB, ICS, ICU, IM, IN, LAA, LBB, LCC,\n     $                   LDA, LDAS, LDB, LDBS, LDC, LDCS, M, MS, N, NA,\n     $                   NARGS, NC, NS\n      LOGICAL            CONJ, LEFT, NULL, RESET, SAME\n      CHARACTER*1        SIDE, SIDES, UPLO, UPLOS\n      CHARACTER*2        ICHS, ICHU\n*     .. Local Arrays ..\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LCE, LCERES\n      EXTERNAL           LCE, LCERES\n*     .. External Subroutines ..\n      EXTERNAL           CHEMM, CMAKE, CMMCH, CSYMM\n*     .. Intrinsic Functions ..\n      INTRINSIC          MAX\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICHS/'LR'/, ICHU/'UL'/\n*     .. Executable Statements ..\n      CONJ = SNAME( 2: 3 ).EQ.'HE'\n*\n      NARGS = 12\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = RZERO\n*\n      DO 100 IM = 1, NIDIM\n         M = IDIM( IM )\n*\n         DO 90 IN = 1, NIDIM\n            N = IDIM( IN )\n*           Set LDC to 1 more than minimum value if room.\n            LDC = M\n            IF( LDC.LT.NMAX )\n     $         LDC = LDC + 1\n*           Skip tests if not enough room.\n            IF( LDC.GT.NMAX )\n     $         GO TO 90\n            LCC = LDC*N\n            NULL = N.LE.0.OR.M.LE.0\n*           Set LDB to 1 more than minimum value if room.\n            LDB = M\n            IF( LDB.LT.NMAX )\n     $         LDB = LDB + 1\n*           Skip tests if not enough room.\n            IF( LDB.GT.NMAX )\n     $         GO TO 90\n            LBB = LDB*N\n*\n*           Generate the matrix B.\n*\n            CALL CMAKE( 'GE', ' ', ' ', M, N, B, NMAX, BB, LDB, RESET,\n     $                  ZERO )\n*\n            DO 80 ICS = 1, 2\n               SIDE = ICHS( ICS: ICS )\n               LEFT = SIDE.EQ.'L'\n*\n               IF( LEFT )THEN\n                  NA = M\n               ELSE\n                  NA = N\n               END IF\n*              Set LDA to 1 more than minimum value if room.\n               LDA = NA\n               IF( LDA.LT.NMAX )\n     $            LDA = LDA + 1\n*              Skip tests if not enough room.\n               IF( LDA.GT.NMAX )\n     $            GO TO 80\n               LAA = LDA*NA\n*\n               DO 70 ICU = 1, 2\n                  UPLO = ICHU( ICU: ICU )\n*\n*                 Generate the hermitian or symmetric matrix A.\n*\n                  CALL CMAKE( SNAME( 2: 3 ), UPLO, ' ', NA, NA, A, NMAX,\n     $                        AA, LDA, RESET, ZERO )\n*\n                  DO 60 IA = 1, NALF\n                     ALPHA = ALF( IA )\n*\n                     DO 50 IB = 1, NBET\n                        BETA = BET( IB )\n*\n*                       Generate the matrix C.\n*\n                        CALL CMAKE( 'GE', ' ', ' ', M, N, C, NMAX, CC,\n     $                              LDC, RESET, ZERO )\n*\n                        NC = NC + 1\n*\n*                       Save every datum before calling the\n*                       subroutine.\n*\n                        SIDES = SIDE\n                        UPLOS = UPLO\n                        MS = M\n                        NS = N\n                        ALS = ALPHA\n                        DO 10 I = 1, LAA\n                           AS( I ) = AA( I )\n   10                   CONTINUE\n                        LDAS = LDA\n                        DO 20 I = 1, LBB\n                           BS( I ) = BB( I )\n   20                   CONTINUE\n                        LDBS = LDB\n                        BLS = BETA\n                        DO 30 I = 1, LCC\n                           CS( I ) = CC( I )\n   30                   CONTINUE\n                        LDCS = LDC\n*\n*                       Call the subroutine.\n*\n                        IF( TRACE )\n     $                     WRITE( NTRA, FMT = 9995 )NC, SNAME, SIDE,\n     $                     UPLO, M, N, ALPHA, LDA, LDB, BETA, LDC\n                        IF( REWI )\n     $                     REWIND NTRA\n                        IF( CONJ )THEN\n                           CALL CHEMM( SIDE, UPLO, M, N, ALPHA, AA, LDA,\n     $                                 BB, LDB, BETA, CC, LDC )\n                        ELSE\n                           CALL CSYMM( SIDE, UPLO, M, N, ALPHA, AA, LDA,\n     $                                 BB, LDB, BETA, CC, LDC )\n                        END IF\n*\n*                       Check if error-exit was taken incorrectly.\n*\n                        IF( .NOT.OK )THEN\n                           WRITE( NOUT, FMT = 9994 )\n                           FATAL = .TRUE.\n                           GO TO 110\n                        END IF\n*\n*                       See what data changed inside subroutines.\n*\n                        ISAME( 1 ) = SIDES.EQ.SIDE\n                        ISAME( 2 ) = UPLOS.EQ.UPLO\n                        ISAME( 3 ) = MS.EQ.M\n                        ISAME( 4 ) = NS.EQ.N\n                        ISAME( 5 ) = ALS.EQ.ALPHA\n                        ISAME( 6 ) = LCE( AS, AA, LAA )\n                        ISAME( 7 ) = LDAS.EQ.LDA\n                        ISAME( 8 ) = LCE( BS, BB, LBB )\n                        ISAME( 9 ) = LDBS.EQ.LDB\n                        ISAME( 10 ) = BLS.EQ.BETA\n                        IF( NULL )THEN\n                           ISAME( 11 ) = LCE( CS, CC, LCC )\n                        ELSE\n                           ISAME( 11 ) = LCERES( 'GE', ' ', M, N, CS,\n     $                                   CC, LDC )\n                        END IF\n                        ISAME( 12 ) = LDCS.EQ.LDC\n*\n*                       If data was incorrectly changed, report and\n*                       return.\n*\n                        SAME = .TRUE.\n                        DO 40 I = 1, NARGS\n                           SAME = SAME.AND.ISAME( I )\n                           IF( .NOT.ISAME( I ) )\n     $                        WRITE( NOUT, FMT = 9998 )I\n   40                   CONTINUE\n                        IF( .NOT.SAME )THEN\n                           FATAL = .TRUE.\n                           GO TO 110\n                        END IF\n*\n                        IF( .NOT.NULL )THEN\n*\n*                          Check the result.\n*\n                           IF( LEFT )THEN\n                              CALL CMMCH( 'N', 'N', M, N, M, ALPHA, A,\n     $                                    NMAX, B, NMAX, BETA, C, NMAX,\n     $                                    CT, G, CC, LDC, EPS, ERR,\n     $                                    FATAL, NOUT, .TRUE. )\n                           ELSE\n                              CALL CMMCH( 'N', 'N', M, N, N, ALPHA, B,\n     $                                    NMAX, A, NMAX, BETA, C, NMAX,\n     $                                    CT, G, CC, LDC, EPS, ERR,\n     $                                    FATAL, NOUT, .TRUE. )\n                           END IF\n                           ERRMAX = MAX( ERRMAX, ERR )\n*                          If got really bad answer, report and\n*                          return.\n                           IF( FATAL )\n     $                        GO TO 110\n                        END IF\n*\n   50                CONTINUE\n*\n   60             CONTINUE\n*\n   70          CONTINUE\n*\n   80       CONTINUE\n*\n   90    CONTINUE\n*\n  100 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 120\n*\n  110 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      WRITE( NOUT, FMT = 9995 )NC, SNAME, SIDE, UPLO, M, N, ALPHA, LDA,\n     $   LDB, BETA, LDC\n*\n  120 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( 1X, I6, ': ', A6, '(', 2( '''', A1, ''',' ), 2( I3, ',' ),\n     $      '(', F4.1, ',', F4.1, '), A,', I3, ', B,', I3, ',(', F4.1,\n     $      ',', F4.1, '), C,', I3, ')    .' )\n 9994 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of CCHK2.\n*\n      END\n      SUBROUTINE CCHK3( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NALF, ALF, NMAX, A, AA, AS,\n     $                  B, BB, BS, CT, G, C )\n*\n*  Tests CTRMM and CTRSM.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Parameters ..\n      COMPLEX            ZERO, ONE\n      PARAMETER          ( ZERO = ( 0.0, 0.0 ), ONE = ( 1.0, 0.0 ) )\n      REAL               RZERO\n      PARAMETER          ( RZERO = 0.0 )\n*     .. Scalar Arguments ..\n      REAL               EPS, THRESH\n      INTEGER            NALF, NIDIM, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      COMPLEX            A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), B( NMAX, NMAX ),\n     $                   BB( NMAX*NMAX ), BS( NMAX*NMAX ),\n     $                   C( NMAX, NMAX ), CT( NMAX )\n      REAL               G( NMAX )\n      INTEGER            IDIM( NIDIM )\n*     .. Local Scalars ..\n      COMPLEX            ALPHA, ALS\n      REAL               ERR, ERRMAX\n      INTEGER            I, IA, ICD, ICS, ICT, ICU, IM, IN, J, LAA, LBB,\n     $                   LDA, LDAS, LDB, LDBS, M, MS, N, NA, NARGS, NC,\n     $                   NS\n      LOGICAL            LEFT, NULL, RESET, SAME\n      CHARACTER*1        DIAG, DIAGS, SIDE, SIDES, TRANAS, TRANSA, UPLO,\n     $                   UPLOS\n      CHARACTER*2        ICHD, ICHS, ICHU\n      CHARACTER*3        ICHT\n*     .. Local Arrays ..\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LCE, LCERES\n      EXTERNAL           LCE, LCERES\n*     .. External Subroutines ..\n      EXTERNAL           CMAKE, CMMCH, CTRMM, CTRSM\n*     .. Intrinsic Functions ..\n      INTRINSIC          MAX\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICHU/'UL'/, ICHT/'NTC'/, ICHD/'UN'/, ICHS/'LR'/\n*     .. Executable Statements ..\n*\n      NARGS = 11\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = RZERO\n*     Set up zero matrix for CMMCH.\n      DO 20 J = 1, NMAX\n         DO 10 I = 1, NMAX\n            C( I, J ) = ZERO\n   10    CONTINUE\n   20 CONTINUE\n*\n      DO 140 IM = 1, NIDIM\n         M = IDIM( IM )\n*\n         DO 130 IN = 1, NIDIM\n            N = IDIM( IN )\n*           Set LDB to 1 more than minimum value if room.\n            LDB = M\n            IF( LDB.LT.NMAX )\n     $         LDB = LDB + 1\n*           Skip tests if not enough room.\n            IF( LDB.GT.NMAX )\n     $         GO TO 130\n            LBB = LDB*N\n            NULL = M.LE.0.OR.N.LE.0\n*\n            DO 120 ICS = 1, 2\n               SIDE = ICHS( ICS: ICS )\n               LEFT = SIDE.EQ.'L'\n               IF( LEFT )THEN\n                  NA = M\n               ELSE\n                  NA = N\n               END IF\n*              Set LDA to 1 more than minimum value if room.\n               LDA = NA\n               IF( LDA.LT.NMAX )\n     $            LDA = LDA + 1\n*              Skip tests if not enough room.\n               IF( LDA.GT.NMAX )\n     $            GO TO 130\n               LAA = LDA*NA\n*\n               DO 110 ICU = 1, 2\n                  UPLO = ICHU( ICU: ICU )\n*\n                  DO 100 ICT = 1, 3\n                     TRANSA = ICHT( ICT: ICT )\n*\n                     DO 90 ICD = 1, 2\n                        DIAG = ICHD( ICD: ICD )\n*\n                        DO 80 IA = 1, NALF\n                           ALPHA = ALF( IA )\n*\n*                          Generate the matrix A.\n*\n                           CALL CMAKE( 'TR', UPLO, DIAG, NA, NA, A,\n     $                                 NMAX, AA, LDA, RESET, ZERO )\n*\n*                          Generate the matrix B.\n*\n                           CALL CMAKE( 'GE', ' ', ' ', M, N, B, NMAX,\n     $                                 BB, LDB, RESET, ZERO )\n*\n                           NC = NC + 1\n*\n*                          Save every datum before calling the\n*                          subroutine.\n*\n                           SIDES = SIDE\n                           UPLOS = UPLO\n                           TRANAS = TRANSA\n                           DIAGS = DIAG\n                           MS = M\n                           NS = N\n                           ALS = ALPHA\n                           DO 30 I = 1, LAA\n                              AS( I ) = AA( I )\n   30                      CONTINUE\n                           LDAS = LDA\n                           DO 40 I = 1, LBB\n                              BS( I ) = BB( I )\n   40                      CONTINUE\n                           LDBS = LDB\n*\n*                          Call the subroutine.\n*\n                           IF( SNAME( 4: 5 ).EQ.'MM' )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9995 )NC, SNAME,\n     $                           SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA,\n     $                           LDA, LDB\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL CTRMM( SIDE, UPLO, TRANSA, DIAG, M,\n     $                                    N, ALPHA, AA, LDA, BB, LDB )\n                           ELSE IF( SNAME( 4: 5 ).EQ.'SM' )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9995 )NC, SNAME,\n     $                           SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA,\n     $                           LDA, LDB\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL CTRSM( SIDE, UPLO, TRANSA, DIAG, M,\n     $                                    N, ALPHA, AA, LDA, BB, LDB )\n                           END IF\n*\n*                          Check if error-exit was taken incorrectly.\n*\n                           IF( .NOT.OK )THEN\n                              WRITE( NOUT, FMT = 9994 )\n                              FATAL = .TRUE.\n                              GO TO 150\n                           END IF\n*\n*                          See what data changed inside subroutines.\n*\n                           ISAME( 1 ) = SIDES.EQ.SIDE\n                           ISAME( 2 ) = UPLOS.EQ.UPLO\n                           ISAME( 3 ) = TRANAS.EQ.TRANSA\n                           ISAME( 4 ) = DIAGS.EQ.DIAG\n                           ISAME( 5 ) = MS.EQ.M\n                           ISAME( 6 ) = NS.EQ.N\n                           ISAME( 7 ) = ALS.EQ.ALPHA\n                           ISAME( 8 ) = LCE( AS, AA, LAA )\n                           ISAME( 9 ) = LDAS.EQ.LDA\n                           IF( NULL )THEN\n                              ISAME( 10 ) = LCE( BS, BB, LBB )\n                           ELSE\n                              ISAME( 10 ) = LCERES( 'GE', ' ', M, N, BS,\n     $                                      BB, LDB )\n                           END IF\n                           ISAME( 11 ) = LDBS.EQ.LDB\n*\n*                          If data was incorrectly changed, report and\n*                          return.\n*\n                           SAME = .TRUE.\n                           DO 50 I = 1, NARGS\n                              SAME = SAME.AND.ISAME( I )\n                              IF( .NOT.ISAME( I ) )\n     $                           WRITE( NOUT, FMT = 9998 )I\n   50                      CONTINUE\n                           IF( .NOT.SAME )THEN\n                              FATAL = .TRUE.\n                              GO TO 150\n                           END IF\n*\n                           IF( .NOT.NULL )THEN\n                              IF( SNAME( 4: 5 ).EQ.'MM' )THEN\n*\n*                                Check the result.\n*\n                                 IF( LEFT )THEN\n                                    CALL CMMCH( TRANSA, 'N', M, N, M,\n     $                                          ALPHA, A, NMAX, B, NMAX,\n     $                                          ZERO, C, NMAX, CT, G,\n     $                                          BB, LDB, EPS, ERR,\n     $                                          FATAL, NOUT, .TRUE. )\n                                 ELSE\n                                    CALL CMMCH( 'N', TRANSA, M, N, N,\n     $                                          ALPHA, B, NMAX, A, NMAX,\n     $                                          ZERO, C, NMAX, CT, G,\n     $                                          BB, LDB, EPS, ERR,\n     $                                          FATAL, NOUT, .TRUE. )\n                                 END IF\n                              ELSE IF( SNAME( 4: 5 ).EQ.'SM' )THEN\n*\n*                                Compute approximation to original\n*                                matrix.\n*\n                                 DO 70 J = 1, N\n                                    DO 60 I = 1, M\n                                       C( I, J ) = BB( I + ( J - 1 )*\n     $                                             LDB )\n                                       BB( I + ( J - 1 )*LDB ) = ALPHA*\n     $                                    B( I, J )\n   60                               CONTINUE\n   70                            CONTINUE\n*\n                                 IF( LEFT )THEN\n                                    CALL CMMCH( TRANSA, 'N', M, N, M,\n     $                                          ONE, A, NMAX, C, NMAX,\n     $                                          ZERO, B, NMAX, CT, G,\n     $                                          BB, LDB, EPS, ERR,\n     $                                          FATAL, NOUT, .FALSE. )\n                                 ELSE\n                                    CALL CMMCH( 'N', TRANSA, M, N, N,\n     $                                          ONE, C, NMAX, A, NMAX,\n     $                                          ZERO, B, NMAX, CT, G,\n     $                                          BB, LDB, EPS, ERR,\n     $                                          FATAL, NOUT, .FALSE. )\n                                 END IF\n                              END IF\n                              ERRMAX = MAX( ERRMAX, ERR )\n*                             If got really bad answer, report and\n*                             return.\n                              IF( FATAL )\n     $                           GO TO 150\n                           END IF\n*\n   80                   CONTINUE\n*\n   90                CONTINUE\n*\n  100             CONTINUE\n*\n  110          CONTINUE\n*\n  120       CONTINUE\n*\n  130    CONTINUE\n*\n  140 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 160\n*\n  150 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      WRITE( NOUT, FMT = 9995 )NC, SNAME, SIDE, UPLO, TRANSA, DIAG, M,\n     $   N, ALPHA, LDA, LDB\n*\n  160 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( 1X, I6, ': ', A6, '(', 4( '''', A1, ''',' ), 2( I3, ',' ),\n     $      '(', F4.1, ',', F4.1, '), A,', I3, ', B,', I3, ')         ',\n     $      '      .' )\n 9994 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of CCHK3.\n*\n      END\n      SUBROUTINE CCHK4( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET, NMAX,\n     $                  A, AA, AS, B, BB, BS, C, CC, CS, CT, G )\n*\n*  Tests CHERK and CSYRK.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Parameters ..\n      COMPLEX            ZERO\n      PARAMETER          ( ZERO = ( 0.0, 0.0 ) )\n      REAL               RONE, RZERO\n      PARAMETER          ( RONE = 1.0, RZERO = 0.0 )\n*     .. Scalar Arguments ..\n      REAL               EPS, THRESH\n      INTEGER            NALF, NBET, NIDIM, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      COMPLEX            A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), B( NMAX, NMAX ),\n     $                   BB( NMAX*NMAX ), BET( NBET ), BS( NMAX*NMAX ),\n     $                   C( NMAX, NMAX ), CC( NMAX*NMAX ),\n     $                   CS( NMAX*NMAX ), CT( NMAX )\n      REAL               G( NMAX )\n      INTEGER            IDIM( NIDIM )\n*     .. Local Scalars ..\n      COMPLEX            ALPHA, ALS, BETA, BETS\n      REAL               ERR, ERRMAX, RALPHA, RALS, RBETA, RBETS\n      INTEGER            I, IA, IB, ICT, ICU, IK, IN, J, JC, JJ, K, KS,\n     $                   LAA, LCC, LDA, LDAS, LDC, LDCS, LJ, MA, N, NA,\n     $                   NARGS, NC, NS\n      LOGICAL            CONJ, NULL, RESET, SAME, TRAN, UPPER\n      CHARACTER*1        TRANS, TRANSS, TRANST, UPLO, UPLOS\n      CHARACTER*2        ICHT, ICHU\n*     .. Local Arrays ..\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LCE, LCERES\n      EXTERNAL           LCE, LCERES\n*     .. External Subroutines ..\n      EXTERNAL           CHERK, CMAKE, CMMCH, CSYRK\n*     .. Intrinsic Functions ..\n      INTRINSIC          CMPLX, MAX, REAL\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICHT/'NC'/, ICHU/'UL'/\n*     .. Executable Statements ..\n      CONJ = SNAME( 2: 3 ).EQ.'HE'\n*\n      NARGS = 10\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = RZERO\n*\n      DO 100 IN = 1, NIDIM\n         N = IDIM( IN )\n*        Set LDC to 1 more than minimum value if room.\n         LDC = N\n         IF( LDC.LT.NMAX )\n     $      LDC = LDC + 1\n*        Skip tests if not enough room.\n         IF( LDC.GT.NMAX )\n     $      GO TO 100\n         LCC = LDC*N\n*\n         DO 90 IK = 1, NIDIM\n            K = IDIM( IK )\n*\n            DO 80 ICT = 1, 2\n               TRANS = ICHT( ICT: ICT )\n               TRAN = TRANS.EQ.'C'\n               IF( TRAN.AND..NOT.CONJ )\n     $            TRANS = 'T'\n               IF( TRAN )THEN\n                  MA = K\n                  NA = N\n               ELSE\n                  MA = N\n                  NA = K\n               END IF\n*              Set LDA to 1 more than minimum value if room.\n               LDA = MA\n               IF( LDA.LT.NMAX )\n     $            LDA = LDA + 1\n*              Skip tests if not enough room.\n               IF( LDA.GT.NMAX )\n     $            GO TO 80\n               LAA = LDA*NA\n*\n*              Generate the matrix A.\n*\n               CALL CMAKE( 'GE', ' ', ' ', MA, NA, A, NMAX, AA, LDA,\n     $                     RESET, ZERO )\n*\n               DO 70 ICU = 1, 2\n                  UPLO = ICHU( ICU: ICU )\n                  UPPER = UPLO.EQ.'U'\n*\n                  DO 60 IA = 1, NALF\n                     ALPHA = ALF( IA )\n                     IF( CONJ )THEN\n                        RALPHA = REAL( ALPHA )\n                        ALPHA = CMPLX( RALPHA, RZERO )\n                     END IF\n*\n                     DO 50 IB = 1, NBET\n                        BETA = BET( IB )\n                        IF( CONJ )THEN\n                           RBETA = REAL( BETA )\n                           BETA = CMPLX( RBETA, RZERO )\n                        END IF\n                        NULL = N.LE.0\n                        IF( CONJ )\n     $                     NULL = NULL.OR.( ( K.LE.0.OR.RALPHA.EQ.\n     $                            RZERO ).AND.RBETA.EQ.RONE )\n*\n*                       Generate the matrix C.\n*\n                        CALL CMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, C,\n     $                              NMAX, CC, LDC, RESET, ZERO )\n*\n                        NC = NC + 1\n*\n*                       Save every datum before calling the subroutine.\n*\n                        UPLOS = UPLO\n                        TRANSS = TRANS\n                        NS = N\n                        KS = K\n                        IF( CONJ )THEN\n                           RALS = RALPHA\n                        ELSE\n                           ALS = ALPHA\n                        END IF\n                        DO 10 I = 1, LAA\n                           AS( I ) = AA( I )\n   10                   CONTINUE\n                        LDAS = LDA\n                        IF( CONJ )THEN\n                           RBETS = RBETA\n                        ELSE\n                           BETS = BETA\n                        END IF\n                        DO 20 I = 1, LCC\n                           CS( I ) = CC( I )\n   20                   CONTINUE\n                        LDCS = LDC\n*\n*                       Call the subroutine.\n*\n                        IF( CONJ )THEN\n                           IF( TRACE )\n     $                        WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO,\n     $                        TRANS, N, K, RALPHA, LDA, RBETA, LDC\n                           IF( REWI )\n     $                        REWIND NTRA\n                           CALL CHERK( UPLO, TRANS, N, K, RALPHA, AA,\n     $                                 LDA, RBETA, CC, LDC )\n                        ELSE\n                           IF( TRACE )\n     $                        WRITE( NTRA, FMT = 9993 )NC, SNAME, UPLO,\n     $                        TRANS, N, K, ALPHA, LDA, BETA, LDC\n                           IF( REWI )\n     $                        REWIND NTRA\n                           CALL CSYRK( UPLO, TRANS, N, K, ALPHA, AA,\n     $                                 LDA, BETA, CC, LDC )\n                        END IF\n*\n*                       Check if error-exit was taken incorrectly.\n*\n                        IF( .NOT.OK )THEN\n                           WRITE( NOUT, FMT = 9992 )\n                           FATAL = .TRUE.\n                           GO TO 120\n                        END IF\n*\n*                       See what data changed inside subroutines.\n*\n                        ISAME( 1 ) = UPLOS.EQ.UPLO\n                        ISAME( 2 ) = TRANSS.EQ.TRANS\n                        ISAME( 3 ) = NS.EQ.N\n                        ISAME( 4 ) = KS.EQ.K\n                        IF( CONJ )THEN\n                           ISAME( 5 ) = RALS.EQ.RALPHA\n                        ELSE\n                           ISAME( 5 ) = ALS.EQ.ALPHA\n                        END IF\n                        ISAME( 6 ) = LCE( AS, AA, LAA )\n                        ISAME( 7 ) = LDAS.EQ.LDA\n                        IF( CONJ )THEN\n                           ISAME( 8 ) = RBETS.EQ.RBETA\n                        ELSE\n                           ISAME( 8 ) = BETS.EQ.BETA\n                        END IF\n                        IF( NULL )THEN\n                           ISAME( 9 ) = LCE( CS, CC, LCC )\n                        ELSE\n                           ISAME( 9 ) = LCERES( SNAME( 2: 3 ), UPLO, N,\n     $                                  N, CS, CC, LDC )\n                        END IF\n                        ISAME( 10 ) = LDCS.EQ.LDC\n*\n*                       If data was incorrectly changed, report and\n*                       return.\n*\n                        SAME = .TRUE.\n                        DO 30 I = 1, NARGS\n                           SAME = SAME.AND.ISAME( I )\n                           IF( .NOT.ISAME( I ) )\n     $                        WRITE( NOUT, FMT = 9998 )I\n   30                   CONTINUE\n                        IF( .NOT.SAME )THEN\n                           FATAL = .TRUE.\n                           GO TO 120\n                        END IF\n*\n                        IF( .NOT.NULL )THEN\n*\n*                          Check the result column by column.\n*\n                           IF( CONJ )THEN\n                              TRANST = 'C'\n                           ELSE\n                              TRANST = 'T'\n                           END IF\n                           JC = 1\n                           DO 40 J = 1, N\n                              IF( UPPER )THEN\n                                 JJ = 1\n                                 LJ = J\n                              ELSE\n                                 JJ = J\n                                 LJ = N - J + 1\n                              END IF\n                              IF( TRAN )THEN\n                                 CALL CMMCH( TRANST, 'N', LJ, 1, K,\n     $                                       ALPHA, A( 1, JJ ), NMAX,\n     $                                       A( 1, J ), NMAX, BETA,\n     $                                       C( JJ, J ), NMAX, CT, G,\n     $                                       CC( JC ), LDC, EPS, ERR,\n     $                                       FATAL, NOUT, .TRUE. )\n                              ELSE\n                                 CALL CMMCH( 'N', TRANST, LJ, 1, K,\n     $                                       ALPHA, A( JJ, 1 ), NMAX,\n     $                                       A( J, 1 ), NMAX, BETA,\n     $                                       C( JJ, J ), NMAX, CT, G,\n     $                                       CC( JC ), LDC, EPS, ERR,\n     $                                       FATAL, NOUT, .TRUE. )\n                              END IF\n                              IF( UPPER )THEN\n                                 JC = JC + LDC\n                              ELSE\n                                 JC = JC + LDC + 1\n                              END IF\n                              ERRMAX = MAX( ERRMAX, ERR )\n*                             If got really bad answer, report and\n*                             return.\n                              IF( FATAL )\n     $                           GO TO 110\n   40                      CONTINUE\n                        END IF\n*\n   50                CONTINUE\n*\n   60             CONTINUE\n*\n   70          CONTINUE\n*\n   80       CONTINUE\n*\n   90    CONTINUE\n*\n  100 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 130\n*\n  110 CONTINUE\n      IF( N.GT.1 )\n     $   WRITE( NOUT, FMT = 9995 )J\n*\n  120 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      IF( CONJ )THEN\n         WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, TRANS, N, K, RALPHA,\n     $      LDA, RBETA, LDC\n      ELSE\n         WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, TRANS, N, K, ALPHA,\n     $      LDA, BETA, LDC\n      END IF\n*\n  130 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( '      THESE ARE THE RESULTS FOR COLUMN ', I3 )\n 9994 FORMAT( 1X, I6, ': ', A6, '(', 2( '''', A1, ''',' ), 2( I3, ',' ),\n     $      F4.1, ', A,', I3, ',', F4.1, ', C,', I3, ')               ',\n     $      '          .' )\n 9993 FORMAT( 1X, I6, ': ', A6, '(', 2( '''', A1, ''',' ), 2( I3, ',' ),\n     $      '(', F4.1, ',', F4.1, ') , A,', I3, ',(', F4.1, ',', F4.1,\n     $      '), C,', I3, ')          .' )\n 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of CCHK4.\n*\n      END\n      SUBROUTINE CCHK5( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET, NMAX,\n     $                  AB, AA, AS, BB, BS, C, CC, CS, CT, G, W )\n*\n*  Tests CHER2K and CSYR2K.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Parameters ..\n      COMPLEX            ZERO, ONE\n      PARAMETER          ( ZERO = ( 0.0, 0.0 ), ONE = ( 1.0, 0.0 ) )\n      REAL               RONE, RZERO\n      PARAMETER          ( RONE = 1.0, RZERO = 0.0 )\n*     .. Scalar Arguments ..\n      REAL               EPS, THRESH\n      INTEGER            NALF, NBET, NIDIM, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      COMPLEX            AA( NMAX*NMAX ), AB( 2*NMAX*NMAX ),\n     $                   ALF( NALF ), AS( NMAX*NMAX ), BB( NMAX*NMAX ),\n     $                   BET( NBET ), BS( NMAX*NMAX ), C( NMAX, NMAX ),\n     $                   CC( NMAX*NMAX ), CS( NMAX*NMAX ), CT( NMAX ),\n     $                   W( 2*NMAX )\n      REAL               G( NMAX )\n      INTEGER            IDIM( NIDIM )\n*     .. Local Scalars ..\n      COMPLEX            ALPHA, ALS, BETA, BETS\n      REAL               ERR, ERRMAX, RBETA, RBETS\n      INTEGER            I, IA, IB, ICT, ICU, IK, IN, J, JC, JJ, JJAB,\n     $                   K, KS, LAA, LBB, LCC, LDA, LDAS, LDB, LDBS,\n     $                   LDC, LDCS, LJ, MA, N, NA, NARGS, NC, NS\n      LOGICAL            CONJ, NULL, RESET, SAME, TRAN, UPPER\n      CHARACTER*1        TRANS, TRANSS, TRANST, UPLO, UPLOS\n      CHARACTER*2        ICHT, ICHU\n*     .. Local Arrays ..\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LCE, LCERES\n      EXTERNAL           LCE, LCERES\n*     .. External Subroutines ..\n      EXTERNAL           CHER2K, CMAKE, CMMCH, CSYR2K\n*     .. Intrinsic Functions ..\n      INTRINSIC          CMPLX, CONJG, MAX, REAL\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICHT/'NC'/, ICHU/'UL'/\n*     .. Executable Statements ..\n      CONJ = SNAME( 2: 3 ).EQ.'HE'\n*\n      NARGS = 12\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = RZERO\n*\n      DO 130 IN = 1, NIDIM\n         N = IDIM( IN )\n*        Set LDC to 1 more than minimum value if room.\n         LDC = N\n         IF( LDC.LT.NMAX )\n     $      LDC = LDC + 1\n*        Skip tests if not enough room.\n         IF( LDC.GT.NMAX )\n     $      GO TO 130\n         LCC = LDC*N\n*\n         DO 120 IK = 1, NIDIM\n            K = IDIM( IK )\n*\n            DO 110 ICT = 1, 2\n               TRANS = ICHT( ICT: ICT )\n               TRAN = TRANS.EQ.'C'\n               IF( TRAN.AND..NOT.CONJ )\n     $            TRANS = 'T'\n               IF( TRAN )THEN\n                  MA = K\n                  NA = N\n               ELSE\n                  MA = N\n                  NA = K\n               END IF\n*              Set LDA to 1 more than minimum value if room.\n               LDA = MA\n               IF( LDA.LT.NMAX )\n     $            LDA = LDA + 1\n*              Skip tests if not enough room.\n               IF( LDA.GT.NMAX )\n     $            GO TO 110\n               LAA = LDA*NA\n*\n*              Generate the matrix A.\n*\n               IF( TRAN )THEN\n                  CALL CMAKE( 'GE', ' ', ' ', MA, NA, AB, 2*NMAX, AA,\n     $                        LDA, RESET, ZERO )\n               ELSE\n                  CALL CMAKE( 'GE', ' ', ' ', MA, NA, AB, NMAX, AA, LDA,\n     $                        RESET, ZERO )\n               END IF\n*\n*              Generate the matrix B.\n*\n               LDB = LDA\n               LBB = LAA\n               IF( TRAN )THEN\n                  CALL CMAKE( 'GE', ' ', ' ', MA, NA, AB( K + 1 ),\n     $                        2*NMAX, BB, LDB, RESET, ZERO )\n               ELSE\n                  CALL CMAKE( 'GE', ' ', ' ', MA, NA, AB( K*NMAX + 1 ),\n     $                        NMAX, BB, LDB, RESET, ZERO )\n               END IF\n*\n               DO 100 ICU = 1, 2\n                  UPLO = ICHU( ICU: ICU )\n                  UPPER = UPLO.EQ.'U'\n*\n                  DO 90 IA = 1, NALF\n                     ALPHA = ALF( IA )\n*\n                     DO 80 IB = 1, NBET\n                        BETA = BET( IB )\n                        IF( CONJ )THEN\n                           RBETA = REAL( BETA )\n                           BETA = CMPLX( RBETA, RZERO )\n                        END IF\n                        NULL = N.LE.0\n                        IF( CONJ )\n     $                     NULL = NULL.OR.( ( K.LE.0.OR.ALPHA.EQ.\n     $                            ZERO ).AND.RBETA.EQ.RONE )\n*\n*                       Generate the matrix C.\n*\n                        CALL CMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, C,\n     $                              NMAX, CC, LDC, RESET, ZERO )\n*\n                        NC = NC + 1\n*\n*                       Save every datum before calling the subroutine.\n*\n                        UPLOS = UPLO\n                        TRANSS = TRANS\n                        NS = N\n                        KS = K\n                        ALS = ALPHA\n                        DO 10 I = 1, LAA\n                           AS( I ) = AA( I )\n   10                   CONTINUE\n                        LDAS = LDA\n                        DO 20 I = 1, LBB\n                           BS( I ) = BB( I )\n   20                   CONTINUE\n                        LDBS = LDB\n                        IF( CONJ )THEN\n                           RBETS = RBETA\n                        ELSE\n                           BETS = BETA\n                        END IF\n                        DO 30 I = 1, LCC\n                           CS( I ) = CC( I )\n   30                   CONTINUE\n                        LDCS = LDC\n*\n*                       Call the subroutine.\n*\n                        IF( CONJ )THEN\n                           IF( TRACE )\n     $                        WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO,\n     $                        TRANS, N, K, ALPHA, LDA, LDB, RBETA, LDC\n                           IF( REWI )\n     $                        REWIND NTRA\n                           CALL CHER2K( UPLO, TRANS, N, K, ALPHA, AA,\n     $                                  LDA, BB, LDB, RBETA, CC, LDC )\n                        ELSE\n                           IF( TRACE )\n     $                        WRITE( NTRA, FMT = 9993 )NC, SNAME, UPLO,\n     $                        TRANS, N, K, ALPHA, LDA, LDB, BETA, LDC\n                           IF( REWI )\n     $                        REWIND NTRA\n                           CALL CSYR2K( UPLO, TRANS, N, K, ALPHA, AA,\n     $                                  LDA, BB, LDB, BETA, CC, LDC )\n                        END IF\n*\n*                       Check if error-exit was taken incorrectly.\n*\n                        IF( .NOT.OK )THEN\n                           WRITE( NOUT, FMT = 9992 )\n                           FATAL = .TRUE.\n                           GO TO 150\n                        END IF\n*\n*                       See what data changed inside subroutines.\n*\n                        ISAME( 1 ) = UPLOS.EQ.UPLO\n                        ISAME( 2 ) = TRANSS.EQ.TRANS\n                        ISAME( 3 ) = NS.EQ.N\n                        ISAME( 4 ) = KS.EQ.K\n                        ISAME( 5 ) = ALS.EQ.ALPHA\n                        ISAME( 6 ) = LCE( AS, AA, LAA )\n                        ISAME( 7 ) = LDAS.EQ.LDA\n                        ISAME( 8 ) = LCE( BS, BB, LBB )\n                        ISAME( 9 ) = LDBS.EQ.LDB\n                        IF( CONJ )THEN\n                           ISAME( 10 ) = RBETS.EQ.RBETA\n                        ELSE\n                           ISAME( 10 ) = BETS.EQ.BETA\n                        END IF\n                        IF( NULL )THEN\n                           ISAME( 11 ) = LCE( CS, CC, LCC )\n                        ELSE\n                           ISAME( 11 ) = LCERES( 'HE', UPLO, N, N, CS,\n     $                                   CC, LDC )\n                        END IF\n                        ISAME( 12 ) = LDCS.EQ.LDC\n*\n*                       If data was incorrectly changed, report and\n*                       return.\n*\n                        SAME = .TRUE.\n                        DO 40 I = 1, NARGS\n                           SAME = SAME.AND.ISAME( I )\n                           IF( .NOT.ISAME( I ) )\n     $                        WRITE( NOUT, FMT = 9998 )I\n   40                   CONTINUE\n                        IF( .NOT.SAME )THEN\n                           FATAL = .TRUE.\n                           GO TO 150\n                        END IF\n*\n                        IF( .NOT.NULL )THEN\n*\n*                          Check the result column by column.\n*\n                           IF( CONJ )THEN\n                              TRANST = 'C'\n                           ELSE\n                              TRANST = 'T'\n                           END IF\n                           JJAB = 1\n                           JC = 1\n                           DO 70 J = 1, N\n                              IF( UPPER )THEN\n                                 JJ = 1\n                                 LJ = J\n                              ELSE\n                                 JJ = J\n                                 LJ = N - J + 1\n                              END IF\n                              IF( TRAN )THEN\n                                 DO 50 I = 1, K\n                                    W( I ) = ALPHA*AB( ( J - 1 )*2*\n     $                                       NMAX + K + I )\n                                    IF( CONJ )THEN\n                                       W( K + I ) = CONJG( ALPHA )*\n     $                                              AB( ( J - 1 )*2*\n     $                                              NMAX + I )\n                                    ELSE\n                                       W( K + I ) = ALPHA*\n     $                                              AB( ( J - 1 )*2*\n     $                                              NMAX + I )\n                                    END IF\n   50                            CONTINUE\n                                 CALL CMMCH( TRANST, 'N', LJ, 1, 2*K,\n     $                                       ONE, AB( JJAB ), 2*NMAX, W,\n     $                                       2*NMAX, BETA, C( JJ, J ),\n     $                                       NMAX, CT, G, CC( JC ), LDC,\n     $                                       EPS, ERR, FATAL, NOUT,\n     $                                       .TRUE. )\n                              ELSE\n                                 DO 60 I = 1, K\n                                    IF( CONJ )THEN\n                                       W( I ) = ALPHA*CONJG( AB( ( K +\n     $                                          I - 1 )*NMAX + J ) )\n                                       W( K + I ) = CONJG( ALPHA*\n     $                                              AB( ( I - 1 )*NMAX +\n     $                                              J ) )\n                                    ELSE\n                                       W( I ) = ALPHA*AB( ( K + I - 1 )*\n     $                                          NMAX + J )\n                                       W( K + I ) = ALPHA*\n     $                                              AB( ( I - 1 )*NMAX +\n     $                                              J )\n                                    END IF\n   60                            CONTINUE\n                                 CALL CMMCH( 'N', 'N', LJ, 1, 2*K, ONE,\n     $                                       AB( JJ ), NMAX, W, 2*NMAX,\n     $                                       BETA, C( JJ, J ), NMAX, CT,\n     $                                       G, CC( JC ), LDC, EPS, ERR,\n     $                                       FATAL, NOUT, .TRUE. )\n                              END IF\n                              IF( UPPER )THEN\n                                 JC = JC + LDC\n                              ELSE\n                                 JC = JC + LDC + 1\n                                 IF( TRAN )\n     $                              JJAB = JJAB + 2*NMAX\n                              END IF\n                              ERRMAX = MAX( ERRMAX, ERR )\n*                             If got really bad answer, report and\n*                             return.\n                              IF( FATAL )\n     $                           GO TO 140\n   70                      CONTINUE\n                        END IF\n*\n   80                CONTINUE\n*\n   90             CONTINUE\n*\n  100          CONTINUE\n*\n  110       CONTINUE\n*\n  120    CONTINUE\n*\n  130 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 160\n*\n  140 CONTINUE\n      IF( N.GT.1 )\n     $   WRITE( NOUT, FMT = 9995 )J\n*\n  150 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      IF( CONJ )THEN\n         WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, TRANS, N, K, ALPHA,\n     $      LDA, LDB, RBETA, LDC\n      ELSE\n         WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, TRANS, N, K, ALPHA,\n     $      LDA, LDB, BETA, LDC\n      END IF\n*\n  160 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( '      THESE ARE THE RESULTS FOR COLUMN ', I3 )\n 9994 FORMAT( 1X, I6, ': ', A6, '(', 2( '''', A1, ''',' ), 2( I3, ',' ),\n     $      '(', F4.1, ',', F4.1, '), A,', I3, ', B,', I3, ',', F4.1,\n     $      ', C,', I3, ')           .' )\n 9993 FORMAT( 1X, I6, ': ', A6, '(', 2( '''', A1, ''',' ), 2( I3, ',' ),\n     $      '(', F4.1, ',', F4.1, '), A,', I3, ', B,', I3, ',(', F4.1,\n     $      ',', F4.1, '), C,', I3, ')    .' )\n 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of CCHK5.\n*\n      END\n      SUBROUTINE CCHKE( ISNUM, SRNAMT, NOUT )\n*\n*  Tests the error exits from the Level 3 Blas.\n*  Requires a special version of the error-handling routine XERBLA.\n*  A, B and C should not need to be defined.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*  3-19-92:  Initialize ALPHA, BETA, RALPHA, and RBETA  (eca)\n*  3-19-92:  Fix argument 12 in calls to CSYMM and CHEMM\n*            with INFOT = 9  (eca)\n*\n*     .. Scalar Arguments ..\n      INTEGER            ISNUM, NOUT\n      CHARACTER*6        SRNAMT\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Parameters ..\n      REAL               ONE, TWO\n      PARAMETER          ( ONE = 1.0E0, TWO = 2.0E0 )\n*     .. Local Scalars ..\n      COMPLEX            ALPHA, BETA\n      REAL               RALPHA, RBETA\n*     .. Local Arrays ..\n      COMPLEX            A( 2, 1 ), B( 2, 1 ), C( 2, 1 )\n*     .. External Subroutines ..\n      EXTERNAL           CGEMM, CHEMM, CHER2K, CHERK, CHKXER, CSYMM,\n     $                   CSYR2K, CSYRK, CTRMM, CTRSM\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Executable Statements ..\n*     OK is set to .FALSE. by the special version of XERBLA or by CHKXER\n*     if anything is wrong.\n      OK = .TRUE.\n*     LERR is set to .TRUE. by the special version of XERBLA each time\n*     it is called, and is then tested and re-set by CHKXER.\n      LERR = .FALSE.\n*\n*     Initialize ALPHA, BETA, RALPHA, and RBETA.\n*\n      ALPHA = CMPLX( ONE, -ONE )\n      BETA = CMPLX( TWO, -TWO )\n      RALPHA = ONE\n      RBETA = TWO\n*\n      GO TO ( 10, 20, 30, 40, 50, 60, 70, 80,\n     $        90 )ISNUM\n   10 INFOT = 1\n      CALL CGEMM( '/', 'N', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 1\n      CALL CGEMM( '/', 'C', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 1\n      CALL CGEMM( '/', 'T', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL CGEMM( 'N', '/', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL CGEMM( 'C', '/', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL CGEMM( 'T', '/', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CGEMM( 'N', 'N', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CGEMM( 'N', 'C', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CGEMM( 'N', 'T', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CGEMM( 'C', 'N', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CGEMM( 'C', 'C', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CGEMM( 'C', 'T', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CGEMM( 'T', 'N', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CGEMM( 'T', 'C', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CGEMM( 'T', 'T', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CGEMM( 'N', 'N', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CGEMM( 'N', 'C', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CGEMM( 'N', 'T', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CGEMM( 'C', 'N', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CGEMM( 'C', 'C', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CGEMM( 'C', 'T', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CGEMM( 'T', 'N', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CGEMM( 'T', 'C', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CGEMM( 'T', 'T', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CGEMM( 'N', 'N', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CGEMM( 'N', 'C', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CGEMM( 'N', 'T', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CGEMM( 'C', 'N', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CGEMM( 'C', 'C', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CGEMM( 'C', 'T', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CGEMM( 'T', 'N', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CGEMM( 'T', 'C', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CGEMM( 'T', 'T', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL CGEMM( 'N', 'N', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL CGEMM( 'N', 'C', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL CGEMM( 'N', 'T', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL CGEMM( 'C', 'N', 0, 0, 2, ALPHA, A, 1, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL CGEMM( 'C', 'C', 0, 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL CGEMM( 'C', 'T', 0, 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL CGEMM( 'T', 'N', 0, 0, 2, ALPHA, A, 1, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL CGEMM( 'T', 'C', 0, 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL CGEMM( 'T', 'T', 0, 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL CGEMM( 'N', 'N', 0, 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL CGEMM( 'C', 'N', 0, 0, 2, ALPHA, A, 2, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL CGEMM( 'T', 'N', 0, 0, 2, ALPHA, A, 2, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL CGEMM( 'N', 'C', 0, 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL CGEMM( 'C', 'C', 0, 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL CGEMM( 'T', 'C', 0, 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL CGEMM( 'N', 'T', 0, 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL CGEMM( 'C', 'T', 0, 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL CGEMM( 'T', 'T', 0, 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 13\n      CALL CGEMM( 'N', 'N', 2, 0, 0, ALPHA, A, 2, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 13\n      CALL CGEMM( 'N', 'C', 2, 0, 0, ALPHA, A, 2, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 13\n      CALL CGEMM( 'N', 'T', 2, 0, 0, ALPHA, A, 2, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 13\n      CALL CGEMM( 'C', 'N', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 13\n      CALL CGEMM( 'C', 'C', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 13\n      CALL CGEMM( 'C', 'T', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 13\n      CALL CGEMM( 'T', 'N', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 13\n      CALL CGEMM( 'T', 'C', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 13\n      CALL CGEMM( 'T', 'T', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 100\n   20 INFOT = 1\n      CALL CHEMM( '/', 'U', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL CHEMM( 'L', '/', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CHEMM( 'L', 'U', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CHEMM( 'R', 'U', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CHEMM( 'L', 'L', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CHEMM( 'R', 'L', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CHEMM( 'L', 'U', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CHEMM( 'R', 'U', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CHEMM( 'L', 'L', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CHEMM( 'R', 'L', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL CHEMM( 'L', 'U', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL CHEMM( 'R', 'U', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL CHEMM( 'L', 'L', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL CHEMM( 'R', 'L', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CHEMM( 'L', 'U', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CHEMM( 'R', 'U', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CHEMM( 'L', 'L', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CHEMM( 'R', 'L', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL CHEMM( 'L', 'U', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL CHEMM( 'R', 'U', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL CHEMM( 'L', 'L', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL CHEMM( 'R', 'L', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 100\n   30 INFOT = 1\n      CALL CSYMM( '/', 'U', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL CSYMM( 'L', '/', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CSYMM( 'L', 'U', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CSYMM( 'R', 'U', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CSYMM( 'L', 'L', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CSYMM( 'R', 'L', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CSYMM( 'L', 'U', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CSYMM( 'R', 'U', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CSYMM( 'L', 'L', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CSYMM( 'R', 'L', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL CSYMM( 'L', 'U', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL CSYMM( 'R', 'U', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL CSYMM( 'L', 'L', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL CSYMM( 'R', 'L', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CSYMM( 'L', 'U', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CSYMM( 'R', 'U', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CSYMM( 'L', 'L', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CSYMM( 'R', 'L', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL CSYMM( 'L', 'U', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL CSYMM( 'R', 'U', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL CSYMM( 'L', 'L', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL CSYMM( 'R', 'L', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 100\n   40 INFOT = 1\n      CALL CTRMM( '/', 'U', 'N', 'N', 0, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL CTRMM( 'L', '/', 'N', 'N', 0, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CTRMM( 'L', 'U', '/', 'N', 0, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CTRMM( 'L', 'U', 'N', '/', 0, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CTRMM( 'L', 'U', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CTRMM( 'L', 'U', 'C', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CTRMM( 'L', 'U', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CTRMM( 'R', 'U', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CTRMM( 'R', 'U', 'C', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CTRMM( 'R', 'U', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CTRMM( 'L', 'L', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CTRMM( 'L', 'L', 'C', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CTRMM( 'L', 'L', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CTRMM( 'R', 'L', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CTRMM( 'R', 'L', 'C', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CTRMM( 'R', 'L', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL CTRMM( 'L', 'U', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL CTRMM( 'L', 'U', 'C', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL CTRMM( 'L', 'U', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL CTRMM( 'R', 'U', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL CTRMM( 'R', 'U', 'C', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL CTRMM( 'R', 'U', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL CTRMM( 'L', 'L', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL CTRMM( 'L', 'L', 'C', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL CTRMM( 'L', 'L', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL CTRMM( 'R', 'L', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL CTRMM( 'R', 'L', 'C', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL CTRMM( 'R', 'L', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CTRMM( 'L', 'U', 'N', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CTRMM( 'L', 'U', 'C', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CTRMM( 'L', 'U', 'T', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CTRMM( 'R', 'U', 'N', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CTRMM( 'R', 'U', 'C', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CTRMM( 'R', 'U', 'T', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CTRMM( 'L', 'L', 'N', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CTRMM( 'L', 'L', 'C', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CTRMM( 'L', 'L', 'T', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CTRMM( 'R', 'L', 'N', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CTRMM( 'R', 'L', 'C', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CTRMM( 'R', 'L', 'T', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL CTRMM( 'L', 'U', 'N', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL CTRMM( 'L', 'U', 'C', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL CTRMM( 'L', 'U', 'T', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL CTRMM( 'R', 'U', 'N', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL CTRMM( 'R', 'U', 'C', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL CTRMM( 'R', 'U', 'T', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL CTRMM( 'L', 'L', 'N', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL CTRMM( 'L', 'L', 'C', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL CTRMM( 'L', 'L', 'T', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL CTRMM( 'R', 'L', 'N', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL CTRMM( 'R', 'L', 'C', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL CTRMM( 'R', 'L', 'T', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 100\n   50 INFOT = 1\n      CALL CTRSM( '/', 'U', 'N', 'N', 0, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL CTRSM( 'L', '/', 'N', 'N', 0, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CTRSM( 'L', 'U', '/', 'N', 0, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CTRSM( 'L', 'U', 'N', '/', 0, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CTRSM( 'L', 'U', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CTRSM( 'L', 'U', 'C', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CTRSM( 'L', 'U', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CTRSM( 'R', 'U', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CTRSM( 'R', 'U', 'C', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CTRSM( 'R', 'U', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CTRSM( 'L', 'L', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CTRSM( 'L', 'L', 'C', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CTRSM( 'L', 'L', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CTRSM( 'R', 'L', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CTRSM( 'R', 'L', 'C', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL CTRSM( 'R', 'L', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL CTRSM( 'L', 'U', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL CTRSM( 'L', 'U', 'C', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL CTRSM( 'L', 'U', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL CTRSM( 'R', 'U', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL CTRSM( 'R', 'U', 'C', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL CTRSM( 'R', 'U', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL CTRSM( 'L', 'L', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL CTRSM( 'L', 'L', 'C', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL CTRSM( 'L', 'L', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL CTRSM( 'R', 'L', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL CTRSM( 'R', 'L', 'C', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL CTRSM( 'R', 'L', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CTRSM( 'L', 'U', 'N', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CTRSM( 'L', 'U', 'C', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CTRSM( 'L', 'U', 'T', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CTRSM( 'R', 'U', 'N', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CTRSM( 'R', 'U', 'C', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CTRSM( 'R', 'U', 'T', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CTRSM( 'L', 'L', 'N', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CTRSM( 'L', 'L', 'C', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CTRSM( 'L', 'L', 'T', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CTRSM( 'R', 'L', 'N', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CTRSM( 'R', 'L', 'C', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CTRSM( 'R', 'L', 'T', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL CTRSM( 'L', 'U', 'N', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL CTRSM( 'L', 'U', 'C', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL CTRSM( 'L', 'U', 'T', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL CTRSM( 'R', 'U', 'N', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL CTRSM( 'R', 'U', 'C', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL CTRSM( 'R', 'U', 'T', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL CTRSM( 'L', 'L', 'N', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL CTRSM( 'L', 'L', 'C', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL CTRSM( 'L', 'L', 'T', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL CTRSM( 'R', 'L', 'N', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL CTRSM( 'R', 'L', 'C', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL CTRSM( 'R', 'L', 'T', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 100\n   60 INFOT = 1\n      CALL CHERK( '/', 'N', 0, 0, RALPHA, A, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL CHERK( 'U', 'T', 0, 0, RALPHA, A, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CHERK( 'U', 'N', -1, 0, RALPHA, A, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CHERK( 'U', 'C', -1, 0, RALPHA, A, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CHERK( 'L', 'N', -1, 0, RALPHA, A, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CHERK( 'L', 'C', -1, 0, RALPHA, A, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CHERK( 'U', 'N', 0, -1, RALPHA, A, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CHERK( 'U', 'C', 0, -1, RALPHA, A, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CHERK( 'L', 'N', 0, -1, RALPHA, A, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CHERK( 'L', 'C', 0, -1, RALPHA, A, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL CHERK( 'U', 'N', 2, 0, RALPHA, A, 1, RBETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL CHERK( 'U', 'C', 0, 2, RALPHA, A, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL CHERK( 'L', 'N', 2, 0, RALPHA, A, 1, RBETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL CHERK( 'L', 'C', 0, 2, RALPHA, A, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL CHERK( 'U', 'N', 2, 0, RALPHA, A, 2, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL CHERK( 'U', 'C', 2, 0, RALPHA, A, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL CHERK( 'L', 'N', 2, 0, RALPHA, A, 2, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL CHERK( 'L', 'C', 2, 0, RALPHA, A, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 100\n   70 INFOT = 1\n      CALL CSYRK( '/', 'N', 0, 0, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL CSYRK( 'U', 'C', 0, 0, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CSYRK( 'U', 'N', -1, 0, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CSYRK( 'U', 'T', -1, 0, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CSYRK( 'L', 'N', -1, 0, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CSYRK( 'L', 'T', -1, 0, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CSYRK( 'U', 'N', 0, -1, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CSYRK( 'U', 'T', 0, -1, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CSYRK( 'L', 'N', 0, -1, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CSYRK( 'L', 'T', 0, -1, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL CSYRK( 'U', 'N', 2, 0, ALPHA, A, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL CSYRK( 'U', 'T', 0, 2, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL CSYRK( 'L', 'N', 2, 0, ALPHA, A, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL CSYRK( 'L', 'T', 0, 2, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL CSYRK( 'U', 'N', 2, 0, ALPHA, A, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL CSYRK( 'U', 'T', 2, 0, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL CSYRK( 'L', 'N', 2, 0, ALPHA, A, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL CSYRK( 'L', 'T', 2, 0, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 100\n   80 INFOT = 1\n      CALL CHER2K( '/', 'N', 0, 0, ALPHA, A, 1, B, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL CHER2K( 'U', 'T', 0, 0, ALPHA, A, 1, B, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CHER2K( 'U', 'N', -1, 0, ALPHA, A, 1, B, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CHER2K( 'U', 'C', -1, 0, ALPHA, A, 1, B, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CHER2K( 'L', 'N', -1, 0, ALPHA, A, 1, B, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CHER2K( 'L', 'C', -1, 0, ALPHA, A, 1, B, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CHER2K( 'U', 'N', 0, -1, ALPHA, A, 1, B, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CHER2K( 'U', 'C', 0, -1, ALPHA, A, 1, B, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CHER2K( 'L', 'N', 0, -1, ALPHA, A, 1, B, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CHER2K( 'L', 'C', 0, -1, ALPHA, A, 1, B, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL CHER2K( 'U', 'N', 2, 0, ALPHA, A, 1, B, 1, RBETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL CHER2K( 'U', 'C', 0, 2, ALPHA, A, 1, B, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL CHER2K( 'L', 'N', 2, 0, ALPHA, A, 1, B, 1, RBETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL CHER2K( 'L', 'C', 0, 2, ALPHA, A, 1, B, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CHER2K( 'U', 'N', 2, 0, ALPHA, A, 2, B, 1, RBETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CHER2K( 'U', 'C', 0, 2, ALPHA, A, 2, B, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CHER2K( 'L', 'N', 2, 0, ALPHA, A, 2, B, 1, RBETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CHER2K( 'L', 'C', 0, 2, ALPHA, A, 2, B, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL CHER2K( 'U', 'N', 2, 0, ALPHA, A, 2, B, 2, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL CHER2K( 'U', 'C', 2, 0, ALPHA, A, 1, B, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL CHER2K( 'L', 'N', 2, 0, ALPHA, A, 2, B, 2, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL CHER2K( 'L', 'C', 2, 0, ALPHA, A, 1, B, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 100\n   90 INFOT = 1\n      CALL CSYR2K( '/', 'N', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL CSYR2K( 'U', 'C', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CSYR2K( 'U', 'N', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CSYR2K( 'U', 'T', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CSYR2K( 'L', 'N', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL CSYR2K( 'L', 'T', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CSYR2K( 'U', 'N', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CSYR2K( 'U', 'T', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CSYR2K( 'L', 'N', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL CSYR2K( 'L', 'T', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL CSYR2K( 'U', 'N', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL CSYR2K( 'U', 'T', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL CSYR2K( 'L', 'N', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL CSYR2K( 'L', 'T', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CSYR2K( 'U', 'N', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CSYR2K( 'U', 'T', 0, 2, ALPHA, A, 2, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CSYR2K( 'L', 'N', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL CSYR2K( 'L', 'T', 0, 2, ALPHA, A, 2, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL CSYR2K( 'U', 'N', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL CSYR2K( 'U', 'T', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL CSYR2K( 'L', 'N', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL CSYR2K( 'L', 'T', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n*\n  100 IF( OK )THEN\n         WRITE( NOUT, FMT = 9999 )SRNAMT\n      ELSE\n         WRITE( NOUT, FMT = 9998 )SRNAMT\n      END IF\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE TESTS OF ERROR-EXITS' )\n 9998 FORMAT( ' ******* ', A6, ' FAILED THE TESTS OF ERROR-EXITS *****',\n     $      '**' )\n*\n*     End of CCHKE.\n*\n      END\n      SUBROUTINE CMAKE( TYPE, UPLO, DIAG, M, N, A, NMAX, AA, LDA, RESET,\n     $                  TRANSL )\n*\n*  Generates values for an M by N matrix A.\n*  Stores the values in the array AA in the data structure required\n*  by the routine, with unwanted elements set to rogue value.\n*\n*  TYPE is 'GE', 'HE', 'SY' or 'TR'.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Parameters ..\n      COMPLEX            ZERO, ONE\n      PARAMETER          ( ZERO = ( 0.0, 0.0 ), ONE = ( 1.0, 0.0 ) )\n      COMPLEX            ROGUE\n      PARAMETER          ( ROGUE = ( -1.0E10, 1.0E10 ) )\n      REAL               RZERO\n      PARAMETER          ( RZERO = 0.0 )\n      REAL               RROGUE\n      PARAMETER          ( RROGUE = -1.0E10 )\n*     .. Scalar Arguments ..\n      COMPLEX            TRANSL\n      INTEGER            LDA, M, N, NMAX\n      LOGICAL            RESET\n      CHARACTER*1        DIAG, UPLO\n      CHARACTER*2        TYPE\n*     .. Array Arguments ..\n      COMPLEX            A( NMAX, * ), AA( * )\n*     .. Local Scalars ..\n      INTEGER            I, IBEG, IEND, J, JJ\n      LOGICAL            GEN, HER, LOWER, SYM, TRI, UNIT, UPPER\n*     .. External Functions ..\n      COMPLEX            CBEG\n      EXTERNAL           CBEG\n*     .. Intrinsic Functions ..\n      INTRINSIC          CMPLX, CONJG, REAL\n*     .. Executable Statements ..\n      GEN = TYPE.EQ.'GE'\n      HER = TYPE.EQ.'HE'\n      SYM = TYPE.EQ.'SY'\n      TRI = TYPE.EQ.'TR'\n      UPPER = ( HER.OR.SYM.OR.TRI ).AND.UPLO.EQ.'U'\n      LOWER = ( HER.OR.SYM.OR.TRI ).AND.UPLO.EQ.'L'\n      UNIT = TRI.AND.DIAG.EQ.'U'\n*\n*     Generate data in array A.\n*\n      DO 20 J = 1, N\n         DO 10 I = 1, M\n            IF( GEN.OR.( UPPER.AND.I.LE.J ).OR.( LOWER.AND.I.GE.J ) )\n     $          THEN\n               A( I, J ) = CBEG( RESET ) + TRANSL\n               IF( I.NE.J )THEN\n*                 Set some elements to zero\n                  IF( N.GT.3.AND.J.EQ.N/2 )\n     $               A( I, J ) = ZERO\n                  IF( HER )THEN\n                     A( J, I ) = CONJG( A( I, J ) )\n                  ELSE IF( SYM )THEN\n                     A( J, I ) = A( I, J )\n                  ELSE IF( TRI )THEN\n                     A( J, I ) = ZERO\n                  END IF\n               END IF\n            END IF\n   10    CONTINUE\n         IF( HER )\n     $      A( J, J ) = CMPLX( REAL( A( J, J ) ), RZERO )\n         IF( TRI )\n     $      A( J, J ) = A( J, J ) + ONE\n         IF( UNIT )\n     $      A( J, J ) = ONE\n   20 CONTINUE\n*\n*     Store elements in array AS in data structure required by routine.\n*\n      IF( TYPE.EQ.'GE' )THEN\n         DO 50 J = 1, N\n            DO 30 I = 1, M\n               AA( I + ( J - 1 )*LDA ) = A( I, J )\n   30       CONTINUE\n            DO 40 I = M + 1, LDA\n               AA( I + ( J - 1 )*LDA ) = ROGUE\n   40       CONTINUE\n   50    CONTINUE\n      ELSE IF( TYPE.EQ.'HE'.OR.TYPE.EQ.'SY'.OR.TYPE.EQ.'TR' )THEN\n         DO 90 J = 1, N\n            IF( UPPER )THEN\n               IBEG = 1\n               IF( UNIT )THEN\n                  IEND = J - 1\n               ELSE\n                  IEND = J\n               END IF\n            ELSE\n               IF( UNIT )THEN\n                  IBEG = J + 1\n               ELSE\n                  IBEG = J\n               END IF\n               IEND = N\n            END IF\n            DO 60 I = 1, IBEG - 1\n               AA( I + ( J - 1 )*LDA ) = ROGUE\n   60       CONTINUE\n            DO 70 I = IBEG, IEND\n               AA( I + ( J - 1 )*LDA ) = A( I, J )\n   70       CONTINUE\n            DO 80 I = IEND + 1, LDA\n               AA( I + ( J - 1 )*LDA ) = ROGUE\n   80       CONTINUE\n            IF( HER )THEN\n               JJ = J + ( J - 1 )*LDA\n               AA( JJ ) = CMPLX( REAL( AA( JJ ) ), RROGUE )\n            END IF\n   90    CONTINUE\n      END IF\n      RETURN\n*\n*     End of CMAKE.\n*\n      END\n      SUBROUTINE CMMCH( TRANSA, TRANSB, M, N, KK, ALPHA, A, LDA, B, LDB,\n     $                  BETA, C, LDC, CT, G, CC, LDCC, EPS, ERR, FATAL,\n     $                  NOUT, MV )\n*\n*  Checks the results of the computational tests.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Parameters ..\n      COMPLEX            ZERO\n      PARAMETER          ( ZERO = ( 0.0, 0.0 ) )\n      REAL               RZERO, RONE\n      PARAMETER          ( RZERO = 0.0, RONE = 1.0 )\n*     .. Scalar Arguments ..\n      COMPLEX            ALPHA, BETA\n      REAL               EPS, ERR\n      INTEGER            KK, LDA, LDB, LDC, LDCC, M, N, NOUT\n      LOGICAL            FATAL, MV\n      CHARACTER*1        TRANSA, TRANSB\n*     .. Array Arguments ..\n      COMPLEX            A( LDA, * ), B( LDB, * ), C( LDC, * ),\n     $                   CC( LDCC, * ), CT( * )\n      REAL               G( * )\n*     .. Local Scalars ..\n      COMPLEX            CL\n      REAL               ERRI\n      INTEGER            I, J, K\n      LOGICAL            CTRANA, CTRANB, TRANA, TRANB\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, AIMAG, CONJG, MAX, REAL, SQRT\n*     .. Statement Functions ..\n      REAL               ABS1\n*     .. Statement Function definitions ..\n      ABS1( CL ) = ABS( REAL( CL ) ) + ABS( AIMAG( CL ) )\n*     .. Executable Statements ..\n      TRANA = TRANSA.EQ.'T'.OR.TRANSA.EQ.'C'\n      TRANB = TRANSB.EQ.'T'.OR.TRANSB.EQ.'C'\n      CTRANA = TRANSA.EQ.'C'\n      CTRANB = TRANSB.EQ.'C'\n*\n*     Compute expected result, one column at a time, in CT using data\n*     in A, B and C.\n*     Compute gauges in G.\n*\n      DO 220 J = 1, N\n*\n         DO 10 I = 1, M\n            CT( I ) = ZERO\n            G( I ) = RZERO\n   10    CONTINUE\n         IF( .NOT.TRANA.AND..NOT.TRANB )THEN\n            DO 30 K = 1, KK\n               DO 20 I = 1, M\n                  CT( I ) = CT( I ) + A( I, K )*B( K, J )\n                  G( I ) = G( I ) + ABS1( A( I, K ) )*ABS1( B( K, J ) )\n   20          CONTINUE\n   30       CONTINUE\n         ELSE IF( TRANA.AND..NOT.TRANB )THEN\n            IF( CTRANA )THEN\n               DO 50 K = 1, KK\n                  DO 40 I = 1, M\n                     CT( I ) = CT( I ) + CONJG( A( K, I ) )*B( K, J )\n                     G( I ) = G( I ) + ABS1( A( K, I ) )*\n     $                        ABS1( B( K, J ) )\n   40             CONTINUE\n   50          CONTINUE\n            ELSE\n               DO 70 K = 1, KK\n                  DO 60 I = 1, M\n                     CT( I ) = CT( I ) + A( K, I )*B( K, J )\n                     G( I ) = G( I ) + ABS1( A( K, I ) )*\n     $                        ABS1( B( K, J ) )\n   60             CONTINUE\n   70          CONTINUE\n            END IF\n         ELSE IF( .NOT.TRANA.AND.TRANB )THEN\n            IF( CTRANB )THEN\n               DO 90 K = 1, KK\n                  DO 80 I = 1, M\n                     CT( I ) = CT( I ) + A( I, K )*CONJG( B( J, K ) )\n                     G( I ) = G( I ) + ABS1( A( I, K ) )*\n     $                        ABS1( B( J, K ) )\n   80             CONTINUE\n   90          CONTINUE\n            ELSE\n               DO 110 K = 1, KK\n                  DO 100 I = 1, M\n                     CT( I ) = CT( I ) + A( I, K )*B( J, K )\n                     G( I ) = G( I ) + ABS1( A( I, K ) )*\n     $                        ABS1( B( J, K ) )\n  100             CONTINUE\n  110          CONTINUE\n            END IF\n         ELSE IF( TRANA.AND.TRANB )THEN\n            IF( CTRANA )THEN\n               IF( CTRANB )THEN\n                  DO 130 K = 1, KK\n                     DO 120 I = 1, M\n                        CT( I ) = CT( I ) + CONJG( A( K, I ) )*\n     $                            CONJG( B( J, K ) )\n                        G( I ) = G( I ) + ABS1( A( K, I ) )*\n     $                           ABS1( B( J, K ) )\n  120                CONTINUE\n  130             CONTINUE\n               ELSE\n                  DO 150 K = 1, KK\n                     DO 140 I = 1, M\n                        CT( I ) = CT( I ) + CONJG( A( K, I ) )*B( J, K )\n                        G( I ) = G( I ) + ABS1( A( K, I ) )*\n     $                           ABS1( B( J, K ) )\n  140                CONTINUE\n  150             CONTINUE\n               END IF\n            ELSE\n               IF( CTRANB )THEN\n                  DO 170 K = 1, KK\n                     DO 160 I = 1, M\n                        CT( I ) = CT( I ) + A( K, I )*CONJG( B( J, K ) )\n                        G( I ) = G( I ) + ABS1( A( K, I ) )*\n     $                           ABS1( B( J, K ) )\n  160                CONTINUE\n  170             CONTINUE\n               ELSE\n                  DO 190 K = 1, KK\n                     DO 180 I = 1, M\n                        CT( I ) = CT( I ) + A( K, I )*B( J, K )\n                        G( I ) = G( I ) + ABS1( A( K, I ) )*\n     $                           ABS1( B( J, K ) )\n  180                CONTINUE\n  190             CONTINUE\n               END IF\n            END IF\n         END IF\n         DO 200 I = 1, M\n            CT( I ) = ALPHA*CT( I ) + BETA*C( I, J )\n            G( I ) = ABS1( ALPHA )*G( I ) +\n     $               ABS1( BETA )*ABS1( C( I, J ) )\n  200    CONTINUE\n*\n*        Compute the error ratio for this result.\n*\n         ERR = ZERO\n         DO 210 I = 1, M\n            ERRI = ABS1( CT( I ) - CC( I, J ) )/EPS\n            IF( G( I ).NE.RZERO )\n     $         ERRI = ERRI/G( I )\n            ERR = MAX( ERR, ERRI )\n            IF( ERR*SQRT( EPS ).GE.RONE )\n     $         GO TO 230\n  210    CONTINUE\n*\n  220 CONTINUE\n*\n*     If the loop completes, all results are at least half accurate.\n      GO TO 250\n*\n*     Report fatal error.\n*\n  230 FATAL = .TRUE.\n      WRITE( NOUT, FMT = 9999 )\n      DO 240 I = 1, M\n         IF( MV )THEN\n            WRITE( NOUT, FMT = 9998 )I, CT( I ), CC( I, J )\n         ELSE\n            WRITE( NOUT, FMT = 9998 )I, CC( I, J ), CT( I )\n         END IF\n  240 CONTINUE\n      IF( N.GT.1 )\n     $   WRITE( NOUT, FMT = 9997 )J\n*\n  250 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ******* FATAL ERROR - COMPUTED RESULT IS LESS THAN HAL',\n     $      'F ACCURATE *******', /'                       EXPECTED RE',\n     $      'SULT                    COMPUTED RESULT' )\n 9998 FORMAT( 1X, I7, 2( '  (', G15.6, ',', G15.6, ')' ) )\n 9997 FORMAT( '      THESE ARE THE RESULTS FOR COLUMN ', I3 )\n*\n*     End of CMMCH.\n*\n      END\n      LOGICAL FUNCTION LCE( RI, RJ, LR )\n*\n*  Tests if two arrays are identical.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Scalar Arguments ..\n      INTEGER            LR\n*     .. Array Arguments ..\n      COMPLEX            RI( * ), RJ( * )\n*     .. Local Scalars ..\n      INTEGER            I\n*     .. Executable Statements ..\n      DO 10 I = 1, LR\n         IF( RI( I ).NE.RJ( I ) )\n     $      GO TO 20\n   10 CONTINUE\n      LCE = .TRUE.\n      GO TO 30\n   20 CONTINUE\n      LCE = .FALSE.\n   30 RETURN\n*\n*     End of LCE.\n*\n      END\n      LOGICAL FUNCTION LCERES( TYPE, UPLO, M, N, AA, AS, LDA )\n*\n*  Tests if selected elements in two arrays are equal.\n*\n*  TYPE is 'GE' or 'HE' or 'SY'.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Scalar Arguments ..\n      INTEGER            LDA, M, N\n      CHARACTER*1        UPLO\n      CHARACTER*2        TYPE\n*     .. Array Arguments ..\n      COMPLEX            AA( LDA, * ), AS( LDA, * )\n*     .. Local Scalars ..\n      INTEGER            I, IBEG, IEND, J\n      LOGICAL            UPPER\n*     .. Executable Statements ..\n      UPPER = UPLO.EQ.'U'\n      IF( TYPE.EQ.'GE' )THEN\n         DO 20 J = 1, N\n            DO 10 I = M + 1, LDA\n               IF( AA( I, J ).NE.AS( I, J ) )\n     $            GO TO 70\n   10       CONTINUE\n   20    CONTINUE\n      ELSE IF( TYPE.EQ.'HE'.OR.TYPE.EQ.'SY' )THEN\n         DO 50 J = 1, N\n            IF( UPPER )THEN\n               IBEG = 1\n               IEND = J\n            ELSE\n               IBEG = J\n               IEND = N\n            END IF\n            DO 30 I = 1, IBEG - 1\n               IF( AA( I, J ).NE.AS( I, J ) )\n     $            GO TO 70\n   30       CONTINUE\n            DO 40 I = IEND + 1, LDA\n               IF( AA( I, J ).NE.AS( I, J ) )\n     $            GO TO 70\n   40       CONTINUE\n   50    CONTINUE\n      END IF\n*\n      LCERES = .TRUE.\n      GO TO 80\n   70 CONTINUE\n      LCERES = .FALSE.\n   80 RETURN\n*\n*     End of LCERES.\n*\n      END\n      COMPLEX FUNCTION CBEG( RESET )\n*\n*  Generates complex numbers as pairs of random numbers uniformly\n*  distributed between -0.5 and 0.5.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Scalar Arguments ..\n      LOGICAL            RESET\n*     .. Local Scalars ..\n      INTEGER            I, IC, J, MI, MJ\n*     .. Save statement ..\n      SAVE               I, IC, J, MI, MJ\n*     .. Intrinsic Functions ..\n      INTRINSIC          CMPLX\n*     .. Executable Statements ..\n      IF( RESET )THEN\n*        Initialize local variables.\n         MI = 891\n         MJ = 457\n         I = 7\n         J = 7\n         IC = 0\n         RESET = .FALSE.\n      END IF\n*\n*     The sequence of values of I or J is bounded between 1 and 999.\n*     If initial I or J = 1,2,3,6,7 or 9, the period will be 50.\n*     If initial I or J = 4 or 8, the period will be 25.\n*     If initial I or J = 5, the period will be 10.\n*     IC is used to break up the period by skipping 1 value of I or J\n*     in 6.\n*\n      IC = IC + 1\n   10 I = I*MI\n      J = J*MJ\n      I = I - 1000*( I/1000 )\n      J = J - 1000*( J/1000 )\n      IF( IC.GE.5 )THEN\n         IC = 0\n         GO TO 10\n      END IF\n      CBEG = CMPLX( ( I - 500 )/1001.0, ( J - 500 )/1001.0 )\n      RETURN\n*\n*     End of CBEG.\n*\n      END\n      REAL FUNCTION SDIFF( X, Y )\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Scalar Arguments ..\n      REAL               X, Y\n*     .. Executable Statements ..\n      SDIFF = X - Y\n      RETURN\n*\n*     End of SDIFF.\n*\n      END\n      SUBROUTINE CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n*\n*  Tests whether XERBLA has detected an error when it should.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Scalar Arguments ..\n      INTEGER            INFOT, NOUT\n      LOGICAL            LERR, OK\n      CHARACTER*6        SRNAMT\n*     .. Executable Statements ..\n      IF( .NOT.LERR )THEN\n         WRITE( NOUT, FMT = 9999 )INFOT, SRNAMT\n         OK = .FALSE.\n      END IF\n      LERR = .FALSE.\n      RETURN\n*\n 9999 FORMAT( ' ***** ILLEGAL VALUE OF PARAMETER NUMBER ', I2, ' NOT D',\n     $      'ETECTED BY ', A6, ' *****' )\n*\n*     End of CHKXER.\n*\n      END\n      SUBROUTINE XERBLA( SRNAME, INFO )\n*\n*  This is a special version of XERBLA to be used only as part of\n*  the test program for testing error exits from the Level 3 BLAS\n*  routines.\n*\n*  XERBLA  is an error handler for the Level 3 BLAS routines.\n*\n*  It is called by the Level 3 BLAS routines if an input parameter is\n*  invalid.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Scalar Arguments ..\n      INTEGER            INFO\n      CHARACTER*6        SRNAME\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUT\n      LOGICAL            LERR, OK\n      CHARACTER*6        SRNAMT\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUT, OK, LERR\n      COMMON             /SRNAMC/SRNAMT\n*     .. Executable Statements ..\n      LERR = .TRUE.\n      IF( INFO.NE.INFOT )THEN\n         IF( INFOT.NE.0 )THEN\n            WRITE( NOUT, FMT = 9999 )INFO, INFOT\n         ELSE\n            WRITE( NOUT, FMT = 9997 )INFO\n         END IF\n         OK = .FALSE.\n      END IF\n      IF( SRNAME.NE.SRNAMT )THEN\n         WRITE( NOUT, FMT = 9998 )SRNAME, SRNAMT\n         OK = .FALSE.\n      END IF\n      RETURN\n*\n 9999 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6, ' INSTEAD',\n     $      ' OF ', I2, ' *******' )\n 9998 FORMAT( ' ******* XERBLA WAS CALLED WITH SRNAME = ', A6, ' INSTE',\n     $      'AD OF ', A6, ' *******' )\n 9997 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6,\n     $      ' *******' )\n*\n*     End of XERBLA\n*\n      END\n\n"
  },
  {
    "path": "include/eigen3/blas/testing/dblat1.f",
    "content": "*> \\brief \\b DBLAT1\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*  Definition:\n*  ===========\n*\n*       PROGRAM DBLAT1\n* \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*>    Test program for the DOUBLE PRECISION Level 1 BLAS.\n*>\n*>    Based upon the original BLAS test routine together with:\n*>    F06EAF Example Program Text\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date April 2012\n*\n*> \\ingroup double_blas_testing\n*\n*  =====================================================================\n      PROGRAM DBLAT1\n*\n*  -- Reference BLAS test routine (version 3.4.1) --\n*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     April 2012\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      INTEGER          NOUT\n      PARAMETER        (NOUT=6)\n*     .. Scalars in Common ..\n      INTEGER          ICASE, INCX, INCY, N\n      LOGICAL          PASS\n*     .. Local Scalars ..\n      DOUBLE PRECISION SFAC\n      INTEGER          IC\n*     .. External Subroutines ..\n      EXTERNAL         CHECK0, CHECK1, CHECK2, CHECK3, HEADER\n*     .. Common blocks ..\n      COMMON           /COMBLA/ICASE, N, INCX, INCY, PASS\n*     .. Data statements ..\n      DATA             SFAC/9.765625D-4/\n*     .. Executable Statements ..\n      WRITE (NOUT,99999)\n      DO 20 IC = 1, 13\n         ICASE = IC\n         CALL HEADER\n*\n*        .. Initialize  PASS,  INCX,  and INCY for a new case. ..\n*        .. the value 9999 for INCX or INCY will appear in the ..\n*        .. detailed  output, if any, for cases  that do not involve ..\n*        .. these parameters ..\n*\n         PASS = .TRUE.\n         INCX = 9999\n         INCY = 9999\n         IF (ICASE.EQ.3 .OR. ICASE.EQ.11) THEN\n            CALL CHECK0(SFAC)\n         ELSE IF (ICASE.EQ.7 .OR. ICASE.EQ.8 .OR. ICASE.EQ.9 .OR.\n     +            ICASE.EQ.10) THEN\n            CALL CHECK1(SFAC)\n         ELSE IF (ICASE.EQ.1 .OR. ICASE.EQ.2 .OR. ICASE.EQ.5 .OR.\n     +            ICASE.EQ.6 .OR. ICASE.EQ.12 .OR. ICASE.EQ.13) THEN\n            CALL CHECK2(SFAC)\n         ELSE IF (ICASE.EQ.4) THEN\n            CALL CHECK3(SFAC)\n         END IF\n*        -- Print\n         IF (PASS) WRITE (NOUT,99998)\n   20 CONTINUE\n      STOP\n*\n99999 FORMAT (' Real BLAS Test Program Results',/1X)\n99998 FORMAT ('                                    ----- PASS -----')\n      END\n      SUBROUTINE HEADER\n*     .. Parameters ..\n      INTEGER          NOUT\n      PARAMETER        (NOUT=6)\n*     .. Scalars in Common ..\n      INTEGER          ICASE, INCX, INCY, N\n      LOGICAL          PASS\n*     .. Local Arrays ..\n      CHARACTER*6      L(13)\n*     .. Common blocks ..\n      COMMON           /COMBLA/ICASE, N, INCX, INCY, PASS\n*     .. Data statements ..\n      DATA             L(1)/' DDOT '/\n      DATA             L(2)/'DAXPY '/\n      DATA             L(3)/'DROTG '/\n      DATA             L(4)/' DROT '/\n      DATA             L(5)/'DCOPY '/\n      DATA             L(6)/'DSWAP '/\n      DATA             L(7)/'DNRM2 '/\n      DATA             L(8)/'DASUM '/\n      DATA             L(9)/'DSCAL '/\n      DATA             L(10)/'IDAMAX'/\n      DATA             L(11)/'DROTMG'/\n      DATA             L(12)/'DROTM '/\n      DATA             L(13)/'DSDOT '/\n*     .. Executable Statements ..\n      WRITE (NOUT,99999) ICASE, L(ICASE)\n      RETURN\n*\n99999 FORMAT (/' Test of subprogram number',I3,12X,A6)\n      END\n      SUBROUTINE CHECK0(SFAC)\n*     .. Parameters ..\n      INTEGER           NOUT\n      PARAMETER         (NOUT=6)\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION  SFAC\n*     .. Scalars in Common ..\n      INTEGER           ICASE, INCX, INCY, N\n      LOGICAL           PASS\n*     .. Local Scalars ..\n      DOUBLE PRECISION  SA, SB, SC, SS, D12\n      INTEGER           I, K\n*     .. Local Arrays ..\n      DOUBLE PRECISION  DA1(8), DATRUE(8), DB1(8), DBTRUE(8), DC1(8),\n     $                  DS1(8), DAB(4,9), DTEMP(9), DTRUE(9,9)\n*     .. External Subroutines ..\n      EXTERNAL          DROTG, DROTMG, STEST1\n*     .. Common blocks ..\n      COMMON            /COMBLA/ICASE, N, INCX, INCY, PASS\n*     .. Data statements ..\n      DATA              DA1/0.3D0, 0.4D0, -0.3D0, -0.4D0, -0.3D0, 0.0D0,\n     +                  0.0D0, 1.0D0/\n      DATA              DB1/0.4D0, 0.3D0, 0.4D0, 0.3D0, -0.4D0, 0.0D0,\n     +                  1.0D0, 0.0D0/\n      DATA              DC1/0.6D0, 0.8D0, -0.6D0, 0.8D0, 0.6D0, 1.0D0,\n     +                  0.0D0, 1.0D0/\n      DATA              DS1/0.8D0, 0.6D0, 0.8D0, -0.6D0, 0.8D0, 0.0D0,\n     +                  1.0D0, 0.0D0/\n      DATA              DATRUE/0.5D0, 0.5D0, 0.5D0, -0.5D0, -0.5D0,\n     +                  0.0D0, 1.0D0, 1.0D0/\n      DATA              DBTRUE/0.0D0, 0.6D0, 0.0D0, -0.6D0, 0.0D0,\n     +                  0.0D0, 1.0D0, 0.0D0/\n*     INPUT FOR MODIFIED GIVENS\n      DATA DAB/ .1D0,.3D0,1.2D0,.2D0,\n     A          .7D0, .2D0, .6D0, 4.2D0,\n     B          0.D0,0.D0,0.D0,0.D0,\n     C          4.D0, -1.D0, 2.D0, 4.D0,\n     D          6.D-10, 2.D-2, 1.D5, 10.D0,\n     E          4.D10, 2.D-2, 1.D-5, 10.D0,\n     F          2.D-10, 4.D-2, 1.D5, 10.D0,\n     G          2.D10, 4.D-2, 1.D-5, 10.D0,\n     H          4.D0, -2.D0, 8.D0, 4.D0    /\n*    TRUE RESULTS FOR MODIFIED GIVENS\n      DATA DTRUE/0.D0,0.D0, 1.3D0, .2D0, 0.D0,0.D0,0.D0, .5D0, 0.D0,\n     A           0.D0,0.D0, 4.5D0, 4.2D0, 1.D0, .5D0, 0.D0,0.D0,0.D0,\n     B           0.D0,0.D0,0.D0,0.D0, -2.D0, 0.D0,0.D0,0.D0,0.D0,\n     C           0.D0,0.D0,0.D0, 4.D0, -1.D0, 0.D0,0.D0,0.D0,0.D0,\n     D           0.D0, 15.D-3, 0.D0, 10.D0, -1.D0, 0.D0, -1.D-4,\n     E           0.D0, 1.D0,\n     F           0.D0,0.D0, 6144.D-5, 10.D0, -1.D0, 4096.D0, -1.D6,\n     G           0.D0, 1.D0,\n     H           0.D0,0.D0,15.D0,10.D0,-1.D0, 5.D-5, 0.D0,1.D0,0.D0,\n     I           0.D0,0.D0, 15.D0, 10.D0, -1. D0, 5.D5, -4096.D0,\n     J           1.D0, 4096.D-6,\n     K           0.D0,0.D0, 7.D0, 4.D0, 0.D0,0.D0, -.5D0, -.25D0, 0.D0/\n*                   4096 = 2 ** 12\n      DATA D12  /4096.D0/\n      DTRUE(1,1) = 12.D0 / 130.D0\n      DTRUE(2,1) = 36.D0 / 130.D0\n      DTRUE(7,1) = -1.D0 / 6.D0\n      DTRUE(1,2) = 14.D0 / 75.D0\n      DTRUE(2,2) = 49.D0 / 75.D0\n      DTRUE(9,2) = 1.D0 / 7.D0\n      DTRUE(1,5) = 45.D-11 * (D12 * D12)\n      DTRUE(3,5) = 4.D5 / (3.D0 * D12)\n      DTRUE(6,5) = 1.D0 / D12\n      DTRUE(8,5) = 1.D4 / (3.D0 * D12)\n      DTRUE(1,6) = 4.D10 / (1.5D0 * D12 * D12)\n      DTRUE(2,6) = 2.D-2 / 1.5D0\n      DTRUE(8,6) = 5.D-7 * D12\n      DTRUE(1,7) = 4.D0 / 150.D0\n      DTRUE(2,7) = (2.D-10 / 1.5D0) * (D12 * D12)\n      DTRUE(7,7) = -DTRUE(6,5)\n      DTRUE(9,7) = 1.D4 / D12\n      DTRUE(1,8) = DTRUE(1,7)\n      DTRUE(2,8) = 2.D10 / (1.5D0 * D12 * D12)\n      DTRUE(1,9) = 32.D0 / 7.D0\n      DTRUE(2,9) = -16.D0 / 7.D0\n*     .. Executable Statements ..\n*\n*     Compute true values which cannot be prestored\n*     in decimal notation\n*\n      DBTRUE(1) = 1.0D0/0.6D0\n      DBTRUE(3) = -1.0D0/0.6D0\n      DBTRUE(5) = 1.0D0/0.6D0\n*\n      DO 20 K = 1, 8\n*        .. Set N=K for identification in output if any ..\n         N = K\n         IF (ICASE.EQ.3) THEN\n*           .. DROTG ..\n            IF (K.GT.8) GO TO 40\n            SA = DA1(K)\n            SB = DB1(K)\n            CALL DROTG(SA,SB,SC,SS)\n            CALL STEST1(SA,DATRUE(K),DATRUE(K),SFAC)\n            CALL STEST1(SB,DBTRUE(K),DBTRUE(K),SFAC)\n            CALL STEST1(SC,DC1(K),DC1(K),SFAC)\n            CALL STEST1(SS,DS1(K),DS1(K),SFAC)\n         ELSEIF (ICASE.EQ.11) THEN\n*           .. DROTMG ..\n            DO I=1,4\n               DTEMP(I)= DAB(I,K)\n               DTEMP(I+4) = 0.0\n            END DO\n            DTEMP(9) = 0.0\n            CALL DROTMG(DTEMP(1),DTEMP(2),DTEMP(3),DTEMP(4),DTEMP(5))\n            CALL STEST(9,DTEMP,DTRUE(1,K),DTRUE(1,K),SFAC)\n         ELSE\n            WRITE (NOUT,*) ' Shouldn''t be here in CHECK0'\n            STOP\n         END IF\n   20 CONTINUE\n   40 RETURN\n      END\n      SUBROUTINE CHECK1(SFAC)\n*     .. Parameters ..\n      INTEGER           NOUT\n      PARAMETER         (NOUT=6)\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION  SFAC\n*     .. Scalars in Common ..\n      INTEGER           ICASE, INCX, INCY, N\n      LOGICAL           PASS\n*     .. Local Scalars ..\n      INTEGER           I, LEN, NP1\n*     .. Local Arrays ..\n      DOUBLE PRECISION  DTRUE1(5), DTRUE3(5), DTRUE5(8,5,2), DV(8,5,2),\n     +                  SA(10), STEMP(1), STRUE(8), SX(8)\n      INTEGER           ITRUE2(5)\n*     .. External Functions ..\n      DOUBLE PRECISION  DASUM, DNRM2\n      INTEGER           IDAMAX\n      EXTERNAL          DASUM, DNRM2, IDAMAX\n*     .. External Subroutines ..\n      EXTERNAL          ITEST1, DSCAL, STEST, STEST1\n*     .. Intrinsic Functions ..\n      INTRINSIC         MAX\n*     .. Common blocks ..\n      COMMON            /COMBLA/ICASE, N, INCX, INCY, PASS\n*     .. Data statements ..\n      DATA              SA/0.3D0, -1.0D0, 0.0D0, 1.0D0, 0.3D0, 0.3D0,\n     +                  0.3D0, 0.3D0, 0.3D0, 0.3D0/\n      DATA              DV/0.1D0, 2.0D0, 2.0D0, 2.0D0, 2.0D0, 2.0D0,\n     +                  2.0D0, 2.0D0, 0.3D0, 3.0D0, 3.0D0, 3.0D0, 3.0D0,\n     +                  3.0D0, 3.0D0, 3.0D0, 0.3D0, -0.4D0, 4.0D0,\n     +                  4.0D0, 4.0D0, 4.0D0, 4.0D0, 4.0D0, 0.2D0,\n     +                  -0.6D0, 0.3D0, 5.0D0, 5.0D0, 5.0D0, 5.0D0,\n     +                  5.0D0, 0.1D0, -0.3D0, 0.5D0, -0.1D0, 6.0D0,\n     +                  6.0D0, 6.0D0, 6.0D0, 0.1D0, 8.0D0, 8.0D0, 8.0D0,\n     +                  8.0D0, 8.0D0, 8.0D0, 8.0D0, 0.3D0, 9.0D0, 9.0D0,\n     +                  9.0D0, 9.0D0, 9.0D0, 9.0D0, 9.0D0, 0.3D0, 2.0D0,\n     +                  -0.4D0, 2.0D0, 2.0D0, 2.0D0, 2.0D0, 2.0D0,\n     +                  0.2D0, 3.0D0, -0.6D0, 5.0D0, 0.3D0, 2.0D0,\n     +                  2.0D0, 2.0D0, 0.1D0, 4.0D0, -0.3D0, 6.0D0,\n     +                  -0.5D0, 7.0D0, -0.1D0, 3.0D0/\n      DATA              DTRUE1/0.0D0, 0.3D0, 0.5D0, 0.7D0, 0.6D0/\n      DATA              DTRUE3/0.0D0, 0.3D0, 0.7D0, 1.1D0, 1.0D0/\n      DATA              DTRUE5/0.10D0, 2.0D0, 2.0D0, 2.0D0, 2.0D0,\n     +                  2.0D0, 2.0D0, 2.0D0, -0.3D0, 3.0D0, 3.0D0,\n     +                  3.0D0, 3.0D0, 3.0D0, 3.0D0, 3.0D0, 0.0D0, 0.0D0,\n     +                  4.0D0, 4.0D0, 4.0D0, 4.0D0, 4.0D0, 4.0D0,\n     +                  0.20D0, -0.60D0, 0.30D0, 5.0D0, 5.0D0, 5.0D0,\n     +                  5.0D0, 5.0D0, 0.03D0, -0.09D0, 0.15D0, -0.03D0,\n     +                  6.0D0, 6.0D0, 6.0D0, 6.0D0, 0.10D0, 8.0D0,\n     +                  8.0D0, 8.0D0, 8.0D0, 8.0D0, 8.0D0, 8.0D0,\n     +                  0.09D0, 9.0D0, 9.0D0, 9.0D0, 9.0D0, 9.0D0,\n     +                  9.0D0, 9.0D0, 0.09D0, 2.0D0, -0.12D0, 2.0D0,\n     +                  2.0D0, 2.0D0, 2.0D0, 2.0D0, 0.06D0, 3.0D0,\n     +                  -0.18D0, 5.0D0, 0.09D0, 2.0D0, 2.0D0, 2.0D0,\n     +                  0.03D0, 4.0D0, -0.09D0, 6.0D0, -0.15D0, 7.0D0,\n     +                  -0.03D0, 3.0D0/\n      DATA              ITRUE2/0, 1, 2, 2, 3/\n*     .. Executable Statements ..\n      DO 80 INCX = 1, 2\n         DO 60 NP1 = 1, 5\n            N = NP1 - 1\n            LEN = 2*MAX(N,1)\n*           .. Set vector arguments ..\n            DO 20 I = 1, LEN\n               SX(I) = DV(I,NP1,INCX)\n   20       CONTINUE\n*\n            IF (ICASE.EQ.7) THEN\n*              .. DNRM2 ..\n               STEMP(1) = DTRUE1(NP1)\n               CALL STEST1(DNRM2(N,SX,INCX),STEMP(1),STEMP,SFAC)\n            ELSE IF (ICASE.EQ.8) THEN\n*              .. DASUM ..\n               STEMP(1) = DTRUE3(NP1)\n               CALL STEST1(DASUM(N,SX,INCX),STEMP(1),STEMP,SFAC)\n            ELSE IF (ICASE.EQ.9) THEN\n*              .. DSCAL ..\n               CALL DSCAL(N,SA((INCX-1)*5+NP1),SX,INCX)\n               DO 40 I = 1, LEN\n                  STRUE(I) = DTRUE5(I,NP1,INCX)\n   40          CONTINUE\n               CALL STEST(LEN,SX,STRUE,STRUE,SFAC)\n            ELSE IF (ICASE.EQ.10) THEN\n*              .. IDAMAX ..\n               CALL ITEST1(IDAMAX(N,SX,INCX),ITRUE2(NP1))\n            ELSE\n               WRITE (NOUT,*) ' Shouldn''t be here in CHECK1'\n               STOP\n            END IF\n   60    CONTINUE\n   80 CONTINUE\n      RETURN\n      END\n      SUBROUTINE CHECK2(SFAC)\n*     .. Parameters ..\n      INTEGER           NOUT\n      PARAMETER         (NOUT=6)\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION  SFAC\n*     .. Scalars in Common ..\n      INTEGER           ICASE, INCX, INCY, N\n      LOGICAL           PASS\n*     .. Local Scalars ..\n      DOUBLE PRECISION  SA\n      INTEGER           I, J, KI, KN, KNI, KPAR, KSIZE, LENX, LENY,\n     $                  MX, MY \n*     .. Local Arrays ..\n      DOUBLE PRECISION  DT10X(7,4,4), DT10Y(7,4,4), DT7(4,4),\n     $                  DT8(7,4,4), DX1(7),\n     $                  DY1(7), SSIZE1(4), SSIZE2(14,2), SSIZE(7),\n     $                  STX(7), STY(7), SX(7), SY(7),\n     $                  DPAR(5,4), DT19X(7,4,16),DT19XA(7,4,4),\n     $                  DT19XB(7,4,4), DT19XC(7,4,4),DT19XD(7,4,4),\n     $                  DT19Y(7,4,16), DT19YA(7,4,4),DT19YB(7,4,4),\n     $                  DT19YC(7,4,4), DT19YD(7,4,4), DTEMP(5)\n      INTEGER           INCXS(4), INCYS(4), LENS(4,2), NS(4)\n*     .. External Functions ..\n      DOUBLE PRECISION  DDOT, DSDOT\n      EXTERNAL          DDOT, DSDOT\n*     .. External Subroutines ..\n      EXTERNAL          DAXPY, DCOPY, DROTM, DSWAP, STEST, STEST1\n*     .. Intrinsic Functions ..\n      INTRINSIC         ABS, MIN\n*     .. Common blocks ..\n      COMMON            /COMBLA/ICASE, N, INCX, INCY, PASS\n*     .. Data statements ..\n      EQUIVALENCE (DT19X(1,1,1),DT19XA(1,1,1)),(DT19X(1,1,5),\n     A   DT19XB(1,1,1)),(DT19X(1,1,9),DT19XC(1,1,1)),\n     B   (DT19X(1,1,13),DT19XD(1,1,1))\n      EQUIVALENCE (DT19Y(1,1,1),DT19YA(1,1,1)),(DT19Y(1,1,5),\n     A   DT19YB(1,1,1)),(DT19Y(1,1,9),DT19YC(1,1,1)),\n     B   (DT19Y(1,1,13),DT19YD(1,1,1))\n\n      DATA              SA/0.3D0/\n      DATA              INCXS/1, 2, -2, -1/\n      DATA              INCYS/1, -2, 1, -2/\n      DATA              LENS/1, 1, 2, 4, 1, 1, 3, 7/\n      DATA              NS/0, 1, 2, 4/\n      DATA              DX1/0.6D0, 0.1D0, -0.5D0, 0.8D0, 0.9D0, -0.3D0,\n     +                  -0.4D0/\n      DATA              DY1/0.5D0, -0.9D0, 0.3D0, 0.7D0, -0.6D0, 0.2D0,\n     +                  0.8D0/\n      DATA              DT7/0.0D0, 0.30D0, 0.21D0, 0.62D0, 0.0D0,\n     +                  0.30D0, -0.07D0, 0.85D0, 0.0D0, 0.30D0, -0.79D0,\n     +                  -0.74D0, 0.0D0, 0.30D0, 0.33D0, 1.27D0/\n      DATA              DT8/0.5D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.68D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.0D0, 0.68D0, -0.87D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.0D0, 0.0D0, 0.68D0, -0.87D0, 0.15D0,\n     +                  0.94D0, 0.0D0, 0.0D0, 0.0D0, 0.5D0, 0.0D0,\n     +                  0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.68D0,\n     +                  0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.35D0, -0.9D0, 0.48D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.38D0, -0.9D0, 0.57D0, 0.7D0, -0.75D0,\n     +                  0.2D0, 0.98D0, 0.5D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.0D0, 0.0D0, 0.68D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.35D0, -0.72D0,\n     +                  0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.38D0,\n     +                  -0.63D0, 0.15D0, 0.88D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.5D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.68D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.68D0, -0.9D0, 0.33D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.0D0, 0.68D0, -0.9D0, 0.33D0, 0.7D0,\n     +                  -0.75D0, 0.2D0, 1.04D0/\n      DATA              DT10X/0.6D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.5D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.5D0, -0.9D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.0D0, 0.5D0, -0.9D0, 0.3D0, 0.7D0,\n     +                  0.0D0, 0.0D0, 0.0D0, 0.6D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.0D0, 0.0D0, 0.5D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.0D0, 0.0D0, 0.3D0, 0.1D0, 0.5D0, 0.0D0,\n     +                  0.0D0, 0.0D0, 0.0D0, 0.8D0, 0.1D0, -0.6D0,\n     +                  0.8D0, 0.3D0, -0.3D0, 0.5D0, 0.6D0, 0.0D0,\n     +                  0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.5D0, 0.0D0,\n     +                  0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, -0.9D0,\n     +                  0.1D0, 0.5D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.7D0,\n     +                  0.1D0, 0.3D0, 0.8D0, -0.9D0, -0.3D0, 0.5D0,\n     +                  0.6D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.5D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.5D0, 0.3D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.5D0, 0.3D0, -0.6D0, 0.8D0, 0.0D0, 0.0D0,\n     +                  0.0D0/\n      DATA              DT10Y/0.5D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.6D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.6D0, 0.1D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.6D0, 0.1D0, -0.5D0, 0.8D0, 0.0D0,\n     +                  0.0D0, 0.0D0, 0.5D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.0D0, 0.6D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.0D0, -0.5D0, -0.9D0, 0.6D0, 0.0D0,\n     +                  0.0D0, 0.0D0, 0.0D0, -0.4D0, -0.9D0, 0.9D0,\n     +                  0.7D0, -0.5D0, 0.2D0, 0.6D0, 0.5D0, 0.0D0,\n     +                  0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.6D0, 0.0D0,\n     +                  0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, -0.5D0,\n     +                  0.6D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  -0.4D0, 0.9D0, -0.5D0, 0.6D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.5D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.6D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.6D0, -0.9D0, 0.1D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.0D0, 0.6D0, -0.9D0, 0.1D0, 0.7D0,\n     +                  -0.5D0, 0.2D0, 0.8D0/\n      DATA              SSIZE1/0.0D0, 0.3D0, 1.6D0, 3.2D0/\n      DATA              SSIZE2/0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 1.17D0, 1.17D0, 1.17D0, 1.17D0, 1.17D0,\n     +                  1.17D0, 1.17D0, 1.17D0, 1.17D0, 1.17D0, 1.17D0,\n     +                  1.17D0, 1.17D0, 1.17D0/\n*\n*                         FOR DROTM\n*\n      DATA DPAR/-2.D0,  0.D0,0.D0,0.D0,0.D0,\n     A          -1.D0,  2.D0, -3.D0, -4.D0,  5.D0,\n     B           0.D0,  0.D0,  2.D0, -3.D0,  0.D0,\n     C           1.D0,  5.D0,  2.D0,  0.D0, -4.D0/\n*                        TRUE X RESULTS F0R ROTATIONS DROTM\n      DATA DT19XA/.6D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     A            .6D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     B            .6D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     C            .6D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     D            .6D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     E           -.8D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     F           -.9D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     G           3.5D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     H            .6D0,   .1D0,             0.D0,0.D0,0.D0,0.D0,0.D0,\n     I           -.8D0,  3.8D0,             0.D0,0.D0,0.D0,0.D0,0.D0,\n     J           -.9D0,  2.8D0,             0.D0,0.D0,0.D0,0.D0,0.D0,\n     K           3.5D0,  -.4D0,             0.D0,0.D0,0.D0,0.D0,0.D0,\n     L            .6D0,   .1D0,  -.5D0,   .8D0,          0.D0,0.D0,0.D0,\n     M           -.8D0,  3.8D0, -2.2D0, -1.2D0,          0.D0,0.D0,0.D0,\n     N           -.9D0,  2.8D0, -1.4D0, -1.3D0,          0.D0,0.D0,0.D0,\n     O           3.5D0,  -.4D0, -2.2D0,  4.7D0,          0.D0,0.D0,0.D0/\n*\n      DATA DT19XB/.6D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     A            .6D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     B            .6D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     C            .6D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     D            .6D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     E           -.8D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     F           -.9D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     G           3.5D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     H            .6D0,   .1D0,  -.5D0,             0.D0,0.D0,0.D0,0.D0,\n     I           0.D0,    .1D0, -3.0D0,             0.D0,0.D0,0.D0,0.D0,\n     J           -.3D0,   .1D0, -2.0D0,             0.D0,0.D0,0.D0,0.D0,\n     K           3.3D0,   .1D0, -2.0D0,             0.D0,0.D0,0.D0,0.D0,\n     L            .6D0,   .1D0,  -.5D0,   .8D0,   .9D0,  -.3D0,  -.4D0,\n     M          -2.0D0,   .1D0,  1.4D0,   .8D0,   .6D0,  -.3D0, -2.8D0,\n     N          -1.8D0,   .1D0,  1.3D0,   .8D0,  0.D0,   -.3D0, -1.9D0,\n     O           3.8D0,   .1D0, -3.1D0,   .8D0,  4.8D0,  -.3D0, -1.5D0 /\n*\n      DATA DT19XC/.6D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     A            .6D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     B            .6D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     C            .6D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     D            .6D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     E           -.8D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     F           -.9D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     G           3.5D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     H            .6D0,   .1D0,  -.5D0,             0.D0,0.D0,0.D0,0.D0,\n     I           4.8D0,   .1D0, -3.0D0,             0.D0,0.D0,0.D0,0.D0,\n     J           3.3D0,   .1D0, -2.0D0,             0.D0,0.D0,0.D0,0.D0,\n     K           2.1D0,   .1D0, -2.0D0,             0.D0,0.D0,0.D0,0.D0,\n     L            .6D0,   .1D0,  -.5D0,   .8D0,   .9D0,  -.3D0,  -.4D0,\n     M          -1.6D0,   .1D0, -2.2D0,   .8D0,  5.4D0,  -.3D0, -2.8D0,\n     N          -1.5D0,   .1D0, -1.4D0,   .8D0,  3.6D0,  -.3D0, -1.9D0,\n     O           3.7D0,   .1D0, -2.2D0,   .8D0,  3.6D0,  -.3D0, -1.5D0 /\n*\n      DATA DT19XD/.6D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     A            .6D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     B            .6D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     C            .6D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     D            .6D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     E           -.8D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     F           -.9D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     G           3.5D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     H            .6D0,   .1D0,             0.D0,0.D0,0.D0,0.D0,0.D0,\n     I           -.8D0, -1.0D0,             0.D0,0.D0,0.D0,0.D0,0.D0,\n     J           -.9D0,  -.8D0,             0.D0,0.D0,0.D0,0.D0,0.D0,\n     K           3.5D0,   .8D0,             0.D0,0.D0,0.D0,0.D0,0.D0,\n     L            .6D0,   .1D0,  -.5D0,   .8D0,          0.D0,0.D0,0.D0,\n     M           -.8D0, -1.0D0,  1.4D0, -1.6D0,          0.D0,0.D0,0.D0,\n     N           -.9D0,  -.8D0,  1.3D0, -1.6D0,          0.D0,0.D0,0.D0,\n     O           3.5D0,   .8D0, -3.1D0,  4.8D0,          0.D0,0.D0,0.D0/\n*                        TRUE Y RESULTS FOR ROTATIONS DROTM\n      DATA DT19YA/.5D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     A            .5D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     B            .5D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     C            .5D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     D            .5D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     E            .7D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     F           1.7D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     G          -2.6D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     H            .5D0,  -.9D0,             0.D0,0.D0,0.D0,0.D0,0.D0,\n     I            .7D0, -4.8D0,             0.D0,0.D0,0.D0,0.D0,0.D0,\n     J           1.7D0,  -.7D0,             0.D0,0.D0,0.D0,0.D0,0.D0,\n     K          -2.6D0,  3.5D0,             0.D0,0.D0,0.D0,0.D0,0.D0,\n     L            .5D0,  -.9D0,   .3D0,   .7D0,          0.D0,0.D0,0.D0,\n     M            .7D0, -4.8D0,  3.0D0,  1.1D0,          0.D0,0.D0,0.D0,\n     N           1.7D0,  -.7D0,  -.7D0,  2.3D0,          0.D0,0.D0,0.D0,\n     O          -2.6D0,  3.5D0,  -.7D0, -3.6D0,          0.D0,0.D0,0.D0/\n*\n      DATA DT19YB/.5D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     A            .5D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     B            .5D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     C            .5D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     D            .5D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     E            .7D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     F           1.7D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     G          -2.6D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     H            .5D0,  -.9D0,   .3D0,             0.D0,0.D0,0.D0,0.D0,\n     I           4.0D0,  -.9D0,  -.3D0,             0.D0,0.D0,0.D0,0.D0,\n     J           -.5D0,  -.9D0,  1.5D0,             0.D0,0.D0,0.D0,0.D0,\n     K          -1.5D0,  -.9D0, -1.8D0,             0.D0,0.D0,0.D0,0.D0,\n     L            .5D0,  -.9D0,   .3D0,   .7D0,  -.6D0,   .2D0,   .8D0,\n     M           3.7D0,  -.9D0, -1.2D0,   .7D0, -1.5D0,   .2D0,  2.2D0,\n     N           -.3D0,  -.9D0,  2.1D0,   .7D0, -1.6D0,   .2D0,  2.0D0,\n     O          -1.6D0,  -.9D0, -2.1D0,   .7D0,  2.9D0,   .2D0, -3.8D0 /\n*\n      DATA DT19YC/.5D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     A            .5D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     B            .5D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     C            .5D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     D            .5D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     E            .7D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     F           1.7D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     G          -2.6D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     H            .5D0,  -.9D0,             0.D0,0.D0,0.D0,0.D0,0.D0,\n     I           4.0D0, -6.3D0,             0.D0,0.D0,0.D0,0.D0,0.D0,\n     J           -.5D0,   .3D0,             0.D0,0.D0,0.D0,0.D0,0.D0,\n     K          -1.5D0,  3.0D0,             0.D0,0.D0,0.D0,0.D0,0.D0,\n     L            .5D0,  -.9D0,   .3D0,   .7D0,          0.D0,0.D0,0.D0,\n     M           3.7D0, -7.2D0,  3.0D0,  1.7D0,          0.D0,0.D0,0.D0,\n     N           -.3D0,   .9D0,  -.7D0,  1.9D0,          0.D0,0.D0,0.D0,\n     O          -1.6D0,  2.7D0,  -.7D0, -3.4D0,          0.D0,0.D0,0.D0/\n*\n      DATA DT19YD/.5D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     A            .5D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     B            .5D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     C            .5D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     D            .5D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     E            .7D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     F           1.7D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     G          -2.6D0,                  0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,\n     H            .5D0,  -.9D0,   .3D0,             0.D0,0.D0,0.D0,0.D0,\n     I            .7D0,  -.9D0,  1.2D0,             0.D0,0.D0,0.D0,0.D0,\n     J           1.7D0,  -.9D0,   .5D0,             0.D0,0.D0,0.D0,0.D0,\n     K          -2.6D0,  -.9D0, -1.3D0,             0.D0,0.D0,0.D0,0.D0,\n     L            .5D0,  -.9D0,   .3D0,   .7D0,  -.6D0,   .2D0,   .8D0,\n     M            .7D0,  -.9D0,  1.2D0,   .7D0, -1.5D0,   .2D0,  1.6D0,\n     N           1.7D0,  -.9D0,   .5D0,   .7D0, -1.6D0,   .2D0,  2.4D0,\n     O          -2.6D0,  -.9D0, -1.3D0,   .7D0,  2.9D0,   .2D0, -4.0D0 /\n*    \n*     .. Executable Statements ..\n*\n      DO 120 KI = 1, 4\n         INCX = INCXS(KI)\n         INCY = INCYS(KI)\n         MX = ABS(INCX)\n         MY = ABS(INCY)\n*\n         DO 100 KN = 1, 4\n            N = NS(KN)\n            KSIZE = MIN(2,KN)\n            LENX = LENS(KN,MX)\n            LENY = LENS(KN,MY)\n*           .. Initialize all argument arrays ..\n            DO 20 I = 1, 7\n               SX(I) = DX1(I)\n               SY(I) = DY1(I)\n   20       CONTINUE\n*\n            IF (ICASE.EQ.1) THEN\n*              .. DDOT ..\n               CALL STEST1(DDOT(N,SX,INCX,SY,INCY),DT7(KN,KI),SSIZE1(KN)\n     +                     ,SFAC)\n            ELSE IF (ICASE.EQ.2) THEN\n*              .. DAXPY ..\n               CALL DAXPY(N,SA,SX,INCX,SY,INCY)\n               DO 40 J = 1, LENY\n                  STY(J) = DT8(J,KN,KI)\n   40          CONTINUE\n               CALL STEST(LENY,SY,STY,SSIZE2(1,KSIZE),SFAC)\n            ELSE IF (ICASE.EQ.5) THEN\n*              .. DCOPY ..\n               DO 60 I = 1, 7\n                  STY(I) = DT10Y(I,KN,KI)\n   60          CONTINUE\n               CALL DCOPY(N,SX,INCX,SY,INCY)\n               CALL STEST(LENY,SY,STY,SSIZE2(1,1),1.0D0)\n            ELSE IF (ICASE.EQ.6) THEN\n*              .. DSWAP ..\n               CALL DSWAP(N,SX,INCX,SY,INCY)\n               DO 80 I = 1, 7\n                  STX(I) = DT10X(I,KN,KI)\n                  STY(I) = DT10Y(I,KN,KI)\n   80          CONTINUE\n               CALL STEST(LENX,SX,STX,SSIZE2(1,1),1.0D0)\n               CALL STEST(LENY,SY,STY,SSIZE2(1,1),1.0D0)\n            ELSE IF (ICASE.EQ.12) THEN\n*              .. DROTM ..\n               KNI=KN+4*(KI-1)\n               DO KPAR=1,4\n                  DO I=1,7\n                     SX(I) = DX1(I)\n                     SY(I) = DY1(I)\n                     STX(I)= DT19X(I,KPAR,KNI)\n                     STY(I)= DT19Y(I,KPAR,KNI)\n                  END DO\n*\n                  DO I=1,5\n                     DTEMP(I) = DPAR(I,KPAR)\n                  END DO\n*\n                  DO  I=1,LENX\n                     SSIZE(I)=STX(I)\n                  END DO\n*                   SEE REMARK ABOVE ABOUT DT11X(1,2,7)\n*                       AND DT11X(5,3,8).\n                  IF ((KPAR .EQ. 2) .AND. (KNI .EQ. 7))\n     $               SSIZE(1) = 2.4D0\n                  IF ((KPAR .EQ. 3) .AND. (KNI .EQ. 8))\n     $               SSIZE(5) = 1.8D0\n*\n                  CALL   DROTM(N,SX,INCX,SY,INCY,DTEMP)\n                  CALL   STEST(LENX,SX,STX,SSIZE,SFAC)\n                  CALL   STEST(LENY,SY,STY,STY,SFAC)\n               END DO\n            ELSE IF (ICASE.EQ.13) THEN\n*              .. DSDOT ..\n            CALL TESTDSDOT(REAL(DSDOT(N,REAL(SX),INCX,REAL(SY),INCY)),\n     $                 REAL(DT7(KN,KI)),REAL(SSIZE1(KN)), .3125E-1)\n            ELSE\n               WRITE (NOUT,*) ' Shouldn''t be here in CHECK2'\n               STOP\n            END IF\n  100    CONTINUE\n  120 CONTINUE\n      RETURN\n      END\n      SUBROUTINE CHECK3(SFAC)\n*     .. Parameters ..\n      INTEGER           NOUT\n      PARAMETER         (NOUT=6)\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION  SFAC\n*     .. Scalars in Common ..\n      INTEGER           ICASE, INCX, INCY, N\n      LOGICAL           PASS\n*     .. Local Scalars ..\n      DOUBLE PRECISION  SC, SS\n      INTEGER           I, K, KI, KN, KSIZE, LENX, LENY, MX, MY\n*     .. Local Arrays ..\n      DOUBLE PRECISION  COPYX(5), COPYY(5), DT9X(7,4,4), DT9Y(7,4,4),\n     +                  DX1(7), DY1(7), MWPC(11), MWPS(11), MWPSTX(5),\n     +                  MWPSTY(5), MWPTX(11,5), MWPTY(11,5), MWPX(5),\n     +                  MWPY(5), SSIZE2(14,2), STX(7), STY(7), SX(7),\n     +                  SY(7)\n      INTEGER           INCXS(4), INCYS(4), LENS(4,2), MWPINX(11),\n     +                  MWPINY(11), MWPN(11), NS(4)\n*     .. External Subroutines ..\n      EXTERNAL          DROT, STEST\n*     .. Intrinsic Functions ..\n      INTRINSIC         ABS, MIN\n*     .. Common blocks ..\n      COMMON            /COMBLA/ICASE, N, INCX, INCY, PASS\n*     .. Data statements ..\n      DATA              INCXS/1, 2, -2, -1/\n      DATA              INCYS/1, -2, 1, -2/\n      DATA              LENS/1, 1, 2, 4, 1, 1, 3, 7/\n      DATA              NS/0, 1, 2, 4/\n      DATA              DX1/0.6D0, 0.1D0, -0.5D0, 0.8D0, 0.9D0, -0.3D0,\n     +                  -0.4D0/\n      DATA              DY1/0.5D0, -0.9D0, 0.3D0, 0.7D0, -0.6D0, 0.2D0,\n     +                  0.8D0/\n      DATA              SC, SS/0.8D0, 0.6D0/\n      DATA              DT9X/0.6D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.78D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.0D0, 0.78D0, -0.46D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.0D0, 0.0D0, 0.78D0, -0.46D0, -0.22D0,\n     +                  1.06D0, 0.0D0, 0.0D0, 0.0D0, 0.6D0, 0.0D0,\n     +                  0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.78D0,\n     +                  0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.66D0, 0.1D0, -0.1D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.96D0, 0.1D0, -0.76D0, 0.8D0, 0.90D0,\n     +                  -0.3D0, -0.02D0, 0.6D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.0D0, 0.0D0, 0.78D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.0D0, 0.0D0, 0.0D0, -0.06D0, 0.1D0,\n     +                  -0.1D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.90D0,\n     +                  0.1D0, -0.22D0, 0.8D0, 0.18D0, -0.3D0, -0.02D0,\n     +                  0.6D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.78D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.78D0, 0.26D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.0D0, 0.78D0, 0.26D0, -0.76D0, 1.12D0,\n     +                  0.0D0, 0.0D0, 0.0D0/\n      DATA              DT9Y/0.5D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.04D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.0D0, 0.04D0, -0.78D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.0D0, 0.0D0, 0.04D0, -0.78D0, 0.54D0,\n     +                  0.08D0, 0.0D0, 0.0D0, 0.0D0, 0.5D0, 0.0D0,\n     +                  0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.04D0,\n     +                  0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.7D0,\n     +                  -0.9D0, -0.12D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.64D0, -0.9D0, -0.30D0, 0.7D0, -0.18D0, 0.2D0,\n     +                  0.28D0, 0.5D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.0D0, 0.04D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.0D0, 0.0D0, 0.7D0, -1.08D0, 0.0D0,\n     +                  0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.64D0, -1.26D0,\n     +                  0.54D0, 0.20D0, 0.0D0, 0.0D0, 0.0D0, 0.5D0,\n     +                  0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.04D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.04D0, -0.9D0, 0.18D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.0D0, 0.04D0, -0.9D0, 0.18D0, 0.7D0,\n     +                  -0.18D0, 0.2D0, 0.16D0/\n      DATA              SSIZE2/0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,\n     +                  0.0D0, 1.17D0, 1.17D0, 1.17D0, 1.17D0, 1.17D0,\n     +                  1.17D0, 1.17D0, 1.17D0, 1.17D0, 1.17D0, 1.17D0,\n     +                  1.17D0, 1.17D0, 1.17D0/\n*     .. Executable Statements ..\n*\n      DO 60 KI = 1, 4\n         INCX = INCXS(KI)\n         INCY = INCYS(KI)\n         MX = ABS(INCX)\n         MY = ABS(INCY)\n*\n         DO 40 KN = 1, 4\n            N = NS(KN)\n            KSIZE = MIN(2,KN)\n            LENX = LENS(KN,MX)\n            LENY = LENS(KN,MY)\n*\n            IF (ICASE.EQ.4) THEN\n*              .. DROT ..\n               DO 20 I = 1, 7\n                  SX(I) = DX1(I)\n                  SY(I) = DY1(I)\n                  STX(I) = DT9X(I,KN,KI)\n                  STY(I) = DT9Y(I,KN,KI)\n   20          CONTINUE\n               CALL DROT(N,SX,INCX,SY,INCY,SC,SS)\n               CALL STEST(LENX,SX,STX,SSIZE2(1,KSIZE),SFAC)\n               CALL STEST(LENY,SY,STY,SSIZE2(1,KSIZE),SFAC)\n            ELSE\n               WRITE (NOUT,*) ' Shouldn''t be here in CHECK3'\n               STOP\n            END IF\n   40    CONTINUE\n   60 CONTINUE\n*\n      MWPC(1) = 1\n      DO 80 I = 2, 11\n         MWPC(I) = 0\n   80 CONTINUE\n      MWPS(1) = 0\n      DO 100 I = 2, 6\n         MWPS(I) = 1\n  100 CONTINUE\n      DO 120 I = 7, 11\n         MWPS(I) = -1\n  120 CONTINUE\n      MWPINX(1) = 1\n      MWPINX(2) = 1\n      MWPINX(3) = 1\n      MWPINX(4) = -1\n      MWPINX(5) = 1\n      MWPINX(6) = -1\n      MWPINX(7) = 1\n      MWPINX(8) = 1\n      MWPINX(9) = -1\n      MWPINX(10) = 1\n      MWPINX(11) = -1\n      MWPINY(1) = 1\n      MWPINY(2) = 1\n      MWPINY(3) = -1\n      MWPINY(4) = -1\n      MWPINY(5) = 2\n      MWPINY(6) = 1\n      MWPINY(7) = 1\n      MWPINY(8) = -1\n      MWPINY(9) = -1\n      MWPINY(10) = 2\n      MWPINY(11) = 1\n      DO 140 I = 1, 11\n         MWPN(I) = 5\n  140 CONTINUE\n      MWPN(5) = 3\n      MWPN(10) = 3\n      DO 160 I = 1, 5\n         MWPX(I) = I\n         MWPY(I) = I\n         MWPTX(1,I) = I\n         MWPTY(1,I) = I\n         MWPTX(2,I) = I\n         MWPTY(2,I) = -I\n         MWPTX(3,I) = 6 - I\n         MWPTY(3,I) = I - 6\n         MWPTX(4,I) = I\n         MWPTY(4,I) = -I\n         MWPTX(6,I) = 6 - I\n         MWPTY(6,I) = I - 6\n         MWPTX(7,I) = -I\n         MWPTY(7,I) = I\n         MWPTX(8,I) = I - 6\n         MWPTY(8,I) = 6 - I\n         MWPTX(9,I) = -I\n         MWPTY(9,I) = I\n         MWPTX(11,I) = I - 6\n         MWPTY(11,I) = 6 - I\n  160 CONTINUE\n      MWPTX(5,1) = 1\n      MWPTX(5,2) = 3\n      MWPTX(5,3) = 5\n      MWPTX(5,4) = 4\n      MWPTX(5,5) = 5\n      MWPTY(5,1) = -1\n      MWPTY(5,2) = 2\n      MWPTY(5,3) = -2\n      MWPTY(5,4) = 4\n      MWPTY(5,5) = -3\n      MWPTX(10,1) = -1\n      MWPTX(10,2) = -3\n      MWPTX(10,3) = -5\n      MWPTX(10,4) = 4\n      MWPTX(10,5) = 5\n      MWPTY(10,1) = 1\n      MWPTY(10,2) = 2\n      MWPTY(10,3) = 2\n      MWPTY(10,4) = 4\n      MWPTY(10,5) = 3\n      DO 200 I = 1, 11\n         INCX = MWPINX(I)\n         INCY = MWPINY(I)\n         DO 180 K = 1, 5\n            COPYX(K) = MWPX(K)\n            COPYY(K) = MWPY(K)\n            MWPSTX(K) = MWPTX(I,K)\n            MWPSTY(K) = MWPTY(I,K)\n  180    CONTINUE\n         CALL DROT(MWPN(I),COPYX,INCX,COPYY,INCY,MWPC(I),MWPS(I))\n         CALL STEST(5,COPYX,MWPSTX,MWPSTX,SFAC)\n         CALL STEST(5,COPYY,MWPSTY,MWPSTY,SFAC)\n  200 CONTINUE\n      RETURN\n      END\n      SUBROUTINE STEST(LEN,SCOMP,STRUE,SSIZE,SFAC)\n*     ********************************* STEST **************************\n*\n*     THIS SUBR COMPARES ARRAYS  SCOMP() AND STRUE() OF LENGTH LEN TO\n*     SEE IF THE TERM BY TERM DIFFERENCES, MULTIPLIED BY SFAC, ARE\n*     NEGLIGIBLE.\n*\n*     C. L. LAWSON, JPL, 1974 DEC 10\n*\n*     .. Parameters ..\n      INTEGER          NOUT\n      DOUBLE PRECISION ZERO\n      PARAMETER        (NOUT=6, ZERO=0.0D0)\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION SFAC\n      INTEGER          LEN\n*     .. Array Arguments ..\n      DOUBLE PRECISION SCOMP(LEN), SSIZE(LEN), STRUE(LEN)\n*     .. Scalars in Common ..\n      INTEGER          ICASE, INCX, INCY, N\n      LOGICAL          PASS\n*     .. Local Scalars ..\n      DOUBLE PRECISION SD\n      INTEGER          I\n*     .. External Functions ..\n      DOUBLE PRECISION SDIFF\n      EXTERNAL         SDIFF\n*     .. Intrinsic Functions ..\n      INTRINSIC        ABS\n*     .. Common blocks ..\n      COMMON           /COMBLA/ICASE, N, INCX, INCY, PASS\n*     .. Executable Statements ..\n*\n      DO 40 I = 1, LEN\n         SD = SCOMP(I) - STRUE(I)\n         IF (ABS(SFAC*SD) .LE. ABS(SSIZE(I))*EPSILON(ZERO))\n     +       GO TO 40\n*\n*                             HERE    SCOMP(I) IS NOT CLOSE TO STRUE(I).\n*\n         IF ( .NOT. PASS) GO TO 20\n*                             PRINT FAIL MESSAGE AND HEADER.\n         PASS = .FALSE.\n         WRITE (NOUT,99999)\n         WRITE (NOUT,99998)\n   20    WRITE (NOUT,99997) ICASE, N, INCX, INCY, I, SCOMP(I),\n     +     STRUE(I), SD, SSIZE(I)\n   40 CONTINUE\n      RETURN\n*\n99999 FORMAT ('                                       FAIL')\n99998 FORMAT (/' CASE  N INCX INCY  I                            ',\n     +       ' COMP(I)                             TRUE(I)  DIFFERENCE',\n     +       '     SIZE(I)',/1X)\n99997 FORMAT (1X,I4,I3,2I5,I3,2D36.8,2D12.4)\n      END\n      SUBROUTINE TESTDSDOT(SCOMP,STRUE,SSIZE,SFAC)\n*     ********************************* STEST **************************\n*\n*     THIS SUBR COMPARES ARRAYS  SCOMP() AND STRUE() OF LENGTH LEN TO\n*     SEE IF THE TERM BY TERM DIFFERENCES, MULTIPLIED BY SFAC, ARE\n*     NEGLIGIBLE.\n*\n*     C. L. LAWSON, JPL, 1974 DEC 10\n*\n*     .. Parameters ..\n      INTEGER          NOUT\n      REAL             ZERO\n      PARAMETER        (NOUT=6, ZERO=0.0E0)\n*     .. Scalar Arguments ..\n      REAL             SFAC, SCOMP, SSIZE, STRUE\n*     .. Scalars in Common ..\n      INTEGER          ICASE, INCX, INCY, N\n      LOGICAL          PASS\n*     .. Local Scalars ..\n      REAL             SD\n*     .. Intrinsic Functions ..\n      INTRINSIC        ABS\n*     .. Common blocks ..\n      COMMON           /COMBLA/ICASE, N, INCX, INCY, PASS\n*     .. Executable Statements ..\n*\n         SD = SCOMP - STRUE\n         IF (ABS(SFAC*SD) .LE. ABS(SSIZE) * EPSILON(ZERO))\n     +       GO TO 40\n*\n*                             HERE    SCOMP(I) IS NOT CLOSE TO STRUE(I).\n*\n         IF ( .NOT. PASS) GO TO 20\n*                             PRINT FAIL MESSAGE AND HEADER.\n         PASS = .FALSE.\n         WRITE (NOUT,99999)\n         WRITE (NOUT,99998)\n   20    WRITE (NOUT,99997) ICASE, N, INCX, INCY, SCOMP,\n     +     STRUE, SD, SSIZE\n   40 CONTINUE\n      RETURN\n*\n99999 FORMAT ('                                       FAIL')\n99998 FORMAT (/' CASE  N INCX INCY                           ',\n     +       ' COMP(I)                             TRUE(I)  DIFFERENCE',\n     +       '     SIZE(I)',/1X)\n99997 FORMAT (1X,I4,I3,1I5,I3,2E36.8,2E12.4)\n      END\n      SUBROUTINE STEST1(SCOMP1,STRUE1,SSIZE,SFAC)\n*     ************************* STEST1 *****************************\n*\n*     THIS IS AN INTERFACE SUBROUTINE TO ACCOMODATE THE FORTRAN\n*     REQUIREMENT THAT WHEN A DUMMY ARGUMENT IS AN ARRAY, THE\n*     ACTUAL ARGUMENT MUST ALSO BE AN ARRAY OR AN ARRAY ELEMENT.\n*\n*     C.L. LAWSON, JPL, 1978 DEC 6\n*\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION  SCOMP1, SFAC, STRUE1\n*     .. Array Arguments ..\n      DOUBLE PRECISION  SSIZE(*)\n*     .. Local Arrays ..\n      DOUBLE PRECISION  SCOMP(1), STRUE(1)\n*     .. External Subroutines ..\n      EXTERNAL          STEST\n*     .. Executable Statements ..\n*\n      SCOMP(1) = SCOMP1\n      STRUE(1) = STRUE1\n      CALL STEST(1,SCOMP,STRUE,SSIZE,SFAC)\n*\n      RETURN\n      END\n      DOUBLE PRECISION FUNCTION SDIFF(SA,SB)\n*     ********************************* SDIFF **************************\n*     COMPUTES DIFFERENCE OF TWO NUMBERS.  C. L. LAWSON, JPL 1974 FEB 15\n*\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION                SA, SB\n*     .. Executable Statements ..\n      SDIFF = SA - SB\n      RETURN\n      END\n      SUBROUTINE ITEST1(ICOMP,ITRUE)\n*     ********************************* ITEST1 *************************\n*\n*     THIS SUBROUTINE COMPARES THE VARIABLES ICOMP AND ITRUE FOR\n*     EQUALITY.\n*     C. L. LAWSON, JPL, 1974 DEC 10\n*\n*     .. Parameters ..\n      INTEGER           NOUT\n      PARAMETER         (NOUT=6)\n*     .. Scalar Arguments ..\n      INTEGER           ICOMP, ITRUE\n*     .. Scalars in Common ..\n      INTEGER           ICASE, INCX, INCY, N\n      LOGICAL           PASS\n*     .. Local Scalars ..\n      INTEGER           ID\n*     .. Common blocks ..\n      COMMON            /COMBLA/ICASE, N, INCX, INCY, PASS\n*     .. Executable Statements ..\n*\n      IF (ICOMP.EQ.ITRUE) GO TO 40\n*\n*                            HERE ICOMP IS NOT EQUAL TO ITRUE.\n*\n      IF ( .NOT. PASS) GO TO 20\n*                             PRINT FAIL MESSAGE AND HEADER.\n      PASS = .FALSE.\n      WRITE (NOUT,99999)\n      WRITE (NOUT,99998)\n   20 ID = ICOMP - ITRUE\n      WRITE (NOUT,99997) ICASE, N, INCX, INCY, ICOMP, ITRUE, ID\n   40 CONTINUE\n      RETURN\n*\n99999 FORMAT ('                                       FAIL')\n99998 FORMAT (/' CASE  N INCX INCY                               ',\n     +       ' COMP                                TRUE     DIFFERENCE',\n     +       /1X)\n99997 FORMAT (1X,I4,I3,2I5,2I36,I12)\n      END\n"
  },
  {
    "path": "include/eigen3/blas/testing/dblat2.f",
    "content": "*> \\brief \\b DBLAT2\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*  Definition:\n*  ===========\n*\n*       PROGRAM DBLAT2\n* \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> Test program for the DOUBLE PRECISION Level 2 Blas.\n*>\n*> The program must be driven by a short data file. The first 18 records\n*> of the file are read using list-directed input, the last 16 records\n*> are read using the format ( A6, L2 ). An annotated example of a data\n*> file can be obtained by deleting the first 3 characters from the\n*> following 34 lines:\n*> 'dblat2.out'      NAME OF SUMMARY OUTPUT FILE\n*> 6                 UNIT NUMBER OF SUMMARY FILE\n*> 'DBLAT2.SNAP'     NAME OF SNAPSHOT OUTPUT FILE\n*> -1                UNIT NUMBER OF SNAPSHOT FILE (NOT USED IF .LT. 0)\n*> F        LOGICAL FLAG, T TO REWIND SNAPSHOT FILE AFTER EACH RECORD.\n*> F        LOGICAL FLAG, T TO STOP ON FAILURES.\n*> T        LOGICAL FLAG, T TO TEST ERROR EXITS.\n*> 16.0     THRESHOLD VALUE OF TEST RATIO\n*> 6                 NUMBER OF VALUES OF N\n*> 0 1 2 3 5 9       VALUES OF N\n*> 4                 NUMBER OF VALUES OF K\n*> 0 1 2 4           VALUES OF K\n*> 4                 NUMBER OF VALUES OF INCX AND INCY\n*> 1 2 -1 -2         VALUES OF INCX AND INCY\n*> 3                 NUMBER OF VALUES OF ALPHA\n*> 0.0 1.0 0.7       VALUES OF ALPHA\n*> 3                 NUMBER OF VALUES OF BETA\n*> 0.0 1.0 0.9       VALUES OF BETAC\n*> DGEMV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> DGBMV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> DSYMV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> DSBMV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> DSPMV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> DTRMV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> DTBMV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> DTPMV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> DTRSV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> DTBSV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> DTPSV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> DGER   T PUT F FOR NO TEST. SAME COLUMNS.\n*> DSYR   T PUT F FOR NO TEST. SAME COLUMNS.\n*> DSPR   T PUT F FOR NO TEST. SAME COLUMNS.\n*> DSYR2  T PUT F FOR NO TEST. SAME COLUMNS.\n*> DSPR2  T PUT F FOR NO TEST. SAME COLUMNS.\n*>\n*> Further Details\n*> ===============\n*>\n*>    See:\n*>\n*>       Dongarra J. J., Du Croz J. J., Hammarling S.  and Hanson R. J..\n*>       An  extended  set of Fortran  Basic Linear Algebra Subprograms.\n*>\n*>       Technical  Memoranda  Nos. 41 (revision 3) and 81,  Mathematics\n*>       and  Computer Science  Division,  Argonne  National Laboratory,\n*>       9700 South Cass Avenue, Argonne, Illinois 60439, US.\n*>\n*>       Or\n*>\n*>       NAG  Technical Reports TR3/87 and TR4/87,  Numerical Algorithms\n*>       Group  Ltd.,  NAG  Central  Office,  256  Banbury  Road, Oxford\n*>       OX2 7DE, UK,  and  Numerical Algorithms Group Inc.,  1101  31st\n*>       Street,  Suite 100,  Downers Grove,  Illinois 60515-1263,  USA.\n*>\n*>\n*> -- Written on 10-August-1987.\n*>    Richard Hanson, Sandia National Labs.\n*>    Jeremy Du Croz, NAG Central Office.\n*>\n*>    10-9-00:  Change STATUS='NEW' to 'UNKNOWN' so that the testers\n*>              can be run multiple times without deleting generated\n*>              output files (susan)\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date April 2012\n*\n*> \\ingroup double_blas_testing\n*\n*  =====================================================================\n      PROGRAM DBLAT2\n*\n*  -- Reference BLAS test routine (version 3.4.1) --\n*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     April 2012\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      INTEGER            NIN\n      PARAMETER          ( NIN = 5 )\n      INTEGER            NSUBS\n      PARAMETER          ( NSUBS = 16 )\n      DOUBLE PRECISION   ZERO, ONE\n      PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )\n      INTEGER            NMAX, INCMAX\n      PARAMETER          ( NMAX = 65, INCMAX = 2 )\n      INTEGER            NINMAX, NIDMAX, NKBMAX, NALMAX, NBEMAX\n      PARAMETER          ( NINMAX = 7, NIDMAX = 9, NKBMAX = 7,\n     $                   NALMAX = 7, NBEMAX = 7 )\n*     .. Local Scalars ..\n      DOUBLE PRECISION   EPS, ERR, THRESH\n      INTEGER            I, ISNUM, J, N, NALF, NBET, NIDIM, NINC, NKB,\n     $                   NOUT, NTRA\n      LOGICAL            FATAL, LTESTT, REWI, SAME, SFATAL, TRACE,\n     $                   TSTERR\n      CHARACTER*1        TRANS\n      CHARACTER*6        SNAMET\n      CHARACTER*32       SNAPS, SUMMRY\n*     .. Local Arrays ..\n      DOUBLE PRECISION   A( NMAX, NMAX ), AA( NMAX*NMAX ),\n     $                   ALF( NALMAX ), AS( NMAX*NMAX ), BET( NBEMAX ),\n     $                   G( NMAX ), X( NMAX ), XS( NMAX*INCMAX ),\n     $                   XX( NMAX*INCMAX ), Y( NMAX ),\n     $                   YS( NMAX*INCMAX ), YT( NMAX ),\n     $                   YY( NMAX*INCMAX ), Z( 2*NMAX )\n      INTEGER            IDIM( NIDMAX ), INC( NINMAX ), KB( NKBMAX )\n      LOGICAL            LTEST( NSUBS )\n      CHARACTER*6        SNAMES( NSUBS )\n*     .. External Functions ..\n      DOUBLE PRECISION   DDIFF\n      LOGICAL            LDE\n      EXTERNAL           DDIFF, LDE\n*     .. External Subroutines ..\n      EXTERNAL           DCHK1, DCHK2, DCHK3, DCHK4, DCHK5, DCHK6,\n     $                   DCHKE, DMVCH\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, MAX, MIN\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n      CHARACTER*6        SRNAMT\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n      COMMON             /SRNAMC/SRNAMT\n*     .. Data statements ..\n      DATA               SNAMES/'DGEMV ', 'DGBMV ', 'DSYMV ', 'DSBMV ',\n     $                   'DSPMV ', 'DTRMV ', 'DTBMV ', 'DTPMV ',\n     $                   'DTRSV ', 'DTBSV ', 'DTPSV ', 'DGER  ',\n     $                   'DSYR  ', 'DSPR  ', 'DSYR2 ', 'DSPR2 '/\n*     .. Executable Statements ..\n*\n*     Read name and unit number for summary output file and open file.\n*\n      READ( NIN, FMT = * )SUMMRY\n      READ( NIN, FMT = * )NOUT\n      OPEN( NOUT, FILE = SUMMRY, STATUS = 'UNKNOWN' )\n      NOUTC = NOUT\n*\n*     Read name and unit number for snapshot output file and open file.\n*\n      READ( NIN, FMT = * )SNAPS\n      READ( NIN, FMT = * )NTRA\n      TRACE = NTRA.GE.0\n      IF( TRACE )THEN\n         OPEN( NTRA, FILE = SNAPS, STATUS = 'UNKNOWN' )\n      END IF\n*     Read the flag that directs rewinding of the snapshot file.\n      READ( NIN, FMT = * )REWI\n      REWI = REWI.AND.TRACE\n*     Read the flag that directs stopping on any failure.\n      READ( NIN, FMT = * )SFATAL\n*     Read the flag that indicates whether error exits are to be tested.\n      READ( NIN, FMT = * )TSTERR\n*     Read the threshold value of the test ratio\n      READ( NIN, FMT = * )THRESH\n*\n*     Read and check the parameter values for the tests.\n*\n*     Values of N\n      READ( NIN, FMT = * )NIDIM\n      IF( NIDIM.LT.1.OR.NIDIM.GT.NIDMAX )THEN\n         WRITE( NOUT, FMT = 9997 )'N', NIDMAX\n         GO TO 230\n      END IF\n      READ( NIN, FMT = * )( IDIM( I ), I = 1, NIDIM )\n      DO 10 I = 1, NIDIM\n         IF( IDIM( I ).LT.0.OR.IDIM( I ).GT.NMAX )THEN\n            WRITE( NOUT, FMT = 9996 )NMAX\n            GO TO 230\n         END IF\n   10 CONTINUE\n*     Values of K\n      READ( NIN, FMT = * )NKB\n      IF( NKB.LT.1.OR.NKB.GT.NKBMAX )THEN\n         WRITE( NOUT, FMT = 9997 )'K', NKBMAX\n         GO TO 230\n      END IF\n      READ( NIN, FMT = * )( KB( I ), I = 1, NKB )\n      DO 20 I = 1, NKB\n         IF( KB( I ).LT.0 )THEN\n            WRITE( NOUT, FMT = 9995 )\n            GO TO 230\n         END IF\n   20 CONTINUE\n*     Values of INCX and INCY\n      READ( NIN, FMT = * )NINC\n      IF( NINC.LT.1.OR.NINC.GT.NINMAX )THEN\n         WRITE( NOUT, FMT = 9997 )'INCX AND INCY', NINMAX\n         GO TO 230\n      END IF\n      READ( NIN, FMT = * )( INC( I ), I = 1, NINC )\n      DO 30 I = 1, NINC\n         IF( INC( I ).EQ.0.OR.ABS( INC( I ) ).GT.INCMAX )THEN\n            WRITE( NOUT, FMT = 9994 )INCMAX\n            GO TO 230\n         END IF\n   30 CONTINUE\n*     Values of ALPHA\n      READ( NIN, FMT = * )NALF\n      IF( NALF.LT.1.OR.NALF.GT.NALMAX )THEN\n         WRITE( NOUT, FMT = 9997 )'ALPHA', NALMAX\n         GO TO 230\n      END IF\n      READ( NIN, FMT = * )( ALF( I ), I = 1, NALF )\n*     Values of BETA\n      READ( NIN, FMT = * )NBET\n      IF( NBET.LT.1.OR.NBET.GT.NBEMAX )THEN\n         WRITE( NOUT, FMT = 9997 )'BETA', NBEMAX\n         GO TO 230\n      END IF\n      READ( NIN, FMT = * )( BET( I ), I = 1, NBET )\n*\n*     Report values of parameters.\n*\n      WRITE( NOUT, FMT = 9993 )\n      WRITE( NOUT, FMT = 9992 )( IDIM( I ), I = 1, NIDIM )\n      WRITE( NOUT, FMT = 9991 )( KB( I ), I = 1, NKB )\n      WRITE( NOUT, FMT = 9990 )( INC( I ), I = 1, NINC )\n      WRITE( NOUT, FMT = 9989 )( ALF( I ), I = 1, NALF )\n      WRITE( NOUT, FMT = 9988 )( BET( I ), I = 1, NBET )\n      IF( .NOT.TSTERR )THEN\n         WRITE( NOUT, FMT = * )\n         WRITE( NOUT, FMT = 9980 )\n      END IF\n      WRITE( NOUT, FMT = * )\n      WRITE( NOUT, FMT = 9999 )THRESH\n      WRITE( NOUT, FMT = * )\n*\n*     Read names of subroutines and flags which indicate\n*     whether they are to be tested.\n*\n      DO 40 I = 1, NSUBS\n         LTEST( I ) = .FALSE.\n   40 CONTINUE\n   50 READ( NIN, FMT = 9984, END = 80 )SNAMET, LTESTT\n      DO 60 I = 1, NSUBS\n         IF( SNAMET.EQ.SNAMES( I ) )\n     $      GO TO 70\n   60 CONTINUE\n      WRITE( NOUT, FMT = 9986 )SNAMET\n      STOP\n   70 LTEST( I ) = LTESTT\n      GO TO 50\n*\n   80 CONTINUE\n      CLOSE ( NIN )\n*\n*     Compute EPS (the machine precision).\n*\n      EPS = EPSILON(ZERO)\n      WRITE( NOUT, FMT = 9998 )EPS\n*\n*     Check the reliability of DMVCH using exact data.\n*\n      N = MIN( 32, NMAX )\n      DO 120 J = 1, N\n         DO 110 I = 1, N\n            A( I, J ) = MAX( I - J + 1, 0 )\n  110    CONTINUE\n         X( J ) = J\n         Y( J ) = ZERO\n  120 CONTINUE\n      DO 130 J = 1, N\n         YY( J ) = J*( ( J + 1 )*J )/2 - ( ( J + 1 )*J*( J - 1 ) )/3\n  130 CONTINUE\n*     YY holds the exact result. On exit from DMVCH YT holds\n*     the result computed by DMVCH.\n      TRANS = 'N'\n      CALL DMVCH( TRANS, N, N, ONE, A, NMAX, X, 1, ZERO, Y, 1, YT, G,\n     $            YY, EPS, ERR, FATAL, NOUT, .TRUE. )\n      SAME = LDE( YY, YT, N )\n      IF( .NOT.SAME.OR.ERR.NE.ZERO )THEN\n         WRITE( NOUT, FMT = 9985 )TRANS, SAME, ERR\n         STOP\n      END IF\n      TRANS = 'T'\n      CALL DMVCH( TRANS, N, N, ONE, A, NMAX, X, -1, ZERO, Y, -1, YT, G,\n     $            YY, EPS, ERR, FATAL, NOUT, .TRUE. )\n      SAME = LDE( YY, YT, N )\n      IF( .NOT.SAME.OR.ERR.NE.ZERO )THEN\n         WRITE( NOUT, FMT = 9985 )TRANS, SAME, ERR\n         STOP\n      END IF\n*\n*     Test each subroutine in turn.\n*\n      DO 210 ISNUM = 1, NSUBS\n         WRITE( NOUT, FMT = * )\n         IF( .NOT.LTEST( ISNUM ) )THEN\n*           Subprogram is not to be tested.\n            WRITE( NOUT, FMT = 9983 )SNAMES( ISNUM )\n         ELSE\n            SRNAMT = SNAMES( ISNUM )\n*           Test error exits.\n            IF( TSTERR )THEN\n               CALL DCHKE( ISNUM, SNAMES( ISNUM ), NOUT )\n               WRITE( NOUT, FMT = * )\n            END IF\n*           Test computations.\n            INFOT = 0\n            OK = .TRUE.\n            FATAL = .FALSE.\n            GO TO ( 140, 140, 150, 150, 150, 160, 160,\n     $              160, 160, 160, 160, 170, 180, 180,\n     $              190, 190 )ISNUM\n*           Test DGEMV, 01, and DGBMV, 02.\n  140       CALL DCHK1( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF,\n     $                  NBET, BET, NINC, INC, NMAX, INCMAX, A, AA, AS,\n     $                  X, XX, XS, Y, YY, YS, YT, G )\n            GO TO 200\n*           Test DSYMV, 03, DSBMV, 04, and DSPMV, 05.\n  150       CALL DCHK2( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF,\n     $                  NBET, BET, NINC, INC, NMAX, INCMAX, A, AA, AS,\n     $                  X, XX, XS, Y, YY, YS, YT, G )\n            GO TO 200\n*           Test DTRMV, 06, DTBMV, 07, DTPMV, 08,\n*           DTRSV, 09, DTBSV, 10, and DTPSV, 11.\n  160       CALL DCHK3( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NKB, KB, NINC, INC,\n     $                  NMAX, INCMAX, A, AA, AS, Y, YY, YS, YT, G, Z )\n            GO TO 200\n*           Test DGER, 12.\n  170       CALL DCHK4( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC,\n     $                  NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS,\n     $                  YT, G, Z )\n            GO TO 200\n*           Test DSYR, 13, and DSPR, 14.\n  180       CALL DCHK5( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC,\n     $                  NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS,\n     $                  YT, G, Z )\n            GO TO 200\n*           Test DSYR2, 15, and DSPR2, 16.\n  190       CALL DCHK6( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC,\n     $                  NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS,\n     $                  YT, G, Z )\n*\n  200       IF( FATAL.AND.SFATAL )\n     $         GO TO 220\n         END IF\n  210 CONTINUE\n      WRITE( NOUT, FMT = 9982 )\n      GO TO 240\n*\n  220 CONTINUE\n      WRITE( NOUT, FMT = 9981 )\n      GO TO 240\n*\n  230 CONTINUE\n      WRITE( NOUT, FMT = 9987 )\n*\n  240 CONTINUE\n      IF( TRACE )\n     $   CLOSE ( NTRA )\n      CLOSE ( NOUT )\n      STOP\n*\n 9999 FORMAT( ' ROUTINES PASS COMPUTATIONAL TESTS IF TEST RATIO IS LES',\n     $      'S THAN', F8.2 )\n 9998 FORMAT( ' RELATIVE MACHINE PRECISION IS TAKEN TO BE', 1P, D9.1 )\n 9997 FORMAT( ' NUMBER OF VALUES OF ', A, ' IS LESS THAN 1 OR GREATER ',\n     $      'THAN ', I2 )\n 9996 FORMAT( ' VALUE OF N IS LESS THAN 0 OR GREATER THAN ', I2 )\n 9995 FORMAT( ' VALUE OF K IS LESS THAN 0' )\n 9994 FORMAT( ' ABSOLUTE VALUE OF INCX OR INCY IS 0 OR GREATER THAN ',\n     $      I2 )\n 9993 FORMAT( ' TESTS OF THE DOUBLE PRECISION LEVEL 2 BLAS', //' THE F',\n     $      'OLLOWING PARAMETER VALUES WILL BE USED:' )\n 9992 FORMAT( '   FOR N              ', 9I6 )\n 9991 FORMAT( '   FOR K              ', 7I6 )\n 9990 FORMAT( '   FOR INCX AND INCY  ', 7I6 )\n 9989 FORMAT( '   FOR ALPHA          ', 7F6.1 )\n 9988 FORMAT( '   FOR BETA           ', 7F6.1 )\n 9987 FORMAT( ' AMEND DATA FILE OR INCREASE ARRAY SIZES IN PROGRAM',\n     $      /' ******* TESTS ABANDONED *******' )\n 9986 FORMAT( ' SUBPROGRAM NAME ', A6, ' NOT RECOGNIZED', /' ******* T',\n     $      'ESTS ABANDONED *******' )\n 9985 FORMAT( ' ERROR IN DMVCH -  IN-LINE DOT PRODUCTS ARE BEING EVALU',\n     $      'ATED WRONGLY.', /' DMVCH WAS CALLED WITH TRANS = ', A1,\n     $      ' AND RETURNED SAME = ', L1, ' AND ERR = ', F12.3, '.', /\n     $   ' THIS MAY BE DUE TO FAULTS IN THE ARITHMETIC OR THE COMPILER.'\n     $      , /' ******* TESTS ABANDONED *******' )\n 9984 FORMAT( A6, L2 )\n 9983 FORMAT( 1X, A6, ' WAS NOT TESTED' )\n 9982 FORMAT( /' END OF TESTS' )\n 9981 FORMAT( /' ******* FATAL ERROR - TESTS ABANDONED *******' )\n 9980 FORMAT( ' ERROR-EXITS WILL NOT BE TESTED' )\n*\n*     End of DBLAT2.\n*\n      END\n      SUBROUTINE DCHK1( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF, NBET,\n     $                  BET, NINC, INC, NMAX, INCMAX, A, AA, AS, X, XX,\n     $                  XS, Y, YY, YS, YT, G )\n*\n*  Tests DGEMV and DGBMV.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Parameters ..\n      DOUBLE PRECISION   ZERO, HALF\n      PARAMETER          ( ZERO = 0.0D0, HALF = 0.5D0 )\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION   EPS, THRESH\n      INTEGER            INCMAX, NALF, NBET, NIDIM, NINC, NKB, NMAX,\n     $                   NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      DOUBLE PRECISION   A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), BET( NBET ), G( NMAX ),\n     $                   X( NMAX ), XS( NMAX*INCMAX ),\n     $                   XX( NMAX*INCMAX ), Y( NMAX ),\n     $                   YS( NMAX*INCMAX ), YT( NMAX ),\n     $                   YY( NMAX*INCMAX )\n      INTEGER            IDIM( NIDIM ), INC( NINC ), KB( NKB )\n*     .. Local Scalars ..\n      DOUBLE PRECISION   ALPHA, ALS, BETA, BLS, ERR, ERRMAX, TRANSL\n      INTEGER            I, IA, IB, IC, IKU, IM, IN, INCX, INCXS, INCY,\n     $                   INCYS, IX, IY, KL, KLS, KU, KUS, LAA, LDA,\n     $                   LDAS, LX, LY, M, ML, MS, N, NARGS, NC, ND, NK,\n     $                   NL, NS\n      LOGICAL            BANDED, FULL, NULL, RESET, SAME, TRAN\n      CHARACTER*1        TRANS, TRANSS\n      CHARACTER*3        ICH\n*     .. Local Arrays ..\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LDE, LDERES\n      EXTERNAL           LDE, LDERES\n*     .. External Subroutines ..\n      EXTERNAL           DGBMV, DGEMV, DMAKE, DMVCH\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, MAX, MIN\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICH/'NTC'/\n*     .. Executable Statements ..\n      FULL = SNAME( 3: 3 ).EQ.'E'\n      BANDED = SNAME( 3: 3 ).EQ.'B'\n*     Define the number of arguments.\n      IF( FULL )THEN\n         NARGS = 11\n      ELSE IF( BANDED )THEN\n         NARGS = 13\n      END IF\n*\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = ZERO\n*\n      DO 120 IN = 1, NIDIM\n         N = IDIM( IN )\n         ND = N/2 + 1\n*\n         DO 110 IM = 1, 2\n            IF( IM.EQ.1 )\n     $         M = MAX( N - ND, 0 )\n            IF( IM.EQ.2 )\n     $         M = MIN( N + ND, NMAX )\n*\n            IF( BANDED )THEN\n               NK = NKB\n            ELSE\n               NK = 1\n            END IF\n            DO 100 IKU = 1, NK\n               IF( BANDED )THEN\n                  KU = KB( IKU )\n                  KL = MAX( KU - 1, 0 )\n               ELSE\n                  KU = N - 1\n                  KL = M - 1\n               END IF\n*              Set LDA to 1 more than minimum value if room.\n               IF( BANDED )THEN\n                  LDA = KL + KU + 1\n               ELSE\n                  LDA = M\n               END IF\n               IF( LDA.LT.NMAX )\n     $            LDA = LDA + 1\n*              Skip tests if not enough room.\n               IF( LDA.GT.NMAX )\n     $            GO TO 100\n               LAA = LDA*N\n               NULL = N.LE.0.OR.M.LE.0\n*\n*              Generate the matrix A.\n*\n               TRANSL = ZERO\n               CALL DMAKE( SNAME( 2: 3 ), ' ', ' ', M, N, A, NMAX, AA,\n     $                     LDA, KL, KU, RESET, TRANSL )\n*\n               DO 90 IC = 1, 3\n                  TRANS = ICH( IC: IC )\n                  TRAN = TRANS.EQ.'T'.OR.TRANS.EQ.'C'\n*\n                  IF( TRAN )THEN\n                     ML = N\n                     NL = M\n                  ELSE\n                     ML = M\n                     NL = N\n                  END IF\n*\n                  DO 80 IX = 1, NINC\n                     INCX = INC( IX )\n                     LX = ABS( INCX )*NL\n*\n*                    Generate the vector X.\n*\n                     TRANSL = HALF\n                     CALL DMAKE( 'GE', ' ', ' ', 1, NL, X, 1, XX,\n     $                           ABS( INCX ), 0, NL - 1, RESET, TRANSL )\n                     IF( NL.GT.1 )THEN\n                        X( NL/2 ) = ZERO\n                        XX( 1 + ABS( INCX )*( NL/2 - 1 ) ) = ZERO\n                     END IF\n*\n                     DO 70 IY = 1, NINC\n                        INCY = INC( IY )\n                        LY = ABS( INCY )*ML\n*\n                        DO 60 IA = 1, NALF\n                           ALPHA = ALF( IA )\n*\n                           DO 50 IB = 1, NBET\n                              BETA = BET( IB )\n*\n*                             Generate the vector Y.\n*\n                              TRANSL = ZERO\n                              CALL DMAKE( 'GE', ' ', ' ', 1, ML, Y, 1,\n     $                                    YY, ABS( INCY ), 0, ML - 1,\n     $                                    RESET, TRANSL )\n*\n                              NC = NC + 1\n*\n*                             Save every datum before calling the\n*                             subroutine.\n*\n                              TRANSS = TRANS\n                              MS = M\n                              NS = N\n                              KLS = KL\n                              KUS = KU\n                              ALS = ALPHA\n                              DO 10 I = 1, LAA\n                                 AS( I ) = AA( I )\n   10                         CONTINUE\n                              LDAS = LDA\n                              DO 20 I = 1, LX\n                                 XS( I ) = XX( I )\n   20                         CONTINUE\n                              INCXS = INCX\n                              BLS = BETA\n                              DO 30 I = 1, LY\n                                 YS( I ) = YY( I )\n   30                         CONTINUE\n                              INCYS = INCY\n*\n*                             Call the subroutine.\n*\n                              IF( FULL )THEN\n                                 IF( TRACE )\n     $                              WRITE( NTRA, FMT = 9994 )NC, SNAME,\n     $                              TRANS, M, N, ALPHA, LDA, INCX, BETA,\n     $                              INCY\n                                 IF( REWI )\n     $                              REWIND NTRA\n                                 CALL DGEMV( TRANS, M, N, ALPHA, AA,\n     $                                       LDA, XX, INCX, BETA, YY,\n     $                                       INCY )\n                              ELSE IF( BANDED )THEN\n                                 IF( TRACE )\n     $                              WRITE( NTRA, FMT = 9995 )NC, SNAME,\n     $                              TRANS, M, N, KL, KU, ALPHA, LDA,\n     $                              INCX, BETA, INCY\n                                 IF( REWI )\n     $                              REWIND NTRA\n                                 CALL DGBMV( TRANS, M, N, KL, KU, ALPHA,\n     $                                       AA, LDA, XX, INCX, BETA,\n     $                                       YY, INCY )\n                              END IF\n*\n*                             Check if error-exit was taken incorrectly.\n*\n                              IF( .NOT.OK )THEN\n                                 WRITE( NOUT, FMT = 9993 )\n                                 FATAL = .TRUE.\n                                 GO TO 130\n                              END IF\n*\n*                             See what data changed inside subroutines.\n*\n                              ISAME( 1 ) = TRANS.EQ.TRANSS\n                              ISAME( 2 ) = MS.EQ.M\n                              ISAME( 3 ) = NS.EQ.N\n                              IF( FULL )THEN\n                                 ISAME( 4 ) = ALS.EQ.ALPHA\n                                 ISAME( 5 ) = LDE( AS, AA, LAA )\n                                 ISAME( 6 ) = LDAS.EQ.LDA\n                                 ISAME( 7 ) = LDE( XS, XX, LX )\n                                 ISAME( 8 ) = INCXS.EQ.INCX\n                                 ISAME( 9 ) = BLS.EQ.BETA\n                                 IF( NULL )THEN\n                                    ISAME( 10 ) = LDE( YS, YY, LY )\n                                 ELSE\n                                    ISAME( 10 ) = LDERES( 'GE', ' ', 1,\n     $                                            ML, YS, YY,\n     $                                            ABS( INCY ) )\n                                 END IF\n                                 ISAME( 11 ) = INCYS.EQ.INCY\n                              ELSE IF( BANDED )THEN\n                                 ISAME( 4 ) = KLS.EQ.KL\n                                 ISAME( 5 ) = KUS.EQ.KU\n                                 ISAME( 6 ) = ALS.EQ.ALPHA\n                                 ISAME( 7 ) = LDE( AS, AA, LAA )\n                                 ISAME( 8 ) = LDAS.EQ.LDA\n                                 ISAME( 9 ) = LDE( XS, XX, LX )\n                                 ISAME( 10 ) = INCXS.EQ.INCX\n                                 ISAME( 11 ) = BLS.EQ.BETA\n                                 IF( NULL )THEN\n                                    ISAME( 12 ) = LDE( YS, YY, LY )\n                                 ELSE\n                                    ISAME( 12 ) = LDERES( 'GE', ' ', 1,\n     $                                            ML, YS, YY,\n     $                                            ABS( INCY ) )\n                                 END IF\n                                 ISAME( 13 ) = INCYS.EQ.INCY\n                              END IF\n*\n*                             If data was incorrectly changed, report\n*                             and return.\n*\n                              SAME = .TRUE.\n                              DO 40 I = 1, NARGS\n                                 SAME = SAME.AND.ISAME( I )\n                                 IF( .NOT.ISAME( I ) )\n     $                              WRITE( NOUT, FMT = 9998 )I\n   40                         CONTINUE\n                              IF( .NOT.SAME )THEN\n                                 FATAL = .TRUE.\n                                 GO TO 130\n                              END IF\n*\n                              IF( .NOT.NULL )THEN\n*\n*                                Check the result.\n*\n                                 CALL DMVCH( TRANS, M, N, ALPHA, A,\n     $                                       NMAX, X, INCX, BETA, Y,\n     $                                       INCY, YT, G, YY, EPS, ERR,\n     $                                       FATAL, NOUT, .TRUE. )\n                                 ERRMAX = MAX( ERRMAX, ERR )\n*                                If got really bad answer, report and\n*                                return.\n                                 IF( FATAL )\n     $                              GO TO 130\n                              ELSE\n*                                Avoid repeating tests with M.le.0 or\n*                                N.le.0.\n                                 GO TO 110\n                              END IF\n*\n   50                      CONTINUE\n*\n   60                   CONTINUE\n*\n   70                CONTINUE\n*\n   80             CONTINUE\n*\n   90          CONTINUE\n*\n  100       CONTINUE\n*\n  110    CONTINUE\n*\n  120 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 140\n*\n  130 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      IF( FULL )THEN\n         WRITE( NOUT, FMT = 9994 )NC, SNAME, TRANS, M, N, ALPHA, LDA,\n     $      INCX, BETA, INCY\n      ELSE IF( BANDED )THEN\n         WRITE( NOUT, FMT = 9995 )NC, SNAME, TRANS, M, N, KL, KU,\n     $      ALPHA, LDA, INCX, BETA, INCY\n      END IF\n*\n  140 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 4( I3, ',' ), F4.1,\n     $      ', A,', I3, ', X,', I2, ',', F4.1, ', Y,', I2, ') .' )\n 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 2( I3, ',' ), F4.1,\n     $      ', A,', I3, ', X,', I2, ',', F4.1, ', Y,', I2,\n     $      ')         .' )\n 9993 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of DCHK1.\n*\n      END\n      SUBROUTINE DCHK2( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF, NBET,\n     $                  BET, NINC, INC, NMAX, INCMAX, A, AA, AS, X, XX,\n     $                  XS, Y, YY, YS, YT, G )\n*\n*  Tests DSYMV, DSBMV and DSPMV.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Parameters ..\n      DOUBLE PRECISION   ZERO, HALF\n      PARAMETER          ( ZERO = 0.0D0, HALF = 0.5D0 )\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION   EPS, THRESH\n      INTEGER            INCMAX, NALF, NBET, NIDIM, NINC, NKB, NMAX,\n     $                   NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      DOUBLE PRECISION   A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), BET( NBET ), G( NMAX ),\n     $                   X( NMAX ), XS( NMAX*INCMAX ),\n     $                   XX( NMAX*INCMAX ), Y( NMAX ),\n     $                   YS( NMAX*INCMAX ), YT( NMAX ),\n     $                   YY( NMAX*INCMAX )\n      INTEGER            IDIM( NIDIM ), INC( NINC ), KB( NKB )\n*     .. Local Scalars ..\n      DOUBLE PRECISION   ALPHA, ALS, BETA, BLS, ERR, ERRMAX, TRANSL\n      INTEGER            I, IA, IB, IC, IK, IN, INCX, INCXS, INCY,\n     $                   INCYS, IX, IY, K, KS, LAA, LDA, LDAS, LX, LY,\n     $                   N, NARGS, NC, NK, NS\n      LOGICAL            BANDED, FULL, NULL, PACKED, RESET, SAME\n      CHARACTER*1        UPLO, UPLOS\n      CHARACTER*2        ICH\n*     .. Local Arrays ..\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LDE, LDERES\n      EXTERNAL           LDE, LDERES\n*     .. External Subroutines ..\n      EXTERNAL           DMAKE, DMVCH, DSBMV, DSPMV, DSYMV\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, MAX\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICH/'UL'/\n*     .. Executable Statements ..\n      FULL = SNAME( 3: 3 ).EQ.'Y'\n      BANDED = SNAME( 3: 3 ).EQ.'B'\n      PACKED = SNAME( 3: 3 ).EQ.'P'\n*     Define the number of arguments.\n      IF( FULL )THEN\n         NARGS = 10\n      ELSE IF( BANDED )THEN\n         NARGS = 11\n      ELSE IF( PACKED )THEN\n         NARGS = 9\n      END IF\n*\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = ZERO\n*\n      DO 110 IN = 1, NIDIM\n         N = IDIM( IN )\n*\n         IF( BANDED )THEN\n            NK = NKB\n         ELSE\n            NK = 1\n         END IF\n         DO 100 IK = 1, NK\n            IF( BANDED )THEN\n               K = KB( IK )\n            ELSE\n               K = N - 1\n            END IF\n*           Set LDA to 1 more than minimum value if room.\n            IF( BANDED )THEN\n               LDA = K + 1\n            ELSE\n               LDA = N\n            END IF\n            IF( LDA.LT.NMAX )\n     $         LDA = LDA + 1\n*           Skip tests if not enough room.\n            IF( LDA.GT.NMAX )\n     $         GO TO 100\n            IF( PACKED )THEN\n               LAA = ( N*( N + 1 ) )/2\n            ELSE\n               LAA = LDA*N\n            END IF\n            NULL = N.LE.0\n*\n            DO 90 IC = 1, 2\n               UPLO = ICH( IC: IC )\n*\n*              Generate the matrix A.\n*\n               TRANSL = ZERO\n               CALL DMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A, NMAX, AA,\n     $                     LDA, K, K, RESET, TRANSL )\n*\n               DO 80 IX = 1, NINC\n                  INCX = INC( IX )\n                  LX = ABS( INCX )*N\n*\n*                 Generate the vector X.\n*\n                  TRANSL = HALF\n                  CALL DMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX,\n     $                        ABS( INCX ), 0, N - 1, RESET, TRANSL )\n                  IF( N.GT.1 )THEN\n                     X( N/2 ) = ZERO\n                     XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO\n                  END IF\n*\n                  DO 70 IY = 1, NINC\n                     INCY = INC( IY )\n                     LY = ABS( INCY )*N\n*\n                     DO 60 IA = 1, NALF\n                        ALPHA = ALF( IA )\n*\n                        DO 50 IB = 1, NBET\n                           BETA = BET( IB )\n*\n*                          Generate the vector Y.\n*\n                           TRANSL = ZERO\n                           CALL DMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY,\n     $                                 ABS( INCY ), 0, N - 1, RESET,\n     $                                 TRANSL )\n*\n                           NC = NC + 1\n*\n*                          Save every datum before calling the\n*                          subroutine.\n*\n                           UPLOS = UPLO\n                           NS = N\n                           KS = K\n                           ALS = ALPHA\n                           DO 10 I = 1, LAA\n                              AS( I ) = AA( I )\n   10                      CONTINUE\n                           LDAS = LDA\n                           DO 20 I = 1, LX\n                              XS( I ) = XX( I )\n   20                      CONTINUE\n                           INCXS = INCX\n                           BLS = BETA\n                           DO 30 I = 1, LY\n                              YS( I ) = YY( I )\n   30                      CONTINUE\n                           INCYS = INCY\n*\n*                          Call the subroutine.\n*\n                           IF( FULL )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9993 )NC, SNAME,\n     $                           UPLO, N, ALPHA, LDA, INCX, BETA, INCY\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL DSYMV( UPLO, N, ALPHA, AA, LDA, XX,\n     $                                    INCX, BETA, YY, INCY )\n                           ELSE IF( BANDED )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9994 )NC, SNAME,\n     $                           UPLO, N, K, ALPHA, LDA, INCX, BETA,\n     $                           INCY\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL DSBMV( UPLO, N, K, ALPHA, AA, LDA,\n     $                                    XX, INCX, BETA, YY, INCY )\n                           ELSE IF( PACKED )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9995 )NC, SNAME,\n     $                           UPLO, N, ALPHA, INCX, BETA, INCY\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL DSPMV( UPLO, N, ALPHA, AA, XX, INCX,\n     $                                    BETA, YY, INCY )\n                           END IF\n*\n*                          Check if error-exit was taken incorrectly.\n*\n                           IF( .NOT.OK )THEN\n                              WRITE( NOUT, FMT = 9992 )\n                              FATAL = .TRUE.\n                              GO TO 120\n                           END IF\n*\n*                          See what data changed inside subroutines.\n*\n                           ISAME( 1 ) = UPLO.EQ.UPLOS\n                           ISAME( 2 ) = NS.EQ.N\n                           IF( FULL )THEN\n                              ISAME( 3 ) = ALS.EQ.ALPHA\n                              ISAME( 4 ) = LDE( AS, AA, LAA )\n                              ISAME( 5 ) = LDAS.EQ.LDA\n                              ISAME( 6 ) = LDE( XS, XX, LX )\n                              ISAME( 7 ) = INCXS.EQ.INCX\n                              ISAME( 8 ) = BLS.EQ.BETA\n                              IF( NULL )THEN\n                                 ISAME( 9 ) = LDE( YS, YY, LY )\n                              ELSE\n                                 ISAME( 9 ) = LDERES( 'GE', ' ', 1, N,\n     $                                        YS, YY, ABS( INCY ) )\n                              END IF\n                              ISAME( 10 ) = INCYS.EQ.INCY\n                           ELSE IF( BANDED )THEN\n                              ISAME( 3 ) = KS.EQ.K\n                              ISAME( 4 ) = ALS.EQ.ALPHA\n                              ISAME( 5 ) = LDE( AS, AA, LAA )\n                              ISAME( 6 ) = LDAS.EQ.LDA\n                              ISAME( 7 ) = LDE( XS, XX, LX )\n                              ISAME( 8 ) = INCXS.EQ.INCX\n                              ISAME( 9 ) = BLS.EQ.BETA\n                              IF( NULL )THEN\n                                 ISAME( 10 ) = LDE( YS, YY, LY )\n                              ELSE\n                                 ISAME( 10 ) = LDERES( 'GE', ' ', 1, N,\n     $                                         YS, YY, ABS( INCY ) )\n                              END IF\n                              ISAME( 11 ) = INCYS.EQ.INCY\n                           ELSE IF( PACKED )THEN\n                              ISAME( 3 ) = ALS.EQ.ALPHA\n                              ISAME( 4 ) = LDE( AS, AA, LAA )\n                              ISAME( 5 ) = LDE( XS, XX, LX )\n                              ISAME( 6 ) = INCXS.EQ.INCX\n                              ISAME( 7 ) = BLS.EQ.BETA\n                              IF( NULL )THEN\n                                 ISAME( 8 ) = LDE( YS, YY, LY )\n                              ELSE\n                                 ISAME( 8 ) = LDERES( 'GE', ' ', 1, N,\n     $                                        YS, YY, ABS( INCY ) )\n                              END IF\n                              ISAME( 9 ) = INCYS.EQ.INCY\n                           END IF\n*\n*                          If data was incorrectly changed, report and\n*                          return.\n*\n                           SAME = .TRUE.\n                           DO 40 I = 1, NARGS\n                              SAME = SAME.AND.ISAME( I )\n                              IF( .NOT.ISAME( I ) )\n     $                           WRITE( NOUT, FMT = 9998 )I\n   40                      CONTINUE\n                           IF( .NOT.SAME )THEN\n                              FATAL = .TRUE.\n                              GO TO 120\n                           END IF\n*\n                           IF( .NOT.NULL )THEN\n*\n*                             Check the result.\n*\n                              CALL DMVCH( 'N', N, N, ALPHA, A, NMAX, X,\n     $                                    INCX, BETA, Y, INCY, YT, G,\n     $                                    YY, EPS, ERR, FATAL, NOUT,\n     $                                    .TRUE. )\n                              ERRMAX = MAX( ERRMAX, ERR )\n*                             If got really bad answer, report and\n*                             return.\n                              IF( FATAL )\n     $                           GO TO 120\n                           ELSE\n*                             Avoid repeating tests with N.le.0\n                              GO TO 110\n                           END IF\n*\n   50                   CONTINUE\n*\n   60                CONTINUE\n*\n   70             CONTINUE\n*\n   80          CONTINUE\n*\n   90       CONTINUE\n*\n  100    CONTINUE\n*\n  110 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 130\n*\n  120 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      IF( FULL )THEN\n         WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, ALPHA, LDA, INCX,\n     $      BETA, INCY\n      ELSE IF( BANDED )THEN\n         WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, K, ALPHA, LDA,\n     $      INCX, BETA, INCY\n      ELSE IF( PACKED )THEN\n         WRITE( NOUT, FMT = 9995 )NC, SNAME, UPLO, N, ALPHA, INCX,\n     $      BETA, INCY\n      END IF\n*\n  130 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', AP',\n     $      ', X,', I2, ',', F4.1, ', Y,', I2, ')                .' )\n 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 2( I3, ',' ), F4.1,\n     $      ', A,', I3, ', X,', I2, ',', F4.1, ', Y,', I2,\n     $      ')         .' )\n 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', A,',\n     $      I3, ', X,', I2, ',', F4.1, ', Y,', I2, ')             .' )\n 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of DCHK2.\n*\n      END\n      SUBROUTINE DCHK3( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NKB, KB, NINC, INC, NMAX,\n     $                  INCMAX, A, AA, AS, X, XX, XS, XT, G, Z )\n*\n*  Tests DTRMV, DTBMV, DTPMV, DTRSV, DTBSV and DTPSV.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Parameters ..\n      DOUBLE PRECISION   ZERO, HALF, ONE\n      PARAMETER          ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0 )\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION   EPS, THRESH\n      INTEGER            INCMAX, NIDIM, NINC, NKB, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      DOUBLE PRECISION   A( NMAX, NMAX ), AA( NMAX*NMAX ),\n     $                   AS( NMAX*NMAX ), G( NMAX ), X( NMAX ),\n     $                   XS( NMAX*INCMAX ), XT( NMAX ),\n     $                   XX( NMAX*INCMAX ), Z( NMAX )\n      INTEGER            IDIM( NIDIM ), INC( NINC ), KB( NKB )\n*     .. Local Scalars ..\n      DOUBLE PRECISION   ERR, ERRMAX, TRANSL\n      INTEGER            I, ICD, ICT, ICU, IK, IN, INCX, INCXS, IX, K,\n     $                   KS, LAA, LDA, LDAS, LX, N, NARGS, NC, NK, NS\n      LOGICAL            BANDED, FULL, NULL, PACKED, RESET, SAME\n      CHARACTER*1        DIAG, DIAGS, TRANS, TRANSS, UPLO, UPLOS\n      CHARACTER*2        ICHD, ICHU\n      CHARACTER*3        ICHT\n*     .. Local Arrays ..\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LDE, LDERES\n      EXTERNAL           LDE, LDERES\n*     .. External Subroutines ..\n      EXTERNAL           DMAKE, DMVCH, DTBMV, DTBSV, DTPMV, DTPSV,\n     $                   DTRMV, DTRSV\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, MAX\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICHU/'UL'/, ICHT/'NTC'/, ICHD/'UN'/\n*     .. Executable Statements ..\n      FULL = SNAME( 3: 3 ).EQ.'R'\n      BANDED = SNAME( 3: 3 ).EQ.'B'\n      PACKED = SNAME( 3: 3 ).EQ.'P'\n*     Define the number of arguments.\n      IF( FULL )THEN\n         NARGS = 8\n      ELSE IF( BANDED )THEN\n         NARGS = 9\n      ELSE IF( PACKED )THEN\n         NARGS = 7\n      END IF\n*\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = ZERO\n*     Set up zero vector for DMVCH.\n      DO 10 I = 1, NMAX\n         Z( I ) = ZERO\n   10 CONTINUE\n*\n      DO 110 IN = 1, NIDIM\n         N = IDIM( IN )\n*\n         IF( BANDED )THEN\n            NK = NKB\n         ELSE\n            NK = 1\n         END IF\n         DO 100 IK = 1, NK\n            IF( BANDED )THEN\n               K = KB( IK )\n            ELSE\n               K = N - 1\n            END IF\n*           Set LDA to 1 more than minimum value if room.\n            IF( BANDED )THEN\n               LDA = K + 1\n            ELSE\n               LDA = N\n            END IF\n            IF( LDA.LT.NMAX )\n     $         LDA = LDA + 1\n*           Skip tests if not enough room.\n            IF( LDA.GT.NMAX )\n     $         GO TO 100\n            IF( PACKED )THEN\n               LAA = ( N*( N + 1 ) )/2\n            ELSE\n               LAA = LDA*N\n            END IF\n            NULL = N.LE.0\n*\n            DO 90 ICU = 1, 2\n               UPLO = ICHU( ICU: ICU )\n*\n               DO 80 ICT = 1, 3\n                  TRANS = ICHT( ICT: ICT )\n*\n                  DO 70 ICD = 1, 2\n                     DIAG = ICHD( ICD: ICD )\n*\n*                    Generate the matrix A.\n*\n                     TRANSL = ZERO\n                     CALL DMAKE( SNAME( 2: 3 ), UPLO, DIAG, N, N, A,\n     $                           NMAX, AA, LDA, K, K, RESET, TRANSL )\n*\n                     DO 60 IX = 1, NINC\n                        INCX = INC( IX )\n                        LX = ABS( INCX )*N\n*\n*                       Generate the vector X.\n*\n                        TRANSL = HALF\n                        CALL DMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX,\n     $                              ABS( INCX ), 0, N - 1, RESET,\n     $                              TRANSL )\n                        IF( N.GT.1 )THEN\n                           X( N/2 ) = ZERO\n                           XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO\n                        END IF\n*\n                        NC = NC + 1\n*\n*                       Save every datum before calling the subroutine.\n*\n                        UPLOS = UPLO\n                        TRANSS = TRANS\n                        DIAGS = DIAG\n                        NS = N\n                        KS = K\n                        DO 20 I = 1, LAA\n                           AS( I ) = AA( I )\n   20                   CONTINUE\n                        LDAS = LDA\n                        DO 30 I = 1, LX\n                           XS( I ) = XX( I )\n   30                   CONTINUE\n                        INCXS = INCX\n*\n*                       Call the subroutine.\n*\n                        IF( SNAME( 4: 5 ).EQ.'MV' )THEN\n                           IF( FULL )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9993 )NC, SNAME,\n     $                           UPLO, TRANS, DIAG, N, LDA, INCX\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL DTRMV( UPLO, TRANS, DIAG, N, AA, LDA,\n     $                                    XX, INCX )\n                           ELSE IF( BANDED )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9994 )NC, SNAME,\n     $                           UPLO, TRANS, DIAG, N, K, LDA, INCX\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL DTBMV( UPLO, TRANS, DIAG, N, K, AA,\n     $                                    LDA, XX, INCX )\n                           ELSE IF( PACKED )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9995 )NC, SNAME,\n     $                           UPLO, TRANS, DIAG, N, INCX\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL DTPMV( UPLO, TRANS, DIAG, N, AA, XX,\n     $                                    INCX )\n                           END IF\n                        ELSE IF( SNAME( 4: 5 ).EQ.'SV' )THEN\n                           IF( FULL )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9993 )NC, SNAME,\n     $                           UPLO, TRANS, DIAG, N, LDA, INCX\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL DTRSV( UPLO, TRANS, DIAG, N, AA, LDA,\n     $                                    XX, INCX )\n                           ELSE IF( BANDED )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9994 )NC, SNAME,\n     $                           UPLO, TRANS, DIAG, N, K, LDA, INCX\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL DTBSV( UPLO, TRANS, DIAG, N, K, AA,\n     $                                    LDA, XX, INCX )\n                           ELSE IF( PACKED )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9995 )NC, SNAME,\n     $                           UPLO, TRANS, DIAG, N, INCX\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL DTPSV( UPLO, TRANS, DIAG, N, AA, XX,\n     $                                    INCX )\n                           END IF\n                        END IF\n*\n*                       Check if error-exit was taken incorrectly.\n*\n                        IF( .NOT.OK )THEN\n                           WRITE( NOUT, FMT = 9992 )\n                           FATAL = .TRUE.\n                           GO TO 120\n                        END IF\n*\n*                       See what data changed inside subroutines.\n*\n                        ISAME( 1 ) = UPLO.EQ.UPLOS\n                        ISAME( 2 ) = TRANS.EQ.TRANSS\n                        ISAME( 3 ) = DIAG.EQ.DIAGS\n                        ISAME( 4 ) = NS.EQ.N\n                        IF( FULL )THEN\n                           ISAME( 5 ) = LDE( AS, AA, LAA )\n                           ISAME( 6 ) = LDAS.EQ.LDA\n                           IF( NULL )THEN\n                              ISAME( 7 ) = LDE( XS, XX, LX )\n                           ELSE\n                              ISAME( 7 ) = LDERES( 'GE', ' ', 1, N, XS,\n     $                                     XX, ABS( INCX ) )\n                           END IF\n                           ISAME( 8 ) = INCXS.EQ.INCX\n                        ELSE IF( BANDED )THEN\n                           ISAME( 5 ) = KS.EQ.K\n                           ISAME( 6 ) = LDE( AS, AA, LAA )\n                           ISAME( 7 ) = LDAS.EQ.LDA\n                           IF( NULL )THEN\n                              ISAME( 8 ) = LDE( XS, XX, LX )\n                           ELSE\n                              ISAME( 8 ) = LDERES( 'GE', ' ', 1, N, XS,\n     $                                     XX, ABS( INCX ) )\n                           END IF\n                           ISAME( 9 ) = INCXS.EQ.INCX\n                        ELSE IF( PACKED )THEN\n                           ISAME( 5 ) = LDE( AS, AA, LAA )\n                           IF( NULL )THEN\n                              ISAME( 6 ) = LDE( XS, XX, LX )\n                           ELSE\n                              ISAME( 6 ) = LDERES( 'GE', ' ', 1, N, XS,\n     $                                     XX, ABS( INCX ) )\n                           END IF\n                           ISAME( 7 ) = INCXS.EQ.INCX\n                        END IF\n*\n*                       If data was incorrectly changed, report and\n*                       return.\n*\n                        SAME = .TRUE.\n                        DO 40 I = 1, NARGS\n                           SAME = SAME.AND.ISAME( I )\n                           IF( .NOT.ISAME( I ) )\n     $                        WRITE( NOUT, FMT = 9998 )I\n   40                   CONTINUE\n                        IF( .NOT.SAME )THEN\n                           FATAL = .TRUE.\n                           GO TO 120\n                        END IF\n*\n                        IF( .NOT.NULL )THEN\n                           IF( SNAME( 4: 5 ).EQ.'MV' )THEN\n*\n*                             Check the result.\n*\n                              CALL DMVCH( TRANS, N, N, ONE, A, NMAX, X,\n     $                                    INCX, ZERO, Z, INCX, XT, G,\n     $                                    XX, EPS, ERR, FATAL, NOUT,\n     $                                    .TRUE. )\n                           ELSE IF( SNAME( 4: 5 ).EQ.'SV' )THEN\n*\n*                             Compute approximation to original vector.\n*\n                              DO 50 I = 1, N\n                                 Z( I ) = XX( 1 + ( I - 1 )*\n     $                                    ABS( INCX ) )\n                                 XX( 1 + ( I - 1 )*ABS( INCX ) )\n     $                              = X( I )\n   50                         CONTINUE\n                              CALL DMVCH( TRANS, N, N, ONE, A, NMAX, Z,\n     $                                    INCX, ZERO, X, INCX, XT, G,\n     $                                    XX, EPS, ERR, FATAL, NOUT,\n     $                                    .FALSE. )\n                           END IF\n                           ERRMAX = MAX( ERRMAX, ERR )\n*                          If got really bad answer, report and return.\n                           IF( FATAL )\n     $                        GO TO 120\n                        ELSE\n*                          Avoid repeating tests with N.le.0.\n                           GO TO 110\n                        END IF\n*\n   60                CONTINUE\n*\n   70             CONTINUE\n*\n   80          CONTINUE\n*\n   90       CONTINUE\n*\n  100    CONTINUE\n*\n  110 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 130\n*\n  120 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      IF( FULL )THEN\n         WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, TRANS, DIAG, N, LDA,\n     $      INCX\n      ELSE IF( BANDED )THEN\n         WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, TRANS, DIAG, N, K,\n     $      LDA, INCX\n      ELSE IF( PACKED )THEN\n         WRITE( NOUT, FMT = 9995 )NC, SNAME, UPLO, TRANS, DIAG, N, INCX\n      END IF\n*\n  130 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), I3, ', AP, ',\n     $      'X,', I2, ')                        .' )\n 9994 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), 2( I3, ',' ),\n     $      ' A,', I3, ', X,', I2, ')                 .' )\n 9993 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), I3, ', A,',\n     $      I3, ', X,', I2, ')                     .' )\n 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of DCHK3.\n*\n      END\n      SUBROUTINE DCHK4( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX,\n     $                  INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G,\n     $                  Z )\n*\n*  Tests DGER.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Parameters ..\n      DOUBLE PRECISION   ZERO, HALF, ONE\n      PARAMETER          ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0 )\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION   EPS, THRESH\n      INTEGER            INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      DOUBLE PRECISION   A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), G( NMAX ), X( NMAX ),\n     $                   XS( NMAX*INCMAX ), XX( NMAX*INCMAX ),\n     $                   Y( NMAX ), YS( NMAX*INCMAX ), YT( NMAX ),\n     $                   YY( NMAX*INCMAX ), Z( NMAX )\n      INTEGER            IDIM( NIDIM ), INC( NINC )\n*     .. Local Scalars ..\n      DOUBLE PRECISION   ALPHA, ALS, ERR, ERRMAX, TRANSL\n      INTEGER            I, IA, IM, IN, INCX, INCXS, INCY, INCYS, IX,\n     $                   IY, J, LAA, LDA, LDAS, LX, LY, M, MS, N, NARGS,\n     $                   NC, ND, NS\n      LOGICAL            NULL, RESET, SAME\n*     .. Local Arrays ..\n      DOUBLE PRECISION   W( 1 )\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LDE, LDERES\n      EXTERNAL           LDE, LDERES\n*     .. External Subroutines ..\n      EXTERNAL           DGER, DMAKE, DMVCH\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, MAX, MIN\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Executable Statements ..\n*     Define the number of arguments.\n      NARGS = 9\n*\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = ZERO\n*\n      DO 120 IN = 1, NIDIM\n         N = IDIM( IN )\n         ND = N/2 + 1\n*\n         DO 110 IM = 1, 2\n            IF( IM.EQ.1 )\n     $         M = MAX( N - ND, 0 )\n            IF( IM.EQ.2 )\n     $         M = MIN( N + ND, NMAX )\n*\n*           Set LDA to 1 more than minimum value if room.\n            LDA = M\n            IF( LDA.LT.NMAX )\n     $         LDA = LDA + 1\n*           Skip tests if not enough room.\n            IF( LDA.GT.NMAX )\n     $         GO TO 110\n            LAA = LDA*N\n            NULL = N.LE.0.OR.M.LE.0\n*\n            DO 100 IX = 1, NINC\n               INCX = INC( IX )\n               LX = ABS( INCX )*M\n*\n*              Generate the vector X.\n*\n               TRANSL = HALF\n               CALL DMAKE( 'GE', ' ', ' ', 1, M, X, 1, XX, ABS( INCX ),\n     $                     0, M - 1, RESET, TRANSL )\n               IF( M.GT.1 )THEN\n                  X( M/2 ) = ZERO\n                  XX( 1 + ABS( INCX )*( M/2 - 1 ) ) = ZERO\n               END IF\n*\n               DO 90 IY = 1, NINC\n                  INCY = INC( IY )\n                  LY = ABS( INCY )*N\n*\n*                 Generate the vector Y.\n*\n                  TRANSL = ZERO\n                  CALL DMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY,\n     $                        ABS( INCY ), 0, N - 1, RESET, TRANSL )\n                  IF( N.GT.1 )THEN\n                     Y( N/2 ) = ZERO\n                     YY( 1 + ABS( INCY )*( N/2 - 1 ) ) = ZERO\n                  END IF\n*\n                  DO 80 IA = 1, NALF\n                     ALPHA = ALF( IA )\n*\n*                    Generate the matrix A.\n*\n                     TRANSL = ZERO\n                     CALL DMAKE( SNAME( 2: 3 ), ' ', ' ', M, N, A, NMAX,\n     $                           AA, LDA, M - 1, N - 1, RESET, TRANSL )\n*\n                     NC = NC + 1\n*\n*                    Save every datum before calling the subroutine.\n*\n                     MS = M\n                     NS = N\n                     ALS = ALPHA\n                     DO 10 I = 1, LAA\n                        AS( I ) = AA( I )\n   10                CONTINUE\n                     LDAS = LDA\n                     DO 20 I = 1, LX\n                        XS( I ) = XX( I )\n   20                CONTINUE\n                     INCXS = INCX\n                     DO 30 I = 1, LY\n                        YS( I ) = YY( I )\n   30                CONTINUE\n                     INCYS = INCY\n*\n*                    Call the subroutine.\n*\n                     IF( TRACE )\n     $                  WRITE( NTRA, FMT = 9994 )NC, SNAME, M, N,\n     $                  ALPHA, INCX, INCY, LDA\n                     IF( REWI )\n     $                  REWIND NTRA\n                     CALL DGER( M, N, ALPHA, XX, INCX, YY, INCY, AA,\n     $                          LDA )\n*\n*                    Check if error-exit was taken incorrectly.\n*\n                     IF( .NOT.OK )THEN\n                        WRITE( NOUT, FMT = 9993 )\n                        FATAL = .TRUE.\n                        GO TO 140\n                     END IF\n*\n*                    See what data changed inside subroutine.\n*\n                     ISAME( 1 ) = MS.EQ.M\n                     ISAME( 2 ) = NS.EQ.N\n                     ISAME( 3 ) = ALS.EQ.ALPHA\n                     ISAME( 4 ) = LDE( XS, XX, LX )\n                     ISAME( 5 ) = INCXS.EQ.INCX\n                     ISAME( 6 ) = LDE( YS, YY, LY )\n                     ISAME( 7 ) = INCYS.EQ.INCY\n                     IF( NULL )THEN\n                        ISAME( 8 ) = LDE( AS, AA, LAA )\n                     ELSE\n                        ISAME( 8 ) = LDERES( 'GE', ' ', M, N, AS, AA,\n     $                               LDA )\n                     END IF\n                     ISAME( 9 ) = LDAS.EQ.LDA\n*\n*                    If data was incorrectly changed, report and return.\n*\n                     SAME = .TRUE.\n                     DO 40 I = 1, NARGS\n                        SAME = SAME.AND.ISAME( I )\n                        IF( .NOT.ISAME( I ) )\n     $                     WRITE( NOUT, FMT = 9998 )I\n   40                CONTINUE\n                     IF( .NOT.SAME )THEN\n                        FATAL = .TRUE.\n                        GO TO 140\n                     END IF\n*\n                     IF( .NOT.NULL )THEN\n*\n*                       Check the result column by column.\n*\n                        IF( INCX.GT.0 )THEN\n                           DO 50 I = 1, M\n                              Z( I ) = X( I )\n   50                      CONTINUE\n                        ELSE\n                           DO 60 I = 1, M\n                              Z( I ) = X( M - I + 1 )\n   60                      CONTINUE\n                        END IF\n                        DO 70 J = 1, N\n                           IF( INCY.GT.0 )THEN\n                              W( 1 ) = Y( J )\n                           ELSE\n                              W( 1 ) = Y( N - J + 1 )\n                           END IF\n                           CALL DMVCH( 'N', M, 1, ALPHA, Z, NMAX, W, 1,\n     $                                 ONE, A( 1, J ), 1, YT, G,\n     $                                 AA( 1 + ( J - 1 )*LDA ), EPS,\n     $                                 ERR, FATAL, NOUT, .TRUE. )\n                           ERRMAX = MAX( ERRMAX, ERR )\n*                          If got really bad answer, report and return.\n                           IF( FATAL )\n     $                        GO TO 130\n   70                   CONTINUE\n                     ELSE\n*                       Avoid repeating tests with M.le.0 or N.le.0.\n                        GO TO 110\n                     END IF\n*\n   80             CONTINUE\n*\n   90          CONTINUE\n*\n  100       CONTINUE\n*\n  110    CONTINUE\n*\n  120 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 150\n*\n  130 CONTINUE\n      WRITE( NOUT, FMT = 9995 )J\n*\n  140 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      WRITE( NOUT, FMT = 9994 )NC, SNAME, M, N, ALPHA, INCX, INCY, LDA\n*\n  150 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( '      THESE ARE THE RESULTS FOR COLUMN ', I3 )\n 9994 FORMAT( 1X, I6, ': ', A6, '(', 2( I3, ',' ), F4.1, ', X,', I2,\n     $      ', Y,', I2, ', A,', I3, ')                  .' )\n 9993 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of DCHK4.\n*\n      END\n      SUBROUTINE DCHK5( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX,\n     $                  INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G,\n     $                  Z )\n*\n*  Tests DSYR and DSPR.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Parameters ..\n      DOUBLE PRECISION   ZERO, HALF, ONE\n      PARAMETER          ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0 )\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION   EPS, THRESH\n      INTEGER            INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      DOUBLE PRECISION   A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), G( NMAX ), X( NMAX ),\n     $                   XS( NMAX*INCMAX ), XX( NMAX*INCMAX ),\n     $                   Y( NMAX ), YS( NMAX*INCMAX ), YT( NMAX ),\n     $                   YY( NMAX*INCMAX ), Z( NMAX )\n      INTEGER            IDIM( NIDIM ), INC( NINC )\n*     .. Local Scalars ..\n      DOUBLE PRECISION   ALPHA, ALS, ERR, ERRMAX, TRANSL\n      INTEGER            I, IA, IC, IN, INCX, INCXS, IX, J, JA, JJ, LAA,\n     $                   LDA, LDAS, LJ, LX, N, NARGS, NC, NS\n      LOGICAL            FULL, NULL, PACKED, RESET, SAME, UPPER\n      CHARACTER*1        UPLO, UPLOS\n      CHARACTER*2        ICH\n*     .. Local Arrays ..\n      DOUBLE PRECISION   W( 1 )\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LDE, LDERES\n      EXTERNAL           LDE, LDERES\n*     .. External Subroutines ..\n      EXTERNAL           DMAKE, DMVCH, DSPR, DSYR\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, MAX\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICH/'UL'/\n*     .. Executable Statements ..\n      FULL = SNAME( 3: 3 ).EQ.'Y'\n      PACKED = SNAME( 3: 3 ).EQ.'P'\n*     Define the number of arguments.\n      IF( FULL )THEN\n         NARGS = 7\n      ELSE IF( PACKED )THEN\n         NARGS = 6\n      END IF\n*\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = ZERO\n*\n      DO 100 IN = 1, NIDIM\n         N = IDIM( IN )\n*        Set LDA to 1 more than minimum value if room.\n         LDA = N\n         IF( LDA.LT.NMAX )\n     $      LDA = LDA + 1\n*        Skip tests if not enough room.\n         IF( LDA.GT.NMAX )\n     $      GO TO 100\n         IF( PACKED )THEN\n            LAA = ( N*( N + 1 ) )/2\n         ELSE\n            LAA = LDA*N\n         END IF\n*\n         DO 90 IC = 1, 2\n            UPLO = ICH( IC: IC )\n            UPPER = UPLO.EQ.'U'\n*\n            DO 80 IX = 1, NINC\n               INCX = INC( IX )\n               LX = ABS( INCX )*N\n*\n*              Generate the vector X.\n*\n               TRANSL = HALF\n               CALL DMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX, ABS( INCX ),\n     $                     0, N - 1, RESET, TRANSL )\n               IF( N.GT.1 )THEN\n                  X( N/2 ) = ZERO\n                  XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO\n               END IF\n*\n               DO 70 IA = 1, NALF\n                  ALPHA = ALF( IA )\n                  NULL = N.LE.0.OR.ALPHA.EQ.ZERO\n*\n*                 Generate the matrix A.\n*\n                  TRANSL = ZERO\n                  CALL DMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A, NMAX,\n     $                        AA, LDA, N - 1, N - 1, RESET, TRANSL )\n*\n                  NC = NC + 1\n*\n*                 Save every datum before calling the subroutine.\n*\n                  UPLOS = UPLO\n                  NS = N\n                  ALS = ALPHA\n                  DO 10 I = 1, LAA\n                     AS( I ) = AA( I )\n   10             CONTINUE\n                  LDAS = LDA\n                  DO 20 I = 1, LX\n                     XS( I ) = XX( I )\n   20             CONTINUE\n                  INCXS = INCX\n*\n*                 Call the subroutine.\n*\n                  IF( FULL )THEN\n                     IF( TRACE )\n     $                  WRITE( NTRA, FMT = 9993 )NC, SNAME, UPLO, N,\n     $                  ALPHA, INCX, LDA\n                     IF( REWI )\n     $                  REWIND NTRA\n                     CALL DSYR( UPLO, N, ALPHA, XX, INCX, AA, LDA )\n                  ELSE IF( PACKED )THEN\n                     IF( TRACE )\n     $                  WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO, N,\n     $                  ALPHA, INCX\n                     IF( REWI )\n     $                  REWIND NTRA\n                     CALL DSPR( UPLO, N, ALPHA, XX, INCX, AA )\n                  END IF\n*\n*                 Check if error-exit was taken incorrectly.\n*\n                  IF( .NOT.OK )THEN\n                     WRITE( NOUT, FMT = 9992 )\n                     FATAL = .TRUE.\n                     GO TO 120\n                  END IF\n*\n*                 See what data changed inside subroutines.\n*\n                  ISAME( 1 ) = UPLO.EQ.UPLOS\n                  ISAME( 2 ) = NS.EQ.N\n                  ISAME( 3 ) = ALS.EQ.ALPHA\n                  ISAME( 4 ) = LDE( XS, XX, LX )\n                  ISAME( 5 ) = INCXS.EQ.INCX\n                  IF( NULL )THEN\n                     ISAME( 6 ) = LDE( AS, AA, LAA )\n                  ELSE\n                     ISAME( 6 ) = LDERES( SNAME( 2: 3 ), UPLO, N, N, AS,\n     $                            AA, LDA )\n                  END IF\n                  IF( .NOT.PACKED )THEN\n                     ISAME( 7 ) = LDAS.EQ.LDA\n                  END IF\n*\n*                 If data was incorrectly changed, report and return.\n*\n                  SAME = .TRUE.\n                  DO 30 I = 1, NARGS\n                     SAME = SAME.AND.ISAME( I )\n                     IF( .NOT.ISAME( I ) )\n     $                  WRITE( NOUT, FMT = 9998 )I\n   30             CONTINUE\n                  IF( .NOT.SAME )THEN\n                     FATAL = .TRUE.\n                     GO TO 120\n                  END IF\n*\n                  IF( .NOT.NULL )THEN\n*\n*                    Check the result column by column.\n*\n                     IF( INCX.GT.0 )THEN\n                        DO 40 I = 1, N\n                           Z( I ) = X( I )\n   40                   CONTINUE\n                     ELSE\n                        DO 50 I = 1, N\n                           Z( I ) = X( N - I + 1 )\n   50                   CONTINUE\n                     END IF\n                     JA = 1\n                     DO 60 J = 1, N\n                        W( 1 ) = Z( J )\n                        IF( UPPER )THEN\n                           JJ = 1\n                           LJ = J\n                        ELSE\n                           JJ = J\n                           LJ = N - J + 1\n                        END IF\n                        CALL DMVCH( 'N', LJ, 1, ALPHA, Z( JJ ), LJ, W,\n     $                              1, ONE, A( JJ, J ), 1, YT, G,\n     $                              AA( JA ), EPS, ERR, FATAL, NOUT,\n     $                              .TRUE. )\n                        IF( FULL )THEN\n                           IF( UPPER )THEN\n                              JA = JA + LDA\n                           ELSE\n                              JA = JA + LDA + 1\n                           END IF\n                        ELSE\n                           JA = JA + LJ\n                        END IF\n                        ERRMAX = MAX( ERRMAX, ERR )\n*                       If got really bad answer, report and return.\n                        IF( FATAL )\n     $                     GO TO 110\n   60                CONTINUE\n                  ELSE\n*                    Avoid repeating tests if N.le.0.\n                     IF( N.LE.0 )\n     $                  GO TO 100\n                  END IF\n*\n   70          CONTINUE\n*\n   80       CONTINUE\n*\n   90    CONTINUE\n*\n  100 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 130\n*\n  110 CONTINUE\n      WRITE( NOUT, FMT = 9995 )J\n*\n  120 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      IF( FULL )THEN\n         WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, ALPHA, INCX, LDA\n      ELSE IF( PACKED )THEN\n         WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, ALPHA, INCX\n      END IF\n*\n  130 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( '      THESE ARE THE RESULTS FOR COLUMN ', I3 )\n 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,',\n     $      I2, ', AP)                           .' )\n 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,',\n     $      I2, ', A,', I3, ')                        .' )\n 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of DCHK5.\n*\n      END\n      SUBROUTINE DCHK6( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX,\n     $                  INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G,\n     $                  Z )\n*\n*  Tests DSYR2 and DSPR2.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Parameters ..\n      DOUBLE PRECISION   ZERO, HALF, ONE\n      PARAMETER          ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0 )\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION   EPS, THRESH\n      INTEGER            INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      DOUBLE PRECISION   A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), G( NMAX ), X( NMAX ),\n     $                   XS( NMAX*INCMAX ), XX( NMAX*INCMAX ),\n     $                   Y( NMAX ), YS( NMAX*INCMAX ), YT( NMAX ),\n     $                   YY( NMAX*INCMAX ), Z( NMAX, 2 )\n      INTEGER            IDIM( NIDIM ), INC( NINC )\n*     .. Local Scalars ..\n      DOUBLE PRECISION   ALPHA, ALS, ERR, ERRMAX, TRANSL\n      INTEGER            I, IA, IC, IN, INCX, INCXS, INCY, INCYS, IX,\n     $                   IY, J, JA, JJ, LAA, LDA, LDAS, LJ, LX, LY, N,\n     $                   NARGS, NC, NS\n      LOGICAL            FULL, NULL, PACKED, RESET, SAME, UPPER\n      CHARACTER*1        UPLO, UPLOS\n      CHARACTER*2        ICH\n*     .. Local Arrays ..\n      DOUBLE PRECISION   W( 2 )\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LDE, LDERES\n      EXTERNAL           LDE, LDERES\n*     .. External Subroutines ..\n      EXTERNAL           DMAKE, DMVCH, DSPR2, DSYR2\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, MAX\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICH/'UL'/\n*     .. Executable Statements ..\n      FULL = SNAME( 3: 3 ).EQ.'Y'\n      PACKED = SNAME( 3: 3 ).EQ.'P'\n*     Define the number of arguments.\n      IF( FULL )THEN\n         NARGS = 9\n      ELSE IF( PACKED )THEN\n         NARGS = 8\n      END IF\n*\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = ZERO\n*\n      DO 140 IN = 1, NIDIM\n         N = IDIM( IN )\n*        Set LDA to 1 more than minimum value if room.\n         LDA = N\n         IF( LDA.LT.NMAX )\n     $      LDA = LDA + 1\n*        Skip tests if not enough room.\n         IF( LDA.GT.NMAX )\n     $      GO TO 140\n         IF( PACKED )THEN\n            LAA = ( N*( N + 1 ) )/2\n         ELSE\n            LAA = LDA*N\n         END IF\n*\n         DO 130 IC = 1, 2\n            UPLO = ICH( IC: IC )\n            UPPER = UPLO.EQ.'U'\n*\n            DO 120 IX = 1, NINC\n               INCX = INC( IX )\n               LX = ABS( INCX )*N\n*\n*              Generate the vector X.\n*\n               TRANSL = HALF\n               CALL DMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX, ABS( INCX ),\n     $                     0, N - 1, RESET, TRANSL )\n               IF( N.GT.1 )THEN\n                  X( N/2 ) = ZERO\n                  XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO\n               END IF\n*\n               DO 110 IY = 1, NINC\n                  INCY = INC( IY )\n                  LY = ABS( INCY )*N\n*\n*                 Generate the vector Y.\n*\n                  TRANSL = ZERO\n                  CALL DMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY,\n     $                        ABS( INCY ), 0, N - 1, RESET, TRANSL )\n                  IF( N.GT.1 )THEN\n                     Y( N/2 ) = ZERO\n                     YY( 1 + ABS( INCY )*( N/2 - 1 ) ) = ZERO\n                  END IF\n*\n                  DO 100 IA = 1, NALF\n                     ALPHA = ALF( IA )\n                     NULL = N.LE.0.OR.ALPHA.EQ.ZERO\n*\n*                    Generate the matrix A.\n*\n                     TRANSL = ZERO\n                     CALL DMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A,\n     $                           NMAX, AA, LDA, N - 1, N - 1, RESET,\n     $                           TRANSL )\n*\n                     NC = NC + 1\n*\n*                    Save every datum before calling the subroutine.\n*\n                     UPLOS = UPLO\n                     NS = N\n                     ALS = ALPHA\n                     DO 10 I = 1, LAA\n                        AS( I ) = AA( I )\n   10                CONTINUE\n                     LDAS = LDA\n                     DO 20 I = 1, LX\n                        XS( I ) = XX( I )\n   20                CONTINUE\n                     INCXS = INCX\n                     DO 30 I = 1, LY\n                        YS( I ) = YY( I )\n   30                CONTINUE\n                     INCYS = INCY\n*\n*                    Call the subroutine.\n*\n                     IF( FULL )THEN\n                        IF( TRACE )\n     $                     WRITE( NTRA, FMT = 9993 )NC, SNAME, UPLO, N,\n     $                     ALPHA, INCX, INCY, LDA\n                        IF( REWI )\n     $                     REWIND NTRA\n                        CALL DSYR2( UPLO, N, ALPHA, XX, INCX, YY, INCY,\n     $                              AA, LDA )\n                     ELSE IF( PACKED )THEN\n                        IF( TRACE )\n     $                     WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO, N,\n     $                     ALPHA, INCX, INCY\n                        IF( REWI )\n     $                     REWIND NTRA\n                        CALL DSPR2( UPLO, N, ALPHA, XX, INCX, YY, INCY,\n     $                              AA )\n                     END IF\n*\n*                    Check if error-exit was taken incorrectly.\n*\n                     IF( .NOT.OK )THEN\n                        WRITE( NOUT, FMT = 9992 )\n                        FATAL = .TRUE.\n                        GO TO 160\n                     END IF\n*\n*                    See what data changed inside subroutines.\n*\n                     ISAME( 1 ) = UPLO.EQ.UPLOS\n                     ISAME( 2 ) = NS.EQ.N\n                     ISAME( 3 ) = ALS.EQ.ALPHA\n                     ISAME( 4 ) = LDE( XS, XX, LX )\n                     ISAME( 5 ) = INCXS.EQ.INCX\n                     ISAME( 6 ) = LDE( YS, YY, LY )\n                     ISAME( 7 ) = INCYS.EQ.INCY\n                     IF( NULL )THEN\n                        ISAME( 8 ) = LDE( AS, AA, LAA )\n                     ELSE\n                        ISAME( 8 ) = LDERES( SNAME( 2: 3 ), UPLO, N, N,\n     $                               AS, AA, LDA )\n                     END IF\n                     IF( .NOT.PACKED )THEN\n                        ISAME( 9 ) = LDAS.EQ.LDA\n                     END IF\n*\n*                    If data was incorrectly changed, report and return.\n*\n                     SAME = .TRUE.\n                     DO 40 I = 1, NARGS\n                        SAME = SAME.AND.ISAME( I )\n                        IF( .NOT.ISAME( I ) )\n     $                     WRITE( NOUT, FMT = 9998 )I\n   40                CONTINUE\n                     IF( .NOT.SAME )THEN\n                        FATAL = .TRUE.\n                        GO TO 160\n                     END IF\n*\n                     IF( .NOT.NULL )THEN\n*\n*                       Check the result column by column.\n*\n                        IF( INCX.GT.0 )THEN\n                           DO 50 I = 1, N\n                              Z( I, 1 ) = X( I )\n   50                      CONTINUE\n                        ELSE\n                           DO 60 I = 1, N\n                              Z( I, 1 ) = X( N - I + 1 )\n   60                      CONTINUE\n                        END IF\n                        IF( INCY.GT.0 )THEN\n                           DO 70 I = 1, N\n                              Z( I, 2 ) = Y( I )\n   70                      CONTINUE\n                        ELSE\n                           DO 80 I = 1, N\n                              Z( I, 2 ) = Y( N - I + 1 )\n   80                      CONTINUE\n                        END IF\n                        JA = 1\n                        DO 90 J = 1, N\n                           W( 1 ) = Z( J, 2 )\n                           W( 2 ) = Z( J, 1 )\n                           IF( UPPER )THEN\n                              JJ = 1\n                              LJ = J\n                           ELSE\n                              JJ = J\n                              LJ = N - J + 1\n                           END IF\n                           CALL DMVCH( 'N', LJ, 2, ALPHA, Z( JJ, 1 ),\n     $                                 NMAX, W, 1, ONE, A( JJ, J ), 1,\n     $                                 YT, G, AA( JA ), EPS, ERR, FATAL,\n     $                                 NOUT, .TRUE. )\n                           IF( FULL )THEN\n                              IF( UPPER )THEN\n                                 JA = JA + LDA\n                              ELSE\n                                 JA = JA + LDA + 1\n                              END IF\n                           ELSE\n                              JA = JA + LJ\n                           END IF\n                           ERRMAX = MAX( ERRMAX, ERR )\n*                          If got really bad answer, report and return.\n                           IF( FATAL )\n     $                        GO TO 150\n   90                   CONTINUE\n                     ELSE\n*                       Avoid repeating tests with N.le.0.\n                        IF( N.LE.0 )\n     $                     GO TO 140\n                     END IF\n*\n  100             CONTINUE\n*\n  110          CONTINUE\n*\n  120       CONTINUE\n*\n  130    CONTINUE\n*\n  140 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 170\n*\n  150 CONTINUE\n      WRITE( NOUT, FMT = 9995 )J\n*\n  160 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      IF( FULL )THEN\n         WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, ALPHA, INCX,\n     $      INCY, LDA\n      ELSE IF( PACKED )THEN\n         WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, ALPHA, INCX, INCY\n      END IF\n*\n  170 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( '      THESE ARE THE RESULTS FOR COLUMN ', I3 )\n 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,',\n     $      I2, ', Y,', I2, ', AP)                     .' )\n 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,',\n     $      I2, ', Y,', I2, ', A,', I3, ')                  .' )\n 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of DCHK6.\n*\n      END\n      SUBROUTINE DCHKE( ISNUM, SRNAMT, NOUT )\n*\n*  Tests the error exits from the Level 2 Blas.\n*  Requires a special version of the error-handling routine XERBLA.\n*  ALPHA, BETA, A, X and Y should not need to be defined.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Scalar Arguments ..\n      INTEGER            ISNUM, NOUT\n      CHARACTER*6        SRNAMT\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Local Scalars ..\n      DOUBLE PRECISION   ALPHA, BETA\n*     .. Local Arrays ..\n      DOUBLE PRECISION   A( 1, 1 ), X( 1 ), Y( 1 )\n*     .. External Subroutines ..\n      EXTERNAL           CHKXER, DGBMV, DGEMV, DGER, DSBMV, DSPMV, DSPR,\n     $                   DSPR2, DSYMV, DSYR, DSYR2, DTBMV, DTBSV, DTPMV,\n     $                   DTPSV, DTRMV, DTRSV\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Executable Statements ..\n*     OK is set to .FALSE. by the special version of XERBLA or by CHKXER\n*     if anything is wrong.\n      OK = .TRUE.\n*     LERR is set to .TRUE. by the special version of XERBLA each time\n*     it is called, and is then tested and re-set by CHKXER.\n      LERR = .FALSE.\n      GO TO ( 10, 20, 30, 40, 50, 60, 70, 80,\n     $        90, 100, 110, 120, 130, 140, 150,\n     $        160 )ISNUM\n   10 INFOT = 1\n      CALL DGEMV( '/', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL DGEMV( 'N', -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL DGEMV( 'N', 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL DGEMV( 'N', 2, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL DGEMV( 'N', 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL DGEMV( 'N', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 170\n   20 INFOT = 1\n      CALL DGBMV( '/', 0, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL DGBMV( 'N', -1, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL DGBMV( 'N', 0, -1, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL DGBMV( 'N', 0, 0, -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL DGBMV( 'N', 2, 0, 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL DGBMV( 'N', 0, 0, 1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL DGBMV( 'N', 0, 0, 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 13\n      CALL DGBMV( 'N', 0, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 170\n   30 INFOT = 1\n      CALL DSYMV( '/', 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL DSYMV( 'U', -1, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL DSYMV( 'U', 2, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL DSYMV( 'U', 0, ALPHA, A, 1, X, 0, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL DSYMV( 'U', 0, ALPHA, A, 1, X, 1, BETA, Y, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 170\n   40 INFOT = 1\n      CALL DSBMV( '/', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL DSBMV( 'U', -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL DSBMV( 'U', 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL DSBMV( 'U', 0, 1, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL DSBMV( 'U', 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL DSBMV( 'U', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 170\n   50 INFOT = 1\n      CALL DSPMV( '/', 0, ALPHA, A, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL DSPMV( 'U', -1, ALPHA, A, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL DSPMV( 'U', 0, ALPHA, A, X, 0, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL DSPMV( 'U', 0, ALPHA, A, X, 1, BETA, Y, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 170\n   60 INFOT = 1\n      CALL DTRMV( '/', 'N', 'N', 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL DTRMV( 'U', '/', 'N', 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL DTRMV( 'U', 'N', '/', 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL DTRMV( 'U', 'N', 'N', -1, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL DTRMV( 'U', 'N', 'N', 2, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL DTRMV( 'U', 'N', 'N', 0, A, 1, X, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 170\n   70 INFOT = 1\n      CALL DTBMV( '/', 'N', 'N', 0, 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL DTBMV( 'U', '/', 'N', 0, 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL DTBMV( 'U', 'N', '/', 0, 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL DTBMV( 'U', 'N', 'N', -1, 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL DTBMV( 'U', 'N', 'N', 0, -1, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL DTBMV( 'U', 'N', 'N', 0, 1, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL DTBMV( 'U', 'N', 'N', 0, 0, A, 1, X, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 170\n   80 INFOT = 1\n      CALL DTPMV( '/', 'N', 'N', 0, A, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL DTPMV( 'U', '/', 'N', 0, A, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL DTPMV( 'U', 'N', '/', 0, A, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL DTPMV( 'U', 'N', 'N', -1, A, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL DTPMV( 'U', 'N', 'N', 0, A, X, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 170\n   90 INFOT = 1\n      CALL DTRSV( '/', 'N', 'N', 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL DTRSV( 'U', '/', 'N', 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL DTRSV( 'U', 'N', '/', 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL DTRSV( 'U', 'N', 'N', -1, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL DTRSV( 'U', 'N', 'N', 2, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL DTRSV( 'U', 'N', 'N', 0, A, 1, X, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 170\n  100 INFOT = 1\n      CALL DTBSV( '/', 'N', 'N', 0, 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL DTBSV( 'U', '/', 'N', 0, 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL DTBSV( 'U', 'N', '/', 0, 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL DTBSV( 'U', 'N', 'N', -1, 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL DTBSV( 'U', 'N', 'N', 0, -1, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL DTBSV( 'U', 'N', 'N', 0, 1, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL DTBSV( 'U', 'N', 'N', 0, 0, A, 1, X, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 170\n  110 INFOT = 1\n      CALL DTPSV( '/', 'N', 'N', 0, A, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL DTPSV( 'U', '/', 'N', 0, A, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL DTPSV( 'U', 'N', '/', 0, A, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL DTPSV( 'U', 'N', 'N', -1, A, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL DTPSV( 'U', 'N', 'N', 0, A, X, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 170\n  120 INFOT = 1\n      CALL DGER( -1, 0, ALPHA, X, 1, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL DGER( 0, -1, ALPHA, X, 1, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL DGER( 0, 0, ALPHA, X, 0, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL DGER( 0, 0, ALPHA, X, 1, Y, 0, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL DGER( 2, 0, ALPHA, X, 1, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 170\n  130 INFOT = 1\n      CALL DSYR( '/', 0, ALPHA, X, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL DSYR( 'U', -1, ALPHA, X, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL DSYR( 'U', 0, ALPHA, X, 0, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL DSYR( 'U', 2, ALPHA, X, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 170\n  140 INFOT = 1\n      CALL DSPR( '/', 0, ALPHA, X, 1, A )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL DSPR( 'U', -1, ALPHA, X, 1, A )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL DSPR( 'U', 0, ALPHA, X, 0, A )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 170\n  150 INFOT = 1\n      CALL DSYR2( '/', 0, ALPHA, X, 1, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL DSYR2( 'U', -1, ALPHA, X, 1, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL DSYR2( 'U', 0, ALPHA, X, 0, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL DSYR2( 'U', 0, ALPHA, X, 1, Y, 0, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL DSYR2( 'U', 2, ALPHA, X, 1, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 170\n  160 INFOT = 1\n      CALL DSPR2( '/', 0, ALPHA, X, 1, Y, 1, A )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL DSPR2( 'U', -1, ALPHA, X, 1, Y, 1, A )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL DSPR2( 'U', 0, ALPHA, X, 0, Y, 1, A )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL DSPR2( 'U', 0, ALPHA, X, 1, Y, 0, A )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n*\n  170 IF( OK )THEN\n         WRITE( NOUT, FMT = 9999 )SRNAMT\n      ELSE\n         WRITE( NOUT, FMT = 9998 )SRNAMT\n      END IF\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE TESTS OF ERROR-EXITS' )\n 9998 FORMAT( ' ******* ', A6, ' FAILED THE TESTS OF ERROR-EXITS *****',\n     $      '**' )\n*\n*     End of DCHKE.\n*\n      END\n      SUBROUTINE DMAKE( TYPE, UPLO, DIAG, M, N, A, NMAX, AA, LDA, KL,\n     $                  KU, RESET, TRANSL )\n*\n*  Generates values for an M by N matrix A within the bandwidth\n*  defined by KL and KU.\n*  Stores the values in the array AA in the data structure required\n*  by the routine, with unwanted elements set to rogue value.\n*\n*  TYPE is 'GE', 'GB', 'SY', 'SB', 'SP', 'TR', 'TB' OR 'TP'.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Parameters ..\n      DOUBLE PRECISION   ZERO, ONE\n      PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )\n      DOUBLE PRECISION   ROGUE\n      PARAMETER          ( ROGUE = -1.0D10 )\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION   TRANSL\n      INTEGER            KL, KU, LDA, M, N, NMAX\n      LOGICAL            RESET\n      CHARACTER*1        DIAG, UPLO\n      CHARACTER*2        TYPE\n*     .. Array Arguments ..\n      DOUBLE PRECISION   A( NMAX, * ), AA( * )\n*     .. Local Scalars ..\n      INTEGER            I, I1, I2, I3, IBEG, IEND, IOFF, J, KK\n      LOGICAL            GEN, LOWER, SYM, TRI, UNIT, UPPER\n*     .. External Functions ..\n      DOUBLE PRECISION   DBEG\n      EXTERNAL           DBEG\n*     .. Intrinsic Functions ..\n      INTRINSIC          MAX, MIN\n*     .. Executable Statements ..\n      GEN = TYPE( 1: 1 ).EQ.'G'\n      SYM = TYPE( 1: 1 ).EQ.'S'\n      TRI = TYPE( 1: 1 ).EQ.'T'\n      UPPER = ( SYM.OR.TRI ).AND.UPLO.EQ.'U'\n      LOWER = ( SYM.OR.TRI ).AND.UPLO.EQ.'L'\n      UNIT = TRI.AND.DIAG.EQ.'U'\n*\n*     Generate data in array A.\n*\n      DO 20 J = 1, N\n         DO 10 I = 1, M\n            IF( GEN.OR.( UPPER.AND.I.LE.J ).OR.( LOWER.AND.I.GE.J ) )\n     $          THEN\n               IF( ( I.LE.J.AND.J - I.LE.KU ).OR.\n     $             ( I.GE.J.AND.I - J.LE.KL ) )THEN\n                  A( I, J ) = DBEG( RESET ) + TRANSL\n               ELSE\n                  A( I, J ) = ZERO\n               END IF\n               IF( I.NE.J )THEN\n                  IF( SYM )THEN\n                     A( J, I ) = A( I, J )\n                  ELSE IF( TRI )THEN\n                     A( J, I ) = ZERO\n                  END IF\n               END IF\n            END IF\n   10    CONTINUE\n         IF( TRI )\n     $      A( J, J ) = A( J, J ) + ONE\n         IF( UNIT )\n     $      A( J, J ) = ONE\n   20 CONTINUE\n*\n*     Store elements in array AS in data structure required by routine.\n*\n      IF( TYPE.EQ.'GE' )THEN\n         DO 50 J = 1, N\n            DO 30 I = 1, M\n               AA( I + ( J - 1 )*LDA ) = A( I, J )\n   30       CONTINUE\n            DO 40 I = M + 1, LDA\n               AA( I + ( J - 1 )*LDA ) = ROGUE\n   40       CONTINUE\n   50    CONTINUE\n      ELSE IF( TYPE.EQ.'GB' )THEN\n         DO 90 J = 1, N\n            DO 60 I1 = 1, KU + 1 - J\n               AA( I1 + ( J - 1 )*LDA ) = ROGUE\n   60       CONTINUE\n            DO 70 I2 = I1, MIN( KL + KU + 1, KU + 1 + M - J )\n               AA( I2 + ( J - 1 )*LDA ) = A( I2 + J - KU - 1, J )\n   70       CONTINUE\n            DO 80 I3 = I2, LDA\n               AA( I3 + ( J - 1 )*LDA ) = ROGUE\n   80       CONTINUE\n   90    CONTINUE\n      ELSE IF( TYPE.EQ.'SY'.OR.TYPE.EQ.'TR' )THEN\n         DO 130 J = 1, N\n            IF( UPPER )THEN\n               IBEG = 1\n               IF( UNIT )THEN\n                  IEND = J - 1\n               ELSE\n                  IEND = J\n               END IF\n            ELSE\n               IF( UNIT )THEN\n                  IBEG = J + 1\n               ELSE\n                  IBEG = J\n               END IF\n               IEND = N\n            END IF\n            DO 100 I = 1, IBEG - 1\n               AA( I + ( J - 1 )*LDA ) = ROGUE\n  100       CONTINUE\n            DO 110 I = IBEG, IEND\n               AA( I + ( J - 1 )*LDA ) = A( I, J )\n  110       CONTINUE\n            DO 120 I = IEND + 1, LDA\n               AA( I + ( J - 1 )*LDA ) = ROGUE\n  120       CONTINUE\n  130    CONTINUE\n      ELSE IF( TYPE.EQ.'SB'.OR.TYPE.EQ.'TB' )THEN\n         DO 170 J = 1, N\n            IF( UPPER )THEN\n               KK = KL + 1\n               IBEG = MAX( 1, KL + 2 - J )\n               IF( UNIT )THEN\n                  IEND = KL\n               ELSE\n                  IEND = KL + 1\n               END IF\n            ELSE\n               KK = 1\n               IF( UNIT )THEN\n                  IBEG = 2\n               ELSE\n                  IBEG = 1\n               END IF\n               IEND = MIN( KL + 1, 1 + M - J )\n            END IF\n            DO 140 I = 1, IBEG - 1\n               AA( I + ( J - 1 )*LDA ) = ROGUE\n  140       CONTINUE\n            DO 150 I = IBEG, IEND\n               AA( I + ( J - 1 )*LDA ) = A( I + J - KK, J )\n  150       CONTINUE\n            DO 160 I = IEND + 1, LDA\n               AA( I + ( J - 1 )*LDA ) = ROGUE\n  160       CONTINUE\n  170    CONTINUE\n      ELSE IF( TYPE.EQ.'SP'.OR.TYPE.EQ.'TP' )THEN\n         IOFF = 0\n         DO 190 J = 1, N\n            IF( UPPER )THEN\n               IBEG = 1\n               IEND = J\n            ELSE\n               IBEG = J\n               IEND = N\n            END IF\n            DO 180 I = IBEG, IEND\n               IOFF = IOFF + 1\n               AA( IOFF ) = A( I, J )\n               IF( I.EQ.J )THEN\n                  IF( UNIT )\n     $               AA( IOFF ) = ROGUE\n               END IF\n  180       CONTINUE\n  190    CONTINUE\n      END IF\n      RETURN\n*\n*     End of DMAKE.\n*\n      END\n      SUBROUTINE DMVCH( TRANS, M, N, ALPHA, A, NMAX, X, INCX, BETA, Y,\n     $                  INCY, YT, G, YY, EPS, ERR, FATAL, NOUT, MV )\n*\n*  Checks the results of the computational tests.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Parameters ..\n      DOUBLE PRECISION   ZERO, ONE\n      PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION   ALPHA, BETA, EPS, ERR\n      INTEGER            INCX, INCY, M, N, NMAX, NOUT\n      LOGICAL            FATAL, MV\n      CHARACTER*1        TRANS\n*     .. Array Arguments ..\n      DOUBLE PRECISION   A( NMAX, * ), G( * ), X( * ), Y( * ), YT( * ),\n     $                   YY( * )\n*     .. Local Scalars ..\n      DOUBLE PRECISION   ERRI\n      INTEGER            I, INCXL, INCYL, IY, J, JX, KX, KY, ML, NL\n      LOGICAL            TRAN\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, MAX, SQRT\n*     .. Executable Statements ..\n      TRAN = TRANS.EQ.'T'.OR.TRANS.EQ.'C'\n      IF( TRAN )THEN\n         ML = N\n         NL = M\n      ELSE\n         ML = M\n         NL = N\n      END IF\n      IF( INCX.LT.0 )THEN\n         KX = NL\n         INCXL = -1\n      ELSE\n         KX = 1\n         INCXL = 1\n      END IF\n      IF( INCY.LT.0 )THEN\n         KY = ML\n         INCYL = -1\n      ELSE\n         KY = 1\n         INCYL = 1\n      END IF\n*\n*     Compute expected result in YT using data in A, X and Y.\n*     Compute gauges in G.\n*\n      IY = KY\n      DO 30 I = 1, ML\n         YT( IY ) = ZERO\n         G( IY ) = ZERO\n         JX = KX\n         IF( TRAN )THEN\n            DO 10 J = 1, NL\n               YT( IY ) = YT( IY ) + A( J, I )*X( JX )\n               G( IY ) = G( IY ) + ABS( A( J, I )*X( JX ) )\n               JX = JX + INCXL\n   10       CONTINUE\n         ELSE\n            DO 20 J = 1, NL\n               YT( IY ) = YT( IY ) + A( I, J )*X( JX )\n               G( IY ) = G( IY ) + ABS( A( I, J )*X( JX ) )\n               JX = JX + INCXL\n   20       CONTINUE\n         END IF\n         YT( IY ) = ALPHA*YT( IY ) + BETA*Y( IY )\n         G( IY ) = ABS( ALPHA )*G( IY ) + ABS( BETA*Y( IY ) )\n         IY = IY + INCYL\n   30 CONTINUE\n*\n*     Compute the error ratio for this result.\n*\n      ERR = ZERO\n      DO 40 I = 1, ML\n         ERRI = ABS( YT( I ) - YY( 1 + ( I - 1 )*ABS( INCY ) ) )/EPS\n         IF( G( I ).NE.ZERO )\n     $      ERRI = ERRI/G( I )\n         ERR = MAX( ERR, ERRI )\n         IF( ERR*SQRT( EPS ).GE.ONE )\n     $      GO TO 50\n   40 CONTINUE\n*     If the loop completes, all results are at least half accurate.\n      GO TO 70\n*\n*     Report fatal error.\n*\n   50 FATAL = .TRUE.\n      WRITE( NOUT, FMT = 9999 )\n      DO 60 I = 1, ML\n         IF( MV )THEN\n            WRITE( NOUT, FMT = 9998 )I, YT( I ),\n     $         YY( 1 + ( I - 1 )*ABS( INCY ) )\n         ELSE\n            WRITE( NOUT, FMT = 9998 )I,\n     $         YY( 1 + ( I - 1 )*ABS( INCY ) ), YT( I )\n         END IF\n   60 CONTINUE\n*\n   70 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ******* FATAL ERROR - COMPUTED RESULT IS LESS THAN HAL',\n     $      'F ACCURATE *******', /'           EXPECTED RESULT   COMPU',\n     $      'TED RESULT' )\n 9998 FORMAT( 1X, I7, 2G18.6 )\n*\n*     End of DMVCH.\n*\n      END\n      LOGICAL FUNCTION LDE( RI, RJ, LR )\n*\n*  Tests if two arrays are identical.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Scalar Arguments ..\n      INTEGER            LR\n*     .. Array Arguments ..\n      DOUBLE PRECISION   RI( * ), RJ( * )\n*     .. Local Scalars ..\n      INTEGER            I\n*     .. Executable Statements ..\n      DO 10 I = 1, LR\n         IF( RI( I ).NE.RJ( I ) )\n     $      GO TO 20\n   10 CONTINUE\n      LDE = .TRUE.\n      GO TO 30\n   20 CONTINUE\n      LDE = .FALSE.\n   30 RETURN\n*\n*     End of LDE.\n*\n      END\n      LOGICAL FUNCTION LDERES( TYPE, UPLO, M, N, AA, AS, LDA )\n*\n*  Tests if selected elements in two arrays are equal.\n*\n*  TYPE is 'GE', 'SY' or 'SP'.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Scalar Arguments ..\n      INTEGER            LDA, M, N\n      CHARACTER*1        UPLO\n      CHARACTER*2        TYPE\n*     .. Array Arguments ..\n      DOUBLE PRECISION   AA( LDA, * ), AS( LDA, * )\n*     .. Local Scalars ..\n      INTEGER            I, IBEG, IEND, J\n      LOGICAL            UPPER\n*     .. Executable Statements ..\n      UPPER = UPLO.EQ.'U'\n      IF( TYPE.EQ.'GE' )THEN\n         DO 20 J = 1, N\n            DO 10 I = M + 1, LDA\n               IF( AA( I, J ).NE.AS( I, J ) )\n     $            GO TO 70\n   10       CONTINUE\n   20    CONTINUE\n      ELSE IF( TYPE.EQ.'SY' )THEN\n         DO 50 J = 1, N\n            IF( UPPER )THEN\n               IBEG = 1\n               IEND = J\n            ELSE\n               IBEG = J\n               IEND = N\n            END IF\n            DO 30 I = 1, IBEG - 1\n               IF( AA( I, J ).NE.AS( I, J ) )\n     $            GO TO 70\n   30       CONTINUE\n            DO 40 I = IEND + 1, LDA\n               IF( AA( I, J ).NE.AS( I, J ) )\n     $            GO TO 70\n   40       CONTINUE\n   50    CONTINUE\n      END IF\n*\n      LDERES = .TRUE.\n      GO TO 80\n   70 CONTINUE\n      LDERES = .FALSE.\n   80 RETURN\n*\n*     End of LDERES.\n*\n      END\n      DOUBLE PRECISION FUNCTION DBEG( RESET )\n*\n*  Generates random numbers uniformly distributed between -0.5 and 0.5.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Scalar Arguments ..\n      LOGICAL            RESET\n*     .. Local Scalars ..\n      INTEGER            I, IC, MI\n*     .. Save statement ..\n      SAVE               I, IC, MI\n*     .. Intrinsic Functions ..\n      INTRINSIC          DBLE\n*     .. Executable Statements ..\n      IF( RESET )THEN\n*        Initialize local variables.\n         MI = 891\n         I = 7\n         IC = 0\n         RESET = .FALSE.\n      END IF\n*\n*     The sequence of values of I is bounded between 1 and 999.\n*     If initial I = 1,2,3,6,7 or 9, the period will be 50.\n*     If initial I = 4 or 8, the period will be 25.\n*     If initial I = 5, the period will be 10.\n*     IC is used to break up the period by skipping 1 value of I in 6.\n*\n      IC = IC + 1\n   10 I = I*MI\n      I = I - 1000*( I/1000 )\n      IF( IC.GE.5 )THEN\n         IC = 0\n         GO TO 10\n      END IF\n      DBEG = DBLE( I - 500 )/1001.0D0\n      RETURN\n*\n*     End of DBEG.\n*\n      END\n      DOUBLE PRECISION FUNCTION DDIFF( X, Y )\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION   X, Y\n*     .. Executable Statements ..\n      DDIFF = X - Y\n      RETURN\n*\n*     End of DDIFF.\n*\n      END\n      SUBROUTINE CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n*\n*  Tests whether XERBLA has detected an error when it should.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Scalar Arguments ..\n      INTEGER            INFOT, NOUT\n      LOGICAL            LERR, OK\n      CHARACTER*6        SRNAMT\n*     .. Executable Statements ..\n      IF( .NOT.LERR )THEN\n         WRITE( NOUT, FMT = 9999 )INFOT, SRNAMT\n         OK = .FALSE.\n      END IF\n      LERR = .FALSE.\n      RETURN\n*\n 9999 FORMAT( ' ***** ILLEGAL VALUE OF PARAMETER NUMBER ', I2, ' NOT D',\n     $      'ETECTED BY ', A6, ' *****' )\n*\n*     End of CHKXER.\n*\n      END\n      SUBROUTINE XERBLA( SRNAME, INFO )\n*\n*  This is a special version of XERBLA to be used only as part of\n*  the test program for testing error exits from the Level 2 BLAS\n*  routines.\n*\n*  XERBLA  is an error handler for the Level 2 BLAS routines.\n*\n*  It is called by the Level 2 BLAS routines if an input parameter is\n*  invalid.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Scalar Arguments ..\n      INTEGER            INFO\n      CHARACTER*6        SRNAME\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUT\n      LOGICAL            LERR, OK\n      CHARACTER*6        SRNAMT\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUT, OK, LERR\n      COMMON             /SRNAMC/SRNAMT\n*     .. Executable Statements ..\n      LERR = .TRUE.\n      IF( INFO.NE.INFOT )THEN\n         IF( INFOT.NE.0 )THEN\n            WRITE( NOUT, FMT = 9999 )INFO, INFOT\n         ELSE\n            WRITE( NOUT, FMT = 9997 )INFO\n         END IF\n         OK = .FALSE.\n      END IF\n      IF( SRNAME.NE.SRNAMT )THEN\n         WRITE( NOUT, FMT = 9998 )SRNAME, SRNAMT\n         OK = .FALSE.\n      END IF\n      RETURN\n*\n 9999 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6, ' INSTEAD',\n     $      ' OF ', I2, ' *******' )\n 9998 FORMAT( ' ******* XERBLA WAS CALLED WITH SRNAME = ', A6, ' INSTE',\n     $      'AD OF ', A6, ' *******' )\n 9997 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6,\n     $      ' *******' )\n*\n*     End of XERBLA\n*\n      END\n\n"
  },
  {
    "path": "include/eigen3/blas/testing/dblat3.f",
    "content": "*> \\brief \\b DBLAT3\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*  Definition:\n*  ===========\n*\n*       PROGRAM DBLAT3\n* \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> Test program for the DOUBLE PRECISION Level 3 Blas.\n*>\n*> The program must be driven by a short data file. The first 14 records\n*> of the file are read using list-directed input, the last 6 records\n*> are read using the format ( A6, L2 ). An annotated example of a data\n*> file can be obtained by deleting the first 3 characters from the\n*> following 20 lines:\n*> 'dblat3.out'      NAME OF SUMMARY OUTPUT FILE\n*> 6                 UNIT NUMBER OF SUMMARY FILE\n*> 'DBLAT3.SNAP'     NAME OF SNAPSHOT OUTPUT FILE\n*> -1                UNIT NUMBER OF SNAPSHOT FILE (NOT USED IF .LT. 0)\n*> F        LOGICAL FLAG, T TO REWIND SNAPSHOT FILE AFTER EACH RECORD.\n*> F        LOGICAL FLAG, T TO STOP ON FAILURES.\n*> T        LOGICAL FLAG, T TO TEST ERROR EXITS.\n*> 16.0     THRESHOLD VALUE OF TEST RATIO\n*> 6                 NUMBER OF VALUES OF N\n*> 0 1 2 3 5 9       VALUES OF N\n*> 3                 NUMBER OF VALUES OF ALPHA\n*> 0.0 1.0 0.7       VALUES OF ALPHA\n*> 3                 NUMBER OF VALUES OF BETA\n*> 0.0 1.0 1.3       VALUES OF BETA\n*> DGEMM  T PUT F FOR NO TEST. SAME COLUMNS.\n*> DSYMM  T PUT F FOR NO TEST. SAME COLUMNS.\n*> DTRMM  T PUT F FOR NO TEST. SAME COLUMNS.\n*> DTRSM  T PUT F FOR NO TEST. SAME COLUMNS.\n*> DSYRK  T PUT F FOR NO TEST. SAME COLUMNS.\n*> DSYR2K T PUT F FOR NO TEST. SAME COLUMNS.\n*>\n*> Further Details\n*> ===============\n*>\n*> See:\n*>\n*>    Dongarra J. J., Du Croz J. J., Duff I. S. and Hammarling S.\n*>    A Set of Level 3 Basic Linear Algebra Subprograms.\n*>\n*>    Technical Memorandum No.88 (Revision 1), Mathematics and\n*>    Computer Science Division, Argonne National Laboratory, 9700\n*>    South Cass Avenue, Argonne, Illinois 60439, US.\n*>\n*> -- Written on 8-February-1989.\n*>    Jack Dongarra, Argonne National Laboratory.\n*>    Iain Duff, AERE Harwell.\n*>    Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*>    Sven Hammarling, Numerical Algorithms Group Ltd.\n*>\n*>    10-9-00:  Change STATUS='NEW' to 'UNKNOWN' so that the testers\n*>              can be run multiple times without deleting generated\n*>              output files (susan)\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date April 2012\n*\n*> \\ingroup double_blas_testing\n*\n*  =====================================================================\n      PROGRAM DBLAT3\n*\n*  -- Reference BLAS test routine (version 3.4.1) --\n*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     April 2012\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      INTEGER            NIN\n      PARAMETER          ( NIN = 5 )\n      INTEGER            NSUBS\n      PARAMETER          ( NSUBS = 6 )\n      DOUBLE PRECISION   ZERO, ONE\n      PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )\n      INTEGER            NMAX\n      PARAMETER          ( NMAX = 65 )\n      INTEGER            NIDMAX, NALMAX, NBEMAX\n      PARAMETER          ( NIDMAX = 9, NALMAX = 7, NBEMAX = 7 )\n*     .. Local Scalars ..\n      DOUBLE PRECISION   EPS, ERR, THRESH\n      INTEGER            I, ISNUM, J, N, NALF, NBET, NIDIM, NOUT, NTRA\n      LOGICAL            FATAL, LTESTT, REWI, SAME, SFATAL, TRACE,\n     $                   TSTERR\n      CHARACTER*1        TRANSA, TRANSB\n      CHARACTER*6        SNAMET\n      CHARACTER*32       SNAPS, SUMMRY\n*     .. Local Arrays ..\n      DOUBLE PRECISION   AA( NMAX*NMAX ), AB( NMAX, 2*NMAX ),\n     $                   ALF( NALMAX ), AS( NMAX*NMAX ),\n     $                   BB( NMAX*NMAX ), BET( NBEMAX ),\n     $                   BS( NMAX*NMAX ), C( NMAX, NMAX ),\n     $                   CC( NMAX*NMAX ), CS( NMAX*NMAX ), CT( NMAX ),\n     $                   G( NMAX ), W( 2*NMAX )\n      INTEGER            IDIM( NIDMAX )\n      LOGICAL            LTEST( NSUBS )\n      CHARACTER*6        SNAMES( NSUBS )\n*     .. External Functions ..\n      DOUBLE PRECISION   DDIFF\n      LOGICAL            LDE\n      EXTERNAL           DDIFF, LDE\n*     .. External Subroutines ..\n      EXTERNAL           DCHK1, DCHK2, DCHK3, DCHK4, DCHK5, DCHKE, DMMCH\n*     .. Intrinsic Functions ..\n      INTRINSIC          MAX, MIN\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n      CHARACTER*6        SRNAMT\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n      COMMON             /SRNAMC/SRNAMT\n*     .. Data statements ..\n      DATA               SNAMES/'DGEMM ', 'DSYMM ', 'DTRMM ', 'DTRSM ',\n     $                   'DSYRK ', 'DSYR2K'/\n*     .. Executable Statements ..\n*\n*     Read name and unit number for summary output file and open file.\n*\n      READ( NIN, FMT = * )SUMMRY\n      READ( NIN, FMT = * )NOUT\n      OPEN( NOUT, FILE = SUMMRY, STATUS = 'UNKNOWN' )\n      NOUTC = NOUT\n*\n*     Read name and unit number for snapshot output file and open file.\n*\n      READ( NIN, FMT = * )SNAPS\n      READ( NIN, FMT = * )NTRA\n      TRACE = NTRA.GE.0\n      IF( TRACE )THEN\n         OPEN( NTRA, FILE = SNAPS, STATUS = 'UNKNOWN' )\n      END IF\n*     Read the flag that directs rewinding of the snapshot file.\n      READ( NIN, FMT = * )REWI\n      REWI = REWI.AND.TRACE\n*     Read the flag that directs stopping on any failure.\n      READ( NIN, FMT = * )SFATAL\n*     Read the flag that indicates whether error exits are to be tested.\n      READ( NIN, FMT = * )TSTERR\n*     Read the threshold value of the test ratio\n      READ( NIN, FMT = * )THRESH\n*\n*     Read and check the parameter values for the tests.\n*\n*     Values of N\n      READ( NIN, FMT = * )NIDIM\n      IF( NIDIM.LT.1.OR.NIDIM.GT.NIDMAX )THEN\n         WRITE( NOUT, FMT = 9997 )'N', NIDMAX\n         GO TO 220\n      END IF\n      READ( NIN, FMT = * )( IDIM( I ), I = 1, NIDIM )\n      DO 10 I = 1, NIDIM\n         IF( IDIM( I ).LT.0.OR.IDIM( I ).GT.NMAX )THEN\n            WRITE( NOUT, FMT = 9996 )NMAX\n            GO TO 220\n         END IF\n   10 CONTINUE\n*     Values of ALPHA\n      READ( NIN, FMT = * )NALF\n      IF( NALF.LT.1.OR.NALF.GT.NALMAX )THEN\n         WRITE( NOUT, FMT = 9997 )'ALPHA', NALMAX\n         GO TO 220\n      END IF\n      READ( NIN, FMT = * )( ALF( I ), I = 1, NALF )\n*     Values of BETA\n      READ( NIN, FMT = * )NBET\n      IF( NBET.LT.1.OR.NBET.GT.NBEMAX )THEN\n         WRITE( NOUT, FMT = 9997 )'BETA', NBEMAX\n         GO TO 220\n      END IF\n      READ( NIN, FMT = * )( BET( I ), I = 1, NBET )\n*\n*     Report values of parameters.\n*\n      WRITE( NOUT, FMT = 9995 )\n      WRITE( NOUT, FMT = 9994 )( IDIM( I ), I = 1, NIDIM )\n      WRITE( NOUT, FMT = 9993 )( ALF( I ), I = 1, NALF )\n      WRITE( NOUT, FMT = 9992 )( BET( I ), I = 1, NBET )\n      IF( .NOT.TSTERR )THEN\n         WRITE( NOUT, FMT = * )\n         WRITE( NOUT, FMT = 9984 )\n      END IF\n      WRITE( NOUT, FMT = * )\n      WRITE( NOUT, FMT = 9999 )THRESH\n      WRITE( NOUT, FMT = * )\n*\n*     Read names of subroutines and flags which indicate\n*     whether they are to be tested.\n*\n      DO 20 I = 1, NSUBS\n         LTEST( I ) = .FALSE.\n   20 CONTINUE\n   30 READ( NIN, FMT = 9988, END = 60 )SNAMET, LTESTT\n      DO 40 I = 1, NSUBS\n         IF( SNAMET.EQ.SNAMES( I ) )\n     $      GO TO 50\n   40 CONTINUE\n      WRITE( NOUT, FMT = 9990 )SNAMET\n      STOP\n   50 LTEST( I ) = LTESTT\n      GO TO 30\n*\n   60 CONTINUE\n      CLOSE ( NIN )\n*\n*     Compute EPS (the machine precision).\n*\n      EPS = EPSILON(ZERO)\n      WRITE( NOUT, FMT = 9998 )EPS\n*\n*     Check the reliability of DMMCH using exact data.\n*\n      N = MIN( 32, NMAX )\n      DO 100 J = 1, N\n         DO 90 I = 1, N\n            AB( I, J ) = MAX( I - J + 1, 0 )\n   90    CONTINUE\n         AB( J, NMAX + 1 ) = J\n         AB( 1, NMAX + J ) = J\n         C( J, 1 ) = ZERO\n  100 CONTINUE\n      DO 110 J = 1, N\n         CC( J ) = J*( ( J + 1 )*J )/2 - ( ( J + 1 )*J*( J - 1 ) )/3\n  110 CONTINUE\n*     CC holds the exact result. On exit from DMMCH CT holds\n*     the result computed by DMMCH.\n      TRANSA = 'N'\n      TRANSB = 'N'\n      CALL DMMCH( TRANSA, TRANSB, N, 1, N, ONE, AB, NMAX,\n     $            AB( 1, NMAX + 1 ), NMAX, ZERO, C, NMAX, CT, G, CC,\n     $            NMAX, EPS, ERR, FATAL, NOUT, .TRUE. )\n      SAME = LDE( CC, CT, N )\n      IF( .NOT.SAME.OR.ERR.NE.ZERO )THEN\n         WRITE( NOUT, FMT = 9989 )TRANSA, TRANSB, SAME, ERR\n         STOP\n      END IF\n      TRANSB = 'T'\n      CALL DMMCH( TRANSA, TRANSB, N, 1, N, ONE, AB, NMAX,\n     $            AB( 1, NMAX + 1 ), NMAX, ZERO, C, NMAX, CT, G, CC,\n     $            NMAX, EPS, ERR, FATAL, NOUT, .TRUE. )\n      SAME = LDE( CC, CT, N )\n      IF( .NOT.SAME.OR.ERR.NE.ZERO )THEN\n         WRITE( NOUT, FMT = 9989 )TRANSA, TRANSB, SAME, ERR\n         STOP\n      END IF\n      DO 120 J = 1, N\n         AB( J, NMAX + 1 ) = N - J + 1\n         AB( 1, NMAX + J ) = N - J + 1\n  120 CONTINUE\n      DO 130 J = 1, N\n         CC( N - J + 1 ) = J*( ( J + 1 )*J )/2 -\n     $                     ( ( J + 1 )*J*( J - 1 ) )/3\n  130 CONTINUE\n      TRANSA = 'T'\n      TRANSB = 'N'\n      CALL DMMCH( TRANSA, TRANSB, N, 1, N, ONE, AB, NMAX,\n     $            AB( 1, NMAX + 1 ), NMAX, ZERO, C, NMAX, CT, G, CC,\n     $            NMAX, EPS, ERR, FATAL, NOUT, .TRUE. )\n      SAME = LDE( CC, CT, N )\n      IF( .NOT.SAME.OR.ERR.NE.ZERO )THEN\n         WRITE( NOUT, FMT = 9989 )TRANSA, TRANSB, SAME, ERR\n         STOP\n      END IF\n      TRANSB = 'T'\n      CALL DMMCH( TRANSA, TRANSB, N, 1, N, ONE, AB, NMAX,\n     $            AB( 1, NMAX + 1 ), NMAX, ZERO, C, NMAX, CT, G, CC,\n     $            NMAX, EPS, ERR, FATAL, NOUT, .TRUE. )\n      SAME = LDE( CC, CT, N )\n      IF( .NOT.SAME.OR.ERR.NE.ZERO )THEN\n         WRITE( NOUT, FMT = 9989 )TRANSA, TRANSB, SAME, ERR\n         STOP\n      END IF\n*\n*     Test each subroutine in turn.\n*\n      DO 200 ISNUM = 1, NSUBS\n         WRITE( NOUT, FMT = * )\n         IF( .NOT.LTEST( ISNUM ) )THEN\n*           Subprogram is not to be tested.\n            WRITE( NOUT, FMT = 9987 )SNAMES( ISNUM )\n         ELSE\n            SRNAMT = SNAMES( ISNUM )\n*           Test error exits.\n            IF( TSTERR )THEN\n               CALL DCHKE( ISNUM, SNAMES( ISNUM ), NOUT )\n               WRITE( NOUT, FMT = * )\n            END IF\n*           Test computations.\n            INFOT = 0\n            OK = .TRUE.\n            FATAL = .FALSE.\n            GO TO ( 140, 150, 160, 160, 170, 180 )ISNUM\n*           Test DGEMM, 01.\n  140       CALL DCHK1( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET,\n     $                  NMAX, AB, AA, AS, AB( 1, NMAX + 1 ), BB, BS, C,\n     $                  CC, CS, CT, G )\n            GO TO 190\n*           Test DSYMM, 02.\n  150       CALL DCHK2( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET,\n     $                  NMAX, AB, AA, AS, AB( 1, NMAX + 1 ), BB, BS, C,\n     $                  CC, CS, CT, G )\n            GO TO 190\n*           Test DTRMM, 03, DTRSM, 04.\n  160       CALL DCHK3( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NALF, ALF, NMAX, AB,\n     $                  AA, AS, AB( 1, NMAX + 1 ), BB, BS, CT, G, C )\n            GO TO 190\n*           Test DSYRK, 05.\n  170       CALL DCHK4( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET,\n     $                  NMAX, AB, AA, AS, AB( 1, NMAX + 1 ), BB, BS, C,\n     $                  CC, CS, CT, G )\n            GO TO 190\n*           Test DSYR2K, 06.\n  180       CALL DCHK5( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET,\n     $                  NMAX, AB, AA, AS, BB, BS, C, CC, CS, CT, G, W )\n            GO TO 190\n*\n  190       IF( FATAL.AND.SFATAL )\n     $         GO TO 210\n         END IF\n  200 CONTINUE\n      WRITE( NOUT, FMT = 9986 )\n      GO TO 230\n*\n  210 CONTINUE\n      WRITE( NOUT, FMT = 9985 )\n      GO TO 230\n*\n  220 CONTINUE\n      WRITE( NOUT, FMT = 9991 )\n*\n  230 CONTINUE\n      IF( TRACE )\n     $   CLOSE ( NTRA )\n      CLOSE ( NOUT )\n      STOP\n*\n 9999 FORMAT( ' ROUTINES PASS COMPUTATIONAL TESTS IF TEST RATIO IS LES',\n     $      'S THAN', F8.2 )\n 9998 FORMAT( ' RELATIVE MACHINE PRECISION IS TAKEN TO BE', 1P, D9.1 )\n 9997 FORMAT( ' NUMBER OF VALUES OF ', A, ' IS LESS THAN 1 OR GREATER ',\n     $      'THAN ', I2 )\n 9996 FORMAT( ' VALUE OF N IS LESS THAN 0 OR GREATER THAN ', I2 )\n 9995 FORMAT( ' TESTS OF THE DOUBLE PRECISION LEVEL 3 BLAS', //' THE F',\n     $      'OLLOWING PARAMETER VALUES WILL BE USED:' )\n 9994 FORMAT( '   FOR N              ', 9I6 )\n 9993 FORMAT( '   FOR ALPHA          ', 7F6.1 )\n 9992 FORMAT( '   FOR BETA           ', 7F6.1 )\n 9991 FORMAT( ' AMEND DATA FILE OR INCREASE ARRAY SIZES IN PROGRAM',\n     $      /' ******* TESTS ABANDONED *******' )\n 9990 FORMAT( ' SUBPROGRAM NAME ', A6, ' NOT RECOGNIZED', /' ******* T',\n     $      'ESTS ABANDONED *******' )\n 9989 FORMAT( ' ERROR IN DMMCH -  IN-LINE DOT PRODUCTS ARE BEING EVALU',\n     $      'ATED WRONGLY.', /' DMMCH WAS CALLED WITH TRANSA = ', A1,\n     $      ' AND TRANSB = ', A1, /' AND RETURNED SAME = ', L1, ' AND ',\n     $      'ERR = ', F12.3, '.', /' THIS MAY BE DUE TO FAULTS IN THE ',\n     $      'ARITHMETIC OR THE COMPILER.', /' ******* TESTS ABANDONED ',\n     $      '*******' )\n 9988 FORMAT( A6, L2 )\n 9987 FORMAT( 1X, A6, ' WAS NOT TESTED' )\n 9986 FORMAT( /' END OF TESTS' )\n 9985 FORMAT( /' ******* FATAL ERROR - TESTS ABANDONED *******' )\n 9984 FORMAT( ' ERROR-EXITS WILL NOT BE TESTED' )\n*\n*     End of DBLAT3.\n*\n      END\n      SUBROUTINE DCHK1( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET, NMAX,\n     $                  A, AA, AS, B, BB, BS, C, CC, CS, CT, G )\n*\n*  Tests DGEMM.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Parameters ..\n      DOUBLE PRECISION   ZERO\n      PARAMETER          ( ZERO = 0.0D0 )\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION   EPS, THRESH\n      INTEGER            NALF, NBET, NIDIM, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      DOUBLE PRECISION   A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), B( NMAX, NMAX ),\n     $                   BB( NMAX*NMAX ), BET( NBET ), BS( NMAX*NMAX ),\n     $                   C( NMAX, NMAX ), CC( NMAX*NMAX ),\n     $                   CS( NMAX*NMAX ), CT( NMAX ), G( NMAX )\n      INTEGER            IDIM( NIDIM )\n*     .. Local Scalars ..\n      DOUBLE PRECISION   ALPHA, ALS, BETA, BLS, ERR, ERRMAX\n      INTEGER            I, IA, IB, ICA, ICB, IK, IM, IN, K, KS, LAA,\n     $                   LBB, LCC, LDA, LDAS, LDB, LDBS, LDC, LDCS, M,\n     $                   MA, MB, MS, N, NA, NARGS, NB, NC, NS\n      LOGICAL            NULL, RESET, SAME, TRANA, TRANB\n      CHARACTER*1        TRANAS, TRANBS, TRANSA, TRANSB\n      CHARACTER*3        ICH\n*     .. Local Arrays ..\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LDE, LDERES\n      EXTERNAL           LDE, LDERES\n*     .. External Subroutines ..\n      EXTERNAL           DGEMM, DMAKE, DMMCH\n*     .. Intrinsic Functions ..\n      INTRINSIC          MAX\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICH/'NTC'/\n*     .. Executable Statements ..\n*\n      NARGS = 13\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = ZERO\n*\n      DO 110 IM = 1, NIDIM\n         M = IDIM( IM )\n*\n         DO 100 IN = 1, NIDIM\n            N = IDIM( IN )\n*           Set LDC to 1 more than minimum value if room.\n            LDC = M\n            IF( LDC.LT.NMAX )\n     $         LDC = LDC + 1\n*           Skip tests if not enough room.\n            IF( LDC.GT.NMAX )\n     $         GO TO 100\n            LCC = LDC*N\n            NULL = N.LE.0.OR.M.LE.0\n*\n            DO 90 IK = 1, NIDIM\n               K = IDIM( IK )\n*\n               DO 80 ICA = 1, 3\n                  TRANSA = ICH( ICA: ICA )\n                  TRANA = TRANSA.EQ.'T'.OR.TRANSA.EQ.'C'\n*\n                  IF( TRANA )THEN\n                     MA = K\n                     NA = M\n                  ELSE\n                     MA = M\n                     NA = K\n                  END IF\n*                 Set LDA to 1 more than minimum value if room.\n                  LDA = MA\n                  IF( LDA.LT.NMAX )\n     $               LDA = LDA + 1\n*                 Skip tests if not enough room.\n                  IF( LDA.GT.NMAX )\n     $               GO TO 80\n                  LAA = LDA*NA\n*\n*                 Generate the matrix A.\n*\n                  CALL DMAKE( 'GE', ' ', ' ', MA, NA, A, NMAX, AA, LDA,\n     $                        RESET, ZERO )\n*\n                  DO 70 ICB = 1, 3\n                     TRANSB = ICH( ICB: ICB )\n                     TRANB = TRANSB.EQ.'T'.OR.TRANSB.EQ.'C'\n*\n                     IF( TRANB )THEN\n                        MB = N\n                        NB = K\n                     ELSE\n                        MB = K\n                        NB = N\n                     END IF\n*                    Set LDB to 1 more than minimum value if room.\n                     LDB = MB\n                     IF( LDB.LT.NMAX )\n     $                  LDB = LDB + 1\n*                    Skip tests if not enough room.\n                     IF( LDB.GT.NMAX )\n     $                  GO TO 70\n                     LBB = LDB*NB\n*\n*                    Generate the matrix B.\n*\n                     CALL DMAKE( 'GE', ' ', ' ', MB, NB, B, NMAX, BB,\n     $                           LDB, RESET, ZERO )\n*\n                     DO 60 IA = 1, NALF\n                        ALPHA = ALF( IA )\n*\n                        DO 50 IB = 1, NBET\n                           BETA = BET( IB )\n*\n*                          Generate the matrix C.\n*\n                           CALL DMAKE( 'GE', ' ', ' ', M, N, C, NMAX,\n     $                                 CC, LDC, RESET, ZERO )\n*\n                           NC = NC + 1\n*\n*                          Save every datum before calling the\n*                          subroutine.\n*\n                           TRANAS = TRANSA\n                           TRANBS = TRANSB\n                           MS = M\n                           NS = N\n                           KS = K\n                           ALS = ALPHA\n                           DO 10 I = 1, LAA\n                              AS( I ) = AA( I )\n   10                      CONTINUE\n                           LDAS = LDA\n                           DO 20 I = 1, LBB\n                              BS( I ) = BB( I )\n   20                      CONTINUE\n                           LDBS = LDB\n                           BLS = BETA\n                           DO 30 I = 1, LCC\n                              CS( I ) = CC( I )\n   30                      CONTINUE\n                           LDCS = LDC\n*\n*                          Call the subroutine.\n*\n                           IF( TRACE )\n     $                        WRITE( NTRA, FMT = 9995 )NC, SNAME,\n     $                        TRANSA, TRANSB, M, N, K, ALPHA, LDA, LDB,\n     $                        BETA, LDC\n                           IF( REWI )\n     $                        REWIND NTRA\n                           CALL DGEMM( TRANSA, TRANSB, M, N, K, ALPHA,\n     $                                 AA, LDA, BB, LDB, BETA, CC, LDC )\n*\n*                          Check if error-exit was taken incorrectly.\n*\n                           IF( .NOT.OK )THEN\n                              WRITE( NOUT, FMT = 9994 )\n                              FATAL = .TRUE.\n                              GO TO 120\n                           END IF\n*\n*                          See what data changed inside subroutines.\n*\n                           ISAME( 1 ) = TRANSA.EQ.TRANAS\n                           ISAME( 2 ) = TRANSB.EQ.TRANBS\n                           ISAME( 3 ) = MS.EQ.M\n                           ISAME( 4 ) = NS.EQ.N\n                           ISAME( 5 ) = KS.EQ.K\n                           ISAME( 6 ) = ALS.EQ.ALPHA\n                           ISAME( 7 ) = LDE( AS, AA, LAA )\n                           ISAME( 8 ) = LDAS.EQ.LDA\n                           ISAME( 9 ) = LDE( BS, BB, LBB )\n                           ISAME( 10 ) = LDBS.EQ.LDB\n                           ISAME( 11 ) = BLS.EQ.BETA\n                           IF( NULL )THEN\n                              ISAME( 12 ) = LDE( CS, CC, LCC )\n                           ELSE\n                              ISAME( 12 ) = LDERES( 'GE', ' ', M, N, CS,\n     $                                      CC, LDC )\n                           END IF\n                           ISAME( 13 ) = LDCS.EQ.LDC\n*\n*                          If data was incorrectly changed, report\n*                          and return.\n*\n                           SAME = .TRUE.\n                           DO 40 I = 1, NARGS\n                              SAME = SAME.AND.ISAME( I )\n                              IF( .NOT.ISAME( I ) )\n     $                           WRITE( NOUT, FMT = 9998 )I\n   40                      CONTINUE\n                           IF( .NOT.SAME )THEN\n                              FATAL = .TRUE.\n                              GO TO 120\n                           END IF\n*\n                           IF( .NOT.NULL )THEN\n*\n*                             Check the result.\n*\n                              CALL DMMCH( TRANSA, TRANSB, M, N, K,\n     $                                    ALPHA, A, NMAX, B, NMAX, BETA,\n     $                                    C, NMAX, CT, G, CC, LDC, EPS,\n     $                                    ERR, FATAL, NOUT, .TRUE. )\n                              ERRMAX = MAX( ERRMAX, ERR )\n*                             If got really bad answer, report and\n*                             return.\n                              IF( FATAL )\n     $                           GO TO 120\n                           END IF\n*\n   50                   CONTINUE\n*\n   60                CONTINUE\n*\n   70             CONTINUE\n*\n   80          CONTINUE\n*\n   90       CONTINUE\n*\n  100    CONTINUE\n*\n  110 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 130\n*\n  120 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      WRITE( NOUT, FMT = 9995 )NC, SNAME, TRANSA, TRANSB, M, N, K,\n     $   ALPHA, LDA, LDB, BETA, LDC\n*\n  130 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',''', A1, ''',',\n     $      3( I3, ',' ), F4.1, ', A,', I3, ', B,', I3, ',', F4.1, ', ',\n     $      'C,', I3, ').' )\n 9994 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of DCHK1.\n*\n      END\n      SUBROUTINE DCHK2( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET, NMAX,\n     $                  A, AA, AS, B, BB, BS, C, CC, CS, CT, G )\n*\n*  Tests DSYMM.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Parameters ..\n      DOUBLE PRECISION   ZERO\n      PARAMETER          ( ZERO = 0.0D0 )\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION   EPS, THRESH\n      INTEGER            NALF, NBET, NIDIM, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      DOUBLE PRECISION   A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), B( NMAX, NMAX ),\n     $                   BB( NMAX*NMAX ), BET( NBET ), BS( NMAX*NMAX ),\n     $                   C( NMAX, NMAX ), CC( NMAX*NMAX ),\n     $                   CS( NMAX*NMAX ), CT( NMAX ), G( NMAX )\n      INTEGER            IDIM( NIDIM )\n*     .. Local Scalars ..\n      DOUBLE PRECISION   ALPHA, ALS, BETA, BLS, ERR, ERRMAX\n      INTEGER            I, IA, IB, ICS, ICU, IM, IN, LAA, LBB, LCC,\n     $                   LDA, LDAS, LDB, LDBS, LDC, LDCS, M, MS, N, NA,\n     $                   NARGS, NC, NS\n      LOGICAL            LEFT, NULL, RESET, SAME\n      CHARACTER*1        SIDE, SIDES, UPLO, UPLOS\n      CHARACTER*2        ICHS, ICHU\n*     .. Local Arrays ..\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LDE, LDERES\n      EXTERNAL           LDE, LDERES\n*     .. External Subroutines ..\n      EXTERNAL           DMAKE, DMMCH, DSYMM\n*     .. Intrinsic Functions ..\n      INTRINSIC          MAX\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICHS/'LR'/, ICHU/'UL'/\n*     .. Executable Statements ..\n*\n      NARGS = 12\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = ZERO\n*\n      DO 100 IM = 1, NIDIM\n         M = IDIM( IM )\n*\n         DO 90 IN = 1, NIDIM\n            N = IDIM( IN )\n*           Set LDC to 1 more than minimum value if room.\n            LDC = M\n            IF( LDC.LT.NMAX )\n     $         LDC = LDC + 1\n*           Skip tests if not enough room.\n            IF( LDC.GT.NMAX )\n     $         GO TO 90\n            LCC = LDC*N\n            NULL = N.LE.0.OR.M.LE.0\n*\n*           Set LDB to 1 more than minimum value if room.\n            LDB = M\n            IF( LDB.LT.NMAX )\n     $         LDB = LDB + 1\n*           Skip tests if not enough room.\n            IF( LDB.GT.NMAX )\n     $         GO TO 90\n            LBB = LDB*N\n*\n*           Generate the matrix B.\n*\n            CALL DMAKE( 'GE', ' ', ' ', M, N, B, NMAX, BB, LDB, RESET,\n     $                  ZERO )\n*\n            DO 80 ICS = 1, 2\n               SIDE = ICHS( ICS: ICS )\n               LEFT = SIDE.EQ.'L'\n*\n               IF( LEFT )THEN\n                  NA = M\n               ELSE\n                  NA = N\n               END IF\n*              Set LDA to 1 more than minimum value if room.\n               LDA = NA\n               IF( LDA.LT.NMAX )\n     $            LDA = LDA + 1\n*              Skip tests if not enough room.\n               IF( LDA.GT.NMAX )\n     $            GO TO 80\n               LAA = LDA*NA\n*\n               DO 70 ICU = 1, 2\n                  UPLO = ICHU( ICU: ICU )\n*\n*                 Generate the symmetric matrix A.\n*\n                  CALL DMAKE( 'SY', UPLO, ' ', NA, NA, A, NMAX, AA, LDA,\n     $                        RESET, ZERO )\n*\n                  DO 60 IA = 1, NALF\n                     ALPHA = ALF( IA )\n*\n                     DO 50 IB = 1, NBET\n                        BETA = BET( IB )\n*\n*                       Generate the matrix C.\n*\n                        CALL DMAKE( 'GE', ' ', ' ', M, N, C, NMAX, CC,\n     $                              LDC, RESET, ZERO )\n*\n                        NC = NC + 1\n*\n*                       Save every datum before calling the\n*                       subroutine.\n*\n                        SIDES = SIDE\n                        UPLOS = UPLO\n                        MS = M\n                        NS = N\n                        ALS = ALPHA\n                        DO 10 I = 1, LAA\n                           AS( I ) = AA( I )\n   10                   CONTINUE\n                        LDAS = LDA\n                        DO 20 I = 1, LBB\n                           BS( I ) = BB( I )\n   20                   CONTINUE\n                        LDBS = LDB\n                        BLS = BETA\n                        DO 30 I = 1, LCC\n                           CS( I ) = CC( I )\n   30                   CONTINUE\n                        LDCS = LDC\n*\n*                       Call the subroutine.\n*\n                        IF( TRACE )\n     $                     WRITE( NTRA, FMT = 9995 )NC, SNAME, SIDE,\n     $                     UPLO, M, N, ALPHA, LDA, LDB, BETA, LDC\n                        IF( REWI )\n     $                     REWIND NTRA\n                        CALL DSYMM( SIDE, UPLO, M, N, ALPHA, AA, LDA,\n     $                              BB, LDB, BETA, CC, LDC )\n*\n*                       Check if error-exit was taken incorrectly.\n*\n                        IF( .NOT.OK )THEN\n                           WRITE( NOUT, FMT = 9994 )\n                           FATAL = .TRUE.\n                           GO TO 110\n                        END IF\n*\n*                       See what data changed inside subroutines.\n*\n                        ISAME( 1 ) = SIDES.EQ.SIDE\n                        ISAME( 2 ) = UPLOS.EQ.UPLO\n                        ISAME( 3 ) = MS.EQ.M\n                        ISAME( 4 ) = NS.EQ.N\n                        ISAME( 5 ) = ALS.EQ.ALPHA\n                        ISAME( 6 ) = LDE( AS, AA, LAA )\n                        ISAME( 7 ) = LDAS.EQ.LDA\n                        ISAME( 8 ) = LDE( BS, BB, LBB )\n                        ISAME( 9 ) = LDBS.EQ.LDB\n                        ISAME( 10 ) = BLS.EQ.BETA\n                        IF( NULL )THEN\n                           ISAME( 11 ) = LDE( CS, CC, LCC )\n                        ELSE\n                           ISAME( 11 ) = LDERES( 'GE', ' ', M, N, CS,\n     $                                   CC, LDC )\n                        END IF\n                        ISAME( 12 ) = LDCS.EQ.LDC\n*\n*                       If data was incorrectly changed, report and\n*                       return.\n*\n                        SAME = .TRUE.\n                        DO 40 I = 1, NARGS\n                           SAME = SAME.AND.ISAME( I )\n                           IF( .NOT.ISAME( I ) )\n     $                        WRITE( NOUT, FMT = 9998 )I\n   40                   CONTINUE\n                        IF( .NOT.SAME )THEN\n                           FATAL = .TRUE.\n                           GO TO 110\n                        END IF\n*\n                        IF( .NOT.NULL )THEN\n*\n*                          Check the result.\n*\n                           IF( LEFT )THEN\n                              CALL DMMCH( 'N', 'N', M, N, M, ALPHA, A,\n     $                                    NMAX, B, NMAX, BETA, C, NMAX,\n     $                                    CT, G, CC, LDC, EPS, ERR,\n     $                                    FATAL, NOUT, .TRUE. )\n                           ELSE\n                              CALL DMMCH( 'N', 'N', M, N, N, ALPHA, B,\n     $                                    NMAX, A, NMAX, BETA, C, NMAX,\n     $                                    CT, G, CC, LDC, EPS, ERR,\n     $                                    FATAL, NOUT, .TRUE. )\n                           END IF\n                           ERRMAX = MAX( ERRMAX, ERR )\n*                          If got really bad answer, report and\n*                          return.\n                           IF( FATAL )\n     $                        GO TO 110\n                        END IF\n*\n   50                CONTINUE\n*\n   60             CONTINUE\n*\n   70          CONTINUE\n*\n   80       CONTINUE\n*\n   90    CONTINUE\n*\n  100 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 120\n*\n  110 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      WRITE( NOUT, FMT = 9995 )NC, SNAME, SIDE, UPLO, M, N, ALPHA, LDA,\n     $   LDB, BETA, LDC\n*\n  120 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( 1X, I6, ': ', A6, '(', 2( '''', A1, ''',' ), 2( I3, ',' ),\n     $      F4.1, ', A,', I3, ', B,', I3, ',', F4.1, ', C,', I3, ')   ',\n     $      ' .' )\n 9994 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of DCHK2.\n*\n      END\n      SUBROUTINE DCHK3( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NALF, ALF, NMAX, A, AA, AS,\n     $                  B, BB, BS, CT, G, C )\n*\n*  Tests DTRMM and DTRSM.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Parameters ..\n      DOUBLE PRECISION   ZERO, ONE\n      PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION   EPS, THRESH\n      INTEGER            NALF, NIDIM, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      DOUBLE PRECISION   A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), B( NMAX, NMAX ),\n     $                   BB( NMAX*NMAX ), BS( NMAX*NMAX ),\n     $                   C( NMAX, NMAX ), CT( NMAX ), G( NMAX )\n      INTEGER            IDIM( NIDIM )\n*     .. Local Scalars ..\n      DOUBLE PRECISION   ALPHA, ALS, ERR, ERRMAX\n      INTEGER            I, IA, ICD, ICS, ICT, ICU, IM, IN, J, LAA, LBB,\n     $                   LDA, LDAS, LDB, LDBS, M, MS, N, NA, NARGS, NC,\n     $                   NS\n      LOGICAL            LEFT, NULL, RESET, SAME\n      CHARACTER*1        DIAG, DIAGS, SIDE, SIDES, TRANAS, TRANSA, UPLO,\n     $                   UPLOS\n      CHARACTER*2        ICHD, ICHS, ICHU\n      CHARACTER*3        ICHT\n*     .. Local Arrays ..\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LDE, LDERES\n      EXTERNAL           LDE, LDERES\n*     .. External Subroutines ..\n      EXTERNAL           DMAKE, DMMCH, DTRMM, DTRSM\n*     .. Intrinsic Functions ..\n      INTRINSIC          MAX\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICHU/'UL'/, ICHT/'NTC'/, ICHD/'UN'/, ICHS/'LR'/\n*     .. Executable Statements ..\n*\n      NARGS = 11\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = ZERO\n*     Set up zero matrix for DMMCH.\n      DO 20 J = 1, NMAX\n         DO 10 I = 1, NMAX\n            C( I, J ) = ZERO\n   10    CONTINUE\n   20 CONTINUE\n*\n      DO 140 IM = 1, NIDIM\n         M = IDIM( IM )\n*\n         DO 130 IN = 1, NIDIM\n            N = IDIM( IN )\n*           Set LDB to 1 more than minimum value if room.\n            LDB = M\n            IF( LDB.LT.NMAX )\n     $         LDB = LDB + 1\n*           Skip tests if not enough room.\n            IF( LDB.GT.NMAX )\n     $         GO TO 130\n            LBB = LDB*N\n            NULL = M.LE.0.OR.N.LE.0\n*\n            DO 120 ICS = 1, 2\n               SIDE = ICHS( ICS: ICS )\n               LEFT = SIDE.EQ.'L'\n               IF( LEFT )THEN\n                  NA = M\n               ELSE\n                  NA = N\n               END IF\n*              Set LDA to 1 more than minimum value if room.\n               LDA = NA\n               IF( LDA.LT.NMAX )\n     $            LDA = LDA + 1\n*              Skip tests if not enough room.\n               IF( LDA.GT.NMAX )\n     $            GO TO 130\n               LAA = LDA*NA\n*\n               DO 110 ICU = 1, 2\n                  UPLO = ICHU( ICU: ICU )\n*\n                  DO 100 ICT = 1, 3\n                     TRANSA = ICHT( ICT: ICT )\n*\n                     DO 90 ICD = 1, 2\n                        DIAG = ICHD( ICD: ICD )\n*\n                        DO 80 IA = 1, NALF\n                           ALPHA = ALF( IA )\n*\n*                          Generate the matrix A.\n*\n                           CALL DMAKE( 'TR', UPLO, DIAG, NA, NA, A,\n     $                                 NMAX, AA, LDA, RESET, ZERO )\n*\n*                          Generate the matrix B.\n*\n                           CALL DMAKE( 'GE', ' ', ' ', M, N, B, NMAX,\n     $                                 BB, LDB, RESET, ZERO )\n*\n                           NC = NC + 1\n*\n*                          Save every datum before calling the\n*                          subroutine.\n*\n                           SIDES = SIDE\n                           UPLOS = UPLO\n                           TRANAS = TRANSA\n                           DIAGS = DIAG\n                           MS = M\n                           NS = N\n                           ALS = ALPHA\n                           DO 30 I = 1, LAA\n                              AS( I ) = AA( I )\n   30                      CONTINUE\n                           LDAS = LDA\n                           DO 40 I = 1, LBB\n                              BS( I ) = BB( I )\n   40                      CONTINUE\n                           LDBS = LDB\n*\n*                          Call the subroutine.\n*\n                           IF( SNAME( 4: 5 ).EQ.'MM' )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9995 )NC, SNAME,\n     $                           SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA,\n     $                           LDA, LDB\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL DTRMM( SIDE, UPLO, TRANSA, DIAG, M,\n     $                                    N, ALPHA, AA, LDA, BB, LDB )\n                           ELSE IF( SNAME( 4: 5 ).EQ.'SM' )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9995 )NC, SNAME,\n     $                           SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA,\n     $                           LDA, LDB\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL DTRSM( SIDE, UPLO, TRANSA, DIAG, M,\n     $                                    N, ALPHA, AA, LDA, BB, LDB )\n                           END IF\n*\n*                          Check if error-exit was taken incorrectly.\n*\n                           IF( .NOT.OK )THEN\n                              WRITE( NOUT, FMT = 9994 )\n                              FATAL = .TRUE.\n                              GO TO 150\n                           END IF\n*\n*                          See what data changed inside subroutines.\n*\n                           ISAME( 1 ) = SIDES.EQ.SIDE\n                           ISAME( 2 ) = UPLOS.EQ.UPLO\n                           ISAME( 3 ) = TRANAS.EQ.TRANSA\n                           ISAME( 4 ) = DIAGS.EQ.DIAG\n                           ISAME( 5 ) = MS.EQ.M\n                           ISAME( 6 ) = NS.EQ.N\n                           ISAME( 7 ) = ALS.EQ.ALPHA\n                           ISAME( 8 ) = LDE( AS, AA, LAA )\n                           ISAME( 9 ) = LDAS.EQ.LDA\n                           IF( NULL )THEN\n                              ISAME( 10 ) = LDE( BS, BB, LBB )\n                           ELSE\n                              ISAME( 10 ) = LDERES( 'GE', ' ', M, N, BS,\n     $                                      BB, LDB )\n                           END IF\n                           ISAME( 11 ) = LDBS.EQ.LDB\n*\n*                          If data was incorrectly changed, report and\n*                          return.\n*\n                           SAME = .TRUE.\n                           DO 50 I = 1, NARGS\n                              SAME = SAME.AND.ISAME( I )\n                              IF( .NOT.ISAME( I ) )\n     $                           WRITE( NOUT, FMT = 9998 )I\n   50                      CONTINUE\n                           IF( .NOT.SAME )THEN\n                              FATAL = .TRUE.\n                              GO TO 150\n                           END IF\n*\n                           IF( .NOT.NULL )THEN\n                              IF( SNAME( 4: 5 ).EQ.'MM' )THEN\n*\n*                                Check the result.\n*\n                                 IF( LEFT )THEN\n                                    CALL DMMCH( TRANSA, 'N', M, N, M,\n     $                                          ALPHA, A, NMAX, B, NMAX,\n     $                                          ZERO, C, NMAX, CT, G,\n     $                                          BB, LDB, EPS, ERR,\n     $                                          FATAL, NOUT, .TRUE. )\n                                 ELSE\n                                    CALL DMMCH( 'N', TRANSA, M, N, N,\n     $                                          ALPHA, B, NMAX, A, NMAX,\n     $                                          ZERO, C, NMAX, CT, G,\n     $                                          BB, LDB, EPS, ERR,\n     $                                          FATAL, NOUT, .TRUE. )\n                                 END IF\n                              ELSE IF( SNAME( 4: 5 ).EQ.'SM' )THEN\n*\n*                                Compute approximation to original\n*                                matrix.\n*\n                                 DO 70 J = 1, N\n                                    DO 60 I = 1, M\n                                       C( I, J ) = BB( I + ( J - 1 )*\n     $                                             LDB )\n                                       BB( I + ( J - 1 )*LDB ) = ALPHA*\n     $                                    B( I, J )\n   60                               CONTINUE\n   70                            CONTINUE\n*\n                                 IF( LEFT )THEN\n                                    CALL DMMCH( TRANSA, 'N', M, N, M,\n     $                                          ONE, A, NMAX, C, NMAX,\n     $                                          ZERO, B, NMAX, CT, G,\n     $                                          BB, LDB, EPS, ERR,\n     $                                          FATAL, NOUT, .FALSE. )\n                                 ELSE\n                                    CALL DMMCH( 'N', TRANSA, M, N, N,\n     $                                          ONE, C, NMAX, A, NMAX,\n     $                                          ZERO, B, NMAX, CT, G,\n     $                                          BB, LDB, EPS, ERR,\n     $                                          FATAL, NOUT, .FALSE. )\n                                 END IF\n                              END IF\n                              ERRMAX = MAX( ERRMAX, ERR )\n*                             If got really bad answer, report and\n*                             return.\n                              IF( FATAL )\n     $                           GO TO 150\n                           END IF\n*\n   80                   CONTINUE\n*\n   90                CONTINUE\n*\n  100             CONTINUE\n*\n  110          CONTINUE\n*\n  120       CONTINUE\n*\n  130    CONTINUE\n*\n  140 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 160\n*\n  150 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      WRITE( NOUT, FMT = 9995 )NC, SNAME, SIDE, UPLO, TRANSA, DIAG, M,\n     $   N, ALPHA, LDA, LDB\n*\n  160 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( 1X, I6, ': ', A6, '(', 4( '''', A1, ''',' ), 2( I3, ',' ),\n     $      F4.1, ', A,', I3, ', B,', I3, ')        .' )\n 9994 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of DCHK3.\n*\n      END\n      SUBROUTINE DCHK4( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET, NMAX,\n     $                  A, AA, AS, B, BB, BS, C, CC, CS, CT, G )\n*\n*  Tests DSYRK.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Parameters ..\n      DOUBLE PRECISION   ZERO\n      PARAMETER          ( ZERO = 0.0D0 )\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION   EPS, THRESH\n      INTEGER            NALF, NBET, NIDIM, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      DOUBLE PRECISION   A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), B( NMAX, NMAX ),\n     $                   BB( NMAX*NMAX ), BET( NBET ), BS( NMAX*NMAX ),\n     $                   C( NMAX, NMAX ), CC( NMAX*NMAX ),\n     $                   CS( NMAX*NMAX ), CT( NMAX ), G( NMAX )\n      INTEGER            IDIM( NIDIM )\n*     .. Local Scalars ..\n      DOUBLE PRECISION   ALPHA, ALS, BETA, BETS, ERR, ERRMAX\n      INTEGER            I, IA, IB, ICT, ICU, IK, IN, J, JC, JJ, K, KS,\n     $                   LAA, LCC, LDA, LDAS, LDC, LDCS, LJ, MA, N, NA,\n     $                   NARGS, NC, NS\n      LOGICAL            NULL, RESET, SAME, TRAN, UPPER\n      CHARACTER*1        TRANS, TRANSS, UPLO, UPLOS\n      CHARACTER*2        ICHU\n      CHARACTER*3        ICHT\n*     .. Local Arrays ..\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LDE, LDERES\n      EXTERNAL           LDE, LDERES\n*     .. External Subroutines ..\n      EXTERNAL           DMAKE, DMMCH, DSYRK\n*     .. Intrinsic Functions ..\n      INTRINSIC          MAX\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICHT/'NTC'/, ICHU/'UL'/\n*     .. Executable Statements ..\n*\n      NARGS = 10\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = ZERO\n*\n      DO 100 IN = 1, NIDIM\n         N = IDIM( IN )\n*        Set LDC to 1 more than minimum value if room.\n         LDC = N\n         IF( LDC.LT.NMAX )\n     $      LDC = LDC + 1\n*        Skip tests if not enough room.\n         IF( LDC.GT.NMAX )\n     $      GO TO 100\n         LCC = LDC*N\n         NULL = N.LE.0\n*\n         DO 90 IK = 1, NIDIM\n            K = IDIM( IK )\n*\n            DO 80 ICT = 1, 3\n               TRANS = ICHT( ICT: ICT )\n               TRAN = TRANS.EQ.'T'.OR.TRANS.EQ.'C'\n               IF( TRAN )THEN\n                  MA = K\n                  NA = N\n               ELSE\n                  MA = N\n                  NA = K\n               END IF\n*              Set LDA to 1 more than minimum value if room.\n               LDA = MA\n               IF( LDA.LT.NMAX )\n     $            LDA = LDA + 1\n*              Skip tests if not enough room.\n               IF( LDA.GT.NMAX )\n     $            GO TO 80\n               LAA = LDA*NA\n*\n*              Generate the matrix A.\n*\n               CALL DMAKE( 'GE', ' ', ' ', MA, NA, A, NMAX, AA, LDA,\n     $                     RESET, ZERO )\n*\n               DO 70 ICU = 1, 2\n                  UPLO = ICHU( ICU: ICU )\n                  UPPER = UPLO.EQ.'U'\n*\n                  DO 60 IA = 1, NALF\n                     ALPHA = ALF( IA )\n*\n                     DO 50 IB = 1, NBET\n                        BETA = BET( IB )\n*\n*                       Generate the matrix C.\n*\n                        CALL DMAKE( 'SY', UPLO, ' ', N, N, C, NMAX, CC,\n     $                              LDC, RESET, ZERO )\n*\n                        NC = NC + 1\n*\n*                       Save every datum before calling the subroutine.\n*\n                        UPLOS = UPLO\n                        TRANSS = TRANS\n                        NS = N\n                        KS = K\n                        ALS = ALPHA\n                        DO 10 I = 1, LAA\n                           AS( I ) = AA( I )\n   10                   CONTINUE\n                        LDAS = LDA\n                        BETS = BETA\n                        DO 20 I = 1, LCC\n                           CS( I ) = CC( I )\n   20                   CONTINUE\n                        LDCS = LDC\n*\n*                       Call the subroutine.\n*\n                        IF( TRACE )\n     $                     WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO,\n     $                     TRANS, N, K, ALPHA, LDA, BETA, LDC\n                        IF( REWI )\n     $                     REWIND NTRA\n                        CALL DSYRK( UPLO, TRANS, N, K, ALPHA, AA, LDA,\n     $                              BETA, CC, LDC )\n*\n*                       Check if error-exit was taken incorrectly.\n*\n                        IF( .NOT.OK )THEN\n                           WRITE( NOUT, FMT = 9993 )\n                           FATAL = .TRUE.\n                           GO TO 120\n                        END IF\n*\n*                       See what data changed inside subroutines.\n*\n                        ISAME( 1 ) = UPLOS.EQ.UPLO\n                        ISAME( 2 ) = TRANSS.EQ.TRANS\n                        ISAME( 3 ) = NS.EQ.N\n                        ISAME( 4 ) = KS.EQ.K\n                        ISAME( 5 ) = ALS.EQ.ALPHA\n                        ISAME( 6 ) = LDE( AS, AA, LAA )\n                        ISAME( 7 ) = LDAS.EQ.LDA\n                        ISAME( 8 ) = BETS.EQ.BETA\n                        IF( NULL )THEN\n                           ISAME( 9 ) = LDE( CS, CC, LCC )\n                        ELSE\n                           ISAME( 9 ) = LDERES( 'SY', UPLO, N, N, CS,\n     $                                  CC, LDC )\n                        END IF\n                        ISAME( 10 ) = LDCS.EQ.LDC\n*\n*                       If data was incorrectly changed, report and\n*                       return.\n*\n                        SAME = .TRUE.\n                        DO 30 I = 1, NARGS\n                           SAME = SAME.AND.ISAME( I )\n                           IF( .NOT.ISAME( I ) )\n     $                        WRITE( NOUT, FMT = 9998 )I\n   30                   CONTINUE\n                        IF( .NOT.SAME )THEN\n                           FATAL = .TRUE.\n                           GO TO 120\n                        END IF\n*\n                        IF( .NOT.NULL )THEN\n*\n*                          Check the result column by column.\n*\n                           JC = 1\n                           DO 40 J = 1, N\n                              IF( UPPER )THEN\n                                 JJ = 1\n                                 LJ = J\n                              ELSE\n                                 JJ = J\n                                 LJ = N - J + 1\n                              END IF\n                              IF( TRAN )THEN\n                                 CALL DMMCH( 'T', 'N', LJ, 1, K, ALPHA,\n     $                                       A( 1, JJ ), NMAX,\n     $                                       A( 1, J ), NMAX, BETA,\n     $                                       C( JJ, J ), NMAX, CT, G,\n     $                                       CC( JC ), LDC, EPS, ERR,\n     $                                       FATAL, NOUT, .TRUE. )\n                              ELSE\n                                 CALL DMMCH( 'N', 'T', LJ, 1, K, ALPHA,\n     $                                       A( JJ, 1 ), NMAX,\n     $                                       A( J, 1 ), NMAX, BETA,\n     $                                       C( JJ, J ), NMAX, CT, G,\n     $                                       CC( JC ), LDC, EPS, ERR,\n     $                                       FATAL, NOUT, .TRUE. )\n                              END IF\n                              IF( UPPER )THEN\n                                 JC = JC + LDC\n                              ELSE\n                                 JC = JC + LDC + 1\n                              END IF\n                              ERRMAX = MAX( ERRMAX, ERR )\n*                             If got really bad answer, report and\n*                             return.\n                              IF( FATAL )\n     $                           GO TO 110\n   40                      CONTINUE\n                        END IF\n*\n   50                CONTINUE\n*\n   60             CONTINUE\n*\n   70          CONTINUE\n*\n   80       CONTINUE\n*\n   90    CONTINUE\n*\n  100 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 130\n*\n  110 CONTINUE\n      IF( N.GT.1 )\n     $   WRITE( NOUT, FMT = 9995 )J\n*\n  120 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, TRANS, N, K, ALPHA,\n     $   LDA, BETA, LDC\n*\n  130 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( '      THESE ARE THE RESULTS FOR COLUMN ', I3 )\n 9994 FORMAT( 1X, I6, ': ', A6, '(', 2( '''', A1, ''',' ), 2( I3, ',' ),\n     $      F4.1, ', A,', I3, ',', F4.1, ', C,', I3, ')           .' )\n 9993 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of DCHK4.\n*\n      END\n      SUBROUTINE DCHK5( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET, NMAX,\n     $                  AB, AA, AS, BB, BS, C, CC, CS, CT, G, W )\n*\n*  Tests DSYR2K.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Parameters ..\n      DOUBLE PRECISION   ZERO\n      PARAMETER          ( ZERO = 0.0D0 )\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION   EPS, THRESH\n      INTEGER            NALF, NBET, NIDIM, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      DOUBLE PRECISION   AA( NMAX*NMAX ), AB( 2*NMAX*NMAX ),\n     $                   ALF( NALF ), AS( NMAX*NMAX ), BB( NMAX*NMAX ),\n     $                   BET( NBET ), BS( NMAX*NMAX ), C( NMAX, NMAX ),\n     $                   CC( NMAX*NMAX ), CS( NMAX*NMAX ), CT( NMAX ),\n     $                   G( NMAX ), W( 2*NMAX )\n      INTEGER            IDIM( NIDIM )\n*     .. Local Scalars ..\n      DOUBLE PRECISION   ALPHA, ALS, BETA, BETS, ERR, ERRMAX\n      INTEGER            I, IA, IB, ICT, ICU, IK, IN, J, JC, JJ, JJAB,\n     $                   K, KS, LAA, LBB, LCC, LDA, LDAS, LDB, LDBS,\n     $                   LDC, LDCS, LJ, MA, N, NA, NARGS, NC, NS\n      LOGICAL            NULL, RESET, SAME, TRAN, UPPER\n      CHARACTER*1        TRANS, TRANSS, UPLO, UPLOS\n      CHARACTER*2        ICHU\n      CHARACTER*3        ICHT\n*     .. Local Arrays ..\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LDE, LDERES\n      EXTERNAL           LDE, LDERES\n*     .. External Subroutines ..\n      EXTERNAL           DMAKE, DMMCH, DSYR2K\n*     .. Intrinsic Functions ..\n      INTRINSIC          MAX\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICHT/'NTC'/, ICHU/'UL'/\n*     .. Executable Statements ..\n*\n      NARGS = 12\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = ZERO\n*\n      DO 130 IN = 1, NIDIM\n         N = IDIM( IN )\n*        Set LDC to 1 more than minimum value if room.\n         LDC = N\n         IF( LDC.LT.NMAX )\n     $      LDC = LDC + 1\n*        Skip tests if not enough room.\n         IF( LDC.GT.NMAX )\n     $      GO TO 130\n         LCC = LDC*N\n         NULL = N.LE.0\n*\n         DO 120 IK = 1, NIDIM\n            K = IDIM( IK )\n*\n            DO 110 ICT = 1, 3\n               TRANS = ICHT( ICT: ICT )\n               TRAN = TRANS.EQ.'T'.OR.TRANS.EQ.'C'\n               IF( TRAN )THEN\n                  MA = K\n                  NA = N\n               ELSE\n                  MA = N\n                  NA = K\n               END IF\n*              Set LDA to 1 more than minimum value if room.\n               LDA = MA\n               IF( LDA.LT.NMAX )\n     $            LDA = LDA + 1\n*              Skip tests if not enough room.\n               IF( LDA.GT.NMAX )\n     $            GO TO 110\n               LAA = LDA*NA\n*\n*              Generate the matrix A.\n*\n               IF( TRAN )THEN\n                  CALL DMAKE( 'GE', ' ', ' ', MA, NA, AB, 2*NMAX, AA,\n     $                        LDA, RESET, ZERO )\n               ELSE\n                  CALL DMAKE( 'GE', ' ', ' ', MA, NA, AB, NMAX, AA, LDA,\n     $                        RESET, ZERO )\n               END IF\n*\n*              Generate the matrix B.\n*\n               LDB = LDA\n               LBB = LAA\n               IF( TRAN )THEN\n                  CALL DMAKE( 'GE', ' ', ' ', MA, NA, AB( K + 1 ),\n     $                        2*NMAX, BB, LDB, RESET, ZERO )\n               ELSE\n                  CALL DMAKE( 'GE', ' ', ' ', MA, NA, AB( K*NMAX + 1 ),\n     $                        NMAX, BB, LDB, RESET, ZERO )\n               END IF\n*\n               DO 100 ICU = 1, 2\n                  UPLO = ICHU( ICU: ICU )\n                  UPPER = UPLO.EQ.'U'\n*\n                  DO 90 IA = 1, NALF\n                     ALPHA = ALF( IA )\n*\n                     DO 80 IB = 1, NBET\n                        BETA = BET( IB )\n*\n*                       Generate the matrix C.\n*\n                        CALL DMAKE( 'SY', UPLO, ' ', N, N, C, NMAX, CC,\n     $                              LDC, RESET, ZERO )\n*\n                        NC = NC + 1\n*\n*                       Save every datum before calling the subroutine.\n*\n                        UPLOS = UPLO\n                        TRANSS = TRANS\n                        NS = N\n                        KS = K\n                        ALS = ALPHA\n                        DO 10 I = 1, LAA\n                           AS( I ) = AA( I )\n   10                   CONTINUE\n                        LDAS = LDA\n                        DO 20 I = 1, LBB\n                           BS( I ) = BB( I )\n   20                   CONTINUE\n                        LDBS = LDB\n                        BETS = BETA\n                        DO 30 I = 1, LCC\n                           CS( I ) = CC( I )\n   30                   CONTINUE\n                        LDCS = LDC\n*\n*                       Call the subroutine.\n*\n                        IF( TRACE )\n     $                     WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO,\n     $                     TRANS, N, K, ALPHA, LDA, LDB, BETA, LDC\n                        IF( REWI )\n     $                     REWIND NTRA\n                        CALL DSYR2K( UPLO, TRANS, N, K, ALPHA, AA, LDA,\n     $                               BB, LDB, BETA, CC, LDC )\n*\n*                       Check if error-exit was taken incorrectly.\n*\n                        IF( .NOT.OK )THEN\n                           WRITE( NOUT, FMT = 9993 )\n                           FATAL = .TRUE.\n                           GO TO 150\n                        END IF\n*\n*                       See what data changed inside subroutines.\n*\n                        ISAME( 1 ) = UPLOS.EQ.UPLO\n                        ISAME( 2 ) = TRANSS.EQ.TRANS\n                        ISAME( 3 ) = NS.EQ.N\n                        ISAME( 4 ) = KS.EQ.K\n                        ISAME( 5 ) = ALS.EQ.ALPHA\n                        ISAME( 6 ) = LDE( AS, AA, LAA )\n                        ISAME( 7 ) = LDAS.EQ.LDA\n                        ISAME( 8 ) = LDE( BS, BB, LBB )\n                        ISAME( 9 ) = LDBS.EQ.LDB\n                        ISAME( 10 ) = BETS.EQ.BETA\n                        IF( NULL )THEN\n                           ISAME( 11 ) = LDE( CS, CC, LCC )\n                        ELSE\n                           ISAME( 11 ) = LDERES( 'SY', UPLO, N, N, CS,\n     $                                   CC, LDC )\n                        END IF\n                        ISAME( 12 ) = LDCS.EQ.LDC\n*\n*                       If data was incorrectly changed, report and\n*                       return.\n*\n                        SAME = .TRUE.\n                        DO 40 I = 1, NARGS\n                           SAME = SAME.AND.ISAME( I )\n                           IF( .NOT.ISAME( I ) )\n     $                        WRITE( NOUT, FMT = 9998 )I\n   40                   CONTINUE\n                        IF( .NOT.SAME )THEN\n                           FATAL = .TRUE.\n                           GO TO 150\n                        END IF\n*\n                        IF( .NOT.NULL )THEN\n*\n*                          Check the result column by column.\n*\n                           JJAB = 1\n                           JC = 1\n                           DO 70 J = 1, N\n                              IF( UPPER )THEN\n                                 JJ = 1\n                                 LJ = J\n                              ELSE\n                                 JJ = J\n                                 LJ = N - J + 1\n                              END IF\n                              IF( TRAN )THEN\n                                 DO 50 I = 1, K\n                                    W( I ) = AB( ( J - 1 )*2*NMAX + K +\n     $                                       I )\n                                    W( K + I ) = AB( ( J - 1 )*2*NMAX +\n     $                                           I )\n   50                            CONTINUE\n                                 CALL DMMCH( 'T', 'N', LJ, 1, 2*K,\n     $                                       ALPHA, AB( JJAB ), 2*NMAX,\n     $                                       W, 2*NMAX, BETA,\n     $                                       C( JJ, J ), NMAX, CT, G,\n     $                                       CC( JC ), LDC, EPS, ERR,\n     $                                       FATAL, NOUT, .TRUE. )\n                              ELSE\n                                 DO 60 I = 1, K\n                                    W( I ) = AB( ( K + I - 1 )*NMAX +\n     $                                       J )\n                                    W( K + I ) = AB( ( I - 1 )*NMAX +\n     $                                           J )\n   60                            CONTINUE\n                                 CALL DMMCH( 'N', 'N', LJ, 1, 2*K,\n     $                                       ALPHA, AB( JJ ), NMAX, W,\n     $                                       2*NMAX, BETA, C( JJ, J ),\n     $                                       NMAX, CT, G, CC( JC ), LDC,\n     $                                       EPS, ERR, FATAL, NOUT,\n     $                                       .TRUE. )\n                              END IF\n                              IF( UPPER )THEN\n                                 JC = JC + LDC\n                              ELSE\n                                 JC = JC + LDC + 1\n                                 IF( TRAN )\n     $                              JJAB = JJAB + 2*NMAX\n                              END IF\n                              ERRMAX = MAX( ERRMAX, ERR )\n*                             If got really bad answer, report and\n*                             return.\n                              IF( FATAL )\n     $                           GO TO 140\n   70                      CONTINUE\n                        END IF\n*\n   80                CONTINUE\n*\n   90             CONTINUE\n*\n  100          CONTINUE\n*\n  110       CONTINUE\n*\n  120    CONTINUE\n*\n  130 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 160\n*\n  140 CONTINUE\n      IF( N.GT.1 )\n     $   WRITE( NOUT, FMT = 9995 )J\n*\n  150 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, TRANS, N, K, ALPHA,\n     $   LDA, LDB, BETA, LDC\n*\n  160 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( '      THESE ARE THE RESULTS FOR COLUMN ', I3 )\n 9994 FORMAT( 1X, I6, ': ', A6, '(', 2( '''', A1, ''',' ), 2( I3, ',' ),\n     $      F4.1, ', A,', I3, ', B,', I3, ',', F4.1, ', C,', I3, ')   ',\n     $      ' .' )\n 9993 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of DCHK5.\n*\n      END\n      SUBROUTINE DCHKE( ISNUM, SRNAMT, NOUT )\n*\n*  Tests the error exits from the Level 3 Blas.\n*  Requires a special version of the error-handling routine XERBLA.\n*  A, B and C should not need to be defined.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*  3-19-92:  Initialize ALPHA and BETA  (eca)\n*  3-19-92:  Fix argument 12 in calls to SSYMM with INFOT = 9  (eca)\n*\n*     .. Scalar Arguments ..\n      INTEGER            ISNUM, NOUT\n      CHARACTER*6        SRNAMT\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Parameters ..\n      DOUBLE PRECISION   ONE, TWO\n      PARAMETER          ( ONE = 1.0D0, TWO = 2.0D0 )\n*     .. Local Scalars ..\n      DOUBLE PRECISION   ALPHA, BETA\n*     .. Local Arrays ..\n      DOUBLE PRECISION   A( 2, 1 ), B( 2, 1 ), C( 2, 1 )\n*     .. External Subroutines ..\n      EXTERNAL           CHKXER, DGEMM, DSYMM, DSYR2K, DSYRK, DTRMM,\n     $                   DTRSM\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Executable Statements ..\n*     OK is set to .FALSE. by the special version of XERBLA or by CHKXER\n*     if anything is wrong.\n      OK = .TRUE.\n*     LERR is set to .TRUE. by the special version of XERBLA each time\n*     it is called, and is then tested and re-set by CHKXER.\n      LERR = .FALSE.\n*\n*     Initialize ALPHA and BETA.\n*\n      ALPHA = ONE\n      BETA = TWO\n*\n      GO TO ( 10, 20, 30, 40, 50, 60 )ISNUM\n   10 INFOT = 1\n      CALL DGEMM( '/', 'N', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 1\n      CALL DGEMM( '/', 'T', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL DGEMM( 'N', '/', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL DGEMM( 'T', '/', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL DGEMM( 'N', 'N', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL DGEMM( 'N', 'T', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL DGEMM( 'T', 'N', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL DGEMM( 'T', 'T', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL DGEMM( 'N', 'N', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL DGEMM( 'N', 'T', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL DGEMM( 'T', 'N', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL DGEMM( 'T', 'T', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL DGEMM( 'N', 'N', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL DGEMM( 'N', 'T', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL DGEMM( 'T', 'N', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL DGEMM( 'T', 'T', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL DGEMM( 'N', 'N', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL DGEMM( 'N', 'T', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL DGEMM( 'T', 'N', 0, 0, 2, ALPHA, A, 1, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL DGEMM( 'T', 'T', 0, 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL DGEMM( 'N', 'N', 0, 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL DGEMM( 'T', 'N', 0, 0, 2, ALPHA, A, 2, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL DGEMM( 'N', 'T', 0, 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL DGEMM( 'T', 'T', 0, 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 13\n      CALL DGEMM( 'N', 'N', 2, 0, 0, ALPHA, A, 2, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 13\n      CALL DGEMM( 'N', 'T', 2, 0, 0, ALPHA, A, 2, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 13\n      CALL DGEMM( 'T', 'N', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 13\n      CALL DGEMM( 'T', 'T', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 70\n   20 INFOT = 1\n      CALL DSYMM( '/', 'U', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL DSYMM( 'L', '/', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL DSYMM( 'L', 'U', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL DSYMM( 'R', 'U', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL DSYMM( 'L', 'L', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL DSYMM( 'R', 'L', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL DSYMM( 'L', 'U', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL DSYMM( 'R', 'U', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL DSYMM( 'L', 'L', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL DSYMM( 'R', 'L', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL DSYMM( 'L', 'U', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL DSYMM( 'R', 'U', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL DSYMM( 'L', 'L', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL DSYMM( 'R', 'L', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL DSYMM( 'L', 'U', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL DSYMM( 'R', 'U', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL DSYMM( 'L', 'L', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL DSYMM( 'R', 'L', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL DSYMM( 'L', 'U', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL DSYMM( 'R', 'U', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL DSYMM( 'L', 'L', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL DSYMM( 'R', 'L', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 70\n   30 INFOT = 1\n      CALL DTRMM( '/', 'U', 'N', 'N', 0, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL DTRMM( 'L', '/', 'N', 'N', 0, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL DTRMM( 'L', 'U', '/', 'N', 0, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL DTRMM( 'L', 'U', 'N', '/', 0, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL DTRMM( 'L', 'U', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL DTRMM( 'L', 'U', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL DTRMM( 'R', 'U', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL DTRMM( 'R', 'U', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL DTRMM( 'L', 'L', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL DTRMM( 'L', 'L', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL DTRMM( 'R', 'L', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL DTRMM( 'R', 'L', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL DTRMM( 'L', 'U', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL DTRMM( 'L', 'U', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL DTRMM( 'R', 'U', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL DTRMM( 'R', 'U', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL DTRMM( 'L', 'L', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL DTRMM( 'L', 'L', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL DTRMM( 'R', 'L', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL DTRMM( 'R', 'L', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL DTRMM( 'L', 'U', 'N', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL DTRMM( 'L', 'U', 'T', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL DTRMM( 'R', 'U', 'N', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL DTRMM( 'R', 'U', 'T', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL DTRMM( 'L', 'L', 'N', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL DTRMM( 'L', 'L', 'T', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL DTRMM( 'R', 'L', 'N', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL DTRMM( 'R', 'L', 'T', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL DTRMM( 'L', 'U', 'N', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL DTRMM( 'L', 'U', 'T', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL DTRMM( 'R', 'U', 'N', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL DTRMM( 'R', 'U', 'T', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL DTRMM( 'L', 'L', 'N', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL DTRMM( 'L', 'L', 'T', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL DTRMM( 'R', 'L', 'N', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL DTRMM( 'R', 'L', 'T', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 70\n   40 INFOT = 1\n      CALL DTRSM( '/', 'U', 'N', 'N', 0, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL DTRSM( 'L', '/', 'N', 'N', 0, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL DTRSM( 'L', 'U', '/', 'N', 0, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL DTRSM( 'L', 'U', 'N', '/', 0, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL DTRSM( 'L', 'U', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL DTRSM( 'L', 'U', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL DTRSM( 'R', 'U', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL DTRSM( 'R', 'U', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL DTRSM( 'L', 'L', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL DTRSM( 'L', 'L', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL DTRSM( 'R', 'L', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL DTRSM( 'R', 'L', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL DTRSM( 'L', 'U', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL DTRSM( 'L', 'U', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL DTRSM( 'R', 'U', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL DTRSM( 'R', 'U', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL DTRSM( 'L', 'L', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL DTRSM( 'L', 'L', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL DTRSM( 'R', 'L', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL DTRSM( 'R', 'L', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL DTRSM( 'L', 'U', 'N', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL DTRSM( 'L', 'U', 'T', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL DTRSM( 'R', 'U', 'N', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL DTRSM( 'R', 'U', 'T', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL DTRSM( 'L', 'L', 'N', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL DTRSM( 'L', 'L', 'T', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL DTRSM( 'R', 'L', 'N', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL DTRSM( 'R', 'L', 'T', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL DTRSM( 'L', 'U', 'N', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL DTRSM( 'L', 'U', 'T', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL DTRSM( 'R', 'U', 'N', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL DTRSM( 'R', 'U', 'T', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL DTRSM( 'L', 'L', 'N', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL DTRSM( 'L', 'L', 'T', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL DTRSM( 'R', 'L', 'N', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL DTRSM( 'R', 'L', 'T', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 70\n   50 INFOT = 1\n      CALL DSYRK( '/', 'N', 0, 0, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL DSYRK( 'U', '/', 0, 0, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL DSYRK( 'U', 'N', -1, 0, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL DSYRK( 'U', 'T', -1, 0, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL DSYRK( 'L', 'N', -1, 0, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL DSYRK( 'L', 'T', -1, 0, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL DSYRK( 'U', 'N', 0, -1, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL DSYRK( 'U', 'T', 0, -1, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL DSYRK( 'L', 'N', 0, -1, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL DSYRK( 'L', 'T', 0, -1, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL DSYRK( 'U', 'N', 2, 0, ALPHA, A, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL DSYRK( 'U', 'T', 0, 2, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL DSYRK( 'L', 'N', 2, 0, ALPHA, A, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL DSYRK( 'L', 'T', 0, 2, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL DSYRK( 'U', 'N', 2, 0, ALPHA, A, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL DSYRK( 'U', 'T', 2, 0, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL DSYRK( 'L', 'N', 2, 0, ALPHA, A, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL DSYRK( 'L', 'T', 2, 0, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 70\n   60 INFOT = 1\n      CALL DSYR2K( '/', 'N', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL DSYR2K( 'U', '/', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL DSYR2K( 'U', 'N', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL DSYR2K( 'U', 'T', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL DSYR2K( 'L', 'N', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL DSYR2K( 'L', 'T', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL DSYR2K( 'U', 'N', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL DSYR2K( 'U', 'T', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL DSYR2K( 'L', 'N', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL DSYR2K( 'L', 'T', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL DSYR2K( 'U', 'N', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL DSYR2K( 'U', 'T', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL DSYR2K( 'L', 'N', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL DSYR2K( 'L', 'T', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL DSYR2K( 'U', 'N', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL DSYR2K( 'U', 'T', 0, 2, ALPHA, A, 2, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL DSYR2K( 'L', 'N', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL DSYR2K( 'L', 'T', 0, 2, ALPHA, A, 2, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL DSYR2K( 'U', 'N', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL DSYR2K( 'U', 'T', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL DSYR2K( 'L', 'N', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL DSYR2K( 'L', 'T', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n*\n   70 IF( OK )THEN\n         WRITE( NOUT, FMT = 9999 )SRNAMT\n      ELSE\n         WRITE( NOUT, FMT = 9998 )SRNAMT\n      END IF\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE TESTS OF ERROR-EXITS' )\n 9998 FORMAT( ' ******* ', A6, ' FAILED THE TESTS OF ERROR-EXITS *****',\n     $      '**' )\n*\n*     End of DCHKE.\n*\n      END\n      SUBROUTINE DMAKE( TYPE, UPLO, DIAG, M, N, A, NMAX, AA, LDA, RESET,\n     $                  TRANSL )\n*\n*  Generates values for an M by N matrix A.\n*  Stores the values in the array AA in the data structure required\n*  by the routine, with unwanted elements set to rogue value.\n*\n*  TYPE is 'GE', 'SY' or 'TR'.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Parameters ..\n      DOUBLE PRECISION   ZERO, ONE\n      PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )\n      DOUBLE PRECISION   ROGUE\n      PARAMETER          ( ROGUE = -1.0D10 )\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION   TRANSL\n      INTEGER            LDA, M, N, NMAX\n      LOGICAL            RESET\n      CHARACTER*1        DIAG, UPLO\n      CHARACTER*2        TYPE\n*     .. Array Arguments ..\n      DOUBLE PRECISION   A( NMAX, * ), AA( * )\n*     .. Local Scalars ..\n      INTEGER            I, IBEG, IEND, J\n      LOGICAL            GEN, LOWER, SYM, TRI, UNIT, UPPER\n*     .. External Functions ..\n      DOUBLE PRECISION   DBEG\n      EXTERNAL           DBEG\n*     .. Executable Statements ..\n      GEN = TYPE.EQ.'GE'\n      SYM = TYPE.EQ.'SY'\n      TRI = TYPE.EQ.'TR'\n      UPPER = ( SYM.OR.TRI ).AND.UPLO.EQ.'U'\n      LOWER = ( SYM.OR.TRI ).AND.UPLO.EQ.'L'\n      UNIT = TRI.AND.DIAG.EQ.'U'\n*\n*     Generate data in array A.\n*\n      DO 20 J = 1, N\n         DO 10 I = 1, M\n            IF( GEN.OR.( UPPER.AND.I.LE.J ).OR.( LOWER.AND.I.GE.J ) )\n     $          THEN\n               A( I, J ) = DBEG( RESET ) + TRANSL\n               IF( I.NE.J )THEN\n*                 Set some elements to zero\n                  IF( N.GT.3.AND.J.EQ.N/2 )\n     $               A( I, J ) = ZERO\n                  IF( SYM )THEN\n                     A( J, I ) = A( I, J )\n                  ELSE IF( TRI )THEN\n                     A( J, I ) = ZERO\n                  END IF\n               END IF\n            END IF\n   10    CONTINUE\n         IF( TRI )\n     $      A( J, J ) = A( J, J ) + ONE\n         IF( UNIT )\n     $      A( J, J ) = ONE\n   20 CONTINUE\n*\n*     Store elements in array AS in data structure required by routine.\n*\n      IF( TYPE.EQ.'GE' )THEN\n         DO 50 J = 1, N\n            DO 30 I = 1, M\n               AA( I + ( J - 1 )*LDA ) = A( I, J )\n   30       CONTINUE\n            DO 40 I = M + 1, LDA\n               AA( I + ( J - 1 )*LDA ) = ROGUE\n   40       CONTINUE\n   50    CONTINUE\n      ELSE IF( TYPE.EQ.'SY'.OR.TYPE.EQ.'TR' )THEN\n         DO 90 J = 1, N\n            IF( UPPER )THEN\n               IBEG = 1\n               IF( UNIT )THEN\n                  IEND = J - 1\n               ELSE\n                  IEND = J\n               END IF\n            ELSE\n               IF( UNIT )THEN\n                  IBEG = J + 1\n               ELSE\n                  IBEG = J\n               END IF\n               IEND = N\n            END IF\n            DO 60 I = 1, IBEG - 1\n               AA( I + ( J - 1 )*LDA ) = ROGUE\n   60       CONTINUE\n            DO 70 I = IBEG, IEND\n               AA( I + ( J - 1 )*LDA ) = A( I, J )\n   70       CONTINUE\n            DO 80 I = IEND + 1, LDA\n               AA( I + ( J - 1 )*LDA ) = ROGUE\n   80       CONTINUE\n   90    CONTINUE\n      END IF\n      RETURN\n*\n*     End of DMAKE.\n*\n      END\n      SUBROUTINE DMMCH( TRANSA, TRANSB, M, N, KK, ALPHA, A, LDA, B, LDB,\n     $                  BETA, C, LDC, CT, G, CC, LDCC, EPS, ERR, FATAL,\n     $                  NOUT, MV )\n*\n*  Checks the results of the computational tests.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Parameters ..\n      DOUBLE PRECISION   ZERO, ONE\n      PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION   ALPHA, BETA, EPS, ERR\n      INTEGER            KK, LDA, LDB, LDC, LDCC, M, N, NOUT\n      LOGICAL            FATAL, MV\n      CHARACTER*1        TRANSA, TRANSB\n*     .. Array Arguments ..\n      DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), C( LDC, * ),\n     $                   CC( LDCC, * ), CT( * ), G( * )\n*     .. Local Scalars ..\n      DOUBLE PRECISION   ERRI\n      INTEGER            I, J, K\n      LOGICAL            TRANA, TRANB\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, MAX, SQRT\n*     .. Executable Statements ..\n      TRANA = TRANSA.EQ.'T'.OR.TRANSA.EQ.'C'\n      TRANB = TRANSB.EQ.'T'.OR.TRANSB.EQ.'C'\n*\n*     Compute expected result, one column at a time, in CT using data\n*     in A, B and C.\n*     Compute gauges in G.\n*\n      DO 120 J = 1, N\n*\n         DO 10 I = 1, M\n            CT( I ) = ZERO\n            G( I ) = ZERO\n   10    CONTINUE\n         IF( .NOT.TRANA.AND..NOT.TRANB )THEN\n            DO 30 K = 1, KK\n               DO 20 I = 1, M\n                  CT( I ) = CT( I ) + A( I, K )*B( K, J )\n                  G( I ) = G( I ) + ABS( A( I, K ) )*ABS( B( K, J ) )\n   20          CONTINUE\n   30       CONTINUE\n         ELSE IF( TRANA.AND..NOT.TRANB )THEN\n            DO 50 K = 1, KK\n               DO 40 I = 1, M\n                  CT( I ) = CT( I ) + A( K, I )*B( K, J )\n                  G( I ) = G( I ) + ABS( A( K, I ) )*ABS( B( K, J ) )\n   40          CONTINUE\n   50       CONTINUE\n         ELSE IF( .NOT.TRANA.AND.TRANB )THEN\n            DO 70 K = 1, KK\n               DO 60 I = 1, M\n                  CT( I ) = CT( I ) + A( I, K )*B( J, K )\n                  G( I ) = G( I ) + ABS( A( I, K ) )*ABS( B( J, K ) )\n   60          CONTINUE\n   70       CONTINUE\n         ELSE IF( TRANA.AND.TRANB )THEN\n            DO 90 K = 1, KK\n               DO 80 I = 1, M\n                  CT( I ) = CT( I ) + A( K, I )*B( J, K )\n                  G( I ) = G( I ) + ABS( A( K, I ) )*ABS( B( J, K ) )\n   80          CONTINUE\n   90       CONTINUE\n         END IF\n         DO 100 I = 1, M\n            CT( I ) = ALPHA*CT( I ) + BETA*C( I, J )\n            G( I ) = ABS( ALPHA )*G( I ) + ABS( BETA )*ABS( C( I, J ) )\n  100    CONTINUE\n*\n*        Compute the error ratio for this result.\n*\n         ERR = ZERO\n         DO 110 I = 1, M\n            ERRI = ABS( CT( I ) - CC( I, J ) )/EPS\n            IF( G( I ).NE.ZERO )\n     $         ERRI = ERRI/G( I )\n            ERR = MAX( ERR, ERRI )\n            IF( ERR*SQRT( EPS ).GE.ONE )\n     $         GO TO 130\n  110    CONTINUE\n*\n  120 CONTINUE\n*\n*     If the loop completes, all results are at least half accurate.\n      GO TO 150\n*\n*     Report fatal error.\n*\n  130 FATAL = .TRUE.\n      WRITE( NOUT, FMT = 9999 )\n      DO 140 I = 1, M\n         IF( MV )THEN\n            WRITE( NOUT, FMT = 9998 )I, CT( I ), CC( I, J )\n         ELSE\n            WRITE( NOUT, FMT = 9998 )I, CC( I, J ), CT( I )\n         END IF\n  140 CONTINUE\n      IF( N.GT.1 )\n     $   WRITE( NOUT, FMT = 9997 )J\n*\n  150 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ******* FATAL ERROR - COMPUTED RESULT IS LESS THAN HAL',\n     $      'F ACCURATE *******', /'           EXPECTED RESULT   COMPU',\n     $      'TED RESULT' )\n 9998 FORMAT( 1X, I7, 2G18.6 )\n 9997 FORMAT( '      THESE ARE THE RESULTS FOR COLUMN ', I3 )\n*\n*     End of DMMCH.\n*\n      END\n      LOGICAL FUNCTION LDE( RI, RJ, LR )\n*\n*  Tests if two arrays are identical.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Scalar Arguments ..\n      INTEGER            LR\n*     .. Array Arguments ..\n      DOUBLE PRECISION   RI( * ), RJ( * )\n*     .. Local Scalars ..\n      INTEGER            I\n*     .. Executable Statements ..\n      DO 10 I = 1, LR\n         IF( RI( I ).NE.RJ( I ) )\n     $      GO TO 20\n   10 CONTINUE\n      LDE = .TRUE.\n      GO TO 30\n   20 CONTINUE\n      LDE = .FALSE.\n   30 RETURN\n*\n*     End of LDE.\n*\n      END\n      LOGICAL FUNCTION LDERES( TYPE, UPLO, M, N, AA, AS, LDA )\n*\n*  Tests if selected elements in two arrays are equal.\n*\n*  TYPE is 'GE' or 'SY'.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Scalar Arguments ..\n      INTEGER            LDA, M, N\n      CHARACTER*1        UPLO\n      CHARACTER*2        TYPE\n*     .. Array Arguments ..\n      DOUBLE PRECISION   AA( LDA, * ), AS( LDA, * )\n*     .. Local Scalars ..\n      INTEGER            I, IBEG, IEND, J\n      LOGICAL            UPPER\n*     .. Executable Statements ..\n      UPPER = UPLO.EQ.'U'\n      IF( TYPE.EQ.'GE' )THEN\n         DO 20 J = 1, N\n            DO 10 I = M + 1, LDA\n               IF( AA( I, J ).NE.AS( I, J ) )\n     $            GO TO 70\n   10       CONTINUE\n   20    CONTINUE\n      ELSE IF( TYPE.EQ.'SY' )THEN\n         DO 50 J = 1, N\n            IF( UPPER )THEN\n               IBEG = 1\n               IEND = J\n            ELSE\n               IBEG = J\n               IEND = N\n            END IF\n            DO 30 I = 1, IBEG - 1\n               IF( AA( I, J ).NE.AS( I, J ) )\n     $            GO TO 70\n   30       CONTINUE\n            DO 40 I = IEND + 1, LDA\n               IF( AA( I, J ).NE.AS( I, J ) )\n     $            GO TO 70\n   40       CONTINUE\n   50    CONTINUE\n      END IF\n*\n      LDERES = .TRUE.\n      GO TO 80\n   70 CONTINUE\n      LDERES = .FALSE.\n   80 RETURN\n*\n*     End of LDERES.\n*\n      END\n      DOUBLE PRECISION FUNCTION DBEG( RESET )\n*\n*  Generates random numbers uniformly distributed between -0.5 and 0.5.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Scalar Arguments ..\n      LOGICAL            RESET\n*     .. Local Scalars ..\n      INTEGER            I, IC, MI\n*     .. Save statement ..\n      SAVE               I, IC, MI\n*     .. Executable Statements ..\n      IF( RESET )THEN\n*        Initialize local variables.\n         MI = 891\n         I = 7\n         IC = 0\n         RESET = .FALSE.\n      END IF\n*\n*     The sequence of values of I is bounded between 1 and 999.\n*     If initial I = 1,2,3,6,7 or 9, the period will be 50.\n*     If initial I = 4 or 8, the period will be 25.\n*     If initial I = 5, the period will be 10.\n*     IC is used to break up the period by skipping 1 value of I in 6.\n*\n      IC = IC + 1\n   10 I = I*MI\n      I = I - 1000*( I/1000 )\n      IF( IC.GE.5 )THEN\n         IC = 0\n         GO TO 10\n      END IF\n      DBEG = ( I - 500 )/1001.0D0\n      RETURN\n*\n*     End of DBEG.\n*\n      END\n      DOUBLE PRECISION FUNCTION DDIFF( X, Y )\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION   X, Y\n*     .. Executable Statements ..\n      DDIFF = X - Y\n      RETURN\n*\n*     End of DDIFF.\n*\n      END\n      SUBROUTINE CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n*\n*  Tests whether XERBLA has detected an error when it should.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Scalar Arguments ..\n      INTEGER            INFOT, NOUT\n      LOGICAL            LERR, OK\n      CHARACTER*6        SRNAMT\n*     .. Executable Statements ..\n      IF( .NOT.LERR )THEN\n         WRITE( NOUT, FMT = 9999 )INFOT, SRNAMT\n         OK = .FALSE.\n      END IF\n      LERR = .FALSE.\n      RETURN\n*\n 9999 FORMAT( ' ***** ILLEGAL VALUE OF PARAMETER NUMBER ', I2, ' NOT D',\n     $      'ETECTED BY ', A6, ' *****' )\n*\n*     End of CHKXER.\n*\n      END\n      SUBROUTINE XERBLA( SRNAME, INFO )\n*\n*  This is a special version of XERBLA to be used only as part of\n*  the test program for testing error exits from the Level 3 BLAS\n*  routines.\n*\n*  XERBLA  is an error handler for the Level 3 BLAS routines.\n*\n*  It is called by the Level 3 BLAS routines if an input parameter is\n*  invalid.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Scalar Arguments ..\n      INTEGER            INFO\n      CHARACTER*6        SRNAME\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUT\n      LOGICAL            LERR, OK\n      CHARACTER*6        SRNAMT\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUT, OK, LERR\n      COMMON             /SRNAMC/SRNAMT\n*     .. Executable Statements ..\n      LERR = .TRUE.\n      IF( INFO.NE.INFOT )THEN\n         IF( INFOT.NE.0 )THEN\n            WRITE( NOUT, FMT = 9999 )INFO, INFOT\n         ELSE\n            WRITE( NOUT, FMT = 9997 )INFO\n         END IF\n         OK = .FALSE.\n      END IF\n      IF( SRNAME.NE.SRNAMT )THEN\n         WRITE( NOUT, FMT = 9998 )SRNAME, SRNAMT\n         OK = .FALSE.\n      END IF\n      RETURN\n*\n 9999 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6, ' INSTEAD',\n     $      ' OF ', I2, ' *******' )\n 9998 FORMAT( ' ******* XERBLA WAS CALLED WITH SRNAME = ', A6, ' INSTE',\n     $      'AD OF ', A6, ' *******' )\n 9997 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6,\n     $      ' *******' )\n*\n*     End of XERBLA\n*\n      END\n\n"
  },
  {
    "path": "include/eigen3/blas/testing/runblastest.sh",
    "content": "#!/bin/bash\n\nblack='\\E[30m'\nred='\\E[31m'\ngreen='\\E[32m'\nyellow='\\E[33m'\nblue='\\E[34m'\nmagenta='\\E[35m'\ncyan='\\E[36m'\nwhite='\\E[37m'\n\nif [ -f $2 ]; then\n  data=$2\n  if [ -f $1.summ ]; then rm $1.summ; fi\n  if [ -f $1.snap ]; then rm $1.snap; fi\nelse\n  data=$1\nfi\n\nif ! ./$1 < $data > /dev/null 2> .runtest.log ; then\n  echo -e  $red Test $1 failed: $black\n  echo -e $blue\n  cat .runtest.log\n  echo -e $black\n  exit 1\nelse\n  if [ -f $1.summ ]; then\n    if [ `grep \"FATAL ERROR\" $1.summ | wc -l` -gt 0 ]; then\n      echo -e  $red \"Test $1 failed (FATAL ERROR, read the file $1.summ for details)\" $black\n      echo -e $blue\n      cat .runtest.log\n      echo -e $black\n      exit 1;\n    fi\n\n    if [ `grep \"FAILED THE TESTS OF ERROR-EXITS\" $1.summ | wc -l` -gt 0 ]; then\n      echo -e  $red \"Test $1 failed (FAILED THE TESTS OF ERROR-EXITS, read the file $1.summ for details)\" $black\n      echo -e $blue\n      cat .runtest.log\n      echo -e $black\n      exit 1;\n    fi      \n  fi\n  echo -e $green Test $1 passed$black\nfi\n"
  },
  {
    "path": "include/eigen3/blas/testing/sblat1.f",
    "content": "*> \\brief \\b SBLAT1\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*  Definition:\n*  ===========\n*\n*       PROGRAM SBLAT1\n* \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*>    Test program for the REAL Level 1 BLAS.\n*>\n*>    Based upon the original BLAS test routine together with:\n*>    F06EAF Example Program Text\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date April 2012\n*\n*> \\ingroup single_blas_testing\n*\n*  =====================================================================\n      PROGRAM SBLAT1\n*\n*  -- Reference BLAS test routine (version 3.4.1) --\n*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     April 2012\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      INTEGER          NOUT\n      PARAMETER        (NOUT=6)\n*     .. Scalars in Common ..\n      INTEGER          ICASE, INCX, INCY, N\n      LOGICAL          PASS\n*     .. Local Scalars ..\n      REAL             SFAC\n      INTEGER          IC\n*     .. External Subroutines ..\n      EXTERNAL         CHECK0, CHECK1, CHECK2, CHECK3, HEADER\n*     .. Common blocks ..\n      COMMON           /COMBLA/ICASE, N, INCX, INCY, PASS\n*     .. Data statements ..\n      DATA             SFAC/9.765625E-4/\n*     .. Executable Statements ..\n      WRITE (NOUT,99999)\n      DO 20 IC = 1, 13\n         ICASE = IC\n         CALL HEADER\n*\n*        .. Initialize  PASS,  INCX,  and INCY for a new case. ..\n*        .. the value 9999 for INCX or INCY will appear in the ..\n*        .. detailed  output, if any, for cases  that do not involve ..\n*        .. these parameters ..\n*\n         PASS = .TRUE.\n         INCX = 9999\n         INCY = 9999\n         IF (ICASE.EQ.3 .OR. ICASE.EQ.11) THEN\n            CALL CHECK0(SFAC)\n         ELSE IF (ICASE.EQ.7 .OR. ICASE.EQ.8 .OR. ICASE.EQ.9 .OR.\n     +            ICASE.EQ.10) THEN\n            CALL CHECK1(SFAC)\n         ELSE IF (ICASE.EQ.1 .OR. ICASE.EQ.2 .OR. ICASE.EQ.5 .OR.\n     +            ICASE.EQ.6 .OR. ICASE.EQ.12 .OR. ICASE.EQ.13) THEN\n            CALL CHECK2(SFAC)\n         ELSE IF (ICASE.EQ.4) THEN\n            CALL CHECK3(SFAC)\n         END IF\n*        -- Print\n         IF (PASS) WRITE (NOUT,99998)\n   20 CONTINUE\n      STOP\n*\n99999 FORMAT (' Real BLAS Test Program Results',/1X)\n99998 FORMAT ('                                    ----- PASS -----')\n      END\n      SUBROUTINE HEADER\n*     .. Parameters ..\n      INTEGER          NOUT\n      PARAMETER        (NOUT=6)\n*     .. Scalars in Common ..\n      INTEGER          ICASE, INCX, INCY, N\n      LOGICAL          PASS\n*     .. Local Arrays ..\n      CHARACTER*6      L(13)\n*     .. Common blocks ..\n      COMMON           /COMBLA/ICASE, N, INCX, INCY, PASS\n*     .. Data statements ..\n      DATA             L(1)/' SDOT '/\n      DATA             L(2)/'SAXPY '/\n      DATA             L(3)/'SROTG '/\n      DATA             L(4)/' SROT '/\n      DATA             L(5)/'SCOPY '/\n      DATA             L(6)/'SSWAP '/\n      DATA             L(7)/'SNRM2 '/\n      DATA             L(8)/'SASUM '/\n      DATA             L(9)/'SSCAL '/\n      DATA             L(10)/'ISAMAX'/\n      DATA             L(11)/'SROTMG'/\n      DATA             L(12)/'SROTM '/\n      DATA             L(13)/'SDSDOT'/\n*     .. Executable Statements ..\n      WRITE (NOUT,99999) ICASE, L(ICASE)\n      RETURN\n*\n99999 FORMAT (/' Test of subprogram number',I3,12X,A6)\n      END\n      SUBROUTINE CHECK0(SFAC)\n*     .. Parameters ..\n      INTEGER           NOUT\n      PARAMETER         (NOUT=6)\n*     .. Scalar Arguments ..\n      REAL              SFAC\n*     .. Scalars in Common ..\n      INTEGER           ICASE, INCX, INCY, N\n      LOGICAL           PASS\n*     .. Local Scalars ..\n      REAL              D12, SA, SB, SC, SS\n      INTEGER           I, K\n*     .. Local Arrays ..\n      REAL              DA1(8), DATRUE(8), DB1(8), DBTRUE(8), DC1(8),\n     +                  DS1(8), DAB(4,9), DTEMP(9), DTRUE(9,9)\n*     .. External Subroutines ..\n      EXTERNAL          SROTG, SROTMG, STEST1\n*     .. Common blocks ..\n      COMMON            /COMBLA/ICASE, N, INCX, INCY, PASS\n*     .. Data statements ..\n      DATA              DA1/0.3E0, 0.4E0, -0.3E0, -0.4E0, -0.3E0, 0.0E0,\n     +                  0.0E0, 1.0E0/\n      DATA              DB1/0.4E0, 0.3E0, 0.4E0, 0.3E0, -0.4E0, 0.0E0,\n     +                  1.0E0, 0.0E0/\n      DATA              DC1/0.6E0, 0.8E0, -0.6E0, 0.8E0, 0.6E0, 1.0E0,\n     +                  0.0E0, 1.0E0/\n      DATA              DS1/0.8E0, 0.6E0, 0.8E0, -0.6E0, 0.8E0, 0.0E0,\n     +                  1.0E0, 0.0E0/\n      DATA              DATRUE/0.5E0, 0.5E0, 0.5E0, -0.5E0, -0.5E0,\n     +                  0.0E0, 1.0E0, 1.0E0/\n      DATA              DBTRUE/0.0E0, 0.6E0, 0.0E0, -0.6E0, 0.0E0,\n     +                  0.0E0, 1.0E0, 0.0E0/\n*     INPUT FOR MODIFIED GIVENS\n      DATA DAB/ .1E0,.3E0,1.2E0,.2E0,\n     A          .7E0, .2E0, .6E0, 4.2E0,\n     B          0.E0,0.E0,0.E0,0.E0,\n     C          4.E0, -1.E0, 2.E0, 4.E0,\n     D          6.E-10, 2.E-2, 1.E5, 10.E0,\n     E          4.E10, 2.E-2, 1.E-5, 10.E0,\n     F          2.E-10, 4.E-2, 1.E5, 10.E0,\n     G          2.E10, 4.E-2, 1.E-5, 10.E0,\n     H          4.E0, -2.E0, 8.E0, 4.E0    /\n*    TRUE RESULTS FOR MODIFIED GIVENS\n      DATA DTRUE/0.E0,0.E0, 1.3E0, .2E0, 0.E0,0.E0,0.E0, .5E0, 0.E0,\n     A           0.E0,0.E0, 4.5E0, 4.2E0, 1.E0, .5E0, 0.E0,0.E0,0.E0,\n     B           0.E0,0.E0,0.E0,0.E0, -2.E0, 0.E0,0.E0,0.E0,0.E0,\n     C           0.E0,0.E0,0.E0, 4.E0, -1.E0, 0.E0,0.E0,0.E0,0.E0,\n     D           0.E0, 15.E-3, 0.E0, 10.E0, -1.E0, 0.E0, -1.E-4,\n     E           0.E0, 1.E0,\n     F           0.E0,0.E0, 6144.E-5, 10.E0, -1.E0, 4096.E0, -1.E6,\n     G           0.E0, 1.E0,\n     H           0.E0,0.E0,15.E0,10.E0,-1.E0, 5.E-5, 0.E0,1.E0,0.E0,\n     I           0.E0,0.E0, 15.E0, 10.E0, -1. E0, 5.E5, -4096.E0,\n     J           1.E0, 4096.E-6,\n     K           0.E0,0.E0, 7.E0, 4.E0, 0.E0,0.E0, -.5E0, -.25E0, 0.E0/\n*                   4096 = 2 ** 12\n      DATA D12  /4096.E0/\n      DTRUE(1,1) = 12.E0 / 130.E0\n      DTRUE(2,1) = 36.E0 / 130.E0\n      DTRUE(7,1) = -1.E0 / 6.E0\n      DTRUE(1,2) = 14.E0 / 75.E0\n      DTRUE(2,2) = 49.E0 / 75.E0\n      DTRUE(9,2) = 1.E0 / 7.E0\n      DTRUE(1,5) = 45.E-11 * (D12 * D12)\n      DTRUE(3,5) = 4.E5 / (3.E0 * D12)\n      DTRUE(6,5) = 1.E0 / D12\n      DTRUE(8,5) = 1.E4 / (3.E0 * D12)\n      DTRUE(1,6) = 4.E10 / (1.5E0 * D12 * D12)\n      DTRUE(2,6) = 2.E-2 / 1.5E0\n      DTRUE(8,6) = 5.E-7 * D12\n      DTRUE(1,7) = 4.E0 / 150.E0\n      DTRUE(2,7) = (2.E-10 / 1.5E0) * (D12 * D12)\n      DTRUE(7,7) = -DTRUE(6,5)\n      DTRUE(9,7) = 1.E4 / D12\n      DTRUE(1,8) = DTRUE(1,7)\n      DTRUE(2,8) = 2.E10 / (1.5E0 * D12 * D12)\n      DTRUE(1,9) = 32.E0 / 7.E0\n      DTRUE(2,9) = -16.E0 / 7.E0\n*     .. Executable Statements ..\n*\n*     Compute true values which cannot be prestored\n*     in decimal notation\n*\n      DBTRUE(1) = 1.0E0/0.6E0\n      DBTRUE(3) = -1.0E0/0.6E0\n      DBTRUE(5) = 1.0E0/0.6E0\n*\n      DO 20 K = 1, 8\n*        .. Set N=K for identification in output if any ..\n         N = K\n         IF (ICASE.EQ.3) THEN\n*           .. SROTG ..\n            IF (K.GT.8) GO TO 40\n            SA = DA1(K)\n            SB = DB1(K)\n            CALL SROTG(SA,SB,SC,SS)\n            CALL STEST1(SA,DATRUE(K),DATRUE(K),SFAC)\n            CALL STEST1(SB,DBTRUE(K),DBTRUE(K),SFAC)\n            CALL STEST1(SC,DC1(K),DC1(K),SFAC)\n            CALL STEST1(SS,DS1(K),DS1(K),SFAC)\n         ELSEIF (ICASE.EQ.11) THEN\n*           .. SROTMG ..\n            DO I=1,4\n               DTEMP(I)= DAB(I,K)\n               DTEMP(I+4) = 0.0\n            END DO\n            DTEMP(9) = 0.0\n            CALL SROTMG(DTEMP(1),DTEMP(2),DTEMP(3),DTEMP(4),DTEMP(5))\n            CALL STEST(9,DTEMP,DTRUE(1,K),DTRUE(1,K),SFAC)\n         ELSE\n            WRITE (NOUT,*) ' Shouldn''t be here in CHECK0'\n            STOP\n         END IF\n   20 CONTINUE\n   40 RETURN\n      END\n      SUBROUTINE CHECK1(SFAC)\n*     .. Parameters ..\n      INTEGER           NOUT\n      PARAMETER         (NOUT=6)\n*     .. Scalar Arguments ..\n      REAL              SFAC\n*     .. Scalars in Common ..\n      INTEGER           ICASE, INCX, INCY, N\n      LOGICAL           PASS\n*     .. Local Scalars ..\n      INTEGER           I, LEN, NP1\n*     .. Local Arrays ..\n      REAL              DTRUE1(5), DTRUE3(5), DTRUE5(8,5,2), DV(8,5,2),\n     +                  SA(10), STEMP(1), STRUE(8), SX(8)\n      INTEGER           ITRUE2(5)\n*     .. External Functions ..\n      REAL              SASUM, SNRM2\n      INTEGER           ISAMAX\n      EXTERNAL          SASUM, SNRM2, ISAMAX\n*     .. External Subroutines ..\n      EXTERNAL          ITEST1, SSCAL, STEST, STEST1\n*     .. Intrinsic Functions ..\n      INTRINSIC         MAX\n*     .. Common blocks ..\n      COMMON            /COMBLA/ICASE, N, INCX, INCY, PASS\n*     .. Data statements ..\n      DATA              SA/0.3E0, -1.0E0, 0.0E0, 1.0E0, 0.3E0, 0.3E0,\n     +                  0.3E0, 0.3E0, 0.3E0, 0.3E0/\n      DATA              DV/0.1E0, 2.0E0, 2.0E0, 2.0E0, 2.0E0, 2.0E0,\n     +                  2.0E0, 2.0E0, 0.3E0, 3.0E0, 3.0E0, 3.0E0, 3.0E0,\n     +                  3.0E0, 3.0E0, 3.0E0, 0.3E0, -0.4E0, 4.0E0,\n     +                  4.0E0, 4.0E0, 4.0E0, 4.0E0, 4.0E0, 0.2E0,\n     +                  -0.6E0, 0.3E0, 5.0E0, 5.0E0, 5.0E0, 5.0E0,\n     +                  5.0E0, 0.1E0, -0.3E0, 0.5E0, -0.1E0, 6.0E0,\n     +                  6.0E0, 6.0E0, 6.0E0, 0.1E0, 8.0E0, 8.0E0, 8.0E0,\n     +                  8.0E0, 8.0E0, 8.0E0, 8.0E0, 0.3E0, 9.0E0, 9.0E0,\n     +                  9.0E0, 9.0E0, 9.0E0, 9.0E0, 9.0E0, 0.3E0, 2.0E0,\n     +                  -0.4E0, 2.0E0, 2.0E0, 2.0E0, 2.0E0, 2.0E0,\n     +                  0.2E0, 3.0E0, -0.6E0, 5.0E0, 0.3E0, 2.0E0,\n     +                  2.0E0, 2.0E0, 0.1E0, 4.0E0, -0.3E0, 6.0E0,\n     +                  -0.5E0, 7.0E0, -0.1E0, 3.0E0/\n      DATA              DTRUE1/0.0E0, 0.3E0, 0.5E0, 0.7E0, 0.6E0/\n      DATA              DTRUE3/0.0E0, 0.3E0, 0.7E0, 1.1E0, 1.0E0/\n      DATA              DTRUE5/0.10E0, 2.0E0, 2.0E0, 2.0E0, 2.0E0,\n     +                  2.0E0, 2.0E0, 2.0E0, -0.3E0, 3.0E0, 3.0E0,\n     +                  3.0E0, 3.0E0, 3.0E0, 3.0E0, 3.0E0, 0.0E0, 0.0E0,\n     +                  4.0E0, 4.0E0, 4.0E0, 4.0E0, 4.0E0, 4.0E0,\n     +                  0.20E0, -0.60E0, 0.30E0, 5.0E0, 5.0E0, 5.0E0,\n     +                  5.0E0, 5.0E0, 0.03E0, -0.09E0, 0.15E0, -0.03E0,\n     +                  6.0E0, 6.0E0, 6.0E0, 6.0E0, 0.10E0, 8.0E0,\n     +                  8.0E0, 8.0E0, 8.0E0, 8.0E0, 8.0E0, 8.0E0,\n     +                  0.09E0, 9.0E0, 9.0E0, 9.0E0, 9.0E0, 9.0E0,\n     +                  9.0E0, 9.0E0, 0.09E0, 2.0E0, -0.12E0, 2.0E0,\n     +                  2.0E0, 2.0E0, 2.0E0, 2.0E0, 0.06E0, 3.0E0,\n     +                  -0.18E0, 5.0E0, 0.09E0, 2.0E0, 2.0E0, 2.0E0,\n     +                  0.03E0, 4.0E0, -0.09E0, 6.0E0, -0.15E0, 7.0E0,\n     +                  -0.03E0, 3.0E0/\n      DATA              ITRUE2/0, 1, 2, 2, 3/\n*     .. Executable Statements ..\n      DO 80 INCX = 1, 2\n         DO 60 NP1 = 1, 5\n            N = NP1 - 1\n            LEN = 2*MAX(N,1)\n*           .. Set vector arguments ..\n            DO 20 I = 1, LEN\n               SX(I) = DV(I,NP1,INCX)\n   20       CONTINUE\n*\n            IF (ICASE.EQ.7) THEN\n*              .. SNRM2 ..\n               STEMP(1) = DTRUE1(NP1)\n               CALL STEST1(SNRM2(N,SX,INCX),STEMP(1),STEMP,SFAC)\n            ELSE IF (ICASE.EQ.8) THEN\n*              .. SASUM ..\n               STEMP(1) = DTRUE3(NP1)\n               CALL STEST1(SASUM(N,SX,INCX),STEMP(1),STEMP,SFAC)\n            ELSE IF (ICASE.EQ.9) THEN\n*              .. SSCAL ..\n               CALL SSCAL(N,SA((INCX-1)*5+NP1),SX,INCX)\n               DO 40 I = 1, LEN\n                  STRUE(I) = DTRUE5(I,NP1,INCX)\n   40          CONTINUE\n               CALL STEST(LEN,SX,STRUE,STRUE,SFAC)\n            ELSE IF (ICASE.EQ.10) THEN\n*              .. ISAMAX ..\n               CALL ITEST1(ISAMAX(N,SX,INCX),ITRUE2(NP1))\n            ELSE\n               WRITE (NOUT,*) ' Shouldn''t be here in CHECK1'\n               STOP\n            END IF\n   60    CONTINUE\n   80 CONTINUE\n      RETURN\n      END\n      SUBROUTINE CHECK2(SFAC)\n*     .. Parameters ..\n      INTEGER           NOUT\n      PARAMETER         (NOUT=6)\n*     .. Scalar Arguments ..\n      REAL              SFAC\n*     .. Scalars in Common ..\n      INTEGER           ICASE, INCX, INCY, N\n      LOGICAL           PASS\n*     .. Local Scalars ..\n      REAL              SA\n      INTEGER           I, J, KI, KN, KNI, KPAR, KSIZE, LENX, LENY,\n     $                  MX, MY \n*     .. Local Arrays ..\n      REAL              DT10X(7,4,4), DT10Y(7,4,4), DT7(4,4),\n     $                  DT8(7,4,4), DX1(7),\n     $                  DY1(7), SSIZE1(4), SSIZE2(14,2), SSIZE3(4),\n     $                  SSIZE(7), STX(7), STY(7), SX(7), SY(7),\n     $                  DPAR(5,4), DT19X(7,4,16),DT19XA(7,4,4),\n     $                  DT19XB(7,4,4), DT19XC(7,4,4),DT19XD(7,4,4),\n     $                  DT19Y(7,4,16), DT19YA(7,4,4),DT19YB(7,4,4),\n     $                  DT19YC(7,4,4), DT19YD(7,4,4), DTEMP(5),\n     $                  ST7B(4,4)\n      INTEGER           INCXS(4), INCYS(4), LENS(4,2), NS(4)\n*     .. External Functions ..\n      REAL              SDOT, SDSDOT\n      EXTERNAL          SDOT, SDSDOT\n*     .. External Subroutines ..\n      EXTERNAL          SAXPY, SCOPY, SROTM, SSWAP, STEST, STEST1\n*     .. Intrinsic Functions ..\n      INTRINSIC         ABS, MIN\n*     .. Common blocks ..\n      COMMON            /COMBLA/ICASE, N, INCX, INCY, PASS\n*     .. Data statements ..\n      EQUIVALENCE (DT19X(1,1,1),DT19XA(1,1,1)),(DT19X(1,1,5),\n     A   DT19XB(1,1,1)),(DT19X(1,1,9),DT19XC(1,1,1)),\n     B   (DT19X(1,1,13),DT19XD(1,1,1))\n      EQUIVALENCE (DT19Y(1,1,1),DT19YA(1,1,1)),(DT19Y(1,1,5),\n     A   DT19YB(1,1,1)),(DT19Y(1,1,9),DT19YC(1,1,1)),\n     B   (DT19Y(1,1,13),DT19YD(1,1,1))\n\n      DATA              SA/0.3E0/\n      DATA              INCXS/1, 2, -2, -1/\n      DATA              INCYS/1, -2, 1, -2/\n      DATA              LENS/1, 1, 2, 4, 1, 1, 3, 7/\n      DATA              NS/0, 1, 2, 4/\n      DATA              DX1/0.6E0, 0.1E0, -0.5E0, 0.8E0, 0.9E0, -0.3E0,\n     +                  -0.4E0/\n      DATA              DY1/0.5E0, -0.9E0, 0.3E0, 0.7E0, -0.6E0, 0.2E0,\n     +                  0.8E0/\n      DATA              DT7/0.0E0, 0.30E0, 0.21E0, 0.62E0, 0.0E0,\n     +                  0.30E0, -0.07E0, 0.85E0, 0.0E0, 0.30E0, -0.79E0,\n     +                  -0.74E0, 0.0E0, 0.30E0, 0.33E0, 1.27E0/\n      DATA              ST7B/ .1, .4, .31, .72,     .1, .4, .03, .95,\n     +                  .1, .4, -.69, -.64,   .1, .4, .43, 1.37/\n      DATA              DT8/0.5E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.68E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.0E0, 0.68E0, -0.87E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.0E0, 0.0E0, 0.68E0, -0.87E0, 0.15E0,\n     +                  0.94E0, 0.0E0, 0.0E0, 0.0E0, 0.5E0, 0.0E0,\n     +                  0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.68E0,\n     +                  0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.35E0, -0.9E0, 0.48E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.38E0, -0.9E0, 0.57E0, 0.7E0, -0.75E0,\n     +                  0.2E0, 0.98E0, 0.5E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.0E0, 0.0E0, 0.68E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.35E0, -0.72E0,\n     +                  0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.38E0,\n     +                  -0.63E0, 0.15E0, 0.88E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.5E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.68E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.68E0, -0.9E0, 0.33E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.0E0, 0.68E0, -0.9E0, 0.33E0, 0.7E0,\n     +                  -0.75E0, 0.2E0, 1.04E0/\n      DATA              DT10X/0.6E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.5E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.5E0, -0.9E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.0E0, 0.5E0, -0.9E0, 0.3E0, 0.7E0,\n     +                  0.0E0, 0.0E0, 0.0E0, 0.6E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.0E0, 0.0E0, 0.5E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.0E0, 0.0E0, 0.3E0, 0.1E0, 0.5E0, 0.0E0,\n     +                  0.0E0, 0.0E0, 0.0E0, 0.8E0, 0.1E0, -0.6E0,\n     +                  0.8E0, 0.3E0, -0.3E0, 0.5E0, 0.6E0, 0.0E0,\n     +                  0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.5E0, 0.0E0,\n     +                  0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, -0.9E0,\n     +                  0.1E0, 0.5E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.7E0,\n     +                  0.1E0, 0.3E0, 0.8E0, -0.9E0, -0.3E0, 0.5E0,\n     +                  0.6E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.5E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.5E0, 0.3E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.5E0, 0.3E0, -0.6E0, 0.8E0, 0.0E0, 0.0E0,\n     +                  0.0E0/\n      DATA              DT10Y/0.5E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.6E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.6E0, 0.1E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.6E0, 0.1E0, -0.5E0, 0.8E0, 0.0E0,\n     +                  0.0E0, 0.0E0, 0.5E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.0E0, 0.6E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.0E0, -0.5E0, -0.9E0, 0.6E0, 0.0E0,\n     +                  0.0E0, 0.0E0, 0.0E0, -0.4E0, -0.9E0, 0.9E0,\n     +                  0.7E0, -0.5E0, 0.2E0, 0.6E0, 0.5E0, 0.0E0,\n     +                  0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.6E0, 0.0E0,\n     +                  0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, -0.5E0,\n     +                  0.6E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  -0.4E0, 0.9E0, -0.5E0, 0.6E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.5E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.6E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.6E0, -0.9E0, 0.1E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.0E0, 0.6E0, -0.9E0, 0.1E0, 0.7E0,\n     +                  -0.5E0, 0.2E0, 0.8E0/\n      DATA              SSIZE1/0.0E0, 0.3E0, 1.6E0, 3.2E0/\n      DATA              SSIZE2/0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 1.17E0, 1.17E0, 1.17E0, 1.17E0, 1.17E0,\n     +                  1.17E0, 1.17E0, 1.17E0, 1.17E0, 1.17E0, 1.17E0,\n     +                  1.17E0, 1.17E0, 1.17E0/\n      DATA              SSIZE3/ .1, .4, 1.7, 3.3 /\n*\n*                         FOR DROTM\n*\n      DATA DPAR/-2.E0,  0.E0,0.E0,0.E0,0.E0,\n     A          -1.E0,  2.E0, -3.E0, -4.E0,  5.E0,\n     B           0.E0,  0.E0,  2.E0, -3.E0,  0.E0,\n     C           1.E0,  5.E0,  2.E0,  0.E0, -4.E0/\n*                        TRUE X RESULTS F0R ROTATIONS DROTM\n      DATA DT19XA/.6E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     A            .6E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     B            .6E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     C            .6E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     D            .6E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     E           -.8E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     F           -.9E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     G           3.5E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     H            .6E0,   .1E0,             0.E0,0.E0,0.E0,0.E0,0.E0,\n     I           -.8E0,  3.8E0,             0.E0,0.E0,0.E0,0.E0,0.E0,\n     J           -.9E0,  2.8E0,             0.E0,0.E0,0.E0,0.E0,0.E0,\n     K           3.5E0,  -.4E0,             0.E0,0.E0,0.E0,0.E0,0.E0,\n     L            .6E0,   .1E0,  -.5E0,   .8E0,          0.E0,0.E0,0.E0,\n     M           -.8E0,  3.8E0, -2.2E0, -1.2E0,          0.E0,0.E0,0.E0,\n     N           -.9E0,  2.8E0, -1.4E0, -1.3E0,          0.E0,0.E0,0.E0,\n     O           3.5E0,  -.4E0, -2.2E0,  4.7E0,          0.E0,0.E0,0.E0/\n*\n      DATA DT19XB/.6E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     A            .6E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     B            .6E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     C            .6E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     D            .6E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     E           -.8E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     F           -.9E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     G           3.5E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     H            .6E0,   .1E0,  -.5E0,             0.E0,0.E0,0.E0,0.E0,\n     I           0.E0,    .1E0, -3.0E0,             0.E0,0.E0,0.E0,0.E0,\n     J           -.3E0,   .1E0, -2.0E0,             0.E0,0.E0,0.E0,0.E0,\n     K           3.3E0,   .1E0, -2.0E0,             0.E0,0.E0,0.E0,0.E0,\n     L            .6E0,   .1E0,  -.5E0,   .8E0,   .9E0,  -.3E0,  -.4E0,\n     M          -2.0E0,   .1E0,  1.4E0,   .8E0,   .6E0,  -.3E0, -2.8E0,\n     N          -1.8E0,   .1E0,  1.3E0,   .8E0,  0.E0,   -.3E0, -1.9E0,\n     O           3.8E0,   .1E0, -3.1E0,   .8E0,  4.8E0,  -.3E0, -1.5E0 /\n*\n      DATA DT19XC/.6E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     A            .6E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     B            .6E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     C            .6E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     D            .6E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     E           -.8E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     F           -.9E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     G           3.5E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     H            .6E0,   .1E0,  -.5E0,             0.E0,0.E0,0.E0,0.E0,\n     I           4.8E0,   .1E0, -3.0E0,             0.E0,0.E0,0.E0,0.E0,\n     J           3.3E0,   .1E0, -2.0E0,             0.E0,0.E0,0.E0,0.E0,\n     K           2.1E0,   .1E0, -2.0E0,             0.E0,0.E0,0.E0,0.E0,\n     L            .6E0,   .1E0,  -.5E0,   .8E0,   .9E0,  -.3E0,  -.4E0,\n     M          -1.6E0,   .1E0, -2.2E0,   .8E0,  5.4E0,  -.3E0, -2.8E0,\n     N          -1.5E0,   .1E0, -1.4E0,   .8E0,  3.6E0,  -.3E0, -1.9E0,\n     O           3.7E0,   .1E0, -2.2E0,   .8E0,  3.6E0,  -.3E0, -1.5E0 /\n*\n      DATA DT19XD/.6E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     A            .6E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     B            .6E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     C            .6E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     D            .6E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     E           -.8E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     F           -.9E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     G           3.5E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     H            .6E0,   .1E0,             0.E0,0.E0,0.E0,0.E0,0.E0,\n     I           -.8E0, -1.0E0,             0.E0,0.E0,0.E0,0.E0,0.E0,\n     J           -.9E0,  -.8E0,             0.E0,0.E0,0.E0,0.E0,0.E0,\n     K           3.5E0,   .8E0,             0.E0,0.E0,0.E0,0.E0,0.E0,\n     L            .6E0,   .1E0,  -.5E0,   .8E0,          0.E0,0.E0,0.E0,\n     M           -.8E0, -1.0E0,  1.4E0, -1.6E0,          0.E0,0.E0,0.E0,\n     N           -.9E0,  -.8E0,  1.3E0, -1.6E0,          0.E0,0.E0,0.E0,\n     O           3.5E0,   .8E0, -3.1E0,  4.8E0,          0.E0,0.E0,0.E0/\n*                        TRUE Y RESULTS FOR ROTATIONS DROTM\n      DATA DT19YA/.5E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     A            .5E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     B            .5E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     C            .5E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     D            .5E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     E            .7E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     F           1.7E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     G          -2.6E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     H            .5E0,  -.9E0,             0.E0,0.E0,0.E0,0.E0,0.E0,\n     I            .7E0, -4.8E0,             0.E0,0.E0,0.E0,0.E0,0.E0,\n     J           1.7E0,  -.7E0,             0.E0,0.E0,0.E0,0.E0,0.E0,\n     K          -2.6E0,  3.5E0,             0.E0,0.E0,0.E0,0.E0,0.E0,\n     L            .5E0,  -.9E0,   .3E0,   .7E0,          0.E0,0.E0,0.E0,\n     M            .7E0, -4.8E0,  3.0E0,  1.1E0,          0.E0,0.E0,0.E0,\n     N           1.7E0,  -.7E0,  -.7E0,  2.3E0,          0.E0,0.E0,0.E0,\n     O          -2.6E0,  3.5E0,  -.7E0, -3.6E0,          0.E0,0.E0,0.E0/\n*\n      DATA DT19YB/.5E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     A            .5E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     B            .5E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     C            .5E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     D            .5E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     E            .7E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     F           1.7E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     G          -2.6E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     H            .5E0,  -.9E0,   .3E0,             0.E0,0.E0,0.E0,0.E0,\n     I           4.0E0,  -.9E0,  -.3E0,             0.E0,0.E0,0.E0,0.E0,\n     J           -.5E0,  -.9E0,  1.5E0,             0.E0,0.E0,0.E0,0.E0,\n     K          -1.5E0,  -.9E0, -1.8E0,             0.E0,0.E0,0.E0,0.E0,\n     L            .5E0,  -.9E0,   .3E0,   .7E0,  -.6E0,   .2E0,   .8E0,\n     M           3.7E0,  -.9E0, -1.2E0,   .7E0, -1.5E0,   .2E0,  2.2E0,\n     N           -.3E0,  -.9E0,  2.1E0,   .7E0, -1.6E0,   .2E0,  2.0E0,\n     O          -1.6E0,  -.9E0, -2.1E0,   .7E0,  2.9E0,   .2E0, -3.8E0 /\n*\n      DATA DT19YC/.5E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     A            .5E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     B            .5E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     C            .5E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     D            .5E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     E            .7E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     F           1.7E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     G          -2.6E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     H            .5E0,  -.9E0,             0.E0,0.E0,0.E0,0.E0,0.E0,\n     I           4.0E0, -6.3E0,             0.E0,0.E0,0.E0,0.E0,0.E0,\n     J           -.5E0,   .3E0,             0.E0,0.E0,0.E0,0.E0,0.E0,\n     K          -1.5E0,  3.0E0,             0.E0,0.E0,0.E0,0.E0,0.E0,\n     L            .5E0,  -.9E0,   .3E0,   .7E0,          0.E0,0.E0,0.E0,\n     M           3.7E0, -7.2E0,  3.0E0,  1.7E0,          0.E0,0.E0,0.E0,\n     N           -.3E0,   .9E0,  -.7E0,  1.9E0,          0.E0,0.E0,0.E0,\n     O          -1.6E0,  2.7E0,  -.7E0, -3.4E0,          0.E0,0.E0,0.E0/\n*\n      DATA DT19YD/.5E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     A            .5E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     B            .5E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     C            .5E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     D            .5E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     E            .7E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     F           1.7E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     G          -2.6E0,                  0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,\n     H            .5E0,  -.9E0,   .3E0,             0.E0,0.E0,0.E0,0.E0,\n     I            .7E0,  -.9E0,  1.2E0,             0.E0,0.E0,0.E0,0.E0,\n     J           1.7E0,  -.9E0,   .5E0,             0.E0,0.E0,0.E0,0.E0,\n     K          -2.6E0,  -.9E0, -1.3E0,             0.E0,0.E0,0.E0,0.E0,\n     L            .5E0,  -.9E0,   .3E0,   .7E0,  -.6E0,   .2E0,   .8E0,\n     M            .7E0,  -.9E0,  1.2E0,   .7E0, -1.5E0,   .2E0,  1.6E0,\n     N           1.7E0,  -.9E0,   .5E0,   .7E0, -1.6E0,   .2E0,  2.4E0,\n     O          -2.6E0,  -.9E0, -1.3E0,   .7E0,  2.9E0,   .2E0, -4.0E0 /\n*\n*     .. Executable Statements ..\n*\n      DO 120 KI = 1, 4\n         INCX = INCXS(KI)\n         INCY = INCYS(KI)\n         MX = ABS(INCX)\n         MY = ABS(INCY)\n*\n         DO 100 KN = 1, 4\n            N = NS(KN)\n            KSIZE = MIN(2,KN)\n            LENX = LENS(KN,MX)\n            LENY = LENS(KN,MY)\n*           .. Initialize all argument arrays ..\n            DO 20 I = 1, 7\n               SX(I) = DX1(I)\n               SY(I) = DY1(I)\n   20       CONTINUE\n*\n            IF (ICASE.EQ.1) THEN\n*              .. SDOT ..\n               CALL STEST1(SDOT(N,SX,INCX,SY,INCY),DT7(KN,KI),SSIZE1(KN)\n     +                     ,SFAC)\n            ELSE IF (ICASE.EQ.2) THEN\n*              .. SAXPY ..\n               CALL SAXPY(N,SA,SX,INCX,SY,INCY)\n               DO 40 J = 1, LENY\n                  STY(J) = DT8(J,KN,KI)\n   40          CONTINUE\n               CALL STEST(LENY,SY,STY,SSIZE2(1,KSIZE),SFAC)\n            ELSE IF (ICASE.EQ.5) THEN\n*              .. SCOPY ..\n               DO 60 I = 1, 7\n                  STY(I) = DT10Y(I,KN,KI)\n   60          CONTINUE\n               CALL SCOPY(N,SX,INCX,SY,INCY)\n               CALL STEST(LENY,SY,STY,SSIZE2(1,1),1.0E0)\n            ELSE IF (ICASE.EQ.6) THEN\n*              .. SSWAP ..\n               CALL SSWAP(N,SX,INCX,SY,INCY)\n               DO 80 I = 1, 7\n                  STX(I) = DT10X(I,KN,KI)\n                  STY(I) = DT10Y(I,KN,KI)\n   80          CONTINUE\n               CALL STEST(LENX,SX,STX,SSIZE2(1,1),1.0E0)\n               CALL STEST(LENY,SY,STY,SSIZE2(1,1),1.0E0)\n            ELSEIF (ICASE.EQ.12) THEN\n*              .. SROTM ..\n               KNI=KN+4*(KI-1)\n               DO KPAR=1,4\n                  DO I=1,7\n                     SX(I) = DX1(I)\n                     SY(I) = DY1(I)\n                     STX(I)= DT19X(I,KPAR,KNI)\n                     STY(I)= DT19Y(I,KPAR,KNI)\n                  END DO\n*\n                  DO I=1,5\n                     DTEMP(I) = DPAR(I,KPAR)\n                  END DO\n*\n                  DO  I=1,LENX\n                     SSIZE(I)=STX(I)\n                  END DO\n*                   SEE REMARK ABOVE ABOUT DT11X(1,2,7)\n*                       AND DT11X(5,3,8).\n                  IF ((KPAR .EQ. 2) .AND. (KNI .EQ. 7))\n     $               SSIZE(1) = 2.4E0\n                  IF ((KPAR .EQ. 3) .AND. (KNI .EQ. 8))\n     $               SSIZE(5) = 1.8E0\n*\n                  CALL   SROTM(N,SX,INCX,SY,INCY,DTEMP)\n                  CALL   STEST(LENX,SX,STX,SSIZE,SFAC)\n                  CALL   STEST(LENY,SY,STY,STY,SFAC)\n               END DO\n            ELSEIF (ICASE.EQ.13) THEN\n*              .. SDSROT ..\n               CALL STEST1 (SDSDOT(N,.1,SX,INCX,SY,INCY),\n     $                 ST7B(KN,KI),SSIZE3(KN),SFAC)\n            ELSE\n               WRITE (NOUT,*) ' Shouldn''t be here in CHECK2'\n               STOP\n            END IF\n  100    CONTINUE\n  120 CONTINUE\n      RETURN\n      END\n      SUBROUTINE CHECK3(SFAC)\n*     .. Parameters ..\n      INTEGER           NOUT\n      PARAMETER         (NOUT=6)\n*     .. Scalar Arguments ..\n      REAL              SFAC\n*     .. Scalars in Common ..\n      INTEGER           ICASE, INCX, INCY, N\n      LOGICAL           PASS\n*     .. Local Scalars ..\n      REAL              SC, SS\n      INTEGER           I, K, KI, KN, KSIZE, LENX, LENY, MX, MY\n*     .. Local Arrays ..\n      REAL              COPYX(5), COPYY(5), DT9X(7,4,4), DT9Y(7,4,4),\n     +                  DX1(7), DY1(7), MWPC(11), MWPS(11), MWPSTX(5),\n     +                  MWPSTY(5), MWPTX(11,5), MWPTY(11,5), MWPX(5),\n     +                  MWPY(5), SSIZE2(14,2), STX(7), STY(7), SX(7),\n     +                  SY(7)\n      INTEGER           INCXS(4), INCYS(4), LENS(4,2), MWPINX(11),\n     +                  MWPINY(11), MWPN(11), NS(4)\n*     .. External Subroutines ..\n      EXTERNAL          SROT, STEST\n*     .. Intrinsic Functions ..\n      INTRINSIC         ABS, MIN\n*     .. Common blocks ..\n      COMMON            /COMBLA/ICASE, N, INCX, INCY, PASS\n*     .. Data statements ..\n      DATA              INCXS/1, 2, -2, -1/\n      DATA              INCYS/1, -2, 1, -2/\n      DATA              LENS/1, 1, 2, 4, 1, 1, 3, 7/\n      DATA              NS/0, 1, 2, 4/\n      DATA              DX1/0.6E0, 0.1E0, -0.5E0, 0.8E0, 0.9E0, -0.3E0,\n     +                  -0.4E0/\n      DATA              DY1/0.5E0, -0.9E0, 0.3E0, 0.7E0, -0.6E0, 0.2E0,\n     +                  0.8E0/\n      DATA              SC, SS/0.8E0, 0.6E0/\n      DATA              DT9X/0.6E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.78E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.0E0, 0.78E0, -0.46E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.0E0, 0.0E0, 0.78E0, -0.46E0, -0.22E0,\n     +                  1.06E0, 0.0E0, 0.0E0, 0.0E0, 0.6E0, 0.0E0,\n     +                  0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.78E0,\n     +                  0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.66E0, 0.1E0, -0.1E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.96E0, 0.1E0, -0.76E0, 0.8E0, 0.90E0,\n     +                  -0.3E0, -0.02E0, 0.6E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.0E0, 0.0E0, 0.78E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.0E0, 0.0E0, 0.0E0, -0.06E0, 0.1E0,\n     +                  -0.1E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.90E0,\n     +                  0.1E0, -0.22E0, 0.8E0, 0.18E0, -0.3E0, -0.02E0,\n     +                  0.6E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.78E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.78E0, 0.26E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.0E0, 0.78E0, 0.26E0, -0.76E0, 1.12E0,\n     +                  0.0E0, 0.0E0, 0.0E0/\n      DATA              DT9Y/0.5E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.04E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.0E0, 0.04E0, -0.78E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.0E0, 0.0E0, 0.04E0, -0.78E0, 0.54E0,\n     +                  0.08E0, 0.0E0, 0.0E0, 0.0E0, 0.5E0, 0.0E0,\n     +                  0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.04E0,\n     +                  0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.7E0,\n     +                  -0.9E0, -0.12E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.64E0, -0.9E0, -0.30E0, 0.7E0, -0.18E0, 0.2E0,\n     +                  0.28E0, 0.5E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.0E0, 0.04E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.0E0, 0.0E0, 0.7E0, -1.08E0, 0.0E0,\n     +                  0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.64E0, -1.26E0,\n     +                  0.54E0, 0.20E0, 0.0E0, 0.0E0, 0.0E0, 0.5E0,\n     +                  0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.04E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.04E0, -0.9E0, 0.18E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.0E0, 0.04E0, -0.9E0, 0.18E0, 0.7E0,\n     +                  -0.18E0, 0.2E0, 0.16E0/\n      DATA              SSIZE2/0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,\n     +                  0.0E0, 1.17E0, 1.17E0, 1.17E0, 1.17E0, 1.17E0,\n     +                  1.17E0, 1.17E0, 1.17E0, 1.17E0, 1.17E0, 1.17E0,\n     +                  1.17E0, 1.17E0, 1.17E0/\n*     .. Executable Statements ..\n*\n      DO 60 KI = 1, 4\n         INCX = INCXS(KI)\n         INCY = INCYS(KI)\n         MX = ABS(INCX)\n         MY = ABS(INCY)\n*\n         DO 40 KN = 1, 4\n            N = NS(KN)\n            KSIZE = MIN(2,KN)\n            LENX = LENS(KN,MX)\n            LENY = LENS(KN,MY)\n*\n            IF (ICASE.EQ.4) THEN\n*              .. SROT ..\n               DO 20 I = 1, 7\n                  SX(I) = DX1(I)\n                  SY(I) = DY1(I)\n                  STX(I) = DT9X(I,KN,KI)\n                  STY(I) = DT9Y(I,KN,KI)\n   20          CONTINUE\n               CALL SROT(N,SX,INCX,SY,INCY,SC,SS)\n               CALL STEST(LENX,SX,STX,SSIZE2(1,KSIZE),SFAC)\n               CALL STEST(LENY,SY,STY,SSIZE2(1,KSIZE),SFAC)\n            ELSE\n               WRITE (NOUT,*) ' Shouldn''t be here in CHECK3'\n               STOP\n            END IF\n   40    CONTINUE\n   60 CONTINUE\n*\n      MWPC(1) = 1\n      DO 80 I = 2, 11\n         MWPC(I) = 0\n   80 CONTINUE\n      MWPS(1) = 0\n      DO 100 I = 2, 6\n         MWPS(I) = 1\n  100 CONTINUE\n      DO 120 I = 7, 11\n         MWPS(I) = -1\n  120 CONTINUE\n      MWPINX(1) = 1\n      MWPINX(2) = 1\n      MWPINX(3) = 1\n      MWPINX(4) = -1\n      MWPINX(5) = 1\n      MWPINX(6) = -1\n      MWPINX(7) = 1\n      MWPINX(8) = 1\n      MWPINX(9) = -1\n      MWPINX(10) = 1\n      MWPINX(11) = -1\n      MWPINY(1) = 1\n      MWPINY(2) = 1\n      MWPINY(3) = -1\n      MWPINY(4) = -1\n      MWPINY(5) = 2\n      MWPINY(6) = 1\n      MWPINY(7) = 1\n      MWPINY(8) = -1\n      MWPINY(9) = -1\n      MWPINY(10) = 2\n      MWPINY(11) = 1\n      DO 140 I = 1, 11\n         MWPN(I) = 5\n  140 CONTINUE\n      MWPN(5) = 3\n      MWPN(10) = 3\n      DO 160 I = 1, 5\n         MWPX(I) = I\n         MWPY(I) = I\n         MWPTX(1,I) = I\n         MWPTY(1,I) = I\n         MWPTX(2,I) = I\n         MWPTY(2,I) = -I\n         MWPTX(3,I) = 6 - I\n         MWPTY(3,I) = I - 6\n         MWPTX(4,I) = I\n         MWPTY(4,I) = -I\n         MWPTX(6,I) = 6 - I\n         MWPTY(6,I) = I - 6\n         MWPTX(7,I) = -I\n         MWPTY(7,I) = I\n         MWPTX(8,I) = I - 6\n         MWPTY(8,I) = 6 - I\n         MWPTX(9,I) = -I\n         MWPTY(9,I) = I\n         MWPTX(11,I) = I - 6\n         MWPTY(11,I) = 6 - I\n  160 CONTINUE\n      MWPTX(5,1) = 1\n      MWPTX(5,2) = 3\n      MWPTX(5,3) = 5\n      MWPTX(5,4) = 4\n      MWPTX(5,5) = 5\n      MWPTY(5,1) = -1\n      MWPTY(5,2) = 2\n      MWPTY(5,3) = -2\n      MWPTY(5,4) = 4\n      MWPTY(5,5) = -3\n      MWPTX(10,1) = -1\n      MWPTX(10,2) = -3\n      MWPTX(10,3) = -5\n      MWPTX(10,4) = 4\n      MWPTX(10,5) = 5\n      MWPTY(10,1) = 1\n      MWPTY(10,2) = 2\n      MWPTY(10,3) = 2\n      MWPTY(10,4) = 4\n      MWPTY(10,5) = 3\n      DO 200 I = 1, 11\n         INCX = MWPINX(I)\n         INCY = MWPINY(I)\n         DO 180 K = 1, 5\n            COPYX(K) = MWPX(K)\n            COPYY(K) = MWPY(K)\n            MWPSTX(K) = MWPTX(I,K)\n            MWPSTY(K) = MWPTY(I,K)\n  180    CONTINUE\n         CALL SROT(MWPN(I),COPYX,INCX,COPYY,INCY,MWPC(I),MWPS(I))\n         CALL STEST(5,COPYX,MWPSTX,MWPSTX,SFAC)\n         CALL STEST(5,COPYY,MWPSTY,MWPSTY,SFAC)\n  200 CONTINUE\n      RETURN\n      END\n      SUBROUTINE STEST(LEN,SCOMP,STRUE,SSIZE,SFAC)\n*     ********************************* STEST **************************\n*\n*     THIS SUBR COMPARES ARRAYS  SCOMP() AND STRUE() OF LENGTH LEN TO\n*     SEE IF THE TERM BY TERM DIFFERENCES, MULTIPLIED BY SFAC, ARE\n*     NEGLIGIBLE.\n*\n*     C. L. LAWSON, JPL, 1974 DEC 10\n*\n*     .. Parameters ..\n      INTEGER          NOUT\n      REAL             ZERO\n      PARAMETER        (NOUT=6, ZERO=0.0E0)\n*     .. Scalar Arguments ..\n      REAL             SFAC\n      INTEGER          LEN\n*     .. Array Arguments ..\n      REAL             SCOMP(LEN), SSIZE(LEN), STRUE(LEN)\n*     .. Scalars in Common ..\n      INTEGER          ICASE, INCX, INCY, N\n      LOGICAL          PASS\n*     .. Local Scalars ..\n      REAL             SD\n      INTEGER          I\n*     .. External Functions ..\n      REAL             SDIFF\n      EXTERNAL         SDIFF\n*     .. Intrinsic Functions ..\n      INTRINSIC        ABS\n*     .. Common blocks ..\n      COMMON           /COMBLA/ICASE, N, INCX, INCY, PASS\n*     .. Executable Statements ..\n*\n      DO 40 I = 1, LEN\n         SD = SCOMP(I) - STRUE(I)\n         IF (ABS(SFAC*SD) .LE. ABS(SSIZE(I))*EPSILON(ZERO))\n     +       GO TO 40\n*\n*                             HERE    SCOMP(I) IS NOT CLOSE TO STRUE(I).\n*\n         IF ( .NOT. PASS) GO TO 20\n*                             PRINT FAIL MESSAGE AND HEADER.\n         PASS = .FALSE.\n         WRITE (NOUT,99999)\n         WRITE (NOUT,99998)\n   20    WRITE (NOUT,99997) ICASE, N, INCX, INCY, I, SCOMP(I),\n     +     STRUE(I), SD, SSIZE(I)\n   40 CONTINUE\n      RETURN\n*\n99999 FORMAT ('                                       FAIL')\n99998 FORMAT (/' CASE  N INCX INCY  I                            ',\n     +       ' COMP(I)                             TRUE(I)  DIFFERENCE',\n     +       '     SIZE(I)',/1X)\n99997 FORMAT (1X,I4,I3,2I5,I3,2E36.8,2E12.4)\n      END\n      SUBROUTINE STEST1(SCOMP1,STRUE1,SSIZE,SFAC)\n*     ************************* STEST1 *****************************\n*\n*     THIS IS AN INTERFACE SUBROUTINE TO ACCOMODATE THE FORTRAN\n*     REQUIREMENT THAT WHEN A DUMMY ARGUMENT IS AN ARRAY, THE\n*     ACTUAL ARGUMENT MUST ALSO BE AN ARRAY OR AN ARRAY ELEMENT.\n*\n*     C.L. LAWSON, JPL, 1978 DEC 6\n*\n*     .. Scalar Arguments ..\n      REAL              SCOMP1, SFAC, STRUE1\n*     .. Array Arguments ..\n      REAL              SSIZE(*)\n*     .. Local Arrays ..\n      REAL              SCOMP(1), STRUE(1)\n*     .. External Subroutines ..\n      EXTERNAL          STEST\n*     .. Executable Statements ..\n*\n      SCOMP(1) = SCOMP1\n      STRUE(1) = STRUE1\n      CALL STEST(1,SCOMP,STRUE,SSIZE,SFAC)\n*\n      RETURN\n      END\n      REAL             FUNCTION SDIFF(SA,SB)\n*     ********************************* SDIFF **************************\n*     COMPUTES DIFFERENCE OF TWO NUMBERS.  C. L. LAWSON, JPL 1974 FEB 15\n*\n*     .. Scalar Arguments ..\n      REAL                            SA, SB\n*     .. Executable Statements ..\n      SDIFF = SA - SB\n      RETURN\n      END\n      SUBROUTINE ITEST1(ICOMP,ITRUE)\n*     ********************************* ITEST1 *************************\n*\n*     THIS SUBROUTINE COMPARES THE VARIABLES ICOMP AND ITRUE FOR\n*     EQUALITY.\n*     C. L. LAWSON, JPL, 1974 DEC 10\n*\n*     .. Parameters ..\n      INTEGER           NOUT\n      PARAMETER         (NOUT=6)\n*     .. Scalar Arguments ..\n      INTEGER           ICOMP, ITRUE\n*     .. Scalars in Common ..\n      INTEGER           ICASE, INCX, INCY, N\n      LOGICAL           PASS\n*     .. Local Scalars ..\n      INTEGER           ID\n*     .. Common blocks ..\n      COMMON            /COMBLA/ICASE, N, INCX, INCY, PASS\n*     .. Executable Statements ..\n*\n      IF (ICOMP.EQ.ITRUE) GO TO 40\n*\n*                            HERE ICOMP IS NOT EQUAL TO ITRUE.\n*\n      IF ( .NOT. PASS) GO TO 20\n*                             PRINT FAIL MESSAGE AND HEADER.\n      PASS = .FALSE.\n      WRITE (NOUT,99999)\n      WRITE (NOUT,99998)\n   20 ID = ICOMP - ITRUE\n      WRITE (NOUT,99997) ICASE, N, INCX, INCY, ICOMP, ITRUE, ID\n   40 CONTINUE\n      RETURN\n*\n99999 FORMAT ('                                       FAIL')\n99998 FORMAT (/' CASE  N INCX INCY                               ',\n     +       ' COMP                                TRUE     DIFFERENCE',\n     +       /1X)\n99997 FORMAT (1X,I4,I3,2I5,2I36,I12)\n      END\n"
  },
  {
    "path": "include/eigen3/blas/testing/sblat2.f",
    "content": "*> \\brief \\b SBLAT2\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*  Definition:\n*  ===========\n*\n*       PROGRAM SBLAT2\n* \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> Test program for the REAL Level 2 Blas.\n*>\n*> The program must be driven by a short data file. The first 18 records\n*> of the file are read using list-directed input, the last 16 records\n*> are read using the format ( A6, L2 ). An annotated example of a data\n*> file can be obtained by deleting the first 3 characters from the\n*> following 34 lines:\n*> 'sblat2.out'      NAME OF SUMMARY OUTPUT FILE\n*> 6                 UNIT NUMBER OF SUMMARY FILE\n*> 'SBLAT2.SNAP'     NAME OF SNAPSHOT OUTPUT FILE\n*> -1                UNIT NUMBER OF SNAPSHOT FILE (NOT USED IF .LT. 0)\n*> F        LOGICAL FLAG, T TO REWIND SNAPSHOT FILE AFTER EACH RECORD.\n*> F        LOGICAL FLAG, T TO STOP ON FAILURES.\n*> T        LOGICAL FLAG, T TO TEST ERROR EXITS.\n*> 16.0     THRESHOLD VALUE OF TEST RATIO\n*> 6                 NUMBER OF VALUES OF N\n*> 0 1 2 3 5 9       VALUES OF N\n*> 4                 NUMBER OF VALUES OF K\n*> 0 1 2 4           VALUES OF K\n*> 4                 NUMBER OF VALUES OF INCX AND INCY\n*> 1 2 -1 -2         VALUES OF INCX AND INCY\n*> 3                 NUMBER OF VALUES OF ALPHA\n*> 0.0 1.0 0.7       VALUES OF ALPHA\n*> 3                 NUMBER OF VALUES OF BETA\n*> 0.0 1.0 0.9       VALUES OF BETA\n*> SGEMV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> SGBMV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> SSYMV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> SSBMV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> SSPMV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> STRMV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> STBMV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> STPMV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> STRSV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> STBSV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> STPSV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> SGER   T PUT F FOR NO TEST. SAME COLUMNS.\n*> SSYR   T PUT F FOR NO TEST. SAME COLUMNS.\n*> SSPR   T PUT F FOR NO TEST. SAME COLUMNS.\n*> SSYR2  T PUT F FOR NO TEST. SAME COLUMNS.\n*> SSPR2  T PUT F FOR NO TEST. SAME COLUMNS.\n*>\n*> Further Details\n*> ===============\n*>\n*>    See:\n*>\n*>       Dongarra J. J., Du Croz J. J., Hammarling S.  and Hanson R. J..\n*>       An  extended  set of Fortran  Basic Linear Algebra Subprograms.\n*>\n*>       Technical  Memoranda  Nos. 41 (revision 3) and 81,  Mathematics\n*>       and  Computer Science  Division,  Argonne  National Laboratory,\n*>       9700 South Cass Avenue, Argonne, Illinois 60439, US.\n*>\n*>       Or\n*>\n*>       NAG  Technical Reports TR3/87 and TR4/87,  Numerical Algorithms\n*>       Group  Ltd.,  NAG  Central  Office,  256  Banbury  Road, Oxford\n*>       OX2 7DE, UK,  and  Numerical Algorithms Group Inc.,  1101  31st\n*>       Street,  Suite 100,  Downers Grove,  Illinois 60515-1263,  USA.\n*>\n*>\n*> -- Written on 10-August-1987.\n*>    Richard Hanson, Sandia National Labs.\n*>    Jeremy Du Croz, NAG Central Office.\n*>\n*>    10-9-00:  Change STATUS='NEW' to 'UNKNOWN' so that the testers\n*>              can be run multiple times without deleting generated\n*>              output files (susan)\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date April 2012\n*\n*> \\ingroup single_blas_testing\n*\n*  =====================================================================\n      PROGRAM SBLAT2\n*\n*  -- Reference BLAS test routine (version 3.4.1) --\n*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     April 2012\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      INTEGER            NIN\n      PARAMETER          ( NIN = 5 )\n      INTEGER            NSUBS\n      PARAMETER          ( NSUBS = 16 )\n      REAL               ZERO, ONE\n      PARAMETER          ( ZERO = 0.0, ONE = 1.0 )\n      INTEGER            NMAX, INCMAX\n      PARAMETER          ( NMAX = 65, INCMAX = 2 )\n      INTEGER            NINMAX, NIDMAX, NKBMAX, NALMAX, NBEMAX\n      PARAMETER          ( NINMAX = 7, NIDMAX = 9, NKBMAX = 7,\n     $                   NALMAX = 7, NBEMAX = 7 )\n*     .. Local Scalars ..\n      REAL               EPS, ERR, THRESH\n      INTEGER            I, ISNUM, J, N, NALF, NBET, NIDIM, NINC, NKB,\n     $                   NOUT, NTRA\n      LOGICAL            FATAL, LTESTT, REWI, SAME, SFATAL, TRACE,\n     $                   TSTERR\n      CHARACTER*1        TRANS\n      CHARACTER*6        SNAMET\n      CHARACTER*32       SNAPS, SUMMRY\n*     .. Local Arrays ..\n      REAL               A( NMAX, NMAX ), AA( NMAX*NMAX ),\n     $                   ALF( NALMAX ), AS( NMAX*NMAX ), BET( NBEMAX ),\n     $                   G( NMAX ), X( NMAX ), XS( NMAX*INCMAX ),\n     $                   XX( NMAX*INCMAX ), Y( NMAX ),\n     $                   YS( NMAX*INCMAX ), YT( NMAX ),\n     $                   YY( NMAX*INCMAX ), Z( 2*NMAX )\n      INTEGER            IDIM( NIDMAX ), INC( NINMAX ), KB( NKBMAX )\n      LOGICAL            LTEST( NSUBS )\n      CHARACTER*6        SNAMES( NSUBS )\n*     .. External Functions ..\n      REAL               SDIFF\n      LOGICAL            LSE\n      EXTERNAL           SDIFF, LSE\n*     .. External Subroutines ..\n      EXTERNAL           SCHK1, SCHK2, SCHK3, SCHK4, SCHK5, SCHK6,\n     $                   SCHKE, SMVCH\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, MAX, MIN\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n      CHARACTER*6        SRNAMT\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n      COMMON             /SRNAMC/SRNAMT\n*     .. Data statements ..\n      DATA               SNAMES/'SGEMV ', 'SGBMV ', 'SSYMV ', 'SSBMV ',\n     $                   'SSPMV ', 'STRMV ', 'STBMV ', 'STPMV ',\n     $                   'STRSV ', 'STBSV ', 'STPSV ', 'SGER  ',\n     $                   'SSYR  ', 'SSPR  ', 'SSYR2 ', 'SSPR2 '/\n*     .. Executable Statements ..\n*\n*     Read name and unit number for summary output file and open file.\n*\n      READ( NIN, FMT = * )SUMMRY\n      READ( NIN, FMT = * )NOUT\n      OPEN( NOUT, FILE = SUMMRY, STATUS = 'UNKNOWN' )\n      NOUTC = NOUT\n*\n*     Read name and unit number for snapshot output file and open file.\n*\n      READ( NIN, FMT = * )SNAPS\n      READ( NIN, FMT = * )NTRA\n      TRACE = NTRA.GE.0\n      IF( TRACE )THEN\n         OPEN( NTRA, FILE = SNAPS, STATUS = 'UNKNOWN' )\n      END IF\n*     Read the flag that directs rewinding of the snapshot file.\n      READ( NIN, FMT = * )REWI\n      REWI = REWI.AND.TRACE\n*     Read the flag that directs stopping on any failure.\n      READ( NIN, FMT = * )SFATAL\n*     Read the flag that indicates whether error exits are to be tested.\n      READ( NIN, FMT = * )TSTERR\n*     Read the threshold value of the test ratio\n      READ( NIN, FMT = * )THRESH\n*\n*     Read and check the parameter values for the tests.\n*\n*     Values of N\n      READ( NIN, FMT = * )NIDIM\n      IF( NIDIM.LT.1.OR.NIDIM.GT.NIDMAX )THEN\n         WRITE( NOUT, FMT = 9997 )'N', NIDMAX\n         GO TO 230\n      END IF\n      READ( NIN, FMT = * )( IDIM( I ), I = 1, NIDIM )\n      DO 10 I = 1, NIDIM\n         IF( IDIM( I ).LT.0.OR.IDIM( I ).GT.NMAX )THEN\n            WRITE( NOUT, FMT = 9996 )NMAX\n            GO TO 230\n         END IF\n   10 CONTINUE\n*     Values of K\n      READ( NIN, FMT = * )NKB\n      IF( NKB.LT.1.OR.NKB.GT.NKBMAX )THEN\n         WRITE( NOUT, FMT = 9997 )'K', NKBMAX\n         GO TO 230\n      END IF\n      READ( NIN, FMT = * )( KB( I ), I = 1, NKB )\n      DO 20 I = 1, NKB\n         IF( KB( I ).LT.0 )THEN\n            WRITE( NOUT, FMT = 9995 )\n            GO TO 230\n         END IF\n   20 CONTINUE\n*     Values of INCX and INCY\n      READ( NIN, FMT = * )NINC\n      IF( NINC.LT.1.OR.NINC.GT.NINMAX )THEN\n         WRITE( NOUT, FMT = 9997 )'INCX AND INCY', NINMAX\n         GO TO 230\n      END IF\n      READ( NIN, FMT = * )( INC( I ), I = 1, NINC )\n      DO 30 I = 1, NINC\n         IF( INC( I ).EQ.0.OR.ABS( INC( I ) ).GT.INCMAX )THEN\n            WRITE( NOUT, FMT = 9994 )INCMAX\n            GO TO 230\n         END IF\n   30 CONTINUE\n*     Values of ALPHA\n      READ( NIN, FMT = * )NALF\n      IF( NALF.LT.1.OR.NALF.GT.NALMAX )THEN\n         WRITE( NOUT, FMT = 9997 )'ALPHA', NALMAX\n         GO TO 230\n      END IF\n      READ( NIN, FMT = * )( ALF( I ), I = 1, NALF )\n*     Values of BETA\n      READ( NIN, FMT = * )NBET\n      IF( NBET.LT.1.OR.NBET.GT.NBEMAX )THEN\n         WRITE( NOUT, FMT = 9997 )'BETA', NBEMAX\n         GO TO 230\n      END IF\n      READ( NIN, FMT = * )( BET( I ), I = 1, NBET )\n*\n*     Report values of parameters.\n*\n      WRITE( NOUT, FMT = 9993 )\n      WRITE( NOUT, FMT = 9992 )( IDIM( I ), I = 1, NIDIM )\n      WRITE( NOUT, FMT = 9991 )( KB( I ), I = 1, NKB )\n      WRITE( NOUT, FMT = 9990 )( INC( I ), I = 1, NINC )\n      WRITE( NOUT, FMT = 9989 )( ALF( I ), I = 1, NALF )\n      WRITE( NOUT, FMT = 9988 )( BET( I ), I = 1, NBET )\n      IF( .NOT.TSTERR )THEN\n         WRITE( NOUT, FMT = * )\n         WRITE( NOUT, FMT = 9980 )\n      END IF\n      WRITE( NOUT, FMT = * )\n      WRITE( NOUT, FMT = 9999 )THRESH\n      WRITE( NOUT, FMT = * )\n*\n*     Read names of subroutines and flags which indicate\n*     whether they are to be tested.\n*\n      DO 40 I = 1, NSUBS\n         LTEST( I ) = .FALSE.\n   40 CONTINUE\n   50 READ( NIN, FMT = 9984, END = 80 )SNAMET, LTESTT\n      DO 60 I = 1, NSUBS\n         IF( SNAMET.EQ.SNAMES( I ) )\n     $      GO TO 70\n   60 CONTINUE\n      WRITE( NOUT, FMT = 9986 )SNAMET\n      STOP\n   70 LTEST( I ) = LTESTT\n      GO TO 50\n*\n   80 CONTINUE\n      CLOSE ( NIN )\n*\n*     Compute EPS (the machine precision).\n*\n      EPS = EPSILON(ZERO)\n      WRITE( NOUT, FMT = 9998 )EPS\n*\n*     Check the reliability of SMVCH using exact data.\n*\n      N = MIN( 32, NMAX )\n      DO 120 J = 1, N\n         DO 110 I = 1, N\n            A( I, J ) = MAX( I - J + 1, 0 )\n  110    CONTINUE\n         X( J ) = J\n         Y( J ) = ZERO\n  120 CONTINUE\n      DO 130 J = 1, N\n         YY( J ) = J*( ( J + 1 )*J )/2 - ( ( J + 1 )*J*( J - 1 ) )/3\n  130 CONTINUE\n*     YY holds the exact result. On exit from SMVCH YT holds\n*     the result computed by SMVCH.\n      TRANS = 'N'\n      CALL SMVCH( TRANS, N, N, ONE, A, NMAX, X, 1, ZERO, Y, 1, YT, G,\n     $            YY, EPS, ERR, FATAL, NOUT, .TRUE. )\n      SAME = LSE( YY, YT, N )\n      IF( .NOT.SAME.OR.ERR.NE.ZERO )THEN\n         WRITE( NOUT, FMT = 9985 )TRANS, SAME, ERR\n         STOP\n      END IF\n      TRANS = 'T'\n      CALL SMVCH( TRANS, N, N, ONE, A, NMAX, X, -1, ZERO, Y, -1, YT, G,\n     $            YY, EPS, ERR, FATAL, NOUT, .TRUE. )\n      SAME = LSE( YY, YT, N )\n      IF( .NOT.SAME.OR.ERR.NE.ZERO )THEN\n         WRITE( NOUT, FMT = 9985 )TRANS, SAME, ERR\n         STOP\n      END IF\n*\n*     Test each subroutine in turn.\n*\n      DO 210 ISNUM = 1, NSUBS\n         WRITE( NOUT, FMT = * )\n         IF( .NOT.LTEST( ISNUM ) )THEN\n*           Subprogram is not to be tested.\n            WRITE( NOUT, FMT = 9983 )SNAMES( ISNUM )\n         ELSE\n            SRNAMT = SNAMES( ISNUM )\n*           Test error exits.\n            IF( TSTERR )THEN\n               CALL SCHKE( ISNUM, SNAMES( ISNUM ), NOUT )\n               WRITE( NOUT, FMT = * )\n            END IF\n*           Test computations.\n            INFOT = 0\n            OK = .TRUE.\n            FATAL = .FALSE.\n            GO TO ( 140, 140, 150, 150, 150, 160, 160,\n     $              160, 160, 160, 160, 170, 180, 180,\n     $              190, 190 )ISNUM\n*           Test SGEMV, 01, and SGBMV, 02.\n  140       CALL SCHK1( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF,\n     $                  NBET, BET, NINC, INC, NMAX, INCMAX, A, AA, AS,\n     $                  X, XX, XS, Y, YY, YS, YT, G )\n            GO TO 200\n*           Test SSYMV, 03, SSBMV, 04, and SSPMV, 05.\n  150       CALL SCHK2( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF,\n     $                  NBET, BET, NINC, INC, NMAX, INCMAX, A, AA, AS,\n     $                  X, XX, XS, Y, YY, YS, YT, G )\n            GO TO 200\n*           Test STRMV, 06, STBMV, 07, STPMV, 08,\n*           STRSV, 09, STBSV, 10, and STPSV, 11.\n  160       CALL SCHK3( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NKB, KB, NINC, INC,\n     $                  NMAX, INCMAX, A, AA, AS, Y, YY, YS, YT, G, Z )\n            GO TO 200\n*           Test SGER, 12.\n  170       CALL SCHK4( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC,\n     $                  NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS,\n     $                  YT, G, Z )\n            GO TO 200\n*           Test SSYR, 13, and SSPR, 14.\n  180       CALL SCHK5( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC,\n     $                  NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS,\n     $                  YT, G, Z )\n            GO TO 200\n*           Test SSYR2, 15, and SSPR2, 16.\n  190       CALL SCHK6( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC,\n     $                  NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS,\n     $                  YT, G, Z )\n*\n  200       IF( FATAL.AND.SFATAL )\n     $         GO TO 220\n         END IF\n  210 CONTINUE\n      WRITE( NOUT, FMT = 9982 )\n      GO TO 240\n*\n  220 CONTINUE\n      WRITE( NOUT, FMT = 9981 )\n      GO TO 240\n*\n  230 CONTINUE\n      WRITE( NOUT, FMT = 9987 )\n*\n  240 CONTINUE\n      IF( TRACE )\n     $   CLOSE ( NTRA )\n      CLOSE ( NOUT )\n      STOP\n*\n 9999 FORMAT( ' ROUTINES PASS COMPUTATIONAL TESTS IF TEST RATIO IS LES',\n     $      'S THAN', F8.2 )\n 9998 FORMAT( ' RELATIVE MACHINE PRECISION IS TAKEN TO BE', 1P, E9.1 )\n 9997 FORMAT( ' NUMBER OF VALUES OF ', A, ' IS LESS THAN 1 OR GREATER ',\n     $      'THAN ', I2 )\n 9996 FORMAT( ' VALUE OF N IS LESS THAN 0 OR GREATER THAN ', I2 )\n 9995 FORMAT( ' VALUE OF K IS LESS THAN 0' )\n 9994 FORMAT( ' ABSOLUTE VALUE OF INCX OR INCY IS 0 OR GREATER THAN ',\n     $      I2 )\n 9993 FORMAT( ' TESTS OF THE REAL             LEVEL 2 BLAS', //' THE F',\n     $      'OLLOWING PARAMETER VALUES WILL BE USED:' )\n 9992 FORMAT( '   FOR N              ', 9I6 )\n 9991 FORMAT( '   FOR K              ', 7I6 )\n 9990 FORMAT( '   FOR INCX AND INCY  ', 7I6 )\n 9989 FORMAT( '   FOR ALPHA          ', 7F6.1 )\n 9988 FORMAT( '   FOR BETA           ', 7F6.1 )\n 9987 FORMAT( ' AMEND DATA FILE OR INCREASE ARRAY SIZES IN PROGRAM',\n     $      /' ******* TESTS ABANDONED *******' )\n 9986 FORMAT( ' SUBPROGRAM NAME ', A6, ' NOT RECOGNIZED', /' ******* T',\n     $      'ESTS ABANDONED *******' )\n 9985 FORMAT( ' ERROR IN SMVCH -  IN-LINE DOT PRODUCTS ARE BEING EVALU',\n     $      'ATED WRONGLY.', /' SMVCH WAS CALLED WITH TRANS = ', A1,\n     $      ' AND RETURNED SAME = ', L1, ' AND ERR = ', F12.3, '.', /\n     $   ' THIS MAY BE DUE TO FAULTS IN THE ARITHMETIC OR THE COMPILER.'\n     $      , /' ******* TESTS ABANDONED *******' )\n 9984 FORMAT( A6, L2 )\n 9983 FORMAT( 1X, A6, ' WAS NOT TESTED' )\n 9982 FORMAT( /' END OF TESTS' )\n 9981 FORMAT( /' ******* FATAL ERROR - TESTS ABANDONED *******' )\n 9980 FORMAT( ' ERROR-EXITS WILL NOT BE TESTED' )\n*\n*     End of SBLAT2.\n*\n      END\n      SUBROUTINE SCHK1( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF, NBET,\n     $                  BET, NINC, INC, NMAX, INCMAX, A, AA, AS, X, XX,\n     $                  XS, Y, YY, YS, YT, G )\n*\n*  Tests SGEMV and SGBMV.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Parameters ..\n      REAL               ZERO, HALF\n      PARAMETER          ( ZERO = 0.0, HALF = 0.5 )\n*     .. Scalar Arguments ..\n      REAL               EPS, THRESH\n      INTEGER            INCMAX, NALF, NBET, NIDIM, NINC, NKB, NMAX,\n     $                   NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      REAL               A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), BET( NBET ), G( NMAX ),\n     $                   X( NMAX ), XS( NMAX*INCMAX ),\n     $                   XX( NMAX*INCMAX ), Y( NMAX ),\n     $                   YS( NMAX*INCMAX ), YT( NMAX ),\n     $                   YY( NMAX*INCMAX )\n      INTEGER            IDIM( NIDIM ), INC( NINC ), KB( NKB )\n*     .. Local Scalars ..\n      REAL               ALPHA, ALS, BETA, BLS, ERR, ERRMAX, TRANSL\n      INTEGER            I, IA, IB, IC, IKU, IM, IN, INCX, INCXS, INCY,\n     $                   INCYS, IX, IY, KL, KLS, KU, KUS, LAA, LDA,\n     $                   LDAS, LX, LY, M, ML, MS, N, NARGS, NC, ND, NK,\n     $                   NL, NS\n      LOGICAL            BANDED, FULL, NULL, RESET, SAME, TRAN\n      CHARACTER*1        TRANS, TRANSS\n      CHARACTER*3        ICH\n*     .. Local Arrays ..\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LSE, LSERES\n      EXTERNAL           LSE, LSERES\n*     .. External Subroutines ..\n      EXTERNAL           SGBMV, SGEMV, SMAKE, SMVCH\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, MAX, MIN\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICH/'NTC'/\n*     .. Executable Statements ..\n      FULL = SNAME( 3: 3 ).EQ.'E'\n      BANDED = SNAME( 3: 3 ).EQ.'B'\n*     Define the number of arguments.\n      IF( FULL )THEN\n         NARGS = 11\n      ELSE IF( BANDED )THEN\n         NARGS = 13\n      END IF\n*\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = ZERO\n*\n      DO 120 IN = 1, NIDIM\n         N = IDIM( IN )\n         ND = N/2 + 1\n*\n         DO 110 IM = 1, 2\n            IF( IM.EQ.1 )\n     $         M = MAX( N - ND, 0 )\n            IF( IM.EQ.2 )\n     $         M = MIN( N + ND, NMAX )\n*\n            IF( BANDED )THEN\n               NK = NKB\n            ELSE\n               NK = 1\n            END IF\n            DO 100 IKU = 1, NK\n               IF( BANDED )THEN\n                  KU = KB( IKU )\n                  KL = MAX( KU - 1, 0 )\n               ELSE\n                  KU = N - 1\n                  KL = M - 1\n               END IF\n*              Set LDA to 1 more than minimum value if room.\n               IF( BANDED )THEN\n                  LDA = KL + KU + 1\n               ELSE\n                  LDA = M\n               END IF\n               IF( LDA.LT.NMAX )\n     $            LDA = LDA + 1\n*              Skip tests if not enough room.\n               IF( LDA.GT.NMAX )\n     $            GO TO 100\n               LAA = LDA*N\n               NULL = N.LE.0.OR.M.LE.0\n*\n*              Generate the matrix A.\n*\n               TRANSL = ZERO\n               CALL SMAKE( SNAME( 2: 3 ), ' ', ' ', M, N, A, NMAX, AA,\n     $                     LDA, KL, KU, RESET, TRANSL )\n*\n               DO 90 IC = 1, 3\n                  TRANS = ICH( IC: IC )\n                  TRAN = TRANS.EQ.'T'.OR.TRANS.EQ.'C'\n*\n                  IF( TRAN )THEN\n                     ML = N\n                     NL = M\n                  ELSE\n                     ML = M\n                     NL = N\n                  END IF\n*\n                  DO 80 IX = 1, NINC\n                     INCX = INC( IX )\n                     LX = ABS( INCX )*NL\n*\n*                    Generate the vector X.\n*\n                     TRANSL = HALF\n                     CALL SMAKE( 'GE', ' ', ' ', 1, NL, X, 1, XX,\n     $                           ABS( INCX ), 0, NL - 1, RESET, TRANSL )\n                     IF( NL.GT.1 )THEN\n                        X( NL/2 ) = ZERO\n                        XX( 1 + ABS( INCX )*( NL/2 - 1 ) ) = ZERO\n                     END IF\n*\n                     DO 70 IY = 1, NINC\n                        INCY = INC( IY )\n                        LY = ABS( INCY )*ML\n*\n                        DO 60 IA = 1, NALF\n                           ALPHA = ALF( IA )\n*\n                           DO 50 IB = 1, NBET\n                              BETA = BET( IB )\n*\n*                             Generate the vector Y.\n*\n                              TRANSL = ZERO\n                              CALL SMAKE( 'GE', ' ', ' ', 1, ML, Y, 1,\n     $                                    YY, ABS( INCY ), 0, ML - 1,\n     $                                    RESET, TRANSL )\n*\n                              NC = NC + 1\n*\n*                             Save every datum before calling the\n*                             subroutine.\n*\n                              TRANSS = TRANS\n                              MS = M\n                              NS = N\n                              KLS = KL\n                              KUS = KU\n                              ALS = ALPHA\n                              DO 10 I = 1, LAA\n                                 AS( I ) = AA( I )\n   10                         CONTINUE\n                              LDAS = LDA\n                              DO 20 I = 1, LX\n                                 XS( I ) = XX( I )\n   20                         CONTINUE\n                              INCXS = INCX\n                              BLS = BETA\n                              DO 30 I = 1, LY\n                                 YS( I ) = YY( I )\n   30                         CONTINUE\n                              INCYS = INCY\n*\n*                             Call the subroutine.\n*\n                              IF( FULL )THEN\n                                 IF( TRACE )\n     $                              WRITE( NTRA, FMT = 9994 )NC, SNAME,\n     $                              TRANS, M, N, ALPHA, LDA, INCX, BETA,\n     $                              INCY\n                                 IF( REWI )\n     $                              REWIND NTRA\n                                 CALL SGEMV( TRANS, M, N, ALPHA, AA,\n     $                                       LDA, XX, INCX, BETA, YY,\n     $                                       INCY )\n                              ELSE IF( BANDED )THEN\n                                 IF( TRACE )\n     $                              WRITE( NTRA, FMT = 9995 )NC, SNAME,\n     $                              TRANS, M, N, KL, KU, ALPHA, LDA,\n     $                              INCX, BETA, INCY\n                                 IF( REWI )\n     $                              REWIND NTRA\n                                 CALL SGBMV( TRANS, M, N, KL, KU, ALPHA,\n     $                                       AA, LDA, XX, INCX, BETA,\n     $                                       YY, INCY )\n                              END IF\n*\n*                             Check if error-exit was taken incorrectly.\n*\n                              IF( .NOT.OK )THEN\n                                 WRITE( NOUT, FMT = 9993 )\n                                 FATAL = .TRUE.\n                                 GO TO 130\n                              END IF\n*\n*                             See what data changed inside subroutines.\n*\n                              ISAME( 1 ) = TRANS.EQ.TRANSS\n                              ISAME( 2 ) = MS.EQ.M\n                              ISAME( 3 ) = NS.EQ.N\n                              IF( FULL )THEN\n                                 ISAME( 4 ) = ALS.EQ.ALPHA\n                                 ISAME( 5 ) = LSE( AS, AA, LAA )\n                                 ISAME( 6 ) = LDAS.EQ.LDA\n                                 ISAME( 7 ) = LSE( XS, XX, LX )\n                                 ISAME( 8 ) = INCXS.EQ.INCX\n                                 ISAME( 9 ) = BLS.EQ.BETA\n                                 IF( NULL )THEN\n                                    ISAME( 10 ) = LSE( YS, YY, LY )\n                                 ELSE\n                                    ISAME( 10 ) = LSERES( 'GE', ' ', 1,\n     $                                            ML, YS, YY,\n     $                                            ABS( INCY ) )\n                                 END IF\n                                 ISAME( 11 ) = INCYS.EQ.INCY\n                              ELSE IF( BANDED )THEN\n                                 ISAME( 4 ) = KLS.EQ.KL\n                                 ISAME( 5 ) = KUS.EQ.KU\n                                 ISAME( 6 ) = ALS.EQ.ALPHA\n                                 ISAME( 7 ) = LSE( AS, AA, LAA )\n                                 ISAME( 8 ) = LDAS.EQ.LDA\n                                 ISAME( 9 ) = LSE( XS, XX, LX )\n                                 ISAME( 10 ) = INCXS.EQ.INCX\n                                 ISAME( 11 ) = BLS.EQ.BETA\n                                 IF( NULL )THEN\n                                    ISAME( 12 ) = LSE( YS, YY, LY )\n                                 ELSE\n                                    ISAME( 12 ) = LSERES( 'GE', ' ', 1,\n     $                                            ML, YS, YY,\n     $                                            ABS( INCY ) )\n                                 END IF\n                                 ISAME( 13 ) = INCYS.EQ.INCY\n                              END IF\n*\n*                             If data was incorrectly changed, report\n*                             and return.\n*\n                              SAME = .TRUE.\n                              DO 40 I = 1, NARGS\n                                 SAME = SAME.AND.ISAME( I )\n                                 IF( .NOT.ISAME( I ) )\n     $                              WRITE( NOUT, FMT = 9998 )I\n   40                         CONTINUE\n                              IF( .NOT.SAME )THEN\n                                 FATAL = .TRUE.\n                                 GO TO 130\n                              END IF\n*\n                              IF( .NOT.NULL )THEN\n*\n*                                Check the result.\n*\n                                 CALL SMVCH( TRANS, M, N, ALPHA, A,\n     $                                       NMAX, X, INCX, BETA, Y,\n     $                                       INCY, YT, G, YY, EPS, ERR,\n     $                                       FATAL, NOUT, .TRUE. )\n                                 ERRMAX = MAX( ERRMAX, ERR )\n*                                If got really bad answer, report and\n*                                return.\n                                 IF( FATAL )\n     $                              GO TO 130\n                              ELSE\n*                                Avoid repeating tests with M.le.0 or\n*                                N.le.0.\n                                 GO TO 110\n                              END IF\n*\n   50                      CONTINUE\n*\n   60                   CONTINUE\n*\n   70                CONTINUE\n*\n   80             CONTINUE\n*\n   90          CONTINUE\n*\n  100       CONTINUE\n*\n  110    CONTINUE\n*\n  120 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 140\n*\n  130 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      IF( FULL )THEN\n         WRITE( NOUT, FMT = 9994 )NC, SNAME, TRANS, M, N, ALPHA, LDA,\n     $      INCX, BETA, INCY\n      ELSE IF( BANDED )THEN\n         WRITE( NOUT, FMT = 9995 )NC, SNAME, TRANS, M, N, KL, KU,\n     $      ALPHA, LDA, INCX, BETA, INCY\n      END IF\n*\n  140 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 4( I3, ',' ), F4.1,\n     $      ', A,', I3, ', X,', I2, ',', F4.1, ', Y,', I2, ') .' )\n 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 2( I3, ',' ), F4.1,\n     $      ', A,', I3, ', X,', I2, ',', F4.1, ', Y,', I2,\n     $      ')         .' )\n 9993 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of SCHK1.\n*\n      END\n      SUBROUTINE SCHK2( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF, NBET,\n     $                  BET, NINC, INC, NMAX, INCMAX, A, AA, AS, X, XX,\n     $                  XS, Y, YY, YS, YT, G )\n*\n*  Tests SSYMV, SSBMV and SSPMV.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Parameters ..\n      REAL               ZERO, HALF\n      PARAMETER          ( ZERO = 0.0, HALF = 0.5 )\n*     .. Scalar Arguments ..\n      REAL               EPS, THRESH\n      INTEGER            INCMAX, NALF, NBET, NIDIM, NINC, NKB, NMAX,\n     $                   NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      REAL               A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), BET( NBET ), G( NMAX ),\n     $                   X( NMAX ), XS( NMAX*INCMAX ),\n     $                   XX( NMAX*INCMAX ), Y( NMAX ),\n     $                   YS( NMAX*INCMAX ), YT( NMAX ),\n     $                   YY( NMAX*INCMAX )\n      INTEGER            IDIM( NIDIM ), INC( NINC ), KB( NKB )\n*     .. Local Scalars ..\n      REAL               ALPHA, ALS, BETA, BLS, ERR, ERRMAX, TRANSL\n      INTEGER            I, IA, IB, IC, IK, IN, INCX, INCXS, INCY,\n     $                   INCYS, IX, IY, K, KS, LAA, LDA, LDAS, LX, LY,\n     $                   N, NARGS, NC, NK, NS\n      LOGICAL            BANDED, FULL, NULL, PACKED, RESET, SAME\n      CHARACTER*1        UPLO, UPLOS\n      CHARACTER*2        ICH\n*     .. Local Arrays ..\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LSE, LSERES\n      EXTERNAL           LSE, LSERES\n*     .. External Subroutines ..\n      EXTERNAL           SMAKE, SMVCH, SSBMV, SSPMV, SSYMV\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, MAX\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICH/'UL'/\n*     .. Executable Statements ..\n      FULL = SNAME( 3: 3 ).EQ.'Y'\n      BANDED = SNAME( 3: 3 ).EQ.'B'\n      PACKED = SNAME( 3: 3 ).EQ.'P'\n*     Define the number of arguments.\n      IF( FULL )THEN\n         NARGS = 10\n      ELSE IF( BANDED )THEN\n         NARGS = 11\n      ELSE IF( PACKED )THEN\n         NARGS = 9\n      END IF\n*\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = ZERO\n*\n      DO 110 IN = 1, NIDIM\n         N = IDIM( IN )\n*\n         IF( BANDED )THEN\n            NK = NKB\n         ELSE\n            NK = 1\n         END IF\n         DO 100 IK = 1, NK\n            IF( BANDED )THEN\n               K = KB( IK )\n            ELSE\n               K = N - 1\n            END IF\n*           Set LDA to 1 more than minimum value if room.\n            IF( BANDED )THEN\n               LDA = K + 1\n            ELSE\n               LDA = N\n            END IF\n            IF( LDA.LT.NMAX )\n     $         LDA = LDA + 1\n*           Skip tests if not enough room.\n            IF( LDA.GT.NMAX )\n     $         GO TO 100\n            IF( PACKED )THEN\n               LAA = ( N*( N + 1 ) )/2\n            ELSE\n               LAA = LDA*N\n            END IF\n            NULL = N.LE.0\n*\n            DO 90 IC = 1, 2\n               UPLO = ICH( IC: IC )\n*\n*              Generate the matrix A.\n*\n               TRANSL = ZERO\n               CALL SMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A, NMAX, AA,\n     $                     LDA, K, K, RESET, TRANSL )\n*\n               DO 80 IX = 1, NINC\n                  INCX = INC( IX )\n                  LX = ABS( INCX )*N\n*\n*                 Generate the vector X.\n*\n                  TRANSL = HALF\n                  CALL SMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX,\n     $                        ABS( INCX ), 0, N - 1, RESET, TRANSL )\n                  IF( N.GT.1 )THEN\n                     X( N/2 ) = ZERO\n                     XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO\n                  END IF\n*\n                  DO 70 IY = 1, NINC\n                     INCY = INC( IY )\n                     LY = ABS( INCY )*N\n*\n                     DO 60 IA = 1, NALF\n                        ALPHA = ALF( IA )\n*\n                        DO 50 IB = 1, NBET\n                           BETA = BET( IB )\n*\n*                          Generate the vector Y.\n*\n                           TRANSL = ZERO\n                           CALL SMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY,\n     $                                 ABS( INCY ), 0, N - 1, RESET,\n     $                                 TRANSL )\n*\n                           NC = NC + 1\n*\n*                          Save every datum before calling the\n*                          subroutine.\n*\n                           UPLOS = UPLO\n                           NS = N\n                           KS = K\n                           ALS = ALPHA\n                           DO 10 I = 1, LAA\n                              AS( I ) = AA( I )\n   10                      CONTINUE\n                           LDAS = LDA\n                           DO 20 I = 1, LX\n                              XS( I ) = XX( I )\n   20                      CONTINUE\n                           INCXS = INCX\n                           BLS = BETA\n                           DO 30 I = 1, LY\n                              YS( I ) = YY( I )\n   30                      CONTINUE\n                           INCYS = INCY\n*\n*                          Call the subroutine.\n*\n                           IF( FULL )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9993 )NC, SNAME,\n     $                           UPLO, N, ALPHA, LDA, INCX, BETA, INCY\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL SSYMV( UPLO, N, ALPHA, AA, LDA, XX,\n     $                                    INCX, BETA, YY, INCY )\n                           ELSE IF( BANDED )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9994 )NC, SNAME,\n     $                           UPLO, N, K, ALPHA, LDA, INCX, BETA,\n     $                           INCY\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL SSBMV( UPLO, N, K, ALPHA, AA, LDA,\n     $                                    XX, INCX, BETA, YY, INCY )\n                           ELSE IF( PACKED )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9995 )NC, SNAME,\n     $                           UPLO, N, ALPHA, INCX, BETA, INCY\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL SSPMV( UPLO, N, ALPHA, AA, XX, INCX,\n     $                                    BETA, YY, INCY )\n                           END IF\n*\n*                          Check if error-exit was taken incorrectly.\n*\n                           IF( .NOT.OK )THEN\n                              WRITE( NOUT, FMT = 9992 )\n                              FATAL = .TRUE.\n                              GO TO 120\n                           END IF\n*\n*                          See what data changed inside subroutines.\n*\n                           ISAME( 1 ) = UPLO.EQ.UPLOS\n                           ISAME( 2 ) = NS.EQ.N\n                           IF( FULL )THEN\n                              ISAME( 3 ) = ALS.EQ.ALPHA\n                              ISAME( 4 ) = LSE( AS, AA, LAA )\n                              ISAME( 5 ) = LDAS.EQ.LDA\n                              ISAME( 6 ) = LSE( XS, XX, LX )\n                              ISAME( 7 ) = INCXS.EQ.INCX\n                              ISAME( 8 ) = BLS.EQ.BETA\n                              IF( NULL )THEN\n                                 ISAME( 9 ) = LSE( YS, YY, LY )\n                              ELSE\n                                 ISAME( 9 ) = LSERES( 'GE', ' ', 1, N,\n     $                                        YS, YY, ABS( INCY ) )\n                              END IF\n                              ISAME( 10 ) = INCYS.EQ.INCY\n                           ELSE IF( BANDED )THEN\n                              ISAME( 3 ) = KS.EQ.K\n                              ISAME( 4 ) = ALS.EQ.ALPHA\n                              ISAME( 5 ) = LSE( AS, AA, LAA )\n                              ISAME( 6 ) = LDAS.EQ.LDA\n                              ISAME( 7 ) = LSE( XS, XX, LX )\n                              ISAME( 8 ) = INCXS.EQ.INCX\n                              ISAME( 9 ) = BLS.EQ.BETA\n                              IF( NULL )THEN\n                                 ISAME( 10 ) = LSE( YS, YY, LY )\n                              ELSE\n                                 ISAME( 10 ) = LSERES( 'GE', ' ', 1, N,\n     $                                         YS, YY, ABS( INCY ) )\n                              END IF\n                              ISAME( 11 ) = INCYS.EQ.INCY\n                           ELSE IF( PACKED )THEN\n                              ISAME( 3 ) = ALS.EQ.ALPHA\n                              ISAME( 4 ) = LSE( AS, AA, LAA )\n                              ISAME( 5 ) = LSE( XS, XX, LX )\n                              ISAME( 6 ) = INCXS.EQ.INCX\n                              ISAME( 7 ) = BLS.EQ.BETA\n                              IF( NULL )THEN\n                                 ISAME( 8 ) = LSE( YS, YY, LY )\n                              ELSE\n                                 ISAME( 8 ) = LSERES( 'GE', ' ', 1, N,\n     $                                        YS, YY, ABS( INCY ) )\n                              END IF\n                              ISAME( 9 ) = INCYS.EQ.INCY\n                           END IF\n*\n*                          If data was incorrectly changed, report and\n*                          return.\n*\n                           SAME = .TRUE.\n                           DO 40 I = 1, NARGS\n                              SAME = SAME.AND.ISAME( I )\n                              IF( .NOT.ISAME( I ) )\n     $                           WRITE( NOUT, FMT = 9998 )I\n   40                      CONTINUE\n                           IF( .NOT.SAME )THEN\n                              FATAL = .TRUE.\n                              GO TO 120\n                           END IF\n*\n                           IF( .NOT.NULL )THEN\n*\n*                             Check the result.\n*\n                              CALL SMVCH( 'N', N, N, ALPHA, A, NMAX, X,\n     $                                    INCX, BETA, Y, INCY, YT, G,\n     $                                    YY, EPS, ERR, FATAL, NOUT,\n     $                                    .TRUE. )\n                              ERRMAX = MAX( ERRMAX, ERR )\n*                             If got really bad answer, report and\n*                             return.\n                              IF( FATAL )\n     $                           GO TO 120\n                           ELSE\n*                             Avoid repeating tests with N.le.0\n                              GO TO 110\n                           END IF\n*\n   50                   CONTINUE\n*\n   60                CONTINUE\n*\n   70             CONTINUE\n*\n   80          CONTINUE\n*\n   90       CONTINUE\n*\n  100    CONTINUE\n*\n  110 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 130\n*\n  120 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      IF( FULL )THEN\n         WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, ALPHA, LDA, INCX,\n     $      BETA, INCY\n      ELSE IF( BANDED )THEN\n         WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, K, ALPHA, LDA,\n     $      INCX, BETA, INCY\n      ELSE IF( PACKED )THEN\n         WRITE( NOUT, FMT = 9995 )NC, SNAME, UPLO, N, ALPHA, INCX,\n     $      BETA, INCY\n      END IF\n*\n  130 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', AP',\n     $      ', X,', I2, ',', F4.1, ', Y,', I2, ')                .' )\n 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 2( I3, ',' ), F4.1,\n     $      ', A,', I3, ', X,', I2, ',', F4.1, ', Y,', I2,\n     $      ')         .' )\n 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', A,',\n     $      I3, ', X,', I2, ',', F4.1, ', Y,', I2, ')             .' )\n 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of SCHK2.\n*\n      END\n      SUBROUTINE SCHK3( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NKB, KB, NINC, INC, NMAX,\n     $                  INCMAX, A, AA, AS, X, XX, XS, XT, G, Z )\n*\n*  Tests STRMV, STBMV, STPMV, STRSV, STBSV and STPSV.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Parameters ..\n      REAL               ZERO, HALF, ONE\n      PARAMETER          ( ZERO = 0.0, HALF = 0.5, ONE = 1.0 )\n*     .. Scalar Arguments ..\n      REAL               EPS, THRESH\n      INTEGER            INCMAX, NIDIM, NINC, NKB, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      REAL               A( NMAX, NMAX ), AA( NMAX*NMAX ),\n     $                   AS( NMAX*NMAX ), G( NMAX ), X( NMAX ),\n     $                   XS( NMAX*INCMAX ), XT( NMAX ),\n     $                   XX( NMAX*INCMAX ), Z( NMAX )\n      INTEGER            IDIM( NIDIM ), INC( NINC ), KB( NKB )\n*     .. Local Scalars ..\n      REAL               ERR, ERRMAX, TRANSL\n      INTEGER            I, ICD, ICT, ICU, IK, IN, INCX, INCXS, IX, K,\n     $                   KS, LAA, LDA, LDAS, LX, N, NARGS, NC, NK, NS\n      LOGICAL            BANDED, FULL, NULL, PACKED, RESET, SAME\n      CHARACTER*1        DIAG, DIAGS, TRANS, TRANSS, UPLO, UPLOS\n      CHARACTER*2        ICHD, ICHU\n      CHARACTER*3        ICHT\n*     .. Local Arrays ..\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LSE, LSERES\n      EXTERNAL           LSE, LSERES\n*     .. External Subroutines ..\n      EXTERNAL           SMAKE, SMVCH, STBMV, STBSV, STPMV, STPSV,\n     $                   STRMV, STRSV\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, MAX\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICHU/'UL'/, ICHT/'NTC'/, ICHD/'UN'/\n*     .. Executable Statements ..\n      FULL = SNAME( 3: 3 ).EQ.'R'\n      BANDED = SNAME( 3: 3 ).EQ.'B'\n      PACKED = SNAME( 3: 3 ).EQ.'P'\n*     Define the number of arguments.\n      IF( FULL )THEN\n         NARGS = 8\n      ELSE IF( BANDED )THEN\n         NARGS = 9\n      ELSE IF( PACKED )THEN\n         NARGS = 7\n      END IF\n*\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = ZERO\n*     Set up zero vector for SMVCH.\n      DO 10 I = 1, NMAX\n         Z( I ) = ZERO\n   10 CONTINUE\n*\n      DO 110 IN = 1, NIDIM\n         N = IDIM( IN )\n*\n         IF( BANDED )THEN\n            NK = NKB\n         ELSE\n            NK = 1\n         END IF\n         DO 100 IK = 1, NK\n            IF( BANDED )THEN\n               K = KB( IK )\n            ELSE\n               K = N - 1\n            END IF\n*           Set LDA to 1 more than minimum value if room.\n            IF( BANDED )THEN\n               LDA = K + 1\n            ELSE\n               LDA = N\n            END IF\n            IF( LDA.LT.NMAX )\n     $         LDA = LDA + 1\n*           Skip tests if not enough room.\n            IF( LDA.GT.NMAX )\n     $         GO TO 100\n            IF( PACKED )THEN\n               LAA = ( N*( N + 1 ) )/2\n            ELSE\n               LAA = LDA*N\n            END IF\n            NULL = N.LE.0\n*\n            DO 90 ICU = 1, 2\n               UPLO = ICHU( ICU: ICU )\n*\n               DO 80 ICT = 1, 3\n                  TRANS = ICHT( ICT: ICT )\n*\n                  DO 70 ICD = 1, 2\n                     DIAG = ICHD( ICD: ICD )\n*\n*                    Generate the matrix A.\n*\n                     TRANSL = ZERO\n                     CALL SMAKE( SNAME( 2: 3 ), UPLO, DIAG, N, N, A,\n     $                           NMAX, AA, LDA, K, K, RESET, TRANSL )\n*\n                     DO 60 IX = 1, NINC\n                        INCX = INC( IX )\n                        LX = ABS( INCX )*N\n*\n*                       Generate the vector X.\n*\n                        TRANSL = HALF\n                        CALL SMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX,\n     $                              ABS( INCX ), 0, N - 1, RESET,\n     $                              TRANSL )\n                        IF( N.GT.1 )THEN\n                           X( N/2 ) = ZERO\n                           XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO\n                        END IF\n*\n                        NC = NC + 1\n*\n*                       Save every datum before calling the subroutine.\n*\n                        UPLOS = UPLO\n                        TRANSS = TRANS\n                        DIAGS = DIAG\n                        NS = N\n                        KS = K\n                        DO 20 I = 1, LAA\n                           AS( I ) = AA( I )\n   20                   CONTINUE\n                        LDAS = LDA\n                        DO 30 I = 1, LX\n                           XS( I ) = XX( I )\n   30                   CONTINUE\n                        INCXS = INCX\n*\n*                       Call the subroutine.\n*\n                        IF( SNAME( 4: 5 ).EQ.'MV' )THEN\n                           IF( FULL )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9993 )NC, SNAME,\n     $                           UPLO, TRANS, DIAG, N, LDA, INCX\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL STRMV( UPLO, TRANS, DIAG, N, AA, LDA,\n     $                                    XX, INCX )\n                           ELSE IF( BANDED )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9994 )NC, SNAME,\n     $                           UPLO, TRANS, DIAG, N, K, LDA, INCX\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL STBMV( UPLO, TRANS, DIAG, N, K, AA,\n     $                                    LDA, XX, INCX )\n                           ELSE IF( PACKED )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9995 )NC, SNAME,\n     $                           UPLO, TRANS, DIAG, N, INCX\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL STPMV( UPLO, TRANS, DIAG, N, AA, XX,\n     $                                    INCX )\n                           END IF\n                        ELSE IF( SNAME( 4: 5 ).EQ.'SV' )THEN\n                           IF( FULL )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9993 )NC, SNAME,\n     $                           UPLO, TRANS, DIAG, N, LDA, INCX\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL STRSV( UPLO, TRANS, DIAG, N, AA, LDA,\n     $                                    XX, INCX )\n                           ELSE IF( BANDED )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9994 )NC, SNAME,\n     $                           UPLO, TRANS, DIAG, N, K, LDA, INCX\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL STBSV( UPLO, TRANS, DIAG, N, K, AA,\n     $                                    LDA, XX, INCX )\n                           ELSE IF( PACKED )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9995 )NC, SNAME,\n     $                           UPLO, TRANS, DIAG, N, INCX\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL STPSV( UPLO, TRANS, DIAG, N, AA, XX,\n     $                                    INCX )\n                           END IF\n                        END IF\n*\n*                       Check if error-exit was taken incorrectly.\n*\n                        IF( .NOT.OK )THEN\n                           WRITE( NOUT, FMT = 9992 )\n                           FATAL = .TRUE.\n                           GO TO 120\n                        END IF\n*\n*                       See what data changed inside subroutines.\n*\n                        ISAME( 1 ) = UPLO.EQ.UPLOS\n                        ISAME( 2 ) = TRANS.EQ.TRANSS\n                        ISAME( 3 ) = DIAG.EQ.DIAGS\n                        ISAME( 4 ) = NS.EQ.N\n                        IF( FULL )THEN\n                           ISAME( 5 ) = LSE( AS, AA, LAA )\n                           ISAME( 6 ) = LDAS.EQ.LDA\n                           IF( NULL )THEN\n                              ISAME( 7 ) = LSE( XS, XX, LX )\n                           ELSE\n                              ISAME( 7 ) = LSERES( 'GE', ' ', 1, N, XS,\n     $                                     XX, ABS( INCX ) )\n                           END IF\n                           ISAME( 8 ) = INCXS.EQ.INCX\n                        ELSE IF( BANDED )THEN\n                           ISAME( 5 ) = KS.EQ.K\n                           ISAME( 6 ) = LSE( AS, AA, LAA )\n                           ISAME( 7 ) = LDAS.EQ.LDA\n                           IF( NULL )THEN\n                              ISAME( 8 ) = LSE( XS, XX, LX )\n                           ELSE\n                              ISAME( 8 ) = LSERES( 'GE', ' ', 1, N, XS,\n     $                                     XX, ABS( INCX ) )\n                           END IF\n                           ISAME( 9 ) = INCXS.EQ.INCX\n                        ELSE IF( PACKED )THEN\n                           ISAME( 5 ) = LSE( AS, AA, LAA )\n                           IF( NULL )THEN\n                              ISAME( 6 ) = LSE( XS, XX, LX )\n                           ELSE\n                              ISAME( 6 ) = LSERES( 'GE', ' ', 1, N, XS,\n     $                                     XX, ABS( INCX ) )\n                           END IF\n                           ISAME( 7 ) = INCXS.EQ.INCX\n                        END IF\n*\n*                       If data was incorrectly changed, report and\n*                       return.\n*\n                        SAME = .TRUE.\n                        DO 40 I = 1, NARGS\n                           SAME = SAME.AND.ISAME( I )\n                           IF( .NOT.ISAME( I ) )\n     $                        WRITE( NOUT, FMT = 9998 )I\n   40                   CONTINUE\n                        IF( .NOT.SAME )THEN\n                           FATAL = .TRUE.\n                           GO TO 120\n                        END IF\n*\n                        IF( .NOT.NULL )THEN\n                           IF( SNAME( 4: 5 ).EQ.'MV' )THEN\n*\n*                             Check the result.\n*\n                              CALL SMVCH( TRANS, N, N, ONE, A, NMAX, X,\n     $                                    INCX, ZERO, Z, INCX, XT, G,\n     $                                    XX, EPS, ERR, FATAL, NOUT,\n     $                                    .TRUE. )\n                           ELSE IF( SNAME( 4: 5 ).EQ.'SV' )THEN\n*\n*                             Compute approximation to original vector.\n*\n                              DO 50 I = 1, N\n                                 Z( I ) = XX( 1 + ( I - 1 )*\n     $                                    ABS( INCX ) )\n                                 XX( 1 + ( I - 1 )*ABS( INCX ) )\n     $                              = X( I )\n   50                         CONTINUE\n                              CALL SMVCH( TRANS, N, N, ONE, A, NMAX, Z,\n     $                                    INCX, ZERO, X, INCX, XT, G,\n     $                                    XX, EPS, ERR, FATAL, NOUT,\n     $                                    .FALSE. )\n                           END IF\n                           ERRMAX = MAX( ERRMAX, ERR )\n*                          If got really bad answer, report and return.\n                           IF( FATAL )\n     $                        GO TO 120\n                        ELSE\n*                          Avoid repeating tests with N.le.0.\n                           GO TO 110\n                        END IF\n*\n   60                CONTINUE\n*\n   70             CONTINUE\n*\n   80          CONTINUE\n*\n   90       CONTINUE\n*\n  100    CONTINUE\n*\n  110 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 130\n*\n  120 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      IF( FULL )THEN\n         WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, TRANS, DIAG, N, LDA,\n     $      INCX\n      ELSE IF( BANDED )THEN\n         WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, TRANS, DIAG, N, K,\n     $      LDA, INCX\n      ELSE IF( PACKED )THEN\n         WRITE( NOUT, FMT = 9995 )NC, SNAME, UPLO, TRANS, DIAG, N, INCX\n      END IF\n*\n  130 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), I3, ', AP, ',\n     $      'X,', I2, ')                        .' )\n 9994 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), 2( I3, ',' ),\n     $      ' A,', I3, ', X,', I2, ')                 .' )\n 9993 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), I3, ', A,',\n     $      I3, ', X,', I2, ')                     .' )\n 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of SCHK3.\n*\n      END\n      SUBROUTINE SCHK4( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX,\n     $                  INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G,\n     $                  Z )\n*\n*  Tests SGER.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Parameters ..\n      REAL               ZERO, HALF, ONE\n      PARAMETER          ( ZERO = 0.0, HALF = 0.5, ONE = 1.0 )\n*     .. Scalar Arguments ..\n      REAL               EPS, THRESH\n      INTEGER            INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      REAL               A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), G( NMAX ), X( NMAX ),\n     $                   XS( NMAX*INCMAX ), XX( NMAX*INCMAX ),\n     $                   Y( NMAX ), YS( NMAX*INCMAX ), YT( NMAX ),\n     $                   YY( NMAX*INCMAX ), Z( NMAX )\n      INTEGER            IDIM( NIDIM ), INC( NINC )\n*     .. Local Scalars ..\n      REAL               ALPHA, ALS, ERR, ERRMAX, TRANSL\n      INTEGER            I, IA, IM, IN, INCX, INCXS, INCY, INCYS, IX,\n     $                   IY, J, LAA, LDA, LDAS, LX, LY, M, MS, N, NARGS,\n     $                   NC, ND, NS\n      LOGICAL            NULL, RESET, SAME\n*     .. Local Arrays ..\n      REAL               W( 1 )\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LSE, LSERES\n      EXTERNAL           LSE, LSERES\n*     .. External Subroutines ..\n      EXTERNAL           SGER, SMAKE, SMVCH\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, MAX, MIN\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Executable Statements ..\n*     Define the number of arguments.\n      NARGS = 9\n*\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = ZERO\n*\n      DO 120 IN = 1, NIDIM\n         N = IDIM( IN )\n         ND = N/2 + 1\n*\n         DO 110 IM = 1, 2\n            IF( IM.EQ.1 )\n     $         M = MAX( N - ND, 0 )\n            IF( IM.EQ.2 )\n     $         M = MIN( N + ND, NMAX )\n*\n*           Set LDA to 1 more than minimum value if room.\n            LDA = M\n            IF( LDA.LT.NMAX )\n     $         LDA = LDA + 1\n*           Skip tests if not enough room.\n            IF( LDA.GT.NMAX )\n     $         GO TO 110\n            LAA = LDA*N\n            NULL = N.LE.0.OR.M.LE.0\n*\n            DO 100 IX = 1, NINC\n               INCX = INC( IX )\n               LX = ABS( INCX )*M\n*\n*              Generate the vector X.\n*\n               TRANSL = HALF\n               CALL SMAKE( 'GE', ' ', ' ', 1, M, X, 1, XX, ABS( INCX ),\n     $                     0, M - 1, RESET, TRANSL )\n               IF( M.GT.1 )THEN\n                  X( M/2 ) = ZERO\n                  XX( 1 + ABS( INCX )*( M/2 - 1 ) ) = ZERO\n               END IF\n*\n               DO 90 IY = 1, NINC\n                  INCY = INC( IY )\n                  LY = ABS( INCY )*N\n*\n*                 Generate the vector Y.\n*\n                  TRANSL = ZERO\n                  CALL SMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY,\n     $                        ABS( INCY ), 0, N - 1, RESET, TRANSL )\n                  IF( N.GT.1 )THEN\n                     Y( N/2 ) = ZERO\n                     YY( 1 + ABS( INCY )*( N/2 - 1 ) ) = ZERO\n                  END IF\n*\n                  DO 80 IA = 1, NALF\n                     ALPHA = ALF( IA )\n*\n*                    Generate the matrix A.\n*\n                     TRANSL = ZERO\n                     CALL SMAKE( SNAME( 2: 3 ), ' ', ' ', M, N, A, NMAX,\n     $                           AA, LDA, M - 1, N - 1, RESET, TRANSL )\n*\n                     NC = NC + 1\n*\n*                    Save every datum before calling the subroutine.\n*\n                     MS = M\n                     NS = N\n                     ALS = ALPHA\n                     DO 10 I = 1, LAA\n                        AS( I ) = AA( I )\n   10                CONTINUE\n                     LDAS = LDA\n                     DO 20 I = 1, LX\n                        XS( I ) = XX( I )\n   20                CONTINUE\n                     INCXS = INCX\n                     DO 30 I = 1, LY\n                        YS( I ) = YY( I )\n   30                CONTINUE\n                     INCYS = INCY\n*\n*                    Call the subroutine.\n*\n                     IF( TRACE )\n     $                  WRITE( NTRA, FMT = 9994 )NC, SNAME, M, N,\n     $                  ALPHA, INCX, INCY, LDA\n                     IF( REWI )\n     $                  REWIND NTRA\n                     CALL SGER( M, N, ALPHA, XX, INCX, YY, INCY, AA,\n     $                          LDA )\n*\n*                    Check if error-exit was taken incorrectly.\n*\n                     IF( .NOT.OK )THEN\n                        WRITE( NOUT, FMT = 9993 )\n                        FATAL = .TRUE.\n                        GO TO 140\n                     END IF\n*\n*                    See what data changed inside subroutine.\n*\n                     ISAME( 1 ) = MS.EQ.M\n                     ISAME( 2 ) = NS.EQ.N\n                     ISAME( 3 ) = ALS.EQ.ALPHA\n                     ISAME( 4 ) = LSE( XS, XX, LX )\n                     ISAME( 5 ) = INCXS.EQ.INCX\n                     ISAME( 6 ) = LSE( YS, YY, LY )\n                     ISAME( 7 ) = INCYS.EQ.INCY\n                     IF( NULL )THEN\n                        ISAME( 8 ) = LSE( AS, AA, LAA )\n                     ELSE\n                        ISAME( 8 ) = LSERES( 'GE', ' ', M, N, AS, AA,\n     $                               LDA )\n                     END IF\n                     ISAME( 9 ) = LDAS.EQ.LDA\n*\n*                    If data was incorrectly changed, report and return.\n*\n                     SAME = .TRUE.\n                     DO 40 I = 1, NARGS\n                        SAME = SAME.AND.ISAME( I )\n                        IF( .NOT.ISAME( I ) )\n     $                     WRITE( NOUT, FMT = 9998 )I\n   40                CONTINUE\n                     IF( .NOT.SAME )THEN\n                        FATAL = .TRUE.\n                        GO TO 140\n                     END IF\n*\n                     IF( .NOT.NULL )THEN\n*\n*                       Check the result column by column.\n*\n                        IF( INCX.GT.0 )THEN\n                           DO 50 I = 1, M\n                              Z( I ) = X( I )\n   50                      CONTINUE\n                        ELSE\n                           DO 60 I = 1, M\n                              Z( I ) = X( M - I + 1 )\n   60                      CONTINUE\n                        END IF\n                        DO 70 J = 1, N\n                           IF( INCY.GT.0 )THEN\n                              W( 1 ) = Y( J )\n                           ELSE\n                              W( 1 ) = Y( N - J + 1 )\n                           END IF\n                           CALL SMVCH( 'N', M, 1, ALPHA, Z, NMAX, W, 1,\n     $                                 ONE, A( 1, J ), 1, YT, G,\n     $                                 AA( 1 + ( J - 1 )*LDA ), EPS,\n     $                                 ERR, FATAL, NOUT, .TRUE. )\n                           ERRMAX = MAX( ERRMAX, ERR )\n*                          If got really bad answer, report and return.\n                           IF( FATAL )\n     $                        GO TO 130\n   70                   CONTINUE\n                     ELSE\n*                       Avoid repeating tests with M.le.0 or N.le.0.\n                        GO TO 110\n                     END IF\n*\n   80             CONTINUE\n*\n   90          CONTINUE\n*\n  100       CONTINUE\n*\n  110    CONTINUE\n*\n  120 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 150\n*\n  130 CONTINUE\n      WRITE( NOUT, FMT = 9995 )J\n*\n  140 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      WRITE( NOUT, FMT = 9994 )NC, SNAME, M, N, ALPHA, INCX, INCY, LDA\n*\n  150 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( '      THESE ARE THE RESULTS FOR COLUMN ', I3 )\n 9994 FORMAT( 1X, I6, ': ', A6, '(', 2( I3, ',' ), F4.1, ', X,', I2,\n     $      ', Y,', I2, ', A,', I3, ')                  .' )\n 9993 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of SCHK4.\n*\n      END\n      SUBROUTINE SCHK5( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX,\n     $                  INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G,\n     $                  Z )\n*\n*  Tests SSYR and SSPR.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Parameters ..\n      REAL               ZERO, HALF, ONE\n      PARAMETER          ( ZERO = 0.0, HALF = 0.5, ONE = 1.0 )\n*     .. Scalar Arguments ..\n      REAL               EPS, THRESH\n      INTEGER            INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      REAL               A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), G( NMAX ), X( NMAX ),\n     $                   XS( NMAX*INCMAX ), XX( NMAX*INCMAX ),\n     $                   Y( NMAX ), YS( NMAX*INCMAX ), YT( NMAX ),\n     $                   YY( NMAX*INCMAX ), Z( NMAX )\n      INTEGER            IDIM( NIDIM ), INC( NINC )\n*     .. Local Scalars ..\n      REAL               ALPHA, ALS, ERR, ERRMAX, TRANSL\n      INTEGER            I, IA, IC, IN, INCX, INCXS, IX, J, JA, JJ, LAA,\n     $                   LDA, LDAS, LJ, LX, N, NARGS, NC, NS\n      LOGICAL            FULL, NULL, PACKED, RESET, SAME, UPPER\n      CHARACTER*1        UPLO, UPLOS\n      CHARACTER*2        ICH\n*     .. Local Arrays ..\n      REAL               W( 1 )\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LSE, LSERES\n      EXTERNAL           LSE, LSERES\n*     .. External Subroutines ..\n      EXTERNAL           SMAKE, SMVCH, SSPR, SSYR\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, MAX\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICH/'UL'/\n*     .. Executable Statements ..\n      FULL = SNAME( 3: 3 ).EQ.'Y'\n      PACKED = SNAME( 3: 3 ).EQ.'P'\n*     Define the number of arguments.\n      IF( FULL )THEN\n         NARGS = 7\n      ELSE IF( PACKED )THEN\n         NARGS = 6\n      END IF\n*\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = ZERO\n*\n      DO 100 IN = 1, NIDIM\n         N = IDIM( IN )\n*        Set LDA to 1 more than minimum value if room.\n         LDA = N\n         IF( LDA.LT.NMAX )\n     $      LDA = LDA + 1\n*        Skip tests if not enough room.\n         IF( LDA.GT.NMAX )\n     $      GO TO 100\n         IF( PACKED )THEN\n            LAA = ( N*( N + 1 ) )/2\n         ELSE\n            LAA = LDA*N\n         END IF\n*\n         DO 90 IC = 1, 2\n            UPLO = ICH( IC: IC )\n            UPPER = UPLO.EQ.'U'\n*\n            DO 80 IX = 1, NINC\n               INCX = INC( IX )\n               LX = ABS( INCX )*N\n*\n*              Generate the vector X.\n*\n               TRANSL = HALF\n               CALL SMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX, ABS( INCX ),\n     $                     0, N - 1, RESET, TRANSL )\n               IF( N.GT.1 )THEN\n                  X( N/2 ) = ZERO\n                  XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO\n               END IF\n*\n               DO 70 IA = 1, NALF\n                  ALPHA = ALF( IA )\n                  NULL = N.LE.0.OR.ALPHA.EQ.ZERO\n*\n*                 Generate the matrix A.\n*\n                  TRANSL = ZERO\n                  CALL SMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A, NMAX,\n     $                        AA, LDA, N - 1, N - 1, RESET, TRANSL )\n*\n                  NC = NC + 1\n*\n*                 Save every datum before calling the subroutine.\n*\n                  UPLOS = UPLO\n                  NS = N\n                  ALS = ALPHA\n                  DO 10 I = 1, LAA\n                     AS( I ) = AA( I )\n   10             CONTINUE\n                  LDAS = LDA\n                  DO 20 I = 1, LX\n                     XS( I ) = XX( I )\n   20             CONTINUE\n                  INCXS = INCX\n*\n*                 Call the subroutine.\n*\n                  IF( FULL )THEN\n                     IF( TRACE )\n     $                  WRITE( NTRA, FMT = 9993 )NC, SNAME, UPLO, N,\n     $                  ALPHA, INCX, LDA\n                     IF( REWI )\n     $                  REWIND NTRA\n                     CALL SSYR( UPLO, N, ALPHA, XX, INCX, AA, LDA )\n                  ELSE IF( PACKED )THEN\n                     IF( TRACE )\n     $                  WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO, N,\n     $                  ALPHA, INCX\n                     IF( REWI )\n     $                  REWIND NTRA\n                     CALL SSPR( UPLO, N, ALPHA, XX, INCX, AA )\n                  END IF\n*\n*                 Check if error-exit was taken incorrectly.\n*\n                  IF( .NOT.OK )THEN\n                     WRITE( NOUT, FMT = 9992 )\n                     FATAL = .TRUE.\n                     GO TO 120\n                  END IF\n*\n*                 See what data changed inside subroutines.\n*\n                  ISAME( 1 ) = UPLO.EQ.UPLOS\n                  ISAME( 2 ) = NS.EQ.N\n                  ISAME( 3 ) = ALS.EQ.ALPHA\n                  ISAME( 4 ) = LSE( XS, XX, LX )\n                  ISAME( 5 ) = INCXS.EQ.INCX\n                  IF( NULL )THEN\n                     ISAME( 6 ) = LSE( AS, AA, LAA )\n                  ELSE\n                     ISAME( 6 ) = LSERES( SNAME( 2: 3 ), UPLO, N, N, AS,\n     $                            AA, LDA )\n                  END IF\n                  IF( .NOT.PACKED )THEN\n                     ISAME( 7 ) = LDAS.EQ.LDA\n                  END IF\n*\n*                 If data was incorrectly changed, report and return.\n*\n                  SAME = .TRUE.\n                  DO 30 I = 1, NARGS\n                     SAME = SAME.AND.ISAME( I )\n                     IF( .NOT.ISAME( I ) )\n     $                  WRITE( NOUT, FMT = 9998 )I\n   30             CONTINUE\n                  IF( .NOT.SAME )THEN\n                     FATAL = .TRUE.\n                     GO TO 120\n                  END IF\n*\n                  IF( .NOT.NULL )THEN\n*\n*                    Check the result column by column.\n*\n                     IF( INCX.GT.0 )THEN\n                        DO 40 I = 1, N\n                           Z( I ) = X( I )\n   40                   CONTINUE\n                     ELSE\n                        DO 50 I = 1, N\n                           Z( I ) = X( N - I + 1 )\n   50                   CONTINUE\n                     END IF\n                     JA = 1\n                     DO 60 J = 1, N\n                        W( 1 ) = Z( J )\n                        IF( UPPER )THEN\n                           JJ = 1\n                           LJ = J\n                        ELSE\n                           JJ = J\n                           LJ = N - J + 1\n                        END IF\n                        CALL SMVCH( 'N', LJ, 1, ALPHA, Z( JJ ), LJ, W,\n     $                              1, ONE, A( JJ, J ), 1, YT, G,\n     $                              AA( JA ), EPS, ERR, FATAL, NOUT,\n     $                              .TRUE. )\n                        IF( FULL )THEN\n                           IF( UPPER )THEN\n                              JA = JA + LDA\n                           ELSE\n                              JA = JA + LDA + 1\n                           END IF\n                        ELSE\n                           JA = JA + LJ\n                        END IF\n                        ERRMAX = MAX( ERRMAX, ERR )\n*                       If got really bad answer, report and return.\n                        IF( FATAL )\n     $                     GO TO 110\n   60                CONTINUE\n                  ELSE\n*                    Avoid repeating tests if N.le.0.\n                     IF( N.LE.0 )\n     $                  GO TO 100\n                  END IF\n*\n   70          CONTINUE\n*\n   80       CONTINUE\n*\n   90    CONTINUE\n*\n  100 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 130\n*\n  110 CONTINUE\n      WRITE( NOUT, FMT = 9995 )J\n*\n  120 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      IF( FULL )THEN\n         WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, ALPHA, INCX, LDA\n      ELSE IF( PACKED )THEN\n         WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, ALPHA, INCX\n      END IF\n*\n  130 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( '      THESE ARE THE RESULTS FOR COLUMN ', I3 )\n 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,',\n     $      I2, ', AP)                           .' )\n 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,',\n     $      I2, ', A,', I3, ')                        .' )\n 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of SCHK5.\n*\n      END\n      SUBROUTINE SCHK6( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX,\n     $                  INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G,\n     $                  Z )\n*\n*  Tests SSYR2 and SSPR2.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Parameters ..\n      REAL               ZERO, HALF, ONE\n      PARAMETER          ( ZERO = 0.0, HALF = 0.5, ONE = 1.0 )\n*     .. Scalar Arguments ..\n      REAL               EPS, THRESH\n      INTEGER            INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      REAL               A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), G( NMAX ), X( NMAX ),\n     $                   XS( NMAX*INCMAX ), XX( NMAX*INCMAX ),\n     $                   Y( NMAX ), YS( NMAX*INCMAX ), YT( NMAX ),\n     $                   YY( NMAX*INCMAX ), Z( NMAX, 2 )\n      INTEGER            IDIM( NIDIM ), INC( NINC )\n*     .. Local Scalars ..\n      REAL               ALPHA, ALS, ERR, ERRMAX, TRANSL\n      INTEGER            I, IA, IC, IN, INCX, INCXS, INCY, INCYS, IX,\n     $                   IY, J, JA, JJ, LAA, LDA, LDAS, LJ, LX, LY, N,\n     $                   NARGS, NC, NS\n      LOGICAL            FULL, NULL, PACKED, RESET, SAME, UPPER\n      CHARACTER*1        UPLO, UPLOS\n      CHARACTER*2        ICH\n*     .. Local Arrays ..\n      REAL               W( 2 )\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LSE, LSERES\n      EXTERNAL           LSE, LSERES\n*     .. External Subroutines ..\n      EXTERNAL           SMAKE, SMVCH, SSPR2, SSYR2\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, MAX\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICH/'UL'/\n*     .. Executable Statements ..\n      FULL = SNAME( 3: 3 ).EQ.'Y'\n      PACKED = SNAME( 3: 3 ).EQ.'P'\n*     Define the number of arguments.\n      IF( FULL )THEN\n         NARGS = 9\n      ELSE IF( PACKED )THEN\n         NARGS = 8\n      END IF\n*\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = ZERO\n*\n      DO 140 IN = 1, NIDIM\n         N = IDIM( IN )\n*        Set LDA to 1 more than minimum value if room.\n         LDA = N\n         IF( LDA.LT.NMAX )\n     $      LDA = LDA + 1\n*        Skip tests if not enough room.\n         IF( LDA.GT.NMAX )\n     $      GO TO 140\n         IF( PACKED )THEN\n            LAA = ( N*( N + 1 ) )/2\n         ELSE\n            LAA = LDA*N\n         END IF\n*\n         DO 130 IC = 1, 2\n            UPLO = ICH( IC: IC )\n            UPPER = UPLO.EQ.'U'\n*\n            DO 120 IX = 1, NINC\n               INCX = INC( IX )\n               LX = ABS( INCX )*N\n*\n*              Generate the vector X.\n*\n               TRANSL = HALF\n               CALL SMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX, ABS( INCX ),\n     $                     0, N - 1, RESET, TRANSL )\n               IF( N.GT.1 )THEN\n                  X( N/2 ) = ZERO\n                  XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO\n               END IF\n*\n               DO 110 IY = 1, NINC\n                  INCY = INC( IY )\n                  LY = ABS( INCY )*N\n*\n*                 Generate the vector Y.\n*\n                  TRANSL = ZERO\n                  CALL SMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY,\n     $                        ABS( INCY ), 0, N - 1, RESET, TRANSL )\n                  IF( N.GT.1 )THEN\n                     Y( N/2 ) = ZERO\n                     YY( 1 + ABS( INCY )*( N/2 - 1 ) ) = ZERO\n                  END IF\n*\n                  DO 100 IA = 1, NALF\n                     ALPHA = ALF( IA )\n                     NULL = N.LE.0.OR.ALPHA.EQ.ZERO\n*\n*                    Generate the matrix A.\n*\n                     TRANSL = ZERO\n                     CALL SMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A,\n     $                           NMAX, AA, LDA, N - 1, N - 1, RESET,\n     $                           TRANSL )\n*\n                     NC = NC + 1\n*\n*                    Save every datum before calling the subroutine.\n*\n                     UPLOS = UPLO\n                     NS = N\n                     ALS = ALPHA\n                     DO 10 I = 1, LAA\n                        AS( I ) = AA( I )\n   10                CONTINUE\n                     LDAS = LDA\n                     DO 20 I = 1, LX\n                        XS( I ) = XX( I )\n   20                CONTINUE\n                     INCXS = INCX\n                     DO 30 I = 1, LY\n                        YS( I ) = YY( I )\n   30                CONTINUE\n                     INCYS = INCY\n*\n*                    Call the subroutine.\n*\n                     IF( FULL )THEN\n                        IF( TRACE )\n     $                     WRITE( NTRA, FMT = 9993 )NC, SNAME, UPLO, N,\n     $                     ALPHA, INCX, INCY, LDA\n                        IF( REWI )\n     $                     REWIND NTRA\n                        CALL SSYR2( UPLO, N, ALPHA, XX, INCX, YY, INCY,\n     $                              AA, LDA )\n                     ELSE IF( PACKED )THEN\n                        IF( TRACE )\n     $                     WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO, N,\n     $                     ALPHA, INCX, INCY\n                        IF( REWI )\n     $                     REWIND NTRA\n                        CALL SSPR2( UPLO, N, ALPHA, XX, INCX, YY, INCY,\n     $                              AA )\n                     END IF\n*\n*                    Check if error-exit was taken incorrectly.\n*\n                     IF( .NOT.OK )THEN\n                        WRITE( NOUT, FMT = 9992 )\n                        FATAL = .TRUE.\n                        GO TO 160\n                     END IF\n*\n*                    See what data changed inside subroutines.\n*\n                     ISAME( 1 ) = UPLO.EQ.UPLOS\n                     ISAME( 2 ) = NS.EQ.N\n                     ISAME( 3 ) = ALS.EQ.ALPHA\n                     ISAME( 4 ) = LSE( XS, XX, LX )\n                     ISAME( 5 ) = INCXS.EQ.INCX\n                     ISAME( 6 ) = LSE( YS, YY, LY )\n                     ISAME( 7 ) = INCYS.EQ.INCY\n                     IF( NULL )THEN\n                        ISAME( 8 ) = LSE( AS, AA, LAA )\n                     ELSE\n                        ISAME( 8 ) = LSERES( SNAME( 2: 3 ), UPLO, N, N,\n     $                               AS, AA, LDA )\n                     END IF\n                     IF( .NOT.PACKED )THEN\n                        ISAME( 9 ) = LDAS.EQ.LDA\n                     END IF\n*\n*                    If data was incorrectly changed, report and return.\n*\n                     SAME = .TRUE.\n                     DO 40 I = 1, NARGS\n                        SAME = SAME.AND.ISAME( I )\n                        IF( .NOT.ISAME( I ) )\n     $                     WRITE( NOUT, FMT = 9998 )I\n   40                CONTINUE\n                     IF( .NOT.SAME )THEN\n                        FATAL = .TRUE.\n                        GO TO 160\n                     END IF\n*\n                     IF( .NOT.NULL )THEN\n*\n*                       Check the result column by column.\n*\n                        IF( INCX.GT.0 )THEN\n                           DO 50 I = 1, N\n                              Z( I, 1 ) = X( I )\n   50                      CONTINUE\n                        ELSE\n                           DO 60 I = 1, N\n                              Z( I, 1 ) = X( N - I + 1 )\n   60                      CONTINUE\n                        END IF\n                        IF( INCY.GT.0 )THEN\n                           DO 70 I = 1, N\n                              Z( I, 2 ) = Y( I )\n   70                      CONTINUE\n                        ELSE\n                           DO 80 I = 1, N\n                              Z( I, 2 ) = Y( N - I + 1 )\n   80                      CONTINUE\n                        END IF\n                        JA = 1\n                        DO 90 J = 1, N\n                           W( 1 ) = Z( J, 2 )\n                           W( 2 ) = Z( J, 1 )\n                           IF( UPPER )THEN\n                              JJ = 1\n                              LJ = J\n                           ELSE\n                              JJ = J\n                              LJ = N - J + 1\n                           END IF\n                           CALL SMVCH( 'N', LJ, 2, ALPHA, Z( JJ, 1 ),\n     $                                 NMAX, W, 1, ONE, A( JJ, J ), 1,\n     $                                 YT, G, AA( JA ), EPS, ERR, FATAL,\n     $                                 NOUT, .TRUE. )\n                           IF( FULL )THEN\n                              IF( UPPER )THEN\n                                 JA = JA + LDA\n                              ELSE\n                                 JA = JA + LDA + 1\n                              END IF\n                           ELSE\n                              JA = JA + LJ\n                           END IF\n                           ERRMAX = MAX( ERRMAX, ERR )\n*                          If got really bad answer, report and return.\n                           IF( FATAL )\n     $                        GO TO 150\n   90                   CONTINUE\n                     ELSE\n*                       Avoid repeating tests with N.le.0.\n                        IF( N.LE.0 )\n     $                     GO TO 140\n                     END IF\n*\n  100             CONTINUE\n*\n  110          CONTINUE\n*\n  120       CONTINUE\n*\n  130    CONTINUE\n*\n  140 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 170\n*\n  150 CONTINUE\n      WRITE( NOUT, FMT = 9995 )J\n*\n  160 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      IF( FULL )THEN\n         WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, ALPHA, INCX,\n     $      INCY, LDA\n      ELSE IF( PACKED )THEN\n         WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, ALPHA, INCX, INCY\n      END IF\n*\n  170 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( '      THESE ARE THE RESULTS FOR COLUMN ', I3 )\n 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,',\n     $      I2, ', Y,', I2, ', AP)                     .' )\n 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,',\n     $      I2, ', Y,', I2, ', A,', I3, ')                  .' )\n 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of SCHK6.\n*\n      END\n      SUBROUTINE SCHKE( ISNUM, SRNAMT, NOUT )\n*\n*  Tests the error exits from the Level 2 Blas.\n*  Requires a special version of the error-handling routine XERBLA.\n*  ALPHA, BETA, A, X and Y should not need to be defined.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Scalar Arguments ..\n      INTEGER            ISNUM, NOUT\n      CHARACTER*6        SRNAMT\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Local Scalars ..\n      REAL               ALPHA, BETA\n*     .. Local Arrays ..\n      REAL               A( 1, 1 ), X( 1 ), Y( 1 )\n*     .. External Subroutines ..\n      EXTERNAL           CHKXER, SGBMV, SGEMV, SGER, SSBMV, SSPMV, SSPR,\n     $                   SSPR2, SSYMV, SSYR, SSYR2, STBMV, STBSV, STPMV,\n     $                   STPSV, STRMV, STRSV\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Executable Statements ..\n*     OK is set to .FALSE. by the special version of XERBLA or by CHKXER\n*     if anything is wrong.\n      OK = .TRUE.\n*     LERR is set to .TRUE. by the special version of XERBLA each time\n*     it is called, and is then tested and re-set by CHKXER.\n      LERR = .FALSE.\n      GO TO ( 10, 20, 30, 40, 50, 60, 70, 80,\n     $        90, 100, 110, 120, 130, 140, 150,\n     $        160 )ISNUM\n   10 INFOT = 1\n      CALL SGEMV( '/', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL SGEMV( 'N', -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL SGEMV( 'N', 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL SGEMV( 'N', 2, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL SGEMV( 'N', 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL SGEMV( 'N', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 170\n   20 INFOT = 1\n      CALL SGBMV( '/', 0, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL SGBMV( 'N', -1, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL SGBMV( 'N', 0, -1, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL SGBMV( 'N', 0, 0, -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL SGBMV( 'N', 2, 0, 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL SGBMV( 'N', 0, 0, 1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL SGBMV( 'N', 0, 0, 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 13\n      CALL SGBMV( 'N', 0, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 170\n   30 INFOT = 1\n      CALL SSYMV( '/', 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL SSYMV( 'U', -1, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL SSYMV( 'U', 2, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL SSYMV( 'U', 0, ALPHA, A, 1, X, 0, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL SSYMV( 'U', 0, ALPHA, A, 1, X, 1, BETA, Y, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 170\n   40 INFOT = 1\n      CALL SSBMV( '/', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL SSBMV( 'U', -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL SSBMV( 'U', 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL SSBMV( 'U', 0, 1, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL SSBMV( 'U', 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL SSBMV( 'U', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 170\n   50 INFOT = 1\n      CALL SSPMV( '/', 0, ALPHA, A, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL SSPMV( 'U', -1, ALPHA, A, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL SSPMV( 'U', 0, ALPHA, A, X, 0, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL SSPMV( 'U', 0, ALPHA, A, X, 1, BETA, Y, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 170\n   60 INFOT = 1\n      CALL STRMV( '/', 'N', 'N', 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL STRMV( 'U', '/', 'N', 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL STRMV( 'U', 'N', '/', 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL STRMV( 'U', 'N', 'N', -1, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL STRMV( 'U', 'N', 'N', 2, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL STRMV( 'U', 'N', 'N', 0, A, 1, X, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 170\n   70 INFOT = 1\n      CALL STBMV( '/', 'N', 'N', 0, 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL STBMV( 'U', '/', 'N', 0, 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL STBMV( 'U', 'N', '/', 0, 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL STBMV( 'U', 'N', 'N', -1, 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL STBMV( 'U', 'N', 'N', 0, -1, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL STBMV( 'U', 'N', 'N', 0, 1, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL STBMV( 'U', 'N', 'N', 0, 0, A, 1, X, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 170\n   80 INFOT = 1\n      CALL STPMV( '/', 'N', 'N', 0, A, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL STPMV( 'U', '/', 'N', 0, A, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL STPMV( 'U', 'N', '/', 0, A, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL STPMV( 'U', 'N', 'N', -1, A, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL STPMV( 'U', 'N', 'N', 0, A, X, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 170\n   90 INFOT = 1\n      CALL STRSV( '/', 'N', 'N', 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL STRSV( 'U', '/', 'N', 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL STRSV( 'U', 'N', '/', 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL STRSV( 'U', 'N', 'N', -1, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL STRSV( 'U', 'N', 'N', 2, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL STRSV( 'U', 'N', 'N', 0, A, 1, X, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 170\n  100 INFOT = 1\n      CALL STBSV( '/', 'N', 'N', 0, 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL STBSV( 'U', '/', 'N', 0, 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL STBSV( 'U', 'N', '/', 0, 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL STBSV( 'U', 'N', 'N', -1, 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL STBSV( 'U', 'N', 'N', 0, -1, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL STBSV( 'U', 'N', 'N', 0, 1, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL STBSV( 'U', 'N', 'N', 0, 0, A, 1, X, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 170\n  110 INFOT = 1\n      CALL STPSV( '/', 'N', 'N', 0, A, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL STPSV( 'U', '/', 'N', 0, A, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL STPSV( 'U', 'N', '/', 0, A, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL STPSV( 'U', 'N', 'N', -1, A, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL STPSV( 'U', 'N', 'N', 0, A, X, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 170\n  120 INFOT = 1\n      CALL SGER( -1, 0, ALPHA, X, 1, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL SGER( 0, -1, ALPHA, X, 1, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL SGER( 0, 0, ALPHA, X, 0, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL SGER( 0, 0, ALPHA, X, 1, Y, 0, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL SGER( 2, 0, ALPHA, X, 1, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 170\n  130 INFOT = 1\n      CALL SSYR( '/', 0, ALPHA, X, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL SSYR( 'U', -1, ALPHA, X, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL SSYR( 'U', 0, ALPHA, X, 0, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL SSYR( 'U', 2, ALPHA, X, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 170\n  140 INFOT = 1\n      CALL SSPR( '/', 0, ALPHA, X, 1, A )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL SSPR( 'U', -1, ALPHA, X, 1, A )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL SSPR( 'U', 0, ALPHA, X, 0, A )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 170\n  150 INFOT = 1\n      CALL SSYR2( '/', 0, ALPHA, X, 1, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL SSYR2( 'U', -1, ALPHA, X, 1, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL SSYR2( 'U', 0, ALPHA, X, 0, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL SSYR2( 'U', 0, ALPHA, X, 1, Y, 0, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL SSYR2( 'U', 2, ALPHA, X, 1, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 170\n  160 INFOT = 1\n      CALL SSPR2( '/', 0, ALPHA, X, 1, Y, 1, A )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL SSPR2( 'U', -1, ALPHA, X, 1, Y, 1, A )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL SSPR2( 'U', 0, ALPHA, X, 0, Y, 1, A )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL SSPR2( 'U', 0, ALPHA, X, 1, Y, 0, A )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n*\n  170 IF( OK )THEN\n         WRITE( NOUT, FMT = 9999 )SRNAMT\n      ELSE\n         WRITE( NOUT, FMT = 9998 )SRNAMT\n      END IF\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE TESTS OF ERROR-EXITS' )\n 9998 FORMAT( ' ******* ', A6, ' FAILED THE TESTS OF ERROR-EXITS *****',\n     $      '**' )\n*\n*     End of SCHKE.\n*\n      END\n      SUBROUTINE SMAKE( TYPE, UPLO, DIAG, M, N, A, NMAX, AA, LDA, KL,\n     $                  KU, RESET, TRANSL )\n*\n*  Generates values for an M by N matrix A within the bandwidth\n*  defined by KL and KU.\n*  Stores the values in the array AA in the data structure required\n*  by the routine, with unwanted elements set to rogue value.\n*\n*  TYPE is 'GE', 'GB', 'SY', 'SB', 'SP', 'TR', 'TB' OR 'TP'.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Parameters ..\n      REAL               ZERO, ONE\n      PARAMETER          ( ZERO = 0.0, ONE = 1.0 )\n      REAL               ROGUE\n      PARAMETER          ( ROGUE = -1.0E10 )\n*     .. Scalar Arguments ..\n      REAL               TRANSL\n      INTEGER            KL, KU, LDA, M, N, NMAX\n      LOGICAL            RESET\n      CHARACTER*1        DIAG, UPLO\n      CHARACTER*2        TYPE\n*     .. Array Arguments ..\n      REAL               A( NMAX, * ), AA( * )\n*     .. Local Scalars ..\n      INTEGER            I, I1, I2, I3, IBEG, IEND, IOFF, J, KK\n      LOGICAL            GEN, LOWER, SYM, TRI, UNIT, UPPER\n*     .. External Functions ..\n      REAL               SBEG\n      EXTERNAL           SBEG\n*     .. Intrinsic Functions ..\n      INTRINSIC          MAX, MIN\n*     .. Executable Statements ..\n      GEN = TYPE( 1: 1 ).EQ.'G'\n      SYM = TYPE( 1: 1 ).EQ.'S'\n      TRI = TYPE( 1: 1 ).EQ.'T'\n      UPPER = ( SYM.OR.TRI ).AND.UPLO.EQ.'U'\n      LOWER = ( SYM.OR.TRI ).AND.UPLO.EQ.'L'\n      UNIT = TRI.AND.DIAG.EQ.'U'\n*\n*     Generate data in array A.\n*\n      DO 20 J = 1, N\n         DO 10 I = 1, M\n            IF( GEN.OR.( UPPER.AND.I.LE.J ).OR.( LOWER.AND.I.GE.J ) )\n     $          THEN\n               IF( ( I.LE.J.AND.J - I.LE.KU ).OR.\n     $             ( I.GE.J.AND.I - J.LE.KL ) )THEN\n                  A( I, J ) = SBEG( RESET ) + TRANSL\n               ELSE\n                  A( I, J ) = ZERO\n               END IF\n               IF( I.NE.J )THEN\n                  IF( SYM )THEN\n                     A( J, I ) = A( I, J )\n                  ELSE IF( TRI )THEN\n                     A( J, I ) = ZERO\n                  END IF\n               END IF\n            END IF\n   10    CONTINUE\n         IF( TRI )\n     $      A( J, J ) = A( J, J ) + ONE\n         IF( UNIT )\n     $      A( J, J ) = ONE\n   20 CONTINUE\n*\n*     Store elements in array AS in data structure required by routine.\n*\n      IF( TYPE.EQ.'GE' )THEN\n         DO 50 J = 1, N\n            DO 30 I = 1, M\n               AA( I + ( J - 1 )*LDA ) = A( I, J )\n   30       CONTINUE\n            DO 40 I = M + 1, LDA\n               AA( I + ( J - 1 )*LDA ) = ROGUE\n   40       CONTINUE\n   50    CONTINUE\n      ELSE IF( TYPE.EQ.'GB' )THEN\n         DO 90 J = 1, N\n            DO 60 I1 = 1, KU + 1 - J\n               AA( I1 + ( J - 1 )*LDA ) = ROGUE\n   60       CONTINUE\n            DO 70 I2 = I1, MIN( KL + KU + 1, KU + 1 + M - J )\n               AA( I2 + ( J - 1 )*LDA ) = A( I2 + J - KU - 1, J )\n   70       CONTINUE\n            DO 80 I3 = I2, LDA\n               AA( I3 + ( J - 1 )*LDA ) = ROGUE\n   80       CONTINUE\n   90    CONTINUE\n      ELSE IF( TYPE.EQ.'SY'.OR.TYPE.EQ.'TR' )THEN\n         DO 130 J = 1, N\n            IF( UPPER )THEN\n               IBEG = 1\n               IF( UNIT )THEN\n                  IEND = J - 1\n               ELSE\n                  IEND = J\n               END IF\n            ELSE\n               IF( UNIT )THEN\n                  IBEG = J + 1\n               ELSE\n                  IBEG = J\n               END IF\n               IEND = N\n            END IF\n            DO 100 I = 1, IBEG - 1\n               AA( I + ( J - 1 )*LDA ) = ROGUE\n  100       CONTINUE\n            DO 110 I = IBEG, IEND\n               AA( I + ( J - 1 )*LDA ) = A( I, J )\n  110       CONTINUE\n            DO 120 I = IEND + 1, LDA\n               AA( I + ( J - 1 )*LDA ) = ROGUE\n  120       CONTINUE\n  130    CONTINUE\n      ELSE IF( TYPE.EQ.'SB'.OR.TYPE.EQ.'TB' )THEN\n         DO 170 J = 1, N\n            IF( UPPER )THEN\n               KK = KL + 1\n               IBEG = MAX( 1, KL + 2 - J )\n               IF( UNIT )THEN\n                  IEND = KL\n               ELSE\n                  IEND = KL + 1\n               END IF\n            ELSE\n               KK = 1\n               IF( UNIT )THEN\n                  IBEG = 2\n               ELSE\n                  IBEG = 1\n               END IF\n               IEND = MIN( KL + 1, 1 + M - J )\n            END IF\n            DO 140 I = 1, IBEG - 1\n               AA( I + ( J - 1 )*LDA ) = ROGUE\n  140       CONTINUE\n            DO 150 I = IBEG, IEND\n               AA( I + ( J - 1 )*LDA ) = A( I + J - KK, J )\n  150       CONTINUE\n            DO 160 I = IEND + 1, LDA\n               AA( I + ( J - 1 )*LDA ) = ROGUE\n  160       CONTINUE\n  170    CONTINUE\n      ELSE IF( TYPE.EQ.'SP'.OR.TYPE.EQ.'TP' )THEN\n         IOFF = 0\n         DO 190 J = 1, N\n            IF( UPPER )THEN\n               IBEG = 1\n               IEND = J\n            ELSE\n               IBEG = J\n               IEND = N\n            END IF\n            DO 180 I = IBEG, IEND\n               IOFF = IOFF + 1\n               AA( IOFF ) = A( I, J )\n               IF( I.EQ.J )THEN\n                  IF( UNIT )\n     $               AA( IOFF ) = ROGUE\n               END IF\n  180       CONTINUE\n  190    CONTINUE\n      END IF\n      RETURN\n*\n*     End of SMAKE.\n*\n      END\n      SUBROUTINE SMVCH( TRANS, M, N, ALPHA, A, NMAX, X, INCX, BETA, Y,\n     $                  INCY, YT, G, YY, EPS, ERR, FATAL, NOUT, MV )\n*\n*  Checks the results of the computational tests.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Parameters ..\n      REAL               ZERO, ONE\n      PARAMETER          ( ZERO = 0.0, ONE = 1.0 )\n*     .. Scalar Arguments ..\n      REAL               ALPHA, BETA, EPS, ERR\n      INTEGER            INCX, INCY, M, N, NMAX, NOUT\n      LOGICAL            FATAL, MV\n      CHARACTER*1        TRANS\n*     .. Array Arguments ..\n      REAL               A( NMAX, * ), G( * ), X( * ), Y( * ), YT( * ),\n     $                   YY( * )\n*     .. Local Scalars ..\n      REAL               ERRI\n      INTEGER            I, INCXL, INCYL, IY, J, JX, KX, KY, ML, NL\n      LOGICAL            TRAN\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, MAX, SQRT\n*     .. Executable Statements ..\n      TRAN = TRANS.EQ.'T'.OR.TRANS.EQ.'C'\n      IF( TRAN )THEN\n         ML = N\n         NL = M\n      ELSE\n         ML = M\n         NL = N\n      END IF\n      IF( INCX.LT.0 )THEN\n         KX = NL\n         INCXL = -1\n      ELSE\n         KX = 1\n         INCXL = 1\n      END IF\n      IF( INCY.LT.0 )THEN\n         KY = ML\n         INCYL = -1\n      ELSE\n         KY = 1\n         INCYL = 1\n      END IF\n*\n*     Compute expected result in YT using data in A, X and Y.\n*     Compute gauges in G.\n*\n      IY = KY\n      DO 30 I = 1, ML\n         YT( IY ) = ZERO\n         G( IY ) = ZERO\n         JX = KX\n         IF( TRAN )THEN\n            DO 10 J = 1, NL\n               YT( IY ) = YT( IY ) + A( J, I )*X( JX )\n               G( IY ) = G( IY ) + ABS( A( J, I )*X( JX ) )\n               JX = JX + INCXL\n   10       CONTINUE\n         ELSE\n            DO 20 J = 1, NL\n               YT( IY ) = YT( IY ) + A( I, J )*X( JX )\n               G( IY ) = G( IY ) + ABS( A( I, J )*X( JX ) )\n               JX = JX + INCXL\n   20       CONTINUE\n         END IF\n         YT( IY ) = ALPHA*YT( IY ) + BETA*Y( IY )\n         G( IY ) = ABS( ALPHA )*G( IY ) + ABS( BETA*Y( IY ) )\n         IY = IY + INCYL\n   30 CONTINUE\n*\n*     Compute the error ratio for this result.\n*\n      ERR = ZERO\n      DO 40 I = 1, ML\n         ERRI = ABS( YT( I ) - YY( 1 + ( I - 1 )*ABS( INCY ) ) )/EPS\n         IF( G( I ).NE.ZERO )\n     $      ERRI = ERRI/G( I )\n         ERR = MAX( ERR, ERRI )\n         IF( ERR*SQRT( EPS ).GE.ONE )\n     $      GO TO 50\n   40 CONTINUE\n*     If the loop completes, all results are at least half accurate.\n      GO TO 70\n*\n*     Report fatal error.\n*\n   50 FATAL = .TRUE.\n      WRITE( NOUT, FMT = 9999 )\n      DO 60 I = 1, ML\n         IF( MV )THEN\n            WRITE( NOUT, FMT = 9998 )I, YT( I ),\n     $         YY( 1 + ( I - 1 )*ABS( INCY ) )\n         ELSE\n            WRITE( NOUT, FMT = 9998 )I, \n     $         YY( 1 + ( I - 1 )*ABS( INCY ) ), YT(I)\n         END IF\n   60 CONTINUE\n*\n   70 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ******* FATAL ERROR - COMPUTED RESULT IS LESS THAN HAL',\n     $      'F ACCURATE *******', /'           EXPECTED RESULT   COMPU',\n     $      'TED RESULT' )\n 9998 FORMAT( 1X, I7, 2G18.6 )\n*\n*     End of SMVCH.\n*\n      END\n      LOGICAL FUNCTION LSE( RI, RJ, LR )\n*\n*  Tests if two arrays are identical.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Scalar Arguments ..\n      INTEGER            LR\n*     .. Array Arguments ..\n      REAL               RI( * ), RJ( * )\n*     .. Local Scalars ..\n      INTEGER            I\n*     .. Executable Statements ..\n      DO 10 I = 1, LR\n         IF( RI( I ).NE.RJ( I ) )\n     $      GO TO 20\n   10 CONTINUE\n      LSE = .TRUE.\n      GO TO 30\n   20 CONTINUE\n      LSE = .FALSE.\n   30 RETURN\n*\n*     End of LSE.\n*\n      END\n      LOGICAL FUNCTION LSERES( TYPE, UPLO, M, N, AA, AS, LDA )\n*\n*  Tests if selected elements in two arrays are equal.\n*\n*  TYPE is 'GE', 'SY' or 'SP'.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Scalar Arguments ..\n      INTEGER            LDA, M, N\n      CHARACTER*1        UPLO\n      CHARACTER*2        TYPE\n*     .. Array Arguments ..\n      REAL               AA( LDA, * ), AS( LDA, * )\n*     .. Local Scalars ..\n      INTEGER            I, IBEG, IEND, J\n      LOGICAL            UPPER\n*     .. Executable Statements ..\n      UPPER = UPLO.EQ.'U'\n      IF( TYPE.EQ.'GE' )THEN\n         DO 20 J = 1, N\n            DO 10 I = M + 1, LDA\n               IF( AA( I, J ).NE.AS( I, J ) )\n     $            GO TO 70\n   10       CONTINUE\n   20    CONTINUE\n      ELSE IF( TYPE.EQ.'SY' )THEN\n         DO 50 J = 1, N\n            IF( UPPER )THEN\n               IBEG = 1\n               IEND = J\n            ELSE\n               IBEG = J\n               IEND = N\n            END IF\n            DO 30 I = 1, IBEG - 1\n               IF( AA( I, J ).NE.AS( I, J ) )\n     $            GO TO 70\n   30       CONTINUE\n            DO 40 I = IEND + 1, LDA\n               IF( AA( I, J ).NE.AS( I, J ) )\n     $            GO TO 70\n   40       CONTINUE\n   50    CONTINUE\n      END IF\n*\n      LSERES = .TRUE.\n      GO TO 80\n   70 CONTINUE\n      LSERES = .FALSE.\n   80 RETURN\n*\n*     End of LSERES.\n*\n      END\n      REAL FUNCTION SBEG( RESET )\n*\n*  Generates random numbers uniformly distributed between -0.5 and 0.5.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Scalar Arguments ..\n      LOGICAL            RESET\n*     .. Local Scalars ..\n      INTEGER            I, IC, MI\n*     .. Save statement ..\n      SAVE               I, IC, MI\n*     .. Intrinsic Functions ..\n      INTRINSIC          REAL\n*     .. Executable Statements ..\n      IF( RESET )THEN\n*        Initialize local variables.\n         MI = 891\n         I = 7\n         IC = 0\n         RESET = .FALSE.\n      END IF\n*\n*     The sequence of values of I is bounded between 1 and 999.\n*     If initial I = 1,2,3,6,7 or 9, the period will be 50.\n*     If initial I = 4 or 8, the period will be 25.\n*     If initial I = 5, the period will be 10.\n*     IC is used to break up the period by skipping 1 value of I in 6.\n*\n      IC = IC + 1\n   10 I = I*MI\n      I = I - 1000*( I/1000 )\n      IF( IC.GE.5 )THEN\n         IC = 0\n         GO TO 10\n      END IF\n      SBEG = REAL( I - 500 )/1001.0\n      RETURN\n*\n*     End of SBEG.\n*\n      END\n      REAL FUNCTION SDIFF( X, Y )\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*\n*     .. Scalar Arguments ..\n      REAL               X, Y\n*     .. Executable Statements ..\n      SDIFF = X - Y\n      RETURN\n*\n*     End of SDIFF.\n*\n      END\n      SUBROUTINE CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n*\n*  Tests whether XERBLA has detected an error when it should.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Scalar Arguments ..\n      INTEGER            INFOT, NOUT\n      LOGICAL            LERR, OK\n      CHARACTER*6        SRNAMT\n*     .. Executable Statements ..\n      IF( .NOT.LERR )THEN\n         WRITE( NOUT, FMT = 9999 )INFOT, SRNAMT\n         OK = .FALSE.\n      END IF\n      LERR = .FALSE.\n      RETURN\n*\n 9999 FORMAT( ' ***** ILLEGAL VALUE OF PARAMETER NUMBER ', I2, ' NOT D',\n     $      'ETECTED BY ', A6, ' *****' )\n*\n*     End of CHKXER.\n*\n      END\n      SUBROUTINE XERBLA( SRNAME, INFO )\n*\n*  This is a special version of XERBLA to be used only as part of\n*  the test program for testing error exits from the Level 2 BLAS\n*  routines.\n*\n*  XERBLA  is an error handler for the Level 2 BLAS routines.\n*\n*  It is called by the Level 2 BLAS routines if an input parameter is\n*  invalid.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Scalar Arguments ..\n      INTEGER            INFO\n      CHARACTER*6        SRNAME\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUT\n      LOGICAL            LERR, OK\n      CHARACTER*6        SRNAMT\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUT, OK, LERR\n      COMMON             /SRNAMC/SRNAMT\n*     .. Executable Statements ..\n      LERR = .TRUE.\n      IF( INFO.NE.INFOT )THEN\n         IF( INFOT.NE.0 )THEN\n            WRITE( NOUT, FMT = 9999 )INFO, INFOT\n         ELSE\n            WRITE( NOUT, FMT = 9997 )INFO\n         END IF\n         OK = .FALSE.\n      END IF\n      IF( SRNAME.NE.SRNAMT )THEN\n         WRITE( NOUT, FMT = 9998 )SRNAME, SRNAMT\n         OK = .FALSE.\n      END IF\n      RETURN\n*\n 9999 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6, ' INSTEAD',\n     $      ' OF ', I2, ' *******' )\n 9998 FORMAT( ' ******* XERBLA WAS CALLED WITH SRNAME = ', A6, ' INSTE',\n     $      'AD OF ', A6, ' *******' )\n 9997 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6,\n     $      ' *******' )\n*\n*     End of XERBLA\n*\n      END\n\n"
  },
  {
    "path": "include/eigen3/blas/testing/sblat3.f",
    "content": "*> \\brief \\b SBLAT3\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*  Definition:\n*  ===========\n*\n*       PROGRAM SBLAT3\n* \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> Test program for the REAL             Level 3 Blas.\n*>\n*> The program must be driven by a short data file. The first 14 records\n*> of the file are read using list-directed input, the last 6 records\n*> are read using the format ( A6, L2 ). An annotated example of a data\n*> file can be obtained by deleting the first 3 characters from the\n*> following 20 lines:\n*> 'sblat3.out'      NAME OF SUMMARY OUTPUT FILE\n*> 6                 UNIT NUMBER OF SUMMARY FILE\n*> 'SBLAT3.SNAP'     NAME OF SNAPSHOT OUTPUT FILE\n*> -1                UNIT NUMBER OF SNAPSHOT FILE (NOT USED IF .LT. 0)\n*> F        LOGICAL FLAG, T TO REWIND SNAPSHOT FILE AFTER EACH RECORD.\n*> F        LOGICAL FLAG, T TO STOP ON FAILURES.\n*> T        LOGICAL FLAG, T TO TEST ERROR EXITS.\n*> 16.0     THRESHOLD VALUE OF TEST RATIO\n*> 6                 NUMBER OF VALUES OF N\n*> 0 1 2 3 5 9       VALUES OF N\n*> 3                 NUMBER OF VALUES OF ALPHA\n*> 0.0 1.0 0.7       VALUES OF ALPHA\n*> 3                 NUMBER OF VALUES OF BETA\n*> 0.0 1.0 1.3       VALUES OF BETA\n*> SGEMM  T PUT F FOR NO TEST. SAME COLUMNS.\n*> SSYMM  T PUT F FOR NO TEST. SAME COLUMNS.\n*> STRMM  T PUT F FOR NO TEST. SAME COLUMNS.\n*> STRSM  T PUT F FOR NO TEST. SAME COLUMNS.\n*> SSYRK  T PUT F FOR NO TEST. SAME COLUMNS.\n*> SSYR2K T PUT F FOR NO TEST. SAME COLUMNS.\n*>\n*> Further Details\n*> ===============\n*>\n*> See:\n*>\n*>    Dongarra J. J., Du Croz J. J., Duff I. S. and Hammarling S.\n*>    A Set of Level 3 Basic Linear Algebra Subprograms.\n*>\n*>    Technical Memorandum No.88 (Revision 1), Mathematics and\n*>    Computer Science Division, Argonne National Laboratory, 9700\n*>    South Cass Avenue, Argonne, Illinois 60439, US.\n*>\n*> -- Written on 8-February-1989.\n*>    Jack Dongarra, Argonne National Laboratory.\n*>    Iain Duff, AERE Harwell.\n*>    Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*>    Sven Hammarling, Numerical Algorithms Group Ltd.\n*>\n*>    10-9-00:  Change STATUS='NEW' to 'UNKNOWN' so that the testers\n*>              can be run multiple times without deleting generated\n*>              output files (susan)\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date April 2012\n*\n*> \\ingroup single_blas_testing\n*\n*  =====================================================================\n      PROGRAM SBLAT3\n*\n*  -- Reference BLAS test routine (version 3.4.1) --\n*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     April 2012\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      INTEGER            NIN\n      PARAMETER          ( NIN = 5 )\n      INTEGER            NSUBS\n      PARAMETER          ( NSUBS = 6 )\n      REAL               ZERO, ONE\n      PARAMETER          ( ZERO = 0.0, ONE = 1.0 )\n      INTEGER            NMAX\n      PARAMETER          ( NMAX = 65 )\n      INTEGER            NIDMAX, NALMAX, NBEMAX\n      PARAMETER          ( NIDMAX = 9, NALMAX = 7, NBEMAX = 7 )\n*     .. Local Scalars ..\n      REAL               EPS, ERR, THRESH\n      INTEGER            I, ISNUM, J, N, NALF, NBET, NIDIM, NOUT, NTRA\n      LOGICAL            FATAL, LTESTT, REWI, SAME, SFATAL, TRACE,\n     $                   TSTERR\n      CHARACTER*1        TRANSA, TRANSB\n      CHARACTER*6        SNAMET\n      CHARACTER*32       SNAPS, SUMMRY\n*     .. Local Arrays ..\n      REAL               AA( NMAX*NMAX ), AB( NMAX, 2*NMAX ),\n     $                   ALF( NALMAX ), AS( NMAX*NMAX ),\n     $                   BB( NMAX*NMAX ), BET( NBEMAX ),\n     $                   BS( NMAX*NMAX ), C( NMAX, NMAX ),\n     $                   CC( NMAX*NMAX ), CS( NMAX*NMAX ), CT( NMAX ),\n     $                   G( NMAX ), W( 2*NMAX )\n      INTEGER            IDIM( NIDMAX )\n      LOGICAL            LTEST( NSUBS )\n      CHARACTER*6        SNAMES( NSUBS )\n*     .. External Functions ..\n      REAL               SDIFF\n      LOGICAL            LSE\n      EXTERNAL           SDIFF, LSE\n*     .. External Subroutines ..\n      EXTERNAL           SCHK1, SCHK2, SCHK3, SCHK4, SCHK5, SCHKE, SMMCH\n*     .. Intrinsic Functions ..\n      INTRINSIC          MAX, MIN\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n      CHARACTER*6        SRNAMT\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n      COMMON             /SRNAMC/SRNAMT\n*     .. Data statements ..\n      DATA               SNAMES/'SGEMM ', 'SSYMM ', 'STRMM ', 'STRSM ',\n     $                   'SSYRK ', 'SSYR2K'/\n*     .. Executable Statements ..\n*\n*     Read name and unit number for summary output file and open file.\n*\n      READ( NIN, FMT = * )SUMMRY\n      READ( NIN, FMT = * )NOUT\n      OPEN( NOUT, FILE = SUMMRY )\n      NOUTC = NOUT\n*\n*     Read name and unit number for snapshot output file and open file.\n*\n      READ( NIN, FMT = * )SNAPS\n      READ( NIN, FMT = * )NTRA\n      TRACE = NTRA.GE.0\n      IF( TRACE )THEN\n         OPEN( NTRA, FILE = SNAPS )\n      END IF\n*     Read the flag that directs rewinding of the snapshot file.\n      READ( NIN, FMT = * )REWI\n      REWI = REWI.AND.TRACE\n*     Read the flag that directs stopping on any failure.\n      READ( NIN, FMT = * )SFATAL\n*     Read the flag that indicates whether error exits are to be tested.\n      READ( NIN, FMT = * )TSTERR\n*     Read the threshold value of the test ratio\n      READ( NIN, FMT = * )THRESH\n*\n*     Read and check the parameter values for the tests.\n*\n*     Values of N\n      READ( NIN, FMT = * )NIDIM\n      IF( NIDIM.LT.1.OR.NIDIM.GT.NIDMAX )THEN\n         WRITE( NOUT, FMT = 9997 )'N', NIDMAX\n         GO TO 220\n      END IF\n      READ( NIN, FMT = * )( IDIM( I ), I = 1, NIDIM )\n      DO 10 I = 1, NIDIM\n         IF( IDIM( I ).LT.0.OR.IDIM( I ).GT.NMAX )THEN\n            WRITE( NOUT, FMT = 9996 )NMAX\n            GO TO 220\n         END IF\n   10 CONTINUE\n*     Values of ALPHA\n      READ( NIN, FMT = * )NALF\n      IF( NALF.LT.1.OR.NALF.GT.NALMAX )THEN\n         WRITE( NOUT, FMT = 9997 )'ALPHA', NALMAX\n         GO TO 220\n      END IF\n      READ( NIN, FMT = * )( ALF( I ), I = 1, NALF )\n*     Values of BETA\n      READ( NIN, FMT = * )NBET\n      IF( NBET.LT.1.OR.NBET.GT.NBEMAX )THEN\n         WRITE( NOUT, FMT = 9997 )'BETA', NBEMAX\n         GO TO 220\n      END IF\n      READ( NIN, FMT = * )( BET( I ), I = 1, NBET )\n*\n*     Report values of parameters.\n*\n      WRITE( NOUT, FMT = 9995 )\n      WRITE( NOUT, FMT = 9994 )( IDIM( I ), I = 1, NIDIM )\n      WRITE( NOUT, FMT = 9993 )( ALF( I ), I = 1, NALF )\n      WRITE( NOUT, FMT = 9992 )( BET( I ), I = 1, NBET )\n      IF( .NOT.TSTERR )THEN\n         WRITE( NOUT, FMT = * )\n         WRITE( NOUT, FMT = 9984 )\n      END IF\n      WRITE( NOUT, FMT = * )\n      WRITE( NOUT, FMT = 9999 )THRESH\n      WRITE( NOUT, FMT = * )\n*\n*     Read names of subroutines and flags which indicate\n*     whether they are to be tested.\n*\n      DO 20 I = 1, NSUBS\n         LTEST( I ) = .FALSE.\n   20 CONTINUE\n   30 READ( NIN, FMT = 9988, END = 60 )SNAMET, LTESTT\n      DO 40 I = 1, NSUBS\n         IF( SNAMET.EQ.SNAMES( I ) )\n     $      GO TO 50\n   40 CONTINUE\n      WRITE( NOUT, FMT = 9990 )SNAMET\n      STOP\n   50 LTEST( I ) = LTESTT\n      GO TO 30\n*\n   60 CONTINUE\n      CLOSE ( NIN )\n*\n*     Compute EPS (the machine precision).\n*\n      EPS = EPSILON(ZERO)\n      WRITE( NOUT, FMT = 9998 )EPS\n*\n*     Check the reliability of SMMCH using exact data.\n*\n      N = MIN( 32, NMAX )\n      DO 100 J = 1, N\n         DO 90 I = 1, N\n            AB( I, J ) = MAX( I - J + 1, 0 )\n   90    CONTINUE\n         AB( J, NMAX + 1 ) = J\n         AB( 1, NMAX + J ) = J\n         C( J, 1 ) = ZERO\n  100 CONTINUE\n      DO 110 J = 1, N\n         CC( J ) = J*( ( J + 1 )*J )/2 - ( ( J + 1 )*J*( J - 1 ) )/3\n  110 CONTINUE\n*     CC holds the exact result. On exit from SMMCH CT holds\n*     the result computed by SMMCH.\n      TRANSA = 'N'\n      TRANSB = 'N'\n      CALL SMMCH( TRANSA, TRANSB, N, 1, N, ONE, AB, NMAX,\n     $            AB( 1, NMAX + 1 ), NMAX, ZERO, C, NMAX, CT, G, CC,\n     $            NMAX, EPS, ERR, FATAL, NOUT, .TRUE. )\n      SAME = LSE( CC, CT, N )\n      IF( .NOT.SAME.OR.ERR.NE.ZERO )THEN\n         WRITE( NOUT, FMT = 9989 )TRANSA, TRANSB, SAME, ERR\n         STOP\n      END IF\n      TRANSB = 'T'\n      CALL SMMCH( TRANSA, TRANSB, N, 1, N, ONE, AB, NMAX,\n     $            AB( 1, NMAX + 1 ), NMAX, ZERO, C, NMAX, CT, G, CC,\n     $            NMAX, EPS, ERR, FATAL, NOUT, .TRUE. )\n      SAME = LSE( CC, CT, N )\n      IF( .NOT.SAME.OR.ERR.NE.ZERO )THEN\n         WRITE( NOUT, FMT = 9989 )TRANSA, TRANSB, SAME, ERR\n         STOP\n      END IF\n      DO 120 J = 1, N\n         AB( J, NMAX + 1 ) = N - J + 1\n         AB( 1, NMAX + J ) = N - J + 1\n  120 CONTINUE\n      DO 130 J = 1, N\n         CC( N - J + 1 ) = J*( ( J + 1 )*J )/2 -\n     $                     ( ( J + 1 )*J*( J - 1 ) )/3\n  130 CONTINUE\n      TRANSA = 'T'\n      TRANSB = 'N'\n      CALL SMMCH( TRANSA, TRANSB, N, 1, N, ONE, AB, NMAX,\n     $            AB( 1, NMAX + 1 ), NMAX, ZERO, C, NMAX, CT, G, CC,\n     $            NMAX, EPS, ERR, FATAL, NOUT, .TRUE. )\n      SAME = LSE( CC, CT, N )\n      IF( .NOT.SAME.OR.ERR.NE.ZERO )THEN\n         WRITE( NOUT, FMT = 9989 )TRANSA, TRANSB, SAME, ERR\n         STOP\n      END IF\n      TRANSB = 'T'\n      CALL SMMCH( TRANSA, TRANSB, N, 1, N, ONE, AB, NMAX,\n     $            AB( 1, NMAX + 1 ), NMAX, ZERO, C, NMAX, CT, G, CC,\n     $            NMAX, EPS, ERR, FATAL, NOUT, .TRUE. )\n      SAME = LSE( CC, CT, N )\n      IF( .NOT.SAME.OR.ERR.NE.ZERO )THEN\n         WRITE( NOUT, FMT = 9989 )TRANSA, TRANSB, SAME, ERR\n         STOP\n      END IF\n*\n*     Test each subroutine in turn.\n*\n      DO 200 ISNUM = 1, NSUBS\n         WRITE( NOUT, FMT = * )\n         IF( .NOT.LTEST( ISNUM ) )THEN\n*           Subprogram is not to be tested.\n            WRITE( NOUT, FMT = 9987 )SNAMES( ISNUM )\n         ELSE\n            SRNAMT = SNAMES( ISNUM )\n*           Test error exits.\n            IF( TSTERR )THEN\n               CALL SCHKE( ISNUM, SNAMES( ISNUM ), NOUT )\n               WRITE( NOUT, FMT = * )\n            END IF\n*           Test computations.\n            INFOT = 0\n            OK = .TRUE.\n            FATAL = .FALSE.\n            GO TO ( 140, 150, 160, 160, 170, 180 )ISNUM\n*           Test SGEMM, 01.\n  140       CALL SCHK1( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET,\n     $                  NMAX, AB, AA, AS, AB( 1, NMAX + 1 ), BB, BS, C,\n     $                  CC, CS, CT, G )\n            GO TO 190\n*           Test SSYMM, 02.\n  150       CALL SCHK2( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET,\n     $                  NMAX, AB, AA, AS, AB( 1, NMAX + 1 ), BB, BS, C,\n     $                  CC, CS, CT, G )\n            GO TO 190\n*           Test STRMM, 03, STRSM, 04.\n  160       CALL SCHK3( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NALF, ALF, NMAX, AB,\n     $                  AA, AS, AB( 1, NMAX + 1 ), BB, BS, CT, G, C )\n            GO TO 190\n*           Test SSYRK, 05.\n  170       CALL SCHK4( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET,\n     $                  NMAX, AB, AA, AS, AB( 1, NMAX + 1 ), BB, BS, C,\n     $                  CC, CS, CT, G )\n            GO TO 190\n*           Test SSYR2K, 06.\n  180       CALL SCHK5( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET,\n     $                  NMAX, AB, AA, AS, BB, BS, C, CC, CS, CT, G, W )\n            GO TO 190\n*\n  190       IF( FATAL.AND.SFATAL )\n     $         GO TO 210\n         END IF\n  200 CONTINUE\n      WRITE( NOUT, FMT = 9986 )\n      GO TO 230\n*\n  210 CONTINUE\n      WRITE( NOUT, FMT = 9985 )\n      GO TO 230\n*\n  220 CONTINUE\n      WRITE( NOUT, FMT = 9991 )\n*\n  230 CONTINUE\n      IF( TRACE )\n     $   CLOSE ( NTRA )\n      CLOSE ( NOUT )\n      STOP\n*\n 9999 FORMAT( ' ROUTINES PASS COMPUTATIONAL TESTS IF TEST RATIO IS LES',\n     $      'S THAN', F8.2 )\n 9998 FORMAT( ' RELATIVE MACHINE PRECISION IS TAKEN TO BE', 1P, E9.1 )\n 9997 FORMAT( ' NUMBER OF VALUES OF ', A, ' IS LESS THAN 1 OR GREATER ',\n     $      'THAN ', I2 )\n 9996 FORMAT( ' VALUE OF N IS LESS THAN 0 OR GREATER THAN ', I2 )\n 9995 FORMAT( ' TESTS OF THE REAL             LEVEL 3 BLAS', //' THE F',\n     $      'OLLOWING PARAMETER VALUES WILL BE USED:' )\n 9994 FORMAT( '   FOR N              ', 9I6 )\n 9993 FORMAT( '   FOR ALPHA          ', 7F6.1 )\n 9992 FORMAT( '   FOR BETA           ', 7F6.1 )\n 9991 FORMAT( ' AMEND DATA FILE OR INCREASE ARRAY SIZES IN PROGRAM',\n     $      /' ******* TESTS ABANDONED *******' )\n 9990 FORMAT( ' SUBPROGRAM NAME ', A6, ' NOT RECOGNIZED', /' ******* T',\n     $      'ESTS ABANDONED *******' )\n 9989 FORMAT( ' ERROR IN SMMCH -  IN-LINE DOT PRODUCTS ARE BEING EVALU',\n     $      'ATED WRONGLY.', /' SMMCH WAS CALLED WITH TRANSA = ', A1,\n     $      ' AND TRANSB = ', A1, /' AND RETURNED SAME = ', L1, ' AND ',\n     $      'ERR = ', F12.3, '.', /' THIS MAY BE DUE TO FAULTS IN THE ',\n     $      'ARITHMETIC OR THE COMPILER.', /' ******* TESTS ABANDONED ',\n     $      '*******' )\n 9988 FORMAT( A6, L2 )\n 9987 FORMAT( 1X, A6, ' WAS NOT TESTED' )\n 9986 FORMAT( /' END OF TESTS' )\n 9985 FORMAT( /' ******* FATAL ERROR - TESTS ABANDONED *******' )\n 9984 FORMAT( ' ERROR-EXITS WILL NOT BE TESTED' )\n*\n*     End of SBLAT3.\n*\n      END\n      SUBROUTINE SCHK1( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET, NMAX,\n     $                  A, AA, AS, B, BB, BS, C, CC, CS, CT, G )\n*\n*  Tests SGEMM.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Parameters ..\n      REAL               ZERO\n      PARAMETER          ( ZERO = 0.0 )\n*     .. Scalar Arguments ..\n      REAL               EPS, THRESH\n      INTEGER            NALF, NBET, NIDIM, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      REAL               A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), B( NMAX, NMAX ),\n     $                   BB( NMAX*NMAX ), BET( NBET ), BS( NMAX*NMAX ),\n     $                   C( NMAX, NMAX ), CC( NMAX*NMAX ),\n     $                   CS( NMAX*NMAX ), CT( NMAX ), G( NMAX )\n      INTEGER            IDIM( NIDIM )\n*     .. Local Scalars ..\n      REAL               ALPHA, ALS, BETA, BLS, ERR, ERRMAX\n      INTEGER            I, IA, IB, ICA, ICB, IK, IM, IN, K, KS, LAA,\n     $                   LBB, LCC, LDA, LDAS, LDB, LDBS, LDC, LDCS, M,\n     $                   MA, MB, MS, N, NA, NARGS, NB, NC, NS\n      LOGICAL            NULL, RESET, SAME, TRANA, TRANB\n      CHARACTER*1        TRANAS, TRANBS, TRANSA, TRANSB\n      CHARACTER*3        ICH\n*     .. Local Arrays ..\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LSE, LSERES\n      EXTERNAL           LSE, LSERES\n*     .. External Subroutines ..\n      EXTERNAL           SGEMM, SMAKE, SMMCH\n*     .. Intrinsic Functions ..\n      INTRINSIC          MAX\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICH/'NTC'/\n*     .. Executable Statements ..\n*\n      NARGS = 13\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = ZERO\n*\n      DO 110 IM = 1, NIDIM\n         M = IDIM( IM )\n*\n         DO 100 IN = 1, NIDIM\n            N = IDIM( IN )\n*           Set LDC to 1 more than minimum value if room.\n            LDC = M\n            IF( LDC.LT.NMAX )\n     $         LDC = LDC + 1\n*           Skip tests if not enough room.\n            IF( LDC.GT.NMAX )\n     $         GO TO 100\n            LCC = LDC*N\n            NULL = N.LE.0.OR.M.LE.0\n*\n            DO 90 IK = 1, NIDIM\n               K = IDIM( IK )\n*\n               DO 80 ICA = 1, 3\n                  TRANSA = ICH( ICA: ICA )\n                  TRANA = TRANSA.EQ.'T'.OR.TRANSA.EQ.'C'\n*\n                  IF( TRANA )THEN\n                     MA = K\n                     NA = M\n                  ELSE\n                     MA = M\n                     NA = K\n                  END IF\n*                 Set LDA to 1 more than minimum value if room.\n                  LDA = MA\n                  IF( LDA.LT.NMAX )\n     $               LDA = LDA + 1\n*                 Skip tests if not enough room.\n                  IF( LDA.GT.NMAX )\n     $               GO TO 80\n                  LAA = LDA*NA\n*\n*                 Generate the matrix A.\n*\n                  CALL SMAKE( 'GE', ' ', ' ', MA, NA, A, NMAX, AA, LDA,\n     $                        RESET, ZERO )\n*\n                  DO 70 ICB = 1, 3\n                     TRANSB = ICH( ICB: ICB )\n                     TRANB = TRANSB.EQ.'T'.OR.TRANSB.EQ.'C'\n*\n                     IF( TRANB )THEN\n                        MB = N\n                        NB = K\n                     ELSE\n                        MB = K\n                        NB = N\n                     END IF\n*                    Set LDB to 1 more than minimum value if room.\n                     LDB = MB\n                     IF( LDB.LT.NMAX )\n     $                  LDB = LDB + 1\n*                    Skip tests if not enough room.\n                     IF( LDB.GT.NMAX )\n     $                  GO TO 70\n                     LBB = LDB*NB\n*\n*                    Generate the matrix B.\n*\n                     CALL SMAKE( 'GE', ' ', ' ', MB, NB, B, NMAX, BB,\n     $                           LDB, RESET, ZERO )\n*\n                     DO 60 IA = 1, NALF\n                        ALPHA = ALF( IA )\n*\n                        DO 50 IB = 1, NBET\n                           BETA = BET( IB )\n*\n*                          Generate the matrix C.\n*\n                           CALL SMAKE( 'GE', ' ', ' ', M, N, C, NMAX,\n     $                                 CC, LDC, RESET, ZERO )\n*\n                           NC = NC + 1\n*\n*                          Save every datum before calling the\n*                          subroutine.\n*\n                           TRANAS = TRANSA\n                           TRANBS = TRANSB\n                           MS = M\n                           NS = N\n                           KS = K\n                           ALS = ALPHA\n                           DO 10 I = 1, LAA\n                              AS( I ) = AA( I )\n   10                      CONTINUE\n                           LDAS = LDA\n                           DO 20 I = 1, LBB\n                              BS( I ) = BB( I )\n   20                      CONTINUE\n                           LDBS = LDB\n                           BLS = BETA\n                           DO 30 I = 1, LCC\n                              CS( I ) = CC( I )\n   30                      CONTINUE\n                           LDCS = LDC\n*\n*                          Call the subroutine.\n*\n                           IF( TRACE )\n     $                        WRITE( NTRA, FMT = 9995 )NC, SNAME,\n     $                        TRANSA, TRANSB, M, N, K, ALPHA, LDA, LDB,\n     $                        BETA, LDC\n                           IF( REWI )\n     $                        REWIND NTRA\n                           CALL SGEMM( TRANSA, TRANSB, M, N, K, ALPHA,\n     $                                 AA, LDA, BB, LDB, BETA, CC, LDC )\n*\n*                          Check if error-exit was taken incorrectly.\n*\n                           IF( .NOT.OK )THEN\n                              WRITE( NOUT, FMT = 9994 )\n                              FATAL = .TRUE.\n                              GO TO 120\n                           END IF\n*\n*                          See what data changed inside subroutines.\n*\n                           ISAME( 1 ) = TRANSA.EQ.TRANAS\n                           ISAME( 2 ) = TRANSB.EQ.TRANBS\n                           ISAME( 3 ) = MS.EQ.M\n                           ISAME( 4 ) = NS.EQ.N\n                           ISAME( 5 ) = KS.EQ.K\n                           ISAME( 6 ) = ALS.EQ.ALPHA\n                           ISAME( 7 ) = LSE( AS, AA, LAA )\n                           ISAME( 8 ) = LDAS.EQ.LDA\n                           ISAME( 9 ) = LSE( BS, BB, LBB )\n                           ISAME( 10 ) = LDBS.EQ.LDB\n                           ISAME( 11 ) = BLS.EQ.BETA\n                           IF( NULL )THEN\n                              ISAME( 12 ) = LSE( CS, CC, LCC )\n                           ELSE\n                              ISAME( 12 ) = LSERES( 'GE', ' ', M, N, CS,\n     $                                      CC, LDC )\n                           END IF\n                           ISAME( 13 ) = LDCS.EQ.LDC\n*\n*                          If data was incorrectly changed, report\n*                          and return.\n*\n                           SAME = .TRUE.\n                           DO 40 I = 1, NARGS\n                              SAME = SAME.AND.ISAME( I )\n                              IF( .NOT.ISAME( I ) )\n     $                           WRITE( NOUT, FMT = 9998 )I\n   40                      CONTINUE\n                           IF( .NOT.SAME )THEN\n                              FATAL = .TRUE.\n                              GO TO 120\n                           END IF\n*\n                           IF( .NOT.NULL )THEN\n*\n*                             Check the result.\n*\n                              CALL SMMCH( TRANSA, TRANSB, M, N, K,\n     $                                    ALPHA, A, NMAX, B, NMAX, BETA,\n     $                                    C, NMAX, CT, G, CC, LDC, EPS,\n     $                                    ERR, FATAL, NOUT, .TRUE. )\n                              ERRMAX = MAX( ERRMAX, ERR )\n*                             If got really bad answer, report and\n*                             return.\n                              IF( FATAL )\n     $                           GO TO 120\n                           END IF\n*\n   50                   CONTINUE\n*\n   60                CONTINUE\n*\n   70             CONTINUE\n*\n   80          CONTINUE\n*\n   90       CONTINUE\n*\n  100    CONTINUE\n*\n  110 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 130\n*\n  120 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      WRITE( NOUT, FMT = 9995 )NC, SNAME, TRANSA, TRANSB, M, N, K,\n     $   ALPHA, LDA, LDB, BETA, LDC\n*\n  130 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',''', A1, ''',',\n     $      3( I3, ',' ), F4.1, ', A,', I3, ', B,', I3, ',', F4.1, ', ',\n     $      'C,', I3, ').' )\n 9994 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of SCHK1.\n*\n      END\n      SUBROUTINE SCHK2( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET, NMAX,\n     $                  A, AA, AS, B, BB, BS, C, CC, CS, CT, G )\n*\n*  Tests SSYMM.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Parameters ..\n      REAL               ZERO\n      PARAMETER          ( ZERO = 0.0 )\n*     .. Scalar Arguments ..\n      REAL               EPS, THRESH\n      INTEGER            NALF, NBET, NIDIM, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      REAL               A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), B( NMAX, NMAX ),\n     $                   BB( NMAX*NMAX ), BET( NBET ), BS( NMAX*NMAX ),\n     $                   C( NMAX, NMAX ), CC( NMAX*NMAX ),\n     $                   CS( NMAX*NMAX ), CT( NMAX ), G( NMAX )\n      INTEGER            IDIM( NIDIM )\n*     .. Local Scalars ..\n      REAL               ALPHA, ALS, BETA, BLS, ERR, ERRMAX\n      INTEGER            I, IA, IB, ICS, ICU, IM, IN, LAA, LBB, LCC,\n     $                   LDA, LDAS, LDB, LDBS, LDC, LDCS, M, MS, N, NA,\n     $                   NARGS, NC, NS\n      LOGICAL            LEFT, NULL, RESET, SAME\n      CHARACTER*1        SIDE, SIDES, UPLO, UPLOS\n      CHARACTER*2        ICHS, ICHU\n*     .. Local Arrays ..\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LSE, LSERES\n      EXTERNAL           LSE, LSERES\n*     .. External Subroutines ..\n      EXTERNAL           SMAKE, SMMCH, SSYMM\n*     .. Intrinsic Functions ..\n      INTRINSIC          MAX\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICHS/'LR'/, ICHU/'UL'/\n*     .. Executable Statements ..\n*\n      NARGS = 12\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = ZERO\n*\n      DO 100 IM = 1, NIDIM\n         M = IDIM( IM )\n*\n         DO 90 IN = 1, NIDIM\n            N = IDIM( IN )\n*           Set LDC to 1 more than minimum value if room.\n            LDC = M\n            IF( LDC.LT.NMAX )\n     $         LDC = LDC + 1\n*           Skip tests if not enough room.\n            IF( LDC.GT.NMAX )\n     $         GO TO 90\n            LCC = LDC*N\n            NULL = N.LE.0.OR.M.LE.0\n*\n*           Set LDB to 1 more than minimum value if room.\n            LDB = M\n            IF( LDB.LT.NMAX )\n     $         LDB = LDB + 1\n*           Skip tests if not enough room.\n            IF( LDB.GT.NMAX )\n     $         GO TO 90\n            LBB = LDB*N\n*\n*           Generate the matrix B.\n*\n            CALL SMAKE( 'GE', ' ', ' ', M, N, B, NMAX, BB, LDB, RESET,\n     $                  ZERO )\n*\n            DO 80 ICS = 1, 2\n               SIDE = ICHS( ICS: ICS )\n               LEFT = SIDE.EQ.'L'\n*\n               IF( LEFT )THEN\n                  NA = M\n               ELSE\n                  NA = N\n               END IF\n*              Set LDA to 1 more than minimum value if room.\n               LDA = NA\n               IF( LDA.LT.NMAX )\n     $            LDA = LDA + 1\n*              Skip tests if not enough room.\n               IF( LDA.GT.NMAX )\n     $            GO TO 80\n               LAA = LDA*NA\n*\n               DO 70 ICU = 1, 2\n                  UPLO = ICHU( ICU: ICU )\n*\n*                 Generate the symmetric matrix A.\n*\n                  CALL SMAKE( 'SY', UPLO, ' ', NA, NA, A, NMAX, AA, LDA,\n     $                        RESET, ZERO )\n*\n                  DO 60 IA = 1, NALF\n                     ALPHA = ALF( IA )\n*\n                     DO 50 IB = 1, NBET\n                        BETA = BET( IB )\n*\n*                       Generate the matrix C.\n*\n                        CALL SMAKE( 'GE', ' ', ' ', M, N, C, NMAX, CC,\n     $                              LDC, RESET, ZERO )\n*\n                        NC = NC + 1\n*\n*                       Save every datum before calling the\n*                       subroutine.\n*\n                        SIDES = SIDE\n                        UPLOS = UPLO\n                        MS = M\n                        NS = N\n                        ALS = ALPHA\n                        DO 10 I = 1, LAA\n                           AS( I ) = AA( I )\n   10                   CONTINUE\n                        LDAS = LDA\n                        DO 20 I = 1, LBB\n                           BS( I ) = BB( I )\n   20                   CONTINUE\n                        LDBS = LDB\n                        BLS = BETA\n                        DO 30 I = 1, LCC\n                           CS( I ) = CC( I )\n   30                   CONTINUE\n                        LDCS = LDC\n*\n*                       Call the subroutine.\n*\n                        IF( TRACE )\n     $                     WRITE( NTRA, FMT = 9995 )NC, SNAME, SIDE,\n     $                     UPLO, M, N, ALPHA, LDA, LDB, BETA, LDC\n                        IF( REWI )\n     $                     REWIND NTRA\n                        CALL SSYMM( SIDE, UPLO, M, N, ALPHA, AA, LDA,\n     $                              BB, LDB, BETA, CC, LDC )\n*\n*                       Check if error-exit was taken incorrectly.\n*\n                        IF( .NOT.OK )THEN\n                           WRITE( NOUT, FMT = 9994 )\n                           FATAL = .TRUE.\n                           GO TO 110\n                        END IF\n*\n*                       See what data changed inside subroutines.\n*\n                        ISAME( 1 ) = SIDES.EQ.SIDE\n                        ISAME( 2 ) = UPLOS.EQ.UPLO\n                        ISAME( 3 ) = MS.EQ.M\n                        ISAME( 4 ) = NS.EQ.N\n                        ISAME( 5 ) = ALS.EQ.ALPHA\n                        ISAME( 6 ) = LSE( AS, AA, LAA )\n                        ISAME( 7 ) = LDAS.EQ.LDA\n                        ISAME( 8 ) = LSE( BS, BB, LBB )\n                        ISAME( 9 ) = LDBS.EQ.LDB\n                        ISAME( 10 ) = BLS.EQ.BETA\n                        IF( NULL )THEN\n                           ISAME( 11 ) = LSE( CS, CC, LCC )\n                        ELSE\n                           ISAME( 11 ) = LSERES( 'GE', ' ', M, N, CS,\n     $                                   CC, LDC )\n                        END IF\n                        ISAME( 12 ) = LDCS.EQ.LDC\n*\n*                       If data was incorrectly changed, report and\n*                       return.\n*\n                        SAME = .TRUE.\n                        DO 40 I = 1, NARGS\n                           SAME = SAME.AND.ISAME( I )\n                           IF( .NOT.ISAME( I ) )\n     $                        WRITE( NOUT, FMT = 9998 )I\n   40                   CONTINUE\n                        IF( .NOT.SAME )THEN\n                           FATAL = .TRUE.\n                           GO TO 110\n                        END IF\n*\n                        IF( .NOT.NULL )THEN\n*\n*                          Check the result.\n*\n                           IF( LEFT )THEN\n                              CALL SMMCH( 'N', 'N', M, N, M, ALPHA, A,\n     $                                    NMAX, B, NMAX, BETA, C, NMAX,\n     $                                    CT, G, CC, LDC, EPS, ERR,\n     $                                    FATAL, NOUT, .TRUE. )\n                           ELSE\n                              CALL SMMCH( 'N', 'N', M, N, N, ALPHA, B,\n     $                                    NMAX, A, NMAX, BETA, C, NMAX,\n     $                                    CT, G, CC, LDC, EPS, ERR,\n     $                                    FATAL, NOUT, .TRUE. )\n                           END IF\n                           ERRMAX = MAX( ERRMAX, ERR )\n*                          If got really bad answer, report and\n*                          return.\n                           IF( FATAL )\n     $                        GO TO 110\n                        END IF\n*\n   50                CONTINUE\n*\n   60             CONTINUE\n*\n   70          CONTINUE\n*\n   80       CONTINUE\n*\n   90    CONTINUE\n*\n  100 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 120\n*\n  110 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      WRITE( NOUT, FMT = 9995 )NC, SNAME, SIDE, UPLO, M, N, ALPHA, LDA,\n     $   LDB, BETA, LDC\n*\n  120 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( 1X, I6, ': ', A6, '(', 2( '''', A1, ''',' ), 2( I3, ',' ),\n     $      F4.1, ', A,', I3, ', B,', I3, ',', F4.1, ', C,', I3, ')   ',\n     $      ' .' )\n 9994 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of SCHK2.\n*\n      END\n      SUBROUTINE SCHK3( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NALF, ALF, NMAX, A, AA, AS,\n     $                  B, BB, BS, CT, G, C )\n*\n*  Tests STRMM and STRSM.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Parameters ..\n      REAL               ZERO, ONE\n      PARAMETER          ( ZERO = 0.0, ONE = 1.0 )\n*     .. Scalar Arguments ..\n      REAL               EPS, THRESH\n      INTEGER            NALF, NIDIM, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      REAL               A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), B( NMAX, NMAX ),\n     $                   BB( NMAX*NMAX ), BS( NMAX*NMAX ),\n     $                   C( NMAX, NMAX ), CT( NMAX ), G( NMAX )\n      INTEGER            IDIM( NIDIM )\n*     .. Local Scalars ..\n      REAL               ALPHA, ALS, ERR, ERRMAX\n      INTEGER            I, IA, ICD, ICS, ICT, ICU, IM, IN, J, LAA, LBB,\n     $                   LDA, LDAS, LDB, LDBS, M, MS, N, NA, NARGS, NC,\n     $                   NS\n      LOGICAL            LEFT, NULL, RESET, SAME\n      CHARACTER*1        DIAG, DIAGS, SIDE, SIDES, TRANAS, TRANSA, UPLO,\n     $                   UPLOS\n      CHARACTER*2        ICHD, ICHS, ICHU\n      CHARACTER*3        ICHT\n*     .. Local Arrays ..\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LSE, LSERES\n      EXTERNAL           LSE, LSERES\n*     .. External Subroutines ..\n      EXTERNAL           SMAKE, SMMCH, STRMM, STRSM\n*     .. Intrinsic Functions ..\n      INTRINSIC          MAX\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICHU/'UL'/, ICHT/'NTC'/, ICHD/'UN'/, ICHS/'LR'/\n*     .. Executable Statements ..\n*\n      NARGS = 11\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = ZERO\n*     Set up zero matrix for SMMCH.\n      DO 20 J = 1, NMAX\n         DO 10 I = 1, NMAX\n            C( I, J ) = ZERO\n   10    CONTINUE\n   20 CONTINUE\n*\n      DO 140 IM = 1, NIDIM\n         M = IDIM( IM )\n*\n         DO 130 IN = 1, NIDIM\n            N = IDIM( IN )\n*           Set LDB to 1 more than minimum value if room.\n            LDB = M\n            IF( LDB.LT.NMAX )\n     $         LDB = LDB + 1\n*           Skip tests if not enough room.\n            IF( LDB.GT.NMAX )\n     $         GO TO 130\n            LBB = LDB*N\n            NULL = M.LE.0.OR.N.LE.0\n*\n            DO 120 ICS = 1, 2\n               SIDE = ICHS( ICS: ICS )\n               LEFT = SIDE.EQ.'L'\n               IF( LEFT )THEN\n                  NA = M\n               ELSE\n                  NA = N\n               END IF\n*              Set LDA to 1 more than minimum value if room.\n               LDA = NA\n               IF( LDA.LT.NMAX )\n     $            LDA = LDA + 1\n*              Skip tests if not enough room.\n               IF( LDA.GT.NMAX )\n     $            GO TO 130\n               LAA = LDA*NA\n*\n               DO 110 ICU = 1, 2\n                  UPLO = ICHU( ICU: ICU )\n*\n                  DO 100 ICT = 1, 3\n                     TRANSA = ICHT( ICT: ICT )\n*\n                     DO 90 ICD = 1, 2\n                        DIAG = ICHD( ICD: ICD )\n*\n                        DO 80 IA = 1, NALF\n                           ALPHA = ALF( IA )\n*\n*                          Generate the matrix A.\n*\n                           CALL SMAKE( 'TR', UPLO, DIAG, NA, NA, A,\n     $                                 NMAX, AA, LDA, RESET, ZERO )\n*\n*                          Generate the matrix B.\n*\n                           CALL SMAKE( 'GE', ' ', ' ', M, N, B, NMAX,\n     $                                 BB, LDB, RESET, ZERO )\n*\n                           NC = NC + 1\n*\n*                          Save every datum before calling the\n*                          subroutine.\n*\n                           SIDES = SIDE\n                           UPLOS = UPLO\n                           TRANAS = TRANSA\n                           DIAGS = DIAG\n                           MS = M\n                           NS = N\n                           ALS = ALPHA\n                           DO 30 I = 1, LAA\n                              AS( I ) = AA( I )\n   30                      CONTINUE\n                           LDAS = LDA\n                           DO 40 I = 1, LBB\n                              BS( I ) = BB( I )\n   40                      CONTINUE\n                           LDBS = LDB\n*\n*                          Call the subroutine.\n*\n                           IF( SNAME( 4: 5 ).EQ.'MM' )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9995 )NC, SNAME,\n     $                           SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA,\n     $                           LDA, LDB\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL STRMM( SIDE, UPLO, TRANSA, DIAG, M,\n     $                                    N, ALPHA, AA, LDA, BB, LDB )\n                           ELSE IF( SNAME( 4: 5 ).EQ.'SM' )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9995 )NC, SNAME,\n     $                           SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA,\n     $                           LDA, LDB\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL STRSM( SIDE, UPLO, TRANSA, DIAG, M,\n     $                                    N, ALPHA, AA, LDA, BB, LDB )\n                           END IF\n*\n*                          Check if error-exit was taken incorrectly.\n*\n                           IF( .NOT.OK )THEN\n                              WRITE( NOUT, FMT = 9994 )\n                              FATAL = .TRUE.\n                              GO TO 150\n                           END IF\n*\n*                          See what data changed inside subroutines.\n*\n                           ISAME( 1 ) = SIDES.EQ.SIDE\n                           ISAME( 2 ) = UPLOS.EQ.UPLO\n                           ISAME( 3 ) = TRANAS.EQ.TRANSA\n                           ISAME( 4 ) = DIAGS.EQ.DIAG\n                           ISAME( 5 ) = MS.EQ.M\n                           ISAME( 6 ) = NS.EQ.N\n                           ISAME( 7 ) = ALS.EQ.ALPHA\n                           ISAME( 8 ) = LSE( AS, AA, LAA )\n                           ISAME( 9 ) = LDAS.EQ.LDA\n                           IF( NULL )THEN\n                              ISAME( 10 ) = LSE( BS, BB, LBB )\n                           ELSE\n                              ISAME( 10 ) = LSERES( 'GE', ' ', M, N, BS,\n     $                                      BB, LDB )\n                           END IF\n                           ISAME( 11 ) = LDBS.EQ.LDB\n*\n*                          If data was incorrectly changed, report and\n*                          return.\n*\n                           SAME = .TRUE.\n                           DO 50 I = 1, NARGS\n                              SAME = SAME.AND.ISAME( I )\n                              IF( .NOT.ISAME( I ) )\n     $                           WRITE( NOUT, FMT = 9998 )I\n   50                      CONTINUE\n                           IF( .NOT.SAME )THEN\n                              FATAL = .TRUE.\n                              GO TO 150\n                           END IF\n*\n                           IF( .NOT.NULL )THEN\n                              IF( SNAME( 4: 5 ).EQ.'MM' )THEN\n*\n*                                Check the result.\n*\n                                 IF( LEFT )THEN\n                                    CALL SMMCH( TRANSA, 'N', M, N, M,\n     $                                          ALPHA, A, NMAX, B, NMAX,\n     $                                          ZERO, C, NMAX, CT, G,\n     $                                          BB, LDB, EPS, ERR,\n     $                                          FATAL, NOUT, .TRUE. )\n                                 ELSE\n                                    CALL SMMCH( 'N', TRANSA, M, N, N,\n     $                                          ALPHA, B, NMAX, A, NMAX,\n     $                                          ZERO, C, NMAX, CT, G,\n     $                                          BB, LDB, EPS, ERR,\n     $                                          FATAL, NOUT, .TRUE. )\n                                 END IF\n                              ELSE IF( SNAME( 4: 5 ).EQ.'SM' )THEN\n*\n*                                Compute approximation to original\n*                                matrix.\n*\n                                 DO 70 J = 1, N\n                                    DO 60 I = 1, M\n                                       C( I, J ) = BB( I + ( J - 1 )*\n     $                                             LDB )\n                                       BB( I + ( J - 1 )*LDB ) = ALPHA*\n     $                                    B( I, J )\n   60                               CONTINUE\n   70                            CONTINUE\n*\n                                 IF( LEFT )THEN\n                                    CALL SMMCH( TRANSA, 'N', M, N, M,\n     $                                          ONE, A, NMAX, C, NMAX,\n     $                                          ZERO, B, NMAX, CT, G,\n     $                                          BB, LDB, EPS, ERR,\n     $                                          FATAL, NOUT, .FALSE. )\n                                 ELSE\n                                    CALL SMMCH( 'N', TRANSA, M, N, N,\n     $                                          ONE, C, NMAX, A, NMAX,\n     $                                          ZERO, B, NMAX, CT, G,\n     $                                          BB, LDB, EPS, ERR,\n     $                                          FATAL, NOUT, .FALSE. )\n                                 END IF\n                              END IF\n                              ERRMAX = MAX( ERRMAX, ERR )\n*                             If got really bad answer, report and\n*                             return.\n                              IF( FATAL )\n     $                           GO TO 150\n                           END IF\n*\n   80                   CONTINUE\n*\n   90                CONTINUE\n*\n  100             CONTINUE\n*\n  110          CONTINUE\n*\n  120       CONTINUE\n*\n  130    CONTINUE\n*\n  140 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 160\n*\n  150 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      WRITE( NOUT, FMT = 9995 )NC, SNAME, SIDE, UPLO, TRANSA, DIAG, M,\n     $   N, ALPHA, LDA, LDB\n*\n  160 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( 1X, I6, ': ', A6, '(', 4( '''', A1, ''',' ), 2( I3, ',' ),\n     $      F4.1, ', A,', I3, ', B,', I3, ')        .' )\n 9994 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of SCHK3.\n*\n      END\n      SUBROUTINE SCHK4( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET, NMAX,\n     $                  A, AA, AS, B, BB, BS, C, CC, CS, CT, G )\n*\n*  Tests SSYRK.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Parameters ..\n      REAL               ZERO\n      PARAMETER          ( ZERO = 0.0 )\n*     .. Scalar Arguments ..\n      REAL               EPS, THRESH\n      INTEGER            NALF, NBET, NIDIM, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      REAL               A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), B( NMAX, NMAX ),\n     $                   BB( NMAX*NMAX ), BET( NBET ), BS( NMAX*NMAX ),\n     $                   C( NMAX, NMAX ), CC( NMAX*NMAX ),\n     $                   CS( NMAX*NMAX ), CT( NMAX ), G( NMAX )\n      INTEGER            IDIM( NIDIM )\n*     .. Local Scalars ..\n      REAL               ALPHA, ALS, BETA, BETS, ERR, ERRMAX\n      INTEGER            I, IA, IB, ICT, ICU, IK, IN, J, JC, JJ, K, KS,\n     $                   LAA, LCC, LDA, LDAS, LDC, LDCS, LJ, MA, N, NA,\n     $                   NARGS, NC, NS\n      LOGICAL            NULL, RESET, SAME, TRAN, UPPER\n      CHARACTER*1        TRANS, TRANSS, UPLO, UPLOS\n      CHARACTER*2        ICHU\n      CHARACTER*3        ICHT\n*     .. Local Arrays ..\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LSE, LSERES\n      EXTERNAL           LSE, LSERES\n*     .. External Subroutines ..\n      EXTERNAL           SMAKE, SMMCH, SSYRK\n*     .. Intrinsic Functions ..\n      INTRINSIC          MAX\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICHT/'NTC'/, ICHU/'UL'/\n*     .. Executable Statements ..\n*\n      NARGS = 10\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = ZERO\n*\n      DO 100 IN = 1, NIDIM\n         N = IDIM( IN )\n*        Set LDC to 1 more than minimum value if room.\n         LDC = N\n         IF( LDC.LT.NMAX )\n     $      LDC = LDC + 1\n*        Skip tests if not enough room.\n         IF( LDC.GT.NMAX )\n     $      GO TO 100\n         LCC = LDC*N\n         NULL = N.LE.0\n*\n         DO 90 IK = 1, NIDIM\n            K = IDIM( IK )\n*\n            DO 80 ICT = 1, 3\n               TRANS = ICHT( ICT: ICT )\n               TRAN = TRANS.EQ.'T'.OR.TRANS.EQ.'C'\n               IF( TRAN )THEN\n                  MA = K\n                  NA = N\n               ELSE\n                  MA = N\n                  NA = K\n               END IF\n*              Set LDA to 1 more than minimum value if room.\n               LDA = MA\n               IF( LDA.LT.NMAX )\n     $            LDA = LDA + 1\n*              Skip tests if not enough room.\n               IF( LDA.GT.NMAX )\n     $            GO TO 80\n               LAA = LDA*NA\n*\n*              Generate the matrix A.\n*\n               CALL SMAKE( 'GE', ' ', ' ', MA, NA, A, NMAX, AA, LDA,\n     $                     RESET, ZERO )\n*\n               DO 70 ICU = 1, 2\n                  UPLO = ICHU( ICU: ICU )\n                  UPPER = UPLO.EQ.'U'\n*\n                  DO 60 IA = 1, NALF\n                     ALPHA = ALF( IA )\n*\n                     DO 50 IB = 1, NBET\n                        BETA = BET( IB )\n*\n*                       Generate the matrix C.\n*\n                        CALL SMAKE( 'SY', UPLO, ' ', N, N, C, NMAX, CC,\n     $                              LDC, RESET, ZERO )\n*\n                        NC = NC + 1\n*\n*                       Save every datum before calling the subroutine.\n*\n                        UPLOS = UPLO\n                        TRANSS = TRANS\n                        NS = N\n                        KS = K\n                        ALS = ALPHA\n                        DO 10 I = 1, LAA\n                           AS( I ) = AA( I )\n   10                   CONTINUE\n                        LDAS = LDA\n                        BETS = BETA\n                        DO 20 I = 1, LCC\n                           CS( I ) = CC( I )\n   20                   CONTINUE\n                        LDCS = LDC\n*\n*                       Call the subroutine.\n*\n                        IF( TRACE )\n     $                     WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO,\n     $                     TRANS, N, K, ALPHA, LDA, BETA, LDC\n                        IF( REWI )\n     $                     REWIND NTRA\n                        CALL SSYRK( UPLO, TRANS, N, K, ALPHA, AA, LDA,\n     $                              BETA, CC, LDC )\n*\n*                       Check if error-exit was taken incorrectly.\n*\n                        IF( .NOT.OK )THEN\n                           WRITE( NOUT, FMT = 9993 )\n                           FATAL = .TRUE.\n                           GO TO 120\n                        END IF\n*\n*                       See what data changed inside subroutines.\n*\n                        ISAME( 1 ) = UPLOS.EQ.UPLO\n                        ISAME( 2 ) = TRANSS.EQ.TRANS\n                        ISAME( 3 ) = NS.EQ.N\n                        ISAME( 4 ) = KS.EQ.K\n                        ISAME( 5 ) = ALS.EQ.ALPHA\n                        ISAME( 6 ) = LSE( AS, AA, LAA )\n                        ISAME( 7 ) = LDAS.EQ.LDA\n                        ISAME( 8 ) = BETS.EQ.BETA\n                        IF( NULL )THEN\n                           ISAME( 9 ) = LSE( CS, CC, LCC )\n                        ELSE\n                           ISAME( 9 ) = LSERES( 'SY', UPLO, N, N, CS,\n     $                                  CC, LDC )\n                        END IF\n                        ISAME( 10 ) = LDCS.EQ.LDC\n*\n*                       If data was incorrectly changed, report and\n*                       return.\n*\n                        SAME = .TRUE.\n                        DO 30 I = 1, NARGS\n                           SAME = SAME.AND.ISAME( I )\n                           IF( .NOT.ISAME( I ) )\n     $                        WRITE( NOUT, FMT = 9998 )I\n   30                   CONTINUE\n                        IF( .NOT.SAME )THEN\n                           FATAL = .TRUE.\n                           GO TO 120\n                        END IF\n*\n                        IF( .NOT.NULL )THEN\n*\n*                          Check the result column by column.\n*\n                           JC = 1\n                           DO 40 J = 1, N\n                              IF( UPPER )THEN\n                                 JJ = 1\n                                 LJ = J\n                              ELSE\n                                 JJ = J\n                                 LJ = N - J + 1\n                              END IF\n                              IF( TRAN )THEN\n                                 CALL SMMCH( 'T', 'N', LJ, 1, K, ALPHA,\n     $                                       A( 1, JJ ), NMAX,\n     $                                       A( 1, J ), NMAX, BETA,\n     $                                       C( JJ, J ), NMAX, CT, G,\n     $                                       CC( JC ), LDC, EPS, ERR,\n     $                                       FATAL, NOUT, .TRUE. )\n                              ELSE\n                                 CALL SMMCH( 'N', 'T', LJ, 1, K, ALPHA,\n     $                                       A( JJ, 1 ), NMAX,\n     $                                       A( J, 1 ), NMAX, BETA,\n     $                                       C( JJ, J ), NMAX, CT, G,\n     $                                       CC( JC ), LDC, EPS, ERR,\n     $                                       FATAL, NOUT, .TRUE. )\n                              END IF\n                              IF( UPPER )THEN\n                                 JC = JC + LDC\n                              ELSE\n                                 JC = JC + LDC + 1\n                              END IF\n                              ERRMAX = MAX( ERRMAX, ERR )\n*                             If got really bad answer, report and\n*                             return.\n                              IF( FATAL )\n     $                           GO TO 110\n   40                      CONTINUE\n                        END IF\n*\n   50                CONTINUE\n*\n   60             CONTINUE\n*\n   70          CONTINUE\n*\n   80       CONTINUE\n*\n   90    CONTINUE\n*\n  100 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 130\n*\n  110 CONTINUE\n      IF( N.GT.1 )\n     $   WRITE( NOUT, FMT = 9995 )J\n*\n  120 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, TRANS, N, K, ALPHA,\n     $   LDA, BETA, LDC\n*\n  130 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( '      THESE ARE THE RESULTS FOR COLUMN ', I3 )\n 9994 FORMAT( 1X, I6, ': ', A6, '(', 2( '''', A1, ''',' ), 2( I3, ',' ),\n     $      F4.1, ', A,', I3, ',', F4.1, ', C,', I3, ')           .' )\n 9993 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of SCHK4.\n*\n      END\n      SUBROUTINE SCHK5( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET, NMAX,\n     $                  AB, AA, AS, BB, BS, C, CC, CS, CT, G, W )\n*\n*  Tests SSYR2K.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Parameters ..\n      REAL               ZERO\n      PARAMETER          ( ZERO = 0.0 )\n*     .. Scalar Arguments ..\n      REAL               EPS, THRESH\n      INTEGER            NALF, NBET, NIDIM, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      REAL               AA( NMAX*NMAX ), AB( 2*NMAX*NMAX ),\n     $                   ALF( NALF ), AS( NMAX*NMAX ), BB( NMAX*NMAX ),\n     $                   BET( NBET ), BS( NMAX*NMAX ), C( NMAX, NMAX ),\n     $                   CC( NMAX*NMAX ), CS( NMAX*NMAX ), CT( NMAX ),\n     $                   G( NMAX ), W( 2*NMAX )\n      INTEGER            IDIM( NIDIM )\n*     .. Local Scalars ..\n      REAL               ALPHA, ALS, BETA, BETS, ERR, ERRMAX\n      INTEGER            I, IA, IB, ICT, ICU, IK, IN, J, JC, JJ, JJAB,\n     $                   K, KS, LAA, LBB, LCC, LDA, LDAS, LDB, LDBS,\n     $                   LDC, LDCS, LJ, MA, N, NA, NARGS, NC, NS\n      LOGICAL            NULL, RESET, SAME, TRAN, UPPER\n      CHARACTER*1        TRANS, TRANSS, UPLO, UPLOS\n      CHARACTER*2        ICHU\n      CHARACTER*3        ICHT\n*     .. Local Arrays ..\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LSE, LSERES\n      EXTERNAL           LSE, LSERES\n*     .. External Subroutines ..\n      EXTERNAL           SMAKE, SMMCH, SSYR2K\n*     .. Intrinsic Functions ..\n      INTRINSIC          MAX\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICHT/'NTC'/, ICHU/'UL'/\n*     .. Executable Statements ..\n*\n      NARGS = 12\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = ZERO\n*\n      DO 130 IN = 1, NIDIM\n         N = IDIM( IN )\n*        Set LDC to 1 more than minimum value if room.\n         LDC = N\n         IF( LDC.LT.NMAX )\n     $      LDC = LDC + 1\n*        Skip tests if not enough room.\n         IF( LDC.GT.NMAX )\n     $      GO TO 130\n         LCC = LDC*N\n         NULL = N.LE.0\n*\n         DO 120 IK = 1, NIDIM\n            K = IDIM( IK )\n*\n            DO 110 ICT = 1, 3\n               TRANS = ICHT( ICT: ICT )\n               TRAN = TRANS.EQ.'T'.OR.TRANS.EQ.'C'\n               IF( TRAN )THEN\n                  MA = K\n                  NA = N\n               ELSE\n                  MA = N\n                  NA = K\n               END IF\n*              Set LDA to 1 more than minimum value if room.\n               LDA = MA\n               IF( LDA.LT.NMAX )\n     $            LDA = LDA + 1\n*              Skip tests if not enough room.\n               IF( LDA.GT.NMAX )\n     $            GO TO 110\n               LAA = LDA*NA\n*\n*              Generate the matrix A.\n*\n               IF( TRAN )THEN\n                  CALL SMAKE( 'GE', ' ', ' ', MA, NA, AB, 2*NMAX, AA,\n     $                        LDA, RESET, ZERO )\n               ELSE\n                  CALL SMAKE( 'GE', ' ', ' ', MA, NA, AB, NMAX, AA, LDA,\n     $                        RESET, ZERO )\n               END IF\n*\n*              Generate the matrix B.\n*\n               LDB = LDA\n               LBB = LAA\n               IF( TRAN )THEN\n                  CALL SMAKE( 'GE', ' ', ' ', MA, NA, AB( K + 1 ),\n     $                        2*NMAX, BB, LDB, RESET, ZERO )\n               ELSE\n                  CALL SMAKE( 'GE', ' ', ' ', MA, NA, AB( K*NMAX + 1 ),\n     $                        NMAX, BB, LDB, RESET, ZERO )\n               END IF\n*\n               DO 100 ICU = 1, 2\n                  UPLO = ICHU( ICU: ICU )\n                  UPPER = UPLO.EQ.'U'\n*\n                  DO 90 IA = 1, NALF\n                     ALPHA = ALF( IA )\n*\n                     DO 80 IB = 1, NBET\n                        BETA = BET( IB )\n*\n*                       Generate the matrix C.\n*\n                        CALL SMAKE( 'SY', UPLO, ' ', N, N, C, NMAX, CC,\n     $                              LDC, RESET, ZERO )\n*\n                        NC = NC + 1\n*\n*                       Save every datum before calling the subroutine.\n*\n                        UPLOS = UPLO\n                        TRANSS = TRANS\n                        NS = N\n                        KS = K\n                        ALS = ALPHA\n                        DO 10 I = 1, LAA\n                           AS( I ) = AA( I )\n   10                   CONTINUE\n                        LDAS = LDA\n                        DO 20 I = 1, LBB\n                           BS( I ) = BB( I )\n   20                   CONTINUE\n                        LDBS = LDB\n                        BETS = BETA\n                        DO 30 I = 1, LCC\n                           CS( I ) = CC( I )\n   30                   CONTINUE\n                        LDCS = LDC\n*\n*                       Call the subroutine.\n*\n                        IF( TRACE )\n     $                     WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO,\n     $                     TRANS, N, K, ALPHA, LDA, LDB, BETA, LDC\n                        IF( REWI )\n     $                     REWIND NTRA\n                        CALL SSYR2K( UPLO, TRANS, N, K, ALPHA, AA, LDA,\n     $                               BB, LDB, BETA, CC, LDC )\n*\n*                       Check if error-exit was taken incorrectly.\n*\n                        IF( .NOT.OK )THEN\n                           WRITE( NOUT, FMT = 9993 )\n                           FATAL = .TRUE.\n                           GO TO 150\n                        END IF\n*\n*                       See what data changed inside subroutines.\n*\n                        ISAME( 1 ) = UPLOS.EQ.UPLO\n                        ISAME( 2 ) = TRANSS.EQ.TRANS\n                        ISAME( 3 ) = NS.EQ.N\n                        ISAME( 4 ) = KS.EQ.K\n                        ISAME( 5 ) = ALS.EQ.ALPHA\n                        ISAME( 6 ) = LSE( AS, AA, LAA )\n                        ISAME( 7 ) = LDAS.EQ.LDA\n                        ISAME( 8 ) = LSE( BS, BB, LBB )\n                        ISAME( 9 ) = LDBS.EQ.LDB\n                        ISAME( 10 ) = BETS.EQ.BETA\n                        IF( NULL )THEN\n                           ISAME( 11 ) = LSE( CS, CC, LCC )\n                        ELSE\n                           ISAME( 11 ) = LSERES( 'SY', UPLO, N, N, CS,\n     $                                   CC, LDC )\n                        END IF\n                        ISAME( 12 ) = LDCS.EQ.LDC\n*\n*                       If data was incorrectly changed, report and\n*                       return.\n*\n                        SAME = .TRUE.\n                        DO 40 I = 1, NARGS\n                           SAME = SAME.AND.ISAME( I )\n                           IF( .NOT.ISAME( I ) )\n     $                        WRITE( NOUT, FMT = 9998 )I\n   40                   CONTINUE\n                        IF( .NOT.SAME )THEN\n                           FATAL = .TRUE.\n                           GO TO 150\n                        END IF\n*\n                        IF( .NOT.NULL )THEN\n*\n*                          Check the result column by column.\n*\n                           JJAB = 1\n                           JC = 1\n                           DO 70 J = 1, N\n                              IF( UPPER )THEN\n                                 JJ = 1\n                                 LJ = J\n                              ELSE\n                                 JJ = J\n                                 LJ = N - J + 1\n                              END IF\n                              IF( TRAN )THEN\n                                 DO 50 I = 1, K\n                                    W( I ) = AB( ( J - 1 )*2*NMAX + K +\n     $                                       I )\n                                    W( K + I ) = AB( ( J - 1 )*2*NMAX +\n     $                                           I )\n   50                            CONTINUE\n                                 CALL SMMCH( 'T', 'N', LJ, 1, 2*K,\n     $                                       ALPHA, AB( JJAB ), 2*NMAX,\n     $                                       W, 2*NMAX, BETA,\n     $                                       C( JJ, J ), NMAX, CT, G,\n     $                                       CC( JC ), LDC, EPS, ERR,\n     $                                       FATAL, NOUT, .TRUE. )\n                              ELSE\n                                 DO 60 I = 1, K\n                                    W( I ) = AB( ( K + I - 1 )*NMAX +\n     $                                       J )\n                                    W( K + I ) = AB( ( I - 1 )*NMAX +\n     $                                           J )\n   60                            CONTINUE\n                                 CALL SMMCH( 'N', 'N', LJ, 1, 2*K,\n     $                                       ALPHA, AB( JJ ), NMAX, W,\n     $                                       2*NMAX, BETA, C( JJ, J ),\n     $                                       NMAX, CT, G, CC( JC ), LDC,\n     $                                       EPS, ERR, FATAL, NOUT,\n     $                                       .TRUE. )\n                              END IF\n                              IF( UPPER )THEN\n                                 JC = JC + LDC\n                              ELSE\n                                 JC = JC + LDC + 1\n                                 IF( TRAN )\n     $                              JJAB = JJAB + 2*NMAX\n                              END IF\n                              ERRMAX = MAX( ERRMAX, ERR )\n*                             If got really bad answer, report and\n*                             return.\n                              IF( FATAL )\n     $                           GO TO 140\n   70                      CONTINUE\n                        END IF\n*\n   80                CONTINUE\n*\n   90             CONTINUE\n*\n  100          CONTINUE\n*\n  110       CONTINUE\n*\n  120    CONTINUE\n*\n  130 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 160\n*\n  140 CONTINUE\n      IF( N.GT.1 )\n     $   WRITE( NOUT, FMT = 9995 )J\n*\n  150 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, TRANS, N, K, ALPHA,\n     $   LDA, LDB, BETA, LDC\n*\n  160 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( '      THESE ARE THE RESULTS FOR COLUMN ', I3 )\n 9994 FORMAT( 1X, I6, ': ', A6, '(', 2( '''', A1, ''',' ), 2( I3, ',' ),\n     $      F4.1, ', A,', I3, ', B,', I3, ',', F4.1, ', C,', I3, ')   ',\n     $      ' .' )\n 9993 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of SCHK5.\n*\n      END\n      SUBROUTINE SCHKE( ISNUM, SRNAMT, NOUT )\n*\n*  Tests the error exits from the Level 3 Blas.\n*  Requires a special version of the error-handling routine XERBLA.\n*  A, B and C should not need to be defined.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*  3-19-92:  Initialize ALPHA and BETA  (eca)\n*  3-19-92:  Fix argument 12 in calls to SSYMM with INFOT = 9  (eca)\n*\n*     .. Scalar Arguments ..\n      INTEGER            ISNUM, NOUT\n      CHARACTER*6        SRNAMT\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Parameters ..\n      REAL               ONE, TWO\n      PARAMETER          ( ONE = 1.0E0, TWO = 2.0E0 )\n*     .. Local Scalars ..\n      REAL               ALPHA, BETA\n*     .. Local Arrays ..\n      REAL               A( 2, 1 ), B( 2, 1 ), C( 2, 1 )\n*     .. External Subroutines ..\n      EXTERNAL           CHKXER, SGEMM, SSYMM, SSYR2K, SSYRK, STRMM,\n     $                   STRSM\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Executable Statements ..\n*     OK is set to .FALSE. by the special version of XERBLA or by CHKXER\n*     if anything is wrong.\n      OK = .TRUE.\n*     LERR is set to .TRUE. by the special version of XERBLA each time\n*     it is called, and is then tested and re-set by CHKXER.\n      LERR = .FALSE.\n*\n*     Initialize ALPHA and BETA.\n*\n      ALPHA = ONE\n      BETA = TWO\n*\n      GO TO ( 10, 20, 30, 40, 50, 60 )ISNUM\n   10 INFOT = 1\n      CALL SGEMM( '/', 'N', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 1\n      CALL SGEMM( '/', 'T', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL SGEMM( 'N', '/', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL SGEMM( 'T', '/', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL SGEMM( 'N', 'N', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL SGEMM( 'N', 'T', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL SGEMM( 'T', 'N', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL SGEMM( 'T', 'T', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL SGEMM( 'N', 'N', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL SGEMM( 'N', 'T', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL SGEMM( 'T', 'N', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL SGEMM( 'T', 'T', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL SGEMM( 'N', 'N', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL SGEMM( 'N', 'T', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL SGEMM( 'T', 'N', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL SGEMM( 'T', 'T', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL SGEMM( 'N', 'N', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL SGEMM( 'N', 'T', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL SGEMM( 'T', 'N', 0, 0, 2, ALPHA, A, 1, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL SGEMM( 'T', 'T', 0, 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL SGEMM( 'N', 'N', 0, 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL SGEMM( 'T', 'N', 0, 0, 2, ALPHA, A, 2, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL SGEMM( 'N', 'T', 0, 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL SGEMM( 'T', 'T', 0, 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 13\n      CALL SGEMM( 'N', 'N', 2, 0, 0, ALPHA, A, 2, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 13\n      CALL SGEMM( 'N', 'T', 2, 0, 0, ALPHA, A, 2, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 13\n      CALL SGEMM( 'T', 'N', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 13\n      CALL SGEMM( 'T', 'T', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 70\n   20 INFOT = 1\n      CALL SSYMM( '/', 'U', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL SSYMM( 'L', '/', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL SSYMM( 'L', 'U', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL SSYMM( 'R', 'U', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL SSYMM( 'L', 'L', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL SSYMM( 'R', 'L', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL SSYMM( 'L', 'U', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL SSYMM( 'R', 'U', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL SSYMM( 'L', 'L', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL SSYMM( 'R', 'L', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL SSYMM( 'L', 'U', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL SSYMM( 'R', 'U', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL SSYMM( 'L', 'L', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL SSYMM( 'R', 'L', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL SSYMM( 'L', 'U', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL SSYMM( 'R', 'U', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL SSYMM( 'L', 'L', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL SSYMM( 'R', 'L', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL SSYMM( 'L', 'U', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL SSYMM( 'R', 'U', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL SSYMM( 'L', 'L', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL SSYMM( 'R', 'L', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 70\n   30 INFOT = 1\n      CALL STRMM( '/', 'U', 'N', 'N', 0, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL STRMM( 'L', '/', 'N', 'N', 0, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL STRMM( 'L', 'U', '/', 'N', 0, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL STRMM( 'L', 'U', 'N', '/', 0, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL STRMM( 'L', 'U', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL STRMM( 'L', 'U', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL STRMM( 'R', 'U', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL STRMM( 'R', 'U', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL STRMM( 'L', 'L', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL STRMM( 'L', 'L', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL STRMM( 'R', 'L', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL STRMM( 'R', 'L', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL STRMM( 'L', 'U', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL STRMM( 'L', 'U', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL STRMM( 'R', 'U', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL STRMM( 'R', 'U', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL STRMM( 'L', 'L', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL STRMM( 'L', 'L', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL STRMM( 'R', 'L', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL STRMM( 'R', 'L', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL STRMM( 'L', 'U', 'N', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL STRMM( 'L', 'U', 'T', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL STRMM( 'R', 'U', 'N', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL STRMM( 'R', 'U', 'T', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL STRMM( 'L', 'L', 'N', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL STRMM( 'L', 'L', 'T', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL STRMM( 'R', 'L', 'N', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL STRMM( 'R', 'L', 'T', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL STRMM( 'L', 'U', 'N', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL STRMM( 'L', 'U', 'T', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL STRMM( 'R', 'U', 'N', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL STRMM( 'R', 'U', 'T', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL STRMM( 'L', 'L', 'N', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL STRMM( 'L', 'L', 'T', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL STRMM( 'R', 'L', 'N', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL STRMM( 'R', 'L', 'T', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 70\n   40 INFOT = 1\n      CALL STRSM( '/', 'U', 'N', 'N', 0, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL STRSM( 'L', '/', 'N', 'N', 0, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL STRSM( 'L', 'U', '/', 'N', 0, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL STRSM( 'L', 'U', 'N', '/', 0, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL STRSM( 'L', 'U', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL STRSM( 'L', 'U', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL STRSM( 'R', 'U', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL STRSM( 'R', 'U', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL STRSM( 'L', 'L', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL STRSM( 'L', 'L', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL STRSM( 'R', 'L', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL STRSM( 'R', 'L', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL STRSM( 'L', 'U', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL STRSM( 'L', 'U', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL STRSM( 'R', 'U', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL STRSM( 'R', 'U', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL STRSM( 'L', 'L', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL STRSM( 'L', 'L', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL STRSM( 'R', 'L', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL STRSM( 'R', 'L', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL STRSM( 'L', 'U', 'N', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL STRSM( 'L', 'U', 'T', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL STRSM( 'R', 'U', 'N', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL STRSM( 'R', 'U', 'T', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL STRSM( 'L', 'L', 'N', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL STRSM( 'L', 'L', 'T', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL STRSM( 'R', 'L', 'N', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL STRSM( 'R', 'L', 'T', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL STRSM( 'L', 'U', 'N', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL STRSM( 'L', 'U', 'T', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL STRSM( 'R', 'U', 'N', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL STRSM( 'R', 'U', 'T', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL STRSM( 'L', 'L', 'N', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL STRSM( 'L', 'L', 'T', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL STRSM( 'R', 'L', 'N', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL STRSM( 'R', 'L', 'T', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 70\n   50 INFOT = 1\n      CALL SSYRK( '/', 'N', 0, 0, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL SSYRK( 'U', '/', 0, 0, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL SSYRK( 'U', 'N', -1, 0, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL SSYRK( 'U', 'T', -1, 0, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL SSYRK( 'L', 'N', -1, 0, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL SSYRK( 'L', 'T', -1, 0, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL SSYRK( 'U', 'N', 0, -1, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL SSYRK( 'U', 'T', 0, -1, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL SSYRK( 'L', 'N', 0, -1, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL SSYRK( 'L', 'T', 0, -1, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL SSYRK( 'U', 'N', 2, 0, ALPHA, A, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL SSYRK( 'U', 'T', 0, 2, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL SSYRK( 'L', 'N', 2, 0, ALPHA, A, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL SSYRK( 'L', 'T', 0, 2, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL SSYRK( 'U', 'N', 2, 0, ALPHA, A, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL SSYRK( 'U', 'T', 2, 0, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL SSYRK( 'L', 'N', 2, 0, ALPHA, A, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL SSYRK( 'L', 'T', 2, 0, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 70\n   60 INFOT = 1\n      CALL SSYR2K( '/', 'N', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL SSYR2K( 'U', '/', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL SSYR2K( 'U', 'N', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL SSYR2K( 'U', 'T', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL SSYR2K( 'L', 'N', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL SSYR2K( 'L', 'T', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL SSYR2K( 'U', 'N', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL SSYR2K( 'U', 'T', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL SSYR2K( 'L', 'N', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL SSYR2K( 'L', 'T', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL SSYR2K( 'U', 'N', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL SSYR2K( 'U', 'T', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL SSYR2K( 'L', 'N', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL SSYR2K( 'L', 'T', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL SSYR2K( 'U', 'N', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL SSYR2K( 'U', 'T', 0, 2, ALPHA, A, 2, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL SSYR2K( 'L', 'N', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL SSYR2K( 'L', 'T', 0, 2, ALPHA, A, 2, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL SSYR2K( 'U', 'N', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL SSYR2K( 'U', 'T', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL SSYR2K( 'L', 'N', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL SSYR2K( 'L', 'T', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n*\n   70 IF( OK )THEN\n         WRITE( NOUT, FMT = 9999 )SRNAMT\n      ELSE\n         WRITE( NOUT, FMT = 9998 )SRNAMT\n      END IF\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE TESTS OF ERROR-EXITS' )\n 9998 FORMAT( ' ******* ', A6, ' FAILED THE TESTS OF ERROR-EXITS *****',\n     $      '**' )\n*\n*     End of SCHKE.\n*\n      END\n      SUBROUTINE SMAKE( TYPE, UPLO, DIAG, M, N, A, NMAX, AA, LDA, RESET,\n     $                  TRANSL )\n*\n*  Generates values for an M by N matrix A.\n*  Stores the values in the array AA in the data structure required\n*  by the routine, with unwanted elements set to rogue value.\n*\n*  TYPE is 'GE', 'SY' or 'TR'.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Parameters ..\n      REAL               ZERO, ONE\n      PARAMETER          ( ZERO = 0.0, ONE = 1.0 )\n      REAL               ROGUE\n      PARAMETER          ( ROGUE = -1.0E10 )\n*     .. Scalar Arguments ..\n      REAL               TRANSL\n      INTEGER            LDA, M, N, NMAX\n      LOGICAL            RESET\n      CHARACTER*1        DIAG, UPLO\n      CHARACTER*2        TYPE\n*     .. Array Arguments ..\n      REAL               A( NMAX, * ), AA( * )\n*     .. Local Scalars ..\n      INTEGER            I, IBEG, IEND, J\n      LOGICAL            GEN, LOWER, SYM, TRI, UNIT, UPPER\n*     .. External Functions ..\n      REAL               SBEG\n      EXTERNAL           SBEG\n*     .. Executable Statements ..\n      GEN = TYPE.EQ.'GE'\n      SYM = TYPE.EQ.'SY'\n      TRI = TYPE.EQ.'TR'\n      UPPER = ( SYM.OR.TRI ).AND.UPLO.EQ.'U'\n      LOWER = ( SYM.OR.TRI ).AND.UPLO.EQ.'L'\n      UNIT = TRI.AND.DIAG.EQ.'U'\n*\n*     Generate data in array A.\n*\n      DO 20 J = 1, N\n         DO 10 I = 1, M\n            IF( GEN.OR.( UPPER.AND.I.LE.J ).OR.( LOWER.AND.I.GE.J ) )\n     $          THEN\n               A( I, J ) = SBEG( RESET ) + TRANSL\n               IF( I.NE.J )THEN\n*                 Set some elements to zero\n                  IF( N.GT.3.AND.J.EQ.N/2 )\n     $               A( I, J ) = ZERO\n                  IF( SYM )THEN\n                     A( J, I ) = A( I, J )\n                  ELSE IF( TRI )THEN\n                     A( J, I ) = ZERO\n                  END IF\n               END IF\n            END IF\n   10    CONTINUE\n         IF( TRI )\n     $      A( J, J ) = A( J, J ) + ONE\n         IF( UNIT )\n     $      A( J, J ) = ONE\n   20 CONTINUE\n*\n*     Store elements in array AS in data structure required by routine.\n*\n      IF( TYPE.EQ.'GE' )THEN\n         DO 50 J = 1, N\n            DO 30 I = 1, M\n               AA( I + ( J - 1 )*LDA ) = A( I, J )\n   30       CONTINUE\n            DO 40 I = M + 1, LDA\n               AA( I + ( J - 1 )*LDA ) = ROGUE\n   40       CONTINUE\n   50    CONTINUE\n      ELSE IF( TYPE.EQ.'SY'.OR.TYPE.EQ.'TR' )THEN\n         DO 90 J = 1, N\n            IF( UPPER )THEN\n               IBEG = 1\n               IF( UNIT )THEN\n                  IEND = J - 1\n               ELSE\n                  IEND = J\n               END IF\n            ELSE\n               IF( UNIT )THEN\n                  IBEG = J + 1\n               ELSE\n                  IBEG = J\n               END IF\n               IEND = N\n            END IF\n            DO 60 I = 1, IBEG - 1\n               AA( I + ( J - 1 )*LDA ) = ROGUE\n   60       CONTINUE\n            DO 70 I = IBEG, IEND\n               AA( I + ( J - 1 )*LDA ) = A( I, J )\n   70       CONTINUE\n            DO 80 I = IEND + 1, LDA\n               AA( I + ( J - 1 )*LDA ) = ROGUE\n   80       CONTINUE\n   90    CONTINUE\n      END IF\n      RETURN\n*\n*     End of SMAKE.\n*\n      END\n      SUBROUTINE SMMCH( TRANSA, TRANSB, M, N, KK, ALPHA, A, LDA, B, LDB,\n     $                  BETA, C, LDC, CT, G, CC, LDCC, EPS, ERR, FATAL,\n     $                  NOUT, MV )\n*\n*  Checks the results of the computational tests.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Parameters ..\n      REAL               ZERO, ONE\n      PARAMETER          ( ZERO = 0.0, ONE = 1.0 )\n*     .. Scalar Arguments ..\n      REAL               ALPHA, BETA, EPS, ERR\n      INTEGER            KK, LDA, LDB, LDC, LDCC, M, N, NOUT\n      LOGICAL            FATAL, MV\n      CHARACTER*1        TRANSA, TRANSB\n*     .. Array Arguments ..\n      REAL               A( LDA, * ), B( LDB, * ), C( LDC, * ),\n     $                   CC( LDCC, * ), CT( * ), G( * )\n*     .. Local Scalars ..\n      REAL               ERRI\n      INTEGER            I, J, K\n      LOGICAL            TRANA, TRANB\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, MAX, SQRT\n*     .. Executable Statements ..\n      TRANA = TRANSA.EQ.'T'.OR.TRANSA.EQ.'C'\n      TRANB = TRANSB.EQ.'T'.OR.TRANSB.EQ.'C'\n*\n*     Compute expected result, one column at a time, in CT using data\n*     in A, B and C.\n*     Compute gauges in G.\n*\n      DO 120 J = 1, N\n*\n         DO 10 I = 1, M\n            CT( I ) = ZERO\n            G( I ) = ZERO\n   10    CONTINUE\n         IF( .NOT.TRANA.AND..NOT.TRANB )THEN\n            DO 30 K = 1, KK\n               DO 20 I = 1, M\n                  CT( I ) = CT( I ) + A( I, K )*B( K, J )\n                  G( I ) = G( I ) + ABS( A( I, K ) )*ABS( B( K, J ) )\n   20          CONTINUE\n   30       CONTINUE\n         ELSE IF( TRANA.AND..NOT.TRANB )THEN\n            DO 50 K = 1, KK\n               DO 40 I = 1, M\n                  CT( I ) = CT( I ) + A( K, I )*B( K, J )\n                  G( I ) = G( I ) + ABS( A( K, I ) )*ABS( B( K, J ) )\n   40          CONTINUE\n   50       CONTINUE\n         ELSE IF( .NOT.TRANA.AND.TRANB )THEN\n            DO 70 K = 1, KK\n               DO 60 I = 1, M\n                  CT( I ) = CT( I ) + A( I, K )*B( J, K )\n                  G( I ) = G( I ) + ABS( A( I, K ) )*ABS( B( J, K ) )\n   60          CONTINUE\n   70       CONTINUE\n         ELSE IF( TRANA.AND.TRANB )THEN\n            DO 90 K = 1, KK\n               DO 80 I = 1, M\n                  CT( I ) = CT( I ) + A( K, I )*B( J, K )\n                  G( I ) = G( I ) + ABS( A( K, I ) )*ABS( B( J, K ) )\n   80          CONTINUE\n   90       CONTINUE\n         END IF\n         DO 100 I = 1, M\n            CT( I ) = ALPHA*CT( I ) + BETA*C( I, J )\n            G( I ) = ABS( ALPHA )*G( I ) + ABS( BETA )*ABS( C( I, J ) )\n  100    CONTINUE\n*\n*        Compute the error ratio for this result.\n*\n         ERR = ZERO\n         DO 110 I = 1, M\n            ERRI = ABS( CT( I ) - CC( I, J ) )/EPS\n            IF( G( I ).NE.ZERO )\n     $         ERRI = ERRI/G( I )\n            ERR = MAX( ERR, ERRI )\n            IF( ERR*SQRT( EPS ).GE.ONE )\n     $         GO TO 130\n  110    CONTINUE\n*\n  120 CONTINUE\n*\n*     If the loop completes, all results are at least half accurate.\n      GO TO 150\n*\n*     Report fatal error.\n*\n  130 FATAL = .TRUE.\n      WRITE( NOUT, FMT = 9999 )\n      DO 140 I = 1, M\n         IF( MV )THEN\n            WRITE( NOUT, FMT = 9998 )I, CT( I ), CC( I, J )\n         ELSE\n            WRITE( NOUT, FMT = 9998 )I, CC( I, J ), CT( I )\n         END IF\n  140 CONTINUE\n      IF( N.GT.1 )\n     $   WRITE( NOUT, FMT = 9997 )J\n*\n  150 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ******* FATAL ERROR - COMPUTED RESULT IS LESS THAN HAL',\n     $      'F ACCURATE *******', /'           EXPECTED RESULT   COMPU',\n     $      'TED RESULT' )\n 9998 FORMAT( 1X, I7, 2G18.6 )\n 9997 FORMAT( '      THESE ARE THE RESULTS FOR COLUMN ', I3 )\n*\n*     End of SMMCH.\n*\n      END\n      LOGICAL FUNCTION LSE( RI, RJ, LR )\n*\n*  Tests if two arrays are identical.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Scalar Arguments ..\n      INTEGER            LR\n*     .. Array Arguments ..\n      REAL               RI( * ), RJ( * )\n*     .. Local Scalars ..\n      INTEGER            I\n*     .. Executable Statements ..\n      DO 10 I = 1, LR\n         IF( RI( I ).NE.RJ( I ) )\n     $      GO TO 20\n   10 CONTINUE\n      LSE = .TRUE.\n      GO TO 30\n   20 CONTINUE\n      LSE = .FALSE.\n   30 RETURN\n*\n*     End of LSE.\n*\n      END\n      LOGICAL FUNCTION LSERES( TYPE, UPLO, M, N, AA, AS, LDA )\n*\n*  Tests if selected elements in two arrays are equal.\n*\n*  TYPE is 'GE' or 'SY'.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Scalar Arguments ..\n      INTEGER            LDA, M, N\n      CHARACTER*1        UPLO\n      CHARACTER*2        TYPE\n*     .. Array Arguments ..\n      REAL               AA( LDA, * ), AS( LDA, * )\n*     .. Local Scalars ..\n      INTEGER            I, IBEG, IEND, J\n      LOGICAL            UPPER\n*     .. Executable Statements ..\n      UPPER = UPLO.EQ.'U'\n      IF( TYPE.EQ.'GE' )THEN\n         DO 20 J = 1, N\n            DO 10 I = M + 1, LDA\n               IF( AA( I, J ).NE.AS( I, J ) )\n     $            GO TO 70\n   10       CONTINUE\n   20    CONTINUE\n      ELSE IF( TYPE.EQ.'SY' )THEN\n         DO 50 J = 1, N\n            IF( UPPER )THEN\n               IBEG = 1\n               IEND = J\n            ELSE\n               IBEG = J\n               IEND = N\n            END IF\n            DO 30 I = 1, IBEG - 1\n               IF( AA( I, J ).NE.AS( I, J ) )\n     $            GO TO 70\n   30       CONTINUE\n            DO 40 I = IEND + 1, LDA\n               IF( AA( I, J ).NE.AS( I, J ) )\n     $            GO TO 70\n   40       CONTINUE\n   50    CONTINUE\n      END IF\n*\n      LSERES = .TRUE.\n      GO TO 80\n   70 CONTINUE\n      LSERES = .FALSE.\n   80 RETURN\n*\n*     End of LSERES.\n*\n      END\n      REAL FUNCTION SBEG( RESET )\n*\n*  Generates random numbers uniformly distributed between -0.5 and 0.5.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Scalar Arguments ..\n      LOGICAL            RESET\n*     .. Local Scalars ..\n      INTEGER            I, IC, MI\n*     .. Save statement ..\n      SAVE               I, IC, MI\n*     .. Executable Statements ..\n      IF( RESET )THEN\n*        Initialize local variables.\n         MI = 891\n         I = 7\n         IC = 0\n         RESET = .FALSE.\n      END IF\n*\n*     The sequence of values of I is bounded between 1 and 999.\n*     If initial I = 1,2,3,6,7 or 9, the period will be 50.\n*     If initial I = 4 or 8, the period will be 25.\n*     If initial I = 5, the period will be 10.\n*     IC is used to break up the period by skipping 1 value of I in 6.\n*\n      IC = IC + 1\n   10 I = I*MI\n      I = I - 1000*( I/1000 )\n      IF( IC.GE.5 )THEN\n         IC = 0\n         GO TO 10\n      END IF\n      SBEG = ( I - 500 )/1001.0\n      RETURN\n*\n*     End of SBEG.\n*\n      END\n      REAL FUNCTION SDIFF( X, Y )\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Scalar Arguments ..\n      REAL               X, Y\n*     .. Executable Statements ..\n      SDIFF = X - Y\n      RETURN\n*\n*     End of SDIFF.\n*\n      END\n      SUBROUTINE CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n*\n*  Tests whether XERBLA has detected an error when it should.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Scalar Arguments ..\n      INTEGER            INFOT, NOUT\n      LOGICAL            LERR, OK\n      CHARACTER*6        SRNAMT\n*     .. Executable Statements ..\n      IF( .NOT.LERR )THEN\n         WRITE( NOUT, FMT = 9999 )INFOT, SRNAMT\n         OK = .FALSE.\n      END IF\n      LERR = .FALSE.\n      RETURN\n*\n 9999 FORMAT( ' ***** ILLEGAL VALUE OF PARAMETER NUMBER ', I2, ' NOT D',\n     $      'ETECTED BY ', A6, ' *****' )\n*\n*     End of CHKXER.\n*\n      END\n      SUBROUTINE XERBLA( SRNAME, INFO )\n*\n*  This is a special version of XERBLA to be used only as part of\n*  the test program for testing error exits from the Level 3 BLAS\n*  routines.\n*\n*  XERBLA  is an error handler for the Level 3 BLAS routines.\n*\n*  It is called by the Level 3 BLAS routines if an input parameter is\n*  invalid.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Scalar Arguments ..\n      INTEGER            INFO\n      CHARACTER*6        SRNAME\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUT\n      LOGICAL            LERR, OK\n      CHARACTER*6        SRNAMT\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUT, OK, LERR\n      COMMON             /SRNAMC/SRNAMT\n*     .. Executable Statements ..\n      LERR = .TRUE.\n      IF( INFO.NE.INFOT )THEN\n         IF( INFOT.NE.0 )THEN\n            WRITE( NOUT, FMT = 9999 )INFO, INFOT\n         ELSE\n            WRITE( NOUT, FMT = 9997 )INFO\n         END IF\n         OK = .FALSE.\n      END IF\n      IF( SRNAME.NE.SRNAMT )THEN\n         WRITE( NOUT, FMT = 9998 )SRNAME, SRNAMT\n         OK = .FALSE.\n      END IF\n      RETURN\n*\n 9999 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6, ' INSTEAD',\n     $      ' OF ', I2, ' *******' )\n 9998 FORMAT( ' ******* XERBLA WAS CALLED WITH SRNAME = ', A6, ' INSTE',\n     $      'AD OF ', A6, ' *******' )\n 9997 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6,\n     $      ' *******' )\n*\n*     End of XERBLA\n*\n      END\n\n"
  },
  {
    "path": "include/eigen3/blas/testing/zblat1.f",
    "content": "*> \\brief \\b ZBLAT1\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*  Definition:\n*  ===========\n*\n*       PROGRAM ZBLAT1\n* \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*>    Test program for the COMPLEX*16 Level 1 BLAS.\n*>\n*>    Based upon the original BLAS test routine together with:\n*>    F06GAF Example Program Text\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date April 2012\n*\n*> \\ingroup complex16_blas_testing\n*\n*  =====================================================================\n      PROGRAM ZBLAT1\n*\n*  -- Reference BLAS test routine (version 3.4.1) --\n*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     April 2012\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      INTEGER          NOUT\n      PARAMETER        (NOUT=6)\n*     .. Scalars in Common ..\n      INTEGER          ICASE, INCX, INCY, MODE, N\n      LOGICAL          PASS\n*     .. Local Scalars ..\n      DOUBLE PRECISION SFAC\n      INTEGER          IC\n*     .. External Subroutines ..\n      EXTERNAL         CHECK1, CHECK2, HEADER\n*     .. Common blocks ..\n      COMMON           /COMBLA/ICASE, N, INCX, INCY, MODE, PASS\n*     .. Data statements ..\n      DATA             SFAC/9.765625D-4/\n*     .. Executable Statements ..\n      WRITE (NOUT,99999)\n      DO 20 IC = 1, 10\n         ICASE = IC\n         CALL HEADER\n*\n*        Initialize PASS, INCX, INCY, and MODE for a new case.\n*        The value 9999 for INCX, INCY or MODE will appear in the\n*        detailed  output, if any, for cases that do not involve\n*        these parameters.\n*\n         PASS = .TRUE.\n         INCX = 9999\n         INCY = 9999\n         MODE = 9999\n         IF (ICASE.LE.5) THEN\n            CALL CHECK2(SFAC)\n         ELSE IF (ICASE.GE.6) THEN\n            CALL CHECK1(SFAC)\n         END IF\n*        -- Print\n         IF (PASS) WRITE (NOUT,99998)\n   20 CONTINUE\n      STOP\n*\n99999 FORMAT (' Complex BLAS Test Program Results',/1X)\n99998 FORMAT ('                                    ----- PASS -----')\n      END\n      SUBROUTINE HEADER\n*     .. Parameters ..\n      INTEGER          NOUT\n      PARAMETER        (NOUT=6)\n*     .. Scalars in Common ..\n      INTEGER          ICASE, INCX, INCY, MODE, N\n      LOGICAL          PASS\n*     .. Local Arrays ..\n      CHARACTER*6      L(10)\n*     .. Common blocks ..\n      COMMON           /COMBLA/ICASE, N, INCX, INCY, MODE, PASS\n*     .. Data statements ..\n      DATA             L(1)/'ZDOTC '/\n      DATA             L(2)/'ZDOTU '/\n      DATA             L(3)/'ZAXPY '/\n      DATA             L(4)/'ZCOPY '/\n      DATA             L(5)/'ZSWAP '/\n      DATA             L(6)/'DZNRM2'/\n      DATA             L(7)/'DZASUM'/\n      DATA             L(8)/'ZSCAL '/\n      DATA             L(9)/'ZDSCAL'/\n      DATA             L(10)/'IZAMAX'/\n*     .. Executable Statements ..\n      WRITE (NOUT,99999) ICASE, L(ICASE)\n      RETURN\n*\n99999 FORMAT (/' Test of subprogram number',I3,12X,A6)\n      END\n      SUBROUTINE CHECK1(SFAC)\n*     .. Parameters ..\n      INTEGER           NOUT\n      PARAMETER         (NOUT=6)\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION  SFAC\n*     .. Scalars in Common ..\n      INTEGER           ICASE, INCX, INCY, MODE, N\n      LOGICAL           PASS\n*     .. Local Scalars ..\n      COMPLEX*16        CA\n      DOUBLE PRECISION  SA\n      INTEGER           I, J, LEN, NP1\n*     .. Local Arrays ..\n      COMPLEX*16        CTRUE5(8,5,2), CTRUE6(8,5,2), CV(8,5,2), CX(8),\n     +                  MWPCS(5), MWPCT(5)\n      DOUBLE PRECISION  STRUE2(5), STRUE4(5)\n      INTEGER           ITRUE3(5)\n*     .. External Functions ..\n      DOUBLE PRECISION  DZASUM, DZNRM2\n      INTEGER           IZAMAX\n      EXTERNAL          DZASUM, DZNRM2, IZAMAX\n*     .. External Subroutines ..\n      EXTERNAL          ZSCAL, ZDSCAL, CTEST, ITEST1, STEST1\n*     .. Intrinsic Functions ..\n      INTRINSIC         MAX\n*     .. Common blocks ..\n      COMMON            /COMBLA/ICASE, N, INCX, INCY, MODE, PASS\n*     .. Data statements ..\n      DATA              SA, CA/0.3D0, (0.4D0,-0.7D0)/\n      DATA              ((CV(I,J,1),I=1,8),J=1,5)/(0.1D0,0.1D0),\n     +                  (1.0D0,2.0D0), (1.0D0,2.0D0), (1.0D0,2.0D0),\n     +                  (1.0D0,2.0D0), (1.0D0,2.0D0), (1.0D0,2.0D0),\n     +                  (1.0D0,2.0D0), (0.3D0,-0.4D0), (3.0D0,4.0D0),\n     +                  (3.0D0,4.0D0), (3.0D0,4.0D0), (3.0D0,4.0D0),\n     +                  (3.0D0,4.0D0), (3.0D0,4.0D0), (3.0D0,4.0D0),\n     +                  (0.1D0,-0.3D0), (0.5D0,-0.1D0), (5.0D0,6.0D0),\n     +                  (5.0D0,6.0D0), (5.0D0,6.0D0), (5.0D0,6.0D0),\n     +                  (5.0D0,6.0D0), (5.0D0,6.0D0), (0.1D0,0.1D0),\n     +                  (-0.6D0,0.1D0), (0.1D0,-0.3D0), (7.0D0,8.0D0),\n     +                  (7.0D0,8.0D0), (7.0D0,8.0D0), (7.0D0,8.0D0),\n     +                  (7.0D0,8.0D0), (0.3D0,0.1D0), (0.5D0,0.0D0),\n     +                  (0.0D0,0.5D0), (0.0D0,0.2D0), (2.0D0,3.0D0),\n     +                  (2.0D0,3.0D0), (2.0D0,3.0D0), (2.0D0,3.0D0)/\n      DATA              ((CV(I,J,2),I=1,8),J=1,5)/(0.1D0,0.1D0),\n     +                  (4.0D0,5.0D0), (4.0D0,5.0D0), (4.0D0,5.0D0),\n     +                  (4.0D0,5.0D0), (4.0D0,5.0D0), (4.0D0,5.0D0),\n     +                  (4.0D0,5.0D0), (0.3D0,-0.4D0), (6.0D0,7.0D0),\n     +                  (6.0D0,7.0D0), (6.0D0,7.0D0), (6.0D0,7.0D0),\n     +                  (6.0D0,7.0D0), (6.0D0,7.0D0), (6.0D0,7.0D0),\n     +                  (0.1D0,-0.3D0), (8.0D0,9.0D0), (0.5D0,-0.1D0),\n     +                  (2.0D0,5.0D0), (2.0D0,5.0D0), (2.0D0,5.0D0),\n     +                  (2.0D0,5.0D0), (2.0D0,5.0D0), (0.1D0,0.1D0),\n     +                  (3.0D0,6.0D0), (-0.6D0,0.1D0), (4.0D0,7.0D0),\n     +                  (0.1D0,-0.3D0), (7.0D0,2.0D0), (7.0D0,2.0D0),\n     +                  (7.0D0,2.0D0), (0.3D0,0.1D0), (5.0D0,8.0D0),\n     +                  (0.5D0,0.0D0), (6.0D0,9.0D0), (0.0D0,0.5D0),\n     +                  (8.0D0,3.0D0), (0.0D0,0.2D0), (9.0D0,4.0D0)/\n      DATA              STRUE2/0.0D0, 0.5D0, 0.6D0, 0.7D0, 0.8D0/\n      DATA              STRUE4/0.0D0, 0.7D0, 1.0D0, 1.3D0, 1.6D0/\n      DATA              ((CTRUE5(I,J,1),I=1,8),J=1,5)/(0.1D0,0.1D0),\n     +                  (1.0D0,2.0D0), (1.0D0,2.0D0), (1.0D0,2.0D0),\n     +                  (1.0D0,2.0D0), (1.0D0,2.0D0), (1.0D0,2.0D0),\n     +                  (1.0D0,2.0D0), (-0.16D0,-0.37D0), (3.0D0,4.0D0),\n     +                  (3.0D0,4.0D0), (3.0D0,4.0D0), (3.0D0,4.0D0),\n     +                  (3.0D0,4.0D0), (3.0D0,4.0D0), (3.0D0,4.0D0),\n     +                  (-0.17D0,-0.19D0), (0.13D0,-0.39D0),\n     +                  (5.0D0,6.0D0), (5.0D0,6.0D0), (5.0D0,6.0D0),\n     +                  (5.0D0,6.0D0), (5.0D0,6.0D0), (5.0D0,6.0D0),\n     +                  (0.11D0,-0.03D0), (-0.17D0,0.46D0),\n     +                  (-0.17D0,-0.19D0), (7.0D0,8.0D0), (7.0D0,8.0D0),\n     +                  (7.0D0,8.0D0), (7.0D0,8.0D0), (7.0D0,8.0D0),\n     +                  (0.19D0,-0.17D0), (0.20D0,-0.35D0),\n     +                  (0.35D0,0.20D0), (0.14D0,0.08D0),\n     +                  (2.0D0,3.0D0), (2.0D0,3.0D0), (2.0D0,3.0D0),\n     +                  (2.0D0,3.0D0)/\n      DATA              ((CTRUE5(I,J,2),I=1,8),J=1,5)/(0.1D0,0.1D0),\n     +                  (4.0D0,5.0D0), (4.0D0,5.0D0), (4.0D0,5.0D0),\n     +                  (4.0D0,5.0D0), (4.0D0,5.0D0), (4.0D0,5.0D0),\n     +                  (4.0D0,5.0D0), (-0.16D0,-0.37D0), (6.0D0,7.0D0),\n     +                  (6.0D0,7.0D0), (6.0D0,7.0D0), (6.0D0,7.0D0),\n     +                  (6.0D0,7.0D0), (6.0D0,7.0D0), (6.0D0,7.0D0),\n     +                  (-0.17D0,-0.19D0), (8.0D0,9.0D0),\n     +                  (0.13D0,-0.39D0), (2.0D0,5.0D0), (2.0D0,5.0D0),\n     +                  (2.0D0,5.0D0), (2.0D0,5.0D0), (2.0D0,5.0D0),\n     +                  (0.11D0,-0.03D0), (3.0D0,6.0D0),\n     +                  (-0.17D0,0.46D0), (4.0D0,7.0D0),\n     +                  (-0.17D0,-0.19D0), (7.0D0,2.0D0), (7.0D0,2.0D0),\n     +                  (7.0D0,2.0D0), (0.19D0,-0.17D0), (5.0D0,8.0D0),\n     +                  (0.20D0,-0.35D0), (6.0D0,9.0D0),\n     +                  (0.35D0,0.20D0), (8.0D0,3.0D0),\n     +                  (0.14D0,0.08D0), (9.0D0,4.0D0)/\n      DATA              ((CTRUE6(I,J,1),I=1,8),J=1,5)/(0.1D0,0.1D0),\n     +                  (1.0D0,2.0D0), (1.0D0,2.0D0), (1.0D0,2.0D0),\n     +                  (1.0D0,2.0D0), (1.0D0,2.0D0), (1.0D0,2.0D0),\n     +                  (1.0D0,2.0D0), (0.09D0,-0.12D0), (3.0D0,4.0D0),\n     +                  (3.0D0,4.0D0), (3.0D0,4.0D0), (3.0D0,4.0D0),\n     +                  (3.0D0,4.0D0), (3.0D0,4.0D0), (3.0D0,4.0D0),\n     +                  (0.03D0,-0.09D0), (0.15D0,-0.03D0),\n     +                  (5.0D0,6.0D0), (5.0D0,6.0D0), (5.0D0,6.0D0),\n     +                  (5.0D0,6.0D0), (5.0D0,6.0D0), (5.0D0,6.0D0),\n     +                  (0.03D0,0.03D0), (-0.18D0,0.03D0),\n     +                  (0.03D0,-0.09D0), (7.0D0,8.0D0), (7.0D0,8.0D0),\n     +                  (7.0D0,8.0D0), (7.0D0,8.0D0), (7.0D0,8.0D0),\n     +                  (0.09D0,0.03D0), (0.15D0,0.00D0),\n     +                  (0.00D0,0.15D0), (0.00D0,0.06D0), (2.0D0,3.0D0),\n     +                  (2.0D0,3.0D0), (2.0D0,3.0D0), (2.0D0,3.0D0)/\n      DATA              ((CTRUE6(I,J,2),I=1,8),J=1,5)/(0.1D0,0.1D0),\n     +                  (4.0D0,5.0D0), (4.0D0,5.0D0), (4.0D0,5.0D0),\n     +                  (4.0D0,5.0D0), (4.0D0,5.0D0), (4.0D0,5.0D0),\n     +                  (4.0D0,5.0D0), (0.09D0,-0.12D0), (6.0D0,7.0D0),\n     +                  (6.0D0,7.0D0), (6.0D0,7.0D0), (6.0D0,7.0D0),\n     +                  (6.0D0,7.0D0), (6.0D0,7.0D0), (6.0D0,7.0D0),\n     +                  (0.03D0,-0.09D0), (8.0D0,9.0D0),\n     +                  (0.15D0,-0.03D0), (2.0D0,5.0D0), (2.0D0,5.0D0),\n     +                  (2.0D0,5.0D0), (2.0D0,5.0D0), (2.0D0,5.0D0),\n     +                  (0.03D0,0.03D0), (3.0D0,6.0D0),\n     +                  (-0.18D0,0.03D0), (4.0D0,7.0D0),\n     +                  (0.03D0,-0.09D0), (7.0D0,2.0D0), (7.0D0,2.0D0),\n     +                  (7.0D0,2.0D0), (0.09D0,0.03D0), (5.0D0,8.0D0),\n     +                  (0.15D0,0.00D0), (6.0D0,9.0D0), (0.00D0,0.15D0),\n     +                  (8.0D0,3.0D0), (0.00D0,0.06D0), (9.0D0,4.0D0)/\n      DATA              ITRUE3/0, 1, 2, 2, 2/\n*     .. Executable Statements ..\n      DO 60 INCX = 1, 2\n         DO 40 NP1 = 1, 5\n            N = NP1 - 1\n            LEN = 2*MAX(N,1)\n*           .. Set vector arguments ..\n            DO 20 I = 1, LEN\n               CX(I) = CV(I,NP1,INCX)\n   20       CONTINUE\n            IF (ICASE.EQ.6) THEN\n*              .. DZNRM2 ..\n               CALL STEST1(DZNRM2(N,CX,INCX),STRUE2(NP1),STRUE2(NP1),\n     +                     SFAC)\n            ELSE IF (ICASE.EQ.7) THEN\n*              .. DZASUM ..\n               CALL STEST1(DZASUM(N,CX,INCX),STRUE4(NP1),STRUE4(NP1),\n     +                     SFAC)\n            ELSE IF (ICASE.EQ.8) THEN\n*              .. ZSCAL ..\n               CALL ZSCAL(N,CA,CX,INCX)\n               CALL CTEST(LEN,CX,CTRUE5(1,NP1,INCX),CTRUE5(1,NP1,INCX),\n     +                    SFAC)\n            ELSE IF (ICASE.EQ.9) THEN\n*              .. ZDSCAL ..\n               CALL ZDSCAL(N,SA,CX,INCX)\n               CALL CTEST(LEN,CX,CTRUE6(1,NP1,INCX),CTRUE6(1,NP1,INCX),\n     +                    SFAC)\n            ELSE IF (ICASE.EQ.10) THEN\n*              .. IZAMAX ..\n               CALL ITEST1(IZAMAX(N,CX,INCX),ITRUE3(NP1))\n            ELSE\n               WRITE (NOUT,*) ' Shouldn''t be here in CHECK1'\n               STOP\n            END IF\n*\n   40    CONTINUE\n   60 CONTINUE\n*\n      INCX = 1\n      IF (ICASE.EQ.8) THEN\n*        ZSCAL\n*        Add a test for alpha equal to zero.\n         CA = (0.0D0,0.0D0)\n         DO 80 I = 1, 5\n            MWPCT(I) = (0.0D0,0.0D0)\n            MWPCS(I) = (1.0D0,1.0D0)\n   80    CONTINUE\n         CALL ZSCAL(5,CA,CX,INCX)\n         CALL CTEST(5,CX,MWPCT,MWPCS,SFAC)\n      ELSE IF (ICASE.EQ.9) THEN\n*        ZDSCAL\n*        Add a test for alpha equal to zero.\n         SA = 0.0D0\n         DO 100 I = 1, 5\n            MWPCT(I) = (0.0D0,0.0D0)\n            MWPCS(I) = (1.0D0,1.0D0)\n  100    CONTINUE\n         CALL ZDSCAL(5,SA,CX,INCX)\n         CALL CTEST(5,CX,MWPCT,MWPCS,SFAC)\n*        Add a test for alpha equal to one.\n         SA = 1.0D0\n         DO 120 I = 1, 5\n            MWPCT(I) = CX(I)\n            MWPCS(I) = CX(I)\n  120    CONTINUE\n         CALL ZDSCAL(5,SA,CX,INCX)\n         CALL CTEST(5,CX,MWPCT,MWPCS,SFAC)\n*        Add a test for alpha equal to minus one.\n         SA = -1.0D0\n         DO 140 I = 1, 5\n            MWPCT(I) = -CX(I)\n            MWPCS(I) = -CX(I)\n  140    CONTINUE\n         CALL ZDSCAL(5,SA,CX,INCX)\n         CALL CTEST(5,CX,MWPCT,MWPCS,SFAC)\n      END IF\n      RETURN\n      END\n      SUBROUTINE CHECK2(SFAC)\n*     .. Parameters ..\n      INTEGER           NOUT\n      PARAMETER         (NOUT=6)\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION  SFAC\n*     .. Scalars in Common ..\n      INTEGER           ICASE, INCX, INCY, MODE, N\n      LOGICAL           PASS\n*     .. Local Scalars ..\n      COMPLEX*16        CA\n      INTEGER           I, J, KI, KN, KSIZE, LENX, LENY, MX, MY\n*     .. Local Arrays ..\n      COMPLEX*16        CDOT(1), CSIZE1(4), CSIZE2(7,2), CSIZE3(14),\n     +                  CT10X(7,4,4), CT10Y(7,4,4), CT6(4,4), CT7(4,4),\n     +                  CT8(7,4,4), CX(7), CX1(7), CY(7), CY1(7)\n      INTEGER           INCXS(4), INCYS(4), LENS(4,2), NS(4)\n*     .. External Functions ..\n      COMPLEX*16        ZDOTC, ZDOTU\n      EXTERNAL          ZDOTC, ZDOTU\n*     .. External Subroutines ..\n      EXTERNAL          ZAXPY, ZCOPY, ZSWAP, CTEST\n*     .. Intrinsic Functions ..\n      INTRINSIC         ABS, MIN\n*     .. Common blocks ..\n      COMMON            /COMBLA/ICASE, N, INCX, INCY, MODE, PASS\n*     .. Data statements ..\n      DATA              CA/(0.4D0,-0.7D0)/\n      DATA              INCXS/1, 2, -2, -1/\n      DATA              INCYS/1, -2, 1, -2/\n      DATA              LENS/1, 1, 2, 4, 1, 1, 3, 7/\n      DATA              NS/0, 1, 2, 4/\n      DATA              CX1/(0.7D0,-0.8D0), (-0.4D0,-0.7D0),\n     +                  (-0.1D0,-0.9D0), (0.2D0,-0.8D0),\n     +                  (-0.9D0,-0.4D0), (0.1D0,0.4D0), (-0.6D0,0.6D0)/\n      DATA              CY1/(0.6D0,-0.6D0), (-0.9D0,0.5D0),\n     +                  (0.7D0,-0.6D0), (0.1D0,-0.5D0), (-0.1D0,-0.2D0),\n     +                  (-0.5D0,-0.3D0), (0.8D0,-0.7D0)/\n      DATA              ((CT8(I,J,1),I=1,7),J=1,4)/(0.6D0,-0.6D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.32D0,-1.41D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.32D0,-1.41D0),\n     +                  (-1.55D0,0.5D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.32D0,-1.41D0), (-1.55D0,0.5D0),\n     +                  (0.03D0,-0.89D0), (-0.38D0,-0.96D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0)/\n      DATA              ((CT8(I,J,2),I=1,7),J=1,4)/(0.6D0,-0.6D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.32D0,-1.41D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (-0.07D0,-0.89D0),\n     +                  (-0.9D0,0.5D0), (0.42D0,-1.41D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.78D0,0.06D0), (-0.9D0,0.5D0),\n     +                  (0.06D0,-0.13D0), (0.1D0,-0.5D0),\n     +                  (-0.77D0,-0.49D0), (-0.5D0,-0.3D0),\n     +                  (0.52D0,-1.51D0)/\n      DATA              ((CT8(I,J,3),I=1,7),J=1,4)/(0.6D0,-0.6D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.32D0,-1.41D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (-0.07D0,-0.89D0),\n     +                  (-1.18D0,-0.31D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.78D0,0.06D0), (-1.54D0,0.97D0),\n     +                  (0.03D0,-0.89D0), (-0.18D0,-1.31D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0)/\n      DATA              ((CT8(I,J,4),I=1,7),J=1,4)/(0.6D0,-0.6D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.32D0,-1.41D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.32D0,-1.41D0), (-0.9D0,0.5D0),\n     +                  (0.05D0,-0.6D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.32D0,-1.41D0),\n     +                  (-0.9D0,0.5D0), (0.05D0,-0.6D0), (0.1D0,-0.5D0),\n     +                  (-0.77D0,-0.49D0), (-0.5D0,-0.3D0),\n     +                  (0.32D0,-1.16D0)/\n      DATA              CT7/(0.0D0,0.0D0), (-0.06D0,-0.90D0),\n     +                  (0.65D0,-0.47D0), (-0.34D0,-1.22D0),\n     +                  (0.0D0,0.0D0), (-0.06D0,-0.90D0),\n     +                  (-0.59D0,-1.46D0), (-1.04D0,-0.04D0),\n     +                  (0.0D0,0.0D0), (-0.06D0,-0.90D0),\n     +                  (-0.83D0,0.59D0), (0.07D0,-0.37D0),\n     +                  (0.0D0,0.0D0), (-0.06D0,-0.90D0),\n     +                  (-0.76D0,-1.15D0), (-1.33D0,-1.82D0)/\n      DATA              CT6/(0.0D0,0.0D0), (0.90D0,0.06D0),\n     +                  (0.91D0,-0.77D0), (1.80D0,-0.10D0),\n     +                  (0.0D0,0.0D0), (0.90D0,0.06D0), (1.45D0,0.74D0),\n     +                  (0.20D0,0.90D0), (0.0D0,0.0D0), (0.90D0,0.06D0),\n     +                  (-0.55D0,0.23D0), (0.83D0,-0.39D0),\n     +                  (0.0D0,0.0D0), (0.90D0,0.06D0), (1.04D0,0.79D0),\n     +                  (1.95D0,1.22D0)/\n      DATA              ((CT10X(I,J,1),I=1,7),J=1,4)/(0.7D0,-0.8D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.6D0,-0.6D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.6D0,-0.6D0), (-0.9D0,0.5D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.6D0,-0.6D0),\n     +                  (-0.9D0,0.5D0), (0.7D0,-0.6D0), (0.1D0,-0.5D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0)/\n      DATA              ((CT10X(I,J,2),I=1,7),J=1,4)/(0.7D0,-0.8D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.6D0,-0.6D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.7D0,-0.6D0), (-0.4D0,-0.7D0),\n     +                  (0.6D0,-0.6D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.8D0,-0.7D0),\n     +                  (-0.4D0,-0.7D0), (-0.1D0,-0.2D0),\n     +                  (0.2D0,-0.8D0), (0.7D0,-0.6D0), (0.1D0,0.4D0),\n     +                  (0.6D0,-0.6D0)/\n      DATA              ((CT10X(I,J,3),I=1,7),J=1,4)/(0.7D0,-0.8D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.6D0,-0.6D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (-0.9D0,0.5D0), (-0.4D0,-0.7D0),\n     +                  (0.6D0,-0.6D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.1D0,-0.5D0),\n     +                  (-0.4D0,-0.7D0), (0.7D0,-0.6D0), (0.2D0,-0.8D0),\n     +                  (-0.9D0,0.5D0), (0.1D0,0.4D0), (0.6D0,-0.6D0)/\n      DATA              ((CT10X(I,J,4),I=1,7),J=1,4)/(0.7D0,-0.8D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.6D0,-0.6D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.6D0,-0.6D0), (0.7D0,-0.6D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.6D0,-0.6D0),\n     +                  (0.7D0,-0.6D0), (-0.1D0,-0.2D0), (0.8D0,-0.7D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0)/\n      DATA              ((CT10Y(I,J,1),I=1,7),J=1,4)/(0.6D0,-0.6D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.7D0,-0.8D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.7D0,-0.8D0), (-0.4D0,-0.7D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.7D0,-0.8D0),\n     +                  (-0.4D0,-0.7D0), (-0.1D0,-0.9D0),\n     +                  (0.2D0,-0.8D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0)/\n      DATA              ((CT10Y(I,J,2),I=1,7),J=1,4)/(0.6D0,-0.6D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.7D0,-0.8D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (-0.1D0,-0.9D0), (-0.9D0,0.5D0),\n     +                  (0.7D0,-0.8D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (-0.6D0,0.6D0),\n     +                  (-0.9D0,0.5D0), (-0.9D0,-0.4D0), (0.1D0,-0.5D0),\n     +                  (-0.1D0,-0.9D0), (-0.5D0,-0.3D0),\n     +                  (0.7D0,-0.8D0)/\n      DATA              ((CT10Y(I,J,3),I=1,7),J=1,4)/(0.6D0,-0.6D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.7D0,-0.8D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (-0.1D0,-0.9D0), (0.7D0,-0.8D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (-0.6D0,0.6D0),\n     +                  (-0.9D0,-0.4D0), (-0.1D0,-0.9D0),\n     +                  (0.7D0,-0.8D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0)/\n      DATA              ((CT10Y(I,J,4),I=1,7),J=1,4)/(0.6D0,-0.6D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.7D0,-0.8D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.7D0,-0.8D0), (-0.9D0,0.5D0),\n     +                  (-0.4D0,-0.7D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.7D0,-0.8D0),\n     +                  (-0.9D0,0.5D0), (-0.4D0,-0.7D0), (0.1D0,-0.5D0),\n     +                  (-0.1D0,-0.9D0), (-0.5D0,-0.3D0),\n     +                  (0.2D0,-0.8D0)/\n      DATA              CSIZE1/(0.0D0,0.0D0), (0.9D0,0.9D0),\n     +                  (1.63D0,1.73D0), (2.90D0,2.78D0)/\n      DATA              CSIZE3/(0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (1.17D0,1.17D0),\n     +                  (1.17D0,1.17D0), (1.17D0,1.17D0),\n     +                  (1.17D0,1.17D0), (1.17D0,1.17D0),\n     +                  (1.17D0,1.17D0), (1.17D0,1.17D0)/\n      DATA              CSIZE2/(0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),\n     +                  (0.0D0,0.0D0), (0.0D0,0.0D0), (1.54D0,1.54D0),\n     +                  (1.54D0,1.54D0), (1.54D0,1.54D0),\n     +                  (1.54D0,1.54D0), (1.54D0,1.54D0),\n     +                  (1.54D0,1.54D0), (1.54D0,1.54D0)/\n*     .. Executable Statements ..\n      DO 60 KI = 1, 4\n         INCX = INCXS(KI)\n         INCY = INCYS(KI)\n         MX = ABS(INCX)\n         MY = ABS(INCY)\n*\n         DO 40 KN = 1, 4\n            N = NS(KN)\n            KSIZE = MIN(2,KN)\n            LENX = LENS(KN,MX)\n            LENY = LENS(KN,MY)\n*           .. initialize all argument arrays ..\n            DO 20 I = 1, 7\n               CX(I) = CX1(I)\n               CY(I) = CY1(I)\n   20       CONTINUE\n            IF (ICASE.EQ.1) THEN\n*              .. ZDOTC ..\n               CDOT(1) = ZDOTC(N,CX,INCX,CY,INCY)\n               CALL CTEST(1,CDOT,CT6(KN,KI),CSIZE1(KN),SFAC)\n            ELSE IF (ICASE.EQ.2) THEN\n*              .. ZDOTU ..\n               CDOT(1) = ZDOTU(N,CX,INCX,CY,INCY)\n               CALL CTEST(1,CDOT,CT7(KN,KI),CSIZE1(KN),SFAC)\n            ELSE IF (ICASE.EQ.3) THEN\n*              .. ZAXPY ..\n               CALL ZAXPY(N,CA,CX,INCX,CY,INCY)\n               CALL CTEST(LENY,CY,CT8(1,KN,KI),CSIZE2(1,KSIZE),SFAC)\n            ELSE IF (ICASE.EQ.4) THEN\n*              .. ZCOPY ..\n               CALL ZCOPY(N,CX,INCX,CY,INCY)\n               CALL CTEST(LENY,CY,CT10Y(1,KN,KI),CSIZE3,1.0D0)\n            ELSE IF (ICASE.EQ.5) THEN\n*              .. ZSWAP ..\n               CALL ZSWAP(N,CX,INCX,CY,INCY)\n               CALL CTEST(LENX,CX,CT10X(1,KN,KI),CSIZE3,1.0D0)\n               CALL CTEST(LENY,CY,CT10Y(1,KN,KI),CSIZE3,1.0D0)\n            ELSE\n               WRITE (NOUT,*) ' Shouldn''t be here in CHECK2'\n               STOP\n            END IF\n*\n   40    CONTINUE\n   60 CONTINUE\n      RETURN\n      END\n      SUBROUTINE STEST(LEN,SCOMP,STRUE,SSIZE,SFAC)\n*     ********************************* STEST **************************\n*\n*     THIS SUBR COMPARES ARRAYS  SCOMP() AND STRUE() OF LENGTH LEN TO\n*     SEE IF THE TERM BY TERM DIFFERENCES, MULTIPLIED BY SFAC, ARE\n*     NEGLIGIBLE.\n*\n*     C. L. LAWSON, JPL, 1974 DEC 10\n*\n*     .. Parameters ..\n      INTEGER          NOUT\n      DOUBLE PRECISION ZERO\n      PARAMETER        (NOUT=6, ZERO=0.0D0)\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION SFAC\n      INTEGER          LEN\n*     .. Array Arguments ..\n      DOUBLE PRECISION SCOMP(LEN), SSIZE(LEN), STRUE(LEN)\n*     .. Scalars in Common ..\n      INTEGER          ICASE, INCX, INCY, MODE, N\n      LOGICAL          PASS\n*     .. Local Scalars ..\n      DOUBLE PRECISION SD\n      INTEGER          I\n*     .. External Functions ..\n      DOUBLE PRECISION SDIFF\n      EXTERNAL         SDIFF\n*     .. Intrinsic Functions ..\n      INTRINSIC        ABS\n*     .. Common blocks ..\n      COMMON           /COMBLA/ICASE, N, INCX, INCY, MODE, PASS\n*     .. Executable Statements ..\n*\n      DO 40 I = 1, LEN\n         SD = SCOMP(I) - STRUE(I)\n         IF (ABS(SFAC*SD) .LE. ABS(SSIZE(I))*EPSILON(ZERO))\n     +       GO TO 40\n*\n*                             HERE    SCOMP(I) IS NOT CLOSE TO STRUE(I).\n*\n         IF ( .NOT. PASS) GO TO 20\n*                             PRINT FAIL MESSAGE AND HEADER.\n         PASS = .FALSE.\n         WRITE (NOUT,99999)\n         WRITE (NOUT,99998)\n   20    WRITE (NOUT,99997) ICASE, N, INCX, INCY, MODE, I, SCOMP(I),\n     +     STRUE(I), SD, SSIZE(I)\n   40 CONTINUE\n      RETURN\n*\n99999 FORMAT ('                                       FAIL')\n99998 FORMAT (/' CASE  N INCX INCY MODE  I                            ',\n     +       ' COMP(I)                             TRUE(I)  DIFFERENCE',\n     +       '     SIZE(I)',/1X)\n99997 FORMAT (1X,I4,I3,3I5,I3,2D36.8,2D12.4)\n      END\n      SUBROUTINE STEST1(SCOMP1,STRUE1,SSIZE,SFAC)\n*     ************************* STEST1 *****************************\n*\n*     THIS IS AN INTERFACE SUBROUTINE TO ACCOMODATE THE FORTRAN\n*     REQUIREMENT THAT WHEN A DUMMY ARGUMENT IS AN ARRAY, THE\n*     ACTUAL ARGUMENT MUST ALSO BE AN ARRAY OR AN ARRAY ELEMENT.\n*\n*     C.L. LAWSON, JPL, 1978 DEC 6\n*\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION  SCOMP1, SFAC, STRUE1\n*     .. Array Arguments ..\n      DOUBLE PRECISION  SSIZE(*)\n*     .. Local Arrays ..\n      DOUBLE PRECISION  SCOMP(1), STRUE(1)\n*     .. External Subroutines ..\n      EXTERNAL          STEST\n*     .. Executable Statements ..\n*\n      SCOMP(1) = SCOMP1\n      STRUE(1) = STRUE1\n      CALL STEST(1,SCOMP,STRUE,SSIZE,SFAC)\n*\n      RETURN\n      END\n      DOUBLE PRECISION FUNCTION SDIFF(SA,SB)\n*     ********************************* SDIFF **************************\n*     COMPUTES DIFFERENCE OF TWO NUMBERS.  C. L. LAWSON, JPL 1974 FEB 15\n*\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION                SA, SB\n*     .. Executable Statements ..\n      SDIFF = SA - SB\n      RETURN\n      END\n      SUBROUTINE CTEST(LEN,CCOMP,CTRUE,CSIZE,SFAC)\n*     **************************** CTEST *****************************\n*\n*     C.L. LAWSON, JPL, 1978 DEC 6\n*\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION SFAC\n      INTEGER          LEN\n*     .. Array Arguments ..\n      COMPLEX*16       CCOMP(LEN), CSIZE(LEN), CTRUE(LEN)\n*     .. Local Scalars ..\n      INTEGER          I\n*     .. Local Arrays ..\n      DOUBLE PRECISION SCOMP(20), SSIZE(20), STRUE(20)\n*     .. External Subroutines ..\n      EXTERNAL         STEST\n*     .. Intrinsic Functions ..\n      INTRINSIC        DIMAG, DBLE\n*     .. Executable Statements ..\n      DO 20 I = 1, LEN\n         SCOMP(2*I-1) = DBLE(CCOMP(I))\n         SCOMP(2*I) = DIMAG(CCOMP(I))\n         STRUE(2*I-1) = DBLE(CTRUE(I))\n         STRUE(2*I) = DIMAG(CTRUE(I))\n         SSIZE(2*I-1) = DBLE(CSIZE(I))\n         SSIZE(2*I) = DIMAG(CSIZE(I))\n   20 CONTINUE\n*\n      CALL STEST(2*LEN,SCOMP,STRUE,SSIZE,SFAC)\n      RETURN\n      END\n      SUBROUTINE ITEST1(ICOMP,ITRUE)\n*     ********************************* ITEST1 *************************\n*\n*     THIS SUBROUTINE COMPARES THE VARIABLES ICOMP AND ITRUE FOR\n*     EQUALITY.\n*     C. L. LAWSON, JPL, 1974 DEC 10\n*\n*     .. Parameters ..\n      INTEGER           NOUT\n      PARAMETER         (NOUT=6)\n*     .. Scalar Arguments ..\n      INTEGER           ICOMP, ITRUE\n*     .. Scalars in Common ..\n      INTEGER           ICASE, INCX, INCY, MODE, N\n      LOGICAL           PASS\n*     .. Local Scalars ..\n      INTEGER           ID\n*     .. Common blocks ..\n      COMMON            /COMBLA/ICASE, N, INCX, INCY, MODE, PASS\n*     .. Executable Statements ..\n      IF (ICOMP.EQ.ITRUE) GO TO 40\n*\n*                            HERE ICOMP IS NOT EQUAL TO ITRUE.\n*\n      IF ( .NOT. PASS) GO TO 20\n*                             PRINT FAIL MESSAGE AND HEADER.\n      PASS = .FALSE.\n      WRITE (NOUT,99999)\n      WRITE (NOUT,99998)\n   20 ID = ICOMP - ITRUE\n      WRITE (NOUT,99997) ICASE, N, INCX, INCY, MODE, ICOMP, ITRUE, ID\n   40 CONTINUE\n      RETURN\n*\n99999 FORMAT ('                                       FAIL')\n99998 FORMAT (/' CASE  N INCX INCY MODE                               ',\n     +       ' COMP                                TRUE     DIFFERENCE',\n     +       /1X)\n99997 FORMAT (1X,I4,I3,3I5,2I36,I12)\n      END\n"
  },
  {
    "path": "include/eigen3/blas/testing/zblat2.f",
    "content": "*> \\brief \\b ZBLAT2\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*  Definition:\n*  ===========\n*\n*       PROGRAM ZBLAT2\n* \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> Test program for the COMPLEX*16       Level 2 Blas.\n*>\n*> The program must be driven by a short data file. The first 18 records\n*> of the file are read using list-directed input, the last 17 records\n*> are read using the format ( A6, L2 ). An annotated example of a data\n*> file can be obtained by deleting the first 3 characters from the\n*> following 35 lines:\n*> 'zblat2.out'      NAME OF SUMMARY OUTPUT FILE\n*> 6                 UNIT NUMBER OF SUMMARY FILE\n*> 'CBLA2T.SNAP'     NAME OF SNAPSHOT OUTPUT FILE\n*> -1                UNIT NUMBER OF SNAPSHOT FILE (NOT USED IF .LT. 0)\n*> F        LOGICAL FLAG, T TO REWIND SNAPSHOT FILE AFTER EACH RECORD.\n*> F        LOGICAL FLAG, T TO STOP ON FAILURES.\n*> T        LOGICAL FLAG, T TO TEST ERROR EXITS.\n*> 16.0     THRESHOLD VALUE OF TEST RATIO\n*> 6                 NUMBER OF VALUES OF N\n*> 0 1 2 3 5 9       VALUES OF N\n*> 4                 NUMBER OF VALUES OF K\n*> 0 1 2 4           VALUES OF K\n*> 4                 NUMBER OF VALUES OF INCX AND INCY\n*> 1 2 -1 -2         VALUES OF INCX AND INCY\n*> 3                 NUMBER OF VALUES OF ALPHA\n*> (0.0,0.0) (1.0,0.0) (0.7,-0.9)       VALUES OF ALPHA\n*> 3                 NUMBER OF VALUES OF BETA\n*> (0.0,0.0) (1.0,0.0) (1.3,-1.1)       VALUES OF BETA\n*> ZGEMV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> ZGBMV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> ZHEMV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> ZHBMV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> ZHPMV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> ZTRMV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> ZTBMV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> ZTPMV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> ZTRSV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> ZTBSV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> ZTPSV  T PUT F FOR NO TEST. SAME COLUMNS.\n*> ZGERC  T PUT F FOR NO TEST. SAME COLUMNS.\n*> ZGERU  T PUT F FOR NO TEST. SAME COLUMNS.\n*> ZHER   T PUT F FOR NO TEST. SAME COLUMNS.\n*> ZHPR   T PUT F FOR NO TEST. SAME COLUMNS.\n*> ZHER2  T PUT F FOR NO TEST. SAME COLUMNS.\n*> ZHPR2  T PUT F FOR NO TEST. SAME COLUMNS.\n*>\n*> Further Details\n*> ===============\n*>\n*>    See:\n*>\n*>       Dongarra J. J., Du Croz J. J., Hammarling S.  and Hanson R. J..\n*>       An  extended  set of Fortran  Basic Linear Algebra Subprograms.\n*>\n*>       Technical  Memoranda  Nos. 41 (revision 3) and 81,  Mathematics\n*>       and  Computer Science  Division,  Argonne  National Laboratory,\n*>       9700 South Cass Avenue, Argonne, Illinois 60439, US.\n*>\n*>       Or\n*>\n*>       NAG  Technical Reports TR3/87 and TR4/87,  Numerical Algorithms\n*>       Group  Ltd.,  NAG  Central  Office,  256  Banbury  Road, Oxford\n*>       OX2 7DE, UK,  and  Numerical Algorithms Group Inc.,  1101  31st\n*>       Street,  Suite 100,  Downers Grove,  Illinois 60515-1263,  USA.\n*>\n*>\n*> -- Written on 10-August-1987.\n*>    Richard Hanson, Sandia National Labs.\n*>    Jeremy Du Croz, NAG Central Office.\n*>\n*>    10-9-00:  Change STATUS='NEW' to 'UNKNOWN' so that the testers\n*>              can be run multiple times without deleting generated\n*>              output files (susan)\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date April 2012\n*\n*> \\ingroup complex16_blas_testing\n*\n*  =====================================================================\n      PROGRAM ZBLAT2\n*\n*  -- Reference BLAS test routine (version 3.4.1) --\n*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     April 2012\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      INTEGER            NIN\n      PARAMETER          ( NIN = 5 )\n      INTEGER            NSUBS\n      PARAMETER          ( NSUBS = 17 )\n      COMPLEX*16         ZERO, ONE\n      PARAMETER          ( ZERO = ( 0.0D0, 0.0D0 ),\n     $                   ONE = ( 1.0D0, 0.0D0 ) )\n      DOUBLE PRECISION   RZERO\n      PARAMETER          ( RZERO = 0.0D0 )\n      INTEGER            NMAX, INCMAX\n      PARAMETER          ( NMAX = 65, INCMAX = 2 )\n      INTEGER            NINMAX, NIDMAX, NKBMAX, NALMAX, NBEMAX\n      PARAMETER          ( NINMAX = 7, NIDMAX = 9, NKBMAX = 7,\n     $                   NALMAX = 7, NBEMAX = 7 )\n*     .. Local Scalars ..\n      DOUBLE PRECISION   EPS, ERR, THRESH\n      INTEGER            I, ISNUM, J, N, NALF, NBET, NIDIM, NINC, NKB,\n     $                   NOUT, NTRA\n      LOGICAL            FATAL, LTESTT, REWI, SAME, SFATAL, TRACE,\n     $                   TSTERR\n      CHARACTER*1        TRANS\n      CHARACTER*6        SNAMET\n      CHARACTER*32       SNAPS, SUMMRY\n*     .. Local Arrays ..\n      COMPLEX*16         A( NMAX, NMAX ), AA( NMAX*NMAX ),\n     $                   ALF( NALMAX ), AS( NMAX*NMAX ), BET( NBEMAX ),\n     $                   X( NMAX ), XS( NMAX*INCMAX ),\n     $                   XX( NMAX*INCMAX ), Y( NMAX ),\n     $                   YS( NMAX*INCMAX ), YT( NMAX ),\n     $                   YY( NMAX*INCMAX ), Z( 2*NMAX )\n      DOUBLE PRECISION   G( NMAX )\n      INTEGER            IDIM( NIDMAX ), INC( NINMAX ), KB( NKBMAX )\n      LOGICAL            LTEST( NSUBS )\n      CHARACTER*6        SNAMES( NSUBS )\n*     .. External Functions ..\n      DOUBLE PRECISION   DDIFF\n      LOGICAL            LZE\n      EXTERNAL           DDIFF, LZE\n*     .. External Subroutines ..\n      EXTERNAL           ZCHK1, ZCHK2, ZCHK3, ZCHK4, ZCHK5, ZCHK6,\n     $                   ZCHKE, ZMVCH\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, MAX, MIN\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n      CHARACTER*6        SRNAMT\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n      COMMON             /SRNAMC/SRNAMT\n*     .. Data statements ..\n      DATA               SNAMES/'ZGEMV ', 'ZGBMV ', 'ZHEMV ', 'ZHBMV ',\n     $                   'ZHPMV ', 'ZTRMV ', 'ZTBMV ', 'ZTPMV ',\n     $                   'ZTRSV ', 'ZTBSV ', 'ZTPSV ', 'ZGERC ',\n     $                   'ZGERU ', 'ZHER  ', 'ZHPR  ', 'ZHER2 ',\n     $                   'ZHPR2 '/\n*     .. Executable Statements ..\n*\n*     Read name and unit number for summary output file and open file.\n*\n      READ( NIN, FMT = * )SUMMRY\n      READ( NIN, FMT = * )NOUT\n      OPEN( NOUT, FILE = SUMMRY, STATUS = 'UNKNOWN' )\n      NOUTC = NOUT\n*\n*     Read name and unit number for snapshot output file and open file.\n*\n      READ( NIN, FMT = * )SNAPS\n      READ( NIN, FMT = * )NTRA\n      TRACE = NTRA.GE.0\n      IF( TRACE )THEN\n         OPEN( NTRA, FILE = SNAPS, STATUS = 'UNKNOWN' )\n      END IF\n*     Read the flag that directs rewinding of the snapshot file.\n      READ( NIN, FMT = * )REWI\n      REWI = REWI.AND.TRACE\n*     Read the flag that directs stopping on any failure.\n      READ( NIN, FMT = * )SFATAL\n*     Read the flag that indicates whether error exits are to be tested.\n      READ( NIN, FMT = * )TSTERR\n*     Read the threshold value of the test ratio\n      READ( NIN, FMT = * )THRESH\n*\n*     Read and check the parameter values for the tests.\n*\n*     Values of N\n      READ( NIN, FMT = * )NIDIM\n      IF( NIDIM.LT.1.OR.NIDIM.GT.NIDMAX )THEN\n         WRITE( NOUT, FMT = 9997 )'N', NIDMAX\n         GO TO 230\n      END IF\n      READ( NIN, FMT = * )( IDIM( I ), I = 1, NIDIM )\n      DO 10 I = 1, NIDIM\n         IF( IDIM( I ).LT.0.OR.IDIM( I ).GT.NMAX )THEN\n            WRITE( NOUT, FMT = 9996 )NMAX\n            GO TO 230\n         END IF\n   10 CONTINUE\n*     Values of K\n      READ( NIN, FMT = * )NKB\n      IF( NKB.LT.1.OR.NKB.GT.NKBMAX )THEN\n         WRITE( NOUT, FMT = 9997 )'K', NKBMAX\n         GO TO 230\n      END IF\n      READ( NIN, FMT = * )( KB( I ), I = 1, NKB )\n      DO 20 I = 1, NKB\n         IF( KB( I ).LT.0 )THEN\n            WRITE( NOUT, FMT = 9995 )\n            GO TO 230\n         END IF\n   20 CONTINUE\n*     Values of INCX and INCY\n      READ( NIN, FMT = * )NINC\n      IF( NINC.LT.1.OR.NINC.GT.NINMAX )THEN\n         WRITE( NOUT, FMT = 9997 )'INCX AND INCY', NINMAX\n         GO TO 230\n      END IF\n      READ( NIN, FMT = * )( INC( I ), I = 1, NINC )\n      DO 30 I = 1, NINC\n         IF( INC( I ).EQ.0.OR.ABS( INC( I ) ).GT.INCMAX )THEN\n            WRITE( NOUT, FMT = 9994 )INCMAX\n            GO TO 230\n         END IF\n   30 CONTINUE\n*     Values of ALPHA\n      READ( NIN, FMT = * )NALF\n      IF( NALF.LT.1.OR.NALF.GT.NALMAX )THEN\n         WRITE( NOUT, FMT = 9997 )'ALPHA', NALMAX\n         GO TO 230\n      END IF\n      READ( NIN, FMT = * )( ALF( I ), I = 1, NALF )\n*     Values of BETA\n      READ( NIN, FMT = * )NBET\n      IF( NBET.LT.1.OR.NBET.GT.NBEMAX )THEN\n         WRITE( NOUT, FMT = 9997 )'BETA', NBEMAX\n         GO TO 230\n      END IF\n      READ( NIN, FMT = * )( BET( I ), I = 1, NBET )\n*\n*     Report values of parameters.\n*\n      WRITE( NOUT, FMT = 9993 )\n      WRITE( NOUT, FMT = 9992 )( IDIM( I ), I = 1, NIDIM )\n      WRITE( NOUT, FMT = 9991 )( KB( I ), I = 1, NKB )\n      WRITE( NOUT, FMT = 9990 )( INC( I ), I = 1, NINC )\n      WRITE( NOUT, FMT = 9989 )( ALF( I ), I = 1, NALF )\n      WRITE( NOUT, FMT = 9988 )( BET( I ), I = 1, NBET )\n      IF( .NOT.TSTERR )THEN\n         WRITE( NOUT, FMT = * )\n         WRITE( NOUT, FMT = 9980 )\n      END IF\n      WRITE( NOUT, FMT = * )\n      WRITE( NOUT, FMT = 9999 )THRESH\n      WRITE( NOUT, FMT = * )\n*\n*     Read names of subroutines and flags which indicate\n*     whether they are to be tested.\n*\n      DO 40 I = 1, NSUBS\n         LTEST( I ) = .FALSE.\n   40 CONTINUE\n   50 READ( NIN, FMT = 9984, END = 80 )SNAMET, LTESTT\n      DO 60 I = 1, NSUBS\n         IF( SNAMET.EQ.SNAMES( I ) )\n     $      GO TO 70\n   60 CONTINUE\n      WRITE( NOUT, FMT = 9986 )SNAMET\n      STOP\n   70 LTEST( I ) = LTESTT\n      GO TO 50\n*\n   80 CONTINUE\n      CLOSE ( NIN )\n*\n*     Compute EPS (the machine precision).\n*\n      EPS = EPSILON(RZERO)\n      WRITE( NOUT, FMT = 9998 )EPS\n*\n*     Check the reliability of ZMVCH using exact data.\n*\n      N = MIN( 32, NMAX )\n      DO 120 J = 1, N\n         DO 110 I = 1, N\n            A( I, J ) = MAX( I - J + 1, 0 )\n  110    CONTINUE\n         X( J ) = J\n         Y( J ) = ZERO\n  120 CONTINUE\n      DO 130 J = 1, N\n         YY( J ) = J*( ( J + 1 )*J )/2 - ( ( J + 1 )*J*( J - 1 ) )/3\n  130 CONTINUE\n*     YY holds the exact result. On exit from ZMVCH YT holds\n*     the result computed by ZMVCH.\n      TRANS = 'N'\n      CALL ZMVCH( TRANS, N, N, ONE, A, NMAX, X, 1, ZERO, Y, 1, YT, G,\n     $            YY, EPS, ERR, FATAL, NOUT, .TRUE. )\n      SAME = LZE( YY, YT, N )\n      IF( .NOT.SAME.OR.ERR.NE.RZERO )THEN\n         WRITE( NOUT, FMT = 9985 )TRANS, SAME, ERR\n         STOP\n      END IF\n      TRANS = 'T'\n      CALL ZMVCH( TRANS, N, N, ONE, A, NMAX, X, -1, ZERO, Y, -1, YT, G,\n     $            YY, EPS, ERR, FATAL, NOUT, .TRUE. )\n      SAME = LZE( YY, YT, N )\n      IF( .NOT.SAME.OR.ERR.NE.RZERO )THEN\n         WRITE( NOUT, FMT = 9985 )TRANS, SAME, ERR\n         STOP\n      END IF\n*\n*     Test each subroutine in turn.\n*\n      DO 210 ISNUM = 1, NSUBS\n         WRITE( NOUT, FMT = * )\n         IF( .NOT.LTEST( ISNUM ) )THEN\n*           Subprogram is not to be tested.\n            WRITE( NOUT, FMT = 9983 )SNAMES( ISNUM )\n         ELSE\n            SRNAMT = SNAMES( ISNUM )\n*           Test error exits.\n            IF( TSTERR )THEN\n               CALL ZCHKE( ISNUM, SNAMES( ISNUM ), NOUT )\n               WRITE( NOUT, FMT = * )\n            END IF\n*           Test computations.\n            INFOT = 0\n            OK = .TRUE.\n            FATAL = .FALSE.\n            GO TO ( 140, 140, 150, 150, 150, 160, 160,\n     $              160, 160, 160, 160, 170, 170, 180,\n     $              180, 190, 190 )ISNUM\n*           Test ZGEMV, 01, and ZGBMV, 02.\n  140       CALL ZCHK1( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF,\n     $                  NBET, BET, NINC, INC, NMAX, INCMAX, A, AA, AS,\n     $                  X, XX, XS, Y, YY, YS, YT, G )\n            GO TO 200\n*           Test ZHEMV, 03, ZHBMV, 04, and ZHPMV, 05.\n  150       CALL ZCHK2( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF,\n     $                  NBET, BET, NINC, INC, NMAX, INCMAX, A, AA, AS,\n     $                  X, XX, XS, Y, YY, YS, YT, G )\n            GO TO 200\n*           Test ZTRMV, 06, ZTBMV, 07, ZTPMV, 08,\n*           ZTRSV, 09, ZTBSV, 10, and ZTPSV, 11.\n  160       CALL ZCHK3( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NKB, KB, NINC, INC,\n     $                  NMAX, INCMAX, A, AA, AS, Y, YY, YS, YT, G, Z )\n            GO TO 200\n*           Test ZGERC, 12, ZGERU, 13.\n  170       CALL ZCHK4( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC,\n     $                  NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS,\n     $                  YT, G, Z )\n            GO TO 200\n*           Test ZHER, 14, and ZHPR, 15.\n  180       CALL ZCHK5( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC,\n     $                  NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS,\n     $                  YT, G, Z )\n            GO TO 200\n*           Test ZHER2, 16, and ZHPR2, 17.\n  190       CALL ZCHK6( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC,\n     $                  NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS,\n     $                  YT, G, Z )\n*\n  200       IF( FATAL.AND.SFATAL )\n     $         GO TO 220\n         END IF\n  210 CONTINUE\n      WRITE( NOUT, FMT = 9982 )\n      GO TO 240\n*\n  220 CONTINUE\n      WRITE( NOUT, FMT = 9981 )\n      GO TO 240\n*\n  230 CONTINUE\n      WRITE( NOUT, FMT = 9987 )\n*\n  240 CONTINUE\n      IF( TRACE )\n     $   CLOSE ( NTRA )\n      CLOSE ( NOUT )\n      STOP\n*\n 9999 FORMAT( ' ROUTINES PASS COMPUTATIONAL TESTS IF TEST RATIO IS LES',\n     $      'S THAN', F8.2 )\n 9998 FORMAT( ' RELATIVE MACHINE PRECISION IS TAKEN TO BE', 1P, D9.1 )\n 9997 FORMAT( ' NUMBER OF VALUES OF ', A, ' IS LESS THAN 1 OR GREATER ',\n     $      'THAN ', I2 )\n 9996 FORMAT( ' VALUE OF N IS LESS THAN 0 OR GREATER THAN ', I2 )\n 9995 FORMAT( ' VALUE OF K IS LESS THAN 0' )\n 9994 FORMAT( ' ABSOLUTE VALUE OF INCX OR INCY IS 0 OR GREATER THAN ',\n     $      I2 )\n 9993 FORMAT( ' TESTS OF THE COMPLEX*16       LEVEL 2 BLAS', //' THE F',\n     $      'OLLOWING PARAMETER VALUES WILL BE USED:' )\n 9992 FORMAT( '   FOR N              ', 9I6 )\n 9991 FORMAT( '   FOR K              ', 7I6 )\n 9990 FORMAT( '   FOR INCX AND INCY  ', 7I6 )\n 9989 FORMAT( '   FOR ALPHA          ',\n     $      7( '(', F4.1, ',', F4.1, ')  ', : ) )\n 9988 FORMAT( '   FOR BETA           ',\n     $      7( '(', F4.1, ',', F4.1, ')  ', : ) )\n 9987 FORMAT( ' AMEND DATA FILE OR INCREASE ARRAY SIZES IN PROGRAM',\n     $      /' ******* TESTS ABANDONED *******' )\n 9986 FORMAT( ' SUBPROGRAM NAME ', A6, ' NOT RECOGNIZED', /' ******* T',\n     $      'ESTS ABANDONED *******' )\n 9985 FORMAT( ' ERROR IN ZMVCH -  IN-LINE DOT PRODUCTS ARE BEING EVALU',\n     $      'ATED WRONGLY.', /' ZMVCH WAS CALLED WITH TRANS = ', A1,\n     $      ' AND RETURNED SAME = ', L1, ' AND ERR = ', F12.3, '.', /\n     $   ' THIS MAY BE DUE TO FAULTS IN THE ARITHMETIC OR THE COMPILER.'\n     $      , /' ******* TESTS ABANDONED *******' )\n 9984 FORMAT( A6, L2 )\n 9983 FORMAT( 1X, A6, ' WAS NOT TESTED' )\n 9982 FORMAT( /' END OF TESTS' )\n 9981 FORMAT( /' ******* FATAL ERROR - TESTS ABANDONED *******' )\n 9980 FORMAT( ' ERROR-EXITS WILL NOT BE TESTED' )\n*\n*     End of ZBLAT2.\n*\n      END\n      SUBROUTINE ZCHK1( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF, NBET,\n     $                  BET, NINC, INC, NMAX, INCMAX, A, AA, AS, X, XX,\n     $                  XS, Y, YY, YS, YT, G )\n*\n*  Tests ZGEMV and ZGBMV.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Parameters ..\n      COMPLEX*16         ZERO, HALF\n      PARAMETER          ( ZERO = ( 0.0D0, 0.0D0 ),\n     $                   HALF = ( 0.5D0, 0.0D0 ) )\n      DOUBLE PRECISION   RZERO\n      PARAMETER          ( RZERO = 0.0D0 )\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION   EPS, THRESH\n      INTEGER            INCMAX, NALF, NBET, NIDIM, NINC, NKB, NMAX,\n     $                   NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      COMPLEX*16         A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), BET( NBET ), X( NMAX ),\n     $                   XS( NMAX*INCMAX ), XX( NMAX*INCMAX ),\n     $                   Y( NMAX ), YS( NMAX*INCMAX ), YT( NMAX ),\n     $                   YY( NMAX*INCMAX )\n      DOUBLE PRECISION   G( NMAX )\n      INTEGER            IDIM( NIDIM ), INC( NINC ), KB( NKB )\n*     .. Local Scalars ..\n      COMPLEX*16         ALPHA, ALS, BETA, BLS, TRANSL\n      DOUBLE PRECISION   ERR, ERRMAX\n      INTEGER            I, IA, IB, IC, IKU, IM, IN, INCX, INCXS, INCY,\n     $                   INCYS, IX, IY, KL, KLS, KU, KUS, LAA, LDA,\n     $                   LDAS, LX, LY, M, ML, MS, N, NARGS, NC, ND, NK,\n     $                   NL, NS\n      LOGICAL            BANDED, FULL, NULL, RESET, SAME, TRAN\n      CHARACTER*1        TRANS, TRANSS\n      CHARACTER*3        ICH\n*     .. Local Arrays ..\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LZE, LZERES\n      EXTERNAL           LZE, LZERES\n*     .. External Subroutines ..\n      EXTERNAL           ZGBMV, ZGEMV, ZMAKE, ZMVCH\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, MAX, MIN\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICH/'NTC'/\n*     .. Executable Statements ..\n      FULL = SNAME( 3: 3 ).EQ.'E'\n      BANDED = SNAME( 3: 3 ).EQ.'B'\n*     Define the number of arguments.\n      IF( FULL )THEN\n         NARGS = 11\n      ELSE IF( BANDED )THEN\n         NARGS = 13\n      END IF\n*\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = RZERO\n*\n      DO 120 IN = 1, NIDIM\n         N = IDIM( IN )\n         ND = N/2 + 1\n*\n         DO 110 IM = 1, 2\n            IF( IM.EQ.1 )\n     $         M = MAX( N - ND, 0 )\n            IF( IM.EQ.2 )\n     $         M = MIN( N + ND, NMAX )\n*\n            IF( BANDED )THEN\n               NK = NKB\n            ELSE\n               NK = 1\n            END IF\n            DO 100 IKU = 1, NK\n               IF( BANDED )THEN\n                  KU = KB( IKU )\n                  KL = MAX( KU - 1, 0 )\n               ELSE\n                  KU = N - 1\n                  KL = M - 1\n               END IF\n*              Set LDA to 1 more than minimum value if room.\n               IF( BANDED )THEN\n                  LDA = KL + KU + 1\n               ELSE\n                  LDA = M\n               END IF\n               IF( LDA.LT.NMAX )\n     $            LDA = LDA + 1\n*              Skip tests if not enough room.\n               IF( LDA.GT.NMAX )\n     $            GO TO 100\n               LAA = LDA*N\n               NULL = N.LE.0.OR.M.LE.0\n*\n*              Generate the matrix A.\n*\n               TRANSL = ZERO\n               CALL ZMAKE( SNAME( 2: 3 ), ' ', ' ', M, N, A, NMAX, AA,\n     $                     LDA, KL, KU, RESET, TRANSL )\n*\n               DO 90 IC = 1, 3\n                  TRANS = ICH( IC: IC )\n                  TRAN = TRANS.EQ.'T'.OR.TRANS.EQ.'C'\n*\n                  IF( TRAN )THEN\n                     ML = N\n                     NL = M\n                  ELSE\n                     ML = M\n                     NL = N\n                  END IF\n*\n                  DO 80 IX = 1, NINC\n                     INCX = INC( IX )\n                     LX = ABS( INCX )*NL\n*\n*                    Generate the vector X.\n*\n                     TRANSL = HALF\n                     CALL ZMAKE( 'GE', ' ', ' ', 1, NL, X, 1, XX,\n     $                           ABS( INCX ), 0, NL - 1, RESET, TRANSL )\n                     IF( NL.GT.1 )THEN\n                        X( NL/2 ) = ZERO\n                        XX( 1 + ABS( INCX )*( NL/2 - 1 ) ) = ZERO\n                     END IF\n*\n                     DO 70 IY = 1, NINC\n                        INCY = INC( IY )\n                        LY = ABS( INCY )*ML\n*\n                        DO 60 IA = 1, NALF\n                           ALPHA = ALF( IA )\n*\n                           DO 50 IB = 1, NBET\n                              BETA = BET( IB )\n*\n*                             Generate the vector Y.\n*\n                              TRANSL = ZERO\n                              CALL ZMAKE( 'GE', ' ', ' ', 1, ML, Y, 1,\n     $                                    YY, ABS( INCY ), 0, ML - 1,\n     $                                    RESET, TRANSL )\n*\n                              NC = NC + 1\n*\n*                             Save every datum before calling the\n*                             subroutine.\n*\n                              TRANSS = TRANS\n                              MS = M\n                              NS = N\n                              KLS = KL\n                              KUS = KU\n                              ALS = ALPHA\n                              DO 10 I = 1, LAA\n                                 AS( I ) = AA( I )\n   10                         CONTINUE\n                              LDAS = LDA\n                              DO 20 I = 1, LX\n                                 XS( I ) = XX( I )\n   20                         CONTINUE\n                              INCXS = INCX\n                              BLS = BETA\n                              DO 30 I = 1, LY\n                                 YS( I ) = YY( I )\n   30                         CONTINUE\n                              INCYS = INCY\n*\n*                             Call the subroutine.\n*\n                              IF( FULL )THEN\n                                 IF( TRACE )\n     $                              WRITE( NTRA, FMT = 9994 )NC, SNAME,\n     $                              TRANS, M, N, ALPHA, LDA, INCX, BETA,\n     $                              INCY\n                                 IF( REWI )\n     $                              REWIND NTRA\n                                 CALL ZGEMV( TRANS, M, N, ALPHA, AA,\n     $                                       LDA, XX, INCX, BETA, YY,\n     $                                       INCY )\n                              ELSE IF( BANDED )THEN\n                                 IF( TRACE )\n     $                              WRITE( NTRA, FMT = 9995 )NC, SNAME,\n     $                              TRANS, M, N, KL, KU, ALPHA, LDA,\n     $                              INCX, BETA, INCY\n                                 IF( REWI )\n     $                              REWIND NTRA\n                                 CALL ZGBMV( TRANS, M, N, KL, KU, ALPHA,\n     $                                       AA, LDA, XX, INCX, BETA,\n     $                                       YY, INCY )\n                              END IF\n*\n*                             Check if error-exit was taken incorrectly.\n*\n                              IF( .NOT.OK )THEN\n                                 WRITE( NOUT, FMT = 9993 )\n                                 FATAL = .TRUE.\n                                 GO TO 130\n                              END IF\n*\n*                             See what data changed inside subroutines.\n*\n                              ISAME( 1 ) = TRANS.EQ.TRANSS\n                              ISAME( 2 ) = MS.EQ.M\n                              ISAME( 3 ) = NS.EQ.N\n                              IF( FULL )THEN\n                                 ISAME( 4 ) = ALS.EQ.ALPHA\n                                 ISAME( 5 ) = LZE( AS, AA, LAA )\n                                 ISAME( 6 ) = LDAS.EQ.LDA\n                                 ISAME( 7 ) = LZE( XS, XX, LX )\n                                 ISAME( 8 ) = INCXS.EQ.INCX\n                                 ISAME( 9 ) = BLS.EQ.BETA\n                                 IF( NULL )THEN\n                                    ISAME( 10 ) = LZE( YS, YY, LY )\n                                 ELSE\n                                    ISAME( 10 ) = LZERES( 'GE', ' ', 1,\n     $                                            ML, YS, YY,\n     $                                            ABS( INCY ) )\n                                 END IF\n                                 ISAME( 11 ) = INCYS.EQ.INCY\n                              ELSE IF( BANDED )THEN\n                                 ISAME( 4 ) = KLS.EQ.KL\n                                 ISAME( 5 ) = KUS.EQ.KU\n                                 ISAME( 6 ) = ALS.EQ.ALPHA\n                                 ISAME( 7 ) = LZE( AS, AA, LAA )\n                                 ISAME( 8 ) = LDAS.EQ.LDA\n                                 ISAME( 9 ) = LZE( XS, XX, LX )\n                                 ISAME( 10 ) = INCXS.EQ.INCX\n                                 ISAME( 11 ) = BLS.EQ.BETA\n                                 IF( NULL )THEN\n                                    ISAME( 12 ) = LZE( YS, YY, LY )\n                                 ELSE\n                                    ISAME( 12 ) = LZERES( 'GE', ' ', 1,\n     $                                            ML, YS, YY,\n     $                                            ABS( INCY ) )\n                                 END IF\n                                 ISAME( 13 ) = INCYS.EQ.INCY\n                              END IF\n*\n*                             If data was incorrectly changed, report\n*                             and return.\n*\n                              SAME = .TRUE.\n                              DO 40 I = 1, NARGS\n                                 SAME = SAME.AND.ISAME( I )\n                                 IF( .NOT.ISAME( I ) )\n     $                              WRITE( NOUT, FMT = 9998 )I\n   40                         CONTINUE\n                              IF( .NOT.SAME )THEN\n                                 FATAL = .TRUE.\n                                 GO TO 130\n                              END IF\n*\n                              IF( .NOT.NULL )THEN\n*\n*                                Check the result.\n*\n                                 CALL ZMVCH( TRANS, M, N, ALPHA, A,\n     $                                       NMAX, X, INCX, BETA, Y,\n     $                                       INCY, YT, G, YY, EPS, ERR,\n     $                                       FATAL, NOUT, .TRUE. )\n                                 ERRMAX = MAX( ERRMAX, ERR )\n*                                If got really bad answer, report and\n*                                return.\n                                 IF( FATAL )\n     $                              GO TO 130\n                              ELSE\n*                                Avoid repeating tests with M.le.0 or\n*                                N.le.0.\n                                 GO TO 110\n                              END IF\n*\n   50                      CONTINUE\n*\n   60                   CONTINUE\n*\n   70                CONTINUE\n*\n   80             CONTINUE\n*\n   90          CONTINUE\n*\n  100       CONTINUE\n*\n  110    CONTINUE\n*\n  120 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 140\n*\n  130 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      IF( FULL )THEN\n         WRITE( NOUT, FMT = 9994 )NC, SNAME, TRANS, M, N, ALPHA, LDA,\n     $      INCX, BETA, INCY\n      ELSE IF( BANDED )THEN\n         WRITE( NOUT, FMT = 9995 )NC, SNAME, TRANS, M, N, KL, KU,\n     $      ALPHA, LDA, INCX, BETA, INCY\n      END IF\n*\n  140 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 4( I3, ',' ), '(',\n     $      F4.1, ',', F4.1, '), A,', I3, ', X,', I2, ',(', F4.1, ',',\n     $      F4.1, '), Y,', I2, ') .' )\n 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 2( I3, ',' ), '(',\n     $      F4.1, ',', F4.1, '), A,', I3, ', X,', I2, ',(', F4.1, ',',\n     $      F4.1, '), Y,', I2, ')         .' )\n 9993 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of ZCHK1.\n*\n      END\n      SUBROUTINE ZCHK2( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF, NBET,\n     $                  BET, NINC, INC, NMAX, INCMAX, A, AA, AS, X, XX,\n     $                  XS, Y, YY, YS, YT, G )\n*\n*  Tests ZHEMV, ZHBMV and ZHPMV.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Parameters ..\n      COMPLEX*16         ZERO, HALF\n      PARAMETER          ( ZERO = ( 0.0D0, 0.0D0 ),\n     $                   HALF = ( 0.5D0, 0.0D0 ) )\n      DOUBLE PRECISION   RZERO\n      PARAMETER          ( RZERO = 0.0D0 )\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION   EPS, THRESH\n      INTEGER            INCMAX, NALF, NBET, NIDIM, NINC, NKB, NMAX,\n     $                   NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      COMPLEX*16         A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), BET( NBET ), X( NMAX ),\n     $                   XS( NMAX*INCMAX ), XX( NMAX*INCMAX ),\n     $                   Y( NMAX ), YS( NMAX*INCMAX ), YT( NMAX ),\n     $                   YY( NMAX*INCMAX )\n      DOUBLE PRECISION   G( NMAX )\n      INTEGER            IDIM( NIDIM ), INC( NINC ), KB( NKB )\n*     .. Local Scalars ..\n      COMPLEX*16         ALPHA, ALS, BETA, BLS, TRANSL\n      DOUBLE PRECISION   ERR, ERRMAX\n      INTEGER            I, IA, IB, IC, IK, IN, INCX, INCXS, INCY,\n     $                   INCYS, IX, IY, K, KS, LAA, LDA, LDAS, LX, LY,\n     $                   N, NARGS, NC, NK, NS\n      LOGICAL            BANDED, FULL, NULL, PACKED, RESET, SAME\n      CHARACTER*1        UPLO, UPLOS\n      CHARACTER*2        ICH\n*     .. Local Arrays ..\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LZE, LZERES\n      EXTERNAL           LZE, LZERES\n*     .. External Subroutines ..\n      EXTERNAL           ZHBMV, ZHEMV, ZHPMV, ZMAKE, ZMVCH\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, MAX\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICH/'UL'/\n*     .. Executable Statements ..\n      FULL = SNAME( 3: 3 ).EQ.'E'\n      BANDED = SNAME( 3: 3 ).EQ.'B'\n      PACKED = SNAME( 3: 3 ).EQ.'P'\n*     Define the number of arguments.\n      IF( FULL )THEN\n         NARGS = 10\n      ELSE IF( BANDED )THEN\n         NARGS = 11\n      ELSE IF( PACKED )THEN\n         NARGS = 9\n      END IF\n*\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = RZERO\n*\n      DO 110 IN = 1, NIDIM\n         N = IDIM( IN )\n*\n         IF( BANDED )THEN\n            NK = NKB\n         ELSE\n            NK = 1\n         END IF\n         DO 100 IK = 1, NK\n            IF( BANDED )THEN\n               K = KB( IK )\n            ELSE\n               K = N - 1\n            END IF\n*           Set LDA to 1 more than minimum value if room.\n            IF( BANDED )THEN\n               LDA = K + 1\n            ELSE\n               LDA = N\n            END IF\n            IF( LDA.LT.NMAX )\n     $         LDA = LDA + 1\n*           Skip tests if not enough room.\n            IF( LDA.GT.NMAX )\n     $         GO TO 100\n            IF( PACKED )THEN\n               LAA = ( N*( N + 1 ) )/2\n            ELSE\n               LAA = LDA*N\n            END IF\n            NULL = N.LE.0\n*\n            DO 90 IC = 1, 2\n               UPLO = ICH( IC: IC )\n*\n*              Generate the matrix A.\n*\n               TRANSL = ZERO\n               CALL ZMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A, NMAX, AA,\n     $                     LDA, K, K, RESET, TRANSL )\n*\n               DO 80 IX = 1, NINC\n                  INCX = INC( IX )\n                  LX = ABS( INCX )*N\n*\n*                 Generate the vector X.\n*\n                  TRANSL = HALF\n                  CALL ZMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX,\n     $                        ABS( INCX ), 0, N - 1, RESET, TRANSL )\n                  IF( N.GT.1 )THEN\n                     X( N/2 ) = ZERO\n                     XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO\n                  END IF\n*\n                  DO 70 IY = 1, NINC\n                     INCY = INC( IY )\n                     LY = ABS( INCY )*N\n*\n                     DO 60 IA = 1, NALF\n                        ALPHA = ALF( IA )\n*\n                        DO 50 IB = 1, NBET\n                           BETA = BET( IB )\n*\n*                          Generate the vector Y.\n*\n                           TRANSL = ZERO\n                           CALL ZMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY,\n     $                                 ABS( INCY ), 0, N - 1, RESET,\n     $                                 TRANSL )\n*\n                           NC = NC + 1\n*\n*                          Save every datum before calling the\n*                          subroutine.\n*\n                           UPLOS = UPLO\n                           NS = N\n                           KS = K\n                           ALS = ALPHA\n                           DO 10 I = 1, LAA\n                              AS( I ) = AA( I )\n   10                      CONTINUE\n                           LDAS = LDA\n                           DO 20 I = 1, LX\n                              XS( I ) = XX( I )\n   20                      CONTINUE\n                           INCXS = INCX\n                           BLS = BETA\n                           DO 30 I = 1, LY\n                              YS( I ) = YY( I )\n   30                      CONTINUE\n                           INCYS = INCY\n*\n*                          Call the subroutine.\n*\n                           IF( FULL )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9993 )NC, SNAME,\n     $                           UPLO, N, ALPHA, LDA, INCX, BETA, INCY\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL ZHEMV( UPLO, N, ALPHA, AA, LDA, XX,\n     $                                    INCX, BETA, YY, INCY )\n                           ELSE IF( BANDED )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9994 )NC, SNAME,\n     $                           UPLO, N, K, ALPHA, LDA, INCX, BETA,\n     $                           INCY\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL ZHBMV( UPLO, N, K, ALPHA, AA, LDA,\n     $                                    XX, INCX, BETA, YY, INCY )\n                           ELSE IF( PACKED )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9995 )NC, SNAME,\n     $                           UPLO, N, ALPHA, INCX, BETA, INCY\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL ZHPMV( UPLO, N, ALPHA, AA, XX, INCX,\n     $                                    BETA, YY, INCY )\n                           END IF\n*\n*                          Check if error-exit was taken incorrectly.\n*\n                           IF( .NOT.OK )THEN\n                              WRITE( NOUT, FMT = 9992 )\n                              FATAL = .TRUE.\n                              GO TO 120\n                           END IF\n*\n*                          See what data changed inside subroutines.\n*\n                           ISAME( 1 ) = UPLO.EQ.UPLOS\n                           ISAME( 2 ) = NS.EQ.N\n                           IF( FULL )THEN\n                              ISAME( 3 ) = ALS.EQ.ALPHA\n                              ISAME( 4 ) = LZE( AS, AA, LAA )\n                              ISAME( 5 ) = LDAS.EQ.LDA\n                              ISAME( 6 ) = LZE( XS, XX, LX )\n                              ISAME( 7 ) = INCXS.EQ.INCX\n                              ISAME( 8 ) = BLS.EQ.BETA\n                              IF( NULL )THEN\n                                 ISAME( 9 ) = LZE( YS, YY, LY )\n                              ELSE\n                                 ISAME( 9 ) = LZERES( 'GE', ' ', 1, N,\n     $                                        YS, YY, ABS( INCY ) )\n                              END IF\n                              ISAME( 10 ) = INCYS.EQ.INCY\n                           ELSE IF( BANDED )THEN\n                              ISAME( 3 ) = KS.EQ.K\n                              ISAME( 4 ) = ALS.EQ.ALPHA\n                              ISAME( 5 ) = LZE( AS, AA, LAA )\n                              ISAME( 6 ) = LDAS.EQ.LDA\n                              ISAME( 7 ) = LZE( XS, XX, LX )\n                              ISAME( 8 ) = INCXS.EQ.INCX\n                              ISAME( 9 ) = BLS.EQ.BETA\n                              IF( NULL )THEN\n                                 ISAME( 10 ) = LZE( YS, YY, LY )\n                              ELSE\n                                 ISAME( 10 ) = LZERES( 'GE', ' ', 1, N,\n     $                                         YS, YY, ABS( INCY ) )\n                              END IF\n                              ISAME( 11 ) = INCYS.EQ.INCY\n                           ELSE IF( PACKED )THEN\n                              ISAME( 3 ) = ALS.EQ.ALPHA\n                              ISAME( 4 ) = LZE( AS, AA, LAA )\n                              ISAME( 5 ) = LZE( XS, XX, LX )\n                              ISAME( 6 ) = INCXS.EQ.INCX\n                              ISAME( 7 ) = BLS.EQ.BETA\n                              IF( NULL )THEN\n                                 ISAME( 8 ) = LZE( YS, YY, LY )\n                              ELSE\n                                 ISAME( 8 ) = LZERES( 'GE', ' ', 1, N,\n     $                                        YS, YY, ABS( INCY ) )\n                              END IF\n                              ISAME( 9 ) = INCYS.EQ.INCY\n                           END IF\n*\n*                          If data was incorrectly changed, report and\n*                          return.\n*\n                           SAME = .TRUE.\n                           DO 40 I = 1, NARGS\n                              SAME = SAME.AND.ISAME( I )\n                              IF( .NOT.ISAME( I ) )\n     $                           WRITE( NOUT, FMT = 9998 )I\n   40                      CONTINUE\n                           IF( .NOT.SAME )THEN\n                              FATAL = .TRUE.\n                              GO TO 120\n                           END IF\n*\n                           IF( .NOT.NULL )THEN\n*\n*                             Check the result.\n*\n                              CALL ZMVCH( 'N', N, N, ALPHA, A, NMAX, X,\n     $                                    INCX, BETA, Y, INCY, YT, G,\n     $                                    YY, EPS, ERR, FATAL, NOUT,\n     $                                    .TRUE. )\n                              ERRMAX = MAX( ERRMAX, ERR )\n*                             If got really bad answer, report and\n*                             return.\n                              IF( FATAL )\n     $                           GO TO 120\n                           ELSE\n*                             Avoid repeating tests with N.le.0\n                              GO TO 110\n                           END IF\n*\n   50                   CONTINUE\n*\n   60                CONTINUE\n*\n   70             CONTINUE\n*\n   80          CONTINUE\n*\n   90       CONTINUE\n*\n  100    CONTINUE\n*\n  110 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 130\n*\n  120 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      IF( FULL )THEN\n         WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, ALPHA, LDA, INCX,\n     $      BETA, INCY\n      ELSE IF( BANDED )THEN\n         WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, K, ALPHA, LDA,\n     $      INCX, BETA, INCY\n      ELSE IF( PACKED )THEN\n         WRITE( NOUT, FMT = 9995 )NC, SNAME, UPLO, N, ALPHA, INCX,\n     $      BETA, INCY\n      END IF\n*\n  130 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',(', F4.1, ',',\n     $      F4.1, '), AP, X,', I2, ',(', F4.1, ',', F4.1, '), Y,', I2,\n     $      ')                .' )\n 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 2( I3, ',' ), '(',\n     $      F4.1, ',', F4.1, '), A,', I3, ', X,', I2, ',(', F4.1, ',',\n     $      F4.1, '), Y,', I2, ')         .' )\n 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',(', F4.1, ',',\n     $      F4.1, '), A,', I3, ', X,', I2, ',(', F4.1, ',', F4.1, '), ',\n     $      'Y,', I2, ')             .' )\n 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of ZCHK2.\n*\n      END\n      SUBROUTINE ZCHK3( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NKB, KB, NINC, INC, NMAX,\n     $                  INCMAX, A, AA, AS, X, XX, XS, XT, G, Z )\n*\n*  Tests ZTRMV, ZTBMV, ZTPMV, ZTRSV, ZTBSV and ZTPSV.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Parameters ..\n      COMPLEX*16         ZERO, HALF, ONE\n      PARAMETER          ( ZERO = ( 0.0D0, 0.0D0 ),\n     $                   HALF = ( 0.5D0, 0.0D0 ),\n     $                   ONE = ( 1.0D0, 0.0D0 ) )\n      DOUBLE PRECISION   RZERO\n      PARAMETER          ( RZERO = 0.0D0 )\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION   EPS, THRESH\n      INTEGER            INCMAX, NIDIM, NINC, NKB, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      COMPLEX*16         A( NMAX, NMAX ), AA( NMAX*NMAX ),\n     $                   AS( NMAX*NMAX ), X( NMAX ), XS( NMAX*INCMAX ),\n     $                   XT( NMAX ), XX( NMAX*INCMAX ), Z( NMAX )\n      DOUBLE PRECISION   G( NMAX )\n      INTEGER            IDIM( NIDIM ), INC( NINC ), KB( NKB )\n*     .. Local Scalars ..\n      COMPLEX*16         TRANSL\n      DOUBLE PRECISION   ERR, ERRMAX\n      INTEGER            I, ICD, ICT, ICU, IK, IN, INCX, INCXS, IX, K,\n     $                   KS, LAA, LDA, LDAS, LX, N, NARGS, NC, NK, NS\n      LOGICAL            BANDED, FULL, NULL, PACKED, RESET, SAME\n      CHARACTER*1        DIAG, DIAGS, TRANS, TRANSS, UPLO, UPLOS\n      CHARACTER*2        ICHD, ICHU\n      CHARACTER*3        ICHT\n*     .. Local Arrays ..\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LZE, LZERES\n      EXTERNAL           LZE, LZERES\n*     .. External Subroutines ..\n      EXTERNAL           ZMAKE, ZMVCH, ZTBMV, ZTBSV, ZTPMV, ZTPSV,\n     $                   ZTRMV, ZTRSV\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, MAX\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICHU/'UL'/, ICHT/'NTC'/, ICHD/'UN'/\n*     .. Executable Statements ..\n      FULL = SNAME( 3: 3 ).EQ.'R'\n      BANDED = SNAME( 3: 3 ).EQ.'B'\n      PACKED = SNAME( 3: 3 ).EQ.'P'\n*     Define the number of arguments.\n      IF( FULL )THEN\n         NARGS = 8\n      ELSE IF( BANDED )THEN\n         NARGS = 9\n      ELSE IF( PACKED )THEN\n         NARGS = 7\n      END IF\n*\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = RZERO\n*     Set up zero vector for ZMVCH.\n      DO 10 I = 1, NMAX\n         Z( I ) = ZERO\n   10 CONTINUE\n*\n      DO 110 IN = 1, NIDIM\n         N = IDIM( IN )\n*\n         IF( BANDED )THEN\n            NK = NKB\n         ELSE\n            NK = 1\n         END IF\n         DO 100 IK = 1, NK\n            IF( BANDED )THEN\n               K = KB( IK )\n            ELSE\n               K = N - 1\n            END IF\n*           Set LDA to 1 more than minimum value if room.\n            IF( BANDED )THEN\n               LDA = K + 1\n            ELSE\n               LDA = N\n            END IF\n            IF( LDA.LT.NMAX )\n     $         LDA = LDA + 1\n*           Skip tests if not enough room.\n            IF( LDA.GT.NMAX )\n     $         GO TO 100\n            IF( PACKED )THEN\n               LAA = ( N*( N + 1 ) )/2\n            ELSE\n               LAA = LDA*N\n            END IF\n            NULL = N.LE.0\n*\n            DO 90 ICU = 1, 2\n               UPLO = ICHU( ICU: ICU )\n*\n               DO 80 ICT = 1, 3\n                  TRANS = ICHT( ICT: ICT )\n*\n                  DO 70 ICD = 1, 2\n                     DIAG = ICHD( ICD: ICD )\n*\n*                    Generate the matrix A.\n*\n                     TRANSL = ZERO\n                     CALL ZMAKE( SNAME( 2: 3 ), UPLO, DIAG, N, N, A,\n     $                           NMAX, AA, LDA, K, K, RESET, TRANSL )\n*\n                     DO 60 IX = 1, NINC\n                        INCX = INC( IX )\n                        LX = ABS( INCX )*N\n*\n*                       Generate the vector X.\n*\n                        TRANSL = HALF\n                        CALL ZMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX,\n     $                              ABS( INCX ), 0, N - 1, RESET,\n     $                              TRANSL )\n                        IF( N.GT.1 )THEN\n                           X( N/2 ) = ZERO\n                           XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO\n                        END IF\n*\n                        NC = NC + 1\n*\n*                       Save every datum before calling the subroutine.\n*\n                        UPLOS = UPLO\n                        TRANSS = TRANS\n                        DIAGS = DIAG\n                        NS = N\n                        KS = K\n                        DO 20 I = 1, LAA\n                           AS( I ) = AA( I )\n   20                   CONTINUE\n                        LDAS = LDA\n                        DO 30 I = 1, LX\n                           XS( I ) = XX( I )\n   30                   CONTINUE\n                        INCXS = INCX\n*\n*                       Call the subroutine.\n*\n                        IF( SNAME( 4: 5 ).EQ.'MV' )THEN\n                           IF( FULL )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9993 )NC, SNAME,\n     $                           UPLO, TRANS, DIAG, N, LDA, INCX\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL ZTRMV( UPLO, TRANS, DIAG, N, AA, LDA,\n     $                                    XX, INCX )\n                           ELSE IF( BANDED )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9994 )NC, SNAME,\n     $                           UPLO, TRANS, DIAG, N, K, LDA, INCX\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL ZTBMV( UPLO, TRANS, DIAG, N, K, AA,\n     $                                    LDA, XX, INCX )\n                           ELSE IF( PACKED )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9995 )NC, SNAME,\n     $                           UPLO, TRANS, DIAG, N, INCX\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL ZTPMV( UPLO, TRANS, DIAG, N, AA, XX,\n     $                                    INCX )\n                           END IF\n                        ELSE IF( SNAME( 4: 5 ).EQ.'SV' )THEN\n                           IF( FULL )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9993 )NC, SNAME,\n     $                           UPLO, TRANS, DIAG, N, LDA, INCX\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL ZTRSV( UPLO, TRANS, DIAG, N, AA, LDA,\n     $                                    XX, INCX )\n                           ELSE IF( BANDED )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9994 )NC, SNAME,\n     $                           UPLO, TRANS, DIAG, N, K, LDA, INCX\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL ZTBSV( UPLO, TRANS, DIAG, N, K, AA,\n     $                                    LDA, XX, INCX )\n                           ELSE IF( PACKED )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9995 )NC, SNAME,\n     $                           UPLO, TRANS, DIAG, N, INCX\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL ZTPSV( UPLO, TRANS, DIAG, N, AA, XX,\n     $                                    INCX )\n                           END IF\n                        END IF\n*\n*                       Check if error-exit was taken incorrectly.\n*\n                        IF( .NOT.OK )THEN\n                           WRITE( NOUT, FMT = 9992 )\n                           FATAL = .TRUE.\n                           GO TO 120\n                        END IF\n*\n*                       See what data changed inside subroutines.\n*\n                        ISAME( 1 ) = UPLO.EQ.UPLOS\n                        ISAME( 2 ) = TRANS.EQ.TRANSS\n                        ISAME( 3 ) = DIAG.EQ.DIAGS\n                        ISAME( 4 ) = NS.EQ.N\n                        IF( FULL )THEN\n                           ISAME( 5 ) = LZE( AS, AA, LAA )\n                           ISAME( 6 ) = LDAS.EQ.LDA\n                           IF( NULL )THEN\n                              ISAME( 7 ) = LZE( XS, XX, LX )\n                           ELSE\n                              ISAME( 7 ) = LZERES( 'GE', ' ', 1, N, XS,\n     $                                     XX, ABS( INCX ) )\n                           END IF\n                           ISAME( 8 ) = INCXS.EQ.INCX\n                        ELSE IF( BANDED )THEN\n                           ISAME( 5 ) = KS.EQ.K\n                           ISAME( 6 ) = LZE( AS, AA, LAA )\n                           ISAME( 7 ) = LDAS.EQ.LDA\n                           IF( NULL )THEN\n                              ISAME( 8 ) = LZE( XS, XX, LX )\n                           ELSE\n                              ISAME( 8 ) = LZERES( 'GE', ' ', 1, N, XS,\n     $                                     XX, ABS( INCX ) )\n                           END IF\n                           ISAME( 9 ) = INCXS.EQ.INCX\n                        ELSE IF( PACKED )THEN\n                           ISAME( 5 ) = LZE( AS, AA, LAA )\n                           IF( NULL )THEN\n                              ISAME( 6 ) = LZE( XS, XX, LX )\n                           ELSE\n                              ISAME( 6 ) = LZERES( 'GE', ' ', 1, N, XS,\n     $                                     XX, ABS( INCX ) )\n                           END IF\n                           ISAME( 7 ) = INCXS.EQ.INCX\n                        END IF\n*\n*                       If data was incorrectly changed, report and\n*                       return.\n*\n                        SAME = .TRUE.\n                        DO 40 I = 1, NARGS\n                           SAME = SAME.AND.ISAME( I )\n                           IF( .NOT.ISAME( I ) )\n     $                        WRITE( NOUT, FMT = 9998 )I\n   40                   CONTINUE\n                        IF( .NOT.SAME )THEN\n                           FATAL = .TRUE.\n                           GO TO 120\n                        END IF\n*\n                        IF( .NOT.NULL )THEN\n                           IF( SNAME( 4: 5 ).EQ.'MV' )THEN\n*\n*                             Check the result.\n*\n                              CALL ZMVCH( TRANS, N, N, ONE, A, NMAX, X,\n     $                                    INCX, ZERO, Z, INCX, XT, G,\n     $                                    XX, EPS, ERR, FATAL, NOUT,\n     $                                    .TRUE. )\n                           ELSE IF( SNAME( 4: 5 ).EQ.'SV' )THEN\n*\n*                             Compute approximation to original vector.\n*\n                              DO 50 I = 1, N\n                                 Z( I ) = XX( 1 + ( I - 1 )*\n     $                                    ABS( INCX ) )\n                                 XX( 1 + ( I - 1 )*ABS( INCX ) )\n     $                              = X( I )\n   50                         CONTINUE\n                              CALL ZMVCH( TRANS, N, N, ONE, A, NMAX, Z,\n     $                                    INCX, ZERO, X, INCX, XT, G,\n     $                                    XX, EPS, ERR, FATAL, NOUT,\n     $                                    .FALSE. )\n                           END IF\n                           ERRMAX = MAX( ERRMAX, ERR )\n*                          If got really bad answer, report and return.\n                           IF( FATAL )\n     $                        GO TO 120\n                        ELSE\n*                          Avoid repeating tests with N.le.0.\n                           GO TO 110\n                        END IF\n*\n   60                CONTINUE\n*\n   70             CONTINUE\n*\n   80          CONTINUE\n*\n   90       CONTINUE\n*\n  100    CONTINUE\n*\n  110 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 130\n*\n  120 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      IF( FULL )THEN\n         WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, TRANS, DIAG, N, LDA,\n     $      INCX\n      ELSE IF( BANDED )THEN\n         WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, TRANS, DIAG, N, K,\n     $      LDA, INCX\n      ELSE IF( PACKED )THEN\n         WRITE( NOUT, FMT = 9995 )NC, SNAME, UPLO, TRANS, DIAG, N, INCX\n      END IF\n*\n  130 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), I3, ', AP, ',\n     $      'X,', I2, ')                                      .' )\n 9994 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), 2( I3, ',' ),\n     $      ' A,', I3, ', X,', I2, ')                               .' )\n 9993 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), I3, ', A,',\n     $      I3, ', X,', I2, ')                                   .' )\n 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of ZCHK3.\n*\n      END\n      SUBROUTINE ZCHK4( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX,\n     $                  INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G,\n     $                  Z )\n*\n*  Tests ZGERC and ZGERU.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Parameters ..\n      COMPLEX*16         ZERO, HALF, ONE\n      PARAMETER          ( ZERO = ( 0.0D0, 0.0D0 ),\n     $                   HALF = ( 0.5D0, 0.0D0 ),\n     $                   ONE = ( 1.0D0, 0.0D0 ) )\n      DOUBLE PRECISION   RZERO\n      PARAMETER          ( RZERO = 0.0D0 )\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION   EPS, THRESH\n      INTEGER            INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      COMPLEX*16         A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), X( NMAX ), XS( NMAX*INCMAX ),\n     $                   XX( NMAX*INCMAX ), Y( NMAX ),\n     $                   YS( NMAX*INCMAX ), YT( NMAX ),\n     $                   YY( NMAX*INCMAX ), Z( NMAX )\n      DOUBLE PRECISION   G( NMAX )\n      INTEGER            IDIM( NIDIM ), INC( NINC )\n*     .. Local Scalars ..\n      COMPLEX*16         ALPHA, ALS, TRANSL\n      DOUBLE PRECISION   ERR, ERRMAX\n      INTEGER            I, IA, IM, IN, INCX, INCXS, INCY, INCYS, IX,\n     $                   IY, J, LAA, LDA, LDAS, LX, LY, M, MS, N, NARGS,\n     $                   NC, ND, NS\n      LOGICAL            CONJ, NULL, RESET, SAME\n*     .. Local Arrays ..\n      COMPLEX*16         W( 1 )\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LZE, LZERES\n      EXTERNAL           LZE, LZERES\n*     .. External Subroutines ..\n      EXTERNAL           ZGERC, ZGERU, ZMAKE, ZMVCH\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, DCONJG, MAX, MIN\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Executable Statements ..\n      CONJ = SNAME( 5: 5 ).EQ.'C'\n*     Define the number of arguments.\n      NARGS = 9\n*\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = RZERO\n*\n      DO 120 IN = 1, NIDIM\n         N = IDIM( IN )\n         ND = N/2 + 1\n*\n         DO 110 IM = 1, 2\n            IF( IM.EQ.1 )\n     $         M = MAX( N - ND, 0 )\n            IF( IM.EQ.2 )\n     $         M = MIN( N + ND, NMAX )\n*\n*           Set LDA to 1 more than minimum value if room.\n            LDA = M\n            IF( LDA.LT.NMAX )\n     $         LDA = LDA + 1\n*           Skip tests if not enough room.\n            IF( LDA.GT.NMAX )\n     $         GO TO 110\n            LAA = LDA*N\n            NULL = N.LE.0.OR.M.LE.0\n*\n            DO 100 IX = 1, NINC\n               INCX = INC( IX )\n               LX = ABS( INCX )*M\n*\n*              Generate the vector X.\n*\n               TRANSL = HALF\n               CALL ZMAKE( 'GE', ' ', ' ', 1, M, X, 1, XX, ABS( INCX ),\n     $                     0, M - 1, RESET, TRANSL )\n               IF( M.GT.1 )THEN\n                  X( M/2 ) = ZERO\n                  XX( 1 + ABS( INCX )*( M/2 - 1 ) ) = ZERO\n               END IF\n*\n               DO 90 IY = 1, NINC\n                  INCY = INC( IY )\n                  LY = ABS( INCY )*N\n*\n*                 Generate the vector Y.\n*\n                  TRANSL = ZERO\n                  CALL ZMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY,\n     $                        ABS( INCY ), 0, N - 1, RESET, TRANSL )\n                  IF( N.GT.1 )THEN\n                     Y( N/2 ) = ZERO\n                     YY( 1 + ABS( INCY )*( N/2 - 1 ) ) = ZERO\n                  END IF\n*\n                  DO 80 IA = 1, NALF\n                     ALPHA = ALF( IA )\n*\n*                    Generate the matrix A.\n*\n                     TRANSL = ZERO\n                     CALL ZMAKE( SNAME( 2: 3 ), ' ', ' ', M, N, A, NMAX,\n     $                           AA, LDA, M - 1, N - 1, RESET, TRANSL )\n*\n                     NC = NC + 1\n*\n*                    Save every datum before calling the subroutine.\n*\n                     MS = M\n                     NS = N\n                     ALS = ALPHA\n                     DO 10 I = 1, LAA\n                        AS( I ) = AA( I )\n   10                CONTINUE\n                     LDAS = LDA\n                     DO 20 I = 1, LX\n                        XS( I ) = XX( I )\n   20                CONTINUE\n                     INCXS = INCX\n                     DO 30 I = 1, LY\n                        YS( I ) = YY( I )\n   30                CONTINUE\n                     INCYS = INCY\n*\n*                    Call the subroutine.\n*\n                     IF( TRACE )\n     $                  WRITE( NTRA, FMT = 9994 )NC, SNAME, M, N,\n     $                  ALPHA, INCX, INCY, LDA\n                     IF( CONJ )THEN\n                        IF( REWI )\n     $                     REWIND NTRA\n                        CALL ZGERC( M, N, ALPHA, XX, INCX, YY, INCY, AA,\n     $                              LDA )\n                     ELSE\n                        IF( REWI )\n     $                     REWIND NTRA\n                        CALL ZGERU( M, N, ALPHA, XX, INCX, YY, INCY, AA,\n     $                              LDA )\n                     END IF\n*\n*                    Check if error-exit was taken incorrectly.\n*\n                     IF( .NOT.OK )THEN\n                        WRITE( NOUT, FMT = 9993 )\n                        FATAL = .TRUE.\n                        GO TO 140\n                     END IF\n*\n*                    See what data changed inside subroutine.\n*\n                     ISAME( 1 ) = MS.EQ.M\n                     ISAME( 2 ) = NS.EQ.N\n                     ISAME( 3 ) = ALS.EQ.ALPHA\n                     ISAME( 4 ) = LZE( XS, XX, LX )\n                     ISAME( 5 ) = INCXS.EQ.INCX\n                     ISAME( 6 ) = LZE( YS, YY, LY )\n                     ISAME( 7 ) = INCYS.EQ.INCY\n                     IF( NULL )THEN\n                        ISAME( 8 ) = LZE( AS, AA, LAA )\n                     ELSE\n                        ISAME( 8 ) = LZERES( 'GE', ' ', M, N, AS, AA,\n     $                               LDA )\n                     END IF\n                     ISAME( 9 ) = LDAS.EQ.LDA\n*\n*                    If data was incorrectly changed, report and return.\n*\n                     SAME = .TRUE.\n                     DO 40 I = 1, NARGS\n                        SAME = SAME.AND.ISAME( I )\n                        IF( .NOT.ISAME( I ) )\n     $                     WRITE( NOUT, FMT = 9998 )I\n   40                CONTINUE\n                     IF( .NOT.SAME )THEN\n                        FATAL = .TRUE.\n                        GO TO 140\n                     END IF\n*\n                     IF( .NOT.NULL )THEN\n*\n*                       Check the result column by column.\n*\n                        IF( INCX.GT.0 )THEN\n                           DO 50 I = 1, M\n                              Z( I ) = X( I )\n   50                      CONTINUE\n                        ELSE\n                           DO 60 I = 1, M\n                              Z( I ) = X( M - I + 1 )\n   60                      CONTINUE\n                        END IF\n                        DO 70 J = 1, N\n                           IF( INCY.GT.0 )THEN\n                              W( 1 ) = Y( J )\n                           ELSE\n                              W( 1 ) = Y( N - J + 1 )\n                           END IF\n                           IF( CONJ )\n     $                        W( 1 ) = DCONJG( W( 1 ) )\n                           CALL ZMVCH( 'N', M, 1, ALPHA, Z, NMAX, W, 1,\n     $                                 ONE, A( 1, J ), 1, YT, G,\n     $                                 AA( 1 + ( J - 1 )*LDA ), EPS,\n     $                                 ERR, FATAL, NOUT, .TRUE. )\n                           ERRMAX = MAX( ERRMAX, ERR )\n*                          If got really bad answer, report and return.\n                           IF( FATAL )\n     $                        GO TO 130\n   70                   CONTINUE\n                     ELSE\n*                       Avoid repeating tests with M.le.0 or N.le.0.\n                        GO TO 110\n                     END IF\n*\n   80             CONTINUE\n*\n   90          CONTINUE\n*\n  100       CONTINUE\n*\n  110    CONTINUE\n*\n  120 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 150\n*\n  130 CONTINUE\n      WRITE( NOUT, FMT = 9995 )J\n*\n  140 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      WRITE( NOUT, FMT = 9994 )NC, SNAME, M, N, ALPHA, INCX, INCY, LDA\n*\n  150 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( '      THESE ARE THE RESULTS FOR COLUMN ', I3 )\n 9994 FORMAT( 1X, I6, ': ', A6, '(', 2( I3, ',' ), '(', F4.1, ',', F4.1,\n     $      '), X,', I2, ', Y,', I2, ', A,', I3, ')                   ',\n     $      '      .' )\n 9993 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of ZCHK4.\n*\n      END\n      SUBROUTINE ZCHK5( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX,\n     $                  INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G,\n     $                  Z )\n*\n*  Tests ZHER and ZHPR.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Parameters ..\n      COMPLEX*16         ZERO, HALF, ONE\n      PARAMETER          ( ZERO = ( 0.0D0, 0.0D0 ),\n     $                   HALF = ( 0.5D0, 0.0D0 ),\n     $                   ONE = ( 1.0D0, 0.0D0 ) )\n      DOUBLE PRECISION   RZERO\n      PARAMETER          ( RZERO = 0.0D0 )\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION   EPS, THRESH\n      INTEGER            INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      COMPLEX*16         A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), X( NMAX ), XS( NMAX*INCMAX ),\n     $                   XX( NMAX*INCMAX ), Y( NMAX ),\n     $                   YS( NMAX*INCMAX ), YT( NMAX ),\n     $                   YY( NMAX*INCMAX ), Z( NMAX )\n      DOUBLE PRECISION   G( NMAX )\n      INTEGER            IDIM( NIDIM ), INC( NINC )\n*     .. Local Scalars ..\n      COMPLEX*16         ALPHA, TRANSL\n      DOUBLE PRECISION   ERR, ERRMAX, RALPHA, RALS\n      INTEGER            I, IA, IC, IN, INCX, INCXS, IX, J, JA, JJ, LAA,\n     $                   LDA, LDAS, LJ, LX, N, NARGS, NC, NS\n      LOGICAL            FULL, NULL, PACKED, RESET, SAME, UPPER\n      CHARACTER*1        UPLO, UPLOS\n      CHARACTER*2        ICH\n*     .. Local Arrays ..\n      COMPLEX*16         W( 1 )\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LZE, LZERES\n      EXTERNAL           LZE, LZERES\n*     .. External Subroutines ..\n      EXTERNAL           ZHER, ZHPR, ZMAKE, ZMVCH\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, DBLE, DCMPLX, DCONJG, MAX\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICH/'UL'/\n*     .. Executable Statements ..\n      FULL = SNAME( 3: 3 ).EQ.'E'\n      PACKED = SNAME( 3: 3 ).EQ.'P'\n*     Define the number of arguments.\n      IF( FULL )THEN\n         NARGS = 7\n      ELSE IF( PACKED )THEN\n         NARGS = 6\n      END IF\n*\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = RZERO\n*\n      DO 100 IN = 1, NIDIM\n         N = IDIM( IN )\n*        Set LDA to 1 more than minimum value if room.\n         LDA = N\n         IF( LDA.LT.NMAX )\n     $      LDA = LDA + 1\n*        Skip tests if not enough room.\n         IF( LDA.GT.NMAX )\n     $      GO TO 100\n         IF( PACKED )THEN\n            LAA = ( N*( N + 1 ) )/2\n         ELSE\n            LAA = LDA*N\n         END IF\n*\n         DO 90 IC = 1, 2\n            UPLO = ICH( IC: IC )\n            UPPER = UPLO.EQ.'U'\n*\n            DO 80 IX = 1, NINC\n               INCX = INC( IX )\n               LX = ABS( INCX )*N\n*\n*              Generate the vector X.\n*\n               TRANSL = HALF\n               CALL ZMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX, ABS( INCX ),\n     $                     0, N - 1, RESET, TRANSL )\n               IF( N.GT.1 )THEN\n                  X( N/2 ) = ZERO\n                  XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO\n               END IF\n*\n               DO 70 IA = 1, NALF\n                  RALPHA = DBLE( ALF( IA ) )\n                  ALPHA = DCMPLX( RALPHA, RZERO )\n                  NULL = N.LE.0.OR.RALPHA.EQ.RZERO\n*\n*                 Generate the matrix A.\n*\n                  TRANSL = ZERO\n                  CALL ZMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A, NMAX,\n     $                        AA, LDA, N - 1, N - 1, RESET, TRANSL )\n*\n                  NC = NC + 1\n*\n*                 Save every datum before calling the subroutine.\n*\n                  UPLOS = UPLO\n                  NS = N\n                  RALS = RALPHA\n                  DO 10 I = 1, LAA\n                     AS( I ) = AA( I )\n   10             CONTINUE\n                  LDAS = LDA\n                  DO 20 I = 1, LX\n                     XS( I ) = XX( I )\n   20             CONTINUE\n                  INCXS = INCX\n*\n*                 Call the subroutine.\n*\n                  IF( FULL )THEN\n                     IF( TRACE )\n     $                  WRITE( NTRA, FMT = 9993 )NC, SNAME, UPLO, N,\n     $                  RALPHA, INCX, LDA\n                     IF( REWI )\n     $                  REWIND NTRA\n                     CALL ZHER( UPLO, N, RALPHA, XX, INCX, AA, LDA )\n                  ELSE IF( PACKED )THEN\n                     IF( TRACE )\n     $                  WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO, N,\n     $                  RALPHA, INCX\n                     IF( REWI )\n     $                  REWIND NTRA\n                     CALL ZHPR( UPLO, N, RALPHA, XX, INCX, AA )\n                  END IF\n*\n*                 Check if error-exit was taken incorrectly.\n*\n                  IF( .NOT.OK )THEN\n                     WRITE( NOUT, FMT = 9992 )\n                     FATAL = .TRUE.\n                     GO TO 120\n                  END IF\n*\n*                 See what data changed inside subroutines.\n*\n                  ISAME( 1 ) = UPLO.EQ.UPLOS\n                  ISAME( 2 ) = NS.EQ.N\n                  ISAME( 3 ) = RALS.EQ.RALPHA\n                  ISAME( 4 ) = LZE( XS, XX, LX )\n                  ISAME( 5 ) = INCXS.EQ.INCX\n                  IF( NULL )THEN\n                     ISAME( 6 ) = LZE( AS, AA, LAA )\n                  ELSE\n                     ISAME( 6 ) = LZERES( SNAME( 2: 3 ), UPLO, N, N, AS,\n     $                            AA, LDA )\n                  END IF\n                  IF( .NOT.PACKED )THEN\n                     ISAME( 7 ) = LDAS.EQ.LDA\n                  END IF\n*\n*                 If data was incorrectly changed, report and return.\n*\n                  SAME = .TRUE.\n                  DO 30 I = 1, NARGS\n                     SAME = SAME.AND.ISAME( I )\n                     IF( .NOT.ISAME( I ) )\n     $                  WRITE( NOUT, FMT = 9998 )I\n   30             CONTINUE\n                  IF( .NOT.SAME )THEN\n                     FATAL = .TRUE.\n                     GO TO 120\n                  END IF\n*\n                  IF( .NOT.NULL )THEN\n*\n*                    Check the result column by column.\n*\n                     IF( INCX.GT.0 )THEN\n                        DO 40 I = 1, N\n                           Z( I ) = X( I )\n   40                   CONTINUE\n                     ELSE\n                        DO 50 I = 1, N\n                           Z( I ) = X( N - I + 1 )\n   50                   CONTINUE\n                     END IF\n                     JA = 1\n                     DO 60 J = 1, N\n                        W( 1 ) = DCONJG( Z( J ) )\n                        IF( UPPER )THEN\n                           JJ = 1\n                           LJ = J\n                        ELSE\n                           JJ = J\n                           LJ = N - J + 1\n                        END IF\n                        CALL ZMVCH( 'N', LJ, 1, ALPHA, Z( JJ ), LJ, W,\n     $                              1, ONE, A( JJ, J ), 1, YT, G,\n     $                              AA( JA ), EPS, ERR, FATAL, NOUT,\n     $                              .TRUE. )\n                        IF( FULL )THEN\n                           IF( UPPER )THEN\n                              JA = JA + LDA\n                           ELSE\n                              JA = JA + LDA + 1\n                           END IF\n                        ELSE\n                           JA = JA + LJ\n                        END IF\n                        ERRMAX = MAX( ERRMAX, ERR )\n*                       If got really bad answer, report and return.\n                        IF( FATAL )\n     $                     GO TO 110\n   60                CONTINUE\n                  ELSE\n*                    Avoid repeating tests if N.le.0.\n                     IF( N.LE.0 )\n     $                  GO TO 100\n                  END IF\n*\n   70          CONTINUE\n*\n   80       CONTINUE\n*\n   90    CONTINUE\n*\n  100 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 130\n*\n  110 CONTINUE\n      WRITE( NOUT, FMT = 9995 )J\n*\n  120 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      IF( FULL )THEN\n         WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, RALPHA, INCX, LDA\n      ELSE IF( PACKED )THEN\n         WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, RALPHA, INCX\n      END IF\n*\n  130 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( '      THESE ARE THE RESULTS FOR COLUMN ', I3 )\n 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,',\n     $      I2, ', AP)                                         .' )\n 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,',\n     $      I2, ', A,', I3, ')                                      .' )\n 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of ZCHK5.\n*\n      END\n      SUBROUTINE ZCHK6( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX,\n     $                  INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G,\n     $                  Z )\n*\n*  Tests ZHER2 and ZHPR2.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Parameters ..\n      COMPLEX*16         ZERO, HALF, ONE\n      PARAMETER          ( ZERO = ( 0.0D0, 0.0D0 ),\n     $                   HALF = ( 0.5D0, 0.0D0 ),\n     $                   ONE = ( 1.0D0, 0.0D0 ) )\n      DOUBLE PRECISION   RZERO\n      PARAMETER          ( RZERO = 0.0D0 )\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION   EPS, THRESH\n      INTEGER            INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      COMPLEX*16         A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), X( NMAX ), XS( NMAX*INCMAX ),\n     $                   XX( NMAX*INCMAX ), Y( NMAX ),\n     $                   YS( NMAX*INCMAX ), YT( NMAX ),\n     $                   YY( NMAX*INCMAX ), Z( NMAX, 2 )\n      DOUBLE PRECISION   G( NMAX )\n      INTEGER            IDIM( NIDIM ), INC( NINC )\n*     .. Local Scalars ..\n      COMPLEX*16         ALPHA, ALS, TRANSL\n      DOUBLE PRECISION   ERR, ERRMAX\n      INTEGER            I, IA, IC, IN, INCX, INCXS, INCY, INCYS, IX,\n     $                   IY, J, JA, JJ, LAA, LDA, LDAS, LJ, LX, LY, N,\n     $                   NARGS, NC, NS\n      LOGICAL            FULL, NULL, PACKED, RESET, SAME, UPPER\n      CHARACTER*1        UPLO, UPLOS\n      CHARACTER*2        ICH\n*     .. Local Arrays ..\n      COMPLEX*16         W( 2 )\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LZE, LZERES\n      EXTERNAL           LZE, LZERES\n*     .. External Subroutines ..\n      EXTERNAL           ZHER2, ZHPR2, ZMAKE, ZMVCH\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, DCONJG, MAX\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICH/'UL'/\n*     .. Executable Statements ..\n      FULL = SNAME( 3: 3 ).EQ.'E'\n      PACKED = SNAME( 3: 3 ).EQ.'P'\n*     Define the number of arguments.\n      IF( FULL )THEN\n         NARGS = 9\n      ELSE IF( PACKED )THEN\n         NARGS = 8\n      END IF\n*\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = RZERO\n*\n      DO 140 IN = 1, NIDIM\n         N = IDIM( IN )\n*        Set LDA to 1 more than minimum value if room.\n         LDA = N\n         IF( LDA.LT.NMAX )\n     $      LDA = LDA + 1\n*        Skip tests if not enough room.\n         IF( LDA.GT.NMAX )\n     $      GO TO 140\n         IF( PACKED )THEN\n            LAA = ( N*( N + 1 ) )/2\n         ELSE\n            LAA = LDA*N\n         END IF\n*\n         DO 130 IC = 1, 2\n            UPLO = ICH( IC: IC )\n            UPPER = UPLO.EQ.'U'\n*\n            DO 120 IX = 1, NINC\n               INCX = INC( IX )\n               LX = ABS( INCX )*N\n*\n*              Generate the vector X.\n*\n               TRANSL = HALF\n               CALL ZMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX, ABS( INCX ),\n     $                     0, N - 1, RESET, TRANSL )\n               IF( N.GT.1 )THEN\n                  X( N/2 ) = ZERO\n                  XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO\n               END IF\n*\n               DO 110 IY = 1, NINC\n                  INCY = INC( IY )\n                  LY = ABS( INCY )*N\n*\n*                 Generate the vector Y.\n*\n                  TRANSL = ZERO\n                  CALL ZMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY,\n     $                        ABS( INCY ), 0, N - 1, RESET, TRANSL )\n                  IF( N.GT.1 )THEN\n                     Y( N/2 ) = ZERO\n                     YY( 1 + ABS( INCY )*( N/2 - 1 ) ) = ZERO\n                  END IF\n*\n                  DO 100 IA = 1, NALF\n                     ALPHA = ALF( IA )\n                     NULL = N.LE.0.OR.ALPHA.EQ.ZERO\n*\n*                    Generate the matrix A.\n*\n                     TRANSL = ZERO\n                     CALL ZMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A,\n     $                           NMAX, AA, LDA, N - 1, N - 1, RESET,\n     $                           TRANSL )\n*\n                     NC = NC + 1\n*\n*                    Save every datum before calling the subroutine.\n*\n                     UPLOS = UPLO\n                     NS = N\n                     ALS = ALPHA\n                     DO 10 I = 1, LAA\n                        AS( I ) = AA( I )\n   10                CONTINUE\n                     LDAS = LDA\n                     DO 20 I = 1, LX\n                        XS( I ) = XX( I )\n   20                CONTINUE\n                     INCXS = INCX\n                     DO 30 I = 1, LY\n                        YS( I ) = YY( I )\n   30                CONTINUE\n                     INCYS = INCY\n*\n*                    Call the subroutine.\n*\n                     IF( FULL )THEN\n                        IF( TRACE )\n     $                     WRITE( NTRA, FMT = 9993 )NC, SNAME, UPLO, N,\n     $                     ALPHA, INCX, INCY, LDA\n                        IF( REWI )\n     $                     REWIND NTRA\n                        CALL ZHER2( UPLO, N, ALPHA, XX, INCX, YY, INCY,\n     $                              AA, LDA )\n                     ELSE IF( PACKED )THEN\n                        IF( TRACE )\n     $                     WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO, N,\n     $                     ALPHA, INCX, INCY\n                        IF( REWI )\n     $                     REWIND NTRA\n                        CALL ZHPR2( UPLO, N, ALPHA, XX, INCX, YY, INCY,\n     $                              AA )\n                     END IF\n*\n*                    Check if error-exit was taken incorrectly.\n*\n                     IF( .NOT.OK )THEN\n                        WRITE( NOUT, FMT = 9992 )\n                        FATAL = .TRUE.\n                        GO TO 160\n                     END IF\n*\n*                    See what data changed inside subroutines.\n*\n                     ISAME( 1 ) = UPLO.EQ.UPLOS\n                     ISAME( 2 ) = NS.EQ.N\n                     ISAME( 3 ) = ALS.EQ.ALPHA\n                     ISAME( 4 ) = LZE( XS, XX, LX )\n                     ISAME( 5 ) = INCXS.EQ.INCX\n                     ISAME( 6 ) = LZE( YS, YY, LY )\n                     ISAME( 7 ) = INCYS.EQ.INCY\n                     IF( NULL )THEN\n                        ISAME( 8 ) = LZE( AS, AA, LAA )\n                     ELSE\n                        ISAME( 8 ) = LZERES( SNAME( 2: 3 ), UPLO, N, N,\n     $                               AS, AA, LDA )\n                     END IF\n                     IF( .NOT.PACKED )THEN\n                        ISAME( 9 ) = LDAS.EQ.LDA\n                     END IF\n*\n*                    If data was incorrectly changed, report and return.\n*\n                     SAME = .TRUE.\n                     DO 40 I = 1, NARGS\n                        SAME = SAME.AND.ISAME( I )\n                        IF( .NOT.ISAME( I ) )\n     $                     WRITE( NOUT, FMT = 9998 )I\n   40                CONTINUE\n                     IF( .NOT.SAME )THEN\n                        FATAL = .TRUE.\n                        GO TO 160\n                     END IF\n*\n                     IF( .NOT.NULL )THEN\n*\n*                       Check the result column by column.\n*\n                        IF( INCX.GT.0 )THEN\n                           DO 50 I = 1, N\n                              Z( I, 1 ) = X( I )\n   50                      CONTINUE\n                        ELSE\n                           DO 60 I = 1, N\n                              Z( I, 1 ) = X( N - I + 1 )\n   60                      CONTINUE\n                        END IF\n                        IF( INCY.GT.0 )THEN\n                           DO 70 I = 1, N\n                              Z( I, 2 ) = Y( I )\n   70                      CONTINUE\n                        ELSE\n                           DO 80 I = 1, N\n                              Z( I, 2 ) = Y( N - I + 1 )\n   80                      CONTINUE\n                        END IF\n                        JA = 1\n                        DO 90 J = 1, N\n                           W( 1 ) = ALPHA*DCONJG( Z( J, 2 ) )\n                           W( 2 ) = DCONJG( ALPHA )*DCONJG( Z( J, 1 ) )\n                           IF( UPPER )THEN\n                              JJ = 1\n                              LJ = J\n                           ELSE\n                              JJ = J\n                              LJ = N - J + 1\n                           END IF\n                           CALL ZMVCH( 'N', LJ, 2, ONE, Z( JJ, 1 ),\n     $                                 NMAX, W, 1, ONE, A( JJ, J ), 1,\n     $                                 YT, G, AA( JA ), EPS, ERR, FATAL,\n     $                                 NOUT, .TRUE. )\n                           IF( FULL )THEN\n                              IF( UPPER )THEN\n                                 JA = JA + LDA\n                              ELSE\n                                 JA = JA + LDA + 1\n                              END IF\n                           ELSE\n                              JA = JA + LJ\n                           END IF\n                           ERRMAX = MAX( ERRMAX, ERR )\n*                          If got really bad answer, report and return.\n                           IF( FATAL )\n     $                        GO TO 150\n   90                   CONTINUE\n                     ELSE\n*                       Avoid repeating tests with N.le.0.\n                        IF( N.LE.0 )\n     $                     GO TO 140\n                     END IF\n*\n  100             CONTINUE\n*\n  110          CONTINUE\n*\n  120       CONTINUE\n*\n  130    CONTINUE\n*\n  140 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 170\n*\n  150 CONTINUE\n      WRITE( NOUT, FMT = 9995 )J\n*\n  160 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      IF( FULL )THEN\n         WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, ALPHA, INCX,\n     $      INCY, LDA\n      ELSE IF( PACKED )THEN\n         WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, ALPHA, INCX, INCY\n      END IF\n*\n  170 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( '      THESE ARE THE RESULTS FOR COLUMN ', I3 )\n 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',(', F4.1, ',',\n     $      F4.1, '), X,', I2, ', Y,', I2, ', AP)                     ',\n     $      '       .' )\n 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',(', F4.1, ',',\n     $      F4.1, '), X,', I2, ', Y,', I2, ', A,', I3, ')             ',\n     $      '            .' )\n 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of ZCHK6.\n*\n      END\n      SUBROUTINE ZCHKE( ISNUM, SRNAMT, NOUT )\n*\n*  Tests the error exits from the Level 2 Blas.\n*  Requires a special version of the error-handling routine XERBLA.\n*  ALPHA, RALPHA, BETA, A, X and Y should not need to be defined.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Scalar Arguments ..\n      INTEGER            ISNUM, NOUT\n      CHARACTER*6        SRNAMT\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Local Scalars ..\n      COMPLEX*16         ALPHA, BETA\n      DOUBLE PRECISION   RALPHA\n*     .. Local Arrays ..\n      COMPLEX*16         A( 1, 1 ), X( 1 ), Y( 1 )\n*     .. External Subroutines ..\n      EXTERNAL           CHKXER, ZGBMV, ZGEMV, ZGERC, ZGERU, ZHBMV,\n     $                   ZHEMV, ZHER, ZHER2, ZHPMV, ZHPR, ZHPR2, ZTBMV,\n     $                   ZTBSV, ZTPMV, ZTPSV, ZTRMV, ZTRSV\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Executable Statements ..\n*     OK is set to .FALSE. by the special version of XERBLA or by CHKXER\n*     if anything is wrong.\n      OK = .TRUE.\n*     LERR is set to .TRUE. by the special version of XERBLA each time\n*     it is called, and is then tested and re-set by CHKXER.\n      LERR = .FALSE.\n      GO TO ( 10, 20, 30, 40, 50, 60, 70, 80,\n     $        90, 100, 110, 120, 130, 140, 150, 160,\n     $        170 )ISNUM\n   10 INFOT = 1\n      CALL ZGEMV( '/', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL ZGEMV( 'N', -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZGEMV( 'N', 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL ZGEMV( 'N', 2, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL ZGEMV( 'N', 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL ZGEMV( 'N', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 180\n   20 INFOT = 1\n      CALL ZGBMV( '/', 0, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL ZGBMV( 'N', -1, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZGBMV( 'N', 0, -1, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZGBMV( 'N', 0, 0, -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZGBMV( 'N', 2, 0, 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL ZGBMV( 'N', 0, 0, 1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL ZGBMV( 'N', 0, 0, 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 13\n      CALL ZGBMV( 'N', 0, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 180\n   30 INFOT = 1\n      CALL ZHEMV( '/', 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL ZHEMV( 'U', -1, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZHEMV( 'U', 2, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL ZHEMV( 'U', 0, ALPHA, A, 1, X, 0, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL ZHEMV( 'U', 0, ALPHA, A, 1, X, 1, BETA, Y, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 180\n   40 INFOT = 1\n      CALL ZHBMV( '/', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL ZHBMV( 'U', -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZHBMV( 'U', 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL ZHBMV( 'U', 0, 1, ALPHA, A, 1, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL ZHBMV( 'U', 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL ZHBMV( 'U', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 180\n   50 INFOT = 1\n      CALL ZHPMV( '/', 0, ALPHA, A, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL ZHPMV( 'U', -1, ALPHA, A, X, 1, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL ZHPMV( 'U', 0, ALPHA, A, X, 0, BETA, Y, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZHPMV( 'U', 0, ALPHA, A, X, 1, BETA, Y, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 180\n   60 INFOT = 1\n      CALL ZTRMV( '/', 'N', 'N', 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL ZTRMV( 'U', '/', 'N', 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZTRMV( 'U', 'N', '/', 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZTRMV( 'U', 'N', 'N', -1, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL ZTRMV( 'U', 'N', 'N', 2, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL ZTRMV( 'U', 'N', 'N', 0, A, 1, X, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 180\n   70 INFOT = 1\n      CALL ZTBMV( '/', 'N', 'N', 0, 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL ZTBMV( 'U', '/', 'N', 0, 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZTBMV( 'U', 'N', '/', 0, 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZTBMV( 'U', 'N', 'N', -1, 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZTBMV( 'U', 'N', 'N', 0, -1, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL ZTBMV( 'U', 'N', 'N', 0, 1, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZTBMV( 'U', 'N', 'N', 0, 0, A, 1, X, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 180\n   80 INFOT = 1\n      CALL ZTPMV( '/', 'N', 'N', 0, A, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL ZTPMV( 'U', '/', 'N', 0, A, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZTPMV( 'U', 'N', '/', 0, A, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZTPMV( 'U', 'N', 'N', -1, A, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL ZTPMV( 'U', 'N', 'N', 0, A, X, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 180\n   90 INFOT = 1\n      CALL ZTRSV( '/', 'N', 'N', 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL ZTRSV( 'U', '/', 'N', 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZTRSV( 'U', 'N', '/', 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZTRSV( 'U', 'N', 'N', -1, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL ZTRSV( 'U', 'N', 'N', 2, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL ZTRSV( 'U', 'N', 'N', 0, A, 1, X, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 180\n  100 INFOT = 1\n      CALL ZTBSV( '/', 'N', 'N', 0, 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL ZTBSV( 'U', '/', 'N', 0, 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZTBSV( 'U', 'N', '/', 0, 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZTBSV( 'U', 'N', 'N', -1, 0, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZTBSV( 'U', 'N', 'N', 0, -1, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL ZTBSV( 'U', 'N', 'N', 0, 1, A, 1, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZTBSV( 'U', 'N', 'N', 0, 0, A, 1, X, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 180\n  110 INFOT = 1\n      CALL ZTPSV( '/', 'N', 'N', 0, A, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL ZTPSV( 'U', '/', 'N', 0, A, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZTPSV( 'U', 'N', '/', 0, A, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZTPSV( 'U', 'N', 'N', -1, A, X, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL ZTPSV( 'U', 'N', 'N', 0, A, X, 0 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 180\n  120 INFOT = 1\n      CALL ZGERC( -1, 0, ALPHA, X, 1, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL ZGERC( 0, -1, ALPHA, X, 1, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZGERC( 0, 0, ALPHA, X, 0, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL ZGERC( 0, 0, ALPHA, X, 1, Y, 0, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZGERC( 2, 0, ALPHA, X, 1, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 180\n  130 INFOT = 1\n      CALL ZGERU( -1, 0, ALPHA, X, 1, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL ZGERU( 0, -1, ALPHA, X, 1, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZGERU( 0, 0, ALPHA, X, 0, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL ZGERU( 0, 0, ALPHA, X, 1, Y, 0, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZGERU( 2, 0, ALPHA, X, 1, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 180\n  140 INFOT = 1\n      CALL ZHER( '/', 0, RALPHA, X, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL ZHER( 'U', -1, RALPHA, X, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZHER( 'U', 0, RALPHA, X, 0, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL ZHER( 'U', 2, RALPHA, X, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 180\n  150 INFOT = 1\n      CALL ZHPR( '/', 0, RALPHA, X, 1, A )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL ZHPR( 'U', -1, RALPHA, X, 1, A )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZHPR( 'U', 0, RALPHA, X, 0, A )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 180\n  160 INFOT = 1\n      CALL ZHER2( '/', 0, ALPHA, X, 1, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL ZHER2( 'U', -1, ALPHA, X, 1, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZHER2( 'U', 0, ALPHA, X, 0, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL ZHER2( 'U', 0, ALPHA, X, 1, Y, 0, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZHER2( 'U', 2, ALPHA, X, 1, Y, 1, A, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 180\n  170 INFOT = 1\n      CALL ZHPR2( '/', 0, ALPHA, X, 1, Y, 1, A )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL ZHPR2( 'U', -1, ALPHA, X, 1, Y, 1, A )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZHPR2( 'U', 0, ALPHA, X, 0, Y, 1, A )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL ZHPR2( 'U', 0, ALPHA, X, 1, Y, 0, A )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n*\n  180 IF( OK )THEN\n         WRITE( NOUT, FMT = 9999 )SRNAMT\n      ELSE\n         WRITE( NOUT, FMT = 9998 )SRNAMT\n      END IF\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE TESTS OF ERROR-EXITS' )\n 9998 FORMAT( ' ******* ', A6, ' FAILED THE TESTS OF ERROR-EXITS *****',\n     $      '**' )\n*\n*     End of ZCHKE.\n*\n      END\n      SUBROUTINE ZMAKE( TYPE, UPLO, DIAG, M, N, A, NMAX, AA, LDA, KL,\n     $                  KU, RESET, TRANSL )\n*\n*  Generates values for an M by N matrix A within the bandwidth\n*  defined by KL and KU.\n*  Stores the values in the array AA in the data structure required\n*  by the routine, with unwanted elements set to rogue value.\n*\n*  TYPE is 'GE', 'GB', 'HE', 'HB', 'HP', 'TR', 'TB' OR 'TP'.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Parameters ..\n      COMPLEX*16         ZERO, ONE\n      PARAMETER          ( ZERO = ( 0.0D0, 0.0D0 ),\n     $                   ONE = ( 1.0D0, 0.0D0 ) )\n      COMPLEX*16         ROGUE\n      PARAMETER          ( ROGUE = ( -1.0D10, 1.0D10 ) )\n      DOUBLE PRECISION   RZERO\n      PARAMETER          ( RZERO = 0.0D0 )\n      DOUBLE PRECISION   RROGUE\n      PARAMETER          ( RROGUE = -1.0D10 )\n*     .. Scalar Arguments ..\n      COMPLEX*16         TRANSL\n      INTEGER            KL, KU, LDA, M, N, NMAX\n      LOGICAL            RESET\n      CHARACTER*1        DIAG, UPLO\n      CHARACTER*2        TYPE\n*     .. Array Arguments ..\n      COMPLEX*16         A( NMAX, * ), AA( * )\n*     .. Local Scalars ..\n      INTEGER            I, I1, I2, I3, IBEG, IEND, IOFF, J, JJ, KK\n      LOGICAL            GEN, LOWER, SYM, TRI, UNIT, UPPER\n*     .. External Functions ..\n      COMPLEX*16         ZBEG\n      EXTERNAL           ZBEG\n*     .. Intrinsic Functions ..\n      INTRINSIC          DBLE, DCMPLX, DCONJG, MAX, MIN\n*     .. Executable Statements ..\n      GEN = TYPE( 1: 1 ).EQ.'G'\n      SYM = TYPE( 1: 1 ).EQ.'H'\n      TRI = TYPE( 1: 1 ).EQ.'T'\n      UPPER = ( SYM.OR.TRI ).AND.UPLO.EQ.'U'\n      LOWER = ( SYM.OR.TRI ).AND.UPLO.EQ.'L'\n      UNIT = TRI.AND.DIAG.EQ.'U'\n*\n*     Generate data in array A.\n*\n      DO 20 J = 1, N\n         DO 10 I = 1, M\n            IF( GEN.OR.( UPPER.AND.I.LE.J ).OR.( LOWER.AND.I.GE.J ) )\n     $          THEN\n               IF( ( I.LE.J.AND.J - I.LE.KU ).OR.\n     $             ( I.GE.J.AND.I - J.LE.KL ) )THEN\n                  A( I, J ) = ZBEG( RESET ) + TRANSL\n               ELSE\n                  A( I, J ) = ZERO\n               END IF\n               IF( I.NE.J )THEN\n                  IF( SYM )THEN\n                     A( J, I ) = DCONJG( A( I, J ) )\n                  ELSE IF( TRI )THEN\n                     A( J, I ) = ZERO\n                  END IF\n               END IF\n            END IF\n   10    CONTINUE\n         IF( SYM )\n     $      A( J, J ) = DCMPLX( DBLE( A( J, J ) ), RZERO )\n         IF( TRI )\n     $      A( J, J ) = A( J, J ) + ONE\n         IF( UNIT )\n     $      A( J, J ) = ONE\n   20 CONTINUE\n*\n*     Store elements in array AS in data structure required by routine.\n*\n      IF( TYPE.EQ.'GE' )THEN\n         DO 50 J = 1, N\n            DO 30 I = 1, M\n               AA( I + ( J - 1 )*LDA ) = A( I, J )\n   30       CONTINUE\n            DO 40 I = M + 1, LDA\n               AA( I + ( J - 1 )*LDA ) = ROGUE\n   40       CONTINUE\n   50    CONTINUE\n      ELSE IF( TYPE.EQ.'GB' )THEN\n         DO 90 J = 1, N\n            DO 60 I1 = 1, KU + 1 - J\n               AA( I1 + ( J - 1 )*LDA ) = ROGUE\n   60       CONTINUE\n            DO 70 I2 = I1, MIN( KL + KU + 1, KU + 1 + M - J )\n               AA( I2 + ( J - 1 )*LDA ) = A( I2 + J - KU - 1, J )\n   70       CONTINUE\n            DO 80 I3 = I2, LDA\n               AA( I3 + ( J - 1 )*LDA ) = ROGUE\n   80       CONTINUE\n   90    CONTINUE\n      ELSE IF( TYPE.EQ.'HE'.OR.TYPE.EQ.'TR' )THEN\n         DO 130 J = 1, N\n            IF( UPPER )THEN\n               IBEG = 1\n               IF( UNIT )THEN\n                  IEND = J - 1\n               ELSE\n                  IEND = J\n               END IF\n            ELSE\n               IF( UNIT )THEN\n                  IBEG = J + 1\n               ELSE\n                  IBEG = J\n               END IF\n               IEND = N\n            END IF\n            DO 100 I = 1, IBEG - 1\n               AA( I + ( J - 1 )*LDA ) = ROGUE\n  100       CONTINUE\n            DO 110 I = IBEG, IEND\n               AA( I + ( J - 1 )*LDA ) = A( I, J )\n  110       CONTINUE\n            DO 120 I = IEND + 1, LDA\n               AA( I + ( J - 1 )*LDA ) = ROGUE\n  120       CONTINUE\n            IF( SYM )THEN\n               JJ = J + ( J - 1 )*LDA\n               AA( JJ ) = DCMPLX( DBLE( AA( JJ ) ), RROGUE )\n            END IF\n  130    CONTINUE\n      ELSE IF( TYPE.EQ.'HB'.OR.TYPE.EQ.'TB' )THEN\n         DO 170 J = 1, N\n            IF( UPPER )THEN\n               KK = KL + 1\n               IBEG = MAX( 1, KL + 2 - J )\n               IF( UNIT )THEN\n                  IEND = KL\n               ELSE\n                  IEND = KL + 1\n               END IF\n            ELSE\n               KK = 1\n               IF( UNIT )THEN\n                  IBEG = 2\n               ELSE\n                  IBEG = 1\n               END IF\n               IEND = MIN( KL + 1, 1 + M - J )\n            END IF\n            DO 140 I = 1, IBEG - 1\n               AA( I + ( J - 1 )*LDA ) = ROGUE\n  140       CONTINUE\n            DO 150 I = IBEG, IEND\n               AA( I + ( J - 1 )*LDA ) = A( I + J - KK, J )\n  150       CONTINUE\n            DO 160 I = IEND + 1, LDA\n               AA( I + ( J - 1 )*LDA ) = ROGUE\n  160       CONTINUE\n            IF( SYM )THEN\n               JJ = KK + ( J - 1 )*LDA\n               AA( JJ ) = DCMPLX( DBLE( AA( JJ ) ), RROGUE )\n            END IF\n  170    CONTINUE\n      ELSE IF( TYPE.EQ.'HP'.OR.TYPE.EQ.'TP' )THEN\n         IOFF = 0\n         DO 190 J = 1, N\n            IF( UPPER )THEN\n               IBEG = 1\n               IEND = J\n            ELSE\n               IBEG = J\n               IEND = N\n            END IF\n            DO 180 I = IBEG, IEND\n               IOFF = IOFF + 1\n               AA( IOFF ) = A( I, J )\n               IF( I.EQ.J )THEN\n                  IF( UNIT )\n     $               AA( IOFF ) = ROGUE\n                  IF( SYM )\n     $               AA( IOFF ) = DCMPLX( DBLE( AA( IOFF ) ), RROGUE )\n               END IF\n  180       CONTINUE\n  190    CONTINUE\n      END IF\n      RETURN\n*\n*     End of ZMAKE.\n*\n      END\n      SUBROUTINE ZMVCH( TRANS, M, N, ALPHA, A, NMAX, X, INCX, BETA, Y,\n     $                  INCY, YT, G, YY, EPS, ERR, FATAL, NOUT, MV )\n*\n*  Checks the results of the computational tests.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Parameters ..\n      COMPLEX*16         ZERO\n      PARAMETER          ( ZERO = ( 0.0D0, 0.0D0 ) )\n      DOUBLE PRECISION   RZERO, RONE\n      PARAMETER          ( RZERO = 0.0D0, RONE = 1.0D0 )\n*     .. Scalar Arguments ..\n      COMPLEX*16         ALPHA, BETA\n      DOUBLE PRECISION   EPS, ERR\n      INTEGER            INCX, INCY, M, N, NMAX, NOUT\n      LOGICAL            FATAL, MV\n      CHARACTER*1        TRANS\n*     .. Array Arguments ..\n      COMPLEX*16         A( NMAX, * ), X( * ), Y( * ), YT( * ), YY( * )\n      DOUBLE PRECISION   G( * )\n*     .. Local Scalars ..\n      COMPLEX*16         C\n      DOUBLE PRECISION   ERRI\n      INTEGER            I, INCXL, INCYL, IY, J, JX, KX, KY, ML, NL\n      LOGICAL            CTRAN, TRAN\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, DBLE, DCONJG, DIMAG, MAX, SQRT\n*     .. Statement Functions ..\n      DOUBLE PRECISION   ABS1\n*     .. Statement Function definitions ..\n      ABS1( C ) = ABS( DBLE( C ) ) + ABS( DIMAG( C ) )\n*     .. Executable Statements ..\n      TRAN = TRANS.EQ.'T'\n      CTRAN = TRANS.EQ.'C'\n      IF( TRAN.OR.CTRAN )THEN\n         ML = N\n         NL = M\n      ELSE\n         ML = M\n         NL = N\n      END IF\n      IF( INCX.LT.0 )THEN\n         KX = NL\n         INCXL = -1\n      ELSE\n         KX = 1\n         INCXL = 1\n      END IF\n      IF( INCY.LT.0 )THEN\n         KY = ML\n         INCYL = -1\n      ELSE\n         KY = 1\n         INCYL = 1\n      END IF\n*\n*     Compute expected result in YT using data in A, X and Y.\n*     Compute gauges in G.\n*\n      IY = KY\n      DO 40 I = 1, ML\n         YT( IY ) = ZERO\n         G( IY ) = RZERO\n         JX = KX\n         IF( TRAN )THEN\n            DO 10 J = 1, NL\n               YT( IY ) = YT( IY ) + A( J, I )*X( JX )\n               G( IY ) = G( IY ) + ABS1( A( J, I ) )*ABS1( X( JX ) )\n               JX = JX + INCXL\n   10       CONTINUE\n         ELSE IF( CTRAN )THEN\n            DO 20 J = 1, NL\n               YT( IY ) = YT( IY ) + DCONJG( A( J, I ) )*X( JX )\n               G( IY ) = G( IY ) + ABS1( A( J, I ) )*ABS1( X( JX ) )\n               JX = JX + INCXL\n   20       CONTINUE\n         ELSE\n            DO 30 J = 1, NL\n               YT( IY ) = YT( IY ) + A( I, J )*X( JX )\n               G( IY ) = G( IY ) + ABS1( A( I, J ) )*ABS1( X( JX ) )\n               JX = JX + INCXL\n   30       CONTINUE\n         END IF\n         YT( IY ) = ALPHA*YT( IY ) + BETA*Y( IY )\n         G( IY ) = ABS1( ALPHA )*G( IY ) + ABS1( BETA )*ABS1( Y( IY ) )\n         IY = IY + INCYL\n   40 CONTINUE\n*\n*     Compute the error ratio for this result.\n*\n      ERR = ZERO\n      DO 50 I = 1, ML\n         ERRI = ABS( YT( I ) - YY( 1 + ( I - 1 )*ABS( INCY ) ) )/EPS\n         IF( G( I ).NE.RZERO )\n     $      ERRI = ERRI/G( I )\n         ERR = MAX( ERR, ERRI )\n         IF( ERR*SQRT( EPS ).GE.RONE )\n     $      GO TO 60\n   50 CONTINUE\n*     If the loop completes, all results are at least half accurate.\n      GO TO 80\n*\n*     Report fatal error.\n*\n   60 FATAL = .TRUE.\n      WRITE( NOUT, FMT = 9999 )\n      DO 70 I = 1, ML\n         IF( MV )THEN\n            WRITE( NOUT, FMT = 9998 )I, YT( I ),\n     $         YY( 1 + ( I - 1 )*ABS( INCY ) )\n         ELSE\n            WRITE( NOUT, FMT = 9998 )I,\n     $         YY( 1 + ( I - 1 )*ABS( INCY ) ), YT( I )\n         END IF\n   70 CONTINUE\n*\n   80 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ******* FATAL ERROR - COMPUTED RESULT IS LESS THAN HAL',\n     $      'F ACCURATE *******', /'                       EXPECTED RE',\n     $      'SULT                    COMPUTED RESULT' )\n 9998 FORMAT( 1X, I7, 2( '  (', G15.6, ',', G15.6, ')' ) )\n*\n*     End of ZMVCH.\n*\n      END\n      LOGICAL FUNCTION LZE( RI, RJ, LR )\n*\n*  Tests if two arrays are identical.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Scalar Arguments ..\n      INTEGER            LR\n*     .. Array Arguments ..\n      COMPLEX*16         RI( * ), RJ( * )\n*     .. Local Scalars ..\n      INTEGER            I\n*     .. Executable Statements ..\n      DO 10 I = 1, LR\n         IF( RI( I ).NE.RJ( I ) )\n     $      GO TO 20\n   10 CONTINUE\n      LZE = .TRUE.\n      GO TO 30\n   20 CONTINUE\n      LZE = .FALSE.\n   30 RETURN\n*\n*     End of LZE.\n*\n      END\n      LOGICAL FUNCTION LZERES( TYPE, UPLO, M, N, AA, AS, LDA )\n*\n*  Tests if selected elements in two arrays are equal.\n*\n*  TYPE is 'GE', 'HE' or 'HP'.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Scalar Arguments ..\n      INTEGER            LDA, M, N\n      CHARACTER*1        UPLO\n      CHARACTER*2        TYPE\n*     .. Array Arguments ..\n      COMPLEX*16         AA( LDA, * ), AS( LDA, * )\n*     .. Local Scalars ..\n      INTEGER            I, IBEG, IEND, J\n      LOGICAL            UPPER\n*     .. Executable Statements ..\n      UPPER = UPLO.EQ.'U'\n      IF( TYPE.EQ.'GE' )THEN\n         DO 20 J = 1, N\n            DO 10 I = M + 1, LDA\n               IF( AA( I, J ).NE.AS( I, J ) )\n     $            GO TO 70\n   10       CONTINUE\n   20    CONTINUE\n      ELSE IF( TYPE.EQ.'HE' )THEN\n         DO 50 J = 1, N\n            IF( UPPER )THEN\n               IBEG = 1\n               IEND = J\n            ELSE\n               IBEG = J\n               IEND = N\n            END IF\n            DO 30 I = 1, IBEG - 1\n               IF( AA( I, J ).NE.AS( I, J ) )\n     $            GO TO 70\n   30       CONTINUE\n            DO 40 I = IEND + 1, LDA\n               IF( AA( I, J ).NE.AS( I, J ) )\n     $            GO TO 70\n   40       CONTINUE\n   50    CONTINUE\n      END IF\n*\n      LZERES = .TRUE.\n      GO TO 80\n   70 CONTINUE\n      LZERES = .FALSE.\n   80 RETURN\n*\n*     End of LZERES.\n*\n      END\n      COMPLEX*16 FUNCTION ZBEG( RESET )\n*\n*  Generates complex numbers as pairs of random numbers uniformly\n*  distributed between -0.5 and 0.5.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Scalar Arguments ..\n      LOGICAL            RESET\n*     .. Local Scalars ..\n      INTEGER            I, IC, J, MI, MJ\n*     .. Save statement ..\n      SAVE               I, IC, J, MI, MJ\n*     .. Intrinsic Functions ..\n      INTRINSIC          DCMPLX\n*     .. Executable Statements ..\n      IF( RESET )THEN\n*        Initialize local variables.\n         MI = 891\n         MJ = 457\n         I = 7\n         J = 7\n         IC = 0\n         RESET = .FALSE.\n      END IF\n*\n*     The sequence of values of I or J is bounded between 1 and 999.\n*     If initial I or J = 1,2,3,6,7 or 9, the period will be 50.\n*     If initial I or J = 4 or 8, the period will be 25.\n*     If initial I or J = 5, the period will be 10.\n*     IC is used to break up the period by skipping 1 value of I or J\n*     in 6.\n*\n      IC = IC + 1\n   10 I = I*MI\n      J = J*MJ\n      I = I - 1000*( I/1000 )\n      J = J - 1000*( J/1000 )\n      IF( IC.GE.5 )THEN\n         IC = 0\n         GO TO 10\n      END IF\n      ZBEG = DCMPLX( ( I - 500 )/1001.0D0, ( J - 500 )/1001.0D0 )\n      RETURN\n*\n*     End of ZBEG.\n*\n      END\n      DOUBLE PRECISION FUNCTION DDIFF( X, Y )\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION   X, Y\n*     .. Executable Statements ..\n      DDIFF = X - Y\n      RETURN\n*\n*     End of DDIFF.\n*\n      END\n      SUBROUTINE CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n*\n*  Tests whether XERBLA has detected an error when it should.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Scalar Arguments ..\n      INTEGER            INFOT, NOUT\n      LOGICAL            LERR, OK\n      CHARACTER*6        SRNAMT\n*     .. Executable Statements ..\n      IF( .NOT.LERR )THEN\n         WRITE( NOUT, FMT = 9999 )INFOT, SRNAMT\n         OK = .FALSE.\n      END IF\n      LERR = .FALSE.\n      RETURN\n*\n 9999 FORMAT( ' ***** ILLEGAL VALUE OF PARAMETER NUMBER ', I2, ' NOT D',\n     $      'ETECTED BY ', A6, ' *****' )\n*\n*     End of CHKXER.\n*\n      END\n      SUBROUTINE XERBLA( SRNAME, INFO )\n*\n*  This is a special version of XERBLA to be used only as part of\n*  the test program for testing error exits from the Level 2 BLAS\n*  routines.\n*\n*  XERBLA  is an error handler for the Level 2 BLAS routines.\n*\n*  It is called by the Level 2 BLAS routines if an input parameter is\n*  invalid.\n*\n*  Auxiliary routine for test program for Level 2 Blas.\n*\n*  -- Written on 10-August-1987.\n*     Richard Hanson, Sandia National Labs.\n*     Jeremy Du Croz, NAG Central Office.\n*\n*     .. Scalar Arguments ..\n      INTEGER            INFO\n      CHARACTER*6        SRNAME\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUT\n      LOGICAL            LERR, OK\n      CHARACTER*6        SRNAMT\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUT, OK, LERR\n      COMMON             /SRNAMC/SRNAMT\n*     .. Executable Statements ..\n      LERR = .TRUE.\n      IF( INFO.NE.INFOT )THEN\n         IF( INFOT.NE.0 )THEN\n            WRITE( NOUT, FMT = 9999 )INFO, INFOT\n         ELSE\n            WRITE( NOUT, FMT = 9997 )INFO\n         END IF\n         OK = .FALSE.\n      END IF\n      IF( SRNAME.NE.SRNAMT )THEN\n         WRITE( NOUT, FMT = 9998 )SRNAME, SRNAMT\n         OK = .FALSE.\n      END IF\n      RETURN\n*\n 9999 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6, ' INSTEAD',\n     $      ' OF ', I2, ' *******' )\n 9998 FORMAT( ' ******* XERBLA WAS CALLED WITH SRNAME = ', A6, ' INSTE',\n     $      'AD OF ', A6, ' *******' )\n 9997 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6,\n     $      ' *******' )\n*\n*     End of XERBLA\n*\n      END\n\n"
  },
  {
    "path": "include/eigen3/blas/testing/zblat3.f",
    "content": "*> \\brief \\b ZBLAT3\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*  Definition:\n*  ===========\n*\n*       PROGRAM ZBLAT3\n* \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> Test program for the COMPLEX*16       Level 3 Blas.\n*>\n*> The program must be driven by a short data file. The first 14 records\n*> of the file are read using list-directed input, the last 9 records\n*> are read using the format ( A6, L2 ). An annotated example of a data\n*> file can be obtained by deleting the first 3 characters from the\n*> following 23 lines:\n*> 'zblat3.out'      NAME OF SUMMARY OUTPUT FILE\n*> 6                 UNIT NUMBER OF SUMMARY FILE\n*> 'ZBLAT3.SNAP'     NAME OF SNAPSHOT OUTPUT FILE\n*> -1                UNIT NUMBER OF SNAPSHOT FILE (NOT USED IF .LT. 0)\n*> F        LOGICAL FLAG, T TO REWIND SNAPSHOT FILE AFTER EACH RECORD.\n*> F        LOGICAL FLAG, T TO STOP ON FAILURES.\n*> T        LOGICAL FLAG, T TO TEST ERROR EXITS.\n*> 16.0     THRESHOLD VALUE OF TEST RATIO\n*> 6                 NUMBER OF VALUES OF N\n*> 0 1 2 3 5 9       VALUES OF N\n*> 3                 NUMBER OF VALUES OF ALPHA\n*> (0.0,0.0) (1.0,0.0) (0.7,-0.9)       VALUES OF ALPHA\n*> 3                 NUMBER OF VALUES OF BETA\n*> (0.0,0.0) (1.0,0.0) (1.3,-1.1)       VALUES OF BETA\n*> ZGEMM  T PUT F FOR NO TEST. SAME COLUMNS.\n*> ZHEMM  T PUT F FOR NO TEST. SAME COLUMNS.\n*> ZSYMM  T PUT F FOR NO TEST. SAME COLUMNS.\n*> ZTRMM  T PUT F FOR NO TEST. SAME COLUMNS.\n*> ZTRSM  T PUT F FOR NO TEST. SAME COLUMNS.\n*> ZHERK  T PUT F FOR NO TEST. SAME COLUMNS.\n*> ZSYRK  T PUT F FOR NO TEST. SAME COLUMNS.\n*> ZHER2K T PUT F FOR NO TEST. SAME COLUMNS.\n*> ZSYR2K T PUT F FOR NO TEST. SAME COLUMNS.\n*>\n*> \n*> Further Details\n*> ===============\n*>\n*> See:\n*>\n*>    Dongarra J. J., Du Croz J. J., Duff I. S. and Hammarling S.\n*>    A Set of Level 3 Basic Linear Algebra Subprograms.\n*>\n*>    Technical Memorandum No.88 (Revision 1), Mathematics and\n*>    Computer Science Division, Argonne National Laboratory, 9700\n*>    South Cass Avenue, Argonne, Illinois 60439, US.\n*>\n*> -- Written on 8-February-1989.\n*>    Jack Dongarra, Argonne National Laboratory.\n*>    Iain Duff, AERE Harwell.\n*>    Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*>    Sven Hammarling, Numerical Algorithms Group Ltd.\n*>\n*>    10-9-00:  Change STATUS='NEW' to 'UNKNOWN' so that the testers\n*>              can be run multiple times without deleting generated\n*>              output files (susan)\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date April 2012\n*\n*> \\ingroup complex16_blas_testing\n*\n*  =====================================================================\n      PROGRAM ZBLAT3\n*\n*  -- Reference BLAS test routine (version 3.4.1) --\n*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     April 2012\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      INTEGER            NIN\n      PARAMETER          ( NIN = 5 )\n      INTEGER            NSUBS\n      PARAMETER          ( NSUBS = 9 )\n      COMPLEX*16         ZERO, ONE\n      PARAMETER          ( ZERO = ( 0.0D0, 0.0D0 ),\n     $                   ONE = ( 1.0D0, 0.0D0 ) )\n      DOUBLE PRECISION   RZERO\n      PARAMETER          ( RZERO = 0.0D0 )\n      INTEGER            NMAX\n      PARAMETER          ( NMAX = 65 )\n      INTEGER            NIDMAX, NALMAX, NBEMAX\n      PARAMETER          ( NIDMAX = 9, NALMAX = 7, NBEMAX = 7 )\n*     .. Local Scalars ..\n      DOUBLE PRECISION   EPS, ERR, THRESH\n      INTEGER            I, ISNUM, J, N, NALF, NBET, NIDIM, NOUT, NTRA\n      LOGICAL            FATAL, LTESTT, REWI, SAME, SFATAL, TRACE,\n     $                   TSTERR\n      CHARACTER*1        TRANSA, TRANSB\n      CHARACTER*6        SNAMET\n      CHARACTER*32       SNAPS, SUMMRY\n*     .. Local Arrays ..\n      COMPLEX*16         AA( NMAX*NMAX ), AB( NMAX, 2*NMAX ),\n     $                   ALF( NALMAX ), AS( NMAX*NMAX ),\n     $                   BB( NMAX*NMAX ), BET( NBEMAX ),\n     $                   BS( NMAX*NMAX ), C( NMAX, NMAX ),\n     $                   CC( NMAX*NMAX ), CS( NMAX*NMAX ), CT( NMAX ),\n     $                   W( 2*NMAX )\n      DOUBLE PRECISION   G( NMAX )\n      INTEGER            IDIM( NIDMAX )\n      LOGICAL            LTEST( NSUBS )\n      CHARACTER*6        SNAMES( NSUBS )\n*     .. External Functions ..\n      DOUBLE PRECISION   DDIFF\n      LOGICAL            LZE\n      EXTERNAL           DDIFF, LZE\n*     .. External Subroutines ..\n      EXTERNAL           ZCHK1, ZCHK2, ZCHK3, ZCHK4, ZCHK5, ZCHKE, ZMMCH\n*     .. Intrinsic Functions ..\n      INTRINSIC          MAX, MIN\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n      CHARACTER*6        SRNAMT\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n      COMMON             /SRNAMC/SRNAMT\n*     .. Data statements ..\n      DATA               SNAMES/'ZGEMM ', 'ZHEMM ', 'ZSYMM ', 'ZTRMM ',\n     $                   'ZTRSM ', 'ZHERK ', 'ZSYRK ', 'ZHER2K',\n     $                   'ZSYR2K'/\n*     .. Executable Statements ..\n*\n*     Read name and unit number for summary output file and open file.\n*\n      READ( NIN, FMT = * )SUMMRY\n      READ( NIN, FMT = * )NOUT\n      OPEN( NOUT, FILE = SUMMRY, STATUS = 'UNKNOWN' )\n      NOUTC = NOUT\n*\n*     Read name and unit number for snapshot output file and open file.\n*\n      READ( NIN, FMT = * )SNAPS\n      READ( NIN, FMT = * )NTRA\n      TRACE = NTRA.GE.0\n      IF( TRACE )THEN\n         OPEN( NTRA, FILE = SNAPS, STATUS = 'UNKNOWN' )\n      END IF\n*     Read the flag that directs rewinding of the snapshot file.\n      READ( NIN, FMT = * )REWI\n      REWI = REWI.AND.TRACE\n*     Read the flag that directs stopping on any failure.\n      READ( NIN, FMT = * )SFATAL\n*     Read the flag that indicates whether error exits are to be tested.\n      READ( NIN, FMT = * )TSTERR\n*     Read the threshold value of the test ratio\n      READ( NIN, FMT = * )THRESH\n*\n*     Read and check the parameter values for the tests.\n*\n*     Values of N\n      READ( NIN, FMT = * )NIDIM\n      IF( NIDIM.LT.1.OR.NIDIM.GT.NIDMAX )THEN\n         WRITE( NOUT, FMT = 9997 )'N', NIDMAX\n         GO TO 220\n      END IF\n      READ( NIN, FMT = * )( IDIM( I ), I = 1, NIDIM )\n      DO 10 I = 1, NIDIM\n         IF( IDIM( I ).LT.0.OR.IDIM( I ).GT.NMAX )THEN\n            WRITE( NOUT, FMT = 9996 )NMAX\n            GO TO 220\n         END IF\n   10 CONTINUE\n*     Values of ALPHA\n      READ( NIN, FMT = * )NALF\n      IF( NALF.LT.1.OR.NALF.GT.NALMAX )THEN\n         WRITE( NOUT, FMT = 9997 )'ALPHA', NALMAX\n         GO TO 220\n      END IF\n      READ( NIN, FMT = * )( ALF( I ), I = 1, NALF )\n*     Values of BETA\n      READ( NIN, FMT = * )NBET\n      IF( NBET.LT.1.OR.NBET.GT.NBEMAX )THEN\n         WRITE( NOUT, FMT = 9997 )'BETA', NBEMAX\n         GO TO 220\n      END IF\n      READ( NIN, FMT = * )( BET( I ), I = 1, NBET )\n*\n*     Report values of parameters.\n*\n      WRITE( NOUT, FMT = 9995 )\n      WRITE( NOUT, FMT = 9994 )( IDIM( I ), I = 1, NIDIM )\n      WRITE( NOUT, FMT = 9993 )( ALF( I ), I = 1, NALF )\n      WRITE( NOUT, FMT = 9992 )( BET( I ), I = 1, NBET )\n      IF( .NOT.TSTERR )THEN\n         WRITE( NOUT, FMT = * )\n         WRITE( NOUT, FMT = 9984 )\n      END IF\n      WRITE( NOUT, FMT = * )\n      WRITE( NOUT, FMT = 9999 )THRESH\n      WRITE( NOUT, FMT = * )\n*\n*     Read names of subroutines and flags which indicate\n*     whether they are to be tested.\n*\n      DO 20 I = 1, NSUBS\n         LTEST( I ) = .FALSE.\n   20 CONTINUE\n   30 READ( NIN, FMT = 9988, END = 60 )SNAMET, LTESTT\n      DO 40 I = 1, NSUBS\n         IF( SNAMET.EQ.SNAMES( I ) )\n     $      GO TO 50\n   40 CONTINUE\n      WRITE( NOUT, FMT = 9990 )SNAMET\n      STOP\n   50 LTEST( I ) = LTESTT\n      GO TO 30\n*\n   60 CONTINUE\n      CLOSE ( NIN )\n*\n*     Compute EPS (the machine precision).\n*\n      EPS = EPSILON(RZERO)\n      WRITE( NOUT, FMT = 9998 )EPS\n*\n*     Check the reliability of ZMMCH using exact data.\n*\n      N = MIN( 32, NMAX )\n      DO 100 J = 1, N\n         DO 90 I = 1, N\n            AB( I, J ) = MAX( I - J + 1, 0 )\n   90    CONTINUE\n         AB( J, NMAX + 1 ) = J\n         AB( 1, NMAX + J ) = J\n         C( J, 1 ) = ZERO\n  100 CONTINUE\n      DO 110 J = 1, N\n         CC( J ) = J*( ( J + 1 )*J )/2 - ( ( J + 1 )*J*( J - 1 ) )/3\n  110 CONTINUE\n*     CC holds the exact result. On exit from ZMMCH CT holds\n*     the result computed by ZMMCH.\n      TRANSA = 'N'\n      TRANSB = 'N'\n      CALL ZMMCH( TRANSA, TRANSB, N, 1, N, ONE, AB, NMAX,\n     $            AB( 1, NMAX + 1 ), NMAX, ZERO, C, NMAX, CT, G, CC,\n     $            NMAX, EPS, ERR, FATAL, NOUT, .TRUE. )\n      SAME = LZE( CC, CT, N )\n      IF( .NOT.SAME.OR.ERR.NE.RZERO )THEN\n         WRITE( NOUT, FMT = 9989 )TRANSA, TRANSB, SAME, ERR\n         STOP\n      END IF\n      TRANSB = 'C'\n      CALL ZMMCH( TRANSA, TRANSB, N, 1, N, ONE, AB, NMAX,\n     $            AB( 1, NMAX + 1 ), NMAX, ZERO, C, NMAX, CT, G, CC,\n     $            NMAX, EPS, ERR, FATAL, NOUT, .TRUE. )\n      SAME = LZE( CC, CT, N )\n      IF( .NOT.SAME.OR.ERR.NE.RZERO )THEN\n         WRITE( NOUT, FMT = 9989 )TRANSA, TRANSB, SAME, ERR\n         STOP\n      END IF\n      DO 120 J = 1, N\n         AB( J, NMAX + 1 ) = N - J + 1\n         AB( 1, NMAX + J ) = N - J + 1\n  120 CONTINUE\n      DO 130 J = 1, N\n         CC( N - J + 1 ) = J*( ( J + 1 )*J )/2 -\n     $                     ( ( J + 1 )*J*( J - 1 ) )/3\n  130 CONTINUE\n      TRANSA = 'C'\n      TRANSB = 'N'\n      CALL ZMMCH( TRANSA, TRANSB, N, 1, N, ONE, AB, NMAX,\n     $            AB( 1, NMAX + 1 ), NMAX, ZERO, C, NMAX, CT, G, CC,\n     $            NMAX, EPS, ERR, FATAL, NOUT, .TRUE. )\n      SAME = LZE( CC, CT, N )\n      IF( .NOT.SAME.OR.ERR.NE.RZERO )THEN\n         WRITE( NOUT, FMT = 9989 )TRANSA, TRANSB, SAME, ERR\n         STOP\n      END IF\n      TRANSB = 'C'\n      CALL ZMMCH( TRANSA, TRANSB, N, 1, N, ONE, AB, NMAX,\n     $            AB( 1, NMAX + 1 ), NMAX, ZERO, C, NMAX, CT, G, CC,\n     $            NMAX, EPS, ERR, FATAL, NOUT, .TRUE. )\n      SAME = LZE( CC, CT, N )\n      IF( .NOT.SAME.OR.ERR.NE.RZERO )THEN\n         WRITE( NOUT, FMT = 9989 )TRANSA, TRANSB, SAME, ERR\n         STOP\n      END IF\n*\n*     Test each subroutine in turn.\n*\n      DO 200 ISNUM = 1, NSUBS\n         WRITE( NOUT, FMT = * )\n         IF( .NOT.LTEST( ISNUM ) )THEN\n*           Subprogram is not to be tested.\n            WRITE( NOUT, FMT = 9987 )SNAMES( ISNUM )\n         ELSE\n            SRNAMT = SNAMES( ISNUM )\n*           Test error exits.\n            IF( TSTERR )THEN\n               CALL ZCHKE( ISNUM, SNAMES( ISNUM ), NOUT )\n               WRITE( NOUT, FMT = * )\n            END IF\n*           Test computations.\n            INFOT = 0\n            OK = .TRUE.\n            FATAL = .FALSE.\n            GO TO ( 140, 150, 150, 160, 160, 170, 170,\n     $              180, 180 )ISNUM\n*           Test ZGEMM, 01.\n  140       CALL ZCHK1( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET,\n     $                  NMAX, AB, AA, AS, AB( 1, NMAX + 1 ), BB, BS, C,\n     $                  CC, CS, CT, G )\n            GO TO 190\n*           Test ZHEMM, 02, ZSYMM, 03.\n  150       CALL ZCHK2( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET,\n     $                  NMAX, AB, AA, AS, AB( 1, NMAX + 1 ), BB, BS, C,\n     $                  CC, CS, CT, G )\n            GO TO 190\n*           Test ZTRMM, 04, ZTRSM, 05.\n  160       CALL ZCHK3( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NALF, ALF, NMAX, AB,\n     $                  AA, AS, AB( 1, NMAX + 1 ), BB, BS, CT, G, C )\n            GO TO 190\n*           Test ZHERK, 06, ZSYRK, 07.\n  170       CALL ZCHK4( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET,\n     $                  NMAX, AB, AA, AS, AB( 1, NMAX + 1 ), BB, BS, C,\n     $                  CC, CS, CT, G )\n            GO TO 190\n*           Test ZHER2K, 08, ZSYR2K, 09.\n  180       CALL ZCHK5( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,\n     $                  REWI, FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET,\n     $                  NMAX, AB, AA, AS, BB, BS, C, CC, CS, CT, G, W )\n            GO TO 190\n*\n  190       IF( FATAL.AND.SFATAL )\n     $         GO TO 210\n         END IF\n  200 CONTINUE\n      WRITE( NOUT, FMT = 9986 )\n      GO TO 230\n*\n  210 CONTINUE\n      WRITE( NOUT, FMT = 9985 )\n      GO TO 230\n*\n  220 CONTINUE\n      WRITE( NOUT, FMT = 9991 )\n*\n  230 CONTINUE\n      IF( TRACE )\n     $   CLOSE ( NTRA )\n      CLOSE ( NOUT )\n      STOP\n*\n 9999 FORMAT( ' ROUTINES PASS COMPUTATIONAL TESTS IF TEST RATIO IS LES',\n     $      'S THAN', F8.2 )\n 9998 FORMAT( ' RELATIVE MACHINE PRECISION IS TAKEN TO BE', 1P, D9.1 )\n 9997 FORMAT( ' NUMBER OF VALUES OF ', A, ' IS LESS THAN 1 OR GREATER ',\n     $      'THAN ', I2 )\n 9996 FORMAT( ' VALUE OF N IS LESS THAN 0 OR GREATER THAN ', I2 )\n 9995 FORMAT( ' TESTS OF THE COMPLEX*16       LEVEL 3 BLAS', //' THE F',\n     $      'OLLOWING PARAMETER VALUES WILL BE USED:' )\n 9994 FORMAT( '   FOR N              ', 9I6 )\n 9993 FORMAT( '   FOR ALPHA          ',\n     $      7( '(', F4.1, ',', F4.1, ')  ', : ) )\n 9992 FORMAT( '   FOR BETA           ',\n     $      7( '(', F4.1, ',', F4.1, ')  ', : ) )\n 9991 FORMAT( ' AMEND DATA FILE OR INCREASE ARRAY SIZES IN PROGRAM',\n     $      /' ******* TESTS ABANDONED *******' )\n 9990 FORMAT( ' SUBPROGRAM NAME ', A6, ' NOT RECOGNIZED', /' ******* T',\n     $      'ESTS ABANDONED *******' )\n 9989 FORMAT( ' ERROR IN ZMMCH -  IN-LINE DOT PRODUCTS ARE BEING EVALU',\n     $      'ATED WRONGLY.', /' ZMMCH WAS CALLED WITH TRANSA = ', A1,\n     $      ' AND TRANSB = ', A1, /' AND RETURNED SAME = ', L1, ' AND ',\n     $      'ERR = ', F12.3, '.', /' THIS MAY BE DUE TO FAULTS IN THE ',\n     $      'ARITHMETIC OR THE COMPILER.', /' ******* TESTS ABANDONED ',\n     $      '*******' )\n 9988 FORMAT( A6, L2 )\n 9987 FORMAT( 1X, A6, ' WAS NOT TESTED' )\n 9986 FORMAT( /' END OF TESTS' )\n 9985 FORMAT( /' ******* FATAL ERROR - TESTS ABANDONED *******' )\n 9984 FORMAT( ' ERROR-EXITS WILL NOT BE TESTED' )\n*\n*     End of ZBLAT3.\n*\n      END\n      SUBROUTINE ZCHK1( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET, NMAX,\n     $                  A, AA, AS, B, BB, BS, C, CC, CS, CT, G )\n*\n*  Tests ZGEMM.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Parameters ..\n      COMPLEX*16         ZERO\n      PARAMETER          ( ZERO = ( 0.0D0, 0.0D0 ) )\n      DOUBLE PRECISION   RZERO\n      PARAMETER          ( RZERO = 0.0D0 )\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION   EPS, THRESH\n      INTEGER            NALF, NBET, NIDIM, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      COMPLEX*16         A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), B( NMAX, NMAX ),\n     $                   BB( NMAX*NMAX ), BET( NBET ), BS( NMAX*NMAX ),\n     $                   C( NMAX, NMAX ), CC( NMAX*NMAX ),\n     $                   CS( NMAX*NMAX ), CT( NMAX )\n      DOUBLE PRECISION   G( NMAX )\n      INTEGER            IDIM( NIDIM )\n*     .. Local Scalars ..\n      COMPLEX*16         ALPHA, ALS, BETA, BLS\n      DOUBLE PRECISION   ERR, ERRMAX\n      INTEGER            I, IA, IB, ICA, ICB, IK, IM, IN, K, KS, LAA,\n     $                   LBB, LCC, LDA, LDAS, LDB, LDBS, LDC, LDCS, M,\n     $                   MA, MB, MS, N, NA, NARGS, NB, NC, NS\n      LOGICAL            NULL, RESET, SAME, TRANA, TRANB\n      CHARACTER*1        TRANAS, TRANBS, TRANSA, TRANSB\n      CHARACTER*3        ICH\n*     .. Local Arrays ..\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LZE, LZERES\n      EXTERNAL           LZE, LZERES\n*     .. External Subroutines ..\n      EXTERNAL           ZGEMM, ZMAKE, ZMMCH\n*     .. Intrinsic Functions ..\n      INTRINSIC          MAX\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICH/'NTC'/\n*     .. Executable Statements ..\n*\n      NARGS = 13\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = RZERO\n*\n      DO 110 IM = 1, NIDIM\n         M = IDIM( IM )\n*\n         DO 100 IN = 1, NIDIM\n            N = IDIM( IN )\n*           Set LDC to 1 more than minimum value if room.\n            LDC = M\n            IF( LDC.LT.NMAX )\n     $         LDC = LDC + 1\n*           Skip tests if not enough room.\n            IF( LDC.GT.NMAX )\n     $         GO TO 100\n            LCC = LDC*N\n            NULL = N.LE.0.OR.M.LE.0\n*\n            DO 90 IK = 1, NIDIM\n               K = IDIM( IK )\n*\n               DO 80 ICA = 1, 3\n                  TRANSA = ICH( ICA: ICA )\n                  TRANA = TRANSA.EQ.'T'.OR.TRANSA.EQ.'C'\n*\n                  IF( TRANA )THEN\n                     MA = K\n                     NA = M\n                  ELSE\n                     MA = M\n                     NA = K\n                  END IF\n*                 Set LDA to 1 more than minimum value if room.\n                  LDA = MA\n                  IF( LDA.LT.NMAX )\n     $               LDA = LDA + 1\n*                 Skip tests if not enough room.\n                  IF( LDA.GT.NMAX )\n     $               GO TO 80\n                  LAA = LDA*NA\n*\n*                 Generate the matrix A.\n*\n                  CALL ZMAKE( 'GE', ' ', ' ', MA, NA, A, NMAX, AA, LDA,\n     $                        RESET, ZERO )\n*\n                  DO 70 ICB = 1, 3\n                     TRANSB = ICH( ICB: ICB )\n                     TRANB = TRANSB.EQ.'T'.OR.TRANSB.EQ.'C'\n*\n                     IF( TRANB )THEN\n                        MB = N\n                        NB = K\n                     ELSE\n                        MB = K\n                        NB = N\n                     END IF\n*                    Set LDB to 1 more than minimum value if room.\n                     LDB = MB\n                     IF( LDB.LT.NMAX )\n     $                  LDB = LDB + 1\n*                    Skip tests if not enough room.\n                     IF( LDB.GT.NMAX )\n     $                  GO TO 70\n                     LBB = LDB*NB\n*\n*                    Generate the matrix B.\n*\n                     CALL ZMAKE( 'GE', ' ', ' ', MB, NB, B, NMAX, BB,\n     $                           LDB, RESET, ZERO )\n*\n                     DO 60 IA = 1, NALF\n                        ALPHA = ALF( IA )\n*\n                        DO 50 IB = 1, NBET\n                           BETA = BET( IB )\n*\n*                          Generate the matrix C.\n*\n                           CALL ZMAKE( 'GE', ' ', ' ', M, N, C, NMAX,\n     $                                 CC, LDC, RESET, ZERO )\n*\n                           NC = NC + 1\n*\n*                          Save every datum before calling the\n*                          subroutine.\n*\n                           TRANAS = TRANSA\n                           TRANBS = TRANSB\n                           MS = M\n                           NS = N\n                           KS = K\n                           ALS = ALPHA\n                           DO 10 I = 1, LAA\n                              AS( I ) = AA( I )\n   10                      CONTINUE\n                           LDAS = LDA\n                           DO 20 I = 1, LBB\n                              BS( I ) = BB( I )\n   20                      CONTINUE\n                           LDBS = LDB\n                           BLS = BETA\n                           DO 30 I = 1, LCC\n                              CS( I ) = CC( I )\n   30                      CONTINUE\n                           LDCS = LDC\n*\n*                          Call the subroutine.\n*\n                           IF( TRACE )\n     $                        WRITE( NTRA, FMT = 9995 )NC, SNAME,\n     $                        TRANSA, TRANSB, M, N, K, ALPHA, LDA, LDB,\n     $                        BETA, LDC\n                           IF( REWI )\n     $                        REWIND NTRA\n                           CALL ZGEMM( TRANSA, TRANSB, M, N, K, ALPHA,\n     $                                 AA, LDA, BB, LDB, BETA, CC, LDC )\n*\n*                          Check if error-exit was taken incorrectly.\n*\n                           IF( .NOT.OK )THEN\n                              WRITE( NOUT, FMT = 9994 )\n                              FATAL = .TRUE.\n                              GO TO 120\n                           END IF\n*\n*                          See what data changed inside subroutines.\n*\n                           ISAME( 1 ) = TRANSA.EQ.TRANAS\n                           ISAME( 2 ) = TRANSB.EQ.TRANBS\n                           ISAME( 3 ) = MS.EQ.M\n                           ISAME( 4 ) = NS.EQ.N\n                           ISAME( 5 ) = KS.EQ.K\n                           ISAME( 6 ) = ALS.EQ.ALPHA\n                           ISAME( 7 ) = LZE( AS, AA, LAA )\n                           ISAME( 8 ) = LDAS.EQ.LDA\n                           ISAME( 9 ) = LZE( BS, BB, LBB )\n                           ISAME( 10 ) = LDBS.EQ.LDB\n                           ISAME( 11 ) = BLS.EQ.BETA\n                           IF( NULL )THEN\n                              ISAME( 12 ) = LZE( CS, CC, LCC )\n                           ELSE\n                              ISAME( 12 ) = LZERES( 'GE', ' ', M, N, CS,\n     $                                      CC, LDC )\n                           END IF\n                           ISAME( 13 ) = LDCS.EQ.LDC\n*\n*                          If data was incorrectly changed, report\n*                          and return.\n*\n                           SAME = .TRUE.\n                           DO 40 I = 1, NARGS\n                              SAME = SAME.AND.ISAME( I )\n                              IF( .NOT.ISAME( I ) )\n     $                           WRITE( NOUT, FMT = 9998 )I\n   40                      CONTINUE\n                           IF( .NOT.SAME )THEN\n                              FATAL = .TRUE.\n                              GO TO 120\n                           END IF\n*\n                           IF( .NOT.NULL )THEN\n*\n*                             Check the result.\n*\n                              CALL ZMMCH( TRANSA, TRANSB, M, N, K,\n     $                                    ALPHA, A, NMAX, B, NMAX, BETA,\n     $                                    C, NMAX, CT, G, CC, LDC, EPS,\n     $                                    ERR, FATAL, NOUT, .TRUE. )\n                              ERRMAX = MAX( ERRMAX, ERR )\n*                             If got really bad answer, report and\n*                             return.\n                              IF( FATAL )\n     $                           GO TO 120\n                           END IF\n*\n   50                   CONTINUE\n*\n   60                CONTINUE\n*\n   70             CONTINUE\n*\n   80          CONTINUE\n*\n   90       CONTINUE\n*\n  100    CONTINUE\n*\n  110 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 130\n*\n  120 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      WRITE( NOUT, FMT = 9995 )NC, SNAME, TRANSA, TRANSB, M, N, K,\n     $   ALPHA, LDA, LDB, BETA, LDC\n*\n  130 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',''', A1, ''',',\n     $      3( I3, ',' ), '(', F4.1, ',', F4.1, '), A,', I3, ', B,', I3,\n     $      ',(', F4.1, ',', F4.1, '), C,', I3, ').' )\n 9994 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of ZCHK1.\n*\n      END\n      SUBROUTINE ZCHK2( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET, NMAX,\n     $                  A, AA, AS, B, BB, BS, C, CC, CS, CT, G )\n*\n*  Tests ZHEMM and ZSYMM.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Parameters ..\n      COMPLEX*16         ZERO\n      PARAMETER          ( ZERO = ( 0.0D0, 0.0D0 ) )\n      DOUBLE PRECISION   RZERO\n      PARAMETER          ( RZERO = 0.0D0 )\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION   EPS, THRESH\n      INTEGER            NALF, NBET, NIDIM, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      COMPLEX*16         A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), B( NMAX, NMAX ),\n     $                   BB( NMAX*NMAX ), BET( NBET ), BS( NMAX*NMAX ),\n     $                   C( NMAX, NMAX ), CC( NMAX*NMAX ),\n     $                   CS( NMAX*NMAX ), CT( NMAX )\n      DOUBLE PRECISION   G( NMAX )\n      INTEGER            IDIM( NIDIM )\n*     .. Local Scalars ..\n      COMPLEX*16         ALPHA, ALS, BETA, BLS\n      DOUBLE PRECISION   ERR, ERRMAX\n      INTEGER            I, IA, IB, ICS, ICU, IM, IN, LAA, LBB, LCC,\n     $                   LDA, LDAS, LDB, LDBS, LDC, LDCS, M, MS, N, NA,\n     $                   NARGS, NC, NS\n      LOGICAL            CONJ, LEFT, NULL, RESET, SAME\n      CHARACTER*1        SIDE, SIDES, UPLO, UPLOS\n      CHARACTER*2        ICHS, ICHU\n*     .. Local Arrays ..\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LZE, LZERES\n      EXTERNAL           LZE, LZERES\n*     .. External Subroutines ..\n      EXTERNAL           ZHEMM, ZMAKE, ZMMCH, ZSYMM\n*     .. Intrinsic Functions ..\n      INTRINSIC          MAX\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICHS/'LR'/, ICHU/'UL'/\n*     .. Executable Statements ..\n      CONJ = SNAME( 2: 3 ).EQ.'HE'\n*\n      NARGS = 12\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = RZERO\n*\n      DO 100 IM = 1, NIDIM\n         M = IDIM( IM )\n*\n         DO 90 IN = 1, NIDIM\n            N = IDIM( IN )\n*           Set LDC to 1 more than minimum value if room.\n            LDC = M\n            IF( LDC.LT.NMAX )\n     $         LDC = LDC + 1\n*           Skip tests if not enough room.\n            IF( LDC.GT.NMAX )\n     $         GO TO 90\n            LCC = LDC*N\n            NULL = N.LE.0.OR.M.LE.0\n*           Set LDB to 1 more than minimum value if room.\n            LDB = M\n            IF( LDB.LT.NMAX )\n     $         LDB = LDB + 1\n*           Skip tests if not enough room.\n            IF( LDB.GT.NMAX )\n     $         GO TO 90\n            LBB = LDB*N\n*\n*           Generate the matrix B.\n*\n            CALL ZMAKE( 'GE', ' ', ' ', M, N, B, NMAX, BB, LDB, RESET,\n     $                  ZERO )\n*\n            DO 80 ICS = 1, 2\n               SIDE = ICHS( ICS: ICS )\n               LEFT = SIDE.EQ.'L'\n*\n               IF( LEFT )THEN\n                  NA = M\n               ELSE\n                  NA = N\n               END IF\n*              Set LDA to 1 more than minimum value if room.\n               LDA = NA\n               IF( LDA.LT.NMAX )\n     $            LDA = LDA + 1\n*              Skip tests if not enough room.\n               IF( LDA.GT.NMAX )\n     $            GO TO 80\n               LAA = LDA*NA\n*\n               DO 70 ICU = 1, 2\n                  UPLO = ICHU( ICU: ICU )\n*\n*                 Generate the hermitian or symmetric matrix A.\n*\n                  CALL ZMAKE( SNAME( 2: 3 ), UPLO, ' ', NA, NA, A, NMAX,\n     $                        AA, LDA, RESET, ZERO )\n*\n                  DO 60 IA = 1, NALF\n                     ALPHA = ALF( IA )\n*\n                     DO 50 IB = 1, NBET\n                        BETA = BET( IB )\n*\n*                       Generate the matrix C.\n*\n                        CALL ZMAKE( 'GE', ' ', ' ', M, N, C, NMAX, CC,\n     $                              LDC, RESET, ZERO )\n*\n                        NC = NC + 1\n*\n*                       Save every datum before calling the\n*                       subroutine.\n*\n                        SIDES = SIDE\n                        UPLOS = UPLO\n                        MS = M\n                        NS = N\n                        ALS = ALPHA\n                        DO 10 I = 1, LAA\n                           AS( I ) = AA( I )\n   10                   CONTINUE\n                        LDAS = LDA\n                        DO 20 I = 1, LBB\n                           BS( I ) = BB( I )\n   20                   CONTINUE\n                        LDBS = LDB\n                        BLS = BETA\n                        DO 30 I = 1, LCC\n                           CS( I ) = CC( I )\n   30                   CONTINUE\n                        LDCS = LDC\n*\n*                       Call the subroutine.\n*\n                        IF( TRACE )\n     $                     WRITE( NTRA, FMT = 9995 )NC, SNAME, SIDE,\n     $                     UPLO, M, N, ALPHA, LDA, LDB, BETA, LDC\n                        IF( REWI )\n     $                     REWIND NTRA\n                        IF( CONJ )THEN\n                           CALL ZHEMM( SIDE, UPLO, M, N, ALPHA, AA, LDA,\n     $                                 BB, LDB, BETA, CC, LDC )\n                        ELSE\n                           CALL ZSYMM( SIDE, UPLO, M, N, ALPHA, AA, LDA,\n     $                                 BB, LDB, BETA, CC, LDC )\n                        END IF\n*\n*                       Check if error-exit was taken incorrectly.\n*\n                        IF( .NOT.OK )THEN\n                           WRITE( NOUT, FMT = 9994 )\n                           FATAL = .TRUE.\n                           GO TO 110\n                        END IF\n*\n*                       See what data changed inside subroutines.\n*\n                        ISAME( 1 ) = SIDES.EQ.SIDE\n                        ISAME( 2 ) = UPLOS.EQ.UPLO\n                        ISAME( 3 ) = MS.EQ.M\n                        ISAME( 4 ) = NS.EQ.N\n                        ISAME( 5 ) = ALS.EQ.ALPHA\n                        ISAME( 6 ) = LZE( AS, AA, LAA )\n                        ISAME( 7 ) = LDAS.EQ.LDA\n                        ISAME( 8 ) = LZE( BS, BB, LBB )\n                        ISAME( 9 ) = LDBS.EQ.LDB\n                        ISAME( 10 ) = BLS.EQ.BETA\n                        IF( NULL )THEN\n                           ISAME( 11 ) = LZE( CS, CC, LCC )\n                        ELSE\n                           ISAME( 11 ) = LZERES( 'GE', ' ', M, N, CS,\n     $                                   CC, LDC )\n                        END IF\n                        ISAME( 12 ) = LDCS.EQ.LDC\n*\n*                       If data was incorrectly changed, report and\n*                       return.\n*\n                        SAME = .TRUE.\n                        DO 40 I = 1, NARGS\n                           SAME = SAME.AND.ISAME( I )\n                           IF( .NOT.ISAME( I ) )\n     $                        WRITE( NOUT, FMT = 9998 )I\n   40                   CONTINUE\n                        IF( .NOT.SAME )THEN\n                           FATAL = .TRUE.\n                           GO TO 110\n                        END IF\n*\n                        IF( .NOT.NULL )THEN\n*\n*                          Check the result.\n*\n                           IF( LEFT )THEN\n                              CALL ZMMCH( 'N', 'N', M, N, M, ALPHA, A,\n     $                                    NMAX, B, NMAX, BETA, C, NMAX,\n     $                                    CT, G, CC, LDC, EPS, ERR,\n     $                                    FATAL, NOUT, .TRUE. )\n                           ELSE\n                              CALL ZMMCH( 'N', 'N', M, N, N, ALPHA, B,\n     $                                    NMAX, A, NMAX, BETA, C, NMAX,\n     $                                    CT, G, CC, LDC, EPS, ERR,\n     $                                    FATAL, NOUT, .TRUE. )\n                           END IF\n                           ERRMAX = MAX( ERRMAX, ERR )\n*                          If got really bad answer, report and\n*                          return.\n                           IF( FATAL )\n     $                        GO TO 110\n                        END IF\n*\n   50                CONTINUE\n*\n   60             CONTINUE\n*\n   70          CONTINUE\n*\n   80       CONTINUE\n*\n   90    CONTINUE\n*\n  100 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 120\n*\n  110 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      WRITE( NOUT, FMT = 9995 )NC, SNAME, SIDE, UPLO, M, N, ALPHA, LDA,\n     $   LDB, BETA, LDC\n*\n  120 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( 1X, I6, ': ', A6, '(', 2( '''', A1, ''',' ), 2( I3, ',' ),\n     $      '(', F4.1, ',', F4.1, '), A,', I3, ', B,', I3, ',(', F4.1,\n     $      ',', F4.1, '), C,', I3, ')    .' )\n 9994 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of ZCHK2.\n*\n      END\n      SUBROUTINE ZCHK3( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NALF, ALF, NMAX, A, AA, AS,\n     $                  B, BB, BS, CT, G, C )\n*\n*  Tests ZTRMM and ZTRSM.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Parameters ..\n      COMPLEX*16         ZERO, ONE\n      PARAMETER          ( ZERO = ( 0.0D0, 0.0D0 ),\n     $                   ONE = ( 1.0D0, 0.0D0 ) )\n      DOUBLE PRECISION   RZERO\n      PARAMETER          ( RZERO = 0.0D0 )\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION   EPS, THRESH\n      INTEGER            NALF, NIDIM, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      COMPLEX*16         A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), B( NMAX, NMAX ),\n     $                   BB( NMAX*NMAX ), BS( NMAX*NMAX ),\n     $                   C( NMAX, NMAX ), CT( NMAX )\n      DOUBLE PRECISION   G( NMAX )\n      INTEGER            IDIM( NIDIM )\n*     .. Local Scalars ..\n      COMPLEX*16         ALPHA, ALS\n      DOUBLE PRECISION   ERR, ERRMAX\n      INTEGER            I, IA, ICD, ICS, ICT, ICU, IM, IN, J, LAA, LBB,\n     $                   LDA, LDAS, LDB, LDBS, M, MS, N, NA, NARGS, NC,\n     $                   NS\n      LOGICAL            LEFT, NULL, RESET, SAME\n      CHARACTER*1        DIAG, DIAGS, SIDE, SIDES, TRANAS, TRANSA, UPLO,\n     $                   UPLOS\n      CHARACTER*2        ICHD, ICHS, ICHU\n      CHARACTER*3        ICHT\n*     .. Local Arrays ..\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LZE, LZERES\n      EXTERNAL           LZE, LZERES\n*     .. External Subroutines ..\n      EXTERNAL           ZMAKE, ZMMCH, ZTRMM, ZTRSM\n*     .. Intrinsic Functions ..\n      INTRINSIC          MAX\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICHU/'UL'/, ICHT/'NTC'/, ICHD/'UN'/, ICHS/'LR'/\n*     .. Executable Statements ..\n*\n      NARGS = 11\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = RZERO\n*     Set up zero matrix for ZMMCH.\n      DO 20 J = 1, NMAX\n         DO 10 I = 1, NMAX\n            C( I, J ) = ZERO\n   10    CONTINUE\n   20 CONTINUE\n*\n      DO 140 IM = 1, NIDIM\n         M = IDIM( IM )\n*\n         DO 130 IN = 1, NIDIM\n            N = IDIM( IN )\n*           Set LDB to 1 more than minimum value if room.\n            LDB = M\n            IF( LDB.LT.NMAX )\n     $         LDB = LDB + 1\n*           Skip tests if not enough room.\n            IF( LDB.GT.NMAX )\n     $         GO TO 130\n            LBB = LDB*N\n            NULL = M.LE.0.OR.N.LE.0\n*\n            DO 120 ICS = 1, 2\n               SIDE = ICHS( ICS: ICS )\n               LEFT = SIDE.EQ.'L'\n               IF( LEFT )THEN\n                  NA = M\n               ELSE\n                  NA = N\n               END IF\n*              Set LDA to 1 more than minimum value if room.\n               LDA = NA\n               IF( LDA.LT.NMAX )\n     $            LDA = LDA + 1\n*              Skip tests if not enough room.\n               IF( LDA.GT.NMAX )\n     $            GO TO 130\n               LAA = LDA*NA\n*\n               DO 110 ICU = 1, 2\n                  UPLO = ICHU( ICU: ICU )\n*\n                  DO 100 ICT = 1, 3\n                     TRANSA = ICHT( ICT: ICT )\n*\n                     DO 90 ICD = 1, 2\n                        DIAG = ICHD( ICD: ICD )\n*\n                        DO 80 IA = 1, NALF\n                           ALPHA = ALF( IA )\n*\n*                          Generate the matrix A.\n*\n                           CALL ZMAKE( 'TR', UPLO, DIAG, NA, NA, A,\n     $                                 NMAX, AA, LDA, RESET, ZERO )\n*\n*                          Generate the matrix B.\n*\n                           CALL ZMAKE( 'GE', ' ', ' ', M, N, B, NMAX,\n     $                                 BB, LDB, RESET, ZERO )\n*\n                           NC = NC + 1\n*\n*                          Save every datum before calling the\n*                          subroutine.\n*\n                           SIDES = SIDE\n                           UPLOS = UPLO\n                           TRANAS = TRANSA\n                           DIAGS = DIAG\n                           MS = M\n                           NS = N\n                           ALS = ALPHA\n                           DO 30 I = 1, LAA\n                              AS( I ) = AA( I )\n   30                      CONTINUE\n                           LDAS = LDA\n                           DO 40 I = 1, LBB\n                              BS( I ) = BB( I )\n   40                      CONTINUE\n                           LDBS = LDB\n*\n*                          Call the subroutine.\n*\n                           IF( SNAME( 4: 5 ).EQ.'MM' )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9995 )NC, SNAME,\n     $                           SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA,\n     $                           LDA, LDB\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL ZTRMM( SIDE, UPLO, TRANSA, DIAG, M,\n     $                                    N, ALPHA, AA, LDA, BB, LDB )\n                           ELSE IF( SNAME( 4: 5 ).EQ.'SM' )THEN\n                              IF( TRACE )\n     $                           WRITE( NTRA, FMT = 9995 )NC, SNAME,\n     $                           SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA,\n     $                           LDA, LDB\n                              IF( REWI )\n     $                           REWIND NTRA\n                              CALL ZTRSM( SIDE, UPLO, TRANSA, DIAG, M,\n     $                                    N, ALPHA, AA, LDA, BB, LDB )\n                           END IF\n*\n*                          Check if error-exit was taken incorrectly.\n*\n                           IF( .NOT.OK )THEN\n                              WRITE( NOUT, FMT = 9994 )\n                              FATAL = .TRUE.\n                              GO TO 150\n                           END IF\n*\n*                          See what data changed inside subroutines.\n*\n                           ISAME( 1 ) = SIDES.EQ.SIDE\n                           ISAME( 2 ) = UPLOS.EQ.UPLO\n                           ISAME( 3 ) = TRANAS.EQ.TRANSA\n                           ISAME( 4 ) = DIAGS.EQ.DIAG\n                           ISAME( 5 ) = MS.EQ.M\n                           ISAME( 6 ) = NS.EQ.N\n                           ISAME( 7 ) = ALS.EQ.ALPHA\n                           ISAME( 8 ) = LZE( AS, AA, LAA )\n                           ISAME( 9 ) = LDAS.EQ.LDA\n                           IF( NULL )THEN\n                              ISAME( 10 ) = LZE( BS, BB, LBB )\n                           ELSE\n                              ISAME( 10 ) = LZERES( 'GE', ' ', M, N, BS,\n     $                                      BB, LDB )\n                           END IF\n                           ISAME( 11 ) = LDBS.EQ.LDB\n*\n*                          If data was incorrectly changed, report and\n*                          return.\n*\n                           SAME = .TRUE.\n                           DO 50 I = 1, NARGS\n                              SAME = SAME.AND.ISAME( I )\n                              IF( .NOT.ISAME( I ) )\n     $                           WRITE( NOUT, FMT = 9998 )I\n   50                      CONTINUE\n                           IF( .NOT.SAME )THEN\n                              FATAL = .TRUE.\n                              GO TO 150\n                           END IF\n*\n                           IF( .NOT.NULL )THEN\n                              IF( SNAME( 4: 5 ).EQ.'MM' )THEN\n*\n*                                Check the result.\n*\n                                 IF( LEFT )THEN\n                                    CALL ZMMCH( TRANSA, 'N', M, N, M,\n     $                                          ALPHA, A, NMAX, B, NMAX,\n     $                                          ZERO, C, NMAX, CT, G,\n     $                                          BB, LDB, EPS, ERR,\n     $                                          FATAL, NOUT, .TRUE. )\n                                 ELSE\n                                    CALL ZMMCH( 'N', TRANSA, M, N, N,\n     $                                          ALPHA, B, NMAX, A, NMAX,\n     $                                          ZERO, C, NMAX, CT, G,\n     $                                          BB, LDB, EPS, ERR,\n     $                                          FATAL, NOUT, .TRUE. )\n                                 END IF\n                              ELSE IF( SNAME( 4: 5 ).EQ.'SM' )THEN\n*\n*                                Compute approximation to original\n*                                matrix.\n*\n                                 DO 70 J = 1, N\n                                    DO 60 I = 1, M\n                                       C( I, J ) = BB( I + ( J - 1 )*\n     $                                             LDB )\n                                       BB( I + ( J - 1 )*LDB ) = ALPHA*\n     $                                    B( I, J )\n   60                               CONTINUE\n   70                            CONTINUE\n*\n                                 IF( LEFT )THEN\n                                    CALL ZMMCH( TRANSA, 'N', M, N, M,\n     $                                          ONE, A, NMAX, C, NMAX,\n     $                                          ZERO, B, NMAX, CT, G,\n     $                                          BB, LDB, EPS, ERR,\n     $                                          FATAL, NOUT, .FALSE. )\n                                 ELSE\n                                    CALL ZMMCH( 'N', TRANSA, M, N, N,\n     $                                          ONE, C, NMAX, A, NMAX,\n     $                                          ZERO, B, NMAX, CT, G,\n     $                                          BB, LDB, EPS, ERR,\n     $                                          FATAL, NOUT, .FALSE. )\n                                 END IF\n                              END IF\n                              ERRMAX = MAX( ERRMAX, ERR )\n*                             If got really bad answer, report and\n*                             return.\n                              IF( FATAL )\n     $                           GO TO 150\n                           END IF\n*\n   80                   CONTINUE\n*\n   90                CONTINUE\n*\n  100             CONTINUE\n*\n  110          CONTINUE\n*\n  120       CONTINUE\n*\n  130    CONTINUE\n*\n  140 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 160\n*\n  150 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      WRITE( NOUT, FMT = 9995 )NC, SNAME, SIDE, UPLO, TRANSA, DIAG, M,\n     $   N, ALPHA, LDA, LDB\n*\n  160 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( 1X, I6, ': ', A6, '(', 4( '''', A1, ''',' ), 2( I3, ',' ),\n     $      '(', F4.1, ',', F4.1, '), A,', I3, ', B,', I3, ')         ',\n     $      '      .' )\n 9994 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of ZCHK3.\n*\n      END\n      SUBROUTINE ZCHK4( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET, NMAX,\n     $                  A, AA, AS, B, BB, BS, C, CC, CS, CT, G )\n*\n*  Tests ZHERK and ZSYRK.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Parameters ..\n      COMPLEX*16         ZERO\n      PARAMETER          ( ZERO = ( 0.0D0, 0.0D0 ) )\n      DOUBLE PRECISION   RONE, RZERO\n      PARAMETER          ( RONE = 1.0D0, RZERO = 0.0D0 )\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION   EPS, THRESH\n      INTEGER            NALF, NBET, NIDIM, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      COMPLEX*16         A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),\n     $                   AS( NMAX*NMAX ), B( NMAX, NMAX ),\n     $                   BB( NMAX*NMAX ), BET( NBET ), BS( NMAX*NMAX ),\n     $                   C( NMAX, NMAX ), CC( NMAX*NMAX ),\n     $                   CS( NMAX*NMAX ), CT( NMAX )\n      DOUBLE PRECISION   G( NMAX )\n      INTEGER            IDIM( NIDIM )\n*     .. Local Scalars ..\n      COMPLEX*16         ALPHA, ALS, BETA, BETS\n      DOUBLE PRECISION   ERR, ERRMAX, RALPHA, RALS, RBETA, RBETS\n      INTEGER            I, IA, IB, ICT, ICU, IK, IN, J, JC, JJ, K, KS,\n     $                   LAA, LCC, LDA, LDAS, LDC, LDCS, LJ, MA, N, NA,\n     $                   NARGS, NC, NS\n      LOGICAL            CONJ, NULL, RESET, SAME, TRAN, UPPER\n      CHARACTER*1        TRANS, TRANSS, TRANST, UPLO, UPLOS\n      CHARACTER*2        ICHT, ICHU\n*     .. Local Arrays ..\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LZE, LZERES\n      EXTERNAL           LZE, LZERES\n*     .. External Subroutines ..\n      EXTERNAL           ZHERK, ZMAKE, ZMMCH, ZSYRK\n*     .. Intrinsic Functions ..\n      INTRINSIC          DCMPLX, MAX, DBLE\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICHT/'NC'/, ICHU/'UL'/\n*     .. Executable Statements ..\n      CONJ = SNAME( 2: 3 ).EQ.'HE'\n*\n      NARGS = 10\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = RZERO\n*\n      DO 100 IN = 1, NIDIM\n         N = IDIM( IN )\n*        Set LDC to 1 more than minimum value if room.\n         LDC = N\n         IF( LDC.LT.NMAX )\n     $      LDC = LDC + 1\n*        Skip tests if not enough room.\n         IF( LDC.GT.NMAX )\n     $      GO TO 100\n         LCC = LDC*N\n*\n         DO 90 IK = 1, NIDIM\n            K = IDIM( IK )\n*\n            DO 80 ICT = 1, 2\n               TRANS = ICHT( ICT: ICT )\n               TRAN = TRANS.EQ.'C'\n               IF( TRAN.AND..NOT.CONJ )\n     $            TRANS = 'T'\n               IF( TRAN )THEN\n                  MA = K\n                  NA = N\n               ELSE\n                  MA = N\n                  NA = K\n               END IF\n*              Set LDA to 1 more than minimum value if room.\n               LDA = MA\n               IF( LDA.LT.NMAX )\n     $            LDA = LDA + 1\n*              Skip tests if not enough room.\n               IF( LDA.GT.NMAX )\n     $            GO TO 80\n               LAA = LDA*NA\n*\n*              Generate the matrix A.\n*\n               CALL ZMAKE( 'GE', ' ', ' ', MA, NA, A, NMAX, AA, LDA,\n     $                     RESET, ZERO )\n*\n               DO 70 ICU = 1, 2\n                  UPLO = ICHU( ICU: ICU )\n                  UPPER = UPLO.EQ.'U'\n*\n                  DO 60 IA = 1, NALF\n                     ALPHA = ALF( IA )\n                     IF( CONJ )THEN\n                        RALPHA = DBLE( ALPHA )\n                        ALPHA = DCMPLX( RALPHA, RZERO )\n                     END IF\n*\n                     DO 50 IB = 1, NBET\n                        BETA = BET( IB )\n                        IF( CONJ )THEN\n                           RBETA = DBLE( BETA )\n                           BETA = DCMPLX( RBETA, RZERO )\n                        END IF\n                        NULL = N.LE.0\n                        IF( CONJ )\n     $                     NULL = NULL.OR.( ( K.LE.0.OR.RALPHA.EQ.\n     $                            RZERO ).AND.RBETA.EQ.RONE )\n*\n*                       Generate the matrix C.\n*\n                        CALL ZMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, C,\n     $                              NMAX, CC, LDC, RESET, ZERO )\n*\n                        NC = NC + 1\n*\n*                       Save every datum before calling the subroutine.\n*\n                        UPLOS = UPLO\n                        TRANSS = TRANS\n                        NS = N\n                        KS = K\n                        IF( CONJ )THEN\n                           RALS = RALPHA\n                        ELSE\n                           ALS = ALPHA\n                        END IF\n                        DO 10 I = 1, LAA\n                           AS( I ) = AA( I )\n   10                   CONTINUE\n                        LDAS = LDA\n                        IF( CONJ )THEN\n                           RBETS = RBETA\n                        ELSE\n                           BETS = BETA\n                        END IF\n                        DO 20 I = 1, LCC\n                           CS( I ) = CC( I )\n   20                   CONTINUE\n                        LDCS = LDC\n*\n*                       Call the subroutine.\n*\n                        IF( CONJ )THEN\n                           IF( TRACE )\n     $                        WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO,\n     $                        TRANS, N, K, RALPHA, LDA, RBETA, LDC\n                           IF( REWI )\n     $                        REWIND NTRA\n                           CALL ZHERK( UPLO, TRANS, N, K, RALPHA, AA,\n     $                                 LDA, RBETA, CC, LDC )\n                        ELSE\n                           IF( TRACE )\n     $                        WRITE( NTRA, FMT = 9993 )NC, SNAME, UPLO,\n     $                        TRANS, N, K, ALPHA, LDA, BETA, LDC\n                           IF( REWI )\n     $                        REWIND NTRA\n                           CALL ZSYRK( UPLO, TRANS, N, K, ALPHA, AA,\n     $                                 LDA, BETA, CC, LDC )\n                        END IF\n*\n*                       Check if error-exit was taken incorrectly.\n*\n                        IF( .NOT.OK )THEN\n                           WRITE( NOUT, FMT = 9992 )\n                           FATAL = .TRUE.\n                           GO TO 120\n                        END IF\n*\n*                       See what data changed inside subroutines.\n*\n                        ISAME( 1 ) = UPLOS.EQ.UPLO\n                        ISAME( 2 ) = TRANSS.EQ.TRANS\n                        ISAME( 3 ) = NS.EQ.N\n                        ISAME( 4 ) = KS.EQ.K\n                        IF( CONJ )THEN\n                           ISAME( 5 ) = RALS.EQ.RALPHA\n                        ELSE\n                           ISAME( 5 ) = ALS.EQ.ALPHA\n                        END IF\n                        ISAME( 6 ) = LZE( AS, AA, LAA )\n                        ISAME( 7 ) = LDAS.EQ.LDA\n                        IF( CONJ )THEN\n                           ISAME( 8 ) = RBETS.EQ.RBETA\n                        ELSE\n                           ISAME( 8 ) = BETS.EQ.BETA\n                        END IF\n                        IF( NULL )THEN\n                           ISAME( 9 ) = LZE( CS, CC, LCC )\n                        ELSE\n                           ISAME( 9 ) = LZERES( SNAME( 2: 3 ), UPLO, N,\n     $                                  N, CS, CC, LDC )\n                        END IF\n                        ISAME( 10 ) = LDCS.EQ.LDC\n*\n*                       If data was incorrectly changed, report and\n*                       return.\n*\n                        SAME = .TRUE.\n                        DO 30 I = 1, NARGS\n                           SAME = SAME.AND.ISAME( I )\n                           IF( .NOT.ISAME( I ) )\n     $                        WRITE( NOUT, FMT = 9998 )I\n   30                   CONTINUE\n                        IF( .NOT.SAME )THEN\n                           FATAL = .TRUE.\n                           GO TO 120\n                        END IF\n*\n                        IF( .NOT.NULL )THEN\n*\n*                          Check the result column by column.\n*\n                           IF( CONJ )THEN\n                              TRANST = 'C'\n                           ELSE\n                              TRANST = 'T'\n                           END IF\n                           JC = 1\n                           DO 40 J = 1, N\n                              IF( UPPER )THEN\n                                 JJ = 1\n                                 LJ = J\n                              ELSE\n                                 JJ = J\n                                 LJ = N - J + 1\n                              END IF\n                              IF( TRAN )THEN\n                                 CALL ZMMCH( TRANST, 'N', LJ, 1, K,\n     $                                       ALPHA, A( 1, JJ ), NMAX,\n     $                                       A( 1, J ), NMAX, BETA,\n     $                                       C( JJ, J ), NMAX, CT, G,\n     $                                       CC( JC ), LDC, EPS, ERR,\n     $                                       FATAL, NOUT, .TRUE. )\n                              ELSE\n                                 CALL ZMMCH( 'N', TRANST, LJ, 1, K,\n     $                                       ALPHA, A( JJ, 1 ), NMAX,\n     $                                       A( J, 1 ), NMAX, BETA,\n     $                                       C( JJ, J ), NMAX, CT, G,\n     $                                       CC( JC ), LDC, EPS, ERR,\n     $                                       FATAL, NOUT, .TRUE. )\n                              END IF\n                              IF( UPPER )THEN\n                                 JC = JC + LDC\n                              ELSE\n                                 JC = JC + LDC + 1\n                              END IF\n                              ERRMAX = MAX( ERRMAX, ERR )\n*                             If got really bad answer, report and\n*                             return.\n                              IF( FATAL )\n     $                           GO TO 110\n   40                      CONTINUE\n                        END IF\n*\n   50                CONTINUE\n*\n   60             CONTINUE\n*\n   70          CONTINUE\n*\n   80       CONTINUE\n*\n   90    CONTINUE\n*\n  100 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 130\n*\n  110 CONTINUE\n      IF( N.GT.1 )\n     $   WRITE( NOUT, FMT = 9995 )J\n*\n  120 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      IF( CONJ )THEN\n         WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, TRANS, N, K, RALPHA,\n     $      LDA, RBETA, LDC\n      ELSE\n         WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, TRANS, N, K, ALPHA,\n     $      LDA, BETA, LDC\n      END IF\n*\n  130 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( '      THESE ARE THE RESULTS FOR COLUMN ', I3 )\n 9994 FORMAT( 1X, I6, ': ', A6, '(', 2( '''', A1, ''',' ), 2( I3, ',' ),\n     $      F4.1, ', A,', I3, ',', F4.1, ', C,', I3, ')               ',\n     $      '          .' )\n 9993 FORMAT( 1X, I6, ': ', A6, '(', 2( '''', A1, ''',' ), 2( I3, ',' ),\n     $      '(', F4.1, ',', F4.1, ') , A,', I3, ',(', F4.1, ',', F4.1,\n     $      '), C,', I3, ')          .' )\n 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of ZCHK4.\n*\n      END\n      SUBROUTINE ZCHK5( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,\n     $                  FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET, NMAX,\n     $                  AB, AA, AS, BB, BS, C, CC, CS, CT, G, W )\n*\n*  Tests ZHER2K and ZSYR2K.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Parameters ..\n      COMPLEX*16         ZERO, ONE\n      PARAMETER          ( ZERO = ( 0.0D0, 0.0D0 ),\n     $                   ONE = ( 1.0D0, 0.0D0 ) )\n      DOUBLE PRECISION   RONE, RZERO\n      PARAMETER          ( RONE = 1.0D0, RZERO = 0.0D0 )\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION   EPS, THRESH\n      INTEGER            NALF, NBET, NIDIM, NMAX, NOUT, NTRA\n      LOGICAL            FATAL, REWI, TRACE\n      CHARACTER*6        SNAME\n*     .. Array Arguments ..\n      COMPLEX*16         AA( NMAX*NMAX ), AB( 2*NMAX*NMAX ),\n     $                   ALF( NALF ), AS( NMAX*NMAX ), BB( NMAX*NMAX ),\n     $                   BET( NBET ), BS( NMAX*NMAX ), C( NMAX, NMAX ),\n     $                   CC( NMAX*NMAX ), CS( NMAX*NMAX ), CT( NMAX ),\n     $                   W( 2*NMAX )\n      DOUBLE PRECISION   G( NMAX )\n      INTEGER            IDIM( NIDIM )\n*     .. Local Scalars ..\n      COMPLEX*16         ALPHA, ALS, BETA, BETS\n      DOUBLE PRECISION   ERR, ERRMAX, RBETA, RBETS\n      INTEGER            I, IA, IB, ICT, ICU, IK, IN, J, JC, JJ, JJAB,\n     $                   K, KS, LAA, LBB, LCC, LDA, LDAS, LDB, LDBS,\n     $                   LDC, LDCS, LJ, MA, N, NA, NARGS, NC, NS\n      LOGICAL            CONJ, NULL, RESET, SAME, TRAN, UPPER\n      CHARACTER*1        TRANS, TRANSS, TRANST, UPLO, UPLOS\n      CHARACTER*2        ICHT, ICHU\n*     .. Local Arrays ..\n      LOGICAL            ISAME( 13 )\n*     .. External Functions ..\n      LOGICAL            LZE, LZERES\n      EXTERNAL           LZE, LZERES\n*     .. External Subroutines ..\n      EXTERNAL           ZHER2K, ZMAKE, ZMMCH, ZSYR2K\n*     .. Intrinsic Functions ..\n      INTRINSIC          DCMPLX, DCONJG, MAX, DBLE\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Data statements ..\n      DATA               ICHT/'NC'/, ICHU/'UL'/\n*     .. Executable Statements ..\n      CONJ = SNAME( 2: 3 ).EQ.'HE'\n*\n      NARGS = 12\n      NC = 0\n      RESET = .TRUE.\n      ERRMAX = RZERO\n*\n      DO 130 IN = 1, NIDIM\n         N = IDIM( IN )\n*        Set LDC to 1 more than minimum value if room.\n         LDC = N\n         IF( LDC.LT.NMAX )\n     $      LDC = LDC + 1\n*        Skip tests if not enough room.\n         IF( LDC.GT.NMAX )\n     $      GO TO 130\n         LCC = LDC*N\n*\n         DO 120 IK = 1, NIDIM\n            K = IDIM( IK )\n*\n            DO 110 ICT = 1, 2\n               TRANS = ICHT( ICT: ICT )\n               TRAN = TRANS.EQ.'C'\n               IF( TRAN.AND..NOT.CONJ )\n     $            TRANS = 'T'\n               IF( TRAN )THEN\n                  MA = K\n                  NA = N\n               ELSE\n                  MA = N\n                  NA = K\n               END IF\n*              Set LDA to 1 more than minimum value if room.\n               LDA = MA\n               IF( LDA.LT.NMAX )\n     $            LDA = LDA + 1\n*              Skip tests if not enough room.\n               IF( LDA.GT.NMAX )\n     $            GO TO 110\n               LAA = LDA*NA\n*\n*              Generate the matrix A.\n*\n               IF( TRAN )THEN\n                  CALL ZMAKE( 'GE', ' ', ' ', MA, NA, AB, 2*NMAX, AA,\n     $                        LDA, RESET, ZERO )\n               ELSE\n                  CALL ZMAKE( 'GE', ' ', ' ', MA, NA, AB, NMAX, AA, LDA,\n     $                        RESET, ZERO )\n               END IF\n*\n*              Generate the matrix B.\n*\n               LDB = LDA\n               LBB = LAA\n               IF( TRAN )THEN\n                  CALL ZMAKE( 'GE', ' ', ' ', MA, NA, AB( K + 1 ),\n     $                        2*NMAX, BB, LDB, RESET, ZERO )\n               ELSE\n                  CALL ZMAKE( 'GE', ' ', ' ', MA, NA, AB( K*NMAX + 1 ),\n     $                        NMAX, BB, LDB, RESET, ZERO )\n               END IF\n*\n               DO 100 ICU = 1, 2\n                  UPLO = ICHU( ICU: ICU )\n                  UPPER = UPLO.EQ.'U'\n*\n                  DO 90 IA = 1, NALF\n                     ALPHA = ALF( IA )\n*\n                     DO 80 IB = 1, NBET\n                        BETA = BET( IB )\n                        IF( CONJ )THEN\n                           RBETA = DBLE( BETA )\n                           BETA = DCMPLX( RBETA, RZERO )\n                        END IF\n                        NULL = N.LE.0\n                        IF( CONJ )\n     $                     NULL = NULL.OR.( ( K.LE.0.OR.ALPHA.EQ.\n     $                            ZERO ).AND.RBETA.EQ.RONE )\n*\n*                       Generate the matrix C.\n*\n                        CALL ZMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, C,\n     $                              NMAX, CC, LDC, RESET, ZERO )\n*\n                        NC = NC + 1\n*\n*                       Save every datum before calling the subroutine.\n*\n                        UPLOS = UPLO\n                        TRANSS = TRANS\n                        NS = N\n                        KS = K\n                        ALS = ALPHA\n                        DO 10 I = 1, LAA\n                           AS( I ) = AA( I )\n   10                   CONTINUE\n                        LDAS = LDA\n                        DO 20 I = 1, LBB\n                           BS( I ) = BB( I )\n   20                   CONTINUE\n                        LDBS = LDB\n                        IF( CONJ )THEN\n                           RBETS = RBETA\n                        ELSE\n                           BETS = BETA\n                        END IF\n                        DO 30 I = 1, LCC\n                           CS( I ) = CC( I )\n   30                   CONTINUE\n                        LDCS = LDC\n*\n*                       Call the subroutine.\n*\n                        IF( CONJ )THEN\n                           IF( TRACE )\n     $                        WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO,\n     $                        TRANS, N, K, ALPHA, LDA, LDB, RBETA, LDC\n                           IF( REWI )\n     $                        REWIND NTRA\n                           CALL ZHER2K( UPLO, TRANS, N, K, ALPHA, AA,\n     $                                  LDA, BB, LDB, RBETA, CC, LDC )\n                        ELSE\n                           IF( TRACE )\n     $                        WRITE( NTRA, FMT = 9993 )NC, SNAME, UPLO,\n     $                        TRANS, N, K, ALPHA, LDA, LDB, BETA, LDC\n                           IF( REWI )\n     $                        REWIND NTRA\n                           CALL ZSYR2K( UPLO, TRANS, N, K, ALPHA, AA,\n     $                                  LDA, BB, LDB, BETA, CC, LDC )\n                        END IF\n*\n*                       Check if error-exit was taken incorrectly.\n*\n                        IF( .NOT.OK )THEN\n                           WRITE( NOUT, FMT = 9992 )\n                           FATAL = .TRUE.\n                           GO TO 150\n                        END IF\n*\n*                       See what data changed inside subroutines.\n*\n                        ISAME( 1 ) = UPLOS.EQ.UPLO\n                        ISAME( 2 ) = TRANSS.EQ.TRANS\n                        ISAME( 3 ) = NS.EQ.N\n                        ISAME( 4 ) = KS.EQ.K\n                        ISAME( 5 ) = ALS.EQ.ALPHA\n                        ISAME( 6 ) = LZE( AS, AA, LAA )\n                        ISAME( 7 ) = LDAS.EQ.LDA\n                        ISAME( 8 ) = LZE( BS, BB, LBB )\n                        ISAME( 9 ) = LDBS.EQ.LDB\n                        IF( CONJ )THEN\n                           ISAME( 10 ) = RBETS.EQ.RBETA\n                        ELSE\n                           ISAME( 10 ) = BETS.EQ.BETA\n                        END IF\n                        IF( NULL )THEN\n                           ISAME( 11 ) = LZE( CS, CC, LCC )\n                        ELSE\n                           ISAME( 11 ) = LZERES( 'HE', UPLO, N, N, CS,\n     $                                   CC, LDC )\n                        END IF\n                        ISAME( 12 ) = LDCS.EQ.LDC\n*\n*                       If data was incorrectly changed, report and\n*                       return.\n*\n                        SAME = .TRUE.\n                        DO 40 I = 1, NARGS\n                           SAME = SAME.AND.ISAME( I )\n                           IF( .NOT.ISAME( I ) )\n     $                        WRITE( NOUT, FMT = 9998 )I\n   40                   CONTINUE\n                        IF( .NOT.SAME )THEN\n                           FATAL = .TRUE.\n                           GO TO 150\n                        END IF\n*\n                        IF( .NOT.NULL )THEN\n*\n*                          Check the result column by column.\n*\n                           IF( CONJ )THEN\n                              TRANST = 'C'\n                           ELSE\n                              TRANST = 'T'\n                           END IF\n                           JJAB = 1\n                           JC = 1\n                           DO 70 J = 1, N\n                              IF( UPPER )THEN\n                                 JJ = 1\n                                 LJ = J\n                              ELSE\n                                 JJ = J\n                                 LJ = N - J + 1\n                              END IF\n                              IF( TRAN )THEN\n                                 DO 50 I = 1, K\n                                    W( I ) = ALPHA*AB( ( J - 1 )*2*\n     $                                       NMAX + K + I )\n                                    IF( CONJ )THEN\n                                       W( K + I ) = DCONJG( ALPHA )*\n     $                                              AB( ( J - 1 )*2*\n     $                                              NMAX + I )\n                                    ELSE\n                                       W( K + I ) = ALPHA*\n     $                                              AB( ( J - 1 )*2*\n     $                                              NMAX + I )\n                                    END IF\n   50                            CONTINUE\n                                 CALL ZMMCH( TRANST, 'N', LJ, 1, 2*K,\n     $                                       ONE, AB( JJAB ), 2*NMAX, W,\n     $                                       2*NMAX, BETA, C( JJ, J ),\n     $                                       NMAX, CT, G, CC( JC ), LDC,\n     $                                       EPS, ERR, FATAL, NOUT,\n     $                                       .TRUE. )\n                              ELSE\n                                 DO 60 I = 1, K\n                                    IF( CONJ )THEN\n                                       W( I ) = ALPHA*DCONJG( AB( ( K +\n     $                                          I - 1 )*NMAX + J ) )\n                                       W( K + I ) = DCONJG( ALPHA*\n     $                                              AB( ( I - 1 )*NMAX +\n     $                                              J ) )\n                                    ELSE\n                                       W( I ) = ALPHA*AB( ( K + I - 1 )*\n     $                                          NMAX + J )\n                                       W( K + I ) = ALPHA*\n     $                                              AB( ( I - 1 )*NMAX +\n     $                                              J )\n                                    END IF\n   60                            CONTINUE\n                                 CALL ZMMCH( 'N', 'N', LJ, 1, 2*K, ONE,\n     $                                       AB( JJ ), NMAX, W, 2*NMAX,\n     $                                       BETA, C( JJ, J ), NMAX, CT,\n     $                                       G, CC( JC ), LDC, EPS, ERR,\n     $                                       FATAL, NOUT, .TRUE. )\n                              END IF\n                              IF( UPPER )THEN\n                                 JC = JC + LDC\n                              ELSE\n                                 JC = JC + LDC + 1\n                                 IF( TRAN )\n     $                              JJAB = JJAB + 2*NMAX\n                              END IF\n                              ERRMAX = MAX( ERRMAX, ERR )\n*                             If got really bad answer, report and\n*                             return.\n                              IF( FATAL )\n     $                           GO TO 140\n   70                      CONTINUE\n                        END IF\n*\n   80                CONTINUE\n*\n   90             CONTINUE\n*\n  100          CONTINUE\n*\n  110       CONTINUE\n*\n  120    CONTINUE\n*\n  130 CONTINUE\n*\n*     Report result.\n*\n      IF( ERRMAX.LT.THRESH )THEN\n         WRITE( NOUT, FMT = 9999 )SNAME, NC\n      ELSE\n         WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX\n      END IF\n      GO TO 160\n*\n  140 CONTINUE\n      IF( N.GT.1 )\n     $   WRITE( NOUT, FMT = 9995 )J\n*\n  150 CONTINUE\n      WRITE( NOUT, FMT = 9996 )SNAME\n      IF( CONJ )THEN\n         WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, TRANS, N, K, ALPHA,\n     $      LDA, LDB, RBETA, LDC\n      ELSE\n         WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, TRANS, N, K, ALPHA,\n     $      LDA, LDB, BETA, LDC\n      END IF\n*\n  160 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',\n     $      'S)' )\n 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',\n     $      'ANGED INCORRECTLY *******' )\n 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',\n     $      'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,\n     $      ' - SUSPECT *******' )\n 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )\n 9995 FORMAT( '      THESE ARE THE RESULTS FOR COLUMN ', I3 )\n 9994 FORMAT( 1X, I6, ': ', A6, '(', 2( '''', A1, ''',' ), 2( I3, ',' ),\n     $      '(', F4.1, ',', F4.1, '), A,', I3, ', B,', I3, ',', F4.1,\n     $      ', C,', I3, ')           .' )\n 9993 FORMAT( 1X, I6, ': ', A6, '(', 2( '''', A1, ''',' ), 2( I3, ',' ),\n     $      '(', F4.1, ',', F4.1, '), A,', I3, ', B,', I3, ',(', F4.1,\n     $      ',', F4.1, '), C,', I3, ')    .' )\n 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',\n     $      '******' )\n*\n*     End of ZCHK5.\n*\n      END\n      SUBROUTINE ZCHKE( ISNUM, SRNAMT, NOUT )\n*\n*  Tests the error exits from the Level 3 Blas.\n*  Requires a special version of the error-handling routine XERBLA.\n*  A, B and C should not need to be defined.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*  3-19-92:  Initialize ALPHA, BETA, RALPHA, and RBETA  (eca)\n*  3-19-92:  Fix argument 12 in calls to ZSYMM and ZHEMM\n*            with INFOT = 9  (eca)\n*  10-9-00:  Declared INTRINSIC DCMPLX (susan)\n*\n*     .. Scalar Arguments ..\n      INTEGER            ISNUM, NOUT\n      CHARACTER*6        SRNAMT\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUTC\n      LOGICAL            LERR, OK\n*     .. Parameters ..\n      REAL               ONE, TWO\n      PARAMETER          ( ONE = 1.0D0, TWO = 2.0D0 )\n*     .. Local Scalars ..\n      COMPLEX*16         ALPHA, BETA\n      DOUBLE PRECISION   RALPHA, RBETA\n*     .. Local Arrays ..\n      COMPLEX*16         A( 2, 1 ), B( 2, 1 ), C( 2, 1 )\n*     .. External Subroutines ..\n      EXTERNAL           ZGEMM, ZHEMM, ZHER2K, ZHERK, CHKXER, ZSYMM,\n     $                   ZSYR2K, ZSYRK, ZTRMM, ZTRSM\n*     .. Intrinsic Functions ..\n      INTRINSIC          DCMPLX\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUTC, OK, LERR\n*     .. Executable Statements ..\n*     OK is set to .FALSE. by the special version of XERBLA or by CHKXER\n*     if anything is wrong.\n      OK = .TRUE.\n*     LERR is set to .TRUE. by the special version of XERBLA each time\n*     it is called, and is then tested and re-set by CHKXER.\n      LERR = .FALSE.\n*\n*     Initialize ALPHA, BETA, RALPHA, and RBETA.\n*\n      ALPHA = DCMPLX( ONE, -ONE )\n      BETA = DCMPLX( TWO, -TWO )\n      RALPHA = ONE\n      RBETA = TWO\n*\n      GO TO ( 10, 20, 30, 40, 50, 60, 70, 80,\n     $        90 )ISNUM\n   10 INFOT = 1\n      CALL ZGEMM( '/', 'N', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 1\n      CALL ZGEMM( '/', 'C', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 1\n      CALL ZGEMM( '/', 'T', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL ZGEMM( 'N', '/', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL ZGEMM( 'C', '/', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL ZGEMM( 'T', '/', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZGEMM( 'N', 'N', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZGEMM( 'N', 'C', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZGEMM( 'N', 'T', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZGEMM( 'C', 'N', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZGEMM( 'C', 'C', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZGEMM( 'C', 'T', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZGEMM( 'T', 'N', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZGEMM( 'T', 'C', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZGEMM( 'T', 'T', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZGEMM( 'N', 'N', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZGEMM( 'N', 'C', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZGEMM( 'N', 'T', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZGEMM( 'C', 'N', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZGEMM( 'C', 'C', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZGEMM( 'C', 'T', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZGEMM( 'T', 'N', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZGEMM( 'T', 'C', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZGEMM( 'T', 'T', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZGEMM( 'N', 'N', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZGEMM( 'N', 'C', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZGEMM( 'N', 'T', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZGEMM( 'C', 'N', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZGEMM( 'C', 'C', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZGEMM( 'C', 'T', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZGEMM( 'T', 'N', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZGEMM( 'T', 'C', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZGEMM( 'T', 'T', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL ZGEMM( 'N', 'N', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL ZGEMM( 'N', 'C', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL ZGEMM( 'N', 'T', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL ZGEMM( 'C', 'N', 0, 0, 2, ALPHA, A, 1, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL ZGEMM( 'C', 'C', 0, 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL ZGEMM( 'C', 'T', 0, 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL ZGEMM( 'T', 'N', 0, 0, 2, ALPHA, A, 1, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL ZGEMM( 'T', 'C', 0, 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 8\n      CALL ZGEMM( 'T', 'T', 0, 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL ZGEMM( 'N', 'N', 0, 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL ZGEMM( 'C', 'N', 0, 0, 2, ALPHA, A, 2, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL ZGEMM( 'T', 'N', 0, 0, 2, ALPHA, A, 2, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL ZGEMM( 'N', 'C', 0, 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL ZGEMM( 'C', 'C', 0, 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL ZGEMM( 'T', 'C', 0, 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL ZGEMM( 'N', 'T', 0, 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL ZGEMM( 'C', 'T', 0, 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL ZGEMM( 'T', 'T', 0, 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 13\n      CALL ZGEMM( 'N', 'N', 2, 0, 0, ALPHA, A, 2, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 13\n      CALL ZGEMM( 'N', 'C', 2, 0, 0, ALPHA, A, 2, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 13\n      CALL ZGEMM( 'N', 'T', 2, 0, 0, ALPHA, A, 2, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 13\n      CALL ZGEMM( 'C', 'N', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 13\n      CALL ZGEMM( 'C', 'C', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 13\n      CALL ZGEMM( 'C', 'T', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 13\n      CALL ZGEMM( 'T', 'N', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 13\n      CALL ZGEMM( 'T', 'C', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 13\n      CALL ZGEMM( 'T', 'T', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 100\n   20 INFOT = 1\n      CALL ZHEMM( '/', 'U', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL ZHEMM( 'L', '/', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZHEMM( 'L', 'U', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZHEMM( 'R', 'U', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZHEMM( 'L', 'L', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZHEMM( 'R', 'L', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZHEMM( 'L', 'U', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZHEMM( 'R', 'U', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZHEMM( 'L', 'L', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZHEMM( 'R', 'L', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL ZHEMM( 'L', 'U', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL ZHEMM( 'R', 'U', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL ZHEMM( 'L', 'L', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL ZHEMM( 'R', 'L', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZHEMM( 'L', 'U', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZHEMM( 'R', 'U', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZHEMM( 'L', 'L', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZHEMM( 'R', 'L', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL ZHEMM( 'L', 'U', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL ZHEMM( 'R', 'U', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL ZHEMM( 'L', 'L', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL ZHEMM( 'R', 'L', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 100\n   30 INFOT = 1\n      CALL ZSYMM( '/', 'U', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL ZSYMM( 'L', '/', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZSYMM( 'L', 'U', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZSYMM( 'R', 'U', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZSYMM( 'L', 'L', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZSYMM( 'R', 'L', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZSYMM( 'L', 'U', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZSYMM( 'R', 'U', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZSYMM( 'L', 'L', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZSYMM( 'R', 'L', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL ZSYMM( 'L', 'U', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL ZSYMM( 'R', 'U', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL ZSYMM( 'L', 'L', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL ZSYMM( 'R', 'L', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZSYMM( 'L', 'U', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZSYMM( 'R', 'U', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZSYMM( 'L', 'L', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZSYMM( 'R', 'L', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL ZSYMM( 'L', 'U', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL ZSYMM( 'R', 'U', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL ZSYMM( 'L', 'L', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL ZSYMM( 'R', 'L', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 100\n   40 INFOT = 1\n      CALL ZTRMM( '/', 'U', 'N', 'N', 0, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL ZTRMM( 'L', '/', 'N', 'N', 0, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZTRMM( 'L', 'U', '/', 'N', 0, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZTRMM( 'L', 'U', 'N', '/', 0, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZTRMM( 'L', 'U', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZTRMM( 'L', 'U', 'C', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZTRMM( 'L', 'U', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZTRMM( 'R', 'U', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZTRMM( 'R', 'U', 'C', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZTRMM( 'R', 'U', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZTRMM( 'L', 'L', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZTRMM( 'L', 'L', 'C', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZTRMM( 'L', 'L', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZTRMM( 'R', 'L', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZTRMM( 'R', 'L', 'C', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZTRMM( 'R', 'L', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL ZTRMM( 'L', 'U', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL ZTRMM( 'L', 'U', 'C', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL ZTRMM( 'L', 'U', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL ZTRMM( 'R', 'U', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL ZTRMM( 'R', 'U', 'C', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL ZTRMM( 'R', 'U', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL ZTRMM( 'L', 'L', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL ZTRMM( 'L', 'L', 'C', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL ZTRMM( 'L', 'L', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL ZTRMM( 'R', 'L', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL ZTRMM( 'R', 'L', 'C', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL ZTRMM( 'R', 'L', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZTRMM( 'L', 'U', 'N', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZTRMM( 'L', 'U', 'C', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZTRMM( 'L', 'U', 'T', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZTRMM( 'R', 'U', 'N', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZTRMM( 'R', 'U', 'C', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZTRMM( 'R', 'U', 'T', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZTRMM( 'L', 'L', 'N', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZTRMM( 'L', 'L', 'C', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZTRMM( 'L', 'L', 'T', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZTRMM( 'R', 'L', 'N', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZTRMM( 'R', 'L', 'C', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZTRMM( 'R', 'L', 'T', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL ZTRMM( 'L', 'U', 'N', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL ZTRMM( 'L', 'U', 'C', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL ZTRMM( 'L', 'U', 'T', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL ZTRMM( 'R', 'U', 'N', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL ZTRMM( 'R', 'U', 'C', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL ZTRMM( 'R', 'U', 'T', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL ZTRMM( 'L', 'L', 'N', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL ZTRMM( 'L', 'L', 'C', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL ZTRMM( 'L', 'L', 'T', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL ZTRMM( 'R', 'L', 'N', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL ZTRMM( 'R', 'L', 'C', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL ZTRMM( 'R', 'L', 'T', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 100\n   50 INFOT = 1\n      CALL ZTRSM( '/', 'U', 'N', 'N', 0, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL ZTRSM( 'L', '/', 'N', 'N', 0, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZTRSM( 'L', 'U', '/', 'N', 0, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZTRSM( 'L', 'U', 'N', '/', 0, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZTRSM( 'L', 'U', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZTRSM( 'L', 'U', 'C', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZTRSM( 'L', 'U', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZTRSM( 'R', 'U', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZTRSM( 'R', 'U', 'C', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZTRSM( 'R', 'U', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZTRSM( 'L', 'L', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZTRSM( 'L', 'L', 'C', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZTRSM( 'L', 'L', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZTRSM( 'R', 'L', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZTRSM( 'R', 'L', 'C', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 5\n      CALL ZTRSM( 'R', 'L', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL ZTRSM( 'L', 'U', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL ZTRSM( 'L', 'U', 'C', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL ZTRSM( 'L', 'U', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL ZTRSM( 'R', 'U', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL ZTRSM( 'R', 'U', 'C', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL ZTRSM( 'R', 'U', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL ZTRSM( 'L', 'L', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL ZTRSM( 'L', 'L', 'C', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL ZTRSM( 'L', 'L', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL ZTRSM( 'R', 'L', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL ZTRSM( 'R', 'L', 'C', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 6\n      CALL ZTRSM( 'R', 'L', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZTRSM( 'L', 'U', 'N', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZTRSM( 'L', 'U', 'C', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZTRSM( 'L', 'U', 'T', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZTRSM( 'R', 'U', 'N', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZTRSM( 'R', 'U', 'C', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZTRSM( 'R', 'U', 'T', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZTRSM( 'L', 'L', 'N', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZTRSM( 'L', 'L', 'C', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZTRSM( 'L', 'L', 'T', 'N', 2, 0, ALPHA, A, 1, B, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZTRSM( 'R', 'L', 'N', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZTRSM( 'R', 'L', 'C', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZTRSM( 'R', 'L', 'T', 'N', 0, 2, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL ZTRSM( 'L', 'U', 'N', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL ZTRSM( 'L', 'U', 'C', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL ZTRSM( 'L', 'U', 'T', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL ZTRSM( 'R', 'U', 'N', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL ZTRSM( 'R', 'U', 'C', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL ZTRSM( 'R', 'U', 'T', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL ZTRSM( 'L', 'L', 'N', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL ZTRSM( 'L', 'L', 'C', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL ZTRSM( 'L', 'L', 'T', 'N', 2, 0, ALPHA, A, 2, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL ZTRSM( 'R', 'L', 'N', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL ZTRSM( 'R', 'L', 'C', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 11\n      CALL ZTRSM( 'R', 'L', 'T', 'N', 2, 0, ALPHA, A, 1, B, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 100\n   60 INFOT = 1\n      CALL ZHERK( '/', 'N', 0, 0, RALPHA, A, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL ZHERK( 'U', 'T', 0, 0, RALPHA, A, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZHERK( 'U', 'N', -1, 0, RALPHA, A, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZHERK( 'U', 'C', -1, 0, RALPHA, A, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZHERK( 'L', 'N', -1, 0, RALPHA, A, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZHERK( 'L', 'C', -1, 0, RALPHA, A, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZHERK( 'U', 'N', 0, -1, RALPHA, A, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZHERK( 'U', 'C', 0, -1, RALPHA, A, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZHERK( 'L', 'N', 0, -1, RALPHA, A, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZHERK( 'L', 'C', 0, -1, RALPHA, A, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL ZHERK( 'U', 'N', 2, 0, RALPHA, A, 1, RBETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL ZHERK( 'U', 'C', 0, 2, RALPHA, A, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL ZHERK( 'L', 'N', 2, 0, RALPHA, A, 1, RBETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL ZHERK( 'L', 'C', 0, 2, RALPHA, A, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL ZHERK( 'U', 'N', 2, 0, RALPHA, A, 2, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL ZHERK( 'U', 'C', 2, 0, RALPHA, A, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL ZHERK( 'L', 'N', 2, 0, RALPHA, A, 2, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL ZHERK( 'L', 'C', 2, 0, RALPHA, A, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 100\n   70 INFOT = 1\n      CALL ZSYRK( '/', 'N', 0, 0, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL ZSYRK( 'U', 'C', 0, 0, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZSYRK( 'U', 'N', -1, 0, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZSYRK( 'U', 'T', -1, 0, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZSYRK( 'L', 'N', -1, 0, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZSYRK( 'L', 'T', -1, 0, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZSYRK( 'U', 'N', 0, -1, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZSYRK( 'U', 'T', 0, -1, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZSYRK( 'L', 'N', 0, -1, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZSYRK( 'L', 'T', 0, -1, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL ZSYRK( 'U', 'N', 2, 0, ALPHA, A, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL ZSYRK( 'U', 'T', 0, 2, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL ZSYRK( 'L', 'N', 2, 0, ALPHA, A, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL ZSYRK( 'L', 'T', 0, 2, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL ZSYRK( 'U', 'N', 2, 0, ALPHA, A, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL ZSYRK( 'U', 'T', 2, 0, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL ZSYRK( 'L', 'N', 2, 0, ALPHA, A, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 10\n      CALL ZSYRK( 'L', 'T', 2, 0, ALPHA, A, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 100\n   80 INFOT = 1\n      CALL ZHER2K( '/', 'N', 0, 0, ALPHA, A, 1, B, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL ZHER2K( 'U', 'T', 0, 0, ALPHA, A, 1, B, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZHER2K( 'U', 'N', -1, 0, ALPHA, A, 1, B, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZHER2K( 'U', 'C', -1, 0, ALPHA, A, 1, B, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZHER2K( 'L', 'N', -1, 0, ALPHA, A, 1, B, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZHER2K( 'L', 'C', -1, 0, ALPHA, A, 1, B, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZHER2K( 'U', 'N', 0, -1, ALPHA, A, 1, B, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZHER2K( 'U', 'C', 0, -1, ALPHA, A, 1, B, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZHER2K( 'L', 'N', 0, -1, ALPHA, A, 1, B, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZHER2K( 'L', 'C', 0, -1, ALPHA, A, 1, B, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL ZHER2K( 'U', 'N', 2, 0, ALPHA, A, 1, B, 1, RBETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL ZHER2K( 'U', 'C', 0, 2, ALPHA, A, 1, B, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL ZHER2K( 'L', 'N', 2, 0, ALPHA, A, 1, B, 1, RBETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL ZHER2K( 'L', 'C', 0, 2, ALPHA, A, 1, B, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZHER2K( 'U', 'N', 2, 0, ALPHA, A, 2, B, 1, RBETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZHER2K( 'U', 'C', 0, 2, ALPHA, A, 2, B, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZHER2K( 'L', 'N', 2, 0, ALPHA, A, 2, B, 1, RBETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZHER2K( 'L', 'C', 0, 2, ALPHA, A, 2, B, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL ZHER2K( 'U', 'N', 2, 0, ALPHA, A, 2, B, 2, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL ZHER2K( 'U', 'C', 2, 0, ALPHA, A, 1, B, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL ZHER2K( 'L', 'N', 2, 0, ALPHA, A, 2, B, 2, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL ZHER2K( 'L', 'C', 2, 0, ALPHA, A, 1, B, 1, RBETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      GO TO 100\n   90 INFOT = 1\n      CALL ZSYR2K( '/', 'N', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 2\n      CALL ZSYR2K( 'U', 'C', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZSYR2K( 'U', 'N', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZSYR2K( 'U', 'T', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZSYR2K( 'L', 'N', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 3\n      CALL ZSYR2K( 'L', 'T', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZSYR2K( 'U', 'N', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZSYR2K( 'U', 'T', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZSYR2K( 'L', 'N', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 4\n      CALL ZSYR2K( 'L', 'T', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL ZSYR2K( 'U', 'N', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL ZSYR2K( 'U', 'T', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL ZSYR2K( 'L', 'N', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 7\n      CALL ZSYR2K( 'L', 'T', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZSYR2K( 'U', 'N', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZSYR2K( 'U', 'T', 0, 2, ALPHA, A, 2, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZSYR2K( 'L', 'N', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 9\n      CALL ZSYR2K( 'L', 'T', 0, 2, ALPHA, A, 2, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL ZSYR2K( 'U', 'N', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL ZSYR2K( 'U', 'T', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL ZSYR2K( 'L', 'N', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n      INFOT = 12\n      CALL ZSYR2K( 'L', 'T', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )\n      CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n*\n  100 IF( OK )THEN\n         WRITE( NOUT, FMT = 9999 )SRNAMT\n      ELSE\n         WRITE( NOUT, FMT = 9998 )SRNAMT\n      END IF\n      RETURN\n*\n 9999 FORMAT( ' ', A6, ' PASSED THE TESTS OF ERROR-EXITS' )\n 9998 FORMAT( ' ******* ', A6, ' FAILED THE TESTS OF ERROR-EXITS *****',\n     $      '**' )\n*\n*     End of ZCHKE.\n*\n      END\n      SUBROUTINE ZMAKE( TYPE, UPLO, DIAG, M, N, A, NMAX, AA, LDA, RESET,\n     $                  TRANSL )\n*\n*  Generates values for an M by N matrix A.\n*  Stores the values in the array AA in the data structure required\n*  by the routine, with unwanted elements set to rogue value.\n*\n*  TYPE is 'GE', 'HE', 'SY' or 'TR'.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Parameters ..\n      COMPLEX*16         ZERO, ONE\n      PARAMETER          ( ZERO = ( 0.0D0, 0.0D0 ),\n     $                   ONE = ( 1.0D0, 0.0D0 ) )\n      COMPLEX*16         ROGUE\n      PARAMETER          ( ROGUE = ( -1.0D10, 1.0D10 ) )\n      DOUBLE PRECISION   RZERO\n      PARAMETER          ( RZERO = 0.0D0 )\n      DOUBLE PRECISION   RROGUE\n      PARAMETER          ( RROGUE = -1.0D10 )\n*     .. Scalar Arguments ..\n      COMPLEX*16         TRANSL\n      INTEGER            LDA, M, N, NMAX\n      LOGICAL            RESET\n      CHARACTER*1        DIAG, UPLO\n      CHARACTER*2        TYPE\n*     .. Array Arguments ..\n      COMPLEX*16         A( NMAX, * ), AA( * )\n*     .. Local Scalars ..\n      INTEGER            I, IBEG, IEND, J, JJ\n      LOGICAL            GEN, HER, LOWER, SYM, TRI, UNIT, UPPER\n*     .. External Functions ..\n      COMPLEX*16         ZBEG\n      EXTERNAL           ZBEG\n*     .. Intrinsic Functions ..\n      INTRINSIC          DCMPLX, DCONJG, DBLE\n*     .. Executable Statements ..\n      GEN = TYPE.EQ.'GE'\n      HER = TYPE.EQ.'HE'\n      SYM = TYPE.EQ.'SY'\n      TRI = TYPE.EQ.'TR'\n      UPPER = ( HER.OR.SYM.OR.TRI ).AND.UPLO.EQ.'U'\n      LOWER = ( HER.OR.SYM.OR.TRI ).AND.UPLO.EQ.'L'\n      UNIT = TRI.AND.DIAG.EQ.'U'\n*\n*     Generate data in array A.\n*\n      DO 20 J = 1, N\n         DO 10 I = 1, M\n            IF( GEN.OR.( UPPER.AND.I.LE.J ).OR.( LOWER.AND.I.GE.J ) )\n     $          THEN\n               A( I, J ) = ZBEG( RESET ) + TRANSL\n               IF( I.NE.J )THEN\n*                 Set some elements to zero\n                  IF( N.GT.3.AND.J.EQ.N/2 )\n     $               A( I, J ) = ZERO\n                  IF( HER )THEN\n                     A( J, I ) = DCONJG( A( I, J ) )\n                  ELSE IF( SYM )THEN\n                     A( J, I ) = A( I, J )\n                  ELSE IF( TRI )THEN\n                     A( J, I ) = ZERO\n                  END IF\n               END IF\n            END IF\n   10    CONTINUE\n         IF( HER )\n     $      A( J, J ) = DCMPLX( DBLE( A( J, J ) ), RZERO )\n         IF( TRI )\n     $      A( J, J ) = A( J, J ) + ONE\n         IF( UNIT )\n     $      A( J, J ) = ONE\n   20 CONTINUE\n*\n*     Store elements in array AS in data structure required by routine.\n*\n      IF( TYPE.EQ.'GE' )THEN\n         DO 50 J = 1, N\n            DO 30 I = 1, M\n               AA( I + ( J - 1 )*LDA ) = A( I, J )\n   30       CONTINUE\n            DO 40 I = M + 1, LDA\n               AA( I + ( J - 1 )*LDA ) = ROGUE\n   40       CONTINUE\n   50    CONTINUE\n      ELSE IF( TYPE.EQ.'HE'.OR.TYPE.EQ.'SY'.OR.TYPE.EQ.'TR' )THEN\n         DO 90 J = 1, N\n            IF( UPPER )THEN\n               IBEG = 1\n               IF( UNIT )THEN\n                  IEND = J - 1\n               ELSE\n                  IEND = J\n               END IF\n            ELSE\n               IF( UNIT )THEN\n                  IBEG = J + 1\n               ELSE\n                  IBEG = J\n               END IF\n               IEND = N\n            END IF\n            DO 60 I = 1, IBEG - 1\n               AA( I + ( J - 1 )*LDA ) = ROGUE\n   60       CONTINUE\n            DO 70 I = IBEG, IEND\n               AA( I + ( J - 1 )*LDA ) = A( I, J )\n   70       CONTINUE\n            DO 80 I = IEND + 1, LDA\n               AA( I + ( J - 1 )*LDA ) = ROGUE\n   80       CONTINUE\n            IF( HER )THEN\n               JJ = J + ( J - 1 )*LDA\n               AA( JJ ) = DCMPLX( DBLE( AA( JJ ) ), RROGUE )\n            END IF\n   90    CONTINUE\n      END IF\n      RETURN\n*\n*     End of ZMAKE.\n*\n      END\n      SUBROUTINE ZMMCH( TRANSA, TRANSB, M, N, KK, ALPHA, A, LDA, B, LDB,\n     $                  BETA, C, LDC, CT, G, CC, LDCC, EPS, ERR, FATAL,\n     $                  NOUT, MV )\n*\n*  Checks the results of the computational tests.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Parameters ..\n      COMPLEX*16         ZERO\n      PARAMETER          ( ZERO = ( 0.0D0, 0.0D0 ) )\n      DOUBLE PRECISION   RZERO, RONE\n      PARAMETER          ( RZERO = 0.0D0, RONE = 1.0D0 )\n*     .. Scalar Arguments ..\n      COMPLEX*16         ALPHA, BETA\n      DOUBLE PRECISION   EPS, ERR\n      INTEGER            KK, LDA, LDB, LDC, LDCC, M, N, NOUT\n      LOGICAL            FATAL, MV\n      CHARACTER*1        TRANSA, TRANSB\n*     .. Array Arguments ..\n      COMPLEX*16         A( LDA, * ), B( LDB, * ), C( LDC, * ),\n     $                   CC( LDCC, * ), CT( * )\n      DOUBLE PRECISION   G( * )\n*     .. Local Scalars ..\n      COMPLEX*16         CL\n      DOUBLE PRECISION   ERRI\n      INTEGER            I, J, K\n      LOGICAL            CTRANA, CTRANB, TRANA, TRANB\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, DIMAG, DCONJG, MAX, DBLE, SQRT\n*     .. Statement Functions ..\n      DOUBLE PRECISION   ABS1\n*     .. Statement Function definitions ..\n      ABS1( CL ) = ABS( DBLE( CL ) ) + ABS( DIMAG( CL ) )\n*     .. Executable Statements ..\n      TRANA = TRANSA.EQ.'T'.OR.TRANSA.EQ.'C'\n      TRANB = TRANSB.EQ.'T'.OR.TRANSB.EQ.'C'\n      CTRANA = TRANSA.EQ.'C'\n      CTRANB = TRANSB.EQ.'C'\n*\n*     Compute expected result, one column at a time, in CT using data\n*     in A, B and C.\n*     Compute gauges in G.\n*\n      DO 220 J = 1, N\n*\n         DO 10 I = 1, M\n            CT( I ) = ZERO\n            G( I ) = RZERO\n   10    CONTINUE\n         IF( .NOT.TRANA.AND..NOT.TRANB )THEN\n            DO 30 K = 1, KK\n               DO 20 I = 1, M\n                  CT( I ) = CT( I ) + A( I, K )*B( K, J )\n                  G( I ) = G( I ) + ABS1( A( I, K ) )*ABS1( B( K, J ) )\n   20          CONTINUE\n   30       CONTINUE\n         ELSE IF( TRANA.AND..NOT.TRANB )THEN\n            IF( CTRANA )THEN\n               DO 50 K = 1, KK\n                  DO 40 I = 1, M\n                     CT( I ) = CT( I ) + DCONJG( A( K, I ) )*B( K, J )\n                     G( I ) = G( I ) + ABS1( A( K, I ) )*\n     $                        ABS1( B( K, J ) )\n   40             CONTINUE\n   50          CONTINUE\n            ELSE\n               DO 70 K = 1, KK\n                  DO 60 I = 1, M\n                     CT( I ) = CT( I ) + A( K, I )*B( K, J )\n                     G( I ) = G( I ) + ABS1( A( K, I ) )*\n     $                        ABS1( B( K, J ) )\n   60             CONTINUE\n   70          CONTINUE\n            END IF\n         ELSE IF( .NOT.TRANA.AND.TRANB )THEN\n            IF( CTRANB )THEN\n               DO 90 K = 1, KK\n                  DO 80 I = 1, M\n                     CT( I ) = CT( I ) + A( I, K )*DCONJG( B( J, K ) )\n                     G( I ) = G( I ) + ABS1( A( I, K ) )*\n     $                        ABS1( B( J, K ) )\n   80             CONTINUE\n   90          CONTINUE\n            ELSE\n               DO 110 K = 1, KK\n                  DO 100 I = 1, M\n                     CT( I ) = CT( I ) + A( I, K )*B( J, K )\n                     G( I ) = G( I ) + ABS1( A( I, K ) )*\n     $                        ABS1( B( J, K ) )\n  100             CONTINUE\n  110          CONTINUE\n            END IF\n         ELSE IF( TRANA.AND.TRANB )THEN\n            IF( CTRANA )THEN\n               IF( CTRANB )THEN\n                  DO 130 K = 1, KK\n                     DO 120 I = 1, M\n                        CT( I ) = CT( I ) + DCONJG( A( K, I ) )*\n     $                            DCONJG( B( J, K ) )\n                        G( I ) = G( I ) + ABS1( A( K, I ) )*\n     $                           ABS1( B( J, K ) )\n  120                CONTINUE\n  130             CONTINUE\n               ELSE\n                  DO 150 K = 1, KK\n                     DO 140 I = 1, M\n                        CT( I ) = CT( I ) + DCONJG( A( K, I ) )*\n     $                            B( J, K )\n                        G( I ) = G( I ) + ABS1( A( K, I ) )*\n     $                           ABS1( B( J, K ) )\n  140                CONTINUE\n  150             CONTINUE\n               END IF\n            ELSE\n               IF( CTRANB )THEN\n                  DO 170 K = 1, KK\n                     DO 160 I = 1, M\n                        CT( I ) = CT( I ) + A( K, I )*\n     $                            DCONJG( B( J, K ) )\n                        G( I ) = G( I ) + ABS1( A( K, I ) )*\n     $                           ABS1( B( J, K ) )\n  160                CONTINUE\n  170             CONTINUE\n               ELSE\n                  DO 190 K = 1, KK\n                     DO 180 I = 1, M\n                        CT( I ) = CT( I ) + A( K, I )*B( J, K )\n                        G( I ) = G( I ) + ABS1( A( K, I ) )*\n     $                           ABS1( B( J, K ) )\n  180                CONTINUE\n  190             CONTINUE\n               END IF\n            END IF\n         END IF\n         DO 200 I = 1, M\n            CT( I ) = ALPHA*CT( I ) + BETA*C( I, J )\n            G( I ) = ABS1( ALPHA )*G( I ) +\n     $               ABS1( BETA )*ABS1( C( I, J ) )\n  200    CONTINUE\n*\n*        Compute the error ratio for this result.\n*\n         ERR = ZERO\n         DO 210 I = 1, M\n            ERRI = ABS1( CT( I ) - CC( I, J ) )/EPS\n            IF( G( I ).NE.RZERO )\n     $         ERRI = ERRI/G( I )\n            ERR = MAX( ERR, ERRI )\n            IF( ERR*SQRT( EPS ).GE.RONE )\n     $         GO TO 230\n  210    CONTINUE\n*\n  220 CONTINUE\n*\n*     If the loop completes, all results are at least half accurate.\n      GO TO 250\n*\n*     Report fatal error.\n*\n  230 FATAL = .TRUE.\n      WRITE( NOUT, FMT = 9999 )\n      DO 240 I = 1, M\n         IF( MV )THEN\n            WRITE( NOUT, FMT = 9998 )I, CT( I ), CC( I, J )\n         ELSE\n            WRITE( NOUT, FMT = 9998 )I, CC( I, J ), CT( I )\n         END IF\n  240 CONTINUE\n      IF( N.GT.1 )\n     $   WRITE( NOUT, FMT = 9997 )J\n*\n  250 CONTINUE\n      RETURN\n*\n 9999 FORMAT( ' ******* FATAL ERROR - COMPUTED RESULT IS LESS THAN HAL',\n     $      'F ACCURATE *******', /'                       EXPECTED RE',\n     $      'SULT                    COMPUTED RESULT' )\n 9998 FORMAT( 1X, I7, 2( '  (', G15.6, ',', G15.6, ')' ) )\n 9997 FORMAT( '      THESE ARE THE RESULTS FOR COLUMN ', I3 )\n*\n*     End of ZMMCH.\n*\n      END\n      LOGICAL FUNCTION LZE( RI, RJ, LR )\n*\n*  Tests if two arrays are identical.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Scalar Arguments ..\n      INTEGER            LR\n*     .. Array Arguments ..\n      COMPLEX*16         RI( * ), RJ( * )\n*     .. Local Scalars ..\n      INTEGER            I\n*     .. Executable Statements ..\n      DO 10 I = 1, LR\n         IF( RI( I ).NE.RJ( I ) )\n     $      GO TO 20\n   10 CONTINUE\n      LZE = .TRUE.\n      GO TO 30\n   20 CONTINUE\n      LZE = .FALSE.\n   30 RETURN\n*\n*     End of LZE.\n*\n      END\n      LOGICAL FUNCTION LZERES( TYPE, UPLO, M, N, AA, AS, LDA )\n*\n*  Tests if selected elements in two arrays are equal.\n*\n*  TYPE is 'GE' or 'HE' or 'SY'.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Scalar Arguments ..\n      INTEGER            LDA, M, N\n      CHARACTER*1        UPLO\n      CHARACTER*2        TYPE\n*     .. Array Arguments ..\n      COMPLEX*16         AA( LDA, * ), AS( LDA, * )\n*     .. Local Scalars ..\n      INTEGER            I, IBEG, IEND, J\n      LOGICAL            UPPER\n*     .. Executable Statements ..\n      UPPER = UPLO.EQ.'U'\n      IF( TYPE.EQ.'GE' )THEN\n         DO 20 J = 1, N\n            DO 10 I = M + 1, LDA\n               IF( AA( I, J ).NE.AS( I, J ) )\n     $            GO TO 70\n   10       CONTINUE\n   20    CONTINUE\n      ELSE IF( TYPE.EQ.'HE'.OR.TYPE.EQ.'SY' )THEN\n         DO 50 J = 1, N\n            IF( UPPER )THEN\n               IBEG = 1\n               IEND = J\n            ELSE\n               IBEG = J\n               IEND = N\n            END IF\n            DO 30 I = 1, IBEG - 1\n               IF( AA( I, J ).NE.AS( I, J ) )\n     $            GO TO 70\n   30       CONTINUE\n            DO 40 I = IEND + 1, LDA\n               IF( AA( I, J ).NE.AS( I, J ) )\n     $            GO TO 70\n   40       CONTINUE\n   50    CONTINUE\n      END IF\n*\n      LZERES = .TRUE.\n      GO TO 80\n   70 CONTINUE\n      LZERES = .FALSE.\n   80 RETURN\n*\n*     End of LZERES.\n*\n      END\n      COMPLEX*16     FUNCTION ZBEG( RESET )\n*\n*  Generates complex numbers as pairs of random numbers uniformly\n*  distributed between -0.5 and 0.5.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Scalar Arguments ..\n      LOGICAL            RESET\n*     .. Local Scalars ..\n      INTEGER            I, IC, J, MI, MJ\n*     .. Save statement ..\n      SAVE               I, IC, J, MI, MJ\n*     .. Intrinsic Functions ..\n      INTRINSIC          DCMPLX\n*     .. Executable Statements ..\n      IF( RESET )THEN\n*        Initialize local variables.\n         MI = 891\n         MJ = 457\n         I = 7\n         J = 7\n         IC = 0\n         RESET = .FALSE.\n      END IF\n*\n*     The sequence of values of I or J is bounded between 1 and 999.\n*     If initial I or J = 1,2,3,6,7 or 9, the period will be 50.\n*     If initial I or J = 4 or 8, the period will be 25.\n*     If initial I or J = 5, the period will be 10.\n*     IC is used to break up the period by skipping 1 value of I or J\n*     in 6.\n*\n      IC = IC + 1\n   10 I = I*MI\n      J = J*MJ\n      I = I - 1000*( I/1000 )\n      J = J - 1000*( J/1000 )\n      IF( IC.GE.5 )THEN\n         IC = 0\n         GO TO 10\n      END IF\n      ZBEG = DCMPLX( ( I - 500 )/1001.0D0, ( J - 500 )/1001.0D0 )\n      RETURN\n*\n*     End of ZBEG.\n*\n      END\n      DOUBLE PRECISION FUNCTION DDIFF( X, Y )\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION   X, Y\n*     .. Executable Statements ..\n      DDIFF = X - Y\n      RETURN\n*\n*     End of DDIFF.\n*\n      END\n      SUBROUTINE CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )\n*\n*  Tests whether XERBLA has detected an error when it should.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Scalar Arguments ..\n      INTEGER            INFOT, NOUT\n      LOGICAL            LERR, OK\n      CHARACTER*6        SRNAMT\n*     .. Executable Statements ..\n      IF( .NOT.LERR )THEN\n         WRITE( NOUT, FMT = 9999 )INFOT, SRNAMT\n         OK = .FALSE.\n      END IF\n      LERR = .FALSE.\n      RETURN\n*\n 9999 FORMAT( ' ***** ILLEGAL VALUE OF PARAMETER NUMBER ', I2, ' NOT D',\n     $      'ETECTED BY ', A6, ' *****' )\n*\n*     End of CHKXER.\n*\n      END\n      SUBROUTINE XERBLA( SRNAME, INFO )\n*\n*  This is a special version of XERBLA to be used only as part of\n*  the test program for testing error exits from the Level 3 BLAS\n*  routines.\n*\n*  XERBLA  is an error handler for the Level 3 BLAS routines.\n*\n*  It is called by the Level 3 BLAS routines if an input parameter is\n*  invalid.\n*\n*  Auxiliary routine for test program for Level 3 Blas.\n*\n*  -- Written on 8-February-1989.\n*     Jack Dongarra, Argonne National Laboratory.\n*     Iain Duff, AERE Harwell.\n*     Jeremy Du Croz, Numerical Algorithms Group Ltd.\n*     Sven Hammarling, Numerical Algorithms Group Ltd.\n*\n*     .. Scalar Arguments ..\n      INTEGER            INFO\n      CHARACTER*6        SRNAME\n*     .. Scalars in Common ..\n      INTEGER            INFOT, NOUT\n      LOGICAL            LERR, OK\n      CHARACTER*6        SRNAMT\n*     .. Common blocks ..\n      COMMON             /INFOC/INFOT, NOUT, OK, LERR\n      COMMON             /SRNAMC/SRNAMT\n*     .. Executable Statements ..\n      LERR = .TRUE.\n      IF( INFO.NE.INFOT )THEN\n         IF( INFOT.NE.0 )THEN\n            WRITE( NOUT, FMT = 9999 )INFO, INFOT\n         ELSE\n            WRITE( NOUT, FMT = 9997 )INFO\n         END IF\n         OK = .FALSE.\n      END IF\n      IF( SRNAME.NE.SRNAMT )THEN\n         WRITE( NOUT, FMT = 9998 )SRNAME, SRNAMT\n         OK = .FALSE.\n      END IF\n      RETURN\n*\n 9999 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6, ' INSTEAD',\n     $      ' OF ', I2, ' *******' )\n 9998 FORMAT( ' ******* XERBLA WAS CALLED WITH SRNAME = ', A6, ' INSTE',\n     $      'AD OF ', A6, ' *******' )\n 9997 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6,\n     $      ' *******' )\n*\n*     End of XERBLA\n*\n      END\n\n"
  },
  {
    "path": "include/eigen3/blas/xerbla.cpp",
    "content": "\n#include <stdio.h>\n\n#if (defined __GNUC__) && (!defined __MINGW32__) && (!defined __CYGWIN__)\n#define EIGEN_WEAK_LINKING __attribute__ ((weak))\n#else\n#define EIGEN_WEAK_LINKING\n#endif\n\n#ifdef __cplusplus\nextern \"C\"\n{\n#endif\n\nEIGEN_WEAK_LINKING int xerbla_(const char * msg, int *info, int)\n{\n  printf(\"Eigen BLAS ERROR #%i: %s\\n\", *info, msg );\n  return 0;\n}\n\n#ifdef __cplusplus\n}\n#endif\n"
  },
  {
    "path": "include/eigen3/cmake/Eigen3Config.cmake.in",
    "content": "# This file exports the Eigen3::Eigen CMake target which should be passed to the\n# target_link_libraries command.\n\n@PACKAGE_INIT@\n\ninclude (\"${CMAKE_CURRENT_LIST_DIR}/Eigen3Targets.cmake\")\n\n# Legacy variables, do *not* use. May be removed in the future.\n\nset (EIGEN3_FOUND 1)\nset (EIGEN3_USE_FILE    \"${CMAKE_CURRENT_LIST_DIR}/UseEigen3.cmake\")\n\nset (EIGEN3_DEFINITIONS  \"@EIGEN_DEFINITIONS@\")\nset (EIGEN3_INCLUDE_DIR  \"@PACKAGE_EIGEN_INCLUDE_DIR@\")\nset (EIGEN3_INCLUDE_DIRS \"@PACKAGE_EIGEN_INCLUDE_DIR@\")\nset (EIGEN3_ROOT_DIR     \"@PACKAGE_EIGEN_ROOT_DIR@\")\n\nset (EIGEN3_VERSION_STRING \"@EIGEN_VERSION_STRING@\")\nset (EIGEN3_VERSION_MAJOR  \"@EIGEN_VERSION_MAJOR@\")\nset (EIGEN3_VERSION_MINOR  \"@EIGEN_VERSION_MINOR@\")\nset (EIGEN3_VERSION_PATCH  \"@EIGEN_VERSION_PATCH@\")\n"
  },
  {
    "path": "include/eigen3/cmake/Eigen3ConfigLegacy.cmake.in",
    "content": "#                                               -*- cmake -*-\n#\n#  Eigen3Config.cmake(.in)\n\n# Use the following variables to compile and link against Eigen:\n#  EIGEN3_FOUND              - True if Eigen was found on your system\n#  EIGEN3_USE_FILE           - The file making Eigen usable\n#  EIGEN3_DEFINITIONS        - Definitions needed to build with Eigen\n#  EIGEN3_INCLUDE_DIR        - Directory where signature_of_eigen3_matrix_library can be found\n#  EIGEN3_INCLUDE_DIRS       - List of directories of Eigen and it's dependencies\n#  EIGEN3_ROOT_DIR           - The base directory of Eigen\n#  EIGEN3_VERSION_STRING     - A human-readable string containing the version\n#  EIGEN3_VERSION_MAJOR      - The major version of Eigen\n#  EIGEN3_VERSION_MINOR      - The minor version of Eigen\n#  EIGEN3_VERSION_PATCH      - The patch version of Eigen\n\n@PACKAGE_INIT@\n\nset ( EIGEN3_FOUND 1 )\nset ( EIGEN3_USE_FILE     \"${CMAKE_CURRENT_LIST_DIR}/UseEigen3.cmake\" )\n\nset ( EIGEN3_DEFINITIONS  \"@EIGEN_DEFINITIONS@\" )\nset ( EIGEN3_INCLUDE_DIR  \"@PACKAGE_EIGEN_INCLUDE_DIR@\" )\nset ( EIGEN3_INCLUDE_DIRS \"@PACKAGE_EIGEN_INCLUDE_DIR@\" )\nset ( EIGEN3_ROOT_DIR     \"@PACKAGE_EIGEN_ROOT_DIR@\" )\n\nset ( EIGEN3_VERSION_STRING \"@EIGEN_VERSION_STRING@\" )\nset ( EIGEN3_VERSION_MAJOR  \"@EIGEN_VERSION_MAJOR@\" )\nset ( EIGEN3_VERSION_MINOR  \"@EIGEN_VERSION_MINOR@\" )\nset ( EIGEN3_VERSION_PATCH  \"@EIGEN_VERSION_PATCH@\" )\n"
  },
  {
    "path": "include/eigen3/cmake/EigenConfigureTesting.cmake",
    "content": "include(EigenTesting)\ninclude(CheckCXXSourceCompiles)\n\n# configure the \"site\" and \"buildname\" \nei_set_sitename()\n\n# retrieve and store the build string\nei_set_build_string()\n\nadd_custom_target(buildtests)\nadd_custom_target(check COMMAND \"ctest\")\nadd_dependencies(check buildtests)\n\n# check whether /bin/bash exists\nfind_file(EIGEN_BIN_BASH_EXISTS \"/bin/bash\" PATHS \"/\" NO_DEFAULT_PATH)\n\n# This call activates testing and generates the DartConfiguration.tcl\ninclude(CTest)\n\nset(EIGEN_TEST_BUILD_FLAGS \"\" CACHE STRING \"Options passed to the build command of unit tests\")\n\n# Overwrite default DartConfiguration.tcl such that ctest can build our unit tests.\n# Recall that our unit tests are not in the \"all\" target, so we have to explicitely ask ctest to build our custom 'buildtests' target.\n# At this stage, we can also add custom flags to the build tool through the user defined EIGEN_TEST_BUILD_FLAGS variable.\nfile(READ  \"${CMAKE_CURRENT_BINARY_DIR}/DartConfiguration.tcl\" EIGEN_DART_CONFIG_FILE)\n# try to grab the default flags\nstring(REGEX MATCH \"MakeCommand:.*-- (.*)\\nDefaultCTestConfigurationType\" EIGEN_DUMMY ${EIGEN_DART_CONFIG_FILE})\nif(NOT CMAKE_MATCH_1)\nstring(REGEX MATCH \"MakeCommand:.*[^c]make (.*)\\nDefaultCTestConfigurationType\" EIGEN_DUMMY ${EIGEN_DART_CONFIG_FILE})\nendif()\nstring(REGEX REPLACE \"MakeCommand:.*DefaultCTestConfigurationType\" \"MakeCommand: ${CMAKE_COMMAND} --build . --target buildtests --config \\\"\\${CTEST_CONFIGURATION_TYPE}\\\" -- ${CMAKE_MATCH_1} ${EIGEN_TEST_BUILD_FLAGS}\\nDefaultCTestConfigurationType\"\n       EIGEN_DART_CONFIG_FILE2 ${EIGEN_DART_CONFIG_FILE})\nfile(WRITE \"${CMAKE_CURRENT_BINARY_DIR}/DartConfiguration.tcl\" ${EIGEN_DART_CONFIG_FILE2})\n\nconfigure_file(${CMAKE_CURRENT_SOURCE_DIR}/CTestCustom.cmake.in ${CMAKE_BINARY_DIR}/CTestCustom.cmake)\n\n# some documentation of this function would be nice\nei_init_testing()\n\n# configure Eigen related testing options\noption(EIGEN_NO_ASSERTION_CHECKING \"Disable checking of assertions using exceptions\" OFF)\noption(EIGEN_DEBUG_ASSERTS \"Enable advanced debuging of assertions\" OFF)\n\nif(CMAKE_COMPILER_IS_GNUCXX)\n  option(EIGEN_COVERAGE_TESTING \"Enable/disable gcov\" OFF)\n  if(EIGEN_COVERAGE_TESTING)\n    set(COVERAGE_FLAGS \"-fprofile-arcs -ftest-coverage\")\n    set(CTEST_CUSTOM_COVERAGE_EXCLUDE \"/test/\")\n    set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} ${COVERAGE_FLAGS}\")\n  endif(EIGEN_COVERAGE_TESTING)\n  \nelseif(MSVC)\n  set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} /D_CRT_SECURE_NO_WARNINGS /D_SCL_SECURE_NO_WARNINGS\")\nendif(CMAKE_COMPILER_IS_GNUCXX)\n\n\ncheck_cxx_compiler_flag(\"-std=c++11\" EIGEN_COMPILER_SUPPORT_CXX11)\n\nif(EIGEN_TEST_CXX11 AND EIGEN_COMPILER_SUPPORT_CXX11)\n  set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} -std=c++11\")\nendif()\n"
  },
  {
    "path": "include/eigen3/cmake/EigenDetermineOSVersion.cmake",
    "content": "# The utility function DetermineOSVersion aims at providing an\n# improved version of the CMake variable ${CMAKE_SYSTEM} on Windows\n# machines.\n#\n# Usage:\n#  include(EigenDetermineOSVersion)\n#  DetermineOSVersion(OS_VERSION)\n#  message(\"OS: ${OS_VERSION}\")\n\n# - A little helper variable which should not be directly called\nfunction(DetermineShortWindowsName WIN_VERSION win_num_version)\n   if    (${win_num_version} VERSION_EQUAL \"6.1\")\n       set(_version \"win7\")\n   elseif(${win_num_version} VERSION_EQUAL \"6.0\")\n       set(_version \"winVista\")\n   elseif(${win_num_version} VERSION_EQUAL \"5.2\")\n       set(_version \"winXpProf\")\n   elseif(${win_num_version} VERSION_EQUAL \"5.1\")\n       set(_version \"winXp\")\n   elseif(${win_num_version} VERSION_EQUAL \"5.0\")\n       set(_version \"win2000Prof\")\n   else()\n       set(_version \"unknownWin\")\n   endif()\n   set(${WIN_VERSION} ${_version} PARENT_SCOPE)\nendfunction()\n\nfunction(DetermineOSVersion OS_VERSION)\n  if (WIN32 AND CMAKE_HOST_SYSTEM_NAME MATCHES Windows)\n    file (TO_NATIVE_PATH \"$ENV{COMSPEC}\" SHELL)\n    exec_program( ${SHELL} ARGS \"/c\" \"ver\" OUTPUT_VARIABLE ver_output)\n\t\t\t\t\n      string(REGEX MATCHALL \"[0-9]+\"\n           ver_list \"${ver_output}\")\n      list(GET ver_list 0 _major)\t\t   \n      list(GET ver_list 1 _minor)\n\t\t\t\t\n    set(win_num_version ${_major}.${_minor})\n    DetermineShortWindowsName(win_version \"${win_num_version}\")\n    if(win_version)\n      set(${OS_VERSION} ${win_version} PARENT_SCOPE)\n    endif()\n  else()\n    set(${OS_VERSION} ${CMAKE_SYSTEM} PARENT_SCOPE)\n  endif()\nendfunction()\n"
  },
  {
    "path": "include/eigen3/cmake/EigenDetermineVSServicePack.cmake",
    "content": "include(CMakeDetermineVSServicePack)\n\n# The code is almost identical to the CMake version. The only difference is that we remove\n# _DetermineVSServicePack_FastCheckVersionWithCompiler which lead to errors on some systems.\nfunction(EigenDetermineVSServicePack _pack)\n    if(NOT DETERMINED_VS_SERVICE_PACK OR NOT ${_pack})\n        if(NOT DETERMINED_VS_SERVICE_PACK)\n            _DetermineVSServicePack_CheckVersionWithTryCompile(DETERMINED_VS_SERVICE_PACK _cl_version)\n            if(NOT DETERMINED_VS_SERVICE_PACK)\n                _DetermineVSServicePack_CheckVersionWithTryRun(DETERMINED_VS_SERVICE_PACK _cl_version)\n            endif()\n        endif()\n\n        if(DETERMINED_VS_SERVICE_PACK)\n            if(_cl_version)\n                # Call helper function to determine VS version\n                _DetermineVSServicePackFromCompiler(_sp \"${_cl_version}\")\n              \n                # temporary fix, until CMake catches up\n                if (NOT _sp)\n                    if(${_cl_version} VERSION_EQUAL \"17.00.50727.1\")\n                        set(_sp \"vc110\")\n                    elseif(${_cl_version} VERSION_EQUAL \"17.00.51106.1\")\n                        set(_sp \"vc110sp1\")\n                    elseif(${_cl_version} VERSION_EQUAL \"17.00.60315.1\")\n                        set(_sp \"vc110sp2\")\n                    elseif(${_cl_version} VERSION_EQUAL \"17.00.60610.1\")\n                        set(_sp \"vc110sp3\")\n                    else()\n                        set(_sp ${CMAKE_CXX_COMPILER_VERSION})\n                    endif()\n                endif()\n                \n                if(_sp)\n                    set(${_pack} ${_sp} CACHE INTERNAL\n                        \"The Visual Studio Release with Service Pack\")\n                endif()\n            endif()\n        endif()\n    endif()\nendfunction()\n"
  },
  {
    "path": "include/eigen3/cmake/EigenTesting.cmake",
    "content": "\nmacro(ei_add_property prop value)\n  get_property(previous GLOBAL PROPERTY ${prop})\n  if ((NOT previous) OR (previous STREQUAL \"\"))\n    set_property(GLOBAL PROPERTY ${prop} \"${value}\")\n  else()\n    set_property(GLOBAL PROPERTY ${prop} \"${previous} ${value}\")\n  endif()\nendmacro(ei_add_property)\n\n#internal. See documentation of ei_add_test for details.\nmacro(ei_add_test_internal testname testname_with_suffix)\n  set(targetname ${testname_with_suffix})\n\n  if(EIGEN_ADD_TEST_FILENAME_EXTENSION)\n    set(filename ${testname}.${EIGEN_ADD_TEST_FILENAME_EXTENSION})\n  else()\n    set(filename ${testname}.cpp)\n  endif()\n\n  if(EIGEN_ADD_TEST_FILENAME_EXTENSION STREQUAL cu)\n    if(EIGEN_TEST_CUDA_CLANG)\n      set_source_files_properties(${filename} PROPERTIES LANGUAGE CXX)\n      if(CUDA_64_BIT_DEVICE_CODE)\n        link_directories(\"${CUDA_TOOLKIT_ROOT_DIR}/lib64\")\n      else()\n        link_directories(\"${CUDA_TOOLKIT_ROOT_DIR}/lib\")\n      endif()\n      if (${ARGC} GREATER 2)\n        add_executable(${targetname} ${filename})\n      else()\n        add_executable(${targetname} ${filename} OPTIONS ${ARGV2})\n      endif()\n      target_link_libraries(${targetname} \"cudart_static\" \"cuda\" \"dl\" \"rt\" \"pthread\")\n    else()\n      if (${ARGC} GREATER 2)\n        cuda_add_executable(${targetname} ${filename} OPTIONS ${ARGV2})\n      else()\n        cuda_add_executable(${targetname} ${filename})\n      endif()\n    endif()\n  else()\n    add_executable(${targetname} ${filename})\n  endif()\n\n  if (targetname MATCHES \"^eigen2_\")\n    add_dependencies(eigen2_buildtests ${targetname})\n  else()\n    add_dependencies(buildtests ${targetname})\n  endif()\n\n  if(EIGEN_NO_ASSERTION_CHECKING)\n    ei_add_target_property(${targetname} COMPILE_FLAGS \"-DEIGEN_NO_ASSERTION_CHECKING=1\")\n  else(EIGEN_NO_ASSERTION_CHECKING)\n    if(EIGEN_DEBUG_ASSERTS)\n      ei_add_target_property(${targetname} COMPILE_FLAGS \"-DEIGEN_DEBUG_ASSERTS=1\")\n    endif(EIGEN_DEBUG_ASSERTS)\n  endif(EIGEN_NO_ASSERTION_CHECKING)\n\n  ei_add_target_property(${targetname} COMPILE_FLAGS \"-DEIGEN_TEST_MAX_SIZE=${EIGEN_TEST_MAX_SIZE}\")\n\n  ei_add_target_property(${targetname} COMPILE_FLAGS \"-DEIGEN_TEST_FUNC=${testname}\")\n\n  if(MSVC)\n    ei_add_target_property(${targetname} COMPILE_FLAGS \"/bigobj\")\n  endif()\n\n  # let the user pass flags.\n  if(${ARGC} GREATER 2)\n    ei_add_target_property(${targetname} COMPILE_FLAGS \"${ARGV2}\")\n  endif(${ARGC} GREATER 2)\n\n  if(EIGEN_TEST_CUSTOM_CXX_FLAGS)\n    ei_add_target_property(${targetname} COMPILE_FLAGS \"${EIGEN_TEST_CUSTOM_CXX_FLAGS}\")\n  endif()\n\n  if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO)\n    target_link_libraries(${targetname} ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO})\n  endif()\n  if(EXTERNAL_LIBS)\n    target_link_libraries(${targetname} ${EXTERNAL_LIBS})\n  endif()\n  if(EIGEN_TEST_CUSTOM_LINKER_FLAGS)\n    target_link_libraries(${targetname} ${EIGEN_TEST_CUSTOM_LINKER_FLAGS})\n  endif()\n\n  if(${ARGC} GREATER 3)\n    set(libs_to_link ${ARGV3})\n    # it could be that some cmake module provides a bad library string \" \"  (just spaces),\n    # and that severely breaks target_link_libraries (\"can't link to -l-lstdc++\" errors).\n    # so we check for strings containing only spaces.\n    string(STRIP \"${libs_to_link}\" libs_to_link_stripped)\n    string(LENGTH \"${libs_to_link_stripped}\" libs_to_link_stripped_length)\n    if(${libs_to_link_stripped_length} GREATER 0)\n      # notice: no double quotes around ${libs_to_link} here. It may be a list.\n      target_link_libraries(${targetname} ${libs_to_link})\n    endif()\n  endif()\n\n  add_test(${testname_with_suffix} \"${targetname}\")\n\n  # Specify target and test labels accoirding to EIGEN_CURRENT_SUBPROJECT\n  get_property(current_subproject GLOBAL PROPERTY EIGEN_CURRENT_SUBPROJECT)\n  if ((current_subproject) AND (NOT (current_subproject STREQUAL \"\")))\n    set_property(TARGET ${targetname} PROPERTY LABELS \"Build${current_subproject}\")\n    add_dependencies(\"Build${current_subproject}\" ${targetname})\n    set_property(TEST ${testname_with_suffix} PROPERTY LABELS \"${current_subproject}\")\n  endif()\n\nendmacro(ei_add_test_internal)\n\n# SYCL\nmacro(ei_add_test_internal_sycl testname testname_with_suffix)\n  include_directories( SYSTEM ${COMPUTECPP_PACKAGE_ROOT_DIR}/include)\n  set(targetname ${testname_with_suffix})\n\n  if(EIGEN_ADD_TEST_FILENAME_EXTENSION)\n    set(filename ${testname}.${EIGEN_ADD_TEST_FILENAME_EXTENSION})\n  else()\n    set(filename ${testname}.cpp)\n  endif()\n\n  set( include_file ${CMAKE_CURRENT_BINARY_DIR}/inc_${filename})\n  set( bc_file ${CMAKE_CURRENT_BINARY_DIR}/${filename})\n  set( host_file ${CMAKE_CURRENT_SOURCE_DIR}/${filename})\n\n  ADD_CUSTOM_COMMAND(\n    OUTPUT ${include_file}\n    COMMAND ${CMAKE_COMMAND} -E echo \"\\\\#include \\\\\\\"${host_file}\\\\\\\"\" > ${include_file}\n    COMMAND ${CMAKE_COMMAND} -E echo \"\\\\#include \\\\\\\"${bc_file}.sycl\\\\\\\"\" >> ${include_file}\n    DEPENDS ${filename} ${bc_file}.sycl\n    COMMENT \"Building ComputeCpp integration header file ${include_file}\"\n  )\n  # Add a custom target for the generated integration header\n  add_custom_target(${testname}_integration_header_sycl DEPENDS ${include_file})\n\n  add_executable(${targetname} ${include_file})\n  add_dependencies(${targetname} ${testname}_integration_header_sycl)\n  add_sycl_to_target(${targetname} ${filename} ${CMAKE_CURRENT_BINARY_DIR})\n\n  if (targetname MATCHES \"^eigen2_\")\n    add_dependencies(eigen2_buildtests ${targetname})\n  else()\n    add_dependencies(buildtests ${targetname})\n  endif()\n\n  if(EIGEN_NO_ASSERTION_CHECKING)\n    ei_add_target_property(${targetname} COMPILE_FLAGS \"-DEIGEN_NO_ASSERTION_CHECKING=1\")\n  else(EIGEN_NO_ASSERTION_CHECKING)\n    if(EIGEN_DEBUG_ASSERTS)\n      ei_add_target_property(${targetname} COMPILE_FLAGS \"-DEIGEN_DEBUG_ASSERTS=1\")\n    endif(EIGEN_DEBUG_ASSERTS)\n  endif(EIGEN_NO_ASSERTION_CHECKING)\n\n  ei_add_target_property(${targetname} COMPILE_FLAGS \"-DEIGEN_TEST_MAX_SIZE=${EIGEN_TEST_MAX_SIZE}\")\n\n  ei_add_target_property(${targetname} COMPILE_FLAGS \"-DEIGEN_TEST_FUNC=${testname}\")\n\n  if(MSVC AND NOT EIGEN_SPLIT_LARGE_TESTS)\n    ei_add_target_property(${targetname} COMPILE_FLAGS \"/bigobj\")\n  endif()\n\n  # let the user pass flags.\n  if(${ARGC} GREATER 2)\n    ei_add_target_property(${targetname} COMPILE_FLAGS \"${ARGV2}\")\n  endif(${ARGC} GREATER 2)\n\n  if(EIGEN_TEST_CUSTOM_CXX_FLAGS)\n    ei_add_target_property(${targetname} COMPILE_FLAGS \"${EIGEN_TEST_CUSTOM_CXX_FLAGS}\")\n  endif()\n\n  if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO)\n    target_link_libraries(${targetname} ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO})\n  endif()\n  if(EXTERNAL_LIBS)\n    target_link_libraries(${targetname} ${EXTERNAL_LIBS})\n  endif()\n  if(EIGEN_TEST_CUSTOM_LINKER_FLAGS)\n    target_link_libraries(${targetname} ${EIGEN_TEST_CUSTOM_LINKER_FLAGS})\n  endif()\n\n  if(${ARGC} GREATER 3)\n    set(libs_to_link ${ARGV3})\n    # it could be that some cmake module provides a bad library string \" \"  (just spaces),\n    # and that severely breaks target_link_libraries (\"can't link to -l-lstdc++\" errors).\n    # so we check for strings containing only spaces.\n    string(STRIP \"${libs_to_link}\" libs_to_link_stripped)\n    string(LENGTH \"${libs_to_link_stripped}\" libs_to_link_stripped_length)\n    if(${libs_to_link_stripped_length} GREATER 0)\n      # notice: no double quotes around ${libs_to_link} here. It may be a list.\n      target_link_libraries(${targetname} ${libs_to_link})\n    endif()\n  endif()\n\n  add_test(${testname_with_suffix} \"${targetname}\")\n\n  # Specify target and test labels according to EIGEN_CURRENT_SUBPROJECT\n  get_property(current_subproject GLOBAL PROPERTY EIGEN_CURRENT_SUBPROJECT)\n  if ((current_subproject) AND (NOT (current_subproject STREQUAL \"\")))\n    set_property(TARGET ${targetname} PROPERTY LABELS \"Build${current_subproject}\")\n    add_dependencies(\"Build${current_subproject}\" ${targetname})\n    set_property(TEST ${testname_with_suffix} PROPERTY LABELS \"${current_subproject}\")\n  endif()\n\n\nendmacro(ei_add_test_internal_sycl)\n\n\n# Macro to add a test\n#\n# the unique mandatory parameter testname must correspond to a file\n# <testname>.cpp which follows this pattern:\n#\n# #include \"main.h\"\n# void test_<testname>() { ... }\n#\n# Depending on the contents of that file, this macro can have 2 behaviors,\n# see below.\n#\n# The optional 2nd parameter is libraries to link to.\n#\n# A. Default behavior\n#\n# this macro adds an executable <testname> as well as a ctest test\n# named <testname> too.\n#\n# On platforms with bash simply run:\n#   \"ctest -V\" or \"ctest -V -R <testname>\"\n# On other platform use ctest as usual\n#\n# B. Multi-part behavior\n#\n# If the source file matches the regexp\n#    CALL_SUBTEST_[0-9]+|EIGEN_TEST_PART_[0-9]+\n# then it is interpreted as a multi-part test. The behavior then depends on the\n# CMake option EIGEN_SPLIT_LARGE_TESTS, which is ON by default.\n#\n# If EIGEN_SPLIT_LARGE_TESTS is OFF, the behavior is the same as in A (the multi-part\n# aspect is ignored).\n#\n# If EIGEN_SPLIT_LARGE_TESTS is ON, the test is split into multiple executables\n#   test_<testname>_<N>\n# where N runs from 1 to the greatest occurence found in the source file. Each of these\n# executables is built passing -DEIGEN_TEST_PART_N. This allows to split large tests\n# into smaller executables.\n#\n# Moreover, targets <testname> are still generated, they\n# have the effect of building all the parts of the test.\n#\n# Again, ctest -R allows to run all matching tests.\nmacro(ei_add_test testname)\n  get_property(EIGEN_TESTS_LIST GLOBAL PROPERTY EIGEN_TESTS_LIST)\n  set(EIGEN_TESTS_LIST \"${EIGEN_TESTS_LIST}${testname}\\n\")\n  set_property(GLOBAL PROPERTY EIGEN_TESTS_LIST \"${EIGEN_TESTS_LIST}\")\n\n  if(EIGEN_ADD_TEST_FILENAME_EXTENSION)\n    set(filename ${testname}.${EIGEN_ADD_TEST_FILENAME_EXTENSION})\n  else()\n    set(filename ${testname}.cpp)\n  endif()\n\n  file(READ \"${filename}\" test_source)\n  set(parts 0)\n  string(REGEX MATCHALL \"CALL_SUBTEST_[0-9]+|EIGEN_TEST_PART_[0-9]+|EIGEN_SUFFIXES(;[0-9]+)+\"\n         occurences \"${test_source}\")\n  string(REGEX REPLACE \"CALL_SUBTEST_|EIGEN_TEST_PART_|EIGEN_SUFFIXES\" \"\" suffixes \"${occurences}\")\n  list(REMOVE_DUPLICATES suffixes)\n  if(EIGEN_SPLIT_LARGE_TESTS AND suffixes)\n    add_custom_target(${testname})\n    foreach(suffix ${suffixes})\n      ei_add_test_internal(${testname} ${testname}_${suffix}\n        \"${ARGV1} -DEIGEN_TEST_PART_${suffix}=1\" \"${ARGV2}\")\n      add_dependencies(${testname} ${testname}_${suffix})\n    endforeach(suffix)\n  else(EIGEN_SPLIT_LARGE_TESTS AND suffixes)\n    set(symbols_to_enable_all_parts \"\")\n    foreach(suffix ${suffixes})\n      set(symbols_to_enable_all_parts\n        \"${symbols_to_enable_all_parts} -DEIGEN_TEST_PART_${suffix}=1\")\n    endforeach(suffix)\n    ei_add_test_internal(${testname} ${testname} \"${ARGV1} ${symbols_to_enable_all_parts}\" \"${ARGV2}\")\n  endif(EIGEN_SPLIT_LARGE_TESTS AND suffixes)\nendmacro(ei_add_test)\n\nmacro(ei_add_test_sycl testname)\n  get_property(EIGEN_TESTS_LIST GLOBAL PROPERTY EIGEN_TESTS_LIST)\n  set(EIGEN_TESTS_LIST \"${EIGEN_TESTS_LIST}${testname}\\n\")\n  set_property(GLOBAL PROPERTY EIGEN_TESTS_LIST \"${EIGEN_TESTS_LIST}\")\n\n  if(EIGEN_ADD_TEST_FILENAME_EXTENSION)\n    set(filename ${testname}.${EIGEN_ADD_TEST_FILENAME_EXTENSION})\n  else()\n    set(filename ${testname}.cpp)\n  endif()\n\n  file(READ \"${filename}\" test_source)\n  set(parts 0)\n  string(REGEX MATCHALL \"CALL_SUBTEST_[0-9]+|EIGEN_TEST_PART_[0-9]+|EIGEN_SUFFIXES(;[0-9]+)+\"\n         occurences \"${test_source}\")\n  string(REGEX REPLACE \"CALL_SUBTEST_|EIGEN_TEST_PART_|EIGEN_SUFFIXES\" \"\" suffixes \"${occurences}\")\n  list(REMOVE_DUPLICATES suffixes)\n  if(EIGEN_SPLIT_LARGE_TESTS AND suffixes)\n    add_custom_target(${testname})\n    foreach(suffix ${suffixes})\n      ei_add_test_internal_sycl(${testname} ${testname}_${suffix}\n        \"${ARGV1} -DEIGEN_TEST_PART_${suffix}=1\" \"${ARGV2}\")\n      add_dependencies(${testname} ${testname}_${suffix})\n    endforeach(suffix)\n  else(EIGEN_SPLIT_LARGE_TESTS AND suffixes)\n    set(symbols_to_enable_all_parts \"\")\n    foreach(suffix ${suffixes})\n      set(symbols_to_enable_all_parts\n        \"${symbols_to_enable_all_parts} -DEIGEN_TEST_PART_${suffix}=1\")\n    endforeach(suffix)\n    ei_add_test_internal_sycl(${testname} ${testname} \"${ARGV1} ${symbols_to_enable_all_parts}\" \"${ARGV2}\")\n  endif(EIGEN_SPLIT_LARGE_TESTS AND suffixes)\nendmacro(ei_add_test_sycl)\n\n# adds a failtest, i.e. a test that succeed if the program fails to compile\n# note that the test runner for these is CMake itself, when passed -DEIGEN_FAILTEST=ON\n# so here we're just running CMake commands immediately, we're not adding any targets.\nmacro(ei_add_failtest testname)\n  get_property(EIGEN_FAILTEST_FAILURE_COUNT GLOBAL PROPERTY EIGEN_FAILTEST_FAILURE_COUNT)\n  get_property(EIGEN_FAILTEST_COUNT GLOBAL PROPERTY EIGEN_FAILTEST_COUNT)\n\n  message(STATUS \"Checking failtest: ${testname}\")\n  set(filename \"${testname}.cpp\")\n  file(READ \"${filename}\" test_source)\n\n  try_compile(succeeds_when_it_should_fail\n              \"${CMAKE_CURRENT_BINARY_DIR}\"\n              \"${CMAKE_CURRENT_SOURCE_DIR}/${filename}\"\n              COMPILE_DEFINITIONS \"-DEIGEN_SHOULD_FAIL_TO_BUILD\")\n  if (succeeds_when_it_should_fail)\n    message(STATUS \"FAILED: ${testname} build succeeded when it should have failed\")\n  endif()\n\n  try_compile(succeeds_when_it_should_succeed\n              \"${CMAKE_CURRENT_BINARY_DIR}\"\n              \"${CMAKE_CURRENT_SOURCE_DIR}/${filename}\"\n              COMPILE_DEFINITIONS)\n  if (NOT succeeds_when_it_should_succeed)\n    message(STATUS \"FAILED: ${testname} build failed when it should have succeeded\")\n  endif()\n\n  if (succeeds_when_it_should_fail OR NOT succeeds_when_it_should_succeed)\n    math(EXPR EIGEN_FAILTEST_FAILURE_COUNT ${EIGEN_FAILTEST_FAILURE_COUNT}+1)\n  endif()\n\n  math(EXPR EIGEN_FAILTEST_COUNT ${EIGEN_FAILTEST_COUNT}+1)\n\n  set_property(GLOBAL PROPERTY EIGEN_FAILTEST_FAILURE_COUNT ${EIGEN_FAILTEST_FAILURE_COUNT})\n  set_property(GLOBAL PROPERTY EIGEN_FAILTEST_COUNT ${EIGEN_FAILTEST_COUNT})\nendmacro(ei_add_failtest)\n\n# print a summary of the different options\nmacro(ei_testing_print_summary)\n  message(STATUS \"************************************************************\")\n  message(STATUS \"***    Eigen's unit tests configuration summary          ***\")\n  message(STATUS \"************************************************************\")\n  message(STATUS \"\")\n  message(STATUS \"Build type:        ${CMAKE_BUILD_TYPE}\")\n  message(STATUS \"Build site:        ${SITE}\")\n  message(STATUS \"Build string:      ${BUILDNAME}\")\n  get_property(EIGEN_TESTING_SUMMARY GLOBAL PROPERTY EIGEN_TESTING_SUMMARY)\n  get_property(EIGEN_TESTED_BACKENDS GLOBAL PROPERTY EIGEN_TESTED_BACKENDS)\n  get_property(EIGEN_MISSING_BACKENDS GLOBAL PROPERTY EIGEN_MISSING_BACKENDS)\n  message(STATUS \"Enabled backends:  ${EIGEN_TESTED_BACKENDS}\")\n  message(STATUS \"Disabled backends: ${EIGEN_MISSING_BACKENDS}\")\n\n  if(EIGEN_DEFAULT_TO_ROW_MAJOR)\n    message(STATUS \"Default order:     Row-major\")\n  else()\n    message(STATUS \"Default order:     Column-major\")\n  endif()\n\n  if(EIGEN_TEST_NO_EXPLICIT_ALIGNMENT)\n    message(STATUS \"Explicit alignment (hence vectorization) disabled\")\n  elseif(EIGEN_TEST_NO_EXPLICIT_VECTORIZATION)\n    message(STATUS \"Explicit vectorization disabled (alignment kept enabled)\")\n  else()\n\n  message(STATUS \"Maximal matrix/vector size: ${EIGEN_TEST_MAX_SIZE}\")\n\n    if(EIGEN_TEST_SSE2)\n      message(STATUS \"SSE2:              ON\")\n    else()\n      message(STATUS \"SSE2:              Using architecture defaults\")\n    endif()\n\n    if(EIGEN_TEST_SSE3)\n      message(STATUS \"SSE3:              ON\")\n    else()\n      message(STATUS \"SSE3:              Using architecture defaults\")\n    endif()\n\n    if(EIGEN_TEST_SSSE3)\n      message(STATUS \"SSSE3:             ON\")\n    else()\n      message(STATUS \"SSSE3:             Using architecture defaults\")\n    endif()\n\n    if(EIGEN_TEST_SSE4_1)\n      message(STATUS \"SSE4.1:            ON\")\n    else()\n      message(STATUS \"SSE4.1:            Using architecture defaults\")\n    endif()\n\n    if(EIGEN_TEST_SSE4_2)\n      message(STATUS \"SSE4.2:            ON\")\n    else()\n      message(STATUS \"SSE4.2:            Using architecture defaults\")\n    endif()\n\n    if(EIGEN_TEST_AVX)\n      message(STATUS \"AVX:               ON\")\n    else()\n      message(STATUS \"AVX:               Using architecture defaults\")\n    endif()\n\n    if(EIGEN_TEST_FMA)\n      message(STATUS \"FMA:               ON\")\n    else()\n      message(STATUS \"FMA:               Using architecture defaults\")\n    endif()\n\n    if(EIGEN_TEST_AVX512)\n      message(STATUS \"AVX512:            ON\")\n    else()\n      message(STATUS \"AVX512:            Using architecture defaults\")\n    endif()\n\n    if(EIGEN_TEST_ALTIVEC)\n      message(STATUS \"Altivec:           ON\")\n    else()\n      message(STATUS \"Altivec:           Using architecture defaults\")\n    endif()\n\n    if(EIGEN_TEST_VSX)\n      message(STATUS \"VSX:               ON\")\n    else()\n      message(STATUS \"VSX:               Using architecture defaults\")\n    endif()\n\n    if(EIGEN_TEST_NEON)\n      message(STATUS \"ARM NEON:          ON\")\n    else()\n      message(STATUS \"ARM NEON:          Using architecture defaults\")\n    endif()\n\n    if(EIGEN_TEST_NEON64)\n      message(STATUS \"ARMv8 NEON:        ON\")\n    else()\n      message(STATUS \"ARMv8 NEON:        Using architecture defaults\")\n    endif()\n\n    if(EIGEN_TEST_ZVECTOR)\n      message(STATUS \"S390X ZVECTOR:     ON\")\n    else()\n      message(STATUS \"S390X ZVECTOR:     Using architecture defaults\")\n    endif()\n\n    if(EIGEN_TEST_CXX11)\n      message(STATUS \"C++11:             ON\")\n    else()\n      message(STATUS \"C++11:             OFF\")\n    endif()\n\n    if(EIGEN_TEST_SYCL)\n      message(STATUS \"SYCL:              ON\")\n    else()\n      message(STATUS \"SYCL:              OFF\")\n    endif()\n    if(EIGEN_TEST_CUDA)\n      if(EIGEN_TEST_CUDA_CLANG)\n        message(STATUS \"CUDA:              ON (using clang)\")\n      else()\n        message(STATUS \"CUDA:              ON (using nvcc)\")\n      endif()\n    else()\n      message(STATUS \"CUDA:              OFF\")\n    endif()\n\n  endif() # vectorization / alignment options\n\n  message(STATUS \"\\n${EIGEN_TESTING_SUMMARY}\")\n\n  message(STATUS \"************************************************************\")\nendmacro(ei_testing_print_summary)\n\nmacro(ei_init_testing)\n  define_property(GLOBAL PROPERTY EIGEN_CURRENT_SUBPROJECT BRIEF_DOCS \" \" FULL_DOCS \" \")\n  define_property(GLOBAL PROPERTY EIGEN_TESTED_BACKENDS BRIEF_DOCS \" \" FULL_DOCS \" \")\n  define_property(GLOBAL PROPERTY EIGEN_MISSING_BACKENDS BRIEF_DOCS \" \" FULL_DOCS \" \")\n  define_property(GLOBAL PROPERTY EIGEN_TESTING_SUMMARY BRIEF_DOCS \" \" FULL_DOCS \" \")\n  define_property(GLOBAL PROPERTY EIGEN_TESTS_LIST BRIEF_DOCS \" \" FULL_DOCS \" \")\n\n  set_property(GLOBAL PROPERTY EIGEN_TESTED_BACKENDS \"\")\n  set_property(GLOBAL PROPERTY EIGEN_MISSING_BACKENDS \"\")\n  set_property(GLOBAL PROPERTY EIGEN_TESTING_SUMMARY \"\")\n  set_property(GLOBAL PROPERTY EIGEN_TESTS_LIST \"\")\n\n  define_property(GLOBAL PROPERTY EIGEN_FAILTEST_FAILURE_COUNT BRIEF_DOCS \" \" FULL_DOCS \" \")\n  define_property(GLOBAL PROPERTY EIGEN_FAILTEST_COUNT BRIEF_DOCS \" \" FULL_DOCS \" \")\n\n  set_property(GLOBAL PROPERTY EIGEN_FAILTEST_FAILURE_COUNT \"0\")\n  set_property(GLOBAL PROPERTY EIGEN_FAILTEST_COUNT \"0\")\n\n  # uncomment anytime you change the ei_get_compilerver_from_cxx_version_string macro\n  # ei_test_get_compilerver_from_cxx_version_string()\nendmacro(ei_init_testing)\n\nmacro(ei_set_sitename)\n  # if the sitename is not yet set, try to set it\n  if(NOT ${SITE} OR ${SITE} STREQUAL \"\")\n    set(eigen_computername $ENV{COMPUTERNAME})\n    set(eigen_hostname $ENV{HOSTNAME})\n    if(eigen_hostname)\n      set(SITE ${eigen_hostname})\n    elseif(eigen_computername)\n      set(SITE ${eigen_computername})\n    endif()\n  endif()\n  # in case it is already set, enforce lower case\n  if(SITE)\n    string(TOLOWER ${SITE} SITE)\n  endif()\nendmacro(ei_set_sitename)\n\nmacro(ei_get_compilerver VAR)\n    if(MSVC)\n      # on windows system, we use a modified CMake script\n      include(EigenDetermineVSServicePack)\n      EigenDetermineVSServicePack( my_service_pack )\n\n      if( my_service_pack )\n        set(${VAR} ${my_service_pack})\n      else()\n        set(${VAR} \"na\")\n      endif()\n    else()\n    # on all other system we rely on ${CMAKE_CXX_COMPILER}\n    # supporting a \"--version\" or \"/version\" flag\n\n    if(WIN32 AND ${CMAKE_CXX_COMPILER_ID} EQUAL \"Intel\")\n      set(EIGEN_CXX_FLAG_VERSION \"/version\")\n    else()\n      set(EIGEN_CXX_FLAG_VERSION \"--version\")\n    endif()\n\n    execute_process(COMMAND ${CMAKE_CXX_COMPILER} ${EIGEN_CXX_FLAG_VERSION}\n                    OUTPUT_VARIABLE eigen_cxx_compiler_version_string OUTPUT_STRIP_TRAILING_WHITESPACE)\n    string(REGEX REPLACE \"[\\n\\r].*\"  \"\"  eigen_cxx_compiler_version_string  ${eigen_cxx_compiler_version_string})\n\n    ei_get_compilerver_from_cxx_version_string(\"${eigen_cxx_compiler_version_string}\" CNAME CVER)\n    set(${VAR} \"${CNAME}-${CVER}\")\n\n  endif()\nendmacro(ei_get_compilerver)\n\n# Extract compiler name and version from a raw version string\n# WARNING: if you edit thid macro, then please test it by  uncommenting\n# the testing macro call in ei_init_testing() of the EigenTesting.cmake file.\n# See also the ei_test_get_compilerver_from_cxx_version_string macro at the end of the file\nmacro(ei_get_compilerver_from_cxx_version_string VERSTRING CNAME CVER)\n  # extract possible compiler names\n  string(REGEX MATCH \"g\\\\+\\\\+\"      ei_has_gpp    ${VERSTRING})\n  string(REGEX MATCH \"llvm|LLVM\"    ei_has_llvm   ${VERSTRING})\n  string(REGEX MATCH \"gcc|GCC\"      ei_has_gcc    ${VERSTRING})\n  string(REGEX MATCH \"icpc|ICC\"     ei_has_icpc   ${VERSTRING})\n  string(REGEX MATCH \"clang|CLANG\"  ei_has_clang  ${VERSTRING})\n\n  # combine them\n  if((ei_has_llvm) AND (ei_has_gpp OR ei_has_gcc))\n    set(${CNAME} \"llvm-g++\")\n  elseif((ei_has_llvm) AND (ei_has_clang))\n    set(${CNAME} \"llvm-clang++\")\n  elseif(ei_has_clang)\n    set(${CNAME} \"clang++\")\n  elseif(ei_has_icpc)\n    set(${CNAME} \"icpc\")\n  elseif(ei_has_gpp OR ei_has_gcc)\n    set(${CNAME} \"g++\")\n  else()\n    set(${CNAME} \"_\")\n  endif()\n\n  # extract possible version numbers\n  # first try to extract 3 isolated numbers:\n  string(REGEX MATCH \" [0-9]+\\\\.[0-9]+\\\\.[0-9]+\" eicver ${VERSTRING})\n  if(NOT eicver)\n    # try to extract 2 isolated ones:\n    string(REGEX MATCH \" [0-9]+\\\\.[0-9]+\" eicver ${VERSTRING})\n    if(NOT eicver)\n      # try to extract 3:\n      string(REGEX MATCH \"[^0-9][0-9]+\\\\.[0-9]+\\\\.[0-9]+\" eicver ${VERSTRING})\n      if(NOT eicver)\n        # try to extract 2:\n        string(REGEX MATCH \"[^0-9][0-9]+\\\\.[0-9]+\" eicver ${VERSTRING})\n      else()\n        set(eicver \" _\")\n      endif()\n    endif()\n  endif()\n\n  string(REGEX REPLACE \".(.*)\" \"\\\\1\" ${CVER} ${eicver})\n\nendmacro(ei_get_compilerver_from_cxx_version_string)\n\nmacro(ei_get_cxxflags VAR)\n  set(${VAR} \"\")\n  ei_is_64bit_env(IS_64BIT_ENV)\n  if(EIGEN_TEST_NEON)\n    set(${VAR} NEON)\n  elseif(EIGEN_TEST_NEON64)\n    set(${VAR} NEON)\n  elseif(EIGEN_TEST_ZVECTOR)\n    set(${VAR} ZVECTOR)\n  elseif(EIGEN_TEST_VSX)\n    set(${VAR} VSX)\n  elseif(EIGEN_TEST_ALTIVEC)\n    set(${VAR} ALVEC)\n  elseif(EIGEN_TEST_FMA)\n    set(${VAR} FMA)\n  elseif(EIGEN_TEST_AVX)\n    set(${VAR} AVX)\n  elseif(EIGEN_TEST_SSE4_2)\n    set(${VAR} SSE42)\n  elseif(EIGEN_TEST_SSE4_1)\n    set(${VAR} SSE41)\n  elseif(EIGEN_TEST_SSSE3)\n    set(${VAR} SSSE3)\n  elseif(EIGEN_TEST_SSE3)\n    set(${VAR} SSE3)\n  elseif(EIGEN_TEST_SSE2 OR IS_64BIT_ENV)\n    set(${VAR} SSE2)\n  endif()\n\n  if(EIGEN_TEST_OPENMP)\n    if (${VAR} STREQUAL \"\")\n      set(${VAR} OMP)\n    else()\n      set(${VAR} ${${VAR}}-OMP)\n    endif()\n  endif()\n\n  if(EIGEN_DEFAULT_TO_ROW_MAJOR)\n    if (${VAR} STREQUAL \"\")\n      set(${VAR} ROW)\n    else()\n      set(${VAR} ${${VAR}}-ROWMAJ)\n    endif()\n  endif()\nendmacro(ei_get_cxxflags)\n\nmacro(ei_set_build_string)\n  ei_get_compilerver(LOCAL_COMPILER_VERSION)\n  ei_get_cxxflags(LOCAL_COMPILER_FLAGS)\n\n  include(EigenDetermineOSVersion)\n  DetermineOSVersion(OS_VERSION)\n\n  set(TMP_BUILD_STRING ${OS_VERSION}-${LOCAL_COMPILER_VERSION})\n\n  if (NOT ${LOCAL_COMPILER_FLAGS} STREQUAL  \"\")\n    set(TMP_BUILD_STRING ${TMP_BUILD_STRING}-${LOCAL_COMPILER_FLAGS})\n  endif()\n\n  ei_is_64bit_env(IS_64BIT_ENV)\n  if(NOT IS_64BIT_ENV)\n    set(TMP_BUILD_STRING ${TMP_BUILD_STRING}-32bit)\n  else()\n    set(TMP_BUILD_STRING ${TMP_BUILD_STRING}-64bit)\n  endif()\n\n  if(EIGEN_TEST_CXX11)\n    set(TMP_BUILD_STRING ${TMP_BUILD_STRING}-cxx11)\n  endif()\n\n  if(EIGEN_BUILD_STRING_SUFFIX)\n    set(TMP_BUILD_STRING ${TMP_BUILD_STRING}-${EIGEN_BUILD_STRING_SUFFIX})\n  endif()\n\n  string(TOLOWER ${TMP_BUILD_STRING} BUILDNAME)\nendmacro(ei_set_build_string)\n\nmacro(ei_is_64bit_env VAR)\n  if(CMAKE_SIZEOF_VOID_P EQUAL 8)\n    set(${VAR} 1)\n  elseif(CMAKE_SIZEOF_VOID_P EQUAL 4)\n    set(${VAR} 0)\n  else()\n    message(WARNING \"Unsupported pointer size. Please contact the authors.\")\n  endif()\nendmacro(ei_is_64bit_env)\n\n\n# helper macro for testing ei_get_compilerver_from_cxx_version_string\n# STR: raw version string\n# REFNAME: expected compiler name\n# REFVER: expected compiler version\nmacro(ei_test1_get_compilerver_from_cxx_version_string STR REFNAME REFVER)\n  ei_get_compilerver_from_cxx_version_string(${STR} CNAME CVER)\n  if((NOT ${REFNAME} STREQUAL ${CNAME}) OR (NOT ${REFVER} STREQUAL ${CVER}))\n    message(\"STATUS ei_get_compilerver_from_cxx_version_string error:\")\n    message(\"Expected \\\"${REFNAME}-${REFVER}\\\", got \\\"${CNAME}-${CVER}\\\"\")\n  endif()\nendmacro(ei_test1_get_compilerver_from_cxx_version_string)\n\n# macro for testing ei_get_compilerver_from_cxx_version_string\n# feel free to add more version strings\nmacro(ei_test_get_compilerver_from_cxx_version_string)\n  ei_test1_get_compilerver_from_cxx_version_string(\"g++ (SUSE Linux) 4.5.3 20110428 [gcc-4_5-branch revision 173117]\" \"g++\" \"4.5.3\")\n  ei_test1_get_compilerver_from_cxx_version_string(\"c++ (GCC) 4.5.1 20100924 (Red Hat 4.5.1-4)\" \"g++\" \"4.5.1\")\n  ei_test1_get_compilerver_from_cxx_version_string(\"icpc (ICC) 11.0 20081105\" \"icpc\" \"11.0\")\n  ei_test1_get_compilerver_from_cxx_version_string(\"g++-3.4 (GCC) 3.4.6\" \"g++\" \"3.4.6\")\n  ei_test1_get_compilerver_from_cxx_version_string(\"SUSE Linux clang version 3.0 (branches/release_30 145598) (based on LLVM 3.0)\" \"llvm-clang++\" \"3.0\")\n  ei_test1_get_compilerver_from_cxx_version_string(\"icpc (ICC) 12.0.5 20110719\" \"icpc\" \"12.0.5\")\n  ei_test1_get_compilerver_from_cxx_version_string(\"Apple clang version 2.1 (tags/Apple/clang-163.7.1) (based on LLVM 3.0svn)\" \"llvm-clang++\" \"2.1\")\n  ei_test1_get_compilerver_from_cxx_version_string(\"i686-apple-darwin11-llvm-g++-4.2 (GCC) 4.2.1 (Based on Apple Inc. build 5658) (LLVM build 2335.15.00)\" \"llvm-g++\" \"4.2.1\")\n  ei_test1_get_compilerver_from_cxx_version_string(\"g++-mp-4.4 (GCC) 4.4.6\" \"g++\" \"4.4.6\")\n  ei_test1_get_compilerver_from_cxx_version_string(\"g++-mp-4.4 (GCC) 2011\" \"g++\" \"4.4\")\nendmacro(ei_test_get_compilerver_from_cxx_version_string)\n"
  },
  {
    "path": "include/eigen3/cmake/EigenUninstall.cmake",
    "content": "################ CMake Uninstall Template #######################\n# CMake Template file for uninstallation of files\n# mentioned in 'install_manifest.txt'\n#\n# Used by uinstall target\n#################################################################\n\nset(MANIFEST \"${CMAKE_CURRENT_BINARY_DIR}/install_manifest.txt\")\n\nif(EXISTS ${MANIFEST})\n  message(STATUS \"============== Uninstalling Eigen  ===================\")\n\n  file(STRINGS ${MANIFEST} files)\n  foreach(file ${files})\n    if(EXISTS ${file})\n      message(STATUS \"Removing file: '${file}'\")\n\n      execute_process(\n        COMMAND ${CMAKE_COMMAND} -E remove ${file}\n        OUTPUT_VARIABLE rm_out\n        RESULT_VARIABLE rm_retval\n        )\n\n      if(NOT \"${rm_retval}\" STREQUAL 0)\n        message(FATAL_ERROR \"Failed to remove file: '${file}'.\")\n      endif()\n    else()\n      message(STATUS \"File '${file}' does not exist.\")\n    endif()\n  endforeach(file)\n\n  message(STATUS \"========== Finished Uninstalling Eigen  ==============\")\nelse()\n  message(STATUS \"Cannot find install manifest: '${MANIFEST}'\")\n  message(STATUS \"Probably make install has not been performed\")\n  message(STATUS \"   or install_manifest.txt has been deleted.\")\nendif()\n\n\n\n"
  },
  {
    "path": "include/eigen3/cmake/FindAdolc.cmake",
    "content": "\nif (ADOLC_INCLUDES AND ADOLC_LIBRARIES)\n  set(ADOLC_FIND_QUIETLY TRUE)\nendif (ADOLC_INCLUDES AND ADOLC_LIBRARIES)\n\nfind_path(ADOLC_INCLUDES\n  NAMES\n  adolc/adtl.h\n  PATHS\n  $ENV{ADOLCDIR}\n  ${INCLUDE_INSTALL_DIR}\n)\n\nfind_library(ADOLC_LIBRARIES adolc PATHS $ENV{ADOLCDIR} ${LIB_INSTALL_DIR})\n\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(ADOLC DEFAULT_MSG\n                                  ADOLC_INCLUDES ADOLC_LIBRARIES)\n\nmark_as_advanced(ADOLC_INCLUDES ADOLC_LIBRARIES)\n"
  },
  {
    "path": "include/eigen3/cmake/FindBLAS.cmake",
    "content": "###\n#\n# @copyright (c) 2009-2014 The University of Tennessee and The University\n#                          of Tennessee Research Foundation.\n#                          All rights reserved.\n# @copyright (c) 2012-2016 Inria. All rights reserved.\n# @copyright (c) 2012-2014 Bordeaux INP, CNRS (LaBRI UMR 5800), Inria, Univ. Bordeaux. All rights reserved.\n#\n###\n#\n# - Find BLAS library\n# This module finds an installed fortran library that implements the BLAS\n# linear-algebra interface (see http://www.netlib.org/blas/).\n# The list of libraries searched for is taken\n# from the autoconf macro file, acx_blas.m4 (distributed at\n# http://ac-archive.sourceforge.net/ac-archive/acx_blas.html).\n#\n# This module sets the following variables:\n#  BLAS_FOUND - set to true if a library implementing the BLAS interface\n#    is found\n#  BLAS_LINKER_FLAGS - uncached list of required linker flags (excluding -l\n#    and -L).\n#  BLAS_COMPILER_FLAGS - uncached list of required compiler flags (including -I for mkl headers).\n#  BLAS_LIBRARIES - uncached list of libraries (using full path name) to\n#    link against to use BLAS\n#  BLAS95_LIBRARIES - uncached list of libraries (using full path name)\n#    to link against to use BLAS95 interface\n#  BLAS95_FOUND - set to true if a library implementing the BLAS f95 interface\n#    is found\n#  BLA_STATIC  if set on this determines what kind of linkage we do (static)\n#  BLA_VENDOR  if set checks only the specified vendor, if not set checks\n#     all the possibilities\n#  BLAS_VENDOR_FOUND stores the BLAS vendor found \n#  BLA_F95     if set on tries to find the f95 interfaces for BLAS/LAPACK\n# The user can give specific paths where to find the libraries adding cmake\n# options at configure (ex: cmake path/to/project -DBLAS_DIR=path/to/blas):\n#  BLAS_DIR            - Where to find the base directory of blas\n#  BLAS_INCDIR         - Where to find the header files\n#  BLAS_LIBDIR         - Where to find the library files\n# The module can also look for the following environment variables if paths\n# are not given as cmake variable: BLAS_DIR, BLAS_INCDIR, BLAS_LIBDIR\n# For MKL case and if no paths are given as hints, we will try to use the MKLROOT\n# environment variable\n#  BLAS_VERBOSE Print some additional information during BLAS libraries detection\n##########\n### List of vendors (BLA_VENDOR) valid in this module\n########## List of vendors (BLA_VENDOR) valid in this module\n##  Open (for OpenBlas), Eigen (for EigenBlas), Goto, ATLAS PhiPACK,\n##  CXML, DXML, SunPerf, SCSL, SGIMATH, IBMESSL, IBMESSLMT\n##  Intel10_32 (intel mkl v10 32 bit), Intel10_64lp (intel mkl v10 64 bit,lp thread model, lp64 model),\n##  Intel10_64lp_seq (intel mkl v10 64 bit,sequential code, lp64 model),\n##  Intel( older versions of mkl 32 and 64 bit),\n##  ACML, ACML_MP, ACML_GPU, Apple, NAS, Generic\n# C/CXX should be enabled to use Intel mkl\n###\n# We handle different modes to find the dependency\n#\n# - Detection if already installed on the system\n#   - BLAS libraries can be detected from different ways\n#     Here is the order of precedence:\n#     1) we look in cmake variable BLAS_LIBDIR or BLAS_DIR (we guess the libdirs) if defined\n#     2) we look in environment variable BLAS_LIBDIR or BLAS_DIR (we guess the libdirs) if defined\n#     3) we look in common environnment variables depending on the system (INCLUDE, C_INCLUDE_PATH, CPATH - LIB, DYLD_LIBRARY_PATH, LD_LIBRARY_PATH)\n#     4) we look in common system paths depending on the system, see for example paths contained in the following cmake variables:\n#       - CMAKE_PLATFORM_IMPLICIT_INCLUDE_DIRECTORIES, CMAKE_PLATFORM_IMPLICIT_LINK_DIRECTORIES\n#       - CMAKE_C_IMPLICIT_INCLUDE_DIRECTORIES, CMAKE_C_IMPLICIT_LINK_DIRECTORIES\n#\n\n#=============================================================================\n# Copyright 2007-2009 Kitware, Inc.\n#\n# Distributed under the OSI-approved BSD License (the \"License\");\n# see accompanying file Copyright.txt for details.\n#\n# This software is distributed WITHOUT ANY WARRANTY; without even the\n# implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.\n# See the License for more information.\n#=============================================================================\n# (To distribute this file outside of CMake, substitute the full\n#  License text for the above reference.)\n\n## Some macros to print status when search for headers and libs\n# This macro informs why the _lib_to_find file has not been found\nmacro(Print_Find_Library_Blas_Status _libname _lib_to_find)\n\n  # save _libname upper/lower case\n  string(TOUPPER ${_libname} LIBNAME)\n  string(TOLOWER ${_libname} libname)\n\n  # print status\n  #message(\" \")\n  if(${LIBNAME}_LIBDIR)\n    message(\"${Yellow}${LIBNAME}_LIBDIR is defined but ${_lib_to_find}\"\n      \"has not been found in ${ARGN}${ColourReset}\")\n  else()\n    if(${LIBNAME}_DIR)\n      message(\"${Yellow}${LIBNAME}_DIR is defined but ${_lib_to_find}\"\n\t\"has not been found in ${ARGN}${ColourReset}\")\n    else()\n      message(\"${Yellow}${_lib_to_find} not found.\"\n\t\"Nor ${LIBNAME}_DIR neither ${LIBNAME}_LIBDIR\"\n\t\"are defined so that we look for ${_lib_to_find} in\"\n\t\"system paths (Linux: LD_LIBRARY_PATH, Windows: LIB,\"\n\t\"Mac: DYLD_LIBRARY_PATH,\"\n\t\"CMAKE_PLATFORM_IMPLICIT_LINK_DIRECTORIES,\"\n\t\"CMAKE_C_IMPLICIT_LINK_DIRECTORIES)${ColourReset}\")\n      if(_lib_env)\n\tmessage(\"${Yellow}${_lib_to_find} has not been found in\"\n\t  \"${_lib_env}${ColourReset}\")\n      endif()\n    endif()\n  endif()\n  message(\"${BoldYellow}Please indicate where to find ${_lib_to_find}. You have three options:\\n\"\n    \"- Option 1: Provide the Installation directory of BLAS library with cmake option: -D${LIBNAME}_DIR=your/path/to/${libname}/\\n\"\n    \"- Option 2: Provide the directory where to find the library with cmake option: -D${LIBNAME}_LIBDIR=your/path/to/${libname}/lib/\\n\"\n    \"- Option 3: Update your environment variable (Linux: LD_LIBRARY_PATH, Windows: LIB, Mac: DYLD_LIBRARY_PATH)\\n\"\n    \"- Option 4: If your library provides a PkgConfig file, make sure pkg-config finds your library${ColourReset}\")\n\nendmacro()\n\n# This macro informs why the _lib_to_find file has not been found\nmacro(Print_Find_Library_Blas_CheckFunc_Status _name)\n\n  # save _libname upper/lower case\n  string(TOUPPER ${_name} FUNCNAME)\n  string(TOLOWER ${_name} funcname)\n\n  # print status\n  #message(\" \")\n  message(\"${Red}Libs have been found but check of symbol ${_name} failed \"\n    \"with following libraries ${ARGN}${ColourReset}\")\n  message(\"${BoldRed}Please open your error file CMakeFiles/CMakeError.log\"\n    \"to figure out why it fails${ColourReset}\")\n  #message(\" \")\n\nendmacro()\n\nif (NOT BLAS_FOUND)\n  set(BLAS_DIR \"\" CACHE PATH \"Installation directory of BLAS library\")\n  if (NOT BLAS_FIND_QUIETLY)\n    message(STATUS \"A cache variable, namely BLAS_DIR, has been set to specify the install directory of BLAS\")\n  endif()\nendif()\n\noption(BLAS_VERBOSE \"Print some additional information during BLAS libraries detection\" OFF)\nmark_as_advanced(BLAS_VERBOSE)\n\ninclude(CheckFunctionExists)\ninclude(CheckFortranFunctionExists)\n\nset(_blas_ORIG_CMAKE_FIND_LIBRARY_SUFFIXES ${CMAKE_FIND_LIBRARY_SUFFIXES})\n\n# Check the language being used\nget_property( _LANGUAGES_ GLOBAL PROPERTY ENABLED_LANGUAGES )\nif( _LANGUAGES_ MATCHES Fortran AND CMAKE_Fortran_COMPILER)\n  set( _CHECK_FORTRAN TRUE )\nelseif( (_LANGUAGES_ MATCHES C) OR (_LANGUAGES_ MATCHES CXX) )\n  set( _CHECK_FORTRAN FALSE )\nelse()\n  if(BLAS_FIND_REQUIRED)\n    message(FATAL_ERROR \"FindBLAS requires Fortran, C, or C++ to be enabled.\")\n  else()\n    message(STATUS \"Looking for BLAS... - NOT found (Unsupported languages)\")\n    return()\n  endif()\nendif()\n\nmacro(Check_Fortran_Libraries LIBRARIES _prefix _name _flags _list _thread)\n  # This macro checks for the existence of the combination of fortran libraries\n  # given by _list.  If the combination is found, this macro checks (using the\n  # Check_Fortran_Function_Exists macro) whether can link against that library\n  # combination using the name of a routine given by _name using the linker\n  # flags given by _flags.  If the combination of libraries is found and passes\n  # the link test, LIBRARIES is set to the list of complete library paths that\n  # have been found.  Otherwise, LIBRARIES is set to FALSE.\n\n  # N.B. _prefix is the prefix applied to the names of all cached variables that\n  # are generated internally and marked advanced by this macro.\n\n  set(_libdir ${ARGN})\n\n  set(_libraries_work TRUE)\n  set(${LIBRARIES})\n  set(_combined_name)\n  set(ENV_MKLROOT \"$ENV{MKLROOT}\")\n  set(ENV_BLAS_DIR \"$ENV{BLAS_DIR}\")\n  set(ENV_BLAS_LIBDIR \"$ENV{BLAS_LIBDIR}\")\n  if (NOT _libdir)\n    if (BLAS_LIBDIR)\n      list(APPEND _libdir \"${BLAS_LIBDIR}\")\n    elseif (BLAS_DIR)\n      list(APPEND _libdir \"${BLAS_DIR}\")\n      list(APPEND _libdir \"${BLAS_DIR}/lib\")\n      if(\"${CMAKE_SIZEOF_VOID_P}\" EQUAL \"8\")\n\tlist(APPEND _libdir \"${BLAS_DIR}/lib64\")\n\tlist(APPEND _libdir \"${BLAS_DIR}/lib/intel64\")\n      else()\n\tlist(APPEND _libdir \"${BLAS_DIR}/lib32\")\n\tlist(APPEND _libdir \"${BLAS_DIR}/lib/ia32\")\n      endif()\n    elseif(ENV_BLAS_LIBDIR)\n      list(APPEND _libdir \"${ENV_BLAS_LIBDIR}\")\n    elseif(ENV_BLAS_DIR)\n      list(APPEND _libdir \"${ENV_BLAS_DIR}\")\n      list(APPEND _libdir \"${ENV_BLAS_DIR}/lib\")\n      if(\"${CMAKE_SIZEOF_VOID_P}\" EQUAL \"8\")\n\tlist(APPEND _libdir \"${ENV_BLAS_DIR}/lib64\")\n\tlist(APPEND _libdir \"${ENV_BLAS_DIR}/lib/intel64\")\n      else()\n\tlist(APPEND _libdir \"${ENV_BLAS_DIR}/lib32\")\n\tlist(APPEND _libdir \"${ENV_BLAS_DIR}/lib/ia32\")\n      endif()\n    else()\n      if (ENV_MKLROOT)\n\tlist(APPEND _libdir \"${ENV_MKLROOT}/lib\")\n\tif(\"${CMAKE_SIZEOF_VOID_P}\" EQUAL \"8\")\n\t  list(APPEND _libdir \"${ENV_MKLROOT}/lib64\")\n\t  list(APPEND _libdir \"${ENV_MKLROOT}/lib/intel64\")\n\telse()\n\t  list(APPEND _libdir \"${ENV_MKLROOT}/lib32\")\n\t  list(APPEND _libdir \"${ENV_MKLROOT}/lib/ia32\")\n\tendif()\n      endif()\n      if (WIN32)\n\tstring(REPLACE \":\" \";\" _libdir2 \"$ENV{LIB}\")\n      elseif (APPLE)\n\tstring(REPLACE \":\" \";\" _libdir2 \"$ENV{DYLD_LIBRARY_PATH}\")\n      else ()\n\tstring(REPLACE \":\" \";\" _libdir2 \"$ENV{LD_LIBRARY_PATH}\")\n      endif ()\n      list(APPEND _libdir \"${_libdir2}\")\n      list(APPEND _libdir \"${CMAKE_PLATFORM_IMPLICIT_LINK_DIRECTORIES}\")\n      list(APPEND _libdir \"${CMAKE_C_IMPLICIT_LINK_DIRECTORIES}\")\n    endif()\n  endif ()\n\n  if (BLAS_VERBOSE)\n    message(\"${Cyan}Try to find BLAS libraries: ${_list}\")\n  endif ()\n\n  foreach(_library ${_list})\n    set(_combined_name ${_combined_name}_${_library})\n\n    if(_libraries_work)\n      if (BLA_STATIC)\n\tif (WIN32)\n\t  set(CMAKE_FIND_LIBRARY_SUFFIXES .lib ${CMAKE_FIND_LIBRARY_SUFFIXES})\n\tendif ()\n\tif (APPLE)\n\t  set(CMAKE_FIND_LIBRARY_SUFFIXES .lib ${CMAKE_FIND_LIBRARY_SUFFIXES})\n\telse ()\n\t  set(CMAKE_FIND_LIBRARY_SUFFIXES .a ${CMAKE_FIND_LIBRARY_SUFFIXES})\n\tendif ()\n      else ()\n\tif (CMAKE_SYSTEM_NAME STREQUAL \"Linux\")\n\t  # for ubuntu's libblas3gf and liblapack3gf packages\n\t  set(CMAKE_FIND_LIBRARY_SUFFIXES ${CMAKE_FIND_LIBRARY_SUFFIXES} .so.3gf)\n\tendif ()\n      endif ()\n      find_library(${_prefix}_${_library}_LIBRARY\n\tNAMES ${_library}\n\tHINTS ${_libdir}\n\tNO_DEFAULT_PATH\n\t)\n      mark_as_advanced(${_prefix}_${_library}_LIBRARY)\n      # Print status if not found\n      # -------------------------\n      if (NOT ${_prefix}_${_library}_LIBRARY AND NOT BLAS_FIND_QUIETLY AND BLAS_VERBOSE)\n\tPrint_Find_Library_Blas_Status(blas ${_library} ${_libdir})\n      endif ()\n      set(${LIBRARIES} ${${LIBRARIES}} ${${_prefix}_${_library}_LIBRARY})\n      set(_libraries_work ${${_prefix}_${_library}_LIBRARY})\n    endif(_libraries_work)\n  endforeach(_library ${_list})\n\n  if(_libraries_work)\n    # Test this combination of libraries.\n    if (CMAKE_SYSTEM_NAME STREQUAL \"Linux\" AND BLA_STATIC)\n      list(INSERT ${LIBRARIES} 0 \"-Wl,--start-group\")\n      list(APPEND ${LIBRARIES} \"-Wl,--end-group\")\n    endif()\n    set(CMAKE_REQUIRED_LIBRARIES \"${_flags};${${LIBRARIES}};${_thread}\")\n    set(CMAKE_REQUIRED_FLAGS \"${BLAS_COMPILER_FLAGS}\")\n    if (BLAS_VERBOSE)\n      message(\"${Cyan}BLAS libs found for BLA_VENDOR ${BLA_VENDOR}.\"\n\t\"Try to compile symbol ${_name} with following libraries:\"\n\t\"${CMAKE_REQUIRED_LIBRARIES}\")\n    endif ()\n    if(NOT BLAS_FOUND)\n      unset(${_prefix}${_combined_name}_WORKS CACHE)\n    endif()\n    if (_CHECK_FORTRAN)\n      if (CMAKE_Fortran_COMPILER_ID STREQUAL \"GNU\")\n\tstring(REPLACE \"mkl_intel_lp64\" \"mkl_gf_lp64\" CMAKE_REQUIRED_LIBRARIES \"${CMAKE_REQUIRED_LIBRARIES}\")\n\tstring(REPLACE \"mkl_intel_ilp64\" \"mkl_gf_ilp64\" CMAKE_REQUIRED_LIBRARIES \"${CMAKE_REQUIRED_LIBRARIES}\")\n      endif()\n      check_fortran_function_exists(\"${_name}\" ${_prefix}${_combined_name}_WORKS)\n    else()\n      check_function_exists(\"${_name}_\" ${_prefix}${_combined_name}_WORKS)\n    endif()\n    mark_as_advanced(${_prefix}${_combined_name}_WORKS)\n    set(_libraries_work ${${_prefix}${_combined_name}_WORKS})\n    # Print status if not found\n    # -------------------------\n    if (NOT _libraries_work AND NOT BLAS_FIND_QUIETLY AND BLAS_VERBOSE)\n      Print_Find_Library_Blas_CheckFunc_Status(${_name} ${CMAKE_REQUIRED_LIBRARIES})\n    endif ()\n    set(CMAKE_REQUIRED_LIBRARIES)\n  endif()\n\n  if(_libraries_work)\n    set(${LIBRARIES} ${${LIBRARIES}} ${_thread})\n  else(_libraries_work)\n    set(${LIBRARIES} FALSE)\n  endif(_libraries_work)\n\nendmacro(Check_Fortran_Libraries)\n\n\nset(BLAS_LINKER_FLAGS)\nset(BLAS_LIBRARIES)\nset(BLAS95_LIBRARIES)\nif ($ENV{BLA_VENDOR} MATCHES \".+\")\n  set(BLA_VENDOR $ENV{BLA_VENDOR})\nelse ()\n  if(NOT BLA_VENDOR)\n    set(BLA_VENDOR \"All\")\n  endif()\nendif ()\n\n#BLAS in intel mkl 10 library? (em64t 64bit)\nif (BLA_VENDOR MATCHES \"Intel*\" OR BLA_VENDOR STREQUAL \"All\")\n\n  if(NOT BLAS_LIBRARIES OR BLA_VENDOR MATCHES \"Intel*\")\n    # Looking for include\n    # -------------------\n\n    # Add system include paths to search include\n    # ------------------------------------------\n    unset(_inc_env)\n    set(ENV_MKLROOT \"$ENV{MKLROOT}\")\n    set(ENV_BLAS_DIR \"$ENV{BLAS_DIR}\")\n    set(ENV_BLAS_INCDIR \"$ENV{BLAS_INCDIR}\")\n    if(ENV_BLAS_INCDIR)\n      list(APPEND _inc_env \"${ENV_BLAS_INCDIR}\")\n    elseif(ENV_BLAS_DIR)\n      list(APPEND _inc_env \"${ENV_BLAS_DIR}\")\n      list(APPEND _inc_env \"${ENV_BLAS_DIR}/include\")\n    else()\n      if (ENV_MKLROOT)\n\tlist(APPEND _inc_env \"${ENV_MKLROOT}/include\")\n      endif()\n      # system variables\n      if(WIN32)\n\tstring(REPLACE \":\" \";\" _path_env \"$ENV{INCLUDE}\")\n\tlist(APPEND _inc_env \"${_path_env}\")\n      else()\n\tstring(REPLACE \":\" \";\" _path_env \"$ENV{INCLUDE}\")\n\tlist(APPEND _inc_env \"${_path_env}\")\n\tstring(REPLACE \":\" \";\" _path_env \"$ENV{C_INCLUDE_PATH}\")\n\tlist(APPEND _inc_env \"${_path_env}\")\n\tstring(REPLACE \":\" \";\" _path_env \"$ENV{CPATH}\")\n\tlist(APPEND _inc_env \"${_path_env}\")\n\tstring(REPLACE \":\" \";\" _path_env \"$ENV{INCLUDE_PATH}\")\n\tlist(APPEND _inc_env \"${_path_env}\")\n      endif()\n    endif()\n    list(APPEND _inc_env \"${CMAKE_PLATFORM_IMPLICIT_INCLUDE_DIRECTORIES}\")\n    list(APPEND _inc_env \"${CMAKE_C_IMPLICIT_INCLUDE_DIRECTORIES}\")\n    list(REMOVE_DUPLICATES _inc_env)\n\n    # set paths where to look for\n    set(PATH_TO_LOOK_FOR \"${_inc_env}\")\n\n    # Try to find the fftw header in the given paths\n    # -------------------------------------------------\n    # call cmake macro to find the header path\n    if(BLAS_INCDIR)\n      set(BLAS_mkl.h_DIRS \"BLAS_mkl.h_DIRS-NOTFOUND\")\n      find_path(BLAS_mkl.h_DIRS\n\tNAMES mkl.h\n\tHINTS ${BLAS_INCDIR})\n    else()\n      if(BLAS_DIR)\n\tset(BLAS_mkl.h_DIRS \"BLAS_mkl.h_DIRS-NOTFOUND\")\n\tfind_path(BLAS_mkl.h_DIRS\n\t  NAMES mkl.h\n\t  HINTS ${BLAS_DIR}\n\t  PATH_SUFFIXES \"include\")\n      else()\n\tset(BLAS_mkl.h_DIRS \"BLAS_mkl.h_DIRS-NOTFOUND\")\n\tfind_path(BLAS_mkl.h_DIRS\n\t  NAMES mkl.h\n\t  HINTS ${PATH_TO_LOOK_FOR})\n      endif()\n    endif()\n    mark_as_advanced(BLAS_mkl.h_DIRS)\n\n    # If found, add path to cmake variable\n    # ------------------------------------\n    if (BLAS_mkl.h_DIRS)\n      set(BLAS_INCLUDE_DIRS \"${BLAS_mkl.h_DIRS}\")\n    else ()\n      set(BLAS_INCLUDE_DIRS \"BLAS_INCLUDE_DIRS-NOTFOUND\")\n      if(NOT BLAS_FIND_QUIETLY)\n\tmessage(STATUS \"Looking for BLAS -- mkl.h not found\")\n      endif()\n    endif()\n\n    if (WIN32)\n      string(REPLACE \":\" \";\" _libdir \"$ENV{LIB}\")\n    elseif (APPLE)\n      string(REPLACE \":\" \";\" _libdir \"$ENV{DYLD_LIBRARY_PATH}\")\n    else ()\n      string(REPLACE \":\" \";\" _libdir \"$ENV{LD_LIBRARY_PATH}\")\n    endif ()\n    list(APPEND _libdir \"${CMAKE_PLATFORM_IMPLICIT_LINK_DIRECTORIES}\")\n    list(APPEND _libdir \"${CMAKE_C_IMPLICIT_LINK_DIRECTORIES}\")\n    # libiomp5\n    # --------\n    set(OMP_iomp5_LIBRARY \"OMP_iomp5_LIBRARY-NOTFOUND\")\n    find_library(OMP_iomp5_LIBRARY\n      NAMES iomp5\n      HINTS ${_libdir}\n      )\n    mark_as_advanced(OMP_iomp5_LIBRARY)\n    set(OMP_LIB \"\")\n    # libgomp\n    # -------\n    set(OMP_gomp_LIBRARY \"OMP_gomp_LIBRARY-NOTFOUND\")\n    find_library(OMP_gomp_LIBRARY\n      NAMES gomp\n      HINTS ${_libdir}\n      )\n    mark_as_advanced(OMP_gomp_LIBRARY)\n    # choose one or another depending on the compilo\n    if (CMAKE_C_COMPILER_ID STREQUAL \"GNU\")\n      if (OMP_gomp_LIBRARY)\n\tset(OMP_LIB \"${OMP_gomp_LIBRARY}\")\n      endif()\n    else(CMAKE_C_COMPILER_ID STREQUAL \"Intel\")\n      if (OMP_iomp5_LIBRARY)\n\tset(OMP_LIB \"${OMP_iomp5_LIBRARY}\")\n      endif()\n    endif()\n\n    if (UNIX AND NOT WIN32)\n      # m\n      find_library(M_LIBRARY\n\tNAMES m\n\tHINTS ${_libdir})\n      mark_as_advanced(M_LIBRARY)\n      if(M_LIBRARY)\n\tset(LM \"-lm\")\n      else()\n\tset(LM \"\")\n      endif()\n      # Fortran\n      set(LGFORTRAN \"\")\n      if (CMAKE_C_COMPILER_ID MATCHES \"GNU\")\n\tfind_library(\n\t  FORTRAN_gfortran_LIBRARY\n\t  NAMES gfortran\n\t  HINTS ${_libdir}\n\t  )\n\tmark_as_advanced(FORTRAN_gfortran_LIBRARY)\n\tif (FORTRAN_gfortran_LIBRARY)\n\t  set(LGFORTRAN \"${FORTRAN_gfortran_LIBRARY}\")\n\tendif()\n      elseif (CMAKE_C_COMPILER_ID MATCHES \"Intel\")\n\tfind_library(\n\t  FORTRAN_ifcore_LIBRARY\n\t  NAMES ifcore\n\t  HINTS ${_libdir}\n\t  )\n\tmark_as_advanced(FORTRAN_ifcore_LIBRARY)\n\tif (FORTRAN_ifcore_LIBRARY)\n\t  set(LGFORTRAN \"{FORTRAN_ifcore_LIBRARY}\")\n\tendif()\n      endif()\n      set(BLAS_COMPILER_FLAGS \"\")\n      if (NOT BLA_VENDOR STREQUAL \"Intel10_64lp_seq\")\n\tif (CMAKE_C_COMPILER_ID STREQUAL \"Intel\")\n\t  list(APPEND BLAS_COMPILER_FLAGS \"-openmp\")\n\tendif()\n\tif (CMAKE_C_COMPILER_ID STREQUAL \"GNU\")\n\t  list(APPEND BLAS_COMPILER_FLAGS \"-fopenmp\")\n\tendif()\n      endif()\n      if (CMAKE_C_COMPILER_ID STREQUAL \"GNU\")\n\tif (BLA_VENDOR STREQUAL \"Intel10_32\")\n\t  list(APPEND BLAS_COMPILER_FLAGS \"-m32\")\n\telse()\n\t  list(APPEND BLAS_COMPILER_FLAGS \"-m64\")\n\tendif()\n\tif (NOT BLA_VENDOR STREQUAL \"Intel10_64lp_seq\")\n\t  list(APPEND OMP_LIB \"-ldl\")\n\tendif()\n\tif (ENV_MKLROOT)\n\t  list(APPEND BLAS_COMPILER_FLAGS \"-I${ENV_MKLROOT}/include\")\n\tendif()\n      endif()\n\n      set(additional_flags \"\")\n      if (CMAKE_C_COMPILER_ID STREQUAL \"GNU\" AND CMAKE_SYSTEM_NAME STREQUAL \"Linux\")\n\tset(additional_flags \"-Wl,--no-as-needed\")\n      endif()\n    endif ()\n\n    if (_LANGUAGES_ MATCHES C OR _LANGUAGES_ MATCHES CXX)\n      if(BLAS_FIND_QUIETLY OR NOT BLAS_FIND_REQUIRED)\n\tfind_package(Threads)\n      else()\n\tfind_package(Threads REQUIRED)\n      endif()\n\n      set(BLAS_SEARCH_LIBS \"\")\n\n      if(BLA_F95)\n\n\tset(BLAS_mkl_SEARCH_SYMBOL SGEMM)\n\tset(_LIBRARIES BLAS95_LIBRARIES)\n\tif (WIN32)\n\t  if (BLA_STATIC)\n\t    set(BLAS_mkl_DLL_SUFFIX \"\")\n\t  else()\n\t    set(BLAS_mkl_DLL_SUFFIX \"_dll\")\n\t  endif()\n\n\t  # Find the main file (32-bit or 64-bit)\n\t  set(BLAS_SEARCH_LIBS_WIN_MAIN \"\")\n\t  if (BLA_VENDOR STREQUAL \"Intel10_32\" OR BLA_VENDOR STREQUAL \"All\")\n\t    list(APPEND BLAS_SEARCH_LIBS_WIN_MAIN\n\t      \"mkl_blas95${BLAS_mkl_DLL_SUFFIX} mkl_intel_c${BLAS_mkl_DLL_SUFFIX}\")\n\t  endif()\n\t  if (BLA_VENDOR STREQUAL \"Intel10_64lp*\" OR BLA_VENDOR STREQUAL \"All\")\n\t    list(APPEND BLAS_SEARCH_LIBS_WIN_MAIN\n\t      \"mkl_blas95_lp64${BLAS_mkl_DLL_SUFFIX} mkl_intel_lp64${BLAS_mkl_DLL_SUFFIX}\")\n\t  endif ()\n\n\t  # Add threading/sequential libs\n\t  set(BLAS_SEARCH_LIBS_WIN_THREAD \"\")\n\t  if (BLA_VENDOR STREQUAL \"*_seq\" OR BLA_VENDOR STREQUAL \"All\")\n\t    list(APPEND BLAS_SEARCH_LIBS_WIN_THREAD\n\t      \"mkl_sequential${BLAS_mkl_DLL_SUFFIX}\")\n\t  endif()\n\t  if (NOT BLA_VENDOR STREQUAL \"*_seq\" OR BLA_VENDOR STREQUAL \"All\")\n\t    # old version\n\t    list(APPEND BLAS_SEARCH_LIBS_WIN_THREAD\n\t      \"libguide40 mkl_intel_thread${BLAS_mkl_DLL_SUFFIX}\")\n\t    # mkl >= 10.3\n\t    list(APPEND BLAS_SEARCH_LIBS_WIN_THREAD\n\t      \"libiomp5md mkl_intel_thread${BLAS_mkl_DLL_SUFFIX}\")\n\t  endif()\n\n\t  # Cartesian product of the above\n\t  foreach (MAIN ${BLAS_SEARCH_LIBS_WIN_MAIN})\n\t    foreach (THREAD ${BLAS_SEARCH_LIBS_WIN_THREAD})\n\t      list(APPEND BLAS_SEARCH_LIBS\n\t\t\"${MAIN} ${THREAD} mkl_core${BLAS_mkl_DLL_SUFFIX}\")\n\t    endforeach()\n\t  endforeach()\n\telse (WIN32)\n\t  if (BLA_VENDOR STREQUAL \"Intel10_32\" OR BLA_VENDOR STREQUAL \"All\")\n\t    list(APPEND BLAS_SEARCH_LIBS\n\t      \"mkl_blas95 mkl_intel mkl_intel_thread mkl_core guide\")\n\t  endif ()\n\t  if (BLA_VENDOR STREQUAL \"Intel10_64lp\" OR BLA_VENDOR STREQUAL \"All\")\n\t    # old version\n\t    list(APPEND BLAS_SEARCH_LIBS\n\t      \"mkl_blas95 mkl_intel_lp64 mkl_intel_thread mkl_core guide\")\n\t    # mkl >= 10.3\n\t    if (CMAKE_C_COMPILER_ID STREQUAL \"Intel\")\n\t      list(APPEND BLAS_SEARCH_LIBS\n\t\t\"mkl_blas95_lp64 mkl_intel_lp64 mkl_intel_thread mkl_core\")\n\t    endif()\n\t    if (CMAKE_C_COMPILER_ID STREQUAL \"GNU\")\n\t      list(APPEND BLAS_SEARCH_LIBS\n\t\t\"mkl_blas95_lp64 mkl_intel_lp64 mkl_gnu_thread mkl_core\")\n\t    endif()\n\t  endif ()\n\t  if (BLA_VENDOR STREQUAL \"Intel10_64lp_seq\" OR BLA_VENDOR STREQUAL \"All\")\n\t    list(APPEND BLAS_SEARCH_LIBS\n\t      \"mkl_intel_lp64 mkl_sequential mkl_core\")\n\t    if (BLA_VENDOR STREQUAL \"Intel10_64lp_seq\")\n\t      set(OMP_LIB \"\")\n\t    endif()\n\t  endif ()\n\tendif (WIN32)\n\n      else (BLA_F95)\n\n\tset(BLAS_mkl_SEARCH_SYMBOL sgemm)\n\tset(_LIBRARIES BLAS_LIBRARIES)\n\tif (WIN32)\n\t  if (BLA_STATIC)\n\t    set(BLAS_mkl_DLL_SUFFIX \"\")\n\t  else()\n\t    set(BLAS_mkl_DLL_SUFFIX \"_dll\")\n\t  endif()\n\n\t  # Find the main file (32-bit or 64-bit)\n\t  set(BLAS_SEARCH_LIBS_WIN_MAIN \"\")\n\t  if (BLA_VENDOR STREQUAL \"Intel10_32\" OR BLA_VENDOR STREQUAL \"All\")\n\t    list(APPEND BLAS_SEARCH_LIBS_WIN_MAIN\n\t      \"mkl_intel_c${BLAS_mkl_DLL_SUFFIX}\")\n\t  endif()\n\t  if (BLA_VENDOR STREQUAL \"Intel10_64lp*\" OR BLA_VENDOR STREQUAL \"All\")\n\t    list(APPEND BLAS_SEARCH_LIBS_WIN_MAIN\n\t      \"mkl_intel_lp64${BLAS_mkl_DLL_SUFFIX}\")\n\t  endif ()\n\n\t  # Add threading/sequential libs\n\t  set(BLAS_SEARCH_LIBS_WIN_THREAD \"\")\n\t  if (NOT BLA_VENDOR STREQUAL \"*_seq\" OR BLA_VENDOR STREQUAL \"All\")\n\t    # old version\n\t    list(APPEND BLAS_SEARCH_LIBS_WIN_THREAD\n\t      \"libguide40 mkl_intel_thread${BLAS_mkl_DLL_SUFFIX}\")\n\t    # mkl >= 10.3\n\t    list(APPEND BLAS_SEARCH_LIBS_WIN_THREAD\n\t      \"libiomp5md mkl_intel_thread${BLAS_mkl_DLL_SUFFIX}\")\n\t  endif()\n\t  if (BLA_VENDOR STREQUAL \"*_seq\" OR BLA_VENDOR STREQUAL \"All\")\n\t    list(APPEND BLAS_SEARCH_LIBS_WIN_THREAD\n\t      \"mkl_sequential${BLAS_mkl_DLL_SUFFIX}\")\n\t  endif()\n\n\t  # Cartesian product of the above\n\t  foreach (MAIN ${BLAS_SEARCH_LIBS_WIN_MAIN})\n\t    foreach (THREAD ${BLAS_SEARCH_LIBS_WIN_THREAD})\n\t      list(APPEND BLAS_SEARCH_LIBS\n\t\t\"${MAIN} ${THREAD} mkl_core${BLAS_mkl_DLL_SUFFIX}\")\n\t    endforeach()\n\t  endforeach()\n\telse (WIN32)\n\t  if (BLA_VENDOR STREQUAL \"Intel10_32\" OR BLA_VENDOR STREQUAL \"All\")\n\t    list(APPEND BLAS_SEARCH_LIBS\n\t      \"mkl_intel mkl_intel_thread mkl_core guide\")\n\t  endif ()\n\t  if (BLA_VENDOR STREQUAL \"Intel10_64lp\" OR BLA_VENDOR STREQUAL \"All\")\n\t    # old version\n\t    list(APPEND BLAS_SEARCH_LIBS\n\t      \"mkl_intel_lp64 mkl_intel_thread mkl_core guide\")\n\t    # mkl >= 10.3\n\t    if (CMAKE_C_COMPILER_ID STREQUAL \"Intel\")\n\t      list(APPEND BLAS_SEARCH_LIBS\n\t\t\"mkl_intel_lp64 mkl_intel_thread mkl_core\")\n\t    endif()\n\t    if (CMAKE_C_COMPILER_ID STREQUAL \"GNU\")\n\t      list(APPEND BLAS_SEARCH_LIBS\n\t\t\"mkl_intel_lp64 mkl_gnu_thread mkl_core\")\n\t    endif()\n\t  endif ()\n\t  if (BLA_VENDOR STREQUAL \"Intel10_64lp_seq\" OR BLA_VENDOR STREQUAL \"All\")\n\t    list(APPEND BLAS_SEARCH_LIBS\n\t      \"mkl_intel_lp64 mkl_sequential mkl_core\")\n\t    if (BLA_VENDOR STREQUAL \"Intel10_64lp_seq\")\n\t      set(OMP_LIB \"\")\n\t    endif()\n\t  endif ()\n\t  #older vesions of intel mkl libs\n\t  if (BLA_VENDOR STREQUAL \"Intel\" OR BLA_VENDOR STREQUAL \"All\")\n\t    list(APPEND BLAS_SEARCH_LIBS\n\t      \"mkl\")\n\t    list(APPEND BLAS_SEARCH_LIBS\n\t      \"mkl_ia32\")\n\t    list(APPEND BLAS_SEARCH_LIBS\n\t      \"mkl_em64t\")\n\t  endif ()\n\tendif (WIN32)\n\n      endif (BLA_F95)\n\n      foreach (IT ${BLAS_SEARCH_LIBS})\n\tstring(REPLACE \" \" \";\" SEARCH_LIBS ${IT})\n\tif (${_LIBRARIES})\n\telse ()\n\t  check_fortran_libraries(\n\t    ${_LIBRARIES}\n\t    BLAS\n\t    ${BLAS_mkl_SEARCH_SYMBOL}\n\t    \"${additional_flags}\"\n\t    \"${SEARCH_LIBS}\"\n\t    \"${OMP_LIB};${CMAKE_THREAD_LIBS_INIT};${LM}\"\n\t    )\n\t  if(_LIBRARIES)\n\t    set(BLAS_LINKER_FLAGS \"${additional_flags}\")\n\t  endif()\n\tendif()\n      endforeach ()\n      if(NOT BLAS_FIND_QUIETLY)\n        if(${_LIBRARIES})\n          message(STATUS \"Looking for MKL BLAS: found\")\n        else()\n          message(STATUS \"Looking for MKL BLAS: not found\")\n        endif()\n      endif()\n      if (${_LIBRARIES} AND NOT BLAS_VENDOR_FOUND)\n          set (BLAS_VENDOR_FOUND \"Intel MKL\")\n      endif()\n    endif (_LANGUAGES_ MATCHES C OR _LANGUAGES_ MATCHES CXX)\n  endif(NOT BLAS_LIBRARIES OR BLA_VENDOR MATCHES \"Intel*\")\nendif (BLA_VENDOR MATCHES \"Intel*\" OR BLA_VENDOR STREQUAL \"All\")\n\n\nif (BLA_VENDOR STREQUAL \"Goto\" OR BLA_VENDOR STREQUAL \"All\")\n\n  if(NOT BLAS_LIBRARIES)\n    # gotoblas (http://www.tacc.utexas.edu/tacc-projects/gotoblas2)\n    check_fortran_libraries(\n      BLAS_LIBRARIES\n      BLAS\n      sgemm\n      \"\"\n      \"goto2\"\n      \"\"\n      )\n    if(NOT BLAS_FIND_QUIETLY)\n      if(BLAS_LIBRARIES)\n\tmessage(STATUS \"Looking for Goto BLAS: found\")\n      else()\n\tmessage(STATUS \"Looking for Goto BLAS: not found\")\n      endif()\n    endif()\n  endif()\n  if (BLAS_LIBRARIES AND NOT BLAS_VENDOR_FOUND)\n      set (BLAS_VENDOR_FOUND \"Goto\")\n  endif()\n\nendif (BLA_VENDOR STREQUAL \"Goto\" OR BLA_VENDOR STREQUAL \"All\")\n\n\n# OpenBlas\nif (BLA_VENDOR STREQUAL \"Open\" OR BLA_VENDOR STREQUAL \"All\")\n\n  if(NOT BLAS_LIBRARIES)\n    # openblas (http://www.openblas.net/)\n    check_fortran_libraries(\n      BLAS_LIBRARIES\n      BLAS\n      sgemm\n      \"\"\n      \"openblas\"\n      \"\"\n      )\n    if(NOT BLAS_FIND_QUIETLY)\n      if(BLAS_LIBRARIES)\n\tmessage(STATUS \"Looking for Open BLAS: found\")\n      else()\n\tmessage(STATUS \"Looking for Open BLAS: not found\")\n      endif()\n    endif()\n  endif()\n  if (BLAS_LIBRARIES AND NOT BLAS_VENDOR_FOUND)\n      set (BLAS_VENDOR_FOUND \"Openblas\")\n  endif()\n\nendif (BLA_VENDOR STREQUAL \"Open\" OR BLA_VENDOR STREQUAL \"All\")\n\n\n# EigenBlas\nif (BLA_VENDOR STREQUAL \"Eigen\" OR BLA_VENDOR STREQUAL \"All\")\n\n  if(NOT BLAS_LIBRARIES)\n    # eigenblas (http://eigen.tuxfamily.org/index.php?title=Main_Page)\n    check_fortran_libraries(\n      BLAS_LIBRARIES\n      BLAS\n      sgemm\n      \"\"\n      \"eigen_blas\"\n      \"\"\n      )\n    if(NOT BLAS_FIND_QUIETLY)\n      if(BLAS_LIBRARIES AND NOT BLAS_VENDOR_FOUND)\n\tmessage(STATUS \"Looking for Eigen BLAS: found\")\n      else()\n\tmessage(STATUS \"Looking for Eigen BLAS: not found\")\n      endif()\n    endif()\n  endif()\n\n  if(NOT BLAS_LIBRARIES)\n    # eigenblas (http://eigen.tuxfamily.org/index.php?title=Main_Page)\n    check_fortran_libraries(\n      BLAS_LIBRARIES\n      BLAS\n      sgemm\n      \"\"\n      \"eigen_blas_static\"\n      \"\"\n      )\n    if(NOT BLAS_FIND_QUIETLY)\n      if(BLAS_LIBRARIES)\n\tmessage(STATUS \"Looking for Eigen BLAS: found\")\n      else()\n\tmessage(STATUS \"Looking for Eigen BLAS: not found\")\n      endif()\n    endif()\n  endif()\n  if (BLAS_LIBRARIES AND NOT BLAS_VENDOR_FOUND)\n      set (BLAS_VENDOR_FOUND \"Eigen\")\n  endif()\n\nendif (BLA_VENDOR STREQUAL \"Eigen\" OR BLA_VENDOR STREQUAL \"All\")\n\n\nif (BLA_VENDOR STREQUAL \"ATLAS\" OR BLA_VENDOR STREQUAL \"All\")\n\n  if(NOT BLAS_LIBRARIES)\n    # BLAS in ATLAS library? (http://math-atlas.sourceforge.net/)\n    check_fortran_libraries(\n      BLAS_LIBRARIES\n      BLAS\n      dgemm\n      \"\"\n      \"f77blas;atlas\"\n      \"\"\n      )\n    if(NOT BLAS_FIND_QUIETLY)\n      if(BLAS_LIBRARIES)\n\tmessage(STATUS \"Looking for Atlas BLAS: found\")\n      else()\n\tmessage(STATUS \"Looking for Atlas BLAS: not found\")\n      endif()\n    endif()\n  endif()\n\n  if (BLAS_LIBRARIES AND NOT BLAS_VENDOR_FOUND)\n      set (BLAS_VENDOR_FOUND \"Atlas\")\n  endif()\n\nendif (BLA_VENDOR STREQUAL \"ATLAS\" OR BLA_VENDOR STREQUAL \"All\")\n\n\n# BLAS in PhiPACK libraries? (requires generic BLAS lib, too)\nif (BLA_VENDOR STREQUAL \"PhiPACK\" OR BLA_VENDOR STREQUAL \"All\")\n\n  if(NOT BLAS_LIBRARIES)\n    check_fortran_libraries(\n      BLAS_LIBRARIES\n      BLAS\n      sgemm\n      \"\"\n      \"sgemm;dgemm;blas\"\n      \"\"\n      )\n    if(NOT BLAS_FIND_QUIETLY)\n      if(BLAS_LIBRARIES)\n\tmessage(STATUS \"Looking for PhiPACK BLAS: found\")\n      else()\n\tmessage(STATUS \"Looking for PhiPACK BLAS: not found\")\n      endif()\n    endif()\n  endif()\n\n  if (BLAS_LIBRARIES AND NOT BLAS_VENDOR_FOUND)\n      set (BLAS_VENDOR_FOUND \"PhiPACK\")\n  endif()\n\nendif (BLA_VENDOR STREQUAL \"PhiPACK\" OR BLA_VENDOR STREQUAL \"All\")\n\n\n# BLAS in Alpha CXML library?\nif (BLA_VENDOR STREQUAL \"CXML\" OR BLA_VENDOR STREQUAL \"All\")\n\n  if(NOT BLAS_LIBRARIES)\n    check_fortran_libraries(\n      BLAS_LIBRARIES\n      BLAS\n      sgemm\n      \"\"\n      \"cxml\"\n      \"\"\n      )\n    if(NOT BLAS_FIND_QUIETLY)\n      if(BLAS_LIBRARIES)\n\tmessage(STATUS \"Looking for CXML BLAS: found\")\n      else()\n\tmessage(STATUS \"Looking for CXML BLAS: not found\")\n      endif()\n    endif()\n  endif()\n\n  if (BLAS_LIBRARIES AND NOT BLAS_VENDOR_FOUND)\n      set (BLAS_VENDOR_FOUND \"CXML\")\n  endif()\n\nendif (BLA_VENDOR STREQUAL \"CXML\" OR BLA_VENDOR STREQUAL \"All\")\n\n\n# BLAS in Alpha DXML library? (now called CXML, see above)\nif (BLA_VENDOR STREQUAL \"DXML\" OR BLA_VENDOR STREQUAL \"All\")\n\n  if(NOT BLAS_LIBRARIES)\n    check_fortran_libraries(\n      BLAS_LIBRARIES\n      BLAS\n      sgemm\n      \"\"\n      \"dxml\"\n      \"\"\n      )\n    if(NOT BLAS_FIND_QUIETLY)\n      if(BLAS_LIBRARIES)\n\tmessage(STATUS \"Looking for DXML BLAS: found\")\n      else()\n\tmessage(STATUS \"Looking for DXML BLAS: not found\")\n      endif()\n    endif()\n  endif()\n\n  if (BLAS_LIBRARIES AND NOT BLAS_VENDOR_FOUND)\n      set (BLAS_VENDOR_FOUND \"DXML\")\n  endif()\n  \nendif (BLA_VENDOR STREQUAL \"DXML\" OR BLA_VENDOR STREQUAL \"All\")\n\n\n# BLAS in Sun Performance library?\nif (BLA_VENDOR STREQUAL \"SunPerf\" OR BLA_VENDOR STREQUAL \"All\")\n\n  if(NOT BLAS_LIBRARIES)\n    check_fortran_libraries(\n      BLAS_LIBRARIES\n      BLAS\n      sgemm\n      \"-xlic_lib=sunperf\"\n      \"sunperf;sunmath\"\n      \"\"\n      )\n    if(BLAS_LIBRARIES)\n      set(BLAS_LINKER_FLAGS \"-xlic_lib=sunperf\")\n    endif()\n    if(NOT BLAS_FIND_QUIETLY)\n      if(BLAS_LIBRARIES)\n\tmessage(STATUS \"Looking for SunPerf BLAS: found\")\n      else()\n\tmessage(STATUS \"Looking for SunPerf BLAS: not found\")\n      endif()\n    endif()\n  endif()\n\n  if (BLAS_LIBRARIES AND NOT BLAS_VENDOR_FOUND)\n      set (BLAS_VENDOR_FOUND \"SunPerf\")\n  endif()\n\nendif ()\n\n\n# BLAS in SCSL library?  (SGI/Cray Scientific Library)\nif (BLA_VENDOR STREQUAL \"SCSL\" OR BLA_VENDOR STREQUAL \"All\")\n\n  if(NOT BLAS_LIBRARIES)\n    check_fortran_libraries(\n      BLAS_LIBRARIES\n      BLAS\n      sgemm\n      \"\"\n      \"scsl\"\n      \"\"\n      )\n    if(NOT BLAS_FIND_QUIETLY)\n      if(BLAS_LIBRARIES)\n\tmessage(STATUS \"Looking for SCSL BLAS: found\")\n      else()\n\tmessage(STATUS \"Looking for SCSL BLAS: not found\")\n      endif()\n    endif()\n  endif()\n\n  if (BLAS_LIBRARIES AND NOT BLAS_VENDOR_FOUND)\n      set (BLAS_VENDOR_FOUND \"SunPerf\")\n  endif()\n\nendif ()\n\n\n# BLAS in SGIMATH library?\nif (BLA_VENDOR STREQUAL \"SGIMATH\" OR BLA_VENDOR STREQUAL \"All\")\n\n  if(NOT BLAS_LIBRARIES)\n    check_fortran_libraries(\n      BLAS_LIBRARIES\n      BLAS\n      sgemm\n      \"\"\n      \"complib.sgimath\"\n      \"\"\n      )\n    if(NOT BLAS_FIND_QUIETLY)\n      if(BLAS_LIBRARIES)\n\tmessage(STATUS \"Looking for SGIMATH BLAS: found\")\n      else()\n\tmessage(STATUS \"Looking for SGIMATH BLAS: not found\")\n      endif()\n    endif()\n  endif()\n\n  if (BLAS_LIBRARIES AND NOT BLAS_VENDOR_FOUND)\n      set (BLAS_VENDOR_FOUND \"SGIMATH\")\n  endif()\n\nendif ()\n\n\n# BLAS in IBM ESSL library (requires generic BLAS lib, too)\nif (BLA_VENDOR STREQUAL \"IBMESSL\" OR BLA_VENDOR STREQUAL \"All\")\n\n  if(NOT BLAS_LIBRARIES)\n    check_fortran_libraries(\n      BLAS_LIBRARIES\n      BLAS\n      sgemm\n      \"\"\n      \"essl;xlfmath;xlf90_r;blas\"\n      \"\"\n      )\n    if(NOT BLAS_FIND_QUIETLY)\n      if(BLAS_LIBRARIES)\n\tmessage(STATUS \"Looking for IBM ESSL BLAS: found\")\n      else()\n\tmessage(STATUS \"Looking for IBM ESSL BLAS: not found\")\n      endif()\n    endif()\n  endif()\n\n  if (BLAS_LIBRARIES AND NOT BLAS_VENDOR_FOUND)\n      set (BLAS_VENDOR_FOUND \"IBM ESSL\")\n  endif()\n\nendif ()\n\n# BLAS in IBM ESSL_MT library (requires generic BLAS lib, too)\nif (BLA_VENDOR STREQUAL \"IBMESSLMT\" OR BLA_VENDOR STREQUAL \"All\")\n\n  if(NOT BLAS_LIBRARIES)\n    check_fortran_libraries(\n      BLAS_LIBRARIES\n      BLAS\n      sgemm\n      \"\"\n      \"esslsmp;xlsmp;xlfmath;xlf90_r;blas\"\n      \"\"\n      )\n    if(NOT BLAS_FIND_QUIETLY)\n      if(BLAS_LIBRARIES)\n\tmessage(STATUS \"Looking for IBM ESSL MT BLAS: found\")\n      else()\n\tmessage(STATUS \"Looking for IBM ESSL MT BLAS: not found\")\n      endif()\n    endif()\n  endif()\n\n  if (BLAS_LIBRARIES AND NOT BLAS_VENDOR_FOUND)\n      set (BLAS_VENDOR_FOUND \"IBM ESSL MT\")\n  endif()\n\nendif ()\n\n\n#BLAS in acml library?\nif (BLA_VENDOR MATCHES \"ACML.*\" OR BLA_VENDOR STREQUAL \"All\")\n\n  if( ((BLA_VENDOR STREQUAL \"ACML\") AND (NOT BLAS_ACML_LIB_DIRS)) OR\n      ((BLA_VENDOR STREQUAL \"ACML_MP\") AND (NOT BLAS_ACML_MP_LIB_DIRS)) OR\n      ((BLA_VENDOR STREQUAL \"ACML_GPU\") AND (NOT BLAS_ACML_GPU_LIB_DIRS)))\n\n    # try to find acml in \"standard\" paths\n    if( WIN32 )\n      file( GLOB _ACML_ROOT \"C:/AMD/acml*/ACML-EULA.txt\" )\n    else()\n      file( GLOB _ACML_ROOT \"/opt/acml*/ACML-EULA.txt\" )\n    endif()\n    if( WIN32 )\n      file( GLOB _ACML_GPU_ROOT \"C:/AMD/acml*/GPGPUexamples\" )\n    else()\n      file( GLOB _ACML_GPU_ROOT \"/opt/acml*/GPGPUexamples\" )\n    endif()\n    list(GET _ACML_ROOT 0 _ACML_ROOT)\n    list(GET _ACML_GPU_ROOT 0 _ACML_GPU_ROOT)\n\n    if( _ACML_ROOT )\n\n      get_filename_component( _ACML_ROOT ${_ACML_ROOT} PATH )\n      if( SIZEOF_INTEGER EQUAL 8 )\n\tset( _ACML_PATH_SUFFIX \"_int64\" )\n      else()\n\tset( _ACML_PATH_SUFFIX \"\" )\n      endif()\n      if( CMAKE_Fortran_COMPILER_ID STREQUAL \"Intel\" )\n\tset( _ACML_COMPILER32 \"ifort32\" )\n\tset( _ACML_COMPILER64 \"ifort64\" )\n      elseif( CMAKE_Fortran_COMPILER_ID STREQUAL \"SunPro\" )\n\tset( _ACML_COMPILER32 \"sun32\" )\n\tset( _ACML_COMPILER64 \"sun64\" )\n      elseif( CMAKE_Fortran_COMPILER_ID STREQUAL \"PGI\" )\n\tset( _ACML_COMPILER32 \"pgi32\" )\n\tif( WIN32 )\n\t  set( _ACML_COMPILER64 \"win64\" )\n\telse()\n\t  set( _ACML_COMPILER64 \"pgi64\" )\n\tendif()\n      elseif( CMAKE_Fortran_COMPILER_ID STREQUAL \"Open64\" )\n\t# 32 bit builds not supported on Open64 but for code simplicity\n\t# We'll just use the same directory twice\n\tset( _ACML_COMPILER32 \"open64_64\" )\n\tset( _ACML_COMPILER64 \"open64_64\" )\n      elseif( CMAKE_Fortran_COMPILER_ID STREQUAL \"NAG\" )\n\tset( _ACML_COMPILER32 \"nag32\" )\n\tset( _ACML_COMPILER64 \"nag64\" )\n      else()\n\tset( _ACML_COMPILER32 \"gfortran32\" )\n\tset( _ACML_COMPILER64 \"gfortran64\" )\n      endif()\n\n      if( BLA_VENDOR STREQUAL \"ACML_MP\" )\n\tset(_ACML_MP_LIB_DIRS\n\t  \"${_ACML_ROOT}/${_ACML_COMPILER32}_mp${_ACML_PATH_SUFFIX}/lib\"\n\t  \"${_ACML_ROOT}/${_ACML_COMPILER64}_mp${_ACML_PATH_SUFFIX}/lib\" )\n      else()\n\tset(_ACML_LIB_DIRS\n\t  \"${_ACML_ROOT}/${_ACML_COMPILER32}${_ACML_PATH_SUFFIX}/lib\"\n\t  \"${_ACML_ROOT}/${_ACML_COMPILER64}${_ACML_PATH_SUFFIX}/lib\" )\n      endif()\n\n    endif(_ACML_ROOT)\n\n  elseif(BLAS_${BLA_VENDOR}_LIB_DIRS)\n\n    set(_${BLA_VENDOR}_LIB_DIRS ${BLAS_${BLA_VENDOR}_LIB_DIRS})\n\n  endif()\n\n  if( BLA_VENDOR STREQUAL \"ACML_MP\" )\n    foreach( BLAS_ACML_MP_LIB_DIRS ${_ACML_MP_LIB_DIRS})\n      check_fortran_libraries (\n\tBLAS_LIBRARIES\n\tBLAS\n\tsgemm\n\t\"\" \"acml_mp;acml_mv\" \"\" ${BLAS_ACML_MP_LIB_DIRS}\n\t)\n      if( BLAS_LIBRARIES )\n\tbreak()\n      endif()\n    endforeach()\n  elseif( BLA_VENDOR STREQUAL \"ACML_GPU\" )\n    foreach( BLAS_ACML_GPU_LIB_DIRS ${_ACML_GPU_LIB_DIRS})\n      check_fortran_libraries (\n\tBLAS_LIBRARIES\n\tBLAS\n\tsgemm\n\t\"\" \"acml;acml_mv;CALBLAS\" \"\" ${BLAS_ACML_GPU_LIB_DIRS}\n\t)\n      if( BLAS_LIBRARIES )\n\tbreak()\n      endif()\n    endforeach()\n  else()\n    foreach( BLAS_ACML_LIB_DIRS ${_ACML_LIB_DIRS} )\n      check_fortran_libraries (\n\tBLAS_LIBRARIES\n\tBLAS\n\tsgemm\n\t\"\" \"acml;acml_mv\" \"\" ${BLAS_ACML_LIB_DIRS}\n\t)\n      if( BLAS_LIBRARIES )\n\tbreak()\n      endif()\n    endforeach()\n  endif()\n\n  # Either acml or acml_mp should be in LD_LIBRARY_PATH but not both\n  if(NOT BLAS_LIBRARIES)\n    check_fortran_libraries(\n      BLAS_LIBRARIES\n      BLAS\n      sgemm\n      \"\"\n      \"acml;acml_mv\"\n      \"\"\n      )\n    if(NOT BLAS_FIND_QUIETLY)\n      if(BLAS_LIBRARIES)\n\tmessage(STATUS \"Looking for ACML BLAS: found\")\n      else()\n\tmessage(STATUS \"Looking for ACML BLAS: not found\")\n      endif()\n    endif()\n  endif()\n\n  if(NOT BLAS_LIBRARIES)\n    check_fortran_libraries(\n      BLAS_LIBRARIES\n      BLAS\n      sgemm\n      \"\"\n      \"acml_mp;acml_mv\"\n      \"\"\n      )\n    if(NOT BLAS_FIND_QUIETLY)\n      if(BLAS_LIBRARIES)\n\tmessage(STATUS \"Looking for ACML BLAS: found\")\n      else()\n\tmessage(STATUS \"Looking for ACML BLAS: not found\")\n      endif()\n    endif()\n  endif()\n\n  if(NOT BLAS_LIBRARIES)\n    check_fortran_libraries(\n      BLAS_LIBRARIES\n      BLAS\n      sgemm\n      \"\"\n      \"acml;acml_mv;CALBLAS\"\n      \"\"\n      )\n    if(NOT BLAS_FIND_QUIETLY)\n      if(BLAS_LIBRARIES)\n\tmessage(STATUS \"Looking for ACML BLAS: found\")\n      else()\n\tmessage(STATUS \"Looking for ACML BLAS: not found\")\n      endif()\n    endif()\n  endif()\n\n  if (BLAS_LIBRARIES AND NOT BLAS_VENDOR_FOUND)\n      set (BLAS_VENDOR_FOUND \"ACML\")\n  endif()\n\nendif (BLA_VENDOR MATCHES \"ACML.*\" OR BLA_VENDOR STREQUAL \"All\") # ACML\n\n\n# Apple BLAS library?\nif (BLA_VENDOR STREQUAL \"Apple\" OR BLA_VENDOR STREQUAL \"All\")\n\n  if(NOT BLAS_LIBRARIES)\n    check_fortran_libraries(\n      BLAS_LIBRARIES\n      BLAS\n      dgemm\n      \"\"\n      \"Accelerate\"\n      \"\"\n      )\n    if(NOT BLAS_FIND_QUIETLY)\n      if(BLAS_LIBRARIES)\n\tmessage(STATUS \"Looking for Apple BLAS: found\")\n      else()\n\tmessage(STATUS \"Looking for Apple BLAS: not found\")\n      endif()\n    endif()\n  endif()\n\n  if (BLAS_LIBRARIES AND NOT BLAS_VENDOR_FOUND)\n      set (BLAS_VENDOR_FOUND \"Apple Accelerate\")\n  endif()\n\nendif (BLA_VENDOR STREQUAL \"Apple\" OR BLA_VENDOR STREQUAL \"All\")\n\n\nif (BLA_VENDOR STREQUAL \"NAS\" OR BLA_VENDOR STREQUAL \"All\")\n\n  if ( NOT BLAS_LIBRARIES )\n    check_fortran_libraries(\n      BLAS_LIBRARIES\n      BLAS\n      dgemm\n      \"\"\n      \"vecLib\"\n      \"\"\n      )\n    if(NOT BLAS_FIND_QUIETLY)\n      if(BLAS_LIBRARIES)\n\tmessage(STATUS \"Looking for NAS BLAS: found\")\n      else()\n\tmessage(STATUS \"Looking for NAS BLAS: not found\")\n      endif()\n    endif()\n  endif ()\n\n  if (BLAS_LIBRARIES AND NOT BLAS_VENDOR_FOUND)\n      set (BLAS_VENDOR_FOUND \"NAS\")\n  endif()\n\nendif (BLA_VENDOR STREQUAL \"NAS\" OR BLA_VENDOR STREQUAL \"All\")\n\n\n# Generic BLAS library?\nif (BLA_VENDOR STREQUAL \"Generic\" OR BLA_VENDOR STREQUAL \"All\")\n\n  set(BLAS_SEARCH_LIBS \"blas;blas_LINUX;blas_MAC;blas_WINDOWS;refblas\")\n  foreach (SEARCH_LIB ${BLAS_SEARCH_LIBS})\n    if (BLAS_LIBRARIES)\n    else ()\n      check_fortran_libraries(\n\tBLAS_LIBRARIES\n\tBLAS\n\tsgemm\n\t\"\"\n\t\"${SEARCH_LIB}\"\n\t\"${LGFORTRAN}\"\n\t)\n      if(NOT BLAS_FIND_QUIETLY)\n\tif(BLAS_LIBRARIES)\n\t  message(STATUS \"Looking for Generic BLAS: found\")\n\telse()\n\t  message(STATUS \"Looking for Generic BLAS: not found\")\n\tendif()\n      endif()\n    endif()\n  endforeach ()\n\n  if (BLAS_LIBRARIES AND NOT BLAS_VENDOR_FOUND)\n      set (BLAS_VENDOR_FOUND \"Netlib or other Generic libblas\")\n  endif()\n\nendif (BLA_VENDOR STREQUAL \"Generic\" OR BLA_VENDOR STREQUAL \"All\")\n\n\nif(BLA_F95)\n\n  if(BLAS95_LIBRARIES)\n    set(BLAS95_FOUND TRUE)\n  else()\n    set(BLAS95_FOUND FALSE)\n  endif()\n\n  if(NOT BLAS_FIND_QUIETLY)\n    if(BLAS95_FOUND)\n      message(STATUS \"A library with BLAS95 API found.\")\n      message(STATUS \"BLAS_LIBRARIES ${BLAS_LIBRARIES}\")\n    else(BLAS95_FOUND)\n      message(WARNING \"BLA_VENDOR has been set to ${BLA_VENDOR} but blas 95 libraries could not be found or check of symbols failed.\"\n\t\"\\nPlease indicate where to find blas libraries. You have three options:\\n\"\n\t\"- Option 1: Provide the installation directory of BLAS library with cmake option: -DBLAS_DIR=your/path/to/blas\\n\"\n\t\"- Option 2: Provide the directory where to find BLAS libraries with cmake option: -DBLAS_LIBDIR=your/path/to/blas/libs\\n\"\n\t\"- Option 3: Update your environment variable (Linux: LD_LIBRARY_PATH, Windows: LIB, Mac: DYLD_LIBRARY_PATH)\\n\"\n\t\"\\nTo follow libraries detection more precisely you can activate a verbose mode with -DBLAS_VERBOSE=ON at cmake configure.\"\n\t\"\\nYou could also specify a BLAS vendor to look for by setting -DBLA_VENDOR=blas_vendor_name.\"\n\t\"\\nList of possible BLAS vendor: Goto, ATLAS PhiPACK, CXML, DXML, SunPerf, SCSL, SGIMATH, IBMESSL, Intel10_32 (intel mkl v10 32 bit),\"\n\t\"Intel10_64lp (intel mkl v10 64 bit, lp thread model, lp64 model), Intel10_64lp_seq (intel mkl v10 64 bit, sequential code, lp64 model),\"\n\t\"Intel( older versions of mkl 32 and 64 bit), ACML, ACML_MP, ACML_GPU, Apple, NAS, Generic\")\n      if(BLAS_FIND_REQUIRED)\n\tmessage(FATAL_ERROR\n\t  \"A required library with BLAS95 API not found. Please specify library location.\")\n      else()\n\tmessage(STATUS\n\t  \"A library with BLAS95 API not found. Please specify library location.\")\n      endif()\n    endif(BLAS95_FOUND)\n  endif(NOT BLAS_FIND_QUIETLY)\n\n  set(BLAS_FOUND TRUE)\n  set(BLAS_LIBRARIES \"${BLAS95_LIBRARIES}\")\n\nelse(BLA_F95)\n\n  if(BLAS_LIBRARIES)\n    set(BLAS_FOUND TRUE)\n  else()\n    set(BLAS_FOUND FALSE)\n  endif()\n\n  if(NOT BLAS_FIND_QUIETLY)\n    if(BLAS_FOUND)\n      message(STATUS \"A library with BLAS API found.\")\n      message(STATUS \"BLAS_LIBRARIES ${BLAS_LIBRARIES}\")\n    else(BLAS_FOUND)\n      message(WARNING \"BLA_VENDOR has been set to ${BLA_VENDOR} but blas libraries could not be found or check of symbols failed.\"\n\t\"\\nPlease indicate where to find blas libraries. You have three options:\\n\"\n\t\"- Option 1: Provide the installation directory of BLAS library with cmake option: -DBLAS_DIR=your/path/to/blas\\n\"\n\t\"- Option 2: Provide the directory where to find BLAS libraries with cmake option: -DBLAS_LIBDIR=your/path/to/blas/libs\\n\"\n\t\"- Option 3: Update your environment variable (Linux: LD_LIBRARY_PATH, Windows: LIB, Mac: DYLD_LIBRARY_PATH)\\n\"\n\t\"\\nTo follow libraries detection more precisely you can activate a verbose mode with -DBLAS_VERBOSE=ON at cmake configure.\"\n\t\"\\nYou could also specify a BLAS vendor to look for by setting -DBLA_VENDOR=blas_vendor_name.\"\n\t\"\\nList of possible BLAS vendor: Goto, ATLAS PhiPACK, CXML, DXML, SunPerf, SCSL, SGIMATH, IBMESSL, Intel10_32 (intel mkl v10 32 bit),\"\n\t\"Intel10_64lp (intel mkl v10 64 bit, lp thread model, lp64 model), Intel10_64lp_seq (intel mkl v10 64 bit, sequential code, lp64 model),\"\n\t\"Intel( older versions of mkl 32 and 64 bit), ACML, ACML_MP, ACML_GPU, Apple, NAS, Generic\")\n      if(BLAS_FIND_REQUIRED)\n\tmessage(FATAL_ERROR\n\t  \"A required library with BLAS API not found. Please specify library location.\")\n      else()\n\tmessage(STATUS\n\t  \"A library with BLAS API not found. Please specify library location.\")\n      endif()\n    endif(BLAS_FOUND)\n  endif(NOT BLAS_FIND_QUIETLY)\n\nendif(BLA_F95)\n\nset(CMAKE_FIND_LIBRARY_SUFFIXES ${_blas_ORIG_CMAKE_FIND_LIBRARY_SUFFIXES})\n\nif (BLAS_FOUND)\n  list(GET BLAS_LIBRARIES 0 first_lib)\n  get_filename_component(first_lib_path \"${first_lib}\" PATH)\n  if (${first_lib_path} MATCHES \"(/lib(32|64)?$)|(/lib/intel64$|/lib/ia32$)\")\n    string(REGEX REPLACE \"(/lib(32|64)?$)|(/lib/intel64$|/lib/ia32$)\" \"\" not_cached_dir \"${first_lib_path}\")\n    set(BLAS_DIR_FOUND \"${not_cached_dir}\" CACHE PATH \"Installation directory of BLAS library\" FORCE)\n  else()\n    set(BLAS_DIR_FOUND \"${first_lib_path}\" CACHE PATH \"Installation directory of BLAS library\" FORCE)\n  endif()\nendif()\nmark_as_advanced(BLAS_DIR)\nmark_as_advanced(BLAS_DIR_FOUND)\n"
  },
  {
    "path": "include/eigen3/cmake/FindBLASEXT.cmake",
    "content": "###\n#\n# @copyright (c) 2009-2014 The University of Tennessee and The University\n#                          of Tennessee Research Foundation.\n#                          All rights reserved.\n# @copyright (c) 2012-2016 Inria. All rights reserved.\n# @copyright (c) 2012-2014 Bordeaux INP, CNRS (LaBRI UMR 5800), Inria, Univ. Bordeaux. All rights reserved.\n#\n###\n#\n# - Find BLAS EXTENDED for MORSE projects: find include dirs and libraries\n#\n# This module allows to find BLAS libraries by calling the official FindBLAS module\n# and handles the creation of different library lists whether the user wishes to link\n# with a sequential BLAS or a multihreaded (BLAS_SEQ_LIBRARIES and BLAS_PAR_LIBRARIES).\n# BLAS is detected with a FindBLAS call then if the BLAS vendor is Intel10_64lp, ACML\n# or IBMESSLMT then the module attempts to find the corresponding multithreaded libraries.\n#\n# The following variables have been added to manage links with sequential or multithreaded\n# versions:\n#  BLAS_INCLUDE_DIRS  - BLAS include directories\n#  BLAS_LIBRARY_DIRS  - Link directories for BLAS libraries\n#  BLAS_SEQ_LIBRARIES - BLAS component libraries to be linked (sequential)\n#  BLAS_PAR_LIBRARIES - BLAS component libraries to be linked (multithreaded)\n\n#=============================================================================\n# Copyright 2012-2013 Inria\n# Copyright 2012-2013 Emmanuel Agullo\n# Copyright 2012-2013 Mathieu Faverge\n# Copyright 2012      Cedric Castagnede\n# Copyright 2013-2016 Florent Pruvost\n#\n# Distributed under the OSI-approved BSD License (the \"License\");\n# see accompanying file MORSE-Copyright.txt for details.\n#\n# This software is distributed WITHOUT ANY WARRANTY; without even the\n# implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.\n# See the License for more information.\n#=============================================================================\n# (To distribute this file outside of Morse, substitute the full\n#  License text for the above reference.)\n\n# macro to factorize this call\nmacro(find_package_blas)\n  if(BLASEXT_FIND_REQUIRED)\n    if(BLASEXT_FIND_QUIETLY)\n      find_package(BLAS REQUIRED QUIET)\n    else()\n      find_package(BLAS REQUIRED)\n    endif()\n  else()\n    if(BLASEXT_FIND_QUIETLY)\n      find_package(BLAS QUIET)\n    else()\n      find_package(BLAS)\n    endif()\n  endif()\nendmacro()\n\n# add a cache variable to let the user specify the BLAS vendor\nset(BLA_VENDOR \"\" CACHE STRING \"list of possible BLAS vendor:\n    Open, Eigen, Goto, ATLAS PhiPACK, CXML, DXML, SunPerf, SCSL, SGIMATH, IBMESSL, IBMESSLMT,\n    Intel10_32 (intel mkl v10 32 bit),\n    Intel10_64lp (intel mkl v10 64 bit, lp thread model, lp64 model),\n    Intel10_64lp_seq (intel mkl v10 64 bit, sequential code, lp64 model),\n    Intel( older versions of mkl 32 and 64 bit),\n    ACML, ACML_MP, ACML_GPU, Apple, NAS, Generic\")\n\nif(NOT BLASEXT_FIND_QUIETLY)\n  message(STATUS \"In FindBLASEXT\")\n  message(STATUS \"If you want to force the use of one specific library, \"\n    \"\\n   please specify the BLAS vendor by setting -DBLA_VENDOR=blas_vendor_name\"\n    \"\\n   at cmake configure.\")\n  message(STATUS \"List of possible BLAS vendor: Goto, ATLAS PhiPACK, CXML, \"\n    \"\\n   DXML, SunPerf, SCSL, SGIMATH, IBMESSL, IBMESSLMT, Intel10_32 (intel mkl v10 32 bit),\"\n    \"\\n   Intel10_64lp (intel mkl v10 64 bit, lp thread model, lp64 model),\"\n    \"\\n   Intel10_64lp_seq (intel mkl v10 64 bit, sequential code, lp64 model),\"\n    \"\\n   Intel( older versions of mkl 32 and 64 bit),\"\n    \"\\n   ACML, ACML_MP, ACML_GPU, Apple, NAS, Generic\")\nendif()\n\nif (NOT BLAS_FOUND)\n  # First try to detect two cases:\n  # 1: only SEQ libs are handled\n  # 2: both SEQ and PAR libs are handled\n  find_package_blas()\nendif ()\n\n# detect the cases where SEQ and PAR libs are handled\nif(BLA_VENDOR STREQUAL \"All\" AND\n    (BLAS_mkl_core_LIBRARY OR BLAS_mkl_core_dll_LIBRARY)\n    )\n  set(BLA_VENDOR \"Intel\")\n  if(BLAS_mkl_intel_LIBRARY)\n    set(BLA_VENDOR \"Intel10_32\")\n  endif()\n  if(BLAS_mkl_intel_lp64_LIBRARY)\n    set(BLA_VENDOR \"Intel10_64lp\")\n  endif()\n  if(NOT BLASEXT_FIND_QUIETLY)\n    message(STATUS \"A BLAS library has been found (${BLAS_LIBRARIES}) but we\"\n      \"\\n   have also potentially detected some multithreaded BLAS libraries from the MKL.\"\n      \"\\n   We try to find both libraries lists (Sequential/Multithreaded).\")\n  endif()\n  set(BLAS_FOUND \"\")\nelseif(BLA_VENDOR STREQUAL \"All\" AND BLAS_acml_LIBRARY)\n  set(BLA_VENDOR \"ACML\")\n  if(NOT BLASEXT_FIND_QUIETLY)\n    message(STATUS \"A BLAS library has been found (${BLAS_LIBRARIES}) but we\"\n      \"\\n   have also potentially detected some multithreaded BLAS libraries from the ACML.\"\n      \"\\n   We try to find both libraries lists (Sequential/Multithreaded).\")\n  endif()\n  set(BLAS_FOUND \"\")\nelseif(BLA_VENDOR STREQUAL \"All\" AND BLAS_essl_LIBRARY)\n  set(BLA_VENDOR \"IBMESSL\")\n  if(NOT BLASEXT_FIND_QUIETLY)\n    message(STATUS \"A BLAS library has been found (${BLAS_LIBRARIES}) but we\"\n      \"\\n   have also potentially detected some multithreaded BLAS libraries from the ESSL.\"\n      \"\\n   We try to find both libraries lists (Sequential/Multithreaded).\")\n  endif()\n  set(BLAS_FOUND \"\")\nendif()\n\n# Intel case\nif(BLA_VENDOR MATCHES \"Intel*\")\n\n  ###\n  # look for include path if the BLAS vendor is Intel\n  ###\n\n  # gather system include paths\n  unset(_inc_env)\n  if(WIN32)\n    string(REPLACE \":\" \";\" _inc_env \"$ENV{INCLUDE}\")\n  else()\n    string(REPLACE \":\" \";\" _path_env \"$ENV{INCLUDE}\")\n    list(APPEND _inc_env \"${_path_env}\")\n    string(REPLACE \":\" \";\" _path_env \"$ENV{C_INCLUDE_PATH}\")\n    list(APPEND _inc_env \"${_path_env}\")\n    string(REPLACE \":\" \";\" _path_env \"$ENV{CPATH}\")\n    list(APPEND _inc_env \"${_path_env}\")\n    string(REPLACE \":\" \";\" _path_env \"$ENV{INCLUDE_PATH}\")\n    list(APPEND _inc_env \"${_path_env}\")\n  endif()\n  list(APPEND _inc_env \"${CMAKE_PLATFORM_IMPLICIT_INCLUDE_DIRECTORIES}\")\n  list(APPEND _inc_env \"${CMAKE_C_IMPLICIT_INCLUDE_DIRECTORIES}\")\n  set(ENV_MKLROOT \"$ENV{MKLROOT}\")\n  if (ENV_MKLROOT)\n    list(APPEND _inc_env \"${ENV_MKLROOT}/include\")\n  endif()\n  list(REMOVE_DUPLICATES _inc_env)\n\n  # find mkl.h inside known include paths\n  set(BLAS_mkl.h_INCLUDE_DIRS \"BLAS_mkl.h_INCLUDE_DIRS-NOTFOUND\")\n  if(BLAS_INCDIR)\n    set(BLAS_mkl.h_INCLUDE_DIRS \"BLAS_mkl.h_INCLUDE_DIRS-NOTFOUND\")\n    find_path(BLAS_mkl.h_INCLUDE_DIRS\n      NAMES mkl.h\n      HINTS ${BLAS_INCDIR})\n  else()\n    if(BLAS_DIR)\n      set(BLAS_mkl.h_INCLUDE_DIRS \"BLAS_mkl.h_INCLUDE_DIRS-NOTFOUND\")\n      find_path(BLAS_mkl.h_INCLUDE_DIRS\n\tNAMES mkl.h\n\tHINTS ${BLAS_DIR}\n\tPATH_SUFFIXES include)\n    else()\n      set(BLAS_mkl.h_INCLUDE_DIRS \"BLAS_mkl.h_INCLUDE_DIRS-NOTFOUND\")\n      find_path(BLAS_mkl.h_INCLUDE_DIRS\n\tNAMES mkl.h\n\tHINTS ${_inc_env})\n    endif()\n  endif()\n  mark_as_advanced(BLAS_mkl.h_INCLUDE_DIRS)\n  ## Print status if not found\n  ## -------------------------\n  #if (NOT BLAS_mkl.h_INCLUDE_DIRS AND MORSE_VERBOSE)\n  #    Print_Find_Header_Status(blas mkl.h)\n  #endif ()\n  set(BLAS_INCLUDE_DIRS \"\")\n  if(BLAS_mkl.h_INCLUDE_DIRS)\n    list(APPEND BLAS_INCLUDE_DIRS \"${BLAS_mkl.h_INCLUDE_DIRS}\" )\n  endif()\n\n  ###\n  # look for libs\n  ###\n  # if Intel 10 64 bit -> look for sequential and multithreaded versions\n  if(BLA_VENDOR MATCHES \"Intel10_64lp*\")\n\n    ## look for the sequential version\n    set(BLA_VENDOR \"Intel10_64lp_seq\")\n    if(NOT BLASEXT_FIND_QUIETLY)\n      message(STATUS \"Look for the sequential version Intel10_64lp_seq\")\n    endif()\n    find_package_blas()\n    if(BLAS_FOUND)\n      set(BLAS_SEQ_LIBRARIES \"${BLAS_LIBRARIES}\")\n    else()\n      set(BLAS_SEQ_LIBRARIES \"${BLAS_SEQ_LIBRARIES-NOTFOUND}\")\n    endif()\n\n    ## look for the multithreaded version\n    set(BLA_VENDOR \"Intel10_64lp\")\n    if(NOT BLASEXT_FIND_QUIETLY)\n      message(STATUS \"Look for the multithreaded version Intel10_64lp\")\n    endif()\n    find_package_blas()\n    if(BLAS_FOUND)\n      set(BLAS_PAR_LIBRARIES \"${BLAS_LIBRARIES}\")\n    else()\n      set(BLAS_PAR_LIBRARIES \"${BLAS_PAR_LIBRARIES-NOTFOUND}\")\n    endif()\n\n  else()\n\n    if(BLAS_FOUND)\n      set(BLAS_SEQ_LIBRARIES \"${BLAS_LIBRARIES}\")\n    else()\n      set(BLAS_SEQ_LIBRARIES \"${BLAS_SEQ_LIBRARIES-NOTFOUND}\")\n    endif()\n\n  endif()\n\n  # ACML case\nelseif(BLA_VENDOR MATCHES \"ACML*\")\n\n  ## look for the sequential version\n  set(BLA_VENDOR \"ACML\")\n  find_package_blas()\n  if(BLAS_FOUND)\n    set(BLAS_SEQ_LIBRARIES \"${BLAS_LIBRARIES}\")\n  else()\n    set(BLAS_SEQ_LIBRARIES \"${BLAS_SEQ_LIBRARIES-NOTFOUND}\")\n  endif()\n\n  ## look for the multithreaded version\n  set(BLA_VENDOR \"ACML_MP\")\n  find_package_blas()\n  if(BLAS_FOUND)\n    set(BLAS_PAR_LIBRARIES \"${BLAS_LIBRARIES}\")\n  else()\n    set(BLAS_PAR_LIBRARIES \"${BLAS_PAR_LIBRARIES-NOTFOUND}\")\n  endif()\n\n  # IBMESSL case\nelseif(BLA_VENDOR MATCHES \"IBMESSL*\")\n\n  ## look for the sequential version\n  set(BLA_VENDOR \"IBMESSL\")\n  find_package_blas()\n  if(BLAS_FOUND)\n    set(BLAS_SEQ_LIBRARIES \"${BLAS_LIBRARIES}\")\n  else()\n    set(BLAS_SEQ_LIBRARIES \"${BLAS_SEQ_LIBRARIES-NOTFOUND}\")\n  endif()\n\n  ## look for the multithreaded version\n  set(BLA_VENDOR \"IBMESSLMT\")\n  find_package_blas()\n  if(BLAS_FOUND)\n    set(BLAS_PAR_LIBRARIES \"${BLAS_LIBRARIES}\")\n  else()\n    set(BLAS_PAR_LIBRARIES \"${BLAS_PAR_LIBRARIES-NOTFOUND}\")\n  endif()\n\nelse()\n\n  if(BLAS_FOUND)\n    # define the SEQ libs as the BLAS_LIBRARIES\n    set(BLAS_SEQ_LIBRARIES \"${BLAS_LIBRARIES}\")\n  else()\n    set(BLAS_SEQ_LIBRARIES \"${BLAS_SEQ_LIBRARIES-NOTFOUND}\")\n  endif()\n  set(BLAS_PAR_LIBRARIES \"${BLAS_PAR_LIBRARIES-NOTFOUND}\")\n\nendif()\n\n\nif(BLAS_SEQ_LIBRARIES)\n  set(BLAS_LIBRARIES \"${BLAS_SEQ_LIBRARIES}\")\nendif()\n\n# extract libs paths\n# remark: because it is not given by find_package(BLAS)\nset(BLAS_LIBRARY_DIRS \"\")\nstring(REPLACE \" \" \";\" BLAS_LIBRARIES \"${BLAS_LIBRARIES}\")\nforeach(blas_lib ${BLAS_LIBRARIES})\n  if (EXISTS \"${blas_lib}\")\n    get_filename_component(a_blas_lib_dir \"${blas_lib}\" PATH)\n    list(APPEND BLAS_LIBRARY_DIRS \"${a_blas_lib_dir}\" )\n  else()\n    string(REPLACE \"-L\" \"\" blas_lib \"${blas_lib}\")\n    if (EXISTS \"${blas_lib}\")\n      list(APPEND BLAS_LIBRARY_DIRS \"${blas_lib}\" )\n    else()\n      get_filename_component(a_blas_lib_dir \"${blas_lib}\" PATH)\n      if (EXISTS \"${a_blas_lib_dir}\")\n\tlist(APPEND BLAS_LIBRARY_DIRS \"${a_blas_lib_dir}\" )\n      endif()\n    endif()\n  endif()\nendforeach()\nif (BLAS_LIBRARY_DIRS)\n  list(REMOVE_DUPLICATES BLAS_LIBRARY_DIRS)\nendif ()\n\n# check that BLAS has been found\n# ---------------------------------\ninclude(FindPackageHandleStandardArgs)\nif(BLA_VENDOR MATCHES \"Intel*\")\n  if(BLA_VENDOR MATCHES \"Intel10_64lp*\")\n    if(NOT BLASEXT_FIND_QUIETLY)\n      message(STATUS \"BLAS found is Intel MKL:\"\n\t\"\\n   we manage two lists of libs, one sequential and one parallel if found\"\n\t\"\\n   (see BLAS_SEQ_LIBRARIES and BLAS_PAR_LIBRARIES)\")\n      message(STATUS \"BLAS sequential libraries stored in BLAS_SEQ_LIBRARIES\")\n    endif()\n    find_package_handle_standard_args(BLAS DEFAULT_MSG\n      BLAS_SEQ_LIBRARIES\n      BLAS_LIBRARY_DIRS\n      BLAS_INCLUDE_DIRS)\n    if(BLAS_PAR_LIBRARIES)\n      if(NOT BLASEXT_FIND_QUIETLY)\n\tmessage(STATUS \"BLAS parallel libraries stored in BLAS_PAR_LIBRARIES\")\n      endif()\n      find_package_handle_standard_args(BLAS DEFAULT_MSG\n\tBLAS_PAR_LIBRARIES)\n    endif()\n  else()\n    if(NOT BLASEXT_FIND_QUIETLY)\n      message(STATUS \"BLAS sequential libraries stored in BLAS_SEQ_LIBRARIES\")\n    endif()\n    find_package_handle_standard_args(BLAS DEFAULT_MSG\n      BLAS_SEQ_LIBRARIES\n      BLAS_LIBRARY_DIRS\n      BLAS_INCLUDE_DIRS)\n  endif()\nelseif(BLA_VENDOR MATCHES \"ACML*\")\n  if(NOT BLASEXT_FIND_QUIETLY)\n    message(STATUS \"BLAS found is ACML:\"\n      \"\\n   we manage two lists of libs, one sequential and one parallel if found\"\n      \"\\n   (see BLAS_SEQ_LIBRARIES and BLAS_PAR_LIBRARIES)\")\n    message(STATUS \"BLAS sequential libraries stored in BLAS_SEQ_LIBRARIES\")\n  endif()\n  find_package_handle_standard_args(BLAS DEFAULT_MSG\n    BLAS_SEQ_LIBRARIES\n    BLAS_LIBRARY_DIRS)\n  if(BLAS_PAR_LIBRARIES)\n    if(NOT BLASEXT_FIND_QUIETLY)\n      message(STATUS \"BLAS parallel libraries stored in BLAS_PAR_LIBRARIES\")\n    endif()\n    find_package_handle_standard_args(BLAS DEFAULT_MSG\n      BLAS_PAR_LIBRARIES)\n  endif()\nelseif(BLA_VENDOR MATCHES \"IBMESSL*\")\n  if(NOT BLASEXT_FIND_QUIETLY)\n    message(STATUS \"BLAS found is ESSL:\"\n      \"\\n   we manage two lists of libs, one sequential and one parallel if found\"\n      \"\\n   (see BLAS_SEQ_LIBRARIES and BLAS_PAR_LIBRARIES)\")\n    message(STATUS \"BLAS sequential libraries stored in BLAS_SEQ_LIBRARIES\")\n  endif()\n  find_package_handle_standard_args(BLAS DEFAULT_MSG\n    BLAS_SEQ_LIBRARIES\n    BLAS_LIBRARY_DIRS)\n  if(BLAS_PAR_LIBRARIES)\n    if(NOT BLASEXT_FIND_QUIETLY)\n      message(STATUS \"BLAS parallel libraries stored in BLAS_PAR_LIBRARIES\")\n    endif()\n    find_package_handle_standard_args(BLAS DEFAULT_MSG\n      BLAS_PAR_LIBRARIES)\n  endif()\nelse()\n  if(NOT BLASEXT_FIND_QUIETLY)\n    message(STATUS \"BLAS sequential libraries stored in BLAS_SEQ_LIBRARIES\")\n  endif()\n  find_package_handle_standard_args(BLAS DEFAULT_MSG\n    BLAS_SEQ_LIBRARIES\n    BLAS_LIBRARY_DIRS)\nendif()\n"
  },
  {
    "path": "include/eigen3/cmake/FindCholmod.cmake",
    "content": "# Cholmod lib usually requires linking to a blas and lapack library.\n# It is up to the user of this module to find a BLAS and link to it.\n\nif (CHOLMOD_INCLUDES AND CHOLMOD_LIBRARIES)\n  set(CHOLMOD_FIND_QUIETLY TRUE)\nendif (CHOLMOD_INCLUDES AND CHOLMOD_LIBRARIES)\n\nfind_path(CHOLMOD_INCLUDES\n  NAMES\n  cholmod.h\n  PATHS\n  $ENV{CHOLMODDIR}\n  ${INCLUDE_INSTALL_DIR}\n  PATH_SUFFIXES\n  suitesparse\n  ufsparse\n)\n\nfind_library(CHOLMOD_LIBRARIES cholmod PATHS $ENV{CHOLMODDIR} ${LIB_INSTALL_DIR})\n\nif(CHOLMOD_LIBRARIES)\n\n  get_filename_component(CHOLMOD_LIBDIR ${CHOLMOD_LIBRARIES} PATH)\n\n  find_library(AMD_LIBRARY amd PATHS ${CHOLMOD_LIBDIR} $ENV{CHOLMODDIR} ${LIB_INSTALL_DIR})\n  if (AMD_LIBRARY)\n    set(CHOLMOD_LIBRARIES ${CHOLMOD_LIBRARIES} ${AMD_LIBRARY})\n  else ()\n    set(CHOLMOD_LIBRARIES FALSE)\n  endif ()\n\nendif(CHOLMOD_LIBRARIES)\n\nif(CHOLMOD_LIBRARIES)\n\n  find_library(COLAMD_LIBRARY colamd PATHS ${CHOLMOD_LIBDIR} $ENV{CHOLMODDIR} ${LIB_INSTALL_DIR})\n  if (COLAMD_LIBRARY)\n    set(CHOLMOD_LIBRARIES ${CHOLMOD_LIBRARIES} ${COLAMD_LIBRARY})\n  else ()\n    set(CHOLMOD_LIBRARIES FALSE)\n  endif ()\n\nendif(CHOLMOD_LIBRARIES)\n\nif(CHOLMOD_LIBRARIES)\n\n  find_library(CAMD_LIBRARY camd PATHS ${CHOLMOD_LIBDIR} $ENV{CHOLMODDIR} ${LIB_INSTALL_DIR})\n  if (CAMD_LIBRARY)\n    set(CHOLMOD_LIBRARIES ${CHOLMOD_LIBRARIES} ${CAMD_LIBRARY})\n  else ()\n    set(CHOLMOD_LIBRARIES FALSE)\n  endif ()\n\nendif(CHOLMOD_LIBRARIES)\n\nif(CHOLMOD_LIBRARIES)\n\n  find_library(CCOLAMD_LIBRARY ccolamd PATHS ${CHOLMOD_LIBDIR} $ENV{CHOLMODDIR} ${LIB_INSTALL_DIR})\n  if (CCOLAMD_LIBRARY)\n    set(CHOLMOD_LIBRARIES ${CHOLMOD_LIBRARIES} ${CCOLAMD_LIBRARY})\n  else ()\n    set(CHOLMOD_LIBRARIES FALSE)\n  endif ()\n\nendif(CHOLMOD_LIBRARIES)\n\nif(CHOLMOD_LIBRARIES)\n\n  find_library(CHOLMOD_METIS_LIBRARY metis PATHS ${CHOLMOD_LIBDIR} $ENV{CHOLMODDIR} ${LIB_INSTALL_DIR})\n  if (CHOLMOD_METIS_LIBRARY)\n    set(CHOLMOD_LIBRARIES ${CHOLMOD_LIBRARIES} ${CHOLMOD_METIS_LIBRARY})\n  endif ()\n\nendif(CHOLMOD_LIBRARIES)\n\nif(CHOLMOD_LIBRARIES)\n\n  find_library(SUITESPARSE_LIBRARY SuiteSparse PATHS ${CHOLMOD_LIBDIR} $ENV{CHOLMODDIR} ${LIB_INSTALL_DIR})\n  if (SUITESPARSE_LIBRARY)\n    set(CHOLMOD_LIBRARIES ${CHOLMOD_LIBRARIES} ${SUITESPARSE_LIBRARY})\n  endif (SUITESPARSE_LIBRARY)\n  \nendif(CHOLMOD_LIBRARIES)\n\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(CHOLMOD DEFAULT_MSG\n                                  CHOLMOD_INCLUDES CHOLMOD_LIBRARIES)\n\nmark_as_advanced(CHOLMOD_INCLUDES CHOLMOD_LIBRARIES AMD_LIBRARY COLAMD_LIBRARY SUITESPARSE_LIBRARY CAMD_LIBRARY CCOLAMD_LIBRARY CHOLMOD_METIS_LIBRARY)\n"
  },
  {
    "path": "include/eigen3/cmake/FindComputeCpp.cmake",
    "content": "#.rst:\n# FindComputeCpp\n#---------------\n#\n#   Copyright 2016 Codeplay Software Ltd.\n#\n#   Licensed under the Apache License, Version 2.0 (the \"License\");\n#   you may not use these files except in compliance with the License.\n#   You may obtain a copy of the License at\n#\n#       http://www.apache.org/licenses/LICENSE-2.0\n#\n#\n#   Unless required by applicable law or agreed to in writing, software\n#   distributed under the License is distributed on an \"AS IS\" BASIS,\n#   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n#   See the License for the specific language governing permissions and\n#   limitations under the License.\n\n#########################\n#  FindComputeCpp.cmake\n#########################\n#\n#  Tools for finding and building with ComputeCpp.\n#\n#  User must define COMPUTECPP_PACKAGE_ROOT_DIR pointing to the ComputeCpp\n#   installation.\n#\n#  Latest version of this file can be found at:\n#    https://github.com/codeplaysoftware/computecpp-sdk\n\n# Require CMake version 3.2.2 or higher\ncmake_minimum_required(VERSION 3.2.2)\n\n# Check that a supported host compiler can be found\nif(CMAKE_COMPILER_IS_GNUCXX)\n    # Require at least gcc 4.8\n    if (CMAKE_CXX_COMPILER_VERSION VERSION_LESS 4.8)\n      message(FATAL_ERROR\n        \"host compiler - Not found! (gcc version must be at least 4.8)\")\n    # Require the GCC dual ABI to be disabled for 5.1 or higher\n    elseif (CMAKE_CXX_COMPILER_VERSION VERSION_GREATER 5.1)\n      set(COMPUTECPP_DISABLE_GCC_DUAL_ABI \"True\")\n      message(STATUS\n        \"host compiler - gcc ${CMAKE_CXX_COMPILER_VERSION} (note pre 5.1 gcc ABI enabled)\")\n    else()\n      message(STATUS \"host compiler - gcc ${CMAKE_CXX_COMPILER_VERSION}\")\n    endif()\nelseif (\"${CMAKE_CXX_COMPILER_ID}\" STREQUAL \"Clang\")\n    # Require at least clang 3.6\n    if (${CMAKE_CXX_COMPILER_VERSION} VERSION_LESS 3.6)\n      message(FATAL_ERROR\n        \"host compiler - Not found! (clang version must be at least 3.6)\")\n    else()\n      message(STATUS \"host compiler - clang ${CMAKE_CXX_COMPILER_VERSION}\")\n    endif()\nelse()\n  message(WARNING\n    \"host compiler - Not found! (ComputeCpp supports GCC and Clang, see readme)\")\nendif()\n\nset(COMPUTECPP_64_BIT_DEFAULT ON)\noption(COMPUTECPP_64_BIT_CODE \"Compile device code in 64 bit mode\"\n        ${COMPUTECPP_64_BIT_DEFAULT})\nmark_as_advanced(COMPUTECPP_64_BIT_CODE)\n\n# Find OpenCL package\nfind_package(OpenCL REQUIRED)\n\n# Find ComputeCpp packagee\nif(NOT COMPUTECPP_PACKAGE_ROOT_DIR)\n  message(FATAL_ERROR\n    \"ComputeCpp package - Not found! (please set COMPUTECPP_PACKAGE_ROOT_DIR\")\nelse()\n  message(STATUS \"ComputeCpp package - Found\")\nendif()\noption(COMPUTECPP_PACKAGE_ROOT_DIR \"Path to the ComputeCpp Package\")\n\n# Obtain the path to compute++\nfind_program(COMPUTECPP_DEVICE_COMPILER compute++ PATHS\n  ${COMPUTECPP_PACKAGE_ROOT_DIR} PATH_SUFFIXES bin)\nif (EXISTS ${COMPUTECPP_DEVICE_COMPILER})\n  mark_as_advanced(COMPUTECPP_DEVICE_COMPILER)\n  message(STATUS \"compute++ - Found\")\nelse()\n  message(FATAL_ERROR \"compute++ - Not found! (${COMPUTECPP_DEVICE_COMPILER})\")\nendif()\n\n# Obtain the path to computecpp_info\nfind_program(COMPUTECPP_INFO_TOOL computecpp_info PATHS\n  ${COMPUTECPP_PACKAGE_ROOT_DIR} PATH_SUFFIXES bin)\nif (EXISTS ${COMPUTECPP_INFO_TOOL})\n  mark_as_advanced(${COMPUTECPP_INFO_TOOL})\n  message(STATUS \"computecpp_info - Found\")\nelse()\n  message(FATAL_ERROR \"computecpp_info - Not found! (${COMPUTECPP_INFO_TOOL})\")\nendif()\n\n# Obtain the path to the ComputeCpp runtime library\nfind_library(COMPUTECPP_RUNTIME_LIBRARY ComputeCpp PATHS ${COMPUTECPP_PACKAGE_ROOT_DIR}\n  HINTS ${COMPUTECPP_PACKAGE_ROOT_DIR}/lib PATH_SUFFIXES lib\n  DOC \"ComputeCpp Runtime Library\" NO_DEFAULT_PATH)\n\nif (EXISTS ${COMPUTECPP_RUNTIME_LIBRARY})\n  mark_as_advanced(COMPUTECPP_RUNTIME_LIBRARY)\n  message(STATUS \"libComputeCpp.so - Found\")\nelse()\n  message(FATAL_ERROR \"libComputeCpp.so - Not found!\")\nendif()\n\n# Obtain the ComputeCpp include directory\nset(COMPUTECPP_INCLUDE_DIRECTORY ${COMPUTECPP_PACKAGE_ROOT_DIR}/include/)\nif (NOT EXISTS ${COMPUTECPP_INCLUDE_DIRECTORY})\n  message(FATAL_ERROR \"ComputeCpp includes - Not found!\")\nelse()\n  message(STATUS \"ComputeCpp includes - Found\")\nendif()\n\n# Obtain the package version\nexecute_process(COMMAND ${COMPUTECPP_INFO_TOOL} \"--dump-version\"\n  OUTPUT_VARIABLE COMPUTECPP_PACKAGE_VERSION\n  RESULT_VARIABLE COMPUTECPP_INFO_TOOL_RESULT OUTPUT_STRIP_TRAILING_WHITESPACE)\nif(NOT COMPUTECPP_INFO_TOOL_RESULT EQUAL \"0\")\n  message(FATAL_ERROR \"Package version - Error obtaining version!\")\nelse()\n  mark_as_advanced(COMPUTECPP_PACKAGE_VERSION)\n  message(STATUS \"Package version - ${COMPUTECPP_PACKAGE_VERSION}\")\nendif()\n\n# Obtain the device compiler flags\nexecute_process(COMMAND ${COMPUTECPP_INFO_TOOL} \"--dump-device-compiler-flags\"\n  OUTPUT_VARIABLE COMPUTECPP_DEVICE_COMPILER_FLAGS\n  RESULT_VARIABLE COMPUTECPP_INFO_TOOL_RESULT OUTPUT_STRIP_TRAILING_WHITESPACE)\nif(NOT COMPUTECPP_INFO_TOOL_RESULT EQUAL \"0\")\n  message(FATAL_ERROR \"compute++ flags - Error obtaining compute++ flags!\")\nelse()\n  mark_as_advanced(COMPUTECPP_COMPILER_FLAGS)\n  message(STATUS \"compute++ flags - ${COMPUTECPP_DEVICE_COMPILER_FLAGS}\")\nendif()\n\nset(COMPUTECPP_DEVICE_COMPILER_FLAGS ${COMPUTECPP_DEVICE_COMPILER_FLAGS} -sycl-compress-name -no-serial-memop -DEIGEN_NO_ASSERTION_CHECKING=1)\n\n# Check if the platform is supported\nexecute_process(COMMAND ${COMPUTECPP_INFO_TOOL} \"--dump-is-supported\"\n  OUTPUT_VARIABLE COMPUTECPP_PLATFORM_IS_SUPPORTED\n  RESULT_VARIABLE COMPUTECPP_INFO_TOOL_RESULT OUTPUT_STRIP_TRAILING_WHITESPACE)\nif(NOT COMPUTECPP_INFO_TOOL_RESULT EQUAL \"0\")\n  message(FATAL_ERROR \"platform - Error checking platform support!\")\nelse()\n  mark_as_advanced(COMPUTECPP_PLATFORM_IS_SUPPORTED)\n  if (COMPUTECPP_PLATFORM_IS_SUPPORTED)\n    message(STATUS \"platform - your system can support ComputeCpp\")\n  else()\n    message(STATUS \"platform - your system CANNOT support ComputeCpp\")\n  endif()\nendif()\n\n####################\n#   __build_sycl\n####################\n#\n#  Adds a custom target for running compute++ and adding a dependency for the\n#  resulting integration header.\n#\n#  targetName : Name of the target.\n#  sourceFile : Source file to be compiled.\n#  binaryDir : Intermediate directory to output the integration header.\n#\nfunction(__build_spir targetName sourceFile binaryDir)\n\n  # Retrieve source file name.\n  get_filename_component(sourceFileName ${sourceFile} NAME)\n\n  # Set the path to the Sycl file.\n  set(outputSyclFile ${binaryDir}/${sourceFileName}.sycl)\n\n  # Add any user-defined include to the device compiler\n  get_property(includeDirectories DIRECTORY ${CMAKE_CURRENT_SOURCE_DIR} PROPERTY\n    INCLUDE_DIRECTORIES)\n  set(device_compiler_includes \"\")\n  foreach(directory ${includeDirectories})\n    set(device_compiler_includes \"-I${directory}\" ${device_compiler_includes})\n  endforeach()\n  if (CMAKE_INCLUDE_PATH)\n    foreach(directory ${CMAKE_INCLUDE_PATH})\n      set(device_compiler_includes \"-I${directory}\"\n        ${device_compiler_includes})\n    endforeach()\n  endif()\n\n  # Convert argument list format\n  separate_arguments(COMPUTECPP_DEVICE_COMPILER_FLAGS)\n\n  # Add custom command for running compute++\n  add_custom_command(\n    OUTPUT ${outputSyclFile}\n    COMMAND ${COMPUTECPP_DEVICE_COMPILER}\n            ${COMPUTECPP_DEVICE_COMPILER_FLAGS}\n            -isystem ${COMPUTECPP_INCLUDE_DIRECTORY}\n            ${COMPUTECPP_PLATFORM_SPECIFIC_ARGS}\n            ${device_compiler_includes}\n            -o ${outputSyclFile}\n            -c ${CMAKE_CURRENT_SOURCE_DIR}/${sourceFile}\n    DEPENDS ${sourceFile}\n    WORKING_DIRECTORY ${binaryDir}\n  COMMENT \"Building ComputeCpp integration header file ${outputSyclFile}\")\n\n  # Add a custom target for the generated integration header\n  add_custom_target(${targetName}_integration_header DEPENDS ${outputSyclFile})\n\n  # Add a dependency on the integration header\n  add_dependencies(${targetName} ${targetName}_integration_header)\n\n  # Set the host compiler C++ standard to C++11\n  set_property(TARGET ${targetName} PROPERTY CXX_STANDARD 11)\n\n  # Disable GCC dual ABI on GCC 5.1 and higher\n  if(COMPUTECPP_DISABLE_GCC_DUAL_ABI)\n    set_property(TARGET ${targetName} APPEND PROPERTY COMPILE_DEFINITIONS\n      \"_GLIBCXX_USE_CXX11_ABI=0\")\n  endif()\n\nendfunction()\n\n#######################\n#  add_sycl_to_target\n#######################\n#\n#  Adds a SYCL compilation custom command associated with an existing\n#  target and sets a dependancy on that new command.\n#\n#  targetName : Name of the target to add a SYCL to.\n#  sourceFile : Source file to be compiled for SYCL.\n#  binaryDir : Intermediate directory to output the integration header.\n#\nfunction(add_sycl_to_target targetName sourceFile binaryDir)\n\n  # Add custom target to run compute++ and generate the integration header\n  __build_spir(${targetName} ${sourceFile} ${binaryDir})\n\n  # Link with the ComputeCpp runtime library\n  target_link_libraries(${targetName} PUBLIC ${COMPUTECPP_RUNTIME_LIBRARY}\n                        PUBLIC ${OpenCL_LIBRARIES})\n\nendfunction(add_sycl_to_target)\n"
  },
  {
    "path": "include/eigen3/cmake/FindEigen2.cmake",
    "content": "# - Try to find Eigen2 lib\n#\n# This module supports requiring a minimum version, e.g. you can do\n#   find_package(Eigen2 2.0.3)\n# to require version 2.0.3 to newer of Eigen2.\n#\n# Once done this will define\n#\n#  EIGEN2_FOUND - system has eigen lib with correct version\n#  EIGEN2_INCLUDE_DIR - the eigen include directory\n#  EIGEN2_VERSION - eigen version\n\n# Copyright (c) 2006, 2007 Montel Laurent, <montel@kde.org>\n# Copyright (c) 2008, 2009 Gael Guennebaud, <g.gael@free.fr>\n# Redistribution and use is allowed according to the terms of the BSD license.\n\nif(NOT Eigen2_FIND_VERSION)\n  if(NOT Eigen2_FIND_VERSION_MAJOR)\n    set(Eigen2_FIND_VERSION_MAJOR 2)\n  endif(NOT Eigen2_FIND_VERSION_MAJOR)\n  if(NOT Eigen2_FIND_VERSION_MINOR)\n    set(Eigen2_FIND_VERSION_MINOR 0)\n  endif(NOT Eigen2_FIND_VERSION_MINOR)\n  if(NOT Eigen2_FIND_VERSION_PATCH)\n    set(Eigen2_FIND_VERSION_PATCH 0)\n  endif(NOT Eigen2_FIND_VERSION_PATCH)\n\n  set(Eigen2_FIND_VERSION \"${Eigen2_FIND_VERSION_MAJOR}.${Eigen2_FIND_VERSION_MINOR}.${Eigen2_FIND_VERSION_PATCH}\")\nendif(NOT Eigen2_FIND_VERSION)\n\nmacro(_eigen2_check_version)\n  file(READ \"${EIGEN2_INCLUDE_DIR}/Eigen/src/Core/util/Macros.h\" _eigen2_version_header)\n\n  string(REGEX MATCH \"define[ \\t]+EIGEN_WORLD_VERSION[ \\t]+([0-9]+)\" _eigen2_world_version_match \"${_eigen2_version_header}\")\n  set(EIGEN2_WORLD_VERSION \"${CMAKE_MATCH_1}\")\n  string(REGEX MATCH \"define[ \\t]+EIGEN_MAJOR_VERSION[ \\t]+([0-9]+)\" _eigen2_major_version_match \"${_eigen2_version_header}\")\n  set(EIGEN2_MAJOR_VERSION \"${CMAKE_MATCH_1}\")\n  string(REGEX MATCH \"define[ \\t]+EIGEN_MINOR_VERSION[ \\t]+([0-9]+)\" _eigen2_minor_version_match \"${_eigen2_version_header}\")\n  set(EIGEN2_MINOR_VERSION \"${CMAKE_MATCH_1}\")\n\n  set(EIGEN2_VERSION ${EIGEN2_WORLD_VERSION}.${EIGEN2_MAJOR_VERSION}.${EIGEN2_MINOR_VERSION})\n  if((${EIGEN2_WORLD_VERSION} NOTEQUAL 2) OR (${EIGEN2_MAJOR_VERSION} GREATER 10) OR (${EIGEN2_VERSION} VERSION_LESS ${Eigen2_FIND_VERSION}))\n    set(EIGEN2_VERSION_OK FALSE)\n  else()\n    set(EIGEN2_VERSION_OK TRUE)\n  endif()\n\n  if(NOT EIGEN2_VERSION_OK)\n\n    message(STATUS \"Eigen2 version ${EIGEN2_VERSION} found in ${EIGEN2_INCLUDE_DIR}, \"\n                   \"but at least version ${Eigen2_FIND_VERSION} is required\")\n  endif(NOT EIGEN2_VERSION_OK)\nendmacro(_eigen2_check_version)\n\nif (EIGEN2_INCLUDE_DIR)\n\n  # in cache already\n  _eigen2_check_version()\n  set(EIGEN2_FOUND ${EIGEN2_VERSION_OK})\n\nelse (EIGEN2_INCLUDE_DIR)\n\nfind_path(EIGEN2_INCLUDE_DIR NAMES Eigen/Core\n     PATHS\n     ${INCLUDE_INSTALL_DIR}\n     ${KDE4_INCLUDE_DIR}\n     PATH_SUFFIXES eigen2\n   )\n\nif(EIGEN2_INCLUDE_DIR)\n  _eigen2_check_version()\nendif(EIGEN2_INCLUDE_DIR)\n\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(Eigen2 DEFAULT_MSG EIGEN2_INCLUDE_DIR EIGEN2_VERSION_OK)\n\nmark_as_advanced(EIGEN2_INCLUDE_DIR)\n\nendif(EIGEN2_INCLUDE_DIR)\n\n"
  },
  {
    "path": "include/eigen3/cmake/FindEigen3.cmake",
    "content": "# - Try to find Eigen3 lib\n#\n# This module supports requiring a minimum version, e.g. you can do\n#   find_package(Eigen3 3.1.2)\n# to require version 3.1.2 or newer of Eigen3.\n#\n# Once done this will define\n#\n#  EIGEN3_FOUND - system has eigen lib with correct version\n#  EIGEN3_INCLUDE_DIR - the eigen include directory\n#  EIGEN3_VERSION - eigen version\n#\n# This module reads hints about search locations from \n# the following enviroment variables:\n#\n# EIGEN3_ROOT\n# EIGEN3_ROOT_DIR\n\n# Copyright (c) 2006, 2007 Montel Laurent, <montel@kde.org>\n# Copyright (c) 2008, 2009 Gael Guennebaud, <g.gael@free.fr>\n# Copyright (c) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n# Redistribution and use is allowed according to the terms of the 2-clause BSD license.\n\nif(NOT Eigen3_FIND_VERSION)\n  if(NOT Eigen3_FIND_VERSION_MAJOR)\n    set(Eigen3_FIND_VERSION_MAJOR 2)\n  endif(NOT Eigen3_FIND_VERSION_MAJOR)\n  if(NOT Eigen3_FIND_VERSION_MINOR)\n    set(Eigen3_FIND_VERSION_MINOR 91)\n  endif(NOT Eigen3_FIND_VERSION_MINOR)\n  if(NOT Eigen3_FIND_VERSION_PATCH)\n    set(Eigen3_FIND_VERSION_PATCH 0)\n  endif(NOT Eigen3_FIND_VERSION_PATCH)\n\n  set(Eigen3_FIND_VERSION \"${Eigen3_FIND_VERSION_MAJOR}.${Eigen3_FIND_VERSION_MINOR}.${Eigen3_FIND_VERSION_PATCH}\")\nendif(NOT Eigen3_FIND_VERSION)\n\nmacro(_eigen3_check_version)\n  file(READ \"${EIGEN3_INCLUDE_DIR}/Eigen/src/Core/util/Macros.h\" _eigen3_version_header)\n\n  string(REGEX MATCH \"define[ \\t]+EIGEN_WORLD_VERSION[ \\t]+([0-9]+)\" _eigen3_world_version_match \"${_eigen3_version_header}\")\n  set(EIGEN3_WORLD_VERSION \"${CMAKE_MATCH_1}\")\n  string(REGEX MATCH \"define[ \\t]+EIGEN_MAJOR_VERSION[ \\t]+([0-9]+)\" _eigen3_major_version_match \"${_eigen3_version_header}\")\n  set(EIGEN3_MAJOR_VERSION \"${CMAKE_MATCH_1}\")\n  string(REGEX MATCH \"define[ \\t]+EIGEN_MINOR_VERSION[ \\t]+([0-9]+)\" _eigen3_minor_version_match \"${_eigen3_version_header}\")\n  set(EIGEN3_MINOR_VERSION \"${CMAKE_MATCH_1}\")\n\n  set(EIGEN3_VERSION ${EIGEN3_WORLD_VERSION}.${EIGEN3_MAJOR_VERSION}.${EIGEN3_MINOR_VERSION})\n  if(${EIGEN3_VERSION} VERSION_LESS ${Eigen3_FIND_VERSION})\n    set(EIGEN3_VERSION_OK FALSE)\n  else(${EIGEN3_VERSION} VERSION_LESS ${Eigen3_FIND_VERSION})\n    set(EIGEN3_VERSION_OK TRUE)\n  endif(${EIGEN3_VERSION} VERSION_LESS ${Eigen3_FIND_VERSION})\n\n  if(NOT EIGEN3_VERSION_OK)\n\n    message(STATUS \"Eigen3 version ${EIGEN3_VERSION} found in ${EIGEN3_INCLUDE_DIR}, \"\n                   \"but at least version ${Eigen3_FIND_VERSION} is required\")\n  endif(NOT EIGEN3_VERSION_OK)\nendmacro(_eigen3_check_version)\n\nif (EIGEN3_INCLUDE_DIR)\n\n  # in cache already\n  _eigen3_check_version()\n  set(EIGEN3_FOUND ${EIGEN3_VERSION_OK})\n\nelse (EIGEN3_INCLUDE_DIR)\n  \n  # search first if an Eigen3Config.cmake is available in the system,\n  # if successful this would set EIGEN3_INCLUDE_DIR and the rest of\n  # the script will work as usual\n  find_package(Eigen3 ${Eigen3_FIND_VERSION} NO_MODULE QUIET)\n\n  if(NOT EIGEN3_INCLUDE_DIR)\n    find_path(EIGEN3_INCLUDE_DIR NAMES signature_of_eigen3_matrix_library\n        HINTS\n        ENV EIGEN3_ROOT \n        ENV EIGEN3_ROOT_DIR\n        PATHS\n        ${CMAKE_INSTALL_PREFIX}/include\n        ${KDE4_INCLUDE_DIR}\n        PATH_SUFFIXES eigen3 eigen\n      )\n  endif(NOT EIGEN3_INCLUDE_DIR)\n\n  if(EIGEN3_INCLUDE_DIR)\n    _eigen3_check_version()\n  endif(EIGEN3_INCLUDE_DIR)\n\n  include(FindPackageHandleStandardArgs)\n  find_package_handle_standard_args(Eigen3 DEFAULT_MSG EIGEN3_INCLUDE_DIR EIGEN3_VERSION_OK)\n\n  mark_as_advanced(EIGEN3_INCLUDE_DIR)\n\nendif(EIGEN3_INCLUDE_DIR)\n\n"
  },
  {
    "path": "include/eigen3/cmake/FindFFTW.cmake",
    "content": "# - Find the FFTW library\n#\n# Usage:\n#   find_package(FFTW [REQUIRED] [QUIET] )\n#     \n# It sets the following variables:\n#   FFTW_FOUND               ... true if fftw is found on the system\n#   FFTW_LIBRARIES           ... full path to fftw library\n#   FFTW_INCLUDES            ... fftw include directory\n#\n# The following variables will be checked by the function\n#   FFTW_USE_STATIC_LIBS    ... if true, only static libraries are found\n#   FFTW_ROOT               ... if set, the libraries are exclusively searched\n#                               under this path\n#   FFTW_LIBRARY            ... fftw library to use\n#   FFTW_INCLUDE_DIR        ... fftw include directory\n#\n\n#If environment variable FFTWDIR is specified, it has same effect as FFTW_ROOT\nif( NOT FFTW_ROOT AND ENV{FFTWDIR} )\n  set( FFTW_ROOT $ENV{FFTWDIR} )\nendif()\n\n# Check if we can use PkgConfig\nfind_package(PkgConfig)\n\n#Determine from PKG\nif( PKG_CONFIG_FOUND AND NOT FFTW_ROOT )\n  pkg_check_modules( PKG_FFTW QUIET \"fftw3\" )\nendif()\n\n#Check whether to search static or dynamic libs\nset( CMAKE_FIND_LIBRARY_SUFFIXES_SAV ${CMAKE_FIND_LIBRARY_SUFFIXES} )\n\nif( ${FFTW_USE_STATIC_LIBS} )\n  set( CMAKE_FIND_LIBRARY_SUFFIXES ${CMAKE_STATIC_LIBRARY_SUFFIX} )\nelse()\n  set( CMAKE_FIND_LIBRARY_SUFFIXES ${CMAKE_SHARED_LIBRARY_SUFFIX} )\nendif()\n\nif( FFTW_ROOT )\n\n  #find libs\n  find_library(\n    FFTW_LIB\n    NAMES \"fftw3\"\n    PATHS ${FFTW_ROOT}\n    PATH_SUFFIXES \"lib\" \"lib64\"\n    NO_DEFAULT_PATH\n  )\n\n  find_library(\n    FFTWF_LIB\n    NAMES \"fftw3f\"\n    PATHS ${FFTW_ROOT}\n    PATH_SUFFIXES \"lib\" \"lib64\"\n    NO_DEFAULT_PATH\n  )\n\n  find_library(\n    FFTWL_LIB\n    NAMES \"fftw3l\"\n    PATHS ${FFTW_ROOT}\n    PATH_SUFFIXES \"lib\" \"lib64\"\n    NO_DEFAULT_PATH\n  )\n\n  #find includes\n  find_path(\n    FFTW_INCLUDES\n    NAMES \"fftw3.h\"\n    PATHS ${FFTW_ROOT}\n    PATH_SUFFIXES \"include\"\n    NO_DEFAULT_PATH\n  )\n\nelse()\n\n  find_library(\n    FFTW_LIB\n    NAMES \"fftw3\"\n    PATHS ${PKG_FFTW_LIBRARY_DIRS} ${LIB_INSTALL_DIR}\n  )\n\n  find_library(\n    FFTWF_LIB\n    NAMES \"fftw3f\"\n    PATHS ${PKG_FFTW_LIBRARY_DIRS} ${LIB_INSTALL_DIR}\n  )\n\n\n  find_library(\n    FFTWL_LIB\n    NAMES \"fftw3l\"\n    PATHS ${PKG_FFTW_LIBRARY_DIRS} ${LIB_INSTALL_DIR}\n  )\n\n  find_path(\n    FFTW_INCLUDES\n    NAMES \"fftw3.h\"\n    PATHS ${PKG_FFTW_INCLUDE_DIRS} ${INCLUDE_INSTALL_DIR}\n  )\n\nendif( FFTW_ROOT )\n\nset(FFTW_LIBRARIES ${FFTW_LIB} ${FFTWF_LIB})\n\nif(FFTWL_LIB)\n  set(FFTW_LIBRARIES ${FFTW_LIBRARIES} ${FFTWL_LIB})\nendif()\n\nset( CMAKE_FIND_LIBRARY_SUFFIXES ${CMAKE_FIND_LIBRARY_SUFFIXES_SAV} )\n\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(FFTW DEFAULT_MSG\n                                  FFTW_INCLUDES FFTW_LIBRARIES)\n\nmark_as_advanced(FFTW_INCLUDES FFTW_LIBRARIES FFTW_LIB FFTWF_LIB FFTWL_LIB)\n\n"
  },
  {
    "path": "include/eigen3/cmake/FindGLEW.cmake",
    "content": "# Copyright (c) 2009 Boudewijn Rempt <boud@valdyas.org>                                                                                          \n#                                                                                                                                                \n# Redistribution and use is allowed according to the terms of the BSD license.                                                                   \n# For details see the accompanying COPYING-CMAKE-SCRIPTS file. \n# \n# - try to find glew library and include files\n#  GLEW_INCLUDE_DIR, where to find GL/glew.h, etc.\n#  GLEW_LIBRARIES, the libraries to link against\n#  GLEW_FOUND, If false, do not try to use GLEW.\n# Also defined, but not for general use are:\n#  GLEW_GLEW_LIBRARY = the full path to the glew library.\n\nIF (WIN32)\n\n  IF(CYGWIN)\n\n    FIND_PATH( GLEW_INCLUDE_DIR GL/glew.h)\n\n    FIND_LIBRARY( GLEW_GLEW_LIBRARY glew32\n      ${OPENGL_LIBRARY_DIR}\n      /usr/lib/w32api\n      /usr/X11R6/lib\n    )\n\n\n  ELSE(CYGWIN)\n  \n    FIND_PATH( GLEW_INCLUDE_DIR GL/glew.h\n      $ENV{GLEW_ROOT_PATH}/include\n    )\n\n    FIND_LIBRARY( GLEW_GLEW_LIBRARY\n      NAMES glew glew32\n      PATHS\n      $ENV{GLEW_ROOT_PATH}/lib\n      ${OPENGL_LIBRARY_DIR}\n    )\n\n  ENDIF(CYGWIN)\n\nELSE (WIN32)\n\n  IF (APPLE)\n# These values for Apple could probably do with improvement.\n    FIND_PATH( GLEW_INCLUDE_DIR glew.h\n      /System/Library/Frameworks/GLEW.framework/Versions/A/Headers\n      ${OPENGL_LIBRARY_DIR}\n    )\n    SET(GLEW_GLEW_LIBRARY \"-framework GLEW\" CACHE STRING \"GLEW library for OSX\")\n    SET(GLEW_cocoa_LIBRARY \"-framework Cocoa\" CACHE STRING \"Cocoa framework for OSX\")\n  ELSE (APPLE)\n\n    FIND_PATH( GLEW_INCLUDE_DIR GL/glew.h\n      /usr/include/GL\n      /usr/openwin/share/include\n      /usr/openwin/include\n      /usr/X11R6/include\n      /usr/include/X11\n      /opt/graphics/OpenGL/include\n      /opt/graphics/OpenGL/contrib/libglew\n    )\n\n    FIND_LIBRARY( GLEW_GLEW_LIBRARY GLEW\n      /usr/openwin/lib\n      /usr/X11R6/lib\n    )\n\n  ENDIF (APPLE)\n\nENDIF (WIN32)\n\nSET( GLEW_FOUND \"NO\" )\nIF(GLEW_INCLUDE_DIR)\n  IF(GLEW_GLEW_LIBRARY)\n    # Is -lXi and -lXmu required on all platforms that have it?\n    # If not, we need some way to figure out what platform we are on.\n    SET( GLEW_LIBRARIES\n      ${GLEW_GLEW_LIBRARY}\n      ${GLEW_cocoa_LIBRARY}\n    )\n    SET( GLEW_FOUND \"YES\" )\n\n#The following deprecated settings are for backwards compatibility with CMake1.4\n    SET (GLEW_LIBRARY ${GLEW_LIBRARIES})\n    SET (GLEW_INCLUDE_PATH ${GLEW_INCLUDE_DIR})\n\n  ENDIF(GLEW_GLEW_LIBRARY)\nENDIF(GLEW_INCLUDE_DIR)\n\nIF(GLEW_FOUND)\n  IF(NOT GLEW_FIND_QUIETLY)\n    MESSAGE(STATUS \"Found Glew: ${GLEW_LIBRARIES}\")\n  ENDIF(NOT GLEW_FIND_QUIETLY)\nELSE(GLEW_FOUND)\n  IF(GLEW_FIND_REQUIRED)\n    MESSAGE(FATAL_ERROR \"Could not find Glew\")\n  ENDIF(GLEW_FIND_REQUIRED)\nENDIF(GLEW_FOUND)\n\nMARK_AS_ADVANCED(\n  GLEW_INCLUDE_DIR\n  GLEW_GLEW_LIBRARY\n  GLEW_Xmu_LIBRARY\n  GLEW_Xi_LIBRARY\n)\n"
  },
  {
    "path": "include/eigen3/cmake/FindGMP.cmake",
    "content": "# Try to find the GNU Multiple Precision Arithmetic Library (GMP)\n# See http://gmplib.org/\n\nif (GMP_INCLUDES AND GMP_LIBRARIES)\n  set(GMP_FIND_QUIETLY TRUE)\nendif (GMP_INCLUDES AND GMP_LIBRARIES)\n\nfind_path(GMP_INCLUDES\n  NAMES\n  gmp.h\n  PATHS\n  $ENV{GMPDIR}\n  ${INCLUDE_INSTALL_DIR}\n)\n\nfind_library(GMP_LIBRARIES gmp PATHS $ENV{GMPDIR} ${LIB_INSTALL_DIR})\n\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(GMP DEFAULT_MSG\n                                  GMP_INCLUDES GMP_LIBRARIES)\nmark_as_advanced(GMP_INCLUDES GMP_LIBRARIES)\n"
  },
  {
    "path": "include/eigen3/cmake/FindGSL.cmake",
    "content": "# Try to find gnu scientific library GSL\n# See \n# http://www.gnu.org/software/gsl/  and\n# http://gnuwin32.sourceforge.net/packages/gsl.htm\n#\n# Once run this will define: \n# \n# GSL_FOUND       = system has GSL lib\n#\n# GSL_LIBRARIES   = full path to the libraries\n#    on Unix/Linux with additional linker flags from \"gsl-config --libs\"\n# \n# CMAKE_GSL_CXX_FLAGS  = Unix compiler flags for GSL, essentially \"`gsl-config --cxxflags`\"\n#\n# GSL_INCLUDE_DIR      = where to find headers \n#\n# GSL_LINK_DIRECTORIES = link directories, useful for rpath on Unix\n# GSL_EXE_LINKER_FLAGS = rpath on Unix\n#\n# Felix Woelk 07/2004\n# Jan Woetzel\n#\n# www.mip.informatik.uni-kiel.de\n# --------------------------------\n\nIF(WIN32)\n  # JW tested with gsl-1.8, Windows XP, MSVS 7.1\n  SET(GSL_POSSIBLE_ROOT_DIRS\n    ${GSL_ROOT_DIR}\n    $ENV{GSL_ROOT_DIR}\n    ${GSL_DIR}\n    ${GSL_HOME}    \n    $ENV{GSL_DIR}\n    $ENV{GSL_HOME}\n    $ENV{EXTRA}\n    \"C:/Program Files/GnuWin32\"\n    )\n  FIND_PATH(GSL_INCLUDE_DIR\n    NAMES gsl/gsl_cdf.h gsl/gsl_randist.h\n    PATHS ${GSL_POSSIBLE_ROOT_DIRS}\n    PATH_SUFFIXES include\n    DOC \"GSL header include dir\"\n    )\n  \n  FIND_LIBRARY(GSL_GSL_LIBRARY\n    NAMES libgsl.dll.a gsl libgsl\n    PATHS  ${GSL_POSSIBLE_ROOT_DIRS}\n    PATH_SUFFIXES lib\n    DOC \"GSL library\" )\n  \n  if(NOT GSL_GSL_LIBRARY)\n\tFIND_FILE(GSL_GSL_LIBRARY\n\t\tNAMES libgsl.dll.a\n\t\tPATHS  ${GSL_POSSIBLE_ROOT_DIRS}\n\t\tPATH_SUFFIXES lib\n\t\tDOC \"GSL library\")\n  endif(NOT GSL_GSL_LIBRARY)\n  \n  FIND_LIBRARY(GSL_GSLCBLAS_LIBRARY\n    NAMES libgslcblas.dll.a gslcblas libgslcblas\n    PATHS  ${GSL_POSSIBLE_ROOT_DIRS}\n    PATH_SUFFIXES lib\n    DOC \"GSL cblas library dir\" )\n  \n  if(NOT GSL_GSLCBLAS_LIBRARY)\n\tFIND_FILE(GSL_GSLCBLAS_LIBRARY\n\t\tNAMES libgslcblas.dll.a\n\t\tPATHS  ${GSL_POSSIBLE_ROOT_DIRS}\n\t\tPATH_SUFFIXES lib\n\t\tDOC \"GSL library\")\n  endif(NOT GSL_GSLCBLAS_LIBRARY)\n  \n  SET(GSL_LIBRARIES ${GSL_GSL_LIBRARY})\n\n  #MESSAGE(\"DBG\\n\"\n  #  \"GSL_GSL_LIBRARY=${GSL_GSL_LIBRARY}\\n\"\n  #  \"GSL_GSLCBLAS_LIBRARY=${GSL_GSLCBLAS_LIBRARY}\\n\"\n  #  \"GSL_LIBRARIES=${GSL_LIBRARIES}\")\n\n\nELSE(WIN32)\n  \n  IF(UNIX) \n    SET(GSL_CONFIG_PREFER_PATH \n      \"$ENV{GSL_DIR}/bin\"\n      \"$ENV{GSL_DIR}\"\n      \"$ENV{GSL_HOME}/bin\" \n      \"$ENV{GSL_HOME}\" \n      CACHE STRING \"preferred path to GSL (gsl-config)\")\n    FIND_PROGRAM(GSL_CONFIG gsl-config\n      ${GSL_CONFIG_PREFER_PATH}\n      /usr/bin/\n      )\n    # MESSAGE(\"DBG GSL_CONFIG ${GSL_CONFIG}\")\n    \n    IF (GSL_CONFIG) \n      # set CXXFLAGS to be fed into CXX_FLAGS by the user:\n      SET(GSL_CXX_FLAGS \"`${GSL_CONFIG} --cflags`\")\n      \n      # set INCLUDE_DIRS to prefix+include\n      EXEC_PROGRAM(${GSL_CONFIG}\n        ARGS --prefix\n        OUTPUT_VARIABLE GSL_PREFIX)\n      SET(GSL_INCLUDE_DIR ${GSL_PREFIX}/include CACHE STRING INTERNAL)\n\n      # set link libraries and link flags\n      #SET(GSL_LIBRARIES \"`${GSL_CONFIG} --libs`\")\n      EXEC_PROGRAM(${GSL_CONFIG}\n        ARGS --libs\n        OUTPUT_VARIABLE GSL_LIBRARIES )\n        \n      # extract link dirs for rpath  \n      EXEC_PROGRAM(${GSL_CONFIG}\n        ARGS --libs\n        OUTPUT_VARIABLE GSL_CONFIG_LIBS )\n      \n      # extract version\n      EXEC_PROGRAM(${GSL_CONFIG}\n        ARGS --version\n        OUTPUT_VARIABLE GSL_FULL_VERSION )\n      \n      # split version as major/minor\n      STRING(REGEX MATCH \"(.)\\\\..*\" GSL_VERSION_MAJOR_ \"${GSL_FULL_VERSION}\")\n      SET(GSL_VERSION_MAJOR ${CMAKE_MATCH_1})\n      STRING(REGEX MATCH \".\\\\.(.*)\" GSL_VERSION_MINOR_ \"${GSL_FULL_VERSION}\")\n      SET(GSL_VERSION_MINOR ${CMAKE_MATCH_1})\n\n      # split off the link dirs (for rpath)\n      # use regular expression to match wildcard equivalent \"-L*<endchar>\"\n      # with <endchar> is a space or a semicolon\n      STRING(REGEX MATCHALL \"[-][L]([^ ;])+\" \n        GSL_LINK_DIRECTORIES_WITH_PREFIX \n        \"${GSL_CONFIG_LIBS}\" )\n      #      MESSAGE(\"DBG  GSL_LINK_DIRECTORIES_WITH_PREFIX=${GSL_LINK_DIRECTORIES_WITH_PREFIX}\")\n\n      # remove prefix -L because we need the pure directory for LINK_DIRECTORIES\n      \n      IF (GSL_LINK_DIRECTORIES_WITH_PREFIX)\n        STRING(REGEX REPLACE \"[-][L]\" \"\" GSL_LINK_DIRECTORIES ${GSL_LINK_DIRECTORIES_WITH_PREFIX} )\n      ENDIF (GSL_LINK_DIRECTORIES_WITH_PREFIX)\n      SET(GSL_EXE_LINKER_FLAGS \"-Wl,-rpath,${GSL_LINK_DIRECTORIES}\" CACHE STRING INTERNAL)\n      #      MESSAGE(\"DBG  GSL_LINK_DIRECTORIES=${GSL_LINK_DIRECTORIES}\")\n      #      MESSAGE(\"DBG  GSL_EXE_LINKER_FLAGS=${GSL_EXE_LINKER_FLAGS}\")\n\n      #      ADD_DEFINITIONS(\"-DHAVE_GSL\")\n      #      SET(GSL_DEFINITIONS \"-DHAVE_GSL\")\n      MARK_AS_ADVANCED(\n        GSL_CXX_FLAGS\n        GSL_INCLUDE_DIR\n        GSL_LIBRARIES\n        GSL_LINK_DIRECTORIES\n        GSL_DEFINITIONS\n        )\n      MESSAGE(STATUS \"Using GSL from ${GSL_PREFIX}\")\n      \n    ELSE(GSL_CONFIG)\n      MESSAGE(\"FindGSL.cmake: gsl-config not found. Please set it manually. GSL_CONFIG=${GSL_CONFIG}\")\n    ENDIF(GSL_CONFIG)\n\n  ENDIF(UNIX)\nENDIF(WIN32)\n\n\nIF(GSL_LIBRARIES)\n  IF(GSL_INCLUDE_DIR OR GSL_CXX_FLAGS)\n\n    SET(GSL_FOUND 1)\n    \n  ENDIF(GSL_INCLUDE_DIR OR GSL_CXX_FLAGS)\nENDIF(GSL_LIBRARIES)\n"
  },
  {
    "path": "include/eigen3/cmake/FindGoogleHash.cmake",
    "content": "\nif (GOOGLEHASH_INCLUDES AND GOOGLEHASH_LIBRARIES)\n  set(GOOGLEHASH_FIND_QUIETLY TRUE)\nendif (GOOGLEHASH_INCLUDES AND GOOGLEHASH_LIBRARIES)\n\nfind_path(GOOGLEHASH_INCLUDES\n  NAMES\n  google/dense_hash_map\n  PATHS\n  ${INCLUDE_INSTALL_DIR}\n)\n\nif(GOOGLEHASH_INCLUDES)\n  # let's make sure it compiles with the current compiler\n  file(WRITE ${CMAKE_BINARY_DIR}/googlehash_test.cpp\n  \"#include <google/sparse_hash_map>\\n#include <google/dense_hash_map>\\nint main(int argc, char** argv) { google::dense_hash_map<int,float> a; google::sparse_hash_map<int,float> b; return 0;}\\n\")\n  try_compile(GOOGLEHASH_COMPILE ${CMAKE_BINARY_DIR} ${CMAKE_BINARY_DIR}/googlehash_test.cpp OUTPUT_VARIABLE GOOGLEHASH_COMPILE_RESULT)\nendif(GOOGLEHASH_INCLUDES)\n\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(GOOGLEHASH DEFAULT_MSG GOOGLEHASH_INCLUDES GOOGLEHASH_COMPILE)\n\nmark_as_advanced(GOOGLEHASH_INCLUDES)\n"
  },
  {
    "path": "include/eigen3/cmake/FindHWLOC.cmake",
    "content": "###\n#\n# @copyright (c) 2009-2014 The University of Tennessee and The University\n#                          of Tennessee Research Foundation.\n#                          All rights reserved.\n# @copyright (c) 2012-2014 Inria. All rights reserved.\n# @copyright (c) 2012-2014 Bordeaux INP, CNRS (LaBRI UMR 5800), Inria, Univ. Bordeaux. All rights reserved.\n#\n###\n#\n# - Find HWLOC include dirs and libraries\n# Use this module by invoking find_package with the form:\n#  find_package(HWLOC\n#               [REQUIRED]) # Fail with error if hwloc is not found\n#\n# This module finds headers and hwloc library.\n# Results are reported in variables:\n#  HWLOC_FOUND           - True if headers and requested libraries were found\n#  HWLOC_INCLUDE_DIRS    - hwloc include directories\n#  HWLOC_LIBRARY_DIRS    - Link directories for hwloc libraries\n#  HWLOC_LIBRARIES       - hwloc component libraries to be linked\n#\n# The user can give specific paths where to find the libraries adding cmake\n# options at configure (ex: cmake path/to/project -DHWLOC_DIR=path/to/hwloc):\n#  HWLOC_DIR             - Where to find the base directory of hwloc\n#  HWLOC_INCDIR          - Where to find the header files\n#  HWLOC_LIBDIR          - Where to find the library files\n# The module can also look for the following environment variables if paths\n# are not given as cmake variable: HWLOC_DIR, HWLOC_INCDIR, HWLOC_LIBDIR\n\n#=============================================================================\n# Copyright 2012-2013 Inria\n# Copyright 2012-2013 Emmanuel Agullo\n# Copyright 2012-2013 Mathieu Faverge\n# Copyright 2012      Cedric Castagnede\n# Copyright 2013      Florent Pruvost\n#\n# Distributed under the OSI-approved BSD License (the \"License\");\n# see accompanying file MORSE-Copyright.txt for details.\n#\n# This software is distributed WITHOUT ANY WARRANTY; without even the\n# implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.\n# See the License for more information.\n#=============================================================================\n# (To distribute this file outside of Morse, substitute the full\n#  License text for the above reference.)\n\ninclude(CheckStructHasMember)\ninclude(CheckCSourceCompiles)\n\nif (NOT HWLOC_FOUND)\n  set(HWLOC_DIR \"\" CACHE PATH \"Installation directory of HWLOC library\")\n  if (NOT HWLOC_FIND_QUIETLY)\n    message(STATUS \"A cache variable, namely HWLOC_DIR, has been set to specify the install directory of HWLOC\")\n  endif()\nendif()\n\nset(ENV_HWLOC_DIR \"$ENV{HWLOC_DIR}\")\nset(ENV_HWLOC_INCDIR \"$ENV{HWLOC_INCDIR}\")\nset(ENV_HWLOC_LIBDIR \"$ENV{HWLOC_LIBDIR}\")\nset(HWLOC_GIVEN_BY_USER \"FALSE\")\nif ( HWLOC_DIR OR ( HWLOC_INCDIR AND HWLOC_LIBDIR) OR ENV_HWLOC_DIR OR (ENV_HWLOC_INCDIR AND ENV_HWLOC_LIBDIR) )\n  set(HWLOC_GIVEN_BY_USER \"TRUE\")\nendif()\n\n# Optionally use pkg-config to detect include/library dirs (if pkg-config is available)\n# -------------------------------------------------------------------------------------\ninclude(FindPkgConfig)\nfind_package(PkgConfig QUIET)\nif( PKG_CONFIG_EXECUTABLE AND NOT HWLOC_GIVEN_BY_USER )\n\n  pkg_search_module(HWLOC hwloc)\n  if (NOT HWLOC_FIND_QUIETLY)\n    if (HWLOC_FOUND AND HWLOC_LIBRARIES)\n      message(STATUS \"Looking for HWLOC - found using PkgConfig\")\n      #if(NOT HWLOC_INCLUDE_DIRS)\n      #    message(\"${Magenta}HWLOC_INCLUDE_DIRS is empty using PkgConfig.\"\n      #        \"Perhaps the path to hwloc headers is already present in your\"\n      #        \"C(PLUS)_INCLUDE_PATH environment variable.${ColourReset}\")\n      #endif()\n    else()\n      message(STATUS \"${Magenta}Looking for HWLOC - not found using PkgConfig.\"\n\t\"\\n   Perhaps you should add the directory containing hwloc.pc to\"\n\t\"\\n   the PKG_CONFIG_PATH environment variable.${ColourReset}\")\n    endif()\n  endif()\n\nendif( PKG_CONFIG_EXECUTABLE AND NOT HWLOC_GIVEN_BY_USER )\n\nif( (NOT PKG_CONFIG_EXECUTABLE) OR (PKG_CONFIG_EXECUTABLE AND NOT HWLOC_FOUND) OR (HWLOC_GIVEN_BY_USER) )\n\n  if (NOT HWLOC_FIND_QUIETLY)\n    message(STATUS \"Looking for HWLOC - PkgConfig not used\")\n  endif()\n\n  # Looking for include\n  # -------------------\n\n  # Add system include paths to search include\n  # ------------------------------------------\n  unset(_inc_env)\n  if(ENV_HWLOC_INCDIR)\n    list(APPEND _inc_env \"${ENV_HWLOC_INCDIR}\")\n  elseif(ENV_HWLOC_DIR)\n    list(APPEND _inc_env \"${ENV_HWLOC_DIR}\")\n    list(APPEND _inc_env \"${ENV_HWLOC_DIR}/include\")\n    list(APPEND _inc_env \"${ENV_HWLOC_DIR}/include/hwloc\")\n  else()\n    if(WIN32)\n      string(REPLACE \":\" \";\" _inc_env \"$ENV{INCLUDE}\")\n    else()\n      string(REPLACE \":\" \";\" _path_env \"$ENV{INCLUDE}\")\n      list(APPEND _inc_env \"${_path_env}\")\n      string(REPLACE \":\" \";\" _path_env \"$ENV{C_INCLUDE_PATH}\")\n      list(APPEND _inc_env \"${_path_env}\")\n      string(REPLACE \":\" \";\" _path_env \"$ENV{CPATH}\")\n      list(APPEND _inc_env \"${_path_env}\")\n      string(REPLACE \":\" \";\" _path_env \"$ENV{INCLUDE_PATH}\")\n      list(APPEND _inc_env \"${_path_env}\")\n    endif()\n  endif()\n  list(APPEND _inc_env \"${CMAKE_PLATFORM_IMPLICIT_INCLUDE_DIRECTORIES}\")\n  list(APPEND _inc_env \"${CMAKE_C_IMPLICIT_INCLUDE_DIRECTORIES}\")\n  list(REMOVE_DUPLICATES _inc_env)\n\n  # set paths where to look for\n  set(PATH_TO_LOOK_FOR \"${_inc_env}\")\n\n  # Try to find the hwloc header in the given paths\n  # -------------------------------------------------\n  # call cmake macro to find the header path\n  if(HWLOC_INCDIR)\n    set(HWLOC_hwloc.h_DIRS \"HWLOC_hwloc.h_DIRS-NOTFOUND\")\n    find_path(HWLOC_hwloc.h_DIRS\n      NAMES hwloc.h\n      HINTS ${HWLOC_INCDIR})\n  else()\n    if(HWLOC_DIR)\n      set(HWLOC_hwloc.h_DIRS \"HWLOC_hwloc.h_DIRS-NOTFOUND\")\n      find_path(HWLOC_hwloc.h_DIRS\n\tNAMES hwloc.h\n\tHINTS ${HWLOC_DIR}\n\tPATH_SUFFIXES \"include\" \"include/hwloc\")\n    else()\n      set(HWLOC_hwloc.h_DIRS \"HWLOC_hwloc.h_DIRS-NOTFOUND\")\n      find_path(HWLOC_hwloc.h_DIRS\n\tNAMES hwloc.h\n\tHINTS ${PATH_TO_LOOK_FOR}\n\tPATH_SUFFIXES \"hwloc\")\n    endif()\n  endif()\n  mark_as_advanced(HWLOC_hwloc.h_DIRS)\n\n  # Add path to cmake variable\n  # ------------------------------------\n  if (HWLOC_hwloc.h_DIRS)\n    set(HWLOC_INCLUDE_DIRS \"${HWLOC_hwloc.h_DIRS}\")\n  else ()\n    set(HWLOC_INCLUDE_DIRS \"HWLOC_INCLUDE_DIRS-NOTFOUND\")\n    if(NOT HWLOC_FIND_QUIETLY)\n      message(STATUS \"Looking for hwloc -- hwloc.h not found\")\n    endif()\n  endif ()\n\n  if (HWLOC_INCLUDE_DIRS)\n    list(REMOVE_DUPLICATES HWLOC_INCLUDE_DIRS)\n  endif ()\n\n\n  # Looking for lib\n  # ---------------\n\n  # Add system library paths to search lib\n  # --------------------------------------\n  unset(_lib_env)\n  if(ENV_HWLOC_LIBDIR)\n    list(APPEND _lib_env \"${ENV_HWLOC_LIBDIR}\")\n  elseif(ENV_HWLOC_DIR)\n    list(APPEND _lib_env \"${ENV_HWLOC_DIR}\")\n    list(APPEND _lib_env \"${ENV_HWLOC_DIR}/lib\")\n  else()\n    if(WIN32)\n      string(REPLACE \":\" \";\" _lib_env \"$ENV{LIB}\")\n    else()\n      if(APPLE)\n\tstring(REPLACE \":\" \";\" _lib_env \"$ENV{DYLD_LIBRARY_PATH}\")\n      else()\n\tstring(REPLACE \":\" \";\" _lib_env \"$ENV{LD_LIBRARY_PATH}\")\n      endif()\n      list(APPEND _lib_env \"${CMAKE_PLATFORM_IMPLICIT_LINK_DIRECTORIES}\")\n      list(APPEND _lib_env \"${CMAKE_C_IMPLICIT_LINK_DIRECTORIES}\")\n    endif()\n  endif()\n  list(REMOVE_DUPLICATES _lib_env)\n\n  # set paths where to look for\n  set(PATH_TO_LOOK_FOR \"${_lib_env}\")\n\n  # Try to find the hwloc lib in the given paths\n  # ----------------------------------------------\n\n  # call cmake macro to find the lib path\n  if(HWLOC_LIBDIR)\n    set(HWLOC_hwloc_LIBRARY \"HWLOC_hwloc_LIBRARY-NOTFOUND\")\n    find_library(HWLOC_hwloc_LIBRARY\n      NAMES hwloc\n      HINTS ${HWLOC_LIBDIR})\n  else()\n    if(HWLOC_DIR)\n      set(HWLOC_hwloc_LIBRARY \"HWLOC_hwloc_LIBRARY-NOTFOUND\")\n      find_library(HWLOC_hwloc_LIBRARY\n\tNAMES hwloc\n\tHINTS ${HWLOC_DIR}\n\tPATH_SUFFIXES lib lib32 lib64)\n    else()\n      set(HWLOC_hwloc_LIBRARY \"HWLOC_hwloc_LIBRARY-NOTFOUND\")\n      find_library(HWLOC_hwloc_LIBRARY\n\tNAMES hwloc\n\tHINTS ${PATH_TO_LOOK_FOR})\n    endif()\n  endif()\n  mark_as_advanced(HWLOC_hwloc_LIBRARY)\n\n  # If found, add path to cmake variable\n  # ------------------------------------\n  if (HWLOC_hwloc_LIBRARY)\n    get_filename_component(hwloc_lib_path ${HWLOC_hwloc_LIBRARY} PATH)\n    # set cmake variables (respects naming convention)\n    set(HWLOC_LIBRARIES    \"${HWLOC_hwloc_LIBRARY}\")\n    set(HWLOC_LIBRARY_DIRS \"${hwloc_lib_path}\")\n  else ()\n    set(HWLOC_LIBRARIES    \"HWLOC_LIBRARIES-NOTFOUND\")\n    set(HWLOC_LIBRARY_DIRS \"HWLOC_LIBRARY_DIRS-NOTFOUND\")\n    if(NOT HWLOC_FIND_QUIETLY)\n      message(STATUS \"Looking for hwloc -- lib hwloc not found\")\n    endif()\n  endif ()\n\n  if (HWLOC_LIBRARY_DIRS)\n    list(REMOVE_DUPLICATES HWLOC_LIBRARY_DIRS)\n  endif ()\n\n  # check a function to validate the find\n  if(HWLOC_LIBRARIES)\n\n    set(REQUIRED_INCDIRS)\n    set(REQUIRED_LIBDIRS)\n    set(REQUIRED_LIBS)\n\n    # HWLOC\n    if (HWLOC_INCLUDE_DIRS)\n      set(REQUIRED_INCDIRS \"${HWLOC_INCLUDE_DIRS}\")\n    endif()\n    if (HWLOC_LIBRARY_DIRS)\n      set(REQUIRED_LIBDIRS \"${HWLOC_LIBRARY_DIRS}\")\n    endif()\n    set(REQUIRED_LIBS \"${HWLOC_LIBRARIES}\")\n\n    # set required libraries for link\n    set(CMAKE_REQUIRED_INCLUDES \"${REQUIRED_INCDIRS}\")\n    set(CMAKE_REQUIRED_LIBRARIES)\n    foreach(lib_dir ${REQUIRED_LIBDIRS})\n      list(APPEND CMAKE_REQUIRED_LIBRARIES \"-L${lib_dir}\")\n    endforeach()\n    list(APPEND CMAKE_REQUIRED_LIBRARIES \"${REQUIRED_LIBS}\")\n    string(REGEX REPLACE \"^ -\" \"-\" CMAKE_REQUIRED_LIBRARIES \"${CMAKE_REQUIRED_LIBRARIES}\")\n\n    # test link\n    unset(HWLOC_WORKS CACHE)\n    include(CheckFunctionExists)\n    check_function_exists(hwloc_topology_init HWLOC_WORKS)\n    mark_as_advanced(HWLOC_WORKS)\n\n    if(NOT HWLOC_WORKS)\n      if(NOT HWLOC_FIND_QUIETLY)\n\tmessage(STATUS \"Looking for hwloc : test of hwloc_topology_init with hwloc library fails\")\n\tmessage(STATUS \"CMAKE_REQUIRED_LIBRARIES: ${CMAKE_REQUIRED_LIBRARIES}\")\n\tmessage(STATUS \"CMAKE_REQUIRED_INCLUDES: ${CMAKE_REQUIRED_INCLUDES}\")\n\tmessage(STATUS \"Check in CMakeFiles/CMakeError.log to figure out why it fails\")\n      endif()\n    endif()\n    set(CMAKE_REQUIRED_INCLUDES)\n    set(CMAKE_REQUIRED_FLAGS)\n    set(CMAKE_REQUIRED_LIBRARIES)\n  endif(HWLOC_LIBRARIES)\n\nendif( (NOT PKG_CONFIG_EXECUTABLE) OR (PKG_CONFIG_EXECUTABLE AND NOT HWLOC_FOUND) OR (HWLOC_GIVEN_BY_USER) )\n\nif (HWLOC_LIBRARIES)\n  if (HWLOC_LIBRARY_DIRS)\n    list(GET HWLOC_LIBRARY_DIRS 0 first_lib_path)\n  else()\n    list(GET HWLOC_LIBRARIES 0 first_lib)\n    get_filename_component(first_lib_path \"${first_lib}\" PATH)\n  endif()\n  if (${first_lib_path} MATCHES \"/lib(32|64)?$\")\n    string(REGEX REPLACE \"/lib(32|64)?$\" \"\" not_cached_dir \"${first_lib_path}\")\n    set(HWLOC_DIR_FOUND \"${not_cached_dir}\" CACHE PATH \"Installation directory of HWLOC library\" FORCE)\n  else()\n    set(HWLOC_DIR_FOUND \"${first_lib_path}\" CACHE PATH \"Installation directory of HWLOC library\" FORCE)\n  endif()\nendif()\nmark_as_advanced(HWLOC_DIR)\nmark_as_advanced(HWLOC_DIR_FOUND)\n\n# check that HWLOC has been found\n# -------------------------------\ninclude(FindPackageHandleStandardArgs)\nif (PKG_CONFIG_EXECUTABLE AND HWLOC_FOUND)\n  find_package_handle_standard_args(HWLOC DEFAULT_MSG\n    HWLOC_LIBRARIES)\nelse()\n  find_package_handle_standard_args(HWLOC DEFAULT_MSG\n    HWLOC_LIBRARIES\n    HWLOC_WORKS)\nendif()\n\nif (HWLOC_FOUND)\n  set(HWLOC_SAVE_CMAKE_REQUIRED_INCLUDES ${CMAKE_REQUIRED_INCLUDES})\n  list(APPEND CMAKE_REQUIRED_INCLUDES ${HWLOC_INCLUDE_DIRS})\n\n  # test headers to guess the version\n  check_struct_has_member( \"struct hwloc_obj\" parent hwloc.h HAVE_HWLOC_PARENT_MEMBER )\n  check_struct_has_member( \"struct hwloc_cache_attr_s\" size hwloc.h HAVE_HWLOC_CACHE_ATTR )\n  check_c_source_compiles( \"#include <hwloc.h>\n\t    int main(void) { hwloc_obj_t o; o->type = HWLOC_OBJ_PU; return 0;}\" HAVE_HWLOC_OBJ_PU)\n  include(CheckLibraryExists)\n  check_library_exists(${HWLOC_LIBRARIES} hwloc_bitmap_free \"\" HAVE_HWLOC_BITMAP)\n\n  set(CMAKE_REQUIRED_INCLUDES ${HWLOC_SAVE_CMAKE_REQUIRED_INCLUDES})\nendif()\n"
  },
  {
    "path": "include/eigen3/cmake/FindLAPACK.cmake",
    "content": "# Find LAPACK library\n#\n# This module finds an installed library that implements the LAPACK\n# linear-algebra interface (see http://www.netlib.org/lapack/).\n# The approach follows mostly that taken for the autoconf macro file, acx_lapack.m4\n# (distributed at http://ac-archive.sourceforge.net/ac-archive/acx_lapack.html).\n#\n# This module sets the following variables:\n#  LAPACK_FOUND - set to true if a library implementing the LAPACK interface\n#    is found\n#  LAPACK_INCLUDE_DIR - Directories containing the LAPACK header files\n#  LAPACK_DEFINITIONS - Compilation options to use LAPACK\n#  LAPACK_LINKER_FLAGS - Linker flags to use LAPACK (excluding -l\n#    and -L).\n#  LAPACK_LIBRARIES_DIR - Directories containing the LAPACK libraries.\n#     May be null if LAPACK_LIBRARIES contains libraries name using full path.\n#  LAPACK_LIBRARIES - List of libraries to link against LAPACK interface.\n#     May be null if the compiler supports auto-link (e.g. VC++).\n#  LAPACK_USE_FILE - The name of the cmake module to include to compile\n#     applications or libraries using LAPACK.\n#\n# This module was modified by CGAL team:\n# - find libraries for a C++ compiler, instead of Fortran\n# - added LAPACK_INCLUDE_DIR, LAPACK_DEFINITIONS and LAPACK_LIBRARIES_DIR\n# - removed LAPACK95_LIBRARIES\n\n\ninclude(CheckFunctionExists)\n\n# This macro checks for the existence of the combination of fortran libraries\n# given by _list.  If the combination is found, this macro checks (using the\n# check_function_exists macro) whether can link against that library\n# combination using the name of a routine given by _name using the linker\n# flags given by _flags.  If the combination of libraries is found and passes\n# the link test, LIBRARIES is set to the list of complete library paths that\n# have been found and DEFINITIONS to the required definitions.\n# Otherwise, LIBRARIES is set to FALSE.\n# N.B. _prefix is the prefix applied to the names of all cached variables that\n# are generated internally and marked advanced by this macro.\nmacro(check_lapack_libraries DEFINITIONS LIBRARIES _prefix _name _flags _list _blas _path)\n  #message(\"DEBUG: check_lapack_libraries(${_list} in ${_path} with ${_blas})\")\n\n  # Check for the existence of the libraries given by _list\n  set(_libraries_found TRUE)\n  set(_libraries_work FALSE)\n  set(${DEFINITIONS} \"\")\n  set(${LIBRARIES} \"\")\n  set(_combined_name)\n  foreach(_library ${_list})\n    set(_combined_name ${_combined_name}_${_library})\n\n    if(_libraries_found)\n      # search first in ${_path}\n      find_library(${_prefix}_${_library}_LIBRARY\n                  NAMES ${_library}\n                  PATHS ${_path} NO_DEFAULT_PATH\n                  )\n      # if not found, search in environment variables and system\n      if ( WIN32 )\n        find_library(${_prefix}_${_library}_LIBRARY\n                    NAMES ${_library}\n                    PATHS ENV LIB\n                    )\n      elseif ( APPLE )\n        find_library(${_prefix}_${_library}_LIBRARY\n                    NAMES ${_library}\n                    PATHS /usr/local/lib /usr/lib /usr/local/lib64 /usr/lib64 ENV DYLD_LIBRARY_PATH\n                    )\n      else ()\n        find_library(${_prefix}_${_library}_LIBRARY\n                    NAMES ${_library}\n                    PATHS /usr/local/lib /usr/lib /usr/local/lib64 /usr/lib64 ENV LD_LIBRARY_PATH\n                    )\n      endif()\n      mark_as_advanced(${_prefix}_${_library}_LIBRARY)\n      set(${LIBRARIES} ${${LIBRARIES}} ${${_prefix}_${_library}_LIBRARY})\n      set(_libraries_found ${${_prefix}_${_library}_LIBRARY})\n    endif(_libraries_found)\n  endforeach(_library ${_list})\n  if(_libraries_found)\n    set(_libraries_found ${${LIBRARIES}})\n  endif()\n\n  # Test this combination of libraries with the Fortran/f2c interface.\n  # We test the Fortran interface first as it is well standardized.\n  if(_libraries_found AND NOT _libraries_work)\n    set(${DEFINITIONS}  \"-D${_prefix}_USE_F2C\")\n    set(${LIBRARIES}    ${_libraries_found})\n    # Some C++ linkers require the f2c library to link with Fortran libraries.\n    # I do not know which ones, thus I just add the f2c library if it is available.\n    find_package( F2C QUIET )\n    if ( F2C_FOUND )\n      set(${DEFINITIONS}  ${${DEFINITIONS}} ${F2C_DEFINITIONS})\n      set(${LIBRARIES}    ${${LIBRARIES}} ${F2C_LIBRARIES})\n    endif()\n    set(CMAKE_REQUIRED_DEFINITIONS  ${${DEFINITIONS}})\n    set(CMAKE_REQUIRED_LIBRARIES    ${_flags} ${${LIBRARIES}} ${_blas})\n    #message(\"DEBUG: CMAKE_REQUIRED_DEFINITIONS = ${CMAKE_REQUIRED_DEFINITIONS}\")\n    #message(\"DEBUG: CMAKE_REQUIRED_LIBRARIES = ${CMAKE_REQUIRED_LIBRARIES}\")\n    # Check if function exists with f2c calling convention (ie a trailing underscore)\n    check_function_exists(${_name}_ ${_prefix}_${_name}_${_combined_name}_f2c_WORKS)\n    set(CMAKE_REQUIRED_DEFINITIONS} \"\")\n    set(CMAKE_REQUIRED_LIBRARIES    \"\")\n    mark_as_advanced(${_prefix}_${_name}_${_combined_name}_f2c_WORKS)\n    set(_libraries_work ${${_prefix}_${_name}_${_combined_name}_f2c_WORKS})\n  endif(_libraries_found AND NOT _libraries_work)\n\n  # If not found, test this combination of libraries with a C interface.\n  # A few implementations (ie ACML) provide a C interface. Unfortunately, there is no standard.\n  if(_libraries_found AND NOT _libraries_work)\n    set(${DEFINITIONS} \"\")\n    set(${LIBRARIES}   ${_libraries_found})\n    set(CMAKE_REQUIRED_DEFINITIONS \"\")\n    set(CMAKE_REQUIRED_LIBRARIES   ${_flags} ${${LIBRARIES}} ${_blas})\n    #message(\"DEBUG: CMAKE_REQUIRED_LIBRARIES = ${CMAKE_REQUIRED_LIBRARIES}\")\n    check_function_exists(${_name} ${_prefix}_${_name}${_combined_name}_WORKS)\n    set(CMAKE_REQUIRED_LIBRARIES \"\")\n    mark_as_advanced(${_prefix}_${_name}${_combined_name}_WORKS)\n    set(_libraries_work ${${_prefix}_${_name}${_combined_name}_WORKS})\n  endif(_libraries_found AND NOT _libraries_work)\n\n  # on failure\n  if(NOT _libraries_work)\n    set(${DEFINITIONS} \"\")\n    set(${LIBRARIES}   FALSE)\n  endif()\n  #message(\"DEBUG: ${DEFINITIONS} = ${${DEFINITIONS}}\")\n  #message(\"DEBUG: ${LIBRARIES} = ${${LIBRARIES}}\")\nendmacro(check_lapack_libraries)\n\n\n#\n# main\n#\n\n# LAPACK requires BLAS\nif(LAPACK_FIND_QUIETLY OR NOT LAPACK_FIND_REQUIRED)\n  find_package(BLAS)\nelse()\n  find_package(BLAS REQUIRED)\nendif()\n\nif (NOT BLAS_FOUND)\n\n  message(STATUS \"LAPACK requires BLAS.\")\n  set(LAPACK_FOUND FALSE)\n\n# Is it already configured?\nelseif (LAPACK_LIBRARIES_DIR OR LAPACK_LIBRARIES)\n\n  set(LAPACK_FOUND TRUE)\n\nelse()\n\n  # reset variables\n  set( LAPACK_INCLUDE_DIR \"\" )\n  set( LAPACK_DEFINITIONS \"\" )\n  set( LAPACK_LINKER_FLAGS \"\" ) # unused (yet)\n  set( LAPACK_LIBRARIES \"\" )\n  set( LAPACK_LIBRARIES_DIR \"\" )\n\n    #\n    # If Unix, search for LAPACK function in possible libraries\n    #\n\n    #intel mkl lapack?\n    if(NOT LAPACK_LIBRARIES)\n      check_lapack_libraries(\n      LAPACK_DEFINITIONS\n      LAPACK_LIBRARIES\n      LAPACK\n      cheev\n      \"\"\n      \"mkl_lapack\"\n      \"${BLAS_LIBRARIES}\"\n      \"${CGAL_TAUCS_LIBRARIES_DIR} ENV LAPACK_LIB_DIR\"\n      )\n    endif()\n\n    #acml lapack?\n    if(NOT LAPACK_LIBRARIES)\n      check_lapack_libraries(\n      LAPACK_DEFINITIONS\n      LAPACK_LIBRARIES\n      LAPACK\n      cheev\n      \"\"\n      \"acml\"\n      \"${BLAS_LIBRARIES}\"\n      \"${CGAL_TAUCS_LIBRARIES_DIR} ENV LAPACK_LIB_DIR\"\n      )\n    endif()\n\n    # Apple LAPACK library?\n    if(NOT LAPACK_LIBRARIES)\n      check_lapack_libraries(\n      LAPACK_DEFINITIONS\n      LAPACK_LIBRARIES\n      LAPACK\n      cheev\n      \"\"\n      \"Accelerate\"\n      \"${BLAS_LIBRARIES}\"\n      \"${CGAL_TAUCS_LIBRARIES_DIR} ENV LAPACK_LIB_DIR\"\n      )\n    endif()\n\n    if ( NOT LAPACK_LIBRARIES )\n      check_lapack_libraries(\n      LAPACK_DEFINITIONS\n      LAPACK_LIBRARIES\n      LAPACK\n      cheev\n      \"\"\n      \"vecLib\"\n      \"${BLAS_LIBRARIES}\"\n      \"${CGAL_TAUCS_LIBRARIES_DIR} ENV LAPACK_LIB_DIR\"\n      )\n    endif ( NOT LAPACK_LIBRARIES )\n\n    # Generic LAPACK library?\n    # This configuration *must* be the last try as this library is notably slow.\n    if ( NOT LAPACK_LIBRARIES )\n      check_lapack_libraries(\n      LAPACK_DEFINITIONS\n      LAPACK_LIBRARIES\n      LAPACK\n      cheev\n      \"\"\n      \"lapack\"\n      \"${BLAS_LIBRARIES}\"\n      \"${CGAL_TAUCS_LIBRARIES_DIR} ENV LAPACK_LIB_DIR\"\n      )\n    endif()\n\n  if(LAPACK_LIBRARIES_DIR OR LAPACK_LIBRARIES)\n    set(LAPACK_FOUND TRUE)\n  else()\n    set(LAPACK_FOUND FALSE)\n  endif()\n\n  if(NOT LAPACK_FIND_QUIETLY)\n    if(LAPACK_FOUND)\n      message(STATUS \"A library with LAPACK API found.\")\n    else(LAPACK_FOUND)\n      if(LAPACK_FIND_REQUIRED)\n        message(FATAL_ERROR \"A required library with LAPACK API not found. Please specify library location.\")\n      else()\n        message(STATUS \"A library with LAPACK API not found. Please specify library location.\")\n      endif()\n    endif(LAPACK_FOUND)\n  endif(NOT LAPACK_FIND_QUIETLY)\n\n  # Add variables to cache\n  set( LAPACK_INCLUDE_DIR   \"${LAPACK_INCLUDE_DIR}\"\n                            CACHE PATH \"Directories containing the LAPACK header files\" FORCE )\n  set( LAPACK_DEFINITIONS   \"${LAPACK_DEFINITIONS}\"\n                            CACHE STRING \"Compilation options to use LAPACK\" FORCE )\n  set( LAPACK_LINKER_FLAGS  \"${LAPACK_LINKER_FLAGS}\"\n                            CACHE STRING \"Linker flags to use LAPACK\" FORCE )\n  set( LAPACK_LIBRARIES     \"${LAPACK_LIBRARIES}\"\n                            CACHE FILEPATH \"LAPACK libraries name\" FORCE )\n  set( LAPACK_LIBRARIES_DIR \"${LAPACK_LIBRARIES_DIR}\"\n                            CACHE PATH \"Directories containing the LAPACK libraries\" FORCE )\n\n  #message(\"DEBUG: LAPACK_INCLUDE_DIR = ${LAPACK_INCLUDE_DIR}\")\n  #message(\"DEBUG: LAPACK_DEFINITIONS = ${LAPACK_DEFINITIONS}\")\n  #message(\"DEBUG: LAPACK_LINKER_FLAGS = ${LAPACK_LINKER_FLAGS}\")\n  #message(\"DEBUG: LAPACK_LIBRARIES = ${LAPACK_LIBRARIES}\")\n  #message(\"DEBUG: LAPACK_LIBRARIES_DIR = ${LAPACK_LIBRARIES_DIR}\")\n  #message(\"DEBUG: LAPACK_FOUND = ${LAPACK_FOUND}\")\n\nendif(NOT BLAS_FOUND)\n"
  },
  {
    "path": "include/eigen3/cmake/FindMPFR.cmake",
    "content": "# Try to find the MPFR library\n# See http://www.mpfr.org/\n#\n# This module supports requiring a minimum version, e.g. you can do\n#   find_package(MPFR 2.3.0)\n# to require version 2.3.0 to newer of MPFR.\n#\n# Once done this will define\n#\n#  MPFR_FOUND - system has MPFR lib with correct version\n#  MPFR_INCLUDES - the MPFR include directory\n#  MPFR_LIBRARIES - the MPFR library\n#  MPFR_VERSION - MPFR version\n\n# Copyright (c) 2006, 2007 Montel Laurent, <montel@kde.org>\n# Copyright (c) 2008, 2009 Gael Guennebaud, <g.gael@free.fr>\n# Copyright (c) 2010 Jitse Niesen, <jitse@maths.leeds.ac.uk>\n# Redistribution and use is allowed according to the terms of the BSD license.\n\n# Set MPFR_INCLUDES\n\nfind_path(MPFR_INCLUDES\n  NAMES\n  mpfr.h\n  PATHS\n  $ENV{GMPDIR}\n  ${INCLUDE_INSTALL_DIR}\n)\n\n# Set MPFR_FIND_VERSION to 1.0.0 if no minimum version is specified\n\nif(NOT MPFR_FIND_VERSION)\n  if(NOT MPFR_FIND_VERSION_MAJOR)\n    set(MPFR_FIND_VERSION_MAJOR 1)\n  endif(NOT MPFR_FIND_VERSION_MAJOR)\n  if(NOT MPFR_FIND_VERSION_MINOR)\n    set(MPFR_FIND_VERSION_MINOR 0)\n  endif(NOT MPFR_FIND_VERSION_MINOR)\n  if(NOT MPFR_FIND_VERSION_PATCH)\n    set(MPFR_FIND_VERSION_PATCH 0)\n  endif(NOT MPFR_FIND_VERSION_PATCH)\n\n  set(MPFR_FIND_VERSION \"${MPFR_FIND_VERSION_MAJOR}.${MPFR_FIND_VERSION_MINOR}.${MPFR_FIND_VERSION_PATCH}\")\nendif(NOT MPFR_FIND_VERSION)\n\n\nif(MPFR_INCLUDES)\n\n  # Set MPFR_VERSION\n  \n  file(READ \"${MPFR_INCLUDES}/mpfr.h\" _mpfr_version_header)\n  \n  string(REGEX MATCH \"define[ \\t]+MPFR_VERSION_MAJOR[ \\t]+([0-9]+)\" _mpfr_major_version_match \"${_mpfr_version_header}\")\n  set(MPFR_MAJOR_VERSION \"${CMAKE_MATCH_1}\")\n  string(REGEX MATCH \"define[ \\t]+MPFR_VERSION_MINOR[ \\t]+([0-9]+)\" _mpfr_minor_version_match \"${_mpfr_version_header}\")\n  set(MPFR_MINOR_VERSION \"${CMAKE_MATCH_1}\")\n  string(REGEX MATCH \"define[ \\t]+MPFR_VERSION_PATCHLEVEL[ \\t]+([0-9]+)\" _mpfr_patchlevel_version_match \"${_mpfr_version_header}\")\n  set(MPFR_PATCHLEVEL_VERSION \"${CMAKE_MATCH_1}\")\n  \n  set(MPFR_VERSION ${MPFR_MAJOR_VERSION}.${MPFR_MINOR_VERSION}.${MPFR_PATCHLEVEL_VERSION})\n  \n  # Check whether found version exceeds minimum version\n  \n  if(${MPFR_VERSION} VERSION_LESS ${MPFR_FIND_VERSION})\n    set(MPFR_VERSION_OK FALSE)\n    message(STATUS \"MPFR version ${MPFR_VERSION} found in ${MPFR_INCLUDES}, \"\n                   \"but at least version ${MPFR_FIND_VERSION} is required\")\n  else(${MPFR_VERSION} VERSION_LESS ${MPFR_FIND_VERSION})\n    set(MPFR_VERSION_OK TRUE)\n  endif(${MPFR_VERSION} VERSION_LESS ${MPFR_FIND_VERSION})\n\nendif(MPFR_INCLUDES)\n\n# Set MPFR_LIBRARIES\n\nfind_library(MPFR_LIBRARIES mpfr PATHS $ENV{GMPDIR} ${LIB_INSTALL_DIR})\n\n# Epilogue\n\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(MPFR DEFAULT_MSG\n                                  MPFR_INCLUDES MPFR_LIBRARIES MPFR_VERSION_OK)\nmark_as_advanced(MPFR_INCLUDES MPFR_LIBRARIES)\n"
  },
  {
    "path": "include/eigen3/cmake/FindMetis.cmake",
    "content": "###\n#\n# @copyright (c) 2009-2014 The University of Tennessee and The University\n#                          of Tennessee Research Foundation.\n#                          All rights reserved.\n# @copyright (c) 2012-2014 Inria. All rights reserved.\n# @copyright (c) 2012-2014 Bordeaux INP, CNRS (LaBRI UMR 5800), Inria, Univ. Bordeaux. All rights reserved.\n#\n###\n#\n# - Find METIS include dirs and libraries\n# Use this module by invoking find_package with the form:\n#  find_package(METIS\n#               [REQUIRED]             # Fail with error if metis is not found\n#              )\n#\n# This module finds headers and metis library.\n# Results are reported in variables:\n#  METIS_FOUND           - True if headers and requested libraries were found\n#  METIS_INCLUDE_DIRS    - metis include directories\n#  METIS_LIBRARY_DIRS    - Link directories for metis libraries\n#  METIS_LIBRARIES       - metis component libraries to be linked\n#\n# The user can give specific paths where to find the libraries adding cmake\n# options at configure (ex: cmake path/to/project -DMETIS_DIR=path/to/metis):\n#  METIS_DIR             - Where to find the base directory of metis\n#  METIS_INCDIR          - Where to find the header files\n#  METIS_LIBDIR          - Where to find the library files\n# The module can also look for the following environment variables if paths\n# are not given as cmake variable: METIS_DIR, METIS_INCDIR, METIS_LIBDIR\n\n#=============================================================================\n# Copyright 2012-2013 Inria\n# Copyright 2012-2013 Emmanuel Agullo\n# Copyright 2012-2013 Mathieu Faverge\n# Copyright 2012      Cedric Castagnede\n# Copyright 2013      Florent Pruvost\n#\n# Distributed under the OSI-approved BSD License (the \"License\");\n# see accompanying file MORSE-Copyright.txt for details.\n#\n# This software is distributed WITHOUT ANY WARRANTY; without even the\n# implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.\n# See the License for more information.\n#=============================================================================\n# (To distribute this file outside of Morse, substitute the full\n#  License text for the above reference.)\n\nif (NOT METIS_FOUND)\n  set(METIS_DIR \"\" CACHE PATH \"Installation directory of METIS library\")\n  if (NOT METIS_FIND_QUIETLY)\n    message(STATUS \"A cache variable, namely METIS_DIR, has been set to specify the install directory of METIS\")\n  endif()\nendif()\n\n# Looking for include\n# -------------------\n\n# Add system include paths to search include\n# ------------------------------------------\nunset(_inc_env)\nset(ENV_METIS_DIR \"$ENV{METIS_DIR}\")\nset(ENV_METIS_INCDIR \"$ENV{METIS_INCDIR}\")\nif(ENV_METIS_INCDIR)\n  list(APPEND _inc_env \"${ENV_METIS_INCDIR}\")\nelseif(ENV_METIS_DIR)\n  list(APPEND _inc_env \"${ENV_METIS_DIR}\")\n  list(APPEND _inc_env \"${ENV_METIS_DIR}/include\")\n  list(APPEND _inc_env \"${ENV_METIS_DIR}/include/metis\")\nelse()\n  if(WIN32)\n    string(REPLACE \":\" \";\" _inc_env \"$ENV{INCLUDE}\")\n  else()\n    string(REPLACE \":\" \";\" _path_env \"$ENV{INCLUDE}\")\n    list(APPEND _inc_env \"${_path_env}\")\n    string(REPLACE \":\" \";\" _path_env \"$ENV{C_INCLUDE_PATH}\")\n    list(APPEND _inc_env \"${_path_env}\")\n    string(REPLACE \":\" \";\" _path_env \"$ENV{CPATH}\")\n    list(APPEND _inc_env \"${_path_env}\")\n    string(REPLACE \":\" \";\" _path_env \"$ENV{INCLUDE_PATH}\")\n    list(APPEND _inc_env \"${_path_env}\")\n  endif()\nendif()\nlist(APPEND _inc_env \"${CMAKE_PLATFORM_IMPLICIT_INCLUDE_DIRECTORIES}\")\nlist(APPEND _inc_env \"${CMAKE_C_IMPLICIT_INCLUDE_DIRECTORIES}\")\nlist(REMOVE_DUPLICATES _inc_env)\n\n\n# Try to find the metis header in the given paths\n# -------------------------------------------------\n# call cmake macro to find the header path\nif(METIS_INCDIR)\n  set(METIS_metis.h_DIRS \"METIS_metis.h_DIRS-NOTFOUND\")\n  find_path(METIS_metis.h_DIRS\n    NAMES metis.h\n    HINTS ${METIS_INCDIR})\nelse()\n  if(METIS_DIR)\n    set(METIS_metis.h_DIRS \"METIS_metis.h_DIRS-NOTFOUND\")\n    find_path(METIS_metis.h_DIRS\n      NAMES metis.h\n      HINTS ${METIS_DIR}\n      PATH_SUFFIXES \"include\" \"include/metis\")\n  else()\n    set(METIS_metis.h_DIRS \"METIS_metis.h_DIRS-NOTFOUND\")\n    find_path(METIS_metis.h_DIRS\n      NAMES metis.h\n      HINTS ${_inc_env})\n  endif()\nendif()\nmark_as_advanced(METIS_metis.h_DIRS)\n\n\n# If found, add path to cmake variable\n# ------------------------------------\nif (METIS_metis.h_DIRS)\n  set(METIS_INCLUDE_DIRS \"${METIS_metis.h_DIRS}\")\nelse ()\n  set(METIS_INCLUDE_DIRS \"METIS_INCLUDE_DIRS-NOTFOUND\")\n  if(NOT METIS_FIND_QUIETLY)\n    message(STATUS \"Looking for metis -- metis.h not found\")\n  endif()\nendif()\n\n\n# Looking for lib\n# ---------------\n\n# Add system library paths to search lib\n# --------------------------------------\nunset(_lib_env)\nset(ENV_METIS_LIBDIR \"$ENV{METIS_LIBDIR}\")\nif(ENV_METIS_LIBDIR)\n  list(APPEND _lib_env \"${ENV_METIS_LIBDIR}\")\nelseif(ENV_METIS_DIR)\n  list(APPEND _lib_env \"${ENV_METIS_DIR}\")\n  list(APPEND _lib_env \"${ENV_METIS_DIR}/lib\")\nelse()\n  if(WIN32)\n    string(REPLACE \":\" \";\" _lib_env \"$ENV{LIB}\")\n  else()\n    if(APPLE)\n      string(REPLACE \":\" \";\" _lib_env \"$ENV{DYLD_LIBRARY_PATH}\")\n    else()\n      string(REPLACE \":\" \";\" _lib_env \"$ENV{LD_LIBRARY_PATH}\")\n    endif()\n    list(APPEND _lib_env \"${CMAKE_PLATFORM_IMPLICIT_LINK_DIRECTORIES}\")\n    list(APPEND _lib_env \"${CMAKE_C_IMPLICIT_LINK_DIRECTORIES}\")\n  endif()\nendif()\nlist(REMOVE_DUPLICATES _lib_env)\n\n# Try to find the metis lib in the given paths\n# ----------------------------------------------\n# call cmake macro to find the lib path\nif(METIS_LIBDIR)\n  set(METIS_metis_LIBRARY \"METIS_metis_LIBRARY-NOTFOUND\")\n  find_library(METIS_metis_LIBRARY\n    NAMES metis\n    HINTS ${METIS_LIBDIR})\nelse()\n  if(METIS_DIR)\n    set(METIS_metis_LIBRARY \"METIS_metis_LIBRARY-NOTFOUND\")\n    find_library(METIS_metis_LIBRARY\n      NAMES metis\n      HINTS ${METIS_DIR}\n      PATH_SUFFIXES lib lib32 lib64)\n  else()\n    set(METIS_metis_LIBRARY \"METIS_metis_LIBRARY-NOTFOUND\")\n    find_library(METIS_metis_LIBRARY\n      NAMES metis\n      HINTS ${_lib_env})\n  endif()\nendif()\nmark_as_advanced(METIS_metis_LIBRARY)\n\n\n# If found, add path to cmake variable\n# ------------------------------------\nif (METIS_metis_LIBRARY)\n  get_filename_component(metis_lib_path \"${METIS_metis_LIBRARY}\" PATH)\n  # set cmake variables\n  set(METIS_LIBRARIES    \"${METIS_metis_LIBRARY}\")\n  set(METIS_LIBRARY_DIRS \"${metis_lib_path}\")\nelse ()\n  set(METIS_LIBRARIES    \"METIS_LIBRARIES-NOTFOUND\")\n  set(METIS_LIBRARY_DIRS \"METIS_LIBRARY_DIRS-NOTFOUND\")\n  if(NOT METIS_FIND_QUIETLY)\n    message(STATUS \"Looking for metis -- lib metis not found\")\n  endif()\nendif ()\n\n# check a function to validate the find\nif(METIS_LIBRARIES)\n\n  set(REQUIRED_INCDIRS)\n  set(REQUIRED_LIBDIRS)\n  set(REQUIRED_LIBS)\n\n  # METIS\n  if (METIS_INCLUDE_DIRS)\n    set(REQUIRED_INCDIRS  \"${METIS_INCLUDE_DIRS}\")\n  endif()\n  if (METIS_LIBRARY_DIRS)\n    set(REQUIRED_LIBDIRS \"${METIS_LIBRARY_DIRS}\")\n  endif()\n  set(REQUIRED_LIBS \"${METIS_LIBRARIES}\")\n  # m\n  find_library(M_LIBRARY NAMES m)\n  mark_as_advanced(M_LIBRARY)\n  if(M_LIBRARY)\n    list(APPEND REQUIRED_LIBS \"-lm\")\n  endif()\n\n  # set required libraries for link\n  set(CMAKE_REQUIRED_INCLUDES \"${REQUIRED_INCDIRS}\")\n  set(CMAKE_REQUIRED_LIBRARIES)\n  foreach(lib_dir ${REQUIRED_LIBDIRS})\n    list(APPEND CMAKE_REQUIRED_LIBRARIES \"-L${lib_dir}\")\n  endforeach()\n  list(APPEND CMAKE_REQUIRED_LIBRARIES \"${REQUIRED_LIBS}\")\n  string(REGEX REPLACE \"^ -\" \"-\" CMAKE_REQUIRED_LIBRARIES \"${CMAKE_REQUIRED_LIBRARIES}\")\n\n  # test link\n  unset(METIS_WORKS CACHE)\n  include(CheckFunctionExists)\n  check_function_exists(METIS_NodeND METIS_WORKS)\n  mark_as_advanced(METIS_WORKS)\n\n  if(NOT METIS_WORKS)\n    if(NOT METIS_FIND_QUIETLY)\n      message(STATUS \"Looking for METIS : test of METIS_NodeND with METIS library fails\")\n      message(STATUS \"CMAKE_REQUIRED_LIBRARIES: ${CMAKE_REQUIRED_LIBRARIES}\")\n      message(STATUS \"CMAKE_REQUIRED_INCLUDES: ${CMAKE_REQUIRED_INCLUDES}\")\n      message(STATUS \"Check in CMakeFiles/CMakeError.log to figure out why it fails\")\n    endif()\n  endif()\n  set(CMAKE_REQUIRED_INCLUDES)\n  set(CMAKE_REQUIRED_FLAGS)\n  set(CMAKE_REQUIRED_LIBRARIES)\nendif(METIS_LIBRARIES)\n\nif (METIS_LIBRARIES)\n  list(GET METIS_LIBRARIES 0 first_lib)\n  get_filename_component(first_lib_path \"${first_lib}\" PATH)\n  if (${first_lib_path} MATCHES \"/lib(32|64)?$\")\n    string(REGEX REPLACE \"/lib(32|64)?$\" \"\" not_cached_dir \"${first_lib_path}\")\n    set(METIS_DIR_FOUND \"${not_cached_dir}\" CACHE PATH \"Installation directory of METIS library\" FORCE)\n  else()\n    set(METIS_DIR_FOUND \"${first_lib_path}\" CACHE PATH \"Installation directory of METIS library\" FORCE)\n  endif()\nendif()\nmark_as_advanced(METIS_DIR)\nmark_as_advanced(METIS_DIR_FOUND)\n\n# check that METIS has been found\n# ---------------------------------\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(METIS DEFAULT_MSG\n  METIS_LIBRARIES\n  METIS_WORKS)\n#\n# TODO: Add possibility to check for specific functions in the library\n#\n"
  },
  {
    "path": "include/eigen3/cmake/FindPTSCOTCH.cmake",
    "content": "###\n#\n# @copyright (c) 2009-2014 The University of Tennessee and The University\n#                          of Tennessee Research Foundation.\n#                          All rights reserved.\n# @copyright (c) 2012-2016 Inria. All rights reserved.\n# @copyright (c) 2012-2014 Bordeaux INP, CNRS (LaBRI UMR 5800), Inria, Univ. Bordeaux. All rights reserved.\n#\n###\n#\n# - Find PTSCOTCH include dirs and libraries\n# Use this module by invoking find_package with the form:\n#  find_package(PTSCOTCH\n#               [REQUIRED]             # Fail with error if ptscotch is not found\n#               [COMPONENTS <comp1> <comp2> ...] # dependencies\n#              )\n#\n#  PTSCOTCH depends on the following libraries:\n#   - Threads\n#   - MPI\n#\n#  COMPONENTS can be some of the following:\n#   - ESMUMPS: to activate detection of PT-Scotch with the esmumps interface\n#\n# This module finds headers and ptscotch library.\n# Results are reported in variables:\n#  PTSCOTCH_FOUND            - True if headers and requested libraries were found\n#  PTSCOTCH_LINKER_FLAGS     - list of required linker flags (excluding -l and -L)\n#  PTSCOTCH_INCLUDE_DIRS     - ptscotch include directories\n#  PTSCOTCH_LIBRARY_DIRS     - Link directories for ptscotch libraries\n#  PTSCOTCH_LIBRARIES        - ptscotch component libraries to be linked\n#  PTSCOTCH_INCLUDE_DIRS_DEP - ptscotch + dependencies include directories\n#  PTSCOTCH_LIBRARY_DIRS_DEP - ptscotch + dependencies link directories\n#  PTSCOTCH_LIBRARIES_DEP    - ptscotch libraries + dependencies\n#  PTSCOTCH_INTSIZE          - Number of octets occupied by a SCOTCH_Num\n#\n# The user can give specific paths where to find the libraries adding cmake\n# options at configure (ex: cmake path/to/project -DPTSCOTCH=path/to/ptscotch):\n#  PTSCOTCH_DIR              - Where to find the base directory of ptscotch\n#  PTSCOTCH_INCDIR           - Where to find the header files\n#  PTSCOTCH_LIBDIR           - Where to find the library files\n# The module can also look for the following environment variables if paths\n# are not given as cmake variable: PTSCOTCH_DIR, PTSCOTCH_INCDIR, PTSCOTCH_LIBDIR\n\n#=============================================================================\n# Copyright 2012-2013 Inria\n# Copyright 2012-2013 Emmanuel Agullo\n# Copyright 2012-2013 Mathieu Faverge\n# Copyright 2012      Cedric Castagnede\n# Copyright 2013-2016 Florent Pruvost\n#\n# Distributed under the OSI-approved BSD License (the \"License\");\n# see accompanying file MORSE-Copyright.txt for details.\n#\n# This software is distributed WITHOUT ANY WARRANTY; without even the\n# implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.\n# See the License for more information.\n#=============================================================================\n# (To distribute this file outside of Morse, substitute the full\n#  License text for the above reference.)\n\nif (NOT PTSCOTCH_FOUND)\n  set(PTSCOTCH_DIR \"\" CACHE PATH \"Installation directory of PTSCOTCH library\")\n  if (NOT PTSCOTCH_FIND_QUIETLY)\n    message(STATUS \"A cache variable, namely PTSCOTCH_DIR, has been set to specify the install directory of PTSCOTCH\")\n  endif()\nendif()\n\n# Set the version to find\nset(PTSCOTCH_LOOK_FOR_ESMUMPS OFF)\n\nif( PTSCOTCH_FIND_COMPONENTS )\n  foreach( component ${PTSCOTCH_FIND_COMPONENTS} )\n    if (${component} STREQUAL \"ESMUMPS\")\n      # means we look for esmumps library\n      set(PTSCOTCH_LOOK_FOR_ESMUMPS ON)\n    endif()\n  endforeach()\nendif()\n\n# PTSCOTCH depends on Threads, try to find it\nif (NOT THREADS_FOUND)\n  if (PTSCOTCH_FIND_REQUIRED)\n    find_package(Threads REQUIRED)\n  else()\n    find_package(Threads)\n  endif()\nendif()\n\n# PTSCOTCH depends on MPI, try to find it\nif (NOT MPI_FOUND)\n  if (PTSCOTCH_FIND_REQUIRED)\n    find_package(MPI REQUIRED)\n  else()\n    find_package(MPI)\n  endif()\nendif()\n\n# Looking for include\n# -------------------\n\n# Add system include paths to search include\n# ------------------------------------------\nunset(_inc_env)\nset(ENV_PTSCOTCH_DIR \"$ENV{PTSCOTCH_DIR}\")\nset(ENV_PTSCOTCH_INCDIR \"$ENV{PTSCOTCH_INCDIR}\")\nif(ENV_PTSCOTCH_INCDIR)\n  list(APPEND _inc_env \"${ENV_PTSCOTCH_INCDIR}\")\nelseif(ENV_PTSCOTCH_DIR)\n  list(APPEND _inc_env \"${ENV_PTSCOTCH_DIR}\")\n  list(APPEND _inc_env \"${ENV_PTSCOTCH_DIR}/include\")\n  list(APPEND _inc_env \"${ENV_PTSCOTCH_DIR}/include/ptscotch\")\nelse()\n  if(WIN32)\n    string(REPLACE \":\" \";\" _inc_env \"$ENV{INCLUDE}\")\n  else()\n    string(REPLACE \":\" \";\" _path_env \"$ENV{INCLUDE}\")\n    list(APPEND _inc_env \"${_path_env}\")\n    string(REPLACE \":\" \";\" _path_env \"$ENV{C_INCLUDE_PATH}\")\n    list(APPEND _inc_env \"${_path_env}\")\n    string(REPLACE \":\" \";\" _path_env \"$ENV{CPATH}\")\n    list(APPEND _inc_env \"${_path_env}\")\n    string(REPLACE \":\" \";\" _path_env \"$ENV{INCLUDE_PATH}\")\n    list(APPEND _inc_env \"${_path_env}\")\n  endif()\nendif()\nlist(APPEND _inc_env \"${CMAKE_PLATFORM_IMPLICIT_INCLUDE_DIRECTORIES}\")\nlist(APPEND _inc_env \"${CMAKE_C_IMPLICIT_INCLUDE_DIRECTORIES}\")\nlist(REMOVE_DUPLICATES _inc_env)\n\n\n# Try to find the ptscotch header in the given paths\n# -------------------------------------------------\n\nset(PTSCOTCH_hdrs_to_find \"ptscotch.h;scotch.h\")\n\n# call cmake macro to find the header path\nif(PTSCOTCH_INCDIR)\n  foreach(ptscotch_hdr ${PTSCOTCH_hdrs_to_find})\n    set(PTSCOTCH_${ptscotch_hdr}_DIRS \"PTSCOTCH_${ptscotch_hdr}_DIRS-NOTFOUND\")\n    find_path(PTSCOTCH_${ptscotch_hdr}_DIRS\n      NAMES ${ptscotch_hdr}\n      HINTS ${PTSCOTCH_INCDIR})\n    mark_as_advanced(PTSCOTCH_${ptscotch_hdr}_DIRS)\n  endforeach()\nelse()\n  if(PTSCOTCH_DIR)\n    foreach(ptscotch_hdr ${PTSCOTCH_hdrs_to_find})\n      set(PTSCOTCH_${ptscotch_hdr}_DIRS \"PTSCOTCH_${ptscotch_hdr}_DIRS-NOTFOUND\")\n      find_path(PTSCOTCH_${ptscotch_hdr}_DIRS\n\tNAMES ${ptscotch_hdr}\n\tHINTS ${PTSCOTCH_DIR}\n\tPATH_SUFFIXES \"include\" \"include/scotch\")\n      mark_as_advanced(PTSCOTCH_${ptscotch_hdr}_DIRS)\n    endforeach()\n  else()\n    foreach(ptscotch_hdr ${PTSCOTCH_hdrs_to_find})\n      set(PTSCOTCH_${ptscotch_hdr}_DIRS \"PTSCOTCH_${ptscotch_hdr}_DIRS-NOTFOUND\")\n      find_path(PTSCOTCH_${ptscotch_hdr}_DIRS\n\tNAMES ${ptscotch_hdr}\n\tHINTS ${_inc_env}\n\tPATH_SUFFIXES \"scotch\")\n      mark_as_advanced(PTSCOTCH_${ptscotch_hdr}_DIRS)\n    endforeach()\n  endif()\nendif()\n\n# If found, add path to cmake variable\n# ------------------------------------\nforeach(ptscotch_hdr ${PTSCOTCH_hdrs_to_find})\n  if (PTSCOTCH_${ptscotch_hdr}_DIRS)\n    list(APPEND PTSCOTCH_INCLUDE_DIRS \"${PTSCOTCH_${ptscotch_hdr}_DIRS}\")\n  else ()\n    set(PTSCOTCH_INCLUDE_DIRS \"PTSCOTCH_INCLUDE_DIRS-NOTFOUND\")\n    if (NOT PTSCOTCH_FIND_QUIETLY)\n      message(STATUS \"Looking for ptscotch -- ${ptscotch_hdr} not found\")\n    endif()\n  endif()\nendforeach()\nlist(REMOVE_DUPLICATES PTSCOTCH_INCLUDE_DIRS)\n\n# Looking for lib\n# ---------------\n\n# Add system library paths to search lib\n# --------------------------------------\nunset(_lib_env)\nset(ENV_PTSCOTCH_LIBDIR \"$ENV{PTSCOTCH_LIBDIR}\")\nif(ENV_PTSCOTCH_LIBDIR)\n  list(APPEND _lib_env \"${ENV_PTSCOTCH_LIBDIR}\")\nelseif(ENV_PTSCOTCH_DIR)\n  list(APPEND _lib_env \"${ENV_PTSCOTCH_DIR}\")\n  list(APPEND _lib_env \"${ENV_PTSCOTCH_DIR}/lib\")\nelse()\n  if(WIN32)\n    string(REPLACE \":\" \";\" _lib_env \"$ENV{LIB}\")\n  else()\n    if(APPLE)\n      string(REPLACE \":\" \";\" _lib_env \"$ENV{DYLD_LIBRARY_PATH}\")\n    else()\n      string(REPLACE \":\" \";\" _lib_env \"$ENV{LD_LIBRARY_PATH}\")\n    endif()\n    list(APPEND _lib_env \"${CMAKE_PLATFORM_IMPLICIT_LINK_DIRECTORIES}\")\n    list(APPEND _lib_env \"${CMAKE_C_IMPLICIT_LINK_DIRECTORIES}\")\n  endif()\nendif()\nlist(REMOVE_DUPLICATES _lib_env)\n\n# Try to find the ptscotch lib in the given paths\n# ----------------------------------------------\n\nset(PTSCOTCH_libs_to_find \"ptscotch;ptscotcherr\")\nif (PTSCOTCH_LOOK_FOR_ESMUMPS)\n  list(INSERT PTSCOTCH_libs_to_find 0 \"ptesmumps\")\n  list(APPEND PTSCOTCH_libs_to_find   \"esmumps\"  )\nendif()\nlist(APPEND PTSCOTCH_libs_to_find \"scotch;scotcherr\")\n\n# call cmake macro to find the lib path\nif(PTSCOTCH_LIBDIR)\n  foreach(ptscotch_lib ${PTSCOTCH_libs_to_find})\n    set(PTSCOTCH_${ptscotch_lib}_LIBRARY \"PTSCOTCH_${ptscotch_lib}_LIBRARY-NOTFOUND\")\n    find_library(PTSCOTCH_${ptscotch_lib}_LIBRARY\n      NAMES ${ptscotch_lib}\n      HINTS ${PTSCOTCH_LIBDIR})\n  endforeach()\nelse()\n  if(PTSCOTCH_DIR)\n    foreach(ptscotch_lib ${PTSCOTCH_libs_to_find})\n      set(PTSCOTCH_${ptscotch_lib}_LIBRARY \"PTSCOTCH_${ptscotch_lib}_LIBRARY-NOTFOUND\")\n      find_library(PTSCOTCH_${ptscotch_lib}_LIBRARY\n\tNAMES ${ptscotch_lib}\n\tHINTS ${PTSCOTCH_DIR}\n\tPATH_SUFFIXES lib lib32 lib64)\n    endforeach()\n  else()\n    foreach(ptscotch_lib ${PTSCOTCH_libs_to_find})\n      set(PTSCOTCH_${ptscotch_lib}_LIBRARY \"PTSCOTCH_${ptscotch_lib}_LIBRARY-NOTFOUND\")\n      find_library(PTSCOTCH_${ptscotch_lib}_LIBRARY\n\tNAMES ${ptscotch_lib}\n\tHINTS ${_lib_env})\n    endforeach()\n  endif()\nendif()\n\nset(PTSCOTCH_LIBRARIES \"\")\nset(PTSCOTCH_LIBRARY_DIRS \"\")\n# If found, add path to cmake variable\n# ------------------------------------\nforeach(ptscotch_lib ${PTSCOTCH_libs_to_find})\n\n  if (PTSCOTCH_${ptscotch_lib}_LIBRARY)\n    get_filename_component(${ptscotch_lib}_lib_path \"${PTSCOTCH_${ptscotch_lib}_LIBRARY}\" PATH)\n    # set cmake variables\n    list(APPEND PTSCOTCH_LIBRARIES \"${PTSCOTCH_${ptscotch_lib}_LIBRARY}\")\n    list(APPEND PTSCOTCH_LIBRARY_DIRS \"${${ptscotch_lib}_lib_path}\")\n  else ()\n    list(APPEND PTSCOTCH_LIBRARIES \"${PTSCOTCH_${ptscotch_lib}_LIBRARY}\")\n    if (NOT PTSCOTCH_FIND_QUIETLY)\n      message(STATUS \"Looking for ptscotch -- lib ${ptscotch_lib} not found\")\n    endif()\n  endif ()\n\n  mark_as_advanced(PTSCOTCH_${ptscotch_lib}_LIBRARY)\n\nendforeach()\nlist(REMOVE_DUPLICATES PTSCOTCH_LIBRARY_DIRS)\n\n# check a function to validate the find\nif(PTSCOTCH_LIBRARIES)\n\n  set(REQUIRED_LDFLAGS)\n  set(REQUIRED_INCDIRS)\n  set(REQUIRED_LIBDIRS)\n  set(REQUIRED_LIBS)\n\n  # PTSCOTCH\n  if (PTSCOTCH_INCLUDE_DIRS)\n    set(REQUIRED_INCDIRS  \"${PTSCOTCH_INCLUDE_DIRS}\")\n  endif()\n  if (PTSCOTCH_LIBRARY_DIRS)\n    set(REQUIRED_LIBDIRS \"${PTSCOTCH_LIBRARY_DIRS}\")\n  endif()\n  set(REQUIRED_LIBS \"${PTSCOTCH_LIBRARIES}\")\n  # MPI\n  if (MPI_FOUND)\n    if (MPI_C_INCLUDE_PATH)\n      list(APPEND CMAKE_REQUIRED_INCLUDES \"${MPI_C_INCLUDE_PATH}\")\n    endif()\n    if (MPI_C_LINK_FLAGS)\n      if (${MPI_C_LINK_FLAGS} MATCHES \"  -\")\n\tstring(REGEX REPLACE \" -\" \"-\" MPI_C_LINK_FLAGS ${MPI_C_LINK_FLAGS})\n      endif()\n      list(APPEND REQUIRED_LDFLAGS \"${MPI_C_LINK_FLAGS}\")\n    endif()\n    list(APPEND REQUIRED_LIBS \"${MPI_C_LIBRARIES}\")\n  endif()\n  # THREADS\n  if(CMAKE_THREAD_LIBS_INIT)\n    list(APPEND REQUIRED_LIBS \"${CMAKE_THREAD_LIBS_INIT}\")\n  endif()\n  set(Z_LIBRARY \"Z_LIBRARY-NOTFOUND\")\n  find_library(Z_LIBRARY NAMES z)\n  mark_as_advanced(Z_LIBRARY)\n  if(Z_LIBRARY)\n    list(APPEND REQUIRED_LIBS \"-lz\")\n  endif()\n  set(M_LIBRARY \"M_LIBRARY-NOTFOUND\")\n  find_library(M_LIBRARY NAMES m)\n  mark_as_advanced(M_LIBRARY)\n  if(M_LIBRARY)\n    list(APPEND REQUIRED_LIBS \"-lm\")\n  endif()\n  set(RT_LIBRARY \"RT_LIBRARY-NOTFOUND\")\n  find_library(RT_LIBRARY NAMES rt)\n  mark_as_advanced(RT_LIBRARY)\n  if(RT_LIBRARY)\n    list(APPEND REQUIRED_LIBS \"-lrt\")\n  endif()\n\n  # set required libraries for link\n  set(CMAKE_REQUIRED_INCLUDES \"${REQUIRED_INCDIRS}\")\n  set(CMAKE_REQUIRED_LIBRARIES)\n  list(APPEND CMAKE_REQUIRED_LIBRARIES \"${REQUIRED_LDFLAGS}\")\n  foreach(lib_dir ${REQUIRED_LIBDIRS})\n    list(APPEND CMAKE_REQUIRED_LIBRARIES \"-L${lib_dir}\")\n  endforeach()\n  list(APPEND CMAKE_REQUIRED_LIBRARIES \"${REQUIRED_LIBS}\")\n  list(APPEND CMAKE_REQUIRED_FLAGS \"${REQUIRED_FLAGS}\")\n  string(REGEX REPLACE \"^ -\" \"-\" CMAKE_REQUIRED_LIBRARIES \"${CMAKE_REQUIRED_LIBRARIES}\")\n\n  # test link\n  unset(PTSCOTCH_WORKS CACHE)\n  include(CheckFunctionExists)\n  check_function_exists(SCOTCH_dgraphInit PTSCOTCH_WORKS)\n  mark_as_advanced(PTSCOTCH_WORKS)\n\n  if(PTSCOTCH_WORKS)\n    # save link with dependencies\n    set(PTSCOTCH_LIBRARIES_DEP \"${REQUIRED_LIBS}\")\n    set(PTSCOTCH_LIBRARY_DIRS_DEP \"${REQUIRED_LIBDIRS}\")\n    set(PTSCOTCH_INCLUDE_DIRS_DEP \"${REQUIRED_INCDIRS}\")\n    set(PTSCOTCH_LINKER_FLAGS \"${REQUIRED_LDFLAGS}\")\n    list(REMOVE_DUPLICATES PTSCOTCH_LIBRARY_DIRS_DEP)\n    list(REMOVE_DUPLICATES PTSCOTCH_INCLUDE_DIRS_DEP)\n    list(REMOVE_DUPLICATES PTSCOTCH_LINKER_FLAGS)\n  else()\n    if(NOT PTSCOTCH_FIND_QUIETLY)\n      message(STATUS \"Looking for PTSCOTCH : test of SCOTCH_dgraphInit with PTSCOTCH library fails\")\n      message(STATUS \"CMAKE_REQUIRED_LIBRARIES: ${CMAKE_REQUIRED_LIBRARIES}\")\n      message(STATUS \"CMAKE_REQUIRED_INCLUDES: ${CMAKE_REQUIRED_INCLUDES}\")\n      message(STATUS \"Check in CMakeFiles/CMakeError.log to figure out why it fails\")\n    endif()\n  endif()\n  set(CMAKE_REQUIRED_INCLUDES)\n  set(CMAKE_REQUIRED_FLAGS)\n  set(CMAKE_REQUIRED_LIBRARIES)\nendif(PTSCOTCH_LIBRARIES)\n\nif (PTSCOTCH_LIBRARIES)\n  list(GET PTSCOTCH_LIBRARIES 0 first_lib)\n  get_filename_component(first_lib_path \"${first_lib}\" PATH)\n  if (${first_lib_path} MATCHES \"/lib(32|64)?$\")\n    string(REGEX REPLACE \"/lib(32|64)?$\" \"\" not_cached_dir \"${first_lib_path}\")\n    set(PTSCOTCH_DIR_FOUND \"${not_cached_dir}\" CACHE PATH \"Installation directory of PTSCOTCH library\" FORCE)\n  else()\n    set(PTSCOTCH_DIR_FOUND \"${first_lib_path}\" CACHE PATH \"Installation directory of PTSCOTCH library\" FORCE)\n  endif()\nendif()\nmark_as_advanced(PTSCOTCH_DIR)\nmark_as_advanced(PTSCOTCH_DIR_FOUND)\n\n# Check the size of SCOTCH_Num\n# ---------------------------------\nset(CMAKE_REQUIRED_INCLUDES ${PTSCOTCH_INCLUDE_DIRS})\n\ninclude(CheckCSourceRuns)\n#stdio.h and stdint.h should be included by scotch.h directly\nset(PTSCOTCH_C_TEST_SCOTCH_Num_4 \"\n#include <stdio.h>\n#include <stdint.h>\n#include <ptscotch.h>\nint main(int argc, char **argv) {\n  if (sizeof(SCOTCH_Num) == 4)\n    return 0;\n  else\n    return 1;\n}\n\")\n\nset(PTSCOTCH_C_TEST_SCOTCH_Num_8 \"\n#include <stdio.h>\n#include <stdint.h>\n#include <ptscotch.h>\nint main(int argc, char **argv) {\n  if (sizeof(SCOTCH_Num) == 8)\n    return 0;\n  else\n    return 1;\n}\n\")\ncheck_c_source_runs(\"${PTSCOTCH_C_TEST_SCOTCH_Num_4}\" PTSCOTCH_Num_4)\nif(NOT PTSCOTCH_Num_4)\n  check_c_source_runs(\"${PTSCOTCH_C_TEST_SCOTCH_Num_8}\" PTSCOTCH_Num_8)\n  if(NOT PTSCOTCH_Num_8)\n    set(PTSCOTCH_INTSIZE -1)\n  else()\n    set(PTSCOTCH_INTSIZE 8)\n  endif()\nelse()\n  set(PTSCOTCH_INTSIZE 4)\nendif()\nset(CMAKE_REQUIRED_INCLUDES \"\")\n\n# check that PTSCOTCH has been found\n# ---------------------------------\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(PTSCOTCH DEFAULT_MSG\n  PTSCOTCH_LIBRARIES\n  PTSCOTCH_WORKS)\n#\n# TODO: Add possibility to check for specific functions in the library\n#\n"
  },
  {
    "path": "include/eigen3/cmake/FindPastix.cmake",
    "content": "###\n#\n# @copyright (c) 2009-2014 The University of Tennessee and The University\n#                          of Tennessee Research Foundation.\n#                          All rights reserved.\n# @copyright (c) 2012-2014 Inria. All rights reserved.\n# @copyright (c) 2012-2014 Bordeaux INP, CNRS (LaBRI UMR 5800), Inria, Univ. Bordeaux. All rights reserved.\n#\n###\n#\n# - Find PASTIX include dirs and libraries\n# Use this module by invoking find_package with the form:\n#  find_package(PASTIX\n#               [REQUIRED] # Fail with error if pastix is not found\n#               [COMPONENTS <comp1> <comp2> ...] # dependencies\n#              )\n#\n#  PASTIX depends on the following libraries:\n#   - Threads, m, rt\n#   - MPI\n#   - HWLOC\n#   - BLAS\n#\n#  COMPONENTS are optional libraries PASTIX could be linked with,\n#  Use it to drive detection of a specific compilation chain\n#  COMPONENTS can be some of the following:\n#   - MPI: to activate detection of the parallel MPI version (default)\n#        it looks for Threads, HWLOC, BLAS, MPI and ScaLAPACK libraries\n#   - SEQ: to activate detection of the sequential version (exclude MPI version)\n#   - STARPU: to activate detection of StarPU version\n#   it looks for MPI version of StarPU (default behaviour)\n#   if SEQ and STARPU are given, it looks for a StarPU without MPI\n#   - STARPU_CUDA: to activate detection of StarPU with CUDA\n#   - STARPU_FXT: to activate detection of StarPU with FxT\n#   - SCOTCH: to activate detection of PASTIX linked with SCOTCH\n#   - PTSCOTCH: to activate detection of PASTIX linked with SCOTCH\n#   - METIS: to activate detection of PASTIX linked with SCOTCH\n#\n# This module finds headers and pastix library.\n# Results are reported in variables:\n#  PASTIX_FOUND            - True if headers and requested libraries were found\n#  PASTIX_LINKER_FLAGS     - list of required linker flags (excluding -l and -L)\n#  PASTIX_INCLUDE_DIRS     - pastix include directories\n#  PASTIX_LIBRARY_DIRS     - Link directories for pastix libraries\n#  PASTIX_LIBRARIES        - pastix libraries\n#  PASTIX_INCLUDE_DIRS_DEP - pastix + dependencies include directories\n#  PASTIX_LIBRARY_DIRS_DEP - pastix + dependencies link directories\n#  PASTIX_LIBRARIES_DEP    - pastix libraries + dependencies\n#\n# The user can give specific paths where to find the libraries adding cmake\n# options at configure (ex: cmake path/to/project -DPASTIX_DIR=path/to/pastix):\n#  PASTIX_DIR              - Where to find the base directory of pastix\n#  PASTIX_INCDIR           - Where to find the header files\n#  PASTIX_LIBDIR           - Where to find the library files\n# The module can also look for the following environment variables if paths\n# are not given as cmake variable: PASTIX_DIR, PASTIX_INCDIR, PASTIX_LIBDIR\n\n#=============================================================================\n# Copyright 2012-2013 Inria\n# Copyright 2012-2013 Emmanuel Agullo\n# Copyright 2012-2013 Mathieu Faverge\n# Copyright 2012      Cedric Castagnede\n# Copyright 2013      Florent Pruvost\n#\n# Distributed under the OSI-approved BSD License (the \"License\");\n# see accompanying file MORSE-Copyright.txt for details.\n#\n# This software is distributed WITHOUT ANY WARRANTY; without even the\n# implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.\n# See the License for more information.\n#=============================================================================\n# (To distribute this file outside of Morse, substitute the full\n#  License text for the above reference.)\n\n\nif (NOT PASTIX_FOUND)\n  set(PASTIX_DIR \"\" CACHE PATH \"Installation directory of PASTIX library\")\n  if (NOT PASTIX_FIND_QUIETLY)\n    message(STATUS \"A cache variable, namely PASTIX_DIR, has been set to specify the install directory of PASTIX\")\n  endif()\nendif()\n\n# Set the version to find\nset(PASTIX_LOOK_FOR_MPI ON)\nset(PASTIX_LOOK_FOR_SEQ OFF)\nset(PASTIX_LOOK_FOR_STARPU OFF)\nset(PASTIX_LOOK_FOR_STARPU_CUDA OFF)\nset(PASTIX_LOOK_FOR_STARPU_FXT OFF)\nset(PASTIX_LOOK_FOR_SCOTCH ON)\nset(PASTIX_LOOK_FOR_PTSCOTCH OFF)\nset(PASTIX_LOOK_FOR_METIS OFF)\n\nif( PASTIX_FIND_COMPONENTS )\n  foreach( component ${PASTIX_FIND_COMPONENTS} )\n    if (${component} STREQUAL \"SEQ\")\n      # means we look for the sequential version of PaStiX (without MPI)\n      set(PASTIX_LOOK_FOR_SEQ ON)\n      set(PASTIX_LOOK_FOR_MPI OFF)\n    endif()\n    if (${component} STREQUAL \"MPI\")\n      # means we look for the MPI version of PaStiX (default)\n      set(PASTIX_LOOK_FOR_SEQ OFF)\n      set(PASTIX_LOOK_FOR_MPI ON)\n    endif()\n    if (${component} STREQUAL \"STARPU\")\n      # means we look for PaStiX with StarPU\n      set(PASTIX_LOOK_FOR_STARPU ON)\n    endif()\n    if (${component} STREQUAL \"STARPU_CUDA\")\n      # means we look for PaStiX with StarPU + CUDA\n      set(PASTIX_LOOK_FOR_STARPU ON)\n      set(PASTIX_LOOK_FOR_STARPU_CUDA ON)\n    endif()\n    if (${component} STREQUAL \"STARPU_FXT\")\n      # means we look for PaStiX with StarPU + FxT\n      set(PASTIX_LOOK_FOR_STARPU_FXT ON)\n    endif()\n    if (${component} STREQUAL \"SCOTCH\")\n      set(PASTIX_LOOK_FOR_SCOTCH ON)\n    endif()\n    if (${component} STREQUAL \"SCOTCH\")\n      set(PASTIX_LOOK_FOR_PTSCOTCH ON)\n    endif()\n    if (${component} STREQUAL \"METIS\")\n      set(PASTIX_LOOK_FOR_METIS ON)\n    endif()\n  endforeach()\nendif()\n\n# Dependencies detection\n# ----------------------\n\n\n# Required dependencies\n# ---------------------\n\nif (NOT PASTIX_FIND_QUIETLY)\n  message(STATUS \"Looking for PASTIX - Try to detect pthread\")\nendif()\nif (PASTIX_FIND_REQUIRED)\n  find_package(Threads REQUIRED QUIET)\nelse()\n  find_package(Threads QUIET)\nendif()\nset(PASTIX_EXTRA_LIBRARIES \"\")\nif( THREADS_FOUND )\n  list(APPEND PASTIX_EXTRA_LIBRARIES ${CMAKE_THREAD_LIBS_INIT})\nendif ()\n\n# Add math library to the list of extra\n# it normally exists on all common systems provided with a C compiler\nif (NOT PASTIX_FIND_QUIETLY)\n  message(STATUS \"Looking for PASTIX - Try to detect libm\")\nendif()\nset(PASTIX_M_LIBRARIES \"\")\nif(UNIX OR WIN32)\n  find_library(\n    PASTIX_M_m_LIBRARY\n    NAMES m\n    )\n  mark_as_advanced(PASTIX_M_m_LIBRARY)\n  if (PASTIX_M_m_LIBRARY)\n    list(APPEND PASTIX_M_LIBRARIES \"${PASTIX_M_m_LIBRARY}\")\n    list(APPEND PASTIX_EXTRA_LIBRARIES \"${PASTIX_M_m_LIBRARY}\")\n  else()\n    if (PASTIX_FIND_REQUIRED)\n      message(FATAL_ERROR \"Could NOT find libm on your system.\"\n\t\"Are you sure to a have a C compiler installed?\")\n    endif()\n  endif()\nendif()\n\n# Try to find librt (libposix4 - POSIX.1b Realtime Extensions library)\n# on Unix systems except Apple ones because it does not exist on it\nif (NOT PASTIX_FIND_QUIETLY)\n  message(STATUS \"Looking for PASTIX - Try to detect librt\")\nendif()\nset(PASTIX_RT_LIBRARIES \"\")\nif(UNIX AND NOT APPLE)\n  find_library(\n    PASTIX_RT_rt_LIBRARY\n    NAMES rt\n    )\n  mark_as_advanced(PASTIX_RT_rt_LIBRARY)\n  if (PASTIX_RT_rt_LIBRARY)\n    list(APPEND PASTIX_RT_LIBRARIES \"${PASTIX_RT_rt_LIBRARY}\")\n    list(APPEND PASTIX_EXTRA_LIBRARIES \"${PASTIX_RT_rt_LIBRARY}\")\n  else()\n    if (PASTIX_FIND_REQUIRED)\n      message(FATAL_ERROR \"Could NOT find librt on your system\")\n    endif()\n  endif()\nendif()\n\n# PASTIX depends on HWLOC\n#------------------------\nif (NOT PASTIX_FIND_QUIETLY)\n  message(STATUS \"Looking for PASTIX - Try to detect HWLOC\")\nendif()\nif (PASTIX_FIND_REQUIRED)\n  find_package(HWLOC REQUIRED QUIET)\nelse()\n  find_package(HWLOC QUIET)\nendif()\n\n# PASTIX depends on BLAS\n#-----------------------\nif (NOT PASTIX_FIND_QUIETLY)\n  message(STATUS \"Looking for PASTIX - Try to detect BLAS\")\nendif()\nif (PASTIX_FIND_REQUIRED)\n  find_package(BLASEXT REQUIRED QUIET)\nelse()\n  find_package(BLASEXT QUIET)\nendif()\n\n# Optional dependencies\n# ---------------------\n\n# PASTIX may depend on MPI\n#-------------------------\nif (NOT MPI_FOUND AND PASTIX_LOOK_FOR_MPI)\n  if (NOT PASTIX_FIND_QUIETLY)\n    message(STATUS \"Looking for PASTIX - Try to detect MPI\")\n  endif()\n  # allows to use an external mpi compilation by setting compilers with\n  # -DMPI_C_COMPILER=path/to/mpicc -DMPI_Fortran_COMPILER=path/to/mpif90\n  # at cmake configure\n  if(NOT MPI_C_COMPILER)\n    set(MPI_C_COMPILER mpicc)\n  endif()\n  if (PASTIX_FIND_REQUIRED AND PASTIX_FIND_REQUIRED_MPI)\n    find_package(MPI REQUIRED QUIET)\n  else()\n    find_package(MPI QUIET)\n  endif()\n  if (MPI_FOUND)\n    mark_as_advanced(MPI_LIBRARY)\n    mark_as_advanced(MPI_EXTRA_LIBRARY)\n  endif()\nendif (NOT MPI_FOUND AND PASTIX_LOOK_FOR_MPI)\n\n# PASTIX may depend on STARPU\n#----------------------------\nif( NOT STARPU_FOUND AND PASTIX_LOOK_FOR_STARPU)\n\n  if (NOT PASTIX_FIND_QUIETLY)\n    message(STATUS \"Looking for PASTIX - Try to detect StarPU\")\n  endif()\n\n  set(PASTIX_STARPU_VERSION \"1.1\" CACHE STRING \"oldest STARPU version desired\")\n\n  # create list of components in order to make a single call to find_package(starpu...)\n  # we explicitly need a StarPU version built with hwloc\n  set(STARPU_COMPONENT_LIST \"HWLOC\")\n\n  # StarPU may depend on MPI\n  # allows to use an external mpi compilation by setting compilers with\n  # -DMPI_C_COMPILER=path/to/mpicc -DMPI_Fortran_COMPILER=path/to/mpif90\n  # at cmake configure\n  if (PASTIX_LOOK_FOR_MPI)\n    if(NOT MPI_C_COMPILER)\n      set(MPI_C_COMPILER mpicc)\n    endif()\n    list(APPEND STARPU_COMPONENT_LIST \"MPI\")\n  endif()\n  if (PASTIX_LOOK_FOR_STARPU_CUDA)\n    list(APPEND STARPU_COMPONENT_LIST \"CUDA\")\n  endif()\n  if (PASTIX_LOOK_FOR_STARPU_FXT)\n    list(APPEND STARPU_COMPONENT_LIST \"FXT\")\n  endif()\n  # set the list of optional dependencies we may discover\n  if (PASTIX_FIND_REQUIRED AND PASTIX_FIND_REQUIRED_STARPU)\n    find_package(STARPU ${PASTIX_STARPU_VERSION} REQUIRED\n      COMPONENTS ${STARPU_COMPONENT_LIST})\n  else()\n    find_package(STARPU ${PASTIX_STARPU_VERSION}\n      COMPONENTS ${STARPU_COMPONENT_LIST})\n  endif()\n\nendif( NOT STARPU_FOUND AND PASTIX_LOOK_FOR_STARPU)\n\n# PASTIX may depends on SCOTCH\n#-----------------------------\nif (NOT SCOTCH_FOUND AND PASTIX_LOOK_FOR_SCOTCH)\n  if (NOT PASTIX_FIND_QUIETLY)\n    message(STATUS \"Looking for PASTIX - Try to detect SCOTCH\")\n  endif()\n  if (PASTIX_FIND_REQUIRED AND PASTIX_FIND_REQUIRED_SCOTCH)\n    find_package(SCOTCH REQUIRED QUIET)\n  else()\n    find_package(SCOTCH QUIET)\n  endif()\nendif()\n\n# PASTIX may depends on PTSCOTCH\n#-------------------------------\nif (NOT PTSCOTCH_FOUND AND PASTIX_LOOK_FOR_PTSCOTCH)\n  if (NOT PASTIX_FIND_QUIETLY)\n    message(STATUS \"Looking for PASTIX - Try to detect PTSCOTCH\")\n  endif()\n  if (PASTIX_FIND_REQUIRED AND PASTIX_FIND_REQUIRED_PTSCOTCH)\n    find_package(PTSCOTCH REQUIRED QUIET)\n  else()\n    find_package(PTSCOTCH QUIET)\n  endif()\nendif()\n\n# PASTIX may depends on METIS\n#----------------------------\nif (NOT METIS_FOUND AND PASTIX_LOOK_FOR_METIS)\n  if (NOT PASTIX_FIND_QUIETLY)\n    message(STATUS \"Looking for PASTIX - Try to detect METIS\")\n  endif()\n  if (PASTIX_FIND_REQUIRED AND PASTIX_FIND_REQUIRED_METIS)\n    find_package(METIS REQUIRED QUIET)\n  else()\n    find_package(METIS QUIET)\n  endif()\nendif()\n\n# Error if pastix required and no partitioning lib found\nif (PASTIX_FIND_REQUIRED AND NOT SCOTCH_FOUND AND NOT PTSCOTCH_FOUND AND NOT METIS_FOUND)\n  message(FATAL_ERROR \"Could NOT find any partitioning library on your system\"\n    \" (install scotch, ptscotch or metis)\")\nendif()\n\n\n# Looking for PaStiX\n# ------------------\n\n# Looking for include\n# -------------------\n\n# Add system include paths to search include\n# ------------------------------------------\nunset(_inc_env)\nset(ENV_PASTIX_DIR \"$ENV{PASTIX_DIR}\")\nset(ENV_PASTIX_INCDIR \"$ENV{PASTIX_INCDIR}\")\nif(ENV_PASTIX_INCDIR)\n  list(APPEND _inc_env \"${ENV_PASTIX_INCDIR}\")\nelseif(ENV_PASTIX_DIR)\n  list(APPEND _inc_env \"${ENV_PASTIX_DIR}\")\n  list(APPEND _inc_env \"${ENV_PASTIX_DIR}/include\")\n  list(APPEND _inc_env \"${ENV_PASTIX_DIR}/include/pastix\")\nelse()\n  if(WIN32)\n    string(REPLACE \":\" \";\" _inc_env \"$ENV{INCLUDE}\")\n  else()\n    string(REPLACE \":\" \";\" _path_env \"$ENV{INCLUDE}\")\n    list(APPEND _inc_env \"${_path_env}\")\n    string(REPLACE \":\" \";\" _path_env \"$ENV{C_INCLUDE_PATH}\")\n    list(APPEND _inc_env \"${_path_env}\")\n    string(REPLACE \":\" \";\" _path_env \"$ENV{CPATH}\")\n    list(APPEND _inc_env \"${_path_env}\")\n    string(REPLACE \":\" \";\" _path_env \"$ENV{INCLUDE_PATH}\")\n    list(APPEND _inc_env \"${_path_env}\")\n  endif()\nendif()\nlist(APPEND _inc_env \"${CMAKE_PLATFORM_IMPLICIT_INCLUDE_DIRECTORIES}\")\nlist(APPEND _inc_env \"${CMAKE_C_IMPLICIT_INCLUDE_DIRECTORIES}\")\nlist(REMOVE_DUPLICATES _inc_env)\n\n\n# Try to find the pastix header in the given paths\n# ---------------------------------------------------\n# call cmake macro to find the header path\nif(PASTIX_INCDIR)\n  set(PASTIX_pastix.h_DIRS \"PASTIX_pastix.h_DIRS-NOTFOUND\")\n  find_path(PASTIX_pastix.h_DIRS\n    NAMES pastix.h\n    HINTS ${PASTIX_INCDIR})\nelse()\n  if(PASTIX_DIR)\n    set(PASTIX_pastix.h_DIRS \"PASTIX_pastix.h_DIRS-NOTFOUND\")\n    find_path(PASTIX_pastix.h_DIRS\n      NAMES pastix.h\n      HINTS ${PASTIX_DIR}\n      PATH_SUFFIXES \"include\" \"include/pastix\")\n  else()\n    set(PASTIX_pastix.h_DIRS \"PASTIX_pastix.h_DIRS-NOTFOUND\")\n    find_path(PASTIX_pastix.h_DIRS\n      NAMES pastix.h\n      HINTS ${_inc_env}\n      PATH_SUFFIXES \"pastix\")\n  endif()\nendif()\nmark_as_advanced(PASTIX_pastix.h_DIRS)\n\n# If found, add path to cmake variable\n# ------------------------------------\nif (PASTIX_pastix.h_DIRS)\n  set(PASTIX_INCLUDE_DIRS \"${PASTIX_pastix.h_DIRS}\")\nelse ()\n  set(PASTIX_INCLUDE_DIRS \"PASTIX_INCLUDE_DIRS-NOTFOUND\")\n  if(NOT PASTIX_FIND_QUIETLY)\n    message(STATUS \"Looking for pastix -- pastix.h not found\")\n  endif()\nendif()\n\n\n# Looking for lib\n# ---------------\n\n# Add system library paths to search lib\n# --------------------------------------\nunset(_lib_env)\nset(ENV_PASTIX_LIBDIR \"$ENV{PASTIX_LIBDIR}\")\nif(ENV_PASTIX_LIBDIR)\n  list(APPEND _lib_env \"${ENV_PASTIX_LIBDIR}\")\nelseif(ENV_PASTIX_DIR)\n  list(APPEND _lib_env \"${ENV_PASTIX_DIR}\")\n  list(APPEND _lib_env \"${ENV_PASTIX_DIR}/lib\")\nelse()\n  if(WIN32)\n    string(REPLACE \":\" \";\" _lib_env \"$ENV{LIB}\")\n  else()\n    if(APPLE)\n      string(REPLACE \":\" \";\" _lib_env \"$ENV{DYLD_LIBRARY_PATH}\")\n    else()\n      string(REPLACE \":\" \";\" _lib_env \"$ENV{LD_LIBRARY_PATH}\")\n    endif()\n    list(APPEND _lib_env \"${CMAKE_PLATFORM_IMPLICIT_LINK_DIRECTORIES}\")\n    list(APPEND _lib_env \"${CMAKE_C_IMPLICIT_LINK_DIRECTORIES}\")\n  endif()\nendif()\nlist(REMOVE_DUPLICATES _lib_env)\n\n# Try to find the pastix lib in the given paths\n# ------------------------------------------------\n\n# create list of libs to find\nset(PASTIX_libs_to_find \"pastix_murge;pastix\")\n\n# call cmake macro to find the lib path\nif(PASTIX_LIBDIR)\n  foreach(pastix_lib ${PASTIX_libs_to_find})\n    set(PASTIX_${pastix_lib}_LIBRARY \"PASTIX_${pastix_lib}_LIBRARY-NOTFOUND\")\n    find_library(PASTIX_${pastix_lib}_LIBRARY\n      NAMES ${pastix_lib}\n      HINTS ${PASTIX_LIBDIR})\n  endforeach()\nelse()\n  if(PASTIX_DIR)\n    foreach(pastix_lib ${PASTIX_libs_to_find})\n      set(PASTIX_${pastix_lib}_LIBRARY \"PASTIX_${pastix_lib}_LIBRARY-NOTFOUND\")\n      find_library(PASTIX_${pastix_lib}_LIBRARY\n\tNAMES ${pastix_lib}\n\tHINTS ${PASTIX_DIR}\n\tPATH_SUFFIXES lib lib32 lib64)\n    endforeach()\n  else()\n    foreach(pastix_lib ${PASTIX_libs_to_find})\n      set(PASTIX_${pastix_lib}_LIBRARY \"PASTIX_${pastix_lib}_LIBRARY-NOTFOUND\")\n      find_library(PASTIX_${pastix_lib}_LIBRARY\n\tNAMES ${pastix_lib}\n\tHINTS ${_lib_env})\n    endforeach()\n  endif()\nendif()\n\n# If found, add path to cmake variable\n# ------------------------------------\nforeach(pastix_lib ${PASTIX_libs_to_find})\n\n  get_filename_component(${pastix_lib}_lib_path ${PASTIX_${pastix_lib}_LIBRARY} PATH)\n  # set cmake variables (respects naming convention)\n  if (PASTIX_LIBRARIES)\n    list(APPEND PASTIX_LIBRARIES \"${PASTIX_${pastix_lib}_LIBRARY}\")\n  else()\n    set(PASTIX_LIBRARIES \"${PASTIX_${pastix_lib}_LIBRARY}\")\n  endif()\n  if (PASTIX_LIBRARY_DIRS)\n    list(APPEND PASTIX_LIBRARY_DIRS \"${${pastix_lib}_lib_path}\")\n  else()\n    set(PASTIX_LIBRARY_DIRS \"${${pastix_lib}_lib_path}\")\n  endif()\n  mark_as_advanced(PASTIX_${pastix_lib}_LIBRARY)\n\nendforeach(pastix_lib ${PASTIX_libs_to_find})\n\n# check a function to validate the find\nif(PASTIX_LIBRARIES)\n\n  set(REQUIRED_LDFLAGS)\n  set(REQUIRED_INCDIRS)\n  set(REQUIRED_LIBDIRS)\n  set(REQUIRED_LIBS)\n\n  # PASTIX\n  if (PASTIX_INCLUDE_DIRS)\n    set(REQUIRED_INCDIRS \"${PASTIX_INCLUDE_DIRS}\")\n  endif()\n  foreach(libdir ${PASTIX_LIBRARY_DIRS})\n    if (libdir)\n      list(APPEND REQUIRED_LIBDIRS \"${libdir}\")\n    endif()\n  endforeach()\n  set(REQUIRED_LIBS \"${PASTIX_LIBRARIES}\")\n  # STARPU\n  if (PASTIX_LOOK_FOR_STARPU AND STARPU_FOUND)\n    if (STARPU_INCLUDE_DIRS_DEP)\n      list(APPEND REQUIRED_INCDIRS \"${STARPU_INCLUDE_DIRS_DEP}\")\n    elseif (STARPU_INCLUDE_DIRS)\n      list(APPEND REQUIRED_INCDIRS \"${STARPU_INCLUDE_DIRS}\")\n    endif()\n    if(STARPU_LIBRARY_DIRS_DEP)\n      list(APPEND REQUIRED_LIBDIRS \"${STARPU_LIBRARY_DIRS_DEP}\")\n    elseif(STARPU_LIBRARY_DIRS)\n      list(APPEND REQUIRED_LIBDIRS \"${STARPU_LIBRARY_DIRS}\")\n    endif()\n    if (STARPU_LIBRARIES_DEP)\n      list(APPEND REQUIRED_LIBS \"${STARPU_LIBRARIES_DEP}\")\n    elseif (STARPU_LIBRARIES)\n      foreach(lib ${STARPU_LIBRARIES})\n\tif (EXISTS ${lib} OR ${lib} MATCHES \"^-\")\n\t  list(APPEND REQUIRED_LIBS \"${lib}\")\n\telse()\n\t  list(APPEND REQUIRED_LIBS \"-l${lib}\")\n\tendif()\n      endforeach()\n    endif()\n  endif()\n  # CUDA\n  if (PASTIX_LOOK_FOR_STARPU_CUDA AND CUDA_FOUND)\n    if (CUDA_INCLUDE_DIRS)\n      list(APPEND REQUIRED_INCDIRS \"${CUDA_INCLUDE_DIRS}\")\n    endif()\n    foreach(libdir ${CUDA_LIBRARY_DIRS})\n      if (libdir)\n\tlist(APPEND REQUIRED_LIBDIRS \"${libdir}\")\n      endif()\n    endforeach()\n    list(APPEND REQUIRED_LIBS \"${CUDA_CUBLAS_LIBRARIES};${CUDA_LIBRARIES}\")\n  endif()\n  # MPI\n  if (PASTIX_LOOK_FOR_MPI AND MPI_FOUND)\n    if (MPI_C_INCLUDE_PATH)\n      list(APPEND REQUIRED_INCDIRS \"${MPI_C_INCLUDE_PATH}\")\n    endif()\n    if (MPI_C_LINK_FLAGS)\n      if (${MPI_C_LINK_FLAGS} MATCHES \"  -\")\n\tstring(REGEX REPLACE \" -\" \"-\" MPI_C_LINK_FLAGS ${MPI_C_LINK_FLAGS})\n      endif()\n      list(APPEND REQUIRED_LDFLAGS \"${MPI_C_LINK_FLAGS}\")\n    endif()\n    list(APPEND REQUIRED_LIBS \"${MPI_C_LIBRARIES}\")\n  endif()\n  # HWLOC\n  if (HWLOC_FOUND)\n    if (HWLOC_INCLUDE_DIRS)\n      list(APPEND REQUIRED_INCDIRS \"${HWLOC_INCLUDE_DIRS}\")\n    endif()\n    foreach(libdir ${HWLOC_LIBRARY_DIRS})\n      if (libdir)\n\tlist(APPEND REQUIRED_LIBDIRS \"${libdir}\")\n      endif()\n    endforeach()\n    foreach(lib ${HWLOC_LIBRARIES})\n      if (EXISTS ${lib} OR ${lib} MATCHES \"^-\")\n\tlist(APPEND REQUIRED_LIBS \"${lib}\")\n      else()\n\tlist(APPEND REQUIRED_LIBS \"-l${lib}\")\n      endif()\n    endforeach()\n  endif()\n  # BLAS\n  if (BLAS_FOUND)\n    if (BLAS_INCLUDE_DIRS)\n      list(APPEND REQUIRED_INCDIRS \"${BLAS_INCLUDE_DIRS}\")\n    endif()\n    foreach(libdir ${BLAS_LIBRARY_DIRS})\n      if (libdir)\n\tlist(APPEND REQUIRED_LIBDIRS \"${libdir}\")\n      endif()\n    endforeach()\n    list(APPEND REQUIRED_LIBS \"${BLAS_LIBRARIES}\")\n    if (BLAS_LINKER_FLAGS)\n      list(APPEND REQUIRED_LDFLAGS \"${BLAS_LINKER_FLAGS}\")\n    endif()\n  endif()\n  # SCOTCH\n  if (PASTIX_LOOK_FOR_SCOTCH AND SCOTCH_FOUND)\n    if (SCOTCH_INCLUDE_DIRS)\n      list(APPEND REQUIRED_INCDIRS \"${SCOTCH_INCLUDE_DIRS}\")\n    endif()\n    foreach(libdir ${SCOTCH_LIBRARY_DIRS})\n      if (libdir)\n\tlist(APPEND REQUIRED_LIBDIRS \"${libdir}\")\n      endif()\n    endforeach()\n    list(APPEND REQUIRED_LIBS \"${SCOTCH_LIBRARIES}\")\n  endif()\n  # PTSCOTCH\n  if (PASTIX_LOOK_FOR_PTSCOTCH AND PTSCOTCH_FOUND)\n    if (PTSCOTCH_INCLUDE_DIRS)\n      list(APPEND REQUIRED_INCDIRS \"${PTSCOTCH_INCLUDE_DIRS}\")\n    endif()\n    foreach(libdir ${PTSCOTCH_LIBRARY_DIRS})\n      if (libdir)\n\tlist(APPEND REQUIRED_LIBDIRS \"${libdir}\")\n      endif()\n    endforeach()\n    list(APPEND REQUIRED_LIBS \"${PTSCOTCH_LIBRARIES}\")\n  endif()\n  # METIS\n  if (PASTIX_LOOK_FOR_METIS AND METIS_FOUND)\n    if (METIS_INCLUDE_DIRS)\n      list(APPEND REQUIRED_INCDIRS \"${METIS_INCLUDE_DIRS}\")\n    endif()\n    foreach(libdir ${METIS_LIBRARY_DIRS})\n      if (libdir)\n\tlist(APPEND REQUIRED_LIBDIRS \"${libdir}\")\n      endif()\n    endforeach()\n    list(APPEND REQUIRED_LIBS \"${METIS_LIBRARIES}\")\n  endif()\n  # Fortran\n  if (CMAKE_C_COMPILER_ID MATCHES \"GNU\")\n    find_library(\n      FORTRAN_gfortran_LIBRARY\n      NAMES gfortran\n      HINTS ${_lib_env}\n      )\n    mark_as_advanced(FORTRAN_gfortran_LIBRARY)\n    if (FORTRAN_gfortran_LIBRARY)\n      list(APPEND REQUIRED_LIBS \"${FORTRAN_gfortran_LIBRARY}\")\n    endif()\n  elseif (CMAKE_C_COMPILER_ID MATCHES \"Intel\")\n    find_library(\n      FORTRAN_ifcore_LIBRARY\n      NAMES ifcore\n      HINTS ${_lib_env}\n      )\n    mark_as_advanced(FORTRAN_ifcore_LIBRARY)\n    if (FORTRAN_ifcore_LIBRARY)\n      list(APPEND REQUIRED_LIBS \"${FORTRAN_ifcore_LIBRARY}\")\n    endif()\n  endif()\n  # EXTRA LIBS such that pthread, m, rt\n  list(APPEND REQUIRED_LIBS ${PASTIX_EXTRA_LIBRARIES})\n\n  # set required libraries for link\n  set(CMAKE_REQUIRED_INCLUDES \"${REQUIRED_INCDIRS}\")\n  set(CMAKE_REQUIRED_LIBRARIES)\n  list(APPEND CMAKE_REQUIRED_LIBRARIES \"${REQUIRED_LDFLAGS}\")\n  foreach(lib_dir ${REQUIRED_LIBDIRS})\n    list(APPEND CMAKE_REQUIRED_LIBRARIES \"-L${lib_dir}\")\n  endforeach()\n  list(APPEND CMAKE_REQUIRED_LIBRARIES \"${REQUIRED_LIBS}\")\n  list(APPEND CMAKE_REQUIRED_FLAGS \"${REQUIRED_FLAGS}\")\n  string(REGEX REPLACE \"^ -\" \"-\" CMAKE_REQUIRED_LIBRARIES \"${CMAKE_REQUIRED_LIBRARIES}\")\n\n  # test link\n  unset(PASTIX_WORKS CACHE)\n  include(CheckFunctionExists)\n  check_function_exists(pastix PASTIX_WORKS)\n  mark_as_advanced(PASTIX_WORKS)\n\n  if(PASTIX_WORKS)\n    # save link with dependencies\n    set(PASTIX_LIBRARIES_DEP \"${REQUIRED_LIBS}\")\n    set(PASTIX_LIBRARY_DIRS_DEP \"${REQUIRED_LIBDIRS}\")\n    set(PASTIX_INCLUDE_DIRS_DEP \"${REQUIRED_INCDIRS}\")\n    set(PASTIX_LINKER_FLAGS \"${REQUIRED_LDFLAGS}\")\n    list(REMOVE_DUPLICATES PASTIX_LIBRARY_DIRS_DEP)\n    list(REMOVE_DUPLICATES PASTIX_INCLUDE_DIRS_DEP)\n    list(REMOVE_DUPLICATES PASTIX_LINKER_FLAGS)\n  else()\n    if(NOT PASTIX_FIND_QUIETLY)\n      message(STATUS \"Looking for PASTIX : test of pastix() fails\")\n      message(STATUS \"CMAKE_REQUIRED_LIBRARIES: ${CMAKE_REQUIRED_LIBRARIES}\")\n      message(STATUS \"CMAKE_REQUIRED_INCLUDES: ${CMAKE_REQUIRED_INCLUDES}\")\n      message(STATUS \"Check in CMakeFiles/CMakeError.log to figure out why it fails\")\n      message(STATUS \"Maybe PASTIX is linked with specific libraries. \"\n\t\"Have you tried with COMPONENTS (MPI/SEQ, STARPU, STARPU_CUDA, SCOTCH, PTSCOTCH, METIS)? \"\n\t\"See the explanation in FindPASTIX.cmake.\")\n    endif()\n  endif()\n  set(CMAKE_REQUIRED_INCLUDES)\n  set(CMAKE_REQUIRED_FLAGS)\n  set(CMAKE_REQUIRED_LIBRARIES)\nendif(PASTIX_LIBRARIES)\n\nif (PASTIX_LIBRARIES)\n  list(GET PASTIX_LIBRARIES 0 first_lib)\n  get_filename_component(first_lib_path \"${first_lib}\" PATH)\n  if (${first_lib_path} MATCHES \"/lib(32|64)?$\")\n    string(REGEX REPLACE \"/lib(32|64)?$\" \"\" not_cached_dir \"${first_lib_path}\")\n    set(PASTIX_DIR_FOUND \"${not_cached_dir}\" CACHE PATH \"Installation directory of PASTIX library\" FORCE)\n  else()\n    set(PASTIX_DIR_FOUND \"${first_lib_path}\" CACHE PATH \"Installation directory of PASTIX library\" FORCE)\n  endif()\nendif()\nmark_as_advanced(PASTIX_DIR)\nmark_as_advanced(PASTIX_DIR_FOUND)\n\n# check that PASTIX has been found\n# ---------------------------------\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(PASTIX DEFAULT_MSG\n  PASTIX_LIBRARIES\n  PASTIX_WORKS)\n"
  },
  {
    "path": "include/eigen3/cmake/FindSPQR.cmake",
    "content": "# SPQR lib usually requires linking to a blas and lapack library.\n# It is up to the user of this module to find a BLAS and link to it.\n\n# SPQR lib requires Cholmod, colamd and amd as well. \n# FindCholmod.cmake can be used to find those packages before finding spqr\n\nif (SPQR_INCLUDES AND SPQR_LIBRARIES)\n  set(SPQR_FIND_QUIETLY TRUE)\nendif (SPQR_INCLUDES AND SPQR_LIBRARIES)\n\nfind_path(SPQR_INCLUDES\n  NAMES\n  SuiteSparseQR.hpp\n  PATHS\n  $ENV{SPQRDIR}\n  ${INCLUDE_INSTALL_DIR}\n  PATH_SUFFIXES\n  suitesparse\n  ufsparse\n)\n\nfind_library(SPQR_LIBRARIES spqr $ENV{SPQRDIR} ${LIB_INSTALL_DIR})\n\nif(SPQR_LIBRARIES)\n\n  find_library(SUITESPARSE_LIBRARY SuiteSparse PATHS $ENV{SPQRDIR} ${LIB_INSTALL_DIR})\n  if (SUITESPARSE_LIBRARY)\n    set(SPQR_LIBRARIES ${SPQR_LIBRARIES} ${SUITESPARSE_LIBRARY})\n  endif()\n\n  find_library(CHOLMOD_LIBRARY cholmod PATHS $ENV{UMFPACK_LIBDIR} $ENV{UMFPACKDIR} ${LIB_INSTALL_DIR})\n  if(CHOLMOD_LIBRARY)\n    set(SPQR_LIBRARIES ${SPQR_LIBRARIES} ${CHOLMOD_LIBRARY})\n  endif()\n  \nendif(SPQR_LIBRARIES)\n\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(SPQR DEFAULT_MSG SPQR_INCLUDES SPQR_LIBRARIES)\n\nmark_as_advanced(SPQR_INCLUDES SPQR_LIBRARIES)"
  },
  {
    "path": "include/eigen3/cmake/FindScotch.cmake",
    "content": "###\n#\n# @copyright (c) 2009-2014 The University of Tennessee and The University\n#                          of Tennessee Research Foundation.\n#                          All rights reserved.\n# @copyright (c) 2012-2014 Inria. All rights reserved.\n# @copyright (c) 2012-2014 Bordeaux INP, CNRS (LaBRI UMR 5800), Inria, Univ. Bordeaux. All rights reserved.\n#\n###\n#\n# - Find SCOTCH include dirs and libraries\n# Use this module by invoking find_package with the form:\n#  find_package(SCOTCH\n#               [REQUIRED]             # Fail with error if scotch is not found\n#               [COMPONENTS <comp1> <comp2> ...] # dependencies\n#              )\n#\n#  COMPONENTS can be some of the following:\n#   - ESMUMPS: to activate detection of Scotch with the esmumps interface\n#\n# This module finds headers and scotch library.\n# Results are reported in variables:\n#  SCOTCH_FOUND           - True if headers and requested libraries were found\n#  SCOTCH_INCLUDE_DIRS    - scotch include directories\n#  SCOTCH_LIBRARY_DIRS    - Link directories for scotch libraries\n#  SCOTCH_LIBRARIES       - scotch component libraries to be linked\n#  SCOTCH_INTSIZE         - Number of octets occupied by a SCOTCH_Num\n#\n# The user can give specific paths where to find the libraries adding cmake\n# options at configure (ex: cmake path/to/project -DSCOTCH=path/to/scotch):\n#  SCOTCH_DIR             - Where to find the base directory of scotch\n#  SCOTCH_INCDIR          - Where to find the header files\n#  SCOTCH_LIBDIR          - Where to find the library files\n# The module can also look for the following environment variables if paths\n# are not given as cmake variable: SCOTCH_DIR, SCOTCH_INCDIR, SCOTCH_LIBDIR\n\n#=============================================================================\n# Copyright 2012-2013 Inria\n# Copyright 2012-2013 Emmanuel Agullo\n# Copyright 2012-2013 Mathieu Faverge\n# Copyright 2012      Cedric Castagnede\n# Copyright 2013      Florent Pruvost\n#\n# Distributed under the OSI-approved BSD License (the \"License\");\n# see accompanying file MORSE-Copyright.txt for details.\n#\n# This software is distributed WITHOUT ANY WARRANTY; without even the\n# implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.\n# See the License for more information.\n#=============================================================================\n# (To distribute this file outside of Morse, substitute the full\n#  License text for the above reference.)\n\nif (NOT SCOTCH_FOUND)\n  set(SCOTCH_DIR \"\" CACHE PATH \"Installation directory of SCOTCH library\")\n  if (NOT SCOTCH_FIND_QUIETLY)\n    message(STATUS \"A cache variable, namely SCOTCH_DIR, has been set to specify the install directory of SCOTCH\")\n  endif()\nendif()\n\n# Set the version to find\nset(SCOTCH_LOOK_FOR_ESMUMPS OFF)\n\nif( SCOTCH_FIND_COMPONENTS )\n  foreach( component ${SCOTCH_FIND_COMPONENTS} )\n    if (${component} STREQUAL \"ESMUMPS\")\n      # means we look for esmumps library\n      set(SCOTCH_LOOK_FOR_ESMUMPS ON)\n    endif()\n  endforeach()\nendif()\n\n# SCOTCH may depend on Threads, try to find it\nif (NOT THREADS_FOUND)\n  if (SCOTCH_FIND_REQUIRED)\n    find_package(Threads REQUIRED)\n  else()\n    find_package(Threads)\n  endif()\nendif()\n\n# Looking for include\n# -------------------\n\n# Add system include paths to search include\n# ------------------------------------------\nunset(_inc_env)\nset(ENV_SCOTCH_DIR \"$ENV{SCOTCH_DIR}\")\nset(ENV_SCOTCH_INCDIR \"$ENV{SCOTCH_INCDIR}\")\nif(ENV_SCOTCH_INCDIR)\n  list(APPEND _inc_env \"${ENV_SCOTCH_INCDIR}\")\nelseif(ENV_SCOTCH_DIR)\n  list(APPEND _inc_env \"${ENV_SCOTCH_DIR}\")\n  list(APPEND _inc_env \"${ENV_SCOTCH_DIR}/include\")\n  list(APPEND _inc_env \"${ENV_SCOTCH_DIR}/include/scotch\")\nelse()\n  if(WIN32)\n    string(REPLACE \":\" \";\" _inc_env \"$ENV{INCLUDE}\")\n  else()\n    string(REPLACE \":\" \";\" _path_env \"$ENV{INCLUDE}\")\n    list(APPEND _inc_env \"${_path_env}\")\n    string(REPLACE \":\" \";\" _path_env \"$ENV{C_INCLUDE_PATH}\")\n    list(APPEND _inc_env \"${_path_env}\")\n    string(REPLACE \":\" \";\" _path_env \"$ENV{CPATH}\")\n    list(APPEND _inc_env \"${_path_env}\")\n    string(REPLACE \":\" \";\" _path_env \"$ENV{INCLUDE_PATH}\")\n    list(APPEND _inc_env \"${_path_env}\")\n  endif()\nendif()\nlist(APPEND _inc_env \"${CMAKE_PLATFORM_IMPLICIT_INCLUDE_DIRECTORIES}\")\nlist(APPEND _inc_env \"${CMAKE_C_IMPLICIT_INCLUDE_DIRECTORIES}\")\nlist(REMOVE_DUPLICATES _inc_env)\n\n\n# Try to find the scotch header in the given paths\n# -------------------------------------------------\n# call cmake macro to find the header path\nif(SCOTCH_INCDIR)\n  set(SCOTCH_scotch.h_DIRS \"SCOTCH_scotch.h_DIRS-NOTFOUND\")\n  find_path(SCOTCH_scotch.h_DIRS\n    NAMES scotch.h\n    HINTS ${SCOTCH_INCDIR})\nelse()\n  if(SCOTCH_DIR)\n    set(SCOTCH_scotch.h_DIRS \"SCOTCH_scotch.h_DIRS-NOTFOUND\")\n    find_path(SCOTCH_scotch.h_DIRS\n      NAMES scotch.h\n      HINTS ${SCOTCH_DIR}\n      PATH_SUFFIXES \"include\" \"include/scotch\")\n  else()\n    set(SCOTCH_scotch.h_DIRS \"SCOTCH_scotch.h_DIRS-NOTFOUND\")\n    find_path(SCOTCH_scotch.h_DIRS\n      NAMES scotch.h\n      HINTS ${_inc_env}\n      PATH_SUFFIXES \"scotch\")\n  endif()\nendif()\nmark_as_advanced(SCOTCH_scotch.h_DIRS)\n\n# If found, add path to cmake variable\n# ------------------------------------\nif (SCOTCH_scotch.h_DIRS)\n  set(SCOTCH_INCLUDE_DIRS \"${SCOTCH_scotch.h_DIRS}\")\nelse ()\n  set(SCOTCH_INCLUDE_DIRS \"SCOTCH_INCLUDE_DIRS-NOTFOUND\")\n  if (NOT SCOTCH_FIND_QUIETLY)\n    message(STATUS \"Looking for scotch -- scotch.h not found\")\n  endif()\nendif()\nlist(REMOVE_DUPLICATES SCOTCH_INCLUDE_DIRS)\n\n# Looking for lib\n# ---------------\n\n# Add system library paths to search lib\n# --------------------------------------\nunset(_lib_env)\nset(ENV_SCOTCH_LIBDIR \"$ENV{SCOTCH_LIBDIR}\")\nif(ENV_SCOTCH_LIBDIR)\n  list(APPEND _lib_env \"${ENV_SCOTCH_LIBDIR}\")\nelseif(ENV_SCOTCH_DIR)\n  list(APPEND _lib_env \"${ENV_SCOTCH_DIR}\")\n  list(APPEND _lib_env \"${ENV_SCOTCH_DIR}/lib\")\nelse()\n  if(WIN32)\n    string(REPLACE \":\" \";\" _lib_env \"$ENV{LIB}\")\n  else()\n    if(APPLE)\n      string(REPLACE \":\" \";\" _lib_env \"$ENV{DYLD_LIBRARY_PATH}\")\n    else()\n      string(REPLACE \":\" \";\" _lib_env \"$ENV{LD_LIBRARY_PATH}\")\n    endif()\n    list(APPEND _lib_env \"${CMAKE_PLATFORM_IMPLICIT_LINK_DIRECTORIES}\")\n    list(APPEND _lib_env \"${CMAKE_C_IMPLICIT_LINK_DIRECTORIES}\")\n  endif()\nendif()\nlist(REMOVE_DUPLICATES _lib_env)\n\n# Try to find the scotch lib in the given paths\n# ----------------------------------------------\n\nset(SCOTCH_libs_to_find \"scotch;scotcherrexit\")\nif (SCOTCH_LOOK_FOR_ESMUMPS)\n  list(INSERT SCOTCH_libs_to_find 0 \"esmumps\")\nendif()\n\n# call cmake macro to find the lib path\nif(SCOTCH_LIBDIR)\n  foreach(scotch_lib ${SCOTCH_libs_to_find})\n    set(SCOTCH_${scotch_lib}_LIBRARY \"SCOTCH_${scotch_lib}_LIBRARY-NOTFOUND\")\n    find_library(SCOTCH_${scotch_lib}_LIBRARY\n      NAMES ${scotch_lib}\n      HINTS ${SCOTCH_LIBDIR})\n  endforeach()\nelse()\n  if(SCOTCH_DIR)\n    foreach(scotch_lib ${SCOTCH_libs_to_find})\n      set(SCOTCH_${scotch_lib}_LIBRARY \"SCOTCH_${scotch_lib}_LIBRARY-NOTFOUND\")\n      find_library(SCOTCH_${scotch_lib}_LIBRARY\n\tNAMES ${scotch_lib}\n\tHINTS ${SCOTCH_DIR}\n\tPATH_SUFFIXES lib lib32 lib64)\n    endforeach()\n  else()\n    foreach(scotch_lib ${SCOTCH_libs_to_find})\n      set(SCOTCH_${scotch_lib}_LIBRARY \"SCOTCH_${scotch_lib}_LIBRARY-NOTFOUND\")\n      find_library(SCOTCH_${scotch_lib}_LIBRARY\n\tNAMES ${scotch_lib}\n\tHINTS ${_lib_env})\n    endforeach()\n  endif()\nendif()\n\nset(SCOTCH_LIBRARIES \"\")\nset(SCOTCH_LIBRARY_DIRS \"\")\n# If found, add path to cmake variable\n# ------------------------------------\nforeach(scotch_lib ${SCOTCH_libs_to_find})\n\n  if (SCOTCH_${scotch_lib}_LIBRARY)\n    get_filename_component(${scotch_lib}_lib_path \"${SCOTCH_${scotch_lib}_LIBRARY}\" PATH)\n    # set cmake variables\n    list(APPEND SCOTCH_LIBRARIES \"${SCOTCH_${scotch_lib}_LIBRARY}\")\n    list(APPEND SCOTCH_LIBRARY_DIRS \"${${scotch_lib}_lib_path}\")\n  else ()\n    list(APPEND SCOTCH_LIBRARIES \"${SCOTCH_${scotch_lib}_LIBRARY}\")\n    if (NOT SCOTCH_FIND_QUIETLY)\n      message(STATUS \"Looking for scotch -- lib ${scotch_lib} not found\")\n    endif()\n  endif ()\n\n  mark_as_advanced(SCOTCH_${scotch_lib}_LIBRARY)\n\nendforeach()\nlist(REMOVE_DUPLICATES SCOTCH_LIBRARY_DIRS)\n\n# check a function to validate the find\nif(SCOTCH_LIBRARIES)\n\n  set(REQUIRED_INCDIRS)\n  set(REQUIRED_LIBDIRS)\n  set(REQUIRED_LIBS)\n\n  # SCOTCH\n  if (SCOTCH_INCLUDE_DIRS)\n    set(REQUIRED_INCDIRS  \"${SCOTCH_INCLUDE_DIRS}\")\n  endif()\n  if (SCOTCH_LIBRARY_DIRS)\n    set(REQUIRED_LIBDIRS \"${SCOTCH_LIBRARY_DIRS}\")\n  endif()\n  set(REQUIRED_LIBS \"${SCOTCH_LIBRARIES}\")\n  # THREADS\n  if(CMAKE_THREAD_LIBS_INIT)\n    list(APPEND REQUIRED_LIBS \"${CMAKE_THREAD_LIBS_INIT}\")\n  endif()\n  set(Z_LIBRARY \"Z_LIBRARY-NOTFOUND\")\n  find_library(Z_LIBRARY NAMES z)\n  mark_as_advanced(Z_LIBRARY)\n  if(Z_LIBRARY)\n    list(APPEND REQUIRED_LIBS \"-lz\")\n  endif()\n  set(M_LIBRARY \"M_LIBRARY-NOTFOUND\")\n  find_library(M_LIBRARY NAMES m)\n  mark_as_advanced(M_LIBRARY)\n  if(M_LIBRARY)\n    list(APPEND REQUIRED_LIBS \"-lm\")\n  endif()\n  set(RT_LIBRARY \"RT_LIBRARY-NOTFOUND\")\n  find_library(RT_LIBRARY NAMES rt)\n  mark_as_advanced(RT_LIBRARY)\n  if(RT_LIBRARY)\n    list(APPEND REQUIRED_LIBS \"-lrt\")\n  endif()\n\n  # set required libraries for link\n  set(CMAKE_REQUIRED_INCLUDES \"${REQUIRED_INCDIRS}\")\n  set(CMAKE_REQUIRED_LIBRARIES)\n  foreach(lib_dir ${REQUIRED_LIBDIRS})\n    list(APPEND CMAKE_REQUIRED_LIBRARIES \"-L${lib_dir}\")\n  endforeach()\n  list(APPEND CMAKE_REQUIRED_LIBRARIES \"${REQUIRED_LIBS}\")\n  string(REGEX REPLACE \"^ -\" \"-\" CMAKE_REQUIRED_LIBRARIES \"${CMAKE_REQUIRED_LIBRARIES}\")\n\n  # test link\n  unset(SCOTCH_WORKS CACHE)\n  include(CheckFunctionExists)\n  check_function_exists(SCOTCH_graphInit SCOTCH_WORKS)\n  mark_as_advanced(SCOTCH_WORKS)\n\n  if(SCOTCH_WORKS)\n    # save link with dependencies\n    set(SCOTCH_LIBRARIES \"${REQUIRED_LIBS}\")\n  else()\n    if(NOT SCOTCH_FIND_QUIETLY)\n      message(STATUS \"Looking for SCOTCH : test of SCOTCH_graphInit with SCOTCH library fails\")\n      message(STATUS \"CMAKE_REQUIRED_LIBRARIES: ${CMAKE_REQUIRED_LIBRARIES}\")\n      message(STATUS \"CMAKE_REQUIRED_INCLUDES: ${CMAKE_REQUIRED_INCLUDES}\")\n      message(STATUS \"Check in CMakeFiles/CMakeError.log to figure out why it fails\")\n    endif()\n  endif()\n  set(CMAKE_REQUIRED_INCLUDES)\n  set(CMAKE_REQUIRED_FLAGS)\n  set(CMAKE_REQUIRED_LIBRARIES)\nendif(SCOTCH_LIBRARIES)\n\nif (SCOTCH_LIBRARIES)\n  list(GET SCOTCH_LIBRARIES 0 first_lib)\n  get_filename_component(first_lib_path \"${first_lib}\" PATH)\n  if (${first_lib_path} MATCHES \"/lib(32|64)?$\")\n    string(REGEX REPLACE \"/lib(32|64)?$\" \"\" not_cached_dir \"${first_lib_path}\")\n    set(SCOTCH_DIR_FOUND \"${not_cached_dir}\" CACHE PATH \"Installation directory of SCOTCH library\" FORCE)\n  else()\n    set(SCOTCH_DIR_FOUND \"${first_lib_path}\" CACHE PATH \"Installation directory of SCOTCH library\" FORCE)\n  endif()\nendif()\nmark_as_advanced(SCOTCH_DIR)\nmark_as_advanced(SCOTCH_DIR_FOUND)\n\n# Check the size of SCOTCH_Num\n# ---------------------------------\nset(CMAKE_REQUIRED_INCLUDES ${SCOTCH_INCLUDE_DIRS})\n\ninclude(CheckCSourceRuns)\n#stdio.h and stdint.h should be included by scotch.h directly\nset(SCOTCH_C_TEST_SCOTCH_Num_4 \"\n#include <stdio.h>\n#include <stdint.h>\n#include <scotch.h>\nint main(int argc, char **argv) {\n  if (sizeof(SCOTCH_Num) == 4)\n    return 0;\n  else\n    return 1;\n}\n\")\n\nset(SCOTCH_C_TEST_SCOTCH_Num_8 \"\n#include <stdio.h>\n#include <stdint.h>\n#include <scotch.h>\nint main(int argc, char **argv) {\n  if (sizeof(SCOTCH_Num) == 8)\n    return 0;\n  else\n    return 1;\n}\n\")\ncheck_c_source_runs(\"${SCOTCH_C_TEST_SCOTCH_Num_4}\" SCOTCH_Num_4)\nif(NOT SCOTCH_Num_4)\n  check_c_source_runs(\"${SCOTCH_C_TEST_SCOTCH_Num_8}\" SCOTCH_Num_8)\n  if(NOT SCOTCH_Num_8)\n    set(SCOTCH_INTSIZE -1)\n  else()\n    set(SCOTCH_INTSIZE 8)\n  endif()\nelse()\n  set(SCOTCH_INTSIZE 4)\nendif()\nset(CMAKE_REQUIRED_INCLUDES \"\")\n\n# check that SCOTCH has been found\n# ---------------------------------\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(SCOTCH DEFAULT_MSG\n  SCOTCH_LIBRARIES\n  SCOTCH_WORKS)\n#\n# TODO: Add possibility to check for specific functions in the library\n#\n"
  },
  {
    "path": "include/eigen3/cmake/FindStandardMathLibrary.cmake",
    "content": "# - Try to find how to link to the standard math library, if anything at all is needed to do.\n# On most platforms this is automatic, but for example it's not automatic on QNX.\n#\n# Once done this will define\n#\n#  STANDARD_MATH_LIBRARY_FOUND - we found how to successfully link to the standard math library\n#  STANDARD_MATH_LIBRARY - the name of the standard library that one has to link to.\n#                            -- this will be left empty if it's automatic (most platforms).\n#                            -- this will be set to \"m\" on platforms where one must explicitly\n#                               pass the \"-lm\" linker flag.\n#\n# Copyright (c) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>\n# Redistribution and use is allowed according to the terms of the 2-clause BSD license.\n\n\ninclude(CheckCXXSourceCompiles)\n\n# a little test program for c++ math functions.\n# notice the std:: is required on some platforms such as QNX\n\nset(find_standard_math_library_test_program\n\"#include<cmath>\nint main() { std::sin(0.0); std::log(0.0f); }\")\n\n# first try compiling/linking the test program without any linker flags\n\nset(CMAKE_REQUIRED_FLAGS \"\")\nset(CMAKE_REQUIRED_LIBRARIES \"\")\nCHECK_CXX_SOURCE_COMPILES(\n  \"${find_standard_math_library_test_program}\"\n  standard_math_library_linked_to_automatically\n)\n\nif(standard_math_library_linked_to_automatically)\n\n  # the test program linked successfully without any linker flag.\n  set(STANDARD_MATH_LIBRARY \"\")\n  set(STANDARD_MATH_LIBRARY_FOUND TRUE)\n\nelse()\n\n  # the test program did not link successfully without any linker flag.\n  # This is a very uncommon case that so far we only saw on QNX. The next try is the\n  # standard name 'm' for the standard math library.\n\n  set(CMAKE_REQUIRED_LIBRARIES \"m\")\n  CHECK_CXX_SOURCE_COMPILES(\n    \"${find_standard_math_library_test_program}\"\n    standard_math_library_linked_to_as_m)\n\n  if(standard_math_library_linked_to_as_m)\n\n    # the test program linked successfully when linking to the 'm' library\n    set(STANDARD_MATH_LIBRARY \"m\")\n    set(STANDARD_MATH_LIBRARY_FOUND TRUE)\n\n  else()\n\n    # the test program still doesn't link successfully\n    set(STANDARD_MATH_LIBRARY_FOUND FALSE)\n\n  endif()\n\nendif()\n"
  },
  {
    "path": "include/eigen3/cmake/FindSuperLU.cmake",
    "content": "\n# Umfpack lib usually requires linking to a blas library.\n# It is up to the user of this module to find a BLAS and link to it.\n\nif (SUPERLU_INCLUDES AND SUPERLU_LIBRARIES)\n  set(SUPERLU_FIND_QUIETLY TRUE)\nendif (SUPERLU_INCLUDES AND SUPERLU_LIBRARIES)\n\nfind_path(SUPERLU_INCLUDES\n  NAMES\n  supermatrix.h\n  PATHS\n  $ENV{SUPERLUDIR}\n  ${INCLUDE_INSTALL_DIR}\n  PATH_SUFFIXES\n  superlu\n  SRC\n)\n\nfind_library(SUPERLU_LIBRARIES\n  NAMES \"superlu_5.2.1\" \"superlu_5.2\" \"superlu_5.1.1\" \"superlu_5.1\" \"superlu_5.0\" \"superlu_4.3\" \"superlu_4.2\" \"superlu_4.1\" \"superlu_4.0\" \"superlu_3.1\" \"superlu_3.0\" \"superlu\"\n  PATHS $ENV{SUPERLUDIR} ${LIB_INSTALL_DIR}\n  PATH_SUFFIXES lib)\n\nif(SUPERLU_INCLUDES AND SUPERLU_LIBRARIES)\n\ninclude(CheckCXXSourceCompiles)\ninclude(CMakePushCheckState)\ncmake_push_check_state()\n\nset(CMAKE_REQUIRED_INCLUDES ${CMAKE_REQUIRED_INCLUDES} ${SUPERLU_INCLUDES})\n\n# check whether struct mem_usage_t is globally defined\ncheck_cxx_source_compiles(\"\ntypedef int int_t;\n#include <supermatrix.h>\n#include <slu_util.h>\nint main() {\n  mem_usage_t mem;\n  return 0;\n}\"\nSUPERLU_HAS_GLOBAL_MEM_USAGE_T)\n\n\ncheck_cxx_source_compiles(\"\ntypedef int int_t;\n#include <supermatrix.h>\n#include <superlu_enum_consts.h>\nint main() {\n  return SLU_SINGLE;\n}\"\nSUPERLU_HAS_CLEAN_ENUMS)\n\ncheck_cxx_source_compiles(\"\ntypedef int int_t;\n#include <supermatrix.h>\n#include <slu_util.h>\nint main(void)\n{\n  GlobalLU_t glu;\n  return 0;\n}\"\nSUPERLU_HAS_GLOBALLU_T)\n\nif(SUPERLU_HAS_GLOBALLU_T)\n  # at least 5.0\n  set(SUPERLU_VERSION_VAR \"5.0\")\nelseif(SUPERLU_HAS_CLEAN_ENUMS)\n  # at least 4.3\n  set(SUPERLU_VERSION_VAR \"4.3\")\nelseif(SUPERLU_HAS_GLOBAL_MEM_USAGE_T)\n  # at least 4.0\n  set(SUPERLU_VERSION_VAR \"4.0\")\nelse()\n  set(SUPERLU_VERSION_VAR \"3.0\")\nendif()\n\ncmake_pop_check_state()\n\nif(SuperLU_FIND_VERSION)\n  if(${SUPERLU_VERSION_VAR} VERSION_LESS ${SuperLU_FIND_VERSION})\n    set(SUPERLU_VERSION_OK FALSE)\n  else()\n    set(SUPERLU_VERSION_OK TRUE)\n  endif()\nelse()\n  set(SUPERLU_VERSION_OK TRUE)\nendif()\n\nendif()\n\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(SUPERLU\n                                  REQUIRED_VARS SUPERLU_INCLUDES SUPERLU_LIBRARIES SUPERLU_VERSION_OK\n                                  VERSION_VAR SUPERLU_VERSION_VAR)\n\nmark_as_advanced(SUPERLU_INCLUDES SUPERLU_LIBRARIES)\n"
  },
  {
    "path": "include/eigen3/cmake/FindUmfpack.cmake",
    "content": "# Umfpack lib usually requires linking to a blas library.\n# It is up to the user of this module to find a BLAS and link to it.\n\nif (UMFPACK_INCLUDES AND UMFPACK_LIBRARIES)\n  set(UMFPACK_FIND_QUIETLY TRUE)\nendif (UMFPACK_INCLUDES AND UMFPACK_LIBRARIES)\n\nfind_path(UMFPACK_INCLUDES\n  NAMES\n  umfpack.h\n  PATHS\n  $ENV{UMFPACKDIR}\n  ${INCLUDE_INSTALL_DIR}\n  PATH_SUFFIXES\n  suitesparse\n  ufsparse\n)\n\nfind_library(UMFPACK_LIBRARIES umfpack PATHS $ENV{UMFPACKDIR} ${LIB_INSTALL_DIR})\n\nif(UMFPACK_LIBRARIES)\n\n  if(NOT UMFPACK_LIBDIR)\n    get_filename_component(UMFPACK_LIBDIR ${UMFPACK_LIBRARIES} PATH)\n  endif(NOT UMFPACK_LIBDIR)\n\n  find_library(COLAMD_LIBRARY colamd PATHS ${UMFPACK_LIBDIR} $ENV{UMFPACKDIR} ${LIB_INSTALL_DIR})\n  if(COLAMD_LIBRARY)\n    set(UMFPACK_LIBRARIES ${UMFPACK_LIBRARIES} ${COLAMD_LIBRARY})\n  endif ()\n  \n  find_library(AMD_LIBRARY amd PATHS ${UMFPACK_LIBDIR} $ENV{UMFPACKDIR} ${LIB_INSTALL_DIR})\n  if(AMD_LIBRARY)\n    set(UMFPACK_LIBRARIES ${UMFPACK_LIBRARIES} ${AMD_LIBRARY})\n  endif ()\n\n  find_library(SUITESPARSE_LIBRARY SuiteSparse PATHS ${UMFPACK_LIBDIR} $ENV{UMFPACKDIR} ${LIB_INSTALL_DIR})\n  if(SUITESPARSE_LIBRARY)\n    set(UMFPACK_LIBRARIES ${UMFPACK_LIBRARIES} ${SUITESPARSE_LIBRARY})\n  endif ()\n\n  find_library(CHOLMOD_LIBRARY cholmod PATHS $ENV{UMFPACK_LIBDIR} $ENV{UMFPACKDIR} ${LIB_INSTALL_DIR})\n  if(CHOLMOD_LIBRARY)\n    set(UMFPACK_LIBRARIES ${UMFPACK_LIBRARIES} ${CHOLMOD_LIBRARY})\n  endif()\n\nendif(UMFPACK_LIBRARIES)\n\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(UMFPACK DEFAULT_MSG\n                                  UMFPACK_INCLUDES UMFPACK_LIBRARIES)\n\nmark_as_advanced(UMFPACK_INCLUDES UMFPACK_LIBRARIES AMD_LIBRARY COLAMD_LIBRARY CHOLMOD_LIBRARY SUITESPARSE_LIBRARY)\n"
  },
  {
    "path": "include/eigen3/cmake/RegexUtils.cmake",
    "content": "function(escape_string_as_regex _str_out _str_in)\n  STRING(REGEX REPLACE \"\\\\\\\\\" \"\\\\\\\\\\\\\\\\\" FILETEST2 \"${_str_in}\")\n  STRING(REGEX REPLACE \"([.$+*?|-])\" \"\\\\\\\\\\\\1\" FILETEST2 \"${FILETEST2}\")\n  STRING(REGEX REPLACE \"\\\\^\" \"\\\\\\\\^\" FILETEST2 \"${FILETEST2}\")\n  STRING(REGEX REPLACE \"\\\\(\" \"\\\\\\\\(\" FILETEST2 \"${FILETEST2}\")\n  STRING(REGEX REPLACE \"\\\\)\" \"\\\\\\\\)\" FILETEST2 \"${FILETEST2}\")\n  STRING(REGEX REPLACE \"\\\\[\" \"\\\\\\\\[\" FILETEST2 \"${FILETEST2}\")\n  STRING(REGEX REPLACE \"\\\\]\" \"\\\\\\\\]\" FILETEST2 \"${FILETEST2}\")\n  SET(${_str_out} \"${FILETEST2}\" PARENT_SCOPE)\nendfunction()\n\nfunction(test_escape_string_as_regex)\n  SET(test1 \"\\\\.^$-+*()[]?|\")\n  escape_string_as_regex(test2 \"${test1}\")\n  SET(testRef \"\\\\\\\\\\\\.\\\\^\\\\$\\\\-\\\\+\\\\*\\\\(\\\\)\\\\[\\\\]\\\\?\\\\|\")\n  if(NOT test2 STREQUAL testRef)\n\tmessage(\"Error in the escape_string_for_regex function : \\n   ${test1} was escaped as ${test2}, should be ${testRef}\")\n  endif(NOT test2 STREQUAL testRef)\nendfunction()"
  },
  {
    "path": "include/eigen3/cmake/UseEigen3.cmake",
    "content": "#                                               -*- cmake -*-\n#\n#  UseEigen3.cmake\n\nadd_definitions     ( ${EIGEN3_DEFINITIONS} )\ninclude_directories ( ${EIGEN3_INCLUDE_DIRS} )\n"
  },
  {
    "path": "include/eigen3/cmake/language_support.cmake",
    "content": "# cmake/modules/language_support.cmake\n#\n# Temporary additional general language support is contained within this\n# file.  \n\n# This additional function definition is needed to provide a workaround for\n# CMake bug 9220.\n\n# On debian testing (cmake 2.6.2), I get return code zero when calling \n# cmake the first time, but cmake crashes when running a second time\n# as follows:\n#\n#  -- The Fortran compiler identification is unknown\n#  CMake Error at /usr/share/cmake-2.6/Modules/CMakeFortranInformation.cmake:7 (GET_FILENAME_COMPONENT):\n#    get_filename_component called with incorrect number of arguments\n#  Call Stack (most recent call first):\n#    CMakeLists.txt:3 (enable_language)\n#\n# My workaround is to invoke cmake twice.  If both return codes are zero, \n# it is safe to invoke ENABLE_LANGUAGE(Fortran OPTIONAL)\n\nfunction(workaround_9220 language language_works)\n  #message(\"DEBUG: language = ${language}\")\n  set(text\n    \"project(test NONE)\n    cmake_minimum_required(VERSION 2.8.0)\n    set (CMAKE_Fortran_FLAGS \\\"${CMAKE_Fortran_FLAGS}\\\")\n    set (CMAKE_EXE_LINKER_FLAGS \\\"${CMAKE_EXE_LINKER_FLAGS}\\\")\n    enable_language(${language})\n  \")\n  file(REMOVE_RECURSE ${CMAKE_BINARY_DIR}/language_tests/${language})\n  file(MAKE_DIRECTORY ${CMAKE_BINARY_DIR}/language_tests/${language})\n  file(WRITE ${CMAKE_BINARY_DIR}/language_tests/${language}/CMakeLists.txt\n    ${text})\n  execute_process(\n    COMMAND ${CMAKE_COMMAND} . -G \"${CMAKE_GENERATOR}\"\n    WORKING_DIRECTORY ${CMAKE_BINARY_DIR}/language_tests/${language}\n    RESULT_VARIABLE return_code\n    OUTPUT_QUIET\n    ERROR_QUIET\n    )\n\n  if(return_code EQUAL 0)\n    # Second run\n    execute_process (\n      COMMAND ${CMAKE_COMMAND} . -G \"${CMAKE_GENERATOR}\"\n      WORKING_DIRECTORY ${CMAKE_BINARY_DIR}/language_tests/${language}\n      RESULT_VARIABLE return_code\n      OUTPUT_QUIET\n      ERROR_QUIET\n      )\n    if(return_code EQUAL 0)\n      set(${language_works} ON PARENT_SCOPE)\n    else(return_code EQUAL 0)\n      set(${language_works} OFF PARENT_SCOPE)\n    endif(return_code EQUAL 0)\n  else(return_code EQUAL 0)\n    set(${language_works} OFF PARENT_SCOPE)\n  endif(return_code EQUAL 0)\nendfunction(workaround_9220)\n\n# Temporary tests of the above function.\n#workaround_9220(CXX CXX_language_works)\n#message(\"CXX_language_works = ${CXX_language_works}\")\n#workaround_9220(CXXp CXXp_language_works)\n#message(\"CXXp_language_works = ${CXXp_language_works}\")\n\n"
  },
  {
    "path": "include/eigen3/debug/gdb/__init__.py",
    "content": "# Intentionally empty\n"
  },
  {
    "path": "include/eigen3/debug/gdb/printers.py",
    "content": "# -*- coding: utf-8 -*-\n# This file is part of Eigen, a lightweight C++ template library\n# for linear algebra.\n#\n# Copyright (C) 2009 Benjamin Schindler <bschindler@inf.ethz.ch>\n#\n# This Source Code Form is subject to the terms of the Mozilla Public\n# License, v. 2.0. If a copy of the MPL was not distributed with this\n# file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n# Pretty printers for Eigen::Matrix\n# This is still pretty basic as the python extension to gdb is still pretty basic. \n# It cannot handle complex eigen types and it doesn't support any of the other eigen types\n# Such as quaternion or some other type. \n# This code supports fixed size as well as dynamic size matrices\n\n# To use it:\n#\n# * Create a directory and put the file as well as an empty __init__.py in \n#   that directory.\n# * Create a ~/.gdbinit file, that contains the following:\n#      python\n#      import sys\n#      sys.path.insert(0, '/path/to/eigen/printer/directory')\n#      from printers import register_eigen_printers\n#      register_eigen_printers (None)\n#      end\n\nimport gdb\nimport re\nimport itertools\n\n\nclass EigenMatrixPrinter:\n\t\"Print Eigen Matrix or Array of some kind\"\n\n\tdef __init__(self, variety, val):\n\t\t\"Extract all the necessary information\"\n\t\t\n\t\t# Save the variety (presumably \"Matrix\" or \"Array\") for later usage\n\t\tself.variety = variety\n\t\t\n\t\t# The gdb extension does not support value template arguments - need to extract them by hand\n\t\ttype = val.type\n\t\tif type.code == gdb.TYPE_CODE_REF:\n\t\t\ttype = type.target()\n\t\tself.type = type.unqualified().strip_typedefs()\n\t\ttag = self.type.tag\n\t\tregex = re.compile('\\<.*\\>')\n\t\tm = regex.findall(tag)[0][1:-1]\n\t\ttemplate_params = m.split(',')\n\t\ttemplate_params = [x.replace(\" \", \"\") for x in template_params]\n\t\t\n\t\tif template_params[1] == '-0x00000000000000001' or template_params[1] == '-0x000000001' or template_params[1] == '-1':\n\t\t\tself.rows = val['m_storage']['m_rows']\n\t\telse:\n\t\t\tself.rows = int(template_params[1])\n\t\t\n\t\tif template_params[2] == '-0x00000000000000001' or template_params[2] == '-0x000000001' or template_params[2] == '-1':\n\t\t\tself.cols = val['m_storage']['m_cols']\n\t\telse:\n\t\t\tself.cols = int(template_params[2])\n\t\t\n\t\tself.options = 0 # default value\n\t\tif len(template_params) > 3:\n\t\t\tself.options = template_params[3];\n\t\t\n\t\tself.rowMajor = (int(self.options) & 0x1)\n\t\t\n\t\tself.innerType = self.type.template_argument(0)\n\t\t\n\t\tself.val = val\n\t\t\n\t\t# Fixed size matrices have a struct as their storage, so we need to walk through this\n\t\tself.data = self.val['m_storage']['m_data']\n\t\tif self.data.type.code == gdb.TYPE_CODE_STRUCT:\n\t\t\tself.data = self.data['array']\n\t\t\tself.data = self.data.cast(self.innerType.pointer())\n\t\t\t\n\tclass _iterator:\n\t\tdef __init__ (self, rows, cols, dataPtr, rowMajor):\n\t\t\tself.rows = rows\n\t\t\tself.cols = cols\n\t\t\tself.dataPtr = dataPtr\n\t\t\tself.currentRow = 0\n\t\t\tself.currentCol = 0\n\t\t\tself.rowMajor = rowMajor\n\t\t\t\n\t\tdef __iter__ (self):\n\t\t\treturn self\n\n\t\tdef next(self):\n                        return self.__next__()  # Python 2.x compatibility\n\n\t\tdef __next__(self):\n\t\t\t\n\t\t\trow = self.currentRow\n\t\t\tcol = self.currentCol\n\t\t\tif self.rowMajor == 0:\n\t\t\t\tif self.currentCol >= self.cols:\n\t\t\t\t\traise StopIteration\n\t\t\t\t\t\n\t\t\t\tself.currentRow = self.currentRow + 1\n\t\t\t\tif self.currentRow >= self.rows:\n\t\t\t\t\tself.currentRow = 0\n\t\t\t\t\tself.currentCol = self.currentCol + 1\n\t\t\telse:\n\t\t\t\tif self.currentRow >= self.rows:\n\t\t\t\t\traise StopIteration\n\t\t\t\t\t\n\t\t\t\tself.currentCol = self.currentCol + 1\n\t\t\t\tif self.currentCol >= self.cols:\n\t\t\t\t\tself.currentCol = 0\n\t\t\t\t\tself.currentRow = self.currentRow + 1\n\t\t\t\t\n\t\t\t\n\t\t\titem = self.dataPtr.dereference()\n\t\t\tself.dataPtr = self.dataPtr + 1\n\t\t\tif (self.cols == 1): #if it's a column vector\n\t\t\t\treturn ('[%d]' % (row,), item)\n\t\t\telif (self.rows == 1): #if it's a row vector\n\t\t\t\treturn ('[%d]' % (col,), item)\n\t\t\treturn ('[%d,%d]' % (row, col), item)\n\t\t\t\n\tdef children(self):\n\t\t\n\t\treturn self._iterator(self.rows, self.cols, self.data, self.rowMajor)\n\t\t\n\tdef to_string(self):\n\t\treturn \"Eigen::%s<%s,%d,%d,%s> (data ptr: %s)\" % (self.variety, self.innerType, self.rows, self.cols, \"RowMajor\" if self.rowMajor else  \"ColMajor\", self.data)\n\nclass EigenQuaternionPrinter:\n\t\"Print an Eigen Quaternion\"\n\t\n\tdef __init__(self, val):\n\t\t\"Extract all the necessary information\"\n\t\t# The gdb extension does not support value template arguments - need to extract them by hand\n\t\ttype = val.type\n\t\tif type.code == gdb.TYPE_CODE_REF:\n\t\t\ttype = type.target()\n\t\tself.type = type.unqualified().strip_typedefs()\n\t\tself.innerType = self.type.template_argument(0)\n\t\tself.val = val\n\t\t\n\t\t# Quaternions have a struct as their storage, so we need to walk through this\n\t\tself.data = self.val['m_coeffs']['m_storage']['m_data']['array']\n\t\tself.data = self.data.cast(self.innerType.pointer())\n\t\t\t\n\tclass _iterator:\n\t\tdef __init__ (self, dataPtr):\n\t\t\tself.dataPtr = dataPtr\n\t\t\tself.currentElement = 0\n\t\t\tself.elementNames = ['x', 'y', 'z', 'w']\n\t\t\t\n\t\tdef __iter__ (self):\n\t\t\treturn self\n\t\n\t\tdef next(self):\n                        return self.__next__()  # Python 2.x compatibility\n\n\t\tdef __next__(self):\n\t\t\telement = self.currentElement\n\t\t\t\n\t\t\tif self.currentElement >= 4: #there are 4 elements in a quanternion\n\t\t\t\traise StopIteration\n\t\t\t\n\t\t\tself.currentElement = self.currentElement + 1\n\t\t\t\n\t\t\titem = self.dataPtr.dereference()\n\t\t\tself.dataPtr = self.dataPtr + 1\n\t\t\treturn ('[%s]' % (self.elementNames[element],), item)\n\t\t\t\n\tdef children(self):\n\t\t\n\t\treturn self._iterator(self.data)\n\t\n\tdef to_string(self):\n\t\treturn \"Eigen::Quaternion<%s> (data ptr: %s)\" % (self.innerType, self.data)\n\ndef build_eigen_dictionary ():\n\tpretty_printers_dict[re.compile('^Eigen::Quaternion<.*>$')] = lambda val: EigenQuaternionPrinter(val)\n\tpretty_printers_dict[re.compile('^Eigen::Matrix<.*>$')] = lambda val: EigenMatrixPrinter(\"Matrix\", val)\n\tpretty_printers_dict[re.compile('^Eigen::Array<.*>$')]  = lambda val: EigenMatrixPrinter(\"Array\",  val)\n\ndef register_eigen_printers(obj):\n\t\"Register eigen pretty-printers with objfile Obj\"\n\n\tif obj == None:\n\t\tobj = gdb\n\tobj.pretty_printers.append(lookup_function)\n\ndef lookup_function(val):\n\t\"Look-up and return a pretty-printer that can print va.\"\n\t\n\ttype = val.type\n\t\n\tif type.code == gdb.TYPE_CODE_REF:\n\t\ttype = type.target()\n\t\n\ttype = type.unqualified().strip_typedefs()\n\t\n\ttypename = type.tag\n\tif typename == None:\n\t\treturn None\n\t\n\tfor function in pretty_printers_dict:\n\t\tif function.search(typename):\n\t\t\treturn pretty_printers_dict[function](val)\n\t\n\treturn None\n\npretty_printers_dict = {}\n\nbuild_eigen_dictionary ()\n"
  },
  {
    "path": "include/eigen3/debug/msvc/eigen.natvis",
    "content": "<?xml version=\"1.0\" encoding=\"utf-8\"?>\n\n<AutoVisualizer xmlns=\"http://schemas.microsoft.com/vstudio/debugger/natvis/2010\">\n\n  <!-- Fixed x Fixed Matrix -->\n  <Type Name=\"Eigen::Matrix&lt;*,*,*,*,*,*&gt;\">      \n      <AlternativeType Name=\"Eigen::Array&lt;*,-1,-1,*,*,*&gt;\"/>\n      <DisplayString>[{$T2}, {$T3}] (fixed matrix)</DisplayString>\n      <Expand>\n        <ArrayItems Condition=\"Flags%2\"> <!-- row major layout -->\n          <Rank>2</Rank>\n          <Size>$i==0 ? $T2 : $T3</Size>\n          <ValuePointer>m_storage.m_data.array</ValuePointer>\n        </ArrayItems>\n        <ArrayItems Condition=\"!(Flags%2)\"> <!-- column major layout -->\n          <Direction>Backward</Direction>\n          <Rank>2</Rank>\n          <Size>$i==0 ? $T2 : $T3</Size>\n          <ValuePointer>m_storage.m_data.array</ValuePointer>\n        </ArrayItems>\n      </Expand>\n  </Type>\n  \n  <!-- 2 x 2 Matrix -->\n  <Type Name=\"Eigen::Matrix&lt;*,2,2,*,*,*&gt;\">      \n      <AlternativeType Name=\"Eigen::Array&lt;*,2,2,*,*,*&gt;\"/>\n      <DisplayString>[2, 2] (fixed matrix)</DisplayString>\n      <Expand>\n        <Synthetic Name=\"[row 0]\" Condition=\"Flags%2\">\n          <DisplayString>({m_storage.m_data.array[0]}, {m_storage.m_data.array[1]})</DisplayString>\n        </Synthetic>\n        <Synthetic Name=\"[row 0]\" Condition=\"!(Flags%2)\">\n          <DisplayString>({m_storage.m_data.array[0]}, {m_storage.m_data.array[2]})</DisplayString>\n        </Synthetic>\n        <Synthetic Name=\"[row 1]\" Condition=\"Flags%2\">\n          <DisplayString>({m_storage.m_data.array[2]}, {m_storage.m_data.array[3]})</DisplayString>\n        </Synthetic>\n        <Synthetic Name=\"[row 1]\" Condition=\"!(Flags%2)\">\n          <DisplayString>({m_storage.m_data.array[1]}, {m_storage.m_data.array[3]})</DisplayString>\n        </Synthetic>        \n      </Expand>\n  </Type>\n  \n  <!-- 3 x 3 Matrix -->\n  <Type Name=\"Eigen::Matrix&lt;*,3,3,*,*,*&gt;\">      \n      <AlternativeType Name=\"Eigen::Array&lt;*,3,3,*,*,*&gt;\"/>\n      <DisplayString>[3, 3] (fixed matrix)</DisplayString>\n      <Expand>\n        <Synthetic Name=\"[row 0]\" Condition=\"Flags%2\">\n          <DisplayString>({m_storage.m_data.array[0]}, {m_storage.m_data.array[1]}, {m_storage.m_data.array[2]})</DisplayString>\n        </Synthetic>\n        <Synthetic Name=\"[row 0]\" Condition=\"!(Flags%2)\">\n          <DisplayString>({m_storage.m_data.array[0]}, {m_storage.m_data.array[3]}, {m_storage.m_data.array[6]})</DisplayString>\n        </Synthetic>\n        <Synthetic Name=\"[row 1]\" Condition=\"Flags%2\">\n          <DisplayString>({m_storage.m_data.array[3]}, {m_storage.m_data.array[4]}, {m_storage.m_data.array[5]})</DisplayString>\n        </Synthetic>\n        <Synthetic Name=\"[row 1]\" Condition=\"!(Flags%2)\">\n          <DisplayString>({m_storage.m_data.array[1]}, {m_storage.m_data.array[4]}, {m_storage.m_data.array[7]})</DisplayString>\n        </Synthetic>\n        <Synthetic Name=\"[row 2]\" Condition=\"Flags%2\">\n          <DisplayString>({m_storage.m_data.array[6]}, {m_storage.m_data.array[7]}, {m_storage.m_data.array[8]})</DisplayString>\n        </Synthetic>\n        <Synthetic Name=\"[row 2]\" Condition=\"!(Flags%2)\">\n          <DisplayString>({m_storage.m_data.array[2]}, {m_storage.m_data.array[5]}, {m_storage.m_data.array[8]})</DisplayString>\n        </Synthetic>        \n      </Expand>\n  </Type>\n  \n  <!-- 4 x 4 Matrix -->\n  <Type Name=\"Eigen::Matrix&lt;*,4,4,*,*,*&gt;\">      \n      <AlternativeType Name=\"Eigen::Array&lt;*,4,4,*,*,*&gt;\"/>\n      <DisplayString>[4, 4] (fixed matrix)</DisplayString>\n      <Expand>\n        <Synthetic Name=\"[row 0]\" Condition=\"Flags%2\">\n          <DisplayString>({m_storage.m_data.array[0]}, {m_storage.m_data.array[1]}, {m_storage.m_data.array[2]}, {m_storage.m_data.array[3]})</DisplayString>\n        </Synthetic>\n        <Synthetic Name=\"[row 0]\" Condition=\"!(Flags%2)\">\n          <DisplayString>({m_storage.m_data.array[0]}, {m_storage.m_data.array[4]}, {m_storage.m_data.array[8]}, {m_storage.m_data.array[12]})</DisplayString>\n        </Synthetic>\n        <Synthetic Name=\"[row 1]\" Condition=\"Flags%2\">\n          <DisplayString>({m_storage.m_data.array[4]}, {m_storage.m_data.array[5]}, {m_storage.m_data.array[6]}, {m_storage.m_data.array[7]})</DisplayString>\n        </Synthetic>\n        <Synthetic Name=\"[row 1]\" Condition=\"!(Flags%2)\">\n          <DisplayString>({m_storage.m_data.array[1]}, {m_storage.m_data.array[5]}, {m_storage.m_data.array[9]}, {m_storage.m_data.array[13]})</DisplayString>\n        </Synthetic>\n        <Synthetic Name=\"[row 2]\" Condition=\"Flags%2\">\n          <DisplayString>({m_storage.m_data.array[8]}, {m_storage.m_data.array[9]}, {m_storage.m_data.array[10]}, {m_storage.m_data.array[11]})</DisplayString>\n        </Synthetic>\n        <Synthetic Name=\"[row 2]\" Condition=\"!(Flags%2)\">\n          <DisplayString>({m_storage.m_data.array[2]}, {m_storage.m_data.array[6]}, {m_storage.m_data.array[10]}, {m_storage.m_data.array[14]})</DisplayString>\n        </Synthetic>\n        <Synthetic Name=\"[row 3]\" Condition=\"Flags%2\">\n          <DisplayString>({m_storage.m_data.array[12]}, {m_storage.m_data.array[13]}, {m_storage.m_data.array[14]}, {m_storage.m_data.array[15]})</DisplayString>\n        </Synthetic>\n        <Synthetic Name=\"[row 3]\" Condition=\"!(Flags%2)\">\n          <DisplayString>({m_storage.m_data.array[3]}, {m_storage.m_data.array[7]}, {m_storage.m_data.array[11]}, {m_storage.m_data.array[15]})</DisplayString>\n        </Synthetic>        \n      </Expand>\n  </Type>  \n  \n  <!-- Dynamic x Dynamic Matrix -->\n  <Type Name=\"Eigen::Matrix&lt;*,-1,-1,*,*,*&gt;\">      \n      <AlternativeType Name=\"Eigen::Array&lt;*,-1,-1,*,*,*&gt;\"/>\n      <DisplayString Condition=\"m_storage.m_data == 0\">empty</DisplayString>\n      <DisplayString Condition=\"m_storage.m_data != 0\">[{m_storage.m_rows}, {m_storage.m_cols}] (dynamic matrix)</DisplayString>\n      <Expand>\n        <ArrayItems Condition=\"Flags%2\"> <!-- row major layout -->\n          <Rank>2</Rank>\n          <Size>$i==0 ? m_storage.m_rows : m_storage.m_cols</Size>\n          <ValuePointer>m_storage.m_data</ValuePointer>\n        </ArrayItems>\n        <ArrayItems Condition=\"!(Flags%2)\"> <!-- column major layout -->\n          <Direction>Backward</Direction>\n          <Rank>2</Rank>\n          <Size>$i==0 ? m_storage.m_rows : m_storage.m_cols</Size>\n          <ValuePointer>m_storage.m_data</ValuePointer>\n        </ArrayItems>\n      </Expand>\n  </Type>\n  \n  <!-- Fixed x Dynamic Matrix -->\n  <Type Name=\"Eigen::Matrix&lt;*,*,-1,*,*,*&gt;\">\n      <AlternativeType Name=\"Eigen::Array&lt;*,*,-1,*,*,*&gt;\"/>\n      <DisplayString Condition=\"m_storage.m_data == 0\">empty</DisplayString>\n      <DisplayString Condition=\"m_storage.m_data != 0\">[{$T2}, {m_storage.m_cols}] (dynamic column matrix)</DisplayString>\n      <Expand>\n        <ArrayItems Condition=\"Flags%2\"> <!-- row major layout -->\n          <Rank>2</Rank>\n          <Size>$i==0 ? $T2 : m_storage.m_cols</Size>\n          <ValuePointer>m_storage.m_data</ValuePointer>\n        </ArrayItems>\n        <ArrayItems Condition=\"!(Flags%2)\"> <!-- column major layout -->\n          <Direction>Backward</Direction>\n          <Rank>2</Rank>\n          <Size>$i==0 ? $T2 : m_storage.m_cols</Size>\n          <ValuePointer>m_storage.m_data</ValuePointer>\n        </ArrayItems>\n      </Expand>\n  </Type>\n  \n  <!-- Dynamic x Fixed Matrix -->\n  <Type Name=\"Eigen::Matrix&lt;*,-1,*,*,*,*&gt;\">\n      <AlternativeType Name=\"Eigen::Array&lt;*,-1,*,*,*,*&gt;\"/>\n      <DisplayString Condition=\"m_storage.m_data == 0\">empty</DisplayString>\n      <DisplayString Condition=\"m_storage.m_data != 0\">[{m_storage.m_rows}, {$T2}] (dynamic row matrix)</DisplayString>\n      <Expand>\n        <ArrayItems Condition=\"Flags%2\"> <!-- row major layout -->\n          <Rank>2</Rank>\n          <Size>$i==0 ? m_storage.m_rows : $T2</Size>\n          <ValuePointer>m_storage.m_data</ValuePointer>\n        </ArrayItems>\n        <ArrayItems Condition=\"!(Flags%2)\"> <!-- column major layout -->\n          <Direction>Backward</Direction>\n          <Rank>2</Rank>\n          <Size>$i==0 ? m_storage.m_rows : $T2</Size>\n          <ValuePointer>m_storage.m_data</ValuePointer>\n        </ArrayItems>\n      </Expand>\n  </Type>\n  \n  <!-- Dynamic Column Vector -->\n  <Type Name=\"Eigen::Matrix&lt;*,1,-1,*,*,*&gt;\">\n      <AlternativeType Name=\"Eigen::Array&lt;*,1,-1,*,*,*&gt;\"/>\n      <DisplayString Condition=\"m_storage.m_data == 0\">empty</DisplayString>\n      <DisplayString Condition=\"m_storage.m_data != 0\">[{m_storage.m_cols}] (dynamic column vector)</DisplayString>\n      <Expand>\n        <Item Name=\"[size]\">m_storage.m_cols</Item>\n        <ArrayItems>\n          <Size>m_storage.m_cols</Size>\n          <ValuePointer>m_storage.m_data</ValuePointer>\n        </ArrayItems>\n      </Expand>\n  </Type>\n  \n  <!-- Dynamic Row Vector -->\n  <Type Name=\"Eigen::Matrix&lt;*,-1,1,*,*,*&gt;\">\n      <AlternativeType Name=\"Eigen::Array&lt;*,-1,1,*,*,*&gt;\"/>\n      <DisplayString Condition=\"m_storage.m_data == 0\">empty</DisplayString>\n      <DisplayString Condition=\"m_storage.m_data != 0\">[{m_storage.m_rows}] (dynamic row vector)</DisplayString>\n      <Expand>\n        <Item Name=\"[size]\">m_storage.m_rows</Item>\n        <ArrayItems>\n          <Size>m_storage.m_rows</Size>\n          <ValuePointer>m_storage.m_data</ValuePointer>\n        </ArrayItems>\n      </Expand>\n  </Type>\n  \n  <!-- Fixed Vector -->\n  <Type Name=\"Eigen::Matrix&lt;*,1,1,*,*,*&gt;\">\n      <AlternativeType Name=\"Eigen::Array&lt;*,1,1,*,*,*&gt;\"/>\n      <DisplayString>[1] ({m_storage.m_data.array[0]})</DisplayString>\n      <Expand>\n        <Item Name=\"[x]\">m_storage.m_data.array[0]</Item>\n      </Expand>\n  </Type>\n  \n  <Type Name=\"Eigen::Matrix&lt;*,2,1,*,*,*&gt;\">\n      <AlternativeType Name=\"Eigen::Matrix&lt;*,1,2,*,*,*&gt;\"/>\n      <AlternativeType Name=\"Eigen::Array&lt;*,2,1,*,*,*&gt;\"/>\n      <AlternativeType Name=\"Eigen::Array&lt;*,1,2,*,*,*&gt;\"/>\n      <DisplayString>[2] ({m_storage.m_data.array[0]}, {m_storage.m_data.array[1]})</DisplayString>\n      <Expand>\n        <Item Name=\"[x]\">m_storage.m_data.array[0]</Item>\n        <Item Name=\"[y]\">m_storage.m_data.array[1]</Item>\n      </Expand>\n  </Type>\n  \n  <Type Name=\"Eigen::Matrix&lt;*,3,1,*,*,*&gt;\">\n      <AlternativeType Name=\"Eigen::Matrix&lt;*,1,3,*,*,*&gt;\"/>\n      <AlternativeType Name=\"Eigen::Array&lt;*,3,1,*,*,*&gt;\"/>\n      <AlternativeType Name=\"Eigen::Array&lt;*,1,3,*,*,*&gt;\"/>\n      <DisplayString>[3] ({m_storage.m_data.array[0]}, {m_storage.m_data.array[1]}, {m_storage.m_data.array[2]})</DisplayString>\n      <Expand>\n        <Item Name=\"[x]\">m_storage.m_data.array[0]</Item>\n        <Item Name=\"[y]\">m_storage.m_data.array[1]</Item>\n        <Item Name=\"[z]\">m_storage.m_data.array[2]</Item>\n      </Expand>\n  </Type>\n  \n    <Type Name=\"Eigen::Matrix&lt;*,4,1,*,*,*&gt;\">\n      <AlternativeType Name=\"Eigen::Matrix&lt;*,1,4,*,*,*&gt;\"/>\n      <AlternativeType Name=\"Eigen::Array&lt;*,4,1,*,*,*&gt;\"/>\n      <AlternativeType Name=\"Eigen::Array&lt;*,1,4,*,*,*&gt;\"/>\n      <DisplayString>[4] ({m_storage.m_data.array[0]}, {m_storage.m_data.array[1]}, {m_storage.m_data.array[2]}, {m_storage.m_data.array[3]})</DisplayString>\n      <Expand>\n        <Item Name=\"[x]\">m_storage.m_data.array[0]</Item>\n        <Item Name=\"[y]\">m_storage.m_data.array[1]</Item>\n        <Item Name=\"[z]\">m_storage.m_data.array[2]</Item>\n        <Item Name=\"[w]\">m_storage.m_data.array[3]</Item>\n      </Expand>\n  </Type>\n\n</AutoVisualizer>\n"
  },
  {
    "path": "include/eigen3/demos/CMakeLists.txt",
    "content": "project(EigenDemos)\n\nadd_custom_target(demos)\n\nif(NOT EIGEN_TEST_NOQT)\n  find_package(Qt4)\n  if(QT4_FOUND)\n    add_subdirectory(mandelbrot)\n    add_subdirectory(opengl)\n  else(QT4_FOUND)\n    message(STATUS \"Qt4 not found, so disabling the mandelbrot and opengl demos\")\n  endif(QT4_FOUND)\nendif()\n"
  },
  {
    "path": "include/eigen3/demos/mandelbrot/CMakeLists.txt",
    "content": "find_package(Qt4 REQUIRED)\n\nset(CMAKE_INCLUDE_CURRENT_DIR ON)\n\nif (CMAKE_COMPILER_IS_GNUCXX)\n   set ( CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} -O2\")\n   add_definitions ( \"-DNDEBUG\" )\nendif (CMAKE_COMPILER_IS_GNUCXX)\n\ninclude_directories( ${QT_INCLUDE_DIR} )\n\nset(mandelbrot_SRCS\n    mandelbrot.cpp\n)\n\nqt4_automoc(${mandelbrot_SRCS})\n\nadd_executable(mandelbrot ${mandelbrot_SRCS})\nadd_dependencies(demos mandelbrot)\n\ntarget_link_libraries(mandelbrot ${QT_QTCORE_LIBRARY} ${QT_QTGUI_LIBRARY})\n"
  },
  {
    "path": "include/eigen3/demos/mandelbrot/README",
    "content": "*** Mandelbrot demo ***\n\nControls:\n* Left mouse button to center view at a point.\n* Drag vertically with left mouse button to zoom in and out.\n\nBe sure to enable SSE2 or AltiVec to improve performance.\n\nThe number of iterations, and the choice between single and double precision, are\ndetermined at runtime depending on the zoom level.\n"
  },
  {
    "path": "include/eigen3/demos/mandelbrot/mandelbrot.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"mandelbrot.h\"\n#include <iostream>\n#include<QtGui/QPainter>\n#include<QtGui/QImage>\n#include<QtGui/QMouseEvent>\n#include<QtCore/QTime>\n\nvoid MandelbrotWidget::resizeEvent(QResizeEvent *)\n{\n  if(size < width() * height())\n  {\n    std::cout << \"reallocate buffer\" << std::endl;\n    size = width() * height();\n    if(buffer) delete[]buffer;\n    buffer = new unsigned char[4*size];\n  }\n}\n\ntemplate<typename T> struct iters_before_test { enum { ret = 8 }; };\ntemplate<> struct iters_before_test<double> { enum { ret = 16 }; };\n\ntemplate<typename Real> void MandelbrotThread::render(int img_width, int img_height)\n{\n  enum { packetSize = Eigen::internal::packet_traits<Real>::size }; // number of reals in a Packet\n  typedef Eigen::Array<Real, packetSize, 1> Packet; // wrap a Packet as a vector\n\n  enum { iters_before_test = iters_before_test<Real>::ret };\n  max_iter = (max_iter / iters_before_test) * iters_before_test;\n  const int alignedWidth = (img_width/packetSize)*packetSize;\n  unsigned char *const buffer = widget->buffer;\n  const double xradius = widget->xradius;\n  const double yradius = xradius * img_height / img_width;\n  const int threadcount = widget->threadcount;\n  typedef Eigen::Array<Real, 2, 1> Vector2;\n  Vector2 start(widget->center.x() - widget->xradius, widget->center.y() - yradius);\n  Vector2 step(2*widget->xradius/img_width, 2*yradius/img_height);\n  total_iter = 0;\n\n  for(int y = id; y < img_height; y += threadcount)\n  {\n    int pix = y * img_width;\n\n    // for each pixel, we're going to do the iteration z := z^2 + c where z and c are complex numbers, \n    // starting with z = c = complex coord of the pixel. pzi and pzr denote the real and imaginary parts of z.\n    // pci and pcr denote the real and imaginary parts of c.\n\n    Packet pzi_start, pci_start;\n    for(int i = 0; i < packetSize; i++) pzi_start[i] = pci_start[i] = start.y() + y * step.y();\n\n    for(int x = 0; x < alignedWidth; x += packetSize, pix += packetSize)\n    {\n      Packet pcr, pci = pci_start, pzr, pzi = pzi_start, pzr_buf;\n      for(int i = 0; i < packetSize; i++) pzr[i] = pcr[i] = start.x() + (x+i) * step.x();\n\n      // do the iterations. Every iters_before_test iterations we check for divergence,\n      // in which case we can stop iterating.\n      int j = 0;\n      typedef Eigen::Matrix<int, packetSize, 1> Packeti;\n      Packeti pix_iter = Packeti::Zero(), // number of iteration per pixel in the packet\n              pix_dont_diverge; // whether or not each pixel has already diverged\n      do\n      {\n        for(int i = 0; i < iters_before_test/4; i++) // peel the inner loop by 4\n        {\n#         define ITERATE \\\n            pzr_buf = pzr; \\\n            pzr = pzr.square(); \\\n            pzr -= pzi.square(); \\\n            pzr += pcr; \\\n            pzi = (2*pzr_buf)*pzi; \\\n            pzi += pci;\n          ITERATE ITERATE ITERATE ITERATE\n        }\n        pix_dont_diverge = ((pzr.square() + pzi.square())\n                           .eval() // temporary fix as what follows is not yet vectorized by Eigen\n                           <= Packet::Constant(4))\n                                // the 4 here is not a magic value, it's a math fact that if\n                                // the square modulus is >4 then divergence is inevitable.\n                           .template cast<int>();\n        pix_iter += iters_before_test * pix_dont_diverge;\n        j++;\n        total_iter += iters_before_test * packetSize;\n      }\n      while(j < max_iter/iters_before_test && pix_dont_diverge.any()); // any() is not yet vectorized by Eigen\n\n      // compute pixel colors\n      for(int i = 0; i < packetSize; i++)\n      {\n        buffer[4*(pix+i)] = 255*pix_iter[i]/max_iter;\n        buffer[4*(pix+i)+1] = 0;\n        buffer[4*(pix+i)+2] = 0;\n      }\n    }\n\n    // if the width is not a multiple of packetSize, fill the remainder in black\n    for(int x = alignedWidth; x < img_width; x++, pix++)\n      buffer[4*pix] = buffer[4*pix+1] = buffer[4*pix+2] = 0;\n  }\n  return;\n}\n\nvoid MandelbrotThread::run()\n{\n  setTerminationEnabled(true);\n  double resolution = widget->xradius*2/widget->width();\n  max_iter = 128;\n  if(resolution < 1e-4f) max_iter += 128 * ( - 4 - std::log10(resolution));\n  int img_width = widget->width()/widget->draft;\n  int img_height = widget->height()/widget->draft;\n  single_precision = resolution > 1e-7f;\n\n  if(single_precision)\n    render<float>(img_width, img_height);\n  else\n    render<double>(img_width, img_height);\n}\n\nvoid MandelbrotWidget::paintEvent(QPaintEvent *)\n{\n  static float max_speed = 0;\n  long long total_iter = 0;\n\n  QTime time;\n  time.start();\n  for(int th = 0; th < threadcount; th++)\n    threads[th]->start(QThread::LowPriority);\n  for(int th = 0; th < threadcount; th++)\n  {\n    threads[th]->wait();\n    total_iter += threads[th]->total_iter;\n  }\n  int elapsed = time.elapsed();\n\n  if(draft == 1)\n  {\n    float speed = elapsed ? float(total_iter)*1000/elapsed : 0;\n    max_speed = std::max(max_speed, speed);\n    std::cout << threadcount << \" threads, \"\n              << elapsed << \" ms, \"\n              << speed << \" iters/s (max \" << max_speed << \")\" << std::endl;\n    int packetSize = threads[0]->single_precision\n                   ? int(Eigen::internal::packet_traits<float>::size)\n                   : int(Eigen::internal::packet_traits<double>::size);\n    setWindowTitle(QString(\"resolution \")+QString::number(xradius*2/width(), 'e', 2)\n                  +QString(\", %1 iterations per pixel, \").arg(threads[0]->max_iter)\n                  +(threads[0]->single_precision ? QString(\"single \") : QString(\"double \"))\n                  +QString(\"precision, \")\n                  +(packetSize==1 ? QString(\"no vectorization\")\n                                  : QString(\"vectorized (%1 per packet)\").arg(packetSize)));\n  }\n  \n  QImage image(buffer, width()/draft, height()/draft, QImage::Format_RGB32);\n  QPainter painter(this);\n  painter.drawImage(QPoint(0, 0), image.scaled(width(), height()));\n\n  if(draft>1)\n  {\n    draft /= 2;\n    setWindowTitle(QString(\"recomputing at 1/%1 resolution...\").arg(draft));\n    update();\n  }\n}\n\nvoid MandelbrotWidget::mousePressEvent(QMouseEvent *event)\n{\n  if( event->buttons() & Qt::LeftButton )\n  {\n    lastpos = event->pos();\n    double yradius = xradius * height() / width();\n    center = Eigen::Vector2d(center.x() + (event->pos().x() - width()/2) * xradius * 2 / width(),\n                             center.y() + (event->pos().y() - height()/2) * yradius * 2 / height());\n    draft = 16;\n    for(int th = 0; th < threadcount; th++)\n      threads[th]->terminate();\n    update();\n  }\n}\n\nvoid MandelbrotWidget::mouseMoveEvent(QMouseEvent *event)\n{\n  QPoint delta = event->pos() - lastpos;\n  lastpos = event->pos();\n  if( event->buttons() & Qt::LeftButton )\n  {\n    double t = 1 + 5 * double(delta.y()) / height();\n    if(t < 0.5) t = 0.5;\n    if(t > 2) t = 2;\n    xradius *= t;\n    draft = 16;\n    for(int th = 0; th < threadcount; th++)\n      threads[th]->terminate();\n    update();\n  }\n}\n\nint main(int argc, char *argv[])\n{\n  QApplication app(argc, argv);\n  MandelbrotWidget w;\n  w.show();\n  return app.exec();\n}\n\n#include \"mandelbrot.moc\"\n"
  },
  {
    "path": "include/eigen3/demos/mandelbrot/mandelbrot.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef MANDELBROT_H\n#define MANDELBROT_H\n\n#include <Eigen/Core>\n#include <QtGui/QApplication>\n#include <QtGui/QWidget>\n#include <QtCore/QThread>\n\nclass MandelbrotWidget;\n\nclass MandelbrotThread : public QThread\n{\n    friend class MandelbrotWidget;\n    MandelbrotWidget *widget;\n    long long total_iter;\n    int id, max_iter;\n    bool single_precision;\n\n  public:\n    MandelbrotThread(MandelbrotWidget *w, int i) : widget(w), id(i) {}\n    void run();\n    template<typename Real> void render(int img_width, int img_height);\n};\n\nclass MandelbrotWidget : public QWidget\n{\n    Q_OBJECT\n\n    friend class MandelbrotThread;\n    Eigen::Vector2d center;\n    double xradius;\n    int size;\n    unsigned char *buffer;\n    QPoint lastpos;\n    int draft;\n    MandelbrotThread **threads;\n    int threadcount;\n\n  protected:\n    void resizeEvent(QResizeEvent *);\n    void paintEvent(QPaintEvent *);\n    void mousePressEvent(QMouseEvent *event);\n    void mouseMoveEvent(QMouseEvent *event);\n\n  public:\n    MandelbrotWidget() : QWidget(), center(0,0), xradius(2),\n                         size(0), buffer(0), draft(16)\n    {\n      setAutoFillBackground(false);\n      threadcount = QThread::idealThreadCount();\n      threads = new MandelbrotThread*[threadcount];\n      for(int th = 0; th < threadcount; th++) threads[th] = new MandelbrotThread(this, th);\n    }\n    ~MandelbrotWidget()\n    {\n      if(buffer) delete[]buffer;\n      for(int th = 0; th < threadcount; th++) delete threads[th];\n      delete[] threads;\n    }\n};\n\n#endif // MANDELBROT_H\n"
  },
  {
    "path": "include/eigen3/demos/mix_eigen_and_c/README",
    "content": "This is an example of how one can wrap some of Eigen into a C library.\n\nTo try this with GCC, do:\n\n  g++ -c binary_library.cpp -O2 -msse2 -I ../..\n  gcc example.c binary_library.o -o example -lstdc++\n  ./example\n\nTODO: add CMakeLists, add more explanations here"
  },
  {
    "path": "include/eigen3/demos/mix_eigen_and_c/binary_library.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n// This C++ file compiles to binary code that can be linked to by your C program,\n// thanks to the extern \"C\" syntax used in the declarations in binary_library.h.\n\n#include \"binary_library.h\"\n\n#include <Eigen/Core>\n\nusing namespace Eigen;\n\n/************************* pointer conversion methods **********************************************/\n\n////// class MatrixXd //////\n\ninline MatrixXd& c_to_eigen(C_MatrixXd* ptr)\n{\n  return *reinterpret_cast<MatrixXd*>(ptr);\n}\n\ninline const MatrixXd& c_to_eigen(const C_MatrixXd* ptr)\n{\n  return *reinterpret_cast<const MatrixXd*>(ptr);\n}\n\ninline C_MatrixXd* eigen_to_c(MatrixXd& ref)\n{\n  return reinterpret_cast<C_MatrixXd*>(&ref);\n}\n\ninline const C_MatrixXd* eigen_to_c(const MatrixXd& ref)\n{\n  return reinterpret_cast<const C_MatrixXd*>(&ref);\n}\n\n////// class Map<MatrixXd> //////\n\ninline Map<MatrixXd>& c_to_eigen(C_Map_MatrixXd* ptr)\n{\n  return *reinterpret_cast<Map<MatrixXd>*>(ptr);\n}\n\ninline const Map<MatrixXd>& c_to_eigen(const C_Map_MatrixXd* ptr)\n{\n  return *reinterpret_cast<const Map<MatrixXd>*>(ptr);\n}\n\ninline C_Map_MatrixXd* eigen_to_c(Map<MatrixXd>& ref)\n{\n  return reinterpret_cast<C_Map_MatrixXd*>(&ref);\n}\n\ninline const C_Map_MatrixXd* eigen_to_c(const Map<MatrixXd>& ref)\n{\n  return reinterpret_cast<const C_Map_MatrixXd*>(&ref);\n}\n\n\n/************************* implementation of classes **********************************************/\n\n\n////// class MatrixXd //////\n\n\nC_MatrixXd* MatrixXd_new(int rows, int cols)\n{\n  return eigen_to_c(*new MatrixXd(rows,cols));\n}\n\nvoid MatrixXd_delete(C_MatrixXd *m)\n{\n  delete &c_to_eigen(m);\n}\n\ndouble* MatrixXd_data(C_MatrixXd *m)\n{\n  return c_to_eigen(m).data();\n}\n\nvoid MatrixXd_set_zero(C_MatrixXd *m)\n{\n  c_to_eigen(m).setZero();\n}\n\nvoid MatrixXd_resize(C_MatrixXd *m, int rows, int cols)\n{\n  c_to_eigen(m).resize(rows,cols);\n}\n\nvoid MatrixXd_copy(C_MatrixXd *dst, const C_MatrixXd *src)\n{\n  c_to_eigen(dst) = c_to_eigen(src);\n}\n\nvoid MatrixXd_copy_map(C_MatrixXd *dst, const C_Map_MatrixXd *src)\n{\n  c_to_eigen(dst) = c_to_eigen(src);\n}\n\nvoid MatrixXd_set_coeff(C_MatrixXd *m, int i, int j, double coeff)\n{\n  c_to_eigen(m)(i,j) = coeff;\n}\n\ndouble MatrixXd_get_coeff(const C_MatrixXd *m, int i, int j)\n{\n  return c_to_eigen(m)(i,j);\n}\n\nvoid MatrixXd_print(const C_MatrixXd *m)\n{\n  std::cout << c_to_eigen(m) << std::endl;\n}\n\nvoid MatrixXd_multiply(const C_MatrixXd *m1, const C_MatrixXd *m2, C_MatrixXd *result)\n{\n  c_to_eigen(result) = c_to_eigen(m1) * c_to_eigen(m2);\n}\n\nvoid MatrixXd_add(const C_MatrixXd *m1, const C_MatrixXd *m2, C_MatrixXd *result)\n{\n  c_to_eigen(result) = c_to_eigen(m1) + c_to_eigen(m2);\n}\n\n\n\n////// class Map_MatrixXd //////\n\n\nC_Map_MatrixXd* Map_MatrixXd_new(double *array, int rows, int cols)\n{\n  return eigen_to_c(*new Map<MatrixXd>(array,rows,cols));\n}\n\nvoid Map_MatrixXd_delete(C_Map_MatrixXd *m)\n{\n  delete &c_to_eigen(m);\n}\n\nvoid Map_MatrixXd_set_zero(C_Map_MatrixXd *m)\n{\n  c_to_eigen(m).setZero();\n}\n\nvoid Map_MatrixXd_copy(C_Map_MatrixXd *dst, const C_Map_MatrixXd *src)\n{\n  c_to_eigen(dst) = c_to_eigen(src);\n}\n\nvoid Map_MatrixXd_copy_matrix(C_Map_MatrixXd *dst, const C_MatrixXd *src)\n{\n  c_to_eigen(dst) = c_to_eigen(src);\n}\n\nvoid Map_MatrixXd_set_coeff(C_Map_MatrixXd *m, int i, int j, double coeff)\n{\n  c_to_eigen(m)(i,j) = coeff;\n}\n\ndouble Map_MatrixXd_get_coeff(const C_Map_MatrixXd *m, int i, int j)\n{\n  return c_to_eigen(m)(i,j);\n}\n\nvoid Map_MatrixXd_print(const C_Map_MatrixXd *m)\n{\n  std::cout << c_to_eigen(m) << std::endl;\n}\n\nvoid Map_MatrixXd_multiply(const C_Map_MatrixXd *m1, const C_Map_MatrixXd *m2, C_Map_MatrixXd *result)\n{\n  c_to_eigen(result) = c_to_eigen(m1) * c_to_eigen(m2);\n}\n\nvoid Map_MatrixXd_add(const C_Map_MatrixXd *m1, const C_Map_MatrixXd *m2, C_Map_MatrixXd *result)\n{\n  c_to_eigen(result) = c_to_eigen(m1) + c_to_eigen(m2);\n}\n"
  },
  {
    "path": "include/eigen3/demos/mix_eigen_and_c/binary_library.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n// This is a pure C header, no C++ here.\n// The functions declared here will be implemented in C++ but\n// we don't have to know, because thanks to the extern \"C\" syntax,\n// they will be compiled to C object code.\n\n#ifdef __cplusplus\nextern \"C\"\n{\n#endif\n\n  // just dummy empty structs to give different pointer types,\n  // instead of using void* which would be type unsafe\n  struct C_MatrixXd {};\n  struct C_Map_MatrixXd {};\n\n  // the C_MatrixXd class, wraps some of the functionality\n  // of Eigen::MatrixXd.\n  struct C_MatrixXd* MatrixXd_new(int rows, int cols);\n  void    MatrixXd_delete     (struct C_MatrixXd *m);\n  double* MatrixXd_data       (struct C_MatrixXd *m);\n  void    MatrixXd_set_zero   (struct C_MatrixXd *m);\n  void    MatrixXd_resize     (struct C_MatrixXd *m, int rows, int cols);\n  void    MatrixXd_copy       (struct C_MatrixXd *dst,\n                               const struct C_MatrixXd *src);\n  void    MatrixXd_copy_map   (struct C_MatrixXd *dst,\n                               const struct C_Map_MatrixXd *src);  \n  void    MatrixXd_set_coeff  (struct C_MatrixXd *m,\n                               int i, int j, double coeff);\n  double  MatrixXd_get_coeff  (const struct C_MatrixXd *m,\n                               int i, int j);\n  void    MatrixXd_print      (const struct C_MatrixXd *m);\n  void    MatrixXd_add        (const struct C_MatrixXd *m1,\n                               const struct C_MatrixXd *m2,\n                               struct C_MatrixXd *result);  \n  void    MatrixXd_multiply   (const struct C_MatrixXd *m1,\n                               const struct C_MatrixXd *m2,\n                               struct C_MatrixXd *result);\n  \n  // the C_Map_MatrixXd class, wraps some of the functionality\n  // of Eigen::Map<MatrixXd>\n  struct C_Map_MatrixXd* Map_MatrixXd_new(double *array, int rows, int cols);\n  void   Map_MatrixXd_delete     (struct C_Map_MatrixXd *m);\n  void   Map_MatrixXd_set_zero   (struct C_Map_MatrixXd *m);\n  void   Map_MatrixXd_copy       (struct C_Map_MatrixXd *dst,\n                                  const struct C_Map_MatrixXd *src);\n  void   Map_MatrixXd_copy_matrix(struct C_Map_MatrixXd *dst,\n                                  const struct C_MatrixXd *src);  \n  void   Map_MatrixXd_set_coeff  (struct C_Map_MatrixXd *m,\n                                  int i, int j, double coeff);\n  double Map_MatrixXd_get_coeff  (const struct C_Map_MatrixXd *m,\n                                  int i, int j);\n  void   Map_MatrixXd_print      (const struct C_Map_MatrixXd *m);\n  void   Map_MatrixXd_add        (const struct C_Map_MatrixXd *m1,\n                                  const struct C_Map_MatrixXd *m2,\n                                  struct C_Map_MatrixXd *result);  \n  void   Map_MatrixXd_multiply   (const struct C_Map_MatrixXd *m1,\n                                  const struct C_Map_MatrixXd *m2,\n                                  struct C_Map_MatrixXd *result);\n\n#ifdef __cplusplus\n} // end extern \"C\"\n#endif"
  },
  {
    "path": "include/eigen3/demos/mix_eigen_and_c/example.c",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"binary_library.h\"\n#include \"stdio.h\"\n\nvoid demo_MatrixXd()\n{\n  struct C_MatrixXd *matrix1, *matrix2, *result;\n  printf(\"*** demo_MatrixXd ***\\n\");\n  \n  matrix1 = MatrixXd_new(3, 3);\n  MatrixXd_set_zero(matrix1);\n  MatrixXd_set_coeff(matrix1, 0, 1, 2.5);\n  MatrixXd_set_coeff(matrix1, 1, 0, 1.4);\n  printf(\"Here is matrix1:\\n\");\n  MatrixXd_print(matrix1);\n\n  matrix2 = MatrixXd_new(3, 3);\n  MatrixXd_multiply(matrix1, matrix1, matrix2);\n  printf(\"Here is matrix1*matrix1:\\n\");\n  MatrixXd_print(matrix2);\n\n  MatrixXd_delete(matrix1);\n  MatrixXd_delete(matrix2);\n}\n\n// this helper function takes a plain C array and prints it in one line\nvoid print_array(double *array, int n)\n{\n  struct C_Map_MatrixXd *m = Map_MatrixXd_new(array, 1, n);\n  Map_MatrixXd_print(m);\n  Map_MatrixXd_delete(m);\n}\n\nvoid demo_Map_MatrixXd()\n{\n  struct C_Map_MatrixXd *map;\n  double array[5];\n  int i;\n  printf(\"*** demo_Map_MatrixXd ***\\n\");\n  \n  for(i = 0; i < 5; ++i) array[i] = i;\n  printf(\"Initially, the array is:\\n\");\n  print_array(array, 5);\n  \n  map = Map_MatrixXd_new(array, 5, 1);\n  Map_MatrixXd_add(map, map, map);\n  Map_MatrixXd_delete(map);\n\n  printf(\"Now the array is:\\n\");\n  print_array(array, 5);\n}\n\nint main()\n{\n  demo_MatrixXd();\n  demo_Map_MatrixXd();\n}\n"
  },
  {
    "path": "include/eigen3/demos/opengl/CMakeLists.txt",
    "content": "find_package(Qt4)\nfind_package(OpenGL)\n\nif(QT4_FOUND AND OPENGL_FOUND)\n\n  set(QT_USE_QTOPENGL TRUE)\n  include(${QT_USE_FILE})\n\n  set(CMAKE_INCLUDE_CURRENT_DIR ON)\n\n  include_directories( ${QT_INCLUDE_DIR} )\n\n  set(quaternion_demo_SRCS  gpuhelper.cpp icosphere.cpp camera.cpp trackball.cpp quaternion_demo.cpp)\n\n  qt4_automoc(${quaternion_demo_SRCS})\n\n  add_executable(quaternion_demo ${quaternion_demo_SRCS})\n  add_dependencies(demos quaternion_demo)\n\n  target_link_libraries(quaternion_demo\n    ${QT_QTCORE_LIBRARY}    ${QT_QTGUI_LIBRARY}\n    ${QT_QTOPENGL_LIBRARY}  ${OPENGL_LIBRARIES} )\n\nelse()\n\n  message(STATUS \"OpenGL demo disabled because Qt4 and/or OpenGL have not been found.\")\n\nendif()"
  },
  {
    "path": "include/eigen3/demos/opengl/README",
    "content": "\nNavigation:\n left button:           rotate around the target\n middle button:         zoom\n left button + ctrl     quake rotate (rotate around camera position)\n middle button + ctrl   walk (progress along camera's z direction)\n left button:           pan (translate in the XY camera's plane)\n\nR : move the camera to initial position\nA : start/stop animation\nC : clear the animation\nG : add a key frame\n\n"
  },
  {
    "path": "include/eigen3/demos/opengl/camera.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"camera.h\"\n\n#include \"gpuhelper.h\"\n#include <GL/glu.h>\n\n#include \"Eigen/LU\"\nusing namespace Eigen;\n\nCamera::Camera()\n    : mViewIsUptodate(false), mProjIsUptodate(false)\n{\n    mViewMatrix.setIdentity();\n    \n    mFovY = M_PI/3.;\n    mNearDist = 1.;\n    mFarDist = 50000.;\n    \n    mVpX = 0;\n    mVpY = 0;\n\n    setPosition(Vector3f::Constant(100.));\n    setTarget(Vector3f::Zero());\n}\n\nCamera& Camera::operator=(const Camera& other)\n{\n    mViewIsUptodate = false;\n    mProjIsUptodate = false;\n    \n    mVpX = other.mVpX;\n    mVpY = other.mVpY;\n    mVpWidth = other.mVpWidth;\n    mVpHeight = other.mVpHeight;\n\n    mTarget = other.mTarget;\n    mFovY = other.mFovY;\n    mNearDist = other.mNearDist;\n    mFarDist = other.mFarDist;\n    \n    mViewMatrix = other.mViewMatrix;\n    mProjectionMatrix = other.mProjectionMatrix;\n\n    return *this;\n}\n\nCamera::Camera(const Camera& other)\n{\n    *this = other;\n}\n\nCamera::~Camera()\n{\n}\n\n\nvoid Camera::setViewport(uint offsetx, uint offsety, uint width, uint height)\n{\n    mVpX = offsetx;\n    mVpY = offsety;\n    mVpWidth = width;\n    mVpHeight = height;\n    \n    mProjIsUptodate = false;\n}\n\nvoid Camera::setViewport(uint width, uint height)\n{\n    mVpWidth = width;\n    mVpHeight = height;\n    \n    mProjIsUptodate = false;\n}\n\nvoid Camera::setFovY(float value)\n{\n    mFovY = value;\n    mProjIsUptodate = false;\n}\n\nVector3f Camera::direction(void) const\n{\n    return - (orientation() * Vector3f::UnitZ());\n}\nVector3f Camera::up(void) const\n{\n    return orientation() * Vector3f::UnitY();\n}\nVector3f Camera::right(void) const\n{\n    return orientation() * Vector3f::UnitX();\n}\n\nvoid Camera::setDirection(const Vector3f& newDirection)\n{\n    // TODO implement it computing the rotation between newDirection and current dir ?\n    Vector3f up = this->up();\n    \n    Matrix3f camAxes;\n\n    camAxes.col(2) = (-newDirection).normalized();\n    camAxes.col(0) = up.cross( camAxes.col(2) ).normalized();\n    camAxes.col(1) = camAxes.col(2).cross( camAxes.col(0) ).normalized();\n    setOrientation(Quaternionf(camAxes));\n    \n    mViewIsUptodate = false;\n}\n\nvoid Camera::setTarget(const Vector3f& target)\n{\n    mTarget = target;\n    if (!mTarget.isApprox(position()))\n    {\n        Vector3f newDirection = mTarget - position();\n        setDirection(newDirection.normalized());\n    }\n}\n\nvoid Camera::setPosition(const Vector3f& p)\n{\n    mFrame.position = p;\n    mViewIsUptodate = false;\n}\n\nvoid Camera::setOrientation(const Quaternionf& q)\n{\n    mFrame.orientation = q;\n    mViewIsUptodate = false;\n}\n\nvoid Camera::setFrame(const Frame& f)\n{\n  mFrame = f;\n  mViewIsUptodate = false;\n}\n\nvoid Camera::rotateAroundTarget(const Quaternionf& q)\n{\n    Matrix4f mrot, mt, mtm;\n    \n    // update the transform matrix\n    updateViewMatrix();\n    Vector3f t = mViewMatrix * mTarget;\n\n    mViewMatrix = Translation3f(t)\n                * q\n                * Translation3f(-t)\n                * mViewMatrix;\n    \n    Quaternionf qa(mViewMatrix.linear());\n    qa = qa.conjugate();\n    setOrientation(qa);\n    setPosition(- (qa * mViewMatrix.translation()) );\n\n    mViewIsUptodate = true;\n}\n\nvoid Camera::localRotate(const Quaternionf& q)\n{\n    float dist = (position() - mTarget).norm();\n    setOrientation(orientation() * q);\n    mTarget = position() + dist * direction();\n    mViewIsUptodate = false;\n}\n\nvoid Camera::zoom(float d)\n{\n    float dist = (position() - mTarget).norm();\n    if(dist > d)\n    {\n        setPosition(position() + direction() * d);\n        mViewIsUptodate = false;\n    }\n}\n\nvoid Camera::localTranslate(const Vector3f& t)\n{\n  Vector3f trans = orientation() * t;\n  setPosition( position() + trans );\n  setTarget( mTarget + trans );\n\n  mViewIsUptodate = false;\n}\n\nvoid Camera::updateViewMatrix(void) const\n{\n    if(!mViewIsUptodate)\n    {\n        Quaternionf q = orientation().conjugate();\n        mViewMatrix.linear() = q.toRotationMatrix();\n        mViewMatrix.translation() = - (mViewMatrix.linear() * position());\n\n        mViewIsUptodate = true;\n    }\n}\n\nconst Affine3f& Camera::viewMatrix(void) const\n{\n  updateViewMatrix();\n  return mViewMatrix;\n}\n\nvoid Camera::updateProjectionMatrix(void) const\n{\n  if(!mProjIsUptodate)\n  {\n    mProjectionMatrix.setIdentity();\n    float aspect = float(mVpWidth)/float(mVpHeight);\n    float theta = mFovY*0.5;\n    float range = mFarDist - mNearDist;\n    float invtan = 1./tan(theta);\n\n    mProjectionMatrix(0,0) = invtan / aspect;\n    mProjectionMatrix(1,1) = invtan;\n    mProjectionMatrix(2,2) = -(mNearDist + mFarDist) / range;\n    mProjectionMatrix(3,2) = -1;\n    mProjectionMatrix(2,3) = -2 * mNearDist * mFarDist / range;\n    mProjectionMatrix(3,3) = 0;\n    \n    mProjIsUptodate = true;\n  }\n}\n\nconst Matrix4f& Camera::projectionMatrix(void) const\n{\n  updateProjectionMatrix();\n  return mProjectionMatrix;\n}\n\nvoid Camera::activateGL(void)\n{\n  glViewport(vpX(), vpY(), vpWidth(), vpHeight());\n  gpu.loadMatrix(projectionMatrix(),GL_PROJECTION);\n  gpu.loadMatrix(viewMatrix().matrix(),GL_MODELVIEW);\n}\n\n\nVector3f Camera::unProject(const Vector2f& uv, float depth) const\n{\n    Matrix4f inv = mViewMatrix.inverse().matrix();\n    return unProject(uv, depth, inv);\n}\n\nVector3f Camera::unProject(const Vector2f& uv, float depth, const Matrix4f& invModelview) const\n{\n    updateViewMatrix();\n    updateProjectionMatrix();\n    \n    Vector3f a(2.*uv.x()/float(mVpWidth)-1., 2.*uv.y()/float(mVpHeight)-1., 1.);\n    a.x() *= depth/mProjectionMatrix(0,0);\n    a.y() *= depth/mProjectionMatrix(1,1);\n    a.z() = -depth;\n    // FIXME /\\/|\n    Vector4f b = invModelview * Vector4f(a.x(), a.y(), a.z(), 1.);\n    return Vector3f(b.x(), b.y(), b.z());\n}\n"
  },
  {
    "path": "include/eigen3/demos/opengl/camera.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CAMERA_H\n#define EIGEN_CAMERA_H\n\n#include <Eigen/Geometry>\n#include <QObject>\n// #include <frame.h>\n\nclass Frame\n{\n  public:\n    EIGEN_MAKE_ALIGNED_OPERATOR_NEW\n    \n    inline Frame(const Eigen::Vector3f& pos = Eigen::Vector3f::Zero(),\n                 const Eigen::Quaternionf& o = Eigen::Quaternionf())\n      : orientation(o), position(pos)\n    {}\n    Frame lerp(float alpha, const Frame& other) const\n    {\n      return Frame((1.f-alpha)*position + alpha * other.position,\n                   orientation.slerp(alpha,other.orientation));\n    }\n\n    Eigen::Quaternionf orientation;\n    Eigen::Vector3f position;\n};\n\nclass Camera\n{\n  public:\n    EIGEN_MAKE_ALIGNED_OPERATOR_NEW\n\n    Camera(void);\n    \n    Camera(const Camera& other);\n    \n    virtual ~Camera();\n    \n    Camera& operator=(const Camera& other);\n    \n    void setViewport(uint offsetx, uint offsety, uint width, uint height);\n    void setViewport(uint width, uint height);\n    \n    inline uint vpX(void) const { return mVpX; }\n    inline uint vpY(void) const { return mVpY; }\n    inline uint vpWidth(void) const { return mVpWidth; }\n    inline uint vpHeight(void) const { return mVpHeight; }\n\n    inline float fovY(void) const { return mFovY; }\n    void setFovY(float value);\n    \n    void setPosition(const Eigen::Vector3f& pos);\n    inline const Eigen::Vector3f& position(void) const { return mFrame.position; }\n\n    void setOrientation(const Eigen::Quaternionf& q);\n    inline const Eigen::Quaternionf& orientation(void) const { return mFrame.orientation; }\n\n    void setFrame(const Frame& f);\n    const Frame& frame(void) const { return mFrame; }\n    \n    void setDirection(const Eigen::Vector3f& newDirection);\n    Eigen::Vector3f direction(void) const;\n    void setUp(const Eigen::Vector3f& vectorUp);\n    Eigen::Vector3f up(void) const;\n    Eigen::Vector3f right(void) const;\n    \n    void setTarget(const Eigen::Vector3f& target);\n    inline const Eigen::Vector3f& target(void) { return mTarget; }\n    \n    const Eigen::Affine3f& viewMatrix(void) const;\n    const Eigen::Matrix4f& projectionMatrix(void) const;\n    \n    void rotateAroundTarget(const Eigen::Quaternionf& q);\n    void localRotate(const Eigen::Quaternionf& q);\n    void zoom(float d);\n    \n    void localTranslate(const Eigen::Vector3f& t);\n    \n    /** Setup OpenGL matrices and viewport */\n    void activateGL(void);\n    \n    Eigen::Vector3f unProject(const Eigen::Vector2f& uv, float depth, const Eigen::Matrix4f& invModelview) const;\n    Eigen::Vector3f unProject(const Eigen::Vector2f& uv, float depth) const;\n    \n  protected:\n    void updateViewMatrix(void) const;\n    void updateProjectionMatrix(void) const;\n\n  protected:\n\n    uint mVpX, mVpY;\n    uint mVpWidth, mVpHeight;\n\n    Frame mFrame;\n    \n    mutable Eigen::Affine3f mViewMatrix;\n    mutable Eigen::Matrix4f mProjectionMatrix;\n\n    mutable bool mViewIsUptodate;\n    mutable bool mProjIsUptodate;\n\n    // used by rotateAroundTarget\n    Eigen::Vector3f mTarget;\n    \n    float mFovY;\n    float mNearDist;\n    float mFarDist;\n};\n\n#endif // EIGEN_CAMERA_H\n"
  },
  {
    "path": "include/eigen3/demos/opengl/gpuhelper.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"gpuhelper.h\"\n#include \"icosphere.h\"\n#include <GL/glu.h>\n// PLEASE don't look at this old code... ;)\n\n#include <fstream>\n#include <algorithm>\n\nGpuHelper gpu;\n\nGpuHelper::GpuHelper()\n{\n    mVpWidth = mVpHeight = 0;\n    mCurrentMatrixTarget = 0;\n    mInitialized = false;\n}\n\nGpuHelper::~GpuHelper()\n{\n}\n\nvoid GpuHelper::pushProjectionMode2D(ProjectionMode2D pm)\n{\n    // switch to 2D projection\n    pushMatrix(Matrix4f::Identity(),GL_PROJECTION);\n\n    if(pm==PM_Normalized)\n    {\n        //glOrtho(-1., 1., -1., 1., 0., 1.);\n    }\n    else if(pm==PM_Viewport)\n    {\n        GLint vp[4];\n        glGetIntegerv(GL_VIEWPORT, vp);\n        glOrtho(0., vp[2], 0., vp[3], -1., 1.);\n    }\n\n    pushMatrix(Matrix4f::Identity(),GL_MODELVIEW);\n}\n\nvoid GpuHelper::popProjectionMode2D(void)\n{\n    popMatrix(GL_PROJECTION);\n    popMatrix(GL_MODELVIEW);\n}\n\nvoid GpuHelper::drawVector(const Vector3f& position, const Vector3f& vec, const Color& color, float aspect /* = 50.*/)\n{\n    static GLUquadricObj *cylindre = gluNewQuadric();\n    glColor4fv(color.data());\n    float length = vec.norm();\n    pushMatrix(GL_MODELVIEW);\n    glTranslatef(position.x(), position.y(), position.z());\n    Vector3f ax = Matrix3f::Identity().col(2).cross(vec);\n    ax.normalize();\n    Vector3f tmp = vec;\n    tmp.normalize();\n    float angle = 180.f/M_PI * acos(tmp.z());\n    if (angle>1e-3)\n        glRotatef(angle, ax.x(), ax.y(), ax.z());\n    gluCylinder(cylindre, length/aspect, length/aspect, 0.8*length, 10, 10);\n    glTranslatef(0.0,0.0,0.8*length);\n    gluCylinder(cylindre, 2.0*length/aspect, 0.0, 0.2*length, 10, 10);\n\n    popMatrix(GL_MODELVIEW);\n}\n\nvoid GpuHelper::drawVectorBox(const Vector3f& position, const Vector3f& vec, const Color& color, float aspect)\n{\n    static GLUquadricObj *cylindre = gluNewQuadric();\n    glColor4fv(color.data());\n    float length = vec.norm();\n    pushMatrix(GL_MODELVIEW);\n    glTranslatef(position.x(), position.y(), position.z());\n    Vector3f ax = Matrix3f::Identity().col(2).cross(vec);\n    ax.normalize();\n    Vector3f tmp = vec;\n    tmp.normalize();\n    float angle = 180.f/M_PI * acos(tmp.z());\n    if (angle>1e-3)\n        glRotatef(angle, ax.x(), ax.y(), ax.z());\n    gluCylinder(cylindre, length/aspect, length/aspect, 0.8*length, 10, 10);\n    glTranslatef(0.0,0.0,0.8*length);\n    glScalef(4.0*length/aspect,4.0*length/aspect,4.0*length/aspect);\n    drawUnitCube();\n    popMatrix(GL_MODELVIEW);\n}\n\nvoid GpuHelper::drawUnitCube(void)\n{\n    static float vertices[][3] = {\n        {-0.5,-0.5,-0.5},\n        { 0.5,-0.5,-0.5},\n        {-0.5, 0.5,-0.5},\n        { 0.5, 0.5,-0.5},\n        {-0.5,-0.5, 0.5},\n        { 0.5,-0.5, 0.5},\n        {-0.5, 0.5, 0.5},\n        { 0.5, 0.5, 0.5}};\n\n    glBegin(GL_QUADS);\n    glNormal3f(0,0,-1); glVertex3fv(vertices[0]); glVertex3fv(vertices[2]); glVertex3fv(vertices[3]); glVertex3fv(vertices[1]);\n    glNormal3f(0,0, 1); glVertex3fv(vertices[4]); glVertex3fv(vertices[5]); glVertex3fv(vertices[7]); glVertex3fv(vertices[6]);\n    glNormal3f(0,-1,0); glVertex3fv(vertices[0]); glVertex3fv(vertices[1]); glVertex3fv(vertices[5]); glVertex3fv(vertices[4]);\n    glNormal3f(0, 1,0); glVertex3fv(vertices[2]); glVertex3fv(vertices[6]); glVertex3fv(vertices[7]); glVertex3fv(vertices[3]);\n    glNormal3f(-1,0,0); glVertex3fv(vertices[0]); glVertex3fv(vertices[4]); glVertex3fv(vertices[6]); glVertex3fv(vertices[2]);\n    glNormal3f( 1,0,0); glVertex3fv(vertices[1]); glVertex3fv(vertices[3]); glVertex3fv(vertices[7]); glVertex3fv(vertices[5]);\n    glEnd();\n}\n\nvoid GpuHelper::drawUnitSphere(int level)\n{\n  static IcoSphere sphere;\n  sphere.draw(level);\n}\n\n\n"
  },
  {
    "path": "include/eigen3/demos/opengl/gpuhelper.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_GPUHELPER_H\n#define EIGEN_GPUHELPER_H\n\n#include <Eigen/Geometry>\n#include <GL/gl.h>\n#include <vector>\n\nusing namespace Eigen;\n\ntypedef Vector4f Color;\n\nclass GpuHelper\n{\n  public:\n\n    GpuHelper();\n\n    ~GpuHelper();\n\n    enum ProjectionMode2D { PM_Normalized = 1, PM_Viewport = 2 };\n    void pushProjectionMode2D(ProjectionMode2D pm);\n    void popProjectionMode2D();\n\n    /** Multiply the OpenGL matrix \\a matrixTarget by the matrix \\a mat.\n        Essentially, this helper function automatically calls glMatrixMode(matrixTarget) if required\n        and does a proper call to the right glMultMatrix*() function according to the scalar type\n        and storage order.\n        \\warning glMatrixMode() must never be called directly. If your're unsure, use forceMatrixMode().\n        \\sa Matrix, loadMatrix(), forceMatrixMode()\n    */\n    template<typename Scalar, int _Flags>\n    void multMatrix(const Matrix<Scalar,4,4, _Flags, 4,4>& mat, GLenum matrixTarget);\n\n    /** Load the matrix \\a mat to the OpenGL matrix \\a matrixTarget.\n        Essentially, this helper function automatically calls glMatrixMode(matrixTarget) if required\n        and does a proper call to the right glLoadMatrix*() or glLoadIdentity() function according to the scalar type\n        and storage order.\n        \\warning glMatrixMode() must never be called directly. If your're unsure, use forceMatrixMode().\n        \\sa Matrix, multMatrix(), forceMatrixMode()\n    */\n    template<typename Scalar, int _Flags>\n    void loadMatrix(const Eigen::Matrix<Scalar,4,4, _Flags, 4,4>& mat, GLenum matrixTarget);\n\n    template<typename Scalar, typename Derived>\n    void loadMatrix(\n        const Eigen::CwiseNullaryOp<Eigen::internal::scalar_identity_op<Scalar>,Derived>&,\n        GLenum matrixTarget);\n\n    /** Make the matrix \\a matrixTarget the current OpenGL matrix target.\n        Call this function before loadMatrix() or multMatrix() if you cannot guarantee that glMatrixMode()\n        has never been called after the last loadMatrix() or multMatrix() calls.\n        \\todo provides a debug mode checking the sanity of the cached matrix mode.\n    */\n    inline void forceMatrixTarget(GLenum matrixTarget) {glMatrixMode(mCurrentMatrixTarget=matrixTarget);}\n\n    inline void setMatrixTarget(GLenum matrixTarget);\n\n    /** Push the OpenGL matrix \\a matrixTarget and load \\a mat.\n    */\n    template<typename Scalar, int _Flags>\n    inline void pushMatrix(const Matrix<Scalar,4,4, _Flags, 4,4>& mat, GLenum matrixTarget);\n\n    template<typename Scalar, typename Derived>\n    void pushMatrix(\n        const Eigen::CwiseNullaryOp<Eigen::internal::scalar_identity_op<Scalar>,Derived>&,\n        GLenum matrixTarget);\n\n    /** Push and clone the OpenGL matrix \\a matrixTarget\n    */\n    inline void pushMatrix(GLenum matrixTarget);\n\n    /** Pop the OpenGL matrix \\a matrixTarget\n    */\n    inline void popMatrix(GLenum matrixTarget);\n\n    void drawVector(const Vector3f& position, const Vector3f& vec, const Color& color, float aspect = 50.);\n    void drawVectorBox(const Vector3f& position, const Vector3f& vec, const Color& color, float aspect = 50.);\n    void drawUnitCube(void);\n    void drawUnitSphere(int level=0);\n\n    /// draw the \\a nofElement first elements\n    inline void draw(GLenum mode, uint nofElement);\n\n    /// draw a range of elements\n    inline void draw(GLenum mode, uint start, uint end);\n\n    /// draw an indexed subset\n    inline void draw(GLenum mode, const std::vector<uint>* pIndexes);\n\nprotected:\n\n    void update(void);\n\n    GLuint mColorBufferId;\n    int mVpWidth, mVpHeight;\n    GLenum mCurrentMatrixTarget;\n    bool mInitialized;\n};\n\n/** Singleton shortcut\n*/\nextern GpuHelper gpu;\n\n\n/** \\internal\n*/\ntemplate<bool RowMajor, int _Flags> struct GlMatrixHelper;\n\ntemplate<int _Flags> struct GlMatrixHelper<false,_Flags>\n{\n    static void loadMatrix(const Matrix<float, 4,4, _Flags, 4,4>&  mat) { glLoadMatrixf(mat.data()); }\n    static void loadMatrix(const Matrix<double,4,4, _Flags, 4,4>& mat) { glLoadMatrixd(mat.data()); }\n    static void multMatrix(const Matrix<float, 4,4, _Flags, 4,4>&  mat) { glMultMatrixf(mat.data()); }\n    static void multMatrix(const Matrix<double,4,4, _Flags, 4,4>& mat) { glMultMatrixd(mat.data()); }\n};\n\ntemplate<int _Flags> struct GlMatrixHelper<true,_Flags>\n{\n    static void loadMatrix(const Matrix<float, 4,4, _Flags, 4,4>&  mat) { glLoadMatrixf(mat.transpose().eval().data()); }\n    static void loadMatrix(const Matrix<double,4,4, _Flags, 4,4>& mat) { glLoadMatrixd(mat.transpose().eval().data()); }\n    static void multMatrix(const Matrix<float, 4,4, _Flags, 4,4>&  mat) { glMultMatrixf(mat.transpose().eval().data()); }\n    static void multMatrix(const Matrix<double,4,4, _Flags, 4,4>& mat) { glMultMatrixd(mat.transpose().eval().data()); }\n};\n\ninline void GpuHelper::setMatrixTarget(GLenum matrixTarget)\n{\n    if (matrixTarget != mCurrentMatrixTarget)\n        glMatrixMode(mCurrentMatrixTarget=matrixTarget);\n}\n\ntemplate<typename Scalar, int _Flags>\nvoid GpuHelper::multMatrix(const Matrix<Scalar,4,4, _Flags, 4,4>& mat, GLenum matrixTarget)\n{\n    setMatrixTarget(matrixTarget);\n    GlMatrixHelper<_Flags&Eigen::RowMajorBit, _Flags>::multMatrix(mat);\n}\n\ntemplate<typename Scalar, typename Derived>\nvoid GpuHelper::loadMatrix(\n    const Eigen::CwiseNullaryOp<Eigen::internal::scalar_identity_op<Scalar>,Derived>&,\n    GLenum matrixTarget)\n{\n    setMatrixTarget(matrixTarget);\n    glLoadIdentity();\n}\n\ntemplate<typename Scalar, int _Flags>\nvoid GpuHelper::loadMatrix(const Eigen::Matrix<Scalar,4,4, _Flags, 4,4>& mat, GLenum matrixTarget)\n{\n    setMatrixTarget(matrixTarget);\n    GlMatrixHelper<(_Flags&Eigen::RowMajorBit)!=0, _Flags>::loadMatrix(mat);\n}\n\ninline void GpuHelper::pushMatrix(GLenum matrixTarget)\n{\n    setMatrixTarget(matrixTarget);\n    glPushMatrix();\n}\n\ntemplate<typename Scalar, int _Flags>\ninline void GpuHelper::pushMatrix(const Matrix<Scalar,4,4, _Flags, 4,4>& mat, GLenum matrixTarget)\n{\n    pushMatrix(matrixTarget);\n    GlMatrixHelper<_Flags&Eigen::RowMajorBit,_Flags>::loadMatrix(mat);\n}\n\ntemplate<typename Scalar, typename Derived>\nvoid GpuHelper::pushMatrix(\n    const Eigen::CwiseNullaryOp<Eigen::internal::scalar_identity_op<Scalar>,Derived>&,\n    GLenum matrixTarget)\n{\n    pushMatrix(matrixTarget);\n    glLoadIdentity();\n}\n\ninline void GpuHelper::popMatrix(GLenum matrixTarget)\n{\n    setMatrixTarget(matrixTarget);\n    glPopMatrix();\n}\n\ninline void GpuHelper::draw(GLenum mode, uint nofElement)\n{\n    glDrawArrays(mode, 0, nofElement);\n}\n\n\ninline void GpuHelper::draw(GLenum mode, const std::vector<uint>* pIndexes)\n{\n    glDrawElements(mode, pIndexes->size(), GL_UNSIGNED_INT, &(pIndexes->front()));\n}\n\ninline void GpuHelper::draw(GLenum mode, uint start, uint end)\n{\n    glDrawArrays(mode, start, end-start);\n}\n\n#endif // EIGEN_GPUHELPER_H\n"
  },
  {
    "path": "include/eigen3/demos/opengl/icosphere.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"icosphere.h\"\n\n#include <GL/gl.h>\n#include <map>\n\nusing namespace Eigen;\n\n//--------------------------------------------------------------------------------\n// icosahedron data\n//--------------------------------------------------------------------------------\n#define X .525731112119133606\n#define Z .850650808352039932\n\nstatic GLfloat vdata[12][3] = {\n   {-X, 0.0, Z}, {X, 0.0, Z}, {-X, 0.0, -Z}, {X, 0.0, -Z},\n   {0.0, Z, X}, {0.0, Z, -X}, {0.0, -Z, X}, {0.0, -Z, -X},\n   {Z, X, 0.0}, {-Z, X, 0.0}, {Z, -X, 0.0}, {-Z, -X, 0.0}\n};\n\nstatic GLint tindices[20][3] = {\n   {0,4,1}, {0,9,4}, {9,5,4}, {4,5,8}, {4,8,1},\n   {8,10,1}, {8,3,10}, {5,3,8}, {5,2,3}, {2,7,3},\n   {7,10,3}, {7,6,10}, {7,11,6}, {11,0,6}, {0,1,6},\n   {6,1,10}, {9,0,11}, {9,11,2}, {9,2,5}, {7,2,11} };\n//--------------------------------------------------------------------------------\n\nIcoSphere::IcoSphere(unsigned int levels)\n{\n  // init with an icosahedron\n  for (int i = 0; i < 12; i++)\n    mVertices.push_back(Map<Vector3f>(vdata[i]));\n  mIndices.push_back(new std::vector<int>);\n  std::vector<int>& indices = *mIndices.back();\n  for (int i = 0; i < 20; i++)\n  {\n    for (int k = 0; k < 3; k++)\n      indices.push_back(tindices[i][k]);\n  }\n  mListIds.push_back(0);\n\n  while(mIndices.size()<levels)\n    _subdivide();\n}\n\nconst std::vector<int>& IcoSphere::indices(int level) const\n{\n  while (level>=int(mIndices.size()))\n    const_cast<IcoSphere*>(this)->_subdivide();\n  return *mIndices[level];\n}\n\nvoid IcoSphere::_subdivide(void)\n{\n  typedef unsigned long long Key;\n  std::map<Key,int> edgeMap;\n  const std::vector<int>& indices = *mIndices.back();\n  mIndices.push_back(new std::vector<int>);\n  std::vector<int>& refinedIndices = *mIndices.back();\n  int end = indices.size();\n  for (int i=0; i<end; i+=3)\n  {\n    int ids0[3],  // indices of outer vertices\n        ids1[3];  // indices of edge vertices\n    for (int k=0; k<3; ++k)\n    {\n      int k1 = (k+1)%3;\n      int e0 = indices[i+k];\n      int e1 = indices[i+k1];\n      ids0[k] = e0;\n      if (e1>e0)\n        std::swap(e0,e1);\n      Key edgeKey = Key(e0) | (Key(e1)<<32);\n      std::map<Key,int>::iterator it = edgeMap.find(edgeKey);\n      if (it==edgeMap.end())\n      {\n        ids1[k] = mVertices.size();\n        edgeMap[edgeKey] = ids1[k];\n        mVertices.push_back( (mVertices[e0]+mVertices[e1]).normalized() );\n      }\n      else\n        ids1[k] = it->second;\n    }\n    refinedIndices.push_back(ids0[0]); refinedIndices.push_back(ids1[0]); refinedIndices.push_back(ids1[2]);\n    refinedIndices.push_back(ids0[1]); refinedIndices.push_back(ids1[1]); refinedIndices.push_back(ids1[0]);\n    refinedIndices.push_back(ids0[2]); refinedIndices.push_back(ids1[2]); refinedIndices.push_back(ids1[1]);\n    refinedIndices.push_back(ids1[0]); refinedIndices.push_back(ids1[1]); refinedIndices.push_back(ids1[2]);\n  }\n  mListIds.push_back(0);\n}\n\nvoid IcoSphere::draw(int level)\n{\n  while (level>=int(mIndices.size()))\n    const_cast<IcoSphere*>(this)->_subdivide();\n  if (mListIds[level]==0)\n  {\n    mListIds[level] = glGenLists(1);\n    glNewList(mListIds[level], GL_COMPILE);\n      glVertexPointer(3, GL_FLOAT, 0, mVertices[0].data());\n      glNormalPointer(GL_FLOAT, 0, mVertices[0].data());\n      glEnableClientState(GL_VERTEX_ARRAY);\n      glEnableClientState(GL_NORMAL_ARRAY);\n      glDrawElements(GL_TRIANGLES, mIndices[level]->size(), GL_UNSIGNED_INT, &(mIndices[level]->at(0)));\n      glDisableClientState(GL_VERTEX_ARRAY);\n      glDisableClientState(GL_NORMAL_ARRAY);\n    glEndList();\n  }\n  glCallList(mListIds[level]);\n}\n\n\n"
  },
  {
    "path": "include/eigen3/demos/opengl/icosphere.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_ICOSPHERE_H\n#define EIGEN_ICOSPHERE_H\n\n#include <Eigen/Core>\n#include <vector>\n\nclass IcoSphere\n{\n  public:\n    IcoSphere(unsigned int levels=1);\n    const std::vector<Eigen::Vector3f>& vertices() const { return mVertices; }\n    const std::vector<int>& indices(int level) const;\n    void draw(int level);\n  protected:\n    void _subdivide();\n    std::vector<Eigen::Vector3f> mVertices;\n    std::vector<std::vector<int>*> mIndices;\n    std::vector<int> mListIds;\n};\n\n#endif // EIGEN_ICOSPHERE_H\n"
  },
  {
    "path": "include/eigen3/demos/opengl/quaternion_demo.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"quaternion_demo.h\"\n#include \"icosphere.h\"\n\n#include <Eigen/Geometry>\n#include <Eigen/QR>\n#include <Eigen/LU>\n\n#include <iostream>\n#include <QEvent>\n#include <QMouseEvent>\n#include <QInputDialog>\n#include <QGridLayout>\n#include <QButtonGroup>\n#include <QRadioButton>\n#include <QDockWidget>\n#include <QPushButton>\n#include <QGroupBox>\n\nusing namespace Eigen;\n\nclass FancySpheres\n{\n  public:\n    EIGEN_MAKE_ALIGNED_OPERATOR_NEW\n    \n    FancySpheres()\n    {\n      const int levels = 4;\n      const float scale = 0.33;\n      float radius = 100;\n      std::vector<int> parents;\n\n      // leval 0\n      mCenters.push_back(Vector3f::Zero());\n      parents.push_back(-1);\n      mRadii.push_back(radius);\n\n      // generate level 1 using icosphere vertices\n      radius *= 0.45;\n      {\n        float dist = mRadii[0]*0.9;\n        for (int i=0; i<12; ++i)\n        {\n          mCenters.push_back(mIcoSphere.vertices()[i] * dist);\n          mRadii.push_back(radius);\n          parents.push_back(0);\n        }\n      }\n\n      static const float angles [10] = {\n        0, 0,\n        M_PI, 0.*M_PI,\n        M_PI, 0.5*M_PI,\n        M_PI, 1.*M_PI,\n        M_PI, 1.5*M_PI\n      };\n\n      // generate other levels\n      int start = 1;\n      for (int l=1; l<levels; l++)\n      {\n        radius *= scale;\n        int end = mCenters.size();\n        for (int i=start; i<end; ++i)\n        {\n          Vector3f c = mCenters[i];\n          Vector3f ax0 = (c - mCenters[parents[i]]).normalized();\n          Vector3f ax1 = ax0.unitOrthogonal();\n          Quaternionf q;\n          q.setFromTwoVectors(Vector3f::UnitZ(), ax0);\n          Affine3f t = Translation3f(c) * q * Scaling(mRadii[i]+radius);\n          for (int j=0; j<5; ++j)\n          {\n            Vector3f newC = c + ( (AngleAxisf(angles[j*2+1], ax0)\n                                * AngleAxisf(angles[j*2+0] * (l==1 ? 0.35 : 0.5), ax1)) * ax0)\n                                * (mRadii[i] + radius*0.8);\n            mCenters.push_back(newC);\n            mRadii.push_back(radius);\n            parents.push_back(i);\n          }\n        }\n        start = end;\n      }\n    }\n\n    void draw()\n    {\n      int end = mCenters.size();\n      glEnable(GL_NORMALIZE);\n      for (int i=0; i<end; ++i)\n      {\n        Affine3f t = Translation3f(mCenters[i]) * Scaling(mRadii[i]);\n        gpu.pushMatrix(GL_MODELVIEW);\n        gpu.multMatrix(t.matrix(),GL_MODELVIEW);\n        mIcoSphere.draw(2);\n        gpu.popMatrix(GL_MODELVIEW);\n      }\n      glDisable(GL_NORMALIZE);\n    }\n  protected:\n    std::vector<Vector3f> mCenters;\n    std::vector<float> mRadii;\n    IcoSphere mIcoSphere;\n};\n\n\n// generic linear interpolation method\ntemplate<typename T> T lerp(float t, const T& a, const T& b)\n{\n  return a*(1-t) + b*t;\n}\n\n// quaternion slerp\ntemplate<> Quaternionf lerp(float t, const Quaternionf& a, const Quaternionf& b)\n{ return a.slerp(t,b); }\n\n// linear interpolation of a frame using the type OrientationType\n// to perform the interpolation of the orientations\ntemplate<typename OrientationType>\ninline static Frame lerpFrame(float alpha, const Frame& a, const Frame& b)\n{\n  return Frame(lerp(alpha,a.position,b.position),\n               Quaternionf(lerp(alpha,OrientationType(a.orientation),OrientationType(b.orientation))));\n}\n\ntemplate<typename _Scalar> class EulerAngles\n{\npublic:\n  enum { Dim = 3 };\n  typedef _Scalar Scalar;\n  typedef Matrix<Scalar,3,3> Matrix3;\n  typedef Matrix<Scalar,3,1> Vector3;\n  typedef Quaternion<Scalar> QuaternionType;\n\nprotected:\n\n  Vector3 m_angles;\n\npublic:\n\n  EulerAngles() {}\n  inline EulerAngles(Scalar a0, Scalar a1, Scalar a2) : m_angles(a0, a1, a2) {}\n  inline EulerAngles(const QuaternionType& q) { *this = q; }\n\n  const Vector3& coeffs() const { return m_angles; }\n  Vector3& coeffs() { return m_angles; }\n\n  EulerAngles& operator=(const QuaternionType& q)\n  {\n    Matrix3 m = q.toRotationMatrix();\n    return *this = m;\n  }\n\n  EulerAngles& operator=(const Matrix3& m)\n  {\n    // mat =  cy*cz          -cy*sz           sy\n    //        cz*sx*sy+cx*sz  cx*cz-sx*sy*sz -cy*sx\n    //       -cx*cz*sy+sx*sz  cz*sx+cx*sy*sz  cx*cy\n    m_angles.coeffRef(1) = std::asin(m.coeff(0,2));\n    m_angles.coeffRef(0) = std::atan2(-m.coeff(1,2),m.coeff(2,2));\n    m_angles.coeffRef(2) = std::atan2(-m.coeff(0,1),m.coeff(0,0));\n    return *this;\n  }\n\n  Matrix3 toRotationMatrix(void) const\n  {\n    Vector3 c = m_angles.array().cos();\n    Vector3 s = m_angles.array().sin();\n    Matrix3 res;\n    res <<  c.y()*c.z(),                    -c.y()*s.z(),                   s.y(),\n            c.z()*s.x()*s.y()+c.x()*s.z(),  c.x()*c.z()-s.x()*s.y()*s.z(),  -c.y()*s.x(),\n            -c.x()*c.z()*s.y()+s.x()*s.z(), c.z()*s.x()+c.x()*s.y()*s.z(),  c.x()*c.y();\n    return res;\n  }\n\n  operator QuaternionType() { return QuaternionType(toRotationMatrix()); }\n};\n\n// Euler angles slerp\ntemplate<> EulerAngles<float> lerp(float t, const EulerAngles<float>& a, const EulerAngles<float>& b)\n{\n  EulerAngles<float> res;\n  res.coeffs() = lerp(t, a.coeffs(), b.coeffs());\n  return res;\n}\n\n\nRenderingWidget::RenderingWidget()\n{\n  mAnimate = false;\n  mCurrentTrackingMode = TM_NO_TRACK;\n  mNavMode = NavTurnAround;\n  mLerpMode = LerpQuaternion;\n  mRotationMode = RotationStable;\n  mTrackball.setCamera(&mCamera);\n\n  // required to capture key press events\n  setFocusPolicy(Qt::ClickFocus);\n}\n\nvoid RenderingWidget::grabFrame(void)\n{\n    // ask user for a time\n    bool ok = false;\n    double t = 0;\n    if (!m_timeline.empty())\n      t = (--m_timeline.end())->first + 1.;\n    t = QInputDialog::getDouble(this, \"Eigen's RenderingWidget\", \"time value: \",\n      t, 0, 1e3, 1, &ok);\n    if (ok)\n    {\n      Frame aux;\n      aux.orientation = mCamera.viewMatrix().linear();\n      aux.position = mCamera.viewMatrix().translation();\n      m_timeline[t] = aux;\n    }\n}\n\nvoid RenderingWidget::drawScene()\n{\n  static FancySpheres sFancySpheres;\n  float length = 50;\n  gpu.drawVector(Vector3f::Zero(), length*Vector3f::UnitX(), Color(1,0,0,1));\n  gpu.drawVector(Vector3f::Zero(), length*Vector3f::UnitY(), Color(0,1,0,1));\n  gpu.drawVector(Vector3f::Zero(), length*Vector3f::UnitZ(), Color(0,0,1,1));\n\n  // draw the fractal object\n  float sqrt3 = std::sqrt(3.);\n  glLightfv(GL_LIGHT0, GL_AMBIENT, Vector4f(0.5,0.5,0.5,1).data());\n  glLightfv(GL_LIGHT0, GL_DIFFUSE, Vector4f(0.5,1,0.5,1).data());\n  glLightfv(GL_LIGHT0, GL_SPECULAR, Vector4f(1,1,1,1).data());\n  glLightfv(GL_LIGHT0, GL_POSITION, Vector4f(-sqrt3,-sqrt3,sqrt3,0).data());\n\n  glLightfv(GL_LIGHT1, GL_AMBIENT, Vector4f(0,0,0,1).data());\n  glLightfv(GL_LIGHT1, GL_DIFFUSE, Vector4f(1,0.5,0.5,1).data());\n  glLightfv(GL_LIGHT1, GL_SPECULAR, Vector4f(1,1,1,1).data());\n  glLightfv(GL_LIGHT1, GL_POSITION, Vector4f(-sqrt3,sqrt3,-sqrt3,0).data());\n\n  glMaterialfv(GL_FRONT_AND_BACK, GL_AMBIENT, Vector4f(0.7, 0.7, 0.7, 1).data());\n  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, Vector4f(0.8, 0.75, 0.6, 1).data());\n  glMaterialfv(GL_FRONT_AND_BACK, GL_SPECULAR, Vector4f(1, 1, 1, 1).data());\n  glMaterialf(GL_FRONT_AND_BACK, GL_SHININESS, 64);\n\n  glEnable(GL_LIGHTING);\n  glEnable(GL_LIGHT0);\n  glEnable(GL_LIGHT1);\n\n  sFancySpheres.draw();\n  glVertexPointer(3, GL_FLOAT, 0, mVertices[0].data());\n  glNormalPointer(GL_FLOAT, 0, mNormals[0].data());\n  glEnableClientState(GL_VERTEX_ARRAY);\n  glEnableClientState(GL_NORMAL_ARRAY);\n  glDrawArrays(GL_TRIANGLES, 0, mVertices.size());\n  glDisableClientState(GL_VERTEX_ARRAY);\n  glDisableClientState(GL_NORMAL_ARRAY);\n\n  glDisable(GL_LIGHTING);\n}\n\nvoid RenderingWidget::animate()\n{\n  m_alpha += double(m_timer.interval()) * 1e-3;\n\n  TimeLine::const_iterator hi = m_timeline.upper_bound(m_alpha);\n  TimeLine::const_iterator lo = hi;\n  --lo;\n\n  Frame currentFrame;\n\n  if(hi==m_timeline.end())\n  {\n    // end\n    currentFrame = lo->second;\n    stopAnimation();\n  }\n  else if(hi==m_timeline.begin())\n  {\n    // start\n    currentFrame = hi->second;\n  }\n  else\n  {\n    float s = (m_alpha - lo->first)/(hi->first - lo->first);\n    if (mLerpMode==LerpEulerAngles)\n      currentFrame = ::lerpFrame<EulerAngles<float> >(s, lo->second, hi->second);\n    else if (mLerpMode==LerpQuaternion)\n      currentFrame = ::lerpFrame<Eigen::Quaternionf>(s, lo->second, hi->second);\n    else\n    {\n      std::cerr << \"Invalid rotation interpolation mode (abort)\\n\";\n      exit(2);\n    }\n    currentFrame.orientation.coeffs().normalize();\n  }\n\n  currentFrame.orientation = currentFrame.orientation.inverse();\n  currentFrame.position = - (currentFrame.orientation * currentFrame.position);\n  mCamera.setFrame(currentFrame);\n\n  updateGL();\n}\n\nvoid RenderingWidget::keyPressEvent(QKeyEvent * e)\n{\n    switch(e->key())\n    {\n      case Qt::Key_Up:\n        mCamera.zoom(2);\n        break;\n      case Qt::Key_Down:\n        mCamera.zoom(-2);\n        break;\n      // add a frame\n      case Qt::Key_G:\n        grabFrame();\n        break;\n      // clear the time line\n      case Qt::Key_C:\n        m_timeline.clear();\n        break;\n      // move the camera to initial pos\n      case Qt::Key_R:\n        resetCamera();\n        break;\n      // start/stop the animation\n      case Qt::Key_A:\n        if (mAnimate)\n        {\n          stopAnimation();\n        }\n        else\n        {\n          m_alpha = 0;\n          connect(&m_timer, SIGNAL(timeout()), this, SLOT(animate()));\n          m_timer.start(1000/30);\n          mAnimate = true;\n        }\n        break;\n      default:\n        break;\n    }\n\n    updateGL();\n}\n\nvoid RenderingWidget::stopAnimation()\n{\n  disconnect(&m_timer, SIGNAL(timeout()), this, SLOT(animate()));\n  m_timer.stop();\n  mAnimate = false;\n  m_alpha = 0;\n}\n\nvoid RenderingWidget::mousePressEvent(QMouseEvent* e)\n{\n  mMouseCoords = Vector2i(e->pos().x(), e->pos().y());\n  bool fly = (mNavMode==NavFly) || (e->modifiers()&Qt::ControlModifier);\n  switch(e->button())\n  {\n    case Qt::LeftButton:\n      if(fly)\n      {\n        mCurrentTrackingMode = TM_LOCAL_ROTATE;\n        mTrackball.start(Trackball::Local);\n      }\n      else\n      {\n        mCurrentTrackingMode = TM_ROTATE_AROUND;\n        mTrackball.start(Trackball::Around);\n      }\n      mTrackball.track(mMouseCoords);\n      break;\n    case Qt::MidButton:\n      if(fly)\n        mCurrentTrackingMode = TM_FLY_Z;\n      else\n        mCurrentTrackingMode = TM_ZOOM;\n      break;\n    case Qt::RightButton:\n        mCurrentTrackingMode = TM_FLY_PAN;\n      break;\n    default:\n      break;\n  }\n}\nvoid RenderingWidget::mouseReleaseEvent(QMouseEvent*)\n{\n    mCurrentTrackingMode = TM_NO_TRACK;\n    updateGL();\n}\n\nvoid RenderingWidget::mouseMoveEvent(QMouseEvent* e)\n{\n    // tracking\n    if(mCurrentTrackingMode != TM_NO_TRACK)\n    {\n        float dx =   float(e->x() - mMouseCoords.x()) / float(mCamera.vpWidth());\n        float dy = - float(e->y() - mMouseCoords.y()) / float(mCamera.vpHeight());\n\n        // speedup the transformations\n        if(e->modifiers() & Qt::ShiftModifier)\n        {\n          dx *= 10.;\n          dy *= 10.;\n        }\n\n        switch(mCurrentTrackingMode)\n        {\n          case TM_ROTATE_AROUND:\n          case TM_LOCAL_ROTATE:\n            if (mRotationMode==RotationStable)\n            {\n              // use the stable trackball implementation mapping\n              // the 2D coordinates to 3D points on a sphere.\n              mTrackball.track(Vector2i(e->pos().x(), e->pos().y()));\n            }\n            else\n            {\n              // standard approach mapping the x and y displacements as rotations\n              // around the camera's X and Y axes.\n              Quaternionf q = AngleAxisf( dx*M_PI, Vector3f::UnitY())\n                            * AngleAxisf(-dy*M_PI, Vector3f::UnitX());\n              if (mCurrentTrackingMode==TM_LOCAL_ROTATE)\n                mCamera.localRotate(q);\n              else\n                mCamera.rotateAroundTarget(q);\n            }\n            break;\n          case TM_ZOOM :\n            mCamera.zoom(dy*100);\n            break;\n          case TM_FLY_Z :\n            mCamera.localTranslate(Vector3f(0, 0, -dy*200));\n            break;\n          case TM_FLY_PAN :\n            mCamera.localTranslate(Vector3f(dx*200, dy*200, 0));\n            break;\n          default:\n            break;\n        }\n\n        updateGL();\n    }\n\n    mMouseCoords = Vector2i(e->pos().x(), e->pos().y());\n}\n\nvoid RenderingWidget::paintGL()\n{\n  glEnable(GL_DEPTH_TEST);\n  glDisable(GL_CULL_FACE);\n  glPolygonMode(GL_FRONT_AND_BACK,GL_FILL);\n  glDisable(GL_COLOR_MATERIAL);\n  glDisable(GL_BLEND);\n  glDisable(GL_ALPHA_TEST);\n  glDisable(GL_TEXTURE_1D);\n  glDisable(GL_TEXTURE_2D);\n  glDisable(GL_TEXTURE_3D);\n\n  // Clear buffers\n  glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);\n\n  mCamera.activateGL();\n\n  drawScene();\n}\n\nvoid RenderingWidget::initializeGL()\n{\n  glClearColor(1., 1., 1., 0.);\n  glLightModeli(GL_LIGHT_MODEL_LOCAL_VIEWER, 1);\n  glDepthMask(GL_TRUE);\n  glColorMask(GL_TRUE, GL_TRUE, GL_TRUE, GL_TRUE);\n\n  mCamera.setPosition(Vector3f(-200, -200, -200));\n  mCamera.setTarget(Vector3f(0, 0, 0));\n  mInitFrame.orientation = mCamera.orientation().inverse();\n  mInitFrame.position = mCamera.viewMatrix().translation();\n}\n\nvoid RenderingWidget::resizeGL(int width, int height)\n{\n    mCamera.setViewport(width,height);\n}\n\nvoid RenderingWidget::setNavMode(int m)\n{\n  mNavMode = NavMode(m);\n}\n\nvoid RenderingWidget::setLerpMode(int m)\n{\n  mLerpMode = LerpMode(m);\n}\n\nvoid RenderingWidget::setRotationMode(int m)\n{\n  mRotationMode = RotationMode(m);\n}\n\nvoid RenderingWidget::resetCamera()\n{\n  if (mAnimate)\n    stopAnimation();\n  m_timeline.clear();\n  Frame aux0 = mCamera.frame();\n  aux0.orientation = aux0.orientation.inverse();\n  aux0.position = mCamera.viewMatrix().translation();\n  m_timeline[0] = aux0;\n\n  Vector3f currentTarget = mCamera.target();\n  mCamera.setTarget(Vector3f::Zero());\n\n  // compute the rotation duration to move the camera to the target\n  Frame aux1 = mCamera.frame();\n  aux1.orientation = aux1.orientation.inverse();\n  aux1.position = mCamera.viewMatrix().translation();\n  float duration = aux0.orientation.angularDistance(aux1.orientation) * 0.9;\n  if (duration<0.1) duration = 0.1;\n\n  // put the camera at that time step:\n  aux1 = aux0.lerp(duration/2,mInitFrame);\n  // and make it look at the target again\n  aux1.orientation = aux1.orientation.inverse();\n  aux1.position = - (aux1.orientation * aux1.position);\n  mCamera.setFrame(aux1);\n  mCamera.setTarget(Vector3f::Zero());\n\n  // add this camera keyframe\n  aux1.orientation = aux1.orientation.inverse();\n  aux1.position = mCamera.viewMatrix().translation();\n  m_timeline[duration] = aux1;\n\n  m_timeline[2] = mInitFrame;\n  m_alpha = 0;\n  animate();\n  connect(&m_timer, SIGNAL(timeout()), this, SLOT(animate()));\n  m_timer.start(1000/30);\n  mAnimate = true;\n}\n\nQWidget* RenderingWidget::createNavigationControlWidget()\n{\n  QWidget* panel = new QWidget();\n  QVBoxLayout* layout = new QVBoxLayout();\n\n  {\n    QPushButton* but = new QPushButton(\"reset\");\n    but->setToolTip(\"move the camera to initial position (with animation)\");\n    layout->addWidget(but);\n    connect(but, SIGNAL(clicked()), this, SLOT(resetCamera()));\n  }\n  {\n    // navigation mode\n    QGroupBox* box = new QGroupBox(\"navigation mode\");\n    QVBoxLayout* boxLayout = new QVBoxLayout;\n    QButtonGroup* group = new QButtonGroup(panel);\n    QRadioButton* but;\n    but = new QRadioButton(\"turn around\");\n    but->setToolTip(\"look around an object\");\n    group->addButton(but, NavTurnAround);\n    boxLayout->addWidget(but);\n    but = new QRadioButton(\"fly\");\n    but->setToolTip(\"free navigation like a spaceship\\n(this mode can also be enabled pressing the \\\"shift\\\" key)\");\n    group->addButton(but, NavFly);\n    boxLayout->addWidget(but);\n    group->button(mNavMode)->setChecked(true);\n    connect(group, SIGNAL(buttonClicked(int)), this, SLOT(setNavMode(int)));\n    box->setLayout(boxLayout);\n    layout->addWidget(box);\n  }\n  {\n    // track ball, rotation mode\n    QGroupBox* box = new QGroupBox(\"rotation mode\");\n    QVBoxLayout* boxLayout = new QVBoxLayout;\n    QButtonGroup* group = new QButtonGroup(panel);\n    QRadioButton* but;\n    but = new QRadioButton(\"stable trackball\");\n    group->addButton(but, RotationStable);\n    boxLayout->addWidget(but);\n    but->setToolTip(\"use the stable trackball implementation mapping\\nthe 2D coordinates to 3D points on a sphere\");\n    but = new QRadioButton(\"standard rotation\");\n    group->addButton(but, RotationStandard);\n    boxLayout->addWidget(but);\n    but->setToolTip(\"standard approach mapping the x and y displacements\\nas rotations around the camera's X and Y axes\");\n    group->button(mRotationMode)->setChecked(true);\n    connect(group, SIGNAL(buttonClicked(int)), this, SLOT(setRotationMode(int)));\n    box->setLayout(boxLayout);\n    layout->addWidget(box);\n  }\n  {\n    // interpolation mode\n    QGroupBox* box = new QGroupBox(\"spherical interpolation\");\n    QVBoxLayout* boxLayout = new QVBoxLayout;\n    QButtonGroup* group = new QButtonGroup(panel);\n    QRadioButton* but;\n    but = new QRadioButton(\"quaternion slerp\");\n    group->addButton(but, LerpQuaternion);\n    boxLayout->addWidget(but);\n    but->setToolTip(\"use quaternion spherical interpolation\\nto interpolate orientations\");\n    but = new QRadioButton(\"euler angles\");\n    group->addButton(but, LerpEulerAngles);\n    boxLayout->addWidget(but);\n    but->setToolTip(\"use Euler angles to interpolate orientations\");\n    group->button(mNavMode)->setChecked(true);\n    connect(group, SIGNAL(buttonClicked(int)), this, SLOT(setLerpMode(int)));\n    box->setLayout(boxLayout);\n    layout->addWidget(box);\n  }\n  layout->addItem(new QSpacerItem(0,0,QSizePolicy::Minimum,QSizePolicy::Expanding));\n  panel->setLayout(layout);\n  return panel;\n}\n\nQuaternionDemo::QuaternionDemo()\n{\n  mRenderingWidget = new RenderingWidget();\n  setCentralWidget(mRenderingWidget);\n\n  QDockWidget* panel = new QDockWidget(\"navigation\", this);\n  panel->setAllowedAreas((QFlags<Qt::DockWidgetArea>)(Qt::RightDockWidgetArea | Qt::LeftDockWidgetArea));\n  addDockWidget(Qt::RightDockWidgetArea, panel);\n  panel->setWidget(mRenderingWidget->createNavigationControlWidget());\n}\n\nint main(int argc, char *argv[])\n{\n  std::cout << \"Navigation:\\n\";\n  std::cout << \"  left button:           rotate around the target\\n\";\n  std::cout << \"  middle button:         zoom\\n\";\n  std::cout << \"  left button + ctrl     quake rotate (rotate around camera position)\\n\";\n  std::cout << \"  middle button + ctrl   walk (progress along camera's z direction)\\n\";\n  std::cout << \"  left button:           pan (translate in the XY camera's plane)\\n\\n\";\n  std::cout << \"R : move the camera to initial position\\n\";\n  std::cout << \"A : start/stop animation\\n\";\n  std::cout << \"C : clear the animation\\n\";\n  std::cout << \"G : add a key frame\\n\";\n\n  QApplication app(argc, argv);\n  QuaternionDemo demo;\n  demo.resize(600,500);\n  demo.show();\n  return app.exec();\n}\n\n#include \"quaternion_demo.moc\"\n\n"
  },
  {
    "path": "include/eigen3/demos/opengl/quaternion_demo.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_QUATERNION_DEMO_H\n#define EIGEN_QUATERNION_DEMO_H\n\n#include \"gpuhelper.h\"\n#include \"camera.h\"\n#include \"trackball.h\"\n#include <map>\n#include <QTimer>\n#include <QtGui/QApplication>\n#include <QtOpenGL/QGLWidget>\n#include <QtGui/QMainWindow>\n\nclass RenderingWidget : public QGLWidget\n{\n  Q_OBJECT\n\n    typedef std::map<float,Frame> TimeLine;\n    TimeLine m_timeline;\n    Frame lerpFrame(float t);\n\n    Frame mInitFrame;\n    bool mAnimate;\n    float m_alpha;\n\n    enum TrackMode {\n      TM_NO_TRACK=0, TM_ROTATE_AROUND, TM_ZOOM,\n      TM_LOCAL_ROTATE, TM_FLY_Z, TM_FLY_PAN\n    };\n\n    enum NavMode {\n      NavTurnAround,\n      NavFly\n    };\n\n    enum LerpMode {\n      LerpQuaternion,\n      LerpEulerAngles\n    };\n\n    enum RotationMode {\n      RotationStable,\n      RotationStandard\n    };\n\n    Camera mCamera;\n    TrackMode mCurrentTrackingMode;\n    NavMode mNavMode;\n    LerpMode mLerpMode;\n    RotationMode mRotationMode;\n    Vector2i mMouseCoords;\n    Trackball mTrackball;\n\n    QTimer m_timer;\n\n    void setupCamera();\n\n    std::vector<Vector3f> mVertices;\n    std::vector<Vector3f> mNormals;\n    std::vector<int> mIndices;\n\n  protected slots:\n\n    virtual void animate(void);\n    virtual void drawScene(void);\n\n    virtual void grabFrame(void);\n    virtual void stopAnimation();\n\n    virtual void setNavMode(int);\n    virtual void setLerpMode(int);\n    virtual void setRotationMode(int);\n    virtual void resetCamera();\n\n  protected:\n\n    virtual void initializeGL();\n    virtual void resizeGL(int width, int height);\n    virtual void paintGL();\n    \n    //--------------------------------------------------------------------------------\n    virtual void mousePressEvent(QMouseEvent * e);\n    virtual void mouseReleaseEvent(QMouseEvent * e);\n    virtual void mouseMoveEvent(QMouseEvent * e);\n    virtual void keyPressEvent(QKeyEvent * e);\n    //--------------------------------------------------------------------------------\n\n  public: \n    EIGEN_MAKE_ALIGNED_OPERATOR_NEW\n    \n    RenderingWidget();\n    ~RenderingWidget() { }\n\n    QWidget* createNavigationControlWidget();\n};\n\nclass QuaternionDemo : public QMainWindow\n{\n  Q_OBJECT\n  public:\n    QuaternionDemo();\n  protected:\n    RenderingWidget* mRenderingWidget;\n};\n\n#endif // EIGEN_QUATERNION_DEMO_H\n"
  },
  {
    "path": "include/eigen3/demos/opengl/trackball.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"trackball.h\"\n#include \"camera.h\"\n\nusing namespace Eigen;\n\nvoid Trackball::track(const Vector2i& point2D)\n{\n  if (mpCamera==0)\n    return;\n  Vector3f newPoint3D;\n  bool newPointOk = mapToSphere(point2D, newPoint3D);\n\n  if (mLastPointOk && newPointOk)\n  {\n    Vector3f axis = mLastPoint3D.cross(newPoint3D).normalized();\n    float cos_angle = mLastPoint3D.dot(newPoint3D);\n    if ( std::abs(cos_angle) < 1.0 )\n    {\n      float angle = 2. * acos(cos_angle);\n      if (mMode==Around)\n        mpCamera->rotateAroundTarget(Quaternionf(AngleAxisf(angle, axis)));\n      else\n        mpCamera->localRotate(Quaternionf(AngleAxisf(-angle, axis)));\n    }\n  }\n\n  mLastPoint3D = newPoint3D;\n  mLastPointOk = newPointOk;\n}\n\nbool Trackball::mapToSphere(const Vector2i& p2, Vector3f& v3)\n{\n  if ((p2.x() >= 0) && (p2.x() <= int(mpCamera->vpWidth())) &&\n      (p2.y() >= 0) && (p2.y() <= int(mpCamera->vpHeight())) )\n  {\n    double x  = (double)(p2.x() - 0.5*mpCamera->vpWidth())  / (double)mpCamera->vpWidth();\n    double y  = (double)(0.5*mpCamera->vpHeight() - p2.y()) / (double)mpCamera->vpHeight();\n    double sinx         = sin(M_PI * x * 0.5);\n    double siny         = sin(M_PI * y * 0.5);\n    double sinx2siny2   = sinx * sinx + siny * siny;\n\n    v3.x() = sinx;\n    v3.y() = siny;\n    v3.z() = sinx2siny2 < 1.0 ? sqrt(1.0 - sinx2siny2) : 0.0;\n\n    return true;\n  }\n  else\n    return false;\n}\n"
  },
  {
    "path": "include/eigen3/demos/opengl/trackball.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_TRACKBALL_H\n#define EIGEN_TRACKBALL_H\n\n#include <Eigen/Geometry>\n\nclass Camera;\n\nclass Trackball\n{\n  public:\n\n    enum Mode {Around, Local};\n\n    Trackball() : mpCamera(0) {}\n\n    void start(Mode m = Around) { mMode = m; mLastPointOk = false; }\n\n    void setCamera(Camera* pCam) { mpCamera = pCam; }\n\n    void track(const Eigen::Vector2i& newPoint2D);\n\n  protected:\n\n    bool mapToSphere( const Eigen::Vector2i& p2, Eigen::Vector3f& v3);\n\n    Camera* mpCamera;\n    Eigen::Vector3f mLastPoint3D;\n    Mode mMode;\n    bool mLastPointOk;\n\n};\n\n#endif // EIGEN_TRACKBALL_H\n"
  },
  {
    "path": "include/eigen3/doc/A05_PortingFrom2To3.dox",
    "content": "namespace Eigen {\n\n/** \\page Eigen2ToEigen3 Porting from Eigen2 to Eigen3\n\nThis page lists the most important API changes between Eigen2 and Eigen3,\nand gives tips to help porting your application from Eigen2 to Eigen3.\n\n\\eigenAutoToc\n\n\\section CompatibilitySupport Eigen2 compatibility support\n\nUp to version 3.2 %Eigen provides <a href=\"http://eigen.tuxfamily.org/dox-3.2/Eigen2SupportModes.html\">Eigen2 support modes</a>. These are removed now, because they were barely used anymore and became hard to maintain after internal re-designs.\nYou can still use them by first <a href=\"http://eigen.tuxfamily.org/dox-3.2/Eigen2ToEigen3.html\">porting your code to Eigen 3.2</a>.\n\n\\section Using The USING_PART_OF_NAMESPACE_EIGEN macro\n\nThe USING_PART_OF_NAMESPACE_EIGEN macro has been removed. In Eigen 3, just do:\n\\code\nusing namespace Eigen;\n\\endcode\n\n\\section ComplexDot Dot products over complex numbers\n\nThis is the single trickiest change between Eigen 2 and Eigen 3. It only affects code using \\c std::complex numbers as scalar type.\n\nEigen 2's dot product was linear in the first variable. Eigen 3's dot product is linear in the second variable. In other words, the Eigen 2 code \\code x.dot(y) \\endcode is equivalent to the Eigen 3 code \\code y.dot(x) \\endcode In yet other words, dot products are complex-conjugated in Eigen 3 compared to Eigen 2. The switch to the new convention was commanded by common usage, especially with the notation \\f$ x^Ty \\f$ for dot products of column-vectors.\n\n\\section VectorBlocks Vector blocks\n\n<table class=\"manual\">\n<tr><th>Eigen 2</th><th>Eigen 3</th></th>\n<tr><td>\\code\nvector.start(length)\nvector.start<length>()\nvector.end(length)\nvector.end<length>()\n\\endcode</td><td>\\code\nvector.head(length)\nvector.head<length>()\nvector.tail(length)\nvector.tail<length>()\n\\endcode</td></tr>\n</table>\n\n\n\\section Corners Matrix Corners\n\n<table class=\"manual\">\n<tr><th>Eigen 2</th><th>Eigen 3</th></th>\n<tr><td>\\code\nmatrix.corner(TopLeft,r,c)\nmatrix.corner(TopRight,r,c)\nmatrix.corner(BottomLeft,r,c)\nmatrix.corner(BottomRight,r,c)\nmatrix.corner<r,c>(TopLeft)\nmatrix.corner<r,c>(TopRight)\nmatrix.corner<r,c>(BottomLeft)\nmatrix.corner<r,c>(BottomRight)\n\\endcode</td><td>\\code\nmatrix.topLeftCorner(r,c)\nmatrix.topRightCorner(r,c)\nmatrix.bottomLeftCorner(r,c)\nmatrix.bottomRightCorner(r,c)\nmatrix.topLeftCorner<r,c>()\nmatrix.topRightCorner<r,c>()\nmatrix.bottomLeftCorner<r,c>()\nmatrix.bottomRightCorner<r,c>()\n\\endcode</td>\n</tr>\n</table>\n\nNotice that Eigen3 also provides these new convenience methods: topRows(), bottomRows(), leftCols(), rightCols(). See in class DenseBase.\n\n\\section CoefficientWiseOperations Coefficient wise operations\n\nIn Eigen2, coefficient wise operations which have no proper mathematical definition (as a coefficient wise product)\nwere achieved using the .cwise() prefix, e.g.:\n\\code a.cwise() * b \\endcode\nIn Eigen3 this .cwise() prefix has been superseded by a new kind of matrix type called\nArray for which all operations are performed coefficient wise. You can easily view a matrix as an array and vice versa using\nthe MatrixBase::array() and ArrayBase::matrix() functions respectively. Here is an example:\n\\code\nVector4f a, b, c;\nc = a.array() * b.array();\n\\endcode\nNote that the .array() function is not at all a synonym of the deprecated .cwise() prefix.\nWhile the .cwise() prefix changed the behavior of the following operator, the array() function performs\na permanent conversion to the array world. Therefore, for binary operations such as the coefficient wise product,\nboth sides must be converted to an \\em array as in the above example. On the other hand, when you\nconcatenate multiple coefficient wise operations you only have to do the conversion once, e.g.:\n\\code\nVector4f a, b, c;\nc = a.array().abs().pow(3) * b.array().abs().sin();\n\\endcode\nWith Eigen2 you would have written:\n\\code\nc = (a.cwise().abs().cwise().pow(3)).cwise() * (b.cwise().abs().cwise().sin());\n\\endcode\n\n\\section PartAndExtract Triangular and self-adjoint matrices\n\nIn Eigen 2 you had to play with the part, extract, and marked functions to deal with triangular and selfadjoint matrices. In Eigen 3, all these functions have been removed in favor of the concept of \\em views:\n\n<table class=\"manual\">\n<tr><th>Eigen 2</th><th>Eigen 3</th></tr>\n<tr><td>\\code\nA.part<UpperTriangular>();\nA.part<StrictlyLowerTriangular>(); \\endcode</td>\n<td>\\code\nA.triangularView<Upper>()\nA.triangularView<StrictlyLower>()\\endcode</td></tr>\n<tr><td>\\code\nA.extract<UpperTriangular>();\nA.extract<StrictlyLowerTriangular>();\\endcode</td>\n<td>\\code\nA.triangularView<Upper>()\nA.triangularView<StrictlyLower>()\\endcode</td></tr>\n<tr><td>\\code\nA.marked<UpperTriangular>();\nA.marked<StrictlyLowerTriangular>();\\endcode</td>\n<td>\\code\nA.triangularView<Upper>()\nA.triangularView<StrictlyLower>()\\endcode</td></tr>\n<tr><td colspan=\"2\"></td></tr>\n<tr><td>\\code\nA.part<SelfAdfjoint|UpperTriangular>();\nA.extract<SelfAdfjoint|LowerTriangular>();\\endcode</td>\n<td>\\code\nA.selfadjointView<Upper>()\nA.selfadjointView<Lower>()\\endcode</td></tr>\n<tr><td colspan=\"2\"></td></tr>\n<tr><td>\\code\nUpperTriangular\nLowerTriangular\nUnitUpperTriangular\nUnitLowerTriangular\nStrictlyUpperTriangular\nStrictlyLowerTriangular\n\\endcode</td><td>\\code\nUpper\nLower\nUnitUpper\nUnitLower\nStrictlyUpper\nStrictlyLower\n\\endcode</td>\n</tr>\n</table>\n\n\\sa class TriangularView, class SelfAdjointView\n\n\\section TriangularSolveInPlace Triangular in-place solving\n\n<table class=\"manual\">\n<tr><th>Eigen 2</th><th>Eigen 3</th></tr>\n<tr><td>\\code A.triangularSolveInPlace<XxxTriangular>(Y);\\endcode</td><td>\\code A.triangularView<Xxx>().solveInPlace(Y);\\endcode</td></tr>\n</table>\n\n\n\\section Decompositions Matrix decompositions\n\nSome of Eigen 2's matrix decompositions have been renamed in Eigen 3, while some others have been removed and are replaced by other decompositions in Eigen 3.\n\n<table class=\"manual\">\n  <tr>\n    <th>Eigen 2</th>\n    <th>Eigen 3</th>\n    <th>Notes</th>\n  </tr>\n  <tr>\n    <td>LU</td>\n    <td>FullPivLU</td>\n    <td class=\"alt\">See also the new PartialPivLU, it's much faster</td>\n  </tr>\n  <tr>\n    <td>QR</td>\n    <td>HouseholderQR</td>\n    <td class=\"alt\">See also the new ColPivHouseholderQR, it's more reliable</td>\n  </tr>\n  <tr>\n    <td>SVD</td>\n    <td>JacobiSVD</td>\n    <td class=\"alt\">We currently don't have a bidiagonalizing SVD; of course this is planned.</td>\n  </tr>\n  <tr>\n    <td>EigenSolver and friends</td>\n    <td>\\code #include<Eigen/Eigenvalues> \\endcode </td>\n    <td class=\"alt\">Moved to separate module</td>\n  </tr>\n</table>\n\n\\section LinearSolvers Linear solvers\n\n<table class=\"manual\">\n<tr><th>Eigen 2</th><th>Eigen 3</th><th>Notes</th></tr>\n<tr><td>\\code A.lu();\\endcode</td>\n<td>\\code A.fullPivLu();\\endcode</td>\n<td class=\"alt\">Now A.lu() returns a PartialPivLU</td></tr>\n<tr><td>\\code A.lu().solve(B,&X);\\endcode</td>\n<td>\\code X = A.lu().solve(B);\n X = A.fullPivLu().solve(B);\\endcode</td>\n<td class=\"alt\">The returned by value is fully optimized</td></tr>\n<tr><td>\\code A.llt().solve(B,&X);\\endcode</td>\n<td>\\code X = A.llt().solve(B);\n X = A.selfadjointView<Lower>.llt().solve(B);\n X = A.selfadjointView<Upper>.llt().solve(B);\\endcode</td>\n<td class=\"alt\">The returned by value is fully optimized and \\n\nthe selfadjointView API allows you to select the \\n\ntriangular part to work on (default is lower part)</td></tr>\n<tr><td>\\code A.llt().solveInPlace(B);\\endcode</td>\n<td>\\code B = A.llt().solve(B);\n B = A.selfadjointView<Lower>.llt().solve(B);\n B = A.selfadjointView<Upper>.llt().solve(B);\\endcode</td>\n<td class=\"alt\">In place solving</td></tr>\n<tr><td>\\code A.ldlt().solve(B,&X);\\endcode</td>\n<td>\\code X = A.ldlt().solve(B);\n X = A.selfadjointView<Lower>.ldlt().solve(B);\n X = A.selfadjointView<Upper>.ldlt().solve(B);\\endcode</td>\n<td class=\"alt\">The returned by value is fully optimized and \\n\nthe selfadjointView API allows you to select the \\n\ntriangular part to work on</td></tr>\n</table>\n\n\\section GeometryModule Changes in the Geometry module\n\nThe Geometry module is the one that changed the most. If you rely heavily on it, it's probably a good idea to use the <a href=\"http://eigen.tuxfamily.org/dox-3.2/Eigen2SupportModes.html\">\"Eigen 2 support modes\"</a> to perform your migration.\n\n\\section Transform The Transform class\n\nIn Eigen 2, the Transform class didn't really know whether it was a projective or affine transformation. In Eigen 3, it takes a new \\a Mode template parameter, which indicates whether it's \\a Projective or \\a Affine transform. There is no default value.\n\nThe Transform3f (etc) typedefs are no more. In Eigen 3, the Transform typedefs explicitly refer to the \\a Projective and \\a Affine modes:\n\n<table class=\"manual\">\n<tr><th>Eigen 2</th><th>Eigen 3</th><th>Notes</th></tr>\n<tr>\n  <td> Transform3f </td>\n  <td> Affine3f or Projective3f </td>\n  <td> Of course 3f is just an example here </td>\n</tr>\n</table>\n\n\n\\section LazyVsNoalias Lazy evaluation and noalias\n\nIn Eigen all operations are performed in a lazy fashion except the matrix products which are always evaluated into a temporary by default.\nIn Eigen2, lazy evaluation could be enforced by tagging a product using the .lazy() function. However, in complex expressions it was not\neasy to determine where to put the lazy() function. In Eigen3, the lazy() feature has been superseded by the MatrixBase::noalias() function\nwhich can be used on the left hand side of an assignment when no aliasing can occur. Here is an example:\n\\code\nMatrixXf a, b, c;\n...\nc.noalias() += 2 * a.transpose() * b;\n\\endcode\nHowever, the noalias mechanism does not cover all the features of the old .lazy(). Indeed, in some extremely rare cases,\nit might be useful to explicit request for a lay product, i.e., for a product which will be evaluated one coefficient at once, on request,\njust like any other expressions. To this end you can use the MatrixBase::lazyProduct() function, however we strongly discourage you to\nuse it unless you are sure of what you are doing, i.e., you have rigourosly measured a speed improvement.\n\n\\section AlignMacros Alignment-related macros\n\nThe EIGEN_ALIGN_128 macro has been renamed to EIGEN_ALIGN16. Don't be surprised, it's just that we switched to counting in bytes ;-)\n\nThe \\link TopicPreprocessorDirectivesPerformance EIGEN_DONT_ALIGN \\endlink option still exists in Eigen 3, but it has a new cousin: \\link TopicPreprocessorDirectivesPerformance  EIGEN_DONT_ALIGN_STATICALLY.\\endlink It allows to get rid of all static alignment issues while keeping alignment of dynamic-size heap-allocated arrays. Vectorization of statically allocated arrays is still preserved (unless you define \\link TopicPreprocessorDirectivesPerformance EIGEN_UNALIGNED_VECTORIZE \\endlink =0), at the cost of unaligned memory stores.\n\n\\section AlignedMap Aligned Map objects\n\nA common issue with Eigen 2 was that when mapping an array with Map, there was no way to tell Eigen that your array was aligned. There was a ForceAligned option but it didn't mean that; it was just confusing and has been removed.\n\nNew in Eigen3 is the #Aligned option. See the documentation of class Map. Use it like this:\n\\code\nMap<Vector4f, Aligned> myMappedVector(some_aligned_array);\n\\endcode\nThere also are related convenience static methods, which actually are the preferred way as they take care of such things as constness:\n\\code\nresult = Vector4f::MapAligned(some_aligned_array);\n\\endcode\n\n\\section StdContainers STL Containers\n\nIn Eigen2, <tt>\\#include\\<Eigen/StdVector\\></tt> tweaked std::vector to automatically align elements. The problem was that that was quite invasive. In Eigen3, we only override standard behavior if you use Eigen::aligned_allocator<T> as your allocator type. So for example, if you use std::vector<Matrix4f>, you need to do the following change (note that aligned_allocator is under namespace Eigen):\n\n<table class=\"manual\">\n<tr><th>Eigen 2</th><th>Eigen 3</th></tr>\n<tr>\n  <td> \\code std::vector<Matrix4f> \\endcode </td>\n  <td> \\code std::vector<Matrix4f, aligned_allocator<Matrix4f> > \\endcode </td>\n</tr>\n</table>\n\n\\section eiPrefix Internal ei_ prefix\n\nIn Eigen2, global internal functions and structures were prefixed by \\c ei_. In Eigen3, they all have been moved into the more explicit \\c internal namespace. So, e.g., \\c ei_sqrt(x) now becomes \\c internal::sqrt(x). Of course it is not recommended to rely on Eigen's internal features.\n\n\n\n*/\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/AsciiQuickReference.txt",
    "content": "// A simple quickref for Eigen. Add anything that's missing.\n// Main author: Keir Mierle\n\n#include <Eigen/Dense>\n\nMatrix<double, 3, 3> A;               // Fixed rows and cols. Same as Matrix3d.\nMatrix<double, 3, Dynamic> B;         // Fixed rows, dynamic cols.\nMatrix<double, Dynamic, Dynamic> C;   // Full dynamic. Same as MatrixXd.\nMatrix<double, 3, 3, RowMajor> E;     // Row major; default is column-major.\nMatrix3f P, Q, R;                     // 3x3 float matrix.\nVector3f x, y, z;                     // 3x1 float matrix.\nRowVector3f a, b, c;                  // 1x3 float matrix.\nVectorXd v;                           // Dynamic column vector of doubles\ndouble s;                            \n\n// Basic usage\n// Eigen          // Matlab           // comments\nx.size()          // length(x)        // vector size\nC.rows()          // size(C,1)        // number of rows\nC.cols()          // size(C,2)        // number of columns\nx(i)              // x(i+1)           // Matlab is 1-based\nC(i,j)            // C(i+1,j+1)       //\n\nA.resize(4, 4);   // Runtime error if assertions are on.\nB.resize(4, 9);   // Runtime error if assertions are on.\nA.resize(3, 3);   // Ok; size didn't change.\nB.resize(3, 9);   // Ok; only dynamic cols changed.\n                  \nA << 1, 2, 3,     // Initialize A. The elements can also be\n     4, 5, 6,     // matrices, which are stacked along cols\n     7, 8, 9;     // and then the rows are stacked.\nB << A, A, A;     // B is three horizontally stacked A's.\nA.fill(10);       // Fill A with all 10's.\n\n// Eigen                                    // Matlab\nMatrixXd::Identity(rows,cols)               // eye(rows,cols)\nC.setIdentity(rows,cols)                    // C = eye(rows,cols)\nMatrixXd::Zero(rows,cols)                   // zeros(rows,cols)\nC.setZero(rows,cols)                        // C = zeros(rows,cols)\nMatrixXd::Ones(rows,cols)                   // ones(rows,cols)\nC.setOnes(rows,cols)                        // C = ones(rows,cols)\nMatrixXd::Random(rows,cols)                 // rand(rows,cols)*2-1            // MatrixXd::Random returns uniform random numbers in (-1, 1).\nC.setRandom(rows,cols)                      // C = rand(rows,cols)*2-1\nVectorXd::LinSpaced(size,low,high)          // linspace(low,high,size)'\nv.setLinSpaced(size,low,high)               // v = linspace(low,high,size)'\nVectorXi::LinSpaced(((hi-low)/step)+1,      // low:step:hi\n                    low,low+step*(size-1))  //\n\n\n// Matrix slicing and blocks. All expressions listed here are read/write.\n// Templated size versions are faster. Note that Matlab is 1-based (a size N\n// vector is x(1)...x(N)).\n// Eigen                           // Matlab\nx.head(n)                          // x(1:n)\nx.head<n>()                        // x(1:n)\nx.tail(n)                          // x(end - n + 1: end)\nx.tail<n>()                        // x(end - n + 1: end)\nx.segment(i, n)                    // x(i+1 : i+n)\nx.segment<n>(i)                    // x(i+1 : i+n)\nP.block(i, j, rows, cols)          // P(i+1 : i+rows, j+1 : j+cols)\nP.block<rows, cols>(i, j)          // P(i+1 : i+rows, j+1 : j+cols)\nP.row(i)                           // P(i+1, :)\nP.col(j)                           // P(:, j+1)\nP.leftCols<cols>()                 // P(:, 1:cols)\nP.leftCols(cols)                   // P(:, 1:cols)\nP.middleCols<cols>(j)              // P(:, j+1:j+cols)\nP.middleCols(j, cols)              // P(:, j+1:j+cols)\nP.rightCols<cols>()                // P(:, end-cols+1:end)\nP.rightCols(cols)                  // P(:, end-cols+1:end)\nP.topRows<rows>()                  // P(1:rows, :)\nP.topRows(rows)                    // P(1:rows, :)\nP.middleRows<rows>(i)              // P(i+1:i+rows, :)\nP.middleRows(i, rows)              // P(i+1:i+rows, :)\nP.bottomRows<rows>()               // P(end-rows+1:end, :)\nP.bottomRows(rows)                 // P(end-rows+1:end, :)\nP.topLeftCorner(rows, cols)        // P(1:rows, 1:cols)\nP.topRightCorner(rows, cols)       // P(1:rows, end-cols+1:end)\nP.bottomLeftCorner(rows, cols)     // P(end-rows+1:end, 1:cols)\nP.bottomRightCorner(rows, cols)    // P(end-rows+1:end, end-cols+1:end)\nP.topLeftCorner<rows,cols>()       // P(1:rows, 1:cols)\nP.topRightCorner<rows,cols>()      // P(1:rows, end-cols+1:end)\nP.bottomLeftCorner<rows,cols>()    // P(end-rows+1:end, 1:cols)\nP.bottomRightCorner<rows,cols>()   // P(end-rows+1:end, end-cols+1:end)\n\n// Of particular note is Eigen's swap function which is highly optimized.\n// Eigen                           // Matlab\nR.row(i) = P.col(j);               // R(i, :) = P(:, j)\nR.col(j1).swap(mat1.col(j2));      // R(:, [j1 j2]) = R(:, [j2, j1])\n\n// Views, transpose, etc;\n// Eigen                           // Matlab\nR.adjoint()                        // R'\nR.transpose()                      // R.' or conj(R')       // Read-write\nR.diagonal()                       // diag(R)               // Read-write\nx.asDiagonal()                     // diag(x)\nR.transpose().colwise().reverse()  // rot90(R)              // Read-write\nR.rowwise().reverse()              // fliplr(R)\nR.colwise().reverse()              // flipud(R)\nR.replicate(i,j)                   // repmat(P,i,j)\n\n\n// All the same as Matlab, but matlab doesn't have *= style operators.\n// Matrix-vector.  Matrix-matrix.   Matrix-scalar.\ny  = M*x;          R  = P*Q;        R  = P*s;\na  = b*M;          R  = P - Q;      R  = s*P;\na *= M;            R  = P + Q;      R  = P/s;\n                   R *= Q;          R  = s*P;\n                   R += Q;          R *= s;\n                   R -= Q;          R /= s;\n\n// Vectorized operations on each element independently\n// Eigen                       // Matlab\nR = P.cwiseProduct(Q);         // R = P .* Q\nR = P.array() * s.array();     // R = P .* s\nR = P.cwiseQuotient(Q);        // R = P ./ Q\nR = P.array() / Q.array();     // R = P ./ Q\nR = P.array() + s.array();     // R = P + s\nR = P.array() - s.array();     // R = P - s\nR.array() += s;                // R = R + s\nR.array() -= s;                // R = R - s\nR.array() < Q.array();         // R < Q\nR.array() <= Q.array();        // R <= Q\nR.cwiseInverse();              // 1 ./ P\nR.array().inverse();           // 1 ./ P\nR.array().sin()                // sin(P)\nR.array().cos()                // cos(P)\nR.array().pow(s)               // P .^ s\nR.array().square()             // P .^ 2\nR.array().cube()               // P .^ 3\nR.cwiseSqrt()                  // sqrt(P)\nR.array().sqrt()               // sqrt(P)\nR.array().exp()                // exp(P)\nR.array().log()                // log(P)\nR.cwiseMax(P)                  // max(R, P)\nR.array().max(P.array())       // max(R, P)\nR.cwiseMin(P)                  // min(R, P)\nR.array().min(P.array())       // min(R, P)\nR.cwiseAbs()                   // abs(P)\nR.array().abs()                // abs(P)\nR.cwiseAbs2()                  // abs(P.^2)\nR.array().abs2()               // abs(P.^2)\n(R.array() < s).select(P,Q );  // (R < s ? P : Q)\nR = (Q.array()==0).select(P,R) // R(Q==0) = P(Q==0)\nR = P.unaryExpr(ptr_fun(func)) // R = arrayfun(func, P)   // with: scalar func(const scalar &x);\n\n\n// Reductions.\nint r, c;\n// Eigen                  // Matlab\nR.minCoeff()              // min(R(:))\nR.maxCoeff()              // max(R(:))\ns = R.minCoeff(&r, &c)    // [s, i] = min(R(:)); [r, c] = ind2sub(size(R), i);\ns = R.maxCoeff(&r, &c)    // [s, i] = max(R(:)); [r, c] = ind2sub(size(R), i);\nR.sum()                   // sum(R(:))\nR.colwise().sum()         // sum(R)\nR.rowwise().sum()         // sum(R, 2) or sum(R')'\nR.prod()                  // prod(R(:))\nR.colwise().prod()        // prod(R)\nR.rowwise().prod()        // prod(R, 2) or prod(R')'\nR.trace()                 // trace(R)\nR.all()                   // all(R(:))\nR.colwise().all()         // all(R)\nR.rowwise().all()         // all(R, 2)\nR.any()                   // any(R(:))\nR.colwise().any()         // any(R)\nR.rowwise().any()         // any(R, 2)\n\n// Dot products, norms, etc.\n// Eigen                  // Matlab\nx.norm()                  // norm(x).    Note that norm(R) doesn't work in Eigen.\nx.squaredNorm()           // dot(x, x)   Note the equivalence is not true for complex\nx.dot(y)                  // dot(x, y)\nx.cross(y)                // cross(x, y) Requires #include <Eigen/Geometry>\n\n//// Type conversion\n// Eigen                  // Matlab\nA.cast<double>();         // double(A)\nA.cast<float>();          // single(A)\nA.cast<int>();            // int32(A)\nA.real();                 // real(A)\nA.imag();                 // imag(A)\n// if the original type equals destination type, no work is done\n\n// Note that for most operations Eigen requires all operands to have the same type:\nMatrixXf F = MatrixXf::Zero(3,3);\nA += F;                // illegal in Eigen. In Matlab A = A+F is allowed\nA += F.cast<double>(); // F converted to double and then added (generally, conversion happens on-the-fly)\n\n// Eigen can map existing memory into Eigen matrices.\nfloat array[3];\nVector3f::Map(array).fill(10);            // create a temporary Map over array and sets entries to 10\nint data[4] = {1, 2, 3, 4};\nMatrix2i mat2x2(data);                    // copies data into mat2x2\nMatrix2i::Map(data) = 2*mat2x2;           // overwrite elements of data with 2*mat2x2\nMatrixXi::Map(data, 2, 2) += mat2x2;      // adds mat2x2 to elements of data (alternative syntax if size is not know at compile time)\n\n// Solve Ax = b. Result stored in x. Matlab: x = A \\ b.\nx = A.ldlt().solve(b));  // A sym. p.s.d.    #include <Eigen/Cholesky>\nx = A.llt() .solve(b));  // A sym. p.d.      #include <Eigen/Cholesky>\nx = A.lu()  .solve(b));  // Stable and fast. #include <Eigen/LU>\nx = A.qr()  .solve(b));  // No pivoting.     #include <Eigen/QR>\nx = A.svd() .solve(b));  // Stable, slowest. #include <Eigen/SVD>\n// .ldlt() -> .matrixL() and .matrixD()\n// .llt()  -> .matrixL()\n// .lu()   -> .matrixL() and .matrixU()\n// .qr()   -> .matrixQ() and .matrixR()\n// .svd()  -> .matrixU(), .singularValues(), and .matrixV()\n\n// Eigenvalue problems\n// Eigen                          // Matlab\nA.eigenvalues();                  // eig(A);\nEigenSolver<Matrix3d> eig(A);     // [vec val] = eig(A)\neig.eigenvalues();                // diag(val)\neig.eigenvectors();               // vec\n// For self-adjoint matrices use SelfAdjointEigenSolver<>\n"
  },
  {
    "path": "include/eigen3/doc/B01_Experimental.dox",
    "content": "namespace Eigen {\n\n/** \\page Experimental Experimental parts of Eigen\n\n\\eigenAutoToc\n\n\\section Experimental_summary Summary\n\nWith the 2.0 release, Eigen's API is, to a large extent, stable. However, we wish to retain the freedom to make API incompatible changes. To that effect, we call many parts of Eigen \"experimental\" which means that they are not subject to API stability guarantee.\n\nOur goal is that for the 2.1 release (expected in July 2009) most of these parts become API-stable too.\n\nWe are aware that API stability is a major concern for our users. That's why it's a priority for us to reach it, but at the same time we're being serious about not calling Eigen API-stable too early.\n\nExperimental features may at any time:\n\\li be removed;\n\\li be subject to an API incompatible change;\n\\li introduce API or ABI incompatible changes in your own code if you let them affect your API or ABI.\n\n\\section Experimental_modules Experimental modules\n\nThe following modules are considered entirely experimental, and we make no firm API stability guarantee about them for the time being:\n\\li SVD\n\\li QR\n\\li Cholesky\n\\li Sparse\n\\li Geometry (this one should be mostly stable, but it's a little too early to make a formal guarantee)\n\n\\section Experimental_core Experimental parts of the Core module\n\nIn the Core module, the only classes subject to ABI stability guarantee (meaning that you can use it for data members in your public ABI) is:\n\\li Matrix\n\\li Map\n\nAll other classes offer no ABI guarantee, e.g. the layout of their data can be changed.\n\nThe only classes subject to (even partial) API stability guarantee (meaning that you can safely construct and use objects) are:\n\\li MatrixBase : partial API stability (see below)\n\\li Matrix : full API stability (except for experimental stuff inherited from MatrixBase)\n\\li Map : full API stability (except for experimental stuff inherited from MatrixBase)\n\nAll other classes offer no direct API guarantee, e.g. their methods can be changed; however notice that most classes inherit MatrixBase and that this is where most of their API comes from -- so in practice most of the API is stable.\n\nA few MatrixBase methods are considered experimental, hence not part of any API stability guarantee:\n\\li all methods documented as internal\n\\li all methods hidden in the Doxygen documentation\n\\li all methods marked as experimental\n\\li all methods defined in experimental modules\n\n*/\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/CMakeLists.txt",
    "content": "project(EigenDoc)\n\nset_directory_properties(PROPERTIES EXCLUDE_FROM_ALL TRUE)\n\nproject(EigenDoc)\n\nif(CMAKE_COMPILER_IS_GNUCXX)\n  if(CMAKE_SYSTEM_NAME MATCHES Linux)\n    set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} -O1 -g1\")\n  endif(CMAKE_SYSTEM_NAME MATCHES Linux)\nendif(CMAKE_COMPILER_IS_GNUCXX)\n\noption(EIGEN_INTERNAL_DOCUMENTATION \"Build internal documentation\" OFF)\n\n\n# Set some Doxygen flags\nset(EIGEN_DOXY_PROJECT_NAME             \"Eigen\")\nset(EIGEN_DOXY_OUTPUT_DIRECTORY_SUFFIX  \"\")\nset(EIGEN_DOXY_INPUT                    \"\\\"${Eigen_SOURCE_DIR}/Eigen\\\" \\\"${Eigen_SOURCE_DIR}/doc\\\"\")\nset(EIGEN_DOXY_HTML_COLORSTYLE_HUE      \"220\")\nset(EIGEN_DOXY_TAGFILES                 \"\")\nif(EIGEN_INTERNAL_DOCUMENTATION)\n  set(EIGEN_DOXY_INTERNAL                 \"YES\")\nelse(EIGEN_INTERNAL_DOCUMENTATION)\n  set(EIGEN_DOXY_INTERNAL                 \"NO\")\nendif(EIGEN_INTERNAL_DOCUMENTATION)\n\nconfigure_file(\n  ${CMAKE_CURRENT_SOURCE_DIR}/Doxyfile.in\n  ${CMAKE_CURRENT_BINARY_DIR}/Doxyfile\n)\n\nset(EIGEN_DOXY_PROJECT_NAME             \"Eigen-unsupported\")\nset(EIGEN_DOXY_OUTPUT_DIRECTORY_SUFFIX  \"/unsupported\")\nset(EIGEN_DOXY_INPUT                    \"\\\"${Eigen_SOURCE_DIR}/unsupported/Eigen\\\" \\\"${Eigen_SOURCE_DIR}/unsupported/doc\\\"\")\nset(EIGEN_DOXY_HTML_COLORSTYLE_HUE      \"0\")\n# set(EIGEN_DOXY_TAGFILES                 \"\\\"${Eigen_BINARY_DIR}/doc/eigen.doxytags =../\\\"\")\nset(EIGEN_DOXY_TAGFILES                 \"\")\n\nconfigure_file(\n  ${CMAKE_CURRENT_SOURCE_DIR}/Doxyfile.in\n  ${CMAKE_CURRENT_BINARY_DIR}/Doxyfile-unsupported\n)\n\nconfigure_file(\n  ${CMAKE_CURRENT_SOURCE_DIR}/eigendoxy_header.html.in\n  ${CMAKE_CURRENT_BINARY_DIR}/eigendoxy_header.html\n)\n\nconfigure_file(\n  ${CMAKE_CURRENT_SOURCE_DIR}/eigendoxy_footer.html.in\n  ${CMAKE_CURRENT_BINARY_DIR}/eigendoxy_footer.html\n)\n\nconfigure_file(\n  ${CMAKE_CURRENT_SOURCE_DIR}/eigendoxy_layout.xml.in\n  ${CMAKE_CURRENT_BINARY_DIR}/eigendoxy_layout.xml\n)\n\nconfigure_file(\n  ${Eigen_SOURCE_DIR}/unsupported/doc/eigendoxy_layout.xml.in\n  ${Eigen_BINARY_DIR}/doc/unsupported/eigendoxy_layout.xml\n)\n\nset(examples_targets \"\")\nset(snippets_targets \"\")\n\nadd_definitions(\"-DEIGEN_MAKING_DOCS\")\nadd_custom_target(all_examples)\n\nadd_subdirectory(examples)\nadd_subdirectory(special_examples)\nadd_subdirectory(snippets)\n\nadd_custom_target(\n  doc-eigen-prerequisites\n  ALL\n  COMMAND ${CMAKE_COMMAND} -E make_directory ${CMAKE_CURRENT_BINARY_DIR}/html/\n  COMMAND ${CMAKE_COMMAND} -E copy ${CMAKE_CURRENT_SOURCE_DIR}/eigen_navtree_hacks.js           ${CMAKE_CURRENT_BINARY_DIR}/html/\n  COMMAND ${CMAKE_COMMAND} -E copy ${CMAKE_CURRENT_SOURCE_DIR}/Eigen_Silly_Professor_64x64.png  ${CMAKE_CURRENT_BINARY_DIR}/html/\n  COMMAND ${CMAKE_COMMAND} -E copy ${CMAKE_CURRENT_SOURCE_DIR}/ftv2pnode.png                    ${CMAKE_CURRENT_BINARY_DIR}/html/\n  COMMAND ${CMAKE_COMMAND} -E copy ${CMAKE_CURRENT_SOURCE_DIR}/ftv2node.png                     ${CMAKE_CURRENT_BINARY_DIR}/html/\n  COMMAND ${CMAKE_COMMAND} -E copy ${CMAKE_CURRENT_SOURCE_DIR}/AsciiQuickReference.txt          ${CMAKE_CURRENT_BINARY_DIR}/html/\n  WORKING_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}\n)\n\nadd_custom_target(\n  doc-unsupported-prerequisites\n  ALL\n  COMMAND ${CMAKE_COMMAND} -E make_directory ${Eigen_BINARY_DIR}/doc/html/unsupported\n  COMMAND ${CMAKE_COMMAND} -E copy ${CMAKE_CURRENT_SOURCE_DIR}/eigen_navtree_hacks.js           ${CMAKE_CURRENT_BINARY_DIR}/html/unsupported/\n  COMMAND ${CMAKE_COMMAND} -E copy ${CMAKE_CURRENT_SOURCE_DIR}/Eigen_Silly_Professor_64x64.png  ${CMAKE_CURRENT_BINARY_DIR}/html/unsupported/\n  COMMAND ${CMAKE_COMMAND} -E copy ${CMAKE_CURRENT_SOURCE_DIR}/ftv2pnode.png                    ${CMAKE_CURRENT_BINARY_DIR}/html/unsupported/\n  COMMAND ${CMAKE_COMMAND} -E copy ${CMAKE_CURRENT_SOURCE_DIR}/ftv2node.png                     ${CMAKE_CURRENT_BINARY_DIR}/html/unsupported/\n  WORKING_DIRECTORY ${Eigen_BINARY_DIR}/doc\n)\n\nadd_dependencies(doc-eigen-prerequisites all_snippets all_examples)\nadd_dependencies(doc-unsupported-prerequisites unsupported_snippets unsupported_examples)\n\nadd_custom_target(doc ALL\n  COMMAND doxygen\n  COMMAND doxygen Doxyfile-unsupported\n  COMMAND ${CMAKE_COMMAND} -E copy ${Eigen_BINARY_DIR}/doc/html/group__TopicUnalignedArrayAssert.html ${Eigen_BINARY_DIR}/doc/html/TopicUnalignedArrayAssert.html\n  COMMAND ${CMAKE_COMMAND} -E rename html eigen-doc\n  COMMAND ${CMAKE_COMMAND} -E remove eigen-doc/eigen-doc.tgz\n  COMMAND ${CMAKE_COMMAND} -E tar cfz eigen-doc.tgz eigen-doc\n  COMMAND ${CMAKE_COMMAND} -E rename eigen-doc.tgz eigen-doc/eigen-doc.tgz\n  COMMAND ${CMAKE_COMMAND} -E rename eigen-doc html\n  WORKING_DIRECTORY ${Eigen_BINARY_DIR}/doc)\n\nadd_dependencies(doc doc-eigen-prerequisites doc-unsupported-prerequisites)\n"
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  {
    "path": "include/eigen3/doc/ClassHierarchy.dox",
    "content": "namespace Eigen {\n\n/** \\page TopicClassHierarchy The class hierarchy\n\nThis page explains the design of the core classes in Eigen's class hierarchy and how they fit together. Casual\nusers probably need not concern themselves with these details, but it may be useful for both advanced users\nand Eigen developers.\n\n\\eigenAutoToc\n\n\n\\section TopicClassHierarchyPrinciples Principles\n\nEigen's class hierarchy is designed so that virtual functions are avoided where their overhead would\nsignificantly impair performance. Instead, Eigen achieves polymorphism with the Curiously Recurring Template\nPattern (CRTP). In this pattern, the base class (for instance, \\c MatrixBase) is in fact a template class, and\nthe derived class (for instance, \\c Matrix) inherits the base class with the derived class itself as a\ntemplate argument (in this case, \\c Matrix inherits from \\c MatrixBase&lt;Matrix&gt;). This allows Eigen to\nresolve the polymorphic function calls at compile time.\n\nIn addition, the design avoids multiple inheritance. One reason for this is that in our experience, some\ncompilers (like MSVC) fail to perform empty base class optimization, which is crucial for our fixed-size\ntypes.\n\n\n\\section TopicClassHierarchyCoreClasses The core classes\n\nThese are the classes that you need to know about if you want to write functions that accept or return Eigen\nobjects.\n\n  - Matrix means plain dense matrix. If \\c m is a \\c %Matrix, then, for instance, \\c m+m is no longer a \n    \\c %Matrix, it is a \"matrix expression\".\n  - MatrixBase means dense matrix expression. This means that a \\c %MatrixBase is something that can be\n    added, matrix-multiplied, LU-decomposed, QR-decomposed... All matrix expression classes, including \n    \\c %Matrix itself, inherit \\c %MatrixBase.\n  - Array means plain dense array. If \\c x is an \\c %Array, then, for instance, \\c x+x is no longer an \n    \\c %Array, it is an \"array expression\".\n  - ArrayBase means dense array expression. This means that an \\c %ArrayBase is something that can be\n    added, array-multiplied, and on which you can perform all sorts of array operations... All array\n    expression classes, including \\c %Array itself, inherit \\c %ArrayBase.\n  - DenseBase means dense (matrix or array) expression. Both \\c %ArrayBase and \\c %MatrixBase inherit\n    \\c %DenseBase. \\c %DenseBase is where all the methods go that apply to dense expressions regardless of\n    whether they are matrix or array expressions. For example, the \\link DenseBase::block() block(...) \\endlink\n    methods are in \\c %DenseBase.\n\n\\section TopicClassHierarchyBaseClasses Base classes\n\nThese classes serve as base classes for the five core classes mentioned above. They are more internal and so\nless interesting for users of the Eigen library.\n\n  - PlainObjectBase means dense (matrix or array) plain object, i.e. something that stores its own dense\n    array of coefficients. This is where, for instance, the \\link PlainObjectBase::resize() resize() \\endlink\n    methods go. \\c %PlainObjectBase is inherited by \\c %Matrix and by \\c %Array. But above, we said that \n    \\c %Matrix inherits \\c %MatrixBase and \\c %Array inherits \\c %ArrayBase. So does that mean multiple\n    inheritance? No, because \\c %PlainObjectBase \\e itself inherits \\c %MatrixBase or \\c %ArrayBase depending\n    on whether we are in the matrix or array case. When we said above that \\c %Matrix inherited \n    \\c %MatrixBase, we omitted to say it does so indirectly via \\c %PlainObjectBase. Same for \\c %Array.\n  - DenseCoeffsBase means something that has dense coefficient accessors. It is a base class for\n    \\c %DenseBase. The reason for \\c %DenseCoeffsBase to exist is that the set of available coefficient\n    accessors is very different depending on whether a dense expression has direct memory access or not (the\n    \\c DirectAccessBit flag). For example, if \\c x is a plain matrix, then \\c x has direct access, and \n    \\c x.transpose() and \\c x.block(...) also have direct access, because their coefficients can be read right\n    off memory, but for example, \\c x+x does not have direct memory access, because obtaining any of its\n    coefficients requires a computation (an addition), it can't be just read off memory.\n  - EigenBase means anything that can be evaluated into a plain dense matrix or array (even if that would\n    be a bad idea). \\c %EigenBase is really the absolute base class for anything that remotely looks like a\n    matrix or array. It is a base class for \\c %DenseCoeffsBase, so it sits below all our dense class\n    hierarchy, but it is not limited to dense expressions. For example, \\c %EigenBase is also inherited by\n    diagonal matrices, sparse matrices, etc...\n\n\n\\section TopicClassHierarchyInheritanceDiagrams Inheritance diagrams\n\nThe inheritance diagram for Matrix looks as follows:\n\n<pre>\nEigenBase&lt;%Matrix&gt;\n  <-- DenseCoeffsBase&lt;%Matrix&gt;    (direct access case)\n    <-- DenseBase&lt;%Matrix&gt;\n      <-- MatrixBase&lt;%Matrix&gt;\n        <-- PlainObjectBase&lt;%Matrix&gt;    (matrix case)\n          <-- Matrix\n</pre>\n\nThe inheritance diagram for Array looks as follows:\n\n<pre>\nEigenBase&lt;%Array&gt;\n  <-- DenseCoeffsBase&lt;%Array&gt;    (direct access case)\n    <-- DenseBase&lt;%Array&gt;\n      <-- ArrayBase&lt;%Array&gt;\n        <-- PlainObjectBase&lt;%Array&gt;    (array case)\n          <-- Array\n</pre>\n\nThe inheritance diagram for some other matrix expression class, here denoted by \\c SomeMatrixXpr, looks as\nfollows:\n\n<pre>\nEigenBase&lt;SomeMatrixXpr&gt;\n  <-- DenseCoeffsBase&lt;SomeMatrixXpr&gt;    (direct access or no direct access case)\n    <-- DenseBase&lt;SomeMatrixXpr&gt;\n      <-- MatrixBase&lt;SomeMatrixXpr&gt;\n        <-- SomeMatrixXpr\n</pre>\n\nThe inheritance diagram for some other array expression class, here denoted by \\c SomeArrayXpr, looks as\nfollows:\n\n<pre>\nEigenBase&lt;SomeArrayXpr&gt;\n  <-- DenseCoeffsBase&lt;SomeArrayXpr&gt;    (direct access or no direct access case)\n    <-- DenseBase&lt;SomeArrayXpr&gt;\n      <-- ArrayBase&lt;SomeArrayXpr&gt;\n        <-- SomeArrayXpr\n</pre>\n\nFinally, consider an example of something that is not a dense expression, for instance a diagonal matrix. The\ncorresponding inheritance diagram is:\n\n<pre>\nEigenBase&lt;%DiagonalMatrix&gt;\n  <-- DiagonalBase&lt;%DiagonalMatrix&gt;\n    <-- DiagonalMatrix\n</pre>\n\n\n*/\n}\n"
  },
  {
    "path": "include/eigen3/doc/CoeffwiseMathFunctionsTable.dox",
    "content": "namespace Eigen {\n\n/** \\eigenManualPage CoeffwiseMathFunctions Catalog of coefficient-wise math functions\n\n\n<!-- <span style=\"font-size:300%; color:red; font-weight: 900;\">!WORK IN PROGRESS!</span> -->\n\nThis table presents a catalog of the coefficient-wise math functions supported by %Eigen.\nIn this table, \\c a, \\c b, refer to Array objects or expressions, and \\c m refers to a linear algebra Matrix/Vector object. Standard scalar types are abbreviated as follows:\n  - \\c int: \\c i32\n  - \\c float: \\c f\n  - \\c double: \\c d\n  - \\c std::complex<float>: \\c cf\n  - \\c std::complex<double>: \\c cd\n\nFor each row, the first column list the equivalent calls for arrays, and matrices when supported. Of course, all functions are available for matrices by first casting it as an array: \\c m.array().\n\nThe third column gives some hints in the underlying scalar implementation. In most cases, %Eigen does not implement itself the math function but relies on the STL for standard scalar types, or user-provided functions for custom scalar types.\nFor instance, some simply calls the respective function of the STL while preserving <a href=\"http://en.cppreference.com/w/cpp/language/adl\">argument-dependent lookup</a> for custom types.\nThe following:\n\\code\nusing std::foo;\nfoo(a[i]);\n\\endcode\nmeans that the STL's function \\c std::foo will be potentially called if it is compatible with the underlying scalar type. If not, then the user must ensure that an overload of the function foo is available for the given scalar type (usually defined in the same namespace as the given scalar type).\nThis also means that, unless specified, if the function \\c std::foo is available only in some recent c++ versions (e.g., c++11), then the respective %Eigen's function/method will be usable on standard types only if the compiler support the required c++ version.\n\n<table class=\"manual-hl\">\n<tr>\n<th>API</th><th>Description</th><th>Default scalar implementation</th><th>SIMD</th>\n</tr>\n<tr><td colspan=\"4\"></td></tr>\n<tr><th colspan=\"4\">Basic operations</th></tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_abs\n  a.\\link ArrayBase::abs abs\\endlink(); \\n\n  \\link Eigen::abs abs\\endlink(a); \\n\n  m.\\link MatrixBase::cwiseAbs cwiseAbs\\endlink();\n  </td>\n  <td>absolute value (\\f$ |a_i| \\f$) </td>\n  <td class=\"code\">\n  using <a href=\"http://en.cppreference.com/w/cpp/numeric/math/fabs\">std::abs</a>; \\n\n  abs(a[i]);\n  </td>\n  <td>SSE2, AVX (i32,f,d)</td>\n</tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_inverse\n  a.\\link ArrayBase::inverse inverse\\endlink(); \\n\n  \\link Eigen::inverse inverse\\endlink(a); \\n\n  m.\\link MatrixBase::cwiseInverse cwiseInverse\\endlink();\n  </td>\n  <td>inverse value (\\f$ 1/a_i \\f$) </td>\n  <td class=\"code\">\n  1/a[i];\n  </td>\n  <td>All engines (f,d,fc,fd)</td>\n</tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_conj\n  a.\\link ArrayBase::conjugate conjugate\\endlink(); \\n\n  \\link Eigen::conj conj\\endlink(a); \\n\n  m.\\link MatrixBase::conjugate conjugate();\n  </td>\n  <td><a href=\"https://en.wikipedia.org/wiki/Complex_conjugate\">complex conjugate</a> (\\f$ \\bar{a_i} \\f$),\\n\n  no-op for real </td>\n  <td class=\"code\">\n  using <a href=\"http://en.cppreference.com/w/cpp/numeric/complex/conj\">std::conj</a>; \\n\n  conj(a[i]);\n  </td>\n  <td>All engines (fc,fd)</td>\n</tr>\n<tr>\n<th colspan=\"4\">Exponential functions</th>\n</tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_exp\n  a.\\link ArrayBase::exp exp\\endlink(); \\n\n  \\link Eigen::exp exp\\endlink(a);\n  </td>\n  <td>\\f$ e \\f$ raised to the given power (\\f$ e^{a_i} \\f$) </td>\n  <td class=\"code\">\n  using <a href=\"http://en.cppreference.com/w/cpp/numeric/math/exp\">std::exp</a>; \\n\n  exp(a[i]);\n  </td>\n  <td>SSE2, AVX (f,d)</td>\n</tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_log\n  a.\\link ArrayBase::log log\\endlink(); \\n\n  \\link Eigen::log log\\endlink(a);\n  </td>\n  <td>natural (base \\f$ e \\f$) logarithm (\\f$ \\ln({a_i}) \\f$)</td>\n  <td class=\"code\">\n  using <a href=\"http://en.cppreference.com/w/cpp/numeric/math/log\">std::log</a>; \\n\n  log(a[i]);\n  </td>\n  <td>SSE2, AVX (f)</td>\n</tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_log1p\n  a.\\link ArrayBase::log1p log1p\\endlink(); \\n\n  \\link Eigen::log1p log1p\\endlink(a);\n  </td>\n  <td>natural (base \\f$ e \\f$) logarithm of 1 plus \\n the given number (\\f$ \\ln({1+a_i}) \\f$)</td>\n  <td>built-in generic implementation based on \\c log,\\n\n  plus \\c using <a href=\"http://en.cppreference.com/w/cpp/numeric/math/log1p\">\\c std::log1p </a>; \\cpp11</td>\n  <td></td>\n</tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_log10\n  a.\\link ArrayBase::log10 log10\\endlink(); \\n\n  \\link Eigen::log10 log10\\endlink(a);\n  </td>\n  <td>base 10 logarithm (\\f$ \\log_{10}({a_i}) \\f$)</td>\n  <td class=\"code\">\n  using <a href=\"http://en.cppreference.com/w/cpp/numeric/math/log10\">std::log10</a>; \\n\n  log10(a[i]);\n  </td>\n  <td></td>\n</tr>\n<tr>\n<th colspan=\"4\">Power functions</th>\n</tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_pow\n  a.\\link ArrayBase::pow pow\\endlink(b); \\n\n  \\link Eigen::pow pow\\endlink(a,b);\n  </td>\n  <td>raises a number to the given power (\\f$ a_i ^ {b_i} \\f$) \\n \\c a and \\c b can be either an array or scalar.</td>\n  <td class=\"code\">\n  using <a href=\"http://en.cppreference.com/w/cpp/numeric/math/pow\">std::pow</a>; \\n\n  pow(a[i],b[i]);\\n\n  (plus builtin for integer types)</td>\n  <td></td>\n</tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_sqrt\n  a.\\link ArrayBase::sqrt sqrt\\endlink(); \\n\n  \\link Eigen::sqrt sqrt\\endlink(a);\\n\n  m.\\link MatrixBase::cwiseSqrt cwiseSqrt\\endlink();\n  </td>\n  <td>computes square root (\\f$ \\sqrt a_i \\f$)</td>\n  <td class=\"code\">\n  using <a href=\"http://en.cppreference.com/w/cpp/numeric/math/sqrt\">std::sqrt</a>; \\n\n  sqrt(a[i]);</td>\n  <td>SSE2, AVX (f,d)</td>\n</tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_rsqrt\n  a.\\link ArrayBase::rsqrt rsqrt\\endlink(); \\n\n  \\link Eigen::rsqrt rsqrt\\endlink(a);\n  </td>\n  <td><a href=\"https://en.wikipedia.org/wiki/Fast_inverse_square_root\">reciprocal square root</a> (\\f$ 1/{\\sqrt a_i} \\f$)</td>\n  <td class=\"code\">\n  using <a href=\"http://en.cppreference.com/w/cpp/numeric/math/sqrt\">std::sqrt</a>; \\n\n  1/sqrt(a[i]); \\n\n  </td>\n  <td>SSE2, AVX, AltiVec, ZVector (f,d)\\n\n  (approx + 1 Newton iteration)</td>\n</tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_square\n  a.\\link ArrayBase::square square\\endlink(); \\n\n  \\link Eigen::square square\\endlink(a);\n  </td>\n  <td>computes square power (\\f$ a_i^2 \\f$)</td>\n  <td class=\"code\">\n  a[i]*a[i]</td>\n  <td>All (i32,f,d,cf,cd)</td>\n</tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_cube\n  a.\\link ArrayBase::cube cube\\endlink(); \\n\n  \\link Eigen::cube cube\\endlink(a);\n  </td>\n  <td>computes cubic power (\\f$ a_i^3 \\f$)</td>\n  <td class=\"code\">\n  a[i]*a[i]*a[i]</td>\n  <td>All (i32,f,d,cf,cd)</td>\n</tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_abs2\n  a.\\link ArrayBase::abs2 abs2\\endlink(); \\n\n  \\link Eigen::abs2 abs2\\endlink(a);\\n\n  m.\\link MatrixBase::cwiseAbs2 cwiseAbs2\\endlink();\n  </td>\n  <td>computes the squared absolute value (\\f$ |a_i|^2 \\f$)</td>\n  <td class=\"code\">\n  real:    a[i]*a[i] \\n\n  complex:  real(a[i])*real(a[i]) \\n\n  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; + imag(a[i])*imag(a[i])</td>\n  <td>All (i32,f,d)</td>\n</tr>\n<tr>\n<th colspan=\"4\">Trigonometric functions</th>\n</tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_sin\n  a.\\link ArrayBase::sin sin\\endlink(); \\n\n  \\link Eigen::sin sin\\endlink(a);\n  </td>\n  <td>computes sine</td>\n  <td class=\"code\">\n  using <a href=\"http://en.cppreference.com/w/cpp/numeric/math/sin\">std::sin</a>; \\n\n  sin(a[i]);</td>\n  <td>SSE2, AVX (f)</td>\n</tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_cos\n  a.\\link ArrayBase::cos cos\\endlink(); \\n\n  \\link Eigen::cos cos\\endlink(a);\n  </td>\n  <td>computes cosine</td>\n  <td class=\"code\">\n  using <a href=\"http://en.cppreference.com/w/cpp/numeric/math/cos\">std::cos</a>; \\n\n  cos(a[i]);</td>\n  <td>SSE2, AVX (f)</td>\n</tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_tan\n  a.\\link ArrayBase::tan tan\\endlink(); \\n\n  \\link Eigen::tan tan\\endlink(a);\n  </td>\n  <td>computes tangent</td>\n  <td class=\"code\">\n  using <a href=\"http://en.cppreference.com/w/cpp/numeric/math/tan\">std::tan</a>; \\n\n  tan(a[i]);</td>\n  <td></td>\n</tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_asin\n  a.\\link ArrayBase::asin asin\\endlink(); \\n\n  \\link Eigen::asin asin\\endlink(a);\n  </td>\n  <td>computes arc sine (\\f$ \\sin^{-1} a_i \\f$)</td>\n  <td class=\"code\">\n  using <a href=\"http://en.cppreference.com/w/cpp/numeric/math/asin\">std::asin</a>; \\n\n  asin(a[i]);</td>\n  <td></td>\n</tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_acos\n  a.\\link ArrayBase::acos acos\\endlink(); \\n\n  \\link Eigen::acos acos\\endlink(a);\n  </td>\n  <td>computes arc cosine  (\\f$ \\cos^{-1} a_i \\f$)</td>\n  <td class=\"code\">\n  using <a href=\"http://en.cppreference.com/w/cpp/numeric/math/acos\">std::acos</a>; \\n\n  acos(a[i]);</td>\n  <td></td>\n</tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_atan\n  a.\\link ArrayBase::atan tan\\endlink(); \\n\n  \\link Eigen::atan atan\\endlink(a);\n  </td>\n  <td>computes arc tangent (\\f$ \\tan^{-1} a_i \\f$)</td>\n  <td class=\"code\">\n  using <a href=\"http://en.cppreference.com/w/cpp/numeric/math/atan\">std::atan</a>; \\n\n  atan(a[i]);</td>\n  <td></td>\n</tr>\n<tr>\n<th colspan=\"4\">Hyperbolic functions</th>\n</tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_sinh\n  a.\\link ArrayBase::sinh sinh\\endlink(); \\n\n  \\link Eigen::sinh sinh\\endlink(a);\n  </td>\n  <td>computes hyperbolic sine</td>\n  <td class=\"code\">\n  using <a href=\"http://en.cppreference.com/w/cpp/numeric/math/sinh\">std::sinh</a>; \\n\n  sinh(a[i]);</td>\n  <td></td>\n</tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_cosh\n  a.\\link ArrayBase::cosh cohs\\endlink(); \\n\n  \\link Eigen::cosh cosh\\endlink(a);\n  </td>\n  <td>computes hyperbolic cosine</td>\n  <td class=\"code\">\n  using <a href=\"http://en.cppreference.com/w/cpp/numeric/math/cosh\">std::cosh</a>; \\n\n  cosh(a[i]);</td>\n  <td></td>\n</tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_tanh\n  a.\\link ArrayBase::tanh tanh\\endlink(); \\n\n  \\link Eigen::tanh tanh\\endlink(a);\n  </td>\n  <td>computes hyperbolic tangent</td>\n  <td class=\"code\">\n  using <a href=\"http://en.cppreference.com/w/cpp/numeric/math/tanh\">std::tanh</a>; \\n\n  tanh(a[i]);</td>\n  <td></td>\n</tr>\n<tr>\n<th colspan=\"4\">Nearest integer floating point operations</th>\n</tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_ceil\n  a.\\link ArrayBase::ceil ceil\\endlink(); \\n\n  \\link Eigen::ceil ceil\\endlink(a);\n  </td>\n  <td>nearest integer not less than the given value</td>\n  <td class=\"code\">\n  using <a href=\"http://en.cppreference.com/w/cpp/numeric/math/ceil\">std::ceil</a>; \\n\n  ceil(a[i]);</td>\n  <td>SSE4,AVX,ZVector (f,d)</td>\n</tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_floor\n  a.\\link ArrayBase::floor floor\\endlink(); \\n\n  \\link Eigen::floor floor\\endlink(a);\n  </td>\n  <td>nearest integer not greater than the given value</td>\n  <td class=\"code\">\n  using <a href=\"http://en.cppreference.com/w/cpp/numeric/math/floor\">std::floor</a>; \\n\n  floor(a[i]);</td>\n  <td>SSE4,AVX,ZVector (f,d)</td>\n</tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_round\n  a.\\link ArrayBase::round round\\endlink(); \\n\n  \\link Eigen::round round\\endlink(a);\n  </td>\n  <td>nearest integer, \\n rounding away from zero in halfway cases</td>\n  <td>built-in generic implementation \\n based on \\c floor and \\c ceil,\\n\n  plus \\c using <a href=\"http://en.cppreference.com/w/cpp/numeric/math/round\">\\c std::round </a>; \\cpp11</td>\n  <td>SSE4,AVX,ZVector (f,d)</td>\n</tr>\n<tr>\n<th colspan=\"4\">Floating point manipulation functions</th>\n</tr>\n<tr>\n<th colspan=\"4\">Classification and comparison</th>\n</tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_isfinite\n  a.\\link ArrayBase::isFinite isFinite\\endlink(); \\n\n  \\link Eigen::isfinite isfinite\\endlink(a);\n  </td>\n  <td>checks if the given number has finite value</td>\n  <td>built-in generic implementation,\\n\n  plus \\c using <a href=\"http://en.cppreference.com/w/cpp/numeric/math/isfinite\">\\c std::isfinite </a>; \\cpp11</td>\n  <td></td>\n</tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_isinf\n  a.\\link ArrayBase::isInf isInf\\endlink(); \\n\n  \\link Eigen::isinf isinf\\endlink(a);\n  </td>\n  <td>checks if the given number is infinite</td>\n  <td>built-in generic implementation,\\n\n  plus \\c using <a href=\"http://en.cppreference.com/w/cpp/numeric/math/isinf\">\\c std::isinf </a>; \\cpp11</td>\n  <td></td>\n</tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_isnan\n  a.\\link ArrayBase::isNaN isNaN\\endlink(); \\n\n  \\link Eigen::isnan isnan\\endlink(a);\n  </td>\n  <td>checks if the given number is not a number</td>\n  <td>built-in generic implementation,\\n\n  plus \\c using <a href=\"http://en.cppreference.com/w/cpp/numeric/math/isnan\">\\c std::isnan </a>; \\cpp11</td>\n  <td></td>\n</tr>\n<tr>\n<th colspan=\"4\">Error and gamma functions</th>\n</tr>\n<tr> <td colspan=\"4\">  Require \\c \\#include \\c <unsupported/Eigen/SpecialFunctions> </td></tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_erf\n  a.\\link ArrayBase::erf erf\\endlink(); \\n\n  \\link Eigen::erf erf\\endlink(a);\n  </td>\n  <td>error function</td>\n  <td class=\"code\">\n  using <a href=\"http://en.cppreference.com/w/cpp/numeric/math/erf\">std::erf</a>; \\cpp11 \\n\n  erf(a[i]);\n  </td>\n  <td></td>\n</tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_erfc\n  a.\\link ArrayBase::erfc erfc\\endlink(); \\n\n  \\link Eigen::erfc erfc\\endlink(a);\n  </td>\n  <td>complementary error function</td>\n  <td class=\"code\">\n  using <a href=\"http://en.cppreference.com/w/cpp/numeric/math/erfc\">std::erfc</a>; \\cpp11 \\n\n  erfc(a[i]);\n  </td>\n  <td></td>\n</tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_lgamma\n  a.\\link ArrayBase::lgamma lgamma\\endlink(); \\n\n  \\link Eigen::lgamma lgamma\\endlink(a);\n  </td>\n  <td>natural logarithm of the gamma function</td>\n  <td class=\"code\">\n  using <a href=\"http://en.cppreference.com/w/cpp/numeric/math/lgamma\">std::lgamma</a>; \\cpp11 \\n\n  lgamma(a[i]);\n  </td>\n  <td></td>\n</tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_digamma\n  a.\\link ArrayBase::digamma digamma\\endlink(); \\n\n  \\link Eigen::digamma digamma\\endlink(a);\n  </td>\n  <td><a href=\"https://en.wikipedia.org/wiki/Digamma_function\">logarithmic derivative of the gamma function</a></td>\n  <td>\n  built-in for float and double\n  </td>\n  <td></td>\n</tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_igamma\n  \\link Eigen::igamma igamma\\endlink(a,x);\n  </td>\n  <td><a href=\"https://en.wikipedia.org/wiki/Incomplete_gamma_function\">lower incomplete gamma integral</a>\n  \\n \\f$ \\gamma(a_i,x_i)= \\frac{1}{|a_i|} \\int_{0}^{x_i}e^{\\text{-}t} t^{a_i-1} \\mathrm{d} t \\f$</td>\n  <td>\n  built-in for float and double,\\n but requires \\cpp11\n  </td>\n  <td></td>\n</tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_igammac\n  \\link Eigen::igammac igammac\\endlink(a,x);\n  </td>\n  <td><a href=\"https://en.wikipedia.org/wiki/Incomplete_gamma_function\">upper incomplete gamma integral</a>\n  \\n \\f$ \\Gamma(a_i,x_i) = \\frac{1}{|a_i|} \\int_{x_i}^{\\infty}e^{\\text{-}t} t^{a_i-1} \\mathrm{d} t \\f$</td>\n  <td>\n  built-in for float and double,\\n but requires \\cpp11\n  </td>\n  <td></td>\n</tr>\n<tr>\n<th colspan=\"4\">Special functions</th>\n</tr>\n<tr> <td colspan=\"4\">  Require \\c \\#include \\c <unsupported/Eigen/SpecialFunctions> </td></tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_polygamma\n  \\link Eigen::polygamma polygamma\\endlink(n,x);\n  </td>\n  <td><a href=\"https://en.wikipedia.org/wiki/Polygamma_function\">n-th derivative of digamma at x</a></td>\n  <td>\n  built-in generic based on\\n <a href=\"#cwisetable_lgamma\">\\c lgamma </a>,\n  <a href=\"#cwisetable_digamma\"> \\c digamma </a>\n  and <a href=\"#cwisetable_zeta\">\\c zeta </a>.\n  </td>\n  <td></td>\n</tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_betainc\n  \\link Eigen::betainc betainc\\endlink(a,b,x);\n  </td>\n  <td><a href=\"https://en.wikipedia.org/wiki/Beta_function#Incomplete_beta_function\">Incomplete beta function</a></td>\n  <td>\n  built-in for float and double,\\n but requires \\cpp11\n  </td>\n  <td></td>\n</tr>\n<tr>\n  <td class=\"code\">\n  \\anchor cwisetable_zeta\n  \\link Eigen::zeta zeta\\endlink(a,b);\n  </td>\n  <td><a href=\"https://en.wikipedia.org/wiki/Hurwitz_zeta_function\">Hurwitz zeta function</a>\n  \\n \\f$ \\zeta(a_i,b_i)=\\sum_{k=0}^{\\infty}(b_i+k)^{\\text{-}a_i} \\f$</td>\n  <td>\n  built-in for float and double\n  </td>\n  <td></td>\n</tr>\n<tr><td colspan=\"4\"></td></tr>\n</table>\n\n\\n\n\n*/\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/CustomizingEigen_CustomScalar.dox",
    "content": "namespace Eigen {\n\n/** \\page TopicCustomizing_CustomScalar Using custom scalar types\n\\anchor user_defined_scalars\n\nBy default, Eigen currently supports standard floating-point types (\\c float, \\c double, \\c std::complex<float>, \\c std::complex<double>, \\c long \\c double), as well as all native integer types (e.g., \\c int, \\c unsigned \\c int, \\c short, etc.), and \\c bool.\nOn x86-64 systems, \\c long \\c double permits to locally enforces the use of x87 registers with extended accuracy (in comparison to SSE).\n\nIn order to add support for a custom type \\c T you need:\n-# make sure the common operator (+,-,*,/,etc.) are supported by the type \\c T\n-# add a specialization of struct Eigen::NumTraits<T> (see \\ref NumTraits)\n-# define the math functions that makes sense for your type. This includes standard ones like sqrt, pow, sin, tan, conj, real, imag, etc, as well as abs2 which is Eigen specific.\n     (see the file Eigen/src/Core/MathFunctions.h)\n\nThe math function should be defined in the same namespace than \\c T, or in the \\c std namespace though that second approach is not recommended.\n\nHere is a concrete example adding support for the Adolc's \\c adouble type. <a href=\"https://projects.coin-or.org/ADOL-C\">Adolc</a> is an automatic differentiation library. The type \\c adouble is basically a real value tracking the values of any number of partial derivatives.\n\n\\code\n#ifndef ADOLCSUPPORT_H\n#define ADOLCSUPPORT_H\n\n#define ADOLC_TAPELESS\n#include <adolc/adouble.h>\n#include <Eigen/Core>\n\nnamespace Eigen {\n\ntemplate<> struct NumTraits<adtl::adouble>\n : NumTraits<double> // permits to get the epsilon, dummy_precision, lowest, highest functions\n{\n  typedef adtl::adouble Real;\n  typedef adtl::adouble NonInteger;\n  typedef adtl::adouble Nested;\n\n  enum {\n    IsComplex = 0,\n    IsInteger = 0,\n    IsSigned = 1,\n    RequireInitialization = 1,\n    ReadCost = 1,\n    AddCost = 3,\n    MulCost = 3\n  };\n};\n\n}\n\nnamespace adtl {\n\ninline const adouble& conj(const adouble& x)  { return x; }\ninline const adouble& real(const adouble& x)  { return x; }\ninline adouble imag(const adouble&)    { return 0.; }\ninline adouble abs(const adouble&  x)  { return fabs(x); }\ninline adouble abs2(const adouble& x)  { return x*x; }\n\n}\n\n#endif // ADOLCSUPPORT_H\n\\endcode\n\nThis other example adds support for the \\c mpq_class type from <a href=\"https://gmplib.org/\">GMP</a>. It shows in particular how to change the way Eigen picks the best pivot during LU factorization. It selects the coefficient with the highest score, where the score is by default the absolute value of a number, but we can define a different score, for instance to prefer pivots with a more compact representation (this is an example, not a recommendation). Note that the scores should always be non-negative and only zero is allowed to have a score of zero. Also, this can interact badly with thresholds for inexact scalar types.\n\n\\code\n#include <gmpxx.h>\n#include <Eigen/Core>\n#include <boost/operators.hpp>\n\nnamespace Eigen {\n  template<> struct NumTraits<mpq_class> : GenericNumTraits<mpq_class>\n  {\n    typedef mpq_class Real;\n    typedef mpq_class NonInteger;\n    typedef mpq_class Nested;\n\n    static inline Real epsilon() { return 0; }\n    static inline Real dummy_precision() { return 0; }\n    static inline Real digits10() { return 0; }\n\n    enum {\n      IsInteger = 0,\n      IsSigned = 1,\n      IsComplex = 0,\n      RequireInitialization = 1,\n      ReadCost = 6,\n      AddCost = 150,\n      MulCost = 100\n    };\n  };\n\n  namespace internal {\n\n    template<> struct scalar_score_coeff_op<mpq_class> {\n      struct result_type : boost::totally_ordered1<result_type> {\n        std::size_t len;\n        result_type(int i = 0) : len(i) {} // Eigen uses Score(0) and Score()\n        result_type(mpq_class const& q) :\n          len(mpz_size(q.get_num_mpz_t())+\n              mpz_size(q.get_den_mpz_t())-1) {}\n        friend bool operator<(result_type x, result_type y) {\n          // 0 is the worst possible pivot\n          if (x.len == 0) return y.len > 0;\n          if (y.len == 0) return false;\n          // Prefer a pivot with a small representation\n          return x.len > y.len;\n        }\n        friend bool operator==(result_type x, result_type y) {\n          // Only used to test if the score is 0\n          return x.len == y.len;\n        }\n      };\n      result_type operator()(mpq_class const& x) const { return x; }\n    };\n  }\n}\n\\endcode\n\n*/\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/CustomizingEigen_InheritingMatrix.dox",
    "content": "namespace Eigen {\n\n/** \\page TopicCustomizing_InheritingMatrix Inheriting from Matrix\n\nBefore inheriting from Matrix, be really, I mean REALLY, sure that using\nEIGEN_MATRIX_PLUGIN is not what you really want (see previous section).\nIf you just need to add few members to Matrix, this is the way to go.\n\nAn example of when you actually need to inherit Matrix, is when you\nhave several layers of heritage such as \nMyVerySpecificVector1, MyVerySpecificVector2 -> MyVector1 -> Matrix and\nMyVerySpecificVector3, MyVerySpecificVector4 -> MyVector2 -> Matrix.\n\nIn order for your object to work within the %Eigen framework, you need to\ndefine a few members in your inherited class.\n\nHere is a minimalistic example:\n\n\\include CustomizingEigen_Inheritance.cpp\n\nOutput: \\verbinclude CustomizingEigen_Inheritance.out\n\nThis is the kind of error you can get if you don't provide those methods\n\\verbatim\nerror: no match for ‘operator=’ in ‘v = Eigen::operator*(\nconst Eigen::MatrixBase<Eigen::Matrix<double, -0x000000001, 1, 0, -0x000000001, 1> >::Scalar&, \nconst Eigen::MatrixBase<Eigen::Matrix<double, -0x000000001, 1> >::StorageBaseType&)\n(((const Eigen::MatrixBase<Eigen::Matrix<double, -0x000000001, 1> >::StorageBaseType&)\n((const Eigen::MatrixBase<Eigen::Matrix<double, -0x000000001, 1> >::StorageBaseType*)(& v))))’\n\\endverbatim\n\n*/\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/CustomizingEigen_NullaryExpr.dox",
    "content": "namespace Eigen {\n\n/** \\page TopicCustomizing_NullaryExpr Matrix manipulation via nullary-expressions\n\n\nThe main purpose of the class CwiseNullaryOp is to define \\em procedural matrices such as constant or random matrices as returned by the Ones(), Zero(), Constant(), Identity() and Random() methods.\nNevertheless, with some imagination it is possible to accomplish very sophisticated matrix manipulation with minimal efforts such that \\ref TopicNewExpressionType \"implementing new expression\" is rarely needed.\n\n\\section NullaryExpr_Circulant Example 1: circulant matrix\n\nTo explore these possibilities let us start with the  \\em circulant example of the \\ref TopicNewExpressionType \"implementing new expression\" topic.\nLet us recall that a circulant matrix is a matrix where each column is the same as the\ncolumn to the left, except that it is cyclically shifted downwards.\nFor example, here is a 4-by-4 circulant matrix:\n\\f[ \\begin{bmatrix}\n    1 & 8 & 4 & 2 \\\\\n    2 & 1 & 8 & 4 \\\\\n    4 & 2 & 1 & 8 \\\\\n    8 & 4 & 2 & 1\n\\end{bmatrix} \\f]\nA circulant matrix is uniquely determined by its first column. We wish\nto write a function \\c makeCirculant which, given the first column,\nreturns an expression representing the circulant matrix.\n\nFor this exercise, the return type of \\c makeCirculant will be a CwiseNullaryOp that we need to instantiate with:\n1 - a proper \\c circulant_functor storing the input vector and implementing the adequate coefficient accessor \\c operator(i,j)\n2 - a template instantiation of class Matrix conveying compile-time information such as the scalar type, sizes, and preferred storage layout.\n\nCalling \\c ArgType the type of the input vector, we can construct the equivalent squared Matrix type as follows:\n\n\\snippet make_circulant2.cpp square\n\nThis little helper structure will help us to implement our \\c makeCirculant function as follows:\n\n\\snippet make_circulant2.cpp makeCirculant\n\nAs usual, our function takes as argument a \\c MatrixBase (see this \\ref TopicFunctionTakingEigenTypes \"page\" for more details).\nThen, the CwiseNullaryOp object is constructed through the DenseBase::NullaryExpr static method with the adequate runtime sizes.\n\nThen, we need to implement our \\c circulant_functor, which is a straightforward exercise:\n\n\\snippet make_circulant2.cpp circulant_func\n\nWe are now all set to try our new feature:\n\n\\snippet make_circulant2.cpp main\n\n\nIf all the fragments are combined, the following output is produced,\nshowing that the program works as expected:\n\n\\include make_circulant2.out\n\nThis implementation of \\c makeCirculant is much simpler than \\ref TopicNewExpressionType \"defining a new expression\" from scratch.\n\n\n\\section NullaryExpr_Indexing Example 2: indexing rows and columns\n\nThe goal here is to mimic MatLab's ability to index a matrix through two vectors of indices referencing the rows and columns to be picked respectively, like this:\n\n\\snippet nullary_indexing.out main1\n\nTo this end, let us first write a nullary-functor storing references to the input matrix and to the two arrays of indices, and implementing the required \\c operator()(i,j):\n\n\\snippet nullary_indexing.cpp functor\n\nThen, let's create an \\c indexing(A,rows,cols) function creating the nullary expression:\n\n\\snippet nullary_indexing.cpp function\n\nFinally, here is an example of how this function can be used:\n\n\\snippet nullary_indexing.cpp main1\n\nThis straightforward implementation is already quite powerful as the row or column index arrays can also be expressions to perform offsetting, modulo, striding, reverse, etc.\n\n\\snippet nullary_indexing.cpp main2\n\nand the output is:\n\n\\snippet nullary_indexing.out main2\n\n*/\n\n}\n\n"
  },
  {
    "path": "include/eigen3/doc/CustomizingEigen_Plugins.dox",
    "content": "namespace Eigen {\n\n/** \\page TopicCustomizing_Plugins Extending MatrixBase (and other classes)\n\nIn this section we will see how to add custom methods to MatrixBase. Since all expressions and matrix types inherit MatrixBase, adding a method to MatrixBase make it immediately available to all expressions ! A typical use case is, for instance, to make Eigen compatible with another API.\n\nYou certainly know that in C++ it is not possible to add methods to an existing class. So how that's possible ? Here the trick is to include in the declaration of MatrixBase a file defined by the preprocessor token \\c EIGEN_MATRIXBASE_PLUGIN:\n\\code\nclass MatrixBase {\n  // ...\n  #ifdef EIGEN_MATRIXBASE_PLUGIN\n  #include EIGEN_MATRIXBASE_PLUGIN\n  #endif\n};\n\\endcode\nTherefore to extend MatrixBase with your own methods you just have to create a file with your method declaration and define EIGEN_MATRIXBASE_PLUGIN before you include any Eigen's header file.\n\nYou can extend many of the other classes used in Eigen by defining similarly named preprocessor symbols. For instance, define \\c EIGEN_ARRAYBASE_PLUGIN if you want to extend the ArrayBase class. A full list of classes that can be extended in this way and the corresponding preprocessor symbols can be found on our page \\ref TopicPreprocessorDirectives.\n\nHere is an example of an extension file for adding methods to MatrixBase: \\n\n\\b MatrixBaseAddons.h\n\\code\ninline Scalar at(uint i, uint j) const { return this->operator()(i,j); }\ninline Scalar& at(uint i, uint j) { return this->operator()(i,j); }\ninline Scalar at(uint i) const { return this->operator[](i); }\ninline Scalar& at(uint i) { return this->operator[](i); }\n\ninline RealScalar squaredLength() const { return squaredNorm(); }\ninline RealScalar length() const { return norm(); }\ninline RealScalar invLength(void) const { return fast_inv_sqrt(squaredNorm()); }\n\ntemplate<typename OtherDerived>\ninline Scalar squaredDistanceTo(const MatrixBase<OtherDerived>& other) const\n{ return (derived() - other.derived()).squaredNorm(); }\n\ntemplate<typename OtherDerived>\ninline RealScalar distanceTo(const MatrixBase<OtherDerived>& other) const\n{ return internal::sqrt(derived().squaredDistanceTo(other)); }\n\ninline void scaleTo(RealScalar l) { RealScalar vl = norm(); if (vl>1e-9) derived() *= (l/vl); }\n\ninline Transpose<Derived> transposed() {return this->transpose();}\ninline const Transpose<Derived> transposed() const {return this->transpose();}\n\ninline uint minComponentId(void) const  { int i; this->minCoeff(&i); return i; }\ninline uint maxComponentId(void) const  { int i; this->maxCoeff(&i); return i; }\n\ntemplate<typename OtherDerived>\nvoid makeFloor(const MatrixBase<OtherDerived>& other) { derived() = derived().cwiseMin(other.derived()); }\ntemplate<typename OtherDerived>\nvoid makeCeil(const MatrixBase<OtherDerived>& other) { derived() = derived().cwiseMax(other.derived()); }\n\nconst CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const Derived, const ConstantReturnType>\noperator+(const Scalar& scalar) const\n{ return CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const Derived, const ConstantReturnType>(derived(), Constant(rows(),cols(),scalar)); }\n\nfriend const CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const ConstantReturnType, Derived>\noperator+(const Scalar& scalar, const MatrixBase<Derived>& mat)\n{ return CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const ConstantReturnType, Derived>(Constant(rows(),cols(),scalar), mat.derived()); }\n\\endcode\n\nThen one can the following declaration in the config.h or whatever prerequisites header file of his project:\n\\code\n#define EIGEN_MATRIXBASE_PLUGIN \"MatrixBaseAddons.h\"\n\\endcode\n\n*/\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/DenseDecompositionBenchmark.dox",
    "content": "namespace Eigen {\n\n/** \\eigenManualPage DenseDecompositionBenchmark Benchmark of dense decompositions\n\nThis page presents a speed comparison of the dense matrix decompositions offered by %Eigen for a wide range of square matrices and overconstrained problems.\n\nFor a more general overview on the features and numerical robustness of linear solvers and decompositions, check this \\link TopicLinearAlgebraDecompositions table \\endlink.\n\nThis benchmark has been run on a laptop equipped with an Intel core i7 \\@ 2,6 GHz, and compiled with clang with \\b AVX and \\b FMA instruction sets enabled but without multi-threading.\nIt uses \\b single \\b precision \\b float numbers. For double, you can get a good estimate by multiplying the timings by a factor 2.\n\nThe square matrices are symmetric, and for the overconstrained matrices, the reported timmings include the cost to compute the symmetric covariance matrix \\f$ A^T A \\f$ for the first four solvers based on Cholesky and LU, as denoted by the \\b * symbol (top-right corner part of the table).\nTimings are in \\b milliseconds, and factors are relative to the LLT decomposition which is the fastest but also the least general and robust.\n\n<table class=\"manual\">\n<tr><th>solver/size</th>\n  <th>8x8</th>  <th>100x100</th>  <th>1000x1000</th>  <th>4000x4000</th>  <th>10000x8</th>  <th>10000x100</th>  <th>10000x1000</th>  <th>10000x4000</th></tr>\n<tr><td>LLT</td><td>0.05</td><td>0.42</td><td>5.83</td><td>374.55</td><td>6.79 <sup><a href=\"#note_ls\">*</a></sup></td><td>30.15 <sup><a href=\"#note_ls\">*</a></sup></td><td>236.34 <sup><a href=\"#note_ls\">*</a></sup></td><td>3847.17 <sup><a href=\"#note_ls\">*</a></sup></td></tr>\n<tr class=\"alt\"><td>LDLT</td><td>0.07 (x1.3)</td><td>0.65 (x1.5)</td><td>26.86 (x4.6)</td><td>2361.18 (x6.3)</td><td>6.81 (x1) <sup><a href=\"#note_ls\">*</a></sup></td><td>31.91 (x1.1) <sup><a href=\"#note_ls\">*</a></sup></td><td>252.61 (x1.1) <sup><a href=\"#note_ls\">*</a></sup></td><td>5807.66 (x1.5) <sup><a href=\"#note_ls\">*</a></sup></td></tr>\n<tr><td>PartialPivLU</td><td>0.08 (x1.5)</td><td>0.69 (x1.6)</td><td>15.63 (x2.7)</td><td>709.32 (x1.9)</td><td>6.81 (x1) <sup><a href=\"#note_ls\">*</a></sup></td><td>31.32 (x1) <sup><a href=\"#note_ls\">*</a></sup></td><td>241.68 (x1) <sup><a href=\"#note_ls\">*</a></sup></td><td>4270.48 (x1.1) <sup><a href=\"#note_ls\">*</a></sup></td></tr>\n<tr class=\"alt\"><td>FullPivLU</td><td>0.1 (x1.9)</td><td>4.48 (x10.6)</td><td>281.33 (x48.2)</td><td>-</td><td>6.83 (x1) <sup><a href=\"#note_ls\">*</a></sup></td><td>32.67 (x1.1) <sup><a href=\"#note_ls\">*</a></sup></td><td>498.25 (x2.1) <sup><a href=\"#note_ls\">*</a></sup></td><td>-</td></tr>\n<tr><td>HouseholderQR</td><td>0.19 (x3.5)</td><td>2.18 (x5.2)</td><td>23.42 (x4)</td><td>1337.52 (x3.6)</td><td>34.26 (x5)</td><td>129.01 (x4.3)</td><td>377.37 (x1.6)</td><td>4839.1 (x1.3)</td></tr>\n<tr class=\"alt\"><td>ColPivHouseholderQR</td><td>0.23 (x4.3)</td><td>2.23 (x5.3)</td><td>103.34 (x17.7)</td><td>9987.16 (x26.7)</td><td>36.05 (x5.3)</td><td>163.18 (x5.4)</td><td>2354.08 (x10)</td><td>37860.5 (x9.8)</td></tr>\n<tr><td>CompleteOrthogonalDecomposition</td><td>0.23 (x4.3)</td><td>2.22 (x5.2)</td><td>99.44 (x17.1)</td><td>10555.3 (x28.2)</td><td>35.75 (x5.3)</td><td>169.39 (x5.6)</td><td>2150.56 (x9.1)</td><td>36981.8 (x9.6)</td></tr>\n<tr class=\"alt\"><td>FullPivHouseholderQR</td><td>0.23 (x4.3)</td><td>4.64 (x11)</td><td>289.1 (x49.6)</td><td>-</td><td>69.38 (x10.2)</td><td>446.73 (x14.8)</td><td>4852.12 (x20.5)</td><td>-</td></tr>\n<tr><td>JacobiSVD</td><td>1.01 (x18.6)</td><td>71.43 (x168.4)</td><td>-</td><td>-</td><td>113.81 (x16.7)</td><td>1179.66 (x39.1)</td><td>-</td><td>-</td></tr>\n<tr class=\"alt\"><td>BDCSVD</td><td>1.07 (x19.7)</td><td>21.83 (x51.5)</td><td>331.77 (x56.9)</td><td>18587.9 (x49.6)</td><td>110.53 (x16.3)</td><td>397.67 (x13.2)</td><td>2975 (x12.6)</td><td>48593.2 (x12.6)</td></tr>\n</table>\n\n<a name=\"note_ls\">\\b *: </a> This decomposition do not support direct least-square solving for over-constrained problems, and the reported timing include the cost to form the symmetric covariance matrix \\f$ A^T A \\f$.\n\n\\b Observations:\n + LLT is always the fastest solvers.\n + For largely over-constrained problems, the cost of Cholesky/LU decompositions is dominated by the computation of the symmetric covariance matrix.\n + For large problem sizes, only the decomposition implementing a cache-friendly blocking strategy scale well. Those include LLT, PartialPivLU, HouseholderQR, and BDCSVD. This explain why for a 4k x 4k matrix, HouseholderQR is faster than LDLT. In the future, LDLT and ColPivHouseholderQR will also implement blocking strategies.\n + CompleteOrthogonalDecomposition is based on ColPivHouseholderQR and they thus achieve the same level of performance.\n\nThe above table has been generated by the <a href=\"https://bitbucket.org/eigen/eigen/raw/default/bench/dense_solvers.cpp\">bench/dense_solvers.cpp</a> file, feel-free to hack it to generate a table matching your hardware, compiler, and favorite problem sizes.\n\n*/\n\n}\n"
  },
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The cache size is given by this formula:\n# 2^(16+SYMBOL_CACHE_SIZE). The valid range is 0..9, the default is 0,\n# corresponding to a cache size of 2^16 = 65536 symbols.\n\n# SYMBOL_CACHE_SIZE      = 0\n\n# Similar to the SYMBOL_CACHE_SIZE the size of the symbol lookup cache can be\n# set using LOOKUP_CACHE_SIZE. This cache is used to resolve symbols given\n# their name and scope. Since this can be an expensive process and often the\n# same symbol appear multiple times in the code, doxygen keeps a cache of\n# pre-resolved symbols. If the cache is too small doxygen will become slower.\n# If the cache is too large, memory is wasted. The cache size is given by this\n# formula: 2^(16+LOOKUP_CACHE_SIZE). The valid range is 0..9, the default is 0,\n# corresponding to a cache size of 2^16 = 65536 symbols.\n\nLOOKUP_CACHE_SIZE      = 0\n\n#---------------------------------------------------------------------------\n# Build related configuration options\n#---------------------------------------------------------------------------\n\n# If the EXTRACT_ALL tag is set to YES doxygen will assume all entities in\n# documentation are documented, even if no documentation was available.\n# Private class members and static file members will be hidden unless\n# the EXTRACT_PRIVATE and EXTRACT_STATIC tags are set to YES\n\nEXTRACT_ALL            = NO\n\n# If the EXTRACT_PRIVATE tag is set to YES all private members of a class\n# will be included in the documentation.\n\nEXTRACT_PRIVATE        = NO\n\n# If the EXTRACT_PACKAGE tag is set to YES all members with package or internal scope will be included in the documentation.\n\nEXTRACT_PACKAGE        = NO\n\n# If the EXTRACT_STATIC tag is set to YES all static members of a file\n# will be included in the documentation.\n\nEXTRACT_STATIC         = NO\n\n# If the EXTRACT_LOCAL_CLASSES tag is set to YES classes (and structs)\n# defined locally in source files will be included in the documentation.\n# If set to NO only classes defined in header files are included.\n\nEXTRACT_LOCAL_CLASSES  = NO\n\n# This flag is only useful for Objective-C code. When set to YES local\n# methods, which are defined in the implementation section but not in\n# the interface are included in the documentation.\n# If set to NO (the default) only methods in the interface are included.\n\nEXTRACT_LOCAL_METHODS  = NO\n\n# If this flag is set to YES, the members of anonymous namespaces will be\n# extracted and appear in the documentation as a namespace called\n# 'anonymous_namespace{file}', where file will be replaced with the base\n# name of the file that contains the anonymous namespace. By default\n# anonymous namespaces are hidden.\n\nEXTRACT_ANON_NSPACES   = NO\n\n# If the HIDE_UNDOC_MEMBERS tag is set to YES, Doxygen will hide all\n# undocumented members of documented classes, files or namespaces.\n# If set to NO (the default) these members will be included in the\n# various overviews, but no documentation section is generated.\n# This option has no effect if EXTRACT_ALL is enabled.\n\nHIDE_UNDOC_MEMBERS     = YES\n\n# If the HIDE_UNDOC_CLASSES tag is set to YES, Doxygen will hide all\n# undocumented classes that are normally visible in the class hierarchy.\n# If set to NO (the default) these classes will be included in the various\n# overviews. This option has no effect if EXTRACT_ALL is enabled.\n\nHIDE_UNDOC_CLASSES     = YES\n\n# If the HIDE_FRIEND_COMPOUNDS tag is set to YES, Doxygen will hide all\n# friend (class|struct|union) declarations.\n# If set to NO (the default) these declarations will be included in the\n# documentation.\n\nHIDE_FRIEND_COMPOUNDS  = YES\n\n# If the HIDE_IN_BODY_DOCS tag is set to YES, Doxygen will hide any\n# documentation blocks found inside the body of a function.\n# If set to NO (the default) these blocks will be appended to the\n# function's detailed documentation block.\n\nHIDE_IN_BODY_DOCS      = NO\n\n# The INTERNAL_DOCS tag determines if documentation\n# that is typed after a \\internal command is included. If the tag is set\n# to NO (the default) then the documentation will be excluded.\n# Set it to YES to include the internal documentation.\n\nINTERNAL_DOCS          = ${EIGEN_DOXY_INTERNAL}\n\n# If the CASE_SENSE_NAMES tag is set to NO then Doxygen will only generate\n# file names in lower-case letters. If set to YES upper-case letters are also\n# allowed. This is useful if you have classes or files whose names only differ\n# in case and if your file system supports case sensitive file names. Windows\n# and Mac users are advised to set this option to NO.\n\nCASE_SENSE_NAMES       = YES\n\n# If the HIDE_SCOPE_NAMES tag is set to NO (the default) then Doxygen\n# will show members with their full class and namespace scopes in the\n# documentation. If set to YES the scope will be hidden.\n\nHIDE_SCOPE_NAMES       = NO\n\n# If the SHOW_INCLUDE_FILES tag is set to YES (the default) then Doxygen\n# will put a list of the files that are included by a file in the documentation\n# of that file.\n\nSHOW_INCLUDE_FILES     = ${EIGEN_DOXY_INTERNAL}\n\n# If the FORCE_LOCAL_INCLUDES tag is set to YES then Doxygen\n# will list include files with double quotes in the documentation\n# rather than with sharp brackets.\n\nFORCE_LOCAL_INCLUDES   = NO\n\n# If the INLINE_INFO tag is set to YES (the default) then a tag [inline]\n# is inserted in the documentation for inline members.\n\nINLINE_INFO            = YES\n\n# If the SORT_MEMBER_DOCS tag is set to YES (the default) then doxygen\n# will sort the (detailed) documentation of file and class members\n# alphabetically by member name. If set to NO the members will appear in\n# declaration order.\n\nSORT_MEMBER_DOCS       = YES\n\n# If the SORT_BRIEF_DOCS tag is set to YES then doxygen will sort the\n# brief documentation of file, namespace and class members alphabetically\n# by member name. If set to NO (the default) the members will appear in\n# declaration order.\n\nSORT_BRIEF_DOCS        = YES\n\n# If the SORT_MEMBERS_CTORS_1ST tag is set to YES then doxygen\n# will sort the (brief and detailed) documentation of class members so that\n# constructors and destructors are listed first. If set to NO (the default)\n# the constructors will appear in the respective orders defined by\n# SORT_MEMBER_DOCS and SORT_BRIEF_DOCS.\n# This tag will be ignored for brief docs if SORT_BRIEF_DOCS is set to NO\n# and ignored for detailed docs if SORT_MEMBER_DOCS is set to NO.\n\nSORT_MEMBERS_CTORS_1ST = NO\n\n# If the SORT_GROUP_NAMES tag is set to YES then doxygen will sort the\n# hierarchy of group names into alphabetical order. If set to NO (the default)\n# the group names will appear in their defined order.\n\nSORT_GROUP_NAMES       = NO\n\n# If the SORT_BY_SCOPE_NAME tag is set to YES, the class list will be\n# sorted by fully-qualified names, including namespaces. If set to\n# NO (the default), the class list will be sorted only by class name,\n# not including the namespace part.\n# Note: This option is not very useful if HIDE_SCOPE_NAMES is set to YES.\n# Note: This option applies only to the class list, not to the\n# alphabetical list.\n\nSORT_BY_SCOPE_NAME     = NO\n\n# If the STRICT_PROTO_MATCHING option is enabled and doxygen fails to\n# do proper type resolution of all parameters of a function it will reject a\n# match between the prototype and the implementation of a member function even\n# if there is only one candidate or it is obvious which candidate to choose\n# by doing a simple string match. By disabling STRICT_PROTO_MATCHING doxygen\n# will still accept a match between prototype and implementation in such cases.\n\nSTRICT_PROTO_MATCHING  = NO\n\n# The GENERATE_TODOLIST tag can be used to enable (YES) or\n# disable (NO) the todo list. This list is created by putting \\todo\n# commands in the documentation.\n\nGENERATE_TODOLIST      = ${EIGEN_DOXY_INTERNAL}\n\n# The GENERATE_TESTLIST tag can be used to enable (YES) or\n# disable (NO) the test list. This list is created by putting \\test\n# commands in the documentation.\n\nGENERATE_TESTLIST      = NO\n\n# The GENERATE_BUGLIST tag can be used to enable (YES) or\n# disable (NO) the bug list. This list is created by putting \\bug\n# commands in the documentation.\n\nGENERATE_BUGLIST       = ${EIGEN_DOXY_INTERNAL}\n\n# The GENERATE_DEPRECATEDLIST tag can be used to enable (YES) or\n# disable (NO) the deprecated list. This list is created by putting\n# \\deprecated commands in the documentation.\n\nGENERATE_DEPRECATEDLIST= YES\n\n# The ENABLED_SECTIONS tag can be used to enable conditional\n# documentation sections, marked by \\if sectionname ... \\endif.\n\nENABLED_SECTIONS       =\n\n# The MAX_INITIALIZER_LINES tag determines the maximum number of lines\n# the initial value of a variable or macro consists of for it to appear in\n# the documentation. If the initializer consists of more lines than specified\n# here it will be hidden. Use a value of 0 to hide initializers completely.\n# The appearance of the initializer of individual variables and macros in the\n# documentation can be controlled using \\showinitializer or \\hideinitializer\n# command in the documentation regardless of this setting.\n\nMAX_INITIALIZER_LINES  = 0\n\n# Set the SHOW_USED_FILES tag to NO to disable the list of files generated\n# at the bottom of the documentation of classes and structs. If set to YES the\n# list will mention the files that were used to generate the documentation.\n\nSHOW_USED_FILES        = YES\n\n# Set the SHOW_FILES tag to NO to disable the generation of the Files page.\n# This will remove the Files entry from the Quick Index and from the\n# Folder Tree View (if specified). The default is YES.\n\nSHOW_FILES             = YES\n\n# Set the SHOW_NAMESPACES tag to NO to disable the generation of the\n# Namespaces page.\n# This will remove the Namespaces entry from the Quick Index\n# and from the Folder Tree View (if specified). The default is YES.\n\nSHOW_NAMESPACES        = NO\n\n# The FILE_VERSION_FILTER tag can be used to specify a program or script that\n# doxygen should invoke to get the current version for each file (typically from\n# the version control system). Doxygen will invoke the program by executing (via\n# popen()) the command <command> <input-file>, where <command> is the value of\n# the FILE_VERSION_FILTER tag, and <input-file> is the name of an input file\n# provided by doxygen. Whatever the program writes to standard output\n# is used as the file version. See the manual for examples.\n\nFILE_VERSION_FILTER    =\n\n# The LAYOUT_FILE tag can be used to specify a layout file which will be parsed\n# by doxygen. The layout file controls the global structure of the generated\n# output files in an output format independent way. To create the layout file\n# that represents doxygen's defaults, run doxygen with the -l option.\n# You can optionally specify a file name after the option, if omitted\n# DoxygenLayout.xml will be used as the name of the layout file.\n\nLAYOUT_FILE            = \"${Eigen_BINARY_DIR}/doc${EIGEN_DOXY_OUTPUT_DIRECTORY_SUFFIX}/eigendoxy_layout.xml\"\n\n# The CITE_BIB_FILES tag can be used to specify one or more bib files\n# containing the references data. This must be a list of .bib files. The\n# .bib extension is automatically appended if omitted. Using this command\n# requires the bibtex tool to be installed. See also\n# http://en.wikipedia.org/wiki/BibTeX for more info. For LaTeX the style\n# of the bibliography can be controlled using LATEX_BIB_STYLE. To use this\n# feature you need bibtex and perl available in the search path.\n\nCITE_BIB_FILES         =\n\n#---------------------------------------------------------------------------\n# configuration options related to warning and progress messages\n#---------------------------------------------------------------------------\n\n# The QUIET tag can be used to turn on/off the messages that are generated\n# by doxygen. Possible values are YES and NO. If left blank NO is used.\n\nQUIET                  = NO\n\n# The WARNINGS tag can be used to turn on/off the warning messages that are\n# generated by doxygen. Possible values are YES and NO. If left blank\n# NO is used.\n\nWARNINGS               = YES\n\n# If WARN_IF_UNDOCUMENTED is set to YES, then doxygen will generate warnings\n# for undocumented members. If EXTRACT_ALL is set to YES then this flag will\n# automatically be disabled.\n\nWARN_IF_UNDOCUMENTED   = NO\n\n# If WARN_IF_DOC_ERROR is set to YES, doxygen will generate warnings for\n# potential errors in the documentation, such as not documenting some\n# parameters in a documented function, or documenting parameters that\n# don't exist or using markup commands wrongly.\n\nWARN_IF_DOC_ERROR      = YES\n\n# The WARN_NO_PARAMDOC option can be enabled to get warnings for\n# functions that are documented, but have no documentation for their parameters\n# or return value. If set to NO (the default) doxygen will only warn about\n# wrong or incomplete parameter documentation, but not about the absence of\n# documentation.\n\nWARN_NO_PARAMDOC       = NO\n\n# The WARN_FORMAT tag determines the format of the warning messages that\n# doxygen can produce. The string should contain the $file, $line, and $text\n# tags, which will be replaced by the file and line number from which the\n# warning originated and the warning text. Optionally the format may contain\n# $version, which will be replaced by the version of the file (if it could\n# be obtained via FILE_VERSION_FILTER)\n\nWARN_FORMAT            = \"$file:$line: $text\"\n\n# The WARN_LOGFILE tag can be used to specify a file to which warning\n# and error messages should be written. If left blank the output is written\n# to stderr.\n\nWARN_LOGFILE           =\n\n#---------------------------------------------------------------------------\n# configuration options related to the input files\n#---------------------------------------------------------------------------\n\n# The INPUT tag can be used to specify the files and/or directories that contain\n# documented source files. You may enter file names like \"myfile.cpp\" or\n# directories like \"/usr/src/myproject\". Separate the files or directories\n# with spaces.\n\nINPUT                  = ${EIGEN_DOXY_INPUT}\n\n# This tag can be used to specify the character encoding of the source files\n# that doxygen parses. Internally doxygen uses the UTF-8 encoding, which is\n# also the default input encoding. Doxygen uses libiconv (or the iconv built\n# into libc) for the transcoding. See http://www.gnu.org/software/libiconv for\n# the list of possible encodings.\n\nINPUT_ENCODING         = UTF-8\n\n# If the value of the INPUT tag contains directories, you can use the\n# FILE_PATTERNS tag to specify one or more wildcard pattern (like *.cpp\n# and *.h) to filter out the source-files in the directories. If left\n# blank the following patterns are tested:\n# *.c *.cc *.cxx *.cpp *.c++ *.d *.java *.ii *.ixx *.ipp *.i++ *.inl *.h *.hh\n# *.hxx *.hpp *.h++ *.idl *.odl *.cs *.php *.php3 *.inc *.m *.mm *.dox *.py\n# *.f90 *.f *.for *.vhd *.vhdl\n\nFILE_PATTERNS          = *\n\n# The RECURSIVE tag can be used to turn specify whether or not subdirectories\n# should be searched for input files as well. Possible values are YES and NO.\n# If left blank NO is used.\n\nRECURSIVE              = YES\n\n# The EXCLUDE tag can be used to specify files and/or directories that should be\n# excluded from the INPUT source files. This way you can easily exclude a\n# subdirectory from a directory tree whose root is specified with the INPUT tag.\n# Note that relative paths are relative to the directory from which doxygen is\n# run.\n\nEXCLUDE                = \"${Eigen_SOURCE_DIR}/Eigen/src/Core/products\" \\\n                         \"${Eigen_SOURCE_DIR}/Eigen/Eigen2Support\" \\\n                         \"${Eigen_SOURCE_DIR}/Eigen/src/Eigen2Support\" \\\n                         \"${Eigen_SOURCE_DIR}/doc/examples\" \\\n                         \"${Eigen_SOURCE_DIR}/doc/special_examples\" \\\n                         \"${Eigen_SOURCE_DIR}/doc/snippets\" \\\n                         \"${Eigen_SOURCE_DIR}/unsupported/doc/examples\" \\\n                         \"${Eigen_SOURCE_DIR}/unsupported/doc/snippets\"\n\n# The EXCLUDE_SYMLINKS tag can be used to select whether or not files or\n# directories that are symbolic links (a Unix file system feature) are excluded\n# from the input.\n\nEXCLUDE_SYMLINKS       = NO\n\n# If the value of the INPUT tag contains directories, you can use the\n# EXCLUDE_PATTERNS tag to specify one or more wildcard patterns to exclude\n# certain files from those directories. Note that the wildcards are matched\n# against the file with absolute path, so to exclude all test directories\n# for example use the pattern */test/*\n\nEXCLUDE_PATTERNS       = CMake* \\\n                         *.txt \\\n                         *.sh \\\n                         *.orig \\\n                         *.diff \\\n                         diff \\\n                         *~ \\\n                         *. \\\n                         *.sln \\\n                         *.sdf \\\n                         *.tmp \\\n                         *.vcxproj \\\n                         *.filters \\\n                         *.user \\\n                         *.suo\n\n# The EXCLUDE_SYMBOLS tag can be used to specify one or more symbol names\n# (namespaces, classes, functions, etc.) that should be excluded from the\n# output. The symbol name can be a fully qualified name, a word, or if the\n# wildcard * is used, a substring. Examples: ANamespace, AClass,\n# AClass::ANamespace, ANamespace::*Test\n\nEXCLUDE_SYMBOLS        = internal::* \\\n                         Flagged* \\\n                         *InnerIterator* \\\n                         DenseStorage<* \\\n                         \n\n# The EXAMPLE_PATH tag can be used to specify one or more files or\n# directories that contain example code fragments that are included (see\n# the \\include command).\n\nEXAMPLE_PATH           = \"${Eigen_SOURCE_DIR}/doc/snippets\" \\\n                         \"${Eigen_BINARY_DIR}/doc/snippets\" \\\n                         \"${Eigen_SOURCE_DIR}/doc/examples\" \\\n                         \"${Eigen_BINARY_DIR}/doc/examples\" \\\n                         \"${Eigen_SOURCE_DIR}/doc/special_examples\" \\\n                         \"${Eigen_BINARY_DIR}/doc/special_examples\" \\\n                         \"${Eigen_SOURCE_DIR}/unsupported/doc/snippets\" \\\n                         \"${Eigen_BINARY_DIR}/unsupported/doc/snippets\" \\\n                         \"${Eigen_SOURCE_DIR}/unsupported/doc/examples\" \\\n                         \"${Eigen_BINARY_DIR}/unsupported/doc/examples\"\n\n# If the value of the EXAMPLE_PATH tag contains directories, you can use the\n# EXAMPLE_PATTERNS tag to specify one or more wildcard pattern (like *.cpp\n# and *.h) to filter out the source-files in the directories. If left\n# blank all files are included.\n\nEXAMPLE_PATTERNS       = *\n\n# If the EXAMPLE_RECURSIVE tag is set to YES then subdirectories will be\n# searched for input files to be used with the \\include or \\dontinclude\n# commands irrespective of the value of the RECURSIVE tag.\n# Possible values are YES and NO. If left blank NO is used.\n\nEXAMPLE_RECURSIVE      = NO\n\n# The IMAGE_PATH tag can be used to specify one or more files or\n# directories that contain image that are included in the documentation (see\n# the \\image command).\n\nIMAGE_PATH             = ${Eigen_BINARY_DIR}/doc/html\n\n# The INPUT_FILTER tag can be used to specify a program that doxygen should\n# invoke to filter for each input file. Doxygen will invoke the filter program\n# by executing (via popen()) the command <filter> <input-file>, where <filter>\n# is the value of the INPUT_FILTER tag, and <input-file> is the name of an\n# input file. Doxygen will then use the output that the filter program writes\n# to standard output.\n# If FILTER_PATTERNS is specified, this tag will be\n# ignored.\n\nINPUT_FILTER           =\n\n# The FILTER_PATTERNS tag can be used to specify filters on a per file pattern\n# basis.\n# Doxygen will compare the file name with each pattern and apply the\n# filter if there is a match.\n# The filters are a list of the form:\n# pattern=filter (like *.cpp=my_cpp_filter). See INPUT_FILTER for further\n# info on how filters are used. If FILTER_PATTERNS is empty or if\n# non of the patterns match the file name, INPUT_FILTER is applied.\n\nFILTER_PATTERNS        =\n\n# If the FILTER_SOURCE_FILES tag is set to YES, the input filter (if set using\n# INPUT_FILTER) will be used to filter the input files when producing source\n# files to browse (i.e. when SOURCE_BROWSER is set to YES).\n\nFILTER_SOURCE_FILES    = NO\n\n# The FILTER_SOURCE_PATTERNS tag can be used to specify source filters per file\n# pattern. A pattern will override the setting for FILTER_PATTERN (if any)\n# and it is also possible to disable source filtering for a specific pattern\n# using *.ext= (so without naming a filter). This option only has effect when\n# FILTER_SOURCE_FILES is enabled.\n\nFILTER_SOURCE_PATTERNS =\n\n#---------------------------------------------------------------------------\n# configuration options related to source browsing\n#---------------------------------------------------------------------------\n\n# If the SOURCE_BROWSER tag is set to YES then a list of source files will\n# be generated. Documented entities will be cross-referenced with these sources.\n# Note: To get rid of all source code in the generated output, make sure also\n# VERBATIM_HEADERS is set to NO.\n\nSOURCE_BROWSER         = NO\n\n# Setting the INLINE_SOURCES tag to YES will include the body\n# of functions and classes directly in the documentation.\n\nINLINE_SOURCES         = NO\n\n# Setting the STRIP_CODE_COMMENTS tag to YES (the default) will instruct\n# doxygen to hide any special comment blocks from generated source code\n# fragments. Normal C, C++ and Fortran comments will always remain visible.\n\nSTRIP_CODE_COMMENTS    = YES\n\n# If the REFERENCED_BY_RELATION tag is set to YES\n# then for each documented function all documented\n# functions referencing it will be listed.\n\nREFERENCED_BY_RELATION = NO\n\n# If the REFERENCES_RELATION tag is set to YES\n# then for each documented function all documented entities\n# called/used by that function will be listed.\n\nREFERENCES_RELATION    = NO\n\n# If the REFERENCES_LINK_SOURCE tag is set to YES (the default)\n# and SOURCE_BROWSER tag is set to YES, then the hyperlinks from\n# functions in REFERENCES_RELATION and REFERENCED_BY_RELATION lists will\n# link to the source code.\n# Otherwise they will link to the documentation.\n\nREFERENCES_LINK_SOURCE = YES\n\n# If the USE_HTAGS tag is set to YES then the references to source code\n# will point to the HTML generated by the htags(1) tool instead of doxygen\n# built-in source browser. The htags tool is part of GNU's global source\n# tagging system (see http://www.gnu.org/software/global/global.html). You\n# will need version 4.8.6 or higher.\n\nUSE_HTAGS              = NO\n\n# If the VERBATIM_HEADERS tag is set to YES (the default) then Doxygen\n# will generate a verbatim copy of the header file for each class for\n# which an include is specified. Set to NO to disable this.\n\nVERBATIM_HEADERS       = YES\n\n#---------------------------------------------------------------------------\n# configuration options related to the alphabetical class index\n#---------------------------------------------------------------------------\n\n# If the ALPHABETICAL_INDEX tag is set to YES, an alphabetical index\n# of all compounds will be generated. Enable this if the project\n# contains a lot of classes, structs, unions or interfaces.\n\nALPHABETICAL_INDEX     = NO\n\n# If the alphabetical index is enabled (see ALPHABETICAL_INDEX) then\n# the COLS_IN_ALPHA_INDEX tag can be used to specify the number of columns\n# in which this list will be split (can be a number in the range [1..20])\n\nCOLS_IN_ALPHA_INDEX    = 5\n\n# In case all classes in a project start with a common prefix, all\n# classes will be put under the same header in the alphabetical index.\n# The IGNORE_PREFIX tag can be used to specify one or more prefixes that\n# should be ignored while generating the index headers.\n\nIGNORE_PREFIX          =\n\n#---------------------------------------------------------------------------\n# configuration options related to the HTML output\n#---------------------------------------------------------------------------\n\n# If the GENERATE_HTML tag is set to YES (the default) Doxygen will\n# generate HTML output.\n\nGENERATE_HTML          = YES\n\n# The HTML_OUTPUT tag is used to specify where the HTML docs will be put.\n# If a relative path is entered the value of OUTPUT_DIRECTORY will be\n# put in front of it. If left blank `html' will be used as the default path.\n\nHTML_OUTPUT            = \"${Eigen_BINARY_DIR}/doc/html${EIGEN_DOXY_OUTPUT_DIRECTORY_SUFFIX}\"\n\n# The HTML_FILE_EXTENSION tag can be used to specify the file extension for\n# each generated HTML page (for example: .htm,.php,.asp). If it is left blank\n# doxygen will generate files with .html extension.\n\nHTML_FILE_EXTENSION    = .html\n\n# The HTML_HEADER tag can be used to specify a personal HTML header for\n# each generated HTML page. If it is left blank doxygen will generate a\n# standard header. Note that when using a custom header you are responsible\n#  for the proper inclusion of any scripts and style sheets that doxygen\n# needs, which is dependent on the configuration options used.\n# It is advised to generate a default header using \"doxygen -w html\n# header.html footer.html stylesheet.css YourConfigFile\" and then modify\n# that header. Note that the header is subject to change so you typically\n# have to redo this when upgrading to a newer version of doxygen or when\n# changing the value of configuration settings such as GENERATE_TREEVIEW!\n\nHTML_HEADER            = \"${Eigen_BINARY_DIR}/doc/eigendoxy_header.html\"\n\n# The HTML_FOOTER tag can be used to specify a personal HTML footer for\n# each generated HTML page. If it is left blank doxygen will generate a\n# standard footer.\n\nHTML_FOOTER            = \"${Eigen_BINARY_DIR}/doc/eigendoxy_footer.html\"\n\n# The HTML_STYLESHEET tag can be used to specify a user-defined cascading\n# style sheet that is used by each HTML page. It can be used to\n# fine-tune the look of the HTML output. If the tag is left blank doxygen\n# will generate a default style sheet. Note that doxygen will try to copy\n# the style sheet file to the HTML output directory, so don't put your own\n# style sheet in the HTML output directory as well, or it will be erased!\n\nHTML_STYLESHEET        = \n\n# The HTML_EXTRA_FILES tag can be used to specify one or more extra images or\n# other source files which should be copied to the HTML output directory. Note\n# that these files will be copied to the base HTML output directory. Use the\n# $relpath$ marker in the HTML_HEADER and/or HTML_FOOTER files to load these\n# files. In the HTML_STYLESHEET file, use the file name only. Also note that\n# the files will be copied as-is; there are no commands or markers available.\n\nHTML_EXTRA_FILES       = \"${Eigen_SOURCE_DIR}/doc/eigendoxy.css\"\n\n# The HTML_COLORSTYLE_HUE tag controls the color of the HTML output.\n# Doxygen will adjust the colors in the style sheet and background images\n# according to this color. Hue is specified as an angle on a colorwheel,\n# see http://en.wikipedia.org/wiki/Hue for more information.\n# For instance the value 0 represents red, 60 is yellow, 120 is green,\n# 180 is cyan, 240 is blue, 300 purple, and 360 is red again.\n# The allowed range is 0 to 359.\n# The default is 220.\n\nHTML_COLORSTYLE_HUE    = ${EIGEN_DOXY_HTML_COLORSTYLE_HUE}\n\n# The HTML_COLORSTYLE_SAT tag controls the purity (or saturation) of\n# the colors in the HTML output. For a value of 0 the output will use\n# grayscales only. A value of 255 will produce the most vivid colors.\n\nHTML_COLORSTYLE_SAT    = 100\n\n# The HTML_COLORSTYLE_GAMMA tag controls the gamma correction applied to\n# the luminance component of the colors in the HTML output. Values below\n# 100 gradually make the output lighter, whereas values above 100 make\n# the output darker. The value divided by 100 is the actual gamma applied,\n# so 80 represents a gamma of 0.8, The value 220 represents a gamma of 2.2,\n# and 100 does not change the gamma.\n\nHTML_COLORSTYLE_GAMMA  = 80\n\n# If the HTML_TIMESTAMP tag is set to YES then the footer of each generated HTML\n# page will contain the date and time when the page was generated. Setting\n# this to NO can help when comparing the output of multiple runs.\n\nHTML_TIMESTAMP         = YES\n\n# If the HTML_DYNAMIC_SECTIONS tag is set to YES then the generated HTML\n# documentation will contain sections that can be hidden and shown after the\n# page has loaded.\n\nHTML_DYNAMIC_SECTIONS  = YES\n\n# With HTML_INDEX_NUM_ENTRIES one can control the preferred number of\n# entries shown in the various tree structured indices initially; the user\n# can expand and collapse entries dynamically later on. Doxygen will expand\n# the tree to such a level that at most the specified number of entries are\n# visible (unless a fully collapsed tree already exceeds this amount).\n# So setting the number of entries 1 will produce a full collapsed tree by\n# default. 0 is a special value representing an infinite number of entries\n# and will result in a full expanded tree by default.\n\nHTML_INDEX_NUM_ENTRIES = 100\n\n# If the GENERATE_DOCSET tag is set to YES, additional index files\n# will be generated that can be used as input for Apple's Xcode 3\n# integrated development environment, introduced with OSX 10.5 (Leopard).\n# To create a documentation set, doxygen will generate a Makefile in the\n# HTML output directory. Running make will produce the docset in that\n# directory and running \"make install\" will install the docset in\n# ~/Library/Developer/Shared/Documentation/DocSets so that Xcode will find\n# it at startup.\n# See http://developer.apple.com/tools/creatingdocsetswithdoxygen.html\n# for more information.\n\nGENERATE_DOCSET        = NO\n\n# When GENERATE_DOCSET tag is set to YES, this tag determines the name of the\n# feed. A documentation feed provides an umbrella under which multiple\n# documentation sets from a single provider (such as a company or product suite)\n# can be grouped.\n\nDOCSET_FEEDNAME        = \"Doxygen generated docs\"\n\n# When GENERATE_DOCSET tag is set to YES, this tag specifies a string that\n# should uniquely identify the documentation set bundle. This should be a\n# reverse domain-name style string, e.g. com.mycompany.MyDocSet. Doxygen\n# will append .docset to the name.\n\nDOCSET_BUNDLE_ID       = org.doxygen.Project\n\n# When GENERATE_PUBLISHER_ID tag specifies a string that should uniquely identify\n# the documentation publisher. This should be a reverse domain-name style\n# string, e.g. com.mycompany.MyDocSet.documentation.\n\nDOCSET_PUBLISHER_ID    = org.doxygen.Publisher\n\n# The GENERATE_PUBLISHER_NAME tag identifies the documentation publisher.\n\nDOCSET_PUBLISHER_NAME  = Publisher\n\n# If the GENERATE_HTMLHELP tag is set to YES, additional index files\n# will be generated that can be used as input for tools like the\n# Microsoft HTML help workshop to generate a compiled HTML help file (.chm)\n# of the generated HTML documentation.\n\nGENERATE_HTMLHELP      = NO\n\n# If the GENERATE_HTMLHELP tag is set to YES, the CHM_FILE tag can\n# be used to specify the file name of the resulting .chm file. You\n# can add a path in front of the file if the result should not be\n# written to the html output directory.\n\nCHM_FILE               =\n\n# If the GENERATE_HTMLHELP tag is set to YES, the HHC_LOCATION tag can\n# be used to specify the location (absolute path including file name) of\n# the HTML help compiler (hhc.exe). If non-empty doxygen will try to run\n# the HTML help compiler on the generated index.hhp.\n\nHHC_LOCATION           =\n\n# If the GENERATE_HTMLHELP tag is set to YES, the GENERATE_CHI flag\n# controls if a separate .chi index file is generated (YES) or that\n# it should be included in the master .chm file (NO).\n\nGENERATE_CHI           = NO\n\n# If the GENERATE_HTMLHELP tag is set to YES, the CHM_INDEX_ENCODING\n# is used to encode HtmlHelp index (hhk), content (hhc) and project file\n# content.\n\nCHM_INDEX_ENCODING     =\n\n# If the GENERATE_HTMLHELP tag is set to YES, the BINARY_TOC flag\n# controls whether a binary table of contents is generated (YES) or a\n# normal table of contents (NO) in the .chm file.\n\nBINARY_TOC             = NO\n\n# The TOC_EXPAND flag can be set to YES to add extra items for group members\n# to the contents of the HTML help documentation and to the tree view.\n\nTOC_EXPAND             = NO\n\n# If the GENERATE_QHP tag is set to YES and both QHP_NAMESPACE and\n# QHP_VIRTUAL_FOLDER are set, an additional index file will be generated\n# that can be used as input for Qt's qhelpgenerator to generate a\n# Qt Compressed Help (.qch) of the generated HTML documentation.\n\nGENERATE_QHP           = NO\n\n# If the QHG_LOCATION tag is specified, the QCH_FILE tag can\n# be used to specify the file name of the resulting .qch file.\n# The path specified is relative to the HTML output folder.\n\nQCH_FILE               =\n\n# The QHP_NAMESPACE tag specifies the namespace to use when generating\n# Qt Help Project output. For more information please see\n# http://doc.trolltech.com/qthelpproject.html#namespace\n\nQHP_NAMESPACE          = org.doxygen.Project\n\n# The QHP_VIRTUAL_FOLDER tag specifies the namespace to use when generating\n# Qt Help Project output. For more information please see\n# http://doc.trolltech.com/qthelpproject.html#virtual-folders\n\nQHP_VIRTUAL_FOLDER     = doc\n\n# If QHP_CUST_FILTER_NAME is set, it specifies the name of a custom filter to\n# add. For more information please see\n# http://doc.trolltech.com/qthelpproject.html#custom-filters\n\nQHP_CUST_FILTER_NAME   =\n\n# The QHP_CUST_FILT_ATTRS tag specifies the list of the attributes of the\n# custom filter to add. For more information please see\n# <a href=\"http://doc.trolltech.com/qthelpproject.html#custom-filters\">\n# Qt Help Project / Custom Filters</a>.\n\nQHP_CUST_FILTER_ATTRS  =\n\n# The QHP_SECT_FILTER_ATTRS tag specifies the list of the attributes this\n# project's\n# filter section matches.\n# <a href=\"http://doc.trolltech.com/qthelpproject.html#filter-attributes\">\n# Qt Help Project / Filter Attributes</a>.\n\nQHP_SECT_FILTER_ATTRS  =\n\n# If the GENERATE_QHP tag is set to YES, the QHG_LOCATION tag can\n# be used to specify the location of Qt's qhelpgenerator.\n# If non-empty doxygen will try to run qhelpgenerator on the generated\n# .qhp file.\n\nQHG_LOCATION           =\n\n# If the GENERATE_ECLIPSEHELP tag is set to YES, additional index files\n#  will be generated, which together with the HTML files, form an Eclipse help\n# plugin. To install this plugin and make it available under the help contents\n# menu in Eclipse, the contents of the directory containing the HTML and XML\n# files needs to be copied into the plugins directory of eclipse. The name of\n# the directory within the plugins directory should be the same as\n# the ECLIPSE_DOC_ID value. After copying Eclipse needs to be restarted before\n# the help appears.\n\nGENERATE_ECLIPSEHELP   = NO\n\n# A unique identifier for the eclipse help plugin. When installing the plugin\n# the directory name containing the HTML and XML files should also have\n# this name.\n\nECLIPSE_DOC_ID         = org.doxygen.Project\n\n# The DISABLE_INDEX tag can be used to turn on/off the condensed index (tabs)\n# at top of each HTML page. The value NO (the default) enables the index and\n# the value YES disables it. Since the tabs have the same information as the\n# navigation tree you can set this option to NO if you already set\n# GENERATE_TREEVIEW to YES.\n\nDISABLE_INDEX          = YES\n\n# The GENERATE_TREEVIEW tag is used to specify whether a tree-like index\n# structure should be generated to display hierarchical information.\n# If the tag value is set to YES, a side panel will be generated\n# containing a tree-like index structure (just like the one that\n# is generated for HTML Help). For this to work a browser that supports\n# JavaScript, DHTML, CSS and frames is required (i.e. any modern browser).\n# Windows users are probably better off using the HTML help feature.\n# Since the tree basically has the same information as the tab index you\n# could consider to set DISABLE_INDEX to NO when enabling this option.\n\nGENERATE_TREEVIEW      = YES\n\n# The ENUM_VALUES_PER_LINE tag can be used to set the number of enum values\n# (range [0,1..20]) that doxygen will group on one line in the generated HTML\n# documentation. Note that a value of 0 will completely suppress the enum\n# values from appearing in the overview section.\n\nENUM_VALUES_PER_LINE   = 1\n\n# If the treeview is enabled (see GENERATE_TREEVIEW) then this tag can be\n# used to set the initial width (in pixels) of the frame in which the tree\n# is shown.\n\nTREEVIEW_WIDTH         = 250\n\n# When the EXT_LINKS_IN_WINDOW option is set to YES doxygen will open\n# links to external symbols imported via tag files in a separate window.\n\nEXT_LINKS_IN_WINDOW    = NO\n\n# Use this tag to change the font size of Latex formulas included\n# as images in the HTML documentation. The default is 10. Note that\n# when you change the font size after a successful doxygen run you need\n# to manually remove any form_*.png images from the HTML output directory\n# to force them to be regenerated.\n\nFORMULA_FONTSIZE       = 12\n\n# Use the FORMULA_TRANPARENT tag to determine whether or not the images\n# generated for formulas are transparent PNGs. Transparent PNGs are\n# not supported properly for IE 6.0, but are supported on all modern browsers.\n# Note that when changing this option you need to delete any form_*.png files\n# in the HTML output before the changes have effect.\n\nFORMULA_TRANSPARENT    = YES\n\n# Enable the USE_MATHJAX option to render LaTeX formulas using MathJax\n# (see http://www.mathjax.org) which uses client side Javascript for the\n# rendering instead of using prerendered bitmaps. Use this if you do not\n# have LaTeX installed or if you want to formulas look prettier in the HTML\n# output. When enabled you may also need to install MathJax separately and\n# configure the path to it using the MATHJAX_RELPATH option.\n\nUSE_MATHJAX            = NO\n\n# When MathJax is enabled you need to specify the location relative to the\n# HTML output directory using the MATHJAX_RELPATH option. The destination\n# directory should contain the MathJax.js script. For instance, if the mathjax\n# directory is located at the same level as the HTML output directory, then\n# MATHJAX_RELPATH should be ../mathjax. The default value points to\n# the MathJax Content Delivery Network so you can quickly see the result without\n# installing MathJax.\n# However, it is strongly recommended to install a local\n# copy of MathJax from http://www.mathjax.org before deployment.\n\nMATHJAX_RELPATH        = http://cdn.mathjax.org/mathjax/latest\n\n# The MATHJAX_EXTENSIONS tag can be used to specify one or MathJax extension\n# names that should be enabled during MathJax rendering.\n\nMATHJAX_EXTENSIONS     =\n\n# When the SEARCHENGINE tag is enabled doxygen will generate a search box\n# for the HTML output. The underlying search engine uses javascript\n# and DHTML and should work on any modern browser. Note that when using\n# HTML help (GENERATE_HTMLHELP), Qt help (GENERATE_QHP), or docsets\n# (GENERATE_DOCSET) there is already a search function so this one should\n# typically be disabled. For large projects the javascript based search engine\n# can be slow, then enabling SERVER_BASED_SEARCH may provide a better solution.\n\nSEARCHENGINE           = YES\n\n# When the SERVER_BASED_SEARCH tag is enabled the search engine will be\n# implemented using a PHP enabled web server instead of at the web client\n# using Javascript. Doxygen will generate the search PHP script and index\n# file to put on the web server. The advantage of the server\n# based approach is that it scales better to large projects and allows\n# full text search. The disadvantages are that it is more difficult to setup\n# and does not have live searching capabilities.\n\nSERVER_BASED_SEARCH    = NO\n\n#---------------------------------------------------------------------------\n# configuration options related to the LaTeX output\n#---------------------------------------------------------------------------\n\n# If the GENERATE_LATEX tag is set to YES (the default) Doxygen will\n# generate Latex output.\n\nGENERATE_LATEX         = NO\n\n# The LATEX_OUTPUT tag is used to specify where the LaTeX docs will be put.\n# If a relative path is entered the value of OUTPUT_DIRECTORY will be\n# put in front of it. If left blank `latex' will be used as the default path.\n\nLATEX_OUTPUT           = latex\n\n# The LATEX_CMD_NAME tag can be used to specify the LaTeX command name to be\n# invoked. If left blank `latex' will be used as the default command name.\n# Note that when enabling USE_PDFLATEX this option is only used for\n# generating bitmaps for formulas in the HTML output, but not in the\n# Makefile that is written to the output directory.\n\nLATEX_CMD_NAME         = latex\n\n# The MAKEINDEX_CMD_NAME tag can be used to specify the command name to\n# generate index for LaTeX. If left blank `makeindex' will be used as the\n# default command name.\n\nMAKEINDEX_CMD_NAME     = makeindex\n\n# If the COMPACT_LATEX tag is set to YES Doxygen generates more compact\n# LaTeX documents. This may be useful for small projects and may help to\n# save some trees in general.\n\nCOMPACT_LATEX          = NO\n\n# The PAPER_TYPE tag can be used to set the paper type that is used\n# by the printer. Possible values are: a4, letter, legal and\n# executive. If left blank a4wide will be used.\n\nPAPER_TYPE             = a4wide\n\n# The EXTRA_PACKAGES tag can be to specify one or more names of LaTeX\n# packages that should be included in the LaTeX output.\n\nEXTRA_PACKAGES         = amssymb \\\n                         amsmath\n\n# The LATEX_HEADER tag can be used to specify a personal LaTeX header for\n# the generated latex document. The header should contain everything until\n# the first chapter. If it is left blank doxygen will generate a\n# standard header. Notice: only use this tag if you know what you are doing!\n\nLATEX_HEADER           =\n\n# The LATEX_FOOTER tag can be used to specify a personal LaTeX footer for\n# the generated latex document. The footer should contain everything after\n# the last chapter. If it is left blank doxygen will generate a\n# standard footer. Notice: only use this tag if you know what you are doing!\n\nLATEX_FOOTER           =\n\n# If the PDF_HYPERLINKS tag is set to YES, the LaTeX that is generated\n# is prepared for conversion to pdf (using ps2pdf). The pdf file will\n# contain links (just like the HTML output) instead of page references\n# This makes the output suitable for online browsing using a pdf viewer.\n\nPDF_HYPERLINKS         = NO\n\n# If the USE_PDFLATEX tag is set to YES, pdflatex will be used instead of\n# plain latex in the generated Makefile. Set this option to YES to get a\n# higher quality PDF documentation.\n\nUSE_PDFLATEX           = NO\n\n# If the LATEX_BATCHMODE tag is set to YES, doxygen will add the \\\\batchmode.\n# command to the generated LaTeX files. This will instruct LaTeX to keep\n# running if errors occur, instead of asking the user for help.\n# This option is also used when generating formulas in HTML.\n\nLATEX_BATCHMODE        = NO\n\n# If LATEX_HIDE_INDICES is set to YES then doxygen will not\n# include the index chapters (such as File Index, Compound Index, etc.)\n# in the output.\n\nLATEX_HIDE_INDICES     = NO\n\n# If LATEX_SOURCE_CODE is set to YES then doxygen will include\n# source code with syntax highlighting in the LaTeX output.\n# Note that which sources are shown also depends on other settings\n# such as SOURCE_BROWSER.\n\nLATEX_SOURCE_CODE      = NO\n\n# The LATEX_BIB_STYLE tag can be used to specify the style to use for the\n# bibliography, e.g. plainnat, or ieeetr. The default style is \"plain\". See\n# http://en.wikipedia.org/wiki/BibTeX for more info.\n\nLATEX_BIB_STYLE        = plain\n\n#---------------------------------------------------------------------------\n# configuration options related to the RTF output\n#---------------------------------------------------------------------------\n\n# If the GENERATE_RTF tag is set to YES Doxygen will generate RTF output\n# The RTF output is optimized for Word 97 and may not look very pretty with\n# other RTF readers or editors.\n\nGENERATE_RTF           = NO\n\n# The RTF_OUTPUT tag is used to specify where the RTF docs will be put.\n# If a relative path is entered the value of OUTPUT_DIRECTORY will be\n# put in front of it. If left blank `rtf' will be used as the default path.\n\nRTF_OUTPUT             = rtf\n\n# If the COMPACT_RTF tag is set to YES Doxygen generates more compact\n# RTF documents. This may be useful for small projects and may help to\n# save some trees in general.\n\nCOMPACT_RTF            = NO\n\n# If the RTF_HYPERLINKS tag is set to YES, the RTF that is generated\n# will contain hyperlink fields. The RTF file will\n# contain links (just like the HTML output) instead of page references.\n# This makes the output suitable for online browsing using WORD or other\n# programs which support those fields.\n# Note: wordpad (write) and others do not support links.\n\nRTF_HYPERLINKS         = NO\n\n# Load style sheet definitions from file. Syntax is similar to doxygen's\n# config file, i.e. a series of assignments. You only have to provide\n# replacements, missing definitions are set to their default value.\n\nRTF_STYLESHEET_FILE    =\n\n# Set optional variables used in the generation of an rtf document.\n# Syntax is similar to doxygen's config file.\n\nRTF_EXTENSIONS_FILE    =\n\n#---------------------------------------------------------------------------\n# configuration options related to the man page output\n#---------------------------------------------------------------------------\n\n# If the GENERATE_MAN tag is set to YES (the default) Doxygen will\n# generate man pages\n\nGENERATE_MAN           = NO\n\n# The MAN_OUTPUT tag is used to specify where the man pages will be put.\n# If a relative path is entered the value of OUTPUT_DIRECTORY will be\n# put in front of it. If left blank `man' will be used as the default path.\n\nMAN_OUTPUT             = man\n\n# The MAN_EXTENSION tag determines the extension that is added to\n# the generated man pages (default is the subroutine's section .3)\n\nMAN_EXTENSION          = .3\n\n# If the MAN_LINKS tag is set to YES and Doxygen generates man output,\n# then it will generate one additional man file for each entity\n# documented in the real man page(s). These additional files\n# only source the real man page, but without them the man command\n# would be unable to find the correct page. The default is NO.\n\nMAN_LINKS              = NO\n\n#---------------------------------------------------------------------------\n# configuration options related to the XML output\n#---------------------------------------------------------------------------\n\n# If the GENERATE_XML tag is set to YES Doxygen will\n# generate an XML file that captures the structure of\n# the code including all documentation.\n\nGENERATE_XML           = NO\n\n# The XML_OUTPUT tag is used to specify where the XML pages will be put.\n# If a relative path is entered the value of OUTPUT_DIRECTORY will be\n# put in front of it. If left blank `xml' will be used as the default path.\n\nXML_OUTPUT             = xml\n\n# The XML_SCHEMA tag can be used to specify an XML schema,\n# which can be used by a validating XML parser to check the\n# syntax of the XML files.\n\n# XML_SCHEMA             =\n\n# The XML_DTD tag can be used to specify an XML DTD,\n# which can be used by a validating XML parser to check the\n# syntax of the XML files.\n\n# XML_DTD                =\n\n# If the XML_PROGRAMLISTING tag is set to YES Doxygen will\n# dump the program listings (including syntax highlighting\n# and cross-referencing information) to the XML output. Note that\n# enabling this will significantly increase the size of the XML output.\n\nXML_PROGRAMLISTING     = YES\n\n#---------------------------------------------------------------------------\n# configuration options for the AutoGen Definitions output\n#---------------------------------------------------------------------------\n\n# If the GENERATE_AUTOGEN_DEF tag is set to YES Doxygen will\n# generate an AutoGen Definitions (see autogen.sf.net) file\n# that captures the structure of the code including all\n# documentation. Note that this feature is still experimental\n# and incomplete at the moment.\n\nGENERATE_AUTOGEN_DEF   = NO\n\n#---------------------------------------------------------------------------\n# configuration options related to the Perl module output\n#---------------------------------------------------------------------------\n\n# If the GENERATE_PERLMOD tag is set to YES Doxygen will\n# generate a Perl module file that captures the structure of\n# the code including all documentation. Note that this\n# feature is still experimental and incomplete at the\n# moment.\n\nGENERATE_PERLMOD       = NO\n\n# If the PERLMOD_LATEX tag is set to YES Doxygen will generate\n# the necessary Makefile rules, Perl scripts and LaTeX code to be able\n# to generate PDF and DVI output from the Perl module output.\n\nPERLMOD_LATEX          = NO\n\n# If the PERLMOD_PRETTY tag is set to YES the Perl module output will be\n# nicely formatted so it can be parsed by a human reader.\n# This is useful\n# if you want to understand what is going on.\n# On the other hand, if this\n# tag is set to NO the size of the Perl module output will be much smaller\n# and Perl will parse it just the same.\n\nPERLMOD_PRETTY         = YES\n\n# The names of the make variables in the generated doxyrules.make file\n# are prefixed with the string contained in PERLMOD_MAKEVAR_PREFIX.\n# This is useful so different doxyrules.make files included by the same\n# Makefile don't overwrite each other's variables.\n\nPERLMOD_MAKEVAR_PREFIX =\n\n#---------------------------------------------------------------------------\n# Configuration options related to the preprocessor\n#---------------------------------------------------------------------------\n\n# If the ENABLE_PREPROCESSING tag is set to YES (the default) Doxygen will\n# evaluate all C-preprocessor directives found in the sources and include\n# files.\n\nENABLE_PREPROCESSING   = YES\n\n# If the MACRO_EXPANSION tag is set to YES Doxygen will expand all macro\n# names in the source code. If set to NO (the default) only conditional\n# compilation will be performed. Macro expansion can be done in a controlled\n# way by setting EXPAND_ONLY_PREDEF to YES.\n\nMACRO_EXPANSION        = YES\n\n# If the EXPAND_ONLY_PREDEF and MACRO_EXPANSION tags are both set to YES\n# then the macro expansion is limited to the macros specified with the\n# PREDEFINED and EXPAND_AS_DEFINED tags.\n\nEXPAND_ONLY_PREDEF     = YES\n\n# If the SEARCH_INCLUDES tag is set to YES (the default) the includes files\n# pointed to by INCLUDE_PATH will be searched when a #include is found.\n\nSEARCH_INCLUDES        = YES\n\n# The INCLUDE_PATH tag can be used to specify one or more directories that\n# contain include files that are not input files but should be processed by\n# the preprocessor.\n\nINCLUDE_PATH           = \"${Eigen_SOURCE_DIR}/Eigen/src/plugins\"\n\n# You can use the INCLUDE_FILE_PATTERNS tag to specify one or more wildcard\n# patterns (like *.h and *.hpp) to filter out the header-files in the\n# directories. If left blank, the patterns specified with FILE_PATTERNS will\n# be used.\n\nINCLUDE_FILE_PATTERNS  =\n\n# The PREDEFINED tag can be used to specify one or more macro names that\n# are defined before the preprocessor is started (similar to the -D option of\n# gcc). The argument of the tag is a list of macros of the form: name\n# or name=definition (no spaces). If the definition and the = are\n# omitted =1 is assumed. To prevent a macro definition from being\n# undefined via #undef or recursively expanded use the := operator\n# instead of the = operator.\n\nPREDEFINED             = EIGEN_EMPTY_STRUCT \\\n                         EIGEN_PARSED_BY_DOXYGEN \\\n                         EIGEN_VECTORIZE \\\n                         EIGEN_QT_SUPPORT \\\n                         EIGEN_STRONG_INLINE=inline \\\n                         EIGEN_DEVICE_FUNC= \\\n                         \"EIGEN_MAKE_CWISE_BINARY_OP(METHOD,FUNCTOR)=template<typename OtherDerived> const CwiseBinaryOp<FUNCTOR<Scalar>, const Derived, const OtherDerived> METHOD(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const;\" \\\n                         \"EIGEN_CWISE_PRODUCT_RETURN_TYPE(LHS,RHS)=CwiseBinaryOp<internal::scalar_product_op<LHS::Scalar,RHS::Scalar>, const LHS, const RHS>\"\\\n                         \"EIGEN_CAT2(a,b)= a ## b\"\\\n                         \"EIGEN_CAT(a,b)=EIGEN_CAT2(a,b)\"\\\n                         \"EIGEN_CWISE_BINARY_RETURN_TYPE(LHS,RHS,OPNAME)=CwiseBinaryOp<EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)<LHS::Scalar, RHS::Scalar>, const LHS, const RHS>\"\\\n                         DOXCOMMA=,\n\n\n# If the MACRO_EXPANSION and EXPAND_ONLY_PREDEF tags are set to YES then\n# this tag can be used to specify a list of macro names that should be expanded.\n# The macro definition that is found in the sources will be used.\n# Use the PREDEFINED tag if you want to use a different macro definition that\n# overrules the definition found in the source code.\n\nEXPAND_AS_DEFINED      = EIGEN_MAKE_TYPEDEFS \\\n                         EIGEN_MAKE_FIXED_TYPEDEFS \\\n                         EIGEN_MAKE_TYPEDEFS_ALL_SIZES \\\n                         EIGEN_CWISE_UNOP_RETURN_TYPE \\\n                         EIGEN_CWISE_BINOP_RETURN_TYPE \\\n                         EIGEN_CURRENT_STORAGE_BASE_CLASS \\\n                         EIGEN_MATHFUNC_IMPL \\\n                         _EIGEN_GENERIC_PUBLIC_INTERFACE \\\n                         EIGEN_ARRAY_DECLARE_GLOBAL_UNARY \\\n                         EIGEN_EMPTY \\\n                         EIGEN_EULER_ANGLES_TYPEDEFS \\\n                         EIGEN_EULER_ANGLES_SINGLE_TYPEDEF \\\n                         EIGEN_EULER_SYSTEM_TYPEDEF \\\n                         EIGEN_DOC_UNARY_ADDONS \\\n                         EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL \\\n                         EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF\n\n\n# If the SKIP_FUNCTION_MACROS tag is set to YES (the default) then\n# doxygen's preprocessor will remove all references to function-like macros\n# that are alone on a line, have an all uppercase name, and do not end with a\n# semicolon, because these will confuse the parser if not removed.\n\nSKIP_FUNCTION_MACROS   = YES\n\n#---------------------------------------------------------------------------\n# Configuration::additions related to external references\n#---------------------------------------------------------------------------\n\n# The TAGFILES option can be used to specify one or more tagfiles. For each\n# tag file the location of the external documentation should be added. The\n# format of a tag file without this location is as follows:\n#\n# TAGFILES = file1 file2 ...\n# Adding location for the tag files is done as follows:\n#\n# TAGFILES = file1=loc1 \"file2 = loc2\" ...\n# where \"loc1\" and \"loc2\" can be relative or absolute paths\n# or URLs. Note that each tag file must have a unique name (where the name does\n# NOT include the path). 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  },
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    "path": "include/eigen3/doc/FixedSizeVectorizable.dox",
    "content": "namespace Eigen {\n\n/** \\eigenManualPage TopicFixedSizeVectorizable Fixed-size vectorizable Eigen objects\n\nThe goal of this page is to explain what we mean by \"fixed-size vectorizable\".\n\n\\section FixedSizeVectorizable_summary Executive Summary\n\nAn Eigen object is called \"fixed-size vectorizable\" if it has fixed size and that size is a multiple of 16 bytes.\n\nExamples include:\n\\li Eigen::Vector2d\n\\li Eigen::Vector4d\n\\li Eigen::Vector4f\n\\li Eigen::Matrix2d\n\\li Eigen::Matrix2f\n\\li Eigen::Matrix4d\n\\li Eigen::Matrix4f\n\\li Eigen::Affine3d\n\\li Eigen::Affine3f\n\\li Eigen::Quaterniond\n\\li Eigen::Quaternionf\n\n\\section FixedSizeVectorizable_explanation Explanation\n\nFirst, \"fixed-size\" should be clear: an Eigen object has fixed size if its number of rows and its number of columns are fixed at compile-time. So for example Matrix3f has fixed size, but MatrixXf doesn't (the opposite of fixed-size is dynamic-size).\n\nThe array of coefficients of a fixed-size Eigen object is a plain \"static array\", it is not dynamically allocated. For example, the data behind a Matrix4f is just a \"float array[16]\".\n\nFixed-size objects are typically very small, which means that we want to handle them with zero runtime overhead -- both in terms of memory usage and of speed.\n\nNow, vectorization (both SSE and AltiVec) works with 128-bit packets. Moreover, for performance reasons, these packets need to be have 128-bit alignment.\n\nSo it turns out that the only way that fixed-size Eigen objects can be vectorized, is if their size is a multiple of 128 bits, or 16 bytes. Eigen will then request 16-byte alignment for these objects, and henceforth rely on these objects being aligned so no runtime check for alignment is performed.\n\n*/\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/FunctionsTakingEigenTypes.dox",
    "content": "namespace Eigen {\n\n/** \\page TopicFunctionTakingEigenTypes Writing Functions Taking %Eigen Types as Parameters\n\n%Eigen's use of expression templates results in potentially every expression being of a different type. If you pass such an expression to a function taking a parameter of type Matrix, your expression will implicitly be evaluated into a temporary Matrix, which will then be passed to the function. This means that you lose the benefit of expression templates. Concretely, this has two drawbacks:\n \\li The evaluation into a temporary may be useless and inefficient;\n \\li This only allows the function to read from the expression, not to write to it.\n\nFortunately, all this myriad of expression types have in common that they all inherit a few common, templated base classes. By letting your function take templated parameters of these base types, you can let them play nicely with %Eigen's expression templates.\n\n\\eigenAutoToc\n\n\\section TopicFirstExamples Some First Examples\n\nThis section will provide simple examples for different types of objects %Eigen is offering. Before starting with the actual examples, we need to recapitulate which base objects we can work with (see also \\ref TopicClassHierarchy).\n\n \\li MatrixBase: The common base class for all dense matrix expressions (as opposed to array expressions, as opposed to sparse and special matrix classes). Use it in functions that are meant to work only on dense matrices.\n \\li ArrayBase: The common base class for all dense array expressions (as opposed to matrix expressions, etc). Use it in functions that are meant to work only on arrays.\n \\li DenseBase: The common base class for all dense matrix expression, that is, the base class for both \\c MatrixBase and \\c ArrayBase. It can be used in functions that are meant to work on both matrices and arrays.\n \\li EigenBase: The base class unifying all types of objects that can be evaluated into dense matrices or arrays, for example special matrix classes such as diagonal matrices, permutation matrices, etc. It can be used in functions that are meant to work on any such general type.\n\n<b> %EigenBase Example </b><br/><br/>\nPrints the dimensions of the most generic object present in %Eigen. It could be any matrix expressions, any dense or sparse matrix and any array.\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include function_taking_eigenbase.cpp\n</td>\n<td>\n\\verbinclude function_taking_eigenbase.out\n</td></tr></table>\n<b> %DenseBase Example </b><br/><br/>\nPrints a sub-block of the dense expression. Accepts any dense matrix or array expression, but no sparse objects and no special matrix classes such as DiagonalMatrix.\n\\code\ntemplate <typename Derived>\nvoid print_block(const DenseBase<Derived>& b, int x, int y, int r, int c)\n{\n  std::cout << \"block: \" << b.block(x,y,r,c) << std::endl;\n}\n\\endcode\n<b> %ArrayBase Example </b><br/><br/>\nPrints the maximum coefficient of the array or array-expression.\n\\code\ntemplate <typename Derived>\nvoid print_max_coeff(const ArrayBase<Derived> &a)\n{\n  std::cout << \"max: \" << a.maxCoeff() << std::endl;\n}\n\\endcode\n<b> %MatrixBase Example </b><br/><br/>\nPrints the inverse condition number of the given matrix or matrix-expression.\n\\code\ntemplate <typename Derived>\nvoid print_inv_cond(const MatrixBase<Derived>& a)\n{\n  const typename JacobiSVD<typename Derived::PlainObject>::SingularValuesType&\n    sing_vals = a.jacobiSvd().singularValues();\n  std::cout << \"inv cond: \" << sing_vals(sing_vals.size()-1) / sing_vals(0) << std::endl;\n}\n\\endcode\n<b> Multiple templated arguments example </b><br/><br/>\nCalculate the Euclidean distance between two points.\n\\code\ntemplate <typename DerivedA,typename DerivedB>\ntypename DerivedA::Scalar squaredist(const MatrixBase<DerivedA>& p1,const MatrixBase<DerivedB>& p2)\n{\n  return (p1-p2).squaredNorm();\n}\n\\endcode\nNotice that we used two template parameters, one per argument. This permits the function to handle inputs of different types, e.g.,\n\\code\nsquaredist(v1,2*v2)\n\\endcode\nwhere the first argument \\c v1 is a vector and the second argument \\c 2*v2 is an expression.\n<br/><br/>\n\nThese examples are just intended to give the reader a first impression of how functions can be written which take a plain and constant Matrix or Array argument. They are also intended to give the reader an idea about the most common base classes being the optimal candidates for functions. In the next section we will look in more detail at an example and the different ways it can be implemented, while discussing each implementation's problems and advantages. For the discussion below, Matrix and Array as well as MatrixBase and ArrayBase can be exchanged and all arguments still hold.\n\n\n\\section TopicUsingRefClass How to write generic, but non-templated function?\n\nIn all the previous examples, the functions had to be template functions. This approach allows to write very generic code, but it is often desirable to write non templated function and still keep some level of genericity to avoid stupid copies of the arguments. The typical example is to write functions accepting both a MatrixXf or a block of a MatrixXf. This exactly the purpose of the Ref class. Here is a simple example:\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include function_taking_ref.cpp\n</td>\n<td>\n\\verbinclude function_taking_ref.out\n</td></tr></table>\nIn the first two calls to inv_cond, no copy occur because the memory layout of the arguments matches the memory layout accepted by Ref<MatrixXf>. However, in the last call, we have a generic expression that will be automatically evaluated into a temporary MatrixXf by the Ref<> object.\n\nA Ref object can also be writable. Here is an example of a function computing the covariance matrix of two input matrices where each row is an observation:\n\\code\nvoid cov(const Ref<const MatrixXf> x, const Ref<const MatrixXf> y, Ref<MatrixXf> C)\n{\n  const float num_observations = static_cast<float>(x.rows());\n  const RowVectorXf x_mean = x.colwise().sum() / num_observations;\n  const RowVectorXf y_mean = y.colwise().sum() / num_observations;\n  C = (x.rowwise() - x_mean).transpose() * (y.rowwise() - y_mean) / num_observations;\n}\n\\endcode\nand here are two examples calling cov without any copy:\n\\code\nMatrixXf m1, m2, m3\ncov(m1, m2, m3);\ncov(m1.leftCols<3>(), m2.leftCols<3>(), m3.topLeftCorner<3,3>());\n\\endcode\nThe Ref<> class has two other optional template arguments allowing to control the kind of memory layout that can be accepted without any copy. See the class Ref documentation for the details.\n\n\\section TopicPlainFunctionsWorking In which cases do functions taking plain Matrix or Array arguments work?\n\nWithout using template functions, and without the Ref class, a naive implementation of the previous cov function might look like this\n\\code\nMatrixXf cov(const MatrixXf& x, const MatrixXf& y)\n{\n  const float num_observations = static_cast<float>(x.rows());\n  const RowVectorXf x_mean = x.colwise().sum() / num_observations;\n  const RowVectorXf y_mean = y.colwise().sum() / num_observations;\n  return (x.rowwise() - x_mean).transpose() * (y.rowwise() - y_mean) / num_observations;\n}\n\\endcode\nand contrary to what one might think at first, this implementation is fine unless you require a generic implementation that works with double matrices too and unless you do not care about temporary objects. Why is that the case? Where are temporaries involved? How can code as given below compile?\n\\code\nMatrixXf x,y,z;\nMatrixXf C = cov(x,y+z);\n\\endcode\nIn this special case, the example is fine and will be working because both parameters are declared as \\e const references. The compiler creates a temporary and evaluates the expression x+z into this temporary. Once the function is processed, the temporary is released and the result is assigned to C.\n\n\\b Note: Functions taking \\e const references to Matrix (or Array) can process expressions at the cost of temporaries.\n\n\n\\section TopicPlainFunctionsFailing In which cases do functions taking a plain Matrix or Array argument fail?\n\nHere, we consider a slightly modified version of the function given above. This time, we do not want to return the result but pass an additional non-const paramter which allows us to store the result. A first naive implementation might look as follows.\n\\code\n// Note: This code is flawed!\nvoid cov(const MatrixXf& x, const MatrixXf& y, MatrixXf& C)\n{\n  const float num_observations = static_cast<float>(x.rows());\n  const RowVectorXf x_mean = x.colwise().sum() / num_observations;\n  const RowVectorXf y_mean = y.colwise().sum() / num_observations;\n  C = (x.rowwise() - x_mean).transpose() * (y.rowwise() - y_mean) / num_observations;\n}\n\\endcode\nWhen trying to execute the following code\n\\code\nMatrixXf C = MatrixXf::Zero(3,6);\ncov(x,y, C.block(0,0,3,3));\n\\endcode\nthe compiler will fail, because it is not possible to convert the expression returned by \\c MatrixXf::block() into a non-const \\c MatrixXf&. This is the case because the compiler wants to protect you from writing your result to a temporary object. In this special case this protection is not intended -- we want to write to a temporary object. So how can we overcome this problem? \n\nThe solution which is preferred at the moment is based on a little \\em hack. One needs to pass a const reference to the matrix and internally the constness needs to be cast away. The correct implementation for C98 compliant compilers would be\n\\code\ntemplate <typename Derived, typename OtherDerived>\nvoid cov(const MatrixBase<Derived>& x, const MatrixBase<Derived>& y, MatrixBase<OtherDerived> const & C)\n{\n  typedef typename Derived::Scalar Scalar;\n  typedef typename internal::plain_row_type<Derived>::type RowVectorType;\n\n  const Scalar num_observations = static_cast<Scalar>(x.rows());\n\n  const RowVectorType x_mean = x.colwise().sum() / num_observations;\n  const RowVectorType y_mean = y.colwise().sum() / num_observations;\n\n  const_cast< MatrixBase<OtherDerived>& >(C) =\n    (x.rowwise() - x_mean).transpose() * (y.rowwise() - y_mean) / num_observations;\n}\n\\endcode\nThe implementation above does now not only work with temporary expressions but it also allows to use the function with matrices of arbitrary floating point scalar types.\n\n\\b Note: The const cast hack will only work with templated functions. It will not work with the MatrixXf implementation because it is not possible to cast a Block expression to a Matrix reference!\n\n\n\n\\section TopicResizingInGenericImplementations How to resize matrices in generic implementations?\n\nOne might think we are done now, right? This is not completely true because in order for our covariance function to be generically applicable, we want the follwing code to work\n\\code\nMatrixXf x = MatrixXf::Random(100,3);\nMatrixXf y = MatrixXf::Random(100,3);\nMatrixXf C;\ncov(x, y, C);\n\\endcode\nThis is not the case anymore, when we are using an implementation taking MatrixBase as a parameter. In general, %Eigen supports automatic resizing but it is not possible to do so on expressions. Why should resizing of a matrix Block be allowed? It is a reference to a sub-matrix and we definitely don't want to resize that. So how can we incorporate resizing if we cannot resize on MatrixBase? The solution is to resize the derived object as in this implementation.\n\\code\ntemplate <typename Derived, typename OtherDerived>\nvoid cov(const MatrixBase<Derived>& x, const MatrixBase<Derived>& y, MatrixBase<OtherDerived> const & C_)\n{\n  typedef typename Derived::Scalar Scalar;\n  typedef typename internal::plain_row_type<Derived>::type RowVectorType;\n\n  const Scalar num_observations = static_cast<Scalar>(x.rows());\n\n  const RowVectorType x_mean = x.colwise().sum() / num_observations;\n  const RowVectorType y_mean = y.colwise().sum() / num_observations;\n\n  MatrixBase<OtherDerived>& C = const_cast< MatrixBase<OtherDerived>& >(C_);\n  \n  C.derived().resize(x.cols(),x.cols()); // resize the derived object\n  C = (x.rowwise() - x_mean).transpose() * (y.rowwise() - y_mean) / num_observations;\n}\n\\endcode\nThis implementation is now working for parameters being expressions and for parameters being matrices and having the wrong size. Resizing the expressions does not do any harm in this case unless they actually require resizing. That means, passing an expression with the wrong dimensions will result in a run-time error (in debug mode only) while passing expressions of the correct size will just work fine.\n\n\\b Note: In the above discussion the terms Matrix and Array and MatrixBase and ArrayBase can be exchanged and all arguments still hold.\n\n\\section TopicSummary Summary\n\n  - To summarize, the implementation of functions taking non-writable (const referenced) objects is not a big issue and does not lead to problematic situations in terms of compiling and running your program. However, a naive implementation is likely to introduce unnecessary temporary objects in your code. In order to avoid evaluating parameters into temporaries, pass them as (const) references to MatrixBase or ArrayBase (so templatize your function).\n\n  - Functions taking writable (non-const) parameters must take const references and cast away constness within the function body.\n\n  - Functions that take as parameters MatrixBase (or ArrayBase) objects, and potentially need to resize them (in the case where they are resizable), must call resize() on the derived class, as returned by derived().\n*/\n}\n"
  },
  {
    "path": "include/eigen3/doc/HiPerformance.dox",
    "content": "\nnamespace Eigen {\n\n/** \\page TopicWritingEfficientProductExpression Writing efficient matrix product expressions\n\nIn general achieving good performance with Eigen does no require any special effort:\nsimply write your expressions in the most high level way. This is especially true\nfor small fixed size matrices. For large matrices, however, it might be useful to\ntake some care when writing your expressions in order to minimize useless evaluations\nand optimize the performance.\nIn this page we will give a brief overview of the Eigen's internal mechanism to simplify\nand evaluate complex product expressions, and discuss the current limitations.\nIn particular we will focus on expressions matching level 2 and 3 BLAS routines, i.e,\nall kind of matrix products and triangular solvers.\n\nIndeed, in Eigen we have implemented a set of highly optimized routines which are very similar\nto BLAS's ones. Unlike BLAS, those routines are made available to user via a high level and\nnatural API. Each of these routines can compute in a single evaluation a wide variety of expressions.\nGiven an expression, the challenge is then to map it to a minimal set of routines.\nAs explained latter, this mechanism has some limitations, and knowing them will allow\nyou to write faster code by making your expressions more Eigen friendly.\n\n\\section GEMM General Matrix-Matrix product (GEMM)\n\nLet's start with the most common primitive: the matrix product of general dense matrices.\nIn the BLAS world this corresponds to the GEMM routine. Our equivalent primitive can\nperform the following operation:\n\\f$ C.noalias() += \\alpha op1(A) op2(B) \\f$\nwhere A, B, and C are column and/or row major matrices (or sub-matrices),\nalpha is a scalar value, and op1, op2 can be transpose, adjoint, conjugate, or the identity.\nWhen Eigen detects a matrix product, it analyzes both sides of the product to extract a\nunique scalar factor alpha, and for each side, its effective storage order, shape, and conjugation states.\nMore precisely each side is simplified by iteratively removing trivial expressions such as scalar multiple,\nnegation and conjugation. Transpose and Block expressions are not evaluated and they only modify the storage order\nand shape. All other expressions are immediately evaluated.\nFor instance, the following expression:\n\\code m1.noalias() -= s4 * (s1 * m2.adjoint() * (-(s3*m3).conjugate()*s2))  \\endcode\nis automatically simplified to:\n\\code m1.noalias() += (s1*s2*conj(s3)*s4) * m2.adjoint() * m3.conjugate() \\endcode\nwhich exactly matches our GEMM routine.\n\n\\subsection GEMM_Limitations Limitations\nUnfortunately, this simplification mechanism is not perfect yet and not all expressions which could be\nhandled by a single GEMM-like call are correctly detected.\n<table class=\"manual\" style=\"width:100%\">\n<tr>\n<th>Not optimal expression</th>\n<th>Evaluated as</th>\n<th>Optimal version (single evaluation)</th>\n<th>Comments</th>\n</tr>\n<tr>\n<td>\\code\nm1 += m2 * m3; \\endcode</td>\n<td>\\code\ntemp = m2 * m3;\nm1 += temp; \\endcode</td>\n<td>\\code\nm1.noalias() += m2 * m3; \\endcode</td>\n<td>Use .noalias() to tell Eigen the result and right-hand-sides do not alias. \n    Otherwise the product m2 * m3 is evaluated into a temporary.</td>\n</tr>\n<tr class=\"alt\">\n<td></td>\n<td></td>\n<td>\\code\nm1.noalias() += s1 * (m2 * m3); \\endcode</td>\n<td>This is a special feature of Eigen. Here the product between a scalar\n    and a matrix product does not evaluate the matrix product but instead it\n    returns a matrix product expression tracking the scalar scaling factor. <br>\n    Without this optimization, the matrix product would be evaluated into a\n    temporary as in the next example.</td>\n</tr>\n<tr>\n<td>\\code\nm1.noalias() += (m2 * m3).adjoint(); \\endcode</td>\n<td>\\code\ntemp = m2 * m3;\nm1 += temp.adjoint(); \\endcode</td>\n<td>\\code\nm1.noalias() += m3.adjoint()\n*              * m2.adjoint(); \\endcode</td>\n<td>This is because the product expression has the EvalBeforeNesting bit which\n    enforces the evaluation of the product by the Tranpose expression.</td>\n</tr>\n<tr class=\"alt\">\n<td>\\code\nm1 = m1 + m2 * m3; \\endcode</td>\n<td>\\code\ntemp = m2 * m3;\nm1 = m1 + temp; \\endcode</td>\n<td>\\code m1.noalias() += m2 * m3; \\endcode</td>\n<td>Here there is no way to detect at compile time that the two m1 are the same,\n    and so the matrix product will be immediately evaluated.</td>\n</tr>\n<tr>\n<td>\\code\nm1.noalias() = m4 + m2 * m3; \\endcode</td>\n<td>\\code\ntemp = m2 * m3;\nm1 = m4 + temp; \\endcode</td>\n<td>\\code\nm1 = m4;\nm1.noalias() += m2 * m3; \\endcode</td>\n<td>First of all, here the .noalias() in the first expression is useless because\n    m2*m3 will be evaluated anyway. However, note how this expression can be rewritten\n    so that no temporary is required. (tip: for very small fixed size matrix\n    it is slighlty better to rewrite it like this: m1.noalias() = m2 * m3; m1 += m4;</td>\n</tr>\n<tr class=\"alt\">\n<td>\\code\nm1.noalias() += (s1*m2).block(..) * m3; \\endcode</td>\n<td>\\code\ntemp = (s1*m2).block(..);\nm1 += temp * m3; \\endcode</td>\n<td>\\code\nm1.noalias() += s1 * m2.block(..) * m3; \\endcode</td>\n<td>This is because our expression analyzer is currently not able to extract trivial\n    expressions nested in a Block expression. Therefore the nested scalar\n    multiple cannot be properly extracted.</td>\n</tr>\n</table>\n\nOf course all these remarks hold for all other kind of products involving triangular or selfadjoint matrices.\n\n*/\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/InplaceDecomposition.dox",
    "content": "namespace Eigen {\n\n/** \\eigenManualPage InplaceDecomposition Inplace matrix decompositions\n\nStarting from %Eigen 3.3, the LU, Cholesky, and QR decompositions can operate \\em inplace, that is, directly within the given input matrix.\nThis feature is especially useful when dealing with huge matrices, and or when the available memory is very limited (embedded systems).\n\nTo this end, the respective decomposition class must be instantiated with a Ref<> matrix type, and the decomposition object must be constructed with the input matrix as argument. As an example, let us consider an inplace LU decomposition with partial pivoting.\n\nLet's start with the basic inclusions, and declaration of a 2x2 matrix \\c A:\n\n<table class=\"example\">\n<tr><th>code</th><th>output</th></tr>\n<tr>\n  <td>\\snippet TutorialInplaceLU.cpp init\n  </td>\n  <td>\\snippet TutorialInplaceLU.out init\n  </td>\n</tr>\n</table>\n\nNo surprise here! Then, let's declare our inplace LU object \\c lu, and check the content of the matrix \\c A:\n\n<table class=\"example\">\n<tr>\n  <td>\\snippet TutorialInplaceLU.cpp declaration\n  </td>\n  <td>\\snippet TutorialInplaceLU.out declaration\n  </td>\n</tr>\n</table>\n\nHere, the \\c lu object computes and stores the \\c L and \\c U factors within the memory held by the matrix \\c A.\nThe coefficients of \\c A have thus been destroyed during the factorization, and replaced by the L and U factors as one can verify:\n\n<table class=\"example\">\n<tr>\n  <td>\\snippet TutorialInplaceLU.cpp matrixLU\n  </td>\n  <td>\\snippet TutorialInplaceLU.out matrixLU\n  </td>\n</tr>\n</table>\n\nThen, one can use the \\c lu object as usual, for instance to solve the Ax=b problem:\n<table class=\"example\">\n<tr>\n  <td>\\snippet TutorialInplaceLU.cpp solve\n  </td>\n  <td>\\snippet TutorialInplaceLU.out solve\n  </td>\n</tr>\n</table>\n\nHere, since the content of the original matrix \\c A has been lost, we had to declared a new matrix \\c A0 to verify the result.\n\nSince the memory is shared between \\c A and \\c lu, modifying the matrix \\c A will make \\c lu invalid.\nThis can easily be verified by modifying the content of \\c A and trying to solve the initial problem again:\n\n<table class=\"example\">\n<tr>\n  <td>\\snippet TutorialInplaceLU.cpp modifyA\n  </td>\n  <td>\\snippet TutorialInplaceLU.out modifyA\n  </td>\n</tr>\n</table>\n\nNote that there is no shared pointer under the hood, it is the \\b responsibility \\b of \\b the \\b user to keep the input matrix \\c A in life as long as \\c lu is living.\n\nIf one wants to update the factorization with the modified A, one has to call the compute method as usual:\n<table class=\"example\">\n<tr>\n  <td>\\snippet TutorialInplaceLU.cpp recompute\n  </td>\n  <td>\\snippet TutorialInplaceLU.out recompute\n  </td>\n</tr>\n</table>\n\nNote that calling compute does not change the memory which is referenced by the \\c lu object. Therefore, if the compute method is called with another matrix \\c A1 different than \\c A, then the content of \\c A1 won't be modified. This is still the content of \\c A that will be used to store the L and U factors of the matrix \\c A1.\nThis can easily be verified as follows:\n<table class=\"example\">\n<tr>\n  <td>\\snippet TutorialInplaceLU.cpp recompute_bis0\n </td>\n  <td>\\snippet TutorialInplaceLU.out recompute_bis0\n </td>\n</tr>\n</table>\nThe matrix \\c A1 is unchanged, and one can thus solve A1*x=b, and directly check the residual without any copy of \\c A1:\n<table class=\"example\">\n<tr>\n  <td>\\snippet TutorialInplaceLU.cpp recompute_bis1\n  </td>\n  <td>\\snippet TutorialInplaceLU.out recompute_bis1\n </td>\n</tr>\n</table>\n\n\nHere is the list of matrix decompositions supporting this inplace mechanism:\n\n- class LLT\n- class LDLT\n- class PartialPivLU\n- class FullPivLU\n- class HouseholderQR\n- class ColPivHouseholderQR\n- class FullPivHouseholderQR\n- class CompleteOrthogonalDecomposition\n\n*/\n\n}"
  },
  {
    "path": "include/eigen3/doc/InsideEigenExample.dox",
    "content": "namespace Eigen {\n\n/** \\page TopicInsideEigenExample What happens inside Eigen, on a simple example\n\n\\eigenAutoToc\n\n<hr>\n\n\nConsider the following example program:\n\n\\code\n#include<Eigen/Core>\n\nint main()\n{\n  int size = 50;\n  // VectorXf is a vector of floats, with dynamic size.\n  Eigen::VectorXf u(size), v(size), w(size);\n  u = v + w;\n}\n\\endcode\n\nThe goal of this page is to understand how Eigen compiles it, assuming that SSE2 vectorization is enabled (GCC option -msse2).\n\n\\section WhyInteresting Why it's interesting\n\nMaybe you think, that the above example program is so simple, that compiling it shouldn't involve anything interesting. So before starting, let us explain what is nontrivial in compiling it correctly -- that is, producing optimized code -- so that the complexity of Eigen, that we'll explain here, is really useful.\n\nLook at the line of code\n\\code\n  u = v + w;   //   (*)\n\\endcode\n\nThe first important thing about compiling it, is that the arrays should be traversed only once, like\n\\code\n  for(int i = 0; i < size; i++) u[i] = v[i] + w[i];\n\\endcode\nThe problem is that if we make a naive C++ library where the VectorXf class has an operator+ returning a VectorXf, then the line of code (*) will amount to:\n\\code\n  VectorXf tmp = v + w;\n  VectorXf u = tmp;\n\\endcode\nObviously, the introduction of the temporary \\a tmp here is useless. It has a very bad effect on performance, first because the creation of \\a tmp requires a dynamic memory allocation in this context, and second as there are now two for loops:\n\\code\n  for(int i = 0; i < size; i++) tmp[i] = v[i] + w[i];\n  for(int i = 0; i < size; i++) u[i] = tmp[i];\n\\endcode\nTraversing the arrays twice instead of once is terrible for performance, as it means that we do many redundant memory accesses.\n\nThe second important thing about compiling the above program, is to make correct use of SSE2 instructions. Notice that Eigen also supports AltiVec and that all the discussion that we make here applies also to AltiVec.\n\nSSE2, like AltiVec, is a set of instructions allowing to perform computations on packets of 128 bits at once. Since a float is 32 bits, this means that SSE2 instructions can handle 4 floats at once. This means that, if correctly used, they can make our computation go up to 4x faster.\n\nHowever, in the above program, we have chosen size=50, so our vectors consist of 50 float's, and 50 is not a multiple of 4. This means that we cannot hope to do all of that computation using SSE2 instructions. The second best thing, to which we should aim, is to handle the 48 first coefficients with SSE2 instructions, since 48 is the biggest multiple of 4 below 50, and then handle separately, without SSE2, the 49th and 50th coefficients. Something like this:\n\n\\code\n  for(int i = 0; i < 4*(size/4); i+=4) u.packet(i)  = v.packet(i) + w.packet(i);\n  for(int i = 4*(size/4); i < size; i++) u[i] = v[i] + w[i];\n\\endcode\n\nSo let us look line by line at our example program, and let's follow Eigen as it compiles it.\n\n\\section ConstructingVectors Constructing vectors\n\nLet's analyze the first line:\n\n\\code\n  Eigen::VectorXf u(size), v(size), w(size);\n\\endcode\n\nFirst of all, VectorXf is the following typedef:\n\\code\n  typedef Matrix<float, Dynamic, 1> VectorXf;\n\\endcode\n\nThe class template Matrix is declared in src/Core/util/ForwardDeclarations.h with 6 template parameters, but the last 3 are automatically determined by the first 3. So you don't need to worry about them for now. Here, Matrix\\<float, Dynamic, 1\\> means a matrix of floats, with a dynamic number of rows and 1 column.\n\nThe Matrix class inherits a base class, MatrixBase. Don't worry about it, for now it suffices to say that MatrixBase is what unifies matrices/vectors and all the expressions types -- more on that below.\n\nWhen we do\n\\code\n  Eigen::VectorXf u(size);\n\\endcode\nthe constructor that is called is Matrix::Matrix(int), in src/Core/Matrix.h. Besides some assertions, all it does is to construct the \\a m_storage member, which is of type DenseStorage\\<float, Dynamic, Dynamic, 1\\>.\n\nYou may wonder, isn't it overengineering to have the storage in a separate class? The reason is that the Matrix class template covers all kinds of matrices and vector: both fixed-size and dynamic-size. The storage method is not the same in these two cases. For fixed-size, the matrix coefficients are stored as a plain member array. For dynamic-size, the coefficients will be stored as a pointer to a dynamically-allocated array. Because of this, we need to abstract storage away from the Matrix class. That's DenseStorage.\n\nLet's look at this constructor, in src/Core/DenseStorage.h. You can see that there are many partial template specializations of DenseStorages here, treating separately the cases where dimensions are Dynamic or fixed at compile-time. The partial specialization that we are looking at is:\n\\code\ntemplate<typename T, int _Cols> class DenseStorage<T, Dynamic, Dynamic, _Cols>\n\\endcode\n\nHere, the constructor called is DenseStorage::DenseStorage(int size, int rows, int columns)\nwith size=50, rows=50, columns=1.\n\nHere is this constructor:\n\\code\ninline DenseStorage(int size, int rows, int) : m_data(internal::aligned_new<T>(size)), m_rows(rows) {}\n\\endcode\n\nHere, the \\a m_data member is the actual array of coefficients of the matrix. As you see, it is dynamically allocated. Rather than calling new[] or malloc(), as you can see, we have our own internal::aligned_new defined in src/Core/util/Memory.h. What it does is that if vectorization is enabled, then it uses a platform-specific call to allocate a 128-bit-aligned array, as that is very useful for vectorization with both SSE2 and AltiVec. If vectorization is disabled, it amounts to the standard new[].\n\nAs you can see, the constructor also sets the \\a m_rows member to \\a size. Notice that there is no \\a m_columns member: indeed, in this partial specialization of DenseStorage, we know the number of columns at compile-time, since the _Cols template parameter is different from Dynamic. Namely, in our case, _Cols is 1, which is to say that our vector is just a matrix with 1 column. Hence, there is no need to store the number of columns as a runtime variable.\n\nWhen you call VectorXf::data() to get the pointer to the array of coefficients, it returns DenseStorage::data() which returns the \\a m_data member.\n\nWhen you call VectorXf::size() to get the size of the vector, this is actually a method in the base class MatrixBase. It determines that the vector is a column-vector, since ColsAtCompileTime==1 (this comes from the template parameters in the typedef VectorXf). It deduces that the size is the number of rows, so it returns VectorXf::rows(), which returns DenseStorage::rows(), which returns the \\a m_rows member, which was set to \\a size by the constructor.\n\n\\section ConstructionOfSumXpr Construction of the sum expression\n\nNow that our vectors are constructed, let's move on to the next line:\n\n\\code\nu = v + w;\n\\endcode\n\nThe executive summary is that operator+ returns a \"sum of vectors\" expression, but doesn't actually perform the computation. It is the operator=, whose call occurs thereafter, that does the computation.\n\nLet us now see what Eigen does when it sees this:\n\n\\code\nv + w\n\\endcode\n\nHere, v and w are of type VectorXf, which is a typedef for a specialization of Matrix (as we explained above), which is a subclass of MatrixBase. So what is being called is\n\n\\code\nMatrixBase::operator+(const MatrixBase&)\n\\endcode\n\nThe return type of this operator is\n\\code\nCwiseBinaryOp<internal::scalar_sum_op<float>, VectorXf, VectorXf>\n\\endcode\nThe CwiseBinaryOp class is our first encounter with an expression template. As we said, the operator+ doesn't by itself perform any computation, it just returns an abstract \"sum of vectors\" expression. Since there are also \"difference of vectors\" and \"coefficient-wise product of vectors\" expressions, we unify them all as \"coefficient-wise binary operations\", which we abbreviate as \"CwiseBinaryOp\". \"Coefficient-wise\" means that the operations is performed coefficient by coefficient. \"binary\" means that there are two operands -- we are adding two vectors with one another.\n\nNow you might ask, what if we did something like\n\n\\code\nv + w + u;\n\\endcode\n\nThe first v + w would return a CwiseBinaryOp as above, so in order for this to compile, we'd need to define an operator+ also in the class CwiseBinaryOp... at this point it starts looking like a nightmare: are we going to have to define all operators in each of the expression classes (as you guessed, CwiseBinaryOp is only one of many) ? This looks like a dead end!\n\nThe solution is that CwiseBinaryOp itself, as well as Matrix and all the other expression types, is a subclass of MatrixBase. So it is enough to define once and for all the operators in class MatrixBase.\n\nSince MatrixBase is the common base class of different subclasses, the aspects that depend on the subclass must be abstracted from MatrixBase. This is called polymorphism.\n\nThe classical approach to polymorphism in C++ is by means of virtual functions. This is dynamic polymorphism. Here we don't want dynamic polymorphism because the whole design of Eigen is based around the assumption that all the complexity, all the abstraction, gets resolved at compile-time. This is crucial: if the abstraction can't get resolved at compile-time, Eigen's compile-time optimization mechanisms become useless, not to mention that if that abstraction has to be resolved at runtime it'll incur an overhead by itself.\n\nHere, what we want is to have a single class MatrixBase as the base of many subclasses, in such a way that each MatrixBase object (be it a matrix, or vector, or any kind of expression) knows at compile-time (as opposed to run-time) of which particular subclass it is an object (i.e. whether it is a matrix, or an expression, and what kind of expression).\n\nThe solution is the <a href=\"http://en.wikipedia.org/wiki/Curiously_Recurring_Template_Pattern\">Curiously Recurring Template Pattern</a>. Let's do the break now. Hopefully you can read this wikipedia page during the break if needed, but it won't be allowed during the exam.\n\nIn short, MatrixBase takes a template parameter \\a Derived. Whenever we define a subclass Subclass, we actually make Subclass inherit MatrixBase\\<Subclass\\>. The point is that different subclasses inherit different MatrixBase types. Thanks to this, whenever we have an object of a subclass, and we call on it some MatrixBase method, we still remember even from inside the MatrixBase method which particular subclass we're talking about.\n\nThis means that we can put almost all the methods and operators in the base class MatrixBase, and have only the bare minimum in the subclasses. If you look at the subclasses in Eigen, like for instance the CwiseBinaryOp class, they have very few methods. There are coeff() and sometimes coeffRef() methods for access to the coefficients, there are rows() and cols() methods returning the number of rows and columns, but there isn't much more than that. All the meat is in MatrixBase, so it only needs to be coded once for all kinds of expressions, matrices, and vectors.\n\nSo let's end this digression and come back to the piece of code from our example program that we were currently analyzing,\n\n\\code\nv + w\n\\endcode\n\nNow that MatrixBase is a good friend, let's write fully the prototype of the operator+ that gets called here (this code is from src/Core/MatrixBase.h):\n\n\\code\ntemplate<typename Derived>\nclass MatrixBase\n{\n  // ...\n\n  template<typename OtherDerived>\n  const CwiseBinaryOp<internal::scalar_sum_op<typename internal::traits<Derived>::Scalar>, Derived, OtherDerived>\n  operator+(const MatrixBase<OtherDerived> &other) const;\n\n  // ...\n};\n\\endcode\n\nHere of course, \\a Derived and \\a OtherDerived are VectorXf.\n\nAs we said, CwiseBinaryOp is also used for other operations such as substration, so it takes another template parameter determining the operation that will be applied to coefficients. This template parameter is a functor, that is, a class in which we have an operator() so it behaves like a function. Here, the functor used is internal::scalar_sum_op. It is defined in src/Core/Functors.h.\n\nLet us now explain the internal::traits here. The internal::scalar_sum_op class takes one template parameter: the type of the numbers to handle. Here of course we want to pass the scalar type (a.k.a. numeric type) of VectorXf, which is \\c float. How do we determine which is the scalar type of \\a Derived ? Throughout Eigen, all matrix and expression types define a typedef \\a Scalar which gives its scalar type. For example, VectorXf::Scalar is a typedef for \\c float. So here, if life was easy, we could find the numeric type of \\a Derived as just\n\\code\ntypename Derived::Scalar\n\\endcode\nUnfortunately, we can't do that here, as the compiler would complain that the type Derived hasn't yet been defined. So we use a workaround: in src/Core/util/ForwardDeclarations.h, we declared (not defined!) all our subclasses, like Matrix, and we also declared the following class template:\n\\code\ntemplate<typename T> struct internal::traits;\n\\endcode\nIn src/Core/Matrix.h, right \\em before the definition of class Matrix, we define a partial specialization of internal::traits for T=Matrix\\<any template parameters\\>. In this specialization of internal::traits, we define the Scalar typedef. So when we actually define Matrix, it is legal to refer to \"typename internal::traits\\<Matrix\\>::Scalar\".\n\nAnyway, we have declared our operator+. In our case, where \\a Derived and \\a OtherDerived are VectorXf, the above declaration amounts to:\n\\code\nclass MatrixBase<VectorXf>\n{\n  // ...\n\n  const CwiseBinaryOp<internal::scalar_sum_op<float>, VectorXf, VectorXf>\n  operator+(const MatrixBase<VectorXf> &other) const;\n\n  // ...\n};\n\\endcode\n\nLet's now jump to src/Core/CwiseBinaryOp.h to see how it is defined. As you can see there, all it does is to return a CwiseBinaryOp object, and this object is just storing references to the left-hand-side and right-hand-side expressions -- here, these are the vectors \\a v and \\a w. Well, the CwiseBinaryOp object is also storing an instance of the (empty) functor class, but you shouldn't worry about it as that is a minor implementation detail.\n\nThus, the operator+ hasn't performed any actual computation. To summarize, the operation \\a v + \\a w just returned an object of type CwiseBinaryOp which did nothing else than just storing references to \\a v and \\a w.\n\n\\section Assignment The assignment\n\nAt this point, the expression \\a v + \\a w has finished evaluating, so, in the process of compiling the line of code\n\\code\nu = v + w;\n\\endcode\nwe now enter the operator=.\n\nWhat operator= is being called here? The vector u is an object of class VectorXf, i.e. Matrix. In src/Core/Matrix.h, inside the definition of class Matrix, we see this:\n\\code\n    template<typename OtherDerived>\n    inline Matrix& operator=(const MatrixBase<OtherDerived>& other)\n    {\n      eigen_assert(m_storage.data()!=0 && \"you cannot use operator= with a non initialized matrix (instead use set()\");\n      return Base::operator=(other.derived());\n    }\n\\endcode\nHere, Base is a typedef for MatrixBase\\<Matrix\\>. So, what is being called is the operator= of MatrixBase. Let's see its prototype in src/Core/MatrixBase.h:\n\\code\n    template<typename OtherDerived>\n    Derived& operator=(const MatrixBase<OtherDerived>& other);\n\\endcode\nHere, \\a Derived is VectorXf (since u is a VectorXf) and \\a OtherDerived is CwiseBinaryOp. More specifically, as explained in the previous section, \\a OtherDerived is:\n\\code\nCwiseBinaryOp<internal::scalar_sum_op<float>, VectorXf, VectorXf>\n\\endcode\nSo the full prototype of the operator= being called is:\n\\code\nVectorXf& MatrixBase<VectorXf>::operator=(const MatrixBase<CwiseBinaryOp<internal::scalar_sum_op<float>, VectorXf, VectorXf> > & other);\n\\endcode\nThis operator= literally reads \"copying a sum of two VectorXf's into another VectorXf\".\n\nLet's now look at the implementation of this operator=. It resides in the file src/Core/Assign.h.\n\nWhat we can see there is:\n\\code\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\ninline Derived& MatrixBase<Derived>\n  ::operator=(const MatrixBase<OtherDerived>& other)\n{\n  return internal::assign_selector<Derived,OtherDerived>::run(derived(), other.derived());\n}\n\\endcode\n\nOK so our next task is to understand internal::assign_selector :)\n\nHere is its declaration (all that is still in the same file src/Core/Assign.h)\n\\code\ntemplate<typename Derived, typename OtherDerived,\n         bool EvalBeforeAssigning = int(OtherDerived::Flags) & EvalBeforeAssigningBit,\n         bool NeedToTranspose = Derived::IsVectorAtCompileTime\n                && OtherDerived::IsVectorAtCompileTime\n                && int(Derived::RowsAtCompileTime) == int(OtherDerived::ColsAtCompileTime)\n                && int(Derived::ColsAtCompileTime) == int(OtherDerived::RowsAtCompileTime)\n                && int(Derived::SizeAtCompileTime) != 1>\nstruct internal::assign_selector;\n\\endcode\n\nSo internal::assign_selector takes 4 template parameters, but the 2 last ones are automatically determined by the 2 first ones.\n\nEvalBeforeAssigning is here to enforce the EvalBeforeAssigningBit. As explained <a href=\"TopicLazyEvaluation.html\">here</a>, certain expressions have this flag which makes them automatically evaluate into temporaries before assigning them to another expression. This is the case of the Product expression, in order to avoid strange aliasing effects when doing \"m = m * m;\" However, of course here our CwiseBinaryOp expression doesn't have the EvalBeforeAssigningBit: we said since the beginning that we didn't want a temporary to be introduced here. So if you go to src/Core/CwiseBinaryOp.h, you'll see that the Flags in internal::traits\\<CwiseBinaryOp\\> don't include the EvalBeforeAssigningBit. The Flags member of CwiseBinaryOp is then imported from the internal::traits by the EIGEN_GENERIC_PUBLIC_INTERFACE macro. Anyway, here the template parameter EvalBeforeAssigning has the value \\c false.\n\nNeedToTranspose is here for the case where the user wants to copy a row-vector into a column-vector. We allow this as a special exception to the general rule that in assignments we require the dimesions to match. Anyway, here both the left-hand and right-hand sides are column vectors, in the sense that ColsAtCompileTime is equal to 1. So NeedToTranspose is \\c false too.\n\nSo, here we are in the partial specialization:\n\\code\ninternal::assign_selector<Derived, OtherDerived, false, false>\n\\endcode\n\nHere's how it is defined:\n\\code\ntemplate<typename Derived, typename OtherDerived>\nstruct internal::assign_selector<Derived,OtherDerived,false,false> {\n  static Derived& run(Derived& dst, const OtherDerived& other) { return dst.lazyAssign(other.derived()); }\n};\n\\endcode\n\nOK so now our next job is to understand how lazyAssign works :)\n\n\\code\ntemplate<typename Derived>\ntemplate<typename OtherDerived>\ninline Derived& MatrixBase<Derived>\n  ::lazyAssign(const MatrixBase<OtherDerived>& other)\n{\n  EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Derived,OtherDerived)\n  eigen_assert(rows() == other.rows() && cols() == other.cols());\n  internal::assign_impl<Derived, OtherDerived>::run(derived(),other.derived());\n  return derived();\n}\n\\endcode\n\nWhat do we see here? Some assertions, and then the only interesting line is:\n\\code\n  internal::assign_impl<Derived, OtherDerived>::run(derived(),other.derived());\n\\endcode\n\nOK so now we want to know what is inside internal::assign_impl.\n\nHere is its declaration:\n\\code\ntemplate<typename Derived1, typename Derived2,\n         int Vectorization = internal::assign_traits<Derived1, Derived2>::Vectorization,\n         int Unrolling = internal::assign_traits<Derived1, Derived2>::Unrolling>\nstruct internal::assign_impl;\n\\endcode\nAgain, internal::assign_selector takes 4 template parameters, but the 2 last ones are automatically determined by the 2 first ones.\n\nThese two parameters \\a Vectorization and \\a Unrolling are determined by a helper class internal::assign_traits. Its job is to determine which vectorization strategy to use (that is \\a Vectorization) and which unrolling strategy to use (that is \\a Unrolling).\n\nWe'll not enter into the details of how these strategies are chosen (this is in the implementation of internal::assign_traits at the top of the same file). Let's just say that here \\a Vectorization has the value \\a LinearVectorization, and \\a Unrolling has the value \\a NoUnrolling (the latter is obvious since our vectors have dynamic size so there's no way to unroll the loop at compile-time).\n\nSo the partial specialization of internal::assign_impl that we're looking at is:\n\\code\ninternal::assign_impl<Derived1, Derived2, LinearVectorization, NoUnrolling>\n\\endcode\n\nHere is how it's defined:\n\\code\ntemplate<typename Derived1, typename Derived2>\nstruct internal::assign_impl<Derived1, Derived2, LinearVectorization, NoUnrolling>\n{\n  static void run(Derived1 &dst, const Derived2 &src)\n  {\n    const int size = dst.size();\n    const int packetSize = internal::packet_traits<typename Derived1::Scalar>::size;\n    const int alignedStart = internal::assign_traits<Derived1,Derived2>::DstIsAligned ? 0\n                           : internal::first_aligned(&dst.coeffRef(0), size);\n    const int alignedEnd = alignedStart + ((size-alignedStart)/packetSize)*packetSize;\n\n    for(int index = 0; index < alignedStart; index++)\n      dst.copyCoeff(index, src);\n\n    for(int index = alignedStart; index < alignedEnd; index += packetSize)\n    {\n      dst.template copyPacket<Derived2, Aligned, internal::assign_traits<Derived1,Derived2>::SrcAlignment>(index, src);\n    }\n\n    for(int index = alignedEnd; index < size; index++)\n      dst.copyCoeff(index, src);\n  }\n};\n\\endcode\n\nHere's how it works. \\a LinearVectorization means that the left-hand and right-hand side expression can be accessed linearly i.e. you can refer to their coefficients by one integer \\a index, as opposed to having to refer to its coefficients by two integers \\a row, \\a column.\n\nAs we said at the beginning, vectorization works with blocks of 4 floats. Here, \\a PacketSize is 4.\n\nThere are two potential problems that we need to deal with:\n\\li first, vectorization works much better if the packets are 128-bit-aligned. This is especially important for write access. So when writing to the coefficients of \\a dst, we want to group these coefficients by packets of 4 such that each of these packets is 128-bit-aligned. In general, this requires to skip a few coefficients at the beginning of \\a dst. This is the purpose of \\a alignedStart. We then copy these first few coefficients one by one, not by packets. However, in our case, the \\a dst expression is a VectorXf and remember that in the construction of the vectors we allocated aligned arrays. Thanks to \\a DstIsAligned, Eigen remembers that without having to do any runtime check, so \\a alignedStart is zero and this part is avoided altogether.\n\\li second, the number of coefficients to copy is not in general a multiple of \\a packetSize. Here, there are 50 coefficients to copy and \\a packetSize is 4. So we'll have to copy the last 2 coefficients one by one, not by packets. Here, \\a alignedEnd is 48.\n\nNow come the actual loops.\n\nFirst, the vectorized part: the 48 first coefficients out of 50 will be copied by packets of 4:\n\\code\n  for(int index = alignedStart; index < alignedEnd; index += packetSize)\n  {\n    dst.template copyPacket<Derived2, Aligned, internal::assign_traits<Derived1,Derived2>::SrcAlignment>(index, src);\n  }\n\\endcode\n\nWhat is copyPacket? It is defined in src/Core/Coeffs.h:\n\\code\ntemplate<typename Derived>\ntemplate<typename OtherDerived, int StoreMode, int LoadMode>\ninline void MatrixBase<Derived>::copyPacket(int index, const MatrixBase<OtherDerived>& other)\n{\n  eigen_internal_assert(index >= 0 && index < size());\n  derived().template writePacket<StoreMode>(index,\n    other.derived().template packet<LoadMode>(index));\n}\n\\endcode\n\nOK, what are writePacket() and packet() here?\n\nFirst, writePacket() here is a method on the left-hand side VectorXf. So we go to src/Core/Matrix.h to look at its definition:\n\\code\ntemplate<int StoreMode>\ninline void writePacket(int index, const PacketScalar& x)\n{\n  internal::pstoret<Scalar, PacketScalar, StoreMode>(m_storage.data() + index, x);\n}\n\\endcode\nHere, \\a StoreMode is \\a #Aligned, indicating that we are doing a 128-bit-aligned write access, \\a PacketScalar is a type representing a \"SSE packet of 4 floats\" and internal::pstoret is a function writing such a packet in memory. Their definitions are architecture-specific, we find them in src/Core/arch/SSE/PacketMath.h:\n\nThe line in src/Core/arch/SSE/PacketMath.h that determines the PacketScalar type (via a typedef in Matrix.h) is:\n\\code\ntemplate<> struct internal::packet_traits<float>  { typedef __m128  type; enum {size=4}; };\n\\endcode\nHere, __m128 is a SSE-specific type. Notice that the enum \\a size here is what was used to define \\a packetSize above.\n\nAnd here is the implementation of internal::pstoret:\n\\code\ntemplate<> inline void internal::pstore(float*  to, const __m128&  from) { _mm_store_ps(to, from); }\n\\endcode\nHere, __mm_store_ps is a SSE-specific intrinsic function, representing a single SSE instruction. The difference between internal::pstore and internal::pstoret is that internal::pstoret is a dispatcher handling both the aligned and unaligned cases, you find its definition in src/Core/GenericPacketMath.h:\n\\code\ntemplate<typename Scalar, typename Packet, int LoadMode>\ninline void internal::pstoret(Scalar* to, const Packet& from)\n{\n  if(LoadMode == Aligned)\n    internal::pstore(to, from);\n  else\n    internal::pstoreu(to, from);\n}\n\\endcode\n\nOK, that explains how writePacket() works. Now let's look into the packet() call. Remember that we are analyzing this line of code inside copyPacket():\n\\code\nderived().template writePacket<StoreMode>(index,\n    other.derived().template packet<LoadMode>(index));\n\\endcode\n\nHere, \\a other is our sum expression \\a v + \\a w. The .derived() is just casting from MatrixBase to the subclass which here is CwiseBinaryOp. So let's go to src/Core/CwiseBinaryOp.h:\n\\code\nclass CwiseBinaryOp\n{\n  // ...\n    template<int LoadMode>\n    inline PacketScalar packet(int index) const\n    {\n      return m_functor.packetOp(m_lhs.template packet<LoadMode>(index), m_rhs.template packet<LoadMode>(index));\n    }\n};\n\\endcode\nHere, \\a m_lhs is the vector \\a v, and \\a m_rhs is the vector \\a w. So the packet() function here is Matrix::packet(). The template parameter \\a LoadMode is \\a #Aligned. So we're looking at\n\\code\nclass Matrix\n{\n  // ...\n    template<int LoadMode>\n    inline PacketScalar packet(int index) const\n    {\n      return internal::ploadt<Scalar, LoadMode>(m_storage.data() + index);\n    }\n};\n\\endcode\nWe let you look up the definition of internal::ploadt in GenericPacketMath.h and the internal::pload in src/Core/arch/SSE/PacketMath.h. It is very similar to the above for internal::pstore.\n\nLet's go back to CwiseBinaryOp::packet(). Once the packets from the vectors \\a v and \\a w have been returned, what does this function do? It calls m_functor.packetOp() on them. What is m_functor? Here we must remember what particular template specialization of CwiseBinaryOp we're dealing with:\n\\code\nCwiseBinaryOp<internal::scalar_sum_op<float>, VectorXf, VectorXf>\n\\endcode\nSo m_functor is an object of the empty class internal::scalar_sum_op<float>. As we mentioned above, don't worry about why we constructed an object of this empty class at all -- it's an implementation detail, the point is that some other functors need to store member data.\n\nAnyway, internal::scalar_sum_op is defined in src/Core/Functors.h:\n\\code\ntemplate<typename Scalar> struct internal::scalar_sum_op EIGEN_EMPTY_STRUCT {\n  inline const Scalar operator() (const Scalar& a, const Scalar& b) const { return a + b; }\n  template<typename PacketScalar>\n  inline const PacketScalar packetOp(const PacketScalar& a, const PacketScalar& b) const\n  { return internal::padd(a,b); }\n};\n\\endcode\nAs you can see, all what packetOp() does is to call internal::padd on the two packets. Here is the definition of internal::padd from src/Core/arch/SSE/PacketMath.h:\n\\code\ntemplate<> inline __m128  internal::padd(const __m128&  a, const __m128&  b) { return _mm_add_ps(a,b); }\n\\endcode\nHere, _mm_add_ps is a SSE-specific intrinsic function, representing a single SSE instruction.\n\nTo summarize, the loop\n\\code\n  for(int index = alignedStart; index < alignedEnd; index += packetSize)\n  {\n    dst.template copyPacket<Derived2, Aligned, internal::assign_traits<Derived1,Derived2>::SrcAlignment>(index, src);\n  }\n\\endcode\nhas been compiled to the following code: for \\a index going from 0 to the 11 ( = 48/4 - 1), read the i-th packet (of 4 floats) from the vector v and the i-th packet from the vector w using two __mm_load_ps SSE instructions, then add them together using a __mm_add_ps instruction, then store the result using a __mm_store_ps instruction.\n\nThere remains the second loop handling the last few (here, the last 2) coefficients:\n\\code\n  for(int index = alignedEnd; index < size; index++)\n    dst.copyCoeff(index, src);\n\\endcode\nHowever, it works just like the one we just explained, it is just simpler because there is no SSE vectorization involved here. copyPacket() becomes copyCoeff(), packet() becomes coeff(), writePacket() becomes coeffRef(). If you followed us this far, you can probably understand this part by yourself.\n\nWe see that all the C++ abstraction of Eigen goes away during compilation and that we indeed are precisely controlling which assembly instructions we emit. Such is the beauty of C++! Since we have such precise control over the emitted assembly instructions, but such complex logic to choose the right instructions, we can say that Eigen really behaves like an optimizing compiler. If you prefer, you could say that Eigen behaves like a script for the compiler. In a sense, C++ template metaprogramming is scripting the compiler -- and it's been shown that this scripting language is Turing-complete. See <a href=\"http://en.wikipedia.org/wiki/Template_metaprogramming\"> Wikipedia</a>.\n\n*/\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/LeastSquares.dox",
    "content": "namespace Eigen {\n\n/** \\eigenManualPage LeastSquares Solving linear least squares systems\n\nThis page describes how to solve linear least squares systems using %Eigen. An overdetermined system\nof equations, say \\a Ax = \\a b, has no solutions. In this case, it makes sense to search for the\nvector \\a x which is closest to being a solution, in the sense that the difference \\a Ax - \\a b is\nas small as possible. This \\a x is called the least square solution (if the Euclidean norm is used).\n\nThe three methods discussed on this page are the SVD decomposition, the QR decomposition and normal\nequations. Of these, the SVD decomposition is generally the most accurate but the slowest, normal\nequations is the fastest but least accurate, and the QR decomposition is in between.\n\n\\eigenAutoToc\n\n\n\\section LeastSquaresSVD Using the SVD decomposition\n\nThe \\link BDCSVD::solve() solve() \\endlink method in the BDCSVD class can be directly used to\nsolve linear squares systems. It is not enough to compute only the singular values (the default for\nthis class); you also need the singular vectors but the thin SVD decomposition suffices for\ncomputing least squares solutions:\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr>\n  <td>\\include TutorialLinAlgSVDSolve.cpp </td>\n  <td>\\verbinclude TutorialLinAlgSVDSolve.out </td>\n</tr>\n</table>\n\nThis is example from the page \\link TutorialLinearAlgebra Linear algebra and decompositions \\endlink.\n\n\n\\section LeastSquaresQR Using the QR decomposition\n\nThe solve() method in QR decomposition classes also computes the least squares solution. There are\nthree QR decomposition classes: HouseholderQR (no pivoting, so fast but unstable),\nColPivHouseholderQR (column pivoting, thus a bit slower but more accurate) and FullPivHouseholderQR\n(full pivoting, so slowest and most stable). Here is an example with column pivoting:\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr>\n  <td>\\include LeastSquaresQR.cpp </td>\n  <td>\\verbinclude LeastSquaresQR.out </td>\n</tr>\n</table>\n\n\n\\section LeastSquaresNormalEquations Using normal equations\n\nFinding the least squares solution of \\a Ax = \\a b is equivalent to solving the normal equation\n<i>A</i><sup>T</sup><i>Ax</i> = <i>A</i><sup>T</sup><i>b</i>. This leads to the following code\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr>\n  <td>\\include LeastSquaresNormalEquations.cpp </td>\n  <td>\\verbinclude LeastSquaresNormalEquations.out </td>\n</tr>\n</table>\n\nIf the matrix \\a A is ill-conditioned, then this is not a good method, because the condition number\nof <i>A</i><sup>T</sup><i>A</i> is the square of the condition number of \\a A. This means that you\nlose twice as many digits using normal equation than if you use the other methods.\n\n*/\n\n}"
  },
  {
    "path": "include/eigen3/doc/Manual.dox",
    "content": "\n// This file strutures pages and modules into a convenient hierarchical structure.\n\nnamespace Eigen {\n\n/** \\page UserManual_CustomizingEigen Extending/Customizing Eigen\n  %Eigen can be extended in several ways, for instance, by defining global methods, by inserting custom methods within main %Eigen's classes through the \\ref TopicCustomizing_Plugins \"plugin\" mechanism, by adding support to \\ref TopicCustomizing_CustomScalar \"custom scalar types\" etc. See below for the respective sub-topics.\n  - \\subpage TopicCustomizing_Plugins\n  - \\subpage TopicCustomizing_InheritingMatrix\n  - \\subpage TopicCustomizing_CustomScalar\n  - \\subpage TopicCustomizing_NullaryExpr\n  - \\subpage TopicNewExpressionType\n  \\sa \\ref TopicPreprocessorDirectives\n*/\n\n\n/** \\page UserManual_Generalities General topics\n  - \\subpage Eigen2ToEigen3\n  - \\subpage TopicFunctionTakingEigenTypes\n  - \\subpage TopicPreprocessorDirectives\n  - \\subpage TopicAssertions\n  - \\subpage TopicMultiThreading\n  - \\subpage TopicUsingBlasLapack\n  - \\subpage TopicUsingIntelMKL\n  - \\subpage TopicCUDA\n  - \\subpage TopicPitfalls\n  - \\subpage TopicTemplateKeyword\n  - \\subpage UserManual_UnderstandingEigen\n  - \\subpage TopicCMakeGuide\n*/\n\n/** \\page UserManual_UnderstandingEigen Understanding Eigen\n  - \\subpage TopicInsideEigenExample\n  - \\subpage TopicClassHierarchy\n  - \\subpage TopicLazyEvaluation\n*/\n\n/** \\page UnclassifiedPages Unclassified pages\n  - \\subpage TopicResizing\n  - \\subpage TopicVectorization\n  - \\subpage TopicEigenExpressionTemplates\n  - \\subpage TopicScalarTypes\n  - \\subpage GettingStarted\n  - \\subpage TutorialSparse_example_details\n  - \\subpage TopicWritingEfficientProductExpression\n  - \\subpage Experimental\n*/\n\n\n/** \\defgroup Support_modules Support modules\n  * Category of modules which add support for external libraries.\n  */\n\n\n/** \\defgroup DenseMatrixManipulation_chapter Dense matrix and array manipulation */\n/** \\defgroup DenseMatrixManipulation_Alignement Alignment issues */\n/** \\defgroup DenseMatrixManipulation_Reference Reference */\n\n/** \\addtogroup TutorialMatrixClass\n    \\ingroup DenseMatrixManipulation_chapter */\n/** \\addtogroup TutorialMatrixArithmetic\n    \\ingroup DenseMatrixManipulation_chapter */\n/** \\addtogroup TutorialArrayClass\n    \\ingroup DenseMatrixManipulation_chapter */\n/** \\addtogroup TutorialBlockOperations\n    \\ingroup DenseMatrixManipulation_chapter */\n/** \\addtogroup TutorialAdvancedInitialization\n    \\ingroup DenseMatrixManipulation_chapter */\n/** \\addtogroup TutorialReductionsVisitorsBroadcasting\n    \\ingroup DenseMatrixManipulation_chapter */\n/** \\addtogroup TutorialMapClass\n    \\ingroup DenseMatrixManipulation_chapter */\n/** \\addtogroup TutorialReshapeSlicing\n    \\ingroup DenseMatrixManipulation_chapter */\n/** \\addtogroup TopicAliasing\n    \\ingroup DenseMatrixManipulation_chapter */\n/** \\addtogroup TopicStorageOrders\n    \\ingroup DenseMatrixManipulation_chapter */\n    \n/** \\addtogroup DenseMatrixManipulation_Alignement\n    \\ingroup DenseMatrixManipulation_chapter */\n/** \\addtogroup TopicUnalignedArrayAssert\n    \\ingroup DenseMatrixManipulation_Alignement */\n/** \\addtogroup TopicFixedSizeVectorizable\n    \\ingroup DenseMatrixManipulation_Alignement */\n/** \\addtogroup TopicStructHavingEigenMembers\n    \\ingroup DenseMatrixManipulation_Alignement */\n/** \\addtogroup TopicStlContainers\n    \\ingroup DenseMatrixManipulation_Alignement */\n/** \\addtogroup TopicPassingByValue\n    \\ingroup DenseMatrixManipulation_Alignement */\n/** \\addtogroup TopicWrongStackAlignment\n    \\ingroup DenseMatrixManipulation_Alignement */\n    \n/** \\addtogroup DenseMatrixManipulation_Reference\n    \\ingroup DenseMatrixManipulation_chapter */\n/** \\addtogroup Core_Module\n    \\ingroup DenseMatrixManipulation_Reference */  \n/** \\addtogroup Jacobi_Module\n    \\ingroup DenseMatrixManipulation_Reference */ \n/** \\addtogroup Householder_Module\n    \\ingroup DenseMatrixManipulation_Reference */ \n\n/** \\addtogroup CoeffwiseMathFunctions\n    \\ingroup DenseMatrixManipulation_chapter */\n\n/** \\addtogroup QuickRefPage\n    \\ingroup DenseMatrixManipulation_chapter */\n\n\n/** \\defgroup DenseLinearSolvers_chapter Dense linear problems and decompositions */\n/** \\defgroup DenseLinearSolvers_Reference Reference */\n\n/** \\addtogroup TutorialLinearAlgebra\n    \\ingroup DenseLinearSolvers_chapter */\n/** \\addtogroup TopicLinearAlgebraDecompositions\n    \\ingroup DenseLinearSolvers_chapter */\n/** \\addtogroup LeastSquares \n    \\ingroup DenseLinearSolvers_chapter */\n/** \\addtogroup InplaceDecomposition\n    \\ingroup DenseLinearSolvers_chapter */\n/** \\addtogroup DenseDecompositionBenchmark\n    \\ingroup DenseLinearSolvers_chapter */\n\n/** \\addtogroup DenseLinearSolvers_Reference\n    \\ingroup DenseLinearSolvers_chapter */\n/** \\addtogroup Cholesky_Module\n    \\ingroup DenseLinearSolvers_Reference */\n/** \\addtogroup LU_Module\n    \\ingroup DenseLinearSolvers_Reference */\n/** \\addtogroup QR_Module\n    \\ingroup DenseLinearSolvers_Reference */\n/** \\addtogroup SVD_Module\n    \\ingroup DenseLinearSolvers_Reference*/\n/** \\addtogroup Eigenvalues_Module\n    \\ingroup DenseLinearSolvers_Reference */\n\n\n\n\n/** \\defgroup Sparse_chapter Sparse linear algebra */\n/** \\defgroup Sparse_Reference Reference */\n\n/** \\addtogroup TutorialSparse\n    \\ingroup Sparse_chapter */\n/** \\addtogroup TopicSparseSystems\n    \\ingroup Sparse_chapter */\n/** \\addtogroup MatrixfreeSolverExample\n    \\ingroup Sparse_chapter */\n\n/** \\addtogroup Sparse_Reference\n    \\ingroup Sparse_chapter */\n/** \\addtogroup SparseCore_Module\n    \\ingroup Sparse_Reference */\n/** \\addtogroup OrderingMethods_Module\n    \\ingroup Sparse_Reference */\n/** \\addtogroup SparseCholesky_Module\n    \\ingroup Sparse_Reference */\n/** \\addtogroup SparseLU_Module\n    \\ingroup Sparse_Reference */\n/** \\addtogroup SparseQR_Module\n    \\ingroup Sparse_Reference */\n/** \\addtogroup IterativeLinearSolvers_Module\n    \\ingroup Sparse_Reference */\n/** \\addtogroup Sparse_Module\n    \\ingroup Sparse_Reference */\n/** \\addtogroup Support_modules\n    \\ingroup Sparse_Reference */    \n\n/** \\addtogroup SparseQuickRefPage\n    \\ingroup Sparse_chapter */\n\n\n/** \\defgroup Geometry_chapter Geometry */\n/** \\defgroup Geometry_Reference Reference */\n\n/** \\addtogroup TutorialGeometry\n    \\ingroup Geometry_chapter */\n    \n/** \\addtogroup Geometry_Reference\n    \\ingroup Geometry_chapter */\n/** \\addtogroup Geometry_Module\n    \\ingroup Geometry_Reference */\n/** \\addtogroup Splines_Module\n    \\ingroup Geometry_Reference */\n\n/** \\internal \\brief Namespace containing low-level routines from the %Eigen library. */\nnamespace internal {}\n}\n"
  },
  {
    "path": "include/eigen3/doc/MatrixfreeSolverExample.dox",
    "content": "\nnamespace Eigen {\n\n/**\n\n\\eigenManualPage MatrixfreeSolverExample Matrix-free solvers\n\nIterative solvers such as ConjugateGradient and BiCGSTAB can be used in a matrix free context. To this end, user must provide a wrapper class inheriting EigenBase<> and implementing the following methods:\n - \\c Index \\c rows() and \\c Index \\c cols(): returns number of rows and columns respectively\n - \\c operator* with your type and an %Eigen dense column vector (its actual implementation goes in a specialization of the internal::generic_product_impl class)\n\n\\c Eigen::internal::traits<> must also be specialized for the wrapper type.\n\nHere is a complete example wrapping an Eigen::SparseMatrix:\n\\include matrixfree_cg.cpp\nOutput: \\verbinclude matrixfree_cg.out\n\n*/\n\n}"
  },
  {
    "path": "include/eigen3/doc/NewExpressionType.dox",
    "content": "namespace Eigen {\n\n/** \\page TopicNewExpressionType Adding a new expression type\n\n<!--<span style=\"font-size:130%; color:red; font-weight: 900;\"></span>-->\n\\warning\nDisclaimer: this page is tailored to very advanced users who are not afraid of dealing with some %Eigen's internal aspects.\nIn most cases, a custom expression can be avoided by either using custom \\ref MatrixBase::unaryExpr \"unary\" or \\ref MatrixBase::binaryExpr \"binary\" functors,\nwhile extremely complex matrix manipulations can be achieved by a nullary functors as described in the \\ref TopicCustomizing_NullaryExpr \"previous page\".\n\nThis page describes with the help of an example how to implement a new\nlight-weight expression type in %Eigen. This consists of three parts:\nthe expression type itself, a traits class containing compile-time\ninformation about the expression, and the evaluator class which is\nused to evaluate the expression to a matrix.\n\n\\b TO \\b DO: Write a page explaining the design, with details on\nvectorization etc., and refer to that page here.\n\n\n\\eigenAutoToc\n\n\\section TopicSetting The setting\n\nA circulant matrix is a matrix where each column is the same as the\ncolumn to the left, except that it is cyclically shifted downwards.\nFor example, here is a 4-by-4 circulant matrix:\n\\f[ \\begin{bmatrix} \n    1 & 8 & 4 & 2 \\\\ \n    2 & 1 & 8 & 4 \\\\\n    4 & 2 & 1 & 8 \\\\\n    8 & 4 & 2 & 1\n\\end{bmatrix} \\f]\nA circulant matrix is uniquely determined by its first column. We wish\nto write a function \\c makeCirculant which, given the first column,\nreturns an expression representing the circulant matrix.\n\nFor simplicity, we restrict the \\c makeCirculant function to dense\nmatrices. It may make sense to also allow arrays, or sparse matrices,\nbut we will not do so here. We also do not want to support\nvectorization.\n\n\n\\section TopicPreamble Getting started\n\nWe will present the file implementing the \\c makeCirculant function\npart by part. We start by including the appropriate header files and\nforward declaring the expression class, which we will call\n\\c Circulant. The \\c makeCirculant function will return an object of\nthis type. The class \\c Circulant is in fact a class template; the\ntemplate argument \\c ArgType refers to the type of the vector passed\nto the \\c makeCirculant function.\n\n\\include make_circulant.cpp.preamble\n\n\n\\section TopicTraits The traits class\n\nFor every expression class \\c X, there should be a traits class \n\\c Traits<X> in the \\c Eigen::internal namespace containing\ninformation about \\c X known as compile time.\n\nAs explained in \\ref TopicSetting, we designed the \\c Circulant\nexpression class to refer to dense matrices. The entries of the\ncirculant matrix have the same type as the entries of the vector\npassed to the \\c makeCirculant function. The type used to index the\nentries is also the same. Again for simplicity, we will only return\ncolumn-major matrices. Finally, the circulant matrix is a square\nmatrix (number of rows equals number of columns), and the number of\nrows equals the number of rows of the column vector passed to the\n\\c makeCirculant function. If this is a dynamic-size vector, then the\nsize of the circulant matrix is not known at compile-time.\n\nThis leads to the following code:\n\n\\include make_circulant.cpp.traits\n\n\n\\section TopicExpression The expression class\n\nThe next step is to define the expression class itself. In our case,\nwe want to inherit from \\c MatrixBase in order to expose the interface\nfor dense matrices. In the constructor, we check that we are passed a\ncolumn vector (see \\ref TopicAssertions) and we store the vector from\nwhich we are going to build the circulant matrix in the member\nvariable \\c m_arg. Finally, the expression class should compute the\nsize of the corresponding circulant matrix. As explained above, this\nis a square matrix with as many columns as the vector used to\nconstruct the matrix.\n\n\\b TO \\b DO: What about the \\c Nested typedef? It seems to be\nnecessary; is this only temporary?\n\n\\include make_circulant.cpp.expression\n\n\n\\section TopicEvaluator The evaluator\n\nThe last big fragment implements the evaluator for the \\c Circulant\nexpression. The evaluator computes the entries of the circulant\nmatrix; this is done in the \\c .coeff() member function. The entries\nare computed by finding the corresponding entry of the vector from\nwhich the circulant matrix is constructed. Getting this entry may\nactually be non-trivial when the circulant matrix is constructed from\na vector which is given by a complicated expression, so we use the\nevaluator which corresponds to the vector.\n\nThe \\c CoeffReadCost constant records the cost of computing an entry\nof the circulant matrix; we ignore the index computation and say that\nthis is the same as the cost of computing an entry of the vector from\nwhich the circulant matrix is constructed.\n\nIn the constructor, we save the evaluator for the column vector which\ndefined the circulant matrix. We also save the size of that vector;\nremember that we can query an expression object to find the size but\nnot the evaluator. \n\n\\include make_circulant.cpp.evaluator\n\n\n\\section TopicEntry The entry point\n\nAfter all this, the \\c makeCirculant function is very simple. It\nsimply creates an expression object and returns it.\n\n\\include make_circulant.cpp.entry\n\n\n\\section TopicMain A simple main function for testing\n\nFinally, a short \\c main function that shows how the \\c makeCirculant\nfunction can be called.\n\n\\include make_circulant.cpp.main\n\nIf all the fragments are combined, the following output is produced,\nshowing that the program works as expected:\n\n\\include make_circulant.out\n\n*/\n}\n\n"
  },
  {
    "path": "include/eigen3/doc/Overview.dox",
    "content": "namespace Eigen {\n\n/** \\mainpage notitle\n\nThis is the API documentation for Eigen3. You can <a href=\"eigen-doc.tgz\">download</a> it as a tgz archive for offline reading.\n\nYou're already an Eigen2 user? Here is a \\link Eigen2ToEigen3 Eigen2 to Eigen3 guide \\endlink to help porting your application.\n\nFor a first contact with Eigen, the best place is to have a look at the \\link GettingStarted getting started \\endlink page that show you how to write and compile your first program with Eigen.\n\nThen, the \\b quick \\b reference \\b pages give you a quite complete description of the API in a very condensed format that is specially useful to recall the syntax of a particular feature, or to have a quick look at the API. They currently cover the two following feature sets, and more will come in the future:\n  - \\link QuickRefPage [QuickRef] Dense matrix and array manipulations \\endlink\n  - \\link SparseQuickRefPage [QuickRef] Sparse linear algebra \\endlink\n\nYou're a MatLab user? There is also a <a href=\"AsciiQuickReference.txt\">short ASCII reference</a> with Matlab translations.\n  \nThe \\b main \\b documentation is organized into \\em chapters covering different domains of features.\nThey are themselves composed of \\em user \\em manual pages describing the different features in a comprehensive way, and \\em reference pages that gives you access to the API documentation through the related Eigen's \\em modules and \\em classes.\n\nUnder the \\subpage UserManual_CustomizingEigen section, you will find discussions and examples on extending %Eigen's features and supporting custom scalar types.\n\nUnder the \\subpage UserManual_Generalities section, you will find documentation on more general topics such as preprocessor directives, controlling assertions, multi-threading, MKL support, some Eigen's internal insights, and much more...\n\nFinally, do not miss the search engine, useful to quickly get to the documentation of a given class or function.\n\nWant more? Checkout the <a href=\"unsupported/index.html\">\\em unsupported \\em modules </a> documentation.\n\n*/\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/PassingByValue.dox",
    "content": "namespace Eigen {\n\n/** \\eigenManualPage TopicPassingByValue Passing Eigen objects by value to functions\n\nPassing objects by value is almost always a very bad idea in C++, as this means useless copies, and one should pass them by reference instead.\n\nWith Eigen, this is even more important: passing \\ref TopicFixedSizeVectorizable \"fixed-size vectorizable Eigen objects\" by value is not only inefficient, it can be illegal or make your program crash! And the reason is that these Eigen objects have alignment modifiers that aren't respected when they are passed by value.\n\nSo for example, a function like this, where v is passed by value:\n\n\\code\nvoid my_function(Eigen::Vector2d v);\n\\endcode\n\nneeds to be rewritten as follows, passing v by reference:\n\n\\code\nvoid my_function(const Eigen::Vector2d& v);\n\\endcode\n\nLikewise if you have a class having a Eigen object as member:\n\n\\code\nstruct Foo\n{\n  Eigen::Vector2d v;\n};\nvoid my_function(Foo v);\n\\endcode\n\nThis function also needs to be rewritten like this:\n\\code\nvoid my_function(const Foo& v);\n\\endcode\n\nNote that on the other hand, there is no problem with functions that return objects by value.\n\n*/\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/Pitfalls.dox",
    "content": "namespace Eigen {\n\n/** \\page TopicPitfalls Common pitfalls\n\n\n\\section TopicPitfalls_template_keyword Compilation error with template methods\n\nSee this \\link TopicTemplateKeyword page \\endlink.\n\n\\section TopicPitfalls_aliasing Aliasing\n\nDon't miss this \\link TopicAliasing page \\endlink on aliasing,\nespecially if you got wrong results in statements where the destination appears on the right hand side of the expression.\n\n\\section TopicPitfalls_auto_keyword C++11 and the auto keyword\n\nIn short: do not use the auto keywords with Eigen's expressions, unless you are 100% sure about what you are doing. In particular, do not use the auto keyword as a replacement for a Matrix<> type. Here is an example:\n\n\\code\nMatrixXd A, B;\nauto C = A*B;\nfor(...) { ... w = C * v;  ...}\n\\endcode\n\nIn this example, the type of C is not a MatrixXd but an abstract expression representing a matrix product and storing references to A and B. Therefore, the product of A*B will be carried out multiple times, once per iteration of the for loop. Moreover, if the coefficients of A or B change during the iteration, then C will evaluate to different values.\n\nHere is another example leading to a segfault:\n\\code\nauto C = ((A+B).eval()).transpose();\n// do something with C\n\\endcode\nThe problem is that eval() returns a temporary object (in this case a MatrixXd) which is then referenced by the Transpose<> expression. However, this temporary is deleted right after the first line, and there the C expression reference a dead object. The same issue might occur when sub expressions are automatically evaluated by Eigen as in the following example:\n\\code\nVectorXd u, v;\nauto C = u + (A*v).normalized();\n// do something with C\n\\endcode\nwhere the normalized() method has to evaluate the expensive product A*v to avoid evaluating it twice. On the other hand, the following example is perfectly fine:\n\\code\nauto C = (u + (A*v).normalized()).eval();\n\\endcode\nIn this case, C will be a regular VectorXd object.\n*/\n}\n"
  },
  {
    "path": "include/eigen3/doc/PreprocessorDirectives.dox",
    "content": "namespace Eigen {\n\n/** \\page TopicPreprocessorDirectives Preprocessor directives\n\nYou can control some aspects of %Eigen by defining the preprocessor tokens using \\c \\#define. These macros\nshould be defined before any %Eigen headers are included. Often they are best set in the project options.\n\nThis page lists the preprocessor tokens recognized by %Eigen.\n\n\\eigenAutoToc\n\n\n\\section TopicPreprocessorDirectivesMajor Macros with major effects\n\nThese macros have a major effect and typically break the API (Application Programming Interface) and/or the\nABI (Application Binary Interface). This can be rather dangerous: if parts of your program are compiled with\none option, and other parts (or libraries that you use) are compiled with another option, your program may\nfail to link or exhibit subtle bugs. Nevertheless, these options can be useful for people who know what they\nare doing.\n\n - \\b EIGEN2_SUPPORT and \\b EIGEN2_SUPPORT_STAGEnn_xxx are disabled starting from the 3.3 release.\n   Defining one of these will raise a compile-error. If you need to compile Eigen2 code,\n   <a href=\"http://eigen.tuxfamily.org/index.php?title=Eigen2\">check this site</a>.\n - \\b EIGEN_DEFAULT_DENSE_INDEX_TYPE - the type for column and row indices in matrices, vectors and array\n   (DenseBase::Index). Set to \\c std::ptrdiff_t by default.\n - \\b EIGEN_DEFAULT_IO_FORMAT - the IOFormat to use when printing a matrix if no %IOFormat is specified.\n   Defaults to the %IOFormat constructed by the default constructor IOFormat::IOFormat().\n - \\b EIGEN_INITIALIZE_MATRICES_BY_ZERO - if defined, all entries of newly constructed matrices and arrays are\n   initialized to zero, as are new entries in matrices and arrays after resizing. Not defined by default.\n   \\warning The unary (resp. binary) constructor of \\c 1x1 (resp. \\c 2x1 or \\c 1x2) fixed size matrices is\n   always interpreted as an initialization constructor where the argument(s) are the coefficient values\n   and not the sizes. For instance, \\code Vector2d v(2,1); \\endcode will create a vector with coeficients [2,1],\n   and \\b not a \\c 2x1 vector initialized with zeros (i.e., [0,0]). If such cases might occur, then it is\n   recommended to use the default constructor with a explicit call to resize:\n   \\code\n   Matrix<?,SizeAtCompileTime,1> v;\n   v.resize(size);\n   Matrix<?,RowsAtCompileTime,ColsAtCompileTime> m;\n   m.resize(rows,cols);\n   \\endcode\n - \\b EIGEN_INITIALIZE_MATRICES_BY_NAN - if defined, all entries of newly constructed matrices and arrays are\n   initialized to NaN, as are new entries in matrices and arrays after resizing. This option is especially\n   useful for debugging purpose, though a memory tool like <a href=\"http://valgrind.org/\">valgrind</a> is\n   preferable. Not defined by default.\n   \\warning See the documentation of \\c EIGEN_INITIALIZE_MATRICES_BY_ZERO for a discussion on a limitations\n   of these macros when applied to \\c 1x1, \\c 1x2, and \\c 2x1 fixed-size matrices.\n - \\b EIGEN_NO_AUTOMATIC_RESIZING - if defined, the matrices (or arrays) on both sides of an assignment \n   <tt>a = b</tt> have to be of the same size; otherwise, %Eigen automatically resizes \\c a so that it is of\n   the correct size. Not defined by default.\n\n\n\\section TopicPreprocessorDirectivesCppVersion C++ standard features\n\nBy default, %Eigen strive to automatically detect and enable langage features at compile-time based on\nthe information provided by the compiler.\n\n - \\b EIGEN_MAX_CPP_VER - disables usage of C++ features requiring a version greater than EIGEN_MAX_CPP_VER.\n   Possible values are: 03, 11, 14, 17, etc. If not defined (the default), %Eigen enables all features supported\n   by the compiler.\n\nIndividual features can be explicitly enabled or disabled by defining the following token to 0 or 1 respectively.\nFor instance, one might limit the C++ version to C++03 by defining EIGEN_MAX_CPP_VER=03, but still enable C99 math\nfunctions by defining EIGEN_HAS_C99_MATH=1.\n\n - \\b EIGEN_HAS_C99_MATH - controls the usage of C99 math functions such as erf, erfc, lgamma, etc.\n   Automatic detection disabled if EIGEN_MAX_CPP_VER<11.\n - \\b EIGEN_HAS_CXX11_MATH - controls the implementation of some functions such as round, logp1, isinf, isnan, etc.\n   Automatic detection disabled if EIGEN_MAX_CPP_VER<11.\n - \\b EIGEN_HAS_RVALUE_REFERENCES - defines whetehr rvalue references are supported\n   Automatic detection disabled if EIGEN_MAX_CPP_VER<11.\n - \\b EIGEN_HAS_STD_RESULT_OF - defines whether std::result_of is supported\n   Automatic detection disabled if EIGEN_MAX_CPP_VER<11.\n - \\b EIGEN_HAS_VARIADIC_TEMPLATES - defines whether variadic templates are supported\n   Automatic detection disabled if EIGEN_MAX_CPP_VER<11.\n - \\b EIGEN_HAS_CONSTEXPR - defines whether relaxed const expression are supported\n   Automatic detection disabled if EIGEN_MAX_CPP_VER<14.\n - \\b EIGEN_HAS_CXX11_CONTAINERS - defines whether STL's containers follows C++11 specifications\n   Automatic detection disabled if EIGEN_MAX_CPP_VER<11.\n - \\b EIGEN_HAS_CXX11_NOEXCEPT - defines whether noexcept is supported\n   Automatic detection disabled if EIGEN_MAX_CPP_VER<11.\n\n\\section TopicPreprocessorDirectivesAssertions Assertions\n\nThe %Eigen library contains many assertions to guard against programming errors, both at compile time and at\nrun time. However, these assertions do cost time and can thus be turned off.\n\n - \\b EIGEN_NO_DEBUG - disables %Eigen's assertions if defined. Not defined by default, unless the\n   \\c NDEBUG macro is defined (this is a standard C++ macro which disables all asserts). \n - \\b EIGEN_NO_STATIC_ASSERT - if defined, compile-time static assertions are replaced by runtime assertions; \n   this saves compilation time. Not defined by default.\n - \\b eigen_assert - macro with one argument that is used inside %Eigen for assertions. By default, it is\n   basically defined to be \\c assert, which aborts the program if the assertion is violated. Redefine this\n   macro if you want to do something else, like throwing an exception.\n - \\b EIGEN_MPL2_ONLY - disable non MPL2 compatible features, or in other words disable the features which\n   are still under the LGPL.\n\n\n\\section TopicPreprocessorDirectivesPerformance Alignment, vectorization and performance tweaking\n\n - \\b \\c EIGEN_MALLOC_ALREADY_ALIGNED - Can be set to 0 or 1 to tell whether default system \\c malloc already\n   returns aligned buffers. In not defined, then this information is automatically deduced from the compiler\n   and system preprocessor tokens.\n - \\b \\c EIGEN_MAX_ALIGN_BYTES - Must be a power of two, or 0. Defines an upper bound on the memory boundary in bytes on which dynamically and statically allocated data may be aligned by %Eigen. If not defined, a default value is automatically computed based on architecture, compiler, and OS.\n This option is typically used to enforce binary compatibility between code/libraries compiled with different SIMD options. For instance, one may compile AVX code and enforce ABI compatibility with existing SSE code by defining \\c EIGEN_MAX_ALIGN_BYTES=16. In the other way round, since by default AVX implies 32 bytes alignment for best performance, one can compile SSE code to be ABI compatible with AVX code by defining \\c EIGEN_MAX_ALIGN_BYTES=32.\n - \\b \\c EIGEN_MAX_STATIC_ALIGN_BYTES - Same as \\c EIGEN_MAX_ALIGN_BYTES but for statically allocated data only. By default, if only  \\c EIGEN_MAX_ALIGN_BYTES is defined, then \\c EIGEN_MAX_STATIC_ALIGN_BYTES == \\c EIGEN_MAX_ALIGN_BYTES, otherwise a default value is automatically computed based on architecture, compiler, and OS (can be smaller than the default value of EIGEN_MAX_ALIGN_BYTES on architectures that do not support stack alignment).\n Let us emphasize that \\c EIGEN_MAX_*_ALIGN_BYTES define only a diserable upper bound. In practice data is aligned to largest power-of-two common divisor of \\c EIGEN_MAX_STATIC_ALIGN_BYTES and the size of the data, such that memory is not wasted.\n - \\b \\c EIGEN_DONT_PARALLELIZE - if defined, this disables multi-threading. This is only relevant if you enabled OpenMP.\n   See \\ref TopicMultiThreading for details.\n - \\b EIGEN_DONT_VECTORIZE - disables explicit vectorization when defined. Not defined by default, unless \n   alignment is disabled by %Eigen's platform test or the user defining \\c EIGEN_DONT_ALIGN.\n - \\b \\c EIGEN_UNALIGNED_VECTORIZE - disables/enables vectorization with unaligned stores. Default is 1 (enabled).\n   If set to 0 (disabled), then expression for which the destination cannot be aligned are not vectorized (e.g., unaligned\n   small fixed size vectors or matrices)\n - \\b \\c EIGEN_FAST_MATH - enables some optimizations which might affect the accuracy of the result. This currently\n   enables the SSE vectorization of sin() and cos(), and speedups sqrt() for single precision. Defined to 1 by default.\n   Define it to 0 to disable.\n - \\b \\c EIGEN_UNROLLING_LIMIT - defines the size of a loop to enable meta unrolling. Set it to zero to disable\n   unrolling. The size of a loop here is expressed in %Eigen's own notion of \"number of FLOPS\", it does not\n   correspond to the number of iterations or the number of instructions. The default is value 100.\n - \\b \\c EIGEN_STACK_ALLOCATION_LIMIT - defines the maximum bytes for a buffer to be allocated on the stack. For internal\n   temporary buffers, dynamic memory allocation is employed as a fall back. For fixed-size matrices or arrays, exceeding\n   this threshold raises a compile time assertion. Use 0 to set no limit. Default is 128 KB.\n - \\b \\c EIGEN_STRONG_INLINE - This macro is used to qualify critical functions and methods that we expect the compiler to inline.\n   By default it is defined to \\c __forceinline for MSVC and ICC, and to \\c inline for other compilers. A tipical usage is to\n   define it to \\c inline for MSVC users wanting faster compilation times, at the risk of performance degradations in some rare\n   cases for which MSVC inliner fails to do a good job.\n\n\n - \\c EIGEN_DONT_ALIGN - Deprecated, it is a synonym for \\c EIGEN_MAX_ALIGN_BYTES=0. It disables alignment completely. %Eigen will not try to align its objects and does not expect that any objects passed to it are aligned. This will turn off vectorization if \\b EIGEN_UNALIGNED_VECTORIZE=1. Not defined by default.\n - \\c EIGEN_DONT_ALIGN_STATICALLY - Deprecated, it is a synonym for \\c EIGEN_MAX_STATIC_ALIGN_BYTES=0. It disables alignment of arrays on the stack. Not defined by default, unless \\c EIGEN_DONT_ALIGN is defined.\n\n\n\\section TopicPreprocessorDirectivesPlugins Plugins\n\nIt is possible to add new methods to many fundamental classes in %Eigen by writing a plugin. As explained in\nthe section \\ref TopicCustomizing_Plugins, the plugin is specified by defining a \\c EIGEN_xxx_PLUGIN macro. The\nfollowing macros are supported; none of them are defined by default.\n\n - \\b EIGEN_ARRAY_PLUGIN - filename of plugin for extending the Array class.\n - \\b EIGEN_ARRAYBASE_PLUGIN - filename of plugin for extending the ArrayBase class.\n - \\b EIGEN_CWISE_PLUGIN - filename of plugin for extending the Cwise class.\n - \\b EIGEN_DENSEBASE_PLUGIN - filename of plugin for extending the DenseBase class.\n - \\b EIGEN_DYNAMICSPARSEMATRIX_PLUGIN - filename of plugin for extending the DynamicSparseMatrix class.\n - \\b EIGEN_MATRIX_PLUGIN - filename of plugin for extending the Matrix class.\n - \\b EIGEN_MATRIXBASE_PLUGIN - filename of plugin for extending the MatrixBase class.\n - \\b EIGEN_PLAINOBJECTBASE_PLUGIN - filename of plugin for extending the PlainObjectBase class.\n - \\b EIGEN_MAPBASE_PLUGIN - filename of plugin for extending the MapBase class.\n - \\b EIGEN_QUATERNION_PLUGIN - filename of plugin for extending the Quaternion class.\n - \\b EIGEN_QUATERNIONBASE_PLUGIN - filename of plugin for extending the QuaternionBase class.\n - \\b EIGEN_SPARSEMATRIX_PLUGIN - filename of plugin for extending the SparseMatrix class.\n - \\b EIGEN_SPARSEMATRIXBASE_PLUGIN - filename of plugin for extending the SparseMatrixBase class.\n - \\b EIGEN_SPARSEVECTOR_PLUGIN - filename of plugin for extending the SparseVector class.\n - \\b EIGEN_TRANSFORM_PLUGIN - filename of plugin for extending the Transform class.\n - \\b EIGEN_FUNCTORS_PLUGIN - filename of plugin for adding new functors and specializations of functor_traits.\n\n\n\\section TopicPreprocessorDirectivesDevelopers Macros for Eigen developers\n\nThese macros are mainly meant for people developing %Eigen and for testing purposes. Even though, they might be useful for power users and the curious for debugging and testing purpose, they \\b should \\b not \\b be \\b used by real-word code.\n\n - \\b EIGEN_DEFAULT_TO_ROW_MAJOR - when defined, the default storage order for matrices becomes row-major\n   instead of column-major. Not defined by default.\n - \\b EIGEN_INTERNAL_DEBUGGING - if defined, enables assertions in %Eigen's internal routines. This is useful\n   for debugging %Eigen itself. Not defined by default.\n - \\b EIGEN_NO_MALLOC - if defined, any request from inside the %Eigen to allocate memory from the heap\n   results in an assertion failure. This is useful to check that some routine does not allocate memory\n   dynamically. Not defined by default.\n - \\b EIGEN_RUNTIME_NO_MALLOC - if defined, a new switch is introduced which can be turned on and off by\n   calling <tt>set_is_malloc_allowed(bool)</tt>. If malloc is not allowed and %Eigen tries to allocate memory\n   dynamically anyway, an assertion failure results. Not defined by default.\n\n*/\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/QuickReference.dox",
    "content": "namespace Eigen {\n\n/** \\eigenManualPage QuickRefPage Quick reference guide\n\n\\eigenAutoToc\n\n<hr>\n\n<a href=\"#\" class=\"top\">top</a>\n\\section QuickRef_Headers Modules and Header files\n\nThe Eigen library is divided in a Core module and several additional modules. Each module has a corresponding header file which has to be included in order to use the module. The \\c %Dense and \\c Eigen header files are provided to conveniently gain access to several modules at once.\n\n<table class=\"manual\">\n<tr><th>Module</th><th>Header file</th><th>Contents</th></tr>\n<tr            ><td>\\link Core_Module Core \\endlink</td><td>\\code#include <Eigen/Core>\\endcode</td><td>Matrix and Array classes, basic linear algebra (including triangular and selfadjoint products), array manipulation</td></tr>\n<tr class=\"alt\"><td>\\link Geometry_Module Geometry \\endlink</td><td>\\code#include <Eigen/Geometry>\\endcode</td><td>Transform, Translation, Scaling, Rotation2D and 3D rotations (Quaternion, AngleAxis)</td></tr>\n<tr            ><td>\\link LU_Module LU \\endlink</td><td>\\code#include <Eigen/LU>\\endcode</td><td>Inverse, determinant, LU decompositions with solver (FullPivLU, PartialPivLU)</td></tr>\n<tr class=\"alt\"><td>\\link Cholesky_Module Cholesky \\endlink</td><td>\\code#include <Eigen/Cholesky>\\endcode</td><td>LLT and LDLT Cholesky factorization with solver</td></tr>\n<tr            ><td>\\link Householder_Module Householder \\endlink</td><td>\\code#include <Eigen/Householder>\\endcode</td><td>Householder transformations; this module is used by several linear algebra modules</td></tr>\n<tr class=\"alt\"><td>\\link SVD_Module SVD \\endlink</td><td>\\code#include <Eigen/SVD>\\endcode</td><td>SVD decompositions with least-squares solver (JacobiSVD, BDCSVD)</td></tr>\n<tr            ><td>\\link QR_Module QR \\endlink</td><td>\\code#include <Eigen/QR>\\endcode</td><td>QR decomposition with solver (HouseholderQR, ColPivHouseholderQR, FullPivHouseholderQR)</td></tr>\n<tr class=\"alt\"><td>\\link Eigenvalues_Module Eigenvalues \\endlink</td><td>\\code#include <Eigen/Eigenvalues>\\endcode</td><td>Eigenvalue, eigenvector decompositions (EigenSolver, SelfAdjointEigenSolver, ComplexEigenSolver)</td></tr>\n<tr            ><td>\\link Sparse_Module Sparse \\endlink</td><td>\\code#include <Eigen/Sparse>\\endcode</td><td>%Sparse matrix storage and related basic linear algebra (SparseMatrix, SparseVector) \\n (see \\ref SparseQuickRefPage for details on sparse modules)</td></tr>\n<tr class=\"alt\"><td></td><td>\\code#include <Eigen/Dense>\\endcode</td><td>Includes Core, Geometry, LU, Cholesky, SVD, QR, and Eigenvalues header files</td></tr>\n<tr            ><td></td><td>\\code#include <Eigen/Eigen>\\endcode</td><td>Includes %Dense and %Sparse header files (the whole Eigen library)</td></tr>\n</table>\n\n<a href=\"#\" class=\"top\">top</a>\n\\section QuickRef_Types Array, matrix and vector types\n\n\n\\b Recall: Eigen provides two kinds of dense objects: mathematical matrices and vectors which are both represented by the template class Matrix, and general 1D and 2D arrays represented by the template class Array:\n\\code\ntypedef Matrix<Scalar, RowsAtCompileTime, ColsAtCompileTime, Options> MyMatrixType;\ntypedef Array<Scalar, RowsAtCompileTime, ColsAtCompileTime, Options> MyArrayType;\n\\endcode\n\n\\li \\c Scalar is the scalar type of the coefficients (e.g., \\c float, \\c double, \\c bool, \\c int, etc.).\n\\li \\c RowsAtCompileTime and \\c ColsAtCompileTime are the number of rows and columns of the matrix as known at compile-time or \\c Dynamic.\n\\li \\c Options can be \\c ColMajor or \\c RowMajor, default is \\c ColMajor. (see class Matrix for more options)\n\nAll combinations are allowed: you can have a matrix with a fixed number of rows and a dynamic number of columns, etc. The following are all valid:\n\\code\nMatrix<double, 6, Dynamic>                  // Dynamic number of columns (heap allocation)\nMatrix<double, Dynamic, 2>                  // Dynamic number of rows (heap allocation)\nMatrix<double, Dynamic, Dynamic, RowMajor>  // Fully dynamic, row major (heap allocation)\nMatrix<double, 13, 3>                       // Fully fixed (usually allocated on stack)\n\\endcode\n\nIn most cases, you can simply use one of the convenience typedefs for \\ref matrixtypedefs \"matrices\" and \\ref arraytypedefs \"arrays\". Some examples:\n<table class=\"example\">\n<tr><th>Matrices</th><th>Arrays</th></tr>\n<tr><td>\\code\nMatrix<float,Dynamic,Dynamic>   <=>   MatrixXf\nMatrix<double,Dynamic,1>        <=>   VectorXd\nMatrix<int,1,Dynamic>           <=>   RowVectorXi\nMatrix<float,3,3>               <=>   Matrix3f\nMatrix<float,4,1>               <=>   Vector4f\n\\endcode</td><td>\\code\nArray<float,Dynamic,Dynamic>    <=>   ArrayXXf\nArray<double,Dynamic,1>         <=>   ArrayXd\nArray<int,1,Dynamic>            <=>   RowArrayXi\nArray<float,3,3>                <=>   Array33f\nArray<float,4,1>                <=>   Array4f\n\\endcode</td></tr>\n</table>\n\nConversion between the matrix and array worlds:\n\\code\nArray44f a1, a1;\nMatrix4f m1, m2;\nm1 = a1 * a2;                     // coeffwise product, implicit conversion from array to matrix.\na1 = m1 * m2;                     // matrix product, implicit conversion from matrix to array.\na2 = a1 + m1.array();             // mixing array and matrix is forbidden\nm2 = a1.matrix() + m1;            // and explicit conversion is required.\nArrayWrapper<Matrix4f> m1a(m1);   // m1a is an alias for m1.array(), they share the same coefficients\nMatrixWrapper<Array44f> a1m(a1);\n\\endcode\n\nIn the rest of this document we will use the following symbols to emphasize the features which are specifics to a given kind of object:\n\\li <a name=\"matrixonly\"></a>\\matrixworld linear algebra matrix and vector only\n\\li <a name=\"arrayonly\"></a>\\arrayworld array objects only\n\n\\subsection QuickRef_Basics Basic matrix manipulation\n\n<table class=\"manual\">\n<tr><th></th><th>1D objects</th><th>2D objects</th><th>Notes</th></tr>\n<tr><td>Constructors</td>\n<td>\\code\nVector4d  v4;\nVector2f  v1(x, y);\nArray3i   v2(x, y, z);\nVector4d  v3(x, y, z, w);\n\nVectorXf  v5; // empty object\nArrayXf   v6(size);\n\\endcode</td><td>\\code\nMatrix4f  m1;\n\n\n\n\nMatrixXf  m5; // empty object\nMatrixXf  m6(nb_rows, nb_columns);\n\\endcode</td><td class=\"note\">\nBy default, the coefficients \\n are left uninitialized</td></tr>\n<tr class=\"alt\"><td>Comma initializer</td>\n<td>\\code\nVector3f  v1;     v1 << x, y, z;\nArrayXf   v2(4);  v2 << 1, 2, 3, 4;\n\n\\endcode</td><td>\\code\nMatrix3f  m1;   m1 << 1, 2, 3,\n                      4, 5, 6,\n                      7, 8, 9;\n\\endcode</td><td></td></tr>\n\n<tr><td>Comma initializer (bis)</td>\n<td colspan=\"2\">\n\\include Tutorial_commainit_02.cpp\n</td>\n<td>\noutput:\n\\verbinclude Tutorial_commainit_02.out\n</td>\n</tr>\n\n<tr class=\"alt\"><td>Runtime info</td>\n<td>\\code\nvector.size();\n\nvector.innerStride();\nvector.data();\n\\endcode</td><td>\\code\nmatrix.rows();          matrix.cols();\nmatrix.innerSize();     matrix.outerSize();\nmatrix.innerStride();   matrix.outerStride();\nmatrix.data();\n\\endcode</td><td class=\"note\">Inner/Outer* are storage order dependent</td></tr>\n<tr><td>Compile-time info</td>\n<td colspan=\"2\">\\code\nObjectType::Scalar              ObjectType::RowsAtCompileTime\nObjectType::RealScalar          ObjectType::ColsAtCompileTime\nObjectType::Index               ObjectType::SizeAtCompileTime\n\\endcode</td><td></td></tr>\n<tr class=\"alt\"><td>Resizing</td>\n<td>\\code\nvector.resize(size);\n\n\nvector.resizeLike(other_vector);\nvector.conservativeResize(size);\n\\endcode</td><td>\\code\nmatrix.resize(nb_rows, nb_cols);\nmatrix.resize(Eigen::NoChange, nb_cols);\nmatrix.resize(nb_rows, Eigen::NoChange);\nmatrix.resizeLike(other_matrix);\nmatrix.conservativeResize(nb_rows, nb_cols);\n\\endcode</td><td class=\"note\">no-op if the new sizes match,<br/>otherwise data are lost<br/><br/>resizing with data preservation</td></tr>\n\n<tr><td>Coeff access with \\n range checking</td>\n<td>\\code\nvector(i)     vector.x()\nvector[i]     vector.y()\n              vector.z()\n              vector.w()\n\\endcode</td><td>\\code\nmatrix(i,j)\n\\endcode</td><td class=\"note\">Range checking is disabled if \\n NDEBUG or EIGEN_NO_DEBUG is defined</td></tr>\n\n<tr class=\"alt\"><td>Coeff access without \\n range checking</td>\n<td>\\code\nvector.coeff(i)\nvector.coeffRef(i)\n\\endcode</td><td>\\code\nmatrix.coeff(i,j)\nmatrix.coeffRef(i,j)\n\\endcode</td><td></td></tr>\n\n<tr><td>Assignment/copy</td>\n<td colspan=\"2\">\\code\nobject = expression;\nobject_of_float = expression_of_double.cast<float>();\n\\endcode</td><td class=\"note\">the destination is automatically resized (if possible)</td></tr>\n\n</table>\n\n\\subsection QuickRef_PredefMat Predefined Matrices\n\n<table class=\"manual\">\n<tr>\n  <th>Fixed-size matrix or vector</th>\n  <th>Dynamic-size matrix</th>\n  <th>Dynamic-size vector</th>\n</tr>\n<tr style=\"border-bottom-style: none;\">\n  <td>\n\\code\ntypedef {Matrix3f|Array33f} FixedXD;\nFixedXD x;\n\nx = FixedXD::Zero();\nx = FixedXD::Ones();\nx = FixedXD::Constant(value);\nx = FixedXD::Random();\nx = FixedXD::LinSpaced(size, low, high);\n\nx.setZero();\nx.setOnes();\nx.setConstant(value);\nx.setRandom();\nx.setLinSpaced(size, low, high);\n\\endcode\n  </td>\n  <td>\n\\code\ntypedef {MatrixXf|ArrayXXf} Dynamic2D;\nDynamic2D x;\n\nx = Dynamic2D::Zero(rows, cols);\nx = Dynamic2D::Ones(rows, cols);\nx = Dynamic2D::Constant(rows, cols, value);\nx = Dynamic2D::Random(rows, cols);\nN/A\n\nx.setZero(rows, cols);\nx.setOnes(rows, cols);\nx.setConstant(rows, cols, value);\nx.setRandom(rows, cols);\nN/A\n\\endcode\n  </td>\n  <td>\n\\code\ntypedef {VectorXf|ArrayXf} Dynamic1D;\nDynamic1D x;\n\nx = Dynamic1D::Zero(size);\nx = Dynamic1D::Ones(size);\nx = Dynamic1D::Constant(size, value);\nx = Dynamic1D::Random(size);\nx = Dynamic1D::LinSpaced(size, low, high);\n\nx.setZero(size);\nx.setOnes(size);\nx.setConstant(size, value);\nx.setRandom(size);\nx.setLinSpaced(size, low, high);\n\\endcode\n  </td>\n</tr>\n\n<tr><td colspan=\"3\">Identity and \\link MatrixBase::Unit basis vectors \\endlink \\matrixworld</td></tr>\n<tr style=\"border-bottom-style: none;\">\n  <td>\n\\code\nx = FixedXD::Identity();\nx.setIdentity();\n\nVector3f::UnitX() // 1 0 0\nVector3f::UnitY() // 0 1 0\nVector3f::UnitZ() // 0 0 1\n\\endcode\n  </td>\n  <td>\n\\code\nx = Dynamic2D::Identity(rows, cols);\nx.setIdentity(rows, cols);\n\n\n\nN/A\n\\endcode\n  </td>\n  <td>\\code\nN/A\n\n\nVectorXf::Unit(size,i)\nVectorXf::Unit(4,1) == Vector4f(0,1,0,0)\n                    == Vector4f::UnitY()\n\\endcode\n  </td>\n</tr>\n</table>\n\n\n\n\\subsection QuickRef_Map Mapping external arrays\n\n<table class=\"manual\">\n<tr>\n<td>Contiguous \\n memory</td>\n<td>\\code\nfloat data[] = {1,2,3,4};\nMap<Vector3f> v1(data);       // uses v1 as a Vector3f object\nMap<ArrayXf>  v2(data,3);     // uses v2 as a ArrayXf object\nMap<Array22f> m1(data);       // uses m1 as a Array22f object\nMap<MatrixXf> m2(data,2,2);   // uses m2 as a MatrixXf object\n\\endcode</td>\n</tr>\n<tr>\n<td>Typical usage \\n of strides</td>\n<td>\\code\nfloat data[] = {1,2,3,4,5,6,7,8,9};\nMap<VectorXf,0,InnerStride<2> >  v1(data,3);                      // = [1,3,5]\nMap<VectorXf,0,InnerStride<> >   v2(data,3,InnerStride<>(3));     // = [1,4,7]\nMap<MatrixXf,0,OuterStride<3> >  m2(data,2,3);                    // both lines     |1,4,7|\nMap<MatrixXf,0,OuterStride<> >   m1(data,2,3,OuterStride<>(3));   // are equal to:  |2,5,8|\n\\endcode</td>\n</tr>\n</table>\n\n\n<a href=\"#\" class=\"top\">top</a>\n\\section QuickRef_ArithmeticOperators Arithmetic Operators\n\n<table class=\"manual\">\n<tr><td>\nadd \\n subtract</td><td>\\code\nmat3 = mat1 + mat2;           mat3 += mat1;\nmat3 = mat1 - mat2;           mat3 -= mat1;\\endcode\n</td></tr>\n<tr class=\"alt\"><td>\nscalar product</td><td>\\code\nmat3 = mat1 * s1;             mat3 *= s1;           mat3 = s1 * mat1;\nmat3 = mat1 / s1;             mat3 /= s1;\\endcode\n</td></tr>\n<tr><td>\nmatrix/vector \\n products \\matrixworld</td><td>\\code\ncol2 = mat1 * col1;\nrow2 = row1 * mat1;           row1 *= mat1;\nmat3 = mat1 * mat2;           mat3 *= mat1; \\endcode\n</td></tr>\n<tr class=\"alt\"><td>\ntransposition \\n adjoint \\matrixworld</td><td>\\code\nmat1 = mat2.transpose();      mat1.transposeInPlace();\nmat1 = mat2.adjoint();        mat1.adjointInPlace();\n\\endcode\n</td></tr>\n<tr><td>\n\\link MatrixBase::dot dot \\endlink product \\n inner product \\matrixworld</td><td>\\code\nscalar = vec1.dot(vec2);\nscalar = col1.adjoint() * col2;\nscalar = (col1.adjoint() * col2).value();\\endcode\n</td></tr>\n<tr class=\"alt\"><td>\nouter product \\matrixworld</td><td>\\code\nmat = col1 * col2.transpose();\\endcode\n</td></tr>\n\n<tr><td>\n\\link MatrixBase::norm() norm \\endlink \\n \\link MatrixBase::normalized() normalization \\endlink \\matrixworld</td><td>\\code\nscalar = vec1.norm();         scalar = vec1.squaredNorm()\nvec2 = vec1.normalized();     vec1.normalize(); // inplace \\endcode\n</td></tr>\n\n<tr class=\"alt\"><td>\n\\link MatrixBase::cross() cross product \\endlink \\matrixworld</td><td>\\code\n#include <Eigen/Geometry>\nvec3 = vec1.cross(vec2);\\endcode</td></tr>\n</table>\n\n<a href=\"#\" class=\"top\">top</a>\n\\section QuickRef_Coeffwise Coefficient-wise \\& Array operators\n\nIn addition to the aforementioned operators, Eigen supports numerous coefficient-wise operator and functions.\nMost of them unambiguously makes sense in array-world\\arrayworld. The following operators are readily available for arrays,\nor available through .array() for vectors and matrices:\n\n<table class=\"manual\">\n<tr><td>Arithmetic operators</td><td>\\code\narray1 * array2     array1 / array2     array1 *= array2    array1 /= array2\narray1 + scalar     array1 - scalar     array1 += scalar    array1 -= scalar\n\\endcode</td></tr>\n<tr><td>Comparisons</td><td>\\code\narray1 < array2     array1 > array2     array1 < scalar     array1 > scalar\narray1 <= array2    array1 >= array2    array1 <= scalar    array1 >= scalar\narray1 == array2    array1 != array2    array1 == scalar    array1 != scalar\narray1.min(array2)  array1.max(array2)  array1.min(scalar)  array1.max(scalar)\n\\endcode</td></tr>\n<tr><td>Trigo, power, and \\n misc functions \\n and the STL-like variants</td><td>\\code\narray1.abs2()\narray1.abs()                  abs(array1)\narray1.sqrt()                 sqrt(array1)\narray1.log()                  log(array1)\narray1.log10()                log10(array1)\narray1.exp()                  exp(array1)\narray1.pow(array2)            pow(array1,array2)\narray1.pow(scalar)            pow(array1,scalar)\n                              pow(scalar,array2)\narray1.square()\narray1.cube()\narray1.inverse()\n\narray1.sin()                  sin(array1)\narray1.cos()                  cos(array1)\narray1.tan()                  tan(array1)\narray1.asin()                 asin(array1)\narray1.acos()                 acos(array1)\narray1.atan()                 atan(array1)\narray1.sinh()                 sinh(array1)\narray1.cosh()                 cosh(array1)\narray1.tanh()                 tanh(array1)\narray1.arg()                  arg(array1)\n\narray1.floor()                floor(array1)\narray1.ceil()                 ceil(array1)\narray1.round()                round(aray1)\n\narray1.isFinite()             isfinite(array1)\narray1.isInf()                isinf(array1)\narray1.isNaN()                isnan(array1)\n\\endcode\n</td></tr>\n</table>\n\n\nThe following coefficient-wise operators are available for all kind of expressions (matrices, vectors, and arrays), and for both real or complex scalar types:\n\n<table class=\"manual\">\n<tr><th>Eigen's API</th><th>STL-like APIs\\arrayworld </th><th>Comments</th></tr>\n<tr><td>\\code\nmat1.real()\nmat1.imag()\nmat1.conjugate()\n\\endcode\n</td><td>\\code\nreal(array1)\nimag(array1)\nconj(array1)\n\\endcode\n</td><td>\n\\code\n // read-write, no-op for real expressions\n // read-only for real, read-write for complexes\n // no-op for real expressions\n\\endcode\n</td></tr>\n</table>\n\nSome coefficient-wise operators are readily available for for matrices and vectors through the following cwise* methods:\n<table class=\"manual\">\n<tr><th>Matrix API \\matrixworld</th><th>Via Array conversions</th></tr>\n<tr><td>\\code\nmat1.cwiseMin(mat2)         mat1.cwiseMin(scalar)\nmat1.cwiseMax(mat2)         mat1.cwiseMax(scalar)\nmat1.cwiseAbs2()\nmat1.cwiseAbs()\nmat1.cwiseSqrt()\nmat1.cwiseInverse()\nmat1.cwiseProduct(mat2)\nmat1.cwiseQuotient(mat2)\nmat1.cwiseEqual(mat2)       mat1.cwiseEqual(scalar)\nmat1.cwiseNotEqual(mat2)\n\\endcode\n</td><td>\\code\nmat1.array().min(mat2.array())    mat1.array().min(scalar)\nmat1.array().max(mat2.array())    mat1.array().max(scalar)\nmat1.array().abs2()\nmat1.array().abs()\nmat1.array().sqrt()\nmat1.array().inverse()\nmat1.array() * mat2.array()\nmat1.array() / mat2.array()\nmat1.array() == mat2.array()      mat1.array() == scalar\nmat1.array() != mat2.array()\n\\endcode</td></tr>\n</table>\nThe main difference between the two API is that the one based on cwise* methods returns an expression in the matrix world,\nwhile the second one (based on .array()) returns an array expression.\nRecall that .array() has no cost, it only changes the available API and interpretation of the data.\n\nIt is also very simple to apply any user defined function \\c foo using DenseBase::unaryExpr together with <a href=\"http://en.cppreference.com/w/cpp/utility/functional/ptr_fun\">std::ptr_fun</a> (c++03), <a href=\"http://en.cppreference.com/w/cpp/utility/functional/ref\">std::ref</a> (c++11), or <a href=\"http://en.cppreference.com/w/cpp/language/lambda\">lambdas</a> (c++11):\n\\code\nmat1.unaryExpr(std::ptr_fun(foo));\nmat1.unaryExpr(std::ref(foo));\nmat1.unaryExpr([](double x) { return foo(x); });\n\\endcode\n\n\n<a href=\"#\" class=\"top\">top</a>\n\\section QuickRef_Reductions Reductions\n\nEigen provides several reduction methods such as:\n\\link DenseBase::minCoeff() minCoeff() \\endlink, \\link DenseBase::maxCoeff() maxCoeff() \\endlink,\n\\link DenseBase::sum() sum() \\endlink, \\link DenseBase::prod() prod() \\endlink,\n\\link MatrixBase::trace() trace() \\endlink \\matrixworld,\n\\link MatrixBase::norm() norm() \\endlink \\matrixworld, \\link MatrixBase::squaredNorm() squaredNorm() \\endlink \\matrixworld,\n\\link DenseBase::all() all() \\endlink, and \\link DenseBase::any() any() \\endlink.\nAll reduction operations can be done matrix-wise,\n\\link DenseBase::colwise() column-wise \\endlink or\n\\link DenseBase::rowwise() row-wise \\endlink. Usage example:\n<table class=\"manual\">\n<tr><td rowspan=\"3\" style=\"border-right-style:dashed;vertical-align:middle\">\\code\n      5 3 1\nmat = 2 7 8\n      9 4 6 \\endcode\n</td> <td>\\code mat.minCoeff(); \\endcode</td><td>\\code 1 \\endcode</td></tr>\n<tr class=\"alt\"><td>\\code mat.colwise().minCoeff(); \\endcode</td><td>\\code 2 3 1 \\endcode</td></tr>\n<tr style=\"vertical-align:middle\"><td>\\code mat.rowwise().minCoeff(); \\endcode</td><td>\\code\n1\n2\n4\n\\endcode</td></tr>\n</table>\n\nSpecial versions of \\link DenseBase::minCoeff(IndexType*,IndexType*) const minCoeff \\endlink and \\link DenseBase::maxCoeff(IndexType*,IndexType*) const maxCoeff \\endlink:\n\\code\nint i, j;\ns = vector.minCoeff(&i);        // s == vector[i]\ns = matrix.maxCoeff(&i, &j);    // s == matrix(i,j)\n\\endcode\nTypical use cases of all() and any():\n\\code\nif((array1 > 0).all()) ...      // if all coefficients of array1 are greater than 0 ...\nif((array1 < array2).any()) ... // if there exist a pair i,j such that array1(i,j) < array2(i,j) ...\n\\endcode\n\n\n<a href=\"#\" class=\"top\">top</a>\\section QuickRef_Blocks Sub-matrices\n\nRead-write access to a \\link DenseBase::col(Index) column \\endlink\nor a \\link DenseBase::row(Index) row \\endlink of a matrix (or array):\n\\code\nmat1.row(i) = mat2.col(j);\nmat1.col(j1).swap(mat1.col(j2));\n\\endcode\n\nRead-write access to sub-vectors:\n<table class=\"manual\">\n<tr>\n<th>Default versions</th>\n<th>Optimized versions when the size \\n is known at compile time</th></tr>\n<th></th>\n\n<tr><td>\\code vec1.head(n)\\endcode</td><td>\\code vec1.head<n>()\\endcode</td><td>the first \\c n coeffs </td></tr>\n<tr><td>\\code vec1.tail(n)\\endcode</td><td>\\code vec1.tail<n>()\\endcode</td><td>the last \\c n coeffs </td></tr>\n<tr><td>\\code vec1.segment(pos,n)\\endcode</td><td>\\code vec1.segment<n>(pos)\\endcode</td>\n    <td>the \\c n coeffs in the \\n range [\\c pos : \\c pos + \\c n - 1]</td></tr>\n<tr class=\"alt\"><td colspan=\"3\">\n\nRead-write access to sub-matrices:</td></tr>\n<tr>\n  <td>\\code mat1.block(i,j,rows,cols)\\endcode\n      \\link DenseBase::block(Index,Index,Index,Index) (more) \\endlink</td>\n  <td>\\code mat1.block<rows,cols>(i,j)\\endcode\n      \\link DenseBase::block(Index,Index) (more) \\endlink</td>\n  <td>the \\c rows x \\c cols sub-matrix \\n starting from position (\\c i,\\c j)</td></tr>\n<tr><td>\\code\n mat1.topLeftCorner(rows,cols)\n mat1.topRightCorner(rows,cols)\n mat1.bottomLeftCorner(rows,cols)\n mat1.bottomRightCorner(rows,cols)\\endcode\n <td>\\code\n mat1.topLeftCorner<rows,cols>()\n mat1.topRightCorner<rows,cols>()\n mat1.bottomLeftCorner<rows,cols>()\n mat1.bottomRightCorner<rows,cols>()\\endcode\n <td>the \\c rows x \\c cols sub-matrix \\n taken in one of the four corners</td></tr>\n <tr><td>\\code\n mat1.topRows(rows)\n mat1.bottomRows(rows)\n mat1.leftCols(cols)\n mat1.rightCols(cols)\\endcode\n <td>\\code\n mat1.topRows<rows>()\n mat1.bottomRows<rows>()\n mat1.leftCols<cols>()\n mat1.rightCols<cols>()\\endcode\n <td>specialized versions of block() \\n when the block fit two corners</td></tr>\n</table>\n\n\n\n<a href=\"#\" class=\"top\">top</a>\\section QuickRef_Misc Miscellaneous operations\n\n\\subsection QuickRef_Reverse Reverse\nVectors, rows, and/or columns of a matrix can be reversed (see DenseBase::reverse(), DenseBase::reverseInPlace(), VectorwiseOp::reverse()).\n\\code\nvec.reverse()           mat.colwise().reverse()   mat.rowwise().reverse()\nvec.reverseInPlace()\n\\endcode\n\n\\subsection QuickRef_Replicate Replicate\nVectors, matrices, rows, and/or columns can be replicated in any direction (see DenseBase::replicate(), VectorwiseOp::replicate())\n\\code\nvec.replicate(times)                                          vec.replicate<Times>\nmat.replicate(vertical_times, horizontal_times)               mat.replicate<VerticalTimes, HorizontalTimes>()\nmat.colwise().replicate(vertical_times, horizontal_times)     mat.colwise().replicate<VerticalTimes, HorizontalTimes>()\nmat.rowwise().replicate(vertical_times, horizontal_times)     mat.rowwise().replicate<VerticalTimes, HorizontalTimes>()\n\\endcode\n\n\n<a href=\"#\" class=\"top\">top</a>\\section QuickRef_DiagTriSymm Diagonal, Triangular, and Self-adjoint matrices\n(matrix world \\matrixworld)\n\n\\subsection QuickRef_Diagonal Diagonal matrices\n\n<table class=\"example\">\n<tr><th>Operation</th><th>Code</th></tr>\n<tr><td>\nview a vector \\link MatrixBase::asDiagonal() as a diagonal matrix \\endlink \\n </td><td>\\code\nmat1 = vec1.asDiagonal();\\endcode\n</td></tr>\n<tr><td>\nDeclare a diagonal matrix</td><td>\\code\nDiagonalMatrix<Scalar,SizeAtCompileTime> diag1(size);\ndiag1.diagonal() = vector;\\endcode\n</td></tr>\n<tr><td>Access the \\link MatrixBase::diagonal() diagonal \\endlink and \\link MatrixBase::diagonal(Index) super/sub diagonals \\endlink of a matrix as a vector (read/write)</td>\n <td>\\code\nvec1 = mat1.diagonal();        mat1.diagonal() = vec1;      // main diagonal\nvec1 = mat1.diagonal(+n);      mat1.diagonal(+n) = vec1;    // n-th super diagonal\nvec1 = mat1.diagonal(-n);      mat1.diagonal(-n) = vec1;    // n-th sub diagonal\nvec1 = mat1.diagonal<1>();     mat1.diagonal<1>() = vec1;   // first super diagonal\nvec1 = mat1.diagonal<-2>();    mat1.diagonal<-2>() = vec1;  // second sub diagonal\n\\endcode</td>\n</tr>\n\n<tr><td>Optimized products and inverse</td>\n <td>\\code\nmat3  = scalar * diag1 * mat1;\nmat3 += scalar * mat1 * vec1.asDiagonal();\nmat3 = vec1.asDiagonal().inverse() * mat1\nmat3 = mat1 * diag1.inverse()\n\\endcode</td>\n</tr>\n\n</table>\n\n\\subsection QuickRef_TriangularView Triangular views\n\nTriangularView gives a view on a triangular part of a dense matrix and allows to perform optimized operations on it. The opposite triangular part is never referenced and can be used to store other information.\n\n\\note The .triangularView() template member function requires the \\c template keyword if it is used on an\nobject of a type that depends on a template parameter; see \\ref TopicTemplateKeyword for details.\n\n<table class=\"example\">\n<tr><th>Operation</th><th>Code</th></tr>\n<tr><td>\nReference to a triangular with optional \\n\nunit or null diagonal (read/write):\n</td><td>\\code\nm.triangularView<Xxx>()\n\\endcode \\n\n\\c Xxx = ::Upper, ::Lower, ::StrictlyUpper, ::StrictlyLower, ::UnitUpper, ::UnitLower\n</td></tr>\n<tr><td>\nWriting to a specific triangular part:\\n (only the referenced triangular part is evaluated)\n</td><td>\\code\nm1.triangularView<Eigen::Lower>() = m2 + m3 \\endcode\n</td></tr>\n<tr><td>\nConversion to a dense matrix setting the opposite triangular part to zero:\n</td><td>\\code\nm2 = m1.triangularView<Eigen::UnitUpper>()\\endcode\n</td></tr>\n<tr><td>\nProducts:\n</td><td>\\code\nm3 += s1 * m1.adjoint().triangularView<Eigen::UnitUpper>() * m2\nm3 -= s1 * m2.conjugate() * m1.adjoint().triangularView<Eigen::Lower>() \\endcode\n</td></tr>\n<tr><td>\nSolving linear equations:\\n\n\\f$ M_2 := L_1^{-1} M_2 \\f$ \\n\n\\f$ M_3 := {L_1^*}^{-1} M_3 \\f$ \\n\n\\f$ M_4 := M_4 U_1^{-1} \\f$\n</td><td>\\n \\code\nL1.triangularView<Eigen::UnitLower>().solveInPlace(M2)\nL1.triangularView<Eigen::Lower>().adjoint().solveInPlace(M3)\nU1.triangularView<Eigen::Upper>().solveInPlace<OnTheRight>(M4)\\endcode\n</td></tr>\n</table>\n\n\\subsection QuickRef_SelfadjointMatrix Symmetric/selfadjoint views\n\nJust as for triangular matrix, you can reference any triangular part of a square matrix to see it as a selfadjoint\nmatrix and perform special and optimized operations. Again the opposite triangular part is never referenced and can be\nused to store other information.\n\n\\note The .selfadjointView() template member function requires the \\c template keyword if it is used on an\nobject of a type that depends on a template parameter; see \\ref TopicTemplateKeyword for details.\n\n<table class=\"example\">\n<tr><th>Operation</th><th>Code</th></tr>\n<tr><td>\nConversion to a dense matrix:\n</td><td>\\code\nm2 = m.selfadjointView<Eigen::Lower>();\\endcode\n</td></tr>\n<tr><td>\nProduct with another general matrix or vector:\n</td><td>\\code\nm3  = s1 * m1.conjugate().selfadjointView<Eigen::Upper>() * m3;\nm3 -= s1 * m3.adjoint() * m1.selfadjointView<Eigen::Lower>();\\endcode\n</td></tr>\n<tr><td>\nRank 1 and rank K update: \\n\n\\f$ upper(M_1) \\mathrel{{+}{=}} s_1 M_2 M_2^* \\f$ \\n\n\\f$ lower(M_1) \\mathbin{{-}{=}} M_2^* M_2 \\f$\n</td><td>\\n \\code\nM1.selfadjointView<Eigen::Upper>().rankUpdate(M2,s1);\nM1.selfadjointView<Eigen::Lower>().rankUpdate(M2.adjoint(),-1); \\endcode\n</td></tr>\n<tr><td>\nRank 2 update: (\\f$ M \\mathrel{{+}{=}} s u v^* + s v u^* \\f$)\n</td><td>\\code\nM.selfadjointView<Eigen::Upper>().rankUpdate(u,v,s);\n\\endcode\n</td></tr>\n<tr><td>\nSolving linear equations:\\n(\\f$ M_2 := M_1^{-1} M_2 \\f$)\n</td><td>\\code\n// via a standard Cholesky factorization\nm2 = m1.selfadjointView<Eigen::Upper>().llt().solve(m2);\n// via a Cholesky factorization with pivoting\nm2 = m1.selfadjointView<Eigen::Lower>().ldlt().solve(m2);\n\\endcode\n</td></tr>\n</table>\n\n*/\n\n/*\n<table class=\"tutorial_code\">\n<tr><td>\n\\link MatrixBase::asDiagonal() make a diagonal matrix \\endlink \\n from a vector </td><td>\\code\nmat1 = vec1.asDiagonal();\\endcode\n</td></tr>\n<tr><td>\nDeclare a diagonal matrix</td><td>\\code\nDiagonalMatrix<Scalar,SizeAtCompileTime> diag1(size);\ndiag1.diagonal() = vector;\\endcode\n</td></tr>\n<tr><td>Access \\link MatrixBase::diagonal() the diagonal and super/sub diagonals of a matrix \\endlink as a vector (read/write)</td>\n <td>\\code\nvec1 = mat1.diagonal();            mat1.diagonal() = vec1;      // main diagonal\nvec1 = mat1.diagonal(+n);          mat1.diagonal(+n) = vec1;    // n-th super diagonal\nvec1 = mat1.diagonal(-n);          mat1.diagonal(-n) = vec1;    // n-th sub diagonal\nvec1 = mat1.diagonal<1>();         mat1.diagonal<1>() = vec1;   // first super diagonal\nvec1 = mat1.diagonal<-2>();        mat1.diagonal<-2>() = vec1;  // second sub diagonal\n\\endcode</td>\n</tr>\n\n<tr><td>View on a triangular part of a matrix (read/write)</td>\n <td>\\code\nmat2 = mat1.triangularView<Xxx>();\n// Xxx = Upper, Lower, StrictlyUpper, StrictlyLower, UnitUpper, UnitLower\nmat1.triangularView<Upper>() = mat2 + mat3; // only the upper part is evaluated and referenced\n\\endcode</td></tr>\n\n<tr><td>View a triangular part as a symmetric/self-adjoint matrix (read/write)</td>\n <td>\\code\nmat2 = mat1.selfadjointView<Xxx>();     // Xxx = Upper or Lower\nmat1.selfadjointView<Upper>() = mat2 + mat2.adjoint();  // evaluated and write to the upper triangular part only\n\\endcode</td></tr>\n\n</table>\n\nOptimized products:\n\\code\nmat3 += scalar * vec1.asDiagonal() * mat1\nmat3 += scalar * mat1 * vec1.asDiagonal()\nmat3.noalias() += scalar * mat1.triangularView<Xxx>() * mat2\nmat3.noalias() += scalar * mat2 * mat1.triangularView<Xxx>()\nmat3.noalias() += scalar * mat1.selfadjointView<Upper or Lower>() * mat2\nmat3.noalias() += scalar * mat2 * mat1.selfadjointView<Upper or Lower>()\nmat1.selfadjointView<Upper or Lower>().rankUpdate(mat2);\nmat1.selfadjointView<Upper or Lower>().rankUpdate(mat2.adjoint(), scalar);\n\\endcode\n\nInverse products: (all are optimized)\n\\code\nmat3 = vec1.asDiagonal().inverse() * mat1\nmat3 = mat1 * diag1.inverse()\nmat1.triangularView<Xxx>().solveInPlace(mat2)\nmat1.triangularView<Xxx>().solveInPlace<OnTheRight>(mat2)\nmat2 = mat1.selfadjointView<Upper or Lower>().llt().solve(mat2)\n\\endcode\n\n*/\n}\n"
  },
  {
    "path": "include/eigen3/doc/QuickStartGuide.dox",
    "content": "namespace Eigen {\n\n/** \\page GettingStarted Getting started\n\n\\eigenAutoToc\n\nThis is a very short guide on how to get started with Eigen. It has a dual purpose. It serves as a minimal introduction to the Eigen library for people who want to start coding as soon as possible. You can also read this page as the first part of the Tutorial, which explains the library in more detail; in this case you will continue with \\ref TutorialMatrixClass.\n\n\\section GettingStartedInstallation How to \"install\" Eigen?\n\nIn order to use Eigen, you just need to download and extract Eigen's source code (see <a href=\"http://eigen.tuxfamily.org/index.php?title=Main_Page#Download\">the wiki</a> for download instructions). In fact, the header files in the \\c Eigen subdirectory are the only files required to compile programs using Eigen. The header files are the same for all platforms. It is not necessary to use CMake or install anything.\n\n\n\\section GettingStartedFirstProgram A simple first program\n\nHere is a rather simple program to get you started.\n\n\\include QuickStart_example.cpp\n\nWe will explain the program after telling you how to compile it.\n\n\n\\section GettingStartedCompiling Compiling and running your first program\n\nThere is no library to link to. The only thing that you need to keep in mind when compiling the above program is that the compiler must be able to find the Eigen header files. The directory in which you placed Eigen's source code must be in the include path. With GCC you use the -I option to achieve this, so you can compile the program with a command like this:\n\n\\code g++ -I /path/to/eigen/ my_program.cpp -o my_program \\endcode\n\nOn Linux or Mac OS X, another option is to symlink or copy the Eigen folder into /usr/local/include/. This way, you can compile the program with:\n\n\\code g++ my_program.cpp -o my_program \\endcode\n\nWhen you run the program, it produces the following output:\n\n\\include QuickStart_example.out\n\n\n\\section GettingStartedExplanation Explanation of the first program\n\nThe Eigen header files define many types, but for simple applications it may be enough to use only the \\c MatrixXd type. This represents a matrix of arbitrary size (hence the \\c X in \\c MatrixXd), in which every entry is a \\c double (hence the \\c d in \\c MatrixXd). See the \\ref QuickRef_Types \"quick reference guide\" for an overview of the different types you can use to represent a matrix.\n\nThe \\c Eigen/Dense header file defines all member functions for the MatrixXd type and related types (see also the \\ref QuickRef_Headers \"table of header files\"). All classes and functions defined in this header file (and other Eigen header files) are in the \\c Eigen namespace. \n\nThe first line of the \\c main function declares a variable of type \\c MatrixXd and specifies that it is a matrix with 2 rows and 2 columns (the entries are not initialized). The statement <tt>m(0,0) = 3</tt> sets the entry in the top-left corner to 3. You need to use round parentheses to refer to entries in the matrix. As usual in computer science, the index of the first index is 0, as opposed to the convention in mathematics that the first index is 1.\n\nThe following three statements sets the other three entries. The final line outputs the matrix \\c m to the standard output stream.\n\n\n\\section GettingStartedExample2 Example 2: Matrices and vectors\n\nHere is another example, which combines matrices with vectors. Concentrate on the left-hand program for now; we will talk about the right-hand program later.\n\n<table class=\"manual\">\n<tr><th>Size set at run time:</th><th>Size set at compile time:</th></tr>\n<tr><td>\n\\include QuickStart_example2_dynamic.cpp\n</td>\n<td>\n\\include QuickStart_example2_fixed.cpp\n</td></tr></table>\n\nThe output is as follows:\n\n\\include QuickStart_example2_dynamic.out\n\n\n\\section GettingStartedExplanation2 Explanation of the second example\n\nThe second example starts by declaring a 3-by-3 matrix \\c m which is initialized using the \\link DenseBase::Random(Index,Index) Random() \\endlink method with random values between -1 and 1. The next line applies a linear mapping such that the values are between 10 and 110. The function call \\link DenseBase::Constant(Index,Index,const Scalar&) MatrixXd::Constant\\endlink(3,3,1.2) returns a 3-by-3 matrix expression having all coefficients equal to 1.2. The rest is standard arithmetics.\n\nThe next line of the \\c main function introduces a new type: \\c VectorXd. This represents a (column) vector of arbitrary size. Here, the vector \\c v is created to contain \\c 3 coefficients which are left unitialized. The one but last line uses the so-called comma-initializer, explained in \\ref TutorialAdvancedInitialization, to set all coefficients of the vector \\c v to be as follows:\n\n\\f[\nv =\n\\begin{bmatrix}\n  1 \\\\\n  2 \\\\\n  3\n\\end{bmatrix}.\n\\f]\n\nThe final line of the program multiplies the matrix \\c m with the vector \\c v and outputs the result.\n\nNow look back at the second example program. We presented two versions of it. In the version in the left column, the matrix is of type \\c MatrixXd which represents matrices of arbitrary size. The version in the right column is similar, except that the matrix is of type \\c Matrix3d, which represents matrices of a fixed size (here 3-by-3). Because the type already encodes the size of the matrix, it is not necessary to specify the size in the constructor; compare <tt>MatrixXd m(3,3)</tt> with <tt>Matrix3d m</tt>. Similarly, we have \\c VectorXd on the left (arbitrary size) versus \\c Vector3d on the right (fixed size). Note that here the coefficients of vector \\c v are directly set in the constructor, though the same syntax of the left example could be used too.\n\nThe use of fixed-size matrices and vectors has two advantages. The compiler emits better (faster) code because it knows the size of the matrices and vectors. Specifying the size in the type also allows for more rigorous checking at compile-time. For instance, the compiler will complain if you try to multiply a \\c Matrix4d (a 4-by-4 matrix) with a \\c Vector3d (a vector of size 3). However, the use of many types increases compilation time and the size of the executable. The size of the matrix may also not be known at compile-time. A rule of thumb is to use fixed-size matrices for size 4-by-4 and smaller.\n\n\n\\section GettingStartedConclusion Where to go from here?\n\nIt's worth taking the time to read the  \\ref TutorialMatrixClass \"long tutorial\".\n\nHowever if you think you don't need it, you can directly use the classes documentation and our \\ref QuickRefPage.\n\n\\li \\b Next: \\ref TutorialMatrixClass\n\n*/\n\n}\n\n"
  },
  {
    "path": "include/eigen3/doc/SparseLinearSystems.dox",
    "content": "namespace Eigen {\n/** \\eigenManualPage TopicSparseSystems Solving Sparse Linear Systems\nIn Eigen, there are several methods available to solve linear systems when the coefficient matrix is sparse. Because of the special representation of this class of matrices, special care should be taken in order to get a good performance. See \\ref TutorialSparse for a detailed introduction about sparse matrices in Eigen. This page lists the sparse solvers available in Eigen. The main steps that are common to all these linear solvers are introduced as well. Depending on the properties of the matrix, the desired accuracy, the end-user is able to tune those steps in order to improve the performance of its code. Note that it is not required to know deeply what's hiding behind these steps: the last section presents a benchmark routine that can be easily used to get an insight on the performance of all the available solvers. \n\n\\eigenAutoToc\n\n\\section TutorialSparseSolverList List of sparse solvers\n\n%Eigen currently provides a wide set of built-in solvers, as well as wrappers to external solver libraries.\nThey are summarized in the following tables:\n\n\\subsection TutorialSparseSolverList_Direct Built-in direct solvers\n\n<table class=\"manual\">\n<tr><th>Class</th><th>Solver kind</th><th>Matrix kind</th><th>Features related to performance</th>\n    <th>License</th><th class=\"width20em\"><p>Notes</p></th></tr>\n\n<tr><td>SimplicialLLT \\n <tt>\\#include<Eigen/\\link SparseCholesky_Module SparseCholesky\\endlink></tt></td><td>Direct LLt factorization</td><td>SPD</td><td>Fill-in reducing</td>\n    <td>LGPL</td>\n    <td>SimplicialLDLT is often preferable</td></tr>\n\n<tr><td>SimplicialLDLT \\n <tt>\\#include<Eigen/\\link SparseCholesky_Module SparseCholesky\\endlink></tt></td><td>Direct LDLt factorization</td><td>SPD</td><td>Fill-in reducing</td>\n    <td>LGPL</td>\n    <td>Recommended for very sparse and not too large problems (e.g., 2D Poisson eq.)</td></tr>\n\n<tr><td>SparseLU \\n <tt>\\#include<Eigen/\\link SparseLU_Module SparseLU\\endlink></tt></td> <td>LU factorization </td>\n    <td>Square </td><td>Fill-in reducing, Leverage fast dense algebra</td>\n    <td>MPL2</td>\n    <td>optimized for small and large problems with irregular patterns </td></tr>\n\n<tr><td>SparseQR \\n <tt>\\#include<Eigen/\\link SparseQR_Module SparseQR\\endlink></tt></td> <td> QR factorization</td>\n    <td>Any, rectangular</td><td> Fill-in reducing</td>\n    <td>MPL2</td>\n    <td>recommended for least-square problems, has a basic rank-revealing feature</td></tr>\n </table>\n\n\\subsection TutorialSparseSolverList_Iterative Built-in iterative solvers\n\n<table class=\"manual\">\n<tr><th>Class</th><th>Solver kind</th><th>Matrix kind</th><th>Supported preconditioners, [default]</th>\n    <th>License</th><th class=\"width20em\"><p>Notes</p></th></tr>\n\n<tr><td>ConjugateGradient \\n <tt>\\#include<Eigen/\\link IterativeLinearSolvers_Module IterativeLinearSolvers\\endlink></tt></td> <td>Classic iterative CG</td><td>SPD</td>\n    <td>IdentityPreconditioner, [DiagonalPreconditioner], IncompleteCholesky</td>\n    <td>MPL2</td>\n    <td>Recommended for large symmetric problems (e.g., 3D Poisson eq.)</td></tr>\n\n<tr><td>LeastSquaresConjugateGradient \\n <tt>\\#include<Eigen/\\link IterativeLinearSolvers_Module IterativeLinearSolvers\\endlink></tt></td><td>CG for rectangular least-square problem</td><td>Rectangular</td>\n    <td>IdentityPreconditioner, [LeastSquareDiagonalPreconditioner]</td>\n    <td>MPL2</td>\n    <td>Solve for min |A'Ax-b|^2 without forming A'A</td></tr>\n\n<tr><td>BiCGSTAB \\n <tt>\\#include<Eigen/\\link IterativeLinearSolvers_Module IterativeLinearSolvers\\endlink></tt></td><td>Iterative stabilized bi-conjugate gradient</td><td>Square</td>\n    <td>IdentityPreconditioner, [DiagonalPreconditioner], IncompleteLUT</td>\n    <td>MPL2</td>\n    <td>To speedup the convergence, try it with the \\ref IncompleteLUT preconditioner.</td></tr>\n</table>\n\n\\subsection TutorialSparseSolverList_Wrapper Wrappers to external solvers\n\n<table class=\"manual\">\n<tr><th>Class</th><th>Module</th><th>Solver kind</th><th>Matrix kind</th><th>Features related to performance</th>\n    <th>Dependencies,License</th><th class=\"width20em\"><p>Notes</p></th></tr>\n<tr><td>PastixLLT \\n PastixLDLT \\n PastixLU</td><td>\\link PaStiXSupport_Module PaStiXSupport \\endlink</td><td>Direct LLt, LDLt, LU factorizations</td><td>SPD \\n SPD \\n Square</td><td>Fill-in reducing, Leverage fast dense algebra, Multithreading</td>\n    <td>Requires the <a href=\"http://pastix.gforge.inria.fr\">PaStiX</a> package, \\b CeCILL-C </td>\n    <td>optimized for tough problems and symmetric patterns</td></tr>\n<tr><td>CholmodSupernodalLLT</td><td>\\link CholmodSupport_Module CholmodSupport \\endlink</td><td>Direct LLt factorization</td><td>SPD</td><td>Fill-in reducing, Leverage fast dense algebra</td>\n    <td>Requires the <a href=\"http://www.suitesparse.com\">SuiteSparse</a> package, \\b GPL </td>\n    <td></td></tr>\n<tr><td>UmfPackLU</td><td>\\link UmfPackSupport_Module UmfPackSupport \\endlink</td><td>Direct LU factorization</td><td>Square</td><td>Fill-in reducing, Leverage fast dense algebra</td>\n    <td>Requires the <a href=\"http://www.suitesparse.com\">SuiteSparse</a> package, \\b GPL </td>\n    <td></td></tr>\n<tr><td>SuperLU</td><td>\\link SuperLUSupport_Module SuperLUSupport \\endlink</td><td>Direct LU factorization</td><td>Square</td><td>Fill-in reducing, Leverage fast dense algebra</td>\n    <td>Requires the <a href=\"http://crd-legacy.lbl.gov/~xiaoye/SuperLU/\">SuperLU</a> library, (BSD-like)</td>\n    <td></td></tr>\n<tr><td>SPQR</td><td>\\link SPQRSupport_Module SPQRSupport \\endlink  </td> <td> QR factorization </td> \n    <td> Any, rectangular</td><td>fill-in reducing, multithreaded, fast dense algebra</td>\n    <td> requires the <a href=\"http://www.suitesparse.com\">SuiteSparse</a> package, \\b GPL </td><td>recommended for linear least-squares problems, has a rank-revealing feature</tr>\n<tr><td>PardisoLLT \\n PardisoLDLT \\n PardisoLU</td><td>\\link PardisoSupport_Module PardisoSupport \\endlink</td><td>Direct LLt, LDLt, LU factorizations</td><td>SPD \\n SPD \\n Square</td><td>Fill-in reducing, Leverage fast dense algebra, Multithreading</td>\n    <td>Requires the <a href=\"http://eigen.tuxfamily.org/Counter/redirect_to_mkl.php\">Intel MKL</a> package, \\b Proprietary </td>\n    <td>optimized for tough problems patterns, see also \\link TopicUsingIntelMKL using MKL with Eigen \\endlink</td></tr>\n</table>\n\nHere \\c SPD means symmetric positive definite.\n\n\\section TutorialSparseSolverConcept Sparse solver concept\n\nAll these solvers follow the same general concept.\nHere is a typical and general example:\n\\code\n#include <Eigen/RequiredModuleName>\n// ...\nSparseMatrix<double> A;\n// fill A\nVectorXd b, x;\n// fill b\n// solve Ax = b\nSolverClassName<SparseMatrix<double> > solver;\nsolver.compute(A);\nif(solver.info()!=Success) {\n  // decomposition failed\n  return;\n}\nx = solver.solve(b);\nif(solver.info()!=Success) {\n  // solving failed\n  return;\n}\n// solve for another right hand side:\nx1 = solver.solve(b1);\n\\endcode\n\nFor \\c SPD solvers, a second optional template argument allows to specify which triangular part have to be used, e.g.:\n\n\\code\n#include <Eigen/IterativeLinearSolvers>\n\nConjugateGradient<SparseMatrix<double>, Eigen::Upper> solver;\nx = solver.compute(A).solve(b);\n\\endcode\nIn the above example, only the upper triangular part of the input matrix A is considered for solving. The opposite triangle might either be empty or contain arbitrary values.\n\nIn the case where multiple problems with the same sparsity pattern have to be solved, then the \"compute\" step can be decomposed as follow:\n\\code\nSolverClassName<SparseMatrix<double> > solver;\nsolver.analyzePattern(A);   // for this step the numerical values of A are not used\nsolver.factorize(A);\nx1 = solver.solve(b1);\nx2 = solver.solve(b2);\n...\nA = ...;                    // modify the values of the nonzeros of A, the nonzeros pattern must stay unchanged\nsolver.factorize(A);\nx1 = solver.solve(b1);\nx2 = solver.solve(b2);\n...\n\\endcode\nThe compute() method is equivalent to calling both analyzePattern() and factorize().\n\nEach solver provides some specific features, such as determinant, access to the factors, controls of the iterations, and so on.\nMore details are available in the documentations of the respective classes.\n\nFinally, most of the iterative solvers, can also be used in a \\b matrix-free context, see the following \\link MatrixfreeSolverExample example \\endlink.\n\n\\section TheSparseCompute The Compute Step\nIn the compute() function, the matrix is generally factorized: LLT for self-adjoint matrices, LDLT for general hermitian matrices, LU for non hermitian matrices and QR for rectangular matrices. These are the results of using direct solvers. For this class of solvers precisely, the compute step is further subdivided into analyzePattern() and factorize(). \n\nThe goal of analyzePattern() is to reorder the nonzero elements of the matrix, such that the factorization step creates less fill-in. This step exploits only the structure of the matrix. Hence, the results of this step can be used for other linear systems where the matrix has the same structure. Note however that sometimes, some external solvers (like SuperLU) require that the values of the matrix are set in this step, for instance to equilibrate the rows and columns of the matrix. In this situation, the results of this step should not be used with other matrices.\n\nEigen provides a limited set of methods to reorder the matrix in this step, either built-in (COLAMD, AMD) or external (METIS). These methods are set in template parameter list of the solver :\n\\code\nDirectSolverClassName<SparseMatrix<double>, OrderingMethod<IndexType> > solver;\n\\endcode \n\nSee the \\link OrderingMethods_Module OrderingMethods module \\endlink for the list of available methods and the associated options. \n\nIn factorize(), the factors of the coefficient matrix are computed. This step should be called each time the values of the matrix change. However, the structural pattern of the matrix should not change between multiple calls. \n\nFor iterative solvers, the compute step is used to eventually setup a preconditioner. For instance, with the ILUT preconditioner, the incomplete factors L and U are computed in this step. Remember that, basically, the goal of the preconditioner is to speedup the convergence of an iterative method by solving a modified linear system where the coefficient matrix has more clustered eigenvalues. For real problems, an iterative solver should always be used with a preconditioner. In Eigen, a preconditioner is  selected by simply adding it as a template parameter to the iterative solver object. \n\\code\nIterativeSolverClassName<SparseMatrix<double>, PreconditionerName<SparseMatrix<double> > solver; \n\\endcode\nThe member function preconditioner() returns a read-write reference to the preconditioner \n to directly interact with it. See the \\link IterativeLinearSolvers_Module Iterative solvers module \\endlink and the documentation of each class for the list of available methods.\n\n\\section TheSparseSolve The Solve step\nThe solve() function computes the solution of the linear systems with one or many right hand sides.\n\\code\nX = solver.solve(B);\n\\endcode \nHere, B  can be a vector or a matrix where the columns form the different right hand sides. The solve() function can be called several times as well, for instance when all the right hand sides are not available at once. \n\\code\nx1 = solver.solve(b1);\n// Get the second right hand side b2\nx2 = solver.solve(b2); \n//  ...\n\\endcode\nFor direct methods, the solution are computed at the machine precision. Sometimes, the solution need not be too accurate. In this case, the iterative methods are more suitable and the desired accuracy can be set before the solve step using \\b setTolerance(). For all the available functions, please, refer to the documentation of the \\link IterativeLinearSolvers_Module Iterative solvers module \\endlink. \n\n\\section BenchmarkRoutine\nMost of the time, all you need is to know how much time it will take to solve your system, and hopefully, what is the most suitable solver. In Eigen, we provide a benchmark routine that can be used for this purpose. It is very easy to use. In the build directory, navigate to bench/spbench and compile the routine by typing \\b make \\e spbenchsolver. Run it with --help option to get the list of all available options. Basically, the matrices to test should be in <a href=\"http://math.nist.gov/MatrixMarket/formats.html\">MatrixMarket Coordinate format</a>, and the routine returns the statistics from all available solvers in Eigen.\n\nTo export your matrices and right-hand-side vectors in the matrix-market format, you can the the unsupported SparseExtra module:\n\\code\n#include <unsupported/Eigen/SparseExtra>\n...\nEigen::saveMarket(A, \"filename.mtx\");\nEigen::saveMarket(A, \"filename_SPD.mtx\", Eigen::Symmetric); // if A is symmetric-positive-definite\nEigen::saveMarketVector(B, \"filename_b.mtx\");\n\\endcode\n\nThe following table gives an example of XML statistics from several Eigen built-in and external solvers. \n<TABLE border=\"1\">\n <TR><TH>Matrix <TH> N <TH> NNZ <TH>  <TH > UMFPACK <TH > SUPERLU <TH > PASTIX LU <TH >BiCGSTAB <TH > BiCGSTAB+ILUT <TH >GMRES+ILUT<TH > LDLT <TH> CHOLMOD LDLT <TH > PASTIX LDLT <TH > LLT <TH > CHOLMOD SP LLT <TH > CHOLMOD LLT <TH > PASTIX LLT <TH> CG</TR>\n<TR><TH rowspan=\"4\">vector_graphics <TD rowspan=\"4\"> 12855 <TD rowspan=\"4\"> 72069 <TH>Compute Time <TD>0.0254549<TD>0.0215677<TD>0.0701827<TD>0.000153388<TD>0.0140107<TD>0.0153709<TD>0.0101601<TD style=\"background-color:red\">0.00930502<TD>0.0649689\n<TR><TH>Solve Time <TD>0.00337835<TD>0.000951826<TD>0.00484373<TD>0.0374886<TD>0.0046445<TD>0.00847754<TD>0.000541813<TD style=\"background-color:red\">0.000293696<TD>0.00485376\n<TR><TH>Total Time <TD>0.0288333<TD>0.0225195<TD>0.0750265<TD>0.037642<TD>0.0186552<TD>0.0238484<TD>0.0107019<TD style=\"background-color:red\">0.00959871<TD>0.0698227\n<TR><TH>Error(Iter) <TD> 1.299e-16 <TD> 2.04207e-16 <TD> 4.83393e-15 <TD> 3.94856e-11 (80)  <TD> 1.03861e-12 (3)  <TD> 5.81088e-14 (6)  <TD> 1.97578e-16 <TD> 1.83927e-16 <TD> 4.24115e-15\n<TR><TH rowspan=\"4\">poisson_SPD <TD rowspan=\"4\"> 19788 <TD rowspan=\"4\"> 308232 <TH>Compute Time <TD>0.425026<TD>1.82378<TD>0.617367<TD>0.000478921<TD>1.34001<TD>1.33471<TD>0.796419<TD>0.857573<TD>0.473007<TD>0.814826<TD style=\"background-color:red\">0.184719<TD>0.861555<TD>0.470559<TD>0.000458188\n<TR><TH>Solve Time <TD>0.0280053<TD>0.0194402<TD>0.0268747<TD>0.249437<TD>0.0548444<TD>0.0926991<TD>0.00850204<TD>0.0053171<TD>0.0258932<TD>0.00874603<TD style=\"background-color:red\">0.00578155<TD>0.00530361<TD>0.0248942<TD>0.239093\n<TR><TH>Total Time <TD>0.453031<TD>1.84322<TD>0.644241<TD>0.249916<TD>1.39486<TD>1.42741<TD>0.804921<TD>0.862891<TD>0.4989<TD>0.823572<TD style=\"background-color:red\">0.190501<TD>0.866859<TD>0.495453<TD>0.239551\n<TR><TH>Error(Iter) <TD> 4.67146e-16 <TD> 1.068e-15 <TD> 1.3397e-15 <TD> 6.29233e-11 (201)  <TD> 3.68527e-11 (6)  <TD> 3.3168e-15 (16)  <TD> 1.86376e-15 <TD> 1.31518e-16 <TD> 1.42593e-15 <TD> 3.45361e-15 <TD> 3.14575e-16 <TD> 2.21723e-15 <TD> 7.21058e-16 <TD> 9.06435e-12 (261) \n<TR><TH rowspan=\"4\">sherman2 <TD rowspan=\"4\"> 1080 <TD rowspan=\"4\"> 23094 <TH>Compute Time <TD style=\"background-color:red\">0.00631754<TD>0.015052<TD>0.0247514 <TD> -<TD>0.0214425<TD>0.0217988\n<TR><TH>Solve Time <TD style=\"background-color:red\">0.000478424<TD>0.000337998<TD>0.0010291 <TD> -<TD>0.00243152<TD>0.00246152\n<TR><TH>Total Time <TD style=\"background-color:red\">0.00679597<TD>0.01539<TD>0.0257805 <TD> -<TD>0.023874<TD>0.0242603\n<TR><TH>Error(Iter) <TD> 1.83099e-15 <TD> 8.19351e-15 <TD> 2.625e-14 <TD> 1.3678e+69 (1080)  <TD> 4.1911e-12 (7)  <TD> 5.0299e-13 (12) \n<TR><TH rowspan=\"4\">bcsstk01_SPD <TD rowspan=\"4\"> 48 <TD rowspan=\"4\"> 400 <TH>Compute Time <TD>0.000169079<TD>0.00010789<TD>0.000572538<TD>1.425e-06<TD>9.1612e-05<TD>8.3985e-05<TD style=\"background-color:red\">5.6489e-05<TD>7.0913e-05<TD>0.000468251<TD>5.7389e-05<TD>8.0212e-05<TD>5.8394e-05<TD>0.000463017<TD>1.333e-06\n<TR><TH>Solve Time <TD>1.2288e-05<TD>1.1124e-05<TD>0.000286387<TD>8.5896e-05<TD>1.6381e-05<TD>1.6984e-05<TD style=\"background-color:red\">3.095e-06<TD>4.115e-06<TD>0.000325438<TD>3.504e-06<TD>7.369e-06<TD>3.454e-06<TD>0.000294095<TD>6.0516e-05\n<TR><TH>Total Time <TD>0.000181367<TD>0.000119014<TD>0.000858925<TD>8.7321e-05<TD>0.000107993<TD>0.000100969<TD style=\"background-color:red\">5.9584e-05<TD>7.5028e-05<TD>0.000793689<TD>6.0893e-05<TD>8.7581e-05<TD>6.1848e-05<TD>0.000757112<TD>6.1849e-05\n<TR><TH>Error(Iter) <TD> 1.03474e-16 <TD> 2.23046e-16 <TD> 2.01273e-16 <TD> 4.87455e-07 (48)  <TD> 1.03553e-16 (2)  <TD> 3.55965e-16 (2)  <TD> 2.48189e-16 <TD> 1.88808e-16 <TD> 1.97976e-16 <TD> 2.37248e-16 <TD> 1.82701e-16 <TD> 2.71474e-16 <TD> 2.11322e-16 <TD> 3.547e-09 (48) \n<TR><TH rowspan=\"4\">sherman1 <TD rowspan=\"4\"> 1000 <TD rowspan=\"4\"> 3750 <TH>Compute Time <TD>0.00228805<TD>0.00209231<TD>0.00528268<TD>9.846e-06<TD>0.00163522<TD>0.00162155<TD>0.000789259<TD style=\"background-color:red\">0.000804495<TD>0.00438269\n<TR><TH>Solve Time <TD>0.000213788<TD>9.7983e-05<TD>0.000938831<TD>0.00629835<TD>0.000361764<TD>0.00078794<TD>4.3989e-05<TD style=\"background-color:red\">2.5331e-05<TD>0.000917166\n<TR><TH>Total Time <TD>0.00250184<TD>0.00219029<TD>0.00622151<TD>0.0063082<TD>0.00199698<TD>0.00240949<TD>0.000833248<TD style=\"background-color:red\">0.000829826<TD>0.00529986\n<TR><TH>Error(Iter) <TD> 1.16839e-16 <TD> 2.25968e-16 <TD> 2.59116e-16 <TD> 3.76779e-11 (248)  <TD> 4.13343e-11 (4)  <TD> 2.22347e-14 (10)  <TD> 2.05861e-16 <TD> 1.83555e-16 <TD> 1.02917e-15\n<TR><TH rowspan=\"4\">young1c <TD rowspan=\"4\"> 841 <TD rowspan=\"4\"> 4089 <TH>Compute Time <TD>0.00235843<TD style=\"background-color:red\">0.00217228<TD>0.00568075<TD>1.2735e-05<TD>0.00264866<TD>0.00258236\n<TR><TH>Solve Time <TD>0.000329599<TD style=\"background-color:red\">0.000168634<TD>0.00080118<TD>0.0534738<TD>0.00187193<TD>0.00450211\n<TR><TH>Total Time <TD>0.00268803<TD style=\"background-color:red\">0.00234091<TD>0.00648193<TD>0.0534865<TD>0.00452059<TD>0.00708447\n<TR><TH>Error(Iter) <TD> 1.27029e-16 <TD> 2.81321e-16 <TD> 5.0492e-15 <TD> 8.0507e-11 (706)  <TD> 3.00447e-12 (8)  <TD> 1.46532e-12 (16) \n<TR><TH rowspan=\"4\">mhd1280b <TD rowspan=\"4\"> 1280 <TD rowspan=\"4\"> 22778 <TH>Compute Time <TD>0.00234898<TD>0.00207079<TD>0.00570918<TD>2.5976e-05<TD>0.00302563<TD>0.00298036<TD>0.00144525<TD style=\"background-color:red\">0.000919922<TD>0.00426444\n<TR><TH>Solve Time <TD>0.00103392<TD>0.000211911<TD>0.00105<TD>0.0110432<TD>0.000628287<TD>0.00392089<TD>0.000138303<TD style=\"background-color:red\">6.2446e-05<TD>0.00097564\n<TR><TH>Total Time <TD>0.0033829<TD>0.0022827<TD>0.00675918<TD>0.0110692<TD>0.00365392<TD>0.00690124<TD>0.00158355<TD style=\"background-color:red\">0.000982368<TD>0.00524008\n<TR><TH>Error(Iter) <TD> 1.32953e-16 <TD> 3.08646e-16 <TD> 6.734e-16 <TD> 8.83132e-11 (40)  <TD> 1.51153e-16 (1)  <TD> 6.08556e-16 (8)  <TD> 1.89264e-16 <TD> 1.97477e-16 <TD> 6.68126e-09\n<TR><TH rowspan=\"4\">crashbasis <TD rowspan=\"4\"> 160000 <TD rowspan=\"4\"> 1750416 <TH>Compute Time <TD>3.2019<TD>5.7892<TD>15.7573<TD style=\"background-color:red\">0.00383515<TD>3.1006<TD>3.09921\n<TR><TH>Solve Time <TD>0.261915<TD>0.106225<TD>0.402141<TD style=\"background-color:red\">1.49089<TD>0.24888<TD>0.443673\n<TR><TH>Total Time <TD>3.46381<TD>5.89542<TD>16.1594<TD style=\"background-color:red\">1.49473<TD>3.34948<TD>3.54288\n<TR><TH>Error(Iter) <TD> 1.76348e-16 <TD> 4.58395e-16 <TD> 1.67982e-14 <TD> 8.64144e-11 (61)  <TD> 8.5996e-12 (2)  <TD> 6.04042e-14 (5) \n\n</TABLE>\n*/\n}\n"
  },
  {
    "path": "include/eigen3/doc/SparseQuickReference.dox",
    "content": "namespace Eigen {\n/** \\eigenManualPage SparseQuickRefPage Quick reference guide for sparse matrices\n\\eigenAutoToc\n\n<hr>\n\nIn this page, we give a quick summary of the main operations available for sparse matrices in the class SparseMatrix. First, it is recommended to read  the introductory tutorial at \\ref TutorialSparse. The important point to have in mind when working on sparse matrices is how they are stored : \ni.e either row major or column major. The default is column major. Most arithmetic operations on sparse matrices will assert that they have the same storage order. \n\n\\section SparseMatrixInit Sparse Matrix Initialization\n<table class=\"manual\">\n<tr><th> Category </th> <th> Operations</th> <th>Notes</th></tr>\n<tr><td>Constructor</td>\n<td>\n\\code\n  SparseMatrix<double> sm1(1000,1000); \n  SparseMatrix<std::complex<double>,RowMajor> sm2;\n\\endcode\n</td> <td> Default is ColMajor</td> </tr>\n<tr class=\"alt\">\n<td> Resize/Reserve</td>\n<td> \n \\code\n    sm1.resize(m,n);      // Change sm1 to a m x n matrix.\n    sm1.reserve(nnz);     // Allocate room for nnz nonzeros elements.   \n  \\endcode \n</td>\n<td> Note that when calling reserve(), it is not required that nnz is the exact number of nonzero elements in the final matrix. However, an exact estimation will avoid multiple reallocations during the insertion phase. </td>\n</tr>\n<tr> \n<td> Assignment </td>\n<td> \n\\code \n  SparseMatrix<double,Colmajor> sm1;\n // Initialize sm2 with sm1.\n  SparseMatrix<double,Rowmajor> sm2(sm1), sm3;        \n  // Assignment and evaluations modify the storage order.\n  sm3 = sm1; \n \\endcode\n</td>\n<td> The copy constructor can be used to convert from a storage order to another</td>\n</tr>\n<tr class=\"alt\">\n<td> Element-wise Insertion</td>\n<td>\n\\code \n// Insert a new element; \n sm1.insert(i, j) = v_ij;  \n\n// Update the value v_ij\n sm1.coeffRef(i,j) = v_ij;\n sm1.coeffRef(i,j) += v_ij;\n sm1.coeffRef(i,j) -= v_ij;\n\\endcode\n</td>\n<td> insert() assumes that the element does not already exist; otherwise, use coeffRef()</td>\n</tr>\n<tr> \n<td> Batch insertion</td>\n<td>\n\\code\n  std::vector< Eigen::Triplet<double> > tripletList;\n  tripletList.reserve(estimation_of_entries);\n  // -- Fill tripletList with nonzero elements...\n  sm1.setFromTriplets(TripletList.begin(), TripletList.end());\n\\endcode\n</td>\n<td>A complete example is available at \\link TutorialSparseFilling Triplet Insertion \\endlink.</td>\n</tr>\n<tr class=\"alt\"> \n<td> Constant or Random Insertion</td>\n<td>\n\\code\nsm1.setZero();\n\\endcode\n</td>\n<td>Remove all non-zero coefficients</td>\n</tr>\n</table>\n\n\n\\section SparseBasicInfos Matrix properties\nBeyond the basic functions rows() and cols(), there are some useful functions that are available to easily get some informations from the matrix. \n<table class=\"manual\">\n<tr>\n  <td> \\code\n  sm1.rows();         // Number of rows\n  sm1.cols();         // Number of columns \n  sm1.nonZeros();     // Number of non zero values   \n  sm1.outerSize();    // Number of columns (resp. rows) for a column major (resp. row major )\n  sm1.innerSize();    // Number of rows (resp. columns) for a row major (resp. column major)\n  sm1.norm();         // Euclidian norm of the matrix\n  sm1.squaredNorm();  // Squared norm of the matrix\n  sm1.blueNorm();\n  sm1.isVector();     // Check if sm1 is a sparse vector or a sparse matrix\n  sm1.isCompressed(); // Check if sm1 is in compressed form\n  ...\n  \\endcode </td>\n</tr>\n</table>\n\n\\section SparseBasicOps Arithmetic operations\nIt is easy to perform arithmetic operations on sparse matrices provided that the dimensions are adequate and that the matrices have the same storage order. Note that the evaluation can always be done in a matrix with a different storage order. In the following, \\b sm denotes a sparse matrix, \\b dm a dense matrix and \\b dv a dense vector.\n<table class=\"manual\">\n<tr><th> Operations </th> <th> Code </th> <th> Notes </th></tr>\n\n<tr>\n  <td> add subtract </td> \n  <td> \\code\n  sm3 = sm1 + sm2; \n  sm3 = sm1 - sm2;\n  sm2 += sm1; \n  sm2 -= sm1; \\endcode\n  </td>\n  <td> \n  sm1 and sm2 should have the same storage order\n  </td> \n</tr>\n\n<tr class=\"alt\"><td>\n  scalar product</td><td>\\code\n  sm3 = sm1 * s1;   sm3 *= s1; \n  sm3 = s1 * sm1 + s2 * sm2; sm3 /= s1;\\endcode\n  </td>\n  <td>\n    Many combinations are possible if the dimensions and the storage order agree.\n</tr>\n\n<tr>\n  <td> %Sparse %Product </td>\n  <td> \\code\n  sm3 = sm1 * sm2;\n  dm2 = sm1 * dm1;\n  dv2 = sm1 * dv1;\n  \\endcode </td>\n  <td>\n  </td>\n</tr> \n\n<tr class='alt'>\n  <td> transposition, adjoint</td>\n  <td> \\code\n  sm2 = sm1.transpose();\n  sm2 = sm1.adjoint();\n  \\endcode </td>\n  <td>\n  Note that the transposition change the storage order. There is no support for transposeInPlace().\n  </td>\n</tr> \n<tr>\n<td> Permutation </td>\n<td> \n\\code \nperm.indices();      // Reference to the vector of indices\nsm1.twistedBy(perm); // Permute rows and columns\nsm2 = sm1 * perm;    // Permute the columns\nsm2 = perm * sm1;    // Permute the columns\n\\endcode \n</td>\n<td> \n\n</td>\n</tr>\n<tr>\n  <td>\n  Component-wise ops\n  </td>\n  <td>\\code \n  sm1.cwiseProduct(sm2);\n  sm1.cwiseQuotient(sm2);\n  sm1.cwiseMin(sm2);\n  sm1.cwiseMax(sm2);\n  sm1.cwiseAbs();\n  sm1.cwiseSqrt();\n  \\endcode</td>\n  <td>\n  sm1 and sm2 should have the same storage order\n  </td>\n</tr>\n</table>\n\n\\section sparseotherops Other supported operations\n<table class=\"manual\">\n<tr><th style=\"min-width:initial\"> Code </th> <th> Notes</th> </tr>\n<tr><td colspan=\"2\">Sub-matrices</td></tr>\n<tr>\n<td> \n\\code \n  sm1.block(startRow, startCol, rows, cols); \n  sm1.block(startRow, startCol); \n  sm1.topLeftCorner(rows, cols); \n  sm1.topRightCorner(rows, cols);\n  sm1.bottomLeftCorner( rows, cols);\n  sm1.bottomRightCorner( rows, cols);\n  \\endcode\n</td><td>\nContrary to dense matrices, here <strong>all these methods are read-only</strong>.\\n\nSee \\ref TutorialSparse_SubMatrices and below for read-write sub-matrices.\n</td>\n</tr>\n<tr class=\"alt\"><td colspan=\"2\"> Range </td></tr>\n<tr class=\"alt\">\n<td> \n\\code \n  sm1.innerVector(outer);           // RW\n  sm1.innerVectors(start, size);    // RW\n  sm1.leftCols(size);               // RW\n  sm2.rightCols(size);              // RO because sm2 is row-major\n  sm1.middleRows(start, numRows);   // RO because sm1 is column-major\n  sm1.middleCols(start, numCols);   // RW\n  sm1.col(j);                       // RW\n\\endcode\n</td>\n<td>\nA inner vector is either a row (for row-major) or a column (for column-major).\\n\nAs stated earlier, for a read-write sub-matrix (RW), the evaluation can be done in a matrix with different storage order.\n</td>\n</tr>\n<tr><td colspan=\"2\"> Triangular and selfadjoint views</td></tr>\n<tr>\n<td> \n\\code\n  sm2 = sm1.triangularview<Lower>();\n  sm2 = sm1.selfadjointview<Lower>();\n\\endcode\n</td>\n<td> Several combination between triangular views and blocks views are possible\n\\code \n  \\endcode </td>\n</tr>\n<tr class=\"alt\"><td colspan=\"2\">Triangular solve </td></tr>\n<tr class=\"alt\">\n<td> \n\\code \n dv2 = sm1.triangularView<Upper>().solve(dv1);\n dv2 = sm1.topLeftCorner(size, size)\n          .triangularView<Lower>().solve(dv1);\n\\endcode \n</td>\n<td> For general sparse solve, Use any suitable module described at \\ref TopicSparseSystems </td>\n</tr>\n<tr><td colspan=\"2\"> Low-level API</td></tr>\n<tr>\n<td>\n\\code\nsm1.valuePtr();      // Pointer to the values\nsm1.innerIndextr();  // Pointer to the indices.\nsm1.outerIndexPtr(); // Pointer to the beginning of each inner vector\n\\endcode\n</td>\n<td>\nIf the matrix is not in compressed form, makeCompressed() should be called before.\\n\nNote that these functions are mostly provided for interoperability purposes with external libraries.\\n\nA better access to the values of the matrix is done by using the InnerIterator class as described in \\link TutorialSparse the Tutorial Sparse \\endlink section</td>\n</tr>\n<tr class=\"alt\"><td colspan=\"2\">Mapping external buffers</td></tr>\n<tr class=\"alt\">\n<td>\n\\code\nint outerIndexPtr[cols+1];\nint innerIndices[nnz];\ndouble values[nnz];\nMap<SparseMatrix<double> > sm1(rows,cols,nnz,outerIndexPtr, // read-write\n                               innerIndices,values);\nMap<const SparseMatrix<double> > sm2(...);                  // read-only\n\\endcode\n</td>\n<td>As for dense matrices, class Map<SparseMatrixType> can be used to see external buffers as an %Eigen's SparseMatrix object. </td>\n</tr>\n</table>\n*/\n}\n"
  },
  {
    "path": "include/eigen3/doc/StlContainers.dox",
    "content": "namespace Eigen {\n\n/** \\eigenManualPage TopicStlContainers Using STL Containers with Eigen\n\n\\eigenAutoToc\n\n\\section StlContainers_summary Executive summary\n\nUsing STL containers on \\ref TopicFixedSizeVectorizable \"fixed-size vectorizable Eigen types\", or classes having members of such types, requires taking the following two steps:\n\n\\li A 16-byte-aligned allocator must be used. Eigen does provide one ready for use: aligned_allocator.\n\\li If you want to use the std::vector container, you need to \\#include <Eigen/StdVector>.\n\nThese issues arise only with \\ref TopicFixedSizeVectorizable \"fixed-size vectorizable Eigen types\" and \\ref TopicStructHavingEigenMembers \"structures having such Eigen objects as member\". For other Eigen types, such as Vector3f or MatrixXd, no special care is needed when using STL containers.\n\n\\section allocator Using an aligned allocator\n\nSTL containers take an optional template parameter, the allocator type. When using STL containers on \\ref TopicFixedSizeVectorizable \"fixed-size vectorizable Eigen types\", you need tell the container to use an allocator that will always allocate memory at 16-byte-aligned locations. Fortunately, Eigen does provide such an allocator: Eigen::aligned_allocator.\n\nFor example, instead of\n\\code\nstd::map<int, Eigen::Vector4f>\n\\endcode\nyou need to use\n\\code\nstd::map<int, Eigen::Vector4f, std::less<int>, \n         Eigen::aligned_allocator<std::pair<const int, Eigen::Vector4f> > >\n\\endcode\nNote that the third parameter \"std::less<int>\" is just the default value, but we have to include it because we want to specify the fourth parameter, which is the allocator type.\n\n\\section StlContainers_vector The case of std::vector\n\nThe situation with std::vector was even worse (explanation below) so we had to specialize it for the Eigen::aligned_allocator type. In practice you \\b must use the Eigen::aligned_allocator (not another aligned allocator), \\b and \\#include <Eigen/StdVector>.\n\nHere is an example:\n\\code\n#include<Eigen/StdVector>\n/* ... */\nstd::vector<Eigen::Vector4f,Eigen::aligned_allocator<Eigen::Vector4f> >\n\\endcode\n\n\\subsection vector_spec An alternative - specializing std::vector for Eigen types\n\nAs an alternative to the recommended approach described above, you have the option to specialize std::vector for Eigen types requiring alignment. \nThe advantage is that you won't need to declare std::vector all over with Eigen::allocator. One drawback on the other hand side is that\nthe specialization needs to be defined before all code pieces in which e.g. std::vector<Vector2d> is used. Otherwise, without knowing the specialization\nthe compiler will compile that particular instance with the default std::allocator and you program is most likely to crash.\n\nHere is an example:\n\\code\n#include<Eigen/StdVector>\n/* ... */\nEIGEN_DEFINE_STL_VECTOR_SPECIALIZATION(Matrix2d)\nstd::vector<Eigen::Vector2d>\n\\endcode\n\n<span class=\"note\">\\b Explanation: The resize() method of std::vector takes a value_type argument (defaulting to value_type()). So with std::vector<Eigen::Vector4f>, some Eigen::Vector4f objects will be passed by value, which discards any alignment modifiers, so a Eigen::Vector4f can be created at an unaligned location. In order to avoid that, the only solution we saw was to specialize std::vector to make it work on a slight modification of, here, Eigen::Vector4f, that is able to deal properly with this situation.\n</span>\n\n*/\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/StorageOrders.dox",
    "content": "namespace Eigen {\n\n/** \\eigenManualPage TopicStorageOrders Storage orders\n\nThere are two different storage orders for matrices and two-dimensional arrays: column-major and row-major.\nThis page explains these storage orders and how to specify which one should be used.\n\n\\eigenAutoToc\n\n\n\\section TopicStorageOrdersIntro Column-major and row-major storage\n\nThe entries of a matrix form a two-dimensional grid. However, when the matrix is stored in memory, the entries\nhave to somehow be laid out linearly. There are two main ways to do this, by row and by column.\n\nWe say that a matrix is stored in \\b row-major order if it is stored row by row. The entire first row is\nstored first, followed by the entire second row, and so on. Consider for example the matrix\n\n\\f[\nA = \\begin{bmatrix}\n8 & 2 & 2 & 9 \\\\\n9 & 1 & 4 & 4 \\\\\n3 & 5 & 4 & 5\n\\end{bmatrix}.\n\\f]\n\nIf this matrix is stored in row-major order, then the entries are laid out in memory as follows:\n\n\\code 8 2 2 9 9 1 4 4 3 5 4 5 \\endcode\n\nOn the other hand, a matrix is stored in \\b column-major order if it is stored column by column, starting with\nthe entire first column, followed by the entire second column, and so on. If the above matrix is stored in\ncolumn-major order, it is laid out as follows:\n\n\\code 8 9 3 2 1 5 2 4 4 9 4 5 \\endcode\n\nThis example is illustrated by the following Eigen code. It uses the PlainObjectBase::data() function, which\nreturns a pointer to the memory location of the first entry of the matrix.\n\n<table class=\"example\">\n<tr><th>Example</th><th>Output</th></tr>\n<tr><td>\n\\include TopicStorageOrders_example.cpp\n</td>\n<td>\n\\verbinclude TopicStorageOrders_example.out\n</td></tr></table>\n\n\n\\section TopicStorageOrdersInEigen Storage orders in Eigen\n\nThe storage order of a matrix or a two-dimensional array can be set by specifying the \\c Options template\nparameter for Matrix or Array. As \\ref TutorialMatrixClass explains, the %Matrix class template has six\ntemplate parameters, of which three are compulsory (\\c Scalar, \\c RowsAtCompileTime and \\c ColsAtCompileTime)\nand three are optional (\\c Options, \\c MaxRowsAtCompileTime and \\c MaxColsAtCompileTime). If the \\c Options\nparameter is set to \\c RowMajor, then the matrix or array is stored in row-major order; if it is set to \n\\c ColMajor, then it is stored in column-major order. This mechanism is used in the above Eigen program to\nspecify the storage order.\n\nIf the storage order is not specified, then Eigen defaults to storing the entry in column-major. This is also\nthe case if one of the convenience typedefs (\\c Matrix3f, \\c ArrayXXd, etc.) is used.\n\nMatrices and arrays using one storage order can be assigned to matrices and arrays using the other storage\norder, as happens in the above program when \\c Arowmajor is initialized using \\c Acolmajor. Eigen will reorder\nthe entries automatically. More generally, row-major and column-major matrices can be mixed in an expression\nas we want.\n\n\n\\section TopicStorageOrdersWhich Which storage order to choose?\n\nSo, which storage order should you use in your program? There is no simple answer to this question; it depends\non your application. Here are some points to keep in mind:\n\n  - Your users may expect you to use a specific storage order. Alternatively, you may use other libraries than\n    Eigen, and these other libraries may expect a certain storage order. In these cases it may be easiest and\n    fastest to use this storage order in your whole program.\n  - Algorithms that traverse a matrix row by row will go faster when the matrix is stored in row-major order\n    because of better data locality. Similarly, column-by-column traversal is faster for column-major\n    matrices. It may be worthwhile to experiment a bit to find out what is faster for your particular\n    application.\n  - The default in Eigen is column-major. Naturally, most of the development and testing of the Eigen library\n    is thus done with column-major matrices. This means that, even though we aim to support column-major and\n    row-major storage orders transparently, the Eigen library may well work best with column-major matrices.\n\n*/\n}\n"
  },
  {
    "path": "include/eigen3/doc/StructHavingEigenMembers.dox",
    "content": "namespace Eigen {\n\n/** \\eigenManualPage TopicStructHavingEigenMembers Structures Having Eigen Members\n\n\\eigenAutoToc\n\n\\section StructHavingEigenMembers_summary Executive Summary\n\nIf you define a structure having members of \\ref TopicFixedSizeVectorizable \"fixed-size vectorizable Eigen types\", you must overload its \"operator new\" so that it generates 16-bytes-aligned pointers. Fortunately, %Eigen provides you with a macro EIGEN_MAKE_ALIGNED_OPERATOR_NEW that does that for you.\n\n\\section StructHavingEigenMembers_what What kind of code needs to be changed?\n\nThe kind of code that needs to be changed is this:\n\n\\code\nclass Foo\n{\n  ...\n  Eigen::Vector2d v;\n  ...\n};\n\n...\n\nFoo *foo = new Foo;\n\\endcode\n\nIn other words: you have a class that has as a member a \\ref TopicFixedSizeVectorizable \"fixed-size vectorizable Eigen object\", and then you dynamically create an object of that class.\n\n\\section StructHavingEigenMembers_how How should such code be modified?\n\nVery easy, you just need to put a EIGEN_MAKE_ALIGNED_OPERATOR_NEW macro in a public part of your class, like this:\n\n\\code\nclass Foo\n{\n  ...\n  Eigen::Vector2d v;\n  ...\npublic:\n  EIGEN_MAKE_ALIGNED_OPERATOR_NEW\n};\n\n...\n\nFoo *foo = new Foo;\n\\endcode\n\nThis macro makes \"new Foo\" always return an aligned pointer.\n\nIf this approach is too intrusive, see also the \\ref StructHavingEigenMembers_othersolutions \"other solutions\".\n\n\\section StructHavingEigenMembers_why Why is this needed?\n\nOK let's say that your code looks like this:\n\n\\code\nclass Foo\n{\n  ...\n  Eigen::Vector2d v;\n  ...\n};\n\n...\n\nFoo *foo = new Foo;\n\\endcode\n\nA Eigen::Vector2d consists of 2 doubles, which is 128 bits. Which is exactly the size of a SSE packet, which makes it possible to use SSE for all sorts of operations on this vector. But SSE instructions (at least the ones that %Eigen uses, which are the fast ones) require 128-bit alignment. Otherwise you get a segmentation fault.\n\nFor this reason, Eigen takes care by itself to require 128-bit alignment for Eigen::Vector2d, by doing two things:\n\\li Eigen requires 128-bit alignment for the Eigen::Vector2d's array (of 2 doubles). With GCC, this is done with a __attribute__ ((aligned(16))).\n\\li Eigen overloads the \"operator new\" of Eigen::Vector2d so it will always return 128-bit aligned pointers.\n\nThus, normally, you don't have to worry about anything, Eigen handles alignment for you...\n\n... except in one case. When you have a class Foo like above, and you dynamically allocate a new Foo as above, then, since Foo doesn't have aligned \"operator new\", the returned pointer foo is not necessarily 128-bit aligned.\n\nThe alignment attribute of the member v is then relative to the start of the class, foo. If the foo pointer wasn't aligned, then foo->v won't be aligned either!\n\nThe solution is to let class Foo have an aligned \"operator new\", as we showed in the previous section.\n\n\\section StructHavingEigenMembers_movetotop Should I then put all the members of Eigen types at the beginning of my class?\n\nThat's not required. Since Eigen takes care of declaring 128-bit alignment, all members that need it are automatically 128-bit aligned relatively to the class. So code like this works fine:\n\n\\code\nclass Foo\n{\n  double x;\n  Eigen::Vector2d v;\npublic:\n  EIGEN_MAKE_ALIGNED_OPERATOR_NEW\n};\n\\endcode\n\n\\section StructHavingEigenMembers_dynamicsize What about dynamic-size matrices and vectors?\n\nDynamic-size matrices and vectors, such as Eigen::VectorXd, allocate dynamically their own array of coefficients, so they take care of requiring absolute alignment automatically. So they don't cause this issue. The issue discussed here is only with \\ref TopicFixedSizeVectorizable  \"fixed-size vectorizable matrices and vectors\".\n\n\\section StructHavingEigenMembers_bugineigen So is this a bug in Eigen?\n\nNo, it's not our bug. It's more like an inherent problem of the C++98 language specification, and seems to be taken care of in the upcoming language revision: <a href=\"http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2007/n2341.pdf\">see this document</a>.\n\n\\section StructHavingEigenMembers_conditional What if I want to do this conditionnally (depending on template parameters) ?\n\nFor this situation, we offer the macro EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(NeedsToAlign). It will generate aligned operators like EIGEN_MAKE_ALIGNED_OPERATOR_NEW if NeedsToAlign is true. It will generate operators with the default alignment if NeedsToAlign is false.\n\nExample:\n\n\\code\ntemplate<int n> class Foo\n{\n  typedef Eigen::Matrix<float,n,1> Vector;\n  enum { NeedsToAlign = (sizeof(Vector)%16)==0 };\n  ...\n  Vector v;\n  ...\npublic:\n  EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(NeedsToAlign)\n};\n\n...\n\nFoo<4> *foo4 = new Foo<4>; // foo4 is guaranteed to be 128bit-aligned\nFoo<3> *foo3 = new Foo<3>; // foo3 has only the system default alignment guarantee\n\\endcode\n\n\n\\section StructHavingEigenMembers_othersolutions Other solutions\n\nIn case putting the EIGEN_MAKE_ALIGNED_OPERATOR_NEW macro everywhere is too intrusive, there exists at least two other solutions.\n\n\\subsection othersolutions1 Disabling alignment\n\nThe first is to disable alignment requirement for the fixed size members:\n\\code\nclass Foo\n{\n  ...\n  Eigen::Matrix<double,2,1,Eigen::DontAlign> v;\n  ...\n};\n\\endcode\nThis has for effect to disable vectorization when using \\c v.\nIf a function of Foo uses it several times, then it still possible to re-enable vectorization by copying it into an aligned temporary vector:\n\\code\nvoid Foo::bar()\n{\n  Eigen::Vector2d av(v);\n  // use av instead of v\n  ...\n  // if av changed, then do:\n  v = av;\n}\n\\endcode\n\n\\subsection othersolutions2 Private structure\n\nThe second consist in storing the fixed-size objects into a private struct which will be dynamically allocated at the construction time of the main object:\n\n\\code\nstruct Foo_d\n{\n  EIGEN_MAKE_ALIGNED_OPERATOR_NEW\n  Vector2d v;\n  ...\n};\n\n\nstruct Foo {\n  Foo() { init_d(); }\n  ~Foo() { delete d; }\n  void bar()\n  {\n    // use d->v instead of v\n    ...\n  }\nprivate:\n  void init_d() { d = new Foo_d; }\n  Foo_d* d;\n};\n\\endcode\n\nThe clear advantage here is that the class Foo remains unchanged regarding alignment issues. The drawback is that a heap allocation will be required whatsoever.\n\n*/\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/TemplateKeyword.dox",
    "content": "namespace Eigen {\n\n/** \\page TopicTemplateKeyword The template and typename keywords in C++\n\nThere are two uses for the \\c template and \\c typename keywords in C++. One of them is fairly well known\namongst programmers: to define templates. The other use is more obscure: to specify that an expression refers\nto a template function or a type. This regularly trips up programmers that use the %Eigen library, often\nleading to error messages from the compiler that are difficult to understand, such as \"expected expression\" or\n\"no match for operator<\".\n\n\\eigenAutoToc\n\n\n\\section TopicTemplateKeywordToDefineTemplates Using the template and typename keywords to define templates\n\nThe \\c template and \\c typename keywords are routinely used to define templates. This is not the topic of this\npage as we assume that the reader is aware of this (otherwise consult a C++ book). The following example\nshould illustrate this use of the \\c template keyword.\n\n\\code\ntemplate <typename T>\nbool isPositive(T x)\n{\n    return x > 0;\n}\n\\endcode\n\nWe could just as well have written <tt>template &lt;class T&gt;</tt>; the keywords \\c typename and \\c class have the\nsame meaning in this context.\n\n\n\\section TopicTemplateKeywordExample An example showing the second use of the template keyword\n\nLet us illustrate the second use of the \\c template keyword with an example. Suppose we want to write a\nfunction which copies all entries in the upper triangular part of a matrix into another matrix, while keeping\nthe lower triangular part unchanged. A straightforward implementation would be as follows:\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include TemplateKeyword_simple.cpp\n</td>\n<td>\n\\verbinclude TemplateKeyword_simple.out\n</td></tr></table>\n\nThat works fine, but it is not very flexible. First, it only works with dynamic-size matrices of\nsingle-precision floats; the function \\c copyUpperTriangularPart() does not accept static-size matrices or\nmatrices with double-precision numbers. Second, if you use an expression such as\n<tt>mat.topLeftCorner(3,3)</tt> as the parameter \\c src, then this is copied into a temporary variable of type\nMatrixXf; this copy can be avoided.\n\nAs explained in \\ref TopicFunctionTakingEigenTypes, both issues can be resolved by making \n\\c copyUpperTriangularPart() accept any object of type MatrixBase. This leads to the following code:\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include TemplateKeyword_flexible.cpp\n</td>\n<td>\n\\verbinclude TemplateKeyword_flexible.out\n</td></tr></table>\n\nThe one line in the body of the function \\c copyUpperTriangularPart() shows the second, more obscure use of\nthe \\c template keyword in C++.  Even though it may look strange, the \\c template keywords are necessary\naccording to the standard. Without it, the compiler may reject the code with an error message like \"no match\nfor operator<\".\n\n\n\\section TopicTemplateKeywordExplanation Explanation\n\nThe reason that the \\c template keyword is necessary in the last example has to do with the rules for how\ntemplates are supposed to be compiled in C++. The compiler has to check the code for correct syntax at the\npoint where the template is defined, without knowing the actual value of the template arguments (\\c Derived1\nand \\c Derived2 in the example). That means that the compiler cannot know that <tt>dst.triangularView</tt> is\na member template and that the following &lt; symbol is part of the delimiter for the template\nparameter. Another possibility would be that <tt>dst.triangularView</tt> is a member variable with the &lt;\nsymbol refering to the <tt>operator&lt;()</tt> function. In fact, the compiler should choose the second\npossibility, according to the standard. If <tt>dst.triangularView</tt> is a member template (as in our case),\nthe programmer should specify this explicitly with the \\c template keyword and write <tt>dst.template\ntriangularView</tt>.\n\nThe precise rules are rather complicated, but ignoring some subtleties we can summarize them as follows:\n- A <em>dependent name</em> is name that depends (directly or indirectly) on a template parameter. In the\n  example, \\c dst is a dependent name because it is of type <tt>MatrixBase&lt;Derived1&gt;</tt> which depends\n  on the template parameter \\c Derived1.\n- If the code contains either one of the constructs <tt>xxx.yyy</tt> or <tt>xxx-&gt;yyy</tt> and \\c xxx is a\n  dependent name and \\c yyy refers to a member template, then the \\c template keyword must be used before \n  \\c yyy, leading to <tt>xxx.template yyy</tt> or <tt>xxx-&gt;template yyy</tt>.\n- If the code contains the construct <tt>xxx::yyy</tt> and \\c xxx is a dependent name and \\c yyy refers to a\n  member typedef, then the \\c typename keyword must be used before the whole construct, leading to\n  <tt>typename xxx::yyy</tt>.\n\nAs an example where the \\c typename keyword is required, consider the following code in \\ref TutorialSparse\nfor iterating over the non-zero entries of a sparse matrix type:\n\n\\code\nSparseMatrixType mat(rows,cols);\nfor (int k=0; k<mat.outerSize(); ++k)\n  for (SparseMatrixType::InnerIterator it(mat,k); it; ++it)\n  {\n    /* ... */\n  }\n\\endcode\n\nIf \\c SparseMatrixType depends on a template parameter, then the \\c typename keyword is required:\n\n\\code\ntemplate <typename T>\nvoid iterateOverSparseMatrix(const SparseMatrix<T>& mat;\n{\n  for (int k=0; k<m1.outerSize(); ++k)\n    for (typename SparseMatrix<T>::InnerIterator it(mat,k); it; ++it)\n    {\n      /* ... */\n    }\n}\n\\endcode\n\n\n\\section TopicTemplateKeywordResources Resources for further reading\n\nFor more information and a fuller explanation of this topic, the reader may consult the following sources:\n- The book \"C++ Template Metaprogramming\" by David Abrahams and Aleksey Gurtovoy contains a very good\n  explanation in Appendix B (\"The typename and template Keywords\") which formed the basis for this page.\n- http://pages.cs.wisc.edu/~driscoll/typename.html\n- http://www.parashift.com/c++-faq-lite/templates.html#faq-35.18\n- http://www.comeaucomputing.com/techtalk/templates/#templateprefix\n- http://www.comeaucomputing.com/techtalk/templates/#typename\n\n*/\n}\n"
  },
  {
    "path": "include/eigen3/doc/TopicAliasing.dox",
    "content": "namespace Eigen {\n\n/** \\eigenManualPage TopicAliasing Aliasing\n\nIn %Eigen, aliasing refers to assignment statement in which the same matrix (or array or vector) appears on the\nleft and on the right of the assignment operators. Statements like <tt>mat = 2 * mat;</tt> or <tt>mat =\nmat.transpose();</tt> exhibit aliasing. The aliasing in the first example is harmless, but the aliasing in the\nsecond example leads to unexpected results. This page explains what aliasing is, when it is harmful, and what\nto do about it.\n\n\\eigenAutoToc\n\n\n\\section TopicAliasingExamples Examples\n\nHere is a simple example exhibiting aliasing:\n\n<table class=\"example\">\n<tr><th>Example</th><th>Output</th></tr>\n<tr><td>\n\\include TopicAliasing_block.cpp\n</td>\n<td>\n\\verbinclude TopicAliasing_block.out\n</td></tr></table>\n\nThe output is not what one would expect. The problem is the assignment\n\\code\nmat.bottomRightCorner(2,2) = mat.topLeftCorner(2,2);\n\\endcode\nThis assignment exhibits aliasing: the coefficient \\c mat(1,1) appears both in the block\n<tt>mat.bottomRightCorner(2,2)</tt> on the left-hand side of the assignment and the block\n<tt>mat.topLeftCorner(2,2)</tt> on the right-hand side. After the assignment, the (2,2) entry in the bottom\nright corner should have the value of \\c mat(1,1) before the assignment, which is 5. However, the output shows\nthat \\c mat(2,2) is actually 1. The problem is that %Eigen uses lazy evaluation (see \n\\ref TopicEigenExpressionTemplates) for <tt>mat.topLeftCorner(2,2)</tt>. The result is similar to\n\\code\nmat(1,1) = mat(0,0);\nmat(1,2) = mat(0,1);\nmat(2,1) = mat(1,0);\nmat(2,2) = mat(1,1);\n\\endcode\nThus, \\c mat(2,2) is assigned the \\e new value of \\c mat(1,1) instead of the old value. The next section\nexplains how to solve this problem by calling \\link DenseBase::eval() eval()\\endlink.\n\nAliasing occurs more naturally when trying to shrink a matrix. For example, the expressions <tt>vec =\nvec.head(n)</tt> and <tt>mat = mat.block(i,j,r,c)</tt> exhibit aliasing.\n\nIn general, aliasing cannot be detected at compile time: if \\c mat in the first example were a bit bigger,\nthen the blocks would not overlap, and there would be no aliasing problem. However, %Eigen does detect some\ninstances of aliasing, albeit at run time.  The following example exhibiting aliasing was mentioned in \\ref\nTutorialMatrixArithmetic :\n\n<table class=\"example\">\n<tr><th>Example</th><th>Output</th></tr>\n<tr><td>\n\\include tut_arithmetic_transpose_aliasing.cpp\n</td>\n<td>\n\\verbinclude tut_arithmetic_transpose_aliasing.out\n</td></tr></table>\n\nAgain, the output shows the aliasing issue. However, by default %Eigen uses a run-time assertion to detect this\nand exits with a message like\n\n\\verbatim\nvoid Eigen::DenseBase<Derived>::checkTransposeAliasing(const OtherDerived&) const \n[with OtherDerived = Eigen::Transpose<Eigen::Matrix<int, 2, 2, 0, 2, 2> >, Derived = Eigen::Matrix<int, 2, 2, 0, 2, 2>]: \nAssertion `(!internal::check_transpose_aliasing_selector<Scalar,internal::blas_traits<Derived>::IsTransposed,OtherDerived>::run(internal::extract_data(derived()), other)) \n&& \"aliasing detected during transposition, use transposeInPlace() or evaluate the rhs into a temporary using .eval()\"' failed.\n\\endverbatim\n\nThe user can turn %Eigen's run-time assertions like the one to detect this aliasing problem off by defining the\nEIGEN_NO_DEBUG macro, and the above program was compiled with this macro turned off in order to illustrate the\naliasing problem. See \\ref TopicAssertions for more information about %Eigen's run-time assertions.\n\n\n\\section TopicAliasingSolution Resolving aliasing issues\n\nIf you understand the cause of the aliasing issue, then it is obvious what must happen to solve it: %Eigen has\nto evaluate the right-hand side fully into a temporary matrix/array and then assign it to the left-hand\nside. The function \\link DenseBase::eval() eval() \\endlink does precisely that.\n\nFor example, here is the corrected version of the first example above:\n\n<table class=\"example\">\n<tr><th>Example</th><th>Output</th></tr>\n<tr><td>\n\\include TopicAliasing_block_correct.cpp\n</td>\n<td>\n\\verbinclude TopicAliasing_block_correct.out\n</td></tr></table>\n\nNow, \\c mat(2,2) equals 5 after the assignment, as it should be.\n\nThe same solution also works for the second example, with the transpose: simply replace the line \n<tt>a = a.transpose();</tt> with <tt>a = a.transpose().eval();</tt>. However, in this common case there is a\nbetter solution. %Eigen provides the special-purpose function \n\\link DenseBase::transposeInPlace() transposeInPlace() \\endlink which replaces a matrix by its transpose. \nThis is shown below:\n\n<table class=\"example\">\n<tr><th>Example</th><th>Output</th></tr>\n<tr><td>\n\\include tut_arithmetic_transpose_inplace.cpp\n</td>\n<td>\n\\verbinclude tut_arithmetic_transpose_inplace.out\n</td></tr></table>\n\nIf an xxxInPlace() function is available, then it is best to use it, because it indicates more clearly what you\nare doing. This may also allow %Eigen to optimize more aggressively. These are some of the xxxInPlace()\nfunctions provided: \n\n<table class=\"manual\">\n<tr><th>Original function</th><th>In-place function</th></tr>\n<tr> <td> MatrixBase::adjoint() </td> <td> MatrixBase::adjointInPlace() </td> </tr>\n<tr class=\"alt\"> <td> DenseBase::reverse() </td> <td> DenseBase::reverseInPlace() </td> </tr>\n<tr> <td> LDLT::solve() </td> <td> LDLT::solveInPlace() </td> </tr>\n<tr class=\"alt\"> <td> LLT::solve() </td> <td> LLT::solveInPlace() </td> </tr>\n<tr> <td> TriangularView::solve() </td> <td> TriangularView::solveInPlace() </td> </tr>\n<tr class=\"alt\"> <td> DenseBase::transpose() </td> <td> DenseBase::transposeInPlace() </td> </tr>\n</table>\n\nIn the special case where a matrix or vector is shrunk using an expression like <tt>vec = vec.head(n)</tt>,\nyou can use \\link PlainObjectBase::conservativeResize() conservativeResize() \\endlink.\n\n\n\\section TopicAliasingCwise Aliasing and component-wise operations\n\nAs explained above, it may be dangerous if the same matrix or array occurs on both the left-hand side and the\nright-hand side of an assignment operator, and it is then often necessary to evaluate the right-hand side\nexplicitly. However, applying component-wise operations (such as matrix addition, scalar multiplication and\narray multiplication) is safe. \n\nThe following example has only component-wise operations. Thus, there is no need for \\link DenseBase::eval()\neval() \\endlink even though the same matrix appears on both sides of the assignments.\n\n<table class=\"example\">\n<tr><th>Example</th><th>Output</th></tr>\n<tr><td>\n\\include TopicAliasing_cwise.cpp\n</td>\n<td>\n\\verbinclude TopicAliasing_cwise.out\n</td></tr></table>\n\nIn general, an assignment is safe if the (i,j) entry of the expression on the right-hand side depends only on\nthe (i,j) entry of the matrix or array on the left-hand side and not on any other entries. In that case it is\nnot necessary to evaluate the right-hand side explicitly.\n\n\n\\section TopicAliasingMatrixMult Aliasing and matrix multiplication\n\nMatrix multiplication is the only operation in %Eigen that assumes aliasing by default, <strong>under the\ncondition that the destination matrix is not resized</strong>.\nThus, if \\c matA is a \\b squared matrix, then the statement <tt>matA = matA * matA;</tt> is safe.\nAll other operations in %Eigen assume that there are no aliasing problems,\neither because the result is assigned to a different matrix or because it is a component-wise operation.\n\n<table class=\"example\">\n<tr><th>Example</th><th>Output</th></tr>\n<tr><td>\n\\include TopicAliasing_mult1.cpp\n</td>\n<td>\n\\verbinclude TopicAliasing_mult1.out\n</td></tr></table>\n\nHowever, this comes at a price. When executing the expression <tt>matA = matA * matA</tt>, %Eigen evaluates the\nproduct in a temporary matrix which is assigned to \\c matA after the computation. This is fine. But %Eigen does\nthe same when the product is assigned to a different matrix (e.g., <tt>matB = matA * matA</tt>). In that case,\nit is more efficient to evaluate the product directly into \\c matB instead of evaluating it first into a\ntemporary matrix and copying that matrix to \\c matB.\n\nThe user can indicate with the \\link MatrixBase::noalias() noalias()\\endlink function that there is no\naliasing, as follows: <tt>matB.noalias() = matA * matA</tt>. This allows %Eigen to evaluate the matrix product\n<tt>matA * matA</tt> directly into \\c matB.\n\n<table class=\"example\">\n<tr><th>Example</th><th>Output</th></tr>\n<tr><td>\n\\include TopicAliasing_mult2.cpp\n</td>\n<td>\n\\verbinclude TopicAliasing_mult2.out\n</td></tr></table>\n\nOf course, you should not use \\c noalias() when there is in fact aliasing taking place. If you do, then you\nmay get wrong results:\n\n<table class=\"example\">\n<tr><th>Example</th><th>Output</th></tr>\n<tr><td>\n\\include TopicAliasing_mult3.cpp\n</td>\n<td>\n\\verbinclude TopicAliasing_mult3.out\n</td></tr></table>\n\nMoreover, starting in Eigen 3.3, aliasing is \\b not assumed if the destination matrix is resized and the product is not directly assigned to the destination.\nTherefore, the following example is also wrong:\n\n<table class=\"example\">\n<tr><th>Example</th><th>Output</th></tr>\n<tr><td>\n\\include TopicAliasing_mult4.cpp\n</td>\n<td>\n\\verbinclude TopicAliasing_mult4.out\n</td></tr></table>\n\nAs for any aliasing issue, you can resolve it by explicitly evaluating the expression prior to assignment:\n<table class=\"example\">\n<tr><th>Example</th><th>Output</th></tr>\n<tr><td>\n\\include TopicAliasing_mult5.cpp\n</td>\n<td>\n\\verbinclude TopicAliasing_mult5.out\n</td></tr></table>\n\n\\section TopicAliasingSummary Summary\n\nAliasing occurs when the same matrix or array coefficients appear both on the left- and the right-hand side of\nan assignment operator.\n - Aliasing is harmless with coefficient-wise computations; this includes scalar multiplication and matrix or\n   array addition.\n - When you multiply two matrices, %Eigen assumes that aliasing occurs. If you know that there is no aliasing,\n   then you can use \\link MatrixBase::noalias() noalias()\\endlink.\n - In all other situations, %Eigen assumes that there is no aliasing issue and thus gives the wrong result if\n   aliasing does in fact occur. To prevent this, you have to use \\link DenseBase::eval() eval() \\endlink or\n   one of the xxxInPlace() functions.\n\n*/\n}\n"
  },
  {
    "path": "include/eigen3/doc/TopicAssertions.dox",
    "content": "namespace Eigen {\n\n/** \\page TopicAssertions Assertions\n\n\\eigenAutoToc\n\n\\section PlainAssert Assertions\n\nThe macro eigen_assert is defined to be \\c eigen_plain_assert by default. We use eigen_plain_assert instead of \\c assert to work around a known bug for GCC <= 4.3. Basically, eigen_plain_assert \\a is \\c assert.\n\n\\subsection RedefineAssert Redefining assertions\n\nBoth eigen_assert and eigen_plain_assert are defined in Macros.h. Defining eigen_assert indirectly gives you a chance to change its behavior. You can redefine this macro if you want to do something else such as throwing an exception, and fall back to its default behavior with eigen_plain_assert. The code below tells Eigen to throw an std::runtime_error:\n\n\\code\n#include <stdexcept>\n#undef eigen_assert\n#define eigen_assert(x) \\\n  if (!(x)) { throw (std::runtime_error(\"Put your message here\")); }\n\\endcode\n\n\\subsection DisableAssert Disabling assertions\n\nAssertions cost run time and can be turned off. You can suppress eigen_assert by defining \\c EIGEN_NO_DEBUG \\b before including Eigen headers. \\c EIGEN_NO_DEBUG is undefined by default unless \\c NDEBUG is defined.\n\n\\section StaticAssert Static assertions\n\nStatic assertions are not standardized until C++11. However, in the Eigen library, there are many conditions can and should be detectedat compile time. For instance, we use static assertions to prevent the code below from compiling.\n\n\\code\nMatrix3d()  + Matrix4d();   // adding matrices of different sizes\nMatrix4cd() * Vector3cd();  // invalid product known at compile time\n\\endcode\n\nStatic assertions are defined in StaticAssert.h. If there is native static_assert, we use it. Otherwise, we have implemented an assertion macro that can show a limited range of messages.\n\nOne can easily come up with static assertions without messages, such as:\n\n\\code\n#define STATIC_ASSERT(x) \\\n  switch(0) { case 0: case x:; }\n\\endcode\n\nHowever, the example above obviously cannot tell why the assertion failed. Therefore, we define a \\c struct in namespace Eigen::internal to handle available messages.\n\n\\code\ntemplate<bool condition>\nstruct static_assertion {};\n\ntemplate<>\nstruct static_assertion<true>\n{\n  enum {\n    YOU_TRIED_CALLING_A_VECTOR_METHOD_ON_A_MATRIX,\n    YOU_MIXED_VECTORS_OF_DIFFERENT_SIZES,\n    // see StaticAssert.h for all enums.\n  };\n};\n\\endcode\n\nAnd then, we define EIGEN_STATIC_ASSERT(CONDITION,MSG) to access Eigen::internal::static_assertion<bool(CONDITION)>::MSG. If the condition evaluates into \\c false, your compiler displays a lot of messages explaining there is no MSG in static_assert<false>. Nevertheless, this is \\a not in what we are interested. As you can see, all members of static_assert<true> are ALL_CAPS_AND_THEY_ARE_SHOUTING.\n\n\\warning\nWhen using this macro, MSG should be a member of static_assertion<true>, or the static assertion \\b always fails.\nCurrently, it can only be used in function scope.\n\n\\subsection DerivedStaticAssert Derived static assertions\n\nThere are other macros derived from EIGEN_STATIC_ASSERT to enhance readability. Their names are self-explanatory.\n\n- \\b EIGEN_STATIC_ASSERT_FIXED_SIZE(TYPE) - passes if \\a TYPE is fixed size.\n- \\b EIGEN_STATIC_ASSERT_DYNAMIC_SIZE(TYPE) - passes if \\a TYPE is dynamic size.\n- \\b EIGEN_STATIC_ASSERT_LVALUE(Derived) - failes if \\a Derived is read-only.\n- \\b EIGEN_STATIC_ASSERT_ARRAYXPR(Derived) - passes if \\a Derived is an array expression.\n- <b>EIGEN_STATIC_ASSERT_SAME_XPR_KIND(Derived1, Derived2)</b> - failes if the two expressions are an array one and a matrix one.\n\nBecause Eigen handles both fixed-size and dynamic-size expressions, some conditions cannot be clearly determined at compile time. We classify them into strict assertions and permissive assertions.\n\n\\subsubsection StrictAssertions Strict assertions\n\nThese assertions fail if the condition <b>may not</b> be met. For example, MatrixXd may not be a vector, so it fails EIGEN_STATIC_ASSERT_VECTOR_ONLY.\n\n- \\b EIGEN_STATIC_ASSERT_VECTOR_ONLY(TYPE) - passes if \\a TYPE must be a vector type.\n- <b>EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(TYPE, SIZE)</b> - passes if \\a TYPE must be a vector of the given size.\n- <b>EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(TYPE, ROWS, COLS)</b> - passes if \\a TYPE must be a matrix with given rows and columns.\n\n\\subsubsection PermissiveAssertions Permissive assertions\n\nThese assertions fail if the condition \\b cannot be met. For example, MatrixXd and Matrix4d may have the same size, so they pass EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE.\n\n- \\b EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(TYPE0,TYPE1) - fails if the two vector expression types must have different sizes.\n- \\b EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(TYPE0,TYPE1) - fails if the two matrix expression types must have different sizes.\n- \\b EIGEN_STATIC_ASSERT_SIZE_1x1(TYPE) - fails if \\a TYPE cannot be an 1x1 expression.\n\nSee StaticAssert.h for details such as what messages they throw.\n\n\\subsection DisableStaticAssert Disabling static assertions\n\nIf \\c EIGEN_NO_STATIC_ASSERT is defined, static assertions turn into <tt>eigen_assert</tt>'s, working like:\n\n\\code\n#define EIGEN_STATIC_ASSERT(CONDITION,MSG) eigen_assert((CONDITION) && #MSG);\n\\endcode\n\nThis saves compile time but consumes more run time. \\c EIGEN_NO_STATIC_ASSERT is undefined by default.\n\n*/\n}\n"
  },
  {
    "path": "include/eigen3/doc/TopicCMakeGuide.dox",
    "content": "namespace Eigen {\n\n/**\n\n\\page TopicCMakeGuide Using %Eigen in CMake Projects\n\n%Eigen provides native CMake support which allows the library to be easily\nused in CMake projects.\n\n\\note %CMake 3.0 (or later) is required to enable this functionality.\n\n%Eigen exports a CMake target called `Eigen3::Eigen` which can be imported\nusing the `find_package` CMake command and used by calling\n`target_link_libraries` as in the following example:\n\\code{.cmake}\ncmake_minimum_required (VERSION 3.0)\nproject (myproject)\n\nfind_package (Eigen3 3.3 REQUIRED NO_MODULE)\n\nadd_executable (example example.cpp)\ntarget_link_libraries (example Eigen3::Eigen)\n\\endcode\n\nThe above code snippet must be placed in a file called `CMakeLists.txt` alongside\n`example.cpp`. After running\n\\code{.sh}\n$ cmake path-to-example-directory\n\\endcode\nCMake will produce project files that generate an executable called `example`\nwhich requires at least version 3.3 of %Eigen. Here, `path-to-example-directory`\nis the path to the directory that contains both `CMakeLists.txt` and\n`example.cpp`.\n\nIf you have multiple installed version of %Eigen, you can pick your favorite one by setting the \\c Eigen3_DIR cmake's variable to the respective path containing the \\c Eigen3*.cmake files. For instance:\n\\code\ncmake path-to-example-directory -DEigen3_DIR=$HOME/mypackages/share/eigen3/cmake/\n\\endcode\n\nIf the `REQUIRED` option is omitted when locating %Eigen using\n`find_package`, one can check whether the package was found as follows:\n\\code{.cmake}\nfind_package (Eigen3 3.3 NO_MODULE)\n\nif (TARGET Eigen3::Eigen)\n  # Use the imported target\nendif (TARGET Eigen3::Eigen)\n\\endcode\n\n*/\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/TopicEigenExpressionTemplates.dox",
    "content": "namespace Eigen {\n\n/** \\page TopicEigenExpressionTemplates Expression templates in Eigen\n\n\nTODO: write this dox page!\n\nIs linked from the tutorial on arithmetic ops.\n\n*/\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/TopicLazyEvaluation.dox",
    "content": "namespace Eigen {\n\n/** \\page TopicLazyEvaluation Lazy Evaluation and Aliasing\n\nExecutive summary: Eigen has intelligent compile-time mechanisms to enable lazy evaluation and removing temporaries where appropriate.\nIt will handle aliasing automatically in most cases, for example with matrix products. The automatic behavior can be overridden\nmanually by using the MatrixBase::eval() and MatrixBase::noalias() methods.\n\nWhen you write a line of code involving a complex expression such as\n\n\\code mat1 = mat2 + mat3 * (mat4 + mat5); \\endcode\n\nEigen determines automatically, for each sub-expression, whether to evaluate it into a temporary variable. Indeed, in certain cases it is better to evaluate immediately a sub-expression into a temporary variable, while in other cases it is better to avoid that.\n\nA traditional math library without expression templates always evaluates all sub-expressions into temporaries. So with this code,\n\n\\code vec1 = vec2 + vec3; \\endcode\n\na traditional library would evaluate \\c vec2 + vec3 into a temporary \\c vec4 and then copy \\c vec4  into \\c vec1. This is of course inefficient: the arrays are traversed twice, so there are a lot of useless load/store operations.\n\nExpression-templates-based libraries can avoid evaluating sub-expressions into temporaries, which in many cases results in large speed improvements. This is called <i>lazy evaluation</i> as an expression is getting evaluated as late as possible, instead of immediately. However, most other expression-templates-based libraries <i>always</i> choose lazy evaluation. There are two problems with that: first, lazy evaluation is not always a good choice for performance; second, lazy evaluation can be very dangerous, for example with matrix products: doing <tt>matrix = matrix*matrix</tt> gives a wrong result if the matrix product is lazy-evaluated, because of the way matrix product works.\n\nFor these reasons, Eigen has intelligent compile-time mechanisms to determine automatically when to use lazy evaluation, and when on the contrary it should evaluate immediately into a temporary variable.\n\nSo in the basic example,\n\n\\code matrix1 = matrix2 + matrix3; \\endcode\n\nEigen chooses lazy evaluation. Thus the arrays are traversed only once, producing optimized code. If you really want to force immediate evaluation, use \\link MatrixBase::eval() eval()\\endlink:\n\n\\code matrix1 = (matrix2 + matrix3).eval(); \\endcode\n\nHere is now a more involved example:\n\n\\code matrix1 = -matrix2 + matrix3 + 5 * matrix4; \\endcode\n\nEigen chooses lazy evaluation at every stage in that example, which is clearly the correct choice. In fact, lazy evaluation is the \"default choice\" and Eigen will choose it except in a few circumstances.\n\n<b>The first circumstance</b> in which Eigen chooses immediate evaluation, is when it sees an assignment <tt>a = b;</tt> and the expression \\c b has the evaluate-before-assigning \\link flags flag\\endlink. The most important example of such an expression is the \\link Product matrix product expression\\endlink. For example, when you do\n\n\\code matrix = matrix * matrix; \\endcode\n\nEigen first evaluates <tt>matrix * matrix</tt> into a temporary matrix, and then copies it into the original \\c matrix. This guarantees a correct result as we saw above that lazy evaluation gives wrong results with matrix products. It also doesn't cost much, as the cost of the matrix product itself is much higher.\n\nWhat if you know that the result does no alias the operand of the product and want to force lazy evaluation? Then use \\link MatrixBase::noalias() .noalias()\\endlink instead. Here is an example:\n\n\\code matrix1.noalias() = matrix2 * matrix2; \\endcode\n\nHere, since we know that matrix2 is not the same matrix as matrix1, we know that lazy evaluation is not dangerous, so we may force lazy evaluation. Concretely, the effect of noalias() here is to bypass the evaluate-before-assigning \\link flags flag\\endlink.\n\n<b>The second circumstance</b> in which Eigen chooses immediate evaluation, is when it sees a nested expression such as <tt>a + b</tt> where \\c b is already an expression having the evaluate-before-nesting \\link flags flag\\endlink. Again, the most important example of such an expression is the \\link Product matrix product expression\\endlink. For example, when you do\n\n\\code matrix1 = matrix2 + matrix3 * matrix4; \\endcode\n\nthe product <tt>matrix3 * matrix4</tt> gets evaluated immediately into a temporary matrix. Indeed, experiments showed that it is often beneficial for performance to evaluate immediately matrix products when they are nested into bigger expressions.\n\n<b>The third circumstance</b> in which Eigen chooses immediate evaluation, is when its cost model shows that the total cost of an operation is reduced if a sub-expression gets evaluated into a temporary. Indeed, in certain cases, an intermediate result is sufficiently costly to compute and is reused sufficiently many times, that is worth \"caching\". Here is an example:\n\n\\code matrix1 = matrix2 * (matrix3 + matrix4); \\endcode\n\nHere, provided the matrices have at least 2 rows and 2 columns, each coefficienct of the expression <tt>matrix3 + matrix4</tt> is going to be used several times in the matrix product. Instead of computing the sum everytime, it is much better to compute it once and store it in a temporary variable. Eigen understands this and evaluates <tt>matrix3 + matrix4</tt> into a temporary variable before evaluating the product.\n\n*/\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/TopicLinearAlgebraDecompositions.dox",
    "content": "namespace Eigen {\n\n/** \\eigenManualPage TopicLinearAlgebraDecompositions Catalogue of dense decompositions\n\nThis page presents a catalogue of the dense matrix decompositions offered by Eigen.\nFor an introduction on linear solvers and decompositions, check this \\link TutorialLinearAlgebra page \\endlink.\nTo get an overview of the true relative speed of the different decompositions, check this \\link DenseDecompositionBenchmark benchmark \\endlink.\n\n\\section TopicLinAlgBigTable Catalogue of decompositions offered by Eigen\n\n<table class=\"manual-vl\">\n    <tr>\n        <th class=\"meta\"></th>\n        <th class=\"meta\" colspan=\"5\">Generic information, not Eigen-specific</th>\n        <th class=\"meta\" colspan=\"3\">Eigen-specific</th>\n    </tr>\n\n    <tr>\n        <th>Decomposition</th>\n        <th>Requirements on the matrix</th>\n        <th>Speed</th>\n        <th>Algorithm reliability and accuracy</th>\n        <th>Rank-revealing</th>\n        <th>Allows to compute (besides linear solving)</th>\n        <th>Linear solver provided by Eigen</th>\n        <th>Maturity of Eigen's implementation</th>\n        <th>Optimizations</th>\n    </tr>\n\n    <tr>\n        <td>PartialPivLU</td>\n        <td>Invertible</td>\n        <td>Fast</td>\n        <td>Depends on condition number</td>\n        <td>-</td>\n        <td>-</td>\n        <td>Yes</td>\n        <td>Excellent</td>\n        <td>Blocking, Implicit MT</td>\n    </tr>\n\n    <tr class=\"alt\">\n        <td>FullPivLU</td>\n        <td>-</td>\n        <td>Slow</td>\n        <td>Proven</td>\n        <td>Yes</td>\n        <td>-</td>\n        <td>Yes</td>\n        <td>Excellent</td>\n        <td>-</td>\n    </tr>\n\n    <tr>\n        <td>HouseholderQR</td>\n        <td>-</td>\n        <td>Fast</td>\n        <td>Depends on condition number</td>\n        <td>-</td>\n        <td>Orthogonalization</td>\n        <td>Yes</td>\n        <td>Excellent</td>\n        <td>Blocking</td>\n    </tr>\n\n    <tr class=\"alt\">\n        <td>ColPivHouseholderQR</td>\n        <td>-</td>\n        <td>Fast</td>\n        <td>Good</td>\n        <td>Yes</td>\n        <td>Orthogonalization</td>\n        <td>Yes</td>\n        <td>Excellent</td>\n        <td><em>Soon: blocking</em></td>\n    </tr>\n\n    <tr>\n        <td>FullPivHouseholderQR</td>\n        <td>-</td>\n        <td>Slow</td>\n        <td>Proven</td>\n        <td>Yes</td>\n        <td>Orthogonalization</td>\n        <td>Yes</td>\n        <td>Average</td>\n        <td>-</td>\n    </tr>\n\n    <tr class=\"alt\">\n        <td>LLT</td>\n        <td>Positive definite</td>\n        <td>Very fast</td>\n        <td>Depends on condition number</td>\n        <td>-</td>\n        <td>-</td>\n        <td>Yes</td>\n        <td>Excellent</td>\n        <td>Blocking</td>\n    </tr>\n\n    <tr>\n        <td>LDLT</td>\n        <td>Positive or negative semidefinite<sup><a href=\"#note1\">1</a></sup></td>\n        <td>Very fast</td>\n        <td>Good</td>\n        <td>-</td>\n        <td>-</td>\n        <td>Yes</td>\n        <td>Excellent</td>\n        <td><em>Soon: blocking</em></td>\n    </tr>\n\n    <tr><th class=\"inter\" colspan=\"9\">\\n Singular values and eigenvalues decompositions</th></tr>\n\n    <tr>\n        <td>BDCSVD (divide \\& conquer)</td>\n        <td>-</td>\n        <td>One of the fastest SVD algorithms</td>\n        <td>Excellent</td>\n        <td>Yes</td>\n        <td>Singular values/vectors, least squares</td>\n        <td>Yes (and does least squares)</td>\n        <td>Excellent</td>\n        <td>Blocked bidiagonalization</td>\n    </tr>\n\n    <tr>\n        <td>JacobiSVD (two-sided)</td>\n        <td>-</td>\n        <td>Slow (but fast for small matrices)</td>\n        <td>Proven<sup><a href=\"#note3\">3</a></sup></td>\n        <td>Yes</td>\n        <td>Singular values/vectors, least squares</td>\n        <td>Yes (and does least squares)</td>\n        <td>Excellent</td>\n        <td>R-SVD</td>\n    </tr>\n\n    <tr class=\"alt\">\n        <td>SelfAdjointEigenSolver</td>\n        <td>Self-adjoint</td>\n        <td>Fast-average<sup><a href=\"#note2\">2</a></sup></td>\n        <td>Good</td>\n        <td>Yes</td>\n        <td>Eigenvalues/vectors</td>\n        <td>-</td>\n        <td>Excellent</td>\n        <td><em>Closed forms for 2x2 and 3x3</em></td>\n    </tr>\n\n    <tr>\n        <td>ComplexEigenSolver</td>\n        <td>Square</td>\n        <td>Slow-very slow<sup><a href=\"#note2\">2</a></sup></td>\n        <td>Depends on condition number</td>\n        <td>Yes</td>\n        <td>Eigenvalues/vectors</td>\n        <td>-</td>\n        <td>Average</td>\n        <td>-</td>\n    </tr>\n\n    <tr class=\"alt\">\n        <td>EigenSolver</td>\n        <td>Square and real</td>\n        <td>Average-slow<sup><a href=\"#note2\">2</a></sup></td>\n        <td>Depends on condition number</td>\n        <td>Yes</td>\n        <td>Eigenvalues/vectors</td>\n        <td>-</td>\n        <td>Average</td>\n        <td>-</td>\n    </tr>\n\n    <tr>\n        <td>GeneralizedSelfAdjointEigenSolver</td>\n        <td>Square</td>\n        <td>Fast-average<sup><a href=\"#note2\">2</a></sup></td>\n        <td>Depends on condition number</td>\n        <td>-</td>\n        <td>Generalized eigenvalues/vectors</td>\n        <td>-</td>\n        <td>Good</td>\n        <td>-</td>\n    </tr>\n\n    <tr><th class=\"inter\" colspan=\"9\">\\n Helper decompositions</th></tr>\n\n    <tr>\n        <td>RealSchur</td>\n        <td>Square and real</td>\n        <td>Average-slow<sup><a href=\"#note2\">2</a></sup></td>\n        <td>Depends on condition number</td>\n        <td>Yes</td>\n        <td>-</td>\n        <td>-</td>\n        <td>Average</td>\n        <td>-</td>\n    </tr>\n\n    <tr class=\"alt\">\n        <td>ComplexSchur</td>\n        <td>Square</td>\n        <td>Slow-very slow<sup><a href=\"#note2\">2</a></sup></td>\n        <td>Depends on condition number</td>\n        <td>Yes</td>\n        <td>-</td>\n        <td>-</td>\n        <td>Average</td>\n        <td>-</td>\n    </tr>\n\n    <tr class=\"alt\">\n        <td>Tridiagonalization</td>\n        <td>Self-adjoint</td>\n        <td>Fast</td>\n        <td>Good</td>\n        <td>-</td>\n        <td>-</td>\n        <td>-</td>\n        <td>Good</td>\n        <td><em>Soon: blocking</em></td>\n    </tr>\n\n    <tr>\n        <td>HessenbergDecomposition</td>\n        <td>Square</td>\n        <td>Average</td>\n        <td>Good</td>\n        <td>-</td>\n        <td>-</td>\n        <td>-</td>\n        <td>Good</td>\n        <td><em>Soon: blocking</em></td>\n    </tr>\n\n</table>\n\n\\b Notes:\n<ul>\n<li><a name=\"note1\">\\b 1: </a>There exist two variants of the LDLT algorithm. Eigen's one produces a pure diagonal D matrix, and therefore it cannot handle indefinite matrices, unlike Lapack's one which produces a block diagonal D matrix.</li>\n<li><a name=\"note2\">\\b 2: </a>Eigenvalues, SVD and Schur decompositions rely on iterative algorithms. Their convergence speed depends on how well the eigenvalues are separated.</li>\n<li><a name=\"note3\">\\b 3: </a>Our JacobiSVD is two-sided, making for proven and optimal precision for square matrices. For non-square matrices, we have to use a QR preconditioner first. The default choice, ColPivHouseholderQR, is already very reliable, but if you want it to be proven, use FullPivHouseholderQR instead.\n</ul>\n\n\\section TopicLinAlgTerminology Terminology\n\n<dl>\n  <dt><b>Selfadjoint</b></dt>\n    <dd>For a real matrix, selfadjoint is a synonym for symmetric. For a complex matrix, selfadjoint is a synonym for \\em hermitian.\n        More generally, a matrix \\f$ A \\f$ is selfadjoint if and only if it is equal to its adjoint \\f$ A^* \\f$. The adjoint is also called the \\em conjugate \\em transpose. </dd>\n  <dt><b>Positive/negative definite</b></dt>\n    <dd>A selfadjoint matrix \\f$ A \\f$ is positive definite if \\f$ v^* A v > 0 \\f$ for any non zero vector \\f$ v \\f$.\n        In the same vein, it is negative definite if \\f$ v^* A v < 0 \\f$ for any non zero vector \\f$ v \\f$ </dd>\n  <dt><b>Positive/negative semidefinite</b></dt>\n    <dd>A selfadjoint matrix \\f$ A \\f$ is positive semi-definite if \\f$ v^* A v \\ge 0 \\f$ for any non zero vector \\f$ v \\f$.\n        In the same vein, it is negative semi-definite if \\f$ v^* A v \\le 0 \\f$ for any non zero vector \\f$ v \\f$ </dd>\n\n  <dt><b>Blocking</b></dt>\n    <dd>Means the algorithm can work per block, whence guaranteeing a good scaling of the performance for large matrices.</dd>\n  <dt><b>Implicit Multi Threading (MT)</b></dt>\n    <dd>Means the algorithm can take advantage of multicore processors via OpenMP. \"Implicit\" means the algortihm itself is not parallelized, but that it relies on parallelized matrix-matrix product rountines.</dd>\n  <dt><b>Explicit Multi Threading (MT)</b></dt>\n    <dd>Means the algorithm is explicitly parallelized to take advantage of multicore processors via OpenMP.</dd>\n  <dt><b>Meta-unroller</b></dt>\n    <dd>Means the algorithm is automatically and explicitly unrolled for very small fixed size matrices.</dd>\n  <dt><b></b></dt>\n    <dd></dd>\n</dl>\n\n\n*/\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/TopicMultithreading.dox",
    "content": "namespace Eigen {\n\n/** \\page TopicMultiThreading Eigen and multi-threading\n\n\\section TopicMultiThreading_MakingEigenMT Make Eigen run in parallel\n\nSome Eigen's algorithms can exploit the multiple cores present in your hardware. To this end, it is enough to enable OpenMP on your compiler, for instance:\n * GCC: \\c -fopenmp\n * ICC: \\c -openmp\n * MSVC: check the respective option in the build properties.\nYou can control the number of thread that will be used using either the OpenMP API or Eigen's API using the following priority:\n\\code\n OMP_NUM_THREADS=n ./my_program\n omp_set_num_threads(n);\n Eigen::setNbThreads(n);\n\\endcode\nUnless setNbThreads has been called, Eigen uses the number of threads specified by OpenMP. You can restore this behavior by calling \\code setNbThreads(0); \\endcode\nYou can query the number of threads that will be used with:\n\\code\nn = Eigen::nbThreads( );\n\\endcode\nYou can disable Eigen's multi threading at compile time by defining the EIGEN_DONT_PARALLELIZE preprocessor token.\n\nCurrently, the following algorithms can make use of multi-threading:\n - general dense matrix - matrix products\n - PartialPivLU\n - row-major-sparse * dense vector/matrix products\n - ConjugateGradient with \\c Lower|Upper as the \\c UpLo template parameter.\n - BiCGSTAB with a row-major sparse matrix format.\n - LeastSquaresConjugateGradient\n\n\\section TopicMultiThreading_UsingEigenWithMT Using Eigen in a multi-threaded application\n\nIn the case your own application is multithreaded, and multiple threads make calls to Eigen, then you have to initialize Eigen by calling the following routine \\b before creating the threads:\n\\code\n#include <Eigen/Core>\n\nint main(int argc, char** argv)\n{\n  Eigen::initParallel();\n  \n  ...\n}\n\\endcode\n\n\\note With Eigen 3.3, and a fully C++11 compliant compiler (i.e., <a href=\"http://en.cppreference.com/w/cpp/language/storage_duration#Static_local_variables\">thread-safe static local variable initialization</a>), then calling \\c initParallel() is optional.\n\n\\warning note that all functions generating random matrices are \\b not re-entrant nor thread-safe. Those include DenseBase::Random(), and DenseBase::setRandom() despite a call to Eigen::initParallel(). This is because these functions are based on std::rand which is not re-entrant. For thread-safe random generator, we recommend the use of boost::random or c++11 random feature.\n\nIn the case your application is parallelized with OpenMP, you might want to disable Eigen's own parallization as detailed in the previous section.\n\n*/\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/TopicResizing.dox",
    "content": "namespace Eigen {\n\n/** \\page TopicResizing Resizing\n\n\nTODO: write this dox page!\n\nIs linked from the tutorial on the Matrix class.\n\n*/\n}\n"
  },
  {
    "path": "include/eigen3/doc/TopicScalarTypes.dox",
    "content": "namespace Eigen {\n\n/** \\page TopicScalarTypes Scalar types\n\n\nTODO: write this dox page!\n\nIs linked from the tutorial on the Matrix class.\n\n*/\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/TopicVectorization.dox",
    "content": "namespace Eigen {\n\n/** \\page TopicVectorization Vectorization\n\n\nTODO: write this dox page!\n\n*/\n}\n"
  },
  {
    "path": "include/eigen3/doc/TutorialAdvancedInitialization.dox",
    "content": "namespace Eigen {\n\n/** \\eigenManualPage TutorialAdvancedInitialization Advanced initialization\n\nThis page discusses several advanced methods for initializing matrices. It gives more details on the\ncomma-initializer, which was introduced before. It also explains how to get special matrices such as the\nidentity matrix and the zero matrix.\n\n\\eigenAutoToc\n\n\\section TutorialAdvancedInitializationCommaInitializer The comma initializer\n\nEigen offers a comma initializer syntax which allows the user to easily set all the coefficients of a matrix,\nvector or array. Simply list the coefficients, starting at the top-left corner and moving from left to right\nand from the top to the bottom. The size of the object needs to be specified beforehand. If you list too few\nor too many coefficients, Eigen will complain.\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include Tutorial_commainit_01.cpp\n</td>\n<td>\n\\verbinclude Tutorial_commainit_01.out\n</td></tr></table>\n\nMoreover, the elements of the initialization list may themselves be vectors or matrices. A common use is\nto join vectors or matrices together. For example, here is how to join two row vectors together. Remember\nthat you have to set the size before you can use the comma initializer.\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include Tutorial_AdvancedInitialization_Join.cpp\n</td>\n<td>\n\\verbinclude Tutorial_AdvancedInitialization_Join.out\n</td></tr></table>\n\nWe can use the same technique to initialize matrices with a block structure.\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include Tutorial_AdvancedInitialization_Block.cpp\n</td>\n<td>\n\\verbinclude Tutorial_AdvancedInitialization_Block.out\n</td></tr></table>\n\nThe comma initializer can also be used to fill block expressions such as <tt>m.row(i)</tt>. Here is a more\ncomplicated way to get the same result as in the first example above:\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include Tutorial_commainit_01b.cpp\n</td>\n<td>\n\\verbinclude Tutorial_commainit_01b.out\n</td></tr></table>\n\n\n\\section TutorialAdvancedInitializationSpecialMatrices Special matrices and arrays\n\nThe Matrix and Array classes have static methods like \\link DenseBase::Zero() Zero()\\endlink, which can be\nused to initialize all coefficients to zero. There are three variants. The first variant takes no arguments\nand can only be used for fixed-size objects. If you want to initialize a dynamic-size object to zero, you need\nto specify the size. Thus, the second variant requires one argument and can be used for one-dimensional\ndynamic-size objects, while the third variant requires two arguments and can be used for two-dimensional\nobjects. All three variants are illustrated in the following example:\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include Tutorial_AdvancedInitialization_Zero.cpp\n</td>\n<td>\n\\verbinclude Tutorial_AdvancedInitialization_Zero.out\n</td></tr></table>\n\nSimilarly, the static method \\link DenseBase::Constant() Constant\\endlink(value) sets all coefficients to \\c value.\nIf the size of the object needs to be specified, the additional arguments go before the \\c value\nargument, as in <tt>MatrixXd::Constant(rows, cols, value)</tt>. The method \\link DenseBase::Random() Random()\n\\endlink fills the matrix or array with random coefficients. The identity matrix can be obtained by calling\n\\link MatrixBase::Identity() Identity()\\endlink; this method is only available for Matrix, not for Array,\nbecause \"identity matrix\" is a linear algebra concept.  The method\n\\link DenseBase::LinSpaced LinSpaced\\endlink(size, low, high) is only available for vectors and\none-dimensional arrays; it yields a vector of the specified size whose coefficients are equally spaced between\n\\c low and \\c high. The method \\c LinSpaced() is illustrated in the following example, which prints a table\nwith angles in degrees, the corresponding angle in radians, and their sine and cosine.\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include Tutorial_AdvancedInitialization_LinSpaced.cpp\n</td>\n<td>\n\\verbinclude Tutorial_AdvancedInitialization_LinSpaced.out\n</td></tr></table>\n\nThis example shows that objects like the ones returned by LinSpaced() can be assigned to variables (and\nexpressions). Eigen defines utility functions like \\link DenseBase::setZero() setZero()\\endlink, \n\\link MatrixBase::setIdentity() \\endlink and \\link DenseBase::setLinSpaced() \\endlink to do this\nconveniently. The following example contrasts three ways to construct the matrix\n\\f$ J = \\bigl[ \\begin{smallmatrix} O & I \\\\ I & O \\end{smallmatrix} \\bigr] \\f$: using static methods and\nassignment, using static methods and the comma-initializer, or using the setXxx() methods.\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include Tutorial_AdvancedInitialization_ThreeWays.cpp\n</td>\n<td>\n\\verbinclude Tutorial_AdvancedInitialization_ThreeWays.out\n</td></tr></table>\n\nA summary of all pre-defined matrix, vector and array objects can be found in the \\ref QuickRefPage.\n\n\n\\section TutorialAdvancedInitializationTemporaryObjects Usage as temporary objects\n\nAs shown above, static methods as Zero() and Constant() can be used to initialize variables at the time of\ndeclaration or at the right-hand side of an assignment operator. You can think of these methods as returning a\nmatrix or array; in fact, they return so-called \\ref TopicEigenExpressionTemplates \"expression objects\" which\nevaluate to a matrix or array when needed, so that this syntax does not incur any overhead.\n\nThese expressions can also be used as a temporary object. The second example in\nthe \\ref GettingStarted guide, which we reproduce here, already illustrates this.\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include QuickStart_example2_dynamic.cpp\n</td>\n<td>\n\\verbinclude QuickStart_example2_dynamic.out\n</td></tr></table>\n\nThe expression <tt>m + MatrixXf::Constant(3,3,1.2)</tt> constructs the 3-by-3 matrix expression with all its coefficients\nequal to 1.2 plus the corresponding coefficient of \\a m.\n\nThe comma-initializer, too, can also be used to construct temporary objects. The following example constructs a random\nmatrix of size 2-by-3, and then multiplies this matrix on the left with \n\\f$ \\bigl[ \\begin{smallmatrix} 0 & 1 \\\\ 1 & 0 \\end{smallmatrix} \\bigr] \\f$.\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include Tutorial_AdvancedInitialization_CommaTemporary.cpp\n</td>\n<td>\n\\verbinclude Tutorial_AdvancedInitialization_CommaTemporary.out\n</td></tr></table>\n\nThe \\link CommaInitializer::finished() finished() \\endlink method is necessary here to get the actual matrix\nobject once the comma initialization of our temporary submatrix is done.\n\n\n*/\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/TutorialArrayClass.dox",
    "content": "namespace Eigen {\n\n/** \\eigenManualPage TutorialArrayClass The Array class and coefficient-wise operations\n\nThis page aims to provide an overview and explanations on how to use\nEigen's Array class.\n\n\\eigenAutoToc\n  \n\\section TutorialArrayClassIntro What is the Array class?\n\nThe Array class provides general-purpose arrays, as opposed to the Matrix class which\nis intended for linear algebra. Furthermore, the Array class provides an easy way to\nperform coefficient-wise operations, which might not have a linear algebraic meaning,\nsuch as adding a constant to every coefficient in the array or multiplying two arrays coefficient-wise.\n\n\n\\section TutorialArrayClassTypes Array types\nArray is a class template taking the same template parameters as Matrix.\nAs with Matrix, the first three template parameters are mandatory:\n\\code\nArray<typename Scalar, int RowsAtCompileTime, int ColsAtCompileTime>\n\\endcode\nThe last three template parameters are optional. Since this is exactly the same as for Matrix,\nwe won't explain it again here and just refer to \\ref TutorialMatrixClass.\n\nEigen also provides typedefs for some common cases, in a way that is similar to the Matrix typedefs\nbut with some slight differences, as the word \"array\" is used for both 1-dimensional and 2-dimensional arrays.\nWe adopt the convention that typedefs of the form ArrayNt stand for 1-dimensional arrays, where N and t are\nthe size and the scalar type, as in the Matrix typedefs explained on \\ref TutorialMatrixClass \"this page\". For 2-dimensional arrays, we\nuse typedefs of the form ArrayNNt. Some examples are shown in the following table:\n\n<table class=\"manual\">\n  <tr>\n    <th>Type </th>\n    <th>Typedef </th>\n  </tr>\n  <tr>\n    <td> \\code Array<float,Dynamic,1> \\endcode </td>\n    <td> \\code ArrayXf \\endcode </td>\n  </tr>\n  <tr>\n    <td> \\code Array<float,3,1> \\endcode </td>\n    <td> \\code Array3f \\endcode </td>\n  </tr>\n  <tr>\n    <td> \\code Array<double,Dynamic,Dynamic> \\endcode </td>\n    <td> \\code ArrayXXd \\endcode </td>\n  </tr>\n  <tr>\n    <td> \\code Array<double,3,3> \\endcode </td>\n    <td> \\code Array33d \\endcode </td>\n  </tr>\n</table>\n\n\n\\section TutorialArrayClassAccess Accessing values inside an Array\n\nThe parenthesis operator is overloaded to provide write and read access to the coefficients of an array, just as with matrices.\nFurthermore, the \\c << operator can be used to initialize arrays (via the comma initializer) or to print them.\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include Tutorial_ArrayClass_accessors.cpp\n</td>\n<td>\n\\verbinclude Tutorial_ArrayClass_accessors.out\n</td></tr></table>\n\nFor more information about the comma initializer, see \\ref TutorialAdvancedInitialization.\n\n\n\\section TutorialArrayClassAddSub Addition and subtraction\n\nAdding and subtracting two arrays is the same as for matrices.\nThe operation is valid if both arrays have the same size, and the addition or subtraction is done coefficient-wise.\n\nArrays also support expressions of the form <tt>array + scalar</tt> which add a scalar to each coefficient in the array.\nThis provides a functionality that is not directly available for Matrix objects.\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include Tutorial_ArrayClass_addition.cpp\n</td>\n<td>\n\\verbinclude Tutorial_ArrayClass_addition.out\n</td></tr></table>\n\n\n\\section TutorialArrayClassMult Array multiplication\n\nFirst of all, of course you can multiply an array by a scalar, this works in the same way as matrices. Where arrays\nare fundamentally different from matrices, is when you multiply two together. Matrices interpret\nmultiplication as matrix product and arrays interpret multiplication as coefficient-wise product. Thus, two \narrays can be multiplied if and only if they have the same dimensions.\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include Tutorial_ArrayClass_mult.cpp\n</td>\n<td>\n\\verbinclude Tutorial_ArrayClass_mult.out\n</td></tr></table>\n\n\n\\section TutorialArrayClassCwiseOther Other coefficient-wise operations\n\nThe Array class defines other coefficient-wise operations besides the addition, subtraction and multiplication\noperators described above. For example, the \\link ArrayBase::abs() .abs() \\endlink method takes the absolute\nvalue of each coefficient, while \\link ArrayBase::sqrt() .sqrt() \\endlink computes the square root of the\ncoefficients. If you have two arrays of the same size, you can call \\link ArrayBase::min(const Eigen::ArrayBase<OtherDerived>&) const .min(.) \\endlink to\nconstruct the array whose coefficients are the minimum of the corresponding coefficients of the two given\narrays. These operations are illustrated in the following example.\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include Tutorial_ArrayClass_cwise_other.cpp\n</td>\n<td>\n\\verbinclude Tutorial_ArrayClass_cwise_other.out\n</td></tr></table>\n\nMore coefficient-wise operations can be found in the \\ref QuickRefPage.\n\n\n\\section TutorialArrayClassConvert Converting between array and matrix expressions\n\nWhen should you use objects of the Matrix class and when should you use objects of the Array class? You cannot\napply Matrix operations on arrays, or Array operations on matrices. Thus, if you need to do linear algebraic\noperations such as matrix multiplication, then you should use matrices; if you need to do coefficient-wise\noperations, then you should use arrays. However, sometimes it is not that simple, but you need to use both\nMatrix and Array operations. In that case, you need to convert a matrix to an array or reversely. This gives\naccess to all operations regardless of the choice of declaring objects as arrays or as matrices.\n\n\\link MatrixBase Matrix expressions \\endlink have an \\link MatrixBase::array() .array() \\endlink method that\n'converts' them into \\link ArrayBase array expressions\\endlink, so that coefficient-wise operations\ncan be applied easily. Conversely, \\link ArrayBase array expressions \\endlink\nhave a \\link ArrayBase::matrix() .matrix() \\endlink method. As with all Eigen expression abstractions,\nthis doesn't have any runtime cost (provided that you let your compiler optimize).\nBoth \\link MatrixBase::array() .array() \\endlink and \\link ArrayBase::matrix() .matrix() \\endlink \ncan be used as rvalues and as lvalues.\n\nMixing matrices and arrays in an expression is forbidden with Eigen. For instance, you cannot add a matrix and\narray directly; the operands of a \\c + operator should either both be matrices or both be arrays. However,\nit is easy to convert from one to the other with \\link MatrixBase::array() .array() \\endlink and \n\\link ArrayBase::matrix() .matrix()\\endlink. The exception to this rule is the assignment operator: it is\nallowed to assign a matrix expression to an array variable, or to assign an array expression to a matrix\nvariable.\n\nThe following example shows how to use array operations on a Matrix object by employing the \n\\link MatrixBase::array() .array() \\endlink method. For example, the statement \n<tt>result = m.array() * n.array()</tt> takes two matrices \\c m and \\c n, converts them both to an array, uses\n* to multiply them coefficient-wise and assigns the result to the matrix variable \\c result (this is legal\nbecause Eigen allows assigning array expressions to matrix variables). \n\nAs a matter of fact, this usage case is so common that Eigen provides a \\link MatrixBase::cwiseProduct const\n.cwiseProduct(.) \\endlink method for matrices to compute the coefficient-wise product. This is also shown in\nthe example program.\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include Tutorial_ArrayClass_interop_matrix.cpp\n</td>\n<td>\n\\verbinclude Tutorial_ArrayClass_interop_matrix.out\n</td></tr></table>\n\nSimilarly, if \\c array1 and \\c array2 are arrays, then the expression <tt>array1.matrix() * array2.matrix()</tt>\ncomputes their matrix product.\n\nHere is a more advanced example. The expression <tt>(m.array() + 4).matrix() * m</tt> adds 4 to every\ncoefficient in the matrix \\c m and then computes the matrix product of the result with \\c m. Similarly, the\nexpression <tt>(m.array() * n.array()).matrix() * m</tt> computes the coefficient-wise product of the matrices\n\\c m and \\c n and then the matrix product of the result with \\c m.\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include Tutorial_ArrayClass_interop.cpp\n</td>\n<td>\n\\verbinclude Tutorial_ArrayClass_interop.out\n</td></tr></table>\n\n*/\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/TutorialBlockOperations.dox",
    "content": "namespace Eigen {\n\n/** \\eigenManualPage TutorialBlockOperations Block operations\n\nThis page explains the essentials of block operations.\nA block is a rectangular part of a matrix or array. Blocks expressions can be used both\nas rvalues and as lvalues. As usual with Eigen expressions, this abstraction has zero runtime cost\nprovided that you let your compiler optimize.\n\n\\eigenAutoToc\n\n\\section TutorialBlockOperationsUsing Using block operations\n\nThe most general block operation in Eigen is called \\link DenseBase::block() .block() \\endlink.\nThere are two versions, whose syntax is as follows:\n\n<table class=\"manual\">\n<tr><th>\\b %Block \\b operation</td>\n<th>Version constructing a \\n dynamic-size block expression</th>\n<th>Version constructing a \\n fixed-size block expression</th></tr>\n<tr><td>%Block of size <tt>(p,q)</tt>, starting at <tt>(i,j)</tt></td>\n    <td>\\code\nmatrix.block(i,j,p,q);\\endcode </td>\n    <td>\\code \nmatrix.block<p,q>(i,j);\\endcode </td>\n</tr>\n</table>\n\nAs always in Eigen, indices start at 0.\n\nBoth versions can be used on fixed-size and dynamic-size matrices and arrays.\nThese two expressions are semantically equivalent.\nThe only difference is that the fixed-size version will typically give you faster code if the block size is small,\nbut requires this size to be known at compile time.\n\nThe following program uses the dynamic-size and fixed-size versions to print the values of several blocks inside a\nmatrix.\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include Tutorial_BlockOperations_print_block.cpp\n</td>\n<td>\n\\verbinclude Tutorial_BlockOperations_print_block.out\n</td></tr></table>\n\nIn the above example the \\link DenseBase::block() .block() \\endlink function was employed as a \\em rvalue, i.e.\nit was only read from. However, blocks can also be used as \\em lvalues, meaning that you can assign to a block.\n\nThis is illustrated in the following example. This example also demonstrates blocks in arrays, which works exactly like the above-demonstrated blocks in matrices.\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include Tutorial_BlockOperations_block_assignment.cpp\n</td>\n<td>\n\\verbinclude Tutorial_BlockOperations_block_assignment.out\n</td></tr></table>\n\nWhile the \\link DenseBase::block() .block() \\endlink method can be used for any block operation, there are\nother methods for special cases, providing more specialized API and/or better performance. On the topic of performance, all what\nmatters is that you give Eigen as much information as possible at compile time. For example, if your block is a single whole column in a matrix,\nusing the specialized \\link DenseBase::col() .col() \\endlink function described below lets Eigen know that, which can give it optimization opportunities.\n\nThe rest of this page describes these specialized methods.\n\n\\section TutorialBlockOperationsSyntaxColumnRows Columns and rows\n\nIndividual columns and rows are special cases of blocks. Eigen provides methods to easily address them:\n\\link DenseBase::col() .col() \\endlink and \\link DenseBase::row() .row()\\endlink.\n\n<table class=\"manual\">\n<tr><th>%Block operation</th>\n<th>Method</th>\n<tr><td>i<sup>th</sup> row\n                    \\link DenseBase::row() * \\endlink</td>\n    <td>\\code\nmatrix.row(i);\\endcode </td>\n</tr>\n<tr><td>j<sup>th</sup> column\n                    \\link DenseBase::col() * \\endlink</td>\n    <td>\\code\nmatrix.col(j);\\endcode </td>\n</tr>\n</table>\n\nThe argument for \\p col() and \\p row() is the index of the column or row to be accessed. As always in Eigen, indices start at 0.\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include Tutorial_BlockOperations_colrow.cpp\n</td>\n<td>\n\\verbinclude Tutorial_BlockOperations_colrow.out\n</td></tr></table>\n\nThat example also demonstrates that block expressions (here columns) can be used in arithmetic like any other expression.\n\n\n\\section TutorialBlockOperationsSyntaxCorners Corner-related operations\n\nEigen also provides special methods for blocks that are flushed against one of the corners or sides of a\nmatrix or array. For instance, \\link DenseBase::topLeftCorner() .topLeftCorner() \\endlink can be used to refer\nto a block in the top-left corner of a matrix.\n\nThe different possibilities are summarized in the following table:\n\n<table class=\"manual\">\n<tr><th>%Block \\b operation</td>\n<th>Version constructing a \\n dynamic-size block expression</th>\n<th>Version constructing a \\n fixed-size block expression</th></tr>\n<tr><td>Top-left p by q block \\link DenseBase::topLeftCorner() * \\endlink</td>\n    <td>\\code\nmatrix.topLeftCorner(p,q);\\endcode </td>\n    <td>\\code \nmatrix.topLeftCorner<p,q>();\\endcode </td>\n</tr>\n<tr><td>Bottom-left p by q block\n              \\link DenseBase::bottomLeftCorner() * \\endlink</td>\n    <td>\\code\nmatrix.bottomLeftCorner(p,q);\\endcode </td>\n    <td>\\code \nmatrix.bottomLeftCorner<p,q>();\\endcode </td>\n</tr>\n<tr><td>Top-right p by q block\n              \\link DenseBase::topRightCorner() * \\endlink</td>\n    <td>\\code\nmatrix.topRightCorner(p,q);\\endcode </td>\n    <td>\\code \nmatrix.topRightCorner<p,q>();\\endcode </td>\n</tr>\n<tr><td>Bottom-right p by q block\n               \\link DenseBase::bottomRightCorner() * \\endlink</td>\n    <td>\\code\nmatrix.bottomRightCorner(p,q);\\endcode </td>\n    <td>\\code \nmatrix.bottomRightCorner<p,q>();\\endcode </td>\n</tr>\n<tr><td>%Block containing the first q rows\n                   \\link DenseBase::topRows() * \\endlink</td>\n    <td>\\code\nmatrix.topRows(q);\\endcode </td>\n    <td>\\code \nmatrix.topRows<q>();\\endcode </td>\n</tr>\n<tr><td>%Block containing the last q rows\n                    \\link DenseBase::bottomRows() * \\endlink</td>\n    <td>\\code\nmatrix.bottomRows(q);\\endcode </td>\n    <td>\\code \nmatrix.bottomRows<q>();\\endcode </td>\n</tr>\n<tr><td>%Block containing the first p columns\n                    \\link DenseBase::leftCols() * \\endlink</td>\n    <td>\\code\nmatrix.leftCols(p);\\endcode </td>\n    <td>\\code \nmatrix.leftCols<p>();\\endcode </td>\n</tr>\n<tr><td>%Block containing the last q columns\n                    \\link DenseBase::rightCols() * \\endlink</td>\n    <td>\\code\nmatrix.rightCols(q);\\endcode </td>\n    <td>\\code \nmatrix.rightCols<q>();\\endcode </td>\n</tr>\n</table>\n\nHere is a simple example illustrating the use of the operations presented above:\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include Tutorial_BlockOperations_corner.cpp\n</td>\n<td>\n\\verbinclude Tutorial_BlockOperations_corner.out\n</td></tr></table>\n\n\n\\section TutorialBlockOperationsSyntaxVectors Block operations for vectors\n\nEigen also provides a set of block operations designed specifically for the special case of vectors and one-dimensional arrays:\n\n<table class=\"manual\">\n<tr><th> %Block operation</th>\n<th>Version constructing a \\n dynamic-size block expression</th>\n<th>Version constructing a \\n fixed-size block expression</th></tr>\n<tr><td>%Block containing the first \\p n elements \n                    \\link DenseBase::head() * \\endlink</td>\n    <td>\\code\nvector.head(n);\\endcode </td>\n    <td>\\code \nvector.head<n>();\\endcode </td>\n</tr>\n<tr><td>%Block containing the last \\p n elements\n                    \\link DenseBase::tail() * \\endlink</td>\n    <td>\\code\nvector.tail(n);\\endcode </td>\n    <td>\\code \nvector.tail<n>();\\endcode </td>\n</tr>\n<tr><td>%Block containing \\p n elements, starting at position \\p i\n                    \\link DenseBase::segment() * \\endlink</td>\n    <td>\\code\nvector.segment(i,n);\\endcode </td>\n    <td>\\code \nvector.segment<n>(i);\\endcode </td>\n</tr>\n</table>\n\n\nAn example is presented below:\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include Tutorial_BlockOperations_vector.cpp\n</td>\n<td>\n\\verbinclude Tutorial_BlockOperations_vector.out\n</td></tr></table>\n\n*/\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/TutorialGeometry.dox",
    "content": "namespace Eigen {\n\n/** \\eigenManualPage TutorialGeometry Space transformations\n\nIn this page, we will introduce the many possibilities offered by the \\ref Geometry_Module \"geometry module\" to deal with 2D and 3D rotations and projective or affine transformations.\n\n\\eigenAutoToc\n\nEigen's Geometry module provides two different kinds of geometric transformations:\n  - Abstract transformations, such as rotations (represented by \\ref AngleAxis \"angle and axis\" or by a \\ref Quaternion \"quaternion\"), \\ref Translation \"translations\", \\ref Scaling \"scalings\". These transformations are NOT represented as matrices, but you can nevertheless mix them with matrices and vectors in expressions, and convert them to matrices if you wish.\n  - Projective or affine transformation matrices: see the Transform class. These are really matrices.\n\n\\note If you are working with OpenGL 4x4 matrices then Affine3f and Affine3d are what you want. Since Eigen defaults to column-major storage, you can directly use the Transform::data() method to pass your transformation matrix to OpenGL.\n\nYou can construct a Transform from an abstract transformation, like this:\n\\code\n  Transform t(AngleAxis(angle,axis));\n\\endcode\nor like this:\n\\code\n  Transform t;\n  t = AngleAxis(angle,axis);\n\\endcode\nBut note that unfortunately, because of how C++ works, you can \\b not do this:\n\\code\n  Transform t = AngleAxis(angle,axis);\n\\endcode\n<span class=\"note\">\\b Explanation: In the C++ language, this would require Transform to have a non-explicit conversion constructor from AngleAxis, but we really don't want to allow implicit casting here.\n</span>\n\n\\section TutorialGeoElementaryTransformations Transformation types\n\n<table class=\"manual\">\n<tr><th>Transformation type</th><th>Typical initialization code</th></tr>\n<tr><td>\n\\ref Rotation2D \"2D rotation\" from an angle</td><td>\\code\nRotation2D<float> rot2(angle_in_radian);\\endcode</td></tr>\n<tr class=\"alt\"><td>\n3D rotation as an \\ref AngleAxis \"angle + axis\"</td><td>\\code\nAngleAxis<float> aa(angle_in_radian, Vector3f(ax,ay,az));\\endcode\n<span class=\"note\">The axis vector must be normalized.</span></td></tr>\n<tr><td>\n3D rotation as a \\ref Quaternion \"quaternion\"</td><td>\\code\nQuaternion<float> q;  q = AngleAxis<float>(angle_in_radian, axis);\\endcode</td></tr>\n<tr class=\"alt\"><td>\nN-D Scaling</td><td>\\code\nScaling(sx, sy)\nScaling(sx, sy, sz)\nScaling(s)\nScaling(vecN)\\endcode</td></tr>\n<tr><td>\nN-D Translation</td><td>\\code\nTranslation<float,2>(tx, ty)\nTranslation<float,3>(tx, ty, tz)\nTranslation<float,N>(s)\nTranslation<float,N>(vecN)\\endcode</td></tr>\n<tr class=\"alt\"><td>\nN-D \\ref TutorialGeoTransform \"Affine transformation\"</td><td>\\code\nTransform<float,N,Affine> t = concatenation_of_any_transformations;\nTransform<float,3,Affine> t = Translation3f(p) * AngleAxisf(a,axis) * Scaling(s);\\endcode</td></tr>\n<tr><td>\nN-D Linear transformations \\n\n<em class=note>(pure rotations, \\n scaling, etc.)</em></td><td>\\code\nMatrix<float,N> t = concatenation_of_rotations_and_scalings;\nMatrix<float,2> t = Rotation2Df(a) * Scaling(s);\nMatrix<float,3> t = AngleAxisf(a,axis) * Scaling(s);\\endcode</td></tr>\n</table>\n\n<strong>Notes on rotations</strong>\\n To transform more than a single vector the preferred\nrepresentations are rotation matrices, while for other usages Quaternion is the\nrepresentation of choice as they are compact, fast and stable. Finally Rotation2D and\nAngleAxis are mainly convenient types to create other rotation objects.\n\n<strong>Notes on Translation and Scaling</strong>\\n Like AngleAxis, these classes were\ndesigned to simplify the creation/initialization of linear (Matrix) and affine (Transform)\ntransformations. Nevertheless, unlike AngleAxis which is inefficient to use, these classes\nmight still be interesting to write generic and efficient algorithms taking as input any\nkind of transformations.\n\nAny of the above transformation types can be converted to any other types of the same nature,\nor to a more generic type. Here are some additional examples:\n<table class=\"manual\">\n<tr><td>\\code\nRotation2Df r;  r  = Matrix2f(..);       // assumes a pure rotation matrix\nAngleAxisf aa;  aa = Quaternionf(..);\nAngleAxisf aa;  aa = Matrix3f(..);       // assumes a pure rotation matrix\nMatrix2f m;     m  = Rotation2Df(..);\nMatrix3f m;     m  = Quaternionf(..);       Matrix3f m;   m = Scaling(..);\nAffine3f m;     m  = AngleAxis3f(..);       Affine3f m;   m = Scaling(..);\nAffine3f m;     m  = Translation3f(..);     Affine3f m;   m = Matrix3f(..);\n\\endcode</td></tr>\n</table>\n\n\n<a href=\"#\" class=\"top\">top</a>\\section TutorialGeoCommontransformationAPI Common API across transformation types\n\nTo some extent, Eigen's \\ref Geometry_Module \"geometry module\" allows you to write\ngeneric algorithms working on any kind of transformation representations:\n<table class=\"manual\">\n<tr><td>\nConcatenation of two transformations</td><td>\\code\ngen1 * gen2;\\endcode</td></tr>\n<tr class=\"alt\"><td>Apply the transformation to a vector</td><td>\\code\nvec2 = gen1 * vec1;\\endcode</td></tr>\n<tr><td>Get the inverse of the transformation</td><td>\\code\ngen2 = gen1.inverse();\\endcode</td></tr>\n<tr class=\"alt\"><td>Spherical interpolation \\n (Rotation2D and Quaternion only)</td><td>\\code\nrot3 = rot1.slerp(alpha,rot2);\\endcode</td></tr>\n</table>\n\n\n\n<a href=\"#\" class=\"top\">top</a>\\section TutorialGeoTransform Affine transformations\nGeneric affine transformations are represented by the Transform class which internaly\nis a (Dim+1)^2 matrix. In Eigen we have chosen to not distinghish between points and\nvectors such that all points are actually represented by displacement vectors from the\norigin ( \\f$ \\mathbf{p} \\equiv \\mathbf{p}-0 \\f$ ). With that in mind, real points and\nvector distinguish when the transformation is applied.\n<table class=\"manual\">\n<tr><td>\nApply the transformation to a \\b point </td><td>\\code\nVectorNf p1, p2;\np2 = t * p1;\\endcode</td></tr>\n<tr class=\"alt\"><td>\nApply the transformation to a \\b vector </td><td>\\code\nVectorNf vec1, vec2;\nvec2 = t.linear() * vec1;\\endcode</td></tr>\n<tr><td>\nApply a \\em general transformation \\n to a \\b normal \\b vector \\n\n</td><td>\\code\nVectorNf n1, n2;\nMatrixNf normalMatrix = t.linear().inverse().transpose();\nn2 = (normalMatrix * n1).normalized();\\endcode</td></tr>\n<tr><td colspan=\"2\">(See subject 5.27 of this <a href=\"http://www.faqs.org/faqs/graphics/algorithms-faq\">faq</a> for the explanations)</td></tr>\n<tr class=\"alt\"><td>\nApply a transformation with \\em pure \\em rotation \\n to a \\b normal \\b vector\n(no scaling, no shear)</td><td>\\code\nn2 = t.linear() * n1;\\endcode</td></tr>\n<tr><td>\nOpenGL compatibility \\b 3D </td><td>\\code\nglLoadMatrixf(t.data());\\endcode</td></tr>\n<tr class=\"alt\"><td>\nOpenGL compatibility \\b 2D </td><td>\\code\nAffine3f aux(Affine3f::Identity());\naux.linear().topLeftCorner<2,2>() = t.linear();\naux.translation().start<2>() = t.translation();\nglLoadMatrixf(aux.data());\\endcode</td></tr>\n</table>\n\n\\b Component \\b accessors\n<table class=\"manual\">\n<tr><td>\nfull read-write access to the internal matrix</td><td>\\code\nt.matrix() = matN1xN1;    // N1 means N+1\nmatN1xN1 = t.matrix();\n\\endcode</td></tr>\n<tr class=\"alt\"><td>\ncoefficient accessors</td><td>\\code\nt(i,j) = scalar;   <=>   t.matrix()(i,j) = scalar;\nscalar = t(i,j);   <=>   scalar = t.matrix()(i,j);\n\\endcode</td></tr>\n<tr><td>\ntranslation part</td><td>\\code\nt.translation() = vecN;\nvecN = t.translation();\n\\endcode</td></tr>\n<tr class=\"alt\"><td>\nlinear part</td><td>\\code\nt.linear() = matNxN;\nmatNxN = t.linear();\n\\endcode</td></tr>\n<tr><td>\nextract the rotation matrix</td><td>\\code\nmatNxN = t.rotation();\n\\endcode</td></tr>\n</table>\n\n\n\\b Transformation \\b creation \\n\nWhile transformation objects can be created and updated concatenating elementary transformations,\nthe Transform class also features a procedural API:\n<table class=\"manual\">\n<tr><th></th><th>procedural API</th><th>equivalent natural API </th></tr>\n<tr><td>Translation</td><td>\\code\nt.translate(Vector_(tx,ty,..));\nt.pretranslate(Vector_(tx,ty,..));\n\\endcode</td><td>\\code\nt *= Translation_(tx,ty,..);\nt = Translation_(tx,ty,..) * t;\n\\endcode</td></tr>\n<tr class=\"alt\"><td>\\b Rotation \\n <em class=\"note\">In 2D and for the procedural API, any_rotation can also \\n be an angle in radian</em></td><td>\\code\nt.rotate(any_rotation);\nt.prerotate(any_rotation);\n\\endcode</td><td>\\code\nt *= any_rotation;\nt = any_rotation * t;\n\\endcode</td></tr>\n<tr><td>Scaling</td><td>\\code\nt.scale(Vector_(sx,sy,..));\nt.scale(s);\nt.prescale(Vector_(sx,sy,..));\nt.prescale(s);\n\\endcode</td><td>\\code\nt *= Scaling(sx,sy,..);\nt *= Scaling(s);\nt = Scaling(sx,sy,..) * t;\nt = Scaling(s) * t;\n\\endcode</td></tr>\n<tr class=\"alt\"><td>Shear transformation \\n ( \\b 2D \\b only ! )</td><td>\\code\nt.shear(sx,sy);\nt.preshear(sx,sy);\n\\endcode</td><td></td></tr>\n</table>\n\nNote that in both API, any many transformations can be concatenated in a single expression as shown in the two following equivalent examples:\n<table class=\"manual\">\n<tr><td>\\code\nt.pretranslate(..).rotate(..).translate(..).scale(..);\n\\endcode</td></tr>\n<tr><td>\\code\nt = Translation_(..) * t * RotationType(..) * Translation_(..) * Scaling(..);\n\\endcode</td></tr>\n</table>\n\n\n\n<a href=\"#\" class=\"top\">top</a>\\section TutorialGeoEulerAngles Euler angles\n<table class=\"manual\">\n<tr><td style=\"max-width:30em;\">\nEuler angles might be convenient to create rotation objects.\nOn the other hand, since there exist 24 different conventions, they are pretty confusing to use. This example shows how\nto create a rotation matrix according to the 2-1-2 convention.</td><td>\\code\nMatrix3f m;\nm = AngleAxisf(angle1, Vector3f::UnitZ())\n  * AngleAxisf(angle2, Vector3f::UnitY())\n  * AngleAxisf(angle3, Vector3f::UnitZ());\n\\endcode</td></tr>\n</table>\n\n*/\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/TutorialLinearAlgebra.dox",
    "content": "namespace Eigen {\n\n/** \\eigenManualPage TutorialLinearAlgebra Linear algebra and decompositions\n\nThis page explains how to solve linear systems, compute various decompositions such as LU,\nQR, %SVD, eigendecompositions... After reading this page, don't miss our\n\\link TopicLinearAlgebraDecompositions catalogue \\endlink of dense matrix decompositions.\n\n\\eigenAutoToc\n\n\\section TutorialLinAlgBasicSolve Basic linear solving\n\n\\b The \\b problem: You have a system of equations, that you have written as a single matrix equation\n    \\f[ Ax \\: = \\: b \\f]\nWhere \\a A and \\a b are matrices (\\a b could be a vector, as a special case). You want to find a solution \\a x.\n\n\\b The \\b solution: You can choose between various decompositions, depending on what your matrix \\a A looks like,\nand depending on whether you favor speed or accuracy. However, let's start with an example that works in all cases,\nand is a good compromise:\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr>\n  <td>\\include TutorialLinAlgExSolveColPivHouseholderQR.cpp </td>\n  <td>\\verbinclude TutorialLinAlgExSolveColPivHouseholderQR.out </td>\n</tr>\n</table>\n\nIn this example, the colPivHouseholderQr() method returns an object of class ColPivHouseholderQR. Since here the\nmatrix is of type Matrix3f, this line could have been replaced by:\n\\code\nColPivHouseholderQR<Matrix3f> dec(A);\nVector3f x = dec.solve(b);\n\\endcode\n\nHere, ColPivHouseholderQR is a QR decomposition with column pivoting. It's a good compromise for this tutorial, as it\nworks for all matrices while being quite fast. Here is a table of some other decompositions that you can choose from,\ndepending on your matrix and the trade-off you want to make:\n\n<table class=\"manual\">\n    <tr>\n        <th>Decomposition</th>\n        <th>Method</th>\n        <th>Requirements<br/>on the matrix</th>\n        <th>Speed<br/> (small-to-medium)</th>\n        <th>Speed<br/> (large)</th>\n        <th>Accuracy</th>\n    </tr>\n    <tr>\n        <td>PartialPivLU</td>\n        <td>partialPivLu()</td>\n        <td>Invertible</td>\n        <td>++</td>\n        <td>++</td>\n        <td>+</td>\n    </tr>\n    <tr class=\"alt\">\n        <td>FullPivLU</td>\n        <td>fullPivLu()</td>\n        <td>None</td>\n        <td>-</td>\n        <td>- -</td>\n        <td>+++</td>\n    </tr>\n    <tr>\n        <td>HouseholderQR</td>\n        <td>householderQr()</td>\n        <td>None</td>\n        <td>++</td>\n        <td>++</td>\n        <td>+</td>\n    </tr>\n    <tr class=\"alt\">\n        <td>ColPivHouseholderQR</td>\n        <td>colPivHouseholderQr()</td>\n        <td>None</td>\n        <td>+</td>\n        <td>-</td>\n        <td>+++</td>\n    </tr>\n    <tr>\n        <td>FullPivHouseholderQR</td>\n        <td>fullPivHouseholderQr()</td>\n        <td>None</td>\n        <td>-</td>\n        <td>- -</td>\n        <td>+++</td>\n    </tr>\n    <tr class=\"alt\">\n        <td>CompleteOrthogonalDecomposition</td>\n        <td>completeOrthogonalDecomposition()</td>\n        <td>None</td>\n        <td>+</td>\n        <td>-</td>\n        <td>+++</td>\n    </tr>\n    <tr class=\"alt\">\n        <td>LLT</td>\n        <td>llt()</td>\n        <td>Positive definite</td>\n        <td>+++</td>\n        <td>+++</td>\n        <td>+</td>\n    </tr>\n    <tr>\n        <td>LDLT</td>\n        <td>ldlt()</td>\n        <td>Positive or negative<br/> semidefinite</td>\n        <td>+++</td>\n        <td>+</td>\n        <td>++</td>\n    </tr>\n    <tr class=\"alt\">\n        <td>BDCSVD</td>\n        <td>bdcSvd()</td>\n        <td>None</td>\n        <td>-</td>\n        <td>-</td>\n        <td>+++</td>\n    </tr>\n    <tr class=\"alt\">\n        <td>JacobiSVD</td>\n        <td>jacobiSvd()</td>\n        <td>None</td>\n        <td>-</td>\n        <td>- - -</td>\n        <td>+++</td>\n    </tr>\n</table>\nTo get an overview of the true relative speed of the different decompositions, check this \\link DenseDecompositionBenchmark benchmark \\endlink.\n\nAll of these decompositions offer a solve() method that works as in the above example.\n\nFor example, if your matrix is positive definite, the above table says that a very good\nchoice is then the LLT or LDLT decomposition. Here's an example, also demonstrating that using a general\nmatrix (not a vector) as right hand side is possible.\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr>\n  <td>\\include TutorialLinAlgExSolveLDLT.cpp </td>\n  <td>\\verbinclude TutorialLinAlgExSolveLDLT.out </td>\n</tr>\n</table>\n\nFor a \\ref TopicLinearAlgebraDecompositions \"much more complete table\" comparing all decompositions supported by Eigen (notice that Eigen\nsupports many other decompositions), see our special page on\n\\ref TopicLinearAlgebraDecompositions \"this topic\".\n\n\\section TutorialLinAlgSolutionExists Checking if a solution really exists\n\nOnly you know what error margin you want to allow for a solution to be considered valid.\nSo Eigen lets you do this computation for yourself, if you want to, as in this example:\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr>\n  <td>\\include TutorialLinAlgExComputeSolveError.cpp </td>\n  <td>\\verbinclude TutorialLinAlgExComputeSolveError.out </td>\n</tr>\n</table>\n\n\\section TutorialLinAlgEigensolving Computing eigenvalues and eigenvectors\n\nYou need an eigendecomposition here, see available such decompositions on \\ref TopicLinearAlgebraDecompositions \"this page\".\nMake sure to check if your matrix is self-adjoint, as is often the case in these problems. Here's an example using\nSelfAdjointEigenSolver, it could easily be adapted to general matrices using EigenSolver or ComplexEigenSolver.\n\nThe computation of eigenvalues and eigenvectors does not necessarily converge, but such failure to converge is\nvery rare. The call to info() is to check for this possibility.\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr>\n  <td>\\include TutorialLinAlgSelfAdjointEigenSolver.cpp </td>\n  <td>\\verbinclude TutorialLinAlgSelfAdjointEigenSolver.out </td>\n</tr>\n</table>\n\n\\section TutorialLinAlgInverse Computing inverse and determinant\n\nFirst of all, make sure that you really want this. While inverse and determinant are fundamental mathematical concepts,\nin \\em numerical linear algebra they are not as popular as in pure mathematics. Inverse computations are often\nadvantageously replaced by solve() operations, and the determinant is often \\em not a good way of checking if a matrix\nis invertible.\n\nHowever, for \\em very \\em small matrices, the above is not true, and inverse and determinant can be very useful.\n\nWhile certain decompositions, such as PartialPivLU and FullPivLU, offer inverse() and determinant() methods, you can also\ncall inverse() and determinant() directly on a matrix. If your matrix is of a very small fixed size (at most 4x4) this\nallows Eigen to avoid performing a LU decomposition, and instead use formulas that are more efficient on such small matrices.\n\nHere is an example:\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr>\n  <td>\\include TutorialLinAlgInverseDeterminant.cpp </td>\n  <td>\\verbinclude TutorialLinAlgInverseDeterminant.out </td>\n</tr>\n</table>\n\n\\section TutorialLinAlgLeastsquares Least squares solving\n\nThe most accurate method to do least squares solving is with a SVD decomposition.\nEigen provides two implementations.\nThe recommended one is the BDCSVD class, which scale well for large problems\nand automatically fall-back to the JacobiSVD class for smaller problems.\nFor both classes, their solve() method is doing least-squares solving.\n\nHere is an example:\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr>\n  <td>\\include TutorialLinAlgSVDSolve.cpp </td>\n  <td>\\verbinclude TutorialLinAlgSVDSolve.out </td>\n</tr>\n</table>\n\nAnother methods, potentially faster but less reliable, are to use a Cholesky decomposition of the\nnormal matrix or a QR decomposition. Our page on \\link LeastSquares least squares solving \\endlink\nhas more details.\n\n\n\\section TutorialLinAlgSeparateComputation Separating the computation from the construction\n\nIn the above examples, the decomposition was computed at the same time that the decomposition object was constructed.\nThere are however situations where you might want to separate these two things, for example if you don't know,\nat the time of the construction, the matrix that you will want to decompose; or if you want to reuse an existing\ndecomposition object.\n\nWhat makes this possible is that:\n\\li all decompositions have a default constructor,\n\\li all decompositions have a compute(matrix) method that does the computation, and that may be called again\n    on an already-computed decomposition, reinitializing it.\n\nFor example:\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr>\n  <td>\\include TutorialLinAlgComputeTwice.cpp </td>\n  <td>\\verbinclude TutorialLinAlgComputeTwice.out </td>\n</tr>\n</table>\n\nFinally, you can tell the decomposition constructor to preallocate storage for decomposing matrices of a given size,\nso that when you subsequently decompose such matrices, no dynamic memory allocation is performed (of course, if you\nare using fixed-size matrices, no dynamic memory allocation happens at all). This is done by just\npassing the size to the decomposition constructor, as in this example:\n\\code\nHouseholderQR<MatrixXf> qr(50,50);\nMatrixXf A = MatrixXf::Random(50,50);\nqr.compute(A); // no dynamic memory allocation\n\\endcode\n\n\\section TutorialLinAlgRankRevealing Rank-revealing decompositions\n\nCertain decompositions are rank-revealing, i.e. are able to compute the rank of a matrix. These are typically\nalso the decompositions that behave best in the face of a non-full-rank matrix (which in the square case means a\nsingular matrix). On \\ref TopicLinearAlgebraDecompositions \"this table\" you can see for all our decompositions\nwhether they are rank-revealing or not.\n\nRank-revealing decompositions offer at least a rank() method. They can also offer convenience methods such as isInvertible(),\nand some are also providing methods to compute the kernel (null-space) and image (column-space) of the matrix, as is the\ncase with FullPivLU:\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr>\n  <td>\\include TutorialLinAlgRankRevealing.cpp </td>\n  <td>\\verbinclude TutorialLinAlgRankRevealing.out </td>\n</tr>\n</table>\n\nOf course, any rank computation depends on the choice of an arbitrary threshold, since practically no\nfloating-point matrix is \\em exactly rank-deficient. Eigen picks a sensible default threshold, which depends\non the decomposition but is typically the diagonal size times machine epsilon. While this is the best default we\ncould pick, only you know what is the right threshold for your application. You can set this by calling setThreshold()\non your decomposition object before calling rank() or any other method that needs to use such a threshold.\nThe decomposition itself, i.e. the compute() method, is independent of the threshold. You don't need to recompute the\ndecomposition after you've changed the threshold.\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr>\n  <td>\\include TutorialLinAlgSetThreshold.cpp </td>\n  <td>\\verbinclude TutorialLinAlgSetThreshold.out </td>\n</tr>\n</table>\n\n*/\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/TutorialMapClass.dox",
    "content": "namespace Eigen {\n\n/** \\eigenManualPage TutorialMapClass Interfacing with raw buffers: the Map class\n\nThis page explains how to work with \"raw\" C/C++ arrays.\nThis can be useful in a variety of contexts, particularly when \"importing\" vectors and matrices from other libraries into %Eigen.\n\n\\eigenAutoToc\n\n\\section TutorialMapIntroduction Introduction\n\nOccasionally you may have a pre-defined array of numbers that you want to use within %Eigen as a vector or matrix. While one option is to make a copy of the data, most commonly you probably want to re-use this memory as an %Eigen type. Fortunately, this is very easy with the Map class.\n\n\\section TutorialMapTypes Map types and declaring Map variables\n\nA Map object has a type defined by its %Eigen equivalent:\n\\code\nMap<Matrix<typename Scalar, int RowsAtCompileTime, int ColsAtCompileTime> >\n\\endcode\nNote that, in this default case, a Map requires just a single template parameter.  \n\nTo construct a Map variable, you need two other pieces of information: a pointer to the region of memory defining the array of coefficients, and the desired shape of the matrix or vector.  For example, to define a matrix of \\c float with sizes determined at compile time, you might do the following:\n\\code\nMap<MatrixXf> mf(pf,rows,columns);\n\\endcode\nwhere \\c pf is a \\c float \\c * pointing to the array of memory.  A fixed-size read-only vector of integers might be declared as\n\\code\nMap<const Vector4i> mi(pi);\n\\endcode\nwhere \\c pi is an \\c int \\c *. In this case the size does not have to be passed to the constructor, because it is already specified by the Matrix/Array type.\n\nNote that Map does not have a default constructor; you \\em must pass a pointer to intialize the object. However, you can work around this requirement (see \\ref TutorialMapPlacementNew).\n\nMap is flexible enough to accomodate a variety of different data representations.  There are two other (optional) template parameters:\n\\code\nMap<typename MatrixType,\n    int MapOptions,\n    typename StrideType>\n\\endcode\n\\li \\c MapOptions specifies whether the pointer is \\c #Aligned, or \\c #Unaligned.  The default is \\c #Unaligned.\n\\li \\c StrideType allows you to specify a custom layout for the memory array, using the Stride class.  One example would be to specify that the data array is organized in row-major format:\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr>\n<td>\\include Tutorial_Map_rowmajor.cpp </td>\n<td>\\verbinclude Tutorial_Map_rowmajor.out </td>\n</table>\nHowever, Stride is even more flexible than this; for details, see the documentation for the Map and Stride classes.\n\n\\section TutorialMapUsing Using Map variables\n\nYou can use a Map object just like any other %Eigen type:\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr>\n<td>\\include Tutorial_Map_using.cpp </td>\n<td>\\verbinclude Tutorial_Map_using.out </td>\n</table>\n\nAll %Eigen functions are written to accept Map objects just like other %Eigen types. However, when writing your own functions taking %Eigen types, this does \\em not happen automatically: a Map type is not identical to its Dense equivalent.  See \\ref TopicFunctionTakingEigenTypes for details.\n\n\\section TutorialMapPlacementNew Changing the mapped array\n\nIt is possible to change the array of a Map object after declaration, using the C++ \"placement new\" syntax:\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr>\n<td>\\include Map_placement_new.cpp </td>\n<td>\\verbinclude Map_placement_new.out </td>\n</table>\nDespite appearances, this does not invoke the memory allocator, because the syntax specifies the location for storing the result.\n\nThis syntax makes it possible to declare a Map object without first knowing the mapped array's location in memory:\n\\code\nMap<Matrix3f> A(NULL);  // don't try to use this matrix yet!\nVectorXf b(n_matrices);\nfor (int i = 0; i < n_matrices; i++)\n{\n  new (&A) Map<Matrix3f>(get_matrix_pointer(i));\n  b(i) = A.trace();\n}\n\\endcode\n\n*/\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/TutorialMatrixArithmetic.dox",
    "content": "namespace Eigen {\n\n/** \\eigenManualPage TutorialMatrixArithmetic Matrix and vector arithmetic\n\nThis page aims to provide an overview and some details on how to perform arithmetic\nbetween matrices, vectors and scalars with Eigen.\n\n\\eigenAutoToc\n\n\\section TutorialArithmeticIntroduction Introduction\n\nEigen offers matrix/vector arithmetic operations either through overloads of common C++ arithmetic operators such as +, -, *,\nor through special methods such as dot(), cross(), etc.\nFor the Matrix class (matrices and vectors), operators are only overloaded to support\nlinear-algebraic operations. For example, \\c matrix1 \\c * \\c matrix2 means matrix-matrix product,\nand \\c vector \\c + \\c scalar is just not allowed. If you want to perform all kinds of array operations,\nnot linear algebra, see the \\ref TutorialArrayClass \"next page\".\n\n\\section TutorialArithmeticAddSub Addition and subtraction\n\nThe left hand side and right hand side must, of course, have the same numbers of rows and of columns. They must\nalso have the same \\c Scalar type, as Eigen doesn't do automatic type promotion. The operators at hand here are:\n\\li binary operator + as in \\c a+b\n\\li binary operator - as in \\c a-b\n\\li unary operator - as in \\c -a\n\\li compound operator += as in \\c a+=b\n\\li compound operator -= as in \\c a-=b\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include tut_arithmetic_add_sub.cpp\n</td>\n<td>\n\\verbinclude tut_arithmetic_add_sub.out\n</td></tr></table>\n\n\\section TutorialArithmeticScalarMulDiv Scalar multiplication and division\n\nMultiplication and division by a scalar is very simple too. The operators at hand here are:\n\\li binary operator * as in \\c matrix*scalar\n\\li binary operator * as in \\c scalar*matrix\n\\li binary operator / as in \\c matrix/scalar\n\\li compound operator *= as in \\c matrix*=scalar\n\\li compound operator /= as in \\c matrix/=scalar\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include tut_arithmetic_scalar_mul_div.cpp\n</td>\n<td>\n\\verbinclude tut_arithmetic_scalar_mul_div.out\n</td></tr></table>\n\n\n\\section TutorialArithmeticMentionXprTemplates A note about expression templates\n\nThis is an advanced topic that we explain on \\ref TopicEigenExpressionTemplates \"this page\",\nbut it is useful to just mention it now. In Eigen, arithmetic operators such as \\c operator+ don't\nperform any computation by themselves, they just return an \"expression object\" describing the computation to be\nperformed. The actual computation happens later, when the whole expression is evaluated, typically in \\c operator=.\nWhile this might sound heavy, any modern optimizing compiler is able to optimize away that abstraction and\nthe result is perfectly optimized code. For example, when you do:\n\\code\nVectorXf a(50), b(50), c(50), d(50);\n...\na = 3*b + 4*c + 5*d;\n\\endcode\nEigen compiles it to just one for loop, so that the arrays are traversed only once. Simplifying (e.g. ignoring\nSIMD optimizations), this loop looks like this:\n\\code\nfor(int i = 0; i < 50; ++i)\n  a[i] = 3*b[i] + 4*c[i] + 5*d[i];\n\\endcode\nThus, you should not be afraid of using relatively large arithmetic expressions with Eigen: it only gives Eigen\nmore opportunities for optimization.\n\n\\section TutorialArithmeticTranspose Transposition and conjugation\n\nThe transpose \\f$ a^T \\f$, conjugate \\f$ \\bar{a} \\f$, and adjoint (i.e., conjugate transpose) \\f$ a^* \\f$ of a matrix or vector \\f$ a \\f$ are obtained by the member functions \\link DenseBase::transpose() transpose()\\endlink, \\link MatrixBase::conjugate() conjugate()\\endlink, and \\link MatrixBase::adjoint() adjoint()\\endlink, respectively.\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include tut_arithmetic_transpose_conjugate.cpp\n</td>\n<td>\n\\verbinclude tut_arithmetic_transpose_conjugate.out\n</td></tr></table>\n\nFor real matrices, \\c conjugate() is a no-operation, and so \\c adjoint() is equivalent to \\c transpose().\n\nAs for basic arithmetic operators, \\c transpose() and \\c adjoint() simply return a proxy object without doing the actual transposition. If you do <tt>b = a.transpose()</tt>, then the transpose is evaluated at the same time as the result is written into \\c b. However, there is a complication here. If you do <tt>a = a.transpose()</tt>, then Eigen starts writing the result into \\c a before the evaluation of the transpose is finished. Therefore, the instruction <tt>a = a.transpose()</tt> does not replace \\c a with its transpose, as one would expect:\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include tut_arithmetic_transpose_aliasing.cpp\n</td>\n<td>\n\\verbinclude tut_arithmetic_transpose_aliasing.out\n</td></tr></table>\nThis is the so-called \\ref TopicAliasing \"aliasing issue\". In \"debug mode\", i.e., when \\ref TopicAssertions \"assertions\" have not been disabled, such common pitfalls are automatically detected. \n\nFor \\em in-place transposition, as for instance in <tt>a = a.transpose()</tt>, simply use the \\link DenseBase::transposeInPlace() transposeInPlace()\\endlink  function:\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include tut_arithmetic_transpose_inplace.cpp\n</td>\n<td>\n\\verbinclude tut_arithmetic_transpose_inplace.out\n</td></tr></table>\nThere is also the \\link MatrixBase::adjointInPlace() adjointInPlace()\\endlink function for complex matrices.\n\n\\section TutorialArithmeticMatrixMul Matrix-matrix and matrix-vector multiplication\n\nMatrix-matrix multiplication is again done with \\c operator*. Since vectors are a special\ncase of matrices, they are implicitly handled there too, so matrix-vector product is really just a special\ncase of matrix-matrix product, and so is vector-vector outer product. Thus, all these cases are handled by just\ntwo operators:\n\\li binary operator * as in \\c a*b\n\\li compound operator *= as in \\c a*=b (this multiplies on the right: \\c a*=b is equivalent to <tt>a = a*b</tt>)\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include tut_arithmetic_matrix_mul.cpp\n</td>\n<td>\n\\verbinclude tut_arithmetic_matrix_mul.out\n</td></tr></table>\n\nNote: if you read the above paragraph on expression templates and are worried that doing \\c m=m*m might cause\naliasing issues, be reassured for now: Eigen treats matrix multiplication as a special case and takes care of\nintroducing a temporary here, so it will compile \\c m=m*m as:\n\\code\ntmp = m*m;\nm = tmp;\n\\endcode\nIf you know your matrix product can be safely evaluated into the destination matrix without aliasing issue, then you can use the \\link MatrixBase::noalias() noalias()\\endlink function to avoid the temporary, e.g.:\n\\code\nc.noalias() += a * b;\n\\endcode\nFor more details on this topic, see the page on \\ref TopicAliasing \"aliasing\".\n\n\\b Note: for BLAS users worried about performance, expressions such as <tt>c.noalias() -= 2 * a.adjoint() * b;</tt> are fully optimized and trigger a single gemm-like function call.\n\n\\section TutorialArithmeticDotAndCross Dot product and cross product\n\nFor dot product and cross product, you need the \\link MatrixBase::dot() dot()\\endlink and \\link MatrixBase::cross() cross()\\endlink methods. Of course, the dot product can also be obtained as a 1x1 matrix as u.adjoint()*v.\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include tut_arithmetic_dot_cross.cpp\n</td>\n<td>\n\\verbinclude tut_arithmetic_dot_cross.out\n</td></tr></table>\n\nRemember that cross product is only for vectors of size 3. Dot product is for vectors of any sizes.\nWhen using complex numbers, Eigen's dot product is conjugate-linear in the first variable and linear in the\nsecond variable.\n\n\\section TutorialArithmeticRedux Basic arithmetic reduction operations\nEigen also provides some reduction operations to reduce a given matrix or vector to a single value such as the sum (computed by \\link DenseBase::sum() sum()\\endlink), product (\\link DenseBase::prod() prod()\\endlink), or the maximum (\\link DenseBase::maxCoeff() maxCoeff()\\endlink) and minimum (\\link DenseBase::minCoeff() minCoeff()\\endlink) of all its coefficients.\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include tut_arithmetic_redux_basic.cpp\n</td>\n<td>\n\\verbinclude tut_arithmetic_redux_basic.out\n</td></tr></table>\n\nThe \\em trace of a matrix, as returned by the function \\link MatrixBase::trace() trace()\\endlink, is the sum of the diagonal coefficients and can also be computed as efficiently using <tt>a.diagonal().sum()</tt>, as we will see later on.\n\nThere also exist variants of the \\c minCoeff and \\c maxCoeff functions returning the coordinates of the respective coefficient via the arguments:\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include tut_arithmetic_redux_minmax.cpp\n</td>\n<td>\n\\verbinclude tut_arithmetic_redux_minmax.out\n</td></tr></table>\n\n\n\\section TutorialArithmeticValidity Validity of operations\nEigen checks the validity of the operations that you perform. When possible,\nit checks them at compile time, producing compilation errors. These error messages can be long and ugly,\nbut Eigen writes the important message in UPPERCASE_LETTERS_SO_IT_STANDS_OUT. For example:\n\\code\n  Matrix3f m;\n  Vector4f v;\n  v = m*v;      // Compile-time error: YOU_MIXED_MATRICES_OF_DIFFERENT_SIZES\n\\endcode\n\nOf course, in many cases, for example when checking dynamic sizes, the check cannot be performed at compile time.\nEigen then uses runtime assertions. This means that the program will abort with an error message when executing an illegal operation if it is run in \"debug mode\", and it will probably crash if assertions are turned off.\n\n\\code\n  MatrixXf m(3,3);\n  VectorXf v(4);\n  v = m * v; // Run-time assertion failure here: \"invalid matrix product\"\n\\endcode\n\nFor more details on this topic, see \\ref TopicAssertions \"this page\".\n\n*/\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/TutorialMatrixClass.dox",
    "content": "namespace Eigen {\n\n/** \\eigenManualPage TutorialMatrixClass The Matrix class\n\n\\eigenAutoToc\n\nIn Eigen, all matrices and vectors are objects of the Matrix template class.\nVectors are just a special case of matrices, with either 1 row or 1 column.\n\n\\section TutorialMatrixFirst3Params The first three template parameters of Matrix\n\nThe Matrix class takes six template parameters, but for now it's enough to\nlearn about the first three first parameters. The three remaining parameters have default\nvalues, which for now we will leave untouched, and which we\n\\ref TutorialMatrixOptTemplParams \"discuss below\".\n\nThe three mandatory template parameters of Matrix are:\n\\code\nMatrix<typename Scalar, int RowsAtCompileTime, int ColsAtCompileTime>\n\\endcode\n\\li \\c Scalar is the scalar type, i.e. the type of the coefficients.\n    That is, if you want a matrix of floats, choose \\c float here.\n    See \\ref TopicScalarTypes \"Scalar types\" for a list of all supported\n    scalar types and for how to extend support to new types.\n\\li \\c RowsAtCompileTime and \\c ColsAtCompileTime are the number of rows\n    and columns of the matrix as known at compile time (see \n    \\ref TutorialMatrixDynamic \"below\" for what to do if the number is not\n    known at compile time).\n\nWe offer a lot of convenience typedefs to cover the usual cases. For example, \\c Matrix4f is\na 4x4 matrix of floats. Here is how it is defined by Eigen:\n\\code\ntypedef Matrix<float, 4, 4> Matrix4f;\n\\endcode\nWe discuss \\ref TutorialMatrixTypedefs \"below\" these convenience typedefs.\n\n\\section TutorialMatrixVectors Vectors\n\nAs mentioned above, in Eigen, vectors are just a special case of\nmatrices, with either 1 row or 1 column. The case where they have 1 column is the most common;\nsuch vectors are called column-vectors, often abbreviated as just vectors. In the other case\nwhere they have 1 row, they are called row-vectors.\n\nFor example, the convenience typedef \\c Vector3f is a (column) vector of 3 floats. It is defined as follows by Eigen:\n\\code\ntypedef Matrix<float, 3, 1> Vector3f;\n\\endcode\nWe also offer convenience typedefs for row-vectors, for example:\n\\code\ntypedef Matrix<int, 1, 2> RowVector2i;\n\\endcode\n\n\\section TutorialMatrixDynamic The special value Dynamic\n\nOf course, Eigen is not limited to matrices whose dimensions are known at compile time.\nThe \\c RowsAtCompileTime and \\c ColsAtCompileTime template parameters can take the special\nvalue \\c Dynamic which indicates that the size is unknown at compile time, so must\nbe handled as a run-time variable. In Eigen terminology, such a size is referred to as a\n\\em dynamic \\em size; while a size that is known at compile time is called a\n\\em fixed \\em size. For example, the convenience typedef \\c MatrixXd, meaning\na matrix of doubles with dynamic size, is defined as follows:\n\\code\ntypedef Matrix<double, Dynamic, Dynamic> MatrixXd;\n\\endcode\nAnd similarly, we define a self-explanatory typedef \\c VectorXi as follows:\n\\code\ntypedef Matrix<int, Dynamic, 1> VectorXi;\n\\endcode\nYou can perfectly have e.g. a fixed number of rows with a dynamic number of columns, as in:\n\\code\nMatrix<float, 3, Dynamic>\n\\endcode\n\n\\section TutorialMatrixConstructors Constructors\n\nA default constructor is always available, never performs any dynamic memory allocation, and never initializes the matrix coefficients. You can do:\n\\code\nMatrix3f a;\nMatrixXf b;\n\\endcode\nHere,\n\\li \\c a is a 3-by-3 matrix, with a plain float[9] array of uninitialized coefficients,\n\\li \\c b is a dynamic-size matrix whose size is currently 0-by-0, and whose array of\ncoefficients hasn't yet been allocated at all.\n\nConstructors taking sizes are also available. For matrices, the number of rows is always passed first.\nFor vectors, just pass the vector size. They allocate the array of coefficients\nwith the given size, but don't initialize the coefficients themselves:\n\\code\nMatrixXf a(10,15);\nVectorXf b(30);\n\\endcode\nHere,\n\\li \\c a is a 10x15 dynamic-size matrix, with allocated but currently uninitialized coefficients.\n\\li \\c b is a dynamic-size vector of size 30, with allocated but currently uninitialized coefficients.\n\nIn order to offer a uniform API across fixed-size and dynamic-size matrices, it is legal to use these\nconstructors on fixed-size matrices, even if passing the sizes is useless in this case. So this is legal:\n\\code\nMatrix3f a(3,3);\n\\endcode\nand is a no-operation.\n\nFinally, we also offer some constructors to initialize the coefficients of small fixed-size vectors up to size 4:\n\\code\nVector2d a(5.0, 6.0);\nVector3d b(5.0, 6.0, 7.0);\nVector4d c(5.0, 6.0, 7.0, 8.0);\n\\endcode\n\n\\section TutorialMatrixCoeffAccessors Coefficient accessors\n\nThe primary coefficient accessors and mutators in Eigen are the overloaded parenthesis operators.\nFor matrices, the row index is always passed first. For vectors, just pass one index.\nThe numbering starts at 0. This example is self-explanatory:\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include tut_matrix_coefficient_accessors.cpp\n</td>\n<td>\n\\verbinclude tut_matrix_coefficient_accessors.out\n</td></tr></table>\n\nNote that the syntax <tt> m(index) </tt>\nis not restricted to vectors, it is also available for general matrices, meaning index-based access\nin the array of coefficients. This however depends on the matrix's storage order. All Eigen matrices default to\ncolumn-major storage order, but this can be changed to row-major, see \\ref TopicStorageOrders \"Storage orders\".\n\nThe operator[] is also overloaded for index-based access in vectors, but keep in mind that C++ doesn't allow operator[] to\ntake more than one argument. We restrict operator[] to vectors, because an awkwardness in the C++ language\nwould make matrix[i,j] compile to the same thing as matrix[j] !\n\n\\section TutorialMatrixCommaInitializer Comma-initialization\n\n%Matrix and vector coefficients can be conveniently set using the so-called \\em comma-initializer syntax.\nFor now, it is enough to know this example:\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr>\n<td>\\include Tutorial_commainit_01.cpp </td>\n<td>\\verbinclude Tutorial_commainit_01.out </td>\n</tr></table>\n\n\nThe right-hand side can also contain matrix expressions as discussed in \\ref TutorialAdvancedInitialization \"this page\".\n\n\\section TutorialMatrixSizesResizing Resizing\n\nThe current size of a matrix can be retrieved by \\link EigenBase::rows() rows()\\endlink, \\link EigenBase::cols() cols() \\endlink and \\link EigenBase::size() size()\\endlink. These methods return the number of rows, the number of columns and the number of coefficients, respectively. Resizing a dynamic-size matrix is done by the \\link PlainObjectBase::resize(Index,Index) resize() \\endlink method.\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr>\n<td>\\include tut_matrix_resize.cpp </td>\n<td>\\verbinclude tut_matrix_resize.out </td>\n</tr></table>\n\nThe resize() method is a no-operation if the actual matrix size doesn't change; otherwise it is destructive: the values of the coefficients may change.\nIf you want a conservative variant of resize() which does not change the coefficients, use \\link PlainObjectBase::conservativeResize() conservativeResize()\\endlink, see \\ref TopicResizing \"this page\" for more details.\n\nAll these methods are still available on fixed-size matrices, for the sake of API uniformity. Of course, you can't actually\nresize a fixed-size matrix. Trying to change a fixed size to an actually different value will trigger an assertion failure;\nbut the following code is legal:\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr>\n<td>\\include tut_matrix_resize_fixed_size.cpp </td>\n<td>\\verbinclude tut_matrix_resize_fixed_size.out </td>\n</tr></table>\n\n\n\\section TutorialMatrixAssignment Assignment and resizing\n\nAssignment is the action of copying a matrix into another, using \\c operator=. Eigen resizes the matrix on the left-hand side automatically so that it matches the size of the matrix on the right-hand size. For example:\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr>\n<td>\\include tut_matrix_assignment_resizing.cpp </td>\n<td>\\verbinclude tut_matrix_assignment_resizing.out </td>\n</tr></table>\n\nOf course, if the left-hand side is of fixed size, resizing it is not allowed.\n\nIf you do not want this automatic resizing to happen (for example for debugging purposes), you can disable it, see\n\\ref TopicResizing \"this page\".\n\n\n\\section TutorialMatrixFixedVsDynamic Fixed vs. Dynamic size\n\nWhen should one use fixed sizes (e.g. \\c Matrix4f), and when should one prefer dynamic sizes (e.g. \\c MatrixXf)?\nThe simple answer is: use fixed\nsizes for very small sizes where you can, and use dynamic sizes for larger sizes or where you have to. For small sizes,\nespecially for sizes smaller than (roughly) 16, using fixed sizes is hugely beneficial\nto performance, as it allows Eigen to avoid dynamic memory allocation and to unroll\nloops. Internally, a fixed-size Eigen matrix is just a plain array, i.e. doing\n\\code Matrix4f mymatrix; \\endcode\nreally amounts to just doing\n\\code float mymatrix[16]; \\endcode\nso this really has zero runtime cost. By contrast, the array of a dynamic-size matrix\nis always allocated on the heap, so doing\n\\code MatrixXf mymatrix(rows,columns); \\endcode\namounts to doing\n\\code float *mymatrix = new float[rows*columns]; \\endcode\nand in addition to that, the MatrixXf object stores its number of rows and columns as\nmember variables.\n\nThe limitation of using fixed sizes, of course, is that this is only possible\nwhen you know the sizes at compile time. Also, for large enough sizes, say for sizes\ngreater than (roughly) 32, the performance benefit of using fixed sizes becomes negligible.\nWorse, trying to create a very large matrix using fixed sizes inside a function could result in a\nstack overflow, since Eigen will try to allocate the array automatically as a local variable, and\nthis is normally done on the stack.\nFinally, depending on circumstances, Eigen can also be more aggressive trying to vectorize\n(use SIMD instructions) when dynamic sizes are used, see \\ref TopicVectorization \"Vectorization\".\n\n\\section TutorialMatrixOptTemplParams Optional template parameters\n\nWe mentioned at the beginning of this page that the Matrix class takes six template parameters,\nbut so far we only discussed the first three. The remaining three parameters are optional. Here is\nthe complete list of template parameters:\n\\code\nMatrix<typename Scalar,\n       int RowsAtCompileTime,\n       int ColsAtCompileTime,\n       int Options = 0,\n       int MaxRowsAtCompileTime = RowsAtCompileTime,\n       int MaxColsAtCompileTime = ColsAtCompileTime>\n\\endcode\n\\li \\c Options is a bit field. Here, we discuss only one bit: \\c RowMajor. It specifies that the matrices\n      of this type use row-major storage order; by default, the storage order is column-major. See the page on\n      \\ref TopicStorageOrders \"storage orders\". For example, this type means row-major 3x3 matrices:\n      \\code\n      Matrix<float, 3, 3, RowMajor>\n      \\endcode\n\\li \\c MaxRowsAtCompileTime and \\c MaxColsAtCompileTime are useful when you want to specify that, even though\n      the exact sizes of your matrices are not known at compile time, a fixed upper bound is known at\n      compile time. The biggest reason why you might want to do that is to avoid dynamic memory allocation.\n      For example the following matrix type uses a plain array of 12 floats, without dynamic memory allocation:\n      \\code\n      Matrix<float, Dynamic, Dynamic, 0, 3, 4>\n      \\endcode\n\n\\section TutorialMatrixTypedefs Convenience typedefs\n\nEigen defines the following Matrix typedefs:\n\\li MatrixNt for Matrix<type, N, N>. For example, MatrixXi for Matrix<int, Dynamic, Dynamic>.\n\\li VectorNt for Matrix<type, N, 1>. For example, Vector2f for Matrix<float, 2, 1>.\n\\li RowVectorNt for Matrix<type, 1, N>. For example, RowVector3d for Matrix<double, 1, 3>.\n\nWhere:\n\\li N can be any one of \\c 2, \\c 3, \\c 4, or \\c X (meaning \\c Dynamic).\n\\li t can be any one of \\c i (meaning int), \\c f (meaning float), \\c d (meaning double),\n      \\c cf (meaning complex<float>), or \\c cd (meaning complex<double>). The fact that typedefs are only\n    defined for these five types doesn't mean that they are the only supported scalar types. For example,\n    all standard integer types are supported, see \\ref TopicScalarTypes \"Scalar types\".\n\n\n*/\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/TutorialReductionsVisitorsBroadcasting.dox",
    "content": "namespace Eigen {\n\n/** \\eigenManualPage TutorialReductionsVisitorsBroadcasting Reductions, visitors and broadcasting\n\nThis page explains Eigen's reductions, visitors and broadcasting and how they are used with\n\\link MatrixBase matrices \\endlink and \\link ArrayBase arrays \\endlink.\n\n\\eigenAutoToc\n\n\\section TutorialReductionsVisitorsBroadcastingReductions Reductions\nIn Eigen, a reduction is a function taking a matrix or array, and returning a single\nscalar value. One of the most used reductions is \\link DenseBase::sum() .sum() \\endlink,\nreturning the sum of all the coefficients inside a given matrix or array.\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include tut_arithmetic_redux_basic.cpp\n</td>\n<td>\n\\verbinclude tut_arithmetic_redux_basic.out\n</td></tr></table>\n\nThe \\em trace of a matrix, as returned by the function \\c trace(), is the sum of the diagonal coefficients and can equivalently be computed <tt>a.diagonal().sum()</tt>.\n\n\n\\subsection TutorialReductionsVisitorsBroadcastingReductionsNorm Norm computations\n\nThe (Euclidean a.k.a. \\f$\\ell^2\\f$) squared norm of a vector can be obtained \\link MatrixBase::squaredNorm() squaredNorm() \\endlink. It is equal to the dot product of the vector by itself, and equivalently to the sum of squared absolute values of its coefficients.\n\nEigen also provides the \\link MatrixBase::norm() norm() \\endlink method, which returns the square root of \\link MatrixBase::squaredNorm() squaredNorm() \\endlink.\n\nThese operations can also operate on matrices; in that case, a n-by-p matrix is seen as a vector of size (n*p), so for example the \\link MatrixBase::norm() norm() \\endlink method returns the \"Frobenius\" or \"Hilbert-Schmidt\" norm. We refrain from speaking of the \\f$\\ell^2\\f$ norm of a matrix because that can mean different things.\n\nIf you want other coefficient-wise \\f$\\ell^p\\f$ norms, use the \\link MatrixBase::lpNorm lpNorm<p>() \\endlink method. The template parameter \\a p can take the special value \\a Infinity if you want the \\f$\\ell^\\infty\\f$ norm, which is the maximum of the absolute values of the coefficients.\n\nThe following example demonstrates these methods.\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include Tutorial_ReductionsVisitorsBroadcasting_reductions_norm.cpp\n</td>\n<td>\n\\verbinclude Tutorial_ReductionsVisitorsBroadcasting_reductions_norm.out\n</td></tr></table>\n\n\\b Operator \\b norm: The 1-norm and \\f$\\infty\\f$-norm <a href=\"https://en.wikipedia.org/wiki/Operator_norm\">matrix operator norms</a> can easily be computed as follows:\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include Tutorial_ReductionsVisitorsBroadcasting_reductions_operatornorm.cpp\n</td>\n<td>\n\\verbinclude Tutorial_ReductionsVisitorsBroadcasting_reductions_operatornorm.out\n</td></tr></table>\nSee below for more explanations on the syntax of these expressions.\n\n\\subsection TutorialReductionsVisitorsBroadcastingReductionsBool Boolean reductions\n\nThe following reductions operate on boolean values:\n  - \\link DenseBase::all() all() \\endlink returns \\b true if all of the coefficients in a given Matrix or Array evaluate to \\b true .\n  - \\link DenseBase::any() any() \\endlink returns \\b true if at least one of the coefficients in a given Matrix or Array evaluates to \\b true .\n  - \\link DenseBase::count() count() \\endlink returns the number of coefficients in a given Matrix or Array that evaluate to  \\b true.\n\nThese are typically used in conjunction with the coefficient-wise comparison and equality operators provided by Array. For instance, <tt>array > 0</tt> is an %Array of the same size as \\c array , with \\b true at those positions where the corresponding coefficient of \\c array is positive. Thus, <tt>(array > 0).all()</tt> tests whether all coefficients of \\c array are positive. This can be seen in the following example:\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include Tutorial_ReductionsVisitorsBroadcasting_reductions_bool.cpp\n</td>\n<td>\n\\verbinclude Tutorial_ReductionsVisitorsBroadcasting_reductions_bool.out\n</td></tr></table>\n\n\\subsection TutorialReductionsVisitorsBroadcastingReductionsUserdefined User defined reductions\n\nTODO\n\nIn the meantime you can have a look at the DenseBase::redux() function.\n\n\\section TutorialReductionsVisitorsBroadcastingVisitors Visitors\nVisitors are useful when one wants to obtain the location of a coefficient inside \na Matrix or Array. The simplest examples are \n\\link MatrixBase::maxCoeff() maxCoeff(&x,&y) \\endlink and \n\\link MatrixBase::minCoeff() minCoeff(&x,&y)\\endlink, which can be used to find\nthe location of the greatest or smallest coefficient in a Matrix or \nArray.\n\nThe arguments passed to a visitor are pointers to the variables where the\nrow and column position are to be stored. These variables should be of type\n\\link Eigen::Index Index \\endlink, as shown below:\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include Tutorial_ReductionsVisitorsBroadcasting_visitors.cpp\n</td>\n<td>\n\\verbinclude Tutorial_ReductionsVisitorsBroadcasting_visitors.out\n</td></tr></table>\n\nBoth functions also return the value of the minimum or maximum coefficient.\n\n\\section TutorialReductionsVisitorsBroadcastingPartialReductions Partial reductions\nPartial reductions are reductions that can operate column- or row-wise on a Matrix or \nArray, applying the reduction operation on each column or row and \nreturning a column or row vector with the corresponding values. Partial reductions are applied \nwith \\link DenseBase::colwise() colwise() \\endlink or \\link DenseBase::rowwise() rowwise() \\endlink.\n\nA simple example is obtaining the maximum of the elements \nin each column in a given matrix, storing the result in a row vector:\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include Tutorial_ReductionsVisitorsBroadcasting_colwise.cpp\n</td>\n<td>\n\\verbinclude Tutorial_ReductionsVisitorsBroadcasting_colwise.out\n</td></tr></table>\n\nThe same operation can be performed row-wise:\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include Tutorial_ReductionsVisitorsBroadcasting_rowwise.cpp\n</td>\n<td>\n\\verbinclude Tutorial_ReductionsVisitorsBroadcasting_rowwise.out\n</td></tr></table>\n\n<b>Note that column-wise operations return a row vector, while row-wise operations return a column vector.</b>\n\n\\subsection TutorialReductionsVisitorsBroadcastingPartialReductionsCombined Combining partial reductions with other operations\nIt is also possible to use the result of a partial reduction to do further processing.\nHere is another example that finds the column whose sum of elements is the maximum\n within a matrix. With column-wise partial reductions this can be coded as:\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include Tutorial_ReductionsVisitorsBroadcasting_maxnorm.cpp\n</td>\n<td>\n\\verbinclude Tutorial_ReductionsVisitorsBroadcasting_maxnorm.out\n</td></tr></table>\n\nThe previous example applies the \\link DenseBase::sum() sum() \\endlink reduction on each column\nthough the \\link DenseBase::colwise() colwise() \\endlink visitor, obtaining a new matrix whose\nsize is 1x4.\n\nTherefore, if\n\\f[\n\\mbox{m} = \\begin{bmatrix} 1 & 2 & 6 & 9 \\\\\n                    3 & 1 & 7 & 2 \\end{bmatrix}\n\\f]\n\nthen\n\n\\f[\n\\mbox{m.colwise().sum()} = \\begin{bmatrix} 4 & 3 & 13 & 11 \\end{bmatrix}\n\\f]\n\nThe \\link DenseBase::maxCoeff() maxCoeff() \\endlink reduction is finally applied \nto obtain the column index where the maximum sum is found, \nwhich is the column index 2 (third column) in this case.\n\n\n\\section TutorialReductionsVisitorsBroadcastingBroadcasting Broadcasting\nThe concept behind broadcasting is similar to partial reductions, with the difference that broadcasting \nconstructs an expression where a vector (column or row) is interpreted as a matrix by replicating it in \none direction.\n\nA simple example is to add a certain column vector to each column in a matrix. \nThis can be accomplished with:\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include Tutorial_ReductionsVisitorsBroadcasting_broadcast_simple.cpp\n</td>\n<td>\n\\verbinclude Tutorial_ReductionsVisitorsBroadcasting_broadcast_simple.out\n</td></tr></table>\n\nWe can interpret the instruction <tt>mat.colwise() += v</tt> in two equivalent ways. It adds the vector \\c v\nto every column of the matrix. Alternatively, it can be interpreted as repeating the vector \\c v four times to\nform a four-by-two matrix which is then added to \\c mat:\n\\f[\n\\begin{bmatrix} 1 & 2 & 6 & 9 \\\\ 3 & 1 & 7 & 2 \\end{bmatrix}\n+ \\begin{bmatrix} 0 & 0 & 0 & 0 \\\\ 1 & 1 & 1 & 1 \\end{bmatrix}\n= \\begin{bmatrix} 1 & 2 & 6 & 9 \\\\ 4 & 2 & 8 & 3 \\end{bmatrix}.\n\\f]\nThe operators <tt>-=</tt>, <tt>+</tt> and <tt>-</tt> can also be used column-wise and row-wise. On arrays, we \ncan also use the operators <tt>*=</tt>, <tt>/=</tt>, <tt>*</tt> and <tt>/</tt> to perform coefficient-wise \nmultiplication and division column-wise or row-wise. These operators are not available on matrices because it\nis not clear what they would do. If you want multiply column 0 of a matrix \\c mat with \\c v(0), column 1 with \n\\c v(1), and so on, then use <tt>mat = mat * v.asDiagonal()</tt>.\n\nIt is important to point out that the vector to be added column-wise or row-wise must be of type Vector,\nand cannot be a Matrix. If this is not met then you will get compile-time error. This also means that\nbroadcasting operations can only be applied with an object of type Vector, when operating with Matrix.\nThe same applies for the Array class, where the equivalent for VectorXf is ArrayXf. As always, you should\nnot mix arrays and matrices in the same expression.\n\nTo perform the same operation row-wise we can do:\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include Tutorial_ReductionsVisitorsBroadcasting_broadcast_simple_rowwise.cpp\n</td>\n<td>\n\\verbinclude Tutorial_ReductionsVisitorsBroadcasting_broadcast_simple_rowwise.out\n</td></tr></table>\n\n\\subsection TutorialReductionsVisitorsBroadcastingBroadcastingCombined Combining broadcasting with other operations\nBroadcasting can also be combined with other operations, such as Matrix or Array operations, \nreductions and partial reductions.\n\nNow that broadcasting, reductions and partial reductions have been introduced, we can dive into a more advanced example that finds\nthe nearest neighbour of a vector <tt>v</tt> within the columns of matrix <tt>m</tt>. The Euclidean distance will be used in this example,\ncomputing the squared Euclidean distance with the partial reduction named \\link MatrixBase::squaredNorm() squaredNorm() \\endlink:\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include Tutorial_ReductionsVisitorsBroadcasting_broadcast_1nn.cpp\n</td>\n<td>\n\\verbinclude Tutorial_ReductionsVisitorsBroadcasting_broadcast_1nn.out\n</td></tr></table>\n\nThe line that does the job is \n\\code\n  (m.colwise() - v).colwise().squaredNorm().minCoeff(&index);\n\\endcode\n\nWe will go step by step to understand what is happening:\n\n  - <tt>m.colwise() - v</tt> is a broadcasting operation, subtracting <tt>v</tt> from each column in <tt>m</tt>. The result of this operation\nis a new matrix whose size is the same as matrix <tt>m</tt>: \\f[\n  \\mbox{m.colwise() - v} = \n  \\begin{bmatrix}\n    -1 & 21 & 4 & 7 \\\\\n     0 & 8  & 4 & -1\n  \\end{bmatrix}\n\\f]\n\n  - <tt>(m.colwise() - v).colwise().squaredNorm()</tt> is a partial reduction, computing the squared norm column-wise. The result of\nthis operation is a row vector where each coefficient is the squared Euclidean distance between each column in <tt>m</tt> and <tt>v</tt>: \\f[\n  \\mbox{(m.colwise() - v).colwise().squaredNorm()} =\n  \\begin{bmatrix}\n     1 & 505 & 32 & 50\n  \\end{bmatrix}\n\\f]\n\n  - Finally, <tt>minCoeff(&index)</tt> is used to obtain the index of the column in <tt>m</tt> that is closest to <tt>v</tt> in terms of Euclidean\ndistance.\n\n*/\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/TutorialReshapeSlicing.dox",
    "content": "namespace Eigen {\n\n/** \\eigenManualPage TutorialReshapeSlicing Reshape and Slicing\n\n%Eigen does not expose convenient methods to take slices or to reshape a matrix yet.\nNonetheless, such features can easily be emulated using the Map class.\n\n\\eigenAutoToc\n\n\\section TutorialReshape Reshape\n\nA reshape operation consists in modifying the sizes of a matrix while keeping the same coefficients.\nInstead of modifying the input matrix itself, which is not possible for compile-time sizes, the approach consist in creating a different \\em view on the storage using class Map.\nHere is a typical example creating a 1D linear view of a matrix:\n\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include Tutorial_ReshapeMat2Vec.cpp\n</td>\n<td>\n\\verbinclude Tutorial_ReshapeMat2Vec.out\n</td></tr></table>\n\nRemark how the storage order of the input matrix modifies the order of the coefficients in the linear view.\nHere is another example reshaping a 2x6 matrix to a 6x2 one:\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include Tutorial_ReshapeMat2Mat.cpp\n</td>\n<td>\n\\verbinclude Tutorial_ReshapeMat2Mat.out\n</td></tr></table>\n\n\n\n\\section TutorialSlicing Slicing\n\nSlicing consists in taking a set of rows, columns, or elements, uniformly spaced within a matrix.\nAgain, the class Map allows to easily mimic this feature.\n\nFor instance, one can skip every P elements in a vector:\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include Tutorial_SlicingVec.cpp\n</td>\n<td>\n\\verbinclude Tutorial_SlicingVec.out\n</td></tr></table>\n\nOne can olso take one column over three using an adequate outer-stride or inner-stride depending on the actual storage order:\n<table class=\"example\">\n<tr><th>Example:</th><th>Output:</th></tr>\n<tr><td>\n\\include Tutorial_SlicingCol.cpp\n</td>\n<td>\n\\verbinclude Tutorial_SlicingCol.out\n</td></tr></table>\n\n*/\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/TutorialSparse.dox",
    "content": "namespace Eigen {\n\n/** \\eigenManualPage TutorialSparse Sparse matrix manipulations\n\n\\eigenAutoToc\n\nManipulating and solving sparse problems involves various modules which are summarized below:\n\n<table class=\"manual\">\n<tr><th>Module</th><th>Header file</th><th>Contents</th></tr>\n<tr><td>\\link SparseCore_Module SparseCore \\endlink</td><td>\\code#include <Eigen/SparseCore>\\endcode</td><td>SparseMatrix and SparseVector classes, matrix assembly, basic sparse linear algebra (including sparse triangular solvers)</td></tr>\n<tr><td>\\link SparseCholesky_Module SparseCholesky \\endlink</td><td>\\code#include <Eigen/SparseCholesky>\\endcode</td><td>Direct sparse LLT and LDLT Cholesky factorization to solve sparse self-adjoint positive definite problems</td></tr>\n<tr><td>\\link SparseLU_Module SparseLU \\endlink</td><td>\\code #include<Eigen/SparseLU> \\endcode</td>\n<td>%Sparse LU factorization to solve general square sparse systems</td></tr>\n<tr><td>\\link SparseQR_Module SparseQR \\endlink</td><td>\\code #include<Eigen/SparseQR>\\endcode </td><td>%Sparse QR factorization for solving sparse linear least-squares problems</td></tr>\n<tr><td>\\link IterativeLinearSolvers_Module IterativeLinearSolvers \\endlink</td><td>\\code#include <Eigen/IterativeLinearSolvers>\\endcode</td><td>Iterative solvers to solve large general linear square problems (including self-adjoint positive definite problems)</td></tr>\n<tr><td>\\link Sparse_Module Sparse \\endlink</td><td>\\code#include <Eigen/Sparse>\\endcode</td><td>Includes all the above modules</td></tr>\n</table>\n\n\\section TutorialSparseIntro Sparse matrix format\n\nIn many applications (e.g., finite element methods) it is common to deal with very large matrices where only a few coefficients are different from zero.  In such cases, memory consumption can be reduced and performance increased by using a specialized representation storing only the nonzero coefficients. Such a matrix is called a sparse matrix.\n\n\\b The \\b %SparseMatrix \\b class\n\nThe class SparseMatrix is the main sparse matrix representation of Eigen's sparse module; it offers high performance and low memory usage.\nIt implements a more versatile variant of the widely-used Compressed Column (or Row) Storage scheme.\nIt consists of four compact arrays:\n - \\c Values: stores the coefficient values of the non-zeros.\n - \\c InnerIndices: stores the row (resp. column) indices of the non-zeros.\n - \\c OuterStarts: stores for each column (resp. row) the index of the first non-zero in the previous two arrays.\n - \\c InnerNNZs: stores the number of non-zeros of each column (resp. row).\nThe word \\c inner refers to an \\em inner \\em vector that is a column for a column-major matrix, or a row for a row-major matrix.\nThe word \\c outer refers to the other direction.\n\nThis storage scheme is better explained on an example. The following matrix\n<table class=\"manual\">\n<tr><td> 0</td><td>3</td><td> 0</td><td>0</td><td> 0</td></tr>\n<tr><td>22</td><td>0</td><td> 0</td><td>0</td><td>17</td></tr>\n<tr><td> 7</td><td>5</td><td> 0</td><td>1</td><td> 0</td></tr>\n<tr><td> 0</td><td>0</td><td> 0</td><td>0</td><td> 0</td></tr>\n<tr><td> 0</td><td>0</td><td>14</td><td>0</td><td> 8</td></tr>\n</table>\n\nand one of its possible sparse, \\b column \\b major representation:\n<table class=\"manual\">\n<tr><td>Values:</td>        <td>22</td><td>7</td><td>_</td><td>3</td><td>5</td><td>14</td><td>_</td><td>_</td><td>1</td><td>_</td><td>17</td><td>8</td></tr>\n<tr><td>InnerIndices:</td>  <td> 1</td><td>2</td><td>_</td><td>0</td><td>2</td><td> 4</td><td>_</td><td>_</td><td>2</td><td>_</td><td> 1</td><td>4</td></tr>\n</table>\n<table class=\"manual\">\n<tr><td>OuterStarts:</td><td>0</td><td>3</td><td>5</td><td>8</td><td>10</td><td>\\em 12 </td></tr>\n<tr><td>InnerNNZs:</td>    <td>2</td><td>2</td><td>1</td><td>1</td><td> 2</td><td></td></tr>\n</table>\n\nCurrently the elements of a given inner vector are guaranteed to be always sorted by increasing inner indices.\nThe \\c \"_\" indicates available free space to quickly insert new elements.\nAssuming no reallocation is needed, the insertion of a random element is therefore in O(nnz_j) where nnz_j is the number of nonzeros of the respective inner vector.\nOn the other hand, inserting elements with increasing inner indices in a given inner vector is much more efficient since this only requires to increase the respective \\c InnerNNZs entry that is a O(1) operation.\n\nThe case where no empty space is available is a special case, and is refered as the \\em compressed mode.\nIt corresponds to the widely used Compressed Column (or Row) Storage schemes (CCS or CRS).\nAny SparseMatrix can be turned to this form by calling the SparseMatrix::makeCompressed() function.\nIn this case, one can remark that the \\c InnerNNZs array is redundant with \\c OuterStarts because we the equality: \\c InnerNNZs[j] = \\c OuterStarts[j+1]-\\c OuterStarts[j].\nTherefore, in practice a call to SparseMatrix::makeCompressed() frees this buffer.\n\nIt is worth noting that most of our wrappers to external libraries requires compressed matrices as inputs.\n\nThe results of %Eigen's operations always produces \\b compressed sparse matrices.\nOn the other hand, the insertion of a new element into a SparseMatrix converts this later to the \\b uncompressed mode.\n\nHere is the previous matrix represented in compressed mode:\n<table class=\"manual\">\n<tr><td>Values:</td>        <td>22</td><td>7</td><td>3</td><td>5</td><td>14</td><td>1</td><td>17</td><td>8</td></tr>\n<tr><td>InnerIndices:</td>  <td> 1</td><td>2</td><td>0</td><td>2</td><td> 4</td><td>2</td><td> 1</td><td>4</td></tr>\n</table>\n<table class=\"manual\">\n<tr><td>OuterStarts:</td><td>0</td><td>2</td><td>4</td><td>5</td><td>6</td><td>\\em 8 </td></tr>\n</table>\n\nA SparseVector is a special case of a SparseMatrix where only the \\c Values and \\c InnerIndices arrays are stored.\nThere is no notion of compressed/uncompressed mode for a SparseVector.\n\n\n\\section TutorialSparseExample First example\n\nBefore describing each individual class, let's start with the following typical example: solving the Laplace equation \\f$ \\Delta u = 0 \\f$ on a regular 2D grid using a finite difference scheme and Dirichlet boundary conditions.\nSuch problem can be mathematically expressed as a linear problem of the form \\f$ Ax=b \\f$ where \\f$ x \\f$ is the vector of \\c m unknowns (in our case, the values of the pixels), \\f$ b \\f$ is the right hand side vector resulting from the boundary conditions, and \\f$ A \\f$ is an \\f$ m \\times m \\f$ matrix containing only a few non-zero elements resulting from the discretization of the Laplacian operator.\n\n<table class=\"manual\">\n<tr><td>\n\\include Tutorial_sparse_example.cpp\n</td>\n<td>\n\\image html Tutorial_sparse_example.jpeg\n</td></tr></table>\n\nIn this example, we start by defining a column-major sparse matrix type of double \\c SparseMatrix<double>, and a triplet list of the same scalar type \\c  Triplet<double>. A triplet is a simple object representing a non-zero entry as the triplet: \\c row index, \\c column index, \\c value.\n\nIn the main function, we declare a list \\c coefficients of triplets (as a std vector) and the right hand side vector \\f$ b \\f$ which are filled by the \\a buildProblem function.\nThe raw and flat list of non-zero entries is then converted to a true SparseMatrix object \\c A.\nNote that the elements of the list do not have to be sorted, and possible duplicate entries will be summed up.\n\nThe last step consists of effectively solving the assembled problem.\nSince the resulting matrix \\c A is symmetric by construction, we can perform a direct Cholesky factorization via the SimplicialLDLT class which behaves like its LDLT counterpart for dense objects.\n\nThe resulting vector \\c x contains the pixel values as a 1D array which is saved to a jpeg file shown on the right of the code above.\n\nDescribing the \\a buildProblem and \\a save functions is out of the scope of this tutorial. They are given \\ref TutorialSparse_example_details \"here\" for the curious and reproducibility purpose.\n\n\n\n\n\\section TutorialSparseSparseMatrix The SparseMatrix class\n\n\\b %Matrix \\b and \\b vector \\b properties \\n\n\nThe SparseMatrix and SparseVector classes take three template arguments:\n * the scalar type (e.g., double)\n * the storage order (ColMajor or RowMajor, the default is ColMajor)\n * the inner index type (default is \\c int).\n\nAs for dense Matrix objects, constructors takes the size of the object.\nHere are some examples:\n\n\\code\nSparseMatrix<std::complex<float> > mat(1000,2000);         // declares a 1000x2000 column-major compressed sparse matrix of complex<float>\nSparseMatrix<double,RowMajor> mat(1000,2000);              // declares a 1000x2000 row-major compressed sparse matrix of double\nSparseVector<std::complex<float> > vec(1000);              // declares a column sparse vector of complex<float> of size 1000\nSparseVector<double,RowMajor> vec(1000);                   // declares a row sparse vector of double of size 1000\n\\endcode\n\nIn the rest of the tutorial, \\c mat and \\c vec represent any sparse-matrix and sparse-vector objects, respectively.\n\nThe dimensions of a matrix can be queried using the following functions:\n<table class=\"manual\">\n<tr><td>Standard \\n dimensions</td><td>\\code\nmat.rows()\nmat.cols()\\endcode</td>\n<td>\\code\nvec.size() \\endcode</td>\n</tr>\n<tr><td>Sizes along the \\n inner/outer dimensions</td><td>\\code\nmat.innerSize()\nmat.outerSize()\\endcode</td>\n<td></td>\n</tr>\n<tr><td>Number of non \\n zero coefficients</td><td>\\code\nmat.nonZeros() \\endcode</td>\n<td>\\code\nvec.nonZeros() \\endcode</td></tr>\n</table>\n\n\n\\b Iterating \\b over \\b the \\b nonzero \\b coefficients \\n\n\nRandom access to the elements of a sparse object can be done through the \\c coeffRef(i,j) function.\nHowever, this function involves a quite expensive binary search.\nIn most cases, one only wants to iterate over the non-zeros elements. This is achieved by a standard loop over the outer dimension, and then by iterating over the non-zeros of the current inner vector via an InnerIterator. Thus, the non-zero entries have to be visited in the same order than the storage order.\nHere is an example:\n<table class=\"manual\">\n<tr><td>\n\\code\nSparseMatrix<double> mat(rows,cols);\nfor (int k=0; k<mat.outerSize(); ++k)\n  for (SparseMatrix<double>::InnerIterator it(mat,k); it; ++it)\n  {\n    it.value();\n    it.row();   // row index\n    it.col();   // col index (here it is equal to k)\n    it.index(); // inner index, here it is equal to it.row()\n  }\n\\endcode\n</td><td>\n\\code\nSparseVector<double> vec(size);\nfor (SparseVector<double>::InnerIterator it(vec); it; ++it)\n{\n  it.value(); // == vec[ it.index() ]\n  it.index();\n}\n\\endcode\n</td></tr>\n</table>\nFor a writable expression, the referenced value can be modified using the valueRef() function.\nIf the type of the sparse matrix or vector depends on a template parameter, then the \\c typename keyword is\nrequired to indicate that \\c InnerIterator denotes a type; see \\ref TopicTemplateKeyword for details.\n\n\n\\section TutorialSparseFilling Filling a sparse matrix\n\nBecause of the special storage scheme of a SparseMatrix, special care has to be taken when adding new nonzero entries.\nFor instance, the cost of a single purely random insertion into a SparseMatrix is \\c O(nnz), where \\c nnz is the current number of non-zero coefficients.\n\nThe simplest way to create a sparse matrix while guaranteeing good performance is thus to first build a list of so-called \\em triplets, and then convert it to a SparseMatrix.\n\nHere is a typical usage example:\n\\code\ntypedef Eigen::Triplet<double> T;\nstd::vector<T> tripletList;\ntripletList.reserve(estimation_of_entries);\nfor(...)\n{\n  // ...\n  tripletList.push_back(T(i,j,v_ij));\n}\nSparseMatrixType mat(rows,cols);\nmat.setFromTriplets(tripletList.begin(), tripletList.end());\n// mat is ready to go!\n\\endcode\nThe \\c std::vector of triplets might contain the elements in arbitrary order, and might even contain duplicated elements that will be summed up by setFromTriplets().\nSee the SparseMatrix::setFromTriplets() function and class Triplet for more details.\n\n\nIn some cases, however, slightly higher performance, and lower memory consumption can be reached by directly inserting the non-zeros into the destination matrix.\nA typical scenario of this approach is illustrated bellow:\n\\code\n1: SparseMatrix<double> mat(rows,cols);         // default is column major\n2: mat.reserve(VectorXi::Constant(cols,6));\n3: for each i,j such that v_ij != 0\n4:   mat.insert(i,j) = v_ij;                    // alternative: mat.coeffRef(i,j) += v_ij;\n5: mat.makeCompressed();                        // optional\n\\endcode\n\n- The key ingredient here is the line 2 where we reserve room for 6 non-zeros per column. In many cases, the number of non-zeros per column or row can easily be known in advance. If it varies significantly for each inner vector, then it is possible to specify a reserve size for each inner vector by providing a vector object with an operator[](int j) returning the reserve size of the \\c j-th inner vector (e.g., via a VectorXi or std::vector<int>). If only a rought estimate of the number of nonzeros per inner-vector can be obtained, it is highly recommended to overestimate it rather than the opposite. If this line is omitted, then the first insertion of a new element will reserve room for 2 elements per inner vector.\n- The line 4 performs a sorted insertion. In this example, the ideal case is when the \\c j-th column is not full and contains non-zeros whose inner-indices are smaller than \\c i. In this case, this operation boils down to trivial O(1) operation.\n- When calling insert(i,j) the element \\c i \\c ,j must not already exists, otherwise use the coeffRef(i,j) method that will allow to, e.g., accumulate values. This method first performs a binary search and finally calls insert(i,j) if the element does not already exist. It is more flexible than insert() but also more costly.\n- The line 5 suppresses the remaining empty space and transforms the matrix into a compressed column storage.\n\n\n\n\\section TutorialSparseFeatureSet Supported operators and functions\n\nBecause of their special storage format, sparse matrices cannot offer the same level of flexibility than dense matrices.\nIn Eigen's sparse module we chose to expose only the subset of the dense matrix API which can be efficiently implemented.\nIn the following \\em sm denotes a sparse matrix, \\em sv a sparse vector, \\em dm a dense matrix, and \\em dv a dense vector.\n\n\\subsection TutorialSparse_BasicOps Basic operations\n\n%Sparse expressions support most of the unary and binary coefficient wise operations:\n\\code\nsm1.real()   sm1.imag()   -sm1                    0.5*sm1\nsm1+sm2      sm1-sm2      sm1.cwiseProduct(sm2)\n\\endcode\nHowever, <strong>a strong restriction is that the storage orders must match</strong>. For instance, in the following example:\n\\code\nsm4 = sm1 + sm2 + sm3;\n\\endcode\nsm1, sm2, and sm3 must all be row-major or all column-major.\nOn the other hand, there is no restriction on the target matrix sm4.\nFor instance, this means that for computing \\f$ A^T + A \\f$, the matrix \\f$ A^T \\f$ must be evaluated into a temporary matrix of compatible storage order:\n\\code\nSparseMatrix<double> A, B;\nB = SparseMatrix<double>(A.transpose()) + A;\n\\endcode\n\nBinary coefficient wise operators can also mix sparse and dense expressions:\n\\code\nsm2 = sm1.cwiseProduct(dm1);\ndm2 = sm1 + dm1;\ndm2 = dm1 - sm1;\n\\endcode\nPerformance-wise, the adding/subtracting sparse and dense matrices is better performed in two steps. For instance, instead of doing <tt>dm2 = sm1 + dm1</tt>, better write:\n\\code\ndm2 = dm1;\ndm2 += sm1;\n\\endcode\nThis version has the advantage to fully exploit the higher performance of dense storage (no indirection, SIMD, etc.), and to pay the cost of slow sparse evaluation on the few non-zeros of the sparse matrix only.\n\n\n%Sparse expressions also support transposition:\n\\code\nsm1 = sm2.transpose();\nsm1 = sm2.adjoint();\n\\endcode\nHowever, there is no transposeInPlace() method.\n\n\n\\subsection TutorialSparse_Products Matrix products\n\n%Eigen supports various kind of sparse matrix products which are summarize below:\n  - \\b sparse-dense:\n    \\code\ndv2 = sm1 * dv1;\ndm2 = dm1 * sm1.adjoint();\ndm2 = 2. * sm1 * dm1;\n    \\endcode\n  - \\b symmetric \\b sparse-dense. The product of a sparse symmetric matrix with a dense matrix (or vector) can also be optimized by specifying the symmetry with selfadjointView():\n    \\code\ndm2 = sm1.selfadjointView<>() * dm1;        // if all coefficients of A are stored\ndm2 = A.selfadjointView<Upper>() * dm1;     // if only the upper part of A is stored\ndm2 = A.selfadjointView<Lower>() * dm1;     // if only the lower part of A is stored\n    \\endcode\n  - \\b sparse-sparse. For sparse-sparse products, two different algorithms are available. The default one is conservative and preserve the explicit zeros that might appear:\n    \\code\nsm3 = sm1 * sm2;\nsm3 = 4 * sm1.adjoint() * sm2;\n    \\endcode\n    The second algorithm prunes on the fly the explicit zeros, or the values smaller than a given threshold. It is enabled and controlled through the prune() functions:\n    \\code\nsm3 = (sm1 * sm2).pruned();                  // removes numerical zeros\nsm3 = (sm1 * sm2).pruned(ref);               // removes elements much smaller than ref\nsm3 = (sm1 * sm2).pruned(ref,epsilon);       // removes elements smaller than ref*epsilon\n    \\endcode\n\n  - \\b permutations. Finally, permutations can be applied to sparse matrices too:\n    \\code\nPermutationMatrix<Dynamic,Dynamic> P = ...;\nsm2 = P * sm1;\nsm2 = sm1 * P.inverse();\nsm2 = sm1.transpose() * P;\n    \\endcode\n\n\n\\subsection TutorialSparse_SubMatrices Block operations\n\nRegarding read-access, sparse matrices expose the same API than for dense matrices to access to sub-matrices such as blocks, columns, and rows. See \\ref TutorialBlockOperations for a detailed introduction.\nHowever, for performance reasons, writing to a sub-sparse-matrix is much more limited, and currently only contiguous sets of columns (resp. rows) of a column-major (resp. row-major) SparseMatrix are writable. Moreover, this information has to be known at compile-time, leaving out methods such as <tt>block(...)</tt> and <tt>corner*(...)</tt>. The available API for write-access to a SparseMatrix are summarized below:\n\\code\nSparseMatrix<double,ColMajor> sm1;\nsm1.col(j) = ...;\nsm1.leftCols(ncols) = ...;\nsm1.middleCols(j,ncols) = ...;\nsm1.rightCols(ncols) = ...;\n\nSparseMatrix<double,RowMajor> sm2;\nsm2.row(i) = ...;\nsm2.topRows(nrows) = ...;\nsm2.middleRows(i,nrows) = ...;\nsm2.bottomRows(nrows) = ...;\n\\endcode\n\nIn addition, sparse matrices expose the SparseMatrixBase::innerVector() and SparseMatrixBase::innerVectors() methods, which are aliases to the col/middleCols methods for a column-major storage, and to the row/middleRows methods for a row-major storage.\n\n\\subsection TutorialSparse_TriangularSelfadjoint Triangular and selfadjoint views\n\nJust as with dense matrices, the triangularView() function can be used to address a triangular part of the matrix, and perform triangular solves with a dense right hand side:\n\\code\ndm2 = sm1.triangularView<Lower>(dm1);\ndv2 = sm1.transpose().triangularView<Upper>(dv1);\n\\endcode\n\nThe selfadjointView() function permits various operations:\n - optimized sparse-dense matrix products:\n    \\code\ndm2 = sm1.selfadjointView<>() * dm1;        // if all coefficients of A are stored\ndm2 = A.selfadjointView<Upper>() * dm1;     // if only the upper part of A is stored\ndm2 = A.selfadjointView<Lower>() * dm1;     // if only the lower part of A is stored\n    \\endcode\n - copy of triangular parts:\n    \\code\nsm2 = sm1.selfadjointView<Upper>();                               // makes a full selfadjoint matrix from the upper triangular part\nsm2.selfadjointView<Lower>() = sm1.selfadjointView<Upper>();      // copies the upper triangular part to the lower triangular part\n    \\endcode\n - application of symmetric permutations:\n \\code\nPermutationMatrix<Dynamic,Dynamic> P = ...;\nsm2 = A.selfadjointView<Upper>().twistedBy(P);                                // compute P S P' from the upper triangular part of A, and make it a full matrix\nsm2.selfadjointView<Lower>() = A.selfadjointView<Lower>().twistedBy(P);       // compute P S P' from the lower triangular part of A, and then only compute the lower part\n \\endcode\n\nPlease, refer to the \\link SparseQuickRefPage Quick Reference \\endlink  guide for the list of supported operations. The list of linear solvers available is \\link TopicSparseSystems here. \\endlink\n\n*/\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/TutorialSparse_example_details.dox",
    "content": "/**\n\\page TutorialSparse_example_details\n\\include Tutorial_sparse_example_details.cpp\n*/\n"
  },
  {
    "path": "include/eigen3/doc/UnalignedArrayAssert.dox",
    "content": "namespace Eigen {\n\n/** \\eigenManualPage TopicUnalignedArrayAssert Explanation of the assertion on unaligned arrays\n\nHello! You are seeing this webpage because your program terminated on an assertion failure like this one:\n<pre>\nmy_program: path/to/eigen/Eigen/src/Core/DenseStorage.h:44:\nEigen::internal::matrix_array<T, Size, MatrixOptions, Align>::internal::matrix_array()\n[with T = double, int Size = 2, int MatrixOptions = 2, bool Align = true]:\nAssertion `(reinterpret_cast<size_t>(array) & (sizemask)) == 0 && \"this assertion\nis explained here: http://eigen.tuxfamily.org/dox-devel/group__TopicUnalignedArrayAssert.html\n**** READ THIS WEB PAGE !!! ****\"' failed.\n</pre>\n\nThere are 4 known causes for this issue. Please read on to understand them and learn how to fix them.\n\n\\eigenAutoToc\n\n\\section where Where in my own code is the cause of the problem?\n\nFirst of all, you need to find out where in your own code this assertion was triggered from. At first glance, the error message doesn't look helpful, as it refers to a file inside Eigen! However, since your program crashed, if you can reproduce the crash, you can get a backtrace using any debugger. For example, if you're using GCC, you can use the GDB debugger as follows:\n\\code\n$ gdb ./my_program          # Start GDB on your program\n> run                       # Start running your program\n...                         # Now reproduce the crash!\n> bt                        # Obtain the backtrace\n\\endcode\nNow that you know precisely where in your own code the problem is happening, read on to understand what you need to change.\n\n\\section c1 Cause 1: Structures having Eigen objects as members\n\nIf you have code like this,\n\n\\code\nclass Foo\n{\n  //...\n  Eigen::Vector2d v;\n  //...\n};\n//...\nFoo *foo = new Foo;\n\\endcode\n\nthen you need to read this separate page: \\ref TopicStructHavingEigenMembers \"Structures Having Eigen Members\".\n\nNote that here, Eigen::Vector2d is only used as an example, more generally the issue arises for all \\ref TopicFixedSizeVectorizable \"fixed-size vectorizable Eigen types\".\n\n\\section c2 Cause 2: STL Containers or manual memory allocation\n\nIf you use STL Containers such as std::vector, std::map, ..., with %Eigen objects, or with classes containing %Eigen objects, like this,\n\n\\code\nstd::vector<Eigen::Matrix2f> my_vector;\nstruct my_class { ... Eigen::Matrix2f m; ... };\nstd::map<int, my_class> my_map;\n\\endcode\n\nthen you need to read this separate page: \\ref TopicStlContainers \"Using STL Containers with Eigen\".\n\nNote that here, Eigen::Matrix2f is only used as an example, more generally the issue arises for all \\ref TopicFixedSizeVectorizable \"fixed-size vectorizable Eigen types\" and \\ref TopicStructHavingEigenMembers \"structures having such Eigen objects as member\".\n\nThe same issue will be exhibited by any classes/functions by-passing operator new to allocate memory, that is, by performing custom memory allocation followed by calls to the placement new operator. This is for instance typically the case of \\c std::make_shared or \\c std::allocate_shared for which is the solution is to use an \\ref aligned_allocator \"aligned allocator\" as detailed in the \\ref TopicStlContainers \"solution for STL containers\".\n\n\\section c3 Cause 3: Passing Eigen objects by value\n\nIf some function in your code is getting an Eigen object passed by value, like this,\n\n\\code\nvoid func(Eigen::Vector4d v);\n\\endcode\n\nthen you need to read this separate page: \\ref TopicPassingByValue \"Passing Eigen objects by value to functions\".\n\nNote that here, Eigen::Vector4d is only used as an example, more generally the issue arises for all \\ref TopicFixedSizeVectorizable \"fixed-size vectorizable Eigen types\".\n\n\\section c4 Cause 4: Compiler making a wrong assumption on stack alignment (for instance GCC on Windows)\n\nThis is a must-read for people using GCC on Windows (like MinGW or TDM-GCC). If you have this assertion failure in an innocent function declaring a local variable like this:\n\n\\code\nvoid foo()\n{\n  Eigen::Quaternionf q;\n  //...\n}\n\\endcode\n\nthen you need to read this separate page: \\ref TopicWrongStackAlignment \"Compiler making a wrong assumption on stack alignment\".\n\nNote that here, Eigen::Quaternionf is only used as an example, more generally the issue arises for all \\ref TopicFixedSizeVectorizable \"fixed-size vectorizable Eigen types\".\n\n\\section explanation General explanation of this assertion\n\n\\ref TopicFixedSizeVectorizable \"fixed-size vectorizable Eigen objects\" must absolutely be created at 16-byte-aligned locations, otherwise SIMD instructions addressing them will crash.\n\nEigen normally takes care of these alignment issues for you, by setting an alignment attribute on them and by overloading their \"operator new\".\n\nHowever there are a few corner cases where these alignment settings get overridden: they are the possible causes for this assertion.\n\n\\section getrid I don't care about optimal vectorization, how do I get rid of that stuff?\n\nThree possibilities:\n<ul>\n  <li>Use the \\c DontAlign option to Matrix, Array, Quaternion, etc. objects that gives you trouble. This way Eigen won't try to align them, and thus won\"t assume any special alignment. On the down side, you will pay the cost of unaligned loads/stores for them, but on modern CPUs, the overhead is either null or marginal. See \\link StructHavingEigenMembers_othersolutions here \\endlink for an example.</li>\n  <li>Define \\link TopicPreprocessorDirectivesPerformance EIGEN_DONT_ALIGN_STATICALLY \\endlink. That disables all 16-byte (and above) static alignment code, while keeping 16-byte (or above) heap alignment. This has the effect of\n      vectorizing fixed-size objects (like Matrix4d) through unaligned stores (as controlled by \\link TopicPreprocessorDirectivesPerformance EIGEN_UNALIGNED_VECTORIZE \\endlink), while keeping unchanged the vectorization of dynamic-size objects\n      (like MatrixXd). But do note that this breaks ABI compatibility with the default behavior of static alignment.</li>\n  <li>Or define both \\link TopicPreprocessorDirectivesPerformance  EIGEN_DONT_VECTORIZE \\endlink and EIGEN_DISABLE_UNALIGNED_ARRAY_ASSERT. This keeps the\n      16-byte alignment code and thus preserves ABI compatibility, but completely disables vectorization.</li>\n</ul>\n\nIf you want to know why defining EIGEN_DONT_VECTORIZE does not by itself disable 16-byte alignment and the assertion, here's the explanation:\n\nIt doesn't disable the assertion, because otherwise code that runs fine without vectorization would suddenly crash when enabling vectorization.\nIt doesn't disable 16-byte alignment, because that would mean that vectorized and non-vectorized code are not mutually ABI-compatible. This ABI compatibility is very important, even for people who develop only an in-house application, as for instance one may want to have in the same application a vectorized path and a non-vectorized path.\n\n*/\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/UsingBlasLapackBackends.dox",
    "content": "/*\n Copyright (c) 2011, Intel Corporation. All rights reserved.\n Copyright (C) 2011-2016 Gael Guennebaud <gael.guennebaud@inria.fr>\n\n Redistribution and use in source and binary forms, with or without modification,\n are permitted provided that the following conditions are met:\n\n * Redistributions of source code must retain the above copyright notice, this\n   list of conditions and the following disclaimer.\n * Redistributions in binary form must reproduce the above copyright notice,\n   this list of conditions and the following disclaimer in the documentation\n   and/or other materials provided with the distribution.\n * Neither the name of Intel Corporation nor the names of its contributors may\n   be used to endorse or promote products derived from this software without\n   specific prior written permission.\n\n THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\" AND\n ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED\n WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\n DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR\n ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES\n (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;\n LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON\n ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT\n (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS\n SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n\n ********************************************************************************\n *   Content : Documentation on the use of BLAS/LAPACK libraries through Eigen\n ********************************************************************************\n*/\n\nnamespace Eigen {\n\n/** \\page TopicUsingBlasLapack Using BLAS/LAPACK from %Eigen\n\n\nSince %Eigen version 3.3 and later, any F77 compatible BLAS or LAPACK libraries can be used as backends for dense matrix products and dense matrix decompositions.\nFor instance, one can use <a href=\"http://eigen.tuxfamily.org/Counter/redirect_to_mkl.php\">Intel® MKL</a>, Apple's Accelerate framework on OSX, <a href=\"http://www.openblas.net/\">OpenBLAS</a>, <a href=\"http://www.netlib.org/lapack\">Netlib LAPACK</a>, etc.\n\nDo not miss this \\link TopicUsingIntelMKL page \\endlink for further discussions on the specific use of Intel® MKL (also includes VML, PARDISO, etc.)\n\nIn order to use an external BLAS and/or LAPACK library, you must link you own application to the respective libraries and their dependencies.\nFor LAPACK, you must also link to the standard <a href=\"http://www.netlib.org/lapack/lapacke.html\">Lapacke</a> library, which is used as a convenient think layer between %Eigen's C++ code and LAPACK F77 interface. Then you must activate their usage by defining one or multiple of the following macros (\\b before including any %Eigen's header):\n\n\\note For Mac users, in order to use the lapack version shipped with the Accelerate framework, you also need the lapacke library.\nUsing <a href=\"https://www.macports.org/\">MacPorts</a>, this is as easy as:\n\\code\nsudo port install lapack\n\\endcode\nand then use the following link flags: \\c -framework \\c Accelerate \\c /opt/local/lib/lapack/liblapacke.dylib\n\n<table class=\"manual\">\n<tr><td>\\c EIGEN_USE_BLAS </td><td>Enables the use of external BLAS level 2 and 3 routines (compatible with any F77 BLAS interface)</td></tr>\n<tr class=\"alt\"><td>\\c EIGEN_USE_LAPACKE </td><td>Enables the use of external Lapack routines via the <a href=\"http://www.netlib.org/lapack/lapacke.html\">Lapacke</a> C interface to Lapack (compatible with any F77 LAPACK interface)</td></tr>\n<tr><td>\\c EIGEN_USE_LAPACKE_STRICT </td><td>Same as \\c EIGEN_USE_LAPACKE but algorithms of lower numerical robustness are disabled. \\n This currently concerns only JacobiSVD which otherwise would be replaced by \\c gesvd that is less robust than Jacobi rotations.</td></tr>\n</table>\n\nWhen doing so, a number of %Eigen's algorithms are silently substituted with calls to BLAS or LAPACK routines.\nThese substitutions apply only for \\b Dynamic \\b or \\b large enough objects with one of the following four standard scalar types: \\c float, \\c double, \\c complex<float>, and \\c complex<double>.\nOperations on other scalar types or mixing reals and complexes will continue to use the built-in algorithms.\n\nThe breadth of %Eigen functionality that can be substituted is listed in the table below.\n<table class=\"manual\">\n<tr><th>Functional domain</th><th>Code example</th><th>BLAS/LAPACK routines</th></tr>\n<tr><td>Matrix-matrix operations \\n \\c EIGEN_USE_BLAS </td><td>\\code\nm1*m2.transpose();\nm1.selfadjointView<Lower>()*m2;\nm1*m2.triangularView<Upper>();\nm1.selfadjointView<Lower>().rankUpdate(m2,1.0);\n\\endcode</td><td>\\code\n?gemm\n?symm/?hemm\n?trmm\ndsyrk/ssyrk\n\\endcode</td></tr>\n<tr class=\"alt\"><td>Matrix-vector operations \\n \\c EIGEN_USE_BLAS </td><td>\\code\nm1.adjoint()*b;\nm1.selfadjointView<Lower>()*b;\nm1.triangularView<Upper>()*b;\n\\endcode</td><td>\\code\n?gemv\n?symv/?hemv\n?trmv\n\\endcode</td></tr>\n<tr><td>LU decomposition \\n \\c EIGEN_USE_LAPACKE \\n \\c EIGEN_USE_LAPACKE_STRICT </td><td>\\code\nv1 = m1.lu().solve(v2);\n\\endcode</td><td>\\code\n?getrf\n\\endcode</td></tr>\n<tr class=\"alt\"><td>Cholesky decomposition \\n \\c EIGEN_USE_LAPACKE \\n \\c EIGEN_USE_LAPACKE_STRICT </td><td>\\code\nv1 = m2.selfadjointView<Upper>().llt().solve(v2);\n\\endcode</td><td>\\code\n?potrf\n\\endcode</td></tr>\n<tr><td>QR decomposition \\n \\c EIGEN_USE_LAPACKE \\n \\c EIGEN_USE_LAPACKE_STRICT </td><td>\\code\nm1.householderQr();\nm1.colPivHouseholderQr();\n\\endcode</td><td>\\code\n?geqrf\n?geqp3\n\\endcode</td></tr>\n<tr class=\"alt\"><td>Singular value decomposition \\n \\c EIGEN_USE_LAPACKE </td><td>\\code\nJacobiSVD<MatrixXd> svd;\nsvd.compute(m1, ComputeThinV);\n\\endcode</td><td>\\code\n?gesvd\n\\endcode</td></tr>\n<tr><td>Eigen-value decompositions \\n \\c EIGEN_USE_LAPACKE \\n \\c EIGEN_USE_LAPACKE_STRICT </td><td>\\code\nEigenSolver<MatrixXd> es(m1);\nComplexEigenSolver<MatrixXcd> ces(m1);\nSelfAdjointEigenSolver<MatrixXd> saes(m1+m1.transpose());\nGeneralizedSelfAdjointEigenSolver<MatrixXd>\n    gsaes(m1+m1.transpose(),m2+m2.transpose());\n\\endcode</td><td>\\code\n?gees\n?gees\n?syev/?heev\n?syev/?heev,\n?potrf\n\\endcode</td></tr>\n<tr class=\"alt\"><td>Schur decomposition \\n \\c EIGEN_USE_LAPACKE \\n \\c EIGEN_USE_LAPACKE_STRICT </td><td>\\code\nRealSchur<MatrixXd> schurR(m1);\nComplexSchur<MatrixXcd> schurC(m1);\n\\endcode</td><td>\\code\n?gees\n\\endcode</td></tr>\n</table>\nIn the examples, m1 and m2 are dense matrices and v1 and v2 are dense vectors.\n\n*/\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/UsingIntelMKL.dox",
    "content": "/*\n Copyright (c) 2011, Intel Corporation. All rights reserved.\n Copyright (C) 2011 Gael Guennebaud <gael.guennebaud@inria.fr>\n\n Redistribution and use in source and binary forms, with or without modification,\n are permitted provided that the following conditions are met:\n\n * Redistributions of source code must retain the above copyright notice, this\n   list of conditions and the following disclaimer.\n * Redistributions in binary form must reproduce the above copyright notice,\n   this list of conditions and the following disclaimer in the documentation\n   and/or other materials provided with the distribution.\n * Neither the name of Intel Corporation nor the names of its contributors may\n   be used to endorse or promote products derived from this software without\n   specific prior written permission.\n\n THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\" AND\n ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED\n WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\n DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR\n ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES\n (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;\n LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON\n ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT\n (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS\n SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n\n ********************************************************************************\n *   Content : Documentation on the use of Intel MKL through Eigen\n ********************************************************************************\n*/\n\nnamespace Eigen {\n\n/** \\page TopicUsingIntelMKL Using Intel® MKL from %Eigen\n\n<!-- \\section TopicUsingIntelMKL_Intro Eigen and Intel® Math Kernel Library (Intel® MKL) -->\n\nSince %Eigen version 3.1 and later, users can benefit from built-in Intel® Math Kernel Library (MKL) optimizations with an installed copy of Intel MKL 10.3 (or later).\n\n<a href=\"http://eigen.tuxfamily.org/Counter/redirect_to_mkl.php\"> Intel MKL </a> provides highly optimized multi-threaded mathematical routines for x86-compatible architectures.\nIntel MKL is available on Linux, Mac and Windows for both Intel64 and IA32 architectures.\n\n\\note\nIntel® MKL is a proprietary software and it is the responsibility of users to buy or register for community (free) Intel MKL licenses for their products. Moreover, the license of the user product has to allow linking to proprietary software that excludes any unmodified versions of the GPL.\n\nUsing Intel MKL through %Eigen is easy:\n-# define the \\c EIGEN_USE_MKL_ALL macro before including any %Eigen's header\n-# link your program to MKL libraries (see the <a href=\"http://software.intel.com/en-us/articles/intel-mkl-link-line-advisor/\">MKL linking advisor</a>)\n-# on a 64bits system, you must use the LP64 interface (not the ILP64 one)\n\nWhen doing so, a number of %Eigen's algorithms are silently substituted with calls to Intel MKL routines.\nThese substitutions apply only for \\b Dynamic \\b or \\b large enough objects with one of the following four standard scalar types: \\c float, \\c double, \\c complex<float>, and \\c complex<double>.\nOperations on other scalar types or mixing reals and complexes will continue to use the built-in algorithms.\n\nIn addition you can choose which parts will be substituted by defining one or multiple of the following macros:\n\n<table class=\"manual\">\n<tr><td>\\c EIGEN_USE_BLAS </td><td>Enables the use of external BLAS level 2 and 3 routines</td></tr>\n<tr class=\"alt\"><td>\\c EIGEN_USE_LAPACKE </td><td>Enables the use of external Lapack routines via the <a href=\"http://www.netlib.org/lapack/lapacke.html\">Lapacke</a> C interface to Lapack</td></tr>\n<tr><td>\\c EIGEN_USE_LAPACKE_STRICT </td><td>Same as \\c EIGEN_USE_LAPACKE but algorithm of lower robustness are disabled. \\n This currently concerns only JacobiSVD which otherwise would be replaced by \\c gesvd that is less robust than Jacobi rotations.</td></tr>\n<tr class=\"alt\"><td>\\c EIGEN_USE_MKL_VML </td><td>Enables the use of Intel VML (vector operations)</td></tr>\n<tr><td>\\c EIGEN_USE_MKL_ALL </td><td>Defines \\c EIGEN_USE_BLAS, \\c EIGEN_USE_LAPACKE, and \\c EIGEN_USE_MKL_VML </td></tr>\n</table>\n\nThe options can be combined with \\b MKL_DIRECT_CALL to enable MKL direct call feature. This may help to increase performance of some MKL BLAS (?GEMM, ?GEMV, ?TRSM, ?AXPY and ?DOT) and LAPACK (LU, Cholesky and QR) routines for very small matrices. To make it work properly, the macro \\c EIGEN_USE_MKL must also be defined in the case none of the other \\c EIGEN_USE_MKL_* macros has been defined.\n\nNote that the BLAS and LAPACKE backends can be enabled for any F77 compatible BLAS and LAPACK libraries. See this \\link TopicUsingBlasLapack page \\endlink for the details.\n\nFinally, the PARDISO sparse solver shipped with Intel MKL can be used through the \\ref PardisoLU, \\ref PardisoLLT and \\ref PardisoLDLT classes of the \\ref PardisoSupport_Module.\n\nThe following table summarizes the list of functions covered by \\c EIGEN_USE_MKL_VML:\n<table class=\"manual\">\n<tr><th>Code example</th><th>MKL routines</th></tr>\n<tr><td>\\code\nv2=v1.array().sin();\nv2=v1.array().asin();\nv2=v1.array().cos();\nv2=v1.array().acos();\nv2=v1.array().tan();\nv2=v1.array().exp();\nv2=v1.array().log();\nv2=v1.array().sqrt();\nv2=v1.array().square();\nv2=v1.array().pow(1.5);\n\\endcode</td><td>\\code\nv?Sin\nv?Asin\nv?Cos\nv?Acos\nv?Tan\nv?Exp\nv?Ln\nv?Sqrt\nv?Sqr\nv?Powx\n\\endcode</td></tr>\n</table>\nIn the examples, v1 and v2 are dense vectors.\n\n\n\\section TopicUsingIntelMKL_Links Links\n- Intel MKL can be purchased and downloaded <a href=\"http://eigen.tuxfamily.org/Counter/redirect_to_mkl.php\">here</a>.\n- Intel MKL is also bundled with <a href=\"http://software.intel.com/en-us/articles/intel-composer-xe/\">Intel Composer XE</a>.\n\n\n*/\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/UsingNVCC.dox",
    "content": "\nnamespace Eigen {\n\n/** \\page TopicCUDA Using Eigen in CUDA kernels\n\n\\b Disclaimer: this page is about an \\b experimental feature in %Eigen.\n\nStaring from CUDA 5.0, the CUDA compiler, \\c nvcc, is able to properly parse %Eigen's code (almost).\nA few adaptations of the %Eigen's code already allows to use some parts of %Eigen in your own CUDA kernels.\nTo this end you need the devel branch of %Eigen, CUDA 5.0 or greater with GCC.\n\nKnown issues:\n\n - \\c nvcc with MS Visual Studio does not work (patch welcome)\n \n - \\c nvcc with \\c clang does not work (patch welcome)\n \n - \\c nvcc 5.5 with gcc-4.7 (or greater) has issues with the standard \\c \\<limits\\> header file. To workaround this, you can add the following before including any other files:\n   \\code\n    // workaround issue between gcc >= 4.7 and cuda 5.5\n    #if (defined __GNUC__) && (__GNUC__>4 || __GNUC_MINOR__>=7)\n      #undef _GLIBCXX_ATOMIC_BUILTINS\n      #undef _GLIBCXX_USE_INT128\n    #endif\n   \\endcode\n   \n - On 64bits system Eigen uses \\c long \\c int as the default type for indexes and sizes. On CUDA device, it would make sense to default to 32 bits \\c int.\n   However, to keep host and CUDA code compatible, this cannot be done automatically by %Eigen, and the user is thus required to define \\c EIGEN_DEFAULT_DENSE_INDEX_TYPE to \\c int throughout his code (or only for CUDA code if there is no interaction between host and CUDA code through %Eigen's object).\n\n*/\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/WrongStackAlignment.dox",
    "content": "namespace Eigen {\n\n/** \\eigenManualPage TopicWrongStackAlignment Compiler making a wrong assumption on stack alignment\n\n<h4>It appears that this was a GCC bug that has been fixed in GCC 4.5.\nIf you hit this issue, please upgrade to GCC 4.5 and report to us, so we can update this page.</h4>\n\nThis is an issue that, so far, we met only with GCC on Windows: for instance, MinGW and TDM-GCC.\n\nBy default, in a function like this,\n\n\\code\nvoid foo()\n{\n  Eigen::Quaternionf q;\n  //...\n}\n\\endcode\n\nGCC assumes that the stack is already 16-byte-aligned so that the object \\a q will be created at a 16-byte-aligned location. For this reason, it doesn't take any special care to explicitly align the object \\a q, as Eigen requires.\n\nThe problem is that, in some particular cases, this assumption can be wrong on Windows, where the stack is only guaranteed to have 4-byte alignment. Indeed, even though GCC takes care of aligning the stack in the main function and does its best to keep it aligned, when a function is called from another thread or from a binary compiled with another compiler, the stack alignment can be corrupted. This results in the object 'q' being created at an unaligned location, making your program crash with the \\ref TopicUnalignedArrayAssert \"assertion on unaligned arrays\". So far we found the three following solutions.\n\n\n\\section sec_sol1 Local solution\n\nA local solution is to mark such a function with this attribute:\n\\code\n__attribute__((force_align_arg_pointer)) void foo()\n{\n  Eigen::Quaternionf q;\n  //...\n}\n\\endcode\nRead <a href=\"http://gcc.gnu.org/onlinedocs/gcc-4.4.0/gcc/Function-Attributes.html#Function-Attributes\">this GCC documentation</a> to understand what this does. Of course this should only be done on GCC on Windows, so for portability you'll have to encapsulate this in a macro which you leave empty on other platforms. The advantage of this solution is that you can finely select which function might have a corrupted stack alignment. Of course on the downside this has to be done for every such function, so you may prefer one of the following two global solutions.\n\n\n\\section sec_sol2 Global solutions\n\nA global solution is to edit your project so that when compiling with GCC on Windows, you pass this option to GCC:\n\\code\n-mincoming-stack-boundary=2\n\\endcode\nExplanation: this tells GCC that the stack is only required to be aligned to 2^2=4 bytes, so that GCC now knows that it really must take extra care to honor the 16 byte alignment of \\ref TopicFixedSizeVectorizable \"fixed-size vectorizable Eigen types\" when needed.\n\nAnother global solution is to pass this option to gcc:\n\\code\n-mstackrealign\n\\endcode\nwhich has the same effect than adding the \\c force_align_arg_pointer attribute to all functions.\n\nThese global solutions are easy to use, but note that they may slowdown your program because they lead to extra prologue/epilogue instructions for every function.\n\n*/\n\n}\n"
  },
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  {
    "path": "include/eigen3/doc/examples/CustomizingEigen_Inheritance.cpp",
    "content": "#include <Eigen/Core>\n#include <iostream>\n\nclass MyVectorType : public Eigen::VectorXd\n{\npublic:\n    MyVectorType(void):Eigen::VectorXd() {}\n\n    // This constructor allows you to construct MyVectorType from Eigen expressions\n    template<typename OtherDerived>\n    MyVectorType(const Eigen::MatrixBase<OtherDerived>& other)\n        : Eigen::VectorXd(other)\n    { }\n\n    // This method allows you to assign Eigen expressions to MyVectorType\n    template<typename OtherDerived>\n    MyVectorType& operator=(const Eigen::MatrixBase <OtherDerived>& other)\n    {\n        this->Eigen::VectorXd::operator=(other);\n        return *this;\n    }\n};\n\nint main()\n{\n  MyVectorType v = MyVectorType::Ones(4);\n  v(2) += 10;\n  v = 2 * v;\n  std::cout << v.transpose() << std::endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/Cwise_erf.cpp",
    "content": "#include <Eigen/Core>\n#include <unsupported/Eigen/SpecialFunctions>\n#include <iostream>\nusing namespace Eigen;\nint main()\n{\n  Array4d v(-0.5,2,0,-7);\n  std::cout << v.erf() << std::endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/Cwise_erfc.cpp",
    "content": "#include <Eigen/Core>\n#include <unsupported/Eigen/SpecialFunctions>\n#include <iostream>\nusing namespace Eigen;\nint main()\n{\n  Array4d v(-0.5,2,0,-7);\n  std::cout << v.erfc() << std::endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/Cwise_lgamma.cpp",
    "content": "#include <Eigen/Core>\n#include <unsupported/Eigen/SpecialFunctions>\n#include <iostream>\nusing namespace Eigen;\nint main()\n{\n  Array4d v(0.5,10,0,-1);\n  std::cout << v.lgamma() << std::endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/DenseBase_middleCols_int.cpp",
    "content": "#include <Eigen/Core>\n#include <iostream>\n\nusing namespace Eigen;\nusing namespace std;\n\nint main(void)\n{\n    int const N = 5;\n    MatrixXi A(N,N);\n    A.setRandom();\n    cout << \"A =\\n\" << A << '\\n' << endl;\n    cout << \"A(1..3,:) =\\n\" << A.middleCols(1,3) << endl;\n    return 0;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/DenseBase_middleRows_int.cpp",
    "content": "#include <Eigen/Core>\n#include <iostream>\n\nusing namespace Eigen;\nusing namespace std;\n\nint main(void)\n{\n    int const N = 5;\n    MatrixXi A(N,N);\n    A.setRandom();\n    cout << \"A =\\n\" << A << '\\n' << endl;\n    cout << \"A(2..3,:) =\\n\" << A.middleRows(2,2) << endl;\n    return 0;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/DenseBase_template_int_middleCols.cpp",
    "content": "#include <Eigen/Core>\n#include <iostream>\n\nusing namespace Eigen;\nusing namespace std;\n\nint main(void)\n{\n    int const N = 5;\n    MatrixXi A(N,N);\n    A.setRandom();\n    cout << \"A =\\n\" << A << '\\n' << endl;\n    cout << \"A(:,1..3) =\\n\" << A.middleCols<3>(1) << endl;\n    return 0;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/DenseBase_template_int_middleRows.cpp",
    "content": "#include <Eigen/Core>\n#include <iostream>\n\nusing namespace Eigen;\nusing namespace std;\n\nint main(void)\n{\n    int const N = 5;\n    MatrixXi A(N,N);\n    A.setRandom();\n    cout << \"A =\\n\" << A << '\\n' << endl;\n    cout << \"A(1..3,:) =\\n\" << A.middleRows<3>(1) << endl;\n    return 0;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/QuickStart_example.cpp",
    "content": "#include <iostream>\n#include <Eigen/Dense>\n\nusing Eigen::MatrixXd;\n\nint main()\n{\n  MatrixXd m(2,2);\n  m(0,0) = 3;\n  m(1,0) = 2.5;\n  m(0,1) = -1;\n  m(1,1) = m(1,0) + m(0,1);\n  std::cout << m << std::endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/QuickStart_example2_dynamic.cpp",
    "content": "#include <iostream>\n#include <Eigen/Dense>\n\nusing namespace Eigen;\nusing namespace std;\n\nint main()\n{\n  MatrixXd m = MatrixXd::Random(3,3);\n  m = (m + MatrixXd::Constant(3,3,1.2)) * 50;\n  cout << \"m =\" << endl << m << endl;\n  VectorXd v(3);\n  v << 1, 2, 3;\n  cout << \"m * v =\" << endl << m * v << endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/QuickStart_example2_fixed.cpp",
    "content": "#include <iostream>\n#include <Eigen/Dense>\n\nusing namespace Eigen;\nusing namespace std;\n\nint main()\n{\n  Matrix3d m = Matrix3d::Random();\n  m = (m + Matrix3d::Constant(1.2)) * 50;\n  cout << \"m =\" << endl << m << endl;\n  Vector3d v(1,2,3);\n  \n  cout << \"m * v =\" << endl << m * v << endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/TemplateKeyword_flexible.cpp",
    "content": "#include <Eigen/Dense>\n#include <iostream>\n\nusing namespace Eigen;\n\ntemplate <typename Derived1, typename Derived2>\nvoid copyUpperTriangularPart(MatrixBase<Derived1>& dst, const MatrixBase<Derived2>& src)\n{\n  /* Note the 'template' keywords in the following line! */\n  dst.template triangularView<Upper>() = src.template triangularView<Upper>();\n}\n\nint main()\n{\n  MatrixXi m1 = MatrixXi::Ones(5,5);\n  MatrixXi m2 = MatrixXi::Random(4,4);\n  std::cout << \"m2 before copy:\" << std::endl;\n  std::cout << m2 << std::endl << std::endl;\n  copyUpperTriangularPart(m2, m1.topLeftCorner(4,4));\n  std::cout << \"m2 after copy:\" << std::endl;\n  std::cout << m2 << std::endl << std::endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/TemplateKeyword_simple.cpp",
    "content": "#include <Eigen/Dense>\n#include <iostream>\n\nusing namespace Eigen;\n\nvoid copyUpperTriangularPart(MatrixXf& dst, const MatrixXf& src)\n{\n  dst.triangularView<Upper>() = src.triangularView<Upper>();\n}\n\nint main()\n{\n  MatrixXf m1 = MatrixXf::Ones(4,4);\n  MatrixXf m2 = MatrixXf::Random(4,4);\n  std::cout << \"m2 before copy:\" << std::endl;\n  std::cout << m2 << std::endl << std::endl;\n  copyUpperTriangularPart(m2, m1);\n  std::cout << \"m2 after copy:\" << std::endl;\n  std::cout << m2 << std::endl << std::endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/TutorialInplaceLU.cpp",
    "content": "#include <iostream>\nstruct init {\n  init() { std::cout << \"[\" << \"init\" << \"]\" << std::endl; }\n};\ninit init_obj;\n// [init]\n#include <iostream>\n#include <Eigen/Dense>\n\nusing namespace std;\nusing namespace Eigen;\n\nint main()\n{\n  MatrixXd A(2,2);\n  A << 2, -1, 1, 3;\n  cout << \"Here is the input matrix A before decomposition:\\n\" << A << endl;\ncout << \"[init]\" << endl;\n\ncout << \"[declaration]\" << endl;\n  PartialPivLU<Ref<MatrixXd> > lu(A);\n  cout << \"Here is the input matrix A after decomposition:\\n\" << A << endl;\ncout << \"[declaration]\" << endl;\n\ncout << \"[matrixLU]\" << endl;\n  cout << \"Here is the matrix storing the L and U factors:\\n\" << lu.matrixLU() << endl;\ncout << \"[matrixLU]\" << endl;\n\ncout << \"[solve]\" << endl;\n  MatrixXd A0(2,2); A0 << 2, -1, 1, 3;\n  VectorXd b(2);    b << 1, 2;\n  VectorXd x = lu.solve(b);\n  cout << \"Residual: \" << (A0 * x - b).norm() << endl;\ncout << \"[solve]\" << endl;\n\ncout << \"[modifyA]\" << endl;\n  A << 3, 4, -2, 1;\n  x = lu.solve(b);\n  cout << \"Residual: \" << (A0 * x - b).norm() << endl;\ncout << \"[modifyA]\" << endl;\n\ncout << \"[recompute]\" << endl;\n  A0 = A; // save A\n  lu.compute(A);\n  x = lu.solve(b);\n  cout << \"Residual: \" << (A0 * x - b).norm() << endl;\ncout << \"[recompute]\" << endl;\n\ncout << \"[recompute_bis0]\" << endl;\n  MatrixXd A1(2,2);\n  A1 << 5,-2,3,4;\n  lu.compute(A1);\n  cout << \"Here is the input matrix A1 after decomposition:\\n\" << A1 << endl;\ncout << \"[recompute_bis0]\" << endl;\n\ncout << \"[recompute_bis1]\" << endl;\n  x = lu.solve(b);\n  cout << \"Residual: \" << (A1 * x - b).norm() << endl;\ncout << \"[recompute_bis1]\" << endl;\n\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/TutorialLinAlgComputeTwice.cpp",
    "content": "#include <iostream>\n#include <Eigen/Dense>\n\nusing namespace std;\nusing namespace Eigen;\n\nint main()\n{\n   Matrix2f A, b;\n   LLT<Matrix2f> llt;\n   A << 2, -1, -1, 3;\n   b << 1, 2, 3, 1;\n   cout << \"Here is the matrix A:\\n\" << A << endl;\n   cout << \"Here is the right hand side b:\\n\" << b << endl;\n   cout << \"Computing LLT decomposition...\" << endl;\n   llt.compute(A);\n   cout << \"The solution is:\\n\" << llt.solve(b) << endl;\n   A(1,1)++;\n   cout << \"The matrix A is now:\\n\" << A << endl;\n   cout << \"Computing LLT decomposition...\" << endl;\n   llt.compute(A);\n   cout << \"The solution is now:\\n\" << llt.solve(b) << endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/TutorialLinAlgExComputeSolveError.cpp",
    "content": "#include <iostream>\n#include <Eigen/Dense>\n\nusing namespace std;\nusing namespace Eigen;\n\nint main()\n{\n   MatrixXd A = MatrixXd::Random(100,100);\n   MatrixXd b = MatrixXd::Random(100,50);\n   MatrixXd x = A.fullPivLu().solve(b);\n   double relative_error = (A*x - b).norm() / b.norm(); // norm() is L2 norm\n   cout << \"The relative error is:\\n\" << relative_error << endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/TutorialLinAlgExSolveColPivHouseholderQR.cpp",
    "content": "#include <iostream>\n#include <Eigen/Dense>\n\nusing namespace std;\nusing namespace Eigen;\n\nint main()\n{\n   Matrix3f A;\n   Vector3f b;\n   A << 1,2,3,  4,5,6,  7,8,10;\n   b << 3, 3, 4;\n   cout << \"Here is the matrix A:\\n\" << A << endl;\n   cout << \"Here is the vector b:\\n\" << b << endl;\n   Vector3f x = A.colPivHouseholderQr().solve(b);\n   cout << \"The solution is:\\n\" << x << endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/TutorialLinAlgExSolveLDLT.cpp",
    "content": "#include <iostream>\n#include <Eigen/Dense>\n\nusing namespace std;\nusing namespace Eigen;\n\nint main()\n{\n   Matrix2f A, b;\n   A << 2, -1, -1, 3;\n   b << 1, 2, 3, 1;\n   cout << \"Here is the matrix A:\\n\" << A << endl;\n   cout << \"Here is the right hand side b:\\n\" << b << endl;\n   Matrix2f x = A.ldlt().solve(b);\n   cout << \"The solution is:\\n\" << x << endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/TutorialLinAlgInverseDeterminant.cpp",
    "content": "#include <iostream>\n#include <Eigen/Dense>\n\nusing namespace std;\nusing namespace Eigen;\n\nint main()\n{\n   Matrix3f A;\n   A << 1, 2, 1,\n        2, 1, 0,\n        -1, 1, 2;\n   cout << \"Here is the matrix A:\\n\" << A << endl;\n   cout << \"The determinant of A is \" << A.determinant() << endl;\n   cout << \"The inverse of A is:\\n\" << A.inverse() << endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/TutorialLinAlgRankRevealing.cpp",
    "content": "#include <iostream>\n#include <Eigen/Dense>\n\nusing namespace std;\nusing namespace Eigen;\n\nint main()\n{\n   Matrix3f A;\n   A << 1, 2, 5,\n        2, 1, 4,\n        3, 0, 3;\n   cout << \"Here is the matrix A:\\n\" << A << endl;\n   FullPivLU<Matrix3f> lu_decomp(A);\n   cout << \"The rank of A is \" << lu_decomp.rank() << endl;\n   cout << \"Here is a matrix whose columns form a basis of the null-space of A:\\n\"\n        << lu_decomp.kernel() << endl;\n   cout << \"Here is a matrix whose columns form a basis of the column-space of A:\\n\"\n        << lu_decomp.image(A) << endl; // yes, have to pass the original A\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/TutorialLinAlgSVDSolve.cpp",
    "content": "#include <iostream>\n#include <Eigen/Dense>\n\nusing namespace std;\nusing namespace Eigen;\n\nint main()\n{\n   MatrixXf A = MatrixXf::Random(3, 2);\n   cout << \"Here is the matrix A:\\n\" << A << endl;\n   VectorXf b = VectorXf::Random(3);\n   cout << \"Here is the right hand side b:\\n\" << b << endl;\n   cout << \"The least-squares solution is:\\n\"\n        << A.bdcSvd(ComputeThinU | ComputeThinV).solve(b) << endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/TutorialLinAlgSelfAdjointEigenSolver.cpp",
    "content": "#include <iostream>\n#include <Eigen/Dense>\n\nusing namespace std;\nusing namespace Eigen;\n\nint main()\n{\n   Matrix2f A;\n   A << 1, 2, 2, 3;\n   cout << \"Here is the matrix A:\\n\" << A << endl;\n   SelfAdjointEigenSolver<Matrix2f> eigensolver(A);\n   if (eigensolver.info() != Success) abort();\n   cout << \"The eigenvalues of A are:\\n\" << eigensolver.eigenvalues() << endl;\n   cout << \"Here's a matrix whose columns are eigenvectors of A \\n\"\n        << \"corresponding to these eigenvalues:\\n\"\n        << eigensolver.eigenvectors() << endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/TutorialLinAlgSetThreshold.cpp",
    "content": "#include <iostream>\n#include <Eigen/Dense>\n\nusing namespace std;\nusing namespace Eigen;\n\nint main()\n{\n   Matrix2d A;\n   A << 2, 1,\n        2, 0.9999999999;\n   FullPivLU<Matrix2d> lu(A);\n   cout << \"By default, the rank of A is found to be \" << lu.rank() << endl;\n   lu.setThreshold(1e-5);\n   cout << \"With threshold 1e-5, the rank of A is found to be \" << lu.rank() << endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/Tutorial_ArrayClass_accessors.cpp",
    "content": "#include <Eigen/Dense>\n#include <iostream>\n\nusing namespace Eigen;\nusing namespace std;\n\nint main()\n{\n  ArrayXXf  m(2,2);\n  \n  // assign some values coefficient by coefficient\n  m(0,0) = 1.0; m(0,1) = 2.0;\n  m(1,0) = 3.0; m(1,1) = m(0,1) + m(1,0);\n  \n  // print values to standard output\n  cout << m << endl << endl;\n \n  // using the comma-initializer is also allowed\n  m << 1.0,2.0,\n       3.0,4.0;\n     \n  // print values to standard output\n  cout << m << endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/Tutorial_ArrayClass_addition.cpp",
    "content": "#include <Eigen/Dense>\n#include <iostream>\n\nusing namespace Eigen;\nusing namespace std;\n\nint main()\n{\n  ArrayXXf a(3,3);\n  ArrayXXf b(3,3);\n  a << 1,2,3,\n       4,5,6,\n       7,8,9;\n  b << 1,2,3,\n       1,2,3,\n       1,2,3;\n       \n  // Adding two arrays\n  cout << \"a + b = \" << endl << a + b << endl << endl;\n\n  // Subtracting a scalar from an array\n  cout << \"a - 2 = \" << endl << a - 2 << endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/Tutorial_ArrayClass_cwise_other.cpp",
    "content": "#include <Eigen/Dense>\n#include <iostream>\n\nusing namespace Eigen;\nusing namespace std;\n\nint main()\n{\n  ArrayXf a = ArrayXf::Random(5);\n  a *= 2;\n  cout << \"a =\" << endl \n       << a << endl;\n  cout << \"a.abs() =\" << endl \n       << a.abs() << endl;\n  cout << \"a.abs().sqrt() =\" << endl \n       << a.abs().sqrt() << endl;\n  cout << \"a.min(a.abs().sqrt()) =\" << endl \n       << a.min(a.abs().sqrt()) << endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/Tutorial_ArrayClass_interop.cpp",
    "content": "#include <Eigen/Dense>\n#include <iostream>\n\nusing namespace Eigen;\nusing namespace std;\n\nint main()\n{\n  MatrixXf m(2,2);\n  MatrixXf n(2,2);\n  MatrixXf result(2,2);\n\n  m << 1,2,\n       3,4;\n  n << 5,6,\n       7,8;\n  \n  result = (m.array() + 4).matrix() * m;\n  cout << \"-- Combination 1: --\" << endl << result << endl << endl;\n  result = (m.array() * n.array()).matrix() * m;\n  cout << \"-- Combination 2: --\" << endl << result << endl << endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/Tutorial_ArrayClass_interop_matrix.cpp",
    "content": "#include <Eigen/Dense>\n#include <iostream>\n\nusing namespace Eigen;\nusing namespace std;\n\nint main()\n{\n  MatrixXf m(2,2);\n  MatrixXf n(2,2);\n  MatrixXf result(2,2);\n\n  m << 1,2,\n       3,4;\n  n << 5,6,\n       7,8;\n\n  result = m * n;\n  cout << \"-- Matrix m*n: --\" << endl << result << endl << endl;\n  result = m.array() * n.array();\n  cout << \"-- Array m*n: --\" << endl << result << endl << endl;\n  result = m.cwiseProduct(n);\n  cout << \"-- With cwiseProduct: --\" << endl << result << endl << endl;\n  result = m.array() + 4;\n  cout << \"-- Array m + 4: --\" << endl << result << endl << endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/Tutorial_ArrayClass_mult.cpp",
    "content": "#include <Eigen/Dense>\n#include <iostream>\n\nusing namespace Eigen;\nusing namespace std;\n\nint main()\n{\n  ArrayXXf a(2,2);\n  ArrayXXf b(2,2);\n  a << 1,2,\n       3,4;\n  b << 5,6,\n       7,8;\n  cout << \"a * b = \" << endl << a * b << endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/Tutorial_BlockOperations_block_assignment.cpp",
    "content": "#include <Eigen/Dense>\n#include <iostream>\n\nusing namespace std;\nusing namespace Eigen;\n\nint main()\n{\n  Array22f m;\n  m << 1,2,\n       3,4;\n  Array44f a = Array44f::Constant(0.6);\n  cout << \"Here is the array a:\" << endl << a << endl << endl;\n  a.block<2,2>(1,1) = m;\n  cout << \"Here is now a with m copied into its central 2x2 block:\" << endl << a << endl << endl;\n  a.block(0,0,2,3) = a.block(2,1,2,3);\n  cout << \"Here is now a with bottom-right 2x3 block copied into top-left 2x2 block:\" << endl << a << endl << endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/Tutorial_BlockOperations_colrow.cpp",
    "content": "#include <Eigen/Dense>\n#include <iostream>\n\nusing namespace std;\n\nint main()\n{\n  Eigen::MatrixXf m(3,3);\n  m << 1,2,3,\n       4,5,6,\n       7,8,9;\n  cout << \"Here is the matrix m:\" << endl << m << endl;\n  cout << \"2nd Row: \" << m.row(1) << endl;\n  m.col(2) += 3 * m.col(0);\n  cout << \"After adding 3 times the first column into the third column, the matrix m is:\\n\";\n  cout << m << endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/Tutorial_BlockOperations_corner.cpp",
    "content": "#include <Eigen/Dense>\n#include <iostream>\n\nusing namespace std;\n\nint main()\n{\n  Eigen::Matrix4f m;\n  m << 1, 2, 3, 4,\n       5, 6, 7, 8,\n       9, 10,11,12,\n       13,14,15,16;\n  cout << \"m.leftCols(2) =\" << endl << m.leftCols(2) << endl << endl;\n  cout << \"m.bottomRows<2>() =\" << endl << m.bottomRows<2>() << endl << endl;\n  m.topLeftCorner(1,3) = m.bottomRightCorner(3,1).transpose();\n  cout << \"After assignment, m = \" << endl << m << endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/Tutorial_BlockOperations_print_block.cpp",
    "content": "#include <Eigen/Dense>\n#include <iostream>\n\nusing namespace std;\n\nint main()\n{\n  Eigen::MatrixXf m(4,4);\n  m <<  1, 2, 3, 4,\n        5, 6, 7, 8,\n        9,10,11,12,\n       13,14,15,16;\n  cout << \"Block in the middle\" << endl;\n  cout << m.block<2,2>(1,1) << endl << endl;\n  for (int i = 1; i <= 3; ++i)\n  {\n    cout << \"Block of size \" << i << \"x\" << i << endl;\n    cout << m.block(0,0,i,i) << endl << endl;\n  }\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/Tutorial_BlockOperations_vector.cpp",
    "content": "#include <Eigen/Dense>\n#include <iostream>\n\nusing namespace std;\n\nint main()\n{\n  Eigen::ArrayXf v(6);\n  v << 1, 2, 3, 4, 5, 6;\n  cout << \"v.head(3) =\" << endl << v.head(3) << endl << endl;\n  cout << \"v.tail<3>() = \" << endl << v.tail<3>() << endl << endl;\n  v.segment(1,4) *= 2;\n  cout << \"after 'v.segment(1,4) *= 2', v =\" << endl << v << endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/Tutorial_PartialLU_solve.cpp",
    "content": "#include <Eigen/Core>\n#include <Eigen/LU>\n#include <iostream>\n\nusing namespace std;\nusing namespace Eigen;\n\nint main()\n{\n   Matrix3f A;\n   Vector3f b;\n   A << 1,2,3,  4,5,6,  7,8,10;\n   b << 3, 3, 4;\n   cout << \"Here is the matrix A:\" << endl << A << endl;\n   cout << \"Here is the vector b:\" << endl << b << endl;\n   Vector3f x = A.lu().solve(b);\n   cout << \"The solution is:\" << endl << x << endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_broadcast_1nn.cpp",
    "content": "#include <iostream>\n#include <Eigen/Dense>\n\nusing namespace std;\nusing namespace Eigen;\n\nint main()\n{\n  Eigen::MatrixXf m(2,4);\n  Eigen::VectorXf v(2);\n  \n  m << 1, 23, 6, 9,\n       3, 11, 7, 2;\n       \n  v << 2,\n       3;\n\n  MatrixXf::Index index;\n  // find nearest neighbour\n  (m.colwise() - v).colwise().squaredNorm().minCoeff(&index);\n\n  cout << \"Nearest neighbour is column \" << index << \":\" << endl;\n  cout << m.col(index) << endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_broadcast_simple.cpp",
    "content": "#include <iostream>\n#include <Eigen/Dense>\n\nusing namespace std;\nint main()\n{\n  Eigen::MatrixXf mat(2,4);\n  Eigen::VectorXf v(2);\n  \n  mat << 1, 2, 6, 9,\n         3, 1, 7, 2;\n         \n  v << 0,\n       1;\n       \n  //add v to each column of m\n  mat.colwise() += v;\n  \n  std::cout << \"Broadcasting result: \" << std::endl;\n  std::cout << mat << std::endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_broadcast_simple_rowwise.cpp",
    "content": "#include <iostream>\n#include <Eigen/Dense>\n\nusing namespace std;\nint main()\n{\n  Eigen::MatrixXf mat(2,4);\n  Eigen::VectorXf v(4);\n  \n  mat << 1, 2, 6, 9,\n         3, 1, 7, 2;\n         \n  v << 0,1,2,3;\n       \n  //add v to each row of m\n  mat.rowwise() += v.transpose();\n  \n  std::cout << \"Broadcasting result: \" << std::endl;\n  std::cout << mat << std::endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_colwise.cpp",
    "content": "#include <iostream>\n#include <Eigen/Dense>\n\nusing namespace std;\nint main()\n{\n  Eigen::MatrixXf mat(2,4);\n  mat << 1, 2, 6, 9,\n         3, 1, 7, 2;\n  \n  std::cout << \"Column's maximum: \" << std::endl\n   << mat.colwise().maxCoeff() << std::endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_maxnorm.cpp",
    "content": "#include <iostream>\n#include <Eigen/Dense>\n\nusing namespace std;\nusing namespace Eigen;\nint main()\n{\n  MatrixXf mat(2,4);\n  mat << 1, 2, 6, 9,\n         3, 1, 7, 2;\n  \n  MatrixXf::Index   maxIndex;\n  float maxNorm = mat.colwise().sum().maxCoeff(&maxIndex);\n  \n  std::cout << \"Maximum sum at position \" << maxIndex << std::endl;\n\n  std::cout << \"The corresponding vector is: \" << std::endl;\n  std::cout << mat.col( maxIndex ) << std::endl;\n  std::cout << \"And its sum is is: \" << maxNorm << std::endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_reductions_bool.cpp",
    "content": "#include <Eigen/Dense>\n#include <iostream>\n\nusing namespace std;\nusing namespace Eigen;\n\nint main()\n{\n  ArrayXXf a(2,2);\n  \n  a << 1,2,\n       3,4;\n\n  cout << \"(a > 0).all()   = \" << (a > 0).all() << endl;\n  cout << \"(a > 0).any()   = \" << (a > 0).any() << endl;\n  cout << \"(a > 0).count() = \" << (a > 0).count() << endl;\n  cout << endl;\n  cout << \"(a > 2).all()   = \" << (a > 2).all() << endl;\n  cout << \"(a > 2).any()   = \" << (a > 2).any() << endl;\n  cout << \"(a > 2).count() = \" << (a > 2).count() << endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_reductions_norm.cpp",
    "content": "#include <Eigen/Dense>\n#include <iostream>\n\nusing namespace std;\nusing namespace Eigen;\n\nint main()\n{\n  VectorXf v(2);\n  MatrixXf m(2,2), n(2,2);\n  \n  v << -1,\n       2;\n  \n  m << 1,-2,\n       -3,4;\n\n  cout << \"v.squaredNorm() = \" << v.squaredNorm() << endl;\n  cout << \"v.norm() = \" << v.norm() << endl;\n  cout << \"v.lpNorm<1>() = \" << v.lpNorm<1>() << endl;\n  cout << \"v.lpNorm<Infinity>() = \" << v.lpNorm<Infinity>() << endl;\n\n  cout << endl;\n  cout << \"m.squaredNorm() = \" << m.squaredNorm() << endl;\n  cout << \"m.norm() = \" << m.norm() << endl;\n  cout << \"m.lpNorm<1>() = \" << m.lpNorm<1>() << endl;\n  cout << \"m.lpNorm<Infinity>() = \" << m.lpNorm<Infinity>() << endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_reductions_operatornorm.cpp",
    "content": "#include <Eigen/Dense>\n#include <iostream>\n\nusing namespace Eigen;\nusing namespace std;\n\nint main()\n{\n  MatrixXf m(2,2);\n  m << 1,-2,\n       -3,4;\n\n  cout << \"1-norm(m)     = \" << m.cwiseAbs().colwise().sum().maxCoeff()\n       << \" == \"             << m.colwise().lpNorm<1>().maxCoeff() << endl;\n\n  cout << \"infty-norm(m) = \" << m.cwiseAbs().rowwise().sum().maxCoeff()\n       << \" == \"             << m.rowwise().lpNorm<1>().maxCoeff() << endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_rowwise.cpp",
    "content": "#include <iostream>\n#include <Eigen/Dense>\n\nusing namespace std;\nint main()\n{\n  Eigen::MatrixXf mat(2,4);\n  mat << 1, 2, 6, 9,\n         3, 1, 7, 2;\n  \n  std::cout << \"Row's maximum: \" << std::endl\n   << mat.rowwise().maxCoeff() << std::endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_visitors.cpp",
    "content": "#include <iostream>\n#include <Eigen/Dense>\n\nusing namespace std;\nusing namespace Eigen;\n\nint main()\n{\n  Eigen::MatrixXf m(2,2);\n  \n  m << 1, 2,\n       3, 4;\n\n  //get location of maximum\n  MatrixXf::Index maxRow, maxCol;\n  float max = m.maxCoeff(&maxRow, &maxCol);\n\n  //get location of minimum\n  MatrixXf::Index minRow, minCol;\n  float min = m.minCoeff(&minRow, &minCol);\n\n  cout << \"Max: \" << max <<  \", at: \" <<\n     maxRow << \",\" << maxCol << endl;\n  cout << \"Min: \" << min << \", at: \" <<\n     minRow << \",\" << minCol << endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/Tutorial_simple_example_dynamic_size.cpp",
    "content": "#include <Eigen/Core>\n#include <iostream>\n\nusing namespace Eigen;\n\nint main()\n{\n  for (int size=1; size<=4; ++size)\n  {\n    MatrixXi m(size,size+1);         // a (size)x(size+1)-matrix of int's\n    for (int j=0; j<m.cols(); ++j)   // loop over columns\n      for (int i=0; i<m.rows(); ++i) // loop over rows\n        m(i,j) = i+j*size;           // to access matrix coefficients,\n                                     // use operator()(int,int)\n    std::cout << m << \"\\n\\n\";\n  }\n\n  VectorXf v(4); // a vector of 4 float's\n  // to access vector coefficients, use either operator () or operator []\n  v[0] = 1; v[1] = 2; v(2) = 3; v(3) = 4;\n  std::cout << \"\\nv:\\n\" << v << std::endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/Tutorial_simple_example_fixed_size.cpp",
    "content": "#include <Eigen/Core>\n#include <iostream>\n\nusing namespace Eigen;\n\nint main()\n{\n  Matrix3f m3;\n  m3 << 1, 2, 3, 4, 5, 6, 7, 8, 9;\n  Matrix4f m4 = Matrix4f::Identity();\n  Vector4i v4(1, 2, 3, 4);\n\n  std::cout << \"m3\\n\" << m3 << \"\\nm4:\\n\"\n    << m4 << \"\\nv4:\\n\" << v4 << std::endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/class_Block.cpp",
    "content": "#include <Eigen/Core>\n#include <iostream>\nusing namespace Eigen;\nusing namespace std;\n\ntemplate<typename Derived>\nEigen::Block<Derived>\ntopLeftCorner(MatrixBase<Derived>& m, int rows, int cols)\n{\n  return Eigen::Block<Derived>(m.derived(), 0, 0, rows, cols);\n}\n\ntemplate<typename Derived>\nconst Eigen::Block<const Derived>\ntopLeftCorner(const MatrixBase<Derived>& m, int rows, int cols)\n{\n  return Eigen::Block<const Derived>(m.derived(), 0, 0, rows, cols);\n}\n\nint main(int, char**)\n{\n  Matrix4d m = Matrix4d::Identity();\n  cout << topLeftCorner(4*m, 2, 3) << endl; // calls the const version\n  topLeftCorner(m, 2, 3) *= 5;              // calls the non-const version\n  cout << \"Now the matrix m is:\" << endl << m << endl;\n  return 0;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/class_CwiseBinaryOp.cpp",
    "content": "#include <Eigen/Core>\n#include <iostream>\nusing namespace Eigen;\nusing namespace std;\n\n// define a custom template binary functor\ntemplate<typename Scalar> struct MakeComplexOp {\n  EIGEN_EMPTY_STRUCT_CTOR(MakeComplexOp)\n  typedef complex<Scalar> result_type;\n  complex<Scalar> operator()(const Scalar& a, const Scalar& b) const { return complex<Scalar>(a,b); }\n};\n\nint main(int, char**)\n{\n  Matrix4d m1 = Matrix4d::Random(), m2 = Matrix4d::Random();\n  cout << m1.binaryExpr(m2, MakeComplexOp<double>()) << endl;\n  return 0;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/class_CwiseUnaryOp.cpp",
    "content": "#include <Eigen/Core>\n#include <iostream>\nusing namespace Eigen;\nusing namespace std;\n\n// define a custom template unary functor\ntemplate<typename Scalar>\nstruct CwiseClampOp {\n  CwiseClampOp(const Scalar& inf, const Scalar& sup) : m_inf(inf), m_sup(sup) {}\n  const Scalar operator()(const Scalar& x) const { return x<m_inf ? m_inf : (x>m_sup ? m_sup : x); }\n  Scalar m_inf, m_sup;\n};\n\nint main(int, char**)\n{\n  Matrix4d m1 = Matrix4d::Random();\n  cout << m1 << endl << \"becomes: \" << endl << m1.unaryExpr(CwiseClampOp<double>(-0.5,0.5)) << endl;\n  return 0;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/class_CwiseUnaryOp_ptrfun.cpp",
    "content": "#include <Eigen/Core>\n#include <iostream>\nusing namespace Eigen;\nusing namespace std;\n\n// define function to be applied coefficient-wise\ndouble ramp(double x)\n{\n  if (x > 0)\n    return x;\n  else \n    return 0;\n}\n\nint main(int, char**)\n{\n  Matrix4d m1 = Matrix4d::Random();\n  cout << m1 << endl << \"becomes: \" << endl << m1.unaryExpr(ptr_fun(ramp)) << endl;\n  return 0;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/class_FixedBlock.cpp",
    "content": "#include <Eigen/Core>\n#include <iostream>\nusing namespace Eigen;\nusing namespace std;\n\ntemplate<typename Derived>\nEigen::Block<Derived, 2, 2>\ntopLeft2x2Corner(MatrixBase<Derived>& m)\n{\n  return Eigen::Block<Derived, 2, 2>(m.derived(), 0, 0);\n}\n\ntemplate<typename Derived>\nconst Eigen::Block<const Derived, 2, 2>\ntopLeft2x2Corner(const MatrixBase<Derived>& m)\n{\n  return Eigen::Block<const Derived, 2, 2>(m.derived(), 0, 0);\n}\n\nint main(int, char**)\n{\n  Matrix3d m = Matrix3d::Identity();\n  cout << topLeft2x2Corner(4*m) << endl; // calls the const version\n  topLeft2x2Corner(m) *= 2;              // calls the non-const version\n  cout << \"Now the matrix m is:\" << endl << m << endl;\n  return 0;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/class_FixedVectorBlock.cpp",
    "content": "#include <Eigen/Core>\n#include <iostream>\nusing namespace Eigen;\nusing namespace std;\n\ntemplate<typename Derived>\nEigen::VectorBlock<Derived, 2>\nfirstTwo(MatrixBase<Derived>& v)\n{\n  return Eigen::VectorBlock<Derived, 2>(v.derived(), 0);\n}\n\ntemplate<typename Derived>\nconst Eigen::VectorBlock<const Derived, 2>\nfirstTwo(const MatrixBase<Derived>& v)\n{\n  return Eigen::VectorBlock<const Derived, 2>(v.derived(), 0);\n}\n\nint main(int, char**)\n{\n  Matrix<int,1,6> v; v << 1,2,3,4,5,6;\n  cout << firstTwo(4*v) << endl; // calls the const version\n  firstTwo(v) *= 2;              // calls the non-const version\n  cout << \"Now the vector v is:\" << endl << v << endl;\n  return 0;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/class_VectorBlock.cpp",
    "content": "#include <Eigen/Core>\n#include <iostream>\nusing namespace Eigen;\nusing namespace std;\n\ntemplate<typename Derived>\nEigen::VectorBlock<Derived>\nsegmentFromRange(MatrixBase<Derived>& v, int start, int end)\n{\n  return Eigen::VectorBlock<Derived>(v.derived(), start, end-start);\n}\n\ntemplate<typename Derived>\nconst Eigen::VectorBlock<const Derived>\nsegmentFromRange(const MatrixBase<Derived>& v, int start, int end)\n{\n  return Eigen::VectorBlock<const Derived>(v.derived(), start, end-start);\n}\n\nint main(int, char**)\n{\n  Matrix<int,1,6> v; v << 1,2,3,4,5,6;\n  cout << segmentFromRange(2*v, 2, 4) << endl; // calls the const version\n  segmentFromRange(v, 1, 3) *= 5;              // calls the non-const version\n  cout << \"Now the vector v is:\" << endl << v << endl;\n  return 0;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/function_taking_eigenbase.cpp",
    "content": "#include <iostream>\n#include <Eigen/Core>\nusing namespace Eigen;\n\ntemplate <typename Derived>\nvoid print_size(const EigenBase<Derived>& b)\n{\n  std::cout << \"size (rows, cols): \" << b.size() << \" (\" << b.rows()\n            << \", \" << b.cols() << \")\" << std::endl;\n}\n\nint main()\n{\n    Vector3f v;\n    print_size(v);\n    // v.asDiagonal() returns a 3x3 diagonal matrix pseudo-expression\n    print_size(v.asDiagonal());\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/function_taking_ref.cpp",
    "content": "#include <iostream>\n#include <Eigen/SVD>\nusing namespace Eigen;\nusing namespace std;\n\nfloat inv_cond(const Ref<const MatrixXf>& a)\n{\n  const VectorXf sing_vals = a.jacobiSvd().singularValues();\n  return sing_vals(sing_vals.size()-1) / sing_vals(0);\n}\n\nint main()\n{\n  Matrix4f m = Matrix4f::Random();\n  cout << \"matrix m:\" << endl << m << endl << endl;\n  cout << \"inv_cond(m):          \" << inv_cond(m)                      << endl;\n  cout << \"inv_cond(m(1:3,1:3)): \" << inv_cond(m.topLeftCorner(3,3))   << endl;\n  cout << \"inv_cond(m+I):        \" << inv_cond(m+Matrix4f::Identity()) << endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/make_circulant.cpp",
    "content": "/*\nThis program is presented in several fragments in the doc page.\nEvery fragment is in its own file; this file simply combines them.\n*/\n\n#include \"make_circulant.cpp.preamble\"\n#include \"make_circulant.cpp.traits\"\n#include \"make_circulant.cpp.expression\"\n#include \"make_circulant.cpp.evaluator\"\n#include \"make_circulant.cpp.entry\"\n#include \"make_circulant.cpp.main\"\n"
  },
  {
    "path": "include/eigen3/doc/examples/make_circulant.cpp.entry",
    "content": "template <class ArgType>\nCirculant<ArgType> makeCirculant(const Eigen::MatrixBase<ArgType>& arg)\n{\n  return Circulant<ArgType>(arg.derived());\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/make_circulant.cpp.evaluator",
    "content": "namespace Eigen {\n  namespace internal {\n    template<typename ArgType>\n    struct evaluator<Circulant<ArgType> >\n      : evaluator_base<Circulant<ArgType> >\n    {\n      typedef Circulant<ArgType> XprType;\n      typedef typename nested_eval<ArgType, XprType::ColsAtCompileTime>::type ArgTypeNested;\n      typedef typename remove_all<ArgTypeNested>::type ArgTypeNestedCleaned;\n      typedef typename XprType::CoeffReturnType CoeffReturnType;\n\n      enum { \n        CoeffReadCost = evaluator<ArgTypeNestedCleaned>::CoeffReadCost,\n        Flags = Eigen::ColMajor \n      };\n      \n      evaluator(const XprType& xpr)\n        : m_argImpl(xpr.m_arg), m_rows(xpr.rows())\n      { }\n\n      CoeffReturnType coeff(Index row, Index col) const\n      {\n        Index index = row - col;\n        if (index < 0) index += m_rows;\n        return m_argImpl.coeff(index);\n      }\n\n      evaluator<ArgTypeNestedCleaned> m_argImpl;\n      const Index m_rows;\n    };\n  }\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/make_circulant.cpp.expression",
    "content": "template <class ArgType>\nclass Circulant : public Eigen::MatrixBase<Circulant<ArgType> >\n{\npublic:\n  Circulant(const ArgType& arg)\n    : m_arg(arg)\n  { \n    EIGEN_STATIC_ASSERT(ArgType::ColsAtCompileTime == 1,\n                        YOU_TRIED_CALLING_A_VECTOR_METHOD_ON_A_MATRIX);\n  }\n\n  typedef typename Eigen::internal::ref_selector<Circulant>::type Nested; \n\n  typedef Eigen::Index Index;\n  Index rows() const { return m_arg.rows(); }\n  Index cols() const { return m_arg.rows(); }\n\n  typedef typename Eigen::internal::ref_selector<ArgType>::type ArgTypeNested;\n  ArgTypeNested m_arg;\n};\n"
  },
  {
    "path": "include/eigen3/doc/examples/make_circulant.cpp.main",
    "content": "int main()\n{\n  Eigen::VectorXd vec(4);\n  vec << 1, 2, 4, 8;\n  Eigen::MatrixXd mat;\n  mat = makeCirculant(vec);\n  std::cout << mat << std::endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/make_circulant.cpp.preamble",
    "content": "#include <Eigen/Core>\n#include <iostream>\n\ntemplate <class ArgType> class Circulant;\n"
  },
  {
    "path": "include/eigen3/doc/examples/make_circulant.cpp.traits",
    "content": "namespace Eigen {\n  namespace internal {\n    template <class ArgType>\n    struct traits<Circulant<ArgType> >\n    {\n      typedef Eigen::Dense StorageKind;\n      typedef Eigen::MatrixXpr XprKind;\n      typedef typename ArgType::StorageIndex StorageIndex;\n      typedef typename ArgType::Scalar Scalar;\n      enum { \n        Flags = Eigen::ColMajor,\n        RowsAtCompileTime = ArgType::RowsAtCompileTime,\n        ColsAtCompileTime = ArgType::RowsAtCompileTime,\n        MaxRowsAtCompileTime = ArgType::MaxRowsAtCompileTime,\n        MaxColsAtCompileTime = ArgType::MaxRowsAtCompileTime\n      };\n    };\n  }\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/make_circulant2.cpp",
    "content": "#include <Eigen/Core>\n#include <iostream>\n\nusing namespace Eigen;\n\n// [circulant_func]\ntemplate<class ArgType>\nclass circulant_functor {\n  const ArgType &m_vec;\npublic:\n  circulant_functor(const ArgType& arg) : m_vec(arg) {}\n\n  const typename ArgType::Scalar& operator() (Index row, Index col) const {\n    Index index = row - col;\n    if (index < 0) index += m_vec.size();\n    return m_vec(index);\n  }\n};\n// [circulant_func]\n\n// [square]\ntemplate<class ArgType>\nstruct circulant_helper {\n  typedef Matrix<typename ArgType::Scalar,\n                 ArgType::SizeAtCompileTime,\n                 ArgType::SizeAtCompileTime,\n                 ColMajor,\n                 ArgType::MaxSizeAtCompileTime,\n                 ArgType::MaxSizeAtCompileTime> MatrixType;\n};\n// [square]\n\n// [makeCirculant]\ntemplate <class ArgType>\nCwiseNullaryOp<circulant_functor<ArgType>, typename circulant_helper<ArgType>::MatrixType>\nmakeCirculant(const Eigen::MatrixBase<ArgType>& arg)\n{\n  typedef typename circulant_helper<ArgType>::MatrixType MatrixType;\n  return MatrixType::NullaryExpr(arg.size(), arg.size(), circulant_functor<ArgType>(arg.derived()));\n}\n// [makeCirculant]\n\n// [main]\nint main()\n{\n  Eigen::VectorXd vec(4);\n  vec << 1, 2, 4, 8;\n  Eigen::MatrixXd mat;\n  mat = makeCirculant(vec);\n  std::cout << mat << std::endl;\n}\n// [main]\n"
  },
  {
    "path": "include/eigen3/doc/examples/matrixfree_cg.cpp",
    "content": "#include <iostream>\n#include <Eigen/Core>\n#include <Eigen/Dense>\n#include <Eigen/IterativeLinearSolvers>\n#include <unsupported/Eigen/IterativeSolvers>\n\nclass MatrixReplacement;\nusing Eigen::SparseMatrix;\n\nnamespace Eigen {\nnamespace internal {\n  // MatrixReplacement looks-like a SparseMatrix, so let's inherits its traits:\n  template<>\n  struct traits<MatrixReplacement> :  public Eigen::internal::traits<Eigen::SparseMatrix<double> >\n  {};\n}\n}\n\n// Example of a matrix-free wrapper from a user type to Eigen's compatible type\n// For the sake of simplicity, this example simply wrap a Eigen::SparseMatrix.\nclass MatrixReplacement : public Eigen::EigenBase<MatrixReplacement> {\npublic:\n  // Required typedefs, constants, and method:\n  typedef double Scalar;\n  typedef double RealScalar;\n  typedef int StorageIndex;\n  enum {\n    ColsAtCompileTime = Eigen::Dynamic,\n    MaxColsAtCompileTime = Eigen::Dynamic,\n    IsRowMajor = false\n  };\n\n  Index rows() const { return mp_mat->rows(); }\n  Index cols() const { return mp_mat->cols(); }\n\n  template<typename Rhs>\n  Eigen::Product<MatrixReplacement,Rhs,Eigen::AliasFreeProduct> operator*(const Eigen::MatrixBase<Rhs>& x) const {\n    return Eigen::Product<MatrixReplacement,Rhs,Eigen::AliasFreeProduct>(*this, x.derived());\n  }\n\n  // Custom API:\n  MatrixReplacement() : mp_mat(0) {}\n\n  void attachMyMatrix(const SparseMatrix<double> &mat) {\n    mp_mat = &mat;\n  }\n  const SparseMatrix<double> my_matrix() const { return *mp_mat; }\n\nprivate:\n  const SparseMatrix<double> *mp_mat;\n};\n\n\n// Implementation of MatrixReplacement * Eigen::DenseVector though a specialization of internal::generic_product_impl:\nnamespace Eigen {\nnamespace internal {\n\n  template<typename Rhs>\n  struct generic_product_impl<MatrixReplacement, Rhs, SparseShape, DenseShape, GemvProduct> // GEMV stands for matrix-vector\n  : generic_product_impl_base<MatrixReplacement,Rhs,generic_product_impl<MatrixReplacement,Rhs> >\n  {\n    typedef typename Product<MatrixReplacement,Rhs>::Scalar Scalar;\n\n    template<typename Dest>\n    static void scaleAndAddTo(Dest& dst, const MatrixReplacement& lhs, const Rhs& rhs, const Scalar& alpha)\n    {\n      // This method should implement \"dst += alpha * lhs * rhs\" inplace,\n      // however, for iterative solvers, alpha is always equal to 1, so let's not bother about it.\n      assert(alpha==Scalar(1) && \"scaling is not implemented\");\n      EIGEN_ONLY_USED_FOR_DEBUG(alpha);\n\n      // Here we could simply call dst.noalias() += lhs.my_matrix() * rhs,\n      // but let's do something fancier (and less efficient):\n      for(Index i=0; i<lhs.cols(); ++i)\n        dst += rhs(i) * lhs.my_matrix().col(i);\n    }\n  };\n\n}\n}\n\nint main()\n{\n  int n = 10;\n  Eigen::SparseMatrix<double> S = Eigen::MatrixXd::Random(n,n).sparseView(0.5,1);\n  S = S.transpose()*S;\n\n  MatrixReplacement A;\n  A.attachMyMatrix(S);\n\n  Eigen::VectorXd b(n), x;\n  b.setRandom();\n\n  // Solve Ax = b using various iterative solver with matrix-free version:\n  {\n    Eigen::ConjugateGradient<MatrixReplacement, Eigen::Lower|Eigen::Upper, Eigen::IdentityPreconditioner> cg;\n    cg.compute(A);\n    x = cg.solve(b);\n    std::cout << \"CG:       #iterations: \" << cg.iterations() << \", estimated error: \" << cg.error() << std::endl;\n  }\n\n  {\n    Eigen::BiCGSTAB<MatrixReplacement, Eigen::IdentityPreconditioner> bicg;\n    bicg.compute(A);\n    x = bicg.solve(b);\n    std::cout << \"BiCGSTAB: #iterations: \" << bicg.iterations() << \", estimated error: \" << bicg.error() << std::endl;\n  }\n\n  {\n    Eigen::GMRES<MatrixReplacement, Eigen::IdentityPreconditioner> gmres;\n    gmres.compute(A);\n    x = gmres.solve(b);\n    std::cout << \"GMRES:    #iterations: \" << gmres.iterations() << \", estimated error: \" << gmres.error() << std::endl;\n  }\n\n  {\n    Eigen::DGMRES<MatrixReplacement, Eigen::IdentityPreconditioner> gmres;\n    gmres.compute(A);\n    x = gmres.solve(b);\n    std::cout << \"DGMRES:   #iterations: \" << gmres.iterations() << \", estimated error: \" << gmres.error() << std::endl;\n  }\n\n  {\n    Eigen::MINRES<MatrixReplacement, Eigen::Lower|Eigen::Upper, Eigen::IdentityPreconditioner> minres;\n    minres.compute(A);\n    x = minres.solve(b);\n    std::cout << \"MINRES:   #iterations: \" << minres.iterations() << \", estimated error: \" << minres.error() << std::endl;\n  }\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/nullary_indexing.cpp",
    "content": "#include <Eigen/Core>\n#include <iostream>\n\nusing namespace Eigen;\n\n// [functor]\ntemplate<class ArgType, class RowIndexType, class ColIndexType>\nclass indexing_functor {\n  const ArgType &m_arg;\n  const RowIndexType &m_rowIndices;\n  const ColIndexType &m_colIndices;\npublic:\n  typedef Matrix<typename ArgType::Scalar,\n                 RowIndexType::SizeAtCompileTime,\n                 ColIndexType::SizeAtCompileTime,\n                 ArgType::Flags&RowMajorBit?RowMajor:ColMajor,\n                 RowIndexType::MaxSizeAtCompileTime,\n                 ColIndexType::MaxSizeAtCompileTime> MatrixType;\n\n  indexing_functor(const ArgType& arg, const RowIndexType& row_indices, const ColIndexType& col_indices)\n    : m_arg(arg), m_rowIndices(row_indices), m_colIndices(col_indices)\n  {}\n\n  const typename ArgType::Scalar& operator() (Index row, Index col) const {\n    return m_arg(m_rowIndices[row], m_colIndices[col]);\n  }\n};\n// [functor]\n\n// [function]\ntemplate <class ArgType, class RowIndexType, class ColIndexType>\nCwiseNullaryOp<indexing_functor<ArgType,RowIndexType,ColIndexType>, typename indexing_functor<ArgType,RowIndexType,ColIndexType>::MatrixType>\nindexing(const Eigen::MatrixBase<ArgType>& arg, const RowIndexType& row_indices, const ColIndexType& col_indices)\n{\n  typedef indexing_functor<ArgType,RowIndexType,ColIndexType> Func;\n  typedef typename Func::MatrixType MatrixType;\n  return MatrixType::NullaryExpr(row_indices.size(), col_indices.size(), Func(arg.derived(), row_indices, col_indices));\n}\n// [function]\n\n\nint main()\n{\n  std::cout << \"[main1]\\n\";\n  Eigen::MatrixXi A = Eigen::MatrixXi::Random(4,4);\n  Array3i ri(1,2,1);\n  ArrayXi ci(6); ci << 3,2,1,0,0,2;\n  Eigen::MatrixXi B = indexing(A, ri, ci);\n  std::cout << \"A =\" << std::endl;\n  std::cout << A << std::endl << std::endl;\n  std::cout << \"A([\" << ri.transpose() << \"], [\" << ci.transpose() << \"]) =\" << std::endl;\n  std::cout << B << std::endl;\n  std::cout << \"[main1]\\n\";\n\n  std::cout << \"[main2]\\n\";\n  B =  indexing(A, ri+1, ci);\n  std::cout << \"A(ri+1,ci) =\" << std::endl;\n  std::cout << B << std::endl << std::endl;\n#if __cplusplus >= 201103L\n  B =  indexing(A, ArrayXi::LinSpaced(13,0,12).unaryExpr([](int x){return x%4;}), ArrayXi::LinSpaced(4,0,3));\n  std::cout << \"A(ArrayXi::LinSpaced(13,0,12).unaryExpr([](int x){return x%4;}), ArrayXi::LinSpaced(4,0,3)) =\" << std::endl;\n  std::cout << B << std::endl << std::endl;\n#endif\n  std::cout << \"[main2]\\n\";\n}\n\n"
  },
  {
    "path": "include/eigen3/doc/examples/tut_arithmetic_add_sub.cpp",
    "content": "#include <iostream>\n#include <Eigen/Dense>\n\nusing namespace Eigen;\n\nint main()\n{\n  Matrix2d a;\n  a << 1, 2,\n       3, 4;\n  MatrixXd b(2,2);\n  b << 2, 3,\n       1, 4;\n  std::cout << \"a + b =\\n\" << a + b << std::endl;\n  std::cout << \"a - b =\\n\" << a - b << std::endl;\n  std::cout << \"Doing a += b;\" << std::endl;\n  a += b;\n  std::cout << \"Now a =\\n\" << a << std::endl;\n  Vector3d v(1,2,3);\n  Vector3d w(1,0,0);\n  std::cout << \"-v + w - v =\\n\" << -v + w - v << std::endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/tut_arithmetic_dot_cross.cpp",
    "content": "#include <iostream>\n#include <Eigen/Dense>\n\nusing namespace Eigen;\nusing namespace std;\nint main()\n{\n  Vector3d v(1,2,3);\n  Vector3d w(0,1,2);\n\n  cout << \"Dot product: \" << v.dot(w) << endl;\n  double dp = v.adjoint()*w; // automatic conversion of the inner product to a scalar\n  cout << \"Dot product via a matrix product: \" << dp << endl;\n  cout << \"Cross product:\\n\" << v.cross(w) << endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/tut_arithmetic_matrix_mul.cpp",
    "content": "#include <iostream>\n#include <Eigen/Dense>\n\nusing namespace Eigen;\nint main()\n{\n  Matrix2d mat;\n  mat << 1, 2,\n         3, 4;\n  Vector2d u(-1,1), v(2,0);\n  std::cout << \"Here is mat*mat:\\n\" << mat*mat << std::endl;\n  std::cout << \"Here is mat*u:\\n\" << mat*u << std::endl;\n  std::cout << \"Here is u^T*mat:\\n\" << u.transpose()*mat << std::endl;\n  std::cout << \"Here is u^T*v:\\n\" << u.transpose()*v << std::endl;\n  std::cout << \"Here is u*v^T:\\n\" << u*v.transpose() << std::endl;\n  std::cout << \"Let's multiply mat by itself\" << std::endl;\n  mat = mat*mat;\n  std::cout << \"Now mat is mat:\\n\" << mat << std::endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/tut_arithmetic_redux_basic.cpp",
    "content": "#include <iostream>\n#include <Eigen/Dense>\n\nusing namespace std;\nint main()\n{\n  Eigen::Matrix2d mat;\n  mat << 1, 2,\n         3, 4;\n  cout << \"Here is mat.sum():       \" << mat.sum()       << endl;\n  cout << \"Here is mat.prod():      \" << mat.prod()      << endl;\n  cout << \"Here is mat.mean():      \" << mat.mean()      << endl;\n  cout << \"Here is mat.minCoeff():  \" << mat.minCoeff()  << endl;\n  cout << \"Here is mat.maxCoeff():  \" << mat.maxCoeff()  << endl;\n  cout << \"Here is mat.trace():     \" << mat.trace()     << endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/tut_arithmetic_scalar_mul_div.cpp",
    "content": "#include <iostream>\n#include <Eigen/Dense>\n\nusing namespace Eigen;\n\nint main()\n{\n  Matrix2d a;\n  a << 1, 2,\n       3, 4;\n  Vector3d v(1,2,3);\n  std::cout << \"a * 2.5 =\\n\" << a * 2.5 << std::endl;\n  std::cout << \"0.1 * v =\\n\" << 0.1 * v << std::endl;\n  std::cout << \"Doing v *= 2;\" << std::endl;\n  v *= 2;\n  std::cout << \"Now v =\\n\" << v << std::endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/tut_matrix_coefficient_accessors.cpp",
    "content": "#include <iostream>\n#include <Eigen/Dense>\n\nusing namespace Eigen;\n\nint main()\n{\n  MatrixXd m(2,2);\n  m(0,0) = 3;\n  m(1,0) = 2.5;\n  m(0,1) = -1;\n  m(1,1) = m(1,0) + m(0,1);\n  std::cout << \"Here is the matrix m:\\n\" << m << std::endl;\n  VectorXd v(2);\n  v(0) = 4;\n  v(1) = v(0) - 1;\n  std::cout << \"Here is the vector v:\\n\" << v << std::endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/tut_matrix_resize.cpp",
    "content": "#include <iostream>\n#include <Eigen/Dense>\n\nusing namespace Eigen;\n\nint main()\n{\n  MatrixXd m(2,5);\n  m.resize(4,3);\n  std::cout << \"The matrix m is of size \"\n            << m.rows() << \"x\" << m.cols() << std::endl;\n  std::cout << \"It has \" << m.size() << \" coefficients\" << std::endl;\n  VectorXd v(2);\n  v.resize(5);\n  std::cout << \"The vector v is of size \" << v.size() << std::endl;\n  std::cout << \"As a matrix, v is of size \"\n            << v.rows() << \"x\" << v.cols() << std::endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/examples/tut_matrix_resize_fixed_size.cpp",
    "content": "#include <iostream>\n#include <Eigen/Dense>\n\nusing namespace Eigen;\n\nint main()\n{\n  Matrix4d m;\n  m.resize(4,4); // no operation\n  std::cout << \"The matrix m is of size \"\n            << m.rows() << \"x\" << m.cols() << std::endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/snippets/.krazy",
    "content": "EXCLUDE copyright\nEXCLUDE license\n"
  },
  {
    "path": "include/eigen3/doc/snippets/AngleAxis_mimic_euler.cpp",
    "content": "Matrix3f m;\nm = AngleAxisf(0.25*M_PI, Vector3f::UnitX())\n  * AngleAxisf(0.5*M_PI,  Vector3f::UnitY())\n  * AngleAxisf(0.33*M_PI, Vector3f::UnitZ());\ncout << m << endl << \"is unitary: \" << m.isUnitary() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/BiCGSTAB_simple.cpp",
    "content": "  int n = 10000;\n  VectorXd x(n), b(n);\n  SparseMatrix<double> A(n,n);\n  /* ... fill A and b ... */ \n  BiCGSTAB<SparseMatrix<double> > solver;\n  solver.compute(A);\n  x = solver.solve(b);\n  std::cout << \"#iterations:     \" << solver.iterations() << std::endl;\n  std::cout << \"estimated error: \" << solver.error()      << std::endl;\n  /* ... update b ... */\n  x = solver.solve(b); // solve again"
  },
  {
    "path": "include/eigen3/doc/snippets/BiCGSTAB_step_by_step.cpp",
    "content": "  int n = 10000;\n  VectorXd x(n), b(n);\n  SparseMatrix<double> A(n,n);\n  /* ... fill A and b ... */ \n  BiCGSTAB<SparseMatrix<double> > solver(A);\n  // start from a random solution\n  x = VectorXd::Random(n);\n  solver.setMaxIterations(1);\n  int i = 0;\n  do {\n    x = solver.solveWithGuess(b,x);\n    std::cout << i << \" : \" << solver.error() << std::endl;\n    ++i;\n  } while (solver.info()!=Success && i<100);"
  },
  {
    "path": "include/eigen3/doc/snippets/CMakeLists.txt",
    "content": "file(GLOB snippets_SRCS \"*.cpp\")\n\nadd_custom_target(all_snippets)\n\nforeach(snippet_src ${snippets_SRCS})\n  get_filename_component(snippet ${snippet_src} NAME_WE)\n  set(compile_snippet_target compile_${snippet})\n  set(compile_snippet_src ${compile_snippet_target}.cpp)\n  file(READ ${snippet_src} snippet_source_code)\n  configure_file(${CMAKE_CURRENT_SOURCE_DIR}/compile_snippet.cpp.in\n                 ${CMAKE_CURRENT_BINARY_DIR}/${compile_snippet_src})\n  add_executable(${compile_snippet_target}\n                 ${CMAKE_CURRENT_BINARY_DIR}/${compile_snippet_src})\n  if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO)\n    target_link_libraries(${compile_snippet_target} ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO})\n  endif()\n  add_custom_command(\n    TARGET ${compile_snippet_target}\n    POST_BUILD\n    COMMAND ${compile_snippet_target}\n    ARGS >${CMAKE_CURRENT_BINARY_DIR}/${snippet}.out\n  )\n  add_dependencies(all_snippets ${compile_snippet_target})\n  set_source_files_properties(${CMAKE_CURRENT_BINARY_DIR}/${compile_snippet_src}\n                              PROPERTIES OBJECT_DEPENDS ${snippet_src})\nendforeach(snippet_src)\n"
  },
  {
    "path": "include/eigen3/doc/snippets/ColPivHouseholderQR_solve.cpp",
    "content": "Matrix3f m = Matrix3f::Random();\nMatrix3f y = Matrix3f::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here is the matrix y:\" << endl << y << endl;\nMatrix3f x;\nx = m.colPivHouseholderQr().solve(y);\nassert(y.isApprox(m*x));\ncout << \"Here is a solution x to the equation mx=y:\" << endl << x << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/ComplexEigenSolver_compute.cpp",
    "content": "MatrixXcf A = MatrixXcf::Random(4,4);\ncout << \"Here is a random 4x4 matrix, A:\" << endl << A << endl << endl;\n\nComplexEigenSolver<MatrixXcf> ces;\nces.compute(A);\ncout << \"The eigenvalues of A are:\" << endl << ces.eigenvalues() << endl;\ncout << \"The matrix of eigenvectors, V, is:\" << endl << ces.eigenvectors() << endl << endl;\n\ncomplex<float> lambda = ces.eigenvalues()[0];\ncout << \"Consider the first eigenvalue, lambda = \" << lambda << endl;\nVectorXcf v = ces.eigenvectors().col(0);\ncout << \"If v is the corresponding eigenvector, then lambda * v = \" << endl << lambda * v << endl;\ncout << \"... and A * v = \" << endl << A * v << endl << endl;\n\ncout << \"Finally, V * D * V^(-1) = \" << endl\n     << ces.eigenvectors() * ces.eigenvalues().asDiagonal() * ces.eigenvectors().inverse() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/ComplexEigenSolver_eigenvalues.cpp",
    "content": "MatrixXcf ones = MatrixXcf::Ones(3,3);\nComplexEigenSolver<MatrixXcf> ces(ones, /* computeEigenvectors = */ false);\ncout << \"The eigenvalues of the 3x3 matrix of ones are:\" \n     << endl << ces.eigenvalues() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/ComplexEigenSolver_eigenvectors.cpp",
    "content": "MatrixXcf ones = MatrixXcf::Ones(3,3);\nComplexEigenSolver<MatrixXcf> ces(ones);\ncout << \"The first eigenvector of the 3x3 matrix of ones is:\" \n     << endl << ces.eigenvectors().col(1) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/ComplexSchur_compute.cpp",
    "content": "MatrixXcf A = MatrixXcf::Random(4,4);\nComplexSchur<MatrixXcf> schur(4);\nschur.compute(A);\ncout << \"The matrix T in the decomposition of A is:\" << endl << schur.matrixT() << endl;\nschur.compute(A.inverse());\ncout << \"The matrix T in the decomposition of A^(-1) is:\" << endl << schur.matrixT() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/ComplexSchur_matrixT.cpp",
    "content": "MatrixXcf A = MatrixXcf::Random(4,4);\ncout << \"Here is a random 4x4 matrix, A:\" << endl << A << endl << endl;\nComplexSchur<MatrixXcf> schurOfA(A, false); // false means do not compute U\ncout << \"The triangular matrix T is:\" << endl << schurOfA.matrixT() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/ComplexSchur_matrixU.cpp",
    "content": "MatrixXcf A = MatrixXcf::Random(4,4);\ncout << \"Here is a random 4x4 matrix, A:\" << endl << A << endl << endl;\nComplexSchur<MatrixXcf> schurOfA(A);\ncout << \"The unitary matrix U is:\" << endl << schurOfA.matrixU() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_abs.cpp",
    "content": "Array3d v(1,-2,-3);\ncout << v.abs() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_abs2.cpp",
    "content": "Array3d v(1,-2,-3);\ncout << v.abs2() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_acos.cpp",
    "content": "Array3d v(0, sqrt(2.)/2, 1);\ncout << v.acos() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_arg.cpp",
    "content": "ArrayXcf v = ArrayXcf::Random(3);\ncout << v << endl << endl;\ncout << arg(v) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_array_power_array.cpp",
    "content": "Array<double,1,3> x(8,25,3),\n                  e(1./3.,0.5,2.);\ncout << \"[\" << x << \"]^[\" << e << \"] = \" << x.pow(e) << endl; // using ArrayBase::pow\ncout << \"[\" << x << \"]^[\" << e << \"] = \" << pow(x,e) << endl; // using Eigen::pow\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_asin.cpp",
    "content": "Array3d v(0, sqrt(2.)/2, 1);\ncout << v.asin() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_atan.cpp",
    "content": "ArrayXd v = ArrayXd::LinSpaced(5,0,1);\ncout << v.atan() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_boolean_and.cpp",
    "content": "Array3d v(-1,2,1), w(-3,2,3);\ncout << ((v<w) && (v<0)) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_boolean_not.cpp",
    "content": "Array3d v(1,2,3);\nv(1) *= 0.0/0.0;\nv(2) /= 0.0;\ncout << v << endl << endl;\ncout << !isfinite(v) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_boolean_or.cpp",
    "content": "Array3d v(-1,2,1), w(-3,2,3);\ncout << ((v<w) || (v<0)) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_boolean_xor.cpp",
    "content": "Array3d v(-1,2,1), w(-3,2,3);\ncout << ((v<w) ^ (v<0)) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_ceil.cpp",
    "content": "ArrayXd v = ArrayXd::LinSpaced(7,-2,2);\ncout << v << endl << endl;\ncout << ceil(v) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_cos.cpp",
    "content": "Array3d v(M_PI, M_PI/2, M_PI/3);\ncout << v.cos() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_cosh.cpp",
    "content": "ArrayXd v = ArrayXd::LinSpaced(5,0,1);\ncout << cosh(v) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_cube.cpp",
    "content": "Array3d v(2,3,4);\ncout << v.cube() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_equal_equal.cpp",
    "content": "Array3d v(1,2,3), w(3,2,1);\ncout << (v==w) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_exp.cpp",
    "content": "Array3d v(1,2,3);\ncout << v.exp() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_floor.cpp",
    "content": "ArrayXd v = ArrayXd::LinSpaced(7,-2,2);\ncout << v << endl << endl;\ncout << floor(v) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_greater.cpp",
    "content": "Array3d v(1,2,3), w(3,2,1);\ncout << (v>w) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_greater_equal.cpp",
    "content": "Array3d v(1,2,3), w(3,2,1);\ncout << (v>=w) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_inverse.cpp",
    "content": "Array3d v(2,3,4);\ncout << v.inverse() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_isFinite.cpp",
    "content": "Array3d v(1,2,3);\nv(1) *= 0.0/0.0;\nv(2) /= 0.0;\ncout << v << endl << endl;\ncout << isfinite(v) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_isInf.cpp",
    "content": "Array3d v(1,2,3);\nv(1) *= 0.0/0.0;\nv(2) /= 0.0;\ncout << v << endl << endl;\ncout << isinf(v) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_isNaN.cpp",
    "content": "Array3d v(1,2,3);\nv(1) *= 0.0/0.0;\nv(2) /= 0.0;\ncout << v << endl << endl;\ncout << isnan(v) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_less.cpp",
    "content": "Array3d v(1,2,3), w(3,2,1);\ncout << (v<w) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_less_equal.cpp",
    "content": "Array3d v(1,2,3), w(3,2,1);\ncout << (v<=w) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_log.cpp",
    "content": "Array3d v(1,2,3);\ncout << v.log() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_log10.cpp",
    "content": "Array4d v(-1,0,1,2);\ncout << log10(v) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_max.cpp",
    "content": "Array3d v(2,3,4), w(4,2,3);\ncout << v.max(w) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_min.cpp",
    "content": "Array3d v(2,3,4), w(4,2,3);\ncout << v.min(w) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_minus.cpp",
    "content": "Array3d v(1,2,3);\ncout << v-5 << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_minus_equal.cpp",
    "content": "Array3d v(1,2,3);\nv -= 5;\ncout << v << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_not_equal.cpp",
    "content": "Array3d v(1,2,3), w(3,2,1);\ncout << (v!=w) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_plus.cpp",
    "content": "Array3d v(1,2,3);\ncout << v+5 << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_plus_equal.cpp",
    "content": "Array3d v(1,2,3);\nv += 5;\ncout << v << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_pow.cpp",
    "content": "Array3d v(8,27,64);\ncout << v.pow(0.333333) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_product.cpp",
    "content": "Array33i a = Array33i::Random(), b = Array33i::Random();\nArray33i c = a * b;\ncout << \"a:\\n\" << a << \"\\nb:\\n\" << b << \"\\nc:\\n\" << c << endl;\n\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_quotient.cpp",
    "content": "Array3d v(2,3,4), w(4,2,3);\ncout << v/w << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_round.cpp",
    "content": "ArrayXd v = ArrayXd::LinSpaced(7,-2,2);\ncout << v << endl << endl;\ncout << round(v) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_scalar_power_array.cpp",
    "content": "Array<double,1,3> e(2,-3,1./3.);\ncout << \"10^[\" << e << \"] = \" << pow(10,e) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_sign.cpp",
    "content": "Array3d v(-3,5,0);\ncout << v.sign() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_sin.cpp",
    "content": "Array3d v(M_PI, M_PI/2, M_PI/3);\ncout << v.sin() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_sinh.cpp",
    "content": "ArrayXd v = ArrayXd::LinSpaced(5,0,1);\ncout << sinh(v) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_slash_equal.cpp",
    "content": "Array3d v(3,2,4), w(5,4,2);\nv /= w;\ncout << v << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_sqrt.cpp",
    "content": "Array3d v(1,2,4);\ncout << v.sqrt() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_square.cpp",
    "content": "Array3d v(2,3,4);\ncout << v.square() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_tan.cpp",
    "content": "Array3d v(M_PI, M_PI/2, M_PI/3);\ncout << v.tan() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_tanh.cpp",
    "content": "ArrayXd v = ArrayXd::LinSpaced(5,0,1);\ncout << tanh(v) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Cwise_times_equal.cpp",
    "content": "Array3d v(1,2,3), w(2,3,0);\nv *= w;\ncout << v << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/DenseBase_LinSpaced.cpp",
    "content": "cout << VectorXi::LinSpaced(4,7,10).transpose() << endl;\ncout << VectorXd::LinSpaced(5,0.0,1.0).transpose() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/DenseBase_LinSpacedInt.cpp",
    "content": "cout << \"Even spacing inputs:\" << endl;\ncout << VectorXi::LinSpaced(8,1,4).transpose() << endl;\ncout << VectorXi::LinSpaced(8,1,8).transpose() << endl;\ncout << VectorXi::LinSpaced(8,1,15).transpose() << endl;\ncout << \"Uneven spacing inputs:\" << endl;\ncout << VectorXi::LinSpaced(8,1,7).transpose() << endl;\ncout << VectorXi::LinSpaced(8,1,9).transpose() << endl;\ncout << VectorXi::LinSpaced(8,1,16).transpose() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/DenseBase_LinSpaced_seq.cpp",
    "content": "cout << VectorXi::LinSpaced(Sequential,4,7,10).transpose() << endl;\ncout << VectorXd::LinSpaced(Sequential,5,0.0,1.0).transpose() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/DenseBase_setLinSpaced.cpp",
    "content": "VectorXf v;\nv.setLinSpaced(5,0.5f,1.5f);\ncout << v << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/DirectionWise_hnormalized.cpp",
    "content": "typedef Matrix<double,4,Dynamic> Matrix4Xd;\nMatrix4Xd M = Matrix4Xd::Random(4,5);\nProjective3d P(Matrix4d::Random());\ncout << \"The matrix M is:\" << endl << M << endl << endl;\ncout << \"M.colwise().hnormalized():\" << endl << M.colwise().hnormalized() << endl << endl;\ncout << \"P*M:\" << endl << P*M << endl << endl;\ncout << \"(P*M).colwise().hnormalized():\" << endl << (P*M).colwise().hnormalized() << endl << endl;"
  },
  {
    "path": "include/eigen3/doc/snippets/DirectionWise_replicate.cpp",
    "content": "MatrixXi m = MatrixXi::Random(2,3);\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"m.colwise().replicate<3>() = ...\" << endl;\ncout << m.colwise().replicate<3>() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/DirectionWise_replicate_int.cpp",
    "content": "Vector3i v = Vector3i::Random();\ncout << \"Here is the vector v:\" << endl << v << endl;\ncout << \"v.rowwise().replicate(5) = ...\" << endl;\ncout << v.rowwise().replicate(5) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/EigenSolver_EigenSolver_MatrixType.cpp",
    "content": "MatrixXd A = MatrixXd::Random(6,6);\ncout << \"Here is a random 6x6 matrix, A:\" << endl << A << endl << endl;\n\nEigenSolver<MatrixXd> es(A);\ncout << \"The eigenvalues of A are:\" << endl << es.eigenvalues() << endl;\ncout << \"The matrix of eigenvectors, V, is:\" << endl << es.eigenvectors() << endl << endl;\n\ncomplex<double> lambda = es.eigenvalues()[0];\ncout << \"Consider the first eigenvalue, lambda = \" << lambda << endl;\nVectorXcd v = es.eigenvectors().col(0);\ncout << \"If v is the corresponding eigenvector, then lambda * v = \" << endl << lambda * v << endl;\ncout << \"... and A * v = \" << endl << A.cast<complex<double> >() * v << endl << endl;\n\nMatrixXcd D = es.eigenvalues().asDiagonal();\nMatrixXcd V = es.eigenvectors();\ncout << \"Finally, V * D * V^(-1) = \" << endl << V * D * V.inverse() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/EigenSolver_compute.cpp",
    "content": "EigenSolver<MatrixXf> es;\nMatrixXf A = MatrixXf::Random(4,4);\nes.compute(A, /* computeEigenvectors = */ false);\ncout << \"The eigenvalues of A are: \" << es.eigenvalues().transpose() << endl;\nes.compute(A + MatrixXf::Identity(4,4), false); // re-use es to compute eigenvalues of A+I\ncout << \"The eigenvalues of A+I are: \" << es.eigenvalues().transpose() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/EigenSolver_eigenvalues.cpp",
    "content": "MatrixXd ones = MatrixXd::Ones(3,3);\nEigenSolver<MatrixXd> es(ones, false);\ncout << \"The eigenvalues of the 3x3 matrix of ones are:\" \n     << endl << es.eigenvalues() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/EigenSolver_eigenvectors.cpp",
    "content": "MatrixXd ones = MatrixXd::Ones(3,3);\nEigenSolver<MatrixXd> es(ones);\ncout << \"The first eigenvector of the 3x3 matrix of ones is:\"\n     << endl << es.eigenvectors().col(0) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/EigenSolver_pseudoEigenvectors.cpp",
    "content": "MatrixXd A = MatrixXd::Random(6,6);\ncout << \"Here is a random 6x6 matrix, A:\" << endl << A << endl << endl;\n\nEigenSolver<MatrixXd> es(A);\nMatrixXd D = es.pseudoEigenvalueMatrix();\nMatrixXd V = es.pseudoEigenvectors();\ncout << \"The pseudo-eigenvalue matrix D is:\" << endl << D << endl;\ncout << \"The pseudo-eigenvector matrix V is:\" << endl << V << endl;\ncout << \"Finally, V * D * V^(-1) = \" << endl << V * D * V.inverse() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/FullPivHouseholderQR_solve.cpp",
    "content": "Matrix3f m = Matrix3f::Random();\nMatrix3f y = Matrix3f::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here is the matrix y:\" << endl << y << endl;\nMatrix3f x;\nx = m.fullPivHouseholderQr().solve(y);\nassert(y.isApprox(m*x));\ncout << \"Here is a solution x to the equation mx=y:\" << endl << x << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/FullPivLU_image.cpp",
    "content": "Matrix3d m;\nm << 1,1,0,\n     1,3,2,\n     0,1,1;\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Notice that the middle column is the sum of the two others, so the \"\n     << \"columns are linearly dependent.\" << endl;\ncout << \"Here is a matrix whose columns have the same span but are linearly independent:\"\n     << endl << m.fullPivLu().image(m) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/FullPivLU_kernel.cpp",
    "content": "MatrixXf m = MatrixXf::Random(3,5);\ncout << \"Here is the matrix m:\" << endl << m << endl;\nMatrixXf ker = m.fullPivLu().kernel();\ncout << \"Here is a matrix whose columns form a basis of the kernel of m:\"\n     << endl << ker << endl;\ncout << \"By definition of the kernel, m*ker is zero:\"\n     << endl << m*ker << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/FullPivLU_solve.cpp",
    "content": "Matrix<float,2,3> m = Matrix<float,2,3>::Random();\nMatrix2f y = Matrix2f::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here is the matrix y:\" << endl << y << endl;\nMatrix<float,3,2> x = m.fullPivLu().solve(y);\nif((m*x).isApprox(y))\n{\n  cout << \"Here is a solution x to the equation mx=y:\" << endl << x << endl;\n}\nelse\n  cout << \"The equation mx=y does not have any solution.\" << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/GeneralizedEigenSolver.cpp",
    "content": "GeneralizedEigenSolver<MatrixXf> ges;\nMatrixXf A = MatrixXf::Random(4,4);\nMatrixXf B = MatrixXf::Random(4,4);\nges.compute(A, B);\ncout << \"The (complex) numerators of the generalzied eigenvalues are: \" << ges.alphas().transpose() << endl;\ncout << \"The (real) denominatore of the generalzied eigenvalues are: \" << ges.betas().transpose() << endl;\ncout << \"The (complex) generalzied eigenvalues are (alphas./beta): \" << ges.eigenvalues().transpose() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/HessenbergDecomposition_compute.cpp",
    "content": "MatrixXcf A = MatrixXcf::Random(4,4);\nHessenbergDecomposition<MatrixXcf> hd(4);\nhd.compute(A);\ncout << \"The matrix H in the decomposition of A is:\" << endl << hd.matrixH() << endl;\nhd.compute(2*A); // re-use hd to compute and store decomposition of 2A\ncout << \"The matrix H in the decomposition of 2A is:\" << endl << hd.matrixH() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/HessenbergDecomposition_matrixH.cpp",
    "content": "Matrix4f A = MatrixXf::Random(4,4);\ncout << \"Here is a random 4x4 matrix:\" << endl << A << endl;\nHessenbergDecomposition<MatrixXf> hessOfA(A);\nMatrixXf H = hessOfA.matrixH();\ncout << \"The Hessenberg matrix H is:\" << endl << H << endl;\nMatrixXf Q = hessOfA.matrixQ();\ncout << \"The orthogonal matrix Q is:\" << endl << Q << endl;\ncout << \"Q H Q^T is:\" << endl << Q * H * Q.transpose() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/HessenbergDecomposition_packedMatrix.cpp",
    "content": "Matrix4d A = Matrix4d::Random(4,4);\ncout << \"Here is a random 4x4 matrix:\" << endl << A << endl;\nHessenbergDecomposition<Matrix4d> hessOfA(A);\nMatrix4d pm = hessOfA.packedMatrix();\ncout << \"The packed matrix M is:\" << endl << pm << endl;\ncout << \"The upper Hessenberg part corresponds to the matrix H, which is:\" \n     << endl << hessOfA.matrixH() << endl;\nVector3d hc = hessOfA.householderCoefficients();\ncout << \"The vector of Householder coefficients is:\" << endl << hc << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/HouseholderQR_householderQ.cpp",
    "content": "MatrixXf A(MatrixXf::Random(5,3)), thinQ(MatrixXf::Identity(5,3)), Q;\nA.setRandom();\nHouseholderQR<MatrixXf> qr(A);\nQ = qr.householderQ();\nthinQ = qr.householderQ() * thinQ;\nstd::cout << \"The complete unitary matrix Q is:\\n\" << Q << \"\\n\\n\";\nstd::cout << \"The thin matrix Q is:\\n\" << thinQ << \"\\n\\n\";\n"
  },
  {
    "path": "include/eigen3/doc/snippets/HouseholderQR_solve.cpp",
    "content": "typedef Matrix<float,3,3> Matrix3x3;\nMatrix3x3 m = Matrix3x3::Random();\nMatrix3f y = Matrix3f::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here is the matrix y:\" << endl << y << endl;\nMatrix3f x;\nx = m.householderQr().solve(y);\nassert(y.isApprox(m*x));\ncout << \"Here is a solution x to the equation mx=y:\" << endl << x << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/HouseholderSequence_HouseholderSequence.cpp",
    "content": "Matrix3d v = Matrix3d::Random();\ncout << \"The matrix v is:\" << endl;\ncout << v << endl;\n\nVector3d v0(1, v(1,0), v(2,0));\ncout << \"The first Householder vector is: v_0 = \" << v0.transpose() << endl;\nVector3d v1(0, 1, v(2,1));\ncout << \"The second Householder vector is: v_1 = \" << v1.transpose()  << endl;\nVector3d v2(0, 0, 1);\ncout << \"The third Householder vector is: v_2 = \" << v2.transpose() << endl;\n\nVector3d h = Vector3d::Random();\ncout << \"The Householder coefficients are: h = \" << h.transpose() << endl;\n\nMatrix3d H0 = Matrix3d::Identity() - h(0) * v0 * v0.adjoint();\ncout << \"The first Householder reflection is represented by H_0 = \" << endl;\ncout << H0 << endl;\nMatrix3d H1 = Matrix3d::Identity() - h(1) * v1 * v1.adjoint();\ncout << \"The second Householder reflection is represented by H_1 = \" << endl;\ncout << H1 << endl;\nMatrix3d H2 = Matrix3d::Identity() - h(2) * v2 * v2.adjoint();\ncout << \"The third Householder reflection is represented by H_2 = \" << endl;\ncout << H2 << endl;\ncout << \"Their product is H_0 H_1 H_2 = \" << endl;\ncout << H0 * H1 * H2 << endl;\n\nHouseholderSequence<Matrix3d, Vector3d> hhSeq(v, h);\nMatrix3d hhSeqAsMatrix(hhSeq);\ncout << \"If we construct a HouseholderSequence from v and h\" << endl;\ncout << \"and convert it to a matrix, we get:\" << endl;\ncout << hhSeqAsMatrix << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/IOFormat.cpp",
    "content": "std::string sep = \"\\n----------------------------------------\\n\";\nMatrix3d m1;\nm1 << 1.111111, 2, 3.33333, 4, 5, 6, 7, 8.888888, 9;\n\nIOFormat CommaInitFmt(StreamPrecision, DontAlignCols, \", \", \", \", \"\", \"\", \" << \", \";\");\nIOFormat CleanFmt(4, 0, \", \", \"\\n\", \"[\", \"]\");\nIOFormat OctaveFmt(StreamPrecision, 0, \", \", \";\\n\", \"\", \"\", \"[\", \"]\");\nIOFormat HeavyFmt(FullPrecision, 0, \", \", \";\\n\", \"[\", \"]\", \"[\", \"]\");\n\nstd::cout << m1 << sep;\nstd::cout << m1.format(CommaInitFmt) << sep;\nstd::cout << m1.format(CleanFmt) << sep;\nstd::cout << m1.format(OctaveFmt) << sep;\nstd::cout << m1.format(HeavyFmt) << sep;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/JacobiSVD_basic.cpp",
    "content": "MatrixXf m = MatrixXf::Random(3,2);\ncout << \"Here is the matrix m:\" << endl << m << endl;\nJacobiSVD<MatrixXf> svd(m, ComputeThinU | ComputeThinV);\ncout << \"Its singular values are:\" << endl << svd.singularValues() << endl;\ncout << \"Its left singular vectors are the columns of the thin U matrix:\" << endl << svd.matrixU() << endl;\ncout << \"Its right singular vectors are the columns of the thin V matrix:\" << endl << svd.matrixV() << endl;\nVector3f rhs(1, 0, 0);\ncout << \"Now consider this rhs vector:\" << endl << rhs << endl;\ncout << \"A least-squares solution of m*x = rhs is:\" << endl << svd.solve(rhs) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Jacobi_makeGivens.cpp",
    "content": "Vector2f v = Vector2f::Random();\nJacobiRotation<float> G;\nG.makeGivens(v.x(), v.y());\ncout << \"Here is the vector v:\" << endl << v << endl;\nv.applyOnTheLeft(0, 1, G.adjoint());\ncout << \"Here is the vector J' * v:\" << endl << v << endl;"
  },
  {
    "path": "include/eigen3/doc/snippets/Jacobi_makeJacobi.cpp",
    "content": "Matrix2f m = Matrix2f::Random();\nm = (m + m.adjoint()).eval();\nJacobiRotation<float> J;\nJ.makeJacobi(m, 0, 1);\ncout << \"Here is the matrix m:\" << endl << m << endl;\nm.applyOnTheLeft(0, 1, J.adjoint());\nm.applyOnTheRight(0, 1, J);\ncout << \"Here is the matrix J' * m * J:\" << endl << m << endl;"
  },
  {
    "path": "include/eigen3/doc/snippets/LLT_example.cpp",
    "content": "MatrixXd A(3,3);\nA << 4,-1,2, -1,6,0, 2,0,5;\ncout << \"The matrix A is\" << endl << A << endl;\n\nLLT<MatrixXd> lltOfA(A); // compute the Cholesky decomposition of A\nMatrixXd L = lltOfA.matrixL(); // retrieve factor L  in the decomposition\n// The previous two lines can also be written as \"L = A.llt().matrixL()\"\n\ncout << \"The Cholesky factor L is\" << endl << L << endl;\ncout << \"To check this, let us compute L * L.transpose()\" << endl;\ncout << L * L.transpose() << endl;\ncout << \"This should equal the matrix A\" << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/LLT_solve.cpp",
    "content": "typedef Matrix<float,Dynamic,2> DataMatrix;\n// let's generate some samples on the 3D plane of equation z = 2x+3y (with some noise)\nDataMatrix samples = DataMatrix::Random(12,2);\nVectorXf elevations = 2*samples.col(0) + 3*samples.col(1) + VectorXf::Random(12)*0.1;\n// and let's solve samples * [x y]^T = elevations in least square sense:\nMatrix<float,2,1> xy\n = (samples.adjoint() * samples).llt().solve((samples.adjoint()*elevations));\ncout << xy << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/LeastSquaresNormalEquations.cpp",
    "content": "MatrixXf A = MatrixXf::Random(3, 2);\nVectorXf b = VectorXf::Random(3);\ncout << \"The solution using normal equations is:\\n\"\n     << (A.transpose() * A).ldlt().solve(A.transpose() * b) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/LeastSquaresQR.cpp",
    "content": "MatrixXf A = MatrixXf::Random(3, 2);\nVectorXf b = VectorXf::Random(3);\ncout << \"The solution using the QR decomposition is:\\n\"\n     << A.colPivHouseholderQr().solve(b) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Map_general_stride.cpp",
    "content": "int array[24];\nfor(int i = 0; i < 24; ++i) array[i] = i;\ncout << Map<MatrixXi, 0, Stride<Dynamic,2> >\n         (array, 3, 3, Stride<Dynamic,2>(8, 2))\n     << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Map_inner_stride.cpp",
    "content": "int array[12];\nfor(int i = 0; i < 12; ++i) array[i] = i;\ncout << Map<VectorXi, 0, InnerStride<2> >\n         (array, 6) // the inner stride has already been passed as template parameter\n     << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Map_outer_stride.cpp",
    "content": "int array[12];\nfor(int i = 0; i < 12; ++i) array[i] = i;\ncout << Map<MatrixXi, 0, OuterStride<> >(array, 3, 3, OuterStride<>(4)) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Map_placement_new.cpp",
    "content": "int data[] = {1,2,3,4,5,6,7,8,9};\nMap<RowVectorXi> v(data,4);\ncout << \"The mapped vector v is: \" << v << \"\\n\";\nnew (&v) Map<RowVectorXi>(data+4,5);\ncout << \"Now v is: \" << v << \"\\n\";"
  },
  {
    "path": "include/eigen3/doc/snippets/Map_simple.cpp",
    "content": "int array[9];\nfor(int i = 0; i < 9; ++i) array[i] = i;\ncout << Map<Matrix3i>(array) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_adjoint.cpp",
    "content": "Matrix2cf m = Matrix2cf::Random();\ncout << \"Here is the 2x2 complex matrix m:\" << endl << m << endl;\ncout << \"Here is the adjoint of m:\" << endl << m.adjoint() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_all.cpp",
    "content": "Vector3f boxMin(Vector3f::Zero()), boxMax(Vector3f::Ones());\nVector3f p0 = Vector3f::Random(), p1 = Vector3f::Random().cwiseAbs();\n// let's check if p0 and p1 are inside the axis aligned box defined by the corners boxMin,boxMax:\ncout << \"Is (\" << p0.transpose() << \") inside the box: \"\n     << ((boxMin.array()<p0.array()).all() && (boxMax.array()>p0.array()).all()) << endl;\ncout << \"Is (\" << p1.transpose() << \") inside the box: \"\n     << ((boxMin.array()<p1.array()).all() && (boxMax.array()>p1.array()).all()) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_applyOnTheLeft.cpp",
    "content": "Matrix3f A = Matrix3f::Random(3,3), B;\nB << 0,1,0,  \n     0,0,1,  \n     1,0,0;\ncout << \"At start, A = \" << endl << A << endl;\nA.applyOnTheLeft(B); \ncout << \"After applyOnTheLeft, A = \" << endl << A << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_applyOnTheRight.cpp",
    "content": "Matrix3f A = Matrix3f::Random(3,3), B;\nB << 0,1,0,  \n     0,0,1,  \n     1,0,0;\ncout << \"At start, A = \" << endl << A << endl;\nA *= B;\ncout << \"After A *= B, A = \" << endl << A << endl;\nA.applyOnTheRight(B);  // equivalent to A *= B\ncout << \"After applyOnTheRight, A = \" << endl << A << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_array.cpp",
    "content": "Vector3d v(1,2,3);\nv.array() += 3;\nv.array() -= 2;\ncout << v << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_array_const.cpp",
    "content": "Vector3d v(-1,2,-3);\ncout << \"the absolute values:\" << endl << v.array().abs() << endl;\ncout << \"the absolute values plus one:\" << endl << v.array().abs()+1 << endl;\ncout << \"sum of the squares: \" << v.array().square().sum() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_asDiagonal.cpp",
    "content": "cout << Matrix3i(Vector3i(2,5,6).asDiagonal()) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_block_int_int.cpp",
    "content": "Matrix4i m = Matrix4i::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here is m.block<2,2>(1,1):\" << endl << m.block<2,2>(1,1) << endl;\nm.block<2,2>(1,1).setZero();\ncout << \"Now the matrix m is:\" << endl << m << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_block_int_int_int_int.cpp",
    "content": "Matrix4i m = Matrix4i::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here is m.block(1, 1, 2, 2):\" << endl << m.block(1, 1, 2, 2) << endl;\nm.block(1, 1, 2, 2).setZero();\ncout << \"Now the matrix m is:\" << endl << m << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_bottomLeftCorner_int_int.cpp",
    "content": "Matrix4i m = Matrix4i::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here is m.bottomLeftCorner(2, 2):\" << endl;\ncout << m.bottomLeftCorner(2, 2) << endl;\nm.bottomLeftCorner(2, 2).setZero();\ncout << \"Now the matrix m is:\" << endl << m << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_bottomRightCorner_int_int.cpp",
    "content": "Matrix4i m = Matrix4i::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here is m.bottomRightCorner(2, 2):\" << endl;\ncout << m.bottomRightCorner(2, 2) << endl;\nm.bottomRightCorner(2, 2).setZero();\ncout << \"Now the matrix m is:\" << endl << m << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_bottomRows_int.cpp",
    "content": "Array44i a = Array44i::Random();\ncout << \"Here is the array a:\" << endl << a << endl;\ncout << \"Here is a.bottomRows(2):\" << endl;\ncout << a.bottomRows(2) << endl;\na.bottomRows(2).setZero();\ncout << \"Now the array a is:\" << endl << a << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_cast.cpp",
    "content": "Matrix2d md = Matrix2d::Identity() * 0.45;\nMatrix2f mf = Matrix2f::Identity();\ncout << md + mf.cast<double>() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_col.cpp",
    "content": "Matrix3d m = Matrix3d::Identity();\nm.col(1) = Vector3d(4,5,6);\ncout << m << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_colwise.cpp",
    "content": "Matrix3d m = Matrix3d::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here is the sum of each column:\" << endl << m.colwise().sum() << endl;\ncout << \"Here is the maximum absolute value of each column:\"\n     << endl << m.cwiseAbs().colwise().maxCoeff() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_computeInverseAndDetWithCheck.cpp",
    "content": "Matrix3d m = Matrix3d::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\nMatrix3d inverse;\nbool invertible;\ndouble determinant;\nm.computeInverseAndDetWithCheck(inverse,determinant,invertible);\ncout << \"Its determinant is \" << determinant << endl;\nif(invertible) {\n  cout << \"It is invertible, and its inverse is:\" << endl << inverse << endl;\n}\nelse {\n  cout << \"It is not invertible.\" << endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_computeInverseWithCheck.cpp",
    "content": "Matrix3d m = Matrix3d::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\nMatrix3d inverse;\nbool invertible;\nm.computeInverseWithCheck(inverse,invertible);\nif(invertible) {\n  cout << \"It is invertible, and its inverse is:\" << endl << inverse << endl;\n}\nelse {\n  cout << \"It is not invertible.\" << endl;\n}\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_cwiseAbs.cpp",
    "content": "MatrixXd m(2,3);\nm << 2, -4, 6,   \n     -5, 1, 0;\ncout << m.cwiseAbs() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_cwiseAbs2.cpp",
    "content": "MatrixXd m(2,3);\nm << 2, -4, 6,   \n     -5, 1, 0;\ncout << m.cwiseAbs2() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_cwiseEqual.cpp",
    "content": "MatrixXi m(2,2);\nm << 1, 0,\n     1, 1;\ncout << \"Comparing m with identity matrix:\" << endl;\ncout << m.cwiseEqual(MatrixXi::Identity(2,2)) << endl;\nint count = m.cwiseEqual(MatrixXi::Identity(2,2)).count();\ncout << \"Number of coefficients that are equal: \" << count << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_cwiseInverse.cpp",
    "content": "MatrixXd m(2,3);\nm << 2, 0.5, 1,   \n     3, 0.25, 1;\ncout << m.cwiseInverse() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_cwiseMax.cpp",
    "content": "Vector3d v(2,3,4), w(4,2,3);\ncout << v.cwiseMax(w) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_cwiseMin.cpp",
    "content": "Vector3d v(2,3,4), w(4,2,3);\ncout << v.cwiseMin(w) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_cwiseNotEqual.cpp",
    "content": "MatrixXi m(2,2);\nm << 1, 0,\n     1, 1;\ncout << \"Comparing m with identity matrix:\" << endl;\ncout << m.cwiseNotEqual(MatrixXi::Identity(2,2)) << endl;\nint count = m.cwiseNotEqual(MatrixXi::Identity(2,2)).count();\ncout << \"Number of coefficients that are not equal: \" << count << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_cwiseProduct.cpp",
    "content": "Matrix3i a = Matrix3i::Random(), b = Matrix3i::Random();\nMatrix3i c = a.cwiseProduct(b);\ncout << \"a:\\n\" << a << \"\\nb:\\n\" << b << \"\\nc:\\n\" << c << endl;\n\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_cwiseQuotient.cpp",
    "content": "Vector3d v(2,3,4), w(4,2,3);\ncout << v.cwiseQuotient(w) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_cwiseSign.cpp",
    "content": "MatrixXd m(2,3);\nm <<  2, -4, 6,\n     -5,  1, 0;\ncout << m.cwiseSign() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_cwiseSqrt.cpp",
    "content": "Vector3d v(1,2,4);\ncout << v.cwiseSqrt() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_diagonal.cpp",
    "content": "Matrix3i m = Matrix3i::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here are the coefficients on the main diagonal of m:\" << endl\n     << m.diagonal() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_diagonal_int.cpp",
    "content": "Matrix4i m = Matrix4i::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m:\" << endl\n     << m.diagonal(1).transpose() << endl\n     << m.diagonal(-2).transpose() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_diagonal_template_int.cpp",
    "content": "Matrix4i m = Matrix4i::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m:\" << endl\n     << m.diagonal<1>().transpose() << endl\n     << m.diagonal<-2>().transpose() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_eigenvalues.cpp",
    "content": "MatrixXd ones = MatrixXd::Ones(3,3);\nVectorXcd eivals = ones.eigenvalues();\ncout << \"The eigenvalues of the 3x3 matrix of ones are:\" << endl << eivals << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_end_int.cpp",
    "content": "RowVector4i v = RowVector4i::Random();\ncout << \"Here is the vector v:\" << endl << v << endl;\ncout << \"Here is v.tail(2):\" << endl << v.tail(2) << endl;\nv.tail(2).setZero();\ncout << \"Now the vector v is:\" << endl << v << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_eval.cpp",
    "content": "Matrix2f M = Matrix2f::Random();\nMatrix2f m;\nm = M;\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Now we want to copy a column into a row.\" << endl;\ncout << \"If we do m.col(1) = m.row(0), then m becomes:\" << endl;\nm.col(1) = m.row(0);\ncout << m << endl << \"which is wrong!\" << endl;\ncout << \"Now let us instead do m.col(1) = m.row(0).eval(). Then m becomes\" << endl;\nm = M;\nm.col(1) = m.row(0).eval();\ncout << m << endl << \"which is right.\" << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_fixedBlock_int_int.cpp",
    "content": "Matrix4d m = Vector4d(1,2,3,4).asDiagonal();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here is m.fixed<2, 2>(2, 2):\" << endl << m.block<2, 2>(2, 2) << endl;\nm.block<2, 2>(2, 0) = m.block<2, 2>(2, 2);\ncout << \"Now the matrix m is:\" << endl << m << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_hnormalized.cpp",
    "content": "Vector4d v = Vector4d::Random();\nProjective3d P(Matrix4d::Random());\ncout << \"v                   = \" << v.transpose() << \"]^T\" << endl;\ncout << \"v.hnormalized()     = \" << v.hnormalized().transpose() << \"]^T\" << endl;\ncout << \"P*v                 = \" << (P*v).transpose() << \"]^T\" << endl;\ncout << \"(P*v).hnormalized() = \" << (P*v).hnormalized().transpose() << \"]^T\" << endl;"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_homogeneous.cpp",
    "content": "Vector3d v = Vector3d::Random(), w;\nProjective3d P(Matrix4d::Random());\ncout << \"v                                   = [\" << v.transpose() << \"]^T\" << endl;\ncout << \"h.homogeneous()                     = [\" << v.homogeneous().transpose() << \"]^T\" << endl;\ncout << \"(P * v.homogeneous())               = [\" << (P * v.homogeneous()).transpose() << \"]^T\" << endl;\ncout << \"(P * v.homogeneous()).hnormalized() = [\" << (P * v.homogeneous()).eval().hnormalized().transpose() << \"]^T\" << endl;"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_identity.cpp",
    "content": "cout << Matrix<double, 3, 4>::Identity() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_identity_int_int.cpp",
    "content": "cout << MatrixXd::Identity(4, 3) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_inverse.cpp",
    "content": "Matrix3d m = Matrix3d::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Its inverse is:\" << endl << m.inverse() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_isDiagonal.cpp",
    "content": "Matrix3d m = 10000 * Matrix3d::Identity();\nm(0,2) = 1;\ncout << \"Here's the matrix m:\" << endl << m << endl;\ncout << \"m.isDiagonal() returns: \" << m.isDiagonal() << endl;\ncout << \"m.isDiagonal(1e-3) returns: \" << m.isDiagonal(1e-3) << endl;\n\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_isIdentity.cpp",
    "content": "Matrix3d m = Matrix3d::Identity();\nm(0,2) = 1e-4;\ncout << \"Here's the matrix m:\" << endl << m << endl;\ncout << \"m.isIdentity() returns: \" << m.isIdentity() << endl;\ncout << \"m.isIdentity(1e-3) returns: \" << m.isIdentity(1e-3) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_isOnes.cpp",
    "content": "Matrix3d m = Matrix3d::Ones();\nm(0,2) += 1e-4;\ncout << \"Here's the matrix m:\" << endl << m << endl;\ncout << \"m.isOnes() returns: \" << m.isOnes() << endl;\ncout << \"m.isOnes(1e-3) returns: \" << m.isOnes(1e-3) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_isOrthogonal.cpp",
    "content": "Vector3d v(1,0,0);\nVector3d w(1e-4,0,1);\ncout << \"Here's the vector v:\" << endl << v << endl;\ncout << \"Here's the vector w:\" << endl << w << endl;\ncout << \"v.isOrthogonal(w) returns: \" << v.isOrthogonal(w) << endl;\ncout << \"v.isOrthogonal(w,1e-3) returns: \" << v.isOrthogonal(w,1e-3) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_isUnitary.cpp",
    "content": "Matrix3d m = Matrix3d::Identity();\nm(0,2) = 1e-4;\ncout << \"Here's the matrix m:\" << endl << m << endl;\ncout << \"m.isUnitary() returns: \" << m.isUnitary() << endl;\ncout << \"m.isUnitary(1e-3) returns: \" << m.isUnitary(1e-3) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_isZero.cpp",
    "content": "Matrix3d m = Matrix3d::Zero();\nm(0,2) = 1e-4;\ncout << \"Here's the matrix m:\" << endl << m << endl;\ncout << \"m.isZero() returns: \" << m.isZero() << endl;\ncout << \"m.isZero(1e-3) returns: \" << m.isZero(1e-3) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_leftCols_int.cpp",
    "content": "Array44i a = Array44i::Random();\ncout << \"Here is the array a:\" << endl << a << endl;\ncout << \"Here is a.leftCols(2):\" << endl;\ncout << a.leftCols(2) << endl;\na.leftCols(2).setZero();\ncout << \"Now the array a is:\" << endl << a << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_noalias.cpp",
    "content": "Matrix2d a, b, c; a << 1,2,3,4; b << 5,6,7,8;\nc.noalias() = a * b; // this computes the product directly to c\ncout << c << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_ones.cpp",
    "content": "cout << Matrix2d::Ones() << endl;\ncout << 6 * RowVector4i::Ones() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_ones_int.cpp",
    "content": "cout << 6 * RowVectorXi::Ones(4) << endl;\ncout << VectorXf::Ones(2) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_ones_int_int.cpp",
    "content": "cout << MatrixXi::Ones(2,3) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_operatorNorm.cpp",
    "content": "MatrixXd ones = MatrixXd::Ones(3,3);\ncout << \"The operator norm of the 3x3 matrix of ones is \"\n     << ones.operatorNorm() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_prod.cpp",
    "content": "Matrix3d m = Matrix3d::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here is the product of all the coefficients:\" << endl << m.prod() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_random.cpp",
    "content": "cout << 100 * Matrix2i::Random() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_random_int.cpp",
    "content": "cout << VectorXi::Random(2) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_random_int_int.cpp",
    "content": "cout << MatrixXi::Random(2,3) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_replicate.cpp",
    "content": "MatrixXi m = MatrixXi::Random(2,3);\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"m.replicate<3,2>() = ...\" << endl;\ncout << m.replicate<3,2>() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_replicate_int_int.cpp",
    "content": "Vector3i v = Vector3i::Random();\ncout << \"Here is the vector v:\" << endl << v << endl;\ncout << \"v.replicate(2,5) = ...\" << endl;\ncout << v.replicate(2,5) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_reverse.cpp",
    "content": "MatrixXi m = MatrixXi::Random(3,4);\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here is the reverse of m:\" << endl << m.reverse() << endl;\ncout << \"Here is the coefficient (1,0) in the reverse of m:\" << endl\n     << m.reverse()(1,0) << endl;\ncout << \"Let us overwrite this coefficient with the value 4.\" << endl;\nm.reverse()(1,0) = 4;\ncout << \"Now the matrix m is:\" << endl << m << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_rightCols_int.cpp",
    "content": "Array44i a = Array44i::Random();\ncout << \"Here is the array a:\" << endl << a << endl;\ncout << \"Here is a.rightCols(2):\" << endl;\ncout << a.rightCols(2) << endl;\na.rightCols(2).setZero();\ncout << \"Now the array a is:\" << endl << a << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_row.cpp",
    "content": "Matrix3d m = Matrix3d::Identity();\nm.row(1) = Vector3d(4,5,6);\ncout << m << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_rowwise.cpp",
    "content": "Matrix3d m = Matrix3d::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here is the sum of each row:\" << endl << m.rowwise().sum() << endl;\ncout << \"Here is the maximum absolute value of each row:\"\n     << endl << m.cwiseAbs().rowwise().maxCoeff() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_segment_int_int.cpp",
    "content": "RowVector4i v = RowVector4i::Random();\ncout << \"Here is the vector v:\" << endl << v << endl;\ncout << \"Here is v.segment(1, 2):\" << endl << v.segment(1, 2) << endl;\nv.segment(1, 2).setZero();\ncout << \"Now the vector v is:\" << endl << v << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_select.cpp",
    "content": "MatrixXi m(3, 3);\nm << 1, 2, 3,\n     4, 5, 6,\n     7, 8, 9;\nm = (m.array() >= 5).select(-m, m);\ncout << m << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_selfadjointView.cpp",
    "content": "Matrix3i m = Matrix3i::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here is the symmetric matrix extracted from the upper part of m:\" << endl\n     << Matrix3i(m.selfadjointView<Upper>()) << endl;\ncout << \"Here is the symmetric matrix extracted from the lower part of m:\" << endl\n     << Matrix3i(m.selfadjointView<Lower>()) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_set.cpp",
    "content": "Matrix3i m1;\nm1 << 1, 2, 3,\n      4, 5, 6,\n      7, 8, 9;\ncout << m1 << endl << endl;\nMatrix3i m2 = Matrix3i::Identity();\nm2.block(0,0, 2,2) << 10, 11, 12, 13;\ncout << m2 << endl << endl;\nVector2i v1;\nv1 << 14, 15;\nm2 << v1.transpose(), 16,\n      v1, m1.block(1,1,2,2);\ncout << m2 << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_setIdentity.cpp",
    "content": "Matrix4i m = Matrix4i::Zero();\nm.block<3,3>(1,0).setIdentity();\ncout << m << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_setOnes.cpp",
    "content": "Matrix4i m = Matrix4i::Random();\nm.row(1).setOnes();\ncout << m << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_setRandom.cpp",
    "content": "Matrix4i m = Matrix4i::Zero();\nm.col(1).setRandom();\ncout << m << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_setZero.cpp",
    "content": "Matrix4i m = Matrix4i::Random();\nm.row(1).setZero();\ncout << m << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_start_int.cpp",
    "content": "RowVector4i v = RowVector4i::Random();\ncout << \"Here is the vector v:\" << endl << v << endl;\ncout << \"Here is v.head(2):\" << endl << v.head(2) << endl;\nv.head(2).setZero();\ncout << \"Now the vector v is:\" << endl << v << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_template_int_bottomRows.cpp",
    "content": "Array44i a = Array44i::Random();\ncout << \"Here is the array a:\" << endl << a << endl;\ncout << \"Here is a.bottomRows<2>():\" << endl;\ncout << a.bottomRows<2>() << endl;\na.bottomRows<2>().setZero();\ncout << \"Now the array a is:\" << endl << a << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_template_int_end.cpp",
    "content": "RowVector4i v = RowVector4i::Random();\ncout << \"Here is the vector v:\" << endl << v << endl;\ncout << \"Here is v.tail(2):\" << endl << v.tail<2>() << endl;\nv.tail<2>().setZero();\ncout << \"Now the vector v is:\" << endl << v << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_template_int_int_block_int_int_int_int.cpp",
    "content": "Matrix4i m = Matrix4i::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here is the block:\" << endl << m.block<2, Dynamic>(1, 1, 2, 3) << endl;\nm.block<2, Dynamic>(1, 1, 2, 3).setZero();\ncout << \"Now the matrix m is:\" << endl << m << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_template_int_int_bottomLeftCorner.cpp",
    "content": "Matrix4i m = Matrix4i::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here is m.bottomLeftCorner<2,2>():\" << endl;\ncout << m.bottomLeftCorner<2,2>() << endl;\nm.bottomLeftCorner<2,2>().setZero();\ncout << \"Now the matrix m is:\" << endl << m << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_template_int_int_bottomLeftCorner_int_int.cpp",
    "content": "Matrix4i m = Matrix4i::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here is m.bottomLeftCorner<2,Dynamic>(2,2):\" << endl;\ncout << m.bottomLeftCorner<2,Dynamic>(2,2) << endl;\nm.bottomLeftCorner<2,Dynamic>(2,2).setZero();\ncout << \"Now the matrix m is:\" << endl << m << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_template_int_int_bottomRightCorner.cpp",
    "content": "Matrix4i m = Matrix4i::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here is m.bottomRightCorner<2,2>():\" << endl;\ncout << m.bottomRightCorner<2,2>() << endl;\nm.bottomRightCorner<2,2>().setZero();\ncout << \"Now the matrix m is:\" << endl << m << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_template_int_int_bottomRightCorner_int_int.cpp",
    "content": "Matrix4i m = Matrix4i::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here is m.bottomRightCorner<2,Dynamic>(2,2):\" << endl;\ncout << m.bottomRightCorner<2,Dynamic>(2,2) << endl;\nm.bottomRightCorner<2,Dynamic>(2,2).setZero();\ncout << \"Now the matrix m is:\" << endl << m << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_template_int_int_topLeftCorner.cpp",
    "content": "Matrix4i m = Matrix4i::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here is m.topLeftCorner<2,2>():\" << endl;\ncout << m.topLeftCorner<2,2>() << endl;\nm.topLeftCorner<2,2>().setZero();\ncout << \"Now the matrix m is:\" << endl << m << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_template_int_int_topLeftCorner_int_int.cpp",
    "content": "Matrix4i m = Matrix4i::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here is m.topLeftCorner<2,Dynamic>(2,2):\" << endl;\ncout << m.topLeftCorner<2,Dynamic>(2,2) << endl;\nm.topLeftCorner<2,Dynamic>(2,2).setZero();\ncout << \"Now the matrix m is:\" << endl << m << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_template_int_int_topRightCorner.cpp",
    "content": "Matrix4i m = Matrix4i::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here is m.topRightCorner<2,2>():\" << endl;\ncout << m.topRightCorner<2,2>() << endl;\nm.topRightCorner<2,2>().setZero();\ncout << \"Now the matrix m is:\" << endl << m << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_template_int_int_topRightCorner_int_int.cpp",
    "content": "Matrix4i m = Matrix4i::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here is m.topRightCorner<2,Dynamic>(2,2):\" << endl;\ncout << m.topRightCorner<2,Dynamic>(2,2) << endl;\nm.topRightCorner<2,Dynamic>(2,2).setZero();\ncout << \"Now the matrix m is:\" << endl << m << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_template_int_leftCols.cpp",
    "content": "Array44i a = Array44i::Random();\ncout << \"Here is the array a:\" << endl << a << endl;\ncout << \"Here is a.leftCols<2>():\" << endl;\ncout << a.leftCols<2>() << endl;\na.leftCols<2>().setZero();\ncout << \"Now the array a is:\" << endl << a << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_template_int_rightCols.cpp",
    "content": "Array44i a = Array44i::Random();\ncout << \"Here is the array a:\" << endl << a << endl;\ncout << \"Here is a.rightCols<2>():\" << endl;\ncout << a.rightCols<2>() << endl;\na.rightCols<2>().setZero();\ncout << \"Now the array a is:\" << endl << a << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_template_int_segment.cpp",
    "content": "RowVector4i v = RowVector4i::Random();\ncout << \"Here is the vector v:\" << endl << v << endl;\ncout << \"Here is v.segment<2>(1):\" << endl << v.segment<2>(1) << endl;\nv.segment<2>(2).setZero();\ncout << \"Now the vector v is:\" << endl << v << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_template_int_start.cpp",
    "content": "RowVector4i v = RowVector4i::Random();\ncout << \"Here is the vector v:\" << endl << v << endl;\ncout << \"Here is v.head(2):\" << endl << v.head<2>() << endl;\nv.head<2>().setZero();\ncout << \"Now the vector v is:\" << endl << v << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_template_int_topRows.cpp",
    "content": "Array44i a = Array44i::Random();\ncout << \"Here is the array a:\" << endl << a << endl;\ncout << \"Here is a.topRows<2>():\" << endl;\ncout << a.topRows<2>() << endl;\na.topRows<2>().setZero();\ncout << \"Now the array a is:\" << endl << a << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_topLeftCorner_int_int.cpp",
    "content": "Matrix4i m = Matrix4i::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here is m.topLeftCorner(2, 2):\" << endl;\ncout << m.topLeftCorner(2, 2) << endl;\nm.topLeftCorner(2, 2).setZero();\ncout << \"Now the matrix m is:\" << endl << m << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_topRightCorner_int_int.cpp",
    "content": "Matrix4i m = Matrix4i::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here is m.topRightCorner(2, 2):\" << endl;\ncout << m.topRightCorner(2, 2) << endl;\nm.topRightCorner(2, 2).setZero();\ncout << \"Now the matrix m is:\" << endl << m << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_topRows_int.cpp",
    "content": "Array44i a = Array44i::Random();\ncout << \"Here is the array a:\" << endl << a << endl;\ncout << \"Here is a.topRows(2):\" << endl;\ncout << a.topRows(2) << endl;\na.topRows(2).setZero();\ncout << \"Now the array a is:\" << endl << a << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_transpose.cpp",
    "content": "Matrix2i m = Matrix2i::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here is the transpose of m:\" << endl << m.transpose() << endl;\ncout << \"Here is the coefficient (1,0) in the transpose of m:\" << endl\n     << m.transpose()(1,0) << endl;\ncout << \"Let us overwrite this coefficient with the value 0.\" << endl;\nm.transpose()(1,0) = 0;\ncout << \"Now the matrix m is:\" << endl << m << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_triangularView.cpp",
    "content": "Matrix3i m = Matrix3i::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here is the upper-triangular matrix extracted from m:\" << endl\n     << Matrix3i(m.triangularView<Eigen::Upper>()) << endl;\ncout << \"Here is the strictly-upper-triangular matrix extracted from m:\" << endl\n     << Matrix3i(m.triangularView<Eigen::StrictlyUpper>()) << endl;\ncout << \"Here is the unit-lower-triangular matrix extracted from m:\" << endl\n     << Matrix3i(m.triangularView<Eigen::UnitLower>()) << endl;\n// FIXME need to implement output for triangularViews (Bug 885)\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_zero.cpp",
    "content": "cout << Matrix2d::Zero() << endl;\ncout << RowVector4i::Zero() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_zero_int.cpp",
    "content": "cout << RowVectorXi::Zero(4) << endl;\ncout << VectorXf::Zero(2) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/MatrixBase_zero_int_int.cpp",
    "content": "cout << MatrixXi::Zero(2,3) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Matrix_Map_stride.cpp",
    "content": "Matrix4i A;\nA << 1,  2,  3,  4,\n     5,  6,  7,  8,\n     9, 10, 11, 12,\n    13, 14, 15, 16;\n\nstd::cout << Matrix2i::Map(&A(1,1),Stride<8,2>()) << std::endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Matrix_resize_NoChange_int.cpp",
    "content": "MatrixXd m(3,4);\nm.resize(NoChange, 5);\ncout << \"m: \" << m.rows() << \" rows, \" << m.cols() << \" cols\" << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Matrix_resize_int.cpp",
    "content": "VectorXd v(10);\nv.resize(3);\nRowVector3d w;\nw.resize(3); // this is legal, but has no effect\ncout << \"v: \" << v.rows() << \" rows, \" << v.cols() << \" cols\" << endl;\ncout << \"w: \" << w.rows() << \" rows, \" << w.cols() << \" cols\" << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Matrix_resize_int_NoChange.cpp",
    "content": "MatrixXd m(3,4);\nm.resize(5, NoChange);\ncout << \"m: \" << m.rows() << \" rows, \" << m.cols() << \" cols\" << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Matrix_resize_int_int.cpp",
    "content": "MatrixXd m(2,3);\nm << 1,2,3,4,5,6;\ncout << \"here's the 2x3 matrix m:\" << endl << m << endl;\ncout << \"let's resize m to 3x2. This is a conservative resizing because 2*3==3*2.\" << endl;\nm.resize(3,2);\ncout << \"here's the 3x2 matrix m:\" << endl << m << endl;\ncout << \"now let's resize m to size 2x2. This is NOT a conservative resizing, so it becomes uninitialized:\" << endl;\nm.resize(2,2);\ncout << m << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Matrix_setConstant_int.cpp",
    "content": "VectorXf v;\nv.setConstant(3, 5);\ncout << v << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Matrix_setConstant_int_int.cpp",
    "content": "MatrixXf m;\nm.setConstant(3, 3, 5);\ncout << m << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Matrix_setIdentity_int_int.cpp",
    "content": "MatrixXf m;\nm.setIdentity(3, 3);\ncout << m << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Matrix_setOnes_int.cpp",
    "content": "VectorXf v;\nv.setOnes(3);\ncout << v << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Matrix_setOnes_int_int.cpp",
    "content": "MatrixXf m;\nm.setOnes(3, 3);\ncout << m << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Matrix_setRandom_int.cpp",
    "content": "VectorXf v;\nv.setRandom(3);\ncout << v << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Matrix_setRandom_int_int.cpp",
    "content": "MatrixXf m;\nm.setRandom(3, 3);\ncout << m << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Matrix_setZero_int.cpp",
    "content": "VectorXf v;\nv.setZero(3);\ncout << v << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Matrix_setZero_int_int.cpp",
    "content": "MatrixXf m;\nm.setZero(3, 3);\ncout << m << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/PartialPivLU_solve.cpp",
    "content": "MatrixXd A = MatrixXd::Random(3,3);\nMatrixXd B = MatrixXd::Random(3,2);\ncout << \"Here is the invertible matrix A:\" << endl << A << endl;\ncout << \"Here is the matrix B:\" << endl << B << endl;\nMatrixXd X = A.lu().solve(B);\ncout << \"Here is the (unique) solution X to the equation AX=B:\" << endl << X << endl;\ncout << \"Relative error: \" << (A*X-B).norm() / B.norm() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/PartialRedux_count.cpp",
    "content": "Matrix3d m = Matrix3d::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\nMatrix<ptrdiff_t, 3, 1> res = (m.array() >= 0.5).rowwise().count();\ncout << \"Here is the count of elements larger or equal than 0.5 of each row:\" << endl;\ncout << res << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/PartialRedux_maxCoeff.cpp",
    "content": "Matrix3d m = Matrix3d::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here is the maximum of each column:\" << endl << m.colwise().maxCoeff() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/PartialRedux_minCoeff.cpp",
    "content": "Matrix3d m = Matrix3d::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here is the minimum of each column:\" << endl << m.colwise().minCoeff() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/PartialRedux_norm.cpp",
    "content": "Matrix3d m = Matrix3d::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here is the norm of each column:\" << endl << m.colwise().norm() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/PartialRedux_prod.cpp",
    "content": "Matrix3d m = Matrix3d::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here is the product of each row:\" << endl << m.rowwise().prod() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/PartialRedux_squaredNorm.cpp",
    "content": "Matrix3d m = Matrix3d::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here is the square norm of each row:\" << endl << m.rowwise().squaredNorm() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/PartialRedux_sum.cpp",
    "content": "Matrix3d m = Matrix3d::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here is the sum of each row:\" << endl << m.rowwise().sum() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/RealQZ_compute.cpp",
    "content": "MatrixXf A = MatrixXf::Random(4,4);\nMatrixXf B = MatrixXf::Random(4,4);\nRealQZ<MatrixXf> qz(4); // preallocate space for 4x4 matrices\nqz.compute(A,B);  // A = Q S Z,  B = Q T Z\n\n// print original matrices and result of decomposition\ncout << \"A:\\n\" << A << \"\\n\" << \"B:\\n\" << B << \"\\n\";\ncout << \"S:\\n\" << qz.matrixS() << \"\\n\" << \"T:\\n\" << qz.matrixT() << \"\\n\";\ncout << \"Q:\\n\" << qz.matrixQ() << \"\\n\" << \"Z:\\n\" << qz.matrixZ() << \"\\n\";\n\n// verify precision\ncout << \"\\nErrors:\"\n  << \"\\n|A-QSZ|: \" << (A-qz.matrixQ()*qz.matrixS()*qz.matrixZ()).norm()\n  << \", |B-QTZ|: \" << (B-qz.matrixQ()*qz.matrixT()*qz.matrixZ()).norm()\n  << \"\\n|QQ* - I|: \" << (qz.matrixQ()*qz.matrixQ().adjoint() - MatrixXf::Identity(4,4)).norm()\n  << \", |ZZ* - I|: \" << (qz.matrixZ()*qz.matrixZ().adjoint() - MatrixXf::Identity(4,4)).norm()\n  << \"\\n\";\n"
  },
  {
    "path": "include/eigen3/doc/snippets/RealSchur_RealSchur_MatrixType.cpp",
    "content": "MatrixXd A = MatrixXd::Random(6,6);\ncout << \"Here is a random 6x6 matrix, A:\" << endl << A << endl << endl;\n\nRealSchur<MatrixXd> schur(A);\ncout << \"The orthogonal matrix U is:\" << endl << schur.matrixU() << endl;\ncout << \"The quasi-triangular matrix T is:\" << endl << schur.matrixT() << endl << endl;\n\nMatrixXd U = schur.matrixU();\nMatrixXd T = schur.matrixT();\ncout << \"U * T * U^T = \" << endl << U * T * U.transpose() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/RealSchur_compute.cpp",
    "content": "MatrixXf A = MatrixXf::Random(4,4);\nRealSchur<MatrixXf> schur(4);\nschur.compute(A, /* computeU = */ false);\ncout << \"The matrix T in the decomposition of A is:\" << endl << schur.matrixT() << endl;\nschur.compute(A.inverse(), /* computeU = */ false);\ncout << \"The matrix T in the decomposition of A^(-1) is:\" << endl << schur.matrixT() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/SelfAdjointEigenSolver_SelfAdjointEigenSolver.cpp",
    "content": "SelfAdjointEigenSolver<Matrix4f> es;\nMatrix4f X = Matrix4f::Random(4,4);\nMatrix4f A = X + X.transpose();\nes.compute(A);\ncout << \"The eigenvalues of A are: \" << es.eigenvalues().transpose() << endl;\nes.compute(A + Matrix4f::Identity(4,4)); // re-use es to compute eigenvalues of A+I\ncout << \"The eigenvalues of A+I are: \" << es.eigenvalues().transpose() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType.cpp",
    "content": "MatrixXd X = MatrixXd::Random(5,5);\nMatrixXd A = X + X.transpose();\ncout << \"Here is a random symmetric 5x5 matrix, A:\" << endl << A << endl << endl;\n\nSelfAdjointEigenSolver<MatrixXd> es(A);\ncout << \"The eigenvalues of A are:\" << endl << es.eigenvalues() << endl;\ncout << \"The matrix of eigenvectors, V, is:\" << endl << es.eigenvectors() << endl << endl;\n\ndouble lambda = es.eigenvalues()[0];\ncout << \"Consider the first eigenvalue, lambda = \" << lambda << endl;\nVectorXd v = es.eigenvectors().col(0);\ncout << \"If v is the corresponding eigenvector, then lambda * v = \" << endl << lambda * v << endl;\ncout << \"... and A * v = \" << endl << A * v << endl << endl;\n\nMatrixXd D = es.eigenvalues().asDiagonal();\nMatrixXd V = es.eigenvectors();\ncout << \"Finally, V * D * V^(-1) = \" << endl << V * D * V.inverse() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType2.cpp",
    "content": "MatrixXd X = MatrixXd::Random(5,5);\nMatrixXd A = X + X.transpose();\ncout << \"Here is a random symmetric matrix, A:\" << endl << A << endl;\nX = MatrixXd::Random(5,5);\nMatrixXd B = X * X.transpose();\ncout << \"and a random postive-definite matrix, B:\" << endl << B << endl << endl;\n\nGeneralizedSelfAdjointEigenSolver<MatrixXd> es(A,B);\ncout << \"The eigenvalues of the pencil (A,B) are:\" << endl << es.eigenvalues() << endl;\ncout << \"The matrix of eigenvectors, V, is:\" << endl << es.eigenvectors() << endl << endl;\n\ndouble lambda = es.eigenvalues()[0];\ncout << \"Consider the first eigenvalue, lambda = \" << lambda << endl;\nVectorXd v = es.eigenvectors().col(0);\ncout << \"If v is the corresponding eigenvector, then A * v = \" << endl << A * v << endl;\ncout << \"... and lambda * B * v = \" << endl << lambda * B * v << endl << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/SelfAdjointEigenSolver_compute_MatrixType.cpp",
    "content": "SelfAdjointEigenSolver<MatrixXf> es(4);\nMatrixXf X = MatrixXf::Random(4,4);\nMatrixXf A = X + X.transpose();\nes.compute(A);\ncout << \"The eigenvalues of A are: \" << es.eigenvalues().transpose() << endl;\nes.compute(A + MatrixXf::Identity(4,4)); // re-use es to compute eigenvalues of A+I\ncout << \"The eigenvalues of A+I are: \" << es.eigenvalues().transpose() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/SelfAdjointEigenSolver_compute_MatrixType2.cpp",
    "content": "MatrixXd X = MatrixXd::Random(5,5);\nMatrixXd A = X * X.transpose();\nX = MatrixXd::Random(5,5);\nMatrixXd B = X * X.transpose();\n\nGeneralizedSelfAdjointEigenSolver<MatrixXd> es(A,B,EigenvaluesOnly);\ncout << \"The eigenvalues of the pencil (A,B) are:\" << endl << es.eigenvalues() << endl;\nes.compute(B,A,false);\ncout << \"The eigenvalues of the pencil (B,A) are:\" << endl << es.eigenvalues() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/SelfAdjointEigenSolver_eigenvalues.cpp",
    "content": "MatrixXd ones = MatrixXd::Ones(3,3);\nSelfAdjointEigenSolver<MatrixXd> es(ones);\ncout << \"The eigenvalues of the 3x3 matrix of ones are:\" \n     << endl << es.eigenvalues() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/SelfAdjointEigenSolver_eigenvectors.cpp",
    "content": "MatrixXd ones = MatrixXd::Ones(3,3);\nSelfAdjointEigenSolver<MatrixXd> es(ones);\ncout << \"The first eigenvector of the 3x3 matrix of ones is:\" \n     << endl << es.eigenvectors().col(1) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/SelfAdjointEigenSolver_operatorInverseSqrt.cpp",
    "content": "MatrixXd X = MatrixXd::Random(4,4);\nMatrixXd A = X * X.transpose();\ncout << \"Here is a random positive-definite matrix, A:\" << endl << A << endl << endl;\n\nSelfAdjointEigenSolver<MatrixXd> es(A);\ncout << \"The inverse square root of A is: \" << endl;\ncout << es.operatorInverseSqrt() << endl;\ncout << \"We can also compute it with operatorSqrt() and inverse(). That yields: \" << endl;\ncout << es.operatorSqrt().inverse() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/SelfAdjointEigenSolver_operatorSqrt.cpp",
    "content": "MatrixXd X = MatrixXd::Random(4,4);\nMatrixXd A = X * X.transpose();\ncout << \"Here is a random positive-definite matrix, A:\" << endl << A << endl << endl;\n\nSelfAdjointEigenSolver<MatrixXd> es(A);\nMatrixXd sqrtA = es.operatorSqrt();\ncout << \"The square root of A is: \" << endl << sqrtA << endl;\ncout << \"If we square this, we get: \" << endl << sqrtA*sqrtA << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/SelfAdjointView_eigenvalues.cpp",
    "content": "MatrixXd ones = MatrixXd::Ones(3,3);\nVectorXd eivals = ones.selfadjointView<Lower>().eigenvalues();\ncout << \"The eigenvalues of the 3x3 matrix of ones are:\" << endl << eivals << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/SelfAdjointView_operatorNorm.cpp",
    "content": "MatrixXd ones = MatrixXd::Ones(3,3);\ncout << \"The operator norm of the 3x3 matrix of ones is \"\n     << ones.selfadjointView<Lower>().operatorNorm() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/SparseMatrix_coeffs.cpp",
    "content": "SparseMatrix<double> A(3,3);\nA.insert(1,2) = 0;\nA.insert(0,1) = 1;\nA.insert(2,0) = 2;\nA.makeCompressed();\ncout << \"The matrix A is:\" << endl << MatrixXd(A) << endl;\ncout << \"it has \" << A.nonZeros() << \" stored non zero coefficients that are: \" << A.coeffs().transpose() << endl;\nA.coeffs() += 10;\ncout << \"After adding 10 to every stored non zero coefficient, the matrix A is:\" << endl << MatrixXd(A) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/TopicAliasing_block.cpp",
    "content": "MatrixXi mat(3,3); \nmat << 1, 2, 3,   4, 5, 6,   7, 8, 9;\ncout << \"Here is the matrix mat:\\n\" << mat << endl;\n\n// This assignment shows the aliasing problem\nmat.bottomRightCorner(2,2) = mat.topLeftCorner(2,2);\ncout << \"After the assignment, mat = \\n\" << mat << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/TopicAliasing_block_correct.cpp",
    "content": "MatrixXi mat(3,3); \nmat << 1, 2, 3,   4, 5, 6,   7, 8, 9;\ncout << \"Here is the matrix mat:\\n\" << mat << endl;\n\n// The eval() solves the aliasing problem\nmat.bottomRightCorner(2,2) = mat.topLeftCorner(2,2).eval();\ncout << \"After the assignment, mat = \\n\" << mat << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/TopicAliasing_cwise.cpp",
    "content": "MatrixXf mat(2,2); \nmat << 1, 2,  4, 7;\ncout << \"Here is the matrix mat:\\n\" << mat << endl << endl;\n\nmat = 2 * mat;\ncout << \"After 'mat = 2 * mat', mat = \\n\" << mat << endl << endl;\n\n\nmat = mat - MatrixXf::Identity(2,2);\ncout << \"After the subtraction, it becomes\\n\" << mat << endl << endl;\n\n\nArrayXXf arr = mat;\narr = arr.square();\ncout << \"After squaring, it becomes\\n\" << arr << endl << endl;\n\n// Combining all operations in one statement:\nmat << 1, 2,  4, 7;\nmat = (2 * mat - MatrixXf::Identity(2,2)).array().square();\ncout << \"Doing everything at once yields\\n\" << mat << endl << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/TopicAliasing_mult1.cpp",
    "content": "MatrixXf matA(2,2); \nmatA << 2, 0,  0, 2;\nmatA = matA * matA;\ncout << matA;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/TopicAliasing_mult2.cpp",
    "content": "MatrixXf matA(2,2), matB(2,2); \nmatA << 2, 0,  0, 2;\n\n// Simple but not quite as efficient\nmatB = matA * matA;\ncout << matB << endl << endl;\n\n// More complicated but also more efficient\nmatB.noalias() = matA * matA;\ncout << matB;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/TopicAliasing_mult3.cpp",
    "content": "MatrixXf matA(2,2); \nmatA << 2, 0,  0, 2;\nmatA.noalias() = matA * matA;\ncout << matA;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/TopicAliasing_mult4.cpp",
    "content": "MatrixXf A(2,2), B(3,2);\nB << 2, 0,  0, 3, 1, 1;\nA << 2, 0, 0, -2;\nA = (B * A).cwiseAbs();\ncout << A;"
  },
  {
    "path": "include/eigen3/doc/snippets/TopicAliasing_mult5.cpp",
    "content": "MatrixXf A(2,2), B(3,2);\nB << 2, 0,  0, 3, 1, 1;\nA << 2, 0, 0, -2;\nA = (B * A).eval().cwiseAbs();\ncout << A;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/TopicStorageOrders_example.cpp",
    "content": "Matrix<int, 3, 4, ColMajor> Acolmajor;\nAcolmajor << 8, 2, 2, 9,\n             9, 1, 4, 4,\n\t     3, 5, 4, 5;\ncout << \"The matrix A:\" << endl;\ncout << Acolmajor << endl << endl; \n\ncout << \"In memory (column-major):\" << endl;\nfor (int i = 0; i < Acolmajor.size(); i++)\n  cout << *(Acolmajor.data() + i) << \"  \";\ncout << endl << endl;\n\nMatrix<int, 3, 4, RowMajor> Arowmajor = Acolmajor;\ncout << \"In memory (row-major):\" << endl;\nfor (int i = 0; i < Arowmajor.size(); i++)\n  cout << *(Arowmajor.data() + i) << \"  \";\ncout << endl;\n\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Triangular_solve.cpp",
    "content": "Matrix3d m = Matrix3d::Zero();\nm.triangularView<Eigen::Upper>().setOnes();\ncout << \"Here is the matrix m:\\n\" << m << endl;\nMatrix3d n = Matrix3d::Ones();\nn.triangularView<Eigen::Lower>() *= 2;\ncout << \"Here is the matrix n:\\n\" << n << endl;\ncout << \"And now here is m.inverse()*n, taking advantage of the fact that\"\n        \" m is upper-triangular:\\n\"\n     << m.triangularView<Eigen::Upper>().solve(n) << endl;\ncout << \"And this is n*m.inverse():\\n\"\n     << m.triangularView<Eigen::Upper>().solve<Eigen::OnTheRight>(n);\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Tridiagonalization_Tridiagonalization_MatrixType.cpp",
    "content": "MatrixXd X = MatrixXd::Random(5,5);\nMatrixXd A = X + X.transpose();\ncout << \"Here is a random symmetric 5x5 matrix:\" << endl << A << endl << endl;\nTridiagonalization<MatrixXd> triOfA(A);\nMatrixXd Q = triOfA.matrixQ();\ncout << \"The orthogonal matrix Q is:\" << endl << Q << endl;\nMatrixXd T = triOfA.matrixT();\ncout << \"The tridiagonal matrix T is:\" << endl << T << endl << endl;\ncout << \"Q * T * Q^T = \" << endl << Q * T * Q.transpose() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Tridiagonalization_compute.cpp",
    "content": "Tridiagonalization<MatrixXf> tri;\nMatrixXf X = MatrixXf::Random(4,4);\nMatrixXf A = X + X.transpose();\ntri.compute(A);\ncout << \"The matrix T in the tridiagonal decomposition of A is: \" << endl;\ncout << tri.matrixT() << endl;\ntri.compute(2*A); // re-use tri to compute eigenvalues of 2A\ncout << \"The matrix T in the tridiagonal decomposition of 2A is: \" << endl;\ncout << tri.matrixT() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Tridiagonalization_decomposeInPlace.cpp",
    "content": "MatrixXd X = MatrixXd::Random(5,5);\nMatrixXd A = X + X.transpose();\ncout << \"Here is a random symmetric 5x5 matrix:\" << endl << A << endl << endl;\n\nVectorXd diag(5);\nVectorXd subdiag(4);\ninternal::tridiagonalization_inplace(A, diag, subdiag, true);\ncout << \"The orthogonal matrix Q is:\" << endl << A << endl;\ncout << \"The diagonal of the tridiagonal matrix T is:\" << endl << diag << endl;\ncout << \"The subdiagonal of the tridiagonal matrix T is:\" << endl << subdiag << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Tridiagonalization_diagonal.cpp",
    "content": "MatrixXcd X = MatrixXcd::Random(4,4);\nMatrixXcd A = X + X.adjoint();\ncout << \"Here is a random self-adjoint 4x4 matrix:\" << endl << A << endl << endl;\n\nTridiagonalization<MatrixXcd> triOfA(A);\nMatrixXd T = triOfA.matrixT();\ncout << \"The tridiagonal matrix T is:\" << endl << T << endl << endl;\n\ncout << \"We can also extract the diagonals of T directly ...\" << endl;\nVectorXd diag = triOfA.diagonal();\ncout << \"The diagonal is:\" << endl << diag << endl; \nVectorXd subdiag = triOfA.subDiagonal();\ncout << \"The subdiagonal is:\" << endl << subdiag << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Tridiagonalization_householderCoefficients.cpp",
    "content": "Matrix4d X = Matrix4d::Random(4,4);\nMatrix4d A = X + X.transpose();\ncout << \"Here is a random symmetric 4x4 matrix:\" << endl << A << endl;\nTridiagonalization<Matrix4d> triOfA(A);\nVector3d hc = triOfA.householderCoefficients();\ncout << \"The vector of Householder coefficients is:\" << endl << hc << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Tridiagonalization_packedMatrix.cpp",
    "content": "Matrix4d X = Matrix4d::Random(4,4);\nMatrix4d A = X + X.transpose();\ncout << \"Here is a random symmetric 4x4 matrix:\" << endl << A << endl;\nTridiagonalization<Matrix4d> triOfA(A);\nMatrix4d pm = triOfA.packedMatrix();\ncout << \"The packed matrix M is:\" << endl << pm << endl;\ncout << \"The diagonal and subdiagonal corresponds to the matrix T, which is:\" \n     << endl << triOfA.matrixT() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Tutorial_AdvancedInitialization_Block.cpp",
    "content": "MatrixXf matA(2, 2);\nmatA << 1, 2, 3, 4;\nMatrixXf matB(4, 4);\nmatB << matA, matA/10, matA/10, matA;\nstd::cout << matB << std::endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Tutorial_AdvancedInitialization_CommaTemporary.cpp",
    "content": "MatrixXf mat = MatrixXf::Random(2, 3);\nstd::cout << mat << std::endl << std::endl;\nmat = (MatrixXf(2,2) << 0, 1, 1, 0).finished() * mat;\nstd::cout << mat << std::endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Tutorial_AdvancedInitialization_Join.cpp",
    "content": "RowVectorXd vec1(3);\nvec1 << 1, 2, 3;\nstd::cout << \"vec1 = \" << vec1 << std::endl;\n\nRowVectorXd vec2(4);\nvec2 << 1, 4, 9, 16;\nstd::cout << \"vec2 = \" << vec2 << std::endl;\n\nRowVectorXd joined(7);\njoined << vec1, vec2;\nstd::cout << \"joined = \" << joined << std::endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Tutorial_AdvancedInitialization_LinSpaced.cpp",
    "content": "ArrayXXf table(10, 4);\ntable.col(0) = ArrayXf::LinSpaced(10, 0, 90);\ntable.col(1) = M_PI / 180 * table.col(0);\ntable.col(2) = table.col(1).sin();\ntable.col(3) = table.col(1).cos();\nstd::cout << \"  Degrees   Radians      Sine    Cosine\\n\";\nstd::cout << table << std::endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Tutorial_AdvancedInitialization_ThreeWays.cpp",
    "content": "const int size = 6;\nMatrixXd mat1(size, size);\nmat1.topLeftCorner(size/2, size/2)     = MatrixXd::Zero(size/2, size/2);\nmat1.topRightCorner(size/2, size/2)    = MatrixXd::Identity(size/2, size/2);\nmat1.bottomLeftCorner(size/2, size/2)  = MatrixXd::Identity(size/2, size/2);\nmat1.bottomRightCorner(size/2, size/2) = MatrixXd::Zero(size/2, size/2);\nstd::cout << mat1 << std::endl << std::endl;\n\nMatrixXd mat2(size, size);\nmat2.topLeftCorner(size/2, size/2).setZero();\nmat2.topRightCorner(size/2, size/2).setIdentity();\nmat2.bottomLeftCorner(size/2, size/2).setIdentity();\nmat2.bottomRightCorner(size/2, size/2).setZero();\nstd::cout << mat2 << std::endl << std::endl;\n\nMatrixXd mat3(size, size);\nmat3 << MatrixXd::Zero(size/2, size/2), MatrixXd::Identity(size/2, size/2),\n        MatrixXd::Identity(size/2, size/2), MatrixXd::Zero(size/2, size/2);\nstd::cout << mat3 << std::endl;\n\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Tutorial_AdvancedInitialization_Zero.cpp",
    "content": "std::cout << \"A fixed-size array:\\n\";\nArray33f a1 = Array33f::Zero();\nstd::cout << a1 << \"\\n\\n\";\n\n\nstd::cout << \"A one-dimensional dynamic-size array:\\n\";\nArrayXf a2 = ArrayXf::Zero(3);\nstd::cout << a2 << \"\\n\\n\";\n\n\nstd::cout << \"A two-dimensional dynamic-size array:\\n\";\nArrayXXf a3 = ArrayXXf::Zero(3, 4);\nstd::cout << a3 << \"\\n\";\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Tutorial_Map_rowmajor.cpp",
    "content": "int array[8];\nfor(int i = 0; i < 8; ++i) array[i] = i;\ncout << \"Column-major:\\n\" << Map<Matrix<int,2,4> >(array) << endl;\ncout << \"Row-major:\\n\" << Map<Matrix<int,2,4,RowMajor> >(array) << endl;\ncout << \"Row-major using stride:\\n\" <<\n  Map<Matrix<int,2,4>, Unaligned, Stride<1,4> >(array) << endl;\n\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Tutorial_Map_using.cpp",
    "content": "typedef Matrix<float,1,Dynamic> MatrixType;\ntypedef Map<MatrixType> MapType;\ntypedef Map<const MatrixType> MapTypeConst;   // a read-only map\nconst int n_dims = 5;\n  \nMatrixType m1(n_dims), m2(n_dims);\nm1.setRandom();\nm2.setRandom();\nfloat *p = &m2(0);  // get the address storing the data for m2\nMapType m2map(p,m2.size());   // m2map shares data with m2\nMapTypeConst m2mapconst(p,m2.size());  // a read-only accessor for m2\n\ncout << \"m1: \" << m1 << endl;\ncout << \"m2: \" << m2 << endl;\ncout << \"Squared euclidean distance: \" << (m1-m2).squaredNorm() << endl;\ncout << \"Squared euclidean distance, using map: \" <<\n  (m1-m2map).squaredNorm() << endl;\nm2map(3) = 7;   // this will change m2, since they share the same array\ncout << \"Updated m2: \" << m2 << endl;\ncout << \"m2 coefficient 2, constant accessor: \" << m2mapconst(2) << endl;\n/* m2mapconst(2) = 5; */   // this yields a compile-time error\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Tutorial_ReshapeMat2Mat.cpp",
    "content": "MatrixXf M1(2,6);    // Column-major storage\nM1 << 1, 2, 3,  4,  5,  6,\n      7, 8, 9, 10, 11, 12;\n\nMap<MatrixXf> M2(M1.data(), 6,2);\ncout << \"M2:\" << endl << M2 << endl;"
  },
  {
    "path": "include/eigen3/doc/snippets/Tutorial_ReshapeMat2Vec.cpp",
    "content": "MatrixXf M1(3,3);    // Column-major storage\nM1 << 1, 2, 3,\n      4, 5, 6,\n      7, 8, 9;\n\nMap<RowVectorXf> v1(M1.data(), M1.size());\ncout << \"v1:\" << endl << v1 << endl;\n\nMatrix<float,Dynamic,Dynamic,RowMajor> M2(M1);\nMap<RowVectorXf> v2(M2.data(), M2.size());\ncout << \"v2:\" << endl << v2 << endl;"
  },
  {
    "path": "include/eigen3/doc/snippets/Tutorial_SlicingCol.cpp",
    "content": "MatrixXf M1 = MatrixXf::Random(3,8);\ncout << \"Column major input:\" << endl << M1 << \"\\n\";\nMap<MatrixXf,0,OuterStride<> > M2(M1.data(), M1.rows(), (M1.cols()+2)/3, OuterStride<>(M1.outerStride()*3));\ncout << \"1 column over 3:\" << endl << M2 << \"\\n\";\n\ntypedef Matrix<float,Dynamic,Dynamic,RowMajor> RowMajorMatrixXf;\nRowMajorMatrixXf M3(M1);\ncout << \"Row major input:\" << endl << M3 << \"\\n\";\nMap<RowMajorMatrixXf,0,Stride<Dynamic,3> > M4(M3.data(), M3.rows(), (M3.cols()+2)/3,\n                                              Stride<Dynamic,3>(M3.outerStride(),3));\ncout << \"1 column over 3:\" << endl << M4 << \"\\n\";"
  },
  {
    "path": "include/eigen3/doc/snippets/Tutorial_SlicingVec.cpp",
    "content": "RowVectorXf v = RowVectorXf::LinSpaced(20,0,19);\ncout << \"Input:\" << endl << v << endl;\nMap<RowVectorXf,0,InnerStride<2> > v2(v.data(), v.size()/2);\ncout << \"Even:\" << v2 << endl;"
  },
  {
    "path": "include/eigen3/doc/snippets/Tutorial_commainit_01.cpp",
    "content": "Matrix3f m;\nm << 1, 2, 3,\n     4, 5, 6,\n     7, 8, 9;\nstd::cout << m;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Tutorial_commainit_01b.cpp",
    "content": "Matrix3f m;\nm.row(0) << 1, 2, 3;\nm.block(1,0,2,2) << 4, 5, 7, 8;\nm.col(2).tail(2) << 6, 9;\t\t    \nstd::cout << m;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Tutorial_commainit_02.cpp",
    "content": "int rows=5, cols=5;\nMatrixXf m(rows,cols);\nm << (Matrix3f() << 1, 2, 3, 4, 5, 6, 7, 8, 9).finished(),\n     MatrixXf::Zero(3,cols-3),\n     MatrixXf::Zero(rows-3,3),\n     MatrixXf::Identity(rows-3,cols-3);\ncout << m;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Tutorial_solve_matrix_inverse.cpp",
    "content": "Matrix3f A;\nVector3f b;\nA << 1,2,3,  4,5,6,  7,8,10;\nb << 3, 3, 4;\nVector3f x = A.inverse() * b;\ncout << \"The solution is:\" << endl << x << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Tutorial_solve_multiple_rhs.cpp",
    "content": "Matrix3f A(3,3);\nA << 1,2,3,  4,5,6,  7,8,10;\nMatrix<float,3,2> B;\nB << 3,1, 3,1, 4,1;\nMatrix<float,3,2> X;\nX = A.fullPivLu().solve(B);\ncout << \"The solution with right-hand side (3,3,4) is:\" << endl;\ncout << X.col(0) << endl;\ncout << \"The solution with right-hand side (1,1,1) is:\" << endl;\ncout << X.col(1) << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Tutorial_solve_reuse_decomposition.cpp",
    "content": "Matrix3f A(3,3);\nA << 1,2,3,  4,5,6,  7,8,10;\nPartialPivLU<Matrix3f> luOfA(A); // compute LU decomposition of A\nVector3f b;\nb << 3,3,4;\nVector3f x;\nx = luOfA.solve(b);\ncout << \"The solution with right-hand side (3,3,4) is:\" << endl;\ncout << x << endl;\nb << 1,1,1;\nx = luOfA.solve(b);\ncout << \"The solution with right-hand side (1,1,1) is:\" << endl;\ncout << x << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Tutorial_solve_singular.cpp",
    "content": "Matrix3f A;\nVector3f b;\nA << 1,2,3,  4,5,6,  7,8,9;\nb << 3, 3, 4;\ncout << \"Here is the matrix A:\" << endl << A << endl;\ncout << \"Here is the vector b:\" << endl << b << endl;\nVector3f x;\nx = A.lu().solve(b);\ncout << \"The solution is:\" << endl << x << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Tutorial_solve_triangular.cpp",
    "content": "Matrix3f A;\nVector3f b;\nA << 1,2,3,  0,5,6,  0,0,10;\nb << 3, 3, 4;\ncout << \"Here is the matrix A:\" << endl << A << endl;\ncout << \"Here is the vector b:\" << endl << b << endl;\nVector3f x = A.triangularView<Upper>().solve(b);\ncout << \"The solution is:\" << endl << x << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/Tutorial_solve_triangular_inplace.cpp",
    "content": "Matrix3f A;\nVector3f b;\nA << 1,2,3,  0,5,6,  0,0,10;\nb << 3, 3, 4;\nA.triangularView<Upper>().solveInPlace(b);\ncout << \"The solution is:\" << endl << b << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/VectorwiseOp_homogeneous.cpp",
    "content": "typedef Matrix<double,3,Dynamic> Matrix3Xd;\nMatrix3Xd M = Matrix3Xd::Random(3,5);\nProjective3d P(Matrix4d::Random());\ncout << \"The matrix M is:\" << endl << M << endl << endl;\ncout << \"M.colwise().homogeneous():\" << endl << M.colwise().homogeneous() << endl << endl;\ncout << \"P * M.colwise().homogeneous():\" << endl << P * M.colwise().homogeneous() << endl << endl;\ncout << \"P * M.colwise().homogeneous().hnormalized(): \" << endl << (P * M.colwise().homogeneous()).colwise().hnormalized() << endl << endl;"
  },
  {
    "path": "include/eigen3/doc/snippets/Vectorwise_reverse.cpp",
    "content": "MatrixXi m = MatrixXi::Random(3,4);\ncout << \"Here is the matrix m:\" << endl << m << endl;\ncout << \"Here is the rowwise reverse of m:\" << endl << m.rowwise().reverse() << endl;\ncout << \"Here is the colwise reverse of m:\" << endl << m.colwise().reverse() << endl;\n\ncout << \"Here is the coefficient (1,0) in the rowise reverse of m:\" << endl\n<< m.rowwise().reverse()(1,0) << endl;\ncout << \"Let us overwrite this coefficient with the value 4.\" << endl;\n//m.colwise().reverse()(1,0) = 4;\ncout << \"Now the matrix m is:\" << endl << m << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/class_FullPivLU.cpp",
    "content": "typedef Matrix<double, 5, 3> Matrix5x3;\ntypedef Matrix<double, 5, 5> Matrix5x5;\nMatrix5x3 m = Matrix5x3::Random();\ncout << \"Here is the matrix m:\" << endl << m << endl;\nEigen::FullPivLU<Matrix5x3> lu(m);\ncout << \"Here is, up to permutations, its LU decomposition matrix:\"\n     << endl << lu.matrixLU() << endl;\ncout << \"Here is the L part:\" << endl;\nMatrix5x5 l = Matrix5x5::Identity();\nl.block<5,3>(0,0).triangularView<StrictlyLower>() = lu.matrixLU();\ncout << l << endl;\ncout << \"Here is the U part:\" << endl;\nMatrix5x3 u = lu.matrixLU().triangularView<Upper>();\ncout << u << endl;\ncout << \"Let us now reconstruct the original matrix m:\" << endl;\ncout << lu.permutationP().inverse() * l * u * lu.permutationQ().inverse() << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/compile_snippet.cpp.in",
    "content": "static bool eigen_did_assert = false;\n#define eigen_assert(X) if(!eigen_did_assert && !(X)){ std::cout << \"### Assertion raised in \" << __FILE__ << \":\" << __LINE__ << \":\\n\" #X << \"\\n### The following would happen without assertions:\\n\"; eigen_did_assert = true;}\n\n#include <iostream>\n#include <Eigen/Eigen>\n\n#ifndef M_PI\n#define M_PI 3.1415926535897932384626433832795\n#endif\n\n\nusing namespace Eigen;\nusing namespace std;\n\nint main(int, char**)\n{\n  cout.precision(3);\n  ${snippet_source_code}\n  return 0;\n}\n"
  },
  {
    "path": "include/eigen3/doc/snippets/tut_arithmetic_redux_minmax.cpp",
    "content": "  Matrix3f m = Matrix3f::Random();\n  std::ptrdiff_t i, j;\n  float minOfM = m.minCoeff(&i,&j);\n  cout << \"Here is the matrix m:\\n\" << m << endl;\n  cout << \"Its minimum coefficient (\" << minOfM \n       << \") is at position (\" << i << \",\" << j << \")\\n\\n\";\n\n  RowVector4i v = RowVector4i::Random();\n  int maxOfV = v.maxCoeff(&i);\n  cout << \"Here is the vector v: \" << v << endl;\n  cout << \"Its maximum coefficient (\" << maxOfV \n       << \") is at position \" << i << endl;\n"
  },
  {
    "path": "include/eigen3/doc/snippets/tut_arithmetic_transpose_aliasing.cpp",
    "content": "Matrix2i a; a << 1, 2, 3, 4;\ncout << \"Here is the matrix a:\\n\" << a << endl;\n\na = a.transpose(); // !!! do NOT do this !!!\ncout << \"and the result of the aliasing effect:\\n\" << a << endl;"
  },
  {
    "path": "include/eigen3/doc/snippets/tut_arithmetic_transpose_conjugate.cpp",
    "content": "MatrixXcf a = MatrixXcf::Random(2,2);\ncout << \"Here is the matrix a\\n\" << a << endl;\n\ncout << \"Here is the matrix a^T\\n\" << a.transpose() << endl;\n\n\ncout << \"Here is the conjugate of a\\n\" << a.conjugate() << endl;\n\n\ncout << \"Here is the matrix a^*\\n\" << a.adjoint() << endl;\n\n\n"
  },
  {
    "path": "include/eigen3/doc/snippets/tut_arithmetic_transpose_inplace.cpp",
    "content": "MatrixXf a(2,3); a << 1, 2, 3, 4, 5, 6;\ncout << \"Here is the initial matrix a:\\n\" << a << endl;\n\n\na.transposeInPlace();\ncout << \"and after being transposed:\\n\" << a << endl;"
  },
  {
    "path": "include/eigen3/doc/snippets/tut_matrix_assignment_resizing.cpp",
    "content": "MatrixXf a(2,2);\nstd::cout << \"a is of size \" << a.rows() << \"x\" << a.cols() << std::endl;\nMatrixXf b(3,3);\na = b;\nstd::cout << \"a is now of size \" << a.rows() << \"x\" << a.cols() << std::endl;\n"
  },
  {
    "path": "include/eigen3/doc/special_examples/CMakeLists.txt",
    "content": "if(NOT EIGEN_TEST_NOQT)\n  find_package(Qt4)\n  if(QT4_FOUND)\n    include(${QT_USE_FILE})\n  endif()\nendif(NOT EIGEN_TEST_NOQT)\n\nif(QT4_FOUND)\n  add_executable(Tutorial_sparse_example Tutorial_sparse_example.cpp Tutorial_sparse_example_details.cpp)\n  target_link_libraries(Tutorial_sparse_example ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO} ${QT_QTCORE_LIBRARY} ${QT_QTGUI_LIBRARY})\n\n  add_custom_command(\n    TARGET Tutorial_sparse_example\n    POST_BUILD\n    COMMAND ${CMAKE_COMMAND} -E make_directory ${CMAKE_CURRENT_BINARY_DIR}/../html/\n    COMMAND Tutorial_sparse_example ARGS ${CMAKE_CURRENT_BINARY_DIR}/../html/Tutorial_sparse_example.jpeg\n  )\n\n  add_dependencies(all_examples Tutorial_sparse_example)\nendif(QT4_FOUND)\n\ncheck_cxx_compiler_flag(\"-std=c++11\" EIGEN_COMPILER_SUPPORT_CPP11)\nif(EIGEN_COMPILER_SUPPORT_CPP11)\n  add_executable(random_cpp11 random_cpp11.cpp)\n  target_link_libraries(random_cpp11 ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO})\n  add_dependencies(all_examples random_cpp11)\n  ei_add_target_property(random_cpp11 COMPILE_FLAGS \"-std=c++11\")\n\n  add_custom_command(\n    TARGET random_cpp11\n    POST_BUILD\n    COMMAND random_cpp11\n    ARGS >${CMAKE_CURRENT_BINARY_DIR}/random_cpp11.out\n  )\nendif()\n"
  },
  {
    "path": "include/eigen3/doc/special_examples/Tutorial_sparse_example.cpp",
    "content": "#include <Eigen/Sparse>\n#include <vector>\n#include <iostream>\n\ntypedef Eigen::SparseMatrix<double> SpMat; // declares a column-major sparse matrix type of double\ntypedef Eigen::Triplet<double> T;\n\nvoid buildProblem(std::vector<T>& coefficients, Eigen::VectorXd& b, int n);\nvoid saveAsBitmap(const Eigen::VectorXd& x, int n, const char* filename);\n\nint main(int argc, char** argv)\n{\n  if(argc!=2) {\n    std::cerr << \"Error: expected one and only one argument.\\n\";\n    return -1;\n  }\n  \n  int n = 300;  // size of the image\n  int m = n*n;  // number of unknows (=number of pixels)\n\n  // Assembly:\n  std::vector<T> coefficients;            // list of non-zeros coefficients\n  Eigen::VectorXd b(m);                   // the right hand side-vector resulting from the constraints\n  buildProblem(coefficients, b, n);\n\n  SpMat A(m,m);\n  A.setFromTriplets(coefficients.begin(), coefficients.end());\n\n  // Solving:\n  Eigen::SimplicialCholesky<SpMat> chol(A);  // performs a Cholesky factorization of A\n  Eigen::VectorXd x = chol.solve(b);         // use the factorization to solve for the given right hand side\n\n  // Export the result to a file:\n  saveAsBitmap(x, n, argv[1]);\n\n  return 0;\n}\n\n"
  },
  {
    "path": "include/eigen3/doc/special_examples/Tutorial_sparse_example_details.cpp",
    "content": "#include <Eigen/Sparse>\n#include <vector>\n#include <QImage>\n\ntypedef Eigen::SparseMatrix<double> SpMat; // declares a column-major sparse matrix type of double\ntypedef Eigen::Triplet<double> T;\n\nvoid insertCoefficient(int id, int i, int j, double w, std::vector<T>& coeffs,\n                       Eigen::VectorXd& b, const Eigen::VectorXd& boundary)\n{\n  int n = int(boundary.size());\n  int id1 = i+j*n;\n\n        if(i==-1 || i==n) b(id) -= w * boundary(j); // constrained coefficient\n  else  if(j==-1 || j==n) b(id) -= w * boundary(i); // constrained coefficient\n  else  coeffs.push_back(T(id,id1,w));              // unknown coefficient\n}\n\nvoid buildProblem(std::vector<T>& coefficients, Eigen::VectorXd& b, int n)\n{\n  b.setZero();\n  Eigen::ArrayXd boundary = Eigen::ArrayXd::LinSpaced(n, 0,M_PI).sin().pow(2);\n  for(int j=0; j<n; ++j)\n  {\n    for(int i=0; i<n; ++i)\n    {\n      int id = i+j*n;\n      insertCoefficient(id, i-1,j, -1, coefficients, b, boundary);\n      insertCoefficient(id, i+1,j, -1, coefficients, b, boundary);\n      insertCoefficient(id, i,j-1, -1, coefficients, b, boundary);\n      insertCoefficient(id, i,j+1, -1, coefficients, b, boundary);\n      insertCoefficient(id, i,j,    4, coefficients, b, boundary);\n    }\n  }\n}\n\nvoid saveAsBitmap(const Eigen::VectorXd& x, int n, const char* filename)\n{\n  Eigen::Array<unsigned char,Eigen::Dynamic,Eigen::Dynamic> bits = (x*255).cast<unsigned char>();\n  QImage img(bits.data(), n,n,QImage::Format_Indexed8);\n  img.setColorCount(256);\n  for(int i=0;i<256;i++) img.setColor(i,qRgb(i,i,i));\n  img.save(filename);\n}\n"
  },
  {
    "path": "include/eigen3/doc/special_examples/random_cpp11.cpp",
    "content": "#include <Eigen/Core>\n#include <iostream>\n#include <random>\n\nusing namespace Eigen;\n\nint main() {\n  std::default_random_engine generator;\n  std::poisson_distribution<int> distribution(4.1);\n  auto poisson = [&] () {return distribution(generator);};\n\n  RowVectorXi v = RowVectorXi::NullaryExpr(10, poisson );\n  std::cout << v << \"\\n\";\n}\n"
  },
  {
    "path": "include/eigen3/doc/tutorial.cpp",
    "content": "#include <Eigen/Array>\n\nint main(int argc, char *argv[])\n{\n  std::cout.precision(2);\n\n  // demo static functions\n  Eigen::Matrix3f m3 = Eigen::Matrix3f::Random();\n  Eigen::Matrix4f m4 = Eigen::Matrix4f::Identity();\n\n  std::cout << \"*** Step 1 ***\\nm3:\\n\" << m3 << \"\\nm4:\\n\" << m4 << std::endl;\n\n  // demo non-static set... functions\n  m4.setZero();\n  m3.diagonal().setOnes();\n  \n  std::cout << \"*** Step 2 ***\\nm3:\\n\" << m3 << \"\\nm4:\\n\" << m4 << std::endl;\n\n  // demo fixed-size block() expression as lvalue and as rvalue\n  m4.block<3,3>(0,1) = m3;\n  m3.row(2) = m4.block<1,3>(2,0);\n\n  std::cout << \"*** Step 3 ***\\nm3:\\n\" << m3 << \"\\nm4:\\n\" << m4 << std::endl;\n\n  // demo dynamic-size block()\n  {\n    int rows = 3, cols = 3;\n    m4.block(0,1,3,3).setIdentity();\n    std::cout << \"*** Step 4 ***\\nm4:\\n\" << m4 << std::endl;\n  }\n\n  // demo vector blocks\n  m4.diagonal().block(1,2).setOnes();\n  std::cout << \"*** Step 5 ***\\nm4.diagonal():\\n\" << m4.diagonal() << std::endl;\n  std::cout << \"m4.diagonal().start(3)\\n\" << m4.diagonal().start(3) << std::endl;\n\n  // demo coeff-wise operations\n  m4 = m4.cwise()*m4;\n  m3 = m3.cwise().cos();\n  std::cout << \"*** Step 6 ***\\nm3:\\n\" << m3 << \"\\nm4:\\n\" << m4 << std::endl;\n\n  // sums of coefficients\n  std::cout << \"*** Step 7 ***\\n m4.sum(): \" << m4.sum() << std::endl;\n  std::cout << \"m4.col(2).sum(): \" << m4.col(2).sum() << std::endl;\n  std::cout << \"m4.colwise().sum():\\n\" << m4.colwise().sum() << std::endl;\n  std::cout << \"m4.rowwise().sum():\\n\" << m4.rowwise().sum() << std::endl;\n\n  // demo intelligent auto-evaluation\n  m4 = m4 * m4; // auto-evaluates so no aliasing problem (performance penalty is low)\n  Eigen::Matrix4f other = (m4 * m4).lazy(); // forces lazy evaluation\n  m4 = m4 + m4; // here Eigen goes for lazy evaluation, as with most expressions\n  m4 = -m4 + m4 + 5 * m4; // same here, Eigen chooses lazy evaluation for all that.\n  m4 = m4 * (m4 + m4); // here Eigen chooses to first evaluate m4 + m4 into a temporary.\n                       // indeed, here it is an optimization to cache this intermediate result.\n  m3 = m3 * m4.block<3,3>(1,1); // here Eigen chooses NOT to evaluate block() into a temporary\n    // because accessing coefficients of that block expression is not more costly than accessing\n    // coefficients of a plain matrix.\n  m4 = m4 * m4.transpose(); // same here, lazy evaluation of the transpose.\n  m4 = m4 * m4.transpose().eval(); // forces immediate evaluation of the transpose\n\n  std::cout << \"*** Step 8 ***\\nm3:\\n\" << m3 << \"\\nm4:\\n\" << m4 << std::endl;\n}\n"
  },
  {
    "path": "include/eigen3/eigen3.pc.in",
    "content": "prefix=@CMAKE_INSTALL_PREFIX@\nexec_prefix=${prefix}\n\nName: Eigen3\nDescription: A C++ template library for linear algebra: vectors, matrices, and related algorithms\nRequires:\nVersion: @EIGEN_VERSION_NUMBER@\nLibs:\nCflags: -I${prefix}/@INCLUDE_INSTALL_DIR@\n"
  },
  {
    "path": "include/eigen3/failtest/CMakeLists.txt",
    "content": "message(STATUS \"Running the failtests\")\n\nei_add_failtest(\"failtest_sanity_check\")\n\nei_add_failtest(\"block_nonconst_ctor_on_const_xpr_0\")\nei_add_failtest(\"block_nonconst_ctor_on_const_xpr_1\")\nei_add_failtest(\"block_nonconst_ctor_on_const_xpr_2\")\nei_add_failtest(\"transpose_nonconst_ctor_on_const_xpr\")\nei_add_failtest(\"diagonal_nonconst_ctor_on_const_xpr\")\nei_add_failtest(\"cwiseunaryview_nonconst_ctor_on_const_xpr\")\nei_add_failtest(\"triangularview_nonconst_ctor_on_const_xpr\")\nei_add_failtest(\"selfadjointview_nonconst_ctor_on_const_xpr\")\n\nei_add_failtest(\"const_qualified_block_method_retval_0\")\nei_add_failtest(\"const_qualified_block_method_retval_1\")\nei_add_failtest(\"const_qualified_transpose_method_retval\")\nei_add_failtest(\"const_qualified_diagonal_method_retval\")\n\nei_add_failtest(\"map_nonconst_ctor_on_const_ptr_0\")\nei_add_failtest(\"map_nonconst_ctor_on_const_ptr_1\")\nei_add_failtest(\"map_nonconst_ctor_on_const_ptr_2\")\nei_add_failtest(\"map_nonconst_ctor_on_const_ptr_3\")\nei_add_failtest(\"map_nonconst_ctor_on_const_ptr_4\")\n\nei_add_failtest(\"map_on_const_type_actually_const_0\")\nei_add_failtest(\"map_on_const_type_actually_const_1\")\nei_add_failtest(\"block_on_const_type_actually_const_0\")\nei_add_failtest(\"block_on_const_type_actually_const_1\")\nei_add_failtest(\"transpose_on_const_type_actually_const\")\nei_add_failtest(\"diagonal_on_const_type_actually_const\")\nei_add_failtest(\"cwiseunaryview_on_const_type_actually_const\")\nei_add_failtest(\"triangularview_on_const_type_actually_const\")\nei_add_failtest(\"selfadjointview_on_const_type_actually_const\")\n\nei_add_failtest(\"ref_1\")\nei_add_failtest(\"ref_2\")\nei_add_failtest(\"ref_3\")\nei_add_failtest(\"ref_4\")\nei_add_failtest(\"ref_5\")\n\nei_add_failtest(\"swap_1\")\nei_add_failtest(\"swap_2\")\n\nei_add_failtest(\"ternary_1\")\nei_add_failtest(\"ternary_2\")\n\nei_add_failtest(\"sparse_ref_1\")\nei_add_failtest(\"sparse_ref_2\")\nei_add_failtest(\"sparse_ref_3\")\nei_add_failtest(\"sparse_ref_4\")\nei_add_failtest(\"sparse_ref_5\")\n\nei_add_failtest(\"sparse_storage_mismatch\")\n\nei_add_failtest(\"partialpivlu_int\")\nei_add_failtest(\"fullpivlu_int\")\nei_add_failtest(\"llt_int\")\nei_add_failtest(\"ldlt_int\")\nei_add_failtest(\"qr_int\")\nei_add_failtest(\"colpivqr_int\")\nei_add_failtest(\"fullpivqr_int\")\nei_add_failtest(\"jacobisvd_int\")\nei_add_failtest(\"bdcsvd_int\")\nei_add_failtest(\"eigensolver_int\")\nei_add_failtest(\"eigensolver_cplx\")\n\nif (EIGEN_FAILTEST_FAILURE_COUNT)\n  message(FATAL_ERROR\n          \"${EIGEN_FAILTEST_FAILURE_COUNT} out of ${EIGEN_FAILTEST_COUNT} failtests FAILED. \"\n          \"To debug these failures, manually compile these programs in ${CMAKE_CURRENT_SOURCE_DIR}, \"\n          \"with and without #define EIGEN_SHOULD_FAIL_TO_BUILD.\")\nelse()\n  message(STATUS \"Failtest SUCCESS: all ${EIGEN_FAILTEST_COUNT} failtests passed.\")\n  message(STATUS \"\")\nendif()\n"
  },
  {
    "path": "include/eigen3/failtest/bdcsvd_int.cpp",
    "content": "#include \"../Eigen/SVD\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define SCALAR int\n#else\n#define SCALAR float\n#endif\n\nusing namespace Eigen;\n\nint main()\n{\n  BDCSVD<Matrix<SCALAR,Dynamic,Dynamic> > qr(Matrix<SCALAR,Dynamic,Dynamic>::Random(10,10));\n}\n"
  },
  {
    "path": "include/eigen3/failtest/block_nonconst_ctor_on_const_xpr_0.cpp",
    "content": "#include \"../Eigen/Core\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define CV_QUALIFIER const\n#else\n#define CV_QUALIFIER\n#endif\n\nusing namespace Eigen;\n\nvoid foo(CV_QUALIFIER Matrix3d &m){\n    Block<Matrix3d,3,3> b(m,0,0);\n}\n\nint main() {}\n"
  },
  {
    "path": "include/eigen3/failtest/block_nonconst_ctor_on_const_xpr_1.cpp",
    "content": "#include \"../Eigen/Core\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define CV_QUALIFIER const\n#else\n#define CV_QUALIFIER\n#endif\n\nusing namespace Eigen;\n\nvoid foo(CV_QUALIFIER Matrix3d &m){\n    Block<Matrix3d> b(m,0,0,3,3);\n}\n\nint main() {}\n"
  },
  {
    "path": "include/eigen3/failtest/block_nonconst_ctor_on_const_xpr_2.cpp",
    "content": "#include \"../Eigen/Core\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define CV_QUALIFIER const\n#else\n#define CV_QUALIFIER\n#endif\n\nusing namespace Eigen;\n\nvoid foo(CV_QUALIFIER Matrix3d &m){\n    // row/column constructor\n    Block<Matrix3d,3,1> b(m,0);\n}\n\nint main() {}\n"
  },
  {
    "path": "include/eigen3/failtest/block_on_const_type_actually_const_0.cpp",
    "content": "#include \"../Eigen/Core\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define CV_QUALIFIER const\n#else\n#define CV_QUALIFIER\n#endif\n\nusing namespace Eigen;\n\nvoid foo(){\n    Matrix3f m;\n    Block<CV_QUALIFIER Matrix3f>(m, 0, 0, 3, 3).coeffRef(0, 0) = 1.0f;\n}\n\nint main() {}\n"
  },
  {
    "path": "include/eigen3/failtest/block_on_const_type_actually_const_1.cpp",
    "content": "#include \"../Eigen/Core\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define CV_QUALIFIER const\n#else\n#define CV_QUALIFIER\n#endif\n\nusing namespace Eigen;\n\nvoid foo(){\n    MatrixXf m;\n    Block<CV_QUALIFIER MatrixXf, 3, 3>(m, 0, 0).coeffRef(0, 0) = 1.0f;\n}\n\nint main() {}\n"
  },
  {
    "path": "include/eigen3/failtest/colpivqr_int.cpp",
    "content": "#include \"../Eigen/QR\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define SCALAR int\n#else\n#define SCALAR float\n#endif\n\nusing namespace Eigen;\n\nint main()\n{\n  ColPivHouseholderQR<Matrix<SCALAR,Dynamic,Dynamic> > qr(Matrix<SCALAR,Dynamic,Dynamic>::Random(10,10));\n}\n"
  },
  {
    "path": "include/eigen3/failtest/const_qualified_block_method_retval_0.cpp",
    "content": "#include \"../Eigen/Core\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define CV_QUALIFIER const\n#else\n#define CV_QUALIFIER\n#endif\n\nusing namespace Eigen;\n\nvoid foo(CV_QUALIFIER Matrix3d &m){\n    Block<Matrix3d,3,3> b(m.block<3,3>(0,0));\n}\n\nint main() {}\n"
  },
  {
    "path": "include/eigen3/failtest/const_qualified_block_method_retval_1.cpp",
    "content": "#include \"../Eigen/Core\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define CV_QUALIFIER const\n#else\n#define CV_QUALIFIER\n#endif\n\nusing namespace Eigen;\n\nvoid foo(CV_QUALIFIER Matrix3d &m){\n    Block<Matrix3d> b(m.block(0,0,3,3));\n}\n\nint main() {}\n"
  },
  {
    "path": "include/eigen3/failtest/const_qualified_diagonal_method_retval.cpp",
    "content": "#include \"../Eigen/Core\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define CV_QUALIFIER const\n#else\n#define CV_QUALIFIER\n#endif\n\nusing namespace Eigen;\n\nvoid foo(CV_QUALIFIER Matrix3d &m){\n    Diagonal<Matrix3d> b(m.diagonal());\n}\n\nint main() {}\n"
  },
  {
    "path": "include/eigen3/failtest/const_qualified_transpose_method_retval.cpp",
    "content": "#include \"../Eigen/Core\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define CV_QUALIFIER const\n#else\n#define CV_QUALIFIER\n#endif\n\nusing namespace Eigen;\n\nvoid foo(CV_QUALIFIER Matrix3d &m){\n    Transpose<Matrix3d> b(m.transpose());\n}\n\nint main() {}\n"
  },
  {
    "path": "include/eigen3/failtest/cwiseunaryview_nonconst_ctor_on_const_xpr.cpp",
    "content": "#include \"../Eigen/Core\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define CV_QUALIFIER const\n#else\n#define CV_QUALIFIER\n#endif\n\nusing namespace Eigen;\n\nvoid foo(CV_QUALIFIER Matrix3d &m){\n    CwiseUnaryView<internal::scalar_real_ref_op<double>,Matrix3d> t(m);\n}\n\nint main() {}\n"
  },
  {
    "path": "include/eigen3/failtest/cwiseunaryview_on_const_type_actually_const.cpp",
    "content": "#include \"../Eigen/Core\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define CV_QUALIFIER const\n#else\n#define CV_QUALIFIER\n#endif\n\nusing namespace Eigen;\n\nvoid foo(){\n    MatrixXf m;\n    CwiseUnaryView<internal::scalar_real_ref_op<double>,CV_QUALIFIER MatrixXf>(m).coeffRef(0, 0) = 1.0f;\n}\n\nint main() {}\n"
  },
  {
    "path": "include/eigen3/failtest/diagonal_nonconst_ctor_on_const_xpr.cpp",
    "content": "#include \"../Eigen/Core\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define CV_QUALIFIER const\n#else\n#define CV_QUALIFIER\n#endif\n\nusing namespace Eigen;\n\nvoid foo(CV_QUALIFIER Matrix3d &m){\n    Diagonal<Matrix3d> d(m);\n}\n\nint main() {}\n"
  },
  {
    "path": "include/eigen3/failtest/diagonal_on_const_type_actually_const.cpp",
    "content": "#include \"../Eigen/Core\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define CV_QUALIFIER const\n#else\n#define CV_QUALIFIER\n#endif\n\nusing namespace Eigen;\n\nvoid foo(){\n    MatrixXf m;\n    Diagonal<CV_QUALIFIER MatrixXf>(m).coeffRef(0) = 1.0f;\n}\n\nint main() {}\n"
  },
  {
    "path": "include/eigen3/failtest/eigensolver_cplx.cpp",
    "content": "#include \"../Eigen/Eigenvalues\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define SCALAR std::complex<double>\n#else\n#define SCALAR float\n#endif\n\nusing namespace Eigen;\n\nint main()\n{\n  EigenSolver<Matrix<SCALAR,Dynamic,Dynamic> > eig(Matrix<SCALAR,Dynamic,Dynamic>::Random(10,10));\n}\n"
  },
  {
    "path": "include/eigen3/failtest/eigensolver_int.cpp",
    "content": "#include \"../Eigen/Eigenvalues\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define SCALAR int\n#else\n#define SCALAR float\n#endif\n\nusing namespace Eigen;\n\nint main()\n{\n  EigenSolver<Matrix<SCALAR,Dynamic,Dynamic> > eig(Matrix<SCALAR,Dynamic,Dynamic>::Random(10,10));\n}\n"
  },
  {
    "path": "include/eigen3/failtest/failtest_sanity_check.cpp",
    "content": "#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\nThis is just some text that won't compile as a C++ file, as a basic sanity check for failtest.\n#else\nint main() {}\n#endif\n"
  },
  {
    "path": "include/eigen3/failtest/fullpivlu_int.cpp",
    "content": "#include \"../Eigen/LU\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define SCALAR int\n#else\n#define SCALAR float\n#endif\n\nusing namespace Eigen;\n\nint main()\n{\n  FullPivLU<Matrix<SCALAR,Dynamic,Dynamic> > lu(Matrix<SCALAR,Dynamic,Dynamic>::Random(10,10));\n}\n"
  },
  {
    "path": "include/eigen3/failtest/fullpivqr_int.cpp",
    "content": "#include \"../Eigen/QR\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define SCALAR int\n#else\n#define SCALAR float\n#endif\n\nusing namespace Eigen;\n\nint main()\n{\n  FullPivHouseholderQR<Matrix<SCALAR,Dynamic,Dynamic> > qr(Matrix<SCALAR,Dynamic,Dynamic>::Random(10,10));\n}\n"
  },
  {
    "path": "include/eigen3/failtest/jacobisvd_int.cpp",
    "content": "#include \"../Eigen/SVD\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define SCALAR int\n#else\n#define SCALAR float\n#endif\n\nusing namespace Eigen;\n\nint main()\n{\n  JacobiSVD<Matrix<SCALAR,Dynamic,Dynamic> > qr(Matrix<SCALAR,Dynamic,Dynamic>::Random(10,10));\n}\n"
  },
  {
    "path": "include/eigen3/failtest/ldlt_int.cpp",
    "content": "#include \"../Eigen/Cholesky\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define SCALAR int\n#else\n#define SCALAR float\n#endif\n\nusing namespace Eigen;\n\nint main()\n{\n  LDLT<Matrix<SCALAR,Dynamic,Dynamic> > ldlt(Matrix<SCALAR,Dynamic,Dynamic>::Random(10,10));\n}\n"
  },
  {
    "path": "include/eigen3/failtest/llt_int.cpp",
    "content": "#include \"../Eigen/Cholesky\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define SCALAR int\n#else\n#define SCALAR float\n#endif\n\nusing namespace Eigen;\n\nint main()\n{\n  LLT<Matrix<SCALAR,Dynamic,Dynamic> > llt(Matrix<SCALAR,Dynamic,Dynamic>::Random(10,10));\n}\n"
  },
  {
    "path": "include/eigen3/failtest/map_nonconst_ctor_on_const_ptr_0.cpp",
    "content": "#include \"../Eigen/Core\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define CV_QUALIFIER const\n#else\n#define CV_QUALIFIER\n#endif\n\nusing namespace Eigen;\n\nvoid foo(CV_QUALIFIER float *ptr){\n    Map<Matrix3f> m(ptr);\n}\n\nint main() {}\n"
  },
  {
    "path": "include/eigen3/failtest/map_nonconst_ctor_on_const_ptr_1.cpp",
    "content": "#include \"../Eigen/Core\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define CV_QUALIFIER const\n#else\n#define CV_QUALIFIER\n#endif\n\nusing namespace Eigen;\n\nvoid foo(CV_QUALIFIER float *ptr, DenseIndex size){\n    Map<ArrayXf> m(ptr, size);\n}\n\nint main() {}\n"
  },
  {
    "path": "include/eigen3/failtest/map_nonconst_ctor_on_const_ptr_2.cpp",
    "content": "#include \"../Eigen/Core\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define CV_QUALIFIER const\n#else\n#define CV_QUALIFIER\n#endif\n\nusing namespace Eigen;\n\nvoid foo(CV_QUALIFIER float *ptr, DenseIndex rows, DenseIndex cols){\n    Map<MatrixXf> m(ptr, rows, cols);\n}\n\nint main() {}\n"
  },
  {
    "path": "include/eigen3/failtest/map_nonconst_ctor_on_const_ptr_3.cpp",
    "content": "#include \"../Eigen/Core\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define CV_QUALIFIER const\n#else\n#define CV_QUALIFIER\n#endif\n\nusing namespace Eigen;\n\nvoid foo(CV_QUALIFIER float *ptr, DenseIndex rows, DenseIndex cols){\n    Map<MatrixXf, Aligned, InnerStride<2> > m(ptr, rows, cols, InnerStride<2>());\n}\n\nint main() {}\n"
  },
  {
    "path": "include/eigen3/failtest/map_nonconst_ctor_on_const_ptr_4.cpp",
    "content": "#include \"../Eigen/Core\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define CV_QUALIFIER\n#else\n#define CV_QUALIFIER const\n#endif\n\nusing namespace Eigen;\n\nvoid foo(const float *ptr, DenseIndex rows, DenseIndex cols){\n    Map<CV_QUALIFIER MatrixXf, Unaligned, OuterStride<> > m(ptr, rows, cols, OuterStride<>(2));\n}\n\nint main() {}\n"
  },
  {
    "path": "include/eigen3/failtest/map_on_const_type_actually_const_0.cpp",
    "content": "#include \"../Eigen/Core\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define CV_QUALIFIER const\n#else\n#define CV_QUALIFIER\n#endif\n\nusing namespace Eigen;\n\nvoid foo(float *ptr){\n    Map<CV_QUALIFIER MatrixXf>(ptr, 1, 1).coeffRef(0,0) = 1.0f;\n}\n\nint main() {}\n"
  },
  {
    "path": "include/eigen3/failtest/map_on_const_type_actually_const_1.cpp",
    "content": "#include \"../Eigen/Core\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define CV_QUALIFIER const\n#else\n#define CV_QUALIFIER\n#endif\n\nusing namespace Eigen;\n\nvoid foo(float *ptr){\n    Map<CV_QUALIFIER Vector3f>(ptr).coeffRef(0) = 1.0f;\n}\n\nint main() {}\n"
  },
  {
    "path": "include/eigen3/failtest/partialpivlu_int.cpp",
    "content": "#include \"../Eigen/LU\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define SCALAR int\n#else\n#define SCALAR float\n#endif\n\nusing namespace Eigen;\n\nint main()\n{\n  PartialPivLU<Matrix<SCALAR,Dynamic,Dynamic> > lu(Matrix<SCALAR,Dynamic,Dynamic>::Random(10,10));\n}\n"
  },
  {
    "path": "include/eigen3/failtest/qr_int.cpp",
    "content": "#include \"../Eigen/QR\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define SCALAR int\n#else\n#define SCALAR float\n#endif\n\nusing namespace Eigen;\n\nint main()\n{\n  HouseholderQR<Matrix<SCALAR,Dynamic,Dynamic> > qr(Matrix<SCALAR,Dynamic,Dynamic>::Random(10,10));\n}\n"
  },
  {
    "path": "include/eigen3/failtest/ref_1.cpp",
    "content": "#include \"../Eigen/Core\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define CV_QUALIFIER const\n#else\n#define CV_QUALIFIER\n#endif\n\nusing namespace Eigen;\n\nvoid call_ref(Ref<VectorXf> a) { }\n\nint main()\n{\n  VectorXf a(10);\n  CV_QUALIFIER VectorXf& ac(a);\n  call_ref(ac);\n}\n"
  },
  {
    "path": "include/eigen3/failtest/ref_2.cpp",
    "content": "#include \"../Eigen/Core\"\n\nusing namespace Eigen;\n\nvoid call_ref(Ref<VectorXf> a) { }\n\nint main()\n{\n  MatrixXf A(10,10);\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n  call_ref(A.row(3));\n#else\n  call_ref(A.col(3));\n#endif\n}\n"
  },
  {
    "path": "include/eigen3/failtest/ref_3.cpp",
    "content": "#include \"../Eigen/Core\"\n\nusing namespace Eigen;\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\nvoid call_ref(Ref<VectorXf> a) { }\n#else\nvoid call_ref(const Ref<const VectorXf> &a) { }\n#endif\n\nint main()\n{\n  VectorXf a(10);\n  call_ref(a+a);\n}\n"
  },
  {
    "path": "include/eigen3/failtest/ref_4.cpp",
    "content": "#include \"../Eigen/Core\"\n\nusing namespace Eigen;\n\nvoid call_ref(Ref<MatrixXf,0,OuterStride<> > a) {}\n\nint main()\n{\n  MatrixXf A(10,10);\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n  call_ref(A.transpose());\n#else\n  call_ref(A);\n#endif\n}\n"
  },
  {
    "path": "include/eigen3/failtest/ref_5.cpp",
    "content": "#include \"../Eigen/Core\"\n\nusing namespace Eigen;\n\nvoid call_ref(Ref<VectorXf> a) { }\n\nint main()\n{\n  VectorXf a(10);\n  DenseBase<VectorXf> &ac(a);\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n  call_ref(ac);\n#else\n  call_ref(ac.derived());\n#endif\n}\n"
  },
  {
    "path": "include/eigen3/failtest/selfadjointview_nonconst_ctor_on_const_xpr.cpp",
    "content": "#include \"../Eigen/Core\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define CV_QUALIFIER const\n#else\n#define CV_QUALIFIER\n#endif\n\nusing namespace Eigen;\n\nvoid foo(CV_QUALIFIER Matrix3d &m){\n    SelfAdjointView<Matrix3d,Upper> t(m);\n}\n\nint main() {}\n"
  },
  {
    "path": "include/eigen3/failtest/selfadjointview_on_const_type_actually_const.cpp",
    "content": "#include \"../Eigen/Core\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define CV_QUALIFIER const\n#else\n#define CV_QUALIFIER\n#endif\n\nusing namespace Eigen;\n\nvoid foo(){\n    MatrixXf m;\n    SelfAdjointView<CV_QUALIFIER MatrixXf,Upper>(m).coeffRef(0, 0) = 1.0f;\n}\n\nint main() {}\n"
  },
  {
    "path": "include/eigen3/failtest/sparse_ref_1.cpp",
    "content": "#include \"../Eigen/Sparse\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define CV_QUALIFIER const\n#else\n#define CV_QUALIFIER\n#endif\n\nusing namespace Eigen;\n\nvoid call_ref(Ref<SparseMatrix<float> > a) { }\n\nint main()\n{\n  SparseMatrix<float> a(10,10);\n  CV_QUALIFIER SparseMatrix<float>& ac(a);\n  call_ref(ac);\n}\n"
  },
  {
    "path": "include/eigen3/failtest/sparse_ref_2.cpp",
    "content": "#include \"../Eigen/Sparse\"\n\nusing namespace Eigen;\n\nvoid call_ref(Ref<SparseMatrix<float> > a) { }\n\nint main()\n{\n  SparseMatrix<float> A(10,10);\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n  call_ref(A.row(3));\n#else\n  call_ref(A.col(3));\n#endif\n}\n"
  },
  {
    "path": "include/eigen3/failtest/sparse_ref_3.cpp",
    "content": "#include \"../Eigen/Sparse\"\n\nusing namespace Eigen;\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\nvoid call_ref(Ref<SparseMatrix<float> > a) { }\n#else\nvoid call_ref(const Ref<const SparseMatrix<float> > &a) { }\n#endif\n\nint main()\n{\n  SparseMatrix<float> a(10,10);\n  call_ref(a+a);\n}\n"
  },
  {
    "path": "include/eigen3/failtest/sparse_ref_4.cpp",
    "content": "#include \"../Eigen/Sparse\"\n\nusing namespace Eigen;\n\nvoid call_ref(Ref<SparseMatrix<float> > a) {}\n\nint main()\n{\n  SparseMatrix<float> A(10,10);\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n  call_ref(A.transpose());\n#else\n  call_ref(A);\n#endif\n}\n"
  },
  {
    "path": "include/eigen3/failtest/sparse_ref_5.cpp",
    "content": "#include \"../Eigen/Sparse\"\n\nusing namespace Eigen;\n\nvoid call_ref(Ref<SparseMatrix<float> > a) { }\n\nint main()\n{\n  SparseMatrix<float> a(10,10);\n  SparseMatrixBase<SparseMatrix<float> > &ac(a);\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n  call_ref(ac);\n#else\n  call_ref(ac.derived());\n#endif\n}\n"
  },
  {
    "path": "include/eigen3/failtest/sparse_storage_mismatch.cpp",
    "content": "#include \"../Eigen/Sparse\"\nusing namespace Eigen;\n\ntypedef SparseMatrix<double,ColMajor> Mat1;\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\ntypedef SparseMatrix<double,RowMajor> Mat2;\n#else\ntypedef SparseMatrix<double,ColMajor> Mat2;\n#endif\n\nint main()\n{\n  Mat1 a(10,10);\n  Mat2 b(10,10);\n  a += b;\n}\n"
  },
  {
    "path": "include/eigen3/failtest/swap_1.cpp",
    "content": "#include \"../Eigen/Core\"\n\nusing namespace Eigen;\n\nint main()\n{\n  VectorXf a(10), b(10);\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n  const DenseBase<VectorXf> &ac(a);\n#else\n  DenseBase<VectorXf> &ac(a);\n#endif\n  b.swap(ac);\n}\n"
  },
  {
    "path": "include/eigen3/failtest/swap_2.cpp",
    "content": "#include \"../Eigen/Core\"\n\nusing namespace Eigen;\n\nint main()\n{\n  VectorXf a(10), b(10);\n  VectorXf const &ac(a);\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n  b.swap(ac);\n#else\n  b.swap(ac.const_cast_derived());\n#endif\n}"
  },
  {
    "path": "include/eigen3/failtest/ternary_1.cpp",
    "content": "#include \"../Eigen/Core\"\n\nusing namespace Eigen;\n\nint main(int argc,char **)\n{\n  VectorXf a(10), b(10);\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n  b = argc>1 ? 2*a : -a;\n#else\n  b = argc>1 ? 2*a : VectorXf(-a);\n#endif\n}\n"
  },
  {
    "path": "include/eigen3/failtest/ternary_2.cpp",
    "content": "#include \"../Eigen/Core\"\n\nusing namespace Eigen;\n\nint main(int argc,char **)\n{\n  VectorXf a(10), b(10);\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n  b = argc>1 ? 2*a : a+a;\n#else\n  b = argc>1 ? VectorXf(2*a) : VectorXf(a+a);\n#endif\n}\n"
  },
  {
    "path": "include/eigen3/failtest/transpose_nonconst_ctor_on_const_xpr.cpp",
    "content": "#include \"../Eigen/Core\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define CV_QUALIFIER const\n#else\n#define CV_QUALIFIER\n#endif\n\nusing namespace Eigen;\n\nvoid foo(CV_QUALIFIER Matrix3d &m){\n    Transpose<Matrix3d> t(m);\n}\n\nint main() {}\n"
  },
  {
    "path": "include/eigen3/failtest/transpose_on_const_type_actually_const.cpp",
    "content": "#include \"../Eigen/Core\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define CV_QUALIFIER const\n#else\n#define CV_QUALIFIER\n#endif\n\nusing namespace Eigen;\n\nvoid foo(){\n    MatrixXf m;\n    Transpose<CV_QUALIFIER MatrixXf>(m).coeffRef(0, 0) = 1.0f;\n}\n\nint main() {}\n"
  },
  {
    "path": "include/eigen3/failtest/triangularview_nonconst_ctor_on_const_xpr.cpp",
    "content": "#include \"../Eigen/Core\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define CV_QUALIFIER const\n#else\n#define CV_QUALIFIER\n#endif\n\nusing namespace Eigen;\n\nvoid foo(CV_QUALIFIER Matrix3d &m){\n  TriangularView<Matrix3d,Upper> t(m);\n}\n\nint main() {}\n"
  },
  {
    "path": "include/eigen3/failtest/triangularview_on_const_type_actually_const.cpp",
    "content": "#include \"../Eigen/Core\"\n\n#ifdef EIGEN_SHOULD_FAIL_TO_BUILD\n#define CV_QUALIFIER const\n#else\n#define CV_QUALIFIER\n#endif\n\nusing namespace Eigen;\n\nvoid foo(){\n    MatrixXf m;\n    TriangularView<CV_QUALIFIER MatrixXf,Upper>(m).coeffRef(0, 0) = 1.0f;\n}\n\nint main() {}\n"
  },
  {
    "path": "include/eigen3/lapack/CMakeLists.txt",
    "content": "\nproject(EigenLapack CXX)\n\ninclude(\"../cmake/language_support.cmake\")\n\nworkaround_9220(Fortran EIGEN_Fortran_COMPILER_WORKS)\n\nif(EIGEN_Fortran_COMPILER_WORKS)\n  enable_language(Fortran OPTIONAL)\n  if(NOT CMAKE_Fortran_COMPILER)\n    set(EIGEN_Fortran_COMPILER_WORKS OFF)\n  endif()\nendif()\n\nadd_custom_target(lapack)\ninclude_directories(../blas)\n\nset(EigenLapack_SRCS\nsingle.cpp double.cpp complex_single.cpp complex_double.cpp ../blas/xerbla.cpp\n)\n\nif(EIGEN_Fortran_COMPILER_WORKS)\n\nset(EigenLapack_SRCS  ${EigenLapack_SRCS}\n  slarft.f  dlarft.f  clarft.f  zlarft.f\n  slarfb.f  dlarfb.f  clarfb.f  zlarfb.f\n  slarfg.f  dlarfg.f  clarfg.f  zlarfg.f\n  slarf.f   dlarf.f   clarf.f   zlarf.f\n  sladiv.f  dladiv.f  cladiv.f  zladiv.f\n  ilaslr.f  iladlr.f  ilaclr.f  ilazlr.f\n  ilaslc.f  iladlc.f  ilaclc.f  ilazlc.f\n  dlapy2.f  dlapy3.f  slapy2.f  slapy3.f\n  clacgv.f  zlacgv.f\n  slamch.f  dlamch.f\n  second_NONE.f dsecnd_NONE.f\n)\n\noption(EIGEN_ENABLE_LAPACK_TESTS OFF \"Enbale the Lapack unit tests\")\n\nif(EIGEN_ENABLE_LAPACK_TESTS)\n\n  get_filename_component(eigen_full_path_to_reference_lapack \"./reference/\" ABSOLUTE)\n  if(NOT EXISTS ${eigen_full_path_to_reference_lapack})\n    # Download lapack and install sources and testing at the right place\n    message(STATUS \"Download lapack_addons_3.4.1.tgz...\")\n    \n    file(DOWNLOAD \"http://downloads.tuxfamily.org/eigen/lapack_addons_3.4.1.tgz\"\n                  \"${CMAKE_CURRENT_SOURCE_DIR}/lapack_addons_3.4.1.tgz\"\n                  INACTIVITY_TIMEOUT 15\n                  TIMEOUT 240\n                  STATUS download_status\n                  EXPECTED_MD5 ab5742640617e3221a873aba44bbdc93\n                  SHOW_PROGRESS)\n                  \n    message(STATUS ${download_status})\n    list(GET download_status 0 download_status_num)\n    set(download_status_num 0)\n    if(download_status_num EQUAL 0)\n      message(STATUS \"Setup lapack reference and lapack unit tests\")\n      execute_process(COMMAND tar xzf  \"lapack_addons_3.4.1.tgz\" WORKING_DIRECTORY ${CMAKE_CURRENT_SOURCE_DIR})\n    else()\n      message(STATUS \"Download of lapack_addons_3.4.1.tgz failed, LAPACK unit tests wont be enabled\")\n      set(EIGEN_ENABLE_LAPACK_TESTS false)\n    endif()\n                  \n  endif()\n  \n  get_filename_component(eigen_full_path_to_reference_lapack \"./reference/\" ABSOLUTE)\n  if(EXISTS ${eigen_full_path_to_reference_lapack})\n    set(EigenLapack_funcfilenames\n        ssyev.f   dsyev.f   csyev.f   zsyev.f\n        spotrf.f  dpotrf.f  cpotrf.f  zpotrf.f\n        spotrs.f  dpotrs.f  cpotrs.f  zpotrs.f\n        sgetrf.f  dgetrf.f  cgetrf.f  zgetrf.f\n        sgetrs.f  dgetrs.f  cgetrs.f  zgetrs.f)\n    \n    FILE(GLOB ReferenceLapack_SRCS0 RELATIVE ${CMAKE_CURRENT_SOURCE_DIR} \"reference/*.f\")\n    foreach(filename1 IN LISTS ReferenceLapack_SRCS0)\n      string(REPLACE \"reference/\" \"\" filename ${filename1})\n      list(FIND EigenLapack_SRCS ${filename} id1)\n      list(FIND EigenLapack_funcfilenames ${filename} id2)\n      if((id1 EQUAL -1) AND (id2 EQUAL -1))\n        set(ReferenceLapack_SRCS ${ReferenceLapack_SRCS} reference/${filename})\n      endif()\n    endforeach()\n  endif()\n  \n  \nendif(EIGEN_ENABLE_LAPACK_TESTS)\n\nendif(EIGEN_Fortran_COMPILER_WORKS)\n\nadd_library(eigen_lapack_static ${EigenLapack_SRCS} ${ReferenceLapack_SRCS})\nadd_library(eigen_lapack SHARED ${EigenLapack_SRCS})\n\ntarget_link_libraries(eigen_lapack  eigen_blas)\n\nif(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO)\n  target_link_libraries(eigen_lapack_static ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO})\n  target_link_libraries(eigen_lapack        ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO})\nendif()\n\nadd_dependencies(lapack eigen_lapack eigen_lapack_static)\n\ninstall(TARGETS eigen_lapack eigen_lapack_static\n        RUNTIME DESTINATION bin\n        LIBRARY DESTINATION lib\n        ARCHIVE DESTINATION lib)\n\n        \n        \nget_filename_component(eigen_full_path_to_testing_lapack \"./testing/\" ABSOLUTE)\nif(EXISTS ${eigen_full_path_to_testing_lapack})\n  \n  # The following comes from lapack/TESTING/CMakeLists.txt\n  # Get Python\n  find_package(PythonInterp)\n  message(STATUS \"Looking for Python found - ${PYTHONINTERP_FOUND}\")\n  if (PYTHONINTERP_FOUND)\n    message(STATUS \"Using Python version ${PYTHON_VERSION_STRING}\")\n  endif()\n\n  set(LAPACK_SOURCE_DIR ${CMAKE_CURRENT_SOURCE_DIR})\n  set(LAPACK_BINARY_DIR ${CMAKE_CURRENT_BINARY_DIR})\n  set(BUILD_SINGLE      true)\n  set(BUILD_DOUBLE      true)\n  set(BUILD_COMPLEX     true)\n  set(BUILD_COMPLEX16E  true)\n  \n  if(MSVC_VERSION)\n#  string(REPLACE \"/STACK:10000000\" \"/STACK:900000000000000000\"\n#    CMAKE_EXE_LINKER_FLAGS \"${CMAKE_EXE_LINKER_FLAGS}\")\n  string(REGEX REPLACE \"(.*)/STACK:(.*) (.*)\" \"\\\\1/STACK:900000000000000000 \\\\3\"\n    CMAKE_EXE_LINKER_FLAGS \"${CMAKE_EXE_LINKER_FLAGS}\")\n  endif()\n  add_subdirectory(testing/MATGEN)\n  add_subdirectory(testing/LIN)\n  add_subdirectory(testing/EIG)\n  macro(add_lapack_test output input target)\n    set(TEST_INPUT \"${LAPACK_SOURCE_DIR}/testing/${input}\")\n    set(TEST_OUTPUT \"${LAPACK_BINARY_DIR}/testing/${output}\")\n    get_target_property(TEST_LOC ${target} LOCATION)\n    string(REPLACE \".\" \"_\" input_name ${input})\n    set(testName \"${target}_${input_name}\")\n    if(EXISTS \"${TEST_INPUT}\")\n      add_test(LAPACK-${testName} \"${CMAKE_COMMAND}\"\n        -DTEST=${TEST_LOC}\n        -DINPUT=${TEST_INPUT} \n        -DOUTPUT=${TEST_OUTPUT} \n        -DINTDIR=${CMAKE_CFG_INTDIR}\n        -P \"${LAPACK_SOURCE_DIR}/testing/runtest.cmake\")\n    endif()\n  endmacro(add_lapack_test)\n\n  if (BUILD_SINGLE)\n  add_lapack_test(stest.out stest.in xlintsts)\n  #\n  # ======== SINGLE RFP LIN TESTS ========================\n  add_lapack_test(stest_rfp.out stest_rfp.in xlintstrfs)\n  #\n  #\n  # ======== SINGLE EIG TESTS ===========================\n  #\n\n  add_lapack_test(snep.out nep.in xeigtsts)\n\n\n  add_lapack_test(ssep.out sep.in xeigtsts)\n\n\n  add_lapack_test(ssvd.out svd.in xeigtsts)\n\n\n  add_lapack_test(sec.out sec.in xeigtsts)\n\n\n  add_lapack_test(sed.out sed.in xeigtsts)\n\n\n  add_lapack_test(sgg.out sgg.in xeigtsts)\n\n\n  add_lapack_test(sgd.out sgd.in xeigtsts)\n\n\n  add_lapack_test(ssb.out ssb.in xeigtsts)\n\n\n  add_lapack_test(ssg.out ssg.in xeigtsts)\n\n\n  add_lapack_test(sbal.out sbal.in xeigtsts)\n\n\n  add_lapack_test(sbak.out sbak.in xeigtsts)\n\n\n  add_lapack_test(sgbal.out sgbal.in xeigtsts)\n\n\n  add_lapack_test(sgbak.out sgbak.in xeigtsts)\n\n\n  add_lapack_test(sbb.out sbb.in xeigtsts)\n\n\n  add_lapack_test(sglm.out glm.in xeigtsts)\n\n\n  add_lapack_test(sgqr.out gqr.in xeigtsts)\n\n\n  add_lapack_test(sgsv.out gsv.in xeigtsts)\n\n\n  add_lapack_test(scsd.out csd.in xeigtsts)\n\n\n  add_lapack_test(slse.out lse.in xeigtsts)\n  endif()\n\n  if (BUILD_DOUBLE)\n  #\n  # ======== DOUBLE LIN TESTS ===========================\n  add_lapack_test(dtest.out dtest.in xlintstd)\n  #\n  # ======== DOUBLE RFP LIN TESTS ========================\n  add_lapack_test(dtest_rfp.out dtest_rfp.in xlintstrfd)\n  #\n  # ======== DOUBLE EIG TESTS ===========================\n\n  add_lapack_test(dnep.out nep.in xeigtstd)\n\n\n  add_lapack_test(dsep.out sep.in xeigtstd)\n\n\n  add_lapack_test(dsvd.out svd.in xeigtstd)\n\n\n  add_lapack_test(dec.out dec.in xeigtstd)\n\n\n  add_lapack_test(ded.out ded.in xeigtstd)\n\n\n  add_lapack_test(dgg.out dgg.in xeigtstd)\n\n\n  add_lapack_test(dgd.out dgd.in xeigtstd)\n\n\n  add_lapack_test(dsb.out dsb.in xeigtstd)\n\n\n  add_lapack_test(dsg.out dsg.in xeigtstd)\n\n\n  add_lapack_test(dbal.out dbal.in xeigtstd)\n\n\n  add_lapack_test(dbak.out dbak.in xeigtstd)\n\n\n  add_lapack_test(dgbal.out dgbal.in xeigtstd)\n\n\n  add_lapack_test(dgbak.out dgbak.in xeigtstd)\n\n\n  add_lapack_test(dbb.out dbb.in xeigtstd)\n\n\n  add_lapack_test(dglm.out glm.in xeigtstd)\n\n\n  add_lapack_test(dgqr.out gqr.in xeigtstd)\n\n\n  add_lapack_test(dgsv.out gsv.in xeigtstd)\n\n\n  add_lapack_test(dcsd.out csd.in xeigtstd)\n\n\n  add_lapack_test(dlse.out lse.in xeigtstd)\n  endif()\n\n  if (BUILD_COMPLEX)\n  add_lapack_test(ctest.out ctest.in xlintstc)\n  #\n  # ======== COMPLEX RFP LIN TESTS ========================\n  add_lapack_test(ctest_rfp.out ctest_rfp.in xlintstrfc)\n  #\n  # ======== COMPLEX EIG TESTS ===========================\n\n  add_lapack_test(cnep.out nep.in xeigtstc)\n\n\n  add_lapack_test(csep.out sep.in xeigtstc)\n\n\n  add_lapack_test(csvd.out svd.in xeigtstc)\n\n\n  add_lapack_test(cec.out cec.in xeigtstc)\n\n\n  add_lapack_test(ced.out ced.in xeigtstc)\n\n\n  add_lapack_test(cgg.out cgg.in xeigtstc)\n\n\n  add_lapack_test(cgd.out cgd.in xeigtstc)\n\n\n  add_lapack_test(csb.out csb.in xeigtstc)\n\n\n  add_lapack_test(csg.out csg.in xeigtstc)\n\n\n  add_lapack_test(cbal.out cbal.in xeigtstc)\n\n\n  add_lapack_test(cbak.out cbak.in xeigtstc)\n\n\n  add_lapack_test(cgbal.out cgbal.in xeigtstc)\n\n\n  add_lapack_test(cgbak.out cgbak.in xeigtstc)\n\n\n  add_lapack_test(cbb.out cbb.in xeigtstc)\n\n\n  add_lapack_test(cglm.out glm.in xeigtstc)\n\n\n  add_lapack_test(cgqr.out gqr.in xeigtstc)\n\n\n  add_lapack_test(cgsv.out gsv.in xeigtstc)\n\n\n  add_lapack_test(ccsd.out csd.in xeigtstc)\n\n\n  add_lapack_test(clse.out lse.in xeigtstc)\n  endif()\n\n  if (BUILD_COMPLEX16)\n  #\n  # ======== COMPLEX16 LIN TESTS ========================\n  add_lapack_test(ztest.out ztest.in xlintstz)\n  #\n  # ======== COMPLEX16 RFP LIN TESTS ========================\n  add_lapack_test(ztest_rfp.out ztest_rfp.in xlintstrfz)\n  #\n  # ======== COMPLEX16 EIG TESTS ===========================\n\n  add_lapack_test(znep.out nep.in xeigtstz)\n\n\n  add_lapack_test(zsep.out sep.in xeigtstz)\n\n\n  add_lapack_test(zsvd.out svd.in xeigtstz)\n\n\n  add_lapack_test(zec.out zec.in xeigtstz)\n\n\n  add_lapack_test(zed.out zed.in xeigtstz)\n\n\n  add_lapack_test(zgg.out zgg.in xeigtstz)\n\n\n  add_lapack_test(zgd.out zgd.in xeigtstz)\n\n\n  add_lapack_test(zsb.out zsb.in xeigtstz)\n\n\n  add_lapack_test(zsg.out zsg.in xeigtstz)\n\n\n  add_lapack_test(zbal.out zbal.in xeigtstz)\n\n\n  add_lapack_test(zbak.out zbak.in xeigtstz)\n\n\n  add_lapack_test(zgbal.out zgbal.in xeigtstz)\n\n\n  add_lapack_test(zgbak.out zgbak.in xeigtstz)\n\n\n  add_lapack_test(zbb.out zbb.in xeigtstz)\n\n\n  add_lapack_test(zglm.out glm.in xeigtstz)\n\n\n  add_lapack_test(zgqr.out gqr.in xeigtstz)\n\n\n  add_lapack_test(zgsv.out gsv.in xeigtstz)\n\n\n  add_lapack_test(zcsd.out csd.in xeigtstz)\n\n\n  add_lapack_test(zlse.out lse.in xeigtstz)\n  endif()\n\n\n  if (BUILD_SIMPLE)\n      if (BUILD_DOUBLE)\n  #\n  # ======== SINGLE-DOUBLE PROTO LIN TESTS ==============\n          add_lapack_test(dstest.out dstest.in xlintstds)\n      endif()\n  endif()\n\n\n  if (BUILD_COMPLEX)\n      if (BUILD_COMPLEX16)\n  #\n  # ======== COMPLEX-COMPLEX16 LIN TESTS ========================\n          add_lapack_test(zctest.out zctest.in xlintstzc)\n      endif()\n  endif()\n\n  # ==============================================================================\n\n  execute_process(COMMAND ${CMAKE_COMMAND} -E copy ${LAPACK_SOURCE_DIR}/testing/lapack_testing.py ${LAPACK_BINARY_DIR})\n  add_test(\n    NAME LAPACK_Test_Summary\n    WORKING_DIRECTORY ${LAPACK_BINARY_DIR}\n    COMMAND ${PYTHON_EXECUTABLE} \"lapack_testing.py\"\n  )\n\nendif()\n\n"
  },
  {
    "path": "include/eigen3/lapack/cholesky.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2010-2011 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"lapack_common.h\"\n#include <Eigen/Cholesky>\n\n// POTRF computes the Cholesky factorization of a real symmetric positive definite matrix A.\nEIGEN_LAPACK_FUNC(potrf,(char* uplo, int *n, RealScalar *pa, int *lda, int *info))\n{\n  *info = 0;\n        if(UPLO(*uplo)==INVALID) *info = -1;\n  else  if(*n<0)                 *info = -2;\n  else  if(*lda<std::max(1,*n))  *info = -4;\n  if(*info!=0)\n  {\n    int e = -*info;\n    return xerbla_(SCALAR_SUFFIX_UP\"POTRF\", &e, 6);\n  }\n\n  Scalar* a = reinterpret_cast<Scalar*>(pa);\n  MatrixType A(a,*n,*n,*lda);\n  int ret;\n  if(UPLO(*uplo)==UP) ret = int(internal::llt_inplace<Scalar, Upper>::blocked(A));\n  else                ret = int(internal::llt_inplace<Scalar, Lower>::blocked(A));\n\n  if(ret>=0)\n    *info = ret+1;\n  \n  return 0;\n}\n\n// POTRS solves a system of linear equations A*X = B with a symmetric\n// positive definite matrix A using the Cholesky factorization\n// A = U**T*U or A = L*L**T computed by DPOTRF.\nEIGEN_LAPACK_FUNC(potrs,(char* uplo, int *n, int *nrhs, RealScalar *pa, int *lda, RealScalar *pb, int *ldb, int *info))\n{\n  *info = 0;\n        if(UPLO(*uplo)==INVALID) *info = -1;\n  else  if(*n<0)                 *info = -2;\n  else  if(*nrhs<0)              *info = -3;\n  else  if(*lda<std::max(1,*n))  *info = -5;\n  else  if(*ldb<std::max(1,*n))  *info = -7;\n  if(*info!=0)\n  {\n    int e = -*info;\n    return xerbla_(SCALAR_SUFFIX_UP\"POTRS\", &e, 6);\n  }\n\n  Scalar* a = reinterpret_cast<Scalar*>(pa);\n  Scalar* b = reinterpret_cast<Scalar*>(pb);\n  MatrixType A(a,*n,*n,*lda);\n  MatrixType B(b,*n,*nrhs,*ldb);\n\n  if(UPLO(*uplo)==UP)\n  {\n    A.triangularView<Upper>().adjoint().solveInPlace(B);\n    A.triangularView<Upper>().solveInPlace(B);\n  }\n  else\n  {\n    A.triangularView<Lower>().solveInPlace(B);\n    A.triangularView<Lower>().adjoint().solveInPlace(B);\n  }\n\n  return 0;\n}\n"
  },
  {
    "path": "include/eigen3/lapack/clacgv.f",
    "content": "*> \\brief \\b CLACGV\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*> \\htmlonly\n*> Download CLACGV + dependencies \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clacgv.f\"> \n*> [TGZ]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clacgv.f\"> \n*> [ZIP]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clacgv.f\"> \n*> [TXT]</a>\n*> \\endhtmlonly \n*\n*  Definition:\n*  ===========\n*\n*       SUBROUTINE CLACGV( N, X, INCX )\n* \n*       .. Scalar Arguments ..\n*       INTEGER            INCX, N\n*       ..\n*       .. Array Arguments ..\n*       COMPLEX            X( * )\n*       ..\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> CLACGV conjugates a complex vector of length N.\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] N\n*> \\verbatim\n*>          N is INTEGER\n*>          The length of the vector X.  N >= 0.\n*> \\endverbatim\n*>\n*> \\param[in,out] X\n*> \\verbatim\n*>          X is COMPLEX array, dimension\n*>                         (1+(N-1)*abs(INCX))\n*>          On entry, the vector of length N to be conjugated.\n*>          On exit, X is overwritten with conjg(X).\n*> \\endverbatim\n*>\n*> \\param[in] INCX\n*> \\verbatim\n*>          INCX is INTEGER\n*>          The spacing between successive elements of X.\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date November 2011\n*\n*> \\ingroup complexOTHERauxiliary\n*\n*  =====================================================================\n      SUBROUTINE CLACGV( N, X, INCX )\n*\n*  -- LAPACK auxiliary routine (version 3.4.0) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     November 2011\n*\n*     .. Scalar Arguments ..\n      INTEGER            INCX, N\n*     ..\n*     .. Array Arguments ..\n      COMPLEX            X( * )\n*     ..\n*\n* =====================================================================\n*\n*     .. Local Scalars ..\n      INTEGER            I, IOFF\n*     ..\n*     .. Intrinsic Functions ..\n      INTRINSIC          CONJG\n*     ..\n*     .. Executable Statements ..\n*\n      IF( INCX.EQ.1 ) THEN\n         DO 10 I = 1, N\n            X( I ) = CONJG( X( I ) )\n   10    CONTINUE\n      ELSE\n         IOFF = 1\n         IF( INCX.LT.0 )\n     $      IOFF = 1 - ( N-1 )*INCX\n         DO 20 I = 1, N\n            X( IOFF ) = CONJG( X( IOFF ) )\n            IOFF = IOFF + INCX\n   20    CONTINUE\n      END IF\n      RETURN\n*\n*     End of CLACGV\n*\n      END\n"
  },
  {
    "path": "include/eigen3/lapack/cladiv.f",
    "content": "*> \\brief \\b CLADIV\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*> \\htmlonly\n*> Download CLADIV + dependencies \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cladiv.f\"> \n*> [TGZ]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cladiv.f\"> \n*> [ZIP]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cladiv.f\"> \n*> [TXT]</a>\n*> \\endhtmlonly \n*\n*  Definition:\n*  ===========\n*\n*       COMPLEX FUNCTION CLADIV( X, Y )\n* \n*       .. Scalar Arguments ..\n*       COMPLEX            X, Y\n*       ..\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> CLADIV := X / Y, where X and Y are complex.  The computation of X / Y\n*> will not overflow on an intermediary step unless the results\n*> overflows.\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] X\n*> \\verbatim\n*>          X is COMPLEX\n*> \\endverbatim\n*>\n*> \\param[in] Y\n*> \\verbatim\n*>          Y is COMPLEX\n*>          The complex scalars X and Y.\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date November 2011\n*\n*> \\ingroup complexOTHERauxiliary\n*\n*  =====================================================================\n      COMPLEX FUNCTION CLADIV( X, Y )\n*\n*  -- LAPACK auxiliary routine (version 3.4.0) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     November 2011\n*\n*     .. Scalar Arguments ..\n      COMPLEX            X, Y\n*     ..\n*\n*  =====================================================================\n*\n*     .. Local Scalars ..\n      REAL               ZI, ZR\n*     ..\n*     .. External Subroutines ..\n      EXTERNAL           SLADIV\n*     ..\n*     .. Intrinsic Functions ..\n      INTRINSIC          AIMAG, CMPLX, REAL\n*     ..\n*     .. Executable Statements ..\n*\n      CALL SLADIV( REAL( X ), AIMAG( X ), REAL( Y ), AIMAG( Y ), ZR,\n     $             ZI )\n      CLADIV = CMPLX( ZR, ZI )\n*\n      RETURN\n*\n*     End of CLADIV\n*\n      END\n"
  },
  {
    "path": "include/eigen3/lapack/clarf.f",
    "content": "*> \\brief \\b CLARF\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*> \\htmlonly\n*> Download CLARF + dependencies \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clarf.f\"> \n*> [TGZ]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clarf.f\"> \n*> [ZIP]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clarf.f\"> \n*> [TXT]</a>\n*> \\endhtmlonly \n*\n*  Definition:\n*  ===========\n*\n*       SUBROUTINE CLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )\n* \n*       .. Scalar Arguments ..\n*       CHARACTER          SIDE\n*       INTEGER            INCV, LDC, M, N\n*       COMPLEX            TAU\n*       ..\n*       .. Array Arguments ..\n*       COMPLEX            C( LDC, * ), V( * ), WORK( * )\n*       ..\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> CLARF applies a complex elementary reflector H to a complex M-by-N\n*> matrix C, from either the left or the right. H is represented in the\n*> form\n*>\n*>       H = I - tau * v * v**H\n*>\n*> where tau is a complex scalar and v is a complex vector.\n*>\n*> If tau = 0, then H is taken to be the unit matrix.\n*>\n*> To apply H**H (the conjugate transpose of H), supply conjg(tau) instead\n*> tau.\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] SIDE\n*> \\verbatim\n*>          SIDE is CHARACTER*1\n*>          = 'L': form  H * C\n*>          = 'R': form  C * H\n*> \\endverbatim\n*>\n*> \\param[in] M\n*> \\verbatim\n*>          M is INTEGER\n*>          The number of rows of the matrix C.\n*> \\endverbatim\n*>\n*> \\param[in] N\n*> \\verbatim\n*>          N is INTEGER\n*>          The number of columns of the matrix C.\n*> \\endverbatim\n*>\n*> \\param[in] V\n*> \\verbatim\n*>          V is COMPLEX array, dimension\n*>                     (1 + (M-1)*abs(INCV)) if SIDE = 'L'\n*>                  or (1 + (N-1)*abs(INCV)) if SIDE = 'R'\n*>          The vector v in the representation of H. V is not used if\n*>          TAU = 0.\n*> \\endverbatim\n*>\n*> \\param[in] INCV\n*> \\verbatim\n*>          INCV is INTEGER\n*>          The increment between elements of v. INCV <> 0.\n*> \\endverbatim\n*>\n*> \\param[in] TAU\n*> \\verbatim\n*>          TAU is COMPLEX\n*>          The value tau in the representation of H.\n*> \\endverbatim\n*>\n*> \\param[in,out] C\n*> \\verbatim\n*>          C is COMPLEX array, dimension (LDC,N)\n*>          On entry, the M-by-N matrix C.\n*>          On exit, C is overwritten by the matrix H * C if SIDE = 'L',\n*>          or C * H if SIDE = 'R'.\n*> \\endverbatim\n*>\n*> \\param[in] LDC\n*> \\verbatim\n*>          LDC is INTEGER\n*>          The leading dimension of the array C. LDC >= max(1,M).\n*> \\endverbatim\n*>\n*> \\param[out] WORK\n*> \\verbatim\n*>          WORK is COMPLEX array, dimension\n*>                         (N) if SIDE = 'L'\n*>                      or (M) if SIDE = 'R'\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date November 2011\n*\n*> \\ingroup complexOTHERauxiliary\n*\n*  =====================================================================\n      SUBROUTINE CLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )\n*\n*  -- LAPACK auxiliary routine (version 3.4.0) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     November 2011\n*\n*     .. Scalar Arguments ..\n      CHARACTER          SIDE\n      INTEGER            INCV, LDC, M, N\n      COMPLEX            TAU\n*     ..\n*     .. Array Arguments ..\n      COMPLEX            C( LDC, * ), V( * ), WORK( * )\n*     ..\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      COMPLEX            ONE, ZERO\n      PARAMETER          ( ONE = ( 1.0E+0, 0.0E+0 ),\n     $                   ZERO = ( 0.0E+0, 0.0E+0 ) )\n*     ..\n*     .. Local Scalars ..\n      LOGICAL            APPLYLEFT\n      INTEGER            I, LASTV, LASTC\n*     ..\n*     .. External Subroutines ..\n      EXTERNAL           CGEMV, CGERC\n*     ..\n*     .. External Functions ..\n      LOGICAL            LSAME\n      INTEGER            ILACLR, ILACLC\n      EXTERNAL           LSAME, ILACLR, ILACLC\n*     ..\n*     .. Executable Statements ..\n*\n      APPLYLEFT = LSAME( SIDE, 'L' )\n      LASTV = 0\n      LASTC = 0\n      IF( TAU.NE.ZERO ) THEN\n!     Set up variables for scanning V.  LASTV begins pointing to the end\n!     of V.\n         IF( APPLYLEFT ) THEN\n            LASTV = M\n         ELSE\n            LASTV = N\n         END IF\n         IF( INCV.GT.0 ) THEN\n            I = 1 + (LASTV-1) * INCV\n         ELSE\n            I = 1\n         END IF\n!     Look for the last non-zero row in V.\n         DO WHILE( LASTV.GT.0 .AND. V( I ).EQ.ZERO )\n            LASTV = LASTV - 1\n            I = I - INCV\n         END DO\n         IF( APPLYLEFT ) THEN\n!     Scan for the last non-zero column in C(1:lastv,:).\n            LASTC = ILACLC(LASTV, N, C, LDC)\n         ELSE\n!     Scan for the last non-zero row in C(:,1:lastv).\n            LASTC = ILACLR(M, LASTV, C, LDC)\n         END IF\n      END IF\n!     Note that lastc.eq.0 renders the BLAS operations null; no special\n!     case is needed at this level.\n      IF( APPLYLEFT ) THEN\n*\n*        Form  H * C\n*\n         IF( LASTV.GT.0 ) THEN\n*\n*           w(1:lastc,1) := C(1:lastv,1:lastc)**H * v(1:lastv,1)\n*\n            CALL CGEMV( 'Conjugate transpose', LASTV, LASTC, ONE,\n     $           C, LDC, V, INCV, ZERO, WORK, 1 )\n*\n*           C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**H\n*\n            CALL CGERC( LASTV, LASTC, -TAU, V, INCV, WORK, 1, C, LDC )\n         END IF\n      ELSE\n*\n*        Form  C * H\n*\n         IF( LASTV.GT.0 ) THEN\n*\n*           w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1)\n*\n            CALL CGEMV( 'No transpose', LASTC, LASTV, ONE, C, LDC,\n     $           V, INCV, ZERO, WORK, 1 )\n*\n*           C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**H\n*\n            CALL CGERC( LASTC, LASTV, -TAU, WORK, 1, V, INCV, C, LDC )\n         END IF\n      END IF\n      RETURN\n*\n*     End of CLARF\n*\n      END\n"
  },
  {
    "path": "include/eigen3/lapack/clarfb.f",
    "content": "*> \\brief \\b CLARFB\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*> \\htmlonly\n*> Download CLARFB + dependencies \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clarfb.f\"> \n*> [TGZ]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clarfb.f\"> \n*> [ZIP]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clarfb.f\"> \n*> [TXT]</a>\n*> \\endhtmlonly \n*\n*  Definition:\n*  ===========\n*\n*       SUBROUTINE CLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV,\n*                          T, LDT, C, LDC, WORK, LDWORK )\n* \n*       .. Scalar Arguments ..\n*       CHARACTER          DIRECT, SIDE, STOREV, TRANS\n*       INTEGER            K, LDC, LDT, LDV, LDWORK, M, N\n*       ..\n*       .. Array Arguments ..\n*       COMPLEX            C( LDC, * ), T( LDT, * ), V( LDV, * ),\n*      $                   WORK( LDWORK, * )\n*       ..\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> CLARFB applies a complex block reflector H or its transpose H**H to a\n*> complex M-by-N matrix C, from either the left or the right.\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] SIDE\n*> \\verbatim\n*>          SIDE is CHARACTER*1\n*>          = 'L': apply H or H**H from the Left\n*>          = 'R': apply H or H**H from the Right\n*> \\endverbatim\n*>\n*> \\param[in] TRANS\n*> \\verbatim\n*>          TRANS is CHARACTER*1\n*>          = 'N': apply H (No transpose)\n*>          = 'C': apply H**H (Conjugate transpose)\n*> \\endverbatim\n*>\n*> \\param[in] DIRECT\n*> \\verbatim\n*>          DIRECT is CHARACTER*1\n*>          Indicates how H is formed from a product of elementary\n*>          reflectors\n*>          = 'F': H = H(1) H(2) . . . H(k) (Forward)\n*>          = 'B': H = H(k) . . . H(2) H(1) (Backward)\n*> \\endverbatim\n*>\n*> \\param[in] STOREV\n*> \\verbatim\n*>          STOREV is CHARACTER*1\n*>          Indicates how the vectors which define the elementary\n*>          reflectors are stored:\n*>          = 'C': Columnwise\n*>          = 'R': Rowwise\n*> \\endverbatim\n*>\n*> \\param[in] M\n*> \\verbatim\n*>          M is INTEGER\n*>          The number of rows of the matrix C.\n*> \\endverbatim\n*>\n*> \\param[in] N\n*> \\verbatim\n*>          N is INTEGER\n*>          The number of columns of the matrix C.\n*> \\endverbatim\n*>\n*> \\param[in] K\n*> \\verbatim\n*>          K is INTEGER\n*>          The order of the matrix T (= the number of elementary\n*>          reflectors whose product defines the block reflector).\n*> \\endverbatim\n*>\n*> \\param[in] V\n*> \\verbatim\n*>          V is COMPLEX array, dimension\n*>                                (LDV,K) if STOREV = 'C'\n*>                                (LDV,M) if STOREV = 'R' and SIDE = 'L'\n*>                                (LDV,N) if STOREV = 'R' and SIDE = 'R'\n*>          The matrix V. See Further Details.\n*> \\endverbatim\n*>\n*> \\param[in] LDV\n*> \\verbatim\n*>          LDV is INTEGER\n*>          The leading dimension of the array V.\n*>          If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M);\n*>          if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N);\n*>          if STOREV = 'R', LDV >= K.\n*> \\endverbatim\n*>\n*> \\param[in] T\n*> \\verbatim\n*>          T is COMPLEX array, dimension (LDT,K)\n*>          The triangular K-by-K matrix T in the representation of the\n*>          block reflector.\n*> \\endverbatim\n*>\n*> \\param[in] LDT\n*> \\verbatim\n*>          LDT is INTEGER\n*>          The leading dimension of the array T. LDT >= K.\n*> \\endverbatim\n*>\n*> \\param[in,out] C\n*> \\verbatim\n*>          C is COMPLEX array, dimension (LDC,N)\n*>          On entry, the M-by-N matrix C.\n*>          On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H.\n*> \\endverbatim\n*>\n*> \\param[in] LDC\n*> \\verbatim\n*>          LDC is INTEGER\n*>          The leading dimension of the array C. LDC >= max(1,M).\n*> \\endverbatim\n*>\n*> \\param[out] WORK\n*> \\verbatim\n*>          WORK is COMPLEX array, dimension (LDWORK,K)\n*> \\endverbatim\n*>\n*> \\param[in] LDWORK\n*> \\verbatim\n*>          LDWORK is INTEGER\n*>          The leading dimension of the array WORK.\n*>          If SIDE = 'L', LDWORK >= max(1,N);\n*>          if SIDE = 'R', LDWORK >= max(1,M).\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date November 2011\n*\n*> \\ingroup complexOTHERauxiliary\n*\n*> \\par Further Details:\n*  =====================\n*>\n*> \\verbatim\n*>\n*>  The shape of the matrix V and the storage of the vectors which define\n*>  the H(i) is best illustrated by the following example with n = 5 and\n*>  k = 3. The elements equal to 1 are not stored; the corresponding\n*>  array elements are modified but restored on exit. The rest of the\n*>  array is not used.\n*>\n*>  DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':\n*>\n*>               V = (  1       )                 V = (  1 v1 v1 v1 v1 )\n*>                   ( v1  1    )                     (     1 v2 v2 v2 )\n*>                   ( v1 v2  1 )                     (        1 v3 v3 )\n*>                   ( v1 v2 v3 )\n*>                   ( v1 v2 v3 )\n*>\n*>  DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':\n*>\n*>               V = ( v1 v2 v3 )                 V = ( v1 v1  1       )\n*>                   ( v1 v2 v3 )                     ( v2 v2 v2  1    )\n*>                   (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )\n*>                   (     1 v3 )\n*>                   (        1 )\n*> \\endverbatim\n*>\n*  =====================================================================\n      SUBROUTINE CLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV,\n     $                   T, LDT, C, LDC, WORK, LDWORK )\n*\n*  -- LAPACK auxiliary routine (version 3.4.0) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     November 2011\n*\n*     .. Scalar Arguments ..\n      CHARACTER          DIRECT, SIDE, STOREV, TRANS\n      INTEGER            K, LDC, LDT, LDV, LDWORK, M, N\n*     ..\n*     .. Array Arguments ..\n      COMPLEX            C( LDC, * ), T( LDT, * ), V( LDV, * ),\n     $                   WORK( LDWORK, * )\n*     ..\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      COMPLEX            ONE\n      PARAMETER          ( ONE = ( 1.0E+0, 0.0E+0 ) )\n*     ..\n*     .. Local Scalars ..\n      CHARACTER          TRANST\n      INTEGER            I, J, LASTV, LASTC\n*     ..\n*     .. External Functions ..\n      LOGICAL            LSAME\n      INTEGER            ILACLR, ILACLC\n      EXTERNAL           LSAME, ILACLR, ILACLC\n*     ..\n*     .. External Subroutines ..\n      EXTERNAL           CCOPY, CGEMM, CLACGV, CTRMM\n*     ..\n*     .. Intrinsic Functions ..\n      INTRINSIC          CONJG\n*     ..\n*     .. Executable Statements ..\n*\n*     Quick return if possible\n*\n      IF( M.LE.0 .OR. N.LE.0 )\n     $   RETURN\n*\n      IF( LSAME( TRANS, 'N' ) ) THEN\n         TRANST = 'C'\n      ELSE\n         TRANST = 'N'\n      END IF\n*\n      IF( LSAME( STOREV, 'C' ) ) THEN\n*\n         IF( LSAME( DIRECT, 'F' ) ) THEN\n*\n*           Let  V =  ( V1 )    (first K rows)\n*                     ( V2 )\n*           where  V1  is unit lower triangular.\n*\n            IF( LSAME( SIDE, 'L' ) ) THEN\n*\n*              Form  H * C  or  H**H * C  where  C = ( C1 )\n*                                                    ( C2 )\n*\n               LASTV = MAX( K, ILACLR( M, K, V, LDV ) )\n               LASTC = ILACLC( LASTV, N, C, LDC )\n*\n*              W := C**H * V  =  (C1**H * V1 + C2**H * V2)  (stored in WORK)\n*\n*              W := C1**H\n*\n               DO 10 J = 1, K\n                  CALL CCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 )\n                  CALL CLACGV( LASTC, WORK( 1, J ), 1 )\n   10          CONTINUE\n*\n*              W := W * V1\n*\n               CALL CTRMM( 'Right', 'Lower', 'No transpose', 'Unit',\n     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )\n               IF( LASTV.GT.K ) THEN\n*\n*                 W := W + C2**H *V2\n*\n                  CALL CGEMM( 'Conjugate transpose', 'No transpose',\n     $                 LASTC, K, LASTV-K, ONE, C( K+1, 1 ), LDC,\n     $                 V( K+1, 1 ), LDV, ONE, WORK, LDWORK )\n               END IF\n*\n*              W := W * T**H  or  W * T\n*\n               CALL CTRMM( 'Right', 'Upper', TRANST, 'Non-unit',\n     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )\n*\n*              C := C - V * W**H\n*\n               IF( M.GT.K ) THEN\n*\n*                 C2 := C2 - V2 * W**H\n*\n                  CALL CGEMM( 'No transpose', 'Conjugate transpose',\n     $                 LASTV-K, LASTC, K, -ONE, V( K+1, 1 ), LDV,\n     $                 WORK, LDWORK, ONE, C( K+1, 1 ), LDC )\n               END IF\n*\n*              W := W * V1**H\n*\n               CALL CTRMM( 'Right', 'Lower', 'Conjugate transpose',\n     $              'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK )\n*\n*              C1 := C1 - W**H\n*\n               DO 30 J = 1, K\n                  DO 20 I = 1, LASTC\n                     C( J, I ) = C( J, I ) - CONJG( WORK( I, J ) )\n   20             CONTINUE\n   30          CONTINUE\n*\n            ELSE IF( LSAME( SIDE, 'R' ) ) THEN\n*\n*              Form  C * H  or  C * H**H  where  C = ( C1  C2 )\n*\n               LASTV = MAX( K, ILACLR( N, K, V, LDV ) )\n               LASTC = ILACLR( M, LASTV, C, LDC )\n*\n*              W := C * V  =  (C1*V1 + C2*V2)  (stored in WORK)\n*\n*              W := C1\n*\n               DO 40 J = 1, K\n                  CALL CCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 )\n   40          CONTINUE\n*\n*              W := W * V1\n*\n               CALL CTRMM( 'Right', 'Lower', 'No transpose', 'Unit',\n     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )\n               IF( LASTV.GT.K ) THEN\n*\n*                 W := W + C2 * V2\n*\n                  CALL CGEMM( 'No transpose', 'No transpose',\n     $                 LASTC, K, LASTV-K,\n     $                 ONE, C( 1, K+1 ), LDC, V( K+1, 1 ), LDV,\n     $                 ONE, WORK, LDWORK )\n               END IF\n*\n*              W := W * T  or  W * T**H\n*\n               CALL CTRMM( 'Right', 'Upper', TRANS, 'Non-unit',\n     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )\n*\n*              C := C - W * V**H\n*\n               IF( LASTV.GT.K ) THEN\n*\n*                 C2 := C2 - W * V2**H\n*\n                  CALL CGEMM( 'No transpose', 'Conjugate transpose',\n     $                 LASTC, LASTV-K, K,\n     $                 -ONE, WORK, LDWORK, V( K+1, 1 ), LDV,\n     $                 ONE, C( 1, K+1 ), LDC )\n               END IF\n*\n*              W := W * V1**H\n*\n               CALL CTRMM( 'Right', 'Lower', 'Conjugate transpose',\n     $              'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK )\n*\n*              C1 := C1 - W\n*\n               DO 60 J = 1, K\n                  DO 50 I = 1, LASTC\n                     C( I, J ) = C( I, J ) - WORK( I, J )\n   50             CONTINUE\n   60          CONTINUE\n            END IF\n*\n         ELSE\n*\n*           Let  V =  ( V1 )\n*                     ( V2 )    (last K rows)\n*           where  V2  is unit upper triangular.\n*\n            IF( LSAME( SIDE, 'L' ) ) THEN\n*\n*              Form  H * C  or  H**H * C  where  C = ( C1 )\n*                                                    ( C2 )\n*\n               LASTV = MAX( K, ILACLR( M, K, V, LDV ) )\n               LASTC = ILACLC( LASTV, N, C, LDC )\n*\n*              W := C**H * V  =  (C1**H * V1 + C2**H * V2)  (stored in WORK)\n*\n*              W := C2**H\n*\n               DO 70 J = 1, K\n                  CALL CCOPY( LASTC, C( LASTV-K+J, 1 ), LDC,\n     $                 WORK( 1, J ), 1 )\n                  CALL CLACGV( LASTC, WORK( 1, J ), 1 )\n   70          CONTINUE\n*\n*              W := W * V2\n*\n               CALL CTRMM( 'Right', 'Upper', 'No transpose', 'Unit',\n     $              LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,\n     $              WORK, LDWORK )\n               IF( LASTV.GT.K ) THEN\n*\n*                 W := W + C1**H*V1\n*\n                  CALL CGEMM( 'Conjugate transpose', 'No transpose',\n     $                 LASTC, K, LASTV-K, ONE, C, LDC, V, LDV,\n     $                 ONE, WORK, LDWORK )\n               END IF\n*\n*              W := W * T**H  or  W * T\n*\n               CALL CTRMM( 'Right', 'Lower', TRANST, 'Non-unit',\n     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )\n*\n*              C := C - V * W**H\n*\n               IF( LASTV.GT.K ) THEN\n*\n*                 C1 := C1 - V1 * W**H\n*\n                  CALL CGEMM( 'No transpose', 'Conjugate transpose',\n     $                 LASTV-K, LASTC, K, -ONE, V, LDV, WORK, LDWORK,\n     $                 ONE, C, LDC )\n               END IF\n*\n*              W := W * V2**H\n*\n               CALL CTRMM( 'Right', 'Upper', 'Conjugate transpose',\n     $              'Unit', LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,\n     $              WORK, LDWORK )\n*\n*              C2 := C2 - W**H\n*\n               DO 90 J = 1, K\n                  DO 80 I = 1, LASTC\n                     C( LASTV-K+J, I ) = C( LASTV-K+J, I ) -\n     $                               CONJG( WORK( I, J ) )\n   80             CONTINUE\n   90          CONTINUE\n*\n            ELSE IF( LSAME( SIDE, 'R' ) ) THEN\n*\n*              Form  C * H  or  C * H**H  where  C = ( C1  C2 )\n*\n               LASTV = MAX( K, ILACLR( N, K, V, LDV ) )\n               LASTC = ILACLR( M, LASTV, C, LDC )\n*\n*              W := C * V  =  (C1*V1 + C2*V2)  (stored in WORK)\n*\n*              W := C2\n*\n               DO 100 J = 1, K\n                  CALL CCOPY( LASTC, C( 1, LASTV-K+J ), 1,\n     $                 WORK( 1, J ), 1 )\n  100          CONTINUE\n*\n*              W := W * V2\n*\n               CALL CTRMM( 'Right', 'Upper', 'No transpose', 'Unit',\n     $              LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,\n     $              WORK, LDWORK )\n               IF( LASTV.GT.K ) THEN\n*\n*                 W := W + C1 * V1\n*\n                  CALL CGEMM( 'No transpose', 'No transpose',\n     $                 LASTC, K, LASTV-K,\n     $                 ONE, C, LDC, V, LDV, ONE, WORK, LDWORK )\n               END IF\n*\n*              W := W * T  or  W * T**H\n*\n               CALL CTRMM( 'Right', 'Lower', TRANS, 'Non-unit',\n     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )\n*\n*              C := C - W * V**H\n*\n               IF( LASTV.GT.K ) THEN\n*\n*                 C1 := C1 - W * V1**H\n*\n                  CALL CGEMM( 'No transpose', 'Conjugate transpose',\n     $                 LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV,\n     $                 ONE, C, LDC )\n               END IF\n*\n*              W := W * V2**H\n*\n               CALL CTRMM( 'Right', 'Upper', 'Conjugate transpose',\n     $              'Unit', LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,\n     $              WORK, LDWORK )\n*\n*              C2 := C2 - W\n*\n               DO 120 J = 1, K\n                  DO 110 I = 1, LASTC\n                     C( I, LASTV-K+J ) = C( I, LASTV-K+J )\n     $                    - WORK( I, J )\n  110             CONTINUE\n  120          CONTINUE\n            END IF\n         END IF\n*\n      ELSE IF( LSAME( STOREV, 'R' ) ) THEN\n*\n         IF( LSAME( DIRECT, 'F' ) ) THEN\n*\n*           Let  V =  ( V1  V2 )    (V1: first K columns)\n*           where  V1  is unit upper triangular.\n*\n            IF( LSAME( SIDE, 'L' ) ) THEN\n*\n*              Form  H * C  or  H**H * C  where  C = ( C1 )\n*                                                    ( C2 )\n*\n               LASTV = MAX( K, ILACLC( K, M, V, LDV ) )\n               LASTC = ILACLC( LASTV, N, C, LDC )\n*\n*              W := C**H * V**H  =  (C1**H * V1**H + C2**H * V2**H) (stored in WORK)\n*\n*              W := C1**H\n*\n               DO 130 J = 1, K\n                  CALL CCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 )\n                  CALL CLACGV( LASTC, WORK( 1, J ), 1 )\n  130          CONTINUE\n*\n*              W := W * V1**H\n*\n               CALL CTRMM( 'Right', 'Upper', 'Conjugate transpose',\n     $                     'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK )\n               IF( LASTV.GT.K ) THEN\n*\n*                 W := W + C2**H*V2**H\n*\n                  CALL CGEMM( 'Conjugate transpose',\n     $                 'Conjugate transpose', LASTC, K, LASTV-K,\n     $                 ONE, C( K+1, 1 ), LDC, V( 1, K+1 ), LDV,\n     $                 ONE, WORK, LDWORK )\n               END IF\n*\n*              W := W * T**H  or  W * T\n*\n               CALL CTRMM( 'Right', 'Upper', TRANST, 'Non-unit',\n     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )\n*\n*              C := C - V**H * W**H\n*\n               IF( LASTV.GT.K ) THEN\n*\n*                 C2 := C2 - V2**H * W**H\n*\n                  CALL CGEMM( 'Conjugate transpose',\n     $                 'Conjugate transpose', LASTV-K, LASTC, K,\n     $                 -ONE, V( 1, K+1 ), LDV, WORK, LDWORK,\n     $                 ONE, C( K+1, 1 ), LDC )\n               END IF\n*\n*              W := W * V1\n*\n               CALL CTRMM( 'Right', 'Upper', 'No transpose', 'Unit',\n     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )\n*\n*              C1 := C1 - W**H\n*\n               DO 150 J = 1, K\n                  DO 140 I = 1, LASTC\n                     C( J, I ) = C( J, I ) - CONJG( WORK( I, J ) )\n  140             CONTINUE\n  150          CONTINUE\n*\n            ELSE IF( LSAME( SIDE, 'R' ) ) THEN\n*\n*              Form  C * H  or  C * H**H  where  C = ( C1  C2 )\n*\n               LASTV = MAX( K, ILACLC( K, N, V, LDV ) )\n               LASTC = ILACLR( M, LASTV, C, LDC )\n*\n*              W := C * V**H  =  (C1*V1**H + C2*V2**H)  (stored in WORK)\n*\n*              W := C1\n*\n               DO 160 J = 1, K\n                  CALL CCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 )\n  160          CONTINUE\n*\n*              W := W * V1**H\n*\n               CALL CTRMM( 'Right', 'Upper', 'Conjugate transpose',\n     $                     'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK )\n               IF( LASTV.GT.K ) THEN\n*\n*                 W := W + C2 * V2**H\n*\n                  CALL CGEMM( 'No transpose', 'Conjugate transpose',\n     $                 LASTC, K, LASTV-K, ONE, C( 1, K+1 ), LDC,\n     $                 V( 1, K+1 ), LDV, ONE, WORK, LDWORK )\n               END IF\n*\n*              W := W * T  or  W * T**H\n*\n               CALL CTRMM( 'Right', 'Upper', TRANS, 'Non-unit',\n     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )\n*\n*              C := C - W * V\n*\n               IF( LASTV.GT.K ) THEN\n*\n*                 C2 := C2 - W * V2\n*\n                  CALL CGEMM( 'No transpose', 'No transpose',\n     $                 LASTC, LASTV-K, K,\n     $                 -ONE, WORK, LDWORK, V( 1, K+1 ), LDV,\n     $                 ONE, C( 1, K+1 ), LDC )\n               END IF\n*\n*              W := W * V1\n*\n               CALL CTRMM( 'Right', 'Upper', 'No transpose', 'Unit',\n     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )\n*\n*              C1 := C1 - W\n*\n               DO 180 J = 1, K\n                  DO 170 I = 1, LASTC\n                     C( I, J ) = C( I, J ) - WORK( I, J )\n  170             CONTINUE\n  180          CONTINUE\n*\n            END IF\n*\n         ELSE\n*\n*           Let  V =  ( V1  V2 )    (V2: last K columns)\n*           where  V2  is unit lower triangular.\n*\n            IF( LSAME( SIDE, 'L' ) ) THEN\n*\n*              Form  H * C  or  H**H * C  where  C = ( C1 )\n*                                                    ( C2 )\n*\n               LASTV = MAX( K, ILACLC( K, M, V, LDV ) )\n               LASTC = ILACLC( LASTV, N, C, LDC )\n*\n*              W := C**H * V**H  =  (C1**H * V1**H + C2**H * V2**H) (stored in WORK)\n*\n*              W := C2**H\n*\n               DO 190 J = 1, K\n                  CALL CCOPY( LASTC, C( LASTV-K+J, 1 ), LDC,\n     $                 WORK( 1, J ), 1 )\n                  CALL CLACGV( LASTC, WORK( 1, J ), 1 )\n  190          CONTINUE\n*\n*              W := W * V2**H\n*\n               CALL CTRMM( 'Right', 'Lower', 'Conjugate transpose',\n     $              'Unit', LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,\n     $              WORK, LDWORK )\n               IF( LASTV.GT.K ) THEN\n*\n*                 W := W + C1**H * V1**H\n*\n                  CALL CGEMM( 'Conjugate transpose',\n     $                 'Conjugate transpose', LASTC, K, LASTV-K,\n     $                 ONE, C, LDC, V, LDV, ONE, WORK, LDWORK )\n               END IF\n*\n*              W := W * T**H  or  W * T\n*\n               CALL CTRMM( 'Right', 'Lower', TRANST, 'Non-unit',\n     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )\n*\n*              C := C - V**H * W**H\n*\n               IF( LASTV.GT.K ) THEN\n*\n*                 C1 := C1 - V1**H * W**H\n*\n                  CALL CGEMM( 'Conjugate transpose',\n     $                 'Conjugate transpose', LASTV-K, LASTC, K,\n     $                 -ONE, V, LDV, WORK, LDWORK, ONE, C, LDC )\n               END IF\n*\n*              W := W * V2\n*\n               CALL CTRMM( 'Right', 'Lower', 'No transpose', 'Unit',\n     $              LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,\n     $              WORK, LDWORK )\n*\n*              C2 := C2 - W**H\n*\n               DO 210 J = 1, K\n                  DO 200 I = 1, LASTC\n                     C( LASTV-K+J, I ) = C( LASTV-K+J, I ) -\n     $                               CONJG( WORK( I, J ) )\n  200             CONTINUE\n  210          CONTINUE\n*\n            ELSE IF( LSAME( SIDE, 'R' ) ) THEN\n*\n*              Form  C * H  or  C * H**H  where  C = ( C1  C2 )\n*\n               LASTV = MAX( K, ILACLC( K, N, V, LDV ) )\n               LASTC = ILACLR( M, LASTV, C, LDC )\n*\n*              W := C * V**H  =  (C1*V1**H + C2*V2**H)  (stored in WORK)\n*\n*              W := C2\n*\n               DO 220 J = 1, K\n                  CALL CCOPY( LASTC, C( 1, LASTV-K+J ), 1,\n     $                 WORK( 1, J ), 1 )\n  220          CONTINUE\n*\n*              W := W * V2**H\n*\n               CALL CTRMM( 'Right', 'Lower', 'Conjugate transpose',\n     $              'Unit', LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,\n     $              WORK, LDWORK )\n               IF( LASTV.GT.K ) THEN\n*\n*                 W := W + C1 * V1**H\n*\n                  CALL CGEMM( 'No transpose', 'Conjugate transpose',\n     $                 LASTC, K, LASTV-K, ONE, C, LDC, V, LDV, ONE,\n     $                 WORK, LDWORK )\n               END IF\n*\n*              W := W * T  or  W * T**H\n*\n               CALL CTRMM( 'Right', 'Lower', TRANS, 'Non-unit',\n     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )\n*\n*              C := C - W * V\n*\n               IF( LASTV.GT.K ) THEN\n*\n*                 C1 := C1 - W * V1\n*\n                  CALL CGEMM( 'No transpose', 'No transpose',\n     $                 LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV,\n     $                 ONE, C, LDC )\n               END IF\n*\n*              W := W * V2\n*\n               CALL CTRMM( 'Right', 'Lower', 'No transpose', 'Unit',\n     $              LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,\n     $              WORK, LDWORK )\n*\n*              C1 := C1 - W\n*\n               DO 240 J = 1, K\n                  DO 230 I = 1, LASTC\n                     C( I, LASTV-K+J ) = C( I, LASTV-K+J )\n     $                    - WORK( I, J )\n  230             CONTINUE\n  240          CONTINUE\n*\n            END IF\n*\n         END IF\n      END IF\n*\n      RETURN\n*\n*     End of CLARFB\n*\n      END\n"
  },
  {
    "path": "include/eigen3/lapack/clarfg.f",
    "content": "*> \\brief \\b CLARFG\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*> \\htmlonly\n*> Download CLARFG + dependencies \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clarfg.f\"> \n*> [TGZ]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clarfg.f\"> \n*> [ZIP]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clarfg.f\"> \n*> [TXT]</a>\n*> \\endhtmlonly \n*\n*  Definition:\n*  ===========\n*\n*       SUBROUTINE CLARFG( N, ALPHA, X, INCX, TAU )\n* \n*       .. Scalar Arguments ..\n*       INTEGER            INCX, N\n*       COMPLEX            ALPHA, TAU\n*       ..\n*       .. Array Arguments ..\n*       COMPLEX            X( * )\n*       ..\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> CLARFG generates a complex elementary reflector H of order n, such\n*> that\n*>\n*>       H**H * ( alpha ) = ( beta ),   H**H * H = I.\n*>              (   x   )   (   0  )\n*>\n*> where alpha and beta are scalars, with beta real, and x is an\n*> (n-1)-element complex vector. H is represented in the form\n*>\n*>       H = I - tau * ( 1 ) * ( 1 v**H ) ,\n*>                     ( v )\n*>\n*> where tau is a complex scalar and v is a complex (n-1)-element\n*> vector. Note that H is not hermitian.\n*>\n*> If the elements of x are all zero and alpha is real, then tau = 0\n*> and H is taken to be the unit matrix.\n*>\n*> Otherwise  1 <= real(tau) <= 2  and  abs(tau-1) <= 1 .\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] N\n*> \\verbatim\n*>          N is INTEGER\n*>          The order of the elementary reflector.\n*> \\endverbatim\n*>\n*> \\param[in,out] ALPHA\n*> \\verbatim\n*>          ALPHA is COMPLEX\n*>          On entry, the value alpha.\n*>          On exit, it is overwritten with the value beta.\n*> \\endverbatim\n*>\n*> \\param[in,out] X\n*> \\verbatim\n*>          X is COMPLEX array, dimension\n*>                         (1+(N-2)*abs(INCX))\n*>          On entry, the vector x.\n*>          On exit, it is overwritten with the vector v.\n*> \\endverbatim\n*>\n*> \\param[in] INCX\n*> \\verbatim\n*>          INCX is INTEGER\n*>          The increment between elements of X. INCX > 0.\n*> \\endverbatim\n*>\n*> \\param[out] TAU\n*> \\verbatim\n*>          TAU is COMPLEX\n*>          The value tau.\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date November 2011\n*\n*> \\ingroup complexOTHERauxiliary\n*\n*  =====================================================================\n      SUBROUTINE CLARFG( N, ALPHA, X, INCX, TAU )\n*\n*  -- LAPACK auxiliary routine (version 3.4.0) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     November 2011\n*\n*     .. Scalar Arguments ..\n      INTEGER            INCX, N\n      COMPLEX            ALPHA, TAU\n*     ..\n*     .. Array Arguments ..\n      COMPLEX            X( * )\n*     ..\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      REAL               ONE, ZERO\n      PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )\n*     ..\n*     .. Local Scalars ..\n      INTEGER            J, KNT\n      REAL               ALPHI, ALPHR, BETA, RSAFMN, SAFMIN, XNORM\n*     ..\n*     .. External Functions ..\n      REAL               SCNRM2, SLAMCH, SLAPY3\n      COMPLEX            CLADIV\n      EXTERNAL           SCNRM2, SLAMCH, SLAPY3, CLADIV\n*     ..\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, AIMAG, CMPLX, REAL, SIGN\n*     ..\n*     .. External Subroutines ..\n      EXTERNAL           CSCAL, CSSCAL\n*     ..\n*     .. Executable Statements ..\n*\n      IF( N.LE.0 ) THEN\n         TAU = ZERO\n         RETURN\n      END IF\n*\n      XNORM = SCNRM2( N-1, X, INCX )\n      ALPHR = REAL( ALPHA )\n      ALPHI = AIMAG( ALPHA )\n*\n      IF( XNORM.EQ.ZERO .AND. ALPHI.EQ.ZERO ) THEN\n*\n*        H  =  I\n*\n         TAU = ZERO\n      ELSE\n*\n*        general case\n*\n         BETA = -SIGN( SLAPY3( ALPHR, ALPHI, XNORM ), ALPHR )\n         SAFMIN = SLAMCH( 'S' ) / SLAMCH( 'E' )\n         RSAFMN = ONE / SAFMIN\n*\n         KNT = 0\n         IF( ABS( BETA ).LT.SAFMIN ) THEN\n*\n*           XNORM, BETA may be inaccurate; scale X and recompute them\n*\n   10       CONTINUE\n            KNT = KNT + 1\n            CALL CSSCAL( N-1, RSAFMN, X, INCX )\n            BETA = BETA*RSAFMN\n            ALPHI = ALPHI*RSAFMN\n            ALPHR = ALPHR*RSAFMN\n            IF( ABS( BETA ).LT.SAFMIN )\n     $         GO TO 10\n*\n*           New BETA is at most 1, at least SAFMIN\n*\n            XNORM = SCNRM2( N-1, X, INCX )\n            ALPHA = CMPLX( ALPHR, ALPHI )\n            BETA = -SIGN( SLAPY3( ALPHR, ALPHI, XNORM ), ALPHR )\n         END IF\n         TAU = CMPLX( ( BETA-ALPHR ) / BETA, -ALPHI / BETA )\n         ALPHA = CLADIV( CMPLX( ONE ), ALPHA-BETA )\n         CALL CSCAL( N-1, ALPHA, X, INCX )\n*\n*        If ALPHA is subnormal, it may lose relative accuracy\n*\n         DO 20 J = 1, KNT\n            BETA = BETA*SAFMIN\n 20      CONTINUE\n         ALPHA = BETA\n      END IF\n*\n      RETURN\n*\n*     End of CLARFG\n*\n      END\n"
  },
  {
    "path": "include/eigen3/lapack/clarft.f",
    "content": "*> \\brief \\b CLARFT\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*> \\htmlonly\n*> Download CLARFT + dependencies \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clarft.f\"> \n*> [TGZ]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clarft.f\"> \n*> [ZIP]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clarft.f\"> \n*> [TXT]</a>\n*> \\endhtmlonly \n*\n*  Definition:\n*  ===========\n*\n*       SUBROUTINE CLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )\n* \n*       .. Scalar Arguments ..\n*       CHARACTER          DIRECT, STOREV\n*       INTEGER            K, LDT, LDV, N\n*       ..\n*       .. Array Arguments ..\n*       COMPLEX            T( LDT, * ), TAU( * ), V( LDV, * )\n*       ..\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> CLARFT forms the triangular factor T of a complex block reflector H\n*> of order n, which is defined as a product of k elementary reflectors.\n*>\n*> If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular;\n*>\n*> If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular.\n*>\n*> If STOREV = 'C', the vector which defines the elementary reflector\n*> H(i) is stored in the i-th column of the array V, and\n*>\n*>    H  =  I - V * T * V**H\n*>\n*> If STOREV = 'R', the vector which defines the elementary reflector\n*> H(i) is stored in the i-th row of the array V, and\n*>\n*>    H  =  I - V**H * T * V\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] DIRECT\n*> \\verbatim\n*>          DIRECT is CHARACTER*1\n*>          Specifies the order in which the elementary reflectors are\n*>          multiplied to form the block reflector:\n*>          = 'F': H = H(1) H(2) . . . H(k) (Forward)\n*>          = 'B': H = H(k) . . . H(2) H(1) (Backward)\n*> \\endverbatim\n*>\n*> \\param[in] STOREV\n*> \\verbatim\n*>          STOREV is CHARACTER*1\n*>          Specifies how the vectors which define the elementary\n*>          reflectors are stored (see also Further Details):\n*>          = 'C': columnwise\n*>          = 'R': rowwise\n*> \\endverbatim\n*>\n*> \\param[in] N\n*> \\verbatim\n*>          N is INTEGER\n*>          The order of the block reflector H. N >= 0.\n*> \\endverbatim\n*>\n*> \\param[in] K\n*> \\verbatim\n*>          K is INTEGER\n*>          The order of the triangular factor T (= the number of\n*>          elementary reflectors). K >= 1.\n*> \\endverbatim\n*>\n*> \\param[in] V\n*> \\verbatim\n*>          V is COMPLEX array, dimension\n*>                               (LDV,K) if STOREV = 'C'\n*>                               (LDV,N) if STOREV = 'R'\n*>          The matrix V. See further details.\n*> \\endverbatim\n*>\n*> \\param[in] LDV\n*> \\verbatim\n*>          LDV is INTEGER\n*>          The leading dimension of the array V.\n*>          If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.\n*> \\endverbatim\n*>\n*> \\param[in] TAU\n*> \\verbatim\n*>          TAU is COMPLEX array, dimension (K)\n*>          TAU(i) must contain the scalar factor of the elementary\n*>          reflector H(i).\n*> \\endverbatim\n*>\n*> \\param[out] T\n*> \\verbatim\n*>          T is COMPLEX array, dimension (LDT,K)\n*>          The k by k triangular factor T of the block reflector.\n*>          If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is\n*>          lower triangular. The rest of the array is not used.\n*> \\endverbatim\n*>\n*> \\param[in] LDT\n*> \\verbatim\n*>          LDT is INTEGER\n*>          The leading dimension of the array T. LDT >= K.\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date April 2012\n*\n*> \\ingroup complexOTHERauxiliary\n*\n*> \\par Further Details:\n*  =====================\n*>\n*> \\verbatim\n*>\n*>  The shape of the matrix V and the storage of the vectors which define\n*>  the H(i) is best illustrated by the following example with n = 5 and\n*>  k = 3. The elements equal to 1 are not stored.\n*>\n*>  DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':\n*>\n*>               V = (  1       )                 V = (  1 v1 v1 v1 v1 )\n*>                   ( v1  1    )                     (     1 v2 v2 v2 )\n*>                   ( v1 v2  1 )                     (        1 v3 v3 )\n*>                   ( v1 v2 v3 )\n*>                   ( v1 v2 v3 )\n*>\n*>  DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':\n*>\n*>               V = ( v1 v2 v3 )                 V = ( v1 v1  1       )\n*>                   ( v1 v2 v3 )                     ( v2 v2 v2  1    )\n*>                   (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )\n*>                   (     1 v3 )\n*>                   (        1 )\n*> \\endverbatim\n*>\n*  =====================================================================\n      SUBROUTINE CLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )\n*\n*  -- LAPACK auxiliary routine (version 3.4.1) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     April 2012\n*\n*     .. Scalar Arguments ..\n      CHARACTER          DIRECT, STOREV\n      INTEGER            K, LDT, LDV, N\n*     ..\n*     .. Array Arguments ..\n      COMPLEX            T( LDT, * ), TAU( * ), V( LDV, * )\n*     ..\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      COMPLEX            ONE, ZERO\n      PARAMETER          ( ONE = ( 1.0E+0, 0.0E+0 ),\n     $                   ZERO = ( 0.0E+0, 0.0E+0 ) )\n*     ..\n*     .. Local Scalars ..\n      INTEGER            I, J, PREVLASTV, LASTV\n*     ..\n*     .. External Subroutines ..\n      EXTERNAL           CGEMV, CLACGV, CTRMV\n*     ..\n*     .. External Functions ..\n      LOGICAL            LSAME\n      EXTERNAL           LSAME\n*     ..\n*     .. Executable Statements ..\n*\n*     Quick return if possible\n*\n      IF( N.EQ.0 )\n     $   RETURN\n*\n      IF( LSAME( DIRECT, 'F' ) ) THEN\n         PREVLASTV = N\n         DO I = 1, K\n            PREVLASTV = MAX( PREVLASTV, I )\n            IF( TAU( I ).EQ.ZERO ) THEN\n*\n*              H(i)  =  I\n*\n               DO J = 1, I\n                  T( J, I ) = ZERO\n               END DO\n            ELSE\n*\n*              general case\n*\n               IF( LSAME( STOREV, 'C' ) ) THEN\n*                 Skip any trailing zeros.\n                  DO LASTV = N, I+1, -1\n                     IF( V( LASTV, I ).NE.ZERO ) EXIT\n                  END DO\n                  DO J = 1, I-1\n                     T( J, I ) = -TAU( I ) * CONJG( V( I , J ) )\n                  END DO                     \n                  J = MIN( LASTV, PREVLASTV )\n*\n*                 T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**H * V(i:j,i)\n*\n                  CALL CGEMV( 'Conjugate transpose', J-I, I-1,\n     $                        -TAU( I ), V( I+1, 1 ), LDV, \n     $                        V( I+1, I ), 1,\n     $                        ONE, T( 1, I ), 1 )\n               ELSE\n*                 Skip any trailing zeros.\n                  DO LASTV = N, I+1, -1\n                     IF( V( I, LASTV ).NE.ZERO ) EXIT\n                  END DO\n                  DO J = 1, I-1\n                     T( J, I ) = -TAU( I ) * V( J , I )\n                  END DO                     \n                  J = MIN( LASTV, PREVLASTV )\n*\n*                 T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**H\n*\n                  CALL CGEMM( 'N', 'C', I-1, 1, J-I, -TAU( I ),\n     $                        V( 1, I+1 ), LDV, V( I, I+1 ), LDV,\n     $                        ONE, T( 1, I ), LDT )                  \n               END IF\n*\n*              T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i)\n*\n               CALL CTRMV( 'Upper', 'No transpose', 'Non-unit', I-1, T,\n     $                     LDT, T( 1, I ), 1 )\n               T( I, I ) = TAU( I )\n               IF( I.GT.1 ) THEN\n                  PREVLASTV = MAX( PREVLASTV, LASTV )\n               ELSE\n                  PREVLASTV = LASTV\n               END IF\n            END IF\n         END DO\n      ELSE\n         PREVLASTV = 1\n         DO I = K, 1, -1\n            IF( TAU( I ).EQ.ZERO ) THEN\n*\n*              H(i)  =  I\n*\n               DO J = I, K\n                  T( J, I ) = ZERO\n               END DO\n            ELSE\n*\n*              general case\n*\n               IF( I.LT.K ) THEN\n                  IF( LSAME( STOREV, 'C' ) ) THEN\n*                    Skip any leading zeros.\n                     DO LASTV = 1, I-1\n                        IF( V( LASTV, I ).NE.ZERO ) EXIT\n                     END DO\n                     DO J = I+1, K\n                        T( J, I ) = -TAU( I ) * CONJG( V( N-K+I , J ) )\n                     END DO                        \n                     J = MAX( LASTV, PREVLASTV )\n*\n*                    T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**H * V(j:n-k+i,i)\n*\n                     CALL CGEMV( 'Conjugate transpose', N-K+I-J, K-I,\n     $                           -TAU( I ), V( J, I+1 ), LDV, V( J, I ),\n     $                           1, ONE, T( I+1, I ), 1 )\n                  ELSE\n*                    Skip any leading zeros.\n                     DO LASTV = 1, I-1\n                        IF( V( I, LASTV ).NE.ZERO ) EXIT\n                     END DO\n                     DO J = I+1, K\n                        T( J, I ) = -TAU( I ) * V( J, N-K+I )\n                     END DO                      \n                     J = MAX( LASTV, PREVLASTV )\n*\n*                    T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**H\n*\n                     CALL CGEMM( 'N', 'C', K-I, 1, N-K+I-J, -TAU( I ),\n     $                           V( I+1, J ), LDV, V( I, J ), LDV,\n     $                           ONE, T( I+1, I ), LDT )                     \n                  END IF\n*\n*                 T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i)\n*\n                  CALL CTRMV( 'Lower', 'No transpose', 'Non-unit', K-I,\n     $                        T( I+1, I+1 ), LDT, T( I+1, I ), 1 )\n                  IF( I.GT.1 ) THEN\n                     PREVLASTV = MIN( PREVLASTV, LASTV )\n                  ELSE\n                     PREVLASTV = LASTV\n                  END IF\n               END IF\n               T( I, I ) = TAU( I )\n            END IF\n         END DO\n      END IF\n      RETURN\n*\n*     End of CLARFT\n*\n      END\n"
  },
  {
    "path": "include/eigen3/lapack/complex_double.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define SCALAR        std::complex<double>\n#define SCALAR_SUFFIX z\n#define SCALAR_SUFFIX_UP \"Z\"\n#define REAL_SCALAR_SUFFIX d\n#define ISCOMPLEX     1\n\n#include \"cholesky.cpp\"\n#include \"lu.cpp\"\n#include \"svd.cpp\"\n"
  },
  {
    "path": "include/eigen3/lapack/complex_single.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define SCALAR        std::complex<float>\n#define SCALAR_SUFFIX c\n#define SCALAR_SUFFIX_UP \"C\"\n#define REAL_SCALAR_SUFFIX s\n#define ISCOMPLEX     1\n\n#include \"cholesky.cpp\"\n#include \"lu.cpp\"\n#include \"svd.cpp\"\n"
  },
  {
    "path": "include/eigen3/lapack/dladiv.f",
    "content": "*> \\brief \\b DLADIV\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*> \\htmlonly\n*> Download DLADIV + dependencies \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dladiv.f\"> \n*> [TGZ]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dladiv.f\"> \n*> [ZIP]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dladiv.f\"> \n*> [TXT]</a>\n*> \\endhtmlonly \n*\n*  Definition:\n*  ===========\n*\n*       SUBROUTINE DLADIV( A, B, C, D, P, Q )\n* \n*       .. Scalar Arguments ..\n*       DOUBLE PRECISION   A, B, C, D, P, Q\n*       ..\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> DLADIV performs complex division in  real arithmetic\n*>\n*>                       a + i*b\n*>            p + i*q = ---------\n*>                       c + i*d\n*>\n*> The algorithm is due to Robert L. Smith and can be found\n*> in D. Knuth, The art of Computer Programming, Vol.2, p.195\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] A\n*> \\verbatim\n*>          A is DOUBLE PRECISION\n*> \\endverbatim\n*>\n*> \\param[in] B\n*> \\verbatim\n*>          B is DOUBLE PRECISION\n*> \\endverbatim\n*>\n*> \\param[in] C\n*> \\verbatim\n*>          C is DOUBLE PRECISION\n*> \\endverbatim\n*>\n*> \\param[in] D\n*> \\verbatim\n*>          D is DOUBLE PRECISION\n*>          The scalars a, b, c, and d in the above expression.\n*> \\endverbatim\n*>\n*> \\param[out] P\n*> \\verbatim\n*>          P is DOUBLE PRECISION\n*> \\endverbatim\n*>\n*> \\param[out] Q\n*> \\verbatim\n*>          Q is DOUBLE PRECISION\n*>          The scalars p and q in the above expression.\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date November 2011\n*\n*> \\ingroup auxOTHERauxiliary\n*\n*  =====================================================================\n      SUBROUTINE DLADIV( A, B, C, D, P, Q )\n*\n*  -- LAPACK auxiliary routine (version 3.4.0) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     November 2011\n*\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION   A, B, C, D, P, Q\n*     ..\n*\n*  =====================================================================\n*\n*     .. Local Scalars ..\n      DOUBLE PRECISION   E, F\n*     ..\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS\n*     ..\n*     .. Executable Statements ..\n*\n      IF( ABS( D ).LT.ABS( C ) ) THEN\n         E = D / C\n         F = C + D*E\n         P = ( A+B*E ) / F\n         Q = ( B-A*E ) / F\n      ELSE\n         E = C / D\n         F = D + C*E\n         P = ( B+A*E ) / F\n         Q = ( -A+B*E ) / F\n      END IF\n*\n      RETURN\n*\n*     End of DLADIV\n*\n      END\n"
  },
  {
    "path": "include/eigen3/lapack/dlamch.f",
    "content": "*> \\brief \\b DLAMCH\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*  Definition:\n*  ===========\n*\n*      DOUBLE PRECISION FUNCTION DLAMCH( CMACH )\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> DLAMCH determines double precision machine parameters.\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] CMACH\n*> \\verbatim\n*>          Specifies the value to be returned by DLAMCH:\n*>          = 'E' or 'e',   DLAMCH := eps\n*>          = 'S' or 's ,   DLAMCH := sfmin\n*>          = 'B' or 'b',   DLAMCH := base\n*>          = 'P' or 'p',   DLAMCH := eps*base\n*>          = 'N' or 'n',   DLAMCH := t\n*>          = 'R' or 'r',   DLAMCH := rnd\n*>          = 'M' or 'm',   DLAMCH := emin\n*>          = 'U' or 'u',   DLAMCH := rmin\n*>          = 'L' or 'l',   DLAMCH := emax\n*>          = 'O' or 'o',   DLAMCH := rmax\n*>          where\n*>          eps   = relative machine precision\n*>          sfmin = safe minimum, such that 1/sfmin does not overflow\n*>          base  = base of the machine\n*>          prec  = eps*base\n*>          t     = number of (base) digits in the mantissa\n*>          rnd   = 1.0 when rounding occurs in addition, 0.0 otherwise\n*>          emin  = minimum exponent before (gradual) underflow\n*>          rmin  = underflow threshold - base**(emin-1)\n*>          emax  = largest exponent before overflow\n*>          rmax  = overflow threshold  - (base**emax)*(1-eps)\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date November 2011\n*\n*> \\ingroup auxOTHERauxiliary\n*\n*  =====================================================================\n      DOUBLE PRECISION FUNCTION DLAMCH( CMACH )\n*\n*  -- LAPACK auxiliary routine (version 3.4.0) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     November 2011\n*\n*     .. Scalar Arguments ..\n      CHARACTER          CMACH\n*     ..\n*\n* =====================================================================\n*\n*     .. Parameters ..\n      DOUBLE PRECISION   ONE, ZERO\n      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )\n*     ..\n*     .. Local Scalars ..\n      DOUBLE PRECISION   RND, EPS, SFMIN, SMALL, RMACH\n*     ..\n*     .. External Functions ..\n      LOGICAL            LSAME\n      EXTERNAL           LSAME\n*     ..\n*     .. Intrinsic Functions ..\n      INTRINSIC          DIGITS, EPSILON, HUGE, MAXEXPONENT,\n     $                   MINEXPONENT, RADIX, TINY\n*     ..\n*     .. Executable Statements ..\n*\n*\n*     Assume rounding, not chopping. Always.\n*\n      RND = ONE\n*\n      IF( ONE.EQ.RND ) THEN\n         EPS = EPSILON(ZERO) * 0.5\n      ELSE\n         EPS = EPSILON(ZERO)\n      END IF\n*\n      IF( LSAME( CMACH, 'E' ) ) THEN\n         RMACH = EPS\n      ELSE IF( LSAME( CMACH, 'S' ) ) THEN\n         SFMIN = TINY(ZERO)\n         SMALL = ONE / HUGE(ZERO)\n         IF( SMALL.GE.SFMIN ) THEN\n*\n*           Use SMALL plus a bit, to avoid the possibility of rounding\n*           causing overflow when computing  1/sfmin.\n*\n            SFMIN = SMALL*( ONE+EPS )\n         END IF\n         RMACH = SFMIN\n      ELSE IF( LSAME( CMACH, 'B' ) ) THEN\n         RMACH = RADIX(ZERO)\n      ELSE IF( LSAME( CMACH, 'P' ) ) THEN\n         RMACH = EPS * RADIX(ZERO)\n      ELSE IF( LSAME( CMACH, 'N' ) ) THEN\n         RMACH = DIGITS(ZERO)\n      ELSE IF( LSAME( CMACH, 'R' ) ) THEN\n         RMACH = RND\n      ELSE IF( LSAME( CMACH, 'M' ) ) THEN\n         RMACH = MINEXPONENT(ZERO)\n      ELSE IF( LSAME( CMACH, 'U' ) ) THEN\n         RMACH = tiny(zero)\n      ELSE IF( LSAME( CMACH, 'L' ) ) THEN\n         RMACH = MAXEXPONENT(ZERO)\n      ELSE IF( LSAME( CMACH, 'O' ) ) THEN\n         RMACH = HUGE(ZERO)\n      ELSE\n         RMACH = ZERO\n      END IF\n*\n      DLAMCH = RMACH\n      RETURN\n*\n*     End of DLAMCH\n*\n      END\n************************************************************************\n*> \\brief \\b DLAMC3\n*> \\details\n*> \\b Purpose:\n*> \\verbatim\n*> DLAMC3  is intended to force  A  and  B  to be stored prior to doing\n*> the addition of  A  and  B ,  for use in situations where optimizers\n*> might hold one of these in a register.\n*> \\endverbatim\n*> \\author LAPACK is a software package provided by Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..\n*> \\date November 2011\n*> \\ingroup auxOTHERauxiliary\n*>\n*> \\param[in] A\n*> \\verbatim\n*>          A is a DOUBLE PRECISION\n*> \\endverbatim\n*>\n*> \\param[in] B\n*> \\verbatim\n*>          B is a DOUBLE PRECISION\n*>          The values A and B.\n*> \\endverbatim\n*>\n      DOUBLE PRECISION FUNCTION DLAMC3( A, B )\n*\n*  -- LAPACK auxiliary routine (version 3.4.0) --\n*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..\n*     November 2010\n*\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION   A, B\n*     ..\n* =====================================================================\n*\n*     .. Executable Statements ..\n*\n      DLAMC3 = A + B\n*\n      RETURN\n*\n*     End of DLAMC3\n*\n      END\n*\n************************************************************************\n"
  },
  {
    "path": "include/eigen3/lapack/dlapy2.f",
    "content": "*> \\brief \\b DLAPY2\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*> \\htmlonly\n*> Download DLAPY2 + dependencies \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlapy2.f\"> \n*> [TGZ]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlapy2.f\"> \n*> [ZIP]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlapy2.f\"> \n*> [TXT]</a>\n*> \\endhtmlonly \n*\n*  Definition:\n*  ===========\n*\n*       DOUBLE PRECISION FUNCTION DLAPY2( X, Y )\n* \n*       .. Scalar Arguments ..\n*       DOUBLE PRECISION   X, Y\n*       ..\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> DLAPY2 returns sqrt(x**2+y**2), taking care not to cause unnecessary\n*> overflow.\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] X\n*> \\verbatim\n*>          X is DOUBLE PRECISION\n*> \\endverbatim\n*>\n*> \\param[in] Y\n*> \\verbatim\n*>          Y is DOUBLE PRECISION\n*>          X and Y specify the values x and y.\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date November 2011\n*\n*> \\ingroup auxOTHERauxiliary\n*\n*  =====================================================================\n      DOUBLE PRECISION FUNCTION DLAPY2( X, Y )\n*\n*  -- LAPACK auxiliary routine (version 3.4.0) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     November 2011\n*\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION   X, Y\n*     ..\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      DOUBLE PRECISION   ZERO\n      PARAMETER          ( ZERO = 0.0D0 )\n      DOUBLE PRECISION   ONE\n      PARAMETER          ( ONE = 1.0D0 )\n*     ..\n*     .. Local Scalars ..\n      DOUBLE PRECISION   W, XABS, YABS, Z\n*     ..\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, MAX, MIN, SQRT\n*     ..\n*     .. Executable Statements ..\n*\n      XABS = ABS( X )\n      YABS = ABS( Y )\n      W = MAX( XABS, YABS )\n      Z = MIN( XABS, YABS )\n      IF( Z.EQ.ZERO ) THEN\n         DLAPY2 = W\n      ELSE\n         DLAPY2 = W*SQRT( ONE+( Z / W )**2 )\n      END IF\n      RETURN\n*\n*     End of DLAPY2\n*\n      END\n"
  },
  {
    "path": "include/eigen3/lapack/dlapy3.f",
    "content": "*> \\brief \\b DLAPY3\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*> \\htmlonly\n*> Download DLAPY3 + dependencies \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlapy3.f\"> \n*> [TGZ]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlapy3.f\"> \n*> [ZIP]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlapy3.f\"> \n*> [TXT]</a>\n*> \\endhtmlonly \n*\n*  Definition:\n*  ===========\n*\n*       DOUBLE PRECISION FUNCTION DLAPY3( X, Y, Z )\n* \n*       .. Scalar Arguments ..\n*       DOUBLE PRECISION   X, Y, Z\n*       ..\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> DLAPY3 returns sqrt(x**2+y**2+z**2), taking care not to cause\n*> unnecessary overflow.\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] X\n*> \\verbatim\n*>          X is DOUBLE PRECISION\n*> \\endverbatim\n*>\n*> \\param[in] Y\n*> \\verbatim\n*>          Y is DOUBLE PRECISION\n*> \\endverbatim\n*>\n*> \\param[in] Z\n*> \\verbatim\n*>          Z is DOUBLE PRECISION\n*>          X, Y and Z specify the values x, y and z.\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date November 2011\n*\n*> \\ingroup auxOTHERauxiliary\n*\n*  =====================================================================\n      DOUBLE PRECISION FUNCTION DLAPY3( X, Y, Z )\n*\n*  -- LAPACK auxiliary routine (version 3.4.0) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     November 2011\n*\n*     .. Scalar Arguments ..\n      DOUBLE PRECISION   X, Y, Z\n*     ..\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      DOUBLE PRECISION   ZERO\n      PARAMETER          ( ZERO = 0.0D0 )\n*     ..\n*     .. Local Scalars ..\n      DOUBLE PRECISION   W, XABS, YABS, ZABS\n*     ..\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, MAX, SQRT\n*     ..\n*     .. Executable Statements ..\n*\n      XABS = ABS( X )\n      YABS = ABS( Y )\n      ZABS = ABS( Z )\n      W = MAX( XABS, YABS, ZABS )\n      IF( W.EQ.ZERO ) THEN\n*     W can be zero for max(0,nan,0)\n*     adding all three entries together will make sure\n*     NaN will not disappear.\n         DLAPY3 =  XABS + YABS + ZABS\n      ELSE\n         DLAPY3 = W*SQRT( ( XABS / W )**2+( YABS / W )**2+\n     $            ( ZABS / W )**2 )\n      END IF\n      RETURN\n*\n*     End of DLAPY3\n*\n      END\n"
  },
  {
    "path": "include/eigen3/lapack/dlarf.f",
    "content": "*> \\brief \\b DLARF\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*> \\htmlonly\n*> Download DLARF + dependencies \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarf.f\"> \n*> [TGZ]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarf.f\"> \n*> [ZIP]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarf.f\"> \n*> [TXT]</a>\n*> \\endhtmlonly \n*\n*  Definition:\n*  ===========\n*\n*       SUBROUTINE DLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )\n* \n*       .. Scalar Arguments ..\n*       CHARACTER          SIDE\n*       INTEGER            INCV, LDC, M, N\n*       DOUBLE PRECISION   TAU\n*       ..\n*       .. Array Arguments ..\n*       DOUBLE PRECISION   C( LDC, * ), V( * ), WORK( * )\n*       ..\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> DLARF applies a real elementary reflector H to a real m by n matrix\n*> C, from either the left or the right. H is represented in the form\n*>\n*>       H = I - tau * v * v**T\n*>\n*> where tau is a real scalar and v is a real vector.\n*>\n*> If tau = 0, then H is taken to be the unit matrix.\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] SIDE\n*> \\verbatim\n*>          SIDE is CHARACTER*1\n*>          = 'L': form  H * C\n*>          = 'R': form  C * H\n*> \\endverbatim\n*>\n*> \\param[in] M\n*> \\verbatim\n*>          M is INTEGER\n*>          The number of rows of the matrix C.\n*> \\endverbatim\n*>\n*> \\param[in] N\n*> \\verbatim\n*>          N is INTEGER\n*>          The number of columns of the matrix C.\n*> \\endverbatim\n*>\n*> \\param[in] V\n*> \\verbatim\n*>          V is DOUBLE PRECISION array, dimension\n*>                     (1 + (M-1)*abs(INCV)) if SIDE = 'L'\n*>                  or (1 + (N-1)*abs(INCV)) if SIDE = 'R'\n*>          The vector v in the representation of H. V is not used if\n*>          TAU = 0.\n*> \\endverbatim\n*>\n*> \\param[in] INCV\n*> \\verbatim\n*>          INCV is INTEGER\n*>          The increment between elements of v. INCV <> 0.\n*> \\endverbatim\n*>\n*> \\param[in] TAU\n*> \\verbatim\n*>          TAU is DOUBLE PRECISION\n*>          The value tau in the representation of H.\n*> \\endverbatim\n*>\n*> \\param[in,out] C\n*> \\verbatim\n*>          C is DOUBLE PRECISION array, dimension (LDC,N)\n*>          On entry, the m by n matrix C.\n*>          On exit, C is overwritten by the matrix H * C if SIDE = 'L',\n*>          or C * H if SIDE = 'R'.\n*> \\endverbatim\n*>\n*> \\param[in] LDC\n*> \\verbatim\n*>          LDC is INTEGER\n*>          The leading dimension of the array C. LDC >= max(1,M).\n*> \\endverbatim\n*>\n*> \\param[out] WORK\n*> \\verbatim\n*>          WORK is DOUBLE PRECISION array, dimension\n*>                         (N) if SIDE = 'L'\n*>                      or (M) if SIDE = 'R'\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date November 2011\n*\n*> \\ingroup doubleOTHERauxiliary\n*\n*  =====================================================================\n      SUBROUTINE DLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )\n*\n*  -- LAPACK auxiliary routine (version 3.4.0) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     November 2011\n*\n*     .. Scalar Arguments ..\n      CHARACTER          SIDE\n      INTEGER            INCV, LDC, M, N\n      DOUBLE PRECISION   TAU\n*     ..\n*     .. Array Arguments ..\n      DOUBLE PRECISION   C( LDC, * ), V( * ), WORK( * )\n*     ..\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      DOUBLE PRECISION   ONE, ZERO\n      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )\n*     ..\n*     .. Local Scalars ..\n      LOGICAL            APPLYLEFT\n      INTEGER            I, LASTV, LASTC\n*     ..\n*     .. External Subroutines ..\n      EXTERNAL           DGEMV, DGER\n*     ..\n*     .. External Functions ..\n      LOGICAL            LSAME\n      INTEGER            ILADLR, ILADLC\n      EXTERNAL           LSAME, ILADLR, ILADLC\n*     ..\n*     .. Executable Statements ..\n*\n      APPLYLEFT = LSAME( SIDE, 'L' )\n      LASTV = 0\n      LASTC = 0\n      IF( TAU.NE.ZERO ) THEN\n!     Set up variables for scanning V.  LASTV begins pointing to the end\n!     of V.\n         IF( APPLYLEFT ) THEN\n            LASTV = M\n         ELSE\n            LASTV = N\n         END IF\n         IF( INCV.GT.0 ) THEN\n            I = 1 + (LASTV-1) * INCV\n         ELSE\n            I = 1\n         END IF\n!     Look for the last non-zero row in V.\n         DO WHILE( LASTV.GT.0 .AND. V( I ).EQ.ZERO )\n            LASTV = LASTV - 1\n            I = I - INCV\n         END DO\n         IF( APPLYLEFT ) THEN\n!     Scan for the last non-zero column in C(1:lastv,:).\n            LASTC = ILADLC(LASTV, N, C, LDC)\n         ELSE\n!     Scan for the last non-zero row in C(:,1:lastv).\n            LASTC = ILADLR(M, LASTV, C, LDC)\n         END IF\n      END IF\n!     Note that lastc.eq.0 renders the BLAS operations null; no special\n!     case is needed at this level.\n      IF( APPLYLEFT ) THEN\n*\n*        Form  H * C\n*\n         IF( LASTV.GT.0 ) THEN\n*\n*           w(1:lastc,1) := C(1:lastv,1:lastc)**T * v(1:lastv,1)\n*\n            CALL DGEMV( 'Transpose', LASTV, LASTC, ONE, C, LDC, V, INCV,\n     $           ZERO, WORK, 1 )\n*\n*           C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**T\n*\n            CALL DGER( LASTV, LASTC, -TAU, V, INCV, WORK, 1, C, LDC )\n         END IF\n      ELSE\n*\n*        Form  C * H\n*\n         IF( LASTV.GT.0 ) THEN\n*\n*           w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1)\n*\n            CALL DGEMV( 'No transpose', LASTC, LASTV, ONE, C, LDC,\n     $           V, INCV, ZERO, WORK, 1 )\n*\n*           C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**T\n*\n            CALL DGER( LASTC, LASTV, -TAU, WORK, 1, V, INCV, C, LDC )\n         END IF\n      END IF\n      RETURN\n*\n*     End of DLARF\n*\n      END\n"
  },
  {
    "path": "include/eigen3/lapack/dlarfb.f",
    "content": "*> \\brief \\b DLARFB\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*> \\htmlonly\n*> Download DLARFB + dependencies \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarfb.f\"> \n*> [TGZ]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarfb.f\"> \n*> [ZIP]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarfb.f\"> \n*> [TXT]</a>\n*> \\endhtmlonly \n*\n*  Definition:\n*  ===========\n*\n*       SUBROUTINE DLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV,\n*                          T, LDT, C, LDC, WORK, LDWORK )\n* \n*       .. Scalar Arguments ..\n*       CHARACTER          DIRECT, SIDE, STOREV, TRANS\n*       INTEGER            K, LDC, LDT, LDV, LDWORK, M, N\n*       ..\n*       .. Array Arguments ..\n*       DOUBLE PRECISION   C( LDC, * ), T( LDT, * ), V( LDV, * ),\n*      $                   WORK( LDWORK, * )\n*       ..\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> DLARFB applies a real block reflector H or its transpose H**T to a\n*> real m by n matrix C, from either the left or the right.\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] SIDE\n*> \\verbatim\n*>          SIDE is CHARACTER*1\n*>          = 'L': apply H or H**T from the Left\n*>          = 'R': apply H or H**T from the Right\n*> \\endverbatim\n*>\n*> \\param[in] TRANS\n*> \\verbatim\n*>          TRANS is CHARACTER*1\n*>          = 'N': apply H (No transpose)\n*>          = 'T': apply H**T (Transpose)\n*> \\endverbatim\n*>\n*> \\param[in] DIRECT\n*> \\verbatim\n*>          DIRECT is CHARACTER*1\n*>          Indicates how H is formed from a product of elementary\n*>          reflectors\n*>          = 'F': H = H(1) H(2) . . . H(k) (Forward)\n*>          = 'B': H = H(k) . . . H(2) H(1) (Backward)\n*> \\endverbatim\n*>\n*> \\param[in] STOREV\n*> \\verbatim\n*>          STOREV is CHARACTER*1\n*>          Indicates how the vectors which define the elementary\n*>          reflectors are stored:\n*>          = 'C': Columnwise\n*>          = 'R': Rowwise\n*> \\endverbatim\n*>\n*> \\param[in] M\n*> \\verbatim\n*>          M is INTEGER\n*>          The number of rows of the matrix C.\n*> \\endverbatim\n*>\n*> \\param[in] N\n*> \\verbatim\n*>          N is INTEGER\n*>          The number of columns of the matrix C.\n*> \\endverbatim\n*>\n*> \\param[in] K\n*> \\verbatim\n*>          K is INTEGER\n*>          The order of the matrix T (= the number of elementary\n*>          reflectors whose product defines the block reflector).\n*> \\endverbatim\n*>\n*> \\param[in] V\n*> \\verbatim\n*>          V is DOUBLE PRECISION array, dimension\n*>                                (LDV,K) if STOREV = 'C'\n*>                                (LDV,M) if STOREV = 'R' and SIDE = 'L'\n*>                                (LDV,N) if STOREV = 'R' and SIDE = 'R'\n*>          The matrix V. See Further Details.\n*> \\endverbatim\n*>\n*> \\param[in] LDV\n*> \\verbatim\n*>          LDV is INTEGER\n*>          The leading dimension of the array V.\n*>          If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M);\n*>          if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N);\n*>          if STOREV = 'R', LDV >= K.\n*> \\endverbatim\n*>\n*> \\param[in] T\n*> \\verbatim\n*>          T is DOUBLE PRECISION array, dimension (LDT,K)\n*>          The triangular k by k matrix T in the representation of the\n*>          block reflector.\n*> \\endverbatim\n*>\n*> \\param[in] LDT\n*> \\verbatim\n*>          LDT is INTEGER\n*>          The leading dimension of the array T. LDT >= K.\n*> \\endverbatim\n*>\n*> \\param[in,out] C\n*> \\verbatim\n*>          C is DOUBLE PRECISION array, dimension (LDC,N)\n*>          On entry, the m by n matrix C.\n*>          On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T.\n*> \\endverbatim\n*>\n*> \\param[in] LDC\n*> \\verbatim\n*>          LDC is INTEGER\n*>          The leading dimension of the array C. LDC >= max(1,M).\n*> \\endverbatim\n*>\n*> \\param[out] WORK\n*> \\verbatim\n*>          WORK is DOUBLE PRECISION array, dimension (LDWORK,K)\n*> \\endverbatim\n*>\n*> \\param[in] LDWORK\n*> \\verbatim\n*>          LDWORK is INTEGER\n*>          The leading dimension of the array WORK.\n*>          If SIDE = 'L', LDWORK >= max(1,N);\n*>          if SIDE = 'R', LDWORK >= max(1,M).\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date November 2011\n*\n*> \\ingroup doubleOTHERauxiliary\n*\n*> \\par Further Details:\n*  =====================\n*>\n*> \\verbatim\n*>\n*>  The shape of the matrix V and the storage of the vectors which define\n*>  the H(i) is best illustrated by the following example with n = 5 and\n*>  k = 3. The elements equal to 1 are not stored; the corresponding\n*>  array elements are modified but restored on exit. The rest of the\n*>  array is not used.\n*>\n*>  DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':\n*>\n*>               V = (  1       )                 V = (  1 v1 v1 v1 v1 )\n*>                   ( v1  1    )                     (     1 v2 v2 v2 )\n*>                   ( v1 v2  1 )                     (        1 v3 v3 )\n*>                   ( v1 v2 v3 )\n*>                   ( v1 v2 v3 )\n*>\n*>  DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':\n*>\n*>               V = ( v1 v2 v3 )                 V = ( v1 v1  1       )\n*>                   ( v1 v2 v3 )                     ( v2 v2 v2  1    )\n*>                   (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )\n*>                   (     1 v3 )\n*>                   (        1 )\n*> \\endverbatim\n*>\n*  =====================================================================\n      SUBROUTINE DLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV,\n     $                   T, LDT, C, LDC, WORK, LDWORK )\n*\n*  -- LAPACK auxiliary routine (version 3.4.0) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     November 2011\n*\n*     .. Scalar Arguments ..\n      CHARACTER          DIRECT, SIDE, STOREV, TRANS\n      INTEGER            K, LDC, LDT, LDV, LDWORK, M, N\n*     ..\n*     .. Array Arguments ..\n      DOUBLE PRECISION   C( LDC, * ), T( LDT, * ), V( LDV, * ),\n     $                   WORK( LDWORK, * )\n*     ..\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      DOUBLE PRECISION   ONE\n      PARAMETER          ( ONE = 1.0D+0 )\n*     ..\n*     .. Local Scalars ..\n      CHARACTER          TRANST\n      INTEGER            I, J, LASTV, LASTC\n*     ..\n*     .. External Functions ..\n      LOGICAL            LSAME\n      INTEGER            ILADLR, ILADLC\n      EXTERNAL           LSAME, ILADLR, ILADLC\n*     ..\n*     .. External Subroutines ..\n      EXTERNAL           DCOPY, DGEMM, DTRMM\n*     ..\n*     .. Executable Statements ..\n*\n*     Quick return if possible\n*\n      IF( M.LE.0 .OR. N.LE.0 )\n     $   RETURN\n*\n      IF( LSAME( TRANS, 'N' ) ) THEN\n         TRANST = 'T'\n      ELSE\n         TRANST = 'N'\n      END IF\n*\n      IF( LSAME( STOREV, 'C' ) ) THEN\n*\n         IF( LSAME( DIRECT, 'F' ) ) THEN\n*\n*           Let  V =  ( V1 )    (first K rows)\n*                     ( V2 )\n*           where  V1  is unit lower triangular.\n*\n            IF( LSAME( SIDE, 'L' ) ) THEN\n*\n*              Form  H * C  or  H**T * C  where  C = ( C1 )\n*                                                    ( C2 )\n*\n               LASTV = MAX( K, ILADLR( M, K, V, LDV ) )\n               LASTC = ILADLC( LASTV, N, C, LDC )\n*\n*              W := C**T * V  =  (C1**T * V1 + C2**T * V2)  (stored in WORK)\n*\n*              W := C1**T\n*\n               DO 10 J = 1, K\n                  CALL DCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 )\n   10          CONTINUE\n*\n*              W := W * V1\n*\n               CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit',\n     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )\n               IF( LASTV.GT.K ) THEN\n*\n*                 W := W + C2**T *V2\n*\n                  CALL DGEMM( 'Transpose', 'No transpose',\n     $                 LASTC, K, LASTV-K,\n     $                 ONE, C( K+1, 1 ), LDC, V( K+1, 1 ), LDV,\n     $                 ONE, WORK, LDWORK )\n               END IF\n*\n*              W := W * T**T  or  W * T\n*\n               CALL DTRMM( 'Right', 'Upper', TRANST, 'Non-unit',\n     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )\n*\n*              C := C - V * W**T\n*\n               IF( LASTV.GT.K ) THEN\n*\n*                 C2 := C2 - V2 * W**T\n*\n                  CALL DGEMM( 'No transpose', 'Transpose',\n     $                 LASTV-K, LASTC, K,\n     $                 -ONE, V( K+1, 1 ), LDV, WORK, LDWORK, ONE,\n     $                 C( K+1, 1 ), LDC )\n               END IF\n*\n*              W := W * V1**T\n*\n               CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit',\n     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )\n*\n*              C1 := C1 - W**T\n*\n               DO 30 J = 1, K\n                  DO 20 I = 1, LASTC\n                     C( J, I ) = C( J, I ) - WORK( I, J )\n   20             CONTINUE\n   30          CONTINUE\n*\n            ELSE IF( LSAME( SIDE, 'R' ) ) THEN\n*\n*              Form  C * H  or  C * H**T  where  C = ( C1  C2 )\n*\n               LASTV = MAX( K, ILADLR( N, K, V, LDV ) )\n               LASTC = ILADLR( M, LASTV, C, LDC )\n*\n*              W := C * V  =  (C1*V1 + C2*V2)  (stored in WORK)\n*\n*              W := C1\n*\n               DO 40 J = 1, K\n                  CALL DCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 )\n   40          CONTINUE\n*\n*              W := W * V1\n*\n               CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit',\n     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )\n               IF( LASTV.GT.K ) THEN\n*\n*                 W := W + C2 * V2\n*\n                  CALL DGEMM( 'No transpose', 'No transpose',\n     $                 LASTC, K, LASTV-K,\n     $                 ONE, C( 1, K+1 ), LDC, V( K+1, 1 ), LDV,\n     $                 ONE, WORK, LDWORK )\n               END IF\n*\n*              W := W * T  or  W * T**T\n*\n               CALL DTRMM( 'Right', 'Upper', TRANS, 'Non-unit',\n     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )\n*\n*              C := C - W * V**T\n*\n               IF( LASTV.GT.K ) THEN\n*\n*                 C2 := C2 - W * V2**T\n*\n                  CALL DGEMM( 'No transpose', 'Transpose',\n     $                 LASTC, LASTV-K, K,\n     $                 -ONE, WORK, LDWORK, V( K+1, 1 ), LDV, ONE,\n     $                 C( 1, K+1 ), LDC )\n               END IF\n*\n*              W := W * V1**T\n*\n               CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit',\n     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )\n*\n*              C1 := C1 - W\n*\n               DO 60 J = 1, K\n                  DO 50 I = 1, LASTC\n                     C( I, J ) = C( I, J ) - WORK( I, J )\n   50             CONTINUE\n   60          CONTINUE\n            END IF\n*\n         ELSE\n*\n*           Let  V =  ( V1 )\n*                     ( V2 )    (last K rows)\n*           where  V2  is unit upper triangular.\n*\n            IF( LSAME( SIDE, 'L' ) ) THEN\n*\n*              Form  H * C  or  H**T * C  where  C = ( C1 )\n*                                                    ( C2 )\n*\n               LASTV = MAX( K, ILADLR( M, K, V, LDV ) )\n               LASTC = ILADLC( LASTV, N, C, LDC )\n*\n*              W := C**T * V  =  (C1**T * V1 + C2**T * V2)  (stored in WORK)\n*\n*              W := C2**T\n*\n               DO 70 J = 1, K\n                  CALL DCOPY( LASTC, C( LASTV-K+J, 1 ), LDC,\n     $                 WORK( 1, J ), 1 )\n   70          CONTINUE\n*\n*              W := W * V2\n*\n               CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit',\n     $              LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,\n     $              WORK, LDWORK )\n               IF( LASTV.GT.K ) THEN\n*\n*                 W := W + C1**T*V1\n*\n                  CALL DGEMM( 'Transpose', 'No transpose',\n     $                 LASTC, K, LASTV-K, ONE, C, LDC, V, LDV,\n     $                 ONE, WORK, LDWORK )\n               END IF\n*\n*              W := W * T**T  or  W * T\n*\n               CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit',\n     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )\n*\n*              C := C - V * W**T\n*\n               IF( LASTV.GT.K ) THEN\n*\n*                 C1 := C1 - V1 * W**T\n*\n                  CALL DGEMM( 'No transpose', 'Transpose',\n     $                 LASTV-K, LASTC, K, -ONE, V, LDV, WORK, LDWORK,\n     $                 ONE, C, LDC )\n               END IF\n*\n*              W := W * V2**T\n*\n               CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit',\n     $              LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,\n     $              WORK, LDWORK )\n*\n*              C2 := C2 - W**T\n*\n               DO 90 J = 1, K\n                  DO 80 I = 1, LASTC\n                     C( LASTV-K+J, I ) = C( LASTV-K+J, I ) - WORK(I, J)\n   80             CONTINUE\n   90          CONTINUE\n*\n            ELSE IF( LSAME( SIDE, 'R' ) ) THEN\n*\n*              Form  C * H  or  C * H**T  where  C = ( C1  C2 )\n*\n               LASTV = MAX( K, ILADLR( N, K, V, LDV ) )\n               LASTC = ILADLR( M, LASTV, C, LDC )\n*\n*              W := C * V  =  (C1*V1 + C2*V2)  (stored in WORK)\n*\n*              W := C2\n*\n               DO 100 J = 1, K\n                  CALL DCOPY( LASTC, C( 1, N-K+J ), 1, WORK( 1, J ), 1 )\n  100          CONTINUE\n*\n*              W := W * V2\n*\n               CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit',\n     $              LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,\n     $              WORK, LDWORK )\n               IF( LASTV.GT.K ) THEN\n*\n*                 W := W + C1 * V1\n*\n                  CALL DGEMM( 'No transpose', 'No transpose',\n     $                 LASTC, K, LASTV-K, ONE, C, LDC, V, LDV,\n     $                 ONE, WORK, LDWORK )\n               END IF\n*\n*              W := W * T  or  W * T**T\n*\n               CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit',\n     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )\n*\n*              C := C - W * V**T\n*\n               IF( LASTV.GT.K ) THEN\n*\n*                 C1 := C1 - W * V1**T\n*\n                  CALL DGEMM( 'No transpose', 'Transpose',\n     $                 LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV,\n     $                 ONE, C, LDC )\n               END IF\n*\n*              W := W * V2**T\n*\n               CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit',\n     $              LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,\n     $              WORK, LDWORK )\n*\n*              C2 := C2 - W\n*\n               DO 120 J = 1, K\n                  DO 110 I = 1, LASTC\n                     C( I, LASTV-K+J ) = C( I, LASTV-K+J ) - WORK(I, J)\n  110             CONTINUE\n  120          CONTINUE\n            END IF\n         END IF\n*\n      ELSE IF( LSAME( STOREV, 'R' ) ) THEN\n*\n         IF( LSAME( DIRECT, 'F' ) ) THEN\n*\n*           Let  V =  ( V1  V2 )    (V1: first K columns)\n*           where  V1  is unit upper triangular.\n*\n            IF( LSAME( SIDE, 'L' ) ) THEN\n*\n*              Form  H * C  or  H**T * C  where  C = ( C1 )\n*                                                    ( C2 )\n*\n               LASTV = MAX( K, ILADLC( K, M, V, LDV ) )\n               LASTC = ILADLC( LASTV, N, C, LDC )\n*\n*              W := C**T * V**T  =  (C1**T * V1**T + C2**T * V2**T) (stored in WORK)\n*\n*              W := C1**T\n*\n               DO 130 J = 1, K\n                  CALL DCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 )\n  130          CONTINUE\n*\n*              W := W * V1**T\n*\n               CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit',\n     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )\n               IF( LASTV.GT.K ) THEN\n*\n*                 W := W + C2**T*V2**T\n*\n                  CALL DGEMM( 'Transpose', 'Transpose',\n     $                 LASTC, K, LASTV-K,\n     $                 ONE, C( K+1, 1 ), LDC, V( 1, K+1 ), LDV,\n     $                 ONE, WORK, LDWORK )\n               END IF\n*\n*              W := W * T**T  or  W * T\n*\n               CALL DTRMM( 'Right', 'Upper', TRANST, 'Non-unit',\n     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )\n*\n*              C := C - V**T * W**T\n*\n               IF( LASTV.GT.K ) THEN\n*\n*                 C2 := C2 - V2**T * W**T\n*\n                  CALL DGEMM( 'Transpose', 'Transpose',\n     $                 LASTV-K, LASTC, K,\n     $                 -ONE, V( 1, K+1 ), LDV, WORK, LDWORK,\n     $                 ONE, C( K+1, 1 ), LDC )\n               END IF\n*\n*              W := W * V1\n*\n               CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit',\n     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )\n*\n*              C1 := C1 - W**T\n*\n               DO 150 J = 1, K\n                  DO 140 I = 1, LASTC\n                     C( J, I ) = C( J, I ) - WORK( I, J )\n  140             CONTINUE\n  150          CONTINUE\n*\n            ELSE IF( LSAME( SIDE, 'R' ) ) THEN\n*\n*              Form  C * H  or  C * H**T  where  C = ( C1  C2 )\n*\n               LASTV = MAX( K, ILADLC( K, N, V, LDV ) )\n               LASTC = ILADLR( M, LASTV, C, LDC )\n*\n*              W := C * V**T  =  (C1*V1**T + C2*V2**T)  (stored in WORK)\n*\n*              W := C1\n*\n               DO 160 J = 1, K\n                  CALL DCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 )\n  160          CONTINUE\n*\n*              W := W * V1**T\n*\n               CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit',\n     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )\n               IF( LASTV.GT.K ) THEN\n*\n*                 W := W + C2 * V2**T\n*\n                  CALL DGEMM( 'No transpose', 'Transpose',\n     $                 LASTC, K, LASTV-K,\n     $                 ONE, C( 1, K+1 ), LDC, V( 1, K+1 ), LDV,\n     $                 ONE, WORK, LDWORK )\n               END IF\n*\n*              W := W * T  or  W * T**T\n*\n               CALL DTRMM( 'Right', 'Upper', TRANS, 'Non-unit',\n     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )\n*\n*              C := C - W * V\n*\n               IF( LASTV.GT.K ) THEN\n*\n*                 C2 := C2 - W * V2\n*\n                  CALL DGEMM( 'No transpose', 'No transpose',\n     $                 LASTC, LASTV-K, K,\n     $                 -ONE, WORK, LDWORK, V( 1, K+1 ), LDV,\n     $                 ONE, C( 1, K+1 ), LDC )\n               END IF\n*\n*              W := W * V1\n*\n               CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit',\n     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )\n*\n*              C1 := C1 - W\n*\n               DO 180 J = 1, K\n                  DO 170 I = 1, LASTC\n                     C( I, J ) = C( I, J ) - WORK( I, J )\n  170             CONTINUE\n  180          CONTINUE\n*\n            END IF\n*\n         ELSE\n*\n*           Let  V =  ( V1  V2 )    (V2: last K columns)\n*           where  V2  is unit lower triangular.\n*\n            IF( LSAME( SIDE, 'L' ) ) THEN\n*\n*              Form  H * C  or  H**T * C  where  C = ( C1 )\n*                                                    ( C2 )\n*\n               LASTV = MAX( K, ILADLC( K, M, V, LDV ) )\n               LASTC = ILADLC( LASTV, N, C, LDC )\n*\n*              W := C**T * V**T  =  (C1**T * V1**T + C2**T * V2**T) (stored in WORK)\n*\n*              W := C2**T\n*\n               DO 190 J = 1, K\n                  CALL DCOPY( LASTC, C( LASTV-K+J, 1 ), LDC,\n     $                 WORK( 1, J ), 1 )\n  190          CONTINUE\n*\n*              W := W * V2**T\n*\n               CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit',\n     $              LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,\n     $              WORK, LDWORK )\n               IF( LASTV.GT.K ) THEN\n*\n*                 W := W + C1**T * V1**T\n*\n                  CALL DGEMM( 'Transpose', 'Transpose',\n     $                 LASTC, K, LASTV-K, ONE, C, LDC, V, LDV,\n     $                 ONE, WORK, LDWORK )\n               END IF\n*\n*              W := W * T**T  or  W * T\n*\n               CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit',\n     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )\n*\n*              C := C - V**T * W**T\n*\n               IF( LASTV.GT.K ) THEN\n*\n*                 C1 := C1 - V1**T * W**T\n*\n                  CALL DGEMM( 'Transpose', 'Transpose',\n     $                 LASTV-K, LASTC, K, -ONE, V, LDV, WORK, LDWORK,\n     $                 ONE, C, LDC )\n               END IF\n*\n*              W := W * V2\n*\n               CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit',\n     $              LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,\n     $              WORK, LDWORK )\n*\n*              C2 := C2 - W**T\n*\n               DO 210 J = 1, K\n                  DO 200 I = 1, LASTC\n                     C( LASTV-K+J, I ) = C( LASTV-K+J, I ) - WORK(I, J)\n  200             CONTINUE\n  210          CONTINUE\n*\n            ELSE IF( LSAME( SIDE, 'R' ) ) THEN\n*\n*              Form  C * H  or  C * H**T  where  C = ( C1  C2 )\n*\n               LASTV = MAX( K, ILADLC( K, N, V, LDV ) )\n               LASTC = ILADLR( M, LASTV, C, LDC )\n*\n*              W := C * V**T  =  (C1*V1**T + C2*V2**T)  (stored in WORK)\n*\n*              W := C2\n*\n               DO 220 J = 1, K\n                  CALL DCOPY( LASTC, C( 1, LASTV-K+J ), 1,\n     $                 WORK( 1, J ), 1 )\n  220          CONTINUE\n*\n*              W := W * V2**T\n*\n               CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit',\n     $              LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,\n     $              WORK, LDWORK )\n               IF( LASTV.GT.K ) THEN\n*\n*                 W := W + C1 * V1**T\n*\n                  CALL DGEMM( 'No transpose', 'Transpose',\n     $                 LASTC, K, LASTV-K, ONE, C, LDC, V, LDV,\n     $                 ONE, WORK, LDWORK )\n               END IF\n*\n*              W := W * T  or  W * T**T\n*\n               CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit',\n     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )\n*\n*              C := C - W * V\n*\n               IF( LASTV.GT.K ) THEN\n*\n*                 C1 := C1 - W * V1\n*\n                  CALL DGEMM( 'No transpose', 'No transpose',\n     $                 LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV,\n     $                 ONE, C, LDC )\n               END IF\n*\n*              W := W * V2\n*\n               CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit',\n     $              LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,\n     $              WORK, LDWORK )\n*\n*              C1 := C1 - W\n*\n               DO 240 J = 1, K\n                  DO 230 I = 1, LASTC\n                     C( I, LASTV-K+J ) = C( I, LASTV-K+J ) - WORK(I, J)\n  230             CONTINUE\n  240          CONTINUE\n*\n            END IF\n*\n         END IF\n      END IF\n*\n      RETURN\n*\n*     End of DLARFB\n*\n      END\n"
  },
  {
    "path": "include/eigen3/lapack/dlarfg.f",
    "content": "*> \\brief \\b DLARFG\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*> \\htmlonly\n*> Download DLARFG + dependencies \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarfg.f\"> \n*> [TGZ]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarfg.f\"> \n*> [ZIP]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarfg.f\"> \n*> [TXT]</a>\n*> \\endhtmlonly \n*\n*  Definition:\n*  ===========\n*\n*       SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU )\n* \n*       .. Scalar Arguments ..\n*       INTEGER            INCX, N\n*       DOUBLE PRECISION   ALPHA, TAU\n*       ..\n*       .. Array Arguments ..\n*       DOUBLE PRECISION   X( * )\n*       ..\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> DLARFG generates a real elementary reflector H of order n, such\n*> that\n*>\n*>       H * ( alpha ) = ( beta ),   H**T * H = I.\n*>           (   x   )   (   0  )\n*>\n*> where alpha and beta are scalars, and x is an (n-1)-element real\n*> vector. H is represented in the form\n*>\n*>       H = I - tau * ( 1 ) * ( 1 v**T ) ,\n*>                     ( v )\n*>\n*> where tau is a real scalar and v is a real (n-1)-element\n*> vector.\n*>\n*> If the elements of x are all zero, then tau = 0 and H is taken to be\n*> the unit matrix.\n*>\n*> Otherwise  1 <= tau <= 2.\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] N\n*> \\verbatim\n*>          N is INTEGER\n*>          The order of the elementary reflector.\n*> \\endverbatim\n*>\n*> \\param[in,out] ALPHA\n*> \\verbatim\n*>          ALPHA is DOUBLE PRECISION\n*>          On entry, the value alpha.\n*>          On exit, it is overwritten with the value beta.\n*> \\endverbatim\n*>\n*> \\param[in,out] X\n*> \\verbatim\n*>          X is DOUBLE PRECISION array, dimension\n*>                         (1+(N-2)*abs(INCX))\n*>          On entry, the vector x.\n*>          On exit, it is overwritten with the vector v.\n*> \\endverbatim\n*>\n*> \\param[in] INCX\n*> \\verbatim\n*>          INCX is INTEGER\n*>          The increment between elements of X. INCX > 0.\n*> \\endverbatim\n*>\n*> \\param[out] TAU\n*> \\verbatim\n*>          TAU is DOUBLE PRECISION\n*>          The value tau.\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date November 2011\n*\n*> \\ingroup doubleOTHERauxiliary\n*\n*  =====================================================================\n      SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU )\n*\n*  -- LAPACK auxiliary routine (version 3.4.0) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     November 2011\n*\n*     .. Scalar Arguments ..\n      INTEGER            INCX, N\n      DOUBLE PRECISION   ALPHA, TAU\n*     ..\n*     .. Array Arguments ..\n      DOUBLE PRECISION   X( * )\n*     ..\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      DOUBLE PRECISION   ONE, ZERO\n      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )\n*     ..\n*     .. Local Scalars ..\n      INTEGER            J, KNT\n      DOUBLE PRECISION   BETA, RSAFMN, SAFMIN, XNORM\n*     ..\n*     .. External Functions ..\n      DOUBLE PRECISION   DLAMCH, DLAPY2, DNRM2\n      EXTERNAL           DLAMCH, DLAPY2, DNRM2\n*     ..\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, SIGN\n*     ..\n*     .. External Subroutines ..\n      EXTERNAL           DSCAL\n*     ..\n*     .. Executable Statements ..\n*\n      IF( N.LE.1 ) THEN\n         TAU = ZERO\n         RETURN\n      END IF\n*\n      XNORM = DNRM2( N-1, X, INCX )\n*\n      IF( XNORM.EQ.ZERO ) THEN\n*\n*        H  =  I\n*\n         TAU = ZERO\n      ELSE\n*\n*        general case\n*\n         BETA = -SIGN( DLAPY2( ALPHA, XNORM ), ALPHA )\n         SAFMIN = DLAMCH( 'S' ) / DLAMCH( 'E' )\n         KNT = 0\n         IF( ABS( BETA ).LT.SAFMIN ) THEN\n*\n*           XNORM, BETA may be inaccurate; scale X and recompute them\n*\n            RSAFMN = ONE / SAFMIN\n   10       CONTINUE\n            KNT = KNT + 1\n            CALL DSCAL( N-1, RSAFMN, X, INCX )\n            BETA = BETA*RSAFMN\n            ALPHA = ALPHA*RSAFMN\n            IF( ABS( BETA ).LT.SAFMIN )\n     $         GO TO 10\n*\n*           New BETA is at most 1, at least SAFMIN\n*\n            XNORM = DNRM2( N-1, X, INCX )\n            BETA = -SIGN( DLAPY2( ALPHA, XNORM ), ALPHA )\n         END IF\n         TAU = ( BETA-ALPHA ) / BETA\n         CALL DSCAL( N-1, ONE / ( ALPHA-BETA ), X, INCX )\n*\n*        If ALPHA is subnormal, it may lose relative accuracy\n*\n         DO 20 J = 1, KNT\n            BETA = BETA*SAFMIN\n 20      CONTINUE\n         ALPHA = BETA\n      END IF\n*\n      RETURN\n*\n*     End of DLARFG\n*\n      END\n"
  },
  {
    "path": "include/eigen3/lapack/dlarft.f",
    "content": "*> \\brief \\b DLARFT\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*> \\htmlonly\n*> Download DLARFT + dependencies \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarft.f\"> \n*> [TGZ]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarft.f\"> \n*> [ZIP]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarft.f\"> \n*> [TXT]</a>\n*> \\endhtmlonly \n*\n*  Definition:\n*  ===========\n*\n*       SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )\n* \n*       .. Scalar Arguments ..\n*       CHARACTER          DIRECT, STOREV\n*       INTEGER            K, LDT, LDV, N\n*       ..\n*       .. Array Arguments ..\n*       DOUBLE PRECISION   T( LDT, * ), TAU( * ), V( LDV, * )\n*       ..\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> DLARFT forms the triangular factor T of a real block reflector H\n*> of order n, which is defined as a product of k elementary reflectors.\n*>\n*> If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular;\n*>\n*> If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular.\n*>\n*> If STOREV = 'C', the vector which defines the elementary reflector\n*> H(i) is stored in the i-th column of the array V, and\n*>\n*>    H  =  I - V * T * V**T\n*>\n*> If STOREV = 'R', the vector which defines the elementary reflector\n*> H(i) is stored in the i-th row of the array V, and\n*>\n*>    H  =  I - V**T * T * V\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] DIRECT\n*> \\verbatim\n*>          DIRECT is CHARACTER*1\n*>          Specifies the order in which the elementary reflectors are\n*>          multiplied to form the block reflector:\n*>          = 'F': H = H(1) H(2) . . . H(k) (Forward)\n*>          = 'B': H = H(k) . . . H(2) H(1) (Backward)\n*> \\endverbatim\n*>\n*> \\param[in] STOREV\n*> \\verbatim\n*>          STOREV is CHARACTER*1\n*>          Specifies how the vectors which define the elementary\n*>          reflectors are stored (see also Further Details):\n*>          = 'C': columnwise\n*>          = 'R': rowwise\n*> \\endverbatim\n*>\n*> \\param[in] N\n*> \\verbatim\n*>          N is INTEGER\n*>          The order of the block reflector H. N >= 0.\n*> \\endverbatim\n*>\n*> \\param[in] K\n*> \\verbatim\n*>          K is INTEGER\n*>          The order of the triangular factor T (= the number of\n*>          elementary reflectors). K >= 1.\n*> \\endverbatim\n*>\n*> \\param[in] V\n*> \\verbatim\n*>          V is DOUBLE PRECISION array, dimension\n*>                               (LDV,K) if STOREV = 'C'\n*>                               (LDV,N) if STOREV = 'R'\n*>          The matrix V. See further details.\n*> \\endverbatim\n*>\n*> \\param[in] LDV\n*> \\verbatim\n*>          LDV is INTEGER\n*>          The leading dimension of the array V.\n*>          If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.\n*> \\endverbatim\n*>\n*> \\param[in] TAU\n*> \\verbatim\n*>          TAU is DOUBLE PRECISION array, dimension (K)\n*>          TAU(i) must contain the scalar factor of the elementary\n*>          reflector H(i).\n*> \\endverbatim\n*>\n*> \\param[out] T\n*> \\verbatim\n*>          T is DOUBLE PRECISION array, dimension (LDT,K)\n*>          The k by k triangular factor T of the block reflector.\n*>          If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is\n*>          lower triangular. The rest of the array is not used.\n*> \\endverbatim\n*>\n*> \\param[in] LDT\n*> \\verbatim\n*>          LDT is INTEGER\n*>          The leading dimension of the array T. LDT >= K.\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date April 2012\n*\n*> \\ingroup doubleOTHERauxiliary\n*\n*> \\par Further Details:\n*  =====================\n*>\n*> \\verbatim\n*>\n*>  The shape of the matrix V and the storage of the vectors which define\n*>  the H(i) is best illustrated by the following example with n = 5 and\n*>  k = 3. The elements equal to 1 are not stored.\n*>\n*>  DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':\n*>\n*>               V = (  1       )                 V = (  1 v1 v1 v1 v1 )\n*>                   ( v1  1    )                     (     1 v2 v2 v2 )\n*>                   ( v1 v2  1 )                     (        1 v3 v3 )\n*>                   ( v1 v2 v3 )\n*>                   ( v1 v2 v3 )\n*>\n*>  DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':\n*>\n*>               V = ( v1 v2 v3 )                 V = ( v1 v1  1       )\n*>                   ( v1 v2 v3 )                     ( v2 v2 v2  1    )\n*>                   (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )\n*>                   (     1 v3 )\n*>                   (        1 )\n*> \\endverbatim\n*>\n*  =====================================================================\n      SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )\n*\n*  -- LAPACK auxiliary routine (version 3.4.1) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     April 2012\n*\n*     .. Scalar Arguments ..\n      CHARACTER          DIRECT, STOREV\n      INTEGER            K, LDT, LDV, N\n*     ..\n*     .. Array Arguments ..\n      DOUBLE PRECISION   T( LDT, * ), TAU( * ), V( LDV, * )\n*     ..\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      DOUBLE PRECISION   ONE, ZERO\n      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )\n*     ..\n*     .. Local Scalars ..\n      INTEGER            I, J, PREVLASTV, LASTV\n*     ..\n*     .. External Subroutines ..\n      EXTERNAL           DGEMV, DTRMV\n*     ..\n*     .. External Functions ..\n      LOGICAL            LSAME\n      EXTERNAL           LSAME\n*     ..\n*     .. Executable Statements ..\n*\n*     Quick return if possible\n*\n      IF( N.EQ.0 )\n     $   RETURN\n*\n      IF( LSAME( DIRECT, 'F' ) ) THEN\n         PREVLASTV = N\n         DO I = 1, K\n            PREVLASTV = MAX( I, PREVLASTV )\n            IF( TAU( I ).EQ.ZERO ) THEN\n*\n*              H(i)  =  I\n*\n               DO J = 1, I\n                  T( J, I ) = ZERO\n               END DO\n            ELSE\n*\n*              general case\n*\n               IF( LSAME( STOREV, 'C' ) ) THEN\n*                 Skip any trailing zeros.\n                  DO LASTV = N, I+1, -1\n                     IF( V( LASTV, I ).NE.ZERO ) EXIT\n                  END DO\n                  DO J = 1, I-1\n                     T( J, I ) = -TAU( I ) * V( I , J )\n                  END DO   \n                  J = MIN( LASTV, PREVLASTV )\n*\n*                 T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**T * V(i:j,i)\n*\n                  CALL DGEMV( 'Transpose', J-I, I-1, -TAU( I ), \n     $                        V( I+1, 1 ), LDV, V( I+1, I ), 1, ONE, \n     $                        T( 1, I ), 1 )\n               ELSE\n*                 Skip any trailing zeros.\n                  DO LASTV = N, I+1, -1\n                     IF( V( I, LASTV ).NE.ZERO ) EXIT\n                  END DO\n                  DO J = 1, I-1\n                     T( J, I ) = -TAU( I ) * V( J , I )\n                  END DO   \n                  J = MIN( LASTV, PREVLASTV )\n*\n*                 T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**T\n*\n                  CALL DGEMV( 'No transpose', I-1, J-I, -TAU( I ),\n     $                        V( 1, I+1 ), LDV, V( I, I+1 ), LDV, ONE,\n     $                        T( 1, I ), 1 )\n               END IF\n*\n*              T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i)\n*\n               CALL DTRMV( 'Upper', 'No transpose', 'Non-unit', I-1, T,\n     $                     LDT, T( 1, I ), 1 )\n               T( I, I ) = TAU( I )\n               IF( I.GT.1 ) THEN\n                  PREVLASTV = MAX( PREVLASTV, LASTV )\n               ELSE\n                  PREVLASTV = LASTV\n               END IF\n            END IF\n         END DO\n      ELSE\n         PREVLASTV = 1\n         DO I = K, 1, -1\n            IF( TAU( I ).EQ.ZERO ) THEN\n*\n*              H(i)  =  I\n*\n               DO J = I, K\n                  T( J, I ) = ZERO\n               END DO\n            ELSE\n*\n*              general case\n*\n               IF( I.LT.K ) THEN\n                  IF( LSAME( STOREV, 'C' ) ) THEN\n*                    Skip any leading zeros.\n                     DO LASTV = 1, I-1\n                        IF( V( LASTV, I ).NE.ZERO ) EXIT\n                     END DO\n                     DO J = I+1, K\n                        T( J, I ) = -TAU( I ) * V( N-K+I , J )\n                     END DO   \n                     J = MAX( LASTV, PREVLASTV )\n*\n*                    T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**T * V(j:n-k+i,i)\n*\n                     CALL DGEMV( 'Transpose', N-K+I-J, K-I, -TAU( I ),\n     $                           V( J, I+1 ), LDV, V( J, I ), 1, ONE,\n     $                           T( I+1, I ), 1 )\n                  ELSE\n*                    Skip any leading zeros.\n                     DO LASTV = 1, I-1\n                        IF( V( I, LASTV ).NE.ZERO ) EXIT\n                     END DO\n                     DO J = I+1, K\n                        T( J, I ) = -TAU( I ) * V( J, N-K+I )\n                     END DO   \n                     J = MAX( LASTV, PREVLASTV )\n*\n*                    T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**T\n*\n                     CALL DGEMV( 'No transpose', K-I, N-K+I-J,\n     $                    -TAU( I ), V( I+1, J ), LDV, V( I, J ), LDV,\n     $                    ONE, T( I+1, I ), 1 )\n                  END IF\n*\n*                 T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i)\n*\n                  CALL DTRMV( 'Lower', 'No transpose', 'Non-unit', K-I,\n     $                        T( I+1, I+1 ), LDT, T( I+1, I ), 1 )\n                  IF( I.GT.1 ) THEN\n                     PREVLASTV = MIN( PREVLASTV, LASTV )\n                  ELSE\n                     PREVLASTV = LASTV\n                  END IF\n               END IF\n               T( I, I ) = TAU( I )\n            END IF\n         END DO\n      END IF\n      RETURN\n*\n*     End of DLARFT\n*\n      END\n"
  },
  {
    "path": "include/eigen3/lapack/double.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define SCALAR        double\n#define SCALAR_SUFFIX d\n#define SCALAR_SUFFIX_UP \"D\"\n#define ISCOMPLEX     0\n\n#include \"cholesky.cpp\"\n#include \"lu.cpp\"\n#include \"eigenvalues.cpp\"\n#include \"svd.cpp\"\n"
  },
  {
    "path": "include/eigen3/lapack/dsecnd_NONE.f",
    "content": "*> \\brief \\b DSECND returns nothing\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*  Definition:\n*  ===========\n*\n*      DOUBLE PRECISION FUNCTION DSECND( )\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*>  DSECND returns nothing instead of returning the user time for a process in seconds.\n*>  If you are using that routine, it means that neither EXTERNAL ETIME,\n*>  EXTERNAL ETIME_, INTERNAL ETIME, INTERNAL CPU_TIME is available  on\n*>  your machine.\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date November 2011\n*\n*> \\ingroup auxOTHERauxiliary\n*\n*  =====================================================================\n      DOUBLE PRECISION FUNCTION DSECND( )\n*\n*  -- LAPACK auxiliary routine (version 3.4.0) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     November 2011\n*\n* =====================================================================\n*\n      DSECND = 0.0D+0\n      RETURN\n*\n*     End of DSECND\n*\n      END\n"
  },
  {
    "path": "include/eigen3/lapack/eigenvalues.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2011 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"lapack_common.h\"\n#include <Eigen/Eigenvalues>\n\n// computes eigen values and vectors of a general N-by-N matrix A\nEIGEN_LAPACK_FUNC(syev,(char *jobz, char *uplo, int* n, Scalar* a, int *lda, Scalar* w, Scalar* /*work*/, int* lwork, int *info))\n{\n  // TODO exploit the work buffer\n  bool query_size = *lwork==-1;\n  \n  *info = 0;\n        if(*jobz!='N' && *jobz!='V')                    *info = -1;\n  else  if(UPLO(*uplo)==INVALID)                        *info = -2;\n  else  if(*n<0)                                        *info = -3;\n  else  if(*lda<std::max(1,*n))                         *info = -5;\n  else  if((!query_size) && *lwork<std::max(1,3**n-1))  *info = -8;\n    \n  if(*info!=0)\n  {\n    int e = -*info;\n    return xerbla_(SCALAR_SUFFIX_UP\"SYEV \", &e, 6);\n  }\n  \n  if(query_size)\n  {\n    *lwork = 0;\n    return 0;\n  }\n  \n  if(*n==0)\n    return 0;\n  \n  PlainMatrixType mat(*n,*n);\n  if(UPLO(*uplo)==UP) mat = matrix(a,*n,*n,*lda).adjoint();\n  else                mat = matrix(a,*n,*n,*lda);\n  \n  bool computeVectors = *jobz=='V' || *jobz=='v';\n  SelfAdjointEigenSolver<PlainMatrixType> eig(mat,computeVectors?ComputeEigenvectors:EigenvaluesOnly);\n  \n  if(eig.info()==NoConvergence)\n  {\n    make_vector(w,*n).setZero();\n    if(computeVectors)\n      matrix(a,*n,*n,*lda).setIdentity();\n    //*info = 1;\n    return 0;\n  }\n  \n  make_vector(w,*n) = eig.eigenvalues();\n  if(computeVectors)\n    matrix(a,*n,*n,*lda) = eig.eigenvectors();\n  \n  return 0;\n}\n"
  },
  {
    "path": "include/eigen3/lapack/ilaclc.f",
    "content": "*> \\brief \\b ILACLC\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*> \\htmlonly\n*> Download ILACLC + dependencies \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ilaclc.f\"> \n*> [TGZ]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ilaclc.f\"> \n*> [ZIP]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ilaclc.f\"> \n*> [TXT]</a>\n*> \\endhtmlonly \n*\n*  Definition:\n*  ===========\n*\n*       INTEGER FUNCTION ILACLC( M, N, A, LDA )\n* \n*       .. Scalar Arguments ..\n*       INTEGER            M, N, LDA\n*       ..\n*       .. Array Arguments ..\n*       COMPLEX            A( LDA, * )\n*       ..\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> ILACLC scans A for its last non-zero column.\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] M\n*> \\verbatim\n*>          M is INTEGER\n*>          The number of rows of the matrix A.\n*> \\endverbatim\n*>\n*> \\param[in] N\n*> \\verbatim\n*>          N is INTEGER\n*>          The number of columns of the matrix A.\n*> \\endverbatim\n*>\n*> \\param[in] A\n*> \\verbatim\n*>          A is COMPLEX array, dimension (LDA,N)\n*>          The m by n matrix A.\n*> \\endverbatim\n*>\n*> \\param[in] LDA\n*> \\verbatim\n*>          LDA is INTEGER\n*>          The leading dimension of the array A. LDA >= max(1,M).\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date November 2011\n*\n*> \\ingroup complexOTHERauxiliary\n*\n*  =====================================================================\n      INTEGER FUNCTION ILACLC( M, N, A, LDA )\n*\n*  -- LAPACK auxiliary routine (version 3.4.0) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     November 2011\n*\n*     .. Scalar Arguments ..\n      INTEGER            M, N, LDA\n*     ..\n*     .. Array Arguments ..\n      COMPLEX            A( LDA, * )\n*     ..\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      COMPLEX          ZERO\n      PARAMETER ( ZERO = (0.0E+0, 0.0E+0) )\n*     ..\n*     .. Local Scalars ..\n      INTEGER I\n*     ..\n*     .. Executable Statements ..\n*\n*     Quick test for the common case where one corner is non-zero.\n      IF( N.EQ.0 ) THEN\n         ILACLC = N\n      ELSE IF( A(1, N).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN\n         ILACLC = N\n      ELSE\n*     Now scan each column from the end, returning with the first non-zero.\n         DO ILACLC = N, 1, -1\n            DO I = 1, M\n               IF( A(I, ILACLC).NE.ZERO ) RETURN\n            END DO\n         END DO\n      END IF\n      RETURN\n      END\n"
  },
  {
    "path": "include/eigen3/lapack/ilaclr.f",
    "content": "*> \\brief \\b ILACLR\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*> \\htmlonly\n*> Download ILACLR + dependencies \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ilaclr.f\"> \n*> [TGZ]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ilaclr.f\"> \n*> [ZIP]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ilaclr.f\"> \n*> [TXT]</a>\n*> \\endhtmlonly \n*\n*  Definition:\n*  ===========\n*\n*       INTEGER FUNCTION ILACLR( M, N, A, LDA )\n* \n*       .. Scalar Arguments ..\n*       INTEGER            M, N, LDA\n*       ..\n*       .. Array Arguments ..\n*       COMPLEX            A( LDA, * )\n*       ..\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> ILACLR scans A for its last non-zero row.\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] M\n*> \\verbatim\n*>          M is INTEGER\n*>          The number of rows of the matrix A.\n*> \\endverbatim\n*>\n*> \\param[in] N\n*> \\verbatim\n*>          N is INTEGER\n*>          The number of columns of the matrix A.\n*> \\endverbatim\n*>\n*> \\param[in] A\n*> \\verbatim\n*>          A is array, dimension (LDA,N)\n*>          The m by n matrix A.\n*> \\endverbatim\n*>\n*> \\param[in] LDA\n*> \\verbatim\n*>          LDA is INTEGER\n*>          The leading dimension of the array A. LDA >= max(1,M).\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date April 2012\n*\n*> \\ingroup complexOTHERauxiliary\n*\n*  =====================================================================\n      INTEGER FUNCTION ILACLR( M, N, A, LDA )\n*\n*  -- LAPACK auxiliary routine (version 3.4.1) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     April 2012\n*\n*     .. Scalar Arguments ..\n      INTEGER            M, N, LDA\n*     ..\n*     .. Array Arguments ..\n      COMPLEX            A( LDA, * )\n*     ..\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      COMPLEX          ZERO\n      PARAMETER ( ZERO = (0.0E+0, 0.0E+0) )\n*     ..\n*     .. Local Scalars ..\n      INTEGER I, J\n*     ..\n*     .. Executable Statements ..\n*\n*     Quick test for the common case where one corner is non-zero.\n      IF( M.EQ.0 ) THEN\n         ILACLR = M\n      ELSE IF( A(M, 1).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN\n         ILACLR = M\n      ELSE\n*     Scan up each column tracking the last zero row seen.\n         ILACLR = 0\n         DO J = 1, N\n            I=M\n            DO WHILE((A(MAX(I,1),J).EQ.ZERO).AND.(I.GE.1))\n               I=I-1\n            ENDDO\n            ILACLR = MAX( ILACLR, I )\n         END DO\n      END IF\n      RETURN\n      END\n"
  },
  {
    "path": "include/eigen3/lapack/iladlc.f",
    "content": "*> \\brief \\b ILADLC\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*> \\htmlonly\n*> Download ILADLC + dependencies \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/iladlc.f\"> \n*> [TGZ]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/iladlc.f\"> \n*> [ZIP]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/iladlc.f\"> \n*> [TXT]</a>\n*> \\endhtmlonly \n*\n*  Definition:\n*  ===========\n*\n*       INTEGER FUNCTION ILADLC( M, N, A, LDA )\n* \n*       .. Scalar Arguments ..\n*       INTEGER            M, N, LDA\n*       ..\n*       .. Array Arguments ..\n*       DOUBLE PRECISION   A( LDA, * )\n*       ..\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> ILADLC scans A for its last non-zero column.\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] M\n*> \\verbatim\n*>          M is INTEGER\n*>          The number of rows of the matrix A.\n*> \\endverbatim\n*>\n*> \\param[in] N\n*> \\verbatim\n*>          N is INTEGER\n*>          The number of columns of the matrix A.\n*> \\endverbatim\n*>\n*> \\param[in] A\n*> \\verbatim\n*>          A is DOUBLE PRECISION array, dimension (LDA,N)\n*>          The m by n matrix A.\n*> \\endverbatim\n*>\n*> \\param[in] LDA\n*> \\verbatim\n*>          LDA is INTEGER\n*>          The leading dimension of the array A. LDA >= max(1,M).\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date November 2011\n*\n*> \\ingroup auxOTHERauxiliary\n*\n*  =====================================================================\n      INTEGER FUNCTION ILADLC( M, N, A, LDA )\n*\n*  -- LAPACK auxiliary routine (version 3.4.0) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     November 2011\n*\n*     .. Scalar Arguments ..\n      INTEGER            M, N, LDA\n*     ..\n*     .. Array Arguments ..\n      DOUBLE PRECISION   A( LDA, * )\n*     ..\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      DOUBLE PRECISION ZERO\n      PARAMETER ( ZERO = 0.0D+0 )\n*     ..\n*     .. Local Scalars ..\n      INTEGER I\n*     ..\n*     .. Executable Statements ..\n*\n*     Quick test for the common case where one corner is non-zero.\n      IF( N.EQ.0 ) THEN\n         ILADLC = N\n      ELSE IF( A(1, N).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN\n         ILADLC = N\n      ELSE\n*     Now scan each column from the end, returning with the first non-zero.\n         DO ILADLC = N, 1, -1\n            DO I = 1, M\n               IF( A(I, ILADLC).NE.ZERO ) RETURN\n            END DO\n         END DO\n      END IF\n      RETURN\n      END\n"
  },
  {
    "path": "include/eigen3/lapack/iladlr.f",
    "content": "*> \\brief \\b ILADLR\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*> \\htmlonly\n*> Download ILADLR + dependencies \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/iladlr.f\"> \n*> [TGZ]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/iladlr.f\"> \n*> [ZIP]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/iladlr.f\"> \n*> [TXT]</a>\n*> \\endhtmlonly \n*\n*  Definition:\n*  ===========\n*\n*       INTEGER FUNCTION ILADLR( M, N, A, LDA )\n* \n*       .. Scalar Arguments ..\n*       INTEGER            M, N, LDA\n*       ..\n*       .. Array Arguments ..\n*       DOUBLE PRECISION   A( LDA, * )\n*       ..\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> ILADLR scans A for its last non-zero row.\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] M\n*> \\verbatim\n*>          M is INTEGER\n*>          The number of rows of the matrix A.\n*> \\endverbatim\n*>\n*> \\param[in] N\n*> \\verbatim\n*>          N is INTEGER\n*>          The number of columns of the matrix A.\n*> \\endverbatim\n*>\n*> \\param[in] A\n*> \\verbatim\n*>          A is DOUBLE PRECISION array, dimension (LDA,N)\n*>          The m by n matrix A.\n*> \\endverbatim\n*>\n*> \\param[in] LDA\n*> \\verbatim\n*>          LDA is INTEGER\n*>          The leading dimension of the array A. LDA >= max(1,M).\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date April 2012\n*\n*> \\ingroup auxOTHERauxiliary\n*\n*  =====================================================================\n      INTEGER FUNCTION ILADLR( M, N, A, LDA )\n*\n*  -- LAPACK auxiliary routine (version 3.4.1) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     April 2012\n*\n*     .. Scalar Arguments ..\n      INTEGER            M, N, LDA\n*     ..\n*     .. Array Arguments ..\n      DOUBLE PRECISION   A( LDA, * )\n*     ..\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      DOUBLE PRECISION ZERO\n      PARAMETER ( ZERO = 0.0D+0 )\n*     ..\n*     .. Local Scalars ..\n      INTEGER I, J\n*     ..\n*     .. Executable Statements ..\n*\n*     Quick test for the common case where one corner is non-zero.\n      IF( M.EQ.0 ) THEN\n         ILADLR = M\n      ELSE IF( A(M, 1).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN\n         ILADLR = M\n      ELSE\n*     Scan up each column tracking the last zero row seen.\n         ILADLR = 0\n         DO J = 1, N\n            I=M\n            DO WHILE((A(MAX(I,1),J).EQ.ZERO).AND.(I.GE.1))\n               I=I-1\n            ENDDO\n            ILADLR = MAX( ILADLR, I )\n         END DO\n      END IF\n      RETURN\n      END\n"
  },
  {
    "path": "include/eigen3/lapack/ilaslc.f",
    "content": "*> \\brief \\b ILASLC\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*> \\htmlonly\n*> Download ILASLC + dependencies \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ilaslc.f\"> \n*> [TGZ]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ilaslc.f\"> \n*> [ZIP]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ilaslc.f\"> \n*> [TXT]</a>\n*> \\endhtmlonly \n*\n*  Definition:\n*  ===========\n*\n*       INTEGER FUNCTION ILASLC( M, N, A, LDA )\n* \n*       .. Scalar Arguments ..\n*       INTEGER            M, N, LDA\n*       ..\n*       .. Array Arguments ..\n*       REAL               A( LDA, * )\n*       ..\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> ILASLC scans A for its last non-zero column.\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] M\n*> \\verbatim\n*>          M is INTEGER\n*>          The number of rows of the matrix A.\n*> \\endverbatim\n*>\n*> \\param[in] N\n*> \\verbatim\n*>          N is INTEGER\n*>          The number of columns of the matrix A.\n*> \\endverbatim\n*>\n*> \\param[in] A\n*> \\verbatim\n*>          A is REAL array, dimension (LDA,N)\n*>          The m by n matrix A.\n*> \\endverbatim\n*>\n*> \\param[in] LDA\n*> \\verbatim\n*>          LDA is INTEGER\n*>          The leading dimension of the array A. LDA >= max(1,M).\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date November 2011\n*\n*> \\ingroup realOTHERauxiliary\n*\n*  =====================================================================\n      INTEGER FUNCTION ILASLC( M, N, A, LDA )\n*\n*  -- LAPACK auxiliary routine (version 3.4.0) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     November 2011\n*\n*     .. Scalar Arguments ..\n      INTEGER            M, N, LDA\n*     ..\n*     .. Array Arguments ..\n      REAL               A( LDA, * )\n*     ..\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      REAL             ZERO\n      PARAMETER ( ZERO = 0.0D+0 )\n*     ..\n*     .. Local Scalars ..\n      INTEGER I\n*     ..\n*     .. Executable Statements ..\n*\n*     Quick test for the common case where one corner is non-zero.\n      IF( N.EQ.0 ) THEN\n         ILASLC = N\n      ELSE IF( A(1, N).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN\n         ILASLC = N\n      ELSE\n*     Now scan each column from the end, returning with the first non-zero.\n         DO ILASLC = N, 1, -1\n            DO I = 1, M\n               IF( A(I, ILASLC).NE.ZERO ) RETURN\n            END DO\n         END DO\n      END IF\n      RETURN\n      END\n"
  },
  {
    "path": "include/eigen3/lapack/ilaslr.f",
    "content": "*> \\brief \\b ILASLR\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*> \\htmlonly\n*> Download ILASLR + dependencies \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ilaslr.f\"> \n*> [TGZ]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ilaslr.f\"> \n*> [ZIP]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ilaslr.f\"> \n*> [TXT]</a>\n*> \\endhtmlonly \n*\n*  Definition:\n*  ===========\n*\n*       INTEGER FUNCTION ILASLR( M, N, A, LDA )\n* \n*       .. Scalar Arguments ..\n*       INTEGER            M, N, LDA\n*       ..\n*       .. Array Arguments ..\n*       REAL               A( LDA, * )\n*       ..\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> ILASLR scans A for its last non-zero row.\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] M\n*> \\verbatim\n*>          M is INTEGER\n*>          The number of rows of the matrix A.\n*> \\endverbatim\n*>\n*> \\param[in] N\n*> \\verbatim\n*>          N is INTEGER\n*>          The number of columns of the matrix A.\n*> \\endverbatim\n*>\n*> \\param[in] A\n*> \\verbatim\n*>          A is REAL array, dimension (LDA,N)\n*>          The m by n matrix A.\n*> \\endverbatim\n*>\n*> \\param[in] LDA\n*> \\verbatim\n*>          LDA is INTEGER\n*>          The leading dimension of the array A. LDA >= max(1,M).\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date April 2012\n*\n*> \\ingroup realOTHERauxiliary\n*\n*  =====================================================================\n      INTEGER FUNCTION ILASLR( M, N, A, LDA )\n*\n*  -- LAPACK auxiliary routine (version 3.4.1) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     April 2012\n*\n*     .. Scalar Arguments ..\n      INTEGER            M, N, LDA\n*     ..\n*     .. Array Arguments ..\n      REAL               A( LDA, * )\n*     ..\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      REAL             ZERO\n      PARAMETER ( ZERO = 0.0E+0 )\n*     ..\n*     .. Local Scalars ..\n      INTEGER I, J\n*     ..\n*     .. Executable Statements ..\n*\n*     Quick test for the common case where one corner is non-zero.\n      IF( M.EQ.0 ) THEN\n         ILASLR = M\n      ELSEIF( A(M, 1).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN\n         ILASLR = M\n      ELSE\n*     Scan up each column tracking the last zero row seen.\n         ILASLR = 0\n         DO J = 1, N\n            I=M\n            DO WHILE((A(MAX(I,1),J).EQ.ZERO).AND.(I.GE.1))\n               I=I-1\n            ENDDO\n            ILASLR = MAX( ILASLR, I )\n         END DO\n      END IF\n      RETURN\n      END\n"
  },
  {
    "path": "include/eigen3/lapack/ilazlc.f",
    "content": "*> \\brief \\b ILAZLC\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*> \\htmlonly\n*> Download ILAZLC + dependencies \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ilazlc.f\"> \n*> [TGZ]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ilazlc.f\"> \n*> [ZIP]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ilazlc.f\"> \n*> [TXT]</a>\n*> \\endhtmlonly \n*\n*  Definition:\n*  ===========\n*\n*       INTEGER FUNCTION ILAZLC( M, N, A, LDA )\n* \n*       .. Scalar Arguments ..\n*       INTEGER            M, N, LDA\n*       ..\n*       .. Array Arguments ..\n*       COMPLEX*16         A( LDA, * )\n*       ..\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> ILAZLC scans A for its last non-zero column.\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] M\n*> \\verbatim\n*>          M is INTEGER\n*>          The number of rows of the matrix A.\n*> \\endverbatim\n*>\n*> \\param[in] N\n*> \\verbatim\n*>          N is INTEGER\n*>          The number of columns of the matrix A.\n*> \\endverbatim\n*>\n*> \\param[in] A\n*> \\verbatim\n*>          A is COMPLEX*16 array, dimension (LDA,N)\n*>          The m by n matrix A.\n*> \\endverbatim\n*>\n*> \\param[in] LDA\n*> \\verbatim\n*>          LDA is INTEGER\n*>          The leading dimension of the array A. LDA >= max(1,M).\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date November 2011\n*\n*> \\ingroup complex16OTHERauxiliary\n*\n*  =====================================================================\n      INTEGER FUNCTION ILAZLC( M, N, A, LDA )\n*\n*  -- LAPACK auxiliary routine (version 3.4.0) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     November 2011\n*\n*     .. Scalar Arguments ..\n      INTEGER            M, N, LDA\n*     ..\n*     .. Array Arguments ..\n      COMPLEX*16         A( LDA, * )\n*     ..\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      COMPLEX*16       ZERO\n      PARAMETER ( ZERO = (0.0D+0, 0.0D+0) )\n*     ..\n*     .. Local Scalars ..\n      INTEGER I\n*     ..\n*     .. Executable Statements ..\n*\n*     Quick test for the common case where one corner is non-zero.\n      IF( N.EQ.0 ) THEN\n         ILAZLC = N\n      ELSE IF( A(1, N).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN\n         ILAZLC = N\n      ELSE\n*     Now scan each column from the end, returning with the first non-zero.\n         DO ILAZLC = N, 1, -1\n            DO I = 1, M\n               IF( A(I, ILAZLC).NE.ZERO ) RETURN\n            END DO\n         END DO\n      END IF\n      RETURN\n      END\n"
  },
  {
    "path": "include/eigen3/lapack/ilazlr.f",
    "content": "*> \\brief \\b ILAZLR\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*> \\htmlonly\n*> Download ILAZLR + dependencies \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ilazlr.f\"> \n*> [TGZ]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ilazlr.f\"> \n*> [ZIP]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ilazlr.f\"> \n*> [TXT]</a>\n*> \\endhtmlonly \n*\n*  Definition:\n*  ===========\n*\n*       INTEGER FUNCTION ILAZLR( M, N, A, LDA )\n* \n*       .. Scalar Arguments ..\n*       INTEGER            M, N, LDA\n*       ..\n*       .. Array Arguments ..\n*       COMPLEX*16         A( LDA, * )\n*       ..\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> ILAZLR scans A for its last non-zero row.\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] M\n*> \\verbatim\n*>          M is INTEGER\n*>          The number of rows of the matrix A.\n*> \\endverbatim\n*>\n*> \\param[in] N\n*> \\verbatim\n*>          N is INTEGER\n*>          The number of columns of the matrix A.\n*> \\endverbatim\n*>\n*> \\param[in] A\n*> \\verbatim\n*>          A is COMPLEX*16 array, dimension (LDA,N)\n*>          The m by n matrix A.\n*> \\endverbatim\n*>\n*> \\param[in] LDA\n*> \\verbatim\n*>          LDA is INTEGER\n*>          The leading dimension of the array A. LDA >= max(1,M).\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date April 2012\n*\n*> \\ingroup complex16OTHERauxiliary\n*\n*  =====================================================================\n      INTEGER FUNCTION ILAZLR( M, N, A, LDA )\n*\n*  -- LAPACK auxiliary routine (version 3.4.1) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     April 2012\n*\n*     .. Scalar Arguments ..\n      INTEGER            M, N, LDA\n*     ..\n*     .. Array Arguments ..\n      COMPLEX*16         A( LDA, * )\n*     ..\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      COMPLEX*16       ZERO\n      PARAMETER ( ZERO = (0.0D+0, 0.0D+0) )\n*     ..\n*     .. Local Scalars ..\n      INTEGER I, J\n*     ..\n*     .. Executable Statements ..\n*\n*     Quick test for the common case where one corner is non-zero.\n      IF( M.EQ.0 ) THEN\n         ILAZLR = M\n      ELSE IF( A(M, 1).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN\n         ILAZLR = M\n      ELSE\n*     Scan up each column tracking the last zero row seen.\n         ILAZLR = 0\n         DO J = 1, N\n            I=M\n            DO WHILE((A(MAX(I,1),J).EQ.ZERO).AND.(I.GE.1))\n               I=I-1\n            ENDDO\n            ILAZLR = MAX( ILAZLR, I )\n         END DO\n      END IF\n      RETURN\n      END\n"
  },
  {
    "path": "include/eigen3/lapack/lapack_common.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2010-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_LAPACK_COMMON_H\n#define EIGEN_LAPACK_COMMON_H\n\n#include \"../blas/common.h\"\n#include \"../Eigen/src/misc/lapack.h\"\n\n#define EIGEN_LAPACK_FUNC(FUNC,ARGLIST)               \\\n  extern \"C\" { int EIGEN_BLAS_FUNC(FUNC) ARGLIST; }   \\\n  int EIGEN_BLAS_FUNC(FUNC) ARGLIST\n\ntypedef Eigen::Map<Eigen::Transpositions<Eigen::Dynamic,Eigen::Dynamic,int> > PivotsType;\n\n#if ISCOMPLEX\n#define EIGEN_LAPACK_ARG_IF_COMPLEX(X) X,\n#else\n#define EIGEN_LAPACK_ARG_IF_COMPLEX(X)\n#endif\n\n\n#endif // EIGEN_LAPACK_COMMON_H\n"
  },
  {
    "path": "include/eigen3/lapack/lu.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2010-2011 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"common.h\"\n#include <Eigen/LU>\n\n// computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges\nEIGEN_LAPACK_FUNC(getrf,(int *m, int *n, RealScalar *pa, int *lda, int *ipiv, int *info))\n{\n  *info = 0;\n        if(*m<0)                  *info = -1;\n  else  if(*n<0)                  *info = -2;\n  else  if(*lda<std::max(1,*m))   *info = -4;\n  if(*info!=0)\n  {\n    int e = -*info;\n    return xerbla_(SCALAR_SUFFIX_UP\"GETRF\", &e, 6);\n  }\n\n  if(*m==0 || *n==0)\n    return 0;\n\n  Scalar* a = reinterpret_cast<Scalar*>(pa);\n  int nb_transpositions;\n  int ret = int(Eigen::internal::partial_lu_impl<Scalar,ColMajor,int>\n                     ::blocked_lu(*m, *n, a, *lda, ipiv, nb_transpositions));\n\n  for(int i=0; i<std::min(*m,*n); ++i)\n    ipiv[i]++;\n\n  if(ret>=0)\n    *info = ret+1;\n\n  return 0;\n}\n\n//GETRS solves a system of linear equations\n//    A * X = B  or  A' * X = B\n//  with a general N-by-N matrix A using the LU factorization computed  by GETRF\nEIGEN_LAPACK_FUNC(getrs,(char *trans, int *n, int *nrhs, RealScalar *pa, int *lda, int *ipiv, RealScalar *pb, int *ldb, int *info))\n{\n  *info = 0;\n        if(OP(*trans)==INVALID)  *info = -1;\n  else  if(*n<0)                 *info = -2;\n  else  if(*nrhs<0)              *info = -3;\n  else  if(*lda<std::max(1,*n))  *info = -5;\n  else  if(*ldb<std::max(1,*n))  *info = -8;\n  if(*info!=0)\n  {\n    int e = -*info;\n    return xerbla_(SCALAR_SUFFIX_UP\"GETRS\", &e, 6);\n  }\n\n  Scalar* a = reinterpret_cast<Scalar*>(pa);\n  Scalar* b = reinterpret_cast<Scalar*>(pb);\n  MatrixType lu(a,*n,*n,*lda);\n  MatrixType B(b,*n,*nrhs,*ldb);\n\n  for(int i=0; i<*n; ++i)\n    ipiv[i]--;\n  if(OP(*trans)==NOTR)\n  {\n    B = PivotsType(ipiv,*n) * B;\n    lu.triangularView<UnitLower>().solveInPlace(B);\n    lu.triangularView<Upper>().solveInPlace(B);\n  }\n  else if(OP(*trans)==TR)\n  {\n    lu.triangularView<Upper>().transpose().solveInPlace(B);\n    lu.triangularView<UnitLower>().transpose().solveInPlace(B);\n    B = PivotsType(ipiv,*n).transpose() * B;\n  }\n  else if(OP(*trans)==ADJ)\n  {\n    lu.triangularView<Upper>().adjoint().solveInPlace(B);\n    lu.triangularView<UnitLower>().adjoint().solveInPlace(B);\n    B = PivotsType(ipiv,*n).transpose() * B;\n  }\n  for(int i=0; i<*n; ++i)\n    ipiv[i]++;\n\n  return 0;\n}\n"
  },
  {
    "path": "include/eigen3/lapack/second_NONE.f",
    "content": "*> \\brief \\b SECOND returns nothing\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*  Definition:\n*  ===========\n*\n*      REAL FUNCTION SECOND( )\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*>  SECOND returns nothing instead of returning the user time for a process in seconds.\n*>  If you are using that routine, it means that neither EXTERNAL ETIME,\n*>  EXTERNAL ETIME_, INTERNAL ETIME, INTERNAL CPU_TIME is available  on\n*>  your machine.\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date November 2011\n*\n*> \\ingroup auxOTHERauxiliary\n*\n*  =====================================================================\n      REAL FUNCTION SECOND( )\n*\n*  -- LAPACK auxiliary routine (version 3.4.0) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     November 2011\n*\n* =====================================================================\n*\n      SECOND = 0.0E+0\n      RETURN\n*\n*     End of SECOND\n*\n      END\n"
  },
  {
    "path": "include/eigen3/lapack/single.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define SCALAR        float\n#define SCALAR_SUFFIX s\n#define SCALAR_SUFFIX_UP \"S\"\n#define ISCOMPLEX     0\n\n#include \"cholesky.cpp\"\n#include \"lu.cpp\"\n#include \"eigenvalues.cpp\"\n#include \"svd.cpp\"\n"
  },
  {
    "path": "include/eigen3/lapack/sladiv.f",
    "content": "*> \\brief \\b SLADIV\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*> \\htmlonly\n*> Download SLADIV + dependencies \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sladiv.f\"> \n*> [TGZ]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sladiv.f\"> \n*> [ZIP]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sladiv.f\"> \n*> [TXT]</a>\n*> \\endhtmlonly \n*\n*  Definition:\n*  ===========\n*\n*       SUBROUTINE SLADIV( A, B, C, D, P, Q )\n* \n*       .. Scalar Arguments ..\n*       REAL               A, B, C, D, P, Q\n*       ..\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> SLADIV performs complex division in  real arithmetic\n*>\n*>                       a + i*b\n*>            p + i*q = ---------\n*>                       c + i*d\n*>\n*> The algorithm is due to Robert L. Smith and can be found\n*> in D. Knuth, The art of Computer Programming, Vol.2, p.195\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] A\n*> \\verbatim\n*>          A is REAL\n*> \\endverbatim\n*>\n*> \\param[in] B\n*> \\verbatim\n*>          B is REAL\n*> \\endverbatim\n*>\n*> \\param[in] C\n*> \\verbatim\n*>          C is REAL\n*> \\endverbatim\n*>\n*> \\param[in] D\n*> \\verbatim\n*>          D is REAL\n*>          The scalars a, b, c, and d in the above expression.\n*> \\endverbatim\n*>\n*> \\param[out] P\n*> \\verbatim\n*>          P is REAL\n*> \\endverbatim\n*>\n*> \\param[out] Q\n*> \\verbatim\n*>          Q is REAL\n*>          The scalars p and q in the above expression.\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date November 2011\n*\n*> \\ingroup auxOTHERauxiliary\n*\n*  =====================================================================\n      SUBROUTINE SLADIV( A, B, C, D, P, Q )\n*\n*  -- LAPACK auxiliary routine (version 3.4.0) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     November 2011\n*\n*     .. Scalar Arguments ..\n      REAL               A, B, C, D, P, Q\n*     ..\n*\n*  =====================================================================\n*\n*     .. Local Scalars ..\n      REAL               E, F\n*     ..\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS\n*     ..\n*     .. Executable Statements ..\n*\n      IF( ABS( D ).LT.ABS( C ) ) THEN\n         E = D / C\n         F = C + D*E\n         P = ( A+B*E ) / F\n         Q = ( B-A*E ) / F\n      ELSE\n         E = C / D\n         F = D + C*E\n         P = ( B+A*E ) / F\n         Q = ( -A+B*E ) / F\n      END IF\n*\n      RETURN\n*\n*     End of SLADIV\n*\n      END\n"
  },
  {
    "path": "include/eigen3/lapack/slamch.f",
    "content": "*> \\brief \\b SLAMCH\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*  Definition:\n*  ===========\n*\n*      REAL             FUNCTION SLAMCH( CMACH )\n*\n*     .. Scalar Arguments ..\n*      CHARACTER          CMACH\n*     ..\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> SLAMCH determines single precision machine parameters.\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] CMACH\n*> \\verbatim\n*>          Specifies the value to be returned by SLAMCH:\n*>          = 'E' or 'e',   SLAMCH := eps\n*>          = 'S' or 's ,   SLAMCH := sfmin\n*>          = 'B' or 'b',   SLAMCH := base\n*>          = 'P' or 'p',   SLAMCH := eps*base\n*>          = 'N' or 'n',   SLAMCH := t\n*>          = 'R' or 'r',   SLAMCH := rnd\n*>          = 'M' or 'm',   SLAMCH := emin\n*>          = 'U' or 'u',   SLAMCH := rmin\n*>          = 'L' or 'l',   SLAMCH := emax\n*>          = 'O' or 'o',   SLAMCH := rmax\n*>          where\n*>          eps   = relative machine precision\n*>          sfmin = safe minimum, such that 1/sfmin does not overflow\n*>          base  = base of the machine\n*>          prec  = eps*base\n*>          t     = number of (base) digits in the mantissa\n*>          rnd   = 1.0 when rounding occurs in addition, 0.0 otherwise\n*>          emin  = minimum exponent before (gradual) underflow\n*>          rmin  = underflow threshold - base**(emin-1)\n*>          emax  = largest exponent before overflow\n*>          rmax  = overflow threshold  - (base**emax)*(1-eps)\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date November 2011\n*\n*> \\ingroup auxOTHERauxiliary\n*\n*  =====================================================================\n      REAL             FUNCTION SLAMCH( CMACH )\n*\n*  -- LAPACK auxiliary routine (version 3.4.0) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     November 2011\n*\n*     .. Scalar Arguments ..\n      CHARACTER          CMACH\n*     ..\n*\n* =====================================================================\n*\n*     .. Parameters ..\n      REAL               ONE, ZERO\n      PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )\n*     ..\n*     .. Local Scalars ..\n      REAL               RND, EPS, SFMIN, SMALL, RMACH\n*     ..\n*     .. External Functions ..\n      LOGICAL            LSAME\n      EXTERNAL           LSAME\n*     ..\n*     .. Intrinsic Functions ..\n      INTRINSIC          DIGITS, EPSILON, HUGE, MAXEXPONENT,\n     $                   MINEXPONENT, RADIX, TINY\n*     ..\n*     .. Executable Statements ..\n*\n*\n*     Assume rounding, not chopping. Always.\n*\n      RND = ONE\n*\n      IF( ONE.EQ.RND ) THEN\n         EPS = EPSILON(ZERO) * 0.5\n      ELSE\n         EPS = EPSILON(ZERO)\n      END IF\n*\n      IF( LSAME( CMACH, 'E' ) ) THEN\n         RMACH = EPS\n      ELSE IF( LSAME( CMACH, 'S' ) ) THEN\n         SFMIN = TINY(ZERO)\n         SMALL = ONE / HUGE(ZERO)\n         IF( SMALL.GE.SFMIN ) THEN\n*\n*           Use SMALL plus a bit, to avoid the possibility of rounding\n*           causing overflow when computing  1/sfmin.\n*\n            SFMIN = SMALL*( ONE+EPS )\n         END IF\n         RMACH = SFMIN\n      ELSE IF( LSAME( CMACH, 'B' ) ) THEN\n         RMACH = RADIX(ZERO)\n      ELSE IF( LSAME( CMACH, 'P' ) ) THEN\n         RMACH = EPS * RADIX(ZERO)\n      ELSE IF( LSAME( CMACH, 'N' ) ) THEN\n         RMACH = DIGITS(ZERO)\n      ELSE IF( LSAME( CMACH, 'R' ) ) THEN\n         RMACH = RND\n      ELSE IF( LSAME( CMACH, 'M' ) ) THEN\n         RMACH = MINEXPONENT(ZERO)\n      ELSE IF( LSAME( CMACH, 'U' ) ) THEN\n         RMACH = tiny(zero)\n      ELSE IF( LSAME( CMACH, 'L' ) ) THEN\n         RMACH = MAXEXPONENT(ZERO)\n      ELSE IF( LSAME( CMACH, 'O' ) ) THEN\n         RMACH = HUGE(ZERO)\n      ELSE\n         RMACH = ZERO\n      END IF\n*\n      SLAMCH = RMACH\n      RETURN\n*\n*     End of SLAMCH\n*\n      END\n************************************************************************\n*> \\brief \\b SLAMC3\n*> \\details\n*> \\b Purpose:\n*> \\verbatim\n*> SLAMC3  is intended to force  A  and  B  to be stored prior to doing\n*> the addition of  A  and  B ,  for use in situations where optimizers\n*> might hold one of these in a register.\n*> \\endverbatim\n*> \\author LAPACK is a software package provided by Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..\n*> \\date November 2011\n*> \\ingroup auxOTHERauxiliary\n*>\n*> \\param[in] A\n*> \\verbatim\n*> \\endverbatim\n*>\n*> \\param[in] B\n*> \\verbatim\n*>          The values A and B.\n*> \\endverbatim\n*>\n*\n      REAL             FUNCTION SLAMC3( A, B )\n*\n*  -- LAPACK auxiliary routine (version 3.4.0) --\n*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..\n*     November 2010\n*\n*     .. Scalar Arguments ..\n      REAL               A, B\n*     ..\n* =====================================================================\n*\n*     .. Executable Statements ..\n*\n      SLAMC3 = A + B\n*\n      RETURN\n*\n*     End of SLAMC3\n*\n      END\n*\n************************************************************************\n"
  },
  {
    "path": "include/eigen3/lapack/slapy2.f",
    "content": "*> \\brief \\b SLAPY2\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*> \\htmlonly\n*> Download SLAPY2 + dependencies \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slapy2.f\"> \n*> [TGZ]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slapy2.f\"> \n*> [ZIP]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slapy2.f\"> \n*> [TXT]</a>\n*> \\endhtmlonly \n*\n*  Definition:\n*  ===========\n*\n*       REAL             FUNCTION SLAPY2( X, Y )\n* \n*       .. Scalar Arguments ..\n*       REAL               X, Y\n*       ..\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> SLAPY2 returns sqrt(x**2+y**2), taking care not to cause unnecessary\n*> overflow.\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] X\n*> \\verbatim\n*>          X is REAL\n*> \\endverbatim\n*>\n*> \\param[in] Y\n*> \\verbatim\n*>          Y is REAL\n*>          X and Y specify the values x and y.\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date November 2011\n*\n*> \\ingroup auxOTHERauxiliary\n*\n*  =====================================================================\n      REAL             FUNCTION SLAPY2( X, Y )\n*\n*  -- LAPACK auxiliary routine (version 3.4.0) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     November 2011\n*\n*     .. Scalar Arguments ..\n      REAL               X, Y\n*     ..\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      REAL               ZERO\n      PARAMETER          ( ZERO = 0.0E0 )\n      REAL               ONE\n      PARAMETER          ( ONE = 1.0E0 )\n*     ..\n*     .. Local Scalars ..\n      REAL               W, XABS, YABS, Z\n*     ..\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, MAX, MIN, SQRT\n*     ..\n*     .. Executable Statements ..\n*\n      XABS = ABS( X )\n      YABS = ABS( Y )\n      W = MAX( XABS, YABS )\n      Z = MIN( XABS, YABS )\n      IF( Z.EQ.ZERO ) THEN\n         SLAPY2 = W\n      ELSE\n         SLAPY2 = W*SQRT( ONE+( Z / W )**2 )\n      END IF\n      RETURN\n*\n*     End of SLAPY2\n*\n      END\n"
  },
  {
    "path": "include/eigen3/lapack/slapy3.f",
    "content": "*> \\brief \\b SLAPY3\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*> \\htmlonly\n*> Download SLAPY3 + dependencies \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slapy3.f\"> \n*> [TGZ]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slapy3.f\"> \n*> [ZIP]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slapy3.f\"> \n*> [TXT]</a>\n*> \\endhtmlonly \n*\n*  Definition:\n*  ===========\n*\n*       REAL             FUNCTION SLAPY3( X, Y, Z )\n* \n*       .. Scalar Arguments ..\n*       REAL               X, Y, Z\n*       ..\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> SLAPY3 returns sqrt(x**2+y**2+z**2), taking care not to cause\n*> unnecessary overflow.\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] X\n*> \\verbatim\n*>          X is REAL\n*> \\endverbatim\n*>\n*> \\param[in] Y\n*> \\verbatim\n*>          Y is REAL\n*> \\endverbatim\n*>\n*> \\param[in] Z\n*> \\verbatim\n*>          Z is REAL\n*>          X, Y and Z specify the values x, y and z.\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date November 2011\n*\n*> \\ingroup auxOTHERauxiliary\n*\n*  =====================================================================\n      REAL             FUNCTION SLAPY3( X, Y, Z )\n*\n*  -- LAPACK auxiliary routine (version 3.4.0) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     November 2011\n*\n*     .. Scalar Arguments ..\n      REAL               X, Y, Z\n*     ..\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      REAL               ZERO\n      PARAMETER          ( ZERO = 0.0E0 )\n*     ..\n*     .. Local Scalars ..\n      REAL               W, XABS, YABS, ZABS\n*     ..\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, MAX, SQRT\n*     ..\n*     .. Executable Statements ..\n*\n      XABS = ABS( X )\n      YABS = ABS( Y )\n      ZABS = ABS( Z )\n      W = MAX( XABS, YABS, ZABS )\n      IF( W.EQ.ZERO ) THEN\n*     W can be zero for max(0,nan,0)\n*     adding all three entries together will make sure\n*     NaN will not disappear.\n         SLAPY3 =  XABS + YABS + ZABS\n      ELSE\n         SLAPY3 = W*SQRT( ( XABS / W )**2+( YABS / W )**2+\n     $            ( ZABS / W )**2 )\n      END IF\n      RETURN\n*\n*     End of SLAPY3\n*\n      END\n"
  },
  {
    "path": "include/eigen3/lapack/slarf.f",
    "content": "*> \\brief \\b SLARF\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*> \\htmlonly\n*> Download SLARF + dependencies \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slarf.f\"> \n*> [TGZ]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slarf.f\"> \n*> [ZIP]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slarf.f\"> \n*> [TXT]</a>\n*> \\endhtmlonly \n*\n*  Definition:\n*  ===========\n*\n*       SUBROUTINE SLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )\n* \n*       .. Scalar Arguments ..\n*       CHARACTER          SIDE\n*       INTEGER            INCV, LDC, M, N\n*       REAL               TAU\n*       ..\n*       .. Array Arguments ..\n*       REAL               C( LDC, * ), V( * ), WORK( * )\n*       ..\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> SLARF applies a real elementary reflector H to a real m by n matrix\n*> C, from either the left or the right. H is represented in the form\n*>\n*>       H = I - tau * v * v**T\n*>\n*> where tau is a real scalar and v is a real vector.\n*>\n*> If tau = 0, then H is taken to be the unit matrix.\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] SIDE\n*> \\verbatim\n*>          SIDE is CHARACTER*1\n*>          = 'L': form  H * C\n*>          = 'R': form  C * H\n*> \\endverbatim\n*>\n*> \\param[in] M\n*> \\verbatim\n*>          M is INTEGER\n*>          The number of rows of the matrix C.\n*> \\endverbatim\n*>\n*> \\param[in] N\n*> \\verbatim\n*>          N is INTEGER\n*>          The number of columns of the matrix C.\n*> \\endverbatim\n*>\n*> \\param[in] V\n*> \\verbatim\n*>          V is REAL array, dimension\n*>                     (1 + (M-1)*abs(INCV)) if SIDE = 'L'\n*>                  or (1 + (N-1)*abs(INCV)) if SIDE = 'R'\n*>          The vector v in the representation of H. V is not used if\n*>          TAU = 0.\n*> \\endverbatim\n*>\n*> \\param[in] INCV\n*> \\verbatim\n*>          INCV is INTEGER\n*>          The increment between elements of v. INCV <> 0.\n*> \\endverbatim\n*>\n*> \\param[in] TAU\n*> \\verbatim\n*>          TAU is REAL\n*>          The value tau in the representation of H.\n*> \\endverbatim\n*>\n*> \\param[in,out] C\n*> \\verbatim\n*>          C is REAL array, dimension (LDC,N)\n*>          On entry, the m by n matrix C.\n*>          On exit, C is overwritten by the matrix H * C if SIDE = 'L',\n*>          or C * H if SIDE = 'R'.\n*> \\endverbatim\n*>\n*> \\param[in] LDC\n*> \\verbatim\n*>          LDC is INTEGER\n*>          The leading dimension of the array C. LDC >= max(1,M).\n*> \\endverbatim\n*>\n*> \\param[out] WORK\n*> \\verbatim\n*>          WORK is REAL array, dimension\n*>                         (N) if SIDE = 'L'\n*>                      or (M) if SIDE = 'R'\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date November 2011\n*\n*> \\ingroup realOTHERauxiliary\n*\n*  =====================================================================\n      SUBROUTINE SLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )\n*\n*  -- LAPACK auxiliary routine (version 3.4.0) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     November 2011\n*\n*     .. Scalar Arguments ..\n      CHARACTER          SIDE\n      INTEGER            INCV, LDC, M, N\n      REAL               TAU\n*     ..\n*     .. Array Arguments ..\n      REAL               C( LDC, * ), V( * ), WORK( * )\n*     ..\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      REAL               ONE, ZERO\n      PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )\n*     ..\n*     .. Local Scalars ..\n      LOGICAL            APPLYLEFT\n      INTEGER            I, LASTV, LASTC\n*     ..\n*     .. External Subroutines ..\n      EXTERNAL           SGEMV, SGER\n*     ..\n*     .. External Functions ..\n      LOGICAL            LSAME\n      INTEGER            ILASLR, ILASLC\n      EXTERNAL           LSAME, ILASLR, ILASLC\n*     ..\n*     .. Executable Statements ..\n*\n      APPLYLEFT = LSAME( SIDE, 'L' )\n      LASTV = 0\n      LASTC = 0\n      IF( TAU.NE.ZERO ) THEN\n!     Set up variables for scanning V.  LASTV begins pointing to the end\n!     of V.\n         IF( APPLYLEFT ) THEN\n            LASTV = M\n         ELSE\n            LASTV = N\n         END IF\n         IF( INCV.GT.0 ) THEN\n            I = 1 + (LASTV-1) * INCV\n         ELSE\n            I = 1\n         END IF\n!     Look for the last non-zero row in V.\n         DO WHILE( LASTV.GT.0 .AND. V( I ).EQ.ZERO )\n            LASTV = LASTV - 1\n            I = I - INCV\n         END DO\n         IF( APPLYLEFT ) THEN\n!     Scan for the last non-zero column in C(1:lastv,:).\n            LASTC = ILASLC(LASTV, N, C, LDC)\n         ELSE\n!     Scan for the last non-zero row in C(:,1:lastv).\n            LASTC = ILASLR(M, LASTV, C, LDC)\n         END IF\n      END IF\n!     Note that lastc.eq.0 renders the BLAS operations null; no special\n!     case is needed at this level.\n      IF( APPLYLEFT ) THEN\n*\n*        Form  H * C\n*\n         IF( LASTV.GT.0 ) THEN\n*\n*           w(1:lastc,1) := C(1:lastv,1:lastc)**T * v(1:lastv,1)\n*\n            CALL SGEMV( 'Transpose', LASTV, LASTC, ONE, C, LDC, V, INCV,\n     $           ZERO, WORK, 1 )\n*\n*           C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**T\n*\n            CALL SGER( LASTV, LASTC, -TAU, V, INCV, WORK, 1, C, LDC )\n         END IF\n      ELSE\n*\n*        Form  C * H\n*\n         IF( LASTV.GT.0 ) THEN\n*\n*           w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1)\n*\n            CALL SGEMV( 'No transpose', LASTC, LASTV, ONE, C, LDC,\n     $           V, INCV, ZERO, WORK, 1 )\n*\n*           C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**T\n*\n            CALL SGER( LASTC, LASTV, -TAU, WORK, 1, V, INCV, C, LDC )\n         END IF\n      END IF\n      RETURN\n*\n*     End of SLARF\n*\n      END\n"
  },
  {
    "path": "include/eigen3/lapack/slarfb.f",
    "content": "*> \\brief \\b SLARFB\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*> \\htmlonly\n*> Download SLARFB + dependencies \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slarfb.f\"> \n*> [TGZ]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slarfb.f\"> \n*> [ZIP]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slarfb.f\"> \n*> [TXT]</a>\n*> \\endhtmlonly \n*\n*  Definition:\n*  ===========\n*\n*       SUBROUTINE SLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV,\n*                          T, LDT, C, LDC, WORK, LDWORK )\n* \n*       .. Scalar Arguments ..\n*       CHARACTER          DIRECT, SIDE, STOREV, TRANS\n*       INTEGER            K, LDC, LDT, LDV, LDWORK, M, N\n*       ..\n*       .. Array Arguments ..\n*       REAL               C( LDC, * ), T( LDT, * ), V( LDV, * ),\n*      $                   WORK( LDWORK, * )\n*       ..\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> SLARFB applies a real block reflector H or its transpose H**T to a\n*> real m by n matrix C, from either the left or the right.\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] SIDE\n*> \\verbatim\n*>          SIDE is CHARACTER*1\n*>          = 'L': apply H or H**T from the Left\n*>          = 'R': apply H or H**T from the Right\n*> \\endverbatim\n*>\n*> \\param[in] TRANS\n*> \\verbatim\n*>          TRANS is CHARACTER*1\n*>          = 'N': apply H (No transpose)\n*>          = 'T': apply H**T (Transpose)\n*> \\endverbatim\n*>\n*> \\param[in] DIRECT\n*> \\verbatim\n*>          DIRECT is CHARACTER*1\n*>          Indicates how H is formed from a product of elementary\n*>          reflectors\n*>          = 'F': H = H(1) H(2) . . . H(k) (Forward)\n*>          = 'B': H = H(k) . . . H(2) H(1) (Backward)\n*> \\endverbatim\n*>\n*> \\param[in] STOREV\n*> \\verbatim\n*>          STOREV is CHARACTER*1\n*>          Indicates how the vectors which define the elementary\n*>          reflectors are stored:\n*>          = 'C': Columnwise\n*>          = 'R': Rowwise\n*> \\endverbatim\n*>\n*> \\param[in] M\n*> \\verbatim\n*>          M is INTEGER\n*>          The number of rows of the matrix C.\n*> \\endverbatim\n*>\n*> \\param[in] N\n*> \\verbatim\n*>          N is INTEGER\n*>          The number of columns of the matrix C.\n*> \\endverbatim\n*>\n*> \\param[in] K\n*> \\verbatim\n*>          K is INTEGER\n*>          The order of the matrix T (= the number of elementary\n*>          reflectors whose product defines the block reflector).\n*> \\endverbatim\n*>\n*> \\param[in] V\n*> \\verbatim\n*>          V is REAL array, dimension\n*>                                (LDV,K) if STOREV = 'C'\n*>                                (LDV,M) if STOREV = 'R' and SIDE = 'L'\n*>                                (LDV,N) if STOREV = 'R' and SIDE = 'R'\n*>          The matrix V. See Further Details.\n*> \\endverbatim\n*>\n*> \\param[in] LDV\n*> \\verbatim\n*>          LDV is INTEGER\n*>          The leading dimension of the array V.\n*>          If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M);\n*>          if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N);\n*>          if STOREV = 'R', LDV >= K.\n*> \\endverbatim\n*>\n*> \\param[in] T\n*> \\verbatim\n*>          T is REAL array, dimension (LDT,K)\n*>          The triangular k by k matrix T in the representation of the\n*>          block reflector.\n*> \\endverbatim\n*>\n*> \\param[in] LDT\n*> \\verbatim\n*>          LDT is INTEGER\n*>          The leading dimension of the array T. LDT >= K.\n*> \\endverbatim\n*>\n*> \\param[in,out] C\n*> \\verbatim\n*>          C is REAL array, dimension (LDC,N)\n*>          On entry, the m by n matrix C.\n*>          On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T.\n*> \\endverbatim\n*>\n*> \\param[in] LDC\n*> \\verbatim\n*>          LDC is INTEGER\n*>          The leading dimension of the array C. LDC >= max(1,M).\n*> \\endverbatim\n*>\n*> \\param[out] WORK\n*> \\verbatim\n*>          WORK is REAL array, dimension (LDWORK,K)\n*> \\endverbatim\n*>\n*> \\param[in] LDWORK\n*> \\verbatim\n*>          LDWORK is INTEGER\n*>          The leading dimension of the array WORK.\n*>          If SIDE = 'L', LDWORK >= max(1,N);\n*>          if SIDE = 'R', LDWORK >= max(1,M).\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date November 2011\n*\n*> \\ingroup realOTHERauxiliary\n*\n*> \\par Further Details:\n*  =====================\n*>\n*> \\verbatim\n*>\n*>  The shape of the matrix V and the storage of the vectors which define\n*>  the H(i) is best illustrated by the following example with n = 5 and\n*>  k = 3. The elements equal to 1 are not stored; the corresponding\n*>  array elements are modified but restored on exit. The rest of the\n*>  array is not used.\n*>\n*>  DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':\n*>\n*>               V = (  1       )                 V = (  1 v1 v1 v1 v1 )\n*>                   ( v1  1    )                     (     1 v2 v2 v2 )\n*>                   ( v1 v2  1 )                     (        1 v3 v3 )\n*>                   ( v1 v2 v3 )\n*>                   ( v1 v2 v3 )\n*>\n*>  DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':\n*>\n*>               V = ( v1 v2 v3 )                 V = ( v1 v1  1       )\n*>                   ( v1 v2 v3 )                     ( v2 v2 v2  1    )\n*>                   (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )\n*>                   (     1 v3 )\n*>                   (        1 )\n*> \\endverbatim\n*>\n*  =====================================================================\n      SUBROUTINE SLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV,\n     $                   T, LDT, C, LDC, WORK, LDWORK )\n*\n*  -- LAPACK auxiliary routine (version 3.4.0) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     November 2011\n*\n*     .. Scalar Arguments ..\n      CHARACTER          DIRECT, SIDE, STOREV, TRANS\n      INTEGER            K, LDC, LDT, LDV, LDWORK, M, N\n*     ..\n*     .. Array Arguments ..\n      REAL               C( LDC, * ), T( LDT, * ), V( LDV, * ),\n     $                   WORK( LDWORK, * )\n*     ..\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      REAL               ONE\n      PARAMETER          ( ONE = 1.0E+0 )\n*     ..\n*     .. Local Scalars ..\n      CHARACTER          TRANST\n      INTEGER            I, J, LASTV, LASTC\n*     ..\n*     .. External Functions ..\n      LOGICAL            LSAME\n      INTEGER            ILASLR, ILASLC\n      EXTERNAL           LSAME, ILASLR, ILASLC\n*     ..\n*     .. External Subroutines ..\n      EXTERNAL           SCOPY, SGEMM, STRMM\n*     ..\n*     .. Executable Statements ..\n*\n*     Quick return if possible\n*\n      IF( M.LE.0 .OR. N.LE.0 )\n     $   RETURN\n*\n      IF( LSAME( TRANS, 'N' ) ) THEN\n         TRANST = 'T'\n      ELSE\n         TRANST = 'N'\n      END IF\n*\n      IF( LSAME( STOREV, 'C' ) ) THEN\n*\n         IF( LSAME( DIRECT, 'F' ) ) THEN\n*\n*           Let  V =  ( V1 )    (first K rows)\n*                     ( V2 )\n*           where  V1  is unit lower triangular.\n*\n            IF( LSAME( SIDE, 'L' ) ) THEN\n*\n*              Form  H * C  or  H**T * C  where  C = ( C1 )\n*                                                    ( C2 )\n*\n               LASTV = MAX( K, ILASLR( M, K, V, LDV ) )\n               LASTC = ILASLC( LASTV, N, C, LDC )\n*\n*              W := C**T * V  =  (C1**T * V1 + C2**T * V2)  (stored in WORK)\n*\n*              W := C1**T\n*\n               DO 10 J = 1, K\n                  CALL SCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 )\n   10          CONTINUE\n*\n*              W := W * V1\n*\n               CALL STRMM( 'Right', 'Lower', 'No transpose', 'Unit',\n     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )\n               IF( LASTV.GT.K ) THEN\n*\n*                 W := W + C2**T *V2\n*\n                  CALL SGEMM( 'Transpose', 'No transpose',\n     $                 LASTC, K, LASTV-K,\n     $                 ONE, C( K+1, 1 ), LDC, V( K+1, 1 ), LDV,\n     $                 ONE, WORK, LDWORK )\n               END IF\n*\n*              W := W * T**T  or  W * T\n*\n               CALL STRMM( 'Right', 'Upper', TRANST, 'Non-unit',\n     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )\n*\n*              C := C - V * W**T\n*\n               IF( LASTV.GT.K ) THEN\n*\n*                 C2 := C2 - V2 * W**T\n*\n                  CALL SGEMM( 'No transpose', 'Transpose',\n     $                 LASTV-K, LASTC, K,\n     $                 -ONE, V( K+1, 1 ), LDV, WORK, LDWORK, ONE,\n     $                 C( K+1, 1 ), LDC )\n               END IF\n*\n*              W := W * V1**T\n*\n               CALL STRMM( 'Right', 'Lower', 'Transpose', 'Unit',\n     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )\n*\n*              C1 := C1 - W**T\n*\n               DO 30 J = 1, K\n                  DO 20 I = 1, LASTC\n                     C( J, I ) = C( J, I ) - WORK( I, J )\n   20             CONTINUE\n   30          CONTINUE\n*\n            ELSE IF( LSAME( SIDE, 'R' ) ) THEN\n*\n*              Form  C * H  or  C * H**T  where  C = ( C1  C2 )\n*\n               LASTV = MAX( K, ILASLR( N, K, V, LDV ) )\n               LASTC = ILASLR( M, LASTV, C, LDC )\n*\n*              W := C * V  =  (C1*V1 + C2*V2)  (stored in WORK)\n*\n*              W := C1\n*\n               DO 40 J = 1, K\n                  CALL SCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 )\n   40          CONTINUE\n*\n*              W := W * V1\n*\n               CALL STRMM( 'Right', 'Lower', 'No transpose', 'Unit',\n     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )\n               IF( LASTV.GT.K ) THEN\n*\n*                 W := W + C2 * V2\n*\n                  CALL SGEMM( 'No transpose', 'No transpose',\n     $                 LASTC, K, LASTV-K,\n     $                 ONE, C( 1, K+1 ), LDC, V( K+1, 1 ), LDV,\n     $                 ONE, WORK, LDWORK )\n               END IF\n*\n*              W := W * T  or  W * T**T\n*\n               CALL STRMM( 'Right', 'Upper', TRANS, 'Non-unit',\n     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )\n*\n*              C := C - W * V**T\n*\n               IF( LASTV.GT.K ) THEN\n*\n*                 C2 := C2 - W * V2**T\n*\n                  CALL SGEMM( 'No transpose', 'Transpose',\n     $                 LASTC, LASTV-K, K,\n     $                 -ONE, WORK, LDWORK, V( K+1, 1 ), LDV, ONE,\n     $                 C( 1, K+1 ), LDC )\n               END IF\n*\n*              W := W * V1**T\n*\n               CALL STRMM( 'Right', 'Lower', 'Transpose', 'Unit',\n     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )\n*\n*              C1 := C1 - W\n*\n               DO 60 J = 1, K\n                  DO 50 I = 1, LASTC\n                     C( I, J ) = C( I, J ) - WORK( I, J )\n   50             CONTINUE\n   60          CONTINUE\n            END IF\n*\n         ELSE\n*\n*           Let  V =  ( V1 )\n*                     ( V2 )    (last K rows)\n*           where  V2  is unit upper triangular.\n*\n            IF( LSAME( SIDE, 'L' ) ) THEN\n*\n*              Form  H * C  or  H**T * C  where  C = ( C1 )\n*                                                    ( C2 )\n*\n               LASTV = MAX( K, ILASLR( M, K, V, LDV ) )\n               LASTC = ILASLC( LASTV, N, C, LDC )\n*\n*              W := C**T * V  =  (C1**T * V1 + C2**T * V2)  (stored in WORK)\n*\n*              W := C2**T\n*\n               DO 70 J = 1, K\n                  CALL SCOPY( LASTC, C( LASTV-K+J, 1 ), LDC,\n     $                 WORK( 1, J ), 1 )\n   70          CONTINUE\n*\n*              W := W * V2\n*\n               CALL STRMM( 'Right', 'Upper', 'No transpose', 'Unit',\n     $              LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,\n     $              WORK, LDWORK )\n               IF( LASTV.GT.K ) THEN\n*\n*                 W := W + C1**T*V1\n*\n                  CALL SGEMM( 'Transpose', 'No transpose',\n     $                 LASTC, K, LASTV-K, ONE, C, LDC, V, LDV,\n     $                 ONE, WORK, LDWORK )\n               END IF\n*\n*              W := W * T**T  or  W * T\n*\n               CALL STRMM( 'Right', 'Lower', TRANST, 'Non-unit',\n     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )\n*\n*              C := C - V * W**T\n*\n               IF( LASTV.GT.K ) THEN\n*\n*                 C1 := C1 - V1 * W**T\n*\n                  CALL SGEMM( 'No transpose', 'Transpose',\n     $                 LASTV-K, LASTC, K, -ONE, V, LDV, WORK, LDWORK,\n     $                 ONE, C, LDC )\n               END IF\n*\n*              W := W * V2**T\n*\n               CALL STRMM( 'Right', 'Upper', 'Transpose', 'Unit',\n     $              LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,\n     $              WORK, LDWORK )\n*\n*              C2 := C2 - W**T\n*\n               DO 90 J = 1, K\n                  DO 80 I = 1, LASTC\n                     C( LASTV-K+J, I ) = C( LASTV-K+J, I ) - WORK(I, J)\n   80             CONTINUE\n   90          CONTINUE\n*\n            ELSE IF( LSAME( SIDE, 'R' ) ) THEN\n*\n*              Form  C * H  or  C * H**T  where  C = ( C1  C2 )\n*\n               LASTV = MAX( K, ILASLR( N, K, V, LDV ) )\n               LASTC = ILASLR( M, LASTV, C, LDC )\n*\n*              W := C * V  =  (C1*V1 + C2*V2)  (stored in WORK)\n*\n*              W := C2\n*\n               DO 100 J = 1, K\n                  CALL SCOPY( LASTC, C( 1, N-K+J ), 1, WORK( 1, J ), 1 )\n  100          CONTINUE\n*\n*              W := W * V2\n*\n               CALL STRMM( 'Right', 'Upper', 'No transpose', 'Unit',\n     $              LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,\n     $              WORK, LDWORK )\n               IF( LASTV.GT.K ) THEN\n*\n*                 W := W + C1 * V1\n*\n                  CALL SGEMM( 'No transpose', 'No transpose',\n     $                 LASTC, K, LASTV-K, ONE, C, LDC, V, LDV,\n     $                 ONE, WORK, LDWORK )\n               END IF\n*\n*              W := W * T  or  W * T**T\n*\n               CALL STRMM( 'Right', 'Lower', TRANS, 'Non-unit',\n     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )\n*\n*              C := C - W * V**T\n*\n               IF( LASTV.GT.K ) THEN\n*\n*                 C1 := C1 - W * V1**T\n*\n                  CALL SGEMM( 'No transpose', 'Transpose',\n     $                 LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV,\n     $                 ONE, C, LDC )\n               END IF\n*\n*              W := W * V2**T\n*\n               CALL STRMM( 'Right', 'Upper', 'Transpose', 'Unit',\n     $              LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,\n     $              WORK, LDWORK )\n*\n*              C2 := C2 - W\n*\n               DO 120 J = 1, K\n                  DO 110 I = 1, LASTC\n                     C( I, LASTV-K+J ) = C( I, LASTV-K+J ) - WORK(I, J)\n  110             CONTINUE\n  120          CONTINUE\n            END IF\n         END IF\n*\n      ELSE IF( LSAME( STOREV, 'R' ) ) THEN\n*\n         IF( LSAME( DIRECT, 'F' ) ) THEN\n*\n*           Let  V =  ( V1  V2 )    (V1: first K columns)\n*           where  V1  is unit upper triangular.\n*\n            IF( LSAME( SIDE, 'L' ) ) THEN\n*\n*              Form  H * C  or  H**T * C  where  C = ( C1 )\n*                                                    ( C2 )\n*\n               LASTV = MAX( K, ILASLC( K, M, V, LDV ) )\n               LASTC = ILASLC( LASTV, N, C, LDC )\n*\n*              W := C**T * V**T  =  (C1**T * V1**T + C2**T * V2**T) (stored in WORK)\n*\n*              W := C1**T\n*\n               DO 130 J = 1, K\n                  CALL SCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 )\n  130          CONTINUE\n*\n*              W := W * V1**T\n*\n               CALL STRMM( 'Right', 'Upper', 'Transpose', 'Unit',\n     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )\n               IF( LASTV.GT.K ) THEN\n*\n*                 W := W + C2**T*V2**T\n*\n                  CALL SGEMM( 'Transpose', 'Transpose',\n     $                 LASTC, K, LASTV-K,\n     $                 ONE, C( K+1, 1 ), LDC, V( 1, K+1 ), LDV,\n     $                 ONE, WORK, LDWORK )\n               END IF\n*\n*              W := W * T**T  or  W * T\n*\n               CALL STRMM( 'Right', 'Upper', TRANST, 'Non-unit',\n     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )\n*\n*              C := C - V**T * W**T\n*\n               IF( LASTV.GT.K ) THEN\n*\n*                 C2 := C2 - V2**T * W**T\n*\n                  CALL SGEMM( 'Transpose', 'Transpose',\n     $                 LASTV-K, LASTC, K,\n     $                 -ONE, V( 1, K+1 ), LDV, WORK, LDWORK,\n     $                 ONE, C( K+1, 1 ), LDC )\n               END IF\n*\n*              W := W * V1\n*\n               CALL STRMM( 'Right', 'Upper', 'No transpose', 'Unit',\n     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )\n*\n*              C1 := C1 - W**T\n*\n               DO 150 J = 1, K\n                  DO 140 I = 1, LASTC\n                     C( J, I ) = C( J, I ) - WORK( I, J )\n  140             CONTINUE\n  150          CONTINUE\n*\n            ELSE IF( LSAME( SIDE, 'R' ) ) THEN\n*\n*              Form  C * H  or  C * H**T  where  C = ( C1  C2 )\n*\n               LASTV = MAX( K, ILASLC( K, N, V, LDV ) )\n               LASTC = ILASLR( M, LASTV, C, LDC )\n*\n*              W := C * V**T  =  (C1*V1**T + C2*V2**T)  (stored in WORK)\n*\n*              W := C1\n*\n               DO 160 J = 1, K\n                  CALL SCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 )\n  160          CONTINUE\n*\n*              W := W * V1**T\n*\n               CALL STRMM( 'Right', 'Upper', 'Transpose', 'Unit',\n     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )\n               IF( LASTV.GT.K ) THEN\n*\n*                 W := W + C2 * V2**T\n*\n                  CALL SGEMM( 'No transpose', 'Transpose',\n     $                 LASTC, K, LASTV-K,\n     $                 ONE, C( 1, K+1 ), LDC, V( 1, K+1 ), LDV,\n     $                 ONE, WORK, LDWORK )\n               END IF\n*\n*              W := W * T  or  W * T**T\n*\n               CALL STRMM( 'Right', 'Upper', TRANS, 'Non-unit',\n     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )\n*\n*              C := C - W * V\n*\n               IF( LASTV.GT.K ) THEN\n*\n*                 C2 := C2 - W * V2\n*\n                  CALL SGEMM( 'No transpose', 'No transpose',\n     $                 LASTC, LASTV-K, K,\n     $                 -ONE, WORK, LDWORK, V( 1, K+1 ), LDV,\n     $                 ONE, C( 1, K+1 ), LDC )\n               END IF\n*\n*              W := W * V1\n*\n               CALL STRMM( 'Right', 'Upper', 'No transpose', 'Unit',\n     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )\n*\n*              C1 := C1 - W\n*\n               DO 180 J = 1, K\n                  DO 170 I = 1, LASTC\n                     C( I, J ) = C( I, J ) - WORK( I, J )\n  170             CONTINUE\n  180          CONTINUE\n*\n            END IF\n*\n         ELSE\n*\n*           Let  V =  ( V1  V2 )    (V2: last K columns)\n*           where  V2  is unit lower triangular.\n*\n            IF( LSAME( SIDE, 'L' ) ) THEN\n*\n*              Form  H * C  or  H**T * C  where  C = ( C1 )\n*                                                    ( C2 )\n*\n               LASTV = MAX( K, ILASLC( K, M, V, LDV ) )\n               LASTC = ILASLC( LASTV, N, C, LDC )\n*\n*              W := C**T * V**T  =  (C1**T * V1**T + C2**T * V2**T) (stored in WORK)\n*\n*              W := C2**T\n*\n               DO 190 J = 1, K\n                  CALL SCOPY( LASTC, C( LASTV-K+J, 1 ), LDC,\n     $                 WORK( 1, J ), 1 )\n  190          CONTINUE\n*\n*              W := W * V2**T\n*\n               CALL STRMM( 'Right', 'Lower', 'Transpose', 'Unit',\n     $              LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,\n     $              WORK, LDWORK )\n               IF( LASTV.GT.K ) THEN\n*\n*                 W := W + C1**T * V1**T\n*\n                  CALL SGEMM( 'Transpose', 'Transpose',\n     $                 LASTC, K, LASTV-K, ONE, C, LDC, V, LDV,\n     $                 ONE, WORK, LDWORK )\n               END IF\n*\n*              W := W * T**T  or  W * T\n*\n               CALL STRMM( 'Right', 'Lower', TRANST, 'Non-unit',\n     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )\n*\n*              C := C - V**T * W**T\n*\n               IF( LASTV.GT.K ) THEN\n*\n*                 C1 := C1 - V1**T * W**T\n*\n                  CALL SGEMM( 'Transpose', 'Transpose',\n     $                 LASTV-K, LASTC, K, -ONE, V, LDV, WORK, LDWORK,\n     $                 ONE, C, LDC )\n               END IF\n*\n*              W := W * V2\n*\n               CALL STRMM( 'Right', 'Lower', 'No transpose', 'Unit',\n     $              LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,\n     $              WORK, LDWORK )\n*\n*              C2 := C2 - W**T\n*\n               DO 210 J = 1, K\n                  DO 200 I = 1, LASTC\n                     C( LASTV-K+J, I ) = C( LASTV-K+J, I ) - WORK(I, J)\n  200             CONTINUE\n  210          CONTINUE\n*\n            ELSE IF( LSAME( SIDE, 'R' ) ) THEN\n*\n*              Form  C * H  or  C * H**T  where  C = ( C1  C2 )\n*\n               LASTV = MAX( K, ILASLC( K, N, V, LDV ) )\n               LASTC = ILASLR( M, LASTV, C, LDC )\n*\n*              W := C * V**T  =  (C1*V1**T + C2*V2**T)  (stored in WORK)\n*\n*              W := C2\n*\n               DO 220 J = 1, K\n                  CALL SCOPY( LASTC, C( 1, LASTV-K+J ), 1,\n     $                 WORK( 1, J ), 1 )\n  220          CONTINUE\n*\n*              W := W * V2**T\n*\n               CALL STRMM( 'Right', 'Lower', 'Transpose', 'Unit',\n     $              LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,\n     $              WORK, LDWORK )\n               IF( LASTV.GT.K ) THEN\n*\n*                 W := W + C1 * V1**T\n*\n                  CALL SGEMM( 'No transpose', 'Transpose',\n     $                 LASTC, K, LASTV-K, ONE, C, LDC, V, LDV,\n     $                 ONE, WORK, LDWORK )\n               END IF\n*\n*              W := W * T  or  W * T**T\n*\n               CALL STRMM( 'Right', 'Lower', TRANS, 'Non-unit',\n     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )\n*\n*              C := C - W * V\n*\n               IF( LASTV.GT.K ) THEN\n*\n*                 C1 := C1 - W * V1\n*\n                  CALL SGEMM( 'No transpose', 'No transpose',\n     $                 LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV,\n     $                 ONE, C, LDC )\n               END IF\n*\n*              W := W * V2\n*\n               CALL STRMM( 'Right', 'Lower', 'No transpose', 'Unit',\n     $              LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,\n     $              WORK, LDWORK )\n*\n*              C1 := C1 - W\n*\n               DO 240 J = 1, K\n                  DO 230 I = 1, LASTC\n                     C( I, LASTV-K+J ) = C( I, LASTV-K+J )\n     $                    - WORK( I, J )\n  230             CONTINUE\n  240          CONTINUE\n*\n            END IF\n*\n         END IF\n      END IF\n*\n      RETURN\n*\n*     End of SLARFB\n*\n      END\n"
  },
  {
    "path": "include/eigen3/lapack/slarfg.f",
    "content": "*> \\brief \\b SLARFG\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*> \\htmlonly\n*> Download SLARFG + dependencies \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slarfg.f\"> \n*> [TGZ]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slarfg.f\"> \n*> [ZIP]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slarfg.f\"> \n*> [TXT]</a>\n*> \\endhtmlonly \n*\n*  Definition:\n*  ===========\n*\n*       SUBROUTINE SLARFG( N, ALPHA, X, INCX, TAU )\n* \n*       .. Scalar Arguments ..\n*       INTEGER            INCX, N\n*       REAL               ALPHA, TAU\n*       ..\n*       .. Array Arguments ..\n*       REAL               X( * )\n*       ..\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> SLARFG generates a real elementary reflector H of order n, such\n*> that\n*>\n*>       H * ( alpha ) = ( beta ),   H**T * H = I.\n*>           (   x   )   (   0  )\n*>\n*> where alpha and beta are scalars, and x is an (n-1)-element real\n*> vector. H is represented in the form\n*>\n*>       H = I - tau * ( 1 ) * ( 1 v**T ) ,\n*>                     ( v )\n*>\n*> where tau is a real scalar and v is a real (n-1)-element\n*> vector.\n*>\n*> If the elements of x are all zero, then tau = 0 and H is taken to be\n*> the unit matrix.\n*>\n*> Otherwise  1 <= tau <= 2.\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] N\n*> \\verbatim\n*>          N is INTEGER\n*>          The order of the elementary reflector.\n*> \\endverbatim\n*>\n*> \\param[in,out] ALPHA\n*> \\verbatim\n*>          ALPHA is REAL\n*>          On entry, the value alpha.\n*>          On exit, it is overwritten with the value beta.\n*> \\endverbatim\n*>\n*> \\param[in,out] X\n*> \\verbatim\n*>          X is REAL array, dimension\n*>                         (1+(N-2)*abs(INCX))\n*>          On entry, the vector x.\n*>          On exit, it is overwritten with the vector v.\n*> \\endverbatim\n*>\n*> \\param[in] INCX\n*> \\verbatim\n*>          INCX is INTEGER\n*>          The increment between elements of X. INCX > 0.\n*> \\endverbatim\n*>\n*> \\param[out] TAU\n*> \\verbatim\n*>          TAU is REAL\n*>          The value tau.\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date November 2011\n*\n*> \\ingroup realOTHERauxiliary\n*\n*  =====================================================================\n      SUBROUTINE SLARFG( N, ALPHA, X, INCX, TAU )\n*\n*  -- LAPACK auxiliary routine (version 3.4.0) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     November 2011\n*\n*     .. Scalar Arguments ..\n      INTEGER            INCX, N\n      REAL               ALPHA, TAU\n*     ..\n*     .. Array Arguments ..\n      REAL               X( * )\n*     ..\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      REAL               ONE, ZERO\n      PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )\n*     ..\n*     .. Local Scalars ..\n      INTEGER            J, KNT\n      REAL               BETA, RSAFMN, SAFMIN, XNORM\n*     ..\n*     .. External Functions ..\n      REAL               SLAMCH, SLAPY2, SNRM2\n      EXTERNAL           SLAMCH, SLAPY2, SNRM2\n*     ..\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, SIGN\n*     ..\n*     .. External Subroutines ..\n      EXTERNAL           SSCAL\n*     ..\n*     .. Executable Statements ..\n*\n      IF( N.LE.1 ) THEN\n         TAU = ZERO\n         RETURN\n      END IF\n*\n      XNORM = SNRM2( N-1, X, INCX )\n*\n      IF( XNORM.EQ.ZERO ) THEN\n*\n*        H  =  I\n*\n         TAU = ZERO\n      ELSE\n*\n*        general case\n*\n         BETA = -SIGN( SLAPY2( ALPHA, XNORM ), ALPHA )\n         SAFMIN = SLAMCH( 'S' ) / SLAMCH( 'E' )\n         KNT = 0\n         IF( ABS( BETA ).LT.SAFMIN ) THEN\n*\n*           XNORM, BETA may be inaccurate; scale X and recompute them\n*\n            RSAFMN = ONE / SAFMIN\n   10       CONTINUE\n            KNT = KNT + 1\n            CALL SSCAL( N-1, RSAFMN, X, INCX )\n            BETA = BETA*RSAFMN\n            ALPHA = ALPHA*RSAFMN\n            IF( ABS( BETA ).LT.SAFMIN )\n     $         GO TO 10\n*\n*           New BETA is at most 1, at least SAFMIN\n*\n            XNORM = SNRM2( N-1, X, INCX )\n            BETA = -SIGN( SLAPY2( ALPHA, XNORM ), ALPHA )\n         END IF\n         TAU = ( BETA-ALPHA ) / BETA\n         CALL SSCAL( N-1, ONE / ( ALPHA-BETA ), X, INCX )\n*\n*        If ALPHA is subnormal, it may lose relative accuracy\n*\n         DO 20 J = 1, KNT\n            BETA = BETA*SAFMIN\n 20      CONTINUE\n         ALPHA = BETA\n      END IF\n*\n      RETURN\n*\n*     End of SLARFG\n*\n      END\n"
  },
  {
    "path": "include/eigen3/lapack/slarft.f",
    "content": "*> \\brief \\b SLARFT\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*> \\htmlonly\n*> Download SLARFT + dependencies \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slarft.f\"> \n*> [TGZ]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slarft.f\"> \n*> [ZIP]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slarft.f\"> \n*> [TXT]</a>\n*> \\endhtmlonly \n*\n*  Definition:\n*  ===========\n*\n*       SUBROUTINE SLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )\n* \n*       .. Scalar Arguments ..\n*       CHARACTER          DIRECT, STOREV\n*       INTEGER            K, LDT, LDV, N\n*       ..\n*       .. Array Arguments ..\n*       REAL               T( LDT, * ), TAU( * ), V( LDV, * )\n*       ..\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> SLARFT forms the triangular factor T of a real block reflector H\n*> of order n, which is defined as a product of k elementary reflectors.\n*>\n*> If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular;\n*>\n*> If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular.\n*>\n*> If STOREV = 'C', the vector which defines the elementary reflector\n*> H(i) is stored in the i-th column of the array V, and\n*>\n*>    H  =  I - V * T * V**T\n*>\n*> If STOREV = 'R', the vector which defines the elementary reflector\n*> H(i) is stored in the i-th row of the array V, and\n*>\n*>    H  =  I - V**T * T * V\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] DIRECT\n*> \\verbatim\n*>          DIRECT is CHARACTER*1\n*>          Specifies the order in which the elementary reflectors are\n*>          multiplied to form the block reflector:\n*>          = 'F': H = H(1) H(2) . . . H(k) (Forward)\n*>          = 'B': H = H(k) . . . H(2) H(1) (Backward)\n*> \\endverbatim\n*>\n*> \\param[in] STOREV\n*> \\verbatim\n*>          STOREV is CHARACTER*1\n*>          Specifies how the vectors which define the elementary\n*>          reflectors are stored (see also Further Details):\n*>          = 'C': columnwise\n*>          = 'R': rowwise\n*> \\endverbatim\n*>\n*> \\param[in] N\n*> \\verbatim\n*>          N is INTEGER\n*>          The order of the block reflector H. N >= 0.\n*> \\endverbatim\n*>\n*> \\param[in] K\n*> \\verbatim\n*>          K is INTEGER\n*>          The order of the triangular factor T (= the number of\n*>          elementary reflectors). K >= 1.\n*> \\endverbatim\n*>\n*> \\param[in] V\n*> \\verbatim\n*>          V is REAL array, dimension\n*>                               (LDV,K) if STOREV = 'C'\n*>                               (LDV,N) if STOREV = 'R'\n*>          The matrix V. See further details.\n*> \\endverbatim\n*>\n*> \\param[in] LDV\n*> \\verbatim\n*>          LDV is INTEGER\n*>          The leading dimension of the array V.\n*>          If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.\n*> \\endverbatim\n*>\n*> \\param[in] TAU\n*> \\verbatim\n*>          TAU is REAL array, dimension (K)\n*>          TAU(i) must contain the scalar factor of the elementary\n*>          reflector H(i).\n*> \\endverbatim\n*>\n*> \\param[out] T\n*> \\verbatim\n*>          T is REAL array, dimension (LDT,K)\n*>          The k by k triangular factor T of the block reflector.\n*>          If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is\n*>          lower triangular. The rest of the array is not used.\n*> \\endverbatim\n*>\n*> \\param[in] LDT\n*> \\verbatim\n*>          LDT is INTEGER\n*>          The leading dimension of the array T. LDT >= K.\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date April 2012\n*\n*> \\ingroup realOTHERauxiliary\n*\n*> \\par Further Details:\n*  =====================\n*>\n*> \\verbatim\n*>\n*>  The shape of the matrix V and the storage of the vectors which define\n*>  the H(i) is best illustrated by the following example with n = 5 and\n*>  k = 3. The elements equal to 1 are not stored.\n*>\n*>  DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':\n*>\n*>               V = (  1       )                 V = (  1 v1 v1 v1 v1 )\n*>                   ( v1  1    )                     (     1 v2 v2 v2 )\n*>                   ( v1 v2  1 )                     (        1 v3 v3 )\n*>                   ( v1 v2 v3 )\n*>                   ( v1 v2 v3 )\n*>\n*>  DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':\n*>\n*>               V = ( v1 v2 v3 )                 V = ( v1 v1  1       )\n*>                   ( v1 v2 v3 )                     ( v2 v2 v2  1    )\n*>                   (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )\n*>                   (     1 v3 )\n*>                   (        1 )\n*> \\endverbatim\n*>\n*  =====================================================================\n      SUBROUTINE SLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )\n*\n*  -- LAPACK auxiliary routine (version 3.4.1) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     April 2012\n*\n*     .. Scalar Arguments ..\n      CHARACTER          DIRECT, STOREV\n      INTEGER            K, LDT, LDV, N\n*     ..\n*     .. Array Arguments ..\n      REAL               T( LDT, * ), TAU( * ), V( LDV, * )\n*     ..\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      REAL               ONE, ZERO\n      PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )\n*     ..\n*     .. Local Scalars ..\n      INTEGER            I, J, PREVLASTV, LASTV\n*     ..\n*     .. External Subroutines ..\n      EXTERNAL           SGEMV, STRMV\n*     ..\n*     .. External Functions ..\n      LOGICAL            LSAME\n      EXTERNAL           LSAME\n*     ..\n*     .. Executable Statements ..\n*\n*     Quick return if possible\n*\n      IF( N.EQ.0 )\n     $   RETURN\n*\n      IF( LSAME( DIRECT, 'F' ) ) THEN\n         PREVLASTV = N\n         DO I = 1, K\n            PREVLASTV = MAX( I, PREVLASTV )\n            IF( TAU( I ).EQ.ZERO ) THEN\n*\n*              H(i)  =  I\n*\n               DO J = 1, I\n                  T( J, I ) = ZERO\n               END DO\n            ELSE\n*\n*              general case\n*\n               IF( LSAME( STOREV, 'C' ) ) THEN\n*                 Skip any trailing zeros.\n                  DO LASTV = N, I+1, -1\n                     IF( V( LASTV, I ).NE.ZERO ) EXIT\n                  END DO\n                  DO J = 1, I-1\n                     T( J, I ) = -TAU( I ) * V( I , J )\n                  END DO   \n                  J = MIN( LASTV, PREVLASTV )\n*\n*                 T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**T * V(i:j,i)\n*\n                  CALL SGEMV( 'Transpose', J-I, I-1, -TAU( I ),\n     $                        V( I+1, 1 ), LDV, V( I+1, I ), 1, ONE,\n     $                        T( 1, I ), 1 )\n               ELSE\n*                 Skip any trailing zeros.\n                  DO LASTV = N, I+1, -1\n                     IF( V( I, LASTV ).NE.ZERO ) EXIT\n                  END DO\n                  DO J = 1, I-1\n                     T( J, I ) = -TAU( I ) * V( J , I )\n                  END DO   \n                  J = MIN( LASTV, PREVLASTV )\n*\n*                 T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**T\n*\n                  CALL SGEMV( 'No transpose', I-1, J-I, -TAU( I ),\n     $                        V( 1, I+1 ), LDV, V( I, I+1 ), LDV, \n     $                        ONE, T( 1, I ), 1 )\n               END IF\n*\n*              T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i)\n*\n               CALL STRMV( 'Upper', 'No transpose', 'Non-unit', I-1, T,\n     $                     LDT, T( 1, I ), 1 )\n               T( I, I ) = TAU( I )\n               IF( I.GT.1 ) THEN\n                  PREVLASTV = MAX( PREVLASTV, LASTV )\n               ELSE\n                  PREVLASTV = LASTV\n               END IF\n            END IF\n         END DO\n      ELSE\n         PREVLASTV = 1\n         DO I = K, 1, -1\n            IF( TAU( I ).EQ.ZERO ) THEN\n*\n*              H(i)  =  I\n*\n               DO J = I, K\n                  T( J, I ) = ZERO\n               END DO\n            ELSE\n*\n*              general case\n*\n               IF( I.LT.K ) THEN\n                  IF( LSAME( STOREV, 'C' ) ) THEN\n*                    Skip any leading zeros.\n                     DO LASTV = 1, I-1\n                        IF( V( LASTV, I ).NE.ZERO ) EXIT\n                     END DO\n                     DO J = I+1, K\n                        T( J, I ) = -TAU( I ) * V( N-K+I , J )\n                     END DO   \n                     J = MAX( LASTV, PREVLASTV )\n*\n*                    T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**T * V(j:n-k+i,i)\n*\n                     CALL SGEMV( 'Transpose', N-K+I-J, K-I, -TAU( I ),\n     $                           V( J, I+1 ), LDV, V( J, I ), 1, ONE,\n     $                           T( I+1, I ), 1 )\n                  ELSE\n*                    Skip any leading zeros.\n                     DO LASTV = 1, I-1\n                        IF( V( I, LASTV ).NE.ZERO ) EXIT\n                     END DO\n                     DO J = I+1, K\n                        T( J, I ) = -TAU( I ) * V( J, N-K+I )\n                     END DO   \n                     J = MAX( LASTV, PREVLASTV )\n*\n*                    T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**T\n*\n                     CALL SGEMV( 'No transpose', K-I, N-K+I-J,\n     $                    -TAU( I ), V( I+1, J ), LDV, V( I, J ), LDV,\n     $                    ONE, T( I+1, I ), 1 )\n                  END IF\n*\n*                 T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i)\n*\n                  CALL STRMV( 'Lower', 'No transpose', 'Non-unit', K-I,\n     $                        T( I+1, I+1 ), LDT, T( I+1, I ), 1 )\n                  IF( I.GT.1 ) THEN\n                     PREVLASTV = MIN( PREVLASTV, LASTV )\n                  ELSE\n                     PREVLASTV = LASTV\n                  END IF\n               END IF\n               T( I, I ) = TAU( I )\n            END IF\n         END DO\n      END IF\n      RETURN\n*\n*     End of SLARFT\n*\n      END\n"
  },
  {
    "path": "include/eigen3/lapack/svd.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"lapack_common.h\"\n#include <Eigen/SVD>\n\n// computes the singular values/vectors a general M-by-N matrix A using divide-and-conquer\nEIGEN_LAPACK_FUNC(gesdd,(char *jobz, int *m, int* n, Scalar* a, int *lda, RealScalar *s, Scalar *u, int *ldu, Scalar *vt, int *ldvt, Scalar* /*work*/, int* lwork,\n                         EIGEN_LAPACK_ARG_IF_COMPLEX(RealScalar */*rwork*/) int * /*iwork*/, int *info))\n{\n  // TODO exploit the work buffer\n  bool query_size = *lwork==-1;\n  int diag_size = (std::min)(*m,*n);\n  \n  *info = 0;\n        if(*jobz!='A' && *jobz!='S' && *jobz!='O' && *jobz!='N')  *info = -1;\n  else  if(*m<0)                                                  *info = -2;\n  else  if(*n<0)                                                  *info = -3;\n  else  if(*lda<std::max(1,*m))                                   *info = -5;\n  else  if(*lda<std::max(1,*m))                                   *info = -8;\n  else  if(*ldu <1 || (*jobz=='A' && *ldu <*m)\n                   || (*jobz=='O' && *m<*n && *ldu<*m))           *info = -8;\n  else  if(*ldvt<1 || (*jobz=='A' && *ldvt<*n)\n                   || (*jobz=='S' && *ldvt<diag_size)\n                   || (*jobz=='O' && *m>=*n && *ldvt<*n))         *info = -10;\n  \n  if(*info!=0)\n  {\n    int e = -*info;\n    return xerbla_(SCALAR_SUFFIX_UP\"GESDD \", &e, 6);\n  }\n  \n  if(query_size)\n  {\n    *lwork = 0;\n    return 0;\n  }\n  \n  if(*n==0 || *m==0)\n    return 0;\n  \n  PlainMatrixType mat(*m,*n);\n  mat = matrix(a,*m,*n,*lda);\n  \n  int option = *jobz=='A' ? ComputeFullU|ComputeFullV\n             : *jobz=='S' ? ComputeThinU|ComputeThinV\n             : *jobz=='O' ? ComputeThinU|ComputeThinV\n             : 0;\n\n  BDCSVD<PlainMatrixType> svd(mat,option);\n  \n  make_vector(s,diag_size) = svd.singularValues().head(diag_size);\n\n  if(*jobz=='A')\n  {\n    matrix(u,*m,*m,*ldu)   = svd.matrixU();\n    matrix(vt,*n,*n,*ldvt) = svd.matrixV().adjoint();\n  }\n  else if(*jobz=='S')\n  {\n    matrix(u,*m,diag_size,*ldu)   = svd.matrixU();\n    matrix(vt,diag_size,*n,*ldvt) = svd.matrixV().adjoint();\n  }\n  else if(*jobz=='O' && *m>=*n)\n  {\n    matrix(a,*m,*n,*lda)   = svd.matrixU();\n    matrix(vt,*n,*n,*ldvt) = svd.matrixV().adjoint();\n  }\n  else if(*jobz=='O')\n  {\n    matrix(u,*m,*m,*ldu)        = svd.matrixU();\n    matrix(a,diag_size,*n,*lda) = svd.matrixV().adjoint();\n  }\n    \n  return 0;\n}\n\n// computes the singular values/vectors a general M-by-N matrix A using two sided jacobi algorithm\nEIGEN_LAPACK_FUNC(gesvd,(char *jobu, char *jobv, int *m, int* n, Scalar* a, int *lda, RealScalar *s, Scalar *u, int *ldu, Scalar *vt, int *ldvt, Scalar* /*work*/, int* lwork,\n                         EIGEN_LAPACK_ARG_IF_COMPLEX(RealScalar */*rwork*/) int *info))\n{\n  // TODO exploit the work buffer\n  bool query_size = *lwork==-1;\n  int diag_size = (std::min)(*m,*n);\n  \n  *info = 0;\n        if( *jobu!='A' && *jobu!='S' && *jobu!='O' && *jobu!='N') *info = -1;\n  else  if((*jobv!='A' && *jobv!='S' && *jobv!='O' && *jobv!='N')\n           || (*jobu=='O' && *jobv=='O'))                         *info = -2;\n  else  if(*m<0)                                                  *info = -3;\n  else  if(*n<0)                                                  *info = -4;\n  else  if(*lda<std::max(1,*m))                                   *info = -6;\n  else  if(*ldu <1 || ((*jobu=='A' || *jobu=='S') && *ldu<*m))    *info = -9;\n  else  if(*ldvt<1 || (*jobv=='A' && *ldvt<*n)\n                   || (*jobv=='S' && *ldvt<diag_size))            *info = -11;\n  \n  if(*info!=0)\n  {\n    int e = -*info;\n    return xerbla_(SCALAR_SUFFIX_UP\"GESVD \", &e, 6);\n  }\n  \n  if(query_size)\n  {\n    *lwork = 0;\n    return 0;\n  }\n  \n  if(*n==0 || *m==0)\n    return 0;\n  \n  PlainMatrixType mat(*m,*n);\n  mat = matrix(a,*m,*n,*lda);\n  \n  int option = (*jobu=='A' ? ComputeFullU : *jobu=='S' || *jobu=='O' ? ComputeThinU : 0)\n             | (*jobv=='A' ? ComputeFullV : *jobv=='S' || *jobv=='O' ? ComputeThinV : 0);\n  \n  JacobiSVD<PlainMatrixType> svd(mat,option);\n  \n  make_vector(s,diag_size) = svd.singularValues().head(diag_size);\n  {\n        if(*jobu=='A') matrix(u,*m,*m,*ldu)           = svd.matrixU();\n  else  if(*jobu=='S') matrix(u,*m,diag_size,*ldu)    = svd.matrixU();\n  else  if(*jobu=='O') matrix(a,*m,diag_size,*lda)    = svd.matrixU();\n  }\n  {\n        if(*jobv=='A') matrix(vt,*n,*n,*ldvt)         = svd.matrixV().adjoint();\n  else  if(*jobv=='S') matrix(vt,diag_size,*n,*ldvt)  = svd.matrixV().adjoint();\n  else  if(*jobv=='O') matrix(a,diag_size,*n,*lda)    = svd.matrixV().adjoint();\n  }\n  return 0;\n}\n"
  },
  {
    "path": "include/eigen3/lapack/zlacgv.f",
    "content": "*> \\brief \\b ZLACGV\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*> \\htmlonly\n*> Download ZLACGV + dependencies \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlacgv.f\"> \n*> [TGZ]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlacgv.f\"> \n*> [ZIP]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlacgv.f\"> \n*> [TXT]</a>\n*> \\endhtmlonly \n*\n*  Definition:\n*  ===========\n*\n*       SUBROUTINE ZLACGV( N, X, INCX )\n* \n*       .. Scalar Arguments ..\n*       INTEGER            INCX, N\n*       ..\n*       .. Array Arguments ..\n*       COMPLEX*16         X( * )\n*       ..\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> ZLACGV conjugates a complex vector of length N.\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] N\n*> \\verbatim\n*>          N is INTEGER\n*>          The length of the vector X.  N >= 0.\n*> \\endverbatim\n*>\n*> \\param[in,out] X\n*> \\verbatim\n*>          X is COMPLEX*16 array, dimension\n*>                         (1+(N-1)*abs(INCX))\n*>          On entry, the vector of length N to be conjugated.\n*>          On exit, X is overwritten with conjg(X).\n*> \\endverbatim\n*>\n*> \\param[in] INCX\n*> \\verbatim\n*>          INCX is INTEGER\n*>          The spacing between successive elements of X.\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date November 2011\n*\n*> \\ingroup complex16OTHERauxiliary\n*\n*  =====================================================================\n      SUBROUTINE ZLACGV( N, X, INCX )\n*\n*  -- LAPACK auxiliary routine (version 3.4.0) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     November 2011\n*\n*     .. Scalar Arguments ..\n      INTEGER            INCX, N\n*     ..\n*     .. Array Arguments ..\n      COMPLEX*16         X( * )\n*     ..\n*\n* =====================================================================\n*\n*     .. Local Scalars ..\n      INTEGER            I, IOFF\n*     ..\n*     .. Intrinsic Functions ..\n      INTRINSIC          DCONJG\n*     ..\n*     .. Executable Statements ..\n*\n      IF( INCX.EQ.1 ) THEN\n         DO 10 I = 1, N\n            X( I ) = DCONJG( X( I ) )\n   10    CONTINUE\n      ELSE\n         IOFF = 1\n         IF( INCX.LT.0 )\n     $      IOFF = 1 - ( N-1 )*INCX\n         DO 20 I = 1, N\n            X( IOFF ) = DCONJG( X( IOFF ) )\n            IOFF = IOFF + INCX\n   20    CONTINUE\n      END IF\n      RETURN\n*\n*     End of ZLACGV\n*\n      END\n"
  },
  {
    "path": "include/eigen3/lapack/zladiv.f",
    "content": "*> \\brief \\b ZLADIV\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*> \\htmlonly\n*> Download ZLADIV + dependencies \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zladiv.f\"> \n*> [TGZ]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zladiv.f\"> \n*> [ZIP]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zladiv.f\"> \n*> [TXT]</a>\n*> \\endhtmlonly \n*\n*  Definition:\n*  ===========\n*\n*       COMPLEX*16     FUNCTION ZLADIV( X, Y )\n* \n*       .. Scalar Arguments ..\n*       COMPLEX*16         X, Y\n*       ..\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> ZLADIV := X / Y, where X and Y are complex.  The computation of X / Y\n*> will not overflow on an intermediary step unless the results\n*> overflows.\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] X\n*> \\verbatim\n*>          X is COMPLEX*16\n*> \\endverbatim\n*>\n*> \\param[in] Y\n*> \\verbatim\n*>          Y is COMPLEX*16\n*>          The complex scalars X and Y.\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date November 2011\n*\n*> \\ingroup complex16OTHERauxiliary\n*\n*  =====================================================================\n      COMPLEX*16     FUNCTION ZLADIV( X, Y )\n*\n*  -- LAPACK auxiliary routine (version 3.4.0) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     November 2011\n*\n*     .. Scalar Arguments ..\n      COMPLEX*16         X, Y\n*     ..\n*\n*  =====================================================================\n*\n*     .. Local Scalars ..\n      DOUBLE PRECISION   ZI, ZR\n*     ..\n*     .. External Subroutines ..\n      EXTERNAL           DLADIV\n*     ..\n*     .. Intrinsic Functions ..\n      INTRINSIC          DBLE, DCMPLX, DIMAG\n*     ..\n*     .. Executable Statements ..\n*\n      CALL DLADIV( DBLE( X ), DIMAG( X ), DBLE( Y ), DIMAG( Y ), ZR,\n     $             ZI )\n      ZLADIV = DCMPLX( ZR, ZI )\n*\n      RETURN\n*\n*     End of ZLADIV\n*\n      END\n"
  },
  {
    "path": "include/eigen3/lapack/zlarf.f",
    "content": "*> \\brief \\b ZLARF\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*> \\htmlonly\n*> Download ZLARF + dependencies \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlarf.f\"> \n*> [TGZ]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlarf.f\"> \n*> [ZIP]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlarf.f\"> \n*> [TXT]</a>\n*> \\endhtmlonly \n*\n*  Definition:\n*  ===========\n*\n*       SUBROUTINE ZLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )\n* \n*       .. Scalar Arguments ..\n*       CHARACTER          SIDE\n*       INTEGER            INCV, LDC, M, N\n*       COMPLEX*16         TAU\n*       ..\n*       .. Array Arguments ..\n*       COMPLEX*16         C( LDC, * ), V( * ), WORK( * )\n*       ..\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> ZLARF applies a complex elementary reflector H to a complex M-by-N\n*> matrix C, from either the left or the right. H is represented in the\n*> form\n*>\n*>       H = I - tau * v * v**H\n*>\n*> where tau is a complex scalar and v is a complex vector.\n*>\n*> If tau = 0, then H is taken to be the unit matrix.\n*>\n*> To apply H**H, supply conjg(tau) instead\n*> tau.\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] SIDE\n*> \\verbatim\n*>          SIDE is CHARACTER*1\n*>          = 'L': form  H * C\n*>          = 'R': form  C * H\n*> \\endverbatim\n*>\n*> \\param[in] M\n*> \\verbatim\n*>          M is INTEGER\n*>          The number of rows of the matrix C.\n*> \\endverbatim\n*>\n*> \\param[in] N\n*> \\verbatim\n*>          N is INTEGER\n*>          The number of columns of the matrix C.\n*> \\endverbatim\n*>\n*> \\param[in] V\n*> \\verbatim\n*>          V is COMPLEX*16 array, dimension\n*>                     (1 + (M-1)*abs(INCV)) if SIDE = 'L'\n*>                  or (1 + (N-1)*abs(INCV)) if SIDE = 'R'\n*>          The vector v in the representation of H. V is not used if\n*>          TAU = 0.\n*> \\endverbatim\n*>\n*> \\param[in] INCV\n*> \\verbatim\n*>          INCV is INTEGER\n*>          The increment between elements of v. INCV <> 0.\n*> \\endverbatim\n*>\n*> \\param[in] TAU\n*> \\verbatim\n*>          TAU is COMPLEX*16\n*>          The value tau in the representation of H.\n*> \\endverbatim\n*>\n*> \\param[in,out] C\n*> \\verbatim\n*>          C is COMPLEX*16 array, dimension (LDC,N)\n*>          On entry, the M-by-N matrix C.\n*>          On exit, C is overwritten by the matrix H * C if SIDE = 'L',\n*>          or C * H if SIDE = 'R'.\n*> \\endverbatim\n*>\n*> \\param[in] LDC\n*> \\verbatim\n*>          LDC is INTEGER\n*>          The leading dimension of the array C. LDC >= max(1,M).\n*> \\endverbatim\n*>\n*> \\param[out] WORK\n*> \\verbatim\n*>          WORK is COMPLEX*16 array, dimension\n*>                         (N) if SIDE = 'L'\n*>                      or (M) if SIDE = 'R'\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date November 2011\n*\n*> \\ingroup complex16OTHERauxiliary\n*\n*  =====================================================================\n      SUBROUTINE ZLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )\n*\n*  -- LAPACK auxiliary routine (version 3.4.0) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     November 2011\n*\n*     .. Scalar Arguments ..\n      CHARACTER          SIDE\n      INTEGER            INCV, LDC, M, N\n      COMPLEX*16         TAU\n*     ..\n*     .. Array Arguments ..\n      COMPLEX*16         C( LDC, * ), V( * ), WORK( * )\n*     ..\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      COMPLEX*16         ONE, ZERO\n      PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ),\n     $                   ZERO = ( 0.0D+0, 0.0D+0 ) )\n*     ..\n*     .. Local Scalars ..\n      LOGICAL            APPLYLEFT\n      INTEGER            I, LASTV, LASTC\n*     ..\n*     .. External Subroutines ..\n      EXTERNAL           ZGEMV, ZGERC\n*     ..\n*     .. External Functions ..\n      LOGICAL            LSAME\n      INTEGER            ILAZLR, ILAZLC\n      EXTERNAL           LSAME, ILAZLR, ILAZLC\n*     ..\n*     .. Executable Statements ..\n*\n      APPLYLEFT = LSAME( SIDE, 'L' )\n      LASTV = 0\n      LASTC = 0\n      IF( TAU.NE.ZERO ) THEN\n*     Set up variables for scanning V.  LASTV begins pointing to the end\n*     of V.\n         IF( APPLYLEFT ) THEN\n            LASTV = M\n         ELSE\n            LASTV = N\n         END IF\n         IF( INCV.GT.0 ) THEN\n            I = 1 + (LASTV-1) * INCV\n         ELSE\n            I = 1\n         END IF\n*     Look for the last non-zero row in V.\n         DO WHILE( LASTV.GT.0 .AND. V( I ).EQ.ZERO )\n            LASTV = LASTV - 1\n            I = I - INCV\n         END DO\n         IF( APPLYLEFT ) THEN\n*     Scan for the last non-zero column in C(1:lastv,:).\n            LASTC = ILAZLC(LASTV, N, C, LDC)\n         ELSE\n*     Scan for the last non-zero row in C(:,1:lastv).\n            LASTC = ILAZLR(M, LASTV, C, LDC)\n         END IF\n      END IF\n*     Note that lastc.eq.0 renders the BLAS operations null; no special\n*     case is needed at this level.\n      IF( APPLYLEFT ) THEN\n*\n*        Form  H * C\n*\n         IF( LASTV.GT.0 ) THEN\n*\n*           w(1:lastc,1) := C(1:lastv,1:lastc)**H * v(1:lastv,1)\n*\n            CALL ZGEMV( 'Conjugate transpose', LASTV, LASTC, ONE,\n     $           C, LDC, V, INCV, ZERO, WORK, 1 )\n*\n*           C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**H\n*\n            CALL ZGERC( LASTV, LASTC, -TAU, V, INCV, WORK, 1, C, LDC )\n         END IF\n      ELSE\n*\n*        Form  C * H\n*\n         IF( LASTV.GT.0 ) THEN\n*\n*           w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1)\n*\n            CALL ZGEMV( 'No transpose', LASTC, LASTV, ONE, C, LDC,\n     $           V, INCV, ZERO, WORK, 1 )\n*\n*           C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**H\n*\n            CALL ZGERC( LASTC, LASTV, -TAU, WORK, 1, V, INCV, C, LDC )\n         END IF\n      END IF\n      RETURN\n*\n*     End of ZLARF\n*\n      END\n"
  },
  {
    "path": "include/eigen3/lapack/zlarfb.f",
    "content": "*> \\brief \\b ZLARFB\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*> \\htmlonly\n*> Download ZLARFB + dependencies \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlarfb.f\"> \n*> [TGZ]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlarfb.f\"> \n*> [ZIP]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlarfb.f\"> \n*> [TXT]</a>\n*> \\endhtmlonly \n*\n*  Definition:\n*  ===========\n*\n*       SUBROUTINE ZLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV,\n*                          T, LDT, C, LDC, WORK, LDWORK )\n* \n*       .. Scalar Arguments ..\n*       CHARACTER          DIRECT, SIDE, STOREV, TRANS\n*       INTEGER            K, LDC, LDT, LDV, LDWORK, M, N\n*       ..\n*       .. Array Arguments ..\n*       COMPLEX*16         C( LDC, * ), T( LDT, * ), V( LDV, * ),\n*      $                   WORK( LDWORK, * )\n*       ..\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> ZLARFB applies a complex block reflector H or its transpose H**H to a\n*> complex M-by-N matrix C, from either the left or the right.\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] SIDE\n*> \\verbatim\n*>          SIDE is CHARACTER*1\n*>          = 'L': apply H or H**H from the Left\n*>          = 'R': apply H or H**H from the Right\n*> \\endverbatim\n*>\n*> \\param[in] TRANS\n*> \\verbatim\n*>          TRANS is CHARACTER*1\n*>          = 'N': apply H (No transpose)\n*>          = 'C': apply H**H (Conjugate transpose)\n*> \\endverbatim\n*>\n*> \\param[in] DIRECT\n*> \\verbatim\n*>          DIRECT is CHARACTER*1\n*>          Indicates how H is formed from a product of elementary\n*>          reflectors\n*>          = 'F': H = H(1) H(2) . . . H(k) (Forward)\n*>          = 'B': H = H(k) . . . H(2) H(1) (Backward)\n*> \\endverbatim\n*>\n*> \\param[in] STOREV\n*> \\verbatim\n*>          STOREV is CHARACTER*1\n*>          Indicates how the vectors which define the elementary\n*>          reflectors are stored:\n*>          = 'C': Columnwise\n*>          = 'R': Rowwise\n*> \\endverbatim\n*>\n*> \\param[in] M\n*> \\verbatim\n*>          M is INTEGER\n*>          The number of rows of the matrix C.\n*> \\endverbatim\n*>\n*> \\param[in] N\n*> \\verbatim\n*>          N is INTEGER\n*>          The number of columns of the matrix C.\n*> \\endverbatim\n*>\n*> \\param[in] K\n*> \\verbatim\n*>          K is INTEGER\n*>          The order of the matrix T (= the number of elementary\n*>          reflectors whose product defines the block reflector).\n*> \\endverbatim\n*>\n*> \\param[in] V\n*> \\verbatim\n*>          V is COMPLEX*16 array, dimension\n*>                                (LDV,K) if STOREV = 'C'\n*>                                (LDV,M) if STOREV = 'R' and SIDE = 'L'\n*>                                (LDV,N) if STOREV = 'R' and SIDE = 'R'\n*>          See Further Details.\n*> \\endverbatim\n*>\n*> \\param[in] LDV\n*> \\verbatim\n*>          LDV is INTEGER\n*>          The leading dimension of the array V.\n*>          If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M);\n*>          if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N);\n*>          if STOREV = 'R', LDV >= K.\n*> \\endverbatim\n*>\n*> \\param[in] T\n*> \\verbatim\n*>          T is COMPLEX*16 array, dimension (LDT,K)\n*>          The triangular K-by-K matrix T in the representation of the\n*>          block reflector.\n*> \\endverbatim\n*>\n*> \\param[in] LDT\n*> \\verbatim\n*>          LDT is INTEGER\n*>          The leading dimension of the array T. LDT >= K.\n*> \\endverbatim\n*>\n*> \\param[in,out] C\n*> \\verbatim\n*>          C is COMPLEX*16 array, dimension (LDC,N)\n*>          On entry, the M-by-N matrix C.\n*>          On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H.\n*> \\endverbatim\n*>\n*> \\param[in] LDC\n*> \\verbatim\n*>          LDC is INTEGER\n*>          The leading dimension of the array C. LDC >= max(1,M).\n*> \\endverbatim\n*>\n*> \\param[out] WORK\n*> \\verbatim\n*>          WORK is COMPLEX*16 array, dimension (LDWORK,K)\n*> \\endverbatim\n*>\n*> \\param[in] LDWORK\n*> \\verbatim\n*>          LDWORK is INTEGER\n*>          The leading dimension of the array WORK.\n*>          If SIDE = 'L', LDWORK >= max(1,N);\n*>          if SIDE = 'R', LDWORK >= max(1,M).\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date November 2011\n*\n*> \\ingroup complex16OTHERauxiliary\n*\n*> \\par Further Details:\n*  =====================\n*>\n*> \\verbatim\n*>\n*>  The shape of the matrix V and the storage of the vectors which define\n*>  the H(i) is best illustrated by the following example with n = 5 and\n*>  k = 3. The elements equal to 1 are not stored; the corresponding\n*>  array elements are modified but restored on exit. The rest of the\n*>  array is not used.\n*>\n*>  DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':\n*>\n*>               V = (  1       )                 V = (  1 v1 v1 v1 v1 )\n*>                   ( v1  1    )                     (     1 v2 v2 v2 )\n*>                   ( v1 v2  1 )                     (        1 v3 v3 )\n*>                   ( v1 v2 v3 )\n*>                   ( v1 v2 v3 )\n*>\n*>  DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':\n*>\n*>               V = ( v1 v2 v3 )                 V = ( v1 v1  1       )\n*>                   ( v1 v2 v3 )                     ( v2 v2 v2  1    )\n*>                   (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )\n*>                   (     1 v3 )\n*>                   (        1 )\n*> \\endverbatim\n*>\n*  =====================================================================\n      SUBROUTINE ZLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV,\n     $                   T, LDT, C, LDC, WORK, LDWORK )\n*\n*  -- LAPACK auxiliary routine (version 3.4.0) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     November 2011\n*\n*     .. Scalar Arguments ..\n      CHARACTER          DIRECT, SIDE, STOREV, TRANS\n      INTEGER            K, LDC, LDT, LDV, LDWORK, M, N\n*     ..\n*     .. Array Arguments ..\n      COMPLEX*16         C( LDC, * ), T( LDT, * ), V( LDV, * ),\n     $                   WORK( LDWORK, * )\n*     ..\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      COMPLEX*16         ONE\n      PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ) )\n*     ..\n*     .. Local Scalars ..\n      CHARACTER          TRANST\n      INTEGER            I, J, LASTV, LASTC\n*     ..\n*     .. External Functions ..\n      LOGICAL            LSAME\n      INTEGER            ILAZLR, ILAZLC\n      EXTERNAL           LSAME, ILAZLR, ILAZLC\n*     ..\n*     .. External Subroutines ..\n      EXTERNAL           ZCOPY, ZGEMM, ZLACGV, ZTRMM\n*     ..\n*     .. Intrinsic Functions ..\n      INTRINSIC          DCONJG\n*     ..\n*     .. Executable Statements ..\n*\n*     Quick return if possible\n*\n      IF( M.LE.0 .OR. N.LE.0 )\n     $   RETURN\n*\n      IF( LSAME( TRANS, 'N' ) ) THEN\n         TRANST = 'C'\n      ELSE\n         TRANST = 'N'\n      END IF\n*\n      IF( LSAME( STOREV, 'C' ) ) THEN\n*\n         IF( LSAME( DIRECT, 'F' ) ) THEN\n*\n*           Let  V =  ( V1 )    (first K rows)\n*                     ( V2 )\n*           where  V1  is unit lower triangular.\n*\n            IF( LSAME( SIDE, 'L' ) ) THEN\n*\n*              Form  H * C  or  H**H * C  where  C = ( C1 )\n*                                                    ( C2 )\n*\n               LASTV = MAX( K, ILAZLR( M, K, V, LDV ) )\n               LASTC = ILAZLC( LASTV, N, C, LDC )\n*\n*              W := C**H * V  =  (C1**H * V1 + C2**H * V2)  (stored in WORK)\n*\n*              W := C1**H\n*\n               DO 10 J = 1, K\n                  CALL ZCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 )\n                  CALL ZLACGV( LASTC, WORK( 1, J ), 1 )\n   10          CONTINUE\n*\n*              W := W * V1\n*\n               CALL ZTRMM( 'Right', 'Lower', 'No transpose', 'Unit',\n     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )\n               IF( LASTV.GT.K ) THEN\n*\n*                 W := W + C2**H *V2\n*\n                  CALL ZGEMM( 'Conjugate transpose', 'No transpose',\n     $                 LASTC, K, LASTV-K, ONE, C( K+1, 1 ), LDC,\n     $                 V( K+1, 1 ), LDV, ONE, WORK, LDWORK )\n               END IF\n*\n*              W := W * T**H  or  W * T\n*\n               CALL ZTRMM( 'Right', 'Upper', TRANST, 'Non-unit',\n     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )\n*\n*              C := C - V * W**H\n*\n               IF( M.GT.K ) THEN\n*\n*                 C2 := C2 - V2 * W**H\n*\n                  CALL ZGEMM( 'No transpose', 'Conjugate transpose',\n     $                 LASTV-K, LASTC, K,\n     $                 -ONE, V( K+1, 1 ), LDV, WORK, LDWORK,\n     $                 ONE, C( K+1, 1 ), LDC )\n               END IF\n*\n*              W := W * V1**H\n*\n               CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose',\n     $              'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK )\n*\n*              C1 := C1 - W**H\n*\n               DO 30 J = 1, K\n                  DO 20 I = 1, LASTC\n                     C( J, I ) = C( J, I ) - DCONJG( WORK( I, J ) )\n   20             CONTINUE\n   30          CONTINUE\n*\n            ELSE IF( LSAME( SIDE, 'R' ) ) THEN\n*\n*              Form  C * H  or  C * H**H  where  C = ( C1  C2 )\n*\n               LASTV = MAX( K, ILAZLR( N, K, V, LDV ) )\n               LASTC = ILAZLR( M, LASTV, C, LDC )\n*\n*              W := C * V  =  (C1*V1 + C2*V2)  (stored in WORK)\n*\n*              W := C1\n*\n               DO 40 J = 1, K\n                  CALL ZCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 )\n   40          CONTINUE\n*\n*              W := W * V1\n*\n               CALL ZTRMM( 'Right', 'Lower', 'No transpose', 'Unit',\n     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )\n               IF( LASTV.GT.K ) THEN\n*\n*                 W := W + C2 * V2\n*\n                  CALL ZGEMM( 'No transpose', 'No transpose',\n     $                 LASTC, K, LASTV-K,\n     $                 ONE, C( 1, K+1 ), LDC, V( K+1, 1 ), LDV,\n     $                 ONE, WORK, LDWORK )\n               END IF\n*\n*              W := W * T  or  W * T**H\n*\n               CALL ZTRMM( 'Right', 'Upper', TRANS, 'Non-unit',\n     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )\n*\n*              C := C - W * V**H\n*\n               IF( LASTV.GT.K ) THEN\n*\n*                 C2 := C2 - W * V2**H\n*\n                  CALL ZGEMM( 'No transpose', 'Conjugate transpose',\n     $                 LASTC, LASTV-K, K,\n     $                 -ONE, WORK, LDWORK, V( K+1, 1 ), LDV,\n     $                 ONE, C( 1, K+1 ), LDC )\n               END IF\n*\n*              W := W * V1**H\n*\n               CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose',\n     $              'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK )\n*\n*              C1 := C1 - W\n*\n               DO 60 J = 1, K\n                  DO 50 I = 1, LASTC\n                     C( I, J ) = C( I, J ) - WORK( I, J )\n   50             CONTINUE\n   60          CONTINUE\n            END IF\n*\n         ELSE\n*\n*           Let  V =  ( V1 )\n*                     ( V2 )    (last K rows)\n*           where  V2  is unit upper triangular.\n*\n            IF( LSAME( SIDE, 'L' ) ) THEN\n*\n*              Form  H * C  or  H**H * C  where  C = ( C1 )\n*                                                    ( C2 )\n*\n               LASTV = MAX( K, ILAZLR( M, K, V, LDV ) )\n               LASTC = ILAZLC( LASTV, N, C, LDC )\n*\n*              W := C**H * V  =  (C1**H * V1 + C2**H * V2)  (stored in WORK)\n*\n*              W := C2**H\n*\n               DO 70 J = 1, K\n                  CALL ZCOPY( LASTC, C( LASTV-K+J, 1 ), LDC,\n     $                 WORK( 1, J ), 1 )\n                  CALL ZLACGV( LASTC, WORK( 1, J ), 1 )\n   70          CONTINUE\n*\n*              W := W * V2\n*\n               CALL ZTRMM( 'Right', 'Upper', 'No transpose', 'Unit',\n     $              LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,\n     $              WORK, LDWORK )\n               IF( LASTV.GT.K ) THEN\n*\n*                 W := W + C1**H*V1\n*\n                  CALL ZGEMM( 'Conjugate transpose', 'No transpose',\n     $                 LASTC, K, LASTV-K,\n     $                 ONE, C, LDC, V, LDV,\n     $                 ONE, WORK, LDWORK )\n               END IF\n*\n*              W := W * T**H  or  W * T\n*\n               CALL ZTRMM( 'Right', 'Lower', TRANST, 'Non-unit',\n     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )\n*\n*              C := C - V * W**H\n*\n               IF( LASTV.GT.K ) THEN\n*\n*                 C1 := C1 - V1 * W**H\n*\n                  CALL ZGEMM( 'No transpose', 'Conjugate transpose',\n     $                 LASTV-K, LASTC, K,\n     $                 -ONE, V, LDV, WORK, LDWORK,\n     $                 ONE, C, LDC )\n               END IF\n*\n*              W := W * V2**H\n*\n               CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose',\n     $              'Unit', LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,\n     $              WORK, LDWORK )\n*\n*              C2 := C2 - W**H\n*\n               DO 90 J = 1, K\n                  DO 80 I = 1, LASTC\n                     C( LASTV-K+J, I ) = C( LASTV-K+J, I ) -\n     $                               DCONJG( WORK( I, J ) )\n   80             CONTINUE\n   90          CONTINUE\n*\n            ELSE IF( LSAME( SIDE, 'R' ) ) THEN\n*\n*              Form  C * H  or  C * H**H  where  C = ( C1  C2 )\n*\n               LASTV = MAX( K, ILAZLR( N, K, V, LDV ) )\n               LASTC = ILAZLR( M, LASTV, C, LDC )\n*\n*              W := C * V  =  (C1*V1 + C2*V2)  (stored in WORK)\n*\n*              W := C2\n*\n               DO 100 J = 1, K\n                  CALL ZCOPY( LASTC, C( 1, LASTV-K+J ), 1,\n     $                 WORK( 1, J ), 1 )\n  100          CONTINUE\n*\n*              W := W * V2\n*\n               CALL ZTRMM( 'Right', 'Upper', 'No transpose', 'Unit',\n     $              LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,\n     $              WORK, LDWORK )\n               IF( LASTV.GT.K ) THEN\n*\n*                 W := W + C1 * V1\n*\n                  CALL ZGEMM( 'No transpose', 'No transpose',\n     $                 LASTC, K, LASTV-K,\n     $                 ONE, C, LDC, V, LDV, ONE, WORK, LDWORK )\n               END IF\n*\n*              W := W * T  or  W * T**H\n*\n               CALL ZTRMM( 'Right', 'Lower', TRANS, 'Non-unit',\n     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )\n*\n*              C := C - W * V**H\n*\n               IF( LASTV.GT.K ) THEN\n*\n*                 C1 := C1 - W * V1**H\n*\n                  CALL ZGEMM( 'No transpose', 'Conjugate transpose',\n     $                 LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV,\n     $                 ONE, C, LDC )\n               END IF\n*\n*              W := W * V2**H\n*\n               CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose',\n     $              'Unit', LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,\n     $              WORK, LDWORK )\n*\n*              C2 := C2 - W\n*\n               DO 120 J = 1, K\n                  DO 110 I = 1, LASTC\n                     C( I, LASTV-K+J ) = C( I, LASTV-K+J )\n     $                    - WORK( I, J )\n  110             CONTINUE\n  120          CONTINUE\n            END IF\n         END IF\n*\n      ELSE IF( LSAME( STOREV, 'R' ) ) THEN\n*\n         IF( LSAME( DIRECT, 'F' ) ) THEN\n*\n*           Let  V =  ( V1  V2 )    (V1: first K columns)\n*           where  V1  is unit upper triangular.\n*\n            IF( LSAME( SIDE, 'L' ) ) THEN\n*\n*              Form  H * C  or  H**H * C  where  C = ( C1 )\n*                                                    ( C2 )\n*\n               LASTV = MAX( K, ILAZLC( K, M, V, LDV ) )\n               LASTC = ILAZLC( LASTV, N, C, LDC )\n*\n*              W := C**H * V**H  =  (C1**H * V1**H + C2**H * V2**H) (stored in WORK)\n*\n*              W := C1**H\n*\n               DO 130 J = 1, K\n                  CALL ZCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 )\n                  CALL ZLACGV( LASTC, WORK( 1, J ), 1 )\n  130          CONTINUE\n*\n*              W := W * V1**H\n*\n               CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose',\n     $                     'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK )\n               IF( LASTV.GT.K ) THEN\n*\n*                 W := W + C2**H*V2**H\n*\n                  CALL ZGEMM( 'Conjugate transpose',\n     $                 'Conjugate transpose', LASTC, K, LASTV-K,\n     $                 ONE, C( K+1, 1 ), LDC, V( 1, K+1 ), LDV,\n     $                 ONE, WORK, LDWORK )\n               END IF\n*\n*              W := W * T**H  or  W * T\n*\n               CALL ZTRMM( 'Right', 'Upper', TRANST, 'Non-unit',\n     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )\n*\n*              C := C - V**H * W**H\n*\n               IF( LASTV.GT.K ) THEN\n*\n*                 C2 := C2 - V2**H * W**H\n*\n                  CALL ZGEMM( 'Conjugate transpose',\n     $                 'Conjugate transpose', LASTV-K, LASTC, K,\n     $                 -ONE, V( 1, K+1 ), LDV, WORK, LDWORK,\n     $                 ONE, C( K+1, 1 ), LDC )\n               END IF\n*\n*              W := W * V1\n*\n               CALL ZTRMM( 'Right', 'Upper', 'No transpose', 'Unit',\n     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )\n*\n*              C1 := C1 - W**H\n*\n               DO 150 J = 1, K\n                  DO 140 I = 1, LASTC\n                     C( J, I ) = C( J, I ) - DCONJG( WORK( I, J ) )\n  140             CONTINUE\n  150          CONTINUE\n*\n            ELSE IF( LSAME( SIDE, 'R' ) ) THEN\n*\n*              Form  C * H  or  C * H**H  where  C = ( C1  C2 )\n*\n               LASTV = MAX( K, ILAZLC( K, N, V, LDV ) )\n               LASTC = ILAZLR( M, LASTV, C, LDC )\n*\n*              W := C * V**H  =  (C1*V1**H + C2*V2**H)  (stored in WORK)\n*\n*              W := C1\n*\n               DO 160 J = 1, K\n                  CALL ZCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 )\n  160          CONTINUE\n*\n*              W := W * V1**H\n*\n               CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose',\n     $                     'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK )\n               IF( LASTV.GT.K ) THEN\n*\n*                 W := W + C2 * V2**H\n*\n                  CALL ZGEMM( 'No transpose', 'Conjugate transpose',\n     $                 LASTC, K, LASTV-K, ONE, C( 1, K+1 ), LDC,\n     $                 V( 1, K+1 ), LDV, ONE, WORK, LDWORK )\n               END IF\n*\n*              W := W * T  or  W * T**H\n*\n               CALL ZTRMM( 'Right', 'Upper', TRANS, 'Non-unit',\n     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )\n*\n*              C := C - W * V\n*\n               IF( LASTV.GT.K ) THEN\n*\n*                 C2 := C2 - W * V2\n*\n                  CALL ZGEMM( 'No transpose', 'No transpose',\n     $                 LASTC, LASTV-K, K,\n     $                 -ONE, WORK, LDWORK, V( 1, K+1 ), LDV,\n     $                 ONE, C( 1, K+1 ), LDC )\n               END IF\n*\n*              W := W * V1\n*\n               CALL ZTRMM( 'Right', 'Upper', 'No transpose', 'Unit',\n     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )\n*\n*              C1 := C1 - W\n*\n               DO 180 J = 1, K\n                  DO 170 I = 1, LASTC\n                     C( I, J ) = C( I, J ) - WORK( I, J )\n  170             CONTINUE\n  180          CONTINUE\n*\n            END IF\n*\n         ELSE\n*\n*           Let  V =  ( V1  V2 )    (V2: last K columns)\n*           where  V2  is unit lower triangular.\n*\n            IF( LSAME( SIDE, 'L' ) ) THEN\n*\n*              Form  H * C  or  H**H * C  where  C = ( C1 )\n*                                                    ( C2 )\n*\n               LASTV = MAX( K, ILAZLC( K, M, V, LDV ) )\n               LASTC = ILAZLC( LASTV, N, C, LDC )\n*\n*              W := C**H * V**H  =  (C1**H * V1**H + C2**H * V2**H) (stored in WORK)\n*\n*              W := C2**H\n*\n               DO 190 J = 1, K\n                  CALL ZCOPY( LASTC, C( LASTV-K+J, 1 ), LDC,\n     $                 WORK( 1, J ), 1 )\n                  CALL ZLACGV( LASTC, WORK( 1, J ), 1 )\n  190          CONTINUE\n*\n*              W := W * V2**H\n*\n               CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose',\n     $              'Unit', LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,\n     $              WORK, LDWORK )\n               IF( LASTV.GT.K ) THEN\n*\n*                 W := W + C1**H * V1**H\n*\n                  CALL ZGEMM( 'Conjugate transpose',\n     $                 'Conjugate transpose', LASTC, K, LASTV-K,\n     $                 ONE, C, LDC, V, LDV, ONE, WORK, LDWORK )\n               END IF\n*\n*              W := W * T**H  or  W * T\n*\n               CALL ZTRMM( 'Right', 'Lower', TRANST, 'Non-unit',\n     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )\n*\n*              C := C - V**H * W**H\n*\n               IF( LASTV.GT.K ) THEN\n*\n*                 C1 := C1 - V1**H * W**H\n*\n                  CALL ZGEMM( 'Conjugate transpose',\n     $                 'Conjugate transpose', LASTV-K, LASTC, K,\n     $                 -ONE, V, LDV, WORK, LDWORK, ONE, C, LDC )\n               END IF\n*\n*              W := W * V2\n*\n               CALL ZTRMM( 'Right', 'Lower', 'No transpose', 'Unit',\n     $              LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,\n     $              WORK, LDWORK )\n*\n*              C2 := C2 - W**H\n*\n               DO 210 J = 1, K\n                  DO 200 I = 1, LASTC\n                     C( LASTV-K+J, I ) = C( LASTV-K+J, I ) -\n     $                               DCONJG( WORK( I, J ) )\n  200             CONTINUE\n  210          CONTINUE\n*\n            ELSE IF( LSAME( SIDE, 'R' ) ) THEN\n*\n*              Form  C * H  or  C * H**H  where  C = ( C1  C2 )\n*\n               LASTV = MAX( K, ILAZLC( K, N, V, LDV ) )\n               LASTC = ILAZLR( M, LASTV, C, LDC )\n*\n*              W := C * V**H  =  (C1*V1**H + C2*V2**H)  (stored in WORK)\n*\n*              W := C2\n*\n               DO 220 J = 1, K\n                  CALL ZCOPY( LASTC, C( 1, LASTV-K+J ), 1,\n     $                 WORK( 1, J ), 1 )\n  220          CONTINUE\n*\n*              W := W * V2**H\n*\n               CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose',\n     $              'Unit', LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,\n     $              WORK, LDWORK )\n               IF( LASTV.GT.K ) THEN\n*\n*                 W := W + C1 * V1**H\n*\n                  CALL ZGEMM( 'No transpose', 'Conjugate transpose',\n     $                 LASTC, K, LASTV-K, ONE, C, LDC, V, LDV, ONE,\n     $                 WORK, LDWORK )\n               END IF\n*\n*              W := W * T  or  W * T**H\n*\n               CALL ZTRMM( 'Right', 'Lower', TRANS, 'Non-unit',\n     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )\n*\n*              C := C - W * V\n*\n               IF( LASTV.GT.K ) THEN\n*\n*                 C1 := C1 - W * V1\n*\n                  CALL ZGEMM( 'No transpose', 'No transpose',\n     $                 LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV,\n     $                 ONE, C, LDC )\n               END IF\n*\n*              W := W * V2\n*\n               CALL ZTRMM( 'Right', 'Lower', 'No transpose', 'Unit',\n     $              LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,\n     $              WORK, LDWORK )\n*\n*              C1 := C1 - W\n*\n               DO 240 J = 1, K\n                  DO 230 I = 1, LASTC\n                     C( I, LASTV-K+J ) = C( I, LASTV-K+J )\n     $                    - WORK( I, J )\n  230             CONTINUE\n  240          CONTINUE\n*\n            END IF\n*\n         END IF\n      END IF\n*\n      RETURN\n*\n*     End of ZLARFB\n*\n      END\n"
  },
  {
    "path": "include/eigen3/lapack/zlarfg.f",
    "content": "*> \\brief \\b ZLARFG\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*> \\htmlonly\n*> Download ZLARFG + dependencies \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlarfg.f\"> \n*> [TGZ]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlarfg.f\"> \n*> [ZIP]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlarfg.f\"> \n*> [TXT]</a>\n*> \\endhtmlonly \n*\n*  Definition:\n*  ===========\n*\n*       SUBROUTINE ZLARFG( N, ALPHA, X, INCX, TAU )\n* \n*       .. Scalar Arguments ..\n*       INTEGER            INCX, N\n*       COMPLEX*16         ALPHA, TAU\n*       ..\n*       .. Array Arguments ..\n*       COMPLEX*16         X( * )\n*       ..\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> ZLARFG generates a complex elementary reflector H of order n, such\n*> that\n*>\n*>       H**H * ( alpha ) = ( beta ),   H**H * H = I.\n*>              (   x   )   (   0  )\n*>\n*> where alpha and beta are scalars, with beta real, and x is an\n*> (n-1)-element complex vector. H is represented in the form\n*>\n*>       H = I - tau * ( 1 ) * ( 1 v**H ) ,\n*>                     ( v )\n*>\n*> where tau is a complex scalar and v is a complex (n-1)-element\n*> vector. Note that H is not hermitian.\n*>\n*> If the elements of x are all zero and alpha is real, then tau = 0\n*> and H is taken to be the unit matrix.\n*>\n*> Otherwise  1 <= real(tau) <= 2  and  abs(tau-1) <= 1 .\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] N\n*> \\verbatim\n*>          N is INTEGER\n*>          The order of the elementary reflector.\n*> \\endverbatim\n*>\n*> \\param[in,out] ALPHA\n*> \\verbatim\n*>          ALPHA is COMPLEX*16\n*>          On entry, the value alpha.\n*>          On exit, it is overwritten with the value beta.\n*> \\endverbatim\n*>\n*> \\param[in,out] X\n*> \\verbatim\n*>          X is COMPLEX*16 array, dimension\n*>                         (1+(N-2)*abs(INCX))\n*>          On entry, the vector x.\n*>          On exit, it is overwritten with the vector v.\n*> \\endverbatim\n*>\n*> \\param[in] INCX\n*> \\verbatim\n*>          INCX is INTEGER\n*>          The increment between elements of X. INCX > 0.\n*> \\endverbatim\n*>\n*> \\param[out] TAU\n*> \\verbatim\n*>          TAU is COMPLEX*16\n*>          The value tau.\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date November 2011\n*\n*> \\ingroup complex16OTHERauxiliary\n*\n*  =====================================================================\n      SUBROUTINE ZLARFG( N, ALPHA, X, INCX, TAU )\n*\n*  -- LAPACK auxiliary routine (version 3.4.0) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     November 2011\n*\n*     .. Scalar Arguments ..\n      INTEGER            INCX, N\n      COMPLEX*16         ALPHA, TAU\n*     ..\n*     .. Array Arguments ..\n      COMPLEX*16         X( * )\n*     ..\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      DOUBLE PRECISION   ONE, ZERO\n      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )\n*     ..\n*     .. Local Scalars ..\n      INTEGER            J, KNT\n      DOUBLE PRECISION   ALPHI, ALPHR, BETA, RSAFMN, SAFMIN, XNORM\n*     ..\n*     .. External Functions ..\n      DOUBLE PRECISION   DLAMCH, DLAPY3, DZNRM2\n      COMPLEX*16         ZLADIV\n      EXTERNAL           DLAMCH, DLAPY3, DZNRM2, ZLADIV\n*     ..\n*     .. Intrinsic Functions ..\n      INTRINSIC          ABS, DBLE, DCMPLX, DIMAG, SIGN\n*     ..\n*     .. External Subroutines ..\n      EXTERNAL           ZDSCAL, ZSCAL\n*     ..\n*     .. Executable Statements ..\n*\n      IF( N.LE.0 ) THEN\n         TAU = ZERO\n         RETURN\n      END IF\n*\n      XNORM = DZNRM2( N-1, X, INCX )\n      ALPHR = DBLE( ALPHA )\n      ALPHI = DIMAG( ALPHA )\n*\n      IF( XNORM.EQ.ZERO .AND. ALPHI.EQ.ZERO ) THEN\n*\n*        H  =  I\n*\n         TAU = ZERO\n      ELSE\n*\n*        general case\n*\n         BETA = -SIGN( DLAPY3( ALPHR, ALPHI, XNORM ), ALPHR )\n         SAFMIN = DLAMCH( 'S' ) / DLAMCH( 'E' )\n         RSAFMN = ONE / SAFMIN\n*\n         KNT = 0\n         IF( ABS( BETA ).LT.SAFMIN ) THEN\n*\n*           XNORM, BETA may be inaccurate; scale X and recompute them\n*\n   10       CONTINUE\n            KNT = KNT + 1\n            CALL ZDSCAL( N-1, RSAFMN, X, INCX )\n            BETA = BETA*RSAFMN\n            ALPHI = ALPHI*RSAFMN\n            ALPHR = ALPHR*RSAFMN\n            IF( ABS( BETA ).LT.SAFMIN )\n     $         GO TO 10\n*\n*           New BETA is at most 1, at least SAFMIN\n*\n            XNORM = DZNRM2( N-1, X, INCX )\n            ALPHA = DCMPLX( ALPHR, ALPHI )\n            BETA = -SIGN( DLAPY3( ALPHR, ALPHI, XNORM ), ALPHR )\n         END IF\n         TAU = DCMPLX( ( BETA-ALPHR ) / BETA, -ALPHI / BETA )\n         ALPHA = ZLADIV( DCMPLX( ONE ), ALPHA-BETA )\n         CALL ZSCAL( N-1, ALPHA, X, INCX )\n*\n*        If ALPHA is subnormal, it may lose relative accuracy\n*\n         DO 20 J = 1, KNT\n            BETA = BETA*SAFMIN\n 20      CONTINUE\n         ALPHA = BETA\n      END IF\n*\n      RETURN\n*\n*     End of ZLARFG\n*\n      END\n"
  },
  {
    "path": "include/eigen3/lapack/zlarft.f",
    "content": "*> \\brief \\b ZLARFT\n*\n*  =========== DOCUMENTATION ===========\n*\n* Online html documentation available at \n*            http://www.netlib.org/lapack/explore-html/ \n*\n*> \\htmlonly\n*> Download ZLARFT + dependencies \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlarft.f\"> \n*> [TGZ]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlarft.f\"> \n*> [ZIP]</a> \n*> <a href=\"http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlarft.f\"> \n*> [TXT]</a>\n*> \\endhtmlonly \n*\n*  Definition:\n*  ===========\n*\n*       SUBROUTINE ZLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )\n* \n*       .. Scalar Arguments ..\n*       CHARACTER          DIRECT, STOREV\n*       INTEGER            K, LDT, LDV, N\n*       ..\n*       .. Array Arguments ..\n*       COMPLEX*16         T( LDT, * ), TAU( * ), V( LDV, * )\n*       ..\n*  \n*\n*> \\par Purpose:\n*  =============\n*>\n*> \\verbatim\n*>\n*> ZLARFT forms the triangular factor T of a complex block reflector H\n*> of order n, which is defined as a product of k elementary reflectors.\n*>\n*> If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular;\n*>\n*> If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular.\n*>\n*> If STOREV = 'C', the vector which defines the elementary reflector\n*> H(i) is stored in the i-th column of the array V, and\n*>\n*>    H  =  I - V * T * V**H\n*>\n*> If STOREV = 'R', the vector which defines the elementary reflector\n*> H(i) is stored in the i-th row of the array V, and\n*>\n*>    H  =  I - V**H * T * V\n*> \\endverbatim\n*\n*  Arguments:\n*  ==========\n*\n*> \\param[in] DIRECT\n*> \\verbatim\n*>          DIRECT is CHARACTER*1\n*>          Specifies the order in which the elementary reflectors are\n*>          multiplied to form the block reflector:\n*>          = 'F': H = H(1) H(2) . . . H(k) (Forward)\n*>          = 'B': H = H(k) . . . H(2) H(1) (Backward)\n*> \\endverbatim\n*>\n*> \\param[in] STOREV\n*> \\verbatim\n*>          STOREV is CHARACTER*1\n*>          Specifies how the vectors which define the elementary\n*>          reflectors are stored (see also Further Details):\n*>          = 'C': columnwise\n*>          = 'R': rowwise\n*> \\endverbatim\n*>\n*> \\param[in] N\n*> \\verbatim\n*>          N is INTEGER\n*>          The order of the block reflector H. N >= 0.\n*> \\endverbatim\n*>\n*> \\param[in] K\n*> \\verbatim\n*>          K is INTEGER\n*>          The order of the triangular factor T (= the number of\n*>          elementary reflectors). K >= 1.\n*> \\endverbatim\n*>\n*> \\param[in] V\n*> \\verbatim\n*>          V is COMPLEX*16 array, dimension\n*>                               (LDV,K) if STOREV = 'C'\n*>                               (LDV,N) if STOREV = 'R'\n*>          The matrix V. See further details.\n*> \\endverbatim\n*>\n*> \\param[in] LDV\n*> \\verbatim\n*>          LDV is INTEGER\n*>          The leading dimension of the array V.\n*>          If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.\n*> \\endverbatim\n*>\n*> \\param[in] TAU\n*> \\verbatim\n*>          TAU is COMPLEX*16 array, dimension (K)\n*>          TAU(i) must contain the scalar factor of the elementary\n*>          reflector H(i).\n*> \\endverbatim\n*>\n*> \\param[out] T\n*> \\verbatim\n*>          T is COMPLEX*16 array, dimension (LDT,K)\n*>          The k by k triangular factor T of the block reflector.\n*>          If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is\n*>          lower triangular. The rest of the array is not used.\n*> \\endverbatim\n*>\n*> \\param[in] LDT\n*> \\verbatim\n*>          LDT is INTEGER\n*>          The leading dimension of the array T. LDT >= K.\n*> \\endverbatim\n*\n*  Authors:\n*  ========\n*\n*> \\author Univ. of Tennessee \n*> \\author Univ. of California Berkeley \n*> \\author Univ. of Colorado Denver \n*> \\author NAG Ltd. \n*\n*> \\date April 2012\n*\n*> \\ingroup complex16OTHERauxiliary\n*\n*> \\par Further Details:\n*  =====================\n*>\n*> \\verbatim\n*>\n*>  The shape of the matrix V and the storage of the vectors which define\n*>  the H(i) is best illustrated by the following example with n = 5 and\n*>  k = 3. The elements equal to 1 are not stored.\n*>\n*>  DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':\n*>\n*>               V = (  1       )                 V = (  1 v1 v1 v1 v1 )\n*>                   ( v1  1    )                     (     1 v2 v2 v2 )\n*>                   ( v1 v2  1 )                     (        1 v3 v3 )\n*>                   ( v1 v2 v3 )\n*>                   ( v1 v2 v3 )\n*>\n*>  DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':\n*>\n*>               V = ( v1 v2 v3 )                 V = ( v1 v1  1       )\n*>                   ( v1 v2 v3 )                     ( v2 v2 v2  1    )\n*>                   (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )\n*>                   (     1 v3 )\n*>                   (        1 )\n*> \\endverbatim\n*>\n*  =====================================================================\n      SUBROUTINE ZLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )\n*\n*  -- LAPACK auxiliary routine (version 3.4.1) --\n*  -- LAPACK is a software package provided by Univ. of Tennessee,    --\n*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--\n*     April 2012\n*\n*     .. Scalar Arguments ..\n      CHARACTER          DIRECT, STOREV\n      INTEGER            K, LDT, LDV, N\n*     ..\n*     .. Array Arguments ..\n      COMPLEX*16         T( LDT, * ), TAU( * ), V( LDV, * )\n*     ..\n*\n*  =====================================================================\n*\n*     .. Parameters ..\n      COMPLEX*16         ONE, ZERO\n      PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ),\n     $                   ZERO = ( 0.0D+0, 0.0D+0 ) )\n*     ..\n*     .. Local Scalars ..\n      INTEGER            I, J, PREVLASTV, LASTV\n*     ..\n*     .. External Subroutines ..\n      EXTERNAL           ZGEMV, ZLACGV, ZTRMV\n*     ..\n*     .. External Functions ..\n      LOGICAL            LSAME\n      EXTERNAL           LSAME\n*     ..\n*     .. Executable Statements ..\n*\n*     Quick return if possible\n*\n      IF( N.EQ.0 )\n     $   RETURN\n*\n      IF( LSAME( DIRECT, 'F' ) ) THEN\n         PREVLASTV = N\n         DO I = 1, K\n            PREVLASTV = MAX( PREVLASTV, I )\n            IF( TAU( I ).EQ.ZERO ) THEN\n*\n*              H(i)  =  I\n*\n               DO J = 1, I\n                  T( J, I ) = ZERO\n               END DO\n            ELSE\n*\n*              general case\n*\n               IF( LSAME( STOREV, 'C' ) ) THEN\n*                 Skip any trailing zeros.\n                  DO LASTV = N, I+1, -1\n                     IF( V( LASTV, I ).NE.ZERO ) EXIT\n                  END DO\n                  DO J = 1, I-1\n                     T( J, I ) = -TAU( I ) * CONJG( V( I , J ) )\n                  END DO                     \n                  J = MIN( LASTV, PREVLASTV )\n*\n*                 T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**H * V(i:j,i)\n*\n                  CALL ZGEMV( 'Conjugate transpose', J-I, I-1,\n     $                        -TAU( I ), V( I+1, 1 ), LDV, \n     $                        V( I+1, I ), 1, ONE, T( 1, I ), 1 )\n               ELSE\n*                 Skip any trailing zeros.\n                  DO LASTV = N, I+1, -1\n                     IF( V( I, LASTV ).NE.ZERO ) EXIT\n                  END DO\n                  DO J = 1, I-1\n                     T( J, I ) = -TAU( I ) * V( J , I )\n                  END DO                     \n                  J = MIN( LASTV, PREVLASTV )\n*\n*                 T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**H\n*\n                  CALL ZGEMM( 'N', 'C', I-1, 1, J-I, -TAU( I ),\n     $                        V( 1, I+1 ), LDV, V( I, I+1 ), LDV,\n     $                        ONE, T( 1, I ), LDT )                  \n               END IF\n*\n*              T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i)\n*\n               CALL ZTRMV( 'Upper', 'No transpose', 'Non-unit', I-1, T,\n     $                     LDT, T( 1, I ), 1 )\n               T( I, I ) = TAU( I )\n               IF( I.GT.1 ) THEN\n                  PREVLASTV = MAX( PREVLASTV, LASTV )\n               ELSE\n                  PREVLASTV = LASTV\n               END IF\n             END IF\n         END DO\n      ELSE\n         PREVLASTV = 1\n         DO I = K, 1, -1\n            IF( TAU( I ).EQ.ZERO ) THEN\n*\n*              H(i)  =  I\n*\n               DO J = I, K\n                  T( J, I ) = ZERO\n               END DO\n            ELSE\n*\n*              general case\n*\n               IF( I.LT.K ) THEN\n                  IF( LSAME( STOREV, 'C' ) ) THEN\n*                    Skip any leading zeros.\n                     DO LASTV = 1, I-1\n                        IF( V( LASTV, I ).NE.ZERO ) EXIT\n                     END DO\n                     DO J = I+1, K\n                        T( J, I ) = -TAU( I ) * CONJG( V( N-K+I , J ) )\n                     END DO                        \n                     J = MAX( LASTV, PREVLASTV )\n*\n*                    T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**H * V(j:n-k+i,i)\n*\n                     CALL ZGEMV( 'Conjugate transpose', N-K+I-J, K-I,\n     $                           -TAU( I ), V( J, I+1 ), LDV, V( J, I ),\n     $                           1, ONE, T( I+1, I ), 1 )\n                  ELSE\n*                    Skip any leading zeros.\n                     DO LASTV = 1, I-1\n                        IF( V( I, LASTV ).NE.ZERO ) EXIT\n                     END DO\n                     DO J = I+1, K\n                        T( J, I ) = -TAU( I ) * V( J, N-K+I )\n                     END DO                                           \n                     J = MAX( LASTV, PREVLASTV )\n*\n*                    T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**H\n*\n                     CALL ZGEMM( 'N', 'C', K-I, 1, N-K+I-J, -TAU( I ),\n     $                           V( I+1, J ), LDV, V( I, J ), LDV,\n     $                           ONE, T( I+1, I ), LDT )                     \n                  END IF\n*\n*                 T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i)\n*\n                  CALL ZTRMV( 'Lower', 'No transpose', 'Non-unit', K-I,\n     $                        T( I+1, I+1 ), LDT, T( I+1, I ), 1 )\n                  IF( I.GT.1 ) THEN\n                     PREVLASTV = MIN( PREVLASTV, LASTV )\n                  ELSE\n                     PREVLASTV = LASTV\n                  END IF\n               END IF\n               T( I, I ) = TAU( I )\n            END IF\n         END DO\n      END IF\n      RETURN\n*\n*     End of ZLARFT\n*\n      END\n"
  },
  {
    "path": "include/eigen3/scripts/CMakeLists.txt",
    "content": "get_property(EIGEN_TESTS_LIST GLOBAL PROPERTY EIGEN_TESTS_LIST)\nconfigure_file(buildtests.in ${CMAKE_BINARY_DIR}/buildtests.sh @ONLY)\n\nconfigure_file(check.in ${CMAKE_BINARY_DIR}/check.sh COPYONLY)\nconfigure_file(debug.in ${CMAKE_BINARY_DIR}/debug.sh COPYONLY)\nconfigure_file(release.in ${CMAKE_BINARY_DIR}/release.sh COPYONLY)\n"
  },
  {
    "path": "include/eigen3/scripts/buildtests.in",
    "content": "#!/bin/bash\n\nif [[ $# != 1 || $1 == *help ]]\nthen\n  echo \"usage: $0 regexp\"\n  echo \"  Builds tests matching the regexp.\"\n  echo \"  The EIGEN_MAKE_ARGS environment variable allows to pass args to 'make'.\"\n  echo \"    For example, to launch 5 concurrent builds, use EIGEN_MAKE_ARGS='-j5'\"\n  exit 0\nfi\n\nTESTSLIST=\"@EIGEN_TESTS_LIST@\"\ntargets_to_make=`echo \"$TESTSLIST\" | egrep \"$1\" | xargs echo`\n\nif [ -n \"${EIGEN_MAKE_ARGS:+x}\" ]\nthen\n  @CMAKE_MAKE_PROGRAM@ $targets_to_make ${EIGEN_MAKE_ARGS}\nelse\n  @CMAKE_MAKE_PROGRAM@ $targets_to_make @EIGEN_TEST_BUILD_FLAGS@\nfi\nexit $?\n\n"
  },
  {
    "path": "include/eigen3/scripts/cdashtesting.cmake.in",
    "content": "\nset(CTEST_SOURCE_DIRECTORY  \"@CMAKE_SOURCE_DIR@\")\nset(CTEST_BINARY_DIRECTORY  \"@CMAKE_BINARY_DIR@\")\nset(CTEST_CMAKE_GENERATOR   \"@CMAKE_GENERATOR@\")\nset(CTEST_BUILD_NAME        \"@BUILDNAME@\")\nset(CTEST_SITE              \"@SITE@\")\n\nset(MODEL Experimental)\nif(${CTEST_SCRIPT_ARG} MATCHES Nightly)\n  set(MODEL Nightly)\nelseif(${CTEST_SCRIPT_ARG} MATCHES Continuous)\n  set(MODEL Continuous)\nendif()\n\nfind_program(CTEST_HG_COMMAND NAMES hg)\nset(CTEST_UPDATE_COMMAND \"${CTEST_HG_COMMAND}\")\n\nctest_start(${MODEL} ${CTEST_SOURCE_DIRECTORY} ${CTEST_BINARY_DIRECTORY})\n\nctest_update(SOURCE \"${CTEST_SOURCE_DIRECTORY}\")\nctest_submit(PARTS Update Notes)\n\n# to get CTEST_PROJECT_SUBPROJECTS definition:\ninclude(\"${CTEST_SOURCE_DIRECTORY}/CTestConfig.cmake\")\n\nforeach(subproject ${CTEST_PROJECT_SUBPROJECTS})\n  message(\"\")\n  message(\"Process ${subproject}\")\n  \n  set_property(GLOBAL PROPERTY SubProject ${subproject})\n  set_property(GLOBAL PROPERTY Label ${subproject})\n\n  ctest_configure(BUILD ${CTEST_BINARY_DIRECTORY} SOURCE ${CTEST_SOURCE_DIRECTORY} )\n  ctest_submit(PARTS Configure)\n\n  set(CTEST_BUILD_TARGET \"Build${subproject}\")\n  message(\"Build ${CTEST_BUILD_TARGET}\")\n  ctest_build(BUILD \"${CTEST_BINARY_DIRECTORY}\" APPEND)\n  # builds target ${CTEST_BUILD_TARGET}\n  ctest_submit(PARTS Build)\n\n  ctest_test(BUILD \"${CTEST_BINARY_DIRECTORY}\" INCLUDE_LABEL \"${subproject}\" )\n  # runs only tests that have a LABELS property matching \"${subproject}\"\n  \n  ctest_coverage(BUILD \"${CTEST_BINARY_DIRECTORY}\" LABELS \"${subproject}\" )\n  \n  ctest_submit(PARTS Test)\n  \nendforeach()\n"
  },
  {
    "path": "include/eigen3/scripts/check.in",
    "content": "#!/bin/bash\n# check : shorthand for make and ctest -R\n\nif [[ $# != 1 || $1 == *help ]]\nthen\n  echo \"usage: $0 regexp\"\n  echo \"  Builds and runs tests matching the regexp.\"\n  echo \"  The EIGEN_MAKE_ARGS environment variable allows to pass args to 'make'.\"\n  echo \"    For example, to launch 5 concurrent builds, use EIGEN_MAKE_ARGS='-j5'\"\n  echo \"  The EIGEN_CTEST_ARGS environment variable allows to pass args to 'ctest'.\"\n  echo \"    For example, with CTest 2.8, you can use EIGEN_CTEST_ARGS='-j5'.\"\n  exit 0\nfi\n\nif [ -n \"${EIGEN_CTEST_ARGS:+x}\" ]\nthen\n  ./buildtests.sh \"$1\" && ctest -R \"$1\" ${EIGEN_CTEST_ARGS}\nelse\n  ./buildtests.sh \"$1\" && ctest -R \"$1\"\nfi\nexit $?\n"
  },
  {
    "path": "include/eigen3/scripts/debug.in",
    "content": "#!/bin/sh\n\ncmake -DCMAKE_BUILD_TYPE=Debug .\n"
  },
  {
    "path": "include/eigen3/scripts/eigen_gen_credits.cpp",
    "content": "#include <string>\n#include <sstream>\n#include <iostream>\n#include <fstream>\n#include <iomanip>\n#include <map>\n#include <list>\n\nusing namespace std;\n\n// this function takes a line that may contain a name and/or email address,\n// and returns just the name, while fixing the \"bad cases\".\nstd::string contributor_name(const std::string& line)\n{\n  string result;\n\n  // let's first take care of the case of isolated email addresses, like\n  // \"user@localhost.localdomain\" entries\n  if(line.find(\"markb@localhost.localdomain\") != string::npos)\n  {\n    return \"Mark Borgerding\";\n  }\n\n  if(line.find(\"kayhman@contact.intra.cea.fr\") != string::npos)\n  {\n    return \"Guillaume Saupin\";\n  }\n\n  // from there on we assume that we have a entry of the form\n  // either:\n  //   Bla bli Blurp\n  // or:\n  //   Bla bli Blurp <bblurp@email.com>\n  \n  size_t position_of_email_address = line.find_first_of('<');\n  if(position_of_email_address != string::npos)\n  {\n    // there is an e-mail address in <...>.\n    \n    // Hauke once committed as \"John Smith\", fix that.\n    if(line.find(\"hauke.heibel\") != string::npos)\n      result = \"Hauke Heibel\";\n    else\n    {\n      // just remove the e-mail address\n      result = line.substr(0, position_of_email_address);\n    }\n  }\n  else\n  {\n    // there is no e-mail address in <...>.\n    \n    if(line.find(\"convert-repo\") != string::npos)\n      result = \"\";\n    else\n      result = line;\n  }\n\n  // remove trailing spaces\n  size_t length = result.length();\n  while(length >= 1 && result[length-1] == ' ') result.erase(--length);\n\n  return result;\n}\n\n// parses hg churn output to generate a contributors map.\nmap<string,int> contributors_map_from_churn_output(const char *filename)\n{\n  map<string,int> contributors_map;\n\n  string line;\n  ifstream churn_out;\n  churn_out.open(filename, ios::in);\n  while(!getline(churn_out,line).eof())\n  {\n    // remove the histograms \"******\" that hg churn may draw at the end of some lines\n    size_t first_star = line.find_first_of('*');\n    if(first_star != string::npos) line.erase(first_star);\n    \n    // remove trailing spaces\n    size_t length = line.length();\n    while(length >= 1 && line[length-1] == ' ') line.erase(--length);\n\n    // now the last space indicates where the number starts\n    size_t last_space = line.find_last_of(' ');\n    \n    // get the number (of changesets or of modified lines for each contributor)\n    int number;\n    istringstream(line.substr(last_space+1)) >> number;\n\n    // get the name of the contributor\n    line.erase(last_space);    \n    string name = contributor_name(line);\n    \n    map<string,int>::iterator it = contributors_map.find(name);\n    // if new contributor, insert\n    if(it == contributors_map.end())\n      contributors_map.insert(pair<string,int>(name, number));\n    // if duplicate, just add the number\n    else\n      it->second += number;\n  }\n  churn_out.close();\n\n  return contributors_map;\n}\n\n// find the last name, i.e. the last word.\n// for \"van den Schbling\" types of last names, that's not a problem, that's actually what we want.\nstring lastname(const string& name)\n{\n  size_t last_space = name.find_last_of(' ');\n  if(last_space >= name.length()-1) return name;\n  else return name.substr(last_space+1);\n}\n\nstruct contributor\n{\n  string name;\n  int changedlines;\n  int changesets;\n  string url;\n  string misc;\n  \n  contributor() : changedlines(0), changesets(0) {}\n  \n  bool operator < (const contributor& other)\n  {\n    return lastname(name).compare(lastname(other.name)) < 0;\n  }\n};\n\nvoid add_online_info_into_contributors_list(list<contributor>& contributors_list, const char *filename)\n{\n  string line;\n  ifstream online_info;\n  online_info.open(filename, ios::in);\n  while(!getline(online_info,line).eof())\n  {\n    string hgname, realname, url, misc;\n    \n    size_t last_bar = line.find_last_of('|');\n    if(last_bar == string::npos) continue;\n    if(last_bar < line.length())\n      misc = line.substr(last_bar+1);\n    line.erase(last_bar);\n    \n    last_bar = line.find_last_of('|');\n    if(last_bar == string::npos) continue;\n    if(last_bar < line.length())\n      url = line.substr(last_bar+1);\n    line.erase(last_bar);\n\n    last_bar = line.find_last_of('|');\n    if(last_bar == string::npos) continue;\n    if(last_bar < line.length())\n      realname = line.substr(last_bar+1);\n    line.erase(last_bar);\n\n    hgname = line;\n    \n    // remove the example line\n    if(hgname.find(\"MercurialName\") != string::npos) continue;\n    \n    list<contributor>::iterator it;\n    for(it=contributors_list.begin(); it != contributors_list.end() && it->name != hgname; ++it)\n    {}\n    \n    if(it == contributors_list.end())\n    {\n      contributor c;\n      c.name = realname;\n      c.url = url;\n      c.misc = misc;\n      contributors_list.push_back(c);\n    }\n    else\n    {\n      it->name = realname;\n      it->url = url;\n      it->misc = misc;\n    }\n  }\n}\n\nint main()\n{\n  // parse the hg churn output files\n  map<string,int> contributors_map_for_changedlines = contributors_map_from_churn_output(\"churn-changedlines.out\");\n  //map<string,int> contributors_map_for_changesets = contributors_map_from_churn_output(\"churn-changesets.out\");\n  \n  // merge into the contributors list\n  list<contributor> contributors_list;\n  map<string,int>::iterator it;\n  for(it=contributors_map_for_changedlines.begin(); it != contributors_map_for_changedlines.end(); ++it)\n  {\n    contributor c;\n    c.name = it->first;\n    c.changedlines = it->second;\n    c.changesets = 0; //contributors_map_for_changesets.find(it->first)->second;\n    contributors_list.push_back(c);\n  }\n  \n  add_online_info_into_contributors_list(contributors_list, \"online-info.out\");\n  \n  contributors_list.sort();\n  \n  cout << \"{| cellpadding=\\\"5\\\"\\n\";\n  cout << \"!\\n\";\n  cout << \"! Lines changed\\n\";\n  cout << \"!\\n\";\n\n  list<contributor>::iterator itc;\n  int i = 0;\n  for(itc=contributors_list.begin(); itc != contributors_list.end(); ++itc)\n  {\n    if(itc->name.length() == 0) continue;\n    if(i%2) cout << \"|-\\n\";\n    else cout << \"|- style=\\\"background:#FFFFD0\\\"\\n\";\n    if(itc->url.length())\n      cout << \"| [\" << itc->url << \" \" << itc->name << \"]\\n\";\n    else\n      cout << \"| \" << itc->name << \"\\n\";\n    if(itc->changedlines)\n      cout << \"| \" << itc->changedlines << \"\\n\";\n    else\n      cout << \"| (no information)\\n\";\n    cout << \"| \" << itc->misc << \"\\n\";\n    i++;\n  }\n  cout << \"|}\" << endl;\n}\n"
  },
  {
    "path": "include/eigen3/scripts/eigen_gen_docs",
    "content": "#!/bin/sh\n\n# configuration\n# You should call this script with USER set as you want, else some default\n# will be used\nUSER=${USER:-'orzel'}\nUPLOAD_DIR=dox-devel\n\n#ulimit -v 1024000\n\n# step 1 : build\nrm build/doc/html -Rf\nmkdir build -p\n(cd build && cmake .. && make doc) || { echo \"make failed\"; exit 1; }\n\n#step 2 : upload\n# (the '/' at the end of path is very important, see rsync documentation)\nrsync -az --no-p --delete build/doc/html/ $USER@ssh.tuxfamily.org:eigen/eigen.tuxfamily.org-web/htdocs/$UPLOAD_DIR/ || { echo \"upload failed\"; exit 1; }\n\n#step 3 : fix the perm\nssh $USER@ssh.tuxfamily.org \"chmod -R g+w /home/eigen/eigen.tuxfamily.org-web/htdocs/$UPLOAD_DIR\" || { echo \"perm failed\"; exit 1; }\n\necho \"Uploaded successfully\"\n\n"
  },
  {
    "path": "include/eigen3/scripts/release.in",
    "content": "#!/bin/sh\n\ncmake -DCMAKE_BUILD_TYPE=Release .\n"
  },
  {
    "path": "include/eigen3/scripts/relicense.py",
    "content": "# This file is part of Eigen, a lightweight C++ template library\n# for linear algebra.\n#\n# Copyright (C) 2012 Keir Mierle <mierle@gmail.com>\n#\n# This Source Code Form is subject to the terms of the Mozilla\n# Public License v. 2.0. If a copy of the MPL was not distributed\n# with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n#\n# Author: mierle@gmail.com (Keir Mierle)\n#\n# Make the long-awaited conversion to MPL.\n\nlgpl3_header = '''\n// Eigen is free software; you can redistribute it and/or\n// modify it under the terms of the GNU Lesser General Public\n// License as published by the Free Software Foundation; either\n// version 3 of the License, or (at your option) any later version.\n//\n// Alternatively, you can redistribute it and/or\n// modify it under the terms of the GNU General Public License as\n// published by the Free Software Foundation; either version 2 of\n// the License, or (at your option) any later version.\n//\n// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY\n// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS\n// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the\n// GNU General Public License for more details.\n//\n// You should have received a copy of the GNU Lesser General Public\n// License and a copy of the GNU General Public License along with\n// Eigen. If not, see <http://www.gnu.org/licenses/>.\n'''\n\nmpl2_header = \"\"\"\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\"\"\"\n\nimport os\nimport sys\n\nexclusions = set(['relicense.py'])\n\ndef update(text):\n  if text.find(lgpl3_header) == -1:\n    return text, False\n  return text.replace(lgpl3_header, mpl2_header), True\n\nrootdir = sys.argv[1]\nfor root, sub_folders, files in os.walk(rootdir):\n    for basename in files:\n        if basename in exclusions:\n          print 'SKIPPED', filename\n          continue\n        filename = os.path.join(root, basename)\n        fo = file(filename)\n        text = fo.read()\n        fo.close()\n\n        text, updated = update(text)\n        if updated:\n          fo = file(filename, \"w\")\n          fo.write(text)\n          fo.close()\n          print 'UPDATED', filename\n        else:\n          print '       ', filename\n"
  },
  {
    "path": "include/eigen3/signature_of_eigen3_matrix_library",
    "content": "This file is just there as a signature to help identify directories containing Eigen3. When writing a script looking for Eigen3, just look for this file. This is especially useful to help disambiguate with Eigen2...\n"
  },
  {
    "path": "include/eigen3/test/CMakeLists.txt",
    "content": "# generate split test header file only if it does not yet exist\n# in order to prevent a rebuild everytime cmake is configured\nif(NOT EXISTS ${CMAKE_CURRENT_BINARY_DIR}/split_test_helper.h)  \n  file(WRITE ${CMAKE_CURRENT_BINARY_DIR}/split_test_helper.h \"\")\n  foreach(i RANGE 1 999)\n    file(APPEND ${CMAKE_CURRENT_BINARY_DIR}/split_test_helper.h\n      \"#ifdef EIGEN_TEST_PART_${i}\\n\"\n      \"#define CALL_SUBTEST_${i}(FUNC) CALL_SUBTEST(FUNC)\\n\"\n      \"#else\\n\"\n      \"#define CALL_SUBTEST_${i}(FUNC)\\n\"\n      \"#endif\\n\\n\"\n    )\n  endforeach()\nendif()\n\n# check if we have a Fortran compiler\ninclude(\"../cmake/language_support.cmake\")\n\nworkaround_9220(Fortran EIGEN_Fortran_COMPILER_WORKS)\n\nif(EIGEN_Fortran_COMPILER_WORKS)\n  enable_language(Fortran OPTIONAL)\n  if(NOT CMAKE_Fortran_COMPILER)\n    set(EIGEN_Fortran_COMPILER_WORKS OFF)\n  endif()\nendif()\n\nif(NOT EIGEN_Fortran_COMPILER_WORKS)\n  # search for a default Lapack library to complete Eigen's one\n  find_package(LAPACK QUIET)\nendif()\n\n# configure blas/lapack (use Eigen's ones)\nset(EIGEN_BLAS_LIBRARIES eigen_blas)\nset(EIGEN_LAPACK_LIBRARIES eigen_lapack)\n\nset(EIGEN_TEST_MATRIX_DIR \"\" CACHE STRING \"Enable testing of realword sparse matrices contained in the specified path\")\nif(EIGEN_TEST_MATRIX_DIR)\n  if(NOT WIN32)\n    message(STATUS \"Test realworld sparse matrices: ${EIGEN_TEST_MATRIX_DIR}\")\n    add_definitions( -DTEST_REAL_CASES=\"${EIGEN_TEST_MATRIX_DIR}\" )\n  else(NOT WIN32)\n    message(STATUS \"REAL CASES CAN NOT BE CURRENTLY TESTED ON WIN32\")\n  endif(NOT WIN32)\nendif(EIGEN_TEST_MATRIX_DIR)\n\nset(SPARSE_LIBS \" \")\n\nfind_package(Cholmod)\nif(CHOLMOD_FOUND)\n  add_definitions(\"-DEIGEN_CHOLMOD_SUPPORT\")\n  include_directories(${CHOLMOD_INCLUDES})\n  set(SPARSE_LIBS ${SPARSE_LIBS} ${CHOLMOD_LIBRARIES} ${EIGEN_BLAS_LIBRARIES} ${EIGEN_LAPACK_LIBRARIES})\n  set(CHOLMOD_ALL_LIBS  ${CHOLMOD_LIBRARIES} ${EIGEN_BLAS_LIBRARIES} ${EIGEN_LAPACK_LIBRARIES})\n  ei_add_property(EIGEN_TESTED_BACKENDS \"Cholmod, \")\nelse()\n  ei_add_property(EIGEN_MISSING_BACKENDS \"Cholmod, \")\nendif()\n\nfind_package(Umfpack)\nif(UMFPACK_FOUND)\n  add_definitions(\"-DEIGEN_UMFPACK_SUPPORT\")\n  include_directories(${UMFPACK_INCLUDES})\n  set(SPARSE_LIBS ${SPARSE_LIBS} ${UMFPACK_LIBRARIES} ${EIGEN_BLAS_LIBRARIES})\n  set(UMFPACK_ALL_LIBS ${UMFPACK_LIBRARIES} ${EIGEN_BLAS_LIBRARIES})\n  ei_add_property(EIGEN_TESTED_BACKENDS \"UmfPack, \")\nelse()\n  ei_add_property(EIGEN_MISSING_BACKENDS \"UmfPack, \")\nendif()\n\nfind_package(SuperLU 4.0)\nif(SUPERLU_FOUND)\n  add_definitions(\"-DEIGEN_SUPERLU_SUPPORT\")\n  include_directories(${SUPERLU_INCLUDES})\n  set(SPARSE_LIBS ${SPARSE_LIBS} ${SUPERLU_LIBRARIES} ${EIGEN_BLAS_LIBRARIES})\n  set(SUPERLU_ALL_LIBS ${SUPERLU_LIBRARIES} ${EIGEN_BLAS_LIBRARIES})\n  ei_add_property(EIGEN_TESTED_BACKENDS  \"SuperLU, \")\nelse()\n  ei_add_property(EIGEN_MISSING_BACKENDS  \"SuperLU, \")\nendif()\n\n\nfind_package(PASTIX QUIET COMPONENTS METIS SCOTCH)\n# check that the PASTIX found is a version without MPI\nfind_path(PASTIX_pastix_nompi.h_INCLUDE_DIRS\n  NAMES pastix_nompi.h\n  HINTS ${PASTIX_INCLUDE_DIRS}\n)\nif (NOT PASTIX_pastix_nompi.h_INCLUDE_DIRS)\n  message(STATUS \"A version of Pastix has been found but pastix_nompi.h does not exist in the include directory.\"\n                 \" Because Eigen tests require a version without MPI, we disable the Pastix backend.\")\nendif()\nif(PASTIX_FOUND AND PASTIX_pastix_nompi.h_INCLUDE_DIRS)\n  add_definitions(\"-DEIGEN_PASTIX_SUPPORT\")\n  include_directories(${PASTIX_INCLUDE_DIRS_DEP})\n  if(SCOTCH_FOUND)\n    include_directories(${SCOTCH_INCLUDE_DIRS})\n    set(PASTIX_LIBRARIES ${PASTIX_LIBRARIES} ${SCOTCH_LIBRARIES})\n  elseif(METIS_FOUND)\n    include_directories(${METIS_INCLUDE_DIRS})\n    set(PASTIX_LIBRARIES ${PASTIX_LIBRARIES} ${METIS_LIBRARIES})\n  else(SCOTCH_FOUND)\n    ei_add_property(EIGEN_MISSING_BACKENDS  \"PaStiX, \")\n  endif(SCOTCH_FOUND)\n  set(SPARSE_LIBS ${SPARSE_LIBS} ${PASTIX_LIBRARIES_DEP} ${ORDERING_LIBRARIES})\n  set(PASTIX_ALL_LIBS ${PASTIX_LIBRARIES_DEP})\n  ei_add_property(EIGEN_TESTED_BACKENDS  \"PaStiX, \")\nelse()\n  ei_add_property(EIGEN_MISSING_BACKENDS  \"PaStiX, \")\nendif()\n\nif(METIS_FOUND)\n  add_definitions(\"-DEIGEN_METIS_SUPPORT\")\n  include_directories(${METIS_INCLUDE_DIRS})\n  ei_add_property(EIGEN_TESTED_BACKENDS \"METIS, \")\nelse()\n  ei_add_property(EIGEN_MISSING_BACKENDS \"METIS, \")\nendif()\n\nfind_package(SPQR)\nif(SPQR_FOUND AND CHOLMOD_FOUND AND (EIGEN_Fortran_COMPILER_WORKS OR LAPACK_FOUND) )\n  add_definitions(\"-DEIGEN_SPQR_SUPPORT\")\n  include_directories(${SPQR_INCLUDES})\n  set(SPQR_ALL_LIBS ${SPQR_LIBRARIES} ${CHOLMOD_LIBRARIES} ${EIGEN_LAPACK_LIBRARIES} ${EIGEN_BLAS_LIBRARIES} ${LAPACK_LIBRARIES})\n  set(SPARSE_LIBS ${SPARSE_LIBS} ${SPQR_ALL_LIBS})\n  ei_add_property(EIGEN_TESTED_BACKENDS \"SPQR, \")\nelse()\n  ei_add_property(EIGEN_MISSING_BACKENDS \"SPQR, \")\nendif()\n\noption(EIGEN_TEST_NOQT \"Disable Qt support in unit tests\" OFF)\nif(NOT EIGEN_TEST_NOQT)\n  find_package(Qt4)\n  if(QT4_FOUND)\n    include(${QT_USE_FILE})\n    ei_add_property(EIGEN_TESTED_BACKENDS  \"Qt4 support, \")\n  else()\n    ei_add_property(EIGEN_MISSING_BACKENDS  \"Qt4 support, \")\n  endif()\nendif(NOT EIGEN_TEST_NOQT)\n\nif(TEST_LIB)\n  add_definitions(\"-DEIGEN_EXTERN_INSTANTIATIONS=1\")\nendif(TEST_LIB)\n\nset_property(GLOBAL PROPERTY EIGEN_CURRENT_SUBPROJECT \"Official\")\nadd_custom_target(BuildOfficial)\n\nei_add_test(rand)\nei_add_test(meta)\nei_add_test(numext)\nei_add_test(sizeof)\nei_add_test(dynalloc)\nei_add_test(nomalloc)\nei_add_test(first_aligned)\nei_add_test(nullary)\nei_add_test(mixingtypes)\nei_add_test(packetmath \"-DEIGEN_FAST_MATH=1\")\nei_add_test(unalignedassert)\nei_add_test(vectorization_logic)\nei_add_test(basicstuff)\nei_add_test(constructor)\nei_add_test(linearstructure)\nei_add_test(integer_types)\nei_add_test(unalignedcount)\nif(NOT EIGEN_TEST_NO_EXCEPTIONS)\n  ei_add_test(exceptions)\nendif()\nei_add_test(redux)\nei_add_test(visitor)\nei_add_test(block)\nei_add_test(corners)\nei_add_test(swap)\nei_add_test(resize)\nei_add_test(conservative_resize)\nei_add_test(product_small)\nei_add_test(product_large)\nei_add_test(product_extra)\nei_add_test(diagonalmatrices)\nei_add_test(adjoint)\nei_add_test(diagonal)\nei_add_test(miscmatrices)\nei_add_test(commainitializer)\nei_add_test(smallvectors)\nei_add_test(mapped_matrix)\nei_add_test(mapstride)\nei_add_test(mapstaticmethods)\nei_add_test(array)\nei_add_test(array_for_matrix)\nei_add_test(array_replicate)\nei_add_test(array_reverse)\nei_add_test(ref)\nei_add_test(is_same_dense)\nei_add_test(triangular)\nei_add_test(selfadjoint)\nei_add_test(product_selfadjoint)\nei_add_test(product_symm)\nei_add_test(product_syrk)\nei_add_test(product_trmv)\nei_add_test(product_trmm)\nei_add_test(product_trsolve)\nei_add_test(product_mmtr)\nei_add_test(product_notemporary)\nei_add_test(stable_norm)\nei_add_test(permutationmatrices)\nei_add_test(bandmatrix)\nei_add_test(cholesky)\nei_add_test(lu)\nei_add_test(determinant)\nei_add_test(inverse)\nei_add_test(qr)\nei_add_test(qr_colpivoting)\nei_add_test(qr_fullpivoting)\nei_add_test(upperbidiagonalization)\nei_add_test(hessenberg)\nei_add_test(schur_real)\nei_add_test(schur_complex)\nei_add_test(eigensolver_selfadjoint)\nei_add_test(eigensolver_generic)\nei_add_test(eigensolver_complex)\nei_add_test(real_qz)\nei_add_test(eigensolver_generalized_real)\nei_add_test(jacobi)\nei_add_test(jacobisvd)\nei_add_test(bdcsvd)\nei_add_test(householder)\nei_add_test(geo_orthomethods)\nei_add_test(geo_quaternion)\nei_add_test(geo_eulerangles)\nei_add_test(geo_parametrizedline)\nei_add_test(geo_alignedbox)\nei_add_test(geo_hyperplane)\nei_add_test(geo_transformations)\nei_add_test(geo_homogeneous)\nei_add_test(stdvector)\nei_add_test(stdvector_overload)\nei_add_test(stdlist)\nei_add_test(stdlist_overload)\nei_add_test(stddeque)\nei_add_test(stddeque_overload)\nei_add_test(sparse_basic)\nei_add_test(sparse_block)\nei_add_test(sparse_vector)\nei_add_test(sparse_product)\nei_add_test(sparse_ref)\nei_add_test(sparse_solvers)\nei_add_test(sparse_permutations)\nei_add_test(simplicial_cholesky)\nei_add_test(conjugate_gradient)\nei_add_test(incomplete_cholesky)\nei_add_test(bicgstab)\nei_add_test(lscg)\nei_add_test(sparselu)\nei_add_test(sparseqr)\nei_add_test(umeyama)\nei_add_test(nesting_ops \"${CMAKE_CXX_FLAGS_DEBUG}\")\nei_add_test(zerosized)\nei_add_test(dontalign)\nei_add_test(evaluators)\nif(NOT EIGEN_TEST_NO_EXCEPTIONS)\n  ei_add_test(sizeoverflow)\nendif()\nei_add_test(prec_inverse_4x4)\nei_add_test(vectorwiseop)\nei_add_test(special_numbers)\nei_add_test(rvalue_types)\nei_add_test(dense_storage)\nei_add_test(ctorleak)\nei_add_test(mpl2only)\nei_add_test(inplace_decomposition)\nei_add_test(half_float)\nei_add_test(array_of_string)\n\nadd_executable(bug1213 bug1213.cpp bug1213_main.cpp)\n\ncheck_cxx_compiler_flag(\"-ffast-math\" COMPILER_SUPPORT_FASTMATH)\nif(COMPILER_SUPPORT_FASTMATH)\n  set(EIGEN_FASTMATH_FLAGS \"-ffast-math\")\nelse()\n  check_cxx_compiler_flag(\"/fp:fast\" COMPILER_SUPPORT_FPFAST)\n  if(COMPILER_SUPPORT_FPFAST)\n    set(EIGEN_FASTMATH_FLAGS \"/fp:fast\")\n  endif()\nendif()\n\nei_add_test(fastmath \" ${EIGEN_FASTMATH_FLAGS} \")\n\n# # ei_add_test(denseLM)\n\nif(QT4_FOUND)\n  ei_add_test(qtvector \"\" \"${QT_QTCORE_LIBRARY}\")\nendif(QT4_FOUND)\n\nif(UMFPACK_FOUND)\n  ei_add_test(umfpack_support \"\" \"${UMFPACK_ALL_LIBS}\")\nendif()\n\nif(SUPERLU_FOUND)\n  ei_add_test(superlu_support \"\" \"${SUPERLU_ALL_LIBS}\")\nendif()\n\nif(CHOLMOD_FOUND)\n  ei_add_test(cholmod_support \"\" \"${CHOLMOD_ALL_LIBS}\")\nendif()\n\nif(PARDISO_FOUND)\n  ei_add_test(pardiso_support \"\" \"${PARDISO_ALL_LIBS}\")\nendif()\n\nif(PASTIX_FOUND AND (SCOTCH_FOUND OR METIS_FOUND))\n  ei_add_test(pastix_support \"\" \"${PASTIX_ALL_LIBS}\")\nendif()\n\nif(SPQR_FOUND AND CHOLMOD_FOUND)\n  ei_add_test(spqr_support \"\" \"${SPQR_ALL_LIBS}\")\nendif()\n\nif(METIS_FOUND)\nei_add_test(metis_support \"\" \"${METIS_LIBRARIES}\")\nendif()\n\nstring(TOLOWER \"${CMAKE_CXX_COMPILER}\" cmake_cxx_compiler_tolower)\nif(cmake_cxx_compiler_tolower MATCHES \"qcc\")\n  set(CXX_IS_QCC \"ON\")\nendif()\n\nei_add_property(EIGEN_TESTING_SUMMARY \"CXX:               ${CMAKE_CXX_COMPILER}\\n\")\nif(CMAKE_COMPILER_IS_GNUCXX AND NOT CXX_IS_QCC)\n  execute_process(COMMAND ${CMAKE_CXX_COMPILER} --version COMMAND head -n 1 OUTPUT_VARIABLE EIGEN_CXX_VERSION_STRING OUTPUT_STRIP_TRAILING_WHITESPACE)\n  ei_add_property(EIGEN_TESTING_SUMMARY \"CXX_VERSION:       ${EIGEN_CXX_VERSION_STRING}\\n\")\nendif()\nei_add_property(EIGEN_TESTING_SUMMARY \"CXX_FLAGS:         ${CMAKE_CXX_FLAGS}\\n\")\nei_add_property(EIGEN_TESTING_SUMMARY \"Sparse lib flags:  ${SPARSE_LIBS}\\n\")\n\noption(EIGEN_TEST_EIGEN2 \"Run whole Eigen2 test suite against EIGEN2_SUPPORT\" OFF)\nmark_as_advanced(EIGEN_TEST_EIGEN2)\nif(EIGEN_TEST_EIGEN2)\n  message(WARNING \"The Eigen2 test suite has been removed\")\nendif()\n\n# boost MP unit test\nfind_package(Boost)\nif(Boost_FOUND)\n  include_directories(${Boost_INCLUDE_DIRS})\n  ei_add_test(boostmultiprec \"\" \"${Boost_LIBRARIES}\")\n  ei_add_property(EIGEN_TESTED_BACKENDS \"Boost.Multiprecision, \")\nelse()\n  ei_add_property(EIGEN_MISSING_BACKENDS \"Boost.Multiprecision, \")\nendif()\n\n\n# CUDA unit tests\noption(EIGEN_TEST_CUDA \"Enable CUDA support in unit tests\" OFF)\noption(EIGEN_TEST_CUDA_CLANG \"Use clang instead of nvcc to compile the CUDA tests\" OFF)\n\nif(EIGEN_TEST_CUDA_CLANG AND NOT CMAKE_CXX_COMPILER MATCHES \"clang\")\n  message(WARNING \"EIGEN_TEST_CUDA_CLANG is set, but CMAKE_CXX_COMPILER does not appear to be clang.\")\nendif()\n\nif(EIGEN_TEST_CUDA)\n\nfind_package(CUDA 5.0)\nif(CUDA_FOUND)\n  \n  set(CUDA_PROPAGATE_HOST_FLAGS OFF)\n  if(\"${CMAKE_CXX_COMPILER_ID}\" STREQUAL \"Clang\") \n    set(CUDA_NVCC_FLAGS \"-ccbin ${CMAKE_C_COMPILER}\" CACHE STRING \"nvcc flags\" FORCE)\n  endif()\n  if(EIGEN_TEST_CUDA_CLANG)\n   set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} -std=c++11 --cuda-gpu-arch=sm_30\")\n  endif()\n  cuda_include_directories(${CMAKE_CURRENT_BINARY_DIR})\n  set(EIGEN_ADD_TEST_FILENAME_EXTENSION  \"cu\")\n  \n  ei_add_test(cuda_basic)\n  \n  unset(EIGEN_ADD_TEST_FILENAME_EXTENSION)\n\nendif(CUDA_FOUND)\n\nendif(EIGEN_TEST_CUDA)\n\n\nfile(MAKE_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}/failtests)    \nadd_test(NAME failtests WORKING_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}/failtests COMMAND ${CMAKE_COMMAND} ${Eigen_SOURCE_DIR} -G \"${CMAKE_GENERATOR}\" -DEIGEN_FAILTEST=ON)\n\noption(EIGEN_TEST_BUILD_DOCUMENTATION \"Test building the doxygen documentation\" OFF)\nIF(EIGEN_TEST_BUILD_DOCUMENTATION)\n  add_dependencies(buildtests doc)\nENDIF()\n"
  },
  {
    "path": "include/eigen3/test/adjoint.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define EIGEN_NO_STATIC_ASSERT\n\n#include \"main.h\"\n\ntemplate<bool IsInteger> struct adjoint_specific;\n\ntemplate<> struct adjoint_specific<true> {\n  template<typename Vec, typename Mat, typename Scalar>\n  static void run(const Vec& v1, const Vec& v2, Vec& v3, const Mat& square, Scalar s1, Scalar s2) {\n    VERIFY(test_isApproxWithRef((s1 * v1 + s2 * v2).dot(v3),     numext::conj(s1) * v1.dot(v3) + numext::conj(s2) * v2.dot(v3), 0));\n    VERIFY(test_isApproxWithRef(v3.dot(s1 * v1 + s2 * v2),       s1*v3.dot(v1)+s2*v3.dot(v2), 0));\n    \n    // check compatibility of dot and adjoint\n    VERIFY(test_isApproxWithRef(v1.dot(square * v2), (square.adjoint() * v1).dot(v2), 0));\n  }\n};\n\ntemplate<> struct adjoint_specific<false> {\n  template<typename Vec, typename Mat, typename Scalar>\n  static void run(const Vec& v1, const Vec& v2, Vec& v3, const Mat& square, Scalar s1, Scalar s2) {\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n    using std::abs;\n    \n    RealScalar ref = NumTraits<Scalar>::IsInteger ? RealScalar(0) : (std::max)((s1 * v1 + s2 * v2).norm(),v3.norm());\n    VERIFY(test_isApproxWithRef((s1 * v1 + s2 * v2).dot(v3),     numext::conj(s1) * v1.dot(v3) + numext::conj(s2) * v2.dot(v3), ref));\n    VERIFY(test_isApproxWithRef(v3.dot(s1 * v1 + s2 * v2),       s1*v3.dot(v1)+s2*v3.dot(v2), ref));\n  \n    VERIFY_IS_APPROX(v1.squaredNorm(),                v1.norm() * v1.norm());\n    // check normalized() and normalize()\n    VERIFY_IS_APPROX(v1, v1.norm() * v1.normalized());\n    v3 = v1;\n    v3.normalize();\n    VERIFY_IS_APPROX(v1, v1.norm() * v3);\n    VERIFY_IS_APPROX(v3, v1.normalized());\n    VERIFY_IS_APPROX(v3.norm(), RealScalar(1));\n\n    // check null inputs\n    VERIFY_IS_APPROX((v1*0).normalized(), (v1*0));\n#if (!EIGEN_ARCH_i386) || defined(EIGEN_VECTORIZE)\n    RealScalar very_small = (std::numeric_limits<RealScalar>::min)();\n    VERIFY( (v1*very_small).norm() == 0 );\n    VERIFY_IS_APPROX((v1*very_small).normalized(), (v1*very_small));\n    v3 = v1*very_small;\n    v3.normalize();\n    VERIFY_IS_APPROX(v3, (v1*very_small));\n#endif\n    \n    // check compatibility of dot and adjoint\n    ref = NumTraits<Scalar>::IsInteger ? 0 : (std::max)((std::max)(v1.norm(),v2.norm()),(std::max)((square * v2).norm(),(square.adjoint() * v1).norm()));\n    VERIFY(internal::isMuchSmallerThan(abs(v1.dot(square * v2) - (square.adjoint() * v1).dot(v2)), ref, test_precision<Scalar>()));\n    \n    // check that Random().normalized() works: tricky as the random xpr must be evaluated by\n    // normalized() in order to produce a consistent result.\n    VERIFY_IS_APPROX(Vec::Random(v1.size()).normalized().norm(), RealScalar(1));\n  }\n};\n\ntemplate<typename MatrixType> void adjoint(const MatrixType& m)\n{\n  /* this test covers the following files:\n     Transpose.h Conjugate.h Dot.h\n  */\n  using std::abs;\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;\n  const Index PacketSize = internal::packet_traits<Scalar>::size;\n  \n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  MatrixType m1 = MatrixType::Random(rows, cols),\n             m2 = MatrixType::Random(rows, cols),\n             m3(rows, cols),\n             square = SquareMatrixType::Random(rows, rows);\n  VectorType v1 = VectorType::Random(rows),\n             v2 = VectorType::Random(rows),\n             v3 = VectorType::Random(rows),\n             vzero = VectorType::Zero(rows);\n\n  Scalar s1 = internal::random<Scalar>(),\n         s2 = internal::random<Scalar>();\n\n  // check basic compatibility of adjoint, transpose, conjugate\n  VERIFY_IS_APPROX(m1.transpose().conjugate().adjoint(),    m1);\n  VERIFY_IS_APPROX(m1.adjoint().conjugate().transpose(),    m1);\n\n  // check multiplicative behavior\n  VERIFY_IS_APPROX((m1.adjoint() * m2).adjoint(),           m2.adjoint() * m1);\n  VERIFY_IS_APPROX((s1 * m1).adjoint(),                     numext::conj(s1) * m1.adjoint());\n\n  // check basic properties of dot, squaredNorm\n  VERIFY_IS_APPROX(numext::conj(v1.dot(v2)),               v2.dot(v1));\n  VERIFY_IS_APPROX(numext::real(v1.dot(v1)),               v1.squaredNorm());\n  \n  adjoint_specific<NumTraits<Scalar>::IsInteger>::run(v1, v2, v3, square, s1, s2);\n  \n  VERIFY_IS_MUCH_SMALLER_THAN(abs(vzero.dot(v1)),  static_cast<RealScalar>(1));\n  \n  // like in testBasicStuff, test operator() to check const-qualification\n  Index r = internal::random<Index>(0, rows-1),\n      c = internal::random<Index>(0, cols-1);\n  VERIFY_IS_APPROX(m1.conjugate()(r,c), numext::conj(m1(r,c)));\n  VERIFY_IS_APPROX(m1.adjoint()(c,r), numext::conj(m1(r,c)));\n\n  // check inplace transpose\n  m3 = m1;\n  m3.transposeInPlace();\n  VERIFY_IS_APPROX(m3,m1.transpose());\n  m3.transposeInPlace();\n  VERIFY_IS_APPROX(m3,m1);\n  \n  if(PacketSize<m3.rows() && PacketSize<m3.cols())\n  {\n    m3 = m1;\n    Index i = internal::random<Index>(0,m3.rows()-PacketSize);\n    Index j = internal::random<Index>(0,m3.cols()-PacketSize);\n    m3.template block<PacketSize,PacketSize>(i,j).transposeInPlace();\n    VERIFY_IS_APPROX( (m3.template block<PacketSize,PacketSize>(i,j)), (m1.template block<PacketSize,PacketSize>(i,j).transpose()) );\n    m3.template block<PacketSize,PacketSize>(i,j).transposeInPlace();\n    VERIFY_IS_APPROX(m3,m1);\n  }\n\n  // check inplace adjoint\n  m3 = m1;\n  m3.adjointInPlace();\n  VERIFY_IS_APPROX(m3,m1.adjoint());\n  m3.transposeInPlace();\n  VERIFY_IS_APPROX(m3,m1.conjugate());\n\n  // check mixed dot product\n  typedef Matrix<RealScalar, MatrixType::RowsAtCompileTime, 1> RealVectorType;\n  RealVectorType rv1 = RealVectorType::Random(rows);\n  VERIFY_IS_APPROX(v1.dot(rv1.template cast<Scalar>()), v1.dot(rv1));\n  VERIFY_IS_APPROX(rv1.template cast<Scalar>().dot(v1), rv1.dot(v1));\n}\n\nvoid test_adjoint()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( adjoint(Matrix<float, 1, 1>()) );\n    CALL_SUBTEST_2( adjoint(Matrix3d()) );\n    CALL_SUBTEST_3( adjoint(Matrix4f()) );\n    \n    CALL_SUBTEST_4( adjoint(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2), internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))) );\n    CALL_SUBTEST_5( adjoint(MatrixXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_6( adjoint(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    \n    // Complement for 128 bits vectorization:\n    CALL_SUBTEST_8( adjoint(Matrix2d()) );\n    CALL_SUBTEST_9( adjoint(Matrix<int,4,4>()) );\n    \n    // 256 bits vectorization:\n    CALL_SUBTEST_10( adjoint(Matrix<float,8,8>()) );\n    CALL_SUBTEST_11( adjoint(Matrix<double,4,4>()) );\n    CALL_SUBTEST_12( adjoint(Matrix<int,8,8>()) );\n  }\n  // test a large static matrix only once\n  CALL_SUBTEST_7( adjoint(Matrix<float, 100, 100>()) );\n\n#ifdef EIGEN_TEST_PART_13\n  {\n    MatrixXcf a(10,10), b(10,10);\n    VERIFY_RAISES_ASSERT(a = a.transpose());\n    VERIFY_RAISES_ASSERT(a = a.transpose() + b);\n    VERIFY_RAISES_ASSERT(a = b + a.transpose());\n    VERIFY_RAISES_ASSERT(a = a.conjugate().transpose());\n    VERIFY_RAISES_ASSERT(a = a.adjoint());\n    VERIFY_RAISES_ASSERT(a = a.adjoint() + b);\n    VERIFY_RAISES_ASSERT(a = b + a.adjoint());\n\n    // no assertion should be triggered for these cases:\n    a.transpose() = a.transpose();\n    a.transpose() += a.transpose();\n    a.transpose() += a.transpose() + b;\n    a.transpose() = a.adjoint();\n    a.transpose() += a.adjoint();\n    a.transpose() += a.adjoint() + b;\n\n    // regression tests for check_for_aliasing\n    MatrixXd c(10,10);\n    c = 1.0 * MatrixXd::Ones(10,10) + c;\n    c = MatrixXd::Ones(10,10) * 1.0 + c;\n    c = c + MatrixXd::Ones(10,10) .cwiseProduct( MatrixXd::Zero(10,10) );\n    c = MatrixXd::Ones(10,10) * MatrixXd::Zero(10,10);\n  }\n#endif\n}\n\n"
  },
  {
    "path": "include/eigen3/test/array.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\ntemplate<typename ArrayType> void array(const ArrayType& m)\n{\n  typedef typename ArrayType::Index Index;\n  typedef typename ArrayType::Scalar Scalar;\n  typedef typename ArrayType::RealScalar RealScalar;\n  typedef Array<Scalar, ArrayType::RowsAtCompileTime, 1> ColVectorType;\n  typedef Array<Scalar, 1, ArrayType::ColsAtCompileTime> RowVectorType;\n\n  Index rows = m.rows();\n  Index cols = m.cols(); \n\n  ArrayType m1 = ArrayType::Random(rows, cols),\n             m2 = ArrayType::Random(rows, cols),\n             m3(rows, cols);\n  ArrayType m4 = m1; // copy constructor\n  VERIFY_IS_APPROX(m1, m4);\n\n  ColVectorType cv1 = ColVectorType::Random(rows);\n  RowVectorType rv1 = RowVectorType::Random(cols);\n\n  Scalar  s1 = internal::random<Scalar>(),\n          s2 = internal::random<Scalar>();\n\n  // scalar addition\n  VERIFY_IS_APPROX(m1 + s1, s1 + m1);\n  VERIFY_IS_APPROX(m1 + s1, ArrayType::Constant(rows,cols,s1) + m1);\n  VERIFY_IS_APPROX(s1 - m1, (-m1)+s1 );\n  VERIFY_IS_APPROX(m1 - s1, m1 - ArrayType::Constant(rows,cols,s1));\n  VERIFY_IS_APPROX(s1 - m1, ArrayType::Constant(rows,cols,s1) - m1);\n  VERIFY_IS_APPROX((m1*Scalar(2)) - s2, (m1+m1) - ArrayType::Constant(rows,cols,s2) );\n  m3 = m1;\n  m3 += s2;\n  VERIFY_IS_APPROX(m3, m1 + s2);\n  m3 = m1;\n  m3 -= s1;\n  VERIFY_IS_APPROX(m3, m1 - s1);  \n  \n  // scalar operators via Maps\n  m3 = m1;\n  ArrayType::Map(m1.data(), m1.rows(), m1.cols()) -= ArrayType::Map(m2.data(), m2.rows(), m2.cols());\n  VERIFY_IS_APPROX(m1, m3 - m2);\n  \n  m3 = m1;\n  ArrayType::Map(m1.data(), m1.rows(), m1.cols()) += ArrayType::Map(m2.data(), m2.rows(), m2.cols());\n  VERIFY_IS_APPROX(m1, m3 + m2);\n  \n  m3 = m1;\n  ArrayType::Map(m1.data(), m1.rows(), m1.cols()) *= ArrayType::Map(m2.data(), m2.rows(), m2.cols());\n  VERIFY_IS_APPROX(m1, m3 * m2);\n  \n  m3 = m1;\n  m2 = ArrayType::Random(rows,cols);\n  m2 = (m2==0).select(1,m2);\n  ArrayType::Map(m1.data(), m1.rows(), m1.cols()) /= ArrayType::Map(m2.data(), m2.rows(), m2.cols());  \n  VERIFY_IS_APPROX(m1, m3 / m2);\n\n  // reductions\n  VERIFY_IS_APPROX(m1.abs().colwise().sum().sum(), m1.abs().sum());\n  VERIFY_IS_APPROX(m1.abs().rowwise().sum().sum(), m1.abs().sum());\n  using std::abs;\n  VERIFY_IS_MUCH_SMALLER_THAN(abs(m1.colwise().sum().sum() - m1.sum()), m1.abs().sum());\n  VERIFY_IS_MUCH_SMALLER_THAN(abs(m1.rowwise().sum().sum() - m1.sum()), m1.abs().sum());\n  if (!internal::isMuchSmallerThan(abs(m1.sum() - (m1+m2).sum()), m1.abs().sum(), test_precision<Scalar>()))\n      VERIFY_IS_NOT_APPROX(((m1+m2).rowwise().sum()).sum(), m1.sum());\n  VERIFY_IS_APPROX(m1.colwise().sum(), m1.colwise().redux(internal::scalar_sum_op<Scalar,Scalar>()));\n\n  // vector-wise ops\n  m3 = m1;\n  VERIFY_IS_APPROX(m3.colwise() += cv1, m1.colwise() + cv1);\n  m3 = m1;\n  VERIFY_IS_APPROX(m3.colwise() -= cv1, m1.colwise() - cv1);\n  m3 = m1;\n  VERIFY_IS_APPROX(m3.rowwise() += rv1, m1.rowwise() + rv1);\n  m3 = m1;\n  VERIFY_IS_APPROX(m3.rowwise() -= rv1, m1.rowwise() - rv1);\n  \n  // Conversion from scalar\n  VERIFY_IS_APPROX((m3 = s1), ArrayType::Constant(rows,cols,s1));\n  VERIFY_IS_APPROX((m3 = 1),  ArrayType::Constant(rows,cols,1));\n  VERIFY_IS_APPROX((m3.topLeftCorner(rows,cols) = 1),  ArrayType::Constant(rows,cols,1));\n  typedef Array<Scalar,\n                ArrayType::RowsAtCompileTime==Dynamic?2:ArrayType::RowsAtCompileTime,\n                ArrayType::ColsAtCompileTime==Dynamic?2:ArrayType::ColsAtCompileTime,\n                ArrayType::Options> FixedArrayType;\n  FixedArrayType f1(s1);\n  VERIFY_IS_APPROX(f1, FixedArrayType::Constant(s1));\n  FixedArrayType f2(numext::real(s1));\n  VERIFY_IS_APPROX(f2, FixedArrayType::Constant(numext::real(s1)));\n  FixedArrayType f3((int)100*numext::real(s1));\n  VERIFY_IS_APPROX(f3, FixedArrayType::Constant((int)100*numext::real(s1)));\n  f1.setRandom();\n  FixedArrayType f4(f1.data());\n  VERIFY_IS_APPROX(f4, f1);\n  \n  // pow\n  VERIFY_IS_APPROX(m1.pow(2), m1.square());\n  VERIFY_IS_APPROX(pow(m1,2), m1.square());\n  VERIFY_IS_APPROX(m1.pow(3), m1.cube());\n  VERIFY_IS_APPROX(pow(m1,3), m1.cube());\n  VERIFY_IS_APPROX((-m1).pow(3), -m1.cube());\n  VERIFY_IS_APPROX(pow(2*m1,3), 8*m1.cube());\n  ArrayType exponents = ArrayType::Constant(rows, cols, RealScalar(2));\n  VERIFY_IS_APPROX(Eigen::pow(m1,exponents), m1.square());\n  VERIFY_IS_APPROX(m1.pow(exponents), m1.square());\n  VERIFY_IS_APPROX(Eigen::pow(2*m1,exponents), 4*m1.square());\n  VERIFY_IS_APPROX((2*m1).pow(exponents), 4*m1.square());\n  VERIFY_IS_APPROX(Eigen::pow(m1,2*exponents), m1.square().square());\n  VERIFY_IS_APPROX(m1.pow(2*exponents), m1.square().square());\n  VERIFY_IS_APPROX(Eigen::pow(m1(0,0), exponents), ArrayType::Constant(rows,cols,m1(0,0)*m1(0,0)));\n\n  // Check possible conflicts with 1D ctor\n  typedef Array<Scalar, Dynamic, 1> OneDArrayType;\n  OneDArrayType o1(rows);\n  VERIFY(o1.size()==rows);\n  OneDArrayType o4((int)rows);\n  VERIFY(o4.size()==rows);\n}\n\ntemplate<typename ArrayType> void comparisons(const ArrayType& m)\n{\n  using std::abs;\n  typedef typename ArrayType::Index Index;\n  typedef typename ArrayType::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  Index r = internal::random<Index>(0, rows-1),\n        c = internal::random<Index>(0, cols-1);\n\n  ArrayType m1 = ArrayType::Random(rows, cols),\n            m2 = ArrayType::Random(rows, cols),\n            m3(rows, cols),\n            m4 = m1;\n  \n  m4 = (m4.abs()==Scalar(0)).select(1,m4);\n\n  VERIFY(((m1 + Scalar(1)) > m1).all());\n  VERIFY(((m1 - Scalar(1)) < m1).all());\n  if (rows*cols>1)\n  {\n    m3 = m1;\n    m3(r,c) += 1;\n    VERIFY(! (m1 < m3).all() );\n    VERIFY(! (m1 > m3).all() );\n  }\n  VERIFY(!(m1 > m2 && m1 < m2).any());\n  VERIFY((m1 <= m2 || m1 >= m2).all());\n\n  // comparisons array to scalar\n  VERIFY( (m1 != (m1(r,c)+1) ).any() );\n  VERIFY( (m1 >  (m1(r,c)-1) ).any() );\n  VERIFY( (m1 <  (m1(r,c)+1) ).any() );\n  VERIFY( (m1 ==  m1(r,c)    ).any() );\n\n  // comparisons scalar to array\n  VERIFY( ( (m1(r,c)+1) != m1).any() );\n  VERIFY( ( (m1(r,c)-1) <  m1).any() );\n  VERIFY( ( (m1(r,c)+1) >  m1).any() );\n  VERIFY( (  m1(r,c)    == m1).any() );\n\n  // test Select\n  VERIFY_IS_APPROX( (m1<m2).select(m1,m2), m1.cwiseMin(m2) );\n  VERIFY_IS_APPROX( (m1>m2).select(m1,m2), m1.cwiseMax(m2) );\n  Scalar mid = (m1.cwiseAbs().minCoeff() + m1.cwiseAbs().maxCoeff())/Scalar(2);\n  for (int j=0; j<cols; ++j)\n  for (int i=0; i<rows; ++i)\n    m3(i,j) = abs(m1(i,j))<mid ? 0 : m1(i,j);\n  VERIFY_IS_APPROX( (m1.abs()<ArrayType::Constant(rows,cols,mid))\n                        .select(ArrayType::Zero(rows,cols),m1), m3);\n  // shorter versions:\n  VERIFY_IS_APPROX( (m1.abs()<ArrayType::Constant(rows,cols,mid))\n                        .select(0,m1), m3);\n  VERIFY_IS_APPROX( (m1.abs()>=ArrayType::Constant(rows,cols,mid))\n                        .select(m1,0), m3);\n  // even shorter version:\n  VERIFY_IS_APPROX( (m1.abs()<mid).select(0,m1), m3);\n\n  // count\n  VERIFY(((m1.abs()+1)>RealScalar(0.1)).count() == rows*cols);\n\n  // and/or\n  VERIFY( (m1<RealScalar(0) && m1>RealScalar(0)).count() == 0);\n  VERIFY( (m1<RealScalar(0) || m1>=RealScalar(0)).count() == rows*cols);\n  RealScalar a = m1.abs().mean();\n  VERIFY( (m1<-a || m1>a).count() == (m1.abs()>a).count());\n\n  typedef Array<typename ArrayType::Index, Dynamic, 1> ArrayOfIndices;\n\n  // TODO allows colwise/rowwise for array\n  VERIFY_IS_APPROX(((m1.abs()+1)>RealScalar(0.1)).colwise().count(), ArrayOfIndices::Constant(cols,rows).transpose());\n  VERIFY_IS_APPROX(((m1.abs()+1)>RealScalar(0.1)).rowwise().count(), ArrayOfIndices::Constant(rows, cols));\n}\n\ntemplate<typename ArrayType> void array_real(const ArrayType& m)\n{\n  using std::abs;\n  using std::sqrt;\n  typedef typename ArrayType::Index Index;\n  typedef typename ArrayType::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  ArrayType m1 = ArrayType::Random(rows, cols),\n            m2 = ArrayType::Random(rows, cols),\n            m3(rows, cols),\n            m4 = m1;\n\n  m4 = (m4.abs()==Scalar(0)).select(1,m4);\n\n  Scalar  s1 = internal::random<Scalar>();\n\n  // these tests are mostly to check possible compilation issues with free-functions.\n  VERIFY_IS_APPROX(m1.sin(), sin(m1));\n  VERIFY_IS_APPROX(m1.cos(), cos(m1));\n  VERIFY_IS_APPROX(m1.tan(), tan(m1));\n  VERIFY_IS_APPROX(m1.asin(), asin(m1));\n  VERIFY_IS_APPROX(m1.acos(), acos(m1));\n  VERIFY_IS_APPROX(m1.atan(), atan(m1));\n  VERIFY_IS_APPROX(m1.sinh(), sinh(m1));\n  VERIFY_IS_APPROX(m1.cosh(), cosh(m1));\n  VERIFY_IS_APPROX(m1.tanh(), tanh(m1));\n\n  VERIFY_IS_APPROX(m1.arg(), arg(m1));\n  VERIFY_IS_APPROX(m1.round(), round(m1));\n  VERIFY_IS_APPROX(m1.floor(), floor(m1));\n  VERIFY_IS_APPROX(m1.ceil(), ceil(m1));\n  VERIFY((m1.isNaN() == (Eigen::isnan)(m1)).all());\n  VERIFY((m1.isInf() == (Eigen::isinf)(m1)).all());\n  VERIFY((m1.isFinite() == (Eigen::isfinite)(m1)).all());\n  VERIFY_IS_APPROX(m1.inverse(), inverse(m1));\n  VERIFY_IS_APPROX(m1.abs(), abs(m1));\n  VERIFY_IS_APPROX(m1.abs2(), abs2(m1));\n  VERIFY_IS_APPROX(m1.square(), square(m1));\n  VERIFY_IS_APPROX(m1.cube(), cube(m1));\n  VERIFY_IS_APPROX(cos(m1+RealScalar(3)*m2), cos((m1+RealScalar(3)*m2).eval()));\n  VERIFY_IS_APPROX(m1.sign(), sign(m1));\n\n\n  // avoid NaNs with abs() so verification doesn't fail\n  m3 = m1.abs();\n  VERIFY_IS_APPROX(m3.sqrt(), sqrt(abs(m1)));\n  VERIFY_IS_APPROX(m3.rsqrt(), Scalar(1)/sqrt(abs(m1)));\n  VERIFY_IS_APPROX(rsqrt(m3), Scalar(1)/sqrt(abs(m1)));\n  VERIFY_IS_APPROX(m3.log(), log(m3));\n  VERIFY_IS_APPROX(m3.log1p(), log1p(m3));\n  VERIFY_IS_APPROX(m3.log10(), log10(m3));\n\n\n  VERIFY((!(m1>m2) == (m1<=m2)).all());\n\n  VERIFY_IS_APPROX(sin(m1.asin()), m1);\n  VERIFY_IS_APPROX(cos(m1.acos()), m1);\n  VERIFY_IS_APPROX(tan(m1.atan()), m1);\n  VERIFY_IS_APPROX(sinh(m1), 0.5*(exp(m1)-exp(-m1)));\n  VERIFY_IS_APPROX(cosh(m1), 0.5*(exp(m1)+exp(-m1)));\n  VERIFY_IS_APPROX(tanh(m1), (0.5*(exp(m1)-exp(-m1)))/(0.5*(exp(m1)+exp(-m1))));\n  VERIFY_IS_APPROX(arg(m1), ((m1<0).template cast<Scalar>())*std::acos(-1.0));\n  VERIFY((round(m1) <= ceil(m1) && round(m1) >= floor(m1)).all());\n  VERIFY((Eigen::isnan)((m1*0.0)/0.0).all());\n  VERIFY((Eigen::isinf)(m4/0.0).all());\n  VERIFY(((Eigen::isfinite)(m1) && (!(Eigen::isfinite)(m1*0.0/0.0)) && (!(Eigen::isfinite)(m4/0.0))).all());\n  VERIFY_IS_APPROX(inverse(inverse(m1)),m1);\n  VERIFY((abs(m1) == m1 || abs(m1) == -m1).all());\n  VERIFY_IS_APPROX(m3, sqrt(abs2(m1)));\n  VERIFY_IS_APPROX( m1.sign(), -(-m1).sign() );\n  VERIFY_IS_APPROX( m1*m1.sign(),m1.abs());\n  VERIFY_IS_APPROX(m1.sign() * m1.abs(), m1);\n\n  VERIFY_IS_APPROX(numext::abs2(numext::real(m1)) + numext::abs2(numext::imag(m1)), numext::abs2(m1));\n  VERIFY_IS_APPROX(numext::abs2(real(m1)) + numext::abs2(imag(m1)), numext::abs2(m1));\n  if(!NumTraits<Scalar>::IsComplex)\n    VERIFY_IS_APPROX(numext::real(m1), m1);\n\n  // shift argument of logarithm so that it is not zero\n  Scalar smallNumber = NumTraits<Scalar>::dummy_precision();\n  VERIFY_IS_APPROX((m3 + smallNumber).log() , log(abs(m1) + smallNumber));\n  VERIFY_IS_APPROX((m3 + smallNumber + 1).log() , log1p(abs(m1) + smallNumber));\n\n  VERIFY_IS_APPROX(m1.exp() * m2.exp(), exp(m1+m2));\n  VERIFY_IS_APPROX(m1.exp(), exp(m1));\n  VERIFY_IS_APPROX(m1.exp() / m2.exp(),(m1-m2).exp());\n\n  VERIFY_IS_APPROX(m3.pow(RealScalar(0.5)), m3.sqrt());\n  VERIFY_IS_APPROX(pow(m3,RealScalar(0.5)), m3.sqrt());\n\n  VERIFY_IS_APPROX(m3.pow(RealScalar(-0.5)), m3.rsqrt());\n  VERIFY_IS_APPROX(pow(m3,RealScalar(-0.5)), m3.rsqrt());\n\n  VERIFY_IS_APPROX(log10(m3), log(m3)/log(10));\n\n  // scalar by array division\n  const RealScalar tiny = sqrt(std::numeric_limits<RealScalar>::epsilon());\n  s1 += Scalar(tiny);\n  m1 += ArrayType::Constant(rows,cols,Scalar(tiny));\n  VERIFY_IS_APPROX(s1/m1, s1 * m1.inverse());\n\n  // check inplace transpose\n  m3 = m1;\n  m3.transposeInPlace();\n  VERIFY_IS_APPROX(m3, m1.transpose());\n  m3.transposeInPlace();\n  VERIFY_IS_APPROX(m3, m1);\n}\n\ntemplate<typename ArrayType> void array_complex(const ArrayType& m)\n{\n  typedef typename ArrayType::Index Index;\n  typedef typename ArrayType::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  ArrayType m1 = ArrayType::Random(rows, cols),\n            m2(rows, cols),\n            m4 = m1;\n  \n  m4.real() = (m4.real().abs()==RealScalar(0)).select(RealScalar(1),m4.real());\n  m4.imag() = (m4.imag().abs()==RealScalar(0)).select(RealScalar(1),m4.imag());\n\n  Array<RealScalar, -1, -1> m3(rows, cols);\n\n  for (Index i = 0; i < m.rows(); ++i)\n    for (Index j = 0; j < m.cols(); ++j)\n      m2(i,j) = sqrt(m1(i,j));\n\n  // these tests are mostly to check possible compilation issues with free-functions.\n  VERIFY_IS_APPROX(m1.sin(), sin(m1));\n  VERIFY_IS_APPROX(m1.cos(), cos(m1));\n  VERIFY_IS_APPROX(m1.tan(), tan(m1));\n  VERIFY_IS_APPROX(m1.sinh(), sinh(m1));\n  VERIFY_IS_APPROX(m1.cosh(), cosh(m1));\n  VERIFY_IS_APPROX(m1.tanh(), tanh(m1));\n  VERIFY_IS_APPROX(m1.arg(), arg(m1));\n  VERIFY((m1.isNaN() == (Eigen::isnan)(m1)).all());\n  VERIFY((m1.isInf() == (Eigen::isinf)(m1)).all());\n  VERIFY((m1.isFinite() == (Eigen::isfinite)(m1)).all());\n  VERIFY_IS_APPROX(m1.inverse(), inverse(m1));\n  VERIFY_IS_APPROX(m1.log(), log(m1));\n  VERIFY_IS_APPROX(m1.log10(), log10(m1));\n  VERIFY_IS_APPROX(m1.abs(), abs(m1));\n  VERIFY_IS_APPROX(m1.abs2(), abs2(m1));\n  VERIFY_IS_APPROX(m1.sqrt(), sqrt(m1));\n  VERIFY_IS_APPROX(m1.square(), square(m1));\n  VERIFY_IS_APPROX(m1.cube(), cube(m1));\n  VERIFY_IS_APPROX(cos(m1+RealScalar(3)*m2), cos((m1+RealScalar(3)*m2).eval()));\n  VERIFY_IS_APPROX(m1.sign(), sign(m1));\n\n\n  VERIFY_IS_APPROX(m1.exp() * m2.exp(), exp(m1+m2));\n  VERIFY_IS_APPROX(m1.exp(), exp(m1));\n  VERIFY_IS_APPROX(m1.exp() / m2.exp(),(m1-m2).exp());\n\n  VERIFY_IS_APPROX(sinh(m1), 0.5*(exp(m1)-exp(-m1)));\n  VERIFY_IS_APPROX(cosh(m1), 0.5*(exp(m1)+exp(-m1)));\n  VERIFY_IS_APPROX(tanh(m1), (0.5*(exp(m1)-exp(-m1)))/(0.5*(exp(m1)+exp(-m1))));\n\n  for (Index i = 0; i < m.rows(); ++i)\n    for (Index j = 0; j < m.cols(); ++j)\n      m3(i,j) = std::atan2(imag(m1(i,j)), real(m1(i,j)));\n  VERIFY_IS_APPROX(arg(m1), m3);\n\n  std::complex<RealScalar> zero(0.0,0.0);\n  VERIFY((Eigen::isnan)(m1*zero/zero).all());\n#if EIGEN_COMP_MSVC\n  // msvc complex division is not robust\n  VERIFY((Eigen::isinf)(m4/RealScalar(0)).all());\n#else\n#if EIGEN_COMP_CLANG\n  // clang's complex division is notoriously broken too\n  if((numext::isinf)(m4(0,0)/RealScalar(0))) {\n#endif\n    VERIFY((Eigen::isinf)(m4/zero).all());\n#if EIGEN_COMP_CLANG\n  }\n  else\n  {\n    VERIFY((Eigen::isinf)(m4.real()/zero.real()).all());\n  }\n#endif\n#endif // MSVC\n\n  VERIFY(((Eigen::isfinite)(m1) && (!(Eigen::isfinite)(m1*zero/zero)) && (!(Eigen::isfinite)(m1/zero))).all());\n\n  VERIFY_IS_APPROX(inverse(inverse(m1)),m1);\n  VERIFY_IS_APPROX(conj(m1.conjugate()), m1);\n  VERIFY_IS_APPROX(abs(m1), sqrt(square(real(m1))+square(imag(m1))));\n  VERIFY_IS_APPROX(abs(m1), sqrt(abs2(m1)));\n  VERIFY_IS_APPROX(log10(m1), log(m1)/log(10));\n\n  VERIFY_IS_APPROX( m1.sign(), -(-m1).sign() );\n  VERIFY_IS_APPROX( m1.sign() * m1.abs(), m1);\n\n  // scalar by array division\n  Scalar  s1 = internal::random<Scalar>();\n  const RealScalar tiny = std::sqrt(std::numeric_limits<RealScalar>::epsilon());\n  s1 += Scalar(tiny);\n  m1 += ArrayType::Constant(rows,cols,Scalar(tiny));\n  VERIFY_IS_APPROX(s1/m1, s1 * m1.inverse());\n\n  // check inplace transpose\n  m2 = m1;\n  m2.transposeInPlace();\n  VERIFY_IS_APPROX(m2, m1.transpose());\n  m2.transposeInPlace();\n  VERIFY_IS_APPROX(m2, m1);\n\n}\n\ntemplate<typename ArrayType> void min_max(const ArrayType& m)\n{\n  typedef typename ArrayType::Index Index;\n  typedef typename ArrayType::Scalar Scalar;\n\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  ArrayType m1 = ArrayType::Random(rows, cols);\n\n  // min/max with array\n  Scalar maxM1 = m1.maxCoeff();\n  Scalar minM1 = m1.minCoeff();\n\n  VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, minM1), (m1.min)(ArrayType::Constant(rows,cols, minM1)));\n  VERIFY_IS_APPROX(m1, (m1.min)(ArrayType::Constant(rows,cols, maxM1)));\n\n  VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, maxM1), (m1.max)(ArrayType::Constant(rows,cols, maxM1)));\n  VERIFY_IS_APPROX(m1, (m1.max)(ArrayType::Constant(rows,cols, minM1)));\n\n  // min/max with scalar input\n  VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, minM1), (m1.min)( minM1));\n  VERIFY_IS_APPROX(m1, (m1.min)( maxM1));\n\n  VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, maxM1), (m1.max)( maxM1));\n  VERIFY_IS_APPROX(m1, (m1.max)( minM1));\n\n}\n\nvoid test_array()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( array(Array<float, 1, 1>()) );\n    CALL_SUBTEST_2( array(Array22f()) );\n    CALL_SUBTEST_3( array(Array44d()) );\n    CALL_SUBTEST_4( array(ArrayXXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_5( array(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_6( array(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n  }\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( comparisons(Array<float, 1, 1>()) );\n    CALL_SUBTEST_2( comparisons(Array22f()) );\n    CALL_SUBTEST_3( comparisons(Array44d()) );\n    CALL_SUBTEST_5( comparisons(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_6( comparisons(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n  }\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( min_max(Array<float, 1, 1>()) );\n    CALL_SUBTEST_2( min_max(Array22f()) );\n    CALL_SUBTEST_3( min_max(Array44d()) );\n    CALL_SUBTEST_5( min_max(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_6( min_max(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n  }\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( array_real(Array<float, 1, 1>()) );\n    CALL_SUBTEST_2( array_real(Array22f()) );\n    CALL_SUBTEST_3( array_real(Array44d()) );\n    CALL_SUBTEST_5( array_real(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n  }\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_4( array_complex(ArrayXXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n  }\n\n  VERIFY((internal::is_same< internal::global_math_functions_filtering_base<int>::type, int >::value));\n  VERIFY((internal::is_same< internal::global_math_functions_filtering_base<float>::type, float >::value));\n  VERIFY((internal::is_same< internal::global_math_functions_filtering_base<Array2i>::type, ArrayBase<Array2i> >::value));\n  typedef CwiseUnaryOp<internal::scalar_abs_op<double>, ArrayXd > Xpr;\n  VERIFY((internal::is_same< internal::global_math_functions_filtering_base<Xpr>::type,\n                           ArrayBase<Xpr>\n                         >::value));\n}\n"
  },
  {
    "path": "include/eigen3/test/array_for_matrix.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\ntemplate<typename MatrixType> void array_for_matrix(const MatrixType& m)\n{\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> ColVectorType;\n  typedef Matrix<Scalar, 1, MatrixType::ColsAtCompileTime> RowVectorType; \n\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  MatrixType m1 = MatrixType::Random(rows, cols),\n             m2 = MatrixType::Random(rows, cols),\n             m3(rows, cols);\n\n  ColVectorType cv1 = ColVectorType::Random(rows);\n  RowVectorType rv1 = RowVectorType::Random(cols);\n  \n  Scalar  s1 = internal::random<Scalar>(),\n          s2 = internal::random<Scalar>();\n          \n  // scalar addition\n  VERIFY_IS_APPROX(m1.array() + s1, s1 + m1.array());\n  VERIFY_IS_APPROX((m1.array() + s1).matrix(), MatrixType::Constant(rows,cols,s1) + m1);\n  VERIFY_IS_APPROX(((m1*Scalar(2)).array() - s2).matrix(), (m1+m1) - MatrixType::Constant(rows,cols,s2) );\n  m3 = m1;\n  m3.array() += s2;\n  VERIFY_IS_APPROX(m3, (m1.array() + s2).matrix());\n  m3 = m1;\n  m3.array() -= s1;\n  VERIFY_IS_APPROX(m3, (m1.array() - s1).matrix());\n\n  // reductions\n  VERIFY_IS_MUCH_SMALLER_THAN(m1.colwise().sum().sum() - m1.sum(), m1.squaredNorm());\n  VERIFY_IS_MUCH_SMALLER_THAN(m1.rowwise().sum().sum() - m1.sum(), m1.squaredNorm());\n  VERIFY_IS_MUCH_SMALLER_THAN(m1.colwise().sum() + m2.colwise().sum() - (m1+m2).colwise().sum(), (m1+m2).squaredNorm());\n  VERIFY_IS_MUCH_SMALLER_THAN(m1.rowwise().sum() - m2.rowwise().sum() - (m1-m2).rowwise().sum(), (m1-m2).squaredNorm());\n  VERIFY_IS_APPROX(m1.colwise().sum(), m1.colwise().redux(internal::scalar_sum_op<Scalar,Scalar>()));\n\n  // vector-wise ops\n  m3 = m1;\n  VERIFY_IS_APPROX(m3.colwise() += cv1, m1.colwise() + cv1);\n  m3 = m1;\n  VERIFY_IS_APPROX(m3.colwise() -= cv1, m1.colwise() - cv1);\n  m3 = m1;\n  VERIFY_IS_APPROX(m3.rowwise() += rv1, m1.rowwise() + rv1);\n  m3 = m1;\n  VERIFY_IS_APPROX(m3.rowwise() -= rv1, m1.rowwise() - rv1);\n  \n  // empty objects\n  VERIFY_IS_APPROX(m1.block(0,0,0,cols).colwise().sum(),  RowVectorType::Zero(cols));\n  VERIFY_IS_APPROX(m1.block(0,0,rows,0).rowwise().prod(), ColVectorType::Ones(rows));\n  \n  // verify the const accessors exist\n  const Scalar& ref_m1 = m.matrix().array().coeffRef(0);\n  const Scalar& ref_m2 = m.matrix().array().coeffRef(0,0);\n  const Scalar& ref_a1 = m.array().matrix().coeffRef(0);\n  const Scalar& ref_a2 = m.array().matrix().coeffRef(0,0);\n  VERIFY(&ref_a1 == &ref_m1);\n  VERIFY(&ref_a2 == &ref_m2);\n\n  // Check write accessors:\n  m1.array().coeffRef(0,0) = 1;\n  VERIFY_IS_APPROX(m1(0,0),Scalar(1));\n  m1.array()(0,0) = 2;\n  VERIFY_IS_APPROX(m1(0,0),Scalar(2));\n  m1.array().matrix().coeffRef(0,0) = 3;\n  VERIFY_IS_APPROX(m1(0,0),Scalar(3));\n  m1.array().matrix()(0,0) = 4;\n  VERIFY_IS_APPROX(m1(0,0),Scalar(4));\n}\n\ntemplate<typename MatrixType> void comparisons(const MatrixType& m)\n{\n  using std::abs;\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  Index r = internal::random<Index>(0, rows-1),\n        c = internal::random<Index>(0, cols-1);\n\n  MatrixType m1 = MatrixType::Random(rows, cols),\n             m2 = MatrixType::Random(rows, cols),\n             m3(rows, cols);\n\n  VERIFY(((m1.array() + Scalar(1)) > m1.array()).all());\n  VERIFY(((m1.array() - Scalar(1)) < m1.array()).all());\n  if (rows*cols>1)\n  {\n    m3 = m1;\n    m3(r,c) += 1;\n    VERIFY(! (m1.array() < m3.array()).all() );\n    VERIFY(! (m1.array() > m3.array()).all() );\n  }\n\n  // comparisons to scalar\n  VERIFY( (m1.array() != (m1(r,c)+1) ).any() );\n  VERIFY( (m1.array() > (m1(r,c)-1) ).any() );\n  VERIFY( (m1.array() < (m1(r,c)+1) ).any() );\n  VERIFY( (m1.array() == m1(r,c) ).any() );\n  VERIFY( m1.cwiseEqual(m1(r,c)).any() );\n\n  // test Select\n  VERIFY_IS_APPROX( (m1.array()<m2.array()).select(m1,m2), m1.cwiseMin(m2) );\n  VERIFY_IS_APPROX( (m1.array()>m2.array()).select(m1,m2), m1.cwiseMax(m2) );\n  Scalar mid = (m1.cwiseAbs().minCoeff() + m1.cwiseAbs().maxCoeff())/Scalar(2);\n  for (int j=0; j<cols; ++j)\n  for (int i=0; i<rows; ++i)\n    m3(i,j) = abs(m1(i,j))<mid ? 0 : m1(i,j);\n  VERIFY_IS_APPROX( (m1.array().abs()<MatrixType::Constant(rows,cols,mid).array())\n                        .select(MatrixType::Zero(rows,cols),m1), m3);\n  // shorter versions:\n  VERIFY_IS_APPROX( (m1.array().abs()<MatrixType::Constant(rows,cols,mid).array())\n                        .select(0,m1), m3);\n  VERIFY_IS_APPROX( (m1.array().abs()>=MatrixType::Constant(rows,cols,mid).array())\n                        .select(m1,0), m3);\n  // even shorter version:\n  VERIFY_IS_APPROX( (m1.array().abs()<mid).select(0,m1), m3);\n\n  // count\n  VERIFY(((m1.array().abs()+1)>RealScalar(0.1)).count() == rows*cols);\n\n  // and/or\n  VERIFY( ((m1.array()<RealScalar(0)).matrix() && (m1.array()>RealScalar(0)).matrix()).count() == 0);\n  VERIFY( ((m1.array()<RealScalar(0)).matrix() || (m1.array()>=RealScalar(0)).matrix()).count() == rows*cols);\n  RealScalar a = m1.cwiseAbs().mean();\n  VERIFY( ((m1.array()<-a).matrix() || (m1.array()>a).matrix()).count() == (m1.cwiseAbs().array()>a).count());\n\n  typedef Matrix<typename MatrixType::Index, Dynamic, 1> VectorOfIndices;\n\n  // TODO allows colwise/rowwise for array\n  VERIFY_IS_APPROX(((m1.array().abs()+1)>RealScalar(0.1)).matrix().colwise().count(), VectorOfIndices::Constant(cols,rows).transpose());\n  VERIFY_IS_APPROX(((m1.array().abs()+1)>RealScalar(0.1)).matrix().rowwise().count(), VectorOfIndices::Constant(rows, cols));\n}\n\ntemplate<typename VectorType> void lpNorm(const VectorType& v)\n{\n  using std::sqrt;\n  typedef typename VectorType::RealScalar RealScalar;\n  VectorType u = VectorType::Random(v.size());\n\n  if(v.size()==0)\n  {\n    VERIFY_IS_APPROX(u.template lpNorm<Infinity>(), RealScalar(0));\n    VERIFY_IS_APPROX(u.template lpNorm<1>(), RealScalar(0));\n    VERIFY_IS_APPROX(u.template lpNorm<2>(), RealScalar(0));\n    VERIFY_IS_APPROX(u.template lpNorm<5>(), RealScalar(0));\n  }\n  else\n  {\n    VERIFY_IS_APPROX(u.template lpNorm<Infinity>(), u.cwiseAbs().maxCoeff());\n  }\n\n  VERIFY_IS_APPROX(u.template lpNorm<1>(), u.cwiseAbs().sum());\n  VERIFY_IS_APPROX(u.template lpNorm<2>(), sqrt(u.array().abs().square().sum()));\n  VERIFY_IS_APPROX(numext::pow(u.template lpNorm<5>(), typename VectorType::RealScalar(5)), u.array().abs().pow(5).sum());\n}\n\ntemplate<typename MatrixType> void cwise_min_max(const MatrixType& m)\n{\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  MatrixType m1 = MatrixType::Random(rows, cols);\n\n  // min/max with array\n  Scalar maxM1 = m1.maxCoeff();\n  Scalar minM1 = m1.minCoeff();\n\n  VERIFY_IS_APPROX(MatrixType::Constant(rows,cols, minM1), m1.cwiseMin(MatrixType::Constant(rows,cols, minM1)));\n  VERIFY_IS_APPROX(m1, m1.cwiseMin(MatrixType::Constant(rows,cols, maxM1)));\n\n  VERIFY_IS_APPROX(MatrixType::Constant(rows,cols, maxM1), m1.cwiseMax(MatrixType::Constant(rows,cols, maxM1)));\n  VERIFY_IS_APPROX(m1, m1.cwiseMax(MatrixType::Constant(rows,cols, minM1)));\n\n  // min/max with scalar input\n  VERIFY_IS_APPROX(MatrixType::Constant(rows,cols, minM1), m1.cwiseMin( minM1));\n  VERIFY_IS_APPROX(m1, m1.cwiseMin(maxM1));\n  VERIFY_IS_APPROX(-m1, (-m1).cwiseMin(-minM1));\n  VERIFY_IS_APPROX(-m1.array(), ((-m1).array().min)( -minM1));\n\n  VERIFY_IS_APPROX(MatrixType::Constant(rows,cols, maxM1), m1.cwiseMax( maxM1));\n  VERIFY_IS_APPROX(m1, m1.cwiseMax(minM1));\n  VERIFY_IS_APPROX(-m1, (-m1).cwiseMax(-maxM1));\n  VERIFY_IS_APPROX(-m1.array(), ((-m1).array().max)(-maxM1));\n\n  VERIFY_IS_APPROX(MatrixType::Constant(rows,cols, minM1).array(), (m1.array().min)( minM1));\n  VERIFY_IS_APPROX(m1.array(), (m1.array().min)( maxM1));\n\n  VERIFY_IS_APPROX(MatrixType::Constant(rows,cols, maxM1).array(), (m1.array().max)( maxM1));\n  VERIFY_IS_APPROX(m1.array(), (m1.array().max)( minM1));\n\n}\n\ntemplate<typename MatrixTraits> void resize(const MatrixTraits& t)\n{\n  typedef typename MatrixTraits::Index Index;\n  typedef typename MatrixTraits::Scalar Scalar;\n  typedef Matrix<Scalar,Dynamic,Dynamic> MatrixType;\n  typedef Array<Scalar,Dynamic,Dynamic> Array2DType;\n  typedef Matrix<Scalar,Dynamic,1> VectorType;\n  typedef Array<Scalar,Dynamic,1> Array1DType;\n\n  Index rows = t.rows(), cols = t.cols();\n\n  MatrixType m(rows,cols);\n  VectorType v(rows);\n  Array2DType a2(rows,cols);\n  Array1DType a1(rows);\n\n  m.array().resize(rows+1,cols+1);\n  VERIFY(m.rows()==rows+1 && m.cols()==cols+1);\n  a2.matrix().resize(rows+1,cols+1);\n  VERIFY(a2.rows()==rows+1 && a2.cols()==cols+1);\n  v.array().resize(cols);\n  VERIFY(v.size()==cols);\n  a1.matrix().resize(cols);\n  VERIFY(a1.size()==cols);\n}\n\ntemplate<int>\nvoid regression_bug_654()\n{\n  ArrayXf a = RowVectorXf(3);\n  VectorXf v = Array<float,1,Dynamic>(3);\n}\n\n// Check propagation of LvalueBit through Array/Matrix-Wrapper\ntemplate<int>\nvoid regrrssion_bug_1410()\n{\n  const Matrix4i M;\n  const Array4i A;\n  ArrayWrapper<const Matrix4i> MA = M.array();\n  MA.row(0);\n  MatrixWrapper<const Array4i> AM = A.matrix();\n  AM.row(0);\n\n  VERIFY((internal::traits<ArrayWrapper<const Matrix4i> >::Flags&LvalueBit)==0);\n  VERIFY((internal::traits<MatrixWrapper<const Array4i> >::Flags&LvalueBit)==0);\n\n  VERIFY((internal::traits<ArrayWrapper<Matrix4i> >::Flags&LvalueBit)==LvalueBit);\n  VERIFY((internal::traits<MatrixWrapper<Array4i> >::Flags&LvalueBit)==LvalueBit);\n}\n\nvoid test_array_for_matrix()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( array_for_matrix(Matrix<float, 1, 1>()) );\n    CALL_SUBTEST_2( array_for_matrix(Matrix2f()) );\n    CALL_SUBTEST_3( array_for_matrix(Matrix4d()) );\n    CALL_SUBTEST_4( array_for_matrix(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_5( array_for_matrix(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_6( array_for_matrix(MatrixXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n  }\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( comparisons(Matrix<float, 1, 1>()) );\n    CALL_SUBTEST_2( comparisons(Matrix2f()) );\n    CALL_SUBTEST_3( comparisons(Matrix4d()) );\n    CALL_SUBTEST_5( comparisons(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_6( comparisons(MatrixXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n  }\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( cwise_min_max(Matrix<float, 1, 1>()) );\n    CALL_SUBTEST_2( cwise_min_max(Matrix2f()) );\n    CALL_SUBTEST_3( cwise_min_max(Matrix4d()) );\n    CALL_SUBTEST_5( cwise_min_max(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_6( cwise_min_max(MatrixXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n  }\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( lpNorm(Matrix<float, 1, 1>()) );\n    CALL_SUBTEST_2( lpNorm(Vector2f()) );\n    CALL_SUBTEST_7( lpNorm(Vector3d()) );\n    CALL_SUBTEST_8( lpNorm(Vector4f()) );\n    CALL_SUBTEST_5( lpNorm(VectorXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_4( lpNorm(VectorXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n  }\n  CALL_SUBTEST_5( lpNorm(VectorXf(0)) );\n  CALL_SUBTEST_4( lpNorm(VectorXcf(0)) );\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_4( resize(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_5( resize(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_6( resize(MatrixXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n  }\n  CALL_SUBTEST_6( regression_bug_654<0>() );\n  CALL_SUBTEST_6( regrrssion_bug_1410<0>() );\n}\n"
  },
  {
    "path": "include/eigen3/test/array_of_string.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\nvoid test_array_of_string()\n{\n  typedef Array<std::string,1,Dynamic> ArrayXs;\n  ArrayXs a1(3), a2(3), a3(3), a3ref(3);\n  a1 << \"one\", \"two\", \"three\";\n  a2 << \"1\", \"2\", \"3\";\n  a3ref << \"one (1)\", \"two (2)\", \"three (3)\";\n  std::stringstream s1;\n  s1 << a1;\n  VERIFY_IS_EQUAL(s1.str(), std::string(\"  one    two  three\"));\n  a3 = a1 + std::string(\" (\") + a2 + std::string(\")\");\n  VERIFY((a3==a3ref).all());\n\n  a3 = a1;\n  a3 += std::string(\" (\") + a2 + std::string(\")\");\n  VERIFY((a3==a3ref).all());\n\n  a1.swap(a3);\n  VERIFY((a1==a3ref).all());\n  VERIFY((a3!=a3ref).all());\n}\n"
  },
  {
    "path": "include/eigen3/test/array_replicate.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\ntemplate<typename MatrixType> void replicate(const MatrixType& m)\n{\n  /* this test covers the following files:\n     Replicate.cpp\n  */\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;\n  typedef Matrix<Scalar, Dynamic, Dynamic> MatrixX;\n  typedef Matrix<Scalar, Dynamic, 1> VectorX;\n\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  MatrixType m1 = MatrixType::Random(rows, cols),\n             m2 = MatrixType::Random(rows, cols);\n\n  VectorType v1 = VectorType::Random(rows);\n\n  MatrixX x1, x2;\n  VectorX vx1;\n\n  int  f1 = internal::random<int>(1,10),\n       f2 = internal::random<int>(1,10);\n\n  x1.resize(rows*f1,cols*f2);\n  for(int j=0; j<f2; j++)\n  for(int i=0; i<f1; i++)\n    x1.block(i*rows,j*cols,rows,cols) = m1;\n  VERIFY_IS_APPROX(x1, m1.replicate(f1,f2));\n\n  x2.resize(2*rows,3*cols);\n  x2 << m2, m2, m2,\n        m2, m2, m2;\n  VERIFY_IS_APPROX(x2, (m2.template replicate<2,3>()));\n  \n  x2.resize(rows,3*cols);\n  x2 << m2, m2, m2;\n  VERIFY_IS_APPROX(x2, (m2.template replicate<1,3>()));\n  \n  vx1.resize(3*rows,cols);\n  vx1 << m2, m2, m2;\n  VERIFY_IS_APPROX(vx1+vx1, vx1+(m2.template replicate<3,1>()));\n  \n  vx1=m2+(m2.colwise().replicate(1));\n  \n  if(m2.cols()==1)\n    VERIFY_IS_APPROX(m2.coeff(0), (m2.template replicate<3,1>().coeff(m2.rows())));\n\n  x2.resize(rows,f1);\n  for (int j=0; j<f1; ++j)\n    x2.col(j) = v1;\n  VERIFY_IS_APPROX(x2, v1.rowwise().replicate(f1));\n\n  vx1.resize(rows*f2);\n  for (int j=0; j<f2; ++j)\n    vx1.segment(j*rows,rows) = v1;\n  VERIFY_IS_APPROX(vx1, v1.colwise().replicate(f2));\n}\n\nvoid test_array_replicate()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( replicate(Matrix<float, 1, 1>()) );\n    CALL_SUBTEST_2( replicate(Vector2f()) );\n    CALL_SUBTEST_3( replicate(Vector3d()) );\n    CALL_SUBTEST_4( replicate(Vector4f()) );\n    CALL_SUBTEST_5( replicate(VectorXf(16)) );\n    CALL_SUBTEST_6( replicate(VectorXcd(10)) );\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/array_reverse.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2009 Ricard Marxer <email@ricardmarxer.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <iostream>\n\nusing namespace std;\n\ntemplate<typename MatrixType> void reverse(const MatrixType& m)\n{\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;\n\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  // this test relies a lot on Random.h, and there's not much more that we can do\n  // to test it, hence I consider that we will have tested Random.h\n  MatrixType m1 = MatrixType::Random(rows, cols), m2;\n  VectorType v1 = VectorType::Random(rows);\n\n  MatrixType m1_r = m1.reverse();\n  // Verify that MatrixBase::reverse() works\n  for ( int i = 0; i < rows; i++ ) {\n    for ( int j = 0; j < cols; j++ ) {\n      VERIFY_IS_APPROX(m1_r(i, j), m1(rows - 1 - i, cols - 1 - j));\n    }\n  }\n\n  Reverse<MatrixType> m1_rd(m1);\n  // Verify that a Reverse default (in both directions) of an expression works\n  for ( int i = 0; i < rows; i++ ) {\n    for ( int j = 0; j < cols; j++ ) {\n      VERIFY_IS_APPROX(m1_rd(i, j), m1(rows - 1 - i, cols - 1 - j));\n    }\n  }\n\n  Reverse<MatrixType, BothDirections> m1_rb(m1);\n  // Verify that a Reverse in both directions of an expression works\n  for ( int i = 0; i < rows; i++ ) {\n    for ( int j = 0; j < cols; j++ ) {\n      VERIFY_IS_APPROX(m1_rb(i, j), m1(rows - 1 - i, cols - 1 - j));\n    }\n  }\n\n  Reverse<MatrixType, Vertical> m1_rv(m1);\n  // Verify that a Reverse in the vertical directions of an expression works\n  for ( int i = 0; i < rows; i++ ) {\n    for ( int j = 0; j < cols; j++ ) {\n      VERIFY_IS_APPROX(m1_rv(i, j), m1(rows - 1 - i, j));\n    }\n  }\n\n  Reverse<MatrixType, Horizontal> m1_rh(m1);\n  // Verify that a Reverse in the horizontal directions of an expression works\n  for ( int i = 0; i < rows; i++ ) {\n    for ( int j = 0; j < cols; j++ ) {\n      VERIFY_IS_APPROX(m1_rh(i, j), m1(i, cols - 1 - j));\n    }\n  }\n\n  VectorType v1_r = v1.reverse();\n  // Verify that a VectorType::reverse() of an expression works\n  for ( int i = 0; i < rows; i++ ) {\n    VERIFY_IS_APPROX(v1_r(i), v1(rows - 1 - i));\n  }\n\n  MatrixType m1_cr = m1.colwise().reverse();\n  // Verify that PartialRedux::reverse() works (for colwise())\n  for ( int i = 0; i < rows; i++ ) {\n    for ( int j = 0; j < cols; j++ ) {\n      VERIFY_IS_APPROX(m1_cr(i, j), m1(rows - 1 - i, j));\n    }\n  }\n\n  MatrixType m1_rr = m1.rowwise().reverse();\n  // Verify that PartialRedux::reverse() works (for rowwise())\n  for ( int i = 0; i < rows; i++ ) {\n    for ( int j = 0; j < cols; j++ ) {\n      VERIFY_IS_APPROX(m1_rr(i, j), m1(i, cols - 1 - j));\n    }\n  }\n\n  Scalar x = internal::random<Scalar>();\n\n  Index r = internal::random<Index>(0, rows-1),\n        c = internal::random<Index>(0, cols-1);\n\n  m1.reverse()(r, c) = x;\n  VERIFY_IS_APPROX(x, m1(rows - 1 - r, cols - 1 - c));\n  \n  m2 = m1;\n  m2.reverseInPlace();\n  VERIFY_IS_APPROX(m2,m1.reverse().eval());\n  \n  m2 = m1;\n  m2.col(0).reverseInPlace();\n  VERIFY_IS_APPROX(m2.col(0),m1.col(0).reverse().eval());\n  \n  m2 = m1;\n  m2.row(0).reverseInPlace();\n  VERIFY_IS_APPROX(m2.row(0),m1.row(0).reverse().eval());\n  \n  m2 = m1;\n  m2.rowwise().reverseInPlace();\n  VERIFY_IS_APPROX(m2,m1.rowwise().reverse().eval());\n  \n  m2 = m1;\n  m2.colwise().reverseInPlace();\n  VERIFY_IS_APPROX(m2,m1.colwise().reverse().eval());\n\n  m1.colwise().reverse()(r, c) = x;\n  VERIFY_IS_APPROX(x, m1(rows - 1 - r, c));\n\n  m1.rowwise().reverse()(r, c) = x;\n  VERIFY_IS_APPROX(x, m1(r, cols - 1 - c));\n}\n\nvoid test_array_reverse()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( reverse(Matrix<float, 1, 1>()) );\n    CALL_SUBTEST_2( reverse(Matrix2f()) );\n    CALL_SUBTEST_3( reverse(Matrix4f()) );\n    CALL_SUBTEST_4( reverse(Matrix4d()) );\n    CALL_SUBTEST_5( reverse(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_6( reverse(MatrixXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_7( reverse(MatrixXcd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_8( reverse(Matrix<float, 100, 100>()) );\n    CALL_SUBTEST_9( reverse(Matrix<float,Dynamic,Dynamic,RowMajor>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n  }\n#ifdef EIGEN_TEST_PART_3\n  Vector4f x; x << 1, 2, 3, 4;\n  Vector4f y; y << 4, 3, 2, 1;\n  VERIFY(x.reverse()[1] == 3);\n  VERIFY(x.reverse() == y);\n#endif\n}\n"
  },
  {
    "path": "include/eigen3/test/bandmatrix.cpp",
    "content": "// This file is triangularView of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\ntemplate<typename MatrixType> void bandmatrix(const MatrixType& _m)\n{\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrixType;\n\n  Index rows = _m.rows();\n  Index cols = _m.cols();\n  Index supers = _m.supers();\n  Index subs = _m.subs();\n\n  MatrixType m(rows,cols,supers,subs);\n\n  DenseMatrixType dm1(rows,cols);\n  dm1.setZero();\n\n  m.diagonal().setConstant(123);\n  dm1.diagonal().setConstant(123);\n  for (int i=1; i<=m.supers();++i)\n  {\n    m.diagonal(i).setConstant(static_cast<RealScalar>(i));\n    dm1.diagonal(i).setConstant(static_cast<RealScalar>(i));\n  }\n  for (int i=1; i<=m.subs();++i)\n  {\n    m.diagonal(-i).setConstant(-static_cast<RealScalar>(i));\n    dm1.diagonal(-i).setConstant(-static_cast<RealScalar>(i));\n  }\n  //std::cerr << m.m_data << \"\\n\\n\" << m.toDense() << \"\\n\\n\" << dm1 << \"\\n\\n\\n\\n\";\n  VERIFY_IS_APPROX(dm1,m.toDenseMatrix());\n\n  for (int i=0; i<cols; ++i)\n  {\n    m.col(i).setConstant(static_cast<RealScalar>(i+1));\n    dm1.col(i).setConstant(static_cast<RealScalar>(i+1));\n  }\n  Index d = (std::min)(rows,cols);\n  Index a = std::max<Index>(0,cols-d-supers);\n  Index b = std::max<Index>(0,rows-d-subs);\n  if(a>0) dm1.block(0,d+supers,rows,a).setZero();\n  dm1.block(0,supers+1,cols-supers-1-a,cols-supers-1-a).template triangularView<Upper>().setZero();\n  dm1.block(subs+1,0,rows-subs-1-b,rows-subs-1-b).template triangularView<Lower>().setZero();\n  if(b>0) dm1.block(d+subs,0,b,cols).setZero();\n  //std::cerr << m.m_data << \"\\n\\n\" << m.toDense() << \"\\n\\n\" << dm1 << \"\\n\\n\";\n  VERIFY_IS_APPROX(dm1,m.toDenseMatrix());\n\n}\n\nusing Eigen::internal::BandMatrix;\n\nvoid test_bandmatrix()\n{\n  for(int i = 0; i < 10*g_repeat ; i++) {\n    Index rows = internal::random<Index>(1,10);\n    Index cols = internal::random<Index>(1,10);\n    Index sups = internal::random<Index>(0,cols-1);\n    Index subs = internal::random<Index>(0,rows-1);\n    CALL_SUBTEST(bandmatrix(BandMatrix<float>(rows,cols,sups,subs)) );\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/basicstuff.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define EIGEN_NO_STATIC_ASSERT\n\n#include \"main.h\"\n\ntemplate<typename MatrixType> void basicStuff(const MatrixType& m)\n{\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;\n\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  // this test relies a lot on Random.h, and there's not much more that we can do\n  // to test it, hence I consider that we will have tested Random.h\n  MatrixType m1 = MatrixType::Random(rows, cols),\n             m2 = MatrixType::Random(rows, cols),\n             m3(rows, cols),\n             mzero = MatrixType::Zero(rows, cols),\n             square = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>::Random(rows, rows);\n  VectorType v1 = VectorType::Random(rows),\n             vzero = VectorType::Zero(rows);\n  SquareMatrixType sm1 = SquareMatrixType::Random(rows,rows), sm2(rows,rows);\n\n  Scalar x = 0;\n  while(x == Scalar(0)) x = internal::random<Scalar>();\n\n  Index r = internal::random<Index>(0, rows-1),\n        c = internal::random<Index>(0, cols-1);\n\n  m1.coeffRef(r,c) = x;\n  VERIFY_IS_APPROX(x, m1.coeff(r,c));\n  m1(r,c) = x;\n  VERIFY_IS_APPROX(x, m1(r,c));\n  v1.coeffRef(r) = x;\n  VERIFY_IS_APPROX(x, v1.coeff(r));\n  v1(r) = x;\n  VERIFY_IS_APPROX(x, v1(r));\n  v1[r] = x;\n  VERIFY_IS_APPROX(x, v1[r]);\n\n  VERIFY_IS_APPROX(               v1,    v1);\n  VERIFY_IS_NOT_APPROX(           v1,    2*v1);\n  VERIFY_IS_MUCH_SMALLER_THAN(    vzero, v1);\n  VERIFY_IS_MUCH_SMALLER_THAN(  vzero, v1.squaredNorm());\n  VERIFY_IS_NOT_MUCH_SMALLER_THAN(v1,    v1);\n  VERIFY_IS_APPROX(               vzero, v1-v1);\n  VERIFY_IS_APPROX(               m1,    m1);\n  VERIFY_IS_NOT_APPROX(           m1,    2*m1);\n  VERIFY_IS_MUCH_SMALLER_THAN(    mzero, m1);\n  VERIFY_IS_NOT_MUCH_SMALLER_THAN(m1,    m1);\n  VERIFY_IS_APPROX(               mzero, m1-m1);\n\n  // always test operator() on each read-only expression class,\n  // in order to check const-qualifiers.\n  // indeed, if an expression class (here Zero) is meant to be read-only,\n  // hence has no _write() method, the corresponding MatrixBase method (here zero())\n  // should return a const-qualified object so that it is the const-qualified\n  // operator() that gets called, which in turn calls _read().\n  VERIFY_IS_MUCH_SMALLER_THAN(MatrixType::Zero(rows,cols)(r,c), static_cast<Scalar>(1));\n\n  // now test copying a row-vector into a (column-)vector and conversely.\n  square.col(r) = square.row(r).eval();\n  Matrix<Scalar, 1, MatrixType::RowsAtCompileTime> rv(rows);\n  Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> cv(rows);\n  rv = square.row(r);\n  cv = square.col(r);\n  \n  VERIFY_IS_APPROX(rv, cv.transpose());\n\n  if(cols!=1 && rows!=1 && MatrixType::SizeAtCompileTime!=Dynamic)\n  {\n    VERIFY_RAISES_ASSERT(m1 = (m2.block(0,0, rows-1, cols-1)));\n  }\n\n  if(cols!=1 && rows!=1)\n  {\n    VERIFY_RAISES_ASSERT(m1[0]);\n    VERIFY_RAISES_ASSERT((m1+m1)[0]);\n  }\n\n  VERIFY_IS_APPROX(m3 = m1,m1);\n  MatrixType m4;\n  VERIFY_IS_APPROX(m4 = m1,m1);\n\n  m3.real() = m1.real();\n  VERIFY_IS_APPROX(static_cast<const MatrixType&>(m3).real(), static_cast<const MatrixType&>(m1).real());\n  VERIFY_IS_APPROX(static_cast<const MatrixType&>(m3).real(), m1.real());\n\n  // check == / != operators\n  VERIFY(m1==m1);\n  VERIFY(m1!=m2);\n  VERIFY(!(m1==m2));\n  VERIFY(!(m1!=m1));\n  m1 = m2;\n  VERIFY(m1==m2);\n  VERIFY(!(m1!=m2));\n  \n  // check automatic transposition\n  sm2.setZero();\n  for(typename MatrixType::Index i=0;i<rows;++i)\n    sm2.col(i) = sm1.row(i);\n  VERIFY_IS_APPROX(sm2,sm1.transpose());\n  \n  sm2.setZero();\n  for(typename MatrixType::Index i=0;i<rows;++i)\n    sm2.col(i).noalias() = sm1.row(i);\n  VERIFY_IS_APPROX(sm2,sm1.transpose());\n  \n  sm2.setZero();\n  for(typename MatrixType::Index i=0;i<rows;++i)\n    sm2.col(i).noalias() += sm1.row(i);\n  VERIFY_IS_APPROX(sm2,sm1.transpose());\n  \n  sm2.setZero();\n  for(typename MatrixType::Index i=0;i<rows;++i)\n    sm2.col(i).noalias() -= sm1.row(i);\n  VERIFY_IS_APPROX(sm2,-sm1.transpose());\n  \n  // check ternary usage\n  {\n    bool b = internal::random<int>(0,10)>5;\n    m3 = b ? m1 : m2;\n    if(b) VERIFY_IS_APPROX(m3,m1);\n    else  VERIFY_IS_APPROX(m3,m2);\n    m3 = b ? -m1 : m2;\n    if(b) VERIFY_IS_APPROX(m3,-m1);\n    else  VERIFY_IS_APPROX(m3,m2);\n    m3 = b ? m1 : -m2;\n    if(b) VERIFY_IS_APPROX(m3,m1);\n    else  VERIFY_IS_APPROX(m3,-m2);\n  }\n}\n\ntemplate<typename MatrixType> void basicStuffComplex(const MatrixType& m)\n{\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  typedef Matrix<RealScalar, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime> RealMatrixType;\n\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  Scalar s1 = internal::random<Scalar>(),\n         s2 = internal::random<Scalar>();\n\n  VERIFY(numext::real(s1)==numext::real_ref(s1));\n  VERIFY(numext::imag(s1)==numext::imag_ref(s1));\n  numext::real_ref(s1) = numext::real(s2);\n  numext::imag_ref(s1) = numext::imag(s2);\n  VERIFY(internal::isApprox(s1, s2, NumTraits<RealScalar>::epsilon()));\n  // extended precision in Intel FPUs means that s1 == s2 in the line above is not guaranteed.\n\n  RealMatrixType rm1 = RealMatrixType::Random(rows,cols),\n                 rm2 = RealMatrixType::Random(rows,cols);\n  MatrixType cm(rows,cols);\n  cm.real() = rm1;\n  cm.imag() = rm2;\n  VERIFY_IS_APPROX(static_cast<const MatrixType&>(cm).real(), rm1);\n  VERIFY_IS_APPROX(static_cast<const MatrixType&>(cm).imag(), rm2);\n  rm1.setZero();\n  rm2.setZero();\n  rm1 = cm.real();\n  rm2 = cm.imag();\n  VERIFY_IS_APPROX(static_cast<const MatrixType&>(cm).real(), rm1);\n  VERIFY_IS_APPROX(static_cast<const MatrixType&>(cm).imag(), rm2);\n  cm.real().setZero();\n  VERIFY(static_cast<const MatrixType&>(cm).real().isZero());\n  VERIFY(!static_cast<const MatrixType&>(cm).imag().isZero());\n}\n\n#ifdef EIGEN_TEST_PART_2\nvoid casting()\n{\n  Matrix4f m = Matrix4f::Random(), m2;\n  Matrix4d n = m.cast<double>();\n  VERIFY(m.isApprox(n.cast<float>()));\n  m2 = m.cast<float>(); // check the specialization when NewType == Type\n  VERIFY(m.isApprox(m2));\n}\n#endif\n\ntemplate <typename Scalar>\nvoid fixedSizeMatrixConstruction()\n{\n  Scalar raw[4];\n  for(int k=0; k<4; ++k)\n    raw[k] = internal::random<Scalar>();\n  \n  {\n    Matrix<Scalar,4,1> m(raw);\n    Array<Scalar,4,1> a(raw);\n    for(int k=0; k<4; ++k) VERIFY(m(k) == raw[k]);\n    for(int k=0; k<4; ++k) VERIFY(a(k) == raw[k]);    \n    VERIFY_IS_EQUAL(m,(Matrix<Scalar,4,1>(raw[0],raw[1],raw[2],raw[3])));\n    VERIFY((a==(Array<Scalar,4,1>(raw[0],raw[1],raw[2],raw[3]))).all());\n  }\n  {\n    Matrix<Scalar,3,1> m(raw);\n    Array<Scalar,3,1> a(raw);\n    for(int k=0; k<3; ++k) VERIFY(m(k) == raw[k]);\n    for(int k=0; k<3; ++k) VERIFY(a(k) == raw[k]);\n    VERIFY_IS_EQUAL(m,(Matrix<Scalar,3,1>(raw[0],raw[1],raw[2])));\n    VERIFY((a==Array<Scalar,3,1>(raw[0],raw[1],raw[2])).all());\n  }\n  {\n    Matrix<Scalar,2,1> m(raw), m2( (DenseIndex(raw[0])), (DenseIndex(raw[1])) );\n    Array<Scalar,2,1> a(raw),  a2( (DenseIndex(raw[0])), (DenseIndex(raw[1])) );\n    for(int k=0; k<2; ++k) VERIFY(m(k) == raw[k]);\n    for(int k=0; k<2; ++k) VERIFY(a(k) == raw[k]);\n    VERIFY_IS_EQUAL(m,(Matrix<Scalar,2,1>(raw[0],raw[1])));\n    VERIFY((a==Array<Scalar,2,1>(raw[0],raw[1])).all());\n    for(int k=0; k<2; ++k) VERIFY(m2(k) == DenseIndex(raw[k]));\n    for(int k=0; k<2; ++k) VERIFY(a2(k) == DenseIndex(raw[k]));\n  }\n  {\n    Matrix<Scalar,1,2> m(raw),\n                       m2( (DenseIndex(raw[0])), (DenseIndex(raw[1])) ),\n                       m3( (int(raw[0])), (int(raw[1])) ),\n                       m4( (float(raw[0])), (float(raw[1])) );\n    Array<Scalar,1,2> a(raw),  a2( (DenseIndex(raw[0])), (DenseIndex(raw[1])) );\n    for(int k=0; k<2; ++k) VERIFY(m(k) == raw[k]);\n    for(int k=0; k<2; ++k) VERIFY(a(k) == raw[k]);\n    VERIFY_IS_EQUAL(m,(Matrix<Scalar,1,2>(raw[0],raw[1])));\n    VERIFY((a==Array<Scalar,1,2>(raw[0],raw[1])).all());\n    for(int k=0; k<2; ++k) VERIFY(m2(k) == DenseIndex(raw[k]));\n    for(int k=0; k<2; ++k) VERIFY(a2(k) == DenseIndex(raw[k]));\n    for(int k=0; k<2; ++k) VERIFY(m3(k) == int(raw[k]));\n    for(int k=0; k<2; ++k) VERIFY((m4(k)) == Scalar(float(raw[k])));\n  }\n  {\n    Matrix<Scalar,1,1> m(raw), m1(raw[0]), m2( (DenseIndex(raw[0])) ), m3( (int(raw[0])) );\n    Array<Scalar,1,1> a(raw), a1(raw[0]), a2( (DenseIndex(raw[0])) );\n    VERIFY(m(0) == raw[0]);\n    VERIFY(a(0) == raw[0]);\n    VERIFY(m1(0) == raw[0]);\n    VERIFY(a1(0) == raw[0]);\n    VERIFY(m2(0) == DenseIndex(raw[0]));\n    VERIFY(a2(0) == DenseIndex(raw[0]));\n    VERIFY(m3(0) == int(raw[0]));\n    VERIFY_IS_EQUAL(m,(Matrix<Scalar,1,1>(raw[0])));\n    VERIFY((a==Array<Scalar,1,1>(raw[0])).all());\n  }\n}\n\nvoid test_basicstuff()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( basicStuff(Matrix<float, 1, 1>()) );\n    CALL_SUBTEST_2( basicStuff(Matrix4d()) );\n    CALL_SUBTEST_3( basicStuff(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_4( basicStuff(MatrixXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_5( basicStuff(MatrixXcd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_6( basicStuff(Matrix<float, 100, 100>()) );\n    CALL_SUBTEST_7( basicStuff(Matrix<long double,Dynamic,Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n\n    CALL_SUBTEST_3( basicStuffComplex(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_5( basicStuffComplex(MatrixXcd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n  }\n\n  CALL_SUBTEST_1(fixedSizeMatrixConstruction<unsigned char>());\n  CALL_SUBTEST_1(fixedSizeMatrixConstruction<float>());\n  CALL_SUBTEST_1(fixedSizeMatrixConstruction<double>());\n  CALL_SUBTEST_1(fixedSizeMatrixConstruction<int>());\n  CALL_SUBTEST_1(fixedSizeMatrixConstruction<long int>());\n  CALL_SUBTEST_1(fixedSizeMatrixConstruction<std::ptrdiff_t>());\n\n  CALL_SUBTEST_2(casting());\n}\n"
  },
  {
    "path": "include/eigen3/test/bdcsvd.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2013 Gauthier Brun <brun.gauthier@gmail.com>\n// Copyright (C) 2013 Nicolas Carre <nicolas.carre@ensimag.fr>\n// Copyright (C) 2013 Jean Ceccato <jean.ceccato@ensimag.fr>\n// Copyright (C) 2013 Pierre Zoppitelli <pierre.zoppitelli@ensimag.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/\n\n// discard stack allocation as that too bypasses malloc\n#define EIGEN_STACK_ALLOCATION_LIMIT 0\n#define EIGEN_RUNTIME_NO_MALLOC\n\n#include \"main.h\"\n#include <Eigen/SVD>\n#include <iostream>\n#include <Eigen/LU>\n\n\n#define SVD_DEFAULT(M) BDCSVD<M>\n#define SVD_FOR_MIN_NORM(M) BDCSVD<M>\n#include \"svd_common.h\"\n\n// Check all variants of JacobiSVD\ntemplate<typename MatrixType>\nvoid bdcsvd(const MatrixType& a = MatrixType(), bool pickrandom = true)\n{\n  MatrixType m = a;\n  if(pickrandom)\n    svd_fill_random(m);\n\n  CALL_SUBTEST(( svd_test_all_computation_options<BDCSVD<MatrixType> >(m, false)  ));\n}\n\ntemplate<typename MatrixType>\nvoid bdcsvd_method()\n{\n  enum { Size = MatrixType::RowsAtCompileTime };\n  typedef typename MatrixType::RealScalar RealScalar;\n  typedef Matrix<RealScalar, Size, 1> RealVecType;\n  MatrixType m = MatrixType::Identity();\n  VERIFY_IS_APPROX(m.bdcSvd().singularValues(), RealVecType::Ones());\n  VERIFY_RAISES_ASSERT(m.bdcSvd().matrixU());\n  VERIFY_RAISES_ASSERT(m.bdcSvd().matrixV());\n  VERIFY_IS_APPROX(m.bdcSvd(ComputeFullU|ComputeFullV).solve(m), m);\n}\n\n// compare the Singular values returned with Jacobi and Bdc\ntemplate<typename MatrixType> \nvoid compare_bdc_jacobi(const MatrixType& a = MatrixType(), unsigned int computationOptions = 0)\n{\n  MatrixType m = MatrixType::Random(a.rows(), a.cols());\n  BDCSVD<MatrixType> bdc_svd(m);\n  JacobiSVD<MatrixType> jacobi_svd(m);\n  VERIFY_IS_APPROX(bdc_svd.singularValues(), jacobi_svd.singularValues());\n  if(computationOptions & ComputeFullU) VERIFY_IS_APPROX(bdc_svd.matrixU(), jacobi_svd.matrixU());\n  if(computationOptions & ComputeThinU) VERIFY_IS_APPROX(bdc_svd.matrixU(), jacobi_svd.matrixU());\n  if(computationOptions & ComputeFullV) VERIFY_IS_APPROX(bdc_svd.matrixV(), jacobi_svd.matrixV());\n  if(computationOptions & ComputeThinV) VERIFY_IS_APPROX(bdc_svd.matrixV(), jacobi_svd.matrixV());\n}\n\nvoid test_bdcsvd()\n{\n  CALL_SUBTEST_3(( svd_verify_assert<BDCSVD<Matrix3f>  >(Matrix3f()) ));\n  CALL_SUBTEST_4(( svd_verify_assert<BDCSVD<Matrix4d>  >(Matrix4d()) ));\n  CALL_SUBTEST_7(( svd_verify_assert<BDCSVD<MatrixXf>  >(MatrixXf(10,12)) ));\n  CALL_SUBTEST_8(( svd_verify_assert<BDCSVD<MatrixXcd> >(MatrixXcd(7,5)) ));\n  \n  CALL_SUBTEST_101(( svd_all_trivial_2x2(bdcsvd<Matrix2cd>) ));\n  CALL_SUBTEST_102(( svd_all_trivial_2x2(bdcsvd<Matrix2d>) ));\n\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_3(( bdcsvd<Matrix3f>() ));\n    CALL_SUBTEST_4(( bdcsvd<Matrix4d>() ));\n    CALL_SUBTEST_5(( bdcsvd<Matrix<float,3,5> >() ));\n\n    int r = internal::random<int>(1, EIGEN_TEST_MAX_SIZE/2),\n        c = internal::random<int>(1, EIGEN_TEST_MAX_SIZE/2);\n    \n    TEST_SET_BUT_UNUSED_VARIABLE(r)\n    TEST_SET_BUT_UNUSED_VARIABLE(c)\n    \n    CALL_SUBTEST_6((  bdcsvd(Matrix<double,Dynamic,2>(r,2)) ));\n    CALL_SUBTEST_7((  bdcsvd(MatrixXf(r,c)) ));\n    CALL_SUBTEST_7((  compare_bdc_jacobi(MatrixXf(r,c)) ));\n    CALL_SUBTEST_10(( bdcsvd(MatrixXd(r,c)) ));\n    CALL_SUBTEST_10(( compare_bdc_jacobi(MatrixXd(r,c)) ));\n    CALL_SUBTEST_8((  bdcsvd(MatrixXcd(r,c)) ));\n    CALL_SUBTEST_8((  compare_bdc_jacobi(MatrixXcd(r,c)) ));\n\n    // Test on inf/nan matrix\n    CALL_SUBTEST_7(  (svd_inf_nan<BDCSVD<MatrixXf>, MatrixXf>()) );\n    CALL_SUBTEST_10( (svd_inf_nan<BDCSVD<MatrixXd>, MatrixXd>()) );\n  }\n\n  // test matrixbase method\n  CALL_SUBTEST_1(( bdcsvd_method<Matrix2cd>() ));\n  CALL_SUBTEST_3(( bdcsvd_method<Matrix3f>() ));\n\n  // Test problem size constructors\n  CALL_SUBTEST_7( BDCSVD<MatrixXf>(10,10) );\n\n  // Check that preallocation avoids subsequent mallocs\n  // Disbaled because not supported by BDCSVD\n  // CALL_SUBTEST_9( svd_preallocate<void>() );\n\n  CALL_SUBTEST_2( svd_underoverflow<void>() );\n}\n\n"
  },
  {
    "path": "include/eigen3/test/bicgstab.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2011 Gael Guennebaud <g.gael@free.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"sparse_solver.h\"\n#include <Eigen/IterativeLinearSolvers>\n\ntemplate<typename T, typename I> void test_bicgstab_T()\n{\n  BiCGSTAB<SparseMatrix<T,0,I>, DiagonalPreconditioner<T> >     bicgstab_colmajor_diag;\n  BiCGSTAB<SparseMatrix<T,0,I>, IdentityPreconditioner    >     bicgstab_colmajor_I;\n  BiCGSTAB<SparseMatrix<T,0,I>, IncompleteLUT<T,I> >              bicgstab_colmajor_ilut;\n  //BiCGSTAB<SparseMatrix<T>, SSORPreconditioner<T> >     bicgstab_colmajor_ssor;\n\n  bicgstab_colmajor_diag.setTolerance(NumTraits<T>::epsilon()*4);\n  bicgstab_colmajor_ilut.setTolerance(NumTraits<T>::epsilon()*4);\n  \n  CALL_SUBTEST( check_sparse_square_solving(bicgstab_colmajor_diag)  );\n//   CALL_SUBTEST( check_sparse_square_solving(bicgstab_colmajor_I)     );\n  CALL_SUBTEST( check_sparse_square_solving(bicgstab_colmajor_ilut)     );\n  //CALL_SUBTEST( check_sparse_square_solving(bicgstab_colmajor_ssor)     );\n}\n\nvoid test_bicgstab()\n{\n  CALL_SUBTEST_1((test_bicgstab_T<double,int>()) );\n  CALL_SUBTEST_2((test_bicgstab_T<std::complex<double>, int>()));\n  CALL_SUBTEST_3((test_bicgstab_T<double,long int>()));\n}\n"
  },
  {
    "path": "include/eigen3/test/block.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define EIGEN_NO_STATIC_ASSERT // otherwise we fail at compile time on unused paths\n#include \"main.h\"\n\ntemplate<typename MatrixType, typename Index, typename Scalar>\ntypename Eigen::internal::enable_if<!NumTraits<typename MatrixType::Scalar>::IsComplex,typename MatrixType::Scalar>::type\nblock_real_only(const MatrixType &m1, Index r1, Index r2, Index c1, Index c2, const Scalar& s1) {\n  // check cwise-Functions:\n  VERIFY_IS_APPROX(m1.row(r1).cwiseMax(s1), m1.cwiseMax(s1).row(r1));\n  VERIFY_IS_APPROX(m1.col(c1).cwiseMin(s1), m1.cwiseMin(s1).col(c1));\n\n  VERIFY_IS_APPROX(m1.block(r1,c1,r2-r1+1,c2-c1+1).cwiseMin(s1), m1.cwiseMin(s1).block(r1,c1,r2-r1+1,c2-c1+1));\n  VERIFY_IS_APPROX(m1.block(r1,c1,r2-r1+1,c2-c1+1).cwiseMax(s1), m1.cwiseMax(s1).block(r1,c1,r2-r1+1,c2-c1+1));\n  \n  return Scalar(0);\n}\n\ntemplate<typename MatrixType, typename Index, typename Scalar>\ntypename Eigen::internal::enable_if<NumTraits<typename MatrixType::Scalar>::IsComplex,typename MatrixType::Scalar>::type\nblock_real_only(const MatrixType &, Index, Index, Index, Index, const Scalar&) {\n  return Scalar(0);\n}\n\n\ntemplate<typename MatrixType> void block(const MatrixType& m)\n{\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename MatrixType::RealScalar RealScalar;\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;\n  typedef Matrix<Scalar, 1, MatrixType::ColsAtCompileTime> RowVectorType;\n  typedef Matrix<Scalar, Dynamic, Dynamic, MatrixType::IsRowMajor?RowMajor:ColMajor> DynamicMatrixType;\n  typedef Matrix<Scalar, Dynamic, 1> DynamicVectorType;\n  \n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  MatrixType m1 = MatrixType::Random(rows, cols),\n             m1_copy = m1,\n             m2 = MatrixType::Random(rows, cols),\n             m3(rows, cols),\n             ones = MatrixType::Ones(rows, cols);\n  VectorType v1 = VectorType::Random(rows);\n\n  Scalar s1 = internal::random<Scalar>();\n\n  Index r1 = internal::random<Index>(0,rows-1);\n  Index r2 = internal::random<Index>(r1,rows-1);\n  Index c1 = internal::random<Index>(0,cols-1);\n  Index c2 = internal::random<Index>(c1,cols-1);\n\n  block_real_only(m1, r1, r2, c1, c1, s1);\n\n  //check row() and col()\n  VERIFY_IS_EQUAL(m1.col(c1).transpose(), m1.transpose().row(c1));\n  //check operator(), both constant and non-constant, on row() and col()\n  m1 = m1_copy;\n  m1.row(r1) += s1 * m1_copy.row(r2);\n  VERIFY_IS_APPROX(m1.row(r1), m1_copy.row(r1) + s1 * m1_copy.row(r2));\n  // check nested block xpr on lhs\n  m1.row(r1).row(0) += s1 * m1_copy.row(r2);\n  VERIFY_IS_APPROX(m1.row(r1), m1_copy.row(r1) + Scalar(2) * s1 * m1_copy.row(r2));\n  m1 = m1_copy;\n  m1.col(c1) += s1 * m1_copy.col(c2);\n  VERIFY_IS_APPROX(m1.col(c1), m1_copy.col(c1) + s1 * m1_copy.col(c2));\n  m1.col(c1).col(0) += s1 * m1_copy.col(c2);\n  VERIFY_IS_APPROX(m1.col(c1), m1_copy.col(c1) + Scalar(2) * s1 * m1_copy.col(c2));\n  \n  \n  //check block()\n  Matrix<Scalar,Dynamic,Dynamic> b1(1,1); b1(0,0) = m1(r1,c1);\n\n  RowVectorType br1(m1.block(r1,0,1,cols));\n  VectorType bc1(m1.block(0,c1,rows,1));\n  VERIFY_IS_EQUAL(b1, m1.block(r1,c1,1,1));\n  VERIFY_IS_EQUAL(m1.row(r1), br1);\n  VERIFY_IS_EQUAL(m1.col(c1), bc1);\n  //check operator(), both constant and non-constant, on block()\n  m1.block(r1,c1,r2-r1+1,c2-c1+1) = s1 * m2.block(0, 0, r2-r1+1,c2-c1+1);\n  m1.block(r1,c1,r2-r1+1,c2-c1+1)(r2-r1,c2-c1) = m2.block(0, 0, r2-r1+1,c2-c1+1)(0,0);\n\n  enum {\n    BlockRows = 2,\n    BlockCols = 5\n  };\n  if (rows>=5 && cols>=8)\n  {\n    // test fixed block() as lvalue\n    m1.template block<BlockRows,BlockCols>(1,1) *= s1;\n    // test operator() on fixed block() both as constant and non-constant\n    m1.template block<BlockRows,BlockCols>(1,1)(0, 3) = m1.template block<2,5>(1,1)(1,2);\n    // check that fixed block() and block() agree\n    Matrix<Scalar,Dynamic,Dynamic> b = m1.template block<BlockRows,BlockCols>(3,3);\n    VERIFY_IS_EQUAL(b, m1.block(3,3,BlockRows,BlockCols));\n\n    // same tests with mixed fixed/dynamic size\n    m1.template block<BlockRows,Dynamic>(1,1,BlockRows,BlockCols) *= s1;\n    m1.template block<BlockRows,Dynamic>(1,1,BlockRows,BlockCols)(0,3) = m1.template block<2,5>(1,1)(1,2);\n    Matrix<Scalar,Dynamic,Dynamic> b2 = m1.template block<Dynamic,BlockCols>(3,3,2,5);\n    VERIFY_IS_EQUAL(b2, m1.block(3,3,BlockRows,BlockCols));\n  }\n\n  if (rows>2)\n  {\n    // test sub vectors\n    VERIFY_IS_EQUAL(v1.template head<2>(), v1.block(0,0,2,1));\n    VERIFY_IS_EQUAL(v1.template head<2>(), v1.head(2));\n    VERIFY_IS_EQUAL(v1.template head<2>(), v1.segment(0,2));\n    VERIFY_IS_EQUAL(v1.template head<2>(), v1.template segment<2>(0));\n    Index i = rows-2;\n    VERIFY_IS_EQUAL(v1.template tail<2>(), v1.block(i,0,2,1));\n    VERIFY_IS_EQUAL(v1.template tail<2>(), v1.tail(2));\n    VERIFY_IS_EQUAL(v1.template tail<2>(), v1.segment(i,2));\n    VERIFY_IS_EQUAL(v1.template tail<2>(), v1.template segment<2>(i));\n    i = internal::random<Index>(0,rows-2);\n    VERIFY_IS_EQUAL(v1.segment(i,2), v1.template segment<2>(i));\n  }\n\n  // stress some basic stuffs with block matrices\n  VERIFY(numext::real(ones.col(c1).sum()) == RealScalar(rows));\n  VERIFY(numext::real(ones.row(r1).sum()) == RealScalar(cols));\n\n  VERIFY(numext::real(ones.col(c1).dot(ones.col(c2))) == RealScalar(rows));\n  VERIFY(numext::real(ones.row(r1).dot(ones.row(r2))) == RealScalar(cols));\n  \n  // check that linear acccessors works on blocks\n  m1 = m1_copy;\n  if((MatrixType::Flags&RowMajorBit)==0)\n    VERIFY_IS_EQUAL(m1.leftCols(c1).coeff(r1+c1*rows), m1(r1,c1));\n  else\n    VERIFY_IS_EQUAL(m1.topRows(r1).coeff(c1+r1*cols), m1(r1,c1));\n  \n\n  // now test some block-inside-of-block.\n  \n  // expressions with direct access\n  VERIFY_IS_EQUAL( (m1.block(r1,c1,rows-r1,cols-c1).block(r2-r1,c2-c1,rows-r2,cols-c2)) , (m1.block(r2,c2,rows-r2,cols-c2)) );\n  VERIFY_IS_EQUAL( (m1.block(r1,c1,r2-r1+1,c2-c1+1).row(0)) , (m1.row(r1).segment(c1,c2-c1+1)) );\n  VERIFY_IS_EQUAL( (m1.block(r1,c1,r2-r1+1,c2-c1+1).col(0)) , (m1.col(c1).segment(r1,r2-r1+1)) );\n  VERIFY_IS_EQUAL( (m1.block(r1,c1,r2-r1+1,c2-c1+1).transpose().col(0)) , (m1.row(r1).segment(c1,c2-c1+1)).transpose() );\n  VERIFY_IS_EQUAL( (m1.transpose().block(c1,r1,c2-c1+1,r2-r1+1).col(0)) , (m1.row(r1).segment(c1,c2-c1+1)).transpose() );\n\n  // expressions without direct access\n  VERIFY_IS_APPROX( ((m1+m2).block(r1,c1,rows-r1,cols-c1).block(r2-r1,c2-c1,rows-r2,cols-c2)) , ((m1+m2).block(r2,c2,rows-r2,cols-c2)) );\n  VERIFY_IS_APPROX( ((m1+m2).block(r1,c1,r2-r1+1,c2-c1+1).row(0)) , ((m1+m2).row(r1).segment(c1,c2-c1+1)) );\n  VERIFY_IS_APPROX( ((m1+m2).block(r1,c1,r2-r1+1,c2-c1+1).col(0)) , ((m1+m2).col(c1).segment(r1,r2-r1+1)) );\n  VERIFY_IS_APPROX( ((m1+m2).block(r1,c1,r2-r1+1,c2-c1+1).transpose().col(0)) , ((m1+m2).row(r1).segment(c1,c2-c1+1)).transpose() );\n  VERIFY_IS_APPROX( ((m1+m2).transpose().block(c1,r1,c2-c1+1,r2-r1+1).col(0)) , ((m1+m2).row(r1).segment(c1,c2-c1+1)).transpose() );\n\n  VERIFY_IS_APPROX( (m1*1).topRows(r1),  m1.topRows(r1) );\n  VERIFY_IS_APPROX( (m1*1).leftCols(c1), m1.leftCols(c1) );\n  VERIFY_IS_APPROX( (m1*1).transpose().topRows(c1), m1.transpose().topRows(c1) );\n  VERIFY_IS_APPROX( (m1*1).transpose().leftCols(r1), m1.transpose().leftCols(r1) );\n  VERIFY_IS_APPROX( (m1*1).transpose().middleRows(c1,c2-c1+1), m1.transpose().middleRows(c1,c2-c1+1) );\n  VERIFY_IS_APPROX( (m1*1).transpose().middleCols(r1,r2-r1+1), m1.transpose().middleCols(r1,r2-r1+1) );\n\n  // evaluation into plain matrices from expressions with direct access (stress MapBase)\n  DynamicMatrixType dm;\n  DynamicVectorType dv;\n  dm.setZero();\n  dm = m1.block(r1,c1,rows-r1,cols-c1).block(r2-r1,c2-c1,rows-r2,cols-c2);\n  VERIFY_IS_EQUAL(dm, (m1.block(r2,c2,rows-r2,cols-c2)));\n  dm.setZero();\n  dv.setZero();\n  dm = m1.block(r1,c1,r2-r1+1,c2-c1+1).row(0).transpose();\n  dv = m1.row(r1).segment(c1,c2-c1+1);\n  VERIFY_IS_EQUAL(dv, dm);\n  dm.setZero();\n  dv.setZero();\n  dm = m1.col(c1).segment(r1,r2-r1+1);\n  dv = m1.block(r1,c1,r2-r1+1,c2-c1+1).col(0);\n  VERIFY_IS_EQUAL(dv, dm);\n  dm.setZero();\n  dv.setZero();\n  dm = m1.block(r1,c1,r2-r1+1,c2-c1+1).transpose().col(0);\n  dv = m1.row(r1).segment(c1,c2-c1+1);\n  VERIFY_IS_EQUAL(dv, dm);\n  dm.setZero();\n  dv.setZero();\n  dm = m1.row(r1).segment(c1,c2-c1+1).transpose();\n  dv = m1.transpose().block(c1,r1,c2-c1+1,r2-r1+1).col(0);\n  VERIFY_IS_EQUAL(dv, dm);\n\n  VERIFY_IS_EQUAL( (m1.template block<Dynamic,1>(1,0,0,1)), m1.block(1,0,0,1));\n  VERIFY_IS_EQUAL( (m1.template block<1,Dynamic>(0,1,1,0)), m1.block(0,1,1,0));\n  VERIFY_IS_EQUAL( ((m1*1).template block<Dynamic,1>(1,0,0,1)), m1.block(1,0,0,1));\n  VERIFY_IS_EQUAL( ((m1*1).template block<1,Dynamic>(0,1,1,0)), m1.block(0,1,1,0));\n\n  if (rows>=2 && cols>=2)\n  {\n    VERIFY_RAISES_ASSERT( m1 += m1.col(0) );\n    VERIFY_RAISES_ASSERT( m1 -= m1.col(0) );\n    VERIFY_RAISES_ASSERT( m1.array() *= m1.col(0).array() );\n    VERIFY_RAISES_ASSERT( m1.array() /= m1.col(0).array() );\n  }\n}\n\n\ntemplate<typename MatrixType>\nvoid compare_using_data_and_stride(const MatrixType& m)\n{\n  typedef typename MatrixType::Index Index;\n  Index rows = m.rows();\n  Index cols = m.cols();\n  Index size = m.size();\n  Index innerStride = m.innerStride();\n  Index outerStride = m.outerStride();\n  Index rowStride = m.rowStride();\n  Index colStride = m.colStride();\n  const typename MatrixType::Scalar* data = m.data();\n\n  for(int j=0;j<cols;++j)\n    for(int i=0;i<rows;++i)\n      VERIFY(m.coeff(i,j) == data[i*rowStride + j*colStride]);\n\n  if(!MatrixType::IsVectorAtCompileTime)\n  {\n    for(int j=0;j<cols;++j)\n      for(int i=0;i<rows;++i)\n        VERIFY(m.coeff(i,j) == data[(MatrixType::Flags&RowMajorBit)\n                                     ? i*outerStride + j*innerStride\n                                     : j*outerStride + i*innerStride]);\n  }\n\n  if(MatrixType::IsVectorAtCompileTime)\n  {\n    VERIFY(innerStride == int((&m.coeff(1))-(&m.coeff(0))));\n    for (int i=0;i<size;++i)\n      VERIFY(m.coeff(i) == data[i*innerStride]);\n  }\n}\n\ntemplate<typename MatrixType>\nvoid data_and_stride(const MatrixType& m)\n{\n  typedef typename MatrixType::Index Index;\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  Index r1 = internal::random<Index>(0,rows-1);\n  Index r2 = internal::random<Index>(r1,rows-1);\n  Index c1 = internal::random<Index>(0,cols-1);\n  Index c2 = internal::random<Index>(c1,cols-1);\n\n  MatrixType m1 = MatrixType::Random(rows, cols);\n  compare_using_data_and_stride(m1.block(r1, c1, r2-r1+1, c2-c1+1));\n  compare_using_data_and_stride(m1.transpose().block(c1, r1, c2-c1+1, r2-r1+1));\n  compare_using_data_and_stride(m1.row(r1));\n  compare_using_data_and_stride(m1.col(c1));\n  compare_using_data_and_stride(m1.row(r1).transpose());\n  compare_using_data_and_stride(m1.col(c1).transpose());\n}\n\nvoid test_block()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( block(Matrix<float, 1, 1>()) );\n    CALL_SUBTEST_2( block(Matrix4d()) );\n    CALL_SUBTEST_3( block(MatrixXcf(3, 3)) );\n    CALL_SUBTEST_4( block(MatrixXi(8, 12)) );\n    CALL_SUBTEST_5( block(MatrixXcd(20, 20)) );\n    CALL_SUBTEST_6( block(MatrixXf(20, 20)) );\n\n    CALL_SUBTEST_8( block(Matrix<float,Dynamic,4>(3, 4)) );\n\n#ifndef EIGEN_DEFAULT_TO_ROW_MAJOR\n    CALL_SUBTEST_6( data_and_stride(MatrixXf(internal::random(5,50), internal::random(5,50))) );\n    CALL_SUBTEST_7( data_and_stride(Matrix<int,Dynamic,Dynamic,RowMajor>(internal::random(5,50), internal::random(5,50))) );\n#endif\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/boostmultiprec.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include <sstream>\n\n#ifdef EIGEN_TEST_MAX_SIZE\n#undef EIGEN_TEST_MAX_SIZE\n#endif\n\n#define EIGEN_TEST_MAX_SIZE 50\n\n#ifdef EIGEN_TEST_PART_1\n#include \"cholesky.cpp\"\n#endif\n\n#ifdef EIGEN_TEST_PART_2\n#include \"lu.cpp\"\n#endif\n\n#ifdef EIGEN_TEST_PART_3\n#include \"qr.cpp\"\n#endif\n\n#ifdef EIGEN_TEST_PART_4\n#include \"qr_colpivoting.cpp\"\n#endif\n\n#ifdef EIGEN_TEST_PART_5\n#include \"qr_fullpivoting.cpp\"\n#endif\n\n#ifdef EIGEN_TEST_PART_6\n#include \"eigensolver_selfadjoint.cpp\"\n#endif\n\n#ifdef EIGEN_TEST_PART_7\n#include \"eigensolver_generic.cpp\"\n#endif\n\n#ifdef EIGEN_TEST_PART_8\n#include \"eigensolver_generalized_real.cpp\"\n#endif\n\n#ifdef EIGEN_TEST_PART_9\n#include \"jacobisvd.cpp\"\n#endif\n\n#ifdef EIGEN_TEST_PART_10\n#include \"bdcsvd.cpp\"\n#endif\n\n#include <Eigen/Dense>\n\n#undef min\n#undef max\n#undef isnan\n#undef isinf\n#undef isfinite\n\n#include <boost/multiprecision/cpp_dec_float.hpp>\n#include <boost/multiprecision/number.hpp>\n#include <boost/math/special_functions.hpp>\n#include <boost/math/complex.hpp>\n\nnamespace mp = boost::multiprecision;\ntypedef mp::number<mp::cpp_dec_float<100>, mp::et_on> Real;\n\nnamespace Eigen {\n  template<> struct NumTraits<Real> : GenericNumTraits<Real> {\n    static inline Real dummy_precision() { return 1e-50; }\n  };\n\n  template<typename T1,typename T2,typename T3,typename T4,typename T5>\n  struct NumTraits<boost::multiprecision::detail::expression<T1,T2,T3,T4,T5> > : NumTraits<Real> {};\n\n  template<>\n  Real test_precision<Real>() { return 1e-50; }\n\n  // needed in C++93 mode where number does not support explicit cast.\n  namespace internal {\n    template<typename NewType>\n    struct cast_impl<Real,NewType> {\n      static inline NewType run(const Real& x) {\n        return x.template convert_to<NewType>();\n      }\n    };\n\n    template<>\n    struct cast_impl<Real,std::complex<Real> > {\n      static inline std::complex<Real>  run(const Real& x) {\n        return std::complex<Real>(x);\n      }\n    };\n  }\n}\n\nnamespace boost {\nnamespace multiprecision {\n  // to make ADL works as expected:\n  using boost::math::isfinite;\n  using boost::math::isnan;\n  using boost::math::isinf;\n  using boost::math::copysign;\n  using boost::math::hypot;\n\n  // The following is needed for std::complex<Real>:\n  Real fabs(const Real& a) { return abs EIGEN_NOT_A_MACRO (a); }\n  Real fmax(const Real& a, const Real& b) { using std::max; return max(a,b); }\n\n  // some specialization for the unit tests:\n  inline bool test_isMuchSmallerThan(const Real& a, const Real& b) {\n    return internal::isMuchSmallerThan(a, b, test_precision<Real>());\n  }\n\n  inline bool test_isApprox(const Real& a, const Real& b) {\n    return internal::isApprox(a, b, test_precision<Real>());\n  }\n\n  inline bool test_isApproxOrLessThan(const Real& a, const Real& b) {\n    return internal::isApproxOrLessThan(a, b, test_precision<Real>());\n  }\n\n  Real get_test_precision(const Real&) {\n    return test_precision<Real>();\n  }\n\n  Real test_relative_error(const Real &a, const Real &b) {\n    using Eigen::numext::abs2;\n    return sqrt(abs2<Real>(a-b)/Eigen::numext::mini<Real>(abs2(a),abs2(b)));\n  }\n}\n}\n\nnamespace Eigen {\n\n}\n\nvoid test_boostmultiprec()\n{\n  typedef Matrix<Real,Dynamic,Dynamic> Mat;\n  typedef Matrix<std::complex<Real>,Dynamic,Dynamic> MatC;\n\n  std::cout << \"NumTraits<Real>::epsilon()         = \" << NumTraits<Real>::epsilon() << std::endl;\n  std::cout << \"NumTraits<Real>::dummy_precision() = \" << NumTraits<Real>::dummy_precision() << std::endl;\n  std::cout << \"NumTraits<Real>::lowest()          = \" << NumTraits<Real>::lowest() << std::endl;\n  std::cout << \"NumTraits<Real>::highest()         = \" << NumTraits<Real>::highest() << std::endl;\n  std::cout << \"NumTraits<Real>::digits10()        = \" << NumTraits<Real>::digits10() << std::endl;\n\n  // chekc stream output\n  {\n    Mat A(10,10);\n    A.setRandom();\n    std::stringstream ss;\n    ss << A;\n  }\n  {\n    MatC A(10,10);\n    A.setRandom();\n    std::stringstream ss;\n    ss << A;\n  }\n\n  for(int i = 0; i < g_repeat; i++) {\n    int s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE);\n\n    CALL_SUBTEST_1( cholesky(Mat(s,s)) );\n\n    CALL_SUBTEST_2( lu_non_invertible<Mat>() );\n    CALL_SUBTEST_2( lu_invertible<Mat>() );\n    CALL_SUBTEST_2( lu_non_invertible<MatC>() );\n    CALL_SUBTEST_2( lu_invertible<MatC>() );\n\n    CALL_SUBTEST_3( qr(Mat(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_3( qr_invertible<Mat>() );\n\n    CALL_SUBTEST_4( qr<Mat>() );\n    CALL_SUBTEST_4( cod<Mat>() );\n    CALL_SUBTEST_4( qr_invertible<Mat>() );\n\n    CALL_SUBTEST_5( qr<Mat>() );\n    CALL_SUBTEST_5( qr_invertible<Mat>() );\n\n    CALL_SUBTEST_6( selfadjointeigensolver(Mat(s,s)) );\n\n    CALL_SUBTEST_7( eigensolver(Mat(s,s)) );\n\n    CALL_SUBTEST_8( generalized_eigensolver_real(Mat(s,s)) );\n\n    TEST_SET_BUT_UNUSED_VARIABLE(s)\n  }\n\n  CALL_SUBTEST_9(( jacobisvd(Mat(internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE), internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/2))) ));\n  CALL_SUBTEST_10(( bdcsvd(Mat(internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE), internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/2))) ));\n}\n\n"
  },
  {
    "path": "include/eigen3/test/bug1213.cpp",
    "content": "\n// This anonymous enum is essential to trigger the linking issue\nenum {\n  Foo\n};\n\n#include \"bug1213.h\"\n\nbool bug1213_1(const Eigen::Vector3f& x)\n{\n  return bug1213_2(x);\n}\n\n"
  },
  {
    "path": "include/eigen3/test/bug1213.h",
    "content": "\n#include <Eigen/Core>\n\ntemplate<typename T, int dim>\nbool bug1213_2(const Eigen::Matrix<T,dim,1>& x);\n\nbool bug1213_1(const Eigen::Vector3f& x);\n\n"
  },
  {
    "path": "include/eigen3/test/bug1213_main.cpp",
    "content": "\n// This is a regression unit regarding a weird linking issue with gcc.\n\n#include \"bug1213.h\"\n\nint main()\n{\n  return 0;\n}\n\n\ntemplate<typename T, int dim>\nbool bug1213_2(const Eigen::Matrix<T,dim,1>& )\n{\n  return true;\n}\n\ntemplate bool bug1213_2<float,3>(const Eigen::Vector3f&);\n"
  },
  {
    "path": "include/eigen3/test/cholesky.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_NO_ASSERTION_CHECKING\n#define EIGEN_NO_ASSERTION_CHECKING\n#endif\n\n#define TEST_ENABLE_TEMPORARY_TRACKING\n\n#include \"main.h\"\n#include <Eigen/Cholesky>\n#include <Eigen/QR>\n\ntemplate<typename MatrixType, int UpLo>\ntypename MatrixType::RealScalar matrix_l1_norm(const MatrixType& m) {\n  MatrixType symm = m.template selfadjointView<UpLo>();\n  return symm.cwiseAbs().colwise().sum().maxCoeff();\n}\n\ntemplate<typename MatrixType,template <typename,int> class CholType> void test_chol_update(const MatrixType& symm)\n{\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename MatrixType::RealScalar RealScalar;\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;\n\n  MatrixType symmLo = symm.template triangularView<Lower>();\n  MatrixType symmUp = symm.template triangularView<Upper>();\n  MatrixType symmCpy = symm;\n\n  CholType<MatrixType,Lower> chollo(symmLo);\n  CholType<MatrixType,Upper> cholup(symmUp);\n\n  for (int k=0; k<10; ++k)\n  {\n    VectorType vec = VectorType::Random(symm.rows());\n    RealScalar sigma = internal::random<RealScalar>();\n    symmCpy += sigma * vec * vec.adjoint();\n\n    // we are doing some downdates, so it might be the case that the matrix is not SPD anymore\n    CholType<MatrixType,Lower> chol(symmCpy);\n    if(chol.info()!=Success)\n      break;\n\n    chollo.rankUpdate(vec, sigma);\n    VERIFY_IS_APPROX(symmCpy, chollo.reconstructedMatrix());\n\n    cholup.rankUpdate(vec, sigma);\n    VERIFY_IS_APPROX(symmCpy, cholup.reconstructedMatrix());\n  }\n}\n\ntemplate<typename MatrixType> void cholesky(const MatrixType& m)\n{\n  typedef typename MatrixType::Index Index;\n  /* this test covers the following files:\n     LLT.h LDLT.h\n  */\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;\n\n  MatrixType a0 = MatrixType::Random(rows,cols);\n  VectorType vecB = VectorType::Random(rows), vecX(rows);\n  MatrixType matB = MatrixType::Random(rows,cols), matX(rows,cols);\n  SquareMatrixType symm =  a0 * a0.adjoint();\n  // let's make sure the matrix is not singular or near singular\n  for (int k=0; k<3; ++k)\n  {\n    MatrixType a1 = MatrixType::Random(rows,cols);\n    symm += a1 * a1.adjoint();\n  }\n\n  {\n    SquareMatrixType symmUp = symm.template triangularView<Upper>();\n    SquareMatrixType symmLo = symm.template triangularView<Lower>();\n\n    LLT<SquareMatrixType,Lower> chollo(symmLo);\n    VERIFY_IS_APPROX(symm, chollo.reconstructedMatrix());\n    vecX = chollo.solve(vecB);\n    VERIFY_IS_APPROX(symm * vecX, vecB);\n    matX = chollo.solve(matB);\n    VERIFY_IS_APPROX(symm * matX, matB);\n\n    const MatrixType symmLo_inverse = chollo.solve(MatrixType::Identity(rows,cols));\n    RealScalar rcond = (RealScalar(1) / matrix_l1_norm<MatrixType, Lower>(symmLo)) /\n                             matrix_l1_norm<MatrixType, Lower>(symmLo_inverse);\n    RealScalar rcond_est = chollo.rcond();\n    // Verify that the estimated condition number is within a factor of 10 of the\n    // truth.\n    VERIFY(rcond_est > rcond / 10 && rcond_est < rcond * 10);\n\n    // test the upper mode\n    LLT<SquareMatrixType,Upper> cholup(symmUp);\n    VERIFY_IS_APPROX(symm, cholup.reconstructedMatrix());\n    vecX = cholup.solve(vecB);\n    VERIFY_IS_APPROX(symm * vecX, vecB);\n    matX = cholup.solve(matB);\n    VERIFY_IS_APPROX(symm * matX, matB);\n\n    // Verify that the estimated condition number is within a factor of 10 of the\n    // truth.\n    const MatrixType symmUp_inverse = cholup.solve(MatrixType::Identity(rows,cols));\n    rcond = (RealScalar(1) / matrix_l1_norm<MatrixType, Upper>(symmUp)) /\n                             matrix_l1_norm<MatrixType, Upper>(symmUp_inverse);\n    rcond_est = cholup.rcond();\n    VERIFY(rcond_est > rcond / 10 && rcond_est < rcond * 10);\n\n\n    MatrixType neg = -symmLo;\n    chollo.compute(neg);\n    VERIFY(chollo.info()==NumericalIssue);\n\n    VERIFY_IS_APPROX(MatrixType(chollo.matrixL().transpose().conjugate()), MatrixType(chollo.matrixU()));\n    VERIFY_IS_APPROX(MatrixType(chollo.matrixU().transpose().conjugate()), MatrixType(chollo.matrixL()));\n    VERIFY_IS_APPROX(MatrixType(cholup.matrixL().transpose().conjugate()), MatrixType(cholup.matrixU()));\n    VERIFY_IS_APPROX(MatrixType(cholup.matrixU().transpose().conjugate()), MatrixType(cholup.matrixL()));\n\n    // test some special use cases of SelfCwiseBinaryOp:\n    MatrixType m1 = MatrixType::Random(rows,cols), m2(rows,cols);\n    m2 = m1;\n    m2 += symmLo.template selfadjointView<Lower>().llt().solve(matB);\n    VERIFY_IS_APPROX(m2, m1 + symmLo.template selfadjointView<Lower>().llt().solve(matB));\n    m2 = m1;\n    m2 -= symmLo.template selfadjointView<Lower>().llt().solve(matB);\n    VERIFY_IS_APPROX(m2, m1 - symmLo.template selfadjointView<Lower>().llt().solve(matB));\n    m2 = m1;\n    m2.noalias() += symmLo.template selfadjointView<Lower>().llt().solve(matB);\n    VERIFY_IS_APPROX(m2, m1 + symmLo.template selfadjointView<Lower>().llt().solve(matB));\n    m2 = m1;\n    m2.noalias() -= symmLo.template selfadjointView<Lower>().llt().solve(matB);\n    VERIFY_IS_APPROX(m2, m1 - symmLo.template selfadjointView<Lower>().llt().solve(matB));\n  }\n\n  // LDLT\n  {\n    int sign = internal::random<int>()%2 ? 1 : -1;\n\n    if(sign == -1)\n    {\n      symm = -symm; // test a negative matrix\n    }\n\n    SquareMatrixType symmUp = symm.template triangularView<Upper>();\n    SquareMatrixType symmLo = symm.template triangularView<Lower>();\n\n    LDLT<SquareMatrixType,Lower> ldltlo(symmLo);\n    VERIFY(ldltlo.info()==Success);\n    VERIFY_IS_APPROX(symm, ldltlo.reconstructedMatrix());\n    vecX = ldltlo.solve(vecB);\n    VERIFY_IS_APPROX(symm * vecX, vecB);\n    matX = ldltlo.solve(matB);\n    VERIFY_IS_APPROX(symm * matX, matB);\n\n    const MatrixType symmLo_inverse = ldltlo.solve(MatrixType::Identity(rows,cols));\n    RealScalar rcond = (RealScalar(1) / matrix_l1_norm<MatrixType, Lower>(symmLo)) /\n                             matrix_l1_norm<MatrixType, Lower>(symmLo_inverse);\n    RealScalar rcond_est = ldltlo.rcond();\n    // Verify that the estimated condition number is within a factor of 10 of the\n    // truth.\n    VERIFY(rcond_est > rcond / 10 && rcond_est < rcond * 10);\n\n\n    LDLT<SquareMatrixType,Upper> ldltup(symmUp);\n    VERIFY(ldltup.info()==Success);\n    VERIFY_IS_APPROX(symm, ldltup.reconstructedMatrix());\n    vecX = ldltup.solve(vecB);\n    VERIFY_IS_APPROX(symm * vecX, vecB);\n    matX = ldltup.solve(matB);\n    VERIFY_IS_APPROX(symm * matX, matB);\n\n    // Verify that the estimated condition number is within a factor of 10 of the\n    // truth.\n    const MatrixType symmUp_inverse = ldltup.solve(MatrixType::Identity(rows,cols));\n    rcond = (RealScalar(1) / matrix_l1_norm<MatrixType, Upper>(symmUp)) /\n                             matrix_l1_norm<MatrixType, Upper>(symmUp_inverse);\n    rcond_est = ldltup.rcond();\n    VERIFY(rcond_est > rcond / 10 && rcond_est < rcond * 10);\n\n    VERIFY_IS_APPROX(MatrixType(ldltlo.matrixL().transpose().conjugate()), MatrixType(ldltlo.matrixU()));\n    VERIFY_IS_APPROX(MatrixType(ldltlo.matrixU().transpose().conjugate()), MatrixType(ldltlo.matrixL()));\n    VERIFY_IS_APPROX(MatrixType(ldltup.matrixL().transpose().conjugate()), MatrixType(ldltup.matrixU()));\n    VERIFY_IS_APPROX(MatrixType(ldltup.matrixU().transpose().conjugate()), MatrixType(ldltup.matrixL()));\n\n    if(MatrixType::RowsAtCompileTime==Dynamic)\n    {\n      // note : each inplace permutation requires a small temporary vector (mask)\n\n      // check inplace solve\n      matX = matB;\n      VERIFY_EVALUATION_COUNT(matX = ldltlo.solve(matX), 0);\n      VERIFY_IS_APPROX(matX, ldltlo.solve(matB).eval());\n\n\n      matX = matB;\n      VERIFY_EVALUATION_COUNT(matX = ldltup.solve(matX), 0);\n      VERIFY_IS_APPROX(matX, ldltup.solve(matB).eval());\n    }\n\n    // restore\n    if(sign == -1)\n      symm = -symm;\n\n    // check matrices coming from linear constraints with Lagrange multipliers\n    if(rows>=3)\n    {\n      SquareMatrixType A = symm;\n      Index c = internal::random<Index>(0,rows-2);\n      A.bottomRightCorner(c,c).setZero();\n      // Make sure a solution exists:\n      vecX.setRandom();\n      vecB = A * vecX;\n      vecX.setZero();\n      ldltlo.compute(A);\n      VERIFY_IS_APPROX(A, ldltlo.reconstructedMatrix());\n      vecX = ldltlo.solve(vecB);\n      VERIFY_IS_APPROX(A * vecX, vecB);\n    }\n\n    // check non-full rank matrices\n    if(rows>=3)\n    {\n      Index r = internal::random<Index>(1,rows-1);\n      Matrix<Scalar,Dynamic,Dynamic> a = Matrix<Scalar,Dynamic,Dynamic>::Random(rows,r);\n      SquareMatrixType A = a * a.adjoint();\n      // Make sure a solution exists:\n      vecX.setRandom();\n      vecB = A * vecX;\n      vecX.setZero();\n      ldltlo.compute(A);\n      VERIFY_IS_APPROX(A, ldltlo.reconstructedMatrix());\n      vecX = ldltlo.solve(vecB);\n      VERIFY_IS_APPROX(A * vecX, vecB);\n    }\n\n    // check matrices with a wide spectrum\n    if(rows>=3)\n    {\n      using std::pow;\n      using std::sqrt;\n      RealScalar s = (std::min)(16,std::numeric_limits<RealScalar>::max_exponent10/8);\n      Matrix<Scalar,Dynamic,Dynamic> a = Matrix<Scalar,Dynamic,Dynamic>::Random(rows,rows);\n      Matrix<RealScalar,Dynamic,1> d =  Matrix<RealScalar,Dynamic,1>::Random(rows);\n      for(Index k=0; k<rows; ++k)\n        d(k) = d(k)*pow(RealScalar(10),internal::random<RealScalar>(-s,s));\n      SquareMatrixType A = a * d.asDiagonal() * a.adjoint();\n      // Make sure a solution exists:\n      vecX.setRandom();\n      vecB = A * vecX;\n      vecX.setZero();\n      ldltlo.compute(A);\n      VERIFY_IS_APPROX(A, ldltlo.reconstructedMatrix());\n      vecX = ldltlo.solve(vecB);\n\n      if(ldltlo.vectorD().real().cwiseAbs().minCoeff()>RealScalar(0))\n      {\n        VERIFY_IS_APPROX(A * vecX,vecB);\n      }\n      else\n      {\n        RealScalar large_tol =  sqrt(test_precision<RealScalar>());\n        VERIFY((A * vecX).isApprox(vecB, large_tol));\n\n        ++g_test_level;\n        VERIFY_IS_APPROX(A * vecX,vecB);\n        --g_test_level;\n      }\n    }\n  }\n\n  // update/downdate\n  CALL_SUBTEST(( test_chol_update<SquareMatrixType,LLT>(symm)  ));\n  CALL_SUBTEST(( test_chol_update<SquareMatrixType,LDLT>(symm) ));\n}\n\ntemplate<typename MatrixType> void cholesky_cplx(const MatrixType& m)\n{\n  // classic test\n  cholesky(m);\n\n  // test mixing real/scalar types\n\n  typedef typename MatrixType::Index Index;\n\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  typedef Matrix<RealScalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> RealMatrixType;\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;\n\n  RealMatrixType a0 = RealMatrixType::Random(rows,cols);\n  VectorType vecB = VectorType::Random(rows), vecX(rows);\n  MatrixType matB = MatrixType::Random(rows,cols), matX(rows,cols);\n  RealMatrixType symm =  a0 * a0.adjoint();\n  // let's make sure the matrix is not singular or near singular\n  for (int k=0; k<3; ++k)\n  {\n    RealMatrixType a1 = RealMatrixType::Random(rows,cols);\n    symm += a1 * a1.adjoint();\n  }\n\n  {\n    RealMatrixType symmLo = symm.template triangularView<Lower>();\n\n    LLT<RealMatrixType,Lower> chollo(symmLo);\n    VERIFY_IS_APPROX(symm, chollo.reconstructedMatrix());\n    vecX = chollo.solve(vecB);\n    VERIFY_IS_APPROX(symm * vecX, vecB);\n//     matX = chollo.solve(matB);\n//     VERIFY_IS_APPROX(symm * matX, matB);\n  }\n\n  // LDLT\n  {\n    int sign = internal::random<int>()%2 ? 1 : -1;\n\n    if(sign == -1)\n    {\n      symm = -symm; // test a negative matrix\n    }\n\n    RealMatrixType symmLo = symm.template triangularView<Lower>();\n\n    LDLT<RealMatrixType,Lower> ldltlo(symmLo);\n    VERIFY(ldltlo.info()==Success);\n    VERIFY_IS_APPROX(symm, ldltlo.reconstructedMatrix());\n    vecX = ldltlo.solve(vecB);\n    VERIFY_IS_APPROX(symm * vecX, vecB);\n//     matX = ldltlo.solve(matB);\n//     VERIFY_IS_APPROX(symm * matX, matB);\n  }\n}\n\n// regression test for bug 241\ntemplate<typename MatrixType> void cholesky_bug241(const MatrixType& m)\n{\n  eigen_assert(m.rows() == 2 && m.cols() == 2);\n\n  typedef typename MatrixType::Scalar Scalar;\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;\n\n  MatrixType matA;\n  matA << 1, 1, 1, 1;\n  VectorType vecB;\n  vecB << 1, 1;\n  VectorType vecX = matA.ldlt().solve(vecB);\n  VERIFY_IS_APPROX(matA * vecX, vecB);\n}\n\n// LDLT is not guaranteed to work for indefinite matrices, but happens to work fine if matrix is diagonal.\n// This test checks that LDLT reports correctly that matrix is indefinite.\n// See http://forum.kde.org/viewtopic.php?f=74&t=106942 and bug 736\ntemplate<typename MatrixType> void cholesky_definiteness(const MatrixType& m)\n{\n  eigen_assert(m.rows() == 2 && m.cols() == 2);\n  MatrixType mat;\n  LDLT<MatrixType> ldlt(2);\n\n  {\n    mat << 1, 0, 0, -1;\n    ldlt.compute(mat);\n    VERIFY(ldlt.info()==Success);\n    VERIFY(!ldlt.isNegative());\n    VERIFY(!ldlt.isPositive());\n    VERIFY_IS_APPROX(mat,ldlt.reconstructedMatrix());\n  }\n  {\n    mat << 1, 2, 2, 1;\n    ldlt.compute(mat);\n    VERIFY(ldlt.info()==Success);\n    VERIFY(!ldlt.isNegative());\n    VERIFY(!ldlt.isPositive());\n    VERIFY_IS_APPROX(mat,ldlt.reconstructedMatrix());\n  }\n  {\n    mat << 0, 0, 0, 0;\n    ldlt.compute(mat);\n    VERIFY(ldlt.info()==Success);\n    VERIFY(ldlt.isNegative());\n    VERIFY(ldlt.isPositive());\n    VERIFY_IS_APPROX(mat,ldlt.reconstructedMatrix());\n  }\n  {\n    mat << 0, 0, 0, 1;\n    ldlt.compute(mat);\n    VERIFY(ldlt.info()==Success);\n    VERIFY(!ldlt.isNegative());\n    VERIFY(ldlt.isPositive());\n    VERIFY_IS_APPROX(mat,ldlt.reconstructedMatrix());\n  }\n  {\n    mat << -1, 0, 0, 0;\n    ldlt.compute(mat);\n    VERIFY(ldlt.info()==Success);\n    VERIFY(ldlt.isNegative());\n    VERIFY(!ldlt.isPositive());\n    VERIFY_IS_APPROX(mat,ldlt.reconstructedMatrix());\n  }\n}\n\ntemplate<typename>\nvoid cholesky_faillure_cases()\n{\n  MatrixXd mat;\n  LDLT<MatrixXd> ldlt;\n\n  {\n    mat.resize(2,2);\n    mat << 0, 1, 1, 0;\n    ldlt.compute(mat);\n    VERIFY_IS_NOT_APPROX(mat,ldlt.reconstructedMatrix());\n    VERIFY(ldlt.info()==NumericalIssue);\n  }\n#if (!EIGEN_ARCH_i386) || defined(EIGEN_VECTORIZE_SSE2)\n  {\n    mat.resize(3,3);\n    mat << -1, -3, 3,\n           -3, -8.9999999999999999999, 1,\n            3, 1, 0;\n    ldlt.compute(mat);\n    VERIFY(ldlt.info()==NumericalIssue);\n    VERIFY_IS_NOT_APPROX(mat,ldlt.reconstructedMatrix());\n  }\n#endif\n  {\n    mat.resize(3,3);\n    mat <<  1, 2, 3,\n            2, 4, 1,\n            3, 1, 0;\n    ldlt.compute(mat);\n    VERIFY(ldlt.info()==NumericalIssue);\n    VERIFY_IS_NOT_APPROX(mat,ldlt.reconstructedMatrix());\n  }\n\n  {\n    mat.resize(8,8);\n    mat <<  0.1, 0, -0.1, 0, 0, 0, 1, 0,\n            0, 4.24667, 0, 2.00333, 0, 0, 0, 0,\n            -0.1, 0, 0.2, 0, -0.1, 0, 0, 0,\n            0, 2.00333, 0, 8.49333, 0, 2.00333, 0, 0,\n            0, 0, -0.1, 0, 0.1, 0, 0, 1,\n            0, 0, 0, 2.00333, 0, 4.24667, 0, 0,\n            1, 0, 0, 0, 0, 0, 0, 0,\n            0, 0, 0, 0, 1, 0, 0, 0;\n    ldlt.compute(mat);\n    VERIFY(ldlt.info()==NumericalIssue);\n    VERIFY_IS_NOT_APPROX(mat,ldlt.reconstructedMatrix());\n  }\n\n  // bug 1479\n  {\n    mat.resize(4,4);\n    mat <<  1, 2, 0, 1,\n            2, 4, 0, 2,\n            0, 0, 0, 1,\n            1, 2, 1, 1;\n    ldlt.compute(mat);\n    VERIFY(ldlt.info()==NumericalIssue);\n    VERIFY_IS_NOT_APPROX(mat,ldlt.reconstructedMatrix());\n  }\n}\n\ntemplate<typename MatrixType> void cholesky_verify_assert()\n{\n  MatrixType tmp;\n\n  LLT<MatrixType> llt;\n  VERIFY_RAISES_ASSERT(llt.matrixL())\n  VERIFY_RAISES_ASSERT(llt.matrixU())\n  VERIFY_RAISES_ASSERT(llt.solve(tmp))\n  VERIFY_RAISES_ASSERT(llt.solveInPlace(&tmp))\n\n  LDLT<MatrixType> ldlt;\n  VERIFY_RAISES_ASSERT(ldlt.matrixL())\n  VERIFY_RAISES_ASSERT(ldlt.permutationP())\n  VERIFY_RAISES_ASSERT(ldlt.vectorD())\n  VERIFY_RAISES_ASSERT(ldlt.isPositive())\n  VERIFY_RAISES_ASSERT(ldlt.isNegative())\n  VERIFY_RAISES_ASSERT(ldlt.solve(tmp))\n  VERIFY_RAISES_ASSERT(ldlt.solveInPlace(&tmp))\n}\n\nvoid test_cholesky()\n{\n  int s = 0;\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( cholesky(Matrix<double,1,1>()) );\n    CALL_SUBTEST_3( cholesky(Matrix2d()) );\n    CALL_SUBTEST_3( cholesky_bug241(Matrix2d()) );\n    CALL_SUBTEST_3( cholesky_definiteness(Matrix2d()) );\n    CALL_SUBTEST_4( cholesky(Matrix3f()) );\n    CALL_SUBTEST_5( cholesky(Matrix4d()) );\n\n    s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE);\n    CALL_SUBTEST_2( cholesky(MatrixXd(s,s)) );\n    TEST_SET_BUT_UNUSED_VARIABLE(s)\n\n    s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2);\n    CALL_SUBTEST_6( cholesky_cplx(MatrixXcd(s,s)) );\n    TEST_SET_BUT_UNUSED_VARIABLE(s)\n  }\n\n  CALL_SUBTEST_4( cholesky_verify_assert<Matrix3f>() );\n  CALL_SUBTEST_7( cholesky_verify_assert<Matrix3d>() );\n  CALL_SUBTEST_8( cholesky_verify_assert<MatrixXf>() );\n  CALL_SUBTEST_2( cholesky_verify_assert<MatrixXd>() );\n\n  // Test problem size constructors\n  CALL_SUBTEST_9( LLT<MatrixXf>(10) );\n  CALL_SUBTEST_9( LDLT<MatrixXf>(10) );\n\n  CALL_SUBTEST_2( cholesky_faillure_cases<void>() );\n\n  TEST_SET_BUT_UNUSED_VARIABLE(nb_temporaries)\n}\n"
  },
  {
    "path": "include/eigen3/test/cholmod_support.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2011 Gael Guennebaud <g.gael@free.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define EIGEN_NO_DEBUG_SMALL_PRODUCT_BLOCKS\n#include \"sparse_solver.h\"\n\n#include <Eigen/CholmodSupport>\n\ntemplate<typename T> void test_cholmod_T()\n{\n  CholmodDecomposition<SparseMatrix<T>, Lower> g_chol_colmajor_lower; g_chol_colmajor_lower.setMode(CholmodSupernodalLLt);\n  CholmodDecomposition<SparseMatrix<T>, Upper> g_chol_colmajor_upper; g_chol_colmajor_upper.setMode(CholmodSupernodalLLt);\n  CholmodDecomposition<SparseMatrix<T>, Lower> g_llt_colmajor_lower;  g_llt_colmajor_lower.setMode(CholmodSimplicialLLt);\n  CholmodDecomposition<SparseMatrix<T>, Upper> g_llt_colmajor_upper;  g_llt_colmajor_upper.setMode(CholmodSimplicialLLt);\n  CholmodDecomposition<SparseMatrix<T>, Lower> g_ldlt_colmajor_lower; g_ldlt_colmajor_lower.setMode(CholmodLDLt);\n  CholmodDecomposition<SparseMatrix<T>, Upper> g_ldlt_colmajor_upper; g_ldlt_colmajor_upper.setMode(CholmodLDLt);\n  \n  CholmodSupernodalLLT<SparseMatrix<T>, Lower> chol_colmajor_lower;\n  CholmodSupernodalLLT<SparseMatrix<T>, Upper> chol_colmajor_upper;\n  CholmodSimplicialLLT<SparseMatrix<T>, Lower> llt_colmajor_lower;\n  CholmodSimplicialLLT<SparseMatrix<T>, Upper> llt_colmajor_upper;\n  CholmodSimplicialLDLT<SparseMatrix<T>, Lower> ldlt_colmajor_lower;\n  CholmodSimplicialLDLT<SparseMatrix<T>, Upper> ldlt_colmajor_upper;\n\n  check_sparse_spd_solving(g_chol_colmajor_lower);\n  check_sparse_spd_solving(g_chol_colmajor_upper);\n  check_sparse_spd_solving(g_llt_colmajor_lower);\n  check_sparse_spd_solving(g_llt_colmajor_upper);\n  check_sparse_spd_solving(g_ldlt_colmajor_lower);\n  check_sparse_spd_solving(g_ldlt_colmajor_upper);\n  \n  check_sparse_spd_solving(chol_colmajor_lower);\n  check_sparse_spd_solving(chol_colmajor_upper);\n  check_sparse_spd_solving(llt_colmajor_lower);\n  check_sparse_spd_solving(llt_colmajor_upper);\n  check_sparse_spd_solving(ldlt_colmajor_lower);\n  check_sparse_spd_solving(ldlt_colmajor_upper);\n\n  check_sparse_spd_determinant(chol_colmajor_lower);\n  check_sparse_spd_determinant(chol_colmajor_upper);\n  check_sparse_spd_determinant(llt_colmajor_lower);\n  check_sparse_spd_determinant(llt_colmajor_upper);\n  check_sparse_spd_determinant(ldlt_colmajor_lower);\n  check_sparse_spd_determinant(ldlt_colmajor_upper);\n}\n\nvoid test_cholmod_support()\n{\n  CALL_SUBTEST_1(test_cholmod_T<double>());\n  CALL_SUBTEST_2(test_cholmod_T<std::complex<double> >());\n}\n"
  },
  {
    "path": "include/eigen3/test/commainitializer.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n\ntemplate<int M1, int M2, int N1, int N2>\nvoid test_blocks()\n{\n  Matrix<int, M1+M2, N1+N2> m_fixed;\n  MatrixXi m_dynamic(M1+M2, N1+N2);\n\n  Matrix<int, M1, N1> mat11; mat11.setRandom();\n  Matrix<int, M1, N2> mat12; mat12.setRandom();\n  Matrix<int, M2, N1> mat21; mat21.setRandom();\n  Matrix<int, M2, N2> mat22; mat22.setRandom();\n\n  MatrixXi matx11 = mat11, matx12 = mat12, matx21 = mat21, matx22 = mat22;\n\n  {\n    VERIFY_IS_EQUAL((m_fixed << mat11, mat12, mat21, matx22).finished(), (m_dynamic << mat11, matx12, mat21, matx22).finished());\n    VERIFY_IS_EQUAL((m_fixed.template topLeftCorner<M1,N1>()), mat11);\n    VERIFY_IS_EQUAL((m_fixed.template topRightCorner<M1,N2>()), mat12);\n    VERIFY_IS_EQUAL((m_fixed.template bottomLeftCorner<M2,N1>()), mat21);\n    VERIFY_IS_EQUAL((m_fixed.template bottomRightCorner<M2,N2>()), mat22);\n    VERIFY_IS_EQUAL((m_fixed << mat12, mat11, matx21, mat22).finished(), (m_dynamic << mat12, matx11, matx21, mat22).finished());\n  }\n\n  if(N1 > 0)\n  {\n    VERIFY_RAISES_ASSERT((m_fixed << mat11, mat12, mat11, mat21, mat22));\n    VERIFY_RAISES_ASSERT((m_fixed << mat11, mat12, mat21, mat21, mat22));\n  }\n  else\n  {\n    // allow insertion of zero-column blocks:\n    VERIFY_IS_EQUAL((m_fixed << mat11, mat12, mat11, mat11, mat21, mat21, mat22).finished(), (m_dynamic << mat12, mat22).finished());\n  }\n  if(M1 != M2)\n  {\n    VERIFY_RAISES_ASSERT((m_fixed << mat11, mat21, mat12, mat22));\n  }\n}\n\n\ntemplate<int N>\nstruct test_block_recursion\n{\n  static void run()\n  {\n    test_blocks<(N>>6)&3, (N>>4)&3, (N>>2)&3, N & 3>();\n    test_block_recursion<N-1>::run();\n  }\n};\n\ntemplate<>\nstruct test_block_recursion<-1>\n{\n  static void run() { }\n};\n\nvoid test_commainitializer()\n{\n  Matrix3d m3;\n  Matrix4d m4;\n\n  VERIFY_RAISES_ASSERT( (m3 << 1, 2, 3, 4, 5, 6, 7, 8) );\n  \n  #ifndef _MSC_VER\n  VERIFY_RAISES_ASSERT( (m3 << 1, 2, 3, 4, 5, 6, 7, 8, 9, 10) );\n  #endif\n\n  double data[] = {1, 2, 3, 4, 5, 6, 7, 8, 9};\n  Matrix3d ref = Map<Matrix<double,3,3,RowMajor> >(data);\n\n  m3 = Matrix3d::Random();\n  m3 << 1, 2, 3, 4, 5, 6, 7, 8, 9;\n  VERIFY_IS_APPROX(m3, ref );\n\n  Vector3d vec[3];\n  vec[0] << 1, 4, 7;\n  vec[1] << 2, 5, 8;\n  vec[2] << 3, 6, 9;\n  m3 = Matrix3d::Random();\n  m3 << vec[0], vec[1], vec[2];\n  VERIFY_IS_APPROX(m3, ref);\n\n  vec[0] << 1, 2, 3;\n  vec[1] << 4, 5, 6;\n  vec[2] << 7, 8, 9;\n  m3 = Matrix3d::Random();\n  m3 << vec[0].transpose(),\n        4, 5, 6,\n        vec[2].transpose();\n  VERIFY_IS_APPROX(m3, ref);\n\n\n  // recursively test all block-sizes from 0 to 3:\n  test_block_recursion<(1<<8) - 1>();\n}\n"
  },
  {
    "path": "include/eigen3/test/conjugate_gradient.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2011 Gael Guennebaud <g.gael@free.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"sparse_solver.h\"\n#include <Eigen/IterativeLinearSolvers>\n\ntemplate<typename T, typename I> void test_conjugate_gradient_T()\n{\n  typedef SparseMatrix<T,0,I> SparseMatrixType;\n  ConjugateGradient<SparseMatrixType, Lower      > cg_colmajor_lower_diag;\n  ConjugateGradient<SparseMatrixType, Upper      > cg_colmajor_upper_diag;\n  ConjugateGradient<SparseMatrixType, Lower|Upper> cg_colmajor_loup_diag;\n  ConjugateGradient<SparseMatrixType, Lower, IdentityPreconditioner> cg_colmajor_lower_I;\n  ConjugateGradient<SparseMatrixType, Upper, IdentityPreconditioner> cg_colmajor_upper_I;\n\n  CALL_SUBTEST( check_sparse_spd_solving(cg_colmajor_lower_diag)  );\n  CALL_SUBTEST( check_sparse_spd_solving(cg_colmajor_upper_diag)  );\n  CALL_SUBTEST( check_sparse_spd_solving(cg_colmajor_loup_diag)   );\n  CALL_SUBTEST( check_sparse_spd_solving(cg_colmajor_lower_I)     );\n  CALL_SUBTEST( check_sparse_spd_solving(cg_colmajor_upper_I)     );\n}\n\nvoid test_conjugate_gradient()\n{\n  CALL_SUBTEST_1(( test_conjugate_gradient_T<double,int>() ));\n  CALL_SUBTEST_2(( test_conjugate_gradient_T<std::complex<double>, int>() ));\n  CALL_SUBTEST_3(( test_conjugate_gradient_T<double,long int>() ));\n}\n"
  },
  {
    "path": "include/eigen3/test/conservative_resize.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Hauke Heibel <hauke.heibel@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/Core>\n\nusing namespace Eigen;\n\ntemplate <typename Scalar, int Storage>\nvoid run_matrix_tests()\n{\n  typedef Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic, Storage> MatrixType;\n  typedef typename MatrixType::Index Index;\n\n  MatrixType m, n;\n\n  // boundary cases ...\n  m = n = MatrixType::Random(50,50);\n  m.conservativeResize(1,50);\n  VERIFY_IS_APPROX(m, n.block(0,0,1,50));\n\n  m = n = MatrixType::Random(50,50);\n  m.conservativeResize(50,1);\n  VERIFY_IS_APPROX(m, n.block(0,0,50,1));\n\n  m = n = MatrixType::Random(50,50);\n  m.conservativeResize(50,50);\n  VERIFY_IS_APPROX(m, n.block(0,0,50,50));\n\n  // random shrinking ...\n  for (int i=0; i<25; ++i)\n  {\n    const Index rows = internal::random<Index>(1,50);\n    const Index cols = internal::random<Index>(1,50);\n    m = n = MatrixType::Random(50,50);\n    m.conservativeResize(rows,cols);\n    VERIFY_IS_APPROX(m, n.block(0,0,rows,cols));\n  }\n\n  // random growing with zeroing ...\n  for (int i=0; i<25; ++i)\n  {\n    const Index rows = internal::random<Index>(50,75);\n    const Index cols = internal::random<Index>(50,75);\n    m = n = MatrixType::Random(50,50);\n    m.conservativeResizeLike(MatrixType::Zero(rows,cols));\n    VERIFY_IS_APPROX(m.block(0,0,n.rows(),n.cols()), n);\n    VERIFY( rows<=50 || m.block(50,0,rows-50,cols).sum() == Scalar(0) );\n    VERIFY( cols<=50 || m.block(0,50,rows,cols-50).sum() == Scalar(0) );\n  }\n}\n\ntemplate <typename Scalar>\nvoid run_vector_tests()\n{\n  typedef Matrix<Scalar, 1, Eigen::Dynamic> VectorType;\n\n  VectorType m, n;\n\n  // boundary cases ...\n  m = n = VectorType::Random(50);\n  m.conservativeResize(1);\n  VERIFY_IS_APPROX(m, n.segment(0,1));\n\n  m = n = VectorType::Random(50);\n  m.conservativeResize(50);\n  VERIFY_IS_APPROX(m, n.segment(0,50));\n  \n  m = n = VectorType::Random(50);\n  m.conservativeResize(m.rows(),1);\n  VERIFY_IS_APPROX(m, n.segment(0,1));\n\n  m = n = VectorType::Random(50);\n  m.conservativeResize(m.rows(),50);\n  VERIFY_IS_APPROX(m, n.segment(0,50));\n\n  // random shrinking ...\n  for (int i=0; i<50; ++i)\n  {\n    const int size = internal::random<int>(1,50);\n    m = n = VectorType::Random(50);\n    m.conservativeResize(size);\n    VERIFY_IS_APPROX(m, n.segment(0,size));\n    \n    m = n = VectorType::Random(50);\n    m.conservativeResize(m.rows(), size);\n    VERIFY_IS_APPROX(m, n.segment(0,size));\n  }\n\n  // random growing with zeroing ...\n  for (int i=0; i<50; ++i)\n  {\n    const int size = internal::random<int>(50,100);\n    m = n = VectorType::Random(50);\n    m.conservativeResizeLike(VectorType::Zero(size));\n    VERIFY_IS_APPROX(m.segment(0,50), n);\n    VERIFY( size<=50 || m.segment(50,size-50).sum() == Scalar(0) );\n    \n    m = n = VectorType::Random(50);\n    m.conservativeResizeLike(Matrix<Scalar,Dynamic,Dynamic>::Zero(1,size));\n    VERIFY_IS_APPROX(m.segment(0,50), n);\n    VERIFY( size<=50 || m.segment(50,size-50).sum() == Scalar(0) );\n  }\n}\n\nvoid test_conservative_resize()\n{\n  for(int i=0; i<g_repeat; ++i)\n  {\n    CALL_SUBTEST_1((run_matrix_tests<int, Eigen::RowMajor>()));\n    CALL_SUBTEST_1((run_matrix_tests<int, Eigen::ColMajor>()));\n    CALL_SUBTEST_2((run_matrix_tests<float, Eigen::RowMajor>()));\n    CALL_SUBTEST_2((run_matrix_tests<float, Eigen::ColMajor>()));\n    CALL_SUBTEST_3((run_matrix_tests<double, Eigen::RowMajor>()));\n    CALL_SUBTEST_3((run_matrix_tests<double, Eigen::ColMajor>()));\n    CALL_SUBTEST_4((run_matrix_tests<std::complex<float>, Eigen::RowMajor>()));\n    CALL_SUBTEST_4((run_matrix_tests<std::complex<float>, Eigen::ColMajor>()));\n    CALL_SUBTEST_5((run_matrix_tests<std::complex<double>, Eigen::RowMajor>()));\n    CALL_SUBTEST_6((run_matrix_tests<std::complex<double>, Eigen::ColMajor>()));\n\n    CALL_SUBTEST_1((run_vector_tests<int>()));\n    CALL_SUBTEST_2((run_vector_tests<float>()));\n    CALL_SUBTEST_3((run_vector_tests<double>()));\n    CALL_SUBTEST_4((run_vector_tests<std::complex<float> >()));\n    CALL_SUBTEST_5((run_vector_tests<std::complex<double> >()));\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/constructor.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2017 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n\n#define TEST_ENABLE_TEMPORARY_TRACKING\n\n#include \"main.h\"\n\ntemplate<typename MatrixType> struct Wrapper\n{\n  MatrixType m_mat;\n  inline Wrapper(const MatrixType &x) : m_mat(x) {}\n  inline operator const MatrixType& () const { return m_mat; }\n  inline operator MatrixType& () { return m_mat; }\n};\n\ntemplate<typename MatrixType> void ctor_init1(const MatrixType& m)\n{\n  // Check logic in PlainObjectBase::_init1\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  MatrixType m0 = MatrixType::Random(rows,cols);\n\n  VERIFY_EVALUATION_COUNT( MatrixType m1(m0), 1);\n  VERIFY_EVALUATION_COUNT( MatrixType m2(m0+m0), 1);\n  VERIFY_EVALUATION_COUNT( MatrixType m2(m0.block(0,0,rows,cols)) , 1);\n\n  Wrapper<MatrixType> wrapper(m0);\n  VERIFY_EVALUATION_COUNT( MatrixType m3(wrapper) , 1);\n}\n\n\nvoid test_constructor()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( ctor_init1(Matrix<float, 1, 1>()) );\n    CALL_SUBTEST_1( ctor_init1(Matrix4d()) );\n    CALL_SUBTEST_1( ctor_init1(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_1( ctor_init1(MatrixXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n  }\n  {\n    Matrix<Index,1,1> a(123);\n    VERIFY_IS_EQUAL(a[0], 123);\n  }\n  {\n    Matrix<Index,1,1> a(123.0);\n    VERIFY_IS_EQUAL(a[0], 123);\n  }\n  {\n    Matrix<float,1,1> a(123);\n    VERIFY_IS_EQUAL(a[0], 123.f);\n  }\n  {\n    Array<Index,1,1> a(123);\n    VERIFY_IS_EQUAL(a[0], 123);\n  }\n  {\n    Array<Index,1,1> a(123.0);\n    VERIFY_IS_EQUAL(a[0], 123);\n  }\n  {\n    Array<float,1,1> a(123);\n    VERIFY_IS_EQUAL(a[0], 123.f);\n  }\n  {\n    Array<Index,3,3> a(123);\n    VERIFY_IS_EQUAL(a(4), 123);\n  }\n  {\n    Array<Index,3,3> a(123.0);\n    VERIFY_IS_EQUAL(a(4), 123);\n  }\n  {\n    Array<float,3,3> a(123);\n    VERIFY_IS_EQUAL(a(4), 123.f);\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/corners.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#define COMPARE_CORNER(A,B) \\\n  VERIFY_IS_EQUAL(matrix.A, matrix.B); \\\n  VERIFY_IS_EQUAL(const_matrix.A, const_matrix.B);\n\ntemplate<typename MatrixType> void corners(const MatrixType& m)\n{\n  typedef typename MatrixType::Index Index;\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  Index r = internal::random<Index>(1,rows);\n  Index c = internal::random<Index>(1,cols);\n\n  MatrixType matrix = MatrixType::Random(rows,cols);\n  const MatrixType const_matrix = MatrixType::Random(rows,cols);\n\n  COMPARE_CORNER(topLeftCorner(r,c), block(0,0,r,c));\n  COMPARE_CORNER(topRightCorner(r,c), block(0,cols-c,r,c));\n  COMPARE_CORNER(bottomLeftCorner(r,c), block(rows-r,0,r,c));\n  COMPARE_CORNER(bottomRightCorner(r,c), block(rows-r,cols-c,r,c));\n\n  Index sr = internal::random<Index>(1,rows) - 1;\n  Index nr = internal::random<Index>(1,rows-sr);\n  Index sc = internal::random<Index>(1,cols) - 1;\n  Index nc = internal::random<Index>(1,cols-sc);\n\n  COMPARE_CORNER(topRows(r), block(0,0,r,cols));\n  COMPARE_CORNER(middleRows(sr,nr), block(sr,0,nr,cols));\n  COMPARE_CORNER(bottomRows(r), block(rows-r,0,r,cols));\n  COMPARE_CORNER(leftCols(c), block(0,0,rows,c));\n  COMPARE_CORNER(middleCols(sc,nc), block(0,sc,rows,nc));\n  COMPARE_CORNER(rightCols(c), block(0,cols-c,rows,c));\n}\n\ntemplate<typename MatrixType, int CRows, int CCols, int SRows, int SCols> void corners_fixedsize()\n{\n  MatrixType matrix = MatrixType::Random();\n  const MatrixType const_matrix = MatrixType::Random();\n\n  enum {\n    rows = MatrixType::RowsAtCompileTime,\n    cols = MatrixType::ColsAtCompileTime,\n    r = CRows,\n    c = CCols,\n\tsr = SRows,\n\tsc = SCols\n  };\n\n  VERIFY_IS_EQUAL((matrix.template topLeftCorner<r,c>()), (matrix.template block<r,c>(0,0)));\n  VERIFY_IS_EQUAL((matrix.template topRightCorner<r,c>()), (matrix.template block<r,c>(0,cols-c)));\n  VERIFY_IS_EQUAL((matrix.template bottomLeftCorner<r,c>()), (matrix.template block<r,c>(rows-r,0)));\n  VERIFY_IS_EQUAL((matrix.template bottomRightCorner<r,c>()), (matrix.template block<r,c>(rows-r,cols-c)));\n\n  VERIFY_IS_EQUAL((matrix.template topLeftCorner<r,c>()), (matrix.template topLeftCorner<r,Dynamic>(r,c)));\n  VERIFY_IS_EQUAL((matrix.template topRightCorner<r,c>()), (matrix.template topRightCorner<r,Dynamic>(r,c)));\n  VERIFY_IS_EQUAL((matrix.template bottomLeftCorner<r,c>()), (matrix.template bottomLeftCorner<r,Dynamic>(r,c)));\n  VERIFY_IS_EQUAL((matrix.template bottomRightCorner<r,c>()), (matrix.template bottomRightCorner<r,Dynamic>(r,c)));\n\n  VERIFY_IS_EQUAL((matrix.template topLeftCorner<r,c>()), (matrix.template topLeftCorner<Dynamic,c>(r,c)));\n  VERIFY_IS_EQUAL((matrix.template topRightCorner<r,c>()), (matrix.template topRightCorner<Dynamic,c>(r,c)));\n  VERIFY_IS_EQUAL((matrix.template bottomLeftCorner<r,c>()), (matrix.template bottomLeftCorner<Dynamic,c>(r,c)));\n  VERIFY_IS_EQUAL((matrix.template bottomRightCorner<r,c>()), (matrix.template bottomRightCorner<Dynamic,c>(r,c)));\n\n  VERIFY_IS_EQUAL((matrix.template topRows<r>()), (matrix.template block<r,cols>(0,0)));\n  VERIFY_IS_EQUAL((matrix.template middleRows<r>(sr)), (matrix.template block<r,cols>(sr,0)));\n  VERIFY_IS_EQUAL((matrix.template bottomRows<r>()), (matrix.template block<r,cols>(rows-r,0)));\n  VERIFY_IS_EQUAL((matrix.template leftCols<c>()), (matrix.template block<rows,c>(0,0)));\n  VERIFY_IS_EQUAL((matrix.template middleCols<c>(sc)), (matrix.template block<rows,c>(0,sc)));\n  VERIFY_IS_EQUAL((matrix.template rightCols<c>()), (matrix.template block<rows,c>(0,cols-c)));\n\n  VERIFY_IS_EQUAL((const_matrix.template topLeftCorner<r,c>()), (const_matrix.template block<r,c>(0,0)));\n  VERIFY_IS_EQUAL((const_matrix.template topRightCorner<r,c>()), (const_matrix.template block<r,c>(0,cols-c)));\n  VERIFY_IS_EQUAL((const_matrix.template bottomLeftCorner<r,c>()), (const_matrix.template block<r,c>(rows-r,0)));\n  VERIFY_IS_EQUAL((const_matrix.template bottomRightCorner<r,c>()), (const_matrix.template block<r,c>(rows-r,cols-c)));\n\n  VERIFY_IS_EQUAL((const_matrix.template topLeftCorner<r,c>()), (const_matrix.template topLeftCorner<r,Dynamic>(r,c)));\n  VERIFY_IS_EQUAL((const_matrix.template topRightCorner<r,c>()), (const_matrix.template topRightCorner<r,Dynamic>(r,c)));\n  VERIFY_IS_EQUAL((const_matrix.template bottomLeftCorner<r,c>()), (const_matrix.template bottomLeftCorner<r,Dynamic>(r,c)));\n  VERIFY_IS_EQUAL((const_matrix.template bottomRightCorner<r,c>()), (const_matrix.template bottomRightCorner<r,Dynamic>(r,c)));\n\n  VERIFY_IS_EQUAL((const_matrix.template topLeftCorner<r,c>()), (const_matrix.template topLeftCorner<Dynamic,c>(r,c)));\n  VERIFY_IS_EQUAL((const_matrix.template topRightCorner<r,c>()), (const_matrix.template topRightCorner<Dynamic,c>(r,c)));\n  VERIFY_IS_EQUAL((const_matrix.template bottomLeftCorner<r,c>()), (const_matrix.template bottomLeftCorner<Dynamic,c>(r,c)));\n  VERIFY_IS_EQUAL((const_matrix.template bottomRightCorner<r,c>()), (const_matrix.template bottomRightCorner<Dynamic,c>(r,c)));\n\n  VERIFY_IS_EQUAL((const_matrix.template topRows<r>()), (const_matrix.template block<r,cols>(0,0)));\n  VERIFY_IS_EQUAL((const_matrix.template middleRows<r>(sr)), (const_matrix.template block<r,cols>(sr,0)));\n  VERIFY_IS_EQUAL((const_matrix.template bottomRows<r>()), (const_matrix.template block<r,cols>(rows-r,0)));\n  VERIFY_IS_EQUAL((const_matrix.template leftCols<c>()), (const_matrix.template block<rows,c>(0,0)));\n  VERIFY_IS_EQUAL((const_matrix.template middleCols<c>(sc)), (const_matrix.template block<rows,c>(0,sc)));\n  VERIFY_IS_EQUAL((const_matrix.template rightCols<c>()), (const_matrix.template block<rows,c>(0,cols-c)));\n}\n\nvoid test_corners()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( corners(Matrix<float, 1, 1>()) );\n    CALL_SUBTEST_2( corners(Matrix4d()) );\n    CALL_SUBTEST_3( corners(Matrix<int,10,12>()) );\n    CALL_SUBTEST_4( corners(MatrixXcf(5, 7)) );\n    CALL_SUBTEST_5( corners(MatrixXf(21, 20)) );\n\n    CALL_SUBTEST_1(( corners_fixedsize<Matrix<float, 1, 1>, 1, 1, 0, 0>() ));\n    CALL_SUBTEST_2(( corners_fixedsize<Matrix4d,2,2,1,1>() ));\n    CALL_SUBTEST_3(( corners_fixedsize<Matrix<int,10,12>,4,7,5,2>() ));\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/ctorleak.cpp",
    "content": "#include \"main.h\"\n\n#include <exception>  // std::exception\n\nstruct Foo\n{\n  static Index object_count;\n  static Index object_limit;\n  int dummy;\n\n  Foo()\n  {\n#ifdef EIGEN_EXCEPTIONS\n    // TODO: Is this the correct way to handle this?\n    if (Foo::object_count > Foo::object_limit) { std::cout << \"\\nThrow!\\n\"; throw Foo::Fail(); }\n#endif\n\t  std::cout << '+';\n    ++Foo::object_count;\n  }\n\n  ~Foo()\n  {\n\t  std::cout << '-';\n    --Foo::object_count;\n  }\n\n  class Fail : public std::exception {};\n};\n\nIndex Foo::object_count = 0;\nIndex Foo::object_limit = 0;\n\n#undef EIGEN_TEST_MAX_SIZE\n#define EIGEN_TEST_MAX_SIZE 3\n\nvoid test_ctorleak()\n{\n  typedef Matrix<Foo, Dynamic, Dynamic> MatrixX;\n  typedef Matrix<Foo, Dynamic, 1> VectorX;\n  Foo::object_count = 0;\n  for(int i = 0; i < g_repeat; i++) {\n    Index rows = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE), cols = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE);\n    Foo::object_limit = internal::random<Index>(0, rows*cols - 2);\n    std::cout << \"object_limit =\" << Foo::object_limit << std::endl;\n#ifdef EIGEN_EXCEPTIONS\n    try\n    {\n#endif\n    \tstd::cout <<       \"\\nMatrixX m(\" << rows << \", \" << cols << \");\\n\";\n      MatrixX m(rows, cols);\n#ifdef EIGEN_EXCEPTIONS\n      VERIFY(false);  // not reached if exceptions are enabled\n    }\n    catch (const Foo::Fail&) { /* ignore */ }\n#endif\n    VERIFY_IS_EQUAL(Index(0), Foo::object_count);\n\n    {\n      Foo::object_limit = (rows+1)*(cols+1);\n      MatrixX A(rows, cols);\n      VERIFY_IS_EQUAL(Foo::object_count, rows*cols);\n      VectorX v=A.row(0);\n      VERIFY_IS_EQUAL(Foo::object_count, (rows+1)*cols);\n      v = A.col(0);\n      VERIFY_IS_EQUAL(Foo::object_count, rows*(cols+1));\n    }\n    VERIFY_IS_EQUAL(Index(0), Foo::object_count);\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/cuda_basic.cu",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015-2016 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n// workaround issue between gcc >= 4.7 and cuda 5.5\n#if (defined __GNUC__) && (__GNUC__>4 || __GNUC_MINOR__>=7)\n  #undef _GLIBCXX_ATOMIC_BUILTINS\n  #undef _GLIBCXX_USE_INT128\n#endif\n\n#define EIGEN_TEST_NO_LONGDOUBLE\n#define EIGEN_TEST_NO_COMPLEX\n#define EIGEN_TEST_FUNC cuda_basic\n#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int\n\n#include <math_constants.h>\n#include <cuda.h>\n#include \"main.h\"\n#include \"cuda_common.h\"\n\n// Check that dense modules can be properly parsed by nvcc\n#include <Eigen/Dense>\n\n// struct Foo{\n//   EIGEN_DEVICE_FUNC\n//   void operator()(int i, const float* mats, float* vecs) const {\n//     using namespace Eigen;\n//   //   Matrix3f M(data);\n//   //   Vector3f x(data+9);\n//   //   Map<Vector3f>(data+9) = M.inverse() * x;\n//     Matrix3f M(mats+i/16);\n//     Vector3f x(vecs+i*3);\n//   //   using std::min;\n//   //   using std::sqrt;\n//     Map<Vector3f>(vecs+i*3) << x.minCoeff(), 1, 2;// / x.dot(x);//(M.inverse() *  x) / x.x();\n//     //x = x*2 + x.y() * x + x * x.maxCoeff() - x / x.sum();\n//   }\n// };\n\ntemplate<typename T>\nstruct coeff_wise {\n  EIGEN_DEVICE_FUNC\n  void operator()(int i, const typename T::Scalar* in, typename T::Scalar* out) const\n  {\n    using namespace Eigen;\n    T x1(in+i);\n    T x2(in+i+1);\n    T x3(in+i+2);\n    Map<T> res(out+i*T::MaxSizeAtCompileTime);\n    \n    res.array() += (in[0] * x1 + x2).array() * x3.array();\n  }\n};\n\ntemplate<typename T>\nstruct replicate {\n  EIGEN_DEVICE_FUNC\n  void operator()(int i, const typename T::Scalar* in, typename T::Scalar* out) const\n  {\n    using namespace Eigen;\n    T x1(in+i);\n    int step   = x1.size() * 4;\n    int stride = 3 * step;\n    \n    typedef Map<Array<typename T::Scalar,Dynamic,Dynamic> > MapType;\n    MapType(out+i*stride+0*step, x1.rows()*2, x1.cols()*2) = x1.replicate(2,2);\n    MapType(out+i*stride+1*step, x1.rows()*3, x1.cols()) = in[i] * x1.colwise().replicate(3);\n    MapType(out+i*stride+2*step, x1.rows(), x1.cols()*3) = in[i] * x1.rowwise().replicate(3);\n  }\n};\n\ntemplate<typename T>\nstruct redux {\n  EIGEN_DEVICE_FUNC\n  void operator()(int i, const typename T::Scalar* in, typename T::Scalar* out) const\n  {\n    using namespace Eigen;\n    int N = 10;\n    T x1(in+i);\n    out[i*N+0] = x1.minCoeff();\n    out[i*N+1] = x1.maxCoeff();\n    out[i*N+2] = x1.sum();\n    out[i*N+3] = x1.prod();\n    out[i*N+4] = x1.matrix().squaredNorm();\n    out[i*N+5] = x1.matrix().norm();\n    out[i*N+6] = x1.colwise().sum().maxCoeff();\n    out[i*N+7] = x1.rowwise().maxCoeff().sum();\n    out[i*N+8] = x1.matrix().colwise().squaredNorm().sum();\n  }\n};\n\ntemplate<typename T1, typename T2>\nstruct prod_test {\n  EIGEN_DEVICE_FUNC\n  void operator()(int i, const typename T1::Scalar* in, typename T1::Scalar* out) const\n  {\n    using namespace Eigen;\n    typedef Matrix<typename T1::Scalar, T1::RowsAtCompileTime, T2::ColsAtCompileTime> T3;\n    T1 x1(in+i);\n    T2 x2(in+i+1);\n    Map<T3> res(out+i*T3::MaxSizeAtCompileTime);\n    res += in[i] * x1 * x2;\n  }\n};\n\ntemplate<typename T1, typename T2>\nstruct diagonal {\n  EIGEN_DEVICE_FUNC\n  void operator()(int i, const typename T1::Scalar* in, typename T1::Scalar* out) const\n  {\n    using namespace Eigen;\n    T1 x1(in+i);\n    Map<T2> res(out+i*T2::MaxSizeAtCompileTime);\n    res += x1.diagonal();\n  }\n};\n\ntemplate<typename T>\nstruct eigenvalues {\n  EIGEN_DEVICE_FUNC\n  void operator()(int i, const typename T::Scalar* in, typename T::Scalar* out) const\n  {\n    using namespace Eigen;\n    typedef Matrix<typename T::Scalar, T::RowsAtCompileTime, 1> Vec;\n    T M(in+i);\n    Map<Vec> res(out+i*Vec::MaxSizeAtCompileTime);\n    T A = M*M.adjoint();\n    SelfAdjointEigenSolver<T> eig;\n    eig.computeDirect(M);\n    res = eig.eigenvalues();\n  }\n};\n\nvoid test_cuda_basic()\n{\n  ei_test_init_cuda();\n  \n  int nthreads = 100;\n  Eigen::VectorXf in, out;\n  \n  #ifndef __CUDA_ARCH__\n  int data_size = nthreads * 512;\n  in.setRandom(data_size);\n  out.setRandom(data_size);\n  #endif\n  \n  CALL_SUBTEST( run_and_compare_to_cuda(coeff_wise<Vector3f>(), nthreads, in, out) );\n  CALL_SUBTEST( run_and_compare_to_cuda(coeff_wise<Array44f>(), nthreads, in, out) );\n  \n  CALL_SUBTEST( run_and_compare_to_cuda(replicate<Array4f>(), nthreads, in, out) );\n  CALL_SUBTEST( run_and_compare_to_cuda(replicate<Array33f>(), nthreads, in, out) );\n  \n  CALL_SUBTEST( run_and_compare_to_cuda(redux<Array4f>(), nthreads, in, out) );\n  CALL_SUBTEST( run_and_compare_to_cuda(redux<Matrix3f>(), nthreads, in, out) );\n  \n  CALL_SUBTEST( run_and_compare_to_cuda(prod_test<Matrix3f,Matrix3f>(), nthreads, in, out) );\n  CALL_SUBTEST( run_and_compare_to_cuda(prod_test<Matrix4f,Vector4f>(), nthreads, in, out) );\n  \n  CALL_SUBTEST( run_and_compare_to_cuda(diagonal<Matrix3f,Vector3f>(), nthreads, in, out) );\n  CALL_SUBTEST( run_and_compare_to_cuda(diagonal<Matrix4f,Vector4f>(), nthreads, in, out) );\n  \n  CALL_SUBTEST( run_and_compare_to_cuda(eigenvalues<Matrix3f>(), nthreads, in, out) );\n  CALL_SUBTEST( run_and_compare_to_cuda(eigenvalues<Matrix2f>(), nthreads, in, out) );\n\n}\n"
  },
  {
    "path": "include/eigen3/test/cuda_common.h",
    "content": "\n#ifndef EIGEN_TEST_CUDA_COMMON_H\n#define EIGEN_TEST_CUDA_COMMON_H\n\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <cuda_runtime_api.h>\n#include <iostream>\n\n#ifndef __CUDACC__\ndim3 threadIdx, blockDim, blockIdx;\n#endif\n\ntemplate<typename Kernel, typename Input, typename Output>\nvoid run_on_cpu(const Kernel& ker, int n, const Input& in, Output& out)\n{\n  for(int i=0; i<n; i++)\n    ker(i, in.data(), out.data());\n}\n\n\ntemplate<typename Kernel, typename Input, typename Output>\n__global__\nvoid run_on_cuda_meta_kernel(const Kernel ker, int n, const Input* in, Output* out)\n{\n  int i = threadIdx.x + blockIdx.x*blockDim.x;\n  if(i<n) {\n    ker(i, in, out);\n  }\n}\n\n\ntemplate<typename Kernel, typename Input, typename Output>\nvoid run_on_cuda(const Kernel& ker, int n, const Input& in, Output& out)\n{\n  typename Input::Scalar*  d_in;\n  typename Output::Scalar* d_out;\n  std::ptrdiff_t in_bytes  = in.size()  * sizeof(typename Input::Scalar);\n  std::ptrdiff_t out_bytes = out.size() * sizeof(typename Output::Scalar);\n  \n  cudaMalloc((void**)(&d_in),  in_bytes);\n  cudaMalloc((void**)(&d_out), out_bytes);\n  \n  cudaMemcpy(d_in,  in.data(),  in_bytes,  cudaMemcpyHostToDevice);\n  cudaMemcpy(d_out, out.data(), out_bytes, cudaMemcpyHostToDevice);\n  \n  // Simple and non-optimal 1D mapping assuming n is not too large\n  // That's only for unit testing!\n  dim3 Blocks(128);\n  dim3 Grids( (n+int(Blocks.x)-1)/int(Blocks.x) );\n\n  cudaThreadSynchronize();\n  run_on_cuda_meta_kernel<<<Grids,Blocks>>>(ker, n, d_in, d_out);\n  cudaThreadSynchronize();\n  \n  // check inputs have not been modified\n  cudaMemcpy(const_cast<typename Input::Scalar*>(in.data()),  d_in,  in_bytes,  cudaMemcpyDeviceToHost);\n  cudaMemcpy(out.data(), d_out, out_bytes, cudaMemcpyDeviceToHost);\n  \n  cudaFree(d_in);\n  cudaFree(d_out);\n}\n\n\ntemplate<typename Kernel, typename Input, typename Output>\nvoid run_and_compare_to_cuda(const Kernel& ker, int n, const Input& in, Output& out)\n{\n  Input  in_ref,  in_cuda;\n  Output out_ref, out_cuda;\n  #ifndef __CUDA_ARCH__\n  in_ref = in_cuda = in;\n  out_ref = out_cuda = out;\n  #endif\n  run_on_cpu (ker, n, in_ref,  out_ref);\n  run_on_cuda(ker, n, in_cuda, out_cuda);\n  #ifndef __CUDA_ARCH__\n  VERIFY_IS_APPROX(in_ref, in_cuda);\n  VERIFY_IS_APPROX(out_ref, out_cuda);\n  #endif\n}\n\n\nvoid ei_test_init_cuda()\n{\n  int device = 0;\n  cudaDeviceProp deviceProp;\n  cudaGetDeviceProperties(&deviceProp, device);\n  std::cout << \"CUDA device info:\\n\";\n  std::cout << \"  name:                        \" << deviceProp.name << \"\\n\";\n  std::cout << \"  capability:                  \" << deviceProp.major << \".\" << deviceProp.minor << \"\\n\";\n  std::cout << \"  multiProcessorCount:         \" << deviceProp.multiProcessorCount << \"\\n\";\n  std::cout << \"  maxThreadsPerMultiProcessor: \" << deviceProp.maxThreadsPerMultiProcessor << \"\\n\";\n  std::cout << \"  warpSize:                    \" << deviceProp.warpSize << \"\\n\";\n  std::cout << \"  regsPerBlock:                \" << deviceProp.regsPerBlock << \"\\n\";\n  std::cout << \"  concurrentKernels:           \" << deviceProp.concurrentKernels << \"\\n\";\n  std::cout << \"  clockRate:                   \" << deviceProp.clockRate << \"\\n\";\n  std::cout << \"  canMapHostMemory:            \" << deviceProp.canMapHostMemory << \"\\n\";\n  std::cout << \"  computeMode:                 \" << deviceProp.computeMode << \"\\n\";\n}\n\n#endif // EIGEN_TEST_CUDA_COMMON_H\n"
  },
  {
    "path": "include/eigen3/test/denseLM.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Desire Nuentsa <desire.nuentsa_wakam@inria.fr>\n// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include <iostream>\n#include <fstream>\n#include <iomanip>\n\n#include \"main.h\"\n#include <Eigen/LevenbergMarquardt>\nusing namespace std;\nusing namespace Eigen;\n\ntemplate<typename Scalar>\nstruct DenseLM : DenseFunctor<Scalar>\n{\n  typedef DenseFunctor<Scalar> Base;\n  typedef typename Base::JacobianType JacobianType;\n  typedef Matrix<Scalar,Dynamic,1> VectorType;\n  \n  DenseLM(int n, int m) : DenseFunctor<Scalar>(n,m) \n  { }\n \n  VectorType model(const VectorType& uv, VectorType& x)\n  {\n    VectorType y; // Should change to use expression template\n    int m = Base::values(); \n    int n = Base::inputs();\n    eigen_assert(uv.size()%2 == 0);\n    eigen_assert(uv.size() == n);\n    eigen_assert(x.size() == m);\n    y.setZero(m);\n    int half = n/2;\n    VectorBlock<const VectorType> u(uv, 0, half);\n    VectorBlock<const VectorType> v(uv, half, half);\n    for (int j = 0; j < m; j++)\n    {\n      for (int i = 0; i < half; i++)\n        y(j) += u(i)*std::exp(-(x(j)-i)*(x(j)-i)/(v(i)*v(i)));\n    }\n    return y;\n    \n  }\n  void initPoints(VectorType& uv_ref, VectorType& x)\n  {\n    m_x = x;\n    m_y = this->model(uv_ref, x);\n  }\n  \n  int operator()(const VectorType& uv, VectorType& fvec)\n  {\n    \n    int m = Base::values(); \n    int n = Base::inputs();\n    eigen_assert(uv.size()%2 == 0);\n    eigen_assert(uv.size() == n);\n    eigen_assert(fvec.size() == m);\n    int half = n/2;\n    VectorBlock<const VectorType> u(uv, 0, half);\n    VectorBlock<const VectorType> v(uv, half, half);\n    for (int j = 0; j < m; j++)\n    {\n      fvec(j) = m_y(j);\n      for (int i = 0; i < half; i++)\n      {\n        fvec(j) -= u(i) *std::exp(-(m_x(j)-i)*(m_x(j)-i)/(v(i)*v(i)));\n      }\n    }\n    \n    return 0;\n  }\n  int df(const VectorType& uv, JacobianType& fjac)\n  {\n    int m = Base::values(); \n    int n = Base::inputs();\n    eigen_assert(n == uv.size());\n    eigen_assert(fjac.rows() == m);\n    eigen_assert(fjac.cols() == n);\n    int half = n/2;\n    VectorBlock<const VectorType> u(uv, 0, half);\n    VectorBlock<const VectorType> v(uv, half, half);\n    for (int j = 0; j < m; j++)\n    {\n      for (int i = 0; i < half; i++)\n      {\n        fjac.coeffRef(j,i) = -std::exp(-(m_x(j)-i)*(m_x(j)-i)/(v(i)*v(i)));\n        fjac.coeffRef(j,i+half) = -2.*u(i)*(m_x(j)-i)*(m_x(j)-i)/(std::pow(v(i),3)) * std::exp(-(m_x(j)-i)*(m_x(j)-i)/(v(i)*v(i)));\n      }\n    }\n    return 0;\n  }\n  VectorType m_x, m_y; //Data Points\n};\n\ntemplate<typename FunctorType, typename VectorType>\nint test_minimizeLM(FunctorType& functor, VectorType& uv)\n{\n  LevenbergMarquardt<FunctorType> lm(functor);\n  LevenbergMarquardtSpace::Status info; \n  \n  info = lm.minimize(uv);\n  \n  VERIFY_IS_EQUAL(info, 1);\n  //FIXME Check other parameters\n  return info;\n}\n\ntemplate<typename FunctorType, typename VectorType>\nint test_lmder(FunctorType& functor, VectorType& uv)\n{\n  typedef typename VectorType::Scalar Scalar;\n  LevenbergMarquardtSpace::Status info; \n  LevenbergMarquardt<FunctorType> lm(functor);\n  info = lm.lmder1(uv);\n  \n  VERIFY_IS_EQUAL(info, 1);\n  //FIXME Check other parameters\n  return info;\n}\n\ntemplate<typename FunctorType, typename VectorType>\nint test_minimizeSteps(FunctorType& functor, VectorType& uv)\n{\n  LevenbergMarquardtSpace::Status info;   \n  LevenbergMarquardt<FunctorType> lm(functor);\n  info = lm.minimizeInit(uv);\n  if (info==LevenbergMarquardtSpace::ImproperInputParameters)\n      return info;\n  do \n  {\n    info = lm.minimizeOneStep(uv);\n  } while (info==LevenbergMarquardtSpace::Running);\n  \n  VERIFY_IS_EQUAL(info, 1);\n  //FIXME Check other parameters\n  return info;\n}\n\ntemplate<typename T>\nvoid test_denseLM_T()\n{\n  typedef Matrix<T,Dynamic,1> VectorType;\n  \n  int inputs = 10; \n  int values = 1000; \n  DenseLM<T> dense_gaussian(inputs, values);\n  VectorType uv(inputs),uv_ref(inputs);\n  VectorType x(values);\n  \n  // Generate the reference solution \n  uv_ref << -2, 1, 4 ,8, 6, 1.8, 1.2, 1.1, 1.9 , 3;\n  \n  //Generate the reference data points\n  x.setRandom();\n  x = 10*x;\n  x.array() += 10;\n  dense_gaussian.initPoints(uv_ref, x);\n  \n  // Generate the initial parameters \n  VectorBlock<VectorType> u(uv, 0, inputs/2); \n  VectorBlock<VectorType> v(uv, inputs/2, inputs/2);\n  \n  // Solve the optimization problem\n  \n  //Solve in one go\n  u.setOnes(); v.setOnes();\n  test_minimizeLM(dense_gaussian, uv);\n  \n  //Solve until the machine precision\n  u.setOnes(); v.setOnes();\n  test_lmder(dense_gaussian, uv); \n  \n  // Solve step by step\n  v.setOnes(); u.setOnes();\n  test_minimizeSteps(dense_gaussian, uv);\n  \n}\n\nvoid test_denseLM()\n{\n  CALL_SUBTEST_2(test_denseLM_T<double>());\n  \n  // CALL_SUBTEST_2(test_sparseLM_T<std::complex<double>());\n}\n"
  },
  {
    "path": "include/eigen3/test/dense_storage.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2013 Hauke Heibel <hauke.heibel@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/Core>\n\ntemplate <typename T, int Rows, int Cols>\nvoid dense_storage_copy()\n{\n  static const int Size = ((Rows==Dynamic || Cols==Dynamic) ? Dynamic : Rows*Cols);\n  typedef DenseStorage<T,Size, Rows,Cols, 0> DenseStorageType;\n  \n  const int rows = (Rows==Dynamic) ? 4 : Rows;\n  const int cols = (Cols==Dynamic) ? 3 : Cols;\n  const int size = rows*cols;\n  DenseStorageType reference(size, rows, cols);\n  T* raw_reference = reference.data();\n  for (int i=0; i<size; ++i)\n    raw_reference[i] = static_cast<T>(i);\n    \n  DenseStorageType copied_reference(reference);\n  const T* raw_copied_reference = copied_reference.data();\n  for (int i=0; i<size; ++i)\n    VERIFY_IS_EQUAL(raw_reference[i], raw_copied_reference[i]);\n}\n\ntemplate <typename T, int Rows, int Cols>\nvoid dense_storage_assignment()\n{\n  static const int Size = ((Rows==Dynamic || Cols==Dynamic) ? Dynamic : Rows*Cols);\n  typedef DenseStorage<T,Size, Rows,Cols, 0> DenseStorageType;\n  \n  const int rows = (Rows==Dynamic) ? 4 : Rows;\n  const int cols = (Cols==Dynamic) ? 3 : Cols;\n  const int size = rows*cols;\n  DenseStorageType reference(size, rows, cols);\n  T* raw_reference = reference.data();\n  for (int i=0; i<size; ++i)\n    raw_reference[i] = static_cast<T>(i);\n    \n  DenseStorageType copied_reference;\n  copied_reference = reference;\n  const T* raw_copied_reference = copied_reference.data();\n  for (int i=0; i<size; ++i)\n    VERIFY_IS_EQUAL(raw_reference[i], raw_copied_reference[i]);\n}\n\nvoid test_dense_storage()\n{\n  dense_storage_copy<int,Dynamic,Dynamic>();  \n  dense_storage_copy<int,Dynamic,3>();\n  dense_storage_copy<int,4,Dynamic>();\n  dense_storage_copy<int,4,3>();\n\n  dense_storage_copy<float,Dynamic,Dynamic>();\n  dense_storage_copy<float,Dynamic,3>();\n  dense_storage_copy<float,4,Dynamic>();  \n  dense_storage_copy<float,4,3>();\n  \n  dense_storage_assignment<int,Dynamic,Dynamic>();  \n  dense_storage_assignment<int,Dynamic,3>();\n  dense_storage_assignment<int,4,Dynamic>();\n  dense_storage_assignment<int,4,3>();\n\n  dense_storage_assignment<float,Dynamic,Dynamic>();\n  dense_storage_assignment<float,Dynamic,3>();\n  dense_storage_assignment<float,4,Dynamic>();  \n  dense_storage_assignment<float,4,3>();  \n}\n"
  },
  {
    "path": "include/eigen3/test/determinant.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <Eigen/LU>\n\ntemplate<typename MatrixType> void determinant(const MatrixType& m)\n{\n  /* this test covers the following files:\n     Determinant.h\n  */\n  typedef typename MatrixType::Index Index;\n  Index size = m.rows();\n\n  MatrixType m1(size, size), m2(size, size);\n  m1.setRandom();\n  m2.setRandom();\n  typedef typename MatrixType::Scalar Scalar;\n  Scalar x = internal::random<Scalar>();\n  VERIFY_IS_APPROX(MatrixType::Identity(size, size).determinant(), Scalar(1));\n  VERIFY_IS_APPROX((m1*m2).eval().determinant(), m1.determinant() * m2.determinant());\n  if(size==1) return;\n  Index i = internal::random<Index>(0, size-1);\n  Index j;\n  do {\n    j = internal::random<Index>(0, size-1);\n  } while(j==i);\n  m2 = m1;\n  m2.row(i).swap(m2.row(j));\n  VERIFY_IS_APPROX(m2.determinant(), -m1.determinant());\n  m2 = m1;\n  m2.col(i).swap(m2.col(j));\n  VERIFY_IS_APPROX(m2.determinant(), -m1.determinant());\n  VERIFY_IS_APPROX(m2.determinant(), m2.transpose().determinant());\n  VERIFY_IS_APPROX(numext::conj(m2.determinant()), m2.adjoint().determinant());\n  m2 = m1;\n  m2.row(i) += x*m2.row(j);\n  VERIFY_IS_APPROX(m2.determinant(), m1.determinant());\n  m2 = m1;\n  m2.row(i) *= x;\n  VERIFY_IS_APPROX(m2.determinant(), m1.determinant() * x);\n  \n  // check empty matrix\n  VERIFY_IS_APPROX(m2.block(0,0,0,0).determinant(), Scalar(1));\n}\n\nvoid test_determinant()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    int s = 0;\n    CALL_SUBTEST_1( determinant(Matrix<float, 1, 1>()) );\n    CALL_SUBTEST_2( determinant(Matrix<double, 2, 2>()) );\n    CALL_SUBTEST_3( determinant(Matrix<double, 3, 3>()) );\n    CALL_SUBTEST_4( determinant(Matrix<double, 4, 4>()) );\n    CALL_SUBTEST_5( determinant(Matrix<std::complex<double>, 10, 10>()) );\n    s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);\n    CALL_SUBTEST_6( determinant(MatrixXd(s, s)) );\n    TEST_SET_BUT_UNUSED_VARIABLE(s)\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/diagonal.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\ntemplate<typename MatrixType> void diagonal(const MatrixType& m)\n{\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  MatrixType m1 = MatrixType::Random(rows, cols),\n             m2 = MatrixType::Random(rows, cols);\n\n  Scalar s1 = internal::random<Scalar>();\n\n  //check diagonal()\n  VERIFY_IS_APPROX(m1.diagonal(), m1.transpose().diagonal());\n  m2.diagonal() = 2 * m1.diagonal();\n  m2.diagonal()[0] *= 3;\n\n  if (rows>2)\n  {\n    enum {\n      N1 = MatrixType::RowsAtCompileTime>2 ?  2 : 0,\n      N2 = MatrixType::RowsAtCompileTime>1 ? -1 : 0\n    };\n\n    // check sub/super diagonal\n    if(MatrixType::SizeAtCompileTime!=Dynamic)\n    {\n      VERIFY(m1.template diagonal<N1>().RowsAtCompileTime == m1.diagonal(N1).size());\n      VERIFY(m1.template diagonal<N2>().RowsAtCompileTime == m1.diagonal(N2).size());\n    }\n\n    m2.template diagonal<N1>() = 2 * m1.template diagonal<N1>();\n    VERIFY_IS_APPROX(m2.template diagonal<N1>(), static_cast<Scalar>(2) * m1.diagonal(N1));\n    m2.template diagonal<N1>()[0] *= 3;\n    VERIFY_IS_APPROX(m2.template diagonal<N1>()[0], static_cast<Scalar>(6) * m1.template diagonal<N1>()[0]);\n\n\n    m2.template diagonal<N2>() = 2 * m1.template diagonal<N2>();\n    m2.template diagonal<N2>()[0] *= 3;\n    VERIFY_IS_APPROX(m2.template diagonal<N2>()[0], static_cast<Scalar>(6) * m1.template diagonal<N2>()[0]);\n\n    m2.diagonal(N1) = 2 * m1.diagonal(N1);\n    VERIFY_IS_APPROX(m2.template diagonal<N1>(), static_cast<Scalar>(2) * m1.diagonal(N1));\n    m2.diagonal(N1)[0] *= 3;\n    VERIFY_IS_APPROX(m2.diagonal(N1)[0], static_cast<Scalar>(6) * m1.diagonal(N1)[0]);\n\n    m2.diagonal(N2) = 2 * m1.diagonal(N2);\n    VERIFY_IS_APPROX(m2.template diagonal<N2>(), static_cast<Scalar>(2) * m1.diagonal(N2));\n    m2.diagonal(N2)[0] *= 3;\n    VERIFY_IS_APPROX(m2.diagonal(N2)[0], static_cast<Scalar>(6) * m1.diagonal(N2)[0]);\n\n    m2.diagonal(N2).x() = s1;\n    VERIFY_IS_APPROX(m2.diagonal(N2).x(), s1);\n    m2.diagonal(N2).coeffRef(0) = Scalar(2)*s1;\n    VERIFY_IS_APPROX(m2.diagonal(N2).coeff(0), Scalar(2)*s1);\n  }\n\n  VERIFY( m1.diagonal( cols).size()==0 );\n  VERIFY( m1.diagonal(-rows).size()==0 );\n}\n\ntemplate<typename MatrixType> void diagonal_assert(const MatrixType& m) {\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  MatrixType m1 = MatrixType::Random(rows, cols);\n\n  if (rows>=2 && cols>=2)\n  {\n    VERIFY_RAISES_ASSERT( m1 += m1.diagonal() );\n    VERIFY_RAISES_ASSERT( m1 -= m1.diagonal() );\n    VERIFY_RAISES_ASSERT( m1.array() *= m1.diagonal().array() );\n    VERIFY_RAISES_ASSERT( m1.array() /= m1.diagonal().array() );\n  }\n\n  VERIFY_RAISES_ASSERT( m1.diagonal(cols+1) );\n  VERIFY_RAISES_ASSERT( m1.diagonal(-(rows+1)) );\n}\n\nvoid test_diagonal()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( diagonal(Matrix<float, 1, 1>()) );\n    CALL_SUBTEST_1( diagonal(Matrix<float, 4, 9>()) );\n    CALL_SUBTEST_1( diagonal(Matrix<float, 7, 3>()) );\n    CALL_SUBTEST_2( diagonal(Matrix4d()) );\n    CALL_SUBTEST_2( diagonal(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_2( diagonal(MatrixXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_2( diagonal(MatrixXcd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_1( diagonal(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_1( diagonal(Matrix<float,Dynamic,4>(3, 4)) );\n    CALL_SUBTEST_1( diagonal_assert(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/diagonalmatrices.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\nusing namespace std;\ntemplate<typename MatrixType> void diagonalmatrices(const MatrixType& m)\n{\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n  enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };\n  typedef Matrix<Scalar, Rows, 1> VectorType;\n  typedef Matrix<Scalar, 1, Cols> RowVectorType;\n  typedef Matrix<Scalar, Rows, Rows> SquareMatrixType;\n  typedef Matrix<Scalar, Dynamic, Dynamic> DynMatrixType;\n  typedef DiagonalMatrix<Scalar, Rows> LeftDiagonalMatrix;\n  typedef DiagonalMatrix<Scalar, Cols> RightDiagonalMatrix;\n  typedef Matrix<Scalar, Rows==Dynamic?Dynamic:2*Rows, Cols==Dynamic?Dynamic:2*Cols> BigMatrix;\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  MatrixType m1 = MatrixType::Random(rows, cols),\n             m2 = MatrixType::Random(rows, cols);\n  VectorType v1 = VectorType::Random(rows),\n             v2 = VectorType::Random(rows);\n  RowVectorType rv1 = RowVectorType::Random(cols),\n             rv2 = RowVectorType::Random(cols);\n\n  LeftDiagonalMatrix ldm1(v1), ldm2(v2);\n  RightDiagonalMatrix rdm1(rv1), rdm2(rv2);\n  \n  Scalar s1 = internal::random<Scalar>();\n\n  SquareMatrixType sq_m1 (v1.asDiagonal());\n  VERIFY_IS_APPROX(sq_m1, v1.asDiagonal().toDenseMatrix());\n  sq_m1 = v1.asDiagonal();\n  VERIFY_IS_APPROX(sq_m1, v1.asDiagonal().toDenseMatrix());\n  SquareMatrixType sq_m2 = v1.asDiagonal();\n  VERIFY_IS_APPROX(sq_m1, sq_m2);\n  \n  ldm1 = v1.asDiagonal();\n  LeftDiagonalMatrix ldm3(v1);\n  VERIFY_IS_APPROX(ldm1.diagonal(), ldm3.diagonal());\n  LeftDiagonalMatrix ldm4 = v1.asDiagonal();\n  VERIFY_IS_APPROX(ldm1.diagonal(), ldm4.diagonal());\n  \n  sq_m1.block(0,0,rows,rows) = ldm1;\n  VERIFY_IS_APPROX(sq_m1, ldm1.toDenseMatrix());\n  sq_m1.transpose() = ldm1;\n  VERIFY_IS_APPROX(sq_m1, ldm1.toDenseMatrix());\n  \n  Index i = internal::random<Index>(0, rows-1);\n  Index j = internal::random<Index>(0, cols-1);\n  \n  VERIFY_IS_APPROX( ((ldm1 * m1)(i,j))  , ldm1.diagonal()(i) * m1(i,j) );\n  VERIFY_IS_APPROX( ((ldm1 * (m1+m2))(i,j))  , ldm1.diagonal()(i) * (m1+m2)(i,j) );\n  VERIFY_IS_APPROX( ((m1 * rdm1)(i,j))  , rdm1.diagonal()(j) * m1(i,j) );\n  VERIFY_IS_APPROX( ((v1.asDiagonal() * m1)(i,j))  , v1(i) * m1(i,j) );\n  VERIFY_IS_APPROX( ((m1 * rv1.asDiagonal())(i,j))  , rv1(j) * m1(i,j) );\n  VERIFY_IS_APPROX( (((v1+v2).asDiagonal() * m1)(i,j))  , (v1+v2)(i) * m1(i,j) );\n  VERIFY_IS_APPROX( (((v1+v2).asDiagonal() * (m1+m2))(i,j))  , (v1+v2)(i) * (m1+m2)(i,j) );\n  VERIFY_IS_APPROX( ((m1 * (rv1+rv2).asDiagonal())(i,j))  , (rv1+rv2)(j) * m1(i,j) );\n  VERIFY_IS_APPROX( (((m1+m2) * (rv1+rv2).asDiagonal())(i,j))  , (rv1+rv2)(j) * (m1+m2)(i,j) );\n  \n  if(rows>1)\n  {\n    DynMatrixType tmp = m1.topRows(rows/2), res;\n    VERIFY_IS_APPROX( (res = m1.topRows(rows/2) * rv1.asDiagonal()), tmp * rv1.asDiagonal() );\n    VERIFY_IS_APPROX( (res = v1.head(rows/2).asDiagonal()*m1.topRows(rows/2)), v1.head(rows/2).asDiagonal()*tmp );\n  }\n\n  BigMatrix big;\n  big.setZero(2*rows, 2*cols);\n  \n  big.block(i,j,rows,cols) = m1;\n  big.block(i,j,rows,cols) = v1.asDiagonal() * big.block(i,j,rows,cols);\n  \n  VERIFY_IS_APPROX((big.block(i,j,rows,cols)) , v1.asDiagonal() * m1 );\n  \n  big.block(i,j,rows,cols) = m1;\n  big.block(i,j,rows,cols) = big.block(i,j,rows,cols) * rv1.asDiagonal();\n  VERIFY_IS_APPROX((big.block(i,j,rows,cols)) , m1 * rv1.asDiagonal() );\n  \n  \n  // scalar multiple\n  VERIFY_IS_APPROX(LeftDiagonalMatrix(ldm1*s1).diagonal(), ldm1.diagonal() * s1);\n  VERIFY_IS_APPROX(LeftDiagonalMatrix(s1*ldm1).diagonal(), s1 * ldm1.diagonal());\n  \n  VERIFY_IS_APPROX(m1 * (rdm1 * s1), (m1 * rdm1) * s1);\n  VERIFY_IS_APPROX(m1 * (s1 * rdm1), (m1 * rdm1) * s1);\n  \n  // Diagonal to dense\n  sq_m1.setRandom();\n  sq_m2 = sq_m1;\n  VERIFY_IS_APPROX( (sq_m1 += (s1*v1).asDiagonal()), sq_m2 += (s1*v1).asDiagonal().toDenseMatrix() );\n  VERIFY_IS_APPROX( (sq_m1 -= (s1*v1).asDiagonal()), sq_m2 -= (s1*v1).asDiagonal().toDenseMatrix() );\n  VERIFY_IS_APPROX( (sq_m1 = (s1*v1).asDiagonal()), (s1*v1).asDiagonal().toDenseMatrix() );\n\n  sq_m1.setRandom();\n  sq_m2 = v1.asDiagonal();\n  sq_m2 = sq_m1 * sq_m2;\n  VERIFY_IS_APPROX( (sq_m1*v1.asDiagonal()).col(i), sq_m2.col(i) );\n  VERIFY_IS_APPROX( (sq_m1*v1.asDiagonal()).row(i), sq_m2.row(i) );\n}\n\ntemplate<typename MatrixType> void as_scalar_product(const MatrixType& m)\n{\n  typedef typename MatrixType::Scalar Scalar;\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;\n  typedef Matrix<Scalar, Dynamic, Dynamic> DynMatrixType;\n  typedef Matrix<Scalar, Dynamic, 1> DynVectorType;\n  typedef Matrix<Scalar, 1, Dynamic> DynRowVectorType;\n\n  Index rows = m.rows();\n  Index depth = internal::random<Index>(1,EIGEN_TEST_MAX_SIZE);\n\n  VectorType v1 = VectorType::Random(rows);  \n  DynVectorType     dv1  = DynVectorType::Random(depth);\n  DynRowVectorType  drv1 = DynRowVectorType::Random(depth);\n  DynMatrixType     dm1  = dv1;\n  DynMatrixType     drm1 = drv1;\n  \n  Scalar s = v1(0);\n\n  VERIFY_IS_APPROX( v1.asDiagonal() * drv1, s*drv1 );\n  VERIFY_IS_APPROX( dv1 * v1.asDiagonal(), dv1*s );\n\n  VERIFY_IS_APPROX( v1.asDiagonal() * drm1, s*drm1 );\n  VERIFY_IS_APPROX( dm1 * v1.asDiagonal(), dm1*s );\n}\n\ntemplate<int>\nvoid bug987()\n{\n  Matrix3Xd points = Matrix3Xd::Random(3, 3);\n  Vector2d diag = Vector2d::Random();\n  Matrix2Xd tmp1 = points.topRows<2>(), res1, res2;\n  VERIFY_IS_APPROX( res1 = diag.asDiagonal() * points.topRows<2>(), res2 = diag.asDiagonal() * tmp1 );\n  Matrix2d tmp2 = points.topLeftCorner<2,2>();\n  VERIFY_IS_APPROX(( res1 = points.topLeftCorner<2,2>()*diag.asDiagonal()) , res2 = tmp2*diag.asDiagonal() );\n}\n\nvoid test_diagonalmatrices()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( diagonalmatrices(Matrix<float, 1, 1>()) );\n    CALL_SUBTEST_1( as_scalar_product(Matrix<float, 1, 1>()) );\n\n    CALL_SUBTEST_2( diagonalmatrices(Matrix3f()) );\n    CALL_SUBTEST_3( diagonalmatrices(Matrix<double,3,3,RowMajor>()) );\n    CALL_SUBTEST_4( diagonalmatrices(Matrix4d()) );\n    CALL_SUBTEST_5( diagonalmatrices(Matrix<float,4,4,RowMajor>()) );\n    CALL_SUBTEST_6( diagonalmatrices(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_6( as_scalar_product(MatrixXcf(1,1)) );\n    CALL_SUBTEST_7( diagonalmatrices(MatrixXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_8( diagonalmatrices(Matrix<double,Dynamic,Dynamic,RowMajor>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_9( diagonalmatrices(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_9( diagonalmatrices(MatrixXf(1,1)) );\n    CALL_SUBTEST_9( as_scalar_product(MatrixXf(1,1)) );\n  }\n  CALL_SUBTEST_10( bug987<0>() );\n}\n"
  },
  {
    "path": "include/eigen3/test/dontalign.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2011 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#if defined EIGEN_TEST_PART_1 || defined EIGEN_TEST_PART_2 || defined EIGEN_TEST_PART_3 || defined EIGEN_TEST_PART_4\n#define EIGEN_DONT_ALIGN\n#elif defined EIGEN_TEST_PART_5 || defined EIGEN_TEST_PART_6 || defined EIGEN_TEST_PART_7 || defined EIGEN_TEST_PART_8\n#define EIGEN_DONT_ALIGN_STATICALLY\n#endif\n\n#include \"main.h\"\n#include <Eigen/Dense>\n\ntemplate<typename MatrixType>\nvoid dontalign(const MatrixType& m)\n{\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;\n\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  MatrixType a = MatrixType::Random(rows,cols);\n  SquareMatrixType square = SquareMatrixType::Random(rows,rows);\n  VectorType v = VectorType::Random(rows);\n\n  VERIFY_IS_APPROX(v, square * square.colPivHouseholderQr().solve(v));\n  square = square.inverse().eval();\n  a = square * a;\n  square = square*square;\n  v = square * v;\n  v = a.adjoint() * v;\n  VERIFY(square.determinant() != Scalar(0));\n\n  // bug 219: MapAligned() was giving an assert with EIGEN_DONT_ALIGN, because Map Flags were miscomputed\n  Scalar* array = internal::aligned_new<Scalar>(rows);\n  v = VectorType::MapAligned(array, rows);\n  internal::aligned_delete(array, rows);\n}\n\nvoid test_dontalign()\n{\n#if defined EIGEN_TEST_PART_1 || defined EIGEN_TEST_PART_5\n  dontalign(Matrix3d());\n  dontalign(Matrix4f());\n#elif defined EIGEN_TEST_PART_2 || defined EIGEN_TEST_PART_6\n  dontalign(Matrix3cd());\n  dontalign(Matrix4cf());\n#elif defined EIGEN_TEST_PART_3 || defined EIGEN_TEST_PART_7\n  dontalign(Matrix<float, 32, 32>());\n  dontalign(Matrix<std::complex<float>, 32, 32>());\n#elif defined EIGEN_TEST_PART_4 || defined EIGEN_TEST_PART_8\n  dontalign(MatrixXd(32, 32));\n  dontalign(MatrixXcf(32, 32));\n#endif\n}\n"
  },
  {
    "path": "include/eigen3/test/dynalloc.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#if EIGEN_MAX_ALIGN_BYTES>0\n#define ALIGNMENT EIGEN_MAX_ALIGN_BYTES\n#else\n#define ALIGNMENT 1\n#endif\n\ntypedef Matrix<float,8,1> Vector8f;\n\nvoid check_handmade_aligned_malloc()\n{\n  for(int i = 1; i < 1000; i++)\n  {\n    char *p = (char*)internal::handmade_aligned_malloc(i);\n    VERIFY(internal::UIntPtr(p)%ALIGNMENT==0);\n    // if the buffer is wrongly allocated this will give a bad write --> check with valgrind\n    for(int j = 0; j < i; j++) p[j]=0;\n    internal::handmade_aligned_free(p);\n  }\n}\n\nvoid check_aligned_malloc()\n{\n  for(int i = ALIGNMENT; i < 1000; i++)\n  {\n    char *p = (char*)internal::aligned_malloc(i);\n    VERIFY(internal::UIntPtr(p)%ALIGNMENT==0);\n    // if the buffer is wrongly allocated this will give a bad write --> check with valgrind\n    for(int j = 0; j < i; j++) p[j]=0;\n    internal::aligned_free(p);\n  }\n}\n\nvoid check_aligned_new()\n{\n  for(int i = ALIGNMENT; i < 1000; i++)\n  {\n    float *p = internal::aligned_new<float>(i);\n    VERIFY(internal::UIntPtr(p)%ALIGNMENT==0);\n    // if the buffer is wrongly allocated this will give a bad write --> check with valgrind\n    for(int j = 0; j < i; j++) p[j]=0;\n    internal::aligned_delete(p,i);\n  }\n}\n\nvoid check_aligned_stack_alloc()\n{\n  for(int i = ALIGNMENT; i < 400; i++)\n  {\n    ei_declare_aligned_stack_constructed_variable(float,p,i,0);\n    VERIFY(internal::UIntPtr(p)%ALIGNMENT==0);\n    // if the buffer is wrongly allocated this will give a bad write --> check with valgrind\n    for(int j = 0; j < i; j++) p[j]=0;\n  }\n}\n\n\n// test compilation with both a struct and a class...\nstruct MyStruct\n{\n  EIGEN_MAKE_ALIGNED_OPERATOR_NEW\n  char dummychar;\n  Vector8f avec;\n};\n\nclass MyClassA\n{\n  public:\n    EIGEN_MAKE_ALIGNED_OPERATOR_NEW\n    char dummychar;\n    Vector8f avec;\n};\n\ntemplate<typename T> void check_dynaligned()\n{\n  // TODO have to be updated once we support multiple alignment values\n  if(T::SizeAtCompileTime % ALIGNMENT == 0)\n  {\n    T* obj = new T;\n    VERIFY(T::NeedsToAlign==1);\n    VERIFY(internal::UIntPtr(obj)%ALIGNMENT==0);\n    delete obj;\n  }\n}\n\ntemplate<typename T> void check_custom_new_delete()\n{\n  {\n    T* t = new T;\n    delete t;\n  }\n  \n  {\n    std::size_t N = internal::random<std::size_t>(1,10);\n    T* t = new T[N];\n    delete[] t;\n  }\n  \n#if EIGEN_MAX_ALIGN_BYTES>0\n  {\n    T* t = static_cast<T *>((T::operator new)(sizeof(T)));\n    (T::operator delete)(t, sizeof(T));\n  }\n  \n  {\n    T* t = static_cast<T *>((T::operator new)(sizeof(T)));\n    (T::operator delete)(t);\n  }\n#endif\n}\n\nvoid test_dynalloc()\n{\n  // low level dynamic memory allocation\n  CALL_SUBTEST(check_handmade_aligned_malloc());\n  CALL_SUBTEST(check_aligned_malloc());\n  CALL_SUBTEST(check_aligned_new());\n  CALL_SUBTEST(check_aligned_stack_alloc());\n\n  for (int i=0; i<g_repeat*100; ++i)\n  {\n    CALL_SUBTEST( check_custom_new_delete<Vector4f>() );\n    CALL_SUBTEST( check_custom_new_delete<Vector2f>() );\n    CALL_SUBTEST( check_custom_new_delete<Matrix4f>() );\n    CALL_SUBTEST( check_custom_new_delete<MatrixXi>() );\n  }\n  \n  // check static allocation, who knows ?\n  #if EIGEN_MAX_STATIC_ALIGN_BYTES\n  for (int i=0; i<g_repeat*100; ++i)\n  {\n    CALL_SUBTEST(check_dynaligned<Vector4f>() );\n    CALL_SUBTEST(check_dynaligned<Vector2d>() );\n    CALL_SUBTEST(check_dynaligned<Matrix4f>() );\n    CALL_SUBTEST(check_dynaligned<Vector4d>() );\n    CALL_SUBTEST(check_dynaligned<Vector4i>() );\n    CALL_SUBTEST(check_dynaligned<Vector8f>() );\n  }\n\n  {\n    MyStruct foo0;  VERIFY(internal::UIntPtr(foo0.avec.data())%ALIGNMENT==0);\n    MyClassA fooA;  VERIFY(internal::UIntPtr(fooA.avec.data())%ALIGNMENT==0);\n  }\n  \n  // dynamic allocation, single object\n  for (int i=0; i<g_repeat*100; ++i)\n  {\n    MyStruct *foo0 = new MyStruct();  VERIFY(internal::UIntPtr(foo0->avec.data())%ALIGNMENT==0);\n    MyClassA *fooA = new MyClassA();  VERIFY(internal::UIntPtr(fooA->avec.data())%ALIGNMENT==0);\n    delete foo0;\n    delete fooA;\n  }\n\n  // dynamic allocation, array\n  const int N = 10;\n  for (int i=0; i<g_repeat*100; ++i)\n  {\n    MyStruct *foo0 = new MyStruct[N];  VERIFY(internal::UIntPtr(foo0->avec.data())%ALIGNMENT==0);\n    MyClassA *fooA = new MyClassA[N];  VERIFY(internal::UIntPtr(fooA->avec.data())%ALIGNMENT==0);\n    delete[] foo0;\n    delete[] fooA;\n  }\n  #endif\n  \n}\n"
  },
  {
    "path": "include/eigen3/test/eigen2support.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define EIGEN2_SUPPORT\n\n#include \"main.h\"\n\ntemplate<typename MatrixType> void eigen2support(const MatrixType& m)\n{\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  MatrixType m1 = MatrixType::Random(rows, cols),\n             m3(rows, cols);\n\n  Scalar  s1 = internal::random<Scalar>(),\n          s2 = internal::random<Scalar>();\n\n  // scalar addition\n  VERIFY_IS_APPROX(m1.cwise() + s1, s1 + m1.cwise());\n  VERIFY_IS_APPROX(m1.cwise() + s1, MatrixType::Constant(rows,cols,s1) + m1);\n  VERIFY_IS_APPROX((m1*Scalar(2)).cwise() - s2, (m1+m1) - MatrixType::Constant(rows,cols,s2) );\n  m3 = m1;\n  m3.cwise() += s2;\n  VERIFY_IS_APPROX(m3, m1.cwise() + s2);\n  m3 = m1;\n  m3.cwise() -= s1;\n  VERIFY_IS_APPROX(m3, m1.cwise() - s1);\n\n  VERIFY_IS_EQUAL((m1.corner(TopLeft,1,1)), (m1.block(0,0,1,1)));\n  VERIFY_IS_EQUAL((m1.template corner<1,1>(TopLeft)), (m1.template block<1,1>(0,0)));\n  VERIFY_IS_EQUAL((m1.col(0).start(1)), (m1.col(0).segment(0,1)));\n  VERIFY_IS_EQUAL((m1.col(0).template start<1>()), (m1.col(0).segment(0,1)));\n  VERIFY_IS_EQUAL((m1.col(0).end(1)), (m1.col(0).segment(rows-1,1)));\n  VERIFY_IS_EQUAL((m1.col(0).template end<1>()), (m1.col(0).segment(rows-1,1)));\n  \n  using std::cos;\n  using numext::real;\n  using numext::abs2;\n  VERIFY_IS_EQUAL(ei_cos(s1), cos(s1));\n  VERIFY_IS_EQUAL(ei_real(s1), real(s1));\n  VERIFY_IS_EQUAL(ei_abs2(s1), abs2(s1));\n\n  m1.minor(0,0);\n}\n\nvoid test_eigen2support()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( eigen2support(Matrix<double,1,1>()) );\n    CALL_SUBTEST_2( eigen2support(MatrixXd(1,1)) );\n    CALL_SUBTEST_4( eigen2support(Matrix3f()) );\n    CALL_SUBTEST_5( eigen2support(Matrix4d()) );\n    CALL_SUBTEST_2( eigen2support(MatrixXf(200,200)) );\n    CALL_SUBTEST_6( eigen2support(MatrixXcd(100,100)) );\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/eigensolver_complex.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <limits>\n#include <Eigen/Eigenvalues>\n#include <Eigen/LU>\n\ntemplate<typename MatrixType> bool find_pivot(typename MatrixType::Scalar tol, MatrixType &diffs, Index col=0)\n{\n  bool match = diffs.diagonal().sum() <= tol;\n  if(match || col==diffs.cols())\n  {\n    return match;\n  }\n  else\n  {\n    Index n = diffs.cols();\n    std::vector<std::pair<Index,Index> > transpositions;\n    for(Index i=col; i<n; ++i)\n    {\n      Index best_index(0);\n      if(diffs.col(col).segment(col,n-i).minCoeff(&best_index) > tol)\n        break;\n      \n      best_index += col;\n      \n      diffs.row(col).swap(diffs.row(best_index));\n      if(find_pivot(tol,diffs,col+1)) return true;\n      diffs.row(col).swap(diffs.row(best_index));\n      \n      // move current pivot to the end\n      diffs.row(n-(i-col)-1).swap(diffs.row(best_index));\n      transpositions.push_back(std::pair<Index,Index>(n-(i-col)-1,best_index));\n    }\n    // restore\n    for(Index k=transpositions.size()-1; k>=0; --k)\n      diffs.row(transpositions[k].first).swap(diffs.row(transpositions[k].second));\n  }\n  return false;\n}\n\n/* Check that two column vectors are approximately equal upto permutations.\n * Initially, this method checked that the k-th power sums are equal for all k = 1, ..., vec1.rows(),\n * however this strategy is numerically inacurate because of numerical cancellation issues.\n */\ntemplate<typename VectorType>\nvoid verify_is_approx_upto_permutation(const VectorType& vec1, const VectorType& vec2)\n{\n  typedef typename VectorType::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n\n  VERIFY(vec1.cols() == 1);\n  VERIFY(vec2.cols() == 1);\n  VERIFY(vec1.rows() == vec2.rows());\n  \n  Index n = vec1.rows();\n  RealScalar tol = test_precision<RealScalar>()*test_precision<RealScalar>()*numext::maxi(vec1.squaredNorm(),vec2.squaredNorm());\n  Matrix<RealScalar,Dynamic,Dynamic> diffs = (vec1.rowwise().replicate(n) - vec2.rowwise().replicate(n).transpose()).cwiseAbs2();\n  \n  VERIFY( find_pivot(tol, diffs) );\n}\n\n\ntemplate<typename MatrixType> void eigensolver(const MatrixType& m)\n{\n  typedef typename MatrixType::Index Index;\n  /* this test covers the following files:\n     ComplexEigenSolver.h, and indirectly ComplexSchur.h\n  */\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n\n  MatrixType a = MatrixType::Random(rows,cols);\n  MatrixType symmA =  a.adjoint() * a;\n\n  ComplexEigenSolver<MatrixType> ei0(symmA);\n  VERIFY_IS_EQUAL(ei0.info(), Success);\n  VERIFY_IS_APPROX(symmA * ei0.eigenvectors(), ei0.eigenvectors() * ei0.eigenvalues().asDiagonal());\n\n  ComplexEigenSolver<MatrixType> ei1(a);\n  VERIFY_IS_EQUAL(ei1.info(), Success);\n  VERIFY_IS_APPROX(a * ei1.eigenvectors(), ei1.eigenvectors() * ei1.eigenvalues().asDiagonal());\n  // Note: If MatrixType is real then a.eigenvalues() uses EigenSolver and thus\n  // another algorithm so results may differ slightly\n  verify_is_approx_upto_permutation(a.eigenvalues(), ei1.eigenvalues());\n\n  ComplexEigenSolver<MatrixType> ei2;\n  ei2.setMaxIterations(ComplexSchur<MatrixType>::m_maxIterationsPerRow * rows).compute(a);\n  VERIFY_IS_EQUAL(ei2.info(), Success);\n  VERIFY_IS_EQUAL(ei2.eigenvectors(), ei1.eigenvectors());\n  VERIFY_IS_EQUAL(ei2.eigenvalues(), ei1.eigenvalues());\n  if (rows > 2) {\n    ei2.setMaxIterations(1).compute(a);\n    VERIFY_IS_EQUAL(ei2.info(), NoConvergence);\n    VERIFY_IS_EQUAL(ei2.getMaxIterations(), 1);\n  }\n\n  ComplexEigenSolver<MatrixType> eiNoEivecs(a, false);\n  VERIFY_IS_EQUAL(eiNoEivecs.info(), Success);\n  VERIFY_IS_APPROX(ei1.eigenvalues(), eiNoEivecs.eigenvalues());\n\n  // Regression test for issue #66\n  MatrixType z = MatrixType::Zero(rows,cols);\n  ComplexEigenSolver<MatrixType> eiz(z);\n  VERIFY((eiz.eigenvalues().cwiseEqual(0)).all());\n\n  MatrixType id = MatrixType::Identity(rows, cols);\n  VERIFY_IS_APPROX(id.operatorNorm(), RealScalar(1));\n\n  if (rows > 1 && rows < 20)\n  {\n    // Test matrix with NaN\n    a(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();\n    ComplexEigenSolver<MatrixType> eiNaN(a);\n    VERIFY_IS_EQUAL(eiNaN.info(), NoConvergence);\n  }\n\n  // regression test for bug 1098\n  {\n    ComplexEigenSolver<MatrixType> eig(a.adjoint() * a);\n    eig.compute(a.adjoint() * a);\n  }\n\n  // regression test for bug 478\n  {\n    a.setZero();\n    ComplexEigenSolver<MatrixType> ei3(a);\n    VERIFY_IS_EQUAL(ei3.info(), Success);\n    VERIFY_IS_MUCH_SMALLER_THAN(ei3.eigenvalues().norm(),RealScalar(1));\n    VERIFY((ei3.eigenvectors().transpose()*ei3.eigenvectors().transpose()).eval().isIdentity());\n  }\n}\n\ntemplate<typename MatrixType> void eigensolver_verify_assert(const MatrixType& m)\n{\n  ComplexEigenSolver<MatrixType> eig;\n  VERIFY_RAISES_ASSERT(eig.eigenvectors());\n  VERIFY_RAISES_ASSERT(eig.eigenvalues());\n\n  MatrixType a = MatrixType::Random(m.rows(),m.cols());\n  eig.compute(a, false);\n  VERIFY_RAISES_ASSERT(eig.eigenvectors());\n}\n\nvoid test_eigensolver_complex()\n{\n  int s = 0;\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( eigensolver(Matrix4cf()) );\n    s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);\n    CALL_SUBTEST_2( eigensolver(MatrixXcd(s,s)) );\n    CALL_SUBTEST_3( eigensolver(Matrix<std::complex<float>, 1, 1>()) );\n    CALL_SUBTEST_4( eigensolver(Matrix3f()) );\n    TEST_SET_BUT_UNUSED_VARIABLE(s)\n  }\n  CALL_SUBTEST_1( eigensolver_verify_assert(Matrix4cf()) );\n  s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);\n  CALL_SUBTEST_2( eigensolver_verify_assert(MatrixXcd(s,s)) );\n  CALL_SUBTEST_3( eigensolver_verify_assert(Matrix<std::complex<float>, 1, 1>()) );\n  CALL_SUBTEST_4( eigensolver_verify_assert(Matrix3f()) );\n\n  // Test problem size constructors\n  CALL_SUBTEST_5(ComplexEigenSolver<MatrixXf> tmp(s));\n  \n  TEST_SET_BUT_UNUSED_VARIABLE(s)\n}\n"
  },
  {
    "path": "include/eigen3/test/eigensolver_generalized_real.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012-2016 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define EIGEN_RUNTIME_NO_MALLOC\n#include \"main.h\"\n#include <limits>\n#include <Eigen/Eigenvalues>\n#include <Eigen/LU>\n\ntemplate<typename MatrixType> void generalized_eigensolver_real(const MatrixType& m)\n{\n  typedef typename MatrixType::Index Index;\n  /* this test covers the following files:\n     GeneralizedEigenSolver.h\n  */\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  typedef typename MatrixType::Scalar Scalar;\n  typedef std::complex<Scalar> ComplexScalar;\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;\n\n  MatrixType a = MatrixType::Random(rows,cols);\n  MatrixType b = MatrixType::Random(rows,cols);\n  MatrixType a1 = MatrixType::Random(rows,cols);\n  MatrixType b1 = MatrixType::Random(rows,cols);\n  MatrixType spdA =  a.adjoint() * a + a1.adjoint() * a1;\n  MatrixType spdB =  b.adjoint() * b + b1.adjoint() * b1;\n\n  // lets compare to GeneralizedSelfAdjointEigenSolver\n  {\n    GeneralizedSelfAdjointEigenSolver<MatrixType> symmEig(spdA, spdB);\n    GeneralizedEigenSolver<MatrixType> eig(spdA, spdB);\n\n    VERIFY_IS_EQUAL(eig.eigenvalues().imag().cwiseAbs().maxCoeff(), 0);\n\n    VectorType realEigenvalues = eig.eigenvalues().real();\n    std::sort(realEigenvalues.data(), realEigenvalues.data()+realEigenvalues.size());\n    VERIFY_IS_APPROX(realEigenvalues, symmEig.eigenvalues());\n\n    // check eigenvectors\n    typename GeneralizedEigenSolver<MatrixType>::EigenvectorsType D = eig.eigenvalues().asDiagonal();\n    typename GeneralizedEigenSolver<MatrixType>::EigenvectorsType V = eig.eigenvectors();\n    VERIFY_IS_APPROX(spdA*V, spdB*V*D);\n  }\n\n  // non symmetric case:\n  {\n    GeneralizedEigenSolver<MatrixType> eig(rows);\n    // TODO enable full-prealocation of required memory, this probably requires an in-place mode for HessenbergDecomposition\n    //Eigen::internal::set_is_malloc_allowed(false);\n    eig.compute(a,b);\n    //Eigen::internal::set_is_malloc_allowed(true);\n    for(Index k=0; k<cols; ++k)\n    {\n      Matrix<ComplexScalar,Dynamic,Dynamic> tmp = (eig.betas()(k)*a).template cast<ComplexScalar>() - eig.alphas()(k)*b;\n      if(tmp.size()>1 && tmp.norm()>(std::numeric_limits<Scalar>::min)())\n        tmp /= tmp.norm();\n      VERIFY_IS_MUCH_SMALLER_THAN( std::abs(tmp.determinant()), Scalar(1) );\n    }\n    // check eigenvectors\n    typename GeneralizedEigenSolver<MatrixType>::EigenvectorsType D = eig.eigenvalues().asDiagonal();\n    typename GeneralizedEigenSolver<MatrixType>::EigenvectorsType V = eig.eigenvectors();\n    VERIFY_IS_APPROX(a*V, b*V*D);\n  }\n\n  // regression test for bug 1098\n  {\n    GeneralizedSelfAdjointEigenSolver<MatrixType> eig1(a.adjoint() * a,b.adjoint() * b);\n    eig1.compute(a.adjoint() * a,b.adjoint() * b);\n    GeneralizedEigenSolver<MatrixType> eig2(a.adjoint() * a,b.adjoint() * b);\n    eig2.compute(a.adjoint() * a,b.adjoint() * b);\n  }\n\n  // check without eigenvectors\n  {\n    GeneralizedEigenSolver<MatrixType> eig1(spdA, spdB, true);\n    GeneralizedEigenSolver<MatrixType> eig2(spdA, spdB, false);\n    VERIFY_IS_APPROX(eig1.eigenvalues(), eig2.eigenvalues());\n  }\n}\n\nvoid test_eigensolver_generalized_real()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    int s = 0;\n    CALL_SUBTEST_1( generalized_eigensolver_real(Matrix4f()) );\n    s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);\n    CALL_SUBTEST_2( generalized_eigensolver_real(MatrixXd(s,s)) );\n\n    // some trivial but implementation-wise special cases\n    CALL_SUBTEST_2( generalized_eigensolver_real(MatrixXd(1,1)) );\n    CALL_SUBTEST_2( generalized_eigensolver_real(MatrixXd(2,2)) );\n    CALL_SUBTEST_3( generalized_eigensolver_real(Matrix<double,1,1>()) );\n    CALL_SUBTEST_4( generalized_eigensolver_real(Matrix2d()) );\n    TEST_SET_BUT_UNUSED_VARIABLE(s)\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/eigensolver_generic.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <limits>\n#include <Eigen/Eigenvalues>\n\ntemplate<typename MatrixType> void eigensolver(const MatrixType& m)\n{\n  typedef typename MatrixType::Index Index;\n  /* this test covers the following files:\n     EigenSolver.h\n  */\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  typedef Matrix<RealScalar, MatrixType::RowsAtCompileTime, 1> RealVectorType;\n  typedef typename std::complex<typename NumTraits<typename MatrixType::Scalar>::Real> Complex;\n\n  MatrixType a = MatrixType::Random(rows,cols);\n  MatrixType a1 = MatrixType::Random(rows,cols);\n  MatrixType symmA =  a.adjoint() * a + a1.adjoint() * a1;\n\n  EigenSolver<MatrixType> ei0(symmA);\n  VERIFY_IS_EQUAL(ei0.info(), Success);\n  VERIFY_IS_APPROX(symmA * ei0.pseudoEigenvectors(), ei0.pseudoEigenvectors() * ei0.pseudoEigenvalueMatrix());\n  VERIFY_IS_APPROX((symmA.template cast<Complex>()) * (ei0.pseudoEigenvectors().template cast<Complex>()),\n    (ei0.pseudoEigenvectors().template cast<Complex>()) * (ei0.eigenvalues().asDiagonal()));\n\n  EigenSolver<MatrixType> ei1(a);\n  VERIFY_IS_EQUAL(ei1.info(), Success);\n  VERIFY_IS_APPROX(a * ei1.pseudoEigenvectors(), ei1.pseudoEigenvectors() * ei1.pseudoEigenvalueMatrix());\n  VERIFY_IS_APPROX(a.template cast<Complex>() * ei1.eigenvectors(),\n                   ei1.eigenvectors() * ei1.eigenvalues().asDiagonal());\n  VERIFY_IS_APPROX(ei1.eigenvectors().colwise().norm(), RealVectorType::Ones(rows).transpose());\n  VERIFY_IS_APPROX(a.eigenvalues(), ei1.eigenvalues());\n\n  EigenSolver<MatrixType> ei2;\n  ei2.setMaxIterations(RealSchur<MatrixType>::m_maxIterationsPerRow * rows).compute(a);\n  VERIFY_IS_EQUAL(ei2.info(), Success);\n  VERIFY_IS_EQUAL(ei2.eigenvectors(), ei1.eigenvectors());\n  VERIFY_IS_EQUAL(ei2.eigenvalues(), ei1.eigenvalues());\n  if (rows > 2) {\n    ei2.setMaxIterations(1).compute(a);\n    VERIFY_IS_EQUAL(ei2.info(), NoConvergence);\n    VERIFY_IS_EQUAL(ei2.getMaxIterations(), 1);\n  }\n\n  EigenSolver<MatrixType> eiNoEivecs(a, false);\n  VERIFY_IS_EQUAL(eiNoEivecs.info(), Success);\n  VERIFY_IS_APPROX(ei1.eigenvalues(), eiNoEivecs.eigenvalues());\n  VERIFY_IS_APPROX(ei1.pseudoEigenvalueMatrix(), eiNoEivecs.pseudoEigenvalueMatrix());\n\n  MatrixType id = MatrixType::Identity(rows, cols);\n  VERIFY_IS_APPROX(id.operatorNorm(), RealScalar(1));\n\n  if (rows > 2 && rows < 20)\n  {\n    // Test matrix with NaN\n    a(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();\n    EigenSolver<MatrixType> eiNaN(a);\n    VERIFY_IS_EQUAL(eiNaN.info(), NoConvergence);\n  }\n\n  // regression test for bug 1098\n  {\n    EigenSolver<MatrixType> eig(a.adjoint() * a);\n    eig.compute(a.adjoint() * a);\n  }\n\n  // regression test for bug 478\n  {\n    a.setZero();\n    EigenSolver<MatrixType> ei3(a);\n    VERIFY_IS_EQUAL(ei3.info(), Success);\n    VERIFY_IS_MUCH_SMALLER_THAN(ei3.eigenvalues().norm(),RealScalar(1));\n    VERIFY((ei3.eigenvectors().transpose()*ei3.eigenvectors().transpose()).eval().isIdentity());\n  }\n}\n\ntemplate<typename MatrixType> void eigensolver_verify_assert(const MatrixType& m)\n{\n  EigenSolver<MatrixType> eig;\n  VERIFY_RAISES_ASSERT(eig.eigenvectors());\n  VERIFY_RAISES_ASSERT(eig.pseudoEigenvectors());\n  VERIFY_RAISES_ASSERT(eig.pseudoEigenvalueMatrix());\n  VERIFY_RAISES_ASSERT(eig.eigenvalues());\n\n  MatrixType a = MatrixType::Random(m.rows(),m.cols());\n  eig.compute(a, false);\n  VERIFY_RAISES_ASSERT(eig.eigenvectors());\n  VERIFY_RAISES_ASSERT(eig.pseudoEigenvectors());\n}\n\nvoid test_eigensolver_generic()\n{\n  int s = 0;\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( eigensolver(Matrix4f()) );\n    s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);\n    CALL_SUBTEST_2( eigensolver(MatrixXd(s,s)) );\n    TEST_SET_BUT_UNUSED_VARIABLE(s)\n\n    // some trivial but implementation-wise tricky cases\n    CALL_SUBTEST_2( eigensolver(MatrixXd(1,1)) );\n    CALL_SUBTEST_2( eigensolver(MatrixXd(2,2)) );\n    CALL_SUBTEST_3( eigensolver(Matrix<double,1,1>()) );\n    CALL_SUBTEST_4( eigensolver(Matrix2d()) );\n  }\n\n  CALL_SUBTEST_1( eigensolver_verify_assert(Matrix4f()) );\n  s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);\n  CALL_SUBTEST_2( eigensolver_verify_assert(MatrixXd(s,s)) );\n  CALL_SUBTEST_3( eigensolver_verify_assert(Matrix<double,1,1>()) );\n  CALL_SUBTEST_4( eigensolver_verify_assert(Matrix2d()) );\n\n  // Test problem size constructors\n  CALL_SUBTEST_5(EigenSolver<MatrixXf> tmp(s));\n\n  // regression test for bug 410\n  CALL_SUBTEST_2(\n  {\n     MatrixXd A(1,1);\n     A(0,0) = std::sqrt(-1.); // is Not-a-Number\n     Eigen::EigenSolver<MatrixXd> solver(A);\n     VERIFY_IS_EQUAL(solver.info(), NumericalIssue);\n  }\n  );\n  \n#ifdef EIGEN_TEST_PART_2\n  {\n    // regression test for bug 793\n    MatrixXd a(3,3);\n    a << 0,  0,  1,\n        1,  1, 1,\n        1, 1e+200,  1;\n    Eigen::EigenSolver<MatrixXd> eig(a);\n    double scale = 1e-200; // scale to avoid overflow during the comparisons\n    VERIFY_IS_APPROX(a * eig.pseudoEigenvectors()*scale, eig.pseudoEigenvectors() * eig.pseudoEigenvalueMatrix()*scale);\n    VERIFY_IS_APPROX(a * eig.eigenvectors()*scale, eig.eigenvectors() * eig.eigenvalues().asDiagonal()*scale);\n  }\n  {\n    // check a case where all eigenvalues are null.\n    MatrixXd a(2,2);\n    a << 1,  1,\n        -1, -1;\n    Eigen::EigenSolver<MatrixXd> eig(a);\n    VERIFY_IS_APPROX(eig.pseudoEigenvectors().squaredNorm(), 2.);\n    VERIFY_IS_APPROX((a * eig.pseudoEigenvectors()).norm()+1., 1.);\n    VERIFY_IS_APPROX((eig.pseudoEigenvectors() * eig.pseudoEigenvalueMatrix()).norm()+1., 1.);\n    VERIFY_IS_APPROX((a * eig.eigenvectors()).norm()+1., 1.);\n    VERIFY_IS_APPROX((eig.eigenvectors() * eig.eigenvalues().asDiagonal()).norm()+1., 1.);\n  }\n#endif\n  \n  TEST_SET_BUT_UNUSED_VARIABLE(s)\n}\n"
  },
  {
    "path": "include/eigen3/test/eigensolver_selfadjoint.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include \"svd_fill.h\"\n#include <limits>\n#include <Eigen/Eigenvalues>\n#include <Eigen/SparseCore>\n\n\ntemplate<typename MatrixType> void selfadjointeigensolver_essential_check(const MatrixType& m)\n{\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  RealScalar eival_eps = numext::mini<RealScalar>(test_precision<RealScalar>(),  NumTraits<Scalar>::dummy_precision()*20000);\n  \n  SelfAdjointEigenSolver<MatrixType> eiSymm(m);\n  VERIFY_IS_EQUAL(eiSymm.info(), Success);\n\n  RealScalar scaling = m.cwiseAbs().maxCoeff();\n\n  if(scaling<(std::numeric_limits<RealScalar>::min)())\n  {\n    VERIFY(eiSymm.eigenvalues().cwiseAbs().maxCoeff() <= (std::numeric_limits<RealScalar>::min)());\n  }\n  else\n  {\n    VERIFY_IS_APPROX((m.template selfadjointView<Lower>() * eiSymm.eigenvectors())/scaling,\n                     (eiSymm.eigenvectors() * eiSymm.eigenvalues().asDiagonal())/scaling);\n  }\n  VERIFY_IS_APPROX(m.template selfadjointView<Lower>().eigenvalues(), eiSymm.eigenvalues());\n  VERIFY_IS_UNITARY(eiSymm.eigenvectors());\n\n  if(m.cols()<=4)\n  {\n    SelfAdjointEigenSolver<MatrixType> eiDirect;\n    eiDirect.computeDirect(m);  \n    VERIFY_IS_EQUAL(eiDirect.info(), Success);\n    if(! eiSymm.eigenvalues().isApprox(eiDirect.eigenvalues(), eival_eps) )\n    {\n      std::cerr << \"reference eigenvalues: \" << eiSymm.eigenvalues().transpose() << \"\\n\"\n                << \"obtained eigenvalues:  \" << eiDirect.eigenvalues().transpose() << \"\\n\"\n                << \"diff:                  \" << (eiSymm.eigenvalues()-eiDirect.eigenvalues()).transpose() << \"\\n\"\n                << \"error (eps):           \" << (eiSymm.eigenvalues()-eiDirect.eigenvalues()).norm() / eiSymm.eigenvalues().norm() << \"  (\" << eival_eps << \")\\n\";\n    }\n    if(scaling<(std::numeric_limits<RealScalar>::min)())\n    {\n      VERIFY(eiDirect.eigenvalues().cwiseAbs().maxCoeff() <= (std::numeric_limits<RealScalar>::min)());\n    }\n    else\n    {\n      VERIFY_IS_APPROX(eiSymm.eigenvalues()/scaling, eiDirect.eigenvalues()/scaling);\n      VERIFY_IS_APPROX((m.template selfadjointView<Lower>() * eiDirect.eigenvectors())/scaling,\n                       (eiDirect.eigenvectors() * eiDirect.eigenvalues().asDiagonal())/scaling);\n      VERIFY_IS_APPROX(m.template selfadjointView<Lower>().eigenvalues()/scaling, eiDirect.eigenvalues()/scaling);\n    }\n\n    VERIFY_IS_UNITARY(eiDirect.eigenvectors());\n  }\n}\n\ntemplate<typename MatrixType> void selfadjointeigensolver(const MatrixType& m)\n{\n  typedef typename MatrixType::Index Index;\n  /* this test covers the following files:\n     EigenSolver.h, SelfAdjointEigenSolver.h (and indirectly: Tridiagonalization.h)\n  */\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n\n  RealScalar largerEps = 10*test_precision<RealScalar>();\n\n  MatrixType a = MatrixType::Random(rows,cols);\n  MatrixType a1 = MatrixType::Random(rows,cols);\n  MatrixType symmA =  a.adjoint() * a + a1.adjoint() * a1;\n  MatrixType symmC = symmA;\n  \n  svd_fill_random(symmA,Symmetric);\n\n  symmA.template triangularView<StrictlyUpper>().setZero();\n  symmC.template triangularView<StrictlyUpper>().setZero();\n\n  MatrixType b = MatrixType::Random(rows,cols);\n  MatrixType b1 = MatrixType::Random(rows,cols);\n  MatrixType symmB = b.adjoint() * b + b1.adjoint() * b1;\n  symmB.template triangularView<StrictlyUpper>().setZero();\n  \n  CALL_SUBTEST( selfadjointeigensolver_essential_check(symmA) );\n\n  SelfAdjointEigenSolver<MatrixType> eiSymm(symmA);\n  // generalized eigen pb\n  GeneralizedSelfAdjointEigenSolver<MatrixType> eiSymmGen(symmC, symmB);\n\n  SelfAdjointEigenSolver<MatrixType> eiSymmNoEivecs(symmA, false);\n  VERIFY_IS_EQUAL(eiSymmNoEivecs.info(), Success);\n  VERIFY_IS_APPROX(eiSymm.eigenvalues(), eiSymmNoEivecs.eigenvalues());\n  \n  // generalized eigen problem Ax = lBx\n  eiSymmGen.compute(symmC, symmB,Ax_lBx);\n  VERIFY_IS_EQUAL(eiSymmGen.info(), Success);\n  VERIFY((symmC.template selfadjointView<Lower>() * eiSymmGen.eigenvectors()).isApprox(\n          symmB.template selfadjointView<Lower>() * (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps));\n\n  // generalized eigen problem BAx = lx\n  eiSymmGen.compute(symmC, symmB,BAx_lx);\n  VERIFY_IS_EQUAL(eiSymmGen.info(), Success);\n  VERIFY((symmB.template selfadjointView<Lower>() * (symmC.template selfadjointView<Lower>() * eiSymmGen.eigenvectors())).isApprox(\n         (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps));\n\n  // generalized eigen problem ABx = lx\n  eiSymmGen.compute(symmC, symmB,ABx_lx);\n  VERIFY_IS_EQUAL(eiSymmGen.info(), Success);\n  VERIFY((symmC.template selfadjointView<Lower>() * (symmB.template selfadjointView<Lower>() * eiSymmGen.eigenvectors())).isApprox(\n         (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps));\n\n\n  eiSymm.compute(symmC);\n  MatrixType sqrtSymmA = eiSymm.operatorSqrt();\n  VERIFY_IS_APPROX(MatrixType(symmC.template selfadjointView<Lower>()), sqrtSymmA*sqrtSymmA);\n  VERIFY_IS_APPROX(sqrtSymmA, symmC.template selfadjointView<Lower>()*eiSymm.operatorInverseSqrt());\n\n  MatrixType id = MatrixType::Identity(rows, cols);\n  VERIFY_IS_APPROX(id.template selfadjointView<Lower>().operatorNorm(), RealScalar(1));\n\n  SelfAdjointEigenSolver<MatrixType> eiSymmUninitialized;\n  VERIFY_RAISES_ASSERT(eiSymmUninitialized.info());\n  VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvalues());\n  VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors());\n  VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt());\n  VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt());\n\n  eiSymmUninitialized.compute(symmA, false);\n  VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors());\n  VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt());\n  VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt());\n\n  // test Tridiagonalization's methods\n  Tridiagonalization<MatrixType> tridiag(symmC);\n  VERIFY_IS_APPROX(tridiag.diagonal(), tridiag.matrixT().diagonal());\n  VERIFY_IS_APPROX(tridiag.subDiagonal(), tridiag.matrixT().template diagonal<-1>());\n  Matrix<RealScalar,Dynamic,Dynamic> T = tridiag.matrixT();\n  if(rows>1 && cols>1) {\n    // FIXME check that upper and lower part are 0:\n    //VERIFY(T.topRightCorner(rows-2, cols-2).template triangularView<Upper>().isZero());\n  }\n  VERIFY_IS_APPROX(tridiag.diagonal(), T.diagonal());\n  VERIFY_IS_APPROX(tridiag.subDiagonal(), T.template diagonal<1>());\n  VERIFY_IS_APPROX(MatrixType(symmC.template selfadjointView<Lower>()), tridiag.matrixQ() * tridiag.matrixT().eval() * MatrixType(tridiag.matrixQ()).adjoint());\n  VERIFY_IS_APPROX(MatrixType(symmC.template selfadjointView<Lower>()), tridiag.matrixQ() * tridiag.matrixT() * tridiag.matrixQ().adjoint());\n  \n  // Test computation of eigenvalues from tridiagonal matrix\n  if(rows > 1)\n  {\n    SelfAdjointEigenSolver<MatrixType> eiSymmTridiag;\n    eiSymmTridiag.computeFromTridiagonal(tridiag.matrixT().diagonal(), tridiag.matrixT().diagonal(-1), ComputeEigenvectors);\n    VERIFY_IS_APPROX(eiSymm.eigenvalues(), eiSymmTridiag.eigenvalues());\n    VERIFY_IS_APPROX(tridiag.matrixT(), eiSymmTridiag.eigenvectors().real() * eiSymmTridiag.eigenvalues().asDiagonal() * eiSymmTridiag.eigenvectors().real().transpose());\n  }\n\n  if (rows > 1 && rows < 20)\n  {\n    // Test matrix with NaN\n    symmC(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();\n    SelfAdjointEigenSolver<MatrixType> eiSymmNaN(symmC);\n    VERIFY_IS_EQUAL(eiSymmNaN.info(), NoConvergence);\n  }\n\n  // regression test for bug 1098\n  {\n    SelfAdjointEigenSolver<MatrixType> eig(a.adjoint() * a);\n    eig.compute(a.adjoint() * a);\n  }\n\n  // regression test for bug 478\n  {\n    a.setZero();\n    SelfAdjointEigenSolver<MatrixType> ei3(a);\n    VERIFY_IS_EQUAL(ei3.info(), Success);\n    VERIFY_IS_MUCH_SMALLER_THAN(ei3.eigenvalues().norm(),RealScalar(1));\n    VERIFY((ei3.eigenvectors().transpose()*ei3.eigenvectors().transpose()).eval().isIdentity());\n  }\n}\n\ntemplate<int>\nvoid bug_854()\n{\n  Matrix3d m;\n  m << 850.961, 51.966, 0,\n       51.966, 254.841, 0,\n            0,       0, 0;\n  selfadjointeigensolver_essential_check(m);\n}\n\ntemplate<int>\nvoid bug_1014()\n{\n  Matrix3d m;\n  m <<        0.11111111111111114658, 0, 0,\n       0,     0.11111111111111109107, 0,\n       0, 0,  0.11111111111111107719;\n  selfadjointeigensolver_essential_check(m);\n}\n\ntemplate<int>\nvoid bug_1225()\n{\n  Matrix3d m1, m2;\n  m1.setRandom();\n  m1 = m1*m1.transpose();\n  m2 = m1.triangularView<Upper>();\n  SelfAdjointEigenSolver<Matrix3d> eig1(m1);\n  SelfAdjointEigenSolver<Matrix3d> eig2(m2.selfadjointView<Upper>());\n  VERIFY_IS_APPROX(eig1.eigenvalues(), eig2.eigenvalues());\n}\n\ntemplate<int>\nvoid bug_1204()\n{\n  SparseMatrix<double> A(2,2);\n  A.setIdentity();\n  SelfAdjointEigenSolver<Eigen::SparseMatrix<double> > eig(A);\n}\n\nvoid test_eigensolver_selfadjoint()\n{\n  int s = 0;\n  for(int i = 0; i < g_repeat; i++) {\n    // trivial test for 1x1 matrices:\n    CALL_SUBTEST_1( selfadjointeigensolver(Matrix<float, 1, 1>()));\n    CALL_SUBTEST_1( selfadjointeigensolver(Matrix<double, 1, 1>()));\n    // very important to test 3x3 and 2x2 matrices since we provide special paths for them\n    CALL_SUBTEST_12( selfadjointeigensolver(Matrix2f()) );\n    CALL_SUBTEST_12( selfadjointeigensolver(Matrix2d()) );\n    CALL_SUBTEST_13( selfadjointeigensolver(Matrix3f()) );\n    CALL_SUBTEST_13( selfadjointeigensolver(Matrix3d()) );\n    CALL_SUBTEST_2( selfadjointeigensolver(Matrix4d()) );\n    \n    s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);\n    CALL_SUBTEST_3( selfadjointeigensolver(MatrixXf(s,s)) );\n    CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(s,s)) );\n    CALL_SUBTEST_5( selfadjointeigensolver(MatrixXcd(s,s)) );\n    CALL_SUBTEST_9( selfadjointeigensolver(Matrix<std::complex<double>,Dynamic,Dynamic,RowMajor>(s,s)) );\n    TEST_SET_BUT_UNUSED_VARIABLE(s)\n\n    // some trivial but implementation-wise tricky cases\n    CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(1,1)) );\n    CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(2,2)) );\n    CALL_SUBTEST_6( selfadjointeigensolver(Matrix<double,1,1>()) );\n    CALL_SUBTEST_7( selfadjointeigensolver(Matrix<double,2,2>()) );\n  }\n  \n  CALL_SUBTEST_13( bug_854<0>() );\n  CALL_SUBTEST_13( bug_1014<0>() );\n  CALL_SUBTEST_13( bug_1204<0>() );\n  CALL_SUBTEST_13( bug_1225<0>() );\n\n  // Test problem size constructors\n  s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);\n  CALL_SUBTEST_8(SelfAdjointEigenSolver<MatrixXf> tmp1(s));\n  CALL_SUBTEST_8(Tridiagonalization<MatrixXf> tmp2(s));\n  \n  TEST_SET_BUT_UNUSED_VARIABLE(s)\n}\n\n"
  },
  {
    "path": "include/eigen3/test/evaluator_common.h",
    "content": ""
  },
  {
    "path": "include/eigen3/test/evaluators.cpp",
    "content": "\n#include \"main.h\"\n\nnamespace Eigen {\n\n  template<typename Lhs,typename Rhs>\n  const Product<Lhs,Rhs>\n  prod(const Lhs& lhs, const Rhs& rhs)\n  {\n    return Product<Lhs,Rhs>(lhs,rhs);\n  }\n\n  template<typename Lhs,typename Rhs>\n  const Product<Lhs,Rhs,LazyProduct>\n  lazyprod(const Lhs& lhs, const Rhs& rhs)\n  {\n    return Product<Lhs,Rhs,LazyProduct>(lhs,rhs);\n  }\n  \n  template<typename DstXprType, typename SrcXprType>\n  EIGEN_STRONG_INLINE\n  DstXprType& copy_using_evaluator(const EigenBase<DstXprType> &dst, const SrcXprType &src)\n  {\n    call_assignment(dst.const_cast_derived(), src.derived(), internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar>());\n    return dst.const_cast_derived();\n  }\n  \n  template<typename DstXprType, template <typename> class StorageBase, typename SrcXprType>\n  EIGEN_STRONG_INLINE\n  const DstXprType& copy_using_evaluator(const NoAlias<DstXprType, StorageBase>& dst, const SrcXprType &src)\n  {\n    call_assignment(dst, src.derived(), internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar>());\n    return dst.expression();\n  }\n  \n  template<typename DstXprType, typename SrcXprType>\n  EIGEN_STRONG_INLINE\n  DstXprType& copy_using_evaluator(const PlainObjectBase<DstXprType> &dst, const SrcXprType &src)\n  {\n    #ifdef EIGEN_NO_AUTOMATIC_RESIZING\n    eigen_assert((dst.size()==0 || (IsVectorAtCompileTime ? (dst.size() == src.size())\n                                                          : (dst.rows() == src.rows() && dst.cols() == src.cols())))\n                && \"Size mismatch. Automatic resizing is disabled because EIGEN_NO_AUTOMATIC_RESIZING is defined\");\n  #else\n    dst.const_cast_derived().resizeLike(src.derived());\n  #endif\n    \n    call_assignment(dst.const_cast_derived(), src.derived(), internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar>());\n    return dst.const_cast_derived();\n  }\n\n  template<typename DstXprType, typename SrcXprType>\n  void add_assign_using_evaluator(const DstXprType& dst, const SrcXprType& src)\n  {\n    typedef typename DstXprType::Scalar Scalar;\n    call_assignment(const_cast<DstXprType&>(dst), src.derived(), internal::add_assign_op<Scalar,typename SrcXprType::Scalar>());\n  }\n\n  template<typename DstXprType, typename SrcXprType>\n  void subtract_assign_using_evaluator(const DstXprType& dst, const SrcXprType& src)\n  {\n    typedef typename DstXprType::Scalar Scalar;\n    call_assignment(const_cast<DstXprType&>(dst), src.derived(), internal::sub_assign_op<Scalar,typename SrcXprType::Scalar>());\n  }\n\n  template<typename DstXprType, typename SrcXprType>\n  void multiply_assign_using_evaluator(const DstXprType& dst, const SrcXprType& src)\n  {\n    typedef typename DstXprType::Scalar Scalar;\n    call_assignment(dst.const_cast_derived(), src.derived(), internal::mul_assign_op<Scalar,typename SrcXprType::Scalar>());\n  }\n\n  template<typename DstXprType, typename SrcXprType>\n  void divide_assign_using_evaluator(const DstXprType& dst, const SrcXprType& src)\n  {\n    typedef typename DstXprType::Scalar Scalar;\n    call_assignment(dst.const_cast_derived(), src.derived(), internal::div_assign_op<Scalar,typename SrcXprType::Scalar>());\n  }\n  \n  template<typename DstXprType, typename SrcXprType>\n  void swap_using_evaluator(const DstXprType& dst, const SrcXprType& src)\n  {\n    typedef typename DstXprType::Scalar Scalar;\n    call_assignment(dst.const_cast_derived(), src.const_cast_derived(), internal::swap_assign_op<Scalar>());\n  }\n\n  namespace internal {\n    template<typename Dst, template <typename> class StorageBase, typename Src, typename Func>\n    EIGEN_DEVICE_FUNC void call_assignment(const NoAlias<Dst,StorageBase>& dst, const Src& src, const Func& func)\n    {\n      call_assignment_no_alias(dst.expression(), src, func);\n    }\n  }\n  \n}\n\ntemplate<typename XprType> long get_cost(const XprType& ) { return Eigen::internal::evaluator<XprType>::CoeffReadCost; }\n\nusing namespace std;\n\n#define VERIFY_IS_APPROX_EVALUATOR(DEST,EXPR) VERIFY_IS_APPROX(copy_using_evaluator(DEST,(EXPR)), (EXPR).eval());\n#define VERIFY_IS_APPROX_EVALUATOR2(DEST,EXPR,REF) VERIFY_IS_APPROX(copy_using_evaluator(DEST,(EXPR)), (REF).eval());\n\nvoid test_evaluators()\n{\n  // Testing Matrix evaluator and Transpose\n  Vector2d v = Vector2d::Random();\n  const Vector2d v_const(v);\n  Vector2d v2;\n  RowVector2d w;\n\n  VERIFY_IS_APPROX_EVALUATOR(v2, v);\n  VERIFY_IS_APPROX_EVALUATOR(v2, v_const);\n\n  // Testing Transpose\n  VERIFY_IS_APPROX_EVALUATOR(w, v.transpose()); // Transpose as rvalue\n  VERIFY_IS_APPROX_EVALUATOR(w, v_const.transpose());\n\n  copy_using_evaluator(w.transpose(), v); // Transpose as lvalue\n  VERIFY_IS_APPROX(w,v.transpose().eval());\n\n  copy_using_evaluator(w.transpose(), v_const);\n  VERIFY_IS_APPROX(w,v_const.transpose().eval());\n\n  // Testing Array evaluator\n  {\n    ArrayXXf a(2,3);\n    ArrayXXf b(3,2);\n    a << 1,2,3, 4,5,6;\n    const ArrayXXf a_const(a);\n\n    VERIFY_IS_APPROX_EVALUATOR(b, a.transpose());\n\n    VERIFY_IS_APPROX_EVALUATOR(b, a_const.transpose());\n\n    // Testing CwiseNullaryOp evaluator\n    copy_using_evaluator(w, RowVector2d::Random());\n    VERIFY((w.array() >= -1).all() && (w.array() <= 1).all()); // not easy to test ...\n\n    VERIFY_IS_APPROX_EVALUATOR(w, RowVector2d::Zero());\n\n    VERIFY_IS_APPROX_EVALUATOR(w, RowVector2d::Constant(3));\n    \n    // mix CwiseNullaryOp and transpose\n    VERIFY_IS_APPROX_EVALUATOR(w, Vector2d::Zero().transpose());\n  }\n\n  {\n    // test product expressions\n    int s = internal::random<int>(1,100);\n    MatrixXf a(s,s), b(s,s), c(s,s), d(s,s);\n    a.setRandom();\n    b.setRandom();\n    c.setRandom();\n    d.setRandom();\n    VERIFY_IS_APPROX_EVALUATOR(d, (a + b));\n    VERIFY_IS_APPROX_EVALUATOR(d, (a + b).transpose());\n    VERIFY_IS_APPROX_EVALUATOR2(d, prod(a,b), a*b);\n    VERIFY_IS_APPROX_EVALUATOR2(d.noalias(), prod(a,b), a*b);\n    VERIFY_IS_APPROX_EVALUATOR2(d, prod(a,b) + c, a*b + c);\n    VERIFY_IS_APPROX_EVALUATOR2(d, s * prod(a,b), s * a*b);\n    VERIFY_IS_APPROX_EVALUATOR2(d, prod(a,b).transpose(), (a*b).transpose());\n    VERIFY_IS_APPROX_EVALUATOR2(d, prod(a,b) + prod(b,c), a*b + b*c);\n\n    // check that prod works even with aliasing present\n    c = a*a;\n    copy_using_evaluator(a, prod(a,a));\n    VERIFY_IS_APPROX(a,c);\n\n    // check compound assignment of products\n    d = c;\n    add_assign_using_evaluator(c.noalias(), prod(a,b));\n    d.noalias() += a*b;\n    VERIFY_IS_APPROX(c, d);\n\n    d = c;\n    subtract_assign_using_evaluator(c.noalias(), prod(a,b));\n    d.noalias() -= a*b;\n    VERIFY_IS_APPROX(c, d);\n  }\n\n  {\n    // test product with all possible sizes\n    int s = internal::random<int>(1,100);\n    Matrix<float,      1,      1> m11, res11;  m11.setRandom(1,1);\n    Matrix<float,      1,      4> m14, res14;  m14.setRandom(1,4);\n    Matrix<float,      1,Dynamic> m1X, res1X;  m1X.setRandom(1,s);\n    Matrix<float,      4,      1> m41, res41;  m41.setRandom(4,1);\n    Matrix<float,      4,      4> m44, res44;  m44.setRandom(4,4);\n    Matrix<float,      4,Dynamic> m4X, res4X;  m4X.setRandom(4,s);\n    Matrix<float,Dynamic,      1> mX1, resX1;  mX1.setRandom(s,1);\n    Matrix<float,Dynamic,      4> mX4, resX4;  mX4.setRandom(s,4);\n    Matrix<float,Dynamic,Dynamic> mXX, resXX;  mXX.setRandom(s,s);\n\n    VERIFY_IS_APPROX_EVALUATOR2(res11, prod(m11,m11), m11*m11);\n    VERIFY_IS_APPROX_EVALUATOR2(res11, prod(m14,m41), m14*m41);\n    VERIFY_IS_APPROX_EVALUATOR2(res11, prod(m1X,mX1), m1X*mX1);\n    VERIFY_IS_APPROX_EVALUATOR2(res14, prod(m11,m14), m11*m14);\n    VERIFY_IS_APPROX_EVALUATOR2(res14, prod(m14,m44), m14*m44);\n    VERIFY_IS_APPROX_EVALUATOR2(res14, prod(m1X,mX4), m1X*mX4);\n    VERIFY_IS_APPROX_EVALUATOR2(res1X, prod(m11,m1X), m11*m1X);\n    VERIFY_IS_APPROX_EVALUATOR2(res1X, prod(m14,m4X), m14*m4X);\n    VERIFY_IS_APPROX_EVALUATOR2(res1X, prod(m1X,mXX), m1X*mXX);\n    VERIFY_IS_APPROX_EVALUATOR2(res41, prod(m41,m11), m41*m11);\n    VERIFY_IS_APPROX_EVALUATOR2(res41, prod(m44,m41), m44*m41);\n    VERIFY_IS_APPROX_EVALUATOR2(res41, prod(m4X,mX1), m4X*mX1);\n    VERIFY_IS_APPROX_EVALUATOR2(res44, prod(m41,m14), m41*m14);\n    VERIFY_IS_APPROX_EVALUATOR2(res44, prod(m44,m44), m44*m44);\n    VERIFY_IS_APPROX_EVALUATOR2(res44, prod(m4X,mX4), m4X*mX4);\n    VERIFY_IS_APPROX_EVALUATOR2(res4X, prod(m41,m1X), m41*m1X);\n    VERIFY_IS_APPROX_EVALUATOR2(res4X, prod(m44,m4X), m44*m4X);\n    VERIFY_IS_APPROX_EVALUATOR2(res4X, prod(m4X,mXX), m4X*mXX);\n    VERIFY_IS_APPROX_EVALUATOR2(resX1, prod(mX1,m11), mX1*m11);\n    VERIFY_IS_APPROX_EVALUATOR2(resX1, prod(mX4,m41), mX4*m41);\n    VERIFY_IS_APPROX_EVALUATOR2(resX1, prod(mXX,mX1), mXX*mX1);\n    VERIFY_IS_APPROX_EVALUATOR2(resX4, prod(mX1,m14), mX1*m14);\n    VERIFY_IS_APPROX_EVALUATOR2(resX4, prod(mX4,m44), mX4*m44);\n    VERIFY_IS_APPROX_EVALUATOR2(resX4, prod(mXX,mX4), mXX*mX4);\n    VERIFY_IS_APPROX_EVALUATOR2(resXX, prod(mX1,m1X), mX1*m1X);\n    VERIFY_IS_APPROX_EVALUATOR2(resXX, prod(mX4,m4X), mX4*m4X);\n    VERIFY_IS_APPROX_EVALUATOR2(resXX, prod(mXX,mXX), mXX*mXX);\n  }\n\n  {\n    ArrayXXf a(2,3);\n    ArrayXXf b(3,2);\n    a << 1,2,3, 4,5,6;\n    const ArrayXXf a_const(a);\n    \n    // this does not work because Random is eval-before-nested: \n    // copy_using_evaluator(w, Vector2d::Random().transpose());\n\n    // test CwiseUnaryOp\n    VERIFY_IS_APPROX_EVALUATOR(v2, 3 * v);\n    VERIFY_IS_APPROX_EVALUATOR(w, (3 * v).transpose());\n    VERIFY_IS_APPROX_EVALUATOR(b, (a + 3).transpose());\n    VERIFY_IS_APPROX_EVALUATOR(b, (2 * a_const + 3).transpose());\n\n    // test CwiseBinaryOp\n    VERIFY_IS_APPROX_EVALUATOR(v2, v + Vector2d::Ones());\n    VERIFY_IS_APPROX_EVALUATOR(w, (v + Vector2d::Ones()).transpose().cwiseProduct(RowVector2d::Constant(3)));\n\n    // dynamic matrices and arrays\n    MatrixXd mat1(6,6), mat2(6,6);\n    VERIFY_IS_APPROX_EVALUATOR(mat1, MatrixXd::Identity(6,6));\n    VERIFY_IS_APPROX_EVALUATOR(mat2, mat1);\n    copy_using_evaluator(mat2.transpose(), mat1);\n    VERIFY_IS_APPROX(mat2.transpose(), mat1);\n\n    ArrayXXd arr1(6,6), arr2(6,6);\n    VERIFY_IS_APPROX_EVALUATOR(arr1, ArrayXXd::Constant(6,6, 3.0));\n    VERIFY_IS_APPROX_EVALUATOR(arr2, arr1);\n    \n    // test automatic resizing\n    mat2.resize(3,3);\n    VERIFY_IS_APPROX_EVALUATOR(mat2, mat1);\n    arr2.resize(9,9);\n    VERIFY_IS_APPROX_EVALUATOR(arr2, arr1);\n\n    // test direct traversal\n    Matrix3f m3;\n    Array33f a3;\n    VERIFY_IS_APPROX_EVALUATOR(m3, Matrix3f::Identity());  // matrix, nullary\n    // TODO: find a way to test direct traversal with array\n    VERIFY_IS_APPROX_EVALUATOR(m3.transpose(), Matrix3f::Identity().transpose());  // transpose\n    VERIFY_IS_APPROX_EVALUATOR(m3, 2 * Matrix3f::Identity());  // unary\n    VERIFY_IS_APPROX_EVALUATOR(m3, Matrix3f::Identity() + Matrix3f::Zero());  // binary\n    VERIFY_IS_APPROX_EVALUATOR(m3.block(0,0,2,2), Matrix3f::Identity().block(1,1,2,2));  // block\n\n    // test linear traversal\n    VERIFY_IS_APPROX_EVALUATOR(m3, Matrix3f::Zero());  // matrix, nullary\n    VERIFY_IS_APPROX_EVALUATOR(a3, Array33f::Zero());  // array\n    VERIFY_IS_APPROX_EVALUATOR(m3.transpose(), Matrix3f::Zero().transpose());  // transpose\n    VERIFY_IS_APPROX_EVALUATOR(m3, 2 * Matrix3f::Zero());  // unary\n    VERIFY_IS_APPROX_EVALUATOR(m3, Matrix3f::Zero() + m3);  // binary  \n\n    // test inner vectorization\n    Matrix4f m4, m4src = Matrix4f::Random();\n    Array44f a4, a4src = Matrix4f::Random();\n    VERIFY_IS_APPROX_EVALUATOR(m4, m4src);  // matrix\n    VERIFY_IS_APPROX_EVALUATOR(a4, a4src);  // array\n    VERIFY_IS_APPROX_EVALUATOR(m4.transpose(), m4src.transpose());  // transpose\n    // TODO: find out why Matrix4f::Zero() does not allow inner vectorization\n    VERIFY_IS_APPROX_EVALUATOR(m4, 2 * m4src);  // unary\n    VERIFY_IS_APPROX_EVALUATOR(m4, m4src + m4src);  // binary\n\n    // test linear vectorization\n    MatrixXf mX(6,6), mXsrc = MatrixXf::Random(6,6);\n    ArrayXXf aX(6,6), aXsrc = ArrayXXf::Random(6,6);\n    VERIFY_IS_APPROX_EVALUATOR(mX, mXsrc);  // matrix\n    VERIFY_IS_APPROX_EVALUATOR(aX, aXsrc);  // array\n    VERIFY_IS_APPROX_EVALUATOR(mX.transpose(), mXsrc.transpose());  // transpose\n    VERIFY_IS_APPROX_EVALUATOR(mX, MatrixXf::Zero(6,6));  // nullary\n    VERIFY_IS_APPROX_EVALUATOR(mX, 2 * mXsrc);  // unary\n    VERIFY_IS_APPROX_EVALUATOR(mX, mXsrc + mXsrc);  // binary\n\n    // test blocks and slice vectorization\n    VERIFY_IS_APPROX_EVALUATOR(m4, (mXsrc.block<4,4>(1,0)));\n    VERIFY_IS_APPROX_EVALUATOR(aX, ArrayXXf::Constant(10, 10, 3.0).block(2, 3, 6, 6));\n\n    Matrix4f m4ref = m4;\n    copy_using_evaluator(m4.block(1, 1, 2, 3), m3.bottomRows(2));\n    m4ref.block(1, 1, 2, 3) = m3.bottomRows(2);\n    VERIFY_IS_APPROX(m4, m4ref);\n\n    mX.setIdentity(20,20);\n    MatrixXf mXref = MatrixXf::Identity(20,20);\n    mXsrc = MatrixXf::Random(9,12);\n    copy_using_evaluator(mX.block(4, 4, 9, 12), mXsrc);\n    mXref.block(4, 4, 9, 12) = mXsrc;\n    VERIFY_IS_APPROX(mX, mXref);\n\n    // test Map\n    const float raw[3] = {1,2,3};\n    float buffer[3] = {0,0,0};\n    Vector3f v3;\n    Array3f a3f;\n    VERIFY_IS_APPROX_EVALUATOR(v3, Map<const Vector3f>(raw));\n    VERIFY_IS_APPROX_EVALUATOR(a3f, Map<const Array3f>(raw));\n    Vector3f::Map(buffer) = 2*v3;\n    VERIFY(buffer[0] == 2);\n    VERIFY(buffer[1] == 4);\n    VERIFY(buffer[2] == 6);\n\n    // test CwiseUnaryView\n    mat1.setRandom();\n    mat2.setIdentity();\n    MatrixXcd matXcd(6,6), matXcd_ref(6,6);\n    copy_using_evaluator(matXcd.real(), mat1);\n    copy_using_evaluator(matXcd.imag(), mat2);\n    matXcd_ref.real() = mat1;\n    matXcd_ref.imag() = mat2;\n    VERIFY_IS_APPROX(matXcd, matXcd_ref);\n\n    // test Select\n    VERIFY_IS_APPROX_EVALUATOR(aX, (aXsrc > 0).select(aXsrc, -aXsrc));\n\n    // test Replicate\n    mXsrc = MatrixXf::Random(6, 6);\n    VectorXf vX = VectorXf::Random(6);\n    mX.resize(6, 6);\n    VERIFY_IS_APPROX_EVALUATOR(mX, mXsrc.colwise() + vX);\n    matXcd.resize(12, 12);\n    VERIFY_IS_APPROX_EVALUATOR(matXcd, matXcd_ref.replicate(2,2));\n    VERIFY_IS_APPROX_EVALUATOR(matXcd, (matXcd_ref.replicate<2,2>()));\n\n    // test partial reductions\n    VectorXd vec1(6);\n    VERIFY_IS_APPROX_EVALUATOR(vec1, mat1.rowwise().sum());\n    VERIFY_IS_APPROX_EVALUATOR(vec1, mat1.colwise().sum().transpose());\n\n    // test MatrixWrapper and ArrayWrapper\n    mat1.setRandom(6,6);\n    arr1.setRandom(6,6);\n    VERIFY_IS_APPROX_EVALUATOR(mat2, arr1.matrix());\n    VERIFY_IS_APPROX_EVALUATOR(arr2, mat1.array());\n    VERIFY_IS_APPROX_EVALUATOR(mat2, (arr1 + 2).matrix());\n    VERIFY_IS_APPROX_EVALUATOR(arr2, mat1.array() + 2);\n    mat2.array() = arr1 * arr1;\n    VERIFY_IS_APPROX(mat2, (arr1 * arr1).matrix());\n    arr2.matrix() = MatrixXd::Identity(6,6);\n    VERIFY_IS_APPROX(arr2, MatrixXd::Identity(6,6).array());\n\n    // test Reverse\n    VERIFY_IS_APPROX_EVALUATOR(arr2, arr1.reverse());\n    VERIFY_IS_APPROX_EVALUATOR(arr2, arr1.colwise().reverse());\n    VERIFY_IS_APPROX_EVALUATOR(arr2, arr1.rowwise().reverse());\n    arr2.reverse() = arr1;\n    VERIFY_IS_APPROX(arr2, arr1.reverse());\n    mat2.array() = mat1.array().reverse();\n    VERIFY_IS_APPROX(mat2.array(), mat1.array().reverse());\n\n    // test Diagonal\n    VERIFY_IS_APPROX_EVALUATOR(vec1, mat1.diagonal());\n    vec1.resize(5);\n    VERIFY_IS_APPROX_EVALUATOR(vec1, mat1.diagonal(1));\n    VERIFY_IS_APPROX_EVALUATOR(vec1, mat1.diagonal<-1>());\n    vec1.setRandom();\n\n    mat2 = mat1;\n    copy_using_evaluator(mat1.diagonal(1), vec1);\n    mat2.diagonal(1) = vec1;\n    VERIFY_IS_APPROX(mat1, mat2);\n\n    copy_using_evaluator(mat1.diagonal<-1>(), mat1.diagonal(1));\n    mat2.diagonal<-1>() = mat2.diagonal(1);\n    VERIFY_IS_APPROX(mat1, mat2);\n  }\n  \n  {\n    // test swapping\n    MatrixXd mat1, mat2, mat1ref, mat2ref;\n    mat1ref = mat1 = MatrixXd::Random(6, 6);\n    mat2ref = mat2 = 2 * mat1 + MatrixXd::Identity(6, 6);\n    swap_using_evaluator(mat1, mat2);\n    mat1ref.swap(mat2ref);\n    VERIFY_IS_APPROX(mat1, mat1ref);\n    VERIFY_IS_APPROX(mat2, mat2ref);\n\n    swap_using_evaluator(mat1.block(0, 0, 3, 3), mat2.block(3, 3, 3, 3));\n    mat1ref.block(0, 0, 3, 3).swap(mat2ref.block(3, 3, 3, 3));\n    VERIFY_IS_APPROX(mat1, mat1ref);\n    VERIFY_IS_APPROX(mat2, mat2ref);\n\n    swap_using_evaluator(mat1.row(2), mat2.col(3).transpose());\n    mat1.row(2).swap(mat2.col(3).transpose());\n    VERIFY_IS_APPROX(mat1, mat1ref);\n    VERIFY_IS_APPROX(mat2, mat2ref);\n  }\n\n  {\n    // test compound assignment\n    const Matrix4d mat_const = Matrix4d::Random(); \n    Matrix4d mat, mat_ref;\n    mat = mat_ref = Matrix4d::Identity();\n    add_assign_using_evaluator(mat, mat_const);\n    mat_ref += mat_const;\n    VERIFY_IS_APPROX(mat, mat_ref);\n\n    subtract_assign_using_evaluator(mat.row(1), 2*mat.row(2));\n    mat_ref.row(1) -= 2*mat_ref.row(2);\n    VERIFY_IS_APPROX(mat, mat_ref);\n\n    const ArrayXXf arr_const = ArrayXXf::Random(5,3); \n    ArrayXXf arr, arr_ref;\n    arr = arr_ref = ArrayXXf::Constant(5, 3, 0.5);\n    multiply_assign_using_evaluator(arr, arr_const);\n    arr_ref *= arr_const;\n    VERIFY_IS_APPROX(arr, arr_ref);\n\n    divide_assign_using_evaluator(arr.row(1), arr.row(2) + 1);\n    arr_ref.row(1) /= (arr_ref.row(2) + 1);\n    VERIFY_IS_APPROX(arr, arr_ref);\n  }\n  \n  {\n    // test triangular shapes\n    MatrixXd A = MatrixXd::Random(6,6), B(6,6), C(6,6), D(6,6);\n    A.setRandom();B.setRandom();\n    VERIFY_IS_APPROX_EVALUATOR2(B, A.triangularView<Upper>(), MatrixXd(A.triangularView<Upper>()));\n    \n    A.setRandom();B.setRandom();\n    VERIFY_IS_APPROX_EVALUATOR2(B, A.triangularView<UnitLower>(), MatrixXd(A.triangularView<UnitLower>()));\n    \n    A.setRandom();B.setRandom();\n    VERIFY_IS_APPROX_EVALUATOR2(B, A.triangularView<UnitUpper>(), MatrixXd(A.triangularView<UnitUpper>()));\n    \n    A.setRandom();B.setRandom();\n    C = B; C.triangularView<Upper>() = A;\n    copy_using_evaluator(B.triangularView<Upper>(), A);\n    VERIFY(B.isApprox(C) && \"copy_using_evaluator(B.triangularView<Upper>(), A)\");\n    \n    A.setRandom();B.setRandom();\n    C = B; C.triangularView<Lower>() = A.triangularView<Lower>();\n    copy_using_evaluator(B.triangularView<Lower>(), A.triangularView<Lower>());\n    VERIFY(B.isApprox(C) && \"copy_using_evaluator(B.triangularView<Lower>(), A.triangularView<Lower>())\");\n    \n    \n    A.setRandom();B.setRandom();\n    C = B; C.triangularView<Lower>() = A.triangularView<Upper>().transpose();\n    copy_using_evaluator(B.triangularView<Lower>(), A.triangularView<Upper>().transpose());\n    VERIFY(B.isApprox(C) && \"copy_using_evaluator(B.triangularView<Lower>(), A.triangularView<Lower>().transpose())\");\n    \n    \n    A.setRandom();B.setRandom(); C = B; D = A;\n    C.triangularView<Upper>().swap(D.triangularView<Upper>());\n    swap_using_evaluator(B.triangularView<Upper>(), A.triangularView<Upper>());\n    VERIFY(B.isApprox(C) && \"swap_using_evaluator(B.triangularView<Upper>(), A.triangularView<Upper>())\");\n    \n    \n    VERIFY_IS_APPROX_EVALUATOR2(B, prod(A.triangularView<Upper>(),A), MatrixXd(A.triangularView<Upper>()*A));\n    \n    VERIFY_IS_APPROX_EVALUATOR2(B, prod(A.selfadjointView<Upper>(),A), MatrixXd(A.selfadjointView<Upper>()*A));\n  }\n\n  {\n    // test diagonal shapes\n    VectorXd d = VectorXd::Random(6);\n    MatrixXd A = MatrixXd::Random(6,6), B(6,6);\n    A.setRandom();B.setRandom();\n    \n    VERIFY_IS_APPROX_EVALUATOR2(B, lazyprod(d.asDiagonal(),A), MatrixXd(d.asDiagonal()*A));\n    VERIFY_IS_APPROX_EVALUATOR2(B, lazyprod(A,d.asDiagonal()), MatrixXd(A*d.asDiagonal()));\n  }\n\n  {\n    // test CoeffReadCost\n    Matrix4d a, b;\n    VERIFY_IS_EQUAL( get_cost(a), 1 );\n    VERIFY_IS_EQUAL( get_cost(a+b), 3);\n    VERIFY_IS_EQUAL( get_cost(2*a+b), 4);\n    VERIFY_IS_EQUAL( get_cost(a*b), 1);\n    VERIFY_IS_EQUAL( get_cost(a.lazyProduct(b)), 15);\n    VERIFY_IS_EQUAL( get_cost(a*(a*b)), 1);\n    VERIFY_IS_EQUAL( get_cost(a.lazyProduct(a*b)), 15);\n    VERIFY_IS_EQUAL( get_cost(a*(a+b)), 1);\n    VERIFY_IS_EQUAL( get_cost(a.lazyProduct(a+b)), 15);\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/exceptions.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2011 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n\n// Various sanity tests with exceptions:\n//  - no memory leak when a custom scalar type trow an exceptions\n//  - todo: complete the list of tests!\n\n#define EIGEN_STACK_ALLOCATION_LIMIT 100000000\n\n#include \"main.h\"\n\nstruct my_exception\n{\n  my_exception() {}\n  ~my_exception() {}\n};\n    \nclass ScalarWithExceptions\n{\n  public:\n    ScalarWithExceptions() { init(); }\n    ScalarWithExceptions(const float& _v) { init(); *v = _v; }\n    ScalarWithExceptions(const ScalarWithExceptions& other) { init(); *v = *(other.v); }\n    ~ScalarWithExceptions() {\n      delete v;\n      instances--;\n    }\n\n    void init() {\n      v = new float;\n      instances++;\n    }\n\n    ScalarWithExceptions operator+(const ScalarWithExceptions& other) const\n    {\n      countdown--;\n      if(countdown<=0)\n        throw my_exception();\n      return ScalarWithExceptions(*v+*other.v);\n    }\n    \n    ScalarWithExceptions operator-(const ScalarWithExceptions& other) const\n    { return ScalarWithExceptions(*v-*other.v); }\n    \n    ScalarWithExceptions operator*(const ScalarWithExceptions& other) const\n    { return ScalarWithExceptions((*v)*(*other.v)); }\n    \n    ScalarWithExceptions& operator+=(const ScalarWithExceptions& other)\n    { *v+=*other.v; return *this; }\n    ScalarWithExceptions& operator-=(const ScalarWithExceptions& other)\n    { *v-=*other.v; return *this; }\n    ScalarWithExceptions& operator=(const ScalarWithExceptions& other)\n    { *v = *(other.v); return *this; }\n  \n    bool operator==(const ScalarWithExceptions& other) const\n    { return *v==*other.v; }\n    bool operator!=(const ScalarWithExceptions& other) const\n    { return *v!=*other.v; }\n    \n    float* v;\n    static int instances;\n    static int countdown;\n};\n\nScalarWithExceptions real(const ScalarWithExceptions &x) { return x; }\nScalarWithExceptions imag(const ScalarWithExceptions & ) { return 0; }\nScalarWithExceptions conj(const ScalarWithExceptions &x) { return x; }\n\nint ScalarWithExceptions::instances = 0;\nint ScalarWithExceptions::countdown = 0;\n\n\n#define CHECK_MEMLEAK(OP) {                                 \\\n    ScalarWithExceptions::countdown = 100;                  \\\n    int before = ScalarWithExceptions::instances;           \\\n    bool exception_thrown = false;                         \\\n    try { OP; }                              \\\n    catch (my_exception) {                                  \\\n      exception_thrown = true;                              \\\n      VERIFY(ScalarWithExceptions::instances==before && \"memory leak detected in \" && EIGEN_MAKESTRING(OP)); \\\n    } \\\n    VERIFY(exception_thrown && \" no exception thrown in \" && EIGEN_MAKESTRING(OP)); \\\n  }\n\nvoid memoryleak()\n{\n  typedef Eigen::Matrix<ScalarWithExceptions,Dynamic,1> VectorType;\n  typedef Eigen::Matrix<ScalarWithExceptions,Dynamic,Dynamic> MatrixType;\n  \n  {\n    int n = 50;\n    VectorType v0(n), v1(n);\n    MatrixType m0(n,n), m1(n,n), m2(n,n);\n    v0.setOnes(); v1.setOnes();\n    m0.setOnes(); m1.setOnes(); m2.setOnes();\n    CHECK_MEMLEAK(v0 = m0 * m1 * v1);\n    CHECK_MEMLEAK(m2 = m0 * m1 * m2);\n    CHECK_MEMLEAK((v0+v1).dot(v0+v1));\n  }\n  VERIFY(ScalarWithExceptions::instances==0 && \"global memory leak detected in \" && EIGEN_MAKESTRING(OP)); \\\n}\n\nvoid test_exceptions()\n{\n  CALL_SUBTEST( memoryleak() );\n}\n"
  },
  {
    "path": "include/eigen3/test/fastmath.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\nvoid check(bool b, bool ref)\n{\n  std::cout << b;\n  if(b==ref)\n    std::cout << \" OK  \";\n  else\n    std::cout << \" BAD \";\n}\n\n#if EIGEN_COMP_MSVC && EIGEN_COMP_MSVC < 1800\nnamespace std {\n  template<typename T> bool (isfinite)(T x) { return _finite(x); }\n  template<typename T> bool (isnan)(T x) { return _isnan(x); }\n  template<typename T> bool (isinf)(T x) { return _fpclass(x)==_FPCLASS_NINF || _fpclass(x)==_FPCLASS_PINF; }\n}\n#endif\n\ntemplate<typename T>\nvoid check_inf_nan(bool dryrun) {\n  Matrix<T,Dynamic,1> m(10);\n  m.setRandom();\n  m(3) = std::numeric_limits<T>::quiet_NaN();\n\n  if(dryrun)\n  {\n    std::cout << \"std::isfinite(\" << m(3) << \") = \"; check((std::isfinite)(m(3)),false); std::cout << \"  ; numext::isfinite = \"; check((numext::isfinite)(m(3)), false); std::cout << \"\\n\";\n    std::cout << \"std::isinf(\" << m(3) << \")    = \"; check((std::isinf)(m(3)),false);    std::cout << \"  ; numext::isinf    = \"; check((numext::isinf)(m(3)), false); std::cout << \"\\n\";\n    std::cout << \"std::isnan(\" << m(3) << \")    = \"; check((std::isnan)(m(3)),true);     std::cout << \"  ; numext::isnan    = \"; check((numext::isnan)(m(3)), true); std::cout << \"\\n\";\n    std::cout << \"allFinite: \"; check(m.allFinite(), 0); std::cout << \"\\n\";\n    std::cout << \"hasNaN:    \"; check(m.hasNaN(), 1);    std::cout << \"\\n\";\n    std::cout << \"\\n\";\n  }\n  else\n  {\n    VERIFY( !(numext::isfinite)(m(3)) );\n    VERIFY( !(numext::isinf)(m(3)) );\n    VERIFY(  (numext::isnan)(m(3)) );\n    VERIFY( !m.allFinite() );\n    VERIFY(  m.hasNaN() );\n  }\n  T hidden_zero = (std::numeric_limits<T>::min)()*(std::numeric_limits<T>::min)();\n  m(4) /= hidden_zero;\n  if(dryrun)\n  {\n    std::cout << \"std::isfinite(\" << m(4) << \") = \"; check((std::isfinite)(m(4)),false); std::cout << \"  ; numext::isfinite = \"; check((numext::isfinite)(m(4)), false); std::cout << \"\\n\";\n    std::cout << \"std::isinf(\" << m(4) << \")    = \"; check((std::isinf)(m(4)),true);     std::cout << \"  ; numext::isinf    = \"; check((numext::isinf)(m(4)), true); std::cout << \"\\n\";\n    std::cout << \"std::isnan(\" << m(4) << \")    = \"; check((std::isnan)(m(4)),false);    std::cout << \"  ; numext::isnan    = \"; check((numext::isnan)(m(4)), false); std::cout << \"\\n\";\n    std::cout << \"allFinite: \"; check(m.allFinite(), 0); std::cout << \"\\n\";\n    std::cout << \"hasNaN:    \"; check(m.hasNaN(), 1);    std::cout << \"\\n\";\n    std::cout << \"\\n\";\n  }\n  else\n  {\n    VERIFY( !(numext::isfinite)(m(4)) );\n    VERIFY(  (numext::isinf)(m(4)) );\n    VERIFY( !(numext::isnan)(m(4)) );\n    VERIFY( !m.allFinite() );\n    VERIFY(  m.hasNaN() );\n  }\n  m(3) = 0;\n  if(dryrun)\n  {\n    std::cout << \"std::isfinite(\" << m(3) << \") = \"; check((std::isfinite)(m(3)),true); std::cout << \"  ; numext::isfinite = \"; check((numext::isfinite)(m(3)), true); std::cout << \"\\n\";\n    std::cout << \"std::isinf(\" << m(3) << \")    = \"; check((std::isinf)(m(3)),false);    std::cout << \"  ; numext::isinf    = \"; check((numext::isinf)(m(3)), false); std::cout << \"\\n\";\n    std::cout << \"std::isnan(\" << m(3) << \")    = \"; check((std::isnan)(m(3)),false);     std::cout << \"  ; numext::isnan    = \"; check((numext::isnan)(m(3)), false); std::cout << \"\\n\";\n    std::cout << \"allFinite: \"; check(m.allFinite(), 0); std::cout << \"\\n\";\n    std::cout << \"hasNaN:    \"; check(m.hasNaN(), 0);    std::cout << \"\\n\";\n    std::cout << \"\\n\\n\";\n  }\n  else\n  {\n    VERIFY(  (numext::isfinite)(m(3)) );\n    VERIFY( !(numext::isinf)(m(3)) );\n    VERIFY( !(numext::isnan)(m(3)) );\n    VERIFY( !m.allFinite() );\n    VERIFY( !m.hasNaN() );\n  }\n}\n\nvoid test_fastmath() {\n  std::cout << \"*** float *** \\n\\n\"; check_inf_nan<float>(true);\n  std::cout << \"*** double ***\\n\\n\"; check_inf_nan<double>(true);\n  std::cout << \"*** long double *** \\n\\n\"; check_inf_nan<long double>(true);\n\n  check_inf_nan<float>(false);\n  check_inf_nan<double>(false);\n  check_inf_nan<long double>(false);\n}\n"
  },
  {
    "path": "include/eigen3/test/first_aligned.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\ntemplate<typename Scalar>\nvoid test_first_aligned_helper(Scalar *array, int size)\n{\n  const int packet_size = sizeof(Scalar) * internal::packet_traits<Scalar>::size;\n  VERIFY(((size_t(array) + sizeof(Scalar) * internal::first_default_aligned(array, size)) % packet_size) == 0);\n}\n\ntemplate<typename Scalar>\nvoid test_none_aligned_helper(Scalar *array, int size)\n{\n  EIGEN_UNUSED_VARIABLE(array);\n  EIGEN_UNUSED_VARIABLE(size);\n  VERIFY(internal::packet_traits<Scalar>::size == 1 || internal::first_default_aligned(array, size) == size);\n}\n\nstruct some_non_vectorizable_type { float x; };\n\nvoid test_first_aligned()\n{\n  EIGEN_ALIGN16 float array_float[100];\n  test_first_aligned_helper(array_float, 50);\n  test_first_aligned_helper(array_float+1, 50);\n  test_first_aligned_helper(array_float+2, 50);\n  test_first_aligned_helper(array_float+3, 50);\n  test_first_aligned_helper(array_float+4, 50);\n  test_first_aligned_helper(array_float+5, 50);\n  \n  EIGEN_ALIGN16 double array_double[100];\n  test_first_aligned_helper(array_double, 50);\n  test_first_aligned_helper(array_double+1, 50);\n  test_first_aligned_helper(array_double+2, 50);\n  \n  double *array_double_plus_4_bytes = (double*)(internal::UIntPtr(array_double)+4);\n  test_none_aligned_helper(array_double_plus_4_bytes, 50);\n  test_none_aligned_helper(array_double_plus_4_bytes+1, 50);\n  \n  some_non_vectorizable_type array_nonvec[100];\n  test_first_aligned_helper(array_nonvec, 100);\n  test_none_aligned_helper(array_nonvec, 100);\n}\n"
  },
  {
    "path": "include/eigen3/test/geo_alignedbox.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <Eigen/Geometry>\n#include <Eigen/LU>\n#include <Eigen/QR>\n\n#include<iostream>\nusing namespace std;\n\ntemplate<typename T> EIGEN_DONT_INLINE\nvoid kill_extra_precision(T& x) { eigen_assert((void*)(&x) != (void*)0); }\n\n\ntemplate<typename BoxType> void alignedbox(const BoxType& _box)\n{\n  /* this test covers the following files:\n     AlignedBox.h\n  */\n  typedef typename BoxType::Index Index;  \n  typedef typename BoxType::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  typedef Matrix<Scalar, BoxType::AmbientDimAtCompileTime, 1> VectorType;\n\n  const Index dim = _box.dim();\n\n  VectorType p0 = VectorType::Random(dim);\n  VectorType p1 = VectorType::Random(dim);\n  while( p1 == p0 ){\n      p1 =  VectorType::Random(dim); }\n  RealScalar s1 = internal::random<RealScalar>(0,1);\n\n  BoxType b0(dim);\n  BoxType b1(VectorType::Random(dim),VectorType::Random(dim));\n  BoxType b2;\n  \n  kill_extra_precision(b1);\n  kill_extra_precision(p0);\n  kill_extra_precision(p1);\n\n  b0.extend(p0);\n  b0.extend(p1);\n  VERIFY(b0.contains(p0*s1+(Scalar(1)-s1)*p1));\n  VERIFY(b0.contains(b0.center()));\n  VERIFY_IS_APPROX(b0.center(),(p0+p1)/Scalar(2));\n\n  (b2 = b0).extend(b1);\n  VERIFY(b2.contains(b0));\n  VERIFY(b2.contains(b1));\n  VERIFY_IS_APPROX(b2.clamp(b0), b0);\n\n  // intersection\n  BoxType box1(VectorType::Random(dim));\n  box1.extend(VectorType::Random(dim));\n  BoxType box2(VectorType::Random(dim));\n  box2.extend(VectorType::Random(dim));\n\n  VERIFY(box1.intersects(box2) == !box1.intersection(box2).isEmpty()); \n\n  // alignment -- make sure there is no memory alignment assertion\n  BoxType *bp0 = new BoxType(dim);\n  BoxType *bp1 = new BoxType(dim);\n  bp0->extend(*bp1);\n  delete bp0;\n  delete bp1;\n\n  // sampling\n  for( int i=0; i<10; ++i )\n  {\n      VectorType r = b0.sample();\n      VERIFY(b0.contains(r));\n  }\n\n}\n\n\n\ntemplate<typename BoxType>\nvoid alignedboxCastTests(const BoxType& _box)\n{\n  // casting  \n  typedef typename BoxType::Index Index;\n  typedef typename BoxType::Scalar Scalar;\n  typedef Matrix<Scalar, BoxType::AmbientDimAtCompileTime, 1> VectorType;\n\n  const Index dim = _box.dim();\n\n  VectorType p0 = VectorType::Random(dim);\n  VectorType p1 = VectorType::Random(dim);\n\n  BoxType b0(dim);\n\n  b0.extend(p0);\n  b0.extend(p1);\n\n  const int Dim = BoxType::AmbientDimAtCompileTime;\n  typedef typename GetDifferentType<Scalar>::type OtherScalar;\n  AlignedBox<OtherScalar,Dim> hp1f = b0.template cast<OtherScalar>();\n  VERIFY_IS_APPROX(hp1f.template cast<Scalar>(),b0);\n  AlignedBox<Scalar,Dim> hp1d = b0.template cast<Scalar>();\n  VERIFY_IS_APPROX(hp1d.template cast<Scalar>(),b0);\n}\n\n\nvoid specificTest1()\n{\n    Vector2f m; m << -1.0f, -2.0f;\n    Vector2f M; M <<  1.0f,  5.0f;\n\n    typedef AlignedBox2f  BoxType;\n    BoxType box( m, M );\n\n    Vector2f sides = M-m;\n    VERIFY_IS_APPROX(sides, box.sizes() );\n    VERIFY_IS_APPROX(sides[1], box.sizes()[1] );\n    VERIFY_IS_APPROX(sides[1], box.sizes().maxCoeff() );\n    VERIFY_IS_APPROX(sides[0], box.sizes().minCoeff() );\n\n    VERIFY_IS_APPROX( 14.0f, box.volume() );\n    VERIFY_IS_APPROX( 53.0f, box.diagonal().squaredNorm() );\n    VERIFY_IS_APPROX( std::sqrt( 53.0f ), box.diagonal().norm() );\n\n    VERIFY_IS_APPROX( m, box.corner( BoxType::BottomLeft ) );\n    VERIFY_IS_APPROX( M, box.corner( BoxType::TopRight ) );\n    Vector2f bottomRight; bottomRight << M[0], m[1];\n    Vector2f topLeft; topLeft << m[0], M[1];\n    VERIFY_IS_APPROX( bottomRight, box.corner( BoxType::BottomRight ) );\n    VERIFY_IS_APPROX( topLeft, box.corner( BoxType::TopLeft ) );\n}\n\n\nvoid specificTest2()\n{\n    Vector3i m; m << -1, -2, 0;\n    Vector3i M; M <<  1,  5, 3;\n\n    typedef AlignedBox3i  BoxType;\n    BoxType box( m, M );\n\n    Vector3i sides = M-m;\n    VERIFY_IS_APPROX(sides, box.sizes() );\n    VERIFY_IS_APPROX(sides[1], box.sizes()[1] );\n    VERIFY_IS_APPROX(sides[1], box.sizes().maxCoeff() );\n    VERIFY_IS_APPROX(sides[0], box.sizes().minCoeff() );\n\n    VERIFY_IS_APPROX( 42, box.volume() );\n    VERIFY_IS_APPROX( 62, box.diagonal().squaredNorm() );\n\n    VERIFY_IS_APPROX( m, box.corner( BoxType::BottomLeftFloor ) );\n    VERIFY_IS_APPROX( M, box.corner( BoxType::TopRightCeil ) );\n    Vector3i bottomRightFloor; bottomRightFloor << M[0], m[1], m[2];\n    Vector3i topLeftFloor; topLeftFloor << m[0], M[1], m[2];\n    VERIFY_IS_APPROX( bottomRightFloor, box.corner( BoxType::BottomRightFloor ) );\n    VERIFY_IS_APPROX( topLeftFloor, box.corner( BoxType::TopLeftFloor ) );\n}\n\n\nvoid test_geo_alignedbox()\n{\n  for(int i = 0; i < g_repeat; i++)\n  {\n    CALL_SUBTEST_1( alignedbox(AlignedBox2f()) );\n    CALL_SUBTEST_2( alignedboxCastTests(AlignedBox2f()) );\n\n    CALL_SUBTEST_3( alignedbox(AlignedBox3f()) );\n    CALL_SUBTEST_4( alignedboxCastTests(AlignedBox3f()) );\n\n    CALL_SUBTEST_5( alignedbox(AlignedBox4d()) );\n    CALL_SUBTEST_6( alignedboxCastTests(AlignedBox4d()) );\n\n    CALL_SUBTEST_7( alignedbox(AlignedBox1d()) );\n    CALL_SUBTEST_8( alignedboxCastTests(AlignedBox1d()) );\n\n    CALL_SUBTEST_9( alignedbox(AlignedBox1i()) );\n    CALL_SUBTEST_10( alignedbox(AlignedBox2i()) );\n    CALL_SUBTEST_11( alignedbox(AlignedBox3i()) );\n\n    CALL_SUBTEST_14( alignedbox(AlignedBox<double,Dynamic>(4)) );\n  }\n  CALL_SUBTEST_12( specificTest1() );\n  CALL_SUBTEST_13( specificTest2() );\n}\n"
  },
  {
    "path": "include/eigen3/test/geo_eulerangles.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2012 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <Eigen/Geometry>\n#include <Eigen/LU>\n#include <Eigen/SVD>\n\n\ntemplate<typename Scalar>\nvoid verify_euler(const Matrix<Scalar,3,1>& ea, int i, int j, int k)\n{\n  typedef Matrix<Scalar,3,3> Matrix3;\n  typedef Matrix<Scalar,3,1> Vector3;\n  typedef AngleAxis<Scalar> AngleAxisx;\n  using std::abs;\n  Matrix3 m(AngleAxisx(ea[0], Vector3::Unit(i)) * AngleAxisx(ea[1], Vector3::Unit(j)) * AngleAxisx(ea[2], Vector3::Unit(k)));\n  Vector3 eabis = m.eulerAngles(i, j, k);\n  Matrix3 mbis(AngleAxisx(eabis[0], Vector3::Unit(i)) * AngleAxisx(eabis[1], Vector3::Unit(j)) * AngleAxisx(eabis[2], Vector3::Unit(k))); \n  VERIFY_IS_APPROX(m,  mbis); \n  /* If I==K, and ea[1]==0, then there no unique solution. */ \n  /* The remark apply in the case where I!=K, and |ea[1]| is close to pi/2. */ \n  if( (i!=k || ea[1]!=0) && (i==k || !internal::isApprox(abs(ea[1]),Scalar(EIGEN_PI/2),test_precision<Scalar>())) ) \n    VERIFY((ea-eabis).norm() <= test_precision<Scalar>());\n  \n  // approx_or_less_than does not work for 0\n  VERIFY(0 < eabis[0] || test_isMuchSmallerThan(eabis[0], Scalar(1)));\n  VERIFY_IS_APPROX_OR_LESS_THAN(eabis[0], Scalar(EIGEN_PI));\n  VERIFY_IS_APPROX_OR_LESS_THAN(-Scalar(EIGEN_PI), eabis[1]);\n  VERIFY_IS_APPROX_OR_LESS_THAN(eabis[1], Scalar(EIGEN_PI));\n  VERIFY_IS_APPROX_OR_LESS_THAN(-Scalar(EIGEN_PI), eabis[2]);\n  VERIFY_IS_APPROX_OR_LESS_THAN(eabis[2], Scalar(EIGEN_PI));\n}\n\ntemplate<typename Scalar> void check_all_var(const Matrix<Scalar,3,1>& ea)\n{\n  verify_euler(ea, 0,1,2);\n  verify_euler(ea, 0,1,0);\n  verify_euler(ea, 0,2,1);\n  verify_euler(ea, 0,2,0);\n\n  verify_euler(ea, 1,2,0);\n  verify_euler(ea, 1,2,1);\n  verify_euler(ea, 1,0,2);\n  verify_euler(ea, 1,0,1);\n\n  verify_euler(ea, 2,0,1);\n  verify_euler(ea, 2,0,2);\n  verify_euler(ea, 2,1,0);\n  verify_euler(ea, 2,1,2);\n}\n\ntemplate<typename Scalar> void eulerangles()\n{\n  typedef Matrix<Scalar,3,3> Matrix3;\n  typedef Matrix<Scalar,3,1> Vector3;\n  typedef Array<Scalar,3,1> Array3;\n  typedef Quaternion<Scalar> Quaternionx;\n  typedef AngleAxis<Scalar> AngleAxisx;\n\n  Scalar a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI));\n  Quaternionx q1;\n  q1 = AngleAxisx(a, Vector3::Random().normalized());\n  Matrix3 m;\n  m = q1;\n  \n  Vector3 ea = m.eulerAngles(0,1,2);\n  check_all_var(ea);\n  ea = m.eulerAngles(0,1,0);\n  check_all_var(ea);\n  \n  // Check with purely random Quaternion:\n  q1.coeffs() = Quaternionx::Coefficients::Random().normalized();\n  m = q1;\n  ea = m.eulerAngles(0,1,2);\n  check_all_var(ea);\n  ea = m.eulerAngles(0,1,0);\n  check_all_var(ea);\n  \n  // Check with random angles in range [0:pi]x[-pi:pi]x[-pi:pi].\n  ea = (Array3::Random() + Array3(1,0,0))*Scalar(EIGEN_PI)*Array3(0.5,1,1);\n  check_all_var(ea);\n  \n  ea[2] = ea[0] = internal::random<Scalar>(0,Scalar(EIGEN_PI));\n  check_all_var(ea);\n  \n  ea[0] = ea[1] = internal::random<Scalar>(0,Scalar(EIGEN_PI));\n  check_all_var(ea);\n  \n  ea[1] = 0;\n  check_all_var(ea);\n  \n  ea.head(2).setZero();\n  check_all_var(ea);\n  \n  ea.setZero();\n  check_all_var(ea);\n}\n\nvoid test_geo_eulerangles()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( eulerangles<float>() );\n    CALL_SUBTEST_2( eulerangles<double>() );\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/geo_homogeneous.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <Eigen/Geometry>\n\ntemplate<typename Scalar,int Size> void homogeneous(void)\n{\n  /* this test covers the following files:\n     Homogeneous.h\n  */\n\n  typedef Matrix<Scalar,Size,Size> MatrixType;\n  typedef Matrix<Scalar,Size,1, ColMajor> VectorType;\n\n  typedef Matrix<Scalar,Size+1,Size> HMatrixType;\n  typedef Matrix<Scalar,Size+1,1> HVectorType;\n\n  typedef Matrix<Scalar,Size,Size+1>   T1MatrixType;\n  typedef Matrix<Scalar,Size+1,Size+1> T2MatrixType;\n  typedef Matrix<Scalar,Size+1,Size> T3MatrixType;\n\n  VectorType v0 = VectorType::Random(),\n             ones = VectorType::Ones();\n\n  HVectorType hv0 = HVectorType::Random();\n\n  MatrixType m0 = MatrixType::Random();\n\n  HMatrixType hm0 = HMatrixType::Random();\n\n  hv0 << v0, 1;\n  VERIFY_IS_APPROX(v0.homogeneous(), hv0);\n  VERIFY_IS_APPROX(v0, hv0.hnormalized());\n  \n  VERIFY_IS_APPROX(v0.homogeneous().sum(), hv0.sum());\n  VERIFY_IS_APPROX(v0.homogeneous().minCoeff(), hv0.minCoeff());\n  VERIFY_IS_APPROX(v0.homogeneous().maxCoeff(), hv0.maxCoeff());\n\n  hm0 << m0, ones.transpose();\n  VERIFY_IS_APPROX(m0.colwise().homogeneous(), hm0);\n  VERIFY_IS_APPROX(m0, hm0.colwise().hnormalized());\n  hm0.row(Size-1).setRandom();\n  for(int j=0; j<Size; ++j)\n    m0.col(j) = hm0.col(j).head(Size) / hm0(Size,j);\n  VERIFY_IS_APPROX(m0, hm0.colwise().hnormalized());\n\n  T1MatrixType t1 = T1MatrixType::Random();\n  VERIFY_IS_APPROX(t1 * (v0.homogeneous().eval()), t1 * v0.homogeneous());\n  VERIFY_IS_APPROX(t1 * (m0.colwise().homogeneous().eval()), t1 * m0.colwise().homogeneous());\n\n  T2MatrixType t2 = T2MatrixType::Random();\n  VERIFY_IS_APPROX(t2 * (v0.homogeneous().eval()), t2 * v0.homogeneous());\n  VERIFY_IS_APPROX(t2 * (m0.colwise().homogeneous().eval()), t2 * m0.colwise().homogeneous());\n  VERIFY_IS_APPROX(t2 * (v0.homogeneous().asDiagonal()), t2 * hv0.asDiagonal());\n  VERIFY_IS_APPROX((v0.homogeneous().asDiagonal()) * t2, hv0.asDiagonal() * t2);\n\n  VERIFY_IS_APPROX((v0.transpose().rowwise().homogeneous().eval()) * t2,\n                    v0.transpose().rowwise().homogeneous() * t2);\n  VERIFY_IS_APPROX((m0.transpose().rowwise().homogeneous().eval()) * t2,\n                    m0.transpose().rowwise().homogeneous() * t2);\n\n  T3MatrixType t3 = T3MatrixType::Random();\n  VERIFY_IS_APPROX((v0.transpose().rowwise().homogeneous().eval()) * t3,\n                    v0.transpose().rowwise().homogeneous() * t3);\n  VERIFY_IS_APPROX((m0.transpose().rowwise().homogeneous().eval()) * t3,\n                    m0.transpose().rowwise().homogeneous() * t3);\n\n  // test product with a Transform object\n  Transform<Scalar, Size, Affine> aff;\n  Transform<Scalar, Size, AffineCompact> caff;\n  Transform<Scalar, Size, Projective> proj;\n  Matrix<Scalar, Size, Dynamic>   pts;\n  Matrix<Scalar, Size+1, Dynamic> pts1, pts2;\n\n  aff.affine().setRandom();\n  proj = caff = aff;\n  pts.setRandom(Size,internal::random<int>(1,20));\n  \n  pts1 = pts.colwise().homogeneous();\n  VERIFY_IS_APPROX(aff  * pts.colwise().homogeneous(), (aff  * pts1).colwise().hnormalized());\n  VERIFY_IS_APPROX(caff * pts.colwise().homogeneous(), (caff * pts1).colwise().hnormalized());\n  VERIFY_IS_APPROX(proj * pts.colwise().homogeneous(), (proj * pts1));\n\n  VERIFY_IS_APPROX((aff  * pts1).colwise().hnormalized(),  aff  * pts);\n  VERIFY_IS_APPROX((caff * pts1).colwise().hnormalized(), caff * pts);\n  \n  pts2 = pts1;\n  pts2.row(Size).setRandom();\n  VERIFY_IS_APPROX((aff  * pts2).colwise().hnormalized(), aff  * pts2.colwise().hnormalized());\n  VERIFY_IS_APPROX((caff * pts2).colwise().hnormalized(), caff * pts2.colwise().hnormalized());\n  VERIFY_IS_APPROX((proj * pts2).colwise().hnormalized(), (proj * pts2.colwise().hnormalized().colwise().homogeneous()).colwise().hnormalized());\n  \n  // Test combination of homogeneous\n  \n  VERIFY_IS_APPROX( (t2 * v0.homogeneous()).hnormalized(),\n                       (t2.template topLeftCorner<Size,Size>() * v0 + t2.template topRightCorner<Size,1>())\n                     / ((t2.template bottomLeftCorner<1,Size>()*v0).value() + t2(Size,Size)) );\n  \n  VERIFY_IS_APPROX( (t2 * pts.colwise().homogeneous()).colwise().hnormalized(),\n                    (Matrix<Scalar, Size+1, Dynamic>(t2 * pts1).colwise().hnormalized()) );\n  \n  VERIFY_IS_APPROX( (t2 .lazyProduct( v0.homogeneous() )).hnormalized(), (t2 * v0.homogeneous()).hnormalized() );\n  VERIFY_IS_APPROX( (t2 .lazyProduct  ( pts.colwise().homogeneous() )).colwise().hnormalized(), (t2 * pts1).colwise().hnormalized() );\n  \n  VERIFY_IS_APPROX( (v0.transpose().homogeneous() .lazyProduct( t2 )).hnormalized(), (v0.transpose().homogeneous()*t2).hnormalized() );\n  VERIFY_IS_APPROX( (pts.transpose().rowwise().homogeneous() .lazyProduct( t2 )).rowwise().hnormalized(), (pts1.transpose()*t2).rowwise().hnormalized() );\n\n  VERIFY_IS_APPROX( (t2.template triangularView<Lower>() * v0.homogeneous()).eval(), (t2.template triangularView<Lower>()*hv0) );\n}\n\nvoid test_geo_homogeneous()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1(( homogeneous<float,1>() ));\n    CALL_SUBTEST_2(( homogeneous<double,3>() ));\n    CALL_SUBTEST_3(( homogeneous<double,8>() ));\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/geo_hyperplane.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <Eigen/Geometry>\n#include <Eigen/LU>\n#include <Eigen/QR>\n\ntemplate<typename HyperplaneType> void hyperplane(const HyperplaneType& _plane)\n{\n  /* this test covers the following files:\n     Hyperplane.h\n  */\n  using std::abs;\n  typedef typename HyperplaneType::Index Index;\n  const Index dim = _plane.dim();\n  enum { Options = HyperplaneType::Options };\n  typedef typename HyperplaneType::Scalar Scalar;\n  typedef typename HyperplaneType::RealScalar RealScalar;\n  typedef Matrix<Scalar, HyperplaneType::AmbientDimAtCompileTime, 1> VectorType;\n  typedef Matrix<Scalar, HyperplaneType::AmbientDimAtCompileTime,\n                         HyperplaneType::AmbientDimAtCompileTime> MatrixType;\n\n  VectorType p0 = VectorType::Random(dim);\n  VectorType p1 = VectorType::Random(dim);\n\n  VectorType n0 = VectorType::Random(dim).normalized();\n  VectorType n1 = VectorType::Random(dim).normalized();\n\n  HyperplaneType pl0(n0, p0);\n  HyperplaneType pl1(n1, p1);\n  HyperplaneType pl2 = pl1;\n\n  Scalar s0 = internal::random<Scalar>();\n  Scalar s1 = internal::random<Scalar>();\n\n  VERIFY_IS_APPROX( n1.dot(n1), Scalar(1) );\n\n  VERIFY_IS_MUCH_SMALLER_THAN( pl0.absDistance(p0), Scalar(1) );\n  if(numext::abs2(s0)>RealScalar(1e-6))\n    VERIFY_IS_APPROX( pl1.signedDistance(p1 + n1 * s0), s0);\n  else\n    VERIFY_IS_MUCH_SMALLER_THAN( abs(pl1.signedDistance(p1 + n1 * s0) - s0), Scalar(1) );\n  VERIFY_IS_MUCH_SMALLER_THAN( pl1.signedDistance(pl1.projection(p0)), Scalar(1) );\n  VERIFY_IS_MUCH_SMALLER_THAN( pl1.absDistance(p1 +  pl1.normal().unitOrthogonal() * s1), Scalar(1) );\n\n  // transform\n  if (!NumTraits<Scalar>::IsComplex)\n  {\n    MatrixType rot = MatrixType::Random(dim,dim).householderQr().householderQ();\n    DiagonalMatrix<Scalar,HyperplaneType::AmbientDimAtCompileTime> scaling(VectorType::Random());\n    Translation<Scalar,HyperplaneType::AmbientDimAtCompileTime> translation(VectorType::Random());\n    \n    while(scaling.diagonal().cwiseAbs().minCoeff()<RealScalar(1e-4)) scaling.diagonal() = VectorType::Random();\n\n    pl2 = pl1;\n    VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot).absDistance(rot * p1), Scalar(1) );\n    pl2 = pl1;\n    VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot,Isometry).absDistance(rot * p1), Scalar(1) );\n    pl2 = pl1;\n    VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*scaling).absDistance((rot*scaling) * p1), Scalar(1) );\n    VERIFY_IS_APPROX( pl2.normal().norm(), RealScalar(1) );\n    pl2 = pl1;\n    VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*scaling*translation)\n                                  .absDistance((rot*scaling*translation) * p1), Scalar(1) );\n    VERIFY_IS_APPROX( pl2.normal().norm(), RealScalar(1) );\n    pl2 = pl1;\n    VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*translation,Isometry)\n                                 .absDistance((rot*translation) * p1), Scalar(1) );\n    VERIFY_IS_APPROX( pl2.normal().norm(), RealScalar(1) );\n  }\n\n  // casting\n  const int Dim = HyperplaneType::AmbientDimAtCompileTime;\n  typedef typename GetDifferentType<Scalar>::type OtherScalar;\n  Hyperplane<OtherScalar,Dim,Options> hp1f = pl1.template cast<OtherScalar>();\n  VERIFY_IS_APPROX(hp1f.template cast<Scalar>(),pl1);\n  Hyperplane<Scalar,Dim,Options> hp1d = pl1.template cast<Scalar>();\n  VERIFY_IS_APPROX(hp1d.template cast<Scalar>(),pl1);\n}\n\ntemplate<typename Scalar> void lines()\n{\n  using std::abs;\n  typedef Hyperplane<Scalar, 2> HLine;\n  typedef ParametrizedLine<Scalar, 2> PLine;\n  typedef Matrix<Scalar,2,1> Vector;\n  typedef Matrix<Scalar,3,1> CoeffsType;\n\n  for(int i = 0; i < 10; i++)\n  {\n    Vector center = Vector::Random();\n    Vector u = Vector::Random();\n    Vector v = Vector::Random();\n    Scalar a = internal::random<Scalar>();\n    while (abs(a-1) < Scalar(1e-4)) a = internal::random<Scalar>();\n    while (u.norm() < Scalar(1e-4)) u = Vector::Random();\n    while (v.norm() < Scalar(1e-4)) v = Vector::Random();\n\n    HLine line_u = HLine::Through(center + u, center + a*u);\n    HLine line_v = HLine::Through(center + v, center + a*v);\n\n    // the line equations should be normalized so that a^2+b^2=1\n    VERIFY_IS_APPROX(line_u.normal().norm(), Scalar(1));\n    VERIFY_IS_APPROX(line_v.normal().norm(), Scalar(1));\n\n    Vector result = line_u.intersection(line_v);\n\n    // the lines should intersect at the point we called \"center\"\n    if(abs(a-1) > Scalar(1e-2) && abs(v.normalized().dot(u.normalized()))<Scalar(0.9))\n      VERIFY_IS_APPROX(result, center);\n\n    // check conversions between two types of lines\n    PLine pl(line_u); // gcc 3.3 will commit suicide if we don't name this variable\n    HLine line_u2(pl);\n    CoeffsType converted_coeffs = line_u2.coeffs();\n    if(line_u2.normal().dot(line_u.normal())<Scalar(0))\n      converted_coeffs = -line_u2.coeffs();\n    VERIFY(line_u.coeffs().isApprox(converted_coeffs));\n  }\n}\n\ntemplate<typename Scalar> void planes()\n{\n  using std::abs;\n  typedef Hyperplane<Scalar, 3> Plane;\n  typedef Matrix<Scalar,3,1> Vector;\n\n  for(int i = 0; i < 10; i++)\n  {\n    Vector v0 = Vector::Random();\n    Vector v1(v0), v2(v0);\n    if(internal::random<double>(0,1)>0.25)\n      v1 += Vector::Random();\n    if(internal::random<double>(0,1)>0.25)\n      v2 += v1 * std::pow(internal::random<Scalar>(0,1),internal::random<int>(1,16));\n    if(internal::random<double>(0,1)>0.25)\n      v2 += Vector::Random() * std::pow(internal::random<Scalar>(0,1),internal::random<int>(1,16));\n\n    Plane p0 = Plane::Through(v0, v1, v2);\n\n    VERIFY_IS_APPROX(p0.normal().norm(), Scalar(1));\n    VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v0), Scalar(1));\n    VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v1), Scalar(1));\n    VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v2), Scalar(1));\n  }\n}\n\ntemplate<typename Scalar> void hyperplane_alignment()\n{\n  typedef Hyperplane<Scalar,3,AutoAlign> Plane3a;\n  typedef Hyperplane<Scalar,3,DontAlign> Plane3u;\n\n  EIGEN_ALIGN_MAX Scalar array1[4];\n  EIGEN_ALIGN_MAX Scalar array2[4];\n  EIGEN_ALIGN_MAX Scalar array3[4+1];\n  Scalar* array3u = array3+1;\n\n  Plane3a *p1 = ::new(reinterpret_cast<void*>(array1)) Plane3a;\n  Plane3u *p2 = ::new(reinterpret_cast<void*>(array2)) Plane3u;\n  Plane3u *p3 = ::new(reinterpret_cast<void*>(array3u)) Plane3u;\n  \n  p1->coeffs().setRandom();\n  *p2 = *p1;\n  *p3 = *p1;\n\n  VERIFY_IS_APPROX(p1->coeffs(), p2->coeffs());\n  VERIFY_IS_APPROX(p1->coeffs(), p3->coeffs());\n  \n  #if defined(EIGEN_VECTORIZE) && EIGEN_MAX_STATIC_ALIGN_BYTES > 0\n  if(internal::packet_traits<Scalar>::Vectorizable && internal::packet_traits<Scalar>::size<=4)\n    VERIFY_RAISES_ASSERT((::new(reinterpret_cast<void*>(array3u)) Plane3a));\n  #endif\n}\n\n\nvoid test_geo_hyperplane()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( hyperplane(Hyperplane<float,2>()) );\n    CALL_SUBTEST_2( hyperplane(Hyperplane<float,3>()) );\n    CALL_SUBTEST_2( hyperplane(Hyperplane<float,3,DontAlign>()) );\n    CALL_SUBTEST_2( hyperplane_alignment<float>() );\n    CALL_SUBTEST_3( hyperplane(Hyperplane<double,4>()) );\n    CALL_SUBTEST_4( hyperplane(Hyperplane<std::complex<double>,5>()) );\n    CALL_SUBTEST_1( lines<float>() );\n    CALL_SUBTEST_3( lines<double>() );\n    CALL_SUBTEST_2( planes<float>() );\n    CALL_SUBTEST_5( planes<double>() );\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/geo_orthomethods.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <Eigen/Geometry>\n#include <Eigen/LU>\n#include <Eigen/SVD>\n\n/* this test covers the following files:\n   Geometry/OrthoMethods.h\n*/\n\ntemplate<typename Scalar> void orthomethods_3()\n{\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  typedef Matrix<Scalar,3,3> Matrix3;\n  typedef Matrix<Scalar,3,1> Vector3;\n\n  typedef Matrix<Scalar,4,1> Vector4;\n\n  Vector3 v0 = Vector3::Random(),\n          v1 = Vector3::Random(),\n          v2 = Vector3::Random();\n\n  // cross product\n  VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(v2).dot(v1), Scalar(1));\n  VERIFY_IS_MUCH_SMALLER_THAN(v1.dot(v1.cross(v2)), Scalar(1));\n  VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(v2).dot(v2), Scalar(1));\n  VERIFY_IS_MUCH_SMALLER_THAN(v2.dot(v1.cross(v2)), Scalar(1));\n  VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(Vector3::Random()).dot(v1), Scalar(1));\n  Matrix3 mat3;\n  mat3 << v0.normalized(),\n         (v0.cross(v1)).normalized(),\n         (v0.cross(v1).cross(v0)).normalized();\n  VERIFY(mat3.isUnitary());\n  \n  mat3.setRandom();\n  VERIFY_IS_APPROX(v0.cross(mat3*v1), -(mat3*v1).cross(v0));\n  VERIFY_IS_APPROX(v0.cross(mat3.lazyProduct(v1)), -(mat3.lazyProduct(v1)).cross(v0));\n\n  // colwise/rowwise cross product\n  mat3.setRandom();\n  Vector3 vec3 = Vector3::Random();\n  Matrix3 mcross;\n  int i = internal::random<int>(0,2);\n  mcross = mat3.colwise().cross(vec3);\n  VERIFY_IS_APPROX(mcross.col(i), mat3.col(i).cross(vec3));\n  \n  VERIFY_IS_MUCH_SMALLER_THAN((mat3.adjoint() * mat3.colwise().cross(vec3)).diagonal().cwiseAbs().sum(), Scalar(1));\n  VERIFY_IS_MUCH_SMALLER_THAN((mat3.adjoint() * mat3.colwise().cross(Vector3::Random())).diagonal().cwiseAbs().sum(), Scalar(1));\n  \n  VERIFY_IS_MUCH_SMALLER_THAN((vec3.adjoint() * mat3.colwise().cross(vec3)).cwiseAbs().sum(), Scalar(1));\n  VERIFY_IS_MUCH_SMALLER_THAN((vec3.adjoint() * Matrix3::Random().colwise().cross(vec3)).cwiseAbs().sum(), Scalar(1));\n  \n  mcross = mat3.rowwise().cross(vec3);\n  VERIFY_IS_APPROX(mcross.row(i), mat3.row(i).cross(vec3));\n\n  // cross3\n  Vector4 v40 = Vector4::Random(),\n          v41 = Vector4::Random(),\n          v42 = Vector4::Random();\n  v40.w() = v41.w() = v42.w() = 0;\n  v42.template head<3>() = v40.template head<3>().cross(v41.template head<3>());\n  VERIFY_IS_APPROX(v40.cross3(v41), v42);\n  VERIFY_IS_MUCH_SMALLER_THAN(v40.cross3(Vector4::Random()).dot(v40), Scalar(1));\n  \n  // check mixed product\n  typedef Matrix<RealScalar, 3, 1> RealVector3;\n  RealVector3 rv1 = RealVector3::Random();\n  VERIFY_IS_APPROX(v1.cross(rv1.template cast<Scalar>()), v1.cross(rv1));\n  VERIFY_IS_APPROX(rv1.template cast<Scalar>().cross(v1), rv1.cross(v1));\n}\n\ntemplate<typename Scalar, int Size> void orthomethods(int size=Size)\n{\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  typedef Matrix<Scalar,Size,1> VectorType;\n  typedef Matrix<Scalar,3,Size> Matrix3N;\n  typedef Matrix<Scalar,Size,3> MatrixN3;\n  typedef Matrix<Scalar,3,1> Vector3;\n\n  VectorType v0 = VectorType::Random(size);\n\n  // unitOrthogonal\n  VERIFY_IS_MUCH_SMALLER_THAN(v0.unitOrthogonal().dot(v0), Scalar(1));\n  VERIFY_IS_APPROX(v0.unitOrthogonal().norm(), RealScalar(1));\n\n  if (size>=3)\n  {\n    v0.template head<2>().setZero();\n    v0.tail(size-2).setRandom();\n\n    VERIFY_IS_MUCH_SMALLER_THAN(v0.unitOrthogonal().dot(v0), Scalar(1));\n    VERIFY_IS_APPROX(v0.unitOrthogonal().norm(), RealScalar(1));\n  }\n\n  // colwise/rowwise cross product\n  Vector3 vec3 = Vector3::Random();\n  int i = internal::random<int>(0,size-1);\n\n  Matrix3N mat3N(3,size), mcross3N(3,size);\n  mat3N.setRandom();\n  mcross3N = mat3N.colwise().cross(vec3);\n  VERIFY_IS_APPROX(mcross3N.col(i), mat3N.col(i).cross(vec3));\n\n  MatrixN3 matN3(size,3), mcrossN3(size,3);\n  matN3.setRandom();\n  mcrossN3 = matN3.rowwise().cross(vec3);\n  VERIFY_IS_APPROX(mcrossN3.row(i), matN3.row(i).cross(vec3));\n}\n\nvoid test_geo_orthomethods()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( orthomethods_3<float>() );\n    CALL_SUBTEST_2( orthomethods_3<double>() );\n    CALL_SUBTEST_4( orthomethods_3<std::complex<double> >() );\n    CALL_SUBTEST_1( (orthomethods<float,2>()) );\n    CALL_SUBTEST_2( (orthomethods<double,2>()) );\n    CALL_SUBTEST_1( (orthomethods<float,3>()) );\n    CALL_SUBTEST_2( (orthomethods<double,3>()) );\n    CALL_SUBTEST_3( (orthomethods<float,7>()) );\n    CALL_SUBTEST_4( (orthomethods<std::complex<double>,8>()) );\n    CALL_SUBTEST_5( (orthomethods<float,Dynamic>(36)) );\n    CALL_SUBTEST_6( (orthomethods<double,Dynamic>(35)) );\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/geo_parametrizedline.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <Eigen/Geometry>\n#include <Eigen/LU>\n#include <Eigen/QR>\n\ntemplate<typename LineType> void parametrizedline(const LineType& _line)\n{\n  /* this test covers the following files:\n     ParametrizedLine.h\n  */\n  using std::abs;\n  typedef typename LineType::Index Index;\n  const Index dim = _line.dim();\n  typedef typename LineType::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  typedef Matrix<Scalar, LineType::AmbientDimAtCompileTime, 1> VectorType;\n  typedef Hyperplane<Scalar,LineType::AmbientDimAtCompileTime> HyperplaneType;\n\n  VectorType p0 = VectorType::Random(dim);\n  VectorType p1 = VectorType::Random(dim);\n\n  VectorType d0 = VectorType::Random(dim).normalized();\n\n  LineType l0(p0, d0);\n\n  Scalar s0 = internal::random<Scalar>();\n  Scalar s1 = abs(internal::random<Scalar>());\n\n  VERIFY_IS_MUCH_SMALLER_THAN( l0.distance(p0), RealScalar(1) );\n  VERIFY_IS_MUCH_SMALLER_THAN( l0.distance(p0+s0*d0), RealScalar(1) );\n  VERIFY_IS_APPROX( (l0.projection(p1)-p1).norm(), l0.distance(p1) );\n  VERIFY_IS_MUCH_SMALLER_THAN( l0.distance(l0.projection(p1)), RealScalar(1) );\n  VERIFY_IS_APPROX( Scalar(l0.distance((p0+s0*d0) + d0.unitOrthogonal() * s1)), s1 );\n\n  // casting\n  const int Dim = LineType::AmbientDimAtCompileTime;\n  typedef typename GetDifferentType<Scalar>::type OtherScalar;\n  ParametrizedLine<OtherScalar,Dim> hp1f = l0.template cast<OtherScalar>();\n  VERIFY_IS_APPROX(hp1f.template cast<Scalar>(),l0);\n  ParametrizedLine<Scalar,Dim> hp1d = l0.template cast<Scalar>();\n  VERIFY_IS_APPROX(hp1d.template cast<Scalar>(),l0);\n\n  // intersections\n  VectorType p2 = VectorType::Random(dim);\n  VectorType n2 = VectorType::Random(dim).normalized();\n  HyperplaneType hp(p2,n2);\n  Scalar t = l0.intersectionParameter(hp);\n  VectorType pi = l0.pointAt(t);\n  VERIFY_IS_MUCH_SMALLER_THAN(hp.signedDistance(pi), RealScalar(1));\n  VERIFY_IS_MUCH_SMALLER_THAN(l0.distance(pi), RealScalar(1));\n  VERIFY_IS_APPROX(l0.intersectionPoint(hp), pi);\n}\n\ntemplate<typename Scalar> void parametrizedline_alignment()\n{\n  typedef ParametrizedLine<Scalar,4,AutoAlign> Line4a;\n  typedef ParametrizedLine<Scalar,4,DontAlign> Line4u;\n\n  EIGEN_ALIGN_MAX Scalar array1[16];\n  EIGEN_ALIGN_MAX Scalar array2[16];\n  EIGEN_ALIGN_MAX Scalar array3[16+1];\n  Scalar* array3u = array3+1;\n\n  Line4a *p1 = ::new(reinterpret_cast<void*>(array1)) Line4a;\n  Line4u *p2 = ::new(reinterpret_cast<void*>(array2)) Line4u;\n  Line4u *p3 = ::new(reinterpret_cast<void*>(array3u)) Line4u;\n  \n  p1->origin().setRandom();\n  p1->direction().setRandom();\n  *p2 = *p1;\n  *p3 = *p1;\n\n  VERIFY_IS_APPROX(p1->origin(), p2->origin());\n  VERIFY_IS_APPROX(p1->origin(), p3->origin());\n  VERIFY_IS_APPROX(p1->direction(), p2->direction());\n  VERIFY_IS_APPROX(p1->direction(), p3->direction());\n  \n  #if defined(EIGEN_VECTORIZE) && EIGEN_MAX_STATIC_ALIGN_BYTES>0\n  if(internal::packet_traits<Scalar>::Vectorizable && internal::packet_traits<Scalar>::size<=4)\n    VERIFY_RAISES_ASSERT((::new(reinterpret_cast<void*>(array3u)) Line4a));\n  #endif\n}\n\nvoid test_geo_parametrizedline()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( parametrizedline(ParametrizedLine<float,2>()) );\n    CALL_SUBTEST_2( parametrizedline(ParametrizedLine<float,3>()) );\n    CALL_SUBTEST_2( parametrizedline_alignment<float>() );\n    CALL_SUBTEST_3( parametrizedline(ParametrizedLine<double,4>()) );\n    CALL_SUBTEST_3( parametrizedline_alignment<double>() );\n    CALL_SUBTEST_4( parametrizedline(ParametrizedLine<std::complex<double>,5>()) );\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/geo_quaternion.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2009 Mathieu Gautier <mathieu.gautier@cea.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <Eigen/Geometry>\n#include <Eigen/LU>\n#include <Eigen/SVD>\n\ntemplate<typename T> T bounded_acos(T v)\n{\n  using std::acos;\n  using std::min;\n  using std::max;\n  return acos((max)(T(-1),(min)(v,T(1))));\n}\n\ntemplate<typename QuatType> void check_slerp(const QuatType& q0, const QuatType& q1)\n{\n  using std::abs;\n  typedef typename QuatType::Scalar Scalar;\n  typedef AngleAxis<Scalar> AA;\n\n  Scalar largeEps = test_precision<Scalar>();\n\n  Scalar theta_tot = AA(q1*q0.inverse()).angle();\n  if(theta_tot>Scalar(EIGEN_PI))\n    theta_tot = Scalar(2.)*Scalar(EIGEN_PI)-theta_tot;\n  for(Scalar t=0; t<=Scalar(1.001); t+=Scalar(0.1))\n  {\n    QuatType q = q0.slerp(t,q1);\n    Scalar theta = AA(q*q0.inverse()).angle();\n    VERIFY(abs(q.norm() - 1) < largeEps);\n    if(theta_tot==0)  VERIFY(theta_tot==0);\n    else              VERIFY(abs(theta - t * theta_tot) < largeEps);\n  }\n}\n\ntemplate<typename Scalar, int Options> void quaternion(void)\n{\n  /* this test covers the following files:\n     Quaternion.h\n  */\n  using std::abs;\n  typedef Matrix<Scalar,3,1> Vector3;\n  typedef Matrix<Scalar,3,3> Matrix3;\n  typedef Quaternion<Scalar,Options> Quaternionx;\n  typedef AngleAxis<Scalar> AngleAxisx;\n\n  Scalar largeEps = test_precision<Scalar>();\n  if (internal::is_same<Scalar,float>::value)\n    largeEps = Scalar(1e-3);\n\n  Scalar eps = internal::random<Scalar>() * Scalar(1e-2);\n\n  Vector3 v0 = Vector3::Random(),\n          v1 = Vector3::Random(),\n          v2 = Vector3::Random(),\n          v3 = Vector3::Random();\n\n  Scalar  a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI)),\n          b = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI));\n\n  // Quaternion: Identity(), setIdentity();\n  Quaternionx q1, q2;\n  q2.setIdentity();\n  VERIFY_IS_APPROX(Quaternionx(Quaternionx::Identity()).coeffs(), q2.coeffs());\n  q1.coeffs().setRandom();\n  VERIFY_IS_APPROX(q1.coeffs(), (q1*q2).coeffs());\n\n  // concatenation\n  q1 *= q2;\n\n  q1 = AngleAxisx(a, v0.normalized());\n  q2 = AngleAxisx(a, v1.normalized());\n\n  // angular distance\n  Scalar refangle = abs(AngleAxisx(q1.inverse()*q2).angle());\n  if (refangle>Scalar(EIGEN_PI))\n    refangle = Scalar(2)*Scalar(EIGEN_PI) - refangle;\n\n  if((q1.coeffs()-q2.coeffs()).norm() > 10*largeEps)\n  {\n    VERIFY_IS_MUCH_SMALLER_THAN(abs(q1.angularDistance(q2) - refangle), Scalar(1));\n  }\n\n  // rotation matrix conversion\n  VERIFY_IS_APPROX(q1 * v2, q1.toRotationMatrix() * v2);\n  VERIFY_IS_APPROX(q1 * q2 * v2,\n    q1.toRotationMatrix() * q2.toRotationMatrix() * v2);\n\n  VERIFY(  (q2*q1).isApprox(q1*q2, largeEps)\n        || !(q2 * q1 * v2).isApprox(q1.toRotationMatrix() * q2.toRotationMatrix() * v2));\n\n  q2 = q1.toRotationMatrix();\n  VERIFY_IS_APPROX(q1*v1,q2*v1);\n\n  Matrix3 rot1(q1);\n  VERIFY_IS_APPROX(q1*v1,rot1*v1);\n  Quaternionx q3(rot1.transpose()*rot1);\n  VERIFY_IS_APPROX(q3*v1,v1);\n\n\n  // angle-axis conversion\n  AngleAxisx aa = AngleAxisx(q1);\n  VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1);\n\n  // Do not execute the test if the rotation angle is almost zero, or\n  // the rotation axis and v1 are almost parallel.\n  if (abs(aa.angle()) > 5*test_precision<Scalar>()\n      && (aa.axis() - v1.normalized()).norm() < Scalar(1.99)\n      && (aa.axis() + v1.normalized()).norm() < Scalar(1.99))\n  {\n    VERIFY_IS_NOT_APPROX(q1 * v1, Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1);\n  }\n\n  // from two vector creation\n  VERIFY_IS_APPROX( v2.normalized(),(q2.setFromTwoVectors(v1, v2)*v1).normalized());\n  VERIFY_IS_APPROX( v1.normalized(),(q2.setFromTwoVectors(v1, v1)*v1).normalized());\n  VERIFY_IS_APPROX(-v1.normalized(),(q2.setFromTwoVectors(v1,-v1)*v1).normalized());\n  if (internal::is_same<Scalar,double>::value)\n  {\n    v3 = (v1.array()+eps).matrix();\n    VERIFY_IS_APPROX( v3.normalized(),(q2.setFromTwoVectors(v1, v3)*v1).normalized());\n    VERIFY_IS_APPROX(-v3.normalized(),(q2.setFromTwoVectors(v1,-v3)*v1).normalized());\n  }\n\n  // from two vector creation static function\n  VERIFY_IS_APPROX( v2.normalized(),(Quaternionx::FromTwoVectors(v1, v2)*v1).normalized());\n  VERIFY_IS_APPROX( v1.normalized(),(Quaternionx::FromTwoVectors(v1, v1)*v1).normalized());\n  VERIFY_IS_APPROX(-v1.normalized(),(Quaternionx::FromTwoVectors(v1,-v1)*v1).normalized());\n  if (internal::is_same<Scalar,double>::value)\n  {\n    v3 = (v1.array()+eps).matrix();\n    VERIFY_IS_APPROX( v3.normalized(),(Quaternionx::FromTwoVectors(v1, v3)*v1).normalized());\n    VERIFY_IS_APPROX(-v3.normalized(),(Quaternionx::FromTwoVectors(v1,-v3)*v1).normalized());\n  }\n\n  // inverse and conjugate\n  VERIFY_IS_APPROX(q1 * (q1.inverse() * v1), v1);\n  VERIFY_IS_APPROX(q1 * (q1.conjugate() * v1), v1);\n\n  // test casting\n  Quaternion<float> q1f = q1.template cast<float>();\n  VERIFY_IS_APPROX(q1f.template cast<Scalar>(),q1);\n  Quaternion<double> q1d = q1.template cast<double>();\n  VERIFY_IS_APPROX(q1d.template cast<Scalar>(),q1);\n\n  // test bug 369 - improper alignment.\n  Quaternionx *q = new Quaternionx;\n  delete q;\n\n  q1 = Quaternionx::UnitRandom();\n  q2 = Quaternionx::UnitRandom();\n  check_slerp(q1,q2);\n\n  q1 = AngleAxisx(b, v1.normalized());\n  q2 = AngleAxisx(b+Scalar(EIGEN_PI), v1.normalized());\n  check_slerp(q1,q2);\n\n  q1 = AngleAxisx(b,  v1.normalized());\n  q2 = AngleAxisx(-b, -v1.normalized());\n  check_slerp(q1,q2);\n\n  q1 = Quaternionx::UnitRandom();\n  q2.coeffs() = -q1.coeffs();\n  check_slerp(q1,q2);\n}\n\ntemplate<typename Scalar> void mapQuaternion(void){\n  typedef Map<Quaternion<Scalar>, Aligned> MQuaternionA;\n  typedef Map<const Quaternion<Scalar>, Aligned> MCQuaternionA;\n  typedef Map<Quaternion<Scalar> > MQuaternionUA;\n  typedef Map<const Quaternion<Scalar> > MCQuaternionUA;\n  typedef Quaternion<Scalar> Quaternionx;\n  typedef Matrix<Scalar,3,1> Vector3;\n  typedef AngleAxis<Scalar> AngleAxisx;\n  \n  Vector3 v0 = Vector3::Random(),\n          v1 = Vector3::Random();\n  Scalar  a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI));\n\n  EIGEN_ALIGN_MAX Scalar array1[4];\n  EIGEN_ALIGN_MAX Scalar array2[4];\n  EIGEN_ALIGN_MAX Scalar array3[4+1];\n  Scalar* array3unaligned = array3+1;\n  \n  MQuaternionA    mq1(array1);\n  MCQuaternionA   mcq1(array1);\n  MQuaternionA    mq2(array2);\n  MQuaternionUA   mq3(array3unaligned);\n  MCQuaternionUA  mcq3(array3unaligned);\n\n//  std::cerr << array1 << \" \" << array2 << \" \" << array3 << \"\\n\";\n  mq1 = AngleAxisx(a, v0.normalized());\n  mq2 = mq1;\n  mq3 = mq1;\n\n  Quaternionx q1 = mq1;\n  Quaternionx q2 = mq2;\n  Quaternionx q3 = mq3;\n  Quaternionx q4 = MCQuaternionUA(array3unaligned);\n\n  VERIFY_IS_APPROX(q1.coeffs(), q2.coeffs());\n  VERIFY_IS_APPROX(q1.coeffs(), q3.coeffs());\n  VERIFY_IS_APPROX(q4.coeffs(), q3.coeffs());\n  #ifdef EIGEN_VECTORIZE\n  if(internal::packet_traits<Scalar>::Vectorizable)\n    VERIFY_RAISES_ASSERT((MQuaternionA(array3unaligned)));\n  #endif\n    \n  VERIFY_IS_APPROX(mq1 * (mq1.inverse() * v1), v1);\n  VERIFY_IS_APPROX(mq1 * (mq1.conjugate() * v1), v1);\n  \n  VERIFY_IS_APPROX(mcq1 * (mcq1.inverse() * v1), v1);\n  VERIFY_IS_APPROX(mcq1 * (mcq1.conjugate() * v1), v1);\n  \n  VERIFY_IS_APPROX(mq3 * (mq3.inverse() * v1), v1);\n  VERIFY_IS_APPROX(mq3 * (mq3.conjugate() * v1), v1);\n  \n  VERIFY_IS_APPROX(mcq3 * (mcq3.inverse() * v1), v1);\n  VERIFY_IS_APPROX(mcq3 * (mcq3.conjugate() * v1), v1);\n  \n  VERIFY_IS_APPROX(mq1*mq2, q1*q2);\n  VERIFY_IS_APPROX(mq3*mq2, q3*q2);\n  VERIFY_IS_APPROX(mcq1*mq2, q1*q2);\n  VERIFY_IS_APPROX(mcq3*mq2, q3*q2);\n\n  // Bug 1461, compilation issue with Map<const Quat>::w(), and other reference/constness checks:\n  VERIFY_IS_APPROX(mcq3.coeffs().x() + mcq3.coeffs().y() + mcq3.coeffs().z() + mcq3.coeffs().w(), mcq3.coeffs().sum());\n  VERIFY_IS_APPROX(mcq3.x() + mcq3.y() + mcq3.z() + mcq3.w(), mcq3.coeffs().sum());\n  mq3.w() = 1;\n  const Quaternionx& cq3(q3);\n  VERIFY( &cq3.x() == &q3.x() );\n  const MQuaternionUA& cmq3(mq3);\n  VERIFY( &cmq3.x() == &mq3.x() );\n  // FIXME the following should be ok. The problem is that currently the LValueBit flag\n  // is used to determine wether we can return a coeff by reference or not, which is not enough for Map<const ...>.\n  //const MCQuaternionUA& cmcq3(mcq3);\n  //VERIFY( &cmcq3.x() == &mcq3.x() );\n}\n\ntemplate<typename Scalar> void quaternionAlignment(void){\n  typedef Quaternion<Scalar,AutoAlign> QuaternionA;\n  typedef Quaternion<Scalar,DontAlign> QuaternionUA;\n\n  EIGEN_ALIGN_MAX Scalar array1[4];\n  EIGEN_ALIGN_MAX Scalar array2[4];\n  EIGEN_ALIGN_MAX Scalar array3[4+1];\n  Scalar* arrayunaligned = array3+1;\n\n  QuaternionA *q1 = ::new(reinterpret_cast<void*>(array1)) QuaternionA;\n  QuaternionUA *q2 = ::new(reinterpret_cast<void*>(array2)) QuaternionUA;\n  QuaternionUA *q3 = ::new(reinterpret_cast<void*>(arrayunaligned)) QuaternionUA;\n\n  q1->coeffs().setRandom();\n  *q2 = *q1;\n  *q3 = *q1;\n\n  VERIFY_IS_APPROX(q1->coeffs(), q2->coeffs());\n  VERIFY_IS_APPROX(q1->coeffs(), q3->coeffs());\n  #if defined(EIGEN_VECTORIZE) && EIGEN_MAX_STATIC_ALIGN_BYTES>0\n  if(internal::packet_traits<Scalar>::Vectorizable && internal::packet_traits<Scalar>::size<=4)\n    VERIFY_RAISES_ASSERT((::new(reinterpret_cast<void*>(arrayunaligned)) QuaternionA));\n  #endif\n}\n\ntemplate<typename PlainObjectType> void check_const_correctness(const PlainObjectType&)\n{\n  // there's a lot that we can't test here while still having this test compile!\n  // the only possible approach would be to run a script trying to compile stuff and checking that it fails.\n  // CMake can help with that.\n\n  // verify that map-to-const don't have LvalueBit\n  typedef typename internal::add_const<PlainObjectType>::type ConstPlainObjectType;\n  VERIFY( !(internal::traits<Map<ConstPlainObjectType> >::Flags & LvalueBit) );\n  VERIFY( !(internal::traits<Map<ConstPlainObjectType, Aligned> >::Flags & LvalueBit) );\n  VERIFY( !(Map<ConstPlainObjectType>::Flags & LvalueBit) );\n  VERIFY( !(Map<ConstPlainObjectType, Aligned>::Flags & LvalueBit) );\n}\n\nvoid test_geo_quaternion()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1(( quaternion<float,AutoAlign>() ));\n    CALL_SUBTEST_1( check_const_correctness(Quaternionf()) );\n    CALL_SUBTEST_2(( quaternion<double,AutoAlign>() ));\n    CALL_SUBTEST_2( check_const_correctness(Quaterniond()) );\n    CALL_SUBTEST_3(( quaternion<float,DontAlign>() ));\n    CALL_SUBTEST_4(( quaternion<double,DontAlign>() ));\n    CALL_SUBTEST_5(( quaternionAlignment<float>() ));\n    CALL_SUBTEST_6(( quaternionAlignment<double>() ));\n    CALL_SUBTEST_1( mapQuaternion<float>() );\n    CALL_SUBTEST_2( mapQuaternion<double>() );\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/geo_transformations.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <Eigen/Geometry>\n#include <Eigen/LU>\n#include <Eigen/SVD>\n\ntemplate<typename T>\nMatrix<T,2,1> angleToVec(T a)\n{\n  return Matrix<T,2,1>(std::cos(a), std::sin(a));\n}\n\n// This permits to workaround a bug in clang/llvm code generation.\ntemplate<typename T>\nEIGEN_DONT_INLINE\nvoid dont_over_optimize(T& x) { volatile typename T::Scalar tmp = x(0); x(0) = tmp; }\n\ntemplate<typename Scalar, int Mode, int Options> void non_projective_only()\n{\n    /* this test covers the following files:\n     Cross.h Quaternion.h, Transform.cpp\n  */\n  typedef Matrix<Scalar,3,1> Vector3;\n  typedef Quaternion<Scalar> Quaternionx;\n  typedef AngleAxis<Scalar> AngleAxisx;\n  typedef Transform<Scalar,3,Mode,Options> Transform3;\n  typedef DiagonalMatrix<Scalar,3> AlignedScaling3;\n  typedef Translation<Scalar,3> Translation3;\n\n  Vector3 v0 = Vector3::Random(),\n          v1 = Vector3::Random();\n\n  Transform3 t0, t1, t2;\n\n  Scalar a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI));\n\n  Quaternionx q1, q2;\n\n  q1 = AngleAxisx(a, v0.normalized());\n\n  t0 = Transform3::Identity();\n  VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity());\n\n  t0.linear() = q1.toRotationMatrix();\n\n  v0 << 50, 2, 1;\n  t0.scale(v0);\n\n  VERIFY_IS_APPROX( (t0 * Vector3(1,0,0)).template head<3>().norm(), v0.x());\n\n  t0.setIdentity();\n  t1.setIdentity();\n  v1 << 1, 2, 3;\n  t0.linear() = q1.toRotationMatrix();\n  t0.pretranslate(v0);\n  t0.scale(v1);\n  t1.linear() = q1.conjugate().toRotationMatrix();\n  t1.prescale(v1.cwiseInverse());\n  t1.translate(-v0);\n\n  VERIFY((t0 * t1).matrix().isIdentity(test_precision<Scalar>()));\n\n  t1.fromPositionOrientationScale(v0, q1, v1);\n  VERIFY_IS_APPROX(t1.matrix(), t0.matrix());\n  VERIFY_IS_APPROX(t1*v1, t0*v1);\n\n  // translation * vector\n  t0.setIdentity();\n  t0.translate(v0);\n  VERIFY_IS_APPROX((t0 * v1).template head<3>(), Translation3(v0) * v1);\n\n  // AlignedScaling * vector\n  t0.setIdentity();\n  t0.scale(v0);\n  VERIFY_IS_APPROX((t0 * v1).template head<3>(), AlignedScaling3(v0) * v1);\n}\n\ntemplate<typename Scalar, int Mode, int Options> void transformations()\n{\n  /* this test covers the following files:\n     Cross.h Quaternion.h, Transform.cpp\n  */\n  using std::cos;\n  using std::abs;\n  typedef Matrix<Scalar,3,3> Matrix3;\n  typedef Matrix<Scalar,4,4> Matrix4;\n  typedef Matrix<Scalar,2,1> Vector2;\n  typedef Matrix<Scalar,3,1> Vector3;\n  typedef Matrix<Scalar,4,1> Vector4;\n  typedef Quaternion<Scalar> Quaternionx;\n  typedef AngleAxis<Scalar> AngleAxisx;\n  typedef Transform<Scalar,2,Mode,Options> Transform2;\n  typedef Transform<Scalar,3,Mode,Options> Transform3;\n  typedef typename Transform3::MatrixType MatrixType;\n  typedef DiagonalMatrix<Scalar,3> AlignedScaling3;\n  typedef Translation<Scalar,2> Translation2;\n  typedef Translation<Scalar,3> Translation3;\n\n  Vector3 v0 = Vector3::Random(),\n          v1 = Vector3::Random();\n  Matrix3 matrot1, m;\n\n  Scalar a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI));\n  Scalar s0 = internal::random<Scalar>(), s1 = internal::random<Scalar>();\n  \n  while(v0.norm() < test_precision<Scalar>()) v0 = Vector3::Random();\n  while(v1.norm() < test_precision<Scalar>()) v1 = Vector3::Random();\n\n  VERIFY_IS_APPROX(v0, AngleAxisx(a, v0.normalized()) * v0);\n  VERIFY_IS_APPROX(-v0, AngleAxisx(Scalar(EIGEN_PI), v0.unitOrthogonal()) * v0);\n  if(abs(cos(a)) > test_precision<Scalar>())\n  {\n    VERIFY_IS_APPROX(cos(a)*v0.squaredNorm(), v0.dot(AngleAxisx(a, v0.unitOrthogonal()) * v0));\n  }\n  m = AngleAxisx(a, v0.normalized()).toRotationMatrix().adjoint();\n  VERIFY_IS_APPROX(Matrix3::Identity(), m * AngleAxisx(a, v0.normalized()));\n  VERIFY_IS_APPROX(Matrix3::Identity(), AngleAxisx(a, v0.normalized()) * m);\n\n  Quaternionx q1, q2;\n  q1 = AngleAxisx(a, v0.normalized());\n  q2 = AngleAxisx(a, v1.normalized());\n\n  // rotation matrix conversion\n  matrot1 = AngleAxisx(Scalar(0.1), Vector3::UnitX())\n          * AngleAxisx(Scalar(0.2), Vector3::UnitY())\n          * AngleAxisx(Scalar(0.3), Vector3::UnitZ());\n  VERIFY_IS_APPROX(matrot1 * v1,\n       AngleAxisx(Scalar(0.1), Vector3(1,0,0)).toRotationMatrix()\n    * (AngleAxisx(Scalar(0.2), Vector3(0,1,0)).toRotationMatrix()\n    * (AngleAxisx(Scalar(0.3), Vector3(0,0,1)).toRotationMatrix() * v1)));\n\n  // angle-axis conversion\n  AngleAxisx aa = AngleAxisx(q1);\n  VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1);\n  \n  // The following test is stable only if 2*angle != angle and v1 is not colinear with axis\n  if( (abs(aa.angle()) > test_precision<Scalar>()) && (abs(aa.axis().dot(v1.normalized()))<(Scalar(1)-Scalar(4)*test_precision<Scalar>())) )\n  {\n    VERIFY( !(q1 * v1).isApprox(Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1) );\n  }\n\n  aa.fromRotationMatrix(aa.toRotationMatrix());\n  VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1);\n  // The following test is stable only if 2*angle != angle and v1 is not colinear with axis\n  if( (abs(aa.angle()) > test_precision<Scalar>()) && (abs(aa.axis().dot(v1.normalized()))<(Scalar(1)-Scalar(4)*test_precision<Scalar>())) )\n  {\n    VERIFY( !(q1 * v1).isApprox(Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1) );\n  }\n\n  // AngleAxis\n  VERIFY_IS_APPROX(AngleAxisx(a,v1.normalized()).toRotationMatrix(),\n    Quaternionx(AngleAxisx(a,v1.normalized())).toRotationMatrix());\n\n  AngleAxisx aa1;\n  m = q1.toRotationMatrix();\n  aa1 = m;\n  VERIFY_IS_APPROX(AngleAxisx(m).toRotationMatrix(),\n    Quaternionx(m).toRotationMatrix());\n\n  // Transform\n  // TODO complete the tests !\n  a = 0;\n  while (abs(a)<Scalar(0.1))\n    a = internal::random<Scalar>(-Scalar(0.4)*Scalar(EIGEN_PI), Scalar(0.4)*Scalar(EIGEN_PI));\n  q1 = AngleAxisx(a, v0.normalized());\n  Transform3 t0, t1, t2;\n\n  // first test setIdentity() and Identity()\n  t0.setIdentity();\n  VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity());\n  t0.matrix().setZero();\n  t0 = Transform3::Identity();\n  VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity());\n\n  t0.setIdentity();\n  t1.setIdentity();\n  v1 << 1, 2, 3;\n  t0.linear() = q1.toRotationMatrix();\n  t0.pretranslate(v0);\n  t0.scale(v1);\n  t1.linear() = q1.conjugate().toRotationMatrix();\n  t1.prescale(v1.cwiseInverse());\n  t1.translate(-v0);\n\n  VERIFY((t0 * t1).matrix().isIdentity(test_precision<Scalar>()));\n\n  t1.fromPositionOrientationScale(v0, q1, v1);\n  VERIFY_IS_APPROX(t1.matrix(), t0.matrix());\n\n  t0.setIdentity(); t0.scale(v0).rotate(q1.toRotationMatrix());\n  t1.setIdentity(); t1.scale(v0).rotate(q1);\n  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());\n\n  t0.setIdentity(); t0.scale(v0).rotate(AngleAxisx(q1));\n  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());\n\n  VERIFY_IS_APPROX(t0.scale(a).matrix(), t1.scale(Vector3::Constant(a)).matrix());\n  VERIFY_IS_APPROX(t0.prescale(a).matrix(), t1.prescale(Vector3::Constant(a)).matrix());\n\n  // More transform constructors, operator=, operator*=\n\n  Matrix3 mat3 = Matrix3::Random();\n  Matrix4 mat4;\n  mat4 << mat3 , Vector3::Zero() , Vector4::Zero().transpose();\n  Transform3 tmat3(mat3), tmat4(mat4);\n  if(Mode!=int(AffineCompact))\n    tmat4.matrix()(3,3) = Scalar(1);\n  VERIFY_IS_APPROX(tmat3.matrix(), tmat4.matrix());\n\n  Scalar a3 = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI));\n  Vector3 v3 = Vector3::Random().normalized();\n  AngleAxisx aa3(a3, v3);\n  Transform3 t3(aa3);\n  Transform3 t4;\n  t4 = aa3;\n  VERIFY_IS_APPROX(t3.matrix(), t4.matrix());\n  t4.rotate(AngleAxisx(-a3,v3));\n  VERIFY_IS_APPROX(t4.matrix(), MatrixType::Identity());\n  t4 *= aa3;\n  VERIFY_IS_APPROX(t3.matrix(), t4.matrix());\n\n  do {\n    v3 = Vector3::Random();\n    dont_over_optimize(v3);\n  } while (v3.cwiseAbs().minCoeff()<NumTraits<Scalar>::epsilon());\n  Translation3 tv3(v3);\n  Transform3 t5(tv3);\n  t4 = tv3;\n  VERIFY_IS_APPROX(t5.matrix(), t4.matrix());\n  t4.translate((-v3).eval());\n  VERIFY_IS_APPROX(t4.matrix(), MatrixType::Identity());\n  t4 *= tv3;\n  VERIFY_IS_APPROX(t5.matrix(), t4.matrix());\n\n  AlignedScaling3 sv3(v3);\n  Transform3 t6(sv3);\n  t4 = sv3;\n  VERIFY_IS_APPROX(t6.matrix(), t4.matrix());\n  t4.scale(v3.cwiseInverse());\n  VERIFY_IS_APPROX(t4.matrix(), MatrixType::Identity());\n  t4 *= sv3;\n  VERIFY_IS_APPROX(t6.matrix(), t4.matrix());\n\n  // matrix * transform\n  VERIFY_IS_APPROX((t3.matrix()*t4).matrix(), (t3*t4).matrix());\n\n  // chained Transform product\n  VERIFY_IS_APPROX(((t3*t4)*t5).matrix(), (t3*(t4*t5)).matrix());\n\n  // check that Transform product doesn't have aliasing problems\n  t5 = t4;\n  t5 = t5*t5;\n  VERIFY_IS_APPROX(t5, t4*t4);\n\n  // 2D transformation\n  Transform2 t20, t21;\n  Vector2 v20 = Vector2::Random();\n  Vector2 v21 = Vector2::Random();\n  for (int k=0; k<2; ++k)\n    if (abs(v21[k])<Scalar(1e-3)) v21[k] = Scalar(1e-3);\n  t21.setIdentity();\n  t21.linear() = Rotation2D<Scalar>(a).toRotationMatrix();\n  VERIFY_IS_APPROX(t20.fromPositionOrientationScale(v20,a,v21).matrix(),\n    t21.pretranslate(v20).scale(v21).matrix());\n\n  t21.setIdentity();\n  t21.linear() = Rotation2D<Scalar>(-a).toRotationMatrix();\n  VERIFY( (t20.fromPositionOrientationScale(v20,a,v21)\n        * (t21.prescale(v21.cwiseInverse()).translate(-v20))).matrix().isIdentity(test_precision<Scalar>()) );\n\n  // Transform - new API\n  // 3D\n  t0.setIdentity();\n  t0.rotate(q1).scale(v0).translate(v0);\n  // mat * aligned scaling and mat * translation\n  t1 = (Matrix3(q1) * AlignedScaling3(v0)) * Translation3(v0);\n  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());\n  t1 = (Matrix3(q1) * Eigen::Scaling(v0)) * Translation3(v0);\n  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());\n  t1 = (q1 * Eigen::Scaling(v0)) * Translation3(v0);\n  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());\n  // mat * transformation and aligned scaling * translation\n  t1 = Matrix3(q1) * (AlignedScaling3(v0) * Translation3(v0));\n  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());\n\n\n  t0.setIdentity();\n  t0.scale(s0).translate(v0);\n  t1 = Eigen::Scaling(s0) * Translation3(v0);\n  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());\n  t0.prescale(s0);\n  t1 = Eigen::Scaling(s0) * t1;\n  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());\n  \n  t0 = t3;\n  t0.scale(s0);\n  t1 = t3 * Eigen::Scaling(s0,s0,s0);\n  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());\n  t0.prescale(s0);\n  t1 = Eigen::Scaling(s0,s0,s0) * t1;\n  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());\n\n  t0 = t3;\n  t0.scale(s0);\n  t1 = t3 * Eigen::Scaling(s0);\n  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());\n  t0.prescale(s0);\n  t1 = Eigen::Scaling(s0) * t1;\n  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());\n\n  t0.setIdentity();\n  t0.prerotate(q1).prescale(v0).pretranslate(v0);\n  // translation * aligned scaling and transformation * mat\n  t1 = (Translation3(v0) * AlignedScaling3(v0)) * Transform3(q1);\n  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());\n  // scaling * mat and translation * mat\n  t1 = Translation3(v0) * (AlignedScaling3(v0) * Transform3(q1));\n  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());\n\n  t0.setIdentity();\n  t0.scale(v0).translate(v0).rotate(q1);\n  // translation * mat and aligned scaling * transformation\n  t1 = AlignedScaling3(v0) * (Translation3(v0) * Transform3(q1));\n  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());\n  // transformation * aligned scaling\n  t0.scale(v0);\n  t1 *= AlignedScaling3(v0);\n  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());\n  t1 = AlignedScaling3(v0) * (Translation3(v0) * Transform3(q1));\n  t1 = t1 * v0.asDiagonal();\n  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());\n  // transformation * translation\n  t0.translate(v0);\n  t1 = t1 * Translation3(v0);\n  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());\n  // translation * transformation\n  t0.pretranslate(v0);\n  t1 = Translation3(v0) * t1;\n  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());\n\n  // transform * quaternion\n  t0.rotate(q1);\n  t1 = t1 * q1;\n  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());\n\n  // translation * quaternion\n  t0.translate(v1).rotate(q1);\n  t1 = t1 * (Translation3(v1) * q1);\n  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());\n\n  // aligned scaling * quaternion\n  t0.scale(v1).rotate(q1);\n  t1 = t1 * (AlignedScaling3(v1) * q1);\n  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());\n\n  // quaternion * transform\n  t0.prerotate(q1);\n  t1 = q1 * t1;\n  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());\n\n  // quaternion * translation\n  t0.rotate(q1).translate(v1);\n  t1 = t1 * (q1 * Translation3(v1));\n  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());\n\n  // quaternion * aligned scaling\n  t0.rotate(q1).scale(v1);\n  t1 = t1 * (q1 * AlignedScaling3(v1));\n  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());\n\n  // test transform inversion\n  t0.setIdentity();\n  t0.translate(v0);\n  do {\n    t0.linear().setRandom();\n  } while(t0.linear().jacobiSvd().singularValues()(2)<test_precision<Scalar>());\n  Matrix4 t044 = Matrix4::Zero();\n  t044(3,3) = 1;\n  t044.block(0,0,t0.matrix().rows(),4) = t0.matrix();\n  VERIFY_IS_APPROX(t0.inverse(Affine).matrix(), t044.inverse().block(0,0,t0.matrix().rows(),4));\n  t0.setIdentity();\n  t0.translate(v0).rotate(q1);\n  t044 = Matrix4::Zero();\n  t044(3,3) = 1;\n  t044.block(0,0,t0.matrix().rows(),4) = t0.matrix();\n  VERIFY_IS_APPROX(t0.inverse(Isometry).matrix(), t044.inverse().block(0,0,t0.matrix().rows(),4));\n\n  Matrix3 mat_rotation, mat_scaling;\n  t0.setIdentity();\n  t0.translate(v0).rotate(q1).scale(v1);\n  t0.computeRotationScaling(&mat_rotation, &mat_scaling);\n  VERIFY_IS_APPROX(t0.linear(), mat_rotation * mat_scaling);\n  VERIFY_IS_APPROX(mat_rotation*mat_rotation.adjoint(), Matrix3::Identity());\n  VERIFY_IS_APPROX(mat_rotation.determinant(), Scalar(1));\n  t0.computeScalingRotation(&mat_scaling, &mat_rotation);\n  VERIFY_IS_APPROX(t0.linear(), mat_scaling * mat_rotation);\n  VERIFY_IS_APPROX(mat_rotation*mat_rotation.adjoint(), Matrix3::Identity());\n  VERIFY_IS_APPROX(mat_rotation.determinant(), Scalar(1));\n\n  // test casting\n  Transform<float,3,Mode> t1f = t1.template cast<float>();\n  VERIFY_IS_APPROX(t1f.template cast<Scalar>(),t1);\n  Transform<double,3,Mode> t1d = t1.template cast<double>();\n  VERIFY_IS_APPROX(t1d.template cast<Scalar>(),t1);\n\n  Translation3 tr1(v0);\n  Translation<float,3> tr1f = tr1.template cast<float>();\n  VERIFY_IS_APPROX(tr1f.template cast<Scalar>(),tr1);\n  Translation<double,3> tr1d = tr1.template cast<double>();\n  VERIFY_IS_APPROX(tr1d.template cast<Scalar>(),tr1);\n\n  AngleAxis<float> aa1f = aa1.template cast<float>();\n  VERIFY_IS_APPROX(aa1f.template cast<Scalar>(),aa1);\n  AngleAxis<double> aa1d = aa1.template cast<double>();\n  VERIFY_IS_APPROX(aa1d.template cast<Scalar>(),aa1);\n\n  Rotation2D<Scalar> r2d1(internal::random<Scalar>());\n  Rotation2D<float> r2d1f = r2d1.template cast<float>();\n  VERIFY_IS_APPROX(r2d1f.template cast<Scalar>(),r2d1);\n  Rotation2D<double> r2d1d = r2d1.template cast<double>();\n  VERIFY_IS_APPROX(r2d1d.template cast<Scalar>(),r2d1);\n  \n  for(int k=0; k<100; ++k)\n  {\n    Scalar angle = internal::random<Scalar>(-100,100);\n    Rotation2D<Scalar> rot2(angle);\n    VERIFY( rot2.smallestPositiveAngle() >= 0 );\n    VERIFY( rot2.smallestPositiveAngle() <= Scalar(2)*Scalar(EIGEN_PI) );\n    VERIFY_IS_APPROX( angleToVec(rot2.smallestPositiveAngle()), angleToVec(rot2.angle()) );\n    \n    VERIFY( rot2.smallestAngle() >= -Scalar(EIGEN_PI) );\n    VERIFY( rot2.smallestAngle() <=  Scalar(EIGEN_PI) );\n    VERIFY_IS_APPROX( angleToVec(rot2.smallestAngle()), angleToVec(rot2.angle()) );\n\n    Matrix<Scalar,2,2> rot2_as_mat(rot2);\n    Rotation2D<Scalar> rot3(rot2_as_mat);\n    VERIFY_IS_APPROX( angleToVec(rot2.smallestAngle()),  angleToVec(rot3.angle()) );\n  }\n\n  s0 = internal::random<Scalar>(-100,100);\n  s1 = internal::random<Scalar>(-100,100);\n  Rotation2D<Scalar> R0(s0), R1(s1);\n  \n  t20 = Translation2(v20) * (R0 * Eigen::Scaling(s0));\n  t21 = Translation2(v20) * R0 * Eigen::Scaling(s0);\n  VERIFY_IS_APPROX(t20,t21);\n  \n  t20 = Translation2(v20) * (R0 * R0.inverse() * Eigen::Scaling(s0));\n  t21 = Translation2(v20) * Eigen::Scaling(s0);\n  VERIFY_IS_APPROX(t20,t21);\n  \n  VERIFY_IS_APPROX(s0, (R0.slerp(0, R1)).angle());\n  VERIFY_IS_APPROX( angleToVec(R1.smallestPositiveAngle()), angleToVec((R0.slerp(1, R1)).smallestPositiveAngle()) );\n  VERIFY_IS_APPROX(R0.smallestPositiveAngle(), (R0.slerp(0.5, R0)).smallestPositiveAngle());\n\n  if(std::cos(s0)>0)\n    VERIFY_IS_MUCH_SMALLER_THAN((R0.slerp(0.5, R0.inverse())).smallestAngle(), Scalar(1));\n  else\n    VERIFY_IS_APPROX(Scalar(EIGEN_PI), (R0.slerp(0.5, R0.inverse())).smallestPositiveAngle());\n  \n  // Check path length\n  Scalar l = 0;\n  int path_steps = 100;\n  for(int k=0; k<path_steps; ++k)\n  {\n    Scalar a1 = R0.slerp(Scalar(k)/Scalar(path_steps), R1).angle();\n    Scalar a2 = R0.slerp(Scalar(k+1)/Scalar(path_steps), R1).angle();\n    l += std::abs(a2-a1);\n  }\n  VERIFY(l<=Scalar(EIGEN_PI)*(Scalar(1)+NumTraits<Scalar>::epsilon()*Scalar(path_steps/2)));\n  \n  // check basic features\n  {\n    Rotation2D<Scalar> r1;           // default ctor\n    r1 = Rotation2D<Scalar>(s0);     // copy assignment\n    VERIFY_IS_APPROX(r1.angle(),s0);\n    Rotation2D<Scalar> r2(r1);       // copy ctor\n    VERIFY_IS_APPROX(r2.angle(),s0);\n  }\n\n  {\n    Transform3 t32(Matrix4::Random()), t33, t34;\n    t34 = t33 = t32;\n    t32.scale(v0);\n    t33*=AlignedScaling3(v0);\n    VERIFY_IS_APPROX(t32.matrix(), t33.matrix());\n    t33 = t34 * AlignedScaling3(v0);\n    VERIFY_IS_APPROX(t32.matrix(), t33.matrix());\n  }\n\n}\n\ntemplate<typename A1, typename A2, typename P, typename Q, typename V, typename H>\nvoid transform_associativity_left(const A1& a1, const A2& a2, const P& p, const Q& q, const V& v, const H& h)\n{\n  VERIFY_IS_APPROX( q*(a1*v), (q*a1)*v );\n  VERIFY_IS_APPROX( q*(a2*v), (q*a2)*v );\n  VERIFY_IS_APPROX( q*(p*h).hnormalized(),  ((q*p)*h).hnormalized() );\n}\n\ntemplate<typename A1, typename A2, typename P, typename Q, typename V, typename H>\nvoid transform_associativity2(const A1& a1, const A2& a2, const P& p, const Q& q, const V& v, const H& h)\n{\n  VERIFY_IS_APPROX( a1*(q*v), (a1*q)*v );\n  VERIFY_IS_APPROX( a2*(q*v), (a2*q)*v );\n  VERIFY_IS_APPROX( p *(q*v).homogeneous(), (p *q)*v.homogeneous() );\n\n  transform_associativity_left(a1, a2,p, q, v, h);\n}\n\ntemplate<typename Scalar, int Dim, int Options,typename RotationType>\nvoid transform_associativity(const RotationType& R)\n{\n  typedef Matrix<Scalar,Dim,1> VectorType;\n  typedef Matrix<Scalar,Dim+1,1> HVectorType;\n  typedef Matrix<Scalar,Dim,Dim> LinearType;\n  typedef Matrix<Scalar,Dim+1,Dim+1> MatrixType;\n  typedef Transform<Scalar,Dim,AffineCompact,Options> AffineCompactType;\n  typedef Transform<Scalar,Dim,Affine,Options> AffineType;\n  typedef Transform<Scalar,Dim,Projective,Options> ProjectiveType;\n  typedef DiagonalMatrix<Scalar,Dim> ScalingType;\n  typedef Translation<Scalar,Dim> TranslationType;\n\n  AffineCompactType A1c; A1c.matrix().setRandom();\n  AffineCompactType A2c; A2c.matrix().setRandom();\n  AffineType A1(A1c);\n  AffineType A2(A2c);\n  ProjectiveType P1; P1.matrix().setRandom();\n  VectorType v1 = VectorType::Random();\n  VectorType v2 = VectorType::Random();\n  HVectorType h1 = HVectorType::Random();\n  Scalar s1 = internal::random<Scalar>();\n  LinearType L = LinearType::Random();\n  MatrixType M = MatrixType::Random();\n\n  CALL_SUBTEST( transform_associativity2(A1c, A1, P1, A2, v2, h1) );\n  CALL_SUBTEST( transform_associativity2(A1c, A1, P1, A2c, v2, h1) );\n  CALL_SUBTEST( transform_associativity2(A1c, A1, P1, v1.asDiagonal(), v2, h1) );\n  CALL_SUBTEST( transform_associativity2(A1c, A1, P1, ScalingType(v1), v2, h1) );\n  CALL_SUBTEST( transform_associativity2(A1c, A1, P1, Scaling(v1), v2, h1) );\n  CALL_SUBTEST( transform_associativity2(A1c, A1, P1, Scaling(s1), v2, h1) );\n  CALL_SUBTEST( transform_associativity2(A1c, A1, P1, TranslationType(v1), v2, h1) );\n  CALL_SUBTEST( transform_associativity_left(A1c, A1, P1, L, v2, h1) );\n  CALL_SUBTEST( transform_associativity2(A1c, A1, P1, R, v2, h1) );\n\n  VERIFY_IS_APPROX( A1*(M*h1), (A1*M)*h1 );\n  VERIFY_IS_APPROX( A1c*(M*h1), (A1c*M)*h1 );\n  VERIFY_IS_APPROX( P1*(M*h1), (P1*M)*h1 );\n\n  VERIFY_IS_APPROX( M*(A1*h1), (M*A1)*h1 );\n  VERIFY_IS_APPROX( M*(A1c*h1), (M*A1c)*h1 );\n  VERIFY_IS_APPROX( M*(P1*h1),  ((M*P1)*h1) );\n}\n\ntemplate<typename Scalar> void transform_alignment()\n{\n  typedef Transform<Scalar,3,Projective,AutoAlign> Projective3a;\n  typedef Transform<Scalar,3,Projective,DontAlign> Projective3u;\n\n  EIGEN_ALIGN_MAX Scalar array1[16];\n  EIGEN_ALIGN_MAX Scalar array2[16];\n  EIGEN_ALIGN_MAX Scalar array3[16+1];\n  Scalar* array3u = array3+1;\n\n  Projective3a *p1 = ::new(reinterpret_cast<void*>(array1)) Projective3a;\n  Projective3u *p2 = ::new(reinterpret_cast<void*>(array2)) Projective3u;\n  Projective3u *p3 = ::new(reinterpret_cast<void*>(array3u)) Projective3u;\n  \n  p1->matrix().setRandom();\n  *p2 = *p1;\n  *p3 = *p1;\n\n  VERIFY_IS_APPROX(p1->matrix(), p2->matrix());\n  VERIFY_IS_APPROX(p1->matrix(), p3->matrix());\n  \n  VERIFY_IS_APPROX( (*p1) * (*p1), (*p2)*(*p3));\n  \n  #if defined(EIGEN_VECTORIZE) && EIGEN_MAX_STATIC_ALIGN_BYTES>0\n  if(internal::packet_traits<Scalar>::Vectorizable)\n    VERIFY_RAISES_ASSERT((::new(reinterpret_cast<void*>(array3u)) Projective3a));\n  #endif\n}\n\ntemplate<typename Scalar, int Dim, int Options> void transform_products()\n{\n  typedef Matrix<Scalar,Dim+1,Dim+1> Mat;\n  typedef Transform<Scalar,Dim,Projective,Options> Proj;\n  typedef Transform<Scalar,Dim,Affine,Options> Aff;\n  typedef Transform<Scalar,Dim,AffineCompact,Options> AffC;\n\n  Proj p; p.matrix().setRandom();\n  Aff a; a.linear().setRandom(); a.translation().setRandom();\n  AffC ac = a;\n\n  Mat p_m(p.matrix()), a_m(a.matrix());\n\n  VERIFY_IS_APPROX((p*p).matrix(), p_m*p_m);\n  VERIFY_IS_APPROX((a*a).matrix(), a_m*a_m);\n  VERIFY_IS_APPROX((p*a).matrix(), p_m*a_m);\n  VERIFY_IS_APPROX((a*p).matrix(), a_m*p_m);\n  VERIFY_IS_APPROX((ac*a).matrix(), a_m*a_m);\n  VERIFY_IS_APPROX((a*ac).matrix(), a_m*a_m);\n  VERIFY_IS_APPROX((p*ac).matrix(), p_m*a_m);\n  VERIFY_IS_APPROX((ac*p).matrix(), a_m*p_m);\n}\n\nvoid test_geo_transformations()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1(( transformations<double,Affine,AutoAlign>() ));\n    CALL_SUBTEST_1(( non_projective_only<double,Affine,AutoAlign>() ));\n    \n    CALL_SUBTEST_2(( transformations<float,AffineCompact,AutoAlign>() ));\n    CALL_SUBTEST_2(( non_projective_only<float,AffineCompact,AutoAlign>() ));\n    CALL_SUBTEST_2(( transform_alignment<float>() ));\n    \n    CALL_SUBTEST_3(( transformations<double,Projective,AutoAlign>() ));\n    CALL_SUBTEST_3(( transformations<double,Projective,DontAlign>() ));\n    CALL_SUBTEST_3(( transform_alignment<double>() ));\n    \n    CALL_SUBTEST_4(( transformations<float,Affine,RowMajor|AutoAlign>() ));\n    CALL_SUBTEST_4(( non_projective_only<float,Affine,RowMajor>() ));\n    \n    CALL_SUBTEST_5(( transformations<double,AffineCompact,RowMajor|AutoAlign>() ));\n    CALL_SUBTEST_5(( non_projective_only<double,AffineCompact,RowMajor>() ));\n\n    CALL_SUBTEST_6(( transformations<double,Projective,RowMajor|AutoAlign>() ));\n    CALL_SUBTEST_6(( transformations<double,Projective,RowMajor|DontAlign>() ));\n\n\n    CALL_SUBTEST_7(( transform_products<double,3,RowMajor|AutoAlign>() ));\n    CALL_SUBTEST_7(( transform_products<float,2,AutoAlign>() ));\n\n    CALL_SUBTEST_8(( transform_associativity<double,2,ColMajor>(Rotation2D<double>(internal::random<double>()*double(EIGEN_PI))) ));\n    CALL_SUBTEST_8(( transform_associativity<double,3,ColMajor>(Quaterniond::UnitRandom()) ));\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/half_float.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include <sstream>\n\n#include \"main.h\"\n\n#include <Eigen/src/Core/arch/CUDA/Half.h>\n\n// Make sure it's possible to forward declare Eigen::half\nnamespace Eigen {\nstruct half;\n}\n\nusing Eigen::half;\n\nvoid test_conversion()\n{\n  using Eigen::half_impl::__half;\n\n  // Conversion from float.\n  VERIFY_IS_EQUAL(half(1.0f).x, 0x3c00);\n  VERIFY_IS_EQUAL(half(0.5f).x, 0x3800);\n  VERIFY_IS_EQUAL(half(0.33333f).x, 0x3555);\n  VERIFY_IS_EQUAL(half(0.0f).x, 0x0000);\n  VERIFY_IS_EQUAL(half(-0.0f).x, 0x8000);\n  VERIFY_IS_EQUAL(half(65504.0f).x, 0x7bff);\n  VERIFY_IS_EQUAL(half(65536.0f).x, 0x7c00);  // Becomes infinity.\n\n  // Denormals.\n  VERIFY_IS_EQUAL(half(-5.96046e-08f).x, 0x8001);\n  VERIFY_IS_EQUAL(half(5.96046e-08f).x, 0x0001);\n  VERIFY_IS_EQUAL(half(1.19209e-07f).x, 0x0002);\n\n  // Verify round-to-nearest-even behavior.\n  float val1 = float(half(__half(0x3c00)));\n  float val2 = float(half(__half(0x3c01)));\n  float val3 = float(half(__half(0x3c02)));\n  VERIFY_IS_EQUAL(half(0.5f * (val1 + val2)).x, 0x3c00);\n  VERIFY_IS_EQUAL(half(0.5f * (val2 + val3)).x, 0x3c02);\n\n  // Conversion from int.\n  VERIFY_IS_EQUAL(half(-1).x, 0xbc00);\n  VERIFY_IS_EQUAL(half(0).x, 0x0000);\n  VERIFY_IS_EQUAL(half(1).x, 0x3c00);\n  VERIFY_IS_EQUAL(half(2).x, 0x4000);\n  VERIFY_IS_EQUAL(half(3).x, 0x4200);\n\n  // Conversion from bool.\n  VERIFY_IS_EQUAL(half(false).x, 0x0000);\n  VERIFY_IS_EQUAL(half(true).x, 0x3c00);\n\n  // Conversion to float.\n  VERIFY_IS_EQUAL(float(half(__half(0x0000))), 0.0f);\n  VERIFY_IS_EQUAL(float(half(__half(0x3c00))), 1.0f);\n\n  // Denormals.\n  VERIFY_IS_APPROX(float(half(__half(0x8001))), -5.96046e-08f);\n  VERIFY_IS_APPROX(float(half(__half(0x0001))), 5.96046e-08f);\n  VERIFY_IS_APPROX(float(half(__half(0x0002))), 1.19209e-07f);\n\n  // NaNs and infinities.\n  VERIFY(!(numext::isinf)(float(half(65504.0f))));  // Largest finite number.\n  VERIFY(!(numext::isnan)(float(half(0.0f))));\n  VERIFY((numext::isinf)(float(half(__half(0xfc00)))));\n  VERIFY((numext::isnan)(float(half(__half(0xfc01)))));\n  VERIFY((numext::isinf)(float(half(__half(0x7c00)))));\n  VERIFY((numext::isnan)(float(half(__half(0x7c01)))));\n\n#if !EIGEN_COMP_MSVC\n  // Visual Studio errors out on divisions by 0\n  VERIFY((numext::isnan)(float(half(0.0 / 0.0))));\n  VERIFY((numext::isinf)(float(half(1.0 / 0.0))));\n  VERIFY((numext::isinf)(float(half(-1.0 / 0.0))));\n#endif\n\n  // Exactly same checks as above, just directly on the half representation.\n  VERIFY(!(numext::isinf)(half(__half(0x7bff))));\n  VERIFY(!(numext::isnan)(half(__half(0x0000))));\n  VERIFY((numext::isinf)(half(__half(0xfc00))));\n  VERIFY((numext::isnan)(half(__half(0xfc01))));\n  VERIFY((numext::isinf)(half(__half(0x7c00))));\n  VERIFY((numext::isnan)(half(__half(0x7c01))));\n\n#if !EIGEN_COMP_MSVC\n  // Visual Studio errors out on divisions by 0\n  VERIFY((numext::isnan)(half(0.0 / 0.0)));\n  VERIFY((numext::isinf)(half(1.0 / 0.0)));\n  VERIFY((numext::isinf)(half(-1.0 / 0.0)));\n#endif\n}\n\nvoid test_numtraits()\n{\n  std::cout << \"epsilon       = \" << NumTraits<half>::epsilon() << \"  (0x\" << std::hex << NumTraits<half>::epsilon().x << \")\" << std::endl;\n  std::cout << \"highest       = \" << NumTraits<half>::highest() << \"  (0x\" << std::hex << NumTraits<half>::highest().x << \")\" << std::endl;\n  std::cout << \"lowest        = \" << NumTraits<half>::lowest() << \"  (0x\" << std::hex << NumTraits<half>::lowest().x << \")\" << std::endl;\n  std::cout << \"min           = \" << (std::numeric_limits<half>::min)() << \"  (0x\" << std::hex << half((std::numeric_limits<half>::min)()).x << \")\" << std::endl;\n  std::cout << \"denorm min    = \" << (std::numeric_limits<half>::denorm_min)() << \"  (0x\" << std::hex << half((std::numeric_limits<half>::denorm_min)()).x << \")\" << std::endl;\n  std::cout << \"infinity      = \" << NumTraits<half>::infinity() << \"  (0x\" << std::hex << NumTraits<half>::infinity().x << \")\" << std::endl;\n  std::cout << \"quiet nan     = \" << NumTraits<half>::quiet_NaN() << \"  (0x\" << std::hex << NumTraits<half>::quiet_NaN().x << \")\" << std::endl;\n  std::cout << \"signaling nan = \" << std::numeric_limits<half>::signaling_NaN() << \"  (0x\" << std::hex << std::numeric_limits<half>::signaling_NaN().x << \")\" << std::endl;\n\n  VERIFY(NumTraits<half>::IsSigned);\n\n  VERIFY_IS_EQUAL( std::numeric_limits<half>::infinity().x, half(std::numeric_limits<float>::infinity()).x );\n  VERIFY_IS_EQUAL( std::numeric_limits<half>::quiet_NaN().x, half(std::numeric_limits<float>::quiet_NaN()).x );\n  VERIFY_IS_EQUAL( std::numeric_limits<half>::signaling_NaN().x, half(std::numeric_limits<float>::signaling_NaN()).x );\n  VERIFY( (std::numeric_limits<half>::min)() > half(0.f) );\n  VERIFY( (std::numeric_limits<half>::denorm_min)() > half(0.f) );\n  VERIFY( (std::numeric_limits<half>::min)()/half(2) > half(0.f) );\n  VERIFY_IS_EQUAL( (std::numeric_limits<half>::denorm_min)()/half(2), half(0.f) );\n}\n\nvoid test_arithmetic()\n{\n  VERIFY_IS_EQUAL(float(half(2) + half(2)), 4);\n  VERIFY_IS_EQUAL(float(half(2) + half(-2)), 0);\n  VERIFY_IS_APPROX(float(half(0.33333f) + half(0.66667f)), 1.0f);\n  VERIFY_IS_EQUAL(float(half(2.0f) * half(-5.5f)), -11.0f);\n  VERIFY_IS_APPROX(float(half(1.0f) / half(3.0f)), 0.33333f);\n  VERIFY_IS_EQUAL(float(-half(4096.0f)), -4096.0f);\n  VERIFY_IS_EQUAL(float(-half(-4096.0f)), 4096.0f);\n}\n\nvoid test_comparison()\n{\n  VERIFY(half(1.0f) > half(0.5f));\n  VERIFY(half(0.5f) < half(1.0f));\n  VERIFY(!(half(1.0f) < half(0.5f)));\n  VERIFY(!(half(0.5f) > half(1.0f)));\n\n  VERIFY(!(half(4.0f) > half(4.0f)));\n  VERIFY(!(half(4.0f) < half(4.0f)));\n\n  VERIFY(!(half(0.0f) < half(-0.0f)));\n  VERIFY(!(half(-0.0f) < half(0.0f)));\n  VERIFY(!(half(0.0f) > half(-0.0f)));\n  VERIFY(!(half(-0.0f) > half(0.0f)));\n\n  VERIFY(half(0.2f) > half(-1.0f));\n  VERIFY(half(-1.0f) < half(0.2f));\n  VERIFY(half(-16.0f) < half(-15.0f));\n\n  VERIFY(half(1.0f) == half(1.0f));\n  VERIFY(half(1.0f) != half(2.0f));\n\n  // Comparisons with NaNs and infinities.\n#if !EIGEN_COMP_MSVC\n  // Visual Studio errors out on divisions by 0\n  VERIFY(!(half(0.0 / 0.0) == half(0.0 / 0.0)));\n  VERIFY(half(0.0 / 0.0) != half(0.0 / 0.0));\n\n  VERIFY(!(half(1.0) == half(0.0 / 0.0)));\n  VERIFY(!(half(1.0) < half(0.0 / 0.0)));\n  VERIFY(!(half(1.0) > half(0.0 / 0.0)));\n  VERIFY(half(1.0) != half(0.0 / 0.0));\n\n  VERIFY(half(1.0) < half(1.0 / 0.0));\n  VERIFY(half(1.0) > half(-1.0 / 0.0));\n#endif\n}\n\nvoid test_basic_functions()\n{\n  VERIFY_IS_EQUAL(float(numext::abs(half(3.5f))), 3.5f);\n  VERIFY_IS_EQUAL(float(abs(half(3.5f))), 3.5f);\n  VERIFY_IS_EQUAL(float(numext::abs(half(-3.5f))), 3.5f);\n  VERIFY_IS_EQUAL(float(abs(half(-3.5f))), 3.5f);\n\n  VERIFY_IS_EQUAL(float(numext::floor(half(3.5f))), 3.0f);\n  VERIFY_IS_EQUAL(float(floor(half(3.5f))), 3.0f);\n  VERIFY_IS_EQUAL(float(numext::floor(half(-3.5f))), -4.0f);\n  VERIFY_IS_EQUAL(float(floor(half(-3.5f))), -4.0f);\n\n  VERIFY_IS_EQUAL(float(numext::ceil(half(3.5f))), 4.0f);\n  VERIFY_IS_EQUAL(float(ceil(half(3.5f))), 4.0f);\n  VERIFY_IS_EQUAL(float(numext::ceil(half(-3.5f))), -3.0f);\n  VERIFY_IS_EQUAL(float(ceil(half(-3.5f))), -3.0f);\n\n  VERIFY_IS_APPROX(float(numext::sqrt(half(0.0f))), 0.0f);\n  VERIFY_IS_APPROX(float(sqrt(half(0.0f))), 0.0f);\n  VERIFY_IS_APPROX(float(numext::sqrt(half(4.0f))), 2.0f);\n  VERIFY_IS_APPROX(float(sqrt(half(4.0f))), 2.0f);\n\n  VERIFY_IS_APPROX(float(numext::pow(half(0.0f), half(1.0f))), 0.0f);\n  VERIFY_IS_APPROX(float(pow(half(0.0f), half(1.0f))), 0.0f);\n  VERIFY_IS_APPROX(float(numext::pow(half(2.0f), half(2.0f))), 4.0f);\n  VERIFY_IS_APPROX(float(pow(half(2.0f), half(2.0f))), 4.0f);\n\n  VERIFY_IS_EQUAL(float(numext::exp(half(0.0f))), 1.0f);\n  VERIFY_IS_EQUAL(float(exp(half(0.0f))), 1.0f);\n  VERIFY_IS_APPROX(float(numext::exp(half(EIGEN_PI))), 20.f + float(EIGEN_PI));\n  VERIFY_IS_APPROX(float(exp(half(EIGEN_PI))), 20.f + float(EIGEN_PI));\n\n  VERIFY_IS_EQUAL(float(numext::log(half(1.0f))), 0.0f);\n  VERIFY_IS_EQUAL(float(log(half(1.0f))), 0.0f);\n  VERIFY_IS_APPROX(float(numext::log(half(10.0f))), 2.30273f);\n  VERIFY_IS_APPROX(float(log(half(10.0f))), 2.30273f);\n\n  VERIFY_IS_EQUAL(float(numext::log1p(half(0.0f))), 0.0f);\n  VERIFY_IS_EQUAL(float(log1p(half(0.0f))), 0.0f);\n  VERIFY_IS_APPROX(float(numext::log1p(half(10.0f))), 2.3978953f);\n  VERIFY_IS_APPROX(float(log1p(half(10.0f))), 2.3978953f);\n}\n\nvoid test_trigonometric_functions()\n{\n  VERIFY_IS_APPROX(numext::cos(half(0.0f)), half(cosf(0.0f)));\n  VERIFY_IS_APPROX(cos(half(0.0f)), half(cosf(0.0f)));\n  VERIFY_IS_APPROX(numext::cos(half(EIGEN_PI)), half(cosf(EIGEN_PI)));\n  //VERIFY_IS_APPROX(numext::cos(half(EIGEN_PI/2)), half(cosf(EIGEN_PI/2)));\n  //VERIFY_IS_APPROX(numext::cos(half(3*EIGEN_PI/2)), half(cosf(3*EIGEN_PI/2)));\n  VERIFY_IS_APPROX(numext::cos(half(3.5f)), half(cosf(3.5f)));\n\n  VERIFY_IS_APPROX(numext::sin(half(0.0f)), half(sinf(0.0f)));\n  VERIFY_IS_APPROX(sin(half(0.0f)), half(sinf(0.0f)));\n  //  VERIFY_IS_APPROX(numext::sin(half(EIGEN_PI)), half(sinf(EIGEN_PI)));\n  VERIFY_IS_APPROX(numext::sin(half(EIGEN_PI/2)), half(sinf(EIGEN_PI/2)));\n  VERIFY_IS_APPROX(numext::sin(half(3*EIGEN_PI/2)), half(sinf(3*EIGEN_PI/2)));\n  VERIFY_IS_APPROX(numext::sin(half(3.5f)), half(sinf(3.5f)));\n\n  VERIFY_IS_APPROX(numext::tan(half(0.0f)), half(tanf(0.0f)));\n  VERIFY_IS_APPROX(tan(half(0.0f)), half(tanf(0.0f)));\n  //  VERIFY_IS_APPROX(numext::tan(half(EIGEN_PI)), half(tanf(EIGEN_PI)));\n  //  VERIFY_IS_APPROX(numext::tan(half(EIGEN_PI/2)), half(tanf(EIGEN_PI/2)));\n  //VERIFY_IS_APPROX(numext::tan(half(3*EIGEN_PI/2)), half(tanf(3*EIGEN_PI/2)));\n  VERIFY_IS_APPROX(numext::tan(half(3.5f)), half(tanf(3.5f)));\n}\n\nvoid test_array()\n{\n  typedef Array<half,1,Dynamic> ArrayXh;\n  Index size = internal::random<Index>(1,10);\n  Index i = internal::random<Index>(0,size-1);\n  ArrayXh a1 = ArrayXh::Random(size), a2 = ArrayXh::Random(size);\n  VERIFY_IS_APPROX( a1+a1, half(2)*a1 );\n  VERIFY( (a1.abs() >= half(0)).all() );\n  VERIFY_IS_APPROX( (a1*a1).sqrt(), a1.abs() );\n\n  VERIFY( ((a1.min)(a2) <= (a1.max)(a2)).all() );\n  a1(i) = half(-10.);\n  VERIFY_IS_EQUAL( a1.minCoeff(), half(-10.) );\n  a1(i) = half(10.);\n  VERIFY_IS_EQUAL( a1.maxCoeff(), half(10.) );\n\n  std::stringstream ss;\n  ss << a1;\n}\n\nvoid test_half_float()\n{\n  CALL_SUBTEST(test_conversion());\n  CALL_SUBTEST(test_numtraits());\n  CALL_SUBTEST(test_arithmetic());\n  CALL_SUBTEST(test_comparison());\n  CALL_SUBTEST(test_basic_functions());\n  CALL_SUBTEST(test_trigonometric_functions());\n  CALL_SUBTEST(test_array());\n}\n"
  },
  {
    "path": "include/eigen3/test/hessenberg.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <Eigen/Eigenvalues>\n\ntemplate<typename Scalar,int Size> void hessenberg(int size = Size)\n{\n  typedef Matrix<Scalar,Size,Size> MatrixType;\n\n  // Test basic functionality: A = U H U* and H is Hessenberg\n  for(int counter = 0; counter < g_repeat; ++counter) {\n    MatrixType m = MatrixType::Random(size,size);\n    HessenbergDecomposition<MatrixType> hess(m);\n    MatrixType Q = hess.matrixQ();\n    MatrixType H = hess.matrixH();\n    VERIFY_IS_APPROX(m, Q * H * Q.adjoint());\n    for(int row = 2; row < size; ++row) {\n      for(int col = 0; col < row-1; ++col) {\n\tVERIFY(H(row,col) == (typename MatrixType::Scalar)0);\n      }\n    }\n  }\n\n  // Test whether compute() and constructor returns same result\n  MatrixType A = MatrixType::Random(size, size);\n  HessenbergDecomposition<MatrixType> cs1;\n  cs1.compute(A);\n  HessenbergDecomposition<MatrixType> cs2(A);\n  VERIFY_IS_EQUAL(cs1.matrixH().eval(), cs2.matrixH().eval());\n  MatrixType cs1Q = cs1.matrixQ();\n  MatrixType cs2Q = cs2.matrixQ();  \n  VERIFY_IS_EQUAL(cs1Q, cs2Q);\n\n  // Test assertions for when used uninitialized\n  HessenbergDecomposition<MatrixType> hessUninitialized;\n  VERIFY_RAISES_ASSERT( hessUninitialized.matrixH() );\n  VERIFY_RAISES_ASSERT( hessUninitialized.matrixQ() );\n  VERIFY_RAISES_ASSERT( hessUninitialized.householderCoefficients() );\n  VERIFY_RAISES_ASSERT( hessUninitialized.packedMatrix() );\n\n  // TODO: Add tests for packedMatrix() and householderCoefficients()\n}\n\nvoid test_hessenberg()\n{\n  CALL_SUBTEST_1(( hessenberg<std::complex<double>,1>() ));\n  CALL_SUBTEST_2(( hessenberg<std::complex<double>,2>() ));\n  CALL_SUBTEST_3(( hessenberg<std::complex<float>,4>() ));\n  CALL_SUBTEST_4(( hessenberg<float,Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE)) ));\n  CALL_SUBTEST_5(( hessenberg<std::complex<double>,Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE)) ));\n\n  // Test problem size constructors\n  CALL_SUBTEST_6(HessenbergDecomposition<MatrixXf>(10));\n}\n"
  },
  {
    "path": "include/eigen3/test/householder.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <Eigen/QR>\n\ntemplate<typename MatrixType> void householder(const MatrixType& m)\n{\n  typedef typename MatrixType::Index Index;\n  static bool even = true;\n  even = !even;\n  /* this test covers the following files:\n     Householder.h\n  */\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;\n  typedef Matrix<Scalar, internal::decrement_size<MatrixType::RowsAtCompileTime>::ret, 1> EssentialVectorType;\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;\n  typedef Matrix<Scalar, Dynamic, MatrixType::ColsAtCompileTime> HBlockMatrixType;\n  typedef Matrix<Scalar, Dynamic, 1> HCoeffsVectorType;\n\n  typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::RowsAtCompileTime> TMatrixType;\n  \n  Matrix<Scalar, EIGEN_SIZE_MAX(MatrixType::RowsAtCompileTime,MatrixType::ColsAtCompileTime), 1> _tmp((std::max)(rows,cols));\n  Scalar* tmp = &_tmp.coeffRef(0,0);\n\n  Scalar beta;\n  RealScalar alpha;\n  EssentialVectorType essential;\n\n  VectorType v1 = VectorType::Random(rows), v2;\n  v2 = v1;\n  v1.makeHouseholder(essential, beta, alpha);\n  v1.applyHouseholderOnTheLeft(essential,beta,tmp);\n  VERIFY_IS_APPROX(v1.norm(), v2.norm());\n  if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(v1.tail(rows-1).norm(), v1.norm());\n  v1 = VectorType::Random(rows);\n  v2 = v1;\n  v1.applyHouseholderOnTheLeft(essential,beta,tmp);\n  VERIFY_IS_APPROX(v1.norm(), v2.norm());\n\n  MatrixType m1(rows, cols),\n             m2(rows, cols);\n\n  v1 = VectorType::Random(rows);\n  if(even) v1.tail(rows-1).setZero();\n  m1.colwise() = v1;\n  m2 = m1;\n  m1.col(0).makeHouseholder(essential, beta, alpha);\n  m1.applyHouseholderOnTheLeft(essential,beta,tmp);\n  VERIFY_IS_APPROX(m1.norm(), m2.norm());\n  if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(m1.block(1,0,rows-1,cols).norm(), m1.norm());\n  VERIFY_IS_MUCH_SMALLER_THAN(numext::imag(m1(0,0)), numext::real(m1(0,0)));\n  VERIFY_IS_APPROX(numext::real(m1(0,0)), alpha);\n\n  v1 = VectorType::Random(rows);\n  if(even) v1.tail(rows-1).setZero();\n  SquareMatrixType m3(rows,rows), m4(rows,rows);\n  m3.rowwise() = v1.transpose();\n  m4 = m3;\n  m3.row(0).makeHouseholder(essential, beta, alpha);\n  m3.applyHouseholderOnTheRight(essential,beta,tmp);\n  VERIFY_IS_APPROX(m3.norm(), m4.norm());\n  if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(m3.block(0,1,rows,rows-1).norm(), m3.norm());\n  VERIFY_IS_MUCH_SMALLER_THAN(numext::imag(m3(0,0)), numext::real(m3(0,0)));\n  VERIFY_IS_APPROX(numext::real(m3(0,0)), alpha);\n\n  // test householder sequence on the left with a shift\n\n  Index shift = internal::random<Index>(0, std::max<Index>(rows-2,0));\n  Index brows = rows - shift;\n  m1.setRandom(rows, cols);\n  HBlockMatrixType hbm = m1.block(shift,0,brows,cols);\n  HouseholderQR<HBlockMatrixType> qr(hbm);\n  m2 = m1;\n  m2.block(shift,0,brows,cols) = qr.matrixQR();\n  HCoeffsVectorType hc = qr.hCoeffs().conjugate();\n  HouseholderSequence<MatrixType, HCoeffsVectorType> hseq(m2, hc);\n  hseq.setLength(hc.size()).setShift(shift);\n  VERIFY(hseq.length() == hc.size());\n  VERIFY(hseq.shift() == shift);\n  \n  MatrixType m5 = m2;\n  m5.block(shift,0,brows,cols).template triangularView<StrictlyLower>().setZero();\n  VERIFY_IS_APPROX(hseq * m5, m1); // test applying hseq directly\n  m3 = hseq;\n  VERIFY_IS_APPROX(m3 * m5, m1); // test evaluating hseq to a dense matrix, then applying\n  \n  SquareMatrixType hseq_mat = hseq;\n  SquareMatrixType hseq_mat_conj = hseq.conjugate();\n  SquareMatrixType hseq_mat_adj = hseq.adjoint();\n  SquareMatrixType hseq_mat_trans = hseq.transpose();\n  SquareMatrixType m6 = SquareMatrixType::Random(rows, rows);\n  VERIFY_IS_APPROX(hseq_mat.adjoint(),    hseq_mat_adj);\n  VERIFY_IS_APPROX(hseq_mat.conjugate(),  hseq_mat_conj);\n  VERIFY_IS_APPROX(hseq_mat.transpose(),  hseq_mat_trans);\n  VERIFY_IS_APPROX(hseq_mat * m6,             hseq_mat * m6);\n  VERIFY_IS_APPROX(hseq_mat.adjoint() * m6,   hseq_mat_adj * m6);\n  VERIFY_IS_APPROX(hseq_mat.conjugate() * m6, hseq_mat_conj * m6);\n  VERIFY_IS_APPROX(hseq_mat.transpose() * m6, hseq_mat_trans * m6);\n  VERIFY_IS_APPROX(m6 * hseq_mat,             m6 * hseq_mat);\n  VERIFY_IS_APPROX(m6 * hseq_mat.adjoint(),   m6 * hseq_mat_adj);\n  VERIFY_IS_APPROX(m6 * hseq_mat.conjugate(), m6 * hseq_mat_conj);\n  VERIFY_IS_APPROX(m6 * hseq_mat.transpose(), m6 * hseq_mat_trans);\n\n  // test householder sequence on the right with a shift\n\n  TMatrixType tm2 = m2.transpose();\n  HouseholderSequence<TMatrixType, HCoeffsVectorType, OnTheRight> rhseq(tm2, hc);\n  rhseq.setLength(hc.size()).setShift(shift);\n  VERIFY_IS_APPROX(rhseq * m5, m1); // test applying rhseq directly\n  m3 = rhseq;\n  VERIFY_IS_APPROX(m3 * m5, m1); // test evaluating rhseq to a dense matrix, then applying\n}\n\nvoid test_householder()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( householder(Matrix<double,2,2>()) );\n    CALL_SUBTEST_2( householder(Matrix<float,2,3>()) );\n    CALL_SUBTEST_3( householder(Matrix<double,3,5>()) );\n    CALL_SUBTEST_4( householder(Matrix<float,4,4>()) );\n    CALL_SUBTEST_5( householder(MatrixXd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_6( householder(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_7( householder(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_8( householder(Matrix<double,1,1>()) );\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/incomplete_cholesky.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015-2016 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n// #define EIGEN_DONT_VECTORIZE\n// #define EIGEN_MAX_ALIGN_BYTES 0\n#include \"sparse_solver.h\"\n#include <Eigen/IterativeLinearSolvers>\n#include <unsupported/Eigen/IterativeSolvers>\n\ntemplate<typename T, typename I> void test_incomplete_cholesky_T()\n{\n  typedef SparseMatrix<T,0,I> SparseMatrixType;\n  ConjugateGradient<SparseMatrixType, Lower, IncompleteCholesky<T, Lower, AMDOrdering<I> > >        cg_illt_lower_amd;\n  ConjugateGradient<SparseMatrixType, Lower, IncompleteCholesky<T, Lower, NaturalOrdering<I> > >    cg_illt_lower_nat;\n  ConjugateGradient<SparseMatrixType, Upper, IncompleteCholesky<T, Upper, AMDOrdering<I> > >        cg_illt_upper_amd;\n  ConjugateGradient<SparseMatrixType, Upper, IncompleteCholesky<T, Upper, NaturalOrdering<I> > >    cg_illt_upper_nat;\n  ConjugateGradient<SparseMatrixType, Upper|Lower, IncompleteCholesky<T, Lower, AMDOrdering<I> > >  cg_illt_uplo_amd;\n  \n\n  CALL_SUBTEST( check_sparse_spd_solving(cg_illt_lower_amd) );\n  CALL_SUBTEST( check_sparse_spd_solving(cg_illt_lower_nat) );\n  CALL_SUBTEST( check_sparse_spd_solving(cg_illt_upper_amd) );\n  CALL_SUBTEST( check_sparse_spd_solving(cg_illt_upper_nat) );\n  CALL_SUBTEST( check_sparse_spd_solving(cg_illt_uplo_amd) );\n}\n\nvoid test_incomplete_cholesky()\n{\n  CALL_SUBTEST_1(( test_incomplete_cholesky_T<double,int>() ));\n  CALL_SUBTEST_2(( test_incomplete_cholesky_T<std::complex<double>, int>() ));\n  CALL_SUBTEST_3(( test_incomplete_cholesky_T<double,long int>() ));\n\n#ifdef EIGEN_TEST_PART_1\n    // regression for bug 1150\n  for(int N = 1; N<20; ++N)\n  {\n    Eigen::MatrixXd b( N, N );\n    b.setOnes();\n\n    Eigen::SparseMatrix<double> m( N, N );\n    m.reserve(Eigen::VectorXi::Constant(N,4));\n    for( int i = 0; i < N; ++i )\n    {\n        m.insert( i, i ) = 1;\n        m.coeffRef( i, i / 2 ) = 2;\n        m.coeffRef( i, i / 3 ) = 2;\n        m.coeffRef( i, i / 4 ) = 2;\n    }\n\n    Eigen::SparseMatrix<double> A;\n    A = m * m.transpose();\n\n    Eigen::ConjugateGradient<Eigen::SparseMatrix<double>,\n        Eigen::Lower | Eigen::Upper,\n        Eigen::IncompleteCholesky<double> > solver( A );\n    VERIFY(solver.preconditioner().info() == Eigen::Success);\n    VERIFY(solver.info() == Eigen::Success);\n  }\n#endif\n}\n"
  },
  {
    "path": "include/eigen3/test/inplace_decomposition.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <Eigen/LU>\n#include <Eigen/Cholesky>\n#include <Eigen/QR>\n\n// This file test inplace decomposition through Ref<>, as supported by Cholesky, LU, and QR decompositions.\n\ntemplate<typename DecType,typename MatrixType> void inplace(bool square = false, bool SPD = false)\n{\n  typedef typename MatrixType::Scalar Scalar;\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> RhsType;\n  typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> ResType;\n\n  Index rows = MatrixType::RowsAtCompileTime==Dynamic ? internal::random<Index>(2,EIGEN_TEST_MAX_SIZE/2) : Index(MatrixType::RowsAtCompileTime);\n  Index cols = MatrixType::ColsAtCompileTime==Dynamic ? (square?rows:internal::random<Index>(2,rows))    : Index(MatrixType::ColsAtCompileTime);\n\n  MatrixType A = MatrixType::Random(rows,cols);\n  RhsType b = RhsType::Random(rows);\n  ResType x(cols);\n\n  if(SPD)\n  {\n    assert(square);\n    A.topRows(cols) = A.topRows(cols).adjoint() * A.topRows(cols);\n    A.diagonal().array() += 1e-3;\n  }\n\n  MatrixType A0 = A;\n  MatrixType A1 = A;\n\n  DecType dec(A);\n\n  // Check that the content of A has been modified\n  VERIFY_IS_NOT_APPROX( A, A0 );\n\n  // Check that the decomposition is correct:\n  if(rows==cols)\n  {\n    VERIFY_IS_APPROX( A0 * (x = dec.solve(b)), b );\n  }\n  else\n  {\n    VERIFY_IS_APPROX( A0.transpose() * A0 * (x = dec.solve(b)), A0.transpose() * b );\n  }\n\n  // Check that modifying A breaks the current dec:\n  A.setRandom();\n  if(rows==cols)\n  {\n    VERIFY_IS_NOT_APPROX( A0 * (x = dec.solve(b)), b );\n  }\n  else\n  {\n    VERIFY_IS_NOT_APPROX( A0.transpose() * A0 * (x = dec.solve(b)), A0.transpose() * b );\n  }\n\n  // Check that calling compute(A1) does not modify A1:\n  A = A0;\n  dec.compute(A1);\n  VERIFY_IS_EQUAL(A0,A1);\n  VERIFY_IS_NOT_APPROX( A, A0 );\n  if(rows==cols)\n  {\n    VERIFY_IS_APPROX( A0 * (x = dec.solve(b)), b );\n  }\n  else\n  {\n    VERIFY_IS_APPROX( A0.transpose() * A0 * (x = dec.solve(b)), A0.transpose() * b );\n  }\n}\n\n\nvoid test_inplace_decomposition()\n{\n  EIGEN_UNUSED typedef Matrix<double,4,3> Matrix43d;\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1(( inplace<LLT<Ref<MatrixXd> >, MatrixXd>(true,true) ));\n    CALL_SUBTEST_1(( inplace<LLT<Ref<Matrix4d> >, Matrix4d>(true,true) ));\n\n    CALL_SUBTEST_2(( inplace<LDLT<Ref<MatrixXd> >, MatrixXd>(true,true) ));\n    CALL_SUBTEST_2(( inplace<LDLT<Ref<Matrix4d> >, Matrix4d>(true,true) ));\n\n    CALL_SUBTEST_3(( inplace<PartialPivLU<Ref<MatrixXd> >, MatrixXd>(true,false) ));\n    CALL_SUBTEST_3(( inplace<PartialPivLU<Ref<Matrix4d> >, Matrix4d>(true,false) ));\n\n    CALL_SUBTEST_4(( inplace<FullPivLU<Ref<MatrixXd> >, MatrixXd>(true,false) ));\n    CALL_SUBTEST_4(( inplace<FullPivLU<Ref<Matrix4d> >, Matrix4d>(true,false) ));\n\n    CALL_SUBTEST_5(( inplace<HouseholderQR<Ref<MatrixXd> >, MatrixXd>(false,false) ));\n    CALL_SUBTEST_5(( inplace<HouseholderQR<Ref<Matrix43d> >, Matrix43d>(false,false) ));\n\n    CALL_SUBTEST_6(( inplace<ColPivHouseholderQR<Ref<MatrixXd> >, MatrixXd>(false,false) ));\n    CALL_SUBTEST_6(( inplace<ColPivHouseholderQR<Ref<Matrix43d> >, Matrix43d>(false,false) ));\n\n    CALL_SUBTEST_7(( inplace<FullPivHouseholderQR<Ref<MatrixXd> >, MatrixXd>(false,false) ));\n    CALL_SUBTEST_7(( inplace<FullPivHouseholderQR<Ref<Matrix43d> >, Matrix43d>(false,false) ));\n\n    CALL_SUBTEST_8(( inplace<CompleteOrthogonalDecomposition<Ref<MatrixXd> >, MatrixXd>(false,false) ));\n    CALL_SUBTEST_8(( inplace<CompleteOrthogonalDecomposition<Ref<Matrix43d> >, Matrix43d>(false,false) ));\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/integer_types.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define EIGEN_NO_STATIC_ASSERT\n\n#include \"main.h\"\n\n#undef VERIFY_IS_APPROX\n#define VERIFY_IS_APPROX(a, b) VERIFY((a)==(b));\n#undef VERIFY_IS_NOT_APPROX\n#define VERIFY_IS_NOT_APPROX(a, b) VERIFY((a)!=(b));\n\ntemplate<typename MatrixType> void signed_integer_type_tests(const MatrixType& m)\n{\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n\n  enum { is_signed = (Scalar(-1) > Scalar(0)) ? 0 : 1 };\n  VERIFY(is_signed == 1);\n\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  MatrixType m1(rows, cols),\n             m2 = MatrixType::Random(rows, cols),\n             mzero = MatrixType::Zero(rows, cols);\n\n  do {\n    m1 = MatrixType::Random(rows, cols);\n  } while(m1 == mzero || m1 == m2);\n\n  // check linear structure\n\n  Scalar s1;\n  do {\n    s1 = internal::random<Scalar>();\n  } while(s1 == 0);\n\n  VERIFY_IS_EQUAL(-(-m1),                  m1);\n  VERIFY_IS_EQUAL(-m2+m1+m2,               m1);\n  VERIFY_IS_EQUAL((-m1+m2)*s1,             -s1*m1+s1*m2);\n}\n\ntemplate<typename MatrixType> void integer_type_tests(const MatrixType& m)\n{\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n\n  VERIFY(NumTraits<Scalar>::IsInteger);\n  enum { is_signed = (Scalar(-1) > Scalar(0)) ? 0 : 1 };\n  VERIFY(int(NumTraits<Scalar>::IsSigned) == is_signed);\n\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;\n\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  // this test relies a lot on Random.h, and there's not much more that we can do\n  // to test it, hence I consider that we will have tested Random.h\n  MatrixType m1(rows, cols),\n             m2 = MatrixType::Random(rows, cols),\n             m3(rows, cols),\n             mzero = MatrixType::Zero(rows, cols);\n\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;\n  SquareMatrixType identity = SquareMatrixType::Identity(rows, rows),\n                   square = SquareMatrixType::Random(rows, rows);\n  VectorType v1(rows),\n             v2 = VectorType::Random(rows),\n             vzero = VectorType::Zero(rows);\n\n  do {\n    m1 = MatrixType::Random(rows, cols);\n  } while(m1 == mzero || m1 == m2);\n\n  do {\n    v1 = VectorType::Random(rows);\n  } while(v1 == vzero || v1 == v2);\n\n  VERIFY_IS_APPROX(               v1,    v1);\n  VERIFY_IS_NOT_APPROX(           v1,    2*v1);\n  VERIFY_IS_APPROX(               vzero, v1-v1);\n  VERIFY_IS_APPROX(               m1,    m1);\n  VERIFY_IS_NOT_APPROX(           m1,    2*m1);\n  VERIFY_IS_APPROX(               mzero, m1-m1);\n\n  VERIFY_IS_APPROX(m3 = m1,m1);\n  MatrixType m4;\n  VERIFY_IS_APPROX(m4 = m1,m1);\n\n  m3.real() = m1.real();\n  VERIFY_IS_APPROX(static_cast<const MatrixType&>(m3).real(), static_cast<const MatrixType&>(m1).real());\n  VERIFY_IS_APPROX(static_cast<const MatrixType&>(m3).real(), m1.real());\n\n  // check == / != operators\n  VERIFY(m1==m1);\n  VERIFY(m1!=m2);\n  VERIFY(!(m1==m2));\n  VERIFY(!(m1!=m1));\n  m1 = m2;\n  VERIFY(m1==m2);\n  VERIFY(!(m1!=m2));\n\n  // check linear structure\n\n  Scalar s1;\n  do {\n    s1 = internal::random<Scalar>();\n  } while(s1 == 0);\n\n  VERIFY_IS_EQUAL(m1+m1,                   2*m1);\n  VERIFY_IS_EQUAL(m1+m2-m1,                m2);\n  VERIFY_IS_EQUAL(m1*s1,                   s1*m1);\n  VERIFY_IS_EQUAL((m1+m2)*s1,              s1*m1+s1*m2);\n  m3 = m2; m3 += m1;\n  VERIFY_IS_EQUAL(m3,                      m1+m2);\n  m3 = m2; m3 -= m1;\n  VERIFY_IS_EQUAL(m3,                      m2-m1);\n  m3 = m2; m3 *= s1;\n  VERIFY_IS_EQUAL(m3,                      s1*m2);\n\n  // check matrix product.\n\n  VERIFY_IS_APPROX(identity * m1, m1);\n  VERIFY_IS_APPROX(square * (m1 + m2), square * m1 + square * m2);\n  VERIFY_IS_APPROX((m1 + m2).transpose() * square, m1.transpose() * square + m2.transpose() * square);\n  VERIFY_IS_APPROX((m1 * m2.transpose()) * m1, m1 * (m2.transpose() * m1));\n}\n\nvoid test_integer_types()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( integer_type_tests(Matrix<unsigned int, 1, 1>()) );\n    CALL_SUBTEST_1( integer_type_tests(Matrix<unsigned long, 3, 4>()) );\n\n    CALL_SUBTEST_2( integer_type_tests(Matrix<long, 2, 2>()) );\n    CALL_SUBTEST_2( signed_integer_type_tests(Matrix<long, 2, 2>()) );\n\n    CALL_SUBTEST_3( integer_type_tests(Matrix<char, 2, Dynamic>(2, 10)) );\n    CALL_SUBTEST_3( signed_integer_type_tests(Matrix<signed char, 2, Dynamic>(2, 10)) );\n\n    CALL_SUBTEST_4( integer_type_tests(Matrix<unsigned char, 3, 3>()) );\n    CALL_SUBTEST_4( integer_type_tests(Matrix<unsigned char, Dynamic, Dynamic>(20, 20)) );\n\n    CALL_SUBTEST_5( integer_type_tests(Matrix<short, Dynamic, 4>(7, 4)) );\n    CALL_SUBTEST_5( signed_integer_type_tests(Matrix<short, Dynamic, 4>(7, 4)) );\n\n    CALL_SUBTEST_6( integer_type_tests(Matrix<unsigned short, 4, 4>()) );\n\n    CALL_SUBTEST_7( integer_type_tests(Matrix<long long, 11, 13>()) );\n    CALL_SUBTEST_7( signed_integer_type_tests(Matrix<long long, 11, 13>()) );\n\n    CALL_SUBTEST_8( integer_type_tests(Matrix<unsigned long long, Dynamic, 5>(1, 5)) );\n  }\n#ifdef EIGEN_TEST_PART_9\n  VERIFY_IS_EQUAL(internal::scalar_div_cost<int>::value, 8);\n  VERIFY_IS_EQUAL(internal::scalar_div_cost<unsigned int>::value, 8);\n  if(sizeof(long)>sizeof(int)) {\n    VERIFY(int(internal::scalar_div_cost<long>::value) > int(internal::scalar_div_cost<int>::value));\n    VERIFY(int(internal::scalar_div_cost<unsigned long>::value) > int(internal::scalar_div_cost<int>::value));\n  }\n#endif\n}\n"
  },
  {
    "path": "include/eigen3/test/inverse.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <Eigen/LU>\n\ntemplate<typename MatrixType> void inverse(const MatrixType& m)\n{\n  using std::abs;\n  typedef typename MatrixType::Index Index;\n  /* this test covers the following files:\n     Inverse.h\n  */\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  typedef typename MatrixType::Scalar Scalar;\n\n  MatrixType m1(rows, cols),\n             m2(rows, cols),\n             identity = MatrixType::Identity(rows, rows);\n  createRandomPIMatrixOfRank(rows,rows,rows,m1);\n  m2 = m1.inverse();\n  VERIFY_IS_APPROX(m1, m2.inverse() );\n\n  VERIFY_IS_APPROX((Scalar(2)*m2).inverse(), m2.inverse()*Scalar(0.5));\n\n  VERIFY_IS_APPROX(identity, m1.inverse() * m1 );\n  VERIFY_IS_APPROX(identity, m1 * m1.inverse() );\n\n  VERIFY_IS_APPROX(m1, m1.inverse().inverse() );\n\n  // since for the general case we implement separately row-major and col-major, test that\n  VERIFY_IS_APPROX(MatrixType(m1.transpose().inverse()), MatrixType(m1.inverse().transpose()));\n\n#if !defined(EIGEN_TEST_PART_5) && !defined(EIGEN_TEST_PART_6)\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType;\n  \n  //computeInverseAndDetWithCheck tests\n  //First: an invertible matrix\n  bool invertible;\n  Scalar det;\n\n  m2.setZero();\n  m1.computeInverseAndDetWithCheck(m2, det, invertible);\n  VERIFY(invertible);\n  VERIFY_IS_APPROX(identity, m1*m2);\n  VERIFY_IS_APPROX(det, m1.determinant());\n\n  m2.setZero();\n  m1.computeInverseWithCheck(m2, invertible);\n  VERIFY(invertible);\n  VERIFY_IS_APPROX(identity, m1*m2);\n\n  //Second: a rank one matrix (not invertible, except for 1x1 matrices)\n  VectorType v3 = VectorType::Random(rows);\n  MatrixType m3 = v3*v3.transpose(), m4(rows,cols);\n  m3.computeInverseAndDetWithCheck(m4, det, invertible);\n  VERIFY( rows==1 ? invertible : !invertible );\n  VERIFY_IS_MUCH_SMALLER_THAN(abs(det-m3.determinant()), RealScalar(1));\n  m3.computeInverseWithCheck(m4, invertible);\n  VERIFY( rows==1 ? invertible : !invertible );\n  \n  // check with submatrices\n  {\n    Matrix<Scalar, MatrixType::RowsAtCompileTime+1, MatrixType::RowsAtCompileTime+1, MatrixType::Options> m5;\n    m5.setRandom();\n    m5.topLeftCorner(rows,rows) = m1;\n    m2 = m5.template topLeftCorner<MatrixType::RowsAtCompileTime,MatrixType::ColsAtCompileTime>().inverse();\n    VERIFY_IS_APPROX( (m5.template topLeftCorner<MatrixType::RowsAtCompileTime,MatrixType::ColsAtCompileTime>()), m2.inverse() );\n  }\n#endif\n\n  // check in-place inversion\n  if(MatrixType::RowsAtCompileTime>=2 && MatrixType::RowsAtCompileTime<=4)\n  {\n    // in-place is forbidden\n    VERIFY_RAISES_ASSERT(m1 = m1.inverse());\n  }\n  else\n  {\n    m2 = m1.inverse();\n    m1 = m1.inverse();\n    VERIFY_IS_APPROX(m1,m2);\n  }\n}\n\nvoid test_inverse()\n{\n  int s = 0;\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( inverse(Matrix<double,1,1>()) );\n    CALL_SUBTEST_2( inverse(Matrix2d()) );\n    CALL_SUBTEST_3( inverse(Matrix3f()) );\n    CALL_SUBTEST_4( inverse(Matrix4f()) );\n    CALL_SUBTEST_4( inverse(Matrix<float,4,4,DontAlign>()) );\n    \n    s = internal::random<int>(50,320); \n    CALL_SUBTEST_5( inverse(MatrixXf(s,s)) );\n    TEST_SET_BUT_UNUSED_VARIABLE(s)\n    \n    s = internal::random<int>(25,100);\n    CALL_SUBTEST_6( inverse(MatrixXcd(s,s)) );\n    TEST_SET_BUT_UNUSED_VARIABLE(s)\n    \n    CALL_SUBTEST_7( inverse(Matrix4d()) );\n    CALL_SUBTEST_7( inverse(Matrix<double,4,4,DontAlign>()) );\n\n    CALL_SUBTEST_8( inverse(Matrix4cd()) );\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/is_same_dense.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\nusing internal::is_same_dense;\n\nvoid test_is_same_dense()\n{\n  typedef Matrix<double,Dynamic,Dynamic,ColMajor> ColMatrixXd;\n  ColMatrixXd m1(10,10);\n  Ref<ColMatrixXd> ref_m1(m1);\n  Ref<const ColMatrixXd> const_ref_m1(m1);\n  VERIFY(is_same_dense(m1,m1));\n  VERIFY(is_same_dense(m1,ref_m1));\n  VERIFY(is_same_dense(const_ref_m1,m1));\n  VERIFY(is_same_dense(const_ref_m1,ref_m1));\n  \n  VERIFY(is_same_dense(m1.block(0,0,m1.rows(),m1.cols()),m1));\n  VERIFY(!is_same_dense(m1.row(0),m1.col(0)));\n  \n  Ref<const ColMatrixXd> const_ref_m1_row(m1.row(1));\n  VERIFY(!is_same_dense(m1.row(1),const_ref_m1_row));\n  \n  Ref<const ColMatrixXd> const_ref_m1_col(m1.col(1));\n  VERIFY(is_same_dense(m1.col(1),const_ref_m1_col));\n}\n"
  },
  {
    "path": "include/eigen3/test/jacobi.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <Eigen/SVD>\n\ntemplate<typename MatrixType, typename JacobiScalar>\nvoid jacobi(const MatrixType& m = MatrixType())\n{\n  typedef typename MatrixType::Index Index;\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  enum {\n    RowsAtCompileTime = MatrixType::RowsAtCompileTime,\n    ColsAtCompileTime = MatrixType::ColsAtCompileTime\n  };\n\n  typedef Matrix<JacobiScalar, 2, 1> JacobiVector;\n\n  const MatrixType a(MatrixType::Random(rows, cols));\n\n  JacobiVector v = JacobiVector::Random().normalized();\n  JacobiScalar c = v.x(), s = v.y();\n  JacobiRotation<JacobiScalar> rot(c, s);\n\n  {\n    Index p = internal::random<Index>(0, rows-1);\n    Index q;\n    do {\n      q = internal::random<Index>(0, rows-1);\n    } while (q == p);\n\n    MatrixType b = a;\n    b.applyOnTheLeft(p, q, rot);\n    VERIFY_IS_APPROX(b.row(p), c * a.row(p) + numext::conj(s) * a.row(q));\n    VERIFY_IS_APPROX(b.row(q), -s * a.row(p) + numext::conj(c) * a.row(q));\n  }\n\n  {\n    Index p = internal::random<Index>(0, cols-1);\n    Index q;\n    do {\n      q = internal::random<Index>(0, cols-1);\n    } while (q == p);\n\n    MatrixType b = a;\n    b.applyOnTheRight(p, q, rot);\n    VERIFY_IS_APPROX(b.col(p), c * a.col(p) - s * a.col(q));\n    VERIFY_IS_APPROX(b.col(q), numext::conj(s) * a.col(p) + numext::conj(c) * a.col(q));\n  }\n}\n\nvoid test_jacobi()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1(( jacobi<Matrix3f, float>() ));\n    CALL_SUBTEST_2(( jacobi<Matrix4d, double>() ));\n    CALL_SUBTEST_3(( jacobi<Matrix4cf, float>() ));\n    CALL_SUBTEST_3(( jacobi<Matrix4cf, std::complex<float> >() ));\n\n    int r = internal::random<int>(2, internal::random<int>(1,EIGEN_TEST_MAX_SIZE)/2),\n        c = internal::random<int>(2, internal::random<int>(1,EIGEN_TEST_MAX_SIZE)/2);\n    CALL_SUBTEST_4(( jacobi<MatrixXf, float>(MatrixXf(r,c)) ));\n    CALL_SUBTEST_5(( jacobi<MatrixXcd, double>(MatrixXcd(r,c)) ));\n    CALL_SUBTEST_5(( jacobi<MatrixXcd, std::complex<double> >(MatrixXcd(r,c)) ));\n    // complex<float> is really important to test as it is the only way to cover conjugation issues in certain unaligned paths\n    CALL_SUBTEST_6(( jacobi<MatrixXcf, float>(MatrixXcf(r,c)) ));\n    CALL_SUBTEST_6(( jacobi<MatrixXcf, std::complex<float> >(MatrixXcf(r,c)) ));\n    \n    TEST_SET_BUT_UNUSED_VARIABLE(r);\n    TEST_SET_BUT_UNUSED_VARIABLE(c);\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/jacobisvd.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n// discard stack allocation as that too bypasses malloc\n#define EIGEN_STACK_ALLOCATION_LIMIT 0\n#define EIGEN_RUNTIME_NO_MALLOC\n#include \"main.h\"\n#include <Eigen/SVD>\n\n#define SVD_DEFAULT(M) JacobiSVD<M>\n#define SVD_FOR_MIN_NORM(M) JacobiSVD<M,ColPivHouseholderQRPreconditioner>\n#include \"svd_common.h\"\n\n// Check all variants of JacobiSVD\ntemplate<typename MatrixType>\nvoid jacobisvd(const MatrixType& a = MatrixType(), bool pickrandom = true)\n{\n  MatrixType m = a;\n  if(pickrandom)\n    svd_fill_random(m);\n\n  CALL_SUBTEST(( svd_test_all_computation_options<JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner> >(m, true)  )); // check full only\n  CALL_SUBTEST(( svd_test_all_computation_options<JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>  >(m, false) ));\n  CALL_SUBTEST(( svd_test_all_computation_options<JacobiSVD<MatrixType, HouseholderQRPreconditioner>        >(m, false) ));\n  if(m.rows()==m.cols())\n    CALL_SUBTEST(( svd_test_all_computation_options<JacobiSVD<MatrixType, NoQRPreconditioner>               >(m, false) ));\n}\n\ntemplate<typename MatrixType> void jacobisvd_verify_assert(const MatrixType& m)\n{\n  svd_verify_assert<JacobiSVD<MatrixType> >(m);\n  typedef typename MatrixType::Index Index;\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  enum {\n    ColsAtCompileTime = MatrixType::ColsAtCompileTime\n  };\n\n\n  MatrixType a = MatrixType::Zero(rows, cols);\n  a.setZero();\n\n  if (ColsAtCompileTime == Dynamic)\n  {\n    JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner> svd_fullqr;\n    VERIFY_RAISES_ASSERT(svd_fullqr.compute(a, ComputeFullU|ComputeThinV))\n    VERIFY_RAISES_ASSERT(svd_fullqr.compute(a, ComputeThinU|ComputeThinV))\n    VERIFY_RAISES_ASSERT(svd_fullqr.compute(a, ComputeThinU|ComputeFullV))\n  }\n}\n\ntemplate<typename MatrixType>\nvoid jacobisvd_method()\n{\n  enum { Size = MatrixType::RowsAtCompileTime };\n  typedef typename MatrixType::RealScalar RealScalar;\n  typedef Matrix<RealScalar, Size, 1> RealVecType;\n  MatrixType m = MatrixType::Identity();\n  VERIFY_IS_APPROX(m.jacobiSvd().singularValues(), RealVecType::Ones());\n  VERIFY_RAISES_ASSERT(m.jacobiSvd().matrixU());\n  VERIFY_RAISES_ASSERT(m.jacobiSvd().matrixV());\n  VERIFY_IS_APPROX(m.jacobiSvd(ComputeFullU|ComputeFullV).solve(m), m);\n}\n\nvoid test_jacobisvd()\n{\n  CALL_SUBTEST_3(( jacobisvd_verify_assert(Matrix3f()) ));\n  CALL_SUBTEST_4(( jacobisvd_verify_assert(Matrix4d()) ));\n  CALL_SUBTEST_7(( jacobisvd_verify_assert(MatrixXf(10,12)) ));\n  CALL_SUBTEST_8(( jacobisvd_verify_assert(MatrixXcd(7,5)) ));\n  \n  CALL_SUBTEST_11(svd_all_trivial_2x2(jacobisvd<Matrix2cd>));\n  CALL_SUBTEST_12(svd_all_trivial_2x2(jacobisvd<Matrix2d>));\n\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_3(( jacobisvd<Matrix3f>() ));\n    CALL_SUBTEST_4(( jacobisvd<Matrix4d>() ));\n    CALL_SUBTEST_5(( jacobisvd<Matrix<float,3,5> >() ));\n    CALL_SUBTEST_6(( jacobisvd<Matrix<double,Dynamic,2> >(Matrix<double,Dynamic,2>(10,2)) ));\n\n    int r = internal::random<int>(1, 30),\n        c = internal::random<int>(1, 30);\n    \n    TEST_SET_BUT_UNUSED_VARIABLE(r)\n    TEST_SET_BUT_UNUSED_VARIABLE(c)\n    \n    CALL_SUBTEST_10(( jacobisvd<MatrixXd>(MatrixXd(r,c)) ));\n    CALL_SUBTEST_7(( jacobisvd<MatrixXf>(MatrixXf(r,c)) ));\n    CALL_SUBTEST_8(( jacobisvd<MatrixXcd>(MatrixXcd(r,c)) ));\n    (void) r;\n    (void) c;\n\n    // Test on inf/nan matrix\n    CALL_SUBTEST_7(  (svd_inf_nan<JacobiSVD<MatrixXf>, MatrixXf>()) );\n    CALL_SUBTEST_10( (svd_inf_nan<JacobiSVD<MatrixXd>, MatrixXd>()) );\n\n    // bug1395 test compile-time vectors as input\n    CALL_SUBTEST_13(( jacobisvd_verify_assert(Matrix<double,6,1>()) ));\n    CALL_SUBTEST_13(( jacobisvd_verify_assert(Matrix<double,1,6>()) ));\n    CALL_SUBTEST_13(( jacobisvd_verify_assert(Matrix<double,Dynamic,1>(r)) ));\n    CALL_SUBTEST_13(( jacobisvd_verify_assert(Matrix<double,1,Dynamic>(c)) ));\n  }\n\n  CALL_SUBTEST_7(( jacobisvd<MatrixXf>(MatrixXf(internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/2), internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/2))) ));\n  CALL_SUBTEST_8(( jacobisvd<MatrixXcd>(MatrixXcd(internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/3), internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/3))) ));\n\n  // test matrixbase method\n  CALL_SUBTEST_1(( jacobisvd_method<Matrix2cd>() ));\n  CALL_SUBTEST_3(( jacobisvd_method<Matrix3f>() ));\n\n  // Test problem size constructors\n  CALL_SUBTEST_7( JacobiSVD<MatrixXf>(10,10) );\n\n  // Check that preallocation avoids subsequent mallocs\n  CALL_SUBTEST_9( svd_preallocate<void>() );\n\n  CALL_SUBTEST_2( svd_underoverflow<void>() );\n}\n"
  },
  {
    "path": "include/eigen3/test/linearstructure.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\nstatic bool g_called;\n#define EIGEN_SCALAR_BINARY_OP_PLUGIN { g_called |= (!internal::is_same<LhsScalar,RhsScalar>::value); }\n\n#include \"main.h\"\n\ntemplate<typename MatrixType> void linearStructure(const MatrixType& m)\n{\n  using std::abs;\n  /* this test covers the following files:\n     CwiseUnaryOp.h, CwiseBinaryOp.h, SelfCwiseBinaryOp.h \n  */\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename MatrixType::RealScalar RealScalar;\n\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  // this test relies a lot on Random.h, and there's not much more that we can do\n  // to test it, hence I consider that we will have tested Random.h\n  MatrixType m1 = MatrixType::Random(rows, cols),\n             m2 = MatrixType::Random(rows, cols),\n             m3(rows, cols);\n\n  Scalar s1 = internal::random<Scalar>();\n  while (abs(s1)<RealScalar(1e-3)) s1 = internal::random<Scalar>();\n\n  Index r = internal::random<Index>(0, rows-1),\n        c = internal::random<Index>(0, cols-1);\n\n  VERIFY_IS_APPROX(-(-m1),                  m1);\n  VERIFY_IS_APPROX(m1+m1,                   2*m1);\n  VERIFY_IS_APPROX(m1+m2-m1,                m2);\n  VERIFY_IS_APPROX(-m2+m1+m2,               m1);\n  VERIFY_IS_APPROX(m1*s1,                   s1*m1);\n  VERIFY_IS_APPROX((m1+m2)*s1,              s1*m1+s1*m2);\n  VERIFY_IS_APPROX((-m1+m2)*s1,             -s1*m1+s1*m2);\n  m3 = m2; m3 += m1;\n  VERIFY_IS_APPROX(m3,                      m1+m2);\n  m3 = m2; m3 -= m1;\n  VERIFY_IS_APPROX(m3,                      m2-m1);\n  m3 = m2; m3 *= s1;\n  VERIFY_IS_APPROX(m3,                      s1*m2);\n  if(!NumTraits<Scalar>::IsInteger)\n  {\n    m3 = m2; m3 /= s1;\n    VERIFY_IS_APPROX(m3,                    m2/s1);\n  }\n\n  // again, test operator() to check const-qualification\n  VERIFY_IS_APPROX((-m1)(r,c), -(m1(r,c)));\n  VERIFY_IS_APPROX((m1-m2)(r,c), (m1(r,c))-(m2(r,c)));\n  VERIFY_IS_APPROX((m1+m2)(r,c), (m1(r,c))+(m2(r,c)));\n  VERIFY_IS_APPROX((s1*m1)(r,c), s1*(m1(r,c)));\n  VERIFY_IS_APPROX((m1*s1)(r,c), (m1(r,c))*s1);\n  if(!NumTraits<Scalar>::IsInteger)\n    VERIFY_IS_APPROX((m1/s1)(r,c), (m1(r,c))/s1);\n\n  // use .block to disable vectorization and compare to the vectorized version\n  VERIFY_IS_APPROX(m1+m1.block(0,0,rows,cols), m1+m1);\n  VERIFY_IS_APPROX(m1.cwiseProduct(m1.block(0,0,rows,cols)), m1.cwiseProduct(m1));\n  VERIFY_IS_APPROX(m1 - m1.block(0,0,rows,cols), m1 - m1);\n  VERIFY_IS_APPROX(m1.block(0,0,rows,cols) * s1, m1 * s1);\n}\n\n// Make sure that complex * real and real * complex are properly optimized\ntemplate<typename MatrixType> void real_complex(DenseIndex rows = MatrixType::RowsAtCompileTime, DenseIndex cols = MatrixType::ColsAtCompileTime)\n{\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename MatrixType::RealScalar RealScalar;\n  \n  RealScalar s = internal::random<RealScalar>();\n  MatrixType m1 = MatrixType::Random(rows, cols);\n  \n  g_called = false;\n  VERIFY_IS_APPROX(s*m1, Scalar(s)*m1);\n  VERIFY(g_called && \"real * matrix<complex> not properly optimized\");\n  \n  g_called = false;\n  VERIFY_IS_APPROX(m1*s, m1*Scalar(s));\n  VERIFY(g_called && \"matrix<complex> * real not properly optimized\");\n  \n  g_called = false;\n  VERIFY_IS_APPROX(m1/s, m1/Scalar(s));\n  VERIFY(g_called && \"matrix<complex> / real not properly optimized\");\n\n  g_called = false;\n  VERIFY_IS_APPROX(s+m1.array(), Scalar(s)+m1.array());\n  VERIFY(g_called && \"real + matrix<complex> not properly optimized\");\n\n  g_called = false;\n  VERIFY_IS_APPROX(m1.array()+s, m1.array()+Scalar(s));\n  VERIFY(g_called && \"matrix<complex> + real not properly optimized\");\n\n  g_called = false;\n  VERIFY_IS_APPROX(s-m1.array(), Scalar(s)-m1.array());\n  VERIFY(g_called && \"real - matrix<complex> not properly optimized\");\n\n  g_called = false;\n  VERIFY_IS_APPROX(m1.array()-s, m1.array()-Scalar(s));\n  VERIFY(g_called && \"matrix<complex> - real not properly optimized\");\n}\n\nvoid test_linearstructure()\n{\n  g_called = true;\n  VERIFY(g_called); // avoid `unneeded-internal-declaration` warning.\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( linearStructure(Matrix<float, 1, 1>()) );\n    CALL_SUBTEST_2( linearStructure(Matrix2f()) );\n    CALL_SUBTEST_3( linearStructure(Vector3d()) );\n    CALL_SUBTEST_4( linearStructure(Matrix4d()) );\n    CALL_SUBTEST_5( linearStructure(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2), internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))) );\n    CALL_SUBTEST_6( linearStructure(MatrixXf (internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_7( linearStructure(MatrixXi (internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_8( linearStructure(MatrixXcd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2), internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))) );\n    CALL_SUBTEST_9( linearStructure(ArrayXXf (internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_10( linearStructure(ArrayXXcf (internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    \n    CALL_SUBTEST_11( real_complex<Matrix4cd>() );\n    CALL_SUBTEST_11( real_complex<MatrixXcf>(10,10) );\n    CALL_SUBTEST_11( real_complex<ArrayXXcf>(10,10) );\n  }\n  \n#ifdef EIGEN_TEST_PART_4\n  {\n    // make sure that /=scalar and /scalar do not overflow\n    // rational: 1.0/4.94e-320 overflow, but m/4.94e-320 should not\n    Matrix4d m2, m3;\n    m3 = m2 =  Matrix4d::Random()*1e-20;\n    m2 = m2 / 4.9e-320;\n    VERIFY_IS_APPROX(m2.cwiseQuotient(m2), Matrix4d::Ones());\n    m3 /= 4.9e-320;\n    VERIFY_IS_APPROX(m3.cwiseQuotient(m3), Matrix4d::Ones());\n    \n    \n  }\n#endif\n}\n"
  },
  {
    "path": "include/eigen3/test/lscg.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2011 Gael Guennebaud <g.gael@free.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"sparse_solver.h\"\n#include <Eigen/IterativeLinearSolvers>\n\ntemplate<typename T> void test_lscg_T()\n{\n  LeastSquaresConjugateGradient<SparseMatrix<T> > lscg_colmajor_diag;\n  LeastSquaresConjugateGradient<SparseMatrix<T>, IdentityPreconditioner> lscg_colmajor_I;\n  LeastSquaresConjugateGradient<SparseMatrix<T,RowMajor> > lscg_rowmajor_diag;\n  LeastSquaresConjugateGradient<SparseMatrix<T,RowMajor>, IdentityPreconditioner> lscg_rowmajor_I;\n\n  CALL_SUBTEST( check_sparse_square_solving(lscg_colmajor_diag)  );\n  CALL_SUBTEST( check_sparse_square_solving(lscg_colmajor_I)     );\n  \n  CALL_SUBTEST( check_sparse_leastsquare_solving(lscg_colmajor_diag)  );\n  CALL_SUBTEST( check_sparse_leastsquare_solving(lscg_colmajor_I)     );\n\n  CALL_SUBTEST( check_sparse_square_solving(lscg_rowmajor_diag)  );\n  CALL_SUBTEST( check_sparse_square_solving(lscg_rowmajor_I)     );\n\n  CALL_SUBTEST( check_sparse_leastsquare_solving(lscg_rowmajor_diag)  );\n  CALL_SUBTEST( check_sparse_leastsquare_solving(lscg_rowmajor_I)     );\n}\n\nvoid test_lscg()\n{\n  CALL_SUBTEST_1(test_lscg_T<double>());\n  CALL_SUBTEST_2(test_lscg_T<std::complex<double> >());\n}\n"
  },
  {
    "path": "include/eigen3/test/lu.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <Eigen/LU>\nusing namespace std;\n\ntemplate<typename MatrixType>\ntypename MatrixType::RealScalar matrix_l1_norm(const MatrixType& m) {\n  return m.cwiseAbs().colwise().sum().maxCoeff();\n}\n\ntemplate<typename MatrixType> void lu_non_invertible()\n{\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::RealScalar RealScalar;\n  /* this test covers the following files:\n     LU.h\n  */\n  Index rows, cols, cols2;\n  if(MatrixType::RowsAtCompileTime==Dynamic)\n  {\n    rows = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE);\n  }\n  else\n  {\n    rows = MatrixType::RowsAtCompileTime;\n  }\n  if(MatrixType::ColsAtCompileTime==Dynamic)\n  {\n    cols = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE);\n    cols2 = internal::random<int>(2,EIGEN_TEST_MAX_SIZE);\n  }\n  else\n  {\n    cols2 = cols = MatrixType::ColsAtCompileTime;\n  }\n\n  enum {\n    RowsAtCompileTime = MatrixType::RowsAtCompileTime,\n    ColsAtCompileTime = MatrixType::ColsAtCompileTime\n  };\n  typedef typename internal::kernel_retval_base<FullPivLU<MatrixType> >::ReturnType KernelMatrixType;\n  typedef typename internal::image_retval_base<FullPivLU<MatrixType> >::ReturnType ImageMatrixType;\n  typedef Matrix<typename MatrixType::Scalar, ColsAtCompileTime, ColsAtCompileTime>\n          CMatrixType;\n  typedef Matrix<typename MatrixType::Scalar, RowsAtCompileTime, RowsAtCompileTime>\n          RMatrixType;\n\n  Index rank = internal::random<Index>(1, (std::min)(rows, cols)-1);\n\n  // The image of the zero matrix should consist of a single (zero) column vector\n  VERIFY((MatrixType::Zero(rows,cols).fullPivLu().image(MatrixType::Zero(rows,cols)).cols() == 1));\n\n  MatrixType m1(rows, cols), m3(rows, cols2);\n  CMatrixType m2(cols, cols2);\n  createRandomPIMatrixOfRank(rank, rows, cols, m1);\n\n  FullPivLU<MatrixType> lu;\n\n  // The special value 0.01 below works well in tests. Keep in mind that we're only computing the rank\n  // of singular values are either 0 or 1.\n  // So it's not clear at all that the epsilon should play any role there.\n  lu.setThreshold(RealScalar(0.01));\n  lu.compute(m1);\n\n  MatrixType u(rows,cols);\n  u = lu.matrixLU().template triangularView<Upper>();\n  RMatrixType l = RMatrixType::Identity(rows,rows);\n  l.block(0,0,rows,(std::min)(rows,cols)).template triangularView<StrictlyLower>()\n    = lu.matrixLU().block(0,0,rows,(std::min)(rows,cols));\n\n  VERIFY_IS_APPROX(lu.permutationP() * m1 * lu.permutationQ(), l*u);\n\n  KernelMatrixType m1kernel = lu.kernel();\n  ImageMatrixType m1image = lu.image(m1);\n\n  VERIFY_IS_APPROX(m1, lu.reconstructedMatrix());\n  VERIFY(rank == lu.rank());\n  VERIFY(cols - lu.rank() == lu.dimensionOfKernel());\n  VERIFY(!lu.isInjective());\n  VERIFY(!lu.isInvertible());\n  VERIFY(!lu.isSurjective());\n  VERIFY((m1 * m1kernel).isMuchSmallerThan(m1));\n  VERIFY(m1image.fullPivLu().rank() == rank);\n  VERIFY_IS_APPROX(m1 * m1.adjoint() * m1image, m1image);\n\n  m2 = CMatrixType::Random(cols,cols2);\n  m3 = m1*m2;\n  m2 = CMatrixType::Random(cols,cols2);\n  // test that the code, which does resize(), may be applied to an xpr\n  m2.block(0,0,m2.rows(),m2.cols()) = lu.solve(m3);\n  VERIFY_IS_APPROX(m3, m1*m2);\n\n  // test solve with transposed\n  m3 = MatrixType::Random(rows,cols2);\n  m2 = m1.transpose()*m3;\n  m3 = MatrixType::Random(rows,cols2);\n  lu.template _solve_impl_transposed<false>(m2, m3);\n  VERIFY_IS_APPROX(m2, m1.transpose()*m3);\n  m3 = MatrixType::Random(rows,cols2);\n  m3 = lu.transpose().solve(m2);\n  VERIFY_IS_APPROX(m2, m1.transpose()*m3);\n\n  // test solve with conjugate transposed\n  m3 = MatrixType::Random(rows,cols2);\n  m2 = m1.adjoint()*m3;\n  m3 = MatrixType::Random(rows,cols2);\n  lu.template _solve_impl_transposed<true>(m2, m3);\n  VERIFY_IS_APPROX(m2, m1.adjoint()*m3);\n  m3 = MatrixType::Random(rows,cols2);\n  m3 = lu.adjoint().solve(m2);\n  VERIFY_IS_APPROX(m2, m1.adjoint()*m3);\n}\n\ntemplate<typename MatrixType> void lu_invertible()\n{\n  /* this test covers the following files:\n     LU.h\n  */\n  typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;\n  Index size = MatrixType::RowsAtCompileTime;\n  if( size==Dynamic)\n    size = internal::random<Index>(1,EIGEN_TEST_MAX_SIZE);\n\n  MatrixType m1(size, size), m2(size, size), m3(size, size);\n  FullPivLU<MatrixType> lu;\n  lu.setThreshold(RealScalar(0.01));\n  do {\n    m1 = MatrixType::Random(size,size);\n    lu.compute(m1);\n  } while(!lu.isInvertible());\n\n  VERIFY_IS_APPROX(m1, lu.reconstructedMatrix());\n  VERIFY(0 == lu.dimensionOfKernel());\n  VERIFY(lu.kernel().cols() == 1); // the kernel() should consist of a single (zero) column vector\n  VERIFY(size == lu.rank());\n  VERIFY(lu.isInjective());\n  VERIFY(lu.isSurjective());\n  VERIFY(lu.isInvertible());\n  VERIFY(lu.image(m1).fullPivLu().isInvertible());\n  m3 = MatrixType::Random(size,size);\n  m2 = lu.solve(m3);\n  VERIFY_IS_APPROX(m3, m1*m2);\n  MatrixType m1_inverse = lu.inverse();\n  VERIFY_IS_APPROX(m2, m1_inverse*m3);\n\n  RealScalar rcond = (RealScalar(1) / matrix_l1_norm(m1)) / matrix_l1_norm(m1_inverse);\n  const RealScalar rcond_est = lu.rcond();\n  // Verify that the estimated condition number is within a factor of 10 of the\n  // truth.\n  VERIFY(rcond_est > rcond / 10 && rcond_est < rcond * 10);\n\n  // test solve with transposed\n  lu.template _solve_impl_transposed<false>(m3, m2);\n  VERIFY_IS_APPROX(m3, m1.transpose()*m2);\n  m3 = MatrixType::Random(size,size);\n  m3 = lu.transpose().solve(m2);\n  VERIFY_IS_APPROX(m2, m1.transpose()*m3);\n\n  // test solve with conjugate transposed\n  lu.template _solve_impl_transposed<true>(m3, m2);\n  VERIFY_IS_APPROX(m3, m1.adjoint()*m2);\n  m3 = MatrixType::Random(size,size);\n  m3 = lu.adjoint().solve(m2);\n  VERIFY_IS_APPROX(m2, m1.adjoint()*m3);\n\n  // Regression test for Bug 302\n  MatrixType m4 = MatrixType::Random(size,size);\n  VERIFY_IS_APPROX(lu.solve(m3*m4), lu.solve(m3)*m4);\n}\n\ntemplate<typename MatrixType> void lu_partial_piv()\n{\n  /* this test covers the following files:\n     PartialPivLU.h\n  */\n  typedef typename MatrixType::Index Index;\n  typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;\n  Index size = internal::random<Index>(1,4);\n\n  MatrixType m1(size, size), m2(size, size), m3(size, size);\n  m1.setRandom();\n  PartialPivLU<MatrixType> plu(m1);\n\n  VERIFY_IS_APPROX(m1, plu.reconstructedMatrix());\n\n  m3 = MatrixType::Random(size,size);\n  m2 = plu.solve(m3);\n  VERIFY_IS_APPROX(m3, m1*m2);\n  MatrixType m1_inverse = plu.inverse();\n  VERIFY_IS_APPROX(m2, m1_inverse*m3);\n\n  RealScalar rcond = (RealScalar(1) / matrix_l1_norm(m1)) / matrix_l1_norm(m1_inverse);\n  const RealScalar rcond_est = plu.rcond();\n  // Verify that the estimate is within a factor of 10 of the truth.\n  VERIFY(rcond_est > rcond / 10 && rcond_est < rcond * 10);\n\n  // test solve with transposed\n  plu.template _solve_impl_transposed<false>(m3, m2);\n  VERIFY_IS_APPROX(m3, m1.transpose()*m2);\n  m3 = MatrixType::Random(size,size);\n  m3 = plu.transpose().solve(m2);\n  VERIFY_IS_APPROX(m2, m1.transpose()*m3);\n\n  // test solve with conjugate transposed\n  plu.template _solve_impl_transposed<true>(m3, m2);\n  VERIFY_IS_APPROX(m3, m1.adjoint()*m2);\n  m3 = MatrixType::Random(size,size);\n  m3 = plu.adjoint().solve(m2);\n  VERIFY_IS_APPROX(m2, m1.adjoint()*m3);\n}\n\ntemplate<typename MatrixType> void lu_verify_assert()\n{\n  MatrixType tmp;\n\n  FullPivLU<MatrixType> lu;\n  VERIFY_RAISES_ASSERT(lu.matrixLU())\n  VERIFY_RAISES_ASSERT(lu.permutationP())\n  VERIFY_RAISES_ASSERT(lu.permutationQ())\n  VERIFY_RAISES_ASSERT(lu.kernel())\n  VERIFY_RAISES_ASSERT(lu.image(tmp))\n  VERIFY_RAISES_ASSERT(lu.solve(tmp))\n  VERIFY_RAISES_ASSERT(lu.determinant())\n  VERIFY_RAISES_ASSERT(lu.rank())\n  VERIFY_RAISES_ASSERT(lu.dimensionOfKernel())\n  VERIFY_RAISES_ASSERT(lu.isInjective())\n  VERIFY_RAISES_ASSERT(lu.isSurjective())\n  VERIFY_RAISES_ASSERT(lu.isInvertible())\n  VERIFY_RAISES_ASSERT(lu.inverse())\n\n  PartialPivLU<MatrixType> plu;\n  VERIFY_RAISES_ASSERT(plu.matrixLU())\n  VERIFY_RAISES_ASSERT(plu.permutationP())\n  VERIFY_RAISES_ASSERT(plu.solve(tmp))\n  VERIFY_RAISES_ASSERT(plu.determinant())\n  VERIFY_RAISES_ASSERT(plu.inverse())\n}\n\nvoid test_lu()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( lu_non_invertible<Matrix3f>() );\n    CALL_SUBTEST_1( lu_invertible<Matrix3f>() );\n    CALL_SUBTEST_1( lu_verify_assert<Matrix3f>() );\n\n    CALL_SUBTEST_2( (lu_non_invertible<Matrix<double, 4, 6> >()) );\n    CALL_SUBTEST_2( (lu_verify_assert<Matrix<double, 4, 6> >()) );\n\n    CALL_SUBTEST_3( lu_non_invertible<MatrixXf>() );\n    CALL_SUBTEST_3( lu_invertible<MatrixXf>() );\n    CALL_SUBTEST_3( lu_verify_assert<MatrixXf>() );\n\n    CALL_SUBTEST_4( lu_non_invertible<MatrixXd>() );\n    CALL_SUBTEST_4( lu_invertible<MatrixXd>() );\n    CALL_SUBTEST_4( lu_partial_piv<MatrixXd>() );\n    CALL_SUBTEST_4( lu_verify_assert<MatrixXd>() );\n\n    CALL_SUBTEST_5( lu_non_invertible<MatrixXcf>() );\n    CALL_SUBTEST_5( lu_invertible<MatrixXcf>() );\n    CALL_SUBTEST_5( lu_verify_assert<MatrixXcf>() );\n\n    CALL_SUBTEST_6( lu_non_invertible<MatrixXcd>() );\n    CALL_SUBTEST_6( lu_invertible<MatrixXcd>() );\n    CALL_SUBTEST_6( lu_partial_piv<MatrixXcd>() );\n    CALL_SUBTEST_6( lu_verify_assert<MatrixXcd>() );\n\n    CALL_SUBTEST_7(( lu_non_invertible<Matrix<float,Dynamic,16> >() ));\n\n    // Test problem size constructors\n    CALL_SUBTEST_9( PartialPivLU<MatrixXf>(10) );\n    CALL_SUBTEST_9( FullPivLU<MatrixXf>(10, 20); );\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/main.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include <cstdlib>\n#include <cerrno>\n#include <ctime>\n#include <iostream>\n#include <fstream>\n#include <string>\n#include <sstream>\n#include <vector>\n#include <typeinfo>\n\n// The following includes of STL headers have to be done _before_ the\n// definition of macros min() and max().  The reason is that many STL\n// implementations will not work properly as the min and max symbols collide\n// with the STL functions std:min() and std::max().  The STL headers may check\n// for the macro definition of min/max and issue a warning or undefine the\n// macros.\n//\n// Still, Windows defines min() and max() in windef.h as part of the regular\n// Windows system interfaces and many other Windows APIs depend on these\n// macros being available.  To prevent the macro expansion of min/max and to\n// make Eigen compatible with the Windows environment all function calls of\n// std::min() and std::max() have to be written with parenthesis around the\n// function name.\n//\n// All STL headers used by Eigen should be included here.  Because main.h is\n// included before any Eigen header and because the STL headers are guarded\n// against multiple inclusions, no STL header will see our own min/max macro\n// definitions.\n#include <limits>\n#include <algorithm>\n#include <complex>\n#include <deque>\n#include <queue>\n#include <cassert>\n#include <list>\n#if __cplusplus >= 201103L\n#include <random>\n#ifdef EIGEN_USE_THREADS\n#include <future>\n#endif\n#endif\n\n// Same for cuda_fp16.h\n#if defined(__CUDACC_VER_MAJOR__) && (__CUDACC_VER_MAJOR__ >= 9)\n#define EIGEN_TEST_CUDACC_VER  ((__CUDACC_VER_MAJOR__ * 10000) + (__CUDACC_VER_MINOR__ * 100))\n#elif defined(__CUDACC_VER__)\n#define EIGEN_TEST_CUDACC_VER __CUDACC_VER__\n#else\n#define EIGEN_TEST_CUDACC_VER 0\n#endif\n\n#if EIGEN_TEST_CUDACC_VER >= 70500\n#include <cuda_fp16.h>\n#endif\n\n// To test that all calls from Eigen code to std::min() and std::max() are\n// protected by parenthesis against macro expansion, the min()/max() macros\n// are defined here and any not-parenthesized min/max call will cause a\n// compiler error.\n#define min(A,B) please_protect_your_min_with_parentheses\n#define max(A,B) please_protect_your_max_with_parentheses\n#define isnan(X) please_protect_your_isnan_with_parentheses\n#define isinf(X) please_protect_your_isinf_with_parentheses\n#define isfinite(X) please_protect_your_isfinite_with_parentheses\n#ifdef M_PI\n#undef M_PI\n#endif\n#define M_PI please_use_EIGEN_PI_instead_of_M_PI\n\n#define FORBIDDEN_IDENTIFIER (this_identifier_is_forbidden_to_avoid_clashes) this_identifier_is_forbidden_to_avoid_clashes\n// B0 is defined in POSIX header termios.h\n#define B0 FORBIDDEN_IDENTIFIER\n\n// Unit tests calling Eigen's blas library must preserve the default blocking size\n// to avoid troubles.\n#ifndef EIGEN_NO_DEBUG_SMALL_PRODUCT_BLOCKS\n#define EIGEN_DEBUG_SMALL_PRODUCT_BLOCKS\n#endif\n\n// shuts down ICC's remark #593: variable \"XXX\" was set but never used\n#define TEST_SET_BUT_UNUSED_VARIABLE(X) EIGEN_UNUSED_VARIABLE(X)\n\n#ifdef TEST_ENABLE_TEMPORARY_TRACKING\n\nstatic long int nb_temporaries;\nstatic long int nb_temporaries_on_assert = -1;\n\ninline void on_temporary_creation(long int size) {\n  // here's a great place to set a breakpoint when debugging failures in this test!\n  if(size!=0) nb_temporaries++;\n  if(nb_temporaries_on_assert>0) assert(nb_temporaries<nb_temporaries_on_assert);\n}\n\n#define EIGEN_DENSE_STORAGE_CTOR_PLUGIN { on_temporary_creation(size); }\n\n#define VERIFY_EVALUATION_COUNT(XPR,N) {\\\n    nb_temporaries = 0; \\\n    XPR; \\\n    if(nb_temporaries!=N) { std::cerr << \"nb_temporaries == \" << nb_temporaries << \"\\n\"; }\\\n    VERIFY( (#XPR) && nb_temporaries==N ); \\\n  }\n  \n#endif\n\n// the following file is automatically generated by cmake\n#include \"split_test_helper.h\"\n\n#ifdef NDEBUG\n#undef NDEBUG\n#endif\n\n// On windows CE, NDEBUG is automatically defined <assert.h> if NDEBUG is not defined.\n#ifndef DEBUG\n#define DEBUG\n#endif\n\n// bounds integer values for AltiVec\n#if defined(__ALTIVEC__) || defined(__VSX__)\n#define EIGEN_MAKING_DOCS\n#endif\n\n#ifndef EIGEN_TEST_FUNC\n#error EIGEN_TEST_FUNC must be defined\n#endif\n\n#define DEFAULT_REPEAT 10\n\nnamespace Eigen\n{\n  static std::vector<std::string> g_test_stack;\n  // level == 0 <=> abort if test fail\n  // level >= 1 <=> warning message to std::cerr if test fail\n  static int g_test_level = 0;\n  static int g_repeat;\n  static unsigned int g_seed;\n  static bool g_has_set_repeat, g_has_set_seed;\n}\n\n#define TRACK std::cerr << __FILE__ << \" \" << __LINE__ << std::endl\n// #define TRACK while()\n\n#define EI_PP_MAKE_STRING2(S) #S\n#define EI_PP_MAKE_STRING(S) EI_PP_MAKE_STRING2(S)\n\n#define EIGEN_DEFAULT_IO_FORMAT IOFormat(4, 0, \"  \", \"\\n\", \"\", \"\", \"\", \"\")\n\n#if (defined(_CPPUNWIND) || defined(__EXCEPTIONS)) && !defined(__CUDA_ARCH__)\n  #define EIGEN_EXCEPTIONS\n#endif\n\n#ifndef EIGEN_NO_ASSERTION_CHECKING\n\n  namespace Eigen\n  {\n    static const bool should_raise_an_assert = false;\n\n    // Used to avoid to raise two exceptions at a time in which\n    // case the exception is not properly caught.\n    // This may happen when a second exceptions is triggered in a destructor.\n    static bool no_more_assert = false;\n    static bool report_on_cerr_on_assert_failure = true;\n\n    struct eigen_assert_exception\n    {\n      eigen_assert_exception(void) {}\n      ~eigen_assert_exception() { Eigen::no_more_assert = false; }\n    };\n\n    struct eigen_static_assert_exception\n    {\n      eigen_static_assert_exception(void) {}\n      ~eigen_static_assert_exception() { Eigen::no_more_assert = false; }\n    };\n  }\n  // If EIGEN_DEBUG_ASSERTS is defined and if no assertion is triggered while\n  // one should have been, then the list of excecuted assertions is printed out.\n  //\n  // EIGEN_DEBUG_ASSERTS is not enabled by default as it\n  // significantly increases the compilation time\n  // and might even introduce side effects that would hide\n  // some memory errors.\n  #ifdef EIGEN_DEBUG_ASSERTS\n\n    namespace Eigen\n    {\n      namespace internal\n      {\n        static bool push_assert = false;\n      }\n      static std::vector<std::string> eigen_assert_list;\n    }\n    #define eigen_assert(a)                       \\\n      if( (!(a)) && (!no_more_assert) )     \\\n      { \\\n        if(report_on_cerr_on_assert_failure) \\\n          std::cerr <<  #a << \" \" __FILE__ << \"(\" << __LINE__ << \")\\n\"; \\\n        Eigen::no_more_assert = true;       \\\n        EIGEN_THROW_X(Eigen::eigen_assert_exception()); \\\n      }                                     \\\n      else if (Eigen::internal::push_assert)       \\\n      {                                     \\\n        eigen_assert_list.push_back(std::string(EI_PP_MAKE_STRING(__FILE__) \" (\" EI_PP_MAKE_STRING(__LINE__) \") : \" #a) ); \\\n      }\n\n    #ifdef EIGEN_EXCEPTIONS\n    #define VERIFY_RAISES_ASSERT(a)                                                   \\\n      {                                                                               \\\n        Eigen::no_more_assert = false;                                                \\\n        Eigen::eigen_assert_list.clear();                                             \\\n        Eigen::internal::push_assert = true;                                          \\\n        Eigen::report_on_cerr_on_assert_failure = false;                              \\\n        try {                                                                         \\\n          a;                                                                          \\\n          std::cerr << \"One of the following asserts should have been triggered:\\n\";  \\\n          for (uint ai=0 ; ai<eigen_assert_list.size() ; ++ai)                        \\\n            std::cerr << \"  \" << eigen_assert_list[ai] << \"\\n\";                       \\\n          VERIFY(Eigen::should_raise_an_assert && # a);                               \\\n        } catch (Eigen::eigen_assert_exception) {                                     \\\n          Eigen::internal::push_assert = false; VERIFY(true);                         \\\n        }                                                                             \\\n        Eigen::report_on_cerr_on_assert_failure = true;                               \\\n        Eigen::internal::push_assert = false;                                         \\\n      }\n    #endif //EIGEN_EXCEPTIONS\n\n  #elif !defined(__CUDACC__) // EIGEN_DEBUG_ASSERTS\n    // see bug 89. The copy_bool here is working around a bug in gcc <= 4.3\n    #define eigen_assert(a) \\\n      if( (!Eigen::internal::copy_bool(a)) && (!no_more_assert) )\\\n      {                                       \\\n        Eigen::no_more_assert = true;         \\\n        if(report_on_cerr_on_assert_failure)  \\\n          eigen_plain_assert(a);              \\\n        else                                  \\\n          EIGEN_THROW_X(Eigen::eigen_assert_exception()); \\\n      }\n\n    #ifdef EIGEN_EXCEPTIONS\n      #define VERIFY_RAISES_ASSERT(a) {                           \\\n        Eigen::no_more_assert = false;                            \\\n        Eigen::report_on_cerr_on_assert_failure = false;          \\\n        try {                                                     \\\n          a;                                                      \\\n          VERIFY(Eigen::should_raise_an_assert && # a);           \\\n        }                                                         \\\n        catch (Eigen::eigen_assert_exception&) { VERIFY(true); }  \\\n        Eigen::report_on_cerr_on_assert_failure = true;           \\\n      }\n    #endif // EIGEN_EXCEPTIONS\n  #endif // EIGEN_DEBUG_ASSERTS\n\n  #if defined(TEST_CHECK_STATIC_ASSERTIONS) && defined(EIGEN_EXCEPTIONS)\n    #define EIGEN_STATIC_ASSERT(a,MSG) \\\n      if( (!Eigen::internal::copy_bool(a)) && (!no_more_assert) )\\\n      {                                       \\\n        Eigen::no_more_assert = true;         \\\n        if(report_on_cerr_on_assert_failure)  \\\n          eigen_plain_assert((a) && #MSG);      \\\n        else                                  \\\n          EIGEN_THROW_X(Eigen::eigen_static_assert_exception()); \\\n      }\n    #define VERIFY_RAISES_STATIC_ASSERT(a) {                    \\\n      Eigen::no_more_assert = false;                            \\\n      Eigen::report_on_cerr_on_assert_failure = false;          \\\n      try {                                                     \\\n        a;                                                      \\\n        VERIFY(Eigen::should_raise_an_assert && # a);           \\\n      }                                                         \\\n      catch (Eigen::eigen_static_assert_exception&) { VERIFY(true); }  \\\n      Eigen::report_on_cerr_on_assert_failure = true;           \\\n    }\n  #endif // TEST_CHECK_STATIC_ASSERTIONS\n\n#ifndef VERIFY_RAISES_ASSERT\n  #define VERIFY_RAISES_ASSERT(a) \\\n    std::cout << \"Can't VERIFY_RAISES_ASSERT( \" #a \" ) with exceptions disabled\\n\";\n#endif\n#ifndef VERIFY_RAISES_STATIC_ASSERT\n  #define VERIFY_RAISES_STATIC_ASSERT(a) \\\n    std::cout << \"Can't VERIFY_RAISES_STATIC_ASSERT( \" #a \" ) with exceptions disabled\\n\";\n#endif\n    \n  #if !defined(__CUDACC__)\n  #define EIGEN_USE_CUSTOM_ASSERT\n  #endif\n\n#else // EIGEN_NO_ASSERTION_CHECKING\n\n  #define VERIFY_RAISES_ASSERT(a) {}\n  #define VERIFY_RAISES_STATIC_ASSERT(a) {}\n\n#endif // EIGEN_NO_ASSERTION_CHECKING\n\n#define EIGEN_INTERNAL_DEBUGGING\n#include <Eigen/QR> // required for createRandomPIMatrixOfRank\n\ninline void verify_impl(bool condition, const char *testname, const char *file, int line, const char *condition_as_string)\n{\n  if (!condition)\n  {\n    if(Eigen::g_test_level>0)\n      std::cerr << \"WARNING: \";\n    std::cerr << \"Test \" << testname << \" failed in \" << file << \" (\" << line << \")\"\n      << std::endl << \"    \" << condition_as_string << std::endl;\n    std::cerr << \"Stack:\\n\";\n    const int test_stack_size = static_cast<int>(Eigen::g_test_stack.size());\n    for(int i=test_stack_size-1; i>=0; --i)\n      std::cerr << \"  - \" << Eigen::g_test_stack[i] << \"\\n\";\n    std::cerr << \"\\n\";\n    if(Eigen::g_test_level==0)\n      abort();\n  }\n}\n\n#define VERIFY(a) ::verify_impl(a, g_test_stack.back().c_str(), __FILE__, __LINE__, EI_PP_MAKE_STRING(a))\n\n#define VERIFY_GE(a, b) ::verify_impl(a >= b, g_test_stack.back().c_str(), __FILE__, __LINE__, EI_PP_MAKE_STRING(a >= b))\n#define VERIFY_LE(a, b) ::verify_impl(a <= b, g_test_stack.back().c_str(), __FILE__, __LINE__, EI_PP_MAKE_STRING(a <= b))\n\n\n#define VERIFY_IS_EQUAL(a, b) VERIFY(test_is_equal(a, b, true))\n#define VERIFY_IS_NOT_EQUAL(a, b) VERIFY(test_is_equal(a, b, false))\n#define VERIFY_IS_APPROX(a, b) VERIFY(verifyIsApprox(a, b))\n#define VERIFY_IS_NOT_APPROX(a, b) VERIFY(!test_isApprox(a, b))\n#define VERIFY_IS_MUCH_SMALLER_THAN(a, b) VERIFY(test_isMuchSmallerThan(a, b))\n#define VERIFY_IS_NOT_MUCH_SMALLER_THAN(a, b) VERIFY(!test_isMuchSmallerThan(a, b))\n#define VERIFY_IS_APPROX_OR_LESS_THAN(a, b) VERIFY(test_isApproxOrLessThan(a, b))\n#define VERIFY_IS_NOT_APPROX_OR_LESS_THAN(a, b) VERIFY(!test_isApproxOrLessThan(a, b))\n\n#define VERIFY_IS_UNITARY(a) VERIFY(test_isUnitary(a))\n\n#define CALL_SUBTEST(FUNC) do { \\\n    g_test_stack.push_back(EI_PP_MAKE_STRING(FUNC)); \\\n    FUNC; \\\n    g_test_stack.pop_back(); \\\n  } while (0)\n\n\nnamespace Eigen {\n\ntemplate<typename T> inline typename NumTraits<T>::Real test_precision() { return NumTraits<T>::dummy_precision(); }\ntemplate<> inline float test_precision<float>() { return 1e-3f; }\ntemplate<> inline double test_precision<double>() { return 1e-6; }\ntemplate<> inline long double test_precision<long double>() { return 1e-6l; }\ntemplate<> inline float test_precision<std::complex<float> >() { return test_precision<float>(); }\ntemplate<> inline double test_precision<std::complex<double> >() { return test_precision<double>(); }\ntemplate<> inline long double test_precision<std::complex<long double> >() { return test_precision<long double>(); }\n\ninline bool test_isApprox(const short& a, const short& b)\n{ return internal::isApprox(a, b, test_precision<short>()); }\ninline bool test_isApprox(const unsigned short& a, const unsigned short& b)\n{ return internal::isApprox(a, b, test_precision<unsigned short>()); }\ninline bool test_isApprox(const unsigned int& a, const unsigned int& b)\n{ return internal::isApprox(a, b, test_precision<unsigned int>()); }\ninline bool test_isApprox(const long& a, const long& b)\n{ return internal::isApprox(a, b, test_precision<long>()); }\ninline bool test_isApprox(const unsigned long& a, const unsigned long& b)\n{ return internal::isApprox(a, b, test_precision<unsigned long>()); }\n\ninline bool test_isApprox(const int& a, const int& b)\n{ return internal::isApprox(a, b, test_precision<int>()); }\ninline bool test_isMuchSmallerThan(const int& a, const int& b)\n{ return internal::isMuchSmallerThan(a, b, test_precision<int>()); }\ninline bool test_isApproxOrLessThan(const int& a, const int& b)\n{ return internal::isApproxOrLessThan(a, b, test_precision<int>()); }\n\ninline bool test_isApprox(const float& a, const float& b)\n{ return internal::isApprox(a, b, test_precision<float>()); }\ninline bool test_isMuchSmallerThan(const float& a, const float& b)\n{ return internal::isMuchSmallerThan(a, b, test_precision<float>()); }\ninline bool test_isApproxOrLessThan(const float& a, const float& b)\n{ return internal::isApproxOrLessThan(a, b, test_precision<float>()); }\n\ninline bool test_isApprox(const double& a, const double& b)\n{ return internal::isApprox(a, b, test_precision<double>()); }\ninline bool test_isMuchSmallerThan(const double& a, const double& b)\n{ return internal::isMuchSmallerThan(a, b, test_precision<double>()); }\ninline bool test_isApproxOrLessThan(const double& a, const double& b)\n{ return internal::isApproxOrLessThan(a, b, test_precision<double>()); }\n\n#ifndef EIGEN_TEST_NO_COMPLEX\ninline bool test_isApprox(const std::complex<float>& a, const std::complex<float>& b)\n{ return internal::isApprox(a, b, test_precision<std::complex<float> >()); }\ninline bool test_isMuchSmallerThan(const std::complex<float>& a, const std::complex<float>& b)\n{ return internal::isMuchSmallerThan(a, b, test_precision<std::complex<float> >()); }\n\ninline bool test_isApprox(const std::complex<double>& a, const std::complex<double>& b)\n{ return internal::isApprox(a, b, test_precision<std::complex<double> >()); }\ninline bool test_isMuchSmallerThan(const std::complex<double>& a, const std::complex<double>& b)\n{ return internal::isMuchSmallerThan(a, b, test_precision<std::complex<double> >()); }\n\n#ifndef EIGEN_TEST_NO_LONGDOUBLE\ninline bool test_isApprox(const std::complex<long double>& a, const std::complex<long double>& b)\n{ return internal::isApprox(a, b, test_precision<std::complex<long double> >()); }\ninline bool test_isMuchSmallerThan(const std::complex<long double>& a, const std::complex<long double>& b)\n{ return internal::isMuchSmallerThan(a, b, test_precision<std::complex<long double> >()); }\n#endif\n#endif\n\n#ifndef EIGEN_TEST_NO_LONGDOUBLE\ninline bool test_isApprox(const long double& a, const long double& b)\n{\n    bool ret = internal::isApprox(a, b, test_precision<long double>());\n    if (!ret) std::cerr\n        << std::endl << \"    actual   = \" << a\n        << std::endl << \"    expected = \" << b << std::endl << std::endl;\n    return ret;\n}\n\ninline bool test_isMuchSmallerThan(const long double& a, const long double& b)\n{ return internal::isMuchSmallerThan(a, b, test_precision<long double>()); }\ninline bool test_isApproxOrLessThan(const long double& a, const long double& b)\n{ return internal::isApproxOrLessThan(a, b, test_precision<long double>()); }\n#endif // EIGEN_TEST_NO_LONGDOUBLE\n\ninline bool test_isApprox(const half& a, const half& b)\n{ return internal::isApprox(a, b, test_precision<half>()); }\ninline bool test_isMuchSmallerThan(const half& a, const half& b)\n{ return internal::isMuchSmallerThan(a, b, test_precision<half>()); }\ninline bool test_isApproxOrLessThan(const half& a, const half& b)\n{ return internal::isApproxOrLessThan(a, b, test_precision<half>()); }\n\n// test_relative_error returns the relative difference between a and b as a real scalar as used in isApprox.\ntemplate<typename T1,typename T2>\ntypename NumTraits<typename T1::RealScalar>::NonInteger test_relative_error(const EigenBase<T1> &a, const EigenBase<T2> &b)\n{\n  using std::sqrt;\n  typedef typename NumTraits<typename T1::RealScalar>::NonInteger RealScalar;\n  typename internal::nested_eval<T1,2>::type ea(a.derived());\n  typename internal::nested_eval<T2,2>::type eb(b.derived());\n  return sqrt(RealScalar((ea-eb).cwiseAbs2().sum()) / RealScalar((std::min)(eb.cwiseAbs2().sum(),ea.cwiseAbs2().sum())));\n}\n\ntemplate<typename T1,typename T2>\ntypename T1::RealScalar test_relative_error(const T1 &a, const T2 &b, const typename T1::Coefficients* = 0)\n{\n  return test_relative_error(a.coeffs(), b.coeffs());\n}\n\ntemplate<typename T1,typename T2>\ntypename T1::Scalar test_relative_error(const T1 &a, const T2 &b, const typename T1::MatrixType* = 0)\n{\n  return test_relative_error(a.matrix(), b.matrix());\n}\n\ntemplate<typename S, int D>\nS test_relative_error(const Translation<S,D> &a, const Translation<S,D> &b)\n{\n  return test_relative_error(a.vector(), b.vector());\n}\n\ntemplate <typename S, int D, int O>\nS test_relative_error(const ParametrizedLine<S,D,O> &a, const ParametrizedLine<S,D,O> &b)\n{\n  return (std::max)(test_relative_error(a.origin(), b.origin()), test_relative_error(a.origin(), b.origin()));\n}\n\ntemplate <typename S, int D>\nS test_relative_error(const AlignedBox<S,D> &a, const AlignedBox<S,D> &b)\n{\n  return (std::max)(test_relative_error((a.min)(), (b.min)()), test_relative_error((a.max)(), (b.max)()));\n}\n\ntemplate<typename Derived> class SparseMatrixBase;\ntemplate<typename T1,typename T2>\ntypename T1::RealScalar test_relative_error(const MatrixBase<T1> &a, const SparseMatrixBase<T2> &b)\n{\n  return test_relative_error(a,b.toDense());\n}\n\ntemplate<typename Derived> class SparseMatrixBase;\ntemplate<typename T1,typename T2>\ntypename T1::RealScalar test_relative_error(const SparseMatrixBase<T1> &a, const MatrixBase<T2> &b)\n{\n  return test_relative_error(a.toDense(),b);\n}\n\ntemplate<typename Derived> class SparseMatrixBase;\ntemplate<typename T1,typename T2>\ntypename T1::RealScalar test_relative_error(const SparseMatrixBase<T1> &a, const SparseMatrixBase<T2> &b)\n{\n  return test_relative_error(a.toDense(),b.toDense());\n}\n\ntemplate<typename T1,typename T2>\ntypename NumTraits<typename NumTraits<T1>::Real>::NonInteger test_relative_error(const T1 &a, const T2 &b, typename internal::enable_if<internal::is_arithmetic<typename NumTraits<T1>::Real>::value, T1>::type* = 0)\n{\n  typedef typename NumTraits<typename NumTraits<T1>::Real>::NonInteger RealScalar;\n  return numext::sqrt(RealScalar(numext::abs2(a-b))/RealScalar((numext::mini)(numext::abs2(a),numext::abs2(b))));\n}\n\ntemplate<typename T>\nT test_relative_error(const Rotation2D<T> &a, const Rotation2D<T> &b)\n{\n  return test_relative_error(a.angle(), b.angle());\n}\n\ntemplate<typename T>\nT test_relative_error(const AngleAxis<T> &a, const AngleAxis<T> &b)\n{\n  return (std::max)(test_relative_error(a.angle(), b.angle()), test_relative_error(a.axis(), b.axis()));\n}\n\ntemplate<typename Type1, typename Type2>\ninline bool test_isApprox(const Type1& a, const Type2& b, typename Type1::Scalar* = 0) // Enabled for Eigen's type only\n{\n  return a.isApprox(b, test_precision<typename Type1::Scalar>());\n}\n\n// get_test_precision is a small wrapper to test_precision allowing to return the scalar precision for either scalars or expressions\ntemplate<typename T>\ntypename NumTraits<typename T::Scalar>::Real get_test_precision(const T&, const typename T::Scalar* = 0)\n{\n  return test_precision<typename NumTraits<typename T::Scalar>::Real>();\n}\n\ntemplate<typename T>\ntypename NumTraits<T>::Real get_test_precision(const T&,typename internal::enable_if<internal::is_arithmetic<typename NumTraits<T>::Real>::value, T>::type* = 0)\n{\n  return test_precision<typename NumTraits<T>::Real>();\n}\n\n// verifyIsApprox is a wrapper to test_isApprox that outputs the relative difference magnitude if the test fails.\ntemplate<typename Type1, typename Type2>\ninline bool verifyIsApprox(const Type1& a, const Type2& b)\n{\n  bool ret = test_isApprox(a,b);\n  if(!ret)\n  {\n    std::cerr << \"Difference too large wrt tolerance \" << get_test_precision(a)  << \", relative error is: \" << test_relative_error(a,b) << std::endl;\n  }\n  return ret;\n}\n\n// The idea behind this function is to compare the two scalars a and b where\n// the scalar ref is a hint about the expected order of magnitude of a and b.\n// WARNING: the scalar a and b must be positive\n// Therefore, if for some reason a and b are very small compared to ref,\n// we won't issue a false negative.\n// This test could be: abs(a-b) <= eps * ref\n// However, it seems that simply comparing a+ref and b+ref is more sensitive to true error.\ntemplate<typename Scalar,typename ScalarRef>\ninline bool test_isApproxWithRef(const Scalar& a, const Scalar& b, const ScalarRef& ref)\n{\n  return test_isApprox(a+ref, b+ref);\n}\n\ntemplate<typename Derived1, typename Derived2>\ninline bool test_isMuchSmallerThan(const MatrixBase<Derived1>& m1,\n                                   const MatrixBase<Derived2>& m2)\n{\n  return m1.isMuchSmallerThan(m2, test_precision<typename internal::traits<Derived1>::Scalar>());\n}\n\ntemplate<typename Derived>\ninline bool test_isMuchSmallerThan(const MatrixBase<Derived>& m,\n                                   const typename NumTraits<typename internal::traits<Derived>::Scalar>::Real& s)\n{\n  return m.isMuchSmallerThan(s, test_precision<typename internal::traits<Derived>::Scalar>());\n}\n\ntemplate<typename Derived>\ninline bool test_isUnitary(const MatrixBase<Derived>& m)\n{\n  return m.isUnitary(test_precision<typename internal::traits<Derived>::Scalar>());\n}\n\n// Forward declaration to avoid ICC warning\ntemplate<typename T, typename U>\nbool test_is_equal(const T& actual, const U& expected, bool expect_equal=true);\n\ntemplate<typename T, typename U>\nbool test_is_equal(const T& actual, const U& expected, bool expect_equal)\n{\n    if ((actual==expected) == expect_equal)\n        return true;\n    // false:\n    std::cerr\n        << \"\\n    actual   = \" << actual\n        << \"\\n    expected \" << (expect_equal ? \"= \" : \"!=\") << expected << \"\\n\\n\";\n    return false;\n}\n\n/** Creates a random Partial Isometry matrix of given rank.\n  *\n  * A partial isometry is a matrix all of whose singular values are either 0 or 1.\n  * This is very useful to test rank-revealing algorithms.\n  */\n// Forward declaration to avoid ICC warning\ntemplate<typename MatrixType>\nvoid createRandomPIMatrixOfRank(Index desired_rank, Index rows, Index cols, MatrixType& m);\ntemplate<typename MatrixType>\nvoid createRandomPIMatrixOfRank(Index desired_rank, Index rows, Index cols, MatrixType& m)\n{\n  typedef typename internal::traits<MatrixType>::Scalar Scalar;\n  enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };\n\n  typedef Matrix<Scalar, Dynamic, 1> VectorType;\n  typedef Matrix<Scalar, Rows, Rows> MatrixAType;\n  typedef Matrix<Scalar, Cols, Cols> MatrixBType;\n\n  if(desired_rank == 0)\n  {\n    m.setZero(rows,cols);\n    return;\n  }\n\n  if(desired_rank == 1)\n  {\n    // here we normalize the vectors to get a partial isometry\n    m = VectorType::Random(rows).normalized() * VectorType::Random(cols).normalized().transpose();\n    return;\n  }\n\n  MatrixAType a = MatrixAType::Random(rows,rows);\n  MatrixType d = MatrixType::Identity(rows,cols);\n  MatrixBType  b = MatrixBType::Random(cols,cols);\n\n  // set the diagonal such that only desired_rank non-zero entries reamain\n  const Index diag_size = (std::min)(d.rows(),d.cols());\n  if(diag_size != desired_rank)\n    d.diagonal().segment(desired_rank, diag_size-desired_rank) = VectorType::Zero(diag_size-desired_rank);\n\n  HouseholderQR<MatrixAType> qra(a);\n  HouseholderQR<MatrixBType> qrb(b);\n  m = qra.householderQ() * d * qrb.householderQ();\n}\n\n// Forward declaration to avoid ICC warning\ntemplate<typename PermutationVectorType>\nvoid randomPermutationVector(PermutationVectorType& v, Index size);\ntemplate<typename PermutationVectorType>\nvoid randomPermutationVector(PermutationVectorType& v, Index size)\n{\n  typedef typename PermutationVectorType::Scalar Scalar;\n  v.resize(size);\n  for(Index i = 0; i < size; ++i) v(i) = Scalar(i);\n  if(size == 1) return;\n  for(Index n = 0; n < 3 * size; ++n)\n  {\n    Index i = internal::random<Index>(0, size-1);\n    Index j;\n    do j = internal::random<Index>(0, size-1); while(j==i);\n    std::swap(v(i), v(j));\n  }\n}\n\ntemplate<typename T> bool isNotNaN(const T& x)\n{\n  return x==x;\n}\n\ntemplate<typename T> bool isPlusInf(const T& x)\n{\n  return x > NumTraits<T>::highest();\n}\n\ntemplate<typename T> bool isMinusInf(const T& x)\n{\n  return x < NumTraits<T>::lowest();\n}\n\n} // end namespace Eigen\n\ntemplate<typename T> struct GetDifferentType;\n\ntemplate<> struct GetDifferentType<float> { typedef double type; };\ntemplate<> struct GetDifferentType<double> { typedef float type; };\ntemplate<typename T> struct GetDifferentType<std::complex<T> >\n{ typedef std::complex<typename GetDifferentType<T>::type> type; };\n\n// Forward declaration to avoid ICC warning\ntemplate<typename T> std::string type_name();\ntemplate<typename T> std::string type_name()                    { return \"other\"; }\ntemplate<> std::string type_name<float>()                       { return \"float\"; }\ntemplate<> std::string type_name<double>()                      { return \"double\"; }\ntemplate<> std::string type_name<long double>()                 { return \"long double\"; }\ntemplate<> std::string type_name<int>()                         { return \"int\"; }\ntemplate<> std::string type_name<std::complex<float> >()        { return \"complex<float>\"; }\ntemplate<> std::string type_name<std::complex<double> >()       { return \"complex<double>\"; }\ntemplate<> std::string type_name<std::complex<long double> >()  { return \"complex<long double>\"; }\ntemplate<> std::string type_name<std::complex<int> >()          { return \"complex<int>\"; }\n\n// forward declaration of the main test function\nvoid EIGEN_CAT(test_,EIGEN_TEST_FUNC)();\n\nusing namespace Eigen;\n\ninline void set_repeat_from_string(const char *str)\n{\n  errno = 0;\n  g_repeat = int(strtoul(str, 0, 10));\n  if(errno || g_repeat <= 0)\n  {\n    std::cout << \"Invalid repeat value \" << str << std::endl;\n    exit(EXIT_FAILURE);\n  }\n  g_has_set_repeat = true;\n}\n\ninline void set_seed_from_string(const char *str)\n{\n  errno = 0;\n  g_seed = int(strtoul(str, 0, 10));\n  if(errno || g_seed == 0)\n  {\n    std::cout << \"Invalid seed value \" << str << std::endl;\n    exit(EXIT_FAILURE);\n  }\n  g_has_set_seed = true;\n}\n\nint main(int argc, char *argv[])\n{\n    g_has_set_repeat = false;\n    g_has_set_seed = false;\n    bool need_help = false;\n\n    for(int i = 1; i < argc; i++)\n    {\n      if(argv[i][0] == 'r')\n      {\n        if(g_has_set_repeat)\n        {\n          std::cout << \"Argument \" << argv[i] << \" conflicting with a former argument\" << std::endl;\n          return 1;\n        }\n        set_repeat_from_string(argv[i]+1);\n      }\n      else if(argv[i][0] == 's')\n      {\n        if(g_has_set_seed)\n        {\n          std::cout << \"Argument \" << argv[i] << \" conflicting with a former argument\" << std::endl;\n          return 1;\n        }\n         set_seed_from_string(argv[i]+1);\n      }\n      else\n      {\n        need_help = true;\n      }\n    }\n\n    if(need_help)\n    {\n      std::cout << \"This test application takes the following optional arguments:\" << std::endl;\n      std::cout << \"  rN     Repeat each test N times (default: \" << DEFAULT_REPEAT << \")\" << std::endl;\n      std::cout << \"  sN     Use N as seed for random numbers (default: based on current time)\" << std::endl;\n      std::cout << std::endl;\n      std::cout << \"If defined, the environment variables EIGEN_REPEAT and EIGEN_SEED\" << std::endl;\n      std::cout << \"will be used as default values for these parameters.\" << std::endl;\n      return 1;\n    }\n\n    char *env_EIGEN_REPEAT = getenv(\"EIGEN_REPEAT\");\n    if(!g_has_set_repeat && env_EIGEN_REPEAT)\n      set_repeat_from_string(env_EIGEN_REPEAT);\n    char *env_EIGEN_SEED = getenv(\"EIGEN_SEED\");\n    if(!g_has_set_seed && env_EIGEN_SEED)\n      set_seed_from_string(env_EIGEN_SEED);\n\n    if(!g_has_set_seed) g_seed = (unsigned int) time(NULL);\n    if(!g_has_set_repeat) g_repeat = DEFAULT_REPEAT;\n\n    std::cout << \"Initializing random number generator with seed \" << g_seed << std::endl;\n    std::stringstream ss;\n    ss << \"Seed: \" << g_seed;\n    g_test_stack.push_back(ss.str());\n    srand(g_seed);\n    std::cout << \"Repeating each test \" << g_repeat << \" times\" << std::endl;\n\n    Eigen::g_test_stack.push_back(std::string(EI_PP_MAKE_STRING(EIGEN_TEST_FUNC)));\n\n    EIGEN_CAT(test_,EIGEN_TEST_FUNC)();\n    return 0;\n}\n\n// These warning are disabled here such that they are still ON when parsing Eigen's header files.\n#if defined __INTEL_COMPILER\n  // remark #383: value copied to temporary, reference to temporary used\n  //  -> this warning is raised even for legal usage as: g_test_stack.push_back(\"foo\"); where g_test_stack is a std::vector<std::string>\n  // remark #1418: external function definition with no prior declaration\n  //  -> this warning is raised for all our test functions. Declaring them static would fix the issue.\n  // warning #279: controlling expression is constant\n  // remark #1572: floating-point equality and inequality comparisons are unreliable\n  #pragma warning disable 279 383 1418 1572\n#endif\n\n#ifdef _MSC_VER\n  // 4503 - decorated name length exceeded, name was truncated\n  #pragma warning( disable : 4503)\n#endif\n"
  },
  {
    "path": "include/eigen3/test/mapped_matrix.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_NO_STATIC_ASSERT\n#define EIGEN_NO_STATIC_ASSERT // turn static asserts into runtime asserts in order to check them\n#endif\n\n#include \"main.h\"\n\n#define EIGEN_TESTMAP_MAX_SIZE 256\n\ntemplate<typename VectorType> void map_class_vector(const VectorType& m)\n{\n  typedef typename VectorType::Index Index;\n  typedef typename VectorType::Scalar Scalar;\n\n  Index size = m.size();\n\n  Scalar* array1 = internal::aligned_new<Scalar>(size);\n  Scalar* array2 = internal::aligned_new<Scalar>(size);\n  Scalar* array3 = new Scalar[size+1];\n  Scalar* array3unaligned = (internal::UIntPtr(array3)%EIGEN_MAX_ALIGN_BYTES) == 0 ? array3+1 : array3;\n  Scalar  array4[EIGEN_TESTMAP_MAX_SIZE];\n\n  Map<VectorType, AlignedMax>(array1, size) = VectorType::Random(size);\n  Map<VectorType, AlignedMax>(array2, size) = Map<VectorType,AlignedMax>(array1, size);\n  Map<VectorType>(array3unaligned, size) = Map<VectorType>(array1, size);\n  Map<VectorType>(array4, size)          = Map<VectorType,AlignedMax>(array1, size);\n  VectorType ma1 = Map<VectorType, AlignedMax>(array1, size);\n  VectorType ma2 = Map<VectorType, AlignedMax>(array2, size);\n  VectorType ma3 = Map<VectorType>(array3unaligned, size);\n  VectorType ma4 = Map<VectorType>(array4, size);\n  VERIFY_IS_EQUAL(ma1, ma2);\n  VERIFY_IS_EQUAL(ma1, ma3);\n  VERIFY_IS_EQUAL(ma1, ma4);\n  #ifdef EIGEN_VECTORIZE\n  if(internal::packet_traits<Scalar>::Vectorizable && size>=AlignedMax)\n    VERIFY_RAISES_ASSERT((Map<VectorType,AlignedMax>(array3unaligned, size)))\n  #endif\n\n  internal::aligned_delete(array1, size);\n  internal::aligned_delete(array2, size);\n  delete[] array3;\n}\n\ntemplate<typename MatrixType> void map_class_matrix(const MatrixType& m)\n{\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n\n  Index rows = m.rows(), cols = m.cols(), size = rows*cols;\n  Scalar s1 = internal::random<Scalar>();\n\n  // array1 and array2 -> aligned heap allocation\n  Scalar* array1 = internal::aligned_new<Scalar>(size);\n  for(int i = 0; i < size; i++) array1[i] = Scalar(1);\n  Scalar* array2 = internal::aligned_new<Scalar>(size);\n  for(int i = 0; i < size; i++) array2[i] = Scalar(1);\n  // array3unaligned -> unaligned pointer to heap\n  Scalar* array3 = new Scalar[size+1];\n  Index sizep1 = size + 1; // <- without this temporary MSVC 2103 generates bad code\n  for(Index i = 0; i < sizep1; i++) array3[i] = Scalar(1);\n  Scalar* array3unaligned = (internal::UIntPtr(array3)%EIGEN_MAX_ALIGN_BYTES) == 0 ? array3+1 : array3;\n  Scalar array4[256];\n  if(size<=256)\n    for(int i = 0; i < size; i++) array4[i] = Scalar(1);\n  \n  Map<MatrixType> map1(array1, rows, cols);\n  Map<MatrixType, AlignedMax> map2(array2, rows, cols);\n  Map<MatrixType> map3(array3unaligned, rows, cols);\n  Map<MatrixType> map4(array4, rows, cols);\n  \n  VERIFY_IS_EQUAL(map1, MatrixType::Ones(rows,cols));\n  VERIFY_IS_EQUAL(map2, MatrixType::Ones(rows,cols));\n  VERIFY_IS_EQUAL(map3, MatrixType::Ones(rows,cols));\n  map1 = MatrixType::Random(rows,cols);\n  map2 = map1;\n  map3 = map1;\n  MatrixType ma1 = map1;\n  MatrixType ma2 = map2;\n  MatrixType ma3 = map3;\n  VERIFY_IS_EQUAL(map1, map2);\n  VERIFY_IS_EQUAL(map1, map3);\n  VERIFY_IS_EQUAL(ma1, ma2);\n  VERIFY_IS_EQUAL(ma1, ma3);\n  VERIFY_IS_EQUAL(ma1, map3);\n  \n  VERIFY_IS_APPROX(s1*map1, s1*map2);\n  VERIFY_IS_APPROX(s1*ma1, s1*ma2);\n  VERIFY_IS_EQUAL(s1*ma1, s1*ma3);\n  VERIFY_IS_APPROX(s1*map1, s1*map3);\n  \n  map2 *= s1;\n  map3 *= s1;\n  VERIFY_IS_APPROX(s1*map1, map2);\n  VERIFY_IS_APPROX(s1*map1, map3);\n  \n  if(size<=256)\n  {\n    VERIFY_IS_EQUAL(map4, MatrixType::Ones(rows,cols));\n    map4 = map1;\n    MatrixType ma4 = map4;\n    VERIFY_IS_EQUAL(map1, map4);\n    VERIFY_IS_EQUAL(ma1, map4);\n    VERIFY_IS_EQUAL(ma1, ma4);\n    VERIFY_IS_APPROX(s1*map1, s1*map4);\n    \n    map4 *= s1;\n    VERIFY_IS_APPROX(s1*map1, map4);\n  }\n\n  internal::aligned_delete(array1, size);\n  internal::aligned_delete(array2, size);\n  delete[] array3;\n}\n\ntemplate<typename VectorType> void map_static_methods(const VectorType& m)\n{\n  typedef typename VectorType::Index Index;\n  typedef typename VectorType::Scalar Scalar;\n\n  Index size = m.size();\n\n  Scalar* array1 = internal::aligned_new<Scalar>(size);\n  Scalar* array2 = internal::aligned_new<Scalar>(size);\n  Scalar* array3 = new Scalar[size+1];\n  Scalar* array3unaligned = internal::UIntPtr(array3)%EIGEN_MAX_ALIGN_BYTES == 0 ? array3+1 : array3;\n\n  VectorType::MapAligned(array1, size) = VectorType::Random(size);\n  VectorType::Map(array2, size) = VectorType::Map(array1, size);\n  VectorType::Map(array3unaligned, size) = VectorType::Map(array1, size);\n  VectorType ma1 = VectorType::Map(array1, size);\n  VectorType ma2 = VectorType::MapAligned(array2, size);\n  VectorType ma3 = VectorType::Map(array3unaligned, size);\n  VERIFY_IS_EQUAL(ma1, ma2);\n  VERIFY_IS_EQUAL(ma1, ma3);\n\n  internal::aligned_delete(array1, size);\n  internal::aligned_delete(array2, size);\n  delete[] array3;\n}\n\ntemplate<typename PlainObjectType> void check_const_correctness(const PlainObjectType&)\n{\n  // there's a lot that we can't test here while still having this test compile!\n  // the only possible approach would be to run a script trying to compile stuff and checking that it fails.\n  // CMake can help with that.\n\n  // verify that map-to-const don't have LvalueBit\n  typedef typename internal::add_const<PlainObjectType>::type ConstPlainObjectType;\n  VERIFY( !(internal::traits<Map<ConstPlainObjectType> >::Flags & LvalueBit) );\n  VERIFY( !(internal::traits<Map<ConstPlainObjectType, AlignedMax> >::Flags & LvalueBit) );\n  VERIFY( !(Map<ConstPlainObjectType>::Flags & LvalueBit) );\n  VERIFY( !(Map<ConstPlainObjectType, AlignedMax>::Flags & LvalueBit) );\n}\n\ntemplate<typename Scalar>\nvoid map_not_aligned_on_scalar()\n{\n  typedef Matrix<Scalar,Dynamic,Dynamic> MatrixType;\n  typedef typename MatrixType::Index Index;\n  Index size = 11;\n  Scalar* array1 = internal::aligned_new<Scalar>((size+1)*(size+1)+1);\n  Scalar* array2 = reinterpret_cast<Scalar*>(sizeof(Scalar)/2+std::size_t(array1));\n  Map<MatrixType,0,OuterStride<> > map2(array2, size, size, OuterStride<>(size+1));\n  MatrixType m2 = MatrixType::Random(size,size);\n  map2 = m2;\n  VERIFY_IS_EQUAL(m2, map2);\n  \n  typedef Matrix<Scalar,Dynamic,1> VectorType;\n  Map<VectorType> map3(array2, size);\n  MatrixType v3 = VectorType::Random(size);\n  map3 = v3;\n  VERIFY_IS_EQUAL(v3, map3);\n  \n  internal::aligned_delete(array1, (size+1)*(size+1)+1);\n}\n\nvoid test_mapped_matrix()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( map_class_vector(Matrix<float, 1, 1>()) );\n    CALL_SUBTEST_1( check_const_correctness(Matrix<float, 1, 1>()) );\n    CALL_SUBTEST_2( map_class_vector(Vector4d()) );\n    CALL_SUBTEST_2( map_class_vector(VectorXd(13)) );\n    CALL_SUBTEST_2( check_const_correctness(Matrix4d()) );\n    CALL_SUBTEST_3( map_class_vector(RowVector4f()) );\n    CALL_SUBTEST_4( map_class_vector(VectorXcf(8)) );\n    CALL_SUBTEST_5( map_class_vector(VectorXi(12)) );\n    CALL_SUBTEST_5( check_const_correctness(VectorXi(12)) );\n\n    CALL_SUBTEST_1( map_class_matrix(Matrix<float, 1, 1>()) );\n    CALL_SUBTEST_2( map_class_matrix(Matrix4d()) );\n    CALL_SUBTEST_11( map_class_matrix(Matrix<float,3,5>()) );\n    CALL_SUBTEST_4( map_class_matrix(MatrixXcf(internal::random<int>(1,10),internal::random<int>(1,10))) );\n    CALL_SUBTEST_5( map_class_matrix(MatrixXi(internal::random<int>(1,10),internal::random<int>(1,10))) );\n\n    CALL_SUBTEST_6( map_static_methods(Matrix<double, 1, 1>()) );\n    CALL_SUBTEST_7( map_static_methods(Vector3f()) );\n    CALL_SUBTEST_8( map_static_methods(RowVector3d()) );\n    CALL_SUBTEST_9( map_static_methods(VectorXcd(8)) );\n    CALL_SUBTEST_10( map_static_methods(VectorXf(12)) );\n    \n    CALL_SUBTEST_11( map_not_aligned_on_scalar<double>() );\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/mapstaticmethods.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2011 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\nfloat *ptr;\nconst float *const_ptr;\n\ntemplate<typename PlainObjectType,\n         bool IsDynamicSize = PlainObjectType::SizeAtCompileTime == Dynamic,\n         bool IsVector = PlainObjectType::IsVectorAtCompileTime\n>\nstruct mapstaticmethods_impl {};\n\ntemplate<typename PlainObjectType, bool IsVector>\nstruct mapstaticmethods_impl<PlainObjectType, false, IsVector>\n{\n  static void run(const PlainObjectType& m)\n  {\n    mapstaticmethods_impl<PlainObjectType, true, IsVector>::run(m);\n\n    int i = internal::random<int>(2,5), j = internal::random<int>(2,5);\n\n    PlainObjectType::Map(ptr).setZero();\n    PlainObjectType::MapAligned(ptr).setZero();\n    PlainObjectType::Map(const_ptr).sum();\n    PlainObjectType::MapAligned(const_ptr).sum();\n\n    PlainObjectType::Map(ptr, InnerStride<>(i)).setZero();\n    PlainObjectType::MapAligned(ptr, InnerStride<>(i)).setZero();\n    PlainObjectType::Map(const_ptr, InnerStride<>(i)).sum();\n    PlainObjectType::MapAligned(const_ptr, InnerStride<>(i)).sum();\n\n    PlainObjectType::Map(ptr, InnerStride<2>()).setZero();\n    PlainObjectType::MapAligned(ptr, InnerStride<3>()).setZero();\n    PlainObjectType::Map(const_ptr, InnerStride<4>()).sum();\n    PlainObjectType::MapAligned(const_ptr, InnerStride<5>()).sum();\n\n    PlainObjectType::Map(ptr, OuterStride<>(i)).setZero();\n    PlainObjectType::MapAligned(ptr, OuterStride<>(i)).setZero();\n    PlainObjectType::Map(const_ptr, OuterStride<>(i)).sum();\n    PlainObjectType::MapAligned(const_ptr, OuterStride<>(i)).sum();\n\n    PlainObjectType::Map(ptr, OuterStride<2>()).setZero();\n    PlainObjectType::MapAligned(ptr, OuterStride<3>()).setZero();\n    PlainObjectType::Map(const_ptr, OuterStride<4>()).sum();\n    PlainObjectType::MapAligned(const_ptr, OuterStride<5>()).sum();\n\n    PlainObjectType::Map(ptr, Stride<Dynamic, Dynamic>(i,j)).setZero();\n    PlainObjectType::MapAligned(ptr, Stride<2,Dynamic>(2,i)).setZero();\n    PlainObjectType::Map(const_ptr, Stride<Dynamic,3>(i,3)).sum();\n    PlainObjectType::MapAligned(const_ptr, Stride<Dynamic, Dynamic>(i,j)).sum();\n\n    PlainObjectType::Map(ptr, Stride<2,3>()).setZero();\n    PlainObjectType::MapAligned(ptr, Stride<3,4>()).setZero();\n    PlainObjectType::Map(const_ptr, Stride<2,4>()).sum();\n    PlainObjectType::MapAligned(const_ptr, Stride<5,3>()).sum();\n  }\n};\n\ntemplate<typename PlainObjectType>\nstruct mapstaticmethods_impl<PlainObjectType, true, false>\n{\n  static void run(const PlainObjectType& m)\n  {\n    typedef typename PlainObjectType::Index Index;\n    Index rows = m.rows(), cols = m.cols();\n\n    int i = internal::random<int>(2,5), j = internal::random<int>(2,5);\n\n    PlainObjectType::Map(ptr, rows, cols).setZero();\n    PlainObjectType::MapAligned(ptr, rows, cols).setZero();\n    PlainObjectType::Map(const_ptr, rows, cols).sum();\n    PlainObjectType::MapAligned(const_ptr, rows, cols).sum();\n\n    PlainObjectType::Map(ptr, rows, cols, InnerStride<>(i)).setZero();\n    PlainObjectType::MapAligned(ptr, rows, cols, InnerStride<>(i)).setZero();\n    PlainObjectType::Map(const_ptr, rows, cols, InnerStride<>(i)).sum();\n    PlainObjectType::MapAligned(const_ptr, rows, cols, InnerStride<>(i)).sum();\n\n    PlainObjectType::Map(ptr, rows, cols, InnerStride<2>()).setZero();\n    PlainObjectType::MapAligned(ptr, rows, cols, InnerStride<3>()).setZero();\n    PlainObjectType::Map(const_ptr, rows, cols, InnerStride<4>()).sum();\n    PlainObjectType::MapAligned(const_ptr, rows, cols, InnerStride<5>()).sum();\n\n    PlainObjectType::Map(ptr, rows, cols, OuterStride<>(i)).setZero();\n    PlainObjectType::MapAligned(ptr, rows, cols, OuterStride<>(i)).setZero();\n    PlainObjectType::Map(const_ptr, rows, cols, OuterStride<>(i)).sum();\n    PlainObjectType::MapAligned(const_ptr, rows, cols, OuterStride<>(i)).sum();\n\n    PlainObjectType::Map(ptr, rows, cols, OuterStride<2>()).setZero();\n    PlainObjectType::MapAligned(ptr, rows, cols, OuterStride<3>()).setZero();\n    PlainObjectType::Map(const_ptr, rows, cols, OuterStride<4>()).sum();\n    PlainObjectType::MapAligned(const_ptr, rows, cols, OuterStride<5>()).sum();\n\n    PlainObjectType::Map(ptr, rows, cols, Stride<Dynamic, Dynamic>(i,j)).setZero();\n    PlainObjectType::MapAligned(ptr, rows, cols, Stride<2,Dynamic>(2,i)).setZero();\n    PlainObjectType::Map(const_ptr, rows, cols, Stride<Dynamic,3>(i,3)).sum();\n    PlainObjectType::MapAligned(const_ptr, rows, cols, Stride<Dynamic, Dynamic>(i,j)).sum();\n\n    PlainObjectType::Map(ptr, rows, cols, Stride<2,3>()).setZero();\n    PlainObjectType::MapAligned(ptr, rows, cols, Stride<3,4>()).setZero();\n    PlainObjectType::Map(const_ptr, rows, cols, Stride<2,4>()).sum();\n    PlainObjectType::MapAligned(const_ptr, rows, cols, Stride<5,3>()).sum();\n  }\n};\n\ntemplate<typename PlainObjectType>\nstruct mapstaticmethods_impl<PlainObjectType, true, true>\n{\n  static void run(const PlainObjectType& v)\n  {\n    typedef typename PlainObjectType::Index Index;\n    Index size = v.size();\n\n    int i = internal::random<int>(2,5);\n\n    PlainObjectType::Map(ptr, size).setZero();\n    PlainObjectType::MapAligned(ptr, size).setZero();\n    PlainObjectType::Map(const_ptr, size).sum();\n    PlainObjectType::MapAligned(const_ptr, size).sum();\n\n    PlainObjectType::Map(ptr, size, InnerStride<>(i)).setZero();\n    PlainObjectType::MapAligned(ptr, size, InnerStride<>(i)).setZero();\n    PlainObjectType::Map(const_ptr, size, InnerStride<>(i)).sum();\n    PlainObjectType::MapAligned(const_ptr, size, InnerStride<>(i)).sum();\n\n    PlainObjectType::Map(ptr, size, InnerStride<2>()).setZero();\n    PlainObjectType::MapAligned(ptr, size, InnerStride<3>()).setZero();\n    PlainObjectType::Map(const_ptr, size, InnerStride<4>()).sum();\n    PlainObjectType::MapAligned(const_ptr, size, InnerStride<5>()).sum();\n  }\n};\n\ntemplate<typename PlainObjectType>\nvoid mapstaticmethods(const PlainObjectType& m)\n{\n  mapstaticmethods_impl<PlainObjectType>::run(m);\n  VERIFY(true); // just to avoid 'unused function' warning\n}\n\nvoid test_mapstaticmethods()\n{\n  ptr = internal::aligned_new<float>(1000);\n  for(int i = 0; i < 1000; i++) ptr[i] = float(i);\n\n  const_ptr = ptr;\n\n  CALL_SUBTEST_1(( mapstaticmethods(Matrix<float, 1, 1>()) ));\n  CALL_SUBTEST_1(( mapstaticmethods(Vector2f()) ));\n  CALL_SUBTEST_2(( mapstaticmethods(Vector3f()) ));\n  CALL_SUBTEST_2(( mapstaticmethods(Matrix2f()) ));\n  CALL_SUBTEST_3(( mapstaticmethods(Matrix4f()) ));\n  CALL_SUBTEST_3(( mapstaticmethods(Array4f()) ));\n  CALL_SUBTEST_4(( mapstaticmethods(Array3f()) ));\n  CALL_SUBTEST_4(( mapstaticmethods(Array33f()) ));\n  CALL_SUBTEST_5(( mapstaticmethods(Array44f()) ));\n  CALL_SUBTEST_5(( mapstaticmethods(VectorXf(1)) ));\n  CALL_SUBTEST_5(( mapstaticmethods(VectorXf(8)) ));\n  CALL_SUBTEST_6(( mapstaticmethods(MatrixXf(1,1)) ));\n  CALL_SUBTEST_6(( mapstaticmethods(MatrixXf(5,7)) ));\n  CALL_SUBTEST_7(( mapstaticmethods(ArrayXf(1)) ));\n  CALL_SUBTEST_7(( mapstaticmethods(ArrayXf(5)) ));\n  CALL_SUBTEST_8(( mapstaticmethods(ArrayXXf(1,1)) ));\n  CALL_SUBTEST_8(( mapstaticmethods(ArrayXXf(8,6)) ));\n\n  internal::aligned_delete(ptr, 1000);\n}\n\n"
  },
  {
    "path": "include/eigen3/test/mapstride.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\ntemplate<int Alignment,typename VectorType> void map_class_vector(const VectorType& m)\n{\n  typedef typename VectorType::Index Index;\n  typedef typename VectorType::Scalar Scalar;\n\n  Index size = m.size();\n\n  VectorType v = VectorType::Random(size);\n\n  Index arraysize = 3*size;\n  \n  Scalar* a_array = internal::aligned_new<Scalar>(arraysize+1);\n  Scalar* array = a_array;\n  if(Alignment!=Aligned)\n    array = (Scalar*)(internal::IntPtr(a_array) + (internal::packet_traits<Scalar>::AlignedOnScalar?sizeof(Scalar):sizeof(typename NumTraits<Scalar>::Real)));\n\n  {\n    Map<VectorType, Alignment, InnerStride<3> > map(array, size);\n    map = v;\n    for(int i = 0; i < size; ++i)\n    {\n      VERIFY(array[3*i] == v[i]);\n      VERIFY(map[i] == v[i]);\n    }\n  }\n\n  {\n    Map<VectorType, Unaligned, InnerStride<Dynamic> > map(array, size, InnerStride<Dynamic>(2));\n    map = v;\n    for(int i = 0; i < size; ++i)\n    {\n      VERIFY(array[2*i] == v[i]);\n      VERIFY(map[i] == v[i]);\n    }\n  }\n\n  internal::aligned_delete(a_array, arraysize+1);\n}\n\ntemplate<int Alignment,typename MatrixType> void map_class_matrix(const MatrixType& _m)\n{\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n\n  Index rows = _m.rows(), cols = _m.cols();\n\n  MatrixType m = MatrixType::Random(rows,cols);\n  Scalar s1 = internal::random<Scalar>();\n\n  Index arraysize = 4*(rows+4)*(cols+4);\n\n  Scalar* a_array1 = internal::aligned_new<Scalar>(arraysize+1);\n  Scalar* array1 = a_array1;\n  if(Alignment!=Aligned)\n    array1 = (Scalar*)(internal::IntPtr(a_array1) + (internal::packet_traits<Scalar>::AlignedOnScalar?sizeof(Scalar):sizeof(typename NumTraits<Scalar>::Real)));\n\n  Scalar a_array2[256];\n  Scalar* array2 = a_array2;\n  if(Alignment!=Aligned)\n    array2 = (Scalar*)(internal::IntPtr(a_array2) + (internal::packet_traits<Scalar>::AlignedOnScalar?sizeof(Scalar):sizeof(typename NumTraits<Scalar>::Real)));\n  else\n    array2 = (Scalar*)(((internal::UIntPtr(a_array2)+EIGEN_MAX_ALIGN_BYTES-1)/EIGEN_MAX_ALIGN_BYTES)*EIGEN_MAX_ALIGN_BYTES);\n  Index maxsize2 = a_array2 - array2 + 256;\n  \n  // test no inner stride and some dynamic outer stride\n  for(int k=0; k<2; ++k)\n  {\n    if(k==1 && (m.innerSize()+1)*m.outerSize() > maxsize2)\n      break;\n    Scalar* array = (k==0 ? array1 : array2);\n    \n    Map<MatrixType, Alignment, OuterStride<Dynamic> > map(array, rows, cols, OuterStride<Dynamic>(m.innerSize()+1));\n    map = m;\n    VERIFY(map.outerStride() == map.innerSize()+1);\n    for(int i = 0; i < m.outerSize(); ++i)\n      for(int j = 0; j < m.innerSize(); ++j)\n      {\n        VERIFY(array[map.outerStride()*i+j] == m.coeffByOuterInner(i,j));\n        VERIFY(map.coeffByOuterInner(i,j) == m.coeffByOuterInner(i,j));\n      }\n    VERIFY_IS_APPROX(s1*map,s1*m);\n    map *= s1;\n    VERIFY_IS_APPROX(map,s1*m);\n  }\n\n  // test no inner stride and an outer stride of +4. This is quite important as for fixed-size matrices,\n  // this allows to hit the special case where it's vectorizable.\n  for(int k=0; k<2; ++k)\n  {\n    if(k==1 && (m.innerSize()+4)*m.outerSize() > maxsize2)\n      break;\n    Scalar* array = (k==0 ? array1 : array2);\n    \n    enum {\n      InnerSize = MatrixType::InnerSizeAtCompileTime,\n      OuterStrideAtCompileTime = InnerSize==Dynamic ? Dynamic : InnerSize+4\n    };\n    Map<MatrixType, Alignment, OuterStride<OuterStrideAtCompileTime> >\n      map(array, rows, cols, OuterStride<OuterStrideAtCompileTime>(m.innerSize()+4));\n    map = m;\n    VERIFY(map.outerStride() == map.innerSize()+4);\n    for(int i = 0; i < m.outerSize(); ++i)\n      for(int j = 0; j < m.innerSize(); ++j)\n      {\n        VERIFY(array[map.outerStride()*i+j] == m.coeffByOuterInner(i,j));\n        VERIFY(map.coeffByOuterInner(i,j) == m.coeffByOuterInner(i,j));\n      }\n    VERIFY_IS_APPROX(s1*map,s1*m);\n    map *= s1;\n    VERIFY_IS_APPROX(map,s1*m);\n  }\n\n  // test both inner stride and outer stride\n  for(int k=0; k<2; ++k)\n  {\n    if(k==1 && (2*m.innerSize()+1)*(m.outerSize()*2) > maxsize2)\n      break;\n    Scalar* array = (k==0 ? array1 : array2);\n    \n    Map<MatrixType, Alignment, Stride<Dynamic,Dynamic> > map(array, rows, cols, Stride<Dynamic,Dynamic>(2*m.innerSize()+1, 2));\n    map = m;\n    VERIFY(map.outerStride() == 2*map.innerSize()+1);\n    VERIFY(map.innerStride() == 2);\n    for(int i = 0; i < m.outerSize(); ++i)\n      for(int j = 0; j < m.innerSize(); ++j)\n      {\n        VERIFY(array[map.outerStride()*i+map.innerStride()*j] == m.coeffByOuterInner(i,j));\n        VERIFY(map.coeffByOuterInner(i,j) == m.coeffByOuterInner(i,j));\n      }\n    VERIFY_IS_APPROX(s1*map,s1*m);\n    map *= s1;\n    VERIFY_IS_APPROX(map,s1*m);\n  }\n\n  // test inner stride and no outer stride\n  for(int k=0; k<2; ++k)\n  {\n    if(k==1 && (m.innerSize()*2)*m.outerSize() > maxsize2)\n      break;\n    Scalar* array = (k==0 ? array1 : array2);\n\n    Map<MatrixType, Alignment, InnerStride<Dynamic> > map(array, rows, cols, InnerStride<Dynamic>(2));\n    map = m;\n    VERIFY(map.outerStride() == map.innerSize()*2);\n    for(int i = 0; i < m.outerSize(); ++i)\n      for(int j = 0; j < m.innerSize(); ++j)\n      {\n        VERIFY(array[map.innerSize()*i*2+j*2] == m.coeffByOuterInner(i,j));\n        VERIFY(map.coeffByOuterInner(i,j) == m.coeffByOuterInner(i,j));\n      }\n    VERIFY_IS_APPROX(s1*map,s1*m);\n    map *= s1;\n    VERIFY_IS_APPROX(map,s1*m);\n  }\n\n  internal::aligned_delete(a_array1, arraysize+1);\n}\n\n// Additional tests for inner-stride but no outer-stride\ntemplate<int>\nvoid bug1453()\n{\n  const int data[] = {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31};\n  typedef Matrix<int,Dynamic,Dynamic,RowMajor> RowMatrixXi;\n  typedef Matrix<int,2,3,ColMajor> ColMatrix23i;\n  typedef Matrix<int,3,2,ColMajor> ColMatrix32i;\n  typedef Matrix<int,2,3,RowMajor> RowMatrix23i;\n  typedef Matrix<int,3,2,RowMajor> RowMatrix32i;\n\n  VERIFY_IS_APPROX(MatrixXi::Map(data, 2, 3, InnerStride<2>()), MatrixXi::Map(data, 2, 3, Stride<4,2>()));\n  VERIFY_IS_APPROX(MatrixXi::Map(data, 2, 3, InnerStride<>(2)), MatrixXi::Map(data, 2, 3, Stride<4,2>()));\n  VERIFY_IS_APPROX(MatrixXi::Map(data, 3, 2, InnerStride<2>()), MatrixXi::Map(data, 3, 2, Stride<6,2>()));\n  VERIFY_IS_APPROX(MatrixXi::Map(data, 3, 2, InnerStride<>(2)), MatrixXi::Map(data, 3, 2, Stride<6,2>()));\n\n  VERIFY_IS_APPROX(RowMatrixXi::Map(data, 2, 3, InnerStride<2>()), RowMatrixXi::Map(data, 2, 3, Stride<6,2>()));\n  VERIFY_IS_APPROX(RowMatrixXi::Map(data, 2, 3, InnerStride<>(2)), RowMatrixXi::Map(data, 2, 3, Stride<6,2>()));\n  VERIFY_IS_APPROX(RowMatrixXi::Map(data, 3, 2, InnerStride<2>()), RowMatrixXi::Map(data, 3, 2, Stride<4,2>()));\n  VERIFY_IS_APPROX(RowMatrixXi::Map(data, 3, 2, InnerStride<>(2)), RowMatrixXi::Map(data, 3, 2, Stride<4,2>()));\n\n  VERIFY_IS_APPROX(ColMatrix23i::Map(data, InnerStride<2>()), MatrixXi::Map(data, 2, 3, Stride<4,2>()));\n  VERIFY_IS_APPROX(ColMatrix23i::Map(data, InnerStride<>(2)), MatrixXi::Map(data, 2, 3, Stride<4,2>()));\n  VERIFY_IS_APPROX(ColMatrix32i::Map(data, InnerStride<2>()), MatrixXi::Map(data, 3, 2, Stride<6,2>()));\n  VERIFY_IS_APPROX(ColMatrix32i::Map(data, InnerStride<>(2)), MatrixXi::Map(data, 3, 2, Stride<6,2>()));\n\n  VERIFY_IS_APPROX(RowMatrix23i::Map(data, InnerStride<2>()), RowMatrixXi::Map(data, 2, 3, Stride<6,2>()));\n  VERIFY_IS_APPROX(RowMatrix23i::Map(data, InnerStride<>(2)), RowMatrixXi::Map(data, 2, 3, Stride<6,2>()));\n  VERIFY_IS_APPROX(RowMatrix32i::Map(data, InnerStride<2>()), RowMatrixXi::Map(data, 3, 2, Stride<4,2>()));\n  VERIFY_IS_APPROX(RowMatrix32i::Map(data, InnerStride<>(2)), RowMatrixXi::Map(data, 3, 2, Stride<4,2>()));\n}\n\nvoid test_mapstride()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    int maxn = 30;\n    CALL_SUBTEST_1( map_class_vector<Aligned>(Matrix<float, 1, 1>()) );\n    CALL_SUBTEST_1( map_class_vector<Unaligned>(Matrix<float, 1, 1>()) );\n    CALL_SUBTEST_2( map_class_vector<Aligned>(Vector4d()) );\n    CALL_SUBTEST_2( map_class_vector<Unaligned>(Vector4d()) );\n    CALL_SUBTEST_3( map_class_vector<Aligned>(RowVector4f()) );\n    CALL_SUBTEST_3( map_class_vector<Unaligned>(RowVector4f()) );\n    CALL_SUBTEST_4( map_class_vector<Aligned>(VectorXcf(internal::random<int>(1,maxn))) );\n    CALL_SUBTEST_4( map_class_vector<Unaligned>(VectorXcf(internal::random<int>(1,maxn))) );\n    CALL_SUBTEST_5( map_class_vector<Aligned>(VectorXi(internal::random<int>(1,maxn))) );\n    CALL_SUBTEST_5( map_class_vector<Unaligned>(VectorXi(internal::random<int>(1,maxn))) );\n\n    CALL_SUBTEST_1( map_class_matrix<Aligned>(Matrix<float, 1, 1>()) );\n    CALL_SUBTEST_1( map_class_matrix<Unaligned>(Matrix<float, 1, 1>()) );\n    CALL_SUBTEST_2( map_class_matrix<Aligned>(Matrix4d()) );\n    CALL_SUBTEST_2( map_class_matrix<Unaligned>(Matrix4d()) );\n    CALL_SUBTEST_3( map_class_matrix<Aligned>(Matrix<float,3,5>()) );\n    CALL_SUBTEST_3( map_class_matrix<Unaligned>(Matrix<float,3,5>()) );\n    CALL_SUBTEST_3( map_class_matrix<Aligned>(Matrix<float,4,8>()) );\n    CALL_SUBTEST_3( map_class_matrix<Unaligned>(Matrix<float,4,8>()) );\n    CALL_SUBTEST_4( map_class_matrix<Aligned>(MatrixXcf(internal::random<int>(1,maxn),internal::random<int>(1,maxn))) );\n    CALL_SUBTEST_4( map_class_matrix<Unaligned>(MatrixXcf(internal::random<int>(1,maxn),internal::random<int>(1,maxn))) );\n    CALL_SUBTEST_5( map_class_matrix<Aligned>(MatrixXi(internal::random<int>(1,maxn),internal::random<int>(1,maxn))) );\n    CALL_SUBTEST_5( map_class_matrix<Unaligned>(MatrixXi(internal::random<int>(1,maxn),internal::random<int>(1,maxn))) );\n    CALL_SUBTEST_6( map_class_matrix<Aligned>(MatrixXcd(internal::random<int>(1,maxn),internal::random<int>(1,maxn))) );\n    CALL_SUBTEST_6( map_class_matrix<Unaligned>(MatrixXcd(internal::random<int>(1,maxn),internal::random<int>(1,maxn))) );\n\n    CALL_SUBTEST_5( bug1453<0>() );\n    \n    TEST_SET_BUT_UNUSED_VARIABLE(maxn);\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/meta.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\ntemplate<typename From, typename To>\nbool check_is_convertible(const From&, const To&)\n{\n  return internal::is_convertible<From,To>::value;\n}\n\nvoid test_meta()\n{\n  VERIFY((internal::conditional<(3<4),internal::true_type, internal::false_type>::type::value));\n  VERIFY(( internal::is_same<float,float>::value));\n  VERIFY((!internal::is_same<float,double>::value));\n  VERIFY((!internal::is_same<float,float&>::value));\n  VERIFY((!internal::is_same<float,const float&>::value));\n  \n  VERIFY(( internal::is_same<float,internal::remove_all<const float&>::type >::value));\n  VERIFY(( internal::is_same<float,internal::remove_all<const float*>::type >::value));\n  VERIFY(( internal::is_same<float,internal::remove_all<const float*&>::type >::value));\n  VERIFY(( internal::is_same<float,internal::remove_all<float**>::type >::value));\n  VERIFY(( internal::is_same<float,internal::remove_all<float**&>::type >::value));\n  VERIFY(( internal::is_same<float,internal::remove_all<float* const *&>::type >::value));\n  VERIFY(( internal::is_same<float,internal::remove_all<float* const>::type >::value));\n\n  // test add_const\n  VERIFY(( internal::is_same< internal::add_const<float>::type, const float >::value));\n  VERIFY(( internal::is_same< internal::add_const<float*>::type, float* const>::value));\n  VERIFY(( internal::is_same< internal::add_const<float const*>::type, float const* const>::value));\n  VERIFY(( internal::is_same< internal::add_const<float&>::type, float& >::value));\n\n  // test remove_const\n  VERIFY(( internal::is_same< internal::remove_const<float const* const>::type, float const* >::value));\n  VERIFY(( internal::is_same< internal::remove_const<float const*>::type, float const* >::value));\n  VERIFY(( internal::is_same< internal::remove_const<float* const>::type, float* >::value));\n\n  // test add_const_on_value_type\n  VERIFY(( internal::is_same< internal::add_const_on_value_type<float&>::type, float const& >::value));\n  VERIFY(( internal::is_same< internal::add_const_on_value_type<float*>::type, float const* >::value));\n\n  VERIFY(( internal::is_same< internal::add_const_on_value_type<float>::type, const float >::value));\n  VERIFY(( internal::is_same< internal::add_const_on_value_type<const float>::type, const float >::value));\n\n  VERIFY(( internal::is_same< internal::add_const_on_value_type<const float* const>::type, const float* const>::value));\n  VERIFY(( internal::is_same< internal::add_const_on_value_type<float* const>::type, const float* const>::value));\n  \n  VERIFY(( internal::is_same<float,internal::remove_reference<float&>::type >::value));\n  VERIFY(( internal::is_same<const float,internal::remove_reference<const float&>::type >::value));\n  VERIFY(( internal::is_same<float,internal::remove_pointer<float*>::type >::value));\n  VERIFY(( internal::is_same<const float,internal::remove_pointer<const float*>::type >::value));\n  VERIFY(( internal::is_same<float,internal::remove_pointer<float* const >::type >::value));\n  \n  VERIFY(( internal::is_convertible<float,double>::value ));\n  VERIFY(( internal::is_convertible<int,double>::value ));\n  VERIFY(( internal::is_convertible<double,int>::value ));\n  VERIFY((!internal::is_convertible<std::complex<double>,double>::value ));\n  VERIFY(( internal::is_convertible<Array33f,Matrix3f>::value ));\n//   VERIFY((!internal::is_convertible<Matrix3f,Matrix3d>::value )); //does not work because the conversion is prevented by a static assertion\n  VERIFY((!internal::is_convertible<Array33f,int>::value ));\n  VERIFY((!internal::is_convertible<MatrixXf,float>::value ));\n  {\n    float f;\n    MatrixXf A, B;\n    VectorXf a, b;\n    VERIFY(( check_is_convertible(a.dot(b), f) ));\n    VERIFY(( check_is_convertible(a.transpose()*b, f) ));\n    VERIFY((!check_is_convertible(A*B, f) ));\n    VERIFY(( check_is_convertible(A*B, A) ));\n  }\n  \n  VERIFY(internal::meta_sqrt<1>::ret == 1);\n  #define VERIFY_META_SQRT(X) VERIFY(internal::meta_sqrt<X>::ret == int(std::sqrt(double(X))))\n  VERIFY_META_SQRT(2);\n  VERIFY_META_SQRT(3);\n  VERIFY_META_SQRT(4);\n  VERIFY_META_SQRT(5);\n  VERIFY_META_SQRT(6);\n  VERIFY_META_SQRT(8);\n  VERIFY_META_SQRT(9);\n  VERIFY_META_SQRT(15);\n  VERIFY_META_SQRT(16);\n  VERIFY_META_SQRT(17);\n  VERIFY_META_SQRT(255);\n  VERIFY_META_SQRT(256);\n  VERIFY_META_SQRT(257);\n  VERIFY_META_SQRT(1023);\n  VERIFY_META_SQRT(1024);\n  VERIFY_META_SQRT(1025);\n}\n"
  },
  {
    "path": "include/eigen3/test/metis_support.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"sparse_solver.h\"\n#include <Eigen/SparseLU>\n#include <Eigen/MetisSupport>\n#include <unsupported/Eigen/SparseExtra>\n\ntemplate<typename T> void test_metis_T()\n{\n  SparseLU<SparseMatrix<T, ColMajor>, MetisOrdering<int> > sparselu_metis;\n  \n  check_sparse_square_solving(sparselu_metis); \n}\n\nvoid test_metis_support()\n{\n  CALL_SUBTEST_1(test_metis_T<double>());\n}\n"
  },
  {
    "path": "include/eigen3/test/miscmatrices.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\ntemplate<typename MatrixType> void miscMatrices(const MatrixType& m)\n{\n  /* this test covers the following files:\n     DiagonalMatrix.h Ones.h\n  */\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  Index r = internal::random<Index>(0, rows-1), r2 = internal::random<Index>(0, rows-1), c = internal::random<Index>(0, cols-1);\n  VERIFY_IS_APPROX(MatrixType::Ones(rows,cols)(r,c), static_cast<Scalar>(1));\n  MatrixType m1 = MatrixType::Ones(rows,cols);\n  VERIFY_IS_APPROX(m1(r,c), static_cast<Scalar>(1));\n  VectorType v1 = VectorType::Random(rows);\n  v1[0];\n  Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>\n  square(v1.asDiagonal());\n  if(r==r2) VERIFY_IS_APPROX(square(r,r2), v1[r]);\n  else VERIFY_IS_MUCH_SMALLER_THAN(square(r,r2), static_cast<Scalar>(1));\n  square = MatrixType::Zero(rows, rows);\n  square.diagonal() = VectorType::Ones(rows);\n  VERIFY_IS_APPROX(square, MatrixType::Identity(rows, rows));\n}\n\nvoid test_miscmatrices()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( miscMatrices(Matrix<float, 1, 1>()) );\n    CALL_SUBTEST_2( miscMatrices(Matrix4d()) );\n    CALL_SUBTEST_3( miscMatrices(MatrixXcf(3, 3)) );\n    CALL_SUBTEST_4( miscMatrices(MatrixXi(8, 12)) );\n    CALL_SUBTEST_5( miscMatrices(MatrixXcd(20, 20)) );\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/mixingtypes.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n// work around \"uninitialized\" warnings and give that option some testing\n#define EIGEN_INITIALIZE_MATRICES_BY_ZERO\n\n#ifndef EIGEN_NO_STATIC_ASSERT\n#define EIGEN_NO_STATIC_ASSERT // turn static asserts into runtime asserts in order to check them\n#endif\n\n#if defined(EIGEN_TEST_PART_1) || defined(EIGEN_TEST_PART_2) || defined(EIGEN_TEST_PART_3)\n\n#ifndef EIGEN_DONT_VECTORIZE\n#define EIGEN_DONT_VECTORIZE\n#endif\n\n#endif\n\nstatic bool g_called;\n#define EIGEN_SCALAR_BINARY_OP_PLUGIN { g_called |= (!internal::is_same<LhsScalar,RhsScalar>::value); }\n\n#include \"main.h\"\n\nusing namespace std;\n\n#define VERIFY_MIX_SCALAR(XPR,REF) \\\n  g_called = false; \\\n  VERIFY_IS_APPROX(XPR,REF); \\\n  VERIFY( g_called && #XPR\" not properly optimized\");\n\ntemplate<int SizeAtCompileType> void mixingtypes(int size = SizeAtCompileType)\n{\n  typedef std::complex<float>   CF;\n  typedef std::complex<double>  CD;\n  typedef Matrix<float, SizeAtCompileType, SizeAtCompileType> Mat_f;\n  typedef Matrix<double, SizeAtCompileType, SizeAtCompileType> Mat_d;\n  typedef Matrix<std::complex<float>, SizeAtCompileType, SizeAtCompileType> Mat_cf;\n  typedef Matrix<std::complex<double>, SizeAtCompileType, SizeAtCompileType> Mat_cd;\n  typedef Matrix<float, SizeAtCompileType, 1> Vec_f;\n  typedef Matrix<double, SizeAtCompileType, 1> Vec_d;\n  typedef Matrix<std::complex<float>, SizeAtCompileType, 1> Vec_cf;\n  typedef Matrix<std::complex<double>, SizeAtCompileType, 1> Vec_cd;\n\n  Mat_f mf    = Mat_f::Random(size,size);\n  Mat_d md    = mf.template cast<double>();\n  //Mat_d rd    = md;\n  Mat_cf mcf  = Mat_cf::Random(size,size);\n  Mat_cd mcd  = mcf.template cast<complex<double> >();\n  Mat_cd rcd = mcd;\n  Vec_f vf    = Vec_f::Random(size,1);\n  Vec_d vd    = vf.template cast<double>();\n  Vec_cf vcf  = Vec_cf::Random(size,1);\n  Vec_cd vcd  = vcf.template cast<complex<double> >();\n  float           sf  = internal::random<float>();\n  double          sd  = internal::random<double>();\n  complex<float>  scf = internal::random<complex<float> >();\n  complex<double> scd = internal::random<complex<double> >();\n\n  mf+mf;\n\n  float  epsf = std::sqrt(std::numeric_limits<float> ::min EIGEN_EMPTY ());\n  double epsd = std::sqrt(std::numeric_limits<double>::min EIGEN_EMPTY ());\n\n  while(std::abs(sf )<epsf) sf  = internal::random<float>();\n  while(std::abs(sd )<epsd) sf  = internal::random<double>();\n  while(std::abs(scf)<epsf) scf = internal::random<CF>();\n  while(std::abs(scd)<epsd) scd = internal::random<CD>();\n\n//   VERIFY_RAISES_ASSERT(mf+md); // does not even compile\n\n#ifdef EIGEN_DONT_VECTORIZE\n  VERIFY_RAISES_ASSERT(vf=vd);\n  VERIFY_RAISES_ASSERT(vf+=vd);\n#endif\n  \n  // check scalar products\n  VERIFY_MIX_SCALAR(vcf * sf , vcf * complex<float>(sf));\n  VERIFY_MIX_SCALAR(sd * vcd , complex<double>(sd) * vcd);\n  VERIFY_MIX_SCALAR(vf * scf , vf.template cast<complex<float> >() * scf);\n  VERIFY_MIX_SCALAR(scd * vd , scd * vd.template cast<complex<double> >());\n\n  VERIFY_MIX_SCALAR(vcf * 2 , vcf * complex<float>(2));\n  VERIFY_MIX_SCALAR(vcf * 2.1 , vcf * complex<float>(2.1));\n  VERIFY_MIX_SCALAR(2 * vcf, vcf * complex<float>(2));\n  VERIFY_MIX_SCALAR(2.1 * vcf , vcf * complex<float>(2.1));\n\n  // check scalar quotients\n  VERIFY_MIX_SCALAR(vcf / sf , vcf / complex<float>(sf));\n  VERIFY_MIX_SCALAR(vf / scf , vf.template cast<complex<float> >() / scf);\n  VERIFY_MIX_SCALAR(vf.array()  / scf, vf.template cast<complex<float> >().array() / scf);\n  VERIFY_MIX_SCALAR(scd / vd.array() , scd / vd.template cast<complex<double> >().array());\n\n  // check scalar increment\n  VERIFY_MIX_SCALAR(vcf.array() + sf , vcf.array() + complex<float>(sf));\n  VERIFY_MIX_SCALAR(sd  + vcd.array(), complex<double>(sd) + vcd.array());\n  VERIFY_MIX_SCALAR(vf.array()  + scf, vf.template cast<complex<float> >().array() + scf);\n  VERIFY_MIX_SCALAR(scd + vd.array() , scd + vd.template cast<complex<double> >().array());\n\n  // check scalar subtractions\n  VERIFY_MIX_SCALAR(vcf.array() - sf , vcf.array() - complex<float>(sf));\n  VERIFY_MIX_SCALAR(sd  - vcd.array(), complex<double>(sd) - vcd.array());\n  VERIFY_MIX_SCALAR(vf.array()  - scf, vf.template cast<complex<float> >().array() - scf);\n  VERIFY_MIX_SCALAR(scd - vd.array() , scd - vd.template cast<complex<double> >().array());\n\n  // check scalar powers\n  VERIFY_MIX_SCALAR( pow(vcf.array(), sf),        Eigen::pow(vcf.array(), complex<float>(sf)) );\n  VERIFY_MIX_SCALAR( vcf.array().pow(sf) ,        Eigen::pow(vcf.array(), complex<float>(sf)) );\n  VERIFY_MIX_SCALAR( pow(sd, vcd.array()),        Eigen::pow(complex<double>(sd), vcd.array()) );\n  VERIFY_MIX_SCALAR( Eigen::pow(vf.array(), scf), Eigen::pow(vf.template cast<complex<float> >().array(), scf) );\n  VERIFY_MIX_SCALAR( vf.array().pow(scf) ,        Eigen::pow(vf.template cast<complex<float> >().array(), scf) );\n  VERIFY_MIX_SCALAR( Eigen::pow(scd, vd.array()), Eigen::pow(scd, vd.template cast<complex<double> >().array()) );\n\n  // check dot product\n  vf.dot(vf);\n#if 0 // we get other compilation errors here than just static asserts\n  VERIFY_RAISES_ASSERT(vd.dot(vf));\n#endif\n  VERIFY_IS_APPROX(vcf.dot(vf), vcf.dot(vf.template cast<complex<float> >()));\n\n  // check diagonal product\n  VERIFY_IS_APPROX(vf.asDiagonal() * mcf, vf.template cast<complex<float> >().asDiagonal() * mcf);\n  VERIFY_IS_APPROX(vcd.asDiagonal() * md, vcd.asDiagonal() * md.template cast<complex<double> >());\n  VERIFY_IS_APPROX(mcf * vf.asDiagonal(), mcf * vf.template cast<complex<float> >().asDiagonal());\n  VERIFY_IS_APPROX(md * vcd.asDiagonal(), md.template cast<complex<double> >() * vcd.asDiagonal());\n\n//   vd.asDiagonal() * mf;    // does not even compile\n//   vcd.asDiagonal() * mf;   // does not even compile\n\n  // check inner product\n  VERIFY_IS_APPROX((vf.transpose() * vcf).value(), (vf.template cast<complex<float> >().transpose() * vcf).value());\n\n  // check outer product\n  VERIFY_IS_APPROX((vf * vcf.transpose()).eval(), (vf.template cast<complex<float> >() * vcf.transpose()).eval());\n\n  // coeff wise product\n\n  VERIFY_IS_APPROX((vf * vcf.transpose()).eval(), (vf.template cast<complex<float> >() * vcf.transpose()).eval());\n\n  Mat_cd mcd2 = mcd;\n  VERIFY_IS_APPROX(mcd.array() *= md.array(), mcd2.array() *= md.array().template cast<std::complex<double> >());\n  \n  // check matrix-matrix products\n  VERIFY_IS_APPROX(sd*md*mcd, (sd*md).template cast<CD>().eval()*mcd);\n  VERIFY_IS_APPROX(sd*mcd*md, sd*mcd*md.template cast<CD>());\n  VERIFY_IS_APPROX(scd*md*mcd, scd*md.template cast<CD>().eval()*mcd);\n  VERIFY_IS_APPROX(scd*mcd*md, scd*mcd*md.template cast<CD>());\n\n  VERIFY_IS_APPROX(sf*mf*mcf, sf*mf.template cast<CF>()*mcf);\n  VERIFY_IS_APPROX(sf*mcf*mf, sf*mcf*mf.template cast<CF>());\n  VERIFY_IS_APPROX(scf*mf*mcf, scf*mf.template cast<CF>()*mcf);\n  VERIFY_IS_APPROX(scf*mcf*mf, scf*mcf*mf.template cast<CF>());\n\n  VERIFY_IS_APPROX(sd*md.adjoint()*mcd, (sd*md).template cast<CD>().eval().adjoint()*mcd);\n  VERIFY_IS_APPROX(sd*mcd.adjoint()*md, sd*mcd.adjoint()*md.template cast<CD>());\n  VERIFY_IS_APPROX(sd*md.adjoint()*mcd.adjoint(), (sd*md).template cast<CD>().eval().adjoint()*mcd.adjoint());\n  VERIFY_IS_APPROX(sd*mcd.adjoint()*md.adjoint(), sd*mcd.adjoint()*md.template cast<CD>().adjoint());\n  VERIFY_IS_APPROX(sd*md*mcd.adjoint(), (sd*md).template cast<CD>().eval()*mcd.adjoint());\n  VERIFY_IS_APPROX(sd*mcd*md.adjoint(), sd*mcd*md.template cast<CD>().adjoint());\n\n  VERIFY_IS_APPROX(sf*mf.adjoint()*mcf, (sf*mf).template cast<CF>().eval().adjoint()*mcf);\n  VERIFY_IS_APPROX(sf*mcf.adjoint()*mf, sf*mcf.adjoint()*mf.template cast<CF>());\n  VERIFY_IS_APPROX(sf*mf.adjoint()*mcf.adjoint(), (sf*mf).template cast<CF>().eval().adjoint()*mcf.adjoint());\n  VERIFY_IS_APPROX(sf*mcf.adjoint()*mf.adjoint(), sf*mcf.adjoint()*mf.template cast<CF>().adjoint());\n  VERIFY_IS_APPROX(sf*mf*mcf.adjoint(), (sf*mf).template cast<CF>().eval()*mcf.adjoint());\n  VERIFY_IS_APPROX(sf*mcf*mf.adjoint(), sf*mcf*mf.template cast<CF>().adjoint());\n\n  VERIFY_IS_APPROX(sf*mf*vcf, (sf*mf).template cast<CF>().eval()*vcf);\n  VERIFY_IS_APPROX(scf*mf*vcf,(scf*mf.template cast<CF>()).eval()*vcf);\n  VERIFY_IS_APPROX(sf*mcf*vf, sf*mcf*vf.template cast<CF>());\n  VERIFY_IS_APPROX(scf*mcf*vf,scf*mcf*vf.template cast<CF>());\n\n  VERIFY_IS_APPROX(sf*vcf.adjoint()*mf,  sf*vcf.adjoint()*mf.template cast<CF>().eval());\n  VERIFY_IS_APPROX(scf*vcf.adjoint()*mf, scf*vcf.adjoint()*mf.template cast<CF>().eval());\n  VERIFY_IS_APPROX(sf*vf.adjoint()*mcf,  sf*vf.adjoint().template cast<CF>().eval()*mcf);\n  VERIFY_IS_APPROX(scf*vf.adjoint()*mcf, scf*vf.adjoint().template cast<CF>().eval()*mcf);\n\n  VERIFY_IS_APPROX(sd*md*vcd, (sd*md).template cast<CD>().eval()*vcd);\n  VERIFY_IS_APPROX(scd*md*vcd,(scd*md.template cast<CD>()).eval()*vcd);\n  VERIFY_IS_APPROX(sd*mcd*vd, sd*mcd*vd.template cast<CD>().eval());\n  VERIFY_IS_APPROX(scd*mcd*vd,scd*mcd*vd.template cast<CD>().eval());\n\n  VERIFY_IS_APPROX(sd*vcd.adjoint()*md,  sd*vcd.adjoint()*md.template cast<CD>().eval());\n  VERIFY_IS_APPROX(scd*vcd.adjoint()*md, scd*vcd.adjoint()*md.template cast<CD>().eval());\n  VERIFY_IS_APPROX(sd*vd.adjoint()*mcd,  sd*vd.adjoint().template cast<CD>().eval()*mcd);\n  VERIFY_IS_APPROX(scd*vd.adjoint()*mcd, scd*vd.adjoint().template cast<CD>().eval()*mcd);\n\n  VERIFY_IS_APPROX( sd*vcd.adjoint()*md.template triangularView<Upper>(),  sd*vcd.adjoint()*md.template cast<CD>().eval().template triangularView<Upper>());\n  VERIFY_IS_APPROX(scd*vcd.adjoint()*md.template triangularView<Lower>(), scd*vcd.adjoint()*md.template cast<CD>().eval().template triangularView<Lower>());\n  VERIFY_IS_APPROX( sd*vcd.adjoint()*md.transpose().template triangularView<Upper>(),  sd*vcd.adjoint()*md.transpose().template cast<CD>().eval().template triangularView<Upper>());\n  VERIFY_IS_APPROX(scd*vcd.adjoint()*md.transpose().template triangularView<Lower>(), scd*vcd.adjoint()*md.transpose().template cast<CD>().eval().template triangularView<Lower>());\n  VERIFY_IS_APPROX( sd*vd.adjoint()*mcd.template triangularView<Lower>(),  sd*vd.adjoint().template cast<CD>().eval()*mcd.template triangularView<Lower>());\n  VERIFY_IS_APPROX(scd*vd.adjoint()*mcd.template triangularView<Upper>(), scd*vd.adjoint().template cast<CD>().eval()*mcd.template triangularView<Upper>());\n  VERIFY_IS_APPROX( sd*vd.adjoint()*mcd.transpose().template triangularView<Lower>(),  sd*vd.adjoint().template cast<CD>().eval()*mcd.transpose().template triangularView<Lower>());\n  VERIFY_IS_APPROX(scd*vd.adjoint()*mcd.transpose().template triangularView<Upper>(), scd*vd.adjoint().template cast<CD>().eval()*mcd.transpose().template triangularView<Upper>());\n\n  // Not supported yet: trmm\n//   VERIFY_IS_APPROX(sd*mcd*md.template triangularView<Lower>(),  sd*mcd*md.template cast<CD>().eval().template triangularView<Lower>());\n//   VERIFY_IS_APPROX(scd*mcd*md.template triangularView<Upper>(), scd*mcd*md.template cast<CD>().eval().template triangularView<Upper>());\n//   VERIFY_IS_APPROX(sd*md*mcd.template triangularView<Lower>(),  sd*md.template cast<CD>().eval()*mcd.template triangularView<Lower>());\n//   VERIFY_IS_APPROX(scd*md*mcd.template triangularView<Upper>(), scd*md.template cast<CD>().eval()*mcd.template triangularView<Upper>());\n\n  // Not supported yet: symv\n//   VERIFY_IS_APPROX(sd*vcd.adjoint()*md.template selfadjointView<Upper>(),  sd*vcd.adjoint()*md.template cast<CD>().eval().template selfadjointView<Upper>());\n//   VERIFY_IS_APPROX(scd*vcd.adjoint()*md.template selfadjointView<Lower>(), scd*vcd.adjoint()*md.template cast<CD>().eval().template selfadjointView<Lower>());\n//   VERIFY_IS_APPROX(sd*vd.adjoint()*mcd.template selfadjointView<Lower>(),  sd*vd.adjoint().template cast<CD>().eval()*mcd.template selfadjointView<Lower>());\n//   VERIFY_IS_APPROX(scd*vd.adjoint()*mcd.template selfadjointView<Upper>(), scd*vd.adjoint().template cast<CD>().eval()*mcd.template selfadjointView<Upper>());\n\n  // Not supported yet: symm\n//   VERIFY_IS_APPROX(sd*vcd.adjoint()*md.template selfadjointView<Upper>(),  sd*vcd.adjoint()*md.template cast<CD>().eval().template selfadjointView<Upper>());\n//   VERIFY_IS_APPROX(scd*vcd.adjoint()*md.template selfadjointView<Upper>(), scd*vcd.adjoint()*md.template cast<CD>().eval().template selfadjointView<Upper>());\n//   VERIFY_IS_APPROX(sd*vd.adjoint()*mcd.template selfadjointView<Upper>(),  sd*vd.adjoint().template cast<CD>().eval()*mcd.template selfadjointView<Upper>());\n//   VERIFY_IS_APPROX(scd*vd.adjoint()*mcd.template selfadjointView<Upper>(), scd*vd.adjoint().template cast<CD>().eval()*mcd.template selfadjointView<Upper>());\n\n  rcd.setZero();\n  VERIFY_IS_APPROX(Mat_cd(rcd.template triangularView<Upper>() = sd * mcd * md),\n                   Mat_cd((sd * mcd * md.template cast<CD>().eval()).template triangularView<Upper>()));\n  VERIFY_IS_APPROX(Mat_cd(rcd.template triangularView<Upper>() = sd * md * mcd),\n                   Mat_cd((sd * md.template cast<CD>().eval() * mcd).template triangularView<Upper>()));\n  VERIFY_IS_APPROX(Mat_cd(rcd.template triangularView<Upper>() = scd * mcd * md),\n                   Mat_cd((scd * mcd * md.template cast<CD>().eval()).template triangularView<Upper>()));\n  VERIFY_IS_APPROX(Mat_cd(rcd.template triangularView<Upper>() = scd * md * mcd),\n                   Mat_cd((scd * md.template cast<CD>().eval() * mcd).template triangularView<Upper>()));\n\n\n  VERIFY_IS_APPROX( md.array()  * mcd.array(), md.template cast<CD>().eval().array() * mcd.array() );\n  VERIFY_IS_APPROX( mcd.array() * md.array(),  mcd.array() * md.template cast<CD>().eval().array() );\n\n  VERIFY_IS_APPROX( md.array()  + mcd.array(), md.template cast<CD>().eval().array() + mcd.array() );\n  VERIFY_IS_APPROX( mcd.array() + md.array(),  mcd.array() + md.template cast<CD>().eval().array() );\n\n  VERIFY_IS_APPROX( md.array()  - mcd.array(), md.template cast<CD>().eval().array() - mcd.array() );\n  VERIFY_IS_APPROX( mcd.array() - md.array(),  mcd.array() - md.template cast<CD>().eval().array() );\n\n  if(mcd.array().abs().minCoeff()>epsd)\n  {\n    VERIFY_IS_APPROX( md.array() / mcd.array(), md.template cast<CD>().eval().array() / mcd.array() );\n  }\n  if(md.array().abs().minCoeff()>epsd)\n  {\n    VERIFY_IS_APPROX( mcd.array() / md.array(), mcd.array() / md.template cast<CD>().eval().array() );\n  }\n\n  if(md.array().abs().minCoeff()>epsd || mcd.array().abs().minCoeff()>epsd)\n  {\n    VERIFY_IS_APPROX( md.array().pow(mcd.array()), md.template cast<CD>().eval().array().pow(mcd.array()) );\n    VERIFY_IS_APPROX( mcd.array().pow(md.array()),  mcd.array().pow(md.template cast<CD>().eval().array()) );\n\n    VERIFY_IS_APPROX( pow(md.array(),mcd.array()), md.template cast<CD>().eval().array().pow(mcd.array()) );\n    VERIFY_IS_APPROX( pow(mcd.array(),md.array()),  mcd.array().pow(md.template cast<CD>().eval().array()) );\n  }\n\n  rcd = mcd;\n  VERIFY_IS_APPROX( rcd = md, md.template cast<CD>().eval() );\n  rcd = mcd;\n  VERIFY_IS_APPROX( rcd += md, mcd + md.template cast<CD>().eval() );\n  rcd = mcd;\n  VERIFY_IS_APPROX( rcd -= md, mcd - md.template cast<CD>().eval() );\n  rcd = mcd;\n  VERIFY_IS_APPROX( rcd.array() *= md.array(), mcd.array() * md.template cast<CD>().eval().array() );\n  rcd = mcd;\n  if(md.array().abs().minCoeff()>epsd)\n  {\n    VERIFY_IS_APPROX( rcd.array() /= md.array(), mcd.array() / md.template cast<CD>().eval().array() );\n  }\n\n  rcd = mcd;\n  VERIFY_IS_APPROX( rcd.noalias() += md + mcd*md, mcd + (md.template cast<CD>().eval()) + mcd*(md.template cast<CD>().eval()));\n\n  VERIFY_IS_APPROX( rcd.noalias()  = md*md,       ((md*md).eval().template cast<CD>()) );\n  rcd = mcd;\n  VERIFY_IS_APPROX( rcd.noalias() += md*md, mcd + ((md*md).eval().template cast<CD>()) );\n  rcd = mcd;\n  VERIFY_IS_APPROX( rcd.noalias() -= md*md, mcd - ((md*md).eval().template cast<CD>()) );\n\n  VERIFY_IS_APPROX( rcd.noalias()  = mcd + md*md,       mcd + ((md*md).eval().template cast<CD>()) );\n  rcd = mcd;\n  VERIFY_IS_APPROX( rcd.noalias() += mcd + md*md, mcd + mcd + ((md*md).eval().template cast<CD>()) );\n  rcd = mcd;\n  VERIFY_IS_APPROX( rcd.noalias() -= mcd + md*md,           - ((md*md).eval().template cast<CD>()) );\n}\n\nvoid test_mixingtypes()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1(mixingtypes<3>());\n    CALL_SUBTEST_2(mixingtypes<4>());\n    CALL_SUBTEST_3(mixingtypes<Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE)));\n\n    CALL_SUBTEST_4(mixingtypes<3>());\n    CALL_SUBTEST_5(mixingtypes<4>());\n    CALL_SUBTEST_6(mixingtypes<Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE)));\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/mpl2only.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define EIGEN_MPL2_ONLY\n#include <Eigen/Dense>\n#include <Eigen/SparseCore>\n#include <Eigen/SparseLU>\n#include <Eigen/SparseQR>\n#include <Eigen/Sparse>\n#include <Eigen/IterativeLinearSolvers>\n#include <Eigen/Eigen>\n\nint main()\n{\n  return 0;\n}\n"
  },
  {
    "path": "include/eigen3/test/nesting_ops.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2010 Hauke Heibel <hauke.heibel@gmail.com>\n// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define TEST_ENABLE_TEMPORARY_TRACKING\n\n#include \"main.h\"\n\ntemplate <int N, typename XprType>\nvoid use_n_times(const XprType &xpr)\n{\n  typename internal::nested_eval<XprType,N>::type mat(xpr);\n  typename XprType::PlainObject res(mat.rows(), mat.cols());\n  nb_temporaries--; // remove res\n  res.setZero();\n  for(int i=0; i<N; ++i)\n    res += mat;\n}\n\ntemplate <int N, typename ReferenceType, typename XprType>\nbool verify_eval_type(const XprType &, const ReferenceType&)\n{\n  typedef typename internal::nested_eval<XprType,N>::type EvalType;\n  return internal::is_same<typename internal::remove_all<EvalType>::type, typename internal::remove_all<ReferenceType>::type>::value;\n}\n\ntemplate <typename MatrixType> void run_nesting_ops_1(const MatrixType& _m)\n{\n  typename internal::nested_eval<MatrixType,2>::type m(_m);\n\n  // Make really sure that we are in debug mode!\n  VERIFY_RAISES_ASSERT(eigen_assert(false));\n\n  // The only intention of these tests is to ensure that this code does\n  // not trigger any asserts or segmentation faults... more to come.\n  VERIFY_IS_APPROX( (m.transpose() * m).diagonal().sum(), (m.transpose() * m).diagonal().sum() );\n  VERIFY_IS_APPROX( (m.transpose() * m).diagonal().array().abs().sum(), (m.transpose() * m).diagonal().array().abs().sum() );\n\n  VERIFY_IS_APPROX( (m.transpose() * m).array().abs().sum(), (m.transpose() * m).array().abs().sum() );\n}\n\ntemplate <typename MatrixType> void run_nesting_ops_2(const MatrixType& _m)\n{\n  typedef typename MatrixType::Scalar Scalar;\n  Index rows = _m.rows();\n  Index cols = _m.cols();\n  MatrixType m1 = MatrixType::Random(rows,cols);\n  Matrix<Scalar,MatrixType::RowsAtCompileTime,MatrixType::ColsAtCompileTime,ColMajor> m2;\n\n  if((MatrixType::SizeAtCompileTime==Dynamic))\n  {\n    VERIFY_EVALUATION_COUNT( use_n_times<1>(m1 + m1*m1), 1 );\n    VERIFY_EVALUATION_COUNT( use_n_times<10>(m1 + m1*m1), 1 );\n\n    VERIFY_EVALUATION_COUNT( use_n_times<1>(m1.template triangularView<Lower>().solve(m1.col(0))), 1 );\n    VERIFY_EVALUATION_COUNT( use_n_times<10>(m1.template triangularView<Lower>().solve(m1.col(0))), 1 );\n\n    VERIFY_EVALUATION_COUNT( use_n_times<1>(Scalar(2)*m1.template triangularView<Lower>().solve(m1.col(0))), 2 ); // FIXME could be one by applying the scaling in-place on the solve result\n    VERIFY_EVALUATION_COUNT( use_n_times<1>(m1.col(0)+m1.template triangularView<Lower>().solve(m1.col(0))), 2 ); // FIXME could be one by adding m1.col() inplace\n    VERIFY_EVALUATION_COUNT( use_n_times<10>(m1.col(0)+m1.template triangularView<Lower>().solve(m1.col(0))), 2 );\n  }\n\n  {\n    VERIFY( verify_eval_type<10>(m1, m1) );\n    if(!NumTraits<Scalar>::IsComplex)\n    {\n      VERIFY( verify_eval_type<3>(2*m1, 2*m1) );\n      VERIFY( verify_eval_type<4>(2*m1, m1) );\n    }\n    else\n    {\n      VERIFY( verify_eval_type<2>(2*m1, 2*m1) );\n      VERIFY( verify_eval_type<3>(2*m1, m1) );\n    }\n    VERIFY( verify_eval_type<2>(m1+m1, m1+m1) );\n    VERIFY( verify_eval_type<3>(m1+m1, m1) );\n    VERIFY( verify_eval_type<1>(m1*m1.transpose(), m2) );\n    VERIFY( verify_eval_type<1>(m1*(m1+m1).transpose(), m2) );\n    VERIFY( verify_eval_type<2>(m1*m1.transpose(), m2) );\n    VERIFY( verify_eval_type<1>(m1+m1*m1, m1) );\n\n    VERIFY( verify_eval_type<1>(m1.template triangularView<Lower>().solve(m1), m1) );\n    VERIFY( verify_eval_type<1>(m1+m1.template triangularView<Lower>().solve(m1), m1) );\n  }\n}\n\n\nvoid test_nesting_ops()\n{\n  CALL_SUBTEST_1(run_nesting_ops_1(MatrixXf::Random(25,25)));\n  CALL_SUBTEST_2(run_nesting_ops_1(MatrixXcd::Random(25,25)));\n  CALL_SUBTEST_3(run_nesting_ops_1(Matrix4f::Random()));\n  CALL_SUBTEST_4(run_nesting_ops_1(Matrix2d::Random()));\n\n  Index s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE);\n  CALL_SUBTEST_1( run_nesting_ops_2(MatrixXf(s,s)) );\n  CALL_SUBTEST_2( run_nesting_ops_2(MatrixXcd(s,s)) );\n  CALL_SUBTEST_3( run_nesting_ops_2(Matrix4f()) );\n  CALL_SUBTEST_4( run_nesting_ops_2(Matrix2d()) );\n  TEST_SET_BUT_UNUSED_VARIABLE(s)\n}\n"
  },
  {
    "path": "include/eigen3/test/nomalloc.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n// discard stack allocation as that too bypasses malloc\n#define EIGEN_STACK_ALLOCATION_LIMIT 0\n// heap allocation will raise an assert if enabled at runtime\n#define EIGEN_RUNTIME_NO_MALLOC\n\n#include \"main.h\"\n#include <Eigen/Cholesky>\n#include <Eigen/Eigenvalues>\n#include <Eigen/LU>\n#include <Eigen/QR>\n#include <Eigen/SVD>\n\ntemplate<typename MatrixType> void nomalloc(const MatrixType& m)\n{\n  /* this test check no dynamic memory allocation are issued with fixed-size matrices\n  */\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  MatrixType m1 = MatrixType::Random(rows, cols),\n             m2 = MatrixType::Random(rows, cols),\n             m3(rows, cols);\n\n  Scalar s1 = internal::random<Scalar>();\n\n  Index r = internal::random<Index>(0, rows-1),\n        c = internal::random<Index>(0, cols-1);\n\n  VERIFY_IS_APPROX((m1+m2)*s1,              s1*m1+s1*m2);\n  VERIFY_IS_APPROX((m1+m2)(r,c), (m1(r,c))+(m2(r,c)));\n  VERIFY_IS_APPROX(m1.cwiseProduct(m1.block(0,0,rows,cols)), (m1.array()*m1.array()).matrix());\n  VERIFY_IS_APPROX((m1*m1.transpose())*m2,  m1*(m1.transpose()*m2));\n  \n  m2.col(0).noalias() = m1 * m1.col(0);\n  m2.col(0).noalias() -= m1.adjoint() * m1.col(0);\n  m2.col(0).noalias() -= m1 * m1.row(0).adjoint();\n  m2.col(0).noalias() -= m1.adjoint() * m1.row(0).adjoint();\n\n  m2.row(0).noalias() = m1.row(0) * m1;\n  m2.row(0).noalias() -= m1.row(0) * m1.adjoint();\n  m2.row(0).noalias() -= m1.col(0).adjoint() * m1;\n  m2.row(0).noalias() -= m1.col(0).adjoint() * m1.adjoint();\n  VERIFY_IS_APPROX(m2,m2);\n  \n  m2.col(0).noalias() = m1.template triangularView<Upper>() * m1.col(0);\n  m2.col(0).noalias() -= m1.adjoint().template triangularView<Upper>() * m1.col(0);\n  m2.col(0).noalias() -= m1.template triangularView<Upper>() * m1.row(0).adjoint();\n  m2.col(0).noalias() -= m1.adjoint().template triangularView<Upper>() * m1.row(0).adjoint();\n\n  m2.row(0).noalias() = m1.row(0) * m1.template triangularView<Upper>();\n  m2.row(0).noalias() -= m1.row(0) * m1.adjoint().template triangularView<Upper>();\n  m2.row(0).noalias() -= m1.col(0).adjoint() * m1.template triangularView<Upper>();\n  m2.row(0).noalias() -= m1.col(0).adjoint() * m1.adjoint().template triangularView<Upper>();\n  VERIFY_IS_APPROX(m2,m2);\n  \n  m2.col(0).noalias() = m1.template selfadjointView<Upper>() * m1.col(0);\n  m2.col(0).noalias() -= m1.adjoint().template selfadjointView<Upper>() * m1.col(0);\n  m2.col(0).noalias() -= m1.template selfadjointView<Upper>() * m1.row(0).adjoint();\n  m2.col(0).noalias() -= m1.adjoint().template selfadjointView<Upper>() * m1.row(0).adjoint();\n\n  m2.row(0).noalias() = m1.row(0) * m1.template selfadjointView<Upper>();\n  m2.row(0).noalias() -= m1.row(0) * m1.adjoint().template selfadjointView<Upper>();\n  m2.row(0).noalias() -= m1.col(0).adjoint() * m1.template selfadjointView<Upper>();\n  m2.row(0).noalias() -= m1.col(0).adjoint() * m1.adjoint().template selfadjointView<Upper>();\n  VERIFY_IS_APPROX(m2,m2);\n  \n  m2.template selfadjointView<Lower>().rankUpdate(m1.col(0),-1);\n  m2.template selfadjointView<Upper>().rankUpdate(m1.row(0),-1);\n  m2.template selfadjointView<Lower>().rankUpdate(m1.col(0), m1.col(0)); // rank-2\n\n  // The following fancy matrix-matrix products are not safe yet regarding static allocation\n  m2.template selfadjointView<Lower>().rankUpdate(m1);\n  m2 += m2.template triangularView<Upper>() * m1;\n  m2.template triangularView<Upper>() = m2 * m2;\n  m1 += m1.template selfadjointView<Lower>() * m2;\n  VERIFY_IS_APPROX(m2,m2);\n}\n\ntemplate<typename Scalar>\nvoid ctms_decompositions()\n{\n  const int maxSize = 16;\n  const int size    = 12;\n\n  typedef Eigen::Matrix<Scalar,\n                        Eigen::Dynamic, Eigen::Dynamic,\n                        0,\n                        maxSize, maxSize> Matrix;\n\n  typedef Eigen::Matrix<Scalar,\n                        Eigen::Dynamic, 1,\n                        0,\n                        maxSize, 1> Vector;\n\n  typedef Eigen::Matrix<std::complex<Scalar>,\n                        Eigen::Dynamic, Eigen::Dynamic,\n                        0,\n                        maxSize, maxSize> ComplexMatrix;\n\n  const Matrix A(Matrix::Random(size, size)), B(Matrix::Random(size, size));\n  Matrix X(size,size);\n  const ComplexMatrix complexA(ComplexMatrix::Random(size, size));\n  const Matrix saA = A.adjoint() * A;\n  const Vector b(Vector::Random(size));\n  Vector x(size);\n\n  // Cholesky module\n  Eigen::LLT<Matrix>  LLT;  LLT.compute(A);\n  X = LLT.solve(B);\n  x = LLT.solve(b);\n  Eigen::LDLT<Matrix> LDLT; LDLT.compute(A);\n  X = LDLT.solve(B);\n  x = LDLT.solve(b);\n\n  // Eigenvalues module\n  Eigen::HessenbergDecomposition<ComplexMatrix> hessDecomp;        hessDecomp.compute(complexA);\n  Eigen::ComplexSchur<ComplexMatrix>            cSchur(size);      cSchur.compute(complexA);\n  Eigen::ComplexEigenSolver<ComplexMatrix>      cEigSolver;        cEigSolver.compute(complexA);\n  Eigen::EigenSolver<Matrix>                    eigSolver;         eigSolver.compute(A);\n  Eigen::SelfAdjointEigenSolver<Matrix>         saEigSolver(size); saEigSolver.compute(saA);\n  Eigen::Tridiagonalization<Matrix>             tridiag;           tridiag.compute(saA);\n\n  // LU module\n  Eigen::PartialPivLU<Matrix> ppLU; ppLU.compute(A);\n  X = ppLU.solve(B);\n  x = ppLU.solve(b);\n  Eigen::FullPivLU<Matrix>    fpLU; fpLU.compute(A);\n  X = fpLU.solve(B);\n  x = fpLU.solve(b);\n\n  // QR module\n  Eigen::HouseholderQR<Matrix>        hQR;  hQR.compute(A);\n  X = hQR.solve(B);\n  x = hQR.solve(b);\n  Eigen::ColPivHouseholderQR<Matrix>  cpQR; cpQR.compute(A);\n  X = cpQR.solve(B);\n  x = cpQR.solve(b);\n  Eigen::FullPivHouseholderQR<Matrix> fpQR; fpQR.compute(A);\n  // FIXME X = fpQR.solve(B);\n  x = fpQR.solve(b);\n\n  // SVD module\n  Eigen::JacobiSVD<Matrix> jSVD; jSVD.compute(A, ComputeFullU | ComputeFullV);\n}\n\nvoid test_zerosized() {\n  // default constructors:\n  Eigen::MatrixXd A;\n  Eigen::VectorXd v;\n  // explicit zero-sized:\n  Eigen::ArrayXXd A0(0,0);\n  Eigen::ArrayXd v0(0);\n\n  // assigning empty objects to each other:\n  A=A0;\n  v=v0;\n}\n\ntemplate<typename MatrixType> void test_reference(const MatrixType& m) {\n  typedef typename MatrixType::Scalar Scalar;\n  enum { Flag          =  MatrixType::IsRowMajor ? Eigen::RowMajor : Eigen::ColMajor};\n  enum { TransposeFlag = !MatrixType::IsRowMajor ? Eigen::RowMajor : Eigen::ColMajor};\n  typename MatrixType::Index rows = m.rows(), cols=m.cols();\n  typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic, Flag         > MatrixX;\n  typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic, TransposeFlag> MatrixXT;\n  // Dynamic reference:\n  typedef Eigen::Ref<const MatrixX  > Ref;\n  typedef Eigen::Ref<const MatrixXT > RefT;\n\n  Ref r1(m);\n  Ref r2(m.block(rows/3, cols/4, rows/2, cols/2));\n  RefT r3(m.transpose());\n  RefT r4(m.topLeftCorner(rows/2, cols/2).transpose());\n\n  VERIFY_RAISES_ASSERT(RefT r5(m));\n  VERIFY_RAISES_ASSERT(Ref r6(m.transpose()));\n  VERIFY_RAISES_ASSERT(Ref r7(Scalar(2) * m));\n\n  // Copy constructors shall also never malloc\n  Ref r8 = r1;\n  RefT r9 = r3;\n\n  // Initializing from a compatible Ref shall also never malloc\n  Eigen::Ref<const MatrixX, Unaligned, Stride<Dynamic, Dynamic> > r10=r8, r11=m;\n\n  // Initializing from an incompatible Ref will malloc:\n  typedef Eigen::Ref<const MatrixX, Aligned> RefAligned;\n  VERIFY_RAISES_ASSERT(RefAligned r12=r10);\n  VERIFY_RAISES_ASSERT(Ref r13=r10); // r10 has more dynamic strides\n\n}\n\nvoid test_nomalloc()\n{\n  // create some dynamic objects\n  Eigen::MatrixXd M1 = MatrixXd::Random(3,3);\n  Ref<const MatrixXd> R1 = 2.0*M1; // Ref requires temporary\n\n  // from here on prohibit malloc:\n  Eigen::internal::set_is_malloc_allowed(false);\n\n  // check that our operator new is indeed called:\n  VERIFY_RAISES_ASSERT(MatrixXd dummy(MatrixXd::Random(3,3)));\n  CALL_SUBTEST_1(nomalloc(Matrix<float, 1, 1>()) );\n  CALL_SUBTEST_2(nomalloc(Matrix4d()) );\n  CALL_SUBTEST_3(nomalloc(Matrix<float,32,32>()) );\n  \n  // Check decomposition modules with dynamic matrices that have a known compile-time max size (ctms)\n  CALL_SUBTEST_4(ctms_decompositions<float>());\n\n  CALL_SUBTEST_5(test_zerosized());\n\n  CALL_SUBTEST_6(test_reference(Matrix<float,32,32>()));\n  CALL_SUBTEST_7(test_reference(R1));\n  CALL_SUBTEST_8(Ref<MatrixXd> R2 = M1.topRows<2>(); test_reference(R2));\n}\n"
  },
  {
    "path": "include/eigen3/test/nullary.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2010-2011 Jitse Niesen <jitse@maths.leeds.ac.uk>\n// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\ntemplate<typename MatrixType>\nbool equalsIdentity(const MatrixType& A)\n{\n  typedef typename MatrixType::Scalar Scalar;\n  Scalar zero = static_cast<Scalar>(0);\n\n  bool offDiagOK = true;\n  for (Index i = 0; i < A.rows(); ++i) {\n    for (Index j = i+1; j < A.cols(); ++j) {\n      offDiagOK = offDiagOK && (A(i,j) == zero);\n    }\n  }\n  for (Index i = 0; i < A.rows(); ++i) {\n    for (Index j = 0; j < (std::min)(i, A.cols()); ++j) {\n      offDiagOK = offDiagOK && (A(i,j) == zero);\n    }\n  }\n\n  bool diagOK = (A.diagonal().array() == 1).all();\n  return offDiagOK && diagOK;\n\n}\n\ntemplate<typename VectorType>\nvoid check_extremity_accuracy(const VectorType &v, const typename VectorType::Scalar &low, const typename VectorType::Scalar &high)\n{\n  typedef typename VectorType::Scalar Scalar;\n  typedef typename VectorType::RealScalar RealScalar;\n\n  RealScalar prec = internal::is_same<RealScalar,float>::value ? NumTraits<RealScalar>::dummy_precision()*10 : NumTraits<RealScalar>::dummy_precision()/10;\n  Index size = v.size();\n\n  if(size<20)\n    return;\n\n  for (int i=0; i<size; ++i)\n  {\n    if(i<5 || i>size-6)\n    {\n      Scalar ref = (low*RealScalar(size-i-1))/RealScalar(size-1) + (high*RealScalar(i))/RealScalar(size-1);\n      if(std::abs(ref)>1)\n      {\n        if(!internal::isApprox(v(i), ref, prec))\n          std::cout << v(i) << \" != \" << ref << \"  ; relative error: \" << std::abs((v(i)-ref)/ref) << \"  ; required precision: \" << prec << \"  ; range: \" << low << \",\" << high << \"  ; i: \" << i << \"\\n\";\n        VERIFY(internal::isApprox(v(i), (low*RealScalar(size-i-1))/RealScalar(size-1) + (high*RealScalar(i))/RealScalar(size-1), prec));\n      }\n    }\n  }\n}\n\ntemplate<typename VectorType>\nvoid testVectorType(const VectorType& base)\n{\n  typedef typename VectorType::Scalar Scalar;\n  typedef typename VectorType::RealScalar RealScalar;\n\n  const Index size = base.size();\n  \n  Scalar high = internal::random<Scalar>(-500,500);\n  Scalar low = (size == 1 ? high : internal::random<Scalar>(-500,500));\n  if (low>high) std::swap(low,high);\n\n  // check low==high\n  if(internal::random<float>(0.f,1.f)<0.05f)\n    low = high;\n  // check abs(low) >> abs(high)\n  else if(size>2 && std::numeric_limits<RealScalar>::max_exponent10>0 && internal::random<float>(0.f,1.f)<0.1f)\n    low = -internal::random<Scalar>(1,2) * RealScalar(std::pow(RealScalar(10),std::numeric_limits<RealScalar>::max_exponent10/2));\n\n  const Scalar step = ((size == 1) ? 1 : (high-low)/(size-1));\n\n  // check whether the result yields what we expect it to do\n  VectorType m(base);\n  m.setLinSpaced(size,low,high);\n\n  if(!NumTraits<Scalar>::IsInteger)\n  {\n    VectorType n(size);\n    for (int i=0; i<size; ++i)\n      n(i) = low+i*step;\n    VERIFY_IS_APPROX(m,n);\n\n    CALL_SUBTEST( check_extremity_accuracy(m, low, high) );\n  }\n\n  if((!NumTraits<Scalar>::IsInteger) || ((high-low)>=size && (Index(high-low)%(size-1))==0) || (Index(high-low+1)<size && (size%Index(high-low+1))==0))\n  {\n    VectorType n(size);\n    if((!NumTraits<Scalar>::IsInteger) || (high-low>=size))\n      for (int i=0; i<size; ++i)\n        n(i) = size==1 ? low : (low + ((high-low)*Scalar(i))/(size-1));\n    else\n      for (int i=0; i<size; ++i)\n        n(i) = size==1 ? low : low + Scalar((double(high-low+1)*double(i))/double(size));\n    VERIFY_IS_APPROX(m,n);\n\n    // random access version\n    m = VectorType::LinSpaced(size,low,high);\n    VERIFY_IS_APPROX(m,n);\n    VERIFY( internal::isApprox(m(m.size()-1),high) );\n    VERIFY( size==1 || internal::isApprox(m(0),low) );\n    VERIFY_IS_EQUAL(m(m.size()-1) , high);\n    if(!NumTraits<Scalar>::IsInteger)\n      CALL_SUBTEST( check_extremity_accuracy(m, low, high) );\n  }\n\n  VERIFY( m(m.size()-1) <= high );\n  VERIFY( (m.array() <= high).all() );\n  VERIFY( (m.array() >= low).all() );\n\n\n  VERIFY( m(m.size()-1) >= low );\n  if(size>=1)\n  {\n    VERIFY( internal::isApprox(m(0),low) );\n    VERIFY_IS_EQUAL(m(0) , low);\n  }\n\n  // check whether everything works with row and col major vectors\n  Matrix<Scalar,Dynamic,1> row_vector(size);\n  Matrix<Scalar,1,Dynamic> col_vector(size);\n  row_vector.setLinSpaced(size,low,high);\n  col_vector.setLinSpaced(size,low,high);\n  // when using the extended precision (e.g., FPU) the relative error might exceed 1 bit\n  // when computing the squared sum in isApprox, thus the 2x factor.\n  VERIFY( row_vector.isApprox(col_vector.transpose(), Scalar(2)*NumTraits<Scalar>::epsilon()));\n\n  Matrix<Scalar,Dynamic,1> size_changer(size+50);\n  size_changer.setLinSpaced(size,low,high);\n  VERIFY( size_changer.size() == size );\n\n  typedef Matrix<Scalar,1,1> ScalarMatrix;\n  ScalarMatrix scalar;\n  scalar.setLinSpaced(1,low,high);\n  VERIFY_IS_APPROX( scalar, ScalarMatrix::Constant(high) );\n  VERIFY_IS_APPROX( ScalarMatrix::LinSpaced(1,low,high), ScalarMatrix::Constant(high) );\n\n  // regression test for bug 526 (linear vectorized transversal)\n  if (size > 1 && (!NumTraits<Scalar>::IsInteger)) {\n    m.tail(size-1).setLinSpaced(low, high);\n    VERIFY_IS_APPROX(m(size-1), high);\n  }\n\n  // regression test for bug 1383 (LinSpaced with empty size/range)\n  {\n    Index n0 = VectorType::SizeAtCompileTime==Dynamic ? 0 : VectorType::SizeAtCompileTime;\n    low = internal::random<Scalar>();\n    m = VectorType::LinSpaced(n0,low,low-1);\n    VERIFY(m.size()==n0);\n\n    if(VectorType::SizeAtCompileTime==Dynamic)\n    {\n      VERIFY_IS_EQUAL(VectorType::LinSpaced(n0,0,Scalar(n0-1)).sum(),Scalar(0));\n      VERIFY_IS_EQUAL(VectorType::LinSpaced(n0,low,low-1).sum(),Scalar(0));\n    }\n\n    m.setLinSpaced(n0,0,Scalar(n0-1));\n    VERIFY(m.size()==n0);\n    m.setLinSpaced(n0,low,low-1);\n    VERIFY(m.size()==n0);\n\n    // empty range only:\n    VERIFY_IS_APPROX(VectorType::LinSpaced(size,low,low),VectorType::Constant(size,low));\n    m.setLinSpaced(size,low,low);\n    VERIFY_IS_APPROX(m,VectorType::Constant(size,low));\n\n    if(NumTraits<Scalar>::IsInteger)\n    {\n      VERIFY_IS_APPROX( VectorType::LinSpaced(size,low,Scalar(low+size-1)), VectorType::LinSpaced(size,Scalar(low+size-1),low).reverse() );\n\n      if(VectorType::SizeAtCompileTime==Dynamic)\n      {\n        // Check negative multiplicator path:\n        for(Index k=1; k<5; ++k)\n          VERIFY_IS_APPROX( VectorType::LinSpaced(size,low,Scalar(low+(size-1)*k)), VectorType::LinSpaced(size,Scalar(low+(size-1)*k),low).reverse() );\n        // Check negative divisor path:\n        for(Index k=1; k<5; ++k)\n          VERIFY_IS_APPROX( VectorType::LinSpaced(size*k,low,Scalar(low+size-1)), VectorType::LinSpaced(size*k,Scalar(low+size-1),low).reverse() );\n      }\n    }\n  }\n}\n\ntemplate<typename MatrixType>\nvoid testMatrixType(const MatrixType& m)\n{\n  using std::abs;\n  const Index rows = m.rows();\n  const Index cols = m.cols();\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename MatrixType::RealScalar RealScalar;\n\n  Scalar s1;\n  do {\n    s1 = internal::random<Scalar>();\n  } while(abs(s1)<RealScalar(1e-5) && (!NumTraits<Scalar>::IsInteger));\n\n  MatrixType A;\n  A.setIdentity(rows, cols);\n  VERIFY(equalsIdentity(A));\n  VERIFY(equalsIdentity(MatrixType::Identity(rows, cols)));\n\n\n  A = MatrixType::Constant(rows,cols,s1);\n  Index i = internal::random<Index>(0,rows-1);\n  Index j = internal::random<Index>(0,cols-1);\n  VERIFY_IS_APPROX( MatrixType::Constant(rows,cols,s1)(i,j), s1 );\n  VERIFY_IS_APPROX( MatrixType::Constant(rows,cols,s1).coeff(i,j), s1 );\n  VERIFY_IS_APPROX( A(i,j), s1 );\n}\n\nvoid test_nullary()\n{\n  CALL_SUBTEST_1( testMatrixType(Matrix2d()) );\n  CALL_SUBTEST_2( testMatrixType(MatrixXcf(internal::random<int>(1,300),internal::random<int>(1,300))) );\n  CALL_SUBTEST_3( testMatrixType(MatrixXf(internal::random<int>(1,300),internal::random<int>(1,300))) );\n  \n  for(int i = 0; i < g_repeat*10; i++) {\n    CALL_SUBTEST_4( testVectorType(VectorXd(internal::random<int>(1,30000))) );\n    CALL_SUBTEST_5( testVectorType(Vector4d()) );  // regression test for bug 232\n    CALL_SUBTEST_6( testVectorType(Vector3d()) );\n    CALL_SUBTEST_7( testVectorType(VectorXf(internal::random<int>(1,30000))) );\n    CALL_SUBTEST_8( testVectorType(Vector3f()) );\n    CALL_SUBTEST_8( testVectorType(Vector4f()) );\n    CALL_SUBTEST_8( testVectorType(Matrix<float,8,1>()) );\n    CALL_SUBTEST_8( testVectorType(Matrix<float,1,1>()) );\n\n    CALL_SUBTEST_9( testVectorType(VectorXi(internal::random<int>(1,10))) );\n    CALL_SUBTEST_9( testVectorType(VectorXi(internal::random<int>(9,300))) );\n    CALL_SUBTEST_9( testVectorType(Matrix<int,1,1>()) );\n  }\n\n#ifdef EIGEN_TEST_PART_6\n  // Assignment of a RowVectorXd to a MatrixXd (regression test for bug #79).\n  VERIFY( (MatrixXd(RowVectorXd::LinSpaced(3, 0, 1)) - RowVector3d(0, 0.5, 1)).norm() < std::numeric_limits<double>::epsilon() );\n#endif\n\n#ifdef EIGEN_TEST_PART_9\n  // Check possible overflow issue\n  {\n    int n = 60000;\n    ArrayXi a1(n), a2(n);\n    a1.setLinSpaced(n, 0, n-1);\n    for(int i=0; i<n; ++i)\n      a2(i) = i;\n    VERIFY_IS_APPROX(a1,a2);\n  }\n#endif\n\n#ifdef EIGEN_TEST_PART_10\n  // check some internal logic\n  VERIFY((  internal::has_nullary_operator<internal::scalar_constant_op<double> >::value ));\n  VERIFY(( !internal::has_unary_operator<internal::scalar_constant_op<double> >::value ));\n  VERIFY(( !internal::has_binary_operator<internal::scalar_constant_op<double> >::value ));\n  VERIFY((  internal::functor_has_linear_access<internal::scalar_constant_op<double> >::ret ));\n\n  VERIFY(( !internal::has_nullary_operator<internal::scalar_identity_op<double> >::value ));\n  VERIFY(( !internal::has_unary_operator<internal::scalar_identity_op<double> >::value ));\n  VERIFY((  internal::has_binary_operator<internal::scalar_identity_op<double> >::value ));\n  VERIFY(( !internal::functor_has_linear_access<internal::scalar_identity_op<double> >::ret ));\n\n  VERIFY(( !internal::has_nullary_operator<internal::linspaced_op<float,float> >::value ));\n  VERIFY((  internal::has_unary_operator<internal::linspaced_op<float,float> >::value ));\n  VERIFY(( !internal::has_binary_operator<internal::linspaced_op<float,float> >::value ));\n  VERIFY((  internal::functor_has_linear_access<internal::linspaced_op<float,float> >::ret ));\n\n  // Regression unit test for a weird MSVC bug.\n  // Search \"nullary_wrapper_workaround_msvc\" in CoreEvaluators.h for the details.\n  // See also traits<Ref>::match.\n  {\n    MatrixXf A = MatrixXf::Random(3,3);\n    Ref<const MatrixXf> R = 2.0*A;\n    VERIFY_IS_APPROX(R, A+A);\n\n    Ref<const MatrixXf> R1 = MatrixXf::Random(3,3)+A;\n\n    VectorXi V = VectorXi::Random(3);\n    Ref<const VectorXi> R2 = VectorXi::LinSpaced(3,1,3)+V;\n    VERIFY_IS_APPROX(R2, V+Vector3i(1,2,3));\n\n    VERIFY((  internal::has_nullary_operator<internal::scalar_constant_op<float> >::value ));\n    VERIFY(( !internal::has_unary_operator<internal::scalar_constant_op<float> >::value ));\n    VERIFY(( !internal::has_binary_operator<internal::scalar_constant_op<float> >::value ));\n    VERIFY((  internal::functor_has_linear_access<internal::scalar_constant_op<float> >::ret ));\n\n    VERIFY(( !internal::has_nullary_operator<internal::linspaced_op<int,int> >::value ));\n    VERIFY((  internal::has_unary_operator<internal::linspaced_op<int,int> >::value ));\n    VERIFY(( !internal::has_binary_operator<internal::linspaced_op<int,int> >::value ));\n    VERIFY((  internal::functor_has_linear_access<internal::linspaced_op<int,int> >::ret ));\n  }\n#endif\n}\n"
  },
  {
    "path": "include/eigen3/test/numext.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2017 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\ntemplate<typename T>\nvoid check_abs() {\n  typedef typename NumTraits<T>::Real Real;\n\n  if(NumTraits<T>::IsSigned)\n    VERIFY_IS_EQUAL(numext::abs(-T(1)), T(1));\n  VERIFY_IS_EQUAL(numext::abs(T(0)), T(0));\n  VERIFY_IS_EQUAL(numext::abs(T(1)), T(1));\n\n  for(int k=0; k<g_repeat*100; ++k)\n  {\n    T x = internal::random<T>();\n    if(!internal::is_same<T,bool>::value)\n      x = x/Real(2);\n    if(NumTraits<T>::IsSigned)\n    {\n      VERIFY_IS_EQUAL(numext::abs(x), numext::abs(-x));\n      VERIFY( numext::abs(-x) >= Real(0));\n    }\n    VERIFY( numext::abs(x) >= Real(0));\n    VERIFY_IS_APPROX( numext::abs2(x), numext::abs2(numext::abs(x)) );\n  }\n}\n\nvoid test_numext() {\n  CALL_SUBTEST( check_abs<bool>() );\n  CALL_SUBTEST( check_abs<signed char>() );\n  CALL_SUBTEST( check_abs<unsigned char>() );\n  CALL_SUBTEST( check_abs<short>() );\n  CALL_SUBTEST( check_abs<unsigned short>() );\n  CALL_SUBTEST( check_abs<int>() );\n  CALL_SUBTEST( check_abs<unsigned int>() );\n  CALL_SUBTEST( check_abs<long>() );\n  CALL_SUBTEST( check_abs<unsigned long>() );\n  CALL_SUBTEST( check_abs<half>() );\n  CALL_SUBTEST( check_abs<float>() );\n  CALL_SUBTEST( check_abs<double>() );\n  CALL_SUBTEST( check_abs<long double>() );\n\n  CALL_SUBTEST( check_abs<std::complex<float> >() );\n  CALL_SUBTEST( check_abs<std::complex<double> >() );\n}\n"
  },
  {
    "path": "include/eigen3/test/packetmath.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include \"unsupported/Eigen/SpecialFunctions\"\n\n#if defined __GNUC__ && __GNUC__>=6\n  #pragma GCC diagnostic ignored \"-Wignored-attributes\"\n#endif\n// using namespace Eigen;\n\n#ifdef EIGEN_VECTORIZE_SSE\nconst bool g_vectorize_sse = true;\n#else\nconst bool g_vectorize_sse = false;\n#endif\n\nnamespace Eigen {\nnamespace internal {\ntemplate<typename T> T negate(const T& x) { return -x; }\n}\n}\n\n// NOTE: we disbale inlining for this function to workaround a GCC issue when using -O3 and the i387 FPU.\ntemplate<typename Scalar> EIGEN_DONT_INLINE\nbool isApproxAbs(const Scalar& a, const Scalar& b, const typename NumTraits<Scalar>::Real& refvalue)\n{\n  return internal::isMuchSmallerThan(a-b, refvalue);\n}\n\ntemplate<typename Scalar> bool areApproxAbs(const Scalar* a, const Scalar* b, int size, const typename NumTraits<Scalar>::Real& refvalue)\n{\n  for (int i=0; i<size; ++i)\n  {\n    if (!isApproxAbs(a[i],b[i],refvalue))\n    {\n      std::cout << \"ref: [\" << Map<const Matrix<Scalar,1,Dynamic> >(a,size) << \"]\" << \" != vec: [\" << Map<const Matrix<Scalar,1,Dynamic> >(b,size) << \"]\\n\";\n      return false;\n    }\n  }\n  return true;\n}\n\ntemplate<typename Scalar> bool areApprox(const Scalar* a, const Scalar* b, int size)\n{\n  for (int i=0; i<size; ++i)\n  {\n    if (a[i]!=b[i] && !internal::isApprox(a[i],b[i]))\n    {\n      std::cout << \"ref: [\" << Map<const Matrix<Scalar,1,Dynamic> >(a,size) << \"]\" << \" != vec: [\" << Map<const Matrix<Scalar,1,Dynamic> >(b,size) << \"]\\n\";\n      return false;\n    }\n  }\n  return true;\n}\n\n#define CHECK_CWISE1(REFOP, POP) { \\\n  for (int i=0; i<PacketSize; ++i) \\\n    ref[i] = REFOP(data1[i]); \\\n  internal::pstore(data2, POP(internal::pload<Packet>(data1))); \\\n  VERIFY(areApprox(ref, data2, PacketSize) && #POP); \\\n}\n\ntemplate<bool Cond,typename Packet>\nstruct packet_helper\n{\n  template<typename T>\n  inline Packet load(const T* from) const { return internal::pload<Packet>(from); }\n\n  template<typename T>\n  inline void store(T* to, const Packet& x) const { internal::pstore(to,x); }\n};\n\ntemplate<typename Packet>\nstruct packet_helper<false,Packet>\n{\n  template<typename T>\n  inline T load(const T* from) const { return *from; }\n\n  template<typename T>\n  inline void store(T* to, const T& x) const { *to = x; }\n};\n\n#define CHECK_CWISE1_IF(COND, REFOP, POP) if(COND) { \\\n  packet_helper<COND,Packet> h; \\\n  for (int i=0; i<PacketSize; ++i) \\\n    ref[i] = REFOP(data1[i]); \\\n  h.store(data2, POP(h.load(data1))); \\\n  VERIFY(areApprox(ref, data2, PacketSize) && #POP); \\\n}\n\n#define CHECK_CWISE2_IF(COND, REFOP, POP) if(COND) { \\\n  packet_helper<COND,Packet> h; \\\n  for (int i=0; i<PacketSize; ++i) \\\n    ref[i] = REFOP(data1[i], data1[i+PacketSize]); \\\n  h.store(data2, POP(h.load(data1),h.load(data1+PacketSize))); \\\n  VERIFY(areApprox(ref, data2, PacketSize) && #POP); \\\n}\n\n#define REF_ADD(a,b) ((a)+(b))\n#define REF_SUB(a,b) ((a)-(b))\n#define REF_MUL(a,b) ((a)*(b))\n#define REF_DIV(a,b) ((a)/(b))\n\ntemplate<typename Scalar> void packetmath()\n{\n  using std::abs;\n  typedef internal::packet_traits<Scalar> PacketTraits;\n  typedef typename PacketTraits::type Packet;\n  const int PacketSize = PacketTraits::size;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n\n  const int max_size = PacketSize > 4 ? PacketSize : 4;\n  const int size = PacketSize*max_size;\n  EIGEN_ALIGN_MAX Scalar data1[size];\n  EIGEN_ALIGN_MAX Scalar data2[size];\n  EIGEN_ALIGN_MAX Packet packets[PacketSize*2];\n  EIGEN_ALIGN_MAX Scalar ref[size];\n  RealScalar refvalue = 0;\n  for (int i=0; i<size; ++i)\n  {\n    data1[i] = internal::random<Scalar>()/RealScalar(PacketSize);\n    data2[i] = internal::random<Scalar>()/RealScalar(PacketSize);\n    refvalue = (std::max)(refvalue,abs(data1[i]));\n  }\n\n  internal::pstore(data2, internal::pload<Packet>(data1));\n  VERIFY(areApprox(data1, data2, PacketSize) && \"aligned load/store\");\n\n  for (int offset=0; offset<PacketSize; ++offset)\n  {\n    internal::pstore(data2, internal::ploadu<Packet>(data1+offset));\n    VERIFY(areApprox(data1+offset, data2, PacketSize) && \"internal::ploadu\");\n  }\n\n  for (int offset=0; offset<PacketSize; ++offset)\n  {\n    internal::pstoreu(data2+offset, internal::pload<Packet>(data1));\n    VERIFY(areApprox(data1, data2+offset, PacketSize) && \"internal::pstoreu\");\n  }\n\n  for (int offset=0; offset<PacketSize; ++offset)\n  {\n    packets[0] = internal::pload<Packet>(data1);\n    packets[1] = internal::pload<Packet>(data1+PacketSize);\n         if (offset==0) internal::palign<0>(packets[0], packets[1]);\n    else if (offset==1) internal::palign<1>(packets[0], packets[1]);\n    else if (offset==2) internal::palign<2>(packets[0], packets[1]);\n    else if (offset==3) internal::palign<3>(packets[0], packets[1]);\n    else if (offset==4) internal::palign<4>(packets[0], packets[1]);\n    else if (offset==5) internal::palign<5>(packets[0], packets[1]);\n    else if (offset==6) internal::palign<6>(packets[0], packets[1]);\n    else if (offset==7) internal::palign<7>(packets[0], packets[1]);\n    else if (offset==8) internal::palign<8>(packets[0], packets[1]);\n    else if (offset==9) internal::palign<9>(packets[0], packets[1]);\n    else if (offset==10) internal::palign<10>(packets[0], packets[1]);\n    else if (offset==11) internal::palign<11>(packets[0], packets[1]);\n    else if (offset==12) internal::palign<12>(packets[0], packets[1]);\n    else if (offset==13) internal::palign<13>(packets[0], packets[1]);\n    else if (offset==14) internal::palign<14>(packets[0], packets[1]);\n    else if (offset==15) internal::palign<15>(packets[0], packets[1]);\n    internal::pstore(data2, packets[0]);\n\n    for (int i=0; i<PacketSize; ++i)\n      ref[i] = data1[i+offset];\n\n    VERIFY(areApprox(ref, data2, PacketSize) && \"internal::palign\");\n  }\n\n  VERIFY((!PacketTraits::Vectorizable) || PacketTraits::HasAdd);\n  VERIFY((!PacketTraits::Vectorizable) || PacketTraits::HasSub);\n  VERIFY((!PacketTraits::Vectorizable) || PacketTraits::HasMul);\n  VERIFY((!PacketTraits::Vectorizable) || PacketTraits::HasNegate);\n  VERIFY((internal::is_same<Scalar,int>::value) || (!PacketTraits::Vectorizable) || PacketTraits::HasDiv);\n\n  CHECK_CWISE2_IF(PacketTraits::HasAdd, REF_ADD,  internal::padd);\n  CHECK_CWISE2_IF(PacketTraits::HasSub, REF_SUB,  internal::psub);\n  CHECK_CWISE2_IF(PacketTraits::HasMul, REF_MUL,  internal::pmul);\n  CHECK_CWISE2_IF(PacketTraits::HasDiv, REF_DIV, internal::pdiv);\n\n  CHECK_CWISE1(internal::negate, internal::pnegate);\n  CHECK_CWISE1(numext::conj, internal::pconj);\n\n  for(int offset=0;offset<3;++offset)\n  {\n    for (int i=0; i<PacketSize; ++i)\n      ref[i] = data1[offset];\n    internal::pstore(data2, internal::pset1<Packet>(data1[offset]));\n    VERIFY(areApprox(ref, data2, PacketSize) && \"internal::pset1\");\n  }\n\n  {\n    for (int i=0; i<PacketSize*4; ++i)\n      ref[i] = data1[i/PacketSize];\n    Packet A0, A1, A2, A3;\n    internal::pbroadcast4<Packet>(data1, A0, A1, A2, A3);\n    internal::pstore(data2+0*PacketSize, A0);\n    internal::pstore(data2+1*PacketSize, A1);\n    internal::pstore(data2+2*PacketSize, A2);\n    internal::pstore(data2+3*PacketSize, A3);\n    VERIFY(areApprox(ref, data2, 4*PacketSize) && \"internal::pbroadcast4\");\n  }\n\n  {\n    for (int i=0; i<PacketSize*2; ++i)\n      ref[i] = data1[i/PacketSize];\n    Packet A0, A1;\n    internal::pbroadcast2<Packet>(data1, A0, A1);\n    internal::pstore(data2+0*PacketSize, A0);\n    internal::pstore(data2+1*PacketSize, A1);\n    VERIFY(areApprox(ref, data2, 2*PacketSize) && \"internal::pbroadcast2\");\n  }\n\n  VERIFY(internal::isApprox(data1[0], internal::pfirst(internal::pload<Packet>(data1))) && \"internal::pfirst\");\n\n  if(PacketSize>1)\n  {\n    for(int offset=0;offset<4;++offset)\n    {\n      for(int i=0;i<PacketSize/2;++i)\n        ref[2*i+0] = ref[2*i+1] = data1[offset+i];\n      internal::pstore(data2,internal::ploaddup<Packet>(data1+offset));\n      VERIFY(areApprox(ref, data2, PacketSize) && \"ploaddup\");\n    }\n  }\n\n  if(PacketSize>2)\n  {\n    for(int offset=0;offset<4;++offset)\n    {\n      for(int i=0;i<PacketSize/4;++i)\n        ref[4*i+0] = ref[4*i+1] = ref[4*i+2] = ref[4*i+3] = data1[offset+i];\n      internal::pstore(data2,internal::ploadquad<Packet>(data1+offset));\n      VERIFY(areApprox(ref, data2, PacketSize) && \"ploadquad\");\n    }\n  }\n\n  ref[0] = 0;\n  for (int i=0; i<PacketSize; ++i)\n    ref[0] += data1[i];\n  VERIFY(isApproxAbs(ref[0], internal::predux(internal::pload<Packet>(data1)), refvalue) && \"internal::predux\");\n\n  {\n    for (int i=0; i<4; ++i)\n      ref[i] = 0;\n    for (int i=0; i<PacketSize; ++i)\n      ref[i%4] += data1[i];\n    internal::pstore(data2, internal::predux_downto4(internal::pload<Packet>(data1)));\n    VERIFY(areApprox(ref, data2, PacketSize>4?PacketSize/2:PacketSize) && \"internal::predux_downto4\");\n  }\n\n  ref[0] = 1;\n  for (int i=0; i<PacketSize; ++i)\n    ref[0] *= data1[i];\n  VERIFY(internal::isApprox(ref[0], internal::predux_mul(internal::pload<Packet>(data1))) && \"internal::predux_mul\");\n\n  for (int j=0; j<PacketSize; ++j)\n  {\n    ref[j] = 0;\n    for (int i=0; i<PacketSize; ++i)\n      ref[j] += data1[i+j*PacketSize];\n    packets[j] = internal::pload<Packet>(data1+j*PacketSize);\n  }\n  internal::pstore(data2, internal::preduxp(packets));\n  VERIFY(areApproxAbs(ref, data2, PacketSize, refvalue) && \"internal::preduxp\");\n\n  for (int i=0; i<PacketSize; ++i)\n    ref[i] = data1[PacketSize-i-1];\n  internal::pstore(data2, internal::preverse(internal::pload<Packet>(data1)));\n  VERIFY(areApprox(ref, data2, PacketSize) && \"internal::preverse\");\n\n  internal::PacketBlock<Packet> kernel;\n  for (int i=0; i<PacketSize; ++i) {\n    kernel.packet[i] = internal::pload<Packet>(data1+i*PacketSize);\n  }\n  ptranspose(kernel);\n  for (int i=0; i<PacketSize; ++i) {\n    internal::pstore(data2, kernel.packet[i]);\n    for (int j = 0; j < PacketSize; ++j) {\n      VERIFY(isApproxAbs(data2[j], data1[i+j*PacketSize], refvalue) && \"ptranspose\");\n    }\n  }\n\n  if (PacketTraits::HasBlend) {\n    Packet thenPacket = internal::pload<Packet>(data1);\n    Packet elsePacket = internal::pload<Packet>(data2);\n    EIGEN_ALIGN_MAX internal::Selector<PacketSize> selector;\n    for (int i = 0; i < PacketSize; ++i) {\n      selector.select[i] = i;\n    }\n\n    Packet blend = internal::pblend(selector, thenPacket, elsePacket);\n    EIGEN_ALIGN_MAX Scalar result[size];\n    internal::pstore(result, blend);\n    for (int i = 0; i < PacketSize; ++i) {\n      VERIFY(isApproxAbs(result[i], (selector.select[i] ? data1[i] : data2[i]), refvalue));\n    }\n  }\n\n  if (PacketTraits::HasBlend || g_vectorize_sse) {\n    // pinsertfirst\n    for (int i=0; i<PacketSize; ++i)\n      ref[i] = data1[i];\n    Scalar s = internal::random<Scalar>();\n    ref[0] = s;\n    internal::pstore(data2, internal::pinsertfirst(internal::pload<Packet>(data1),s));\n    VERIFY(areApprox(ref, data2, PacketSize) && \"internal::pinsertfirst\");\n  }\n\n  if (PacketTraits::HasBlend || g_vectorize_sse) {\n    // pinsertlast\n    for (int i=0; i<PacketSize; ++i)\n      ref[i] = data1[i];\n    Scalar s = internal::random<Scalar>();\n    ref[PacketSize-1] = s;\n    internal::pstore(data2, internal::pinsertlast(internal::pload<Packet>(data1),s));\n    VERIFY(areApprox(ref, data2, PacketSize) && \"internal::pinsertlast\");\n  }\n}\n\ntemplate<typename Scalar> void packetmath_real()\n{\n  using std::abs;\n  typedef internal::packet_traits<Scalar> PacketTraits;\n  typedef typename PacketTraits::type Packet;\n  const int PacketSize = PacketTraits::size;\n\n  const int size = PacketSize*4;\n  EIGEN_ALIGN_MAX Scalar data1[PacketTraits::size*4];\n  EIGEN_ALIGN_MAX Scalar data2[PacketTraits::size*4];\n  EIGEN_ALIGN_MAX Scalar ref[PacketTraits::size*4];\n\n  for (int i=0; i<size; ++i)\n  {\n    data1[i] = internal::random<Scalar>(-1,1) * std::pow(Scalar(10), internal::random<Scalar>(-3,3));\n    data2[i] = internal::random<Scalar>(-1,1) * std::pow(Scalar(10), internal::random<Scalar>(-3,3));\n  }\n  CHECK_CWISE1_IF(PacketTraits::HasSin, std::sin, internal::psin);\n  CHECK_CWISE1_IF(PacketTraits::HasCos, std::cos, internal::pcos);\n  CHECK_CWISE1_IF(PacketTraits::HasTan, std::tan, internal::ptan);\n\n  CHECK_CWISE1_IF(PacketTraits::HasRound, numext::round, internal::pround);\n  CHECK_CWISE1_IF(PacketTraits::HasCeil, numext::ceil, internal::pceil);\n  CHECK_CWISE1_IF(PacketTraits::HasFloor, numext::floor, internal::pfloor);\n\n  for (int i=0; i<size; ++i)\n  {\n    data1[i] = internal::random<Scalar>(-1,1);\n    data2[i] = internal::random<Scalar>(-1,1);\n  }\n  CHECK_CWISE1_IF(PacketTraits::HasASin, std::asin, internal::pasin);\n  CHECK_CWISE1_IF(PacketTraits::HasACos, std::acos, internal::pacos);\n\n  for (int i=0; i<size; ++i)\n  {\n    data1[i] = internal::random<Scalar>(-87,88);\n    data2[i] = internal::random<Scalar>(-87,88);\n  }\n  CHECK_CWISE1_IF(PacketTraits::HasExp, std::exp, internal::pexp);\n  for (int i=0; i<size; ++i)\n  {\n    data1[i] = internal::random<Scalar>(-1,1) * std::pow(Scalar(10), internal::random<Scalar>(-6,6));\n    data2[i] = internal::random<Scalar>(-1,1) * std::pow(Scalar(10), internal::random<Scalar>(-6,6));\n  }\n  CHECK_CWISE1_IF(PacketTraits::HasTanh, std::tanh, internal::ptanh);\n  if(PacketTraits::HasExp && PacketTraits::size>=2)\n  {\n    data1[0] = std::numeric_limits<Scalar>::quiet_NaN();\n    data1[1] = std::numeric_limits<Scalar>::epsilon();\n    packet_helper<PacketTraits::HasExp,Packet> h;\n    h.store(data2, internal::pexp(h.load(data1)));\n    VERIFY((numext::isnan)(data2[0]));\n    VERIFY_IS_EQUAL(std::exp(std::numeric_limits<Scalar>::epsilon()), data2[1]);\n\n    data1[0] = -std::numeric_limits<Scalar>::epsilon();\n    data1[1] = 0;\n    h.store(data2, internal::pexp(h.load(data1)));\n    VERIFY_IS_EQUAL(std::exp(-std::numeric_limits<Scalar>::epsilon()), data2[0]);\n    VERIFY_IS_EQUAL(std::exp(Scalar(0)), data2[1]);\n\n    data1[0] = (std::numeric_limits<Scalar>::min)();\n    data1[1] = -(std::numeric_limits<Scalar>::min)();\n    h.store(data2, internal::pexp(h.load(data1)));\n    VERIFY_IS_EQUAL(std::exp((std::numeric_limits<Scalar>::min)()), data2[0]);\n    VERIFY_IS_EQUAL(std::exp(-(std::numeric_limits<Scalar>::min)()), data2[1]);\n\n    data1[0] = std::numeric_limits<Scalar>::denorm_min();\n    data1[1] = -std::numeric_limits<Scalar>::denorm_min();\n    h.store(data2, internal::pexp(h.load(data1)));\n    VERIFY_IS_EQUAL(std::exp(std::numeric_limits<Scalar>::denorm_min()), data2[0]);\n    VERIFY_IS_EQUAL(std::exp(-std::numeric_limits<Scalar>::denorm_min()), data2[1]);\n  }\n\n  if (PacketTraits::HasTanh) {\n    // NOTE this test migh fail with GCC prior to 6.3, see MathFunctionsImpl.h for details.\n    data1[0] = std::numeric_limits<Scalar>::quiet_NaN();\n    packet_helper<internal::packet_traits<Scalar>::HasTanh,Packet> h;\n    h.store(data2, internal::ptanh(h.load(data1)));\n    VERIFY((numext::isnan)(data2[0]));\n  }\n\n#if EIGEN_HAS_C99_MATH\n  {\n    data1[0] = std::numeric_limits<Scalar>::quiet_NaN();\n    packet_helper<internal::packet_traits<Scalar>::HasLGamma,Packet> h;\n    h.store(data2, internal::plgamma(h.load(data1)));\n    VERIFY((numext::isnan)(data2[0]));\n  }\n  {\n    data1[0] = std::numeric_limits<Scalar>::quiet_NaN();\n    packet_helper<internal::packet_traits<Scalar>::HasErf,Packet> h;\n    h.store(data2, internal::perf(h.load(data1)));\n    VERIFY((numext::isnan)(data2[0]));\n  }\n  {\n    data1[0] = std::numeric_limits<Scalar>::quiet_NaN();\n    packet_helper<internal::packet_traits<Scalar>::HasErfc,Packet> h;\n    h.store(data2, internal::perfc(h.load(data1)));\n    VERIFY((numext::isnan)(data2[0]));\n  }\n#endif  // EIGEN_HAS_C99_MATH\n\n  for (int i=0; i<size; ++i)\n  {\n    data1[i] = internal::random<Scalar>(0,1) * std::pow(Scalar(10), internal::random<Scalar>(-6,6));\n    data2[i] = internal::random<Scalar>(0,1) * std::pow(Scalar(10), internal::random<Scalar>(-6,6));\n  }\n\n  if(internal::random<float>(0,1)<0.1f)\n    data1[internal::random<int>(0, PacketSize)] = 0;\n  CHECK_CWISE1_IF(PacketTraits::HasSqrt, std::sqrt, internal::psqrt);\n  CHECK_CWISE1_IF(PacketTraits::HasLog, std::log, internal::plog);\n#if EIGEN_HAS_C99_MATH && (__cplusplus > 199711L)\n  CHECK_CWISE1_IF(PacketTraits::HasLog1p, std::log1p, internal::plog1p);\n  CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasLGamma, std::lgamma, internal::plgamma);\n  CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasErf, std::erf, internal::perf);\n  CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasErfc, std::erfc, internal::perfc);\n#endif\n\n  if(PacketTraits::HasLog && PacketTraits::size>=2)\n  {\n    data1[0] = std::numeric_limits<Scalar>::quiet_NaN();\n    data1[1] = std::numeric_limits<Scalar>::epsilon();\n    packet_helper<PacketTraits::HasLog,Packet> h;\n    h.store(data2, internal::plog(h.load(data1)));\n    VERIFY((numext::isnan)(data2[0]));\n    VERIFY_IS_EQUAL(std::log(std::numeric_limits<Scalar>::epsilon()), data2[1]);\n\n    data1[0] = -std::numeric_limits<Scalar>::epsilon();\n    data1[1] = 0;\n    h.store(data2, internal::plog(h.load(data1)));\n    VERIFY((numext::isnan)(data2[0]));\n    VERIFY_IS_EQUAL(std::log(Scalar(0)), data2[1]);\n\n    data1[0] = (std::numeric_limits<Scalar>::min)();\n    data1[1] = -(std::numeric_limits<Scalar>::min)();\n    h.store(data2, internal::plog(h.load(data1)));\n    VERIFY_IS_EQUAL(std::log((std::numeric_limits<Scalar>::min)()), data2[0]);\n    VERIFY((numext::isnan)(data2[1]));\n\n    data1[0] = std::numeric_limits<Scalar>::denorm_min();\n    data1[1] = -std::numeric_limits<Scalar>::denorm_min();\n    h.store(data2, internal::plog(h.load(data1)));\n    // VERIFY_IS_EQUAL(std::log(std::numeric_limits<Scalar>::denorm_min()), data2[0]);\n    VERIFY((numext::isnan)(data2[1]));\n\n    data1[0] = Scalar(-1.0f);\n    h.store(data2, internal::plog(h.load(data1)));\n    VERIFY((numext::isnan)(data2[0]));\n    h.store(data2, internal::psqrt(h.load(data1)));\n    VERIFY((numext::isnan)(data2[0]));\n    VERIFY((numext::isnan)(data2[1]));\n  }\n}\n\ntemplate<typename Scalar> void packetmath_notcomplex()\n{\n  using std::abs;\n  typedef internal::packet_traits<Scalar> PacketTraits;\n  typedef typename PacketTraits::type Packet;\n  const int PacketSize = PacketTraits::size;\n\n  EIGEN_ALIGN_MAX Scalar data1[PacketTraits::size*4];\n  EIGEN_ALIGN_MAX Scalar data2[PacketTraits::size*4];\n  EIGEN_ALIGN_MAX Scalar ref[PacketTraits::size*4];\n\n  Array<Scalar,Dynamic,1>::Map(data1, PacketTraits::size*4).setRandom();\n\n  ref[0] = data1[0];\n  for (int i=0; i<PacketSize; ++i)\n    ref[0] = (std::min)(ref[0],data1[i]);\n  VERIFY(internal::isApprox(ref[0], internal::predux_min(internal::pload<Packet>(data1))) && \"internal::predux_min\");\n\n  VERIFY((!PacketTraits::Vectorizable) || PacketTraits::HasMin);\n  VERIFY((!PacketTraits::Vectorizable) || PacketTraits::HasMax);\n\n  CHECK_CWISE2_IF(PacketTraits::HasMin, (std::min), internal::pmin);\n  CHECK_CWISE2_IF(PacketTraits::HasMax, (std::max), internal::pmax);\n  CHECK_CWISE1(abs, internal::pabs);\n\n  ref[0] = data1[0];\n  for (int i=0; i<PacketSize; ++i)\n    ref[0] = (std::max)(ref[0],data1[i]);\n  VERIFY(internal::isApprox(ref[0], internal::predux_max(internal::pload<Packet>(data1))) && \"internal::predux_max\");\n\n  for (int i=0; i<PacketSize; ++i)\n    ref[i] = data1[0]+Scalar(i);\n  internal::pstore(data2, internal::plset<Packet>(data1[0]));\n  VERIFY(areApprox(ref, data2, PacketSize) && \"internal::plset\");\n}\n\ntemplate<typename Scalar,bool ConjLhs,bool ConjRhs> void test_conj_helper(Scalar* data1, Scalar* data2, Scalar* ref, Scalar* pval)\n{\n  typedef internal::packet_traits<Scalar> PacketTraits;\n  typedef typename PacketTraits::type Packet;\n  const int PacketSize = PacketTraits::size;\n\n  internal::conj_if<ConjLhs> cj0;\n  internal::conj_if<ConjRhs> cj1;\n  internal::conj_helper<Scalar,Scalar,ConjLhs,ConjRhs> cj;\n  internal::conj_helper<Packet,Packet,ConjLhs,ConjRhs> pcj;\n\n  for(int i=0;i<PacketSize;++i)\n  {\n    ref[i] = cj0(data1[i]) * cj1(data2[i]);\n    VERIFY(internal::isApprox(ref[i], cj.pmul(data1[i],data2[i])) && \"conj_helper pmul\");\n  }\n  internal::pstore(pval,pcj.pmul(internal::pload<Packet>(data1),internal::pload<Packet>(data2)));\n  VERIFY(areApprox(ref, pval, PacketSize) && \"conj_helper pmul\");\n\n  for(int i=0;i<PacketSize;++i)\n  {\n    Scalar tmp = ref[i];\n    ref[i] += cj0(data1[i]) * cj1(data2[i]);\n    VERIFY(internal::isApprox(ref[i], cj.pmadd(data1[i],data2[i],tmp)) && \"conj_helper pmadd\");\n  }\n  internal::pstore(pval,pcj.pmadd(internal::pload<Packet>(data1),internal::pload<Packet>(data2),internal::pload<Packet>(pval)));\n  VERIFY(areApprox(ref, pval, PacketSize) && \"conj_helper pmadd\");\n}\n\ntemplate<typename Scalar> void packetmath_complex()\n{\n  typedef internal::packet_traits<Scalar> PacketTraits;\n  typedef typename PacketTraits::type Packet;\n  const int PacketSize = PacketTraits::size;\n\n  const int size = PacketSize*4;\n  EIGEN_ALIGN_MAX Scalar data1[PacketSize*4];\n  EIGEN_ALIGN_MAX Scalar data2[PacketSize*4];\n  EIGEN_ALIGN_MAX Scalar ref[PacketSize*4];\n  EIGEN_ALIGN_MAX Scalar pval[PacketSize*4];\n\n  for (int i=0; i<size; ++i)\n  {\n    data1[i] = internal::random<Scalar>() * Scalar(1e2);\n    data2[i] = internal::random<Scalar>() * Scalar(1e2);\n  }\n\n  test_conj_helper<Scalar,false,false> (data1,data2,ref,pval);\n  test_conj_helper<Scalar,false,true>  (data1,data2,ref,pval);\n  test_conj_helper<Scalar,true,false>  (data1,data2,ref,pval);\n  test_conj_helper<Scalar,true,true>   (data1,data2,ref,pval);\n\n  {\n    for(int i=0;i<PacketSize;++i)\n      ref[i] = Scalar(std::imag(data1[i]),std::real(data1[i]));\n    internal::pstore(pval,internal::pcplxflip(internal::pload<Packet>(data1)));\n    VERIFY(areApprox(ref, pval, PacketSize) && \"pcplxflip\");\n  }\n}\n\ntemplate<typename Scalar> void packetmath_scatter_gather()\n{\n  typedef internal::packet_traits<Scalar> PacketTraits;\n  typedef typename PacketTraits::type Packet;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  const int PacketSize = PacketTraits::size;\n  EIGEN_ALIGN_MAX Scalar data1[PacketSize];\n  RealScalar refvalue = 0;\n  for (int i=0; i<PacketSize; ++i) {\n    data1[i] = internal::random<Scalar>()/RealScalar(PacketSize);\n  }\n\n  int stride = internal::random<int>(1,20);\n\n  EIGEN_ALIGN_MAX Scalar buffer[PacketSize*20];\n  memset(buffer, 0, 20*PacketSize*sizeof(Scalar));\n  Packet packet = internal::pload<Packet>(data1);\n  internal::pscatter<Scalar, Packet>(buffer, packet, stride);\n\n  for (int i = 0; i < PacketSize*20; ++i) {\n    if ((i%stride) == 0 && i<stride*PacketSize) {\n      VERIFY(isApproxAbs(buffer[i], data1[i/stride], refvalue) && \"pscatter\");\n    } else {\n      VERIFY(isApproxAbs(buffer[i], Scalar(0), refvalue) && \"pscatter\");\n    }\n  }\n\n  for (int i=0; i<PacketSize*7; ++i) {\n    buffer[i] = internal::random<Scalar>()/RealScalar(PacketSize);\n  }\n  packet = internal::pgather<Scalar, Packet>(buffer, 7);\n  internal::pstore(data1, packet);\n  for (int i = 0; i < PacketSize; ++i) {\n    VERIFY(isApproxAbs(data1[i], buffer[i*7], refvalue) && \"pgather\");\n  }\n}\n\nvoid test_packetmath()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( packetmath<float>() );\n    CALL_SUBTEST_2( packetmath<double>() );\n    CALL_SUBTEST_3( packetmath<int>() );\n    CALL_SUBTEST_4( packetmath<std::complex<float> >() );\n    CALL_SUBTEST_5( packetmath<std::complex<double> >() );\n\n    CALL_SUBTEST_1( packetmath_notcomplex<float>() );\n    CALL_SUBTEST_2( packetmath_notcomplex<double>() );\n    CALL_SUBTEST_3( packetmath_notcomplex<int>() );\n\n    CALL_SUBTEST_1( packetmath_real<float>() );\n    CALL_SUBTEST_2( packetmath_real<double>() );\n\n    CALL_SUBTEST_4( packetmath_complex<std::complex<float> >() );\n    CALL_SUBTEST_5( packetmath_complex<std::complex<double> >() );\n\n    CALL_SUBTEST_1( packetmath_scatter_gather<float>() );\n    CALL_SUBTEST_2( packetmath_scatter_gather<double>() );\n    CALL_SUBTEST_3( packetmath_scatter_gather<int>() );\n    CALL_SUBTEST_4( packetmath_scatter_gather<std::complex<float> >() );\n    CALL_SUBTEST_5( packetmath_scatter_gather<std::complex<double> >() );\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/pardiso_support.cpp",
    "content": "/* \n   Intel Copyright (C) ....\n*/\n\n#include \"sparse_solver.h\"\n#include <Eigen/PardisoSupport>\n\ntemplate<typename T> void test_pardiso_T()\n{\n  PardisoLLT < SparseMatrix<T, RowMajor>, Lower> pardiso_llt_lower;\n  PardisoLLT < SparseMatrix<T, RowMajor>, Upper> pardiso_llt_upper;\n  PardisoLDLT < SparseMatrix<T, RowMajor>, Lower> pardiso_ldlt_lower;\n  PardisoLDLT < SparseMatrix<T, RowMajor>, Upper> pardiso_ldlt_upper;\n  PardisoLU  < SparseMatrix<T, RowMajor> > pardiso_lu;\n\n  check_sparse_spd_solving(pardiso_llt_lower);\n  check_sparse_spd_solving(pardiso_llt_upper);\n  check_sparse_spd_solving(pardiso_ldlt_lower);\n  check_sparse_spd_solving(pardiso_ldlt_upper);\n  check_sparse_square_solving(pardiso_lu);\n}\n\nvoid test_pardiso_support()\n{\n  CALL_SUBTEST_1(test_pardiso_T<float>());\n  CALL_SUBTEST_2(test_pardiso_T<double>());\n  CALL_SUBTEST_3(test_pardiso_T< std::complex<float> >());\n  CALL_SUBTEST_4(test_pardiso_T< std::complex<double> >());\n}\n"
  },
  {
    "path": "include/eigen3/test/pastix_support.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2012 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define EIGEN_NO_DEBUG_SMALL_PRODUCT_BLOCKS\n#include \"sparse_solver.h\"\n#include <Eigen/PaStiXSupport>\n#include <unsupported/Eigen/SparseExtra>\n\n\ntemplate<typename T> void test_pastix_T()\n{\n  PastixLLT< SparseMatrix<T, ColMajor>, Eigen::Lower > pastix_llt_lower;\n  PastixLDLT< SparseMatrix<T, ColMajor>, Eigen::Lower > pastix_ldlt_lower;\n  PastixLLT< SparseMatrix<T, ColMajor>, Eigen::Upper > pastix_llt_upper;\n  PastixLDLT< SparseMatrix<T, ColMajor>, Eigen::Upper > pastix_ldlt_upper;\n  PastixLU< SparseMatrix<T, ColMajor> > pastix_lu;\n\n  check_sparse_spd_solving(pastix_llt_lower);\n  check_sparse_spd_solving(pastix_ldlt_lower);\n  check_sparse_spd_solving(pastix_llt_upper);\n  check_sparse_spd_solving(pastix_ldlt_upper);\n  check_sparse_square_solving(pastix_lu);\n\n  // Some compilation check:\n  pastix_llt_lower.iparm();\n  pastix_llt_lower.dparm();\n  pastix_ldlt_lower.iparm();\n  pastix_ldlt_lower.dparm();\n  pastix_lu.iparm();\n  pastix_lu.dparm();\n}\n\n// There is no support for selfadjoint matrices with PaStiX. \n// Complex symmetric matrices should pass though\ntemplate<typename T> void test_pastix_T_LU()\n{\n  PastixLU< SparseMatrix<T, ColMajor> > pastix_lu;\n  check_sparse_square_solving(pastix_lu);\n}\n\nvoid test_pastix_support()\n{\n  CALL_SUBTEST_1(test_pastix_T<float>());\n  CALL_SUBTEST_2(test_pastix_T<double>());\n  CALL_SUBTEST_3( (test_pastix_T_LU<std::complex<float> >()) );\n  CALL_SUBTEST_4(test_pastix_T_LU<std::complex<double> >());\n} \n"
  },
  {
    "path": "include/eigen3/test/permutationmatrices.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define TEST_ENABLE_TEMPORARY_TRACKING\n  \n#include \"main.h\"\n\nusing namespace std;\ntemplate<typename MatrixType> void permutationmatrices(const MatrixType& m)\n{\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n  enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime,\n         Options = MatrixType::Options };\n  typedef PermutationMatrix<Rows> LeftPermutationType;\n  typedef Transpositions<Rows> LeftTranspositionsType;\n  typedef Matrix<int, Rows, 1> LeftPermutationVectorType;\n  typedef Map<LeftPermutationType> MapLeftPerm;\n  typedef PermutationMatrix<Cols> RightPermutationType;\n  typedef Transpositions<Cols> RightTranspositionsType;\n  typedef Matrix<int, Cols, 1> RightPermutationVectorType;\n  typedef Map<RightPermutationType> MapRightPerm;\n\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  MatrixType m_original = MatrixType::Random(rows,cols);\n  LeftPermutationVectorType lv;\n  randomPermutationVector(lv, rows);\n  LeftPermutationType lp(lv);\n  RightPermutationVectorType rv;\n  randomPermutationVector(rv, cols);\n  RightPermutationType rp(rv);\n  LeftTranspositionsType lt(lv);\n  RightTranspositionsType rt(rv);\n  MatrixType m_permuted = MatrixType::Random(rows,cols);\n  \n  VERIFY_EVALUATION_COUNT(m_permuted = lp * m_original * rp, 1); // 1 temp for sub expression \"lp * m_original\"\n\n  for (int i=0; i<rows; i++)\n    for (int j=0; j<cols; j++)\n        VERIFY_IS_APPROX(m_permuted(lv(i),j), m_original(i,rv(j)));\n\n  Matrix<Scalar,Rows,Rows> lm(lp);\n  Matrix<Scalar,Cols,Cols> rm(rp);\n\n  VERIFY_IS_APPROX(m_permuted, lm*m_original*rm);\n  \n  m_permuted = m_original;\n  VERIFY_EVALUATION_COUNT(m_permuted = lp * m_permuted * rp, 1);\n  VERIFY_IS_APPROX(m_permuted, lm*m_original*rm);\n  \n  VERIFY_IS_APPROX(lp.inverse()*m_permuted*rp.inverse(), m_original);\n  VERIFY_IS_APPROX(lv.asPermutation().inverse()*m_permuted*rv.asPermutation().inverse(), m_original);\n  VERIFY_IS_APPROX(MapLeftPerm(lv.data(),lv.size()).inverse()*m_permuted*MapRightPerm(rv.data(),rv.size()).inverse(), m_original);\n  \n  VERIFY((lp*lp.inverse()).toDenseMatrix().isIdentity());\n  VERIFY((lv.asPermutation()*lv.asPermutation().inverse()).toDenseMatrix().isIdentity());\n  VERIFY((MapLeftPerm(lv.data(),lv.size())*MapLeftPerm(lv.data(),lv.size()).inverse()).toDenseMatrix().isIdentity());\n\n  LeftPermutationVectorType lv2;\n  randomPermutationVector(lv2, rows);\n  LeftPermutationType lp2(lv2);\n  Matrix<Scalar,Rows,Rows> lm2(lp2);\n  VERIFY_IS_APPROX((lp*lp2).toDenseMatrix().template cast<Scalar>(), lm*lm2);\n  VERIFY_IS_APPROX((lv.asPermutation()*lv2.asPermutation()).toDenseMatrix().template cast<Scalar>(), lm*lm2);\n  VERIFY_IS_APPROX((MapLeftPerm(lv.data(),lv.size())*MapLeftPerm(lv2.data(),lv2.size())).toDenseMatrix().template cast<Scalar>(), lm*lm2);\n\n  LeftPermutationType identityp;\n  identityp.setIdentity(rows);\n  VERIFY_IS_APPROX(m_original, identityp*m_original);\n  \n  // check inplace permutations\n  m_permuted = m_original;\n  VERIFY_EVALUATION_COUNT(m_permuted.noalias()= lp.inverse() * m_permuted, 1); // 1 temp to allocate the mask\n  VERIFY_IS_APPROX(m_permuted, lp.inverse()*m_original);\n  \n  m_permuted = m_original;\n  VERIFY_EVALUATION_COUNT(m_permuted.noalias() = m_permuted * rp.inverse(), 1); // 1 temp to allocate the mask\n  VERIFY_IS_APPROX(m_permuted, m_original*rp.inverse());\n  \n  m_permuted = m_original;\n  VERIFY_EVALUATION_COUNT(m_permuted.noalias() = lp * m_permuted, 1); // 1 temp to allocate the mask\n  VERIFY_IS_APPROX(m_permuted, lp*m_original);\n  \n  m_permuted = m_original;\n  VERIFY_EVALUATION_COUNT(m_permuted.noalias() = m_permuted * rp, 1); // 1 temp to allocate the mask\n  VERIFY_IS_APPROX(m_permuted, m_original*rp);\n\n  if(rows>1 && cols>1)\n  {\n    lp2 = lp;\n    Index i = internal::random<Index>(0, rows-1);\n    Index j;\n    do j = internal::random<Index>(0, rows-1); while(j==i);\n    lp2.applyTranspositionOnTheLeft(i, j);\n    lm = lp;\n    lm.row(i).swap(lm.row(j));\n    VERIFY_IS_APPROX(lm, lp2.toDenseMatrix().template cast<Scalar>());\n\n    RightPermutationType rp2 = rp;\n    i = internal::random<Index>(0, cols-1);\n    do j = internal::random<Index>(0, cols-1); while(j==i);\n    rp2.applyTranspositionOnTheRight(i, j);\n    rm = rp;\n    rm.col(i).swap(rm.col(j));\n    VERIFY_IS_APPROX(rm, rp2.toDenseMatrix().template cast<Scalar>());\n  }\n\n  {\n    // simple compilation check\n    Matrix<Scalar, Cols, Cols> A = rp;\n    Matrix<Scalar, Cols, Cols> B = rp.transpose();\n    VERIFY_IS_APPROX(A, B.transpose());\n  }\n\n  m_permuted = m_original;\n  lp = lt;\n  rp = rt;\n  VERIFY_EVALUATION_COUNT(m_permuted = lt * m_permuted * rt, 1);\n  VERIFY_IS_APPROX(m_permuted, lp*m_original*rp.transpose());\n  \n  VERIFY_IS_APPROX(lt.inverse()*m_permuted*rt.inverse(), m_original);\n}\n\ntemplate<typename T>\nvoid bug890()\n{\n  typedef Matrix<T, Dynamic, Dynamic> MatrixType;\n  typedef Matrix<T, Dynamic, 1> VectorType;\n  typedef Stride<Dynamic,Dynamic> S;\n  typedef Map<MatrixType, Aligned, S> MapType;\n  typedef PermutationMatrix<Dynamic> Perm;\n  \n  VectorType v1(2), v2(2), op(4), rhs(2);\n  v1 << 666,667;\n  op << 1,0,0,1;\n  rhs << 42,42;\n  \n  Perm P(2);\n  P.indices() << 1, 0;\n\n  MapType(v1.data(),2,1,S(1,1)) = P * MapType(rhs.data(),2,1,S(1,1));\n  VERIFY_IS_APPROX(v1, (P * rhs).eval());\n  \n  MapType(v1.data(),2,1,S(1,1)) = P.inverse() * MapType(rhs.data(),2,1,S(1,1));\n  VERIFY_IS_APPROX(v1, (P.inverse() * rhs).eval());\n}\n\nvoid test_permutationmatrices()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( permutationmatrices(Matrix<float, 1, 1>()) );\n    CALL_SUBTEST_2( permutationmatrices(Matrix3f()) );\n    CALL_SUBTEST_3( permutationmatrices(Matrix<double,3,3,RowMajor>()) );\n    CALL_SUBTEST_4( permutationmatrices(Matrix4d()) );\n    CALL_SUBTEST_5( permutationmatrices(Matrix<double,40,60>()) );\n    CALL_SUBTEST_6( permutationmatrices(Matrix<double,Dynamic,Dynamic,RowMajor>(20, 30)) );\n    CALL_SUBTEST_7( permutationmatrices(MatrixXcf(15, 10)) );\n  }\n  CALL_SUBTEST_5( bug890<double>() );\n}\n"
  },
  {
    "path": "include/eigen3/test/prec_inverse_4x4.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <Eigen/LU>\n#include <algorithm>\n\ntemplate<typename MatrixType> void inverse_permutation_4x4()\n{\n  typedef typename MatrixType::Scalar Scalar;\n  Vector4i indices(0,1,2,3);\n  for(int i = 0; i < 24; ++i)\n  {\n    MatrixType m = PermutationMatrix<4>(indices);\n    MatrixType inv = m.inverse();\n    double error = double( (m*inv-MatrixType::Identity()).norm() / NumTraits<Scalar>::epsilon() );\n    EIGEN_DEBUG_VAR(error)\n    VERIFY(error == 0.0);\n    std::next_permutation(indices.data(),indices.data()+4);\n  }\n}\n\ntemplate<typename MatrixType> void inverse_general_4x4(int repeat)\n{\n  using std::abs;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename MatrixType::RealScalar RealScalar;\n  double error_sum = 0., error_max = 0.;\n  for(int i = 0; i < repeat; ++i)\n  {\n    MatrixType m;\n    RealScalar absdet;\n    do {\n      m = MatrixType::Random();\n      absdet = abs(m.determinant());\n    } while(absdet < NumTraits<Scalar>::epsilon());\n    MatrixType inv = m.inverse();\n    double error = double( (m*inv-MatrixType::Identity()).norm() * absdet / NumTraits<Scalar>::epsilon() );\n    error_sum += error;\n    error_max = (std::max)(error_max, error);\n  }\n  std::cerr << \"inverse_general_4x4, Scalar = \" << type_name<Scalar>() << std::endl;\n  double error_avg = error_sum / repeat;\n  EIGEN_DEBUG_VAR(error_avg);\n  EIGEN_DEBUG_VAR(error_max);\n   // FIXME that 1.25 used to be a 1.0 until the NumTraits changes on 28 April 2010, what's going wrong??\n   // FIXME that 1.25 used to be 1.2 until we tested gcc 4.1 on 30 June 2010 and got 1.21.\n  VERIFY(error_avg < (NumTraits<Scalar>::IsComplex ? 8.0 : 1.25));\n  VERIFY(error_max < (NumTraits<Scalar>::IsComplex ? 64.0 : 20.0));\n\n  {\n    int s = 5;//internal::random<int>(4,10);\n    int i = 0;//internal::random<int>(0,s-4);\n    int j = 0;//internal::random<int>(0,s-4);\n    Matrix<Scalar,5,5> mat(s,s);\n    mat.setRandom();\n    MatrixType submat = mat.template block<4,4>(i,j);\n    MatrixType mat_inv = mat.template block<4,4>(i,j).inverse();\n    VERIFY_IS_APPROX(mat_inv, submat.inverse());\n    mat.template block<4,4>(i,j) = submat.inverse();\n    VERIFY_IS_APPROX(mat_inv, (mat.template block<4,4>(i,j)));\n  }\n}\n\nvoid test_prec_inverse_4x4()\n{\n  CALL_SUBTEST_1((inverse_permutation_4x4<Matrix4f>()));\n  CALL_SUBTEST_1(( inverse_general_4x4<Matrix4f>(200000 * g_repeat) ));\n  CALL_SUBTEST_1(( inverse_general_4x4<Matrix<float,4,4,RowMajor> >(200000 * g_repeat) ));\n\n  CALL_SUBTEST_2((inverse_permutation_4x4<Matrix<double,4,4,RowMajor> >()));\n  CALL_SUBTEST_2(( inverse_general_4x4<Matrix<double,4,4,ColMajor> >(200000 * g_repeat) ));\n  CALL_SUBTEST_2(( inverse_general_4x4<Matrix<double,4,4,RowMajor> >(200000 * g_repeat) ));\n\n  CALL_SUBTEST_3((inverse_permutation_4x4<Matrix4cf>()));\n  CALL_SUBTEST_3((inverse_general_4x4<Matrix4cf>(50000 * g_repeat)));\n}\n"
  },
  {
    "path": "include/eigen3/test/product.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <Eigen/QR>\n\ntemplate<typename Derived1, typename Derived2>\nbool areNotApprox(const MatrixBase<Derived1>& m1, const MatrixBase<Derived2>& m2, typename Derived1::RealScalar epsilon = NumTraits<typename Derived1::RealScalar>::dummy_precision())\n{\n  return !((m1-m2).cwiseAbs2().maxCoeff() < epsilon * epsilon\n                          * (std::max)(m1.cwiseAbs2().maxCoeff(), m2.cwiseAbs2().maxCoeff()));\n}\n\ntemplate<typename MatrixType> void product(const MatrixType& m)\n{\n  /* this test covers the following files:\n     Identity.h Product.h\n  */\n  typedef typename MatrixType::Scalar Scalar;\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> RowVectorType;\n  typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> ColVectorType;\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> RowSquareMatrixType;\n  typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> ColSquareMatrixType;\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime,\n                         MatrixType::Flags&RowMajorBit?ColMajor:RowMajor> OtherMajorMatrixType;\n\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  // this test relies a lot on Random.h, and there's not much more that we can do\n  // to test it, hence I consider that we will have tested Random.h\n  MatrixType m1 = MatrixType::Random(rows, cols),\n             m2 = MatrixType::Random(rows, cols),\n             m3(rows, cols);\n  RowSquareMatrixType\n             identity = RowSquareMatrixType::Identity(rows, rows),\n             square = RowSquareMatrixType::Random(rows, rows),\n             res = RowSquareMatrixType::Random(rows, rows);\n  ColSquareMatrixType\n             square2 = ColSquareMatrixType::Random(cols, cols),\n             res2 = ColSquareMatrixType::Random(cols, cols);\n  RowVectorType v1 = RowVectorType::Random(rows);\n  ColVectorType vc2 = ColVectorType::Random(cols), vcres(cols);\n  OtherMajorMatrixType tm1 = m1;\n\n  Scalar s1 = internal::random<Scalar>();\n\n  Index r  = internal::random<Index>(0, rows-1),\n        c  = internal::random<Index>(0, cols-1),\n        c2 = internal::random<Index>(0, cols-1);\n\n  // begin testing Product.h: only associativity for now\n  // (we use Transpose.h but this doesn't count as a test for it)\n  VERIFY_IS_APPROX((m1*m1.transpose())*m2,  m1*(m1.transpose()*m2));\n  m3 = m1;\n  m3 *= m1.transpose() * m2;\n  VERIFY_IS_APPROX(m3,                      m1 * (m1.transpose()*m2));\n  VERIFY_IS_APPROX(m3,                      m1 * (m1.transpose()*m2));\n\n  // continue testing Product.h: distributivity\n  VERIFY_IS_APPROX(square*(m1 + m2),        square*m1+square*m2);\n  VERIFY_IS_APPROX(square*(m1 - m2),        square*m1-square*m2);\n\n  // continue testing Product.h: compatibility with ScalarMultiple.h\n  VERIFY_IS_APPROX(s1*(square*m1),          (s1*square)*m1);\n  VERIFY_IS_APPROX(s1*(square*m1),          square*(m1*s1));\n\n  // test Product.h together with Identity.h\n  VERIFY_IS_APPROX(v1,                      identity*v1);\n  VERIFY_IS_APPROX(v1.transpose(),          v1.transpose() * identity);\n  // again, test operator() to check const-qualification\n  VERIFY_IS_APPROX(MatrixType::Identity(rows, cols)(r,c), static_cast<Scalar>(r==c));\n\n  if (rows!=cols)\n     VERIFY_RAISES_ASSERT(m3 = m1*m1);\n\n  // test the previous tests were not screwed up because operator* returns 0\n  // (we use the more accurate default epsilon)\n  if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1)\n  {\n    VERIFY(areNotApprox(m1.transpose()*m2,m2.transpose()*m1));\n  }\n\n  // test optimized operator+= path\n  res = square;\n  res.noalias() += m1 * m2.transpose();\n  VERIFY_IS_APPROX(res, square + m1 * m2.transpose());\n  if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1)\n  {\n    VERIFY(areNotApprox(res,square + m2 * m1.transpose()));\n  }\n  vcres = vc2;\n  vcres.noalias() += m1.transpose() * v1;\n  VERIFY_IS_APPROX(vcres, vc2 + m1.transpose() * v1);\n\n  // test optimized operator-= path\n  res = square;\n  res.noalias() -= m1 * m2.transpose();\n  VERIFY_IS_APPROX(res, square - (m1 * m2.transpose()));\n  if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1)\n  {\n    VERIFY(areNotApprox(res,square - m2 * m1.transpose()));\n  }\n  vcres = vc2;\n  vcres.noalias() -= m1.transpose() * v1;\n  VERIFY_IS_APPROX(vcres, vc2 - m1.transpose() * v1);\n\n  // test d ?= a+b*c rules\n  res.noalias() = square + m1 * m2.transpose();\n  VERIFY_IS_APPROX(res, square + m1 * m2.transpose());\n  res.noalias() += square + m1 * m2.transpose();\n  VERIFY_IS_APPROX(res, 2*(square + m1 * m2.transpose()));\n  res.noalias() -= square + m1 * m2.transpose();\n  VERIFY_IS_APPROX(res, square + m1 * m2.transpose());\n\n  // test d ?= a-b*c rules\n  res.noalias() = square - m1 * m2.transpose();\n  VERIFY_IS_APPROX(res, square - m1 * m2.transpose());\n  res.noalias() += square - m1 * m2.transpose();\n  VERIFY_IS_APPROX(res, 2*(square - m1 * m2.transpose()));\n  res.noalias() -= square - m1 * m2.transpose();\n  VERIFY_IS_APPROX(res, square - m1 * m2.transpose());\n\n\n  tm1 = m1;\n  VERIFY_IS_APPROX(tm1.transpose() * v1, m1.transpose() * v1);\n  VERIFY_IS_APPROX(v1.transpose() * tm1, v1.transpose() * m1);\n\n  // test submatrix and matrix/vector product\n  for (int i=0; i<rows; ++i)\n    res.row(i) = m1.row(i) * m2.transpose();\n  VERIFY_IS_APPROX(res, m1 * m2.transpose());\n  // the other way round:\n  for (int i=0; i<rows; ++i)\n    res.col(i) = m1 * m2.transpose().col(i);\n  VERIFY_IS_APPROX(res, m1 * m2.transpose());\n\n  res2 = square2;\n  res2.noalias() += m1.transpose() * m2;\n  VERIFY_IS_APPROX(res2, square2 + m1.transpose() * m2);\n  if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1)\n  {\n    VERIFY(areNotApprox(res2,square2 + m2.transpose() * m1));\n  }\n\n  VERIFY_IS_APPROX(res.col(r).noalias() = square.adjoint() * square.col(r), (square.adjoint() * square.col(r)).eval());\n  VERIFY_IS_APPROX(res.col(r).noalias() = square * square.col(r), (square * square.col(r)).eval());\n\n  // vector at runtime (see bug 1166)\n  {\n    RowSquareMatrixType ref(square);\n    ColSquareMatrixType ref2(square2);\n    ref = res = square;\n    VERIFY_IS_APPROX(res.block(0,0,1,rows).noalias() = m1.col(0).transpose() * square.transpose(),            (ref.row(0) = m1.col(0).transpose() * square.transpose()));\n    VERIFY_IS_APPROX(res.block(0,0,1,rows).noalias() = m1.block(0,0,rows,1).transpose() * square.transpose(), (ref.row(0) = m1.col(0).transpose() * square.transpose()));\n    VERIFY_IS_APPROX(res.block(0,0,1,rows).noalias() = m1.col(0).transpose() * square,                        (ref.row(0) = m1.col(0).transpose() * square));\n    VERIFY_IS_APPROX(res.block(0,0,1,rows).noalias() = m1.block(0,0,rows,1).transpose() * square,             (ref.row(0) = m1.col(0).transpose() * square));\n    ref2 = res2 = square2;\n    VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.row(0) * square2.transpose(),                      (ref2.row(0) = m1.row(0) * square2.transpose()));\n    VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.block(0,0,1,cols) * square2.transpose(),           (ref2.row(0) = m1.row(0) * square2.transpose()));\n    VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.row(0) * square2,                                  (ref2.row(0) = m1.row(0) * square2));\n    VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.block(0,0,1,cols) * square2,                       (ref2.row(0) = m1.row(0) * square2));\n  }\n\n  // vector.block() (see bug 1283)\n  {\n    RowVectorType w1(rows);\n    VERIFY_IS_APPROX(square * v1.block(0,0,rows,1), square * v1);\n    VERIFY_IS_APPROX(w1.noalias() = square * v1.block(0,0,rows,1), square * v1);\n    VERIFY_IS_APPROX(w1.block(0,0,rows,1).noalias() = square * v1.block(0,0,rows,1), square * v1);\n\n    Matrix<Scalar,1,MatrixType::ColsAtCompileTime> w2(cols);\n    VERIFY_IS_APPROX(vc2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2);\n    VERIFY_IS_APPROX(w2.noalias() = vc2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2);\n    VERIFY_IS_APPROX(w2.block(0,0,1,cols).noalias() = vc2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2);\n\n    vc2 = square2.block(0,0,1,cols).transpose();\n    VERIFY_IS_APPROX(square2.block(0,0,1,cols) * square2, vc2.transpose() * square2);\n    VERIFY_IS_APPROX(w2.noalias() = square2.block(0,0,1,cols) * square2, vc2.transpose() * square2);\n    VERIFY_IS_APPROX(w2.block(0,0,1,cols).noalias() = square2.block(0,0,1,cols) * square2, vc2.transpose() * square2);\n\n    vc2 = square2.block(0,0,cols,1);\n    VERIFY_IS_APPROX(square2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2);\n    VERIFY_IS_APPROX(w2.noalias() = square2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2);\n    VERIFY_IS_APPROX(w2.block(0,0,1,cols).noalias() = square2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2);\n  }\n\n  // inner product\n  {\n    Scalar x = square2.row(c) * square2.col(c2);\n    VERIFY_IS_APPROX(x, square2.row(c).transpose().cwiseProduct(square2.col(c2)).sum());\n  }\n\n  // outer product\n  {\n    VERIFY_IS_APPROX(m1.col(c) * m1.row(r), m1.block(0,c,rows,1) * m1.block(r,0,1,cols));\n    VERIFY_IS_APPROX(m1.row(r).transpose() * m1.col(c).transpose(), m1.block(r,0,1,cols).transpose() * m1.block(0,c,rows,1).transpose());\n    VERIFY_IS_APPROX(m1.block(0,c,rows,1) * m1.row(r), m1.block(0,c,rows,1) * m1.block(r,0,1,cols));\n    VERIFY_IS_APPROX(m1.col(c) * m1.block(r,0,1,cols), m1.block(0,c,rows,1) * m1.block(r,0,1,cols));\n    VERIFY_IS_APPROX(m1.leftCols(1) * m1.row(r), m1.block(0,0,rows,1) * m1.block(r,0,1,cols));\n    VERIFY_IS_APPROX(m1.col(c) * m1.topRows(1), m1.block(0,c,rows,1) * m1.block(0,0,1,cols));\n  }\n\n  // Aliasing\n  {\n    ColVectorType x(cols); x.setRandom();\n    ColVectorType z(x);\n    ColVectorType y(cols); y.setZero();\n    ColSquareMatrixType A(cols,cols); A.setRandom();\n    // CwiseBinaryOp\n    VERIFY_IS_APPROX(x = y + A*x, A*z);\n    x = z;\n    // CwiseUnaryOp\n    VERIFY_IS_APPROX(x = Scalar(1.)*(A*x), A*z);\n  }\n\n  // regression for blas_trais\n  {\n    VERIFY_IS_APPROX(square * (square*square).transpose(), square * square.transpose() * square.transpose());\n    VERIFY_IS_APPROX(square * (-(square*square)), -square * square * square);\n    VERIFY_IS_APPROX(square * (s1*(square*square)), s1 * square * square * square);\n    VERIFY_IS_APPROX(square * (square*square).conjugate(), square * square.conjugate() * square.conjugate());\n  }\n\n}\n"
  },
  {
    "path": "include/eigen3/test/product_extra.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\ntemplate<typename MatrixType> void product_extra(const MatrixType& m)\n{\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef Matrix<Scalar, 1, Dynamic> RowVectorType;\n  typedef Matrix<Scalar, Dynamic, 1> ColVectorType;\n  typedef Matrix<Scalar, Dynamic, Dynamic,\n                         MatrixType::Flags&RowMajorBit> OtherMajorMatrixType;\n\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  MatrixType m1 = MatrixType::Random(rows, cols),\n             m2 = MatrixType::Random(rows, cols),\n             m3(rows, cols),\n             mzero = MatrixType::Zero(rows, cols),\n             identity = MatrixType::Identity(rows, rows),\n             square = MatrixType::Random(rows, rows),\n             res = MatrixType::Random(rows, rows),\n             square2 = MatrixType::Random(cols, cols),\n             res2 = MatrixType::Random(cols, cols);\n  RowVectorType v1 = RowVectorType::Random(rows), vrres(rows);\n  ColVectorType vc2 = ColVectorType::Random(cols), vcres(cols);\n  OtherMajorMatrixType tm1 = m1;\n\n  Scalar s1 = internal::random<Scalar>(),\n         s2 = internal::random<Scalar>(),\n         s3 = internal::random<Scalar>();\n\n  VERIFY_IS_APPROX(m3.noalias() = m1 * m2.adjoint(),                 m1 * m2.adjoint().eval());\n  VERIFY_IS_APPROX(m3.noalias() = m1.adjoint() * square.adjoint(),   m1.adjoint().eval() * square.adjoint().eval());\n  VERIFY_IS_APPROX(m3.noalias() = m1.adjoint() * m2,                 m1.adjoint().eval() * m2);\n  VERIFY_IS_APPROX(m3.noalias() = (s1 * m1.adjoint()) * m2,          (s1 * m1.adjoint()).eval() * m2);\n  VERIFY_IS_APPROX(m3.noalias() = ((s1 * m1).adjoint()) * m2,        (numext::conj(s1) * m1.adjoint()).eval() * m2);\n  VERIFY_IS_APPROX(m3.noalias() = (- m1.adjoint() * s1) * (s3 * m2), (- m1.adjoint()  * s1).eval() * (s3 * m2).eval());\n  VERIFY_IS_APPROX(m3.noalias() = (s2 * m1.adjoint() * s1) * m2,     (s2 * m1.adjoint()  * s1).eval() * m2);\n  VERIFY_IS_APPROX(m3.noalias() = (-m1*s2) * s1*m2.adjoint(),        (-m1*s2).eval() * (s1*m2.adjoint()).eval());\n\n  // a very tricky case where a scale factor has to be automatically conjugated:\n  VERIFY_IS_APPROX( m1.adjoint() * (s1*m2).conjugate(), (m1.adjoint()).eval() * ((s1*m2).conjugate()).eval());\n\n\n  // test all possible conjugate combinations for the four matrix-vector product cases:\n\n  VERIFY_IS_APPROX((-m1.conjugate() * s2) * (s1 * vc2),\n                   (-m1.conjugate()*s2).eval() * (s1 * vc2).eval());\n  VERIFY_IS_APPROX((-m1 * s2) * (s1 * vc2.conjugate()),\n                   (-m1*s2).eval() * (s1 * vc2.conjugate()).eval());\n  VERIFY_IS_APPROX((-m1.conjugate() * s2) * (s1 * vc2.conjugate()),\n                   (-m1.conjugate()*s2).eval() * (s1 * vc2.conjugate()).eval());\n\n  VERIFY_IS_APPROX((s1 * vc2.transpose()) * (-m1.adjoint() * s2),\n                   (s1 * vc2.transpose()).eval() * (-m1.adjoint()*s2).eval());\n  VERIFY_IS_APPROX((s1 * vc2.adjoint()) * (-m1.transpose() * s2),\n                   (s1 * vc2.adjoint()).eval() * (-m1.transpose()*s2).eval());\n  VERIFY_IS_APPROX((s1 * vc2.adjoint()) * (-m1.adjoint() * s2),\n                   (s1 * vc2.adjoint()).eval() * (-m1.adjoint()*s2).eval());\n\n  VERIFY_IS_APPROX((-m1.adjoint() * s2) * (s1 * v1.transpose()),\n                   (-m1.adjoint()*s2).eval() * (s1 * v1.transpose()).eval());\n  VERIFY_IS_APPROX((-m1.transpose() * s2) * (s1 * v1.adjoint()),\n                   (-m1.transpose()*s2).eval() * (s1 * v1.adjoint()).eval());\n  VERIFY_IS_APPROX((-m1.adjoint() * s2) * (s1 * v1.adjoint()),\n                   (-m1.adjoint()*s2).eval() * (s1 * v1.adjoint()).eval());\n\n  VERIFY_IS_APPROX((s1 * v1) * (-m1.conjugate() * s2),\n                   (s1 * v1).eval() * (-m1.conjugate()*s2).eval());\n  VERIFY_IS_APPROX((s1 * v1.conjugate()) * (-m1 * s2),\n                   (s1 * v1.conjugate()).eval() * (-m1*s2).eval());\n  VERIFY_IS_APPROX((s1 * v1.conjugate()) * (-m1.conjugate() * s2),\n                   (s1 * v1.conjugate()).eval() * (-m1.conjugate()*s2).eval());\n\n  VERIFY_IS_APPROX((-m1.adjoint() * s2) * (s1 * v1.adjoint()),\n                   (-m1.adjoint()*s2).eval() * (s1 * v1.adjoint()).eval());\n\n  // test the vector-matrix product with non aligned starts\n  Index i = internal::random<Index>(0,m1.rows()-2);\n  Index j = internal::random<Index>(0,m1.cols()-2);\n  Index r = internal::random<Index>(1,m1.rows()-i);\n  Index c = internal::random<Index>(1,m1.cols()-j);\n  Index i2 = internal::random<Index>(0,m1.rows()-1);\n  Index j2 = internal::random<Index>(0,m1.cols()-1);\n\n  VERIFY_IS_APPROX(m1.col(j2).adjoint() * m1.block(0,j,m1.rows(),c), m1.col(j2).adjoint().eval() * m1.block(0,j,m1.rows(),c).eval());\n  VERIFY_IS_APPROX(m1.block(i,0,r,m1.cols()) * m1.row(i2).adjoint(), m1.block(i,0,r,m1.cols()).eval() * m1.row(i2).adjoint().eval());\n  \n  // regression test\n  MatrixType tmp = m1 * m1.adjoint() * s1;\n  VERIFY_IS_APPROX(tmp, m1 * m1.adjoint() * s1);\n\n  // regression test for bug 1343, assignment to arrays\n  Array<Scalar,Dynamic,1> a1 = m1 * vc2;\n  VERIFY_IS_APPROX(a1.matrix(),m1*vc2);\n  Array<Scalar,Dynamic,1> a2 = s1 * (m1 * vc2);\n  VERIFY_IS_APPROX(a2.matrix(),s1*m1*vc2);\n  Array<Scalar,1,Dynamic> a3 = v1 * m1;\n  VERIFY_IS_APPROX(a3.matrix(),v1*m1);\n  Array<Scalar,Dynamic,Dynamic> a4 = m1 * m2.adjoint();\n  VERIFY_IS_APPROX(a4.matrix(),m1*m2.adjoint());\n}\n\n// Regression test for bug reported at http://forum.kde.org/viewtopic.php?f=74&t=96947\nvoid mat_mat_scalar_scalar_product()\n{\n  Eigen::Matrix2Xd dNdxy(2, 3);\n  dNdxy << -0.5, 0.5, 0,\n           -0.3, 0, 0.3;\n  double det = 6.0, wt = 0.5;\n  VERIFY_IS_APPROX(dNdxy.transpose()*dNdxy*det*wt, det*wt*dNdxy.transpose()*dNdxy);\n}\n\ntemplate <typename MatrixType> \nvoid zero_sized_objects(const MatrixType& m)\n{\n  typedef typename MatrixType::Scalar Scalar;\n  const int PacketSize  = internal::packet_traits<Scalar>::size;\n  const int PacketSize1 = PacketSize>1 ?  PacketSize-1 : 1;\n  Index rows = m.rows();\n  Index cols = m.cols();\n  \n  {\n    MatrixType res, a(rows,0), b(0,cols);\n    VERIFY_IS_APPROX( (res=a*b), MatrixType::Zero(rows,cols) );\n    VERIFY_IS_APPROX( (res=a*a.transpose()), MatrixType::Zero(rows,rows) );\n    VERIFY_IS_APPROX( (res=b.transpose()*b), MatrixType::Zero(cols,cols) );\n    VERIFY_IS_APPROX( (res=b.transpose()*a.transpose()), MatrixType::Zero(cols,rows) );\n  }\n  \n  {\n    MatrixType res, a(rows,cols), b(cols,0);\n    res = a*b;\n    VERIFY(res.rows()==rows && res.cols()==0);\n    b.resize(0,rows);\n    res = b*a;\n    VERIFY(res.rows()==0 && res.cols()==cols);\n  }\n  \n  {\n    Matrix<Scalar,PacketSize,0> a;\n    Matrix<Scalar,0,1> b;\n    Matrix<Scalar,PacketSize,1> res;\n    VERIFY_IS_APPROX( (res=a*b), MatrixType::Zero(PacketSize,1) );\n    VERIFY_IS_APPROX( (res=a.lazyProduct(b)), MatrixType::Zero(PacketSize,1) );\n  }\n  \n  {\n    Matrix<Scalar,PacketSize1,0> a;\n    Matrix<Scalar,0,1> b;\n    Matrix<Scalar,PacketSize1,1> res;\n    VERIFY_IS_APPROX( (res=a*b), MatrixType::Zero(PacketSize1,1) );\n    VERIFY_IS_APPROX( (res=a.lazyProduct(b)), MatrixType::Zero(PacketSize1,1) );\n  }\n  \n  {\n    Matrix<Scalar,PacketSize,Dynamic> a(PacketSize,0);\n    Matrix<Scalar,Dynamic,1> b(0,1);\n    Matrix<Scalar,PacketSize,1> res;\n    VERIFY_IS_APPROX( (res=a*b), MatrixType::Zero(PacketSize,1) );\n    VERIFY_IS_APPROX( (res=a.lazyProduct(b)), MatrixType::Zero(PacketSize,1) );\n  }\n  \n  {\n    Matrix<Scalar,PacketSize1,Dynamic> a(PacketSize1,0);\n    Matrix<Scalar,Dynamic,1> b(0,1);\n    Matrix<Scalar,PacketSize1,1> res;\n    VERIFY_IS_APPROX( (res=a*b), MatrixType::Zero(PacketSize1,1) );\n    VERIFY_IS_APPROX( (res=a.lazyProduct(b)), MatrixType::Zero(PacketSize1,1) );\n  }\n}\n\ntemplate<int>\nvoid bug_127()\n{\n  // Bug 127\n  //\n  // a product of the form lhs*rhs with\n  //\n  // lhs:\n  // rows = 1, cols = 4\n  // RowsAtCompileTime = 1, ColsAtCompileTime = -1\n  // MaxRowsAtCompileTime = 1, MaxColsAtCompileTime = 5\n  //\n  // rhs:\n  // rows = 4, cols = 0\n  // RowsAtCompileTime = -1, ColsAtCompileTime = -1\n  // MaxRowsAtCompileTime = 5, MaxColsAtCompileTime = 1\n  //\n  // was failing on a runtime assertion, because it had been mis-compiled as a dot product because Product.h was using the\n  // max-sizes to detect size 1 indicating vectors, and that didn't account for 0-sized object with max-size 1.\n\n  Matrix<float,1,Dynamic,RowMajor,1,5> a(1,4);\n  Matrix<float,Dynamic,Dynamic,ColMajor,5,1> b(4,0);\n  a*b;\n}\n\ntemplate<int> void bug_817()\n{\n  ArrayXXf B = ArrayXXf::Random(10,10), C;\n  VectorXf x = VectorXf::Random(10);\n  C = (x.transpose()*B.matrix());\n  B = (x.transpose()*B.matrix());\n  VERIFY_IS_APPROX(B,C);\n}\n\ntemplate<int>\nvoid unaligned_objects()\n{\n  // Regression test for the bug reported here:\n  // http://forum.kde.org/viewtopic.php?f=74&t=107541\n  // Recall the matrix*vector kernel avoid unaligned loads by loading two packets and then reassemble then.\n  // There was a mistake in the computation of the valid range for fully unaligned objects: in some rare cases,\n  // memory was read outside the allocated matrix memory. Though the values were not used, this might raise segfault.\n  for(int m=450;m<460;++m)\n  {\n    for(int n=8;n<12;++n)\n    {\n      MatrixXf M(m, n);\n      VectorXf v1(n), r1(500);\n      RowVectorXf v2(m), r2(16);\n\n      M.setRandom();\n      v1.setRandom();\n      v2.setRandom();\n      for(int o=0; o<4; ++o)\n      {\n        r1.segment(o,m).noalias() = M * v1;\n        VERIFY_IS_APPROX(r1.segment(o,m), M * MatrixXf(v1));\n        r2.segment(o,n).noalias() = v2 * M;\n        VERIFY_IS_APPROX(r2.segment(o,n), MatrixXf(v2) * M);\n      }\n    }\n  }\n}\n\ntemplate<typename T>\nEIGEN_DONT_INLINE\nIndex test_compute_block_size(Index m, Index n, Index k)\n{\n  Index mc(m), nc(n), kc(k);\n  internal::computeProductBlockingSizes<T,T>(kc, mc, nc);\n  return kc+mc+nc;\n}\n\ntemplate<typename T>\nIndex compute_block_size()\n{\n  Index ret = 0;\n  ret += test_compute_block_size<T>(0,1,1);\n  ret += test_compute_block_size<T>(1,0,1);\n  ret += test_compute_block_size<T>(1,1,0);\n  ret += test_compute_block_size<T>(0,0,1);\n  ret += test_compute_block_size<T>(0,1,0);\n  ret += test_compute_block_size<T>(1,0,0);\n  ret += test_compute_block_size<T>(0,0,0);\n  return ret;\n}\n\ntemplate<typename>\nvoid aliasing_with_resize()\n{\n  Index m = internal::random<Index>(10,50);\n  Index n = internal::random<Index>(10,50);\n  MatrixXd A, B, C(m,n), D(m,m);\n  VectorXd a, b, c(n);\n  C.setRandom();\n  D.setRandom();\n  c.setRandom();\n  double s = internal::random<double>(1,10);\n\n  A = C;\n  B = A * A.transpose();\n  A = A * A.transpose();\n  VERIFY_IS_APPROX(A,B);\n\n  A = C;\n  B = (A * A.transpose())/s;\n  A = (A * A.transpose())/s;\n  VERIFY_IS_APPROX(A,B);\n\n  A = C;\n  B = (A * A.transpose()) + D;\n  A = (A * A.transpose()) + D;\n  VERIFY_IS_APPROX(A,B);\n\n  A = C;\n  B = D + (A * A.transpose());\n  A = D + (A * A.transpose());\n  VERIFY_IS_APPROX(A,B);\n\n  A = C;\n  B = s * (A * A.transpose());\n  A = s * (A * A.transpose());\n  VERIFY_IS_APPROX(A,B);\n\n  A = C;\n  a = c;\n  b = (A * a)/s;\n  a = (A * a)/s;\n  VERIFY_IS_APPROX(a,b);\n}\n\ntemplate<int>\nvoid bug_1308()\n{\n  int n = 10;\n  MatrixXd r(n,n);\n  VectorXd v = VectorXd::Random(n);\n  r = v * RowVectorXd::Ones(n);\n  VERIFY_IS_APPROX(r, v.rowwise().replicate(n));\n  r = VectorXd::Ones(n) * v.transpose();\n  VERIFY_IS_APPROX(r, v.rowwise().replicate(n).transpose());\n\n  Matrix4d ones44 = Matrix4d::Ones();\n  Matrix4d m44 = Matrix4d::Ones() * Matrix4d::Ones();\n  VERIFY_IS_APPROX(m44,Matrix4d::Constant(4));\n  VERIFY_IS_APPROX(m44.noalias()=ones44*Matrix4d::Ones(), Matrix4d::Constant(4));\n  VERIFY_IS_APPROX(m44.noalias()=ones44.transpose()*Matrix4d::Ones(), Matrix4d::Constant(4));\n  VERIFY_IS_APPROX(m44.noalias()=Matrix4d::Ones()*ones44, Matrix4d::Constant(4));\n  VERIFY_IS_APPROX(m44.noalias()=Matrix4d::Ones()*ones44.transpose(), Matrix4d::Constant(4));\n\n  typedef Matrix<double,4,4,RowMajor> RMatrix4d;\n  RMatrix4d r44 = Matrix4d::Ones() * Matrix4d::Ones();\n  VERIFY_IS_APPROX(r44,Matrix4d::Constant(4));\n  VERIFY_IS_APPROX(r44.noalias()=ones44*Matrix4d::Ones(), Matrix4d::Constant(4));\n  VERIFY_IS_APPROX(r44.noalias()=ones44.transpose()*Matrix4d::Ones(), Matrix4d::Constant(4));\n  VERIFY_IS_APPROX(r44.noalias()=Matrix4d::Ones()*ones44, Matrix4d::Constant(4));\n  VERIFY_IS_APPROX(r44.noalias()=Matrix4d::Ones()*ones44.transpose(), Matrix4d::Constant(4));\n  VERIFY_IS_APPROX(r44.noalias()=ones44*RMatrix4d::Ones(), Matrix4d::Constant(4));\n  VERIFY_IS_APPROX(r44.noalias()=ones44.transpose()*RMatrix4d::Ones(), Matrix4d::Constant(4));\n  VERIFY_IS_APPROX(r44.noalias()=RMatrix4d::Ones()*ones44, Matrix4d::Constant(4));\n  VERIFY_IS_APPROX(r44.noalias()=RMatrix4d::Ones()*ones44.transpose(), Matrix4d::Constant(4));\n\n//   RowVector4d r4;\n  m44.setOnes();\n  r44.setZero();\n  VERIFY_IS_APPROX(r44.noalias() += m44.row(0).transpose() * RowVector4d::Ones(), ones44);\n  r44.setZero();\n  VERIFY_IS_APPROX(r44.noalias() += m44.col(0) * RowVector4d::Ones(), ones44);\n  r44.setZero();\n  VERIFY_IS_APPROX(r44.noalias() += Vector4d::Ones() * m44.row(0), ones44);\n  r44.setZero();\n  VERIFY_IS_APPROX(r44.noalias() += Vector4d::Ones() * m44.col(0).transpose(), ones44);\n}\n\nvoid test_product_extra()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( product_extra(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_2( product_extra(MatrixXd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_2( mat_mat_scalar_scalar_product() );\n    CALL_SUBTEST_3( product_extra(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2), internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))) );\n    CALL_SUBTEST_4( product_extra(MatrixXcd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2), internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))) );\n    CALL_SUBTEST_1( zero_sized_objects(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n  }\n  CALL_SUBTEST_5( bug_127<0>() );\n  CALL_SUBTEST_5( bug_817<0>() );\n  CALL_SUBTEST_5( bug_1308<0>() );\n  CALL_SUBTEST_6( unaligned_objects<0>() );\n  CALL_SUBTEST_7( compute_block_size<float>() );\n  CALL_SUBTEST_7( compute_block_size<double>() );\n  CALL_SUBTEST_7( compute_block_size<std::complex<double> >() );\n  CALL_SUBTEST_8( aliasing_with_resize<void>() );\n\n}\n"
  },
  {
    "path": "include/eigen3/test/product_large.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"product.h\"\n\ntemplate<typename T>\nvoid test_aliasing()\n{\n  int rows = internal::random<int>(1,12);\n  int cols = internal::random<int>(1,12);\n  typedef Matrix<T,Dynamic,Dynamic> MatrixType;\n  typedef Matrix<T,Dynamic,1> VectorType;\n  VectorType x(cols); x.setRandom();\n  VectorType z(x);\n  VectorType y(rows); y.setZero();\n  MatrixType A(rows,cols); A.setRandom();\n  // CwiseBinaryOp\n  VERIFY_IS_APPROX(x = y + A*x, A*z);     // OK because \"y + A*x\" is marked as \"assume-aliasing\"\n  x = z;\n  // CwiseUnaryOp\n  VERIFY_IS_APPROX(x = T(1.)*(A*x), A*z); // OK because 1*(A*x) is replaced by (1*A*x) which is a Product<> expression\n  x = z;\n  // VERIFY_IS_APPROX(x = y-A*x, -A*z);   // Not OK in 3.3 because x is resized before A*x gets evaluated\n  x = z;\n}\n\nvoid test_product_large()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( product(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_2( product(MatrixXd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_3( product(MatrixXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n    CALL_SUBTEST_4( product(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2), internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))) );\n    CALL_SUBTEST_5( product(Matrix<float,Dynamic,Dynamic,RowMajor>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n\n    CALL_SUBTEST_1( test_aliasing<float>() );\n  }\n\n#if defined EIGEN_TEST_PART_6\n  {\n    // test a specific issue in DiagonalProduct\n    int N = 1000000;\n    VectorXf v = VectorXf::Ones(N);\n    MatrixXf m = MatrixXf::Ones(N,3);\n    m = (v+v).asDiagonal() * m;\n    VERIFY_IS_APPROX(m, MatrixXf::Constant(N,3,2));\n  }\n\n  {\n    // test deferred resizing in Matrix::operator=\n    MatrixXf a = MatrixXf::Random(10,4), b = MatrixXf::Random(4,10), c = a;\n    VERIFY_IS_APPROX((a = a * b), (c * b).eval());\n  }\n\n  {\n    // check the functions to setup blocking sizes compile and do not segfault\n    // FIXME check they do what they are supposed to do !!\n    std::ptrdiff_t l1 = internal::random<int>(10000,20000);\n    std::ptrdiff_t l2 = internal::random<int>(100000,200000);\n    std::ptrdiff_t l3 = internal::random<int>(1000000,2000000);\n    setCpuCacheSizes(l1,l2,l3);\n    VERIFY(l1==l1CacheSize());\n    VERIFY(l2==l2CacheSize());\n    std::ptrdiff_t k1 = internal::random<int>(10,100)*16;\n    std::ptrdiff_t m1 = internal::random<int>(10,100)*16;\n    std::ptrdiff_t n1 = internal::random<int>(10,100)*16;\n    // only makes sure it compiles fine\n    internal::computeProductBlockingSizes<float,float,std::ptrdiff_t>(k1,m1,n1,1);\n  }\n\n  {\n    // test regression in row-vector by matrix (bad Map type)\n    MatrixXf mat1(10,32); mat1.setRandom();\n    MatrixXf mat2(32,32); mat2.setRandom();\n    MatrixXf r1 = mat1.row(2)*mat2.transpose();\n    VERIFY_IS_APPROX(r1, (mat1.row(2)*mat2.transpose()).eval());\n\n    MatrixXf r2 = mat1.row(2)*mat2;\n    VERIFY_IS_APPROX(r2, (mat1.row(2)*mat2).eval());\n  }\n\n  {\n    Eigen::MatrixXd A(10,10), B, C;\n    A.setRandom();\n    C = A;\n    for(int k=0; k<79; ++k)\n      C = C * A;\n    B.noalias() = (((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A)) * ((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A)))\n                * (((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A)) * ((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A)));\n    VERIFY_IS_APPROX(B,C);\n  }\n#endif\n\n  // Regression test for bug 714:\n#if defined EIGEN_HAS_OPENMP\n  omp_set_dynamic(1);\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_6( product(Matrix<float,Dynamic,Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n  }\n#endif\n}\n"
  },
  {
    "path": "include/eigen3/test/product_mmtr.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2010-2017 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#define CHECK_MMTR(DEST, TRI, OP) {                   \\\n    ref3 = DEST;                                      \\\n    ref2 = ref1 = DEST;                               \\\n    DEST.template triangularView<TRI>() OP;           \\\n    ref1 OP;                                          \\\n    ref2.template triangularView<TRI>()               \\\n      = ref1.template triangularView<TRI>();          \\\n    VERIFY_IS_APPROX(DEST,ref2);                      \\\n    \\\n    DEST = ref3;                                      \\\n    ref3 = ref2;                                      \\\n    ref3.diagonal() = DEST.diagonal();                \\\n    DEST.template triangularView<TRI|ZeroDiag>() OP;  \\\n    VERIFY_IS_APPROX(DEST,ref3);                      \\\n  }\n\ntemplate<typename Scalar> void mmtr(int size)\n{\n  typedef Matrix<Scalar,Dynamic,Dynamic,ColMajor> MatrixColMaj;\n  typedef Matrix<Scalar,Dynamic,Dynamic,RowMajor> MatrixRowMaj;\n\n  DenseIndex othersize = internal::random<DenseIndex>(1,200);\n  \n  MatrixColMaj matc = MatrixColMaj::Zero(size, size);\n  MatrixRowMaj matr = MatrixRowMaj::Zero(size, size);\n  MatrixColMaj ref1(size, size), ref2(size, size), ref3(size,size);\n  \n  MatrixColMaj soc(size,othersize); soc.setRandom();\n  MatrixColMaj osc(othersize,size); osc.setRandom();\n  MatrixRowMaj sor(size,othersize); sor.setRandom();\n  MatrixRowMaj osr(othersize,size); osr.setRandom();\n  MatrixColMaj sqc(size,size); sqc.setRandom();\n  MatrixRowMaj sqr(size,size); sqr.setRandom();\n  \n  Scalar s = internal::random<Scalar>();\n  \n  CHECK_MMTR(matc, Lower, = s*soc*sor.adjoint());\n  CHECK_MMTR(matc, Upper, = s*(soc*soc.adjoint()));\n  CHECK_MMTR(matr, Lower, = s*soc*soc.adjoint());\n  CHECK_MMTR(matr, Upper, = soc*(s*sor.adjoint()));\n  \n  CHECK_MMTR(matc, Lower, += s*soc*soc.adjoint());\n  CHECK_MMTR(matc, Upper, += s*(soc*sor.transpose()));\n  CHECK_MMTR(matr, Lower, += s*sor*soc.adjoint());\n  CHECK_MMTR(matr, Upper, += soc*(s*soc.adjoint()));\n  \n  CHECK_MMTR(matc, Lower, -= s*soc*soc.adjoint());\n  CHECK_MMTR(matc, Upper, -= s*(osc.transpose()*osc.conjugate()));\n  CHECK_MMTR(matr, Lower, -= s*soc*soc.adjoint());\n  CHECK_MMTR(matr, Upper, -= soc*(s*soc.adjoint()));\n  \n  CHECK_MMTR(matc, Lower, -= s*sqr*sqc.template triangularView<Upper>());\n  CHECK_MMTR(matc, Upper, = s*sqc*sqr.template triangularView<Upper>());\n  CHECK_MMTR(matc, Lower, += s*sqr*sqc.template triangularView<Lower>());\n  CHECK_MMTR(matc, Upper, = s*sqc*sqc.template triangularView<Lower>());\n  \n  CHECK_MMTR(matc, Lower, = (s*sqr).template triangularView<Upper>()*sqc);\n  CHECK_MMTR(matc, Upper, -= (s*sqc).template triangularView<Upper>()*sqc);\n  CHECK_MMTR(matc, Lower, = (s*sqr).template triangularView<Lower>()*sqc);\n  CHECK_MMTR(matc, Upper, += (s*sqc).template triangularView<Lower>()*sqc);\n\n  // check aliasing\n  ref2 = ref1 = matc;\n  ref1 = sqc.adjoint() * matc * sqc;\n  ref2.template triangularView<Upper>() = ref1.template triangularView<Upper>();\n  matc.template triangularView<Upper>() = sqc.adjoint() * matc * sqc;\n  VERIFY_IS_APPROX(matc, ref2);\n\n  ref2 = ref1 = matc;\n  ref1 = sqc * matc * sqc.adjoint();\n  ref2.template triangularView<Lower>() = ref1.template triangularView<Lower>();\n  matc.template triangularView<Lower>() = sqc * matc * sqc.adjoint();\n  VERIFY_IS_APPROX(matc, ref2);\n}\n\nvoid test_product_mmtr()\n{\n  for(int i = 0; i < g_repeat ; i++)\n  {\n    CALL_SUBTEST_1((mmtr<float>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE))));\n    CALL_SUBTEST_2((mmtr<double>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE))));\n    CALL_SUBTEST_3((mmtr<std::complex<float> >(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))));\n    CALL_SUBTEST_4((mmtr<std::complex<double> >(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))));\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/product_notemporary.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define TEST_ENABLE_TEMPORARY_TRACKING\n\n#include \"main.h\"\n\ntemplate<typename MatrixType> void product_notemporary(const MatrixType& m)\n{\n  /* This test checks the number of temporaries created\n   * during the evaluation of a complex expression */\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename MatrixType::RealScalar RealScalar;\n  typedef Matrix<Scalar, 1, Dynamic> RowVectorType;\n  typedef Matrix<Scalar, Dynamic, 1> ColVectorType;\n  typedef Matrix<Scalar, Dynamic, Dynamic, ColMajor> ColMajorMatrixType;\n  typedef Matrix<Scalar, Dynamic, Dynamic, RowMajor> RowMajorMatrixType;\n\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  ColMajorMatrixType m1 = MatrixType::Random(rows, cols),\n                     m2 = MatrixType::Random(rows, cols),\n                     m3(rows, cols);\n  RowVectorType rv1 = RowVectorType::Random(rows), rvres(rows);\n  ColVectorType cv1 = ColVectorType::Random(cols), cvres(cols);\n  RowMajorMatrixType rm3(rows, cols);\n\n  Scalar s1 = internal::random<Scalar>(),\n         s2 = internal::random<Scalar>(),\n         s3 = internal::random<Scalar>();\n\n  Index c0 = internal::random<Index>(4,cols-8),\n        c1 = internal::random<Index>(8,cols-c0),\n        r0 = internal::random<Index>(4,cols-8),\n        r1 = internal::random<Index>(8,rows-r0);\n\n  VERIFY_EVALUATION_COUNT( m3 = (m1 * m2.adjoint()), 1);\n  VERIFY_EVALUATION_COUNT( m3 = (m1 * m2.adjoint()).transpose(), 1);\n  VERIFY_EVALUATION_COUNT( m3.noalias() = m1 * m2.adjoint(), 0);\n\n  VERIFY_EVALUATION_COUNT( m3 = s1 * (m1 * m2.transpose()), 1);\n//   VERIFY_EVALUATION_COUNT( m3 = m3 + s1 * (m1 * m2.transpose()), 1);\n  VERIFY_EVALUATION_COUNT( m3.noalias() = s1 * (m1 * m2.transpose()), 0);\n\n  VERIFY_EVALUATION_COUNT( m3 = m3 + (m1 * m2.adjoint()), 1);\n  VERIFY_EVALUATION_COUNT( m3 = m3 - (m1 * m2.adjoint()), 1);\n\n  VERIFY_EVALUATION_COUNT( m3 = m3 + (m1 * m2.adjoint()).transpose(), 1);\n  VERIFY_EVALUATION_COUNT( m3.noalias() = m3 + m1 * m2.transpose(), 0);\n  VERIFY_EVALUATION_COUNT( m3.noalias() += m3 + m1 * m2.transpose(), 0);\n  VERIFY_EVALUATION_COUNT( m3.noalias() -= m3 + m1 * m2.transpose(), 0);\n  VERIFY_EVALUATION_COUNT( m3.noalias() =  m3 - m1 * m2.transpose(), 0);\n  VERIFY_EVALUATION_COUNT( m3.noalias() += m3 - m1 * m2.transpose(), 0);\n  VERIFY_EVALUATION_COUNT( m3.noalias() -= m3 - m1 * m2.transpose(), 0);\n\n  VERIFY_EVALUATION_COUNT( m3.noalias() = s1 * m1 * s2 * m2.adjoint(), 0);\n  VERIFY_EVALUATION_COUNT( m3.noalias() = s1 * m1 * s2 * (m1*s3+m2*s2).adjoint(), 1);\n  VERIFY_EVALUATION_COUNT( m3.noalias() = (s1 * m1).adjoint() * s2 * m2, 0);\n  VERIFY_EVALUATION_COUNT( m3.noalias() += s1 * (-m1*s3).adjoint() * (s2 * m2 * s3), 0);\n  VERIFY_EVALUATION_COUNT( m3.noalias() -= s1 * (m1.transpose() * m2), 0);\n\n  VERIFY_EVALUATION_COUNT(( m3.block(r0,r0,r1,r1).noalias() += -m1.block(r0,c0,r1,c1) * (s2*m2.block(r0,c0,r1,c1)).adjoint() ), 0);\n  VERIFY_EVALUATION_COUNT(( m3.block(r0,r0,r1,r1).noalias() -= s1 * m1.block(r0,c0,r1,c1) * m2.block(c0,r0,c1,r1) ), 0);\n\n  // NOTE this is because the Block expression is not handled yet by our expression analyser\n  VERIFY_EVALUATION_COUNT(( m3.block(r0,r0,r1,r1).noalias() = s1 * m1.block(r0,c0,r1,c1) * (s1*m2).block(c0,r0,c1,r1) ), 1);\n\n  VERIFY_EVALUATION_COUNT( m3.noalias() -= (s1 * m1).template triangularView<Lower>() * m2, 0);\n  VERIFY_EVALUATION_COUNT( rm3.noalias() = (s1 * m1.adjoint()).template triangularView<Upper>() * (m2+m2), 1);\n  VERIFY_EVALUATION_COUNT( rm3.noalias() = (s1 * m1.adjoint()).template triangularView<UnitUpper>() * m2.adjoint(), 0);\n\n  VERIFY_EVALUATION_COUNT( m3.template triangularView<Upper>() = (m1 * m2.adjoint()), 0);\n  VERIFY_EVALUATION_COUNT( m3.template triangularView<Upper>() -= (m1 * m2.adjoint()), 0);\n\n  // NOTE this is because the blas_traits require innerstride==1 to avoid a temporary, but that doesn't seem to be actually needed for the triangular products\n  VERIFY_EVALUATION_COUNT( rm3.col(c0).noalias() = (s1 * m1.adjoint()).template triangularView<UnitUpper>() * (s2*m2.row(c0)).adjoint(), 1);\n\n  VERIFY_EVALUATION_COUNT( m1.template triangularView<Lower>().solveInPlace(m3), 0);\n  VERIFY_EVALUATION_COUNT( m1.adjoint().template triangularView<Lower>().solveInPlace(m3.transpose()), 0);\n\n  VERIFY_EVALUATION_COUNT( m3.noalias() -= (s1 * m1).adjoint().template selfadjointView<Lower>() * (-m2*s3).adjoint(), 0);\n  VERIFY_EVALUATION_COUNT( m3.noalias() = s2 * m2.adjoint() * (s1 * m1.adjoint()).template selfadjointView<Upper>(), 0);\n  VERIFY_EVALUATION_COUNT( rm3.noalias() = (s1 * m1.adjoint()).template selfadjointView<Lower>() * m2.adjoint(), 0);\n\n  // NOTE this is because the blas_traits require innerstride==1 to avoid a temporary, but that doesn't seem to be actually needed for the triangular products\n  VERIFY_EVALUATION_COUNT( m3.col(c0).noalias() = (s1 * m1).adjoint().template selfadjointView<Lower>() * (-m2.row(c0)*s3).adjoint(), 1);\n  VERIFY_EVALUATION_COUNT( m3.col(c0).noalias() -= (s1 * m1).adjoint().template selfadjointView<Upper>() * (-m2.row(c0)*s3).adjoint(), 1);\n\n  VERIFY_EVALUATION_COUNT( m3.block(r0,c0,r1,c1).noalias() += m1.block(r0,r0,r1,r1).template selfadjointView<Upper>() * (s1*m2.block(r0,c0,r1,c1)), 0);\n  VERIFY_EVALUATION_COUNT( m3.block(r0,c0,r1,c1).noalias() = m1.block(r0,r0,r1,r1).template selfadjointView<Upper>() * m2.block(r0,c0,r1,c1), 0);\n\n  VERIFY_EVALUATION_COUNT( m3.template selfadjointView<Lower>().rankUpdate(m2.adjoint()), 0);\n\n  // Here we will get 1 temporary for each resize operation of the lhs operator; resize(r1,c1) would lead to zero temporaries\n  m3.resize(1,1);\n  VERIFY_EVALUATION_COUNT( m3.noalias() = m1.block(r0,r0,r1,r1).template selfadjointView<Lower>() * m2.block(r0,c0,r1,c1), 1);\n  m3.resize(1,1);\n  VERIFY_EVALUATION_COUNT( m3.noalias() = m1.block(r0,r0,r1,r1).template triangularView<UnitUpper>()  * m2.block(r0,c0,r1,c1), 1);\n\n  // Zero temporaries for lazy products ...\n  VERIFY_EVALUATION_COUNT( Scalar tmp = 0; tmp += Scalar(RealScalar(1)) /  (m3.transpose().lazyProduct(m3)).diagonal().sum(), 0 );\n\n  // ... and even no temporary for even deeply (>=2) nested products\n  VERIFY_EVALUATION_COUNT( Scalar tmp = 0; tmp += Scalar(RealScalar(1)) /  (m3.transpose() * m3).diagonal().sum(), 0 );\n  VERIFY_EVALUATION_COUNT( Scalar tmp = 0; tmp += Scalar(RealScalar(1)) /  (m3.transpose() * m3).diagonal().array().abs().sum(), 0 );\n\n  // Zero temporaries for ... CoeffBasedProductMode\n  VERIFY_EVALUATION_COUNT( m3.col(0).template head<5>() * m3.col(0).transpose() + m3.col(0).template head<5>() * m3.col(0).transpose(), 0 );\n\n  // Check matrix * vectors\n  VERIFY_EVALUATION_COUNT( cvres.noalias() = m1 * cv1, 0 );\n  VERIFY_EVALUATION_COUNT( cvres.noalias() -= m1 * cv1, 0 );\n  VERIFY_EVALUATION_COUNT( cvres.noalias() -= m1 * m2.col(0), 0 );\n  VERIFY_EVALUATION_COUNT( cvres.noalias() -= m1 * rv1.adjoint(), 0 );\n  VERIFY_EVALUATION_COUNT( cvres.noalias() -= m1 * m2.row(0).transpose(), 0 );\n\n  VERIFY_EVALUATION_COUNT( cvres.noalias() = (m1+m1) * cv1, 0 );\n  VERIFY_EVALUATION_COUNT( cvres.noalias() = (rm3+rm3) * cv1, 0 );\n  VERIFY_EVALUATION_COUNT( cvres.noalias() = (m1+m1) * (m1*cv1), 1 );\n  VERIFY_EVALUATION_COUNT( cvres.noalias() = (rm3+rm3) * (m1*cv1), 1 );\n\n  // Check outer products\n  m3 = cv1 * rv1;\n  VERIFY_EVALUATION_COUNT( m3.noalias() = cv1 * rv1, 0 );\n  VERIFY_EVALUATION_COUNT( m3.noalias() = (cv1+cv1) * (rv1+rv1), 1 );\n  VERIFY_EVALUATION_COUNT( m3.noalias() = (m1*cv1) * (rv1), 1 );\n  VERIFY_EVALUATION_COUNT( m3.noalias() += (m1*cv1) * (rv1), 1 );\n  VERIFY_EVALUATION_COUNT( rm3.noalias() = (cv1) * (rv1 * m1), 1 );\n  VERIFY_EVALUATION_COUNT( rm3.noalias() -= (cv1) * (rv1 * m1), 1 );\n  VERIFY_EVALUATION_COUNT( rm3.noalias() = (m1*cv1) * (rv1 * m1), 2 );\n  VERIFY_EVALUATION_COUNT( rm3.noalias() += (m1*cv1) * (rv1 * m1), 2 );\n\n  // Check nested products\n  VERIFY_EVALUATION_COUNT( cvres.noalias() = m1.adjoint() * m1 * cv1, 1 );\n  VERIFY_EVALUATION_COUNT( rvres.noalias() = rv1 * (m1 * m2.adjoint()), 1 );\n}\n\nvoid test_product_notemporary()\n{\n  int s;\n  for(int i = 0; i < g_repeat; i++) {\n    s = internal::random<int>(16,EIGEN_TEST_MAX_SIZE);\n    CALL_SUBTEST_1( product_notemporary(MatrixXf(s, s)) );\n    CALL_SUBTEST_2( product_notemporary(MatrixXd(s, s)) );\n    TEST_SET_BUT_UNUSED_VARIABLE(s)\n    \n    s = internal::random<int>(16,EIGEN_TEST_MAX_SIZE/2);\n    CALL_SUBTEST_3( product_notemporary(MatrixXcf(s,s)) );\n    CALL_SUBTEST_4( product_notemporary(MatrixXcd(s,s)) );\n    TEST_SET_BUT_UNUSED_VARIABLE(s)\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/product_selfadjoint.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\ntemplate<typename MatrixType> void product_selfadjoint(const MatrixType& m)\n{\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;\n  typedef Matrix<Scalar, 1, MatrixType::RowsAtCompileTime> RowVectorType;\n\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, Dynamic, RowMajor> RhsMatrixType;\n\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  MatrixType m1 = MatrixType::Random(rows, cols),\n             m2 = MatrixType::Random(rows, cols),\n             m3;\n  VectorType v1 = VectorType::Random(rows),\n             v2 = VectorType::Random(rows),\n             v3(rows);\n  RowVectorType r1 = RowVectorType::Random(rows),\n                r2 = RowVectorType::Random(rows);\n  RhsMatrixType m4 = RhsMatrixType::Random(rows,10);\n\n  Scalar s1 = internal::random<Scalar>(),\n         s2 = internal::random<Scalar>(),\n         s3 = internal::random<Scalar>();\n\n  m1 = (m1.adjoint() + m1).eval();\n\n  // rank2 update\n  m2 = m1.template triangularView<Lower>();\n  m2.template selfadjointView<Lower>().rankUpdate(v1,v2);\n  VERIFY_IS_APPROX(m2, (m1 + v1 * v2.adjoint()+ v2 * v1.adjoint()).template triangularView<Lower>().toDenseMatrix());\n\n  m2 = m1.template triangularView<Upper>();\n  m2.template selfadjointView<Upper>().rankUpdate(-v1,s2*v2,s3);\n  VERIFY_IS_APPROX(m2, (m1 + (s3*(-v1)*(s2*v2).adjoint()+numext::conj(s3)*(s2*v2)*(-v1).adjoint())).template triangularView<Upper>().toDenseMatrix());\n\n  m2 = m1.template triangularView<Upper>();\n  m2.template selfadjointView<Upper>().rankUpdate(-s2*r1.adjoint(),r2.adjoint()*s3,s1);\n  VERIFY_IS_APPROX(m2, (m1 + s1*(-s2*r1.adjoint())*(r2.adjoint()*s3).adjoint() + numext::conj(s1)*(r2.adjoint()*s3) * (-s2*r1.adjoint()).adjoint()).template triangularView<Upper>().toDenseMatrix());\n\n  if (rows>1)\n  {\n    m2 = m1.template triangularView<Lower>();\n    m2.block(1,1,rows-1,cols-1).template selfadjointView<Lower>().rankUpdate(v1.tail(rows-1),v2.head(cols-1));\n    m3 = m1;\n    m3.block(1,1,rows-1,cols-1) += v1.tail(rows-1) * v2.head(cols-1).adjoint()+ v2.head(cols-1) * v1.tail(rows-1).adjoint();\n    VERIFY_IS_APPROX(m2, m3.template triangularView<Lower>().toDenseMatrix());\n  }\n}\n\nvoid test_product_selfadjoint()\n{\n  int s = 0;\n  for(int i = 0; i < g_repeat ; i++) {\n    CALL_SUBTEST_1( product_selfadjoint(Matrix<float, 1, 1>()) );\n    CALL_SUBTEST_2( product_selfadjoint(Matrix<float, 2, 2>()) );\n    CALL_SUBTEST_3( product_selfadjoint(Matrix3d()) );\n    \n    s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2);\n    CALL_SUBTEST_4( product_selfadjoint(MatrixXcf(s, s)) );\n    TEST_SET_BUT_UNUSED_VARIABLE(s)\n    \n    s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2);\n    CALL_SUBTEST_5( product_selfadjoint(MatrixXcd(s,s)) );\n    TEST_SET_BUT_UNUSED_VARIABLE(s)\n    \n    s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE);\n    CALL_SUBTEST_6( product_selfadjoint(MatrixXd(s,s)) );\n    TEST_SET_BUT_UNUSED_VARIABLE(s)\n    \n    s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE);\n    CALL_SUBTEST_7( product_selfadjoint(Matrix<float,Dynamic,Dynamic,RowMajor>(s,s)) );\n    TEST_SET_BUT_UNUSED_VARIABLE(s)\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/product_small.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define EIGEN_NO_STATIC_ASSERT\n#include \"product.h\"\n#include <Eigen/LU>\n\n// regression test for bug 447\ntemplate<int>\nvoid product1x1()\n{\n  Matrix<float,1,3> matAstatic;\n  Matrix<float,3,1> matBstatic;\n  matAstatic.setRandom();\n  matBstatic.setRandom();\n  VERIFY_IS_APPROX( (matAstatic * matBstatic).coeff(0,0), \n                    matAstatic.cwiseProduct(matBstatic.transpose()).sum() );\n\n  MatrixXf matAdynamic(1,3);\n  MatrixXf matBdynamic(3,1);\n  matAdynamic.setRandom();\n  matBdynamic.setRandom();\n  VERIFY_IS_APPROX( (matAdynamic * matBdynamic).coeff(0,0), \n                    matAdynamic.cwiseProduct(matBdynamic.transpose()).sum() );\n}\n\ntemplate<typename TC, typename TA, typename TB>\nconst TC& ref_prod(TC &C, const TA &A, const TB &B)\n{\n  for(Index i=0;i<C.rows();++i)\n    for(Index j=0;j<C.cols();++j)\n      for(Index k=0;k<A.cols();++k)\n        C.coeffRef(i,j) += A.coeff(i,k) * B.coeff(k,j);\n  return C;\n}\n\ntemplate<typename T, int Rows, int Cols, int Depth, int OC, int OA, int OB>\ntypename internal::enable_if<! ( (Rows ==1&&Depth!=1&&OA==ColMajor)\n                              || (Depth==1&&Rows !=1&&OA==RowMajor)\n                              || (Cols ==1&&Depth!=1&&OB==RowMajor)\n                              || (Depth==1&&Cols !=1&&OB==ColMajor)\n                              || (Rows ==1&&Cols !=1&&OC==ColMajor)\n                              || (Cols ==1&&Rows !=1&&OC==RowMajor)),void>::type\ntest_lazy_single(int rows, int cols, int depth)\n{\n  Matrix<T,Rows,Depth,OA> A(rows,depth); A.setRandom();\n  Matrix<T,Depth,Cols,OB> B(depth,cols); B.setRandom();\n  Matrix<T,Rows,Cols,OC>  C(rows,cols);  C.setRandom();\n  Matrix<T,Rows,Cols,OC>  D(C);\n  VERIFY_IS_APPROX(C+=A.lazyProduct(B), ref_prod(D,A,B));\n}\n\ntemplate<typename T, int Rows, int Cols, int Depth, int OC, int OA, int OB>\ntypename internal::enable_if<  ( (Rows ==1&&Depth!=1&&OA==ColMajor)\n                              || (Depth==1&&Rows !=1&&OA==RowMajor)\n                              || (Cols ==1&&Depth!=1&&OB==RowMajor)\n                              || (Depth==1&&Cols !=1&&OB==ColMajor)\n                              || (Rows ==1&&Cols !=1&&OC==ColMajor)\n                              || (Cols ==1&&Rows !=1&&OC==RowMajor)),void>::type\ntest_lazy_single(int, int, int)\n{\n}\n\ntemplate<typename T, int Rows, int Cols, int Depth>\nvoid test_lazy_all_layout(int rows=Rows, int cols=Cols, int depth=Depth)\n{\n  CALL_SUBTEST(( test_lazy_single<T,Rows,Cols,Depth,ColMajor,ColMajor,ColMajor>(rows,cols,depth) ));\n  CALL_SUBTEST(( test_lazy_single<T,Rows,Cols,Depth,RowMajor,ColMajor,ColMajor>(rows,cols,depth) ));\n  CALL_SUBTEST(( test_lazy_single<T,Rows,Cols,Depth,ColMajor,RowMajor,ColMajor>(rows,cols,depth) ));\n  CALL_SUBTEST(( test_lazy_single<T,Rows,Cols,Depth,RowMajor,RowMajor,ColMajor>(rows,cols,depth) ));\n  CALL_SUBTEST(( test_lazy_single<T,Rows,Cols,Depth,ColMajor,ColMajor,RowMajor>(rows,cols,depth) ));\n  CALL_SUBTEST(( test_lazy_single<T,Rows,Cols,Depth,RowMajor,ColMajor,RowMajor>(rows,cols,depth) ));\n  CALL_SUBTEST(( test_lazy_single<T,Rows,Cols,Depth,ColMajor,RowMajor,RowMajor>(rows,cols,depth) ));\n  CALL_SUBTEST(( test_lazy_single<T,Rows,Cols,Depth,RowMajor,RowMajor,RowMajor>(rows,cols,depth) ));\n}\n\ntemplate<typename T>\nvoid test_lazy_l1()\n{\n  int rows = internal::random<int>(1,12);\n  int cols = internal::random<int>(1,12);\n  int depth = internal::random<int>(1,12);\n\n  // Inner\n  CALL_SUBTEST(( test_lazy_all_layout<T,1,1,1>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,1,1,2>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,1,1,3>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,1,1,8>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,1,1,9>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,1,1,-1>(1,1,depth) ));\n\n  // Outer\n  CALL_SUBTEST(( test_lazy_all_layout<T,2,1,1>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,1,2,1>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,2,2,1>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,3,3,1>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,4,4,1>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,4,8,1>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,4,-1,1>(4,cols) ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,7,-1,1>(7,cols) ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,-1,8,1>(rows) ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,-1,3,1>(rows) ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,-1,-1,1>(rows,cols) ));\n}\n\ntemplate<typename T>\nvoid test_lazy_l2()\n{\n  int rows = internal::random<int>(1,12);\n  int cols = internal::random<int>(1,12);\n  int depth = internal::random<int>(1,12);\n\n  // mat-vec\n  CALL_SUBTEST(( test_lazy_all_layout<T,2,1,2>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,2,1,4>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,4,1,2>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,4,1,4>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,5,1,4>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,4,1,5>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,4,1,6>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,6,1,4>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,8,1,8>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,-1,1,4>(rows) ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,4,1,-1>(4,1,depth) ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,-1,1,-1>(rows,1,depth) ));\n\n  // vec-mat\n  CALL_SUBTEST(( test_lazy_all_layout<T,1,2,2>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,1,2,4>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,1,4,2>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,1,4,4>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,1,5,4>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,1,4,5>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,1,4,6>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,1,6,4>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,1,8,8>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,1,-1, 4>(1,cols) ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,1, 4,-1>(1,4,depth) ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,1,-1,-1>(1,cols,depth) ));\n}\n\ntemplate<typename T>\nvoid test_lazy_l3()\n{\n  int rows = internal::random<int>(1,12);\n  int cols = internal::random<int>(1,12);\n  int depth = internal::random<int>(1,12);\n  // mat-mat\n  CALL_SUBTEST(( test_lazy_all_layout<T,2,4,2>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,2,6,4>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,4,3,2>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,4,8,4>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,5,6,4>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,4,2,5>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,4,7,6>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,6,8,4>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,8,3,8>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,-1,6,4>(rows) ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,4,3,-1>(4,3,depth) ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,-1,6,-1>(rows,6,depth) ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,8,2,2>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,5,2,4>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,4,4,2>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,8,4,4>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,6,5,4>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,4,4,5>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,3,4,6>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,2,6,4>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,7,8,8>() ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,8,-1, 4>(8,cols) ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,3, 4,-1>(3,4,depth) ));\n  CALL_SUBTEST(( test_lazy_all_layout<T,4,-1,-1>(4,cols,depth) ));\n}\n\ntemplate<typename T,int N,int M,int K>\nvoid test_linear_but_not_vectorizable()\n{\n  // Check tricky cases for which the result of the product is a vector and thus must exhibit the LinearBit flag,\n  // but is not vectorizable along the linear dimension.\n  Index n = N==Dynamic ? internal::random<Index>(1,32) : N;\n  Index m = M==Dynamic ? internal::random<Index>(1,32) : M;\n  Index k = K==Dynamic ? internal::random<Index>(1,32) : K;\n\n  {\n    Matrix<T,N,M+1> A; A.setRandom(n,m+1);\n    Matrix<T,M*2,K> B; B.setRandom(m*2,k);\n    Matrix<T,1,K> C;\n    Matrix<T,1,K> R;\n\n    C.noalias() = A.template topLeftCorner<1,M>() * (B.template topRows<M>()+B.template bottomRows<M>());\n    R.noalias() = A.template topLeftCorner<1,M>() * (B.template topRows<M>()+B.template bottomRows<M>()).eval();\n    VERIFY_IS_APPROX(C,R);\n  }\n\n  {\n    Matrix<T,M+1,N,RowMajor> A; A.setRandom(m+1,n);\n    Matrix<T,K,M*2,RowMajor> B; B.setRandom(k,m*2);\n    Matrix<T,K,1> C;\n    Matrix<T,K,1> R;\n\n    C.noalias() = (B.template leftCols<M>()+B.template rightCols<M>())        * A.template topLeftCorner<M,1>();\n    R.noalias() = (B.template leftCols<M>()+B.template rightCols<M>()).eval() * A.template topLeftCorner<M,1>();\n    VERIFY_IS_APPROX(C,R);\n  }\n}\n\ntemplate<int Rows>\nvoid bug_1311()\n{\n  Matrix< double, Rows, 2 > A;  A.setRandom();\n  Vector2d b = Vector2d::Random() ;\n  Matrix<double,Rows,1> res;\n  res.noalias() = 1. * (A * b);\n  VERIFY_IS_APPROX(res, A*b);\n  res.noalias() = 1.*A * b;\n  VERIFY_IS_APPROX(res, A*b);\n  res.noalias() = (1.*A).lazyProduct(b);\n  VERIFY_IS_APPROX(res, A*b);\n  res.noalias() = (1.*A).lazyProduct(1.*b);\n  VERIFY_IS_APPROX(res, A*b);\n  res.noalias() = (A).lazyProduct(1.*b);\n  VERIFY_IS_APPROX(res, A*b);\n}\n\nvoid test_product_small()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( product(Matrix<float, 3, 2>()) );\n    CALL_SUBTEST_2( product(Matrix<int, 3, 17>()) );\n    CALL_SUBTEST_8( product(Matrix<double, 3, 17>()) );\n    CALL_SUBTEST_3( product(Matrix3d()) );\n    CALL_SUBTEST_4( product(Matrix4d()) );\n    CALL_SUBTEST_5( product(Matrix4f()) );\n    CALL_SUBTEST_6( product1x1<0>() );\n\n    CALL_SUBTEST_11( test_lazy_l1<float>() );\n    CALL_SUBTEST_12( test_lazy_l2<float>() );\n    CALL_SUBTEST_13( test_lazy_l3<float>() );\n\n    CALL_SUBTEST_21( test_lazy_l1<double>() );\n    CALL_SUBTEST_22( test_lazy_l2<double>() );\n    CALL_SUBTEST_23( test_lazy_l3<double>() );\n\n    CALL_SUBTEST_31( test_lazy_l1<std::complex<float> >() );\n    CALL_SUBTEST_32( test_lazy_l2<std::complex<float> >() );\n    CALL_SUBTEST_33( test_lazy_l3<std::complex<float> >() );\n\n    CALL_SUBTEST_41( test_lazy_l1<std::complex<double> >() );\n    CALL_SUBTEST_42( test_lazy_l2<std::complex<double> >() );\n    CALL_SUBTEST_43( test_lazy_l3<std::complex<double> >() );\n\n    CALL_SUBTEST_7(( test_linear_but_not_vectorizable<float,2,1,Dynamic>() ));\n    CALL_SUBTEST_7(( test_linear_but_not_vectorizable<float,3,1,Dynamic>() ));\n    CALL_SUBTEST_7(( test_linear_but_not_vectorizable<float,2,1,16>() ));\n\n    CALL_SUBTEST_6( bug_1311<3>() );\n    CALL_SUBTEST_6( bug_1311<5>() );\n  }\n\n#ifdef EIGEN_TEST_PART_6\n  {\n    // test compilation of (outer_product) * vector\n    Vector3f v = Vector3f::Random();\n    VERIFY_IS_APPROX( (v * v.transpose()) * v, (v * v.transpose()).eval() * v);\n  }\n  \n  {\n    // regression test for pull-request #93\n    Eigen::Matrix<double, 1, 1> A;  A.setRandom();\n    Eigen::Matrix<double, 18, 1> B; B.setRandom();\n    Eigen::Matrix<double, 1, 18> C; C.setRandom();\n    VERIFY_IS_APPROX(B * A.inverse(), B * A.inverse()[0]);\n    VERIFY_IS_APPROX(A.inverse() * C, A.inverse()[0] * C);\n  }\n\n  {\n    Eigen::Matrix<double, 10, 10> A, B, C;\n    A.setRandom();\n    C = A;\n    for(int k=0; k<79; ++k)\n      C = C * A;\n    B.noalias() = (((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A)) * ((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A)))\n                * (((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A)) * ((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A)));\n    VERIFY_IS_APPROX(B,C);\n  }\n#endif\n}\n"
  },
  {
    "path": "include/eigen3/test/product_symm.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\ntemplate<typename Scalar, int Size, int OtherSize> void symm(int size = Size, int othersize = OtherSize)\n{\n  typedef Matrix<Scalar, Size, Size> MatrixType;\n  typedef Matrix<Scalar, Size, OtherSize> Rhs1;\n  typedef Matrix<Scalar, OtherSize, Size> Rhs2;\n  enum { order = OtherSize==1 ? 0 : RowMajor };\n  typedef Matrix<Scalar, Size, OtherSize,order> Rhs3;\n  typedef typename MatrixType::Index Index;\n\n  Index rows = size;\n  Index cols = size;\n\n  MatrixType m1 = MatrixType::Random(rows, cols),\n             m2 = MatrixType::Random(rows, cols), m3;\n\n  m1 = (m1+m1.adjoint()).eval();\n\n  Rhs1 rhs1 = Rhs1::Random(cols, othersize), rhs12(cols, othersize), rhs13(cols, othersize);\n  Rhs2 rhs2 = Rhs2::Random(othersize, rows), rhs22(othersize, rows), rhs23(othersize, rows);\n  Rhs3 rhs3 = Rhs3::Random(cols, othersize), rhs32(cols, othersize), rhs33(cols, othersize);\n\n  Scalar s1 = internal::random<Scalar>(),\n         s2 = internal::random<Scalar>();\n\n  m2 = m1.template triangularView<Lower>();\n  m3 = m2.template selfadjointView<Lower>();\n  VERIFY_IS_EQUAL(m1, m3);\n  VERIFY_IS_APPROX(rhs12 = (s1*m2).template selfadjointView<Lower>() * (s2*rhs1),\n                   rhs13 = (s1*m1) * (s2*rhs1));\n\n  VERIFY_IS_APPROX(rhs12 = (s1*m2).transpose().template selfadjointView<Upper>() * (s2*rhs1),\n                   rhs13 = (s1*m1.transpose()) * (s2*rhs1));\n\n  VERIFY_IS_APPROX(rhs12 = (s1*m2).template selfadjointView<Lower>().transpose() * (s2*rhs1),\n                   rhs13 = (s1*m1.transpose()) * (s2*rhs1));\n\n  VERIFY_IS_APPROX(rhs12 = (s1*m2).conjugate().template selfadjointView<Lower>() * (s2*rhs1),\n                   rhs13 = (s1*m1).conjugate() * (s2*rhs1));\n\n  VERIFY_IS_APPROX(rhs12 = (s1*m2).template selfadjointView<Lower>().conjugate() * (s2*rhs1),\n                   rhs13 = (s1*m1).conjugate() * (s2*rhs1));\n\n  VERIFY_IS_APPROX(rhs12 = (s1*m2).adjoint().template selfadjointView<Upper>() * (s2*rhs1),\n                   rhs13 = (s1*m1).adjoint() * (s2*rhs1));\n\n  VERIFY_IS_APPROX(rhs12 = (s1*m2).template selfadjointView<Lower>().adjoint() * (s2*rhs1),\n                   rhs13 = (s1*m1).adjoint() * (s2*rhs1));\n\n  m2 = m1.template triangularView<Upper>(); rhs12.setRandom(); rhs13 = rhs12;\n  m3 = m2.template selfadjointView<Upper>();\n  VERIFY_IS_EQUAL(m1, m3);\n  VERIFY_IS_APPROX(rhs12 += (s1*m2).template selfadjointView<Upper>() * (s2*rhs1),\n                   rhs13 += (s1*m1) * (s2*rhs1));\n\n  m2 = m1.template triangularView<Lower>();\n  VERIFY_IS_APPROX(rhs12 = (s1*m2).template selfadjointView<Lower>() * (s2*rhs2.adjoint()),\n                   rhs13 = (s1*m1) * (s2*rhs2.adjoint()));\n\n  m2 = m1.template triangularView<Upper>();\n  VERIFY_IS_APPROX(rhs12 = (s1*m2).template selfadjointView<Upper>() * (s2*rhs2.adjoint()),\n                   rhs13 = (s1*m1) * (s2*rhs2.adjoint()));\n\n  m2 = m1.template triangularView<Upper>();\n  VERIFY_IS_APPROX(rhs12 = (s1*m2.adjoint()).template selfadjointView<Lower>() * (s2*rhs2.adjoint()),\n                   rhs13 = (s1*m1.adjoint()) * (s2*rhs2.adjoint()));\n\n  // test row major = <...>\n  m2 = m1.template triangularView<Lower>(); rhs12.setRandom(); rhs13 = rhs12;\n  VERIFY_IS_APPROX(rhs12 -= (s1*m2).template selfadjointView<Lower>() * (s2*rhs3),\n                   rhs13 -= (s1*m1) * (s2 * rhs3));\n\n  m2 = m1.template triangularView<Upper>();\n  VERIFY_IS_APPROX(rhs12 = (s1*m2.adjoint()).template selfadjointView<Lower>() * (s2*rhs3).conjugate(),\n                   rhs13 = (s1*m1.adjoint()) * (s2*rhs3).conjugate());\n\n\n  m2 = m1.template triangularView<Upper>(); rhs13 = rhs12;\n  VERIFY_IS_APPROX(rhs12.noalias() += s1 * ((m2.adjoint()).template selfadjointView<Lower>() * (s2*rhs3).conjugate()),\n                   rhs13 += (s1*m1.adjoint()) * (s2*rhs3).conjugate());\n\n  m2 = m1.template triangularView<Lower>();\n  VERIFY_IS_APPROX(rhs22 = (rhs2) * (m2).template selfadjointView<Lower>(), rhs23 = (rhs2) * (m1));\n  VERIFY_IS_APPROX(rhs22 = (s2*rhs2) * (s1*m2).template selfadjointView<Lower>(), rhs23 = (s2*rhs2) * (s1*m1));\n\n}\n\nvoid test_product_symm()\n{\n  for(int i = 0; i < g_repeat ; i++)\n  {\n    CALL_SUBTEST_1(( symm<float,Dynamic,Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE)) ));\n    CALL_SUBTEST_2(( symm<double,Dynamic,Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE)) ));\n    CALL_SUBTEST_3(( symm<std::complex<float>,Dynamic,Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2),internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2)) ));\n    CALL_SUBTEST_4(( symm<std::complex<double>,Dynamic,Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2),internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2)) ));\n\n    CALL_SUBTEST_5(( symm<float,Dynamic,1>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE)) ));\n    CALL_SUBTEST_6(( symm<double,Dynamic,1>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE)) ));\n    CALL_SUBTEST_7(( symm<std::complex<float>,Dynamic,1>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE)) ));\n    CALL_SUBTEST_8(( symm<std::complex<double>,Dynamic,1>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE)) ));\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/product_syrk.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\ntemplate<typename MatrixType> void syrk(const MatrixType& m)\n{\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime, RowMajor> RMatrixType;\n  typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, Dynamic> Rhs1;\n  typedef Matrix<Scalar, Dynamic, MatrixType::RowsAtCompileTime> Rhs2;\n  typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, Dynamic,RowMajor> Rhs3;\n\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  MatrixType m1 = MatrixType::Random(rows, cols),\n             m2 = MatrixType::Random(rows, cols),\n             m3 = MatrixType::Random(rows, cols);\n  RMatrixType rm2 = MatrixType::Random(rows, cols);\n\n  Rhs1 rhs1 = Rhs1::Random(internal::random<int>(1,320), cols); Rhs1 rhs11 = Rhs1::Random(rhs1.rows(), cols);\n  Rhs2 rhs2 = Rhs2::Random(rows, internal::random<int>(1,320)); Rhs2 rhs22 = Rhs2::Random(rows, rhs2.cols());\n  Rhs3 rhs3 = Rhs3::Random(internal::random<int>(1,320), rows);\n\n  Scalar s1 = internal::random<Scalar>();\n  \n  Index c = internal::random<Index>(0,cols-1);\n\n  m2.setZero();\n  VERIFY_IS_APPROX((m2.template selfadjointView<Lower>().rankUpdate(rhs2,s1)._expression()),\n                   ((s1 * rhs2 * rhs2.adjoint()).eval().template triangularView<Lower>().toDenseMatrix()));\n  m2.setZero();\n  VERIFY_IS_APPROX(((m2.template triangularView<Lower>() += s1 * rhs2  * rhs22.adjoint()).nestedExpression()),\n                   ((s1 * rhs2 * rhs22.adjoint()).eval().template triangularView<Lower>().toDenseMatrix()));\n\n  \n  m2.setZero();\n  VERIFY_IS_APPROX(m2.template selfadjointView<Upper>().rankUpdate(rhs2,s1)._expression(),\n                   (s1 * rhs2 * rhs2.adjoint()).eval().template triangularView<Upper>().toDenseMatrix());\n  m2.setZero();\n  VERIFY_IS_APPROX((m2.template triangularView<Upper>() += s1 * rhs22 * rhs2.adjoint()).nestedExpression(),\n                   (s1 * rhs22 * rhs2.adjoint()).eval().template triangularView<Upper>().toDenseMatrix());\n\n  \n  m2.setZero();\n  VERIFY_IS_APPROX(m2.template selfadjointView<Lower>().rankUpdate(rhs1.adjoint(),s1)._expression(),\n                   (s1 * rhs1.adjoint() * rhs1).eval().template triangularView<Lower>().toDenseMatrix());\n  m2.setZero();\n  VERIFY_IS_APPROX((m2.template triangularView<Lower>() += s1 * rhs11.adjoint() * rhs1).nestedExpression(),\n                   (s1 * rhs11.adjoint() * rhs1).eval().template triangularView<Lower>().toDenseMatrix());\n  \n  \n  m2.setZero();\n  VERIFY_IS_APPROX(m2.template selfadjointView<Upper>().rankUpdate(rhs1.adjoint(),s1)._expression(),\n                   (s1 * rhs1.adjoint() * rhs1).eval().template triangularView<Upper>().toDenseMatrix());\n  VERIFY_IS_APPROX((m2.template triangularView<Upper>() = s1 * rhs1.adjoint() * rhs11).nestedExpression(),\n                   (s1 * rhs1.adjoint() * rhs11).eval().template triangularView<Upper>().toDenseMatrix());\n\n  \n  m2.setZero();\n  VERIFY_IS_APPROX(m2.template selfadjointView<Lower>().rankUpdate(rhs3.adjoint(),s1)._expression(),\n                   (s1 * rhs3.adjoint() * rhs3).eval().template triangularView<Lower>().toDenseMatrix());\n\n  m2.setZero();\n  VERIFY_IS_APPROX(m2.template selfadjointView<Upper>().rankUpdate(rhs3.adjoint(),s1)._expression(),\n                   (s1 * rhs3.adjoint() * rhs3).eval().template triangularView<Upper>().toDenseMatrix());\n                   \n  m2.setZero();\n  VERIFY_IS_APPROX((m2.template selfadjointView<Lower>().rankUpdate(m1.col(c),s1)._expression()),\n                   ((s1 * m1.col(c) * m1.col(c).adjoint()).eval().template triangularView<Lower>().toDenseMatrix()));\n                   \n  m2.setZero();\n  VERIFY_IS_APPROX((m2.template selfadjointView<Upper>().rankUpdate(m1.col(c),s1)._expression()),\n                   ((s1 * m1.col(c) * m1.col(c).adjoint()).eval().template triangularView<Upper>().toDenseMatrix()));\n  rm2.setZero();\n  VERIFY_IS_APPROX((rm2.template selfadjointView<Upper>().rankUpdate(m1.col(c),s1)._expression()),\n                   ((s1 * m1.col(c) * m1.col(c).adjoint()).eval().template triangularView<Upper>().toDenseMatrix()));\n  m2.setZero();\n  VERIFY_IS_APPROX((m2.template triangularView<Upper>() += s1 * m3.col(c) * m1.col(c).adjoint()).nestedExpression(),\n                   ((s1 * m3.col(c) * m1.col(c).adjoint()).eval().template triangularView<Upper>().toDenseMatrix()));\n  rm2.setZero();\n  VERIFY_IS_APPROX((rm2.template triangularView<Upper>() += s1 * m1.col(c) * m3.col(c).adjoint()).nestedExpression(),\n                   ((s1 * m1.col(c) * m3.col(c).adjoint()).eval().template triangularView<Upper>().toDenseMatrix()));\n  \n  m2.setZero();\n  VERIFY_IS_APPROX((m2.template selfadjointView<Lower>().rankUpdate(m1.col(c).conjugate(),s1)._expression()),\n                   ((s1 * m1.col(c).conjugate() * m1.col(c).conjugate().adjoint()).eval().template triangularView<Lower>().toDenseMatrix()));\n                   \n  m2.setZero();\n  VERIFY_IS_APPROX((m2.template selfadjointView<Upper>().rankUpdate(m1.col(c).conjugate(),s1)._expression()),\n                   ((s1 * m1.col(c).conjugate() * m1.col(c).conjugate().adjoint()).eval().template triangularView<Upper>().toDenseMatrix()));\n  \n  \n  m2.setZero();\n  VERIFY_IS_APPROX((m2.template selfadjointView<Lower>().rankUpdate(m1.row(c),s1)._expression()),\n                   ((s1 * m1.row(c).transpose() * m1.row(c).transpose().adjoint()).eval().template triangularView<Lower>().toDenseMatrix()));\n  rm2.setZero();\n  VERIFY_IS_APPROX((rm2.template selfadjointView<Lower>().rankUpdate(m1.row(c),s1)._expression()),\n                   ((s1 * m1.row(c).transpose() * m1.row(c).transpose().adjoint()).eval().template triangularView<Lower>().toDenseMatrix()));\n  m2.setZero();\n  VERIFY_IS_APPROX((m2.template triangularView<Lower>() += s1 * m3.row(c).transpose() * m1.row(c).transpose().adjoint()).nestedExpression(),\n                   ((s1 * m3.row(c).transpose() * m1.row(c).transpose().adjoint()).eval().template triangularView<Lower>().toDenseMatrix()));\n  rm2.setZero();\n  VERIFY_IS_APPROX((rm2.template triangularView<Lower>() += s1 * m3.row(c).transpose() * m1.row(c).transpose().adjoint()).nestedExpression(),\n                   ((s1 * m3.row(c).transpose() * m1.row(c).transpose().adjoint()).eval().template triangularView<Lower>().toDenseMatrix()));\n  \n  \n  m2.setZero();\n  VERIFY_IS_APPROX((m2.template selfadjointView<Upper>().rankUpdate(m1.row(c).adjoint(),s1)._expression()),\n                   ((s1 * m1.row(c).adjoint() * m1.row(c).adjoint().adjoint()).eval().template triangularView<Upper>().toDenseMatrix()));\n}\n\nvoid test_product_syrk()\n{\n  for(int i = 0; i < g_repeat ; i++)\n  {\n    int s;\n    s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE);\n    CALL_SUBTEST_1( syrk(MatrixXf(s, s)) );\n    CALL_SUBTEST_2( syrk(MatrixXd(s, s)) );\n    TEST_SET_BUT_UNUSED_VARIABLE(s)\n    \n    s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2);\n    CALL_SUBTEST_3( syrk(MatrixXcf(s, s)) );\n    CALL_SUBTEST_4( syrk(MatrixXcd(s, s)) );\n    TEST_SET_BUT_UNUSED_VARIABLE(s)\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/product_trmm.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\ntemplate<typename T>\nint get_random_size()\n{\n  const int factor = NumTraits<T>::ReadCost;\n  const int max_test_size = EIGEN_TEST_MAX_SIZE>2*factor ? EIGEN_TEST_MAX_SIZE/factor : EIGEN_TEST_MAX_SIZE;\n  return internal::random<int>(1,max_test_size);\n}\n\ntemplate<typename Scalar, int Mode, int TriOrder, int OtherOrder, int ResOrder, int OtherCols>\nvoid trmm(int rows=get_random_size<Scalar>(),\n          int cols=get_random_size<Scalar>(),\n          int otherCols = OtherCols==Dynamic?get_random_size<Scalar>():OtherCols)\n{\n  typedef Matrix<Scalar,Dynamic,Dynamic,TriOrder> TriMatrix;\n  typedef Matrix<Scalar,Dynamic,OtherCols,OtherCols==1?ColMajor:OtherOrder> OnTheRight;\n  typedef Matrix<Scalar,OtherCols,Dynamic,OtherCols==1?RowMajor:OtherOrder> OnTheLeft;\n  \n  typedef Matrix<Scalar,Dynamic,OtherCols,OtherCols==1?ColMajor:ResOrder> ResXS;\n  typedef Matrix<Scalar,OtherCols,Dynamic,OtherCols==1?RowMajor:ResOrder> ResSX;\n\n  TriMatrix  mat(rows,cols), tri(rows,cols), triTr(cols,rows), s1tri(rows,cols), s1triTr(cols,rows);\n  \n  OnTheRight  ge_right(cols,otherCols);\n  OnTheLeft   ge_left(otherCols,rows);\n  ResSX       ge_sx, ge_sx_save;\n  ResXS       ge_xs, ge_xs_save;\n\n  Scalar s1 = internal::random<Scalar>(),\n         s2 = internal::random<Scalar>();\n\n  mat.setRandom();\n  tri = mat.template triangularView<Mode>();\n  triTr = mat.transpose().template triangularView<Mode>();\n  s1tri = (s1*mat).template triangularView<Mode>();\n  s1triTr = (s1*mat).transpose().template triangularView<Mode>();\n  ge_right.setRandom();\n  ge_left.setRandom();\n\n  VERIFY_IS_APPROX( ge_xs = mat.template triangularView<Mode>() * ge_right, tri * ge_right);\n  VERIFY_IS_APPROX( ge_sx = ge_left * mat.template triangularView<Mode>(), ge_left * tri);\n  \n  VERIFY_IS_APPROX( ge_xs.noalias() = mat.template triangularView<Mode>() * ge_right, tri * ge_right);\n  VERIFY_IS_APPROX( ge_sx.noalias() = ge_left * mat.template triangularView<Mode>(), ge_left * tri);\n\n  if((Mode&UnitDiag)==0)\n    VERIFY_IS_APPROX( ge_xs.noalias() = (s1*mat.adjoint()).template triangularView<Mode>() * (s2*ge_left.transpose()), s1*triTr.conjugate() * (s2*ge_left.transpose()));\n  \n  VERIFY_IS_APPROX( ge_xs.noalias() = (s1*mat.transpose()).template triangularView<Mode>() * (s2*ge_left.transpose()), s1triTr * (s2*ge_left.transpose()));\n  VERIFY_IS_APPROX( ge_sx.noalias() = (s2*ge_left) * (s1*mat).template triangularView<Mode>(), (s2*ge_left)*s1tri);\n\n  VERIFY_IS_APPROX( ge_sx.noalias() = ge_right.transpose() * mat.adjoint().template triangularView<Mode>(), ge_right.transpose() * triTr.conjugate());\n  VERIFY_IS_APPROX( ge_sx.noalias() = ge_right.adjoint() * mat.adjoint().template triangularView<Mode>(), ge_right.adjoint() * triTr.conjugate());\n  \n  ge_xs_save = ge_xs;\n  if((Mode&UnitDiag)==0)\n    VERIFY_IS_APPROX( (ge_xs_save + s1*triTr.conjugate() * (s2*ge_left.adjoint())).eval(), ge_xs.noalias() += (s1*mat.adjoint()).template triangularView<Mode>() * (s2*ge_left.adjoint()) );\n  ge_xs_save = ge_xs;\n  VERIFY_IS_APPROX( (ge_xs_save + s1triTr * (s2*ge_left.adjoint())).eval(), ge_xs.noalias() += (s1*mat.transpose()).template triangularView<Mode>() * (s2*ge_left.adjoint()) );\n  ge_sx.setRandom();\n  ge_sx_save = ge_sx;\n  if((Mode&UnitDiag)==0)\n    VERIFY_IS_APPROX( ge_sx_save - (ge_right.adjoint() * (-s1 * triTr).conjugate()).eval(), ge_sx.noalias() -= (ge_right.adjoint() * (-s1 * mat).adjoint().template triangularView<Mode>()).eval());\n  \n  if((Mode&UnitDiag)==0)\n    VERIFY_IS_APPROX( ge_xs = (s1*mat).adjoint().template triangularView<Mode>() * ge_left.adjoint(), numext::conj(s1) * triTr.conjugate() * ge_left.adjoint());\n  VERIFY_IS_APPROX( ge_xs = (s1*mat).transpose().template triangularView<Mode>() * ge_left.adjoint(), s1triTr * ge_left.adjoint());\n\n  \n  // TODO check with sub-matrix expressions ?\n}\n\ntemplate<typename Scalar, int Mode, int TriOrder>\nvoid trmv(int rows=get_random_size<Scalar>(), int cols=get_random_size<Scalar>())\n{\n  trmm<Scalar,Mode,TriOrder,ColMajor,ColMajor,1>(rows,cols,1);\n}\n\ntemplate<typename Scalar, int Mode, int TriOrder, int OtherOrder, int ResOrder>\nvoid trmm(int rows=get_random_size<Scalar>(), int cols=get_random_size<Scalar>(), int otherCols = get_random_size<Scalar>())\n{\n  trmm<Scalar,Mode,TriOrder,OtherOrder,ResOrder,Dynamic>(rows,cols,otherCols);\n}\n\n#define CALL_ALL_ORDERS(NB,SCALAR,MODE)                                             \\\n  EIGEN_CAT(CALL_SUBTEST_,NB)((trmm<SCALAR, MODE, ColMajor,ColMajor,ColMajor>()));  \\\n  EIGEN_CAT(CALL_SUBTEST_,NB)((trmm<SCALAR, MODE, ColMajor,ColMajor,RowMajor>()));  \\\n  EIGEN_CAT(CALL_SUBTEST_,NB)((trmm<SCALAR, MODE, ColMajor,RowMajor,ColMajor>()));  \\\n  EIGEN_CAT(CALL_SUBTEST_,NB)((trmm<SCALAR, MODE, ColMajor,RowMajor,RowMajor>()));  \\\n  EIGEN_CAT(CALL_SUBTEST_,NB)((trmm<SCALAR, MODE, RowMajor,ColMajor,ColMajor>()));  \\\n  EIGEN_CAT(CALL_SUBTEST_,NB)((trmm<SCALAR, MODE, RowMajor,ColMajor,RowMajor>()));  \\\n  EIGEN_CAT(CALL_SUBTEST_,NB)((trmm<SCALAR, MODE, RowMajor,RowMajor,ColMajor>()));  \\\n  EIGEN_CAT(CALL_SUBTEST_,NB)((trmm<SCALAR, MODE, RowMajor,RowMajor,RowMajor>()));  \\\n  \\\n  EIGEN_CAT(CALL_SUBTEST_1,NB)((trmv<SCALAR, MODE, ColMajor>()));                   \\\n  EIGEN_CAT(CALL_SUBTEST_1,NB)((trmv<SCALAR, MODE, RowMajor>()));\n\n  \n#define CALL_ALL(NB,SCALAR)                 \\\n  CALL_ALL_ORDERS(EIGEN_CAT(1,NB),SCALAR,Upper)          \\\n  CALL_ALL_ORDERS(EIGEN_CAT(2,NB),SCALAR,UnitUpper)      \\\n  CALL_ALL_ORDERS(EIGEN_CAT(3,NB),SCALAR,StrictlyUpper)  \\\n  CALL_ALL_ORDERS(EIGEN_CAT(1,NB),SCALAR,Lower)          \\\n  CALL_ALL_ORDERS(EIGEN_CAT(2,NB),SCALAR,UnitLower)      \\\n  CALL_ALL_ORDERS(EIGEN_CAT(3,NB),SCALAR,StrictlyLower)\n  \n\nvoid test_product_trmm()\n{\n  for(int i = 0; i < g_repeat ; i++)\n  {\n    CALL_ALL(1,float);                //  EIGEN_SUFFIXES;11;111;21;121;31;131\n    CALL_ALL(2,double);               //  EIGEN_SUFFIXES;12;112;22;122;32;132\n    CALL_ALL(3,std::complex<float>);  //  EIGEN_SUFFIXES;13;113;23;123;33;133\n    CALL_ALL(4,std::complex<double>); //  EIGEN_SUFFIXES;14;114;24;124;34;134\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/product_trmv.cpp",
    "content": "// This file is triangularView of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\ntemplate<typename MatrixType> void trmv(const MatrixType& m)\n{\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;\n\n  RealScalar largerEps = 10*test_precision<RealScalar>();\n\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  MatrixType m1 = MatrixType::Random(rows, cols),\n             m3(rows, cols);\n  VectorType v1 = VectorType::Random(rows);\n\n  Scalar s1 = internal::random<Scalar>();\n\n  m1 = MatrixType::Random(rows, cols);\n\n  // check with a column-major matrix\n  m3 = m1.template triangularView<Eigen::Lower>();\n  VERIFY((m3 * v1).isApprox(m1.template triangularView<Eigen::Lower>() * v1, largerEps));\n  m3 = m1.template triangularView<Eigen::Upper>();\n  VERIFY((m3 * v1).isApprox(m1.template triangularView<Eigen::Upper>() * v1, largerEps));\n  m3 = m1.template triangularView<Eigen::UnitLower>();\n  VERIFY((m3 * v1).isApprox(m1.template triangularView<Eigen::UnitLower>() * v1, largerEps));\n  m3 = m1.template triangularView<Eigen::UnitUpper>();\n  VERIFY((m3 * v1).isApprox(m1.template triangularView<Eigen::UnitUpper>() * v1, largerEps));\n\n  // check conjugated and scalar multiple expressions (col-major)\n  m3 = m1.template triangularView<Eigen::Lower>();\n  VERIFY(((s1*m3).conjugate() * v1).isApprox((s1*m1).conjugate().template triangularView<Eigen::Lower>() * v1, largerEps));\n  m3 = m1.template triangularView<Eigen::Upper>();\n  VERIFY((m3.conjugate() * v1.conjugate()).isApprox(m1.conjugate().template triangularView<Eigen::Upper>() * v1.conjugate(), largerEps));\n\n  // check with a row-major matrix\n  m3 = m1.template triangularView<Eigen::Upper>();\n  VERIFY((m3.transpose() * v1).isApprox(m1.transpose().template triangularView<Eigen::Lower>() * v1, largerEps));\n  m3 = m1.template triangularView<Eigen::Lower>();\n  VERIFY((m3.transpose() * v1).isApprox(m1.transpose().template triangularView<Eigen::Upper>() * v1, largerEps));\n  m3 = m1.template triangularView<Eigen::UnitUpper>();\n  VERIFY((m3.transpose() * v1).isApprox(m1.transpose().template triangularView<Eigen::UnitLower>() * v1, largerEps));\n  m3 = m1.template triangularView<Eigen::UnitLower>();\n  VERIFY((m3.transpose() * v1).isApprox(m1.transpose().template triangularView<Eigen::UnitUpper>() * v1, largerEps));\n\n  // check conjugated and scalar multiple expressions (row-major)\n  m3 = m1.template triangularView<Eigen::Upper>();\n  VERIFY((m3.adjoint() * v1).isApprox(m1.adjoint().template triangularView<Eigen::Lower>() * v1, largerEps));\n  m3 = m1.template triangularView<Eigen::Lower>();\n  VERIFY((m3.adjoint() * (s1*v1.conjugate())).isApprox(m1.adjoint().template triangularView<Eigen::Upper>() * (s1*v1.conjugate()), largerEps));\n  m3 = m1.template triangularView<Eigen::UnitUpper>();\n\n  // check transposed cases:\n  m3 = m1.template triangularView<Eigen::Lower>();\n  VERIFY((v1.transpose() * m3).isApprox(v1.transpose() * m1.template triangularView<Eigen::Lower>(), largerEps));\n  VERIFY((v1.adjoint() * m3).isApprox(v1.adjoint() * m1.template triangularView<Eigen::Lower>(), largerEps));\n  VERIFY((v1.adjoint() * m3.adjoint()).isApprox(v1.adjoint() * m1.template triangularView<Eigen::Lower>().adjoint(), largerEps));\n\n  // TODO check with sub-matrices\n}\n\nvoid test_product_trmv()\n{\n  int s = 0;\n  for(int i = 0; i < g_repeat ; i++) {\n    CALL_SUBTEST_1( trmv(Matrix<float, 1, 1>()) );\n    CALL_SUBTEST_2( trmv(Matrix<float, 2, 2>()) );\n    CALL_SUBTEST_3( trmv(Matrix3d()) );\n    \n    s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2);\n    CALL_SUBTEST_4( trmv(MatrixXcf(s,s)) );\n    CALL_SUBTEST_5( trmv(MatrixXcd(s,s)) );\n    TEST_SET_BUT_UNUSED_VARIABLE(s)\n    \n    s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE);\n    CALL_SUBTEST_6( trmv(Matrix<float,Dynamic,Dynamic,RowMajor>(s, s)) );\n    TEST_SET_BUT_UNUSED_VARIABLE(s)\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/product_trsolve.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#define VERIFY_TRSM(TRI,XB) { \\\n    (XB).setRandom(); ref = (XB); \\\n    (TRI).solveInPlace(XB); \\\n    VERIFY_IS_APPROX((TRI).toDenseMatrix() * (XB), ref); \\\n    (XB).setRandom(); ref = (XB); \\\n    (XB) = (TRI).solve(XB); \\\n    VERIFY_IS_APPROX((TRI).toDenseMatrix() * (XB), ref); \\\n  }\n\n#define VERIFY_TRSM_ONTHERIGHT(TRI,XB) { \\\n    (XB).setRandom(); ref = (XB); \\\n    (TRI).transpose().template solveInPlace<OnTheRight>(XB.transpose()); \\\n    VERIFY_IS_APPROX((XB).transpose() * (TRI).transpose().toDenseMatrix(), ref.transpose()); \\\n    (XB).setRandom(); ref = (XB); \\\n    (XB).transpose() = (TRI).transpose().template solve<OnTheRight>(XB.transpose()); \\\n    VERIFY_IS_APPROX((XB).transpose() * (TRI).transpose().toDenseMatrix(), ref.transpose()); \\\n  }\n\ntemplate<typename Scalar,int Size, int Cols> void trsolve(int size=Size,int cols=Cols)\n{\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n\n  Matrix<Scalar,Size,Size,ColMajor> cmLhs(size,size);\n  Matrix<Scalar,Size,Size,RowMajor> rmLhs(size,size);\n\n  enum {  colmajor = Size==1 ? RowMajor : ColMajor,\n          rowmajor = Cols==1 ? ColMajor : RowMajor };\n  Matrix<Scalar,Size,Cols,colmajor> cmRhs(size,cols);\n  Matrix<Scalar,Size,Cols,rowmajor> rmRhs(size,cols);\n  Matrix<Scalar,Dynamic,Dynamic,colmajor> ref(size,cols);\n\n  cmLhs.setRandom(); cmLhs *= static_cast<RealScalar>(0.1); cmLhs.diagonal().array() += static_cast<RealScalar>(1);\n  rmLhs.setRandom(); rmLhs *= static_cast<RealScalar>(0.1); rmLhs.diagonal().array() += static_cast<RealScalar>(1);\n\n  VERIFY_TRSM(cmLhs.conjugate().template triangularView<Lower>(), cmRhs);\n  VERIFY_TRSM(cmLhs.adjoint()  .template triangularView<Lower>(), cmRhs);\n  VERIFY_TRSM(cmLhs            .template triangularView<Upper>(), cmRhs);\n  VERIFY_TRSM(cmLhs            .template triangularView<Lower>(), rmRhs);\n  VERIFY_TRSM(cmLhs.conjugate().template triangularView<Upper>(), rmRhs);\n  VERIFY_TRSM(cmLhs.adjoint()  .template triangularView<Upper>(), rmRhs);\n\n  VERIFY_TRSM(cmLhs.conjugate().template triangularView<UnitLower>(), cmRhs);\n  VERIFY_TRSM(cmLhs            .template triangularView<UnitUpper>(), rmRhs);\n\n  VERIFY_TRSM(rmLhs            .template triangularView<Lower>(), cmRhs);\n  VERIFY_TRSM(rmLhs.conjugate().template triangularView<UnitUpper>(), rmRhs);\n\n\n  VERIFY_TRSM_ONTHERIGHT(cmLhs.conjugate().template triangularView<Lower>(), cmRhs);\n  VERIFY_TRSM_ONTHERIGHT(cmLhs            .template triangularView<Upper>(), cmRhs);\n  VERIFY_TRSM_ONTHERIGHT(cmLhs            .template triangularView<Lower>(), rmRhs);\n  VERIFY_TRSM_ONTHERIGHT(cmLhs.conjugate().template triangularView<Upper>(), rmRhs);\n\n  VERIFY_TRSM_ONTHERIGHT(cmLhs.conjugate().template triangularView<UnitLower>(), cmRhs);\n  VERIFY_TRSM_ONTHERIGHT(cmLhs            .template triangularView<UnitUpper>(), rmRhs);\n\n  VERIFY_TRSM_ONTHERIGHT(rmLhs            .template triangularView<Lower>(), cmRhs);\n  VERIFY_TRSM_ONTHERIGHT(rmLhs.conjugate().template triangularView<UnitUpper>(), rmRhs);\n\n  int c = internal::random<int>(0,cols-1);\n  VERIFY_TRSM(rmLhs.template triangularView<Lower>(), rmRhs.col(c));\n  VERIFY_TRSM(cmLhs.template triangularView<Lower>(), rmRhs.col(c));\n}\n\nvoid test_product_trsolve()\n{\n  for(int i = 0; i < g_repeat ; i++)\n  {\n    // matrices\n    CALL_SUBTEST_1((trsolve<float,Dynamic,Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))));\n    CALL_SUBTEST_2((trsolve<double,Dynamic,Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))));\n    CALL_SUBTEST_3((trsolve<std::complex<float>,Dynamic,Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2),internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))));\n    CALL_SUBTEST_4((trsolve<std::complex<double>,Dynamic,Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2),internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))));\n\n    // vectors\n    CALL_SUBTEST_5((trsolve<float,Dynamic,1>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE))));\n    CALL_SUBTEST_6((trsolve<double,Dynamic,1>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE))));\n    CALL_SUBTEST_7((trsolve<std::complex<float>,Dynamic,1>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE))));\n    CALL_SUBTEST_8((trsolve<std::complex<double>,Dynamic,1>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE))));\n    \n    // meta-unrollers\n    CALL_SUBTEST_9((trsolve<float,4,1>()));\n    CALL_SUBTEST_10((trsolve<double,4,1>()));\n    CALL_SUBTEST_11((trsolve<std::complex<float>,4,1>()));\n    CALL_SUBTEST_12((trsolve<float,1,1>()));\n    CALL_SUBTEST_13((trsolve<float,1,2>()));\n    CALL_SUBTEST_14((trsolve<float,3,1>()));\n    \n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/qr.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <Eigen/QR>\n\ntemplate<typename MatrixType> void qr(const MatrixType& m)\n{\n  typedef typename MatrixType::Index Index;\n\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  typedef typename MatrixType::Scalar Scalar;\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType;\n\n  MatrixType a = MatrixType::Random(rows,cols);\n  HouseholderQR<MatrixType> qrOfA(a);\n\n  MatrixQType q = qrOfA.householderQ();\n  VERIFY_IS_UNITARY(q);\n\n  MatrixType r = qrOfA.matrixQR().template triangularView<Upper>();\n  VERIFY_IS_APPROX(a, qrOfA.householderQ() * r);\n}\n\ntemplate<typename MatrixType, int Cols2> void qr_fixedsize()\n{\n  enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };\n  typedef typename MatrixType::Scalar Scalar;\n  Matrix<Scalar,Rows,Cols> m1 = Matrix<Scalar,Rows,Cols>::Random();\n  HouseholderQR<Matrix<Scalar,Rows,Cols> > qr(m1);\n\n  Matrix<Scalar,Rows,Cols> r = qr.matrixQR();\n  // FIXME need better way to construct trapezoid\n  for(int i = 0; i < Rows; i++) for(int j = 0; j < Cols; j++) if(i>j) r(i,j) = Scalar(0);\n\n  VERIFY_IS_APPROX(m1, qr.householderQ() * r);\n\n  Matrix<Scalar,Cols,Cols2> m2 = Matrix<Scalar,Cols,Cols2>::Random(Cols,Cols2);\n  Matrix<Scalar,Rows,Cols2> m3 = m1*m2;\n  m2 = Matrix<Scalar,Cols,Cols2>::Random(Cols,Cols2);\n  m2 = qr.solve(m3);\n  VERIFY_IS_APPROX(m3, m1*m2);\n}\n\ntemplate<typename MatrixType> void qr_invertible()\n{\n  using std::log;\n  using std::abs;\n  using std::pow;\n  using std::max;\n  typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;\n  typedef typename MatrixType::Scalar Scalar;\n\n  int size = internal::random<int>(10,50);\n\n  MatrixType m1(size, size), m2(size, size), m3(size, size);\n  m1 = MatrixType::Random(size,size);\n\n  if (internal::is_same<RealScalar,float>::value)\n  {\n    // let's build a matrix more stable to inverse\n    MatrixType a = MatrixType::Random(size,size*4);\n    m1 += a * a.adjoint();\n  }\n\n  HouseholderQR<MatrixType> qr(m1);\n  m3 = MatrixType::Random(size,size);\n  m2 = qr.solve(m3);\n  VERIFY_IS_APPROX(m3, m1*m2);\n\n  // now construct a matrix with prescribed determinant\n  m1.setZero();\n  for(int i = 0; i < size; i++) m1(i,i) = internal::random<Scalar>();\n  RealScalar absdet = abs(m1.diagonal().prod());\n  m3 = qr.householderQ(); // get a unitary\n  m1 = m3 * m1 * m3;\n  qr.compute(m1);\n  VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant());\n  // This test is tricky if the determinant becomes too small.\n  // Since we generate random numbers with magnitude rrange [0,1], the average determinant is 0.5^size\n  VERIFY_IS_MUCH_SMALLER_THAN( abs(absdet-qr.absDeterminant()), numext::maxi(RealScalar(pow(0.5,size)),numext::maxi<RealScalar>(abs(absdet),abs(qr.absDeterminant()))) );\n  \n}\n\ntemplate<typename MatrixType> void qr_verify_assert()\n{\n  MatrixType tmp;\n\n  HouseholderQR<MatrixType> qr;\n  VERIFY_RAISES_ASSERT(qr.matrixQR())\n  VERIFY_RAISES_ASSERT(qr.solve(tmp))\n  VERIFY_RAISES_ASSERT(qr.householderQ())\n  VERIFY_RAISES_ASSERT(qr.absDeterminant())\n  VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())\n}\n\nvoid test_qr()\n{\n  for(int i = 0; i < g_repeat; i++) {\n   CALL_SUBTEST_1( qr(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n   CALL_SUBTEST_2( qr(MatrixXcd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2),internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))) );\n   CALL_SUBTEST_3(( qr_fixedsize<Matrix<float,3,4>, 2 >() ));\n   CALL_SUBTEST_4(( qr_fixedsize<Matrix<double,6,2>, 4 >() ));\n   CALL_SUBTEST_5(( qr_fixedsize<Matrix<double,2,5>, 7 >() ));\n   CALL_SUBTEST_11( qr(Matrix<float,1,1>()) );\n  }\n\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( qr_invertible<MatrixXf>() );\n    CALL_SUBTEST_6( qr_invertible<MatrixXd>() );\n    CALL_SUBTEST_7( qr_invertible<MatrixXcf>() );\n    CALL_SUBTEST_8( qr_invertible<MatrixXcd>() );\n  }\n\n  CALL_SUBTEST_9(qr_verify_assert<Matrix3f>());\n  CALL_SUBTEST_10(qr_verify_assert<Matrix3d>());\n  CALL_SUBTEST_1(qr_verify_assert<MatrixXf>());\n  CALL_SUBTEST_6(qr_verify_assert<MatrixXd>());\n  CALL_SUBTEST_7(qr_verify_assert<MatrixXcf>());\n  CALL_SUBTEST_8(qr_verify_assert<MatrixXcd>());\n\n  // Test problem size constructors\n  CALL_SUBTEST_12(HouseholderQR<MatrixXf>(10, 20));\n}\n"
  },
  {
    "path": "include/eigen3/test/qr_colpivoting.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <Eigen/QR>\n#include <Eigen/SVD>\n\ntemplate <typename MatrixType>\nvoid cod() {\n  typedef typename MatrixType::Index Index;\n\n  Index rows = internal::random<Index>(2, EIGEN_TEST_MAX_SIZE);\n  Index cols = internal::random<Index>(2, EIGEN_TEST_MAX_SIZE);\n  Index cols2 = internal::random<Index>(2, EIGEN_TEST_MAX_SIZE);\n  Index rank = internal::random<Index>(1, (std::min)(rows, cols) - 1);\n\n  typedef typename MatrixType::Scalar Scalar;\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime,\n                 MatrixType::RowsAtCompileTime>\n      MatrixQType;\n  MatrixType matrix;\n  createRandomPIMatrixOfRank(rank, rows, cols, matrix);\n  CompleteOrthogonalDecomposition<MatrixType> cod(matrix);\n  VERIFY(rank == cod.rank());\n  VERIFY(cols - cod.rank() == cod.dimensionOfKernel());\n  VERIFY(!cod.isInjective());\n  VERIFY(!cod.isInvertible());\n  VERIFY(!cod.isSurjective());\n\n  MatrixQType q = cod.householderQ();\n  VERIFY_IS_UNITARY(q);\n\n  MatrixType z = cod.matrixZ();\n  VERIFY_IS_UNITARY(z);\n\n  MatrixType t;\n  t.setZero(rows, cols);\n  t.topLeftCorner(rank, rank) =\n      cod.matrixT().topLeftCorner(rank, rank).template triangularView<Upper>();\n\n  MatrixType c = q * t * z * cod.colsPermutation().inverse();\n  VERIFY_IS_APPROX(matrix, c);\n\n  MatrixType exact_solution = MatrixType::Random(cols, cols2);\n  MatrixType rhs = matrix * exact_solution;\n  MatrixType cod_solution = cod.solve(rhs);\n  VERIFY_IS_APPROX(rhs, matrix * cod_solution);\n\n  // Verify that we get the same minimum-norm solution as the SVD.\n  JacobiSVD<MatrixType> svd(matrix, ComputeThinU | ComputeThinV);\n  MatrixType svd_solution = svd.solve(rhs);\n  VERIFY_IS_APPROX(cod_solution, svd_solution);\n\n  MatrixType pinv = cod.pseudoInverse();\n  VERIFY_IS_APPROX(cod_solution, pinv * rhs);\n}\n\ntemplate <typename MatrixType, int Cols2>\nvoid cod_fixedsize() {\n  enum {\n    Rows = MatrixType::RowsAtCompileTime,\n    Cols = MatrixType::ColsAtCompileTime\n  };\n  typedef typename MatrixType::Scalar Scalar;\n  int rank = internal::random<int>(1, (std::min)(int(Rows), int(Cols)) - 1);\n  Matrix<Scalar, Rows, Cols> matrix;\n  createRandomPIMatrixOfRank(rank, Rows, Cols, matrix);\n  CompleteOrthogonalDecomposition<Matrix<Scalar, Rows, Cols> > cod(matrix);\n  VERIFY(rank == cod.rank());\n  VERIFY(Cols - cod.rank() == cod.dimensionOfKernel());\n  VERIFY(cod.isInjective() == (rank == Rows));\n  VERIFY(cod.isSurjective() == (rank == Cols));\n  VERIFY(cod.isInvertible() == (cod.isInjective() && cod.isSurjective()));\n\n  Matrix<Scalar, Cols, Cols2> exact_solution;\n  exact_solution.setRandom(Cols, Cols2);\n  Matrix<Scalar, Rows, Cols2> rhs = matrix * exact_solution;\n  Matrix<Scalar, Cols, Cols2> cod_solution = cod.solve(rhs);\n  VERIFY_IS_APPROX(rhs, matrix * cod_solution);\n\n  // Verify that we get the same minimum-norm solution as the SVD.\n  JacobiSVD<MatrixType> svd(matrix, ComputeFullU | ComputeFullV);\n  Matrix<Scalar, Cols, Cols2> svd_solution = svd.solve(rhs);\n  VERIFY_IS_APPROX(cod_solution, svd_solution);\n}\n\ntemplate<typename MatrixType> void qr()\n{\n  using std::sqrt;\n  typedef typename MatrixType::Index Index;\n\n  Index rows = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE), cols = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE), cols2 = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE);\n  Index rank = internal::random<Index>(1, (std::min)(rows, cols)-1);\n\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename MatrixType::RealScalar RealScalar;\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType;\n  MatrixType m1;\n  createRandomPIMatrixOfRank(rank,rows,cols,m1);\n  ColPivHouseholderQR<MatrixType> qr(m1);\n  VERIFY_IS_EQUAL(rank, qr.rank());\n  VERIFY_IS_EQUAL(cols - qr.rank(), qr.dimensionOfKernel());\n  VERIFY(!qr.isInjective());\n  VERIFY(!qr.isInvertible());\n  VERIFY(!qr.isSurjective());\n\n  MatrixQType q = qr.householderQ();\n  VERIFY_IS_UNITARY(q);\n\n  MatrixType r = qr.matrixQR().template triangularView<Upper>();\n  MatrixType c = q * r * qr.colsPermutation().inverse();\n  VERIFY_IS_APPROX(m1, c);\n\n  // Verify that the absolute value of the diagonal elements in R are\n  // non-increasing until they reach the singularity threshold.\n  RealScalar threshold =\n      sqrt(RealScalar(rows)) * numext::abs(r(0, 0)) * NumTraits<Scalar>::epsilon();\n  for (Index i = 0; i < (std::min)(rows, cols) - 1; ++i) {\n    RealScalar x = numext::abs(r(i, i));\n    RealScalar y = numext::abs(r(i + 1, i + 1));\n    if (x < threshold && y < threshold) continue;\n    if (!test_isApproxOrLessThan(y, x)) {\n      for (Index j = 0; j < (std::min)(rows, cols); ++j) {\n        std::cout << \"i = \" << j << \", |r_ii| = \" << numext::abs(r(j, j)) << std::endl;\n      }\n      std::cout << \"Failure at i=\" << i << \", rank=\" << rank\n                << \", threshold=\" << threshold << std::endl;\n    }\n    VERIFY_IS_APPROX_OR_LESS_THAN(y, x);\n  }\n\n  MatrixType m2 = MatrixType::Random(cols,cols2);\n  MatrixType m3 = m1*m2;\n  m2 = MatrixType::Random(cols,cols2);\n  m2 = qr.solve(m3);\n  VERIFY_IS_APPROX(m3, m1*m2);\n\n  {\n    Index size = rows;\n    do {\n      m1 = MatrixType::Random(size,size);\n      qr.compute(m1);\n    } while(!qr.isInvertible());\n    MatrixType m1_inv = qr.inverse();\n    m3 = m1 * MatrixType::Random(size,cols2);\n    m2 = qr.solve(m3);\n    VERIFY_IS_APPROX(m2, m1_inv*m3);\n  }\n}\n\ntemplate<typename MatrixType, int Cols2> void qr_fixedsize()\n{\n  using std::sqrt;\n  using std::abs;\n  enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename MatrixType::RealScalar RealScalar;\n  int rank = internal::random<int>(1, (std::min)(int(Rows), int(Cols))-1);\n  Matrix<Scalar,Rows,Cols> m1;\n  createRandomPIMatrixOfRank(rank,Rows,Cols,m1);\n  ColPivHouseholderQR<Matrix<Scalar,Rows,Cols> > qr(m1);\n  VERIFY_IS_EQUAL(rank, qr.rank());\n  VERIFY_IS_EQUAL(Cols - qr.rank(), qr.dimensionOfKernel());\n  VERIFY_IS_EQUAL(qr.isInjective(), (rank == Rows));\n  VERIFY_IS_EQUAL(qr.isSurjective(), (rank == Cols));\n  VERIFY_IS_EQUAL(qr.isInvertible(), (qr.isInjective() && qr.isSurjective()));\n\n  Matrix<Scalar,Rows,Cols> r = qr.matrixQR().template triangularView<Upper>();\n  Matrix<Scalar,Rows,Cols> c = qr.householderQ() * r * qr.colsPermutation().inverse();\n  VERIFY_IS_APPROX(m1, c);\n\n  Matrix<Scalar,Cols,Cols2> m2 = Matrix<Scalar,Cols,Cols2>::Random(Cols,Cols2);\n  Matrix<Scalar,Rows,Cols2> m3 = m1*m2;\n  m2 = Matrix<Scalar,Cols,Cols2>::Random(Cols,Cols2);\n  m2 = qr.solve(m3);\n  VERIFY_IS_APPROX(m3, m1*m2);\n  // Verify that the absolute value of the diagonal elements in R are\n  // non-increasing until they reache the singularity threshold.\n  RealScalar threshold =\n      sqrt(RealScalar(Rows)) * (std::abs)(r(0, 0)) * NumTraits<Scalar>::epsilon();\n  for (Index i = 0; i < (std::min)(int(Rows), int(Cols)) - 1; ++i) {\n    RealScalar x = numext::abs(r(i, i));\n    RealScalar y = numext::abs(r(i + 1, i + 1));\n    if (x < threshold && y < threshold) continue;\n    if (!test_isApproxOrLessThan(y, x)) {\n      for (Index j = 0; j < (std::min)(int(Rows), int(Cols)); ++j) {\n        std::cout << \"i = \" << j << \", |r_ii| = \" << numext::abs(r(j, j)) << std::endl;\n      }\n      std::cout << \"Failure at i=\" << i << \", rank=\" << rank\n                << \", threshold=\" << threshold << std::endl;\n    }\n    VERIFY_IS_APPROX_OR_LESS_THAN(y, x);\n  }\n}\n\n// This test is meant to verify that pivots are chosen such that\n// even for a graded matrix, the diagonal of R falls of roughly\n// monotonically until it reaches the threshold for singularity.\n// We use the so-called Kahan matrix, which is a famous counter-example\n// for rank-revealing QR. See\n// http://www.netlib.org/lapack/lawnspdf/lawn176.pdf\n// page 3 for more detail.\ntemplate<typename MatrixType> void qr_kahan_matrix()\n{\n  using std::sqrt;\n  using std::abs;\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename MatrixType::RealScalar RealScalar;\n\n  Index rows = 300, cols = rows;\n\n  MatrixType m1;\n  m1.setZero(rows,cols);\n  RealScalar s = std::pow(NumTraits<RealScalar>::epsilon(), 1.0 / rows);\n  RealScalar c = std::sqrt(1 - s*s);\n  RealScalar pow_s_i(1.0); // pow(s,i)\n  for (Index i = 0; i < rows; ++i) {\n    m1(i, i) = pow_s_i;\n    m1.row(i).tail(rows - i - 1) = -pow_s_i * c * MatrixType::Ones(1, rows - i - 1);\n    pow_s_i *= s;\n  }\n  m1 = (m1 + m1.transpose()).eval();\n  ColPivHouseholderQR<MatrixType> qr(m1);\n  MatrixType r = qr.matrixQR().template triangularView<Upper>();\n\n  RealScalar threshold =\n      std::sqrt(RealScalar(rows)) * numext::abs(r(0, 0)) * NumTraits<Scalar>::epsilon();\n  for (Index i = 0; i < (std::min)(rows, cols) - 1; ++i) {\n    RealScalar x = numext::abs(r(i, i));\n    RealScalar y = numext::abs(r(i + 1, i + 1));\n    if (x < threshold && y < threshold) continue;\n    if (!test_isApproxOrLessThan(y, x)) {\n      for (Index j = 0; j < (std::min)(rows, cols); ++j) {\n        std::cout << \"i = \" << j << \", |r_ii| = \" << numext::abs(r(j, j)) << std::endl;\n      }\n      std::cout << \"Failure at i=\" << i << \", rank=\" << qr.rank()\n                << \", threshold=\" << threshold << std::endl;\n    }\n    VERIFY_IS_APPROX_OR_LESS_THAN(y, x);\n  }\n}\n\ntemplate<typename MatrixType> void qr_invertible()\n{\n  using std::log;\n  using std::abs;\n  typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;\n  typedef typename MatrixType::Scalar Scalar;\n\n  int size = internal::random<int>(10,50);\n\n  MatrixType m1(size, size), m2(size, size), m3(size, size);\n  m1 = MatrixType::Random(size,size);\n\n  if (internal::is_same<RealScalar,float>::value)\n  {\n    // let's build a matrix more stable to inverse\n    MatrixType a = MatrixType::Random(size,size*2);\n    m1 += a * a.adjoint();\n  }\n\n  ColPivHouseholderQR<MatrixType> qr(m1);\n  m3 = MatrixType::Random(size,size);\n  m2 = qr.solve(m3);\n  //VERIFY_IS_APPROX(m3, m1*m2);\n\n  // now construct a matrix with prescribed determinant\n  m1.setZero();\n  for(int i = 0; i < size; i++) m1(i,i) = internal::random<Scalar>();\n  RealScalar absdet = abs(m1.diagonal().prod());\n  m3 = qr.householderQ(); // get a unitary\n  m1 = m3 * m1 * m3;\n  qr.compute(m1);\n  VERIFY_IS_APPROX(absdet, qr.absDeterminant());\n  VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant());\n}\n\ntemplate<typename MatrixType> void qr_verify_assert()\n{\n  MatrixType tmp;\n\n  ColPivHouseholderQR<MatrixType> qr;\n  VERIFY_RAISES_ASSERT(qr.matrixQR())\n  VERIFY_RAISES_ASSERT(qr.solve(tmp))\n  VERIFY_RAISES_ASSERT(qr.householderQ())\n  VERIFY_RAISES_ASSERT(qr.dimensionOfKernel())\n  VERIFY_RAISES_ASSERT(qr.isInjective())\n  VERIFY_RAISES_ASSERT(qr.isSurjective())\n  VERIFY_RAISES_ASSERT(qr.isInvertible())\n  VERIFY_RAISES_ASSERT(qr.inverse())\n  VERIFY_RAISES_ASSERT(qr.absDeterminant())\n  VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())\n}\n\nvoid test_qr_colpivoting()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( qr<MatrixXf>() );\n    CALL_SUBTEST_2( qr<MatrixXd>() );\n    CALL_SUBTEST_3( qr<MatrixXcd>() );\n    CALL_SUBTEST_4(( qr_fixedsize<Matrix<float,3,5>, 4 >() ));\n    CALL_SUBTEST_5(( qr_fixedsize<Matrix<double,6,2>, 3 >() ));\n    CALL_SUBTEST_5(( qr_fixedsize<Matrix<double,1,1>, 1 >() ));\n  }\n\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( cod<MatrixXf>() );\n    CALL_SUBTEST_2( cod<MatrixXd>() );\n    CALL_SUBTEST_3( cod<MatrixXcd>() );\n    CALL_SUBTEST_4(( cod_fixedsize<Matrix<float,3,5>, 4 >() ));\n    CALL_SUBTEST_5(( cod_fixedsize<Matrix<double,6,2>, 3 >() ));\n    CALL_SUBTEST_5(( cod_fixedsize<Matrix<double,1,1>, 1 >() ));\n  }\n\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( qr_invertible<MatrixXf>() );\n    CALL_SUBTEST_2( qr_invertible<MatrixXd>() );\n    CALL_SUBTEST_6( qr_invertible<MatrixXcf>() );\n    CALL_SUBTEST_3( qr_invertible<MatrixXcd>() );\n  }\n\n  CALL_SUBTEST_7(qr_verify_assert<Matrix3f>());\n  CALL_SUBTEST_8(qr_verify_assert<Matrix3d>());\n  CALL_SUBTEST_1(qr_verify_assert<MatrixXf>());\n  CALL_SUBTEST_2(qr_verify_assert<MatrixXd>());\n  CALL_SUBTEST_6(qr_verify_assert<MatrixXcf>());\n  CALL_SUBTEST_3(qr_verify_assert<MatrixXcd>());\n\n  // Test problem size constructors\n  CALL_SUBTEST_9(ColPivHouseholderQR<MatrixXf>(10, 20));\n\n  CALL_SUBTEST_1( qr_kahan_matrix<MatrixXf>() );\n  CALL_SUBTEST_2( qr_kahan_matrix<MatrixXd>() );\n}\n"
  },
  {
    "path": "include/eigen3/test/qr_fullpivoting.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <Eigen/QR>\n\ntemplate<typename MatrixType> void qr()\n{\n  typedef typename MatrixType::Index Index;\n\n  Index max_size = EIGEN_TEST_MAX_SIZE;\n  Index min_size = numext::maxi(1,EIGEN_TEST_MAX_SIZE/10);\n  Index rows  = internal::random<Index>(min_size,max_size),\n        cols  = internal::random<Index>(min_size,max_size),\n        cols2 = internal::random<Index>(min_size,max_size),\n        rank  = internal::random<Index>(1, (std::min)(rows, cols)-1);\n\n  typedef typename MatrixType::Scalar Scalar;\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType;\n  MatrixType m1;\n  createRandomPIMatrixOfRank(rank,rows,cols,m1);\n  FullPivHouseholderQR<MatrixType> qr(m1);\n  VERIFY_IS_EQUAL(rank, qr.rank());\n  VERIFY_IS_EQUAL(cols - qr.rank(), qr.dimensionOfKernel());\n  VERIFY(!qr.isInjective());\n  VERIFY(!qr.isInvertible());\n  VERIFY(!qr.isSurjective());\n\n  MatrixType r = qr.matrixQR();\n  \n  MatrixQType q = qr.matrixQ();\n  VERIFY_IS_UNITARY(q);\n  \n  // FIXME need better way to construct trapezoid\n  for(int i = 0; i < rows; i++) for(int j = 0; j < cols; j++) if(i>j) r(i,j) = Scalar(0);\n\n  MatrixType c = qr.matrixQ() * r * qr.colsPermutation().inverse();\n\n  VERIFY_IS_APPROX(m1, c);\n  \n  // stress the ReturnByValue mechanism\n  MatrixType tmp;\n  VERIFY_IS_APPROX(tmp.noalias() = qr.matrixQ() * r, (qr.matrixQ() * r).eval());\n  \n  MatrixType m2 = MatrixType::Random(cols,cols2);\n  MatrixType m3 = m1*m2;\n  m2 = MatrixType::Random(cols,cols2);\n  m2 = qr.solve(m3);\n  VERIFY_IS_APPROX(m3, m1*m2);\n\n  {\n    Index size = rows;\n    do {\n      m1 = MatrixType::Random(size,size);\n      qr.compute(m1);\n    } while(!qr.isInvertible());\n    MatrixType m1_inv = qr.inverse();\n    m3 = m1 * MatrixType::Random(size,cols2);\n    m2 = qr.solve(m3);\n    VERIFY_IS_APPROX(m2, m1_inv*m3);\n  }\n}\n\ntemplate<typename MatrixType> void qr_invertible()\n{\n  using std::log;\n  using std::abs;\n  typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;\n  typedef typename MatrixType::Scalar Scalar;\n\n  Index max_size = numext::mini(50,EIGEN_TEST_MAX_SIZE);\n  Index min_size = numext::maxi(1,EIGEN_TEST_MAX_SIZE/10);\n  Index size = internal::random<Index>(min_size,max_size);\n\n  MatrixType m1(size, size), m2(size, size), m3(size, size);\n  m1 = MatrixType::Random(size,size);\n\n  if (internal::is_same<RealScalar,float>::value)\n  {\n    // let's build a matrix more stable to inverse\n    MatrixType a = MatrixType::Random(size,size*2);\n    m1 += a * a.adjoint();\n  }\n\n  FullPivHouseholderQR<MatrixType> qr(m1);\n  VERIFY(qr.isInjective());\n  VERIFY(qr.isInvertible());\n  VERIFY(qr.isSurjective());\n\n  m3 = MatrixType::Random(size,size);\n  m2 = qr.solve(m3);\n  VERIFY_IS_APPROX(m3, m1*m2);\n\n  // now construct a matrix with prescribed determinant\n  m1.setZero();\n  for(int i = 0; i < size; i++) m1(i,i) = internal::random<Scalar>();\n  RealScalar absdet = abs(m1.diagonal().prod());\n  m3 = qr.matrixQ(); // get a unitary\n  m1 = m3 * m1 * m3;\n  qr.compute(m1);\n  VERIFY_IS_APPROX(absdet, qr.absDeterminant());\n  VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant());\n}\n\ntemplate<typename MatrixType> void qr_verify_assert()\n{\n  MatrixType tmp;\n\n  FullPivHouseholderQR<MatrixType> qr;\n  VERIFY_RAISES_ASSERT(qr.matrixQR())\n  VERIFY_RAISES_ASSERT(qr.solve(tmp))\n  VERIFY_RAISES_ASSERT(qr.matrixQ())\n  VERIFY_RAISES_ASSERT(qr.dimensionOfKernel())\n  VERIFY_RAISES_ASSERT(qr.isInjective())\n  VERIFY_RAISES_ASSERT(qr.isSurjective())\n  VERIFY_RAISES_ASSERT(qr.isInvertible())\n  VERIFY_RAISES_ASSERT(qr.inverse())\n  VERIFY_RAISES_ASSERT(qr.absDeterminant())\n  VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())\n}\n\nvoid test_qr_fullpivoting()\n{\n for(int i = 0; i < 1; i++) {\n    // FIXME : very weird bug here\n//     CALL_SUBTEST(qr(Matrix2f()) );\n    CALL_SUBTEST_1( qr<MatrixXf>() );\n    CALL_SUBTEST_2( qr<MatrixXd>() );\n    CALL_SUBTEST_3( qr<MatrixXcd>() );\n  }\n\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( qr_invertible<MatrixXf>() );\n    CALL_SUBTEST_2( qr_invertible<MatrixXd>() );\n    CALL_SUBTEST_4( qr_invertible<MatrixXcf>() );\n    CALL_SUBTEST_3( qr_invertible<MatrixXcd>() );\n  }\n\n  CALL_SUBTEST_5(qr_verify_assert<Matrix3f>());\n  CALL_SUBTEST_6(qr_verify_assert<Matrix3d>());\n  CALL_SUBTEST_1(qr_verify_assert<MatrixXf>());\n  CALL_SUBTEST_2(qr_verify_assert<MatrixXd>());\n  CALL_SUBTEST_4(qr_verify_assert<MatrixXcf>());\n  CALL_SUBTEST_3(qr_verify_assert<MatrixXcd>());\n\n  // Test problem size constructors\n  CALL_SUBTEST_7(FullPivHouseholderQR<MatrixXf>(10, 20));\n  CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,10,20> >(10,20)));\n  CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,10,20> >(Matrix<float,10,20>::Random())));\n  CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,20,10> >(20,10)));\n  CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,20,10> >(Matrix<float,20,10>::Random())));\n}\n"
  },
  {
    "path": "include/eigen3/test/qtvector.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define EIGEN_WORK_AROUND_QT_BUG_CALLING_WRONG_OPERATOR_NEW_FIXED_IN_QT_4_5\n\n#include \"main.h\"\n#include <QtCore/QVector>\n#include <Eigen/Geometry>\n#include <Eigen/QtAlignedMalloc>\n\ntemplate<typename MatrixType>\nvoid check_qtvector_matrix(const MatrixType& m)\n{\n  typedef typename MatrixType::Index Index;\n\n  Index rows = m.rows();\n  Index cols = m.cols();\n  MatrixType x = MatrixType::Random(rows,cols), y = MatrixType::Random(rows,cols);\n  QVector<MatrixType> v(10, MatrixType(rows,cols)), w(20, y);\n  for(int i = 0; i < 20; i++)\n  {\n    VERIFY_IS_APPROX(w[i], y);\n  }\n  v[5] = x;\n  w[6] = v[5];\n  VERIFY_IS_APPROX(w[6], v[5]);\n  v = w;\n  for(int i = 0; i < 20; i++)\n  {\n    VERIFY_IS_APPROX(w[i], v[i]);\n  }\n\n  v.resize(21);\n  v[20] = x;\n  VERIFY_IS_APPROX(v[20], x);\n  v.fill(y,22);\n  VERIFY_IS_APPROX(v[21], y);\n  v.push_back(x);\n  VERIFY_IS_APPROX(v[22], x);\n  VERIFY((size_t)&(v[22]) == (size_t)&(v[21]) + sizeof(MatrixType));\n\n  // do a lot of push_back such that the vector gets internally resized\n  // (with memory reallocation)\n  MatrixType* ref = &w[0];\n  for(int i=0; i<30 || ((ref==&w[0]) && i<300); ++i)\n    v.push_back(w[i%w.size()]);\n  for(int i=23; i<v.size(); ++i)\n  {\n    VERIFY(v[i]==w[(i-23)%w.size()]);\n  }\n}\n\ntemplate<typename TransformType>\nvoid check_qtvector_transform(const TransformType&)\n{\n  typedef typename TransformType::MatrixType MatrixType;\n  TransformType x(MatrixType::Random()), y(MatrixType::Random());\n  QVector<TransformType> v(10), w(20, y);\n  v[5] = x;\n  w[6] = v[5];\n  VERIFY_IS_APPROX(w[6], v[5]);\n  v = w;\n  for(int i = 0; i < 20; i++)\n  {\n    VERIFY_IS_APPROX(w[i], v[i]);\n  }\n\n  v.resize(21);\n  v[20] = x;\n  VERIFY_IS_APPROX(v[20], x);\n  v.fill(y,22);\n  VERIFY_IS_APPROX(v[21], y);\n  v.push_back(x);\n  VERIFY_IS_APPROX(v[22], x);\n  VERIFY((size_t)&(v[22]) == (size_t)&(v[21]) + sizeof(TransformType));\n\n  // do a lot of push_back such that the vector gets internally resized\n  // (with memory reallocation)\n  TransformType* ref = &w[0];\n  for(int i=0; i<30 || ((ref==&w[0]) && i<300); ++i)\n    v.push_back(w[i%w.size()]);\n  for(unsigned int i=23; int(i)<v.size(); ++i)\n  {\n    VERIFY(v[i].matrix()==w[(i-23)%w.size()].matrix());\n  }\n}\n\ntemplate<typename QuaternionType>\nvoid check_qtvector_quaternion(const QuaternionType&)\n{\n  typedef typename QuaternionType::Coefficients Coefficients;\n  QuaternionType x(Coefficients::Random()), y(Coefficients::Random());\n  QVector<QuaternionType> v(10), w(20, y);\n  v[5] = x;\n  w[6] = v[5];\n  VERIFY_IS_APPROX(w[6], v[5]);\n  v = w;\n  for(int i = 0; i < 20; i++)\n  {\n    VERIFY_IS_APPROX(w[i], v[i]);\n  }\n\n  v.resize(21);\n  v[20] = x;\n  VERIFY_IS_APPROX(v[20], x);\n  v.fill(y,22);\n  VERIFY_IS_APPROX(v[21], y);\n  v.push_back(x);\n  VERIFY_IS_APPROX(v[22], x);\n  VERIFY((size_t)&(v[22]) == (size_t)&(v[21]) + sizeof(QuaternionType));\n\n  // do a lot of push_back such that the vector gets internally resized\n  // (with memory reallocation)\n  QuaternionType* ref = &w[0];\n  for(int i=0; i<30 || ((ref==&w[0]) && i<300); ++i)\n    v.push_back(w[i%w.size()]);\n  for(unsigned int i=23; int(i)<v.size(); ++i)\n  {\n    VERIFY(v[i].coeffs()==w[(i-23)%w.size()].coeffs());\n  }\n}\n\nvoid test_qtvector()\n{\n  // some non vectorizable fixed sizes\n  CALL_SUBTEST(check_qtvector_matrix(Vector2f()));\n  CALL_SUBTEST(check_qtvector_matrix(Matrix3f()));\n  CALL_SUBTEST(check_qtvector_matrix(Matrix3d()));\n\n  // some vectorizable fixed sizes\n  CALL_SUBTEST(check_qtvector_matrix(Matrix2f()));\n  CALL_SUBTEST(check_qtvector_matrix(Vector4f()));\n  CALL_SUBTEST(check_qtvector_matrix(Matrix4f()));\n  CALL_SUBTEST(check_qtvector_matrix(Matrix4d()));\n\n  // some dynamic sizes\n  CALL_SUBTEST(check_qtvector_matrix(MatrixXd(1,1)));\n  CALL_SUBTEST(check_qtvector_matrix(VectorXd(20)));\n  CALL_SUBTEST(check_qtvector_matrix(RowVectorXf(20)));\n  CALL_SUBTEST(check_qtvector_matrix(MatrixXcf(10,10)));\n\n  // some Transform\n  CALL_SUBTEST(check_qtvector_transform(Affine2f()));\n  CALL_SUBTEST(check_qtvector_transform(Affine3f()));\n  CALL_SUBTEST(check_qtvector_transform(Affine3d()));\n  //CALL_SUBTEST(check_qtvector_transform(Transform4d()));\n\n  // some Quaternion\n  CALL_SUBTEST(check_qtvector_quaternion(Quaternionf()));\n  CALL_SUBTEST(check_qtvector_quaternion(Quaternionf()));\n}\n"
  },
  {
    "path": "include/eigen3/test/rand.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\ntypedef long long int64;\n\ntemplate<typename Scalar> Scalar check_in_range(Scalar x, Scalar y)\n{\n  Scalar r = internal::random<Scalar>(x,y);\n  VERIFY(r>=x);\n  if(y>=x)\n  {\n    VERIFY(r<=y);\n  }\n  return r;\n}\n\ntemplate<typename Scalar> void check_all_in_range(Scalar x, Scalar y)\n{\n  Array<int,1,Dynamic> mask(y-x+1);\n  mask.fill(0);\n  long n = (y-x+1)*32;\n  for(long k=0; k<n; ++k)\n  {\n    mask( check_in_range(x,y)-x )++;\n  }\n  for(Index i=0; i<mask.size(); ++i)\n    if(mask(i)==0)\n      std::cout << \"WARNING: value \" << x+i << \" not reached.\" << std::endl;\n  VERIFY( (mask>0).all() );\n}\n\ntemplate<typename Scalar> void check_histogram(Scalar x, Scalar y, int bins)\n{\n  Array<int,1,Dynamic> hist(bins);\n  hist.fill(0);\n  int f = 100000;\n  int n = bins*f;\n  int64 range = int64(y)-int64(x);\n  int divisor = int((range+1)/bins);\n  assert(((range+1)%bins)==0);\n  for(int k=0; k<n; ++k)\n  {\n    Scalar r = check_in_range(x,y);\n    hist( int((int64(r)-int64(x))/divisor) )++;\n  }\n  VERIFY( (((hist.cast<double>()/double(f))-1.0).abs()<0.02).all() );\n}\n\nvoid test_rand()\n{\n  long long_ref = NumTraits<long>::highest()/10;\n  signed char char_offset = (std::min)(g_repeat,64);\n  signed char short_offset = (std::min)(g_repeat,16000);\n\n  for(int i = 0; i < g_repeat*10000; i++) {\n    CALL_SUBTEST(check_in_range<float>(10,11));\n    CALL_SUBTEST(check_in_range<float>(1.24234523,1.24234523));\n    CALL_SUBTEST(check_in_range<float>(-1,1));\n    CALL_SUBTEST(check_in_range<float>(-1432.2352,-1432.2352));\n\n    CALL_SUBTEST(check_in_range<double>(10,11));\n    CALL_SUBTEST(check_in_range<double>(1.24234523,1.24234523));\n    CALL_SUBTEST(check_in_range<double>(-1,1));\n    CALL_SUBTEST(check_in_range<double>(-1432.2352,-1432.2352));\n\n    CALL_SUBTEST(check_in_range<int>(0,-1));\n    CALL_SUBTEST(check_in_range<short>(0,-1));\n    CALL_SUBTEST(check_in_range<long>(0,-1));\n    CALL_SUBTEST(check_in_range<int>(-673456,673456));\n    CALL_SUBTEST(check_in_range<int>(-RAND_MAX+10,RAND_MAX-10));\n    CALL_SUBTEST(check_in_range<short>(-24345,24345));\n    CALL_SUBTEST(check_in_range<long>(-long_ref,long_ref));\n  }\n\n  CALL_SUBTEST(check_all_in_range<signed char>(11,11));\n  CALL_SUBTEST(check_all_in_range<signed char>(11,11+char_offset));\n  CALL_SUBTEST(check_all_in_range<signed char>(-5,5));\n  CALL_SUBTEST(check_all_in_range<signed char>(-11-char_offset,-11));\n  CALL_SUBTEST(check_all_in_range<signed char>(-126,-126+char_offset));\n  CALL_SUBTEST(check_all_in_range<signed char>(126-char_offset,126));\n  CALL_SUBTEST(check_all_in_range<signed char>(-126,126));\n\n  CALL_SUBTEST(check_all_in_range<short>(11,11));\n  CALL_SUBTEST(check_all_in_range<short>(11,11+short_offset));\n  CALL_SUBTEST(check_all_in_range<short>(-5,5));\n  CALL_SUBTEST(check_all_in_range<short>(-11-short_offset,-11));\n  CALL_SUBTEST(check_all_in_range<short>(-24345,-24345+short_offset));\n  CALL_SUBTEST(check_all_in_range<short>(24345,24345+short_offset));\n\n  CALL_SUBTEST(check_all_in_range<int>(11,11));\n  CALL_SUBTEST(check_all_in_range<int>(11,11+g_repeat));\n  CALL_SUBTEST(check_all_in_range<int>(-5,5));\n  CALL_SUBTEST(check_all_in_range<int>(-11-g_repeat,-11));\n  CALL_SUBTEST(check_all_in_range<int>(-673456,-673456+g_repeat));\n  CALL_SUBTEST(check_all_in_range<int>(673456,673456+g_repeat));\n\n  CALL_SUBTEST(check_all_in_range<long>(11,11));\n  CALL_SUBTEST(check_all_in_range<long>(11,11+g_repeat));\n  CALL_SUBTEST(check_all_in_range<long>(-5,5));\n  CALL_SUBTEST(check_all_in_range<long>(-11-g_repeat,-11));\n  CALL_SUBTEST(check_all_in_range<long>(-long_ref,-long_ref+g_repeat));\n  CALL_SUBTEST(check_all_in_range<long>( long_ref, long_ref+g_repeat));\n\n  CALL_SUBTEST(check_histogram<int>(-5,5,11));\n  int bins = 100;\n  CALL_SUBTEST(check_histogram<int>(-3333,-3333+bins*(3333/bins)-1,bins));\n  bins = 1000;\n  CALL_SUBTEST(check_histogram<int>(-RAND_MAX+10,-RAND_MAX+10+bins*(RAND_MAX/bins)-1,bins));\n  CALL_SUBTEST(check_histogram<int>(-RAND_MAX+10,-int64(RAND_MAX)+10+bins*(2*int64(RAND_MAX)/bins)-1,bins));\n}\n"
  },
  {
    "path": "include/eigen3/test/real_qz.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Alexey Korepanov <kaikaikai@yandex.ru>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define EIGEN_RUNTIME_NO_MALLOC\n#include \"main.h\"\n#include <limits>\n#include <Eigen/Eigenvalues>\n\ntemplate<typename MatrixType> void real_qz(const MatrixType& m)\n{\n  /* this test covers the following files:\n     RealQZ.h\n  */\n  using std::abs;\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n  \n  Index dim = m.cols();\n  \n  MatrixType A = MatrixType::Random(dim,dim),\n             B = MatrixType::Random(dim,dim);\n\n\n  // Regression test for bug 985: Randomly set rows or columns to zero\n  Index k=internal::random<Index>(0, dim-1);\n  switch(internal::random<int>(0,10)) {\n  case 0:\n    A.row(k).setZero(); break;\n  case 1:\n    A.col(k).setZero(); break;\n  case 2:\n    B.row(k).setZero(); break;\n  case 3:\n    B.col(k).setZero(); break;\n  default:\n    break;\n  }\n\n  RealQZ<MatrixType> qz(dim);\n  // TODO enable full-prealocation of required memory, this probably requires an in-place mode for HessenbergDecomposition\n  //Eigen::internal::set_is_malloc_allowed(false);\n  qz.compute(A,B);\n  //Eigen::internal::set_is_malloc_allowed(true);\n  \n  VERIFY_IS_EQUAL(qz.info(), Success);\n  // check for zeros\n  bool all_zeros = true;\n  for (Index i=0; i<A.cols(); i++)\n    for (Index j=0; j<i; j++) {\n      if (abs(qz.matrixT()(i,j))!=Scalar(0.0))\n      {\n        std::cerr << \"Error: T(\" << i << \",\" << j << \") = \" << qz.matrixT()(i,j) << std::endl;\n        all_zeros = false;\n      }\n      if (j<i-1 && abs(qz.matrixS()(i,j))!=Scalar(0.0))\n      {\n        std::cerr << \"Error: S(\" << i << \",\" << j << \") = \" << qz.matrixS()(i,j) << std::endl;\n        all_zeros = false;\n      }\n      if (j==i-1 && j>0 && abs(qz.matrixS()(i,j))!=Scalar(0.0) && abs(qz.matrixS()(i-1,j-1))!=Scalar(0.0))\n      {\n        std::cerr << \"Error: S(\" << i << \",\" << j << \") = \" << qz.matrixS()(i,j)  << \" && S(\" << i-1 << \",\" << j-1 << \") = \" << qz.matrixS()(i-1,j-1) << std::endl;\n        all_zeros = false;\n      }\n    }\n  VERIFY_IS_EQUAL(all_zeros, true);\n  VERIFY_IS_APPROX(qz.matrixQ()*qz.matrixS()*qz.matrixZ(), A);\n  VERIFY_IS_APPROX(qz.matrixQ()*qz.matrixT()*qz.matrixZ(), B);\n  VERIFY_IS_APPROX(qz.matrixQ()*qz.matrixQ().adjoint(), MatrixType::Identity(dim,dim));\n  VERIFY_IS_APPROX(qz.matrixZ()*qz.matrixZ().adjoint(), MatrixType::Identity(dim,dim));\n}\n\nvoid test_real_qz()\n{\n  int s = 0;\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( real_qz(Matrix4f()) );\n    s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);\n    CALL_SUBTEST_2( real_qz(MatrixXd(s,s)) );\n\n    // some trivial but implementation-wise tricky cases\n    CALL_SUBTEST_2( real_qz(MatrixXd(1,1)) );\n    CALL_SUBTEST_2( real_qz(MatrixXd(2,2)) );\n    CALL_SUBTEST_3( real_qz(Matrix<double,1,1>()) );\n    CALL_SUBTEST_4( real_qz(Matrix2d()) );\n  }\n  \n  TEST_SET_BUT_UNUSED_VARIABLE(s)\n}\n"
  },
  {
    "path": "include/eigen3/test/redux.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define TEST_ENABLE_TEMPORARY_TRACKING\n#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 8\n// ^^ see bug 1449\n\n#include \"main.h\"\n\ntemplate<typename MatrixType> void matrixRedux(const MatrixType& m)\n{\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename MatrixType::RealScalar RealScalar;\n\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  MatrixType m1 = MatrixType::Random(rows, cols);\n\n  // The entries of m1 are uniformly distributed in [0,1], so m1.prod() is very small. This may lead to test\n  // failures if we underflow into denormals. Thus, we scale so that entries are close to 1.\n  MatrixType m1_for_prod = MatrixType::Ones(rows, cols) + RealScalar(0.2) * m1;\n\n  VERIFY_IS_MUCH_SMALLER_THAN(MatrixType::Zero(rows, cols).sum(), Scalar(1));\n  VERIFY_IS_APPROX(MatrixType::Ones(rows, cols).sum(), Scalar(float(rows*cols))); // the float() here to shut up excessive MSVC warning about int->complex conversion being lossy\n  Scalar s(0), p(1), minc(numext::real(m1.coeff(0))), maxc(numext::real(m1.coeff(0)));\n  for(int j = 0; j < cols; j++)\n  for(int i = 0; i < rows; i++)\n  {\n    s += m1(i,j);\n    p *= m1_for_prod(i,j);\n    minc = (std::min)(numext::real(minc), numext::real(m1(i,j)));\n    maxc = (std::max)(numext::real(maxc), numext::real(m1(i,j)));\n  }\n  const Scalar mean = s/Scalar(RealScalar(rows*cols));\n\n  VERIFY_IS_APPROX(m1.sum(), s);\n  VERIFY_IS_APPROX(m1.mean(), mean);\n  VERIFY_IS_APPROX(m1_for_prod.prod(), p);\n  VERIFY_IS_APPROX(m1.real().minCoeff(), numext::real(minc));\n  VERIFY_IS_APPROX(m1.real().maxCoeff(), numext::real(maxc));\n\n  // test slice vectorization assuming assign is ok\n  Index r0 = internal::random<Index>(0,rows-1);\n  Index c0 = internal::random<Index>(0,cols-1);\n  Index r1 = internal::random<Index>(r0+1,rows)-r0;\n  Index c1 = internal::random<Index>(c0+1,cols)-c0;\n  VERIFY_IS_APPROX(m1.block(r0,c0,r1,c1).sum(), m1.block(r0,c0,r1,c1).eval().sum());\n  VERIFY_IS_APPROX(m1.block(r0,c0,r1,c1).mean(), m1.block(r0,c0,r1,c1).eval().mean());\n  VERIFY_IS_APPROX(m1_for_prod.block(r0,c0,r1,c1).prod(), m1_for_prod.block(r0,c0,r1,c1).eval().prod());\n  VERIFY_IS_APPROX(m1.block(r0,c0,r1,c1).real().minCoeff(), m1.block(r0,c0,r1,c1).real().eval().minCoeff());\n  VERIFY_IS_APPROX(m1.block(r0,c0,r1,c1).real().maxCoeff(), m1.block(r0,c0,r1,c1).real().eval().maxCoeff());\n\n  // regression for bug 1090\n  const int R1 = MatrixType::RowsAtCompileTime>=2 ? MatrixType::RowsAtCompileTime/2 : 6;\n  const int C1 = MatrixType::ColsAtCompileTime>=2 ? MatrixType::ColsAtCompileTime/2 : 6;\n  if(R1<=rows-r0 && C1<=cols-c0)\n  {\n    VERIFY_IS_APPROX( (m1.template block<R1,C1>(r0,c0).sum()), m1.block(r0,c0,R1,C1).sum() );\n  }\n  \n  // test empty objects\n  VERIFY_IS_APPROX(m1.block(r0,c0,0,0).sum(),   Scalar(0));\n  VERIFY_IS_APPROX(m1.block(r0,c0,0,0).prod(),  Scalar(1));\n\n  // test nesting complex expression\n  VERIFY_EVALUATION_COUNT( (m1.matrix()*m1.matrix().transpose()).sum(), (MatrixType::IsVectorAtCompileTime && MatrixType::SizeAtCompileTime!=1 ? 0 : 1) );\n  Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> m2(rows,rows);\n  m2.setRandom();\n  VERIFY_EVALUATION_COUNT( ((m1.matrix()*m1.matrix().transpose())+m2).sum(),(MatrixType::IsVectorAtCompileTime && MatrixType::SizeAtCompileTime!=1 ? 0 : 1));\n}\n\ntemplate<typename VectorType> void vectorRedux(const VectorType& w)\n{\n  using std::abs;\n  typedef typename VectorType::Index Index;\n  typedef typename VectorType::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  Index size = w.size();\n\n  VectorType v = VectorType::Random(size);\n  VectorType v_for_prod = VectorType::Ones(size) + Scalar(0.2) * v; // see comment above declaration of m1_for_prod\n\n  for(int i = 1; i < size; i++)\n  {\n    Scalar s(0), p(1);\n    RealScalar minc(numext::real(v.coeff(0))), maxc(numext::real(v.coeff(0)));\n    for(int j = 0; j < i; j++)\n    {\n      s += v[j];\n      p *= v_for_prod[j];\n      minc = (std::min)(minc, numext::real(v[j]));\n      maxc = (std::max)(maxc, numext::real(v[j]));\n    }\n    VERIFY_IS_MUCH_SMALLER_THAN(abs(s - v.head(i).sum()), Scalar(1));\n    VERIFY_IS_APPROX(p, v_for_prod.head(i).prod());\n    VERIFY_IS_APPROX(minc, v.real().head(i).minCoeff());\n    VERIFY_IS_APPROX(maxc, v.real().head(i).maxCoeff());\n  }\n\n  for(int i = 0; i < size-1; i++)\n  {\n    Scalar s(0), p(1);\n    RealScalar minc(numext::real(v.coeff(i))), maxc(numext::real(v.coeff(i)));\n    for(int j = i; j < size; j++)\n    {\n      s += v[j];\n      p *= v_for_prod[j];\n      minc = (std::min)(minc, numext::real(v[j]));\n      maxc = (std::max)(maxc, numext::real(v[j]));\n    }\n    VERIFY_IS_MUCH_SMALLER_THAN(abs(s - v.tail(size-i).sum()), Scalar(1));\n    VERIFY_IS_APPROX(p, v_for_prod.tail(size-i).prod());\n    VERIFY_IS_APPROX(minc, v.real().tail(size-i).minCoeff());\n    VERIFY_IS_APPROX(maxc, v.real().tail(size-i).maxCoeff());\n  }\n\n  for(int i = 0; i < size/2; i++)\n  {\n    Scalar s(0), p(1);\n    RealScalar minc(numext::real(v.coeff(i))), maxc(numext::real(v.coeff(i)));\n    for(int j = i; j < size-i; j++)\n    {\n      s += v[j];\n      p *= v_for_prod[j];\n      minc = (std::min)(minc, numext::real(v[j]));\n      maxc = (std::max)(maxc, numext::real(v[j]));\n    }\n    VERIFY_IS_MUCH_SMALLER_THAN(abs(s - v.segment(i, size-2*i).sum()), Scalar(1));\n    VERIFY_IS_APPROX(p, v_for_prod.segment(i, size-2*i).prod());\n    VERIFY_IS_APPROX(minc, v.real().segment(i, size-2*i).minCoeff());\n    VERIFY_IS_APPROX(maxc, v.real().segment(i, size-2*i).maxCoeff());\n  }\n  \n  // test empty objects\n  VERIFY_IS_APPROX(v.head(0).sum(),   Scalar(0));\n  VERIFY_IS_APPROX(v.tail(0).prod(),  Scalar(1));\n  VERIFY_RAISES_ASSERT(v.head(0).mean());\n  VERIFY_RAISES_ASSERT(v.head(0).minCoeff());\n  VERIFY_RAISES_ASSERT(v.head(0).maxCoeff());\n}\n\nvoid test_redux()\n{\n  // the max size cannot be too large, otherwise reduxion operations obviously generate large errors.\n  int maxsize = (std::min)(100,EIGEN_TEST_MAX_SIZE);\n  TEST_SET_BUT_UNUSED_VARIABLE(maxsize);\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( matrixRedux(Matrix<float, 1, 1>()) );\n    CALL_SUBTEST_1( matrixRedux(Array<float, 1, 1>()) );\n    CALL_SUBTEST_2( matrixRedux(Matrix2f()) );\n    CALL_SUBTEST_2( matrixRedux(Array2f()) );\n    CALL_SUBTEST_2( matrixRedux(Array22f()) );\n    CALL_SUBTEST_3( matrixRedux(Matrix4d()) );\n    CALL_SUBTEST_3( matrixRedux(Array4d()) );\n    CALL_SUBTEST_3( matrixRedux(Array44d()) );\n    CALL_SUBTEST_4( matrixRedux(MatrixXcf(internal::random<int>(1,maxsize), internal::random<int>(1,maxsize))) );\n    CALL_SUBTEST_4( matrixRedux(ArrayXXcf(internal::random<int>(1,maxsize), internal::random<int>(1,maxsize))) );\n    CALL_SUBTEST_5( matrixRedux(MatrixXd (internal::random<int>(1,maxsize), internal::random<int>(1,maxsize))) );\n    CALL_SUBTEST_5( matrixRedux(ArrayXXd (internal::random<int>(1,maxsize), internal::random<int>(1,maxsize))) );\n    CALL_SUBTEST_6( matrixRedux(MatrixXi (internal::random<int>(1,maxsize), internal::random<int>(1,maxsize))) );\n    CALL_SUBTEST_6( matrixRedux(ArrayXXi (internal::random<int>(1,maxsize), internal::random<int>(1,maxsize))) );\n  }\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_7( vectorRedux(Vector4f()) );\n    CALL_SUBTEST_7( vectorRedux(Array4f()) );\n    CALL_SUBTEST_5( vectorRedux(VectorXd(internal::random<int>(1,maxsize))) );\n    CALL_SUBTEST_5( vectorRedux(ArrayXd(internal::random<int>(1,maxsize))) );\n    CALL_SUBTEST_8( vectorRedux(VectorXf(internal::random<int>(1,maxsize))) );\n    CALL_SUBTEST_8( vectorRedux(ArrayXf(internal::random<int>(1,maxsize))) );\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/ref.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 20013 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n// This unit test cannot be easily written to work with EIGEN_DEFAULT_TO_ROW_MAJOR\n#ifdef EIGEN_DEFAULT_TO_ROW_MAJOR\n#undef EIGEN_DEFAULT_TO_ROW_MAJOR\n#endif\n\n#define TEST_ENABLE_TEMPORARY_TRACKING\n#define TEST_CHECK_STATIC_ASSERTIONS\n#include \"main.h\"\n\n// test Ref.h\n\n// Deal with i387 extended precision\n#if EIGEN_ARCH_i386 && !(EIGEN_ARCH_x86_64)\n\n#if EIGEN_COMP_GNUC_STRICT && EIGEN_GNUC_AT_LEAST(4,4)\n#pragma GCC optimize (\"-ffloat-store\")\n#else\n#undef VERIFY_IS_EQUAL\n#define VERIFY_IS_EQUAL(X,Y) VERIFY_IS_APPROX(X,Y)\n#endif\n\n#endif\n\ntemplate<typename MatrixType> void ref_matrix(const MatrixType& m)\n{\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename MatrixType::RealScalar RealScalar;\n  typedef Matrix<Scalar,Dynamic,Dynamic,MatrixType::Options> DynMatrixType;\n  typedef Matrix<RealScalar,Dynamic,Dynamic,MatrixType::Options> RealDynMatrixType;\n  \n  typedef Ref<MatrixType> RefMat;\n  typedef Ref<DynMatrixType> RefDynMat;\n  typedef Ref<const DynMatrixType> ConstRefDynMat;\n  typedef Ref<RealDynMatrixType , 0, Stride<Dynamic,Dynamic> > RefRealMatWithStride;\n\n  Index rows = m.rows(), cols = m.cols();\n  \n  MatrixType  m1 = MatrixType::Random(rows, cols),\n              m2 = m1;\n  \n  Index i = internal::random<Index>(0,rows-1);\n  Index j = internal::random<Index>(0,cols-1);\n  Index brows = internal::random<Index>(1,rows-i);\n  Index bcols = internal::random<Index>(1,cols-j);\n  \n  RefMat rm0 = m1;\n  VERIFY_IS_EQUAL(rm0, m1);\n  RefDynMat rm1 = m1;\n  VERIFY_IS_EQUAL(rm1, m1);\n  RefDynMat rm2 = m1.block(i,j,brows,bcols);\n  VERIFY_IS_EQUAL(rm2, m1.block(i,j,brows,bcols));\n  rm2.setOnes();\n  m2.block(i,j,brows,bcols).setOnes();\n  VERIFY_IS_EQUAL(m1, m2);\n  \n  m2.block(i,j,brows,bcols).setRandom();\n  rm2 = m2.block(i,j,brows,bcols);\n  VERIFY_IS_EQUAL(m1, m2);\n  \n  ConstRefDynMat rm3 = m1.block(i,j,brows,bcols);\n  m1.block(i,j,brows,bcols) *= 2;\n  m2.block(i,j,brows,bcols) *= 2;\n  VERIFY_IS_EQUAL(rm3, m2.block(i,j,brows,bcols));\n  RefRealMatWithStride rm4 = m1.real();\n  VERIFY_IS_EQUAL(rm4, m2.real());\n  rm4.array() += 1;\n  m2.real().array() += 1;\n  VERIFY_IS_EQUAL(m1, m2);\n}\n\ntemplate<typename VectorType> void ref_vector(const VectorType& m)\n{\n  typedef typename VectorType::Index Index;\n  typedef typename VectorType::Scalar Scalar;\n  typedef typename VectorType::RealScalar RealScalar;\n  typedef Matrix<Scalar,Dynamic,1,VectorType::Options> DynMatrixType;\n  typedef Matrix<Scalar,Dynamic,Dynamic,ColMajor> MatrixType;\n  typedef Matrix<RealScalar,Dynamic,1,VectorType::Options> RealDynMatrixType;\n  \n  typedef Ref<VectorType> RefMat;\n  typedef Ref<DynMatrixType> RefDynMat;\n  typedef Ref<const DynMatrixType> ConstRefDynMat;\n  typedef Ref<RealDynMatrixType , 0, InnerStride<> > RefRealMatWithStride;\n  typedef Ref<DynMatrixType , 0, InnerStride<> > RefMatWithStride;\n\n  Index size = m.size();\n  \n  VectorType  v1 = VectorType::Random(size),\n              v2 = v1;\n  MatrixType mat1 = MatrixType::Random(size,size),\n             mat2 = mat1,\n             mat3 = MatrixType::Random(size,size);\n  \n  Index i = internal::random<Index>(0,size-1);\n  Index bsize = internal::random<Index>(1,size-i);\n  \n  RefMat rm0 = v1;\n  VERIFY_IS_EQUAL(rm0, v1);\n  RefDynMat rv1 = v1;\n  VERIFY_IS_EQUAL(rv1, v1);\n  RefDynMat rv2 = v1.segment(i,bsize);\n  VERIFY_IS_EQUAL(rv2, v1.segment(i,bsize));\n  rv2.setOnes();\n  v2.segment(i,bsize).setOnes();\n  VERIFY_IS_EQUAL(v1, v2);\n  \n  v2.segment(i,bsize).setRandom();\n  rv2 = v2.segment(i,bsize);\n  VERIFY_IS_EQUAL(v1, v2);\n  \n  ConstRefDynMat rm3 = v1.segment(i,bsize);\n  v1.segment(i,bsize) *= 2;\n  v2.segment(i,bsize) *= 2;\n  VERIFY_IS_EQUAL(rm3, v2.segment(i,bsize));\n  \n  RefRealMatWithStride rm4 = v1.real();\n  VERIFY_IS_EQUAL(rm4, v2.real());\n  rm4.array() += 1;\n  v2.real().array() += 1;\n  VERIFY_IS_EQUAL(v1, v2);\n  \n  RefMatWithStride rm5 = mat1.row(i).transpose();\n  VERIFY_IS_EQUAL(rm5, mat1.row(i).transpose());\n  rm5.array() += 1;\n  mat2.row(i).array() += 1;\n  VERIFY_IS_EQUAL(mat1, mat2);\n  rm5.noalias() = rm4.transpose() * mat3;\n  mat2.row(i) = v2.real().transpose() * mat3;\n  VERIFY_IS_APPROX(mat1, mat2);\n}\n\ntemplate<typename PlainObjectType> void check_const_correctness(const PlainObjectType&)\n{\n  // verify that ref-to-const don't have LvalueBit\n  typedef typename internal::add_const<PlainObjectType>::type ConstPlainObjectType;\n  VERIFY( !(internal::traits<Ref<ConstPlainObjectType> >::Flags & LvalueBit) );\n  VERIFY( !(internal::traits<Ref<ConstPlainObjectType, Aligned> >::Flags & LvalueBit) );\n  VERIFY( !(Ref<ConstPlainObjectType>::Flags & LvalueBit) );\n  VERIFY( !(Ref<ConstPlainObjectType, Aligned>::Flags & LvalueBit) );\n}\n\ntemplate<typename B>\nEIGEN_DONT_INLINE void call_ref_1(Ref<VectorXf> a, const B &b) { VERIFY_IS_EQUAL(a,b); }\ntemplate<typename B>\nEIGEN_DONT_INLINE void call_ref_2(const Ref<const VectorXf>& a, const B &b) { VERIFY_IS_EQUAL(a,b); }\ntemplate<typename B>\nEIGEN_DONT_INLINE void call_ref_3(Ref<VectorXf,0,InnerStride<> > a, const B &b) { VERIFY_IS_EQUAL(a,b); }\ntemplate<typename B>\nEIGEN_DONT_INLINE void call_ref_4(const Ref<const VectorXf,0,InnerStride<> >& a, const B &b) { VERIFY_IS_EQUAL(a,b); }\ntemplate<typename B>\nEIGEN_DONT_INLINE void call_ref_5(Ref<MatrixXf,0,OuterStride<> > a, const B &b) { VERIFY_IS_EQUAL(a,b); }\ntemplate<typename B>\nEIGEN_DONT_INLINE void call_ref_6(const Ref<const MatrixXf,0,OuterStride<> >& a, const B &b) { VERIFY_IS_EQUAL(a,b); }\ntemplate<typename B>\nEIGEN_DONT_INLINE void call_ref_7(Ref<Matrix<float,Dynamic,3> > a, const B &b) { VERIFY_IS_EQUAL(a,b); }\n\nvoid call_ref()\n{\n  VectorXcf ca  = VectorXcf::Random(10);\n  VectorXf a    = VectorXf::Random(10);\n  RowVectorXf b = RowVectorXf::Random(10);\n  MatrixXf A    = MatrixXf::Random(10,10);\n  RowVector3f c = RowVector3f::Random();\n  const VectorXf& ac(a);\n  VectorBlock<VectorXf> ab(a,0,3);\n  const VectorBlock<VectorXf> abc(a,0,3);\n  \n\n  VERIFY_EVALUATION_COUNT( call_ref_1(a,a), 0);\n  VERIFY_EVALUATION_COUNT( call_ref_1(b,b.transpose()), 0);\n//   call_ref_1(ac,a<c);           // does not compile because ac is const\n  VERIFY_EVALUATION_COUNT( call_ref_1(ab,ab), 0);\n  VERIFY_EVALUATION_COUNT( call_ref_1(a.head(4),a.head(4)), 0);\n  VERIFY_EVALUATION_COUNT( call_ref_1(abc,abc), 0);\n  VERIFY_EVALUATION_COUNT( call_ref_1(A.col(3),A.col(3)), 0);\n//   call_ref_1(A.row(3),A.row(3));    // does not compile because innerstride!=1\n  VERIFY_EVALUATION_COUNT( call_ref_3(A.row(3),A.row(3).transpose()), 0);\n  VERIFY_EVALUATION_COUNT( call_ref_4(A.row(3),A.row(3).transpose()), 0);\n//   call_ref_1(a+a, a+a);          // does not compile for obvious reason\n\n  MatrixXf tmp = A*A.col(1);\n  VERIFY_EVALUATION_COUNT( call_ref_2(A*A.col(1), tmp), 1);     // evaluated into a temp\n  VERIFY_EVALUATION_COUNT( call_ref_2(ac.head(5),ac.head(5)), 0);\n  VERIFY_EVALUATION_COUNT( call_ref_2(ac,ac), 0);\n  VERIFY_EVALUATION_COUNT( call_ref_2(a,a), 0);\n  VERIFY_EVALUATION_COUNT( call_ref_2(ab,ab), 0);\n  VERIFY_EVALUATION_COUNT( call_ref_2(a.head(4),a.head(4)), 0);\n  tmp = a+a;\n  VERIFY_EVALUATION_COUNT( call_ref_2(a+a,tmp), 1);            // evaluated into a temp\n  VERIFY_EVALUATION_COUNT( call_ref_2(ca.imag(),ca.imag()), 1);      // evaluated into a temp\n\n  VERIFY_EVALUATION_COUNT( call_ref_4(ac.head(5),ac.head(5)), 0);\n  tmp = a+a;\n  VERIFY_EVALUATION_COUNT( call_ref_4(a+a,tmp), 1);           // evaluated into a temp\n  VERIFY_EVALUATION_COUNT( call_ref_4(ca.imag(),ca.imag()), 0);\n\n  VERIFY_EVALUATION_COUNT( call_ref_5(a,a), 0);\n  VERIFY_EVALUATION_COUNT( call_ref_5(a.head(3),a.head(3)), 0);\n  VERIFY_EVALUATION_COUNT( call_ref_5(A,A), 0);\n//   call_ref_5(A.transpose(),A.transpose());   // does not compile because storage order does not match\n  VERIFY_EVALUATION_COUNT( call_ref_5(A.block(1,1,2,2),A.block(1,1,2,2)), 0);\n  VERIFY_EVALUATION_COUNT( call_ref_5(b,b), 0);             // storage order do not match, but this is a degenerate case that should work\n  VERIFY_EVALUATION_COUNT( call_ref_5(a.row(3),a.row(3)), 0);\n\n  VERIFY_EVALUATION_COUNT( call_ref_6(a,a), 0);\n  VERIFY_EVALUATION_COUNT( call_ref_6(a.head(3),a.head(3)), 0);\n  VERIFY_EVALUATION_COUNT( call_ref_6(A.row(3),A.row(3)), 1);           // evaluated into a temp thouth it could be avoided by viewing it as a 1xn matrix\n  tmp = A+A;\n  VERIFY_EVALUATION_COUNT( call_ref_6(A+A,tmp), 1);                // evaluated into a temp\n  VERIFY_EVALUATION_COUNT( call_ref_6(A,A), 0);\n  VERIFY_EVALUATION_COUNT( call_ref_6(A.transpose(),A.transpose()), 1);      // evaluated into a temp because the storage orders do not match\n  VERIFY_EVALUATION_COUNT( call_ref_6(A.block(1,1,2,2),A.block(1,1,2,2)), 0);\n  \n  VERIFY_EVALUATION_COUNT( call_ref_7(c,c), 0);\n}\n\ntypedef Matrix<double,Dynamic,Dynamic,RowMajor> RowMatrixXd;\nint test_ref_overload_fun1(Ref<MatrixXd> )       { return 1; }\nint test_ref_overload_fun1(Ref<RowMatrixXd> )    { return 2; }\nint test_ref_overload_fun1(Ref<MatrixXf> )       { return 3; }\n\nint test_ref_overload_fun2(Ref<const MatrixXd> ) { return 4; }\nint test_ref_overload_fun2(Ref<const MatrixXf> ) { return 5; }\n\nvoid test_ref_ambiguous(const Ref<const ArrayXd> &A, Ref<ArrayXd> B)\n{\n  B = A;\n  B = A - A;\n}\n\n// See also bug 969\nvoid test_ref_overloads()\n{\n  MatrixXd Ad, Bd;\n  RowMatrixXd rAd, rBd;\n  VERIFY( test_ref_overload_fun1(Ad)==1 );\n  VERIFY( test_ref_overload_fun1(rAd)==2 );\n  \n  MatrixXf Af, Bf;\n  VERIFY( test_ref_overload_fun2(Ad)==4 );\n  VERIFY( test_ref_overload_fun2(Ad+Bd)==4 );\n  VERIFY( test_ref_overload_fun2(Af+Bf)==5 );\n  \n  ArrayXd A, B;\n  test_ref_ambiguous(A, B);\n}\n\nvoid test_ref_fixed_size_assert()\n{\n  Vector4f v4;\n  VectorXf vx(10);\n  VERIFY_RAISES_STATIC_ASSERT( Ref<Vector3f> y = v4; (void)y; );\n  VERIFY_RAISES_STATIC_ASSERT( Ref<Vector3f> y = vx.head<4>(); (void)y; );\n  VERIFY_RAISES_STATIC_ASSERT( Ref<const Vector3f> y = v4; (void)y; );\n  VERIFY_RAISES_STATIC_ASSERT( Ref<const Vector3f> y = vx.head<4>(); (void)y; );\n  VERIFY_RAISES_STATIC_ASSERT( Ref<const Vector3f> y = 2*v4; (void)y; );\n}\n\nvoid test_ref()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( ref_vector(Matrix<float, 1, 1>()) );\n    CALL_SUBTEST_1( check_const_correctness(Matrix<float, 1, 1>()) );\n    CALL_SUBTEST_2( ref_vector(Vector4d()) );\n    CALL_SUBTEST_2( check_const_correctness(Matrix4d()) );\n    CALL_SUBTEST_3( ref_vector(Vector4cf()) );\n    CALL_SUBTEST_4( ref_vector(VectorXcf(8)) );\n    CALL_SUBTEST_5( ref_vector(VectorXi(12)) );\n    CALL_SUBTEST_5( check_const_correctness(VectorXi(12)) );\n\n    CALL_SUBTEST_1( ref_matrix(Matrix<float, 1, 1>()) );\n    CALL_SUBTEST_2( ref_matrix(Matrix4d()) );\n    CALL_SUBTEST_1( ref_matrix(Matrix<float,3,5>()) );\n    CALL_SUBTEST_4( ref_matrix(MatrixXcf(internal::random<int>(1,10),internal::random<int>(1,10))) );\n    CALL_SUBTEST_4( ref_matrix(Matrix<std::complex<double>,10,15>()) );\n    CALL_SUBTEST_5( ref_matrix(MatrixXi(internal::random<int>(1,10),internal::random<int>(1,10))) );\n    CALL_SUBTEST_6( call_ref() );\n  }\n  \n  CALL_SUBTEST_7( test_ref_overloads() );\n  CALL_SUBTEST_7( test_ref_fixed_size_assert() );\n}\n"
  },
  {
    "path": "include/eigen3/test/resize.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Keir Mierle <mierle@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\ntemplate<DenseIndex rows, DenseIndex cols>\nvoid resizeLikeTest()\n{\n  MatrixXf A(rows, cols);\n  MatrixXf B;\n  Matrix<double, rows, cols> C;\n  B.resizeLike(A);\n  C.resizeLike(B);  // Shouldn't crash.\n  VERIFY(B.rows() == rows && B.cols() == cols);\n\n  VectorXf x(rows);\n  RowVectorXf y;\n  y.resizeLike(x);\n  VERIFY(y.rows() == 1 && y.cols() == rows);\n\n  y.resize(cols);\n  x.resizeLike(y);\n  VERIFY(x.rows() == cols && x.cols() == 1);\n}\n\nvoid resizeLikeTest12() { resizeLikeTest<1,2>(); }\nvoid resizeLikeTest1020() { resizeLikeTest<10,20>(); }\nvoid resizeLikeTest31() { resizeLikeTest<3,1>(); }\n\nvoid test_resize()\n{\n  CALL_SUBTEST(resizeLikeTest12() );\n  CALL_SUBTEST(resizeLikeTest1020() );\n  CALL_SUBTEST(resizeLikeTest31() );\n}\n"
  },
  {
    "path": "include/eigen3/test/rvalue_types.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2013 Hauke Heibel <hauke.heibel@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/Core>\n\nusing internal::UIntPtr;\n\n#if EIGEN_HAS_RVALUE_REFERENCES\ntemplate <typename MatrixType>\nvoid rvalue_copyassign(const MatrixType& m)\n{\n\n  typedef typename internal::traits<MatrixType>::Scalar Scalar;\n  \n  // create a temporary which we are about to destroy by moving\n  MatrixType tmp = m;\n  UIntPtr src_address = reinterpret_cast<UIntPtr>(tmp.data());\n  \n  // move the temporary to n\n  MatrixType n = std::move(tmp);\n  UIntPtr dst_address = reinterpret_cast<UIntPtr>(n.data());\n\n  if (MatrixType::RowsAtCompileTime==Dynamic|| MatrixType::ColsAtCompileTime==Dynamic)\n  {\n    // verify that we actually moved the guts\n    VERIFY_IS_EQUAL(src_address, dst_address);\n  }\n\n  // verify that the content did not change\n  Scalar abs_diff = (m-n).array().abs().sum();\n  VERIFY_IS_EQUAL(abs_diff, Scalar(0));\n}\n#else\ntemplate <typename MatrixType>\nvoid rvalue_copyassign(const MatrixType&) {}\n#endif\n\nvoid test_rvalue_types()\n{\n  CALL_SUBTEST_1(rvalue_copyassign( MatrixXf::Random(50,50).eval() ));\n  CALL_SUBTEST_1(rvalue_copyassign( ArrayXXf::Random(50,50).eval() ));\n\n  CALL_SUBTEST_1(rvalue_copyassign( Matrix<float,1,Dynamic>::Random(50).eval() ));\n  CALL_SUBTEST_1(rvalue_copyassign( Array<float,1,Dynamic>::Random(50).eval() ));\n\n  CALL_SUBTEST_1(rvalue_copyassign( Matrix<float,Dynamic,1>::Random(50).eval() ));\n  CALL_SUBTEST_1(rvalue_copyassign( Array<float,Dynamic,1>::Random(50).eval() ));\n  \n  CALL_SUBTEST_2(rvalue_copyassign( Array<float,2,1>::Random().eval() ));\n  CALL_SUBTEST_2(rvalue_copyassign( Array<float,3,1>::Random().eval() ));\n  CALL_SUBTEST_2(rvalue_copyassign( Array<float,4,1>::Random().eval() ));\n\n  CALL_SUBTEST_2(rvalue_copyassign( Array<float,2,2>::Random().eval() ));\n  CALL_SUBTEST_2(rvalue_copyassign( Array<float,3,3>::Random().eval() ));\n  CALL_SUBTEST_2(rvalue_copyassign( Array<float,4,4>::Random().eval() ));\n}\n"
  },
  {
    "path": "include/eigen3/test/schur_complex.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <limits>\n#include <Eigen/Eigenvalues>\n\ntemplate<typename MatrixType> void schur(int size = MatrixType::ColsAtCompileTime)\n{\n  typedef typename ComplexSchur<MatrixType>::ComplexScalar ComplexScalar;\n  typedef typename ComplexSchur<MatrixType>::ComplexMatrixType ComplexMatrixType;\n\n  // Test basic functionality: T is triangular and A = U T U*\n  for(int counter = 0; counter < g_repeat; ++counter) {\n    MatrixType A = MatrixType::Random(size, size);\n    ComplexSchur<MatrixType> schurOfA(A);\n    VERIFY_IS_EQUAL(schurOfA.info(), Success);\n    ComplexMatrixType U = schurOfA.matrixU();\n    ComplexMatrixType T = schurOfA.matrixT();\n    for(int row = 1; row < size; ++row) {\n      for(int col = 0; col < row; ++col) {\n        VERIFY(T(row,col) == (typename MatrixType::Scalar)0);\n      }\n    }\n    VERIFY_IS_APPROX(A.template cast<ComplexScalar>(), U * T * U.adjoint());\n  }\n\n  // Test asserts when not initialized\n  ComplexSchur<MatrixType> csUninitialized;\n  VERIFY_RAISES_ASSERT(csUninitialized.matrixT());\n  VERIFY_RAISES_ASSERT(csUninitialized.matrixU());\n  VERIFY_RAISES_ASSERT(csUninitialized.info());\n  \n  // Test whether compute() and constructor returns same result\n  MatrixType A = MatrixType::Random(size, size);\n  ComplexSchur<MatrixType> cs1;\n  cs1.compute(A);\n  ComplexSchur<MatrixType> cs2(A);\n  VERIFY_IS_EQUAL(cs1.info(), Success);\n  VERIFY_IS_EQUAL(cs2.info(), Success);\n  VERIFY_IS_EQUAL(cs1.matrixT(), cs2.matrixT());\n  VERIFY_IS_EQUAL(cs1.matrixU(), cs2.matrixU());\n\n  // Test maximum number of iterations\n  ComplexSchur<MatrixType> cs3;\n  cs3.setMaxIterations(ComplexSchur<MatrixType>::m_maxIterationsPerRow * size).compute(A);\n  VERIFY_IS_EQUAL(cs3.info(), Success);\n  VERIFY_IS_EQUAL(cs3.matrixT(), cs1.matrixT());\n  VERIFY_IS_EQUAL(cs3.matrixU(), cs1.matrixU());\n  cs3.setMaxIterations(1).compute(A);\n  VERIFY_IS_EQUAL(cs3.info(), size > 1 ? NoConvergence : Success);\n  VERIFY_IS_EQUAL(cs3.getMaxIterations(), 1);\n\n  MatrixType Atriangular = A;\n  Atriangular.template triangularView<StrictlyLower>().setZero(); \n  cs3.setMaxIterations(1).compute(Atriangular); // triangular matrices do not need any iterations\n  VERIFY_IS_EQUAL(cs3.info(), Success);\n  VERIFY_IS_EQUAL(cs3.matrixT(), Atriangular.template cast<ComplexScalar>());\n  VERIFY_IS_EQUAL(cs3.matrixU(), ComplexMatrixType::Identity(size, size));\n\n  // Test computation of only T, not U\n  ComplexSchur<MatrixType> csOnlyT(A, false);\n  VERIFY_IS_EQUAL(csOnlyT.info(), Success);\n  VERIFY_IS_EQUAL(cs1.matrixT(), csOnlyT.matrixT());\n  VERIFY_RAISES_ASSERT(csOnlyT.matrixU());\n\n  if (size > 1 && size < 20)\n  {\n    // Test matrix with NaN\n    A(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();\n    ComplexSchur<MatrixType> csNaN(A);\n    VERIFY_IS_EQUAL(csNaN.info(), NoConvergence);\n  }\n}\n\nvoid test_schur_complex()\n{\n  CALL_SUBTEST_1(( schur<Matrix4cd>() ));\n  CALL_SUBTEST_2(( schur<MatrixXcf>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4)) ));\n  CALL_SUBTEST_3(( schur<Matrix<std::complex<float>, 1, 1> >() ));\n  CALL_SUBTEST_4(( schur<Matrix<float, 3, 3, Eigen::RowMajor> >() ));\n\n  // Test problem size constructors\n  CALL_SUBTEST_5(ComplexSchur<MatrixXf>(10));\n}\n"
  },
  {
    "path": "include/eigen3/test/schur_real.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <limits>\n#include <Eigen/Eigenvalues>\n\ntemplate<typename MatrixType> void verifyIsQuasiTriangular(const MatrixType& T)\n{\n  typedef typename MatrixType::Index Index;\n\n  const Index size = T.cols();\n  typedef typename MatrixType::Scalar Scalar;\n\n  // Check T is lower Hessenberg\n  for(int row = 2; row < size; ++row) {\n    for(int col = 0; col < row - 1; ++col) {\n      VERIFY(T(row,col) == Scalar(0));\n    }\n  }\n\n  // Check that any non-zero on the subdiagonal is followed by a zero and is\n  // part of a 2x2 diagonal block with imaginary eigenvalues.\n  for(int row = 1; row < size; ++row) {\n    if (T(row,row-1) != Scalar(0)) {\n      VERIFY(row == size-1 || T(row+1,row) == 0);\n      Scalar tr = T(row-1,row-1) + T(row,row);\n      Scalar det = T(row-1,row-1) * T(row,row) - T(row-1,row) * T(row,row-1);\n      VERIFY(4 * det > tr * tr);\n    }\n  }\n}\n\ntemplate<typename MatrixType> void schur(int size = MatrixType::ColsAtCompileTime)\n{\n  // Test basic functionality: T is quasi-triangular and A = U T U*\n  for(int counter = 0; counter < g_repeat; ++counter) {\n    MatrixType A = MatrixType::Random(size, size);\n    RealSchur<MatrixType> schurOfA(A);\n    VERIFY_IS_EQUAL(schurOfA.info(), Success);\n    MatrixType U = schurOfA.matrixU();\n    MatrixType T = schurOfA.matrixT();\n    verifyIsQuasiTriangular(T);\n    VERIFY_IS_APPROX(A, U * T * U.transpose());\n  }\n\n  // Test asserts when not initialized\n  RealSchur<MatrixType> rsUninitialized;\n  VERIFY_RAISES_ASSERT(rsUninitialized.matrixT());\n  VERIFY_RAISES_ASSERT(rsUninitialized.matrixU());\n  VERIFY_RAISES_ASSERT(rsUninitialized.info());\n  \n  // Test whether compute() and constructor returns same result\n  MatrixType A = MatrixType::Random(size, size);\n  RealSchur<MatrixType> rs1;\n  rs1.compute(A);\n  RealSchur<MatrixType> rs2(A);\n  VERIFY_IS_EQUAL(rs1.info(), Success);\n  VERIFY_IS_EQUAL(rs2.info(), Success);\n  VERIFY_IS_EQUAL(rs1.matrixT(), rs2.matrixT());\n  VERIFY_IS_EQUAL(rs1.matrixU(), rs2.matrixU());\n\n  // Test maximum number of iterations\n  RealSchur<MatrixType> rs3;\n  rs3.setMaxIterations(RealSchur<MatrixType>::m_maxIterationsPerRow * size).compute(A);\n  VERIFY_IS_EQUAL(rs3.info(), Success);\n  VERIFY_IS_EQUAL(rs3.matrixT(), rs1.matrixT());\n  VERIFY_IS_EQUAL(rs3.matrixU(), rs1.matrixU());\n  if (size > 2) {\n    rs3.setMaxIterations(1).compute(A);\n    VERIFY_IS_EQUAL(rs3.info(), NoConvergence);\n    VERIFY_IS_EQUAL(rs3.getMaxIterations(), 1);\n  }\n\n  MatrixType Atriangular = A;\n  Atriangular.template triangularView<StrictlyLower>().setZero(); \n  rs3.setMaxIterations(1).compute(Atriangular); // triangular matrices do not need any iterations\n  VERIFY_IS_EQUAL(rs3.info(), Success);\n  VERIFY_IS_APPROX(rs3.matrixT(), Atriangular); // approx because of scaling...\n  VERIFY_IS_EQUAL(rs3.matrixU(), MatrixType::Identity(size, size));\n\n  // Test computation of only T, not U\n  RealSchur<MatrixType> rsOnlyT(A, false);\n  VERIFY_IS_EQUAL(rsOnlyT.info(), Success);\n  VERIFY_IS_EQUAL(rs1.matrixT(), rsOnlyT.matrixT());\n  VERIFY_RAISES_ASSERT(rsOnlyT.matrixU());\n\n  if (size > 2 && size < 20)\n  {\n    // Test matrix with NaN\n    A(0,0) = std::numeric_limits<typename MatrixType::Scalar>::quiet_NaN();\n    RealSchur<MatrixType> rsNaN(A);\n    VERIFY_IS_EQUAL(rsNaN.info(), NoConvergence);\n  }\n}\n\nvoid test_schur_real()\n{\n  CALL_SUBTEST_1(( schur<Matrix4f>() ));\n  CALL_SUBTEST_2(( schur<MatrixXd>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4)) ));\n  CALL_SUBTEST_3(( schur<Matrix<float, 1, 1> >() ));\n  CALL_SUBTEST_4(( schur<Matrix<double, 3, 3, Eigen::RowMajor> >() ));\n\n  // Test problem size constructors\n  CALL_SUBTEST_5(RealSchur<MatrixXf>(10));\n}\n"
  },
  {
    "path": "include/eigen3/test/selfadjoint.cpp",
    "content": "// This file is triangularView of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define TEST_CHECK_STATIC_ASSERTIONS\n#include \"main.h\"\n\n// This file tests the basic selfadjointView API,\n// the related products and decompositions are tested in specific files.\n\ntemplate<typename MatrixType> void selfadjoint(const MatrixType& m)\n{\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  MatrixType m1 = MatrixType::Random(rows, cols),\n             m2 = MatrixType::Random(rows, cols),\n             m3(rows, cols),\n             m4(rows, cols);\n\n  m1.diagonal() = m1.diagonal().real().template cast<Scalar>();\n\n  // check selfadjoint to dense\n  m3 = m1.template selfadjointView<Upper>();\n  VERIFY_IS_APPROX(MatrixType(m3.template triangularView<Upper>()), MatrixType(m1.template triangularView<Upper>()));\n  VERIFY_IS_APPROX(m3, m3.adjoint());\n\n  m3 = m1.template selfadjointView<Lower>();\n  VERIFY_IS_APPROX(MatrixType(m3.template triangularView<Lower>()), MatrixType(m1.template triangularView<Lower>()));\n  VERIFY_IS_APPROX(m3, m3.adjoint());\n\n  m3 = m1.template selfadjointView<Upper>();\n  m4 = m2;\n  m4 += m1.template selfadjointView<Upper>();\n  VERIFY_IS_APPROX(m4, m2+m3);\n\n  m3 = m1.template selfadjointView<Lower>();\n  m4 = m2;\n  m4 -= m1.template selfadjointView<Lower>();\n  VERIFY_IS_APPROX(m4, m2-m3);\n\n  VERIFY_RAISES_STATIC_ASSERT(m2.template selfadjointView<StrictlyUpper>());\n  VERIFY_RAISES_STATIC_ASSERT(m2.template selfadjointView<UnitLower>());\n}\n\nvoid bug_159()\n{\n  Matrix3d m = Matrix3d::Random().selfadjointView<Lower>();\n  EIGEN_UNUSED_VARIABLE(m)\n}\n\nvoid test_selfadjoint()\n{\n  for(int i = 0; i < g_repeat ; i++)\n  {\n    int s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE);\n\n    CALL_SUBTEST_1( selfadjoint(Matrix<float, 1, 1>()) );\n    CALL_SUBTEST_2( selfadjoint(Matrix<float, 2, 2>()) );\n    CALL_SUBTEST_3( selfadjoint(Matrix3cf()) );\n    CALL_SUBTEST_4( selfadjoint(MatrixXcd(s,s)) );\n    CALL_SUBTEST_5( selfadjoint(Matrix<float,Dynamic,Dynamic,RowMajor>(s, s)) );\n    \n    TEST_SET_BUT_UNUSED_VARIABLE(s)\n  }\n  \n  CALL_SUBTEST_1( bug_159() );\n}\n"
  },
  {
    "path": "include/eigen3/test/simplicial_cholesky.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2011 Gael Guennebaud <g.gael@free.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"sparse_solver.h\"\n\ntemplate<typename T, typename I> void test_simplicial_cholesky_T()\n{\n  typedef SparseMatrix<T,0,I> SparseMatrixType;\n  SimplicialCholesky<SparseMatrixType, Lower> chol_colmajor_lower_amd;\n  SimplicialCholesky<SparseMatrixType, Upper> chol_colmajor_upper_amd;\n  SimplicialLLT<     SparseMatrixType, Lower> llt_colmajor_lower_amd;\n  SimplicialLLT<     SparseMatrixType, Upper> llt_colmajor_upper_amd;\n  SimplicialLDLT<    SparseMatrixType, Lower> ldlt_colmajor_lower_amd;\n  SimplicialLDLT<    SparseMatrixType, Upper> ldlt_colmajor_upper_amd;\n  SimplicialLDLT<    SparseMatrixType, Lower, NaturalOrdering<I> > ldlt_colmajor_lower_nat;\n  SimplicialLDLT<    SparseMatrixType, Upper, NaturalOrdering<I> > ldlt_colmajor_upper_nat;\n\n  check_sparse_spd_solving(chol_colmajor_lower_amd);\n  check_sparse_spd_solving(chol_colmajor_upper_amd);\n  check_sparse_spd_solving(llt_colmajor_lower_amd);\n  check_sparse_spd_solving(llt_colmajor_upper_amd);\n  check_sparse_spd_solving(ldlt_colmajor_lower_amd);\n  check_sparse_spd_solving(ldlt_colmajor_upper_amd);\n  \n  check_sparse_spd_determinant(chol_colmajor_lower_amd);\n  check_sparse_spd_determinant(chol_colmajor_upper_amd);\n  check_sparse_spd_determinant(llt_colmajor_lower_amd);\n  check_sparse_spd_determinant(llt_colmajor_upper_amd);\n  check_sparse_spd_determinant(ldlt_colmajor_lower_amd);\n  check_sparse_spd_determinant(ldlt_colmajor_upper_amd);\n  \n  check_sparse_spd_solving(ldlt_colmajor_lower_nat, 300, 1000);\n  check_sparse_spd_solving(ldlt_colmajor_upper_nat, 300, 1000);\n}\n\nvoid test_simplicial_cholesky()\n{\n  CALL_SUBTEST_1(( test_simplicial_cholesky_T<double,int>() ));\n  CALL_SUBTEST_2(( test_simplicial_cholesky_T<std::complex<double>, int>() ));\n  CALL_SUBTEST_3(( test_simplicial_cholesky_T<double,long int>() ));\n}\n"
  },
  {
    "path": "include/eigen3/test/sizeof.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\ntemplate<typename MatrixType> void verifySizeOf(const MatrixType&)\n{\n  typedef typename MatrixType::Scalar Scalar;\n  if (MatrixType::RowsAtCompileTime!=Dynamic && MatrixType::ColsAtCompileTime!=Dynamic)\n    VERIFY_IS_EQUAL(std::ptrdiff_t(sizeof(MatrixType)),std::ptrdiff_t(sizeof(Scalar))*std::ptrdiff_t(MatrixType::SizeAtCompileTime));\n  else\n    VERIFY_IS_EQUAL(sizeof(MatrixType),sizeof(Scalar*) + 2 * sizeof(typename MatrixType::Index));\n}\n\nvoid test_sizeof()\n{\n  CALL_SUBTEST(verifySizeOf(Matrix<float, 1, 1>()) );\n  CALL_SUBTEST(verifySizeOf(Array<float, 2, 1>()) );\n  CALL_SUBTEST(verifySizeOf(Array<float, 3, 1>()) );\n  CALL_SUBTEST(verifySizeOf(Array<float, 4, 1>()) );\n  CALL_SUBTEST(verifySizeOf(Array<float, 5, 1>()) );\n  CALL_SUBTEST(verifySizeOf(Array<float, 6, 1>()) );\n  CALL_SUBTEST(verifySizeOf(Array<float, 7, 1>()) );\n  CALL_SUBTEST(verifySizeOf(Array<float, 8, 1>()) );\n  CALL_SUBTEST(verifySizeOf(Array<float, 9, 1>()) );\n  CALL_SUBTEST(verifySizeOf(Array<float, 10, 1>()) );\n  CALL_SUBTEST(verifySizeOf(Array<float, 11, 1>()) );\n  CALL_SUBTEST(verifySizeOf(Array<float, 12, 1>()) );\n  CALL_SUBTEST(verifySizeOf(Vector2d()) );\n  CALL_SUBTEST(verifySizeOf(Vector4f()) );\n  CALL_SUBTEST(verifySizeOf(Matrix4d()) );\n  CALL_SUBTEST(verifySizeOf(Matrix<double, 4, 2>()) );\n  CALL_SUBTEST(verifySizeOf(Matrix<bool, 7, 5>()) );\n  CALL_SUBTEST(verifySizeOf(MatrixXcf(3, 3)) );\n  CALL_SUBTEST(verifySizeOf(MatrixXi(8, 12)) );\n  CALL_SUBTEST(verifySizeOf(MatrixXcd(20, 20)) );\n  CALL_SUBTEST(verifySizeOf(Matrix<float, 100, 100>()) );\n  \n  VERIFY(sizeof(std::complex<float>) == 2*sizeof(float));\n  VERIFY(sizeof(std::complex<double>) == 2*sizeof(double));\n}\n"
  },
  {
    "path": "include/eigen3/test/sizeoverflow.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2011 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#define VERIFY_THROWS_BADALLOC(a) {                           \\\n    bool threw = false;                                       \\\n    try {                                                     \\\n      a;                                                      \\\n    }                                                         \\\n    catch (std::bad_alloc&) { threw = true; }                 \\\n    VERIFY(threw && \"should have thrown bad_alloc: \" #a);     \\\n  }\n\ntemplate<typename MatrixType>\nvoid triggerMatrixBadAlloc(Index rows, Index cols)\n{\n  VERIFY_THROWS_BADALLOC( MatrixType m(rows, cols) );\n  VERIFY_THROWS_BADALLOC( MatrixType m; m.resize(rows, cols) );\n  VERIFY_THROWS_BADALLOC( MatrixType m; m.conservativeResize(rows, cols) );\n}\n\ntemplate<typename VectorType>\nvoid triggerVectorBadAlloc(Index size)\n{\n  VERIFY_THROWS_BADALLOC( VectorType v(size) );\n  VERIFY_THROWS_BADALLOC( VectorType v; v.resize(size) );\n  VERIFY_THROWS_BADALLOC( VectorType v; v.conservativeResize(size) );\n}\n\nvoid test_sizeoverflow()\n{\n  // there are 2 levels of overflow checking. first in PlainObjectBase.h we check for overflow in rows*cols computations.\n  // this is tested in tests of the form times_itself_gives_0 * times_itself_gives_0\n  // Then in Memory.h we check for overflow in size * sizeof(T) computations.\n  // this is tested in tests of the form times_4_gives_0 * sizeof(float)\n  \n  size_t times_itself_gives_0 = size_t(1) << (8 * sizeof(Index) / 2);\n  VERIFY(times_itself_gives_0 * times_itself_gives_0 == 0);\n\n  size_t times_4_gives_0 = size_t(1) << (8 * sizeof(Index) - 2);\n  VERIFY(times_4_gives_0 * 4 == 0);\n\n  size_t times_8_gives_0 = size_t(1) << (8 * sizeof(Index) - 3);\n  VERIFY(times_8_gives_0 * 8 == 0);\n\n  triggerMatrixBadAlloc<MatrixXf>(times_itself_gives_0, times_itself_gives_0);\n  triggerMatrixBadAlloc<MatrixXf>(times_itself_gives_0 / 4, times_itself_gives_0);\n  triggerMatrixBadAlloc<MatrixXf>(times_4_gives_0, 1);\n\n  triggerMatrixBadAlloc<MatrixXd>(times_itself_gives_0, times_itself_gives_0);\n  triggerMatrixBadAlloc<MatrixXd>(times_itself_gives_0 / 8, times_itself_gives_0);\n  triggerMatrixBadAlloc<MatrixXd>(times_8_gives_0, 1);\n  \n  triggerVectorBadAlloc<VectorXf>(times_4_gives_0);\n  \n  triggerVectorBadAlloc<VectorXd>(times_8_gives_0);\n}\n"
  },
  {
    "path": "include/eigen3/test/smallvectors.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define EIGEN_NO_STATIC_ASSERT\n#include \"main.h\"\n\ntemplate<typename Scalar> void smallVectors()\n{\n  typedef Matrix<Scalar, 1, 2> V2;\n  typedef Matrix<Scalar, 3, 1> V3;\n  typedef Matrix<Scalar, 1, 4> V4;\n  typedef Matrix<Scalar, Dynamic, 1> VX;\n  Scalar x1 = internal::random<Scalar>(),\n         x2 = internal::random<Scalar>(),\n         x3 = internal::random<Scalar>(),\n         x4 = internal::random<Scalar>();\n  V2 v2(x1, x2);\n  V3 v3(x1, x2, x3);\n  V4 v4(x1, x2, x3, x4);\n  VERIFY_IS_APPROX(x1, v2.x());\n  VERIFY_IS_APPROX(x1, v3.x());\n  VERIFY_IS_APPROX(x1, v4.x());\n  VERIFY_IS_APPROX(x2, v2.y());\n  VERIFY_IS_APPROX(x2, v3.y());\n  VERIFY_IS_APPROX(x2, v4.y());\n  VERIFY_IS_APPROX(x3, v3.z());\n  VERIFY_IS_APPROX(x3, v4.z());\n  VERIFY_IS_APPROX(x4, v4.w());\n\n  if (!NumTraits<Scalar>::IsInteger)\n  {\n    VERIFY_RAISES_ASSERT(V3(2, 1))\n    VERIFY_RAISES_ASSERT(V3(3, 2))\n    VERIFY_RAISES_ASSERT(V3(Scalar(3), 1))\n    VERIFY_RAISES_ASSERT(V3(3, Scalar(1)))\n    VERIFY_RAISES_ASSERT(V3(Scalar(3), Scalar(1)))\n    VERIFY_RAISES_ASSERT(V3(Scalar(123), Scalar(123)))\n\n    VERIFY_RAISES_ASSERT(V4(1, 3))\n    VERIFY_RAISES_ASSERT(V4(2, 4))\n    VERIFY_RAISES_ASSERT(V4(1, Scalar(4)))\n    VERIFY_RAISES_ASSERT(V4(Scalar(1), 4))\n    VERIFY_RAISES_ASSERT(V4(Scalar(1), Scalar(4)))\n    VERIFY_RAISES_ASSERT(V4(Scalar(123), Scalar(123)))\n\n    VERIFY_RAISES_ASSERT(VX(3, 2))\n    VERIFY_RAISES_ASSERT(VX(Scalar(3), 1))\n    VERIFY_RAISES_ASSERT(VX(3, Scalar(1)))\n    VERIFY_RAISES_ASSERT(VX(Scalar(3), Scalar(1)))\n    VERIFY_RAISES_ASSERT(VX(Scalar(123), Scalar(123)))\n  }\n}\n\nvoid test_smallvectors()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST(smallVectors<int>() );\n    CALL_SUBTEST(smallVectors<float>() );\n    CALL_SUBTEST(smallVectors<double>() );\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/sparse.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_TESTSPARSE_H\n#define EIGEN_TESTSPARSE_H\n\n#define EIGEN_YES_I_KNOW_SPARSE_MODULE_IS_NOT_STABLE_YET\n\n#include \"main.h\"\n\n#if EIGEN_GNUC_AT_LEAST(4,0) && !defined __ICC && !defined(__clang__)\n\n#ifdef min\n#undef min\n#endif\n\n#ifdef max\n#undef max\n#endif\n\n#include <tr1/unordered_map>\n#define EIGEN_UNORDERED_MAP_SUPPORT\nnamespace std {\n  using std::tr1::unordered_map;\n}\n#endif\n\n#ifdef EIGEN_GOOGLEHASH_SUPPORT\n  #include <google/sparse_hash_map>\n#endif\n\n#include <Eigen/Cholesky>\n#include <Eigen/LU>\n#include <Eigen/Sparse>\n\nenum {\n  ForceNonZeroDiag = 1,\n  MakeLowerTriangular = 2,\n  MakeUpperTriangular = 4,\n  ForceRealDiag = 8\n};\n\n/* Initializes both a sparse and dense matrix with same random values,\n * and a ratio of \\a density non zero entries.\n * \\param flags is a union of ForceNonZeroDiag, MakeLowerTriangular and MakeUpperTriangular\n *        allowing to control the shape of the matrix.\n * \\param zeroCoords and nonzeroCoords allows to get the coordinate lists of the non zero,\n *        and zero coefficients respectively.\n */\ntemplate<typename Scalar,int Opt1,int Opt2,typename StorageIndex> void\ninitSparse(double density,\n           Matrix<Scalar,Dynamic,Dynamic,Opt1>& refMat,\n           SparseMatrix<Scalar,Opt2,StorageIndex>& sparseMat,\n           int flags = 0,\n           std::vector<Matrix<StorageIndex,2,1> >* zeroCoords = 0,\n           std::vector<Matrix<StorageIndex,2,1> >* nonzeroCoords = 0)\n{\n  enum { IsRowMajor = SparseMatrix<Scalar,Opt2,StorageIndex>::IsRowMajor };\n  sparseMat.setZero();\n  //sparseMat.reserve(int(refMat.rows()*refMat.cols()*density));\n  sparseMat.reserve(VectorXi::Constant(IsRowMajor ? refMat.rows() : refMat.cols(), int((1.5*density)*(IsRowMajor?refMat.cols():refMat.rows()))));\n  \n  for(Index j=0; j<sparseMat.outerSize(); j++)\n  {\n    //sparseMat.startVec(j);\n    for(Index i=0; i<sparseMat.innerSize(); i++)\n    {\n      Index ai(i), aj(j);\n      if(IsRowMajor)\n        std::swap(ai,aj);\n      Scalar v = (internal::random<double>(0,1) < density) ? internal::random<Scalar>() : Scalar(0);\n      if ((flags&ForceNonZeroDiag) && (i==j))\n      {\n        // FIXME: the following is too conservative\n        v = internal::random<Scalar>()*Scalar(3.);\n        v = v*v;\n        if(numext::real(v)>0) v += Scalar(5);\n        else                  v -= Scalar(5);\n      }\n      if ((flags & MakeLowerTriangular) && aj>ai)\n        v = Scalar(0);\n      else if ((flags & MakeUpperTriangular) && aj<ai)\n        v = Scalar(0);\n\n      if ((flags&ForceRealDiag) && (i==j))\n        v = numext::real(v);\n\n      if (v!=Scalar(0))\n      {\n        //sparseMat.insertBackByOuterInner(j,i) = v;\n        sparseMat.insertByOuterInner(j,i) = v;\n        if (nonzeroCoords)\n          nonzeroCoords->push_back(Matrix<StorageIndex,2,1> (ai,aj));\n      }\n      else if (zeroCoords)\n      {\n        zeroCoords->push_back(Matrix<StorageIndex,2,1> (ai,aj));\n      }\n      refMat(ai,aj) = v;\n    }\n  }\n  //sparseMat.finalize();\n}\n\ntemplate<typename Scalar,int Opt1,int Opt2,typename Index> void\ninitSparse(double density,\n           Matrix<Scalar,Dynamic,Dynamic, Opt1>& refMat,\n           DynamicSparseMatrix<Scalar, Opt2, Index>& sparseMat,\n           int flags = 0,\n           std::vector<Matrix<Index,2,1> >* zeroCoords = 0,\n           std::vector<Matrix<Index,2,1> >* nonzeroCoords = 0)\n{\n  enum { IsRowMajor = DynamicSparseMatrix<Scalar,Opt2,Index>::IsRowMajor };\n  sparseMat.setZero();\n  sparseMat.reserve(int(refMat.rows()*refMat.cols()*density));\n  for(int j=0; j<sparseMat.outerSize(); j++)\n  {\n    sparseMat.startVec(j); // not needed for DynamicSparseMatrix\n    for(int i=0; i<sparseMat.innerSize(); i++)\n    {\n      int ai(i), aj(j);\n      if(IsRowMajor)\n        std::swap(ai,aj);\n      Scalar v = (internal::random<double>(0,1) < density) ? internal::random<Scalar>() : Scalar(0);\n      if ((flags&ForceNonZeroDiag) && (i==j))\n      {\n        v = internal::random<Scalar>()*Scalar(3.);\n        v = v*v + Scalar(5.);\n      }\n      if ((flags & MakeLowerTriangular) && aj>ai)\n        v = Scalar(0);\n      else if ((flags & MakeUpperTriangular) && aj<ai)\n        v = Scalar(0);\n\n      if ((flags&ForceRealDiag) && (i==j))\n        v = numext::real(v);\n\n      if (v!=Scalar(0))\n      {\n        sparseMat.insertBackByOuterInner(j,i) = v;\n        if (nonzeroCoords)\n          nonzeroCoords->push_back(Matrix<Index,2,1> (ai,aj));\n      }\n      else if (zeroCoords)\n      {\n        zeroCoords->push_back(Matrix<Index,2,1> (ai,aj));\n      }\n      refMat(ai,aj) = v;\n    }\n  }\n  sparseMat.finalize();\n}\n\ntemplate<typename Scalar,int Options,typename Index> void\ninitSparse(double density,\n           Matrix<Scalar,Dynamic,1>& refVec,\n           SparseVector<Scalar,Options,Index>& sparseVec,\n           std::vector<int>* zeroCoords = 0,\n           std::vector<int>* nonzeroCoords = 0)\n{\n  sparseVec.reserve(int(refVec.size()*density));\n  sparseVec.setZero();\n  for(int i=0; i<refVec.size(); i++)\n  {\n    Scalar v = (internal::random<double>(0,1) < density) ? internal::random<Scalar>() : Scalar(0);\n    if (v!=Scalar(0))\n    {\n      sparseVec.insertBack(i) = v;\n      if (nonzeroCoords)\n        nonzeroCoords->push_back(i);\n    }\n    else if (zeroCoords)\n        zeroCoords->push_back(i);\n    refVec[i] = v;\n  }\n}\n\ntemplate<typename Scalar,int Options,typename Index> void\ninitSparse(double density,\n           Matrix<Scalar,1,Dynamic>& refVec,\n           SparseVector<Scalar,Options,Index>& sparseVec,\n           std::vector<int>* zeroCoords = 0,\n           std::vector<int>* nonzeroCoords = 0)\n{\n  sparseVec.reserve(int(refVec.size()*density));\n  sparseVec.setZero();\n  for(int i=0; i<refVec.size(); i++)\n  {\n    Scalar v = (internal::random<double>(0,1) < density) ? internal::random<Scalar>() : Scalar(0);\n    if (v!=Scalar(0))\n    {\n      sparseVec.insertBack(i) = v;\n      if (nonzeroCoords)\n        nonzeroCoords->push_back(i);\n    }\n    else if (zeroCoords)\n        zeroCoords->push_back(i);\n    refVec[i] = v;\n  }\n}\n\n\n#include <unsupported/Eigen/SparseExtra>\n#endif // EIGEN_TESTSPARSE_H\n"
  },
  {
    "path": "include/eigen3/test/sparseLM.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Desire Nuentsa <desire.nuentsa_wakam@inria.fr>\n// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n#include <iostream>\n#include <fstream>\n#include <iomanip>\n\n#include \"main.h\"\n#include <Eigen/LevenbergMarquardt>\n\nusing namespace std;\nusing namespace Eigen;\n\ntemplate <typename Scalar>\nstruct sparseGaussianTest : SparseFunctor<Scalar, int>\n{\n  typedef Matrix<Scalar,Dynamic,1> VectorType;\n  typedef SparseFunctor<Scalar,int> Base;\n  typedef typename Base::JacobianType JacobianType;\n  sparseGaussianTest(int inputs, int values) : SparseFunctor<Scalar,int>(inputs,values)\n  { }\n  \n  VectorType model(const VectorType& uv, VectorType& x)\n  {\n    VectorType y; //Change this to use expression template\n    int m = Base::values(); \n    int n = Base::inputs();\n    eigen_assert(uv.size()%2 == 0);\n    eigen_assert(uv.size() == n);\n    eigen_assert(x.size() == m);\n    y.setZero(m);\n    int half = n/2;\n    VectorBlock<const VectorType> u(uv, 0, half);\n    VectorBlock<const VectorType> v(uv, half, half);\n    Scalar coeff;\n    for (int j = 0; j < m; j++)\n    {\n      for (int i = 0; i < half; i++) \n      {\n        coeff = (x(j)-i)/v(i);\n        coeff *= coeff;\n        if (coeff < 1. && coeff > 0.)\n          y(j) += u(i)*std::pow((1-coeff), 2);\n      }\n    }\n    return y;\n  }\n  void initPoints(VectorType& uv_ref, VectorType& x)\n  {\n    m_x = x;\n    m_y = this->model(uv_ref,x);\n  }\n  int operator()(const VectorType& uv, VectorType& fvec)\n  {\n    int m = Base::values(); \n    int n = Base::inputs();\n    eigen_assert(uv.size()%2 == 0);\n    eigen_assert(uv.size() == n);\n    int half = n/2;\n    VectorBlock<const VectorType> u(uv, 0, half);\n    VectorBlock<const VectorType> v(uv, half, half);\n    fvec = m_y;\n    Scalar coeff;\n    for (int j = 0; j < m; j++)\n    {\n      for (int i = 0; i < half; i++)\n      {\n        coeff = (m_x(j)-i)/v(i);\n        coeff *= coeff;\n        if (coeff < 1. && coeff > 0.)\n          fvec(j) -= u(i)*std::pow((1-coeff), 2);\n      }\n    }\n    return 0;\n  }\n  \n  int df(const VectorType& uv, JacobianType& fjac)\n  {\n    int m = Base::values(); \n    int n = Base::inputs();\n    eigen_assert(n == uv.size());\n    eigen_assert(fjac.rows() == m);\n    eigen_assert(fjac.cols() == n);\n    int half = n/2;\n    VectorBlock<const VectorType> u(uv, 0, half);\n    VectorBlock<const VectorType> v(uv, half, half);\n    Scalar coeff;\n    \n    //Derivatives with respect to u\n    for (int col = 0; col < half; col++)\n    {\n      for (int row = 0; row < m; row++)\n      {\n        coeff = (m_x(row)-col)/v(col);\n          coeff = coeff*coeff;\n        if(coeff < 1. && coeff > 0.)\n        {\n          fjac.coeffRef(row,col) = -(1-coeff)*(1-coeff);\n        }\n      }\n    }\n    //Derivatives with respect to v\n    for (int col = 0; col < half; col++)\n    {\n      for (int row = 0; row < m; row++)\n      {\n        coeff = (m_x(row)-col)/v(col);\n        coeff = coeff*coeff;\n        if(coeff < 1. && coeff > 0.)\n        {\n          fjac.coeffRef(row,col+half) = -4 * (u(col)/v(col))*coeff*(1-coeff);\n        }\n      }\n    }\n    return 0;\n  }\n  \n  VectorType m_x, m_y; //Data points\n};\n\n\ntemplate<typename T>\nvoid test_sparseLM_T()\n{\n  typedef Matrix<T,Dynamic,1> VectorType;\n  \n  int inputs = 10;\n  int values = 2000;\n  sparseGaussianTest<T> sparse_gaussian(inputs, values);\n  VectorType uv(inputs),uv_ref(inputs);\n  VectorType x(values);\n  // Generate the reference solution \n  uv_ref << -2, 1, 4 ,8, 6, 1.8, 1.2, 1.1, 1.9 , 3;\n  //Generate the reference data points\n  x.setRandom();\n  x = 10*x;\n  x.array() += 10;\n  sparse_gaussian.initPoints(uv_ref, x);\n  \n  \n  // Generate the initial parameters \n  VectorBlock<VectorType> u(uv, 0, inputs/2); \n  VectorBlock<VectorType> v(uv, inputs/2, inputs/2);\n  v.setOnes();\n  //Generate u or Solve for u from v\n  u.setOnes();\n  \n  // Solve the optimization problem\n  LevenbergMarquardt<sparseGaussianTest<T> > lm(sparse_gaussian);\n  int info;\n//   info = lm.minimize(uv);\n  \n  VERIFY_IS_EQUAL(info,1);\n    // Do a step by step solution and save the residual \n  int maxiter = 200;\n  int iter = 0;\n  MatrixXd Err(values, maxiter);\n  MatrixXd Mod(values, maxiter);\n  LevenbergMarquardtSpace::Status status; \n  status = lm.minimizeInit(uv);\n  if (status==LevenbergMarquardtSpace::ImproperInputParameters)\n      return ;\n\n}\nvoid test_sparseLM()\n{\n  CALL_SUBTEST_1(test_sparseLM_T<double>());\n  \n  // CALL_SUBTEST_2(test_sparseLM_T<std::complex<double>());\n}\n"
  },
  {
    "path": "include/eigen3/test/sparse_basic.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2008 Daniel Gomez Ferro <dgomezferro@gmail.com>\n// Copyright (C) 2013 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\nstatic long g_realloc_count = 0;\n#define EIGEN_SPARSE_COMPRESSED_STORAGE_REALLOCATE_PLUGIN g_realloc_count++;\n\n#include \"sparse.h\"\n\ntemplate<typename SparseMatrixType> void sparse_basic(const SparseMatrixType& ref)\n{\n  typedef typename SparseMatrixType::StorageIndex StorageIndex;\n  typedef Matrix<StorageIndex,2,1> Vector2;\n  \n  const Index rows = ref.rows();\n  const Index cols = ref.cols();\n  //const Index inner = ref.innerSize();\n  //const Index outer = ref.outerSize();\n\n  typedef typename SparseMatrixType::Scalar Scalar;\n  typedef typename SparseMatrixType::RealScalar RealScalar;\n  enum { Flags = SparseMatrixType::Flags };\n\n  double density = (std::max)(8./(rows*cols), 0.01);\n  typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;\n  typedef Matrix<Scalar,Dynamic,1> DenseVector;\n  Scalar eps = 1e-6;\n\n  Scalar s1 = internal::random<Scalar>();\n  {\n    SparseMatrixType m(rows, cols);\n    DenseMatrix refMat = DenseMatrix::Zero(rows, cols);\n    DenseVector vec1 = DenseVector::Random(rows);\n\n    std::vector<Vector2> zeroCoords;\n    std::vector<Vector2> nonzeroCoords;\n    initSparse<Scalar>(density, refMat, m, 0, &zeroCoords, &nonzeroCoords);\n\n    // test coeff and coeffRef\n    for (std::size_t i=0; i<zeroCoords.size(); ++i)\n    {\n      VERIFY_IS_MUCH_SMALLER_THAN( m.coeff(zeroCoords[i].x(),zeroCoords[i].y()), eps );\n      if(internal::is_same<SparseMatrixType,SparseMatrix<Scalar,Flags> >::value)\n        VERIFY_RAISES_ASSERT( m.coeffRef(zeroCoords[i].x(),zeroCoords[i].y()) = 5 );\n    }\n    VERIFY_IS_APPROX(m, refMat);\n\n    if(!nonzeroCoords.empty()) {\n      m.coeffRef(nonzeroCoords[0].x(), nonzeroCoords[0].y()) = Scalar(5);\n      refMat.coeffRef(nonzeroCoords[0].x(), nonzeroCoords[0].y()) = Scalar(5);\n    }\n\n    VERIFY_IS_APPROX(m, refMat);\n\n      // test assertion\n      VERIFY_RAISES_ASSERT( m.coeffRef(-1,1) = 0 );\n      VERIFY_RAISES_ASSERT( m.coeffRef(0,m.cols()) = 0 );\n    }\n\n    // test insert (inner random)\n    {\n      DenseMatrix m1(rows,cols);\n      m1.setZero();\n      SparseMatrixType m2(rows,cols);\n      bool call_reserve = internal::random<int>()%2;\n      Index nnz = internal::random<int>(1,int(rows)/2);\n      if(call_reserve)\n      {\n        if(internal::random<int>()%2)\n          m2.reserve(VectorXi::Constant(m2.outerSize(), int(nnz)));\n        else\n          m2.reserve(m2.outerSize() * nnz);\n      }\n      g_realloc_count = 0;\n      for (Index j=0; j<cols; ++j)\n      {\n        for (Index k=0; k<nnz; ++k)\n        {\n          Index i = internal::random<Index>(0,rows-1);\n          if (m1.coeff(i,j)==Scalar(0))\n            m2.insert(i,j) = m1(i,j) = internal::random<Scalar>();\n        }\n      }\n      \n      if(call_reserve && !SparseMatrixType::IsRowMajor)\n      {\n        VERIFY(g_realloc_count==0);\n      }\n      \n      m2.finalize();\n      VERIFY_IS_APPROX(m2,m1);\n    }\n\n    // test insert (fully random)\n    {\n      DenseMatrix m1(rows,cols);\n      m1.setZero();\n      SparseMatrixType m2(rows,cols);\n      if(internal::random<int>()%2)\n        m2.reserve(VectorXi::Constant(m2.outerSize(), 2));\n      for (int k=0; k<rows*cols; ++k)\n      {\n        Index i = internal::random<Index>(0,rows-1);\n        Index j = internal::random<Index>(0,cols-1);\n        if ((m1.coeff(i,j)==Scalar(0)) && (internal::random<int>()%2))\n          m2.insert(i,j) = m1(i,j) = internal::random<Scalar>();\n        else\n        {\n          Scalar v = internal::random<Scalar>();\n          m2.coeffRef(i,j) += v;\n          m1(i,j) += v;\n        }\n      }\n      VERIFY_IS_APPROX(m2,m1);\n    }\n    \n    // test insert (un-compressed)\n    for(int mode=0;mode<4;++mode)\n    {\n      DenseMatrix m1(rows,cols);\n      m1.setZero();\n      SparseMatrixType m2(rows,cols);\n      VectorXi r(VectorXi::Constant(m2.outerSize(), ((mode%2)==0) ? int(m2.innerSize()) : std::max<int>(1,int(m2.innerSize())/8)));\n      m2.reserve(r);\n      for (Index k=0; k<rows*cols; ++k)\n      {\n        Index i = internal::random<Index>(0,rows-1);\n        Index j = internal::random<Index>(0,cols-1);\n        if (m1.coeff(i,j)==Scalar(0))\n          m2.insert(i,j) = m1(i,j) = internal::random<Scalar>();\n        if(mode==3)\n          m2.reserve(r);\n      }\n      if(internal::random<int>()%2)\n        m2.makeCompressed();\n      VERIFY_IS_APPROX(m2,m1);\n    }\n\n  // test basic computations\n  {\n    DenseMatrix refM1 = DenseMatrix::Zero(rows, cols);\n    DenseMatrix refM2 = DenseMatrix::Zero(rows, cols);\n    DenseMatrix refM3 = DenseMatrix::Zero(rows, cols);\n    DenseMatrix refM4 = DenseMatrix::Zero(rows, cols);\n    SparseMatrixType m1(rows, cols);\n    SparseMatrixType m2(rows, cols);\n    SparseMatrixType m3(rows, cols);\n    SparseMatrixType m4(rows, cols);\n    initSparse<Scalar>(density, refM1, m1);\n    initSparse<Scalar>(density, refM2, m2);\n    initSparse<Scalar>(density, refM3, m3);\n    initSparse<Scalar>(density, refM4, m4);\n\n    if(internal::random<bool>())\n      m1.makeCompressed();\n\n    Index m1_nnz = m1.nonZeros();\n\n    VERIFY_IS_APPROX(m1*s1, refM1*s1);\n    VERIFY_IS_APPROX(m1+m2, refM1+refM2);\n    VERIFY_IS_APPROX(m1+m2+m3, refM1+refM2+refM3);\n    VERIFY_IS_APPROX(m3.cwiseProduct(m1+m2), refM3.cwiseProduct(refM1+refM2));\n    VERIFY_IS_APPROX(m1*s1-m2, refM1*s1-refM2);\n    VERIFY_IS_APPROX(m4=m1/s1, refM1/s1);\n    VERIFY_IS_EQUAL(m4.nonZeros(), m1_nnz);\n\n    if(SparseMatrixType::IsRowMajor)\n      VERIFY_IS_APPROX(m1.innerVector(0).dot(refM2.row(0)), refM1.row(0).dot(refM2.row(0)));\n    else\n      VERIFY_IS_APPROX(m1.innerVector(0).dot(refM2.col(0)), refM1.col(0).dot(refM2.col(0)));\n\n    DenseVector rv = DenseVector::Random(m1.cols());\n    DenseVector cv = DenseVector::Random(m1.rows());\n    Index r = internal::random<Index>(0,m1.rows()-2);\n    Index c = internal::random<Index>(0,m1.cols()-1);\n    VERIFY_IS_APPROX(( m1.template block<1,Dynamic>(r,0,1,m1.cols()).dot(rv)) , refM1.row(r).dot(rv));\n    VERIFY_IS_APPROX(m1.row(r).dot(rv), refM1.row(r).dot(rv));\n    VERIFY_IS_APPROX(m1.col(c).dot(cv), refM1.col(c).dot(cv));\n\n    VERIFY_IS_APPROX(m1.conjugate(), refM1.conjugate());\n    VERIFY_IS_APPROX(m1.real(), refM1.real());\n\n    refM4.setRandom();\n    // sparse cwise* dense\n    VERIFY_IS_APPROX(m3.cwiseProduct(refM4), refM3.cwiseProduct(refM4));\n    // dense cwise* sparse\n    VERIFY_IS_APPROX(refM4.cwiseProduct(m3), refM4.cwiseProduct(refM3));\n//     VERIFY_IS_APPROX(m3.cwise()/refM4, refM3.cwise()/refM4);\n\n    VERIFY_IS_APPROX(refM4 + m3, refM4 + refM3);\n    VERIFY_IS_APPROX(m3 + refM4, refM3 + refM4);\n    VERIFY_IS_APPROX(refM4 - m3, refM4 - refM3);\n    VERIFY_IS_APPROX(m3 - refM4, refM3 - refM4);\n    VERIFY_IS_APPROX((RealScalar(0.5)*refM4 + RealScalar(0.5)*m3).eval(), RealScalar(0.5)*refM4 + RealScalar(0.5)*refM3);\n    VERIFY_IS_APPROX((RealScalar(0.5)*refM4 + m3*RealScalar(0.5)).eval(), RealScalar(0.5)*refM4 + RealScalar(0.5)*refM3);\n    VERIFY_IS_APPROX((RealScalar(0.5)*refM4 + m3.cwiseProduct(m3)).eval(), RealScalar(0.5)*refM4 + refM3.cwiseProduct(refM3));\n\n    VERIFY_IS_APPROX((RealScalar(0.5)*refM4 + RealScalar(0.5)*m3).eval(), RealScalar(0.5)*refM4 + RealScalar(0.5)*refM3);\n    VERIFY_IS_APPROX((RealScalar(0.5)*refM4 + m3*RealScalar(0.5)).eval(), RealScalar(0.5)*refM4 + RealScalar(0.5)*refM3);\n    VERIFY_IS_APPROX((RealScalar(0.5)*refM4 + (m3+m3)).eval(), RealScalar(0.5)*refM4 + (refM3+refM3));\n    VERIFY_IS_APPROX(((refM3+m3)+RealScalar(0.5)*m3).eval(), RealScalar(0.5)*refM3 + (refM3+refM3));\n    VERIFY_IS_APPROX((RealScalar(0.5)*refM4 + (refM3+m3)).eval(), RealScalar(0.5)*refM4 + (refM3+refM3));\n    VERIFY_IS_APPROX((RealScalar(0.5)*refM4 + (m3+refM3)).eval(), RealScalar(0.5)*refM4 + (refM3+refM3));\n\n\n    VERIFY_IS_APPROX(m1.sum(), refM1.sum());\n\n    m4 = m1; refM4 = m4;\n\n    VERIFY_IS_APPROX(m1*=s1, refM1*=s1);\n    VERIFY_IS_EQUAL(m1.nonZeros(), m1_nnz);\n    VERIFY_IS_APPROX(m1/=s1, refM1/=s1);\n    VERIFY_IS_EQUAL(m1.nonZeros(), m1_nnz);\n\n    VERIFY_IS_APPROX(m1+=m2, refM1+=refM2);\n    VERIFY_IS_APPROX(m1-=m2, refM1-=refM2);\n\n    if (rows>=2 && cols>=2)\n    {\n      VERIFY_RAISES_ASSERT( m1 += m1.innerVector(0) );\n      VERIFY_RAISES_ASSERT( m1 -= m1.innerVector(0) );\n      VERIFY_RAISES_ASSERT( refM1 -= m1.innerVector(0) );\n      VERIFY_RAISES_ASSERT( refM1 += m1.innerVector(0) );\n    }\n    m1 = m4; refM1 = refM4;\n\n    // test aliasing\n    VERIFY_IS_APPROX((m1 = -m1), (refM1 = -refM1));\n    VERIFY_IS_EQUAL(m1.nonZeros(), m1_nnz);\n    m1 = m4; refM1 = refM4;\n    VERIFY_IS_APPROX((m1 = m1.transpose()), (refM1 = refM1.transpose().eval()));\n    VERIFY_IS_EQUAL(m1.nonZeros(), m1_nnz);\n    m1 = m4; refM1 = refM4;\n    VERIFY_IS_APPROX((m1 = -m1.transpose()), (refM1 = -refM1.transpose().eval()));\n    VERIFY_IS_EQUAL(m1.nonZeros(), m1_nnz);\n    m1 = m4; refM1 = refM4;\n    VERIFY_IS_APPROX((m1 += -m1), (refM1 += -refM1));\n    VERIFY_IS_EQUAL(m1.nonZeros(), m1_nnz);\n    m1 = m4; refM1 = refM4;\n\n    if(m1.isCompressed())\n    {\n      VERIFY_IS_APPROX(m1.coeffs().sum(), m1.sum());\n      m1.coeffs() += s1;\n      for(Index j = 0; j<m1.outerSize(); ++j)\n        for(typename SparseMatrixType::InnerIterator it(m1,j); it; ++it)\n          refM1(it.row(), it.col()) += s1;\n      VERIFY_IS_APPROX(m1, refM1);\n    }\n\n    // and/or\n    {\n      typedef SparseMatrix<bool, SparseMatrixType::Options, typename SparseMatrixType::StorageIndex> SpBool;\n      SpBool mb1 = m1.real().template cast<bool>();\n      SpBool mb2 = m2.real().template cast<bool>();\n      VERIFY_IS_EQUAL(mb1.template cast<int>().sum(), refM1.real().template cast<bool>().count());\n      VERIFY_IS_EQUAL((mb1 && mb2).template cast<int>().sum(), (refM1.real().template cast<bool>() && refM2.real().template cast<bool>()).count());\n      VERIFY_IS_EQUAL((mb1 || mb2).template cast<int>().sum(), (refM1.real().template cast<bool>() || refM2.real().template cast<bool>()).count());\n      SpBool mb3 = mb1 && mb2;\n      if(mb1.coeffs().all() && mb2.coeffs().all())\n      {\n        VERIFY_IS_EQUAL(mb3.nonZeros(), (refM1.real().template cast<bool>() && refM2.real().template cast<bool>()).count());\n      }\n    }\n  }\n\n  // test reverse iterators\n  {\n    DenseMatrix refMat2 = DenseMatrix::Zero(rows, cols);\n    SparseMatrixType m2(rows, cols);\n    initSparse<Scalar>(density, refMat2, m2);\n    std::vector<Scalar> ref_value(m2.innerSize());\n    std::vector<Index> ref_index(m2.innerSize());\n    if(internal::random<bool>())\n      m2.makeCompressed();\n    for(Index j = 0; j<m2.outerSize(); ++j)\n    {\n      Index count_forward = 0;\n\n      for(typename SparseMatrixType::InnerIterator it(m2,j); it; ++it)\n      {\n        ref_value[ref_value.size()-1-count_forward] = it.value();\n        ref_index[ref_index.size()-1-count_forward] = it.index();\n        count_forward++;\n      }\n      Index count_reverse = 0;\n      for(typename SparseMatrixType::ReverseInnerIterator it(m2,j); it; --it)\n      {\n        VERIFY_IS_APPROX( std::abs(ref_value[ref_value.size()-count_forward+count_reverse])+1, std::abs(it.value())+1);\n        VERIFY_IS_EQUAL( ref_index[ref_index.size()-count_forward+count_reverse] , it.index());\n        count_reverse++;\n      }\n      VERIFY_IS_EQUAL(count_forward, count_reverse);\n    }\n  }\n\n  // test transpose\n  {\n    DenseMatrix refMat2 = DenseMatrix::Zero(rows, cols);\n    SparseMatrixType m2(rows, cols);\n    initSparse<Scalar>(density, refMat2, m2);\n    VERIFY_IS_APPROX(m2.transpose().eval(), refMat2.transpose().eval());\n    VERIFY_IS_APPROX(m2.transpose(), refMat2.transpose());\n\n    VERIFY_IS_APPROX(SparseMatrixType(m2.adjoint()), refMat2.adjoint());\n    \n    // check isApprox handles opposite storage order\n    typename Transpose<SparseMatrixType>::PlainObject m3(m2);\n    VERIFY(m2.isApprox(m3));\n  }\n\n  // test prune\n  {\n    SparseMatrixType m2(rows, cols);\n    DenseMatrix refM2(rows, cols);\n    refM2.setZero();\n    int countFalseNonZero = 0;\n    int countTrueNonZero = 0;\n    m2.reserve(VectorXi::Constant(m2.outerSize(), int(m2.innerSize())));\n    for (Index j=0; j<m2.cols(); ++j)\n    {\n      for (Index i=0; i<m2.rows(); ++i)\n      {\n        float x = internal::random<float>(0,1);\n        if (x<0.1f)\n        {\n          // do nothing\n        }\n        else if (x<0.5f)\n        {\n          countFalseNonZero++;\n          m2.insert(i,j) = Scalar(0);\n        }\n        else\n        {\n          countTrueNonZero++;\n          m2.insert(i,j) = Scalar(1);\n          refM2(i,j) = Scalar(1);\n        }\n      }\n    }\n    if(internal::random<bool>())\n      m2.makeCompressed();\n    VERIFY(countFalseNonZero+countTrueNonZero == m2.nonZeros());\n    if(countTrueNonZero>0)\n      VERIFY_IS_APPROX(m2, refM2);\n    m2.prune(Scalar(1));\n    VERIFY(countTrueNonZero==m2.nonZeros());\n    VERIFY_IS_APPROX(m2, refM2);\n  }\n\n  // test setFromTriplets\n  {\n    typedef Triplet<Scalar,StorageIndex> TripletType;\n    std::vector<TripletType> triplets;\n    Index ntriplets = rows*cols;\n    triplets.reserve(ntriplets);\n    DenseMatrix refMat_sum  = DenseMatrix::Zero(rows,cols);\n    DenseMatrix refMat_prod = DenseMatrix::Zero(rows,cols);\n    DenseMatrix refMat_last = DenseMatrix::Zero(rows,cols);\n\n    for(Index i=0;i<ntriplets;++i)\n    {\n      StorageIndex r = internal::random<StorageIndex>(0,StorageIndex(rows-1));\n      StorageIndex c = internal::random<StorageIndex>(0,StorageIndex(cols-1));\n      Scalar v = internal::random<Scalar>();\n      triplets.push_back(TripletType(r,c,v));\n      refMat_sum(r,c) += v;\n      if(std::abs(refMat_prod(r,c))==0)\n        refMat_prod(r,c) = v;\n      else\n        refMat_prod(r,c) *= v;\n      refMat_last(r,c) = v;\n    }\n    SparseMatrixType m(rows,cols);\n    m.setFromTriplets(triplets.begin(), triplets.end());\n    VERIFY_IS_APPROX(m, refMat_sum);\n\n    m.setFromTriplets(triplets.begin(), triplets.end(), std::multiplies<Scalar>());\n    VERIFY_IS_APPROX(m, refMat_prod);\n#if (defined(__cplusplus) && __cplusplus >= 201103L)\n    m.setFromTriplets(triplets.begin(), triplets.end(), [] (Scalar,Scalar b) { return b; });\n    VERIFY_IS_APPROX(m, refMat_last);\n#endif\n  }\n  \n  // test Map\n  {\n    DenseMatrix refMat2(rows, cols), refMat3(rows, cols);\n    SparseMatrixType m2(rows, cols), m3(rows, cols);\n    initSparse<Scalar>(density, refMat2, m2);\n    initSparse<Scalar>(density, refMat3, m3);\n    {\n      Map<SparseMatrixType> mapMat2(m2.rows(), m2.cols(), m2.nonZeros(), m2.outerIndexPtr(), m2.innerIndexPtr(), m2.valuePtr(), m2.innerNonZeroPtr());\n      Map<SparseMatrixType> mapMat3(m3.rows(), m3.cols(), m3.nonZeros(), m3.outerIndexPtr(), m3.innerIndexPtr(), m3.valuePtr(), m3.innerNonZeroPtr());\n      VERIFY_IS_APPROX(mapMat2+mapMat3, refMat2+refMat3);\n      VERIFY_IS_APPROX(mapMat2+mapMat3, refMat2+refMat3);\n    }\n    {\n      MappedSparseMatrix<Scalar,SparseMatrixType::Options,StorageIndex> mapMat2(m2.rows(), m2.cols(), m2.nonZeros(), m2.outerIndexPtr(), m2.innerIndexPtr(), m2.valuePtr(), m2.innerNonZeroPtr());\n      MappedSparseMatrix<Scalar,SparseMatrixType::Options,StorageIndex> mapMat3(m3.rows(), m3.cols(), m3.nonZeros(), m3.outerIndexPtr(), m3.innerIndexPtr(), m3.valuePtr(), m3.innerNonZeroPtr());\n      VERIFY_IS_APPROX(mapMat2+mapMat3, refMat2+refMat3);\n      VERIFY_IS_APPROX(mapMat2+mapMat3, refMat2+refMat3);\n    }\n\n    Index i = internal::random<Index>(0,rows-1);\n    Index j = internal::random<Index>(0,cols-1);\n    m2.coeffRef(i,j) = 123;\n    if(internal::random<bool>())\n      m2.makeCompressed();\n    Map<SparseMatrixType> mapMat2(rows, cols, m2.nonZeros(), m2.outerIndexPtr(), m2.innerIndexPtr(), m2.valuePtr(),  m2.innerNonZeroPtr());\n    VERIFY_IS_EQUAL(m2.coeff(i,j),Scalar(123));\n    VERIFY_IS_EQUAL(mapMat2.coeff(i,j),Scalar(123));\n    mapMat2.coeffRef(i,j) = -123;\n    VERIFY_IS_EQUAL(m2.coeff(i,j),Scalar(-123));\n  }\n\n  // test triangularView\n  {\n    DenseMatrix refMat2(rows, cols), refMat3(rows, cols);\n    SparseMatrixType m2(rows, cols), m3(rows, cols);\n    initSparse<Scalar>(density, refMat2, m2);\n    refMat3 = refMat2.template triangularView<Lower>();\n    m3 = m2.template triangularView<Lower>();\n    VERIFY_IS_APPROX(m3, refMat3);\n\n    refMat3 = refMat2.template triangularView<Upper>();\n    m3 = m2.template triangularView<Upper>();\n    VERIFY_IS_APPROX(m3, refMat3);\n\n    {\n      refMat3 = refMat2.template triangularView<UnitUpper>();\n      m3 = m2.template triangularView<UnitUpper>();\n      VERIFY_IS_APPROX(m3, refMat3);\n\n      refMat3 = refMat2.template triangularView<UnitLower>();\n      m3 = m2.template triangularView<UnitLower>();\n      VERIFY_IS_APPROX(m3, refMat3);\n    }\n\n    refMat3 = refMat2.template triangularView<StrictlyUpper>();\n    m3 = m2.template triangularView<StrictlyUpper>();\n    VERIFY_IS_APPROX(m3, refMat3);\n\n    refMat3 = refMat2.template triangularView<StrictlyLower>();\n    m3 = m2.template triangularView<StrictlyLower>();\n    VERIFY_IS_APPROX(m3, refMat3);\n\n    // check sparse-triangular to dense\n    refMat3 = m2.template triangularView<StrictlyUpper>();\n    VERIFY_IS_APPROX(refMat3, DenseMatrix(refMat2.template triangularView<StrictlyUpper>()));\n  }\n  \n  // test selfadjointView\n  if(!SparseMatrixType::IsRowMajor)\n  {\n    DenseMatrix refMat2(rows, rows), refMat3(rows, rows);\n    SparseMatrixType m2(rows, rows), m3(rows, rows);\n    initSparse<Scalar>(density, refMat2, m2);\n    refMat3 = refMat2.template selfadjointView<Lower>();\n    m3 = m2.template selfadjointView<Lower>();\n    VERIFY_IS_APPROX(m3, refMat3);\n\n    refMat3 += refMat2.template selfadjointView<Lower>();\n    m3 += m2.template selfadjointView<Lower>();\n    VERIFY_IS_APPROX(m3, refMat3);\n\n    refMat3 -= refMat2.template selfadjointView<Lower>();\n    m3 -= m2.template selfadjointView<Lower>();\n    VERIFY_IS_APPROX(m3, refMat3);\n\n    // selfadjointView only works for square matrices:\n    SparseMatrixType m4(rows, rows+1);\n    VERIFY_RAISES_ASSERT(m4.template selfadjointView<Lower>());\n    VERIFY_RAISES_ASSERT(m4.template selfadjointView<Upper>());\n  }\n  \n  // test sparseView\n  {\n    DenseMatrix refMat2 = DenseMatrix::Zero(rows, rows);\n    SparseMatrixType m2(rows, rows);\n    initSparse<Scalar>(density, refMat2, m2);\n    VERIFY_IS_APPROX(m2.eval(), refMat2.sparseView().eval());\n\n    // sparse view on expressions:\n    VERIFY_IS_APPROX((s1*m2).eval(), (s1*refMat2).sparseView().eval());\n    VERIFY_IS_APPROX((m2+m2).eval(), (refMat2+refMat2).sparseView().eval());\n    VERIFY_IS_APPROX((m2*m2).eval(), (refMat2.lazyProduct(refMat2)).sparseView().eval());\n    VERIFY_IS_APPROX((m2*m2).eval(), (refMat2*refMat2).sparseView().eval());\n  }\n\n  // test diagonal\n  {\n    DenseMatrix refMat2 = DenseMatrix::Zero(rows, cols);\n    SparseMatrixType m2(rows, cols);\n    initSparse<Scalar>(density, refMat2, m2);\n    VERIFY_IS_APPROX(m2.diagonal(), refMat2.diagonal().eval());\n    DenseVector d = m2.diagonal();\n    VERIFY_IS_APPROX(d, refMat2.diagonal().eval());\n    d = m2.diagonal().array();\n    VERIFY_IS_APPROX(d, refMat2.diagonal().eval());\n    VERIFY_IS_APPROX(const_cast<const SparseMatrixType&>(m2).diagonal(), refMat2.diagonal().eval());\n    \n    initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag);\n    m2.diagonal()      += refMat2.diagonal();\n    refMat2.diagonal() += refMat2.diagonal();\n    VERIFY_IS_APPROX(m2, refMat2);\n  }\n  \n  // test diagonal to sparse\n  {\n    DenseVector d = DenseVector::Random(rows);\n    DenseMatrix refMat2 = d.asDiagonal();\n    SparseMatrixType m2(rows, rows);\n    m2 = d.asDiagonal();\n    VERIFY_IS_APPROX(m2, refMat2);\n    SparseMatrixType m3(d.asDiagonal());\n    VERIFY_IS_APPROX(m3, refMat2);\n    refMat2 += d.asDiagonal();\n    m2 += d.asDiagonal();\n    VERIFY_IS_APPROX(m2, refMat2);\n  }\n  \n  // test conservative resize\n  {\n      std::vector< std::pair<StorageIndex,StorageIndex> > inc;\n      if(rows > 3 && cols > 2)\n        inc.push_back(std::pair<StorageIndex,StorageIndex>(-3,-2));\n      inc.push_back(std::pair<StorageIndex,StorageIndex>(0,0));\n      inc.push_back(std::pair<StorageIndex,StorageIndex>(3,2));\n      inc.push_back(std::pair<StorageIndex,StorageIndex>(3,0));\n      inc.push_back(std::pair<StorageIndex,StorageIndex>(0,3));\n      \n      for(size_t i = 0; i< inc.size(); i++) {\n        StorageIndex incRows = inc[i].first;\n        StorageIndex incCols = inc[i].second;\n        SparseMatrixType m1(rows, cols);\n        DenseMatrix refMat1 = DenseMatrix::Zero(rows, cols);\n        initSparse<Scalar>(density, refMat1, m1);\n        \n        m1.conservativeResize(rows+incRows, cols+incCols);\n        refMat1.conservativeResize(rows+incRows, cols+incCols);\n        if (incRows > 0) refMat1.bottomRows(incRows).setZero();\n        if (incCols > 0) refMat1.rightCols(incCols).setZero();\n        \n        VERIFY_IS_APPROX(m1, refMat1);\n        \n        // Insert new values\n        if (incRows > 0) \n          m1.insert(m1.rows()-1, 0) = refMat1(refMat1.rows()-1, 0) = 1;\n        if (incCols > 0) \n          m1.insert(0, m1.cols()-1) = refMat1(0, refMat1.cols()-1) = 1;\n          \n        VERIFY_IS_APPROX(m1, refMat1);\n          \n          \n      }\n  }\n\n  // test Identity matrix\n  {\n    DenseMatrix refMat1 = DenseMatrix::Identity(rows, rows);\n    SparseMatrixType m1(rows, rows);\n    m1.setIdentity();\n    VERIFY_IS_APPROX(m1, refMat1);\n    for(int k=0; k<rows*rows/4; ++k)\n    {\n      Index i = internal::random<Index>(0,rows-1);\n      Index j = internal::random<Index>(0,rows-1);\n      Scalar v = internal::random<Scalar>();\n      m1.coeffRef(i,j) = v;\n      refMat1.coeffRef(i,j) = v;\n      VERIFY_IS_APPROX(m1, refMat1);\n      if(internal::random<Index>(0,10)<2)\n        m1.makeCompressed();\n    }\n    m1.setIdentity();\n    refMat1.setIdentity();\n    VERIFY_IS_APPROX(m1, refMat1);\n  }\n\n  // test array/vector of InnerIterator\n  {\n    typedef typename SparseMatrixType::InnerIterator IteratorType;\n\n    DenseMatrix refMat2 = DenseMatrix::Zero(rows, cols);\n    SparseMatrixType m2(rows, cols);\n    initSparse<Scalar>(density, refMat2, m2);\n    IteratorType static_array[2];\n    static_array[0] = IteratorType(m2,0);\n    static_array[1] = IteratorType(m2,m2.outerSize()-1);\n    VERIFY( static_array[0] || m2.innerVector(static_array[0].outer()).nonZeros() == 0 );\n    VERIFY( static_array[1] || m2.innerVector(static_array[1].outer()).nonZeros() == 0 );\n    if(static_array[0] && static_array[1])\n    {\n      ++(static_array[1]);\n      static_array[1] = IteratorType(m2,0);\n      VERIFY( static_array[1] );\n      VERIFY( static_array[1].index() == static_array[0].index() );\n      VERIFY( static_array[1].outer() == static_array[0].outer() );\n      VERIFY( static_array[1].value() == static_array[0].value() );\n    }\n\n    std::vector<IteratorType> iters(2);\n    iters[0] = IteratorType(m2,0);\n    iters[1] = IteratorType(m2,m2.outerSize()-1);\n  }\n}\n\n\ntemplate<typename SparseMatrixType>\nvoid big_sparse_triplet(Index rows, Index cols, double density) {\n  typedef typename SparseMatrixType::StorageIndex StorageIndex;\n  typedef typename SparseMatrixType::Scalar Scalar;\n  typedef Triplet<Scalar,Index> TripletType;\n  std::vector<TripletType> triplets;\n  double nelements = density * rows*cols;\n  VERIFY(nelements>=0 && nelements <  NumTraits<StorageIndex>::highest());\n  Index ntriplets = Index(nelements);\n  triplets.reserve(ntriplets);\n  Scalar sum = Scalar(0);\n  for(Index i=0;i<ntriplets;++i)\n  {\n    Index r = internal::random<Index>(0,rows-1);\n    Index c = internal::random<Index>(0,cols-1);\n    Scalar v = internal::random<Scalar>();\n    triplets.push_back(TripletType(r,c,v));\n    sum += v;\n  }\n  SparseMatrixType m(rows,cols);\n  m.setFromTriplets(triplets.begin(), triplets.end());\n  VERIFY(m.nonZeros() <= ntriplets);\n  VERIFY_IS_APPROX(sum, m.sum());\n}\n\n\nvoid test_sparse_basic()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    int r = Eigen::internal::random<int>(1,200), c = Eigen::internal::random<int>(1,200);\n    if(Eigen::internal::random<int>(0,4) == 0) {\n      r = c; // check square matrices in 25% of tries\n    }\n    EIGEN_UNUSED_VARIABLE(r+c);\n    CALL_SUBTEST_1(( sparse_basic(SparseMatrix<double>(1, 1)) ));\n    CALL_SUBTEST_1(( sparse_basic(SparseMatrix<double>(8, 8)) ));\n    CALL_SUBTEST_2(( sparse_basic(SparseMatrix<std::complex<double>, ColMajor>(r, c)) ));\n    CALL_SUBTEST_2(( sparse_basic(SparseMatrix<std::complex<double>, RowMajor>(r, c)) ));\n    CALL_SUBTEST_1(( sparse_basic(SparseMatrix<double>(r, c)) ));\n    CALL_SUBTEST_5(( sparse_basic(SparseMatrix<double,ColMajor,long int>(r, c)) ));\n    CALL_SUBTEST_5(( sparse_basic(SparseMatrix<double,RowMajor,long int>(r, c)) ));\n    \n    r = Eigen::internal::random<int>(1,100);\n    c = Eigen::internal::random<int>(1,100);\n    if(Eigen::internal::random<int>(0,4) == 0) {\n      r = c; // check square matrices in 25% of tries\n    }\n    \n    CALL_SUBTEST_6(( sparse_basic(SparseMatrix<double,ColMajor,short int>(short(r), short(c))) ));\n    CALL_SUBTEST_6(( sparse_basic(SparseMatrix<double,RowMajor,short int>(short(r), short(c))) ));\n  }\n\n  // Regression test for bug 900: (manually insert higher values here, if you have enough RAM):\n  CALL_SUBTEST_3((big_sparse_triplet<SparseMatrix<float, RowMajor, int> >(10000, 10000, 0.125)));\n  CALL_SUBTEST_4((big_sparse_triplet<SparseMatrix<double, ColMajor, long int> >(10000, 10000, 0.125)));\n\n  // Regression test for bug 1105\n#ifdef EIGEN_TEST_PART_7\n  {\n    int n = Eigen::internal::random<int>(200,600);\n    SparseMatrix<std::complex<double>,0, long> mat(n, n);\n    std::complex<double> val;\n\n    for(int i=0; i<n; ++i)\n    {\n      mat.coeffRef(i, i%(n/10)) = val;\n      VERIFY(mat.data().allocatedSize()<20*n);\n    }\n  }\n#endif\n}\n"
  },
  {
    "path": "include/eigen3/test/sparse_block.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"sparse.h\"\n\ntemplate<typename T>\ntypename Eigen::internal::enable_if<(T::Flags&RowMajorBit)==RowMajorBit, typename T::RowXpr>::type\ninnervec(T& A, Index i)\n{\n  return A.row(i);\n}\n\ntemplate<typename T>\ntypename Eigen::internal::enable_if<(T::Flags&RowMajorBit)==0, typename T::ColXpr>::type\ninnervec(T& A, Index i)\n{\n  return A.col(i);\n}\n\ntemplate<typename SparseMatrixType> void sparse_block(const SparseMatrixType& ref)\n{\n  const Index rows = ref.rows();\n  const Index cols = ref.cols();\n  const Index inner = ref.innerSize();\n  const Index outer = ref.outerSize();\n\n  typedef typename SparseMatrixType::Scalar Scalar;\n  typedef typename SparseMatrixType::StorageIndex StorageIndex;\n\n  double density = (std::max)(8./(rows*cols), 0.01);\n  typedef Matrix<Scalar,Dynamic,Dynamic,SparseMatrixType::IsRowMajor?RowMajor:ColMajor> DenseMatrix;\n  typedef Matrix<Scalar,Dynamic,1> DenseVector;\n  typedef Matrix<Scalar,1,Dynamic> RowDenseVector;\n  typedef SparseVector<Scalar> SparseVectorType;\n\n  Scalar s1 = internal::random<Scalar>();\n  {\n    SparseMatrixType m(rows, cols);\n    DenseMatrix refMat = DenseMatrix::Zero(rows, cols);\n    initSparse<Scalar>(density, refMat, m);\n\n    VERIFY_IS_APPROX(m, refMat);\n\n    // test InnerIterators and Block expressions\n    for (int t=0; t<10; ++t)\n    {\n      Index j = internal::random<Index>(0,cols-2);\n      Index i = internal::random<Index>(0,rows-2);\n      Index w = internal::random<Index>(1,cols-j);\n      Index h = internal::random<Index>(1,rows-i);\n\n      VERIFY_IS_APPROX(m.block(i,j,h,w), refMat.block(i,j,h,w));\n      for(Index c=0; c<w; c++)\n      {\n        VERIFY_IS_APPROX(m.block(i,j,h,w).col(c), refMat.block(i,j,h,w).col(c));\n        for(Index r=0; r<h; r++)\n        {\n          VERIFY_IS_APPROX(m.block(i,j,h,w).col(c).coeff(r), refMat.block(i,j,h,w).col(c).coeff(r));\n          VERIFY_IS_APPROX(m.block(i,j,h,w).coeff(r,c), refMat.block(i,j,h,w).coeff(r,c));\n        }\n      }\n      for(Index r=0; r<h; r++)\n      {\n        VERIFY_IS_APPROX(m.block(i,j,h,w).row(r), refMat.block(i,j,h,w).row(r));\n        for(Index c=0; c<w; c++)\n        {\n          VERIFY_IS_APPROX(m.block(i,j,h,w).row(r).coeff(c), refMat.block(i,j,h,w).row(r).coeff(c));\n          VERIFY_IS_APPROX(m.block(i,j,h,w).coeff(r,c), refMat.block(i,j,h,w).coeff(r,c));\n        }\n      }\n      \n      VERIFY_IS_APPROX(m.middleCols(j,w), refMat.middleCols(j,w));\n      VERIFY_IS_APPROX(m.middleRows(i,h), refMat.middleRows(i,h));\n      for(Index r=0; r<h; r++)\n      {\n        VERIFY_IS_APPROX(m.middleCols(j,w).row(r), refMat.middleCols(j,w).row(r));\n        VERIFY_IS_APPROX(m.middleRows(i,h).row(r), refMat.middleRows(i,h).row(r));\n        for(Index c=0; c<w; c++)\n        {\n          VERIFY_IS_APPROX(m.col(c).coeff(r), refMat.col(c).coeff(r));\n          VERIFY_IS_APPROX(m.row(r).coeff(c), refMat.row(r).coeff(c));\n          \n          VERIFY_IS_APPROX(m.middleCols(j,w).coeff(r,c), refMat.middleCols(j,w).coeff(r,c));\n          VERIFY_IS_APPROX(m.middleRows(i,h).coeff(r,c), refMat.middleRows(i,h).coeff(r,c));\n          if(m.middleCols(j,w).coeff(r,c) != Scalar(0))\n          {\n            VERIFY_IS_APPROX(m.middleCols(j,w).coeffRef(r,c), refMat.middleCols(j,w).coeff(r,c));\n          }\n          if(m.middleRows(i,h).coeff(r,c) != Scalar(0))\n          {\n            VERIFY_IS_APPROX(m.middleRows(i,h).coeff(r,c), refMat.middleRows(i,h).coeff(r,c));\n          }\n        }\n      }\n      for(Index c=0; c<w; c++)\n      {\n        VERIFY_IS_APPROX(m.middleCols(j,w).col(c), refMat.middleCols(j,w).col(c));\n        VERIFY_IS_APPROX(m.middleRows(i,h).col(c), refMat.middleRows(i,h).col(c));\n      }\n    }\n\n    for(Index c=0; c<cols; c++)\n    {\n      VERIFY_IS_APPROX(m.col(c) + m.col(c), (m + m).col(c));\n      VERIFY_IS_APPROX(m.col(c) + m.col(c), refMat.col(c) + refMat.col(c));\n    }\n\n    for(Index r=0; r<rows; r++)\n    {\n      VERIFY_IS_APPROX(m.row(r) + m.row(r), (m + m).row(r));\n      VERIFY_IS_APPROX(m.row(r) + m.row(r), refMat.row(r) + refMat.row(r));\n    }\n  }\n\n  // test innerVector()\n  {\n    DenseMatrix refMat2 = DenseMatrix::Zero(rows, cols);\n    SparseMatrixType m2(rows, cols);\n    initSparse<Scalar>(density, refMat2, m2);\n    Index j0 = internal::random<Index>(0,outer-1);\n    Index j1 = internal::random<Index>(0,outer-1);\n    Index r0 = internal::random<Index>(0,rows-1);\n    Index c0 = internal::random<Index>(0,cols-1);\n\n    VERIFY_IS_APPROX(m2.innerVector(j0), innervec(refMat2,j0));\n    VERIFY_IS_APPROX(m2.innerVector(j0)+m2.innerVector(j1), innervec(refMat2,j0)+innervec(refMat2,j1));\n\n    m2.innerVector(j0) *= Scalar(2);\n    innervec(refMat2,j0) *= Scalar(2);\n    VERIFY_IS_APPROX(m2, refMat2);\n\n    m2.row(r0) *= Scalar(3);\n    refMat2.row(r0) *= Scalar(3);\n    VERIFY_IS_APPROX(m2, refMat2);\n\n    m2.col(c0) *= Scalar(4);\n    refMat2.col(c0) *= Scalar(4);\n    VERIFY_IS_APPROX(m2, refMat2);\n\n    m2.row(r0) /= Scalar(3);\n    refMat2.row(r0) /= Scalar(3);\n    VERIFY_IS_APPROX(m2, refMat2);\n\n    m2.col(c0) /= Scalar(4);\n    refMat2.col(c0) /= Scalar(4);\n    VERIFY_IS_APPROX(m2, refMat2);\n\n    SparseVectorType v1;\n    VERIFY_IS_APPROX(v1 = m2.col(c0) * 4, refMat2.col(c0)*4);\n    VERIFY_IS_APPROX(v1 = m2.row(r0) * 4, refMat2.row(r0).transpose()*4);\n\n    SparseMatrixType m3(rows,cols);\n    m3.reserve(VectorXi::Constant(outer,int(inner/2)));\n    for(Index j=0; j<outer; ++j)\n      for(Index k=0; k<(std::min)(j,inner); ++k)\n        m3.insertByOuterInner(j,k) = internal::convert_index<StorageIndex>(k+1);\n    for(Index j=0; j<(std::min)(outer, inner); ++j)\n    {\n      VERIFY(j==numext::real(m3.innerVector(j).nonZeros()));\n      if(j>0)\n        VERIFY(j==numext::real(m3.innerVector(j).lastCoeff()));\n    }\n    m3.makeCompressed();\n    for(Index j=0; j<(std::min)(outer, inner); ++j)\n    {\n      VERIFY(j==numext::real(m3.innerVector(j).nonZeros()));\n      if(j>0)\n        VERIFY(j==numext::real(m3.innerVector(j).lastCoeff()));\n    }\n\n    VERIFY(m3.innerVector(j0).nonZeros() == m3.transpose().innerVector(j0).nonZeros());\n\n//     m2.innerVector(j0) = 2*m2.innerVector(j1);\n//     refMat2.col(j0) = 2*refMat2.col(j1);\n//     VERIFY_IS_APPROX(m2, refMat2);\n  }\n\n  // test innerVectors()\n  {\n    DenseMatrix refMat2 = DenseMatrix::Zero(rows, cols);\n    SparseMatrixType m2(rows, cols);\n    initSparse<Scalar>(density, refMat2, m2);\n    if(internal::random<float>(0,1)>0.5f) m2.makeCompressed();\n    Index j0 = internal::random<Index>(0,outer-2);\n    Index j1 = internal::random<Index>(0,outer-2);\n    Index n0 = internal::random<Index>(1,outer-(std::max)(j0,j1));\n    if(SparseMatrixType::IsRowMajor)\n      VERIFY_IS_APPROX(m2.innerVectors(j0,n0), refMat2.block(j0,0,n0,cols));\n    else\n      VERIFY_IS_APPROX(m2.innerVectors(j0,n0), refMat2.block(0,j0,rows,n0));\n    if(SparseMatrixType::IsRowMajor)\n      VERIFY_IS_APPROX(m2.innerVectors(j0,n0)+m2.innerVectors(j1,n0),\n                       refMat2.middleRows(j0,n0)+refMat2.middleRows(j1,n0));\n    else\n      VERIFY_IS_APPROX(m2.innerVectors(j0,n0)+m2.innerVectors(j1,n0),\n                      refMat2.block(0,j0,rows,n0)+refMat2.block(0,j1,rows,n0));\n    \n    VERIFY_IS_APPROX(m2, refMat2);\n    \n    VERIFY(m2.innerVectors(j0,n0).nonZeros() == m2.transpose().innerVectors(j0,n0).nonZeros());\n    \n    m2.innerVectors(j0,n0) = m2.innerVectors(j0,n0) + m2.innerVectors(j1,n0);\n    if(SparseMatrixType::IsRowMajor)\n      refMat2.middleRows(j0,n0) = (refMat2.middleRows(j0,n0) + refMat2.middleRows(j1,n0)).eval();\n    else\n      refMat2.middleCols(j0,n0) = (refMat2.middleCols(j0,n0) + refMat2.middleCols(j1,n0)).eval();\n    \n    VERIFY_IS_APPROX(m2, refMat2);\n  }\n\n  // test generic blocks\n  {\n    DenseMatrix refMat2 = DenseMatrix::Zero(rows, cols);\n    SparseMatrixType m2(rows, cols);\n    initSparse<Scalar>(density, refMat2, m2);\n    Index j0 = internal::random<Index>(0,outer-2);\n    Index j1 = internal::random<Index>(0,outer-2);\n    Index n0 = internal::random<Index>(1,outer-(std::max)(j0,j1));\n    if(SparseMatrixType::IsRowMajor)\n      VERIFY_IS_APPROX(m2.block(j0,0,n0,cols), refMat2.block(j0,0,n0,cols));\n    else\n      VERIFY_IS_APPROX(m2.block(0,j0,rows,n0), refMat2.block(0,j0,rows,n0));\n    \n    if(SparseMatrixType::IsRowMajor)\n      VERIFY_IS_APPROX(m2.block(j0,0,n0,cols)+m2.block(j1,0,n0,cols),\n                      refMat2.block(j0,0,n0,cols)+refMat2.block(j1,0,n0,cols));\n    else\n      VERIFY_IS_APPROX(m2.block(0,j0,rows,n0)+m2.block(0,j1,rows,n0),\n                      refMat2.block(0,j0,rows,n0)+refMat2.block(0,j1,rows,n0));\n      \n    Index i = internal::random<Index>(0,m2.outerSize()-1);\n    if(SparseMatrixType::IsRowMajor) {\n      m2.innerVector(i) = m2.innerVector(i) * s1;\n      refMat2.row(i) = refMat2.row(i) * s1;\n      VERIFY_IS_APPROX(m2,refMat2);\n    } else {\n      m2.innerVector(i) = m2.innerVector(i) * s1;\n      refMat2.col(i) = refMat2.col(i) * s1;\n      VERIFY_IS_APPROX(m2,refMat2);\n    }\n    \n    Index r0 = internal::random<Index>(0,rows-2);\n    Index c0 = internal::random<Index>(0,cols-2);\n    Index r1 = internal::random<Index>(1,rows-r0);\n    Index c1 = internal::random<Index>(1,cols-c0);\n    \n    VERIFY_IS_APPROX(DenseVector(m2.col(c0)), refMat2.col(c0));\n    VERIFY_IS_APPROX(m2.col(c0), refMat2.col(c0));\n    \n    VERIFY_IS_APPROX(RowDenseVector(m2.row(r0)), refMat2.row(r0));\n    VERIFY_IS_APPROX(m2.row(r0), refMat2.row(r0));\n\n    VERIFY_IS_APPROX(m2.block(r0,c0,r1,c1), refMat2.block(r0,c0,r1,c1));\n    VERIFY_IS_APPROX((2*m2).block(r0,c0,r1,c1), (2*refMat2).block(r0,c0,r1,c1));\n\n    if(m2.nonZeros()>0)\n    {\n      VERIFY_IS_APPROX(m2, refMat2);\n      SparseMatrixType m3(rows, cols);\n      DenseMatrix refMat3(rows, cols); refMat3.setZero();\n      Index n = internal::random<Index>(1,10);\n      for(Index k=0; k<n; ++k)\n      {\n        Index o1 = internal::random<Index>(0,outer-1);\n        Index o2 = internal::random<Index>(0,outer-1);\n        if(SparseMatrixType::IsRowMajor)\n        {\n          m3.innerVector(o1) = m2.row(o2);\n          refMat3.row(o1) = refMat2.row(o2);\n        }\n        else\n        {\n          m3.innerVector(o1) = m2.col(o2);\n          refMat3.col(o1) = refMat2.col(o2);\n        }\n        if(internal::random<bool>())\n          m3.makeCompressed();\n      }\n      if(m3.nonZeros()>0)\n      VERIFY_IS_APPROX(m3, refMat3);\n    }\n  }\n}\n\nvoid test_sparse_block()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    int r = Eigen::internal::random<int>(1,200), c = Eigen::internal::random<int>(1,200);\n    if(Eigen::internal::random<int>(0,4) == 0) {\n      r = c; // check square matrices in 25% of tries\n    }\n    EIGEN_UNUSED_VARIABLE(r+c);\n    CALL_SUBTEST_1(( sparse_block(SparseMatrix<double>(1, 1)) ));\n    CALL_SUBTEST_1(( sparse_block(SparseMatrix<double>(8, 8)) ));\n    CALL_SUBTEST_1(( sparse_block(SparseMatrix<double>(r, c)) ));\n    CALL_SUBTEST_2(( sparse_block(SparseMatrix<std::complex<double>, ColMajor>(r, c)) ));\n    CALL_SUBTEST_2(( sparse_block(SparseMatrix<std::complex<double>, RowMajor>(r, c)) ));\n    \n    CALL_SUBTEST_3(( sparse_block(SparseMatrix<double,ColMajor,long int>(r, c)) ));\n    CALL_SUBTEST_3(( sparse_block(SparseMatrix<double,RowMajor,long int>(r, c)) ));\n    \n    r = Eigen::internal::random<int>(1,100);\n    c = Eigen::internal::random<int>(1,100);\n    if(Eigen::internal::random<int>(0,4) == 0) {\n      r = c; // check square matrices in 25% of tries\n    }\n    \n    CALL_SUBTEST_4(( sparse_block(SparseMatrix<double,ColMajor,short int>(short(r), short(c))) ));\n    CALL_SUBTEST_4(( sparse_block(SparseMatrix<double,RowMajor,short int>(short(r), short(c))) ));\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/sparse_permutations.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2011-2015 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n\nstatic long int nb_transposed_copies;\n#define EIGEN_SPARSE_TRANSPOSED_COPY_PLUGIN {nb_transposed_copies++;}\n#define VERIFY_TRANSPOSITION_COUNT(XPR,N) {\\\n    nb_transposed_copies = 0; \\\n    XPR; \\\n    if(nb_transposed_copies!=N) std::cerr << \"nb_transposed_copies == \" << nb_transposed_copies << \"\\n\"; \\\n    VERIFY( (#XPR) && nb_transposed_copies==N ); \\\n  }\n\n#include \"sparse.h\"\n\ntemplate<typename T>\nbool is_sorted(const T& mat) {\n  for(Index k = 0; k<mat.outerSize(); ++k)\n  {\n    Index prev = -1;\n    for(typename T::InnerIterator it(mat,k); it; ++it)\n    {\n      if(prev>=it.index())\n        return false;\n      prev = it.index();\n    }\n  }\n  return true;\n}\n\ntemplate<typename T>\ntypename internal::nested_eval<T,1>::type eval(const T &xpr)\n{\n  VERIFY( int(internal::nested_eval<T,1>::type::Flags&RowMajorBit) == int(internal::evaluator<T>::Flags&RowMajorBit) );\n  return xpr;\n}\n\ntemplate<int OtherStorage, typename SparseMatrixType> void sparse_permutations(const SparseMatrixType& ref)\n{\n  const Index rows = ref.rows();\n  const Index cols = ref.cols();\n  typedef typename SparseMatrixType::Scalar Scalar;\n  typedef typename SparseMatrixType::StorageIndex StorageIndex;\n  typedef SparseMatrix<Scalar, OtherStorage, StorageIndex> OtherSparseMatrixType;\n  typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;\n  typedef Matrix<StorageIndex,Dynamic,1> VectorI;\n//   bool IsRowMajor1 = SparseMatrixType::IsRowMajor;\n//   bool IsRowMajor2 = OtherSparseMatrixType::IsRowMajor;\n  \n  double density = (std::max)(8./(rows*cols), 0.01);\n  \n  SparseMatrixType mat(rows, cols), up(rows,cols), lo(rows,cols);\n  OtherSparseMatrixType res;\n  DenseMatrix mat_d = DenseMatrix::Zero(rows, cols), up_sym_d, lo_sym_d, res_d;\n  \n  initSparse<Scalar>(density, mat_d, mat, 0);\n\n  up = mat.template triangularView<Upper>();\n  lo = mat.template triangularView<Lower>();\n  \n  up_sym_d = mat_d.template selfadjointView<Upper>();\n  lo_sym_d = mat_d.template selfadjointView<Lower>();\n  \n  VERIFY_IS_APPROX(mat, mat_d);\n  VERIFY_IS_APPROX(up, DenseMatrix(mat_d.template triangularView<Upper>()));\n  VERIFY_IS_APPROX(lo, DenseMatrix(mat_d.template triangularView<Lower>()));\n  \n  PermutationMatrix<Dynamic> p, p_null;\n  VectorI pi;\n  randomPermutationVector(pi, cols);\n  p.indices() = pi;\n\n  VERIFY( is_sorted( ::eval(mat*p) ));\n  VERIFY( is_sorted( res = mat*p ));\n  VERIFY_TRANSPOSITION_COUNT( ::eval(mat*p), 0);\n  //VERIFY_TRANSPOSITION_COUNT( res = mat*p, IsRowMajor ? 1 : 0 );\n  res_d = mat_d*p;\n  VERIFY(res.isApprox(res_d) && \"mat*p\");\n\n  VERIFY( is_sorted( ::eval(p*mat) ));\n  VERIFY( is_sorted( res = p*mat ));\n  VERIFY_TRANSPOSITION_COUNT( ::eval(p*mat), 0);\n  res_d = p*mat_d;\n  VERIFY(res.isApprox(res_d) && \"p*mat\");\n\n  VERIFY( is_sorted( (mat*p).eval() ));\n  VERIFY( is_sorted( res = mat*p.inverse() ));\n  VERIFY_TRANSPOSITION_COUNT( ::eval(mat*p.inverse()), 0);\n  res_d = mat*p.inverse();\n  VERIFY(res.isApprox(res_d) && \"mat*inv(p)\");\n\n  VERIFY( is_sorted( (p*mat+p*mat).eval() ));\n  VERIFY( is_sorted( res = p.inverse()*mat ));\n  VERIFY_TRANSPOSITION_COUNT( ::eval(p.inverse()*mat), 0);\n  res_d = p.inverse()*mat_d;\n  VERIFY(res.isApprox(res_d) && \"inv(p)*mat\");\n\n  VERIFY( is_sorted( (p * mat * p.inverse()).eval() ));\n  VERIFY( is_sorted( res = mat.twistedBy(p) ));\n  VERIFY_TRANSPOSITION_COUNT( ::eval(p * mat * p.inverse()), 0);\n  res_d = (p * mat_d) * p.inverse();\n  VERIFY(res.isApprox(res_d) && \"p*mat*inv(p)\");\n\n  \n  VERIFY( is_sorted( res = mat.template selfadjointView<Upper>().twistedBy(p_null) ));\n  res_d = up_sym_d;\n  VERIFY(res.isApprox(res_d) && \"full selfadjoint upper to full\");\n  \n  VERIFY( is_sorted( res = mat.template selfadjointView<Lower>().twistedBy(p_null) ));\n  res_d = lo_sym_d;\n  VERIFY(res.isApprox(res_d) && \"full selfadjoint lower to full\");\n  \n  \n  VERIFY( is_sorted( res = up.template selfadjointView<Upper>().twistedBy(p_null) ));\n  res_d = up_sym_d;\n  VERIFY(res.isApprox(res_d) && \"upper selfadjoint to full\");\n  \n  VERIFY( is_sorted( res = lo.template selfadjointView<Lower>().twistedBy(p_null) ));\n  res_d = lo_sym_d;\n  VERIFY(res.isApprox(res_d) && \"lower selfadjoint full\");\n\n\n  VERIFY( is_sorted( res = mat.template selfadjointView<Upper>() ));\n  res_d = up_sym_d;\n  VERIFY(res.isApprox(res_d) && \"full selfadjoint upper to full\");\n\n  VERIFY( is_sorted( res = mat.template selfadjointView<Lower>() ));\n  res_d = lo_sym_d;\n  VERIFY(res.isApprox(res_d) && \"full selfadjoint lower to full\");\n\n  VERIFY( is_sorted( res = up.template selfadjointView<Upper>() ));\n  res_d = up_sym_d;\n  VERIFY(res.isApprox(res_d) && \"upper selfadjoint to full\");\n\n  VERIFY( is_sorted( res = lo.template selfadjointView<Lower>() ));\n  res_d = lo_sym_d;\n  VERIFY(res.isApprox(res_d) && \"lower selfadjoint full\");\n\n\n  res.template selfadjointView<Upper>() = mat.template selfadjointView<Upper>();\n  res_d = up_sym_d.template triangularView<Upper>();\n  VERIFY(res.isApprox(res_d) && \"full selfadjoint upper to upper\");\n\n  res.template selfadjointView<Lower>() = mat.template selfadjointView<Upper>();\n  res_d = up_sym_d.template triangularView<Lower>();\n  VERIFY(res.isApprox(res_d) && \"full selfadjoint upper to lower\");\n\n  res.template selfadjointView<Upper>() = mat.template selfadjointView<Lower>();\n  res_d = lo_sym_d.template triangularView<Upper>();\n  VERIFY(res.isApprox(res_d) && \"full selfadjoint lower to upper\");\n\n  res.template selfadjointView<Lower>() = mat.template selfadjointView<Lower>();\n  res_d = lo_sym_d.template triangularView<Lower>();\n  VERIFY(res.isApprox(res_d) && \"full selfadjoint lower to lower\");\n\n  \n  \n  res.template selfadjointView<Upper>() = mat.template selfadjointView<Upper>().twistedBy(p);\n  res_d = ((p * up_sym_d) * p.inverse()).eval().template triangularView<Upper>();\n  VERIFY(res.isApprox(res_d) && \"full selfadjoint upper twisted to upper\");\n  \n  res.template selfadjointView<Upper>() = mat.template selfadjointView<Lower>().twistedBy(p);\n  res_d = ((p * lo_sym_d) * p.inverse()).eval().template triangularView<Upper>();\n  VERIFY(res.isApprox(res_d) && \"full selfadjoint lower twisted to upper\");\n  \n  res.template selfadjointView<Lower>() = mat.template selfadjointView<Lower>().twistedBy(p);\n  res_d = ((p * lo_sym_d) * p.inverse()).eval().template triangularView<Lower>();\n  VERIFY(res.isApprox(res_d) && \"full selfadjoint lower twisted to lower\");\n  \n  res.template selfadjointView<Lower>() = mat.template selfadjointView<Upper>().twistedBy(p);\n  res_d = ((p * up_sym_d) * p.inverse()).eval().template triangularView<Lower>();\n  VERIFY(res.isApprox(res_d) && \"full selfadjoint upper twisted to lower\");\n  \n  \n  res.template selfadjointView<Upper>() = up.template selfadjointView<Upper>().twistedBy(p);\n  res_d = ((p * up_sym_d) * p.inverse()).eval().template triangularView<Upper>();\n  VERIFY(res.isApprox(res_d) && \"upper selfadjoint twisted to upper\");\n  \n  res.template selfadjointView<Upper>() = lo.template selfadjointView<Lower>().twistedBy(p);\n  res_d = ((p * lo_sym_d) * p.inverse()).eval().template triangularView<Upper>();\n  VERIFY(res.isApprox(res_d) && \"lower selfadjoint twisted to upper\");\n  \n  res.template selfadjointView<Lower>() = lo.template selfadjointView<Lower>().twistedBy(p);\n  res_d = ((p * lo_sym_d) * p.inverse()).eval().template triangularView<Lower>();\n  VERIFY(res.isApprox(res_d) && \"lower selfadjoint twisted to lower\");\n  \n  res.template selfadjointView<Lower>() = up.template selfadjointView<Upper>().twistedBy(p);\n  res_d = ((p * up_sym_d) * p.inverse()).eval().template triangularView<Lower>();\n  VERIFY(res.isApprox(res_d) && \"upper selfadjoint twisted to lower\");\n\n  \n  VERIFY( is_sorted( res = mat.template selfadjointView<Upper>().twistedBy(p) ));\n  res_d = (p * up_sym_d) * p.inverse();\n  VERIFY(res.isApprox(res_d) && \"full selfadjoint upper twisted to full\");\n  \n  VERIFY( is_sorted( res = mat.template selfadjointView<Lower>().twistedBy(p) ));\n  res_d = (p * lo_sym_d) * p.inverse();\n  VERIFY(res.isApprox(res_d) && \"full selfadjoint lower twisted to full\");\n  \n  VERIFY( is_sorted( res = up.template selfadjointView<Upper>().twistedBy(p) ));\n  res_d = (p * up_sym_d) * p.inverse();\n  VERIFY(res.isApprox(res_d) && \"upper selfadjoint twisted to full\");\n  \n  VERIFY( is_sorted( res = lo.template selfadjointView<Lower>().twistedBy(p) ));\n  res_d = (p * lo_sym_d) * p.inverse();\n  VERIFY(res.isApprox(res_d) && \"lower selfadjoint twisted to full\");\n}\n\ntemplate<typename Scalar> void sparse_permutations_all(int size)\n{\n  CALL_SUBTEST(( sparse_permutations<ColMajor>(SparseMatrix<Scalar, ColMajor>(size,size)) ));\n  CALL_SUBTEST(( sparse_permutations<ColMajor>(SparseMatrix<Scalar, RowMajor>(size,size)) ));\n  CALL_SUBTEST(( sparse_permutations<RowMajor>(SparseMatrix<Scalar, ColMajor>(size,size)) ));\n  CALL_SUBTEST(( sparse_permutations<RowMajor>(SparseMatrix<Scalar, RowMajor>(size,size)) ));\n}\n\nvoid test_sparse_permutations()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    int s = Eigen::internal::random<int>(1,50);\n    CALL_SUBTEST_1((  sparse_permutations_all<double>(s) ));\n    CALL_SUBTEST_2((  sparse_permutations_all<std::complex<double> >(s) ));\n  }\n\n  VERIFY((internal::is_same<internal::permutation_matrix_product<SparseMatrix<double>,OnTheRight,false,SparseShape>::ReturnType,\n                            internal::nested_eval<Product<SparseMatrix<double>,PermutationMatrix<Dynamic,Dynamic>,AliasFreeProduct>,1>::type>::value));\n\n  VERIFY((internal::is_same<internal::permutation_matrix_product<SparseMatrix<double>,OnTheLeft,false,SparseShape>::ReturnType,\n                            internal::nested_eval<Product<PermutationMatrix<Dynamic,Dynamic>,SparseMatrix<double>,AliasFreeProduct>,1>::type>::value));\n}\n"
  },
  {
    "path": "include/eigen3/test/sparse_product.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#if defined(_MSC_VER) && (_MSC_VER==1800)\n// This unit test takes forever to compile in Release mode with MSVC 2013,\n// multiple hours. So let's switch off optimization for this one.\n#pragma optimize(\"\",off)\n#endif\n\nstatic long int nb_temporaries;\n\ninline void on_temporary_creation() {\n  // here's a great place to set a breakpoint when debugging failures in this test!\n  nb_temporaries++;\n}\n\n#define EIGEN_SPARSE_CREATE_TEMPORARY_PLUGIN { on_temporary_creation(); }\n\n#include \"sparse.h\"\n\n#define VERIFY_EVALUATION_COUNT(XPR,N) {\\\n    nb_temporaries = 0; \\\n    CALL_SUBTEST( XPR ); \\\n    if(nb_temporaries!=N) std::cerr << \"nb_temporaries == \" << nb_temporaries << \"\\n\"; \\\n    VERIFY( (#XPR) && nb_temporaries==N ); \\\n  }\n\n\n\ntemplate<typename SparseMatrixType> void sparse_product()\n{\n  typedef typename SparseMatrixType::StorageIndex StorageIndex;\n  Index n = 100;\n  const Index rows  = internal::random<Index>(1,n);\n  const Index cols  = internal::random<Index>(1,n);\n  const Index depth = internal::random<Index>(1,n);\n  typedef typename SparseMatrixType::Scalar Scalar;\n  enum { Flags = SparseMatrixType::Flags };\n\n  double density = (std::max)(8./(rows*cols), 0.2);\n  typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;\n  typedef Matrix<Scalar,Dynamic,1> DenseVector;\n  typedef Matrix<Scalar,1,Dynamic> RowDenseVector;\n  typedef SparseVector<Scalar,0,StorageIndex> ColSpVector;\n  typedef SparseVector<Scalar,RowMajor,StorageIndex> RowSpVector;\n\n  Scalar s1 = internal::random<Scalar>();\n  Scalar s2 = internal::random<Scalar>();\n\n  // test matrix-matrix product\n  {\n    DenseMatrix refMat2  = DenseMatrix::Zero(rows, depth);\n    DenseMatrix refMat2t = DenseMatrix::Zero(depth, rows);\n    DenseMatrix refMat3  = DenseMatrix::Zero(depth, cols);\n    DenseMatrix refMat3t = DenseMatrix::Zero(cols, depth);\n    DenseMatrix refMat4  = DenseMatrix::Zero(rows, cols);\n    DenseMatrix refMat4t = DenseMatrix::Zero(cols, rows);\n    DenseMatrix refMat5  = DenseMatrix::Random(depth, cols);\n    DenseMatrix refMat6  = DenseMatrix::Random(rows, rows);\n    DenseMatrix dm4 = DenseMatrix::Zero(rows, rows);\n//     DenseVector dv1 = DenseVector::Random(rows);\n    SparseMatrixType m2 (rows, depth);\n    SparseMatrixType m2t(depth, rows);\n    SparseMatrixType m3 (depth, cols);\n    SparseMatrixType m3t(cols, depth);\n    SparseMatrixType m4 (rows, cols);\n    SparseMatrixType m4t(cols, rows);\n    SparseMatrixType m6(rows, rows);\n    initSparse(density, refMat2,  m2);\n    initSparse(density, refMat2t, m2t);\n    initSparse(density, refMat3,  m3);\n    initSparse(density, refMat3t, m3t);\n    initSparse(density, refMat4,  m4);\n    initSparse(density, refMat4t, m4t);\n    initSparse(density, refMat6, m6);\n\n//     int c = internal::random<int>(0,depth-1);\n\n    // sparse * sparse\n    VERIFY_IS_APPROX(m4=m2*m3, refMat4=refMat2*refMat3);\n    VERIFY_IS_APPROX(m4=m2t.transpose()*m3, refMat4=refMat2t.transpose()*refMat3);\n    VERIFY_IS_APPROX(m4=m2t.transpose()*m3t.transpose(), refMat4=refMat2t.transpose()*refMat3t.transpose());\n    VERIFY_IS_APPROX(m4=m2*m3t.transpose(), refMat4=refMat2*refMat3t.transpose());\n\n    VERIFY_IS_APPROX(m4 = m2*m3/s1, refMat4 = refMat2*refMat3/s1);\n    VERIFY_IS_APPROX(m4 = m2*m3*s1, refMat4 = refMat2*refMat3*s1);\n    VERIFY_IS_APPROX(m4 = s2*m2*m3*s1, refMat4 = s2*refMat2*refMat3*s1);\n    VERIFY_IS_APPROX(m4 = (m2+m2)*m3, refMat4 = (refMat2+refMat2)*refMat3);\n    VERIFY_IS_APPROX(m4 = m2*m3.leftCols(cols/2), refMat4 = refMat2*refMat3.leftCols(cols/2));\n    VERIFY_IS_APPROX(m4 = m2*(m3+m3).leftCols(cols/2), refMat4 = refMat2*(refMat3+refMat3).leftCols(cols/2));\n\n    VERIFY_IS_APPROX(m4=(m2*m3).pruned(0), refMat4=refMat2*refMat3);\n    VERIFY_IS_APPROX(m4=(m2t.transpose()*m3).pruned(0), refMat4=refMat2t.transpose()*refMat3);\n    VERIFY_IS_APPROX(m4=(m2t.transpose()*m3t.transpose()).pruned(0), refMat4=refMat2t.transpose()*refMat3t.transpose());\n    VERIFY_IS_APPROX(m4=(m2*m3t.transpose()).pruned(0), refMat4=refMat2*refMat3t.transpose());\n\n    // make sure the right product implementation is called:\n    if((!SparseMatrixType::IsRowMajor) && m2.rows()<=m3.cols())\n    {\n      VERIFY_EVALUATION_COUNT(m4 = m2*m3, 3); // 1 temp for the result + 2 for transposing and get a sorted result.\n      VERIFY_EVALUATION_COUNT(m4 = (m2*m3).pruned(0), 1);\n      VERIFY_EVALUATION_COUNT(m4 = (m2*m3).eval().pruned(0), 4);\n    }\n\n    // and that pruning is effective:\n    {\n      DenseMatrix Ad(2,2);\n      Ad << -1, 1, 1, 1;\n      SparseMatrixType As(Ad.sparseView()), B(2,2);\n      VERIFY_IS_EQUAL( (As*As.transpose()).eval().nonZeros(), 4);\n      VERIFY_IS_EQUAL( (Ad*Ad.transpose()).eval().sparseView().eval().nonZeros(), 2);\n      VERIFY_IS_EQUAL( (As*As.transpose()).pruned(1e-6).eval().nonZeros(), 2);\n    }\n\n    // dense ?= sparse * sparse\n    VERIFY_IS_APPROX(dm4 =m2*m3, refMat4 =refMat2*refMat3);\n    VERIFY_IS_APPROX(dm4+=m2*m3, refMat4+=refMat2*refMat3);\n    VERIFY_IS_APPROX(dm4-=m2*m3, refMat4-=refMat2*refMat3);\n    VERIFY_IS_APPROX(dm4 =m2t.transpose()*m3, refMat4 =refMat2t.transpose()*refMat3);\n    VERIFY_IS_APPROX(dm4+=m2t.transpose()*m3, refMat4+=refMat2t.transpose()*refMat3);\n    VERIFY_IS_APPROX(dm4-=m2t.transpose()*m3, refMat4-=refMat2t.transpose()*refMat3);\n    VERIFY_IS_APPROX(dm4 =m2t.transpose()*m3t.transpose(), refMat4 =refMat2t.transpose()*refMat3t.transpose());\n    VERIFY_IS_APPROX(dm4+=m2t.transpose()*m3t.transpose(), refMat4+=refMat2t.transpose()*refMat3t.transpose());\n    VERIFY_IS_APPROX(dm4-=m2t.transpose()*m3t.transpose(), refMat4-=refMat2t.transpose()*refMat3t.transpose());\n    VERIFY_IS_APPROX(dm4 =m2*m3t.transpose(), refMat4 =refMat2*refMat3t.transpose());\n    VERIFY_IS_APPROX(dm4+=m2*m3t.transpose(), refMat4+=refMat2*refMat3t.transpose());\n    VERIFY_IS_APPROX(dm4-=m2*m3t.transpose(), refMat4-=refMat2*refMat3t.transpose());\n    VERIFY_IS_APPROX(dm4 = m2*m3*s1, refMat4 = refMat2*refMat3*s1);\n\n    // test aliasing\n    m4 = m2; refMat4 = refMat2;\n    VERIFY_IS_APPROX(m4=m4*m3, refMat4=refMat4*refMat3);\n\n    // sparse * dense matrix\n    VERIFY_IS_APPROX(dm4=m2*refMat3, refMat4=refMat2*refMat3);\n    VERIFY_IS_APPROX(dm4=m2*refMat3t.transpose(), refMat4=refMat2*refMat3t.transpose());\n    VERIFY_IS_APPROX(dm4=m2t.transpose()*refMat3, refMat4=refMat2t.transpose()*refMat3);\n    VERIFY_IS_APPROX(dm4=m2t.transpose()*refMat3t.transpose(), refMat4=refMat2t.transpose()*refMat3t.transpose());\n\n    VERIFY_IS_APPROX(dm4=m2*refMat3, refMat4=refMat2*refMat3);\n    VERIFY_IS_APPROX(dm4=dm4+m2*refMat3, refMat4=refMat4+refMat2*refMat3);\n    VERIFY_IS_APPROX(dm4+=m2*refMat3, refMat4+=refMat2*refMat3);\n    VERIFY_IS_APPROX(dm4-=m2*refMat3, refMat4-=refMat2*refMat3);\n    VERIFY_IS_APPROX(dm4.noalias()+=m2*refMat3, refMat4+=refMat2*refMat3);\n    VERIFY_IS_APPROX(dm4.noalias()-=m2*refMat3, refMat4-=refMat2*refMat3);\n    VERIFY_IS_APPROX(dm4=m2*(refMat3+refMat3), refMat4=refMat2*(refMat3+refMat3));\n    VERIFY_IS_APPROX(dm4=m2t.transpose()*(refMat3+refMat5)*0.5, refMat4=refMat2t.transpose()*(refMat3+refMat5)*0.5);\n    \n    // sparse * dense vector\n    VERIFY_IS_APPROX(dm4.col(0)=m2*refMat3.col(0), refMat4.col(0)=refMat2*refMat3.col(0));\n    VERIFY_IS_APPROX(dm4.col(0)=m2*refMat3t.transpose().col(0), refMat4.col(0)=refMat2*refMat3t.transpose().col(0));\n    VERIFY_IS_APPROX(dm4.col(0)=m2t.transpose()*refMat3.col(0), refMat4.col(0)=refMat2t.transpose()*refMat3.col(0));\n    VERIFY_IS_APPROX(dm4.col(0)=m2t.transpose()*refMat3t.transpose().col(0), refMat4.col(0)=refMat2t.transpose()*refMat3t.transpose().col(0));\n\n    // dense * sparse\n    VERIFY_IS_APPROX(dm4=refMat2*m3, refMat4=refMat2*refMat3);\n    VERIFY_IS_APPROX(dm4=dm4+refMat2*m3, refMat4=refMat4+refMat2*refMat3);\n    VERIFY_IS_APPROX(dm4+=refMat2*m3, refMat4+=refMat2*refMat3);\n    VERIFY_IS_APPROX(dm4-=refMat2*m3, refMat4-=refMat2*refMat3);\n    VERIFY_IS_APPROX(dm4.noalias()+=refMat2*m3, refMat4+=refMat2*refMat3);\n    VERIFY_IS_APPROX(dm4.noalias()-=refMat2*m3, refMat4-=refMat2*refMat3);\n    VERIFY_IS_APPROX(dm4=refMat2*m3t.transpose(), refMat4=refMat2*refMat3t.transpose());\n    VERIFY_IS_APPROX(dm4=refMat2t.transpose()*m3, refMat4=refMat2t.transpose()*refMat3);\n    VERIFY_IS_APPROX(dm4=refMat2t.transpose()*m3t.transpose(), refMat4=refMat2t.transpose()*refMat3t.transpose());\n\n    // sparse * dense and dense * sparse outer product\n    {\n      Index c  = internal::random<Index>(0,depth-1);\n      Index r  = internal::random<Index>(0,rows-1);\n      Index c1 = internal::random<Index>(0,cols-1);\n      Index r1 = internal::random<Index>(0,depth-1);\n      DenseMatrix dm5  = DenseMatrix::Random(depth, cols);\n\n      VERIFY_IS_APPROX( m4=m2.col(c)*dm5.col(c1).transpose(), refMat4=refMat2.col(c)*dm5.col(c1).transpose());\n      VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());\n      VERIFY_IS_APPROX( m4=m2.middleCols(c,1)*dm5.col(c1).transpose(), refMat4=refMat2.col(c)*dm5.col(c1).transpose());\n      VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());\n      VERIFY_IS_APPROX(dm4=m2.col(c)*dm5.col(c1).transpose(), refMat4=refMat2.col(c)*dm5.col(c1).transpose());\n      \n      VERIFY_IS_APPROX(m4=dm5.col(c1)*m2.col(c).transpose(), refMat4=dm5.col(c1)*refMat2.col(c).transpose());\n      VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());\n      VERIFY_IS_APPROX(m4=dm5.col(c1)*m2.middleCols(c,1).transpose(), refMat4=dm5.col(c1)*refMat2.col(c).transpose());\n      VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());\n      VERIFY_IS_APPROX(dm4=dm5.col(c1)*m2.col(c).transpose(), refMat4=dm5.col(c1)*refMat2.col(c).transpose());\n\n      VERIFY_IS_APPROX( m4=dm5.row(r1).transpose()*m2.col(c).transpose(), refMat4=dm5.row(r1).transpose()*refMat2.col(c).transpose());\n      VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());\n      VERIFY_IS_APPROX(dm4=dm5.row(r1).transpose()*m2.col(c).transpose(), refMat4=dm5.row(r1).transpose()*refMat2.col(c).transpose());\n\n      VERIFY_IS_APPROX( m4=m2.row(r).transpose()*dm5.col(c1).transpose(), refMat4=refMat2.row(r).transpose()*dm5.col(c1).transpose());\n      VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());\n      VERIFY_IS_APPROX( m4=m2.middleRows(r,1).transpose()*dm5.col(c1).transpose(), refMat4=refMat2.row(r).transpose()*dm5.col(c1).transpose());\n      VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());\n      VERIFY_IS_APPROX(dm4=m2.row(r).transpose()*dm5.col(c1).transpose(), refMat4=refMat2.row(r).transpose()*dm5.col(c1).transpose());\n\n      VERIFY_IS_APPROX( m4=dm5.col(c1)*m2.row(r), refMat4=dm5.col(c1)*refMat2.row(r));\n      VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());\n      VERIFY_IS_APPROX( m4=dm5.col(c1)*m2.middleRows(r,1), refMat4=dm5.col(c1)*refMat2.row(r));\n      VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());\n      VERIFY_IS_APPROX(dm4=dm5.col(c1)*m2.row(r), refMat4=dm5.col(c1)*refMat2.row(r));\n\n      VERIFY_IS_APPROX( m4=dm5.row(r1).transpose()*m2.row(r), refMat4=dm5.row(r1).transpose()*refMat2.row(r));\n      VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());\n      VERIFY_IS_APPROX(dm4=dm5.row(r1).transpose()*m2.row(r), refMat4=dm5.row(r1).transpose()*refMat2.row(r));\n    }\n\n    VERIFY_IS_APPROX(m6=m6*m6, refMat6=refMat6*refMat6);\n    \n    // sparse matrix * sparse vector\n    ColSpVector cv0(cols), cv1;\n    DenseVector dcv0(cols), dcv1;\n    initSparse(2*density,dcv0, cv0);\n    \n    RowSpVector rv0(depth), rv1;\n    RowDenseVector drv0(depth), drv1(rv1);\n    initSparse(2*density,drv0, rv0);\n\n    VERIFY_IS_APPROX(cv1=m3*cv0, dcv1=refMat3*dcv0);    \n    VERIFY_IS_APPROX(rv1=rv0*m3, drv1=drv0*refMat3);\n    VERIFY_IS_APPROX(cv1=m3t.adjoint()*cv0, dcv1=refMat3t.adjoint()*dcv0);\n    VERIFY_IS_APPROX(cv1=rv0*m3, dcv1=drv0*refMat3);\n    VERIFY_IS_APPROX(rv1=m3*cv0, drv1=refMat3*dcv0);\n  }\n  \n  // test matrix - diagonal product\n  {\n    DenseMatrix refM2 = DenseMatrix::Zero(rows, cols);\n    DenseMatrix refM3 = DenseMatrix::Zero(rows, cols);\n    DenseMatrix d3 = DenseMatrix::Zero(rows, cols);\n    DiagonalMatrix<Scalar,Dynamic> d1(DenseVector::Random(cols));\n    DiagonalMatrix<Scalar,Dynamic> d2(DenseVector::Random(rows));\n    SparseMatrixType m2(rows, cols);\n    SparseMatrixType m3(rows, cols);\n    initSparse<Scalar>(density, refM2, m2);\n    initSparse<Scalar>(density, refM3, m3);\n    VERIFY_IS_APPROX(m3=m2*d1, refM3=refM2*d1);\n    VERIFY_IS_APPROX(m3=m2.transpose()*d2, refM3=refM2.transpose()*d2);\n    VERIFY_IS_APPROX(m3=d2*m2, refM3=d2*refM2);\n    VERIFY_IS_APPROX(m3=d1*m2.transpose(), refM3=d1*refM2.transpose());\n    \n    // also check with a SparseWrapper:\n    DenseVector v1 = DenseVector::Random(cols);\n    DenseVector v2 = DenseVector::Random(rows);\n    DenseVector v3 = DenseVector::Random(rows);\n    VERIFY_IS_APPROX(m3=m2*v1.asDiagonal(), refM3=refM2*v1.asDiagonal());\n    VERIFY_IS_APPROX(m3=m2.transpose()*v2.asDiagonal(), refM3=refM2.transpose()*v2.asDiagonal());\n    VERIFY_IS_APPROX(m3=v2.asDiagonal()*m2, refM3=v2.asDiagonal()*refM2);\n    VERIFY_IS_APPROX(m3=v1.asDiagonal()*m2.transpose(), refM3=v1.asDiagonal()*refM2.transpose());\n    \n    VERIFY_IS_APPROX(m3=v2.asDiagonal()*m2*v1.asDiagonal(), refM3=v2.asDiagonal()*refM2*v1.asDiagonal());\n\n    VERIFY_IS_APPROX(v2=m2*v1.asDiagonal()*v1, refM2*v1.asDiagonal()*v1);\n    VERIFY_IS_APPROX(v3=v2.asDiagonal()*m2*v1, v2.asDiagonal()*refM2*v1);\n    \n    // evaluate to a dense matrix to check the .row() and .col() iterator functions\n    VERIFY_IS_APPROX(d3=m2*d1, refM3=refM2*d1);\n    VERIFY_IS_APPROX(d3=m2.transpose()*d2, refM3=refM2.transpose()*d2);\n    VERIFY_IS_APPROX(d3=d2*m2, refM3=d2*refM2);\n    VERIFY_IS_APPROX(d3=d1*m2.transpose(), refM3=d1*refM2.transpose());\n  }\n\n  // test self-adjoint and triangular-view products\n  {\n    DenseMatrix b = DenseMatrix::Random(rows, rows);\n    DenseMatrix x = DenseMatrix::Random(rows, rows);\n    DenseMatrix refX = DenseMatrix::Random(rows, rows);\n    DenseMatrix refUp = DenseMatrix::Zero(rows, rows);\n    DenseMatrix refLo = DenseMatrix::Zero(rows, rows);\n    DenseMatrix refS = DenseMatrix::Zero(rows, rows);\n    DenseMatrix refA = DenseMatrix::Zero(rows, rows);\n    SparseMatrixType mUp(rows, rows);\n    SparseMatrixType mLo(rows, rows);\n    SparseMatrixType mS(rows, rows);\n    SparseMatrixType mA(rows, rows);\n    initSparse<Scalar>(density, refA, mA);\n    do {\n      initSparse<Scalar>(density, refUp, mUp, ForceRealDiag|/*ForceNonZeroDiag|*/MakeUpperTriangular);\n    } while (refUp.isZero());\n    refLo = refUp.adjoint();\n    mLo = mUp.adjoint();\n    refS = refUp + refLo;\n    refS.diagonal() *= 0.5;\n    mS = mUp + mLo;\n    // TODO be able to address the diagonal....\n    for (int k=0; k<mS.outerSize(); ++k)\n      for (typename SparseMatrixType::InnerIterator it(mS,k); it; ++it)\n        if (it.index() == k)\n          it.valueRef() *= Scalar(0.5);\n\n    VERIFY_IS_APPROX(refS.adjoint(), refS);\n    VERIFY_IS_APPROX(mS.adjoint(), mS);\n    VERIFY_IS_APPROX(mS, refS);\n    VERIFY_IS_APPROX(x=mS*b, refX=refS*b);\n\n    // sparse selfadjointView with dense matrices\n    VERIFY_IS_APPROX(x=mUp.template selfadjointView<Upper>()*b, refX=refS*b);\n    VERIFY_IS_APPROX(x=mLo.template selfadjointView<Lower>()*b, refX=refS*b);\n    VERIFY_IS_APPROX(x=mS.template selfadjointView<Upper|Lower>()*b, refX=refS*b);\n\n    VERIFY_IS_APPROX(x=b * mUp.template selfadjointView<Upper>(),       refX=b*refS);\n    VERIFY_IS_APPROX(x=b * mLo.template selfadjointView<Lower>(),       refX=b*refS);\n    VERIFY_IS_APPROX(x=b * mS.template selfadjointView<Upper|Lower>(),  refX=b*refS);\n\n    VERIFY_IS_APPROX(x.noalias()+=mUp.template selfadjointView<Upper>()*b, refX+=refS*b);\n    VERIFY_IS_APPROX(x.noalias()-=mLo.template selfadjointView<Lower>()*b, refX-=refS*b);\n    VERIFY_IS_APPROX(x.noalias()+=mS.template selfadjointView<Upper|Lower>()*b, refX+=refS*b);\n    \n    // sparse selfadjointView with sparse matrices\n    SparseMatrixType mSres(rows,rows);\n    VERIFY_IS_APPROX(mSres = mLo.template selfadjointView<Lower>()*mS,\n                     refX = refLo.template selfadjointView<Lower>()*refS);\n    VERIFY_IS_APPROX(mSres = mS * mLo.template selfadjointView<Lower>(),\n                     refX = refS * refLo.template selfadjointView<Lower>());\n    \n    // sparse triangularView with dense matrices\n    VERIFY_IS_APPROX(x=mA.template triangularView<Upper>()*b, refX=refA.template triangularView<Upper>()*b);\n    VERIFY_IS_APPROX(x=mA.template triangularView<Lower>()*b, refX=refA.template triangularView<Lower>()*b);\n    VERIFY_IS_APPROX(x=b*mA.template triangularView<Upper>(), refX=b*refA.template triangularView<Upper>());\n    VERIFY_IS_APPROX(x=b*mA.template triangularView<Lower>(), refX=b*refA.template triangularView<Lower>());\n    \n    // sparse triangularView with sparse matrices\n    VERIFY_IS_APPROX(mSres = mA.template triangularView<Lower>()*mS,   refX = refA.template triangularView<Lower>()*refS);\n    VERIFY_IS_APPROX(mSres = mS * mA.template triangularView<Lower>(), refX = refS * refA.template triangularView<Lower>());\n    VERIFY_IS_APPROX(mSres = mA.template triangularView<Upper>()*mS,   refX = refA.template triangularView<Upper>()*refS);\n    VERIFY_IS_APPROX(mSres = mS * mA.template triangularView<Upper>(), refX = refS * refA.template triangularView<Upper>());\n  }\n}\n\n// New test for Bug in SparseTimeDenseProduct\ntemplate<typename SparseMatrixType, typename DenseMatrixType> void sparse_product_regression_test()\n{\n  // This code does not compile with afflicted versions of the bug\n  SparseMatrixType sm1(3,2);\n  DenseMatrixType m2(2,2);\n  sm1.setZero();\n  m2.setZero();\n\n  DenseMatrixType m3 = sm1*m2;\n\n\n  // This code produces a segfault with afflicted versions of another SparseTimeDenseProduct\n  // bug\n\n  SparseMatrixType sm2(20000,2);\n  sm2.setZero();\n  DenseMatrixType m4(sm2*m2);\n\n  VERIFY_IS_APPROX( m4(0,0), 0.0 );\n}\n\ntemplate<typename Scalar>\nvoid bug_942()\n{\n  typedef Matrix<Scalar, Dynamic, 1>     Vector;\n  typedef SparseMatrix<Scalar, ColMajor> ColSpMat;\n  typedef SparseMatrix<Scalar, RowMajor> RowSpMat;\n  ColSpMat cmA(1,1);\n  cmA.insert(0,0) = 1;\n\n  RowSpMat rmA(1,1);\n  rmA.insert(0,0) = 1;\n\n  Vector d(1);\n  d[0] = 2;\n  \n  double res = 2;\n  \n  VERIFY_IS_APPROX( ( cmA*d.asDiagonal() ).eval().coeff(0,0), res );\n  VERIFY_IS_APPROX( ( d.asDiagonal()*rmA ).eval().coeff(0,0), res );\n  VERIFY_IS_APPROX( ( rmA*d.asDiagonal() ).eval().coeff(0,0), res );\n  VERIFY_IS_APPROX( ( d.asDiagonal()*cmA ).eval().coeff(0,0), res );\n}\n\ntemplate<typename Real>\nvoid test_mixing_types()\n{\n  typedef std::complex<Real> Cplx;\n  typedef SparseMatrix<Real> SpMatReal;\n  typedef SparseMatrix<Cplx> SpMatCplx;\n  typedef SparseMatrix<Cplx,RowMajor> SpRowMatCplx;\n  typedef Matrix<Real,Dynamic,Dynamic> DenseMatReal;\n  typedef Matrix<Cplx,Dynamic,Dynamic> DenseMatCplx;\n\n  Index n = internal::random<Index>(1,100);\n  double density = (std::max)(8./(n*n), 0.2);\n\n  SpMatReal sR1(n,n);\n  SpMatCplx sC1(n,n), sC2(n,n), sC3(n,n);\n  SpRowMatCplx sCR(n,n);\n  DenseMatReal dR1(n,n);\n  DenseMatCplx dC1(n,n), dC2(n,n), dC3(n,n);\n\n  initSparse<Real>(density, dR1, sR1);\n  initSparse<Cplx>(density, dC1, sC1);\n  initSparse<Cplx>(density, dC2, sC2);\n\n  VERIFY_IS_APPROX( sC2 = (sR1 * sC1),                         dC3 = dR1.template cast<Cplx>() * dC1 );\n  VERIFY_IS_APPROX( sC2 = (sC1 * sR1),                         dC3 = dC1 * dR1.template cast<Cplx>() );\n  VERIFY_IS_APPROX( sC2 = (sR1.transpose() * sC1),             dC3 = dR1.template cast<Cplx>().transpose() * dC1 );\n  VERIFY_IS_APPROX( sC2 = (sC1.transpose() * sR1),             dC3 = dC1.transpose() * dR1.template cast<Cplx>() );\n  VERIFY_IS_APPROX( sC2 = (sR1 * sC1.transpose()),             dC3 = dR1.template cast<Cplx>() * dC1.transpose() );\n  VERIFY_IS_APPROX( sC2 = (sC1 * sR1.transpose()),             dC3 = dC1 * dR1.template cast<Cplx>().transpose() );\n  VERIFY_IS_APPROX( sC2 = (sR1.transpose() * sC1.transpose()), dC3 = dR1.template cast<Cplx>().transpose() * dC1.transpose() );\n  VERIFY_IS_APPROX( sC2 = (sC1.transpose() * sR1.transpose()), dC3 = dC1.transpose() * dR1.template cast<Cplx>().transpose() );\n\n  VERIFY_IS_APPROX( sCR = (sR1 * sC1),                         dC3 = dR1.template cast<Cplx>() * dC1 );\n  VERIFY_IS_APPROX( sCR = (sC1 * sR1),                         dC3 = dC1 * dR1.template cast<Cplx>() );\n  VERIFY_IS_APPROX( sCR = (sR1.transpose() * sC1),             dC3 = dR1.template cast<Cplx>().transpose() * dC1 );\n  VERIFY_IS_APPROX( sCR = (sC1.transpose() * sR1),             dC3 = dC1.transpose() * dR1.template cast<Cplx>() );\n  VERIFY_IS_APPROX( sCR = (sR1 * sC1.transpose()),             dC3 = dR1.template cast<Cplx>() * dC1.transpose() );\n  VERIFY_IS_APPROX( sCR = (sC1 * sR1.transpose()),             dC3 = dC1 * dR1.template cast<Cplx>().transpose() );\n  VERIFY_IS_APPROX( sCR = (sR1.transpose() * sC1.transpose()), dC3 = dR1.template cast<Cplx>().transpose() * dC1.transpose() );\n  VERIFY_IS_APPROX( sCR = (sC1.transpose() * sR1.transpose()), dC3 = dC1.transpose() * dR1.template cast<Cplx>().transpose() );\n\n\n  VERIFY_IS_APPROX( sC2 = (sR1 * sC1).pruned(),                         dC3 = dR1.template cast<Cplx>() * dC1 );\n  VERIFY_IS_APPROX( sC2 = (sC1 * sR1).pruned(),                         dC3 = dC1 * dR1.template cast<Cplx>() );\n  VERIFY_IS_APPROX( sC2 = (sR1.transpose() * sC1).pruned(),             dC3 = dR1.template cast<Cplx>().transpose() * dC1 );\n  VERIFY_IS_APPROX( sC2 = (sC1.transpose() * sR1).pruned(),             dC3 = dC1.transpose() * dR1.template cast<Cplx>() );\n  VERIFY_IS_APPROX( sC2 = (sR1 * sC1.transpose()).pruned(),             dC3 = dR1.template cast<Cplx>() * dC1.transpose() );\n  VERIFY_IS_APPROX( sC2 = (sC1 * sR1.transpose()).pruned(),             dC3 = dC1 * dR1.template cast<Cplx>().transpose() );\n  VERIFY_IS_APPROX( sC2 = (sR1.transpose() * sC1.transpose()).pruned(), dC3 = dR1.template cast<Cplx>().transpose() * dC1.transpose() );\n  VERIFY_IS_APPROX( sC2 = (sC1.transpose() * sR1.transpose()).pruned(), dC3 = dC1.transpose() * dR1.template cast<Cplx>().transpose() );\n\n  VERIFY_IS_APPROX( sCR = (sR1 * sC1).pruned(),                         dC3 = dR1.template cast<Cplx>() * dC1 );\n  VERIFY_IS_APPROX( sCR = (sC1 * sR1).pruned(),                         dC3 = dC1 * dR1.template cast<Cplx>() );\n  VERIFY_IS_APPROX( sCR = (sR1.transpose() * sC1).pruned(),             dC3 = dR1.template cast<Cplx>().transpose() * dC1 );\n  VERIFY_IS_APPROX( sCR = (sC1.transpose() * sR1).pruned(),             dC3 = dC1.transpose() * dR1.template cast<Cplx>() );\n  VERIFY_IS_APPROX( sCR = (sR1 * sC1.transpose()).pruned(),             dC3 = dR1.template cast<Cplx>() * dC1.transpose() );\n  VERIFY_IS_APPROX( sCR = (sC1 * sR1.transpose()).pruned(),             dC3 = dC1 * dR1.template cast<Cplx>().transpose() );\n  VERIFY_IS_APPROX( sCR = (sR1.transpose() * sC1.transpose()).pruned(), dC3 = dR1.template cast<Cplx>().transpose() * dC1.transpose() );\n  VERIFY_IS_APPROX( sCR = (sC1.transpose() * sR1.transpose()).pruned(), dC3 = dC1.transpose() * dR1.template cast<Cplx>().transpose() );\n\n\n  VERIFY_IS_APPROX( dC2 = (sR1 * sC1),                         dC3 = dR1.template cast<Cplx>() * dC1 );\n  VERIFY_IS_APPROX( dC2 = (sC1 * sR1),                         dC3 = dC1 * dR1.template cast<Cplx>() );\n  VERIFY_IS_APPROX( dC2 = (sR1.transpose() * sC1),             dC3 = dR1.template cast<Cplx>().transpose() * dC1 );\n  VERIFY_IS_APPROX( dC2 = (sC1.transpose() * sR1),             dC3 = dC1.transpose() * dR1.template cast<Cplx>() );\n  VERIFY_IS_APPROX( dC2 = (sR1 * sC1.transpose()),             dC3 = dR1.template cast<Cplx>() * dC1.transpose() );\n  VERIFY_IS_APPROX( dC2 = (sC1 * sR1.transpose()),             dC3 = dC1 * dR1.template cast<Cplx>().transpose() );\n  VERIFY_IS_APPROX( dC2 = (sR1.transpose() * sC1.transpose()), dC3 = dR1.template cast<Cplx>().transpose() * dC1.transpose() );\n  VERIFY_IS_APPROX( dC2 = (sC1.transpose() * sR1.transpose()), dC3 = dC1.transpose() * dR1.template cast<Cplx>().transpose() );\n\n\n  VERIFY_IS_APPROX( dC2 = dR1 * sC1, dC3 = dR1.template cast<Cplx>() * sC1 );\n  VERIFY_IS_APPROX( dC2 = sR1 * dC1, dC3 = sR1.template cast<Cplx>() * dC1 );\n  VERIFY_IS_APPROX( dC2 = dC1 * sR1, dC3 = dC1 * sR1.template cast<Cplx>() );\n  VERIFY_IS_APPROX( dC2 = sC1 * dR1, dC3 = sC1 * dR1.template cast<Cplx>() );\n\n  VERIFY_IS_APPROX( dC2 = dR1.row(0) * sC1, dC3 = dR1.template cast<Cplx>().row(0) * sC1 );\n  VERIFY_IS_APPROX( dC2 = sR1 * dC1.col(0), dC3 = sR1.template cast<Cplx>() * dC1.col(0) );\n  VERIFY_IS_APPROX( dC2 = dC1.row(0) * sR1, dC3 = dC1.row(0) * sR1.template cast<Cplx>() );\n  VERIFY_IS_APPROX( dC2 = sC1 * dR1.col(0), dC3 = sC1 * dR1.template cast<Cplx>().col(0) );\n}\n\nvoid test_sparse_product()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( (sparse_product<SparseMatrix<double,ColMajor> >()) );\n    CALL_SUBTEST_1( (sparse_product<SparseMatrix<double,RowMajor> >()) );\n    CALL_SUBTEST_1( (bug_942<double>()) );\n    CALL_SUBTEST_2( (sparse_product<SparseMatrix<std::complex<double>, ColMajor > >()) );\n    CALL_SUBTEST_2( (sparse_product<SparseMatrix<std::complex<double>, RowMajor > >()) );\n    CALL_SUBTEST_3( (sparse_product<SparseMatrix<float,ColMajor,long int> >()) );\n    CALL_SUBTEST_4( (sparse_product_regression_test<SparseMatrix<double,RowMajor>, Matrix<double, Dynamic, Dynamic, RowMajor> >()) );\n\n    CALL_SUBTEST_5( (test_mixing_types<float>()) );\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/sparse_ref.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 20015 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n// This unit test cannot be easily written to work with EIGEN_DEFAULT_TO_ROW_MAJOR\n#ifdef EIGEN_DEFAULT_TO_ROW_MAJOR\n#undef EIGEN_DEFAULT_TO_ROW_MAJOR\n#endif\n\nstatic long int nb_temporaries;\n\ninline void on_temporary_creation() {\n  // here's a great place to set a breakpoint when debugging failures in this test!\n  nb_temporaries++;\n}\n\n#define EIGEN_SPARSE_CREATE_TEMPORARY_PLUGIN { on_temporary_creation(); }\n\n#include \"main.h\"\n#include <Eigen/SparseCore>\n\n#define VERIFY_EVALUATION_COUNT(XPR,N) {\\\n    nb_temporaries = 0; \\\n    CALL_SUBTEST( XPR ); \\\n    if(nb_temporaries!=N) std::cerr << \"nb_temporaries == \" << nb_temporaries << \"\\n\"; \\\n    VERIFY( (#XPR) && nb_temporaries==N ); \\\n  }\n\ntemplate<typename PlainObjectType> void check_const_correctness(const PlainObjectType&)\n{\n  // verify that ref-to-const don't have LvalueBit\n  typedef typename internal::add_const<PlainObjectType>::type ConstPlainObjectType;\n  VERIFY( !(internal::traits<Ref<ConstPlainObjectType> >::Flags & LvalueBit) );\n  VERIFY( !(internal::traits<Ref<ConstPlainObjectType, Aligned> >::Flags & LvalueBit) );\n  VERIFY( !(Ref<ConstPlainObjectType>::Flags & LvalueBit) );\n  VERIFY( !(Ref<ConstPlainObjectType, Aligned>::Flags & LvalueBit) );\n}\n\ntemplate<typename B>\nEIGEN_DONT_INLINE void call_ref_1(Ref<SparseMatrix<float> > a, const B &b) { VERIFY_IS_EQUAL(a.toDense(),b.toDense()); }\n\ntemplate<typename B>\nEIGEN_DONT_INLINE void call_ref_2(const Ref<const SparseMatrix<float> >& a, const B &b) { VERIFY_IS_EQUAL(a.toDense(),b.toDense()); }\n\ntemplate<typename B>\nEIGEN_DONT_INLINE void call_ref_3(const Ref<const SparseMatrix<float>, StandardCompressedFormat>& a, const B &b) {\n  VERIFY(a.isCompressed());\n  VERIFY_IS_EQUAL(a.toDense(),b.toDense());\n}\n\ntemplate<typename B>\nEIGEN_DONT_INLINE void call_ref_4(Ref<SparseVector<float> > a, const B &b) { VERIFY_IS_EQUAL(a.toDense(),b.toDense()); }\n\ntemplate<typename B>\nEIGEN_DONT_INLINE void call_ref_5(const Ref<const SparseVector<float> >& a, const B &b) { VERIFY_IS_EQUAL(a.toDense(),b.toDense()); }\n\nvoid call_ref()\n{\n  SparseMatrix<float>               A = MatrixXf::Random(10,10).sparseView(0.5,1);\n  SparseMatrix<float,RowMajor>      B = MatrixXf::Random(10,10).sparseView(0.5,1);\n  SparseMatrix<float>               C = MatrixXf::Random(10,10).sparseView(0.5,1);\n  C.reserve(VectorXi::Constant(C.outerSize(), 2));\n  const SparseMatrix<float>&        Ac(A);\n  Block<SparseMatrix<float> >       Ab(A,0,1, 3,3);\n  const Block<SparseMatrix<float> > Abc(A,0,1,3,3);\n  SparseVector<float>               vc =  VectorXf::Random(10).sparseView(0.5,1);\n  SparseVector<float,RowMajor>      vr =  VectorXf::Random(10).sparseView(0.5,1);\n  SparseMatrix<float> AA = A*A;\n  \n\n  VERIFY_EVALUATION_COUNT( call_ref_1(A, A),  0);\n//   VERIFY_EVALUATION_COUNT( call_ref_1(Ac, Ac),  0); // does not compile on purpose\n  VERIFY_EVALUATION_COUNT( call_ref_2(A, A),  0);\n  VERIFY_EVALUATION_COUNT( call_ref_3(A, A),  0);\n  VERIFY_EVALUATION_COUNT( call_ref_2(A.transpose(), A.transpose()),  1);\n  VERIFY_EVALUATION_COUNT( call_ref_3(A.transpose(), A.transpose()),  1);\n  VERIFY_EVALUATION_COUNT( call_ref_2(Ac,Ac), 0);\n  VERIFY_EVALUATION_COUNT( call_ref_3(Ac,Ac), 0);\n  VERIFY_EVALUATION_COUNT( call_ref_2(A+A,2*Ac), 1);\n  VERIFY_EVALUATION_COUNT( call_ref_3(A+A,2*Ac), 1);\n  VERIFY_EVALUATION_COUNT( call_ref_2(B, B),  1);\n  VERIFY_EVALUATION_COUNT( call_ref_3(B, B),  1);\n  VERIFY_EVALUATION_COUNT( call_ref_2(B.transpose(), B.transpose()),  0);\n  VERIFY_EVALUATION_COUNT( call_ref_3(B.transpose(), B.transpose()),  0);\n  VERIFY_EVALUATION_COUNT( call_ref_2(A*A, AA),  3);\n  VERIFY_EVALUATION_COUNT( call_ref_3(A*A, AA),  3);\n  \n  VERIFY(!C.isCompressed());\n  VERIFY_EVALUATION_COUNT( call_ref_3(C, C),  1);\n  \n  Ref<SparseMatrix<float> > Ar(A);\n  VERIFY_IS_APPROX(Ar+Ar, A+A);\n  VERIFY_EVALUATION_COUNT( call_ref_1(Ar, A),  0);\n  VERIFY_EVALUATION_COUNT( call_ref_2(Ar, A),  0);\n  \n  Ref<SparseMatrix<float,RowMajor> > Br(B);\n  VERIFY_EVALUATION_COUNT( call_ref_1(Br.transpose(), Br.transpose()),  0);\n  VERIFY_EVALUATION_COUNT( call_ref_2(Br, Br),  1);\n  VERIFY_EVALUATION_COUNT( call_ref_2(Br.transpose(), Br.transpose()),  0);\n  \n  Ref<const SparseMatrix<float> > Arc(A);\n//   VERIFY_EVALUATION_COUNT( call_ref_1(Arc, Arc),  0); // does not compile on purpose\n  VERIFY_EVALUATION_COUNT( call_ref_2(Arc, Arc),  0);\n  \n  VERIFY_EVALUATION_COUNT( call_ref_2(A.middleCols(1,3), A.middleCols(1,3)),  0);\n  \n  VERIFY_EVALUATION_COUNT( call_ref_2(A.col(2), A.col(2)),  0);\n  VERIFY_EVALUATION_COUNT( call_ref_2(vc, vc),  0);\n  VERIFY_EVALUATION_COUNT( call_ref_2(vr.transpose(), vr.transpose()),  0);\n  VERIFY_EVALUATION_COUNT( call_ref_2(vr, vr.transpose()),  0);\n  \n  VERIFY_EVALUATION_COUNT( call_ref_2(A.block(1,1,3,3), A.block(1,1,3,3)),  1); // should be 0 (allocate starts/nnz only)\n\n  VERIFY_EVALUATION_COUNT( call_ref_4(vc, vc),  0);\n  VERIFY_EVALUATION_COUNT( call_ref_4(vr, vr.transpose()),  0);\n  VERIFY_EVALUATION_COUNT( call_ref_5(vc, vc),  0);\n  VERIFY_EVALUATION_COUNT( call_ref_5(vr, vr.transpose()),  0);\n  VERIFY_EVALUATION_COUNT( call_ref_4(A.col(2), A.col(2)),  0);\n  VERIFY_EVALUATION_COUNT( call_ref_5(A.col(2), A.col(2)),  0);\n  // VERIFY_EVALUATION_COUNT( call_ref_4(A.row(2), A.row(2).transpose()),  1); // does not compile on purpose\n  VERIFY_EVALUATION_COUNT( call_ref_5(A.row(2), A.row(2).transpose()),  1);\n}\n\nvoid test_sparse_ref()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( check_const_correctness(SparseMatrix<float>()) );\n    CALL_SUBTEST_1( check_const_correctness(SparseMatrix<double,RowMajor>()) );\n    CALL_SUBTEST_2( call_ref() );\n\n    CALL_SUBTEST_3( check_const_correctness(SparseVector<float>()) );\n    CALL_SUBTEST_3( check_const_correctness(SparseVector<double,RowMajor>()) );\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/sparse_solver.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2011 Gael Guennebaud <g.gael@free.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"sparse.h\"\n#include <Eigen/SparseCore>\n#include <sstream>\n\ntemplate<typename Solver, typename Rhs, typename Guess,typename Result>\nvoid solve_with_guess(IterativeSolverBase<Solver>& solver, const MatrixBase<Rhs>& b, const Guess& g, Result &x) {\n  if(internal::random<bool>())\n  {\n    // With a temporary through evaluator<SolveWithGuess>\n    x = solver.derived().solveWithGuess(b,g) + Result::Zero(x.rows(), x.cols());\n  }\n  else\n  {\n    // direct evaluation within x through Assignment<Result,SolveWithGuess>\n    x = solver.derived().solveWithGuess(b.derived(),g);\n  }\n}\n\ntemplate<typename Solver, typename Rhs, typename Guess,typename Result>\nvoid solve_with_guess(SparseSolverBase<Solver>& solver, const MatrixBase<Rhs>& b, const Guess& , Result& x) {\n  if(internal::random<bool>())\n    x = solver.derived().solve(b) + Result::Zero(x.rows(), x.cols());\n  else\n    x = solver.derived().solve(b);\n}\n\ntemplate<typename Solver, typename Rhs, typename Guess,typename Result>\nvoid solve_with_guess(SparseSolverBase<Solver>& solver, const SparseMatrixBase<Rhs>& b, const Guess& , Result& x) {\n  x = solver.derived().solve(b);\n}\n\ntemplate<typename Solver, typename Rhs, typename DenseMat, typename DenseRhs>\nvoid check_sparse_solving(Solver& solver, const typename Solver::MatrixType& A, const Rhs& b, const DenseMat& dA, const DenseRhs& db)\n{\n  typedef typename Solver::MatrixType Mat;\n  typedef typename Mat::Scalar Scalar;\n  typedef typename Mat::StorageIndex StorageIndex;\n\n  DenseRhs refX = dA.householderQr().solve(db);\n  {\n    Rhs x(A.cols(), b.cols());\n    Rhs oldb = b;\n\n    solver.compute(A);\n    if (solver.info() != Success)\n    {\n      std::cerr << \"ERROR | sparse solver testing, factorization failed (\" << typeid(Solver).name() << \")\\n\";\n      VERIFY(solver.info() == Success);\n    }\n    x = solver.solve(b);\n    if (solver.info() != Success)\n    {\n      std::cerr << \"WARNING | sparse solver testing: solving failed (\" << typeid(Solver).name() << \")\\n\";\n      return;\n    }\n    VERIFY(oldb.isApprox(b) && \"sparse solver testing: the rhs should not be modified!\");\n    VERIFY(x.isApprox(refX,test_precision<Scalar>()));\n\n    x.setZero();\n    solve_with_guess(solver, b, x, x);\n    VERIFY(solver.info() == Success && \"solving failed when using analyzePattern/factorize API\");\n    VERIFY(oldb.isApprox(b) && \"sparse solver testing: the rhs should not be modified!\");\n    VERIFY(x.isApprox(refX,test_precision<Scalar>()));\n    \n    x.setZero();\n    // test the analyze/factorize API\n    solver.analyzePattern(A);\n    solver.factorize(A);\n    VERIFY(solver.info() == Success && \"factorization failed when using analyzePattern/factorize API\");\n    x = solver.solve(b);\n    VERIFY(solver.info() == Success && \"solving failed when using analyzePattern/factorize API\");\n    VERIFY(oldb.isApprox(b) && \"sparse solver testing: the rhs should not be modified!\");\n    VERIFY(x.isApprox(refX,test_precision<Scalar>()));\n    \n    x.setZero();\n    // test with Map\n    MappedSparseMatrix<Scalar,Mat::Options,StorageIndex> Am(A.rows(), A.cols(), A.nonZeros(), const_cast<StorageIndex*>(A.outerIndexPtr()), const_cast<StorageIndex*>(A.innerIndexPtr()), const_cast<Scalar*>(A.valuePtr()));\n    solver.compute(Am);\n    VERIFY(solver.info() == Success && \"factorization failed when using Map\");\n    DenseRhs dx(refX);\n    dx.setZero();\n    Map<DenseRhs> xm(dx.data(), dx.rows(), dx.cols());\n    Map<const DenseRhs> bm(db.data(), db.rows(), db.cols());\n    xm = solver.solve(bm);\n    VERIFY(solver.info() == Success && \"solving failed when using Map\");\n    VERIFY(oldb.isApprox(bm) && \"sparse solver testing: the rhs should not be modified!\");\n    VERIFY(xm.isApprox(refX,test_precision<Scalar>()));\n  }\n  \n  // if not too large, do some extra check:\n  if(A.rows()<2000)\n  {\n    // test initialization ctor\n    {\n      Rhs x(b.rows(), b.cols());\n      Solver solver2(A);\n      VERIFY(solver2.info() == Success);\n      x = solver2.solve(b);\n      VERIFY(x.isApprox(refX,test_precision<Scalar>()));\n    }\n\n    // test dense Block as the result and rhs:\n    {\n      DenseRhs x(refX.rows(), refX.cols());\n      DenseRhs oldb(db);\n      x.setZero();\n      x.block(0,0,x.rows(),x.cols()) = solver.solve(db.block(0,0,db.rows(),db.cols()));\n      VERIFY(oldb.isApprox(db) && \"sparse solver testing: the rhs should not be modified!\");\n      VERIFY(x.isApprox(refX,test_precision<Scalar>()));\n    }\n\n    // test uncompressed inputs\n    {\n      Mat A2 = A;\n      A2.reserve((ArrayXf::Random(A.outerSize())+2).template cast<typename Mat::StorageIndex>().eval());\n      solver.compute(A2);\n      Rhs x = solver.solve(b);\n      VERIFY(x.isApprox(refX,test_precision<Scalar>()));\n    }\n\n    // test expression as input\n    {\n      solver.compute(0.5*(A+A));\n      Rhs x = solver.solve(b);\n      VERIFY(x.isApprox(refX,test_precision<Scalar>()));\n\n      Solver solver2(0.5*(A+A));\n      Rhs x2 = solver2.solve(b);\n      VERIFY(x2.isApprox(refX,test_precision<Scalar>()));\n    }\n  }\n}\n\ntemplate<typename Solver, typename Rhs>\nvoid check_sparse_solving_real_cases(Solver& solver, const typename Solver::MatrixType& A, const Rhs& b, const typename Solver::MatrixType& fullA, const Rhs& refX)\n{\n  typedef typename Solver::MatrixType Mat;\n  typedef typename Mat::Scalar Scalar;\n  typedef typename Mat::RealScalar RealScalar;\n  \n  Rhs x(A.cols(), b.cols());\n\n  solver.compute(A);\n  if (solver.info() != Success)\n  {\n    std::cerr << \"ERROR | sparse solver testing, factorization failed (\" << typeid(Solver).name() << \")\\n\";\n    VERIFY(solver.info() == Success);\n  }\n  x = solver.solve(b);\n  \n  if (solver.info() != Success)\n  {\n    std::cerr << \"WARNING | sparse solver testing, solving failed (\" << typeid(Solver).name() << \")\\n\";\n    return;\n  }\n  \n  RealScalar res_error = (fullA*x-b).norm()/b.norm();  \n  VERIFY( (res_error <= test_precision<Scalar>() ) && \"sparse solver failed without noticing it\"); \n\n  \n  if(refX.size() != 0 && (refX - x).norm()/refX.norm() > test_precision<Scalar>())\n  {\n    std::cerr << \"WARNING | found solution is different from the provided reference one\\n\";\n  }\n  \n}\ntemplate<typename Solver, typename DenseMat>\nvoid check_sparse_determinant(Solver& solver, const typename Solver::MatrixType& A, const DenseMat& dA)\n{\n  typedef typename Solver::MatrixType Mat;\n  typedef typename Mat::Scalar Scalar;\n  \n  solver.compute(A);\n  if (solver.info() != Success)\n  {\n    std::cerr << \"WARNING | sparse solver testing: factorization failed (check_sparse_determinant)\\n\";\n    return;\n  }\n\n  Scalar refDet = dA.determinant();\n  VERIFY_IS_APPROX(refDet,solver.determinant());\n}\ntemplate<typename Solver, typename DenseMat>\nvoid check_sparse_abs_determinant(Solver& solver, const typename Solver::MatrixType& A, const DenseMat& dA)\n{\n  using std::abs;\n  typedef typename Solver::MatrixType Mat;\n  typedef typename Mat::Scalar Scalar;\n  \n  solver.compute(A);\n  if (solver.info() != Success)\n  {\n    std::cerr << \"WARNING | sparse solver testing: factorization failed (check_sparse_abs_determinant)\\n\";\n    return;\n  }\n\n  Scalar refDet = abs(dA.determinant());\n  VERIFY_IS_APPROX(refDet,solver.absDeterminant());\n}\n\ntemplate<typename Solver, typename DenseMat>\nint generate_sparse_spd_problem(Solver& , typename Solver::MatrixType& A, typename Solver::MatrixType& halfA, DenseMat& dA, int maxSize = 300)\n{\n  typedef typename Solver::MatrixType Mat;\n  typedef typename Mat::Scalar Scalar;\n  typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;\n\n  int size = internal::random<int>(1,maxSize);\n  double density = (std::max)(8./(size*size), 0.01);\n\n  Mat M(size, size);\n  DenseMatrix dM(size, size);\n\n  initSparse<Scalar>(density, dM, M, ForceNonZeroDiag);\n\n  A = M * M.adjoint();\n  dA = dM * dM.adjoint();\n  \n  halfA.resize(size,size);\n  if(Solver::UpLo==(Lower|Upper))\n    halfA = A;\n  else\n    halfA.template selfadjointView<Solver::UpLo>().rankUpdate(M);\n  \n  return size;\n}\n\n\n#ifdef TEST_REAL_CASES\ntemplate<typename Scalar>\ninline std::string get_matrixfolder()\n{\n  std::string mat_folder = TEST_REAL_CASES; \n  if( internal::is_same<Scalar, std::complex<float> >::value || internal::is_same<Scalar, std::complex<double> >::value )\n    mat_folder  = mat_folder + static_cast<std::string>(\"/complex/\");\n  else\n    mat_folder = mat_folder + static_cast<std::string>(\"/real/\");\n  return mat_folder;\n}\nstd::string sym_to_string(int sym)\n{\n  if(sym==Symmetric) return \"Symmetric \";\n  if(sym==SPD)       return \"SPD \";\n  return \"\";\n}\ntemplate<typename Derived>\nstd::string solver_stats(const IterativeSolverBase<Derived> &solver)\n{\n  std::stringstream ss;\n  ss << solver.iterations() << \" iters, error: \" << solver.error();\n  return ss.str();\n}\ntemplate<typename Derived>\nstd::string solver_stats(const SparseSolverBase<Derived> &/*solver*/)\n{\n  return \"\";\n}\n#endif\n\ntemplate<typename Solver> void check_sparse_spd_solving(Solver& solver, int maxSize = 300, int maxRealWorldSize = 100000)\n{\n  typedef typename Solver::MatrixType Mat;\n  typedef typename Mat::Scalar Scalar;\n  typedef typename Mat::StorageIndex StorageIndex;\n  typedef SparseMatrix<Scalar,ColMajor, StorageIndex> SpMat;\n  typedef SparseVector<Scalar, 0, StorageIndex> SpVec;\n  typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;\n  typedef Matrix<Scalar,Dynamic,1> DenseVector;\n\n  // generate the problem\n  Mat A, halfA;\n  DenseMatrix dA;\n  for (int i = 0; i < g_repeat; i++) {\n    int size = generate_sparse_spd_problem(solver, A, halfA, dA, maxSize);\n\n    // generate the right hand sides\n    int rhsCols = internal::random<int>(1,16);\n    double density = (std::max)(8./(size*rhsCols), 0.1);\n    SpMat B(size,rhsCols);\n    DenseVector b = DenseVector::Random(size);\n    DenseMatrix dB(size,rhsCols);\n    initSparse<Scalar>(density, dB, B, ForceNonZeroDiag);\n    SpVec c = B.col(0);\n    DenseVector dc = dB.col(0);\n  \n    CALL_SUBTEST( check_sparse_solving(solver, A,     b,  dA, b)  );\n    CALL_SUBTEST( check_sparse_solving(solver, halfA, b,  dA, b)  );\n    CALL_SUBTEST( check_sparse_solving(solver, A,     dB, dA, dB) );\n    CALL_SUBTEST( check_sparse_solving(solver, halfA, dB, dA, dB) );\n    CALL_SUBTEST( check_sparse_solving(solver, A,     B,  dA, dB) );\n    CALL_SUBTEST( check_sparse_solving(solver, halfA, B,  dA, dB) );\n    CALL_SUBTEST( check_sparse_solving(solver, A,     c,  dA, dc) );\n    CALL_SUBTEST( check_sparse_solving(solver, halfA, c,  dA, dc) );\n    \n    // check only once\n    if(i==0)\n    {\n      b = DenseVector::Zero(size);\n      check_sparse_solving(solver, A, b, dA, b);\n    }\n  }\n  \n  // First, get the folder \n#ifdef TEST_REAL_CASES\n  // Test real problems with double precision only\n  if (internal::is_same<typename NumTraits<Scalar>::Real, double>::value)\n  {\n    std::string mat_folder = get_matrixfolder<Scalar>();\n    MatrixMarketIterator<Scalar> it(mat_folder);\n    for (; it; ++it)\n    {\n      if (it.sym() == SPD){\n        A = it.matrix();\n        if(A.diagonal().size() <= maxRealWorldSize)\n        {\n          DenseVector b = it.rhs();\n          DenseVector refX = it.refX();\n          PermutationMatrix<Dynamic, Dynamic, StorageIndex> pnull;\n          halfA.resize(A.rows(), A.cols());\n          if(Solver::UpLo == (Lower|Upper))\n            halfA = A;\n          else\n            halfA.template selfadjointView<Solver::UpLo>() = A.template triangularView<Eigen::Lower>().twistedBy(pnull);\n          \n          std::cout << \"INFO | Testing \" << sym_to_string(it.sym()) << \"sparse problem \" << it.matname()\n                  << \" (\" << A.rows() << \"x\" << A.cols() << \") using \" << typeid(Solver).name() << \"...\" << std::endl;\n          CALL_SUBTEST( check_sparse_solving_real_cases(solver, A,     b, A, refX) );\n          std::string stats = solver_stats(solver);\n          if(stats.size()>0)\n            std::cout << \"INFO |  \" << stats << std::endl;\n          CALL_SUBTEST( check_sparse_solving_real_cases(solver, halfA, b, A, refX) );\n        }\n        else\n        {\n          std::cout << \"INFO | Skip sparse problem \\\"\" << it.matname() << \"\\\" (too large)\" << std::endl;\n        }\n      }\n    }\n  }\n#else\n  EIGEN_UNUSED_VARIABLE(maxRealWorldSize);\n#endif\n}\n\ntemplate<typename Solver> void check_sparse_spd_determinant(Solver& solver)\n{\n  typedef typename Solver::MatrixType Mat;\n  typedef typename Mat::Scalar Scalar;\n  typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;\n\n  // generate the problem\n  Mat A, halfA;\n  DenseMatrix dA;\n  generate_sparse_spd_problem(solver, A, halfA, dA, 30);\n  \n  for (int i = 0; i < g_repeat; i++) {\n    check_sparse_determinant(solver, A,     dA);\n    check_sparse_determinant(solver, halfA, dA );\n  }\n}\n\ntemplate<typename Solver, typename DenseMat>\nIndex generate_sparse_square_problem(Solver&, typename Solver::MatrixType& A, DenseMat& dA, int maxSize = 300, int options = ForceNonZeroDiag)\n{\n  typedef typename Solver::MatrixType Mat;\n  typedef typename Mat::Scalar Scalar;\n\n  Index size = internal::random<int>(1,maxSize);\n  double density = (std::max)(8./(size*size), 0.01);\n  \n  A.resize(size,size);\n  dA.resize(size,size);\n\n  initSparse<Scalar>(density, dA, A, options);\n  \n  return size;\n}\n\n\nstruct prune_column {\n  Index m_col;\n  prune_column(Index col) : m_col(col) {}\n  template<class Scalar>\n  bool operator()(Index, Index col, const Scalar&) const {\n    return col != m_col;\n  }\n};\n\n\ntemplate<typename Solver> void check_sparse_square_solving(Solver& solver, int maxSize = 300, int maxRealWorldSize = 100000, bool checkDeficient = false)\n{\n  typedef typename Solver::MatrixType Mat;\n  typedef typename Mat::Scalar Scalar;\n  typedef SparseMatrix<Scalar,ColMajor, typename Mat::StorageIndex> SpMat;\n  typedef SparseVector<Scalar, 0, typename Mat::StorageIndex> SpVec;\n  typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;\n  typedef Matrix<Scalar,Dynamic,1> DenseVector;\n\n  int rhsCols = internal::random<int>(1,16);\n\n  Mat A;\n  DenseMatrix dA;\n  for (int i = 0; i < g_repeat; i++) {\n    Index size = generate_sparse_square_problem(solver, A, dA, maxSize);\n\n    A.makeCompressed();\n    DenseVector b = DenseVector::Random(size);\n    DenseMatrix dB(size,rhsCols);\n    SpMat B(size,rhsCols);\n    double density = (std::max)(8./(size*rhsCols), 0.1);\n    initSparse<Scalar>(density, dB, B, ForceNonZeroDiag);\n    B.makeCompressed();\n    SpVec c = B.col(0);\n    DenseVector dc = dB.col(0);\n    CALL_SUBTEST(check_sparse_solving(solver, A, b,  dA, b));\n    CALL_SUBTEST(check_sparse_solving(solver, A, dB, dA, dB));\n    CALL_SUBTEST(check_sparse_solving(solver, A, B,  dA, dB));\n    CALL_SUBTEST(check_sparse_solving(solver, A, c,  dA, dc));\n    \n    // check only once\n    if(i==0)\n    {\n      b = DenseVector::Zero(size);\n      check_sparse_solving(solver, A, b, dA, b);\n    }\n    // regression test for Bug 792 (structurally rank deficient matrices):\n    if(checkDeficient && size>1) {\n      Index col = internal::random<int>(0,int(size-1));\n      A.prune(prune_column(col));\n      solver.compute(A);\n      VERIFY_IS_EQUAL(solver.info(), NumericalIssue);\n    }\n  }\n  \n  // First, get the folder \n#ifdef TEST_REAL_CASES\n  // Test real problems with double precision only\n  if (internal::is_same<typename NumTraits<Scalar>::Real, double>::value)\n  {\n    std::string mat_folder = get_matrixfolder<Scalar>();\n    MatrixMarketIterator<Scalar> it(mat_folder);\n    for (; it; ++it)\n    {\n      A = it.matrix();\n      if(A.diagonal().size() <= maxRealWorldSize)\n      {\n        DenseVector b = it.rhs();\n        DenseVector refX = it.refX();\n        std::cout << \"INFO | Testing \" << sym_to_string(it.sym()) << \"sparse problem \" << it.matname()\n                  << \" (\" << A.rows() << \"x\" << A.cols() << \") using \" << typeid(Solver).name() << \"...\" << std::endl;\n        CALL_SUBTEST(check_sparse_solving_real_cases(solver, A, b, A, refX));\n        std::string stats = solver_stats(solver);\n        if(stats.size()>0)\n          std::cout << \"INFO |  \" << stats << std::endl;\n      }\n      else\n      {\n        std::cout << \"INFO | SKIP sparse problem \\\"\" << it.matname() << \"\\\" (too large)\" << std::endl;\n      }\n    }\n  }\n#else\n  EIGEN_UNUSED_VARIABLE(maxRealWorldSize);\n#endif\n\n}\n\ntemplate<typename Solver> void check_sparse_square_determinant(Solver& solver)\n{\n  typedef typename Solver::MatrixType Mat;\n  typedef typename Mat::Scalar Scalar;\n  typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;\n  \n  for (int i = 0; i < g_repeat; i++) {\n    // generate the problem\n    Mat A;\n    DenseMatrix dA;\n    \n    int size = internal::random<int>(1,30);\n    dA.setRandom(size,size);\n    \n    dA = (dA.array().abs()<0.3).select(0,dA);\n    dA.diagonal() = (dA.diagonal().array()==0).select(1,dA.diagonal());\n    A = dA.sparseView();\n    A.makeCompressed();\n  \n    check_sparse_determinant(solver, A, dA);\n  }\n}\n\ntemplate<typename Solver> void check_sparse_square_abs_determinant(Solver& solver)\n{\n  typedef typename Solver::MatrixType Mat;\n  typedef typename Mat::Scalar Scalar;\n  typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;\n\n  for (int i = 0; i < g_repeat; i++) {\n    // generate the problem\n    Mat A;\n    DenseMatrix dA;\n    generate_sparse_square_problem(solver, A, dA, 30);\n    A.makeCompressed();\n    check_sparse_abs_determinant(solver, A, dA);\n  }\n}\n\ntemplate<typename Solver, typename DenseMat>\nvoid generate_sparse_leastsquare_problem(Solver&, typename Solver::MatrixType& A, DenseMat& dA, int maxSize = 300, int options = ForceNonZeroDiag)\n{\n  typedef typename Solver::MatrixType Mat;\n  typedef typename Mat::Scalar Scalar;\n\n  int rows = internal::random<int>(1,maxSize);\n  int cols = internal::random<int>(1,rows);\n  double density = (std::max)(8./(rows*cols), 0.01);\n  \n  A.resize(rows,cols);\n  dA.resize(rows,cols);\n\n  initSparse<Scalar>(density, dA, A, options);\n}\n\ntemplate<typename Solver> void check_sparse_leastsquare_solving(Solver& solver)\n{\n  typedef typename Solver::MatrixType Mat;\n  typedef typename Mat::Scalar Scalar;\n  typedef SparseMatrix<Scalar,ColMajor, typename Mat::StorageIndex> SpMat;\n  typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;\n  typedef Matrix<Scalar,Dynamic,1> DenseVector;\n\n  int rhsCols = internal::random<int>(1,16);\n\n  Mat A;\n  DenseMatrix dA;\n  for (int i = 0; i < g_repeat; i++) {\n    generate_sparse_leastsquare_problem(solver, A, dA);\n\n    A.makeCompressed();\n    DenseVector b = DenseVector::Random(A.rows());\n    DenseMatrix dB(A.rows(),rhsCols);\n    SpMat B(A.rows(),rhsCols);\n    double density = (std::max)(8./(A.rows()*rhsCols), 0.1);\n    initSparse<Scalar>(density, dB, B, ForceNonZeroDiag);\n    B.makeCompressed();\n    check_sparse_solving(solver, A, b,  dA, b);\n    check_sparse_solving(solver, A, dB, dA, dB);\n    check_sparse_solving(solver, A, B,  dA, dB);\n    \n    // check only once\n    if(i==0)\n    {\n      b = DenseVector::Zero(A.rows());\n      check_sparse_solving(solver, A, b, dA, b);\n    }\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/sparse_solvers.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"sparse.h\"\n\ntemplate<typename Scalar> void\ninitSPD(double density,\n        Matrix<Scalar,Dynamic,Dynamic>& refMat,\n        SparseMatrix<Scalar>& sparseMat)\n{\n  Matrix<Scalar,Dynamic,Dynamic> aux(refMat.rows(),refMat.cols());\n  initSparse(density,refMat,sparseMat);\n  refMat = refMat * refMat.adjoint();\n  for (int k=0; k<2; ++k)\n  {\n    initSparse(density,aux,sparseMat,ForceNonZeroDiag);\n    refMat += aux * aux.adjoint();\n  }\n  sparseMat.setZero();\n  for (int j=0 ; j<sparseMat.cols(); ++j)\n    for (int i=j ; i<sparseMat.rows(); ++i)\n      if (refMat(i,j)!=Scalar(0))\n        sparseMat.insert(i,j) = refMat(i,j);\n  sparseMat.finalize();\n}\n\ntemplate<typename Scalar> void sparse_solvers(int rows, int cols)\n{\n  double density = (std::max)(8./(rows*cols), 0.01);\n  typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;\n  typedef Matrix<Scalar,Dynamic,1> DenseVector;\n  // Scalar eps = 1e-6;\n\n  DenseVector vec1 = DenseVector::Random(rows);\n\n  std::vector<Vector2i> zeroCoords;\n  std::vector<Vector2i> nonzeroCoords;\n\n  // test triangular solver\n  {\n    DenseVector vec2 = vec1, vec3 = vec1;\n    SparseMatrix<Scalar> m2(rows, cols);\n    DenseMatrix refMat2 = DenseMatrix::Zero(rows, cols);\n\n    // lower - dense\n    initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular, &zeroCoords, &nonzeroCoords);\n    VERIFY_IS_APPROX(refMat2.template triangularView<Lower>().solve(vec2),\n                     m2.template triangularView<Lower>().solve(vec3));\n\n    // upper - dense\n    initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular, &zeroCoords, &nonzeroCoords);\n    VERIFY_IS_APPROX(refMat2.template triangularView<Upper>().solve(vec2),\n                     m2.template triangularView<Upper>().solve(vec3));\n    VERIFY_IS_APPROX(refMat2.conjugate().template triangularView<Upper>().solve(vec2),\n                     m2.conjugate().template triangularView<Upper>().solve(vec3));\n    {\n      SparseMatrix<Scalar> cm2(m2);\n      //Index rows, Index cols, Index nnz, Index* outerIndexPtr, Index* innerIndexPtr, Scalar* valuePtr\n      MappedSparseMatrix<Scalar> mm2(rows, cols, cm2.nonZeros(), cm2.outerIndexPtr(), cm2.innerIndexPtr(), cm2.valuePtr());\n      VERIFY_IS_APPROX(refMat2.conjugate().template triangularView<Upper>().solve(vec2),\n                       mm2.conjugate().template triangularView<Upper>().solve(vec3));\n    }\n\n    // lower - transpose\n    initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular, &zeroCoords, &nonzeroCoords);\n    VERIFY_IS_APPROX(refMat2.transpose().template triangularView<Upper>().solve(vec2),\n                     m2.transpose().template triangularView<Upper>().solve(vec3));\n\n    // upper - transpose\n    initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular, &zeroCoords, &nonzeroCoords);\n    VERIFY_IS_APPROX(refMat2.transpose().template triangularView<Lower>().solve(vec2),\n                     m2.transpose().template triangularView<Lower>().solve(vec3));\n\n    SparseMatrix<Scalar> matB(rows, rows);\n    DenseMatrix refMatB = DenseMatrix::Zero(rows, rows);\n\n    // lower - sparse\n    initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular);\n    initSparse<Scalar>(density, refMatB, matB);\n    refMat2.template triangularView<Lower>().solveInPlace(refMatB);\n    m2.template triangularView<Lower>().solveInPlace(matB);\n    VERIFY_IS_APPROX(matB.toDense(), refMatB);\n\n    // upper - sparse\n    initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular);\n    initSparse<Scalar>(density, refMatB, matB);\n    refMat2.template triangularView<Upper>().solveInPlace(refMatB);\n    m2.template triangularView<Upper>().solveInPlace(matB);\n    VERIFY_IS_APPROX(matB, refMatB);\n\n    // test deprecated API\n    initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular, &zeroCoords, &nonzeroCoords);\n    VERIFY_IS_APPROX(refMat2.template triangularView<Lower>().solve(vec2),\n                     m2.template triangularView<Lower>().solve(vec3));\n  }\n}\n\nvoid test_sparse_solvers()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1(sparse_solvers<double>(8, 8) );\n    int s = internal::random<int>(1,300);\n    CALL_SUBTEST_2(sparse_solvers<std::complex<double> >(s,s) );\n    CALL_SUBTEST_1(sparse_solvers<double>(s,s) );\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/sparse_vector.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"sparse.h\"\n\ntemplate<typename Scalar,typename StorageIndex> void sparse_vector(int rows, int cols)\n{\n  double densityMat = (std::max)(8./(rows*cols), 0.01);\n  double densityVec = (std::max)(8./(rows), 0.1);\n  typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;\n  typedef Matrix<Scalar,Dynamic,1> DenseVector;\n  typedef SparseVector<Scalar,0,StorageIndex> SparseVectorType;\n  typedef SparseMatrix<Scalar,0,StorageIndex> SparseMatrixType;\n  Scalar eps = 1e-6;\n\n  SparseMatrixType m1(rows,rows);\n  SparseVectorType v1(rows), v2(rows), v3(rows);\n  DenseMatrix refM1 = DenseMatrix::Zero(rows, rows);\n  DenseVector refV1 = DenseVector::Random(rows),\n              refV2 = DenseVector::Random(rows),\n              refV3 = DenseVector::Random(rows);\n\n  std::vector<int> zerocoords, nonzerocoords;\n  initSparse<Scalar>(densityVec, refV1, v1, &zerocoords, &nonzerocoords);\n  initSparse<Scalar>(densityMat, refM1, m1);\n\n  initSparse<Scalar>(densityVec, refV2, v2);\n  initSparse<Scalar>(densityVec, refV3, v3);\n\n  Scalar s1 = internal::random<Scalar>();\n\n  // test coeff and coeffRef\n  for (unsigned int i=0; i<zerocoords.size(); ++i)\n  {\n    VERIFY_IS_MUCH_SMALLER_THAN( v1.coeff(zerocoords[i]), eps );\n    //VERIFY_RAISES_ASSERT( v1.coeffRef(zerocoords[i]) = 5 );\n  }\n  {\n    VERIFY(int(nonzerocoords.size()) == v1.nonZeros());\n    int j=0;\n    for (typename SparseVectorType::InnerIterator it(v1); it; ++it,++j)\n    {\n      VERIFY(nonzerocoords[j]==it.index());\n      VERIFY(it.value()==v1.coeff(it.index()));\n      VERIFY(it.value()==refV1.coeff(it.index()));\n    }\n  }\n  VERIFY_IS_APPROX(v1, refV1);\n  \n  // test coeffRef with reallocation\n  {\n    SparseVectorType v4(rows);\n    DenseVector v5 = DenseVector::Zero(rows);\n    for(int k=0; k<rows; ++k)\n    {\n      int i = internal::random<int>(0,rows-1);\n      Scalar v = internal::random<Scalar>();\n      v4.coeffRef(i) += v;\n      v5.coeffRef(i) += v;\n    }\n    VERIFY_IS_APPROX(v4,v5);\n  }\n\n  v1.coeffRef(nonzerocoords[0]) = Scalar(5);\n  refV1.coeffRef(nonzerocoords[0]) = Scalar(5);\n  VERIFY_IS_APPROX(v1, refV1);\n\n  VERIFY_IS_APPROX(v1+v2, refV1+refV2);\n  VERIFY_IS_APPROX(v1+v2+v3, refV1+refV2+refV3);\n\n  VERIFY_IS_APPROX(v1*s1-v2, refV1*s1-refV2);\n\n  VERIFY_IS_APPROX(v1*=s1, refV1*=s1);\n  VERIFY_IS_APPROX(v1/=s1, refV1/=s1);\n\n  VERIFY_IS_APPROX(v1+=v2, refV1+=refV2);\n  VERIFY_IS_APPROX(v1-=v2, refV1-=refV2);\n\n  VERIFY_IS_APPROX(v1.dot(v2), refV1.dot(refV2));\n  VERIFY_IS_APPROX(v1.dot(refV2), refV1.dot(refV2));\n\n  VERIFY_IS_APPROX(m1*v2, refM1*refV2);\n  VERIFY_IS_APPROX(v1.dot(m1*v2), refV1.dot(refM1*refV2));\n  {\n    int i = internal::random<int>(0,rows-1);\n    VERIFY_IS_APPROX(v1.dot(m1.col(i)), refV1.dot(refM1.col(i)));\n  }\n\n\n  VERIFY_IS_APPROX(v1.squaredNorm(), refV1.squaredNorm());\n  \n  VERIFY_IS_APPROX(v1.blueNorm(), refV1.blueNorm());\n\n  // test aliasing\n  VERIFY_IS_APPROX((v1 = -v1), (refV1 = -refV1));\n  VERIFY_IS_APPROX((v1 = v1.transpose()), (refV1 = refV1.transpose().eval()));\n  VERIFY_IS_APPROX((v1 += -v1), (refV1 += -refV1));\n  \n  // sparse matrix to sparse vector\n  SparseMatrixType mv1;\n  VERIFY_IS_APPROX((mv1=v1),v1);\n  VERIFY_IS_APPROX(mv1,(v1=mv1));\n  VERIFY_IS_APPROX(mv1,(v1=mv1.transpose()));\n  \n  // check copy to dense vector with transpose\n  refV3.resize(0);\n  VERIFY_IS_APPROX(refV3 = v1.transpose(),v1.toDense()); \n  VERIFY_IS_APPROX(DenseVector(v1),v1.toDense()); \n\n  // test conservative resize\n  {\n    std::vector<StorageIndex> inc;\n    if(rows > 3)\n      inc.push_back(-3);\n    inc.push_back(0);\n    inc.push_back(3);\n    inc.push_back(1);\n    inc.push_back(10);\n\n    for(std::size_t i = 0; i< inc.size(); i++) {\n      StorageIndex incRows = inc[i];\n      SparseVectorType vec1(rows);\n      DenseVector refVec1 = DenseVector::Zero(rows);\n      initSparse<Scalar>(densityVec, refVec1, vec1);\n\n      vec1.conservativeResize(rows+incRows);\n      refVec1.conservativeResize(rows+incRows);\n      if (incRows > 0) refVec1.tail(incRows).setZero();\n\n      VERIFY_IS_APPROX(vec1, refVec1);\n\n      // Insert new values\n      if (incRows > 0)\n        vec1.insert(vec1.rows()-1) = refVec1(refVec1.rows()-1) = 1;\n\n      VERIFY_IS_APPROX(vec1, refVec1);\n    }\n  }\n\n}\n\nvoid test_sparse_vector()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    int r = Eigen::internal::random<int>(1,500), c = Eigen::internal::random<int>(1,500);\n    if(Eigen::internal::random<int>(0,4) == 0) {\n      r = c; // check square matrices in 25% of tries\n    }\n    EIGEN_UNUSED_VARIABLE(r+c);\n\n    CALL_SUBTEST_1(( sparse_vector<double,int>(8, 8) ));\n    CALL_SUBTEST_2(( sparse_vector<std::complex<double>, int>(r, c) ));\n    CALL_SUBTEST_1(( sparse_vector<double,long int>(r, c) ));\n    CALL_SUBTEST_1(( sparse_vector<double,short>(r, c) ));\n  }\n}\n\n"
  },
  {
    "path": "include/eigen3/test/sparselu.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n// SparseLU solve does not accept column major matrices for the destination.\n// However, as expected, the generic check_sparse_square_solving routines produces row-major\n// rhs and destination matrices when compiled with EIGEN_DEFAULT_TO_ROW_MAJOR\n\n#ifdef EIGEN_DEFAULT_TO_ROW_MAJOR\n#undef EIGEN_DEFAULT_TO_ROW_MAJOR\n#endif\n\n#include \"sparse_solver.h\"\n#include <Eigen/SparseLU>\n#include <unsupported/Eigen/SparseExtra>\n\ntemplate<typename T> void test_sparselu_T()\n{\n  SparseLU<SparseMatrix<T, ColMajor> /*, COLAMDOrdering<int>*/ > sparselu_colamd; // COLAMDOrdering is the default\n  SparseLU<SparseMatrix<T, ColMajor>, AMDOrdering<int> > sparselu_amd; \n  SparseLU<SparseMatrix<T, ColMajor, long int>, NaturalOrdering<long int> > sparselu_natural;\n  \n  check_sparse_square_solving(sparselu_colamd,  300, 100000, true); \n  check_sparse_square_solving(sparselu_amd,     300,  10000, true);\n  check_sparse_square_solving(sparselu_natural, 300,   2000, true);\n  \n  check_sparse_square_abs_determinant(sparselu_colamd);\n  check_sparse_square_abs_determinant(sparselu_amd);\n  \n  check_sparse_square_determinant(sparselu_colamd);\n  check_sparse_square_determinant(sparselu_amd);\n}\n\nvoid test_sparselu()\n{\n  CALL_SUBTEST_1(test_sparselu_T<float>()); \n  CALL_SUBTEST_2(test_sparselu_T<double>());\n  CALL_SUBTEST_3(test_sparselu_T<std::complex<float> >()); \n  CALL_SUBTEST_4(test_sparselu_T<std::complex<double> >());\n}\n"
  },
  {
    "path": "include/eigen3/test/sparseqr.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Desire Nuentsa Wakam <desire.nuentsa_wakam@inria.fr>\n// Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n#include \"sparse.h\"\n#include <Eigen/SparseQR>\n\ntemplate<typename MatrixType,typename DenseMat>\nint generate_sparse_rectangular_problem(MatrixType& A, DenseMat& dA, int maxRows = 300, int maxCols = 150)\n{\n  eigen_assert(maxRows >= maxCols);\n  typedef typename MatrixType::Scalar Scalar;\n  int rows = internal::random<int>(1,maxRows);\n  int cols = internal::random<int>(1,maxCols);\n  double density = (std::max)(8./(rows*cols), 0.01);\n  \n  A.resize(rows,cols);\n  dA.resize(rows,cols);\n  initSparse<Scalar>(density, dA, A,ForceNonZeroDiag);\n  A.makeCompressed();\n  int nop = internal::random<int>(0, internal::random<double>(0,1) > 0.5 ? cols/2 : 0);\n  for(int k=0; k<nop; ++k)\n  {\n    int j0 = internal::random<int>(0,cols-1);\n    int j1 = internal::random<int>(0,cols-1);\n    Scalar s = internal::random<Scalar>();\n    A.col(j0)  = s * A.col(j1);\n    dA.col(j0) = s * dA.col(j1);\n  }\n  \n//   if(rows<cols) {\n//     A.conservativeResize(cols,cols);\n//     dA.conservativeResize(cols,cols);\n//     dA.bottomRows(cols-rows).setZero();\n//   }\n  \n  return rows;\n}\n\ntemplate<typename Scalar> void test_sparseqr_scalar()\n{\n  typedef SparseMatrix<Scalar,ColMajor> MatrixType; \n  typedef Matrix<Scalar,Dynamic,Dynamic> DenseMat;\n  typedef Matrix<Scalar,Dynamic,1> DenseVector;\n  MatrixType A;\n  DenseMat dA;\n  DenseVector refX,x,b; \n  SparseQR<MatrixType, COLAMDOrdering<int> > solver; \n  generate_sparse_rectangular_problem(A,dA);\n  \n  b = dA * DenseVector::Random(A.cols());\n  solver.compute(A);\n\n  // Q should be MxM\n  VERIFY_IS_EQUAL(solver.matrixQ().rows(), A.rows());\n  VERIFY_IS_EQUAL(solver.matrixQ().cols(), A.rows());\n\n  // R should be MxN\n  VERIFY_IS_EQUAL(solver.matrixR().rows(), A.rows());\n  VERIFY_IS_EQUAL(solver.matrixR().cols(), A.cols());\n\n  // Q and R can be multiplied\n  DenseMat recoveredA = solver.matrixQ()\n                      * DenseMat(solver.matrixR().template triangularView<Upper>())\n                      * solver.colsPermutation().transpose();\n  VERIFY_IS_EQUAL(recoveredA.rows(), A.rows());\n  VERIFY_IS_EQUAL(recoveredA.cols(), A.cols());\n\n  // and in the full rank case the original matrix is recovered\n  if (solver.rank() == A.cols())\n  {\n      VERIFY_IS_APPROX(A, recoveredA);\n  }\n\n  if(internal::random<float>(0,1)>0.5f)\n    solver.factorize(A);  // this checks that calling analyzePattern is not needed if the pattern do not change.\n  if (solver.info() != Success)\n  {\n    std::cerr << \"sparse QR factorization failed\\n\";\n    exit(0);\n    return;\n  }\n  x = solver.solve(b);\n  if (solver.info() != Success)\n  {\n    std::cerr << \"sparse QR factorization failed\\n\";\n    exit(0);\n    return;\n  }\n  \n  VERIFY_IS_APPROX(A * x, b);\n  \n  //Compare with a dense QR solver\n  ColPivHouseholderQR<DenseMat> dqr(dA);\n  refX = dqr.solve(b);\n  \n  VERIFY_IS_EQUAL(dqr.rank(), solver.rank());\n  if(solver.rank()==A.cols()) // full rank\n    VERIFY_IS_APPROX(x, refX);\n//   else\n//     VERIFY((dA * refX - b).norm() * 2 > (A * x - b).norm() );\n\n  // Compute explicitly the matrix Q\n  MatrixType Q, QtQ, idM;\n  Q = solver.matrixQ();\n  //Check  ||Q' * Q - I ||\n  QtQ = Q * Q.adjoint();\n  idM.resize(Q.rows(), Q.rows()); idM.setIdentity();\n  VERIFY(idM.isApprox(QtQ));\n  \n  // Q to dense\n  DenseMat dQ;\n  dQ = solver.matrixQ();\n  VERIFY_IS_APPROX(Q, dQ);\n}\nvoid test_sparseqr()\n{\n  for(int i=0; i<g_repeat; ++i)\n  {\n    CALL_SUBTEST_1(test_sparseqr_scalar<double>());\n    CALL_SUBTEST_2(test_sparseqr_scalar<std::complex<double> >());\n  }\n}\n\n"
  },
  {
    "path": "include/eigen3/test/special_numbers.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2013 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\ntemplate<typename Scalar> void special_numbers()\n{\n  typedef Matrix<Scalar, Dynamic,Dynamic> MatType;\n  int rows = internal::random<int>(1,300);\n  int cols = internal::random<int>(1,300);\n  \n  Scalar nan = std::numeric_limits<Scalar>::quiet_NaN();\n  Scalar inf = std::numeric_limits<Scalar>::infinity();\n  Scalar s1 = internal::random<Scalar>();\n  \n  MatType m1    = MatType::Random(rows,cols),\n          mnan  = MatType::Random(rows,cols),\n          minf  = MatType::Random(rows,cols),\n          mboth = MatType::Random(rows,cols);\n          \n  int n = internal::random<int>(1,10);\n  for(int k=0; k<n; ++k)\n  {\n    mnan(internal::random<int>(0,rows-1), internal::random<int>(0,cols-1)) = nan;\n    minf(internal::random<int>(0,rows-1), internal::random<int>(0,cols-1)) = inf;\n  }\n  mboth = mnan + minf;\n  \n  VERIFY(!m1.hasNaN());\n  VERIFY(m1.allFinite());\n  \n  VERIFY(mnan.hasNaN());\n  VERIFY((s1*mnan).hasNaN());\n  VERIFY(!minf.hasNaN());\n  VERIFY(!(2*minf).hasNaN());\n  VERIFY(mboth.hasNaN());\n  VERIFY(mboth.array().hasNaN());\n  \n  VERIFY(!mnan.allFinite());\n  VERIFY(!minf.allFinite());\n  VERIFY(!(minf-mboth).allFinite());\n  VERIFY(!mboth.allFinite());\n  VERIFY(!mboth.array().allFinite());\n}\n\nvoid test_special_numbers()\n{\n  for(int i = 0; i < 10*g_repeat; i++) {\n    CALL_SUBTEST_1( special_numbers<float>() );\n    CALL_SUBTEST_1( special_numbers<double>() );\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/spqr_support.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Desire Nuentsa Wakam <desire.nuentsa_wakam@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n\n#define EIGEN_NO_DEBUG_SMALL_PRODUCT_BLOCKS\n#include \"sparse.h\"\n#include <Eigen/SPQRSupport>\n\n\ntemplate<typename MatrixType,typename DenseMat>\nint generate_sparse_rectangular_problem(MatrixType& A, DenseMat& dA, int maxRows = 300, int maxCols = 300)\n{\n  eigen_assert(maxRows >= maxCols);\n  typedef typename MatrixType::Scalar Scalar;\n  int rows = internal::random<int>(1,maxRows);\n  int cols = internal::random<int>(1,rows);\n  double density = (std::max)(8./(rows*cols), 0.01);\n  \n  A.resize(rows,cols);\n  dA.resize(rows,cols);\n  initSparse<Scalar>(density, dA, A,ForceNonZeroDiag);\n  A.makeCompressed();\n  return rows;\n}\n\ntemplate<typename Scalar> void test_spqr_scalar()\n{\n  typedef SparseMatrix<Scalar,ColMajor> MatrixType; \n  MatrixType A;\n  Matrix<Scalar,Dynamic,Dynamic> dA;\n  typedef Matrix<Scalar,Dynamic,1> DenseVector;\n  DenseVector refX,x,b; \n  SPQR<MatrixType> solver; \n  generate_sparse_rectangular_problem(A,dA);\n  \n  Index m = A.rows();\n  b = DenseVector::Random(m);\n  solver.compute(A);\n  if (solver.info() != Success)\n  {\n    std::cerr << \"sparse QR factorization failed\\n\";\n    exit(0);\n    return;\n  }\n  x = solver.solve(b);\n  if (solver.info() != Success)\n  {\n    std::cerr << \"sparse QR factorization failed\\n\";\n    exit(0);\n    return;\n  }  \n  //Compare with a dense solver\n  refX = dA.colPivHouseholderQr().solve(b);\n  VERIFY(x.isApprox(refX,test_precision<Scalar>()));\n}\nvoid test_spqr_support()\n{\n  CALL_SUBTEST_1(test_spqr_scalar<double>());\n  CALL_SUBTEST_2(test_spqr_scalar<std::complex<double> >());\n}\n"
  },
  {
    "path": "include/eigen3/test/stable_norm.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\ntemplate<typename T> EIGEN_DONT_INLINE T copy(const T& x)\n{\n  return x;\n}\n\ntemplate<typename MatrixType> void stable_norm(const MatrixType& m)\n{\n  /* this test covers the following files:\n     StableNorm.h\n  */\n  using std::sqrt;\n  using std::abs;\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  \n  bool complex_real_product_ok = true;\n\n  // Check the basic machine-dependent constants.\n  {\n    int ibeta, it, iemin, iemax;\n\n    ibeta = std::numeric_limits<RealScalar>::radix;         // base for floating-point numbers\n    it    = std::numeric_limits<RealScalar>::digits;        // number of base-beta digits in mantissa\n    iemin = std::numeric_limits<RealScalar>::min_exponent;  // minimum exponent\n    iemax = std::numeric_limits<RealScalar>::max_exponent;  // maximum exponent\n\n    VERIFY( (!(iemin > 1 - 2*it || 1+it>iemax || (it==2 && ibeta<5) || (it<=4 && ibeta <= 3 ) || it<2))\n           && \"the stable norm algorithm cannot be guaranteed on this computer\");\n    \n    Scalar inf = std::numeric_limits<RealScalar>::infinity();\n    if(NumTraits<Scalar>::IsComplex && (numext::isnan)(inf*RealScalar(1)) )\n    {\n      complex_real_product_ok = false;\n      static bool first = true;\n      if(first)\n        std::cerr << \"WARNING: compiler mess up complex*real product, \" << inf << \" * \" << 1.0 << \" = \" << inf*RealScalar(1) << std::endl;\n      first = false;\n    }\n  }\n\n\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  // get a non-zero random factor\n  Scalar factor = internal::random<Scalar>();\n  while(numext::abs2(factor)<RealScalar(1e-4))\n    factor = internal::random<Scalar>();\n  Scalar big = factor * ((std::numeric_limits<RealScalar>::max)() * RealScalar(1e-4));\n  \n  factor = internal::random<Scalar>();\n  while(numext::abs2(factor)<RealScalar(1e-4))\n    factor = internal::random<Scalar>();\n  Scalar small = factor * ((std::numeric_limits<RealScalar>::min)() * RealScalar(1e4));\n\n  Scalar one(1);\n\n  MatrixType  vzero = MatrixType::Zero(rows, cols),\n              vrand = MatrixType::Random(rows, cols),\n              vbig(rows, cols),\n              vsmall(rows,cols);\n\n  vbig.fill(big);\n  vsmall.fill(small);\n\n  VERIFY_IS_MUCH_SMALLER_THAN(vzero.norm(), static_cast<RealScalar>(1));\n  VERIFY_IS_APPROX(vrand.stableNorm(),      vrand.norm());\n  VERIFY_IS_APPROX(vrand.blueNorm(),        vrand.norm());\n  VERIFY_IS_APPROX(vrand.hypotNorm(),       vrand.norm());\n\n  // test with expressions as input\n  VERIFY_IS_APPROX((one*vrand).stableNorm(),      vrand.norm());\n  VERIFY_IS_APPROX((one*vrand).blueNorm(),        vrand.norm());\n  VERIFY_IS_APPROX((one*vrand).hypotNorm(),       vrand.norm());\n  VERIFY_IS_APPROX((one*vrand+one*vrand-one*vrand).stableNorm(),      vrand.norm());\n  VERIFY_IS_APPROX((one*vrand+one*vrand-one*vrand).blueNorm(),        vrand.norm());\n  VERIFY_IS_APPROX((one*vrand+one*vrand-one*vrand).hypotNorm(),       vrand.norm());\n\n  RealScalar size = static_cast<RealScalar>(m.size());\n\n  // test numext::isfinite\n  VERIFY(!(numext::isfinite)( std::numeric_limits<RealScalar>::infinity()));\n  VERIFY(!(numext::isfinite)(sqrt(-abs(big))));\n\n  // test overflow\n  VERIFY((numext::isfinite)(sqrt(size)*abs(big)));\n  VERIFY_IS_NOT_APPROX(sqrt(copy(vbig.squaredNorm())), abs(sqrt(size)*big)); // here the default norm must fail\n  VERIFY_IS_APPROX(vbig.stableNorm(), sqrt(size)*abs(big));\n  VERIFY_IS_APPROX(vbig.blueNorm(),   sqrt(size)*abs(big));\n  VERIFY_IS_APPROX(vbig.hypotNorm(),  sqrt(size)*abs(big));\n\n  // test underflow\n  VERIFY((numext::isfinite)(sqrt(size)*abs(small)));\n  VERIFY_IS_NOT_APPROX(sqrt(copy(vsmall.squaredNorm())),   abs(sqrt(size)*small)); // here the default norm must fail\n  VERIFY_IS_APPROX(vsmall.stableNorm(), sqrt(size)*abs(small));\n  VERIFY_IS_APPROX(vsmall.blueNorm(),   sqrt(size)*abs(small));\n  VERIFY_IS_APPROX(vsmall.hypotNorm(),  sqrt(size)*abs(small));\n\n  // Test compilation of cwise() version\n  VERIFY_IS_APPROX(vrand.colwise().stableNorm(),      vrand.colwise().norm());\n  VERIFY_IS_APPROX(vrand.colwise().blueNorm(),        vrand.colwise().norm());\n  VERIFY_IS_APPROX(vrand.colwise().hypotNorm(),       vrand.colwise().norm());\n  VERIFY_IS_APPROX(vrand.rowwise().stableNorm(),      vrand.rowwise().norm());\n  VERIFY_IS_APPROX(vrand.rowwise().blueNorm(),        vrand.rowwise().norm());\n  VERIFY_IS_APPROX(vrand.rowwise().hypotNorm(),       vrand.rowwise().norm());\n  \n  // test NaN, +inf, -inf \n  MatrixType v;\n  Index i = internal::random<Index>(0,rows-1);\n  Index j = internal::random<Index>(0,cols-1);\n\n  // NaN\n  {\n    v = vrand;\n    v(i,j) = std::numeric_limits<RealScalar>::quiet_NaN();\n    VERIFY(!(numext::isfinite)(v.squaredNorm()));   VERIFY((numext::isnan)(v.squaredNorm()));\n    VERIFY(!(numext::isfinite)(v.norm()));          VERIFY((numext::isnan)(v.norm()));\n    VERIFY(!(numext::isfinite)(v.stableNorm()));    VERIFY((numext::isnan)(v.stableNorm()));\n    VERIFY(!(numext::isfinite)(v.blueNorm()));      VERIFY((numext::isnan)(v.blueNorm()));\n    VERIFY(!(numext::isfinite)(v.hypotNorm()));     VERIFY((numext::isnan)(v.hypotNorm()));\n  }\n  \n  // +inf\n  {\n    v = vrand;\n    v(i,j) = std::numeric_limits<RealScalar>::infinity();\n    VERIFY(!(numext::isfinite)(v.squaredNorm()));   VERIFY(isPlusInf(v.squaredNorm()));\n    VERIFY(!(numext::isfinite)(v.norm()));          VERIFY(isPlusInf(v.norm()));\n    VERIFY(!(numext::isfinite)(v.stableNorm()));\n    if(complex_real_product_ok){\n      VERIFY(isPlusInf(v.stableNorm()));\n    }\n    VERIFY(!(numext::isfinite)(v.blueNorm()));      VERIFY(isPlusInf(v.blueNorm()));\n    VERIFY(!(numext::isfinite)(v.hypotNorm()));     VERIFY(isPlusInf(v.hypotNorm()));\n  }\n  \n  // -inf\n  {\n    v = vrand;\n    v(i,j) = -std::numeric_limits<RealScalar>::infinity();\n    VERIFY(!(numext::isfinite)(v.squaredNorm()));   VERIFY(isPlusInf(v.squaredNorm()));\n    VERIFY(!(numext::isfinite)(v.norm()));          VERIFY(isPlusInf(v.norm()));\n    VERIFY(!(numext::isfinite)(v.stableNorm()));\n    if(complex_real_product_ok) {\n      VERIFY(isPlusInf(v.stableNorm()));\n    }\n    VERIFY(!(numext::isfinite)(v.blueNorm()));      VERIFY(isPlusInf(v.blueNorm()));\n    VERIFY(!(numext::isfinite)(v.hypotNorm()));     VERIFY(isPlusInf(v.hypotNorm()));\n  }\n  \n  // mix\n  {\n    Index i2 = internal::random<Index>(0,rows-1);\n    Index j2 = internal::random<Index>(0,cols-1);\n    v = vrand;\n    v(i,j) = -std::numeric_limits<RealScalar>::infinity();\n    v(i2,j2) = std::numeric_limits<RealScalar>::quiet_NaN();\n    VERIFY(!(numext::isfinite)(v.squaredNorm()));   VERIFY((numext::isnan)(v.squaredNorm()));\n    VERIFY(!(numext::isfinite)(v.norm()));          VERIFY((numext::isnan)(v.norm()));\n    VERIFY(!(numext::isfinite)(v.stableNorm()));    VERIFY((numext::isnan)(v.stableNorm()));\n    VERIFY(!(numext::isfinite)(v.blueNorm()));      VERIFY((numext::isnan)(v.blueNorm()));\n    VERIFY(!(numext::isfinite)(v.hypotNorm()));     VERIFY((numext::isnan)(v.hypotNorm()));\n  }\n\n  // stableNormalize[d]\n  {\n    VERIFY_IS_APPROX(vrand.stableNormalized(), vrand.normalized());\n    MatrixType vcopy(vrand);\n    vcopy.stableNormalize();\n    VERIFY_IS_APPROX(vcopy, vrand.normalized());\n    VERIFY_IS_APPROX((vrand.stableNormalized()).norm(), RealScalar(1));\n    VERIFY_IS_APPROX(vcopy.norm(), RealScalar(1));\n    VERIFY_IS_APPROX((vbig.stableNormalized()).norm(), RealScalar(1));\n    VERIFY_IS_APPROX((vsmall.stableNormalized()).norm(), RealScalar(1));\n    RealScalar big_scaling = ((std::numeric_limits<RealScalar>::max)() * RealScalar(1e-4));\n    VERIFY_IS_APPROX(vbig/big_scaling, (vbig.stableNorm() * vbig.stableNormalized()).eval()/big_scaling);\n    VERIFY_IS_APPROX(vsmall, vsmall.stableNorm() * vsmall.stableNormalized());\n  }\n}\n\nvoid test_stable_norm()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( stable_norm(Matrix<float, 1, 1>()) );\n    CALL_SUBTEST_2( stable_norm(Vector4d()) );\n    CALL_SUBTEST_3( stable_norm(VectorXd(internal::random<int>(10,2000))) );\n    CALL_SUBTEST_4( stable_norm(VectorXf(internal::random<int>(10,2000))) );\n    CALL_SUBTEST_5( stable_norm(VectorXcd(internal::random<int>(10,2000))) );\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/stddeque.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2010 Hauke Heibel <hauke.heibel@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <Eigen/StdDeque>\n#include <Eigen/Geometry>\n\ntemplate<typename MatrixType>\nvoid check_stddeque_matrix(const MatrixType& m)\n{\n  typedef typename MatrixType::Index Index;\n  \n  Index rows = m.rows();\n  Index cols = m.cols();\n  MatrixType x = MatrixType::Random(rows,cols), y = MatrixType::Random(rows,cols);\n  std::deque<MatrixType,Eigen::aligned_allocator<MatrixType> > v(10, MatrixType(rows,cols)), w(20, y);\n  v.front() = x;\n  w.front() = w.back();\n  VERIFY_IS_APPROX(w.front(), w.back());\n  v = w;\n\n  typename std::deque<MatrixType,Eigen::aligned_allocator<MatrixType> >::iterator vi = v.begin();\n  typename std::deque<MatrixType,Eigen::aligned_allocator<MatrixType> >::iterator wi = w.begin();\n  for(int i = 0; i < 20; i++)\n  {\n    VERIFY_IS_APPROX(*vi, *wi);\n    ++vi;\n    ++wi;\n  }\n\n  v.resize(21);  \n  v.back() = x;\n  VERIFY_IS_APPROX(v.back(), x);\n  v.resize(22,y);\n  VERIFY_IS_APPROX(v.back(), y);\n  v.push_back(x);\n  VERIFY_IS_APPROX(v.back(), x);\n}\n\ntemplate<typename TransformType>\nvoid check_stddeque_transform(const TransformType&)\n{\n  typedef typename TransformType::MatrixType MatrixType;\n  TransformType x(MatrixType::Random()), y(MatrixType::Random());\n  std::deque<TransformType,Eigen::aligned_allocator<TransformType> > v(10), w(20, y);\n  v.front() = x;\n  w.front() = w.back();\n  VERIFY_IS_APPROX(w.front(), w.back());\n  v = w;\n\n  typename std::deque<TransformType,Eigen::aligned_allocator<TransformType> >::iterator vi = v.begin();\n  typename std::deque<TransformType,Eigen::aligned_allocator<TransformType> >::iterator wi = w.begin();\n  for(int i = 0; i < 20; i++)\n  {\n    VERIFY_IS_APPROX(*vi, *wi);\n    ++vi;\n    ++wi;\n  }\n\n  v.resize(21);\n  v.back() = x;\n  VERIFY_IS_APPROX(v.back(), x);\n  v.resize(22,y);\n  VERIFY_IS_APPROX(v.back(), y);\n  v.push_back(x);\n  VERIFY_IS_APPROX(v.back(), x);\n}\n\ntemplate<typename QuaternionType>\nvoid check_stddeque_quaternion(const QuaternionType&)\n{\n  typedef typename QuaternionType::Coefficients Coefficients;\n  QuaternionType x(Coefficients::Random()), y(Coefficients::Random());\n  std::deque<QuaternionType,Eigen::aligned_allocator<QuaternionType> > v(10), w(20, y);\n  v.front() = x;\n  w.front() = w.back();\n  VERIFY_IS_APPROX(w.front(), w.back());\n  v = w;\n\n  typename std::deque<QuaternionType,Eigen::aligned_allocator<QuaternionType> >::iterator vi = v.begin();\n  typename std::deque<QuaternionType,Eigen::aligned_allocator<QuaternionType> >::iterator wi = w.begin();\n  for(int i = 0; i < 20; i++)\n  {\n    VERIFY_IS_APPROX(*vi, *wi);\n    ++vi;\n    ++wi;\n  }\n\n  v.resize(21);\n  v.back() = x;\n  VERIFY_IS_APPROX(v.back(), x);\n  v.resize(22,y);\n  VERIFY_IS_APPROX(v.back(), y);\n  v.push_back(x);\n  VERIFY_IS_APPROX(v.back(), x);\n}\n\nvoid test_stddeque()\n{\n  // some non vectorizable fixed sizes\n  CALL_SUBTEST_1(check_stddeque_matrix(Vector2f()));\n  CALL_SUBTEST_1(check_stddeque_matrix(Matrix3f()));\n  CALL_SUBTEST_2(check_stddeque_matrix(Matrix3d()));\n\n  // some vectorizable fixed sizes\n  CALL_SUBTEST_1(check_stddeque_matrix(Matrix2f()));\n  CALL_SUBTEST_1(check_stddeque_matrix(Vector4f()));\n  CALL_SUBTEST_1(check_stddeque_matrix(Matrix4f()));\n  CALL_SUBTEST_2(check_stddeque_matrix(Matrix4d()));\n\n  // some dynamic sizes\n  CALL_SUBTEST_3(check_stddeque_matrix(MatrixXd(1,1)));\n  CALL_SUBTEST_3(check_stddeque_matrix(VectorXd(20)));\n  CALL_SUBTEST_3(check_stddeque_matrix(RowVectorXf(20)));\n  CALL_SUBTEST_3(check_stddeque_matrix(MatrixXcf(10,10)));\n\n  // some Transform\n  CALL_SUBTEST_4(check_stddeque_transform(Affine2f()));\n  CALL_SUBTEST_4(check_stddeque_transform(Affine3f()));\n  CALL_SUBTEST_4(check_stddeque_transform(Affine3d()));\n\n  // some Quaternion\n  CALL_SUBTEST_5(check_stddeque_quaternion(Quaternionf()));\n  CALL_SUBTEST_5(check_stddeque_quaternion(Quaterniond()));\n}\n"
  },
  {
    "path": "include/eigen3/test/stddeque_overload.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2010 Hauke Heibel <hauke.heibel@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/StdDeque>\n#include <Eigen/Geometry>\n\nEIGEN_DEFINE_STL_DEQUE_SPECIALIZATION(Vector4f)\n\nEIGEN_DEFINE_STL_DEQUE_SPECIALIZATION(Matrix2f)\nEIGEN_DEFINE_STL_DEQUE_SPECIALIZATION(Matrix4f)\nEIGEN_DEFINE_STL_DEQUE_SPECIALIZATION(Matrix4d)\n\nEIGEN_DEFINE_STL_DEQUE_SPECIALIZATION(Affine3f)\nEIGEN_DEFINE_STL_DEQUE_SPECIALIZATION(Affine3d)\n\nEIGEN_DEFINE_STL_DEQUE_SPECIALIZATION(Quaternionf)\nEIGEN_DEFINE_STL_DEQUE_SPECIALIZATION(Quaterniond)\n\ntemplate<typename MatrixType>\nvoid check_stddeque_matrix(const MatrixType& m)\n{\n  typename MatrixType::Index rows = m.rows();\n  typename MatrixType::Index cols = m.cols();\n  MatrixType x = MatrixType::Random(rows,cols), y = MatrixType::Random(rows,cols);\n  std::deque<MatrixType> v(10, MatrixType(rows,cols)), w(20, y);\n  v[5] = x;\n  w[6] = v[5];\n  VERIFY_IS_APPROX(w[6], v[5]);\n  v = w;\n  for(int i = 0; i < 20; i++)\n  {\n    VERIFY_IS_APPROX(w[i], v[i]);\n  }\n\n  v.resize(21);\n  v[20] = x;\n  VERIFY_IS_APPROX(v[20], x);\n  v.resize(22,y);\n  VERIFY_IS_APPROX(v[21], y);\n  v.push_back(x);\n  VERIFY_IS_APPROX(v[22], x);\n\n  // do a lot of push_back such that the deque gets internally resized\n  // (with memory reallocation)\n  MatrixType* ref = &w[0];\n  for(int i=0; i<30 || ((ref==&w[0]) && i<300); ++i)\n    v.push_back(w[i%w.size()]);\n  for(unsigned int i=23; i<v.size(); ++i)\n  {\n    VERIFY(v[i]==w[(i-23)%w.size()]);\n  }\n}\n\ntemplate<typename TransformType>\nvoid check_stddeque_transform(const TransformType&)\n{\n  typedef typename TransformType::MatrixType MatrixType;\n  TransformType x(MatrixType::Random()), y(MatrixType::Random());\n  std::deque<TransformType> v(10), w(20, y);\n  v[5] = x;\n  w[6] = v[5];\n  VERIFY_IS_APPROX(w[6], v[5]);\n  v = w;\n  for(int i = 0; i < 20; i++)\n  {\n    VERIFY_IS_APPROX(w[i], v[i]);\n  }\n\n  v.resize(21);\n  v[20] = x;\n  VERIFY_IS_APPROX(v[20], x);\n  v.resize(22,y);\n  VERIFY_IS_APPROX(v[21], y);\n  v.push_back(x);\n  VERIFY_IS_APPROX(v[22], x);\n\n  // do a lot of push_back such that the deque gets internally resized\n  // (with memory reallocation)\n  TransformType* ref = &w[0];\n  for(int i=0; i<30 || ((ref==&w[0]) && i<300); ++i)\n    v.push_back(w[i%w.size()]);\n  for(unsigned int i=23; i<v.size(); ++i)\n  {\n    VERIFY(v[i].matrix()==w[(i-23)%w.size()].matrix());\n  }\n}\n\ntemplate<typename QuaternionType>\nvoid check_stddeque_quaternion(const QuaternionType&)\n{\n  typedef typename QuaternionType::Coefficients Coefficients;\n  QuaternionType x(Coefficients::Random()), y(Coefficients::Random());\n  std::deque<QuaternionType> v(10), w(20, y);\n  v[5] = x;\n  w[6] = v[5];\n  VERIFY_IS_APPROX(w[6], v[5]);\n  v = w;\n  for(int i = 0; i < 20; i++)\n  {\n    VERIFY_IS_APPROX(w[i], v[i]);\n  }\n\n  v.resize(21);\n  v[20] = x;\n  VERIFY_IS_APPROX(v[20], x);\n  v.resize(22,y);\n  VERIFY_IS_APPROX(v[21], y);\n  v.push_back(x);\n  VERIFY_IS_APPROX(v[22], x);\n\n  // do a lot of push_back such that the deque gets internally resized\n  // (with memory reallocation)\n  QuaternionType* ref = &w[0];\n  for(int i=0; i<30 || ((ref==&w[0]) && i<300); ++i)\n    v.push_back(w[i%w.size()]);\n  for(unsigned int i=23; i<v.size(); ++i)\n  {\n    VERIFY(v[i].coeffs()==w[(i-23)%w.size()].coeffs());\n  }\n}\n\nvoid test_stddeque_overload()\n{\n  // some non vectorizable fixed sizes\n  CALL_SUBTEST_1(check_stddeque_matrix(Vector2f()));\n  CALL_SUBTEST_1(check_stddeque_matrix(Matrix3f()));\n  CALL_SUBTEST_2(check_stddeque_matrix(Matrix3d()));\n\n  // some vectorizable fixed sizes\n  CALL_SUBTEST_1(check_stddeque_matrix(Matrix2f()));\n  CALL_SUBTEST_1(check_stddeque_matrix(Vector4f()));\n  CALL_SUBTEST_1(check_stddeque_matrix(Matrix4f()));\n  CALL_SUBTEST_2(check_stddeque_matrix(Matrix4d()));\n\n  // some dynamic sizes\n  CALL_SUBTEST_3(check_stddeque_matrix(MatrixXd(1,1)));\n  CALL_SUBTEST_3(check_stddeque_matrix(VectorXd(20)));\n  CALL_SUBTEST_3(check_stddeque_matrix(RowVectorXf(20)));\n  CALL_SUBTEST_3(check_stddeque_matrix(MatrixXcf(10,10)));\n\n  // some Transform\n  CALL_SUBTEST_4(check_stddeque_transform(Affine2f())); // does not need the specialization (2+1)^2 = 9\n  CALL_SUBTEST_4(check_stddeque_transform(Affine3f()));\n  CALL_SUBTEST_4(check_stddeque_transform(Affine3d()));\n\n  // some Quaternion\n  CALL_SUBTEST_5(check_stddeque_quaternion(Quaternionf()));\n  CALL_SUBTEST_5(check_stddeque_quaternion(Quaterniond()));\n}\n"
  },
  {
    "path": "include/eigen3/test/stdlist.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2010 Hauke Heibel <hauke.heibel@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <Eigen/StdList>\n#include <Eigen/Geometry>\n\ntemplate<typename MatrixType>\nvoid check_stdlist_matrix(const MatrixType& m)\n{\n  typedef typename MatrixType::Index Index;\n  \n  Index rows = m.rows();\n  Index cols = m.cols();\n  MatrixType x = MatrixType::Random(rows,cols), y = MatrixType::Random(rows,cols);\n  std::list<MatrixType,Eigen::aligned_allocator<MatrixType> > v(10, MatrixType(rows,cols)), w(20, y);\n  v.front() = x;\n  w.front() = w.back();\n  VERIFY_IS_APPROX(w.front(), w.back());\n  v = w;\n\n  typename std::list<MatrixType,Eigen::aligned_allocator<MatrixType> >::iterator vi = v.begin();\n  typename std::list<MatrixType,Eigen::aligned_allocator<MatrixType> >::iterator wi = w.begin();\n  for(int i = 0; i < 20; i++)\n  {\n    VERIFY_IS_APPROX(*vi, *wi);\n    ++vi;\n    ++wi;\n  }\n\n  v.resize(21);  \n  v.back() = x;\n  VERIFY_IS_APPROX(v.back(), x);\n  v.resize(22,y);\n  VERIFY_IS_APPROX(v.back(), y);\n  v.push_back(x);\n  VERIFY_IS_APPROX(v.back(), x);\n}\n\ntemplate<typename TransformType>\nvoid check_stdlist_transform(const TransformType&)\n{\n  typedef typename TransformType::MatrixType MatrixType;\n  TransformType x(MatrixType::Random()), y(MatrixType::Random());\n  std::list<TransformType,Eigen::aligned_allocator<TransformType> > v(10), w(20, y);\n  v.front() = x;\n  w.front() = w.back();\n  VERIFY_IS_APPROX(w.front(), w.back());\n  v = w;\n\n  typename std::list<TransformType,Eigen::aligned_allocator<TransformType> >::iterator vi = v.begin();\n  typename std::list<TransformType,Eigen::aligned_allocator<TransformType> >::iterator wi = w.begin();\n  for(int i = 0; i < 20; i++)\n  {\n    VERIFY_IS_APPROX(*vi, *wi);\n    ++vi;\n    ++wi;\n  }\n\n  v.resize(21);\n  v.back() = x;\n  VERIFY_IS_APPROX(v.back(), x);\n  v.resize(22,y);\n  VERIFY_IS_APPROX(v.back(), y);\n  v.push_back(x);\n  VERIFY_IS_APPROX(v.back(), x);\n}\n\ntemplate<typename QuaternionType>\nvoid check_stdlist_quaternion(const QuaternionType&)\n{\n  typedef typename QuaternionType::Coefficients Coefficients;\n  QuaternionType x(Coefficients::Random()), y(Coefficients::Random());\n  std::list<QuaternionType,Eigen::aligned_allocator<QuaternionType> > v(10), w(20, y);\n  v.front() = x;\n  w.front() = w.back();\n  VERIFY_IS_APPROX(w.front(), w.back());\n  v = w;\n\n  typename std::list<QuaternionType,Eigen::aligned_allocator<QuaternionType> >::iterator vi = v.begin();\n  typename std::list<QuaternionType,Eigen::aligned_allocator<QuaternionType> >::iterator wi = w.begin();\n  for(int i = 0; i < 20; i++)\n  {\n    VERIFY_IS_APPROX(*vi, *wi);\n    ++vi;\n    ++wi;\n  }\n\n  v.resize(21);\n  v.back() = x;\n  VERIFY_IS_APPROX(v.back(), x);\n  v.resize(22,y);\n  VERIFY_IS_APPROX(v.back(), y);\n  v.push_back(x);\n  VERIFY_IS_APPROX(v.back(), x);\n}\n\nvoid test_stdlist()\n{\n  // some non vectorizable fixed sizes\n  CALL_SUBTEST_1(check_stdlist_matrix(Vector2f()));\n  CALL_SUBTEST_1(check_stdlist_matrix(Matrix3f()));\n  CALL_SUBTEST_2(check_stdlist_matrix(Matrix3d()));\n\n  // some vectorizable fixed sizes\n  CALL_SUBTEST_1(check_stdlist_matrix(Matrix2f()));\n  CALL_SUBTEST_1(check_stdlist_matrix(Vector4f()));\n  CALL_SUBTEST_1(check_stdlist_matrix(Matrix4f()));\n  CALL_SUBTEST_2(check_stdlist_matrix(Matrix4d()));\n\n  // some dynamic sizes\n  CALL_SUBTEST_3(check_stdlist_matrix(MatrixXd(1,1)));\n  CALL_SUBTEST_3(check_stdlist_matrix(VectorXd(20)));\n  CALL_SUBTEST_3(check_stdlist_matrix(RowVectorXf(20)));\n  CALL_SUBTEST_3(check_stdlist_matrix(MatrixXcf(10,10)));\n\n  // some Transform\n  CALL_SUBTEST_4(check_stdlist_transform(Affine2f()));\n  CALL_SUBTEST_4(check_stdlist_transform(Affine3f()));\n  CALL_SUBTEST_4(check_stdlist_transform(Affine3d()));\n\n  // some Quaternion\n  CALL_SUBTEST_5(check_stdlist_quaternion(Quaternionf()));\n  CALL_SUBTEST_5(check_stdlist_quaternion(Quaterniond()));\n}\n"
  },
  {
    "path": "include/eigen3/test/stdlist_overload.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2010 Hauke Heibel <hauke.heibel@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/StdList>\n#include <Eigen/Geometry>\n\nEIGEN_DEFINE_STL_LIST_SPECIALIZATION(Vector4f)\n\nEIGEN_DEFINE_STL_LIST_SPECIALIZATION(Matrix2f)\nEIGEN_DEFINE_STL_LIST_SPECIALIZATION(Matrix4f)\nEIGEN_DEFINE_STL_LIST_SPECIALIZATION(Matrix4d)\n\nEIGEN_DEFINE_STL_LIST_SPECIALIZATION(Affine3f)\nEIGEN_DEFINE_STL_LIST_SPECIALIZATION(Affine3d)\n\nEIGEN_DEFINE_STL_LIST_SPECIALIZATION(Quaternionf)\nEIGEN_DEFINE_STL_LIST_SPECIALIZATION(Quaterniond)\n\ntemplate <class Container, class Position>\ntypename Container::iterator get(Container & c, Position position)\n{\n  typename Container::iterator it = c.begin();\n  std::advance(it, position);\n  return it;\n}\n\ntemplate <class Container, class Position, class Value>\nvoid set(Container & c, Position position, const Value & value)\n{\n  typename Container::iterator it = c.begin();\n  std::advance(it, position);\n  *it = value;\n}\n\ntemplate<typename MatrixType>\nvoid check_stdlist_matrix(const MatrixType& m)\n{\n  typename MatrixType::Index rows = m.rows();\n  typename MatrixType::Index cols = m.cols();\n  MatrixType x = MatrixType::Random(rows,cols), y = MatrixType::Random(rows,cols);\n  std::list<MatrixType> v(10, MatrixType(rows,cols)), w(20, y);\n  typename std::list<MatrixType>::iterator itv = get(v, 5);\n  typename std::list<MatrixType>::iterator itw = get(w, 6);\n  *itv = x;\n  *itw = *itv;\n  VERIFY_IS_APPROX(*itw, *itv);\n  v = w;\n  itv = v.begin();\n  itw = w.begin();\n  for(int i = 0; i < 20; i++)\n  {\n    VERIFY_IS_APPROX(*itw, *itv);\n    ++itv;\n    ++itw;\n  }\n\n  v.resize(21);\n  set(v, 20, x);\n  VERIFY_IS_APPROX(*get(v, 20), x);\n  v.resize(22,y);\n  VERIFY_IS_APPROX(*get(v, 21), y);\n  v.push_back(x);\n  VERIFY_IS_APPROX(*get(v, 22), x);\n\n  // do a lot of push_back such that the list gets internally resized\n  // (with memory reallocation)\n  MatrixType* ref = &(*get(w, 0));\n  for(int i=0; i<30 || ((ref==&(*get(w, 0))) && i<300); ++i)\n    v.push_back(*get(w, i%w.size()));\n  for(unsigned int i=23; i<v.size(); ++i)\n  {\n    VERIFY((*get(v, i))==(*get(w, (i-23)%w.size())));\n  }\n}\n\ntemplate<typename TransformType>\nvoid check_stdlist_transform(const TransformType&)\n{\n  typedef typename TransformType::MatrixType MatrixType;\n  TransformType x(MatrixType::Random()), y(MatrixType::Random());\n  std::list<TransformType> v(10), w(20, y);\n  typename std::list<TransformType>::iterator itv = get(v, 5);\n  typename std::list<TransformType>::iterator itw = get(w, 6);\n  *itv = x;\n  *itw = *itv;\n  VERIFY_IS_APPROX(*itw, *itv);\n  v = w;\n  itv = v.begin();\n  itw = w.begin();\n  for(int i = 0; i < 20; i++)\n  {\n    VERIFY_IS_APPROX(*itw, *itv);\n    ++itv;\n    ++itw;\n  }\n\n  v.resize(21);\n  set(v, 20, x);\n  VERIFY_IS_APPROX(*get(v, 20), x);\n  v.resize(22,y);\n  VERIFY_IS_APPROX(*get(v, 21), y);\n  v.push_back(x);\n  VERIFY_IS_APPROX(*get(v, 22), x);\n\n  // do a lot of push_back such that the list gets internally resized\n  // (with memory reallocation)\n  TransformType* ref = &(*get(w, 0));\n  for(int i=0; i<30 || ((ref==&(*get(w, 0))) && i<300); ++i)\n    v.push_back(*get(w, i%w.size()));\n  for(unsigned int i=23; i<v.size(); ++i)\n  {\n    VERIFY(get(v, i)->matrix()==get(w, (i-23)%w.size())->matrix());\n  }\n}\n\ntemplate<typename QuaternionType>\nvoid check_stdlist_quaternion(const QuaternionType&)\n{\n  typedef typename QuaternionType::Coefficients Coefficients;\n  QuaternionType x(Coefficients::Random()), y(Coefficients::Random());\n  std::list<QuaternionType> v(10), w(20, y);\n  typename std::list<QuaternionType>::iterator itv = get(v, 5);\n  typename std::list<QuaternionType>::iterator itw = get(w, 6);\n  *itv = x;\n  *itw = *itv;\n  VERIFY_IS_APPROX(*itw, *itv);\n  v = w;\n  itv = v.begin();\n  itw = w.begin();\n  for(int i = 0; i < 20; i++)\n  {\n    VERIFY_IS_APPROX(*itw, *itv);\n    ++itv;\n    ++itw;\n  }\n\n  v.resize(21);\n  set(v, 20, x);\n  VERIFY_IS_APPROX(*get(v, 20), x);\n  v.resize(22,y);\n  VERIFY_IS_APPROX(*get(v, 21), y);\n  v.push_back(x);\n  VERIFY_IS_APPROX(*get(v, 22), x);\n\n  // do a lot of push_back such that the list gets internally resized\n  // (with memory reallocation)\n  QuaternionType* ref = &(*get(w, 0));\n  for(int i=0; i<30 || ((ref==&(*get(w, 0))) && i<300); ++i)\n    v.push_back(*get(w, i%w.size()));\n  for(unsigned int i=23; i<v.size(); ++i)\n  {\n    VERIFY(get(v, i)->coeffs()==get(w, (i-23)%w.size())->coeffs());\n  }\n}\n\nvoid test_stdlist_overload()\n{\n  // some non vectorizable fixed sizes\n  CALL_SUBTEST_1(check_stdlist_matrix(Vector2f()));\n  CALL_SUBTEST_1(check_stdlist_matrix(Matrix3f()));\n  CALL_SUBTEST_2(check_stdlist_matrix(Matrix3d()));\n\n  // some vectorizable fixed sizes\n  CALL_SUBTEST_1(check_stdlist_matrix(Matrix2f()));\n  CALL_SUBTEST_1(check_stdlist_matrix(Vector4f()));\n  CALL_SUBTEST_1(check_stdlist_matrix(Matrix4f()));\n  CALL_SUBTEST_2(check_stdlist_matrix(Matrix4d()));\n\n  // some dynamic sizes\n  CALL_SUBTEST_3(check_stdlist_matrix(MatrixXd(1,1)));\n  CALL_SUBTEST_3(check_stdlist_matrix(VectorXd(20)));\n  CALL_SUBTEST_3(check_stdlist_matrix(RowVectorXf(20)));\n  CALL_SUBTEST_3(check_stdlist_matrix(MatrixXcf(10,10)));\n\n  // some Transform\n  CALL_SUBTEST_4(check_stdlist_transform(Affine2f())); // does not need the specialization (2+1)^2 = 9\n  CALL_SUBTEST_4(check_stdlist_transform(Affine3f()));\n  CALL_SUBTEST_4(check_stdlist_transform(Affine3d()));\n\n  // some Quaternion\n  CALL_SUBTEST_5(check_stdlist_quaternion(Quaternionf()));\n  CALL_SUBTEST_5(check_stdlist_quaternion(Quaterniond()));\n}\n"
  },
  {
    "path": "include/eigen3/test/stdvector.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <Eigen/StdVector>\n#include <Eigen/Geometry>\n\ntemplate<typename MatrixType>\nvoid check_stdvector_matrix(const MatrixType& m)\n{\n  typename MatrixType::Index rows = m.rows();\n  typename MatrixType::Index cols = m.cols();\n  MatrixType x = MatrixType::Random(rows,cols), y = MatrixType::Random(rows,cols);\n  std::vector<MatrixType,Eigen::aligned_allocator<MatrixType> > v(10, MatrixType(rows,cols)), w(20, y);\n  v[5] = x;\n  w[6] = v[5];\n  VERIFY_IS_APPROX(w[6], v[5]);\n  v = w;\n  for(int i = 0; i < 20; i++)\n  {\n    VERIFY_IS_APPROX(w[i], v[i]);\n  }\n\n  v.resize(21);\n  v[20] = x;\n  VERIFY_IS_APPROX(v[20], x);\n  v.resize(22,y);\n  VERIFY_IS_APPROX(v[21], y);\n  v.push_back(x);\n  VERIFY_IS_APPROX(v[22], x);\n  VERIFY((internal::UIntPtr)&(v[22]) == (internal::UIntPtr)&(v[21]) + sizeof(MatrixType));\n\n  // do a lot of push_back such that the vector gets internally resized\n  // (with memory reallocation)\n  MatrixType* ref = &w[0];\n  for(int i=0; i<30 || ((ref==&w[0]) && i<300); ++i)\n    v.push_back(w[i%w.size()]);\n  for(unsigned int i=23; i<v.size(); ++i)\n  {\n    VERIFY(v[i]==w[(i-23)%w.size()]);\n  }\n}\n\ntemplate<typename TransformType>\nvoid check_stdvector_transform(const TransformType&)\n{\n  typedef typename TransformType::MatrixType MatrixType;\n  TransformType x(MatrixType::Random()), y(MatrixType::Random());\n  std::vector<TransformType,Eigen::aligned_allocator<TransformType> > v(10), w(20, y);\n  v[5] = x;\n  w[6] = v[5];\n  VERIFY_IS_APPROX(w[6], v[5]);\n  v = w;\n  for(int i = 0; i < 20; i++)\n  {\n    VERIFY_IS_APPROX(w[i], v[i]);\n  }\n\n  v.resize(21);\n  v[20] = x;\n  VERIFY_IS_APPROX(v[20], x);\n  v.resize(22,y);\n  VERIFY_IS_APPROX(v[21], y);\n  v.push_back(x);\n  VERIFY_IS_APPROX(v[22], x);\n  VERIFY((internal::UIntPtr)&(v[22]) == (internal::UIntPtr)&(v[21]) + sizeof(TransformType));\n\n  // do a lot of push_back such that the vector gets internally resized\n  // (with memory reallocation)\n  TransformType* ref = &w[0];\n  for(int i=0; i<30 || ((ref==&w[0]) && i<300); ++i)\n    v.push_back(w[i%w.size()]);\n  for(unsigned int i=23; i<v.size(); ++i)\n  {\n    VERIFY(v[i].matrix()==w[(i-23)%w.size()].matrix());\n  }\n}\n\ntemplate<typename QuaternionType>\nvoid check_stdvector_quaternion(const QuaternionType&)\n{\n  typedef typename QuaternionType::Coefficients Coefficients;\n  QuaternionType x(Coefficients::Random()), y(Coefficients::Random());\n  std::vector<QuaternionType,Eigen::aligned_allocator<QuaternionType> > v(10), w(20, y);\n  v[5] = x;\n  w[6] = v[5];\n  VERIFY_IS_APPROX(w[6], v[5]);\n  v = w;\n  for(int i = 0; i < 20; i++)\n  {\n    VERIFY_IS_APPROX(w[i], v[i]);\n  }\n\n  v.resize(21);\n  v[20] = x;\n  VERIFY_IS_APPROX(v[20], x);\n  v.resize(22,y);\n  VERIFY_IS_APPROX(v[21], y);\n  v.push_back(x);\n  VERIFY_IS_APPROX(v[22], x);\n  VERIFY((internal::UIntPtr)&(v[22]) == (internal::UIntPtr)&(v[21]) + sizeof(QuaternionType));\n\n  // do a lot of push_back such that the vector gets internally resized\n  // (with memory reallocation)\n  QuaternionType* ref = &w[0];\n  for(int i=0; i<30 || ((ref==&w[0]) && i<300); ++i)\n    v.push_back(w[i%w.size()]);\n  for(unsigned int i=23; i<v.size(); ++i)\n  {\n    VERIFY(v[i].coeffs()==w[(i-23)%w.size()].coeffs());\n  }\n}\n\nvoid test_stdvector()\n{\n  // some non vectorizable fixed sizes\n  CALL_SUBTEST_1(check_stdvector_matrix(Vector2f()));\n  CALL_SUBTEST_1(check_stdvector_matrix(Matrix3f()));\n  CALL_SUBTEST_2(check_stdvector_matrix(Matrix3d()));\n\n  // some vectorizable fixed sizes\n  CALL_SUBTEST_1(check_stdvector_matrix(Matrix2f()));\n  CALL_SUBTEST_1(check_stdvector_matrix(Vector4f()));\n  CALL_SUBTEST_1(check_stdvector_matrix(Matrix4f()));\n  CALL_SUBTEST_2(check_stdvector_matrix(Matrix4d()));\n\n  // some dynamic sizes\n  CALL_SUBTEST_3(check_stdvector_matrix(MatrixXd(1,1)));\n  CALL_SUBTEST_3(check_stdvector_matrix(VectorXd(20)));\n  CALL_SUBTEST_3(check_stdvector_matrix(RowVectorXf(20)));\n  CALL_SUBTEST_3(check_stdvector_matrix(MatrixXcf(10,10)));\n\n  // some Transform\n  CALL_SUBTEST_4(check_stdvector_transform(Projective2f()));\n  CALL_SUBTEST_4(check_stdvector_transform(Projective3f()));\n  CALL_SUBTEST_4(check_stdvector_transform(Projective3d()));\n  //CALL_SUBTEST(heck_stdvector_transform(Projective4d()));\n\n  // some Quaternion\n  CALL_SUBTEST_5(check_stdvector_quaternion(Quaternionf()));\n  CALL_SUBTEST_5(check_stdvector_quaternion(Quaterniond()));\n}\n"
  },
  {
    "path": "include/eigen3/test/stdvector_overload.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2010 Hauke Heibel <hauke.heibel@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/StdVector>\n#include <Eigen/Geometry>\n\nEIGEN_DEFINE_STL_VECTOR_SPECIALIZATION(Vector4f)\n\nEIGEN_DEFINE_STL_VECTOR_SPECIALIZATION(Matrix2f)\nEIGEN_DEFINE_STL_VECTOR_SPECIALIZATION(Matrix4f)\nEIGEN_DEFINE_STL_VECTOR_SPECIALIZATION(Matrix4d)\n\nEIGEN_DEFINE_STL_VECTOR_SPECIALIZATION(Affine3f)\nEIGEN_DEFINE_STL_VECTOR_SPECIALIZATION(Affine3d)\n\nEIGEN_DEFINE_STL_VECTOR_SPECIALIZATION(Quaternionf)\nEIGEN_DEFINE_STL_VECTOR_SPECIALIZATION(Quaterniond)\n\ntemplate<typename MatrixType>\nvoid check_stdvector_matrix(const MatrixType& m)\n{\n  typename MatrixType::Index rows = m.rows();\n  typename MatrixType::Index cols = m.cols();\n  MatrixType x = MatrixType::Random(rows,cols), y = MatrixType::Random(rows,cols);\n  std::vector<MatrixType> v(10, MatrixType(rows,cols)), w(20, y);\n  v[5] = x;\n  w[6] = v[5];\n  VERIFY_IS_APPROX(w[6], v[5]);\n  v = w;\n  for(int i = 0; i < 20; i++)\n  {\n    VERIFY_IS_APPROX(w[i], v[i]);\n  }\n\n  v.resize(21);\n  v[20] = x;\n  VERIFY_IS_APPROX(v[20], x);\n  v.resize(22,y);\n  VERIFY_IS_APPROX(v[21], y);\n  v.push_back(x);\n  VERIFY_IS_APPROX(v[22], x);\n  VERIFY((internal::UIntPtr)&(v[22]) == (internal::UIntPtr)&(v[21]) + sizeof(MatrixType));\n\n  // do a lot of push_back such that the vector gets internally resized\n  // (with memory reallocation)\n  MatrixType* ref = &w[0];\n  for(int i=0; i<30 || ((ref==&w[0]) && i<300); ++i)\n    v.push_back(w[i%w.size()]);\n  for(unsigned int i=23; i<v.size(); ++i)\n  {\n    VERIFY(v[i]==w[(i-23)%w.size()]);\n  }\n}\n\ntemplate<typename TransformType>\nvoid check_stdvector_transform(const TransformType&)\n{\n  typedef typename TransformType::MatrixType MatrixType;\n  TransformType x(MatrixType::Random()), y(MatrixType::Random());\n  std::vector<TransformType> v(10), w(20, y);\n  v[5] = x;\n  w[6] = v[5];\n  VERIFY_IS_APPROX(w[6], v[5]);\n  v = w;\n  for(int i = 0; i < 20; i++)\n  {\n    VERIFY_IS_APPROX(w[i], v[i]);\n  }\n\n  v.resize(21);\n  v[20] = x;\n  VERIFY_IS_APPROX(v[20], x);\n  v.resize(22,y);\n  VERIFY_IS_APPROX(v[21], y);\n  v.push_back(x);\n  VERIFY_IS_APPROX(v[22], x);\n  VERIFY((internal::UIntPtr)&(v[22]) == (internal::UIntPtr)&(v[21]) + sizeof(TransformType));\n\n  // do a lot of push_back such that the vector gets internally resized\n  // (with memory reallocation)\n  TransformType* ref = &w[0];\n  for(int i=0; i<30 || ((ref==&w[0]) && i<300); ++i)\n    v.push_back(w[i%w.size()]);\n  for(unsigned int i=23; i<v.size(); ++i)\n  {\n    VERIFY(v[i].matrix()==w[(i-23)%w.size()].matrix());\n  }\n}\n\ntemplate<typename QuaternionType>\nvoid check_stdvector_quaternion(const QuaternionType&)\n{\n  typedef typename QuaternionType::Coefficients Coefficients;\n  QuaternionType x(Coefficients::Random()), y(Coefficients::Random());\n  std::vector<QuaternionType> v(10), w(20, y);\n  v[5] = x;\n  w[6] = v[5];\n  VERIFY_IS_APPROX(w[6], v[5]);\n  v = w;\n  for(int i = 0; i < 20; i++)\n  {\n    VERIFY_IS_APPROX(w[i], v[i]);\n  }\n\n  v.resize(21);\n  v[20] = x;\n  VERIFY_IS_APPROX(v[20], x);\n  v.resize(22,y);\n  VERIFY_IS_APPROX(v[21], y);\n  v.push_back(x);\n  VERIFY_IS_APPROX(v[22], x);\n  VERIFY((internal::UIntPtr)&(v[22]) == (internal::UIntPtr)&(v[21]) + sizeof(QuaternionType));\n\n  // do a lot of push_back such that the vector gets internally resized\n  // (with memory reallocation)\n  QuaternionType* ref = &w[0];\n  for(int i=0; i<30 || ((ref==&w[0]) && i<300); ++i)\n    v.push_back(w[i%w.size()]);\n  for(unsigned int i=23; i<v.size(); ++i)\n  {\n    VERIFY(v[i].coeffs()==w[(i-23)%w.size()].coeffs());\n  }\n}\n\nvoid test_stdvector_overload()\n{\n  // some non vectorizable fixed sizes\n  CALL_SUBTEST_1(check_stdvector_matrix(Vector2f()));\n  CALL_SUBTEST_1(check_stdvector_matrix(Matrix3f()));\n  CALL_SUBTEST_2(check_stdvector_matrix(Matrix3d()));\n\n  // some vectorizable fixed sizes\n  CALL_SUBTEST_1(check_stdvector_matrix(Matrix2f()));\n  CALL_SUBTEST_1(check_stdvector_matrix(Vector4f()));\n  CALL_SUBTEST_1(check_stdvector_matrix(Matrix4f()));\n  CALL_SUBTEST_2(check_stdvector_matrix(Matrix4d()));\n\n  // some dynamic sizes\n  CALL_SUBTEST_3(check_stdvector_matrix(MatrixXd(1,1)));\n  CALL_SUBTEST_3(check_stdvector_matrix(VectorXd(20)));\n  CALL_SUBTEST_3(check_stdvector_matrix(RowVectorXf(20)));\n  CALL_SUBTEST_3(check_stdvector_matrix(MatrixXcf(10,10)));\n\n  // some Transform\n  CALL_SUBTEST_4(check_stdvector_transform(Affine2f())); // does not need the specialization (2+1)^2 = 9\n  CALL_SUBTEST_4(check_stdvector_transform(Affine3f()));\n  CALL_SUBTEST_4(check_stdvector_transform(Affine3d()));\n\n  // some Quaternion\n  CALL_SUBTEST_5(check_stdvector_quaternion(Quaternionf()));\n  CALL_SUBTEST_5(check_stdvector_quaternion(Quaterniond()));\n}\n"
  },
  {
    "path": "include/eigen3/test/superlu_support.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2011 Gael Guennebaud <g.gael@free.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define EIGEN_NO_DEBUG_SMALL_PRODUCT_BLOCKS\n#include \"sparse_solver.h\"\n\n#include <Eigen/SuperLUSupport>\n\nvoid test_superlu_support()\n{\n  SuperLU<SparseMatrix<double> > superlu_double_colmajor;\n  SuperLU<SparseMatrix<std::complex<double> > > superlu_cplxdouble_colmajor;\n  CALL_SUBTEST_1( check_sparse_square_solving(superlu_double_colmajor)      );\n  CALL_SUBTEST_2( check_sparse_square_solving(superlu_cplxdouble_colmajor)  );\n  CALL_SUBTEST_1( check_sparse_square_determinant(superlu_double_colmajor)      );\n  CALL_SUBTEST_2( check_sparse_square_determinant(superlu_cplxdouble_colmajor)  );\n}\n"
  },
  {
    "path": "include/eigen3/test/svd_common.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef SVD_DEFAULT\n#error a macro SVD_DEFAULT(MatrixType) must be defined prior to including svd_common.h\n#endif\n\n#ifndef SVD_FOR_MIN_NORM\n#error a macro SVD_FOR_MIN_NORM(MatrixType) must be defined prior to including svd_common.h\n#endif\n\n#include \"svd_fill.h\"\n\n// Check that the matrix m is properly reconstructed and that the U and V factors are unitary\n// The SVD must have already been computed.\ntemplate<typename SvdType, typename MatrixType>\nvoid svd_check_full(const MatrixType& m, const SvdType& svd)\n{\n  typedef typename MatrixType::Index Index;\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  enum {\n    RowsAtCompileTime = MatrixType::RowsAtCompileTime,\n    ColsAtCompileTime = MatrixType::ColsAtCompileTime\n  };\n\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename MatrixType::RealScalar RealScalar;\n  typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime> MatrixUType;\n  typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime> MatrixVType;\n\n  MatrixType sigma = MatrixType::Zero(rows,cols);\n  sigma.diagonal() = svd.singularValues().template cast<Scalar>();\n  MatrixUType u = svd.matrixU();\n  MatrixVType v = svd.matrixV();\n  RealScalar scaling = m.cwiseAbs().maxCoeff();\n  if(scaling<(std::numeric_limits<RealScalar>::min)())\n  {\n    VERIFY(sigma.cwiseAbs().maxCoeff() <= (std::numeric_limits<RealScalar>::min)());\n  }\n  else\n  {\n    VERIFY_IS_APPROX(m/scaling, u * (sigma/scaling) * v.adjoint());\n  }\n  VERIFY_IS_UNITARY(u);\n  VERIFY_IS_UNITARY(v);\n}\n\n// Compare partial SVD defined by computationOptions to a full SVD referenceSvd\ntemplate<typename SvdType, typename MatrixType>\nvoid svd_compare_to_full(const MatrixType& m,\n                         unsigned int computationOptions,\n                         const SvdType& referenceSvd)\n{\n  typedef typename MatrixType::RealScalar RealScalar;\n  Index rows = m.rows();\n  Index cols = m.cols();\n  Index diagSize = (std::min)(rows, cols);\n  RealScalar prec = test_precision<RealScalar>();\n\n  SvdType svd(m, computationOptions);\n\n  VERIFY_IS_APPROX(svd.singularValues(), referenceSvd.singularValues());\n  \n  if(computationOptions & (ComputeFullV|ComputeThinV))\n  {\n    VERIFY( (svd.matrixV().adjoint()*svd.matrixV()).isIdentity(prec) );\n    VERIFY_IS_APPROX( svd.matrixV().leftCols(diagSize) * svd.singularValues().asDiagonal() * svd.matrixV().leftCols(diagSize).adjoint(),\n                      referenceSvd.matrixV().leftCols(diagSize) * referenceSvd.singularValues().asDiagonal() * referenceSvd.matrixV().leftCols(diagSize).adjoint());\n  }\n  \n  if(computationOptions & (ComputeFullU|ComputeThinU))\n  {\n    VERIFY( (svd.matrixU().adjoint()*svd.matrixU()).isIdentity(prec) );\n    VERIFY_IS_APPROX( svd.matrixU().leftCols(diagSize) * svd.singularValues().cwiseAbs2().asDiagonal() * svd.matrixU().leftCols(diagSize).adjoint(),\n                      referenceSvd.matrixU().leftCols(diagSize) * referenceSvd.singularValues().cwiseAbs2().asDiagonal() * referenceSvd.matrixU().leftCols(diagSize).adjoint());\n  }\n  \n  // The following checks are not critical.\n  // For instance, with Dived&Conquer SVD, if only the factor 'V' is computedt then different matrix-matrix product implementation will be used\n  // and the resulting 'V' factor might be significantly different when the SVD decomposition is not unique, especially with single precision float.\n  ++g_test_level;\n  if(computationOptions & ComputeFullU)  VERIFY_IS_APPROX(svd.matrixU(), referenceSvd.matrixU());\n  if(computationOptions & ComputeThinU)  VERIFY_IS_APPROX(svd.matrixU(), referenceSvd.matrixU().leftCols(diagSize));\n  if(computationOptions & ComputeFullV)  VERIFY_IS_APPROX(svd.matrixV().cwiseAbs(), referenceSvd.matrixV().cwiseAbs());\n  if(computationOptions & ComputeThinV)  VERIFY_IS_APPROX(svd.matrixV(), referenceSvd.matrixV().leftCols(diagSize));\n  --g_test_level;\n}\n\n//\ntemplate<typename SvdType, typename MatrixType>\nvoid svd_least_square(const MatrixType& m, unsigned int computationOptions)\n{\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename MatrixType::RealScalar RealScalar;\n  typedef typename MatrixType::Index Index;\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  enum {\n    RowsAtCompileTime = MatrixType::RowsAtCompileTime,\n    ColsAtCompileTime = MatrixType::ColsAtCompileTime\n  };\n\n  typedef Matrix<Scalar, RowsAtCompileTime, Dynamic> RhsType;\n  typedef Matrix<Scalar, ColsAtCompileTime, Dynamic> SolutionType;\n\n  RhsType rhs = RhsType::Random(rows, internal::random<Index>(1, cols));\n  SvdType svd(m, computationOptions);\n\n       if(internal::is_same<RealScalar,double>::value) svd.setThreshold(1e-8);\n  else if(internal::is_same<RealScalar,float>::value)  svd.setThreshold(2e-4);\n\n  SolutionType x = svd.solve(rhs);\n   \n  RealScalar residual = (m*x-rhs).norm();\n  RealScalar rhs_norm = rhs.norm();\n  if(!test_isMuchSmallerThan(residual,rhs.norm()))\n  {\n    // ^^^ If the residual is very small, then we have an exact solution, so we are already good.\n    \n    // evaluate normal equation which works also for least-squares solutions\n    if(internal::is_same<RealScalar,double>::value || svd.rank()==m.diagonal().size())\n    {\n      using std::sqrt;\n      // This test is not stable with single precision.\n      // This is probably because squaring m signicantly affects the precision.      \n      if(internal::is_same<RealScalar,float>::value) ++g_test_level;\n      \n      VERIFY_IS_APPROX(m.adjoint()*(m*x),m.adjoint()*rhs);\n      \n      if(internal::is_same<RealScalar,float>::value) --g_test_level;\n    }\n    \n    // Check that there is no significantly better solution in the neighborhood of x\n    for(Index k=0;k<x.rows();++k)\n    {\n      using std::abs;\n      \n      SolutionType y(x);\n      y.row(k) = (RealScalar(1)+2*NumTraits<RealScalar>::epsilon())*x.row(k);\n      RealScalar residual_y = (m*y-rhs).norm();\n      VERIFY( test_isMuchSmallerThan(abs(residual_y-residual), rhs_norm) || residual < residual_y );\n      if(internal::is_same<RealScalar,float>::value) ++g_test_level;\n      VERIFY( test_isApprox(residual_y,residual) || residual < residual_y );\n      if(internal::is_same<RealScalar,float>::value) --g_test_level;\n      \n      y.row(k) = (RealScalar(1)-2*NumTraits<RealScalar>::epsilon())*x.row(k);\n      residual_y = (m*y-rhs).norm();\n      VERIFY( test_isMuchSmallerThan(abs(residual_y-residual), rhs_norm) || residual < residual_y );\n      if(internal::is_same<RealScalar,float>::value) ++g_test_level;\n      VERIFY( test_isApprox(residual_y,residual) || residual < residual_y );\n      if(internal::is_same<RealScalar,float>::value) --g_test_level;\n    }\n  }\n}\n\n// check minimal norm solutions, the inoput matrix m is only used to recover problem size\ntemplate<typename MatrixType>\nvoid svd_min_norm(const MatrixType& m, unsigned int computationOptions)\n{\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename MatrixType::Index Index;\n  Index cols = m.cols();\n\n  enum {\n    ColsAtCompileTime = MatrixType::ColsAtCompileTime\n  };\n\n  typedef Matrix<Scalar, ColsAtCompileTime, Dynamic> SolutionType;\n\n  // generate a full-rank m x n problem with m<n\n  enum {\n    RankAtCompileTime2 = ColsAtCompileTime==Dynamic ? Dynamic : (ColsAtCompileTime)/2+1,\n    RowsAtCompileTime3 = ColsAtCompileTime==Dynamic ? Dynamic : ColsAtCompileTime+1\n  };\n  typedef Matrix<Scalar, RankAtCompileTime2, ColsAtCompileTime> MatrixType2;\n  typedef Matrix<Scalar, RankAtCompileTime2, 1> RhsType2;\n  typedef Matrix<Scalar, ColsAtCompileTime, RankAtCompileTime2> MatrixType2T;\n  Index rank = RankAtCompileTime2==Dynamic ? internal::random<Index>(1,cols) : Index(RankAtCompileTime2);\n  MatrixType2 m2(rank,cols);\n  int guard = 0;\n  do {\n    m2.setRandom();\n  } while(SVD_FOR_MIN_NORM(MatrixType2)(m2).setThreshold(test_precision<Scalar>()).rank()!=rank && (++guard)<10);\n  VERIFY(guard<10);\n\n  RhsType2 rhs2 = RhsType2::Random(rank);\n  // use QR to find a reference minimal norm solution\n  HouseholderQR<MatrixType2T> qr(m2.adjoint());\n  Matrix<Scalar,Dynamic,1> tmp = qr.matrixQR().topLeftCorner(rank,rank).template triangularView<Upper>().adjoint().solve(rhs2);\n  tmp.conservativeResize(cols);\n  tmp.tail(cols-rank).setZero();\n  SolutionType x21 = qr.householderQ() * tmp;\n  // now check with SVD\n  SVD_FOR_MIN_NORM(MatrixType2) svd2(m2, computationOptions);\n  SolutionType x22 = svd2.solve(rhs2);\n  VERIFY_IS_APPROX(m2*x21, rhs2);\n  VERIFY_IS_APPROX(m2*x22, rhs2);\n  VERIFY_IS_APPROX(x21, x22);\n\n  // Now check with a rank deficient matrix\n  typedef Matrix<Scalar, RowsAtCompileTime3, ColsAtCompileTime> MatrixType3;\n  typedef Matrix<Scalar, RowsAtCompileTime3, 1> RhsType3;\n  Index rows3 = RowsAtCompileTime3==Dynamic ? internal::random<Index>(rank+1,2*cols) : Index(RowsAtCompileTime3);\n  Matrix<Scalar,RowsAtCompileTime3,Dynamic> C = Matrix<Scalar,RowsAtCompileTime3,Dynamic>::Random(rows3,rank);\n  MatrixType3 m3 = C * m2;\n  RhsType3 rhs3 = C * rhs2;\n  SVD_FOR_MIN_NORM(MatrixType3) svd3(m3, computationOptions);\n  SolutionType x3 = svd3.solve(rhs3);\n  VERIFY_IS_APPROX(m3*x3, rhs3);\n  VERIFY_IS_APPROX(m3*x21, rhs3);\n  VERIFY_IS_APPROX(m2*x3, rhs2);\n  VERIFY_IS_APPROX(x21, x3);\n}\n\n// Check full, compare_to_full, least_square, and min_norm for all possible compute-options\ntemplate<typename SvdType, typename MatrixType>\nvoid svd_test_all_computation_options(const MatrixType& m, bool full_only)\n{\n//   if (QRPreconditioner == NoQRPreconditioner && m.rows() != m.cols())\n//     return;\n  SvdType fullSvd(m, ComputeFullU|ComputeFullV);\n  CALL_SUBTEST(( svd_check_full(m, fullSvd) ));\n  CALL_SUBTEST(( svd_least_square<SvdType>(m, ComputeFullU | ComputeFullV) ));\n  CALL_SUBTEST(( svd_min_norm(m, ComputeFullU | ComputeFullV) ));\n  \n  #if defined __INTEL_COMPILER\n  // remark #111: statement is unreachable\n  #pragma warning disable 111\n  #endif\n  if(full_only)\n    return;\n\n  CALL_SUBTEST(( svd_compare_to_full(m, ComputeFullU, fullSvd) ));\n  CALL_SUBTEST(( svd_compare_to_full(m, ComputeFullV, fullSvd) ));\n  CALL_SUBTEST(( svd_compare_to_full(m, 0, fullSvd) ));\n\n  if (MatrixType::ColsAtCompileTime == Dynamic) {\n    // thin U/V are only available with dynamic number of columns\n    CALL_SUBTEST(( svd_compare_to_full(m, ComputeFullU|ComputeThinV, fullSvd) ));\n    CALL_SUBTEST(( svd_compare_to_full(m,              ComputeThinV, fullSvd) ));\n    CALL_SUBTEST(( svd_compare_to_full(m, ComputeThinU|ComputeFullV, fullSvd) ));\n    CALL_SUBTEST(( svd_compare_to_full(m, ComputeThinU             , fullSvd) ));\n    CALL_SUBTEST(( svd_compare_to_full(m, ComputeThinU|ComputeThinV, fullSvd) ));\n    \n    CALL_SUBTEST(( svd_least_square<SvdType>(m, ComputeFullU | ComputeThinV) ));\n    CALL_SUBTEST(( svd_least_square<SvdType>(m, ComputeThinU | ComputeFullV) ));\n    CALL_SUBTEST(( svd_least_square<SvdType>(m, ComputeThinU | ComputeThinV) ));\n\n    CALL_SUBTEST(( svd_min_norm(m, ComputeFullU | ComputeThinV) ));\n    CALL_SUBTEST(( svd_min_norm(m, ComputeThinU | ComputeFullV) ));\n    CALL_SUBTEST(( svd_min_norm(m, ComputeThinU | ComputeThinV) ));\n\n    // test reconstruction\n    typedef typename MatrixType::Index Index;\n    Index diagSize = (std::min)(m.rows(), m.cols());\n    SvdType svd(m, ComputeThinU | ComputeThinV);\n    VERIFY_IS_APPROX(m, svd.matrixU().leftCols(diagSize) * svd.singularValues().asDiagonal() * svd.matrixV().leftCols(diagSize).adjoint());\n  }\n}\n\n\n// work around stupid msvc error when constructing at compile time an expression that involves\n// a division by zero, even if the numeric type has floating point\ntemplate<typename Scalar>\nEIGEN_DONT_INLINE Scalar zero() { return Scalar(0); }\n\n// workaround aggressive optimization in ICC\ntemplate<typename T> EIGEN_DONT_INLINE  T sub(T a, T b) { return a - b; }\n\n// all this function does is verify we don't iterate infinitely on nan/inf values\ntemplate<typename SvdType, typename MatrixType>\nvoid svd_inf_nan()\n{\n  SvdType svd;\n  typedef typename MatrixType::Scalar Scalar;\n  Scalar some_inf = Scalar(1) / zero<Scalar>();\n  VERIFY(sub(some_inf, some_inf) != sub(some_inf, some_inf));\n  svd.compute(MatrixType::Constant(10,10,some_inf), ComputeFullU | ComputeFullV);\n\n  Scalar nan = std::numeric_limits<Scalar>::quiet_NaN();\n  VERIFY(nan != nan);\n  svd.compute(MatrixType::Constant(10,10,nan), ComputeFullU | ComputeFullV);\n\n  MatrixType m = MatrixType::Zero(10,10);\n  m(internal::random<int>(0,9), internal::random<int>(0,9)) = some_inf;\n  svd.compute(m, ComputeFullU | ComputeFullV);\n\n  m = MatrixType::Zero(10,10);\n  m(internal::random<int>(0,9), internal::random<int>(0,9)) = nan;\n  svd.compute(m, ComputeFullU | ComputeFullV);\n  \n  // regression test for bug 791\n  m.resize(3,3);\n  m << 0,    2*NumTraits<Scalar>::epsilon(),  0.5,\n       0,   -0.5,                             0,\n       nan,  0,                               0;\n  svd.compute(m, ComputeFullU | ComputeFullV);\n  \n  m.resize(4,4);\n  m <<  1, 0, 0, 0,\n        0, 3, 1, 2e-308,\n        1, 0, 1, nan,\n        0, nan, nan, 0;\n  svd.compute(m, ComputeFullU | ComputeFullV);\n}\n\n// Regression test for bug 286: JacobiSVD loops indefinitely with some\n// matrices containing denormal numbers.\ntemplate<typename>\nvoid svd_underoverflow()\n{\n#if defined __INTEL_COMPILER\n// shut up warning #239: floating point underflow\n#pragma warning push\n#pragma warning disable 239\n#endif\n  Matrix2d M;\n  M << -7.90884e-313, -4.94e-324,\n                 0, 5.60844e-313;\n  SVD_DEFAULT(Matrix2d) svd;\n  svd.compute(M,ComputeFullU|ComputeFullV);\n  CALL_SUBTEST( svd_check_full(M,svd) );\n  \n  // Check all 2x2 matrices made with the following coefficients:\n  VectorXd value_set(9);\n  value_set << 0, 1, -1, 5.60844e-313, -5.60844e-313, 4.94e-324, -4.94e-324, -4.94e-223, 4.94e-223;\n  Array4i id(0,0,0,0);\n  int k = 0;\n  do\n  {\n    M << value_set(id(0)), value_set(id(1)), value_set(id(2)), value_set(id(3));\n    svd.compute(M,ComputeFullU|ComputeFullV);\n    CALL_SUBTEST( svd_check_full(M,svd) );\n\n    id(k)++;\n    if(id(k)>=value_set.size())\n    {\n      while(k<3 && id(k)>=value_set.size()) id(++k)++;\n      id.head(k).setZero();\n      k=0;\n    }\n\n  } while((id<int(value_set.size())).all());\n  \n#if defined __INTEL_COMPILER\n#pragma warning pop\n#endif\n  \n  // Check for overflow:\n  Matrix3d M3;\n  M3 << 4.4331978442502944e+307, -5.8585363752028680e+307,  6.4527017443412964e+307,\n        3.7841695601406358e+307,  2.4331702789740617e+306, -3.5235707140272905e+307,\n       -8.7190887618028355e+307, -7.3453213709232193e+307, -2.4367363684472105e+307;\n\n  SVD_DEFAULT(Matrix3d) svd3;\n  svd3.compute(M3,ComputeFullU|ComputeFullV); // just check we don't loop indefinitely\n  CALL_SUBTEST( svd_check_full(M3,svd3) );\n}\n\n// void jacobisvd(const MatrixType& a = MatrixType(), bool pickrandom = true)\n\ntemplate<typename MatrixType>\nvoid svd_all_trivial_2x2( void (*cb)(const MatrixType&,bool) )\n{\n  MatrixType M;\n  VectorXd value_set(3);\n  value_set << 0, 1, -1;\n  Array4i id(0,0,0,0);\n  int k = 0;\n  do\n  {\n    M << value_set(id(0)), value_set(id(1)), value_set(id(2)), value_set(id(3));\n    \n    cb(M,false);\n    \n    id(k)++;\n    if(id(k)>=value_set.size())\n    {\n      while(k<3 && id(k)>=value_set.size()) id(++k)++;\n      id.head(k).setZero();\n      k=0;\n    }\n    \n  } while((id<int(value_set.size())).all());\n}\n\ntemplate<typename>\nvoid svd_preallocate()\n{\n  Vector3f v(3.f, 2.f, 1.f);\n  MatrixXf m = v.asDiagonal();\n\n  internal::set_is_malloc_allowed(false);\n  VERIFY_RAISES_ASSERT(VectorXf tmp(10);)\n  SVD_DEFAULT(MatrixXf) svd;\n  internal::set_is_malloc_allowed(true);\n  svd.compute(m);\n  VERIFY_IS_APPROX(svd.singularValues(), v);\n\n  SVD_DEFAULT(MatrixXf) svd2(3,3);\n  internal::set_is_malloc_allowed(false);\n  svd2.compute(m);\n  internal::set_is_malloc_allowed(true);\n  VERIFY_IS_APPROX(svd2.singularValues(), v);\n  VERIFY_RAISES_ASSERT(svd2.matrixU());\n  VERIFY_RAISES_ASSERT(svd2.matrixV());\n  svd2.compute(m, ComputeFullU | ComputeFullV);\n  VERIFY_IS_APPROX(svd2.matrixU(), Matrix3f::Identity());\n  VERIFY_IS_APPROX(svd2.matrixV(), Matrix3f::Identity());\n  internal::set_is_malloc_allowed(false);\n  svd2.compute(m);\n  internal::set_is_malloc_allowed(true);\n\n  SVD_DEFAULT(MatrixXf) svd3(3,3,ComputeFullU|ComputeFullV);\n  internal::set_is_malloc_allowed(false);\n  svd2.compute(m);\n  internal::set_is_malloc_allowed(true);\n  VERIFY_IS_APPROX(svd2.singularValues(), v);\n  VERIFY_IS_APPROX(svd2.matrixU(), Matrix3f::Identity());\n  VERIFY_IS_APPROX(svd2.matrixV(), Matrix3f::Identity());\n  internal::set_is_malloc_allowed(false);\n  svd2.compute(m, ComputeFullU|ComputeFullV);\n  internal::set_is_malloc_allowed(true);\n}\n\ntemplate<typename SvdType,typename MatrixType> \nvoid svd_verify_assert(const MatrixType& m)\n{\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename MatrixType::Index Index;\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  enum {\n    RowsAtCompileTime = MatrixType::RowsAtCompileTime,\n    ColsAtCompileTime = MatrixType::ColsAtCompileTime\n  };\n\n  typedef Matrix<Scalar, RowsAtCompileTime, 1> RhsType;\n  RhsType rhs(rows);\n  SvdType svd;\n  VERIFY_RAISES_ASSERT(svd.matrixU())\n  VERIFY_RAISES_ASSERT(svd.singularValues())\n  VERIFY_RAISES_ASSERT(svd.matrixV())\n  VERIFY_RAISES_ASSERT(svd.solve(rhs))\n  MatrixType a = MatrixType::Zero(rows, cols);\n  a.setZero();\n  svd.compute(a, 0);\n  VERIFY_RAISES_ASSERT(svd.matrixU())\n  VERIFY_RAISES_ASSERT(svd.matrixV())\n  svd.singularValues();\n  VERIFY_RAISES_ASSERT(svd.solve(rhs))\n    \n  if (ColsAtCompileTime == Dynamic)\n  {\n    svd.compute(a, ComputeThinU);\n    svd.matrixU();\n    VERIFY_RAISES_ASSERT(svd.matrixV())\n    VERIFY_RAISES_ASSERT(svd.solve(rhs))\n    svd.compute(a, ComputeThinV);\n    svd.matrixV();\n    VERIFY_RAISES_ASSERT(svd.matrixU())\n    VERIFY_RAISES_ASSERT(svd.solve(rhs))\n  }\n  else\n  {\n    VERIFY_RAISES_ASSERT(svd.compute(a, ComputeThinU))\n    VERIFY_RAISES_ASSERT(svd.compute(a, ComputeThinV))\n  }\n}\n\n#undef SVD_DEFAULT\n#undef SVD_FOR_MIN_NORM\n"
  },
  {
    "path": "include/eigen3/test/svd_fill.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014-2015 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\ntemplate<typename T>\nArray<T,4,1> four_denorms();\n\ntemplate<>\nArray4f four_denorms() { return Array4f(5.60844e-39f, -5.60844e-39f, 4.94e-44f, -4.94e-44f); }\ntemplate<>\nArray4d four_denorms() { return Array4d(5.60844e-313, -5.60844e-313, 4.94e-324, -4.94e-324); }\ntemplate<typename T>\nArray<T,4,1> four_denorms() { return four_denorms<double>().cast<T>(); }\n\ntemplate<typename MatrixType>\nvoid svd_fill_random(MatrixType &m, int Option = 0)\n{\n  using std::pow;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename MatrixType::RealScalar RealScalar;\n  typedef typename MatrixType::Index Index;\n  Index diagSize = (std::min)(m.rows(), m.cols());\n  RealScalar s = std::numeric_limits<RealScalar>::max_exponent10/4;\n  s = internal::random<RealScalar>(1,s);\n  Matrix<RealScalar,Dynamic,1> d =  Matrix<RealScalar,Dynamic,1>::Random(diagSize);\n  for(Index k=0; k<diagSize; ++k)\n    d(k) = d(k)*pow(RealScalar(10),internal::random<RealScalar>(-s,s));\n\n  bool dup     = internal::random<int>(0,10) < 3;\n  bool unit_uv = internal::random<int>(0,10) < (dup?7:3); // if we duplicate some diagonal entries, then increase the chance to preserve them using unitary U and V factors\n  \n  // duplicate some singular values\n  if(dup)\n  {\n    Index n = internal::random<Index>(0,d.size()-1);\n    for(Index i=0; i<n; ++i)\n      d(internal::random<Index>(0,d.size()-1)) = d(internal::random<Index>(0,d.size()-1));\n  }\n  \n  Matrix<Scalar,Dynamic,Dynamic> U(m.rows(),diagSize);\n  Matrix<Scalar,Dynamic,Dynamic> VT(diagSize,m.cols());\n  if(unit_uv)\n  {\n    // in very rare cases let's try with a pure diagonal matrix\n    if(internal::random<int>(0,10) < 1)\n    {\n      U.setIdentity();\n      VT.setIdentity();\n    }\n    else\n    {\n      createRandomPIMatrixOfRank(diagSize,U.rows(), U.cols(), U);\n      createRandomPIMatrixOfRank(diagSize,VT.rows(), VT.cols(), VT);\n    }\n  }\n  else\n  {\n    U.setRandom();\n    VT.setRandom();\n  }\n  \n  Matrix<Scalar,Dynamic,1> samples(9);\n  samples << 0, four_denorms<RealScalar>(),\n            -RealScalar(1)/NumTraits<RealScalar>::highest(), RealScalar(1)/NumTraits<RealScalar>::highest(), (std::numeric_limits<RealScalar>::min)(), pow((std::numeric_limits<RealScalar>::min)(),0.8);\n  \n  if(Option==Symmetric)\n  {\n    m = U * d.asDiagonal() * U.transpose();\n    \n    // randomly nullify some rows/columns\n    {\n      Index count = internal::random<Index>(-diagSize,diagSize);\n      for(Index k=0; k<count; ++k)\n      {\n        Index i = internal::random<Index>(0,diagSize-1);\n        m.row(i).setZero();\n        m.col(i).setZero();\n      }\n      if(count<0)\n      // (partly) cancel some coeffs\n      if(!(dup && unit_uv))\n      {\n        \n        Index n = internal::random<Index>(0,m.size()-1);\n        for(Index k=0; k<n; ++k)\n        {\n          Index i = internal::random<Index>(0,m.rows()-1);\n          Index j = internal::random<Index>(0,m.cols()-1);\n          m(j,i) = m(i,j) = samples(internal::random<Index>(0,samples.size()-1));\n          if(NumTraits<Scalar>::IsComplex)\n            *(&numext::real_ref(m(j,i))+1) = *(&numext::real_ref(m(i,j))+1) = samples.real()(internal::random<Index>(0,samples.size()-1));\n        }\n      }\n    }\n  }\n  else\n  {\n    m = U * d.asDiagonal() * VT;\n    // (partly) cancel some coeffs\n    if(!(dup && unit_uv))\n    {\n      Index n = internal::random<Index>(0,m.size()-1);\n      for(Index k=0; k<n; ++k)\n      {\n        Index i = internal::random<Index>(0,m.rows()-1);\n        Index j = internal::random<Index>(0,m.cols()-1);\n        m(i,j) = samples(internal::random<Index>(0,samples.size()-1));\n        if(NumTraits<Scalar>::IsComplex)\n          *(&numext::real_ref(m(i,j))+1) = samples.real()(internal::random<Index>(0,samples.size()-1));\n      }\n    }\n  }\n}\n\n"
  },
  {
    "path": "include/eigen3/test/swap.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define EIGEN_NO_STATIC_ASSERT\n#include \"main.h\"\n\ntemplate<typename T>\nstruct other_matrix_type\n{\n  typedef int type;\n};\n\ntemplate<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>\nstruct other_matrix_type<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >\n{\n  typedef Matrix<_Scalar, _Rows, _Cols, _Options^RowMajor, _MaxRows, _MaxCols> type;\n};\n\ntemplate<typename MatrixType> void swap(const MatrixType& m)\n{\n  typedef typename other_matrix_type<MatrixType>::type OtherMatrixType;\n  typedef typename MatrixType::Scalar Scalar;\n\n  eigen_assert((!internal::is_same<MatrixType,OtherMatrixType>::value));\n  typename MatrixType::Index rows = m.rows();\n  typename MatrixType::Index cols = m.cols();\n  \n  // construct 3 matrix guaranteed to be distinct\n  MatrixType m1 = MatrixType::Random(rows,cols);\n  MatrixType m2 = MatrixType::Random(rows,cols) + Scalar(100) * MatrixType::Identity(rows,cols);\n  OtherMatrixType m3 = OtherMatrixType::Random(rows,cols) + Scalar(200) * OtherMatrixType::Identity(rows,cols);\n  \n  MatrixType m1_copy = m1;\n  MatrixType m2_copy = m2;\n  OtherMatrixType m3_copy = m3;\n  \n  // test swapping 2 matrices of same type\n  Scalar *d1=m1.data(), *d2=m2.data();\n  m1.swap(m2);\n  VERIFY_IS_APPROX(m1,m2_copy);\n  VERIFY_IS_APPROX(m2,m1_copy);\n  if(MatrixType::SizeAtCompileTime==Dynamic)\n  {\n    VERIFY(m1.data()==d2);\n    VERIFY(m2.data()==d1);\n  }\n  m1 = m1_copy;\n  m2 = m2_copy;\n  \n  // test swapping 2 matrices of different types\n  m1.swap(m3);\n  VERIFY_IS_APPROX(m1,m3_copy);\n  VERIFY_IS_APPROX(m3,m1_copy);\n  m1 = m1_copy;\n  m3 = m3_copy;\n  \n  // test swapping matrix with expression\n  m1.swap(m2.block(0,0,rows,cols));\n  VERIFY_IS_APPROX(m1,m2_copy);\n  VERIFY_IS_APPROX(m2,m1_copy);\n  m1 = m1_copy;\n  m2 = m2_copy;\n\n  // test swapping two expressions of different types\n  m1.transpose().swap(m3.transpose());\n  VERIFY_IS_APPROX(m1,m3_copy);\n  VERIFY_IS_APPROX(m3,m1_copy);\n  m1 = m1_copy;\n  m3 = m3_copy;\n  \n  if(m1.rows()>1)\n  {\n    // test assertion on mismatching size -- matrix case\n    VERIFY_RAISES_ASSERT(m1.swap(m1.row(0)));\n    // test assertion on mismatching size -- xpr case\n    VERIFY_RAISES_ASSERT(m1.row(0).swap(m1));\n  }\n}\n\nvoid test_swap()\n{\n  int s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE);\n  CALL_SUBTEST_1( swap(Matrix3f()) ); // fixed size, no vectorization \n  CALL_SUBTEST_2( swap(Matrix4d()) ); // fixed size, possible vectorization \n  CALL_SUBTEST_3( swap(MatrixXd(s,s)) ); // dyn size, no vectorization \n  CALL_SUBTEST_4( swap(MatrixXf(s,s)) ); // dyn size, possible vectorization \n  TEST_SET_BUT_UNUSED_VARIABLE(s)\n}\n"
  },
  {
    "path": "include/eigen3/test/triangular.cpp",
    "content": "// This file is triangularView of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n\n\ntemplate<typename MatrixType> void triangular_square(const MatrixType& m)\n{\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;\n\n  RealScalar largerEps = 10*test_precision<RealScalar>();\n\n  typename MatrixType::Index rows = m.rows();\n  typename MatrixType::Index cols = m.cols();\n\n  MatrixType m1 = MatrixType::Random(rows, cols),\n             m2 = MatrixType::Random(rows, cols),\n             m3(rows, cols),\n             m4(rows, cols),\n             r1(rows, cols),\n             r2(rows, cols);\n  VectorType v2 = VectorType::Random(rows);\n\n  MatrixType m1up = m1.template triangularView<Upper>();\n  MatrixType m2up = m2.template triangularView<Upper>();\n\n  if (rows*cols>1)\n  {\n    VERIFY(m1up.isUpperTriangular());\n    VERIFY(m2up.transpose().isLowerTriangular());\n    VERIFY(!m2.isLowerTriangular());\n  }\n\n//   VERIFY_IS_APPROX(m1up.transpose() * m2, m1.upper().transpose().lower() * m2);\n\n  // test overloaded operator+=\n  r1.setZero();\n  r2.setZero();\n  r1.template triangularView<Upper>() +=  m1;\n  r2 += m1up;\n  VERIFY_IS_APPROX(r1,r2);\n\n  // test overloaded operator=\n  m1.setZero();\n  m1.template triangularView<Upper>() = m2.transpose() + m2;\n  m3 = m2.transpose() + m2;\n  VERIFY_IS_APPROX(m3.template triangularView<Lower>().transpose().toDenseMatrix(), m1);\n\n  // test overloaded operator=\n  m1.setZero();\n  m1.template triangularView<Lower>() = m2.transpose() + m2;\n  VERIFY_IS_APPROX(m3.template triangularView<Lower>().toDenseMatrix(), m1);\n\n  VERIFY_IS_APPROX(m3.template triangularView<Lower>().conjugate().toDenseMatrix(),\n                   m3.conjugate().template triangularView<Lower>().toDenseMatrix());\n\n  m1 = MatrixType::Random(rows, cols);\n  for (int i=0; i<rows; ++i)\n    while (numext::abs2(m1(i,i))<RealScalar(1e-1)) m1(i,i) = internal::random<Scalar>();\n\n  Transpose<MatrixType> trm4(m4);\n  // test back and forward subsitution with a vector as the rhs\n  m3 = m1.template triangularView<Upper>();\n  VERIFY(v2.isApprox(m3.adjoint() * (m1.adjoint().template triangularView<Lower>().solve(v2)), largerEps));\n  m3 = m1.template triangularView<Lower>();\n  VERIFY(v2.isApprox(m3.transpose() * (m1.transpose().template triangularView<Upper>().solve(v2)), largerEps));\n  m3 = m1.template triangularView<Upper>();\n  VERIFY(v2.isApprox(m3 * (m1.template triangularView<Upper>().solve(v2)), largerEps));\n  m3 = m1.template triangularView<Lower>();\n  VERIFY(v2.isApprox(m3.conjugate() * (m1.conjugate().template triangularView<Lower>().solve(v2)), largerEps));\n\n  // test back and forward substitution with a matrix as the rhs\n  m3 = m1.template triangularView<Upper>();\n  VERIFY(m2.isApprox(m3.adjoint() * (m1.adjoint().template triangularView<Lower>().solve(m2)), largerEps));\n  m3 = m1.template triangularView<Lower>();\n  VERIFY(m2.isApprox(m3.transpose() * (m1.transpose().template triangularView<Upper>().solve(m2)), largerEps));\n  m3 = m1.template triangularView<Upper>();\n  VERIFY(m2.isApprox(m3 * (m1.template triangularView<Upper>().solve(m2)), largerEps));\n  m3 = m1.template triangularView<Lower>();\n  VERIFY(m2.isApprox(m3.conjugate() * (m1.conjugate().template triangularView<Lower>().solve(m2)), largerEps));\n\n  // check M * inv(L) using in place API\n  m4 = m3;\n  m1.transpose().template triangularView<Eigen::Upper>().solveInPlace(trm4);\n  VERIFY_IS_APPROX(m4 * m1.template triangularView<Eigen::Lower>(), m3);\n\n  // check M * inv(U) using in place API\n  m3 = m1.template triangularView<Upper>();\n  m4 = m3;\n  m3.transpose().template triangularView<Eigen::Lower>().solveInPlace(trm4);\n  VERIFY_IS_APPROX(m4 * m1.template triangularView<Eigen::Upper>(), m3);\n\n  // check solve with unit diagonal\n  m3 = m1.template triangularView<UnitUpper>();\n  VERIFY(m2.isApprox(m3 * (m1.template triangularView<UnitUpper>().solve(m2)), largerEps));\n\n//   VERIFY((  m1.template triangularView<Upper>()\n//           * m2.template triangularView<Upper>()).isUpperTriangular());\n\n  // test swap\n  m1.setOnes();\n  m2.setZero();\n  m2.template triangularView<Upper>().swap(m1);\n  m3.setZero();\n  m3.template triangularView<Upper>().setOnes();\n  VERIFY_IS_APPROX(m2,m3);\n  \n  m1.setRandom();\n  m3 = m1.template triangularView<Upper>();\n  Matrix<Scalar, MatrixType::ColsAtCompileTime, Dynamic> m5(cols, internal::random<int>(1,20));  m5.setRandom();\n  Matrix<Scalar, Dynamic, MatrixType::RowsAtCompileTime> m6(internal::random<int>(1,20), rows);  m6.setRandom();\n  VERIFY_IS_APPROX(m1.template triangularView<Upper>() * m5, m3*m5);\n  VERIFY_IS_APPROX(m6*m1.template triangularView<Upper>(), m6*m3);\n\n  m1up = m1.template triangularView<Upper>();\n  VERIFY_IS_APPROX(m1.template selfadjointView<Upper>().template triangularView<Upper>().toDenseMatrix(), m1up);\n  VERIFY_IS_APPROX(m1up.template selfadjointView<Upper>().template triangularView<Upper>().toDenseMatrix(), m1up);\n  VERIFY_IS_APPROX(m1.template selfadjointView<Upper>().template triangularView<Lower>().toDenseMatrix(), m1up.adjoint());\n  VERIFY_IS_APPROX(m1up.template selfadjointView<Upper>().template triangularView<Lower>().toDenseMatrix(), m1up.adjoint());\n\n  VERIFY_IS_APPROX(m1.template selfadjointView<Upper>().diagonal(), m1.diagonal());\n\n}\n\n\ntemplate<typename MatrixType> void triangular_rect(const MatrixType& m)\n{\n  typedef const typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  enum { Rows =  MatrixType::RowsAtCompileTime, Cols =  MatrixType::ColsAtCompileTime };\n\n  Index rows = m.rows();\n  Index cols = m.cols();\n\n  MatrixType m1 = MatrixType::Random(rows, cols),\n             m2 = MatrixType::Random(rows, cols),\n             m3(rows, cols),\n             m4(rows, cols),\n             r1(rows, cols),\n             r2(rows, cols);\n\n  MatrixType m1up = m1.template triangularView<Upper>();\n  MatrixType m2up = m2.template triangularView<Upper>();\n\n  if (rows>1 && cols>1)\n  {\n    VERIFY(m1up.isUpperTriangular());\n    VERIFY(m2up.transpose().isLowerTriangular());\n    VERIFY(!m2.isLowerTriangular());\n  }\n\n  // test overloaded operator+=\n  r1.setZero();\n  r2.setZero();\n  r1.template triangularView<Upper>() +=  m1;\n  r2 += m1up;\n  VERIFY_IS_APPROX(r1,r2);\n\n  // test overloaded operator=\n  m1.setZero();\n  m1.template triangularView<Upper>() = 3 * m2;\n  m3 = 3 * m2;\n  VERIFY_IS_APPROX(m3.template triangularView<Upper>().toDenseMatrix(), m1);\n\n\n  m1.setZero();\n  m1.template triangularView<Lower>() = 3 * m2;\n  VERIFY_IS_APPROX(m3.template triangularView<Lower>().toDenseMatrix(), m1);\n\n  m1.setZero();\n  m1.template triangularView<StrictlyUpper>() = 3 * m2;\n  VERIFY_IS_APPROX(m3.template triangularView<StrictlyUpper>().toDenseMatrix(), m1);\n\n\n  m1.setZero();\n  m1.template triangularView<StrictlyLower>() = 3 * m2;\n  VERIFY_IS_APPROX(m3.template triangularView<StrictlyLower>().toDenseMatrix(), m1);\n  m1.setRandom();\n  m2 = m1.template triangularView<Upper>();\n  VERIFY(m2.isUpperTriangular());\n  VERIFY(!m2.isLowerTriangular());\n  m2 = m1.template triangularView<StrictlyUpper>();\n  VERIFY(m2.isUpperTriangular());\n  VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));\n  m2 = m1.template triangularView<UnitUpper>();\n  VERIFY(m2.isUpperTriangular());\n  m2.diagonal().array() -= Scalar(1);\n  VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));\n  m2 = m1.template triangularView<Lower>();\n  VERIFY(m2.isLowerTriangular());\n  VERIFY(!m2.isUpperTriangular());\n  m2 = m1.template triangularView<StrictlyLower>();\n  VERIFY(m2.isLowerTriangular());\n  VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));\n  m2 = m1.template triangularView<UnitLower>();\n  VERIFY(m2.isLowerTriangular());\n  m2.diagonal().array() -= Scalar(1);\n  VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));\n  // test swap\n  m1.setOnes();\n  m2.setZero();\n  m2.template triangularView<Upper>().swap(m1);\n  m3.setZero();\n  m3.template triangularView<Upper>().setOnes();\n  VERIFY_IS_APPROX(m2,m3);\n}\n\nvoid bug_159()\n{\n  Matrix3d m = Matrix3d::Random().triangularView<Lower>();\n  EIGEN_UNUSED_VARIABLE(m)\n}\n\nvoid test_triangular()\n{\n  int maxsize = (std::min)(EIGEN_TEST_MAX_SIZE,20);\n  for(int i = 0; i < g_repeat ; i++)\n  {\n    int r = internal::random<int>(2,maxsize); TEST_SET_BUT_UNUSED_VARIABLE(r)\n    int c = internal::random<int>(2,maxsize); TEST_SET_BUT_UNUSED_VARIABLE(c)\n\n    CALL_SUBTEST_1( triangular_square(Matrix<float, 1, 1>()) );\n    CALL_SUBTEST_2( triangular_square(Matrix<float, 2, 2>()) );\n    CALL_SUBTEST_3( triangular_square(Matrix3d()) );\n    CALL_SUBTEST_4( triangular_square(Matrix<std::complex<float>,8, 8>()) );\n    CALL_SUBTEST_5( triangular_square(MatrixXcd(r,r)) );\n    CALL_SUBTEST_6( triangular_square(Matrix<float,Dynamic,Dynamic,RowMajor>(r, r)) );\n\n    CALL_SUBTEST_7( triangular_rect(Matrix<float, 4, 5>()) );\n    CALL_SUBTEST_8( triangular_rect(Matrix<double, 6, 2>()) );\n    CALL_SUBTEST_9( triangular_rect(MatrixXcf(r, c)) );\n    CALL_SUBTEST_5( triangular_rect(MatrixXcd(r, c)) );\n    CALL_SUBTEST_6( triangular_rect(Matrix<float,Dynamic,Dynamic,RowMajor>(r, c)) );\n  }\n  \n  CALL_SUBTEST_1( bug_159() );\n}\n"
  },
  {
    "path": "include/eigen3/test/umeyama.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Hauke Heibel <hauke.heibel@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/Core>\n#include <Eigen/Geometry>\n\n#include <Eigen/LU> // required for MatrixBase::determinant\n#include <Eigen/SVD> // required for SVD\n\nusing namespace Eigen;\n\n//  Constructs a random matrix from the unitary group U(size).\ntemplate <typename T>\nEigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> randMatrixUnitary(int size)\n{\n  typedef T Scalar;\n  typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> MatrixType;\n\n  MatrixType Q;\n\n  int max_tries = 40;\n  double is_unitary = false;\n\n  while (!is_unitary && max_tries > 0)\n  {\n    // initialize random matrix\n    Q = MatrixType::Random(size, size);\n\n    // orthogonalize columns using the Gram-Schmidt algorithm\n    for (int col = 0; col < size; ++col)\n    {\n      typename MatrixType::ColXpr colVec = Q.col(col);\n      for (int prevCol = 0; prevCol < col; ++prevCol)\n      {\n        typename MatrixType::ColXpr prevColVec = Q.col(prevCol);\n        colVec -= colVec.dot(prevColVec)*prevColVec;\n      }\n      Q.col(col) = colVec.normalized();\n    }\n\n    // this additional orthogonalization is not necessary in theory but should enhance\n    // the numerical orthogonality of the matrix\n    for (int row = 0; row < size; ++row)\n    {\n      typename MatrixType::RowXpr rowVec = Q.row(row);\n      for (int prevRow = 0; prevRow < row; ++prevRow)\n      {\n        typename MatrixType::RowXpr prevRowVec = Q.row(prevRow);\n        rowVec -= rowVec.dot(prevRowVec)*prevRowVec;\n      }\n      Q.row(row) = rowVec.normalized();\n    }\n\n    // final check\n    is_unitary = Q.isUnitary();\n    --max_tries;\n  }\n\n  if (max_tries == 0)\n    eigen_assert(false && \"randMatrixUnitary: Could not construct unitary matrix!\");\n\n  return Q;\n}\n\n//  Constructs a random matrix from the special unitary group SU(size).\ntemplate <typename T>\nEigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> randMatrixSpecialUnitary(int size)\n{\n  typedef T Scalar;\n\n  typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> MatrixType;\n\n  // initialize unitary matrix\n  MatrixType Q = randMatrixUnitary<Scalar>(size);\n\n  // tweak the first column to make the determinant be 1\n  Q.col(0) *= numext::conj(Q.determinant());\n\n  return Q;\n}\n\ntemplate <typename MatrixType>\nvoid run_test(int dim, int num_elements)\n{\n  using std::abs;\n  typedef typename internal::traits<MatrixType>::Scalar Scalar;\n  typedef Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> MatrixX;\n  typedef Matrix<Scalar, Eigen::Dynamic, 1> VectorX;\n\n  // MUST be positive because in any other case det(cR_t) may become negative for\n  // odd dimensions!\n  const Scalar c = abs(internal::random<Scalar>());\n\n  MatrixX R = randMatrixSpecialUnitary<Scalar>(dim);\n  VectorX t = Scalar(50)*VectorX::Random(dim,1);\n\n  MatrixX cR_t = MatrixX::Identity(dim+1,dim+1);\n  cR_t.block(0,0,dim,dim) = c*R;\n  cR_t.block(0,dim,dim,1) = t;\n\n  MatrixX src = MatrixX::Random(dim+1, num_elements);\n  src.row(dim) = Matrix<Scalar, 1, Dynamic>::Constant(num_elements, Scalar(1));\n\n  MatrixX dst = cR_t*src;\n\n  MatrixX cR_t_umeyama = umeyama(src.block(0,0,dim,num_elements), dst.block(0,0,dim,num_elements));\n\n  const Scalar error = ( cR_t_umeyama*src - dst ).norm() / dst.norm();\n  VERIFY(error < Scalar(40)*std::numeric_limits<Scalar>::epsilon());\n}\n\ntemplate<typename Scalar, int Dimension>\nvoid run_fixed_size_test(int num_elements)\n{\n  using std::abs;\n  typedef Matrix<Scalar, Dimension+1, Dynamic> MatrixX;\n  typedef Matrix<Scalar, Dimension+1, Dimension+1> HomMatrix;\n  typedef Matrix<Scalar, Dimension, Dimension> FixedMatrix;\n  typedef Matrix<Scalar, Dimension, 1> FixedVector;\n\n  const int dim = Dimension;\n\n  // MUST be positive because in any other case det(cR_t) may become negative for\n  // odd dimensions!\n  // Also if c is to small compared to t.norm(), problem is ill-posed (cf. Bug 744)\n  const Scalar c = internal::random<Scalar>(0.5, 2.0);\n\n  FixedMatrix R = randMatrixSpecialUnitary<Scalar>(dim);\n  FixedVector t = Scalar(32)*FixedVector::Random(dim,1);\n\n  HomMatrix cR_t = HomMatrix::Identity(dim+1,dim+1);\n  cR_t.block(0,0,dim,dim) = c*R;\n  cR_t.block(0,dim,dim,1) = t;\n\n  MatrixX src = MatrixX::Random(dim+1, num_elements);\n  src.row(dim) = Matrix<Scalar, 1, Dynamic>::Constant(num_elements, Scalar(1));\n\n  MatrixX dst = cR_t*src;\n\n  Block<MatrixX, Dimension, Dynamic> src_block(src,0,0,dim,num_elements);\n  Block<MatrixX, Dimension, Dynamic> dst_block(dst,0,0,dim,num_elements);\n\n  HomMatrix cR_t_umeyama = umeyama(src_block, dst_block);\n\n  const Scalar error = ( cR_t_umeyama*src - dst ).squaredNorm();\n\n  VERIFY(error < Scalar(16)*std::numeric_limits<Scalar>::epsilon());\n}\n\nvoid test_umeyama()\n{\n  for (int i=0; i<g_repeat; ++i)\n  {\n    const int num_elements = internal::random<int>(40,500);\n\n    // works also for dimensions bigger than 3...\n    for (int dim=2; dim<8; ++dim)\n    {\n      CALL_SUBTEST_1(run_test<MatrixXd>(dim, num_elements));\n      CALL_SUBTEST_2(run_test<MatrixXf>(dim, num_elements));\n    }\n\n    CALL_SUBTEST_3((run_fixed_size_test<float, 2>(num_elements)));\n    CALL_SUBTEST_4((run_fixed_size_test<float, 3>(num_elements)));\n    CALL_SUBTEST_5((run_fixed_size_test<float, 4>(num_elements)));\n\n    CALL_SUBTEST_6((run_fixed_size_test<double, 2>(num_elements)));\n    CALL_SUBTEST_7((run_fixed_size_test<double, 3>(num_elements)));\n    CALL_SUBTEST_8((run_fixed_size_test<double, 4>(num_elements)));\n  }\n\n  // Those two calls don't compile and result in meaningful error messages!\n  // umeyama(MatrixXcf(),MatrixXcf());\n  // umeyama(MatrixXcd(),MatrixXcd());\n}\n"
  },
  {
    "path": "include/eigen3/test/umfpack_support.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2011 Gael Guennebaud <g.gael@free.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define EIGEN_NO_DEBUG_SMALL_PRODUCT_BLOCKS\n#include \"sparse_solver.h\"\n\n#include <Eigen/UmfPackSupport>\n\ntemplate<typename T> void test_umfpack_support_T()\n{\n  UmfPackLU<SparseMatrix<T, ColMajor> > umfpack_colmajor;\n  UmfPackLU<SparseMatrix<T, RowMajor> > umfpack_rowmajor;\n  \n  check_sparse_square_solving(umfpack_colmajor);\n  check_sparse_square_solving(umfpack_rowmajor);\n  \n  check_sparse_square_determinant(umfpack_colmajor);\n  check_sparse_square_determinant(umfpack_rowmajor);\n}\n\nvoid test_umfpack_support()\n{\n  CALL_SUBTEST_1(test_umfpack_support_T<double>());\n  CALL_SUBTEST_2(test_umfpack_support_T<std::complex<double> >());\n}\n\n"
  },
  {
    "path": "include/eigen3/test/unalignedassert.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#if defined(EIGEN_TEST_PART_1)\n  // default\n#elif defined(EIGEN_TEST_PART_2)\n  #define EIGEN_MAX_STATIC_ALIGN_BYTES 16\n  #define EIGEN_MAX_ALIGN_BYTES 16\n#elif defined(EIGEN_TEST_PART_3)\n  #define EIGEN_MAX_STATIC_ALIGN_BYTES 32\n  #define EIGEN_MAX_ALIGN_BYTES 32\n#elif defined(EIGEN_TEST_PART_4)\n  #define EIGEN_MAX_STATIC_ALIGN_BYTES 64\n  #define EIGEN_MAX_ALIGN_BYTES 64\n#endif\n\n#include \"main.h\"\n\ntypedef Matrix<float,  6,1> Vector6f;\ntypedef Matrix<float,  8,1> Vector8f;\ntypedef Matrix<float, 12,1> Vector12f;\n\ntypedef Matrix<double, 5,1> Vector5d;\ntypedef Matrix<double, 6,1> Vector6d;\ntypedef Matrix<double, 7,1> Vector7d;\ntypedef Matrix<double, 8,1> Vector8d;\ntypedef Matrix<double, 9,1> Vector9d;\ntypedef Matrix<double,10,1> Vector10d;\ntypedef Matrix<double,12,1> Vector12d;\n\nstruct TestNew1\n{\n  MatrixXd m; // good: m will allocate its own array, taking care of alignment.\n  TestNew1() : m(20,20) {}\n};\n\nstruct TestNew2\n{\n  Matrix3d m; // good: m's size isn't a multiple of 16 bytes, so m doesn't have to be 16-byte aligned,\n              // 8-byte alignment is good enough here, which we'll get automatically\n};\n\nstruct TestNew3\n{\n  Vector2f m; // good: m's size isn't a multiple of 16 bytes, so m doesn't have to be 16-byte aligned\n};\n\nstruct TestNew4\n{\n  EIGEN_MAKE_ALIGNED_OPERATOR_NEW\n  Vector2d m;\n  float f; // make the struct have sizeof%16!=0 to make it a little more tricky when we allow an array of 2 such objects\n};\n\nstruct TestNew5\n{\n  EIGEN_MAKE_ALIGNED_OPERATOR_NEW\n  float f; // try the f at first -- the EIGEN_ALIGN_MAX attribute of m should make that still work\n  Matrix4f m;\n};\n\nstruct TestNew6\n{\n  Matrix<float,2,2,DontAlign> m; // good: no alignment requested\n  float f;\n};\n\ntemplate<bool Align> struct Depends\n{\n  EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(Align)\n  Vector2d m;\n  float f;\n};\n\ntemplate<typename T>\nvoid check_unalignedassert_good()\n{\n  T *x, *y;\n  x = new T;\n  delete x;\n  y = new T[2];\n  delete[] y;\n}\n\n#if EIGEN_MAX_STATIC_ALIGN_BYTES>0\ntemplate<typename T>\nvoid construct_at_boundary(int boundary)\n{\n  char buf[sizeof(T)+256];\n  size_t _buf = reinterpret_cast<internal::UIntPtr>(buf);\n  _buf += (EIGEN_MAX_ALIGN_BYTES - (_buf % EIGEN_MAX_ALIGN_BYTES)); // make 16/32/...-byte aligned\n  _buf += boundary; // make exact boundary-aligned\n  T *x = ::new(reinterpret_cast<void*>(_buf)) T;\n  x[0].setZero(); // just in order to silence warnings\n  x->~T();\n}\n#endif\n\nvoid unalignedassert()\n{\n#if EIGEN_MAX_STATIC_ALIGN_BYTES>0\n  construct_at_boundary<Vector2f>(4);\n  construct_at_boundary<Vector3f>(4);\n  construct_at_boundary<Vector4f>(16);\n  construct_at_boundary<Vector6f>(4);\n  construct_at_boundary<Vector8f>(EIGEN_MAX_ALIGN_BYTES);\n  construct_at_boundary<Vector12f>(16);\n  construct_at_boundary<Matrix2f>(16);\n  construct_at_boundary<Matrix3f>(4);\n  construct_at_boundary<Matrix4f>(EIGEN_MAX_ALIGN_BYTES);\n\n  construct_at_boundary<Vector2d>(16);\n  construct_at_boundary<Vector3d>(4);\n  construct_at_boundary<Vector4d>(EIGEN_MAX_ALIGN_BYTES);\n  construct_at_boundary<Vector5d>(4);\n  construct_at_boundary<Vector6d>(16);\n  construct_at_boundary<Vector7d>(4);\n  construct_at_boundary<Vector8d>(EIGEN_MAX_ALIGN_BYTES);\n  construct_at_boundary<Vector9d>(4);\n  construct_at_boundary<Vector10d>(16);\n  construct_at_boundary<Vector12d>(EIGEN_MAX_ALIGN_BYTES);\n  construct_at_boundary<Matrix2d>(EIGEN_MAX_ALIGN_BYTES);\n  construct_at_boundary<Matrix3d>(4);\n  construct_at_boundary<Matrix4d>(EIGEN_MAX_ALIGN_BYTES);\n\n  construct_at_boundary<Vector2cf>(16);\n  construct_at_boundary<Vector3cf>(4);\n  construct_at_boundary<Vector2cd>(EIGEN_MAX_ALIGN_BYTES);\n  construct_at_boundary<Vector3cd>(16);\n#endif\n\n  check_unalignedassert_good<TestNew1>();\n  check_unalignedassert_good<TestNew2>();\n  check_unalignedassert_good<TestNew3>();\n\n  check_unalignedassert_good<TestNew4>();\n  check_unalignedassert_good<TestNew5>();\n  check_unalignedassert_good<TestNew6>();\n  check_unalignedassert_good<Depends<true> >();\n\n#if EIGEN_MAX_STATIC_ALIGN_BYTES>0\n  if(EIGEN_MAX_ALIGN_BYTES>=16)\n  {\n    VERIFY_RAISES_ASSERT(construct_at_boundary<Vector4f>(8));\n    VERIFY_RAISES_ASSERT(construct_at_boundary<Vector8f>(8));\n    VERIFY_RAISES_ASSERT(construct_at_boundary<Vector12f>(8));\n    VERIFY_RAISES_ASSERT(construct_at_boundary<Vector2d>(8));\n    VERIFY_RAISES_ASSERT(construct_at_boundary<Vector4d>(8));\n    VERIFY_RAISES_ASSERT(construct_at_boundary<Vector6d>(8));\n    VERIFY_RAISES_ASSERT(construct_at_boundary<Vector8d>(8));\n    VERIFY_RAISES_ASSERT(construct_at_boundary<Vector10d>(8));\n    VERIFY_RAISES_ASSERT(construct_at_boundary<Vector12d>(8));\n    // Complexes are disabled because the compiler might aggressively vectorize\n    // the initialization of complex coeffs to 0 before we can check for alignedness\n    //VERIFY_RAISES_ASSERT(construct_at_boundary<Vector2cf>(8));\n    VERIFY_RAISES_ASSERT(construct_at_boundary<Vector4i>(8));\n  }\n  for(int b=8; b<EIGEN_MAX_ALIGN_BYTES; b+=8)\n  {\n    if(b<32)  VERIFY_RAISES_ASSERT(construct_at_boundary<Vector8f>(b));\n    if(b<64)  VERIFY_RAISES_ASSERT(construct_at_boundary<Matrix4f>(b));\n    if(b<32)  VERIFY_RAISES_ASSERT(construct_at_boundary<Vector4d>(b));\n    if(b<32)  VERIFY_RAISES_ASSERT(construct_at_boundary<Matrix2d>(b));\n    if(b<128) VERIFY_RAISES_ASSERT(construct_at_boundary<Matrix4d>(b));\n    //if(b<32)  VERIFY_RAISES_ASSERT(construct_at_boundary<Vector2cd>(b));\n  }\n#endif\n}\n\nvoid test_unalignedassert()\n{\n  CALL_SUBTEST(unalignedassert());\n}\n"
  },
  {
    "path": "include/eigen3/test/unalignedcount.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\nstatic int nb_load;\nstatic int nb_loadu;\nstatic int nb_store;\nstatic int nb_storeu;\n\n#define EIGEN_DEBUG_ALIGNED_LOAD    { nb_load++;    }\n#define EIGEN_DEBUG_UNALIGNED_LOAD  { nb_loadu++;   }\n#define EIGEN_DEBUG_ALIGNED_STORE   { nb_store++;   }\n#define EIGEN_DEBUG_UNALIGNED_STORE { nb_storeu++;  }\n\n#define VERIFY_ALIGNED_UNALIGNED_COUNT(XPR,AL,UL,AS,US) {\\\n    nb_load = nb_loadu = nb_store = nb_storeu = 0; \\\n    XPR; \\\n    if(!(nb_load==AL && nb_loadu==UL && nb_store==AS && nb_storeu==US)) \\\n      std::cerr << \" >> \" << nb_load << \", \" << nb_loadu << \", \" << nb_store << \", \" << nb_storeu << \"\\n\"; \\\n    VERIFY( (#XPR) && nb_load==AL && nb_loadu==UL && nb_store==AS && nb_storeu==US ); \\\n  }\n\n\n#include \"main.h\"\n\nvoid test_unalignedcount()\n{\n  #if defined(EIGEN_VECTORIZE_AVX)\n  VectorXf a(40), b(40);\n  VERIFY_ALIGNED_UNALIGNED_COUNT(a += b, 10, 0, 5, 0);\n  VERIFY_ALIGNED_UNALIGNED_COUNT(a.segment(0,40) += b.segment(0,40), 5, 5, 5, 0);\n  VERIFY_ALIGNED_UNALIGNED_COUNT(a.segment(0,40) -= b.segment(0,40), 5, 5, 5, 0);\n  VERIFY_ALIGNED_UNALIGNED_COUNT(a.segment(0,40) *= 3.5, 5, 0, 5, 0);\n  VERIFY_ALIGNED_UNALIGNED_COUNT(a.segment(0,40) /= 3.5, 5, 0, 5, 0);\n  #elif defined(EIGEN_VECTORIZE_SSE)\n  VectorXf a(40), b(40);\n  VERIFY_ALIGNED_UNALIGNED_COUNT(a += b, 20, 0, 10, 0);\n  VERIFY_ALIGNED_UNALIGNED_COUNT(a.segment(0,40) += b.segment(0,40), 10, 10, 10, 0);\n  VERIFY_ALIGNED_UNALIGNED_COUNT(a.segment(0,40) -= b.segment(0,40), 10, 10, 10, 0);\n  VERIFY_ALIGNED_UNALIGNED_COUNT(a.segment(0,40) *= 3.5, 10, 0, 10, 0);\n  VERIFY_ALIGNED_UNALIGNED_COUNT(a.segment(0,40) /= 3.5, 10, 0, 10, 0);\n  #else\n  // The following line is to eliminate \"variable not used\" warnings\n  nb_load = nb_loadu = nb_store = nb_storeu = 0;\n  int a(0), b(0);\n  VERIFY(a==b);\n  #endif\n}\n"
  },
  {
    "path": "include/eigen3/test/upperbidiagonalization.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <Eigen/SVD>\n\ntemplate<typename MatrixType> void upperbidiag(const MatrixType& m)\n{\n  const typename MatrixType::Index rows = m.rows();\n  const typename MatrixType::Index cols = m.cols();\n\n  typedef Matrix<typename MatrixType::RealScalar, MatrixType::RowsAtCompileTime,  MatrixType::ColsAtCompileTime> RealMatrixType;\n  typedef Matrix<typename MatrixType::Scalar, MatrixType::ColsAtCompileTime,  MatrixType::RowsAtCompileTime> TransposeMatrixType;\n\n  MatrixType a = MatrixType::Random(rows,cols);\n  internal::UpperBidiagonalization<MatrixType> ubd(a);\n  RealMatrixType b(rows, cols);\n  b.setZero();\n  b.block(0,0,cols,cols) = ubd.bidiagonal();\n  MatrixType c = ubd.householderU() * b * ubd.householderV().adjoint();\n  VERIFY_IS_APPROX(a,c);\n  TransposeMatrixType d = ubd.householderV() * b.adjoint() * ubd.householderU().adjoint();\n  VERIFY_IS_APPROX(a.adjoint(),d);\n}\n\nvoid test_upperbidiagonalization()\n{\n  for(int i = 0; i < g_repeat; i++) {\n   CALL_SUBTEST_1( upperbidiag(MatrixXf(3,3)) );\n   CALL_SUBTEST_2( upperbidiag(MatrixXd(17,12)) );\n   CALL_SUBTEST_3( upperbidiag(MatrixXcf(20,20)) );\n   CALL_SUBTEST_4( upperbidiag(Matrix<std::complex<double>,Dynamic,Dynamic,RowMajor>(16,15)) );\n   CALL_SUBTEST_5( upperbidiag(Matrix<float,6,4>()) );\n   CALL_SUBTEST_6( upperbidiag(Matrix<float,5,5>()) );\n   CALL_SUBTEST_7( upperbidiag(Matrix<double,4,3>()) );\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/vectorization_logic.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifdef EIGEN_TEST_PART_1\n#define EIGEN_UNALIGNED_VECTORIZE 1\n#endif\n\n#ifdef EIGEN_TEST_PART_2\n#define EIGEN_UNALIGNED_VECTORIZE 0\n#endif\n\n#ifdef EIGEN_DEFAULT_TO_ROW_MAJOR\n#undef EIGEN_DEFAULT_TO_ROW_MAJOR\n#endif\n#define EIGEN_DEBUG_ASSIGN\n#include \"main.h\"\n#include <typeinfo>\n\nusing internal::demangle_flags;\nusing internal::demangle_traversal;\nusing internal::demangle_unrolling;\n\ntemplate<typename Dst, typename Src>\nbool test_assign(const Dst&, const Src&, int traversal, int unrolling)\n{\n  typedef internal::copy_using_evaluator_traits<internal::evaluator<Dst>,internal::evaluator<Src>, internal::assign_op<typename Dst::Scalar,typename Src::Scalar> > traits;\n  bool res = traits::Traversal==traversal;\n  if(unrolling==InnerUnrolling+CompleteUnrolling)\n    res = res && (int(traits::Unrolling)==InnerUnrolling || int(traits::Unrolling)==CompleteUnrolling);\n  else\n    res = res && int(traits::Unrolling)==unrolling;\n  if(!res)\n  {\n    std::cerr << \"Src: \" << demangle_flags(Src::Flags) << std::endl;\n    std::cerr << \"     \" << demangle_flags(internal::evaluator<Src>::Flags) << std::endl;\n    std::cerr << \"Dst: \" << demangle_flags(Dst::Flags) << std::endl;\n    std::cerr << \"     \" << demangle_flags(internal::evaluator<Dst>::Flags) << std::endl;\n    traits::debug();\n    std::cerr << \" Expected Traversal == \" << demangle_traversal(traversal)\n              << \" got \" << demangle_traversal(traits::Traversal) << \"\\n\";\n    std::cerr << \" Expected Unrolling == \" << demangle_unrolling(unrolling)\n              << \" got \" << demangle_unrolling(traits::Unrolling) << \"\\n\";\n  }\n  return res;\n}\n\ntemplate<typename Dst, typename Src>\nbool test_assign(int traversal, int unrolling)\n{\n  typedef internal::copy_using_evaluator_traits<internal::evaluator<Dst>,internal::evaluator<Src>, internal::assign_op<typename Dst::Scalar,typename Src::Scalar> > traits;\n  bool res = traits::Traversal==traversal && traits::Unrolling==unrolling;\n  if(!res)\n  {\n    std::cerr << \"Src: \" << demangle_flags(Src::Flags) << std::endl;\n    std::cerr << \"     \" << demangle_flags(internal::evaluator<Src>::Flags) << std::endl;\n    std::cerr << \"Dst: \" << demangle_flags(Dst::Flags) << std::endl;\n    std::cerr << \"     \" << demangle_flags(internal::evaluator<Dst>::Flags) << std::endl;\n    traits::debug();\n    std::cerr << \" Expected Traversal == \" << demangle_traversal(traversal)\n              << \" got \" << demangle_traversal(traits::Traversal) << \"\\n\";\n    std::cerr << \" Expected Unrolling == \" << demangle_unrolling(unrolling)\n              << \" got \" << demangle_unrolling(traits::Unrolling) << \"\\n\";\n  }\n  return res;\n}\n\ntemplate<typename Xpr>\nbool test_redux(const Xpr&, int traversal, int unrolling)\n{\n  typedef typename Xpr::Scalar Scalar;\n  typedef internal::redux_traits<internal::scalar_sum_op<Scalar,Scalar>,internal::redux_evaluator<Xpr> > traits;\n  \n  bool res = traits::Traversal==traversal && traits::Unrolling==unrolling;\n  if(!res)\n  {\n    std::cerr << demangle_flags(Xpr::Flags) << std::endl;\n    std::cerr << demangle_flags(internal::evaluator<Xpr>::Flags) << std::endl;\n    traits::debug();\n    \n    std::cerr << \" Expected Traversal == \" << demangle_traversal(traversal)\n              << \" got \" << demangle_traversal(traits::Traversal) << \"\\n\";\n    std::cerr << \" Expected Unrolling == \" << demangle_unrolling(unrolling)\n              << \" got \" << demangle_unrolling(traits::Unrolling) << \"\\n\";\n  }\n  return res;\n}\n\ntemplate<typename Scalar, bool Enable = internal::packet_traits<Scalar>::Vectorizable>\nstruct vectorization_logic\n{\n  typedef internal::packet_traits<Scalar> PacketTraits;\n  \n  typedef typename internal::packet_traits<Scalar>::type PacketType;\n  typedef typename internal::unpacket_traits<PacketType>::half HalfPacketType;\n  enum {\n    PacketSize = internal::unpacket_traits<PacketType>::size,\n    HalfPacketSize = internal::unpacket_traits<HalfPacketType>::size\n  };\n  static void run()\n  {\n    \n    typedef Matrix<Scalar,PacketSize,1> Vector1;\n    typedef Matrix<Scalar,Dynamic,1> VectorX;\n    typedef Matrix<Scalar,Dynamic,Dynamic> MatrixXX;\n    typedef Matrix<Scalar,PacketSize,PacketSize> Matrix11;\n    typedef Matrix<Scalar,2*PacketSize,2*PacketSize> Matrix22;\n    typedef Matrix<Scalar,(Matrix11::Flags&RowMajorBit)?16:4*PacketSize,(Matrix11::Flags&RowMajorBit)?4*PacketSize:16> Matrix44;\n    typedef Matrix<Scalar,(Matrix11::Flags&RowMajorBit)?16:4*PacketSize,(Matrix11::Flags&RowMajorBit)?4*PacketSize:16,DontAlign|EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION> Matrix44u;\n    typedef Matrix<Scalar,4*PacketSize,4*PacketSize,ColMajor> Matrix44c;\n    typedef Matrix<Scalar,4*PacketSize,4*PacketSize,RowMajor> Matrix44r;\n\n    typedef Matrix<Scalar,\n        (PacketSize==8 ? 4 : PacketSize==4 ? 2 : PacketSize==2 ? 1 : /*PacketSize==1 ?*/ 1),\n        (PacketSize==8 ? 2 : PacketSize==4 ? 2 : PacketSize==2 ? 2 : /*PacketSize==1 ?*/ 1)\n      > Matrix1;\n\n    typedef Matrix<Scalar,\n        (PacketSize==8 ? 4 : PacketSize==4 ? 2 : PacketSize==2 ? 1 : /*PacketSize==1 ?*/ 1),\n        (PacketSize==8 ? 2 : PacketSize==4 ? 2 : PacketSize==2 ? 2 : /*PacketSize==1 ?*/ 1),\n      DontAlign|((Matrix1::Flags&RowMajorBit)?RowMajor:ColMajor)> Matrix1u;\n\n    // this type is made such that it can only be vectorized when viewed as a linear 1D vector\n    typedef Matrix<Scalar,\n        (PacketSize==8 ? 4 : PacketSize==4 ? 6 : PacketSize==2 ? ((Matrix11::Flags&RowMajorBit)?2:3) : /*PacketSize==1 ?*/ 1),\n        (PacketSize==8 ? 6 : PacketSize==4 ? 2 : PacketSize==2 ? ((Matrix11::Flags&RowMajorBit)?3:2) : /*PacketSize==1 ?*/ 3)\n      > Matrix3;\n    \n    #if !EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT\n    VERIFY(test_assign(Vector1(),Vector1(),\n      InnerVectorizedTraversal,CompleteUnrolling));\n    VERIFY(test_assign(Vector1(),Vector1()+Vector1(),\n      InnerVectorizedTraversal,CompleteUnrolling));\n    VERIFY(test_assign(Vector1(),Vector1().cwiseProduct(Vector1()),\n      InnerVectorizedTraversal,CompleteUnrolling));\n    VERIFY(test_assign(Vector1(),Vector1().template cast<Scalar>(),\n      InnerVectorizedTraversal,CompleteUnrolling));\n\n\n    VERIFY(test_assign(Vector1(),Vector1(),\n      InnerVectorizedTraversal,CompleteUnrolling));\n    VERIFY(test_assign(Vector1(),Vector1()+Vector1(),\n      InnerVectorizedTraversal,CompleteUnrolling));\n    VERIFY(test_assign(Vector1(),Vector1().cwiseProduct(Vector1()),\n      InnerVectorizedTraversal,CompleteUnrolling));\n\n    VERIFY(test_assign(Matrix44(),Matrix44()+Matrix44(),\n      InnerVectorizedTraversal,InnerUnrolling));\n\n    VERIFY(test_assign(Matrix44u(),Matrix44()+Matrix44(),\n      EIGEN_UNALIGNED_VECTORIZE ? InnerVectorizedTraversal : LinearTraversal,\n      EIGEN_UNALIGNED_VECTORIZE ? InnerUnrolling : NoUnrolling));\n\n    VERIFY(test_assign(Matrix1(),Matrix1()+Matrix1(),\n      (Matrix1::InnerSizeAtCompileTime % PacketSize)==0 ? InnerVectorizedTraversal : LinearVectorizedTraversal,\n      CompleteUnrolling));\n\n    VERIFY(test_assign(Matrix1u(),Matrix1()+Matrix1(),\n      EIGEN_UNALIGNED_VECTORIZE ? ((Matrix1::InnerSizeAtCompileTime % PacketSize)==0 ? InnerVectorizedTraversal : LinearVectorizedTraversal)\n                                : LinearTraversal, CompleteUnrolling));\n\n    VERIFY(test_assign(Matrix44c().col(1),Matrix44c().col(2)+Matrix44c().col(3),\n      InnerVectorizedTraversal,CompleteUnrolling));\n\n    VERIFY(test_assign(Matrix44r().row(2),Matrix44r().row(1)+Matrix44r().row(1),\n      InnerVectorizedTraversal,CompleteUnrolling));\n\n    if(PacketSize>1)\n    {\n      typedef Matrix<Scalar,3,3,ColMajor> Matrix33c;\n      typedef Matrix<Scalar,3,1,ColMajor> Vector3;\n      VERIFY(test_assign(Matrix33c().row(2),Matrix33c().row(1)+Matrix33c().row(1),\n        LinearTraversal,CompleteUnrolling));\n      VERIFY(test_assign(Vector3(),Vector3()+Vector3(),\n        EIGEN_UNALIGNED_VECTORIZE ? (HalfPacketSize==1 ? InnerVectorizedTraversal : LinearVectorizedTraversal) : (HalfPacketSize==1 ? InnerVectorizedTraversal : LinearTraversal), CompleteUnrolling));\n      VERIFY(test_assign(Matrix33c().col(0),Matrix33c().col(1)+Matrix33c().col(1),\n        EIGEN_UNALIGNED_VECTORIZE ? (HalfPacketSize==1 ? InnerVectorizedTraversal : LinearVectorizedTraversal) : (HalfPacketSize==1 ? SliceVectorizedTraversal : LinearTraversal),\n        ((!EIGEN_UNALIGNED_VECTORIZE) && HalfPacketSize==1) ? NoUnrolling : CompleteUnrolling));\n\n      VERIFY(test_assign(Matrix3(),Matrix3().cwiseProduct(Matrix3()),\n        LinearVectorizedTraversal,CompleteUnrolling));\n\n      VERIFY(test_assign(Matrix<Scalar,17,17>(),Matrix<Scalar,17,17>()+Matrix<Scalar,17,17>(),\n        HalfPacketSize==1             ? InnerVectorizedTraversal  :\n        EIGEN_UNALIGNED_VECTORIZE ? LinearVectorizedTraversal :\n                                        LinearTraversal,\n        NoUnrolling));\n\n      VERIFY(test_assign(Matrix11(), Matrix11()+Matrix11(),InnerVectorizedTraversal,CompleteUnrolling));\n\n\n      VERIFY(test_assign(Matrix11(),Matrix<Scalar,17,17>().template block<PacketSize,PacketSize>(2,3)+Matrix<Scalar,17,17>().template block<PacketSize,PacketSize>(8,4),\n        (EIGEN_UNALIGNED_VECTORIZE) ? InnerVectorizedTraversal : DefaultTraversal, CompleteUnrolling|InnerUnrolling));\n\n      VERIFY(test_assign(Vector1(),Matrix11()*Vector1(),\n                         InnerVectorizedTraversal,CompleteUnrolling));\n\n      VERIFY(test_assign(Matrix11(),Matrix11().lazyProduct(Matrix11()),\n                         InnerVectorizedTraversal,InnerUnrolling+CompleteUnrolling));\n    }\n\n    VERIFY(test_redux(Vector1(),\n      LinearVectorizedTraversal,CompleteUnrolling));\n\n    VERIFY(test_redux(Vector1().array()*Vector1().array(),\n      LinearVectorizedTraversal,CompleteUnrolling));\n\n    VERIFY(test_redux((Vector1().array()*Vector1().array()).col(0),\n      LinearVectorizedTraversal,CompleteUnrolling));\n\n    VERIFY(test_redux(Matrix<Scalar,PacketSize,3>(),\n      LinearVectorizedTraversal,CompleteUnrolling));\n\n    VERIFY(test_redux(Matrix3(),\n      LinearVectorizedTraversal,CompleteUnrolling));\n\n    VERIFY(test_redux(Matrix44(),\n      LinearVectorizedTraversal,NoUnrolling));\n\n    VERIFY(test_redux(Matrix44().template block<(Matrix1::Flags&RowMajorBit)?4:PacketSize,(Matrix1::Flags&RowMajorBit)?PacketSize:4>(1,2),\n      DefaultTraversal,CompleteUnrolling));\n\n    VERIFY(test_redux(Matrix44c().template block<2*PacketSize,1>(1,2),\n      LinearVectorizedTraversal,CompleteUnrolling));\n\n    VERIFY(test_redux(Matrix44r().template block<1,2*PacketSize>(2,1),\n      LinearVectorizedTraversal,CompleteUnrolling));\n\n    VERIFY((test_assign<\n            Map<Matrix22, AlignedMax, OuterStride<3*PacketSize> >,\n            Matrix22\n            >(InnerVectorizedTraversal,CompleteUnrolling)));\n\n    VERIFY((test_assign<\n            Map<Matrix<Scalar,EIGEN_PLAIN_ENUM_MAX(2,PacketSize),EIGEN_PLAIN_ENUM_MAX(2,PacketSize)>, AlignedMax, InnerStride<3*PacketSize> >,\n            Matrix<Scalar,EIGEN_PLAIN_ENUM_MAX(2,PacketSize),EIGEN_PLAIN_ENUM_MAX(2,PacketSize)>\n            >(DefaultTraversal,PacketSize>=8?InnerUnrolling:CompleteUnrolling)));\n\n    VERIFY((test_assign(Matrix11(), Matrix<Scalar,PacketSize,EIGEN_PLAIN_ENUM_MIN(2,PacketSize)>()*Matrix<Scalar,EIGEN_PLAIN_ENUM_MIN(2,PacketSize),PacketSize>(),\n                        InnerVectorizedTraversal, CompleteUnrolling)));\n    #endif\n\n    VERIFY(test_assign(MatrixXX(10,10),MatrixXX(20,20).block(10,10,2,3),\n      SliceVectorizedTraversal,NoUnrolling));\n\n    VERIFY(test_redux(VectorX(10),\n      LinearVectorizedTraversal,NoUnrolling));\n  }\n};\n\ntemplate<typename Scalar> struct vectorization_logic<Scalar,false>\n{\n  static void run() {}\n};\n\ntemplate<typename Scalar, bool Enable = !internal::is_same<typename internal::unpacket_traits<typename internal::packet_traits<Scalar>::type>::half,\n                                                           typename internal::packet_traits<Scalar>::type>::value >\nstruct vectorization_logic_half\n{\n  typedef internal::packet_traits<Scalar> PacketTraits;\n  typedef typename internal::unpacket_traits<typename internal::packet_traits<Scalar>::type>::half PacketType;\n  enum {\n    PacketSize = internal::unpacket_traits<PacketType>::size\n  };\n  static void run()\n  {\n    \n    typedef Matrix<Scalar,PacketSize,1> Vector1;\n    typedef Matrix<Scalar,PacketSize,PacketSize> Matrix11;\n    typedef Matrix<Scalar,5*PacketSize,7,ColMajor> Matrix57;\n    typedef Matrix<Scalar,3*PacketSize,5,ColMajor> Matrix35;\n    typedef Matrix<Scalar,5*PacketSize,7,DontAlign|ColMajor> Matrix57u;\n//     typedef Matrix<Scalar,(Matrix11::Flags&RowMajorBit)?16:4*PacketSize,(Matrix11::Flags&RowMajorBit)?4*PacketSize:16> Matrix44;\n//     typedef Matrix<Scalar,(Matrix11::Flags&RowMajorBit)?16:4*PacketSize,(Matrix11::Flags&RowMajorBit)?4*PacketSize:16,DontAlign|EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION> Matrix44u;\n//     typedef Matrix<Scalar,4*PacketSize,4*PacketSize,ColMajor> Matrix44c;\n//     typedef Matrix<Scalar,4*PacketSize,4*PacketSize,RowMajor> Matrix44r;\n\n    typedef Matrix<Scalar,\n        (PacketSize==8 ? 4 : PacketSize==4 ? 2 : PacketSize==2 ? 1 : /*PacketSize==1 ?*/ 1),\n        (PacketSize==8 ? 2 : PacketSize==4 ? 2 : PacketSize==2 ? 2 : /*PacketSize==1 ?*/ 1)\n      > Matrix1;\n\n    typedef Matrix<Scalar,\n        (PacketSize==8 ? 4 : PacketSize==4 ? 2 : PacketSize==2 ? 1 : /*PacketSize==1 ?*/ 1),\n        (PacketSize==8 ? 2 : PacketSize==4 ? 2 : PacketSize==2 ? 2 : /*PacketSize==1 ?*/ 1),\n      DontAlign|((Matrix1::Flags&RowMajorBit)?RowMajor:ColMajor)> Matrix1u;\n\n    // this type is made such that it can only be vectorized when viewed as a linear 1D vector\n    typedef Matrix<Scalar,\n        (PacketSize==8 ? 4 : PacketSize==4 ? 6 : PacketSize==2 ? ((Matrix11::Flags&RowMajorBit)?2:3) : /*PacketSize==1 ?*/ 1),\n        (PacketSize==8 ? 6 : PacketSize==4 ? 2 : PacketSize==2 ? ((Matrix11::Flags&RowMajorBit)?3:2) : /*PacketSize==1 ?*/ 3)\n      > Matrix3;\n    \n    #if !EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT\n    VERIFY(test_assign(Vector1(),Vector1(),\n      InnerVectorizedTraversal,CompleteUnrolling));\n    VERIFY(test_assign(Vector1(),Vector1()+Vector1(),\n      InnerVectorizedTraversal,CompleteUnrolling));\n    VERIFY(test_assign(Vector1(),Vector1().template segment<PacketSize>(0).derived(),\n      EIGEN_UNALIGNED_VECTORIZE ? InnerVectorizedTraversal : LinearVectorizedTraversal,CompleteUnrolling));\n    VERIFY(test_assign(Vector1(),Scalar(2.1)*Vector1()-Vector1(),\n      InnerVectorizedTraversal,CompleteUnrolling));\n    VERIFY(test_assign(Vector1(),(Scalar(2.1)*Vector1().template segment<PacketSize>(0)-Vector1().template segment<PacketSize>(0)).derived(),\n      EIGEN_UNALIGNED_VECTORIZE ? InnerVectorizedTraversal : LinearVectorizedTraversal,CompleteUnrolling));\n    VERIFY(test_assign(Vector1(),Vector1().cwiseProduct(Vector1()),\n      InnerVectorizedTraversal,CompleteUnrolling));\n    VERIFY(test_assign(Vector1(),Vector1().template cast<Scalar>(),\n      InnerVectorizedTraversal,CompleteUnrolling));\n\n\n    VERIFY(test_assign(Vector1(),Vector1(),\n      InnerVectorizedTraversal,CompleteUnrolling));\n    VERIFY(test_assign(Vector1(),Vector1()+Vector1(),\n      InnerVectorizedTraversal,CompleteUnrolling));\n    VERIFY(test_assign(Vector1(),Vector1().cwiseProduct(Vector1()),\n      InnerVectorizedTraversal,CompleteUnrolling));\n\n    VERIFY(test_assign(Matrix57(),Matrix57()+Matrix57(),\n      InnerVectorizedTraversal,InnerUnrolling));\n\n    VERIFY(test_assign(Matrix57u(),Matrix57()+Matrix57(),\n      EIGEN_UNALIGNED_VECTORIZE ? InnerVectorizedTraversal : LinearTraversal,\n      EIGEN_UNALIGNED_VECTORIZE ? InnerUnrolling : NoUnrolling));\n\n    VERIFY(test_assign(Matrix1u(),Matrix1()+Matrix1(),\n      EIGEN_UNALIGNED_VECTORIZE ? ((Matrix1::InnerSizeAtCompileTime % PacketSize)==0 ? InnerVectorizedTraversal : LinearVectorizedTraversal) : LinearTraversal,CompleteUnrolling));\n        \n    if(PacketSize>1)\n    {\n      typedef Matrix<Scalar,3,3,ColMajor> Matrix33c;\n      VERIFY(test_assign(Matrix33c().row(2),Matrix33c().row(1)+Matrix33c().row(1),\n        LinearTraversal,CompleteUnrolling));\n      VERIFY(test_assign(Matrix33c().col(0),Matrix33c().col(1)+Matrix33c().col(1),\n        EIGEN_UNALIGNED_VECTORIZE ? (PacketSize==1 ? InnerVectorizedTraversal : LinearVectorizedTraversal) : LinearTraversal,CompleteUnrolling));\n              \n      VERIFY(test_assign(Matrix3(),Matrix3().cwiseQuotient(Matrix3()),\n        PacketTraits::HasDiv ? LinearVectorizedTraversal : LinearTraversal,CompleteUnrolling));\n        \n      VERIFY(test_assign(Matrix<Scalar,17,17>(),Matrix<Scalar,17,17>()+Matrix<Scalar,17,17>(),\n        EIGEN_UNALIGNED_VECTORIZE ? (PacketSize==1 ? InnerVectorizedTraversal : LinearVectorizedTraversal) : LinearTraversal,\n        NoUnrolling));\n        \n      VERIFY(test_assign(Matrix11(),Matrix<Scalar,17,17>().template block<PacketSize,PacketSize>(2,3)+Matrix<Scalar,17,17>().template block<PacketSize,PacketSize>(8,4),\n        EIGEN_UNALIGNED_VECTORIZE ? InnerVectorizedTraversal : DefaultTraversal,PacketSize>4?InnerUnrolling:CompleteUnrolling));\n\n      VERIFY(test_assign(Vector1(),Matrix11()*Vector1(),\n                         InnerVectorizedTraversal,CompleteUnrolling));\n\n      VERIFY(test_assign(Matrix11(),Matrix11().lazyProduct(Matrix11()),\n                         InnerVectorizedTraversal,InnerUnrolling+CompleteUnrolling));\n    }\n    \n    VERIFY(test_redux(Vector1(),\n      LinearVectorizedTraversal,CompleteUnrolling));\n\n    VERIFY(test_redux(Matrix<Scalar,PacketSize,3>(),\n      LinearVectorizedTraversal,CompleteUnrolling));\n\n    VERIFY(test_redux(Matrix3(),\n      LinearVectorizedTraversal,CompleteUnrolling));\n\n    VERIFY(test_redux(Matrix35(),\n      LinearVectorizedTraversal,CompleteUnrolling));\n\n    VERIFY(test_redux(Matrix57().template block<PacketSize,3>(1,0),\n      DefaultTraversal,CompleteUnrolling));\n\n    VERIFY((test_assign<\n            Map<Matrix<Scalar,EIGEN_PLAIN_ENUM_MAX(2,PacketSize),EIGEN_PLAIN_ENUM_MAX(2,PacketSize)>, AlignedMax, InnerStride<3*PacketSize> >,\n            Matrix<Scalar,EIGEN_PLAIN_ENUM_MAX(2,PacketSize),EIGEN_PLAIN_ENUM_MAX(2,PacketSize)>\n            >(DefaultTraversal,CompleteUnrolling)));\n\n    VERIFY((test_assign(Matrix57(), Matrix<Scalar,5*PacketSize,3>()*Matrix<Scalar,3,7>(),\n                        InnerVectorizedTraversal, InnerUnrolling|CompleteUnrolling)));\n    #endif\n  }\n};\n\ntemplate<typename Scalar> struct vectorization_logic_half<Scalar,false>\n{\n  static void run() {}\n};\n\nvoid test_vectorization_logic()\n{\n\n#ifdef EIGEN_VECTORIZE\n\n  CALL_SUBTEST( vectorization_logic<int>::run() );\n  CALL_SUBTEST( vectorization_logic<float>::run() );\n  CALL_SUBTEST( vectorization_logic<double>::run() );\n  CALL_SUBTEST( vectorization_logic<std::complex<float> >::run() );\n  CALL_SUBTEST( vectorization_logic<std::complex<double> >::run() );\n  \n  CALL_SUBTEST( vectorization_logic_half<int>::run() );\n  CALL_SUBTEST( vectorization_logic_half<float>::run() );\n  CALL_SUBTEST( vectorization_logic_half<double>::run() );\n  CALL_SUBTEST( vectorization_logic_half<std::complex<float> >::run() );\n  CALL_SUBTEST( vectorization_logic_half<std::complex<double> >::run() );\n  \n  if(internal::packet_traits<float>::Vectorizable)\n  {\n    VERIFY(test_assign(Matrix<float,3,3>(),Matrix<float,3,3>()+Matrix<float,3,3>(),\n      EIGEN_UNALIGNED_VECTORIZE ? LinearVectorizedTraversal : LinearTraversal,CompleteUnrolling));\n      \n    VERIFY(test_redux(Matrix<float,5,2>(),\n      EIGEN_UNALIGNED_VECTORIZE ? LinearVectorizedTraversal : DefaultTraversal,CompleteUnrolling));\n  }\n  \n  if(internal::packet_traits<double>::Vectorizable)\n  {\n    VERIFY(test_assign(Matrix<double,3,3>(),Matrix<double,3,3>()+Matrix<double,3,3>(),\n      EIGEN_UNALIGNED_VECTORIZE ? LinearVectorizedTraversal : LinearTraversal,CompleteUnrolling));\n    \n    VERIFY(test_redux(Matrix<double,7,3>(),\n      EIGEN_UNALIGNED_VECTORIZE ? LinearVectorizedTraversal : DefaultTraversal,CompleteUnrolling));\n  }\n#endif // EIGEN_VECTORIZE\n\n}\n"
  },
  {
    "path": "include/eigen3/test/vectorwiseop.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2011 Benoit Jacob <jacob.benoit.1@gmail.com>\n// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define TEST_ENABLE_TEMPORARY_TRACKING\n#define EIGEN_NO_STATIC_ASSERT\n\n#include \"main.h\"\n\ntemplate<typename ArrayType> void vectorwiseop_array(const ArrayType& m)\n{\n  typedef typename ArrayType::Index Index;\n  typedef typename ArrayType::Scalar Scalar;\n  typedef Array<Scalar, ArrayType::RowsAtCompileTime, 1> ColVectorType;\n  typedef Array<Scalar, 1, ArrayType::ColsAtCompileTime> RowVectorType;\n\n  Index rows = m.rows();\n  Index cols = m.cols();\n  Index r = internal::random<Index>(0, rows-1),\n        c = internal::random<Index>(0, cols-1);\n\n  ArrayType m1 = ArrayType::Random(rows, cols),\n            m2(rows, cols),\n            m3(rows, cols);\n\n  ColVectorType colvec = ColVectorType::Random(rows);\n  RowVectorType rowvec = RowVectorType::Random(cols);\n\n  // test addition\n\n  m2 = m1;\n  m2.colwise() += colvec;\n  VERIFY_IS_APPROX(m2, m1.colwise() + colvec);\n  VERIFY_IS_APPROX(m2.col(c), m1.col(c) + colvec);\n\n  VERIFY_RAISES_ASSERT(m2.colwise() += colvec.transpose());\n  VERIFY_RAISES_ASSERT(m1.colwise() + colvec.transpose());\n\n  m2 = m1;\n  m2.rowwise() += rowvec;\n  VERIFY_IS_APPROX(m2, m1.rowwise() + rowvec);\n  VERIFY_IS_APPROX(m2.row(r), m1.row(r) + rowvec);\n\n  VERIFY_RAISES_ASSERT(m2.rowwise() += rowvec.transpose());\n  VERIFY_RAISES_ASSERT(m1.rowwise() + rowvec.transpose());\n\n  // test substraction\n\n  m2 = m1;\n  m2.colwise() -= colvec;\n  VERIFY_IS_APPROX(m2, m1.colwise() - colvec);\n  VERIFY_IS_APPROX(m2.col(c), m1.col(c) - colvec);\n\n  VERIFY_RAISES_ASSERT(m2.colwise() -= colvec.transpose());\n  VERIFY_RAISES_ASSERT(m1.colwise() - colvec.transpose());\n\n  m2 = m1;\n  m2.rowwise() -= rowvec;\n  VERIFY_IS_APPROX(m2, m1.rowwise() - rowvec);\n  VERIFY_IS_APPROX(m2.row(r), m1.row(r) - rowvec);\n\n  VERIFY_RAISES_ASSERT(m2.rowwise() -= rowvec.transpose());\n  VERIFY_RAISES_ASSERT(m1.rowwise() - rowvec.transpose());\n\n  // test multiplication\n\n  m2 = m1;\n  m2.colwise() *= colvec;\n  VERIFY_IS_APPROX(m2, m1.colwise() * colvec);\n  VERIFY_IS_APPROX(m2.col(c), m1.col(c) * colvec);\n\n  VERIFY_RAISES_ASSERT(m2.colwise() *= colvec.transpose());\n  VERIFY_RAISES_ASSERT(m1.colwise() * colvec.transpose());\n\n  m2 = m1;\n  m2.rowwise() *= rowvec;\n  VERIFY_IS_APPROX(m2, m1.rowwise() * rowvec);\n  VERIFY_IS_APPROX(m2.row(r), m1.row(r) * rowvec);\n\n  VERIFY_RAISES_ASSERT(m2.rowwise() *= rowvec.transpose());\n  VERIFY_RAISES_ASSERT(m1.rowwise() * rowvec.transpose());\n\n  // test quotient\n\n  m2 = m1;\n  m2.colwise() /= colvec;\n  VERIFY_IS_APPROX(m2, m1.colwise() / colvec);\n  VERIFY_IS_APPROX(m2.col(c), m1.col(c) / colvec);\n\n  VERIFY_RAISES_ASSERT(m2.colwise() /= colvec.transpose());\n  VERIFY_RAISES_ASSERT(m1.colwise() / colvec.transpose());\n\n  m2 = m1;\n  m2.rowwise() /= rowvec;\n  VERIFY_IS_APPROX(m2, m1.rowwise() / rowvec);\n  VERIFY_IS_APPROX(m2.row(r), m1.row(r) / rowvec);\n\n  VERIFY_RAISES_ASSERT(m2.rowwise() /= rowvec.transpose());\n  VERIFY_RAISES_ASSERT(m1.rowwise() / rowvec.transpose());\n\n  m2 = m1;\n  // yes, there might be an aliasing issue there but \".rowwise() /=\"\n  // is supposed to evaluate \" m2.colwise().sum()\" into a temporary to avoid\n  // evaluating the reduction multiple times\n  if(ArrayType::RowsAtCompileTime>2 || ArrayType::RowsAtCompileTime==Dynamic)\n  {\n    m2.rowwise() /= m2.colwise().sum();\n    VERIFY_IS_APPROX(m2, m1.rowwise() / m1.colwise().sum());\n  }\n\n  // all/any\n  Array<bool,Dynamic,Dynamic> mb(rows,cols);\n  mb = (m1.real()<=0.7).colwise().all();\n  VERIFY( (mb.col(c) == (m1.real().col(c)<=0.7).all()).all() );\n  mb = (m1.real()<=0.7).rowwise().all();\n  VERIFY( (mb.row(r) == (m1.real().row(r)<=0.7).all()).all() );\n\n  mb = (m1.real()>=0.7).colwise().any();\n  VERIFY( (mb.col(c) == (m1.real().col(c)>=0.7).any()).all() );\n  mb = (m1.real()>=0.7).rowwise().any();\n  VERIFY( (mb.row(r) == (m1.real().row(r)>=0.7).any()).all() );\n}\n\ntemplate<typename MatrixType> void vectorwiseop_matrix(const MatrixType& m)\n{\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> ColVectorType;\n  typedef Matrix<Scalar, 1, MatrixType::ColsAtCompileTime> RowVectorType;\n  typedef Matrix<RealScalar, MatrixType::RowsAtCompileTime, 1> RealColVectorType;\n  typedef Matrix<RealScalar, 1, MatrixType::ColsAtCompileTime> RealRowVectorType;\n\n  Index rows = m.rows();\n  Index cols = m.cols();\n  Index r = internal::random<Index>(0, rows-1),\n        c = internal::random<Index>(0, cols-1);\n\n  MatrixType m1 = MatrixType::Random(rows, cols),\n            m2(rows, cols),\n            m3(rows, cols);\n\n  ColVectorType colvec = ColVectorType::Random(rows);\n  RowVectorType rowvec = RowVectorType::Random(cols);\n  RealColVectorType rcres;\n  RealRowVectorType rrres;\n\n  // test addition\n\n  m2 = m1;\n  m2.colwise() += colvec;\n  VERIFY_IS_APPROX(m2, m1.colwise() + colvec);\n  VERIFY_IS_APPROX(m2.col(c), m1.col(c) + colvec);\n\n  if(rows>1)\n  {\n    VERIFY_RAISES_ASSERT(m2.colwise() += colvec.transpose());\n    VERIFY_RAISES_ASSERT(m1.colwise() + colvec.transpose());\n  }\n\n  m2 = m1;\n  m2.rowwise() += rowvec;\n  VERIFY_IS_APPROX(m2, m1.rowwise() + rowvec);\n  VERIFY_IS_APPROX(m2.row(r), m1.row(r) + rowvec);\n\n  if(cols>1)\n  {\n    VERIFY_RAISES_ASSERT(m2.rowwise() += rowvec.transpose());\n    VERIFY_RAISES_ASSERT(m1.rowwise() + rowvec.transpose());\n  }\n\n  // test substraction\n\n  m2 = m1;\n  m2.colwise() -= colvec;\n  VERIFY_IS_APPROX(m2, m1.colwise() - colvec);\n  VERIFY_IS_APPROX(m2.col(c), m1.col(c) - colvec);\n\n  if(rows>1)\n  {\n    VERIFY_RAISES_ASSERT(m2.colwise() -= colvec.transpose());\n    VERIFY_RAISES_ASSERT(m1.colwise() - colvec.transpose());\n  }\n\n  m2 = m1;\n  m2.rowwise() -= rowvec;\n  VERIFY_IS_APPROX(m2, m1.rowwise() - rowvec);\n  VERIFY_IS_APPROX(m2.row(r), m1.row(r) - rowvec);\n\n  if(cols>1)\n  {\n    VERIFY_RAISES_ASSERT(m2.rowwise() -= rowvec.transpose());\n    VERIFY_RAISES_ASSERT(m1.rowwise() - rowvec.transpose());\n  }\n\n  // test norm\n  rrres = m1.colwise().norm();\n  VERIFY_IS_APPROX(rrres(c), m1.col(c).norm());\n  rcres = m1.rowwise().norm();\n  VERIFY_IS_APPROX(rcres(r), m1.row(r).norm());\n\n  VERIFY_IS_APPROX(m1.cwiseAbs().colwise().sum(), m1.colwise().template lpNorm<1>());\n  VERIFY_IS_APPROX(m1.cwiseAbs().rowwise().sum(), m1.rowwise().template lpNorm<1>());\n  VERIFY_IS_APPROX(m1.cwiseAbs().colwise().maxCoeff(), m1.colwise().template lpNorm<Infinity>());\n  VERIFY_IS_APPROX(m1.cwiseAbs().rowwise().maxCoeff(), m1.rowwise().template lpNorm<Infinity>());\n\n  // regression for bug 1158\n  VERIFY_IS_APPROX(m1.cwiseAbs().colwise().sum().x(), m1.col(0).cwiseAbs().sum());\n\n  // test normalized\n  m2 = m1.colwise().normalized();\n  VERIFY_IS_APPROX(m2.col(c), m1.col(c).normalized());\n  m2 = m1.rowwise().normalized();\n  VERIFY_IS_APPROX(m2.row(r), m1.row(r).normalized());\n\n  // test normalize\n  m2 = m1;\n  m2.colwise().normalize();\n  VERIFY_IS_APPROX(m2.col(c), m1.col(c).normalized());\n  m2 = m1;\n  m2.rowwise().normalize();\n  VERIFY_IS_APPROX(m2.row(r), m1.row(r).normalized());\n\n  // test with partial reduction of products\n  Matrix<Scalar,MatrixType::RowsAtCompileTime,MatrixType::RowsAtCompileTime> m1m1 = m1 * m1.transpose();\n  VERIFY_IS_APPROX( (m1 * m1.transpose()).colwise().sum(), m1m1.colwise().sum());\n  Matrix<Scalar,1,MatrixType::RowsAtCompileTime> tmp(rows);\n  VERIFY_EVALUATION_COUNT( tmp = (m1 * m1.transpose()).colwise().sum(), 1);\n\n  m2 = m1.rowwise() - (m1.colwise().sum()/RealScalar(m1.rows())).eval();\n  m1 = m1.rowwise() - (m1.colwise().sum()/RealScalar(m1.rows()));\n  VERIFY_IS_APPROX( m1, m2 );\n  VERIFY_EVALUATION_COUNT( m2 = (m1.rowwise() - m1.colwise().sum()/RealScalar(m1.rows())), (MatrixType::RowsAtCompileTime!=1 ? 1 : 0) );\n}\n\nvoid test_vectorwiseop()\n{\n  CALL_SUBTEST_1( vectorwiseop_array(Array22cd()) );\n  CALL_SUBTEST_2( vectorwiseop_array(Array<double, 3, 2>()) );\n  CALL_SUBTEST_3( vectorwiseop_array(ArrayXXf(3, 4)) );\n  CALL_SUBTEST_4( vectorwiseop_matrix(Matrix4cf()) );\n  CALL_SUBTEST_5( vectorwiseop_matrix(Matrix<float,4,5>()) );\n  CALL_SUBTEST_6( vectorwiseop_matrix(MatrixXd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n  CALL_SUBTEST_7( vectorwiseop_matrix(VectorXd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n  CALL_SUBTEST_7( vectorwiseop_matrix(RowVectorXd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );\n}\n"
  },
  {
    "path": "include/eigen3/test/visitor.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\ntemplate<typename MatrixType> void matrixVisitor(const MatrixType& p)\n{\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename MatrixType::Index Index;\n\n  Index rows = p.rows();\n  Index cols = p.cols();\n\n  // construct a random matrix where all coefficients are different\n  MatrixType m;\n  m = MatrixType::Random(rows, cols);\n  for(Index i = 0; i < m.size(); i++)\n    for(Index i2 = 0; i2 < i; i2++)\n      while(m(i) == m(i2)) // yes, ==\n        m(i) = internal::random<Scalar>();\n  \n  Scalar minc = Scalar(1000), maxc = Scalar(-1000);\n  Index minrow=0,mincol=0,maxrow=0,maxcol=0;\n  for(Index j = 0; j < cols; j++)\n  for(Index i = 0; i < rows; i++)\n  {\n    if(m(i,j) < minc)\n    {\n      minc = m(i,j);\n      minrow = i;\n      mincol = j;\n    }\n    if(m(i,j) > maxc)\n    {\n      maxc = m(i,j);\n      maxrow = i;\n      maxcol = j;\n    }\n  }\n  Index eigen_minrow, eigen_mincol, eigen_maxrow, eigen_maxcol;\n  Scalar eigen_minc, eigen_maxc;\n  eigen_minc = m.minCoeff(&eigen_minrow,&eigen_mincol);\n  eigen_maxc = m.maxCoeff(&eigen_maxrow,&eigen_maxcol);\n  VERIFY(minrow == eigen_minrow);\n  VERIFY(maxrow == eigen_maxrow);\n  VERIFY(mincol == eigen_mincol);\n  VERIFY(maxcol == eigen_maxcol);\n  VERIFY_IS_APPROX(minc, eigen_minc);\n  VERIFY_IS_APPROX(maxc, eigen_maxc);\n  VERIFY_IS_APPROX(minc, m.minCoeff());\n  VERIFY_IS_APPROX(maxc, m.maxCoeff());\n\n  eigen_maxc = (m.adjoint()*m).maxCoeff(&eigen_maxrow,&eigen_maxcol);\n  eigen_maxc = (m.adjoint()*m).eval().maxCoeff(&maxrow,&maxcol);\n  VERIFY(maxrow == eigen_maxrow);\n  VERIFY(maxcol == eigen_maxcol);\n}\n\ntemplate<typename VectorType> void vectorVisitor(const VectorType& w)\n{\n  typedef typename VectorType::Scalar Scalar;\n  typedef typename VectorType::Index Index;\n\n  Index size = w.size();\n\n  // construct a random vector where all coefficients are different\n  VectorType v;\n  v = VectorType::Random(size);\n  for(Index i = 0; i < size; i++)\n    for(Index i2 = 0; i2 < i; i2++)\n      while(v(i) == v(i2)) // yes, ==\n        v(i) = internal::random<Scalar>();\n  \n  Scalar minc = v(0), maxc = v(0);\n  Index minidx=0, maxidx=0;\n  for(Index i = 0; i < size; i++)\n  {\n    if(v(i) < minc)\n    {\n      minc = v(i);\n      minidx = i;\n    }\n    if(v(i) > maxc)\n    {\n      maxc = v(i);\n      maxidx = i;\n    }\n  }\n  Index eigen_minidx, eigen_maxidx;\n  Scalar eigen_minc, eigen_maxc;\n  eigen_minc = v.minCoeff(&eigen_minidx);\n  eigen_maxc = v.maxCoeff(&eigen_maxidx);\n  VERIFY(minidx == eigen_minidx);\n  VERIFY(maxidx == eigen_maxidx);\n  VERIFY_IS_APPROX(minc, eigen_minc);\n  VERIFY_IS_APPROX(maxc, eigen_maxc);\n  VERIFY_IS_APPROX(minc, v.minCoeff());\n  VERIFY_IS_APPROX(maxc, v.maxCoeff());\n  \n  Index idx0 = internal::random<Index>(0,size-1);\n  Index idx1 = eigen_minidx;\n  Index idx2 = eigen_maxidx;\n  VectorType v1(v), v2(v);\n  v1(idx0) = v1(idx1);\n  v2(idx0) = v2(idx2);\n  v1.minCoeff(&eigen_minidx);\n  v2.maxCoeff(&eigen_maxidx);\n  VERIFY(eigen_minidx == (std::min)(idx0,idx1));\n  VERIFY(eigen_maxidx == (std::min)(idx0,idx2));\n}\n\nvoid test_visitor()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( matrixVisitor(Matrix<float, 1, 1>()) );\n    CALL_SUBTEST_2( matrixVisitor(Matrix2f()) );\n    CALL_SUBTEST_3( matrixVisitor(Matrix4d()) );\n    CALL_SUBTEST_4( matrixVisitor(MatrixXd(8, 12)) );\n    CALL_SUBTEST_5( matrixVisitor(Matrix<double,Dynamic,Dynamic,RowMajor>(20, 20)) );\n    CALL_SUBTEST_6( matrixVisitor(MatrixXi(8, 12)) );\n  }\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_7( vectorVisitor(Vector4f()) );\n    CALL_SUBTEST_7( vectorVisitor(Matrix<int,12,1>()) );\n    CALL_SUBTEST_8( vectorVisitor(VectorXd(10)) );\n    CALL_SUBTEST_9( vectorVisitor(RowVectorXd(10)) );\n    CALL_SUBTEST_10( vectorVisitor(VectorXf(33)) );\n  }\n}\n"
  },
  {
    "path": "include/eigen3/test/zerosized.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2011 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n\ntemplate<typename MatrixType> void zeroReduction(const MatrixType& m) {\n  // Reductions that must hold for zero sized objects\n  VERIFY(m.all());\n  VERIFY(!m.any());\n  VERIFY(m.prod()==1);\n  VERIFY(m.sum()==0);\n  VERIFY(m.count()==0);\n  VERIFY(m.allFinite());\n  VERIFY(!m.hasNaN());\n}\n\n\ntemplate<typename MatrixType> void zeroSizedMatrix()\n{\n  MatrixType t1;\n  typedef typename MatrixType::Scalar Scalar;\n\n  if (MatrixType::SizeAtCompileTime == Dynamic || MatrixType::SizeAtCompileTime == 0)\n  {\n    zeroReduction(t1);\n    if (MatrixType::RowsAtCompileTime == Dynamic)\n      VERIFY(t1.rows() == 0);\n    if (MatrixType::ColsAtCompileTime == Dynamic)\n      VERIFY(t1.cols() == 0);\n\n    if (MatrixType::RowsAtCompileTime == Dynamic && MatrixType::ColsAtCompileTime == Dynamic)\n    {\n\n      MatrixType t2(0, 0), t3(t1);\n      VERIFY(t2.rows() == 0);\n      VERIFY(t2.cols() == 0);\n\n      zeroReduction(t2);\n      VERIFY(t1==t2);\n    }\n  }\n\n  if(MatrixType::MaxColsAtCompileTime!=0 && MatrixType::MaxRowsAtCompileTime!=0)\n  {\n    Index rows = MatrixType::RowsAtCompileTime==Dynamic ? internal::random<Index>(1,10) : Index(MatrixType::RowsAtCompileTime);\n    Index cols = MatrixType::ColsAtCompileTime==Dynamic ? internal::random<Index>(1,10) : Index(MatrixType::ColsAtCompileTime);\n    MatrixType m(rows,cols);\n    zeroReduction(m.template block<0,MatrixType::ColsAtCompileTime>(0,0,0,cols));\n    zeroReduction(m.template block<MatrixType::RowsAtCompileTime,0>(0,0,rows,0));\n    zeroReduction(m.template block<0,1>(0,0));\n    zeroReduction(m.template block<1,0>(0,0));\n    Matrix<Scalar,Dynamic,Dynamic> prod = m.template block<MatrixType::RowsAtCompileTime,0>(0,0,rows,0) * m.template block<0,MatrixType::ColsAtCompileTime>(0,0,0,cols);\n    VERIFY(prod.rows()==rows && prod.cols()==cols);\n    VERIFY(prod.isZero());\n    prod = m.template block<1,0>(0,0) * m.template block<0,1>(0,0);\n    VERIFY(prod.size()==1);\n    VERIFY(prod.isZero());\n  }\n}\n\ntemplate<typename VectorType> void zeroSizedVector()\n{\n  VectorType t1;\n\n  if (VectorType::SizeAtCompileTime == Dynamic || VectorType::SizeAtCompileTime==0)\n  {\n    zeroReduction(t1);\n    VERIFY(t1.size() == 0);\n    VectorType t2(DenseIndex(0)); // DenseIndex disambiguates with 0-the-null-pointer (error with gcc 4.4 and MSVC8)\n    VERIFY(t2.size() == 0);\n    zeroReduction(t2);\n\n    VERIFY(t1==t2);\n  }\n}\n\nvoid test_zerosized()\n{\n  zeroSizedMatrix<Matrix2d>();\n  zeroSizedMatrix<Matrix3i>();\n  zeroSizedMatrix<Matrix<float, 2, Dynamic> >();\n  zeroSizedMatrix<MatrixXf>();\n  zeroSizedMatrix<Matrix<float, 0, 0> >();\n  zeroSizedMatrix<Matrix<float, Dynamic, 0, 0, 0, 0> >();\n  zeroSizedMatrix<Matrix<float, 0, Dynamic, 0, 0, 0> >();\n  zeroSizedMatrix<Matrix<float, Dynamic, Dynamic, 0, 0, 0> >();\n  zeroSizedMatrix<Matrix<float, 0, 4> >();\n  zeroSizedMatrix<Matrix<float, 4, 0> >();\n\n  zeroSizedVector<Vector2d>();\n  zeroSizedVector<Vector3i>();\n  zeroSizedVector<VectorXf>();\n  zeroSizedVector<Matrix<float, 0, 1> >();\n  zeroSizedVector<Matrix<float, 1, 0> >();\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/CMakeLists.txt",
    "content": "add_subdirectory(Eigen)\nadd_subdirectory(doc EXCLUDE_FROM_ALL)\nif(BUILD_TESTING)\n  if(EIGEN_LEAVE_TEST_IN_ALL_TARGET)\n    add_subdirectory(test) # can't do EXCLUDE_FROM_ALL here, breaks CTest\n  else()\n    add_subdirectory(test EXCLUDE_FROM_ALL)\n  endif()\nendif()\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/AdolcForward",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <g.gael@free.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_ADLOC_FORWARD\n#define EIGEN_ADLOC_FORWARD\n\n//--------------------------------------------------------------------------------\n//\n// This file provides support for adolc's adouble type in forward mode.\n// ADOL-C is a C++ automatic differentiation library,\n// see https://projects.coin-or.org/ADOL-C for more information.\n//\n// Note that the maximal number of directions is controlled by\n// the preprocessor token NUMBER_DIRECTIONS. The default is 2.\n//\n//--------------------------------------------------------------------------------\n\n#define ADOLC_TAPELESS\n#ifndef NUMBER_DIRECTIONS\n# define NUMBER_DIRECTIONS 2\n#endif\n#include <adolc/adtl.h>\n\n// adolc defines some very stupid macros:\n#if defined(malloc)\n# undef malloc\n#endif\n\n#if defined(calloc)\n# undef calloc\n#endif\n\n#if defined(realloc)\n# undef realloc\n#endif\n\n#include <Eigen/Core>\n\nnamespace Eigen {\n\n/**\n  * \\defgroup AdolcForward_Module Adolc forward module\n  * This module provides support for adolc's adouble type in forward mode.\n  * ADOL-C is a C++ automatic differentiation library,\n  * see https://projects.coin-or.org/ADOL-C for more information.\n  * It mainly consists in:\n  *  - a struct Eigen::NumTraits<adtl::adouble> specialization\n  *  - overloads of internal::* math function for adtl::adouble type.\n  *\n  * Note that the maximal number of directions is controlled by\n  * the preprocessor token NUMBER_DIRECTIONS. The default is 2.\n  *\n  * \\code\n  * #include <unsupported/Eigen/AdolcSupport>\n  * \\endcode\n  */\n  //@{\n\n} // namespace Eigen\n\n// Eigen's require a few additional functions which must be defined in the same namespace\n// than the custom scalar type own namespace\nnamespace adtl {\n\ninline const adouble& conj(const adouble& x)  { return x; }\ninline const adouble& real(const adouble& x)  { return x; }\ninline adouble imag(const adouble&)    { return 0.; }\ninline adouble abs(const adouble&  x)  { return fabs(x); }\ninline adouble abs2(const adouble& x)  { return x*x; }\n\n}\n\nnamespace Eigen {\n\ntemplate<> struct NumTraits<adtl::adouble>\n    : NumTraits<double>\n{\n  typedef adtl::adouble Real;\n  typedef adtl::adouble NonInteger;\n  typedef adtl::adouble Nested;\n  enum {\n    IsComplex = 0,\n    IsInteger = 0,\n    IsSigned = 1,\n    RequireInitialization = 1,\n    ReadCost = 1,\n    AddCost = 1,\n    MulCost = 1\n  };\n};\n\ntemplate<typename Functor> class AdolcForwardJacobian : public Functor\n{\n  typedef adtl::adouble ActiveScalar;\npublic:\n\n  AdolcForwardJacobian() : Functor() {}\n  AdolcForwardJacobian(const Functor& f) : Functor(f) {}\n\n  // forward constructors\n  template<typename T0>\n  AdolcForwardJacobian(const T0& a0) : Functor(a0) {}\n  template<typename T0, typename T1>\n  AdolcForwardJacobian(const T0& a0, const T1& a1) : Functor(a0, a1) {}\n  template<typename T0, typename T1, typename T2>\n  AdolcForwardJacobian(const T0& a0, const T1& a1, const T1& a2) : Functor(a0, a1, a2) {}\n\n  typedef typename Functor::InputType InputType;\n  typedef typename Functor::ValueType ValueType;\n  typedef typename Functor::JacobianType JacobianType;\n\n  typedef Matrix<ActiveScalar, InputType::SizeAtCompileTime, 1> ActiveInput;\n  typedef Matrix<ActiveScalar, ValueType::SizeAtCompileTime, 1> ActiveValue;\n\n  void operator() (const InputType& x, ValueType* v, JacobianType* _jac) const\n  {\n    eigen_assert(v!=0);\n    if (!_jac)\n    {\n      Functor::operator()(x, v);\n      return;\n    }\n\n    JacobianType& jac = *_jac;\n\n    ActiveInput ax = x.template cast<ActiveScalar>();\n    ActiveValue av(jac.rows());\n\n    for (int j=0; j<jac.cols(); j++)\n      for (int i=0; i<jac.cols(); i++)\n        ax[i].setADValue(j, i==j ? 1 : 0);\n\n    Functor::operator()(ax, &av);\n\n    for (int i=0; i<jac.rows(); i++)\n    {\n      (*v)[i] = av[i].getValue();\n      for (int j=0; j<jac.cols(); j++)\n        jac.coeffRef(i,j) = av[i].getADValue(j);\n    }\n  }\nprotected:\n\n};\n\n//@}\n\n}\n\n#endif // EIGEN_ADLOC_FORWARD\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/AlignedVector3",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Gael Guennebaud <g.gael@free.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_ALIGNED_VECTOR3\n#define EIGEN_ALIGNED_VECTOR3\n\n#include <Eigen/Geometry>\n\nnamespace Eigen {\n\n/**\n  * \\defgroup AlignedVector3_Module Aligned vector3 module\n  *\n  * \\code\n  * #include <unsupported/Eigen/AlignedVector3>\n  * \\endcode\n  */\n  //@{\n\n\n/** \\class AlignedVector3\n  *\n  * \\brief A vectorization friendly 3D vector\n  *\n  * This class represents a 3D vector internally using a 4D vector\n  * such that vectorization can be seamlessly enabled. Of course,\n  * the same result can be achieved by directly using a 4D vector.\n  * This class makes this process simpler.\n  *\n  */\n// TODO specialize Cwise\ntemplate<typename _Scalar> class AlignedVector3;\n\nnamespace internal {\ntemplate<typename _Scalar> struct traits<AlignedVector3<_Scalar> >\n  : traits<Matrix<_Scalar,3,1,0,4,1> >\n{\n};\n}\n\ntemplate<typename _Scalar> class AlignedVector3\n  : public MatrixBase<AlignedVector3<_Scalar> >\n{\n    typedef Matrix<_Scalar,4,1> CoeffType;\n    CoeffType m_coeffs;\n  public:\n\n    typedef MatrixBase<AlignedVector3<_Scalar> > Base;\t\n    EIGEN_DENSE_PUBLIC_INTERFACE(AlignedVector3)\n    using Base::operator*;\n\n    inline Index rows() const { return 3; }\n    inline Index cols() const { return 1; }\n    \n    Scalar* data() { return m_coeffs.data(); }\n    const Scalar* data() const { return m_coeffs.data(); }\n    Index innerStride() const { return 1; }\n    Index outerStride() const { return 3; }\n\n    inline const Scalar& coeff(Index row, Index col) const\n    { return m_coeffs.coeff(row, col); }\n\n    inline Scalar& coeffRef(Index row, Index col)\n    { return m_coeffs.coeffRef(row, col); }\n\n    inline const Scalar& coeff(Index index) const\n    { return m_coeffs.coeff(index); }\n\n    inline Scalar& coeffRef(Index index)\n    { return m_coeffs.coeffRef(index);}\n\n\n    inline AlignedVector3(const Scalar& x, const Scalar& y, const Scalar& z)\n      : m_coeffs(x, y, z, Scalar(0))\n    {}\n\n    inline AlignedVector3(const AlignedVector3& other)\n      : Base(), m_coeffs(other.m_coeffs)\n    {}\n\n    template<typename XprType, int Size=XprType::SizeAtCompileTime>\n    struct generic_assign_selector {};\n\n    template<typename XprType> struct generic_assign_selector<XprType,4>\n    {\n      inline static void run(AlignedVector3& dest, const XprType& src)\n      {\n        dest.m_coeffs = src;\n      }\n    };\n\n    template<typename XprType> struct generic_assign_selector<XprType,3>\n    {\n      inline static void run(AlignedVector3& dest, const XprType& src)\n      {\n        dest.m_coeffs.template head<3>() = src;\n        dest.m_coeffs.w() = Scalar(0);\n      }\n    };\n\n    template<typename Derived>\n    inline AlignedVector3(const MatrixBase<Derived>& other)\n    {\n      generic_assign_selector<Derived>::run(*this,other.derived());\n    }\n\n    inline AlignedVector3& operator=(const AlignedVector3& other)\n    { m_coeffs = other.m_coeffs; return *this; }\n\n    template <typename Derived>\n    inline AlignedVector3& operator=(const MatrixBase<Derived>& other)\n    {\n      generic_assign_selector<Derived>::run(*this,other.derived());\n      return *this;\n    }\n\n    inline AlignedVector3 operator+(const AlignedVector3& other) const\n    { return AlignedVector3(m_coeffs + other.m_coeffs); }\n\n    inline AlignedVector3& operator+=(const AlignedVector3& other)\n    { m_coeffs += other.m_coeffs; return *this; }\n\n    inline AlignedVector3 operator-(const AlignedVector3& other) const\n    { return AlignedVector3(m_coeffs - other.m_coeffs); }\n\n    inline AlignedVector3 operator-=(const AlignedVector3& other)\n    { m_coeffs -= other.m_coeffs; return *this; }\n\n    inline AlignedVector3 operator*(const Scalar& s) const\n    { return AlignedVector3(m_coeffs * s); }\n\n    inline friend AlignedVector3 operator*(const Scalar& s,const AlignedVector3& vec)\n    { return AlignedVector3(s * vec.m_coeffs); }\n\n    inline AlignedVector3& operator*=(const Scalar& s)\n    { m_coeffs *= s; return *this; }\n\n    inline AlignedVector3 operator/(const Scalar& s) const\n    { return AlignedVector3(m_coeffs / s); }\n\n    inline AlignedVector3& operator/=(const Scalar& s)\n    { m_coeffs /= s; return *this; }\n\n    inline Scalar dot(const AlignedVector3& other) const\n    {\n      eigen_assert(m_coeffs.w()==Scalar(0));\n      eigen_assert(other.m_coeffs.w()==Scalar(0));\n      return m_coeffs.dot(other.m_coeffs);\n    }\n\n    inline void normalize()\n    {\n      m_coeffs /= norm();\n    }\n\n    inline AlignedVector3 normalized() const\n    {\n      return AlignedVector3(m_coeffs / norm());\n    }\n\n    inline Scalar sum() const\n    {\n      eigen_assert(m_coeffs.w()==Scalar(0));\n      return m_coeffs.sum();\n    }\n\n    inline Scalar squaredNorm() const\n    {\n      eigen_assert(m_coeffs.w()==Scalar(0));\n      return m_coeffs.squaredNorm();\n    }\n\n    inline Scalar norm() const\n    {\n      using std::sqrt;\n      return sqrt(squaredNorm());\n    }\n\n    inline AlignedVector3 cross(const AlignedVector3& other) const\n    {\n      return AlignedVector3(m_coeffs.cross3(other.m_coeffs));\n    }\n\n    template<typename Derived>\n    inline bool isApprox(const MatrixBase<Derived>& other, const RealScalar& eps=NumTraits<Scalar>::dummy_precision()) const\n    {\n      return m_coeffs.template head<3>().isApprox(other,eps);\n    }\n    \n    CoeffType& coeffs() { return m_coeffs; }\n    const CoeffType& coeffs() const { return m_coeffs; }\n};\n\nnamespace internal {\n\ntemplate<typename _Scalar>\nstruct eval<AlignedVector3<_Scalar>, Dense>\n{\n typedef const AlignedVector3<_Scalar>& type;\n};\n\ntemplate<typename Scalar>\nstruct evaluator<AlignedVector3<Scalar> >\n  : evaluator<Matrix<Scalar,4,1> >\n{\n  typedef AlignedVector3<Scalar> XprType;\n  typedef evaluator<Matrix<Scalar,4,1> > Base;\n  \n  evaluator(const XprType &m) : Base(m.coeffs()) {}  \n};\n\n}\n\n//@}\n\n}\n\n#endif // EIGEN_ALIGNED_VECTOR3\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/ArpackSupport",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_ARPACKSUPPORT_MODULE_H\n#define EIGEN_ARPACKSUPPORT_MODULE_H\n\n#include <Eigen/Core>\n\n#include <Eigen/src/Core/util/DisableStupidWarnings.h>\n\n/** \\defgroup ArpackSupport_Module Arpack support module\n  *\n  * This module provides a wrapper to Arpack, a library for sparse eigenvalue decomposition.\n  *\n  * \\code\n  * #include <Eigen/ArpackSupport>\n  * \\endcode\n  */\n\n#include <Eigen/SparseCholesky>\n#include \"src/Eigenvalues/ArpackSelfAdjointEigenSolver.h\"\n\n#include <Eigen/src/Core/util/ReenableStupidWarnings.h>\n\n#endif // EIGEN_ARPACKSUPPORT_MODULE_H\n/* vim: set filetype=cpp et sw=2 ts=2 ai: */\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/AutoDiff",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <g.gael@free.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_AUTODIFF_MODULE\n#define EIGEN_AUTODIFF_MODULE\n\nnamespace Eigen {\n\n/**\n  * \\defgroup AutoDiff_Module Auto Diff module\n  *\n  * This module features forward automatic differentation via a simple\n  * templated scalar type wrapper AutoDiffScalar.\n  *\n  * Warning : this should NOT be confused with numerical differentiation, which\n  * is a different method and has its own module in Eigen : \\ref NumericalDiff_Module.\n  *\n  * \\code\n  * #include <unsupported/Eigen/AutoDiff>\n  * \\endcode\n  */\n//@{\n\n}\n\n#include \"src/AutoDiff/AutoDiffScalar.h\"\n// #include \"src/AutoDiff/AutoDiffVector.h\"\n#include \"src/AutoDiff/AutoDiffJacobian.h\"\n\nnamespace Eigen {\n//@}\n}\n\n#endif // EIGEN_AUTODIFF_MODULE\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/BVH",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Ilya Baran <ibaran@mit.edu>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_BVH_MODULE_H\n#define EIGEN_BVH_MODULE_H\n\n#include <Eigen/Core>\n#include <Eigen/Geometry>\n#include <Eigen/StdVector>\n#include <algorithm>\n#include <queue>\n\nnamespace Eigen {\n\n/**\n  * \\defgroup BVH_Module BVH module\n  * \\brief This module provides generic bounding volume hierarchy algorithms\n  * and reference tree implementations.\n  *\n  *\n  * \\code\n  * #include <unsupported/Eigen/BVH>\n  * \\endcode\n  *\n  * A bounding volume hierarchy (BVH) can accelerate many geometric queries.  This module provides a generic implementation\n  * of the two basic algorithms over a BVH: intersection of a query object against all objects in the hierarchy and minimization\n  * of a function over the objects in the hierarchy.  It also provides intersection and minimization over a cartesian product of\n  * two BVH's.  A BVH accelerates intersection by using the fact that if a query object does not intersect a volume, then it cannot\n  * intersect any object contained in that volume.  Similarly, a BVH accelerates minimization because the minimum of a function\n  * over a volume is no greater than the minimum of a function over any object contained in it.\n  *\n  * Some sample queries that can be written in terms of intersection are:\n  *   - Determine all points where a ray intersects a triangle mesh\n  *   - Given a set of points, determine which are contained in a query sphere\n  *   - Given a set of spheres, determine which contain the query point\n  *   - Given a set of disks, determine if any is completely contained in a query rectangle (represent each 2D disk as a point \\f$(x,y,r)\\f$\n  *     in 3D and represent the rectangle as a pyramid based on the original rectangle and shrinking in the \\f$r\\f$ direction)\n  *   - Given a set of points, count how many pairs are \\f$d\\pm\\epsilon\\f$ apart (done by looking at the cartesian product of the set\n  *     of points with itself)\n  *\n  * Some sample queries that can be written in terms of function minimization over a set of objects are:\n  *   - Find the intersection between a ray and a triangle mesh closest to the ray origin (function is infinite off the ray)\n  *   - Given a polyline and a query point, determine the closest point on the polyline to the query\n  *   - Find the diameter of a point cloud (done by looking at the cartesian product and using negative distance as the function)\n  *   - Determine how far two meshes are from colliding (this is also a cartesian product query)\n  *\n  * This implementation decouples the basic algorithms both from the type of hierarchy (and the types of the bounding volumes) and\n  * from the particulars of the query.  To enable abstraction from the BVH, the BVH is required to implement a generic mechanism\n  * for traversal.  To abstract from the query, the query is responsible for keeping track of results.\n  *\n  * To be used in the algorithms, a hierarchy must implement the following traversal mechanism (see KdBVH for a sample implementation): \\code\n      typedef Volume  //the type of bounding volume\n      typedef Object  //the type of object in the hierarchy\n      typedef Index   //a reference to a node in the hierarchy--typically an int or a pointer\n      typedef VolumeIterator //an iterator type over node children--returns Index\n      typedef ObjectIterator //an iterator over object (leaf) children--returns const Object &\n      Index getRootIndex() const //returns the index of the hierarchy root\n      const Volume &getVolume(Index index) const //returns the bounding volume of the node at given index\n      void getChildren(Index index, VolumeIterator &outVBegin, VolumeIterator &outVEnd,\n                      ObjectIterator &outOBegin, ObjectIterator &outOEnd) const\n      //getChildren takes a node index and makes [outVBegin, outVEnd) range over its node children\n      //and [outOBegin, outOEnd) range over its object children\n    \\endcode\n  *\n  * To use the hierarchy, call BVIntersect or BVMinimize, passing it a BVH (or two, for cartesian product) and a minimizer or intersector.\n  * For an intersection query on a single BVH, the intersector encapsulates the query and must provide two functions:\n  * \\code\n      bool intersectVolume(const Volume &volume) //returns true if the query intersects the volume\n      bool intersectObject(const Object &object) //returns true if the intersection search should terminate immediately\n    \\endcode\n  * The guarantee that BVIntersect provides is that intersectObject will be called on every object whose bounding volume\n  * intersects the query (but possibly on other objects too) unless the search is terminated prematurely.  It is the\n  * responsibility of the intersectObject function to keep track of the results in whatever manner is appropriate.\n  * The cartesian product intersection and the BVMinimize queries are similar--see their individual documentation.\n  *\n  * The following is a simple but complete example for how to use the BVH to accelerate the search for a closest red-blue point pair:\n  * \\include BVH_Example.cpp\n  * Output: \\verbinclude BVH_Example.out\n  */\n}\n\n//@{\n\n#include \"src/BVH/BVAlgorithms.h\"\n#include \"src/BVH/KdBVH.h\"\n\n//@}\n\n#endif // EIGEN_BVH_MODULE_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CMakeLists.txt",
    "content": "set(Eigen_HEADERS \n  AdolcForward\n  AlignedVector3\n  ArpackSupport\n  AutoDiff\n  BVH\n  EulerAngles\n  FFT\n  IterativeSolvers \n  KroneckerProduct\n  LevenbergMarquardt\n  MatrixFunctions \n  MoreVectorization\n  MPRealSupport\n  NonLinearOptimization\n  NumericalDiff\n  OpenGLSupport\n  Polynomials\n  Skyline \n  SparseExtra\n  SpecialFunctions\n  Splines\n  )\n\ninstall(FILES\n  ${Eigen_HEADERS}\n  DESTINATION ${INCLUDE_INSTALL_DIR}/unsupported/Eigen COMPONENT Devel\n  )\n\ninstall(DIRECTORY src DESTINATION ${INCLUDE_INSTALL_DIR}/unsupported/Eigen COMPONENT Devel FILES_MATCHING PATTERN \"*.h\")\n\nadd_subdirectory(CXX11)\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/CMakeLists.txt",
    "content": "set(Eigen_CXX11_HEADERS Tensor TensorSymmetry ThreadPool)\n\ninstall(FILES\n  ${Eigen_CXX11_HEADERS}\n  DESTINATION ${INCLUDE_INSTALL_DIR}/unsupported/Eigen/CXX11 COMPONENT Devel\n  )\n\ninstall(DIRECTORY src DESTINATION ${INCLUDE_INSTALL_DIR}/unsupported/Eigen/CXX11 COMPONENT Devel FILES_MATCHING PATTERN \"*.h\")\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/Tensor",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n// Copyright (C) 2013 Christian Seiler <christian@iwakd.de>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n//#ifndef EIGEN_CXX11_TENSOR_MODULE\n//#define EIGEN_CXX11_TENSOR_MODULE\n\n#include \"../../../Eigen/Core\"\n\n#ifdef EIGEN_USE_SYCL\n#undef min\n#undef max\n#undef isnan\n#undef isinf\n#undef isfinite\n#include <SYCL/sycl.hpp>\n#include <map>\n#include <memory>\n#include <utility>\n#endif\n\n#include <Eigen/src/Core/util/DisableStupidWarnings.h>\n\n#include \"../SpecialFunctions\"\n#include \"src/util/CXX11Meta.h\"\n#include \"src/util/MaxSizeVector.h\"\n\n/** \\defgroup CXX11_Tensor_Module Tensor Module\n  *\n  * This module provides a Tensor class for storing arbitrarily indexed\n  * objects.\n  *\n  * \\code\n  * #include <Eigen/CXX11/Tensor>\n  * \\endcode\n  */\n\n#include <cmath>\n#include <cstddef>\n#include <cstring>\n\n#ifdef _WIN32\ntypedef __int16 int16_t;\ntypedef unsigned __int16 uint16_t;\ntypedef __int32 int32_t;\ntypedef unsigned __int32 uint32_t;\ntypedef __int64 int64_t;\ntypedef unsigned __int64 uint64_t;\n#else\n#include <stdint.h>\n#endif\n\n#if __cplusplus > 199711 || EIGEN_COMP_MSVC >= 1900\n#include <random>\n#endif\n\n#ifdef _WIN32\n#include <windows.h>\n#elif defined(__APPLE__)\n#include <mach/mach_time.h>\n#else\n#include <time.h>\n#endif\n\n#ifdef EIGEN_USE_THREADS\n#include \"ThreadPool\"\n#endif\n\n#ifdef EIGEN_USE_GPU\n#include <iostream>\n#include <cuda_runtime.h>\n#if __cplusplus >= 201103L\n#include <atomic>\n#include <unistd.h>\n#endif\n#endif\n\n#include \"src/Tensor/TensorMacros.h\"\n#include \"src/Tensor/TensorForwardDeclarations.h\"\n#include \"src/Tensor/TensorMeta.h\"\n#include \"src/Tensor/TensorFunctors.h\"\n#include \"src/Tensor/TensorCostModel.h\"\n#include \"src/Tensor/TensorDeviceDefault.h\"\n#include \"src/Tensor/TensorDeviceThreadPool.h\"\n#include \"src/Tensor/TensorDeviceCuda.h\"\n#include \"src/Tensor/TensorDeviceSycl.h\"\n#include \"src/Tensor/TensorIndexList.h\"\n#include \"src/Tensor/TensorDimensionList.h\"\n#include \"src/Tensor/TensorDimensions.h\"\n#include \"src/Tensor/TensorInitializer.h\"\n#include \"src/Tensor/TensorTraits.h\"\n#include \"src/Tensor/TensorRandom.h\"\n#include \"src/Tensor/TensorUInt128.h\"\n#include \"src/Tensor/TensorIntDiv.h\"\n#include \"src/Tensor/TensorGlobalFunctions.h\"\n\n#include \"src/Tensor/TensorBase.h\"\n\n#include \"src/Tensor/TensorEvaluator.h\"\n#include \"src/Tensor/TensorExpr.h\"\n#include \"src/Tensor/TensorReduction.h\"\n#include \"src/Tensor/TensorReductionCuda.h\"\n#include \"src/Tensor/TensorArgMax.h\"\n#include \"src/Tensor/TensorConcatenation.h\"\n#include \"src/Tensor/TensorContractionMapper.h\"\n#include \"src/Tensor/TensorContractionBlocking.h\"\n#include \"src/Tensor/TensorContraction.h\"\n#include \"src/Tensor/TensorContractionThreadPool.h\"\n#include \"src/Tensor/TensorContractionCuda.h\"\n#include \"src/Tensor/TensorConversion.h\"\n#include \"src/Tensor/TensorConvolution.h\"\n#include \"src/Tensor/TensorFFT.h\"\n#include \"src/Tensor/TensorPatch.h\"\n#include \"src/Tensor/TensorImagePatch.h\"\n#include \"src/Tensor/TensorVolumePatch.h\"\n#include \"src/Tensor/TensorBroadcasting.h\"\n#include \"src/Tensor/TensorChipping.h\"\n#include \"src/Tensor/TensorInflation.h\"\n#include \"src/Tensor/TensorLayoutSwap.h\"\n#include \"src/Tensor/TensorMorphing.h\"\n#include \"src/Tensor/TensorPadding.h\"\n#include \"src/Tensor/TensorReverse.h\"\n#include \"src/Tensor/TensorShuffling.h\"\n#include \"src/Tensor/TensorStriding.h\"\n#include \"src/Tensor/TensorCustomOp.h\"\n#include \"src/Tensor/TensorEvalTo.h\"\n#include \"src/Tensor/TensorForcedEval.h\"\n#include \"src/Tensor/TensorGenerator.h\"\n#include \"src/Tensor/TensorAssign.h\"\n#include \"src/Tensor/TensorScan.h\"\n\n#include \"src/Tensor/TensorSycl.h\"\n#include \"src/Tensor/TensorExecutor.h\"\n#include \"src/Tensor/TensorDevice.h\"\n\n#include \"src/Tensor/TensorStorage.h\"\n#include \"src/Tensor/Tensor.h\"\n#include \"src/Tensor/TensorFixedSize.h\"\n#include \"src/Tensor/TensorMap.h\"\n#include \"src/Tensor/TensorRef.h\"\n\n#include \"src/Tensor/TensorIO.h\"\n\n#include <Eigen/src/Core/util/ReenableStupidWarnings.h>\n\n//#endif // EIGEN_CXX11_TENSOR_MODULE\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/TensorSymmetry",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2013 Christian Seiler <christian@iwakd.de>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSORSYMMETRY_MODULE\n#define EIGEN_CXX11_TENSORSYMMETRY_MODULE\n\n#include <unsupported/Eigen/CXX11/Tensor>\n\n#include <Eigen/src/Core/util/DisableStupidWarnings.h>\n\n#include \"src/util/CXX11Meta.h\"\n\n/** \\defgroup CXX11_TensorSymmetry_Module Tensor Symmetry Module\n  *\n  * This module provides a classes that allow for the definition of\n  * symmetries w.r.t. tensor indices.\n  *\n  * Including this module will implicitly include the Tensor module.\n  *\n  * \\code\n  * #include <Eigen/TensorSymmetry>\n  * \\endcode\n  */\n\n#include \"src/TensorSymmetry/util/TemplateGroupTheory.h\"\n#include \"src/TensorSymmetry/Symmetry.h\"\n#include \"src/TensorSymmetry/StaticSymmetry.h\"\n#include \"src/TensorSymmetry/DynamicSymmetry.h\"\n\n#include <Eigen/src/Core/util/ReenableStupidWarnings.h>\n\n#endif // EIGEN_CXX11_TENSORSYMMETRY_MODULE\n\n/*\n * kate: space-indent on; indent-width 2; mixedindent off; indent-mode cstyle;\n */\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/ThreadPool",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_THREADPOOL_MODULE\n#define EIGEN_CXX11_THREADPOOL_MODULE\n\n#include \"../../../Eigen/Core\"\n\n#include <Eigen/src/Core/util/DisableStupidWarnings.h>\n\n/** \\defgroup CXX11_ThreadPool_Module C++11 ThreadPool Module\n  *\n  * This module provides 2 threadpool implementations\n  *  - a simple reference implementation\n  *  - a faster non blocking implementation\n  *\n  * This module requires C++11.\n  *\n  * \\code\n  * #include <Eigen/CXX11/ThreadPool>\n  * \\endcode\n  */\n\n\n// The code depends on CXX11, so only include the module if the\n// compiler supports it.\n#if __cplusplus > 199711L || EIGEN_COMP_MSVC >= 1900\n#include <cstddef>\n#include <cstring>\n#include <stdint.h>\n#include <time.h>\n\n#include <vector>\n#include <atomic>\n#include <condition_variable>\n#include <deque>\n#include <mutex>\n#include <thread>\n#include <functional>\n#include <memory>\n\n#include \"src/util/CXX11Meta.h\"\n#include \"src/util/MaxSizeVector.h\"\n\n#include \"src/ThreadPool/ThreadLocal.h\"\n#include \"src/ThreadPool/ThreadYield.h\"\n#include \"src/ThreadPool/EventCount.h\"\n#include \"src/ThreadPool/RunQueue.h\"\n#include \"src/ThreadPool/ThreadPoolInterface.h\"\n#include \"src/ThreadPool/ThreadEnvironment.h\"\n#include \"src/ThreadPool/SimpleThreadPool.h\"\n#include \"src/ThreadPool/NonBlockingThreadPool.h\"\n\n#endif\n\n#include <Eigen/src/Core/util/ReenableStupidWarnings.h>\n\n#endif // EIGEN_CXX11_THREADPOOL_MODULE\n\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/README.md",
    "content": "# Eigen Tensors\n\nTensors are multidimensional arrays of elements. Elements are typically scalars,\nbut more complex types such as strings are also supported.\n\n[TOC]\n\n## Tensor Classes\n\nYou can manipulate a tensor with one of the following classes.  They all are in\nthe namespace ```::Eigen.```\n\n\n### Class Tensor<data_type, rank>\n\nThis is the class to use to create a tensor and allocate memory for it.  The\nclass is templatized with the tensor datatype, such as float or int, and the\ntensor rank.  The rank is the number of dimensions, for example rank 2 is a\nmatrix.\n\nTensors of this class are resizable.  For example, if you assign a tensor of a\ndifferent size to a Tensor, that tensor is resized to match its new value.\n\n#### Constructor Tensor<data_type, rank>(size0, size1, ...)\n\nConstructor for a Tensor.  The constructor must be passed ```rank``` integers\nindicating the sizes of the instance along each of the the ```rank```\ndimensions.\n\n    // Create a tensor of rank 3 of sizes 2, 3, 4.  This tensor owns\n    // memory to hold 24 floating point values (24 = 2 x 3 x 4).\n    Tensor<float, 3> t_3d(2, 3, 4);\n\n    // Resize t_3d by assigning a tensor of different sizes, but same rank.\n    t_3d = Tensor<float, 3>(3, 4, 3);\n\n#### Constructor Tensor<data_type, rank>(size_array)\n\nConstructor where the sizes for the constructor are specified as an array of\nvalues instead of an explicitly list of parameters.  The array type to use is\n```Eigen::array<Eigen::Index>```.  The array can be constructed automatically\nfrom an initializer list.\n\n    // Create a tensor of strings of rank 2 with sizes 5, 7.\n    Tensor<string, 2> t_2d({5, 7});\n\n\n### Class TensorFixedSize<data_type, Sizes<size0, size1, ...>>\n\nClass to use for tensors of fixed size, where the size is known at compile\ntime.  Fixed sized tensors can provide very fast computations because all their\ndimensions are known by the compiler.  FixedSize tensors are not resizable.\n\nIf the total number of elements in a fixed size tensor is small enough the\ntensor data is held onto the stack and does not cause heap allocation and free.\n\n    // Create a 4 x 3 tensor of floats.\n    TensorFixedSize<float, Sizes<4, 3>> t_4x3;\n\n### Class TensorMap<Tensor<data_type, rank>>\n\nThis is the class to use to create a tensor on top of memory allocated and\nowned by another part of your code.  It allows to view any piece of allocated\nmemory as a Tensor.  Instances of this class do not own the memory where the\ndata are stored.\n\nA TensorMap is not resizable because it does not own the memory where its data\nare stored.\n\n#### Constructor TensorMap<Tensor<data_type, rank>>(data, size0, size1, ...)\n\nConstructor for a Tensor.  The constructor must be passed a pointer to the\nstorage for the data, and \"rank\" size attributes.  The storage has to be\nlarge enough to hold all the data.\n\n    // Map a tensor of ints on top of stack-allocated storage.\n    int storage[128];  // 2 x 4 x 2 x 8 = 128\n    TensorMap<Tensor<int, 4>> t_4d(storage, 2, 4, 2, 8);\n\n    // The same storage can be viewed as a different tensor.\n    // You can also pass the sizes as an array.\n    TensorMap<Tensor<int, 2>> t_2d(storage, 16, 8);\n\n    // You can also map fixed-size tensors.  Here we get a 1d view of\n    // the 2d fixed-size tensor.\n    Tensor<float, Sizes<4, 5>> t_4x3;\n    TensorMap<Tensor<float, 1>> t_12(t_4x3, 12);\n\n\n#### Class TensorRef\n\nSee Assigning to a TensorRef below.\n\n## Accessing Tensor Elements\n\n#### <data_type> tensor(index0, index1...)\n\nReturn the element at position ```(index0, index1...)``` in tensor\n```tensor```.  You must pass as many parameters as the rank of ```tensor```.\nThe expression can be used as an l-value to set the value of the element at the\nspecified position.  The value returned is of the datatype of the tensor.\n\n    // Set the value of the element at position (0, 1, 0);\n    Tensor<float, 3> t_3d(2, 3, 4);\n    t_3d(0, 1, 0) = 12.0f;\n\n    // Initialize all elements to random values.\n    for (int i = 0; i < 2; ++i) {\n      for (int j = 0; j < 3; ++j) {\n        for (int k = 0; k < 4; ++k) {\n          t_3d(i, j, k) = ...some random value...;\n        }\n      }\n    }\n\n    // Print elements of a tensor.\n    for (int i = 0; i < 2; ++i) {\n      LOG(INFO) << t_3d(i, 0, 0);\n    }\n\n\n## TensorLayout\n\nThe tensor library supports 2 layouts: ```ColMajor``` (the default) and\n```RowMajor```.  Only the default column major layout is currently fully\nsupported, and it is therefore not recommended to attempt to use the row major\nlayout at the moment.\n\nThe layout of a tensor is optionally specified as part of its type. If not\nspecified explicitly column major is assumed.\n\n    Tensor<float, 3, ColMajor> col_major;  // equivalent to Tensor<float, 3>\n    TensorMap<Tensor<float, 3, RowMajor> > row_major(data, ...);\n\nAll the arguments to an expression must use the same layout. Attempting to mix\ndifferent layouts will result in a compilation error.\n\nIt is possible to change the layout of a tensor or an expression using the\n```swap_layout()``` method.  Note that this will also reverse the order of the\ndimensions.\n\n    Tensor<float, 2, ColMajor> col_major(2, 4);\n    Tensor<float, 2, RowMajor> row_major(2, 4);\n\n    Tensor<float, 2> col_major_result = col_major;  // ok, layouts match\n    Tensor<float, 2> col_major_result = row_major;  // will not compile\n\n    // Simple layout swap\n    col_major_result = row_major.swap_layout();\n    eigen_assert(col_major_result.dimension(0) == 4);\n    eigen_assert(col_major_result.dimension(1) == 2);\n\n    // Swap the layout and preserve the order of the dimensions\n    array<int, 2> shuffle(1, 0);\n    col_major_result = row_major.swap_layout().shuffle(shuffle);\n    eigen_assert(col_major_result.dimension(0) == 2);\n    eigen_assert(col_major_result.dimension(1) == 4);\n\n\n## Tensor Operations\n\nThe Eigen Tensor library provides a vast library of operations on Tensors:\nnumerical operations such as addition and multiplication, geometry operations\nsuch as slicing and shuffling, etc.  These operations are available as methods\nof the Tensor classes, and in some cases as operator overloads.  For example\nthe following code computes the elementwise addition of two tensors:\n\n    Tensor<float, 3> t1(2, 3, 4);\n    ...set some values in t1...\n    Tensor<float, 3> t2(2, 3, 4);\n    ...set some values in t2...\n    // Set t3 to the element wise sum of t1 and t2\n    Tensor<float, 3> t3 = t1 + t2;\n\nWhile the code above looks easy enough, it is important to understand that the\nexpression ```t1 + t2``` is not actually adding the values of the tensors.  The\nexpression instead constructs a \"tensor operator\" object of the class\nTensorCwiseBinaryOp<scalar_sum>, which has references to the tensors\n```t1``` and ```t2```.  This is a small C++ object that knows how to add\n```t1``` and ```t2```.  It is only when the value of the expression is assigned\nto the tensor ```t3``` that the addition is actually performed.  Technically,\nthis happens through the overloading of ```operator=()``` in the Tensor class.\n\nThis mechanism for computing tensor expressions allows for lazy evaluation and\noptimizations which are what make the tensor library very fast.\n\nOf course, the tensor operators do nest, and the expression ```t1 + t2 *\n0.3f``` is actually represented with the (approximate) tree of operators:\n\n    TensorCwiseBinaryOp<scalar_sum>(t1, TensorCwiseUnaryOp<scalar_mul>(t2, 0.3f))\n\n\n### Tensor Operations and C++ \"auto\"\n\nBecause Tensor operations create tensor operators, the C++ ```auto``` keyword\ndoes not have its intuitive meaning.  Consider these 2 lines of code:\n\n    Tensor<float, 3> t3 = t1 + t2;\n    auto t4 = t1 + t2;\n\nIn the first line we allocate the tensor ```t3``` and it will contain the\nresult of the addition of ```t1``` and ```t2```.  In the second line, ```t4```\nis actually the tree of tensor operators that will compute the addition of\n```t1``` and ```t2```.  In fact, ```t4``` is *not* a tensor and you cannot get\nthe values of its elements:\n\n    Tensor<float, 3> t3 = t1 + t2;\n    cout << t3(0, 0, 0);  // OK prints the value of t1(0, 0, 0) + t2(0, 0, 0)\n\n    auto t4 = t1 + t2;\n    cout << t4(0, 0, 0);  // Compilation error!\n\nWhen you use ```auto``` you do not get a Tensor as a result but instead a\nnon-evaluated expression.  So only use ```auto``` to delay evaluation.\n\nUnfortunately, there is no single underlying concrete type for holding\nnon-evaluated expressions, hence you have to use auto in the case when you do\nwant to hold non-evaluated expressions.\n\nWhen you need the results of set of tensor computations you have to assign the\nresult to a Tensor that will be capable of holding onto them.  This can be\neither a normal Tensor, a fixed size Tensor, or a TensorMap on an existing\npiece of memory.  All the following will work:\n\n    auto t4 = t1 + t2;\n\n    Tensor<float, 3> result = t4;  // Could also be: result(t4);\n    cout << result(0, 0, 0);\n\n    TensorMap<float, 4> result(<a float* with enough space>, <size0>, ...) = t4;\n    cout << result(0, 0, 0);\n\n    TensorFixedSize<float, Sizes<size0, ...>> result = t4;\n    cout << result(0, 0, 0);\n\nUntil you need the results, you can keep the operation around, and even reuse\nit for additional operations.  As long as you keep the expression as an\noperation, no computation is performed.\n\n    // One way to compute exp((t1 + t2) * 0.2f);\n    auto t3 = t1 + t2;\n    auto t4 = t3 * 0.2f;\n    auto t5 = t4.exp();\n    Tensor<float, 3> result = t5;\n\n    // Another way, exactly as efficient as the previous one:\n    Tensor<float, 3> result = ((t1 + t2) * 0.2f).exp();\n\n### Controlling When Expression are Evaluated\n\nThere are several ways to control when expressions are evaluated:\n\n*   Assignment to a Tensor, TensorFixedSize, or TensorMap.\n*   Use of the eval() method.\n*   Assignment to a TensorRef.\n\n#### Assigning to a Tensor, TensorFixedSize, or TensorMap.\n\nThe most common way to evaluate an expression is to assign it to a Tensor.  In\nthe example below, the ```auto``` declarations make the intermediate values\n\"Operations\", not Tensors, and do not cause the expressions to be evaluated.\nThe assignment to the Tensor ```result``` causes the evaluation of all the\noperations.\n\n    auto t3 = t1 + t2;             // t3 is an Operation.\n    auto t4 = t3 * 0.2f;           // t4 is an Operation.\n    auto t5 = t4.exp();            // t5 is an Operation.\n    Tensor<float, 3> result = t5;  // The operations are evaluated.\n\nIf you know the ranks and sizes of the Operation value you can assign the\nOperation to a TensorFixedSize instead of a Tensor, which is a bit more\nefficient.\n\n    // We know that the result is a 4x4x2 tensor!\n    TensorFixedSize<float, 4, 4, 2> result = t5;\n\nSimiarly, assigning an expression to a TensorMap causes its evaluation.  Like\ntensors of type TensorFixedSize, TensorMaps cannot be resized so they have to\nhave the rank and sizes of the expression that are assigned to them.\n\n#### Calling eval().\n\nWhen you compute large composite expressions, you sometimes want to tell Eigen\nthat an intermediate value in the expression tree is worth evaluating ahead of\ntime.  This is done by inserting a call to the ```eval()``` method of the\nexpression Operation.\n\n    // The previous example could have been written:\n    Tensor<float, 3> result = ((t1 + t2) * 0.2f).exp();\n\n    // If you want to compute (t1 + t2) once ahead of time you can write:\n    Tensor<float, 3> result = ((t1 + t2).eval() * 0.2f).exp();\n\nSemantically, calling ```eval()``` is equivalent to materializing the value of\nthe expression in a temporary Tensor of the right size.  The code above in\neffect does:\n\n    // .eval() knows the size!\n    TensorFixedSize<float, 4, 4, 2> tmp = t1 + t2;\n    Tensor<float, 3> result = (tmp * 0.2f).exp();\n\nNote that the return value of ```eval()``` is itself an Operation, so the\nfollowing code does not do what you may think:\n\n    // Here t3 is an evaluation Operation.  t3 has not been evaluated yet.\n    auto t3 = (t1 + t2).eval();\n\n    // You can use t3 in another expression.  Still no evaluation.\n    auto t4 = (t3 * 0.2f).exp();\n\n    // The value is evaluated when you assign the Operation to a Tensor, using\n    // an intermediate tensor to represent t3.x\n    Tensor<float, 3> result = t4;\n\nWhile in the examples above calling ```eval()``` does not make a difference in\nperformance, in other cases it can make a huge difference.  In the expression\nbelow the ```broadcast()``` expression causes the ```X.maximum()``` expression\nto be evaluated many times:\n\n    Tensor<...> X ...;\n    Tensor<...> Y = ((X - X.maximum(depth_dim).reshape(dims2d).broadcast(bcast))\n                     * beta).exp();\n\nInserting a call to ```eval()``` between the ```maximum()``` and\n```reshape()``` calls guarantees that maximum() is only computed once and\ngreatly speeds-up execution:\n\n    Tensor<...> Y =\n      ((X - X.maximum(depth_dim).eval().reshape(dims2d).broadcast(bcast))\n        * beta).exp();\n\nIn the other example below, the tensor ```Y``` is both used in the expression\nand its assignment.  This is an aliasing problem and if the evaluation is not\ndone in the right order Y will be updated incrementally during the evaluation\nresulting in bogus results:\n\n     Tensor<...> Y ...;\n     Y = Y / (Y.sum(depth_dim).reshape(dims2d).broadcast(bcast));\n\nInserting a call to ```eval()``` between the ```sum()``` and ```reshape()```\nexpressions ensures that the sum is computed before any updates to ```Y``` are\ndone.\n\n     Y = Y / (Y.sum(depth_dim).eval().reshape(dims2d).broadcast(bcast));\n\nNote that an eval around the full right hand side expression is not needed\nbecause the generated has to compute the i-th value of the right hand side\nbefore assigning it to the left hand side.\n\nHowever, if you were assigning the expression value to a shuffle of ```Y```\nthen you would need to force an eval for correctness by adding an ```eval()```\ncall for the right hand side:\n\n     Y.shuffle(...) =\n        (Y / (Y.sum(depth_dim).eval().reshape(dims2d).broadcast(bcast))).eval();\n\n\n#### Assigning to a TensorRef.\n\nIf you need to access only a few elements from the value of an expression you\ncan avoid materializing the value in a full tensor by using a TensorRef.\n\nA TensorRef is a small wrapper class for any Eigen Operation.  It provides\noverloads for the ```()``` operator that let you access individual values in\nthe expression.  TensorRef is convenient, because the Operation themselves do\nnot provide a way to access individual elements.\n\n    // Create a TensorRef for the expression.  The expression is not\n    // evaluated yet.\n    TensorRef<Tensor<float, 3> > ref = ((t1 + t2) * 0.2f).exp();\n\n    // Use \"ref\" to access individual elements.  The expression is evaluated\n    // on the fly.\n    float at_0 = ref(0, 0, 0);\n    cout << ref(0, 1, 0);\n\nOnly use TensorRef when you need a subset of the values of the expression.\nTensorRef only computes the values you access.  However note that if you are\ngoing to access all the values it will be much faster to materialize the\nresults in a Tensor first.\n\nIn some cases, if the full Tensor result would be very large, you may save\nmemory by accessing it as a TensorRef.  But not always.  So don't count on it.\n\n\n### Controlling How Expressions Are Evaluated\n\nThe tensor library provides several implementations of the various operations\nsuch as contractions and convolutions.  The implementations are optimized for\ndifferent environments: single threaded on CPU, multi threaded on CPU, or on a\nGPU using cuda.  Additional implementations may be added later.\n\nYou can choose which implementation to use with the ```device()``` call.  If\nyou do not choose an implementation explicitly the default implementation that\nuses a single thread on the CPU is used.\n\nThe default implementation has been optimized for recent Intel CPUs, taking\nadvantage of SSE, AVX, and FMA instructions.  Work is ongoing to tune the\nlibrary on ARM CPUs.  Note that you need to pass compiler-dependent flags\nto enable the use of SSE, AVX, and other instructions.\n\nFor example, the following code adds two tensors using the default\nsingle-threaded CPU implementation:\n\n    Tensor<float, 2> a(30, 40);\n    Tensor<float, 2> b(30, 40);\n    Tensor<float, 2> c = a + b;\n\nTo choose a different implementation you have to insert a ```device()``` call\nbefore the assignment of the result.  For technical C++ reasons this requires\nthat the Tensor for the result be declared on its own.  This means that you\nhave to know the size of the result.\n\n    Eigen::Tensor<float, 2> c(30, 40);\n    c.device(...) = a + b;\n\nThe call to ```device()``` must be the last call on the left of the operator=.\n\nYou must pass to the ```device()``` call an Eigen device object.  There are\npresently three devices you can use: DefaultDevice, ThreadPoolDevice and\nGpuDevice.\n\n\n#### Evaluating With the DefaultDevice\n\nThis is exactly the same as not inserting a ```device()``` call.\n\n    DefaultDevice my_device;\n    c.device(my_device) = a + b;\n\n#### Evaluating with a Thread Pool\n\n    // Create the Eigen ThreadPoolDevice.\n    Eigen::ThreadPoolDevice my_device(4 /* number of threads to use */);\n\n    // Now just use the device when evaluating expressions.\n    Eigen::Tensor<float, 2> c(30, 50);\n    c.device(my_device) = a.contract(b, dot_product_dims);\n\n\n#### Evaluating On GPU\n\nThis is presently a bit more complicated than just using a thread pool device.\nYou need to create a GPU device but you also need to explicitly allocate the\nmemory for tensors with cuda.\n\n\n## API Reference\n\n### Datatypes\n\nIn the documentation of the tensor methods and Operation we mention datatypes\nthat are tensor-type specific:\n\n#### <Tensor-Type>::Dimensions\n\nActs like an array of ints.  Has an ```int size``` attribute, and can be\nindexed like an array to access individual values.  Used to represent the\ndimensions of a tensor.  See ```dimensions()```.\n\n#### <Tensor-Type>::Index\n\nActs like an ```int```.  Used for indexing tensors along their dimensions.  See\n```operator()```, ```dimension()```, and ```size()```.\n\n#### <Tensor-Type>::Scalar\n\nRepresents the datatype of individual tensor elements.  For example, for a\n```Tensor<float>```, ```Scalar``` is the type ```float```.  See\n```setConstant()```.\n\n#### <Operation>\n\nWe use this pseudo type to indicate that a tensor Operation is returned by a\nmethod.  We indicate in the text the type and dimensions of the tensor that the\nOperation returns after evaluation.\n\nThe Operation will have to be evaluated, for example by assigning it to a\ntensor, before you can access the values of the resulting tensor.  You can also\naccess the values through a TensorRef.\n\n\n## Built-in Tensor Methods\n\nThese are usual C++ methods that act on tensors immediately.  They are not\nOperations which provide delayed evaluation of their results.  Unless specified\notherwise, all the methods listed below are available on all tensor classes:\nTensor, TensorFixedSize, and TensorMap.\n\n## Metadata\n\n### int NumDimensions\n\nConstant value indicating the number of dimensions of a Tensor.  This is also\nknown as the tensor \"rank\".\n\n      Eigen::Tensor<float, 2> a(3, 4);\n      cout << \"Dims \" << a.NumDimensions;\n      => Dims 2\n\n### Dimensions dimensions()\n\nReturns an array-like object representing the dimensions of the tensor.\nThe actual type of the dimensions() result is <Tensor-Type>::Dimensions.\n\n    Eigen::Tensor<float, 2> a(3, 4);\n    const Eigen::Tensor<float, 2>::Dimensions& d = a.dimensions();\n    cout << \"Dim size: \" << d.size << \", dim 0: \" << d[0]\n         << \", dim 1: \" << d[1];\n    => Dim size: 2, dim 0: 3, dim 1: 4\n\nIf you use a C++11 compiler, you can use ```auto``` to simplify the code:\n\n    const auto& d = a.dimensions();\n    cout << \"Dim size: \" << d.size << \", dim 0: \" << d[0]\n         << \", dim 1: \" << d[1];\n    => Dim size: 2, dim 0: 3, dim 1: 4\n\n### Index dimension(Index n)\n\nReturns the n-th dimension of the tensor.  The actual type of the\n```dimension()``` result is ```<Tensor-Type>::Index```, but you can\nalways use it like an int.\n\n      Eigen::Tensor<float, 2> a(3, 4);\n      int dim1 = a.dimension(1);\n      cout << \"Dim 1: \" << dim1;\n      => Dim 1: 4\n\n### Index size()\n\nReturns the total number of elements in the tensor.  This is the product of all\nthe tensor dimensions.  The actual type of the ```size()``` result is\n```<Tensor-Type>::Index```, but you can always use it like an int.\n\n    Eigen::Tensor<float, 2> a(3, 4);\n    cout << \"Size: \" << a.size();\n    => Size: 12\n\n\n### Getting Dimensions From An Operation\n\nA few operations provide ```dimensions()``` directly,\ne.g. ```TensorReslicingOp```.  Most operations defer calculating dimensions\nuntil the operation is being evaluated.  If you need access to the dimensions\nof a deferred operation, you can wrap it in a TensorRef (see Assigning to a\nTensorRef above), which provides ```dimensions()``` and ```dimension()``` as\nabove.\n\nTensorRef can also wrap the plain Tensor types, so this is a useful idiom in\ntemplated contexts where the underlying object could be either a raw Tensor\nor some deferred operation (e.g. a slice of a Tensor).  In this case, the\ntemplate code can wrap the object in a TensorRef and reason about its\ndimensionality while remaining agnostic to the underlying type.\n\n\n## Constructors\n\n### Tensor\n\nCreates a tensor of the specified size. The number of arguments must be equal\nto the rank of the tensor. The content of the tensor is not initialized.\n\n    Eigen::Tensor<float, 2> a(3, 4);\n    cout << \"NumRows: \" << a.dimension(0) << \" NumCols: \" << a.dimension(1) << endl;\n    => NumRows: 3 NumCols: 4\n\n### TensorFixedSize\n\nCreates a tensor of the specified size. The number of arguments in the Size<>\ntemplate parameter determines the rank of the tensor. The content of the tensor\nis not initialized.\n\n    Eigen::TensorFixedSize<float, Size<3, 4>> a;\n    cout << \"Rank: \" << a.rank() << endl;\n    => Rank: 2\n    cout << \"NumRows: \" << a.dimension(0) << \" NumCols: \" << a.dimension(1) << endl;\n    => NumRows: 3 NumCols: 4\n\n### TensorMap\n\nCreates a tensor mapping an existing array of data. The data must not be freed\nuntil the TensorMap is discarded, and the size of the data must be large enough\nto accomodate of the coefficients of the tensor.\n\n    float data[] = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11};\n    Eigen::TensorMap<float, 2> a(data, 3, 4);\n    cout << \"NumRows: \" << a.dimension(0) << \" NumCols: \" << a.dimension(1) << endl;\n    => NumRows: 3 NumCols: 4\n    cout << \"a(1, 2): \" << a(1, 2) << endl;\n    => a(1, 2): 9\n\n\n## Contents Initialization\n\nWhen a new Tensor or a new TensorFixedSize are created, memory is allocated to\nhold all the tensor elements, but the memory is not initialized.  Similarly,\nwhen a new TensorMap is created on top of non-initialized memory the memory its\ncontents are not initialized.\n\nYou can use one of the methods below to initialize the tensor memory.  These\nhave an immediate effect on the tensor and return the tensor itself as a\nresult.  These are not tensor Operations which delay evaluation.\n\n### <Tensor-Type> setConstant(const Scalar& val)\n\nSets all elements of the tensor to the constant value ```val```.  ```Scalar```\nis the type of data stored in the tensor.  You can pass any value that is\nconvertible to that type.\n\nReturns the tensor itself in case you want to chain another call.\n\n    a.setConstant(12.3f);\n    cout << \"Constant: \" << endl << a << endl << endl;\n    =>\n    Constant:\n    12.3 12.3 12.3 12.3\n    12.3 12.3 12.3 12.3\n    12.3 12.3 12.3 12.3\n\nNote that ```setConstant()``` can be used on any tensor where the element type\nhas a copy constructor and an ```operator=()```:\n\n    Eigen::Tensor<string, 2> a(2, 3);\n    a.setConstant(\"yolo\");\n    cout << \"String tensor: \" << endl << a << endl << endl;\n    =>\n    String tensor:\n    yolo yolo yolo\n    yolo yolo yolo\n\n\n### <Tensor-Type> setZero()\n\nFills the tensor with zeros.  Equivalent to ```setConstant(Scalar(0))```.\nReturns the tensor itself in case you want to chain another call.\n\n    a.setZero();\n    cout << \"Zeros: \" << endl << a << endl << endl;\n    =>\n    Zeros:\n    0 0 0 0\n    0 0 0 0\n    0 0 0 0\n\n\n### <Tensor-Type> setValues({..initializer_list})\n\nFills the tensor with explicit values specified in a std::initializer_list.\nThe type of the initializer list depends on the type and rank of the tensor.\n\nIf the tensor has rank N, the initializer list must be nested N times.  The\nmost deeply nested lists must contains P scalars of the Tensor type where P is\nthe size of the last dimension of the Tensor.\n\nFor example, for a ```TensorFixedSize<float, 2, 3>``` the initializer list must\ncontains 2 lists of 3 floats each.\n\n```setValues()``` returns the tensor itself in case you want to chain another\ncall.\n\n    Eigen::Tensor<float, 2> a(2, 3);\n    a.setValues({{0.0f, 1.0f, 2.0f}, {3.0f, 4.0f, 5.0f}});\n    cout << \"a\" << endl << a << endl << endl;\n    =>\n    a\n    0 1 2\n    3 4 5\n\nIf a list is too short, the corresponding elements of the tensor will not be\nchanged.  This is valid at each level of nesting.  For example the following\ncode only sets the values of the first row of the tensor.\n\n    Eigen::Tensor<int, 2> a(2, 3);\n    a.setConstant(1000);\n    a.setValues({{10, 20, 30}});\n    cout << \"a\" << endl << a << endl << endl;\n    =>\n    a\n    10   20   30\n    1000 1000 1000\n\n### <Tensor-Type> setRandom()\n\nFills the tensor with random values.  Returns the tensor itself in case you\nwant to chain another call.\n\n    a.setRandom();\n    cout << \"Random: \" << endl << a << endl << endl;\n    =>\n    Random:\n      0.680375    0.59688  -0.329554    0.10794\n     -0.211234   0.823295   0.536459 -0.0452059\n      0.566198  -0.604897  -0.444451   0.257742\n\nYou can customize ```setRandom()``` by providing your own random number\ngenerator as a template argument:\n\n    a.setRandom<MyRandomGenerator>();\n\nHere, ```MyRandomGenerator``` must be a struct with the following member\nfunctions, where Scalar and Index are the same as ```<Tensor-Type>::Scalar```\nand ```<Tensor-Type>::Index```.\n\nSee ```struct UniformRandomGenerator``` in TensorFunctors.h for an example.\n\n    // Custom number generator for use with setRandom().\n    struct MyRandomGenerator {\n      // Default and copy constructors. Both are needed\n      MyRandomGenerator() { }\n      MyRandomGenerator(const MyRandomGenerator& ) { }\n\n      // Return a random value to be used.  \"element_location\" is the\n      // location of the entry to set in the tensor, it can typically\n      // be ignored.\n      Scalar operator()(Eigen::DenseIndex element_location,\n                        Eigen::DenseIndex /*unused*/ = 0) const {\n        return <randomly generated value of type T>;\n      }\n\n      // Same as above but generates several numbers at a time.\n      typename internal::packet_traits<Scalar>::type packetOp(\n          Eigen::DenseIndex packet_location, Eigen::DenseIndex /*unused*/ = 0) const {\n        return <a packet of randomly generated values>;\n      }\n    };\n\nYou can also use one of the 2 random number generators that are part of the\ntensor library:\n*   UniformRandomGenerator\n*   NormalRandomGenerator\n\n\n## Data Access\n\nThe Tensor, TensorFixedSize, and TensorRef classes provide the following\naccessors to access the tensor coefficients:\n\n    const Scalar& operator()(const array<Index, NumIndices>& indices)\n    const Scalar& operator()(Index firstIndex, IndexTypes... otherIndices)\n    Scalar& operator()(const array<Index, NumIndices>& indices)\n    Scalar& operator()(Index firstIndex, IndexTypes... otherIndices)\n\nThe number of indices must be equal to the rank of the tensor. Moreover, these\naccessors are not available on tensor expressions. In order to access the\nvalues of a tensor expression, the expression must either be evaluated or\nwrapped in a TensorRef.\n\n\n### Scalar* data() and const Scalar* data() const\n\nReturns a pointer to the storage for the tensor.  The pointer is const if the\ntensor was const.  This allows direct access to the data.  The layout of the\ndata depends on the tensor layout: RowMajor or ColMajor.\n\nThis access is usually only needed for special cases, for example when mixing\nEigen Tensor code with other libraries.\n\nScalar is the type of data stored in the tensor.\n\n    Eigen::Tensor<float, 2> a(3, 4);\n    float* a_data = a.data();\n    a_data[0] = 123.45f;\n    cout << \"a(0, 0): \" << a(0, 0);\n    => a(0, 0): 123.45\n\n\n## Tensor Operations\n\nAll the methods documented below return non evaluated tensor ```Operations```.\nThese can be chained: you can apply another Tensor Operation to the value\nreturned by the method.\n\nThe chain of Operation is evaluated lazily, typically when it is assigned to a\ntensor.  See \"Controlling when Expression are Evaluated\" for more details about\ntheir evaluation.\n\n### <Operation> constant(const Scalar& val)\n\nReturns a tensor of the same type and dimensions as the original tensor but\nwhere all elements have the value ```val```.\n\nThis is useful, for example, when you want to add or subtract a constant from a\ntensor, or multiply every element of a tensor by a scalar.\n\n    Eigen::Tensor<float, 2> a(2, 3);\n    a.setConstant(1.0f);\n    Eigen::Tensor<float, 2> b = a + a.constant(2.0f);\n    Eigen::Tensor<float, 2> c = b * b.constant(0.2f);\n    cout << \"a\" << endl << a << endl << endl;\n    cout << \"b\" << endl << b << endl << endl;\n    cout << \"c\" << endl << c << endl << endl;\n    =>\n    a\n    1 1 1\n    1 1 1\n\n    b\n    3 3 3\n    3 3 3\n\n    c\n    0.6 0.6 0.6\n    0.6 0.6 0.6\n\n### <Operation> random()\n\nReturns a tensor of the same type and dimensions as the current tensor\nbut where all elements have random values.\n\nThis is for example useful to add random values to an existing tensor.\nThe generation of random values can be customized in the same manner\nas for ```setRandom()```.\n\n    Eigen::Tensor<float, 2> a(2, 3);\n    a.setConstant(1.0f);\n    Eigen::Tensor<float, 2> b = a + a.random();\n    cout << \"a\" << endl << a << endl << endl;\n    cout << \"b\" << endl << b << endl << endl;\n    =>\n    a\n    1 1 1\n    1 1 1\n\n    b\n    1.68038   1.5662  1.82329\n    0.788766  1.59688 0.395103\n\n\n## Unary Element Wise Operations\n\nAll these operations take a single input tensor as argument and return a tensor\nof the same type and dimensions as the tensor to which they are applied.  The\nrequested operations are applied to each element independently.\n\n### <Operation> operator-()\n\nReturns a tensor of the same type and dimensions as the original tensor\ncontaining the opposite values of the original tensor.\n\n    Eigen::Tensor<float, 2> a(2, 3);\n    a.setConstant(1.0f);\n    Eigen::Tensor<float, 2> b = -a;\n    cout << \"a\" << endl << a << endl << endl;\n    cout << \"b\" << endl << b << endl << endl;\n    =>\n    a\n    1 1 1\n    1 1 1\n\n    b\n    -1 -1 -1\n    -1 -1 -1\n\n### <Operation> sqrt()\n\nReturns a tensor of the same type and dimensions as the original tensor\ncontaining the square roots of the original tensor.\n\n### <Operation> rsqrt()\n\nReturns a tensor of the same type and dimensions as the original tensor\ncontaining the inverse square roots of the original tensor.\n\n### <Operation> square()\n\nReturns a tensor of the same type and dimensions as the original tensor\ncontaining the squares of the original tensor values.\n\n### <Operation> inverse()\n\nReturns a tensor of the same type and dimensions as the original tensor\ncontaining the inverse of the original tensor values.\n\n### <Operation> exp()\n\nReturns a tensor of the same type and dimensions as the original tensor\ncontaining the exponential of the original tensor.\n\n### <Operation> log()\n\nReturns a tensor of the same type and dimensions as the original tensor\ncontaining the natural logarithms of the original tensor.\n\n### <Operation> abs()\n\nReturns a tensor of the same type and dimensions as the original tensor\ncontaining the absolute values of the original tensor.\n\n### <Operation> pow(Scalar exponent)\n\nReturns a tensor of the same type and dimensions as the original tensor\ncontaining the coefficients of the original tensor to the power of the\nexponent.\n\nThe type of the exponent, Scalar, is always the same as the type of the\ntensor coefficients.  For example, only integer exponents can be used in\nconjuntion with tensors of integer values.\n\nYou can use cast() to lift this restriction.  For example this computes\ncubic roots of an int Tensor:\n\n    Eigen::Tensor<int, 2> a(2, 3);\n    a.setValues({{0, 1, 8}, {27, 64, 125}});\n    Eigen::Tensor<double, 2> b = a.cast<double>().pow(1.0 / 3.0);\n    cout << \"a\" << endl << a << endl << endl;\n    cout << \"b\" << endl << b << endl << endl;\n    =>\n    a\n    0   1   8\n    27  64 125\n\n    b\n    0 1 2\n    3 4 5\n\n### <Operation>  operator * (Scalar scale)\n\nMultiplies all the coefficients of the input tensor by the provided scale.\n\n### <Operation>  cwiseMax(Scalar threshold)\nTODO\n\n### <Operation>  cwiseMin(Scalar threshold)\nTODO\n\n### <Operation>  unaryExpr(const CustomUnaryOp& func)\nTODO\n\n\n## Binary Element Wise Operations\n\nThese operations take two input tensors as arguments. The 2 input tensors should\nbe of the same type and dimensions. The result is a tensor of the same\ndimensions as the tensors to which they are applied, and unless otherwise\nspecified it is also of the same type. The requested operations are applied to\neach pair of elements independently.\n\n### <Operation> operator+(const OtherDerived& other)\n\nReturns a tensor of the same type and dimensions as the input tensors\ncontaining the coefficient wise sums of the inputs.\n\n### <Operation> operator-(const OtherDerived& other)\n\nReturns a tensor of the same type and dimensions as the input tensors\ncontaining the coefficient wise differences of the inputs.\n\n### <Operation> operator*(const OtherDerived& other)\n\nReturns a tensor of the same type and dimensions as the input tensors\ncontaining the coefficient wise products of the inputs.\n\n### <Operation> operator/(const OtherDerived& other)\n\nReturns a tensor of the same type and dimensions as the input tensors\ncontaining the coefficient wise quotients of the inputs.\n\nThis operator is not supported for integer types.\n\n### <Operation> cwiseMax(const OtherDerived& other)\n\nReturns a tensor of the same type and dimensions as the input tensors\ncontaining the coefficient wise maximums of the inputs.\n\n### <Operation> cwiseMin(const OtherDerived& other)\n\nReturns a tensor of the same type and dimensions as the input tensors\ncontaining the coefficient wise mimimums of the inputs.\n\n### <Operation> Logical operators\n\nThe following logical operators are supported as well:\n\n*   operator&&(const OtherDerived& other)\n*   operator||(const OtherDerived& other)\n*   operator<(const OtherDerived& other)\n*   operator<=(const OtherDerived& other)\n*   operator>(const OtherDerived& other)\n*   operator>=(const OtherDerived& other)\n*   operator==(const OtherDerived& other)\n*   operator!=(const OtherDerived& other)\n\nThey all return a tensor of boolean values.\n\n\n## Selection (select(const ThenDerived& thenTensor, const ElseDerived& elseTensor)\n\nSelection is a coefficient-wise ternary operator that is the tensor equivalent\nto the if-then-else operation.\n\n    Tensor<bool, 3> if = ...;\n    Tensor<float, 3> then = ...;\n    Tensor<float, 3> else = ...;\n    Tensor<float, 3> result = if.select(then, else);\n\nThe 3 arguments must be of the same dimensions, which will also be the dimension\nof the result.  The 'if' tensor must be of type boolean, the 'then' and the\n'else' tensor must be of the same type, which will also be the type of the\nresult.\n\nEach coefficient in the result is equal to the corresponding coefficient in the\n'then' tensor if the corresponding value in the 'if' tensor is true. If not, the\nresulting coefficient will come from the 'else' tensor.\n\n\n## Contraction\n\nTensor *contractions* are a generalization of the matrix product to the\nmultidimensional case.\n\n    // Create 2 matrices using tensors of rank 2\n    Eigen::Tensor<int, 2> a(2, 3);\n    a.setValues({{1, 2, 3}, {6, 5, 4}});\n    Eigen::Tensor<int, 2> b(3, 2);\n    a.setValues({{1, 2}, {4, 5}, {5, 6}});\n\n    // Compute the traditional matrix product\n    array<IndexPair<int>, 1> product_dims = { IndexPair(1, 0) };\n    Eigen::Tensor<int, 2> AB = a.contract(b, product_dims);\n\n    // Compute the product of the transpose of the matrices\n    array<IndexPair<int>, 1> transpose_product_dims = { IndexPair(0, 1) };\n    Eigen::Tensor<int, 2> AtBt = a.contract(b, transposed_product_dims);\n\n\n## Reduction Operations\n\nA *Reduction* operation returns a tensor with fewer dimensions than the\noriginal tensor.  The values in the returned tensor are computed by applying a\n*reduction operator* to slices of values from the original tensor.  You specify\nthe dimensions along which the slices are made.\n\nThe Eigen Tensor library provides a set of predefined reduction operators such\nas ```maximum()``` and ```sum()``` and lets you define additional operators by\nimplementing a few methods from a reductor template.\n\n### Reduction Dimensions\n\nAll reduction operations take a single parameter of type\n```<TensorType>::Dimensions``` which can always be specified as an array of\nints.  These are called the \"reduction dimensions.\"  The values are the indices\nof the dimensions of the input tensor over which the reduction is done.  The\nparameter can have at most as many element as the rank of the input tensor;\neach element must be less than the tensor rank, as it indicates one of the\ndimensions to reduce.\n\nEach dimension of the input tensor should occur at most once in the reduction\ndimensions as the implementation does not remove duplicates.\n\nThe order of the values in the reduction dimensions does not affect the\nresults, but the code may execute faster if you list the dimensions in\nincreasing order.\n\nExample: Reduction along one dimension.\n\n    // Create a tensor of 2 dimensions\n    Eigen::Tensor<int, 2> a(2, 3);\n    a.setValues({{1, 2, 3}, {6, 5, 4}});\n    // Reduce it along the second dimension (1)...\n    Eigen::array<int, 1> dims({1 /* dimension to reduce */});\n    // ...using the \"maximum\" operator.\n    // The result is a tensor with one dimension.  The size of\n    // that dimension is the same as the first (non-reduced) dimension of a.\n    Eigen::Tensor<int, 1> b = a.maximum(dims);\n    cout << \"a\" << endl << a << endl << endl;\n    cout << \"b\" << endl << b << endl << endl;\n    =>\n    a\n    1 2 3\n    6 5 4\n\n    b\n    3\n    6\n\nExample: Reduction along two dimensions.\n\n    Eigen::Tensor<float, 3, Eigen::ColMajor> a(2, 3, 4);\n    a.setValues({{{0.0f, 1.0f, 2.0f, 3.0f},\n                  {7.0f, 6.0f, 5.0f, 4.0f},\n                  {8.0f, 9.0f, 10.0f, 11.0f}},\n                 {{12.0f, 13.0f, 14.0f, 15.0f},\n                  {19.0f, 18.0f, 17.0f, 16.0f},\n                  {20.0f, 21.0f, 22.0f, 23.0f}}});\n    // The tensor a has 3 dimensions.  We reduce along the\n    // first 2, resulting in a tensor with a single dimension\n    // of size 4 (the last dimension of a.)\n    // Note that we pass the array of reduction dimensions\n    // directly to the maximum() call.\n    Eigen::Tensor<float, 1, Eigen::ColMajor> b =\n        a.maximum(Eigen::array<int, 2>({0, 1}));\n    cout << \"b\" << endl << b << endl << endl;\n    =>\n    b\n    20\n    21\n    22\n    23\n\n#### Reduction along all dimensions\n\nAs a special case, if you pass no parameter to a reduction operation the\noriginal tensor is reduced along *all* its dimensions.  The result is a\nscalar, represented as a zero-dimension tensor.\n\n    Eigen::Tensor<float, 3> a(2, 3, 4);\n    a.setValues({{{0.0f, 1.0f, 2.0f, 3.0f},\n                  {7.0f, 6.0f, 5.0f, 4.0f},\n                  {8.0f, 9.0f, 10.0f, 11.0f}},\n                 {{12.0f, 13.0f, 14.0f, 15.0f},\n                  {19.0f, 18.0f, 17.0f, 16.0f},\n                  {20.0f, 21.0f, 22.0f, 23.0f}}});\n    // Reduce along all dimensions using the sum() operator.\n    Eigen::Tensor<float, 0> b = a.sum();\n    cout << \"b\" << endl << b << endl << endl;\n    =>\n    b\n    276\n\n\n### <Operation> sum(const Dimensions& new_dims)\n### <Operation> sum()\n\nReduce a tensor using the sum() operator.  The resulting values\nare the sum of the reduced values.\n\n### <Operation> mean(const Dimensions& new_dims)\n### <Operation> mean()\n\nReduce a tensor using the mean() operator.  The resulting values\nare the mean of the reduced values.\n\n### <Operation> maximum(const Dimensions& new_dims)\n### <Operation> maximum()\n\nReduce a tensor using the maximum() operator.  The resulting values are the\nlargest of the reduced values.\n\n### <Operation> minimum(const Dimensions& new_dims)\n### <Operation> minimum()\n\nReduce a tensor using the minimum() operator.  The resulting values\nare the smallest of the reduced values.\n\n### <Operation> prod(const Dimensions& new_dims)\n### <Operation> prod()\n\nReduce a tensor using the prod() operator.  The resulting values\nare the product of the reduced values.\n\n### <Operation> all(const Dimensions& new_dims)\n### <Operation> all()\nReduce a tensor using the all() operator.  Casts tensor to bool and then checks\nwhether all elements are true.  Runs through all elements rather than\nshort-circuiting, so may be significantly inefficient.\n\n### <Operation> any(const Dimensions& new_dims)\n### <Operation> any()\nReduce a tensor using the any() operator.  Casts tensor to bool and then checks\nwhether any element is true.  Runs through all elements rather than\nshort-circuiting, so may be significantly inefficient.\n\n\n### <Operation> reduce(const Dimensions& new_dims, const Reducer& reducer)\n\nReduce a tensor using a user-defined reduction operator.  See ```SumReducer```\nin TensorFunctors.h for information on how to implement a reduction operator.\n\n\n## Scan Operations\n\nA *Scan* operation returns a tensor with the same dimensions as the original\ntensor. The operation performs an inclusive scan along the specified\naxis, which means it computes a running total along the axis for a given\nreduction operation.\nIf the reduction operation corresponds to summation, then this computes the\nprefix sum of the tensor along the given axis.\n\nExample:\ndd a comment to this line\n\n    // Create a tensor of 2 dimensions\n    Eigen::Tensor<int, 2> a(2, 3);\n    a.setValues({{1, 2, 3}, {4, 5, 6}});\n    // Scan it along the second dimension (1) using summation\n    Eigen::Tensor<int, 2> b = a.cumsum(1);\n    // The result is a tensor with the same size as the input\n    cout << \"a\" << endl << a << endl << endl;\n    cout << \"b\" << endl << b << endl << endl;\n    =>\n    a\n    1 2 3\n    6 5 4\n\n    b\n    1  3  6\n    4  9 15\n\n### <Operation> cumsum(const Index& axis)\n\nPerform a scan by summing consecutive entries.\n\n### <Operation> cumprod(const Index& axis)\n\nPerform a scan by multiplying consecutive entries.\n\n\n## Convolutions\n\n### <Operation> convolve(const Kernel& kernel, const Dimensions& dims)\n\nReturns a tensor that is the output of the convolution of the input tensor with the kernel,\nalong the specified dimensions of the input tensor. The dimension size for dimensions of the output tensor\nwhich were part of the convolution will be reduced by the formula:\noutput_dim_size = input_dim_size - kernel_dim_size + 1 (requires: input_dim_size >= kernel_dim_size).\nThe dimension sizes for dimensions that were not part of the convolution will remain the same.\nPerformance of the convolution can depend on the length of the stride(s) of the input tensor dimension(s) along which the\nconvolution is computed (the first dimension has the shortest stride for ColMajor, whereas RowMajor's shortest stride is\nfor the last dimension).\n\n    // Compute convolution along the second and third dimension.\n    Tensor<float, 4, DataLayout> input(3, 3, 7, 11);\n    Tensor<float, 2, DataLayout> kernel(2, 2);\n    Tensor<float, 4, DataLayout> output(3, 2, 6, 11);\n    input.setRandom();\n    kernel.setRandom();\n\n    Eigen::array<ptrdiff_t, 2> dims({1, 2});  // Specify second and third dimension for convolution.\n    output = input.convolve(kernel, dims);\n\n    for (int i = 0; i < 3; ++i) {\n      for (int j = 0; j < 2; ++j) {\n        for (int k = 0; k < 6; ++k) {\n          for (int l = 0; l < 11; ++l) {\n            const float result = output(i,j,k,l);\n            const float expected = input(i,j+0,k+0,l) * kernel(0,0) +\n                                   input(i,j+1,k+0,l) * kernel(1,0) +\n                                   input(i,j+0,k+1,l) * kernel(0,1) +\n                                   input(i,j+1,k+1,l) * kernel(1,1);\n            VERIFY_IS_APPROX(result, expected);\n          }\n        }\n      }\n    }\n\n\n## Geometrical Operations\n\nThese operations return a Tensor with different dimensions than the original\nTensor.  They can be used to access slices of tensors, see them with different\ndimensions, or pad tensors with additional data.\n\n### <Operation> reshape(const Dimensions& new_dims)\n\nReturns a view of the input tensor that has been reshaped to the specified\nnew dimensions.  The argument new_dims is an array of Index values.  The\nrank of the resulting tensor is equal to the number of elements in new_dims.\n\nThe product of all the sizes in the new dimension array must be equal to\nthe number of elements in the input tensor.\n\n    // Increase the rank of the input tensor by introducing a new dimension\n    // of size 1.\n    Tensor<float, 2> input(7, 11);\n    array<int, 3> three_dims{{7, 11, 1}};\n    Tensor<float, 3> result = input.reshape(three_dims);\n\n    // Decrease the rank of the input tensor by merging 2 dimensions;\n    array<int, 1> one_dim{{7 * 11}};\n    Tensor<float, 1> result = input.reshape(one_dim);\n\nThis operation does not move any data in the input tensor, so the resulting\ncontents of a reshaped Tensor depend on the data layout of the original Tensor.\n\nFor example this is what happens when you ```reshape()``` a 2D ColMajor tensor\nto one dimension:\n\n    Eigen::Tensor<float, 2, Eigen::ColMajor> a(2, 3);\n    a.setValues({{0.0f, 100.0f, 200.0f}, {300.0f, 400.0f, 500.0f}});\n    Eigen::array<Eigen::DenseIndex, 1> one_dim({3 * 2});\n    Eigen::Tensor<float, 1, Eigen::ColMajor> b = a.reshape(one_dim);\n    cout << \"b\" << endl << b << endl;\n    =>\n    b\n      0\n    300\n    100\n    400\n    200\n    500\n\nThis is what happens when the 2D Tensor is RowMajor:\n\n    Eigen::Tensor<float, 2, Eigen::RowMajor> a(2, 3);\n    a.setValues({{0.0f, 100.0f, 200.0f}, {300.0f, 400.0f, 500.0f}});\n    Eigen::array<Eigen::DenseIndex, 1> one_dim({3 * 2});\n    Eigen::Tensor<float, 1, Eigen::RowMajor> b = a.reshape(one_dim);\n    cout << \"b\" << endl << b << endl;\n    =>\n    b\n      0\n    100\n    200\n    300\n    400\n    500\n\nThe reshape operation is a lvalue. In other words, it can be used on the left\nside of the assignment operator.\n\nThe previous example can be rewritten as follow:\n\n    Eigen::Tensor<float, 2, Eigen::ColMajor> a(2, 3);\n    a.setValues({{0.0f, 100.0f, 200.0f}, {300.0f, 400.0f, 500.0f}});\n    Eigen::array<Eigen::DenseIndex, 2> two_dim({2, 3});\n    Eigen::Tensor<float, 1, Eigen::ColMajor> b;\n    b.reshape(two_dim) = a;\n    cout << \"b\" << endl << b << endl;\n    =>\n    b\n      0\n    300\n    100\n    400\n    200\n    500\n\nNote that \"b\" itself was not reshaped but that instead the assignment is done to\nthe reshape view of b.\n\n\n### <Operation> shuffle(const Shuffle& shuffle)\n\nReturns a copy of the input tensor whose dimensions have been\nreordered according to the specified permutation. The argument shuffle\nis an array of Index values. Its size is the rank of the input\ntensor. It must contain a permutation of 0, 1, ..., rank - 1. The i-th\ndimension of the output tensor equals to the size of the shuffle[i]-th\ndimension of the input tensor. For example:\n\n    // Shuffle all dimensions to the left by 1.\n    Tensor<float, 3> input(20, 30, 50);\n    // ... set some values in input.\n    Tensor<float, 3> output = input.shuffle({1, 2, 0})\n\n    eigen_assert(output.dimension(0) == 30);\n    eigen_assert(output.dimension(1) == 50);\n    eigen_assert(output.dimension(2) == 20);\n\nIndices into the output tensor are shuffled accordingly to formulate\nindices into the input tensor. For example, one can assert in the above\ncode snippet that:\n\n    eigen_assert(output(3, 7, 11) == input(11, 3, 7));\n\nIn general, one can assert that\n\n    eigen_assert(output(..., indices[shuffle[i]], ...) ==\n                 input(..., indices[i], ...))\n\nThe shuffle operation results in a lvalue, which means that it can be assigned\nto. In other words, it can be used on the left side of the assignment operator.\n\nLet's rewrite the previous example to take advantage of this feature:\n\n    // Shuffle all dimensions to the left by 1.\n    Tensor<float, 3> input(20, 30, 50);\n    // ... set some values in input.\n    Tensor<float, 3> output(30, 50, 20);\n    output.shuffle({2, 0, 1}) = input;\n\n\n### <Operation> stride(const Strides& strides)\n\nReturns a view of the input tensor that strides (skips stride-1\nelements) along each of the dimensions.  The argument strides is an\narray of Index values.  The dimensions of the resulting tensor are\nceil(input_dimensions[i] / strides[i]).\n\nFor example this is what happens when you ```stride()``` a 2D tensor:\n\n    Eigen::Tensor<int, 2> a(4, 3);\n    a.setValues({{0, 100, 200}, {300, 400, 500}, {600, 700, 800}, {900, 1000, 1100}});\n    Eigen::array<Eigen::DenseIndex, 2> strides({3, 2});\n    Eigen::Tensor<int, 2> b = a.stride(strides);\n    cout << \"b\" << endl << b << endl;\n    =>\n    b\n       0   200\n     900  1100\n\nIt is possible to assign a tensor to a stride:\n    Tensor<float, 3> input(20, 30, 50);\n    // ... set some values in input.\n    Tensor<float, 3> output(40, 90, 200);\n    output.stride({2, 3, 4}) = input;\n\n\n### <Operation> slice(const StartIndices& offsets, const Sizes& extents)\n\nReturns a sub-tensor of the given tensor. For each dimension i, the slice is\nmade of the coefficients stored between offset[i] and offset[i] + extents[i] in\nthe input tensor.\n\n    Eigen::Tensor<int, 2> a(4, 3);\n    a.setValues({{0, 100, 200}, {300, 400, 500},\n                 {600, 700, 800}, {900, 1000, 1100}});\n    Eigen::array<int, 2> offsets = {1, 0};\n    Eigen::array<int, 2> extents = {2, 2};\n    Eigen::Tensor<int, 1> slice = a.slice(offsets, extents);\n    cout << \"a\" << endl << a << endl;\n    =>\n    a\n       0   100   200\n     300   400   500\n     600   700   800\n     900  1000  1100\n    cout << \"slice\" << endl << slice << endl;\n    =>\n    slice\n     300   400\n     600   700\n\n\n### <Operation> chip(const Index offset, const Index dim)\n\nA chip is a special kind of slice. It is the subtensor at the given offset in\nthe dimension dim. The returned tensor has one fewer dimension than the input\ntensor: the dimension dim is removed.\n\nFor example, a matrix chip would be either a row or a column of the input\nmatrix.\n\n    Eigen::Tensor<int, 2> a(4, 3);\n    a.setValues({{0, 100, 200}, {300, 400, 500},\n                 {600, 700, 800}, {900, 1000, 1100}});\n    Eigen::Tensor<int, 1> row_3 = a.chip(2, 0);\n    Eigen::Tensor<int, 1> col_2 = a.chip(1, 1);\n    cout << \"a\" << endl << a << endl;\n    =>\n    a\n       0   100   200\n     300   400   500\n     600   700   800\n     900  1000  1100\n    cout << \"row_3\" << endl << row_3 << endl;\n    =>\n    row_3\n       600   700   800\n    cout << \"col_2\" << endl << col_2 << endl;\n    =>\n    col_2\n       100   400   700    1000\n\nIt is possible to assign values to a tensor chip since the chip operation is a\nlvalue. For example:\n\n    Eigen::Tensor<int, 1> a(3);\n    a.setValues({{100, 200, 300}});\n    Eigen::Tensor<int, 2> b(2, 3);\n    b.setZero();\n    b.chip(0, 0) = a;\n    cout << \"a\" << endl << a << endl;\n    =>\n    a\n     100\n     200\n     300\n    cout << \"b\" << endl << b << endl;\n    =>\n    b\n       100   200   300\n         0     0     0\n\n\n### <Operation> reverse(const ReverseDimensions& reverse)\n\nReturns a view of the input tensor that reverses the order of the coefficients\nalong a subset of the dimensions.  The argument reverse is an array of boolean\nvalues that indicates whether or not the order of the coefficients should be\nreversed along each of the dimensions.  This operation preserves the dimensions\nof the input tensor.\n\nFor example this is what happens when you ```reverse()``` the first dimension\nof a 2D tensor:\n\n    Eigen::Tensor<int, 2> a(4, 3);\n    a.setValues({{0, 100, 200}, {300, 400, 500},\n                {600, 700, 800}, {900, 1000, 1100}});\n    Eigen::array<bool, 2> reverse({true, false});\n    Eigen::Tensor<int, 2> b = a.reverse(reverse);\n    cout << \"a\" << endl << a << endl << \"b\" << endl << b << endl;\n    =>\n    a\n       0   100   200\n     300   400   500\n     600   700   800\n     900  1000  1100\n    b\n     900  1000  1100\n     600   700   800\n     300   400   500\n       0   100   200\n\n\n### <Operation> broadcast(const Broadcast& broadcast)\n\nReturns a view of the input tensor in which the input is replicated one to many\ntimes.\nThe broadcast argument specifies how many copies of the input tensor need to be\nmade in each of the dimensions.\n\n    Eigen::Tensor<int, 2> a(2, 3);\n    a.setValues({{0, 100, 200}, {300, 400, 500}});\n    Eigen::array<int, 2> bcast({3, 2});\n    Eigen::Tensor<int, 2> b = a.broadcast(bcast);\n    cout << \"a\" << endl << a << endl << \"b\" << endl << b << endl;\n    =>\n    a\n       0   100   200\n     300   400   500\n    b\n       0   100   200    0   100   200\n     300   400   500  300   400   500\n       0   100   200    0   100   200\n     300   400   500  300   400   500\n       0   100   200    0   100   200\n     300   400   500  300   400   500\n\n### <Operation> concatenate(const OtherDerived& other, Axis axis)\n\nTODO\n\n### <Operation>  pad(const PaddingDimensions& padding)\n\nReturns a view of the input tensor in which the input is padded with zeros.\n\n    Eigen::Tensor<int, 2> a(2, 3);\n    a.setValues({{0, 100, 200}, {300, 400, 500}});\n    Eigen::array<pair<int, int>, 2> paddings;\n    paddings[0] = make_pair(0, 1);\n    paddings[1] = make_pair(2, 3);\n    Eigen::Tensor<int, 2> b = a.pad(paddings);\n    cout << \"a\" << endl << a << endl << \"b\" << endl << b << endl;\n    =>\n    a\n       0   100   200\n     300   400   500\n    b\n       0     0     0    0\n       0     0     0    0\n       0   100   200    0\n     300   400   500    0\n       0     0     0    0\n       0     0     0    0\n       0     0     0    0\n\n\n### <Operation>  extract_patches(const PatchDims& patch_dims)\n\nReturns a tensor of coefficient patches extracted from the input tensor, where\neach patch is of dimension specified by 'patch_dims'. The returned tensor has\none greater dimension than the input tensor, which is used to index each patch.\nThe patch index in the output tensor depends on the data layout of the input\ntensor: the patch index is the last dimension ColMajor layout, and the first\ndimension in RowMajor layout.\n\nFor example, given the following input tensor:\n\n  Eigen::Tensor<float, 2, DataLayout> tensor(3,4);\n  tensor.setValues({{0.0f, 1.0f, 2.0f, 3.0f},\n                    {4.0f, 5.0f, 6.0f, 7.0f},\n                    {8.0f, 9.0f, 10.0f, 11.0f}});\n\n  cout << \"tensor: \" << endl << tensor << endl;\n=>\ntensor:\n 0   1   2   3\n 4   5   6   7\n 8   9  10  11\n\nSix 2x2 patches can be extracted and indexed using the following code:\n\n  Eigen::Tensor<float, 3, DataLayout> patch;\n  Eigen::array<ptrdiff_t, 2> patch_dims;\n  patch_dims[0] = 2;\n  patch_dims[1] = 2;\n  patch = tensor.extract_patches(patch_dims);\n  for (int k = 0; k < 6; ++k) {\n    cout << \"patch index: \" << k << endl;\n    for (int i = 0; i < 2; ++i) {\n      for (int j = 0; j < 2; ++j) {\n        if (DataLayout == ColMajor) {\n          cout << patch(i, j, k) << \" \";\n        } else {\n          cout << patch(k, i, j) << \" \";\n        }\n      }\n      cout << endl;\n    }\n  }\n\nThis code results in the following output when the data layout is ColMajor:\n\npatch index: 0\n0 1\n4 5\npatch index: 1\n4 5\n8 9\npatch index: 2\n1 2\n5 6\npatch index: 3\n5 6\n9 10\npatch index: 4\n2 3\n6 7\npatch index: 5\n6 7\n10 11\n\nThis code results in the following output when the data layout is RowMajor:\n(NOTE: the set of patches is the same as in ColMajor, but are indexed differently).\n\npatch index: 0\n0 1\n4 5\npatch index: 1\n1 2\n5 6\npatch index: 2\n2 3\n6 7\npatch index: 3\n4 5\n8 9\npatch index: 4\n5 6\n9 10\npatch index: 5\n6 7\n10 11\n\n### <Operation>  extract_image_patches(const Index patch_rows, const Index patch_cols,\n                          const Index row_stride, const Index col_stride,\n                          const PaddingType padding_type)\n\nReturns a tensor of coefficient image patches extracted from the input tensor,\nwhich is expected to have dimensions ordered as follows (depending on the data\nlayout of the input tensor, and the number of additional dimensions 'N'):\n\n*) ColMajor\n1st dimension: channels (of size d)\n2nd dimension: rows (of size r)\n3rd dimension: columns (of size c)\n4th-Nth dimension: time (for video) or batch (for bulk processing).\n\n*) RowMajor (reverse order of ColMajor)\n1st-Nth dimension: time (for video) or batch (for bulk processing).\nN+1'th dimension: columns (of size c)\nN+2'th dimension: rows (of size r)\nN+3'th dimension: channels (of size d)\n\nThe returned tensor has one greater dimension than the input tensor, which is\nused to index each patch. The patch index in the output tensor depends on the\ndata layout of the input tensor: the patch index is the 4'th dimension in\nColMajor layout, and the 4'th from the last dimension in RowMajor layout.\n\nFor example, given the following input tensor with the following dimension\nsizes:\n *) depth:   2\n *) rows:    3\n *) columns: 5\n *) batch:   7\n\n  Tensor<float, 4> tensor(2,3,5,7);\n  Tensor<float, 4, RowMajor> tensor_row_major = tensor.swap_layout();\n\n2x2 image patches can be extracted and indexed using the following code:\n\n*) 2D patch: ColMajor (patch indexed by second-to-last dimension)\n  Tensor<float, 5> twod_patch;\n  twod_patch = tensor.extract_image_patches<2, 2>();\n  // twod_patch.dimension(0) == 2\n  // twod_patch.dimension(1) == 2\n  // twod_patch.dimension(2) == 2\n  // twod_patch.dimension(3) == 3*5\n  // twod_patch.dimension(4) == 7\n\n*) 2D patch: RowMajor (patch indexed by the second dimension)\n  Tensor<float, 5, RowMajor> twod_patch_row_major;\n  twod_patch_row_major = tensor_row_major.extract_image_patches<2, 2>();\n  // twod_patch_row_major.dimension(0) == 7\n  // twod_patch_row_major.dimension(1) == 3*5\n  // twod_patch_row_major.dimension(2) == 2\n  // twod_patch_row_major.dimension(3) == 2\n  // twod_patch_row_major.dimension(4) == 2\n\n## Special Operations\n\n### <Operation> cast<T>()\n\nReturns a tensor of type T with the same dimensions as the original tensor.\nThe returned tensor contains the values of the original tensor converted to\ntype T.\n\n    Eigen::Tensor<float, 2> a(2, 3);\n    Eigen::Tensor<int, 2> b = a.cast<int>();\n\nThis can be useful for example if you need to do element-wise division of\nTensors of integers.  This is not currently supported by the Tensor library\nbut you can easily cast the tensors to floats to do the division:\n\n    Eigen::Tensor<int, 2> a(2, 3);\n    a.setValues({{0, 1, 2}, {3, 4, 5}});\n    Eigen::Tensor<int, 2> b =\n        (a.cast<float>() / a.constant(2).cast<float>()).cast<int>();\n    cout << \"a\" << endl << a << endl << endl;\n    cout << \"b\" << endl << b << endl << endl;\n    =>\n    a\n    0 1 2\n    3 4 5\n\n    b\n    0 0 1\n    1 2 2\n\n\n### <Operation>     eval()\n\nTODO\n\n\n## Representation of scalar values\n\nScalar values are often represented by tensors of size 1 and rank 1. It would be\nmore logical and user friendly to use tensors of rank 0 instead. For example\nTensor<T, N>::maximum() currently returns a Tensor<T, 1>. Similarly, the inner\nproduct of 2 1d tensors (through contractions) returns a 1d tensor. In the\nfuture these operations might be updated to return 0d tensors instead.\n\n## Limitations\n\n*   The number of tensor dimensions is currently limited to 250 when using a\n    compiler that supports cxx11. It is limited to only 5 for older compilers.\n*   The IndexList class requires a cxx11 compliant compiler. You can use an\n    array of indices instead if you don't have access to a modern compiler.\n*   On GPUs only floating point values are properly tested and optimized for.\n*   Complex and integer values are known to be broken on GPUs. If you try to use\n    them you'll most likely end up triggering a static assertion failure such as\n    EIGEN_STATIC_ASSERT(packetSize > 1, YOU_MADE_A_PROGRAMMING_MISTAKE)\n\n\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/Tensor.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n// Copyright (C) 2013 Christian Seiler <christian@iwakd.de>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_H\n#define EIGEN_CXX11_TENSOR_TENSOR_H\n\nnamespace Eigen {\n\n/** \\class Tensor\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief The tensor class.\n  *\n  * The %Tensor class is the work-horse for all \\em dense tensors within Eigen.\n  *\n  * The %Tensor class encompasses only dynamic-size objects so far.\n  *\n  * The first two template parameters are required:\n  * \\tparam Scalar_ \\anchor tensor_tparam_scalar Numeric type, e.g. float, double, int or std::complex<float>.\n  *                 User defined scalar types are supported as well (see \\ref user_defined_scalars \"here\").\n  * \\tparam NumIndices_ Number of indices (i.e. rank of the tensor)\n  *\n  * The remaining template parameters are optional -- in most cases you don't have to worry about them.\n  * \\tparam Options_ \\anchor tensor_tparam_options A combination of either \\b #RowMajor or \\b #ColMajor, and of either\n  *                 \\b #AutoAlign or \\b #DontAlign.\n  *                 The former controls \\ref TopicStorageOrders \"storage order\", and defaults to column-major. The latter controls alignment, which is required\n  *                 for vectorization. It defaults to aligning tensors. Note that tensors currently do not support any operations that profit from vectorization.\n  *                 Support for such operations (i.e. adding two tensors etc.) is planned.\n  *\n  * You can access elements of tensors using normal subscripting:\n  *\n  * \\code\n  * Eigen::Tensor<double, 4> t(10, 10, 10, 10);\n  * t(0, 1, 2, 3) = 42.0;\n  * \\endcode\n  *\n  * This class can be extended with the help of the plugin mechanism described on the page\n  * \\ref TopicCustomizingEigen by defining the preprocessor symbol \\c EIGEN_TENSOR_PLUGIN.\n  *\n  * <i><b>Some notes:</b></i>\n  *\n  * <dl>\n  * <dt><b>Relation to other parts of Eigen:</b></dt>\n  * <dd>The midterm developement goal for this class is to have a similar hierarchy as Eigen uses for matrices, so that\n  * taking blocks or using tensors in expressions is easily possible, including an interface with the vector/matrix code\n  * by providing .asMatrix() and .asVector() (or similar) methods for rank 2 and 1 tensors. However, currently, the %Tensor\n  * class does not provide any of these features and is only available as a stand-alone class that just allows for\n  * coefficient access. Also, when fixed-size tensors are implemented, the number of template arguments is likely to\n  * change dramatically.</dd>\n  * </dl>\n  *\n  * \\ref TopicStorageOrders\n  */\n\ntemplate<typename Scalar_, int NumIndices_, int Options_, typename IndexType_>\nclass Tensor : public TensorBase<Tensor<Scalar_, NumIndices_, Options_, IndexType_> >\n{\n  public:\n    typedef Tensor<Scalar_, NumIndices_, Options_, IndexType_> Self;\n    typedef TensorBase<Tensor<Scalar_, NumIndices_, Options_, IndexType_> > Base;\n    typedef typename Eigen::internal::nested<Self>::type Nested;\n    typedef typename internal::traits<Self>::StorageKind StorageKind;\n    typedef typename internal::traits<Self>::Index Index;\n    typedef Scalar_ Scalar;\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n    typedef typename Base::CoeffReturnType CoeffReturnType;\n\n    enum {\n      IsAligned = bool(EIGEN_MAX_ALIGN_BYTES>0) & !(Options_&DontAlign),\n      Layout = Options_ & RowMajor ? RowMajor : ColMajor,\n      CoordAccess = true,\n      RawAccess = true\n    };\n\n    static const int Options = Options_;\n    static const int NumIndices = NumIndices_;\n    typedef DSizes<Index, NumIndices_> Dimensions;\n\n  protected:\n    TensorStorage<Scalar, Dimensions, Options> m_storage;\n\n#ifdef EIGEN_HAS_SFINAE\n    template<typename CustomIndices>\n    struct isOfNormalIndex{\n      static const bool is_array = internal::is_base_of<array<Index, NumIndices>, CustomIndices>::value;\n      static const bool is_int = NumTraits<CustomIndices>::IsInteger;\n      static const bool value = is_array | is_int;\n    };\n#endif\n\n  public:\n    // Metadata\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index                         rank()                   const { return NumIndices; }\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index                         dimension(std::size_t n) const { return m_storage.dimensions()[n]; }\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions&             dimensions()             const { return m_storage.dimensions(); }\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index                         size()                   const { return m_storage.size(); }\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar                        *data()                        { return m_storage.data(); }\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar                  *data()                  const { return m_storage.data(); }\n\n    // This makes EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED\n    // work, because that uses base().coeffRef() - and we don't yet\n    // implement a similar class hierarchy\n    inline Self& base()             { return *this; }\n    inline const Self& base() const { return *this; }\n\n#if EIGEN_HAS_VARIADIC_TEMPLATES\n    template<typename... IndexTypes>\n    EIGEN_DEVICE_FUNC inline const Scalar& coeff(Index firstIndex, Index secondIndex, IndexTypes... otherIndices) const\n    {\n      // The number of indices used to access a tensor coefficient must be equal to the rank of the tensor.\n      EIGEN_STATIC_ASSERT(sizeof...(otherIndices) + 2 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)\n      return coeff(array<Index, NumIndices>{{firstIndex, secondIndex, otherIndices...}});\n    }\n#endif\n\n    // normal indices\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& coeff(const array<Index, NumIndices>& indices) const\n    {\n      eigen_internal_assert(checkIndexRange(indices));\n      return m_storage.data()[linearizedIndex(indices)];\n    }\n\n    // custom indices\n#ifdef EIGEN_HAS_SFINAE\n    template<typename CustomIndices,\n             EIGEN_SFINAE_ENABLE_IF( !(isOfNormalIndex<CustomIndices>::value) )\n    >\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& coeff(CustomIndices& indices) const\n    {\n        return coeff(internal::customIndices2Array<Index,NumIndices>(indices));\n    }\n#endif\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& coeff() const\n    {\n      EIGEN_STATIC_ASSERT(NumIndices == 0, YOU_MADE_A_PROGRAMMING_MISTAKE);\n      return m_storage.data()[0];\n    }\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& coeff(Index index) const\n    {\n      eigen_internal_assert(index >= 0 && index < size());\n      return m_storage.data()[index];\n    }\n\n#if EIGEN_HAS_VARIADIC_TEMPLATES\n    template<typename... IndexTypes>\n    inline Scalar& coeffRef(Index firstIndex, Index secondIndex, IndexTypes... otherIndices)\n    {\n      // The number of indices used to access a tensor coefficient must be equal to the rank of the tensor.\n      EIGEN_STATIC_ASSERT(sizeof...(otherIndices) + 2 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)\n      return coeffRef(array<Index, NumIndices>{{firstIndex, secondIndex, otherIndices...}});\n    }\n#endif\n\n    // normal indices\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(const array<Index, NumIndices>& indices)\n    {\n      eigen_internal_assert(checkIndexRange(indices));\n      return m_storage.data()[linearizedIndex(indices)];\n    }\n\n    // custom indices\n#ifdef EIGEN_HAS_SFINAE\n    template<typename CustomIndices,\n             EIGEN_SFINAE_ENABLE_IF( !(isOfNormalIndex<CustomIndices>::value) )\n             >\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(CustomIndices& indices)\n    {\n        return coeffRef(internal::customIndices2Array<Index,NumIndices>(indices));\n    }\n#endif\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef()\n    {\n      EIGEN_STATIC_ASSERT(NumIndices == 0, YOU_MADE_A_PROGRAMMING_MISTAKE);\n      return m_storage.data()[0];\n    }\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index index)\n    {\n      eigen_internal_assert(index >= 0 && index < size());\n      return m_storage.data()[index];\n    }\n\n#if EIGEN_HAS_VARIADIC_TEMPLATES\n    template<typename... IndexTypes>\n    inline const Scalar& operator()(Index firstIndex, Index secondIndex, IndexTypes... otherIndices) const\n    {\n      // The number of indices used to access a tensor coefficient must be equal to the rank of the tensor.\n      EIGEN_STATIC_ASSERT(sizeof...(otherIndices) + 2 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)\n      return this->operator()(array<Index, NumIndices>{{firstIndex, secondIndex, otherIndices...}});\n    }\n#else\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar& operator()(Index i0, Index i1) const\n    {\n      return coeff(array<Index, 2>(i0, i1));\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar& operator()(Index i0, Index i1, Index i2) const\n    {\n      return coeff(array<Index, 3>(i0, i1, i2));\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar& operator()(Index i0, Index i1, Index i2, Index i3) const\n    {\n      return coeff(array<Index, 4>(i0, i1, i2, i3));\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar& operator()(Index i0, Index i1, Index i2, Index i3, Index i4) const\n    {\n      return coeff(array<Index, 5>(i0, i1, i2, i3, i4));\n    }\n#endif\n\n    // custom indices\n#ifdef EIGEN_HAS_SFINAE\n    template<typename CustomIndices,\n             EIGEN_SFINAE_ENABLE_IF( !(isOfNormalIndex<CustomIndices>::value) )\n    >\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& operator()(CustomIndices& indices) const\n    {\n        return coeff(internal::customIndices2Array<Index,NumIndices>(indices));\n    }\n#endif\n\n    // normal indices\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& operator()(const array<Index, NumIndices>& indices) const\n    {\n      return coeff(indices);\n    }\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& operator()(Index index) const\n    {\n      eigen_internal_assert(index >= 0 && index < size());\n      return coeff(index);\n    }\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& operator()() const\n    {\n      EIGEN_STATIC_ASSERT(NumIndices == 0, YOU_MADE_A_PROGRAMMING_MISTAKE);\n      return coeff();\n    }\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& operator[](Index index) const\n    {\n      // The bracket operator is only for vectors, use the parenthesis operator instead.\n      EIGEN_STATIC_ASSERT(NumIndices == 1, YOU_MADE_A_PROGRAMMING_MISTAKE);\n      return coeff(index);\n    }\n\n#if EIGEN_HAS_VARIADIC_TEMPLATES\n    template<typename... IndexTypes>\n    inline Scalar& operator()(Index firstIndex, Index secondIndex, IndexTypes... otherIndices)\n    {\n      // The number of indices used to access a tensor coefficient must be equal to the rank of the tensor.\n      EIGEN_STATIC_ASSERT(sizeof...(otherIndices) + 2 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)\n      return operator()(array<Index, NumIndices>{{firstIndex, secondIndex, otherIndices...}});\n    }\n#else\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar& operator()(Index i0, Index i1)\n    {\n      return coeffRef(array<Index, 2>(i0, i1));\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar& operator()(Index i0, Index i1, Index i2)\n    {\n      return coeffRef(array<Index, 3>(i0, i1, i2));\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar& operator()(Index i0, Index i1, Index i2, Index i3)\n    {\n      return coeffRef(array<Index, 4>(i0, i1, i2, i3));\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar& operator()(Index i0, Index i1, Index i2, Index i3, Index i4)\n    {\n      return coeffRef(array<Index, 5>(i0, i1, i2, i3, i4));\n    }\n#endif\n\n    // normal indices\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& operator()(const array<Index, NumIndices>& indices)\n    {\n      return coeffRef(indices);\n    }\n\n    // custom indices\n#ifdef EIGEN_HAS_SFINAE\n    template<typename CustomIndices,\n             EIGEN_SFINAE_ENABLE_IF( !(isOfNormalIndex<CustomIndices>::value) )\n    >\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& operator()(CustomIndices& indices)\n    {\n      return coeffRef(internal::customIndices2Array<Index,NumIndices>(indices));\n    }\n#endif\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& operator()(Index index)\n    {\n      eigen_assert(index >= 0 && index < size());\n      return coeffRef(index);\n    }\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& operator()()\n    {\n      EIGEN_STATIC_ASSERT(NumIndices == 0, YOU_MADE_A_PROGRAMMING_MISTAKE);\n      return coeffRef();\n    }\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& operator[](Index index)\n    {\n      // The bracket operator is only for vectors, use the parenthesis operator instead\n      EIGEN_STATIC_ASSERT(NumIndices == 1, YOU_MADE_A_PROGRAMMING_MISTAKE)\n      return coeffRef(index);\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Tensor()\n      : m_storage()\n    {\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Tensor(const Self& other)\n      : m_storage(other.m_storage)\n    {\n    }\n\n#if EIGEN_HAS_VARIADIC_TEMPLATES\n    template<typename... IndexTypes>\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Tensor(Index firstDimension, IndexTypes... otherDimensions)\n        : m_storage(firstDimension, otherDimensions...)\n    {\n      // The number of dimensions used to construct a tensor must be equal to the rank of the tensor.\n      EIGEN_STATIC_ASSERT(sizeof...(otherDimensions) + 1 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)\n    }\n#else\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit Tensor(Index dim1)\n      : m_storage(dim1, array<Index, 1>(dim1))\n    {\n      EIGEN_STATIC_ASSERT(1 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)\n    }\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Tensor(Index dim1, Index dim2)\n      : m_storage(dim1*dim2, array<Index, 2>(dim1, dim2))\n    {\n      EIGEN_STATIC_ASSERT(2 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)\n    }\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Tensor(Index dim1, Index dim2, Index dim3)\n      : m_storage(dim1*dim2*dim3, array<Index, 3>(dim1, dim2, dim3))\n    {\n      EIGEN_STATIC_ASSERT(3 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)\n    }\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Tensor(Index dim1, Index dim2, Index dim3, Index dim4)\n      : m_storage(dim1*dim2*dim3*dim4, array<Index, 4>(dim1, dim2, dim3, dim4))\n    {\n      EIGEN_STATIC_ASSERT(4 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)\n    }\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Tensor(Index dim1, Index dim2, Index dim3, Index dim4, Index dim5)\n      : m_storage(dim1*dim2*dim3*dim4*dim5, array<Index, 5>(dim1, dim2, dim3, dim4, dim5))\n    {\n      EIGEN_STATIC_ASSERT(5 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)\n    }\n#endif\n\n    /** Normal Dimension */\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit Tensor(const array<Index, NumIndices>& dimensions)\n        : m_storage(internal::array_prod(dimensions), dimensions)\n    {\n      EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED\n    }\n\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Tensor(const TensorBase<OtherDerived, ReadOnlyAccessors>& other)\n    {\n      typedef TensorAssignOp<Tensor, const OtherDerived> Assign;\n      Assign assign(*this, other.derived());\n      resize(TensorEvaluator<const Assign, DefaultDevice>(assign, DefaultDevice()).dimensions());\n      internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());\n    }\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Tensor(const TensorBase<OtherDerived, WriteAccessors>& other)\n    {\n      typedef TensorAssignOp<Tensor, const OtherDerived> Assign;\n      Assign assign(*this, other.derived());\n      resize(TensorEvaluator<const Assign, DefaultDevice>(assign, DefaultDevice()).dimensions());\n      internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Tensor& operator=(const Tensor& other)\n    {\n      typedef TensorAssignOp<Tensor, const Tensor> Assign;\n      Assign assign(*this, other);\n      resize(TensorEvaluator<const Assign, DefaultDevice>(assign, DefaultDevice()).dimensions());\n      internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());\n      return *this;\n    }\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Tensor& operator=(const OtherDerived& other)\n    {\n      typedef TensorAssignOp<Tensor, const OtherDerived> Assign;\n      Assign assign(*this, other);\n      resize(TensorEvaluator<const Assign, DefaultDevice>(assign, DefaultDevice()).dimensions());\n      internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());\n      return *this;\n    }\n\n#if EIGEN_HAS_VARIADIC_TEMPLATES\n    template<typename... IndexTypes> EIGEN_DEVICE_FUNC\n    void resize(Index firstDimension, IndexTypes... otherDimensions)\n    {\n      // The number of dimensions used to resize a tensor must be equal to the rank of the tensor.\n      EIGEN_STATIC_ASSERT(sizeof...(otherDimensions) + 1 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)\n      resize(array<Index, NumIndices>{{firstDimension, otherDimensions...}});\n    }\n#endif\n\n    /** Normal Dimension */\n    EIGEN_DEVICE_FUNC void resize(const array<Index, NumIndices>& dimensions)\n    {\n      int i;\n      Index size = Index(1);\n      for (i = 0; i < NumIndices; i++) {\n        internal::check_rows_cols_for_overflow<Dynamic>::run(size, dimensions[i]);\n        size *= dimensions[i];\n      }\n      #ifdef EIGEN_INITIALIZE_COEFFS\n        bool size_changed = size != this->size();\n        m_storage.resize(size, dimensions);\n        if(size_changed) EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED\n      #else\n        m_storage.resize(size, dimensions);\n      #endif\n    }\n\n    // Why this overload, DSizes is derived from array ??? //\n    EIGEN_DEVICE_FUNC void resize(const DSizes<Index, NumIndices>& dimensions) {\n      array<Index, NumIndices> dims;\n      for (int i = 0; i < NumIndices; ++i) {\n        dims[i] = dimensions[i];\n      }\n      resize(dims);\n    }\n\n    EIGEN_DEVICE_FUNC\n    void resize()\n    {\n      EIGEN_STATIC_ASSERT(NumIndices == 0, YOU_MADE_A_PROGRAMMING_MISTAKE);\n      // Nothing to do: rank 0 tensors have fixed size\n    }\n\n    /** Custom Dimension */\n#ifdef EIGEN_HAS_SFINAE\n    template<typename CustomDimension,\n             EIGEN_SFINAE_ENABLE_IF( !(isOfNormalIndex<CustomDimension>::value) )\n    >\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void resize(CustomDimension& dimensions)\n    {\n      resize(internal::customIndices2Array<Index,NumIndices>(dimensions));\n    }\n#endif\n\n#ifndef EIGEN_EMULATE_CXX11_META_H\n    template <typename std::ptrdiff_t... Indices>\n    EIGEN_DEVICE_FUNC\n    void resize(const Sizes<Indices...>& dimensions) {\n      array<Index, NumIndices> dims;\n      for (int i = 0; i < NumIndices; ++i) {\n        dims[i] = static_cast<Index>(dimensions[i]);\n      }\n      resize(dims);\n    }\n#else\n    template <std::size_t V1, std::size_t V2, std::size_t V3, std::size_t V4, std::size_t V5>\n    EIGEN_DEVICE_FUNC\n    void resize(const Sizes<V1, V2, V3, V4, V5>& dimensions) {\n      array<Index, NumIndices> dims;\n      for (int i = 0; i < NumIndices; ++i) {\n        dims[i] = static_cast<Index>(dimensions[i]);\n      }\n      resize(dims);\n    }\n#endif\n\n  protected:\n\n    bool checkIndexRange(const array<Index, NumIndices>& indices) const\n    {\n      using internal::array_apply_and_reduce;\n      using internal::array_zip_and_reduce;\n      using internal::greater_equal_zero_op;\n      using internal::logical_and_op;\n      using internal::lesser_op;\n\n      return\n        // check whether the indices are all >= 0\n        array_apply_and_reduce<logical_and_op, greater_equal_zero_op>(indices) &&\n        // check whether the indices fit in the dimensions\n        array_zip_and_reduce<logical_and_op, lesser_op>(indices, m_storage.dimensions());\n    }\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index linearizedIndex(const array<Index, NumIndices>& indices) const\n    {\n      if (Options&RowMajor) {\n        return m_storage.dimensions().IndexOfRowMajor(indices);\n      } else {\n        return m_storage.dimensions().IndexOfColMajor(indices);\n      }\n    }\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorArgMax.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Eugene Brevdo <ebrevdo@gmail.com>\n//                    Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_ARG_MAX_H\n#define EIGEN_CXX11_TENSOR_TENSOR_ARG_MAX_H\n\nnamespace Eigen {\nnamespace internal {\n\n/** \\class TensorIndexTuple\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief Tensor + Index Tuple class.\n  *\n  *\n  */\ntemplate<typename XprType>\nstruct traits<TensorIndexTupleOp<XprType> > : public traits<XprType>\n{\n  typedef traits<XprType> XprTraits;\n  typedef typename XprTraits::StorageKind StorageKind;\n  typedef typename XprTraits::Index Index;\n  typedef Tuple<Index, typename XprTraits::Scalar> Scalar;\n  typedef typename XprType::Nested Nested;\n  typedef typename remove_reference<Nested>::type _Nested;\n  static const int NumDimensions = XprTraits::NumDimensions;\n  static const int Layout = XprTraits::Layout;\n};\n\ntemplate<typename XprType>\nstruct eval<TensorIndexTupleOp<XprType>, Eigen::Dense>\n{\n  typedef const TensorIndexTupleOp<XprType>& type;\n};\n\ntemplate<typename XprType>\nstruct nested<TensorIndexTupleOp<XprType>, 1,\n              typename eval<TensorIndexTupleOp<XprType> >::type>\n{\n  typedef TensorIndexTupleOp<XprType> type;\n};\n\n}  // end namespace internal\n\ntemplate<typename XprType>\nclass TensorIndexTupleOp : public TensorBase<TensorIndexTupleOp<XprType>, ReadOnlyAccessors>\n{\n  public:\n  typedef typename Eigen::internal::traits<TensorIndexTupleOp>::Scalar Scalar;\n  typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;\n  typedef typename Eigen::internal::nested<TensorIndexTupleOp>::type Nested;\n  typedef typename Eigen::internal::traits<TensorIndexTupleOp>::StorageKind StorageKind;\n  typedef typename Eigen::internal::traits<TensorIndexTupleOp>::Index Index;\n  typedef Tuple<Index, typename XprType::CoeffReturnType> CoeffReturnType;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorIndexTupleOp(const XprType& expr)\n      : m_xpr(expr) {}\n\n  EIGEN_DEVICE_FUNC\n  const typename internal::remove_all<typename XprType::Nested>::type&\n  expression() const { return m_xpr; }\n\n  protected:\n    typename XprType::Nested m_xpr;\n};\n\n// Eval as rvalue\ntemplate<typename ArgType, typename Device>\nstruct TensorEvaluator<const TensorIndexTupleOp<ArgType>, Device>\n{\n  typedef TensorIndexTupleOp<ArgType> XprType;\n  typedef typename XprType::Index Index;\n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n\n  typedef typename TensorEvaluator<ArgType, Device>::Dimensions Dimensions;\n  static const int NumDims = internal::array_size<Dimensions>::value;\n\n  enum {\n    IsAligned = /*TensorEvaluator<ArgType, Device>::IsAligned*/ false,\n    PacketAccess = /*TensorEvaluator<ArgType, Device>::PacketAccess*/ false,\n    BlockAccess = false,\n    Layout = TensorEvaluator<ArgType, Device>::Layout,\n    CoordAccess = false,  // to be implemented\n    RawAccess = false\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)\n      : m_impl(op.expression(), device) { }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const {\n    return m_impl.dimensions();\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(Scalar* /*data*/) {\n    m_impl.evalSubExprsIfNeeded(NULL);\n    return true;\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {\n    m_impl.cleanup();\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const\n  {\n    return CoeffReturnType(index, m_impl.coeff(index));\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost\n  costPerCoeff(bool vectorized) const {\n    return m_impl.costPerCoeff(vectorized) + TensorOpCost(0, 0, 1);\n  }\n\n  EIGEN_DEVICE_FUNC Scalar* data() const { return NULL; }\n\n protected:\n  TensorEvaluator<ArgType, Device> m_impl;\n};\n\nnamespace internal {\n\n/** \\class TensorTupleIndex\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief Converts to Tensor<Tuple<Index, Scalar> > and reduces to Tensor<Index>.\n  *\n  */\ntemplate<typename ReduceOp, typename Dims, typename XprType>\nstruct traits<TensorTupleReducerOp<ReduceOp, Dims, XprType> > : public traits<XprType>\n{\n  typedef traits<XprType> XprTraits;\n  typedef typename XprTraits::StorageKind StorageKind;\n  typedef typename XprTraits::Index Index;\n  typedef Index Scalar;\n  typedef typename XprType::Nested Nested;\n  typedef typename remove_reference<Nested>::type _Nested;\n  static const int NumDimensions = XprTraits::NumDimensions - array_size<Dims>::value;\n  static const int Layout = XprTraits::Layout;\n};\n\ntemplate<typename ReduceOp, typename Dims, typename XprType>\nstruct eval<TensorTupleReducerOp<ReduceOp, Dims, XprType>, Eigen::Dense>\n{\n  typedef const TensorTupleReducerOp<ReduceOp, Dims, XprType>& type;\n};\n\ntemplate<typename ReduceOp, typename Dims, typename XprType>\nstruct nested<TensorTupleReducerOp<ReduceOp, Dims, XprType>, 1,\n              typename eval<TensorTupleReducerOp<ReduceOp, Dims, XprType> >::type>\n{\n  typedef TensorTupleReducerOp<ReduceOp, Dims, XprType> type;\n};\n\n}  // end namespace internal\n\ntemplate<typename ReduceOp, typename Dims, typename XprType>\nclass TensorTupleReducerOp : public TensorBase<TensorTupleReducerOp<ReduceOp, Dims, XprType>, ReadOnlyAccessors>\n{\n  public:\n  typedef typename Eigen::internal::traits<TensorTupleReducerOp>::Scalar Scalar;\n  typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;\n  typedef typename Eigen::internal::nested<TensorTupleReducerOp>::type Nested;\n  typedef typename Eigen::internal::traits<TensorTupleReducerOp>::StorageKind StorageKind;\n  typedef typename Eigen::internal::traits<TensorTupleReducerOp>::Index Index;\n  typedef Index CoeffReturnType;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorTupleReducerOp(const XprType& expr,\n                                                          const ReduceOp& reduce_op,\n                                                          const int return_dim,\n                                                          const Dims& reduce_dims)\n      : m_xpr(expr), m_reduce_op(reduce_op), m_return_dim(return_dim), m_reduce_dims(reduce_dims) {}\n\n  EIGEN_DEVICE_FUNC\n  const typename internal::remove_all<typename XprType::Nested>::type&\n  expression() const { return m_xpr; }\n\n  EIGEN_DEVICE_FUNC\n  const ReduceOp& reduce_op() const { return m_reduce_op; }\n\n  EIGEN_DEVICE_FUNC\n  const Dims& reduce_dims() const { return m_reduce_dims; }\n\n  EIGEN_DEVICE_FUNC\n  int return_dim() const { return m_return_dim; }\n\n  protected:\n    typename XprType::Nested m_xpr;\n    const ReduceOp m_reduce_op;\n    const int m_return_dim;\n    const Dims m_reduce_dims;\n};\n\n// Eval as rvalue\ntemplate<typename ReduceOp, typename Dims, typename ArgType, typename Device>\nstruct TensorEvaluator<const TensorTupleReducerOp<ReduceOp, Dims, ArgType>, Device>\n{\n  typedef TensorTupleReducerOp<ReduceOp, Dims, ArgType> XprType;\n  typedef typename XprType::Index Index;\n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename TensorIndexTupleOp<ArgType>::CoeffReturnType TupleType;\n  typedef typename TensorEvaluator<const TensorReductionOp<ReduceOp, Dims, const TensorIndexTupleOp<ArgType> >, Device>::Dimensions Dimensions;\n  typedef typename TensorEvaluator<const TensorIndexTupleOp<ArgType> , Device>::Dimensions InputDimensions;\n  static const int NumDims = internal::array_size<InputDimensions>::value;\n  typedef array<Index, NumDims> StrideDims;\n\n  enum {\n    IsAligned = /*TensorEvaluator<ArgType, Device>::IsAligned*/ false,\n    PacketAccess = /*TensorEvaluator<ArgType, Device>::PacketAccess*/ false,\n    BlockAccess = false,\n    Layout = TensorEvaluator<const TensorReductionOp<ReduceOp, Dims, const TensorIndexTupleOp<ArgType> >, Device>::Layout,\n    CoordAccess = false,  // to be implemented\n    RawAccess = false\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)\n      : m_orig_impl(op.expression(), device),\n        m_impl(op.expression().index_tuples().reduce(op.reduce_dims(), op.reduce_op()), device),\n        m_return_dim(op.return_dim()) {\n\n    gen_strides(m_orig_impl.dimensions(), m_strides);\n    if (Layout == static_cast<int>(ColMajor)) {\n      const Index total_size = internal::array_prod(m_orig_impl.dimensions());\n      m_stride_mod = (m_return_dim < NumDims - 1) ? m_strides[m_return_dim + 1] : total_size;\n    } else {\n      const Index total_size = internal::array_prod(m_orig_impl.dimensions());\n      m_stride_mod = (m_return_dim > 0) ? m_strides[m_return_dim - 1] : total_size;\n    }\n    m_stride_div = m_strides[m_return_dim];\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const {\n    return m_impl.dimensions();\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(Scalar* /*data*/) {\n    m_impl.evalSubExprsIfNeeded(NULL);\n    return true;\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {\n    m_impl.cleanup();\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const {\n    const TupleType v = m_impl.coeff(index);\n    return (m_return_dim < 0) ? v.first : (v.first % m_stride_mod) / m_stride_div;\n  }\n\n  EIGEN_DEVICE_FUNC Scalar* data() const { return NULL; }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost\n  costPerCoeff(bool vectorized) const {\n    const double compute_cost = 1.0 +\n        (m_return_dim < 0 ? 0.0 : (TensorOpCost::ModCost<Index>() + TensorOpCost::DivCost<Index>()));\n    return m_orig_impl.costPerCoeff(vectorized) +\n           m_impl.costPerCoeff(vectorized) + TensorOpCost(0, 0, compute_cost);\n  }\n\n private:\n  EIGEN_DEVICE_FUNC void gen_strides(const InputDimensions& dims, StrideDims& strides) {\n    if (m_return_dim < 0) {\n      return;  // Won't be using the strides.\n    }\n    eigen_assert(m_return_dim < NumDims &&\n                 \"Asking to convert index to a dimension outside of the rank\");\n\n    // Calculate m_stride_div and m_stride_mod, which are used to\n    // calculate the value of an index w.r.t. the m_return_dim.\n    if (Layout == static_cast<int>(ColMajor)) {\n      strides[0] = 1;\n      for (int i = 1; i < NumDims; ++i) {\n        strides[i] = strides[i-1] * dims[i-1];\n      }\n    } else {\n      strides[NumDims-1] = 1;\n      for (int i = NumDims - 2; i >= 0; --i) {\n        strides[i] = strides[i+1] * dims[i+1];\n      }\n    }\n  }\n\n protected:\n  TensorEvaluator<const TensorIndexTupleOp<ArgType>, Device> m_orig_impl;\n  TensorEvaluator<const TensorReductionOp<ReduceOp, Dims, const TensorIndexTupleOp<ArgType> >, Device> m_impl;\n  const int m_return_dim;\n  StrideDims m_strides;\n  Index m_stride_mod;\n  Index m_stride_div;\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_ARG_MAX_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorAssign.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_ASSIGN_H\n#define EIGEN_CXX11_TENSOR_TENSOR_ASSIGN_H\n\nnamespace Eigen {\n\n/** \\class TensorAssign\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief The tensor assignment class.\n  *\n  * This class is represents the assignment of the values resulting from the evaluation of\n  * the rhs expression to the memory locations denoted by the lhs expression.\n  */\nnamespace internal {\ntemplate<typename LhsXprType, typename RhsXprType>\nstruct traits<TensorAssignOp<LhsXprType, RhsXprType> >\n{\n  typedef typename LhsXprType::Scalar Scalar;\n  typedef typename traits<LhsXprType>::StorageKind StorageKind;\n  typedef typename promote_index_type<typename traits<LhsXprType>::Index,\n                                      typename traits<RhsXprType>::Index>::type Index;\n  typedef typename LhsXprType::Nested LhsNested;\n  typedef typename RhsXprType::Nested RhsNested;\n  typedef typename remove_reference<LhsNested>::type _LhsNested;\n  typedef typename remove_reference<RhsNested>::type _RhsNested;\n  static const std::size_t NumDimensions = internal::traits<LhsXprType>::NumDimensions;\n  static const int Layout = internal::traits<LhsXprType>::Layout;\n\n  enum {\n    Flags = 0\n  };\n};\n\ntemplate<typename LhsXprType, typename RhsXprType>\nstruct eval<TensorAssignOp<LhsXprType, RhsXprType>, Eigen::Dense>\n{\n  typedef const TensorAssignOp<LhsXprType, RhsXprType>& type;\n};\n\ntemplate<typename LhsXprType, typename RhsXprType>\nstruct nested<TensorAssignOp<LhsXprType, RhsXprType>, 1, typename eval<TensorAssignOp<LhsXprType, RhsXprType> >::type>\n{\n  typedef TensorAssignOp<LhsXprType, RhsXprType> type;\n};\n\n}  // end namespace internal\n\n\n\ntemplate<typename LhsXprType, typename RhsXprType>\nclass TensorAssignOp : public TensorBase<TensorAssignOp<LhsXprType, RhsXprType> >\n{\n  public:\n  typedef typename Eigen::internal::traits<TensorAssignOp>::Scalar Scalar;\n  typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;\n  typedef typename LhsXprType::CoeffReturnType CoeffReturnType;\n  typedef typename Eigen::internal::nested<TensorAssignOp>::type Nested;\n  typedef typename Eigen::internal::traits<TensorAssignOp>::StorageKind StorageKind;\n  typedef typename Eigen::internal::traits<TensorAssignOp>::Index Index;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorAssignOp(LhsXprType& lhs, const RhsXprType& rhs)\n      : m_lhs_xpr(lhs), m_rhs_xpr(rhs) {}\n\n    /** \\returns the nested expressions */\n    EIGEN_DEVICE_FUNC\n    typename internal::remove_all<typename LhsXprType::Nested>::type&\n    lhsExpression() const { return *((typename internal::remove_all<typename LhsXprType::Nested>::type*)&m_lhs_xpr); }\n\n    EIGEN_DEVICE_FUNC\n    const typename internal::remove_all<typename RhsXprType::Nested>::type&\n    rhsExpression() const { return m_rhs_xpr; }\n\n  protected:\n    typename internal::remove_all<typename LhsXprType::Nested>::type& m_lhs_xpr;\n    const typename internal::remove_all<typename RhsXprType::Nested>::type& m_rhs_xpr;\n};\n\n\ntemplate<typename LeftArgType, typename RightArgType, typename Device>\nstruct TensorEvaluator<const TensorAssignOp<LeftArgType, RightArgType>, Device>\n{\n  typedef TensorAssignOp<LeftArgType, RightArgType> XprType;\n  typedef typename XprType::Index Index;\n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  typedef typename TensorEvaluator<RightArgType, Device>::Dimensions Dimensions;\n  static const int PacketSize = internal::unpacket_traits<PacketReturnType>::size;\n\n  enum {\n    IsAligned = TensorEvaluator<LeftArgType, Device>::IsAligned & TensorEvaluator<RightArgType, Device>::IsAligned,\n    PacketAccess = TensorEvaluator<LeftArgType, Device>::PacketAccess & TensorEvaluator<RightArgType, Device>::PacketAccess,\n    Layout = TensorEvaluator<LeftArgType, Device>::Layout,\n    RawAccess = TensorEvaluator<LeftArgType, Device>::RawAccess\n  };\n\n  EIGEN_DEVICE_FUNC TensorEvaluator(const XprType& op, const Device& device) :\n      m_leftImpl(op.lhsExpression(), device),\n      m_rightImpl(op.rhsExpression(), device)\n  {\n    EIGEN_STATIC_ASSERT((static_cast<int>(TensorEvaluator<LeftArgType, Device>::Layout) == static_cast<int>(TensorEvaluator<RightArgType, Device>::Layout)), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  }\n\n  EIGEN_DEVICE_FUNC const Dimensions& dimensions() const\n  {\n    // The dimensions of the lhs and the rhs tensors should be equal to prevent\n    // overflows and ensure the result is fully initialized.\n    // TODO: use left impl instead if right impl dimensions are known at compile time.\n    return m_rightImpl.dimensions();\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(Scalar*) {\n    eigen_assert(dimensions_match(m_leftImpl.dimensions(), m_rightImpl.dimensions()));\n    m_leftImpl.evalSubExprsIfNeeded(NULL);\n    // If the lhs provides raw access to its storage area (i.e. if m_leftImpl.data() returns a non\n    // null value), attempt to evaluate the rhs expression in place. Returns true iff in place\n    // evaluation isn't supported and the caller still needs to manually assign the values generated\n    // by the rhs to the lhs.\n    return m_rightImpl.evalSubExprsIfNeeded(m_leftImpl.data());\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {\n    m_leftImpl.cleanup();\n    m_rightImpl.cleanup();\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalScalar(Index i) {\n    m_leftImpl.coeffRef(i) = m_rightImpl.coeff(i);\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalPacket(Index i) {\n    const int LhsStoreMode = TensorEvaluator<LeftArgType, Device>::IsAligned ? Aligned : Unaligned;\n    const int RhsLoadMode = TensorEvaluator<RightArgType, Device>::IsAligned ? Aligned : Unaligned;\n    m_leftImpl.template writePacket<LhsStoreMode>(i, m_rightImpl.template packet<RhsLoadMode>(i));\n  }\n  EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index index) const\n  {\n    return m_leftImpl.coeff(index);\n  }\n  template<int LoadMode>\n  EIGEN_DEVICE_FUNC PacketReturnType packet(Index index) const\n  {\n    return m_leftImpl.template packet<LoadMode>(index);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost\n  costPerCoeff(bool vectorized) const {\n    // We assume that evalPacket or evalScalar is called to perform the\n    // assignment and account for the cost of the write here, but reduce left\n    // cost by one load because we are using m_leftImpl.coeffRef.\n    TensorOpCost left = m_leftImpl.costPerCoeff(vectorized);\n    return m_rightImpl.costPerCoeff(vectorized) +\n           TensorOpCost(\n               numext::maxi(0.0, left.bytes_loaded() - sizeof(CoeffReturnType)),\n               left.bytes_stored(), left.compute_cycles()) +\n           TensorOpCost(0, sizeof(CoeffReturnType), 0, vectorized, PacketSize);\n  }\n\n  /// required by sycl in order to extract the accessor\n  const TensorEvaluator<LeftArgType, Device>& left_impl() const { return m_leftImpl; }\n  /// required by sycl in order to extract the accessor\n  const TensorEvaluator<RightArgType, Device>& right_impl() const { return m_rightImpl; }\n\n  EIGEN_DEVICE_FUNC CoeffReturnType* data() const { return m_leftImpl.data(); }\n\n private:\n  TensorEvaluator<LeftArgType, Device> m_leftImpl;\n  TensorEvaluator<RightArgType, Device> m_rightImpl;\n};\n\n}\n\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_ASSIGN_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorBase.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_BASE_H\n#define EIGEN_CXX11_TENSOR_TENSOR_BASE_H\n\n// clang-format off\n\nnamespace Eigen {\n\n/** \\class TensorBase\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief The tensor base class.\n  *\n  * This class is the common parent of the Tensor and TensorMap class, thus\n  * making it possible to use either class interchangably in expressions.\n  */\n\ntemplate<typename Derived>\nclass TensorBase<Derived, ReadOnlyAccessors>\n{\n  public:\n    typedef internal::traits<Derived> DerivedTraits;\n    typedef typename DerivedTraits::Scalar Scalar;\n    typedef typename DerivedTraits::Index Index;\n    typedef typename internal::remove_const<Scalar>::type CoeffReturnType;\n    static const int NumDimensions = DerivedTraits::NumDimensions;\n\n    // Generic nullary operation support.\n    template <typename CustomNullaryOp> EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseNullaryOp<CustomNullaryOp, const Derived>\n    nullaryExpr(const CustomNullaryOp& func) const {\n      return TensorCwiseNullaryOp<CustomNullaryOp, const Derived>(derived(), func);\n    }\n\n    // Coefficient-wise nullary operators\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseNullaryOp<internal::scalar_constant_op<Scalar>, const Derived>\n    constant(const Scalar& value) const {\n      return nullaryExpr(internal::scalar_constant_op<Scalar>(value));\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseNullaryOp<internal::UniformRandomGenerator<Scalar>, const Derived>\n    random() const {\n      return nullaryExpr(internal::UniformRandomGenerator<Scalar>());\n    }\n    template <typename RandomGenerator> EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseNullaryOp<RandomGenerator, const Derived>\n    random(const RandomGenerator& gen = RandomGenerator()) const {\n      return nullaryExpr(gen);\n    }\n\n    // Tensor generation\n    template <typename Generator> EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorGeneratorOp<Generator, const Derived>\n    generate(const Generator& generator) const {\n      return TensorGeneratorOp<Generator, const Derived>(derived(), generator);\n    }\n\n    // Generic unary operation support.\n    template <typename CustomUnaryOp> EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<CustomUnaryOp, const Derived>\n    unaryExpr(const CustomUnaryOp& func) const {\n      return TensorCwiseUnaryOp<CustomUnaryOp, const Derived>(derived(), func);\n    }\n\n    // Coefficient-wise unary operators\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_opposite_op<Scalar>, const Derived>\n    operator-() const {\n      return unaryExpr(internal::scalar_opposite_op<Scalar>());\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_sqrt_op<Scalar>, const Derived>\n    sqrt() const {\n      return unaryExpr(internal::scalar_sqrt_op<Scalar>());\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_sign_op<Scalar>, const Derived>\n    sign() const {\n      return unaryExpr(internal::scalar_sign_op<Scalar>());\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_rsqrt_op<Scalar>, const Derived>\n    rsqrt() const {\n      return unaryExpr(internal::scalar_rsqrt_op<Scalar>());\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_square_op<Scalar>, const Derived>\n    square() const {\n      return unaryExpr(internal::scalar_square_op<Scalar>());\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_cube_op<Scalar>, const Derived>\n    cube() const {\n      return unaryExpr(internal::scalar_cube_op<Scalar>());\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const Derived>\n    inverse() const {\n      return unaryExpr(internal::scalar_inverse_op<Scalar>());\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_tanh_op<Scalar>, const Derived>\n    tanh() const {\n      return unaryExpr(internal::scalar_tanh_op<Scalar>());\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_lgamma_op<Scalar>, const Derived>\n    lgamma() const {\n      return unaryExpr(internal::scalar_lgamma_op<Scalar>());\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_digamma_op<Scalar>, const Derived>\n    digamma() const {\n      return unaryExpr(internal::scalar_digamma_op<Scalar>());\n    }\n\n    // igamma(a = this, x = other)\n    template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorCwiseBinaryOp<internal::scalar_igamma_op<Scalar>, const Derived, const OtherDerived>\n    igamma(const OtherDerived& other) const {\n      return binaryExpr(other.derived(), internal::scalar_igamma_op<Scalar>());\n    }\n\n    // igammac(a = this, x = other)\n    template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorCwiseBinaryOp<internal::scalar_igammac_op<Scalar>, const Derived, const OtherDerived>\n    igammac(const OtherDerived& other) const {\n      return binaryExpr(other.derived(), internal::scalar_igammac_op<Scalar>());\n    }\n\n    // zeta(x = this, q = other)\n    template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorCwiseBinaryOp<internal::scalar_zeta_op<Scalar>, const Derived, const OtherDerived>\n    zeta(const OtherDerived& other) const {\n      return binaryExpr(other.derived(), internal::scalar_zeta_op<Scalar>());\n    }\n\n    // polygamma(n = this, x = other)\n    template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorCwiseBinaryOp<internal::scalar_polygamma_op<Scalar>, const Derived, const OtherDerived>\n    polygamma(const OtherDerived& other) const {\n      return binaryExpr(other.derived(), internal::scalar_polygamma_op<Scalar>());\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_erf_op<Scalar>, const Derived>\n    erf() const {\n      return unaryExpr(internal::scalar_erf_op<Scalar>());\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_erfc_op<Scalar>, const Derived>\n    erfc() const {\n      return unaryExpr(internal::scalar_erfc_op<Scalar>());\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_sigmoid_op<Scalar>, const Derived>\n    sigmoid() const {\n      return unaryExpr(internal::scalar_sigmoid_op<Scalar>());\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_exp_op<Scalar>, const Derived>\n    exp() const {\n      return unaryExpr(internal::scalar_exp_op<Scalar>());\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_log_op<Scalar>, const Derived>\n    log() const {\n      return unaryExpr(internal::scalar_log_op<Scalar>());\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_log1p_op<Scalar>, const Derived>\n    log1p() const {\n      return unaryExpr(internal::scalar_log1p_op<Scalar>());\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_abs_op<Scalar>, const Derived>\n    abs() const {\n      return unaryExpr(internal::scalar_abs_op<Scalar>());\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_conjugate_op<Scalar>, const Derived>\n    conjugate() const {\n      return unaryExpr(internal::scalar_conjugate_op<Scalar>());\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::bind2nd_op<internal::scalar_pow_op<Scalar,Scalar> >, const Derived>\n    pow(Scalar exponent) const {\n      return unaryExpr(internal::bind2nd_op<internal::scalar_pow_op<Scalar,Scalar> >(exponent));\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_real_op<Scalar>, const Derived>\n    real() const {\n      return unaryExpr(internal::scalar_real_op<Scalar>());\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_imag_op<Scalar>, const Derived>\n    imag() const {\n      return unaryExpr(internal::scalar_imag_op<Scalar>());\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::bind2nd_op<internal::scalar_sum_op<Scalar,Scalar> >, const Derived>\n    operator+ (Scalar rhs) const {\n      return unaryExpr(internal::bind2nd_op<internal::scalar_sum_op<Scalar,Scalar> >(rhs));\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE friend\n    const TensorCwiseUnaryOp<internal::bind1st_op<internal::scalar_sum_op<Scalar> >, const Derived>\n    operator+ (Scalar lhs, const Derived& rhs) {\n      return rhs.unaryExpr(internal::bind1st_op<internal::scalar_sum_op<Scalar> >(lhs));\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::bind2nd_op<internal::scalar_difference_op<Scalar,Scalar> >, const Derived>\n    operator- (Scalar rhs) const {\n      EIGEN_STATIC_ASSERT((NumTraits<Scalar>::IsSigned || internal::is_same<Scalar, const std::complex<float> >::value), YOU_MADE_A_PROGRAMMING_MISTAKE);\n      return unaryExpr(internal::bind2nd_op<internal::scalar_difference_op<Scalar,Scalar> >(rhs));\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE friend\n    const TensorCwiseUnaryOp<internal::bind1st_op<internal::scalar_difference_op<Scalar> >, const Derived>\n    operator- (Scalar lhs, const Derived& rhs) {\n      return rhs.unaryExpr(internal::bind1st_op<internal::scalar_difference_op<Scalar> >(lhs));\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::bind2nd_op<internal::scalar_product_op<Scalar,Scalar> >, const Derived>\n    operator* (Scalar rhs) const {\n      return unaryExpr(internal::bind2nd_op<internal::scalar_product_op<Scalar,Scalar> >(rhs));\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE friend\n    const TensorCwiseUnaryOp<internal::bind1st_op<internal::scalar_product_op<Scalar> >, const Derived>\n    operator* (Scalar lhs, const Derived& rhs) {\n      return rhs.unaryExpr(internal::bind1st_op<internal::scalar_product_op<Scalar> >(lhs));\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::bind2nd_op<internal::scalar_quotient_op<Scalar,Scalar> >, const Derived>\n    operator/ (Scalar rhs) const {\n      return unaryExpr(internal::bind2nd_op<internal::scalar_quotient_op<Scalar,Scalar> >(rhs));\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE friend\n    const TensorCwiseUnaryOp<internal::bind1st_op<internal::scalar_quotient_op<Scalar> >, const Derived>\n    operator/ (Scalar lhs, const Derived& rhs) {\n      return rhs.unaryExpr(internal::bind1st_op<internal::scalar_quotient_op<Scalar> >(lhs));\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_mod_op<Scalar>, const Derived>\n    operator% (Scalar rhs) const {\n      EIGEN_STATIC_ASSERT(NumTraits<Scalar>::IsInteger, YOU_MADE_A_PROGRAMMING_MISTAKE_TRY_MOD);\n      return unaryExpr(internal::scalar_mod_op<Scalar>(rhs));\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseBinaryOp<internal::scalar_max_op<Scalar>, const Derived, const TensorCwiseNullaryOp<internal::scalar_constant_op<Scalar>, const Derived> >\n    cwiseMax(Scalar threshold) const {\n      return cwiseMax(constant(threshold));\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseBinaryOp<internal::scalar_min_op<Scalar>, const Derived, const TensorCwiseNullaryOp<internal::scalar_constant_op<Scalar>, const Derived> >\n    cwiseMin(Scalar threshold) const {\n      return cwiseMin(constant(threshold));\n    }\n\n    template <typename NewType> EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorConversionOp<NewType, const Derived>\n    cast() const {\n      return TensorConversionOp<NewType, const Derived>(derived());\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_round_op<Scalar>, const Derived>\n    round() const {\n      return unaryExpr(internal::scalar_round_op<Scalar>());\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_ceil_op<Scalar>, const Derived>\n    ceil() const {\n      return unaryExpr(internal::scalar_ceil_op<Scalar>());\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_floor_op<Scalar>, const Derived>\n    floor() const {\n      return unaryExpr(internal::scalar_floor_op<Scalar>());\n    }\n\n    // Generic binary operation support.\n    template <typename CustomBinaryOp, typename OtherDerived> EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseBinaryOp<CustomBinaryOp, const Derived, const OtherDerived>\n    binaryExpr(const OtherDerived& other, const CustomBinaryOp& func) const {\n      return TensorCwiseBinaryOp<CustomBinaryOp, const Derived, const OtherDerived>(derived(), other, func);\n    }\n\n    // Coefficient-wise binary operators.\n    template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorCwiseBinaryOp<internal::scalar_sum_op<Scalar>, const Derived, const OtherDerived>\n    operator+(const OtherDerived& other) const {\n      return binaryExpr(other.derived(), internal::scalar_sum_op<Scalar>());\n    }\n\n    template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorCwiseBinaryOp<internal::scalar_difference_op<Scalar>, const Derived, const OtherDerived>\n    operator-(const OtherDerived& other) const {\n      return binaryExpr(other.derived(), internal::scalar_difference_op<Scalar>());\n    }\n\n    template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorCwiseBinaryOp<internal::scalar_product_op<Scalar>, const Derived, const OtherDerived>\n    operator*(const OtherDerived& other) const {\n      return binaryExpr(other.derived(), internal::scalar_product_op<Scalar>());\n    }\n\n    template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorCwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const Derived, const OtherDerived>\n    operator/(const OtherDerived& other) const {\n      return binaryExpr(other.derived(), internal::scalar_quotient_op<Scalar>());\n    }\n\n    template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorCwiseBinaryOp<internal::scalar_max_op<Scalar>, const Derived, const OtherDerived>\n    cwiseMax(const OtherDerived& other) const {\n      return binaryExpr(other.derived(), internal::scalar_max_op<Scalar>());\n    }\n\n    template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorCwiseBinaryOp<internal::scalar_min_op<Scalar>, const Derived, const OtherDerived>\n    cwiseMin(const OtherDerived& other) const {\n      return binaryExpr(other.derived(), internal::scalar_min_op<Scalar>());\n    }\n\n    template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorCwiseBinaryOp<internal::scalar_boolean_and_op, const Derived, const OtherDerived>\n    operator&&(const OtherDerived& other) const {\n      return binaryExpr(other.derived(), internal::scalar_boolean_and_op());\n    }\n\n    template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorCwiseBinaryOp<internal::scalar_boolean_or_op, const Derived, const OtherDerived>\n    operator||(const OtherDerived& other) const {\n      return binaryExpr(other.derived(), internal::scalar_boolean_or_op());\n    }\n\n    template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorCwiseBinaryOp<internal::scalar_boolean_xor_op, const Derived, const OtherDerived>\n    operator^(const OtherDerived& other) const {\n      return binaryExpr(other.derived(), internal::scalar_boolean_xor_op());\n    }\n\n    // Comparisons and tests.\n    template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_LT>, const Derived, const OtherDerived>\n    operator<(const OtherDerived& other) const {\n      return binaryExpr(other.derived(), internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_LT>());\n    }\n    template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_LE>, const Derived, const OtherDerived>\n    operator<=(const OtherDerived& other) const {\n      return binaryExpr(other.derived(), internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_LE>());\n    }\n    template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_GT>, const Derived, const OtherDerived>\n    operator>(const OtherDerived& other) const {\n      return binaryExpr(other.derived(), internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_GT>());\n    }\n    template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_GE>, const Derived, const OtherDerived>\n    operator>=(const OtherDerived& other) const {\n      return binaryExpr(other.derived(), internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_GE>());\n    }\n\n    template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_EQ>, const Derived, const OtherDerived>\n    operator==(const OtherDerived& other) const {\n      return binaryExpr(other.derived(), internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_EQ>());\n    }\n\n    template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_NEQ>, const Derived, const OtherDerived>\n    operator!=(const OtherDerived& other) const {\n      return binaryExpr(other.derived(), internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_NEQ>());\n    }\n\n    // comparisons and tests for Scalars\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_LT>, const Derived, const TensorCwiseNullaryOp<internal::scalar_constant_op<Scalar>, const Derived> >\n    operator<(Scalar threshold) const {\n      return operator<(constant(threshold));\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_LE>, const Derived, const TensorCwiseNullaryOp<internal::scalar_constant_op<Scalar>, const Derived> >\n    operator<=(Scalar threshold) const {\n      return operator<=(constant(threshold));\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_GT>, const Derived, const TensorCwiseNullaryOp<internal::scalar_constant_op<Scalar>, const Derived> >\n    operator>(Scalar threshold) const {\n      return operator>(constant(threshold));\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_GE>, const Derived, const TensorCwiseNullaryOp<internal::scalar_constant_op<Scalar>, const Derived> >\n    operator>=(Scalar threshold) const {\n      return operator>=(constant(threshold));\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_EQ>, const Derived, const TensorCwiseNullaryOp<internal::scalar_constant_op<Scalar>, const Derived> >\n    operator==(Scalar threshold) const {\n      return operator==(constant(threshold));\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_NEQ>, const Derived, const TensorCwiseNullaryOp<internal::scalar_constant_op<Scalar>, const Derived> >\n    operator!=(Scalar threshold) const {\n      return operator!=(constant(threshold));\n    }\n\n    // Checks\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_isnan_op<Scalar>, const Derived>\n    (isnan)() const {\n      return unaryExpr(internal::scalar_isnan_op<Scalar>());\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_isinf_op<Scalar>, const Derived>\n    (isinf)() const {\n      return unaryExpr(internal::scalar_isinf_op<Scalar>());\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_isfinite_op<Scalar>, const Derived>\n    (isfinite)() const {\n      return unaryExpr(internal::scalar_isfinite_op<Scalar>());\n    }\n\n    // Coefficient-wise ternary operators.\n    template<typename ThenDerived, typename ElseDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorSelectOp<const Derived, const ThenDerived, const ElseDerived>\n    select(const ThenDerived& thenTensor, const ElseDerived& elseTensor) const {\n      return TensorSelectOp<const Derived, const ThenDerived, const ElseDerived>(derived(), thenTensor.derived(), elseTensor.derived());\n    }\n\n    // Contractions.\n    typedef Eigen::IndexPair<Index> DimensionPair;\n\n    template<typename OtherDerived, typename Dimensions> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorContractionOp<const Dimensions, const Derived, const OtherDerived>\n    contract(const OtherDerived& other, const Dimensions& dims) const {\n      return TensorContractionOp<const Dimensions, const Derived, const OtherDerived>(derived(), other.derived(), dims);\n    }\n\n    // Convolutions.\n    template<typename KernelDerived, typename Dimensions> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorConvolutionOp<const Dimensions, const Derived, const KernelDerived>\n    convolve(const KernelDerived& kernel, const Dimensions& dims) const {\n      return TensorConvolutionOp<const Dimensions, const Derived, const KernelDerived>(derived(), kernel.derived(), dims);\n    }\n\n    // Fourier transforms\n    template <int FFTDataType, int FFTDirection, typename FFT> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorFFTOp<const FFT, const Derived, FFTDataType, FFTDirection>\n    fft(const FFT& fft) const {\n      return TensorFFTOp<const FFT, const Derived, FFTDataType, FFTDirection>(derived(), fft);\n    }\n\n    // Scan.\n    typedef TensorScanOp<internal::SumReducer<CoeffReturnType>, const Derived> TensorScanSumOp;\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorScanSumOp\n    cumsum(const Index& axis, bool exclusive = false) const {\n      return TensorScanSumOp(derived(), axis, exclusive);\n    }\n\n    typedef TensorScanOp<internal::ProdReducer<CoeffReturnType>, const Derived> TensorScanProdOp;\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorScanProdOp\n    cumprod(const Index& axis, bool exclusive = false) const {\n      return TensorScanProdOp(derived(), axis, exclusive);\n    }\n\n    template <typename Reducer>\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorScanOp<Reducer, const Derived>\n    scan(const Index& axis, const Reducer& reducer, bool exclusive = false) const {\n      return TensorScanOp<Reducer, const Derived>(derived(), axis, exclusive, reducer);\n    }\n\n    // Reductions.\n    template <typename Dims> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorReductionOp<internal::SumReducer<CoeffReturnType>, const Dims, const Derived>\n    sum(const Dims& dims) const {\n      return TensorReductionOp<internal::SumReducer<CoeffReturnType>, const Dims, const Derived>(derived(), dims, internal::SumReducer<CoeffReturnType>());\n    }\n\n    const TensorReductionOp<internal::SumReducer<CoeffReturnType>, const DimensionList<Index, NumDimensions>, const Derived>\n    sum() const {\n      DimensionList<Index, NumDimensions> in_dims;\n      return TensorReductionOp<internal::SumReducer<CoeffReturnType>, const DimensionList<Index, NumDimensions>, const Derived>(derived(), in_dims, internal::SumReducer<CoeffReturnType>());\n    }\n\n    template <typename Dims> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorReductionOp<internal::MeanReducer<CoeffReturnType>, const Dims, const Derived>\n    mean(const Dims& dims) const {\n      return TensorReductionOp<internal::MeanReducer<CoeffReturnType>, const Dims, const Derived>(derived(), dims, internal::MeanReducer<CoeffReturnType>());\n    }\n\n    const TensorReductionOp<internal::MeanReducer<CoeffReturnType>, const DimensionList<Index, NumDimensions>, const Derived>\n    mean() const {\n      DimensionList<Index, NumDimensions> in_dims;\n      return TensorReductionOp<internal::MeanReducer<CoeffReturnType>, const DimensionList<Index, NumDimensions>, const Derived>(derived(), in_dims, internal::MeanReducer<CoeffReturnType>());\n    }\n\n    template <typename Dims> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorReductionOp<internal::ProdReducer<CoeffReturnType>, const Dims, const Derived>\n    prod(const Dims& dims) const {\n      return TensorReductionOp<internal::ProdReducer<CoeffReturnType>, const Dims, const Derived>(derived(), dims, internal::ProdReducer<CoeffReturnType>());\n    }\n\n    const TensorReductionOp<internal::ProdReducer<CoeffReturnType>, const DimensionList<Index, NumDimensions>, const Derived>\n    prod() const {\n      DimensionList<Index, NumDimensions> in_dims;\n      return TensorReductionOp<internal::ProdReducer<CoeffReturnType>, const DimensionList<Index, NumDimensions>, const Derived>(derived(), in_dims, internal::ProdReducer<CoeffReturnType>());\n    }\n\n    template <typename Dims> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorReductionOp<internal::MaxReducer<CoeffReturnType>, const Dims, const Derived>\n    maximum(const Dims& dims) const {\n      return TensorReductionOp<internal::MaxReducer<CoeffReturnType>, const Dims, const Derived>(derived(), dims, internal::MaxReducer<CoeffReturnType>());\n    }\n\n    const TensorReductionOp<internal::MaxReducer<CoeffReturnType>, const DimensionList<Index, NumDimensions>, const Derived>\n    maximum() const {\n      DimensionList<Index, NumDimensions> in_dims;\n      return TensorReductionOp<internal::MaxReducer<CoeffReturnType>, const DimensionList<Index, NumDimensions>, const Derived>(derived(), in_dims, internal::MaxReducer<CoeffReturnType>());\n    }\n\n    template <typename Dims> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorReductionOp<internal::MinReducer<CoeffReturnType>, const Dims, const Derived>\n    minimum(const Dims& dims) const {\n      return TensorReductionOp<internal::MinReducer<CoeffReturnType>, const Dims, const Derived>(derived(), dims, internal::MinReducer<CoeffReturnType>());\n    }\n\n    const TensorReductionOp<internal::MinReducer<CoeffReturnType>, const DimensionList<Index, NumDimensions>, const Derived>\n    minimum() const {\n      DimensionList<Index, NumDimensions> in_dims;\n      return TensorReductionOp<internal::MinReducer<CoeffReturnType>, const DimensionList<Index, NumDimensions>, const Derived>(derived(), in_dims, internal::MinReducer<CoeffReturnType>());\n    }\n\n    template <typename Dims> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorReductionOp<internal::AndReducer, const Dims, const TensorConversionOp<bool, const Derived> >\n    all(const Dims& dims) const {\n      return cast<bool>().reduce(dims, internal::AndReducer());\n    }\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorReductionOp<internal::AndReducer, const DimensionList<Index, NumDimensions>, const TensorConversionOp<bool, const Derived> >\n    all() const {\n      DimensionList<Index, NumDimensions> in_dims;\n      return cast<bool>().reduce(in_dims, internal::AndReducer());\n    }\n\n    template <typename Dims> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorReductionOp<internal::OrReducer, const Dims, const TensorConversionOp<bool, const Derived> >\n    any(const Dims& dims) const {\n      return cast<bool>().reduce(dims, internal::OrReducer());\n    }\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorReductionOp<internal::OrReducer, const DimensionList<Index, NumDimensions>, const TensorConversionOp<bool, const Derived> >\n    any() const {\n      DimensionList<Index, NumDimensions> in_dims;\n      return cast<bool>().reduce(in_dims, internal::OrReducer());\n    }\n\n   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorTupleReducerOp<\n      internal::ArgMaxTupleReducer<Tuple<Index, CoeffReturnType> >,\n      const array<Index, NumDimensions>, const Derived>\n    argmax() const {\n      array<Index, NumDimensions> in_dims;\n      for (int d = 0; d < NumDimensions; ++d) in_dims[d] = d;\n      return TensorTupleReducerOp<\n        internal::ArgMaxTupleReducer<Tuple<Index, CoeffReturnType> >,\n        const array<Index, NumDimensions>,\n        const Derived>(derived(), internal::ArgMaxTupleReducer<Tuple<Index, CoeffReturnType> >(), -1, in_dims);\n    }\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorTupleReducerOp<\n      internal::ArgMinTupleReducer<Tuple<Index, CoeffReturnType> >,\n      const array<Index, NumDimensions>, const Derived>\n    argmin() const {\n      array<Index, NumDimensions> in_dims;\n      for (int d = 0; d < NumDimensions; ++d) in_dims[d] = d;\n      return TensorTupleReducerOp<\n        internal::ArgMinTupleReducer<Tuple<Index, CoeffReturnType> >,\n        const array<Index, NumDimensions>,\n        const Derived>(derived(), internal::ArgMinTupleReducer<Tuple<Index, CoeffReturnType> >(), -1, in_dims);\n    }\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorTupleReducerOp<\n      internal::ArgMaxTupleReducer<Tuple<Index, CoeffReturnType> >,\n      const array<Index, 1>, const Derived>\n    argmax(const int return_dim) const {\n      array<Index, 1> in_dims;\n      in_dims[0] = return_dim;\n      return TensorTupleReducerOp<\n        internal::ArgMaxTupleReducer<Tuple<Index, CoeffReturnType> >,\n        const array<Index, 1>,\n        const Derived>(derived(), internal::ArgMaxTupleReducer<Tuple<Index, CoeffReturnType> >(), return_dim, in_dims);\n    }\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorTupleReducerOp<\n      internal::ArgMinTupleReducer<Tuple<Index, CoeffReturnType> >,\n      const array<Index, 1>, const Derived>\n    argmin(const int return_dim) const {\n      array<Index, 1> in_dims;\n      in_dims[0] = return_dim;\n      return TensorTupleReducerOp<\n        internal::ArgMinTupleReducer<Tuple<Index, CoeffReturnType> >,\n        const array<Index, 1>,\n        const Derived>(derived(), internal::ArgMinTupleReducer<Tuple<Index, CoeffReturnType> >(), return_dim, in_dims);\n    }\n\n    template <typename Reducer, typename Dims> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorReductionOp<Reducer, const Dims, const Derived>\n    reduce(const Dims& dims, const Reducer& reducer) const {\n      return TensorReductionOp<Reducer, const Dims, const Derived>(derived(), dims, reducer);\n    }\n\n    template <typename Broadcast> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorBroadcastingOp<const Broadcast, const Derived>\n    broadcast(const Broadcast& broadcast) const {\n      return TensorBroadcastingOp<const Broadcast, const Derived>(derived(), broadcast);\n    }\n\n    template <typename Axis, typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorConcatenationOp<Axis, const Derived, const OtherDerived>\n    concatenate(const OtherDerived& other, Axis axis) const {\n      return TensorConcatenationOp<Axis, const Derived, const OtherDerived>(derived(), other.derived(), axis);\n    }\n\n    template <typename PatchDims> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorPatchOp<const PatchDims, const Derived>\n    extract_patches(const PatchDims& patch_dims) const {\n      return TensorPatchOp<const PatchDims, const Derived>(derived(), patch_dims);\n    }\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorImagePatchOp<Dynamic, Dynamic, const Derived>\n    extract_image_patches(const Index patch_rows = 1, const Index patch_cols = 1,\n                          const Index row_stride = 1, const Index col_stride = 1,\n                          const Index in_row_stride = 1, const Index in_col_stride = 1,\n                          const PaddingType padding_type = PADDING_SAME, const Scalar padding_value = Scalar(0)) const {\n      return TensorImagePatchOp<Dynamic, Dynamic, const Derived>(derived(), patch_rows, patch_cols, row_stride, col_stride,\n                                                                 in_row_stride, in_col_stride, 1, 1, padding_type, padding_value);\n    }\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorImagePatchOp<Dynamic, Dynamic, const Derived>\n    extract_image_patches(const Index patch_rows, const Index patch_cols,\n                          const Index row_stride, const Index col_stride,\n                          const Index in_row_stride, const Index in_col_stride,\n                          const Index row_inflate_stride, const Index col_inflate_stride,\n                          const Index padding_top, const Index padding_bottom,\n                          const Index padding_left,const Index padding_right,\n                          const Scalar padding_value) const {\n      return TensorImagePatchOp<Dynamic, Dynamic, const Derived>(derived(), patch_rows, patch_cols, row_stride, col_stride,\n                                                                 in_row_stride, in_col_stride, row_inflate_stride, col_inflate_stride,\n                                                                 padding_top, padding_bottom, padding_left, padding_right, padding_value);\n    }\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorVolumePatchOp<Dynamic, Dynamic, Dynamic, const Derived>\n    extract_volume_patches(const Index patch_planes, const Index patch_rows, const Index patch_cols,\n                           const Index plane_stride = 1, const Index row_stride = 1, const Index col_stride = 1,\n                           const PaddingType padding_type = PADDING_SAME, const Scalar padding_value = Scalar(0)) const {\n      return TensorVolumePatchOp<Dynamic, Dynamic, Dynamic, const Derived>(derived(), patch_planes, patch_rows, patch_cols, plane_stride, row_stride, col_stride, 1, 1, 1, 1, 1, 1, padding_type, padding_value);\n    }\n\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorVolumePatchOp<Dynamic, Dynamic, Dynamic, const Derived>\n    extract_volume_patches(const Index patch_planes, const Index patch_rows, const Index patch_cols,\n                           const Index plane_stride, const Index row_stride, const Index col_stride,\n                           const Index plane_inflate_stride, const Index row_inflate_stride, const Index col_inflate_stride,\n                           const Index padding_top_z, const Index padding_bottom_z,\n                           const Index padding_top, const Index padding_bottom,\n                           const Index padding_left, const Index padding_right, const Scalar padding_value = Scalar(0)) const {\n      return TensorVolumePatchOp<Dynamic, Dynamic, Dynamic, const Derived>(derived(), patch_planes, patch_rows, patch_cols, plane_stride, row_stride, col_stride, 1, 1, 1, plane_inflate_stride, row_inflate_stride, col_inflate_stride, padding_top_z, padding_bottom_z, padding_top, padding_bottom, padding_left, padding_right, padding_value);\n    }\n\n    // Morphing operators.\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorLayoutSwapOp<const Derived>\n    swap_layout() const {\n      return TensorLayoutSwapOp<const Derived>(derived());\n    }\n    template <typename NewDimensions> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorReshapingOp<const NewDimensions, const Derived>\n    reshape(const NewDimensions& newDimensions) const {\n      return TensorReshapingOp<const NewDimensions, const Derived>(derived(), newDimensions);\n    }\n    template <typename StartIndices, typename Sizes> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorSlicingOp<const StartIndices, const Sizes, const Derived>\n    slice(const StartIndices& startIndices, const Sizes& sizes) const {\n      return TensorSlicingOp<const StartIndices, const Sizes, const Derived>(derived(), startIndices, sizes);\n    }\n    template <typename StartIndices, typename StopIndices, typename Strides> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorStridingSlicingOp<const StartIndices, const StopIndices, const Strides, const Derived>\n    stridedSlice(const StartIndices& startIndices, const StopIndices& stopIndices, const Strides& strides) const {\n      return TensorStridingSlicingOp<const StartIndices, const StopIndices, const Strides,\n                                const Derived>(derived(), startIndices, stopIndices, strides);\n    }\n    template <Index DimId> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorChippingOp<DimId, const Derived>\n    chip(const Index offset) const {\n      return TensorChippingOp<DimId, const Derived>(derived(), offset, DimId);\n    }\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorChippingOp<Dynamic, const Derived>\n    chip(const Index offset, const Index dim) const {\n      return TensorChippingOp<Dynamic, const Derived>(derived(), offset, dim);\n    }\n    template <typename ReverseDimensions> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorReverseOp<const ReverseDimensions, const Derived>\n    reverse(const ReverseDimensions& rev) const {\n      return TensorReverseOp<const ReverseDimensions, const Derived>(derived(), rev);\n    }\n    template <typename PaddingDimensions> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorPaddingOp<const PaddingDimensions, const Derived>\n    pad(const PaddingDimensions& padding) const {\n      return TensorPaddingOp<const PaddingDimensions, const Derived>(derived(), padding, internal::scalar_cast_op<int, Scalar>()(0));\n    }\n    template <typename PaddingDimensions> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorPaddingOp<const PaddingDimensions, const Derived>\n    pad(const PaddingDimensions& padding, const Scalar padding_value) const {\n      return TensorPaddingOp<const PaddingDimensions, const Derived>(derived(), padding, padding_value);\n    }\n    template <typename Shuffle> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorShufflingOp<const Shuffle, const Derived>\n    shuffle(const Shuffle& shuffle) const {\n      return TensorShufflingOp<const Shuffle, const Derived>(derived(), shuffle);\n    }\n    template <typename Strides> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorStridingOp<const Strides, const Derived>\n    stride(const Strides& strides) const {\n      return TensorStridingOp<const Strides, const Derived>(derived(), strides);\n    }\n    template <typename Strides> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorInflationOp<const Strides, const Derived>\n    inflate(const Strides& strides) const {\n      return TensorInflationOp<const Strides, const Derived>(derived(), strides);\n    }\n\n    // Returns a tensor containing index/value tuples\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorIndexTupleOp<const Derived>\n    index_tuples() const {\n      return TensorIndexTupleOp<const Derived>(derived());\n    }\n\n    // Support for custom unary and binary operations\n    template <typename CustomUnaryFunc>\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorCustomUnaryOp<const CustomUnaryFunc, const Derived> customOp(const CustomUnaryFunc& op) const {\n      return TensorCustomUnaryOp<const CustomUnaryFunc, const Derived>(derived(), op);\n    }\n    template <typename OtherDerived, typename CustomBinaryFunc>\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorCustomBinaryOp<const CustomBinaryFunc, const Derived, const OtherDerived> customOp(const OtherDerived& other, const CustomBinaryFunc& op) const {\n      return TensorCustomBinaryOp<const CustomBinaryFunc, const Derived, const OtherDerived>(derived(), other, op);\n    }\n\n    // Force the evaluation of the expression.\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorForcedEvalOp<const Derived> eval() const {\n      return TensorForcedEvalOp<const Derived>(derived());\n    }\n\n  protected:\n    template <typename Scalar, int NumIndices, int Options, typename IndexType> friend class Tensor;\n    template <typename Scalar, typename Dimensions, int Option, typename IndexTypes> friend class TensorFixedSize;\n    template <typename OtherDerived, int AccessLevel> friend class TensorBase;\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Derived& derived() const { return *static_cast<const Derived*>(this); }\n};\n\ntemplate<typename Derived, int AccessLevel = internal::accessors_level<Derived>::value>\nclass TensorBase : public TensorBase<Derived, ReadOnlyAccessors> {\n public:\n    typedef internal::traits<Derived> DerivedTraits;\n    typedef typename DerivedTraits::Scalar Scalar;\n    typedef typename DerivedTraits::Index Index;\n    typedef Scalar CoeffReturnType;\n    static const int NumDimensions = DerivedTraits::NumDimensions;\n\n    template <typename Scalar, int NumIndices, int Options, typename IndexType> friend class Tensor;\n    template <typename Scalar, typename Dimensions, int Option, typename IndexTypes> friend class TensorFixedSize;\n    template <typename OtherDerived, int OtherAccessLevel> friend class TensorBase;\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Derived& setZero() {\n      return setConstant(Scalar(0));\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Derived& setConstant(const Scalar& val) {\n      return derived() = this->constant(val);\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Derived& setRandom() {\n      return derived() = this->random();\n    }\n    template <typename RandomGenerator> EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Derived& setRandom() {\n      return derived() = this->template random<RandomGenerator>();\n    }\n\n#if EIGEN_HAS_VARIADIC_TEMPLATES\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Derived& setValues(\n        const typename internal::Initializer<Derived, NumDimensions>::InitList& vals) {\n      TensorEvaluator<Derived, DefaultDevice> eval(derived(), DefaultDevice());\n      internal::initialize_tensor<Derived, NumDimensions>(eval, vals);\n      return derived();\n    }\n#endif  // EIGEN_HAS_VARIADIC_TEMPLATES\n\n    template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    Derived& operator+=(const OtherDerived& other) {\n      return derived() = derived() + other.derived();\n    }\n    template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    Derived& operator-=(const OtherDerived& other) {\n      return derived() = derived() - other.derived();\n    }\n    template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    Derived& operator*=(const OtherDerived& other) {\n      return derived() = derived() * other.derived();\n    }\n    template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    Derived& operator/=(const OtherDerived& other) {\n      return derived() = derived() / other.derived();\n    }\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorLayoutSwapOp<const Derived>\n    swap_layout() const {\n      return TensorLayoutSwapOp<const Derived>(derived());\n    }\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    TensorLayoutSwapOp<Derived>\n    swap_layout() {\n      return TensorLayoutSwapOp<Derived>(derived());\n    }\n\n    template <typename Axis, typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorConcatenationOp<const Axis, const Derived, const OtherDerived>\n    concatenate(const OtherDerived& other, const Axis& axis) const {\n      return TensorConcatenationOp<const Axis, const Derived, const OtherDerived>(derived(), other, axis);\n    }\n    template <typename Axis, typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    TensorConcatenationOp<const Axis, Derived, OtherDerived>\n    concatenate(const OtherDerived& other, const Axis& axis) {\n      return TensorConcatenationOp<const Axis, Derived, OtherDerived>(derived(), other, axis);\n    }\n\n    template <typename NewDimensions> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorReshapingOp<const NewDimensions, const Derived>\n    reshape(const NewDimensions& newDimensions) const {\n      return TensorReshapingOp<const NewDimensions, const Derived>(derived(), newDimensions);\n    }\n    template <typename NewDimensions> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    TensorReshapingOp<const NewDimensions, Derived>\n    reshape(const NewDimensions& newDimensions) {\n      return TensorReshapingOp<const NewDimensions, Derived>(derived(), newDimensions);\n    }\n\n    template <typename StartIndices, typename Sizes> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorSlicingOp<const StartIndices, const Sizes, const Derived>\n    slice(const StartIndices& startIndices, const Sizes& sizes) const {\n      return TensorSlicingOp<const StartIndices, const Sizes, const Derived>(derived(), startIndices, sizes);\n    }\n    template <typename StartIndices, typename Sizes> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    TensorSlicingOp<const StartIndices, const Sizes, Derived>\n    slice(const StartIndices& startIndices, const Sizes& sizes) {\n      return TensorSlicingOp<const StartIndices, const Sizes, Derived>(derived(), startIndices, sizes);\n    }\n\n    template <typename StartIndices, typename StopIndices, typename Strides> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorStridingSlicingOp<const StartIndices, const StopIndices, const Strides, const Derived>\n    stridedSlice(const StartIndices& startIndices, const StopIndices& stopIndices, const Strides& strides) const {\n      return TensorStridingSlicingOp<const StartIndices, const StopIndices, const Strides,\n                                const Derived>(derived(), startIndices, stopIndices, strides);\n    }\n    template <typename StartIndices, typename StopIndices, typename Strides> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    TensorStridingSlicingOp<const StartIndices, const StopIndices, const Strides, Derived>\n    stridedSlice(const StartIndices& startIndices, const StopIndices& stopIndices, const Strides& strides) {\n      return TensorStridingSlicingOp<const StartIndices, const StopIndices, const Strides,\n                                Derived>(derived(), startIndices, stopIndices, strides);\n    }\n\n    template <DenseIndex DimId> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorChippingOp<DimId, const Derived>\n    chip(const Index offset) const {\n      return TensorChippingOp<DimId, const Derived>(derived(), offset, DimId);\n    }\n    template <Index DimId> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    TensorChippingOp<DimId, Derived>\n    chip(const Index offset) {\n      return TensorChippingOp<DimId, Derived>(derived(), offset, DimId);\n    }\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorChippingOp<Dynamic, const Derived>\n    chip(const Index offset, const Index dim) const {\n      return TensorChippingOp<Dynamic, const Derived>(derived(), offset, dim);\n    }\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    TensorChippingOp<Dynamic, Derived>\n    chip(const Index offset, const Index dim) {\n      return TensorChippingOp<Dynamic, Derived>(derived(), offset, dim);\n    }\n\n    template <typename ReverseDimensions> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorReverseOp<const ReverseDimensions, const Derived>\n    reverse(const ReverseDimensions& rev) const {\n      return TensorReverseOp<const ReverseDimensions, const Derived>(derived(), rev);\n    }\n    template <typename ReverseDimensions> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    TensorReverseOp<const ReverseDimensions, Derived>\n    reverse(const ReverseDimensions& rev) {\n      return TensorReverseOp<const ReverseDimensions, Derived>(derived(), rev);\n    }\n\n    template <typename Shuffle> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorShufflingOp<const Shuffle, const Derived>\n    shuffle(const Shuffle& shuffle) const {\n      return TensorShufflingOp<const Shuffle, const Derived>(derived(), shuffle);\n    }\n    template <typename Shuffle> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    TensorShufflingOp<const Shuffle, Derived>\n    shuffle(const Shuffle& shuffle) {\n      return TensorShufflingOp<const Shuffle, Derived>(derived(), shuffle);\n    }\n\n    template <typename Strides> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const TensorStridingOp<const Strides, const Derived>\n    stride(const Strides& strides) const {\n      return TensorStridingOp<const Strides, const Derived>(derived(), strides);\n    }\n    template <typename Strides> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    TensorStridingOp<const Strides, Derived>\n    stride(const Strides& strides) {\n      return TensorStridingOp<const Strides, Derived>(derived(), strides);\n    }\n\n    // Select the device on which to evaluate the expression.\n    template <typename DeviceType>\n    TensorDevice<Derived, DeviceType> device(const DeviceType& device) {\n      return TensorDevice<Derived, DeviceType>(device, derived());\n    }\n\n protected:\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Derived& derived() { return *static_cast<Derived*>(this); }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Derived& derived() const { return *static_cast<const Derived*>(this); }\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_BASE_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorBroadcasting.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_BROADCASTING_H\n#define EIGEN_CXX11_TENSOR_TENSOR_BROADCASTING_H\n\nnamespace Eigen {\n\n/** \\class TensorBroadcasting\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief Tensor broadcasting class.\n  *\n  *\n  */\nnamespace internal {\ntemplate<typename Broadcast, typename XprType>\nstruct traits<TensorBroadcastingOp<Broadcast, XprType> > : public traits<XprType>\n{\n  typedef typename XprType::Scalar Scalar;\n  typedef traits<XprType> XprTraits;\n  typedef typename XprTraits::StorageKind StorageKind;\n  typedef typename XprTraits::Index Index;\n  typedef typename XprType::Nested Nested;\n  typedef typename remove_reference<Nested>::type _Nested;\n  static const int NumDimensions = XprTraits::NumDimensions;\n  static const int Layout = XprTraits::Layout;\n};\n\ntemplate<typename Broadcast, typename XprType>\nstruct eval<TensorBroadcastingOp<Broadcast, XprType>, Eigen::Dense>\n{\n  typedef const TensorBroadcastingOp<Broadcast, XprType>& type;\n};\n\ntemplate<typename Broadcast, typename XprType>\nstruct nested<TensorBroadcastingOp<Broadcast, XprType>, 1, typename eval<TensorBroadcastingOp<Broadcast, XprType> >::type>\n{\n  typedef TensorBroadcastingOp<Broadcast, XprType> type;\n};\n\ntemplate <typename Dims>\nstruct is_input_scalar {\n  static const bool value = false;\n};\ntemplate <>\nstruct is_input_scalar<Sizes<> > {\n  static const bool value = true;\n};\n#ifndef EIGEN_EMULATE_CXX11_META_H\ntemplate <typename std::size_t... Indices>\nstruct is_input_scalar<Sizes<Indices...> > {\n  static const bool value = (Sizes<Indices...>::total_size == 1);\n};\n#endif\n\n}  // end namespace internal\n\n\n\ntemplate<typename Broadcast, typename XprType>\nclass TensorBroadcastingOp : public TensorBase<TensorBroadcastingOp<Broadcast, XprType>, ReadOnlyAccessors>\n{\n  public:\n  typedef typename Eigen::internal::traits<TensorBroadcastingOp>::Scalar Scalar;\n  typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename Eigen::internal::nested<TensorBroadcastingOp>::type Nested;\n  typedef typename Eigen::internal::traits<TensorBroadcastingOp>::StorageKind StorageKind;\n  typedef typename Eigen::internal::traits<TensorBroadcastingOp>::Index Index;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorBroadcastingOp(const XprType& expr, const Broadcast& broadcast)\n      : m_xpr(expr), m_broadcast(broadcast) {}\n\n    EIGEN_DEVICE_FUNC\n    const Broadcast& broadcast() const { return m_broadcast; }\n\n    EIGEN_DEVICE_FUNC\n    const typename internal::remove_all<typename XprType::Nested>::type&\n    expression() const { return m_xpr; }\n\n  protected:\n    typename XprType::Nested m_xpr;\n    const Broadcast m_broadcast;\n};\n\n\n// Eval as rvalue\ntemplate<typename Broadcast, typename ArgType, typename Device>\nstruct TensorEvaluator<const TensorBroadcastingOp<Broadcast, ArgType>, Device>\n{\n  typedef TensorBroadcastingOp<Broadcast, ArgType> XprType;\n  typedef typename XprType::Index Index;\n  static const int NumDims = internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value;\n  typedef DSizes<Index, NumDims> Dimensions;\n  typedef typename XprType::Scalar Scalar;\n  typedef typename TensorEvaluator<ArgType, Device>::Dimensions InputDimensions;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  static const int PacketSize = internal::unpacket_traits<PacketReturnType>::size;\n\n  enum {\n    IsAligned = true,\n    PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,\n    Layout = TensorEvaluator<ArgType, Device>::Layout,\n    RawAccess = false\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)\n    : m_broadcast(op.broadcast()),m_impl(op.expression(), device)\n  {\n    // The broadcasting op doesn't change the rank of the tensor. One can't broadcast a scalar\n    // and store the result in a scalar. Instead one should reshape the scalar into a a N-D\n    // tensor with N >= 1 of 1 element first and then broadcast.\n    EIGEN_STATIC_ASSERT((NumDims > 0), YOU_MADE_A_PROGRAMMING_MISTAKE);\n    const InputDimensions& input_dims = m_impl.dimensions();\n    const Broadcast& broadcast = op.broadcast();\n    for (int i = 0; i < NumDims; ++i) {\n      eigen_assert(input_dims[i] > 0);\n      m_dimensions[i] = input_dims[i] * broadcast[i];\n    }\n\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      m_inputStrides[0] = 1;\n      m_outputStrides[0] = 1;\n      for (int i = 1; i < NumDims; ++i) {\n        m_inputStrides[i] = m_inputStrides[i-1] * input_dims[i-1];\n        m_outputStrides[i] = m_outputStrides[i-1] * m_dimensions[i-1];\n      }\n    } else {\n      m_inputStrides[NumDims-1] = 1;\n      m_outputStrides[NumDims-1] = 1;\n      for (int i = NumDims-2; i >= 0; --i) {\n        m_inputStrides[i] = m_inputStrides[i+1] * input_dims[i+1];\n        m_outputStrides[i] = m_outputStrides[i+1] * m_dimensions[i+1];\n      }\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(Scalar* /*data*/) {\n    m_impl.evalSubExprsIfNeeded(NULL);\n    return true;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {\n    m_impl.cleanup();\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE CoeffReturnType coeff(Index index) const\n  {\n    if (internal::is_input_scalar<typename internal::remove_all<InputDimensions>::type>::value) {\n      return m_impl.coeff(0);\n    }\n\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      return coeffColMajor(index);\n    } else {\n      return coeffRowMajor(index);\n    }\n  }\n\n  // TODO: attempt to speed this up. The integer divisions and modulo are slow\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeffColMajor(Index index) const\n  {\n    Index inputIndex = 0;\n    for (int i = NumDims - 1; i > 0; --i) {\n      const Index idx = index / m_outputStrides[i];\n      if (internal::index_statically_eq<Broadcast>(i, 1)) {\n        eigen_assert(idx < m_impl.dimensions()[i]);\n        inputIndex += idx * m_inputStrides[i];\n      } else {\n        if (internal::index_statically_eq<InputDimensions>(i, 1)) {\n          eigen_assert(idx % m_impl.dimensions()[i] == 0);\n        } else {\n          inputIndex += (idx % m_impl.dimensions()[i]) * m_inputStrides[i];\n        }\n      }\n      index -= idx * m_outputStrides[i];\n    }\n    if (internal::index_statically_eq<Broadcast>(0, 1)) {\n      eigen_assert(index < m_impl.dimensions()[0]);\n      inputIndex += index;\n    } else {\n      if (internal::index_statically_eq<InputDimensions>(0, 1)) {\n        eigen_assert(index % m_impl.dimensions()[0] == 0);\n      } else {\n        inputIndex += (index % m_impl.dimensions()[0]);\n      }\n    }\n    return m_impl.coeff(inputIndex);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeffRowMajor(Index index) const\n  {\n    Index inputIndex = 0;\n    for (int i = 0; i < NumDims - 1; ++i) {\n      const Index idx = index / m_outputStrides[i];\n      if (internal::index_statically_eq<Broadcast>(i, 1)) {\n        eigen_assert(idx < m_impl.dimensions()[i]);\n        inputIndex += idx * m_inputStrides[i];\n      } else {\n        if (internal::index_statically_eq<InputDimensions>(i, 1)) {\n          eigen_assert(idx % m_impl.dimensions()[i] == 0);\n        } else {\n          inputIndex += (idx % m_impl.dimensions()[i]) * m_inputStrides[i];\n        }\n      }\n      index -= idx * m_outputStrides[i];\n    }\n    if (internal::index_statically_eq<Broadcast>(NumDims-1, 1)) {\n      eigen_assert(index < m_impl.dimensions()[NumDims-1]);\n      inputIndex += index;\n    } else {\n      if (internal::index_statically_eq<InputDimensions>(NumDims-1, 1)) {\n        eigen_assert(index % m_impl.dimensions()[NumDims-1] == 0);\n      } else {\n        inputIndex += (index % m_impl.dimensions()[NumDims-1]);\n      }\n    }\n    return m_impl.coeff(inputIndex);\n  }\n\n  template<int LoadMode>\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketReturnType packet(Index index) const\n  {\n    if (internal::is_input_scalar<typename internal::remove_all<InputDimensions>::type>::value) {\n      return internal::pset1<PacketReturnType>(m_impl.coeff(0));\n    }\n\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      return packetColMajor<LoadMode>(index);\n    } else {\n      return packetRowMajor<LoadMode>(index);\n    }\n  }\n\n  // Ignore the LoadMode and always use unaligned loads since we can't guarantee\n  // the alignment at compile time.\n  template<int LoadMode>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packetColMajor(Index index) const\n  {\n    EIGEN_STATIC_ASSERT((PacketSize > 1), YOU_MADE_A_PROGRAMMING_MISTAKE)\n    eigen_assert(index+PacketSize-1 < dimensions().TotalSize());\n\n    const Index originalIndex = index;\n\n    Index inputIndex = 0;\n    for (int i = NumDims - 1; i > 0; --i) {\n      const Index idx = index / m_outputStrides[i];\n      if (internal::index_statically_eq<Broadcast>(i, 1)) {\n        eigen_assert(idx < m_impl.dimensions()[i]);\n        inputIndex += idx * m_inputStrides[i];\n      } else {\n        if (internal::index_statically_eq<InputDimensions>(i, 1)) {\n          eigen_assert(idx % m_impl.dimensions()[i] == 0);\n        } else {\n          inputIndex += (idx % m_impl.dimensions()[i]) * m_inputStrides[i];\n        }\n      }\n      index -= idx * m_outputStrides[i];\n    }\n    Index innermostLoc;\n    if (internal::index_statically_eq<Broadcast>(0, 1)) {\n      eigen_assert(index < m_impl.dimensions()[0]);\n      innermostLoc = index;\n    } else {\n      if (internal::index_statically_eq<InputDimensions>(0, 1)) {\n        eigen_assert(index % m_impl.dimensions()[0] == 0);\n        innermostLoc = 0;\n      } else {\n        innermostLoc = index % m_impl.dimensions()[0];\n      }\n    }\n    inputIndex += innermostLoc;\n\n    // Todo: this could be extended to the second dimension if we're not\n    // broadcasting alongside the first dimension, and so on.\n    if (innermostLoc + PacketSize <= m_impl.dimensions()[0]) {\n      return m_impl.template packet<Unaligned>(inputIndex);\n    } else {\n      EIGEN_ALIGN_MAX typename internal::remove_const<CoeffReturnType>::type values[PacketSize];\n      values[0] = m_impl.coeff(inputIndex);\n      for (int i = 1; i < PacketSize; ++i) {\n        values[i] = coeffColMajor(originalIndex+i);\n      }\n      PacketReturnType rslt = internal::pload<PacketReturnType>(values);\n      return rslt;\n    }\n  }\n\n  template<int LoadMode>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packetRowMajor(Index index) const\n  {\n    EIGEN_STATIC_ASSERT((PacketSize > 1), YOU_MADE_A_PROGRAMMING_MISTAKE)\n    eigen_assert(index+PacketSize-1 < dimensions().TotalSize());\n\n    const Index originalIndex = index;\n\n    Index inputIndex = 0;\n    for (int i = 0; i < NumDims - 1; ++i) {\n      const Index idx = index / m_outputStrides[i];\n      if (internal::index_statically_eq<Broadcast>(i, 1)) {\n        eigen_assert(idx < m_impl.dimensions()[i]);\n        inputIndex += idx * m_inputStrides[i];\n      } else {\n        if (internal::index_statically_eq<InputDimensions>(i, 1)) {\n          eigen_assert(idx % m_impl.dimensions()[i] == 0);\n        } else {\n          inputIndex += (idx % m_impl.dimensions()[i]) * m_inputStrides[i];\n        }\n      }\n      index -= idx * m_outputStrides[i];\n    }\n    Index innermostLoc;\n    if (internal::index_statically_eq<Broadcast>(NumDims-1, 1)) {\n      eigen_assert(index < m_impl.dimensions()[NumDims-1]);\n      innermostLoc = index;\n    } else {\n      if (internal::index_statically_eq<InputDimensions>(NumDims-1, 1)) {\n        eigen_assert(index % m_impl.dimensions()[NumDims-1] == 0);\n        innermostLoc = 0;\n      } else {\n        innermostLoc = index % m_impl.dimensions()[NumDims-1];\n      }\n    }\n    inputIndex += innermostLoc;\n\n    // Todo: this could be extended to the second dimension if we're not\n    // broadcasting alongside the first dimension, and so on.\n    if (innermostLoc + PacketSize <= m_impl.dimensions()[NumDims-1]) {\n      return m_impl.template packet<Unaligned>(inputIndex);\n    } else {\n      EIGEN_ALIGN_MAX typename internal::remove_const<CoeffReturnType>::type values[PacketSize];\n      values[0] = m_impl.coeff(inputIndex);\n      for (int i = 1; i < PacketSize; ++i) {\n        values[i] = coeffRowMajor(originalIndex+i);\n      }\n      PacketReturnType rslt = internal::pload<PacketReturnType>(values);\n      return rslt;\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost\n  costPerCoeff(bool vectorized) const {\n    double compute_cost = TensorOpCost::AddCost<Index>();\n    if (NumDims > 0) {\n      for (int i = NumDims - 1; i > 0; --i) {\n        compute_cost += TensorOpCost::DivCost<Index>();\n        if (internal::index_statically_eq<Broadcast>(i, 1)) {\n          compute_cost +=\n              TensorOpCost::MulCost<Index>() + TensorOpCost::AddCost<Index>();\n        } else {\n          if (!internal::index_statically_eq<InputDimensions>(i, 1)) {\n            compute_cost += TensorOpCost::MulCost<Index>() +\n                            TensorOpCost::ModCost<Index>() +\n                            TensorOpCost::AddCost<Index>();\n          }\n        }\n        compute_cost +=\n            TensorOpCost::MulCost<Index>() + TensorOpCost::AddCost<Index>();\n      }\n    }\n    return m_impl.costPerCoeff(vectorized) +\n           TensorOpCost(0, 0, compute_cost, vectorized, PacketSize);\n  }\n\n  EIGEN_DEVICE_FUNC Scalar* data() const { return NULL; }\n\n  const TensorEvaluator<ArgType, Device>& impl() const { return m_impl; }\n\n  Broadcast functor() const { return m_broadcast; }\n\n protected:\n  const Broadcast m_broadcast;\n  Dimensions m_dimensions;\n  array<Index, NumDims> m_outputStrides;\n  array<Index, NumDims> m_inputStrides;\n  TensorEvaluator<ArgType, Device> m_impl;\n};\n\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_BROADCASTING_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorChipping.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_CHIPPING_H\n#define EIGEN_CXX11_TENSOR_TENSOR_CHIPPING_H\n\nnamespace Eigen {\n\n/** \\class TensorKChippingReshaping\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief A chip is a thin slice, corresponding to a column or a row in a 2-d tensor.\n  *\n  *\n  */\n\nnamespace internal {\ntemplate<DenseIndex DimId, typename XprType>\nstruct traits<TensorChippingOp<DimId, XprType> > : public traits<XprType>\n{\n  typedef typename XprType::Scalar Scalar;\n  typedef traits<XprType> XprTraits;\n  typedef typename XprTraits::StorageKind StorageKind;\n  typedef typename XprTraits::Index Index;\n  typedef typename XprType::Nested Nested;\n  typedef typename remove_reference<Nested>::type _Nested;\n  static const int NumDimensions = XprTraits::NumDimensions - 1;\n  static const int Layout = XprTraits::Layout;\n};\n\ntemplate<DenseIndex DimId, typename XprType>\nstruct eval<TensorChippingOp<DimId, XprType>, Eigen::Dense>\n{\n  typedef const TensorChippingOp<DimId, XprType>& type;\n};\n\ntemplate<DenseIndex DimId, typename XprType>\nstruct nested<TensorChippingOp<DimId, XprType>, 1, typename eval<TensorChippingOp<DimId, XprType> >::type>\n{\n  typedef TensorChippingOp<DimId, XprType> type;\n};\n\ntemplate <DenseIndex DimId>\nstruct DimensionId\n{\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DimensionId(DenseIndex dim) {\n    eigen_assert(dim == DimId);\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DenseIndex actualDim() const {\n    return DimId;\n  }\n};\ntemplate <>\nstruct DimensionId<Dynamic>\n{\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DimensionId(DenseIndex dim) : actual_dim(dim) {\n    eigen_assert(dim >= 0);\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DenseIndex actualDim() const {\n    return actual_dim;\n  }\n private:\n  const DenseIndex actual_dim;\n};\n\n\n}  // end namespace internal\n\n\n\ntemplate<DenseIndex DimId, typename XprType>\nclass TensorChippingOp : public TensorBase<TensorChippingOp<DimId, XprType> >\n{\n  public:\n  typedef typename Eigen::internal::traits<TensorChippingOp>::Scalar Scalar;\n  typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename Eigen::internal::nested<TensorChippingOp>::type Nested;\n  typedef typename Eigen::internal::traits<TensorChippingOp>::StorageKind StorageKind;\n  typedef typename Eigen::internal::traits<TensorChippingOp>::Index Index;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorChippingOp(const XprType& expr, const Index offset, const Index dim)\n      : m_xpr(expr), m_offset(offset), m_dim(dim) {\n  }\n\n  EIGEN_DEVICE_FUNC\n  const Index offset() const { return m_offset; }\n  EIGEN_DEVICE_FUNC\n  const Index dim() const { return m_dim.actualDim(); }\n\n  EIGEN_DEVICE_FUNC\n  const typename internal::remove_all<typename XprType::Nested>::type&\n  expression() const { return m_xpr; }\n\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE TensorChippingOp& operator = (const TensorChippingOp& other)\n  {\n    typedef TensorAssignOp<TensorChippingOp, const TensorChippingOp> Assign;\n    Assign assign(*this, other);\n    internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());\n    return *this;\n  }\n\n  template<typename OtherDerived>\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE TensorChippingOp& operator = (const OtherDerived& other)\n  {\n    typedef TensorAssignOp<TensorChippingOp, const OtherDerived> Assign;\n    Assign assign(*this, other);\n    internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());\n    return *this;\n  }\n\n  protected:\n    typename XprType::Nested m_xpr;\n    const Index m_offset;\n    const internal::DimensionId<DimId> m_dim;\n};\n\n\n// Eval as rvalue\ntemplate<DenseIndex DimId, typename ArgType, typename Device>\nstruct TensorEvaluator<const TensorChippingOp<DimId, ArgType>, Device>\n{\n  typedef TensorChippingOp<DimId, ArgType> XprType;\n  static const int NumInputDims = internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value;\n  static const int NumDims = NumInputDims-1;\n  typedef typename XprType::Index Index;\n  typedef DSizes<Index, NumDims> Dimensions;\n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  static const int PacketSize = internal::unpacket_traits<PacketReturnType>::size;\n\n\n  enum {\n    // Alignment can't be guaranteed at compile time since it depends on the\n    // slice offsets.\n    IsAligned = false,\n    PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,\n    Layout = TensorEvaluator<ArgType, Device>::Layout,\n    CoordAccess = false,  // to be implemented\n    RawAccess = false\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)\n      : m_impl(op.expression(), device), m_dim(op.dim()), m_device(device)\n  {\n    EIGEN_STATIC_ASSERT((NumInputDims >= 1), YOU_MADE_A_PROGRAMMING_MISTAKE);\n    eigen_assert(NumInputDims > m_dim.actualDim());\n\n    const typename TensorEvaluator<ArgType, Device>::Dimensions& input_dims = m_impl.dimensions();\n    eigen_assert(op.offset() < input_dims[m_dim.actualDim()]);\n\n    int j = 0;\n    for (int i = 0; i < NumInputDims; ++i) {\n      if (i != m_dim.actualDim()) {\n        m_dimensions[j] = input_dims[i];\n        ++j;\n      }\n    }\n\n    m_stride = 1;\n    m_inputStride = 1;\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      for (int i = 0; i < m_dim.actualDim(); ++i) {\n        m_stride *= input_dims[i];\n        m_inputStride *= input_dims[i];\n      }\n    } else {\n      for (int i = NumInputDims-1; i > m_dim.actualDim(); --i) {\n        m_stride *= input_dims[i];\n        m_inputStride *= input_dims[i];\n      }\n    }\n    m_inputStride *= input_dims[m_dim.actualDim()];\n    m_inputOffset = m_stride * op.offset();\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(Scalar* /*data*/) {\n    m_impl.evalSubExprsIfNeeded(NULL);\n    return true;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {\n    m_impl.cleanup();\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const\n  {\n    return m_impl.coeff(srcCoeff(index));\n  }\n\n  template<int LoadMode>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const\n  {\n    EIGEN_STATIC_ASSERT((PacketSize > 1), YOU_MADE_A_PROGRAMMING_MISTAKE)\n    eigen_assert(index+PacketSize-1 < dimensions().TotalSize());\n\n    if ((static_cast<int>(Layout) == static_cast<int>(ColMajor) && m_dim.actualDim() == 0) ||\n\t(static_cast<int>(Layout) == static_cast<int>(RowMajor) && m_dim.actualDim() == NumInputDims-1)) {\n      // m_stride is equal to 1, so let's avoid the integer division.\n      eigen_assert(m_stride == 1);\n      Index inputIndex = index * m_inputStride + m_inputOffset;\n      EIGEN_ALIGN_MAX typename internal::remove_const<CoeffReturnType>::type values[PacketSize];\n      for (int i = 0; i < PacketSize; ++i) {\n        values[i] = m_impl.coeff(inputIndex);\n        inputIndex += m_inputStride;\n      }\n      PacketReturnType rslt = internal::pload<PacketReturnType>(values);\n      return rslt;\n    } else if ((static_cast<int>(Layout) == static_cast<int>(ColMajor) && m_dim.actualDim() == NumInputDims - 1) ||\n\t       (static_cast<int>(Layout) == static_cast<int>(RowMajor) && m_dim.actualDim() == 0)) {\n      // m_stride is aways greater than index, so let's avoid the integer division.\n      eigen_assert(m_stride > index);\n      return m_impl.template packet<LoadMode>(index + m_inputOffset);\n    } else {\n      const Index idx = index / m_stride;\n      const Index rem = index - idx * m_stride;\n      if (rem + PacketSize <= m_stride) {\n        Index inputIndex = idx * m_inputStride + m_inputOffset + rem;\n        return m_impl.template packet<LoadMode>(inputIndex);\n      } else {\n        // Cross the stride boundary. Fallback to slow path.\n        EIGEN_ALIGN_MAX typename internal::remove_const<CoeffReturnType>::type values[PacketSize];\n        for (int i = 0; i < PacketSize; ++i) {\n          values[i] = coeff(index);\n          ++index;\n        }\n        PacketReturnType rslt = internal::pload<PacketReturnType>(values);\n        return rslt;\n      }\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost\n  costPerCoeff(bool vectorized) const {\n    double cost = 0;\n    if ((static_cast<int>(Layout) == static_cast<int>(ColMajor) &&\n         m_dim.actualDim() == 0) ||\n        (static_cast<int>(Layout) == static_cast<int>(RowMajor) &&\n         m_dim.actualDim() == NumInputDims - 1)) {\n      cost += TensorOpCost::MulCost<Index>() + TensorOpCost::AddCost<Index>();\n    } else if ((static_cast<int>(Layout) == static_cast<int>(ColMajor) &&\n                m_dim.actualDim() == NumInputDims - 1) ||\n               (static_cast<int>(Layout) == static_cast<int>(RowMajor) &&\n                m_dim.actualDim() == 0)) {\n      cost += TensorOpCost::AddCost<Index>();\n    } else {\n      cost += 3 * TensorOpCost::MulCost<Index>() + TensorOpCost::DivCost<Index>() +\n              3 * TensorOpCost::AddCost<Index>();\n    }\n\n    return m_impl.costPerCoeff(vectorized) +\n           TensorOpCost(0, 0, cost, vectorized, PacketSize);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType* data() const {\n    CoeffReturnType* result = const_cast<CoeffReturnType*>(m_impl.data());\n    if (((static_cast<int>(Layout) == static_cast<int>(ColMajor) && m_dim.actualDim() == NumDims) ||\n         (static_cast<int>(Layout) == static_cast<int>(RowMajor) && m_dim.actualDim() == 0)) &&\n        result) {\n      return result + m_inputOffset;\n    } else {\n      return NULL;\n    }\n  }\n\n protected:\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index srcCoeff(Index index) const\n  {\n    Index inputIndex;\n    if ((static_cast<int>(Layout) == static_cast<int>(ColMajor) && m_dim.actualDim() == 0) ||\n\t(static_cast<int>(Layout) == static_cast<int>(RowMajor) && m_dim.actualDim() == NumInputDims-1)) {\n      // m_stride is equal to 1, so let's avoid the integer division.\n      eigen_assert(m_stride == 1);\n      inputIndex = index * m_inputStride + m_inputOffset;\n    } else if ((static_cast<int>(Layout) == static_cast<int>(ColMajor) && m_dim.actualDim() == NumInputDims-1) ||\n\t       (static_cast<int>(Layout) == static_cast<int>(RowMajor) && m_dim.actualDim() == 0)) {\n      // m_stride is aways greater than index, so let's avoid the integer division.\n      eigen_assert(m_stride > index);\n      inputIndex = index + m_inputOffset;\n    } else {\n      const Index idx = index / m_stride;\n      inputIndex = idx * m_inputStride + m_inputOffset;\n      index -= idx * m_stride;\n      inputIndex += index;\n    }\n    return inputIndex;\n  }\n\n  Dimensions m_dimensions;\n  Index m_stride;\n  Index m_inputOffset;\n  Index m_inputStride;\n  TensorEvaluator<ArgType, Device> m_impl;\n  const internal::DimensionId<DimId> m_dim;\n  const Device& m_device;\n};\n\n\n// Eval as lvalue\ntemplate<DenseIndex DimId, typename ArgType, typename Device>\nstruct TensorEvaluator<TensorChippingOp<DimId, ArgType>, Device>\n  : public TensorEvaluator<const TensorChippingOp<DimId, ArgType>, Device>\n{\n  typedef TensorEvaluator<const TensorChippingOp<DimId, ArgType>, Device> Base;\n  typedef TensorChippingOp<DimId, ArgType> XprType;\n  static const int NumInputDims = internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value;\n  static const int NumDims = NumInputDims-1;\n  typedef typename XprType::Index Index;\n  typedef DSizes<Index, NumDims> Dimensions;\n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  static const int PacketSize = internal::unpacket_traits<PacketReturnType>::size;\n\n  enum {\n    IsAligned = false,\n    PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,\n    RawAccess = false\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)\n    : Base(op, device)\n    { }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType& coeffRef(Index index)\n  {\n    return this->m_impl.coeffRef(this->srcCoeff(index));\n  }\n\n  template <int StoreMode> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  void writePacket(Index index, const PacketReturnType& x)\n  {\n    EIGEN_STATIC_ASSERT((PacketSize > 1), YOU_MADE_A_PROGRAMMING_MISTAKE)\n\n    if ((static_cast<int>(this->Layout) == static_cast<int>(ColMajor) && this->m_dim.actualDim() == 0) ||\n\t(static_cast<int>(this->Layout) == static_cast<int>(RowMajor) && this->m_dim.actualDim() == NumInputDims-1)) {\n      // m_stride is equal to 1, so let's avoid the integer division.\n      eigen_assert(this->m_stride == 1);\n      EIGEN_ALIGN_MAX typename internal::remove_const<CoeffReturnType>::type values[PacketSize];\n      internal::pstore<CoeffReturnType, PacketReturnType>(values, x);\n      Index inputIndex = index * this->m_inputStride + this->m_inputOffset;\n      for (int i = 0; i < PacketSize; ++i) {\n        this->m_impl.coeffRef(inputIndex) = values[i];\n        inputIndex += this->m_inputStride;\n      }\n    } else if ((static_cast<int>(this->Layout) == static_cast<int>(ColMajor) && this->m_dim.actualDim() == NumInputDims-1) ||\n\t       (static_cast<int>(this->Layout) == static_cast<int>(RowMajor) && this->m_dim.actualDim() == 0)) {\n      // m_stride is aways greater than index, so let's avoid the integer division.\n      eigen_assert(this->m_stride > index);\n      this->m_impl.template writePacket<StoreMode>(index + this->m_inputOffset, x);\n    } else {\n      const Index idx = index / this->m_stride;\n      const Index rem = index - idx * this->m_stride;\n      if (rem + PacketSize <= this->m_stride) {\n        const Index inputIndex = idx * this->m_inputStride + this->m_inputOffset + rem;\n        this->m_impl.template writePacket<StoreMode>(inputIndex, x);\n      } else {\n        // Cross stride boundary. Fallback to slow path.\n        EIGEN_ALIGN_MAX typename internal::remove_const<CoeffReturnType>::type values[PacketSize];\n        internal::pstore<CoeffReturnType, PacketReturnType>(values, x);\n        for (int i = 0; i < PacketSize; ++i) {\n          this->coeffRef(index) = values[i];\n          ++index;\n        }\n      }\n    }\n  }\n};\n\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_CHIPPING_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorConcatenation.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_CONCATENATION_H\n#define EIGEN_CXX11_TENSOR_TENSOR_CONCATENATION_H\n\nnamespace Eigen {\n\n/** \\class TensorConcatenationOp\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief Tensor concatenation class.\n  *\n  *\n  */\nnamespace internal {\ntemplate<typename Axis, typename LhsXprType, typename RhsXprType>\nstruct traits<TensorConcatenationOp<Axis, LhsXprType, RhsXprType> >\n{\n  // Type promotion to handle the case where the types of the lhs and the rhs are different.\n  typedef typename promote_storage_type<typename LhsXprType::Scalar,\n                                        typename RhsXprType::Scalar>::ret Scalar;\n  typedef typename promote_storage_type<typename traits<LhsXprType>::StorageKind,\n                                        typename traits<RhsXprType>::StorageKind>::ret StorageKind;\n  typedef typename promote_index_type<typename traits<LhsXprType>::Index,\n                                      typename traits<RhsXprType>::Index>::type Index;\n  typedef typename LhsXprType::Nested LhsNested;\n  typedef typename RhsXprType::Nested RhsNested;\n  typedef typename remove_reference<LhsNested>::type _LhsNested;\n  typedef typename remove_reference<RhsNested>::type _RhsNested;\n  static const int NumDimensions = traits<LhsXprType>::NumDimensions;\n  static const int Layout = traits<LhsXprType>::Layout;\n  enum { Flags = 0 };\n};\n\ntemplate<typename Axis, typename LhsXprType, typename RhsXprType>\nstruct eval<TensorConcatenationOp<Axis, LhsXprType, RhsXprType>, Eigen::Dense>\n{\n  typedef const TensorConcatenationOp<Axis, LhsXprType, RhsXprType>& type;\n};\n\ntemplate<typename Axis, typename LhsXprType, typename RhsXprType>\nstruct nested<TensorConcatenationOp<Axis, LhsXprType, RhsXprType>, 1, typename eval<TensorConcatenationOp<Axis, LhsXprType, RhsXprType> >::type>\n{\n  typedef TensorConcatenationOp<Axis, LhsXprType, RhsXprType> type;\n};\n\n}  // end namespace internal\n\n\ntemplate<typename Axis, typename LhsXprType, typename RhsXprType>\nclass TensorConcatenationOp : public TensorBase<TensorConcatenationOp<Axis, LhsXprType, RhsXprType>, WriteAccessors>\n{\n  public:\n    typedef typename internal::traits<TensorConcatenationOp>::Scalar Scalar;\n    typedef typename internal::traits<TensorConcatenationOp>::StorageKind StorageKind;\n    typedef typename internal::traits<TensorConcatenationOp>::Index Index;\n    typedef typename internal::nested<TensorConcatenationOp>::type Nested;\n    typedef typename internal::promote_storage_type<typename LhsXprType::CoeffReturnType,\n                                                    typename RhsXprType::CoeffReturnType>::ret CoeffReturnType;\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorConcatenationOp(const LhsXprType& lhs, const RhsXprType& rhs, Axis axis)\n        : m_lhs_xpr(lhs), m_rhs_xpr(rhs), m_axis(axis) {}\n\n    EIGEN_DEVICE_FUNC\n    const typename internal::remove_all<typename LhsXprType::Nested>::type&\n    lhsExpression() const { return m_lhs_xpr; }\n\n    EIGEN_DEVICE_FUNC\n    const typename internal::remove_all<typename RhsXprType::Nested>::type&\n    rhsExpression() const { return m_rhs_xpr; }\n\n    EIGEN_DEVICE_FUNC const Axis& axis() const { return m_axis; }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE TensorConcatenationOp& operator = (const TensorConcatenationOp& other)\n    {\n      typedef TensorAssignOp<TensorConcatenationOp, const TensorConcatenationOp> Assign;\n      Assign assign(*this, other);\n      internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());\n      return *this;\n    }\n\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE TensorConcatenationOp& operator = (const OtherDerived& other)\n    {\n      typedef TensorAssignOp<TensorConcatenationOp, const OtherDerived> Assign;\n      Assign assign(*this, other);\n      internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());\n      return *this;\n    }\n\n  protected:\n    typename LhsXprType::Nested m_lhs_xpr;\n    typename RhsXprType::Nested m_rhs_xpr;\n    const Axis m_axis;\n};\n\n\n// Eval as rvalue\ntemplate<typename Axis, typename LeftArgType, typename RightArgType, typename Device>\nstruct TensorEvaluator<const TensorConcatenationOp<Axis, LeftArgType, RightArgType>, Device>\n{\n  typedef TensorConcatenationOp<Axis, LeftArgType, RightArgType> XprType;\n  typedef typename XprType::Index Index;\n  static const int NumDims = internal::array_size<typename TensorEvaluator<LeftArgType, Device>::Dimensions>::value;\n  static const int RightNumDims = internal::array_size<typename TensorEvaluator<RightArgType, Device>::Dimensions>::value;\n  typedef DSizes<Index, NumDims> Dimensions;\n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  enum {\n    IsAligned = false,\n    PacketAccess = TensorEvaluator<LeftArgType, Device>::PacketAccess & TensorEvaluator<RightArgType, Device>::PacketAccess,\n    Layout = TensorEvaluator<LeftArgType, Device>::Layout,\n    RawAccess = false\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)\n    : m_leftImpl(op.lhsExpression(), device), m_rightImpl(op.rhsExpression(), device), m_axis(op.axis())\n  {\n    EIGEN_STATIC_ASSERT((static_cast<int>(TensorEvaluator<LeftArgType, Device>::Layout) == static_cast<int>(TensorEvaluator<RightArgType, Device>::Layout) || NumDims == 1), YOU_MADE_A_PROGRAMMING_MISTAKE);\n    EIGEN_STATIC_ASSERT((NumDims == RightNumDims), YOU_MADE_A_PROGRAMMING_MISTAKE);\n    EIGEN_STATIC_ASSERT((NumDims > 0), YOU_MADE_A_PROGRAMMING_MISTAKE);\n\n    eigen_assert(0 <= m_axis && m_axis < NumDims);\n    const Dimensions& lhs_dims = m_leftImpl.dimensions();\n    const Dimensions& rhs_dims = m_rightImpl.dimensions();\n    {\n      int i = 0;\n      for (; i < m_axis; ++i) {\n        eigen_assert(lhs_dims[i] > 0);\n        eigen_assert(lhs_dims[i] == rhs_dims[i]);\n        m_dimensions[i] = lhs_dims[i];\n      }\n      eigen_assert(lhs_dims[i] > 0);  // Now i == m_axis.\n      eigen_assert(rhs_dims[i] > 0);\n      m_dimensions[i] = lhs_dims[i] + rhs_dims[i];\n      for (++i; i < NumDims; ++i) {\n        eigen_assert(lhs_dims[i] > 0);\n        eigen_assert(lhs_dims[i] == rhs_dims[i]);\n        m_dimensions[i] = lhs_dims[i];\n      }\n    }\n\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      m_leftStrides[0] = 1;\n      m_rightStrides[0] = 1;\n      m_outputStrides[0] = 1;\n\n      for (int j = 1; j < NumDims; ++j) {\n        m_leftStrides[j] = m_leftStrides[j-1] * lhs_dims[j-1];\n        m_rightStrides[j] = m_rightStrides[j-1] * rhs_dims[j-1];\n        m_outputStrides[j] = m_outputStrides[j-1] * m_dimensions[j-1];\n      }\n    } else {\n      m_leftStrides[NumDims - 1] = 1;\n      m_rightStrides[NumDims - 1] = 1;\n      m_outputStrides[NumDims - 1] = 1;\n\n      for (int j = NumDims - 2; j >= 0; --j) {\n        m_leftStrides[j] = m_leftStrides[j+1] * lhs_dims[j+1];\n        m_rightStrides[j] = m_rightStrides[j+1] * rhs_dims[j+1];\n        m_outputStrides[j] = m_outputStrides[j+1] * m_dimensions[j+1];\n      }\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }\n\n  // TODO(phli): Add short-circuit memcpy evaluation if underlying data are linear?\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(Scalar* /*data*/)\n  {\n    m_leftImpl.evalSubExprsIfNeeded(NULL);\n    m_rightImpl.evalSubExprsIfNeeded(NULL);\n    return true;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup()\n  {\n    m_leftImpl.cleanup();\n    m_rightImpl.cleanup();\n  }\n\n  // TODO(phli): attempt to speed this up. The integer divisions and modulo are slow.\n  // See CL/76180724 comments for more ideas.\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const\n  {\n    // Collect dimension-wise indices (subs).\n    array<Index, NumDims> subs;\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      for (int i = NumDims - 1; i > 0; --i) {\n        subs[i] = index / m_outputStrides[i];\n        index -= subs[i] * m_outputStrides[i];\n      }\n      subs[0] = index;\n    } else {\n      for (int i = 0; i < NumDims - 1; ++i) {\n        subs[i] = index / m_outputStrides[i];\n        index -= subs[i] * m_outputStrides[i];\n      }\n      subs[NumDims - 1] = index;\n    }\n\n    const Dimensions& left_dims = m_leftImpl.dimensions();\n    if (subs[m_axis] < left_dims[m_axis]) {\n      Index left_index;\n      if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n        left_index = subs[0];\n        for (int i = 1; i < NumDims; ++i) {\n          left_index += (subs[i] % left_dims[i]) * m_leftStrides[i];\n        }\n      } else {\n        left_index = subs[NumDims - 1];\n        for (int i = NumDims - 2; i >= 0; --i) {\n          left_index += (subs[i] % left_dims[i]) * m_leftStrides[i];\n        }\n      }\n      return m_leftImpl.coeff(left_index);\n    } else {\n      subs[m_axis] -= left_dims[m_axis];\n      const Dimensions& right_dims = m_rightImpl.dimensions();\n      Index right_index;\n      if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n        right_index = subs[0];\n        for (int i = 1; i < NumDims; ++i) {\n          right_index += (subs[i] % right_dims[i]) * m_rightStrides[i];\n        }\n      } else {\n        right_index = subs[NumDims - 1];\n        for (int i = NumDims - 2; i >= 0; --i) {\n          right_index += (subs[i] % right_dims[i]) * m_rightStrides[i];\n        }\n      }\n      return m_rightImpl.coeff(right_index);\n    }\n  }\n\n  // TODO(phli): Add a real vectorization.\n  template<int LoadMode>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const\n  {\n    const int packetSize = internal::unpacket_traits<PacketReturnType>::size;\n    EIGEN_STATIC_ASSERT((packetSize > 1), YOU_MADE_A_PROGRAMMING_MISTAKE)\n    eigen_assert(index + packetSize - 1 < dimensions().TotalSize());\n\n    EIGEN_ALIGN_MAX CoeffReturnType values[packetSize];\n    for (int i = 0; i < packetSize; ++i) {\n      values[i] = coeff(index+i);\n    }\n    PacketReturnType rslt = internal::pload<PacketReturnType>(values);\n    return rslt;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost\n  costPerCoeff(bool vectorized) const {\n    const double compute_cost = NumDims * (2 * TensorOpCost::AddCost<Index>() +\n                                           2 * TensorOpCost::MulCost<Index>() +\n                                           TensorOpCost::DivCost<Index>() +\n                                           TensorOpCost::ModCost<Index>());\n    const double lhs_size = m_leftImpl.dimensions().TotalSize();\n    const double rhs_size = m_rightImpl.dimensions().TotalSize();\n    return (lhs_size / (lhs_size + rhs_size)) *\n               m_leftImpl.costPerCoeff(vectorized) +\n           (rhs_size / (lhs_size + rhs_size)) *\n               m_rightImpl.costPerCoeff(vectorized) +\n           TensorOpCost(0, 0, compute_cost);\n  }\n\n  EIGEN_DEVICE_FUNC Scalar* data() const { return NULL; }\n\n  protected:\n    Dimensions m_dimensions;\n    array<Index, NumDims> m_outputStrides;\n    array<Index, NumDims> m_leftStrides;\n    array<Index, NumDims> m_rightStrides;\n    TensorEvaluator<LeftArgType, Device> m_leftImpl;\n    TensorEvaluator<RightArgType, Device> m_rightImpl;\n    const Axis m_axis;\n};\n\n// Eval as lvalue\ntemplate<typename Axis, typename LeftArgType, typename RightArgType, typename Device>\n  struct TensorEvaluator<TensorConcatenationOp<Axis, LeftArgType, RightArgType>, Device>\n  : public TensorEvaluator<const TensorConcatenationOp<Axis, LeftArgType, RightArgType>, Device>\n{\n  typedef TensorEvaluator<const TensorConcatenationOp<Axis, LeftArgType, RightArgType>, Device> Base;\n  typedef TensorConcatenationOp<Axis, LeftArgType, RightArgType> XprType;\n  typedef typename Base::Dimensions Dimensions;\n  enum {\n    IsAligned = false,\n    PacketAccess = TensorEvaluator<LeftArgType, Device>::PacketAccess & TensorEvaluator<RightArgType, Device>::PacketAccess,\n    Layout = TensorEvaluator<LeftArgType, Device>::Layout,\n    RawAccess = false\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(XprType& op, const Device& device)\n    : Base(op, device)\n  {\n    EIGEN_STATIC_ASSERT((static_cast<int>(Layout) == static_cast<int>(ColMajor)), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  }\n\n  typedef typename XprType::Index Index;\n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType& coeffRef(Index index)\n  {\n    // Collect dimension-wise indices (subs).\n    array<Index, Base::NumDims> subs;\n    for (int i = Base::NumDims - 1; i > 0; --i) {\n      subs[i] = index / this->m_outputStrides[i];\n      index -= subs[i] * this->m_outputStrides[i];\n    }\n    subs[0] = index;\n\n    const Dimensions& left_dims = this->m_leftImpl.dimensions();\n    if (subs[this->m_axis] < left_dims[this->m_axis]) {\n      Index left_index = subs[0];\n      for (int i = 1; i < Base::NumDims; ++i) {\n        left_index += (subs[i] % left_dims[i]) * this->m_leftStrides[i];\n      }\n      return this->m_leftImpl.coeffRef(left_index);\n    } else {\n      subs[this->m_axis] -= left_dims[this->m_axis];\n      const Dimensions& right_dims = this->m_rightImpl.dimensions();\n      Index right_index = subs[0];\n      for (int i = 1; i < Base::NumDims; ++i) {\n        right_index += (subs[i] % right_dims[i]) * this->m_rightStrides[i];\n      }\n      return this->m_rightImpl.coeffRef(right_index);\n    }\n  }\n\n  template <int StoreMode> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  void writePacket(Index index, const PacketReturnType& x)\n  {\n    const int packetSize = internal::unpacket_traits<PacketReturnType>::size;\n    EIGEN_STATIC_ASSERT((packetSize > 1), YOU_MADE_A_PROGRAMMING_MISTAKE)\n    eigen_assert(index + packetSize - 1 < this->dimensions().TotalSize());\n\n    EIGEN_ALIGN_MAX CoeffReturnType values[packetSize];\n    internal::pstore<CoeffReturnType, PacketReturnType>(values, x);\n    for (int i = 0; i < packetSize; ++i) {\n      coeffRef(index+i) = values[i];\n    }\n  }\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_CONCATENATION_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorContraction.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_H\n#define EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_H\n\nnamespace Eigen {\n\n/** \\class TensorContraction\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief Tensor contraction class.\n  *\n  *\n  */\nnamespace internal {\n\ntemplate<typename Dimensions, typename LhsXprType, typename RhsXprType>\nstruct traits<TensorContractionOp<Dimensions, LhsXprType, RhsXprType> >\n{\n  // Type promotion to handle the case where the types of the lhs and the rhs are different.\n  typedef typename gebp_traits<typename remove_const<typename LhsXprType::Scalar>::type,\n                               typename remove_const<typename RhsXprType::Scalar>::type>::ResScalar Scalar;\n\n  typedef typename promote_storage_type<typename traits<LhsXprType>::StorageKind,\n                                        typename traits<RhsXprType>::StorageKind>::ret StorageKind;\n  typedef typename promote_index_type<typename traits<LhsXprType>::Index,\n                                      typename traits<RhsXprType>::Index>::type Index;\n  typedef typename LhsXprType::Nested LhsNested;\n  typedef typename RhsXprType::Nested RhsNested;\n  typedef typename remove_reference<LhsNested>::type _LhsNested;\n  typedef typename remove_reference<RhsNested>::type _RhsNested;\n\n  // From NumDims below.\n  static const int NumDimensions = traits<RhsXprType>::NumDimensions + traits<RhsXprType>::NumDimensions - 2 * array_size<Dimensions>::value;\n  static const int Layout = traits<LhsXprType>::Layout;\n\n  enum {\n    Flags = 0\n  };\n};\n\ntemplate<typename Dimensions, typename LhsXprType, typename RhsXprType>\nstruct eval<TensorContractionOp<Dimensions, LhsXprType, RhsXprType>, Eigen::Dense>\n{\n  typedef const TensorContractionOp<Dimensions, LhsXprType, RhsXprType>& type;\n};\n\ntemplate<typename Dimensions, typename LhsXprType, typename RhsXprType>\nstruct nested<TensorContractionOp<Dimensions, LhsXprType, RhsXprType>, 1, typename eval<TensorContractionOp<Dimensions, LhsXprType, RhsXprType> >::type>\n{\n  typedef TensorContractionOp<Dimensions, LhsXprType, RhsXprType> type;\n};\n\ntemplate<typename Indices_, typename LeftArgType_, typename RightArgType_, typename Device_>\nstruct traits<TensorEvaluator<const TensorContractionOp<Indices_, LeftArgType_, RightArgType_>, Device_> > {\n  typedef Indices_ Indices;\n  typedef LeftArgType_ LeftArgType;\n  typedef RightArgType_ RightArgType;\n  typedef Device_ Device;\n\n  // From NumDims below.\n  static const int NumDimensions = traits<LeftArgType_>::NumDimensions + traits<RightArgType_>::NumDimensions - 2 * array_size<Indices_>::value;\n};\n\n}  // end namespace internal\n\ntemplate<typename Indices, typename LhsXprType, typename RhsXprType>\nclass TensorContractionOp : public TensorBase<TensorContractionOp<Indices, LhsXprType, RhsXprType>, ReadOnlyAccessors>\n{\n  public:\n  typedef typename Eigen::internal::traits<TensorContractionOp>::Scalar Scalar;\n  typedef typename internal::gebp_traits<typename LhsXprType::CoeffReturnType,\n                                                   typename RhsXprType::CoeffReturnType>::ResScalar CoeffReturnType;\n  typedef typename Eigen::internal::nested<TensorContractionOp>::type Nested;\n  typedef typename Eigen::internal::traits<TensorContractionOp>::StorageKind StorageKind;\n  typedef typename Eigen::internal::traits<TensorContractionOp>::Index Index;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorContractionOp(\n      const LhsXprType& lhs, const RhsXprType& rhs, const Indices& dims)\n      : m_lhs_xpr(lhs), m_rhs_xpr(rhs), m_indices(dims) {}\n\n  EIGEN_DEVICE_FUNC\n  const Indices& indices() const { return m_indices; }\n\n  /** \\returns the nested expressions */\n  EIGEN_DEVICE_FUNC\n  const typename internal::remove_all<typename LhsXprType::Nested>::type&\n  lhsExpression() const { return m_lhs_xpr; }\n\n  EIGEN_DEVICE_FUNC\n  const typename internal::remove_all<typename RhsXprType::Nested>::type&\n  rhsExpression() const { return m_rhs_xpr; }\n\n  protected:\n    typename LhsXprType::Nested m_lhs_xpr;\n    typename RhsXprType::Nested m_rhs_xpr;\n    const Indices m_indices;\n};\n\n\ntemplate<typename Derived>\nstruct TensorContractionEvaluatorBase\n{\n  typedef typename internal::traits<Derived>::Indices Indices;\n  typedef typename internal::traits<Derived>::LeftArgType LeftArgType;\n  typedef typename internal::traits<Derived>::RightArgType RightArgType;\n  typedef typename internal::traits<Derived>::Device Device;\n\n  typedef TensorContractionOp<Indices, LeftArgType, RightArgType> XprType;\n  typedef typename internal::remove_const<typename XprType::Scalar>::type Scalar;\n  typedef typename XprType::Index Index;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n\n  enum {\n    IsAligned = true,\n    PacketAccess = (internal::unpacket_traits<PacketReturnType>::size > 1),\n    Layout = TensorEvaluator<LeftArgType, Device>::Layout,\n    CoordAccess = false,  // to be implemented\n    RawAccess = true\n  };\n\n  // Most of the code is assuming that both input tensors are ColMajor. If the\n  // inputs are RowMajor, we will \"cheat\" by swapping the LHS and RHS:\n  // If we want to compute A * B = C, where A is LHS and B is RHS, the code\n  // will pretend B is LHS and A is RHS.\n  typedef typename internal::conditional<\n    static_cast<int>(Layout) == static_cast<int>(ColMajor), LeftArgType, RightArgType>::type EvalLeftArgType;\n  typedef typename internal::conditional<\n    static_cast<int>(Layout) == static_cast<int>(ColMajor), RightArgType, LeftArgType>::type EvalRightArgType;\n\n  static const int LDims =\n      internal::array_size<typename TensorEvaluator<EvalLeftArgType, Device>::Dimensions>::value;\n  static const int RDims =\n      internal::array_size<typename TensorEvaluator<EvalRightArgType, Device>::Dimensions>::value;\n  static const int ContractDims = internal::array_size<Indices>::value;\n  static const int NumDims = LDims + RDims - 2 * ContractDims;\n\n  typedef array<Index, ContractDims> contract_t;\n  typedef array<Index, LDims - ContractDims> left_nocontract_t;\n  typedef array<Index, RDims - ContractDims> right_nocontract_t;\n\n  typedef DSizes<Index, NumDims> Dimensions;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  TensorContractionEvaluatorBase(const XprType& op, const Device& device)\n    : m_leftImpl(choose(Cond<static_cast<int>(Layout) == static_cast<int>(ColMajor)>(),\n                          op.lhsExpression(), op.rhsExpression()), device),\n    m_rightImpl(choose(Cond<static_cast<int>(Layout) == static_cast<int>(ColMajor)>(),\n                          op.rhsExpression(), op.lhsExpression()), device),\n        m_device(device),\n        m_result(NULL) {\n    EIGEN_STATIC_ASSERT((static_cast<int>(TensorEvaluator<LeftArgType, Device>::Layout) ==\n\t\t\t   static_cast<int>(TensorEvaluator<RightArgType, Device>::Layout)),\n                        YOU_MADE_A_PROGRAMMING_MISTAKE);\n\n\n    DSizes<Index, LDims> eval_left_dims;\n    DSizes<Index, RDims> eval_right_dims;\n    array<IndexPair<Index>, ContractDims> eval_op_indices;\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      // For ColMajor, we keep using the existing dimensions\n      for (int i = 0; i < LDims; i++) {\n        eval_left_dims[i] = m_leftImpl.dimensions()[i];\n      }\n      for (int i = 0; i < RDims; i++) {\n        eval_right_dims[i] = m_rightImpl.dimensions()[i];\n      }\n      // We keep the pairs of contracting indices.\n      for (int i = 0; i < ContractDims; i++) {\n        eval_op_indices[i].first = op.indices()[i].first;\n        eval_op_indices[i].second = op.indices()[i].second;\n      }\n    } else {\n      // For RowMajor, we need to reverse the existing dimensions\n      for (int i = 0; i < LDims; i++) {\n        eval_left_dims[i] = m_leftImpl.dimensions()[LDims - i - 1];\n      }\n      for (int i = 0; i < RDims; i++) {\n        eval_right_dims[i] = m_rightImpl.dimensions()[RDims - i - 1];\n      }\n      // We need to flip all the pairs of contracting indices as well as\n      // reversing the dimensions.\n      for (int i = 0; i < ContractDims; i++) {\n        eval_op_indices[i].first = LDims - 1 - op.indices()[ContractDims - 1 - i].second;\n        eval_op_indices[i].second = RDims - 1 - op.indices()[ContractDims - 1 - i].first;\n      }\n    }\n\n    // Check for duplicate axes and make sure the first index in eval_op_indices\n    // is increasing. Using O(n^2) sorting is OK since ContractDims is small\n    for (int i = 0; i < ContractDims; i++) {\n      for (int j = i + 1; j < ContractDims; j++) {\n        eigen_assert(eval_op_indices[j].first != eval_op_indices[i].first &&\n                     eval_op_indices[j].second != eval_op_indices[i].second &&\n                     \"contraction axes should be unique\");\n        if (eval_op_indices[j].first < eval_op_indices[i].first) {\n          numext::swap(eval_op_indices[j], eval_op_indices[i]);\n        }\n      }\n    }\n\n    array<Index, LDims> lhs_strides;\n    lhs_strides[0] = 1;\n    for (int i = 0; i < LDims-1; ++i) {\n      lhs_strides[i+1] = lhs_strides[i] * eval_left_dims[i];\n    }\n\n    array<Index, RDims> rhs_strides;\n    rhs_strides[0] = 1;\n    for (int i = 0; i < RDims-1; ++i) {\n      rhs_strides[i+1] = rhs_strides[i] * eval_right_dims[i];\n    }\n\n    if (m_i_strides.size() > 0) m_i_strides[0] = 1;\n    if (m_j_strides.size() > 0) m_j_strides[0] = 1;\n    if (m_k_strides.size() > 0) m_k_strides[0] = 1;\n\n    m_i_size = 1;\n    m_j_size = 1;\n    m_k_size = 1;\n\n    // To compute the dimension, we simply concatenate the non-contracting\n    // dimensions of the left and then the right tensor. Additionally, we also\n    // compute the strides corresponding to the left non-contracting\n    // dimensions and right non-contracting dimensions.\n    m_lhs_inner_dim_contiguous = true;\n    int dim_idx = 0;\n    unsigned int nocontract_idx = 0;\n\n    for (int i = 0; i < LDims; i++) {\n      // find if we are contracting on index i of left tensor\n      bool contracting = false;\n      for (int j = 0; j < ContractDims; j++) {\n        if (eval_op_indices[j].first == i) {\n          contracting = true;\n          break;\n        }\n      }\n      if (!contracting) {\n        // add dimension size to output dimensions\n        m_dimensions[dim_idx] = eval_left_dims[i];\n        m_left_nocontract_strides[nocontract_idx] = lhs_strides[i];\n        if (dim_idx != i) {\n          m_lhs_inner_dim_contiguous = false;\n        }\n        if (nocontract_idx+1 < internal::array_size<left_nocontract_t>::value) {\n          m_i_strides[nocontract_idx+1] =\n              m_i_strides[nocontract_idx] * eval_left_dims[i];\n        } else {\n          m_i_size = m_i_strides[nocontract_idx] * eval_left_dims[i];\n        }\n        dim_idx++;\n        nocontract_idx++;\n      }\n    }\n\n    nocontract_idx = 0;\n    for (int i = 0; i < RDims; i++) {\n      bool contracting = false;\n      // find if we are contracting on index i of right tensor\n      for (int j = 0; j < ContractDims; j++) {\n        if (eval_op_indices[j].second == i) {\n          contracting = true;\n          break;\n        }\n      }\n      if (!contracting) {\n        m_dimensions[dim_idx] = eval_right_dims[i];\n        if (nocontract_idx+1 < internal::array_size<right_nocontract_t>::value) {\n          m_j_strides[nocontract_idx+1] =\n              m_j_strides[nocontract_idx] * eval_right_dims[i];\n        } else {\n          m_j_size = m_j_strides[nocontract_idx] * eval_right_dims[i];\n        }\n        m_right_nocontract_strides[nocontract_idx] = rhs_strides[i];\n        dim_idx++;\n        nocontract_idx++;\n      }\n    }\n\n    // Now compute the strides corresponding to the contracting dimensions. We\n    // assumed above that non-contracting axes are represented in the same order\n    // in the matrix as they are in the tensor. This is not the case for\n    // contracting axes. As the contracting axes must be of the same size in\n    // each tensor, we'll only look at the first tensor here.\n    m_rhs_inner_dim_contiguous = true;\n    m_rhs_inner_dim_reordered = false;\n    for (int i = 0; i < ContractDims; i++) {\n      Index left = eval_op_indices[i].first;\n      Index right = eval_op_indices[i].second;\n\n      Index size = eval_left_dims[left];\n      eigen_assert(size == eval_right_dims[right] &&\n                   \"Contraction axes must be same size\");\n\n      if (i+1 < static_cast<int>(internal::array_size<contract_t>::value)) {\n        m_k_strides[i+1] = m_k_strides[i] * size;\n      } else {\n        m_k_size = m_k_strides[i] * size;\n      }\n      m_left_contracting_strides[i] = lhs_strides[left];\n      m_right_contracting_strides[i] = rhs_strides[right];\n\n      if (i > 0 && right < eval_op_indices[i-1].second) {\n        m_rhs_inner_dim_reordered = true;\n      }\n      if (right != i) {\n        m_rhs_inner_dim_contiguous = false;\n      }\n    }\n\n    // If the layout is RowMajor, we need to reverse the m_dimensions\n    if (static_cast<int>(Layout) == static_cast<int>(RowMajor)) {\n      for (int i = 0, j = NumDims - 1; i < j; i++, j--) {\n        numext::swap(m_dimensions[i], m_dimensions[j]);\n      }\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(Scalar* data) {\n    m_leftImpl.evalSubExprsIfNeeded(NULL);\n    m_rightImpl.evalSubExprsIfNeeded(NULL);\n    if (data) {\n      evalTo(data);\n      return false;\n    } else {\n      m_result = static_cast<Scalar *>(m_device.allocate(dimensions().TotalSize() * sizeof(Scalar)));\n      evalTo(m_result);\n      return true;\n    }\n  }\n\n  EIGEN_DEVICE_FUNC void evalTo(Scalar* buffer) const {\n    if (this->m_lhs_inner_dim_contiguous) {\n      if (this->m_rhs_inner_dim_contiguous) {\n        if (this->m_rhs_inner_dim_reordered) {\n          static_cast<const Derived*>(this)->template evalProduct<true, true, true, Unaligned>(buffer);\n        }\n        else {\n          static_cast<const Derived*>(this)->template evalProduct<true, true, false, Unaligned>(buffer);\n        }\n      }\n      else {\n       if (this->m_rhs_inner_dim_reordered) {\n          static_cast<const Derived*>(this)->template evalProduct<true, false, true, Unaligned>(buffer);\n        }\n        else {\n          static_cast<const Derived*>(this)->template evalProduct<true, false, false, Unaligned>(buffer);\n        }\n      }\n    }\n    else {\n      if (this->m_rhs_inner_dim_contiguous) {\n        if (this->m_rhs_inner_dim_reordered) {\n          static_cast<const Derived*>(this)->template evalProduct<false, true, true, Unaligned>(buffer);\n        }\n        else {\n          static_cast<const Derived*>(this)->template evalProduct<false, true, false, Unaligned>(buffer);\n        }\n      }\n      else {\n       if (this->m_rhs_inner_dim_reordered) {\n          static_cast<const Derived*>(this)->template evalProduct<false, false, true, Unaligned>(buffer);\n        }\n        else {\n          static_cast<const Derived*>(this)->template evalProduct<false, false, false, Unaligned>(buffer);\n        }\n      }\n    }\n  }\n\n  template <bool lhs_inner_dim_contiguous, bool rhs_inner_dim_contiguous, bool rhs_inner_dim_reordered, int Alignment>\n  EIGEN_DEVICE_FUNC void evalGemv(Scalar* buffer) const {\n    const Index rows = m_i_size;\n    const Index cols = m_k_size;\n\n    typedef typename internal::remove_const<typename EvalLeftArgType::Scalar>::type LhsScalar;\n    typedef typename internal::remove_const<typename EvalRightArgType::Scalar>::type RhsScalar;\n    typedef TensorEvaluator<EvalLeftArgType, Device> LeftEvaluator;\n    typedef TensorEvaluator<EvalRightArgType, Device> RightEvaluator;\n    const Index lhs_packet_size = internal::unpacket_traits<typename LeftEvaluator::PacketReturnType>::size;\n    const Index rhs_packet_size = internal::unpacket_traits<typename RightEvaluator::PacketReturnType>::size;\n    const int lhs_alignment = LeftEvaluator::IsAligned ? Aligned : Unaligned;\n    const int rhs_alignment = RightEvaluator::IsAligned ? Aligned : Unaligned;\n    typedef internal::TensorContractionInputMapper<LhsScalar, Index, internal::Lhs,\n                                                   LeftEvaluator, left_nocontract_t,\n                                                   contract_t, lhs_packet_size,\n                                                   lhs_inner_dim_contiguous,\n                                                   false, lhs_alignment> LhsMapper;\n\n    typedef internal::TensorContractionInputMapper<RhsScalar, Index, internal::Rhs,\n                                                   RightEvaluator, right_nocontract_t,\n                                                   contract_t, rhs_packet_size,\n                                                   rhs_inner_dim_contiguous,\n                                                   rhs_inner_dim_reordered, rhs_alignment> RhsMapper;\n\n    LhsMapper lhs(m_leftImpl, m_left_nocontract_strides, m_i_strides,\n                  m_left_contracting_strides, m_k_strides);\n    RhsMapper rhs(m_rightImpl, m_right_nocontract_strides, m_j_strides,\n                  m_right_contracting_strides, m_k_strides);\n\n    const Scalar alpha(1);\n    const Index resIncr(1);\n\n    // zero out the result buffer (which must be of size at least rows * sizeof(Scalar)\n    m_device.memset(buffer, 0, rows * sizeof(Scalar));\n\n    internal::general_matrix_vector_product<Index,LhsScalar,LhsMapper,ColMajor,false,RhsScalar,RhsMapper,false>::run(\n        rows, cols, lhs, rhs,\n        buffer, resIncr, alpha);\n  }\n\n  template <bool lhs_inner_dim_contiguous, bool rhs_inner_dim_contiguous, bool rhs_inner_dim_reordered, int Alignment>\n  EIGEN_DEVICE_FUNC void evalGemm(Scalar* buffer) const {\n    // columns in left side, rows in right side\n    const Index k = this->m_k_size;\n\n    // rows in left side\n    const Index m = this->m_i_size;\n\n    // columns in right side\n    const Index n = this->m_j_size;\n\n    // zero out the result buffer (which must be of size at least m * n * sizeof(Scalar)\n    this->m_device.memset(buffer, 0, m * n * sizeof(Scalar));\n\n    // define mr, nr, and all of my data mapper types\n    typedef typename internal::remove_const<typename EvalLeftArgType::Scalar>::type LhsScalar;\n    typedef typename internal::remove_const<typename EvalRightArgType::Scalar>::type RhsScalar;\n    typedef typename internal::gebp_traits<LhsScalar, RhsScalar> Traits;\n\n    const Index nr = Traits::nr;\n    const Index mr = Traits::mr;\n\n    typedef TensorEvaluator<EvalLeftArgType, Device> LeftEvaluator;\n    typedef TensorEvaluator<EvalRightArgType, Device> RightEvaluator;\n\n    const Index lhs_packet_size = internal::unpacket_traits<typename LeftEvaluator::PacketReturnType>::size;\n    const Index rhs_packet_size = internal::unpacket_traits<typename RightEvaluator::PacketReturnType>::size;\n\n    typedef internal::TensorContractionInputMapper<LhsScalar, Index, internal::Lhs,\n                                                   LeftEvaluator, left_nocontract_t,\n                                                   contract_t, lhs_packet_size,\n                                                   lhs_inner_dim_contiguous,\n                                                   false, Unaligned> LhsMapper;\n\n    typedef internal::TensorContractionInputMapper<RhsScalar, Index, internal::Rhs,\n                                                   RightEvaluator, right_nocontract_t,\n                                                   contract_t, rhs_packet_size,\n                                                   rhs_inner_dim_contiguous,\n                                                   rhs_inner_dim_reordered, Unaligned> RhsMapper;\n\n    typedef internal::blas_data_mapper<Scalar, Index, ColMajor> OutputMapper;\n\n    // Declare GEBP packing and kernel structs\n    internal::gemm_pack_lhs<LhsScalar, Index, typename LhsMapper::SubMapper, mr, Traits::LhsProgress, ColMajor> pack_lhs;\n    internal::gemm_pack_rhs<RhsScalar, Index, typename RhsMapper::SubMapper, nr, ColMajor> pack_rhs;\n\n    internal::gebp_kernel<LhsScalar, RhsScalar, Index, OutputMapper, mr, nr, false, false> gebp;\n\n    // initialize data mappers\n    LhsMapper lhs(this->m_leftImpl, this->m_left_nocontract_strides, this->m_i_strides,\n                  this->m_left_contracting_strides, this->m_k_strides);\n\n    RhsMapper rhs(this->m_rightImpl, this->m_right_nocontract_strides, this->m_j_strides,\n                  this->m_right_contracting_strides, this->m_k_strides);\n\n    OutputMapper output(buffer, m);\n\n    // Sizes of the blocks to load in cache. See the Goto paper for details.\n    internal::TensorContractionBlocking<LhsMapper, RhsMapper, Index, internal::ShardByCol> blocking(k, m, n, 1);\n    const Index kc = blocking.kc();\n    const Index mc = numext::mini(m, blocking.mc());\n    const Index nc = numext::mini(n, blocking.nc());\n    const Index sizeA = mc * kc;\n    const Index sizeB = kc * nc;\n\n    LhsScalar* blockA = static_cast<LhsScalar *>(this->m_device.allocate(sizeA * sizeof(LhsScalar)));\n    RhsScalar* blockB = static_cast<RhsScalar *>(this->m_device.allocate(sizeB * sizeof(RhsScalar)));\n\n    for(Index i2=0; i2<m; i2+=mc)\n    {\n      const Index actual_mc = numext::mini(i2+mc,m)-i2;\n      for (Index k2 = 0; k2 < k; k2 += kc) {\n        // make sure we don't overshoot right edge of left matrix, then pack vertical panel\n        const Index actual_kc = numext::mini(k2 + kc, k) - k2;\n        pack_lhs(blockA, lhs.getSubMapper(i2, k2), actual_kc, actual_mc, 0, 0);\n\n        // series of horizontal blocks\n        for (Index j2 = 0; j2 < n; j2 += nc) {\n          // make sure we don't overshoot right edge of right matrix, then pack block\n          const Index actual_nc = numext::mini(j2 + nc, n) - j2;\n          pack_rhs(blockB, rhs.getSubMapper(k2, j2), actual_kc, actual_nc, 0, 0);\n\n          // call gebp (matrix kernel)\n          // The parameters here are copied from Eigen's GEMM implementation\n          gebp(output.getSubMapper(i2, j2), blockA, blockB, actual_mc, actual_kc, actual_nc, Scalar(1), -1, -1, 0, 0);\n        }\n      }\n    }\n\n    this->m_device.deallocate(blockA);\n    this->m_device.deallocate(blockB);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {\n    m_leftImpl.cleanup();\n    m_rightImpl.cleanup();\n\n    if (m_result != NULL) {\n      m_device.deallocate(m_result);\n      m_result = NULL;\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const {\n    return m_result[index];\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool) const {\n    return TensorOpCost(sizeof(CoeffReturnType), 0, 0);\n  }\n\n  template<int LoadMode>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const {\n    return internal::ploadt<PacketReturnType, LoadMode>(m_result + index);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar* data() const { return m_result; }\n\n  protected:\n  // Prevent assignment\n  TensorContractionEvaluatorBase& operator = (const TensorContractionEvaluatorBase&);\n  Dimensions m_dimensions;\n\n  contract_t m_k_strides;\n  contract_t m_left_contracting_strides;\n  contract_t m_right_contracting_strides;\n\n  bool m_lhs_inner_dim_contiguous;\n  bool m_rhs_inner_dim_contiguous;\n  bool m_rhs_inner_dim_reordered;\n\n  left_nocontract_t m_i_strides;\n  right_nocontract_t m_j_strides;\n  left_nocontract_t m_left_nocontract_strides;\n  right_nocontract_t m_right_nocontract_strides;\n\n  Index m_i_size;\n  Index m_j_size;\n  Index m_k_size;\n\n  TensorEvaluator<EvalLeftArgType, Device> m_leftImpl;\n  TensorEvaluator<EvalRightArgType, Device> m_rightImpl;\n  const Device& m_device;\n  Scalar* m_result;\n};\n\n\n// evaluator for default device\ntemplate<typename Indices, typename LeftArgType, typename RightArgType, typename Device>\nstruct TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgType>, Device> :\n    public TensorContractionEvaluatorBase<\n      TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgType>, Device> > {\n  typedef TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgType>, Device> Self;\n  typedef TensorContractionEvaluatorBase<Self> Base;\n\n  typedef TensorContractionOp<Indices, LeftArgType, RightArgType> XprType;\n  typedef typename internal::remove_const<typename XprType::Scalar>::type Scalar;\n  typedef typename XprType::Index Index;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n\n  enum {\n    Layout = TensorEvaluator<LeftArgType, Device>::Layout\n  };\n\n  // Most of the code is assuming that both input tensors are ColMajor. If the\n  // inputs are RowMajor, we will \"cheat\" by swapping the LHS and RHS:\n  // If we want to compute A * B = C, where A is LHS and B is RHS, the code\n  // will pretend B is LHS and A is RHS.\n  typedef typename internal::conditional<\n    static_cast<int>(Layout) == static_cast<int>(ColMajor), LeftArgType, RightArgType>::type EvalLeftArgType;\n  typedef typename internal::conditional<\n    static_cast<int>(Layout) == static_cast<int>(ColMajor), RightArgType, LeftArgType>::type EvalRightArgType;\n\n  static const int LDims =\n      internal::array_size<typename TensorEvaluator<EvalLeftArgType, Device>::Dimensions>::value;\n  static const int RDims =\n      internal::array_size<typename TensorEvaluator<EvalRightArgType, Device>::Dimensions>::value;\n  static const int ContractDims = internal::array_size<Indices>::value;\n\n  typedef array<Index, ContractDims> contract_t;\n  typedef array<Index, LDims - ContractDims> left_nocontract_t;\n  typedef array<Index, RDims - ContractDims> right_nocontract_t;\n\n  static const int NumDims = LDims + RDims - 2 * ContractDims;\n\n  // Could we use NumDimensions here?\n  typedef DSizes<Index, NumDims> Dimensions;\n\n  EIGEN_DEVICE_FUNC TensorEvaluator(const XprType& op, const Device& device) :\n      Base(op, device) { }\n\n  template <bool lhs_inner_dim_contiguous, bool rhs_inner_dim_contiguous, bool rhs_inner_dim_reordered, int Alignment>\n  EIGEN_DEVICE_FUNC void evalProduct(Scalar* buffer) const {\n    if (this->m_j_size == 1) {\n      this->template evalGemv<lhs_inner_dim_contiguous, rhs_inner_dim_contiguous, rhs_inner_dim_reordered, Alignment>(buffer);\n      return;\n    }\n\n    this->template evalGemm<lhs_inner_dim_contiguous, rhs_inner_dim_contiguous, rhs_inner_dim_reordered, Alignment>(buffer);\n  }\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorContractionBlocking.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_BLOCKING_H\n#define EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_BLOCKING_H\n\n\nnamespace Eigen {\nnamespace internal {\n\nenum {\n  ShardByRow = 0,\n  ShardByCol = 1\n};\n\n\n// Default Blocking Strategy\ntemplate <typename LhsMapper, typename RhsMapper, typename Index, int ShardingType=ShardByCol>\nclass TensorContractionBlocking {\n public:\n\n  typedef typename LhsMapper::Scalar LhsScalar;\n  typedef typename RhsMapper::Scalar RhsScalar;\n\n  EIGEN_DEVICE_FUNC TensorContractionBlocking(Index k, Index m, Index n, Index num_threads = 1) :\n      kc_(k), mc_(m), nc_(n)\n  {\n    if (ShardingType == ShardByCol) {\n      computeProductBlockingSizes<LhsScalar, RhsScalar, 1>(kc_, mc_, nc_, num_threads);\n    }\n    else {\n      computeProductBlockingSizes<LhsScalar, RhsScalar, 1>(kc_, nc_, mc_, num_threads);\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Index kc() const { return kc_; }\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Index mc() const { return mc_; }\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Index nc() const { return nc_; }\n\n private:\n  Index kc_;\n  Index mc_;\n  Index nc_;\n};\n\n\n} // end namespace internal\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_BLOCKING_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorContractionCuda.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014-2015 Benoit Steiner <benoit.steiner.goog@gmail.com>\n// Copyright (C) 2015 Navdeep Jaitly <ndjaitly@google.com>\n// Copyright (C) 2014 Eric Martin <eric@ericmart.in>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_CUDA_H\n#define EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_CUDA_H\n\n#if defined(EIGEN_USE_GPU) && defined(__CUDACC__)\n\nnamespace Eigen {\n\ntemplate<typename Scalar, typename Index, typename LhsMapper,\n         typename RhsMapper, typename OutputMapper, bool needs_edge_check>\n__device__ EIGEN_STRONG_INLINE void\nEigenContractionKernelInternal(const LhsMapper lhs, const RhsMapper rhs,\n                               const OutputMapper output, Scalar* lhs_shmem, Scalar* rhs_shmem,\n                       const Index m_size, const Index n_size, const Index k_size) {\n\n  const Index m_block_idx = blockIdx.x;\n  const Index n_block_idx = blockIdx.y;\n\n  const Index base_m = 64 * m_block_idx;\n  const Index base_n = 64 * n_block_idx;\n\n  // declare and initialize 64 registers for output 8x8 block\n\n  // prefetch registers\n  Scalar lhs_pf0;\n  Scalar lhs_pf1;\n  Scalar lhs_pf2;\n  Scalar lhs_pf3;\n  Scalar lhs_pf4;\n  Scalar lhs_pf5;\n  Scalar lhs_pf6;\n  Scalar lhs_pf7;\n\n  Scalar rhs_pf0;\n  Scalar rhs_pf1;\n  Scalar rhs_pf2;\n  Scalar rhs_pf3;\n  Scalar rhs_pf4;\n  Scalar rhs_pf5;\n  Scalar rhs_pf6;\n  Scalar rhs_pf7;\n\n  // shared memory is formatted\n  // (contract idx in block, nocontract idx in block, block idx)\n  // where block idx is column major. This transposition limits the number of\n  // bank conflicts when reading the LHS. The core idea is that since the contracting\n  // index is shared by both sides, then the contracting index should be in threadIdx.x.\n\n  // On the LHS, we pad each row inside of each block with an extra element. This makes\n  // each block 8 rows of 9 elements, which is 72 elements. This gives no bank conflicts\n  // on writes and very few 2-way conflicts on reads. There is an 8x8 grid of these blocks.\n\n  // On the RHS we just add 8 padding elements to the end of each block. This gives no bank\n  // conflicts on writes and also none on reads.\n\n  // storage indices\n  const Index lhs_store_idx_base = threadIdx.y * 72 + threadIdx.x * 9 + threadIdx.z;\n  const Index rhs_store_idx_base = threadIdx.y * 72 + threadIdx.z * 8 + threadIdx.x;\n\n  const Index lhs_store_idx_0 = lhs_store_idx_base + 576 * 0;\n  const Index lhs_store_idx_1 = lhs_store_idx_base + 576 * 1;\n  const Index lhs_store_idx_2 = lhs_store_idx_base + 576 * 2;\n  const Index lhs_store_idx_3 = lhs_store_idx_base + 576 * 3;\n  const Index lhs_store_idx_4 = lhs_store_idx_base + 576 * 4;\n  const Index lhs_store_idx_5 = lhs_store_idx_base + 576 * 5;\n  const Index lhs_store_idx_6 = lhs_store_idx_base + 576 * 6;\n  const Index lhs_store_idx_7 = lhs_store_idx_base + 576 * 7;\n\n  const Index rhs_store_idx_0 = rhs_store_idx_base + 576 * 0;\n  const Index rhs_store_idx_1 = rhs_store_idx_base + 576 * 1;\n  const Index rhs_store_idx_2 = rhs_store_idx_base + 576 * 2;\n  const Index rhs_store_idx_3 = rhs_store_idx_base + 576 * 3;\n  const Index rhs_store_idx_4 = rhs_store_idx_base + 576 * 4;\n  const Index rhs_store_idx_5 = rhs_store_idx_base + 576 * 5;\n  const Index rhs_store_idx_6 = rhs_store_idx_base + 576 * 6;\n  const Index rhs_store_idx_7 = rhs_store_idx_base + 576 * 7;\n\n  // in the loading code, the following variables are important:\n  // threadIdx.x: the vertical position in an 8x8 block\n  // threadIdx.y: the vertical index of the 8x8 block in the grid\n  // threadIdx.z: the horizontal position in an 8x8 block\n  // k: the horizontal index of the 8x8 block in the grid\n  //\n  // The k parameter is implicit (it was the loop counter for a loop that went\n  // from 0 to <8, but now that loop is unrolled in the below code.\n\n  const Index load_idx_vert = threadIdx.x + 8 * threadIdx.y;\n  const Index lhs_vert = base_m + load_idx_vert;\n\n#define prefetchIntoRegisters(base_k)                           \\\n  {                                                             \\\n    lhs_pf0 = conv(0);                                          \\\n    lhs_pf1 = conv(0);                                          \\\n    lhs_pf2 = conv(0);                                          \\\n    lhs_pf3 = conv(0);                                          \\\n    lhs_pf4 = conv(0);                                          \\\n    lhs_pf5 = conv(0);                                          \\\n    lhs_pf6 = conv(0);                                          \\\n    lhs_pf7 = conv(0);                                          \\\n                                                                \\\n    rhs_pf0 = conv(0);                                          \\\n    rhs_pf1 = conv(0);                                          \\\n    rhs_pf2 = conv(0);                                          \\\n    rhs_pf3 = conv(0);                                          \\\n    rhs_pf4 = conv(0);                                          \\\n    rhs_pf5 = conv(0);                                          \\\n    rhs_pf6 = conv(0);                                          \\\n    rhs_pf7 = conv(0);                                          \\\n                                                                \\\n    if (!needs_edge_check || lhs_vert < m_size) {               \\\n      const Index lhs_horiz_0 = base_k + threadIdx.z + 0 * 8;   \\\n      const Index lhs_horiz_1 = base_k + threadIdx.z + 1 * 8;   \\\n      const Index lhs_horiz_2 = base_k + threadIdx.z + 2 * 8;   \\\n      const Index lhs_horiz_3 = base_k + threadIdx.z + 3 * 8;   \\\n      const Index lhs_horiz_4 = base_k + threadIdx.z + 4 * 8;   \\\n      const Index lhs_horiz_5 = base_k + threadIdx.z + 5 * 8;   \\\n      const Index lhs_horiz_6 = base_k + threadIdx.z + 6 * 8;   \\\n      const Index lhs_horiz_7 = base_k + threadIdx.z + 7 * 8;   \\\n                                                                \\\n      if (!needs_edge_check || lhs_horiz_7 < k_size) {          \\\n        lhs_pf0 = lhs(lhs_vert, lhs_horiz_0);                   \\\n        lhs_pf1 = lhs(lhs_vert, lhs_horiz_1);                   \\\n        lhs_pf2 = lhs(lhs_vert, lhs_horiz_2);                   \\\n        lhs_pf3 = lhs(lhs_vert, lhs_horiz_3);                   \\\n        lhs_pf4 = lhs(lhs_vert, lhs_horiz_4);                   \\\n        lhs_pf5 = lhs(lhs_vert, lhs_horiz_5);                   \\\n        lhs_pf6 = lhs(lhs_vert, lhs_horiz_6);                   \\\n        lhs_pf7 = lhs(lhs_vert, lhs_horiz_7);                   \\\n      } else if (lhs_horiz_6 < k_size) {                        \\\n        lhs_pf0 = lhs(lhs_vert, lhs_horiz_0);                   \\\n        lhs_pf1 = lhs(lhs_vert, lhs_horiz_1);                   \\\n        lhs_pf2 = lhs(lhs_vert, lhs_horiz_2);                   \\\n        lhs_pf3 = lhs(lhs_vert, lhs_horiz_3);                   \\\n        lhs_pf4 = lhs(lhs_vert, lhs_horiz_4);                   \\\n        lhs_pf5 = lhs(lhs_vert, lhs_horiz_5);                   \\\n        lhs_pf6 = lhs(lhs_vert, lhs_horiz_6);                   \\\n      } else if (lhs_horiz_5 < k_size) {                        \\\n        lhs_pf0 = lhs(lhs_vert, lhs_horiz_0);                   \\\n        lhs_pf1 = lhs(lhs_vert, lhs_horiz_1);                   \\\n        lhs_pf2 = lhs(lhs_vert, lhs_horiz_2);                   \\\n        lhs_pf3 = lhs(lhs_vert, lhs_horiz_3);                   \\\n        lhs_pf4 = lhs(lhs_vert, lhs_horiz_4);                   \\\n        lhs_pf5 = lhs(lhs_vert, lhs_horiz_5);                   \\\n      } else if (lhs_horiz_4 < k_size) {                        \\\n        lhs_pf0 = lhs(lhs_vert, lhs_horiz_0);                   \\\n        lhs_pf1 = lhs(lhs_vert, lhs_horiz_1);                   \\\n        lhs_pf2 = lhs(lhs_vert, lhs_horiz_2);                   \\\n        lhs_pf3 = lhs(lhs_vert, lhs_horiz_3);                   \\\n        lhs_pf4 = lhs(lhs_vert, lhs_horiz_4);                   \\\n      } else if (lhs_horiz_3 < k_size) {                        \\\n        lhs_pf0 = lhs(lhs_vert, lhs_horiz_0);                   \\\n        lhs_pf1 = lhs(lhs_vert, lhs_horiz_1);                   \\\n        lhs_pf2 = lhs(lhs_vert, lhs_horiz_2);                   \\\n        lhs_pf3 = lhs(lhs_vert, lhs_horiz_3);                   \\\n      } else if (lhs_horiz_2 < k_size) {                        \\\n        lhs_pf0 = lhs(lhs_vert, lhs_horiz_0);                   \\\n        lhs_pf1 = lhs(lhs_vert, lhs_horiz_1);                   \\\n        lhs_pf2 = lhs(lhs_vert, lhs_horiz_2);                   \\\n      } else if (lhs_horiz_1 < k_size) {                        \\\n        lhs_pf0 = lhs(lhs_vert, lhs_horiz_0);                   \\\n        lhs_pf1 = lhs(lhs_vert, lhs_horiz_1);                   \\\n      } else if (lhs_horiz_0 < k_size) {                        \\\n        lhs_pf0 = lhs(lhs_vert, lhs_horiz_0);                   \\\n      }                                                         \\\n    }                                                           \\\n                                                                \\\n    const Index rhs_vert = base_k + load_idx_vert;              \\\n    if (!needs_edge_check || rhs_vert < k_size) {               \\\n      const Index rhs_horiz_0 = base_n + threadIdx.z + 0 * 8;   \\\n      const Index rhs_horiz_1 = base_n + threadIdx.z + 1 * 8;   \\\n      const Index rhs_horiz_2 = base_n + threadIdx.z + 2 * 8;   \\\n      const Index rhs_horiz_3 = base_n + threadIdx.z + 3 * 8;   \\\n      const Index rhs_horiz_4 = base_n + threadIdx.z + 4 * 8;   \\\n      const Index rhs_horiz_5 = base_n + threadIdx.z + 5 * 8;   \\\n      const Index rhs_horiz_6 = base_n + threadIdx.z + 6 * 8;   \\\n      const Index rhs_horiz_7 = base_n + threadIdx.z + 7 * 8;   \\\n                                                                \\\n      if (rhs_horiz_7 < n_size) {                               \\\n        rhs_pf0 = rhs(rhs_vert, rhs_horiz_0);                   \\\n        rhs_pf1 = rhs(rhs_vert, rhs_horiz_1);                   \\\n        rhs_pf2 = rhs(rhs_vert, rhs_horiz_2);                   \\\n        rhs_pf3 = rhs(rhs_vert, rhs_horiz_3);                   \\\n        rhs_pf4 = rhs(rhs_vert, rhs_horiz_4);                   \\\n        rhs_pf5 = rhs(rhs_vert, rhs_horiz_5);                   \\\n        rhs_pf6 = rhs(rhs_vert, rhs_horiz_6);                   \\\n        rhs_pf7 = rhs(rhs_vert, rhs_horiz_7);                   \\\n      } else if (rhs_horiz_6 < n_size) {                        \\\n        rhs_pf0 = rhs(rhs_vert, rhs_horiz_0);                   \\\n        rhs_pf1 = rhs(rhs_vert, rhs_horiz_1);                   \\\n        rhs_pf2 = rhs(rhs_vert, rhs_horiz_2);                   \\\n        rhs_pf3 = rhs(rhs_vert, rhs_horiz_3);                   \\\n        rhs_pf4 = rhs(rhs_vert, rhs_horiz_4);                   \\\n        rhs_pf5 = rhs(rhs_vert, rhs_horiz_5);                   \\\n        rhs_pf6 = rhs(rhs_vert, rhs_horiz_6);                   \\\n      } else if (rhs_horiz_5 < n_size) {                        \\\n        rhs_pf0 = rhs(rhs_vert, rhs_horiz_0);                   \\\n        rhs_pf1 = rhs(rhs_vert, rhs_horiz_1);                   \\\n        rhs_pf2 = rhs(rhs_vert, rhs_horiz_2);                   \\\n        rhs_pf3 = rhs(rhs_vert, rhs_horiz_3);                   \\\n        rhs_pf4 = rhs(rhs_vert, rhs_horiz_4);                   \\\n        rhs_pf5 = rhs(rhs_vert, rhs_horiz_5);                   \\\n      } else if (rhs_horiz_4 < n_size) {                        \\\n        rhs_pf0 = rhs(rhs_vert, rhs_horiz_0);                   \\\n        rhs_pf1 = rhs(rhs_vert, rhs_horiz_1);                   \\\n        rhs_pf2 = rhs(rhs_vert, rhs_horiz_2);                   \\\n        rhs_pf3 = rhs(rhs_vert, rhs_horiz_3);                   \\\n        rhs_pf4 = rhs(rhs_vert, rhs_horiz_4);                   \\\n      } else if (rhs_horiz_3 < n_size) {                        \\\n        rhs_pf0 = rhs(rhs_vert, rhs_horiz_0);                   \\\n        rhs_pf1 = rhs(rhs_vert, rhs_horiz_1);                   \\\n        rhs_pf2 = rhs(rhs_vert, rhs_horiz_2);                   \\\n        rhs_pf3 = rhs(rhs_vert, rhs_horiz_3);                   \\\n      } else if (rhs_horiz_2 < n_size) {                        \\\n        rhs_pf0 = rhs(rhs_vert, rhs_horiz_0);                   \\\n        rhs_pf1 = rhs(rhs_vert, rhs_horiz_1);                   \\\n        rhs_pf2 = rhs(rhs_vert, rhs_horiz_2);                   \\\n      } else if (rhs_horiz_1 < n_size) {                        \\\n        rhs_pf0 = rhs(rhs_vert, rhs_horiz_0);                   \\\n        rhs_pf1 = rhs(rhs_vert, rhs_horiz_1);                   \\\n      } else if (rhs_horiz_0 < n_size) {                        \\\n        rhs_pf0 = rhs(rhs_vert, rhs_horiz_0);                   \\\n      }                                                         \\\n    }                                                           \\\n  }                                                             \\\n\n#define writeRegToShmem(_)                      \\\n  lhs_shmem[lhs_store_idx_0] = lhs_pf0;         \\\n  rhs_shmem[rhs_store_idx_0] = rhs_pf0;         \\\n                                                \\\n  lhs_shmem[lhs_store_idx_1] = lhs_pf1;         \\\n  rhs_shmem[rhs_store_idx_1] = rhs_pf1;         \\\n                                                \\\n  lhs_shmem[lhs_store_idx_2] = lhs_pf2;         \\\n  rhs_shmem[rhs_store_idx_2] = rhs_pf2;         \\\n                                                \\\n  lhs_shmem[lhs_store_idx_3] = lhs_pf3;         \\\n  rhs_shmem[rhs_store_idx_3] = rhs_pf3;         \\\n                                                \\\n  lhs_shmem[lhs_store_idx_4] = lhs_pf4;         \\\n  rhs_shmem[rhs_store_idx_4] = rhs_pf4;         \\\n                                                \\\n  lhs_shmem[lhs_store_idx_5] = lhs_pf5;         \\\n  rhs_shmem[rhs_store_idx_5] = rhs_pf5;         \\\n                                                \\\n  lhs_shmem[lhs_store_idx_6] = lhs_pf6;         \\\n  rhs_shmem[rhs_store_idx_6] = rhs_pf6;         \\\n                                                \\\n  lhs_shmem[lhs_store_idx_7] = lhs_pf7;         \\\n  rhs_shmem[rhs_store_idx_7] = rhs_pf7;         \\\n\n  // declare and initialize result array\n#define res(i, j) _res_##i##j\n#define initResultRow(i)                        \\\n  Scalar res(i, 0) = conv(0);                   \\\n  Scalar res(i, 1) = conv(0);                   \\\n  Scalar res(i, 2) = conv(0);                   \\\n  Scalar res(i, 3) = conv(0);                   \\\n  Scalar res(i, 4) = conv(0);                   \\\n  Scalar res(i, 5) = conv(0);                   \\\n  Scalar res(i, 6) = conv(0);                   \\\n  Scalar res(i, 7) = conv(0);                   \\\n\n  internal::scalar_cast_op<int, Scalar> conv;\n  initResultRow(0);\n  initResultRow(1);\n  initResultRow(2);\n  initResultRow(3);\n  initResultRow(4);\n  initResultRow(5);\n  initResultRow(6);\n  initResultRow(7);\n#undef initResultRow\n\n  for (Index base_k = 0; base_k < k_size; base_k += 64) {\n    // wait for previous iteration to finish with shmem. Despite common sense,\n    // the code is a bit faster with this here then at bottom of loop\n    __syncthreads();\n\n    prefetchIntoRegisters(base_k);\n    writeRegToShmem();\n\n    #undef prefetchIntoRegisters\n    #undef writeRegToShmem\n\n    // wait for shared mem packing to be done before starting computation\n    __syncthreads();\n\n    // compute 8x8 matrix product by outer product. This involves packing one column\n    // of LHS and one row of RHS into registers (takes 16 registers).\n\n#define lcol(i) _lcol##i\n    Scalar lcol(0);\n    Scalar lcol(1);\n    Scalar lcol(2);\n    Scalar lcol(3);\n    Scalar lcol(4);\n    Scalar lcol(5);\n    Scalar lcol(6);\n    Scalar lcol(7);\n\n#define rrow(j) _rrow##j\n    Scalar rrow(0);\n    Scalar rrow(1);\n    Scalar rrow(2);\n    Scalar rrow(3);\n    Scalar rrow(4);\n    Scalar rrow(5);\n    Scalar rrow(6);\n    Scalar rrow(7);\n\n    // Now x corresponds to k, y to m, and z to n\n    const Scalar* lhs_block = &lhs_shmem[threadIdx.x + 9 * threadIdx.y];\n    const Scalar* rhs_block = &rhs_shmem[threadIdx.x + 8 * threadIdx.z];\n\n#define lhs_element(i, j) lhs_block[72 * ((i) + 8 * (j))]\n#define rhs_element(i, j) rhs_block[72 * ((i) + 8 * (j))]\n\n#define loadData(i, j)                          \\\n    lcol(0) = lhs_element(0, j);               \\\n    rrow(0) = rhs_element(i, 0);               \\\n    lcol(1) = lhs_element(1, j);               \\\n    rrow(1) = rhs_element(i, 1);               \\\n    lcol(2) = lhs_element(2, j);               \\\n    rrow(2) = rhs_element(i, 2);               \\\n    lcol(3) = lhs_element(3, j);               \\\n    rrow(3) = rhs_element(i, 3);               \\\n    lcol(4) = lhs_element(4, j);               \\\n    rrow(4) = rhs_element(i, 4);               \\\n    lcol(5) = lhs_element(5, j);               \\\n    rrow(5) = rhs_element(i, 5);               \\\n    lcol(6) = lhs_element(6, j);               \\\n    rrow(6) = rhs_element(i, 6);               \\\n    lcol(7) = lhs_element(7, j);               \\\n    rrow(7) = rhs_element(i, 7);               \\\n\n#define computeCol(j)                           \\\n    res(0, j) += lcol(0) * rrow(j);             \\\n    res(1, j) += lcol(1) * rrow(j);             \\\n    res(2, j) += lcol(2) * rrow(j);             \\\n    res(3, j) += lcol(3) * rrow(j);             \\\n    res(4, j) += lcol(4) * rrow(j);             \\\n    res(5, j) += lcol(5) * rrow(j);             \\\n    res(6, j) += lcol(6) * rrow(j);             \\\n    res(7, j) += lcol(7) * rrow(j);             \\\n\n#define computePass(i)                          \\\n    loadData(i, i);                             \\\n                                                \\\n    computeCol(0);                              \\\n    computeCol(1);                              \\\n    computeCol(2);                              \\\n    computeCol(3);                              \\\n    computeCol(4);                              \\\n    computeCol(5);                              \\\n    computeCol(6);                              \\\n    computeCol(7);                              \\\n\n    computePass(0);\n    computePass(1);\n    computePass(2);\n    computePass(3);\n    computePass(4);\n    computePass(5);\n    computePass(6);\n    computePass(7);\n\n#undef lcol\n#undef rrow\n#undef lhs_element\n#undef rhs_element\n#undef loadData\n#undef computeCol\n#undef computePass\n  } // end loop over k\n\n  // we've now iterated over all of the large (ie width 64) k blocks and\n  // accumulated results in registers. At this point thread (x, y, z) contains\n  // the sum across all big k blocks of the product of little k block of index (x, y)\n  // with block of index (y, z). To compute the final output, we need to reduce\n  // the 8 threads over y by summation.\n#define shuffleInc(i, j, mask) res(i, j) += __shfl_xor(res(i, j), mask)\n\n#define reduceRow(i, mask)                      \\\n  shuffleInc(i, 0, mask);                       \\\n  shuffleInc(i, 1, mask);                       \\\n  shuffleInc(i, 2, mask);                       \\\n  shuffleInc(i, 3, mask);                       \\\n  shuffleInc(i, 4, mask);                       \\\n  shuffleInc(i, 5, mask);                       \\\n  shuffleInc(i, 6, mask);                       \\\n  shuffleInc(i, 7, mask);                       \\\n\n#define reduceMatrix(mask)                      \\\n  reduceRow(0, mask);                           \\\n  reduceRow(1, mask);                           \\\n  reduceRow(2, mask);                           \\\n  reduceRow(3, mask);                           \\\n  reduceRow(4, mask);                           \\\n  reduceRow(5, mask);                           \\\n  reduceRow(6, mask);                           \\\n  reduceRow(7, mask);                           \\\n\n  // actually perform the reduction, now each thread of index (_, y, z)\n  // contains the correct values in its registers that belong in the output\n  // block\n  reduceMatrix(1);\n  reduceMatrix(2);\n  reduceMatrix(4);\n\n#undef shuffleInc\n#undef reduceRow\n#undef reduceMatrix\n\n  // now we need to copy the 64 values into main memory. We can't split work\n  // among threads because all variables are in registers. There's 2 ways\n  // to do this:\n  // (1) have 1 thread do 64 writes from registers into global memory\n  // (2) have 1 thread do 64 writes into shared memory, and then 8 threads\n  //     each do 8 writes into global memory. We can just overwrite the shared\n  //     memory from the problem we just solved.\n  // (2) is slightly faster than (1) due to less branching and more ILP\n\n  // TODO: won't yield much gain, but could just use currently unused shared mem\n  //       and then we won't have to sync\n  // wait for shared mem to be out of use\n  __syncthreads();\n\n#define writeResultShmem(i, j)                                          \\\n  lhs_shmem[i + 8 * threadIdx.y + 64 * threadIdx.z + 512 * j] = res(i, j); \\\n\n#define writeRow(i)                             \\\n  writeResultShmem(i, 0);                       \\\n  writeResultShmem(i, 1);                       \\\n  writeResultShmem(i, 2);                       \\\n  writeResultShmem(i, 3);                       \\\n  writeResultShmem(i, 4);                       \\\n  writeResultShmem(i, 5);                       \\\n  writeResultShmem(i, 6);                       \\\n  writeResultShmem(i, 7);                       \\\n\n  if (threadIdx.x == 0) {\n    writeRow(0);\n    writeRow(1);\n    writeRow(2);\n    writeRow(3);\n    writeRow(4);\n    writeRow(5);\n    writeRow(6);\n    writeRow(7);\n  }\n#undef writeResultShmem\n#undef writeRow\n\n  const int max_i_write = numext::mini((int)((m_size - base_m - threadIdx.y + 7) / 8), 8);\n  const int max_j_write = numext::mini((int)((n_size - base_n - threadIdx.z + 7) / 8), 8);\n\n  if (threadIdx.x < max_i_write) {\n    if (max_j_write == 8) {\n      // TODO: can i trade bank conflicts for coalesced writes?\n      Scalar val0 = lhs_shmem[threadIdx.x + 8 * threadIdx.y + 64 * threadIdx.z + 512 * 0];\n      Scalar val1 = lhs_shmem[threadIdx.x + 8 * threadIdx.y + 64 * threadIdx.z + 512 * 1];\n      Scalar val2 = lhs_shmem[threadIdx.x + 8 * threadIdx.y + 64 * threadIdx.z + 512 * 2];\n      Scalar val3 = lhs_shmem[threadIdx.x + 8 * threadIdx.y + 64 * threadIdx.z + 512 * 3];\n      Scalar val4 = lhs_shmem[threadIdx.x + 8 * threadIdx.y + 64 * threadIdx.z + 512 * 4];\n      Scalar val5 = lhs_shmem[threadIdx.x + 8 * threadIdx.y + 64 * threadIdx.z + 512 * 5];\n      Scalar val6 = lhs_shmem[threadIdx.x + 8 * threadIdx.y + 64 * threadIdx.z + 512 * 6];\n      Scalar val7 = lhs_shmem[threadIdx.x + 8 * threadIdx.y + 64 * threadIdx.z + 512 * 7];\n\n      output(base_m + threadIdx.y + 8 * threadIdx.x, base_n + threadIdx.z + 8 * 0) = val0;\n      output(base_m + threadIdx.y + 8 * threadIdx.x, base_n + threadIdx.z + 8 * 1) = val1;\n      output(base_m + threadIdx.y + 8 * threadIdx.x, base_n + threadIdx.z + 8 * 2) = val2;\n      output(base_m + threadIdx.y + 8 * threadIdx.x, base_n + threadIdx.z + 8 * 3) = val3;\n      output(base_m + threadIdx.y + 8 * threadIdx.x, base_n + threadIdx.z + 8 * 4) = val4;\n      output(base_m + threadIdx.y + 8 * threadIdx.x, base_n + threadIdx.z + 8 * 5) = val5;\n      output(base_m + threadIdx.y + 8 * threadIdx.x, base_n + threadIdx.z + 8 * 6) = val6;\n      output(base_m + threadIdx.y + 8 * threadIdx.x, base_n + threadIdx.z + 8 * 7) = val7;\n    } else {\n#pragma unroll 7\n      for (int j = 0; j < max_j_write; j++) {\n        Scalar val = lhs_shmem[threadIdx.x + 8 * threadIdx.y + 64 * threadIdx.z + 512 * j];\n        output(base_m + threadIdx.y + 8 * threadIdx.x, base_n + threadIdx.z + 8 * j) = val;\n      }\n    }\n  }\n#undef res\n}\n\n\ntemplate<typename Scalar, typename Index, typename LhsMapper,\n         typename RhsMapper, typename OutputMapper>\n__global__ void\n__launch_bounds__(512)\nEigenContractionKernel(const LhsMapper lhs, const RhsMapper rhs,\n                       const OutputMapper output,\n                       const Index m_size, const Index n_size, const Index k_size) {\n  __shared__ Scalar lhs_shmem[72 * 64];\n  __shared__ Scalar rhs_shmem[72 * 64];\n\n  const Index m_block_idx = blockIdx.x;\n  const Index n_block_idx = blockIdx.y;\n\n  const Index base_m = 64 * m_block_idx;\n  const Index base_n = 64 * n_block_idx;\n\n  if (base_m + 63 < m_size && base_n + 63 < n_size) {\n    EigenContractionKernelInternal<Scalar, Index, LhsMapper, RhsMapper, OutputMapper, false>(lhs, rhs, output, lhs_shmem, rhs_shmem, m_size, n_size, k_size);\n  } else {\n    EigenContractionKernelInternal<Scalar, Index, LhsMapper, RhsMapper, OutputMapper, true>(lhs, rhs, output, lhs_shmem, rhs_shmem, m_size, n_size, k_size);\n  }\n}\n\n\ntemplate<typename Index, typename LhsMapper,\n         typename RhsMapper, typename OutputMapper, bool CHECK_LHS_BOUNDARY,\n         bool CHECK_RHS_BOUNDARY>\n__device__ EIGEN_STRONG_INLINE void\nEigenFloatContractionKernelInternal16x16(const LhsMapper lhs, const RhsMapper rhs,\n                       const OutputMapper output, float2 lhs_shmem2[][16],\n                       float2 rhs_shmem2[][8], const Index m_size,\n                       const Index n_size, const Index k_size,\n                       const Index base_m, const Index base_n) {\n  typedef float Scalar;\n\n  // prefetch registers\n  float4 lhs_pf0, rhs_pf0;\n\n  float4 results[4];\n  for (int i=0; i < 4; i++) {\n    results[i].x = results[i].y = results[i].z = results[i].w = 0;\n  }\n\n\n#define prefetch_lhs(reg, row, col)                   \\\n    if (!CHECK_LHS_BOUNDARY) {                        \\\n      if (col < k_size) {                             \\\n        reg =lhs.loadPacket<Unaligned>(row, col);     \\\n      }                                               \\\n    } else {                                          \\\n      if (col < k_size) {                             \\\n        if (row + 3 < m_size) {                       \\\n          reg =lhs.loadPacket<Unaligned>(row, col);   \\\n        } else if (row + 2 < m_size) {                \\\n          reg.x =lhs(row + 0, col);                   \\\n          reg.y =lhs(row + 1, col);                   \\\n          reg.z =lhs(row + 2, col);                   \\\n        } else if (row + 1 < m_size) {                \\\n          reg.x =lhs(row + 0, col);                   \\\n          reg.y =lhs(row + 1, col);                   \\\n        } else if (row  < m_size) {                   \\\n          reg.x =lhs(row + 0, col);                   \\\n        }                                             \\\n      }                                               \\\n    }                                                 \\\n\n\n  Index lhs_vert = base_m+threadIdx.x*4;\n\n  for (Index k = 0; k < k_size; k += 16) {\n    lhs_pf0 = internal::pset1<float4>(0);\n    rhs_pf0 = internal::pset1<float4>(0);\n\n    Index lhs_horiz = threadIdx.y+k;\n    prefetch_lhs(lhs_pf0, lhs_vert, lhs_horiz)\n\n    Index rhs_vert = k+(threadIdx.x%4)*4;\n    Index rhs_horiz0 = (threadIdx.x>>2)+threadIdx.y*4+base_n;\n\n    if (!CHECK_RHS_BOUNDARY) {\n      if ((rhs_vert + 3) < k_size) {\n        // just CHECK_RHS_BOUNDARY\n        rhs_pf0 = rhs.loadPacket<Unaligned>(rhs_vert, rhs_horiz0);\n      } else if (rhs_vert + 2 < k_size) {\n        // just CHECK_RHS_BOUNDARY\n        rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);\n        rhs_pf0.y = rhs(rhs_vert + 1, rhs_horiz0);\n        rhs_pf0.z = rhs(rhs_vert + 2, rhs_horiz0);\n      } else if (rhs_vert + 1 < k_size) {\n        rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);\n        rhs_pf0.y = rhs(rhs_vert + 1, rhs_horiz0);\n      } else if (rhs_vert  < k_size) {\n        rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);\n      }\n    } else {\n      if (rhs_horiz0 < n_size) {\n        if ((rhs_vert + 3) < k_size) {\n          rhs_pf0 = rhs.loadPacket<Unaligned>(rhs_vert, rhs_horiz0);\n        } else if ((rhs_vert + 2) < k_size) {\n          rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);\n          rhs_pf0.y = rhs(rhs_vert + 1, rhs_horiz0);\n          rhs_pf0.z = rhs(rhs_vert + 2, rhs_horiz0);\n        } else if ((rhs_vert + 1) < k_size) {\n          rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);\n          rhs_pf0.y = rhs(rhs_vert + 1, rhs_horiz0);\n        } else if (rhs_vert  < k_size) {\n          rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);\n        }\n      }\n    }\n    float x1, x2 ;\n    // the following can be a bitwise operation..... some day.\n    if((threadIdx.x%8) < 4) {\n      x1 = rhs_pf0.y;\n      x2 = rhs_pf0.w;\n    } else {\n      x1 = rhs_pf0.x;\n      x2 = rhs_pf0.z;\n    }\n    x1 = __shfl_xor(x1, 4);\n    x2 = __shfl_xor(x2, 4);\n    if((threadIdx.x%8) < 4) {\n      rhs_pf0.y = x1;\n      rhs_pf0.w = x2;\n    } else {\n      rhs_pf0.x = x1;\n      rhs_pf0.z = x2;\n    }\n\n    // We have 64 features.\n    // Row 0 -> times (0, 4, 8, 12, 1, 5, 9, 13) for features 0, 1.\n    // Row 1 -> times (0, 4, 8, 12, 1, 5, 9, 13) for features 2, 3.\n    // ...\n    // Row 31 -> times (0, 4, 8, 12, 1, 5, 9, 13) for features 62, 63\n    // Row 32 -> times (2, 6, 10, 14, 3, 7, 11, 15) for features 0, 1\n    // ...\n    rhs_shmem2[(threadIdx.x>>3)+ threadIdx.y*2][threadIdx.x%8] = make_float2(rhs_pf0.x, rhs_pf0.y);\n    rhs_shmem2[(threadIdx.x>>3)+ threadIdx.y*2+32][threadIdx.x%8] = make_float2(rhs_pf0.z, rhs_pf0.w);\n\n    // Row 0 (time 0) -> features (0, 1), (4, 5), .. (28, 29), (32, 33), ..  (60, 61)\n    // Row 1 (time 1) -> features (0, 1), (4, 5), .. (28, 29), (32, 33), ..  (60, 61)\n    // ...\n    // Row 15 (time 15) -> features (0, 1), (4, 5), .. (28, 29), (32, 33), ..  (60, 61)\n    // Row 16 (time 0) -> features (2, 3), (6, 7), .. (30, 31), (34, 35), ..  (62, 63)\n    // ...\n\n    lhs_shmem2[threadIdx.y][threadIdx.x] = make_float2(lhs_pf0.x, lhs_pf0.y);\n    lhs_shmem2[threadIdx.y+16][threadIdx.x] = make_float2(lhs_pf0.z, lhs_pf0.w);\n\n\n#define add_vals(fl1, fl2, fr1, fr2)\\\n    results[0].x += fl1.x * fr1.x;\\\n    results[0].y += fl1.y * fr1.x;\\\n    results[0].z += fl2.x * fr1.x;\\\n    results[0].w += fl2.y * fr1.x;\\\n\\\n    results[1].x += fl1.x * fr1.y;\\\n    results[1].y += fl1.y * fr1.y;\\\n    results[1].z += fl2.x * fr1.y;\\\n    results[1].w += fl2.y * fr1.y;\\\n\\\n    results[2].x += fl1.x * fr2.x;\\\n    results[2].y += fl1.y * fr2.x;\\\n    results[2].z += fl2.x * fr2.x;\\\n    results[2].w += fl2.y * fr2.x;\\\n\\\n    results[3].x += fl1.x * fr2.y;\\\n    results[3].y += fl1.y * fr2.y;\\\n    results[3].z += fl2.x * fr2.y;\\\n    results[3].w += fl2.y * fr2.y;\\\n\n    __syncthreads();\n\n    // Do the multiplies.\n    #pragma unroll\n    for (int koff = 0; koff < 16; koff ++) {\n      // 32 x threads.\n      float2 fl1 = lhs_shmem2[koff][threadIdx.x];\n      float2 fl2 = lhs_shmem2[koff + 16][threadIdx.x];\n\n      int start_feature = threadIdx.y * 4;\n      float2 fr1 = rhs_shmem2[(start_feature>>1) + 32*((koff%4)/2)][koff/4 + (koff%2)*4];\n      float2 fr2 = rhs_shmem2[(start_feature>>1) + 1 + 32*((koff%4)/2)][koff/4 + (koff%2)*4];\n\n      add_vals(fl1, fl2, fr1, fr2)\n    }\n    __syncthreads();\n  }\n\n#undef prefetch_lhs\n#undef add_vals\n\n  Index horiz_base = threadIdx.y*4+base_n;\n  if (!CHECK_LHS_BOUNDARY && !CHECK_RHS_BOUNDARY) {\n    for (int i = 0; i < 4; i++) {\n      output(lhs_vert, horiz_base + i) = results[i].x;\n      output(lhs_vert + 1, horiz_base + i) = results[i].y;\n      output(lhs_vert + 2, horiz_base + i) = results[i].z;\n      output(lhs_vert + 3, horiz_base + i) = results[i].w;\n    }\n  } else if (!CHECK_RHS_BOUNDARY) {\n    // CHECK LHS\n    if (lhs_vert + 3 < m_size) {\n      for (int i = 0; i < 4; i++) {\n        output(lhs_vert, horiz_base + i) = results[i].x;\n        output(lhs_vert + 1, horiz_base + i) = results[i].y;\n        output(lhs_vert + 2, horiz_base + i) = results[i].z;\n        output(lhs_vert + 3, horiz_base + i) = results[i].w;\n      }\n    } else if (lhs_vert + 2 < m_size) {\n      for (int i = 0; i < 4; i++) {\n        output(lhs_vert, horiz_base + i) = results[i].x;\n        output(lhs_vert + 1, horiz_base + i) = results[i].y;\n        output(lhs_vert + 2, horiz_base + i) = results[i].z;\n      }\n    } else if (lhs_vert + 1 < m_size) {\n      for (int i = 0; i < 4; i++) {\n        output(lhs_vert, horiz_base + i) = results[i].x;\n        output(lhs_vert + 1, horiz_base + i) = results[i].y;\n      }\n    } else if (lhs_vert  < m_size) {\n      for (int i = 0; i < 4; i++) {\n        output(lhs_vert, horiz_base + i) = results[i].x;\n      }\n    }\n  } else if (!CHECK_LHS_BOUNDARY) {\n    // CHECK RHS\n    /*\n    int ncols_rem = fminf(n_size- horiz_base, 4);\n    for (int i = 0; i < ncols_rem; i++) {\n      output(lhs_vert, horiz_base + i) = results[i].x;\n      output(lhs_vert + 1, horiz_base + i) = results[i].y;\n      output(lhs_vert + 2, horiz_base + i) = results[i].z;\n      output(lhs_vert + 3, horiz_base + i) = results[i].w;\n    }*/\n    for (int i = 0; i < 4; i++) {\n      if (horiz_base+i < n_size) {\n        output(lhs_vert, horiz_base + i) = results[i].x;\n        output(lhs_vert + 1, horiz_base + i) = results[i].y;\n        output(lhs_vert + 2, horiz_base + i) = results[i].z;\n        output(lhs_vert + 3, horiz_base + i) = results[i].w;\n       }\n    }\n  } else {\n    // CHECK both boundaries.\n    for (int i = 0; i < 4; i++) {\n      if (horiz_base+i < n_size) {\n        if (lhs_vert < m_size)\n          output(lhs_vert, horiz_base + i) = results[i].x;\n        if (lhs_vert + 1 < m_size)\n          output(lhs_vert + 1, horiz_base + i) = results[i].y;\n        if (lhs_vert + 2 < m_size)\n          output(lhs_vert + 2, horiz_base + i) = results[i].z;\n        if (lhs_vert + 3 < m_size)\n          output(lhs_vert + 3, horiz_base + i) = results[i].w;\n      }\n    }\n  }\n}\n\n\ntemplate<typename Index, typename LhsMapper,\n         typename RhsMapper, typename OutputMapper, bool CHECK_LHS_BOUNDARY,\n         bool CHECK_RHS_BOUNDARY>\n__device__ EIGEN_STRONG_INLINE void\nEigenFloatContractionKernelInternal(const LhsMapper lhs, const RhsMapper rhs,\n                       const OutputMapper output, float2 lhs_shmem2[][32],\n                       float2 rhs_shmem2[][8], const Index m_size,\n                       const Index n_size, const Index k_size,\n                       const Index base_m, const Index base_n) {\n  typedef float Scalar;\n\n  // prefetch registers\n  float4 lhs_pf0, lhs_pf1, lhs_pf2, lhs_pf3;\n  float4 rhs_pf0, rhs_pf1;\n\n  float4 results[8];\n  for (int i=0; i < 8; i++) {\n    results[i].x = results[i].y = results[i].z = results[i].w = 0;\n  }\n\n\n  Index lhs_vert = base_m+threadIdx.x*4+(threadIdx.y%4)*32;\n  for (Index k = 0; k < k_size; k += 32) {\n    lhs_pf0 = internal::pset1<float4>(0);\n    lhs_pf1 = internal::pset1<float4>(0);\n    lhs_pf2 = internal::pset1<float4>(0);\n    lhs_pf3 = internal::pset1<float4>(0);\n\n    rhs_pf0 = internal::pset1<float4>(0);\n    rhs_pf1 = internal::pset1<float4>(0);\n\n     if (!CHECK_LHS_BOUNDARY) {\n      if ((threadIdx.y/4+k+24) < k_size) {\n        lhs_pf0 =lhs.loadPacket<Unaligned>(lhs_vert, (threadIdx.y/4+k));\n        lhs_pf1 =lhs.loadPacket<Unaligned>(lhs_vert, (threadIdx.y/4+k+8));\n        lhs_pf2 =lhs.loadPacket<Unaligned>(lhs_vert, (threadIdx.y/4+k+16));\n        lhs_pf3 =lhs.loadPacket<Unaligned>(lhs_vert, (threadIdx.y/4+k+24));\n      } else if ((threadIdx.y/4+k+16) < k_size) {\n        lhs_pf0 =lhs.loadPacket<Unaligned>(lhs_vert, (threadIdx.y/4+k));\n        lhs_pf1 =lhs.loadPacket<Unaligned>(lhs_vert, (threadIdx.y/4+k+8));\n        lhs_pf2 =lhs.loadPacket<Unaligned>(lhs_vert, (threadIdx.y/4+k+16));\n      } else if ((threadIdx.y/4+k+8) < k_size) {\n        lhs_pf0 =lhs.loadPacket<Unaligned>(lhs_vert, (threadIdx.y/4+k));\n        lhs_pf1 =lhs.loadPacket<Unaligned>(lhs_vert, (threadIdx.y/4+k+8));\n      } else if ((threadIdx.y/4+k) < k_size) {\n        lhs_pf0 =lhs.loadPacket<Unaligned>(lhs_vert, (threadIdx.y/4+k));\n      }\n    } else {\n      // just CHECK_LHS_BOUNDARY\n      if (lhs_vert + 3 < m_size) {\n        if ((threadIdx.y/4+k+24) < k_size) {\n          lhs_pf0 =lhs.loadPacket<Unaligned>(lhs_vert, (threadIdx.y/4+k));\n          lhs_pf1 =lhs.loadPacket<Unaligned>(lhs_vert, (threadIdx.y/4+k+8));\n          lhs_pf2 =lhs.loadPacket<Unaligned>(lhs_vert, (threadIdx.y/4+k+16));\n          lhs_pf3 =lhs.loadPacket<Unaligned>(lhs_vert, (threadIdx.y/4+k+24));\n        } else if ((threadIdx.y/4+k+16) < k_size) {\n          lhs_pf0 =lhs.loadPacket<Unaligned>(lhs_vert, (threadIdx.y/4+k));\n          lhs_pf1 =lhs.loadPacket<Unaligned>(lhs_vert, (threadIdx.y/4+k+8));\n          lhs_pf2 =lhs.loadPacket<Unaligned>(lhs_vert, (threadIdx.y/4+k+16));\n        } else if ((threadIdx.y/4+k+8) < k_size) {\n          lhs_pf0 =lhs.loadPacket<Unaligned>(lhs_vert, (threadIdx.y/4+k));\n          lhs_pf1 =lhs.loadPacket<Unaligned>(lhs_vert, (threadIdx.y/4+k+8));\n        } else if ((threadIdx.y/4+k) < k_size) {\n          lhs_pf0 =lhs.loadPacket<Unaligned>(lhs_vert, (threadIdx.y/4+k));\n        }\n      } else if (lhs_vert + 2 < m_size) {\n        if ((threadIdx.y/4+k+24) < k_size) {\n          lhs_pf0.x =lhs(lhs_vert + 0, (threadIdx.y/4+k));\n          lhs_pf0.y =lhs(lhs_vert + 1, (threadIdx.y/4+k));\n          lhs_pf0.z =lhs(lhs_vert + 2, (threadIdx.y/4+k));\n          lhs_pf1.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+8));\n          lhs_pf1.y =lhs(lhs_vert + 1, (threadIdx.y/4+k+8));\n          lhs_pf1.z =lhs(lhs_vert + 2, (threadIdx.y/4+k+8));\n          lhs_pf2.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+16));\n          lhs_pf2.y =lhs(lhs_vert + 1, (threadIdx.y/4+k+16));\n          lhs_pf2.z =lhs(lhs_vert + 2, (threadIdx.y/4+k+16));\n          lhs_pf3.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+24));\n          lhs_pf3.y =lhs(lhs_vert + 1, (threadIdx.y/4+k+24));\n          lhs_pf3.z =lhs(lhs_vert + 2, (threadIdx.y/4+k+24));\n        } else if ((threadIdx.y/4+k+16) < k_size) {\n          lhs_pf0.x =lhs(lhs_vert + 0, (threadIdx.y/4+k));\n          lhs_pf0.y =lhs(lhs_vert + 1, (threadIdx.y/4+k));\n          lhs_pf0.z =lhs(lhs_vert + 2, (threadIdx.y/4+k));\n          lhs_pf1.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+8));\n          lhs_pf1.y =lhs(lhs_vert + 1, (threadIdx.y/4+k+8));\n          lhs_pf1.z =lhs(lhs_vert + 2, (threadIdx.y/4+k+8));\n          lhs_pf2.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+16));\n          lhs_pf2.y =lhs(lhs_vert + 1, (threadIdx.y/4+k+16));\n          lhs_pf2.z =lhs(lhs_vert + 2, (threadIdx.y/4+k+16));\n        } else if ((threadIdx.y/4+k+8) < k_size) {\n          lhs_pf0.x =lhs(lhs_vert + 0, (threadIdx.y/4+k));\n          lhs_pf0.y =lhs(lhs_vert + 1, (threadIdx.y/4+k));\n          lhs_pf0.z =lhs(lhs_vert + 2, (threadIdx.y/4+k));\n          lhs_pf1.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+8));\n          lhs_pf1.y =lhs(lhs_vert + 1, (threadIdx.y/4+k+8));\n          lhs_pf1.z =lhs(lhs_vert + 2, (threadIdx.y/4+k+8));\n        } else if ((threadIdx.y/4+k) < k_size) {\n          lhs_pf0.x =lhs(lhs_vert + 0, (threadIdx.y/4+k));\n          lhs_pf0.y =lhs(lhs_vert + 1, (threadIdx.y/4+k));\n          lhs_pf0.z =lhs(lhs_vert + 2, (threadIdx.y/4+k));\n        }\n      } else if (lhs_vert + 1 < m_size) {\n        if ((threadIdx.y/4+k+24) < k_size) {\n          lhs_pf0.x =lhs(lhs_vert + 0, (threadIdx.y/4+k));\n          lhs_pf0.y =lhs(lhs_vert + 1, (threadIdx.y/4+k));\n          lhs_pf1.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+8));\n          lhs_pf1.y =lhs(lhs_vert + 1, (threadIdx.y/4+k+8));\n          lhs_pf2.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+16));\n          lhs_pf2.y =lhs(lhs_vert + 1, (threadIdx.y/4+k+16));\n          lhs_pf3.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+24));\n          lhs_pf3.y =lhs(lhs_vert + 1, (threadIdx.y/4+k+24));\n        } else if ((threadIdx.y/4+k+16) < k_size) {\n          lhs_pf0.x =lhs(lhs_vert + 0, (threadIdx.y/4+k));\n          lhs_pf0.y =lhs(lhs_vert + 1, (threadIdx.y/4+k));\n          lhs_pf1.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+8));\n          lhs_pf1.y =lhs(lhs_vert + 1, (threadIdx.y/4+k+8));\n          lhs_pf2.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+16));\n          lhs_pf2.y =lhs(lhs_vert + 1, (threadIdx.y/4+k+16));\n        } else if ((threadIdx.y/4+k+8) < k_size) {\n          lhs_pf0.x =lhs(lhs_vert + 0, (threadIdx.y/4+k));\n          lhs_pf0.y =lhs(lhs_vert + 1, (threadIdx.y/4+k));\n          lhs_pf1.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+8));\n          lhs_pf1.y =lhs(lhs_vert + 1, (threadIdx.y/4+k+8));\n        } else if ((threadIdx.y/4+k) < k_size) {\n          lhs_pf0.x =lhs(lhs_vert + 0, (threadIdx.y/4+k));\n          lhs_pf0.y =lhs(lhs_vert + 1, (threadIdx.y/4+k));\n        }\n      } else if (lhs_vert < m_size) {\n        if ((threadIdx.y/4+k+24) < k_size) {\n          lhs_pf0.x =lhs(lhs_vert + 0, (threadIdx.y/4+k));\n          lhs_pf1.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+8));\n          lhs_pf2.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+16));\n          lhs_pf3.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+24));\n        } else if ((threadIdx.y/4+k+16) < k_size) {\n          lhs_pf0.x =lhs(lhs_vert + 0, (threadIdx.y/4+k));\n          lhs_pf1.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+8));\n          lhs_pf2.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+16));\n        } else if ((threadIdx.y/4+k+8) < k_size) {\n          lhs_pf0.x =lhs(lhs_vert + 0, (threadIdx.y/4+k));\n          lhs_pf1.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+8));\n        } else if ((threadIdx.y/4+k) < k_size) {\n          lhs_pf0.x =lhs(lhs_vert + 0, (threadIdx.y/4+k));\n        }\n      }\n    }\n    __syncthreads();\n    Index rhs_vert = k+threadIdx.x*4;\n    Index rhs_horiz0 = threadIdx.y*2+base_n;\n    Index rhs_horiz1 = threadIdx.y*2+1+base_n;\n    if (!CHECK_RHS_BOUNDARY) {\n      if ((rhs_vert + 3) < k_size) {\n        // just CHECK_RHS_BOUNDARY\n        rhs_pf0 = rhs.loadPacket<Unaligned>(rhs_vert, rhs_horiz0);\n        rhs_pf1 = rhs.loadPacket<Unaligned>(rhs_vert, rhs_horiz1);\n      } else if (rhs_vert + 2 < k_size) {\n        // just CHECK_RHS_BOUNDARY\n        rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);\n        rhs_pf0.y = rhs(rhs_vert + 1, rhs_horiz0);\n        rhs_pf0.z = rhs(rhs_vert + 2, rhs_horiz0);\n        rhs_pf1.x = rhs(rhs_vert, rhs_horiz1);\n        rhs_pf1.y = rhs(rhs_vert + 1, rhs_horiz1);\n        rhs_pf1.z = rhs(rhs_vert + 2, rhs_horiz1);\n      } else if (rhs_vert + 1 < k_size) {\n        rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);\n        rhs_pf0.y = rhs(rhs_vert + 1, rhs_horiz0);\n        rhs_pf1.x = rhs(rhs_vert, rhs_horiz1);\n        rhs_pf1.y = rhs(rhs_vert + 1, rhs_horiz1);\n      } else if (rhs_vert  < k_size) {\n        rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);\n        rhs_pf1.x = rhs(rhs_vert, rhs_horiz1);\n      }\n    } else {\n      if (rhs_horiz1 < n_size) {\n        if ((rhs_vert + 3) < k_size) {\n          // just CHECK_RHS_BOUNDARY\n          rhs_pf0 = rhs.loadPacket<Unaligned>(rhs_vert, rhs_horiz0);\n          rhs_pf1 = rhs.loadPacket<Unaligned>(rhs_vert, rhs_horiz1);\n        } else if (rhs_vert + 2 < k_size) {\n          // just CHECK_RHS_BOUNDARY\n          rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);\n          rhs_pf0.y = rhs(rhs_vert + 1, rhs_horiz0);\n          rhs_pf0.z = rhs(rhs_vert + 2, rhs_horiz0);\n          rhs_pf1.x = rhs(rhs_vert, rhs_horiz1);\n          rhs_pf1.y = rhs(rhs_vert + 1, rhs_horiz1);\n          rhs_pf1.z = rhs(rhs_vert + 2, rhs_horiz1);\n        } else if (k+threadIdx.x*4 + 1 < k_size) {\n          rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);\n          rhs_pf0.y = rhs(rhs_vert + 1, rhs_horiz0);\n          rhs_pf1.x = rhs(rhs_vert, rhs_horiz1);\n          rhs_pf1.y = rhs(rhs_vert + 1, rhs_horiz1);\n        } else if (k+threadIdx.x*4  < k_size) {\n          rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);\n          rhs_pf1.x = rhs(rhs_vert, rhs_horiz1);\n        }\n      } else if (rhs_horiz0 < n_size) {\n        if ((rhs_vert + 3) < k_size) {\n          // just CHECK_RHS_BOUNDARY\n          rhs_pf0 = rhs.loadPacket<Unaligned>(rhs_vert, rhs_horiz0);\n        } else if ((rhs_vert + 2) < k_size) {\n          // just CHECK_RHS_BOUNDARY\n          rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);\n          rhs_pf0.y = rhs(rhs_vert + 1, rhs_horiz0);\n          rhs_pf0.z = rhs(rhs_vert + 2, rhs_horiz0);\n        } else if ((rhs_vert + 1) < k_size) {\n          rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);\n          rhs_pf0.y = rhs(rhs_vert + 1, rhs_horiz0);\n        } else if (rhs_vert  < k_size) {\n          rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);\n        }\n      }\n    }\n    __syncthreads();\n    // Loaded. Do computation\n    // Row 0 -> times (0, 4, 8, .. 28) for features 0, 1.\n    // Row 1 -> times (0, 4, 8, .. 28) for features 2, 3.\n    // ..\n    // Row 31 -> times (0, 4, 8, .. 28) for features 62, 63\n    rhs_shmem2[threadIdx.y][threadIdx.x] = make_float2(rhs_pf0.x, rhs_pf1.x);\n    // Row 32 -> times (1, 5, 9, .. 29) for features 0, 1.\n    // Row 33 -> times (1, 5, 9, .. 29) for features 2, 3.\n    // ..\n    rhs_shmem2[threadIdx.y+32][threadIdx.x] = make_float2(rhs_pf0.y, rhs_pf1.y);\n    // Row 64 -> times (2, 6, 10, .. 30) for features 0, 1.\n    // Row 65 -> times (2, 6, 10, .. 30) for features 2, 3.\n    rhs_shmem2[threadIdx.y+64][threadIdx.x] = make_float2(rhs_pf0.z, rhs_pf1.z);\n    // Row 96 -> times (3, 7, 11, .. 31) for features 0, 1.\n    // Row 97 -> times (3, 7, 11, .. 31) for features 2, 3.\n    rhs_shmem2[threadIdx.y+96][threadIdx.x] = make_float2(rhs_pf0.w, rhs_pf1.w);\n\n    // LHS.\n    // Row 0 (time 0) -> features (0, 1), (4, 5), .. (28, 29), (32, 33), ..  (60, 61) .. (124, 125)\n    // Row 1 (time 1) -> features (0, 1), (4, 5), .. (28, 29), (32, 33), ..  (60, 61) .. (124, 125)\n    // ...\n    // Row 8 (time 0) -> features (2, 3), (6, 7), .. (30, 31), (34, 35), ..  (62, 63) .. (126, 127)\n    // Row 15 (time 7) -> features (2, 3), (6, 7), .. (30, 31), (34, 35), ..  (62, 63) .. (126, 127)\n\n\n#define add_vals(a_feat1, a_feat2, f1, f2, f3, f4)\\\n      results[0].x += a_feat1.x * f1.x;\\\n      results[1].x += a_feat1.x * f1.y;\\\n      results[2].x += a_feat1.x * f2.x;\\\n      results[3].x += a_feat1.x * f2.y;\\\n      results[4].x += a_feat1.x * f3.x;\\\n      results[5].x += a_feat1.x * f3.y;\\\n      results[6].x += a_feat1.x * f4.x;\\\n      results[7].x += a_feat1.x * f4.y;\\\n\\\n      results[0].y += a_feat1.y * f1.x;\\\n      results[1].y += a_feat1.y * f1.y;\\\n      results[2].y += a_feat1.y * f2.x;\\\n      results[3].y += a_feat1.y * f2.y;\\\n      results[4].y += a_feat1.y * f3.x;\\\n      results[5].y += a_feat1.y * f3.y;\\\n      results[6].y += a_feat1.y * f4.x;\\\n      results[7].y += a_feat1.y * f4.y;\\\n\\\n      results[0].z += a_feat2.x * f1.x;\\\n      results[1].z += a_feat2.x * f1.y;\\\n      results[2].z += a_feat2.x * f2.x;\\\n      results[3].z += a_feat2.x * f2.y;\\\n      results[4].z += a_feat2.x * f3.x;\\\n      results[5].z += a_feat2.x * f3.y;\\\n      results[6].z += a_feat2.x * f4.x;\\\n      results[7].z += a_feat2.x * f4.y;\\\n\\\n      results[0].w += a_feat2.y * f1.x;\\\n      results[1].w += a_feat2.y * f1.y;\\\n      results[2].w += a_feat2.y * f2.x;\\\n      results[3].w += a_feat2.y * f2.y;\\\n      results[4].w += a_feat2.y * f3.x;\\\n      results[5].w += a_feat2.y * f3.y;\\\n      results[6].w += a_feat2.y * f4.x;\\\n      results[7].w += a_feat2.y * f4.y;\\\n\n    lhs_shmem2[threadIdx.y/4][threadIdx.x+(threadIdx.y%4)*8] = make_float2(lhs_pf0.x, lhs_pf0.y);\n    lhs_shmem2[threadIdx.y/4+8][threadIdx.x+(threadIdx.y%4)*8] = make_float2(lhs_pf1.x, lhs_pf1.y);\n    lhs_shmem2[threadIdx.y/4+16][threadIdx.x+(threadIdx.y%4)*8] = make_float2(lhs_pf2.x, lhs_pf2.y);\n    lhs_shmem2[threadIdx.y/4+24][threadIdx.x+(threadIdx.y%4)*8] = make_float2(lhs_pf3.x, lhs_pf3.y);\n\n    lhs_shmem2[threadIdx.y/4 + 32][threadIdx.x+(threadIdx.y%4)*8] = make_float2(lhs_pf0.z, lhs_pf0.w);\n    lhs_shmem2[threadIdx.y/4 + 40][threadIdx.x+(threadIdx.y%4)*8] = make_float2(lhs_pf1.z, lhs_pf1.w);\n    lhs_shmem2[threadIdx.y/4 + 48][threadIdx.x+(threadIdx.y%4)*8] = make_float2(lhs_pf2.z, lhs_pf2.w);\n    lhs_shmem2[threadIdx.y/4 + 56][threadIdx.x+(threadIdx.y%4)*8] = make_float2(lhs_pf3.z, lhs_pf3.w);\n\n    __syncthreads();\n\n    // Do the multiplies.\n    #pragma unroll\n    for (int koff = 0; koff < 32; koff ++) {\n      float2 a3 = lhs_shmem2[koff][threadIdx.x + (threadIdx.y % 4) * 8];\n      float2 a4 = lhs_shmem2[koff + 32][threadIdx.x + (threadIdx.y % 4) * 8];\n\n      // first feature is at (threadIdx.y/4) * 8 last is at start + 8.\n      int start_feature = (threadIdx.y / 4) * 8;\n\n      float2 br1 = rhs_shmem2[start_feature/2 +     (koff % 4) * 32][koff/4];\n      float2 br2 = rhs_shmem2[start_feature/2 + 1 + (koff % 4) * 32][koff/4];\n      float2 br3 = rhs_shmem2[start_feature/2 + 2 + (koff % 4) * 32][koff/4];\n      float2 br4 = rhs_shmem2[start_feature/2 + 3 + (koff % 4) * 32][koff/4];\n\n      add_vals(a3, a4, br1, br2, br3, br4)\n    }\n    __syncthreads();\n  } // end loop over k\n\n\n  __syncthreads();\n  Index horiz_base = (threadIdx.y/4)*8+base_n;\n  if (!CHECK_LHS_BOUNDARY && !CHECK_RHS_BOUNDARY) {\n    for (int i = 0; i < 8; i++) {\n      output(lhs_vert, horiz_base + i) = results[i].x;\n      output(lhs_vert + 1, horiz_base + i) = results[i].y;\n      output(lhs_vert + 2, horiz_base + i) = results[i].z;\n      output(lhs_vert + 3, horiz_base + i) = results[i].w;\n    }\n  } else if (!CHECK_RHS_BOUNDARY) {\n    if (lhs_vert + 3 < m_size) {\n      for (int i = 0; i < 8; i++) {\n        output(lhs_vert, horiz_base + i) = results[i].x;\n        output(lhs_vert + 1, horiz_base + i) = results[i].y;\n        output(lhs_vert + 2, horiz_base + i) = results[i].z;\n        output(lhs_vert + 3, horiz_base + i) = results[i].w;\n      }\n    } else if (lhs_vert + 2 < m_size) {\n      for (int i = 0; i < 8; i++) {\n        output(lhs_vert, horiz_base + i) = results[i].x;\n        output(lhs_vert + 1, horiz_base + i) = results[i].y;\n        output(lhs_vert + 2, horiz_base + i) = results[i].z;\n      }\n    } else if (lhs_vert + 1 < m_size) {\n      for (int i = 0; i < 8; i++) {\n        output(lhs_vert, horiz_base + i) = results[i].x;\n        output(lhs_vert + 1, horiz_base + i) = results[i].y;\n      }\n    } else if (lhs_vert  < m_size) {\n      for (int i = 0; i < 8; i++) {\n        output(lhs_vert, horiz_base + i) = results[i].x;\n      }\n    }\n  } else if (!CHECK_LHS_BOUNDARY) {\n    // CHECK BOUNDARY_B\n    for (int i = 0; i < 8; i++) {\n      if (horiz_base + i < n_size) {\n        output(lhs_vert, horiz_base + i) = results[i].x;\n        output(lhs_vert + 1, horiz_base + i) = results[i].y;\n        output(lhs_vert + 2, horiz_base + i) = results[i].z;\n        output(lhs_vert + 3, horiz_base + i) = results[i].w;\n      }\n    }\n  } else {\n    // CHECK both boundaries.\n    for (int i = 0; i < 8; i++) {\n      if (horiz_base + i < n_size) {\n        if (lhs_vert < m_size)\n          output(lhs_vert, horiz_base + i) = results[i].x;\n        if (lhs_vert + 1 < m_size)\n          output(lhs_vert + 1, horiz_base + i) = results[i].y;\n        if (lhs_vert + 2 < m_size)\n          output(lhs_vert + 2, horiz_base + i) = results[i].z;\n        if (lhs_vert + 3 < m_size)\n          output(lhs_vert + 3, horiz_base + i) = results[i].w;\n      }\n    }\n  }\n}\n\n\ntemplate<typename Index, typename LhsMapper,\n         typename RhsMapper, typename OutputMapper>\n__global__ void\n__launch_bounds__(256)\nEigenFloatContractionKernel(const LhsMapper lhs, const RhsMapper rhs,\n                       const OutputMapper output,\n                       const Index m_size, const Index n_size, const Index k_size) {\n  __shared__ float2 lhs_shmem[64*32];\n  __shared__ float2 rhs_shmem[128*8];\n\n  typedef float2 LHS_MEM[64][32];\n  typedef float2 RHS_MEM[128][8];\n\n  typedef float2 LHS_MEM16x16[32][16];\n  typedef float2 RHS_MEM16x16[64][8];\n\n  const Index m_block_idx = blockIdx.x;\n  const Index n_block_idx = blockIdx.y;\n\n  const Index base_m = 128 * m_block_idx;\n  const Index base_n = 64 * n_block_idx;\n\n  bool check_rhs = (base_n + 63) >= n_size;\n  bool check_lhs128 = (base_m + 127) >= m_size;\n\n  if (!check_rhs) {\n    if (!check_lhs128) {\n      // >= 128 rows left\n      EigenFloatContractionKernelInternal<Index, LhsMapper, RhsMapper, OutputMapper, false, false>(\n                     lhs, rhs, output, *((LHS_MEM *) lhs_shmem), *((RHS_MEM *) rhs_shmem), m_size, n_size, k_size, base_m, base_n);\n    } else {\n      EigenFloatContractionKernelInternal<Index, LhsMapper, RhsMapper, OutputMapper, true, false>(\n                     lhs, rhs, output, *((LHS_MEM *) lhs_shmem), *((RHS_MEM *) rhs_shmem), m_size, n_size, k_size, base_m, base_n);\n    }\n  } else {\n    if (!check_lhs128) {\n      // >= 128 rows left\n      EigenFloatContractionKernelInternal<Index, LhsMapper, RhsMapper, OutputMapper, false, true>(\n                     lhs, rhs, output, *((LHS_MEM *) lhs_shmem), *((RHS_MEM *) rhs_shmem), m_size, n_size, k_size, base_m, base_n);\n    } else {\n      EigenFloatContractionKernelInternal<Index, LhsMapper, RhsMapper, OutputMapper, true, true>(\n                     lhs, rhs, output, *((LHS_MEM *) lhs_shmem), *((RHS_MEM *) rhs_shmem), m_size, n_size, k_size, base_m, base_n);\n    }\n  }\n}\n\ntemplate<typename Index, typename LhsMapper,\n         typename RhsMapper, typename OutputMapper>\n__global__ void\n__launch_bounds__(256)\nEigenFloatContractionKernel16x16(const LhsMapper lhs, const RhsMapper rhs,\n                       const OutputMapper output,\n                       const Index m_size, const Index n_size, const Index k_size) {\n  __shared__ float2 lhs_shmem[32][16];\n  __shared__ float2 rhs_shmem[64][8];\n\n  const Index m_block_idx = blockIdx.x;\n  const Index n_block_idx = blockIdx.y;\n\n  const Index base_m = 64 * m_block_idx;\n  const Index base_n = 64 * n_block_idx;\n\n  if (base_m + 63 < m_size) {\n    if (base_n + 63 < n_size) {\n      EigenFloatContractionKernelInternal16x16<Index, LhsMapper, RhsMapper, OutputMapper, false, false>(lhs, rhs, output, lhs_shmem, rhs_shmem, m_size, n_size, k_size, base_m, base_n);\n    } else {\n      EigenFloatContractionKernelInternal16x16<Index, LhsMapper, RhsMapper, OutputMapper, false, true>(lhs, rhs, output, lhs_shmem, rhs_shmem, m_size, n_size, k_size, base_m, base_n);\n    }\n  } else {\n    if (base_n + 63 < n_size) {\n      EigenFloatContractionKernelInternal16x16<Index, LhsMapper, RhsMapper, OutputMapper, true, false>(lhs, rhs, output, lhs_shmem, rhs_shmem, m_size, n_size, k_size, base_m, base_n);\n    } else {\n      EigenFloatContractionKernelInternal16x16<Index, LhsMapper, RhsMapper, OutputMapper, true, true>(lhs, rhs, output, lhs_shmem, rhs_shmem, m_size, n_size, k_size, base_m, base_n);\n    }\n  }\n}\n\n\ntemplate<typename Indices, typename LeftArgType, typename RightArgType>\nstruct TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgType>, GpuDevice> :\n    public TensorContractionEvaluatorBase<TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgType>, GpuDevice> > {\n\n  typedef GpuDevice Device;\n\n  typedef TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgType>, Device> Self;\n  typedef TensorContractionEvaluatorBase<Self> Base;\n\n  typedef TensorContractionOp<Indices, LeftArgType, RightArgType> XprType;\n  typedef typename internal::remove_const<typename XprType::Scalar>::type Scalar;\n  typedef typename XprType::Index Index;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, GpuDevice>::type PacketReturnType;\n\n  enum {\n    Layout = TensorEvaluator<LeftArgType, Device>::Layout,\n  };\n\n  // Most of the code is assuming that both input tensors are ColMajor. If the\n  // inputs are RowMajor, we will \"cheat\" by swapping the LHS and RHS:\n  // If we want to compute A * B = C, where A is LHS and B is RHS, the code\n  // will pretend B is LHS and A is RHS.\n  typedef typename internal::conditional<\n    static_cast<int>(Layout) == static_cast<int>(ColMajor), LeftArgType, RightArgType>::type EvalLeftArgType;\n  typedef typename internal::conditional<\n    static_cast<int>(Layout) == static_cast<int>(ColMajor), RightArgType, LeftArgType>::type EvalRightArgType;\n\n  static const int LDims =\n      internal::array_size<typename TensorEvaluator<EvalLeftArgType, Device>::Dimensions>::value;\n  static const int RDims =\n      internal::array_size<typename TensorEvaluator<EvalRightArgType, Device>::Dimensions>::value;\n  static const int ContractDims = internal::array_size<Indices>::value;\n\n  typedef array<Index, LDims> left_dim_mapper_t;\n  typedef array<Index, RDims> right_dim_mapper_t;\n\n  typedef array<Index, ContractDims> contract_t;\n  typedef array<Index, LDims - ContractDims> left_nocontract_t;\n  typedef array<Index, RDims - ContractDims> right_nocontract_t;\n\n  static const int NumDims = LDims + RDims - 2 * ContractDims;\n\n  typedef DSizes<Index, NumDims> Dimensions;\n\n  // typedefs needed in evalTo\n  typedef typename internal::remove_const<typename EvalLeftArgType::Scalar>::type LhsScalar;\n  typedef typename internal::remove_const<typename EvalRightArgType::Scalar>::type RhsScalar;\n\n  typedef TensorEvaluator<EvalLeftArgType, Device> LeftEvaluator;\n  typedef TensorEvaluator<EvalRightArgType, Device> RightEvaluator;\n\n  typedef typename LeftEvaluator::Dimensions LeftDimensions;\n  typedef typename RightEvaluator::Dimensions RightDimensions;\n\n  EIGEN_DEVICE_FUNC TensorEvaluator(const XprType& op, const Device& device) :\n      Base(op, device) {}\n\n  // We need to redefine this method to make nvcc happy\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(Scalar* data) {\n    this->m_leftImpl.evalSubExprsIfNeeded(NULL);\n    this->m_rightImpl.evalSubExprsIfNeeded(NULL);\n    if (data) {\n      evalTo(data);\n      return false;\n    } else {\n      this->m_result = static_cast<Scalar *>(this->m_device.allocate(this->dimensions().TotalSize() * sizeof(Scalar)));\n      evalTo(this->m_result);\n      return true;\n    }\n  }\n\n  void evalTo(Scalar* buffer) const {\n    if (this->m_lhs_inner_dim_contiguous) {\n      if (this->m_rhs_inner_dim_contiguous) {\n        if (this->m_rhs_inner_dim_reordered) {\n          evalTyped<true, true, true, Unaligned>(buffer);\n        }\n        else {\n          evalTyped<true, true, false, Unaligned>(buffer);\n        }\n      }\n      else {\n       if (this->m_rhs_inner_dim_reordered) {\n          evalTyped<true, false, true, Unaligned>(buffer);\n        }\n        else {\n          evalTyped<true, false, false, Unaligned>(buffer);\n        }\n      }\n    }\n    else {\n      if (this->m_rhs_inner_dim_contiguous) {\n        if (this->m_rhs_inner_dim_reordered) {\n          evalTyped<false, true, true, Unaligned>(buffer);\n        }\n        else {\n          evalTyped<false, true, false, Unaligned>(buffer);\n        }\n      }\n      else {\n       if (this->m_rhs_inner_dim_reordered) {\n          evalTyped<false, false, true, Unaligned>(buffer);\n        }\n        else {\n          evalTyped<false, false, false, Unaligned>(buffer);\n        }\n      }\n    }\n  }\n\n  template <typename LhsScalar, typename RhsScalar, typename Index, typename LhsMapper, typename RhsMapper, typename OutputMapper> struct LaunchKernels {\n    static void Run(const LhsMapper& lhs, const RhsMapper& rhs, const OutputMapper& output, Index m, Index n, Index k, const GpuDevice& device) {\n    const Index m_blocks = (m + 63) / 64;\n    const Index n_blocks = (n + 63) / 64;\n    const dim3 num_blocks(m_blocks, n_blocks, 1);\n    const dim3 block_size(8, 8, 8);\n    LAUNCH_CUDA_KERNEL((EigenContractionKernel<Scalar, Index, LhsMapper, RhsMapper, OutputMapper>), num_blocks, block_size, 0, device, lhs, rhs, output, m, n, k);\n    }\n  };\n\n  template <typename Index, typename LhsMapper, typename RhsMapper, typename OutputMapper> struct LaunchKernels<float, float, Index, LhsMapper, RhsMapper, OutputMapper> {\n    static void Run(const LhsMapper& lhs, const RhsMapper& rhs, const OutputMapper& output, Index m, Index n, Index k, const GpuDevice& device) {\n      if (m < 768 || n < 768) {\n        const Index m_blocks = (m + 63) / 64;\n        const Index n_blocks = (n + 63) / 64;\n        const dim3 num_blocks(m_blocks, n_blocks, 1);\n        const dim3 block_size(16, 16, 1);\n        LAUNCH_CUDA_KERNEL((EigenFloatContractionKernel16x16<Index, LhsMapper, RhsMapper, OutputMapper>), num_blocks, block_size, 0, device, lhs, rhs, output, m, n, k);\n      } else {\n        const Index m_blocks = (m + 127) / 128;\n        const Index n_blocks = (n + 63) / 64;\n        const dim3 num_blocks(m_blocks, n_blocks, 1);\n        const dim3 block_size(8, 32, 1);\n        LAUNCH_CUDA_KERNEL((EigenFloatContractionKernel<Index, LhsMapper, RhsMapper, OutputMapper>), num_blocks, block_size, 0, device, lhs, rhs, output, m, n, k);\n      }\n    }\n  };\n\n  template <bool lhs_inner_dim_contiguous, bool rhs_inner_dim_contiguous, bool rhs_inner_dim_reordered, int Alignment>\n  void evalTyped(Scalar* buffer) const {\n    // columns in left side, rows in right side\n    const Index k = this->m_k_size;\n    EIGEN_UNUSED_VARIABLE(k)\n\n    // rows in left side\n    const Index m = this->m_i_size;\n\n    // columns in right side\n    const Index n = this->m_j_size;\n\n    // zero out the result buffer (which must be of size at least m * n * sizeof(Scalar)\n    this->m_device.memset(buffer, 0, m * n * sizeof(Scalar));\n\n    typedef internal::TensorContractionInputMapper<LhsScalar, Index, internal::Lhs,\n                                                   LeftEvaluator, left_nocontract_t,\n                                                   contract_t, 4,\n                                                   lhs_inner_dim_contiguous,\n                                                   false, Unaligned> LhsMapper;\n\n    typedef internal::TensorContractionInputMapper<RhsScalar, Index, internal::Rhs,\n                                                   RightEvaluator, right_nocontract_t,\n                                                   contract_t, 4,\n                                                   rhs_inner_dim_contiguous,\n                                                   rhs_inner_dim_reordered, Unaligned> RhsMapper;\n\n    typedef internal::blas_data_mapper<Scalar, Index, ColMajor> OutputMapper;\n\n\n    // initialize data mappers\n    LhsMapper lhs(this->m_leftImpl, this->m_left_nocontract_strides, this->m_i_strides,\n                  this->m_left_contracting_strides, this->m_k_strides);\n\n    RhsMapper rhs(this->m_rightImpl, this->m_right_nocontract_strides, this->m_j_strides,\n                  this->m_right_contracting_strides, this->m_k_strides);\n\n    OutputMapper output(buffer, m);\n\n    setCudaSharedMemConfig(cudaSharedMemBankSizeEightByte);\n    LaunchKernels<LhsScalar, RhsScalar, Index, LhsMapper, RhsMapper, OutputMapper>::Run(lhs, rhs, output,  m, n, k, this->m_device);\n  }\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_USE_GPU and __CUDACC__\n#endif // EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_CUDA_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorContractionMapper.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_MAPPER_H\n#define EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_MAPPER_H\n\nnamespace Eigen {\n\nnamespace internal {\n\nenum {\n  Rhs = 0,\n  Lhs = 1\n};\n\n/*\n * Implementation of the Eigen blas_data_mapper class for tensors.\n */\n\ntemplate <typename Tensor, bool HasRawAccess> struct CoeffLoader {\n  enum {\n    DirectOffsets = false\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE CoeffLoader(const Tensor& tensor) : m_tensor(tensor) { }\n\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void offsetBuffer(typename Tensor::Index) {\n    eigen_assert(false && \"unsupported\");\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE typename Tensor::Scalar coeff(typename Tensor::Index index) const { return m_tensor.coeff(index); }\n\n template<int LoadMode> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n typename Tensor::PacketReturnType packet(typename Tensor::Index index) const\n  {\n    return m_tensor.template packet<LoadMode>(index);\n  }\n\n\n private:\n  const Tensor m_tensor;\n};\n\ntemplate <typename Tensor> struct CoeffLoader<Tensor, true> {\n  enum {\n    DirectOffsets = true\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE CoeffLoader(const Tensor& tensor) : m_data(tensor.data()) {}\n\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void offsetBuffer(typename Tensor::Index offset) {\n    m_data += offset;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE typename Tensor::Scalar coeff(typename Tensor::Index index) const { return loadConstant(m_data+index); }\n\n template<int LoadMode> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n typename Tensor::PacketReturnType packet(typename Tensor::Index index) const\n  {\n    return internal::ploadt_ro<typename Tensor::PacketReturnType, LoadMode>(m_data + index);\n  }\n private:\n  typedef typename Tensor::Scalar Scalar;\n  const Scalar* m_data;\n};\n\ntemplate<typename Scalar, typename Index, int side,\n         typename Tensor,\n         typename nocontract_t, typename contract_t,\n         int packet_size, bool inner_dim_contiguous, int Alignment>\nclass SimpleTensorContractionMapper {\n  public:\n  EIGEN_DEVICE_FUNC\n  SimpleTensorContractionMapper(const Tensor& tensor,\n                                const nocontract_t& nocontract_strides,\n                                const nocontract_t& ij_strides,\n                                const contract_t& contract_strides,\n                                const contract_t& k_strides) :\n      m_tensor(tensor),\n      m_nocontract_strides(nocontract_strides),\n      m_ij_strides(ij_strides),\n      m_contract_strides(contract_strides),\n      m_k_strides(k_strides) { }\n\n  enum {\n    DirectOffsets = CoeffLoader<Tensor, Tensor::RawAccess>::DirectOffsets\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void offsetBuffer(typename Tensor::Index offset) {\n    m_tensor.offsetBuffer(offset);\n  }\n\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE void prefetch(Index /*i*/) { }\n\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE Scalar operator()(Index row) const {\n    // column major assumption\n    return operator()(row, 0);\n  }\n\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE Scalar operator()(Index row, Index col) const {\n    return m_tensor.coeff(computeIndex(row, col));\n  }\n\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE Index computeIndex(Index row, Index col) const {\n    const bool left = (side == Lhs);\n    Index nocontract_val = left ? row : col;\n    Index linidx = 0;\n    for (int i = static_cast<int>(array_size<nocontract_t>::value) - 1; i > 0; i--) {\n      const Index idx = nocontract_val / m_ij_strides[i];\n      linidx += idx * m_nocontract_strides[i];\n      nocontract_val -= idx * m_ij_strides[i];\n    }\n    if (array_size<typename Tensor::Dimensions>::value > array_size<contract_t>::value) {\n      if (side == Lhs && inner_dim_contiguous) {\n        eigen_assert(m_nocontract_strides[0] == 1);\n        linidx += nocontract_val;\n      } else {\n        linidx += nocontract_val * m_nocontract_strides[0];\n      }\n    }\n\n    Index contract_val = left ? col : row;\n    if(array_size<contract_t>::value > 0) {\n      for (int i = static_cast<int>(array_size<contract_t>::value) - 1; i > 0; i--) {\n        const Index idx = contract_val / m_k_strides[i];\n        linidx += idx * m_contract_strides[i];\n        contract_val -= idx * m_k_strides[i];\n      }\n\n      if (side == Rhs && inner_dim_contiguous) {\n        eigen_assert(m_contract_strides[0] == 1);\n        linidx += contract_val;\n      } else {\n        linidx += contract_val * m_contract_strides[0];\n      }\n    }\n\n    return linidx;\n  }\n\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE IndexPair<Index> computeIndexPair(Index row, Index col, const Index distance) const {\n    const bool left = (side == Lhs);\n    Index nocontract_val[2] = {left ? row : col, left ? row + distance : col};\n    Index linidx[2] = {0, 0};\n    if (array_size<typename Tensor::Dimensions>::value > array_size<contract_t>::value) {\n      for (int i = static_cast<int>(array_size<nocontract_t>::value) - 1; i > 0; i--) {\n        const Index idx0 = nocontract_val[0] / m_ij_strides[i];\n        const Index idx1 = nocontract_val[1] / m_ij_strides[i];\n        linidx[0] += idx0 * m_nocontract_strides[i];\n        linidx[1] += idx1 * m_nocontract_strides[i];\n        nocontract_val[0] -= idx0 * m_ij_strides[i];\n        nocontract_val[1] -= idx1 * m_ij_strides[i];\n      }\n      if (side == Lhs && inner_dim_contiguous) {\n        eigen_assert(m_nocontract_strides[0] == 1);\n        linidx[0] += nocontract_val[0];\n        linidx[1] += nocontract_val[1];\n      } else {\n        linidx[0] += nocontract_val[0] * m_nocontract_strides[0];\n        linidx[1] += nocontract_val[1] * m_nocontract_strides[0];\n      }\n    }\n\n    Index contract_val[2] = {left ? col : row, left ? col : row + distance};\n    if (array_size<contract_t>::value> 0) {\n      for (int i = static_cast<int>(array_size<contract_t>::value) - 1; i > 0; i--) {\n        const Index idx0 = contract_val[0] / m_k_strides[i];\n        const Index idx1 = contract_val[1] / m_k_strides[i];\n        linidx[0] += idx0 * m_contract_strides[i];\n        linidx[1] += idx1 * m_contract_strides[i];\n        contract_val[0] -= idx0 * m_k_strides[i];\n        contract_val[1] -= idx1 * m_k_strides[i];\n      }\n\n      if (side == Rhs && inner_dim_contiguous) {\n        eigen_assert(m_contract_strides[0] == 1);\n        linidx[0] += contract_val[0];\n        linidx[1] += contract_val[1];\n      } else {\n        linidx[0] += contract_val[0] * m_contract_strides[0];\n        linidx[1] += contract_val[1] * m_contract_strides[0];\n      }\n    }\n    return IndexPair<Index>(linidx[0], linidx[1]);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Index firstAligned(Index size) const {\n    // Only claim alignment when we can compute the actual stride (ie when we're\n    // dealing with the lhs with inner_dim_contiguous. This is because the\n    // matrix-vector product relies on the stride when dealing with aligned inputs.\n    return (Alignment == Aligned) && (side == Lhs) && inner_dim_contiguous ? 0 : size;\n  }\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Index stride() const {\n    return ((side == Lhs) && inner_dim_contiguous && array_size<contract_t>::value > 0) ? m_contract_strides[0] : 1;\n  }\n\n protected:\n  CoeffLoader<Tensor, Tensor::RawAccess> m_tensor;\n  const nocontract_t m_nocontract_strides;\n  const nocontract_t m_ij_strides;\n  const contract_t m_contract_strides;\n  const contract_t m_k_strides;\n};\n\n\ntemplate<typename Scalar, typename Index, int side,\n         typename Tensor,\n         typename nocontract_t, typename contract_t,\n         int packet_size, bool inner_dim_contiguous,\n         bool inner_dim_reordered, int Alignment>\nclass BaseTensorContractionMapper : public SimpleTensorContractionMapper<Scalar, Index, side, Tensor, nocontract_t, contract_t, packet_size, inner_dim_contiguous, Alignment>\n{\n public:\n  typedef SimpleTensorContractionMapper<Scalar, Index, side, Tensor, nocontract_t, contract_t, packet_size, inner_dim_contiguous, Alignment> ParentMapper;\n\n  EIGEN_DEVICE_FUNC\n  BaseTensorContractionMapper(const Tensor& tensor,\n                              const nocontract_t& nocontract_strides,\n                              const nocontract_t& ij_strides,\n                              const contract_t& contract_strides,\n                              const contract_t& k_strides) :\n  ParentMapper(tensor, nocontract_strides, ij_strides, contract_strides, k_strides) { }\n\n  typedef typename Tensor::PacketReturnType Packet;\n  typedef typename unpacket_traits<Packet>::half HalfPacket;\n\n  template <int AlignmentType>\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE Packet loadPacket(Index i, Index j) const {\n    // whole method makes column major assumption\n\n    // don't need to add offsets for now (because operator handles that)\n    // current code assumes packet size must be a multiple of 2\n    EIGEN_STATIC_ASSERT(packet_size % 2 == 0, YOU_MADE_A_PROGRAMMING_MISTAKE);\n\n    if (Tensor::PacketAccess && inner_dim_contiguous && !inner_dim_reordered) {\n      const Index index = this->computeIndex(i, j);\n      eigen_assert(this->computeIndex(i+packet_size-1, j) == index + packet_size-1);\n      return this->m_tensor.template packet<AlignmentType>(index);\n    }\n\n    const IndexPair<Index> indexPair = this->computeIndexPair(i, j, packet_size - 1);\n    const Index first = indexPair.first;\n    const Index last = indexPair.second;\n\n    // We can always do optimized packet reads from left hand side right now, because\n    // the vertical matrix dimension on the left hand side is never contracting.\n    // On the right hand side we need to check if the contracting dimensions may have\n    // been shuffled first.\n    if (Tensor::PacketAccess &&\n        (side == Lhs || internal::array_size<contract_t>::value <= 1 || !inner_dim_reordered) &&\n        (last - first) == (packet_size - 1)) {\n\n      return this->m_tensor.template packet<AlignmentType>(first);\n    }\n\n    EIGEN_ALIGN_MAX Scalar data[packet_size];\n\n    data[0] = this->m_tensor.coeff(first);\n    for (Index k = 1; k < packet_size - 1; k += 2) {\n      const IndexPair<Index> internal_pair = this->computeIndexPair(i + k, j, 1);\n      data[k] = this->m_tensor.coeff(internal_pair.first);\n      data[k + 1] = this->m_tensor.coeff(internal_pair.second);\n    }\n    data[packet_size - 1] = this->m_tensor.coeff(last);\n\n    return pload<Packet>(data);\n  }\n\n  template <int AlignmentType>\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE HalfPacket loadHalfPacket(Index i, Index j) const {\n    // whole method makes column major assumption\n\n    // don't need to add offsets for now (because operator handles that)\n    const Index half_packet_size = unpacket_traits<HalfPacket>::size;\n    if (half_packet_size == packet_size) {\n      return loadPacket<AlignmentType>(i, j);\n    }\n    EIGEN_ALIGN_MAX Scalar data[half_packet_size];\n    for (Index k = 0; k < half_packet_size; k++) {\n      data[k] = operator()(i + k, j);\n    }\n    return pload<HalfPacket>(data);\n  }\n};\n\n\ntemplate<typename Scalar, typename Index, int side,\n         typename Tensor,\n         typename nocontract_t, typename contract_t,\n         bool inner_dim_contiguous,\n         bool inner_dim_reordered, int Alignment>\nclass BaseTensorContractionMapper<Scalar, Index, side, Tensor, nocontract_t, contract_t, 1, inner_dim_contiguous, inner_dim_reordered, Alignment> : public SimpleTensorContractionMapper<Scalar, Index, side, Tensor, nocontract_t, contract_t, 1, inner_dim_contiguous, Alignment>\n{\n public:\n  typedef SimpleTensorContractionMapper<Scalar, Index, side, Tensor, nocontract_t, contract_t, 1, inner_dim_contiguous, Alignment> ParentMapper;\n\n  EIGEN_DEVICE_FUNC\n  BaseTensorContractionMapper(const Tensor& tensor,\n                              const nocontract_t& nocontract_strides,\n                              const nocontract_t& ij_strides,\n                              const contract_t& contract_strides,\n                              const contract_t& k_strides) :\n  ParentMapper(tensor, nocontract_strides, ij_strides, contract_strides, k_strides) { }\n\n  typedef typename Tensor::PacketReturnType Packet;\n  template <int> EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE Packet loadPacket(Index i, Index j) const {\n    EIGEN_ALIGN_MAX Scalar data[1];\n    data[0] = this->m_tensor.coeff(this->computeIndex(i, j));\n    return pload<typename Tensor::PacketReturnType>(data);\n  }\n  template <int> EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE Packet loadHalfPacket(Index i, Index j) const {\n    return loadPacket(i, j);\n  }\n};\n\n\ntemplate<typename Scalar, typename Index, int side,\n         typename Tensor,\n         typename nocontract_t, typename contract_t,\n         int packet_size,\n         bool inner_dim_contiguous, bool inner_dim_reordered, int Alignment>\nclass TensorContractionSubMapper {\n public:\n  typedef typename Tensor::PacketReturnType Packet;\n  typedef typename unpacket_traits<Packet>::half HalfPacket;\n\n  typedef BaseTensorContractionMapper<Scalar, Index, side, Tensor, nocontract_t, contract_t, packet_size, inner_dim_contiguous, inner_dim_reordered, Alignment> ParentMapper;\n  typedef TensorContractionSubMapper<Scalar, Index, side, Tensor, nocontract_t, contract_t, packet_size, inner_dim_contiguous, inner_dim_reordered, Alignment> Self;\n  typedef Self LinearMapper;\n\n  enum {\n    // We can use direct offsets iff the parent mapper supports then and we can compute the strides.\n    // TODO: we should also enable direct offsets for the Rhs case.\n    UseDirectOffsets = ParentMapper::DirectOffsets && (side == Lhs) && inner_dim_contiguous && (array_size<contract_t>::value > 0)\n  };\n\n  EIGEN_DEVICE_FUNC TensorContractionSubMapper(const ParentMapper& base_mapper, Index vert_offset, Index horiz_offset)\n      : m_base_mapper(base_mapper), m_vert_offset(vert_offset), m_horiz_offset(horiz_offset) {\n    // Bake the offsets into the buffer used by the base mapper whenever possible. This avoids the need to recompute\n    // this offset every time we attempt to access a coefficient.\n    if (UseDirectOffsets) {\n      Index stride = m_base_mapper.stride();\n      m_base_mapper.offsetBuffer(vert_offset + horiz_offset * stride);\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Scalar operator()(Index i) const {\n    if (UseDirectOffsets) {\n      return m_base_mapper(i, 0);\n    }\n    return m_base_mapper(i + m_vert_offset, m_horiz_offset);\n  }\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Scalar operator()(Index i, Index j) const {\n    if (UseDirectOffsets) {\n      return m_base_mapper(i, j);\n    }\n    return m_base_mapper(i + m_vert_offset, j + m_horiz_offset);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet loadPacket(Index i) const {\n    if (UseDirectOffsets) {\n      return m_base_mapper.template loadPacket<Alignment>(i, 0);\n    }\n    return m_base_mapper.template loadPacket<Alignment>(i + m_vert_offset, m_horiz_offset);\n  }\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet loadPacket(Index i, Index j) const {\n    if (UseDirectOffsets) {\n      return m_base_mapper.template loadPacket<Alignment>(i, j);\n    }\n    return m_base_mapper.template loadPacket<Alignment>(i + m_vert_offset, j + m_horiz_offset);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE HalfPacket loadHalfPacket(Index i) const {\n    if (UseDirectOffsets) {\n      return m_base_mapper.template loadHalfPacket<Alignment>(i, 0);\n    }\n    return m_base_mapper.template loadHalfPacket<Alignment>(i + m_vert_offset, m_horiz_offset);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void storePacket(Index i, Packet p) const {\n    if (UseDirectOffsets) {\n      m_base_mapper.storePacket(i, 0, p);\n    }\n    m_base_mapper.storePacket(i + m_vert_offset, m_horiz_offset, p);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE LinearMapper getLinearMapper(Index i, Index j) const {\n    if (UseDirectOffsets) {\n      return LinearMapper(m_base_mapper, i, j);\n    }\n    return LinearMapper(m_base_mapper, i + m_vert_offset, j + m_horiz_offset);\n  }\n\n  template <typename PacketT, int AlignmentType>\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketT load(Index i) const {\n    EIGEN_STATIC_ASSERT((internal::is_same<PacketT, Packet>::value), YOU_MADE_A_PROGRAMMING_MISTAKE);\n    const int ActualAlignment = (AlignmentType == Aligned) && (Alignment == Aligned) ? Aligned : Unaligned;\n    if (UseDirectOffsets) {\n     return m_base_mapper.template loadPacket<ActualAlignment>(i, 0);\n    }\n    return m_base_mapper.template loadPacket<ActualAlignment>(i + m_vert_offset, m_horiz_offset);\n  }\n\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool aligned(Index) const {\n    return false;\n  }\n\n private:\n  ParentMapper m_base_mapper;\n  const Index m_vert_offset;\n  const Index m_horiz_offset;\n};\n\n\ntemplate<typename Scalar_, typename Index, int side,\n         typename Tensor,\n         typename nocontract_t, typename contract_t,\n         int packet_size,\n         bool inner_dim_contiguous, bool inner_dim_reordered, int Alignment>\nclass TensorContractionInputMapper\n  : public BaseTensorContractionMapper<Scalar_, Index, side, Tensor, nocontract_t, contract_t, packet_size, inner_dim_contiguous, inner_dim_reordered, Alignment> {\n\n public:\n  typedef Scalar_ Scalar;\n  typedef BaseTensorContractionMapper<Scalar, Index, side, Tensor, nocontract_t, contract_t, packet_size, inner_dim_contiguous, inner_dim_reordered, Alignment> Base;\n  typedef TensorContractionSubMapper<Scalar, Index, side, Tensor, nocontract_t, contract_t, packet_size, inner_dim_contiguous, inner_dim_reordered, Alignment> SubMapper;\n  typedef SubMapper VectorMapper;\n\n  EIGEN_DEVICE_FUNC TensorContractionInputMapper(const Tensor& tensor,\n                               const nocontract_t& nocontract_strides,\n                               const nocontract_t& ij_strides,\n                               const contract_t& contract_strides,\n                               const contract_t& k_strides)\n      : Base(tensor, nocontract_strides, ij_strides, contract_strides, k_strides) { }\n\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE SubMapper getSubMapper(Index i, Index j) const {\n    return SubMapper(*this, i, j);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE VectorMapper getVectorMapper(Index i, Index j) const {\n    return VectorMapper(*this, i, j);\n  }\n};\n\n\n\n}  // end namespace internal\n}  // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_MAPPER_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorContractionThreadPool.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_THREAD_POOL_H\n#define EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_THREAD_POOL_H\n\n// evaluator for thread pool device\n#ifdef EIGEN_USE_THREADS\n\nnamespace Eigen {\n\n#ifdef EIGEN_USE_SIMPLE_THREAD_POOL\nnamespace internal {\n\ntemplate<typename LhsScalar, typename LhsMapper, typename Index>\nstruct packLhsArg {\n  LhsScalar* blockA;\n  const LhsMapper& lhs;\n  const Index m_start;\n  const Index k_start;\n  const Index mc;\n  const Index kc;\n};\n\ntemplate<typename LhsScalar, typename RhsScalar, typename RhsMapper, typename OutputMapper, typename Index>\nstruct packRhsAndKernelArg {\n  const MaxSizeVector<LhsScalar*>* blockAs;\n  RhsScalar* blockB;\n  const RhsMapper& rhs;\n  OutputMapper& output;\n  const Index m;\n  const Index k;\n  const Index n;\n  const Index mc;\n  const Index kc;\n  const Index nc;\n  const Index num_threads;\n  const Index num_blockAs;\n  const Index max_m;\n  const Index k_block_idx;\n  const Index m_block_idx;\n  const Index n_block_idx;\n  const Index m_blocks;\n  const Index n_blocks;\n  MaxSizeVector<Notification*>* kernel_notifications;\n  const MaxSizeVector<Notification*>* lhs_notifications;\n  const bool need_to_pack;\n};\n\n}  // end namespace internal\n#endif  // EIGEN_USE_SIMPLE_THREAD_POOL\n\ntemplate<typename Indices, typename LeftArgType, typename RightArgType>\nstruct TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgType>, ThreadPoolDevice> :\n    public TensorContractionEvaluatorBase<TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgType>, ThreadPoolDevice> > {\n\n  typedef ThreadPoolDevice Device;\n\n  typedef TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgType>, Device> Self;\n  typedef TensorContractionEvaluatorBase<Self> Base;\n\n  typedef TensorContractionOp<Indices, LeftArgType, RightArgType> XprType;\n  typedef typename internal::remove_const<typename XprType::Scalar>::type Scalar;\n  typedef typename XprType::Index Index;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n\n  enum {\n    Layout = TensorEvaluator<LeftArgType, Device>::Layout,\n  };\n\n  // Most of the code is assuming that both input tensors are ColMajor. If the\n  // inputs are RowMajor, we will \"cheat\" by swapping the LHS and RHS:\n  // If we want to compute A * B = C, where A is LHS and B is RHS, the code\n  // will pretend B is LHS and A is RHS.\n  typedef typename internal::conditional<\n    static_cast<int>(Layout) == static_cast<int>(ColMajor), LeftArgType, RightArgType>::type EvalLeftArgType;\n  typedef typename internal::conditional<\n    static_cast<int>(Layout) == static_cast<int>(ColMajor), RightArgType, LeftArgType>::type EvalRightArgType;\n\n  static const int LDims =\n      internal::array_size<typename TensorEvaluator<EvalLeftArgType, Device>::Dimensions>::value;\n  static const int RDims =\n      internal::array_size<typename TensorEvaluator<EvalRightArgType, Device>::Dimensions>::value;\n  static const int ContractDims = internal::array_size<Indices>::value;\n\n  typedef array<Index, LDims> left_dim_mapper_t;\n  typedef array<Index, RDims> right_dim_mapper_t;\n\n  typedef array<Index, ContractDims> contract_t;\n  typedef array<Index, LDims - ContractDims> left_nocontract_t;\n  typedef array<Index, RDims - ContractDims> right_nocontract_t;\n\n  static const int NumDims = LDims + RDims - 2 * ContractDims;\n\n  typedef DSizes<Index, NumDims> Dimensions;\n\n  // typedefs needed in evalTo\n  typedef typename internal::remove_const<typename EvalLeftArgType::Scalar>::type LhsScalar;\n  typedef typename internal::remove_const<typename EvalRightArgType::Scalar>::type RhsScalar;\n  typedef typename internal::gebp_traits<LhsScalar, RhsScalar> Traits;\n\n  typedef TensorEvaluator<EvalLeftArgType, Device> LeftEvaluator;\n  typedef TensorEvaluator<EvalRightArgType, Device> RightEvaluator;\n\n  TensorEvaluator(const XprType& op, const Device& device) :\n      Base(op, device) {}\n\n#ifndef EIGEN_USE_SIMPLE_THREAD_POOL\n  template <bool lhs_inner_dim_contiguous, bool rhs_inner_dim_contiguous,\n            bool rhs_inner_dim_reordered, int Alignment>\n  void evalProduct(Scalar* buffer) const {\n    typedef\n        typename internal::remove_const<typename EvalLeftArgType::Scalar>::type\n            LhsScalar;\n    typedef\n        typename internal::remove_const<typename EvalRightArgType::Scalar>::type\n            RhsScalar;\n    typedef typename internal::gebp_traits<LhsScalar, RhsScalar> Traits;\n    typedef TensorEvaluator<EvalLeftArgType, Device> LeftEvaluator;\n    typedef TensorEvaluator<EvalRightArgType, Device> RightEvaluator;\n    typedef internal::TensorContractionInputMapper<\n        LhsScalar, Index, internal::Lhs, LeftEvaluator, left_nocontract_t,\n        contract_t, internal::packet_traits<LhsScalar>::size,\n        lhs_inner_dim_contiguous, false, Unaligned>\n        LhsMapper;\n    typedef internal::TensorContractionInputMapper<\n        RhsScalar, Index, internal::Rhs, RightEvaluator, right_nocontract_t,\n        contract_t, internal::packet_traits<RhsScalar>::size,\n        rhs_inner_dim_contiguous, rhs_inner_dim_reordered, Unaligned>\n        RhsMapper;\n    typedef internal::blas_data_mapper<Scalar, Index, ColMajor> OutputMapper;\n    typedef internal::gemm_pack_lhs<LhsScalar, Index,\n                                    typename LhsMapper::SubMapper, Traits::mr,\n                                    Traits::LhsProgress, ColMajor>\n        LhsPacker;\n    typedef internal::gemm_pack_rhs<\n        RhsScalar, Index, typename RhsMapper::SubMapper, Traits::nr, ColMajor>\n        RhsPacker;\n    typedef internal::gebp_kernel<LhsScalar, RhsScalar, Index, OutputMapper,\n                                  Traits::mr, Traits::nr, false, false>\n        GebpKernel;\n\n    const Index m = this->m_i_size;\n    const Index n = this->m_j_size;\n    const Index k = this->m_k_size;\n    if (m == 0 || n == 0 || k == 0) return;\n\n    // Compute a set of algorithm parameters:\n    // - kernel block sizes (bm, bn, bk)\n    // - task grain sizes (number of kernels executed per task: gm, gn)\n    // - number of threads\n    // - sharding by row/column\n    // - parallel packing or first lhs then rhs\n    // and some derived parameters:\n    // - number of tasks (nm, nn, nk)\n    // - number of kernels (nm0, nn0)\n    // Unfortunately, all these parameters are tightly interdependent.\n    // So in some cases we first compute approximate values, then compute other\n    // values based on these approximations and then refine the approximations.\n\n    // There are lots of heuristics here. There is some reasoning behind them,\n    // but ultimately they are just tuned on contraction benchmarks for\n    // different input configurations, thread counts and instruction sets.\n    // So feel free to question any of them.\n\n    // Compute whether we want to shard by row or by column.\n    // This is a first approximation, it will be refined later. Since we don't\n    // know number of threads yet we use 2, because what's we are most\n    // interested in at this point is whether it makes sense to use\n    // parallelization at all or not.\n    bool shard_by_col = shardByCol(m, n, 2);\n\n    // First approximation of kernel blocking sizes.\n    // Again, we don't know number of threads yet, so we use 2.\n    Index bm, bn, bk;\n    if (shard_by_col) {\n      internal::TensorContractionBlocking<LhsMapper, RhsMapper, Index,\n                                          internal::ShardByCol>\n          blocking(k, m, n, 2);\n      bm = blocking.mc();\n      bn = blocking.nc();\n      bk = blocking.kc();\n    } else {\n      internal::TensorContractionBlocking<LhsMapper, RhsMapper, Index,\n                                          internal::ShardByRow>\n          blocking(k, m, n, 2);\n      bm = blocking.mc();\n      bn = blocking.nc();\n      bk = blocking.kc();\n    }\n\n    // Compute optimal number of threads.\n    // Note: we use bk instead of k here because we are interested in amount of\n    // _parallelizable_ computations, and computations are not parallelizable\n    // across k dimension.\n    const TensorOpCost cost =\n        contractionCost(m, n, bm, bn, bk, shard_by_col, false);\n    int num_threads = TensorCostModel<ThreadPoolDevice>::numThreads(\n        static_cast<double>(n) * m, cost, this->m_device.numThreads());\n\n    // TODO(dvyukov): this is a stop-gap to prevent regressions while the cost\n    // model is not tuned. Remove this when the cost model is tuned.\n    if (n == 1) num_threads = 1;\n\n    if (num_threads == 1) {\n      // The single-threaded algorithm should be faster in this case.\n      if (n == 1)\n        this->template evalGemv<lhs_inner_dim_contiguous,\n                                rhs_inner_dim_contiguous,\n                                rhs_inner_dim_reordered, Alignment>(buffer);\n      else\n        this->template evalGemm<lhs_inner_dim_contiguous,\n                                rhs_inner_dim_contiguous,\n                                rhs_inner_dim_reordered, Alignment>(buffer);\n      return;\n    }\n\n    // Now that we know number of threads, recalculate sharding and blocking.\n    shard_by_col = shardByCol(m, n, num_threads);\n    if (shard_by_col) {\n      internal::TensorContractionBlocking<LhsMapper, RhsMapper, Index,\n                                          internal::ShardByCol>\n          blocking(k, m, n, num_threads);\n      bm = blocking.mc();\n      bn = blocking.nc();\n      bk = blocking.kc();\n    } else {\n      internal::TensorContractionBlocking<LhsMapper, RhsMapper, Index,\n                                          internal::ShardByRow>\n          blocking(k, m, n, num_threads);\n      bm = blocking.mc();\n      bn = blocking.nc();\n      bk = blocking.kc();\n    }\n\n    // Number of kernels for each dimension.\n    Index nm0 = divup(m, bm);\n    Index nn0 = divup(n, bn);\n    Index nk = divup(k, bk);\n\n    // Calculate task grain size (number of kernels executed per task).\n    // This task size coarsening serves two purposes:\n    // 1. It reduces per-task overheads including synchronization overheads.\n    // 2. It allows to use caches better (reuse the same packed rhs in several\n    // consecutive kernels).\n    Index gm = 1;\n    Index gn = 1;\n    // If we are sharding by column, then we prefer to reduce rows first.\n    if (shard_by_col) {\n      gm = coarsenM(m, n, bm, bn, bk, gn, num_threads, shard_by_col);\n      gn = coarsenN(m, n, bm, bn, bk, gm, num_threads, shard_by_col);\n    } else {\n      gn = coarsenN(m, n, bm, bn, bk, gm, num_threads, shard_by_col);\n      gm = coarsenM(m, n, bm, bn, bk, gn, num_threads, shard_by_col);\n    }\n    // Number of tasks in each dimension.\n    Index nm = divup(nm0, gm);\n    Index nn = divup(nn0, gn);\n\n    // Last by not least, decide whether we want to issue both lhs and rhs\n    // packing in parallel; or issue lhs packing first, and then issue rhs\n    // packing when lhs packing completes (for !shard_by_col lhs and rhs are\n    // swapped). Parallel packing allows more parallelism (for both packing and\n    // kernels), while sequential packing provides better locality (once\n    // a thread finishes rhs packing it proceed to kernels with that rhs).\n    // First, we are interested in parallel packing if there are few tasks.\n    bool parallel_pack = num_threads >= nm * nn;\n    // Also do parallel packing if all data fits into L2$.\n    if (m * bk * Index(sizeof(LhsScalar)) + n * bk * Index(sizeof(RhsScalar)) <=\n        l2CacheSize() * num_threads)\n      parallel_pack = true;\n    // But don't do it if we will use each rhs only once. Locality seems to be\n    // more important in this case.\n    if ((shard_by_col ? nm : nn) == 1) parallel_pack = false;\n\n    LhsMapper lhs(this->m_leftImpl, this->m_left_nocontract_strides,\n                  this->m_i_strides, this->m_left_contracting_strides,\n                  this->m_k_strides);\n\n    RhsMapper rhs(this->m_rightImpl, this->m_right_nocontract_strides,\n                  this->m_j_strides, this->m_right_contracting_strides,\n                  this->m_k_strides);\n\n    Context<LhsPacker, RhsPacker, GebpKernel, LhsMapper, RhsMapper,\n            OutputMapper>(this->m_device, num_threads, lhs, rhs, buffer, m, n,\n                          k, bm, bn, bk, nm, nn, nk, gm, gn, nm0, nn0,\n                          shard_by_col, parallel_pack)\n        .run();\n  }\n\n  // Context coordinates a single parallel gemm operation.\n  template <typename LhsPacker, typename RhsPacker, typename GebpKernel,\n            typename LhsMapper, typename RhsMapper, typename OutputMapper>\n  class Context {\n   public:\n    Context(const Device& device, int num_threads, LhsMapper& lhs,\n            RhsMapper& rhs, Scalar* buffer, Index tm, Index tn, Index tk, Index bm,\n            Index bn, Index bk, Index nm, Index nn, Index nk, Index gm,\n            Index gn, Index nm0, Index nn0, bool shard_by_col,\n            bool parallel_pack)\n        : device_(device),\n          lhs_(lhs),\n          rhs_(rhs),\n          buffer_(buffer),\n          output_(buffer, tm),\n          num_threads_(num_threads),\n          shard_by_col_(shard_by_col),\n          parallel_pack_(parallel_pack),\n          m_(tm),\n          n_(tn),\n          k_(tk),\n          bm_(bm),\n          bn_(bn),\n          bk_(bk),\n          nm_(nm),\n          nn_(nn),\n          nk_(nk),\n          gm_(gm),\n          gn_(gn),\n          nm0_(nm0),\n          nn0_(nn0)\n  {\n      for (Index x = 0; x < P; x++) {\n        // Normal number of notifications for k slice switch is\n        // nm_ + nn_ + nm_ * nn_. However, first P - 1 slices will receive only\n        // nm_ + nn_ notifications, because they will not receive notifications\n        // from preceeding kernels.\n        state_switch_[x] =\n            x == 0\n                ? 1\n                : (parallel_pack_ ? nn_ + nm_ : (shard_by_col_ ? nn_ : nm_)) +\n                      (x == P - 1 ? nm_ * nn_ : 0);\n        state_packing_ready_[x] =\n            parallel_pack_ ? 0 : (shard_by_col_ ? nm_ : nn_);\n        state_kernel_[x] = new std::atomic<uint8_t>*[nm_];\n        for (Index m = 0; m < nm_; m++) {\n          state_kernel_[x][m] = new std::atomic<uint8_t>[nn_];\n          // Kernels generally receive 3 notifications (previous kernel + 2\n          // packing), but the first slice won't get notifications from previous\n          // kernels.\n          for (Index n = 0; n < nn_; n++)\n            state_kernel_[x][m][n].store(\n                (x == 0 ? 0 : 1) + (parallel_pack_ ? 2 : 1),\n                std::memory_order_relaxed);\n        }\n      }\n\n      // Allocate memory for packed rhs/lhs matrices.\n      size_t align = numext::maxi(EIGEN_MAX_ALIGN_BYTES, 1);\n      size_t lhs_size =\n          divup<size_t>(bm_ * bk_ * sizeof(LhsScalar), align) * align;\n      size_t rhs_size =\n          divup<size_t>(bn_ * bk_ * sizeof(RhsScalar), align) * align;\n      packed_mem_ = static_cast<char*>(internal::aligned_malloc(\n          (nm0_ * lhs_size + nn0_ * rhs_size) * std::min<size_t>(nk_, P - 1)));\n      char* mem = static_cast<char*>(packed_mem_);\n      for (Index x = 0; x < numext::mini<Index>(nk_, P - 1); x++) {\n        packed_lhs_[x].resize(nm0_);\n        for (Index m = 0; m < nm0_; m++) {\n          packed_lhs_[x][m] = reinterpret_cast<LhsScalar*>(mem);\n          mem += lhs_size;\n        }\n        packed_rhs_[x].resize(nn0_);\n        for (Index n = 0; n < nn0_; n++) {\n          packed_rhs_[x][n] = reinterpret_cast<RhsScalar*>(mem);\n          mem += rhs_size;\n        }\n      }\n    }\n\n    ~Context() {\n      for (Index x = 0; x < P; x++) {\n        for (Index m = 0; m < nm_; m++) delete[] state_kernel_[x][m];\n        delete[] state_kernel_[x];\n      }\n      internal::aligned_free(packed_mem_);\n    }\n\n    void run() {\n      // Kick off packing of the first slice.\n      signal_switch(0, 1);\n      // Wait for overall completion.\n      // TODO(dvyukov): this wait can lead to deadlock.\n      // If nthreads contractions are concurrently submitted from worker\n      // threads, this wait will block all worker threads and the system will\n      // deadlock.\n      done_.Wait();\n    }\n\n   private:\n    Notification done_;\n    const Device& device_;\n    LhsMapper& lhs_;\n    RhsMapper& rhs_;\n    Scalar* const buffer_;\n    OutputMapper output_;\n    const int num_threads_;\n    const bool shard_by_col_;\n    const bool parallel_pack_;\n    // Matrix sizes.\n    const Index m_;\n    const Index n_;\n    const Index k_;\n    // Block sizes.\n    const Index bm_;\n    const Index bn_;\n    const Index bk_;\n    // Number of tasks.\n    const Index nm_;\n    const Index nn_;\n    const Index nk_;\n    // Task grain sizes (number of kernels executed per task).\n    const Index gm_;\n    const Index gn_;\n    // Number of blocks (this is different from ni_/nn_ because of task size\n    // coarsening).\n    const Index nm0_;\n    const Index nn0_;\n\n    // Parallelization strategy.\n    //\n    // Blocks related to the same k block can run in parallel because they write\n    // to different output blocks. So we parallelize within k slices, this\n    // gives us parallelism level of m x n. Before we can start any kernels\n    // related to k-th slice, we need to issue m lhs packing tasks and n rhs\n    // packing tasks.\n    //\n    // However, there is a bottleneck when we are finishing kernels for k-th\n    // slice (at the very end there is only 1 runnable kernel). To mitigate this\n    // bottleneck we allow kernels from k-th and k+1-th slices to run in\n    // parallel. Note that (m, n, k) and (m, n, k+1) kernels write to the same\n    // output block, so they must not run in parallel.\n    //\n    // This gives us the following dependency graph.\n    // On each k slice we have m x n kernel tasks, m lhs paking tasks and n rhs\n    // packing tasks.\n    // Kernel (m, n, k) can start when:\n    //  - kernel (m, n, k-1) has finished\n    //  - lhs packing (m, k) has finished\n    //  - rhs packing (n, k) has finished\n    // Lhs/rhs packing can start when:\n    //  - all k-1 packing has finished (artificially imposed to limit amount of\n    //  parallel packing)\n    //\n    // On top of that we limit runnable tasks to two consecutive k slices.\n    // This is done to limit amount of memory we need for packed lhs/rhs\n    // (for each k slice we need m*bk + n*bk memory in packed_lhs_/packed_rhs_).\n    //\n    // state_switch_ tracks when we are ready to switch to the next k slice.\n    // state_kernel_[m][n] tracks when we are ready to kick off kernel (m, n).\n    // These variable are rolling over 3 consecutive k slices: first two we are\n    // actively executing + one to track completion of kernels in the second\n    // slice.\n    static const Index P = 3;\n    void* packed_mem_;\n    std::vector<LhsScalar*> packed_lhs_[P - 1];\n    std::vector<RhsScalar*> packed_rhs_[P - 1];\n    std::atomic<uint8_t>** state_kernel_[P];\n    // state_switch_ is frequently modified by worker threads, while other\n    // fields are read-only after constructor. Let's move it to a separate cache\n    // line to reduce cache-coherency traffic.\n    char pad_[128];\n    std::atomic<Index> state_packing_ready_[P];\n    std::atomic<Index> state_switch_[P];\n\n    void pack_lhs(Index m, Index k) {\n      const Index mend = m * gm_ + gm(m);\n      for (Index m1 = m * gm_; m1 < mend; m1++)\n        LhsPacker()(packed_lhs_[k % (P - 1)][m1],\n                    lhs_.getSubMapper(m1 * bm_, k * bk_), bk(k), bm(m1));\n\n      if (!parallel_pack_ && shard_by_col_) {\n        signal_packing(k);\n      } else {\n        signal_switch(k + 1);\n        for (Index n = nn_ - 1; n >= 0; n--) signal_kernel(m, n, k, n == 0);\n      }\n    }\n\n    void pack_rhs(Index n, Index k) {\n      const Index nend = n * gn_ + gn(n);\n      for (Index n1 = n * gn_; n1 < nend; n1++) {\n        if (k == 0) {\n          // Zero the output memory in parallel.\n          // On 10000x2x10000 mm zeroing can easily take half of time.\n          // Zero (bn x m) row. Safe to do here because all kernels that will\n          // write to this memory depend on completion of this task.\n          // Note: don't call device_.memset() here. device_.memset() blocks on\n          // thread pool worker thread, which can lead to underutilization and\n          // deadlocks.\n          memset(buffer_ + n1 * bn_ * m_, 0, bn(n1) * m_ * sizeof(Scalar));\n        }\n        RhsPacker()(packed_rhs_[k % (P - 1)][n1],\n                    rhs_.getSubMapper(k * bk_, n1 * bn_), bk(k), bn(n1));\n      }\n\n      if (parallel_pack_ || shard_by_col_) {\n        signal_switch(k + 1);\n        for (Index m = nm_ - 1; m >= 0; m--) signal_kernel(m, n, k, m == 0);\n      } else {\n        signal_packing(k);\n      }\n    }\n\n    void kernel(Index m, Index n, Index k) {\n      // Note: order of iteration matters here. Iteration over m is innermost\n      // because we want to reuse the same packed rhs in consequetive tasks\n      // (rhs fits into L2$ while lhs only into L3$).\n      const Index nend = n * gn_ + gn(n);\n      const Index mend = m * gm_ + gm(m);\n      if (shard_by_col_) {\n        for (Index n1 = n * gn_; n1 < nend; n1++) {\n          for (Index m1 = m * gm_; m1 < mend; m1++)\n            GebpKernel()(output_.getSubMapper(m1 * bm_, n1 * bn_),\n                         packed_lhs_[k % (P - 1)][m1],\n                         packed_rhs_[k % (P - 1)][n1], bm(m1), bk(k), bn(n1),\n                         Scalar(1), -1, -1, 0, 0);\n        }\n      } else {\n        for (Index m1 = m * gm_; m1 < mend; m1++)\n          for (Index n1 = n * gn_; n1 < nend; n1++) {\n            GebpKernel()(output_.getSubMapper(m1 * bm_, n1 * bn_),\n                         packed_lhs_[k % (P - 1)][m1],\n                         packed_rhs_[k % (P - 1)][n1], bm(m1), bk(k), bn(n1),\n                         Scalar(1), -1, -1, 0, 0);\n          }\n      }\n      signal_kernel(m, n, k + 1, false);\n      signal_switch(k + 2);\n    }\n\n    void signal_packing(Index k) {\n      eigen_assert(!parallel_pack_);\n      Index s = state_packing_ready_[k % P].fetch_sub(1);\n      eigen_assert(s > 0);\n      if (s != 1) return;\n      state_packing_ready_[k % P] = shard_by_col_ ? nm_ : nn_;\n      enqueue_packing(k, shard_by_col_);\n    }\n\n    void signal_kernel(Index m, Index n, Index k, bool sync) {\n      std::atomic<uint8_t>* state = &state_kernel_[k % P][m][n];\n      Index s = state->load();\n      eigen_assert(s > 0);\n      if (s != 1 && state->fetch_sub(1) != 1) return;\n      state->store(parallel_pack_ ? 3 : 2, std::memory_order_relaxed);\n      if (sync)\n        kernel(m, n, k);\n      else\n        device_.enqueueNoNotification([=]() { kernel(m, n, k); });\n    }\n\n    void signal_switch(Index k, Index v = 1) {\n      Index s = state_switch_[k % P].fetch_sub(v);\n      eigen_assert(s >= v);\n      if (s != v) return;\n\n      // Ready to switch to the next k slice.\n      // Reset counter for the next iteration.\n      state_switch_[k % P] =\n          (parallel_pack_ ? nm_ + nn_ : (shard_by_col_ ? nn_ : nm_)) +\n          nm_ * nn_;\n      if (k < nk_) {\n        // Issue lhs/rhs packing. Their completion will in turn kick off\n        // kernels.\n        if (parallel_pack_) {\n          enqueue_packing(k, !shard_by_col_);\n          enqueue_packing(k, shard_by_col_);\n        } else if (shard_by_col_) {\n          enqueue_packing(k, false);\n        } else {\n          enqueue_packing(k, true);\n        }\n\n        // Termination handling.\n        // Because kernel completion signals k + 2 switch, we need to finish nk\n        // + 2 slices without issuing any tasks on nk + 1 slice. So here we\n        // pretend that all nk + 1 packing tasks just finish instantly; so that\n        // nk + 2 switch only waits for completion of nk kernels.\n      } else if (k == nk_) {\n        signal_switch(k + 1,\n                      parallel_pack_ ? nm_ + nn_ : (shard_by_col_ ? nn_ : nm_));\n      } else {\n        done_.Notify();\n      }\n    }\n\n    // Enqueue all rhs/lhs packing for k-th slice.\n    void enqueue_packing(Index k, bool rhs) {\n      enqueue_packing_helper(0, rhs ? nn_ : nm_, k, rhs);\n    }\n\n    void enqueue_packing_helper(Index start, Index end, Index k, bool rhs) {\n      if (end - start == 1) {\n        if (rhs)\n          pack_rhs(start, k);\n        else\n          pack_lhs(start, k);\n      } else {\n        Index mid = (start + end) / 2;\n        device_.enqueueNoNotification(\n            [=]() { enqueue_packing_helper(mid, end, k, rhs); });\n        device_.enqueueNoNotification(\n            [=]() { enqueue_packing_helper(start, mid, k, rhs); });\n      }\n    }\n\n    // Block sizes with accounting for potentially incomplete last block.\n    Index bm(Index m) const { return m + 1 < nm0_ ? bm_ : m_ + bm_ - bm_ * nm0_; }\n    Index bn(Index n) const { return n + 1 < nn0_ ? bn_ : n_ + bn_ - bn_ * nn0_; }\n    Index bk(Index k) const { return k + 1 < nk_ ? bk_ : k_ + bk_ - bk_ * nk_; }\n    // Task grain sizes accounting for potentially incomplete last task.\n    Index gm(Index m) const { return m + 1 < nm_ ? gm_ : nm0_ + gm_ - gm_ * nm_; }\n    Index gn(Index n) const { return n + 1 < nn_ ? gn_ : nn0_ + gn_ - gn_ * nn_; }\n\n    Context(const Context&) = delete;\n    void operator=(const Context&) = delete;\n  };\n\n  // Decide whether we want to shard m x n contraction by columns or by rows.\n  static bool shardByCol(Index m, Index n, Index num_threads) {\n    // Note: we are comparing both n and m against Traits::nr, it is not\n    // a mistake. We are trying to figure out how both n and m will fit into\n    // the main sharding dimension.\n\n    // Sharding by column is the default\n    // ... unless there is enough data for vectorization over rows\n    if (m / num_threads >= Traits::nr &&\n        // and not enough data for vectorization over columns\n        (n / num_threads < Traits::nr ||\n         // ... or barely enough data for vectorization over columns,\n         // but it is not evenly dividable across threads\n         (n / num_threads < 4 * Traits::nr &&\n          (n % (num_threads * Traits::nr)) != 0 &&\n          // ... and it is evenly dividable across threads for rows\n          ((m % (num_threads * Traits::nr)) == 0 ||\n           // .. or it is not evenly dividable for both dimensions but\n           // there is much more data over rows so that corner effects are\n           // mitigated.\n           (m / n >= 6)))))\n      return false;\n    // Wait, or if matrices are just substantially prolonged over the other\n    // dimension.\n    if (n / num_threads < 16 * Traits::nr && m > n * 32) return false;\n    return true;\n  }\n\n  Index coarsenM(Index m, Index n, Index bm, Index bn, Index bk, Index gn,\n                 int num_threads, bool shard_by_col) const {\n    Index gm = 1;\n    Index gm1 = 1;\n    Index nm0 = divup(m, bm);\n    Index nm1 = nm0;\n    for (;;) {\n      // Find the next candidate for m grain size. It needs to result in\n      // different number of blocks. E.g. if we have 10 kernels, we want to try\n      // 5 and 10, but not 6, 7, 8 and 9.\n      while (gm1 <= nm0 && nm1 == divup(nm0, gm1)) gm1++;\n      if (gm1 > nm0) break;\n      // Check the candidate.\n      int res = checkGrain(m, n, bm, bn, bk, gm1, gn, gm, gn, num_threads,\n                           shard_by_col);\n      if (res < 0) break;\n      nm1 = divup(nm0, gm1);\n      if (res == 0) continue;\n      // Commit new grain size.\n      gm = gm1;\n    }\n    return gm;\n  }\n\n  Index coarsenN(Index m, Index n, Index bm, Index bn, Index bk, Index gm,\n                 int num_threads, bool shard_by_col) const {\n    Index gn = 1;\n    Index gn1 = 1;\n    Index nn0 = divup(n, bn);\n    Index nn1 = nn0;\n    for (;;) {\n      while (gn1 <= nn0 && nn1 == divup(nn0, gn1)) gn1++;\n      if (gn1 > nn0) break;\n      int res = checkGrain(m, n, bm, bn, bk, gm, gn1, gm, gn, num_threads,\n                           shard_by_col);\n      if (res < 0) break;\n      nn1 = divup(nn0, gn1);\n      if (res == 0) continue;\n      gn = gn1;\n    }\n    return gn;\n  }\n\n  // checkGrain checks whether grain (gm, gn) is suitable and is better than\n  // (oldgm, oldgn).\n  int checkGrain(Index m, Index n, Index bm, Index bn, Index bk, Index gm,\n                 Index gn, Index oldgm, Index oldgn, int num_threads,\n                 bool shard_by_col) const {\n    const TensorOpCost cost =\n        contractionCost(bm * gm, bn * gn, bm, bn, bk, shard_by_col, true);\n    double taskSize = TensorCostModel<ThreadPoolDevice>::taskSize(\n        static_cast<double>(bm) * gm * bn * gn, cost);\n    // If the task is too small, then we agree on it regardless of anything\n    // else. Otherwise synchronization overheads will dominate.\n    if (taskSize < 1) return 1;\n    // If it is too large, then we reject it and all larger tasks.\n    if (taskSize > 2) return -1;\n    // Now we are in presumably good task size range.\n    // The main deciding factor here is parallelism. Consider that we have 12\n    // kernels and 4 threads. Grains of 2, 3 and 4 all yield good task sizes.\n    // But 2/4 yield 6/3 tasks, which gives us parallelism of 0.75 (at most 3/4\n    // of cores will be busy). While grain size 3 gives us 4 tasks, which gives\n    // us parallelism of 1 (we can load all cores).\n    Index nm0 = divup(m, bm);\n    Index nn0 = divup(n, bn);\n    Index new_tasks = divup(nm0, gm) * divup(nn0, gn);\n    double new_parallelism = static_cast<double>(new_tasks) /\n                             (divup<int>(new_tasks, num_threads) * num_threads);\n    Index old_tasks = divup(nm0, oldgm) * divup(nn0, oldgn);\n    double old_parallelism = static_cast<double>(old_tasks) /\n                             (divup<int>(old_tasks, num_threads) * num_threads);\n    if (new_parallelism > old_parallelism || new_parallelism == 1) return 1;\n    return 0;\n  }\n\n#else  // EIGEN_USE_SIMPLE_THREAD_POOL\n\n  template <bool lhs_inner_dim_contiguous, bool rhs_inner_dim_contiguous, bool rhs_inner_dim_reordered, int Alignment>\n  void evalProduct(Scalar* buffer) const {\n    if (this->m_j_size == 1) {\n      this->template evalGemv<lhs_inner_dim_contiguous, rhs_inner_dim_contiguous, rhs_inner_dim_reordered, Alignment>(buffer);\n      return;\n    }\n\n    evalGemm<lhs_inner_dim_contiguous, rhs_inner_dim_contiguous, rhs_inner_dim_reordered, Alignment>(buffer);\n  }\n\n  template <bool lhs_inner_dim_contiguous, bool rhs_inner_dim_contiguous, bool rhs_inner_dim_reordered, int Alignment>\n  void evalGemm(Scalar* buffer) const {\n    // columns in left side, rows in right side\n    const Index k = this->m_k_size;\n\n    // rows in left side\n    const Index m = this->m_i_size;\n\n    // columns in right side\n    const Index n = this->m_j_size;\n\n    // zero out the result buffer (which must be of size at least m * n * sizeof(Scalar)\n    this->m_device.memset(buffer, 0, m * n * sizeof(Scalar));\n\n\n    const int lhs_packet_size = internal::unpacket_traits<typename LeftEvaluator::PacketReturnType>::size;\n    const int rhs_packet_size = internal::unpacket_traits<typename RightEvaluator::PacketReturnType>::size;\n\n    typedef internal::TensorContractionInputMapper<LhsScalar, Index, internal::Lhs,\n                                                   LeftEvaluator, left_nocontract_t,\n                                                   contract_t, lhs_packet_size,\n                                                   lhs_inner_dim_contiguous,\n                                                   false, Unaligned> LhsMapper;\n\n    typedef internal::TensorContractionInputMapper<RhsScalar, Index, internal::Rhs,\n                                                   RightEvaluator, right_nocontract_t,\n                                                   contract_t, rhs_packet_size,\n                                                   rhs_inner_dim_contiguous,\n                                                   rhs_inner_dim_reordered, Unaligned> RhsMapper;\n\n    typedef internal::blas_data_mapper<Scalar, Index, ColMajor> OutputMapper;\n\n    // TODO: packing could be faster sometimes if we supported row major tensor mappers\n    typedef internal::gemm_pack_lhs<LhsScalar, Index, typename LhsMapper::SubMapper, Traits::mr,\n                                    Traits::LhsProgress, ColMajor> LhsPacker;\n    typedef internal::gemm_pack_rhs<RhsScalar, Index, typename RhsMapper::SubMapper, Traits::nr, ColMajor> RhsPacker;\n\n    // TODO: replace false, false with conjugate values?\n    typedef internal::gebp_kernel<LhsScalar, RhsScalar, Index, OutputMapper,\n                                  Traits::mr, Traits::nr, false, false> GebpKernel;\n\n    typedef internal::packLhsArg<LhsScalar, LhsMapper, Index> packLArg;\n    typedef internal::packRhsAndKernelArg<LhsScalar, RhsScalar, RhsMapper, OutputMapper, Index> packRKArg;\n\n    // initialize data mappers\n    LhsMapper lhs(this->m_leftImpl, this->m_left_nocontract_strides, this->m_i_strides,\n                  this->m_left_contracting_strides, this->m_k_strides);\n\n    RhsMapper rhs(this->m_rightImpl, this->m_right_nocontract_strides, this->m_j_strides,\n                  this->m_right_contracting_strides, this->m_k_strides);\n\n    OutputMapper output(buffer, m);\n\n    // compute block sizes (which depend on number of threads)\n    const Index num_threads = this->m_device.numThreads();\n    internal::TensorContractionBlocking<LhsMapper, RhsMapper, Index, internal::ShardByCol> blocking(k, m, n, num_threads);\n    Index mc = blocking.mc();\n    Index nc = blocking.nc();\n    Index kc = blocking.kc();\n    eigen_assert(mc <= m);\n    eigen_assert(nc <= n);\n    eigen_assert(kc <= k);\n\n#define CEIL_DIV(a, b) (((a) + (b) - 1) / (b))\n    const Index k_blocks = CEIL_DIV(k, kc);\n    const Index n_blocks = CEIL_DIV(n, nc);\n    const Index m_blocks = CEIL_DIV(m, mc);\n    const Index sizeA = mc * kc;\n    const Index sizeB = kc * nc;\n\n    /*    cout << \"m: \" << m << \" n: \" << n << \" k: \" << k << endl;\n    cout << \"mc: \" << mc << \" nc: \" << nc << \" kc: \" << kc << endl;\n    cout << \"m_blocks: \" << m_blocks << \" n_blocks: \" << n_blocks << \" k_blocks: \" << k_blocks << endl;\n    cout << \"num threads: \" << num_threads << endl;\n    */\n\n    // note: m_device.allocate should return 16 byte aligned pointers, but if blockA and blockB\n    //       aren't 16 byte aligned segfaults will happen due to SIMD instructions\n    // note: You can get away with allocating just a single blockA and offsets and meet the\n    //       the alignment requirements with the assumption that\n    //       (Traits::mr * sizeof(ResScalar)) % 16 == 0\n    const Index numBlockAs = numext::mini(num_threads, m_blocks);\n    MaxSizeVector<LhsScalar *> blockAs(num_threads);\n    for (int i = 0; i < num_threads; i++) {\n      blockAs.push_back(static_cast<LhsScalar *>(this->m_device.allocate(sizeA * sizeof(LhsScalar))));\n    }\n\n    // To circumvent alignment issues, I'm just going to separately allocate the memory for each thread\n    // TODO: is this too much memory to allocate? This simplifies coding a lot, but is wasteful.\n    //       Other options: (1) reuse memory when a thread finishes. con: tricky\n    //                      (2) allocate block B memory in each thread. con: overhead\n    MaxSizeVector<RhsScalar *> blockBs(n_blocks);\n    for (int i = 0; i < n_blocks; i++) {\n      blockBs.push_back(static_cast<RhsScalar *>(this->m_device.allocate(sizeB * sizeof(RhsScalar))));\n    }\n\n    // lhs_notifications starts with all null Notifications\n    MaxSizeVector<Notification*> lhs_notifications(num_threads, nullptr);\n\n    // this should really be numBlockAs * n_blocks;\n    const Index num_kernel_notifications = num_threads * n_blocks;\n    MaxSizeVector<Notification*> kernel_notifications(num_kernel_notifications,\n                                                    nullptr);\n\n    for (Index k_block_idx = 0; k_block_idx < k_blocks; k_block_idx++) {\n      const Index k_start = k_block_idx * kc;\n      // make sure we don't overshoot right edge of left matrix\n      const Index actual_kc = numext::mini(k_start + kc, k) - k_start;\n\n      for (Index m_block_idx = 0; m_block_idx < m_blocks; m_block_idx += numBlockAs) {\n        const Index num_blocks = numext::mini(m_blocks-m_block_idx, numBlockAs);\n\n        for (Index mt_block_idx = m_block_idx; mt_block_idx < m_block_idx+num_blocks; mt_block_idx++) {\n          const Index m_start = mt_block_idx * mc;\n          const Index actual_mc = numext::mini(m_start + mc, m) - m_start;\n          eigen_assert(actual_mc > 0);\n\n          Index blockAId = (k_block_idx * m_blocks + mt_block_idx) % num_threads;\n\n          for (int i = 0; i < n_blocks; ++i) {\n            Index notification_id = (blockAId * n_blocks + i);\n            // Wait for any current kernels using this slot to complete\n            // before using it.\n            if (kernel_notifications[notification_id]) {\n              wait_until_ready(kernel_notifications[notification_id]);\n              delete kernel_notifications[notification_id];\n            }\n            kernel_notifications[notification_id] = new Notification();\n          }\n          const packLArg arg = {\n            blockAs[blockAId], // blockA\n            lhs,        // lhs\n            m_start,    // m\n            k_start,    // k\n            actual_mc,  // mc\n            actual_kc,  // kc\n          };\n\n          // Delete any existing notification since we may be\n          // replacing it.  The algorithm should ensure that there are\n          // no existing waiters on this notification.\n          delete lhs_notifications[blockAId];\n          lhs_notifications[blockAId] =\n          this->m_device.enqueue(&Self::packLhs<packLArg, LhsPacker>, arg);\n        }\n\n        // now start kernels.\n        const Index m_base_start = m_block_idx * mc;\n        const bool need_to_pack = m_block_idx == 0;\n\n        for (Index n_block_idx = 0; n_block_idx < n_blocks; n_block_idx++) {\n          const Index n_start = n_block_idx * nc;\n          const Index actual_nc = numext::mini(n_start + nc, n) - n_start;\n\n          // first make sure the previous kernels are all done before overwriting rhs. Also wait if\n          // we're going to start new k. In both cases need_to_pack is true.\n          if (need_to_pack) {\n            for (Index i = num_blocks; i < num_threads; ++i) {\n              Index blockAId = (k_block_idx * m_blocks + i + m_block_idx) % num_threads;\n              Index future_id = (blockAId * n_blocks + n_block_idx);\n              wait_until_ready(kernel_notifications[future_id]);\n            }\n          }\n\n          packRKArg arg = {\n            &blockAs, // blockA\n            blockBs[n_block_idx], // blockB\n            rhs,          // rhs\n            output,       // output\n            m_base_start, // m\n            k_start,      // k\n            n_start,      // n\n            mc,           // mc\n            actual_kc,    // kc\n            actual_nc,    // nc\n            num_threads,\n            numBlockAs,\n            m,\n            k_block_idx,\n            m_block_idx,\n            n_block_idx, // n_block_idx\n            m_blocks, // m_blocks\n            n_blocks, // n_blocks\n            &kernel_notifications, // kernel notifications\n            &lhs_notifications,    // lhs notifications\n            need_to_pack, // need_to_pack\n          };\n\n          // We asynchronously kick off this function, which ends up\n          // notifying the appropriate kernel_notifications objects,\n          // which this thread waits on before exiting.\n          this->m_device.enqueueNoNotification(&Self::packRhsAndKernel<packRKArg, RhsPacker, GebpKernel>, arg);\n        }\n      }\n    }\n\n    // Make sure all the kernels are done.\n    for (size_t i = 0; i < kernel_notifications.size(); ++i) {\n      wait_until_ready(kernel_notifications[i]);\n      delete kernel_notifications[i];\n    }\n\n    // No need to wait for lhs notifications since they should have\n    // already been waited on.  Just clean them up.\n    for (size_t i = 0; i < lhs_notifications.size(); ++i) {\n      delete lhs_notifications[i];\n    }\n\n    // deallocate all of the memory for both A and B's\n    for (size_t i = 0; i < blockAs.size(); i++) {\n      this->m_device.deallocate(blockAs[i]);\n    }\n    for (size_t i = 0; i < blockBs.size(); i++) {\n      this->m_device.deallocate(blockBs[i]);\n    }\n\n#undef CEIL_DIV\n  }\n\n  /*\n   * Packs a LHS block of size (mt, kc) starting at lhs(m, k). Before packing\n   * the LHS block, check that all of the kernels that worked on the same\n   * mt_block_idx in the previous m_block are done.\n   */\n  template <typename packLArg, typename LhsPacker>\n  static void packLhs(const packLArg arg) {\n    // perform actual packing\n    LhsPacker pack_lhs;\n    pack_lhs(arg.blockA, arg.lhs.getSubMapper(arg.m_start, arg.k_start), arg.kc, arg.mc);\n  }\n\n  /*\n   * Packs a RHS block of size (kc, nc) starting at (k, n) after checking that\n   * all kernels in the previous block are done.\n   * Then for each LHS future, we wait on the future and then call GEBP\n   * on the area packed by the future (which starts at\n   * blockA + future_idx * mt * kc) on the LHS and with the full packed\n   * RHS block.\n   * The output of this GEBP is written to output(m + i * mt, n).\n   */\n  template <typename packRKArg, typename RhsPacker, typename GebpKernel>\n  static void packRhsAndKernel(packRKArg arg) {\n    if (arg.need_to_pack) {\n      RhsPacker pack_rhs;\n      pack_rhs(arg.blockB, arg.rhs.getSubMapper(arg.k, arg.n), arg.kc, arg.nc);\n    }\n\n    GebpKernel gebp;\n    for (Index mt_block_idx = 0; mt_block_idx < arg.num_blockAs; mt_block_idx++) {\n      const Index m_base_start = arg.m + arg.mc*mt_block_idx;\n      if (m_base_start < arg.max_m) {\n        Index blockAId = (arg.k_block_idx * arg.m_blocks + mt_block_idx + arg.m_block_idx) % arg.num_threads;\n        wait_until_ready((*arg.lhs_notifications)[blockAId]);\n        const Index actual_mc = numext::mini(m_base_start + arg.mc, arg.max_m) - m_base_start;\n        gebp(arg.output.getSubMapper(m_base_start, arg.n),\n             (*arg.blockAs)[blockAId], arg.blockB,\n             actual_mc, arg.kc, arg.nc, Scalar(1), -1, -1, 0, 0);\n\n        // Notify that the kernel is done.\n        const Index set_idx = blockAId * arg.n_blocks + arg.n_block_idx;\n        (*arg.kernel_notifications)[set_idx]->Notify();\n      }\n    }\n  }\n#endif  // EIGEN_USE_SIMPLE_THREAD_POOL\n\n  TensorOpCost contractionCost(Index m, Index n, Index bm, Index bn, Index bk,\n                               bool shard_by_col, bool prepacked) const {\n    const int packed_size = std::min<int>(PacketType<LhsScalar, Device>::size,\n                                          PacketType<RhsScalar, Device>::size);\n    const int output_packet_size = internal::unpacket_traits<PacketReturnType>::size;\n    const double kd = static_cast<double>(bk);\n    // Peak VFMA bandwidth is 0.5. However if we have not enough data for\n    // vectorization bandwidth drops. The 4.0 and 2.0 bandwidth is determined\n    // experimentally.\n    double computeBandwidth = bk == 1 ? 4.0 :\n          (shard_by_col ? bn : bm) < Traits::nr ||\n          (shard_by_col ? bm : bn) < Traits::mr ? 2.0 : 0.5;\n#ifndef EIGEN_VECTORIZE_FMA\n    // Bandwidth of all of VFMA/MULPS/ADDPS is 0.5 on latest Intel processors.\n    // However for MULPS/ADDPS we have dependent sequence of 2 such instructions,\n    // so overall bandwidth is 1.0.\n    if (computeBandwidth == 0.5) computeBandwidth = 1.0;\n#endif\n    // Computations.\n    TensorOpCost cost = TensorOpCost(0, 0, kd * computeBandwidth, true, packed_size);\n    // Output stores.\n    cost += TensorOpCost(0, sizeof(CoeffReturnType), 0, true, output_packet_size);\n    if (prepacked) {\n      // Packing and kernels are executed in different tasks. When we calculate\n      // task grain size we look only at kernel cost assuming that kernel\n      // is more expensive than packing.\n      return cost;\n    }\n    // Lhs/rhs loads + computations.\n    TensorOpCost lhsCost = this->m_leftImpl.costPerCoeff(true) * (kd / n);\n    TensorOpCost rhsCost = this->m_rightImpl.costPerCoeff(true) * (kd / m);\n    // Lhs packing memory cost does not contribute considerably to overall\n    // execution time because lhs is prefetched early and accessed sequentially.\n    if (shard_by_col)\n      lhsCost.dropMemoryCost();\n    else\n      rhsCost.dropMemoryCost();\n    return cost + lhsCost + rhsCost;\n  }\n};\n\n} // end namespace Eigen\n\n#endif  // EIGEN_USE_THREADS\n#endif // EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_THREAD_POOL_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorConversion.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_CONVERSION_H\n#define EIGEN_CXX11_TENSOR_TENSOR_CONVERSION_H\n\nnamespace Eigen {\n\n/** \\class TensorConversionOp\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief Tensor conversion class. This class makes it possible to vectorize\n  * type casting operations when the number of scalars per packet in the source\n  * and the destination type differ\n  */\nnamespace internal {\ntemplate<typename TargetType, typename XprType>\nstruct traits<TensorConversionOp<TargetType, XprType> >\n{\n  // Type promotion to handle the case where the types of the lhs and the rhs are different.\n  typedef TargetType Scalar;\n  typedef typename traits<XprType>::StorageKind StorageKind;\n  typedef typename traits<XprType>::Index Index;\n  typedef typename XprType::Nested Nested;\n  typedef typename remove_reference<Nested>::type _Nested;\n  static const int NumDimensions = traits<XprType>::NumDimensions;\n  static const int Layout = traits<XprType>::Layout;\n  enum { Flags = 0 };\n};\n\ntemplate<typename TargetType, typename XprType>\nstruct eval<TensorConversionOp<TargetType, XprType>, Eigen::Dense>\n{\n  typedef const TensorConversionOp<TargetType, XprType>& type;\n};\n\ntemplate<typename TargetType, typename XprType>\nstruct nested<TensorConversionOp<TargetType, XprType>, 1, typename eval<TensorConversionOp<TargetType, XprType> >::type>\n{\n  typedef TensorConversionOp<TargetType, XprType> type;\n};\n\n}  // end namespace internal\n\n\ntemplate <typename TensorEvaluator, typename SrcPacket, typename TgtPacket, int SrcCoeffRatio, int TgtCoeffRatio>\nstruct PacketConverter {\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  PacketConverter(const TensorEvaluator& impl)\n      : m_impl(impl) {}\n\n  template<int LoadMode, typename Index>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TgtPacket packet(Index index) const {\n    return internal::pcast<SrcPacket, TgtPacket>(m_impl.template packet<LoadMode>(index));\n  }\n\n private:\n  const TensorEvaluator& m_impl;\n};\n\n\ntemplate <typename TensorEvaluator, typename SrcPacket, typename TgtPacket>\nstruct PacketConverter<TensorEvaluator, SrcPacket, TgtPacket, 2, 1> {\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  PacketConverter(const TensorEvaluator& impl)\n      : m_impl(impl) {}\n\n  template<int LoadMode, typename Index>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TgtPacket packet(Index index) const {\n    const int SrcPacketSize = internal::unpacket_traits<SrcPacket>::size;\n\n    SrcPacket src1 = m_impl.template packet<LoadMode>(index);\n    SrcPacket src2 = m_impl.template packet<LoadMode>(index + SrcPacketSize);\n    TgtPacket result = internal::pcast<SrcPacket, TgtPacket>(src1, src2);\n    return result;\n  }\n\n private:\n  const TensorEvaluator& m_impl;\n};\n\ntemplate <typename TensorEvaluator, typename SrcPacket, typename TgtPacket>\nstruct PacketConverter<TensorEvaluator, SrcPacket, TgtPacket, 4, 1> {\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  PacketConverter(const TensorEvaluator& impl)\n      : m_impl(impl) {}\n\n  template<int LoadMode, typename Index>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TgtPacket packet(Index index) const {\n    const int SrcPacketSize = internal::unpacket_traits<SrcPacket>::size;\n\n    SrcPacket src1 = m_impl.template packet<LoadMode>(index);\n    SrcPacket src2 = m_impl.template packet<LoadMode>(index + SrcPacketSize);\n    SrcPacket src3 = m_impl.template packet<LoadMode>(index + 2 * SrcPacketSize);\n    SrcPacket src4 = m_impl.template packet<LoadMode>(index + 3 * SrcPacketSize);\n    TgtPacket result = internal::pcast<SrcPacket, TgtPacket>(src1, src2, src3, src4);\n    return result;\n  }\n\n private:\n  const TensorEvaluator& m_impl;\n};\n\ntemplate <typename TensorEvaluator, typename SrcPacket, typename TgtPacket>\nstruct PacketConverter<TensorEvaluator, SrcPacket, TgtPacket, 1, 2> {\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  PacketConverter(const TensorEvaluator& impl)\n      : m_impl(impl), m_maxIndex(impl.dimensions().TotalSize()) {}\n\n  template<int LoadMode, typename Index>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TgtPacket packet(Index index) const {\n    const int SrcPacketSize = internal::unpacket_traits<SrcPacket>::size;\n    // Only call m_impl.packet() when we have direct access to the underlying data. This\n    // ensures that we don't compute the subexpression twice. We may however load some\n    // coefficients twice, but in practice this doesn't negatively impact performance.\n    if (m_impl.data() && (index + SrcPacketSize < m_maxIndex)) {\n      // Force unaligned memory loads since we can't ensure alignment anymore\n      return internal::pcast<SrcPacket, TgtPacket>(m_impl.template packet<Unaligned>(index));\n    } else {\n      const int TgtPacketSize = internal::unpacket_traits<TgtPacket>::size;\n      typedef typename internal::unpacket_traits<SrcPacket>::type SrcType;\n      typedef typename internal::unpacket_traits<TgtPacket>::type TgtType;\n      internal::scalar_cast_op<SrcType, TgtType> converter;\n      EIGEN_ALIGN_MAX typename internal::unpacket_traits<TgtPacket>::type values[TgtPacketSize];\n      for (int i = 0; i < TgtPacketSize; ++i) {\n        values[i] = converter(m_impl.coeff(index+i));\n      }\n      TgtPacket rslt = internal::pload<TgtPacket>(values);\n      return rslt;\n    }\n  }\n\n private:\n  const TensorEvaluator& m_impl;\n  const typename TensorEvaluator::Index m_maxIndex;\n};\n\ntemplate<typename TargetType, typename XprType>\nclass TensorConversionOp : public TensorBase<TensorConversionOp<TargetType, XprType>, ReadOnlyAccessors>\n{\n  public:\n    typedef typename internal::traits<TensorConversionOp>::Scalar Scalar;\n    typedef typename internal::traits<TensorConversionOp>::StorageKind StorageKind;\n    typedef typename internal::traits<TensorConversionOp>::Index Index;\n    typedef typename internal::nested<TensorConversionOp>::type Nested;\n    typedef Scalar CoeffReturnType;\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorConversionOp(const XprType& xpr)\n        : m_xpr(xpr) {}\n\n    EIGEN_DEVICE_FUNC\n    const typename internal::remove_all<typename XprType::Nested>::type&\n    expression() const { return m_xpr; }\n\n  protected:\n    typename XprType::Nested m_xpr;\n};\n\ntemplate <bool SameType, typename Eval, typename Scalar> struct ConversionSubExprEval {\n  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool run(Eval& impl, Scalar*) {\n    impl.evalSubExprsIfNeeded(NULL);\n    return true;\n  }\n};\n\ntemplate <typename Eval, typename Scalar> struct ConversionSubExprEval<true, Eval, Scalar> {\n  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool run(Eval& impl, Scalar* data) {\n    return impl.evalSubExprsIfNeeded(data);\n  }\n};\n\n\n// Eval as rvalue\ntemplate<typename TargetType, typename ArgType, typename Device>\nstruct TensorEvaluator<const TensorConversionOp<TargetType, ArgType>, Device>\n{\n  typedef TensorConversionOp<TargetType, ArgType> XprType;\n  typedef typename XprType::Index Index;\n  typedef typename TensorEvaluator<ArgType, Device>::Dimensions Dimensions;\n  typedef TargetType Scalar;\n  typedef TargetType CoeffReturnType;\n  typedef typename internal::remove_all<typename internal::traits<ArgType>::Scalar>::type SrcType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  typedef typename PacketType<SrcType, Device>::type PacketSourceType;\n  static const int PacketSize = internal::unpacket_traits<PacketReturnType>::size;\n\n  enum {\n    IsAligned = false,\n    PacketAccess = true,\n    Layout = TensorEvaluator<ArgType, Device>::Layout,\n    RawAccess = false\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)\n    : m_impl(op.expression(), device)\n  {\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_impl.dimensions(); }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(Scalar* data)\n  {\n    return ConversionSubExprEval<internal::is_same<TargetType, SrcType>::value, TensorEvaluator<ArgType, Device>, Scalar>::run(m_impl, data);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup()\n  {\n    m_impl.cleanup();\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const\n  {\n    internal::scalar_cast_op<SrcType, TargetType> converter;\n    return converter(m_impl.coeff(index));\n  }\n\n  template<int LoadMode>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const\n  {\n    const bool Vectorizable = TensorEvaluator<ArgType, Device>::PacketAccess &\n        internal::type_casting_traits<SrcType, TargetType>::VectorizedCast;\n    return PacketConv<LoadMode, Vectorizable>::run(m_impl, index);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost\n  costPerCoeff(bool vectorized) const {\n    const double cast_cost = TensorOpCost::CastCost<SrcType, TargetType>();\n    if (vectorized) {\n      const double SrcCoeffRatio =\n          internal::type_casting_traits<SrcType, TargetType>::SrcCoeffRatio;\n      const double TgtCoeffRatio =\n          internal::type_casting_traits<SrcType, TargetType>::TgtCoeffRatio;\n      return m_impl.costPerCoeff(vectorized) * (SrcCoeffRatio / PacketSize) +\n          TensorOpCost(0, 0, TgtCoeffRatio * (cast_cost / PacketSize));\n    } else {\n      return m_impl.costPerCoeff(vectorized) + TensorOpCost(0, 0, cast_cost);\n    }\n  }\n\n  EIGEN_DEVICE_FUNC Scalar* data() const { return NULL; }\n\n  protected:\n  template <int LoadMode, bool ActuallyVectorize>\n  struct PacketConv {\n    static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType run(const TensorEvaluator<ArgType, Device>& impl, Index index) {\n      internal::scalar_cast_op<SrcType, TargetType> converter;\n      EIGEN_ALIGN_MAX typename internal::remove_const<CoeffReturnType>::type values[PacketSize];\n      for (int i = 0; i < PacketSize; ++i) {\n        values[i] = converter(impl.coeff(index+i));\n      }\n      PacketReturnType rslt = internal::pload<PacketReturnType>(values);\n      return rslt;\n    }\n  };\n\n  template <int LoadMode>\n  struct PacketConv<LoadMode, true> {\n    static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType run(const TensorEvaluator<ArgType, Device>& impl, Index index) {\n      const int SrcCoeffRatio = internal::type_casting_traits<SrcType, TargetType>::SrcCoeffRatio;\n      const int TgtCoeffRatio = internal::type_casting_traits<SrcType, TargetType>::TgtCoeffRatio;\n      PacketConverter<TensorEvaluator<ArgType, Device>, PacketSourceType, PacketReturnType,\n                      SrcCoeffRatio, TgtCoeffRatio> converter(impl);\n      return converter.template packet<LoadMode>(index);\n    }\n  };\n\n  TensorEvaluator<ArgType, Device> m_impl;\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_CONVERSION_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorConvolution.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_CONVOLUTION_H\n#define EIGEN_CXX11_TENSOR_TENSOR_CONVOLUTION_H\n\nnamespace Eigen {\n\n/** \\class TensorConvolution\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief Tensor convolution class.\n  *\n  *\n  */\nnamespace internal {\n\ntemplate <typename Index, typename InputDims, int NumKernelDims, int Layout>\nclass IndexMapper {\n public:\n  IndexMapper(const InputDims& input_dims, const array<Index, NumKernelDims>& kernel_dims,\n              const array<Index, NumKernelDims>& indices) {\n\n    array<Index, NumDims> dimensions = input_dims;\n    for (int i = 0; i < NumKernelDims; ++i) {\n      const Index index = indices[i];\n      const Index input_dim = input_dims[index];\n      const Index kernel_dim = kernel_dims[i];\n      const Index result_dim = input_dim - kernel_dim + 1;\n      dimensions[index] = result_dim;\n    }\n\n    array<Index, NumDims> inputStrides;\n    array<Index, NumDims> outputStrides;\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      inputStrides[0] = 1;\n      outputStrides[0] = 1;\n      for (int i = 1; i < NumDims; ++i) {\n        inputStrides[i] = inputStrides[i-1] * input_dims[i-1];\n        outputStrides[i] = outputStrides[i-1] * dimensions[i-1];\n      }\n    } else {\n      inputStrides[NumDims - 1] = 1;\n      outputStrides[NumDims - 1] = 1;\n      for (int i = static_cast<int>(NumDims) - 2; i >= 0; --i) {\n        inputStrides[i] = inputStrides[i + 1] * input_dims[i + 1];\n        outputStrides[i] = outputStrides[i + 1] * dimensions[i + 1];\n      }\n    }\n\n    array<Index, NumDims> cudaInputDimensions;\n    array<Index, NumDims> cudaOutputDimensions;\n    array<Index, NumDims> tmp = dimensions;\n    array<Index, NumDims> ordering;\n    const size_t offset = static_cast<int>(Layout) == static_cast<int>(ColMajor)\n                              ? 0\n                              : NumDims - NumKernelDims;\n    for (int i = 0; i < NumKernelDims; ++i) {\n      const Index index = i + offset;\n      ordering[index] = indices[i];\n      tmp[indices[i]] = -1;\n      cudaInputDimensions[index] = input_dims[indices[i]];\n      cudaOutputDimensions[index] = dimensions[indices[i]];\n    }\n\n    int written = static_cast<int>(Layout) == static_cast<int>(ColMajor)\n                      ? NumKernelDims\n                      : 0;\n    for (int i = 0; i < NumDims; ++i) {\n      if (tmp[i] >= 0) {\n        ordering[written] = i;\n        cudaInputDimensions[written] = input_dims[i];\n        cudaOutputDimensions[written] = dimensions[i];\n        ++written;\n      }\n    }\n\n    for (int i = 0; i < NumDims; ++i) {\n      m_inputStrides[i] = inputStrides[ordering[i]];\n      m_outputStrides[i] = outputStrides[ordering[i]];\n    }\n\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      for (int i = 0; i < NumDims; ++i) {\n        if (i > NumKernelDims) {\n          m_cudaInputStrides[i] =\n              m_cudaInputStrides[i - 1] * cudaInputDimensions[i - 1];\n          m_cudaOutputStrides[i] =\n              m_cudaOutputStrides[i - 1] * cudaOutputDimensions[i - 1];\n        } else {\n          m_cudaInputStrides[i] = 1;\n          m_cudaOutputStrides[i] = 1;\n        }\n      }\n    } else {\n      for (int i = NumDims - 1; i >= 0; --i) {\n        if (i + 1 < offset) {\n          m_cudaInputStrides[i] =\n              m_cudaInputStrides[i + 1] * cudaInputDimensions[i + 1];\n          m_cudaOutputStrides[i] =\n              m_cudaOutputStrides[i + 1] * cudaOutputDimensions[i + 1];\n        } else {\n          m_cudaInputStrides[i] = 1;\n          m_cudaOutputStrides[i] = 1;\n        }\n      }\n    }\n  }\n\n  EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Index mapCudaInputPlaneToTensorInputOffset(Index p) const {\n    Index inputIndex = 0;\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      for (int d = NumDims - 1; d > NumKernelDims; --d) {\n        const Index idx = p / m_cudaInputStrides[d];\n        inputIndex += idx * m_inputStrides[d];\n        p -= idx * m_cudaInputStrides[d];\n      }\n      inputIndex += p * m_inputStrides[NumKernelDims];\n    } else {\n      std::ptrdiff_t limit = 0;\n      if (NumKernelDims < NumDims) {\n        limit = NumDims - NumKernelDims - 1;\n      }\n      for (int d = 0; d < limit; ++d) {\n        const Index idx = p / m_cudaInputStrides[d];\n        inputIndex += idx * m_inputStrides[d];\n        p -= idx * m_cudaInputStrides[d];\n      }\n      inputIndex += p * m_inputStrides[limit];\n    }\n    return inputIndex;\n  }\n\n  EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Index mapCudaOutputPlaneToTensorOutputOffset(Index p) const {\n    Index outputIndex = 0;\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      for (int d = NumDims - 1; d > NumKernelDims; --d) {\n        const Index idx = p / m_cudaOutputStrides[d];\n        outputIndex += idx * m_outputStrides[d];\n        p -= idx * m_cudaOutputStrides[d];\n      }\n      outputIndex += p * m_outputStrides[NumKernelDims];\n    } else {\n      std::ptrdiff_t limit = 0;\n      if (NumKernelDims < NumDims) {\n        limit = NumDims - NumKernelDims - 1;\n      }\n      for (int d = 0; d < limit; ++d) {\n        const Index idx = p / m_cudaOutputStrides[d];\n        outputIndex += idx * m_outputStrides[d];\n        p -= idx * m_cudaOutputStrides[d];\n      }\n      outputIndex += p * m_outputStrides[limit];\n    }\n    return outputIndex;\n  }\n\n  EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Index mapCudaInputKernelToTensorInputOffset(Index i) const {\n    const size_t offset = static_cast<int>(Layout) == static_cast<int>(ColMajor)\n                              ? 0\n                              : NumDims - NumKernelDims;\n    return i * m_inputStrides[offset];\n  }\n\n  EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Index mapCudaOutputKernelToTensorOutputOffset(Index i) const {\n    const size_t offset = static_cast<int>(Layout) == static_cast<int>(ColMajor)\n                              ? 0\n                              : NumDims - NumKernelDims;\n    return i * m_outputStrides[offset];\n  }\n\n  EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Index mapCudaInputKernelToTensorInputOffset(Index i, Index j) const {\n    const size_t offset = static_cast<int>(Layout) == static_cast<int>(ColMajor)\n                              ? 0\n                              : NumDims - NumKernelDims;\n    return i * m_inputStrides[offset] + j * m_inputStrides[offset + 1];\n  }\n\n  EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Index mapCudaOutputKernelToTensorOutputOffset(Index i, Index j) const {\n    const size_t offset = static_cast<int>(Layout) == static_cast<int>(ColMajor)\n                              ? 0\n                              : NumDims - NumKernelDims;\n    return i * m_outputStrides[offset] + j * m_outputStrides[offset + 1];\n  }\n\n  EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Index mapCudaInputKernelToTensorInputOffset(Index i, Index j, Index k) const {\n    const size_t offset = static_cast<int>(Layout) == static_cast<int>(ColMajor)\n                              ? 0\n                              : NumDims - NumKernelDims;\n    return i * m_inputStrides[offset] + j * m_inputStrides[offset + 1] +\n           k * m_inputStrides[offset + 2];\n  }\n\n  EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Index mapCudaOutputKernelToTensorOutputOffset(Index i, Index j, Index k) const {\n    const size_t offset = static_cast<int>(Layout) == static_cast<int>(ColMajor)\n                              ? 0\n                              : NumDims - NumKernelDims;\n    return i * m_outputStrides[offset] + j * m_outputStrides[offset + 1] +\n           k * m_outputStrides[offset + 2];\n  }\n\n private:\n  static const int NumDims = internal::array_size<InputDims>::value;\n  array<Index, NumDims> m_inputStrides;\n  array<Index, NumDims> m_outputStrides;\n  array<Index, NumDims> m_cudaInputStrides;\n  array<Index, NumDims> m_cudaOutputStrides;\n};\n\n\n\ntemplate<typename Dimensions, typename InputXprType, typename KernelXprType>\nstruct traits<TensorConvolutionOp<Dimensions, InputXprType, KernelXprType> >\n{\n  // Type promotion to handle the case where the types of the lhs and the rhs are different.\n  typedef typename promote_storage_type<typename InputXprType::Scalar,\n                                        typename KernelXprType::Scalar>::ret Scalar;\n  typedef typename promote_storage_type<typename traits<InputXprType>::StorageKind,\n                                        typename traits<KernelXprType>::StorageKind>::ret StorageKind;\n  typedef typename promote_index_type<typename traits<InputXprType>::Index,\n                                      typename traits<KernelXprType>::Index>::type Index;\n  typedef typename InputXprType::Nested LhsNested;\n  typedef typename KernelXprType::Nested RhsNested;\n  typedef typename remove_reference<LhsNested>::type _LhsNested;\n  typedef typename remove_reference<RhsNested>::type _RhsNested;\n  static const int NumDimensions = traits<InputXprType>::NumDimensions;\n  static const int Layout = traits<InputXprType>::Layout;\n\n  enum {\n    Flags = 0\n  };\n};\n\ntemplate<typename Dimensions, typename InputXprType, typename KernelXprType>\nstruct eval<TensorConvolutionOp<Dimensions, InputXprType, KernelXprType>, Eigen::Dense>\n{\n  typedef const TensorConvolutionOp<Dimensions, InputXprType, KernelXprType>& type;\n};\n\ntemplate<typename Dimensions, typename InputXprType, typename KernelXprType>\nstruct nested<TensorConvolutionOp<Dimensions, InputXprType, KernelXprType>, 1, typename eval<TensorConvolutionOp<Dimensions, InputXprType, KernelXprType> >::type>\n{\n  typedef TensorConvolutionOp<Dimensions, InputXprType, KernelXprType> type;\n};\n\n}  // end namespace internal\n\n\n\ntemplate<typename Indices, typename InputXprType, typename KernelXprType>\nclass TensorConvolutionOp : public TensorBase<TensorConvolutionOp<Indices, InputXprType, KernelXprType>, ReadOnlyAccessors>\n{\n  public:\n  typedef typename Eigen::internal::traits<TensorConvolutionOp>::Scalar Scalar;\n  typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;\n  typedef typename internal::promote_storage_type<typename InputXprType::CoeffReturnType,\n                                                  typename KernelXprType::CoeffReturnType>::ret CoeffReturnType;\n  typedef typename Eigen::internal::nested<TensorConvolutionOp>::type Nested;\n  typedef typename Eigen::internal::traits<TensorConvolutionOp>::StorageKind StorageKind;\n  typedef typename Eigen::internal::traits<TensorConvolutionOp>::Index Index;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorConvolutionOp(const InputXprType& input, const KernelXprType& kernel, const Indices& dims)\n      : m_input_xpr(input), m_kernel_xpr(kernel), m_indices(dims) {}\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const Indices& indices() const { return m_indices; }\n\n    /** \\returns the nested expressions */\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const typename internal::remove_all<typename InputXprType::Nested>::type&\n    inputExpression() const { return m_input_xpr; }\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const typename internal::remove_all<typename KernelXprType::Nested>::type&\n    kernelExpression() const { return m_kernel_xpr; }\n\n  protected:\n    typename InputXprType::Nested m_input_xpr;\n    typename KernelXprType::Nested m_kernel_xpr;\n    const Indices m_indices;\n};\n\n\ntemplate<typename Indices, typename InputArgType, typename KernelArgType, typename Device>\nstruct TensorEvaluator<const TensorConvolutionOp<Indices, InputArgType, KernelArgType>, Device>\n{\n  typedef TensorConvolutionOp<Indices, InputArgType, KernelArgType> XprType;\n\n  static const int NumDims = internal::array_size<typename TensorEvaluator<InputArgType, Device>::Dimensions>::value;\n  static const int NumKernelDims = internal::array_size<Indices>::value;\n  typedef typename XprType::Index Index;\n  typedef DSizes<Index, NumDims> Dimensions;\n\n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  static const int PacketSize = internal::unpacket_traits<PacketReturnType>::size;\n\n  enum {\n    IsAligned = TensorEvaluator<InputArgType, Device>::IsAligned & TensorEvaluator<KernelArgType, Device>::IsAligned,\n    PacketAccess = TensorEvaluator<InputArgType, Device>::PacketAccess & TensorEvaluator<KernelArgType, Device>::PacketAccess,\n    Layout = TensorEvaluator<InputArgType, Device>::Layout,\n    CoordAccess = false,  // to be implemented\n    RawAccess = false\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)\n      : m_inputImpl(op.inputExpression(), device), m_kernelImpl(op.kernelExpression(), device), m_kernelArg(op.kernelExpression()), m_kernel(NULL), m_local_kernel(false), m_device(device)\n  {\n    EIGEN_STATIC_ASSERT((static_cast<int>(TensorEvaluator<InputArgType, Device>::Layout) == static_cast<int>(TensorEvaluator<KernelArgType, Device>::Layout)), YOU_MADE_A_PROGRAMMING_MISTAKE);\n\n    const typename TensorEvaluator<InputArgType, Device>::Dimensions& input_dims = m_inputImpl.dimensions();\n    const typename TensorEvaluator<KernelArgType, Device>::Dimensions& kernel_dims = m_kernelImpl.dimensions();\n\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      m_inputStride[0] = 1;\n      for (int i = 1; i < NumDims; ++i) {\n        m_inputStride[i] = m_inputStride[i - 1] * input_dims[i - 1];\n      }\n    } else {\n      m_inputStride[NumDims - 1] = 1;\n      for (int i = NumDims - 2; i >= 0; --i) {\n        m_inputStride[i] = m_inputStride[i + 1] * input_dims[i + 1];\n      }\n    }\n\n    m_dimensions = m_inputImpl.dimensions();\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      for (int i = 0; i < NumKernelDims; ++i) {\n        const Index index = op.indices()[i];\n        const Index input_dim = input_dims[index];\n        const Index kernel_dim = kernel_dims[i];\n        const Index result_dim = input_dim - kernel_dim + 1;\n        m_dimensions[index] = result_dim;\n        if (i > 0) {\n          m_kernelStride[i] = m_kernelStride[i - 1] * kernel_dims[i - 1];\n        } else {\n          m_kernelStride[0] = 1;\n        }\n        m_indexStride[i] = m_inputStride[index];\n      }\n\n      m_outputStride[0] = 1;\n      for (int i = 1; i < NumDims; ++i) {\n        m_outputStride[i] = m_outputStride[i - 1] * m_dimensions[i - 1];\n      }\n    } else {\n      for (int i = NumKernelDims - 1; i >= 0; --i) {\n        const Index index = op.indices()[i];\n        const Index input_dim = input_dims[index];\n        const Index kernel_dim = kernel_dims[i];\n        const Index result_dim = input_dim - kernel_dim + 1;\n        m_dimensions[index] = result_dim;\n        if (i < NumKernelDims - 1) {\n          m_kernelStride[i] = m_kernelStride[i + 1] * kernel_dims[i + 1];\n        } else {\n          m_kernelStride[NumKernelDims - 1] = 1;\n        }\n        m_indexStride[i] = m_inputStride[index];\n      }\n\n      m_outputStride[NumDims - 1] = 1;\n      for (int i = NumDims - 2; i >= 0; --i) {\n        m_outputStride[i] = m_outputStride[i + 1] * m_dimensions[i + 1];\n      }\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(Scalar*) {\n    m_inputImpl.evalSubExprsIfNeeded(NULL);\n    preloadKernel();\n    return true;\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {\n    m_inputImpl.cleanup();\n    if (m_local_kernel) {\n      m_device.deallocate((void*)m_kernel);\n      m_local_kernel = false;\n    }\n    m_kernel = NULL;\n  }\n\n  void evalTo(typename XprType::Scalar* buffer) {\n    evalSubExprsIfNeeded(NULL);\n    for (int i = 0; i < dimensions().TotalSize(); ++i) {\n      buffer[i] += coeff(i);\n    }\n    cleanup();\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const\n  {\n    CoeffReturnType result = CoeffReturnType(0);\n    convolve(firstInput(index), 0, NumKernelDims-1, result);\n    return result;\n  }\n\n  template<int LoadMode>\n  EIGEN_DEVICE_FUNC PacketReturnType packet(const Index index) const\n  {\n    Index indices[2] = {index, index+PacketSize-1};\n    Index startInputs[2] = {0, 0};\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      for (int i = NumDims - 1; i > 0; --i) {\n        const Index idx0 = indices[0] / m_outputStride[i];\n        const Index idx1 = indices[1] / m_outputStride[i];\n        startInputs[0] += idx0 * m_inputStride[i];\n        startInputs[1] += idx1 * m_inputStride[i];\n        indices[0] -= idx0 * m_outputStride[i];\n        indices[1] -= idx1 * m_outputStride[i];\n      }\n    } else {\n      for (int i = 0; i < NumDims - 1; ++i) {\n        const Index idx0 = indices[0] / m_outputStride[i];\n        const Index idx1 = indices[1] / m_outputStride[i];\n        startInputs[0] += idx0 * m_inputStride[i];\n        startInputs[1] += idx1 * m_inputStride[i];\n        indices[0] -= idx0 * m_outputStride[i];\n        indices[1] -= idx1 * m_outputStride[i];\n      }\n    }\n    startInputs[0] += indices[0];\n    startInputs[1] += indices[1];\n\n    if (startInputs[1]-startInputs[0] == PacketSize-1) {\n      PacketReturnType result = internal::pset1<PacketReturnType>(0);\n      convolvePacket(startInputs[0], 0, NumKernelDims-1, result);\n      return result;\n    } else {\n      EIGEN_ALIGN_MAX Scalar data[PacketSize];\n      data[0] = Scalar(0);\n      convolve(startInputs[0], 0, NumKernelDims-1, data[0]);\n      for (int i = 1; i < PacketSize-1; ++i) {\n        data[i] = Scalar(0);\n        convolve(firstInput(index+i), 0, NumKernelDims-1, data[i]);\n      }\n      data[PacketSize-1] = Scalar(0);\n      convolve(startInputs[1], 0, NumKernelDims-1, data[PacketSize-1]);\n      return internal::pload<PacketReturnType>(data);\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost\n  costPerCoeff(bool vectorized) const {\n    const double kernel_size = m_kernelImpl.dimensions().TotalSize();\n    // We ignore the use of fused multiply-add.\n    const double convolve_compute_cost =\n        TensorOpCost::AddCost<Scalar>() + TensorOpCost::MulCost<Scalar>();\n    const double firstIndex_compute_cost =\n        NumDims *\n        (2 * TensorOpCost::AddCost<Index>() + 2 * TensorOpCost::MulCost<Index>() +\n         TensorOpCost::DivCost<Index>());\n    return TensorOpCost(0, 0, firstIndex_compute_cost, vectorized, PacketSize) +\n           kernel_size * (m_inputImpl.costPerCoeff(vectorized) +\n                          m_kernelImpl.costPerCoeff(vectorized) +\n                          TensorOpCost(0, 0, convolve_compute_cost, vectorized,\n                                       PacketSize));\n  }\n\n  EIGEN_DEVICE_FUNC Scalar* data() const { return NULL; }\n\n private:\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index firstInput(Index index) const {\n    Index startInput = 0;\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      for (int i = NumDims - 1; i > 0; --i) {\n        const Index idx = index / m_outputStride[i];\n        startInput += idx * m_inputStride[i];\n        index -= idx * m_outputStride[i];\n      }\n    } else {\n      for (int i = 0; i < NumDims - 1; ++i) {\n        const Index idx = index / m_outputStride[i];\n        startInput += idx * m_inputStride[i];\n        index -= idx * m_outputStride[i];\n      }\n    }\n    startInput += index;\n    return startInput;\n  }\n\n  EIGEN_DEVICE_FUNC void convolve(Index firstIndex, Index firstKernel, int DimIndex, CoeffReturnType& accum) const {\n    for (int j = 0; j < m_kernelImpl.dimensions()[DimIndex]; ++j) {\n      const Index input = firstIndex + j * m_indexStride[DimIndex];\n      const Index kernel = firstKernel + j * m_kernelStride[DimIndex];\n      if (DimIndex > 0) {\n        convolve(input, kernel, DimIndex-1, accum);\n      } else {\n        accum += m_inputImpl.coeff(input) * m_kernel[kernel];\n      }\n    }\n  }\n\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC void convolvePacket(Index firstIndex, Index firstKernel, int DimIndex, Packet& accum) const {\n    for (int j = 0; j < m_kernelImpl.dimensions()[DimIndex]; ++j) {\n      const Index input = firstIndex + j * m_indexStride[DimIndex];\n      const Index kernel = firstKernel + j * m_kernelStride[DimIndex];\n      if (DimIndex > 0) {\n        convolvePacket(input, kernel, DimIndex-1, accum);\n      } else {\n        accum = internal::pmadd<Packet>(m_inputImpl.template packet<Unaligned>(input), internal::pset1<Packet>(m_kernel[kernel]), accum);\n      }\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void preloadKernel() {\n    // Don't make a local copy of the kernel unless we have to (i.e. it's an\n    // expression that needs to be evaluated)\n    const Scalar* in_place = m_kernelImpl.data();\n    if (in_place) {\n      m_kernel = in_place;\n      m_local_kernel = false;\n    } else {\n      size_t kernel_sz = m_kernelImpl.dimensions().TotalSize() * sizeof(Scalar);\n      Scalar* local = (Scalar*)m_device.allocate(kernel_sz);\n      typedef TensorEvalToOp<const KernelArgType> EvalTo;\n      EvalTo evalToTmp(local, m_kernelArg);\n      const bool PacketAccess = internal::IsVectorizable<Device, KernelArgType>::value;\n      internal::TensorExecutor<const EvalTo, Device, PacketAccess>::run(evalToTmp, m_device);\n\n      m_kernel = local;\n      m_local_kernel = true;\n    }\n  }\n\n  array<Index, NumDims> m_inputStride;\n  array<Index, NumDims> m_outputStride;\n\n  array<Index, NumKernelDims> m_indexStride;\n  array<Index, NumKernelDims> m_kernelStride;\n  TensorEvaluator<InputArgType, Device> m_inputImpl;\n  TensorEvaluator<KernelArgType, Device> m_kernelImpl;\n  Dimensions m_dimensions;\n\n  KernelArgType m_kernelArg;\n  const Scalar* m_kernel;\n  bool m_local_kernel;\n  const Device& m_device;\n};\n\n\n\n\n// Use an optimized implementation of the evaluation code for GPUs whenever possible.\n#if defined(EIGEN_USE_GPU) && defined(__CUDACC__)\n\ntemplate <int StaticKernelSize>\nstruct GetKernelSize {\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE int operator() (const int /*kernelSize*/) const {\n    return StaticKernelSize;\n  }\n};\ntemplate <>\nstruct GetKernelSize<Dynamic> {\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE int operator() (const int kernelSize) const {\n    return kernelSize;\n  }\n};\n\ntemplate <typename InputEvaluator, typename Index, typename InputDims,\n          int StaticKernelSize>\n__global__ void EigenConvolutionKernel1D(\n    InputEvaluator eval,\n    const internal::IndexMapper<Index, InputDims, 1, InputEvaluator::Layout>\n        indexMapper,\n    const float* __restrict kernel, const int numPlanes, const int numX,\n    const int maxX, const int kernelSize, float* buffer) {\n  extern __shared__ float s[];\n\n  const int first_x = blockIdx.x * maxX;\n  const int last_x = (first_x + maxX < numX ? first_x + maxX : numX) - 1;\n  const int num_x_input = last_x - first_x + GetKernelSize<StaticKernelSize>()(kernelSize);\n  const int num_x_output = last_x - first_x + 1;\n\n  const int first_plane = blockIdx.y * blockDim.y;\n  const int plane_stride = blockDim.y * gridDim.y;\n\n  for (int p = first_plane + threadIdx.y; p < numPlanes; p += plane_stride) {\n    // Load inputs to shared memory\n    const int plane_input_offset = indexMapper.mapCudaInputPlaneToTensorInputOffset(p);\n    const int plane_kernel_offset = threadIdx.y * num_x_input;\n    #pragma unroll\n    for (int i = threadIdx.x; i < num_x_input; i += blockDim.x) {\n      const int tensor_index = plane_input_offset + indexMapper.mapCudaInputKernelToTensorInputOffset(i+first_x);\n      s[i + plane_kernel_offset] = eval.coeff(tensor_index);\n    }\n\n    __syncthreads();\n\n    // Compute the convolution\n    const int plane_output_offset = indexMapper.mapCudaOutputPlaneToTensorOutputOffset(p);\n\n    #pragma unroll\n    for (int i = threadIdx.x; i < num_x_output; i += blockDim.x) {\n      const int kernel_offset = plane_kernel_offset + i;\n      float result = 0.0f;\n      #pragma unroll\n      for (int k = 0; k < GetKernelSize<StaticKernelSize>()(kernelSize); ++k) {\n        result += s[k + kernel_offset] * kernel[k];\n      }\n      const int tensor_index = plane_output_offset + indexMapper.mapCudaOutputKernelToTensorOutputOffset(i+first_x);\n      buffer[tensor_index] = result;\n    }\n    __syncthreads();\n  }\n};\n\ntemplate <typename InputEvaluator, typename Index, typename InputDims,\n          int StaticKernelSizeX, int StaticKernelSizeY>\n__global__ void EigenConvolutionKernel2D(\n    InputEvaluator eval,\n    const internal::IndexMapper<Index, InputDims, 2, InputEvaluator::Layout>\n        indexMapper,\n    const float* __restrict kernel, const int numPlanes, const int numX,\n    const int maxX, const int numY, const int maxY, const int kernelSizeX,\n    const int kernelSizeY, float* buffer) {\n  extern __shared__ float s[];\n\n  const int first_x = blockIdx.x * maxX;\n  const int last_x = (first_x + maxX < numX ? first_x + maxX : numX) - 1;\n  const int num_x_input = last_x - first_x + GetKernelSize<StaticKernelSizeX>()(kernelSizeX);\n  const int num_x_output = last_x - first_x + 1;\n\n  const int first_y = blockIdx.y * maxY;\n  const int last_y = (first_y + maxY < numY ? first_y + maxY : numY) - 1;\n  const int num_y_input = last_y - first_y + GetKernelSize<StaticKernelSizeY>()(kernelSizeY);\n  const int num_y_output = last_y - first_y + 1;\n\n  const int first_plane = blockIdx.z * blockDim.z;\n  const int plane_stride = blockDim.z * gridDim.z;\n\n  for (int p = first_plane + threadIdx.z; p < numPlanes; p += plane_stride) {\n\n    const int plane_input_offset = indexMapper.mapCudaInputPlaneToTensorInputOffset(p);\n    const int plane_kernel_offset = threadIdx.z * num_y_input;\n\n    // Load inputs to shared memory\n    #pragma unroll\n    for (int j = threadIdx.y; j < num_y_input; j += blockDim.y) {\n      const int input_offset = num_x_input * (j + plane_kernel_offset);\n      #pragma unroll\n      for (int i = threadIdx.x; i < num_x_input; i += blockDim.x) {\n        const int tensor_index = plane_input_offset + indexMapper.mapCudaInputKernelToTensorInputOffset(i+first_x, j+first_y);\n        s[i + input_offset] = eval.coeff(tensor_index);\n      }\n    }\n\n    __syncthreads();\n\n    // Convolution\n    const int plane_output_offset = indexMapper.mapCudaOutputPlaneToTensorOutputOffset(p);\n\n    #pragma unroll\n    for (int j = threadIdx.y; j < num_y_output; j += blockDim.y) {\n      #pragma unroll\n      for (int i = threadIdx.x; i < num_x_output; i += blockDim.x) {\n        float result = 0.0f;\n        #pragma unroll\n        for (int l = 0; l < GetKernelSize<StaticKernelSizeY>()(kernelSizeY); ++l) {\n          const int kernel_offset = kernelSizeX * l;\n          const int input_offset = i + num_x_input * (j + l + plane_kernel_offset);\n          #pragma unroll\n          for (int k = 0; k < GetKernelSize<StaticKernelSizeX>()(kernelSizeX); ++k) {\n            result += s[k + input_offset] * kernel[k + kernel_offset];\n          }\n        }\n        const int tensor_index = plane_output_offset + indexMapper.mapCudaOutputKernelToTensorOutputOffset(i+first_x, j+first_y);\n        buffer[tensor_index] = result;\n      }\n    }\n\n    __syncthreads();\n  }\n};\n\ntemplate <typename InputEvaluator, typename Index, typename InputDims>\n__global__ void EigenConvolutionKernel3D(\n    InputEvaluator eval,\n    const internal::IndexMapper<Index, InputDims, 3, InputEvaluator::Layout>\n        indexMapper,\n    const float* __restrict kernel, const size_t numPlanes, const size_t numX,\n    const size_t maxX, const size_t numY, const size_t maxY, const size_t numZ,\n    const size_t maxZ, const size_t kernelSizeX, const size_t kernelSizeY,\n    const size_t kernelSizeZ, float* buffer) {\n  extern __shared__ float s[];\n\n  // Load inputs to shared memory\n  const int first_x = blockIdx.x * maxX;\n  const int last_x = (first_x + maxX < numX ? first_x + maxX : numX) - 1;\n  const int num_x_input = last_x - first_x + kernelSizeX;\n\n  const int first_y = blockIdx.y * maxY;\n  const int last_y = (first_y + maxY < numY ? first_y + maxY : numY) - 1;\n  const int num_y_input = last_y - first_y + kernelSizeY;\n\n  const int first_z = blockIdx.z * maxZ;\n  const int last_z = (first_z + maxZ < numZ ? first_z + maxZ : numZ) - 1;\n  const int num_z_input = last_z - first_z + kernelSizeZ;\n\n  for (int p = 0; p < numPlanes; ++p) {\n\n    const int plane_input_offset = indexMapper.mapCudaInputPlaneToTensorInputOffset(p);\n    const int plane_kernel_offset = 0;\n\n    for (int k = threadIdx.z; k < num_z_input; k += blockDim.z) {\n      for (int j = threadIdx.y; j < num_y_input; j += blockDim.y) {\n        for (int i = threadIdx.x; i < num_x_input; i += blockDim.x) {\n          const int tensor_index = plane_input_offset + indexMapper.mapCudaInputKernelToTensorInputOffset(i+first_x, j+first_y, k+first_z);\n          s[i + num_x_input * (j + num_y_input * (k + plane_kernel_offset))] = eval.coeff(tensor_index);\n        }\n      }\n    }\n\n    __syncthreads();\n\n    // Convolution\n    const int num_z_output = last_z - first_z + 1;\n    const int num_y_output = last_y - first_y + 1;\n    const int num_x_output = last_x - first_x + 1;\n    const int plane_output_offset = indexMapper.mapCudaOutputPlaneToTensorOutputOffset(p);\n\n    for (int k = threadIdx.z; k < num_z_output; k += blockDim.z) {\n      for (int j = threadIdx.y; j < num_y_output; j += blockDim.y) {\n        for (int i = threadIdx.x; i < num_x_output; i += blockDim.x) {\n          float result = 0.0f;\n          for (int n = 0; n < kernelSizeZ; ++n) {\n            for (int m = 0; m < kernelSizeY; ++m) {\n              for (int l = 0; l < kernelSizeX; ++l) {\n                result += s[i + l + num_x_input * (j + m + num_y_input * (k + n + plane_kernel_offset))] * kernel[l + kernelSizeX * (m + kernelSizeY * n)];\n              }\n            }\n          }\n          const int tensor_index = plane_output_offset + indexMapper.mapCudaOutputKernelToTensorOutputOffset(i+first_x, j+first_y, k+first_z);\n          buffer[tensor_index] = result;\n        }\n      }\n    }\n    __syncthreads();\n  }\n};\n\n\n\ntemplate<typename Indices, typename InputArgType, typename KernelArgType>\nstruct TensorEvaluator<const TensorConvolutionOp<Indices, InputArgType, KernelArgType>, GpuDevice>\n{\n  typedef TensorConvolutionOp<Indices, InputArgType, KernelArgType> XprType;\n\n  static const int NumDims =  internal::array_size<typename TensorEvaluator<InputArgType, GpuDevice>::Dimensions>::value;\n  static const int NumKernelDims = internal::array_size<Indices>::value;\n  typedef typename XprType::Index Index;\n  typedef DSizes<Index, NumDims> Dimensions;\n  typedef typename TensorEvaluator<KernelArgType, GpuDevice>::Dimensions KernelDimensions;\n\n  enum {\n    IsAligned = TensorEvaluator<InputArgType, GpuDevice>::IsAligned & TensorEvaluator<KernelArgType, GpuDevice>::IsAligned,\n    PacketAccess = false,\n    Layout = TensorEvaluator<InputArgType, GpuDevice>::Layout,\n    CoordAccess = false,  // to be implemented\n    RawAccess = false\n  };\n\n  EIGEN_DEVICE_FUNC TensorEvaluator(const XprType& op, const GpuDevice& device)\n      : m_inputImpl(op.inputExpression(), device), m_kernelArg(op.kernelExpression()), m_kernelImpl(op.kernelExpression(), device), m_indices(op.indices()), m_buf(NULL), m_kernel(NULL), m_local_kernel(false), m_device(device)\n  {\n    EIGEN_STATIC_ASSERT((static_cast<int>(TensorEvaluator<InputArgType, GpuDevice>::Layout) == static_cast<int>(TensorEvaluator<KernelArgType, GpuDevice>::Layout)), YOU_MADE_A_PROGRAMMING_MISTAKE);\n\n    const typename TensorEvaluator<InputArgType, GpuDevice>::Dimensions& input_dims = m_inputImpl.dimensions();\n    const typename TensorEvaluator<KernelArgType, GpuDevice>::Dimensions& kernel_dims = m_kernelImpl.dimensions();\n\n    m_dimensions = m_inputImpl.dimensions();\n    for (int i = 0; i < NumKernelDims; ++i) {\n      const Index index = op.indices()[i];\n      const Index input_dim = input_dims[index];\n      const Index kernel_dim = kernel_dims[i];\n      const Index result_dim = input_dim - kernel_dim + 1;\n      m_dimensions[index] = result_dim;\n    }\n  }\n\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, GpuDevice>::type PacketReturnType;\n  typedef typename InputArgType::Scalar Scalar;\n  static const int PacketSize = internal::unpacket_traits<PacketReturnType>::size;\n\n  EIGEN_DEVICE_FUNC const Dimensions& dimensions() const { return m_dimensions; }\n\n  EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(Scalar* data) {\n    preloadKernel();\n    m_inputImpl.evalSubExprsIfNeeded(NULL);\n    if (data) {\n      executeEval(data);\n      return false;\n    } else {\n      m_buf = (Scalar*)m_device.allocate(dimensions().TotalSize() * sizeof(Scalar));\n      executeEval(m_buf);\n      return true;\n    }\n  }\n\n  EIGEN_STRONG_INLINE void cleanup() {\n    m_inputImpl.cleanup();\n    if (m_buf) {\n      m_device.deallocate(m_buf);\n      m_buf = NULL;\n    }\n    if (m_local_kernel) {\n      m_device.deallocate((void*)m_kernel);\n      m_local_kernel = false;\n    }\n    m_kernel = NULL;\n  }\n\n  EIGEN_STRONG_INLINE void preloadKernel() {\n    // Don't make a local copy of the kernel unless we have to (i.e. it's an\n    // expression that needs to be evaluated)\n    const Scalar* in_place = m_kernelImpl.data();\n    if (in_place) {\n      m_kernel = in_place;\n      m_local_kernel = false;\n    } else {\n      size_t kernel_sz = m_kernelImpl.dimensions().TotalSize() * sizeof(Scalar);\n      Scalar* local = (Scalar*)m_device.allocate(kernel_sz);\n      typedef TensorEvalToOp<const KernelArgType> EvalTo;\n      EvalTo evalToTmp(local, m_kernelArg);\n      const bool PacketAccess = internal::IsVectorizable<GpuDevice, KernelArgType>::value;\n      internal::TensorExecutor<const EvalTo, GpuDevice, PacketAccess>::run(evalToTmp, m_device);\n\n      m_kernel = local;\n      m_local_kernel = true;\n    }\n  }\n\n  static unsigned int ceil(unsigned int num, unsigned int denom) {\n    const unsigned int rounded_toward_zero = num / denom;\n    if (num > rounded_toward_zero * denom) {\n      return rounded_toward_zero + 1;\n    }\n    return rounded_toward_zero;\n  }\n\n  void executeEval(Scalar* data) const {\n    typedef typename TensorEvaluator<InputArgType, GpuDevice>::Dimensions InputDims;\n\n    const int maxSharedMem = m_device.sharedMemPerBlock();\n    const int maxThreadsPerBlock = m_device.maxCudaThreadsPerBlock();\n    const int maxBlocksPerProcessor = m_device.maxCudaThreadsPerMultiProcessor() / maxThreadsPerBlock;\n    const int numMultiProcessors = m_device.getNumCudaMultiProcessors();\n    const int warpSize = 32;\n\n    switch (NumKernelDims) {\n      case 1: {\n        const int kernel_size = m_kernelImpl.dimensions().TotalSize();\n\n        const int numX = dimensions()[m_indices[0]];\n        const int numP = dimensions().TotalSize() / numX;\n        int maxX;\n        dim3 block_size;\n\n        const int single_stride_dim =\n            static_cast<int>(Layout) == static_cast<int>(ColMajor)\n                ? 0\n                : m_inputImpl.dimensions().rank() - 1;\n        if (m_indices[0] == single_stride_dim) {\n          // Maximum the reuse\n          const int inner_dim = ((maxSharedMem / (sizeof(Scalar)) - kernel_size + 1 + 31) / 32) * 32;\n          maxX = numext::mini<int>(inner_dim, numX);\n          const int maxP = numext::mini<int>(maxSharedMem / ((kernel_size - 1 + maxX) * sizeof(Scalar)), numP);\n          block_size.x = numext::mini(maxThreadsPerBlock, maxX);\n          block_size.y = numext::mini<int>(maxThreadsPerBlock / block_size.x, maxP);\n        }\n        else {\n          // Read as much as possible alongside the inner most dimension, that is the plane\n          const int inner_dim = maxSharedMem / ((warpSize + kernel_size) * sizeof(Scalar));\n          const int maxP = numext::mini<int>(inner_dim, numP);\n          maxX = numext::mini<int>(maxSharedMem / (inner_dim * sizeof(Scalar)) - kernel_size + 1, numX);\n\n          block_size.x = numext::mini(warpSize, maxX);\n          block_size.y = numext::mini<int>(maxThreadsPerBlock/block_size.x, maxP);\n        }\n\n        const int shared_mem = block_size.y * (maxX + kernel_size - 1) * sizeof(Scalar);\n        assert(shared_mem <= maxSharedMem);\n\n        const int num_x_blocks = ceil(numX, maxX);\n        const int blocksPerProcessor = numext::mini(maxBlocksPerProcessor, maxSharedMem / shared_mem);\n        const int num_y_blocks = ceil(numMultiProcessors * blocksPerProcessor, num_x_blocks);\n\n        dim3 num_blocks(num_x_blocks, numext::mini<int>(num_y_blocks, ceil(numP, block_size.y)));\n\n\n        //cout << \"launching 1D kernel with block_size.x: \" << block_size.x << \" block_size.y: \" << block_size.y << \" num_blocks.x: \" << num_blocks.x << \" num_blocks.y: \" << num_blocks.y << \" maxX: \" << maxX << \" shared_mem: \" << shared_mem << \" in stream \" << m_device.stream() << endl;\n\n        const array<Index, 1> indices(m_indices[0]);\n        const array<Index, 1> kernel_dims(m_kernelImpl.dimensions()[0]);\n        internal::IndexMapper<Index, InputDims, 1, Layout> indexMapper(\n            m_inputImpl.dimensions(), kernel_dims, indices);\n        switch(kernel_size) {\n          case 4: {\n            LAUNCH_CUDA_KERNEL((EigenConvolutionKernel1D<TensorEvaluator<InputArgType, GpuDevice>, Index, InputDims, 4>), num_blocks, block_size, shared_mem, m_device, m_inputImpl, indexMapper, m_kernel, numP, numX, maxX, 4, data);\n            break;\n          }\n          case 7: {\n            LAUNCH_CUDA_KERNEL((EigenConvolutionKernel1D<TensorEvaluator<InputArgType, GpuDevice>, Index, InputDims, 7>), num_blocks, block_size, shared_mem, m_device, m_inputImpl, indexMapper, m_kernel, numP, numX, maxX, 7, data);\n            break;\n          }\n          default: {\n            LAUNCH_CUDA_KERNEL((EigenConvolutionKernel1D<TensorEvaluator<InputArgType, GpuDevice>, Index, InputDims, Dynamic>), num_blocks, block_size, shared_mem, m_device, m_inputImpl, indexMapper, m_kernel, numP, numX, maxX, kernel_size, data);\n          }\n        }\n        break;\n      }\n\n      case 2: {\n        const int idxX =\n            static_cast<int>(Layout) == static_cast<int>(ColMajor) ? 0 : 1;\n        const int idxY =\n            static_cast<int>(Layout) == static_cast<int>(ColMajor) ? 1 : 0;\n        const int kernel_size_x = m_kernelImpl.dimensions()[idxX];\n        const int kernel_size_y = m_kernelImpl.dimensions()[idxY];\n\n        const int numX = dimensions()[m_indices[idxX]];\n        const int numY = dimensions()[m_indices[idxY]];\n        const int numP = dimensions().TotalSize() / (numX*numY);\n\n        const float scaling_factor = sqrtf(static_cast<float>(maxSharedMem) / (sizeof(Scalar) * kernel_size_y * kernel_size_x));\n\n        // Snap maxX to warp size\n        int inner_dim = ((static_cast<int>(scaling_factor * kernel_size_x) - kernel_size_x + 1 + 32) / 32) * 32;\n        const int maxX = numext::mini<int>(inner_dim, numX);\n        const int maxY = numext::mini<int>(maxSharedMem / (sizeof(Scalar) * (maxX + kernel_size_x - 1)) - kernel_size_y + 1, numY);\n        const int maxP = numext::mini<int>(maxSharedMem / ((kernel_size_x - 1 + maxX) * (kernel_size_y - 1 + maxY) * sizeof(Scalar)), numP);\n\n        dim3 block_size;\n        block_size.x = numext::mini(1024, maxX);\n        block_size.y = numext::mini<int>(1024/block_size.x, maxY);\n        block_size.z = numext::mini<int>(1024/(block_size.x*block_size.y), maxP);\n\n        const int shared_mem = block_size.z * (maxX + kernel_size_x - 1) * (maxY + kernel_size_y - 1) * sizeof(Scalar);\n        assert(shared_mem <= maxSharedMem);\n\n        const int num_x_blocks = ceil(numX, maxX);\n        const int num_y_blocks = ceil(numY, maxY);\n        const int blocksPerProcessor = numext::mini(maxBlocksPerProcessor, maxSharedMem / shared_mem);\n        const int num_z_blocks = ceil(numMultiProcessors * blocksPerProcessor, num_x_blocks * num_y_blocks);\n\n        dim3 num_blocks(num_x_blocks, num_y_blocks, numext::mini<int>(num_z_blocks, ceil(numP, block_size.z)));\n\n\n        //cout << \"launching 2D kernel with block_size.x: \" << block_size.x << \" block_size.y: \" << block_size.y  << \" block_size.z: \" << block_size.z << \" num_blocks.x: \" << num_blocks.x << \" num_blocks.y: \" << num_blocks.y << \" num_blocks.z: \" << num_blocks.z << \" maxX: \" << maxX << \" maxY: \" << maxY << \" maxP: \" << maxP << \" shared_mem: \" << shared_mem << \" in stream \" << m_device.stream() << endl;\n\n        const array<Index, 2> indices(m_indices[idxX], m_indices[idxY]);\n        const array<Index, 2> kernel_dims(m_kernelImpl.dimensions()[idxX],\n                                          m_kernelImpl.dimensions()[idxY]);\n        internal::IndexMapper<Index, InputDims, 2, Layout> indexMapper(\n            m_inputImpl.dimensions(), kernel_dims, indices);\n        switch (kernel_size_x) {\n          case 4: {\n            switch (kernel_size_y) {\n              case 7: {\n                LAUNCH_CUDA_KERNEL((EigenConvolutionKernel2D<TensorEvaluator<InputArgType, GpuDevice>, Index, InputDims, 4, 7>), num_blocks, block_size, shared_mem, m_device, m_inputImpl, indexMapper, m_kernel, numP, numX, maxX, numY, maxY, 4, 7, data);\n                break;\n              }\n              default: {\n                LAUNCH_CUDA_KERNEL((EigenConvolutionKernel2D<TensorEvaluator<InputArgType, GpuDevice>, Index, InputDims, 4, Dynamic>), num_blocks, block_size, shared_mem, m_device, m_inputImpl, indexMapper, m_kernel, numP, numX, maxX, numY, maxY, 4, kernel_size_y, data);\n                break;\n              }\n            }\n            break;\n          }\n          case 7: {\n            switch (kernel_size_y) {\n              case 4: {\n                LAUNCH_CUDA_KERNEL((EigenConvolutionKernel2D<TensorEvaluator<InputArgType, GpuDevice>, Index, InputDims, 7, 4>), num_blocks, block_size, shared_mem, m_device, m_inputImpl, indexMapper, m_kernel, numP, numX, maxX, numY, maxY, 7, 4, data);\n                break;\n              }\n              default: {\n                LAUNCH_CUDA_KERNEL((EigenConvolutionKernel2D<TensorEvaluator<InputArgType, GpuDevice>, Index, InputDims, 7, Dynamic>), num_blocks, block_size, shared_mem, m_device, m_inputImpl, indexMapper, m_kernel, numP, numX, maxX, numY, maxY, 7, kernel_size_y, data);\n                break;\n              }\n            }\n            break;\n          }\n          default: {\n            LAUNCH_CUDA_KERNEL((EigenConvolutionKernel2D<TensorEvaluator<InputArgType, GpuDevice>, Index, InputDims, Dynamic, Dynamic>), num_blocks, block_size, shared_mem, m_device, m_inputImpl, indexMapper, m_kernel, numP, numX, maxX, numY, maxY, kernel_size_x, kernel_size_y, data);\n            break;\n          }\n        }\n        break;\n      }\n\n      case 3: {\n        const int idxX =\n            static_cast<int>(Layout) == static_cast<int>(ColMajor) ? 0 : 2;\n        const int idxY =\n            static_cast<int>(Layout) == static_cast<int>(ColMajor) ? 1 : 1;\n        const int idxZ =\n            static_cast<int>(Layout) == static_cast<int>(ColMajor) ? 2 : 0;\n\n        const int kernel_size_x = m_kernelImpl.dimensions()[idxX];\n        const int kernel_size_y = m_kernelImpl.dimensions()[idxY];\n        const int kernel_size_z = m_kernelImpl.dimensions()[idxZ];\n\n        const int numX = dimensions()[m_indices[idxX]];\n        const int numY = dimensions()[m_indices[idxY]];\n        const int numZ = dimensions()[m_indices[idxZ]];\n        const int numP = dimensions().TotalSize() / (numX*numY*numZ);\n\n        const int maxX = numext::mini<int>(128, numext::mini<int>(maxSharedMem / (sizeof(Scalar) * kernel_size_y * kernel_size_z) - kernel_size_x + 1, numX));\n        const int maxY = numext::mini<int>(128, numext::mini<int>(maxSharedMem / (sizeof(Scalar) * (maxX + kernel_size_x - 1) * kernel_size_z) - kernel_size_y + 1, numY));\n        const int maxZ = numext::mini<int>(128, numext::mini<int>(maxSharedMem / (sizeof(Scalar) * (maxX + kernel_size_x - 1) * (maxY + kernel_size_y - 1)) - kernel_size_z + 1, numZ));\n\n        dim3 block_size;\n        block_size.x = numext::mini(32, maxX);\n        block_size.y = numext::mini(32, maxY);\n        block_size.z = numext::mini<int>(1024/(block_size.x*block_size.y), maxZ);\n        dim3 num_blocks(ceil(numX, maxX), ceil(numY, maxY), ceil(numZ, maxZ));\n\n        const int shared_mem = (maxX + kernel_size_x - 1) * (maxY + kernel_size_y - 1) * (maxZ + kernel_size_z - 1) * sizeof(Scalar);\n        assert(shared_mem <= maxSharedMem);\n\n        //cout << \"launching 3D kernel with block_size.x: \" << block_size.x << \" block_size.y: \" << block_size.y  << \" block_size.z: \" << block_size.z << \" num_blocks.x: \" << num_blocks.x << \" num_blocks.y: \" << num_blocks.y << \" num_blocks.z: \" << num_blocks.z  << \" shared_mem: \" << shared_mem << \" in stream \" << m_device.stream() << endl;\n        const array<Index, 3> indices(m_indices[idxX], m_indices[idxY],\n                                      m_indices[idxZ]);\n        const array<Index, 3> kernel_dims(m_kernelImpl.dimensions()[idxX],\n                                          m_kernelImpl.dimensions()[idxY],\n                                          m_kernelImpl.dimensions()[idxZ]);\n        internal::IndexMapper<Index, InputDims, 3, Layout> indexMapper(\n            m_inputImpl.dimensions(), kernel_dims, indices);\n\n        LAUNCH_CUDA_KERNEL((EigenConvolutionKernel3D<TensorEvaluator<InputArgType, GpuDevice>, Index, InputDims>), num_blocks, block_size, shared_mem, m_device, m_inputImpl, indexMapper, m_kernel, numP, numX, maxX, numY, maxY, numZ, maxZ, kernel_size_x, kernel_size_y, kernel_size_z, data);\n        break;\n      }\n\n      default: {\n        EIGEN_STATIC_ASSERT((NumKernelDims >= 1 && NumKernelDims <= 3), THIS_METHOD_IS_ONLY_FOR_OBJECTS_OF_A_SPECIFIC_SIZE);\n      }\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const\n  {\n    eigen_assert(m_buf);\n    eigen_assert(index < m_dimensions.TotalSize());\n    return m_buf[index];\n  }\n\n  template<int LoadMode>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(const Index index) const\n  {\n    eigen_assert(m_buf);\n    eigen_assert(index < m_dimensions.TotalSize());\n    return internal::ploadt<PacketReturnType, LoadMode>(m_buf+index);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost\n  costPerCoeff(bool vectorized) const {\n    // TODO(rmlarsen): FIXME: For now, this is just a copy of the CPU cost\n    // model.\n    const double kernel_size = m_kernelImpl.dimensions().TotalSize();\n    // We ignore the use of fused multiply-add.\n    const double convolve_compute_cost =\n        TensorOpCost::AddCost<Scalar>() + TensorOpCost::MulCost<Scalar>();\n    const double firstIndex_compute_cost =\n        NumDims *\n        (2 * TensorOpCost::AddCost<Index>() + 2 * TensorOpCost::MulCost<Index>() +\n         TensorOpCost::DivCost<Index>());\n    return TensorOpCost(0, 0, firstIndex_compute_cost, vectorized, PacketSize) +\n           kernel_size * (m_inputImpl.costPerCoeff(vectorized) +\n                          m_kernelImpl.costPerCoeff(vectorized) +\n                          TensorOpCost(0, 0, convolve_compute_cost, vectorized,\n                                       PacketSize));\n  }\n\n private:\n  // No assignment (copies are needed by the kernels)\n  TensorEvaluator& operator = (const TensorEvaluator&);\n\n  TensorEvaluator<InputArgType, GpuDevice> m_inputImpl;\n  TensorEvaluator<KernelArgType, GpuDevice> m_kernelImpl;\n  KernelArgType m_kernelArg;\n  Indices m_indices;\n  Dimensions m_dimensions;\n  Scalar* m_buf;\n  const Scalar* m_kernel;\n  bool m_local_kernel;\n\n  const GpuDevice& m_device;\n};\n#endif\n\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_CONVOLUTION_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorCostModel.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Rasmus Munk Larsen <rmlarsen@google.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_COST_MODEL_H\n#define EIGEN_CXX11_TENSOR_TENSOR_COST_MODEL_H\n\nnamespace Eigen {\n\n/** \\class TensorEvaluator\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief A cost model used to limit the number of threads used for evaluating\n  * tensor expression.\n  *\n  */\n\n// Class storing the cost of evaluating a tensor expression in terms of the\n// estimated number of operand bytes loads, bytes stored, and compute cycles.\nclass TensorOpCost {\n public:\n  // TODO(rmlarsen): Fix the scalar op costs in Eigen proper. Even a simple\n  // model based on minimal reciprocal throughput numbers from Intel or\n  // Agner Fog's tables would be better than what is there now.\n  template <typename ArgType>\n  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE int MulCost() {\n    return internal::functor_traits<\n        internal::scalar_product_op<ArgType, ArgType> >::Cost;\n  }\n  template <typename ArgType>\n  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE int AddCost() {\n    return internal::functor_traits<internal::scalar_sum_op<ArgType> >::Cost;\n  }\n  template <typename ArgType>\n  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE int DivCost() {\n    return internal::functor_traits<\n        internal::scalar_quotient_op<ArgType, ArgType> >::Cost;\n  }\n  template <typename ArgType>\n  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE int ModCost() {\n    return internal::functor_traits<internal::scalar_mod_op<ArgType> >::Cost;\n  }\n  template <typename SrcType, typename TargetType>\n  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE int CastCost() {\n    return internal::functor_traits<\n        internal::scalar_cast_op<SrcType, TargetType> >::Cost;\n  }\n\n  EIGEN_DEVICE_FUNC\n  TensorOpCost() : bytes_loaded_(0), bytes_stored_(0), compute_cycles_(0) {}\n  EIGEN_DEVICE_FUNC\n  TensorOpCost(double bytes_loaded, double bytes_stored, double compute_cycles)\n      : bytes_loaded_(bytes_loaded),\n        bytes_stored_(bytes_stored),\n        compute_cycles_(compute_cycles) {}\n\n  EIGEN_DEVICE_FUNC\n  TensorOpCost(double bytes_loaded, double bytes_stored, double compute_cycles,\n               bool vectorized, double packet_size)\n      : bytes_loaded_(bytes_loaded),\n        bytes_stored_(bytes_stored),\n        compute_cycles_(vectorized ? compute_cycles / packet_size\n                                   : compute_cycles) {\n    eigen_assert(bytes_loaded >= 0 && (numext::isfinite)(bytes_loaded));\n    eigen_assert(bytes_stored >= 0 && (numext::isfinite)(bytes_stored));\n    eigen_assert(compute_cycles >= 0 && (numext::isfinite)(compute_cycles));\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double bytes_loaded() const {\n    return bytes_loaded_;\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double bytes_stored() const {\n    return bytes_stored_;\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double compute_cycles() const {\n    return compute_cycles_;\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double total_cost(\n      double load_cost, double store_cost, double compute_cost) const {\n    return load_cost * bytes_loaded_ + store_cost * bytes_stored_ +\n           compute_cost * compute_cycles_;\n  }\n\n  // Drop memory access component. Intended for cases when memory accesses are\n  // sequential or are completely masked by computations.\n  EIGEN_DEVICE_FUNC void dropMemoryCost() {\n    bytes_loaded_ = 0;\n    bytes_stored_ = 0;\n  }\n\n  // TODO(rmlarsen): Define min in terms of total cost, not elementwise.\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost cwiseMin(\n      const TensorOpCost& rhs) const {\n    double bytes_loaded = numext::mini(bytes_loaded_, rhs.bytes_loaded());\n    double bytes_stored = numext::mini(bytes_stored_, rhs.bytes_stored());\n    double compute_cycles = numext::mini(compute_cycles_, rhs.compute_cycles());\n    return TensorOpCost(bytes_loaded, bytes_stored, compute_cycles);\n  }\n\n  // TODO(rmlarsen): Define max in terms of total cost, not elementwise.\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost cwiseMax(\n      const TensorOpCost& rhs) const {\n    double bytes_loaded = numext::maxi(bytes_loaded_, rhs.bytes_loaded());\n    double bytes_stored = numext::maxi(bytes_stored_, rhs.bytes_stored());\n    double compute_cycles = numext::maxi(compute_cycles_, rhs.compute_cycles());\n    return TensorOpCost(bytes_loaded, bytes_stored, compute_cycles);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost& operator+=(\n      const TensorOpCost& rhs) {\n    bytes_loaded_ += rhs.bytes_loaded();\n    bytes_stored_ += rhs.bytes_stored();\n    compute_cycles_ += rhs.compute_cycles();\n    return *this;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost& operator*=(double rhs) {\n    bytes_loaded_ *= rhs;\n    bytes_stored_ *= rhs;\n    compute_cycles_ *= rhs;\n    return *this;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE friend TensorOpCost operator+(\n      TensorOpCost lhs, const TensorOpCost& rhs) {\n    lhs += rhs;\n    return lhs;\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE friend TensorOpCost operator*(\n      TensorOpCost lhs, double rhs) {\n    lhs *= rhs;\n    return lhs;\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE friend TensorOpCost operator*(\n      double lhs, TensorOpCost rhs) {\n    rhs *= lhs;\n    return rhs;\n  }\n\n  friend std::ostream& operator<<(std::ostream& os, const TensorOpCost& tc) {\n    return os << \"[bytes_loaded = \" << tc.bytes_loaded()\n              << \", bytes_stored = \" << tc.bytes_stored()\n              << \", compute_cycles = \" << tc.compute_cycles() << \"]\";\n  }\n\n private:\n  double bytes_loaded_;\n  double bytes_stored_;\n  double compute_cycles_;\n};\n\n// TODO(rmlarsen): Implement a policy that chooses an \"optimal\" number of theads\n// in [1:max_threads] instead of just switching multi-threading off for small\n// work units.\ntemplate <typename Device>\nclass TensorCostModel {\n public:\n  // Scaling from Eigen compute cost to device cycles.\n  static const int kDeviceCyclesPerComputeCycle = 1;\n\n // Costs in device cycles.\n  static const int kStartupCycles = 100000;\n  static const int kPerThreadCycles = 100000;\n  static const int kTaskSize = 40000;\n\n  // Returns the number of threads in [1:max_threads] to use for\n  // evaluating an expression with the given output size and cost per\n  // coefficient.\n  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE int numThreads(\n      double output_size, const TensorOpCost& cost_per_coeff, int max_threads) {\n    double cost = totalCost(output_size, cost_per_coeff);\n    int threads = (cost - kStartupCycles) / kPerThreadCycles + 0.9;\n    return numext::mini(max_threads, numext::maxi(1, threads));\n  }\n\n  // taskSize assesses parallel task size.\n  // Value of 1.0 means ideal parallel task size. Values < 1.0 mean that task\n  // granularity needs to be increased to mitigate parallelization overheads.\n  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double taskSize(\n      double output_size, const TensorOpCost& cost_per_coeff) {\n    return totalCost(output_size, cost_per_coeff) / kTaskSize;\n  }\n\n private:\n  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double totalCost(\n      double output_size, const TensorOpCost& cost_per_coeff) {\n    // Cost of memory fetches from L2 cache. 64 is typical cache line size.\n    // 11 is L2 cache latency on Haswell.\n    // We don't know whether data is in L1, L2 or L3. But we are most interested\n    // in single-threaded computational time around 100us-10ms (smaller time\n    // is too small for parallelization, larger time is not intersting\n    // either because we are probably using all available threads already).\n    // And for the target time range, L2 seems to be what matters. Data set\n    // fitting into L1 is too small to take noticeable time. Data set fitting\n    // only into L3 presumably will take more than 10ms to load and process.\n    const double kLoadCycles = 1.0 / 64 * 11;\n    const double kStoreCycles = 1.0 / 64 * 11;\n    // Scaling from Eigen compute cost to device cycles.\n    return output_size *\n        cost_per_coeff.total_cost(kLoadCycles, kStoreCycles,\n                                  kDeviceCyclesPerComputeCycle);\n  }\n};\n\n}  // namespace Eigen\n\n#endif  // EIGEN_CXX11_TENSOR_TENSOR_COST_MODEL_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorCustomOp.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_CUSTOM_OP_H\n#define EIGEN_CXX11_TENSOR_TENSOR_CUSTOM_OP_H\n\nnamespace Eigen {\n\n/** \\class TensorCustomUnaryOp\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief Tensor custom class.\n  *\n  *\n  */\nnamespace internal {\ntemplate<typename CustomUnaryFunc, typename XprType>\nstruct traits<TensorCustomUnaryOp<CustomUnaryFunc, XprType> >\n{\n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::StorageKind StorageKind;\n  typedef typename XprType::Index Index;\n  typedef typename XprType::Nested Nested;\n  typedef typename remove_reference<Nested>::type _Nested;\n  static const int NumDimensions = traits<XprType>::NumDimensions;\n  static const int Layout = traits<XprType>::Layout;\n};\n\ntemplate<typename CustomUnaryFunc, typename XprType>\nstruct eval<TensorCustomUnaryOp<CustomUnaryFunc, XprType>, Eigen::Dense>\n{\n  typedef const TensorCustomUnaryOp<CustomUnaryFunc, XprType>& type;\n};\n\ntemplate<typename CustomUnaryFunc, typename XprType>\nstruct nested<TensorCustomUnaryOp<CustomUnaryFunc, XprType> >\n{\n  typedef TensorCustomUnaryOp<CustomUnaryFunc, XprType> type;\n};\n\n}  // end namespace internal\n\n\n\ntemplate<typename CustomUnaryFunc, typename XprType>\nclass TensorCustomUnaryOp : public TensorBase<TensorCustomUnaryOp<CustomUnaryFunc, XprType>, ReadOnlyAccessors>\n{\n  public:\n  typedef typename internal::traits<TensorCustomUnaryOp>::Scalar Scalar;\n  typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename internal::nested<TensorCustomUnaryOp>::type Nested;\n  typedef typename internal::traits<TensorCustomUnaryOp>::StorageKind StorageKind;\n  typedef typename internal::traits<TensorCustomUnaryOp>::Index Index;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorCustomUnaryOp(const XprType& expr, const CustomUnaryFunc& func)\n      : m_expr(expr), m_func(func) {}\n\n  EIGEN_DEVICE_FUNC\n  const CustomUnaryFunc& func() const { return m_func; }\n\n  EIGEN_DEVICE_FUNC\n  const typename internal::remove_all<typename XprType::Nested>::type&\n  expression() const { return m_expr; }\n\n  protected:\n    typename XprType::Nested m_expr;\n    const CustomUnaryFunc m_func;\n};\n\n\n// Eval as rvalue\ntemplate<typename CustomUnaryFunc, typename XprType, typename Device>\nstruct TensorEvaluator<const TensorCustomUnaryOp<CustomUnaryFunc, XprType>, Device>\n{\n  typedef TensorCustomUnaryOp<CustomUnaryFunc, XprType> ArgType;\n  typedef typename internal::traits<ArgType>::Index Index;\n  static const int NumDims = internal::traits<ArgType>::NumDimensions;\n  typedef DSizes<Index, NumDims> Dimensions;\n  typedef typename internal::remove_const<typename ArgType::Scalar>::type Scalar;\n  typedef typename internal::remove_const<typename XprType::CoeffReturnType>::type CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  static const int PacketSize = internal::unpacket_traits<PacketReturnType>::size;\n\n  enum {\n    IsAligned = false,\n    PacketAccess = (internal::packet_traits<Scalar>::size > 1),\n    BlockAccess = false,\n    Layout = TensorEvaluator<XprType, Device>::Layout,\n    CoordAccess = false,  // to be implemented\n    RawAccess = false\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const ArgType& op, const Device& device)\n      : m_op(op), m_device(device), m_result(NULL)\n  {\n    m_dimensions = op.func().dimensions(op.expression());\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(CoeffReturnType* data) {\n    if (data) {\n      evalTo(data);\n      return false;\n    } else {\n      m_result = static_cast<CoeffReturnType*>(\n          m_device.allocate(dimensions().TotalSize() * sizeof(Scalar)));\n      evalTo(m_result);\n      return true;\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {\n    if (m_result != NULL) {\n      m_device.deallocate(m_result);\n      m_result = NULL;\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const {\n    return m_result[index];\n  }\n\n  template<int LoadMode>\n  EIGEN_DEVICE_FUNC PacketReturnType packet(Index index) const {\n    return internal::ploadt<PacketReturnType, LoadMode>(m_result + index);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {\n    // TODO(rmlarsen): Extend CustomOp API to return its cost estimate.\n    return TensorOpCost(sizeof(CoeffReturnType), 0, 0, vectorized, PacketSize);\n  }\n\n  EIGEN_DEVICE_FUNC CoeffReturnType* data() const { return m_result; }\n\n protected:\n  EIGEN_DEVICE_FUNC void evalTo(Scalar* data) {\n    TensorMap<Tensor<CoeffReturnType, NumDims, Layout, Index> > result(\n        data, m_dimensions);\n    m_op.func().eval(m_op.expression(), result, m_device);\n  }\n\n  Dimensions m_dimensions;\n  const ArgType m_op;\n  const Device& m_device;\n  CoeffReturnType* m_result;\n};\n\n\n\n/** \\class TensorCustomBinaryOp\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief Tensor custom class.\n  *\n  *\n  */\nnamespace internal {\ntemplate<typename CustomBinaryFunc, typename LhsXprType, typename RhsXprType>\nstruct traits<TensorCustomBinaryOp<CustomBinaryFunc, LhsXprType, RhsXprType> >\n{\n  typedef typename internal::promote_storage_type<typename LhsXprType::Scalar,\n                                                  typename RhsXprType::Scalar>::ret Scalar;\n  typedef typename internal::promote_storage_type<typename LhsXprType::CoeffReturnType,\n                                                  typename RhsXprType::CoeffReturnType>::ret CoeffReturnType;\n  typedef typename promote_storage_type<typename traits<LhsXprType>::StorageKind,\n                                        typename traits<RhsXprType>::StorageKind>::ret StorageKind;\n  typedef typename promote_index_type<typename traits<LhsXprType>::Index,\n                                      typename traits<RhsXprType>::Index>::type Index;\n  typedef typename LhsXprType::Nested LhsNested;\n  typedef typename RhsXprType::Nested RhsNested;\n  typedef typename remove_reference<LhsNested>::type _LhsNested;\n  typedef typename remove_reference<RhsNested>::type _RhsNested;\n  static const int NumDimensions = traits<LhsXprType>::NumDimensions;\n  static const int Layout = traits<LhsXprType>::Layout;\n};\n\ntemplate<typename CustomBinaryFunc, typename LhsXprType, typename RhsXprType>\nstruct eval<TensorCustomBinaryOp<CustomBinaryFunc, LhsXprType, RhsXprType>, Eigen::Dense>\n{\n  typedef const TensorCustomBinaryOp<CustomBinaryFunc, LhsXprType, RhsXprType>& type;\n};\n\ntemplate<typename CustomBinaryFunc, typename LhsXprType, typename RhsXprType>\nstruct nested<TensorCustomBinaryOp<CustomBinaryFunc, LhsXprType, RhsXprType> >\n{\n  typedef TensorCustomBinaryOp<CustomBinaryFunc, LhsXprType, RhsXprType> type;\n};\n\n}  // end namespace internal\n\n\n\ntemplate<typename CustomBinaryFunc, typename LhsXprType, typename RhsXprType>\nclass TensorCustomBinaryOp : public TensorBase<TensorCustomBinaryOp<CustomBinaryFunc, LhsXprType, RhsXprType>, ReadOnlyAccessors>\n{\n  public:\n  typedef typename internal::traits<TensorCustomBinaryOp>::Scalar Scalar;\n  typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;\n  typedef typename internal::traits<TensorCustomBinaryOp>::CoeffReturnType CoeffReturnType;\n  typedef typename internal::nested<TensorCustomBinaryOp>::type Nested;\n  typedef typename internal::traits<TensorCustomBinaryOp>::StorageKind StorageKind;\n  typedef typename internal::traits<TensorCustomBinaryOp>::Index Index;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorCustomBinaryOp(const LhsXprType& lhs, const RhsXprType& rhs, const CustomBinaryFunc& func)\n\n      : m_lhs_xpr(lhs), m_rhs_xpr(rhs), m_func(func) {}\n\n  EIGEN_DEVICE_FUNC\n  const CustomBinaryFunc& func() const { return m_func; }\n\n  EIGEN_DEVICE_FUNC\n  const typename internal::remove_all<typename LhsXprType::Nested>::type&\n  lhsExpression() const { return m_lhs_xpr; }\n\n  EIGEN_DEVICE_FUNC\n  const typename internal::remove_all<typename RhsXprType::Nested>::type&\n  rhsExpression() const { return m_rhs_xpr; }\n\n  protected:\n    typename LhsXprType::Nested m_lhs_xpr;\n    typename RhsXprType::Nested m_rhs_xpr;\n    const CustomBinaryFunc m_func;\n};\n\n\n// Eval as rvalue\ntemplate<typename CustomBinaryFunc, typename LhsXprType, typename RhsXprType, typename Device>\nstruct TensorEvaluator<const TensorCustomBinaryOp<CustomBinaryFunc, LhsXprType, RhsXprType>, Device>\n{\n  typedef TensorCustomBinaryOp<CustomBinaryFunc, LhsXprType, RhsXprType> XprType;\n  typedef typename internal::traits<XprType>::Index Index;\n  static const int NumDims = internal::traits<XprType>::NumDimensions;\n  typedef DSizes<Index, NumDims> Dimensions;\n  typedef typename XprType::Scalar Scalar;\n  typedef typename internal::remove_const<typename XprType::CoeffReturnType>::type CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  static const int PacketSize = internal::unpacket_traits<PacketReturnType>::size;\n\n  enum {\n    IsAligned = false,\n    PacketAccess = (internal::packet_traits<Scalar>::size > 1),\n    BlockAccess = false,\n    Layout = TensorEvaluator<LhsXprType, Device>::Layout,\n    CoordAccess = false,  // to be implemented\n    RawAccess = false\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)\n      : m_op(op), m_device(device), m_result(NULL)\n  {\n    m_dimensions = op.func().dimensions(op.lhsExpression(), op.rhsExpression());\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(CoeffReturnType* data) {\n    if (data) {\n      evalTo(data);\n      return false;\n    } else {\n      m_result = static_cast<Scalar *>(m_device.allocate(dimensions().TotalSize() * sizeof(Scalar)));\n      evalTo(m_result);\n      return true;\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {\n    if (m_result != NULL) {\n      m_device.deallocate(m_result);\n      m_result = NULL;\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const {\n    return m_result[index];\n  }\n\n  template<int LoadMode>\n  EIGEN_DEVICE_FUNC PacketReturnType packet(Index index) const {\n    return internal::ploadt<PacketReturnType, LoadMode>(m_result + index);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {\n    // TODO(rmlarsen): Extend CustomOp API to return its cost estimate.\n    return TensorOpCost(sizeof(CoeffReturnType), 0, 0, vectorized, PacketSize);\n  }\n\n  EIGEN_DEVICE_FUNC CoeffReturnType* data() const { return m_result; }\n\n protected:\n  EIGEN_DEVICE_FUNC void evalTo(Scalar* data) {\n    TensorMap<Tensor<Scalar, NumDims, Layout> > result(data, m_dimensions);\n    m_op.func().eval(m_op.lhsExpression(), m_op.rhsExpression(), result, m_device);\n  }\n\n  Dimensions m_dimensions;\n  const XprType m_op;\n  const Device& m_device;\n  CoeffReturnType* m_result;\n};\n\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_CUSTOM_OP_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorDevice.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_DEVICE_H\n#define EIGEN_CXX11_TENSOR_TENSOR_DEVICE_H\n\nnamespace Eigen {\n\n/** \\class TensorDevice\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief Pseudo expression providing an operator = that will evaluate its argument\n  * on the specified computing 'device' (GPU, thread pool, ...)\n  *\n  * Example:\n  *    C.device(EIGEN_GPU) = A + B;\n  *\n  * Todo: operator *= and /=.\n  */\n\ntemplate <typename ExpressionType, typename DeviceType> class TensorDevice {\n  public:\n    TensorDevice(const DeviceType& device, ExpressionType& expression) : m_device(device), m_expression(expression) {}\n\n    template<typename OtherDerived>\n    EIGEN_STRONG_INLINE TensorDevice& operator=(const OtherDerived& other) {\n      typedef TensorAssignOp<ExpressionType, const OtherDerived> Assign;\n      Assign assign(m_expression, other);\n      internal::TensorExecutor<const Assign, DeviceType>::run(assign, m_device);\n      return *this;\n    }\n\n    template<typename OtherDerived>\n    EIGEN_STRONG_INLINE TensorDevice& operator+=(const OtherDerived& other) {\n      typedef typename OtherDerived::Scalar Scalar;\n      typedef TensorCwiseBinaryOp<internal::scalar_sum_op<Scalar>, const ExpressionType, const OtherDerived> Sum;\n      Sum sum(m_expression, other);\n      typedef TensorAssignOp<ExpressionType, const Sum> Assign;\n      Assign assign(m_expression, sum);\n      internal::TensorExecutor<const Assign, DeviceType>::run(assign, m_device);\n      return *this;\n    }\n\n    template<typename OtherDerived>\n    EIGEN_STRONG_INLINE TensorDevice& operator-=(const OtherDerived& other) {\n      typedef typename OtherDerived::Scalar Scalar;\n      typedef TensorCwiseBinaryOp<internal::scalar_difference_op<Scalar>, const ExpressionType, const OtherDerived> Difference;\n      Difference difference(m_expression, other);\n      typedef TensorAssignOp<ExpressionType, const Difference> Assign;\n      Assign assign(m_expression, difference);\n      internal::TensorExecutor<const Assign, DeviceType>::run(assign, m_device);\n      return *this;\n    }\n\n  protected:\n    const DeviceType& m_device;\n    ExpressionType& m_expression;\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_DEVICE_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceCuda.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#if defined(EIGEN_USE_GPU) && !defined(EIGEN_CXX11_TENSOR_TENSOR_DEVICE_CUDA_H)\n#define EIGEN_CXX11_TENSOR_TENSOR_DEVICE_CUDA_H\n\nnamespace Eigen {\n\nstatic const int kCudaScratchSize = 1024;\n\n// This defines an interface that GPUDevice can take to use\n// CUDA streams underneath.\nclass StreamInterface {\n public:\n  virtual ~StreamInterface() {}\n\n  virtual const cudaStream_t& stream() const = 0;\n  virtual const cudaDeviceProp& deviceProperties() const = 0;\n\n  // Allocate memory on the actual device where the computation will run\n  virtual void* allocate(size_t num_bytes) const = 0;\n  virtual void deallocate(void* buffer) const = 0;\n\n  // Return a scratchpad buffer of size 1k\n  virtual void* scratchpad() const = 0;\n\n  // Return a semaphore. The semaphore is initially initialized to 0, and\n  // each kernel using it is responsible for resetting to 0 upon completion\n  // to maintain the invariant that the semaphore is always equal to 0 upon\n  // each kernel start.\n  virtual unsigned int* semaphore() const = 0;\n};\n\nstatic cudaDeviceProp* m_deviceProperties;\nstatic bool m_devicePropInitialized = false;\n\nstatic void initializeDeviceProp() {\n  if (!m_devicePropInitialized) {\n    // Attempts to ensure proper behavior in the case of multiple threads\n    // calling this function simultaneously. This would be trivial to\n    // implement if we could use std::mutex, but unfortunately mutex don't\n    // compile with nvcc, so we resort to atomics and thread fences instead.\n    // Note that if the caller uses a compiler that doesn't support c++11 we\n    // can't ensure that the initialization is thread safe.\n#if __cplusplus >= 201103L\n    static std::atomic<bool> first(true);\n    if (first.exchange(false)) {\n#else\n    static bool first = true;\n    if (first) {\n      first = false;\n#endif\n      // We're the first thread to reach this point.\n      int num_devices;\n      cudaError_t status = cudaGetDeviceCount(&num_devices);\n      if (status != cudaSuccess) {\n        std::cerr << \"Failed to get the number of CUDA devices: \"\n                  << cudaGetErrorString(status)\n                  << std::endl;\n        assert(status == cudaSuccess);\n      }\n      m_deviceProperties = new cudaDeviceProp[num_devices];\n      for (int i = 0; i < num_devices; ++i) {\n        status = cudaGetDeviceProperties(&m_deviceProperties[i], i);\n        if (status != cudaSuccess) {\n          std::cerr << \"Failed to initialize CUDA device #\"\n                    << i\n                    << \": \"\n                    << cudaGetErrorString(status)\n                    << std::endl;\n          assert(status == cudaSuccess);\n        }\n      }\n\n#if __cplusplus >= 201103L\n      std::atomic_thread_fence(std::memory_order_release);\n#endif\n      m_devicePropInitialized = true;\n    } else {\n      // Wait for the other thread to inititialize the properties.\n      while (!m_devicePropInitialized) {\n#if __cplusplus >= 201103L\n        std::atomic_thread_fence(std::memory_order_acquire);\n#endif\n        sleep(1);\n      }\n    }\n  }\n}\n\nstatic const cudaStream_t default_stream = cudaStreamDefault;\n\nclass CudaStreamDevice : public StreamInterface {\n public:\n  // Use the default stream on the current device\n  CudaStreamDevice() : stream_(&default_stream), scratch_(NULL), semaphore_(NULL) {\n    cudaGetDevice(&device_);\n    initializeDeviceProp();\n  }\n  // Use the default stream on the specified device\n  CudaStreamDevice(int device) : stream_(&default_stream), device_(device), scratch_(NULL), semaphore_(NULL) {\n    initializeDeviceProp();\n  }\n  // Use the specified stream. Note that it's the\n  // caller responsibility to ensure that the stream can run on\n  // the specified device. If no device is specified the code\n  // assumes that the stream is associated to the current gpu device.\n  CudaStreamDevice(const cudaStream_t* stream, int device = -1)\n      : stream_(stream), device_(device), scratch_(NULL), semaphore_(NULL) {\n    if (device < 0) {\n      cudaGetDevice(&device_);\n    } else {\n      int num_devices;\n      cudaError_t err = cudaGetDeviceCount(&num_devices);\n      EIGEN_UNUSED_VARIABLE(err)\n      assert(err == cudaSuccess);\n      assert(device < num_devices);\n      device_ = device;\n    }\n    initializeDeviceProp();\n  }\n\n  virtual ~CudaStreamDevice() {\n    if (scratch_) {\n      deallocate(scratch_);\n    }\n  }\n\n  const cudaStream_t& stream() const { return *stream_; }\n  const cudaDeviceProp& deviceProperties() const {\n    return m_deviceProperties[device_];\n  }\n  virtual void* allocate(size_t num_bytes) const {\n    cudaError_t err = cudaSetDevice(device_);\n    EIGEN_UNUSED_VARIABLE(err)\n    assert(err == cudaSuccess);\n    void* result;\n    err = cudaMalloc(&result, num_bytes);\n    assert(err == cudaSuccess);\n    assert(result != NULL);\n    return result;\n  }\n  virtual void deallocate(void* buffer) const {\n    cudaError_t err = cudaSetDevice(device_);\n    EIGEN_UNUSED_VARIABLE(err)\n    assert(err == cudaSuccess);\n    assert(buffer != NULL);\n    err = cudaFree(buffer);\n    assert(err == cudaSuccess);\n  }\n\n  virtual void* scratchpad() const {\n    if (scratch_ == NULL) {\n      scratch_ = allocate(kCudaScratchSize + sizeof(unsigned int));\n    }\n    return scratch_;\n  }\n\n  virtual unsigned int* semaphore() const {\n    if (semaphore_ == NULL) {\n      char* scratch = static_cast<char*>(scratchpad()) + kCudaScratchSize;\n      semaphore_ = reinterpret_cast<unsigned int*>(scratch);\n      cudaError_t err = cudaMemsetAsync(semaphore_, 0, sizeof(unsigned int), *stream_);\n      EIGEN_UNUSED_VARIABLE(err)\n      assert(err == cudaSuccess);\n    }\n    return semaphore_;\n  }\n\n private:\n  const cudaStream_t* stream_;\n  int device_;\n  mutable void* scratch_;\n  mutable unsigned int* semaphore_;\n};\n\nstruct GpuDevice {\n  // The StreamInterface is not owned: the caller is\n  // responsible for its initialization and eventual destruction.\n  explicit GpuDevice(const StreamInterface* stream) : stream_(stream), max_blocks_(INT_MAX) {\n    eigen_assert(stream);\n  }\n  explicit GpuDevice(const StreamInterface* stream, int num_blocks) : stream_(stream), max_blocks_(num_blocks) {\n    eigen_assert(stream);\n  }\n  // TODO(bsteiner): This is an internal API, we should not expose it.\n  EIGEN_STRONG_INLINE const cudaStream_t& stream() const {\n    return stream_->stream();\n  }\n\n  EIGEN_STRONG_INLINE void* allocate(size_t num_bytes) const {\n    return stream_->allocate(num_bytes);\n  }\n\n  EIGEN_STRONG_INLINE void deallocate(void* buffer) const {\n    stream_->deallocate(buffer);\n  }\n\n  EIGEN_STRONG_INLINE void* scratchpad() const {\n    return stream_->scratchpad();\n  }\n\n  EIGEN_STRONG_INLINE unsigned int* semaphore() const {\n    return stream_->semaphore();\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void memcpy(void* dst, const void* src, size_t n) const {\n#ifndef __CUDA_ARCH__\n    cudaError_t err = cudaMemcpyAsync(dst, src, n, cudaMemcpyDeviceToDevice,\n                                      stream_->stream());\n    EIGEN_UNUSED_VARIABLE(err)\n    assert(err == cudaSuccess);\n#else\n  eigen_assert(false && \"The default device should be used instead to generate kernel code\");\n#endif\n  }\n\n  EIGEN_STRONG_INLINE void memcpyHostToDevice(void* dst, const void* src, size_t n) const {\n    cudaError_t err =\n        cudaMemcpyAsync(dst, src, n, cudaMemcpyHostToDevice, stream_->stream());\n    EIGEN_UNUSED_VARIABLE(err)\n    assert(err == cudaSuccess);\n  }\n\n  EIGEN_STRONG_INLINE void memcpyDeviceToHost(void* dst, const void* src, size_t n) const {\n    cudaError_t err =\n        cudaMemcpyAsync(dst, src, n, cudaMemcpyDeviceToHost, stream_->stream());\n    EIGEN_UNUSED_VARIABLE(err)\n    assert(err == cudaSuccess);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void memset(void* buffer, int c, size_t n) const {\n#ifndef __CUDA_ARCH__\n    cudaError_t err = cudaMemsetAsync(buffer, c, n, stream_->stream());\n    EIGEN_UNUSED_VARIABLE(err)\n    assert(err == cudaSuccess);\n#else\n  eigen_assert(false && \"The default device should be used instead to generate kernel code\");\n#endif\n  }\n\n  EIGEN_STRONG_INLINE size_t numThreads() const {\n    // FIXME\n    return 32;\n  }\n\n  EIGEN_STRONG_INLINE size_t firstLevelCacheSize() const {\n    // FIXME\n    return 48*1024;\n  }\n\n  EIGEN_STRONG_INLINE size_t lastLevelCacheSize() const {\n    // We won't try to take advantage of the l2 cache for the time being, and\n    // there is no l3 cache on cuda devices.\n    return firstLevelCacheSize();\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void synchronize() const {\n#if defined(__CUDACC__) && !defined(__CUDA_ARCH__)\n    cudaError_t err = cudaStreamSynchronize(stream_->stream());\n    if (err != cudaSuccess) {\n      std::cerr << \"Error detected in CUDA stream: \"\n                << cudaGetErrorString(err)\n                << std::endl;\n      assert(err == cudaSuccess);\n    }\n#else\n    assert(false && \"The default device should be used instead to generate kernel code\");\n#endif\n  }\n\n  EIGEN_STRONG_INLINE int getNumCudaMultiProcessors() const {\n    return stream_->deviceProperties().multiProcessorCount;\n  }\n  EIGEN_STRONG_INLINE int maxCudaThreadsPerBlock() const {\n    return stream_->deviceProperties().maxThreadsPerBlock;\n  }\n  EIGEN_STRONG_INLINE int maxCudaThreadsPerMultiProcessor() const {\n    return stream_->deviceProperties().maxThreadsPerMultiProcessor;\n  }\n  EIGEN_STRONG_INLINE int sharedMemPerBlock() const {\n    return stream_->deviceProperties().sharedMemPerBlock;\n  }\n  EIGEN_STRONG_INLINE int majorDeviceVersion() const {\n    return stream_->deviceProperties().major;\n  }\n  EIGEN_STRONG_INLINE int minorDeviceVersion() const {\n    return stream_->deviceProperties().minor;\n  }\n\n  EIGEN_STRONG_INLINE int maxBlocks() const {\n    return max_blocks_;\n  }\n\n  // This function checks if the CUDA runtime recorded an error for the\n  // underlying stream device.\n  inline bool ok() const {\n#ifdef __CUDACC__\n    cudaError_t error = cudaStreamQuery(stream_->stream());\n    return (error == cudaSuccess) || (error == cudaErrorNotReady);\n#else\n    return false;\n#endif\n  }\n\n private:\n  const StreamInterface* stream_;\n  int max_blocks_;\n};\n\n#define LAUNCH_CUDA_KERNEL(kernel, gridsize, blocksize, sharedmem, device, ...)             \\\n  (kernel) <<< (gridsize), (blocksize), (sharedmem), (device).stream() >>> (__VA_ARGS__);   \\\n  assert(cudaGetLastError() == cudaSuccess);\n\n\n// FIXME: Should be device and kernel specific.\n#ifdef __CUDACC__\nstatic EIGEN_DEVICE_FUNC inline void setCudaSharedMemConfig(cudaSharedMemConfig config) {\n#ifndef __CUDA_ARCH__\n  cudaError_t status = cudaDeviceSetSharedMemConfig(config);\n  EIGEN_UNUSED_VARIABLE(status)\n  assert(status == cudaSuccess);\n#else\n  EIGEN_UNUSED_VARIABLE(config)\n#endif\n}\n#endif\n\n}  // end namespace Eigen\n\n#endif  // EIGEN_CXX11_TENSOR_TENSOR_DEVICE_CUDA_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceDefault.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_DEVICE_DEFAULT_H\n#define EIGEN_CXX11_TENSOR_TENSOR_DEVICE_DEFAULT_H\n\n\nnamespace Eigen {\n\n// Default device for the machine (typically a single cpu core)\nstruct DefaultDevice {\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void* allocate(size_t num_bytes) const {\n    return internal::aligned_malloc(num_bytes);\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void deallocate(void* buffer) const {\n    internal::aligned_free(buffer);\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void memcpy(void* dst, const void* src, size_t n) const {\n    ::memcpy(dst, src, n);\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void memcpyHostToDevice(void* dst, const void* src, size_t n) const {\n    memcpy(dst, src, n);\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void memcpyDeviceToHost(void* dst, const void* src, size_t n) const {\n    memcpy(dst, src, n);\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void memset(void* buffer, int c, size_t n) const {\n    ::memset(buffer, c, n);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE size_t numThreads() const {\n#ifndef __CUDA_ARCH__\n    // Running on the host CPU\n    return 1;\n#else\n    // Running on a CUDA device\n    return 32;\n#endif\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE size_t firstLevelCacheSize() const {\n#ifndef __CUDA_ARCH__\n    // Running on the host CPU\n    return l1CacheSize();\n#else\n    // Running on a CUDA device, return the amount of shared memory available.\n    return 48*1024;\n#endif\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE size_t lastLevelCacheSize() const {\n#ifndef __CUDA_ARCH__\n    // Running single threaded on the host CPU\n    return l3CacheSize();\n#else\n    // Running on a CUDA device\n    return firstLevelCacheSize();\n#endif\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE int majorDeviceVersion() const {\n#ifndef __CUDA_ARCH__\n    // Running single threaded on the host CPU\n    // Should return an enum that encodes the ISA supported by the CPU\n    return 1;\n#else\n    // Running on a CUDA device\n    return __CUDA_ARCH__ / 100;\n#endif\n  }\n};\n\n}  // namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_DEVICE_DEFAULT_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceSycl.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Mehdi Goli    Codeplay Software Ltd.\n// Ralph Potter  Codeplay Software Ltd.\n// Luke Iwanski  Codeplay Software Ltd.\n// Contact: <eigen@codeplay.com>\n// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>\n\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#if defined(EIGEN_USE_SYCL) && !defined(EIGEN_CXX11_TENSOR_TENSOR_DEVICE_SYCL_H)\n#define EIGEN_CXX11_TENSOR_TENSOR_DEVICE_SYCL_H\n\nnamespace Eigen {\nstruct SyclDevice {\n  /// class members\n  /// sycl queue\n  mutable cl::sycl::queue m_queue;\n  /// std::map is the container used to make sure that we create only one buffer\n  /// per pointer. The lifespan of the buffer now depends on the lifespan of SyclDevice.\n  /// If a non-read-only pointer is needed to be accessed on the host we should manually deallocate it.\n  mutable std::map<const void *, std::shared_ptr<void>> buffer_map;\n  /// creating device by using selector\n  template<typename dev_Selector> SyclDevice(dev_Selector s)\n  :\n#ifdef EIGEN_EXCEPTIONS\n  m_queue(cl::sycl::queue(s, [=](cl::sycl::exception_list l) {\n    for (const auto& e : l) {\n      try {\n        std::rethrow_exception(e);\n      } catch (cl::sycl::exception e) {\n          std::cout << e.what() << std::endl;\n        }\n    }\n  }))\n#else\n  m_queue(cl::sycl::queue(s))\n#endif\n  {}\n  // destructor\n  ~SyclDevice() { deallocate_all(); }\n\n  template <typename T> void deallocate(T *p) const {\n    auto it = buffer_map.find(p);\n    if (it != buffer_map.end()) {\n      buffer_map.erase(it);\n      internal::aligned_free(p);\n    }\n  }\n  void deallocate_all() const {\n    std::map<const void *, std::shared_ptr<void>>::iterator it=buffer_map.begin();\n    while (it!=buffer_map.end()) {\n      auto p=it->first;\n      buffer_map.erase(it);\n      internal::aligned_free(const_cast<void*>(p));\n      it=buffer_map.begin();\n    }\n    buffer_map.clear();\n  }\n\n  /// creation of sycl accessor for a buffer. This function first tries to find\n  /// the buffer in the buffer_map. If found it gets the accessor from it, if not,\n  ///the function then adds an entry by creating a sycl buffer for that particular pointer.\n  template <cl::sycl::access::mode AcMd, typename T> inline cl::sycl::accessor<T, 1, AcMd, cl::sycl::access::target::global_buffer>\n  get_sycl_accessor(size_t num_bytes, cl::sycl::handler &cgh, const T * ptr) const {\n    return (get_sycl_buffer<T>(num_bytes, ptr)->template get_access<AcMd, cl::sycl::access::target::global_buffer>(cgh));\n  }\n\n  template<typename T> inline  std::pair<std::map<const void *, std::shared_ptr<void>>::iterator,bool> add_sycl_buffer(const T *ptr, size_t num_bytes) const {\n    using Type = cl::sycl::buffer<T, 1>;\n    std::pair<std::map<const void *, std::shared_ptr<void>>::iterator,bool> ret = buffer_map.insert(std::pair<const void *, std::shared_ptr<void>>(ptr, std::shared_ptr<void>(new Type(cl::sycl::range<1>(num_bytes)),\n      [](void *dataMem) { delete static_cast<Type*>(dataMem); })));\n    (static_cast<Type*>(buffer_map.at(ptr).get()))->set_final_data(nullptr);\n    return ret;\n  }\n\n  template <typename T> inline cl::sycl::buffer<T, 1>* get_sycl_buffer(size_t num_bytes,const T * ptr) const {\n    return static_cast<cl::sycl::buffer<T, 1>*>(add_sycl_buffer(ptr, num_bytes).first->second.get());\n  }\n\n  /// allocating memory on the cpu\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void *allocate(size_t) const {\n    return internal::aligned_malloc(8);\n  }\n\n  // some runtime conditions that can be applied here\n  bool isDeviceSuitable() const { return true; }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void memcpy(void *dst, const void *src, size_t n) const {\n    ::memcpy(dst, src, n);\n  }\n\n  template<typename T> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void memcpyHostToDevice(T *dst, const T *src, size_t n) const {\n    auto host_acc= (static_cast<cl::sycl::buffer<T, 1>*>(add_sycl_buffer(dst, n).first->second.get()))-> template get_access<cl::sycl::access::mode::discard_write, cl::sycl::access::target::host_buffer>();\n    memcpy(host_acc.get_pointer(), src, n);\n  }\n /// whith the current implementation of sycl, the data is copied twice from device to host. This will be fixed soon.\n  template<typename T> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void memcpyDeviceToHost(T *dst, const T *src, size_t n) const {\n    auto it = buffer_map.find(src);\n    if (it != buffer_map.end()) {\n      auto host_acc= (static_cast<cl::sycl::buffer<T, 1>*>(it->second.get()))-> template get_access<cl::sycl::access::mode::read, cl::sycl::access::target::host_buffer>();\n      memcpy(dst,host_acc.get_pointer(),  n);\n    } else{\n      eigen_assert(\"no device memory found. The memory might be destroyed before creation\");\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void memset(void *buffer, int c, size_t n) const {\n    ::memset(buffer, c, n);\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE int majorDeviceVersion() const {\n  return 1;\n  }\n};\n\n}  // end namespace Eigen\n\n#endif  // EIGEN_CXX11_TENSOR_TENSOR_DEVICE_SYCL_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceThreadPool.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#if defined(EIGEN_USE_THREADS) && !defined(EIGEN_CXX11_TENSOR_TENSOR_DEVICE_THREAD_POOL_H)\n#define EIGEN_CXX11_TENSOR_TENSOR_DEVICE_THREAD_POOL_H\n\nnamespace Eigen {\n\n// Use the SimpleThreadPool by default. We'll switch to the new non blocking\n// thread pool later.\n#ifndef EIGEN_USE_SIMPLE_THREAD_POOL\ntemplate <typename Env> using ThreadPoolTempl = NonBlockingThreadPoolTempl<Env>;\ntypedef NonBlockingThreadPool ThreadPool;\n#else\ntemplate <typename Env> using ThreadPoolTempl = SimpleThreadPoolTempl<Env>;\ntypedef SimpleThreadPool ThreadPool;\n#endif\n\n\n// Barrier is an object that allows one or more threads to wait until\n// Notify has been called a specified number of times.\nclass Barrier {\n public:\n  Barrier(unsigned int count) : state_(count << 1), notified_(false) {\n    eigen_assert(((count << 1) >> 1) == count);\n  }\n  ~Barrier() {\n    eigen_assert((state_>>1) == 0);\n  }\n\n  void Notify() {\n    unsigned int v = state_.fetch_sub(2, std::memory_order_acq_rel) - 2;\n    if (v != 1) {\n      eigen_assert(((v + 2) & ~1) != 0);\n      return;  // either count has not dropped to 0, or waiter is not waiting\n    }\n    std::unique_lock<std::mutex> l(mu_);\n    eigen_assert(!notified_);\n    notified_ = true;\n    cv_.notify_all();\n  }\n\n  void Wait() {\n    unsigned int v = state_.fetch_or(1, std::memory_order_acq_rel);\n    if ((v >> 1) == 0) return;\n    std::unique_lock<std::mutex> l(mu_);\n    while (!notified_) {\n      cv_.wait(l);\n    }\n  }\n\n private:\n  std::mutex mu_;\n  std::condition_variable cv_;\n  std::atomic<unsigned int> state_;  // low bit is waiter flag\n  bool notified_;\n};\n\n\n// Notification is an object that allows a user to to wait for another\n// thread to signal a notification that an event has occurred.\n//\n// Multiple threads can wait on the same Notification object,\n// but only one caller must call Notify() on the object.\nstruct Notification : Barrier {\n  Notification() : Barrier(1) {};\n};\n\n\n// Runs an arbitrary function and then calls Notify() on the passed in\n// Notification.\ntemplate <typename Function, typename... Args> struct FunctionWrapperWithNotification\n{\n  static void run(Notification* n, Function f, Args... args) {\n    f(args...);\n    if (n) {\n      n->Notify();\n    }\n  }\n};\n\ntemplate <typename Function, typename... Args> struct FunctionWrapperWithBarrier\n{\n  static void run(Barrier* b, Function f, Args... args) {\n    f(args...);\n    if (b) {\n      b->Notify();\n    }\n  }\n};\n\ntemplate <typename SyncType>\nstatic EIGEN_STRONG_INLINE void wait_until_ready(SyncType* n) {\n  if (n) {\n    n->Wait();\n  }\n}\n\n\n// Build a thread pool device on top the an existing pool of threads.\nstruct ThreadPoolDevice {\n  // The ownership of the thread pool remains with the caller.\n  ThreadPoolDevice(ThreadPoolInterface* pool, int num_cores) : pool_(pool), num_threads_(num_cores) { }\n\n  EIGEN_STRONG_INLINE void* allocate(size_t num_bytes) const {\n    return internal::aligned_malloc(num_bytes);\n  }\n\n  EIGEN_STRONG_INLINE void deallocate(void* buffer) const {\n    internal::aligned_free(buffer);\n  }\n\n  EIGEN_STRONG_INLINE void memcpy(void* dst, const void* src, size_t n) const {\n    ::memcpy(dst, src, n);\n  }\n  EIGEN_STRONG_INLINE void memcpyHostToDevice(void* dst, const void* src, size_t n) const {\n    memcpy(dst, src, n);\n  }\n  EIGEN_STRONG_INLINE void memcpyDeviceToHost(void* dst, const void* src, size_t n) const {\n    memcpy(dst, src, n);\n  }\n\n  EIGEN_STRONG_INLINE void memset(void* buffer, int c, size_t n) const {\n    ::memset(buffer, c, n);\n  }\n\n  EIGEN_STRONG_INLINE int numThreads() const {\n    return num_threads_;\n  }\n\n  EIGEN_STRONG_INLINE size_t firstLevelCacheSize() const {\n    return l1CacheSize();\n  }\n\n  EIGEN_STRONG_INLINE size_t lastLevelCacheSize() const {\n    // The l3 cache size is shared between all the cores.\n    return l3CacheSize() / num_threads_;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE int majorDeviceVersion() const {\n    // Should return an enum that encodes the ISA supported by the CPU\n    return 1;\n  }\n\n  template <class Function, class... Args>\n  EIGEN_STRONG_INLINE Notification* enqueue(Function&& f, Args&&... args) const {\n    Notification* n = new Notification();\n    pool_->Schedule(std::bind(&FunctionWrapperWithNotification<Function, Args...>::run, n, f, args...));\n    return n;\n  }\n\n  template <class Function, class... Args>\n  EIGEN_STRONG_INLINE void enqueue_with_barrier(Barrier* b,\n                                                Function&& f,\n                                                Args&&... args) const {\n    pool_->Schedule(std::bind(\n        &FunctionWrapperWithBarrier<Function, Args...>::run, b, f, args...));\n  }\n\n  template <class Function, class... Args>\n  EIGEN_STRONG_INLINE void enqueueNoNotification(Function&& f, Args&&... args) const {\n    pool_->Schedule(std::bind(f, args...));\n  }\n\n  // Returns a logical thread index between 0 and pool_->NumThreads() - 1 if\n  // called from one of the threads in pool_. Returns -1 otherwise.\n  EIGEN_STRONG_INLINE int currentThreadId() const {\n    return pool_->CurrentThreadId();\n  }\n\n  // parallelFor executes f with [0, n) arguments in parallel and waits for\n  // completion. F accepts a half-open interval [first, last).\n  // Block size is choosen based on the iteration cost and resulting parallel\n  // efficiency. If block_align is not nullptr, it is called to round up the\n  // block size.\n  void parallelFor(Index n, const TensorOpCost& cost,\n                   std::function<Index(Index)> block_align,\n                   std::function<void(Index, Index)> f) const {\n    typedef TensorCostModel<ThreadPoolDevice> CostModel;\n    if (n <= 1 || numThreads() == 1 ||\n        CostModel::numThreads(n, cost, static_cast<int>(numThreads())) == 1) {\n      f(0, n);\n      return;\n    }\n\n    // Calculate block size based on (1) the iteration cost and (2) parallel\n    // efficiency. We want blocks to be not too small to mitigate\n    // parallelization overheads; not too large to mitigate tail\n    // effect and potential load imbalance and we also want number\n    // of blocks to be evenly dividable across threads.\n\n    double block_size_f = 1.0 / CostModel::taskSize(1, cost);\n    const Index max_oversharding_factor = 4;\n    Index block_size = numext::mini(\n        n, numext::maxi<Index>(divup<Index>(n, max_oversharding_factor * numThreads()),\n                               block_size_f));\n    const Index max_block_size = numext::mini(n, 2 * block_size);\n    if (block_align) {\n      Index new_block_size = block_align(block_size);\n      eigen_assert(new_block_size >= block_size);\n      block_size = numext::mini(n, new_block_size);\n    }\n    Index block_count = divup(n, block_size);\n    // Calculate parallel efficiency as fraction of total CPU time used for\n    // computations:\n    double max_efficiency =\n        static_cast<double>(block_count) /\n        (divup<int>(block_count, numThreads()) * numThreads());\n    // Now try to increase block size up to max_block_size as long as it\n    // doesn't decrease parallel efficiency.\n    for (Index prev_block_count = block_count;\n         max_efficiency < 1.0 && prev_block_count > 1;) {\n      // This is the next block size that divides size into a smaller number\n      // of blocks than the current block_size.\n      Index coarser_block_size = divup(n, prev_block_count - 1);\n      if (block_align) {\n        Index new_block_size = block_align(coarser_block_size);\n        eigen_assert(new_block_size >= coarser_block_size);\n        coarser_block_size = numext::mini(n, new_block_size);\n      }\n      if (coarser_block_size > max_block_size) {\n        break;  // Reached max block size. Stop.\n      }\n      // Recalculate parallel efficiency.\n      const Index coarser_block_count = divup(n, coarser_block_size);\n      eigen_assert(coarser_block_count < prev_block_count);\n      prev_block_count = coarser_block_count;\n      const double coarser_efficiency =\n          static_cast<double>(coarser_block_count) /\n          (divup<int>(coarser_block_count, numThreads()) * numThreads());\n      if (coarser_efficiency + 0.01 >= max_efficiency) {\n        // Taking it.\n        block_size = coarser_block_size;\n        block_count = coarser_block_count;\n        if (max_efficiency < coarser_efficiency) {\n          max_efficiency = coarser_efficiency;\n        }\n      }\n    }\n\n    // Recursively divide size into halves until we reach block_size.\n    // Division code rounds mid to block_size, so we are guaranteed to get\n    // block_count leaves that do actual computations.\n    Barrier barrier(static_cast<unsigned int>(block_count));\n    std::function<void(Index, Index)> handleRange;\n    handleRange = [=, &handleRange, &barrier, &f](Index first, Index last) {\n      if (last - first <= block_size) {\n        // Single block or less, execute directly.\n        f(first, last);\n        barrier.Notify();\n        return;\n      }\n      // Split into halves and submit to the pool.\n      Index mid = first + divup((last - first) / 2, block_size) * block_size;\n      pool_->Schedule([=, &handleRange]() { handleRange(mid, last); });\n      pool_->Schedule([=, &handleRange]() { handleRange(first, mid); });\n    };\n    handleRange(0, n);\n    barrier.Wait();\n  }\n\n  // Convenience wrapper for parallelFor that does not align blocks.\n  void parallelFor(Index n, const TensorOpCost& cost,\n                   std::function<void(Index, Index)> f) const {\n    parallelFor(n, cost, nullptr, std::move(f));\n  }\n\n private:\n  ThreadPoolInterface* pool_;\n  int num_threads_;\n};\n\n\n}  // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_DEVICE_THREAD_POOL_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorDimensionList.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_DIMENSION_LIST_H\n#define EIGEN_CXX11_TENSOR_TENSOR_DIMENSION_LIST_H\n\nnamespace Eigen {\n\n/** \\internal\n  *\n  * \\class TensorDimensionList\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief Special case of tensor index list used to list all the dimensions of a tensor of rank n.\n  *\n  * \\sa Tensor\n  */\n\ntemplate <typename Index, std::size_t Rank> struct DimensionList {\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\n  const Index operator[] (const Index i) const { return i; }\n};\n\nnamespace internal {\n\ntemplate<typename Index, std::size_t Rank> struct array_size<DimensionList<Index, Rank> > {\n  static const size_t value = Rank;\n};\ntemplate<typename Index, std::size_t Rank> struct array_size<const DimensionList<Index, Rank> > {\n  static const size_t value = Rank;\n};\n\ntemplate<DenseIndex n, typename Index, std::size_t Rank> const Index array_get(DimensionList<Index, Rank>&) {\n  return n;\n}\ntemplate<DenseIndex n, typename Index, std::size_t Rank> const Index array_get(const DimensionList<Index, Rank>&) {\n  return n;\n}\n\n\n#if EIGEN_HAS_CONSTEXPR\ntemplate <typename Index, std::size_t Rank>\nstruct index_known_statically_impl<DimensionList<Index, Rank> > {\n  EIGEN_DEVICE_FUNC static constexpr bool run(const DenseIndex) {\n    return true;\n  }\n};\ntemplate <typename Index, std::size_t Rank>\nstruct index_known_statically_impl<const DimensionList<Index, Rank> > {\n  EIGEN_DEVICE_FUNC static constexpr bool run(const DenseIndex) {\n    return true;\n  }\n};\n\ntemplate <typename Index, std::size_t Rank>\nstruct all_indices_known_statically_impl<DimensionList<Index, Rank> > {\n  EIGEN_DEVICE_FUNC static constexpr bool run() {\n    return true;\n  }\n};\ntemplate <typename Index, std::size_t Rank>\nstruct all_indices_known_statically_impl<const DimensionList<Index, Rank> > {\n  EIGEN_DEVICE_FUNC static constexpr bool run() {\n    return true;\n  }\n};\n\ntemplate <typename Index, std::size_t Rank>\nstruct indices_statically_known_to_increase_impl<DimensionList<Index, Rank> > {\n  EIGEN_DEVICE_FUNC static constexpr bool run() {\n    return true;\n  }\n};\ntemplate <typename Index, std::size_t Rank>\nstruct indices_statically_known_to_increase_impl<const DimensionList<Index, Rank> > {\n  EIGEN_DEVICE_FUNC static constexpr bool run() {\n    return true;\n  }\n};\n\ntemplate <typename Index, std::size_t Rank>\nstruct index_statically_eq_impl<DimensionList<Index, Rank> > {\n  static constexpr bool run(const DenseIndex i, const DenseIndex value) {\n    return i == value;\n  }\n};\ntemplate <typename Index, std::size_t Rank>\nstruct index_statically_eq_impl<const DimensionList<Index, Rank> > {\n  EIGEN_DEVICE_FUNC static constexpr bool run(const DenseIndex i, const DenseIndex value) {\n    return i == value;\n  }\n};\n\ntemplate <typename Index, std::size_t Rank>\nstruct index_statically_ne_impl<DimensionList<Index, Rank> > {\n  EIGEN_DEVICE_FUNC static constexpr bool run(const DenseIndex i, const DenseIndex value) {\n    return i != value;\n  }\n};\ntemplate <typename Index, std::size_t Rank>\nstruct index_statically_ne_impl<const DimensionList<Index, Rank> > {\n  static constexpr bool run(const DenseIndex i, const DenseIndex value) {\n    return i != value;\n  }\n};\n\ntemplate <typename Index, std::size_t Rank>\nstruct index_statically_gt_impl<DimensionList<Index, Rank> > {\n  EIGEN_DEVICE_FUNC static constexpr bool run(const DenseIndex i, const DenseIndex value) {\n    return i > value;\n  }\n};\ntemplate <typename Index, std::size_t Rank>\nstruct index_statically_gt_impl<const DimensionList<Index, Rank> > {\n  EIGEN_DEVICE_FUNC static constexpr bool run(const DenseIndex i, const DenseIndex value) {\n    return i > value;\n  }\n};\n\ntemplate <typename Index, std::size_t Rank>\nstruct index_statically_lt_impl<DimensionList<Index, Rank> > {\n  EIGEN_DEVICE_FUNC static constexpr bool run(const DenseIndex i, const DenseIndex value) {\n    return i < value;\n  }\n};\ntemplate <typename Index, std::size_t Rank>\nstruct index_statically_lt_impl<const DimensionList<Index, Rank> > {\n  EIGEN_DEVICE_FUNC static constexpr bool run(const DenseIndex i, const DenseIndex value) {\n    return i < value;\n  }\n};\n\n#else\ntemplate <typename Index, std::size_t Rank>\nstruct index_known_statically_impl<DimensionList<Index, Rank> > {\n  EIGEN_DEVICE_FUNC static EIGEN_ALWAYS_INLINE bool run(const DenseIndex) {\n    return true;\n  }\n};\ntemplate <typename Index, std::size_t Rank>\nstruct index_known_statically_impl<const DimensionList<Index, Rank> > {\n  EIGEN_DEVICE_FUNC static EIGEN_ALWAYS_INLINE bool run(const DenseIndex) {\n    return true;\n  }\n};\n\ntemplate <typename Index, std::size_t Rank>\nstruct all_indices_known_statically_impl<DimensionList<Index, Rank> > {\n  EIGEN_DEVICE_FUNC static EIGEN_ALWAYS_INLINE bool run() {\n    return true;\n  }\n};\ntemplate <typename Index, std::size_t Rank>\nstruct all_indices_known_statically_impl<const DimensionList<Index, Rank> > {\n  EIGEN_DEVICE_FUNC static EIGEN_ALWAYS_INLINE bool run() {\n    return true;\n  }\n};\n\ntemplate <typename Index, std::size_t Rank>\nstruct indices_statically_known_to_increase_impl<DimensionList<Index, Rank> > {\n  static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool run() {\n    return true;\n  }\n};\ntemplate <typename Index, std::size_t Rank>\nstruct indices_statically_known_to_increase_impl<const DimensionList<Index, Rank> > {\n  static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool run() {\n    return true;\n  }\n};\n\ntemplate <typename Index, std::size_t Rank>\nstruct index_statically_eq_impl<DimensionList<Index, Rank> > {\n  static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool run(const DenseIndex, const DenseIndex) {\n    return false;\n  }\n};\ntemplate <typename Index, std::size_t Rank>\nstruct index_statically_eq_impl<const DimensionList<Index, Rank> > {\n  static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool run(const DenseIndex, const DenseIndex) {\n    return false;\n  }\n};\n\ntemplate <typename Index, std::size_t Rank>\nstruct index_statically_ne_impl<DimensionList<Index, Rank> > {\n  static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool run(const DenseIndex, const DenseIndex){\n    return false;\n  }\n};\ntemplate <typename Index, std::size_t Rank>\nstruct index_statically_ne_impl<const DimensionList<Index, Rank> > {\n  static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool run(const DenseIndex, const DenseIndex) {\n    return false;\n  }\n};\n\ntemplate <typename Index, std::size_t Rank>\nstruct index_statically_gt_impl<DimensionList<Index, Rank> > {\n  static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool run(const DenseIndex, const DenseIndex) {\n    return false;\n  }\n};\ntemplate <typename Index, std::size_t Rank>\nstruct index_statically_gt_impl<const DimensionList<Index, Rank> > {\n  static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool run(const DenseIndex, const DenseIndex) {\n    return false;\n  }\n};\n\ntemplate <typename Index, std::size_t Rank>\nstruct index_statically_lt_impl<DimensionList<Index, Rank> > {\n  static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool run(const DenseIndex, const DenseIndex) {\n    return false;\n  }\n};\ntemplate <typename Index, std::size_t Rank>\nstruct index_statically_lt_impl<const DimensionList<Index, Rank> > {\n  static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool run(const DenseIndex, const DenseIndex) {\n    return false;\n  }\n};\n#endif\n\n}  // end namespace internal\n}  // end namespace Eigen\n\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_DIMENSION_LIST_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorDimensions.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_DIMENSIONS_H\n#define EIGEN_CXX11_TENSOR_TENSOR_DIMENSIONS_H\n\n\nnamespace Eigen {\n\n/** \\internal\n  *\n  * \\class TensorDimensions\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief Set of classes used to encode and store the dimensions of a Tensor.\n  *\n  * The Sizes class encodes as part of the type the number of dimensions and the\n  * sizes corresponding to each dimension. It uses no storage space since it is\n  * entirely known at compile time.\n  * The DSizes class is its dynamic sibling: the number of dimensions is known\n  * at compile time but the sizes are set during execution.\n  *\n  * \\sa Tensor\n  */\n\n// Boilerplate code\nnamespace internal {\n\ntemplate<std::size_t n, typename Dimension> struct dget {\n  static const std::size_t value = get<n, Dimension>::value;\n};\n\n\ntemplate<typename Index, std::size_t NumIndices, std::size_t n, bool RowMajor>\nstruct fixed_size_tensor_index_linearization_helper\n{\n  template <typename Dimensions> EIGEN_DEVICE_FUNC\n  static inline Index run(array<Index, NumIndices> const& indices,\n                          const Dimensions& dimensions)\n  {\n    return array_get<RowMajor ? n - 1 : (NumIndices - n)>(indices) +\n        dget<RowMajor ? n - 1 : (NumIndices - n), Dimensions>::value *\n        fixed_size_tensor_index_linearization_helper<Index, NumIndices, n - 1, RowMajor>::run(indices, dimensions);\n  }\n};\n\ntemplate<typename Index, std::size_t NumIndices, bool RowMajor>\nstruct fixed_size_tensor_index_linearization_helper<Index, NumIndices, 0, RowMajor>\n{\n  template <typename Dimensions> EIGEN_DEVICE_FUNC\n  static inline Index run(array<Index, NumIndices> const&, const Dimensions&)\n  {\n    return 0;\n  }\n};\n\ntemplate<typename Index, std::size_t n>\nstruct fixed_size_tensor_index_extraction_helper\n{\n  template <typename Dimensions> EIGEN_DEVICE_FUNC\n  static inline Index run(const Index index,\n                          const Dimensions& dimensions)\n  {\n    const Index mult = (index == n-1) ? 1 : 0;\n    return array_get<n-1>(dimensions) * mult +\n        fixed_size_tensor_index_extraction_helper<Index, n - 1>::run(index, dimensions);\n  }\n};\n\ntemplate<typename Index>\nstruct fixed_size_tensor_index_extraction_helper<Index, 0>\n{\n  template <typename Dimensions> EIGEN_DEVICE_FUNC\n  static inline Index run(const Index,\n                          const Dimensions&)\n  {\n    return 0;\n  }\n  };\n\n}  // end namespace internal\n\n\n// Fixed size\n#ifndef EIGEN_EMULATE_CXX11_META_H\ntemplate <typename std::ptrdiff_t... Indices>\nstruct Sizes : internal::numeric_list<std::ptrdiff_t, Indices...> {\n  typedef internal::numeric_list<std::ptrdiff_t, Indices...> Base;\n  static const std::ptrdiff_t total_size = internal::arg_prod(Indices...);\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::ptrdiff_t rank() const {\n    return Base::count;\n  }\n\n  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::ptrdiff_t TotalSize() {\n    return internal::arg_prod(Indices...);\n  }\n\n  EIGEN_DEVICE_FUNC Sizes() { }\n  template <typename DenseIndex>\n  explicit EIGEN_DEVICE_FUNC Sizes(const array<DenseIndex, Base::count>& /*indices*/) {\n    // todo: add assertion\n  }\n#if EIGEN_HAS_VARIADIC_TEMPLATES\n  template <typename... DenseIndex> EIGEN_DEVICE_FUNC Sizes(DenseIndex...) { }\n  explicit EIGEN_DEVICE_FUNC Sizes(std::initializer_list<std::ptrdiff_t> /*l*/) {\n    // todo: add assertion\n  }\n#endif\n\n  template <typename T> Sizes& operator = (const T& /*other*/) {\n    // add assertion failure if the size of other is different\n    return *this;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::ptrdiff_t operator[] (const std::size_t index) const {\n    return internal::fixed_size_tensor_index_extraction_helper<std::ptrdiff_t, Base::count>::run(index, *this);\n  }\n\n  template <typename DenseIndex> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  size_t IndexOfColMajor(const array<DenseIndex, Base::count>& indices) const {\n    return internal::fixed_size_tensor_index_linearization_helper<DenseIndex, Base::count, Base::count, false>::run(indices, *static_cast<const Base*>(this));\n  }\n  template <typename DenseIndex> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  size_t IndexOfRowMajor(const array<DenseIndex, Base::count>& indices) const {\n    return internal::fixed_size_tensor_index_linearization_helper<DenseIndex, Base::count, Base::count, true>::run(indices, *static_cast<const Base*>(this));\n  }\n};\n\nnamespace internal {\ntemplate <typename std::ptrdiff_t... Indices>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::ptrdiff_t array_prod(const Sizes<Indices...>&) {\n  return Sizes<Indices...>::total_size;\n}\n}\n\n#else\n\ntemplate <std::size_t n>\nstruct non_zero_size {\n  typedef internal::type2val<std::size_t, n> type;\n};\ntemplate <>\nstruct non_zero_size<0> {\n  typedef internal::null_type type;\n};\n\ntemplate <std::size_t V1=0, std::size_t V2=0, std::size_t V3=0, std::size_t V4=0, std::size_t V5=0> struct Sizes {\n  typedef typename internal::make_type_list<typename non_zero_size<V1>::type, typename non_zero_size<V2>::type, typename non_zero_size<V3>::type, typename non_zero_size<V4>::type, typename non_zero_size<V5>::type >::type Base;\n  static const size_t count = Base::count;\n  static const std::size_t total_size = internal::arg_prod<Base>::value;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE size_t rank() const {\n    return count;\n  }\n\n  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE size_t TotalSize() {\n    return internal::arg_prod<Base>::value;\n  }\n\n  Sizes() { }\n  template <typename DenseIndex>\n  explicit Sizes(const array<DenseIndex, Base::count>& /*indices*/) {\n    // todo: add assertion\n  }\n  template <typename T> Sizes& operator = (const T& /*other*/) {\n    // add assertion failure if the size of other is different\n    return *this;\n  }\n\n#if EIGEN_HAS_VARIADIC_TEMPLATES\n  template <typename... DenseIndex> Sizes(DenseIndex... /*indices*/) { }\n  explicit Sizes(std::initializer_list<std::size_t>) {\n    // todo: add assertion\n  }\n#else\n  EIGEN_DEVICE_FUNC explicit Sizes(const DenseIndex) {\n  }\n  EIGEN_DEVICE_FUNC Sizes(const DenseIndex, const DenseIndex) {\n  }\n  EIGEN_DEVICE_FUNC Sizes(const DenseIndex, const DenseIndex, const DenseIndex) {\n  }\n  EIGEN_DEVICE_FUNC Sizes(const DenseIndex, const DenseIndex, const DenseIndex, const DenseIndex) {\n  }\n  EIGEN_DEVICE_FUNC Sizes(const DenseIndex, const DenseIndex, const DenseIndex, const DenseIndex, const DenseIndex) {\n  }\n#endif\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DenseIndex operator[] (const int index) const {\n    switch (index) {\n      case 0:\n        return internal::get<0, Base>::value;\n      case 1:\n        return internal::get<1, Base>::value;\n      case 2:\n        return internal::get<2, Base>::value;\n      case 3:\n        return internal::get<3, Base>::value;\n      case 4:\n        return internal::get<4, Base>::value;\n      default:\n        eigen_assert(false && \"index overflow\");\n        return static_cast<DenseIndex>(-1);\n    }\n  }\n\n  template <typename DenseIndex> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  size_t IndexOfColMajor(const array<DenseIndex, Base::count>& indices) const {\n    return internal::fixed_size_tensor_index_linearization_helper<DenseIndex, Base::count, Base::count, false>::run(indices, *reinterpret_cast<const Base*>(this));\n  }\n  template <typename DenseIndex> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  size_t IndexOfRowMajor(const array<DenseIndex, Base::count>& indices) const {\n    return internal::fixed_size_tensor_index_linearization_helper<DenseIndex, Base::count, Base::count, true>::run(indices, *reinterpret_cast<const Base*>(this));\n  }\n};\n\nnamespace internal {\ntemplate <std::size_t V1, std::size_t V2, std::size_t V3, std::size_t V4, std::size_t V5>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::size_t array_prod(const Sizes<V1, V2, V3, V4, V5>&) {\n  return Sizes<V1, V2, V3, V4, V5>::total_size;\n}\n}\n\n#endif\n\n// Boilerplate\nnamespace internal {\ntemplate<typename Index, std::size_t NumIndices, std::size_t n, bool RowMajor>\nstruct tensor_index_linearization_helper\n{\n  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  Index run(array<Index, NumIndices> const& indices, array<Index, NumIndices> const& dimensions)\n  {\n    return array_get<RowMajor ? n : (NumIndices - n - 1)>(indices) +\n      array_get<RowMajor ? n : (NumIndices - n - 1)>(dimensions) *\n        tensor_index_linearization_helper<Index, NumIndices, n - 1, RowMajor>::run(indices, dimensions);\n  }\n};\n\ntemplate<typename Index, std::size_t NumIndices, bool RowMajor>\nstruct tensor_index_linearization_helper<Index, NumIndices, 0, RowMajor>\n{\n  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  Index run(array<Index, NumIndices> const& indices, array<Index, NumIndices> const&)\n  {\n    return array_get<RowMajor ? 0 : NumIndices - 1>(indices);\n  }\n};\n}  // end namespace internal\n\n\n\n// Dynamic size\ntemplate <typename DenseIndex, int NumDims>\nstruct DSizes : array<DenseIndex, NumDims> {\n  typedef array<DenseIndex, NumDims> Base;\n  static const int count = NumDims;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE size_t rank() const {\n    return NumDims;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DenseIndex TotalSize() const {\n    return (NumDims == 0) ? 1 : internal::array_prod(*static_cast<const Base*>(this));\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DSizes() {\n    for (int i = 0 ; i < NumDims; ++i) {\n      (*this)[i] = 0;\n    }\n  }\n  EIGEN_DEVICE_FUNC explicit DSizes(const array<DenseIndex, NumDims>& a) : Base(a) { }\n\n  EIGEN_DEVICE_FUNC explicit DSizes(const DenseIndex i0) {\n    eigen_assert(NumDims == 1);\n    (*this)[0] = i0;\n  }\n\n#if EIGEN_HAS_VARIADIC_TEMPLATES\n  template<typename... IndexTypes> EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE explicit DSizes(DenseIndex firstDimension, DenseIndex secondDimension, IndexTypes... otherDimensions) : Base({{firstDimension, secondDimension, otherDimensions...}}) {\n    EIGEN_STATIC_ASSERT(sizeof...(otherDimensions) + 2 == NumDims, YOU_MADE_A_PROGRAMMING_MISTAKE)\n  }\n#else\n  EIGEN_DEVICE_FUNC DSizes(const DenseIndex i0, const DenseIndex i1) {\n    eigen_assert(NumDims == 2);\n    (*this)[0] = i0;\n    (*this)[1] = i1;\n  }\n  EIGEN_DEVICE_FUNC DSizes(const DenseIndex i0, const DenseIndex i1, const DenseIndex i2) {\n    eigen_assert(NumDims == 3);\n    (*this)[0] = i0;\n    (*this)[1] = i1;\n    (*this)[2] = i2;\n  }\n  EIGEN_DEVICE_FUNC DSizes(const DenseIndex i0, const DenseIndex i1, const DenseIndex i2, const DenseIndex i3) {\n    eigen_assert(NumDims == 4);\n    (*this)[0] = i0;\n    (*this)[1] = i1;\n    (*this)[2] = i2;\n    (*this)[3] = i3;\n  }\n  EIGEN_DEVICE_FUNC DSizes(const DenseIndex i0, const DenseIndex i1, const DenseIndex i2, const DenseIndex i3, const DenseIndex i4) {\n    eigen_assert(NumDims == 5);\n    (*this)[0] = i0;\n    (*this)[1] = i1;\n    (*this)[2] = i2;\n    (*this)[3] = i3;\n    (*this)[4] = i4;\n  }\n#endif\n\n  EIGEN_DEVICE_FUNC DSizes& operator = (const array<DenseIndex, NumDims>& other) {\n    *static_cast<Base*>(this) = other;\n    return *this;\n  }\n\n  // A constexpr would be so much better here\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DenseIndex IndexOfColMajor(const array<DenseIndex, NumDims>& indices) const {\n    return internal::tensor_index_linearization_helper<DenseIndex, NumDims, NumDims - 1, false>::run(indices, *static_cast<const Base*>(this));\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DenseIndex IndexOfRowMajor(const array<DenseIndex, NumDims>& indices) const {\n    return internal::tensor_index_linearization_helper<DenseIndex, NumDims, NumDims - 1, true>::run(indices, *static_cast<const Base*>(this));\n  }\n};\n\n\n\n\n// Boilerplate\nnamespace internal {\ntemplate<typename Index, std::size_t NumIndices, std::size_t n, bool RowMajor>\nstruct tensor_vsize_index_linearization_helper\n{\n  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  Index run(array<Index, NumIndices> const& indices, std::vector<DenseIndex> const& dimensions)\n  {\n    return array_get<RowMajor ? n : (NumIndices - n - 1)>(indices) +\n      array_get<RowMajor ? n : (NumIndices - n - 1)>(dimensions) *\n        tensor_vsize_index_linearization_helper<Index, NumIndices, n - 1, RowMajor>::run(indices, dimensions);\n  }\n};\n\ntemplate<typename Index, std::size_t NumIndices, bool RowMajor>\nstruct tensor_vsize_index_linearization_helper<Index, NumIndices, 0, RowMajor>\n{\n  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  Index run(array<Index, NumIndices> const& indices, std::vector<DenseIndex> const&)\n  {\n    return array_get<RowMajor ? 0 : NumIndices - 1>(indices);\n  }\n};\n}  // end namespace internal\n\n\nnamespace internal {\n\ntemplate <typename DenseIndex, int NumDims> struct array_size<const DSizes<DenseIndex, NumDims> > {\n  static const size_t value = NumDims;\n};\ntemplate <typename DenseIndex, int NumDims> struct array_size<DSizes<DenseIndex, NumDims> > {\n  static const size_t value = NumDims;\n};\n#ifndef EIGEN_EMULATE_CXX11_META_H\ntemplate <typename std::ptrdiff_t... Indices> struct array_size<const Sizes<Indices...> > {\nstatic const std::ptrdiff_t value = Sizes<Indices...>::count;\n};\ntemplate <typename std::ptrdiff_t... Indices> struct array_size<Sizes<Indices...> > {\nstatic const std::ptrdiff_t value = Sizes<Indices...>::count;\n};\ntemplate <std::ptrdiff_t n, typename std::ptrdiff_t... Indices> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::ptrdiff_t array_get(const Sizes<Indices...>&) {\n  return get<n, internal::numeric_list<std::size_t, Indices...> >::value;\n}\ntemplate <std::ptrdiff_t n> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::ptrdiff_t array_get(const Sizes<>&) {\n  eigen_assert(false && \"should never be called\");\n  return -1;\n}\n#else\ntemplate <std::size_t V1, std::size_t V2, std::size_t V3, std::size_t V4, std::size_t V5> struct array_size<const Sizes<V1,V2,V3,V4,V5> > {\n  static const size_t value = Sizes<V1,V2,V3,V4,V5>::count;\n};\ntemplate <std::size_t V1, std::size_t V2, std::size_t V3, std::size_t V4, std::size_t V5> struct array_size<Sizes<V1,V2,V3,V4,V5> > {\n  static const size_t value = Sizes<V1,V2,V3,V4,V5>::count;\n};\ntemplate <std::size_t n, std::size_t V1, std::size_t V2, std::size_t V3, std::size_t V4, std::size_t V5> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::size_t array_get(const Sizes<V1,V2,V3,V4,V5>&) {\n  return get<n, typename Sizes<V1,V2,V3,V4,V5>::Base>::value;\n}\n\n#endif\n\n\ntemplate <typename Dims1, typename Dims2, size_t n, size_t m>\nstruct sizes_match_below_dim {\n  static EIGEN_DEVICE_FUNC  inline bool run(Dims1&, Dims2&) {\n    return false;\n  }\n};\ntemplate <typename Dims1, typename Dims2, size_t n>\nstruct sizes_match_below_dim<Dims1, Dims2, n, n> {\n  static EIGEN_DEVICE_FUNC  inline bool run(Dims1& dims1, Dims2& dims2) {\n    return (array_get<n-1>(dims1) == array_get<n-1>(dims2)) &\n        sizes_match_below_dim<Dims1, Dims2, n-1, n-1>::run(dims1, dims2);\n  }\n};\ntemplate <typename Dims1, typename Dims2>\nstruct sizes_match_below_dim<Dims1, Dims2, 0, 0> {\n  static EIGEN_DEVICE_FUNC  inline bool run(Dims1&, Dims2&) {\n    return true;\n  }\n};\n\n} // end namespace internal\n\n\ntemplate <typename Dims1, typename Dims2>\nEIGEN_DEVICE_FUNC bool dimensions_match(Dims1& dims1, Dims2& dims2) {\n  return internal::sizes_match_below_dim<Dims1, Dims2, internal::array_size<Dims1>::value, internal::array_size<Dims2>::value>::run(dims1, dims2);\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_DIMENSIONS_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorEvalTo.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_EVAL_TO_H\n#define EIGEN_CXX11_TENSOR_TENSOR_EVAL_TO_H\n\nnamespace Eigen {\n\n/** \\class TensorForcedEval\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief Tensor reshaping class.\n  *\n  *\n  */\nnamespace internal {\ntemplate<typename XprType, template <class> class MakePointer_>\nstruct traits<TensorEvalToOp<XprType, MakePointer_> >\n{\n  // Type promotion to handle the case where the types of the lhs and the rhs are different.\n  typedef typename XprType::Scalar Scalar;\n  typedef traits<XprType> XprTraits;\n  typedef typename XprTraits::StorageKind StorageKind;\n  typedef typename XprTraits::Index Index;\n  typedef typename XprType::Nested Nested;\n  typedef typename remove_reference<Nested>::type _Nested;\n  static const int NumDimensions = XprTraits::NumDimensions;\n  static const int Layout = XprTraits::Layout;\n\n  enum {\n    Flags = 0\n  };\n  template <class T>\n  struct MakePointer {\n    // Intermediate typedef to workaround MSVC issue.\n    typedef MakePointer_<T> MakePointerT;\n    typedef typename MakePointerT::Type Type;\n  };\n};\n\ntemplate<typename XprType, template <class> class MakePointer_>\nstruct eval<TensorEvalToOp<XprType, MakePointer_>, Eigen::Dense>\n{\n  typedef const TensorEvalToOp<XprType, MakePointer_>& type;\n};\n\ntemplate<typename XprType, template <class> class MakePointer_>\nstruct nested<TensorEvalToOp<XprType, MakePointer_>, 1, typename eval<TensorEvalToOp<XprType, MakePointer_> >::type>\n{\n  typedef TensorEvalToOp<XprType, MakePointer_> type;\n};\n\n}  // end namespace internal\n\n\n\n\ntemplate<typename XprType, template <class> class MakePointer_>\nclass TensorEvalToOp : public TensorBase<TensorEvalToOp<XprType, MakePointer_>, ReadOnlyAccessors>\n{\n  public:\n  typedef typename Eigen::internal::traits<TensorEvalToOp>::Scalar Scalar;\n  typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;\n  typedef typename internal::remove_const<typename XprType::CoeffReturnType>::type CoeffReturnType;\n  typedef typename MakePointer_<CoeffReturnType>::Type PointerType;\n  typedef typename Eigen::internal::nested<TensorEvalToOp>::type Nested;\n  typedef typename Eigen::internal::traits<TensorEvalToOp>::StorageKind StorageKind;\n  typedef typename Eigen::internal::traits<TensorEvalToOp>::Index Index;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvalToOp(PointerType buffer, const XprType& expr)\n      : m_xpr(expr), m_buffer(buffer) {}\n\n    EIGEN_DEVICE_FUNC\n    const typename internal::remove_all<typename XprType::Nested>::type&\n    expression() const { return m_xpr; }\n\n    EIGEN_DEVICE_FUNC PointerType buffer() const { return m_buffer; }\n\n  protected:\n    typename XprType::Nested m_xpr;\n    PointerType m_buffer;\n};\n\n\n\ntemplate<typename ArgType, typename Device, template <class> class MakePointer_>\nstruct TensorEvaluator<const TensorEvalToOp<ArgType, MakePointer_>, Device>\n{\n  typedef TensorEvalToOp<ArgType, MakePointer_> XprType;\n  typedef typename ArgType::Scalar Scalar;\n  typedef typename TensorEvaluator<ArgType, Device>::Dimensions Dimensions;\n  typedef typename XprType::Index Index;\n  typedef typename internal::remove_const<typename XprType::CoeffReturnType>::type CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  static const int PacketSize = internal::unpacket_traits<PacketReturnType>::size;\n\n  enum {\n    IsAligned = TensorEvaluator<ArgType, Device>::IsAligned,\n    PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,\n    Layout = TensorEvaluator<ArgType, Device>::Layout,\n    CoordAccess = false,  // to be implemented\n    RawAccess = true\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)\n      : m_impl(op.expression(), device), m_device(device),\n          m_buffer(op.buffer()), m_op(op), m_expression(op.expression())\n  { }\n\n  // Used for accessor extraction in SYCL Managed TensorMap:\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const XprType& op() const {\n    return m_op;\n  }\n  \n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ~TensorEvaluator() {\n  }\n\n  typedef typename internal::traits<const TensorEvalToOp<ArgType, MakePointer_> >::template MakePointer<CoeffReturnType>::Type DevicePointer;\n  EIGEN_DEVICE_FUNC const Dimensions& dimensions() const { return m_impl.dimensions(); }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(DevicePointer scalar) {\n    EIGEN_UNUSED_VARIABLE(scalar);\n    eigen_assert(scalar == NULL);\n    return m_impl.evalSubExprsIfNeeded(m_buffer);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalScalar(Index i) {\n    m_buffer[i] = m_impl.coeff(i);\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalPacket(Index i) {\n    internal::pstoret<CoeffReturnType, PacketReturnType, Aligned>(m_buffer + i, m_impl.template packet<TensorEvaluator<ArgType, Device>::IsAligned ? Aligned : Unaligned>(i));\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {\n    m_impl.cleanup();\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const\n  {\n    return m_buffer[index];\n  }\n\n  template<int LoadMode>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const\n  {\n    return internal::ploadt<PacketReturnType, LoadMode>(m_buffer + index);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {\n    // We assume that evalPacket or evalScalar is called to perform the\n    // assignment and account for the cost of the write here.\n    return m_impl.costPerCoeff(vectorized) +\n        TensorOpCost(0, sizeof(CoeffReturnType), 0, vectorized, PacketSize);\n  }\n\n  EIGEN_DEVICE_FUNC DevicePointer data() const { return m_buffer; }\n  ArgType expression() const { return m_expression; }\n\n  /// required by sycl in order to extract the accessor\n  const TensorEvaluator<ArgType, Device>& impl() const { return m_impl; }\n  /// added for sycl in order to construct the buffer from the sycl device\n  const Device& device() const{return m_device;}\n\n private:\n  TensorEvaluator<ArgType, Device> m_impl;\n  const Device& m_device;\n  DevicePointer m_buffer;\n  const XprType& m_op;\n  const ArgType m_expression;\n};\n\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_EVAL_TO_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorEvaluator.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_EVALUATOR_H\n#define EIGEN_CXX11_TENSOR_TENSOR_EVALUATOR_H\n\nnamespace Eigen {\n\n/** \\class TensorEvaluator\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief The tensor evaluator classes.\n  *\n  * These classes are responsible for the evaluation of the tensor expression.\n  *\n  * TODO: add support for more types of expressions, in particular expressions\n  * leading to lvalues (slicing, reshaping, etc...)\n  */\n\n// Generic evaluator\ntemplate<typename Derived, typename Device>\nstruct TensorEvaluator\n{\n  typedef typename Derived::Index Index;\n  typedef typename Derived::Scalar Scalar;\n  typedef typename Derived::Scalar CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  typedef typename Derived::Dimensions Dimensions;\n\n  // NumDimensions is -1 for variable dim tensors\n  static const int NumCoords = internal::traits<Derived>::NumDimensions > 0 ?\n                               internal::traits<Derived>::NumDimensions : 0;\n\n  enum {\n    IsAligned = Derived::IsAligned,\n    PacketAccess = (internal::unpacket_traits<PacketReturnType>::size > 1),\n    Layout = Derived::Layout,\n    CoordAccess = NumCoords > 0,\n    RawAccess = true\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const Derived& m, const Device& device)\n      : m_data(const_cast<typename internal::traits<Derived>::template MakePointer<Scalar>::Type>(m.data())), m_dims(m.dimensions()), m_device(device), m_impl(m)\n  { }\n\n  // Used for accessor extraction in SYCL Managed TensorMap:\n  const Derived& derived() const { return m_impl; }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dims; }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(CoeffReturnType* dest) {\n    if (dest) {\n      m_device.memcpy((void*)dest, m_data, sizeof(Scalar) * m_dims.TotalSize());\n      return false;\n    }\n    return true;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() { }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const {\n    eigen_assert(m_data);\n    return m_data[index];\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index index) {\n    eigen_assert(m_data);\n    return m_data[index];\n  }\n\n  template<int LoadMode> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  PacketReturnType packet(Index index) const\n  {\n    return internal::ploadt<PacketReturnType, LoadMode>(m_data + index);\n  }\n\n  template <int StoreMode> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  void writePacket(Index index, const PacketReturnType& x)\n  {\n    return internal::pstoret<Scalar, PacketReturnType, StoreMode>(m_data + index, x);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(const array<DenseIndex, NumCoords>& coords) const {\n    eigen_assert(m_data);\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      return m_data[m_dims.IndexOfColMajor(coords)];\n    } else {\n      return m_data[m_dims.IndexOfRowMajor(coords)];\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(const array<DenseIndex, NumCoords>& coords) {\n    eigen_assert(m_data);\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      return m_data[m_dims.IndexOfColMajor(coords)];\n    } else {\n      return m_data[m_dims.IndexOfRowMajor(coords)];\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {\n    return TensorOpCost(sizeof(CoeffReturnType), 0, 0, vectorized,\n                        internal::unpacket_traits<PacketReturnType>::size);\n  }\n\n  EIGEN_DEVICE_FUNC typename internal::traits<Derived>::template MakePointer<Scalar>::Type data() const { return m_data; }\n\n  /// required by sycl in order to construct sycl buffer from raw pointer\n  const Device& device() const{return m_device;}\n\n protected:\n  typename internal::traits<Derived>::template MakePointer<Scalar>::Type m_data;\n  Dimensions m_dims;\n  const Device& m_device;\n  const Derived& m_impl;\n};\n\nnamespace {\ntemplate <typename T> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nT loadConstant(const T* address) {\n  return *address;\n}\n// Use the texture cache on CUDA devices whenever possible\n#if defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 350\ntemplate <> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nfloat loadConstant(const float* address) {\n  return __ldg(address);\n}\ntemplate <> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\ndouble loadConstant(const double* address) {\n  return __ldg(address);\n}\ntemplate <> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nEigen::half loadConstant(const Eigen::half* address) {\n  return Eigen::half(half_impl::raw_uint16_to_half(__ldg(&address->x)));\n}\n#endif\n}\n\n\n// Default evaluator for rvalues\ntemplate<typename Derived, typename Device>\nstruct TensorEvaluator<const Derived, Device>\n{\n  typedef typename Derived::Index Index;\n  typedef typename Derived::Scalar Scalar;\n  typedef typename Derived::Scalar CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  typedef typename Derived::Dimensions Dimensions;\n\n  // NumDimensions is -1 for variable dim tensors\n  static const int NumCoords = internal::traits<Derived>::NumDimensions > 0 ?\n                               internal::traits<Derived>::NumDimensions : 0;\n\n  enum {\n    IsAligned = Derived::IsAligned,\n    PacketAccess = (internal::unpacket_traits<PacketReturnType>::size > 1),\n    Layout = Derived::Layout,\n    CoordAccess = NumCoords > 0,\n    RawAccess = true\n  };\n\n  // Used for accessor extraction in SYCL Managed TensorMap:\n  const Derived& derived() const { return m_impl; }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const Derived& m, const Device& device)\n      : m_data(m.data()), m_dims(m.dimensions()), m_device(device), m_impl(m)\n  { }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dims; }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(CoeffReturnType* data) {\n    if (!NumTraits<typename internal::remove_const<Scalar>::type>::RequireInitialization && data) {\n      m_device.memcpy((void*)data, m_data, m_dims.TotalSize() * sizeof(Scalar));\n      return false;\n    }\n    return true;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() { }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const {\n    eigen_assert(m_data);\n    return loadConstant(m_data+index);\n  }\n\n  template<int LoadMode> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  PacketReturnType packet(Index index) const\n  {\n    return internal::ploadt_ro<PacketReturnType, LoadMode>(m_data + index);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(const array<DenseIndex, NumCoords>& coords) const {\n    eigen_assert(m_data);\n    const Index index = (static_cast<int>(Layout) == static_cast<int>(ColMajor)) ? m_dims.IndexOfColMajor(coords)\n                        : m_dims.IndexOfRowMajor(coords);\n    return loadConstant(m_data+index);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {\n    return TensorOpCost(sizeof(CoeffReturnType), 0, 0, vectorized,\n                        internal::unpacket_traits<PacketReturnType>::size);\n  }\n\n  EIGEN_DEVICE_FUNC typename internal::traits<Derived>::template MakePointer<const Scalar>::Type data() const { return m_data; }\n\n  /// added for sycl in order to construct the buffer from the sycl device\n  const Device& device() const{return m_device;}\n\n protected:\n  typename internal::traits<Derived>::template MakePointer<const Scalar>::Type m_data;\n  Dimensions m_dims;\n  const Device& m_device;\n  const Derived& m_impl;\n};\n\n\n\n\n// -------------------- CwiseNullaryOp --------------------\n\ntemplate<typename NullaryOp, typename ArgType, typename Device>\nstruct TensorEvaluator<const TensorCwiseNullaryOp<NullaryOp, ArgType>, Device>\n{\n  typedef TensorCwiseNullaryOp<NullaryOp, ArgType> XprType;\n\n  enum {\n    IsAligned = true,\n    PacketAccess = internal::functor_traits<NullaryOp>::PacketAccess,\n    Layout = TensorEvaluator<ArgType, Device>::Layout,\n    CoordAccess = false,  // to be implemented\n    RawAccess = false\n  };\n\n  EIGEN_DEVICE_FUNC\n  TensorEvaluator(const XprType& op, const Device& device)\n      : m_functor(op.functor()), m_argImpl(op.nestedExpression(), device), m_wrapper()\n  { }\n\n  typedef typename XprType::Index Index;\n  typedef typename XprType::Scalar Scalar;\n  typedef typename internal::traits<XprType>::Scalar CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  static const int PacketSize = internal::unpacket_traits<PacketReturnType>::size;\n  typedef typename TensorEvaluator<ArgType, Device>::Dimensions Dimensions;\n\n  EIGEN_DEVICE_FUNC const Dimensions& dimensions() const { return m_argImpl.dimensions(); }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(CoeffReturnType*) { return true; }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() { }\n\n  EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index index) const\n  {\n    return m_wrapper(m_functor, index);\n  }\n\n  template<int LoadMode>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const\n  {\n    return m_wrapper.template packetOp<PacketReturnType, Index>(m_functor, index);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost\n  costPerCoeff(bool vectorized) const {\n    return TensorOpCost(sizeof(CoeffReturnType), 0, 0, vectorized,\n                        internal::unpacket_traits<PacketReturnType>::size);\n  }\n\n  EIGEN_DEVICE_FUNC CoeffReturnType* data() const { return NULL; }\n\n  /// required by sycl in order to extract the accessor\n  const TensorEvaluator<ArgType, Device>& impl() const { return m_argImpl; }\n  /// required by sycl in order to extract the accessor\n  NullaryOp functor() const { return m_functor; }\n\n\n private:\n  const NullaryOp m_functor;\n  TensorEvaluator<ArgType, Device> m_argImpl;\n  const internal::nullary_wrapper<CoeffReturnType,NullaryOp> m_wrapper;\n};\n\n\n\n// -------------------- CwiseUnaryOp --------------------\n\ntemplate<typename UnaryOp, typename ArgType, typename Device>\nstruct TensorEvaluator<const TensorCwiseUnaryOp<UnaryOp, ArgType>, Device>\n{\n  typedef TensorCwiseUnaryOp<UnaryOp, ArgType> XprType;\n\n  enum {\n    IsAligned = TensorEvaluator<ArgType, Device>::IsAligned,\n    PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess & internal::functor_traits<UnaryOp>::PacketAccess,\n    Layout = TensorEvaluator<ArgType, Device>::Layout,\n    CoordAccess = false,  // to be implemented\n    RawAccess = false\n  };\n\n  EIGEN_DEVICE_FUNC TensorEvaluator(const XprType& op, const Device& device)\n    : m_functor(op.functor()),\n      m_argImpl(op.nestedExpression(), device)\n  { }\n\n  typedef typename XprType::Index Index;\n  typedef typename XprType::Scalar Scalar;\n  typedef typename internal::traits<XprType>::Scalar CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  static const int PacketSize = internal::unpacket_traits<PacketReturnType>::size;\n  typedef typename TensorEvaluator<ArgType, Device>::Dimensions Dimensions;\n\n  EIGEN_DEVICE_FUNC const Dimensions& dimensions() const { return m_argImpl.dimensions(); }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(Scalar*) {\n    m_argImpl.evalSubExprsIfNeeded(NULL);\n    return true;\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {\n    m_argImpl.cleanup();\n  }\n\n  EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index index) const\n  {\n    return m_functor(m_argImpl.coeff(index));\n  }\n\n  template<int LoadMode>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const\n  {\n    return m_functor.packetOp(m_argImpl.template packet<LoadMode>(index));\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {\n    const double functor_cost = internal::functor_traits<UnaryOp>::Cost;\n    return m_argImpl.costPerCoeff(vectorized) +\n        TensorOpCost(0, 0, functor_cost, vectorized, PacketSize);\n  }\n\n  EIGEN_DEVICE_FUNC CoeffReturnType* data() const { return NULL; }\n\n  /// required by sycl in order to extract the accessor\n  const TensorEvaluator<ArgType, Device> & impl() const { return m_argImpl; }\n  /// added for sycl in order to construct the buffer from sycl device\n  UnaryOp functor() const { return m_functor; }\n\n\n private:\n  const UnaryOp m_functor;\n  TensorEvaluator<ArgType, Device> m_argImpl;\n};\n\n\n// -------------------- CwiseBinaryOp --------------------\n\ntemplate<typename BinaryOp, typename LeftArgType, typename RightArgType, typename Device>\nstruct TensorEvaluator<const TensorCwiseBinaryOp<BinaryOp, LeftArgType, RightArgType>, Device>\n{\n  typedef TensorCwiseBinaryOp<BinaryOp, LeftArgType, RightArgType> XprType;\n\n  enum {\n    IsAligned = TensorEvaluator<LeftArgType, Device>::IsAligned & TensorEvaluator<RightArgType, Device>::IsAligned,\n    PacketAccess = TensorEvaluator<LeftArgType, Device>::PacketAccess & TensorEvaluator<RightArgType, Device>::PacketAccess &\n                   internal::functor_traits<BinaryOp>::PacketAccess,\n    Layout = TensorEvaluator<LeftArgType, Device>::Layout,\n    CoordAccess = false,  // to be implemented\n    RawAccess = false\n  };\n\n  EIGEN_DEVICE_FUNC TensorEvaluator(const XprType& op, const Device& device)\n    : m_functor(op.functor()),\n      m_leftImpl(op.lhsExpression(), device),\n      m_rightImpl(op.rhsExpression(), device)\n  {\n    EIGEN_STATIC_ASSERT((static_cast<int>(TensorEvaluator<LeftArgType, Device>::Layout) == static_cast<int>(TensorEvaluator<RightArgType, Device>::Layout) || internal::traits<XprType>::NumDimensions <= 1), YOU_MADE_A_PROGRAMMING_MISTAKE);\n    eigen_assert(dimensions_match(m_leftImpl.dimensions(), m_rightImpl.dimensions()));\n  }\n\n  typedef typename XprType::Index Index;\n  typedef typename XprType::Scalar Scalar;\n  typedef typename internal::traits<XprType>::Scalar CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  static const int PacketSize = internal::unpacket_traits<PacketReturnType>::size;\n  typedef typename TensorEvaluator<LeftArgType, Device>::Dimensions Dimensions;\n\n  EIGEN_DEVICE_FUNC const Dimensions& dimensions() const\n  {\n    // TODO: use right impl instead if right impl dimensions are known at compile time.\n    return m_leftImpl.dimensions();\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(CoeffReturnType*) {\n    m_leftImpl.evalSubExprsIfNeeded(NULL);\n    m_rightImpl.evalSubExprsIfNeeded(NULL);\n    return true;\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {\n    m_leftImpl.cleanup();\n    m_rightImpl.cleanup();\n  }\n\n  EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index index) const\n  {\n    return m_functor(m_leftImpl.coeff(index), m_rightImpl.coeff(index));\n  }\n  template<int LoadMode>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const\n  {\n    return m_functor.packetOp(m_leftImpl.template packet<LoadMode>(index), m_rightImpl.template packet<LoadMode>(index));\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost\n  costPerCoeff(bool vectorized) const {\n    const double functor_cost = internal::functor_traits<BinaryOp>::Cost;\n    return m_leftImpl.costPerCoeff(vectorized) +\n           m_rightImpl.costPerCoeff(vectorized) +\n           TensorOpCost(0, 0, functor_cost, vectorized, PacketSize);\n  }\n\n  EIGEN_DEVICE_FUNC CoeffReturnType* data() const { return NULL; }\n  /// required by sycl in order to extract the accessor\n  const TensorEvaluator<LeftArgType, Device>& left_impl() const { return m_leftImpl; }\n  /// required by sycl in order to extract the accessor\n  const TensorEvaluator<RightArgType, Device>& right_impl() const { return m_rightImpl; }\n  /// required by sycl in order to extract the accessor\n  BinaryOp functor() const { return m_functor; }\n\n private:\n  const BinaryOp m_functor;\n  TensorEvaluator<LeftArgType, Device> m_leftImpl;\n  TensorEvaluator<RightArgType, Device> m_rightImpl;\n};\n\n// -------------------- CwiseTernaryOp --------------------\n\ntemplate<typename TernaryOp, typename Arg1Type, typename Arg2Type, typename Arg3Type, typename Device>\nstruct TensorEvaluator<const TensorCwiseTernaryOp<TernaryOp, Arg1Type, Arg2Type, Arg3Type>, Device>\n{\n  typedef TensorCwiseTernaryOp<TernaryOp, Arg1Type, Arg2Type, Arg3Type> XprType;\n\n  enum {\n    IsAligned = TensorEvaluator<Arg1Type, Device>::IsAligned & TensorEvaluator<Arg2Type, Device>::IsAligned & TensorEvaluator<Arg3Type, Device>::IsAligned,\n    PacketAccess = TensorEvaluator<Arg1Type, Device>::PacketAccess & TensorEvaluator<Arg2Type, Device>::PacketAccess & TensorEvaluator<Arg3Type, Device>::PacketAccess &\n                   internal::functor_traits<TernaryOp>::PacketAccess,\n    Layout = TensorEvaluator<Arg1Type, Device>::Layout,\n    CoordAccess = false,  // to be implemented\n    RawAccess = false\n  };\n\n  EIGEN_DEVICE_FUNC TensorEvaluator(const XprType& op, const Device& device)\n    : m_functor(op.functor()),\n      m_arg1Impl(op.arg1Expression(), device),\n      m_arg2Impl(op.arg2Expression(), device),\n      m_arg3Impl(op.arg3Expression(), device)\n  {\n    EIGEN_STATIC_ASSERT((static_cast<int>(TensorEvaluator<Arg1Type, Device>::Layout) == static_cast<int>(TensorEvaluator<Arg3Type, Device>::Layout) || internal::traits<XprType>::NumDimensions <= 1), YOU_MADE_A_PROGRAMMING_MISTAKE);\n\n    EIGEN_STATIC_ASSERT((internal::is_same<typename internal::traits<Arg1Type>::StorageKind,\n                         typename internal::traits<Arg2Type>::StorageKind>::value),\n                        STORAGE_KIND_MUST_MATCH)\n    EIGEN_STATIC_ASSERT((internal::is_same<typename internal::traits<Arg1Type>::StorageKind,\n                         typename internal::traits<Arg3Type>::StorageKind>::value),\n                        STORAGE_KIND_MUST_MATCH)\n    EIGEN_STATIC_ASSERT((internal::is_same<typename internal::traits<Arg1Type>::Index,\n                         typename internal::traits<Arg2Type>::Index>::value),\n                        STORAGE_INDEX_MUST_MATCH)\n    EIGEN_STATIC_ASSERT((internal::is_same<typename internal::traits<Arg1Type>::Index,\n                         typename internal::traits<Arg3Type>::Index>::value),\n                        STORAGE_INDEX_MUST_MATCH)\n\n    eigen_assert(dimensions_match(m_arg1Impl.dimensions(), m_arg2Impl.dimensions()) && dimensions_match(m_arg1Impl.dimensions(), m_arg3Impl.dimensions()));\n  }\n\n  typedef typename XprType::Index Index;\n  typedef typename XprType::Scalar Scalar;\n  typedef typename internal::traits<XprType>::Scalar CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  static const int PacketSize = internal::unpacket_traits<PacketReturnType>::size;\n  typedef typename TensorEvaluator<Arg1Type, Device>::Dimensions Dimensions;\n\n  EIGEN_DEVICE_FUNC const Dimensions& dimensions() const\n  {\n    // TODO: use arg2 or arg3 dimensions if they are known at compile time.\n    return m_arg1Impl.dimensions();\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(CoeffReturnType*) {\n    m_arg1Impl.evalSubExprsIfNeeded(NULL);\n    m_arg2Impl.evalSubExprsIfNeeded(NULL);\n    m_arg3Impl.evalSubExprsIfNeeded(NULL);\n    return true;\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {\n    m_arg1Impl.cleanup();\n    m_arg2Impl.cleanup();\n    m_arg3Impl.cleanup();\n  }\n\n  EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index index) const\n  {\n    return m_functor(m_arg1Impl.coeff(index), m_arg2Impl.coeff(index), m_arg3Impl.coeff(index));\n  }\n  template<int LoadMode>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const\n  {\n    return m_functor.packetOp(m_arg1Impl.template packet<LoadMode>(index),\n                              m_arg2Impl.template packet<LoadMode>(index),\n                              m_arg3Impl.template packet<LoadMode>(index));\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost\n  costPerCoeff(bool vectorized) const {\n    const double functor_cost = internal::functor_traits<TernaryOp>::Cost;\n    return m_arg1Impl.costPerCoeff(vectorized) +\n           m_arg2Impl.costPerCoeff(vectorized) +\n           m_arg3Impl.costPerCoeff(vectorized) +\n           TensorOpCost(0, 0, functor_cost, vectorized, PacketSize);\n  }\n\n  EIGEN_DEVICE_FUNC CoeffReturnType* data() const { return NULL; }\n\n  /// required by sycl in order to extract the accessor\n  const TensorEvaluator<Arg1Type, Device> & arg1Impl() const { return m_arg1Impl; }\n  /// required by sycl in order to extract the accessor\n  const TensorEvaluator<Arg2Type, Device>& arg2Impl() const { return m_arg2Impl; }\n  /// required by sycl in order to extract the accessor\n  const TensorEvaluator<Arg3Type, Device>& arg3Impl() const { return m_arg3Impl; }\n\n private:\n  const TernaryOp m_functor;\n  TensorEvaluator<Arg1Type, Device> m_arg1Impl;\n  TensorEvaluator<Arg2Type, Device> m_arg2Impl;\n  TensorEvaluator<Arg3Type, Device> m_arg3Impl;\n};\n\n\n// -------------------- SelectOp --------------------\n\ntemplate<typename IfArgType, typename ThenArgType, typename ElseArgType, typename Device>\nstruct TensorEvaluator<const TensorSelectOp<IfArgType, ThenArgType, ElseArgType>, Device>\n{\n  typedef TensorSelectOp<IfArgType, ThenArgType, ElseArgType> XprType;\n  typedef typename XprType::Scalar Scalar;\n\n  enum {\n    IsAligned = TensorEvaluator<ThenArgType, Device>::IsAligned & TensorEvaluator<ElseArgType, Device>::IsAligned,\n    PacketAccess = TensorEvaluator<ThenArgType, Device>::PacketAccess & TensorEvaluator<ElseArgType, Device>::PacketAccess &\n                   internal::packet_traits<Scalar>::HasBlend,\n    Layout = TensorEvaluator<IfArgType, Device>::Layout,\n    CoordAccess = false,  // to be implemented\n    RawAccess = false\n  };\n\n  EIGEN_DEVICE_FUNC TensorEvaluator(const XprType& op, const Device& device)\n    : m_condImpl(op.ifExpression(), device),\n      m_thenImpl(op.thenExpression(), device),\n      m_elseImpl(op.elseExpression(), device)\n  {\n    EIGEN_STATIC_ASSERT((static_cast<int>(TensorEvaluator<IfArgType, Device>::Layout) == static_cast<int>(TensorEvaluator<ThenArgType, Device>::Layout)), YOU_MADE_A_PROGRAMMING_MISTAKE);\n    EIGEN_STATIC_ASSERT((static_cast<int>(TensorEvaluator<IfArgType, Device>::Layout) == static_cast<int>(TensorEvaluator<ElseArgType, Device>::Layout)), YOU_MADE_A_PROGRAMMING_MISTAKE);\n    eigen_assert(dimensions_match(m_condImpl.dimensions(), m_thenImpl.dimensions()));\n    eigen_assert(dimensions_match(m_thenImpl.dimensions(), m_elseImpl.dimensions()));\n  }\n\n  typedef typename XprType::Index Index;\n  typedef typename internal::traits<XprType>::Scalar CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  static const int PacketSize = internal::unpacket_traits<PacketReturnType>::size;\n  typedef typename TensorEvaluator<IfArgType, Device>::Dimensions Dimensions;\n\n  EIGEN_DEVICE_FUNC const Dimensions& dimensions() const\n  {\n    // TODO: use then or else impl instead if they happen to be known at compile time.\n    return m_condImpl.dimensions();\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(CoeffReturnType*) {\n    m_condImpl.evalSubExprsIfNeeded(NULL);\n    m_thenImpl.evalSubExprsIfNeeded(NULL);\n    m_elseImpl.evalSubExprsIfNeeded(NULL);\n    return true;\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {\n    m_condImpl.cleanup();\n    m_thenImpl.cleanup();\n    m_elseImpl.cleanup();\n  }\n\n  EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index index) const\n  {\n    return m_condImpl.coeff(index) ? m_thenImpl.coeff(index) : m_elseImpl.coeff(index);\n  }\n  template<int LoadMode>\n  EIGEN_DEVICE_FUNC PacketReturnType packet(Index index) const\n  {\n    internal::Selector<PacketSize> select;\n    for (Index i = 0; i < PacketSize; ++i) {\n      select.select[i] = m_condImpl.coeff(index+i);\n    }\n    return internal::pblend(select,\n                            m_thenImpl.template packet<LoadMode>(index),\n                            m_elseImpl.template packet<LoadMode>(index));\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost\n  costPerCoeff(bool vectorized) const {\n    return m_condImpl.costPerCoeff(vectorized) +\n           m_thenImpl.costPerCoeff(vectorized)\n        .cwiseMax(m_elseImpl.costPerCoeff(vectorized));\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType* data() const { return NULL; }\n  /// required by sycl in order to extract the accessor\n  const TensorEvaluator<IfArgType, Device> & cond_impl() const { return m_condImpl; }\n  /// required by sycl in order to extract the accessor\n  const TensorEvaluator<ThenArgType, Device>& then_impl() const { return m_thenImpl; }\n  /// required by sycl in order to extract the accessor\n  const TensorEvaluator<ElseArgType, Device>& else_impl() const { return m_elseImpl; }\n\n private:\n  TensorEvaluator<IfArgType, Device> m_condImpl;\n  TensorEvaluator<ThenArgType, Device> m_thenImpl;\n  TensorEvaluator<ElseArgType, Device> m_elseImpl;\n};\n\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_EVALUATOR_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorExecutor.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_EXECUTOR_H\n#define EIGEN_CXX11_TENSOR_TENSOR_EXECUTOR_H\n\nnamespace Eigen {\n\n/** \\class TensorExecutor\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief The tensor executor class.\n  *\n  * This class is responsible for launch the evaluation of the expression on\n  * the specified computing device.\n  */\nnamespace internal {\n\n// Default strategy: the expression is evaluated with a single cpu thread.\ntemplate<typename Expression, typename Device, bool Vectorizable>\nclass TensorExecutor\n{\n public:\n  typedef typename Expression::Index Index;\n  EIGEN_DEVICE_FUNC\n  static inline void run(const Expression& expr, const Device& device = Device())\n  {\n    TensorEvaluator<Expression, Device> evaluator(expr, device);\n    const bool needs_assign = evaluator.evalSubExprsIfNeeded(NULL);\n    if (needs_assign)\n    {\n      const Index size = array_prod(evaluator.dimensions());\n      for (Index i = 0; i < size; ++i) {\n        evaluator.evalScalar(i);\n      }\n    }\n    evaluator.cleanup();\n  }\n};\n\n\ntemplate<typename Expression>\nclass TensorExecutor<Expression, DefaultDevice, true>\n{\n public:\n  typedef typename Expression::Index Index;\n  EIGEN_DEVICE_FUNC\n  static inline void run(const Expression& expr, const DefaultDevice& device = DefaultDevice())\n  {\n    TensorEvaluator<Expression, DefaultDevice> evaluator(expr, device);\n    const bool needs_assign = evaluator.evalSubExprsIfNeeded(NULL);\n    if (needs_assign)\n    {\n      const Index size = array_prod(evaluator.dimensions());\n      const int PacketSize = unpacket_traits<typename TensorEvaluator<Expression, DefaultDevice>::PacketReturnType>::size;\n      // Give the compiler a strong hint to unroll the loop. But don't insist\n      // on unrolling, because if the function is expensive the compiler should not\n      // unroll the loop at the expense of inlining.\n      const Index UnrolledSize = (size / (4 * PacketSize)) * 4 * PacketSize;\n      for (Index i = 0; i < UnrolledSize; i += 4*PacketSize) {\n        for (Index j = 0; j < 4; j++) {\n          evaluator.evalPacket(i + j * PacketSize);\n        }\n      }\n      const Index VectorizedSize = (size / PacketSize) * PacketSize;\n      for (Index i = UnrolledSize; i < VectorizedSize; i += PacketSize) {\n        evaluator.evalPacket(i);\n      }\n      for (Index i = VectorizedSize; i < size; ++i) {\n        evaluator.evalScalar(i);\n      }\n    }\n    evaluator.cleanup();\n  }\n};\n\n\n\n// Multicore strategy: the index space is partitioned and each partition is executed on a single core\n#ifdef EIGEN_USE_THREADS\ntemplate <typename Evaluator, typename Index, bool Vectorizable>\nstruct EvalRange {\n  static void run(Evaluator* evaluator_in, const Index first, const Index last) {\n    Evaluator evaluator = *evaluator_in;\n    eigen_assert(last >= first);\n    for (Index i = first; i < last; ++i) {\n      evaluator.evalScalar(i);\n    }\n  }\n\n  static Index alignBlockSize(Index size) {\n    return size;\n  }\n};\n\ntemplate <typename Evaluator, typename Index>\nstruct EvalRange<Evaluator, Index, true> {\n  static const int PacketSize = unpacket_traits<typename Evaluator::PacketReturnType>::size;\n\n  static void run(Evaluator* evaluator_in, const Index first, const Index last) {\n    Evaluator evaluator = *evaluator_in;\n    eigen_assert(last >= first);\n    Index i = first;\n    if (last - first >= PacketSize) {\n      eigen_assert(first % PacketSize == 0);\n      Index last_chunk_offset = last - 4 * PacketSize;\n      // Give the compiler a strong hint to unroll the loop. But don't insist\n      // on unrolling, because if the function is expensive the compiler should not\n      // unroll the loop at the expense of inlining.\n      for (; i <= last_chunk_offset; i += 4*PacketSize) {\n        for (Index j = 0; j < 4; j++) {\n          evaluator.evalPacket(i + j * PacketSize);\n        }\n      }\n      last_chunk_offset = last - PacketSize;\n      for (; i <= last_chunk_offset; i += PacketSize) {\n        evaluator.evalPacket(i);\n      }\n    }\n    for (; i < last; ++i) {\n      evaluator.evalScalar(i);\n    }\n  }\n\n  static Index alignBlockSize(Index size) {\n    // Align block size to packet size and account for unrolling in run above.\n    if (size >= 16 * PacketSize) {\n      return (size + 4 * PacketSize - 1) & ~(4 * PacketSize - 1);\n    }\n    // Aligning to 4 * PacketSize would increase block size by more than 25%.\n    return (size + PacketSize - 1) & ~(PacketSize - 1);\n  }\n};\n\ntemplate <typename Expression, bool Vectorizable>\nclass TensorExecutor<Expression, ThreadPoolDevice, Vectorizable> {\n public:\n  typedef typename Expression::Index Index;\n  static inline void run(const Expression& expr, const ThreadPoolDevice& device)\n  {\n    typedef TensorEvaluator<Expression, ThreadPoolDevice> Evaluator;\n    Evaluator evaluator(expr, device);\n    const bool needs_assign = evaluator.evalSubExprsIfNeeded(NULL);\n    if (needs_assign)\n    {\n      const Index size = array_prod(evaluator.dimensions());\n#if !defined(EIGEN_USE_SIMPLE_THREAD_POOL)\n      device.parallelFor(size, evaluator.costPerCoeff(Vectorizable),\n                         EvalRange<Evaluator, Index, Vectorizable>::alignBlockSize,\n                         [&evaluator](Index first, Index last) {\n                           EvalRange<Evaluator, Index, Vectorizable>::run(&evaluator, first, last);\n                         });\n#else\n      size_t num_threads = device.numThreads();\n      if (num_threads > 1) {\n        num_threads = TensorCostModel<ThreadPoolDevice>::numThreads(\n            size, evaluator.costPerCoeff(Vectorizable), num_threads);\n      }\n      if (num_threads == 1) {\n        EvalRange<Evaluator, Index, Vectorizable>::run(&evaluator, 0, size);\n      } else {\n        const Index PacketSize = Vectorizable ? unpacket_traits<typename Evaluator::PacketReturnType>::size : 1;\n        Index blocksz = std::ceil<Index>(static_cast<float>(size)/num_threads) + PacketSize - 1;\n        const Index blocksize = numext::maxi<Index>(PacketSize, (blocksz - (blocksz % PacketSize)));\n        const Index numblocks = size / blocksize;\n\n        Barrier barrier(numblocks);\n        for (int i = 0; i < numblocks; ++i) {\n          device.enqueue_with_barrier(\n              &barrier, &EvalRange<Evaluator, Index, Vectorizable>::run,\n              &evaluator, i * blocksize, (i + 1) * blocksize);\n        }\n        if (numblocks * blocksize < size) {\n          EvalRange<Evaluator, Index, Vectorizable>::run(\n              &evaluator, numblocks * blocksize, size);\n        }\n        barrier.Wait();\n      }\n#endif  // defined(!EIGEN_USE_SIMPLE_THREAD_POOL)\n    }\n    evaluator.cleanup();\n  }\n};\n#endif  // EIGEN_USE_THREADS\n\n\n// GPU: the evaluation of the expression is offloaded to a GPU.\n#if defined(EIGEN_USE_GPU)\n\ntemplate <typename Expression, bool Vectorizable>\nclass TensorExecutor<Expression, GpuDevice, Vectorizable> {\n public:\n  typedef typename Expression::Index Index;\n  static void run(const Expression& expr, const GpuDevice& device);\n};\n\n\n#if defined(__CUDACC__)\ntemplate <typename Evaluator, typename Index, bool Vectorizable>\nstruct EigenMetaKernelEval {\n  static __device__ EIGEN_ALWAYS_INLINE\n  void run(Evaluator& eval, Index first, Index last, Index step_size) {\n    for (Index i = first; i < last; i += step_size) {\n      eval.evalScalar(i);\n    }\n  }\n};\n\ntemplate <typename Evaluator, typename Index>\nstruct EigenMetaKernelEval<Evaluator, Index, true> {\n  static __device__ EIGEN_ALWAYS_INLINE\n  void run(Evaluator& eval, Index first, Index last, Index step_size) {\n    const Index PacketSize = unpacket_traits<typename Evaluator::PacketReturnType>::size;\n    const Index vectorized_size = (last / PacketSize) * PacketSize;\n    const Index vectorized_step_size = step_size * PacketSize;\n\n    // Use the vector path\n    for (Index i = first * PacketSize; i < vectorized_size;\n         i += vectorized_step_size) {\n      eval.evalPacket(i);\n    }\n    for (Index i = vectorized_size + first; i < last; i += step_size) {\n      eval.evalScalar(i);\n    }\n  }\n};\n\ntemplate <typename Evaluator, typename Index>\n__global__ void\n__launch_bounds__(1024)\nEigenMetaKernel(Evaluator eval, Index size) {\n\n  const Index first_index = blockIdx.x * blockDim.x + threadIdx.x;\n  const Index step_size = blockDim.x * gridDim.x;\n\n  const bool vectorizable = Evaluator::PacketAccess & Evaluator::IsAligned;\n  EigenMetaKernelEval<Evaluator, Index, vectorizable>::run(eval, first_index, size, step_size);\n}\n\n/*static*/\ntemplate <typename Expression, bool Vectorizable>\ninline void TensorExecutor<Expression, GpuDevice, Vectorizable>::run(\n    const Expression& expr, const GpuDevice& device) {\n  TensorEvaluator<Expression, GpuDevice> evaluator(expr, device);\n  const bool needs_assign = evaluator.evalSubExprsIfNeeded(NULL);\n  if (needs_assign) {\n    const int block_size = device.maxCudaThreadsPerBlock();\n    const int max_blocks = device.getNumCudaMultiProcessors() *\n                           device.maxCudaThreadsPerMultiProcessor() / block_size;\n    const Index size = array_prod(evaluator.dimensions());\n    // Create a least one block to ensure we won't crash when tensorflow calls with tensors of size 0.\n    const int num_blocks = numext::maxi<int>(numext::mini<int>(max_blocks, divup<int>(size, block_size)), 1);\n\n    LAUNCH_CUDA_KERNEL(\n        (EigenMetaKernel<TensorEvaluator<Expression, GpuDevice>, Index>),\n        num_blocks, block_size, 0, device, evaluator, size);\n  }\n  evaluator.cleanup();\n}\n\n#endif  // __CUDACC__\n#endif  // EIGEN_USE_GPU\n\n// SYCL Executor policy\n#ifdef EIGEN_USE_SYCL\n\ntemplate <typename Expression, bool Vectorizable>\nclass TensorExecutor<Expression, SyclDevice, Vectorizable> {\npublic:\n  static inline void run(const Expression &expr, const SyclDevice &device) {\n    // call TensorSYCL module\n    TensorSycl::run(expr, device);\n  }\n};\n\n#endif\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_EXECUTOR_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorExpr.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_EXPR_H\n#define EIGEN_CXX11_TENSOR_TENSOR_EXPR_H\n\nnamespace Eigen {\n\n/** \\class TensorExpr\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief Tensor expression classes.\n  *\n  * The TensorCwiseNullaryOp class applies a nullary operators to an expression.\n  * This is typically used to generate constants.\n  *\n  * The TensorCwiseUnaryOp class represents an expression where a unary operator\n  * (e.g. cwiseSqrt) is applied to an expression.\n  *\n  * The TensorCwiseBinaryOp class represents an expression where a binary\n  * operator (e.g. addition) is applied to a lhs and a rhs expression.\n  *\n  */\nnamespace internal {\ntemplate<typename NullaryOp, typename XprType>\nstruct traits<TensorCwiseNullaryOp<NullaryOp, XprType> >\n    : traits<XprType>\n{\n  typedef traits<XprType> XprTraits;\n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::Nested XprTypeNested;\n  typedef typename remove_reference<XprTypeNested>::type _XprTypeNested;\n  static const int NumDimensions = XprTraits::NumDimensions;\n  static const int Layout = XprTraits::Layout;\n\n  enum {\n    Flags = 0\n  };\n};\n\n}  // end namespace internal\n\n\n\ntemplate<typename NullaryOp, typename XprType>\nclass TensorCwiseNullaryOp : public TensorBase<TensorCwiseNullaryOp<NullaryOp, XprType>, ReadOnlyAccessors>\n{\n  public:\n    typedef typename Eigen::internal::traits<TensorCwiseNullaryOp>::Scalar Scalar;\n    typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;\n    typedef typename XprType::CoeffReturnType CoeffReturnType;\n    typedef TensorCwiseNullaryOp<NullaryOp, XprType> Nested;\n    typedef typename Eigen::internal::traits<TensorCwiseNullaryOp>::StorageKind StorageKind;\n    typedef typename Eigen::internal::traits<TensorCwiseNullaryOp>::Index Index;\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorCwiseNullaryOp(const XprType& xpr, const NullaryOp& func = NullaryOp())\n        : m_xpr(xpr), m_functor(func) {}\n\n    EIGEN_DEVICE_FUNC\n    const typename internal::remove_all<typename XprType::Nested>::type&\n    nestedExpression() const { return m_xpr; }\n\n    EIGEN_DEVICE_FUNC\n    const NullaryOp& functor() const { return m_functor; }\n\n  protected:\n    typename XprType::Nested m_xpr;\n    const NullaryOp m_functor;\n};\n\n\n\nnamespace internal {\ntemplate<typename UnaryOp, typename XprType>\nstruct traits<TensorCwiseUnaryOp<UnaryOp, XprType> >\n    : traits<XprType>\n{\n  // TODO(phli): Add InputScalar, InputPacket.  Check references to\n  // current Scalar/Packet to see if the intent is Input or Output.\n  typedef typename result_of<UnaryOp(typename XprType::Scalar)>::type Scalar;\n  typedef traits<XprType> XprTraits;\n  typedef typename XprType::Nested XprTypeNested;\n  typedef typename remove_reference<XprTypeNested>::type _XprTypeNested;\n  static const int NumDimensions = XprTraits::NumDimensions;\n  static const int Layout = XprTraits::Layout;\n};\n\ntemplate<typename UnaryOp, typename XprType>\nstruct eval<TensorCwiseUnaryOp<UnaryOp, XprType>, Eigen::Dense>\n{\n  typedef const TensorCwiseUnaryOp<UnaryOp, XprType>& type;\n};\n\ntemplate<typename UnaryOp, typename XprType>\nstruct nested<TensorCwiseUnaryOp<UnaryOp, XprType>, 1, typename eval<TensorCwiseUnaryOp<UnaryOp, XprType> >::type>\n{\n  typedef TensorCwiseUnaryOp<UnaryOp, XprType> type;\n};\n\n}  // end namespace internal\n\n\n\ntemplate<typename UnaryOp, typename XprType>\nclass TensorCwiseUnaryOp : public TensorBase<TensorCwiseUnaryOp<UnaryOp, XprType>, ReadOnlyAccessors>\n{\n  public:\n    // TODO(phli): Add InputScalar, InputPacket.  Check references to\n    // current Scalar/Packet to see if the intent is Input or Output.\n    typedef typename Eigen::internal::traits<TensorCwiseUnaryOp>::Scalar Scalar;\n    typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;\n    typedef Scalar CoeffReturnType;\n    typedef typename Eigen::internal::nested<TensorCwiseUnaryOp>::type Nested;\n    typedef typename Eigen::internal::traits<TensorCwiseUnaryOp>::StorageKind StorageKind;\n    typedef typename Eigen::internal::traits<TensorCwiseUnaryOp>::Index Index;\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorCwiseUnaryOp(const XprType& xpr, const UnaryOp& func = UnaryOp())\n      : m_xpr(xpr), m_functor(func) {}\n\n    EIGEN_DEVICE_FUNC\n    const UnaryOp& functor() const { return m_functor; }\n\n    /** \\returns the nested expression */\n    EIGEN_DEVICE_FUNC\n    const typename internal::remove_all<typename XprType::Nested>::type&\n    nestedExpression() const { return m_xpr; }\n\n  protected:\n    typename XprType::Nested m_xpr;\n    const UnaryOp m_functor;\n};\n\n\nnamespace internal {\ntemplate<typename BinaryOp, typename LhsXprType, typename RhsXprType>\nstruct traits<TensorCwiseBinaryOp<BinaryOp, LhsXprType, RhsXprType> >\n{\n  // Type promotion to handle the case where the types of the lhs and the rhs\n  // are different.\n  // TODO(phli): Add Lhs/RhsScalar, Lhs/RhsPacket.  Check references to\n  // current Scalar/Packet to see if the intent is Inputs or Output.\n  typedef typename result_of<\n      BinaryOp(typename LhsXprType::Scalar,\n               typename RhsXprType::Scalar)>::type Scalar;\n  typedef traits<LhsXprType> XprTraits;\n  typedef typename promote_storage_type<\n      typename traits<LhsXprType>::StorageKind,\n      typename traits<RhsXprType>::StorageKind>::ret StorageKind;\n  typedef typename promote_index_type<\n      typename traits<LhsXprType>::Index,\n      typename traits<RhsXprType>::Index>::type Index;\n  typedef typename LhsXprType::Nested LhsNested;\n  typedef typename RhsXprType::Nested RhsNested;\n  typedef typename remove_reference<LhsNested>::type _LhsNested;\n  typedef typename remove_reference<RhsNested>::type _RhsNested;\n  static const int NumDimensions = XprTraits::NumDimensions;\n  static const int Layout = XprTraits::Layout;\n\n  enum {\n    Flags = 0\n  };\n};\n\ntemplate<typename BinaryOp, typename LhsXprType, typename RhsXprType>\nstruct eval<TensorCwiseBinaryOp<BinaryOp, LhsXprType, RhsXprType>, Eigen::Dense>\n{\n  typedef const TensorCwiseBinaryOp<BinaryOp, LhsXprType, RhsXprType>& type;\n};\n\ntemplate<typename BinaryOp, typename LhsXprType, typename RhsXprType>\nstruct nested<TensorCwiseBinaryOp<BinaryOp, LhsXprType, RhsXprType>, 1, typename eval<TensorCwiseBinaryOp<BinaryOp, LhsXprType, RhsXprType> >::type>\n{\n  typedef TensorCwiseBinaryOp<BinaryOp, LhsXprType, RhsXprType> type;\n};\n\n}  // end namespace internal\n\n\n\ntemplate<typename BinaryOp, typename LhsXprType, typename RhsXprType>\nclass TensorCwiseBinaryOp : public TensorBase<TensorCwiseBinaryOp<BinaryOp, LhsXprType, RhsXprType>, ReadOnlyAccessors>\n{\n  public:\n    // TODO(phli): Add Lhs/RhsScalar, Lhs/RhsPacket.  Check references to\n    // current Scalar/Packet to see if the intent is Inputs or Output.\n    typedef typename Eigen::internal::traits<TensorCwiseBinaryOp>::Scalar Scalar;\n    typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;\n    typedef Scalar CoeffReturnType;\n    typedef typename Eigen::internal::nested<TensorCwiseBinaryOp>::type Nested;\n    typedef typename Eigen::internal::traits<TensorCwiseBinaryOp>::StorageKind StorageKind;\n    typedef typename Eigen::internal::traits<TensorCwiseBinaryOp>::Index Index;\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorCwiseBinaryOp(const LhsXprType& lhs, const RhsXprType& rhs, const BinaryOp& func = BinaryOp())\n        : m_lhs_xpr(lhs), m_rhs_xpr(rhs), m_functor(func) {}\n\n    EIGEN_DEVICE_FUNC\n    const BinaryOp& functor() const { return m_functor; }\n\n    /** \\returns the nested expressions */\n    EIGEN_DEVICE_FUNC\n    const typename internal::remove_all<typename LhsXprType::Nested>::type&\n    lhsExpression() const { return m_lhs_xpr; }\n\n    EIGEN_DEVICE_FUNC\n    const typename internal::remove_all<typename RhsXprType::Nested>::type&\n    rhsExpression() const { return m_rhs_xpr; }\n\n  protected:\n    typename LhsXprType::Nested m_lhs_xpr;\n    typename RhsXprType::Nested m_rhs_xpr;\n    const BinaryOp m_functor;\n};\n\n\nnamespace internal {\ntemplate<typename TernaryOp, typename Arg1XprType, typename Arg2XprType, typename Arg3XprType>\nstruct traits<TensorCwiseTernaryOp<TernaryOp, Arg1XprType, Arg2XprType, Arg3XprType> >\n{\n  // Type promotion to handle the case where the types of the args are different.\n  typedef typename result_of<\n      TernaryOp(typename Arg1XprType::Scalar,\n                typename Arg2XprType::Scalar,\n                typename Arg3XprType::Scalar)>::type Scalar;\n  typedef traits<Arg1XprType> XprTraits;\n  typedef typename traits<Arg1XprType>::StorageKind StorageKind;\n  typedef typename traits<Arg1XprType>::Index Index;\n  typedef typename Arg1XprType::Nested Arg1Nested;\n  typedef typename Arg2XprType::Nested Arg2Nested;\n  typedef typename Arg3XprType::Nested Arg3Nested;\n  typedef typename remove_reference<Arg1Nested>::type _Arg1Nested;\n  typedef typename remove_reference<Arg2Nested>::type _Arg2Nested;\n  typedef typename remove_reference<Arg3Nested>::type _Arg3Nested;\n  static const int NumDimensions = XprTraits::NumDimensions;\n  static const int Layout = XprTraits::Layout;\n\n  enum {\n    Flags = 0\n  };\n};\n\ntemplate<typename TernaryOp, typename Arg1XprType, typename Arg2XprType, typename Arg3XprType>\nstruct eval<TensorCwiseTernaryOp<TernaryOp, Arg1XprType, Arg2XprType, Arg3XprType>, Eigen::Dense>\n{\n  typedef const TensorCwiseTernaryOp<TernaryOp, Arg1XprType, Arg2XprType, Arg3XprType>& type;\n};\n\ntemplate<typename TernaryOp, typename Arg1XprType, typename Arg2XprType, typename Arg3XprType>\nstruct nested<TensorCwiseTernaryOp<TernaryOp, Arg1XprType, Arg2XprType, Arg3XprType>, 1, typename eval<TensorCwiseTernaryOp<TernaryOp, Arg1XprType, Arg2XprType, Arg3XprType> >::type>\n{\n  typedef TensorCwiseTernaryOp<TernaryOp, Arg1XprType, Arg2XprType, Arg3XprType> type;\n};\n\n}  // end namespace internal\n\n\n\ntemplate<typename TernaryOp, typename Arg1XprType, typename Arg2XprType, typename Arg3XprType>\nclass TensorCwiseTernaryOp : public TensorBase<TensorCwiseTernaryOp<TernaryOp, Arg1XprType, Arg2XprType, Arg3XprType>, ReadOnlyAccessors>\n{\n  public:\n    typedef typename Eigen::internal::traits<TensorCwiseTernaryOp>::Scalar Scalar;\n    typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;\n    typedef Scalar CoeffReturnType;\n    typedef typename Eigen::internal::nested<TensorCwiseTernaryOp>::type Nested;\n    typedef typename Eigen::internal::traits<TensorCwiseTernaryOp>::StorageKind StorageKind;\n    typedef typename Eigen::internal::traits<TensorCwiseTernaryOp>::Index Index;\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorCwiseTernaryOp(const Arg1XprType& arg1, const Arg2XprType& arg2, const Arg3XprType& arg3, const TernaryOp& func = TernaryOp())\n        : m_arg1_xpr(arg1), m_arg2_xpr(arg2), m_arg3_xpr(arg3), m_functor(func) {}\n\n    EIGEN_DEVICE_FUNC\n    const TernaryOp& functor() const { return m_functor; }\n\n    /** \\returns the nested expressions */\n    EIGEN_DEVICE_FUNC\n    const typename internal::remove_all<typename Arg1XprType::Nested>::type&\n    arg1Expression() const { return m_arg1_xpr; }\n\n    EIGEN_DEVICE_FUNC\n    const typename internal::remove_all<typename Arg2XprType::Nested>::type&\n    arg2Expression() const { return m_arg2_xpr; }\n\n    EIGEN_DEVICE_FUNC\n    const typename internal::remove_all<typename Arg3XprType::Nested>::type&\n    arg3Expression() const { return m_arg3_xpr; }\n\n  protected:\n    typename Arg1XprType::Nested m_arg1_xpr;\n    typename Arg2XprType::Nested m_arg2_xpr;\n    typename Arg3XprType::Nested m_arg3_xpr;\n    const TernaryOp m_functor;\n};\n\n\nnamespace internal {\ntemplate<typename IfXprType, typename ThenXprType, typename ElseXprType>\nstruct traits<TensorSelectOp<IfXprType, ThenXprType, ElseXprType> >\n    : traits<ThenXprType>\n{\n  typedef typename traits<ThenXprType>::Scalar Scalar;\n  typedef traits<ThenXprType> XprTraits;\n  typedef typename promote_storage_type<typename traits<ThenXprType>::StorageKind,\n                                        typename traits<ElseXprType>::StorageKind>::ret StorageKind;\n  typedef typename promote_index_type<typename traits<ElseXprType>::Index,\n                                      typename traits<ThenXprType>::Index>::type Index;\n  typedef typename IfXprType::Nested IfNested;\n  typedef typename ThenXprType::Nested ThenNested;\n  typedef typename ElseXprType::Nested ElseNested;\n  static const int NumDimensions = XprTraits::NumDimensions;\n  static const int Layout = XprTraits::Layout;\n};\n\ntemplate<typename IfXprType, typename ThenXprType, typename ElseXprType>\nstruct eval<TensorSelectOp<IfXprType, ThenXprType, ElseXprType>, Eigen::Dense>\n{\n  typedef const TensorSelectOp<IfXprType, ThenXprType, ElseXprType>& type;\n};\n\ntemplate<typename IfXprType, typename ThenXprType, typename ElseXprType>\nstruct nested<TensorSelectOp<IfXprType, ThenXprType, ElseXprType>, 1, typename eval<TensorSelectOp<IfXprType, ThenXprType, ElseXprType> >::type>\n{\n  typedef TensorSelectOp<IfXprType, ThenXprType, ElseXprType> type;\n};\n\n}  // end namespace internal\n\n\ntemplate<typename IfXprType, typename ThenXprType, typename ElseXprType>\nclass TensorSelectOp : public TensorBase<TensorSelectOp<IfXprType, ThenXprType, ElseXprType>, ReadOnlyAccessors>\n{\n  public:\n    typedef typename Eigen::internal::traits<TensorSelectOp>::Scalar Scalar;\n    typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;\n    typedef typename internal::promote_storage_type<typename ThenXprType::CoeffReturnType,\n                                                    typename ElseXprType::CoeffReturnType>::ret CoeffReturnType;\n    typedef typename Eigen::internal::nested<TensorSelectOp>::type Nested;\n    typedef typename Eigen::internal::traits<TensorSelectOp>::StorageKind StorageKind;\n    typedef typename Eigen::internal::traits<TensorSelectOp>::Index Index;\n\n    EIGEN_DEVICE_FUNC\n    TensorSelectOp(const IfXprType& a_condition,\n                   const ThenXprType& a_then,\n                   const ElseXprType& a_else)\n      : m_condition(a_condition), m_then(a_then), m_else(a_else)\n    { }\n\n    EIGEN_DEVICE_FUNC\n    const IfXprType& ifExpression() const { return m_condition; }\n\n    EIGEN_DEVICE_FUNC\n    const ThenXprType& thenExpression() const { return m_then; }\n\n    EIGEN_DEVICE_FUNC\n    const ElseXprType& elseExpression() const { return m_else; }\n\n  protected:\n    typename IfXprType::Nested m_condition;\n    typename ThenXprType::Nested m_then;\n    typename ElseXprType::Nested m_else;\n};\n\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_EXPR_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorFFT.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Jianwei Cui <thucjw@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_FFT_H\n#define EIGEN_CXX11_TENSOR_TENSOR_FFT_H\n\n// This code requires the ability to initialize arrays of constant\n// values directly inside a class.\n#if __cplusplus >= 201103L || EIGEN_COMP_MSVC >= 1900\n\nnamespace Eigen {\n\n/** \\class TensorFFT\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief Tensor FFT class.\n  *\n  * TODO:\n  * Vectorize the Cooley Tukey and the Bluestein algorithm\n  * Add support for multithreaded evaluation\n  * Improve the performance on GPU\n  */\n\ntemplate <bool NeedUprade> struct MakeComplex {\n  template <typename T>\n  EIGEN_DEVICE_FUNC\n  T operator() (const T& val) const { return val; }\n};\n\ntemplate <> struct MakeComplex<true> {\n  template <typename T>\n  EIGEN_DEVICE_FUNC\n  std::complex<T> operator() (const T& val) const { return std::complex<T>(val, 0); }\n};\n\ntemplate <> struct MakeComplex<false> {\n  template <typename T>\n  EIGEN_DEVICE_FUNC\n  std::complex<T> operator() (const std::complex<T>& val) const { return val; }\n};\n\ntemplate <int ResultType> struct PartOf {\n  template <typename T> T operator() (const T& val) const { return val; }\n};\n\ntemplate <> struct PartOf<RealPart> {\n  template <typename T> T operator() (const std::complex<T>& val) const { return val.real(); }\n};\n\ntemplate <> struct PartOf<ImagPart> {\n  template <typename T> T operator() (const std::complex<T>& val) const { return val.imag(); }\n};\n\nnamespace internal {\ntemplate <typename FFT, typename XprType, int FFTResultType, int FFTDir>\nstruct traits<TensorFFTOp<FFT, XprType, FFTResultType, FFTDir> > : public traits<XprType> {\n  typedef traits<XprType> XprTraits;\n  typedef typename NumTraits<typename XprTraits::Scalar>::Real RealScalar;\n  typedef typename std::complex<RealScalar> ComplexScalar;\n  typedef typename XprTraits::Scalar InputScalar;\n  typedef typename conditional<FFTResultType == RealPart || FFTResultType == ImagPart, RealScalar, ComplexScalar>::type OutputScalar;\n  typedef typename XprTraits::StorageKind StorageKind;\n  typedef typename XprTraits::Index Index;\n  typedef typename XprType::Nested Nested;\n  typedef typename remove_reference<Nested>::type _Nested;\n  static const int NumDimensions = XprTraits::NumDimensions;\n  static const int Layout = XprTraits::Layout;\n};\n\ntemplate <typename FFT, typename XprType, int FFTResultType, int FFTDirection>\nstruct eval<TensorFFTOp<FFT, XprType, FFTResultType, FFTDirection>, Eigen::Dense> {\n  typedef const TensorFFTOp<FFT, XprType, FFTResultType, FFTDirection>& type;\n};\n\ntemplate <typename FFT, typename XprType, int FFTResultType, int FFTDirection>\nstruct nested<TensorFFTOp<FFT, XprType, FFTResultType, FFTDirection>, 1, typename eval<TensorFFTOp<FFT, XprType, FFTResultType, FFTDirection> >::type> {\n  typedef TensorFFTOp<FFT, XprType, FFTResultType, FFTDirection> type;\n};\n\n}  // end namespace internal\n\ntemplate <typename FFT, typename XprType, int FFTResultType, int FFTDir>\nclass TensorFFTOp : public TensorBase<TensorFFTOp<FFT, XprType, FFTResultType, FFTDir>, ReadOnlyAccessors> {\n public:\n  typedef typename Eigen::internal::traits<TensorFFTOp>::Scalar Scalar;\n  typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;\n  typedef typename std::complex<RealScalar> ComplexScalar;\n  typedef typename internal::conditional<FFTResultType == RealPart || FFTResultType == ImagPart, RealScalar, ComplexScalar>::type OutputScalar;\n  typedef OutputScalar CoeffReturnType;\n  typedef typename Eigen::internal::nested<TensorFFTOp>::type Nested;\n  typedef typename Eigen::internal::traits<TensorFFTOp>::StorageKind StorageKind;\n  typedef typename Eigen::internal::traits<TensorFFTOp>::Index Index;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorFFTOp(const XprType& expr, const FFT& fft)\n      : m_xpr(expr), m_fft(fft) {}\n\n  EIGEN_DEVICE_FUNC\n  const FFT& fft() const { return m_fft; }\n\n  EIGEN_DEVICE_FUNC\n  const typename internal::remove_all<typename XprType::Nested>::type& expression() const {\n    return m_xpr;\n  }\n\n protected:\n  typename XprType::Nested m_xpr;\n  const FFT m_fft;\n};\n\n// Eval as rvalue\ntemplate <typename FFT, typename ArgType, typename Device, int FFTResultType, int FFTDir>\nstruct TensorEvaluator<const TensorFFTOp<FFT, ArgType, FFTResultType, FFTDir>, Device> {\n  typedef TensorFFTOp<FFT, ArgType, FFTResultType, FFTDir> XprType;\n  typedef typename XprType::Index Index;\n  static const int NumDims = internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value;\n  typedef DSizes<Index, NumDims> Dimensions;\n  typedef typename XprType::Scalar Scalar;\n  typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;\n  typedef typename std::complex<RealScalar> ComplexScalar;\n  typedef typename TensorEvaluator<ArgType, Device>::Dimensions InputDimensions;\n  typedef internal::traits<XprType> XprTraits;\n  typedef typename XprTraits::Scalar InputScalar;\n  typedef typename internal::conditional<FFTResultType == RealPart || FFTResultType == ImagPart, RealScalar, ComplexScalar>::type OutputScalar;\n  typedef OutputScalar CoeffReturnType;\n  typedef typename PacketType<OutputScalar, Device>::type PacketReturnType;\n  static const int PacketSize = internal::unpacket_traits<PacketReturnType>::size;\n\n  enum {\n    IsAligned = false,\n    PacketAccess = true,\n    BlockAccess = false,\n    Layout = TensorEvaluator<ArgType, Device>::Layout,\n    CoordAccess = false,\n    RawAccess = false\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device) : m_fft(op.fft()), m_impl(op.expression(), device), m_data(NULL), m_device(device) {\n    const typename TensorEvaluator<ArgType, Device>::Dimensions& input_dims = m_impl.dimensions();\n    for (int i = 0; i < NumDims; ++i) {\n      eigen_assert(input_dims[i] > 0);\n      m_dimensions[i] = input_dims[i];\n    }\n\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      m_strides[0] = 1;\n      for (int i = 1; i < NumDims; ++i) {\n        m_strides[i] = m_strides[i - 1] * m_dimensions[i - 1];\n      }\n    } else {\n      m_strides[NumDims - 1] = 1;\n      for (int i = NumDims - 2; i >= 0; --i) {\n        m_strides[i] = m_strides[i + 1] * m_dimensions[i + 1];\n      }\n    }\n    m_size = m_dimensions.TotalSize();\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const {\n    return m_dimensions;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(OutputScalar* data) {\n    m_impl.evalSubExprsIfNeeded(NULL);\n    if (data) {\n      evalToBuf(data);\n      return false;\n    } else {\n      m_data = (CoeffReturnType*)m_device.allocate(sizeof(CoeffReturnType) * m_size);\n      evalToBuf(m_data);\n      return true;\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {\n    if (m_data) {\n      m_device.deallocate(m_data);\n      m_data = NULL;\n    }\n    m_impl.cleanup();\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE CoeffReturnType coeff(Index index) const {\n    return m_data[index];\n  }\n\n  template <int LoadMode>\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketReturnType\n  packet(Index index) const {\n    return internal::ploadt<PacketReturnType, LoadMode>(m_data + index);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost\n  costPerCoeff(bool vectorized) const {\n    return TensorOpCost(sizeof(CoeffReturnType), 0, 0, vectorized, PacketSize);\n  }\n\n  EIGEN_DEVICE_FUNC Scalar* data() const { return m_data; }\n\n\n private:\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalToBuf(OutputScalar* data) {\n    const bool write_to_out = internal::is_same<OutputScalar, ComplexScalar>::value;\n    ComplexScalar* buf = write_to_out ? (ComplexScalar*)data : (ComplexScalar*)m_device.allocate(sizeof(ComplexScalar) * m_size);\n\n    for (Index i = 0; i < m_size; ++i) {\n      buf[i] = MakeComplex<internal::is_same<InputScalar, RealScalar>::value>()(m_impl.coeff(i));\n    }\n\n    for (size_t i = 0; i < m_fft.size(); ++i) {\n      Index dim = m_fft[i];\n      eigen_assert(dim >= 0 && dim < NumDims);\n      Index line_len = m_dimensions[dim];\n      eigen_assert(line_len >= 1);\n      ComplexScalar* line_buf = (ComplexScalar*)m_device.allocate(sizeof(ComplexScalar) * line_len);\n      const bool is_power_of_two = isPowerOfTwo(line_len);\n      const Index good_composite = is_power_of_two ? 0 : findGoodComposite(line_len);\n      const Index log_len = is_power_of_two ? getLog2(line_len) : getLog2(good_composite);\n\n      ComplexScalar* a = is_power_of_two ? NULL : (ComplexScalar*)m_device.allocate(sizeof(ComplexScalar) * good_composite);\n      ComplexScalar* b = is_power_of_two ? NULL : (ComplexScalar*)m_device.allocate(sizeof(ComplexScalar) * good_composite);\n      ComplexScalar* pos_j_base_powered = is_power_of_two ? NULL : (ComplexScalar*)m_device.allocate(sizeof(ComplexScalar) * (line_len + 1));\n      if (!is_power_of_two) {\n        // Compute twiddle factors\n        //   t_n = exp(sqrt(-1) * pi * n^2 / line_len)\n        // for n = 0, 1,..., line_len-1.\n        // For n > 2 we use the recurrence t_n = t_{n-1}^2 / t_{n-2} * t_1^2\n        pos_j_base_powered[0] = ComplexScalar(1, 0);\n        if (line_len > 1) {\n          const RealScalar pi_over_len(EIGEN_PI / line_len);\n          const ComplexScalar pos_j_base = ComplexScalar(\n\t       std::cos(pi_over_len), std::sin(pi_over_len));\n          pos_j_base_powered[1] = pos_j_base;\n          if (line_len > 2) {\n            const ComplexScalar pos_j_base_sq = pos_j_base * pos_j_base;\n            for (int j = 2; j < line_len + 1; ++j) {\n              pos_j_base_powered[j] = pos_j_base_powered[j - 1] *\n                                      pos_j_base_powered[j - 1] /\n                                      pos_j_base_powered[j - 2] * pos_j_base_sq;\n            }\n          }\n        }\n      }\n\n      for (Index partial_index = 0; partial_index < m_size / line_len; ++partial_index) {\n        const Index base_offset = getBaseOffsetFromIndex(partial_index, dim);\n\n        // get data into line_buf\n        const Index stride = m_strides[dim];\n        if (stride == 1) {\n          memcpy(line_buf, &buf[base_offset], line_len*sizeof(ComplexScalar));\n        } else {\n          Index offset = base_offset;\n          for (int j = 0; j < line_len; ++j, offset += stride) {\n            line_buf[j] = buf[offset];\n          }\n        }\n\n        // processs the line\n        if (is_power_of_two) {\n          processDataLineCooleyTukey(line_buf, line_len, log_len);\n        }\n        else {\n          processDataLineBluestein(line_buf, line_len, good_composite, log_len, a, b, pos_j_base_powered);\n        }\n\n        // write back\n        if (FFTDir == FFT_FORWARD && stride == 1) {\n          memcpy(&buf[base_offset], line_buf, line_len*sizeof(ComplexScalar));\n        } else {\n          Index offset = base_offset;\n          const ComplexScalar div_factor =  ComplexScalar(1.0 / line_len, 0);\n          for (int j = 0; j < line_len; ++j, offset += stride) {\n             buf[offset] = (FFTDir == FFT_FORWARD) ? line_buf[j] : line_buf[j] * div_factor;\n          }\n        }\n      }\n      m_device.deallocate(line_buf);\n      if (!is_power_of_two) {\n        m_device.deallocate(a);\n        m_device.deallocate(b);\n        m_device.deallocate(pos_j_base_powered);\n      }\n    }\n\n    if(!write_to_out) {\n      for (Index i = 0; i < m_size; ++i) {\n        data[i] = PartOf<FFTResultType>()(buf[i]);\n      }\n      m_device.deallocate(buf);\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE static bool isPowerOfTwo(Index x) {\n    eigen_assert(x > 0);\n    return !(x & (x - 1));\n  }\n\n  // The composite number for padding, used in Bluestein's FFT algorithm\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE static Index findGoodComposite(Index n) {\n    Index i = 2;\n    while (i < 2 * n - 1) i *= 2;\n    return i;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE static Index getLog2(Index m) {\n    Index log2m = 0;\n    while (m >>= 1) log2m++;\n    return log2m;\n  }\n\n  // Call Cooley Tukey algorithm directly, data length must be power of 2\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void processDataLineCooleyTukey(ComplexScalar* line_buf, Index line_len, Index log_len) {\n    eigen_assert(isPowerOfTwo(line_len));\n    scramble_FFT(line_buf, line_len);\n    compute_1D_Butterfly<FFTDir>(line_buf, line_len, log_len);\n  }\n\n  // Call Bluestein's FFT algorithm, m is a good composite number greater than (2 * n - 1), used as the padding length\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void processDataLineBluestein(ComplexScalar* line_buf, Index line_len, Index good_composite, Index log_len, ComplexScalar* a, ComplexScalar* b, const ComplexScalar* pos_j_base_powered) {\n    Index n = line_len;\n    Index m = good_composite;\n    ComplexScalar* data = line_buf;\n\n    for (Index i = 0; i < n; ++i) {\n      if(FFTDir == FFT_FORWARD) {\n        a[i] = data[i] * numext::conj(pos_j_base_powered[i]);\n      }\n      else {\n        a[i] = data[i] * pos_j_base_powered[i];\n      }\n    }\n    for (Index i = n; i < m; ++i) {\n      a[i] = ComplexScalar(0, 0);\n    }\n\n    for (Index i = 0; i < n; ++i) {\n      if(FFTDir == FFT_FORWARD) {\n        b[i] = pos_j_base_powered[i];\n      }\n      else {\n        b[i] = numext::conj(pos_j_base_powered[i]);\n      }\n    }\n    for (Index i = n; i < m - n; ++i) {\n      b[i] = ComplexScalar(0, 0);\n    }\n    for (Index i = m - n; i < m; ++i) {\n      if(FFTDir == FFT_FORWARD) {\n        b[i] = pos_j_base_powered[m-i];\n      }\n      else {\n        b[i] = numext::conj(pos_j_base_powered[m-i]);\n      }\n    }\n\n    scramble_FFT(a, m);\n    compute_1D_Butterfly<FFT_FORWARD>(a, m, log_len);\n\n    scramble_FFT(b, m);\n    compute_1D_Butterfly<FFT_FORWARD>(b, m, log_len);\n\n    for (Index i = 0; i < m; ++i) {\n      a[i] *= b[i];\n    }\n\n    scramble_FFT(a, m);\n    compute_1D_Butterfly<FFT_REVERSE>(a, m, log_len);\n\n    //Do the scaling after ifft\n    for (Index i = 0; i < m; ++i) {\n      a[i] /= m;\n    }\n\n    for (Index i = 0; i < n; ++i) {\n      if(FFTDir == FFT_FORWARD) {\n        data[i] = a[i] * numext::conj(pos_j_base_powered[i]);\n      }\n      else {\n        data[i] = a[i] * pos_j_base_powered[i];\n      }\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE static void scramble_FFT(ComplexScalar* data, Index n) {\n    eigen_assert(isPowerOfTwo(n));\n    Index j = 1;\n    for (Index i = 1; i < n; ++i){\n      if (j > i) {\n        std::swap(data[j-1], data[i-1]);\n      }\n      Index m = n >> 1;\n      while (m >= 2 && j > m) {\n        j -= m;\n        m >>= 1;\n      }\n      j += m;\n    }\n  }\n\n  template <int Dir>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void butterfly_2(ComplexScalar* data) {\n    ComplexScalar tmp = data[1];\n    data[1] = data[0] - data[1];\n    data[0] += tmp;\n  }\n\n  template <int Dir>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void butterfly_4(ComplexScalar* data) {\n    ComplexScalar tmp[4];\n    tmp[0] = data[0] + data[1];\n    tmp[1] = data[0] - data[1];\n    tmp[2] = data[2] + data[3];\n    if (Dir == FFT_FORWARD) {\n      tmp[3] = ComplexScalar(0.0, -1.0) * (data[2] - data[3]);\n    } else {\n      tmp[3] = ComplexScalar(0.0, 1.0) * (data[2] - data[3]);\n    }\n    data[0] = tmp[0] + tmp[2];\n    data[1] = tmp[1] + tmp[3];\n    data[2] = tmp[0] - tmp[2];\n    data[3] = tmp[1] - tmp[3];\n  }\n\n  template <int Dir>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void butterfly_8(ComplexScalar* data) {\n    ComplexScalar tmp_1[8];\n    ComplexScalar tmp_2[8];\n\n    tmp_1[0] = data[0] + data[1];\n    tmp_1[1] = data[0] - data[1];\n    tmp_1[2] = data[2] + data[3];\n    if (Dir == FFT_FORWARD) {\n      tmp_1[3] = (data[2] - data[3]) * ComplexScalar(0, -1);\n    } else {\n      tmp_1[3] = (data[2] - data[3]) * ComplexScalar(0, 1);\n    }\n    tmp_1[4] = data[4] + data[5];\n    tmp_1[5] = data[4] - data[5];\n    tmp_1[6] = data[6] + data[7];\n    if (Dir == FFT_FORWARD) {\n      tmp_1[7] = (data[6] - data[7]) * ComplexScalar(0, -1);\n    } else {\n      tmp_1[7] = (data[6] - data[7]) * ComplexScalar(0, 1);\n    }\n    tmp_2[0] = tmp_1[0] + tmp_1[2];\n    tmp_2[1] = tmp_1[1] + tmp_1[3];\n    tmp_2[2] = tmp_1[0] - tmp_1[2];\n    tmp_2[3] = tmp_1[1] - tmp_1[3];\n    tmp_2[4] = tmp_1[4] + tmp_1[6];\n// SQRT2DIV2 = sqrt(2)/2\n#define SQRT2DIV2 0.7071067811865476\n    if (Dir == FFT_FORWARD) {\n      tmp_2[5] = (tmp_1[5] + tmp_1[7]) * ComplexScalar(SQRT2DIV2, -SQRT2DIV2);\n      tmp_2[6] = (tmp_1[4] - tmp_1[6]) * ComplexScalar(0, -1);\n      tmp_2[7] = (tmp_1[5] - tmp_1[7]) * ComplexScalar(-SQRT2DIV2, -SQRT2DIV2);\n    } else {\n      tmp_2[5] = (tmp_1[5] + tmp_1[7]) * ComplexScalar(SQRT2DIV2, SQRT2DIV2);\n      tmp_2[6] = (tmp_1[4] - tmp_1[6]) * ComplexScalar(0, 1);\n      tmp_2[7] = (tmp_1[5] - tmp_1[7]) * ComplexScalar(-SQRT2DIV2, SQRT2DIV2);\n    }\n    data[0] = tmp_2[0] + tmp_2[4];\n    data[1] = tmp_2[1] + tmp_2[5];\n    data[2] = tmp_2[2] + tmp_2[6];\n    data[3] = tmp_2[3] + tmp_2[7];\n    data[4] = tmp_2[0] - tmp_2[4];\n    data[5] = tmp_2[1] - tmp_2[5];\n    data[6] = tmp_2[2] - tmp_2[6];\n    data[7] = tmp_2[3] - tmp_2[7];\n  }\n\n  template <int Dir>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void butterfly_1D_merge(\n      ComplexScalar* data, Index n, Index n_power_of_2) {\n    // Original code:\n    // RealScalar wtemp = std::sin(M_PI/n);\n    // RealScalar wpi =  -std::sin(2 * M_PI/n);\n    const RealScalar wtemp = m_sin_PI_div_n_LUT[n_power_of_2];\n    const RealScalar wpi = (Dir == FFT_FORWARD)\n                               ? m_minus_sin_2_PI_div_n_LUT[n_power_of_2]\n                               : -m_minus_sin_2_PI_div_n_LUT[n_power_of_2];\n\n    const ComplexScalar wp(wtemp, wpi);\n    const ComplexScalar wp_one = wp + ComplexScalar(1, 0);\n    const ComplexScalar wp_one_2 = wp_one * wp_one;\n    const ComplexScalar wp_one_3 = wp_one_2 * wp_one;\n    const ComplexScalar wp_one_4 = wp_one_3 * wp_one;\n    const Index n2 = n / 2;\n    ComplexScalar w(1.0, 0.0);\n    for (Index i = 0; i < n2; i += 4) {\n       ComplexScalar temp0(data[i + n2] * w);\n       ComplexScalar temp1(data[i + 1 + n2] * w * wp_one);\n       ComplexScalar temp2(data[i + 2 + n2] * w * wp_one_2);\n       ComplexScalar temp3(data[i + 3 + n2] * w * wp_one_3);\n       w = w * wp_one_4;\n\n       data[i + n2] = data[i] - temp0;\n       data[i] += temp0;\n\n       data[i + 1 + n2] = data[i + 1] - temp1;\n       data[i + 1] += temp1;\n\n       data[i + 2 + n2] = data[i + 2] - temp2;\n       data[i + 2] += temp2;\n\n       data[i + 3 + n2] = data[i + 3] - temp3;\n       data[i + 3] += temp3;\n    }\n  }\n\n template <int Dir>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void compute_1D_Butterfly(\n      ComplexScalar* data, Index n, Index n_power_of_2) {\n    eigen_assert(isPowerOfTwo(n));\n    if (n > 8) {\n      compute_1D_Butterfly<Dir>(data, n / 2, n_power_of_2 - 1);\n      compute_1D_Butterfly<Dir>(data + n / 2, n / 2, n_power_of_2 - 1);\n      butterfly_1D_merge<Dir>(data, n, n_power_of_2);\n    } else if (n == 8) {\n      butterfly_8<Dir>(data);\n    } else if (n == 4) {\n      butterfly_4<Dir>(data);\n    } else if (n == 2) {\n      butterfly_2<Dir>(data);\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index getBaseOffsetFromIndex(Index index, Index omitted_dim) const {\n    Index result = 0;\n\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      for (int i = NumDims - 1; i > omitted_dim; --i) {\n        const Index partial_m_stride = m_strides[i] / m_dimensions[omitted_dim];\n        const Index idx = index / partial_m_stride;\n        index -= idx * partial_m_stride;\n        result += idx * m_strides[i];\n      }\n      result += index;\n    }\n    else {\n      for (Index i = 0; i < omitted_dim; ++i) {\n        const Index partial_m_stride = m_strides[i] / m_dimensions[omitted_dim];\n        const Index idx = index / partial_m_stride;\n        index -= idx * partial_m_stride;\n        result += idx * m_strides[i];\n      }\n      result += index;\n    }\n    // Value of index_coords[omitted_dim] is not determined to this step\n    return result;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index getIndexFromOffset(Index base, Index omitted_dim, Index offset) const {\n    Index result = base + offset * m_strides[omitted_dim] ;\n    return result;\n  }\n\n protected:\n  Index m_size;\n  const FFT& m_fft;\n  Dimensions m_dimensions;\n  array<Index, NumDims> m_strides;\n  TensorEvaluator<ArgType, Device> m_impl;\n  CoeffReturnType* m_data;\n  const Device& m_device;\n\n  // This will support a maximum FFT size of 2^32 for each dimension\n  // m_sin_PI_div_n_LUT[i] = (-2) * std::sin(M_PI / std::pow(2,i)) ^ 2;\n  const RealScalar m_sin_PI_div_n_LUT[32] = {\n    RealScalar(0.0),\n    RealScalar(-2),\n    RealScalar(-0.999999999999999),\n    RealScalar(-0.292893218813453),\n    RealScalar(-0.0761204674887130),\n    RealScalar(-0.0192147195967696),\n    RealScalar(-0.00481527332780311),\n    RealScalar(-0.00120454379482761),\n    RealScalar(-3.01181303795779e-04),\n    RealScalar(-7.52981608554592e-05),\n    RealScalar(-1.88247173988574e-05),\n    RealScalar(-4.70619042382852e-06),\n    RealScalar(-1.17654829809007e-06),\n    RealScalar(-2.94137117780840e-07),\n    RealScalar(-7.35342821488550e-08),\n    RealScalar(-1.83835707061916e-08),\n    RealScalar(-4.59589268710903e-09),\n    RealScalar(-1.14897317243732e-09),\n    RealScalar(-2.87243293150586e-10),\n    RealScalar( -7.18108232902250e-11),\n    RealScalar(-1.79527058227174e-11),\n    RealScalar(-4.48817645568941e-12),\n    RealScalar(-1.12204411392298e-12),\n    RealScalar(-2.80511028480785e-13),\n    RealScalar(-7.01277571201985e-14),\n    RealScalar(-1.75319392800498e-14),\n    RealScalar(-4.38298482001247e-15),\n    RealScalar(-1.09574620500312e-15),\n    RealScalar(-2.73936551250781e-16),\n    RealScalar(-6.84841378126949e-17),\n    RealScalar(-1.71210344531737e-17),\n    RealScalar(-4.28025861329343e-18)\n  };\n\n  // m_minus_sin_2_PI_div_n_LUT[i] = -std::sin(2 * M_PI / std::pow(2,i));\n  const RealScalar m_minus_sin_2_PI_div_n_LUT[32] = {\n    RealScalar(0.0),\n    RealScalar(0.0),\n    RealScalar(-1.00000000000000e+00),\n    RealScalar(-7.07106781186547e-01),\n    RealScalar(-3.82683432365090e-01),\n    RealScalar(-1.95090322016128e-01),\n    RealScalar(-9.80171403295606e-02),\n    RealScalar(-4.90676743274180e-02),\n    RealScalar(-2.45412285229123e-02),\n    RealScalar(-1.22715382857199e-02),\n    RealScalar(-6.13588464915448e-03),\n    RealScalar(-3.06795676296598e-03),\n    RealScalar(-1.53398018628477e-03),\n    RealScalar(-7.66990318742704e-04),\n    RealScalar(-3.83495187571396e-04),\n    RealScalar(-1.91747597310703e-04),\n    RealScalar(-9.58737990959773e-05),\n    RealScalar(-4.79368996030669e-05),\n    RealScalar(-2.39684498084182e-05),\n    RealScalar(-1.19842249050697e-05),\n    RealScalar(-5.99211245264243e-06),\n    RealScalar(-2.99605622633466e-06),\n    RealScalar(-1.49802811316901e-06),\n    RealScalar(-7.49014056584716e-07),\n    RealScalar(-3.74507028292384e-07),\n    RealScalar(-1.87253514146195e-07),\n    RealScalar(-9.36267570730981e-08),\n    RealScalar(-4.68133785365491e-08),\n    RealScalar(-2.34066892682746e-08),\n    RealScalar(-1.17033446341373e-08),\n    RealScalar(-5.85167231706864e-09),\n    RealScalar(-2.92583615853432e-09)\n  };\n};\n\n}  // end namespace Eigen\n\n#endif  // EIGEN_HAS_CONSTEXPR\n\n\n#endif  // EIGEN_CXX11_TENSOR_TENSOR_FFT_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorFixedSize.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_FIXED_SIZE_H\n#define EIGEN_CXX11_TENSOR_TENSOR_FIXED_SIZE_H\n\nnamespace Eigen {\n\n/** \\class TensorFixedSize\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief The fixed sized version of the tensor class.\n  *\n  * The fixed sized equivalent of\n  * Eigen::Tensor<float, 3> t(3, 5, 7);\n  * is\n  * Eigen::TensorFixedSize<float, Size<3,5,7>> t;\n  */\n\ntemplate<typename Scalar_, typename Dimensions_, int Options_, typename IndexType>\nclass TensorFixedSize : public TensorBase<TensorFixedSize<Scalar_, Dimensions_, Options_, IndexType> >\n{\n  public:\n    typedef TensorFixedSize<Scalar_, Dimensions_, Options_, IndexType> Self;\n    typedef TensorBase<TensorFixedSize<Scalar_, Dimensions_, Options_, IndexType> > Base;\n    typedef typename Eigen::internal::nested<Self>::type Nested;\n    typedef typename internal::traits<Self>::StorageKind StorageKind;\n    typedef typename internal::traits<Self>::Index Index;\n    typedef Scalar_ Scalar;\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n    typedef typename Base::CoeffReturnType CoeffReturnType;\n\n    static const int Options = Options_;\n\n    enum {\n      IsAligned = bool(EIGEN_MAX_ALIGN_BYTES>0),\n      Layout = Options_ & RowMajor ? RowMajor : ColMajor,\n      CoordAccess = true,\n      RawAccess = true\n    };\n\n  typedef Dimensions_ Dimensions;\n  static const std::size_t NumIndices = Dimensions::count;\n\n  protected:\n  TensorStorage<Scalar, Dimensions, Options> m_storage;\n\n  public:\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index                    rank()                   const { return NumIndices; }\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index                    dimension(std::size_t n) const { return m_storage.dimensions()[n]; }\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions&        dimensions()             const { return m_storage.dimensions(); }\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index                    size()                   const { return m_storage.size(); }\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar                   *data()                        { return m_storage.data(); }\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar             *data()                  const { return m_storage.data(); }\n\n    // This makes EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED\n    // work, because that uses base().coeffRef() - and we don't yet\n    // implement a similar class hierarchy\n    inline Self& base()             { return *this; }\n    inline const Self& base() const { return *this; }\n\n#if EIGEN_HAS_VARIADIC_TEMPLATES\n    template<typename... IndexTypes>\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& coeff(Index firstIndex, IndexTypes... otherIndices) const\n    {\n      // The number of indices used to access a tensor coefficient must be equal to the rank of the tensor.\n      EIGEN_STATIC_ASSERT(sizeof...(otherIndices) + 1 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)\n      return coeff(array<Index, NumIndices>{{firstIndex, otherIndices...}});\n    }\n#endif\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar& coeff(const array<Index, NumIndices>& indices) const\n    {\n      eigen_internal_assert(checkIndexRange(indices));\n      return m_storage.data()[linearizedIndex(indices)];\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar& coeff(Index index) const\n    {\n      eigen_internal_assert(index >= 0 && index < size());\n      return m_storage.data()[index];\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar& coeff() const\n    {\n      EIGEN_STATIC_ASSERT(NumIndices == 0, YOU_MADE_A_PROGRAMMING_MISTAKE);\n      return m_storage.data()[0];\n    }\n\n\n#if EIGEN_HAS_VARIADIC_TEMPLATES\n    template<typename... IndexTypes>\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index firstIndex, IndexTypes... otherIndices)\n    {\n      // The number of indices used to access a tensor coefficient must be equal to the rank of the tensor.\n      EIGEN_STATIC_ASSERT(sizeof...(otherIndices) + 1 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)\n      return coeffRef(array<Index, NumIndices>{{firstIndex, otherIndices...}});\n    }\n#endif\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar& coeffRef(const array<Index, NumIndices>& indices)\n    {\n      eigen_internal_assert(checkIndexRange(indices));\n      return m_storage.data()[linearizedIndex(indices)];\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar& coeffRef(Index index)\n    {\n      eigen_internal_assert(index >= 0 && index < size());\n      return m_storage.data()[index];\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar& coeffRef()\n    {\n      EIGEN_STATIC_ASSERT(NumIndices == 0, YOU_MADE_A_PROGRAMMING_MISTAKE);\n      return m_storage.data()[0];\n    }\n\n#if EIGEN_HAS_VARIADIC_TEMPLATES\n    template<typename... IndexTypes>\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& operator()(Index firstIndex, IndexTypes... otherIndices) const\n    {\n      // The number of indices used to access a tensor coefficient must be equal to the rank of the tensor.\n      EIGEN_STATIC_ASSERT(sizeof...(otherIndices) + 1 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)\n      return this->operator()(array<Index, NumIndices>{{firstIndex, otherIndices...}});\n    }\n#else\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar& operator()(Index i0, Index i1) const\n    {\n      if (Options&RowMajor) {\n        const Index index = i1 + i0 * m_storage.dimensions()[1];\n        return m_storage.data()[index];\n      } else {\n        const Index index = i0 + i1 * m_storage.dimensions()[0];\n        return m_storage.data()[index];\n      }\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar& operator()(Index i0, Index i1, Index i2) const\n    {\n      if (Options&RowMajor) {\n         const Index index = i2 + m_storage.dimensions()[2] * (i1 + m_storage.dimensions()[1] * i0);\n         return m_storage.data()[index];\n      } else {\n         const Index index = i0 + m_storage.dimensions()[0] * (i1 + m_storage.dimensions()[1] * i2);\n        return m_storage.data()[index];\n      }\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar& operator()(Index i0, Index i1, Index i2, Index i3) const\n    {\n      if (Options&RowMajor) {\n        const Index index = i3 + m_storage.dimensions()[3] * (i2 + m_storage.dimensions()[2] * (i1 + m_storage.dimensions()[1] * i0));\n        return m_storage.data()[index];\n      } else {\n        const Index index = i0 + m_storage.dimensions()[0] * (i1 + m_storage.dimensions()[1] * (i2 + m_storage.dimensions()[2] * i3));\n        return m_storage.data()[index];\n      }\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar& operator()(Index i0, Index i1, Index i2, Index i3, Index i4) const\n    {\n      if (Options&RowMajor) {\n        const Index index = i4 + m_storage.dimensions()[4] * (i3 + m_storage.dimensions()[3] * (i2 + m_storage.dimensions()[2] * (i1 + m_storage.dimensions()[1] * i0)));\n        return m_storage.data()[index];\n      } else {\n        const Index index = i0 + m_storage.dimensions()[0] * (i1 + m_storage.dimensions()[1] * (i2 + m_storage.dimensions()[2] * (i3 + m_storage.dimensions()[3] * i4)));\n        return m_storage.data()[index];\n      }\n    }\n#endif\n\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar& operator()(const array<Index, NumIndices>& indices) const\n    {\n      eigen_assert(checkIndexRange(indices));\n      return coeff(indices);\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar& operator()(Index index) const\n    {\n      eigen_internal_assert(index >= 0 && index < size());\n      return coeff(index);\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar& operator()() const\n    {\n      EIGEN_STATIC_ASSERT(NumIndices == 0, YOU_MADE_A_PROGRAMMING_MISTAKE);\n      return coeff();\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar& operator[](Index index) const\n    {\n      // The bracket operator is only for vectors, use the parenthesis operator instead.\n      EIGEN_STATIC_ASSERT(NumIndices == 1, YOU_MADE_A_PROGRAMMING_MISTAKE);\n      return coeff(index);\n    }\n\n#if EIGEN_HAS_VARIADIC_TEMPLATES\n    template<typename... IndexTypes>\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& operator()(Index firstIndex, IndexTypes... otherIndices)\n    {\n      // The number of indices used to access a tensor coefficient must be equal to the rank of the tensor.\n      EIGEN_STATIC_ASSERT(sizeof...(otherIndices) + 1 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)\n      return operator()(array<Index, NumIndices>{{firstIndex, otherIndices...}});\n    }\n#else\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar& operator()(Index i0, Index i1)\n    {\n       if (Options&RowMajor) {\n         const Index index = i1 + i0 * m_storage.dimensions()[1];\n        return m_storage.data()[index];\n      } else {\n        const Index index = i0 + i1 * m_storage.dimensions()[0];\n        return m_storage.data()[index];\n      }\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar& operator()(Index i0, Index i1, Index i2)\n    {\n       if (Options&RowMajor) {\n         const Index index = i2 + m_storage.dimensions()[2] * (i1 + m_storage.dimensions()[1] * i0);\n        return m_storage.data()[index];\n      } else {\n         const Index index = i0 + m_storage.dimensions()[0] * (i1 + m_storage.dimensions()[1] * i2);\n        return m_storage.data()[index];\n      }\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar& operator()(Index i0, Index i1, Index i2, Index i3)\n    {\n      if (Options&RowMajor) {\n        const Index index = i3 + m_storage.dimensions()[3] * (i2 + m_storage.dimensions()[2] * (i1 + m_storage.dimensions()[1] * i0));\n        return m_storage.data()[index];\n      } else {\n        const Index index = i0 + m_storage.dimensions()[0] * (i1 + m_storage.dimensions()[1] * (i2 + m_storage.dimensions()[2] * i3));\n        return m_storage.data()[index];\n      }\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar& operator()(Index i0, Index i1, Index i2, Index i3, Index i4)\n    {\n      if (Options&RowMajor) {\n        const Index index = i4 + m_storage.dimensions()[4] * (i3 + m_storage.dimensions()[3] * (i2 + m_storage.dimensions()[2] * (i1 + m_storage.dimensions()[1] * i0)));\n        return m_storage.data()[index];\n      } else {\n        const Index index = i0 + m_storage.dimensions()[0] * (i1 + m_storage.dimensions()[1] * (i2 + m_storage.dimensions()[2] * (i3 + m_storage.dimensions()[3] * i4)));\n        return m_storage.data()[index];\n      }\n    }\n#endif\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar& operator()(const array<Index, NumIndices>& indices)\n    {\n      eigen_assert(checkIndexRange(indices));\n      return coeffRef(indices);\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar& operator()(Index index)\n    {\n      eigen_assert(index >= 0 && index < size());\n      return coeffRef(index);\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar& operator()()\n    {\n      EIGEN_STATIC_ASSERT(NumIndices == 0, YOU_MADE_A_PROGRAMMING_MISTAKE);\n      return coeffRef();\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar& operator[](Index index)\n    {\n      // The bracket operator is only for vectors, use the parenthesis operator instead\n      EIGEN_STATIC_ASSERT(NumIndices == 1, YOU_MADE_A_PROGRAMMING_MISTAKE)\n      return coeffRef(index);\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE TensorFixedSize()\n      : m_storage()\n    {\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE TensorFixedSize(const Self& other)\n      : m_storage(other.m_storage)\n    {\n    }\n\n#if EIGEN_HAS_RVALUE_REFERENCES\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorFixedSize(Self&& other)\n      : m_storage(other.m_storage)\n    {\n    }\n#endif\n\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE TensorFixedSize(const TensorBase<OtherDerived, ReadOnlyAccessors>& other)\n    {\n      typedef TensorAssignOp<TensorFixedSize, const OtherDerived> Assign;\n      Assign assign(*this, other.derived());\n      internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());\n    }\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE TensorFixedSize(const TensorBase<OtherDerived, WriteAccessors>& other)\n    {\n      typedef TensorAssignOp<TensorFixedSize, const OtherDerived> Assign;\n      Assign assign(*this, other.derived());\n      internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE TensorFixedSize& operator=(const TensorFixedSize& other)\n    {\n      // FIXME: check that the dimensions of other match the dimensions of *this.\n      // Unfortunately this isn't possible yet when the rhs is an expression.\n      typedef TensorAssignOp<Self, const TensorFixedSize> Assign;\n      Assign assign(*this, other);\n      internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());\n      return *this;\n    }\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE TensorFixedSize& operator=(const OtherDerived& other)\n    {\n      // FIXME: check that the dimensions of other match the dimensions of *this.\n      // Unfortunately this isn't possible yet when the rhs is an expression.\n      typedef TensorAssignOp<Self, const OtherDerived> Assign;\n      Assign assign(*this, other);\n      internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());\n      return *this;\n    }\n\n  protected:\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE bool checkIndexRange(const array<Index, NumIndices>& /*indices*/) const\n    {\n      using internal::array_apply_and_reduce;\n      using internal::array_zip_and_reduce;\n      using internal::greater_equal_zero_op;\n      using internal::logical_and_op;\n      using internal::lesser_op;\n\n      return true;\n        // check whether the indices are all >= 0\n          /*       array_apply_and_reduce<logical_and_op, greater_equal_zero_op>(indices) &&\n        // check whether the indices fit in the dimensions\n        array_zip_and_reduce<logical_and_op, lesser_op>(indices, m_storage.dimensions());*/\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Index linearizedIndex(const array<Index, NumIndices>& indices) const\n    {\n      if (Options&RowMajor) {\n        return m_storage.dimensions().IndexOfRowMajor(indices);\n      } else {\n        return m_storage.dimensions().IndexOfColMajor(indices);\n      }\n    }\n};\n\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_FIXED_SIZE_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorForcedEval.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_FORCED_EVAL_H\n#define EIGEN_CXX11_TENSOR_TENSOR_FORCED_EVAL_H\n\nnamespace Eigen {\n\n/** \\class TensorForcedEval\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief Tensor reshaping class.\n  *\n  *\n  */\n/// template <class> class MakePointer_ is added to convert the host pointer to the device pointer.\n/// It is added due to the fact that for our device compiler T* is not allowed.\n/// If we wanted to use the same Evaluator functions we have to convert that type to our pointer T.\n/// This is done through our MakePointer_ class. By default the Type in the MakePointer_<T> is T* .\n/// Therefore, by adding the default value, we managed to convert the type and it does not break any\n/// existing code as its default value is T*.\nnamespace internal {\ntemplate<typename XprType, template <class> class MakePointer_>\nstruct traits<TensorForcedEvalOp<XprType, MakePointer_> >\n{\n  // Type promotion to handle the case where the types of the lhs and the rhs are different.\n  typedef typename XprType::Scalar Scalar;\n  typedef traits<XprType> XprTraits;\n  typedef typename traits<XprType>::StorageKind StorageKind;\n  typedef typename traits<XprType>::Index Index;\n  typedef typename XprType::Nested Nested;\n  typedef typename remove_reference<Nested>::type _Nested;\n  static const int NumDimensions = XprTraits::NumDimensions;\n  static const int Layout = XprTraits::Layout;\n\n  enum {\n    Flags = 0\n  };\n  template <class T> struct MakePointer {\n    // Intermediate typedef to workaround MSVC issue.\n    typedef MakePointer_<T> MakePointerT;\n    typedef typename MakePointerT::Type Type;\n  };\n};\n\ntemplate<typename XprType, template <class> class MakePointer_>\nstruct eval<TensorForcedEvalOp<XprType, MakePointer_>, Eigen::Dense>\n{\n  typedef const TensorForcedEvalOp<XprType, MakePointer_>& type;\n};\n\ntemplate<typename XprType, template <class> class MakePointer_>\nstruct nested<TensorForcedEvalOp<XprType, MakePointer_>, 1, typename eval<TensorForcedEvalOp<XprType, MakePointer_> >::type>\n{\n  typedef TensorForcedEvalOp<XprType, MakePointer_> type;\n};\n\n}  // end namespace internal\n\n\n\ntemplate<typename XprType, template <class> class MakePointer_>\nclass TensorForcedEvalOp : public TensorBase<TensorForcedEvalOp<XprType, MakePointer_>, ReadOnlyAccessors>\n{\n  public:\n  typedef typename Eigen::internal::traits<TensorForcedEvalOp>::Scalar Scalar;\n  typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;\n  typedef typename internal::remove_const<typename XprType::CoeffReturnType>::type CoeffReturnType;\n  typedef typename Eigen::internal::nested<TensorForcedEvalOp>::type Nested;\n  typedef typename Eigen::internal::traits<TensorForcedEvalOp>::StorageKind StorageKind;\n  typedef typename Eigen::internal::traits<TensorForcedEvalOp>::Index Index;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorForcedEvalOp(const XprType& expr)\n      : m_xpr(expr) {}\n\n    EIGEN_DEVICE_FUNC\n    const typename internal::remove_all<typename XprType::Nested>::type&\n    expression() const { return m_xpr; }\n\n  protected:\n    typename XprType::Nested m_xpr;\n};\n\n\ntemplate<typename ArgType, typename Device, template <class> class MakePointer_>\nstruct TensorEvaluator<const TensorForcedEvalOp<ArgType, MakePointer_>, Device>\n{\n  typedef TensorForcedEvalOp<ArgType, MakePointer_> XprType;\n  typedef typename ArgType::Scalar Scalar;\n  typedef typename TensorEvaluator<ArgType, Device>::Dimensions Dimensions;\n  typedef typename XprType::Index Index;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  static const int PacketSize = internal::unpacket_traits<PacketReturnType>::size;\n\n  enum {\n    IsAligned = true,\n    PacketAccess = (PacketSize > 1),\n    Layout = TensorEvaluator<ArgType, Device>::Layout,\n    RawAccess = true\n  };\n\n  EIGEN_DEVICE_FUNC TensorEvaluator(const XprType& op, const Device& device)\n\t/// op_ is used for sycl\n      : m_impl(op.expression(), device), m_op(op.expression()), m_device(device), m_buffer(NULL)\n  { }\n\n  EIGEN_DEVICE_FUNC const Dimensions& dimensions() const { return m_impl.dimensions(); }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(CoeffReturnType*) {\n    const Index numValues =  internal::array_prod(m_impl.dimensions());\n    m_buffer = (CoeffReturnType*)m_device.allocate(numValues * sizeof(CoeffReturnType));\n    // Should initialize the memory in case we're dealing with non POD types.\n    if (NumTraits<CoeffReturnType>::RequireInitialization) {\n      for (Index i = 0; i < numValues; ++i) {\n        new(m_buffer+i) CoeffReturnType();\n      }\n    }\n    typedef TensorEvalToOp< const typename internal::remove_const<ArgType>::type > EvalTo;\n    EvalTo evalToTmp(m_buffer, m_op);\n    const bool PacketAccess = internal::IsVectorizable<Device, const ArgType>::value;\n    internal::TensorExecutor<const EvalTo, typename internal::remove_const<Device>::type, PacketAccess>::run(evalToTmp, m_device);\n    return true;\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {\n    m_device.deallocate(m_buffer);\n    m_buffer = NULL;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const\n  {\n    return m_buffer[index];\n  }\n\n  template<int LoadMode>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const\n  {\n    return internal::ploadt<PacketReturnType, LoadMode>(m_buffer + index);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {\n    return TensorOpCost(sizeof(CoeffReturnType), 0, 0, vectorized, PacketSize);\n  }\n\n  EIGEN_DEVICE_FUNC typename MakePointer<Scalar>::Type data() const { return m_buffer; }\n\n  /// required by sycl in order to extract the sycl accessor\n  const TensorEvaluator<ArgType, Device>& impl() { return m_impl; }\n  /// used by sycl in order to build the sycl buffer\n  const Device& device() const{return m_device;}\n private:\n  TensorEvaluator<ArgType, Device> m_impl;\n  const ArgType m_op;\n  const Device& m_device;\n  typename MakePointer<CoeffReturnType>::Type m_buffer;\n};\n\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_FORCED_EVAL_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorForwardDeclarations.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_FORWARD_DECLARATIONS_H\n#define EIGEN_CXX11_TENSOR_TENSOR_FORWARD_DECLARATIONS_H\n\nnamespace Eigen {\n\n// MakePointer class is used as a container of the adress space of the pointer\n// on the host and on the device. From the host side it generates the T* pointer\n// and when EIGEN_USE_SYCL is used it construct a buffer with a map_allocator to\n// T* m_data on the host. It is always called on the device.\n// Specialisation of MakePointer class for creating the sycl buffer with\n// map_allocator.\ntemplate<typename T> struct MakePointer {\n  typedef T* Type;\n};\n\ntemplate<typename PlainObjectType, int Options_ = Unaligned, template <class> class MakePointer_ = MakePointer> class TensorMap;\ntemplate<typename Scalar_, int NumIndices_, int Options_ = 0, typename IndexType = DenseIndex> class Tensor;\ntemplate<typename Scalar_, typename Dimensions, int Options_ = 0, typename IndexType = DenseIndex> class TensorFixedSize;\ntemplate<typename PlainObjectType> class TensorRef;\ntemplate<typename Derived, int AccessLevel> class TensorBase;\n\ntemplate<typename NullaryOp, typename PlainObjectType> class TensorCwiseNullaryOp;\ntemplate<typename UnaryOp, typename XprType> class TensorCwiseUnaryOp;\ntemplate<typename BinaryOp, typename LeftXprType, typename RightXprType> class TensorCwiseBinaryOp;\ntemplate<typename TernaryOp, typename Arg1XprType, typename Arg2XprType, typename Arg3XprType> class TensorCwiseTernaryOp;\ntemplate<typename IfXprType, typename ThenXprType, typename ElseXprType> class TensorSelectOp;\ntemplate<typename Op, typename Dims, typename XprType, template <class> class MakePointer_ = MakePointer > class TensorReductionOp;\ntemplate<typename XprType> class TensorIndexTupleOp;\ntemplate<typename ReduceOp, typename Dims, typename XprType> class TensorTupleReducerOp;\ntemplate<typename Axis, typename LeftXprType, typename RightXprType> class TensorConcatenationOp;\ntemplate<typename Dimensions, typename LeftXprType, typename RightXprType> class TensorContractionOp;\ntemplate<typename TargetType, typename XprType> class TensorConversionOp;\ntemplate<typename Dimensions, typename InputXprType, typename KernelXprType> class TensorConvolutionOp;\ntemplate<typename FFT, typename XprType, int FFTDataType, int FFTDirection> class TensorFFTOp;\ntemplate<typename PatchDim, typename XprType> class TensorPatchOp;\ntemplate<DenseIndex Rows, DenseIndex Cols, typename XprType> class TensorImagePatchOp;\ntemplate<DenseIndex Planes, DenseIndex Rows, DenseIndex Cols, typename XprType> class TensorVolumePatchOp;\ntemplate<typename Broadcast, typename XprType> class TensorBroadcastingOp;\ntemplate<DenseIndex DimId, typename XprType> class TensorChippingOp;\ntemplate<typename NewDimensions, typename XprType> class TensorReshapingOp;\ntemplate<typename XprType> class TensorLayoutSwapOp;\ntemplate<typename StartIndices, typename Sizes, typename XprType> class TensorSlicingOp;\ntemplate<typename ReverseDimensions, typename XprType> class TensorReverseOp;\ntemplate<typename PaddingDimensions, typename XprType> class TensorPaddingOp;\ntemplate<typename Shuffle, typename XprType> class TensorShufflingOp;\ntemplate<typename Strides, typename XprType> class TensorStridingOp;\ntemplate<typename StartIndices, typename StopIndices, typename Strides, typename XprType> class TensorStridingSlicingOp;\ntemplate<typename Strides, typename XprType> class TensorInflationOp;\ntemplate<typename Generator, typename XprType> class TensorGeneratorOp;\ntemplate<typename LeftXprType, typename RightXprType> class TensorAssignOp;\ntemplate<typename Op, typename XprType> class TensorScanOp;\n\ntemplate<typename CustomUnaryFunc, typename XprType> class TensorCustomUnaryOp;\ntemplate<typename CustomBinaryFunc, typename LhsXprType, typename RhsXprType> class TensorCustomBinaryOp;\n\ntemplate<typename XprType, template <class> class MakePointer_ = MakePointer> class TensorEvalToOp;\ntemplate<typename XprType, template <class> class MakePointer_ = MakePointer> class TensorForcedEvalOp;\n\ntemplate<typename ExpressionType, typename DeviceType> class TensorDevice;\ntemplate<typename Derived, typename Device> struct TensorEvaluator;\n\nstruct DefaultDevice;\nstruct ThreadPoolDevice;\nstruct GpuDevice;\nstruct SyclDevice;\n\nenum FFTResultType {\n  RealPart = 0,\n  ImagPart = 1,\n  BothParts = 2\n};\n\nenum FFTDirection {\n    FFT_FORWARD = 0,\n    FFT_REVERSE = 1\n};\n\n\nnamespace internal {\n\ntemplate <typename Device, typename Expression>\nstruct IsVectorizable {\n  static const bool value = TensorEvaluator<Expression, Device>::PacketAccess;\n};\n\ntemplate <typename Expression>\nstruct IsVectorizable<GpuDevice, Expression> {\n  static const bool value = TensorEvaluator<Expression, GpuDevice>::PacketAccess &&\n                            TensorEvaluator<Expression, GpuDevice>::IsAligned;\n};\n\ntemplate <typename Expression, typename Device,\n          bool Vectorizable = IsVectorizable<Device, Expression>::value>\nclass TensorExecutor;\n\n}  // end namespace internal\n\n}  // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_FORWARD_DECLARATIONS_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorFunctors.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_FUNCTORS_H\n#define EIGEN_CXX11_TENSOR_TENSOR_FUNCTORS_H\n\nnamespace Eigen {\nnamespace internal {\n\n\n/** \\internal\n * \\brief Template functor to compute the modulo between an array and a scalar.\n */\ntemplate <typename Scalar>\nstruct scalar_mod_op {\n  EIGEN_DEVICE_FUNC scalar_mod_op(const Scalar& divisor) : m_divisor(divisor) {}\n  EIGEN_DEVICE_FUNC inline Scalar operator() (const Scalar& a) const { return a % m_divisor; }\n  const Scalar m_divisor;\n};\ntemplate <typename Scalar>\nstruct functor_traits<scalar_mod_op<Scalar> >\n{ enum { Cost = scalar_div_cost<Scalar,false>::value, PacketAccess = false }; };\n\n\n/** \\internal\n * \\brief Template functor to compute the modulo between 2 arrays.\n */\ntemplate <typename Scalar>\nstruct scalar_mod2_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_mod2_op);\n  EIGEN_DEVICE_FUNC inline Scalar operator() (const Scalar& a, const Scalar& b) const { return a % b; }\n};\ntemplate <typename Scalar>\nstruct functor_traits<scalar_mod2_op<Scalar> >\n{ enum { Cost = scalar_div_cost<Scalar,false>::value, PacketAccess = false }; };\n\ntemplate <typename Scalar>\nstruct scalar_fmod_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_fmod_op);\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar\n  operator()(const Scalar& a, const Scalar& b) const {\n    return numext::fmod(a, b);\n  }\n};\ntemplate <typename Scalar>\nstruct functor_traits<scalar_fmod_op<Scalar> > {\n  enum { Cost = 13,  // Reciprocal throughput of FPREM on Haswell.\n         PacketAccess = false };\n};\n\n\n/** \\internal\n  * \\brief Template functor to compute the sigmoid of a scalar\n  * \\sa class CwiseUnaryOp, ArrayBase::sigmoid()\n  */\ntemplate <typename T>\nstruct scalar_sigmoid_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_sigmoid_op)\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T operator()(const T& x) const {\n    const T one = T(1);\n    return one / (one + numext::exp(-x));\n  }\n\n  template <typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  Packet packetOp(const Packet& x) const {\n    const Packet one = pset1<Packet>(T(1));\n    return pdiv(one, padd(one, pexp(pnegate(x))));\n  }\n};\n\ntemplate <typename T>\nstruct functor_traits<scalar_sigmoid_op<T> > {\n  enum {\n    Cost = NumTraits<T>::AddCost * 2 + NumTraits<T>::MulCost * 6,\n    PacketAccess = packet_traits<T>::HasAdd && packet_traits<T>::HasDiv &&\n                   packet_traits<T>::HasNegate && packet_traits<T>::HasExp\n  };\n};\n\n\ntemplate<typename Reducer, typename Device>\nstruct reducer_traits {\n  enum {\n    Cost = 1,\n    PacketAccess = false\n  };\n};\n\n// Standard reduction functors\ntemplate <typename T> struct SumReducer\n{\n  static const bool PacketAccess = packet_traits<T>::HasAdd;\n  static const bool IsStateful = false;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const T t, T* accum) const {\n    internal::scalar_sum_op<T> sum_op;\n    *accum = sum_op(*accum, t);\n  }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reducePacket(const Packet& p, Packet* accum) const {\n    (*accum) = padd<Packet>(*accum, p);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T initialize() const {\n    internal::scalar_cast_op<int, T> conv;\n    return conv(0);\n  }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet initializePacket() const {\n    return pset1<Packet>(initialize());\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T finalize(const T accum) const {\n    return accum;\n  }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet finalizePacket(const Packet& vaccum) const {\n    return vaccum;\n  }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T finalizeBoth(const T saccum, const Packet& vaccum) const {\n    internal::scalar_sum_op<T> sum_op;\n    return sum_op(saccum, predux(vaccum));\n  }\n};\n\ntemplate <typename T, typename Device>\nstruct reducer_traits<SumReducer<T>, Device> {\n  enum {\n    Cost = NumTraits<T>::AddCost,\n    PacketAccess = PacketType<T, Device>::HasAdd\n  };\n};\n\n\ntemplate <typename T> struct MeanReducer\n{\n  static const bool PacketAccess = packet_traits<T>::HasAdd && !NumTraits<T>::IsInteger;\n  static const bool IsStateful = true;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  MeanReducer() : scalarCount_(0), packetCount_(0) { }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const T t, T* accum) {\n    internal::scalar_sum_op<T> sum_op;\n    *accum = sum_op(*accum, t);\n    scalarCount_++;\n  }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reducePacket(const Packet& p, Packet* accum) {\n    (*accum) = padd<Packet>(*accum, p);\n    packetCount_++;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T initialize() const {\n    internal::scalar_cast_op<int, T> conv;\n    return conv(0);\n  }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet initializePacket() const {\n    return pset1<Packet>(initialize());\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T finalize(const T accum) const {\n    return accum / scalarCount_;\n  }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet finalizePacket(const Packet& vaccum) const {\n    return pdiv(vaccum, pset1<Packet>(packetCount_));\n  }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T finalizeBoth(const T saccum, const Packet& vaccum) const {\n    internal::scalar_sum_op<T> sum_op;\n    return sum_op(saccum, predux(vaccum)) / (scalarCount_ + packetCount_ * unpacket_traits<Packet>::size);\n  }\n\n  protected:\n    DenseIndex scalarCount_;\n    DenseIndex packetCount_;\n};\n\ntemplate <typename T, typename Device>\nstruct reducer_traits<MeanReducer<T>, Device> {\n  enum {\n    Cost = NumTraits<T>::AddCost,\n    PacketAccess = PacketType<T, Device>::HasAdd\n  };\n};\n\n\ntemplate <typename T, bool IsMax = true, bool IsInteger = true>\nstruct MinMaxBottomValue {\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE T bottom_value() {\n    return Eigen::NumTraits<T>::lowest();\n  }\n};\ntemplate <typename T>\nstruct MinMaxBottomValue<T, true, false> {\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE T bottom_value() {\n    return -Eigen::NumTraits<T>::infinity();\n  }\n};\ntemplate <typename T>\nstruct MinMaxBottomValue<T, false, true> {\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE T bottom_value() {\n    return Eigen::NumTraits<T>::highest();\n  }\n};\ntemplate <typename T>\nstruct MinMaxBottomValue<T, false, false> {\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE T bottom_value() {\n    return Eigen::NumTraits<T>::infinity();\n  }\n};\n\n\ntemplate <typename T> struct MaxReducer\n{\n  static const bool PacketAccess = packet_traits<T>::HasMax;\n  static const bool IsStateful = false;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const T t, T* accum) const {\n    if (t > *accum) { *accum = t; }\n  }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reducePacket(const Packet& p, Packet* accum) const {\n    (*accum) = pmax<Packet>(*accum, p);\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T initialize() const {\n    return MinMaxBottomValue<T, true, Eigen::NumTraits<T>::IsInteger>::bottom_value();\n  }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet initializePacket() const {\n    return pset1<Packet>(initialize());\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T finalize(const T accum) const {\n    return accum;\n  }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet finalizePacket(const Packet& vaccum) const {\n    return vaccum;\n  }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T finalizeBoth(const T saccum, const Packet& vaccum) const {\n    return numext::maxi(saccum, predux_max(vaccum));\n  }\n};\n\ntemplate <typename T, typename Device>\nstruct reducer_traits<MaxReducer<T>, Device> {\n  enum {\n    Cost = NumTraits<T>::AddCost,\n    PacketAccess = PacketType<T, Device>::HasMax\n  };\n};\n\n\ntemplate <typename T> struct MinReducer\n{\n  static const bool PacketAccess = packet_traits<T>::HasMin;\n  static const bool IsStateful = false;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const T t, T* accum) const {\n    if (t < *accum) { *accum = t; }\n  }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reducePacket(const Packet& p, Packet* accum) const {\n    (*accum) = pmin<Packet>(*accum, p);\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T initialize() const {\n    return MinMaxBottomValue<T, false, Eigen::NumTraits<T>::IsInteger>::bottom_value();\n  }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet initializePacket() const {\n    return pset1<Packet>(initialize());\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T finalize(const T accum) const {\n    return accum;\n  }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet finalizePacket(const Packet& vaccum) const {\n    return vaccum;\n  }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T finalizeBoth(const T saccum, const Packet& vaccum) const {\n    return numext::mini(saccum, predux_min(vaccum));\n  }\n};\n\ntemplate <typename T, typename Device>\nstruct reducer_traits<MinReducer<T>, Device> {\n  enum {\n    Cost = NumTraits<T>::AddCost,\n    PacketAccess = PacketType<T, Device>::HasMin\n  };\n};\n\n\ntemplate <typename T> struct ProdReducer\n{\n  static const bool PacketAccess = packet_traits<T>::HasMul;\n  static const bool IsStateful = false;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const T t, T* accum) const {\n    internal::scalar_product_op<T> prod_op;\n    (*accum) = prod_op(*accum, t);\n  }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reducePacket(const Packet& p, Packet* accum) const {\n    (*accum) = pmul<Packet>(*accum, p);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T initialize() const {\n    internal::scalar_cast_op<int, T> conv;\n    return conv(1);\n  }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet initializePacket() const {\n    return pset1<Packet>(initialize());\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T finalize(const T accum) const {\n    return accum;\n  }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet finalizePacket(const Packet& vaccum) const {\n    return vaccum;\n  }\n  template <typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T finalizeBoth(const T saccum, const Packet& vaccum) const {\n    internal::scalar_product_op<T> prod_op;\n    return prod_op(saccum, predux_mul(vaccum));\n  }\n};\n\ntemplate <typename T, typename Device>\nstruct reducer_traits<ProdReducer<T>, Device> {\n  enum {\n    Cost = NumTraits<T>::MulCost,\n    PacketAccess = PacketType<T, Device>::HasMul\n  };\n};\n\n\nstruct AndReducer\n{\n  static const bool PacketAccess = false;\n  static const bool IsStateful = false;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(bool t, bool* accum) const {\n    *accum = *accum && t;\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool initialize() const {\n    return true;\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool finalize(bool accum) const {\n    return accum;\n  }\n};\n\ntemplate <typename Device>\nstruct reducer_traits<AndReducer, Device> {\n  enum {\n    Cost = 1,\n    PacketAccess = false\n  };\n};\n\n\nstruct OrReducer {\n  static const bool PacketAccess = false;\n  static const bool IsStateful = false;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(bool t, bool* accum) const {\n    *accum = *accum || t;\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool initialize() const {\n    return false;\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool finalize(bool accum) const {\n    return accum;\n  }\n};\n\ntemplate <typename Device>\nstruct reducer_traits<OrReducer, Device> {\n  enum {\n    Cost = 1,\n    PacketAccess = false\n  };\n};\n\n\n// Argmin/Argmax reducers\ntemplate <typename T> struct ArgMaxTupleReducer\n{\n  static const bool PacketAccess = false;\n  static const bool IsStateful = false;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const T t, T* accum) const {\n    if (t.second > accum->second) { *accum = t; }\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T initialize() const {\n    return T(0, NumTraits<typename T::second_type>::lowest());\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T finalize(const T& accum) const {\n    return accum;\n  }\n};\n\ntemplate <typename T, typename Device>\nstruct reducer_traits<ArgMaxTupleReducer<T>, Device> {\n  enum {\n    Cost = NumTraits<T>::AddCost,\n    PacketAccess = false\n  };\n};\n\n\ntemplate <typename T> struct ArgMinTupleReducer\n{\n  static const bool PacketAccess = false;\n  static const bool IsStateful = false;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const T& t, T* accum) const {\n    if (t.second < accum->second) { *accum = t; }\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T initialize() const {\n    return T(0, NumTraits<typename T::second_type>::highest());\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T finalize(const T& accum) const {\n    return accum;\n  }\n};\n\ntemplate <typename T, typename Device>\nstruct reducer_traits<ArgMinTupleReducer<T>, Device> {\n  enum {\n    Cost = NumTraits<T>::AddCost,\n    PacketAccess = false\n  };\n};\n\n\ntemplate <typename T, typename Index, size_t NumDims>\nclass GaussianGenerator {\n public:\n  static const bool PacketAccess = false;\n\n  EIGEN_DEVICE_FUNC GaussianGenerator(const array<T, NumDims>& means,\n                                      const array<T, NumDims>& std_devs)\n      : m_means(means)\n  {\n    for (size_t i = 0; i < NumDims; ++i) {\n      m_two_sigmas[i] = std_devs[i] * std_devs[i] * 2;\n    }\n  }\n\n  EIGEN_DEVICE_FUNC T operator()(const array<Index, NumDims>& coordinates) const {\n    T tmp = T(0);\n    for (size_t i = 0; i < NumDims; ++i) {\n      T offset = coordinates[i] - m_means[i];\n      tmp += offset * offset / m_two_sigmas[i];\n    }\n    return numext::exp(-tmp);\n  }\n\n private:\n  array<T, NumDims> m_means;\n  array<T, NumDims> m_two_sigmas;\n};\n\ntemplate <typename T, typename Index, size_t NumDims>\nstruct functor_traits<GaussianGenerator<T, Index, NumDims> > {\n  enum {\n    Cost = NumDims * (2 * NumTraits<T>::AddCost + NumTraits<T>::MulCost +\n                      functor_traits<scalar_quotient_op<T, T> >::Cost) +\n           functor_traits<scalar_exp_op<T> >::Cost,\n    PacketAccess = GaussianGenerator<T, Index, NumDims>::PacketAccess\n  };\n};\n\n} // end namespace internal\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_FUNCTORS_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorGenerator.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_GENERATOR_H\n#define EIGEN_CXX11_TENSOR_TENSOR_GENERATOR_H\n\nnamespace Eigen {\n\n/** \\class TensorGenerator\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief Tensor generator class.\n  *\n  *\n  */\nnamespace internal {\ntemplate<typename Generator, typename XprType>\nstruct traits<TensorGeneratorOp<Generator, XprType> > : public traits<XprType>\n{\n  typedef typename XprType::Scalar Scalar;\n  typedef traits<XprType> XprTraits;\n  typedef typename XprTraits::StorageKind StorageKind;\n  typedef typename XprTraits::Index Index;\n  typedef typename XprType::Nested Nested;\n  typedef typename remove_reference<Nested>::type _Nested;\n  static const int NumDimensions = XprTraits::NumDimensions;\n  static const int Layout = XprTraits::Layout;\n};\n\ntemplate<typename Generator, typename XprType>\nstruct eval<TensorGeneratorOp<Generator, XprType>, Eigen::Dense>\n{\n  typedef const TensorGeneratorOp<Generator, XprType>& type;\n};\n\ntemplate<typename Generator, typename XprType>\nstruct nested<TensorGeneratorOp<Generator, XprType>, 1, typename eval<TensorGeneratorOp<Generator, XprType> >::type>\n{\n  typedef TensorGeneratorOp<Generator, XprType> type;\n};\n\n}  // end namespace internal\n\n\n\ntemplate<typename Generator, typename XprType>\nclass TensorGeneratorOp : public TensorBase<TensorGeneratorOp<Generator, XprType>, ReadOnlyAccessors>\n{\n  public:\n  typedef typename Eigen::internal::traits<TensorGeneratorOp>::Scalar Scalar;\n  typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename Eigen::internal::nested<TensorGeneratorOp>::type Nested;\n  typedef typename Eigen::internal::traits<TensorGeneratorOp>::StorageKind StorageKind;\n  typedef typename Eigen::internal::traits<TensorGeneratorOp>::Index Index;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorGeneratorOp(const XprType& expr, const Generator& generator)\n      : m_xpr(expr), m_generator(generator) {}\n\n    EIGEN_DEVICE_FUNC\n    const Generator& generator() const { return m_generator; }\n\n    EIGEN_DEVICE_FUNC\n    const typename internal::remove_all<typename XprType::Nested>::type&\n    expression() const { return m_xpr; }\n\n  protected:\n    typename XprType::Nested m_xpr;\n    const Generator m_generator;\n};\n\n\n// Eval as rvalue\ntemplate<typename Generator, typename ArgType, typename Device>\nstruct TensorEvaluator<const TensorGeneratorOp<Generator, ArgType>, Device>\n{\n  typedef TensorGeneratorOp<Generator, ArgType> XprType;\n  typedef typename XprType::Index Index;\n  typedef typename TensorEvaluator<ArgType, Device>::Dimensions Dimensions;\n  static const int NumDims = internal::array_size<Dimensions>::value;\n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  enum {\n    IsAligned = false,\n    PacketAccess = (internal::unpacket_traits<PacketReturnType>::size > 1),\n    BlockAccess = false,\n    Layout = TensorEvaluator<ArgType, Device>::Layout,\n    CoordAccess = false,  // to be implemented\n    RawAccess = false\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)\n      : m_generator(op.generator())\n  {\n    TensorEvaluator<ArgType, Device> impl(op.expression(), device);\n    m_dimensions = impl.dimensions();\n\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      m_strides[0] = 1;\n      for (int i = 1; i < NumDims; ++i) {\n        m_strides[i] = m_strides[i - 1] * m_dimensions[i - 1];\n      }\n    } else {\n      m_strides[NumDims - 1] = 1;\n      for (int i = NumDims - 2; i >= 0; --i) {\n        m_strides[i] = m_strides[i + 1] * m_dimensions[i + 1];\n      }\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(Scalar* /*data*/) {\n    return true;\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const\n  {\n    array<Index, NumDims> coords;\n    extract_coordinates(index, coords);\n    return m_generator(coords);\n  }\n\n  template<int LoadMode>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const\n  {\n    const int packetSize = internal::unpacket_traits<PacketReturnType>::size;\n    EIGEN_STATIC_ASSERT((packetSize > 1), YOU_MADE_A_PROGRAMMING_MISTAKE)\n    eigen_assert(index+packetSize-1 < dimensions().TotalSize());\n\n    EIGEN_ALIGN_MAX typename internal::remove_const<CoeffReturnType>::type values[packetSize];\n    for (int i = 0; i < packetSize; ++i) {\n      values[i] = coeff(index+i);\n    }\n    PacketReturnType rslt = internal::pload<PacketReturnType>(values);\n    return rslt;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost\n  costPerCoeff(bool) const {\n    // TODO(rmlarsen): This is just a placeholder. Define interface to make\n    // generators return their cost.\n    return TensorOpCost(0, 0, TensorOpCost::AddCost<Scalar>() +\n                                  TensorOpCost::MulCost<Scalar>());\n  }\n\n  EIGEN_DEVICE_FUNC Scalar* data() const { return NULL; }\n\n protected:\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  void extract_coordinates(Index index, array<Index, NumDims>& coords) const {\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      for (int i = NumDims - 1; i > 0; --i) {\n        const Index idx = index / m_strides[i];\n        index -= idx * m_strides[i];\n        coords[i] = idx;\n      }\n      coords[0] = index;\n    } else {\n      for (int i = 0; i < NumDims - 1; ++i) {\n        const Index idx = index / m_strides[i];\n        index -= idx * m_strides[i];\n        coords[i] = idx;\n      }\n      coords[NumDims-1] = index;\n    }\n  }\n\n  Dimensions m_dimensions;\n  array<Index, NumDims> m_strides;\n  Generator m_generator;\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_GENERATOR_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorGlobalFunctions.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Eugene Brevdo <ebrevdo@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_GLOBAL_FUNCTIONS_H\n#define EIGEN_CXX11_TENSOR_TENSOR_GLOBAL_FUNCTIONS_H\n\nnamespace Eigen {\n\n/** \\cpp11 \\returns an expression of the coefficient-wise betainc(\\a x, \\a a, \\a b) to the given tensors.\n *\n * This function computes the regularized incomplete beta function (integral).\n *\n */\ntemplate <typename ADerived, typename BDerived, typename XDerived>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const\n    TensorCwiseTernaryOp<internal::scalar_betainc_op<typename XDerived::Scalar>,\n                         const ADerived, const BDerived, const XDerived>\n    betainc(const ADerived& a, const BDerived& b, const XDerived& x) {\n  return TensorCwiseTernaryOp<\n      internal::scalar_betainc_op<typename XDerived::Scalar>, const ADerived,\n      const BDerived, const XDerived>(\n      a, b, x, internal::scalar_betainc_op<typename XDerived::Scalar>());\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_GLOBAL_FUNCTIONS_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorIO.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_IO_H\n#define EIGEN_CXX11_TENSOR_TENSOR_IO_H\n\nnamespace Eigen {\n\nnamespace internal {\n\n// Print the tensor as a 2d matrix\ntemplate <typename Tensor, int Rank>\nstruct TensorPrinter {\n  static void run (std::ostream& os, const Tensor& tensor) {\n    typedef typename internal::remove_const<typename Tensor::Scalar>::type Scalar;\n    typedef typename Tensor::Index Index;\n    const Index total_size = internal::array_prod(tensor.dimensions());\n    if (total_size > 0) {\n      const Index first_dim = Eigen::internal::array_get<0>(tensor.dimensions());\n      static const int layout = Tensor::Layout;\n      Map<const Array<Scalar, Dynamic, Dynamic, layout> > matrix(const_cast<Scalar*>(tensor.data()), first_dim, total_size/first_dim);\n      os << matrix;\n    }\n  }\n};\n\n\n// Print the tensor as a vector\ntemplate <typename Tensor>\nstruct TensorPrinter<Tensor, 1> {\n  static void run (std::ostream& os, const Tensor& tensor) {\n    typedef typename internal::remove_const<typename Tensor::Scalar>::type Scalar;\n    typedef typename Tensor::Index Index;\n    const Index total_size = internal::array_prod(tensor.dimensions());\n    if (total_size > 0) {\n      Map<const Array<Scalar, Dynamic, 1> > array(const_cast<Scalar*>(tensor.data()), total_size);\n      os << array;\n    }\n  }\n};\n\n\n// Print the tensor as a scalar\ntemplate <typename Tensor>\nstruct TensorPrinter<Tensor, 0> {\n  static void run (std::ostream& os, const Tensor& tensor) {\n    os << tensor.coeff(0);\n  }\n};\n}\n\ntemplate <typename T>\nstd::ostream& operator << (std::ostream& os, const TensorBase<T, ReadOnlyAccessors>& expr) {\n  typedef TensorEvaluator<const TensorForcedEvalOp<const T>, DefaultDevice> Evaluator;\n  typedef typename Evaluator::Dimensions Dimensions;\n\n  // Evaluate the expression if needed\n  TensorForcedEvalOp<const T> eval = expr.eval();\n  Evaluator tensor(eval, DefaultDevice());\n  tensor.evalSubExprsIfNeeded(NULL);\n\n  // Print the result\n  static const int rank = internal::array_size<Dimensions>::value;\n  internal::TensorPrinter<Evaluator, rank>::run(os, tensor);\n\n  // Cleanup.\n  tensor.cleanup();\n  return os;\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_IO_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorImagePatch.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_IMAGE_PATCH_H\n#define EIGEN_CXX11_TENSOR_TENSOR_IMAGE_PATCH_H\n\nnamespace Eigen {\n\n/** \\class TensorImagePatch\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief Patch extraction specialized for image processing.\n  * This assumes that the input has a least 3 dimensions ordered as follow:\n  *  1st dimension: channels (of size d)\n  *  2nd dimension: rows (of size r)\n  *  3rd dimension: columns (of size c)\n  *  There can be additional dimensions such as time (for video) or batch (for\n  * bulk processing after the first 3.\n  * Calling the image patch code with patch_rows and patch_cols is equivalent\n  * to calling the regular patch extraction code with parameters d, patch_rows,\n  * patch_cols, and 1 for all the additional dimensions.\n  */\nnamespace internal {\ntemplate<DenseIndex Rows, DenseIndex Cols, typename XprType>\nstruct traits<TensorImagePatchOp<Rows, Cols, XprType> > : public traits<XprType>\n{\n  typedef typename internal::remove_const<typename XprType::Scalar>::type Scalar;\n  typedef traits<XprType> XprTraits;\n  typedef typename XprTraits::StorageKind StorageKind;\n  typedef typename XprTraits::Index Index;\n  typedef typename XprType::Nested Nested;\n  typedef typename remove_reference<Nested>::type _Nested;\n  static const int NumDimensions = XprTraits::NumDimensions + 1;\n  static const int Layout = XprTraits::Layout;\n};\n\ntemplate<DenseIndex Rows, DenseIndex Cols, typename XprType>\nstruct eval<TensorImagePatchOp<Rows, Cols, XprType>, Eigen::Dense>\n{\n  typedef const TensorImagePatchOp<Rows, Cols, XprType>& type;\n};\n\ntemplate<DenseIndex Rows, DenseIndex Cols, typename XprType>\nstruct nested<TensorImagePatchOp<Rows, Cols, XprType>, 1, typename eval<TensorImagePatchOp<Rows, Cols, XprType> >::type>\n{\n  typedef TensorImagePatchOp<Rows, Cols, XprType> type;\n};\n\n}  // end namespace internal\n\ntemplate<DenseIndex Rows, DenseIndex Cols, typename XprType>\nclass TensorImagePatchOp : public TensorBase<TensorImagePatchOp<Rows, Cols, XprType>, ReadOnlyAccessors>\n{\n  public:\n  typedef typename Eigen::internal::traits<TensorImagePatchOp>::Scalar Scalar;\n  typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename Eigen::internal::nested<TensorImagePatchOp>::type Nested;\n  typedef typename Eigen::internal::traits<TensorImagePatchOp>::StorageKind StorageKind;\n  typedef typename Eigen::internal::traits<TensorImagePatchOp>::Index Index;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorImagePatchOp(const XprType& expr, DenseIndex patch_rows, DenseIndex patch_cols,\n                                                           DenseIndex row_strides, DenseIndex col_strides,\n                                                           DenseIndex in_row_strides, DenseIndex in_col_strides,\n                                                           DenseIndex row_inflate_strides, DenseIndex col_inflate_strides,\n                                                           PaddingType padding_type, Scalar padding_value)\n      : m_xpr(expr), m_patch_rows(patch_rows), m_patch_cols(patch_cols),\n        m_row_strides(row_strides), m_col_strides(col_strides),\n        m_in_row_strides(in_row_strides), m_in_col_strides(in_col_strides),\n        m_row_inflate_strides(row_inflate_strides), m_col_inflate_strides(col_inflate_strides),\n        m_padding_explicit(false), m_padding_top(0), m_padding_bottom(0), m_padding_left(0), m_padding_right(0),\n        m_padding_type(padding_type), m_padding_value(padding_value) {}\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorImagePatchOp(const XprType& expr, DenseIndex patch_rows, DenseIndex patch_cols,\n                                                           DenseIndex row_strides, DenseIndex col_strides,\n                                                           DenseIndex in_row_strides, DenseIndex in_col_strides,\n                                                           DenseIndex row_inflate_strides, DenseIndex col_inflate_strides,\n                                                           DenseIndex padding_top, DenseIndex padding_bottom,\n                                                           DenseIndex padding_left, DenseIndex padding_right,\n                                                           Scalar padding_value)\n      : m_xpr(expr), m_patch_rows(patch_rows), m_patch_cols(patch_cols),\n        m_row_strides(row_strides), m_col_strides(col_strides),\n        m_in_row_strides(in_row_strides), m_in_col_strides(in_col_strides),\n        m_row_inflate_strides(row_inflate_strides), m_col_inflate_strides(col_inflate_strides),\n        m_padding_explicit(true), m_padding_top(padding_top), m_padding_bottom(padding_bottom),\n        m_padding_left(padding_left), m_padding_right(padding_right),\n        m_padding_type(PADDING_VALID), m_padding_value(padding_value) {}\n\n    EIGEN_DEVICE_FUNC\n    DenseIndex patch_rows() const { return m_patch_rows; }\n    EIGEN_DEVICE_FUNC\n    DenseIndex patch_cols() const { return m_patch_cols; }\n    EIGEN_DEVICE_FUNC\n    DenseIndex row_strides() const { return m_row_strides; }\n    EIGEN_DEVICE_FUNC\n    DenseIndex col_strides() const { return m_col_strides; }\n    EIGEN_DEVICE_FUNC\n    DenseIndex in_row_strides() const { return m_in_row_strides; }\n    EIGEN_DEVICE_FUNC\n    DenseIndex in_col_strides() const { return m_in_col_strides; }\n    EIGEN_DEVICE_FUNC\n    DenseIndex row_inflate_strides() const { return m_row_inflate_strides; }\n    EIGEN_DEVICE_FUNC\n    DenseIndex col_inflate_strides() const { return m_col_inflate_strides; }\n    EIGEN_DEVICE_FUNC\n    bool padding_explicit() const { return m_padding_explicit; }\n    EIGEN_DEVICE_FUNC\n    DenseIndex padding_top() const { return m_padding_top; }\n    EIGEN_DEVICE_FUNC\n    DenseIndex padding_bottom() const { return m_padding_bottom; }\n    EIGEN_DEVICE_FUNC\n    DenseIndex padding_left() const { return m_padding_left; }\n    EIGEN_DEVICE_FUNC\n    DenseIndex padding_right() const { return m_padding_right; }\n    EIGEN_DEVICE_FUNC\n    PaddingType padding_type() const { return m_padding_type; }\n    EIGEN_DEVICE_FUNC\n    Scalar padding_value() const { return m_padding_value; }\n\n    EIGEN_DEVICE_FUNC\n    const typename internal::remove_all<typename XprType::Nested>::type&\n    expression() const { return m_xpr; }\n\n  protected:\n    typename XprType::Nested m_xpr;\n    const DenseIndex m_patch_rows;\n    const DenseIndex m_patch_cols;\n    const DenseIndex m_row_strides;\n    const DenseIndex m_col_strides;\n    const DenseIndex m_in_row_strides;\n    const DenseIndex m_in_col_strides;\n    const DenseIndex m_row_inflate_strides;\n    const DenseIndex m_col_inflate_strides;\n    const bool m_padding_explicit;\n    const DenseIndex m_padding_top;\n    const DenseIndex m_padding_bottom;\n    const DenseIndex m_padding_left;\n    const DenseIndex m_padding_right;\n    const PaddingType m_padding_type;\n    const Scalar m_padding_value;\n};\n\n// Eval as rvalue\ntemplate<DenseIndex Rows, DenseIndex Cols, typename ArgType, typename Device>\nstruct TensorEvaluator<const TensorImagePatchOp<Rows, Cols, ArgType>, Device>\n{\n  typedef TensorImagePatchOp<Rows, Cols, ArgType> XprType;\n  typedef typename XprType::Index Index;\n  static const int NumInputDims = internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value;\n  static const int NumDims = NumInputDims + 1;\n  typedef DSizes<Index, NumDims> Dimensions;\n  typedef typename internal::remove_const<typename XprType::Scalar>::type Scalar;\n  typedef TensorEvaluator<const TensorImagePatchOp<Rows, Cols, ArgType>,\n                          Device> Self;\n  typedef TensorEvaluator<ArgType, Device> Impl;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  static const int PacketSize = internal::unpacket_traits<PacketReturnType>::size;\n\n  enum {\n    IsAligned = false,\n    PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,\n    Layout = TensorEvaluator<ArgType, Device>::Layout,\n    CoordAccess = false,\n    RawAccess = false\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)\n      : m_impl(op.expression(), device)\n  {\n    EIGEN_STATIC_ASSERT((NumDims >= 4), YOU_MADE_A_PROGRAMMING_MISTAKE);\n\n    m_paddingValue = op.padding_value();\n\n    const typename TensorEvaluator<ArgType, Device>::Dimensions& input_dims = m_impl.dimensions();\n\n    // Caches a few variables.\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      m_inputDepth = input_dims[0];\n      m_inputRows = input_dims[1];\n      m_inputCols = input_dims[2];\n    } else {\n      m_inputDepth = input_dims[NumInputDims-1];\n      m_inputRows = input_dims[NumInputDims-2];\n      m_inputCols = input_dims[NumInputDims-3];\n    }\n\n    m_row_strides = op.row_strides();\n    m_col_strides = op.col_strides();\n\n    // Input strides and effective input/patch size\n    m_in_row_strides = op.in_row_strides();\n    m_in_col_strides = op.in_col_strides();\n    m_row_inflate_strides = op.row_inflate_strides();\n    m_col_inflate_strides = op.col_inflate_strides();\n    // The \"effective\" input rows and input cols are the input rows and cols\n    // after inflating them with zeros.\n    // For examples, a 2x3 matrix with row_inflate_strides and\n    // col_inflate_strides of 2 comes from:\n    //   A B C\n    //   D E F\n    //\n    // to a matrix is 3 x 5:\n    //\n    //   A . B . C\n    //   . . . . .\n    //   D . E . F\n\n    m_input_rows_eff = (m_inputRows - 1) * m_row_inflate_strides + 1;\n    m_input_cols_eff = (m_inputCols - 1) * m_col_inflate_strides + 1;\n    m_patch_rows_eff = op.patch_rows() + (op.patch_rows() - 1) * (m_in_row_strides - 1);\n    m_patch_cols_eff = op.patch_cols() + (op.patch_cols() - 1) * (m_in_col_strides - 1);\n\n    if (op.padding_explicit()) {\n      m_outputRows = numext::ceil((m_input_rows_eff + op.padding_top() + op.padding_bottom() - m_patch_rows_eff + 1.f) / static_cast<float>(m_row_strides));\n      m_outputCols = numext::ceil((m_input_cols_eff + op.padding_left() + op.padding_right() - m_patch_cols_eff + 1.f) / static_cast<float>(m_col_strides));\n      m_rowPaddingTop = op.padding_top();\n      m_colPaddingLeft = op.padding_left();\n    } else {\n      // Computing padding from the type\n      switch (op.padding_type()) {\n        case PADDING_VALID:\n          m_outputRows = numext::ceil((m_input_rows_eff - m_patch_rows_eff + 1.f) / static_cast<float>(m_row_strides));\n          m_outputCols = numext::ceil((m_input_cols_eff - m_patch_cols_eff + 1.f) / static_cast<float>(m_col_strides));\n          // Calculate the padding\n          m_rowPaddingTop = numext::maxi<Index>(0, ((m_outputRows - 1) * m_row_strides + m_patch_rows_eff - m_input_rows_eff) / 2);\n          m_colPaddingLeft = numext::maxi<Index>(0, ((m_outputCols - 1) * m_col_strides + m_patch_cols_eff - m_input_cols_eff) / 2);\n          break;\n        case PADDING_SAME:\n          m_outputRows = numext::ceil(m_input_rows_eff / static_cast<float>(m_row_strides));\n          m_outputCols = numext::ceil(m_input_cols_eff / static_cast<float>(m_col_strides));\n          // Calculate the padding\n          m_rowPaddingTop = ((m_outputRows - 1) * m_row_strides + m_patch_rows_eff - m_input_rows_eff) / 2;\n          m_colPaddingLeft = ((m_outputCols - 1) * m_col_strides + m_patch_cols_eff - m_input_cols_eff) / 2;\n          break;\n        default:\n          eigen_assert(false && \"unexpected padding\");\n      }\n    }\n    eigen_assert(m_outputRows > 0);\n    eigen_assert(m_outputCols > 0);\n\n    // Dimensions for result of extraction.\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      // ColMajor\n      // 0: depth\n      // 1: patch_rows\n      // 2: patch_cols\n      // 3: number of patches\n      // 4 and beyond: anything else (such as batch).\n      m_dimensions[0] = input_dims[0];\n      m_dimensions[1] = op.patch_rows();\n      m_dimensions[2] = op.patch_cols();\n      m_dimensions[3] = m_outputRows * m_outputCols;\n      for (int i = 4; i < NumDims; ++i) {\n        m_dimensions[i] = input_dims[i-1];\n      }\n    } else {\n      // RowMajor\n      // NumDims-1: depth\n      // NumDims-2: patch_rows\n      // NumDims-3: patch_cols\n      // NumDims-4: number of patches\n      // NumDims-5 and beyond: anything else (such as batch).\n      m_dimensions[NumDims-1] = input_dims[NumInputDims-1];\n      m_dimensions[NumDims-2] = op.patch_rows();\n      m_dimensions[NumDims-3] = op.patch_cols();\n      m_dimensions[NumDims-4] = m_outputRows * m_outputCols;\n      for (int i = NumDims-5; i >= 0; --i) {\n        m_dimensions[i] = input_dims[i];\n      }\n    }\n\n    // Strides for moving the patch in various dimensions.\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      m_colStride = m_dimensions[1];\n      m_patchStride = m_colStride * m_dimensions[2] * m_dimensions[0];\n      m_otherStride = m_patchStride * m_dimensions[3];\n    } else {\n      m_colStride = m_dimensions[NumDims-2];\n      m_patchStride = m_colStride * m_dimensions[NumDims-3] * m_dimensions[NumDims-1];\n      m_otherStride = m_patchStride * m_dimensions[NumDims-4];\n    }\n\n    // Strides for navigating through the input tensor.\n    m_rowInputStride = m_inputDepth;\n    m_colInputStride = m_inputDepth * m_inputRows;\n    m_patchInputStride = m_inputDepth * m_inputRows * m_inputCols;\n\n    // Fast representations of different variables.\n    m_fastOtherStride = internal::TensorIntDivisor<Index>(m_otherStride);\n    m_fastPatchStride = internal::TensorIntDivisor<Index>(m_patchStride);\n    m_fastColStride = internal::TensorIntDivisor<Index>(m_colStride);\n    m_fastInflateRowStride = internal::TensorIntDivisor<Index>(m_row_inflate_strides);\n    m_fastInflateColStride = internal::TensorIntDivisor<Index>(m_col_inflate_strides);\n    m_fastInputColsEff = internal::TensorIntDivisor<Index>(m_input_cols_eff);\n\n    // Number of patches in the width dimension.\n    m_fastOutputRows = internal::TensorIntDivisor<Index>(m_outputRows);\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      m_fastOutputDepth = internal::TensorIntDivisor<Index>(m_dimensions[0]);\n    } else {\n      m_fastOutputDepth = internal::TensorIntDivisor<Index>(m_dimensions[NumDims-1]);\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(Scalar* /*data*/) {\n    m_impl.evalSubExprsIfNeeded(NULL);\n    return true;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {\n    m_impl.cleanup();\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const\n  {\n    // Patch index corresponding to the passed in index.\n    const Index patchIndex = index / m_fastPatchStride;\n    // Find the offset of the element wrt the location of the first element.\n    const Index patchOffset = (index - patchIndex * m_patchStride) / m_fastOutputDepth;\n\n    // Other ways to index this element.\n    const Index otherIndex = (NumDims == 4) ? 0 : index / m_fastOtherStride;\n    const Index patch2DIndex = (NumDims == 4) ? patchIndex : (index - otherIndex * m_otherStride) / m_fastPatchStride;\n\n    // Calculate col index in the input original tensor.\n    const Index colIndex = patch2DIndex / m_fastOutputRows;\n    const Index colOffset = patchOffset / m_fastColStride;\n    const Index inputCol = colIndex * m_col_strides + colOffset * m_in_col_strides - m_colPaddingLeft;\n    const Index origInputCol = (m_col_inflate_strides == 1) ? inputCol : ((inputCol >= 0) ? (inputCol / m_fastInflateColStride) : 0);\n    if (inputCol < 0 || inputCol >= m_input_cols_eff ||\n        ((m_col_inflate_strides != 1) && (inputCol != origInputCol * m_col_inflate_strides))) {\n      return Scalar(m_paddingValue);\n    }\n\n    // Calculate row index in the original input tensor.\n    const Index rowIndex = patch2DIndex - colIndex * m_outputRows;\n    const Index rowOffset = patchOffset - colOffset * m_colStride;\n    const Index inputRow = rowIndex * m_row_strides + rowOffset * m_in_row_strides - m_rowPaddingTop;\n    const Index origInputRow = (m_row_inflate_strides == 1) ? inputRow : ((inputRow >= 0) ? (inputRow / m_fastInflateRowStride) : 0);\n    if (inputRow < 0 || inputRow >= m_input_rows_eff ||\n        ((m_row_inflate_strides != 1) && (inputRow != origInputRow * m_row_inflate_strides))) {\n      return Scalar(m_paddingValue);\n    }\n\n    const int depth_index = static_cast<int>(Layout) == static_cast<int>(ColMajor) ? 0 : NumDims - 1;\n    const Index depth = index - (index / m_fastOutputDepth) * m_dimensions[depth_index];\n\n    const Index inputIndex = depth + origInputRow * m_rowInputStride + origInputCol * m_colInputStride + otherIndex * m_patchInputStride;\n    return m_impl.coeff(inputIndex);\n  }\n\n  template<int LoadMode>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const\n  {\n    EIGEN_STATIC_ASSERT((PacketSize > 1), YOU_MADE_A_PROGRAMMING_MISTAKE)\n    eigen_assert(index+PacketSize-1 < dimensions().TotalSize());\n\n    if (m_in_row_strides != 1 || m_in_col_strides != 1 || m_row_inflate_strides != 1 || m_col_inflate_strides != 1) {\n      return packetWithPossibleZero(index);\n    }\n\n    const Index indices[2] = {index, index + PacketSize - 1};\n    const Index patchIndex = indices[0] / m_fastPatchStride;\n    if (patchIndex != indices[1] / m_fastPatchStride) {\n      return packetWithPossibleZero(index);\n    }\n    const Index otherIndex = (NumDims == 4) ? 0 : indices[0] / m_fastOtherStride;\n    eigen_assert(otherIndex == indices[1] / m_fastOtherStride);\n\n    // Find the offset of the element wrt the location of the first element.\n    const Index patchOffsets[2] = {(indices[0] - patchIndex * m_patchStride) / m_fastOutputDepth,\n                                   (indices[1] - patchIndex * m_patchStride) / m_fastOutputDepth};\n\n    const Index patch2DIndex = (NumDims == 4) ? patchIndex : (indices[0] - otherIndex * m_otherStride) / m_fastPatchStride;\n    eigen_assert(patch2DIndex == (indices[1] - otherIndex * m_otherStride) / m_fastPatchStride);\n\n    const Index colIndex = patch2DIndex / m_fastOutputRows;\n    const Index colOffsets[2] = {patchOffsets[0] / m_fastColStride, patchOffsets[1] / m_fastColStride};\n\n    // Calculate col indices in the original input tensor.\n    const Index inputCols[2] = {colIndex * m_col_strides + colOffsets[0] -\n      m_colPaddingLeft, colIndex * m_col_strides + colOffsets[1] - m_colPaddingLeft};\n    if (inputCols[1] < 0 || inputCols[0] >= m_inputCols) {\n      return internal::pset1<PacketReturnType>(Scalar(m_paddingValue));\n    }\n\n    if (inputCols[0] == inputCols[1]) {\n      const Index rowIndex = patch2DIndex - colIndex * m_outputRows;\n      const Index rowOffsets[2] = {patchOffsets[0] - colOffsets[0]*m_colStride, patchOffsets[1] - colOffsets[1]*m_colStride};\n      eigen_assert(rowOffsets[0] <= rowOffsets[1]);\n      // Calculate col indices in the original input tensor.\n      const Index inputRows[2] = {rowIndex * m_row_strides + rowOffsets[0] -\n        m_rowPaddingTop, rowIndex * m_row_strides + rowOffsets[1] - m_rowPaddingTop};\n\n      if (inputRows[1] < 0 || inputRows[0] >= m_inputRows) {\n        return internal::pset1<PacketReturnType>(Scalar(m_paddingValue));\n      }\n\n      if (inputRows[0] >= 0 && inputRows[1] < m_inputRows) {\n        // no padding\n        const int depth_index = static_cast<int>(Layout) == static_cast<int>(ColMajor) ? 0 : NumDims - 1;\n        const Index depth = index - (index / m_fastOutputDepth) * m_dimensions[depth_index];\n        const Index inputIndex = depth + inputRows[0] * m_rowInputStride + inputCols[0] * m_colInputStride + otherIndex * m_patchInputStride;\n        return m_impl.template packet<Unaligned>(inputIndex);\n      }\n    }\n\n    return packetWithPossibleZero(index);\n  }\n\n  EIGEN_DEVICE_FUNC Scalar* data() const { return NULL; }\n\n  const TensorEvaluator<ArgType, Device>& impl() const { return m_impl; }\n\n  Index rowPaddingTop() const { return m_rowPaddingTop; }\n  Index colPaddingLeft() const { return m_colPaddingLeft; }\n  Index outputRows() const { return m_outputRows; }\n  Index outputCols() const { return m_outputCols; }\n  Index userRowStride() const { return m_row_strides; }\n  Index userColStride() const { return m_col_strides; }\n  Index userInRowStride() const { return m_in_row_strides; }\n  Index userInColStride() const { return m_in_col_strides; }\n  Index rowInflateStride() const { return m_row_inflate_strides; }\n  Index colInflateStride() const { return m_col_inflate_strides; }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost\n  costPerCoeff(bool vectorized) const {\n    // We conservatively estimate the cost for the code path where the computed\n    // index is inside the original image and\n    // TensorEvaluator<ArgType, Device>::CoordAccess is false.\n    const double compute_cost = 3 * TensorOpCost::DivCost<Index>() +\n                                6 * TensorOpCost::MulCost<Index>() +\n                                8 * TensorOpCost::MulCost<Index>();\n    return m_impl.costPerCoeff(vectorized) +\n           TensorOpCost(0, 0, compute_cost, vectorized, PacketSize);\n  }\n\n protected:\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packetWithPossibleZero(Index index) const\n  {\n    EIGEN_ALIGN_MAX typename internal::remove_const<CoeffReturnType>::type values[PacketSize];\n    for (int i = 0; i < PacketSize; ++i) {\n      values[i] = coeff(index+i);\n    }\n    PacketReturnType rslt = internal::pload<PacketReturnType>(values);\n    return rslt;\n  }\n\n  Dimensions m_dimensions;\n\n  Index m_otherStride;\n  Index m_patchStride;\n  Index m_colStride;\n  Index m_row_strides;\n  Index m_col_strides;\n\n  Index m_in_row_strides;\n  Index m_in_col_strides;\n  Index m_row_inflate_strides;\n  Index m_col_inflate_strides;\n\n  Index m_input_rows_eff;\n  Index m_input_cols_eff;\n  Index m_patch_rows_eff;\n  Index m_patch_cols_eff;\n\n  internal::TensorIntDivisor<Index> m_fastOtherStride;\n  internal::TensorIntDivisor<Index> m_fastPatchStride;\n  internal::TensorIntDivisor<Index> m_fastColStride;\n  internal::TensorIntDivisor<Index> m_fastInflateRowStride;\n  internal::TensorIntDivisor<Index> m_fastInflateColStride;\n  internal::TensorIntDivisor<Index> m_fastInputColsEff;\n\n  Index m_rowInputStride;\n  Index m_colInputStride;\n  Index m_patchInputStride;\n\n  Index m_inputDepth;\n  Index m_inputRows;\n  Index m_inputCols;\n\n  Index m_outputRows;\n  Index m_outputCols;\n\n  Index m_rowPaddingTop;\n  Index m_colPaddingLeft;\n\n  internal::TensorIntDivisor<Index> m_fastOutputRows;\n  internal::TensorIntDivisor<Index> m_fastOutputDepth;\n\n  Scalar m_paddingValue;\n\n  TensorEvaluator<ArgType, Device> m_impl;\n};\n\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_IMAGE_PATCH_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorIndexList.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_INDEX_LIST_H\n#define EIGEN_CXX11_TENSOR_TENSOR_INDEX_LIST_H\n\n\n#if EIGEN_HAS_CONSTEXPR && EIGEN_HAS_VARIADIC_TEMPLATES\n\n#define EIGEN_HAS_INDEX_LIST\n\nnamespace Eigen {\n\n/** \\internal\n  *\n  * \\class TensorIndexList\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief Set of classes used to encode a set of Tensor dimensions/indices.\n  *\n  * The indices in the list can be known at compile time or at runtime. A mix\n  * of static and dynamic indices can also be provided if needed. The tensor\n  * code will attempt to take advantage of the indices that are known at\n  * compile time to optimize the code it generates.\n  *\n  * This functionality requires a c++11 compliant compiler. If your compiler\n  * is older you need to use arrays of indices instead.\n  *\n  * Several examples are provided in the cxx11_tensor_index_list.cpp file.\n  *\n  * \\sa Tensor\n  */\n\ntemplate <DenseIndex n>\nstruct type2index {\n  static const DenseIndex value = n;\n  EIGEN_DEVICE_FUNC constexpr operator DenseIndex() const { return n; }\n  EIGEN_DEVICE_FUNC void set(DenseIndex val) {\n    eigen_assert(val == n);\n  }\n};\n\n// This can be used with IndexPairList to get compile-time constant pairs,\n// such as IndexPairList<type2indexpair<1,2>, type2indexpair<3,4>>().\ntemplate <DenseIndex f, DenseIndex s>\nstruct type2indexpair {\n  static const DenseIndex first = f;\n  static const DenseIndex second = s;\n\n  constexpr EIGEN_DEVICE_FUNC operator IndexPair<DenseIndex>() const {\n    return IndexPair<DenseIndex>(f, s);\n  }\n\n  EIGEN_DEVICE_FUNC void set(const IndexPair<DenseIndex>& val) {\n    eigen_assert(val.first == f);\n    eigen_assert(val.second == s);\n  }\n};\n\n\ntemplate<DenseIndex n> struct NumTraits<type2index<n> >\n{\n  typedef DenseIndex Real;\n  enum {\n    IsComplex = 0,\n    RequireInitialization = false,\n    ReadCost = 1,\n    AddCost = 1,\n    MulCost = 1\n  };\n\n  EIGEN_DEVICE_FUNC static inline Real epsilon() { return 0; }\n  EIGEN_DEVICE_FUNC static inline Real dummy_precision() { return 0; }\n  EIGEN_DEVICE_FUNC static inline Real highest() { return n; }\n  EIGEN_DEVICE_FUNC static inline Real lowest() { return n; }\n};\n\nnamespace internal {\ntemplate <typename T>\nEIGEN_DEVICE_FUNC void update_value(T& val, DenseIndex new_val) {\n  val = new_val;\n}\ntemplate <DenseIndex n>\nEIGEN_DEVICE_FUNC void update_value(type2index<n>& val, DenseIndex new_val) {\n  val.set(new_val);\n}\n\ntemplate <typename T>\nEIGEN_DEVICE_FUNC void update_value(T& val, IndexPair<DenseIndex> new_val) {\n  val = new_val;\n}\ntemplate <DenseIndex f, DenseIndex s>\nEIGEN_DEVICE_FUNC void update_value(type2indexpair<f, s>& val, IndexPair<DenseIndex> new_val) {\n  val.set(new_val);\n}\n\n\ntemplate <typename T>\nstruct is_compile_time_constant {\n  static constexpr bool value = false;\n};\n\ntemplate <DenseIndex idx>\nstruct is_compile_time_constant<type2index<idx> > {\n  static constexpr bool value = true;\n};\ntemplate <DenseIndex idx>\nstruct is_compile_time_constant<const type2index<idx> > {\n  static constexpr bool value = true;\n};\ntemplate <DenseIndex idx>\nstruct is_compile_time_constant<type2index<idx>& > {\n  static constexpr bool value = true;\n};\ntemplate <DenseIndex idx>\nstruct is_compile_time_constant<const type2index<idx>& > {\n  static constexpr bool value = true;\n};\n\ntemplate <DenseIndex f, DenseIndex s>\nstruct is_compile_time_constant<type2indexpair<f, s> > {\n  static constexpr bool value = true;\n};\ntemplate <DenseIndex f, DenseIndex s>\nstruct is_compile_time_constant<const type2indexpair<f, s> > {\n  static constexpr bool value = true;\n};\ntemplate <DenseIndex f, DenseIndex s>\nstruct is_compile_time_constant<type2indexpair<f, s>& > {\n  static constexpr bool value = true;\n};\ntemplate <DenseIndex f, DenseIndex s>\nstruct is_compile_time_constant<const type2indexpair<f, s>& > {\n  static constexpr bool value = true;\n};\n\n\ntemplate<typename... T>\nstruct IndexTuple;\n\ntemplate<typename T, typename... O>\nstruct IndexTuple<T, O...> {\n  EIGEN_DEVICE_FUNC constexpr IndexTuple() : head(), others() { }\n  EIGEN_DEVICE_FUNC constexpr IndexTuple(const T& v, const O... o) : head(v), others(o...) { }\n\n  constexpr static int count = 1 + sizeof...(O);\n  T head;\n  IndexTuple<O...> others;\n  typedef T Head;\n  typedef IndexTuple<O...> Other;\n};\n\ntemplate<typename T>\n  struct IndexTuple<T> {\n  EIGEN_DEVICE_FUNC constexpr IndexTuple() : head() { }\n  EIGEN_DEVICE_FUNC constexpr IndexTuple(const T& v) : head(v) { }\n\n  constexpr static int count = 1;\n  T head;\n  typedef T Head;\n};\n\n\ntemplate<int N, typename... T>\nstruct IndexTupleExtractor;\n\ntemplate<int N, typename T, typename... O>\nstruct IndexTupleExtractor<N, T, O...> {\n\n  typedef typename IndexTupleExtractor<N-1, O...>::ValType ValType;\n\n  EIGEN_DEVICE_FUNC static constexpr ValType& get_val(IndexTuple<T, O...>& val) {\n    return IndexTupleExtractor<N-1, O...>::get_val(val.others);\n  }\n\n  EIGEN_DEVICE_FUNC static constexpr const ValType& get_val(const IndexTuple<T, O...>& val) {\n    return IndexTupleExtractor<N-1, O...>::get_val(val.others);\n  }\n  template <typename V>\n  EIGEN_DEVICE_FUNC static void set_val(IndexTuple<T, O...>& val, V& new_val) {\n    IndexTupleExtractor<N-1, O...>::set_val(val.others, new_val);\n  }\n\n};\n\ntemplate<typename T, typename... O>\n  struct IndexTupleExtractor<0, T, O...> {\n\n  typedef T ValType;\n\n  EIGEN_DEVICE_FUNC static constexpr ValType& get_val(IndexTuple<T, O...>& val) {\n    return val.head;\n  }\n  EIGEN_DEVICE_FUNC static constexpr const ValType& get_val(const IndexTuple<T, O...>& val) {\n    return val.head;\n  }\n  template <typename V>\n  EIGEN_DEVICE_FUNC static void set_val(IndexTuple<T, O...>& val, V& new_val) {\n    val.head = new_val;\n  }\n};\n\n\n\ntemplate <int N, typename T, typename... O>\nEIGEN_DEVICE_FUNC constexpr typename IndexTupleExtractor<N, T, O...>::ValType& array_get(IndexTuple<T, O...>& tuple) {\n  return IndexTupleExtractor<N, T, O...>::get_val(tuple);\n}\ntemplate <int N, typename T, typename... O>\nEIGEN_DEVICE_FUNC constexpr const typename IndexTupleExtractor<N, T, O...>::ValType& array_get(const IndexTuple<T, O...>& tuple) {\n  return IndexTupleExtractor<N, T, O...>::get_val(tuple);\n}\ntemplate <typename T, typename... O>\n  struct array_size<IndexTuple<T, O...> > {\n  static const size_t value = IndexTuple<T, O...>::count;\n};\ntemplate <typename T, typename... O>\n  struct array_size<const IndexTuple<T, O...> > {\n  static const size_t value = IndexTuple<T, O...>::count;\n};\n\n\n\n\ntemplate <DenseIndex Idx, typename ValueT>\nstruct tuple_coeff {\n  template <typename... T>\n  EIGEN_DEVICE_FUNC static constexpr ValueT get(const DenseIndex i, const IndexTuple<T...>& t) {\n    //    return array_get<Idx>(t) * (i == Idx) + tuple_coeff<Idx-1>::get(i, t) * (i != Idx);\n    return (i == Idx ? array_get<Idx>(t) : tuple_coeff<Idx-1, ValueT>::get(i, t));\n  }\n  template <typename... T>\n  EIGEN_DEVICE_FUNC static void set(const DenseIndex i, IndexTuple<T...>& t, const ValueT& value) {\n    if (i == Idx) {\n      update_value(array_get<Idx>(t), value);\n    } else {\n      tuple_coeff<Idx-1, ValueT>::set(i, t, value);\n    }\n  }\n\n  template <typename... T>\n  EIGEN_DEVICE_FUNC static constexpr bool value_known_statically(const DenseIndex i, const IndexTuple<T...>& t) {\n    return ((i == Idx) & is_compile_time_constant<typename IndexTupleExtractor<Idx, T...>::ValType>::value) ||\n        tuple_coeff<Idx-1, ValueT>::value_known_statically(i, t);\n  }\n\n  template <typename... T>\n  EIGEN_DEVICE_FUNC static constexpr bool values_up_to_known_statically(const IndexTuple<T...>& t) {\n    return is_compile_time_constant<typename IndexTupleExtractor<Idx, T...>::ValType>::value &&\n        tuple_coeff<Idx-1, ValueT>::values_up_to_known_statically(t);\n  }\n\n  template <typename... T>\n  EIGEN_DEVICE_FUNC static constexpr bool values_up_to_statically_known_to_increase(const IndexTuple<T...>& t) {\n    return is_compile_time_constant<typename IndexTupleExtractor<Idx, T...>::ValType>::value &&\n           is_compile_time_constant<typename IndexTupleExtractor<Idx, T...>::ValType>::value &&\n           array_get<Idx>(t) > array_get<Idx-1>(t) &&\n           tuple_coeff<Idx-1, ValueT>::values_up_to_statically_known_to_increase(t);\n  }\n};\n\ntemplate <typename ValueT>\nstruct tuple_coeff<0, ValueT> {\n  template <typename... T>\n  EIGEN_DEVICE_FUNC static constexpr ValueT get(const DenseIndex /*i*/, const IndexTuple<T...>& t) {\n    //  eigen_assert (i == 0);  // gcc fails to compile assertions in constexpr\n    return array_get<0>(t)/* * (i == 0)*/;\n  }\n  template <typename... T>\n  EIGEN_DEVICE_FUNC static void set(const DenseIndex i, IndexTuple<T...>& t, const ValueT value) {\n    eigen_assert (i == 0);\n    update_value(array_get<0>(t), value);\n  }\n  template <typename... T>\n  EIGEN_DEVICE_FUNC static constexpr bool value_known_statically(const DenseIndex i, const IndexTuple<T...>&) {\n    return is_compile_time_constant<typename IndexTupleExtractor<0, T...>::ValType>::value & (i == 0);\n  }\n\n  template <typename... T>\n  EIGEN_DEVICE_FUNC static constexpr bool values_up_to_known_statically(const IndexTuple<T...>&) {\n    return is_compile_time_constant<typename IndexTupleExtractor<0, T...>::ValType>::value;\n  }\n\n  template <typename... T>\n  EIGEN_DEVICE_FUNC static constexpr bool values_up_to_statically_known_to_increase(const IndexTuple<T...>&) {\n    return true;\n  }\n};\n}  // namespace internal\n\n\n\ntemplate<typename FirstType, typename... OtherTypes>\nstruct IndexList : internal::IndexTuple<FirstType, OtherTypes...> {\n  EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC constexpr DenseIndex operator[] (const DenseIndex i) const {\n    return internal::tuple_coeff<internal::array_size<internal::IndexTuple<FirstType, OtherTypes...> >::value-1, DenseIndex>::get(i, *this);\n  }\n  EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC constexpr DenseIndex get(const DenseIndex i) const {\n    return internal::tuple_coeff<internal::array_size<internal::IndexTuple<FirstType, OtherTypes...> >::value-1, DenseIndex>::get(i, *this);\n  }\n  EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC void set(const DenseIndex i, const DenseIndex value) {\n    return internal::tuple_coeff<internal::array_size<internal::IndexTuple<FirstType, OtherTypes...> >::value-1, DenseIndex>::set(i, *this, value);\n  }\n\n  EIGEN_DEVICE_FUNC constexpr IndexList(const internal::IndexTuple<FirstType, OtherTypes...>& other) : internal::IndexTuple<FirstType, OtherTypes...>(other) { }\n  EIGEN_DEVICE_FUNC constexpr IndexList(FirstType& first, OtherTypes... other) : internal::IndexTuple<FirstType, OtherTypes...>(first, other...) { }\n  EIGEN_DEVICE_FUNC constexpr IndexList() : internal::IndexTuple<FirstType, OtherTypes...>() { }\n\n  EIGEN_DEVICE_FUNC constexpr bool value_known_statically(const DenseIndex i) const {\n    return internal::tuple_coeff<internal::array_size<internal::IndexTuple<FirstType, OtherTypes...> >::value-1, DenseIndex>::value_known_statically(i, *this);\n  }\n  EIGEN_DEVICE_FUNC constexpr bool all_values_known_statically() const {\n    return internal::tuple_coeff<internal::array_size<internal::IndexTuple<FirstType, OtherTypes...> >::value-1, DenseIndex>::values_up_to_known_statically(*this);\n  }\n\n  EIGEN_DEVICE_FUNC constexpr bool values_statically_known_to_increase() const {\n    return internal::tuple_coeff<internal::array_size<internal::IndexTuple<FirstType, OtherTypes...> >::value-1, DenseIndex>::values_up_to_statically_known_to_increase(*this);\n  }\n};\n\n\ntemplate<typename FirstType, typename... OtherTypes>\nconstexpr IndexList<FirstType, OtherTypes...> make_index_list(FirstType val1, OtherTypes... other_vals) {\n  return IndexList<FirstType, OtherTypes...>(val1, other_vals...);\n}\n\n\ntemplate<typename FirstType, typename... OtherTypes>\nstruct IndexPairList : internal::IndexTuple<FirstType, OtherTypes...> {\n  EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC constexpr IndexPair<DenseIndex> operator[] (const DenseIndex i) const {\n    return internal::tuple_coeff<internal::array_size<internal::IndexTuple<FirstType, OtherTypes...> >::value-1, IndexPair<DenseIndex>>::get(i, *this);\n  }\n  EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC void set(const DenseIndex i, const IndexPair<DenseIndex> value) {\n    return internal::tuple_coeff<internal::array_size<internal::IndexTuple<FirstType, OtherTypes...>>::value-1, IndexPair<DenseIndex> >::set(i, *this, value);\n  }\n\n  EIGEN_DEVICE_FUNC  constexpr IndexPairList(const internal::IndexTuple<FirstType, OtherTypes...>& other) : internal::IndexTuple<FirstType, OtherTypes...>(other) { }\n  EIGEN_DEVICE_FUNC  constexpr IndexPairList() : internal::IndexTuple<FirstType, OtherTypes...>() { }\n\n  EIGEN_DEVICE_FUNC constexpr bool value_known_statically(const DenseIndex i) const {\n    return internal::tuple_coeff<internal::array_size<internal::IndexTuple<FirstType, OtherTypes...> >::value-1, DenseIndex>::value_known_statically(i, *this);\n  }\n};\n\nnamespace internal {\n\ntemplate<typename FirstType, typename... OtherTypes> size_t array_prod(const IndexList<FirstType, OtherTypes...>& sizes) {\n  size_t result = 1;\n  for (int i = 0; i < array_size<IndexList<FirstType, OtherTypes...> >::value; ++i) {\n    result *= sizes[i];\n  }\n  return result;\n}\n\ntemplate<typename FirstType, typename... OtherTypes> struct array_size<IndexList<FirstType, OtherTypes...> > {\n  static const size_t value = array_size<IndexTuple<FirstType, OtherTypes...> >::value;\n};\ntemplate<typename FirstType, typename... OtherTypes> struct array_size<const IndexList<FirstType, OtherTypes...> > {\n  static const size_t value = array_size<IndexTuple<FirstType, OtherTypes...> >::value;\n};\n\ntemplate<typename FirstType, typename... OtherTypes> struct array_size<IndexPairList<FirstType, OtherTypes...> > {\n  static const size_t value = std::tuple_size<std::tuple<FirstType, OtherTypes...> >::value;\n};\ntemplate<typename FirstType, typename... OtherTypes> struct array_size<const IndexPairList<FirstType, OtherTypes...> > {\n  static const size_t value = std::tuple_size<std::tuple<FirstType, OtherTypes...> >::value;\n};\n\ntemplate<DenseIndex N, typename FirstType, typename... OtherTypes> EIGEN_DEVICE_FUNC constexpr DenseIndex array_get(IndexList<FirstType, OtherTypes...>& a) {\n  return IndexTupleExtractor<N, FirstType, OtherTypes...>::get_val(a);\n}\ntemplate<DenseIndex N, typename FirstType, typename... OtherTypes> EIGEN_DEVICE_FUNC constexpr DenseIndex array_get(const IndexList<FirstType, OtherTypes...>& a) {\n  return IndexTupleExtractor<N, FirstType, OtherTypes...>::get_val(a);\n}\n\ntemplate <typename T>\nstruct index_known_statically_impl {\n  EIGEN_DEVICE_FUNC static constexpr bool run(const DenseIndex) {\n    return false;\n  }\n};\n\ntemplate <typename FirstType, typename... OtherTypes>\nstruct index_known_statically_impl<IndexList<FirstType, OtherTypes...> > {\n  EIGEN_DEVICE_FUNC static constexpr bool run(const DenseIndex i) {\n    return IndexList<FirstType, OtherTypes...>().value_known_statically(i);\n  }\n};\n\ntemplate <typename FirstType, typename... OtherTypes>\nstruct index_known_statically_impl<const IndexList<FirstType, OtherTypes...> > {\n  EIGEN_DEVICE_FUNC static constexpr bool run(const DenseIndex i) {\n    return IndexList<FirstType, OtherTypes...>().value_known_statically(i);\n  }\n};\n\n\ntemplate <typename T>\nstruct all_indices_known_statically_impl {\n  static constexpr bool run() {\n    return false;\n  }\n};\n\ntemplate <typename FirstType, typename... OtherTypes>\nstruct all_indices_known_statically_impl<IndexList<FirstType, OtherTypes...> > {\n  EIGEN_DEVICE_FUNC static constexpr bool run() {\n    return IndexList<FirstType, OtherTypes...>().all_values_known_statically();\n  }\n};\n\ntemplate <typename FirstType, typename... OtherTypes>\nstruct all_indices_known_statically_impl<const IndexList<FirstType, OtherTypes...> > {\n  EIGEN_DEVICE_FUNC static constexpr bool run() {\n    return IndexList<FirstType, OtherTypes...>().all_values_known_statically();\n  }\n};\n\n\ntemplate <typename T>\nstruct indices_statically_known_to_increase_impl {\n  EIGEN_DEVICE_FUNC static constexpr bool run() {\n    return false;\n  }\n};\n\ntemplate <typename FirstType, typename... OtherTypes>\n  struct indices_statically_known_to_increase_impl<IndexList<FirstType, OtherTypes...> > {\n  EIGEN_DEVICE_FUNC static constexpr bool run() {\n    return Eigen::IndexList<FirstType, OtherTypes...>().values_statically_known_to_increase();\n  }\n};\n\ntemplate <typename FirstType, typename... OtherTypes>\n  struct indices_statically_known_to_increase_impl<const IndexList<FirstType, OtherTypes...> > {\n  EIGEN_DEVICE_FUNC static constexpr bool run() {\n    return Eigen::IndexList<FirstType, OtherTypes...>().values_statically_known_to_increase();\n  }\n};\n\n\ntemplate <typename Tx>\nstruct index_statically_eq_impl {\n  EIGEN_DEVICE_FUNC static constexpr bool run(DenseIndex, DenseIndex) {\n    return false;\n  }\n};\n\ntemplate <typename FirstType, typename... OtherTypes>\nstruct index_statically_eq_impl<IndexList<FirstType, OtherTypes...> > {\n  EIGEN_DEVICE_FUNC static constexpr bool run(const DenseIndex i, const DenseIndex value) {\n    return IndexList<FirstType, OtherTypes...>().value_known_statically(i) &\n        (IndexList<FirstType, OtherTypes...>().get(i) == value);\n  }\n};\n\ntemplate <typename FirstType, typename... OtherTypes>\nstruct index_statically_eq_impl<const IndexList<FirstType, OtherTypes...> > {\n  EIGEN_DEVICE_FUNC static constexpr bool run(const DenseIndex i, const DenseIndex value) {\n    return IndexList<FirstType, OtherTypes...>().value_known_statically(i) &\n        (IndexList<FirstType, OtherTypes...>().get(i) == value);\n  }\n};\n\n\ntemplate <typename T>\nstruct index_statically_ne_impl {\n  EIGEN_DEVICE_FUNC static constexpr bool run(DenseIndex, DenseIndex) {\n    return false;\n  }\n};\n\ntemplate <typename FirstType, typename... OtherTypes>\nstruct index_statically_ne_impl<IndexList<FirstType, OtherTypes...> > {\n  EIGEN_DEVICE_FUNC static constexpr bool run(const DenseIndex i, const DenseIndex value) {\n    return IndexList<FirstType, OtherTypes...>().value_known_statically(i) &\n        (IndexList<FirstType, OtherTypes...>().get(i) != value);\n  }\n};\n\ntemplate <typename FirstType, typename... OtherTypes>\nstruct index_statically_ne_impl<const IndexList<FirstType, OtherTypes...> > {\n  EIGEN_DEVICE_FUNC static constexpr bool run(const DenseIndex i, const DenseIndex value) {\n    return IndexList<FirstType, OtherTypes...>().value_known_statically(i) &\n        (IndexList<FirstType, OtherTypes...>().get(i) != value);\n  }\n};\n\n\ntemplate <typename T>\nstruct index_statically_gt_impl {\n  EIGEN_DEVICE_FUNC static constexpr bool run(DenseIndex, DenseIndex) {\n    return false;\n  }\n};\n\ntemplate <typename FirstType, typename... OtherTypes>\nstruct index_statically_gt_impl<IndexList<FirstType, OtherTypes...> > {\n  EIGEN_DEVICE_FUNC static constexpr bool run(const DenseIndex i, const DenseIndex value) {\n    return IndexList<FirstType, OtherTypes...>().value_known_statically(i) &\n        (IndexList<FirstType, OtherTypes...>().get(i) > value);\n  }\n};\n\ntemplate <typename FirstType, typename... OtherTypes>\nstruct index_statically_gt_impl<const IndexList<FirstType, OtherTypes...> > {\n  EIGEN_DEVICE_FUNC static constexpr bool run(const DenseIndex i, const DenseIndex value) {\n    return IndexList<FirstType, OtherTypes...>().value_known_statically(i) &\n        (IndexList<FirstType, OtherTypes...>().get(i) > value);\n  }\n};\n\n\n\ntemplate <typename T>\nstruct index_statically_lt_impl {\n  EIGEN_DEVICE_FUNC static constexpr bool run(DenseIndex, DenseIndex) {\n    return false;\n  }\n};\n\ntemplate <typename FirstType, typename... OtherTypes>\nstruct index_statically_lt_impl<IndexList<FirstType, OtherTypes...> > {\n  EIGEN_DEVICE_FUNC static constexpr bool run(const DenseIndex i, const DenseIndex value) {\n    return IndexList<FirstType, OtherTypes...>().value_known_statically(i) &\n        (IndexList<FirstType, OtherTypes...>().get(i) < value);\n  }\n};\n\ntemplate <typename FirstType, typename... OtherTypes>\nstruct index_statically_lt_impl<const IndexList<FirstType, OtherTypes...> > {\n  EIGEN_DEVICE_FUNC static constexpr bool run(const DenseIndex i, const DenseIndex value) {\n    return IndexList<FirstType, OtherTypes...>().value_known_statically(i) &\n        (IndexList<FirstType, OtherTypes...>().get(i) < value);\n  }\n};\n\n\n\ntemplate <typename Tx>\nstruct index_pair_first_statically_eq_impl {\n  EIGEN_DEVICE_FUNC static constexpr bool run(DenseIndex, DenseIndex) {\n    return false;\n  }\n};\n\ntemplate <typename FirstType, typename... OtherTypes>\nstruct index_pair_first_statically_eq_impl<IndexPairList<FirstType, OtherTypes...> > {\n  EIGEN_DEVICE_FUNC static constexpr bool run(const DenseIndex i, const DenseIndex value) {\n    return IndexPairList<FirstType, OtherTypes...>().value_known_statically(i) &\n        (IndexPairList<FirstType, OtherTypes...>().operator[](i).first == value);\n  }\n};\n\ntemplate <typename FirstType, typename... OtherTypes>\nstruct index_pair_first_statically_eq_impl<const IndexPairList<FirstType, OtherTypes...> > {\n  EIGEN_DEVICE_FUNC static constexpr bool run(const DenseIndex i, const DenseIndex value) {\n    return IndexPairList<FirstType, OtherTypes...>().value_known_statically(i) &\n        (IndexPairList<FirstType, OtherTypes...>().operator[](i).first == value);\n  }\n};\n\n\n\ntemplate <typename Tx>\nstruct index_pair_second_statically_eq_impl {\n  EIGEN_DEVICE_FUNC static constexpr bool run(DenseIndex, DenseIndex) {\n    return false;\n  }\n};\n\ntemplate <typename FirstType, typename... OtherTypes>\nstruct index_pair_second_statically_eq_impl<IndexPairList<FirstType, OtherTypes...> > {\n  EIGEN_DEVICE_FUNC static constexpr bool run(const DenseIndex i, const DenseIndex value) {\n    return IndexPairList<FirstType, OtherTypes...>().value_known_statically(i) &\n        (IndexPairList<FirstType, OtherTypes...>().operator[](i).second == value);\n  }\n};\n\ntemplate <typename FirstType, typename... OtherTypes>\nstruct index_pair_second_statically_eq_impl<const IndexPairList<FirstType, OtherTypes...> > {\n  EIGEN_DEVICE_FUNC static constexpr bool run(const DenseIndex i, const DenseIndex value) {\n    return IndexPairList<FirstType, OtherTypes...>().value_known_statically(i) &\n        (IndexPairList<FirstType, OtherTypes...>().operator[](i).second == value);\n  }\n};\n\n\n}  // end namespace internal\n}  // end namespace Eigen\n\n#else\n\nnamespace Eigen {\nnamespace internal {\n\ntemplate <typename T>\nstruct index_known_statically_impl {\n  static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool run(const DenseIndex) {\n    return false;\n  }\n};\n\ntemplate <typename T>\nstruct all_indices_known_statically_impl {\n  static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool run() {\n    return false;\n  }\n};\n\ntemplate <typename T>\nstruct indices_statically_known_to_increase_impl {\n  static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool run() {\n    return false;\n  }\n};\n\ntemplate <typename T>\nstruct index_statically_eq_impl {\n  static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool run(DenseIndex, DenseIndex) {\n    return false;\n  }\n};\n\ntemplate <typename T>\nstruct index_statically_ne_impl {\n  static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool run(DenseIndex, DenseIndex) {\n    return false;\n  }\n};\n\ntemplate <typename T>\nstruct index_statically_gt_impl {\n  static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool run(DenseIndex, DenseIndex) {\n    return false;\n  }\n};\n\ntemplate <typename T>\nstruct index_statically_lt_impl {\n  static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool run(DenseIndex, DenseIndex) {\n    return false;\n  }\n};\n\ntemplate <typename Tx>\nstruct index_pair_first_statically_eq_impl {\n  static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool run(DenseIndex, DenseIndex) {\n    return false;\n  }\n};\n\ntemplate <typename Tx>\nstruct index_pair_second_statically_eq_impl {\n  static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool run(DenseIndex, DenseIndex) {\n    return false;\n  }\n};\n\n\n\n}  // end namespace internal\n}  // end namespace Eigen\n\n#endif\n\n\nnamespace Eigen {\nnamespace internal {\ntemplate <typename T>\nstatic EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bool index_known_statically(DenseIndex i) {\n  return index_known_statically_impl<T>::run(i);\n}\n\ntemplate <typename T>\nstatic EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bool all_indices_known_statically() {\n  return all_indices_known_statically_impl<T>::run();\n}\n\ntemplate <typename T>\nstatic EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bool indices_statically_known_to_increase() {\n  return indices_statically_known_to_increase_impl<T>::run();\n}\n\ntemplate <typename T>\nstatic EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bool index_statically_eq(DenseIndex i, DenseIndex value) {\n  return index_statically_eq_impl<T>::run(i, value);\n}\n\ntemplate <typename T>\nstatic EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bool index_statically_ne(DenseIndex i, DenseIndex value) {\n  return index_statically_ne_impl<T>::run(i, value);\n}\n\ntemplate <typename T>\nstatic EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bool index_statically_gt(DenseIndex i, DenseIndex value) {\n  return index_statically_gt_impl<T>::run(i, value);\n}\n\ntemplate <typename T>\nstatic EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bool index_statically_lt(DenseIndex i, DenseIndex value) {\n  return index_statically_lt_impl<T>::run(i, value);\n}\n\ntemplate <typename T>\nstatic EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bool index_pair_first_statically_eq(DenseIndex i, DenseIndex value) {\n  return index_pair_first_statically_eq_impl<T>::run(i, value);\n}\n\ntemplate <typename T>\nstatic EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bool index_pair_second_statically_eq(DenseIndex i, DenseIndex value) {\n  return index_pair_second_statically_eq_impl<T>::run(i, value);\n}\n\n}  // end namespace internal\n}  // end namespace Eigen\n\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_INDEX_LIST_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorInflation.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Ke Yang <yangke@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_INFLATION_H\n#define EIGEN_CXX11_TENSOR_TENSOR_INFLATION_H\n\nnamespace Eigen {\n\n/** \\class TensorInflation\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief Tensor inflation class.\n  *\n  *\n  */\nnamespace internal {\ntemplate<typename Strides, typename XprType>\nstruct traits<TensorInflationOp<Strides, XprType> > : public traits<XprType>\n{\n  typedef typename XprType::Scalar Scalar;\n  typedef traits<XprType> XprTraits;\n  typedef typename XprTraits::StorageKind StorageKind;\n  typedef typename XprTraits::Index Index;\n  typedef typename XprType::Nested Nested;\n  typedef typename remove_reference<Nested>::type _Nested;\n  static const int NumDimensions = XprTraits::NumDimensions;\n  static const int Layout = XprTraits::Layout;\n};\n\ntemplate<typename Strides, typename XprType>\nstruct eval<TensorInflationOp<Strides, XprType>, Eigen::Dense>\n{\n  typedef const TensorInflationOp<Strides, XprType>& type;\n};\n\ntemplate<typename Strides, typename XprType>\nstruct nested<TensorInflationOp<Strides, XprType>, 1, typename eval<TensorInflationOp<Strides, XprType> >::type>\n{\n  typedef TensorInflationOp<Strides, XprType> type;\n};\n\n}  // end namespace internal\n\ntemplate<typename Strides, typename XprType>\nclass TensorInflationOp : public TensorBase<TensorInflationOp<Strides, XprType>, ReadOnlyAccessors>\n{\n  public:\n  typedef typename Eigen::internal::traits<TensorInflationOp>::Scalar Scalar;\n  typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename Eigen::internal::nested<TensorInflationOp>::type Nested;\n  typedef typename Eigen::internal::traits<TensorInflationOp>::StorageKind StorageKind;\n  typedef typename Eigen::internal::traits<TensorInflationOp>::Index Index;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorInflationOp(const XprType& expr, const Strides& strides)\n      : m_xpr(expr), m_strides(strides) {}\n\n    EIGEN_DEVICE_FUNC\n    const Strides& strides() const { return m_strides; }\n\n    EIGEN_DEVICE_FUNC\n    const typename internal::remove_all<typename XprType::Nested>::type&\n    expression() const { return m_xpr; }\n\n  protected:\n    typename XprType::Nested m_xpr;\n    const Strides m_strides;\n};\n\n// Eval as rvalue\ntemplate<typename Strides, typename ArgType, typename Device>\nstruct TensorEvaluator<const TensorInflationOp<Strides, ArgType>, Device>\n{\n  typedef TensorInflationOp<Strides, ArgType> XprType;\n  typedef typename XprType::Index Index;\n  static const int NumDims = internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value;\n  typedef DSizes<Index, NumDims> Dimensions;\n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  static const int PacketSize = internal::unpacket_traits<PacketReturnType>::size;\n\n  enum {\n    IsAligned = /*TensorEvaluator<ArgType, Device>::IsAligned*/ false,\n    PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,\n    BlockAccess = false,\n    Layout = TensorEvaluator<ArgType, Device>::Layout,\n    CoordAccess = false,  // to be implemented\n    RawAccess = false\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)\n      : m_impl(op.expression(), device), m_strides(op.strides())\n  {\n    m_dimensions = m_impl.dimensions();\n    // Expand each dimension to the inflated dimension.\n    for (int i = 0; i < NumDims; ++i) {\n      m_dimensions[i] = (m_dimensions[i] - 1) * op.strides()[i] + 1;\n    }\n\n    // Remember the strides for fast division.\n    for (int i = 0; i < NumDims; ++i) {\n      m_fastStrides[i] = internal::TensorIntDivisor<Index>(m_strides[i]);\n    }\n\n    const typename TensorEvaluator<ArgType, Device>::Dimensions& input_dims = m_impl.dimensions();\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      m_outputStrides[0] = 1;\n      m_inputStrides[0] = 1;\n      for (int i = 1; i < NumDims; ++i) {\n        m_outputStrides[i] = m_outputStrides[i-1] * m_dimensions[i-1];\n        m_inputStrides[i] = m_inputStrides[i-1] * input_dims[i-1];\n      }\n    } else {  // RowMajor\n      m_outputStrides[NumDims-1] = 1;\n      m_inputStrides[NumDims-1] = 1;\n      for (int i = NumDims - 2; i >= 0; --i) {\n        m_outputStrides[i] = m_outputStrides[i+1] * m_dimensions[i+1];\n        m_inputStrides[i] = m_inputStrides[i+1] * input_dims[i+1];\n      }\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(Scalar* /*data*/) {\n    m_impl.evalSubExprsIfNeeded(NULL);\n    return true;\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {\n    m_impl.cleanup();\n  }\n\n  // Computes the input index given the output index. Returns true if the output\n  // index doesn't fall into a hole.\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool getInputIndex(Index index, Index* inputIndex) const\n  {\n    eigen_assert(index < dimensions().TotalSize());\n    *inputIndex = 0;\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      for (int i = NumDims - 1; i > 0; --i) {\n        const Index idx = index / m_outputStrides[i];\n        if (idx != idx / m_fastStrides[i] * m_strides[i]) {\n          return false;\n        }\n        *inputIndex += idx / m_strides[i] * m_inputStrides[i];\n        index -= idx * m_outputStrides[i];\n      }\n      if (index != index / m_fastStrides[0] * m_strides[0]) {\n        return false;\n      }\n      *inputIndex += index / m_strides[0];\n      return true;\n    } else {\n      for (int i = 0; i < NumDims - 1; ++i) {\n        const Index idx = index / m_outputStrides[i];\n        if (idx != idx / m_fastStrides[i] * m_strides[i]) {\n          return false;\n        }\n        *inputIndex += idx / m_strides[i] * m_inputStrides[i];\n        index -= idx * m_outputStrides[i];\n      }\n      if (index != index / m_fastStrides[NumDims-1] * m_strides[NumDims-1]) {\n        return false;\n      }\n      *inputIndex += index / m_strides[NumDims - 1];\n    }\n    return true;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const\n  {\n    Index inputIndex = 0;\n    if (getInputIndex(index, &inputIndex)) {\n     return m_impl.coeff(inputIndex);\n    } else {\n     return Scalar(0);\n    }\n  }\n\n  // TODO(yangke): optimize this function so that we can detect and produce\n  // all-zero packets\n  template<int LoadMode>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const\n  {\n    EIGEN_STATIC_ASSERT((PacketSize > 1), YOU_MADE_A_PROGRAMMING_MISTAKE)\n    eigen_assert(index+PacketSize-1 < dimensions().TotalSize());\n\n    EIGEN_ALIGN_MAX typename internal::remove_const<CoeffReturnType>::type values[PacketSize];\n    for (int i = 0; i < PacketSize; ++i) {\n      values[i] = coeff(index+i);\n    }\n    PacketReturnType rslt = internal::pload<PacketReturnType>(values);\n    return rslt;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {\n    const double compute_cost = NumDims * (3 * TensorOpCost::DivCost<Index>() +\n                                           3 * TensorOpCost::MulCost<Index>() +\n                                           2 * TensorOpCost::AddCost<Index>());\n    const double input_size = m_impl.dimensions().TotalSize();\n    const double output_size = m_dimensions.TotalSize();\n    if (output_size == 0)\n      return TensorOpCost();\n    return m_impl.costPerCoeff(vectorized) +\n           TensorOpCost(sizeof(CoeffReturnType) * input_size / output_size, 0,\n                        compute_cost, vectorized, PacketSize);\n  }\n\n  EIGEN_DEVICE_FUNC Scalar* data() const { return NULL; }\n\n protected:\n  Dimensions m_dimensions;\n  array<Index, NumDims> m_outputStrides;\n  array<Index, NumDims> m_inputStrides;\n  TensorEvaluator<ArgType, Device> m_impl;\n  const Strides m_strides;\n  array<internal::TensorIntDivisor<Index>, NumDims> m_fastStrides;\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_INFLATION_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorInitializer.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_INITIALIZER_H\n#define EIGEN_CXX11_TENSOR_TENSOR_INITIALIZER_H\n\n#if EIGEN_HAS_VARIADIC_TEMPLATES\n\n#include <initializer_list>\n\nnamespace Eigen {\n\n/** \\class TensorInitializer\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief Helper template to initialize Tensors from std::initializer_lists.\n  */\nnamespace internal {\n\ntemplate <typename Derived, int N>\nstruct Initializer {\n  typedef std::initializer_list<\n    typename Initializer<Derived, N - 1>::InitList> InitList;\n\n  static void run(TensorEvaluator<Derived, DefaultDevice>& tensor,\n                  Eigen::array<typename traits<Derived>::Index, traits<Derived>::NumDimensions>* indices,\n                  const InitList& vals) {\n    int i = 0;\n    for (auto v : vals) {\n      (*indices)[traits<Derived>::NumDimensions - N] = i++;\n      Initializer<Derived, N - 1>::run(tensor, indices, v);\n    }\n  }\n};\n\ntemplate <typename Derived>\nstruct Initializer<Derived, 1> {\n  typedef std::initializer_list<typename traits<Derived>::Scalar> InitList;\n\n  static void run(TensorEvaluator<Derived, DefaultDevice>& tensor,\n                  Eigen::array<typename traits<Derived>::Index, traits<Derived>::NumDimensions>* indices,\n                  const InitList& vals) {\n    int i = 0;\n    // There is likely a faster way to do that than iterating.\n    for (auto v : vals) {\n      (*indices)[traits<Derived>::NumDimensions - 1] = i++;\n      tensor.coeffRef(*indices) = v;\n    }\n  }\n};\n\ntemplate <typename Derived>\nstruct Initializer<Derived, 0> {\n  typedef typename traits<Derived>::Scalar InitList;\n\n  static void run(TensorEvaluator<Derived, DefaultDevice>& tensor,\n                  Eigen::array<typename traits<Derived>::Index, traits<Derived>::NumDimensions>*,\n                  const InitList& v) {\n    tensor.coeffRef(0) = v;\n  }\n};\n\n\ntemplate <typename Derived, int N>\nvoid initialize_tensor(TensorEvaluator<Derived, DefaultDevice>& tensor,\n                       const typename Initializer<Derived, traits<Derived>::NumDimensions>::InitList& vals) {\n  Eigen::array<typename traits<Derived>::Index, traits<Derived>::NumDimensions> indices;\n  Initializer<Derived, traits<Derived>::NumDimensions>::run(tensor, &indices, vals);\n}\n\n}  // namespace internal\n}  // namespace Eigen\n\n#endif  // EIGEN_HAS_VARIADIC_TEMPLATES\n\n#endif  // EIGEN_CXX11_TENSOR_TENSOR_INITIALIZER_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorIntDiv.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_INTDIV_H\n#define EIGEN_CXX11_TENSOR_TENSOR_INTDIV_H\n\n\nnamespace Eigen {\n\n/** \\internal\n  *\n  * \\class TensorIntDiv\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief Fast integer division by a constant.\n  *\n  * See the paper from Granlund and Montgomery for explanation.\n  *   (at http://dx.doi.org/10.1145/773473.178249)\n  *\n  * \\sa Tensor\n  */\n\nnamespace internal {\n\nnamespace {\n\n  // Note: result is undefined if val == 0\n  template <typename T>\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\n  typename internal::enable_if<sizeof(T)==4,int>::type count_leading_zeros(const T val)\n  {\n#ifdef __CUDA_ARCH__\n    return __clz(val);\n#elif EIGEN_COMP_MSVC\n    unsigned long index;\n    _BitScanReverse(&index, val);\n    return 31 - index;\n#else\n    EIGEN_STATIC_ASSERT(sizeof(unsigned long long) == 8, YOU_MADE_A_PROGRAMMING_MISTAKE);\n    return __builtin_clz(static_cast<uint32_t>(val));\n#endif\n  }\n\n  template <typename T>\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\n  typename internal::enable_if<sizeof(T)==8,int>::type count_leading_zeros(const T val)\n  {\n#ifdef __CUDA_ARCH__\n    return __clzll(val);\n#elif EIGEN_COMP_MSVC && EIGEN_ARCH_x86_64\n    unsigned long index;\n    _BitScanReverse64(&index, val);\n    return 63 - index;\n#elif EIGEN_COMP_MSVC\n    // MSVC's _BitScanReverse64 is not available for 32bits builds.\n    unsigned int lo = (unsigned int)(val&0xffffffff);\n    unsigned int hi = (unsigned int)((val>>32)&0xffffffff);\n    int n;\n    if(hi==0)\n      n = 32 + count_leading_zeros<unsigned int>(lo);\n    else\n      n = count_leading_zeros<unsigned int>(hi);\n    return n;\n#else\n    EIGEN_STATIC_ASSERT(sizeof(unsigned long long) == 8, YOU_MADE_A_PROGRAMMING_MISTAKE);\n    return __builtin_clzll(static_cast<uint64_t>(val));\n#endif\n  }\n\n  template <typename T>\n  struct UnsignedTraits {\n    typedef typename conditional<sizeof(T) == 8, uint64_t, uint32_t>::type type;\n  };\n\n  template <typename T>\n  struct DividerTraits {\n    typedef typename UnsignedTraits<T>::type type;\n    static const int N = sizeof(T) * 8;\n  };\n\n  template <typename T>\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE uint32_t muluh(const uint32_t a, const T b) {\n#if defined(__CUDA_ARCH__)\n    return __umulhi(a, b);\n#else\n    return (static_cast<uint64_t>(a) * b) >> 32;\n#endif\n  }\n\n  template <typename T>\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE uint64_t muluh(const uint64_t a, const T b) {\n#if defined(__CUDA_ARCH__)\n    return __umul64hi(a, b);\n#elif defined(__SIZEOF_INT128__)\n    __uint128_t v = static_cast<__uint128_t>(a) * static_cast<__uint128_t>(b);\n    return static_cast<uint64_t>(v >> 64);\n#else\n    return (TensorUInt128<static_val<0>, uint64_t>(a) * TensorUInt128<static_val<0>, uint64_t>(b)).upper();\n#endif\n  }\n\n  template <int N, typename T>\n  struct DividerHelper {\n    static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE uint32_t computeMultiplier(const int log_div, const T divider) {\n      EIGEN_STATIC_ASSERT(N == 32, YOU_MADE_A_PROGRAMMING_MISTAKE);\n      return static_cast<uint32_t>((static_cast<uint64_t>(1) << (N+log_div)) / divider - (static_cast<uint64_t>(1) << N) + 1);\n    }\n  };\n\n  template <typename T>\n  struct DividerHelper<64, T> {\n    static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE uint64_t computeMultiplier(const int log_div, const T divider) {\n#if defined(__SIZEOF_INT128__) && !defined(__CUDA_ARCH__)\n      return static_cast<uint64_t>((static_cast<__uint128_t>(1) << (64+log_div)) / static_cast<__uint128_t>(divider) - (static_cast<__uint128_t>(1) << 64) + 1);\n#else\n      const uint64_t shift = 1ULL << log_div;\n      TensorUInt128<uint64_t, uint64_t> result = TensorUInt128<uint64_t, static_val<0> >(shift, 0) / TensorUInt128<static_val<0>, uint64_t>(divider)\n                                               - TensorUInt128<static_val<1>, static_val<0> >(1, 0)\n                                               + TensorUInt128<static_val<0>, static_val<1> >(1);\n      return static_cast<uint64_t>(result);\n#endif\n    }\n  };\n}\n\n\ntemplate <typename T, bool div_gt_one = false>\nstruct TensorIntDivisor {\n public:\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorIntDivisor() {\n    multiplier = 0;\n    shift1 = 0;\n    shift2 = 0;\n  }\n\n  // Must have 0 < divider < 2^31. This is relaxed to\n  // 0 < divider < 2^63 when using 64-bit indices on platforms that support\n  // the __uint128_t type.\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorIntDivisor(const T divider) {\n    const int N = DividerTraits<T>::N;\n    eigen_assert(static_cast<typename UnsignedTraits<T>::type>(divider) < NumTraits<UnsignedType>::highest()/2);\n    eigen_assert(divider > 0);\n\n    // fast ln2\n    const int leading_zeros = count_leading_zeros(static_cast<UnsignedType>(divider));\n    int log_div = N - leading_zeros;\n    // if divider is a power of two then log_div is 1 more than it should be.\n    if ((static_cast<typename UnsignedTraits<T>::type>(1) << (log_div-1)) == static_cast<typename UnsignedTraits<T>::type>(divider))\n      log_div--;\n\n    multiplier = DividerHelper<N, T>::computeMultiplier(log_div, divider);\n    shift1 = log_div > 1 ? 1 : log_div;\n    shift2 = log_div > 1 ? log_div-1 : 0;\n  }\n\n  // Must have 0 <= numerator. On platforms that dont support the __uint128_t\n  // type numerator should also be less than 2^32-1.\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T divide(const T numerator) const {\n    eigen_assert(static_cast<typename UnsignedTraits<T>::type>(numerator) < NumTraits<UnsignedType>::highest()/2);\n    //eigen_assert(numerator >= 0); // this is implicitly asserted by the line above\n\n    UnsignedType t1 = muluh(multiplier, numerator);\n    UnsignedType t = (static_cast<UnsignedType>(numerator) - t1) >> shift1;\n    return (t1 + t) >> shift2;\n  }\n\n private:\n  typedef typename DividerTraits<T>::type UnsignedType;\n  UnsignedType multiplier;\n  int32_t shift1;\n  int32_t shift2;\n};\n\n\n// Optimized version for signed 32 bit integers.\n// Derived from Hacker's Delight.\n// Only works for divisors strictly greater than one\ntemplate <>\nclass TensorIntDivisor<int32_t, true> {\n public:\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorIntDivisor() {\n    magic = 0;\n    shift = 0;\n  }\n  // Must have 2 <= divider\n  EIGEN_DEVICE_FUNC TensorIntDivisor(int32_t divider)  {\n    eigen_assert(divider >= 2);\n    calcMagic(divider);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE int divide(const int32_t n) const {\n#ifdef __CUDA_ARCH__\n    return (__umulhi(magic, n) >> shift);\n#else\n    uint64_t v = static_cast<uint64_t>(magic) * static_cast<uint64_t>(n);\n    return (static_cast<uint32_t>(v >> 32) >> shift);\n#endif\n  }\n\nprivate:\n  // Compute the magic numbers. See Hacker's Delight section 10 for an in\n  // depth explanation.\n  EIGEN_DEVICE_FUNC void calcMagic(int32_t d) {\n   const unsigned two31 = 0x80000000;     // 2**31.\n   unsigned ad = d;\n   unsigned t = two31 + (ad >> 31);\n   unsigned anc = t - 1 - t%ad;     // Absolute value of nc.\n   int p = 31;                      // Init. p.\n   unsigned q1 = two31/anc;         // Init. q1 = 2**p/|nc|.\n   unsigned r1 = two31 - q1*anc;    // Init. r1 = rem(2**p, |nc|).\n   unsigned q2 = two31/ad;          // Init. q2 = 2**p/|d|.\n   unsigned r2 = two31 - q2*ad;     // Init. r2 = rem(2**p, |d|).\n   unsigned delta = 0;\n   do {\n      p = p + 1;\n      q1 = 2*q1;           // Update q1 = 2**p/|nc|.\n      r1 = 2*r1;           // Update r1 = rem(2**p, |nc|).\n      if (r1 >= anc) {     // (Must be an unsigned\n         q1 = q1 + 1;      // comparison here).\n         r1 = r1 - anc;}\n      q2 = 2*q2;           // Update q2 = 2**p/|d|.\n      r2 = 2*r2;           // Update r2 = rem(2**p, |d|).\n      if (r2 >= ad) {      // (Must be an unsigned\n         q2 = q2 + 1;      // comparison here).\n         r2 = r2 - ad;}\n      delta = ad - r2;\n   } while (q1 < delta || (q1 == delta && r1 == 0));\n\n   magic = (unsigned)(q2 + 1);\n   shift = p - 32;\n  }\n\n  uint32_t magic;\n  int32_t shift;\n};\n\n\ntemplate <typename T, bool div_gt_one>\nstatic EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T operator / (const T& numerator, const TensorIntDivisor<T, div_gt_one>& divisor) {\n  return divisor.divide(numerator);\n}\n\n\n} // end namespace internal\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_INTDIV_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorLayoutSwap.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_LAYOUT_SWAP_H\n#define EIGEN_CXX11_TENSOR_TENSOR_LAYOUT_SWAP_H\n\nnamespace Eigen {\n\n/** \\class TensorLayoutSwap\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief Swap the layout from col-major to row-major, or row-major\n  * to col-major, and invert the order of the dimensions.\n  *\n  * Beware: the dimensions are reversed by this operation. If you want to\n  * preserve the ordering of the dimensions, you need to combine this\n  * operation with a shuffle.\n  *\n  * \\example:\n  * Tensor<float, 2, ColMajor> input(2, 4);\n  * Tensor<float, 2, RowMajor> output = input.swap_layout();\n  * eigen_assert(output.dimension(0) == 4);\n  * eigen_assert(output.dimension(1) == 2);\n  *\n  * array<int, 2> shuffle(1, 0);\n  * output = input.swap_layout().shuffle(shuffle);\n  * eigen_assert(output.dimension(0) == 2);\n  * eigen_assert(output.dimension(1) == 4);\n  *\n  */\nnamespace internal {\ntemplate<typename XprType>\nstruct traits<TensorLayoutSwapOp<XprType> > : public traits<XprType>\n{\n  typedef typename XprType::Scalar Scalar;\n  typedef traits<XprType> XprTraits;\n  typedef typename XprTraits::StorageKind StorageKind;\n  typedef typename XprTraits::Index Index;\n  typedef typename XprType::Nested Nested;\n  typedef typename remove_reference<Nested>::type _Nested;\n  static const int NumDimensions = traits<XprType>::NumDimensions;\n  static const int Layout = (traits<XprType>::Layout == ColMajor) ? RowMajor : ColMajor;\n};\n\ntemplate<typename XprType>\nstruct eval<TensorLayoutSwapOp<XprType>, Eigen::Dense>\n{\n  typedef const TensorLayoutSwapOp<XprType>& type;\n};\n\ntemplate<typename XprType>\nstruct nested<TensorLayoutSwapOp<XprType>, 1, typename eval<TensorLayoutSwapOp<XprType> >::type>\n{\n  typedef TensorLayoutSwapOp<XprType> type;\n};\n\n}  // end namespace internal\n\n\n\ntemplate<typename XprType>\nclass TensorLayoutSwapOp : public TensorBase<TensorLayoutSwapOp<XprType>, WriteAccessors>\n{\n  public:\n  typedef typename Eigen::internal::traits<TensorLayoutSwapOp>::Scalar Scalar;\n  typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;\n  typedef typename internal::remove_const<typename XprType::CoeffReturnType>::type CoeffReturnType;\n  typedef typename Eigen::internal::nested<TensorLayoutSwapOp>::type Nested;\n  typedef typename Eigen::internal::traits<TensorLayoutSwapOp>::StorageKind StorageKind;\n  typedef typename Eigen::internal::traits<TensorLayoutSwapOp>::Index Index;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorLayoutSwapOp(const XprType& expr)\n      : m_xpr(expr) {}\n\n    EIGEN_DEVICE_FUNC\n    const typename internal::remove_all<typename XprType::Nested>::type&\n    expression() const { return m_xpr; }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE TensorLayoutSwapOp& operator = (const TensorLayoutSwapOp& other)\n    {\n      typedef TensorAssignOp<TensorLayoutSwapOp, const TensorLayoutSwapOp> Assign;\n      Assign assign(*this, other);\n      internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());\n      return *this;\n    }\n\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE TensorLayoutSwapOp& operator = (const OtherDerived& other)\n    {\n      typedef TensorAssignOp<TensorLayoutSwapOp, const OtherDerived> Assign;\n      Assign assign(*this, other);\n      internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());\n      return *this;\n    }\n\n  protected:\n    typename XprType::Nested m_xpr;\n};\n\n\n// Eval as rvalue\ntemplate<typename ArgType, typename Device>\nstruct TensorEvaluator<const TensorLayoutSwapOp<ArgType>, Device>\n{\n  typedef TensorLayoutSwapOp<ArgType> XprType;\n  typedef typename XprType::Index Index;\n  static const int NumDims = internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value;\n  typedef DSizes<Index, NumDims> Dimensions;\n\n  enum {\n    IsAligned = TensorEvaluator<ArgType, Device>::IsAligned,\n    PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,\n    Layout = (static_cast<int>(TensorEvaluator<ArgType, Device>::Layout) == static_cast<int>(ColMajor)) ? RowMajor : ColMajor,\n    CoordAccess = false,  // to be implemented\n    RawAccess = TensorEvaluator<ArgType, Device>::RawAccess\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)\n      : m_impl(op.expression(), device)\n  {\n    for(int i = 0; i < NumDims; ++i) {\n      m_dimensions[i] = m_impl.dimensions()[NumDims-1-i];\n    }\n  }\n\n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(CoeffReturnType* data) {\n    return m_impl.evalSubExprsIfNeeded(data);\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {\n    m_impl.cleanup();\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const\n  {\n    return m_impl.coeff(index);\n  }\n\n  template<int LoadMode>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const\n  {\n    return m_impl.template packet<LoadMode>(index);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {\n    return m_impl.costPerCoeff(vectorized);\n  }\n\n  EIGEN_DEVICE_FUNC Scalar* data() const { return m_impl.data(); }\n\n  const TensorEvaluator<ArgType, Device>& impl() const { return m_impl; }\n\n protected:\n  TensorEvaluator<ArgType, Device> m_impl;\n  Dimensions m_dimensions;\n};\n\n\n// Eval as lvalue\ntemplate<typename ArgType, typename Device>\n  struct TensorEvaluator<TensorLayoutSwapOp<ArgType>, Device>\n  : public TensorEvaluator<const TensorLayoutSwapOp<ArgType>, Device>\n{\n  typedef TensorEvaluator<const TensorLayoutSwapOp<ArgType>, Device> Base;\n  typedef TensorLayoutSwapOp<ArgType> XprType;\n\n  enum {\n    IsAligned = TensorEvaluator<ArgType, Device>::IsAligned,\n    PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,\n    Layout = (static_cast<int>(TensorEvaluator<ArgType, Device>::Layout) == static_cast<int>(ColMajor)) ? RowMajor : ColMajor,\n    CoordAccess = false  // to be implemented\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)\n    : Base(op, device)\n  { }\n\n  typedef typename XprType::Index Index;\n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType& coeffRef(Index index)\n  {\n    return this->m_impl.coeffRef(index);\n  }\n  template <int StoreMode> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  void writePacket(Index index, const PacketReturnType& x)\n  {\n    this->m_impl.template writePacket<StoreMode>(index, x);\n  }\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_LAYOUT_SWAP_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorMacros.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_META_MACROS_H\n#define EIGEN_CXX11_TENSOR_TENSOR_META_MACROS_H\n\n\n/** use this macro in sfinae selection in templated functions\n *\n *   template<typename T,\n *            typename std::enable_if< isBanana<T>::value , int >::type = 0\n *   >\n *   void foo(){}\n *\n *   becomes =>\n *\n *   template<typename TopoType,\n *           SFINAE_ENABLE_IF( isBanana<T>::value )\n *   >\n *   void foo(){}\n */\n\n// SFINAE requires variadic templates\n#ifndef __CUDACC__\n#if EIGEN_HAS_VARIADIC_TEMPLATES\n  // SFINAE doesn't work for gcc <= 4.7\n  #ifdef EIGEN_COMP_GNUC\n    #if EIGEN_GNUC_AT_LEAST(4,8)\n      #define EIGEN_HAS_SFINAE\n    #endif\n  #else\n    #define EIGEN_HAS_SFINAE\n  #endif\n#endif\n#endif\n\n#define EIGEN_SFINAE_ENABLE_IF( __condition__ ) \\\n    typename internal::enable_if< ( __condition__ ) , int >::type = 0\n\n\n#if EIGEN_HAS_CONSTEXPR\n#define EIGEN_CONSTEXPR constexpr\n#else\n#define EIGEN_CONSTEXPR\n#endif\n\n\n#endif\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorMap.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_MAP_H\n#define EIGEN_CXX11_TENSOR_TENSOR_MAP_H\n\nnamespace Eigen {\n\n/** \\class TensorMap\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief A tensor expression mapping an existing array of data.\n  *\n  */\n/// template <class> class MakePointer_ is added to convert the host pointer to the device pointer.\n/// It is added due to the fact that for our device compiler T* is not allowed.\n/// If we wanted to use the same Evaluator functions we have to convert that type to our pointer T.\n/// This is done through our MakePointer_ class. By default the Type in the MakePointer_<T> is T* .\n/// Therefore, by adding the default value, we managed to convert the type and it does not break any\n/// existing code as its default value is T*.\ntemplate<typename PlainObjectType, int Options_, template <class> class MakePointer_> class TensorMap : public TensorBase<TensorMap<PlainObjectType, Options_, MakePointer_> >\n{\n  public:\n    typedef TensorMap<PlainObjectType, Options_, MakePointer_> Self;\n    typedef typename PlainObjectType::Base Base;\n    typedef typename Eigen::internal::nested<Self>::type Nested;\n    typedef typename internal::traits<PlainObjectType>::StorageKind StorageKind;\n    typedef typename internal::traits<PlainObjectType>::Index Index;\n    typedef typename internal::traits<PlainObjectType>::Scalar Scalar;\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n    typedef typename Base::CoeffReturnType CoeffReturnType;\n\n  /*    typedef typename internal::conditional<\n                         bool(internal::is_lvalue<PlainObjectType>::value),\n                         Scalar *,\n                         const Scalar *>::type\n                     PointerType;*/\n    typedef typename MakePointer_<Scalar>::Type PointerType;\n    typedef PointerType PointerArgType;\n\n    static const int Options = Options_;\n\n    static const Index NumIndices = PlainObjectType::NumIndices;\n    typedef typename PlainObjectType::Dimensions Dimensions;\n\n    enum {\n      IsAligned = ((int(Options_)&Aligned)==Aligned),\n      Layout = PlainObjectType::Layout,\n      CoordAccess = true,\n      RawAccess = true\n    };\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE TensorMap(PointerArgType dataPtr) : m_data(dataPtr), m_dimensions() {\n      // The number of dimensions used to construct a tensor must be equal to the rank of the tensor.\n      EIGEN_STATIC_ASSERT((0 == NumIndices || NumIndices == Dynamic), YOU_MADE_A_PROGRAMMING_MISTAKE)\n    }\n\n#if EIGEN_HAS_VARIADIC_TEMPLATES\n    template<typename... IndexTypes> EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE TensorMap(PointerArgType dataPtr, Index firstDimension, IndexTypes... otherDimensions) : m_data(dataPtr), m_dimensions(firstDimension, otherDimensions...) {\n      // The number of dimensions used to construct a tensor must be equal to the rank of the tensor.\n      EIGEN_STATIC_ASSERT((sizeof...(otherDimensions) + 1 == NumIndices || NumIndices == Dynamic), YOU_MADE_A_PROGRAMMING_MISTAKE)\n    }\n#else\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE TensorMap(PointerArgType dataPtr, Index firstDimension) : m_data(dataPtr), m_dimensions(firstDimension) {\n      // The number of dimensions used to construct a tensor must be equal to the rank of the tensor.\n      EIGEN_STATIC_ASSERT((1 == NumIndices || NumIndices == Dynamic), YOU_MADE_A_PROGRAMMING_MISTAKE)\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE TensorMap(PointerArgType dataPtr, Index dim1, Index dim2) : m_data(dataPtr), m_dimensions(dim1, dim2) {\n      EIGEN_STATIC_ASSERT(2 == NumIndices || NumIndices == Dynamic, YOU_MADE_A_PROGRAMMING_MISTAKE)\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE TensorMap(PointerArgType dataPtr, Index dim1, Index dim2, Index dim3) : m_data(dataPtr), m_dimensions(dim1, dim2, dim3) {\n      EIGEN_STATIC_ASSERT(3 == NumIndices || NumIndices == Dynamic, YOU_MADE_A_PROGRAMMING_MISTAKE)\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE TensorMap(PointerArgType dataPtr, Index dim1, Index dim2, Index dim3, Index dim4) : m_data(dataPtr), m_dimensions(dim1, dim2, dim3, dim4) {\n      EIGEN_STATIC_ASSERT(4 == NumIndices || NumIndices == Dynamic, YOU_MADE_A_PROGRAMMING_MISTAKE)\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE TensorMap(PointerArgType dataPtr, Index dim1, Index dim2, Index dim3, Index dim4, Index dim5) : m_data(dataPtr), m_dimensions(dim1, dim2, dim3, dim4, dim5) {\n      EIGEN_STATIC_ASSERT(5 == NumIndices || NumIndices == Dynamic, YOU_MADE_A_PROGRAMMING_MISTAKE)\n    }\n#endif\n\n   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorMap(PointerArgType dataPtr, const array<Index, NumIndices>& dimensions)\n      : m_data(dataPtr), m_dimensions(dimensions)\n    { }\n\n    template <typename Dimensions>\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorMap(PointerArgType dataPtr, const Dimensions& dimensions)\n      : m_data(dataPtr), m_dimensions(dimensions)\n    { }\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorMap(PlainObjectType& tensor)\n      : m_data(tensor.data()), m_dimensions(tensor.dimensions())\n    { }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Index rank() const { return m_dimensions.rank(); }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Index dimension(Index n) const { return m_dimensions[n]; }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Index size() const { return m_dimensions.TotalSize(); }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE PointerType data() { return m_data; }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const PointerType data() const { return m_data; }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar& operator()(const array<Index, NumIndices>& indices) const\n    {\n      //      eigen_assert(checkIndexRange(indices));\n      if (PlainObjectType::Options&RowMajor) {\n        const Index index = m_dimensions.IndexOfRowMajor(indices);\n        return m_data[index];\n      } else {\n        const Index index = m_dimensions.IndexOfColMajor(indices);\n        return m_data[index];\n      }\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar& operator()() const\n    {\n      EIGEN_STATIC_ASSERT(NumIndices == 0, YOU_MADE_A_PROGRAMMING_MISTAKE)\n      return m_data[0];\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar& operator()(Index index) const\n    {\n      eigen_internal_assert(index >= 0 && index < size());\n      return m_data[index];\n    }\n\n#if EIGEN_HAS_VARIADIC_TEMPLATES\n    template<typename... IndexTypes> EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar& operator()(Index firstIndex, Index secondIndex, IndexTypes... otherIndices) const\n    {\n      EIGEN_STATIC_ASSERT(sizeof...(otherIndices) + 2 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)\n      if (PlainObjectType::Options&RowMajor) {\n        const Index index = m_dimensions.IndexOfRowMajor(array<Index, NumIndices>{{firstIndex, secondIndex, otherIndices...}});\n        return m_data[index];\n      } else {\n        const Index index = m_dimensions.IndexOfColMajor(array<Index, NumIndices>{{firstIndex, secondIndex, otherIndices...}});\n        return m_data[index];\n      }\n    }\n#else\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar& operator()(Index i0, Index i1) const\n    {\n      if (PlainObjectType::Options&RowMajor) {\n        const Index index = i1 + i0 * m_dimensions[1];\n        return m_data[index];\n      } else {\n        const Index index = i0 + i1 * m_dimensions[0];\n        return m_data[index];\n      }\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar& operator()(Index i0, Index i1, Index i2) const\n    {\n      if (PlainObjectType::Options&RowMajor) {\n         const Index index = i2 + m_dimensions[2] * (i1 + m_dimensions[1] * i0);\n         return m_data[index];\n      } else {\n         const Index index = i0 + m_dimensions[0] * (i1 + m_dimensions[1] * i2);\n        return m_data[index];\n      }\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar& operator()(Index i0, Index i1, Index i2, Index i3) const\n    {\n      if (PlainObjectType::Options&RowMajor) {\n        const Index index = i3 + m_dimensions[3] * (i2 + m_dimensions[2] * (i1 + m_dimensions[1] * i0));\n        return m_data[index];\n      } else {\n        const Index index = i0 + m_dimensions[0] * (i1 + m_dimensions[1] * (i2 + m_dimensions[2] * i3));\n        return m_data[index];\n      }\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar& operator()(Index i0, Index i1, Index i2, Index i3, Index i4) const\n    {\n      if (PlainObjectType::Options&RowMajor) {\n        const Index index = i4 + m_dimensions[4] * (i3 + m_dimensions[3] * (i2 + m_dimensions[2] * (i1 + m_dimensions[1] * i0)));\n        return m_data[index];\n      } else {\n        const Index index = i0 + m_dimensions[0] * (i1 + m_dimensions[1] * (i2 + m_dimensions[2] * (i3 + m_dimensions[3] * i4)));\n        return m_data[index];\n      }\n    }\n#endif\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar& operator()(const array<Index, NumIndices>& indices)\n    {\n      //      eigen_assert(checkIndexRange(indices));\n      if (PlainObjectType::Options&RowMajor) {\n        const Index index = m_dimensions.IndexOfRowMajor(indices);\n        return m_data[index];\n      } else {\n        const Index index = m_dimensions.IndexOfColMajor(indices);\n        return m_data[index];\n      }\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar& operator()()\n    {\n      EIGEN_STATIC_ASSERT(NumIndices == 0, YOU_MADE_A_PROGRAMMING_MISTAKE)\n      return m_data[0];\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar& operator()(Index index)\n    {\n      eigen_internal_assert(index >= 0 && index < size());\n      return m_data[index];\n    }\n\n#if EIGEN_HAS_VARIADIC_TEMPLATES\n    template<typename... IndexTypes> EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar& operator()(Index firstIndex, Index secondIndex, IndexTypes... otherIndices)\n    {\n      static_assert(sizeof...(otherIndices) + 2 == NumIndices || NumIndices == Dynamic, \"Number of indices used to access a tensor coefficient must be equal to the rank of the tensor.\");\n      const std::size_t NumDims = sizeof...(otherIndices) + 2;\n      if (PlainObjectType::Options&RowMajor) {\n        const Index index = m_dimensions.IndexOfRowMajor(array<Index, NumDims>{{firstIndex, secondIndex, otherIndices...}});\n        return m_data[index];\n      } else {\n        const Index index = m_dimensions.IndexOfColMajor(array<Index, NumDims>{{firstIndex, secondIndex, otherIndices...}});\n        return m_data[index];\n      }\n    }\n#else\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar& operator()(Index i0, Index i1)\n    {\n       if (PlainObjectType::Options&RowMajor) {\n         const Index index = i1 + i0 * m_dimensions[1];\n        return m_data[index];\n      } else {\n        const Index index = i0 + i1 * m_dimensions[0];\n        return m_data[index];\n      }\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar& operator()(Index i0, Index i1, Index i2)\n    {\n       if (PlainObjectType::Options&RowMajor) {\n         const Index index = i2 + m_dimensions[2] * (i1 + m_dimensions[1] * i0);\n        return m_data[index];\n      } else {\n         const Index index = i0 + m_dimensions[0] * (i1 + m_dimensions[1] * i2);\n        return m_data[index];\n      }\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar& operator()(Index i0, Index i1, Index i2, Index i3)\n    {\n      if (PlainObjectType::Options&RowMajor) {\n        const Index index = i3 + m_dimensions[3] * (i2 + m_dimensions[2] * (i1 + m_dimensions[1] * i0));\n        return m_data[index];\n      } else {\n        const Index index = i0 + m_dimensions[0] * (i1 + m_dimensions[1] * (i2 + m_dimensions[2] * i3));\n        return m_data[index];\n      }\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar& operator()(Index i0, Index i1, Index i2, Index i3, Index i4)\n    {\n      if (PlainObjectType::Options&RowMajor) {\n        const Index index = i4 + m_dimensions[4] * (i3 + m_dimensions[3] * (i2 + m_dimensions[2] * (i1 + m_dimensions[1] * i0)));\n        return m_data[index];\n      } else {\n        const Index index = i0 + m_dimensions[0] * (i1 + m_dimensions[1] * (i2 + m_dimensions[2] * (i3 + m_dimensions[3] * i4)));\n        return m_data[index];\n      }\n    }\n#endif\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Self& operator=(const Self& other)\n    {\n      typedef TensorAssignOp<Self, const Self> Assign;\n      Assign assign(*this, other);\n      internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());\n      return *this;\n    }\n\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    Self& operator=(const OtherDerived& other)\n    {\n      typedef TensorAssignOp<Self, const OtherDerived> Assign;\n      Assign assign(*this, other);\n      internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());\n      return *this;\n    }\n\n  private:\n    typename MakePointer_<Scalar>::Type m_data;\n    Dimensions m_dimensions;\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_MAP_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorMeta.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_META_H\n#define EIGEN_CXX11_TENSOR_TENSOR_META_H\n\nnamespace Eigen {\n\ntemplate<bool cond> struct Cond {};\n\ntemplate<typename T1, typename T2> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nconst T1& choose(Cond<true>, const T1& first, const T2&) {\n  return first;\n}\n\ntemplate<typename T1, typename T2> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nconst T2& choose(Cond<false>, const T1&, const T2& second) {\n  return second;\n}\n\n\ntemplate <typename T, typename X, typename Y>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nT divup(const X x, const Y y) {\n  return static_cast<T>((x + y - 1) / y);\n}\n\ntemplate <typename T>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nT divup(const T x, const T y) {\n  return static_cast<T>((x + y - 1) / y);\n}\n\ntemplate <size_t n> struct max_n_1 {\n  static const size_t size = n;\n};\ntemplate <> struct max_n_1<0> {\n  static const size_t size = 1;\n};\n\n\n// Default packet types\ntemplate <typename Scalar, typename Device>\nstruct PacketType : internal::packet_traits<Scalar> {\n  typedef typename internal::packet_traits<Scalar>::type type;\n};\n\n// For CUDA packet types when using a GpuDevice\n#if defined(EIGEN_USE_GPU) && defined(__CUDACC__) && defined(EIGEN_HAS_CUDA_FP16)\ntemplate <>\nstruct PacketType<half, GpuDevice> {\n  typedef half2 type;\n  static const int size = 2;\n  enum {\n    HasAdd    = 1,\n    HasSub    = 1,\n    HasMul    = 1,\n    HasNegate = 1,\n    HasAbs    = 1,\n    HasArg    = 0,\n    HasAbs2   = 0,\n    HasMin    = 1,\n    HasMax    = 1,\n    HasConj   = 0,\n    HasSetLinear = 0,\n    HasBlend  = 0,\n\n    HasDiv    = 1,\n    HasSqrt   = 1,\n    HasRsqrt  = 1,\n    HasExp    = 1,\n    HasLog    = 1,\n    HasLog1p  = 0,\n    HasLog10  = 0,\n    HasPow    = 1,\n  };\n};\n#endif\n\n#if defined(EIGEN_USE_SYCL)\ntemplate <typename T>\n  struct PacketType<T, SyclDevice> {\n  typedef T type;\n  static const int size = 1;\n  enum {\n    HasAdd    = 0,\n    HasSub    = 0,\n    HasMul    = 0,\n    HasNegate = 0,\n    HasAbs    = 0,\n    HasArg    = 0,\n    HasAbs2   = 0,\n    HasMin    = 0,\n    HasMax    = 0,\n    HasConj   = 0,\n    HasSetLinear = 0,\n    HasBlend  = 0\n  };\n};\n#endif\n\n\n// Tuple mimics std::pair but works on e.g. nvcc.\ntemplate <typename U, typename V> struct Tuple {\n public:\n  U first;\n  V second;\n\n  typedef U first_type;\n  typedef V second_type;\n\n  EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  Tuple() : first(), second() {}\n\n  EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  Tuple(const U& f, const V& s) : first(f), second(s) {}\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  Tuple& operator= (const Tuple& rhs) {\n    if (&rhs == this) return *this;\n    first = rhs.first;\n    second = rhs.second;\n    return *this;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  void swap(Tuple& rhs) {\n    using numext::swap;\n    swap(first, rhs.first);\n    swap(second, rhs.second);\n  }\n};\n\ntemplate <typename U, typename V>\nEIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nbool operator==(const Tuple<U, V>& x, const Tuple<U, V>& y) {\n  return (x.first == y.first && x.second == y.second);\n}\n\ntemplate <typename U, typename V>\nEIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nbool operator!=(const Tuple<U, V>& x, const Tuple<U, V>& y) {\n  return !(x == y);\n}\n\n\n// Can't use std::pairs on cuda devices\ntemplate <typename Idx> struct IndexPair {\n  EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE IndexPair() : first(0), second(0) {}\n  EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE IndexPair(Idx f, Idx s) : first(f), second(s) {}\n\n  EIGEN_DEVICE_FUNC void set(IndexPair<Idx> val) {\n    first = val.first;\n    second = val.second;\n  }\n\n  Idx first;\n  Idx second;\n};\n\n\n#ifdef EIGEN_HAS_SFINAE\nnamespace internal {\n\n  template<typename IndexType, Index... Is>\n  EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  array<Index, sizeof...(Is)> customIndices2Array(IndexType& idx, numeric_list<Index, Is...>) {\n    return { idx[Is]... };\n  }\n  template<typename IndexType>\n  EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  array<Index, 0> customIndices2Array(IndexType&, numeric_list<Index>) {\n    return array<Index, 0>();\n  }\n\n  /** Make an array (for index/dimensions) out of a custom index */\n  template<typename Index, std::size_t NumIndices, typename IndexType>\n  EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  array<Index, NumIndices> customIndices2Array(IndexType& idx) {\n    return customIndices2Array(idx, typename gen_numeric_list<Index, NumIndices>::type{});\n  }\n\n\n  template <typename B, typename D>\n  struct is_base_of\n  {\n\n    typedef char (&yes)[1];\n    typedef char (&no)[2];\n\n    template <typename BB, typename DD>\n    struct Host\n    {\n      operator BB*() const;\n      operator DD*();\n    };\n\n    template<typename T>\n    static yes check(D*, T);\n    static no check(B*, int);\n\n    static const bool value = sizeof(check(Host<B,D>(), int())) == sizeof(yes);\n  };\n\n}\n#endif\n\n\n\n}  // namespace Eigen\n\n#endif  // EIGEN_CXX11_TENSOR_TENSOR_META_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorMorphing.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_MORPHING_H\n#define EIGEN_CXX11_TENSOR_TENSOR_MORPHING_H\n\nnamespace Eigen {\n\n/** \\class TensorReshaping\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief Tensor reshaping class.\n  *\n  *\n  */\nnamespace internal {\ntemplate<typename NewDimensions, typename XprType>\nstruct traits<TensorReshapingOp<NewDimensions, XprType> > : public traits<XprType>\n{\n  typedef typename XprType::Scalar Scalar;\n  typedef traits<XprType> XprTraits;\n  typedef typename XprTraits::StorageKind StorageKind;\n  typedef typename XprTraits::Index Index;\n  typedef typename XprType::Nested Nested;\n  typedef typename remove_reference<Nested>::type _Nested;\n  static const int NumDimensions = array_size<NewDimensions>::value;\n  static const int Layout = XprTraits::Layout;\n};\n\ntemplate<typename NewDimensions, typename XprType>\nstruct eval<TensorReshapingOp<NewDimensions, XprType>, Eigen::Dense>\n{\n  typedef const TensorReshapingOp<NewDimensions, XprType>& type;\n};\n\ntemplate<typename NewDimensions, typename XprType>\nstruct nested<TensorReshapingOp<NewDimensions, XprType>, 1, typename eval<TensorReshapingOp<NewDimensions, XprType> >::type>\n{\n  typedef TensorReshapingOp<NewDimensions, XprType> type;\n};\n\n}  // end namespace internal\n\n\n\ntemplate<typename NewDimensions, typename XprType>\nclass TensorReshapingOp : public TensorBase<TensorReshapingOp<NewDimensions, XprType>, WriteAccessors>\n{\n  public:\n  typedef typename Eigen::internal::traits<TensorReshapingOp>::Scalar Scalar;\n  typedef typename internal::remove_const<typename XprType::CoeffReturnType>::type CoeffReturnType;\n  typedef typename Eigen::internal::nested<TensorReshapingOp>::type Nested;\n  typedef typename Eigen::internal::traits<TensorReshapingOp>::StorageKind StorageKind;\n  typedef typename Eigen::internal::traits<TensorReshapingOp>::Index Index;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorReshapingOp(const XprType& expr, const NewDimensions& dims)\n      : m_xpr(expr), m_dims(dims) {}\n\n    EIGEN_DEVICE_FUNC\n    const NewDimensions& dimensions() const { return m_dims; }\n\n    EIGEN_DEVICE_FUNC\n    const typename internal::remove_all<typename XprType::Nested>::type&\n    expression() const { return m_xpr; }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE TensorReshapingOp& operator = (const TensorReshapingOp& other)\n    {\n      typedef TensorAssignOp<TensorReshapingOp, const TensorReshapingOp> Assign;\n      Assign assign(*this, other);\n      internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());\n      return *this;\n    }\n\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE TensorReshapingOp& operator = (const OtherDerived& other)\n    {\n      typedef TensorAssignOp<TensorReshapingOp, const OtherDerived> Assign;\n      Assign assign(*this, other);\n      internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());\n      return *this;\n    }\n\n  protected:\n    typename XprType::Nested m_xpr;\n    const NewDimensions m_dims;\n};\n\n\n// Eval as rvalue\ntemplate<typename NewDimensions, typename ArgType, typename Device>\nstruct TensorEvaluator<const TensorReshapingOp<NewDimensions, ArgType>, Device>\n{\n  typedef TensorReshapingOp<NewDimensions, ArgType> XprType;\n  typedef NewDimensions Dimensions;\n\n  enum {\n    IsAligned = TensorEvaluator<ArgType, Device>::IsAligned,\n    PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,\n    Layout = TensorEvaluator<ArgType, Device>::Layout,\n    CoordAccess = false,  // to be implemented\n    RawAccess = TensorEvaluator<ArgType, Device>::RawAccess\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)\n      : m_impl(op.expression(), device), m_dimensions(op.dimensions())\n  {\n    // The total size of the reshaped tensor must be equal to the total size\n    // of the input tensor.\n    eigen_assert(internal::array_prod(m_impl.dimensions()) == internal::array_prod(op.dimensions()));\n  }\n\n  typedef typename XprType::Index Index;\n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(CoeffReturnType* data) {\n    return m_impl.evalSubExprsIfNeeded(data);\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {\n    m_impl.cleanup();\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const\n  {\n    return m_impl.coeff(index);\n  }\n\n  template<int LoadMode>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const\n  {\n    return m_impl.template packet<LoadMode>(index);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {\n    return m_impl.costPerCoeff(vectorized);\n  }\n\n  EIGEN_DEVICE_FUNC Scalar* data() const { return const_cast<Scalar*>(m_impl.data()); }\n\n  EIGEN_DEVICE_FUNC const TensorEvaluator<ArgType, Device>& impl() const { return m_impl; }\n\n protected:\n  TensorEvaluator<ArgType, Device> m_impl;\n  NewDimensions m_dimensions;\n};\n\n\n// Eval as lvalue\ntemplate<typename NewDimensions, typename ArgType, typename Device>\n  struct TensorEvaluator<TensorReshapingOp<NewDimensions, ArgType>, Device>\n  : public TensorEvaluator<const TensorReshapingOp<NewDimensions, ArgType>, Device>\n\n{\n  typedef TensorEvaluator<const TensorReshapingOp<NewDimensions, ArgType>, Device> Base;\n  typedef TensorReshapingOp<NewDimensions, ArgType> XprType;\n  typedef NewDimensions Dimensions;\n\n  enum {\n    IsAligned = TensorEvaluator<ArgType, Device>::IsAligned,\n    PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,\n    Layout = TensorEvaluator<ArgType, Device>::Layout,\n    CoordAccess = false,  // to be implemented\n    RawAccess = TensorEvaluator<ArgType, Device>::RawAccess\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)\n    : Base(op, device)\n  { }\n\n  typedef typename XprType::Index Index;\n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType& coeffRef(Index index)\n  {\n    return this->m_impl.coeffRef(index);\n  }\n  template <int StoreMode> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  void writePacket(Index index, const PacketReturnType& x)\n  {\n    this->m_impl.template writePacket<StoreMode>(index, x);\n  }\n};\n\n\n/** \\class TensorSlicing\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief Tensor slicing class.\n  *\n  *\n  */\nnamespace internal {\ntemplate<typename StartIndices, typename Sizes, typename XprType>\nstruct traits<TensorSlicingOp<StartIndices, Sizes, XprType> > : public traits<XprType>\n{\n  typedef typename XprType::Scalar Scalar;\n  typedef traits<XprType> XprTraits;\n  typedef typename XprTraits::StorageKind StorageKind;\n  typedef typename XprTraits::Index Index;\n  typedef typename XprType::Nested Nested;\n  typedef typename remove_reference<Nested>::type _Nested;\n  static const int NumDimensions = array_size<StartIndices>::value;\n  static const int Layout = XprTraits::Layout;\n};\n\ntemplate<typename StartIndices, typename Sizes, typename XprType>\nstruct eval<TensorSlicingOp<StartIndices, Sizes, XprType>, Eigen::Dense>\n{\n  typedef const TensorSlicingOp<StartIndices, Sizes, XprType>& type;\n};\n\ntemplate<typename StartIndices, typename Sizes, typename XprType>\nstruct nested<TensorSlicingOp<StartIndices, Sizes, XprType>, 1, typename eval<TensorSlicingOp<StartIndices, Sizes, XprType> >::type>\n{\n  typedef TensorSlicingOp<StartIndices, Sizes, XprType> type;\n};\n\n}  // end namespace internal\n\n\n\ntemplate<typename StartIndices, typename Sizes, typename XprType>\nclass TensorSlicingOp : public TensorBase<TensorSlicingOp<StartIndices, Sizes, XprType> >\n{\n  public:\n  typedef typename Eigen::internal::traits<TensorSlicingOp>::Scalar Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename Eigen::internal::nested<TensorSlicingOp>::type Nested;\n  typedef typename Eigen::internal::traits<TensorSlicingOp>::StorageKind StorageKind;\n  typedef typename Eigen::internal::traits<TensorSlicingOp>::Index Index;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorSlicingOp(const XprType& expr, const StartIndices& indices, const Sizes& sizes)\n      : m_xpr(expr), m_indices(indices), m_sizes(sizes) {}\n\n    EIGEN_DEVICE_FUNC\n    const StartIndices& startIndices() const { return m_indices; }\n    EIGEN_DEVICE_FUNC\n    const Sizes& sizes() const { return m_sizes; }\n\n    EIGEN_DEVICE_FUNC\n    const typename internal::remove_all<typename XprType::Nested>::type&\n    expression() const { return m_xpr; }\n\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE TensorSlicingOp& operator = (const OtherDerived& other)\n    {\n      typedef TensorAssignOp<TensorSlicingOp, const OtherDerived> Assign;\n      Assign assign(*this, other);\n      internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());\n      return *this;\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE TensorSlicingOp& operator = (const TensorSlicingOp& other)\n    {\n      typedef TensorAssignOp<TensorSlicingOp, const TensorSlicingOp> Assign;\n      Assign assign(*this, other);\n      internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());\n      return *this;\n    }\n\n\n  protected:\n    typename XprType::Nested m_xpr;\n    const StartIndices m_indices;\n    const Sizes m_sizes;\n};\n\n\n// Fixme: figure out the exact threshold\nnamespace {\ntemplate <typename Index, typename Device> struct MemcpyTriggerForSlicing {\n  EIGEN_DEVICE_FUNC MemcpyTriggerForSlicing(const Device& device) : threshold_(2 * device.numThreads()) { }\n  EIGEN_DEVICE_FUNC bool operator ()(Index val) const { return val > threshold_; }\n\n private:\n  Index threshold_;\n};\n\n// It is very expensive to start the memcpy kernel on GPU: we therefore only\n// use it for large copies.\n#ifdef EIGEN_USE_GPU\ntemplate <typename Index> struct MemcpyTriggerForSlicing<Index, GpuDevice>  {\n  EIGEN_DEVICE_FUNC MemcpyTriggerForSlicing(const GpuDevice&) { }\n  EIGEN_DEVICE_FUNC bool operator ()(Index val) const { return val > 4*1024*1024; }\n};\n#endif\n}\n\n// Eval as rvalue\ntemplate<typename StartIndices, typename Sizes, typename ArgType, typename Device>\nstruct TensorEvaluator<const TensorSlicingOp<StartIndices, Sizes, ArgType>, Device>\n{\n  typedef TensorSlicingOp<StartIndices, Sizes, ArgType> XprType;\n  static const int NumDims = internal::array_size<Sizes>::value;\n\n  enum {\n    // Alignment can't be guaranteed at compile time since it depends on the\n    // slice offsets and sizes.\n    IsAligned = /*TensorEvaluator<ArgType, Device>::IsAligned*/false,\n    PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,\n    Layout = TensorEvaluator<ArgType, Device>::Layout,\n    CoordAccess = false,\n    RawAccess = false\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)\n      : m_impl(op.expression(), device), m_device(device), m_dimensions(op.sizes()), m_offsets(op.startIndices())\n  {\n    for (std::size_t i = 0; i < internal::array_size<Dimensions>::value; ++i) {\n      eigen_assert(m_impl.dimensions()[i] >= op.sizes()[i] + op.startIndices()[i]);\n    }\n\n    const typename TensorEvaluator<ArgType, Device>::Dimensions& input_dims = m_impl.dimensions();\n    const Sizes& output_dims = op.sizes();\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      m_inputStrides[0] = 1;\n      for (int i = 1; i < NumDims; ++i) {\n        m_inputStrides[i] = m_inputStrides[i-1] * input_dims[i-1];\n      }\n\n     // Don't initialize m_fastOutputStrides[0] since it won't ever be accessed.\n      m_outputStrides[0] = 1;\n      for (int i = 1; i < NumDims; ++i) {\n        m_outputStrides[i] = m_outputStrides[i-1] * output_dims[i-1];\n        m_fastOutputStrides[i] = internal::TensorIntDivisor<Index>(m_outputStrides[i]);\n      }\n    } else {\n      m_inputStrides[NumDims-1] = 1;\n      for (int i = NumDims - 2; i >= 0; --i) {\n        m_inputStrides[i] = m_inputStrides[i+1] * input_dims[i+1];\n      }\n\n     // Don't initialize m_fastOutputStrides[NumDims-1] since it won't ever be accessed.\n      m_outputStrides[NumDims-1] = 1;\n      for (int i = NumDims - 2; i >= 0; --i) {\n        m_outputStrides[i] = m_outputStrides[i+1] * output_dims[i+1];\n        m_fastOutputStrides[i] = internal::TensorIntDivisor<Index>(m_outputStrides[i]);\n      }\n    }\n  }\n\n  typedef typename XprType::Index Index;\n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  typedef Sizes Dimensions;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }\n\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(CoeffReturnType* data) {\n    m_impl.evalSubExprsIfNeeded(NULL);\n    if (!NumTraits<typename internal::remove_const<Scalar>::type>::RequireInitialization && data && m_impl.data()) {\n      Index contiguous_values = 1;\n      if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n        for (int i = 0; i < NumDims; ++i) {\n          contiguous_values *= dimensions()[i];\n          if (dimensions()[i] != m_impl.dimensions()[i]) {\n            break;\n          }\n        }\n      } else {\n        for (int i = NumDims-1; i >= 0; --i) {\n          contiguous_values *= dimensions()[i];\n          if (dimensions()[i] != m_impl.dimensions()[i]) {\n            break;\n          }\n        }\n      }\n      // Use memcpy if it's going to be faster than using the regular evaluation.\n      const MemcpyTriggerForSlicing<Index, Device> trigger(m_device);\n      if (trigger(contiguous_values)) {\n        Scalar* src = (Scalar*)m_impl.data();\n        for (int i = 0; i < internal::array_prod(dimensions()); i += contiguous_values) {\n          Index offset = srcCoeff(i);\n          m_device.memcpy((void*)(data+i), src+offset, contiguous_values * sizeof(Scalar));\n        }\n        return false;\n      }\n    }\n    return true;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {\n    m_impl.cleanup();\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const\n  {\n    return m_impl.coeff(srcCoeff(index));\n  }\n\n  template<int LoadMode>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const\n  {\n    const int packetSize = internal::unpacket_traits<PacketReturnType>::size;\n    EIGEN_STATIC_ASSERT((packetSize > 1), YOU_MADE_A_PROGRAMMING_MISTAKE)\n    eigen_assert(index+packetSize-1 < internal::array_prod(dimensions()));\n\n    Index inputIndices[] = {0, 0};\n    Index indices[] = {index, index + packetSize - 1};\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      for (int i = NumDims - 1; i > 0; --i) {\n        const Index idx0 = indices[0] / m_fastOutputStrides[i];\n        const Index idx1 = indices[1] / m_fastOutputStrides[i];\n        inputIndices[0] += (idx0 + m_offsets[i]) * m_inputStrides[i];\n        inputIndices[1] += (idx1 + m_offsets[i]) * m_inputStrides[i];\n        indices[0] -= idx0 * m_outputStrides[i];\n        indices[1] -= idx1 * m_outputStrides[i];\n      }\n      inputIndices[0] += (indices[0] + m_offsets[0]);\n      inputIndices[1] += (indices[1] + m_offsets[0]);\n    } else {\n      for (int i = 0; i < NumDims - 1; ++i) {\n        const Index idx0 = indices[0] / m_fastOutputStrides[i];\n        const Index idx1 = indices[1] / m_fastOutputStrides[i];\n        inputIndices[0] += (idx0 + m_offsets[i]) * m_inputStrides[i];\n        inputIndices[1] += (idx1 + m_offsets[i]) * m_inputStrides[i];\n        indices[0] -= idx0 * m_outputStrides[i];\n        indices[1] -= idx1 * m_outputStrides[i];\n      }\n      inputIndices[0] += (indices[0] + m_offsets[NumDims-1]);\n      inputIndices[1] += (indices[1] + m_offsets[NumDims-1]);\n    }\n    if (inputIndices[1] - inputIndices[0] == packetSize - 1) {\n      PacketReturnType rslt = m_impl.template packet<Unaligned>(inputIndices[0]);\n      return rslt;\n    }\n    else {\n      EIGEN_ALIGN_MAX typename internal::remove_const<CoeffReturnType>::type values[packetSize];\n      values[0] = m_impl.coeff(inputIndices[0]);\n      values[packetSize-1] = m_impl.coeff(inputIndices[1]);\n      for (int i = 1; i < packetSize-1; ++i) {\n        values[i] = coeff(index+i);\n      }\n      PacketReturnType rslt = internal::pload<PacketReturnType>(values);\n      return rslt;\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {\n    return m_impl.costPerCoeff(vectorized) + TensorOpCost(0, 0, NumDims);\n  }\n\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar* data() const {\n    Scalar* result = m_impl.data();\n    if (result) {\n      Index offset = 0;\n      if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n        for (int i = 0; i < NumDims; ++i) {\n          if (m_dimensions[i] != m_impl.dimensions()[i]) {\n            offset += m_offsets[i] * m_inputStrides[i];\n            for (int j = i+1; j < NumDims; ++j) {\n              if (m_dimensions[j] > 1) {\n                return NULL;\n              }\n              offset += m_offsets[j] * m_inputStrides[j];\n            }\n            break;\n          }\n        }\n      } else {\n        for (int i = NumDims - 1; i >= 0; --i) {\n          if (m_dimensions[i] != m_impl.dimensions()[i]) {\n            offset += m_offsets[i] * m_inputStrides[i];\n            for (int j = i-1; j >= 0; --j) {\n              if (m_dimensions[j] > 1) {\n                return NULL;\n              }\n              offset += m_offsets[j] * m_inputStrides[j];\n            }\n            break;\n          }\n        }\n      }\n      return result + offset;\n    }\n    return NULL;\n  }\n\n protected:\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index srcCoeff(Index index) const\n  {\n    Index inputIndex = 0;\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      for (int i = NumDims - 1; i > 0; --i) {\n        const Index idx = index / m_fastOutputStrides[i];\n        inputIndex += (idx + m_offsets[i]) * m_inputStrides[i];\n        index -= idx * m_outputStrides[i];\n      }\n      inputIndex += (index + m_offsets[0]);\n    } else {\n      for (int i = 0; i < NumDims - 1; ++i) {\n        const Index idx = index / m_fastOutputStrides[i];\n        inputIndex += (idx + m_offsets[i]) * m_inputStrides[i];\n        index -= idx * m_outputStrides[i];\n      }\n      inputIndex += (index + m_offsets[NumDims-1]);\n    }\n    return inputIndex;\n  }\n\n  array<Index, NumDims> m_outputStrides;\n  array<internal::TensorIntDivisor<Index>, NumDims> m_fastOutputStrides;\n  array<Index, NumDims> m_inputStrides;\n  TensorEvaluator<ArgType, Device> m_impl;\n  const Device& m_device;\n  Dimensions m_dimensions;\n  const StartIndices m_offsets;\n};\n\n\n// Eval as lvalue\ntemplate<typename StartIndices, typename Sizes, typename ArgType, typename Device>\nstruct TensorEvaluator<TensorSlicingOp<StartIndices, Sizes, ArgType>, Device>\n  : public TensorEvaluator<const TensorSlicingOp<StartIndices, Sizes, ArgType>, Device>\n{\n  typedef TensorEvaluator<const TensorSlicingOp<StartIndices, Sizes, ArgType>, Device> Base;\n  typedef TensorSlicingOp<StartIndices, Sizes, ArgType> XprType;\n  static const int NumDims = internal::array_size<Sizes>::value;\n\n  enum {\n    IsAligned = /*TensorEvaluator<ArgType, Device>::IsAligned*/false,\n    PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,\n    Layout = TensorEvaluator<ArgType, Device>::Layout,\n    CoordAccess = false,\n    RawAccess = false\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)\n    : Base(op, device)\n    { }\n\n  typedef typename XprType::Index Index;\n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  typedef Sizes Dimensions;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType& coeffRef(Index index)\n  {\n    return this->m_impl.coeffRef(this->srcCoeff(index));\n  }\n\n  template <int StoreMode> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  void writePacket(Index index, const PacketReturnType& x)\n  {\n    const int packetSize = internal::unpacket_traits<PacketReturnType>::size;\n    Index inputIndices[] = {0, 0};\n    Index indices[] = {index, index + packetSize - 1};\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      for (int i = NumDims - 1; i > 0; --i) {\n        const Index idx0 = indices[0] / this->m_fastOutputStrides[i];\n        const Index idx1 = indices[1] / this->m_fastOutputStrides[i];\n        inputIndices[0] += (idx0 + this->m_offsets[i]) * this->m_inputStrides[i];\n        inputIndices[1] += (idx1 + this->m_offsets[i]) * this->m_inputStrides[i];\n        indices[0] -= idx0 * this->m_outputStrides[i];\n        indices[1] -= idx1 * this->m_outputStrides[i];\n      }\n      inputIndices[0] += (indices[0] + this->m_offsets[0]);\n      inputIndices[1] += (indices[1] + this->m_offsets[0]);\n    } else {\n      for (int i = 0; i < NumDims - 1; ++i) {\n        const Index idx0 = indices[0] / this->m_fastOutputStrides[i];\n        const Index idx1 = indices[1] / this->m_fastOutputStrides[i];\n        inputIndices[0] += (idx0 + this->m_offsets[i]) * this->m_inputStrides[i];\n        inputIndices[1] += (idx1 + this->m_offsets[i]) * this->m_inputStrides[i];\n        indices[0] -= idx0 * this->m_outputStrides[i];\n        indices[1] -= idx1 * this->m_outputStrides[i];\n      }\n      inputIndices[0] += (indices[0] + this->m_offsets[NumDims-1]);\n      inputIndices[1] += (indices[1] + this->m_offsets[NumDims-1]);\n    }\n    if (inputIndices[1] - inputIndices[0] == packetSize - 1) {\n      this->m_impl.template writePacket<StoreMode>(inputIndices[0], x);\n    }\n    else {\n      EIGEN_ALIGN_MAX CoeffReturnType values[packetSize];\n      internal::pstore<CoeffReturnType, PacketReturnType>(values, x);\n      this->m_impl.coeffRef(inputIndices[0]) = values[0];\n      this->m_impl.coeffRef(inputIndices[1]) = values[packetSize-1];\n      for (int i = 1; i < packetSize-1; ++i) {\n        this->coeffRef(index+i) = values[i];\n      }\n    }\n  }\n};\n\n\n\nnamespace internal {\ntemplate<typename StartIndices, typename StopIndices, typename Strides, typename XprType>\nstruct traits<TensorStridingSlicingOp<StartIndices, StopIndices, Strides, XprType> > : public traits<XprType>\n{\n  typedef typename XprType::Scalar Scalar;\n  typedef traits<XprType> XprTraits;\n  typedef typename XprTraits::StorageKind StorageKind;\n  typedef typename XprTraits::Index Index;\n  typedef typename XprType::Nested Nested;\n  typedef typename remove_reference<Nested>::type _Nested;\n  static const int NumDimensions = array_size<StartIndices>::value;\n  static const int Layout = XprTraits::Layout;\n};\n\ntemplate<typename StartIndices, typename StopIndices, typename Strides, typename XprType>\nstruct eval<TensorStridingSlicingOp<StartIndices, StopIndices, Strides, XprType>, Eigen::Dense>\n{\n  typedef const TensorStridingSlicingOp<StartIndices, StopIndices, Strides, XprType>& type;\n};\n\ntemplate<typename StartIndices, typename StopIndices, typename Strides, typename XprType>\nstruct nested<TensorStridingSlicingOp<StartIndices, StopIndices, Strides, XprType>, 1, typename eval<TensorStridingSlicingOp<StartIndices, StopIndices, Strides, XprType> >::type>\n{\n  typedef TensorStridingSlicingOp<StartIndices, StopIndices, Strides, XprType> type;\n};\n\n}  // end namespace internal\n\n\ntemplate<typename StartIndices, typename StopIndices, typename Strides, typename XprType>\nclass TensorStridingSlicingOp : public TensorBase<TensorStridingSlicingOp<StartIndices, StopIndices, Strides, XprType> >\n{\n  public:\n  typedef typename internal::traits<TensorStridingSlicingOp>::Scalar Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename internal::nested<TensorStridingSlicingOp>::type Nested;\n  typedef typename internal::traits<TensorStridingSlicingOp>::StorageKind StorageKind;\n  typedef typename internal::traits<TensorStridingSlicingOp>::Index Index;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorStridingSlicingOp(\n    const XprType& expr, const StartIndices& startIndices,\n    const StopIndices& stopIndices, const Strides& strides)\n      : m_xpr(expr), m_startIndices(startIndices), m_stopIndices(stopIndices),\n        m_strides(strides) {}\n\n    EIGEN_DEVICE_FUNC\n    const StartIndices& startIndices() const { return m_startIndices; }\n    EIGEN_DEVICE_FUNC\n    const StartIndices& stopIndices() const { return m_stopIndices; }\n    EIGEN_DEVICE_FUNC\n    const StartIndices& strides() const { return m_strides; }\n\n    EIGEN_DEVICE_FUNC\n    const typename internal::remove_all<typename XprType::Nested>::type&\n    expression() const { return m_xpr; }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE TensorStridingSlicingOp& operator = (const TensorStridingSlicingOp& other)\n    {\n      typedef TensorAssignOp<TensorStridingSlicingOp, const TensorStridingSlicingOp> Assign;\n      Assign assign(*this, other);\n      internal::TensorExecutor<const Assign, DefaultDevice>::run(\n          assign, DefaultDevice());\n      return *this;\n    }\n\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE TensorStridingSlicingOp& operator = (const OtherDerived& other)\n    {\n      typedef TensorAssignOp<TensorStridingSlicingOp, const OtherDerived> Assign;\n      Assign assign(*this, other);\n      internal::TensorExecutor<const Assign, DefaultDevice>::run(\n          assign, DefaultDevice());\n      return *this;\n    }\n\n  protected:\n    typename XprType::Nested m_xpr;\n    const StartIndices m_startIndices;\n    const StopIndices m_stopIndices;\n    const Strides m_strides;\n};\n\n// Eval as rvalue\ntemplate<typename StartIndices, typename StopIndices, typename Strides, typename ArgType, typename Device>\nstruct TensorEvaluator<const TensorStridingSlicingOp<StartIndices, StopIndices, Strides, ArgType>, Device>\n{\n  typedef TensorStridingSlicingOp<StartIndices, StopIndices, Strides, ArgType> XprType;\n  static const int NumDims = internal::array_size<Strides>::value;\n\n  enum {\n    // Alignment can't be guaranteed at compile time since it depends on the\n    // slice offsets and sizes.\n    IsAligned = false,\n    PacketAccess = false,\n    BlockAccess = false,\n    Layout = TensorEvaluator<ArgType, Device>::Layout,\n    RawAccess = false\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)\n      : m_impl(op.expression(), device), m_device(device), m_strides(op.strides())\n  {\n    // Handle degenerate intervals by gracefully clamping and allowing m_dimensions to be zero\n    DSizes<Index,NumDims> startIndicesClamped, stopIndicesClamped;\n    for (size_t i = 0; i < internal::array_size<Dimensions>::value; ++i) {\n      eigen_assert(m_strides[i] != 0 && \"0 stride is invalid\");\n      if(m_strides[i]>0){\n        startIndicesClamped[i] = clamp(op.startIndices()[i], 0, m_impl.dimensions()[i]);\n        stopIndicesClamped[i] = clamp(op.stopIndices()[i], 0, m_impl.dimensions()[i]);\n      }else{\n        /* implies m_strides[i]<0 by assert */\n        startIndicesClamped[i] = clamp(op.startIndices()[i], -1, m_impl.dimensions()[i] - 1);\n        stopIndicesClamped[i] = clamp(op.stopIndices()[i], -1, m_impl.dimensions()[i] - 1);\n      }\n      m_startIndices[i] = startIndicesClamped[i];\n    }\n\n    const typename TensorEvaluator<ArgType, Device>::Dimensions& input_dims = m_impl.dimensions();\n\n    // check for degenerate intervals and compute output tensor shape\n    bool degenerate = false;;\n    for(int i = 0; i < NumDims; i++){\n      Index interval = stopIndicesClamped[i] - startIndicesClamped[i];\n      if(interval == 0 || ((interval<0) != (m_strides[i]<0))){\n        m_dimensions[i] = 0;\n        degenerate = true;\n      }else{\n        m_dimensions[i] = interval / m_strides[i]\n                          + (interval % m_strides[i] != 0 ? 1 : 0);\n        eigen_assert(m_dimensions[i] >= 0);\n      }\n    }\n    Strides output_dims = m_dimensions;\n\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      m_inputStrides[0] = m_strides[0];\n      m_offsets[0] = startIndicesClamped[0];\n      Index previousDimProduct = 1;\n      for (int i = 1; i < NumDims; ++i) {\n        previousDimProduct *= input_dims[i-1];\n        m_inputStrides[i] = previousDimProduct * m_strides[i];\n        m_offsets[i] = startIndicesClamped[i] * previousDimProduct;\n      }\n\n      // Don't initialize m_fastOutputStrides[0] since it won't ever be accessed.\n      m_outputStrides[0] = 1;\n      for (int i = 1; i < NumDims; ++i) {\n        m_outputStrides[i] = m_outputStrides[i-1] * output_dims[i-1];\n        // NOTE: if tensor is degenerate, we send 1 to prevent TensorIntDivisor constructor crash\n        m_fastOutputStrides[i] = internal::TensorIntDivisor<Index>(degenerate ? 1 : m_outputStrides[i]);\n      }\n    } else {\n      m_inputStrides[NumDims-1] = m_strides[NumDims-1];\n      m_offsets[NumDims-1] = startIndicesClamped[NumDims-1];\n      Index previousDimProduct = 1;\n      for (int i = NumDims - 2; i >= 0; --i) {\n        previousDimProduct *= input_dims[i+1];\n        m_inputStrides[i] = previousDimProduct * m_strides[i];\n        m_offsets[i] = startIndicesClamped[i] * previousDimProduct;\n      }\n\n      m_outputStrides[NumDims-1] = 1;\n      for (int i = NumDims - 2; i >= 0; --i) {\n        m_outputStrides[i] = m_outputStrides[i+1] * output_dims[i+1];\n        // NOTE: if tensor is degenerate, we send 1 to prevent TensorIntDivisor constructor crash\n        m_fastOutputStrides[i] = internal::TensorIntDivisor<Index>(degenerate ? 1 : m_outputStrides[i]);\n      }\n    }\n    m_block_total_size_max = numext::maxi(static_cast<std::size_t>(1),\n                                          device.lastLevelCacheSize() /\n                                          sizeof(Scalar));\n  }\n\n  typedef typename XprType::Index Index;\n  typedef typename XprType::Scalar Scalar;\n  typedef typename internal::remove_const<Scalar>::type ScalarNonConst;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  typedef Strides Dimensions;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }\n\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(CoeffReturnType*) {\n    m_impl.evalSubExprsIfNeeded(NULL);\n    return true;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {\n    m_impl.cleanup();\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const\n  {\n    return m_impl.coeff(srcCoeff(index));\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {\n    return m_impl.costPerCoeff(vectorized) + TensorOpCost(0, 0, NumDims);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar* data() const {\n    return NULL;\n  }\n\n protected:\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index srcCoeff(Index index) const\n  {\n    Index inputIndex = 0;\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      for (int i = NumDims - 1; i >= 0; --i) {\n        const Index idx = index / m_fastOutputStrides[i];\n        inputIndex += idx * m_inputStrides[i] + m_offsets[i];\n        index -= idx * m_outputStrides[i];\n      }\n    } else {\n      for (int i = 0; i < NumDims; ++i) {\n        const Index idx = index / m_fastOutputStrides[i];\n        inputIndex += idx * m_inputStrides[i] + m_offsets[i];\n        index -= idx * m_outputStrides[i];\n      }\n    }\n    return inputIndex;\n  }\n\n  static EIGEN_STRONG_INLINE Index clamp(Index value, Index min, Index max) {\n    return numext::maxi(min, numext::mini(max,value));\n  }\n\n  array<Index, NumDims> m_outputStrides;\n  array<internal::TensorIntDivisor<Index>, NumDims> m_fastOutputStrides;\n  array<Index, NumDims> m_inputStrides;\n  TensorEvaluator<ArgType, Device> m_impl;\n  const Device& m_device;\n  DSizes<Index, NumDims> m_startIndices; // clamped startIndices\n  DSizes<Index, NumDims> m_dimensions;\n  DSizes<Index, NumDims> m_offsets; // offset in a flattened shape\n  const Strides m_strides;\n  std::size_t m_block_total_size_max;\n};\n\n// Eval as lvalue\ntemplate<typename StartIndices, typename StopIndices, typename Strides, typename ArgType, typename Device>\nstruct TensorEvaluator<TensorStridingSlicingOp<StartIndices, StopIndices, Strides, ArgType>, Device>\n  : public TensorEvaluator<const TensorStridingSlicingOp<StartIndices, StopIndices, Strides, ArgType>, Device>\n{\n  typedef TensorEvaluator<const TensorStridingSlicingOp<StartIndices, StopIndices, Strides, ArgType>, Device> Base;\n  typedef TensorStridingSlicingOp<StartIndices, StopIndices, Strides, ArgType> XprType;\n  static const int NumDims = internal::array_size<Strides>::value;\n\n  enum {\n    IsAligned = false,\n    PacketAccess = false,\n    BlockAccess = false,\n    Layout = TensorEvaluator<ArgType, Device>::Layout,\n    CoordAccess = TensorEvaluator<ArgType, Device>::CoordAccess,\n    RawAccess = false\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)\n    : Base(op, device)\n    { }\n\n  typedef typename XprType::Index Index;\n  typedef typename XprType::Scalar Scalar;\n  typedef typename internal::remove_const<Scalar>::type ScalarNonConst;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  typedef Strides Dimensions;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType& coeffRef(Index index)\n  {\n    return this->m_impl.coeffRef(this->srcCoeff(index));\n  }\n};\n\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_MORPHING_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorPadding.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_PADDING_H\n#define EIGEN_CXX11_TENSOR_TENSOR_PADDING_H\n\nnamespace Eigen {\n\n/** \\class TensorPadding\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief Tensor padding class.\n  * At the moment only padding with a constant value is supported.\n  *\n  */\nnamespace internal {\ntemplate<typename PaddingDimensions, typename XprType>\nstruct traits<TensorPaddingOp<PaddingDimensions, XprType> > : public traits<XprType>\n{\n  typedef typename XprType::Scalar Scalar;\n  typedef traits<XprType> XprTraits;\n  typedef typename XprTraits::StorageKind StorageKind;\n  typedef typename XprTraits::Index Index;\n  typedef typename XprType::Nested Nested;\n  typedef typename remove_reference<Nested>::type _Nested;\n  static const int NumDimensions = XprTraits::NumDimensions;\n  static const int Layout = XprTraits::Layout;\n};\n\ntemplate<typename PaddingDimensions, typename XprType>\nstruct eval<TensorPaddingOp<PaddingDimensions, XprType>, Eigen::Dense>\n{\n  typedef const TensorPaddingOp<PaddingDimensions, XprType>& type;\n};\n\ntemplate<typename PaddingDimensions, typename XprType>\nstruct nested<TensorPaddingOp<PaddingDimensions, XprType>, 1, typename eval<TensorPaddingOp<PaddingDimensions, XprType> >::type>\n{\n  typedef TensorPaddingOp<PaddingDimensions, XprType> type;\n};\n\n}  // end namespace internal\n\n\n\ntemplate<typename PaddingDimensions, typename XprType>\nclass TensorPaddingOp : public TensorBase<TensorPaddingOp<PaddingDimensions, XprType>, ReadOnlyAccessors>\n{\n  public:\n  typedef typename Eigen::internal::traits<TensorPaddingOp>::Scalar Scalar;\n  typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename Eigen::internal::nested<TensorPaddingOp>::type Nested;\n  typedef typename Eigen::internal::traits<TensorPaddingOp>::StorageKind StorageKind;\n  typedef typename Eigen::internal::traits<TensorPaddingOp>::Index Index;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorPaddingOp(const XprType& expr, const PaddingDimensions& padding_dims, const Scalar padding_value)\n      : m_xpr(expr), m_padding_dims(padding_dims), m_padding_value(padding_value) {}\n\n    EIGEN_DEVICE_FUNC\n    const PaddingDimensions& padding() const { return m_padding_dims; }\n    EIGEN_DEVICE_FUNC\n    Scalar padding_value() const { return m_padding_value; }\n\n    EIGEN_DEVICE_FUNC\n    const typename internal::remove_all<typename XprType::Nested>::type&\n    expression() const { return m_xpr; }\n\n  protected:\n    typename XprType::Nested m_xpr;\n    const PaddingDimensions m_padding_dims;\n    const Scalar m_padding_value;\n};\n\n\n// Eval as rvalue\ntemplate<typename PaddingDimensions, typename ArgType, typename Device>\nstruct TensorEvaluator<const TensorPaddingOp<PaddingDimensions, ArgType>, Device>\n{\n  typedef TensorPaddingOp<PaddingDimensions, ArgType> XprType;\n  typedef typename XprType::Index Index;\n  static const int NumDims = internal::array_size<PaddingDimensions>::value;\n  typedef DSizes<Index, NumDims> Dimensions;\n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  static const int PacketSize = internal::unpacket_traits<PacketReturnType>::size;\n\n  enum {\n    IsAligned = true,\n    PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,\n    Layout = TensorEvaluator<ArgType, Device>::Layout,\n    CoordAccess = true,\n    RawAccess = false\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)\n      : m_impl(op.expression(), device), m_padding(op.padding()), m_paddingValue(op.padding_value())\n  {\n    // The padding op doesn't change the rank of the tensor. Directly padding a scalar would lead\n    // to a vector, which doesn't make sense. Instead one should reshape the scalar into a vector\n    // of 1 element first and then pad.\n    EIGEN_STATIC_ASSERT((NumDims > 0), YOU_MADE_A_PROGRAMMING_MISTAKE);\n\n    // Compute dimensions\n    m_dimensions = m_impl.dimensions();\n    for (int i = 0; i < NumDims; ++i) {\n      m_dimensions[i] += m_padding[i].first + m_padding[i].second;\n    }\n    const typename TensorEvaluator<ArgType, Device>::Dimensions& input_dims = m_impl.dimensions();\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      m_inputStrides[0] = 1;\n      m_outputStrides[0] = 1;\n      for (int i = 1; i < NumDims; ++i) {\n        m_inputStrides[i] = m_inputStrides[i-1] * input_dims[i-1];\n        m_outputStrides[i] = m_outputStrides[i-1] * m_dimensions[i-1];\n      }\n      m_outputStrides[NumDims] = m_outputStrides[NumDims-1] * m_dimensions[NumDims-1];\n    } else {\n      m_inputStrides[NumDims - 1] = 1;\n      m_outputStrides[NumDims] = 1;\n      for (int i = NumDims - 2; i >= 0; --i) {\n        m_inputStrides[i] = m_inputStrides[i+1] * input_dims[i+1];\n        m_outputStrides[i+1] = m_outputStrides[i+2] * m_dimensions[i+1];\n      }\n      m_outputStrides[0] = m_outputStrides[1] * m_dimensions[0];\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(Scalar*) {\n    m_impl.evalSubExprsIfNeeded(NULL);\n    return true;\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {\n    m_impl.cleanup();\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const\n  {\n    eigen_assert(index < dimensions().TotalSize());\n    Index inputIndex = 0;\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      for (int i = NumDims - 1; i > 0; --i) {\n        const Index idx = index / m_outputStrides[i];\n        if (isPaddingAtIndexForDim(idx, i)) {\n          return m_paddingValue;\n        }\n        inputIndex += (idx - m_padding[i].first) * m_inputStrides[i];\n        index -= idx * m_outputStrides[i];\n      }\n      if (isPaddingAtIndexForDim(index, 0)) {\n        return m_paddingValue;\n      }\n      inputIndex += (index - m_padding[0].first);\n    } else {\n      for (int i = 0; i < NumDims - 1; ++i) {\n        const Index idx = index / m_outputStrides[i+1];\n        if (isPaddingAtIndexForDim(idx, i)) {\n          return m_paddingValue;\n        }\n        inputIndex += (idx - m_padding[i].first) * m_inputStrides[i];\n        index -= idx * m_outputStrides[i+1];\n      }\n      if (isPaddingAtIndexForDim(index, NumDims-1)) {\n        return m_paddingValue;\n      }\n      inputIndex += (index - m_padding[NumDims-1].first);\n    }\n    return m_impl.coeff(inputIndex);\n  }\n\n  template<int LoadMode>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const\n  {\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      return packetColMajor(index);\n    }\n    return packetRowMajor(index);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {\n    TensorOpCost cost = m_impl.costPerCoeff(vectorized);\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      for (int i = 0; i < NumDims; ++i)\n        updateCostPerDimension(cost, i, i == 0);\n    } else {\n      for (int i = NumDims - 1; i >= 0; --i)\n        updateCostPerDimension(cost, i, i == NumDims - 1);\n    }\n    return cost;\n  }\n\n  EIGEN_DEVICE_FUNC Scalar* data() const { return NULL; }\n\n private:\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool isPaddingAtIndexForDim(\n      Index index, int dim_index) const {\n#if defined(EIGEN_HAS_INDEX_LIST)\n    return (!internal::index_pair_first_statically_eq<PaddingDimensions>(dim_index, 0) &&\n            index < m_padding[dim_index].first) ||\n        (!internal::index_pair_second_statically_eq<PaddingDimensions>(dim_index, 0) &&\n         index >= m_dimensions[dim_index] - m_padding[dim_index].second);\n#else\n    return (index < m_padding[dim_index].first) ||\n           (index >= m_dimensions[dim_index] - m_padding[dim_index].second);\n#endif\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool isLeftPaddingCompileTimeZero(\n      int dim_index) const {\n#if defined(EIGEN_HAS_INDEX_LIST)\n    return internal::index_pair_first_statically_eq<PaddingDimensions>(dim_index, 0);\n#else\n    EIGEN_UNUSED_VARIABLE(dim_index);\n    return false;\n#endif\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool isRightPaddingCompileTimeZero(\n      int dim_index) const {\n#if defined(EIGEN_HAS_INDEX_LIST)\n    return internal::index_pair_second_statically_eq<PaddingDimensions>(dim_index, 0);\n#else\n    EIGEN_UNUSED_VARIABLE(dim_index);\n    return false;\n#endif\n  }\n\n\n  void updateCostPerDimension(TensorOpCost& cost, int i, bool first) const {\n    const double in = static_cast<double>(m_impl.dimensions()[i]);\n    const double out = in + m_padding[i].first + m_padding[i].second;\n    if (out == 0)\n      return;\n    const double reduction = in / out;\n    cost *= reduction;\n    if (first) {\n      cost += TensorOpCost(0, 0, 2 * TensorOpCost::AddCost<Index>() +\n                    reduction * (1 * TensorOpCost::AddCost<Index>()));\n    } else {\n      cost += TensorOpCost(0, 0, 2 * TensorOpCost::AddCost<Index>() +\n                                 2 * TensorOpCost::MulCost<Index>() +\n                    reduction * (2 * TensorOpCost::MulCost<Index>() +\n                                 1 * TensorOpCost::DivCost<Index>()));\n    }\n  }\n\n protected:\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packetColMajor(Index index) const\n  {\n    EIGEN_STATIC_ASSERT((PacketSize > 1), YOU_MADE_A_PROGRAMMING_MISTAKE)\n    eigen_assert(index+PacketSize-1 < dimensions().TotalSize());\n\n    const Index initialIndex = index;\n    Index inputIndex = 0;\n    for (int i = NumDims - 1; i > 0; --i) {\n      const Index first = index;\n      const Index last = index + PacketSize - 1;\n      const Index lastPaddedLeft = m_padding[i].first * m_outputStrides[i];\n      const Index firstPaddedRight = (m_dimensions[i] - m_padding[i].second) * m_outputStrides[i];\n      const Index lastPaddedRight = m_outputStrides[i+1];\n\n      if (!isLeftPaddingCompileTimeZero(i) && last < lastPaddedLeft) {\n        // all the coefficient are in the padding zone.\n        return internal::pset1<PacketReturnType>(m_paddingValue);\n      }\n      else if (!isRightPaddingCompileTimeZero(i) && first >= firstPaddedRight && last < lastPaddedRight) {\n        // all the coefficient are in the padding zone.\n        return internal::pset1<PacketReturnType>(m_paddingValue);\n      }\n      else if ((isLeftPaddingCompileTimeZero(i) && isRightPaddingCompileTimeZero(i)) || (first >= lastPaddedLeft && last < firstPaddedRight)) {\n        // all the coefficient are between the 2 padding zones.\n        const Index idx = index / m_outputStrides[i];\n        inputIndex += (idx - m_padding[i].first) * m_inputStrides[i];\n        index -= idx * m_outputStrides[i];\n      }\n      else {\n        // Every other case\n        return packetWithPossibleZero(initialIndex);\n      }\n    }\n\n    const Index last = index + PacketSize - 1;\n    const Index first = index;\n    const Index lastPaddedLeft = m_padding[0].first;\n    const Index firstPaddedRight = (m_dimensions[0] - m_padding[0].second);\n    const Index lastPaddedRight = m_outputStrides[1];\n\n    if (!isLeftPaddingCompileTimeZero(0) && last < lastPaddedLeft) {\n      // all the coefficient are in the padding zone.\n      return internal::pset1<PacketReturnType>(m_paddingValue);\n    }\n    else if (!isRightPaddingCompileTimeZero(0) && first >= firstPaddedRight && last < lastPaddedRight) {\n      // all the coefficient are in the padding zone.\n      return internal::pset1<PacketReturnType>(m_paddingValue);\n    }\n    else if ((isLeftPaddingCompileTimeZero(0) && isRightPaddingCompileTimeZero(0)) || (first >= lastPaddedLeft && last < firstPaddedRight)) {\n      // all the coefficient are between the 2 padding zones.\n      inputIndex += (index - m_padding[0].first);\n      return m_impl.template packet<Unaligned>(inputIndex);\n    }\n    // Every other case\n    return packetWithPossibleZero(initialIndex);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packetRowMajor(Index index) const\n  {\n    EIGEN_STATIC_ASSERT((PacketSize > 1), YOU_MADE_A_PROGRAMMING_MISTAKE)\n    eigen_assert(index+PacketSize-1 < dimensions().TotalSize());\n\n    const Index initialIndex = index;\n    Index inputIndex = 0;\n\n    for (int i = 0; i < NumDims - 1; ++i) {\n      const Index first = index;\n      const Index last = index + PacketSize - 1;\n      const Index lastPaddedLeft = m_padding[i].first * m_outputStrides[i+1];\n      const Index firstPaddedRight = (m_dimensions[i] - m_padding[i].second) * m_outputStrides[i+1];\n      const Index lastPaddedRight = m_outputStrides[i];\n\n      if (!isLeftPaddingCompileTimeZero(i) && last < lastPaddedLeft) {\n        // all the coefficient are in the padding zone.\n        return internal::pset1<PacketReturnType>(m_paddingValue);\n      }\n      else if (!isRightPaddingCompileTimeZero(i) && first >= firstPaddedRight && last < lastPaddedRight) {\n        // all the coefficient are in the padding zone.\n        return internal::pset1<PacketReturnType>(m_paddingValue);\n      }\n      else if ((isLeftPaddingCompileTimeZero(i) && isRightPaddingCompileTimeZero(i)) || (first >= lastPaddedLeft && last < firstPaddedRight)) {\n        // all the coefficient are between the 2 padding zones.\n        const Index idx = index / m_outputStrides[i+1];\n        inputIndex += (idx - m_padding[i].first) * m_inputStrides[i];\n        index -= idx * m_outputStrides[i+1];\n      }\n      else {\n        // Every other case\n        return packetWithPossibleZero(initialIndex);\n      }\n    }\n\n    const Index last = index + PacketSize - 1;\n    const Index first = index;\n    const Index lastPaddedLeft = m_padding[NumDims-1].first;\n    const Index firstPaddedRight = (m_dimensions[NumDims-1] - m_padding[NumDims-1].second);\n    const Index lastPaddedRight = m_outputStrides[NumDims-1];\n\n    if (!isLeftPaddingCompileTimeZero(NumDims-1) && last < lastPaddedLeft) {\n      // all the coefficient are in the padding zone.\n      return internal::pset1<PacketReturnType>(m_paddingValue);\n    }\n    else if (!isRightPaddingCompileTimeZero(NumDims-1) && first >= firstPaddedRight && last < lastPaddedRight) {\n      // all the coefficient are in the padding zone.\n      return internal::pset1<PacketReturnType>(m_paddingValue);\n    }\n    else if ((isLeftPaddingCompileTimeZero(NumDims-1) && isRightPaddingCompileTimeZero(NumDims-1)) || (first >= lastPaddedLeft && last < firstPaddedRight)) {\n      // all the coefficient are between the 2 padding zones.\n      inputIndex += (index - m_padding[NumDims-1].first);\n      return m_impl.template packet<Unaligned>(inputIndex);\n    }\n    // Every other case\n    return packetWithPossibleZero(initialIndex);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packetWithPossibleZero(Index index) const\n  {\n    EIGEN_ALIGN_MAX typename internal::remove_const<CoeffReturnType>::type values[PacketSize];\n    for (int i = 0; i < PacketSize; ++i) {\n      values[i] = coeff(index+i);\n    }\n    PacketReturnType rslt = internal::pload<PacketReturnType>(values);\n    return rslt;\n  }\n\n  Dimensions m_dimensions;\n  array<Index, NumDims+1> m_outputStrides;\n  array<Index, NumDims> m_inputStrides;\n  TensorEvaluator<ArgType, Device> m_impl;\n  PaddingDimensions m_padding;\n\n  Scalar m_paddingValue;\n};\n\n\n\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_PADDING_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorPatch.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_PATCH_H\n#define EIGEN_CXX11_TENSOR_TENSOR_PATCH_H\n\nnamespace Eigen {\n\n/** \\class TensorPatch\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief Tensor patch class.\n  *\n  *\n  */\nnamespace internal {\ntemplate<typename PatchDim, typename XprType>\nstruct traits<TensorPatchOp<PatchDim, XprType> > : public traits<XprType>\n{\n  typedef typename XprType::Scalar Scalar;\n  typedef traits<XprType> XprTraits;\n  typedef typename XprTraits::StorageKind StorageKind;\n  typedef typename XprTraits::Index Index;\n  typedef typename XprType::Nested Nested;\n  typedef typename remove_reference<Nested>::type _Nested;\n  static const int NumDimensions = XprTraits::NumDimensions + 1;\n  static const int Layout = XprTraits::Layout;\n};\n\ntemplate<typename PatchDim, typename XprType>\nstruct eval<TensorPatchOp<PatchDim, XprType>, Eigen::Dense>\n{\n  typedef const TensorPatchOp<PatchDim, XprType>& type;\n};\n\ntemplate<typename PatchDim, typename XprType>\nstruct nested<TensorPatchOp<PatchDim, XprType>, 1, typename eval<TensorPatchOp<PatchDim, XprType> >::type>\n{\n  typedef TensorPatchOp<PatchDim, XprType> type;\n};\n\n}  // end namespace internal\n\n\n\ntemplate<typename PatchDim, typename XprType>\nclass TensorPatchOp : public TensorBase<TensorPatchOp<PatchDim, XprType>, ReadOnlyAccessors>\n{\n  public:\n  typedef typename Eigen::internal::traits<TensorPatchOp>::Scalar Scalar;\n  typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename Eigen::internal::nested<TensorPatchOp>::type Nested;\n  typedef typename Eigen::internal::traits<TensorPatchOp>::StorageKind StorageKind;\n  typedef typename Eigen::internal::traits<TensorPatchOp>::Index Index;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorPatchOp(const XprType& expr, const PatchDim& patch_dims)\n      : m_xpr(expr), m_patch_dims(patch_dims) {}\n\n    EIGEN_DEVICE_FUNC\n    const PatchDim& patch_dims() const { return m_patch_dims; }\n\n    EIGEN_DEVICE_FUNC\n    const typename internal::remove_all<typename XprType::Nested>::type&\n    expression() const { return m_xpr; }\n\n  protected:\n    typename XprType::Nested m_xpr;\n    const PatchDim m_patch_dims;\n};\n\n\n// Eval as rvalue\ntemplate<typename PatchDim, typename ArgType, typename Device>\nstruct TensorEvaluator<const TensorPatchOp<PatchDim, ArgType>, Device>\n{\n  typedef TensorPatchOp<PatchDim, ArgType> XprType;\n  typedef typename XprType::Index Index;\n  static const int NumDims = internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value + 1;\n  typedef DSizes<Index, NumDims> Dimensions;\n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  static const int PacketSize = internal::unpacket_traits<PacketReturnType>::size;\n\n\n  enum {\n    IsAligned = false,\n    PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,\n    Layout = TensorEvaluator<ArgType, Device>::Layout,\n    CoordAccess = false,\n    RawAccess = false\n };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)\n      : m_impl(op.expression(), device)\n  {\n    Index num_patches = 1;\n    const typename TensorEvaluator<ArgType, Device>::Dimensions& input_dims = m_impl.dimensions();\n    const PatchDim& patch_dims = op.patch_dims();\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      for (int i = 0; i < NumDims-1; ++i) {\n        m_dimensions[i] = patch_dims[i];\n        num_patches *= (input_dims[i] - patch_dims[i] + 1);\n      }\n      m_dimensions[NumDims-1] = num_patches;\n\n      m_inputStrides[0] = 1;\n      m_patchStrides[0] = 1;\n      for (int i = 1; i < NumDims-1; ++i) {\n        m_inputStrides[i] = m_inputStrides[i-1] * input_dims[i-1];\n        m_patchStrides[i] = m_patchStrides[i-1] * (input_dims[i-1] - patch_dims[i-1] + 1);\n      }\n      m_outputStrides[0] = 1;\n      for (int i = 1; i < NumDims; ++i) {\n        m_outputStrides[i] = m_outputStrides[i-1] * m_dimensions[i-1];\n      }\n    } else {\n      for (int i = 0; i < NumDims-1; ++i) {\n        m_dimensions[i+1] = patch_dims[i];\n        num_patches *= (input_dims[i] - patch_dims[i] + 1);\n      }\n      m_dimensions[0] = num_patches;\n\n      m_inputStrides[NumDims-2] = 1;\n      m_patchStrides[NumDims-2] = 1;\n      for (int i = NumDims-3; i >= 0; --i) {\n        m_inputStrides[i] = m_inputStrides[i+1] * input_dims[i+1];\n        m_patchStrides[i] = m_patchStrides[i+1] * (input_dims[i+1] - patch_dims[i+1] + 1);\n      }\n      m_outputStrides[NumDims-1] = 1;\n      for (int i = NumDims-2; i >= 0; --i) {\n        m_outputStrides[i] = m_outputStrides[i+1] * m_dimensions[i+1];\n      }\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(Scalar* /*data*/) {\n    m_impl.evalSubExprsIfNeeded(NULL);\n    return true;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {\n    m_impl.cleanup();\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const\n  {\n    Index output_stride_index = (static_cast<int>(Layout) == static_cast<int>(ColMajor)) ? NumDims - 1 : 0;\n    // Find the location of the first element of the patch.\n    Index patchIndex = index / m_outputStrides[output_stride_index];\n    // Find the offset of the element wrt the location of the first element.\n    Index patchOffset = index - patchIndex * m_outputStrides[output_stride_index];\n    Index inputIndex = 0;\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      for (int i = NumDims - 2; i > 0; --i) {\n        const Index patchIdx = patchIndex / m_patchStrides[i];\n        patchIndex -= patchIdx * m_patchStrides[i];\n        const Index offsetIdx = patchOffset / m_outputStrides[i];\n        patchOffset -= offsetIdx * m_outputStrides[i];\n        inputIndex += (patchIdx + offsetIdx) * m_inputStrides[i];\n      }\n    } else {\n      for (int i = 0; i < NumDims - 2; ++i) {\n        const Index patchIdx = patchIndex / m_patchStrides[i];\n        patchIndex -= patchIdx * m_patchStrides[i];\n        const Index offsetIdx = patchOffset / m_outputStrides[i+1];\n        patchOffset -= offsetIdx * m_outputStrides[i+1];\n        inputIndex += (patchIdx + offsetIdx) * m_inputStrides[i];\n      }\n    }\n    inputIndex += (patchIndex + patchOffset);\n    return m_impl.coeff(inputIndex);\n  }\n\n  template<int LoadMode>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const\n  {\n    EIGEN_STATIC_ASSERT((PacketSize > 1), YOU_MADE_A_PROGRAMMING_MISTAKE)\n    eigen_assert(index+PacketSize-1 < dimensions().TotalSize());\n\n    Index output_stride_index = (static_cast<int>(Layout) == static_cast<int>(ColMajor)) ? NumDims - 1 : 0;\n    Index indices[2] = {index, index + PacketSize - 1};\n    Index patchIndices[2] = {indices[0] / m_outputStrides[output_stride_index],\n                             indices[1] / m_outputStrides[output_stride_index]};\n    Index patchOffsets[2] = {indices[0] - patchIndices[0] * m_outputStrides[output_stride_index],\n                             indices[1] - patchIndices[1] * m_outputStrides[output_stride_index]};\n\n    Index inputIndices[2] = {0, 0};\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      for (int i = NumDims - 2; i > 0; --i) {\n        const Index patchIdx[2] = {patchIndices[0] / m_patchStrides[i],\n                                   patchIndices[1] / m_patchStrides[i]};\n        patchIndices[0] -= patchIdx[0] * m_patchStrides[i];\n        patchIndices[1] -= patchIdx[1] * m_patchStrides[i];\n\n        const Index offsetIdx[2] = {patchOffsets[0] / m_outputStrides[i],\n                                    patchOffsets[1] / m_outputStrides[i]};\n        patchOffsets[0] -= offsetIdx[0] * m_outputStrides[i];\n        patchOffsets[1] -= offsetIdx[1] * m_outputStrides[i];\n\n        inputIndices[0] += (patchIdx[0] + offsetIdx[0]) * m_inputStrides[i];\n        inputIndices[1] += (patchIdx[1] + offsetIdx[1]) * m_inputStrides[i];\n      }\n    } else {\n      for (int i = 0; i < NumDims - 2; ++i) {\n        const Index patchIdx[2] = {patchIndices[0] / m_patchStrides[i],\n                                   patchIndices[1] / m_patchStrides[i]};\n        patchIndices[0] -= patchIdx[0] * m_patchStrides[i];\n        patchIndices[1] -= patchIdx[1] * m_patchStrides[i];\n\n        const Index offsetIdx[2] = {patchOffsets[0] / m_outputStrides[i+1],\n                                    patchOffsets[1] / m_outputStrides[i+1]};\n        patchOffsets[0] -= offsetIdx[0] * m_outputStrides[i+1];\n        patchOffsets[1] -= offsetIdx[1] * m_outputStrides[i+1];\n\n        inputIndices[0] += (patchIdx[0] + offsetIdx[0]) * m_inputStrides[i];\n        inputIndices[1] += (patchIdx[1] + offsetIdx[1]) * m_inputStrides[i];\n      }\n    }\n    inputIndices[0] += (patchIndices[0] + patchOffsets[0]);\n    inputIndices[1] += (patchIndices[1] + patchOffsets[1]);\n\n    if (inputIndices[1] - inputIndices[0] == PacketSize - 1) {\n      PacketReturnType rslt = m_impl.template packet<Unaligned>(inputIndices[0]);\n      return rslt;\n    }\n    else {\n      EIGEN_ALIGN_MAX CoeffReturnType values[PacketSize];\n      values[0] = m_impl.coeff(inputIndices[0]);\n      values[PacketSize-1] = m_impl.coeff(inputIndices[1]);\n      for (int i = 1; i < PacketSize-1; ++i) {\n        values[i] = coeff(index+i);\n      }\n      PacketReturnType rslt = internal::pload<PacketReturnType>(values);\n      return rslt;\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {\n    const double compute_cost = NumDims * (TensorOpCost::DivCost<Index>() +\n                                           TensorOpCost::MulCost<Index>() +\n                                           2 * TensorOpCost::AddCost<Index>());\n    return m_impl.costPerCoeff(vectorized) +\n           TensorOpCost(0, 0, compute_cost, vectorized, PacketSize);\n  }\n\n  EIGEN_DEVICE_FUNC Scalar* data() const { return NULL; }\n\n protected:\n  Dimensions m_dimensions;\n  array<Index, NumDims> m_outputStrides;\n  array<Index, NumDims-1> m_inputStrides;\n  array<Index, NumDims-1> m_patchStrides;\n\n  TensorEvaluator<ArgType, Device> m_impl;\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_PATCH_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorRandom.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_RANDOM_H\n#define EIGEN_CXX11_TENSOR_TENSOR_RANDOM_H\n\nnamespace Eigen {\nnamespace internal {\n\nnamespace {\n\nEIGEN_DEVICE_FUNC uint64_t get_random_seed() {\n#ifdef __CUDA_ARCH__\n  // We don't support 3d kernels since we currently only use 1 and\n  // 2d kernels.\n  assert(threadIdx.z == 0);\n  return clock64() +\n      blockIdx.x * blockDim.x + threadIdx.x +\n      gridDim.x * blockDim.x * (blockIdx.y * blockDim.y + threadIdx.y);\n\n#elif defined _WIN32\n  // Use the current time as a baseline.\n  SYSTEMTIME st;\n  GetSystemTime(&st);\n  int time = st.wSecond + 1000 * st.wMilliseconds;\n  // Mix in a random number to make sure that we get different seeds if\n  // we try to generate seeds faster than the clock resolution.\n  // We need 2 random values since the generator only generate 16 bits at\n  // a time (https://msdn.microsoft.com/en-us/library/398ax69y.aspx)\n  int rnd1 = ::rand();\n  int rnd2 = ::rand();\n  uint64_t rnd = (rnd1 | rnd2 << 16) ^ time;\n  return rnd;\n\n#elif defined __APPLE__\n  // Same approach as for win32, except that the random number generator\n  // is better (// https://developer.apple.com/legacy/library/documentation/Darwin/Reference/ManPages/man3/random.3.html#//apple_ref/doc/man/3/random).\n  uint64_t rnd = ::random() ^ mach_absolute_time();\n  return rnd;\n\n#else\n  // Augment the current time with pseudo random number generation\n  // to ensure that we get different seeds if we try to generate seeds\n  // faster than the clock resolution.\n  timespec ts;\n  clock_gettime(CLOCK_REALTIME, &ts);\n  uint64_t rnd = ::random() ^ ts.tv_nsec;\n  return rnd;\n#endif\n}\n\nstatic EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE unsigned PCG_XSH_RS_generator(uint64_t* state) {\n  // TODO: Unify with the implementation in the non blocking thread pool.\n  uint64_t current = *state;\n  // Update the internal state\n  *state = current * 6364136223846793005ULL + 0xda3e39cb94b95bdbULL;\n  // Generate the random output (using the PCG-XSH-RS scheme)\n  return static_cast<unsigned>((current ^ (current >> 22)) >> (22 + (current >> 61)));\n}\n\nstatic EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE uint64_t PCG_XSH_RS_state(uint64_t seed) {\n  seed = seed ? seed : get_random_seed();\n  return seed * 6364136223846793005ULL + 0xda3e39cb94b95bdbULL;\n}\n\n}  // namespace\n\n\ntemplate <typename T> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nT RandomToTypeUniform(uint64_t* state) {\n  unsigned rnd = PCG_XSH_RS_generator(state);\n  return static_cast<T>(rnd);\n}\n\n\ntemplate <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nEigen::half RandomToTypeUniform<Eigen::half>(uint64_t* state) {\n  Eigen::half result;\n  // Generate 10 random bits for the mantissa\n  unsigned rnd = PCG_XSH_RS_generator(state);\n  result.x = static_cast<uint16_t>(rnd & 0x3ffu);\n  // Set the exponent\n  result.x |= (static_cast<uint16_t>(15) << 10);\n  // Return the final result\n  return result - Eigen::half(1.0f);\n}\n\n\ntemplate <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nfloat RandomToTypeUniform<float>(uint64_t* state) {\n  typedef union {\n    uint32_t raw;\n    float fp;\n  } internal;\n  internal result;\n  // Generate 23 random bits for the mantissa mantissa\n  const unsigned rnd = PCG_XSH_RS_generator(state);\n  result.raw = rnd & 0x7fffffu;\n  // Set the exponent\n  result.raw |= (static_cast<uint32_t>(127) << 23);\n  // Return the final result\n  return result.fp - 1.0f;\n}\n\ntemplate <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\ndouble RandomToTypeUniform<double>(uint64_t* state) {\n  typedef union {\n    uint64_t raw;\n    double dp;\n  } internal;\n  internal result;\n  result.raw = 0;\n  // Generate 52 random bits for the mantissa\n  // First generate the upper 20 bits\n  unsigned rnd1 = PCG_XSH_RS_generator(state) & 0xfffffu;\n  // The generate the lower 32 bits\n  unsigned rnd2 = PCG_XSH_RS_generator(state);\n  result.raw = (static_cast<uint64_t>(rnd1) << 32) | rnd2;\n  // Set the exponent\n  result.raw |= (static_cast<uint64_t>(1023) << 52);\n  // Return the final result\n  return result.dp - 1.0;\n}\n\ntemplate <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nstd::complex<float> RandomToTypeUniform<std::complex<float> >(uint64_t* state) {\n  return std::complex<float>(RandomToTypeUniform<float>(state),\n                             RandomToTypeUniform<float>(state));\n}\ntemplate <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nstd::complex<double> RandomToTypeUniform<std::complex<double> >(uint64_t* state) {\n  return std::complex<double>(RandomToTypeUniform<double>(state),\n                              RandomToTypeUniform<double>(state));\n}\n\ntemplate <typename T> class UniformRandomGenerator {\n public:\n  static const bool PacketAccess = true;\n\n  // Uses the given \"seed\" if non-zero, otherwise uses a random seed.\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE UniformRandomGenerator(\n      uint64_t seed = 0) {\n    m_state = PCG_XSH_RS_state(seed);\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE UniformRandomGenerator(\n      const UniformRandomGenerator& other) {\n    m_state = other.m_state;\n  }\n\n  template<typename Index> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  T operator()(Index i) const {\n    uint64_t local_state = m_state + i;\n    T result = RandomToTypeUniform<T>(&local_state);\n    m_state = local_state;\n    return result;\n  }\n\n  template<typename Packet, typename Index> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  Packet packetOp(Index i) const {\n    const int packetSize = internal::unpacket_traits<Packet>::size;\n    EIGEN_ALIGN_MAX T values[packetSize];\n    uint64_t local_state = m_state + i;\n    for (int j = 0; j < packetSize; ++j) {\n      values[j] = RandomToTypeUniform<T>(&local_state);\n    }\n    m_state = local_state;\n    return internal::pload<Packet>(values);\n  }\n\n private:\n  mutable uint64_t m_state;\n};\n\ntemplate <typename Scalar>\nstruct functor_traits<UniformRandomGenerator<Scalar> > {\n  enum {\n    // Rough estimate for floating point, multiplied by ceil(sizeof(T) / sizeof(float)).\n    Cost = 12 * NumTraits<Scalar>::AddCost *\n           ((sizeof(Scalar) + sizeof(float) - 1) / sizeof(float)),\n    PacketAccess = UniformRandomGenerator<Scalar>::PacketAccess\n  };\n};\n\n\n\ntemplate <typename T> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nT RandomToTypeNormal(uint64_t* state) {\n  // Use the ratio of uniform method to generate numbers following a normal\n  // distribution. See for example Numerical Recipes chapter 7.3.9 for the\n  // details.\n  T u, v, q;\n  do {\n    u = RandomToTypeUniform<T>(state);\n    v = T(1.7156) * (RandomToTypeUniform<T>(state) - T(0.5));\n    const T x = u - T(0.449871);\n    const T y = numext::abs(v) + T(0.386595);\n    q = x*x + y * (T(0.196)*y - T(0.25472)*x);\n  } while (q > T(0.27597) &&\n           (q > T(0.27846) || v*v > T(-4) * numext::log(u) * u*u));\n\n  return v/u;\n}\n\ntemplate <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nstd::complex<float> RandomToTypeNormal<std::complex<float> >(uint64_t* state) {\n  return std::complex<float>(RandomToTypeNormal<float>(state),\n                             RandomToTypeNormal<float>(state));\n}\ntemplate <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nstd::complex<double> RandomToTypeNormal<std::complex<double> >(uint64_t* state) {\n  return std::complex<double>(RandomToTypeNormal<double>(state),\n                              RandomToTypeNormal<double>(state));\n}\n\n\ntemplate <typename T> class NormalRandomGenerator {\n public:\n  static const bool PacketAccess = true;\n\n  // Uses the given \"seed\" if non-zero, otherwise uses a random seed.\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE NormalRandomGenerator(uint64_t seed = 0) {\n    m_state = PCG_XSH_RS_state(seed);\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE NormalRandomGenerator(\n      const NormalRandomGenerator& other) {\n    m_state = other.m_state;\n  }\n\n template<typename Index> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  T operator()(Index i) const {\n    uint64_t local_state = m_state + i;\n    T result = RandomToTypeNormal<T>(&local_state);\n    m_state = local_state;\n    return result;\n  }\n\n  template<typename Packet, typename Index> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  Packet packetOp(Index i) const {\n    const int packetSize = internal::unpacket_traits<Packet>::size;\n    EIGEN_ALIGN_MAX T values[packetSize];\n    uint64_t local_state = m_state + i;\n    for (int j = 0; j < packetSize; ++j) {\n      values[j] = RandomToTypeNormal<T>(&local_state);\n    }\n    m_state = local_state;\n    return internal::pload<Packet>(values);\n  }\n\n private:\n  mutable uint64_t m_state;\n};\n\n\ntemplate <typename Scalar>\nstruct functor_traits<NormalRandomGenerator<Scalar> > {\n  enum {\n    // On average, we need to generate about 3 random numbers\n    // 15 mul, 8 add, 1.5 logs\n    Cost = 3 * functor_traits<UniformRandomGenerator<Scalar> >::Cost +\n           15 * NumTraits<Scalar>::AddCost + 8 * NumTraits<Scalar>::AddCost +\n           3 * functor_traits<scalar_log_op<Scalar> >::Cost / 2,\n    PacketAccess = NormalRandomGenerator<Scalar>::PacketAccess\n  };\n};\n\n\n} // end namespace internal\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_RANDOM_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorReduction.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n// Copyright (C) 2016 Mehdi Goli, Codeplay Software Ltd <eigen@codeplay.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_REDUCTION_H\n#define EIGEN_CXX11_TENSOR_TENSOR_REDUCTION_H\n\nnamespace Eigen {\n\n/** \\class TensorReduction\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief Tensor reduction class.\n  *\n  */\n\nnamespace internal {\n  template<typename Op, typename Dims, typename XprType,template <class> class MakePointer_ >\n  struct traits<TensorReductionOp<Op, Dims, XprType, MakePointer_> >\n : traits<XprType>\n{\n  typedef traits<XprType> XprTraits;\n  typedef typename XprTraits::Scalar Scalar;\n  typedef typename XprTraits::StorageKind StorageKind;\n  typedef typename XprTraits::Index Index;\n  typedef typename XprType::Nested Nested;\n  static const int NumDimensions = XprTraits::NumDimensions - array_size<Dims>::value;\n  static const int Layout = XprTraits::Layout;\n\n  template <class T> struct MakePointer {\n    // Intermediate typedef to workaround MSVC issue.\n    typedef MakePointer_<T> MakePointerT;\n    typedef typename MakePointerT::Type Type;\n  };\n};\n\ntemplate<typename Op, typename Dims, typename XprType, template <class> class MakePointer_>\nstruct eval<TensorReductionOp<Op, Dims, XprType, MakePointer_>, Eigen::Dense>\n{\n  typedef const TensorReductionOp<Op, Dims, XprType, MakePointer_>& type;\n};\n\ntemplate<typename Op, typename Dims, typename XprType, template <class> class MakePointer_>\nstruct nested<TensorReductionOp<Op, Dims, XprType, MakePointer_>, 1, typename eval<TensorReductionOp<Op, Dims, XprType, MakePointer_> >::type>\n{\n  typedef TensorReductionOp<Op, Dims, XprType, MakePointer_> type;\n};\n\n\ntemplate <typename OutputDims> struct DimInitializer {\n  template <typename InputDims, typename ReducedDims> EIGEN_DEVICE_FUNC\n  static void run(const InputDims& input_dims,\n                  const array<bool, internal::array_size<InputDims>::value>& reduced,\n                  OutputDims* output_dims, ReducedDims* reduced_dims) {\n    const int NumInputDims = internal::array_size<InputDims>::value;\n    int outputIndex = 0;\n    int reduceIndex = 0;\n    for (int i = 0; i < NumInputDims; ++i) {\n      if (reduced[i]) {\n        (*reduced_dims)[reduceIndex] = input_dims[i];\n        ++reduceIndex;\n      } else {\n        (*output_dims)[outputIndex] = input_dims[i];\n        ++outputIndex;\n      }\n    }\n  }\n};\n\ntemplate <> struct DimInitializer<Sizes<> > {\n  template <typename InputDims, typename Index, size_t Rank> EIGEN_DEVICE_FUNC\n  static void run(const InputDims& input_dims, const array<bool, Rank>&,\n                  Sizes<>*, array<Index, Rank>* reduced_dims) {\n    const int NumInputDims = internal::array_size<InputDims>::value;\n    for (int i = 0; i < NumInputDims; ++i) {\n      (*reduced_dims)[i] = input_dims[i];\n    }\n  }\n};\n\n\ntemplate <typename ReducedDims, int NumTensorDims, int Layout>\nstruct are_inner_most_dims {\n  static const bool value = false;\n};\ntemplate <typename ReducedDims, int NumTensorDims, int Layout>\nstruct preserve_inner_most_dims {\n  static const bool value = false;\n};\n\n#if EIGEN_HAS_CONSTEXPR && EIGEN_HAS_VARIADIC_TEMPLATES\ntemplate <typename ReducedDims, int NumTensorDims>\nstruct are_inner_most_dims<ReducedDims, NumTensorDims, ColMajor>{\n  static const bool tmp1 = indices_statically_known_to_increase<ReducedDims>();\n  static const bool tmp2 = index_statically_eq<ReducedDims>(0, 0);\n  static const bool tmp3 = index_statically_eq<ReducedDims>(array_size<ReducedDims>::value-1, array_size<ReducedDims>::value-1);\n  static const bool value = tmp1 & tmp2 & tmp3;\n};\ntemplate <typename ReducedDims, int NumTensorDims>\nstruct are_inner_most_dims<ReducedDims, NumTensorDims, RowMajor>{\n  static const bool tmp1 = indices_statically_known_to_increase<ReducedDims>();\n  static const bool tmp2 = index_statically_eq<ReducedDims>(0, NumTensorDims - array_size<ReducedDims>::value);\n  static const bool tmp3 = index_statically_eq<ReducedDims>(array_size<ReducedDims>::value - 1, NumTensorDims - 1);\n  static const bool value = tmp1 & tmp2 & tmp3;\n\n};\ntemplate <typename ReducedDims, int NumTensorDims>\nstruct preserve_inner_most_dims<ReducedDims, NumTensorDims, ColMajor>{\n  static const bool tmp1 = indices_statically_known_to_increase<ReducedDims>();\n  static const bool tmp2 = index_statically_gt<ReducedDims>(0, 0);\n  static const bool value = tmp1 & tmp2;\n\n};\ntemplate <typename ReducedDims, int NumTensorDims>\nstruct preserve_inner_most_dims<ReducedDims, NumTensorDims, RowMajor>{\n  static const bool tmp1 = indices_statically_known_to_increase<ReducedDims>();\n  static const bool tmp2 = index_statically_lt<ReducedDims>(array_size<ReducedDims>::value - 1, NumTensorDims - 1);\n  static const bool value = tmp1 & tmp2;\n};\n#endif\n\n\ntemplate <int DimIndex, typename Self, typename Op>\nstruct GenericDimReducer {\n  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const Self& self, typename Self::Index firstIndex, Op& reducer, typename Self::CoeffReturnType* accum) {\n    EIGEN_STATIC_ASSERT((DimIndex > 0), YOU_MADE_A_PROGRAMMING_MISTAKE);\n    for (int j = 0; j < self.m_reducedDims[DimIndex]; ++j) {\n      const typename Self::Index input = firstIndex + j * self.m_reducedStrides[DimIndex];\n      GenericDimReducer<DimIndex-1, Self, Op>::reduce(self, input, reducer, accum);\n    }\n  }\n};\ntemplate <typename Self, typename Op>\nstruct GenericDimReducer<0, Self, Op> {\n  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const Self& self, typename Self::Index firstIndex, Op& reducer, typename Self::CoeffReturnType* accum) {\n    for (int j = 0; j < self.m_reducedDims[0]; ++j) {\n      const typename Self::Index input = firstIndex + j * self.m_reducedStrides[0];\n      reducer.reduce(self.m_impl.coeff(input), accum);\n    }\n  }\n};\ntemplate <typename Self, typename Op>\nstruct GenericDimReducer<-1, Self, Op> {\n  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const Self& self, typename Self::Index index, Op& reducer, typename Self::CoeffReturnType* accum) {\n    reducer.reduce(self.m_impl.coeff(index), accum);\n  }\n};\n\ntemplate <typename Self, typename Op, bool Vectorizable = (Self::InputPacketAccess & Op::PacketAccess)>\nstruct InnerMostDimReducer {\n  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename Self::CoeffReturnType reduce(const Self& self, typename Self::Index firstIndex, typename Self::Index numValuesToReduce, Op& reducer) {\n    typename Self::CoeffReturnType accum = reducer.initialize();\n    for (typename Self::Index j = 0; j < numValuesToReduce; ++j) {\n      reducer.reduce(self.m_impl.coeff(firstIndex + j), &accum);\n    }\n    return reducer.finalize(accum);\n  }\n};\n\ntemplate <typename Self, typename Op>\nstruct InnerMostDimReducer<Self, Op, true> {\n  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename Self::CoeffReturnType reduce(const Self& self, typename Self::Index firstIndex, typename Self::Index numValuesToReduce, Op& reducer) {\n    const int packetSize = internal::unpacket_traits<typename Self::PacketReturnType>::size;\n    const typename Self::Index VectorizedSize = (numValuesToReduce / packetSize) * packetSize;\n    typename Self::PacketReturnType p = reducer.template initializePacket<typename Self::PacketReturnType>();\n    for (typename Self::Index j = 0; j < VectorizedSize; j += packetSize) {\n      reducer.reducePacket(self.m_impl.template packet<Unaligned>(firstIndex + j), &p);\n    }\n    typename Self::CoeffReturnType accum = reducer.initialize();\n    for (typename Self::Index j = VectorizedSize; j < numValuesToReduce; ++j) {\n      reducer.reduce(self.m_impl.coeff(firstIndex + j), &accum);\n    }\n    return reducer.finalizeBoth(accum, p);\n  }\n};\n\ntemplate <int DimIndex, typename Self, typename Op, bool vectorizable = (Self::InputPacketAccess & Op::PacketAccess)>\nstruct InnerMostDimPreserver {\n  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const Self&, typename Self::Index, Op&, typename Self::PacketReturnType*) {\n    eigen_assert(false && \"should never be called\");\n  }\n};\n\ntemplate <int DimIndex, typename Self, typename Op>\nstruct InnerMostDimPreserver<DimIndex, Self, Op, true> {\n  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const Self& self, typename Self::Index firstIndex, Op& reducer, typename Self::PacketReturnType* accum) {\n    EIGEN_STATIC_ASSERT((DimIndex > 0), YOU_MADE_A_PROGRAMMING_MISTAKE);\n    for (typename Self::Index j = 0; j < self.m_reducedDims[DimIndex]; ++j) {\n      const typename Self::Index input = firstIndex + j * self.m_reducedStrides[DimIndex];\n      InnerMostDimPreserver<DimIndex-1, Self, Op>::reduce(self, input, reducer, accum);\n    }\n  }\n};\n\ntemplate <typename Self, typename Op>\nstruct InnerMostDimPreserver<0, Self, Op, true> {\n  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const Self& self, typename Self::Index firstIndex, Op& reducer, typename Self::PacketReturnType* accum) {\n    for (typename Self::Index j = 0; j < self.m_reducedDims[0]; ++j) {\n      const typename Self::Index input = firstIndex + j * self.m_reducedStrides[0];\n      reducer.reducePacket(self.m_impl.template packet<Unaligned>(input), accum);\n    }\n  }\n};\ntemplate <typename Self, typename Op>\nstruct InnerMostDimPreserver<-1, Self, Op, true> {\n  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const Self&, typename Self::Index, Op&, typename Self::PacketReturnType*) {\n    eigen_assert(false && \"should never be called\");\n  }\n};\n\n// Default full reducer\ntemplate <typename Self, typename Op, typename Device, bool Vectorizable = (Self::InputPacketAccess & Op::PacketAccess)>\nstruct FullReducer {\n  static const bool HasOptimizedImplementation = false;\n\n  static EIGEN_DEVICE_FUNC void run(const Self& self, Op& reducer, const Device&, typename Self::CoeffReturnType* output) {\n    const typename Self::Index num_coeffs = array_prod(self.m_impl.dimensions());\n    *output = InnerMostDimReducer<Self, Op, Vectorizable>::reduce(self, 0, num_coeffs, reducer);\n  }\n};\n\n\n#ifdef EIGEN_USE_THREADS\n// Multithreaded full reducers\ntemplate <typename Self, typename Op,\n          bool Vectorizable = (Self::InputPacketAccess & Op::PacketAccess)>\nstruct FullReducerShard {\n  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(const Self& self, typename Self::Index firstIndex,\n                  typename Self::Index numValuesToReduce, Op& reducer,\n                  typename Self::CoeffReturnType* output) {\n    *output = InnerMostDimReducer<Self, Op, Vectorizable>::reduce(\n        self, firstIndex, numValuesToReduce, reducer);\n  }\n};\n\n// Multithreaded full reducer\ntemplate <typename Self, typename Op, bool Vectorizable>\nstruct FullReducer<Self, Op, ThreadPoolDevice, Vectorizable> {\n  static const bool HasOptimizedImplementation = !Op::IsStateful;\n  static const int PacketSize =\n      unpacket_traits<typename Self::PacketReturnType>::size;\n\n  // launch one reducer per thread and accumulate the result.\n  static void run(const Self& self, Op& reducer, const ThreadPoolDevice& device,\n                  typename Self::CoeffReturnType* output) {\n    typedef typename Self::Index Index;\n    const Index num_coeffs = array_prod(self.m_impl.dimensions());\n    if (num_coeffs == 0) {\n      *output = reducer.finalize(reducer.initialize());\n      return;\n    }\n    const TensorOpCost cost =\n        self.m_impl.costPerCoeff(Vectorizable) +\n        TensorOpCost(0, 0, internal::functor_traits<Op>::Cost, Vectorizable,\n                     PacketSize);\n    const int num_threads = TensorCostModel<ThreadPoolDevice>::numThreads(\n        num_coeffs, cost, device.numThreads());\n    if (num_threads == 1) {\n      *output =\n          InnerMostDimReducer<Self, Op, Vectorizable>::reduce(self, 0, num_coeffs, reducer);\n      return;\n    }\n    const Index blocksize =\n        std::floor<Index>(static_cast<float>(num_coeffs) / num_threads);\n    const Index numblocks = blocksize > 0 ? num_coeffs / blocksize : 0;\n    eigen_assert(num_coeffs >= numblocks * blocksize);\n\n    Barrier barrier(internal::convert_index<unsigned int>(numblocks));\n    MaxSizeVector<typename Self::CoeffReturnType> shards(numblocks, reducer.initialize());\n    for (Index i = 0; i < numblocks; ++i) {\n      device.enqueue_with_barrier(&barrier, &FullReducerShard<Self, Op, Vectorizable>::run,\n                                  self, i * blocksize, blocksize, reducer,\n                                  &shards[i]);\n    }\n    typename Self::CoeffReturnType finalShard;\n    if (numblocks * blocksize < num_coeffs) {\n      finalShard = InnerMostDimReducer<Self, Op, Vectorizable>::reduce(\n          self, numblocks * blocksize, num_coeffs - numblocks * blocksize,\n          reducer);\n    } else {\n      finalShard = reducer.initialize();\n    }\n    barrier.Wait();\n\n    for (Index i = 0; i < numblocks; ++i) {\n      reducer.reduce(shards[i], &finalShard);\n    }\n    *output = reducer.finalize(finalShard);\n  }\n};\n\n#endif\n\n\n// Default inner reducer\ntemplate <typename Self, typename Op, typename Device>\nstruct InnerReducer {\n  static const bool HasOptimizedImplementation = false;\n\n  EIGEN_DEVICE_FUNC static bool run(const Self&, Op&, const Device&, typename Self::CoeffReturnType*, typename Self::Index, typename Self::Index) {\n    eigen_assert(false && \"Not implemented\");\n    return true;\n  }\n};\n\n// Default outer reducer\ntemplate <typename Self, typename Op, typename Device>\nstruct OuterReducer {\n  static const bool HasOptimizedImplementation = false;\n\n  EIGEN_DEVICE_FUNC static bool run(const Self&, Op&, const Device&, typename Self::CoeffReturnType*, typename Self::Index, typename Self::Index) {\n    eigen_assert(false && \"Not implemented\");\n    return true;\n  }\n};\n\n\n#if defined(EIGEN_USE_GPU) && defined(__CUDACC__)\ntemplate <int B, int N, typename S, typename R, typename I>\n__global__ void FullReductionKernel(R, const S, I, typename S::CoeffReturnType*, unsigned int*);\n\n\n#ifdef EIGEN_HAS_CUDA_FP16\ntemplate <typename S, typename R, typename I>\n__global__ void ReductionInitFullReduxKernelHalfFloat(R, const S, I, half2*);\ntemplate <int B, int N, typename S, typename R, typename I>\n__global__ void FullReductionKernelHalfFloat(R, const S, I, half*, half2*);\ntemplate <int NPT, typename S, typename R, typename I>\n__global__ void InnerReductionKernelHalfFloat(R, const S, I, I, half*);\n\n#endif\n\ntemplate <int NPT, typename S, typename R, typename I>\n__global__ void InnerReductionKernel(R, const S, I, I, typename S::CoeffReturnType*);\n\ntemplate <int NPT, typename S, typename R, typename I>\n__global__ void OuterReductionKernel(R, const S, I, I, typename S::CoeffReturnType*);\n#endif\n\n}  // end namespace internal\n\n\ntemplate <typename Op, typename Dims, typename XprType,  template <class> class MakePointer_>\nclass TensorReductionOp : public TensorBase<TensorReductionOp<Op, Dims, XprType, MakePointer_>, ReadOnlyAccessors> {\n  public:\n    typedef typename Eigen::internal::traits<TensorReductionOp>::Scalar Scalar;\n    typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;\n    typedef typename internal::remove_const<typename XprType::CoeffReturnType>::type CoeffReturnType;\n    typedef typename Eigen::internal::nested<TensorReductionOp>::type Nested;\n    typedef typename Eigen::internal::traits<TensorReductionOp>::StorageKind StorageKind;\n    typedef typename Eigen::internal::traits<TensorReductionOp>::Index Index;\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    TensorReductionOp(const XprType& expr, const Dims& dims) : m_expr(expr), m_dims(dims)\n    { }\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    TensorReductionOp(const XprType& expr, const Dims& dims, const Op& reducer) : m_expr(expr), m_dims(dims), m_reducer(reducer)\n    { }\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const XprType& expression() const { return m_expr; }\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const Dims& dims() const { return m_dims; }\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n    const Op& reducer() const { return m_reducer; }\n\n  protected:\n    typename XprType::Nested m_expr;\n    const Dims m_dims;\n    const Op m_reducer;\n};\n\n\n// Eval as rvalue\ntemplate<typename Op, typename Dims, typename ArgType, template <class> class MakePointer_, typename Device>\nstruct TensorEvaluator<const TensorReductionOp<Op, Dims, ArgType, MakePointer_>, Device>\n{\n  typedef TensorReductionOp<Op, Dims, ArgType, MakePointer_> XprType;\n  typedef typename XprType::Index Index;\n  typedef ArgType ChildType;\n  typedef typename TensorEvaluator<ArgType, Device>::Dimensions InputDimensions;\n  static const int NumInputDims = internal::array_size<InputDimensions>::value;\n  static const int NumReducedDims = internal::array_size<Dims>::value;\n  static const int NumOutputDims = NumInputDims - NumReducedDims;\n  typedef typename internal::conditional<NumOutputDims==0, Sizes<>, DSizes<Index, NumOutputDims> >::type Dimensions;\n  typedef typename XprType::Scalar Scalar;\n  typedef TensorEvaluator<const TensorReductionOp<Op, Dims, ArgType, MakePointer_>, Device> Self;\n  static const bool InputPacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess;\n  typedef typename internal::remove_const<typename XprType::CoeffReturnType>::type CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  static const int PacketSize = internal::unpacket_traits<PacketReturnType>::size;\n\n  enum {\n    IsAligned = false,\n    PacketAccess = Self::InputPacketAccess && Op::PacketAccess,\n    Layout = TensorEvaluator<ArgType, Device>::Layout,\n    CoordAccess = false,  // to be implemented\n    RawAccess = false\n  };\n\n  static const bool ReducingInnerMostDims = internal::are_inner_most_dims<Dims, NumInputDims, Layout>::value;\n  static const bool PreservingInnerMostDims = internal::preserve_inner_most_dims<Dims, NumInputDims, Layout>::value;\n  static const bool RunningFullReduction = (NumOutputDims==0);\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)\n      : m_impl(op.expression(), device), m_reducer(op.reducer()), m_result(NULL), m_device(device), m_xpr_dims(op.dims())\n  {\n    EIGEN_STATIC_ASSERT((NumInputDims >= NumReducedDims), YOU_MADE_A_PROGRAMMING_MISTAKE);\n    EIGEN_STATIC_ASSERT((!ReducingInnerMostDims | !PreservingInnerMostDims | (NumReducedDims == NumInputDims)),\n                        YOU_MADE_A_PROGRAMMING_MISTAKE);\n\n    // Build the bitmap indicating if an input dimension is reduced or not.\n    for (int i = 0; i < NumInputDims; ++i) {\n      m_reduced[i] = false;\n    }\n    for (int i = 0; i < NumReducedDims; ++i) {\n      eigen_assert(op.dims()[i] >= 0);\n      eigen_assert(op.dims()[i] < NumInputDims);\n      m_reduced[op.dims()[i]] = true;\n    }\n\n    const typename TensorEvaluator<ArgType, Device>::Dimensions& input_dims = m_impl.dimensions();\n    internal::DimInitializer<Dimensions>::run(input_dims, m_reduced, &m_dimensions, &m_reducedDims);\n\n    // Precompute output strides.\n    if (NumOutputDims > 0) {\n      if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n        m_outputStrides[0] = 1;\n        for (int i = 1; i < NumOutputDims; ++i) {\n          m_outputStrides[i] = m_outputStrides[i - 1] * m_dimensions[i - 1];\n        }\n      } else {\n        m_outputStrides.back() = 1;\n        for (int i = NumOutputDims - 2; i >= 0; --i) {\n          m_outputStrides[i] = m_outputStrides[i + 1] * m_dimensions[i + 1];\n        }\n      }\n    }\n\n    // Precompute input strides.\n    if (NumInputDims > 0) {\n      array<Index, NumInputDims> input_strides;\n      if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n        input_strides[0] = 1;\n        for (int i = 1; i < NumInputDims; ++i) {\n          input_strides[i] = input_strides[i-1] * input_dims[i-1];\n        }\n      } else {\n        input_strides.back() = 1;\n        for (int i = NumInputDims - 2; i >= 0; --i) {\n          input_strides[i] = input_strides[i + 1] * input_dims[i + 1];\n        }\n      }\n\n      int outputIndex = 0;\n      int reduceIndex = 0;\n      for (int i = 0; i < NumInputDims; ++i) {\n        if (m_reduced[i]) {\n          m_reducedStrides[reduceIndex] = input_strides[i];\n          ++reduceIndex;\n        } else {\n          m_preservedStrides[outputIndex] = input_strides[i];\n          ++outputIndex;\n        }\n      }\n    }\n\n    // Special case for full reductions\n    if (NumOutputDims == 0) {\n      m_preservedStrides[0] = internal::array_prod(input_dims);\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }\n\n  EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool evalSubExprsIfNeeded(typename MakePointer_<CoeffReturnType>::Type data) {\n    m_impl.evalSubExprsIfNeeded(NULL);\n\n    // Use the FullReducer if possible.\n    if ((RunningFullReduction && RunningOnSycl) ||(RunningFullReduction &&\n        internal::FullReducer<Self, Op, Device>::HasOptimizedImplementation &&\n        ((RunningOnGPU && (m_device.majorDeviceVersion() >= 3)) ||\n         !RunningOnGPU))) {\n      bool need_assign = false;\n      if (!data) {\n        m_result = static_cast<CoeffReturnType*>(m_device.allocate(sizeof(CoeffReturnType)));\n        data = m_result;\n        need_assign = true;\n      }\n      Op reducer(m_reducer);\n      internal::FullReducer<Self, Op, Device>::run(*this, reducer, m_device, data);\n      return need_assign;\n    }\n    else if(RunningOnSycl){\n      const Index num_values_to_reduce = internal::array_prod(m_reducedDims);\n      const Index num_coeffs_to_preserve = internal::array_prod(m_dimensions);\n      if (!data) {\n        data = static_cast<CoeffReturnType*>(m_device.allocate(sizeof(CoeffReturnType) * num_coeffs_to_preserve));\n        m_result = data;\n      }\n      Op reducer(m_reducer);\n      internal::InnerReducer<Self, Op, Device>::run(*this, reducer, m_device, data, num_values_to_reduce, num_coeffs_to_preserve);\n      return (m_result != NULL);\n    }\n\n    // Attempt to use an optimized reduction.\n    else if (RunningOnGPU && (m_device.majorDeviceVersion() >= 3)) {\n      bool reducing_inner_dims = true;\n      for (int i = 0; i < NumReducedDims; ++i) {\n        if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n          reducing_inner_dims &= m_reduced[i];\n        } else {\n          reducing_inner_dims &= m_reduced[NumInputDims - 1 - i];\n        }\n      }\n      if (internal::InnerReducer<Self, Op, Device>::HasOptimizedImplementation &&\n          (reducing_inner_dims || ReducingInnerMostDims)) {\n        const Index num_values_to_reduce = internal::array_prod(m_reducedDims);\n        const Index num_coeffs_to_preserve = internal::array_prod(m_dimensions);\n        if (!data) {\n          if (num_coeffs_to_preserve < 1024 && num_values_to_reduce > num_coeffs_to_preserve && num_values_to_reduce > 128) {\n            data = static_cast<CoeffReturnType*>(m_device.allocate(sizeof(CoeffReturnType) * num_coeffs_to_preserve));\n            m_result = data;\n          }\n          else {\n            return true;\n          }\n        }\n        Op reducer(m_reducer);\n        if (internal::InnerReducer<Self, Op, Device>::run(*this, reducer, m_device, data, num_values_to_reduce, num_coeffs_to_preserve)) {\n          if (m_result) {\n            m_device.deallocate(m_result);\n            m_result = NULL;\n          }\n          return true;\n        } else {\n          return (m_result != NULL);\n        }\n      }\n\n      bool preserving_inner_dims = true;\n      for (int i = 0; i < NumReducedDims; ++i) {\n        if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n          preserving_inner_dims &= m_reduced[NumInputDims - 1 - i];\n        } else {\n          preserving_inner_dims &= m_reduced[i];\n        }\n      }\n      if (internal::OuterReducer<Self, Op, Device>::HasOptimizedImplementation &&\n          preserving_inner_dims) {\n        const Index num_values_to_reduce = internal::array_prod(m_reducedDims);\n        const Index num_coeffs_to_preserve = internal::array_prod(m_dimensions);\n        if (!data) {\n          if (num_coeffs_to_preserve < 1024 && num_values_to_reduce > num_coeffs_to_preserve && num_values_to_reduce > 32) {\n            data = static_cast<CoeffReturnType*>(m_device.allocate(sizeof(CoeffReturnType) * num_coeffs_to_preserve));\n            m_result = data;\n          }\n          else {\n            return true;\n          }\n        }\n        Op reducer(m_reducer);\n        if (internal::OuterReducer<Self, Op, Device>::run(*this, reducer, m_device, data, num_values_to_reduce, num_coeffs_to_preserve)) {\n          if (m_result) {\n            m_device.deallocate(m_result);\n            m_result = NULL;\n          }\n          return true;\n        } else {\n          return (m_result != NULL);\n        }\n      }\n    }\n    return true;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {\n    m_impl.cleanup();\n    if (m_result) {\n      m_device.deallocate(m_result);\n      m_result = NULL;\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const\n  {\n    if ((RunningOnSycl || RunningFullReduction || RunningOnGPU) && m_result) {\n      return *(m_result + index);\n    }\n    Op reducer(m_reducer);\n    if (ReducingInnerMostDims || RunningFullReduction) {\n      const Index num_values_to_reduce =\n        (static_cast<int>(Layout) == static_cast<int>(ColMajor)) ? m_preservedStrides[0] : m_preservedStrides[NumPreservedStrides - 1];\n      return internal::InnerMostDimReducer<Self, Op>::reduce(*this, firstInput(index),\n                                                             num_values_to_reduce, reducer);\n    } else {\n      typename Self::CoeffReturnType accum = reducer.initialize();\n      internal::GenericDimReducer<NumReducedDims-1, Self, Op>::reduce(*this, firstInput(index), reducer, &accum);\n      return reducer.finalize(accum);\n    }\n  }\n\n  // TODO(bsteiner): provide a more efficient implementation.\n  template<int LoadMode>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const\n  {\n    EIGEN_STATIC_ASSERT((PacketSize > 1), YOU_MADE_A_PROGRAMMING_MISTAKE)\n    eigen_assert(index + PacketSize - 1 < Index(internal::array_prod(dimensions())));\n\n    if (RunningOnGPU && m_result) {\n      return internal::pload<PacketReturnType>(m_result + index);\n    }\n\n    EIGEN_ALIGN_MAX typename internal::remove_const<CoeffReturnType>::type values[PacketSize];\n    if (ReducingInnerMostDims) {\n      const Index num_values_to_reduce =\n        (static_cast<int>(Layout) == static_cast<int>(ColMajor)) ? m_preservedStrides[0] : m_preservedStrides[NumPreservedStrides - 1];\n      const Index firstIndex = firstInput(index);\n      for (Index i = 0; i < PacketSize; ++i) {\n        Op reducer(m_reducer);\n        values[i] = internal::InnerMostDimReducer<Self, Op>::reduce(*this, firstIndex + i * num_values_to_reduce,\n                                                                    num_values_to_reduce, reducer);\n      }\n    } else if (PreservingInnerMostDims) {\n      const Index firstIndex = firstInput(index);\n      const int innermost_dim = (static_cast<int>(Layout) == static_cast<int>(ColMajor)) ? 0 : NumOutputDims - 1;\n      // TBD: extend this the the n innermost dimensions that we preserve.\n      if (((firstIndex % m_dimensions[innermost_dim]) + PacketSize - 1) < m_dimensions[innermost_dim]) {\n        Op reducer(m_reducer);\n        typename Self::PacketReturnType accum = reducer.template initializePacket<typename Self::PacketReturnType>();\n        internal::InnerMostDimPreserver<NumReducedDims-1, Self, Op>::reduce(*this, firstIndex, reducer, &accum);\n        return reducer.finalizePacket(accum);\n      } else {\n        for (int i = 0; i < PacketSize; ++i) {\n          values[i] = coeff(index + i);\n        }\n      }\n    } else {\n      for (int i = 0; i < PacketSize; ++i) {\n        values[i] = coeff(index + i);\n      }\n    }\n    PacketReturnType rslt = internal::pload<PacketReturnType>(values);\n    return rslt;\n  }\n\n  // Must be called after evalSubExprsIfNeeded().\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {\n    if (RunningFullReduction && m_result) {\n      return TensorOpCost(sizeof(CoeffReturnType), 0, 0, vectorized, PacketSize);\n    } else {\n      const Index num_values_to_reduce = internal::array_prod(m_reducedDims);\n      const double compute_cost = num_values_to_reduce * internal::functor_traits<Op>::Cost;\n      return m_impl.costPerCoeff(vectorized) * num_values_to_reduce +\n          TensorOpCost(0, 0, compute_cost, vectorized, PacketSize);\n    }\n  }\n\n  EIGEN_DEVICE_FUNC typename MakePointer_<Scalar>::Type data() const { return m_result; }\n  /// required by sycl in order to extract the accessor\n  const TensorEvaluator<ArgType, Device>& impl() const { return m_impl; }\n  /// added for sycl in order to construct the buffer from the sycl device\n  const Device& device() const{return m_device;}\n  /// added for sycl in order to re-construct the reduction eval on the device for the sub-kernel\n  const Dims& xprDims() const {return m_xpr_dims;}\n\n\n  private:\n  template <int, typename, typename> friend struct internal::GenericDimReducer;\n  template <typename, typename, bool> friend struct internal::InnerMostDimReducer;\n  template <int, typename, typename, bool> friend struct internal::InnerMostDimPreserver;\n  template <typename S, typename O, typename D, bool V> friend struct internal::FullReducer;\n#ifdef EIGEN_USE_THREADS\n  template <typename S, typename O, bool V> friend struct internal::FullReducerShard;\n#endif\n#if defined(EIGEN_USE_GPU) && defined(__CUDACC__)\n  template <int B, int N, typename S, typename R, typename I> friend void internal::FullReductionKernel(R, const S, I, typename S::CoeffReturnType*, unsigned int*);\n#ifdef EIGEN_HAS_CUDA_FP16\n  template <typename S, typename R, typename I> friend void internal::ReductionInitFullReduxKernelHalfFloat(R, const S, I, half2*);\n  template <int B, int N, typename S, typename R, typename I> friend void internal::FullReductionKernelHalfFloat(R, const S, I, half*, half2*);\n  template <int NPT, typename S, typename R, typename I> friend void internal::InnerReductionKernelHalfFloat(R, const S, I, I, half*);\n#endif\n  template <int NPT, typename S, typename R, typename I> friend void internal::InnerReductionKernel(R, const S, I, I, typename S::CoeffReturnType*);\n\n  template <int NPT, typename S, typename R, typename I> friend void internal::OuterReductionKernel(R, const S, I, I, typename S::CoeffReturnType*);\n#endif\n\n  template <typename S, typename O, typename D> friend struct internal::InnerReducer;\n\n  // Returns the Index in the input tensor of the first value that needs to be\n  // used to compute the reduction at output index \"index\".\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index firstInput(Index index) const {\n    if (ReducingInnerMostDims) {\n      if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n        return index * m_preservedStrides[0];\n      } else {\n        return index * m_preservedStrides[NumPreservedStrides - 1];\n      }\n    }\n    // TBD: optimize the case where we preserve the innermost dimensions.\n    Index startInput = 0;\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      for (int i = NumOutputDims - 1; i > 0; --i) {\n        // This is index_i in the output tensor.\n        const Index idx = index / m_outputStrides[i];\n        startInput += idx * m_preservedStrides[i];\n        index -= idx * m_outputStrides[i];\n      }\n      if (PreservingInnerMostDims) {\n        eigen_assert(m_preservedStrides[0] == 1);\n        startInput += index;\n      } else {\n        startInput += index * m_preservedStrides[0];\n      }\n    } else {\n      for (int i = 0; i < NumOutputDims - 1; ++i) {\n        // This is index_i in the output tensor.\n        const Index idx = index / m_outputStrides[i];\n        startInput += idx * m_preservedStrides[i];\n        index -= idx * m_outputStrides[i];\n      }\n      if (PreservingInnerMostDims) {\n        eigen_assert(m_preservedStrides[NumPreservedStrides - 1] == 1);\n        startInput += index;\n      } else {\n        startInput += index * m_preservedStrides[NumPreservedStrides - 1];\n      }\n    }\n    return startInput;\n  }\n\n  // Bitmap indicating if an input dimension is reduced or not.\n  array<bool, NumInputDims> m_reduced;\n  // Dimensions of the output of the operation.\n  Dimensions m_dimensions;\n  // Precomputed strides for the output tensor.\n  array<Index, NumOutputDims> m_outputStrides;\n  // Subset of strides of the input tensor for the non-reduced dimensions.\n  // Indexed by output dimensions.\n  static const int NumPreservedStrides = max_n_1<NumOutputDims>::size;\n  array<Index, NumPreservedStrides> m_preservedStrides;\n\n  // Subset of strides of the input tensor for the reduced dimensions.\n  // Indexed by reduced dimensions.\n  array<Index, NumReducedDims> m_reducedStrides;\n  // Size of the input dimensions that are reduced.\n  // Indexed by reduced dimensions.\n  array<Index, NumReducedDims> m_reducedDims;\n\n  // Evaluator for the input expression.\n  TensorEvaluator<ArgType, Device> m_impl;\n\n  // Operation to apply for computing the reduction.\n  Op m_reducer;\n\n  // For full reductions\n#if defined(EIGEN_USE_GPU) && defined(__CUDACC__)\n  static const bool RunningOnGPU = internal::is_same<Device, Eigen::GpuDevice>::value;\n  static const bool RunningOnSycl = false;\n#elif defined(EIGEN_USE_SYCL)\nstatic const bool RunningOnSycl = internal::is_same<typename internal::remove_all<Device>::type, Eigen::SyclDevice>::value;\nstatic const bool RunningOnGPU = false;\n#else\n  static const bool RunningOnGPU = false;\n  static const bool RunningOnSycl = false;\n#endif\n  typename MakePointer_<CoeffReturnType>::Type m_result;\n\n  const Device& m_device;\n  const Dims& m_xpr_dims;\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_REDUCTION_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorReductionCuda.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_REDUCTION_CUDA_H\n#define EIGEN_CXX11_TENSOR_TENSOR_REDUCTION_CUDA_H\n\nnamespace Eigen {\nnamespace internal {\n\n\n#if defined(EIGEN_USE_GPU) && defined(__CUDACC__)\n// Full reducers for GPU, don't vectorize for now\n\n// Reducer function that enables multiple cuda thread to safely accumulate at the same\n// output address. It basically reads the current value of the output variable, and\n// attempts to update it with the new value. If in the meantime another cuda thread\n// updated the content of the output address it will try again.\ntemplate <typename T, typename R>\n__device__ EIGEN_ALWAYS_INLINE void atomicReduce(T* output, T accum, R& reducer) {\n#if __CUDA_ARCH__ >= 300\n  if (sizeof(T) == 4)\n  {\n    unsigned int oldval = *reinterpret_cast<unsigned int*>(output);\n    unsigned int newval = oldval;\n    reducer.reduce(accum, reinterpret_cast<T*>(&newval));\n    if (newval == oldval) {\n      return;\n    }\n    unsigned int readback;\n    while ((readback = atomicCAS((unsigned int*)output, oldval, newval)) != oldval) {\n      oldval = readback;\n      newval = oldval;\n      reducer.reduce(accum, reinterpret_cast<T*>(&newval));\n      if (newval == oldval) {\n        return;\n      }\n    }\n  }\n  else if (sizeof(T) == 8) {\n    unsigned long long oldval = *reinterpret_cast<unsigned long long*>(output);\n    unsigned long long newval = oldval;\n    reducer.reduce(accum, reinterpret_cast<T*>(&newval));\n    if (newval == oldval) {\n      return;\n    }\n    unsigned long long readback;\n    while ((readback = atomicCAS((unsigned long long*)output, oldval, newval)) != oldval) {\n      oldval = readback;\n      newval = oldval;\n      reducer.reduce(accum, reinterpret_cast<T*>(&newval));\n      if (newval == oldval) {\n        return;\n      }\n    }\n  }\n  else {\n    assert(0 && \"Wordsize not supported\");\n  }\n#else\n  assert(0 && \"Shouldn't be called on unsupported device\");\n#endif\n}\n\n// We extend atomicExch to support extra data types\ntemplate <typename Type>\n__device__ inline Type atomicExchCustom(Type* address, Type val) {\n  return atomicExch(address, val);\n}\n\ntemplate <>\n__device__ inline double atomicExchCustom(double* address, double val) {\n  unsigned long long int* address_as_ull = reinterpret_cast<unsigned long long int*>(address);\n  return __longlong_as_double(atomicExch(address_as_ull, __double_as_longlong(val)));\n}\n\n#ifdef EIGEN_HAS_CUDA_FP16\ntemplate <template <typename T> class R>\n__device__ inline void atomicReduce(half2* output, half2 accum, R<half>& reducer) {\n  unsigned int oldval = *reinterpret_cast<unsigned int*>(output);\n  unsigned int newval = oldval;\n  reducer.reducePacket(accum, reinterpret_cast<half2*>(&newval));\n  if (newval == oldval) {\n    return;\n  }\n  unsigned int readback;\n  while ((readback = atomicCAS((unsigned int*)output, oldval, newval)) != oldval) {\n    oldval = readback;\n    newval = oldval;\n    reducer.reducePacket(accum, reinterpret_cast<half2*>(&newval));\n    if (newval == oldval) {\n      return;\n    }\n  }\n}\n#endif\n\ntemplate <>\n__device__ inline void atomicReduce(float* output, float accum, SumReducer<float>&) {\n#if __CUDA_ARCH__ >= 300\n  atomicAdd(output, accum);\n#else\n  assert(0 && \"Shouldn't be called on unsupported device\");\n#endif\n}\n\n\ntemplate <typename CoeffType, typename Index>\n__global__ void ReductionInitKernel(const CoeffType val, Index num_preserved_coeffs, CoeffType* output) {\n  const Index thread_id = blockIdx.x * blockDim.x + threadIdx.x;\n  const Index num_threads = blockDim.x * gridDim.x;\n  for (Index i = thread_id; i < num_preserved_coeffs; i += num_threads) {\n    output[i] = val;\n  }\n}\n\n\ntemplate <int BlockSize, int NumPerThread, typename Self,\n          typename Reducer, typename Index>\n__global__ void FullReductionKernel(Reducer reducer, const Self input, Index num_coeffs,\n                                    typename Self::CoeffReturnType* output, unsigned int* semaphore) {\n#if __CUDA_ARCH__ >= 300\n  // Initialize the output value\n  const Index first_index = blockIdx.x * BlockSize * NumPerThread + threadIdx.x;\n  if (gridDim.x == 1) {\n    if (first_index == 0) {\n      *output = reducer.initialize();\n    }\n  }\n  else {\n    if (threadIdx.x == 0) {\n      unsigned int block = atomicCAS(semaphore, 0u, 1u);\n      if (block == 0) {\n        // We're the first block to run, initialize the output value\n        atomicExchCustom(output, reducer.initialize());\n        __threadfence();\n        atomicExch(semaphore, 2u);\n      }\n      else {\n        // Wait for the first block to initialize the output value.\n        // Use atomicCAS here to ensure that the reads aren't cached\n        unsigned int val;\n        do {\n          val = atomicCAS(semaphore, 2u, 2u);\n        }\n        while (val < 2u);\n      }\n    }\n  }\n\n  __syncthreads();\n\n  eigen_assert(gridDim.x == 1 || *semaphore >= 2u);\n\n  typename Self::CoeffReturnType accum = reducer.initialize();\n  Index max_iter = numext::mini<Index>(num_coeffs - first_index, NumPerThread*BlockSize);\n  for (Index i = 0; i < max_iter; i+=BlockSize) {\n    const Index index = first_index + i;\n    eigen_assert(index < num_coeffs);\n    typename Self::CoeffReturnType val = input.m_impl.coeff(index);\n    reducer.reduce(val, &accum);\n  }\n\n#pragma unroll\n  for (int offset = warpSize/2; offset > 0; offset /= 2) {\n    reducer.reduce(__shfl_down(accum, offset, warpSize), &accum);\n  }\n\n  if ((threadIdx.x & (warpSize - 1)) == 0) {\n    atomicReduce(output, accum, reducer);\n  }\n\n  if (gridDim.x > 1 && threadIdx.x == 0) {\n    // Let the last block reset the semaphore\n    atomicInc(semaphore, gridDim.x + 1);\n  }\n#else\n  assert(0 && \"Shouldn't be called on unsupported device\");\n#endif\n}\n\n\n#ifdef EIGEN_HAS_CUDA_FP16\ntemplate <typename Self,\n          typename Reducer, typename Index>\n__global__ void ReductionInitFullReduxKernelHalfFloat(Reducer reducer, const Self input, Index num_coeffs, half2* scratch) {\n  eigen_assert(blockDim.x == 1);\n  eigen_assert(gridDim.x == 1);\n  if (num_coeffs % 2 != 0) {\n    half last = input.m_impl.coeff(num_coeffs-1);\n    *scratch = __halves2half2(last, reducer.initialize());\n  } else {\n    *scratch = reducer.template initializePacket<half2>();\n  }\n}\n\ntemplate <typename Self,\n          typename Reducer, typename Index>\n__global__ void ReductionInitKernelHalfFloat(Reducer reducer, const Self input, Index num_coeffs, half* output) {\n  const Index thread_id = blockIdx.x * blockDim.x + threadIdx.x;\n  const Index num_threads = blockDim.x * gridDim.x;\n  const Index num_packets = num_coeffs / 2;\n  for (Index i = thread_id; i < num_packets; i += num_threads) {\n    ((half2*)output)[i] = reducer.template initializePacket<half2>();\n  }\n\n  if (thread_id == 0 && num_coeffs % 2 != 0) {\n    output[num_coeffs-1] = reducer.initialize();\n  }\n}\n\ntemplate <int BlockSize, int NumPerThread, typename Self,\n          typename Reducer, typename Index>\n__global__ void FullReductionKernelHalfFloat(Reducer reducer, const Self input, Index num_coeffs,\n                                    half* output, half2* scratch) {\n  eigen_assert(NumPerThread % 2 == 0);\n\n  const Index first_index = blockIdx.x * BlockSize * NumPerThread + 2*threadIdx.x;\n\n  // Initialize the output value if it wasn't initialized by the ReductionInitKernel\n  if (gridDim.x == 1 && first_index == 0) {\n    if (num_coeffs % 2 != 0) {\n      half last = input.m_impl.coeff(num_coeffs-1);\n      *scratch = __halves2half2(last, reducer.initialize());\n    } else {\n      *scratch = reducer.template initializePacket<half2>();\n    }\n    __syncthreads();\n  }\n\n  half2 accum = reducer.template initializePacket<half2>();\n  const Index max_iter = numext::mini<Index>((num_coeffs - first_index) / 2, NumPerThread*BlockSize / 2);\n  for (Index i = 0; i < max_iter; i += BlockSize) {\n    const Index index = first_index + 2*i;\n    eigen_assert(index + 1 < num_coeffs);\n    half2 val = input.m_impl.template packet<Unaligned>(index);\n    reducer.reducePacket(val, &accum);\n  }\n\n#pragma unroll\n  for (int offset = warpSize/2; offset > 0; offset /= 2) {\n    reducer.reducePacket(__shfl_down(accum, offset, warpSize), &accum);\n  }\n\n  if ((threadIdx.x & (warpSize - 1)) == 0) {\n    atomicReduce(scratch, accum, reducer);\n  }\n\n  __syncthreads();\n\n  if (gridDim.x == 1 && first_index == 0) {\n    half tmp = __low2half(*scratch);\n    reducer.reduce(__high2half(*scratch), &tmp);\n    *output = tmp;\n  }\n}\n\ntemplate <typename Op>\n__global__ void ReductionCleanupKernelHalfFloat(Op& reducer, half* output, half2* scratch) {\n  eigen_assert(threadIdx.x == 1);\n  half tmp = __low2half(*scratch);\n  reducer.reduce(__high2half(*scratch), &tmp);\n  *output = tmp;\n}\n\n#endif\n\ntemplate <typename Self, typename Op, typename OutputType, bool PacketAccess, typename Enabled = void>\nstruct FullReductionLauncher {\n  static void run(const Self&, Op&, const GpuDevice&, OutputType*, typename Self::Index) {\n    assert(false && \"Should only be called on doubles, floats and half floats\");\n  }\n};\n\n// Specialization for float and double\ntemplate <typename Self, typename Op, typename OutputType, bool PacketAccess>\nstruct FullReductionLauncher<\n    Self, Op, OutputType, PacketAccess,\n    typename internal::enable_if<\n      internal::is_same<float, OutputType>::value ||\n      internal::is_same<double, OutputType>::value,\n    void>::type> {\n  static void run(const Self& self, Op& reducer, const GpuDevice& device, OutputType* output, typename Self::Index num_coeffs) {\n    typedef typename Self::Index Index;\n    typedef typename Self::CoeffReturnType Scalar;\n    const int block_size = 256;\n    const int num_per_thread = 128;\n    const int num_blocks = divup<int>(num_coeffs, block_size * num_per_thread);\n\n    unsigned int* semaphore = NULL;\n    if (num_blocks > 1) {\n      semaphore = device.semaphore();\n    }\n\n    LAUNCH_CUDA_KERNEL((FullReductionKernel<block_size, num_per_thread, Self, Op, Index>),\n                       num_blocks, block_size, 0, device, reducer, self, num_coeffs, output, semaphore);\n  }\n};\n\n#ifdef EIGEN_HAS_CUDA_FP16\ntemplate <typename Self, typename Op>\nstruct FullReductionLauncher<Self, Op, Eigen::half, false> {\n  static void run(const Self&, Op&, const GpuDevice&, half*, typename Self::Index) {\n    assert(false && \"Should not be called since there is no packet accessor\");\n  }\n};\n\ntemplate <typename Self, typename Op>\nstruct FullReductionLauncher<Self, Op, Eigen::half, true> {\n  static void run(const Self& self, Op& reducer, const GpuDevice& device, half* output, typename Self::Index num_coeffs) {\n    typedef typename Self::Index Index;\n\n    const int block_size = 256;\n    const int num_per_thread = 128;\n    const int num_blocks = divup<int>(num_coeffs, block_size * num_per_thread);\n    half2* scratch = static_cast<half2*>(device.scratchpad());\n\n    if (num_blocks > 1) {\n      // We initialize the output and the scrathpad outside the reduction kernel when we can't be sure that there\n      // won't be a race conditions between multiple thread blocks.\n      LAUNCH_CUDA_KERNEL((ReductionInitFullReduxKernelHalfFloat<Self, Op, Index>),\n                         1, 1, 0, device, reducer, self, num_coeffs, scratch);\n    }\n\n    LAUNCH_CUDA_KERNEL((FullReductionKernelHalfFloat<block_size, num_per_thread, Self, Op, Index>),\n                       num_blocks, block_size, 0, device, reducer, self, num_coeffs, output, scratch);\n\n    if (num_blocks > 1) {\n      LAUNCH_CUDA_KERNEL((ReductionCleanupKernelHalfFloat<Op>),\n                         1, 1, 0, device, reducer, output, scratch);\n    }\n  }\n};\n#endif\n\n\ntemplate <typename Self, typename Op, bool Vectorizable>\nstruct FullReducer<Self, Op, GpuDevice, Vectorizable> {\n  // Unfortunately nvidia doesn't support well exotic types such as complex,\n  // so reduce the scope of the optimized version of the code to the simple cases\n  // of doubles, floats and half floats\n#ifdef EIGEN_HAS_CUDA_FP16\n  static const bool HasOptimizedImplementation = !Op::IsStateful &&\n      (internal::is_same<typename Self::CoeffReturnType, float>::value ||\n       internal::is_same<typename Self::CoeffReturnType, double>::value ||\n       (internal::is_same<typename Self::CoeffReturnType, Eigen::half>::value && reducer_traits<Op, GpuDevice>::PacketAccess));\n#else\n  static const bool HasOptimizedImplementation = !Op::IsStateful &&\n                                                (internal::is_same<typename Self::CoeffReturnType, float>::value ||\n                                                 internal::is_same<typename Self::CoeffReturnType, double>::value);\n#endif\n\n  template <typename OutputType>\n  static void run(const Self& self, Op& reducer, const GpuDevice& device, OutputType* output) {\n    assert(HasOptimizedImplementation && \"Should only be called on doubles, floats or half floats\");\n    const Index num_coeffs = array_prod(self.m_impl.dimensions());\n    // Don't crash when we're called with an input tensor of size 0.\n    if (num_coeffs == 0) {\n      return;\n    }\n\n    FullReductionLauncher<Self, Op, OutputType, reducer_traits<Op, GpuDevice>::PacketAccess>::run(self, reducer, device, output, num_coeffs);\n  }\n};\n\n\ntemplate <int NumPerThread, typename Self,\n          typename Reducer, typename Index>\n__global__ void InnerReductionKernel(Reducer reducer, const Self input, Index num_coeffs_to_reduce, Index num_preserved_coeffs,\n                                         typename Self::CoeffReturnType* output) {\n#if __CUDA_ARCH__ >= 300\n  typedef typename Self::CoeffReturnType Type;\n  eigen_assert(blockDim.y == 1);\n  eigen_assert(blockDim.z == 1);\n  eigen_assert(gridDim.y == 1);\n  eigen_assert(gridDim.z == 1);\n\n  const int unroll_times = 16;\n  eigen_assert(NumPerThread % unroll_times == 0);\n\n  const Index input_col_blocks = divup<Index>(num_coeffs_to_reduce, blockDim.x * NumPerThread);\n  const Index num_input_blocks = input_col_blocks * num_preserved_coeffs;\n\n  const Index num_threads = blockDim.x * gridDim.x;\n  const Index thread_id = blockIdx.x * blockDim.x + threadIdx.x;\n\n  // Initialize the output values if they weren't initialized by the ReductionInitKernel\n  if (gridDim.x == 1) {\n    for (Index i = thread_id; i < num_preserved_coeffs; i += num_threads) {\n      output[i] = reducer.initialize();\n    }\n    __syncthreads();\n  }\n\n  for (Index i = blockIdx.x; i < num_input_blocks; i += gridDim.x) {\n    const Index row = i / input_col_blocks;\n\n    if (row < num_preserved_coeffs) {\n      const Index col_block = i % input_col_blocks;\n      const Index col_begin = col_block * blockDim.x * NumPerThread + threadIdx.x;\n\n      Type reduced_val = reducer.initialize();\n\n      for (Index j = 0; j < NumPerThread; j += unroll_times) {\n        const Index last_col = col_begin + blockDim.x * (j + unroll_times - 1);\n        if (last_col >= num_coeffs_to_reduce) {\n          for (Index col = col_begin + blockDim.x * j; col < num_coeffs_to_reduce; col += blockDim.x) {\n            const Type val = input.m_impl.coeff(row * num_coeffs_to_reduce + col);\n            reducer.reduce(val, &reduced_val);\n          }\n          break;\n        } else {\n          // Faster version of the loop with no branches after unrolling.\n#pragma unroll\n          for (int k = 0; k < unroll_times; ++k) {\n            const Index col = col_begin + blockDim.x * (j + k);\n            reducer.reduce(input.m_impl.coeff(row * num_coeffs_to_reduce + col), &reduced_val);\n          }\n        }\n      }\n\n#pragma unroll\n      for (int offset = warpSize/2; offset > 0; offset /= 2) {\n        reducer.reduce(__shfl_down(reduced_val, offset), &reduced_val);\n      }\n\n      if ((threadIdx.x & (warpSize - 1)) == 0) {\n        atomicReduce(&(output[row]), reduced_val, reducer);\n      }\n    }\n  }\n#else\n  assert(0 && \"Shouldn't be called on unsupported device\");\n#endif\n}\n\n#ifdef EIGEN_HAS_CUDA_FP16\n\ntemplate <int NumPerThread, typename Self,\n          typename Reducer, typename Index>\n__global__ void InnerReductionKernelHalfFloat(Reducer reducer, const Self input, Index num_coeffs_to_reduce, Index num_preserved_coeffs,\n                                              half* output) {\n  eigen_assert(blockDim.y == 1);\n  eigen_assert(blockDim.z == 1);\n  eigen_assert(gridDim.y == 1);\n  eigen_assert(gridDim.z == 1);\n\n  const int unroll_times = 16;\n  eigen_assert(NumPerThread % unroll_times == 0);\n  eigen_assert(unroll_times % 2 == 0);\n\n  const Index input_col_blocks = divup<Index>(num_coeffs_to_reduce, blockDim.x * NumPerThread * 2);\n  const Index num_input_blocks = divup<Index>(input_col_blocks * num_preserved_coeffs, 2);\n\n  const Index num_threads = blockDim.x * gridDim.x;\n  const Index thread_id = blockIdx.x * blockDim.x + threadIdx.x;\n\n  // Initialize the output values if they weren't initialized by the ReductionInitKernel\n  if (gridDim.x == 1) {\n    Index i = 2*thread_id;\n    for (; i + 1 < num_preserved_coeffs; i += 2*num_threads) {\n      half* loc = output + i;\n      *((half2*)loc) = reducer.template initializePacket<half2>();\n    }\n    if (i < num_preserved_coeffs) {\n      output[i] = reducer.initialize();\n    }\n    __syncthreads();\n  }\n\n  for (Index i = blockIdx.x; i < num_input_blocks; i += gridDim.x) {\n    const Index row = 2 * (i / input_col_blocks);\n\n    if (row + 1 < num_preserved_coeffs) {\n      const Index col_block = i % input_col_blocks;\n      const Index col_begin = 2 * (col_block * blockDim.x * NumPerThread + threadIdx.x);\n\n      half2 reduced_val1 = reducer.template initializePacket<half2>();\n      half2 reduced_val2 = reducer.template initializePacket<half2>();\n\n      for (Index j = 0; j < NumPerThread; j += unroll_times) {\n        const Index last_col = col_begin + blockDim.x * (j + unroll_times - 1) * 2;\n        if (last_col >= num_coeffs_to_reduce) {\n          Index col = col_begin + blockDim.x * j;\n          for (; col + 1 < num_coeffs_to_reduce; col += blockDim.x) {\n            const half2 val1 = input.m_impl.template packet<Unaligned>(row * num_coeffs_to_reduce + col);\n            reducer.reducePacket(val1, &reduced_val1);\n            const half2 val2 = input.m_impl.template packet<Unaligned>((row+1) * num_coeffs_to_reduce + col);\n            reducer.reducePacket(val2, &reduced_val2);\n          }\n          if (col < num_coeffs_to_reduce) {\n            // Peel;\n            const half last1 = input.m_impl.coeff(row * num_coeffs_to_reduce + col);\n            const half2 val1 = __halves2half2(last1, reducer.initialize());\n            reducer.reducePacket(val1, &reduced_val1);\n            const half last2 = input.m_impl.coeff((row+1) * num_coeffs_to_reduce + col);\n            const half2 val2 = __halves2half2(last2, reducer.initialize());\n            reducer.reducePacket(val2, &reduced_val2);\n          }\n          break;\n        } else {\n          // Faster version of the loop with no branches after unrolling.\n#pragma unroll\n          for (int k = 0; k < unroll_times; ++k) {\n            const Index col = col_begin + blockDim.x * (j + k) * 2;\n            reducer.reducePacket(input.m_impl.template packet<Unaligned>(row * num_coeffs_to_reduce + col), &reduced_val1);\n            reducer.reducePacket(input.m_impl.template packet<Unaligned>((row + 1)* num_coeffs_to_reduce + col), &reduced_val2);\n          }\n        }\n      }\n\n#pragma unroll\n      for (int offset = warpSize/2; offset > 0; offset /= 2) {\n        reducer.reducePacket(__shfl_down(reduced_val1, offset, warpSize), &reduced_val1);\n        reducer.reducePacket(__shfl_down(reduced_val2, offset, warpSize), &reduced_val2);\n      }\n\n      half val1 =  __low2half(reduced_val1);\n      reducer.reduce(__high2half(reduced_val1), &val1);\n      half val2 =  __low2half(reduced_val2);\n      reducer.reduce(__high2half(reduced_val2), &val2);\n      half2 val = __halves2half2(val1, val2);\n\n      if ((threadIdx.x & (warpSize - 1)) == 0) {\n        half* loc = output + row;\n        atomicReduce((half2*)loc, val, reducer);\n      }\n    }\n  }\n}\n\n#endif\n\ntemplate <typename Self, typename Op, typename OutputType, bool PacketAccess, typename Enabled = void>\nstruct InnerReductionLauncher {\n  static EIGEN_DEVICE_FUNC bool run(const Self&, Op&, const GpuDevice&, OutputType*, typename Self::Index, typename Self::Index) {\n    assert(false && \"Should only be called to reduce doubles, floats and half floats on a gpu device\");\n    return true;\n  }\n};\n\n// Specialization for float and double\ntemplate <typename Self, typename Op, typename OutputType, bool PacketAccess>\nstruct InnerReductionLauncher<\n  Self, Op, OutputType, PacketAccess,\n  typename internal::enable_if<\n    internal::is_same<float, OutputType>::value ||\n    internal::is_same<double, OutputType>::value,\n  void>::type> {\n  static bool run(const Self& self, Op& reducer, const GpuDevice& device, OutputType* output, typename Self::Index num_coeffs_to_reduce, typename Self::Index num_preserved_vals) {\n    typedef typename Self::Index Index;\n\n    const Index num_coeffs = num_coeffs_to_reduce * num_preserved_vals;\n    const int block_size = 256;\n    const int num_per_thread = 128;\n    const int dyn_blocks = divup<int>(num_coeffs, block_size * num_per_thread);\n    const int max_blocks = device.getNumCudaMultiProcessors() *\n                           device.maxCudaThreadsPerMultiProcessor() / block_size;\n    const int num_blocks = numext::mini<int>(max_blocks, dyn_blocks);\n\n    if (num_blocks > 1) {\n      // We initialize the outputs outside the reduction kernel when we can't be sure that there\n      // won't be a race conditions between multiple thread blocks.\n      const int dyn_blocks = divup<int>(num_preserved_vals, 1024);\n      const int max_blocks = device.getNumCudaMultiProcessors() *\n                           device.maxCudaThreadsPerMultiProcessor() / 1024;\n      const int num_blocks = numext::mini<int>(max_blocks, dyn_blocks);\n      LAUNCH_CUDA_KERNEL((ReductionInitKernel<OutputType, Index>),\n                         num_blocks, 1024, 0, device, reducer.initialize(),\n                         num_preserved_vals, output);\n    }\n\n    LAUNCH_CUDA_KERNEL((InnerReductionKernel<num_per_thread, Self, Op, Index>),\n                       num_blocks, block_size, 0, device, reducer, self, num_coeffs_to_reduce, num_preserved_vals, output);\n\n    return false;\n  }\n};\n\n#ifdef EIGEN_HAS_CUDA_FP16\ntemplate <typename Self, typename Op>\nstruct InnerReductionLauncher<Self, Op, Eigen::half, false> {\n  static bool run(const Self&, Op&, const GpuDevice&, half*, typename Self::Index, typename Self::Index) {\n    assert(false && \"Should not be called since there is no packet accessor\");\n    return true;\n  }\n};\n\ntemplate <typename Self, typename Op>\nstruct InnerReductionLauncher<Self, Op, Eigen::half, true> {\n  static bool run(const Self& self, Op& reducer, const GpuDevice& device, half* output, typename Self::Index num_coeffs_to_reduce, typename Self::Index num_preserved_vals) {\n    typedef typename Self::Index Index;\n\n    if (num_preserved_vals % 2 != 0) {\n      // Not supported yet, revert to the slower code path\n      return true;\n    }\n\n    const Index num_coeffs = num_coeffs_to_reduce * num_preserved_vals;\n    const int block_size = /*256*/128;\n    const int num_per_thread = /*128*/64;\n    const int dyn_blocks = divup<int>(num_coeffs, block_size * num_per_thread);\n    const int max_blocks = device.getNumCudaMultiProcessors() *\n                           device.maxCudaThreadsPerMultiProcessor() / block_size;\n    const int num_blocks = numext::mini<int>(max_blocks, dyn_blocks);\n\n    if (num_blocks > 1) {\n      // We initialize the outputs outside the reduction kernel when we can't be sure that there\n      // won't be a race conditions between multiple thread blocks.\n      const int dyn_blocks = divup<int>(num_preserved_vals, 1024);\n      const int max_blocks = device.getNumCudaMultiProcessors() *\n                           device.maxCudaThreadsPerMultiProcessor() / 1024;\n      const int num_blocks = numext::mini<int>(max_blocks, dyn_blocks);\n      LAUNCH_CUDA_KERNEL((ReductionInitKernelHalfFloat<Self, Op, Index>),\n                         1, 1, 0, device, reducer, self, num_preserved_vals, output);\n    }\n\n    LAUNCH_CUDA_KERNEL((InnerReductionKernelHalfFloat<num_per_thread, Self, Op, Index>),\n                       num_blocks, block_size, 0, device, reducer, self, num_coeffs_to_reduce, num_preserved_vals, output);\n\n    return false;\n  }\n};\n#endif\n\n\ntemplate <typename Self, typename Op>\nstruct InnerReducer<Self, Op, GpuDevice> {\n  // Unfortunately nvidia doesn't support well exotic types such as complex,\n  // so reduce the scope of the optimized version of the code to the simple case\n  // of floats and half floats.\n#ifdef EIGEN_HAS_CUDA_FP16\n  static const bool HasOptimizedImplementation = !Op::IsStateful &&\n      (internal::is_same<typename Self::CoeffReturnType, float>::value ||\n       internal::is_same<typename Self::CoeffReturnType, double>::value ||\n       (internal::is_same<typename Self::CoeffReturnType, Eigen::half>::value && reducer_traits<Op, GpuDevice>::PacketAccess));\n#else\n  static const bool HasOptimizedImplementation = !Op::IsStateful &&\n                                                 (internal::is_same<typename Self::CoeffReturnType, float>::value ||\n                                                  internal::is_same<typename Self::CoeffReturnType, double>::value);\n#endif\n\n  template <typename OutputType>\n  static bool run(const Self& self, Op& reducer, const GpuDevice& device, OutputType* output, typename Self::Index num_coeffs_to_reduce, typename Self::Index num_preserved_vals) {\n    assert(HasOptimizedImplementation && \"Should only be called on doubles, floats or half floats\");\n    const Index num_coeffs = array_prod(self.m_impl.dimensions());\n    // Don't crash when we're called with an input tensor of size 0.\n    if (num_coeffs == 0) {\n      return true;\n    }\n    // It's faster to use the usual code.\n    if (num_coeffs_to_reduce <= 128) {\n      return true;\n    }\n\n    return InnerReductionLauncher<Self, Op, OutputType, reducer_traits<Op, GpuDevice>::PacketAccess>::run(self, reducer, device, output, num_coeffs_to_reduce, num_preserved_vals);\n  }\n};\n\ntemplate <int NumPerThread, typename Self,\n          typename Reducer, typename Index>\n__global__ void OuterReductionKernel(Reducer reducer, const Self input, Index num_coeffs_to_reduce, Index num_preserved_coeffs,\n                                     typename Self::CoeffReturnType* output) {\n  const Index num_threads = blockDim.x * gridDim.x;\n  const Index thread_id = blockIdx.x * blockDim.x + threadIdx.x;\n  // Initialize the output values if they weren't initialized by the ReductionInitKernel\n  if (gridDim.x == 1) {\n    for (Index i = thread_id; i < num_preserved_coeffs; i += num_threads) {\n      output[i] = reducer.initialize();\n    }\n    __syncthreads();\n  }\n\n  // Do the reduction.\n  const Index max_iter = num_preserved_coeffs * divup<Index>(num_coeffs_to_reduce, NumPerThread);\n  for (Index i = thread_id; i < max_iter; i += num_threads) {\n    const Index input_col = i % num_preserved_coeffs;\n    const Index input_row = (i / num_preserved_coeffs) * NumPerThread;\n    typename Self::CoeffReturnType reduced_val = reducer.initialize();\n    const Index max_row = numext::mini(input_row + NumPerThread, num_coeffs_to_reduce);\n    for (Index j = input_row; j < max_row; j++) {\n      typename Self::CoeffReturnType val = input.m_impl.coeff(j * num_preserved_coeffs + input_col);\n      reducer.reduce(val, &reduced_val);\n    }\n    atomicReduce(&(output[input_col]), reduced_val, reducer);\n  }\n}\n\n\ntemplate <typename Self, typename Op>\nstruct OuterReducer<Self, Op, GpuDevice> {\n  // Unfortunately nvidia doesn't support well exotic types such as complex,\n  // so reduce the scope of the optimized version of the code to the simple case\n  // of floats.\n  static const bool HasOptimizedImplementation = !Op::IsStateful &&\n                                                 (internal::is_same<typename Self::CoeffReturnType, float>::value ||\n                                                  internal::is_same<typename Self::CoeffReturnType, double>::value);\n  template <typename Device, typename OutputType>\n  static EIGEN_DEVICE_FUNC bool run(const Self&, Op&, const Device&, OutputType*, typename Self::Index, typename Self::Index) {\n    assert(false && \"Should only be called to reduce doubles or floats on a gpu device\");\n    return true;\n  }\n\n  static bool run(const Self& self, Op& reducer, const GpuDevice& device, float* output, typename Self::Index num_coeffs_to_reduce, typename Self::Index num_preserved_vals) {\n    typedef typename Self::Index Index;\n\n    // It's faster to use the usual code.\n    if (num_coeffs_to_reduce <= 32) {\n      return true;\n    }\n\n    const Index num_coeffs = num_coeffs_to_reduce * num_preserved_vals;\n    const int block_size = 256;\n    const int num_per_thread = 16;\n    const int dyn_blocks = divup<int>(num_coeffs, block_size * num_per_thread);\n    const int max_blocks = device.getNumCudaMultiProcessors() *\n                           device.maxCudaThreadsPerMultiProcessor() / block_size;\n    const int num_blocks = numext::mini<int>(max_blocks, dyn_blocks);\n\n    if (num_blocks > 1) {\n      // We initialize the outputs in the reduction kernel itself when we don't have to worry\n      // about race conditions between multiple thread blocks.\n      const int dyn_blocks = divup<int>(num_preserved_vals, 1024);\n      const int max_blocks = device.getNumCudaMultiProcessors() *\n                             device.maxCudaThreadsPerMultiProcessor() / 1024;\n      const int num_blocks = numext::mini<int>(max_blocks, dyn_blocks);\n      LAUNCH_CUDA_KERNEL((ReductionInitKernel<float, Index>),\n                         num_blocks, 1024, 0, device, reducer.initialize(),\n                         num_preserved_vals, output);\n    }\n\n    LAUNCH_CUDA_KERNEL((OuterReductionKernel<num_per_thread, Self, Op, Index>),\n                       num_blocks, block_size, 0, device, reducer, self, num_coeffs_to_reduce, num_preserved_vals, output);\n\n    return false;\n  }\n};\n\n#endif\n\n\n} // end namespace internal\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_REDUCTION_CUDA_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorReductionSycl.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Mehdi Goli    Codeplay Software Ltd.\n// Ralph Potter  Codeplay Software Ltd.\n// Luke Iwanski  Codeplay Software Ltd.\n// Contact: <eigen@codeplay.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n/*****************************************************************\n * TensorSyclPlaceHolderExpr.h\n *\n * \\brief:\n *  This is the specialisation of the placeholder expression based on the\n * operation type\n *\n*****************************************************************/\n\n#ifndef UNSUPPORTED_EIGEN_CXX11_SRC_TENSOR_TENSOR_REDUCTION_SYCL_HPP\n#define UNSUPPORTED_EIGEN_CXX11_SRC_TENSOR_TENSOR_REDUCTION_SYCL_HPP\n\nnamespace Eigen {\nnamespace internal {\n\ntemplate<typename CoeffReturnType, typename KernelName> struct syclGenericBufferReducer{\ntemplate<typename BufferTOut, typename BufferTIn>\nstatic void run(BufferTOut* bufOut, BufferTIn& bufI, const Eigen::SyclDevice& dev, size_t length, size_t local){\n  do {\n          auto f = [length, local, bufOut, &bufI](cl::sycl::handler& h) mutable {\n            cl::sycl::nd_range<1> r{cl::sycl::range<1>{std::max(length, local)},\n                                    cl::sycl::range<1>{std::min(length, local)}};\n            /* Two accessors are used: one to the buffer that is being reduced,\n             * and a second to local memory, used to store intermediate data. */\n            auto aI =\n                bufI.template get_access<cl::sycl::access::mode::read_write>(h);\n            auto aOut =\n                bufOut->template get_access<cl::sycl::access::mode::discard_write>(h);\n            cl::sycl::accessor<CoeffReturnType, 1, cl::sycl::access::mode::read_write,\n                               cl::sycl::access::target::local>\n                scratch(cl::sycl::range<1>(local), h);\n\n            /* The parallel_for invocation chosen is the variant with an nd_item\n             * parameter, since the code requires barriers for correctness. */\n            h.parallel_for<KernelName>(\n                r, [aOut, aI, scratch, local, length](cl::sycl::nd_item<1> id) {\n                  size_t globalid = id.get_global(0);\n                  size_t localid = id.get_local(0);\n                  /* All threads collectively read from global memory into local.\n                   * The barrier ensures all threads' IO is resolved before\n                   * execution continues (strictly speaking, all threads within\n                   * a single work-group - there is no co-ordination between\n                   * work-groups, only work-items). */\n                  if (globalid < length) {\n                    scratch[localid] = aI[globalid];\n                  }\n                  id.barrier(cl::sycl::access::fence_space::local_space);\n\n                  /* Apply the reduction operation between the current local\n                   * id and the one on the other half of the vector. */\n                  if (globalid < length) {\n                    int min = (length < local) ? length : local;\n                    for (size_t offset = min / 2; offset > 0; offset /= 2) {\n                      if (localid < offset) {\n                        scratch[localid] += scratch[localid + offset];\n                      }\n                      id.barrier(cl::sycl::access::fence_space::local_space);\n                    }\n                    /* The final result will be stored in local id 0. */\n                    if (localid == 0) {\n                      aI[id.get_group(0)] = scratch[localid];\n                      if((length<=local) && globalid ==0){\n                        aOut[globalid]=scratch[localid];\n                      }\n                    }\n                  }\n                });\n          };\n            dev.m_queue.submit(f);\n            dev.m_queue.throw_asynchronous();\n\n          /* At this point, you could queue::wait_and_throw() to ensure that\n           * errors are caught quickly. However, this would likely impact\n           * performance negatively. */\n          length = length / local;\n\n        } while (length > 1);\n\n\n\n}\n\n};\n\n/// For now let's start with a full reducer\n/// Self is useless here because in expression construction we are going to treat reduction as a leafnode.\n/// we want to take reduction child and then build a construction and apply the full reducer function on it. Fullreducre applies the\n/// reduction operation on the child of the reduction. once it is done the reduction is an empty shell and can be thrown away and treated as\n// a leafNode.\ntemplate <typename Self, typename Op, bool Vectorizable>\nstruct FullReducer<Self, Op, const Eigen::SyclDevice, Vectorizable> {\n\n  typedef typename Self::CoeffReturnType CoeffReturnType;\n  static const bool HasOptimizedImplementation = false;\n\n  static void run(const Self& self, Op& reducer, const Eigen::SyclDevice& dev, CoeffReturnType* output) {\n    typedef const typename Self::ChildType HostExpr; /// this is the child of reduction\n    typedef  typename TensorSycl::internal::createPlaceHolderExpression<HostExpr>::Type PlaceHolderExpr;\n    auto functors = TensorSycl::internal::extractFunctors(self.impl());\n    int red_factor =256; /// initial reduction. If the size is less than red_factor we only creates one thread.\n    size_t inputSize =self.impl().dimensions().TotalSize();\n    size_t rng = inputSize/red_factor; // the total number of thread initially is half the size of the input\n    size_t remaining = inputSize% red_factor;\n    if(rng ==0) {\n      red_factor=1;\n    };\n    size_t tileSize =dev.m_queue.get_device(). template get_info<cl::sycl::info::device::max_work_group_size>()/2;\n    size_t GRange=std::max((size_t )1, rng);\n\n    // convert global range to power of 2 for redecution\n    GRange--;\n    GRange |= GRange >> 1;\n    GRange |= GRange >> 2;\n    GRange |= GRange >> 4;\n    GRange |= GRange >> 8;\n    GRange |= GRange >> 16;\n#if __x86_64__ || __ppc64__ || _WIN64\n    GRange |= GRange >> 32;\n#endif\n    GRange++;\n    size_t  outTileSize = tileSize;\n    /// if the shared memory is less than the GRange, we set shared_mem size to the TotalSize and in this case one kernel would be created for recursion to reduce all to one.\n    if (GRange < outTileSize) outTileSize=GRange;\n    // getting final out buffer at the moment the created buffer is true because there is no need for assign\n    auto out_buffer =dev.template get_sycl_buffer<typename Eigen::internal::remove_all<CoeffReturnType>::type>(self.dimensions().TotalSize(), output);\n    /// creating the shared memory for calculating reduction.\n    /// This one is used to collect all the reduced value of shared memory as we dont have global barrier on GPU. Once it is saved we can\n    /// recursively apply reduction on it in order to reduce the whole.\n    auto temp_global_buffer =cl::sycl::buffer<CoeffReturnType, 1>(cl::sycl::range<1>(GRange));\n    typedef typename Eigen::internal::remove_all<decltype(self.xprDims())>::type Dims;\n    Dims dims= self.xprDims();\n    Op functor = reducer;\n    dev.m_queue.submit([&](cl::sycl::handler &cgh) {\n      // create a tuple of accessors from Evaluator\n      auto tuple_of_accessors =  TensorSycl::internal::createTupleOfAccessors(cgh, self.impl());\n      auto tmp_global_accessor = temp_global_buffer. template get_access<cl::sycl::access::mode::read_write, cl::sycl::access::target::global_buffer>(cgh);\n\n      cgh.parallel_for<PlaceHolderExpr>( cl::sycl::nd_range<1>(cl::sycl::range<1>(GRange), cl::sycl::range<1>(outTileSize)), [=](cl::sycl::nd_item<1> itemID) {\n        typedef typename TensorSycl::internal::ConvertToDeviceExpression<const HostExpr>::Type DevExpr;\n        auto device_expr = TensorSycl::internal::createDeviceExpression<DevExpr, PlaceHolderExpr>(functors, tuple_of_accessors);\n        /// reduction cannot be captured automatically through our device conversion recursion. The reason is that reduction has two behaviour\n        /// the first behaviour is when it is used as a root to lauch the sub-kernel. The second one is when it is treated as a leafnode to pass the\n        /// calculated result to its parent kernel. While the latter is automatically detected through our device expression generator. The former is created here.\n        const auto device_self_expr= TensorReductionOp<Op, Dims, decltype(device_expr.expr) ,MakeGlobalPointer>(device_expr.expr, dims, functor);\n        /// This is the evaluator for device_self_expr. This is exactly similar to the self which has been passed to run function. The difference is\n        /// the device_evaluator is detectable and recognisable on the device.\n        auto device_self_evaluator = Eigen::TensorEvaluator<decltype(device_self_expr), Eigen::DefaultDevice>(device_self_expr, Eigen::DefaultDevice());\n        /// const cast added as a naive solution to solve the qualifier drop error\n        auto globalid=itemID.get_global_linear_id();\n\n        if(globalid<rng)\n          tmp_global_accessor.get_pointer()[globalid]=InnerMostDimReducer<decltype(device_self_evaluator), Op, false>::reduce(device_self_evaluator, red_factor*globalid, red_factor, const_cast<Op&>(functor));\n        else\n          tmp_global_accessor.get_pointer()[globalid]=static_cast<CoeffReturnType>(0);\n\n        if(remaining!=0 && globalid==0 )\n          // this will add the rest of input buffer when the input size is not devidable to red_factor.\n          tmp_global_accessor.get_pointer()[globalid]+=InnerMostDimReducer<decltype(device_self_evaluator), Op, false>::reduce(device_self_evaluator, red_factor*(rng), remaining, const_cast<Op&>(functor));\n      });\n    });\n  dev.m_queue.throw_asynchronous();\n\n/// This is used to recursively reduce the tmp value to an element of 1;\n  syclGenericBufferReducer<CoeffReturnType,HostExpr>::run(out_buffer, temp_global_buffer,dev, GRange,  outTileSize);\n  }\n\n};\n\ntemplate <typename Self, typename Op>\nstruct InnerReducer<Self, Op, const Eigen::SyclDevice> {\n\n  typedef typename Self::CoeffReturnType CoeffReturnType;\n  static const bool HasOptimizedImplementation = false;\n\n  static bool run(const Self& self, Op& reducer, const Eigen::SyclDevice& dev, CoeffReturnType* output, typename Self::Index , typename Self::Index num_coeffs_to_preserve) {\n    typedef const typename Self::ChildType HostExpr; /// this is the child of reduction\n    typedef  typename TensorSycl::internal::createPlaceHolderExpression<HostExpr>::Type PlaceHolderExpr;\n    auto functors = TensorSycl::internal::extractFunctors(self.impl());\n\n    size_t tileSize =dev.m_queue.get_device(). template get_info<cl::sycl::info::device::max_work_group_size>()/2;\n\n    size_t GRange=num_coeffs_to_preserve;\n    if (tileSize>GRange) tileSize=GRange;\n    else if(GRange>tileSize){\n      size_t xMode = GRange % tileSize;\n      if (xMode != 0) GRange += (tileSize - xMode);\n    }\n    // getting final out buffer at the moment the created buffer is true because there is no need for assign\n    /// creating the shared memory for calculating reduction.\n    /// This one is used to collect all the reduced value of shared memory as we dont have global barrier on GPU. Once it is saved we can\n    /// recursively apply reduction on it in order to reduce the whole.\n    typedef typename Eigen::internal::remove_all<decltype(self.xprDims())>::type Dims;\n    Dims dims= self.xprDims();\n    Op functor = reducer;\n\n    dev.m_queue.submit([&](cl::sycl::handler &cgh) {\n      // create a tuple of accessors from Evaluator\n      auto tuple_of_accessors =  TensorSycl::internal::createTupleOfAccessors(cgh, self.impl());\n      auto output_accessor = dev.template get_sycl_accessor<cl::sycl::access::mode::discard_write>(num_coeffs_to_preserve,cgh, output);\n\n      cgh.parallel_for<Self>( cl::sycl::nd_range<1>(cl::sycl::range<1>(GRange), cl::sycl::range<1>(tileSize)), [=](cl::sycl::nd_item<1> itemID) {\n        typedef typename TensorSycl::internal::ConvertToDeviceExpression<const HostExpr>::Type DevExpr;\n        auto device_expr = TensorSycl::internal::createDeviceExpression<DevExpr, PlaceHolderExpr>(functors, tuple_of_accessors);\n        /// reduction cannot be captured automatically through our device conversion recursion. The reason is that reduction has two behaviour\n        /// the first behaviour is when it is used as a root to lauch the sub-kernel. The second one is when it is treated as a leafnode to pass the\n        /// calculated result to its parent kernel. While the latter is automatically detected through our device expression generator. The former is created here.\n        const auto device_self_expr= TensorReductionOp<Op, Dims, decltype(device_expr.expr) ,MakeGlobalPointer>(device_expr.expr, dims, functor);\n        /// This is the evaluator for device_self_expr. This is exactly similar to the self which has been passed to run function. The difference is\n        /// the device_evaluator is detectable and recognisable on the device.\n        typedef Eigen::TensorEvaluator<decltype(device_self_expr), Eigen::DefaultDevice> DeiceSelf;\n        auto device_self_evaluator = Eigen::TensorEvaluator<decltype(device_self_expr), Eigen::DefaultDevice>(device_self_expr, Eigen::DefaultDevice());\n        /// const cast added as a naive solution to solve the qualifier drop error\n        auto globalid=itemID.get_global_linear_id();\n        if (globalid< static_cast<size_t>(num_coeffs_to_preserve)) {\n          typename DeiceSelf::CoeffReturnType accum = functor.initialize();\n          GenericDimReducer<DeiceSelf::NumReducedDims-1, DeiceSelf, Op>::reduce(device_self_evaluator, device_self_evaluator.firstInput(globalid),const_cast<Op&>(functor), &accum);\n          functor.finalize(accum);\n          output_accessor.get_pointer()[globalid]= accum;\n        }\n      });\n    });\n  dev.m_queue.throw_asynchronous();\n    return false;\n  }\n};\n\n}  // end namespace internal\n}  // namespace Eigen\n\n#endif  // UNSUPPORTED_EIGEN_CXX11_SRC_TENSOR_TENSOR_REDUCTION_SYCL_HPP\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorRef.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_REF_H\n#define EIGEN_CXX11_TENSOR_TENSOR_REF_H\n\nnamespace Eigen {\n\nnamespace internal {\n\ntemplate <typename Dimensions, typename Scalar>\nclass TensorLazyBaseEvaluator {\n public:\n  TensorLazyBaseEvaluator() : m_refcount(0) { }\n  virtual ~TensorLazyBaseEvaluator() { }\n\n  EIGEN_DEVICE_FUNC virtual const Dimensions& dimensions() const = 0;\n  EIGEN_DEVICE_FUNC virtual const Scalar* data() const = 0;\n\n  EIGEN_DEVICE_FUNC virtual const Scalar coeff(DenseIndex index) const = 0;\n  EIGEN_DEVICE_FUNC virtual Scalar& coeffRef(DenseIndex index) = 0;\n\n  void incrRefCount() { ++m_refcount; }\n  void decrRefCount() { --m_refcount; }\n  int refCount() const { return m_refcount; }\n\n private:\n  // No copy, no assigment;\n  TensorLazyBaseEvaluator(const TensorLazyBaseEvaluator& other);\n  TensorLazyBaseEvaluator& operator = (const TensorLazyBaseEvaluator& other);\n\n  int m_refcount;\n};\n\n\ntemplate <typename Dimensions, typename Expr, typename Device>\nclass TensorLazyEvaluatorReadOnly : public TensorLazyBaseEvaluator<Dimensions, typename TensorEvaluator<Expr, Device>::Scalar> {\n public:\n  //  typedef typename TensorEvaluator<Expr, Device>::Dimensions Dimensions;\n  typedef typename TensorEvaluator<Expr, Device>::Scalar Scalar;\n\n  TensorLazyEvaluatorReadOnly(const Expr& expr, const Device& device) : m_impl(expr, device), m_dummy(Scalar(0)) {\n    m_dims = m_impl.dimensions();\n    m_impl.evalSubExprsIfNeeded(NULL);\n  }\n  virtual ~TensorLazyEvaluatorReadOnly() {\n    m_impl.cleanup();\n  }\n\n  EIGEN_DEVICE_FUNC virtual const Dimensions& dimensions() const {\n    return m_dims;\n  }\n  EIGEN_DEVICE_FUNC virtual const Scalar* data() const {\n    return m_impl.data();\n  }\n\n  EIGEN_DEVICE_FUNC virtual const Scalar coeff(DenseIndex index) const {\n    return m_impl.coeff(index);\n  }\n  EIGEN_DEVICE_FUNC virtual Scalar& coeffRef(DenseIndex /*index*/) {\n    eigen_assert(false && \"can't reference the coefficient of a rvalue\");\n    return m_dummy;\n  };\n\n protected:\n  TensorEvaluator<Expr, Device> m_impl;\n  Dimensions m_dims;\n  Scalar m_dummy;\n};\n\ntemplate <typename Dimensions, typename Expr, typename Device>\nclass TensorLazyEvaluatorWritable : public TensorLazyEvaluatorReadOnly<Dimensions, Expr, Device> {\n public:\n  typedef TensorLazyEvaluatorReadOnly<Dimensions, Expr, Device> Base;\n  typedef typename Base::Scalar Scalar;\n\n  TensorLazyEvaluatorWritable(const Expr& expr, const Device& device) : Base(expr, device) {\n  }\n  virtual ~TensorLazyEvaluatorWritable() {\n  }\n\n  EIGEN_DEVICE_FUNC virtual Scalar& coeffRef(DenseIndex index) {\n    return this->m_impl.coeffRef(index);\n  }\n};\n\ntemplate <typename Dimensions, typename Expr, typename Device>\nclass TensorLazyEvaluator : public internal::conditional<bool(internal::is_lvalue<Expr>::value),\n                            TensorLazyEvaluatorWritable<Dimensions, Expr, Device>,\n                            TensorLazyEvaluatorReadOnly<Dimensions, const Expr, Device> >::type {\n public:\n  typedef typename internal::conditional<bool(internal::is_lvalue<Expr>::value),\n                                         TensorLazyEvaluatorWritable<Dimensions, Expr, Device>,\n                                         TensorLazyEvaluatorReadOnly<Dimensions, const Expr, Device> >::type Base;\n  typedef typename Base::Scalar Scalar;\n\n  TensorLazyEvaluator(const Expr& expr, const Device& device) : Base(expr, device) {\n  }\n  virtual ~TensorLazyEvaluator() {\n  }\n};\n\n}  // namespace internal\n\n\n/** \\class TensorRef\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief A reference to a tensor expression\n  * The expression will be evaluated lazily (as much as possible).\n  *\n  */\ntemplate<typename PlainObjectType> class TensorRef : public TensorBase<TensorRef<PlainObjectType> >\n{\n  public:\n    typedef TensorRef<PlainObjectType> Self;\n    typedef typename PlainObjectType::Base Base;\n    typedef typename Eigen::internal::nested<Self>::type Nested;\n    typedef typename internal::traits<PlainObjectType>::StorageKind StorageKind;\n    typedef typename internal::traits<PlainObjectType>::Index Index;\n    typedef typename internal::traits<PlainObjectType>::Scalar Scalar;\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n    typedef typename Base::CoeffReturnType CoeffReturnType;\n    typedef Scalar* PointerType;\n    typedef PointerType PointerArgType;\n\n    static const Index NumIndices = PlainObjectType::NumIndices;\n    typedef typename PlainObjectType::Dimensions Dimensions;\n\n    enum {\n      IsAligned = false,\n      PacketAccess = false,\n      Layout = PlainObjectType::Layout,\n      CoordAccess = false,  // to be implemented\n      RawAccess = false\n    };\n\n    EIGEN_STRONG_INLINE TensorRef() : m_evaluator(NULL) {\n    }\n\n    template <typename Expression>\n    EIGEN_STRONG_INLINE TensorRef(const Expression& expr) : m_evaluator(new internal::TensorLazyEvaluator<Dimensions, Expression, DefaultDevice>(expr, DefaultDevice())) {\n      m_evaluator->incrRefCount();\n    }\n\n    template <typename Expression>\n    EIGEN_STRONG_INLINE TensorRef& operator = (const Expression& expr) {\n      unrefEvaluator();\n      m_evaluator = new internal::TensorLazyEvaluator<Dimensions, Expression, DefaultDevice>(expr, DefaultDevice());\n      m_evaluator->incrRefCount();\n      return *this;\n    }\n\n    ~TensorRef() {\n      unrefEvaluator();\n    }\n\n    TensorRef(const TensorRef& other) : m_evaluator(other.m_evaluator) {\n      eigen_assert(m_evaluator->refCount() > 0);\n      m_evaluator->incrRefCount();\n    }\n\n    TensorRef& operator = (const TensorRef& other) {\n      if (this != &other) {\n        unrefEvaluator();\n        m_evaluator = other.m_evaluator;\n        eigen_assert(m_evaluator->refCount() > 0);\n        m_evaluator->incrRefCount();\n      }\n      return *this;\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Index rank() const { return m_evaluator->dimensions().size(); }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Index dimension(Index n) const { return m_evaluator->dimensions()[n]; }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_evaluator->dimensions(); }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Index size() const { return m_evaluator->dimensions().TotalSize(); }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar* data() const { return m_evaluator->data(); }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar operator()(Index index) const\n    {\n      return m_evaluator->coeff(index);\n    }\n\n#if EIGEN_HAS_VARIADIC_TEMPLATES\n    template<typename... IndexTypes> EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar operator()(Index firstIndex, IndexTypes... otherIndices) const\n    {\n      const std::size_t num_indices = (sizeof...(otherIndices) + 1);\n      const array<Index, num_indices> indices{{firstIndex, otherIndices...}};\n      return coeff(indices);\n    }\n    template<typename... IndexTypes> EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar& coeffRef(Index firstIndex, IndexTypes... otherIndices)\n    {\n      const std::size_t num_indices = (sizeof...(otherIndices) + 1);\n      const array<Index, num_indices> indices{{firstIndex, otherIndices...}};\n      return coeffRef(indices);\n    }\n#else\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar operator()(Index i0, Index i1) const\n    {\n      array<Index, 2> indices;\n      indices[0] = i0;\n      indices[1] = i1;\n      return coeff(indices);\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar operator()(Index i0, Index i1, Index i2) const\n    {\n      array<Index, 3> indices;\n      indices[0] = i0;\n      indices[1] = i1;\n      indices[2] = i2;\n      return coeff(indices);\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar operator()(Index i0, Index i1, Index i2, Index i3) const\n    {\n      array<Index, 4> indices;\n      indices[0] = i0;\n      indices[1] = i1;\n      indices[2] = i2;\n      indices[3] = i3;\n      return coeff(indices);\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar operator()(Index i0, Index i1, Index i2, Index i3, Index i4) const\n    {\n      array<Index, 5> indices;\n      indices[0] = i0;\n      indices[1] = i1;\n      indices[2] = i2;\n      indices[3] = i3;\n      indices[4] = i4;\n      return coeff(indices);\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar& coeffRef(Index i0, Index i1)\n    {\n      array<Index, 2> indices;\n      indices[0] = i0;\n      indices[1] = i1;\n      return coeffRef(indices);\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar& coeffRef(Index i0, Index i1, Index i2)\n    {\n      array<Index, 3> indices;\n      indices[0] = i0;\n      indices[1] = i1;\n      indices[2] = i2;\n      return coeffRef(indices);\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar& operator()(Index i0, Index i1, Index i2, Index i3)\n    {\n      array<Index, 4> indices;\n      indices[0] = i0;\n      indices[1] = i1;\n      indices[2] = i2;\n      indices[3] = i3;\n      return coeffRef(indices);\n    }\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar& coeffRef(Index i0, Index i1, Index i2, Index i3, Index i4)\n    {\n      array<Index, 5> indices;\n      indices[0] = i0;\n      indices[1] = i1;\n      indices[2] = i2;\n      indices[3] = i3;\n      indices[4] = i4;\n      return coeffRef(indices);\n    }\n#endif\n\n    template <std::size_t NumIndices> EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar coeff(const array<Index, NumIndices>& indices) const\n    {\n      const Dimensions& dims = this->dimensions();\n      Index index = 0;\n      if (PlainObjectType::Options & RowMajor) {\n        index += indices[0];\n        for (size_t i = 1; i < NumIndices; ++i) {\n          index = index * dims[i] + indices[i];\n        }\n      } else {\n        index += indices[NumIndices-1];\n        for (int i = NumIndices-2; i >= 0; --i) {\n          index = index * dims[i] + indices[i];\n        }\n      }\n      return m_evaluator->coeff(index);\n    }\n    template <std::size_t NumIndices> EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar& coeffRef(const array<Index, NumIndices>& indices)\n    {\n      const Dimensions& dims = this->dimensions();\n      Index index = 0;\n      if (PlainObjectType::Options & RowMajor) {\n        index += indices[0];\n        for (size_t i = 1; i < NumIndices; ++i) {\n          index = index * dims[i] + indices[i];\n        }\n      } else {\n        index += indices[NumIndices-1];\n        for (int i = NumIndices-2; i >= 0; --i) {\n          index = index * dims[i] + indices[i];\n        }\n      }\n      return m_evaluator->coeffRef(index);\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE const Scalar coeff(Index index) const\n    {\n      return m_evaluator->coeff(index);\n    }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE Scalar& coeffRef(Index index)\n    {\n      return m_evaluator->coeffRef(index);\n    }\n\n  private:\n    EIGEN_STRONG_INLINE void unrefEvaluator() {\n      if (m_evaluator) {\n        m_evaluator->decrRefCount();\n        if (m_evaluator->refCount() == 0) {\n          delete m_evaluator;\n        }\n      }\n    }\n\n  internal::TensorLazyBaseEvaluator<Dimensions, Scalar>* m_evaluator;\n};\n\n\n// evaluator for rvalues\ntemplate<typename Derived, typename Device>\nstruct TensorEvaluator<const TensorRef<Derived>, Device>\n{\n  typedef typename Derived::Index Index;\n  typedef typename Derived::Scalar Scalar;\n  typedef typename Derived::Scalar CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  typedef typename Derived::Dimensions Dimensions;\n\n  enum {\n    IsAligned = false,\n    PacketAccess = false,\n    Layout = TensorRef<Derived>::Layout,\n    CoordAccess = false,  // to be implemented\n    RawAccess = false\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const TensorRef<Derived>& m, const Device&)\n      : m_ref(m)\n  { }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_ref.dimensions(); }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(Scalar*) {\n    return true;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() { }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const {\n    return m_ref.coeff(index);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index index) {\n    return m_ref.coeffRef(index);\n  }\n\n  EIGEN_DEVICE_FUNC Scalar* data() const { return m_ref.data(); }\n\n protected:\n  TensorRef<Derived> m_ref;\n};\n\n\n// evaluator for lvalues\ntemplate<typename Derived, typename Device>\nstruct TensorEvaluator<TensorRef<Derived>, Device> : public TensorEvaluator<const TensorRef<Derived>, Device>\n{\n  typedef typename Derived::Index Index;\n  typedef typename Derived::Scalar Scalar;\n  typedef typename Derived::Scalar CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  typedef typename Derived::Dimensions Dimensions;\n\n  typedef TensorEvaluator<const TensorRef<Derived>, Device> Base;\n\n  enum {\n    IsAligned = false,\n    PacketAccess = false,\n    RawAccess = false\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(TensorRef<Derived>& m, const Device& d) : Base(m, d)\n  { }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index index) {\n    return this->m_ref.coeffRef(index);\n  }\n};\n\n\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_REF_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorReverse.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Navdeep Jaitly <ndjaitly@google.com>\n//                    Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_REVERSE_H\n#define EIGEN_CXX11_TENSOR_TENSOR_REVERSE_H\nnamespace Eigen {\n\n/** \\class TensorReverse\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief Tensor reverse elements class.\n  *\n  */\nnamespace internal {\ntemplate<typename ReverseDimensions, typename XprType>\nstruct traits<TensorReverseOp<ReverseDimensions,\n                              XprType> > : public traits<XprType>\n{\n  typedef typename XprType::Scalar Scalar;\n  typedef traits<XprType> XprTraits;\n  typedef typename XprTraits::StorageKind StorageKind;\n  typedef typename XprTraits::Index Index;\n  typedef typename XprType::Nested Nested;\n  typedef typename remove_reference<Nested>::type _Nested;\n  static const int NumDimensions = XprTraits::NumDimensions;\n  static const int Layout = XprTraits::Layout;\n};\n\ntemplate<typename ReverseDimensions, typename XprType>\nstruct eval<TensorReverseOp<ReverseDimensions, XprType>, Eigen::Dense>\n{\n  typedef const TensorReverseOp<ReverseDimensions, XprType>& type;\n};\n\ntemplate<typename ReverseDimensions, typename XprType>\nstruct nested<TensorReverseOp<ReverseDimensions, XprType>, 1,\n            typename eval<TensorReverseOp<ReverseDimensions, XprType> >::type>\n{\n  typedef TensorReverseOp<ReverseDimensions, XprType> type;\n};\n\n}  // end namespace internal\n\ntemplate<typename ReverseDimensions, typename XprType>\nclass TensorReverseOp : public TensorBase<TensorReverseOp<ReverseDimensions,\n                                          XprType>, WriteAccessors>\n{\n  public:\n  typedef typename Eigen::internal::traits<TensorReverseOp>::Scalar Scalar;\n  typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename Eigen::internal::nested<TensorReverseOp>::type Nested;\n  typedef typename Eigen::internal::traits<TensorReverseOp>::StorageKind\n                                                                    StorageKind;\n  typedef typename Eigen::internal::traits<TensorReverseOp>::Index Index;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorReverseOp(\n      const XprType& expr, const ReverseDimensions& reverse_dims)\n      : m_xpr(expr), m_reverse_dims(reverse_dims) { }\n\n    EIGEN_DEVICE_FUNC\n    const ReverseDimensions& reverse() const { return m_reverse_dims; }\n\n    EIGEN_DEVICE_FUNC\n    const typename internal::remove_all<typename XprType::Nested>::type&\n    expression() const { return m_xpr; }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE TensorReverseOp& operator = (const TensorReverseOp& other)\n    {\n      typedef TensorAssignOp<TensorReverseOp, const TensorReverseOp> Assign;\n      Assign assign(*this, other);\n      internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());\n      return *this;\n    }\n\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE TensorReverseOp& operator = (const OtherDerived& other)\n    {\n      typedef TensorAssignOp<TensorReverseOp, const OtherDerived> Assign;\n      Assign assign(*this, other);\n      internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());\n      return *this;\n    }\n\n  protected:\n    typename XprType::Nested m_xpr;\n    const ReverseDimensions m_reverse_dims;\n};\n\n// Eval as rvalue\ntemplate<typename ReverseDimensions, typename ArgType, typename Device>\nstruct TensorEvaluator<const TensorReverseOp<ReverseDimensions, ArgType>, Device>\n{\n  typedef TensorReverseOp<ReverseDimensions, ArgType> XprType;\n  typedef typename XprType::Index Index;\n  static const int NumDims = internal::array_size<ReverseDimensions>::value;\n  typedef DSizes<Index, NumDims> Dimensions;\n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  static const int PacketSize = internal::unpacket_traits<PacketReturnType>::size;\n\n  enum {\n    IsAligned = false,\n    PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,\n    Layout = TensorEvaluator<ArgType, Device>::Layout,\n    CoordAccess = false,  // to be implemented\n    RawAccess = false\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op,\n                                                        const Device& device)\n      : m_impl(op.expression(), device), m_reverse(op.reverse())\n  {\n    // Reversing a scalar isn't supported yet. It would be a no-op anyway.\n    EIGEN_STATIC_ASSERT((NumDims > 0), YOU_MADE_A_PROGRAMMING_MISTAKE);\n\n    // Compute strides\n    m_dimensions = m_impl.dimensions();\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      m_strides[0] = 1;\n      for (int i = 1; i < NumDims; ++i) {\n        m_strides[i] = m_strides[i-1] * m_dimensions[i-1];\n      }\n    } else {\n      m_strides[NumDims-1] = 1;\n      for (int i = NumDims - 2; i >= 0; --i) {\n        m_strides[i] = m_strides[i+1] * m_dimensions[i+1];\n      }\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  const Dimensions& dimensions() const { return m_dimensions; }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(Scalar*) {\n    m_impl.evalSubExprsIfNeeded(NULL);\n    return true;\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {\n    m_impl.cleanup();\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index reverseIndex(\n      Index index) const {\n    eigen_assert(index < dimensions().TotalSize());\n    Index inputIndex = 0;\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      for (int i = NumDims - 1; i > 0; --i) {\n        Index idx = index / m_strides[i];\n        index -= idx * m_strides[i];\n        if (m_reverse[i]) {\n          idx = m_dimensions[i] - idx - 1;\n        }\n        inputIndex += idx * m_strides[i] ;\n      }\n      if (m_reverse[0]) {\n        inputIndex += (m_dimensions[0] - index - 1);\n      } else {\n        inputIndex += index;\n      }\n    } else {\n      for (int i = 0; i < NumDims - 1; ++i) {\n        Index idx = index / m_strides[i];\n        index -= idx * m_strides[i];\n        if (m_reverse[i]) {\n          idx = m_dimensions[i] - idx - 1;\n        }\n        inputIndex += idx * m_strides[i] ;\n      }\n      if (m_reverse[NumDims-1]) {\n        inputIndex += (m_dimensions[NumDims-1] - index - 1);\n      } else {\n        inputIndex += index;\n      }\n    }\n    return inputIndex;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(\n      Index index) const  {\n    return m_impl.coeff(reverseIndex(index));\n  }\n\n  template<int LoadMode>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  PacketReturnType packet(Index index) const\n  {\n    EIGEN_STATIC_ASSERT((PacketSize > 1), YOU_MADE_A_PROGRAMMING_MISTAKE)\n    eigen_assert(index+PacketSize-1 < dimensions().TotalSize());\n\n    // TODO(ndjaitly): write a better packing routine that uses\n    // local structure.\n    EIGEN_ALIGN_MAX typename internal::remove_const<CoeffReturnType>::type\n                                                            values[PacketSize];\n    for (int i = 0; i < PacketSize; ++i) {\n      values[i] = coeff(index+i);\n    }\n    PacketReturnType rslt = internal::pload<PacketReturnType>(values);\n    return rslt;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {\n    double compute_cost = NumDims * (2 * TensorOpCost::AddCost<Index>() +\n                                     2 * TensorOpCost::MulCost<Index>() +\n                                     TensorOpCost::DivCost<Index>());\n    for (int i = 0; i < NumDims; ++i) {\n      if (m_reverse[i]) {\n        compute_cost += 2 * TensorOpCost::AddCost<Index>();\n      }\n    }\n    return m_impl.costPerCoeff(vectorized) +\n           TensorOpCost(0, 0, compute_cost, false /* vectorized */, PacketSize);\n  }\n\n  EIGEN_DEVICE_FUNC Scalar* data() const { return NULL; }\n\n protected:\n  Dimensions m_dimensions;\n  array<Index, NumDims> m_strides;\n  TensorEvaluator<ArgType, Device> m_impl;\n  ReverseDimensions m_reverse;\n};\n\n// Eval as lvalue\n\ntemplate <typename ReverseDimensions, typename ArgType, typename Device>\nstruct TensorEvaluator<TensorReverseOp<ReverseDimensions, ArgType>, Device>\n    : public TensorEvaluator<const TensorReverseOp<ReverseDimensions, ArgType>,\n                             Device> {\n  typedef TensorEvaluator<const TensorReverseOp<ReverseDimensions, ArgType>,\n                          Device> Base;\n  typedef TensorReverseOp<ReverseDimensions, ArgType> XprType;\n  typedef typename XprType::Index Index;\n  static const int NumDims = internal::array_size<ReverseDimensions>::value;\n  typedef DSizes<Index, NumDims> Dimensions;\n\n  enum {\n    IsAligned = false,\n    PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,\n    Layout = TensorEvaluator<ArgType, Device>::Layout,\n    CoordAccess = false,  // to be implemented\n    RawAccess = false\n  };\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op,\n                                                        const Device& device)\n      : Base(op, device) {}\n\n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  static const int PacketSize = internal::unpacket_traits<PacketReturnType>::size;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  const Dimensions& dimensions() const { return this->m_dimensions; }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index index) {\n    return this->m_impl.coeffRef(this->reverseIndex(index));\n  }\n\n  template <int StoreMode> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  void writePacket(Index index, const PacketReturnType& x) {\n    EIGEN_STATIC_ASSERT((PacketSize > 1), YOU_MADE_A_PROGRAMMING_MISTAKE)\n    eigen_assert(index+PacketSize-1 < dimensions().TotalSize());\n\n    // This code is pilfered from TensorMorphing.h\n    EIGEN_ALIGN_MAX CoeffReturnType values[PacketSize];\n    internal::pstore<CoeffReturnType, PacketReturnType>(values, x);\n    for (int i = 0; i < PacketSize; ++i) {\n      this->coeffRef(index+i) = values[i];\n    }\n  }\n\n};\n\n\n}  // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_REVERSE_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorScan.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Igor Babuschkin <igor@babuschk.in>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_SCAN_H\n#define EIGEN_CXX11_TENSOR_TENSOR_SCAN_H\n\nnamespace Eigen {\n\nnamespace internal {\n\ntemplate <typename Op, typename XprType>\nstruct traits<TensorScanOp<Op, XprType> >\n    : public traits<XprType> {\n  typedef typename XprType::Scalar Scalar;\n  typedef traits<XprType> XprTraits;\n  typedef typename XprTraits::StorageKind StorageKind;\n  typedef typename XprType::Nested Nested;\n  typedef typename remove_reference<Nested>::type _Nested;\n  static const int NumDimensions = XprTraits::NumDimensions;\n  static const int Layout = XprTraits::Layout;\n};\n\ntemplate<typename Op, typename XprType>\nstruct eval<TensorScanOp<Op, XprType>, Eigen::Dense>\n{\n  typedef const TensorScanOp<Op, XprType>& type;\n};\n\ntemplate<typename Op, typename XprType>\nstruct nested<TensorScanOp<Op, XprType>, 1,\n            typename eval<TensorScanOp<Op, XprType> >::type>\n{\n  typedef TensorScanOp<Op, XprType> type;\n};\n} // end namespace internal\n\n/** \\class TensorScan\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief Tensor scan class.\n  */\ntemplate <typename Op, typename XprType>\nclass TensorScanOp\n    : public TensorBase<TensorScanOp<Op, XprType>, ReadOnlyAccessors> {\npublic:\n  typedef typename Eigen::internal::traits<TensorScanOp>::Scalar Scalar;\n  typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename Eigen::internal::nested<TensorScanOp>::type Nested;\n  typedef typename Eigen::internal::traits<TensorScanOp>::StorageKind StorageKind;\n  typedef typename Eigen::internal::traits<TensorScanOp>::Index Index;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorScanOp(\n      const XprType& expr, const Index& axis, bool exclusive = false, const Op& op = Op())\n      : m_expr(expr), m_axis(axis), m_accumulator(op), m_exclusive(exclusive) {}\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  const Index axis() const { return m_axis; }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  const XprType& expression() const { return m_expr; }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  const Op accumulator() const { return m_accumulator; }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  bool exclusive() const { return m_exclusive; }\n\nprotected:\n  typename XprType::Nested m_expr;\n  const Index m_axis;\n  const Op m_accumulator;\n  const bool m_exclusive;\n};\n\ntemplate <typename Self, typename Reducer, typename Device>\nstruct ScanLauncher;\n\n// Eval as rvalue\ntemplate <typename Op, typename ArgType, typename Device>\nstruct TensorEvaluator<const TensorScanOp<Op, ArgType>, Device> {\n\n  typedef TensorScanOp<Op, ArgType> XprType;\n  typedef typename XprType::Index Index;\n  static const int NumDims = internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value;\n  typedef DSizes<Index, NumDims> Dimensions;\n  typedef typename internal::remove_const<typename XprType::Scalar>::type Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  typedef TensorEvaluator<const TensorScanOp<Op, ArgType>, Device> Self;\n\n  enum {\n    IsAligned = false,\n    PacketAccess = (internal::unpacket_traits<PacketReturnType>::size > 1),\n    BlockAccess = false,\n    Layout = TensorEvaluator<ArgType, Device>::Layout,\n    CoordAccess = false,\n    RawAccess = true\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op,\n                                                        const Device& device)\n      : m_impl(op.expression(), device),\n        m_device(device),\n        m_exclusive(op.exclusive()),\n        m_accumulator(op.accumulator()),\n        m_size(m_impl.dimensions()[op.axis()]),\n        m_stride(1),\n        m_output(NULL) {\n\n    // Accumulating a scalar isn't supported.\n    EIGEN_STATIC_ASSERT((NumDims > 0), YOU_MADE_A_PROGRAMMING_MISTAKE);\n    eigen_assert(op.axis() >= 0 && op.axis() < NumDims);\n\n    // Compute stride of scan axis\n    const Dimensions& dims = m_impl.dimensions();\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      for (int i = 0; i < op.axis(); ++i) {\n        m_stride = m_stride * dims[i];\n      }\n    } else {\n      for (int i = NumDims - 1; i > op.axis(); --i) {\n        m_stride = m_stride * dims[i];\n      }\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const {\n    return m_impl.dimensions();\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Index& stride() const {\n    return m_stride;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Index& size() const {\n    return m_size;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Op& accumulator() const {\n    return m_accumulator;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool exclusive() const {\n    return m_exclusive;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const TensorEvaluator<ArgType, Device>& inner() const {\n    return m_impl;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Device& device() const {\n    return m_device;\n  }\n\n  EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(Scalar* data) {\n    m_impl.evalSubExprsIfNeeded(NULL);\n    ScanLauncher<Self, Op, Device> launcher;\n    if (data) {\n      launcher(*this, data);\n      return false;\n    }\n\n    const Index total_size = internal::array_prod(dimensions());\n    m_output = static_cast<CoeffReturnType*>(m_device.allocate(total_size * sizeof(Scalar)));\n    launcher(*this, m_output);\n    return true;\n  }\n\n  template<int LoadMode>\n  EIGEN_DEVICE_FUNC PacketReturnType packet(Index index) const {\n    return internal::ploadt<PacketReturnType, LoadMode>(m_output + index);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType* data() const\n  {\n    return m_output;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const\n  {\n    return m_output[index];\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool) const {\n    return TensorOpCost(sizeof(CoeffReturnType), 0, 0);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {\n    if (m_output != NULL) {\n      m_device.deallocate(m_output);\n      m_output = NULL;\n    }\n    m_impl.cleanup();\n  }\n\nprotected:\n  TensorEvaluator<ArgType, Device> m_impl;\n  const Device& m_device;\n  const bool m_exclusive;\n  Op m_accumulator;\n  const Index m_size;\n  Index m_stride;\n  CoeffReturnType* m_output;\n};\n\n// CPU implementation of scan\n// TODO(ibab) This single-threaded implementation should be parallelized,\n// at least by running multiple scans at the same time.\ntemplate <typename Self, typename Reducer, typename Device>\nstruct ScanLauncher {\n  void operator()(Self& self, typename Self::CoeffReturnType *data) {\n    Index total_size = internal::array_prod(self.dimensions());\n\n    // We fix the index along the scan axis to 0 and perform a\n    // scan per remaining entry. The iteration is split into two nested\n    // loops to avoid an integer division by keeping track of each idx1 and idx2.\n    for (Index idx1 = 0; idx1 < total_size; idx1 += self.stride() * self.size()) {\n      for (Index idx2 = 0; idx2 < self.stride(); idx2++) {\n        // Calculate the starting offset for the scan\n        Index offset = idx1 + idx2;\n\n        // Compute the scan along the axis, starting at the calculated offset\n        typename Self::CoeffReturnType accum = self.accumulator().initialize();\n        for (Index idx3 = 0; idx3 < self.size(); idx3++) {\n          Index curr = offset + idx3 * self.stride();\n\n          if (self.exclusive()) {\n            data[curr] = self.accumulator().finalize(accum);\n            self.accumulator().reduce(self.inner().coeff(curr), &accum);\n          } else {\n            self.accumulator().reduce(self.inner().coeff(curr), &accum);\n            data[curr] = self.accumulator().finalize(accum);\n          }\n        }\n      }\n    }\n  }\n};\n\n#if defined(EIGEN_USE_GPU) && defined(__CUDACC__)\n\n// GPU implementation of scan\n// TODO(ibab) This placeholder implementation performs multiple scans in\n// parallel, but it would be better to use a parallel scan algorithm and\n// optimize memory access.\ntemplate <typename Self, typename Reducer>\n__global__ void ScanKernel(Self self, Index total_size, typename Self::CoeffReturnType* data) {\n  // Compute offset as in the CPU version\n  Index val = threadIdx.x + blockIdx.x * blockDim.x;\n  Index offset = (val / self.stride()) * self.stride() * self.size() + val % self.stride();\n\n  if (offset + (self.size() - 1) * self.stride() < total_size) {\n    // Compute the scan along the axis, starting at the calculated offset\n    typename Self::CoeffReturnType accum = self.accumulator().initialize();\n    for (Index idx = 0; idx < self.size(); idx++) {\n      Index curr = offset + idx * self.stride();\n      if (self.exclusive()) {\n        data[curr] = self.accumulator().finalize(accum);\n        self.accumulator().reduce(self.inner().coeff(curr), &accum);\n      } else {\n        self.accumulator().reduce(self.inner().coeff(curr), &accum);\n        data[curr] = self.accumulator().finalize(accum);\n      }\n    }\n  }\n  __syncthreads();\n\n}\n\ntemplate <typename Self, typename Reducer>\nstruct ScanLauncher<Self, Reducer, GpuDevice> {\n  void operator()(const Self& self, typename Self::CoeffReturnType* data) {\n     Index total_size = internal::array_prod(self.dimensions());\n     Index num_blocks = (total_size / self.size() + 63) / 64;\n     Index block_size = 64;\n     LAUNCH_CUDA_KERNEL((ScanKernel<Self, Reducer>), num_blocks, block_size, 0, self.device(), self, total_size, data);\n  }\n};\n#endif  // EIGEN_USE_GPU && __CUDACC__\n\n}  // end namespace Eigen\n\n#endif  // EIGEN_CXX11_TENSOR_TENSOR_SCAN_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorShuffling.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_SHUFFLING_H\n#define EIGEN_CXX11_TENSOR_TENSOR_SHUFFLING_H\n\nnamespace Eigen {\n\n/** \\class TensorShuffling\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief Tensor shuffling class.\n  *\n  *\n  */\nnamespace internal {\ntemplate<typename Shuffle, typename XprType>\nstruct traits<TensorShufflingOp<Shuffle, XprType> > : public traits<XprType>\n{\n  typedef typename XprType::Scalar Scalar;\n  typedef traits<XprType> XprTraits;\n  typedef typename XprTraits::StorageKind StorageKind;\n  typedef typename XprTraits::Index Index;\n  typedef typename XprType::Nested Nested;\n  typedef typename remove_reference<Nested>::type _Nested;\n  static const int NumDimensions = XprTraits::NumDimensions;\n  static const int Layout = XprTraits::Layout;\n};\n\ntemplate<typename Shuffle, typename XprType>\nstruct eval<TensorShufflingOp<Shuffle, XprType>, Eigen::Dense>\n{\n  typedef const TensorShufflingOp<Shuffle, XprType>& type;\n};\n\ntemplate<typename Shuffle, typename XprType>\nstruct nested<TensorShufflingOp<Shuffle, XprType>, 1, typename eval<TensorShufflingOp<Shuffle, XprType> >::type>\n{\n  typedef TensorShufflingOp<Shuffle, XprType> type;\n};\n\n}  // end namespace internal\n\n\n\ntemplate<typename Shuffle, typename XprType>\nclass TensorShufflingOp : public TensorBase<TensorShufflingOp<Shuffle, XprType> >\n{\n  public:\n  typedef typename Eigen::internal::traits<TensorShufflingOp>::Scalar Scalar;\n  typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename Eigen::internal::nested<TensorShufflingOp>::type Nested;\n  typedef typename Eigen::internal::traits<TensorShufflingOp>::StorageKind StorageKind;\n  typedef typename Eigen::internal::traits<TensorShufflingOp>::Index Index;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorShufflingOp(const XprType& expr, const Shuffle& shuffle)\n      : m_xpr(expr), m_shuffle(shuffle) {}\n\n    EIGEN_DEVICE_FUNC\n    const Shuffle& shufflePermutation() const { return m_shuffle; }\n\n    EIGEN_DEVICE_FUNC\n    const typename internal::remove_all<typename XprType::Nested>::type&\n    expression() const { return m_xpr; }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE TensorShufflingOp& operator = (const TensorShufflingOp& other)\n    {\n      typedef TensorAssignOp<TensorShufflingOp, const TensorShufflingOp> Assign;\n      Assign assign(*this, other);\n      internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());\n      return *this;\n    }\n\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE TensorShufflingOp& operator = (const OtherDerived& other)\n    {\n      typedef TensorAssignOp<TensorShufflingOp, const OtherDerived> Assign;\n      Assign assign(*this, other);\n      internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());\n      return *this;\n    }\n\n  protected:\n    typename XprType::Nested m_xpr;\n    const Shuffle m_shuffle;\n};\n\n\n// Eval as rvalue\ntemplate<typename Shuffle, typename ArgType, typename Device>\nstruct TensorEvaluator<const TensorShufflingOp<Shuffle, ArgType>, Device>\n{\n  typedef TensorShufflingOp<Shuffle, ArgType> XprType;\n  typedef typename XprType::Index Index;\n  static const int NumDims = internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value;\n  typedef DSizes<Index, NumDims> Dimensions;\n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  static const int PacketSize = internal::unpacket_traits<PacketReturnType>::size;\n\n  enum {\n    IsAligned = false,\n    PacketAccess = (internal::packet_traits<Scalar>::size > 1),\n    Layout = TensorEvaluator<ArgType, Device>::Layout,\n    CoordAccess = false,  // to be implemented\n    RawAccess = false\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)\n      : m_impl(op.expression(), device)\n  {\n    const typename TensorEvaluator<ArgType, Device>::Dimensions& input_dims = m_impl.dimensions();\n    const Shuffle& shuffle = op.shufflePermutation();\n    for (int i = 0; i < NumDims; ++i) {\n      m_dimensions[i] = input_dims[shuffle[i]];\n    }\n\n    array<Index, NumDims> inputStrides;\n\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      inputStrides[0] = 1;\n      m_outputStrides[0] = 1;\n      for (int i = 1; i < NumDims; ++i) {\n        inputStrides[i] = inputStrides[i - 1] * input_dims[i - 1];\n        m_outputStrides[i] = m_outputStrides[i - 1] * m_dimensions[i - 1];\n      }\n    } else {\n      inputStrides[NumDims - 1] = 1;\n      m_outputStrides[NumDims - 1] = 1;\n      for (int i = NumDims - 2; i >= 0; --i) {\n        inputStrides[i] = inputStrides[i + 1] * input_dims[i + 1];\n        m_outputStrides[i] = m_outputStrides[i + 1] * m_dimensions[i + 1];\n      }\n    }\n\n    for (int i = 0; i < NumDims; ++i) {\n      m_inputStrides[i] = inputStrides[shuffle[i]];\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(Scalar* /*data*/) {\n    m_impl.evalSubExprsIfNeeded(NULL);\n    return true;\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {\n    m_impl.cleanup();\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const\n  {\n    return m_impl.coeff(srcCoeff(index));\n  }\n\n  template<int LoadMode>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const\n  {\n    EIGEN_STATIC_ASSERT((PacketSize > 1), YOU_MADE_A_PROGRAMMING_MISTAKE)\n    eigen_assert(index+PacketSize-1 < dimensions().TotalSize());\n\n    EIGEN_ALIGN_MAX typename internal::remove_const<CoeffReturnType>::type values[PacketSize];\n    for (int i = 0; i < PacketSize; ++i) {\n      values[i] = coeff(index+i);\n    }\n    PacketReturnType rslt = internal::pload<PacketReturnType>(values);\n    return rslt;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {\n    const double compute_cost = NumDims * (2 * TensorOpCost::AddCost<Index>() +\n                                           2 * TensorOpCost::MulCost<Index>() +\n                                           TensorOpCost::DivCost<Index>());\n    return m_impl.costPerCoeff(vectorized) +\n           TensorOpCost(0, 0, compute_cost, false /* vectorized */, PacketSize);\n  }\n\n  EIGEN_DEVICE_FUNC Scalar* data() const { return NULL; }\n\n protected:\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index srcCoeff(Index index) const {\n    Index inputIndex = 0;\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      for (int i = NumDims - 1; i > 0; --i) {\n        const Index idx = index / m_outputStrides[i];\n        inputIndex += idx * m_inputStrides[i];\n        index -= idx * m_outputStrides[i];\n      }\n      return inputIndex + index * m_inputStrides[0];\n    } else {\n      for (int i = 0; i < NumDims - 1; ++i) {\n        const Index idx = index / m_outputStrides[i];\n        inputIndex += idx * m_inputStrides[i];\n        index -= idx * m_outputStrides[i];\n      }\n      return inputIndex + index * m_inputStrides[NumDims - 1];\n    }\n  }\n\n  Dimensions m_dimensions;\n  array<Index, NumDims> m_outputStrides;\n  array<Index, NumDims> m_inputStrides;\n  TensorEvaluator<ArgType, Device> m_impl;\n};\n\n\n// Eval as lvalue\ntemplate<typename Shuffle, typename ArgType, typename Device>\nstruct TensorEvaluator<TensorShufflingOp<Shuffle, ArgType>, Device>\n    : public TensorEvaluator<const TensorShufflingOp<Shuffle, ArgType>, Device>\n{\n  typedef TensorEvaluator<const TensorShufflingOp<Shuffle, ArgType>, Device> Base;\n\n  typedef TensorShufflingOp<Shuffle, ArgType> XprType;\n  typedef typename XprType::Index Index;\n  static const int NumDims = internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value;\n  typedef DSizes<Index, NumDims> Dimensions;\n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  static const int PacketSize = internal::unpacket_traits<PacketReturnType>::size;\n\n  enum {\n    IsAligned = false,\n    PacketAccess = (internal::packet_traits<Scalar>::size > 1),\n    RawAccess = false\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)\n      : Base(op, device)\n  { }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType& coeffRef(Index index)\n  {\n    return this->m_impl.coeffRef(this->srcCoeff(index));\n  }\n\n  template <int StoreMode> EIGEN_STRONG_INLINE\n  void writePacket(Index index, const PacketReturnType& x)\n  {\n    EIGEN_STATIC_ASSERT((PacketSize > 1), YOU_MADE_A_PROGRAMMING_MISTAKE)\n\n    EIGEN_ALIGN_MAX typename internal::remove_const<CoeffReturnType>::type values[PacketSize];\n    internal::pstore<CoeffReturnType, PacketReturnType>(values, x);\n    for (int i = 0; i < PacketSize; ++i) {\n      this->coeffRef(index+i) = values[i];\n    }\n  }\n};\n\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_SHUFFLING_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorStorage.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2013 Christian Seiler <christian@iwakd.de>\n// Copyright (C) 2014-2015 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSORSTORAGE_H\n#define EIGEN_CXX11_TENSOR_TENSORSTORAGE_H\n\n#ifdef EIGEN_TENSOR_STORAGE_CTOR_PLUGIN\n  #define EIGEN_INTERNAL_TENSOR_STORAGE_CTOR_PLUGIN EIGEN_TENSOR_STORAGE_CTOR_PLUGIN;\n#else\n  #define EIGEN_INTERNAL_TENSOR_STORAGE_CTOR_PLUGIN\n#endif\n\nnamespace Eigen {\n\n/** \\internal\n  *\n  * \\class TensorStorage\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief Stores the data of a tensor\n  *\n  * This class stores the data of fixed-size, dynamic-size or mixed tensors\n  * in a way as compact as possible.\n  *\n  * \\sa Tensor\n  */\ntemplate<typename T, typename Dimensions, int Options> class TensorStorage;\n\n\n// Pure fixed-size storage\ntemplate<typename T, typename FixedDimensions, int Options_>\nclass TensorStorage\n{\n private:\n  static const std::size_t Size = FixedDimensions::total_size;\n\n  // Allocate an array of size at least one to prevent compiler warnings.\n  static const std::size_t MinSize = max_n_1<Size>::size;\n  EIGEN_ALIGN_MAX T m_data[MinSize];\n\n  FixedDimensions m_dimensions;\n\n public:\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE TensorStorage() {\n  }\n\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE T *data() { return m_data; }\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE const T *data() const { return m_data; }\n\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE const FixedDimensions& dimensions() const { return m_dimensions; }\n\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE DenseIndex size() const { return m_dimensions.TotalSize(); }\n};\n\n\n// pure dynamic\ntemplate<typename T, typename IndexType, int NumIndices_, int Options_>\nclass TensorStorage<T, DSizes<IndexType, NumIndices_>, Options_>\n{\n  public:\n    typedef IndexType Index;\n    typedef DSizes<IndexType, NumIndices_> Dimensions;\n    typedef TensorStorage<T, DSizes<IndexType, NumIndices_>, Options_> Self;\n\n    EIGEN_DEVICE_FUNC TensorStorage() : m_data(0), m_dimensions() {\n      if (NumIndices_ == 0) {\n\tm_data = internal::conditional_aligned_new_auto<T,(Options_&DontAlign)==0>(1);\n      }\n    }\n    EIGEN_DEVICE_FUNC TensorStorage(internal::constructor_without_unaligned_array_assert)\n      : m_data(0), m_dimensions(internal::template repeat<NumIndices_, Index>(0)) {}\n    EIGEN_DEVICE_FUNC TensorStorage(Index size, const array<Index, NumIndices_>& dimensions)\n        : m_data(internal::conditional_aligned_new_auto<T,(Options_&DontAlign)==0>(size)), m_dimensions(dimensions)\n      { EIGEN_INTERNAL_TENSOR_STORAGE_CTOR_PLUGIN }\n\n#if EIGEN_HAS_VARIADIC_TEMPLATES\n    template <typename... DenseIndex>\n    EIGEN_DEVICE_FUNC TensorStorage(DenseIndex... indices) : m_dimensions(indices...) {\n      m_data = internal::conditional_aligned_new_auto<T,(Options_&DontAlign)==0>(internal::array_prod(m_dimensions));\n    }\n#endif\n\n    EIGEN_DEVICE_FUNC TensorStorage(const Self& other)\n      : m_data(internal::conditional_aligned_new_auto<T,(Options_&DontAlign)==0>(internal::array_prod(other.m_dimensions)))\n      , m_dimensions(other.m_dimensions)\n    {\n      internal::smart_copy(other.m_data, other.m_data+internal::array_prod(other.m_dimensions), m_data);\n    }\n    EIGEN_DEVICE_FUNC Self& operator=(const Self& other)\n    {\n      if (this != &other) {\n        Self tmp(other);\n        this->swap(tmp);\n      }\n      return *this;\n    }\n\n    EIGEN_DEVICE_FUNC  ~TensorStorage() { internal::conditional_aligned_delete_auto<T,(Options_&DontAlign)==0>(m_data, internal::array_prod(m_dimensions)); }\n    EIGEN_DEVICE_FUNC  void swap(Self& other)\n    { numext::swap(m_data,other.m_data); numext::swap(m_dimensions,other.m_dimensions); }\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const {return m_dimensions;}\n\n    EIGEN_DEVICE_FUNC void resize(Index size, const array<Index, NumIndices_>& nbDimensions)\n    {\n      const Index currentSz = internal::array_prod(m_dimensions);\n      if(size != currentSz)\n      {\n        internal::conditional_aligned_delete_auto<T,(Options_&DontAlign)==0>(m_data, currentSz);\n        if (size)\n          m_data = internal::conditional_aligned_new_auto<T,(Options_&DontAlign)==0>(size);\n        else if (NumIndices_ == 0) {\n\t  m_data = internal::conditional_aligned_new_auto<T,(Options_&DontAlign)==0>(1);\n\t}\n\telse \n          m_data = 0;\n        EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({})\n      }\n      m_dimensions = nbDimensions;\n    }\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T *data() { return m_data; }\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const T *data() const { return m_data; }\n\n    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index size() const { return m_dimensions.TotalSize(); }\n\n private:\n  T *m_data;\n  Dimensions m_dimensions;\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSORSTORAGE_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorStriding.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_STRIDING_H\n#define EIGEN_CXX11_TENSOR_TENSOR_STRIDING_H\n\nnamespace Eigen {\n\n/** \\class TensorStriding\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief Tensor striding class.\n  *\n  *\n  */\nnamespace internal {\ntemplate<typename Strides, typename XprType>\nstruct traits<TensorStridingOp<Strides, XprType> > : public traits<XprType>\n{\n  typedef typename XprType::Scalar Scalar;\n  typedef traits<XprType> XprTraits;\n  typedef typename XprTraits::StorageKind StorageKind;\n  typedef typename XprTraits::Index Index;\n  typedef typename XprType::Nested Nested;\n  typedef typename remove_reference<Nested>::type _Nested;\n  static const int NumDimensions = XprTraits::NumDimensions;\n  static const int Layout = XprTraits::Layout;\n};\n\ntemplate<typename Strides, typename XprType>\nstruct eval<TensorStridingOp<Strides, XprType>, Eigen::Dense>\n{\n  typedef const TensorStridingOp<Strides, XprType>& type;\n};\n\ntemplate<typename Strides, typename XprType>\nstruct nested<TensorStridingOp<Strides, XprType>, 1, typename eval<TensorStridingOp<Strides, XprType> >::type>\n{\n  typedef TensorStridingOp<Strides, XprType> type;\n};\n\n}  // end namespace internal\n\n\n\ntemplate<typename Strides, typename XprType>\nclass TensorStridingOp : public TensorBase<TensorStridingOp<Strides, XprType> >\n{\n  public:\n  typedef typename Eigen::internal::traits<TensorStridingOp>::Scalar Scalar;\n  typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename Eigen::internal::nested<TensorStridingOp>::type Nested;\n  typedef typename Eigen::internal::traits<TensorStridingOp>::StorageKind StorageKind;\n  typedef typename Eigen::internal::traits<TensorStridingOp>::Index Index;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorStridingOp(const XprType& expr, const Strides& dims)\n      : m_xpr(expr), m_dims(dims) {}\n\n    EIGEN_DEVICE_FUNC\n    const Strides& strides() const { return m_dims; }\n\n    EIGEN_DEVICE_FUNC\n    const typename internal::remove_all<typename XprType::Nested>::type&\n    expression() const { return m_xpr; }\n\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE TensorStridingOp& operator = (const TensorStridingOp& other)\n    {\n      typedef TensorAssignOp<TensorStridingOp, const TensorStridingOp> Assign;\n      Assign assign(*this, other);\n      internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());\n      return *this;\n    }\n\n    template<typename OtherDerived>\n    EIGEN_DEVICE_FUNC\n    EIGEN_STRONG_INLINE TensorStridingOp& operator = (const OtherDerived& other)\n    {\n      typedef TensorAssignOp<TensorStridingOp, const OtherDerived> Assign;\n      Assign assign(*this, other);\n      internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());\n      return *this;\n    }\n\n  protected:\n    typename XprType::Nested m_xpr;\n    const Strides m_dims;\n};\n\n\n// Eval as rvalue\ntemplate<typename Strides, typename ArgType, typename Device>\nstruct TensorEvaluator<const TensorStridingOp<Strides, ArgType>, Device>\n{\n  typedef TensorStridingOp<Strides, ArgType> XprType;\n  typedef typename XprType::Index Index;\n  static const int NumDims = internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value;\n  typedef DSizes<Index, NumDims> Dimensions;\n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  static const int PacketSize = internal::unpacket_traits<PacketReturnType>::size;\n\n  enum {\n    IsAligned = /*TensorEvaluator<ArgType, Device>::IsAligned*/false,\n    PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,\n    Layout = TensorEvaluator<ArgType, Device>::Layout,\n    CoordAccess = false,  // to be implemented\n    RawAccess = false\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)\n      : m_impl(op.expression(), device)\n  {\n    m_dimensions = m_impl.dimensions();\n    for (int i = 0; i < NumDims; ++i) {\n      m_dimensions[i] = ceilf(static_cast<float>(m_dimensions[i]) / op.strides()[i]);\n    }\n\n    const typename TensorEvaluator<ArgType, Device>::Dimensions& input_dims = m_impl.dimensions();\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      m_outputStrides[0] = 1;\n      m_inputStrides[0] = 1;\n      for (int i = 1; i < NumDims; ++i) {\n        m_outputStrides[i] = m_outputStrides[i-1] * m_dimensions[i-1];\n        m_inputStrides[i] = m_inputStrides[i-1] * input_dims[i-1];\n        m_inputStrides[i-1] *= op.strides()[i-1];\n      }\n      m_inputStrides[NumDims-1] *= op.strides()[NumDims-1];\n    } else {  // RowMajor\n      m_outputStrides[NumDims-1] = 1;\n      m_inputStrides[NumDims-1] = 1;\n      for (int i = NumDims - 2; i >= 0; --i) {\n        m_outputStrides[i] = m_outputStrides[i+1] * m_dimensions[i+1];\n        m_inputStrides[i] = m_inputStrides[i+1] * input_dims[i+1];\n        m_inputStrides[i+1] *= op.strides()[i+1];\n      }\n      m_inputStrides[0] *= op.strides()[0];\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(Scalar* /*data*/) {\n    m_impl.evalSubExprsIfNeeded(NULL);\n    return true;\n  }\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {\n    m_impl.cleanup();\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const\n  {\n    return m_impl.coeff(srcCoeff(index));\n  }\n\n  template<int LoadMode>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const\n  {\n    EIGEN_STATIC_ASSERT((PacketSize > 1), YOU_MADE_A_PROGRAMMING_MISTAKE)\n    eigen_assert(index+PacketSize-1 < dimensions().TotalSize());\n\n    Index inputIndices[] = {0, 0};\n    Index indices[] = {index, index + PacketSize - 1};\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      for (int i = NumDims - 1; i > 0; --i) {\n        const Index idx0 = indices[0] / m_outputStrides[i];\n        const Index idx1 = indices[1] / m_outputStrides[i];\n        inputIndices[0] += idx0 * m_inputStrides[i];\n        inputIndices[1] += idx1 * m_inputStrides[i];\n        indices[0] -= idx0 * m_outputStrides[i];\n        indices[1] -= idx1 * m_outputStrides[i];\n      }\n      inputIndices[0] += indices[0] * m_inputStrides[0];\n      inputIndices[1] += indices[1] * m_inputStrides[0];\n    } else {  // RowMajor\n      for (int i = 0; i < NumDims - 1; ++i) {\n        const Index idx0 = indices[0] / m_outputStrides[i];\n        const Index idx1 = indices[1] / m_outputStrides[i];\n        inputIndices[0] += idx0 * m_inputStrides[i];\n        inputIndices[1] += idx1 * m_inputStrides[i];\n        indices[0] -= idx0 * m_outputStrides[i];\n        indices[1] -= idx1 * m_outputStrides[i];\n      }\n      inputIndices[0] += indices[0] * m_inputStrides[NumDims-1];\n      inputIndices[1] += indices[1] * m_inputStrides[NumDims-1];\n    }\n    if (inputIndices[1] - inputIndices[0] == PacketSize - 1) {\n      PacketReturnType rslt = m_impl.template packet<Unaligned>(inputIndices[0]);\n      return rslt;\n    }\n    else {\n      EIGEN_ALIGN_MAX typename internal::remove_const<CoeffReturnType>::type values[PacketSize];\n      values[0] = m_impl.coeff(inputIndices[0]);\n      values[PacketSize-1] = m_impl.coeff(inputIndices[1]);\n      for (int i = 1; i < PacketSize-1; ++i) {\n        values[i] = coeff(index+i);\n      }\n      PacketReturnType rslt = internal::pload<PacketReturnType>(values);\n      return rslt;\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {\n    double compute_cost = (NumDims - 1) * (TensorOpCost::AddCost<Index>() +\n                                           TensorOpCost::MulCost<Index>() +\n                                           TensorOpCost::DivCost<Index>()) +\n        TensorOpCost::MulCost<Index>();\n    if (vectorized) {\n      compute_cost *= 2;  // packet() computes two indices\n    }\n    const int innerDim = (static_cast<int>(Layout) == static_cast<int>(ColMajor)) ? 0 : (NumDims - 1);\n    return m_impl.costPerCoeff(vectorized && m_inputStrides[innerDim] == 1) +\n        // Computation is not vectorized per se, but it is done once per packet.\n        TensorOpCost(0, 0, compute_cost, vectorized, PacketSize);\n  }\n\n  EIGEN_DEVICE_FUNC Scalar* data() const { return NULL; }\n\n protected:\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index srcCoeff(Index index) const\n  {\n    Index inputIndex = 0;\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      for (int i = NumDims - 1; i > 0; --i) {\n        const Index idx = index / m_outputStrides[i];\n        inputIndex += idx * m_inputStrides[i];\n        index -= idx * m_outputStrides[i];\n      }\n      inputIndex += index * m_inputStrides[0];\n    } else {  // RowMajor\n      for (int i = 0; i < NumDims - 1; ++i) {\n        const Index idx = index / m_outputStrides[i];\n        inputIndex += idx * m_inputStrides[i];\n        index -= idx * m_outputStrides[i];\n      }\n      inputIndex += index * m_inputStrides[NumDims-1];\n    }\n    return inputIndex;\n  }\n\n  Dimensions m_dimensions;\n  array<Index, NumDims> m_outputStrides;\n  array<Index, NumDims> m_inputStrides;\n  TensorEvaluator<ArgType, Device> m_impl;\n};\n\n\n// Eval as lvalue\ntemplate<typename Strides, typename ArgType, typename Device>\nstruct TensorEvaluator<TensorStridingOp<Strides, ArgType>, Device>\n    : public TensorEvaluator<const TensorStridingOp<Strides, ArgType>, Device>\n{\n  typedef TensorStridingOp<Strides, ArgType> XprType;\n  typedef TensorEvaluator<const XprType, Device> Base;\n  //  typedef typename XprType::Index Index;\n  static const int NumDims = internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value;\n  //  typedef DSizes<Index, NumDims> Dimensions;\n\n  enum {\n    IsAligned = /*TensorEvaluator<ArgType, Device>::IsAligned*/false,\n    PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,\n    Layout = TensorEvaluator<ArgType, Device>::Layout,\n    CoordAccess = false,  // to be implemented\n    RawAccess = false\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)\n      : Base(op, device) { }\n\n  typedef typename XprType::Index Index;\n  typedef typename XprType::Scalar Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  static const int PacketSize = internal::unpacket_traits<PacketReturnType>::size;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index index)\n  {\n    return this->m_impl.coeffRef(this->srcCoeff(index));\n  }\n\n  template <int StoreMode> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  void writePacket(Index index, const PacketReturnType& x)\n  {\n    EIGEN_STATIC_ASSERT((PacketSize > 1), YOU_MADE_A_PROGRAMMING_MISTAKE)\n    eigen_assert(index+PacketSize-1 < this->dimensions().TotalSize());\n\n    Index inputIndices[] = {0, 0};\n    Index indices[] = {index, index + PacketSize - 1};\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      for (int i = NumDims - 1; i > 0; --i) {\n        const Index idx0 = indices[0] / this->m_outputStrides[i];\n        const Index idx1 = indices[1] / this->m_outputStrides[i];\n        inputIndices[0] += idx0 * this->m_inputStrides[i];\n        inputIndices[1] += idx1 * this->m_inputStrides[i];\n        indices[0] -= idx0 * this->m_outputStrides[i];\n        indices[1] -= idx1 * this->m_outputStrides[i];\n      }\n      inputIndices[0] += indices[0] * this->m_inputStrides[0];\n      inputIndices[1] += indices[1] * this->m_inputStrides[0];\n    } else {  // RowMajor\n      for (int i = 0; i < NumDims - 1; ++i) {\n        const Index idx0 = indices[0] / this->m_outputStrides[i];\n        const Index idx1 = indices[1] / this->m_outputStrides[i];\n        inputIndices[0] += idx0 * this->m_inputStrides[i];\n        inputIndices[1] += idx1 * this->m_inputStrides[i];\n        indices[0] -= idx0 * this->m_outputStrides[i];\n        indices[1] -= idx1 * this->m_outputStrides[i];\n      }\n      inputIndices[0] += indices[0] * this->m_inputStrides[NumDims-1];\n      inputIndices[1] += indices[1] * this->m_inputStrides[NumDims-1];\n    }\n    if (inputIndices[1] - inputIndices[0] == PacketSize - 1) {\n      this->m_impl.template writePacket<Unaligned>(inputIndices[0], x);\n    }\n    else {\n      EIGEN_ALIGN_MAX Scalar values[PacketSize];\n      internal::pstore<Scalar, PacketReturnType>(values, x);\n      this->m_impl.coeffRef(inputIndices[0]) = values[0];\n      this->m_impl.coeffRef(inputIndices[1]) = values[PacketSize-1];\n      for (int i = 1; i < PacketSize-1; ++i) {\n        this->coeffRef(index+i) = values[i];\n      }\n    }\n  }\n};\n\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_STRIDING_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorSycl.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Mehdi Goli    Codeplay Software Ltd.\n// Ralph Potter  Codeplay Software Ltd.\n// Luke Iwanski  Codeplay Software Ltd.\n// Contact: eigen@codeplay.com\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n// General include header of SYCL target for Tensor Module\n#ifndef UNSUPPORTED_EIGEN_CXX11_SRC_TENSOR_TENSORSYCL_H\n#define UNSUPPORTED_EIGEN_CXX11_SRC_TENSOR_TENSORSYCL_H\n\n#ifdef EIGEN_USE_SYCL\n\n// global pointer to set different attribute state for a class\ntemplate <class T>\nstruct MakeGlobalPointer {\n  typedef typename cl::sycl::global_ptr<T>::pointer_t Type;\n};\n\n// global pointer to set different attribute state for a class\ntemplate <class T>\nstruct MakeLocalPointer {\n  typedef typename cl::sycl::local_ptr<T>::pointer_t Type;\n};\n\n\nnamespace Eigen {\nnamespace TensorSycl {\nnamespace internal {\n\n/// This struct is used for special expression nodes with no operations (for example assign and selectOP).\n  struct NoOP;\n\ntemplate<bool IsConst, typename T> struct GetType{\n  typedef const T Type;\n};\ntemplate<typename T> struct GetType<false, T>{\n  typedef T Type;\n};\n\n}\n}\n}\n\n// tuple construction\n#include \"TensorSyclTuple.h\"\n\n// counting number of leaf at compile time\n#include \"TensorSyclLeafCount.h\"\n\n// The index PlaceHolder takes the actual expression and replaces the actual\n// data on it with the place holder. It uses the same pre-order expression tree\n// traverse as the leaf count in order to give the right access number to each\n// node in the expression\n#include \"TensorSyclPlaceHolderExpr.h\"\n\n// creation of an accessor tuple from a tuple of SYCL buffers\n#include \"TensorSyclExtractAccessor.h\"\n\n// this is used to change the address space type in tensor map for GPU\n#include \"TensorSyclConvertToDeviceExpression.h\"\n\n// this is used to extract the functors\n#include \"TensorSyclExtractFunctors.h\"\n\n// this is used to create tensormap on the device\n// this is used to construct the expression on the device\n#include \"TensorSyclExprConstructor.h\"\n\n/// this is used for extracting tensor reduction\n#include \"TensorReductionSycl.h\"\n\n// kernel execution using fusion\n#include \"TensorSyclRun.h\"\n\n#endif  // end of EIGEN_USE_SYCL\n#endif  // UNSUPPORTED_EIGEN_CXX11_SRC_TENSOR_TENSORSYCL_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorSyclConvertToDeviceExpression.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Mehdi Goli    Codeplay Software Ltd.\n// Ralph Potter  Codeplay Software Ltd.\n// Luke Iwanski  Codeplay Software Ltd.\n// Contact: <eigen@codeplay.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n/*****************************************************************\n * TensorSyclConvertToDeviceExpression.h\n *\n * \\brief:\n *  Conversion from host pointer to device pointer\n *  inside leaf nodes of the expression.\n *\n*****************************************************************/\n\n#ifndef UNSUPPORTED_EIGEN_CXX11_SRC_TENSOR_TENSORSYCL_CONVERT_TO_DEVICE_EXPRESSION_HPP\n#define UNSUPPORTED_EIGEN_CXX11_SRC_TENSOR_TENSORSYCL_CONVERT_TO_DEVICE_EXPRESSION_HPP\n\nnamespace Eigen {\nnamespace TensorSycl {\nnamespace internal {\n\n/// \\struct ConvertToDeviceExpression\n/// \\brief This struct is used to convert the MakePointer in the host expression\n/// to the MakeGlobalPointer for the device expression. For the leafNodes\n/// containing the pointer. This is due to the fact that the address space of\n/// the pointer T* is different on the host and the device.\ntemplate <typename Expr>\nstruct ConvertToDeviceExpression;\n\ntemplate<template<class...> class NonOpCategory, bool IsConst, typename... Args>\nstruct NonOpConversion{\n  typedef typename GetType<IsConst, NonOpCategory<typename ConvertToDeviceExpression<Args>::Type...> >::Type Type;\n};\n\n\ntemplate<template<class, template <class> class > class NonOpCategory, bool IsConst, typename Args>\nstruct DeviceConvertor{\n  typedef typename GetType<IsConst, NonOpCategory<typename ConvertToDeviceExpression<Args>::Type, MakeGlobalPointer> >::Type Type;\n};\n\n/// specialisation of the \\ref ConvertToDeviceExpression struct when the node\n/// type is TensorMap\n#define TENSORMAPCONVERT(CVQual)\\\ntemplate <typename Scalar_, int Options_, int Options2_, int NumIndices_, typename IndexType_, template <class> class MakePointer_>\\\nstruct ConvertToDeviceExpression<CVQual TensorMap<Tensor<Scalar_, NumIndices_, Options_, IndexType_>, Options2_, MakePointer_> > {\\\n  typedef CVQual TensorMap<Tensor<Scalar_, NumIndices_, Options_, IndexType_>, Options2_, MakeGlobalPointer> Type;\\\n};\n\nTENSORMAPCONVERT(const)\nTENSORMAPCONVERT()\n#undef TENSORMAPCONVERT\n\n/// specialisation of the \\ref ConvertToDeviceExpression struct when the node\n/// type is TensorCwiseNullaryOp, TensorCwiseUnaryOp, TensorCwiseBinaryOp, TensorCwiseTernaryOp, TensorBroadcastingOp\n#define CATEGORYCONVERT(CVQual)\\\ntemplate <template<class, class...> class Category, typename OP, typename... subExprs>\\\nstruct ConvertToDeviceExpression<CVQual Category<OP, subExprs...> > {\\\n  typedef CVQual Category<OP, typename ConvertToDeviceExpression<subExprs>::Type... > Type;\\\n};\nCATEGORYCONVERT(const)\nCATEGORYCONVERT()\n#undef CATEGORYCONVERT\n\n\n/// specialisation of the \\ref ConvertToDeviceExpression struct when the node\n/// type is  TensorCwiseSelectOp\n#define SELECTOPCONVERT(CVQual, Res)\\\ntemplate <typename IfExpr, typename ThenExpr, typename ElseExpr>\\\nstruct ConvertToDeviceExpression<CVQual TensorSelectOp<IfExpr, ThenExpr, ElseExpr> >\\\n: NonOpConversion<TensorSelectOp, Res, IfExpr, ThenExpr, ElseExpr> {};\nSELECTOPCONVERT(const, true)\nSELECTOPCONVERT(, false)\n#undef SELECTOPCONVERT\n\n/// specialisation of the \\ref ConvertToDeviceExpression struct when the node\n/// type is const AssingOP\n#define ASSIGNCONVERT(CVQual, Res)\\\ntemplate <typename LHSExpr, typename RHSExpr>\\\nstruct ConvertToDeviceExpression<CVQual TensorAssignOp<LHSExpr, RHSExpr> >\\\n: NonOpConversion<TensorAssignOp, Res, LHSExpr, RHSExpr>{};\n\nASSIGNCONVERT(const, true)\nASSIGNCONVERT(, false)\n#undef ASSIGNCONVERT\n\n/// specialisation of the \\ref ConvertToDeviceExpression struct when the node\n/// type is either TensorForcedEvalOp or TensorEvalToOp\n#define KERNELBROKERCONVERT(CVQual, Res, ExprNode)\\\ntemplate <typename Expr>\\\nstruct ConvertToDeviceExpression<CVQual ExprNode<Expr> > \\\n: DeviceConvertor<ExprNode, Res, Expr>{};\n\nKERNELBROKERCONVERT(const, true, TensorForcedEvalOp)\nKERNELBROKERCONVERT(, false, TensorForcedEvalOp)\nKERNELBROKERCONVERT(const, true, TensorEvalToOp)\nKERNELBROKERCONVERT(, false, TensorEvalToOp)\n#undef KERNELBROKERCONVERT\n\n/// specialisation of the \\ref ConvertToDeviceExpression struct when the node type is TensorReductionOp\n#define KERNELBROKERCONVERTREDUCTION(CVQual)\\\ntemplate <typename OP, typename Dim, typename subExpr, template <class> class MakePointer_>\\\nstruct ConvertToDeviceExpression<CVQual TensorReductionOp<OP, Dim, subExpr, MakePointer_> > {\\\n  typedef CVQual TensorReductionOp<OP, Dim, typename ConvertToDeviceExpression<subExpr>::Type, MakeGlobalPointer> Type;\\\n};\n\nKERNELBROKERCONVERTREDUCTION(const)\nKERNELBROKERCONVERTREDUCTION()\n#undef KERNELBROKERCONVERTREDUCTION\n\n}  // namespace internal\n}  // namespace TensorSycl\n}  // namespace Eigen\n\n#endif  // UNSUPPORTED_EIGEN_CXX1\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorSyclExprConstructor.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Mehdi Goli    Codeplay Software Ltd.\n// Ralph Potter  Codeplay Software Ltd.\n// Luke Iwanski  Codeplay Software Ltd.\n// Contact: <eigen@codeplay.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n/*****************************************************************\n * TensorSyclExprConstructor.h\n *\n * \\brief:\n *  This file re-create an expression on the SYCL device in order\n *  to use the original tensor evaluator.\n *\n*****************************************************************/\n\n#ifndef UNSUPPORTED_EIGEN_CXX11_SRC_TENSOR_TENSORSYCL_EXPR_CONSTRUCTOR_HPP\n#define UNSUPPORTED_EIGEN_CXX11_SRC_TENSOR_TENSORSYCL_EXPR_CONSTRUCTOR_HPP\n\nnamespace Eigen {\nnamespace TensorSycl {\nnamespace internal {\n/// this class is used by EvalToOp in order to create an lhs expression which is\n/// a pointer from an accessor on device-only buffer\ntemplate <typename PtrType, size_t N, typename... Params>\nstruct EvalToLHSConstructor {\n  PtrType expr;\n  EvalToLHSConstructor(const utility::tuple::Tuple<Params...> &t): expr((&(*(utility::tuple::get<N>(t).get_pointer())))) {}\n};\n\n/// \\struct ExprConstructor is used to reconstruct the expression on the device and\n/// recreate the expression with MakeGlobalPointer containing the device address\n/// space for the TensorMap pointers used in eval function.\n/// It receives the original expression type, the functor of the node, the tuple\n/// of accessors, and the device expression type to re-instantiate the\n/// expression tree for the device\ntemplate <typename OrigExpr, typename IndexExpr, typename... Params>\nstruct ExprConstructor;\n\n/// specialisation of the \\ref ExprConstructor struct when the node type is\n/// TensorMap\n#define TENSORMAP(CVQual)\\\ntemplate <typename Scalar_, int Options_, int Options2_, int Options3_, int NumIndices_, typename IndexType_,\\\ntemplate <class> class MakePointer_, size_t N, typename... Params>\\\nstruct ExprConstructor< CVQual TensorMap<Tensor<Scalar_, NumIndices_, Options_, IndexType_>, Options2_, MakeGlobalPointer>,\\\nCVQual PlaceHolder<CVQual TensorMap<Tensor<Scalar_, NumIndices_, Options_, IndexType_>, Options3_, MakePointer_>, N>, Params...>{\\\n  typedef  CVQual TensorMap<Tensor<Scalar_, NumIndices_, Options_, IndexType_>, Options2_, MakeGlobalPointer>  Type;\\\n  Type expr;\\\n  template <typename FuncDetector>\\\n  ExprConstructor(FuncDetector &fd, const utility::tuple::Tuple<Params...> &t)\\\n  : expr(Type((&(*(utility::tuple::get<N>(t).get_pointer()))), fd.dimensions())) {}\\\n};\n\nTENSORMAP(const)\nTENSORMAP()\n#undef TENSORMAP\n\n#define UNARYCATEGORY(CVQual)\\\ntemplate <template<class, class> class UnaryCategory, typename OP, typename OrigRHSExpr, typename RHSExpr, typename... Params>\\\nstruct ExprConstructor<CVQual UnaryCategory<OP, OrigRHSExpr>, CVQual UnaryCategory<OP, RHSExpr>, Params...> {\\\n  typedef  ExprConstructor<OrigRHSExpr, RHSExpr, Params...> my_type;\\\n  my_type rhsExpr;\\\n  typedef CVQual UnaryCategory<OP, typename my_type::Type> Type;\\\n  Type expr;\\\n  template <typename FuncDetector>\\\n  ExprConstructor(FuncDetector &funcD, const utility::tuple::Tuple<Params...> &t)\\\n  : rhsExpr(funcD.rhsExpr, t), expr(rhsExpr.expr, funcD.func) {}\\\n};\n\nUNARYCATEGORY(const)\nUNARYCATEGORY()\n#undef UNARYCATEGORY\n\n/// specialisation of the \\ref ExprConstructor struct when the node type is\n/// TensorBinaryOp\n#define BINARYCATEGORY(CVQual)\\\ntemplate <template<class, class, class> class BinaryCategory, typename OP, typename OrigLHSExpr, typename OrigRHSExpr, typename LHSExpr,\\\ntypename RHSExpr, typename... Params>\\\nstruct ExprConstructor<CVQual BinaryCategory<OP, OrigLHSExpr, OrigRHSExpr>,  CVQual BinaryCategory<OP, LHSExpr, RHSExpr>, Params...> {\\\n  typedef  ExprConstructor<OrigLHSExpr, LHSExpr, Params...> my_left_type;\\\n  typedef  ExprConstructor<OrigRHSExpr, RHSExpr, Params...> my_right_type;\\\n  typedef  CVQual BinaryCategory<OP, typename my_left_type::Type, typename my_right_type::Type> Type;\\\n  my_left_type lhsExpr;\\\n  my_right_type rhsExpr;\\\n  Type expr;\\\n  template <typename FuncDetector>\\\n  ExprConstructor(FuncDetector &funcD, const utility::tuple::Tuple<Params...> &t)\\\n  : lhsExpr(funcD.lhsExpr, t),rhsExpr(funcD.rhsExpr, t), expr(lhsExpr.expr, rhsExpr.expr, funcD.func) {}\\\n};\n\nBINARYCATEGORY(const)\nBINARYCATEGORY()\n#undef BINARYCATEGORY\n\n/// specialisation of the \\ref ExprConstructor struct when the node type is\n/// TensorCwiseTernaryOp\n#define TERNARYCATEGORY(CVQual)\\\ntemplate <template <class, class, class, class> class TernaryCategory, typename OP, typename OrigArg1Expr, typename OrigArg2Expr,typename OrigArg3Expr,\\\ntypename Arg1Expr, typename Arg2Expr, typename Arg3Expr, typename... Params>\\\nstruct ExprConstructor<CVQual TernaryCategory<OP, OrigArg1Expr, OrigArg2Expr, OrigArg3Expr>, CVQual TernaryCategory<OP, Arg1Expr, Arg2Expr, Arg3Expr>, Params...> {\\\n  typedef ExprConstructor<OrigArg1Expr, Arg1Expr, Params...> my_arg1_type;\\\n  typedef ExprConstructor<OrigArg2Expr, Arg2Expr, Params...> my_arg2_type;\\\n  typedef ExprConstructor<OrigArg3Expr, Arg3Expr, Params...> my_arg3_type;\\\n  typedef  CVQual TernaryCategory<OP, typename my_arg1_type::Type, typename my_arg2_type::Type, typename my_arg3_type::Type> Type;\\\n  my_arg1_type arg1Expr;\\\n  my_arg2_type arg2Expr;\\\n  my_arg3_type arg3Expr;\\\n  Type expr;\\\n  template <typename FuncDetector>\\\n  ExprConstructor(FuncDetector &funcD,const utility::tuple::Tuple<Params...> &t)\\\n  : arg1Expr(funcD.arg1Expr, t), arg2Expr(funcD.arg2Expr, t), arg3Expr(funcD.arg3Expr, t), expr(arg1Expr.expr, arg2Expr.expr, arg3Expr.expr, funcD.func) {}\\\n};\n\nTERNARYCATEGORY(const)\nTERNARYCATEGORY()\n#undef TERNARYCATEGORY\n\n/// specialisation of the \\ref ExprConstructor struct when the node type is\n/// TensorCwiseSelectOp\n#define SELECTOP(CVQual)\\\ntemplate <typename OrigIfExpr, typename OrigThenExpr, typename OrigElseExpr, typename IfExpr, typename ThenExpr, typename ElseExpr, typename... Params>\\\nstruct ExprConstructor< CVQual TensorSelectOp<OrigIfExpr, OrigThenExpr, OrigElseExpr>, CVQual TensorSelectOp<IfExpr, ThenExpr, ElseExpr>, Params...> {\\\n  typedef  ExprConstructor<OrigIfExpr, IfExpr, Params...> my_if_type;\\\n  typedef  ExprConstructor<OrigThenExpr, ThenExpr, Params...> my_then_type;\\\n  typedef  ExprConstructor<OrigElseExpr, ElseExpr, Params...> my_else_type;\\\n  typedef CVQual TensorSelectOp<typename my_if_type::Type, typename my_then_type::Type, typename my_else_type::Type> Type;\\\n  my_if_type ifExpr;\\\n  my_then_type thenExpr;\\\n  my_else_type elseExpr;\\\n  Type expr;\\\n  template <typename FuncDetector>\\\n  ExprConstructor(FuncDetector &funcD, const utility::tuple::Tuple<Params...> &t)\\\n  : ifExpr(funcD.ifExpr, t), thenExpr(funcD.thenExpr, t), elseExpr(funcD.elseExpr, t), expr(ifExpr.expr, thenExpr.expr, elseExpr.expr) {}\\\n};\n\nSELECTOP(const)\nSELECTOP()\n#undef SELECTOP\n\n/// specialisation of the \\ref ExprConstructor struct when the node type is\n/// const TensorAssignOp\n#define ASSIGN(CVQual)\\\ntemplate <typename OrigLHSExpr, typename OrigRHSExpr, typename LHSExpr, typename RHSExpr, typename... Params>\\\nstruct ExprConstructor<CVQual TensorAssignOp<OrigLHSExpr, OrigRHSExpr>,  CVQual TensorAssignOp<LHSExpr, RHSExpr>, Params...> {\\\n  typedef ExprConstructor<OrigLHSExpr, LHSExpr, Params...> my_left_type;\\\n  typedef ExprConstructor<OrigRHSExpr, RHSExpr, Params...> my_right_type;\\\n  typedef CVQual TensorAssignOp<typename my_left_type::Type, typename my_right_type::Type>  Type;\\\n  my_left_type lhsExpr;\\\n  my_right_type rhsExpr;\\\n  Type expr;\\\n  template <typename FuncDetector>\\\n  ExprConstructor(FuncDetector &funcD, const utility::tuple::Tuple<Params...> &t)\\\n  : lhsExpr(funcD.lhsExpr, t), rhsExpr(funcD.rhsExpr, t), expr(lhsExpr.expr, rhsExpr.expr) {}\\\n };\n\n ASSIGN(const)\n ASSIGN()\n #undef ASSIGN\n/// specialisation of the \\ref ExprConstructor struct when the node type is\n///  TensorEvalToOp\n#define EVALTO(CVQual)\\\ntemplate <typename OrigExpr, typename Expr, typename... Params>\\\nstruct ExprConstructor<CVQual TensorEvalToOp<OrigExpr, MakeGlobalPointer>, CVQual TensorEvalToOp<Expr>, Params...> {\\\n  typedef ExprConstructor<OrigExpr, Expr, Params...> my_expr_type;\\\n  typedef typename TensorEvalToOp<OrigExpr, MakeGlobalPointer>::PointerType my_buffer_type;\\\n  typedef CVQual TensorEvalToOp<typename my_expr_type::Type, MakeGlobalPointer> Type;\\\n  my_expr_type nestedExpression;\\\n  EvalToLHSConstructor<my_buffer_type, 0, Params...> buffer;\\\n  Type expr;\\\n  template <typename FuncDetector>\\\n  ExprConstructor(FuncDetector &funcD, const utility::tuple::Tuple<Params...> &t)\\\n  : nestedExpression(funcD.rhsExpr, t), buffer(t), expr(buffer.expr, nestedExpression.expr) {}\\\n};\n\nEVALTO(const)\nEVALTO()\n#undef EVALTO\n\n/// specialisation of the \\ref ExprConstructor struct when the node type is\n/// TensorForcedEvalOp\n#define FORCEDEVAL(CVQual)\\\ntemplate <typename OrigExpr, typename DevExpr, size_t N, typename... Params>\\\nstruct ExprConstructor<CVQual TensorForcedEvalOp<OrigExpr, MakeGlobalPointer>,\\\nCVQual PlaceHolder<CVQual TensorForcedEvalOp<DevExpr>, N>, Params...> {\\\n  typedef CVQual TensorMap<Tensor<typename TensorForcedEvalOp<DevExpr, MakeGlobalPointer>::Scalar,\\\n  TensorForcedEvalOp<DevExpr, MakeGlobalPointer>::NumDimensions, 0, typename TensorForcedEvalOp<DevExpr>::Index>, 0, MakeGlobalPointer> Type;\\\n  Type expr;\\\n  template <typename FuncDetector>\\\n  ExprConstructor(FuncDetector &fd, const utility::tuple::Tuple<Params...> &t)\\\n  : expr(Type((&(*(utility::tuple::get<N>(t).get_pointer()))), fd.dimensions())) {}\\\n};\n\nFORCEDEVAL(const)\nFORCEDEVAL()\n#undef FORCEDEVAL\n\ntemplate <bool Conds,  size_t X , size_t Y > struct ValueCondition {\n  static const size_t Res =X;\n};\ntemplate<size_t X, size_t Y> struct ValueCondition<false, X , Y> {\n  static const size_t Res =Y;\n};\n\n/// specialisation of the \\ref ExprConstructor struct when the node type is TensorReductionOp\n#define SYCLREDUCTIONEXPR(CVQual)\\\ntemplate <typename OP, typename Dim, typename OrigExpr, typename DevExpr, size_t N, typename... Params>\\\nstruct ExprConstructor<CVQual TensorReductionOp<OP, Dim, OrigExpr, MakeGlobalPointer>,\\\nCVQual PlaceHolder<CVQual TensorReductionOp<OP, Dim, DevExpr>, N>, Params...> {\\\n  static const size_t NumIndices= ValueCondition< TensorReductionOp<OP, Dim, DevExpr, MakeGlobalPointer>::NumDimensions==0,  1, TensorReductionOp<OP, Dim, DevExpr, MakeGlobalPointer>::NumDimensions >::Res;\\\n  typedef CVQual TensorMap<Tensor<typename TensorReductionOp<OP, Dim, DevExpr, MakeGlobalPointer>::Scalar,\\\n  NumIndices, 0, typename TensorReductionOp<OP, Dim, DevExpr>::Index>, 0, MakeGlobalPointer> Type;\\\n  Type expr;\\\n  template <typename FuncDetector>\\\n  ExprConstructor(FuncDetector &fd, const utility::tuple::Tuple<Params...> &t)\\\n  : expr(Type((&(*(utility::tuple::get<N>(t).get_pointer()))), fd.dimensions())) {}\\\n};\n\nSYCLREDUCTIONEXPR(const)\nSYCLREDUCTIONEXPR()\n#undef SYCLREDUCTIONEXPR\n\n/// template deduction for \\ref ExprConstructor struct\ntemplate <typename OrigExpr, typename IndexExpr, typename FuncD, typename... Params>\nauto createDeviceExpression(FuncD &funcD, const utility::tuple::Tuple<Params...> &t)\n    -> decltype(ExprConstructor<OrigExpr, IndexExpr, Params...>(funcD, t)) {\n  return ExprConstructor<OrigExpr, IndexExpr, Params...>(funcD, t);\n}\n\n} /// namespace TensorSycl\n} /// namespace internal\n} /// namespace Eigen\n\n\n#endif  // UNSUPPORTED_EIGEN_CXX11_SRC_TENSOR_TENSORSYCL_EXPR_CONSTRUCTOR_HPP\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorSyclExtractAccessor.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Mehdi Goli    Codeplay Software Ltd.\n// Ralph Potter  Codeplay Software Ltd.\n// Luke Iwanski  Codeplay Software Ltd.\n// Contact: <eigen@codeplay.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n/*****************************************************************\n * TensorSyclExtractAccessor.h\n *\n * \\brief:\n * ExtractAccessor takes Expression placeHolder expression and the tuple of sycl\n * buffers as an input. Using pre-order tree traversal, ExtractAccessor\n * recursively calls itself for its children in the expression tree. The\n * leaf node in the PlaceHolder expression is nothing but a container preserving\n * the order of the actual data in the tuple of sycl buffer. By invoking the\n * extract accessor for the PlaceHolder<N>, an accessor is created for the Nth\n * buffer in the tuple of buffers. This accessor is then added as an Nth\n * element in the tuple of accessors. In this case we preserve the order of data\n * in the expression tree.\n *\n * This is the specialisation of extract accessor method for different operation\n * type in the PlaceHolder expression.\n *\n*****************************************************************/\n\n#ifndef UNSUPPORTED_EIGEN_CXX11_SRC_TENSOR_TENSORSYCL_EXTRACT_ACCESSOR_HPP\n#define UNSUPPORTED_EIGEN_CXX11_SRC_TENSOR_TENSORSYCL_EXTRACT_ACCESSOR_HPP\n\nnamespace Eigen {\nnamespace TensorSycl {\nnamespace internal {\n/// \\struct ExtractAccessor: Extract Accessor Class is used to extract the\n/// accessor from a buffer.\n/// Depending on the type of the leaf node we can get a read accessor or a\n/// read_write accessor\ntemplate <typename Evaluator>\nstruct ExtractAccessor;\n\nstruct AccessorConstructor{\n  template<typename Arg> static inline auto getTuple(cl::sycl::handler& cgh, Arg eval)\n  -> decltype(ExtractAccessor<Arg>::getTuple(cgh, eval)) {\n  return ExtractAccessor<Arg>::getTuple(cgh, eval);\n  }\n\n  template<typename Arg1, typename Arg2> static inline auto getTuple(cl::sycl::handler& cgh, Arg1 eval1, Arg2 eval2)\n  -> decltype(utility::tuple::append(ExtractAccessor<Arg1>::getTuple(cgh, eval1), ExtractAccessor<Arg2>::getTuple(cgh, eval2))) {\n    return utility::tuple::append(ExtractAccessor<Arg1>::getTuple(cgh, eval1), ExtractAccessor<Arg2>::getTuple(cgh, eval2));\n  }\n  template<typename Arg1, typename Arg2, typename Arg3>\tstatic inline auto getTuple(cl::sycl::handler& cgh, Arg1 eval1 , Arg2 eval2 , Arg3 eval3)\n  -> decltype(utility::tuple::append(ExtractAccessor<Arg1>::getTuple(cgh, eval1),utility::tuple::append(ExtractAccessor<Arg2>::getTuple(cgh, eval2), ExtractAccessor<Arg3>::getTuple(cgh, eval3)))) {\n    return utility::tuple::append(ExtractAccessor<Arg1>::getTuple(cgh, eval1),utility::tuple::append(ExtractAccessor<Arg2>::getTuple(cgh, eval2), ExtractAccessor<Arg3>::getTuple(cgh, eval3)));\n  }\n  template< cl::sycl::access::mode AcM, typename Arg> static inline auto getAccessor(cl::sycl::handler& cgh, Arg eval)\n  -> decltype(utility::tuple::make_tuple( eval.device().template get_sycl_accessor<AcM,\n  typename Eigen::internal::remove_all<typename Arg::CoeffReturnType>::type>(eval.dimensions().TotalSize(), cgh,eval.data()))){\n    return utility::tuple::make_tuple(eval.device().template get_sycl_accessor<AcM, typename Eigen::internal::remove_all<typename Arg::CoeffReturnType>::type>(eval.dimensions().TotalSize(), cgh,eval.data()));\n  }\n};\n\n/// specialisation of the \\ref ExtractAccessor struct when the node type is\n/// const TensorCwiseNullaryOp, const TensorCwiseUnaryOp and const TensorBroadcastingOp\ntemplate <template<class, class> class UnaryCategory, typename OP, typename RHSExpr, typename Dev>\nstruct ExtractAccessor<TensorEvaluator<const UnaryCategory<OP, RHSExpr>, Dev> > {\n  static inline auto getTuple(cl::sycl::handler& cgh, const TensorEvaluator<const UnaryCategory<OP, RHSExpr>, Dev> eval)\n  -> decltype(AccessorConstructor::getTuple(cgh, eval.impl())){\n    return AccessorConstructor::getTuple(cgh, eval.impl());\n  }\n};\n\n/// specialisation of the \\ref ExtractAccessor struct when the node type is TensorCwiseNullaryOp,  TensorCwiseUnaryOp and  TensorBroadcastingOp\ntemplate <template<class, class> class UnaryCategory, typename OP, typename RHSExpr, typename Dev>\nstruct ExtractAccessor<TensorEvaluator<UnaryCategory<OP, RHSExpr>, Dev> >\n: ExtractAccessor<TensorEvaluator<const UnaryCategory<OP, RHSExpr>, Dev> > {};\n\n/// specialisation of the \\ref ExtractAccessor struct when the node type is const TensorCwiseBinaryOp\ntemplate <template<class, class, class> class BinaryCategory, typename OP,  typename LHSExpr, typename RHSExpr, typename Dev>\nstruct ExtractAccessor<TensorEvaluator<const BinaryCategory<OP, LHSExpr, RHSExpr>, Dev> > {\n  static inline auto getTuple(cl::sycl::handler& cgh, const TensorEvaluator<const BinaryCategory<OP, LHSExpr, RHSExpr>, Dev> eval)\n  -> decltype(AccessorConstructor::getTuple(cgh, eval.left_impl(), eval.right_impl())){\n    return AccessorConstructor::getTuple(cgh, eval.left_impl(), eval.right_impl());\n  }\n};\n/// specialisation of the \\ref ExtractAccessor struct when the node type is TensorCwiseBinaryOp\ntemplate <template<class, class, class> class BinaryCategory, typename OP,  typename LHSExpr, typename RHSExpr, typename Dev>\nstruct ExtractAccessor<TensorEvaluator<BinaryCategory<OP, LHSExpr, RHSExpr>, Dev> >\n: ExtractAccessor<TensorEvaluator<const BinaryCategory<OP, LHSExpr, RHSExpr>, Dev> >{};\n\n/// specialisation of the \\ref ExtractAccessor struct when the node type is\n/// const TensorCwiseTernaryOp\ntemplate <template<class, class, class, class> class TernaryCategory, typename OP, typename Arg1Expr, typename Arg2Expr, typename Arg3Expr, typename Dev>\nstruct ExtractAccessor<TensorEvaluator<const TernaryCategory<OP, Arg1Expr, Arg2Expr, Arg3Expr>, Dev> > {\n  static inline auto getTuple(cl::sycl::handler& cgh, const TensorEvaluator<const TernaryCategory<OP, Arg1Expr, Arg2Expr, Arg3Expr>, Dev> eval)\n  -> decltype(AccessorConstructor::getTuple(cgh, eval.arg1Impl(), eval.arg2Impl(), eval.arg3Impl())){\n    return AccessorConstructor::getTuple(cgh, eval.arg1Impl(), eval.arg2Impl(), eval.arg3Impl());\n  }\n};\n\n/// specialisation of the \\ref ExtractAccessor struct when the node type is TensorCwiseTernaryOp\ntemplate <template<class, class, class, class> class TernaryCategory, typename OP, typename Arg1Expr, typename Arg2Expr, typename Arg3Expr, typename Dev>\nstruct ExtractAccessor<TensorEvaluator<TernaryCategory<OP, Arg1Expr, Arg2Expr, Arg3Expr>, Dev> >\n: ExtractAccessor<TensorEvaluator<const TernaryCategory<OP, Arg1Expr, Arg2Expr, Arg3Expr>, Dev> >{};\n\n/// specialisation of the \\ref ExtractAccessor struct when the node type is\n/// const TensorCwiseSelectOp. This is a special case where there is no OP\ntemplate <typename IfExpr, typename ThenExpr, typename ElseExpr, typename Dev>\nstruct ExtractAccessor<TensorEvaluator<const TensorSelectOp<IfExpr, ThenExpr, ElseExpr>, Dev> > {\n  static inline auto getTuple(cl::sycl::handler& cgh, const TensorEvaluator<const TensorSelectOp<IfExpr, ThenExpr, ElseExpr>, Dev> eval)\n  -> decltype(AccessorConstructor::getTuple(cgh, eval.cond_impl(), eval.then_impl(), eval.else_impl())){\n    return AccessorConstructor::getTuple(cgh, eval.cond_impl(), eval.then_impl(), eval.else_impl());\n  }\n};\n\n/// specialisation of the \\ref ExtractAccessor struct when the node type is\n/// TensorCwiseSelectOp. This is a special case where there is no OP\ntemplate <typename IfExpr, typename ThenExpr, typename ElseExpr, typename Dev>\nstruct ExtractAccessor<TensorEvaluator<TensorSelectOp<IfExpr, ThenExpr, ElseExpr>, Dev> >\n: ExtractAccessor<TensorEvaluator<const TensorSelectOp<IfExpr, ThenExpr, ElseExpr>, Dev> >{};\n\n/// specialisation of the \\ref ExtractAccessor struct when the node type is const TensorAssignOp\ntemplate <typename LHSExpr, typename RHSExpr, typename Dev>\nstruct ExtractAccessor<TensorEvaluator<const TensorAssignOp<LHSExpr, RHSExpr>, Dev> > {\n  static inline auto getTuple(cl::sycl::handler& cgh, const TensorEvaluator<const TensorAssignOp<LHSExpr, RHSExpr>, Dev> eval)\n  -> decltype(AccessorConstructor::getTuple(cgh, eval.left_impl(), eval.right_impl())){\n    return AccessorConstructor::getTuple(cgh, eval.left_impl(), eval.right_impl());\n }\n};\n\n/// specialisation of the \\ref ExtractAccessor struct when the node type is TensorAssignOp\ntemplate <typename LHSExpr, typename RHSExpr, typename Dev>\nstruct ExtractAccessor<TensorEvaluator<TensorAssignOp<LHSExpr, RHSExpr>, Dev> >\n: ExtractAccessor<TensorEvaluator<const TensorAssignOp<LHSExpr, RHSExpr>, Dev> >{};\n\n/// specialisation of the \\ref ExtractAccessor struct when the node type is const TensorMap\n#define TENSORMAPEXPR(CVQual, ACCType)\\\ntemplate <typename PlainObjectType, int Options_, typename Dev>\\\nstruct ExtractAccessor<TensorEvaluator<CVQual TensorMap<PlainObjectType, Options_>, Dev> > {\\\n  static inline auto getTuple(cl::sycl::handler& cgh,const TensorEvaluator<CVQual TensorMap<PlainObjectType, Options_>, Dev> eval)\\\n  -> decltype(AccessorConstructor::template getAccessor<ACCType>(cgh, eval)){\\\n    return AccessorConstructor::template getAccessor<ACCType>(cgh, eval);\\\n  }\\\n};\nTENSORMAPEXPR(const, cl::sycl::access::mode::read)\nTENSORMAPEXPR(, cl::sycl::access::mode::read_write)\n#undef TENSORMAPEXPR\n\n/// specialisation of the \\ref ExtractAccessor struct when the node type is const TensorForcedEvalOp\ntemplate <typename Expr, typename Dev>\nstruct ExtractAccessor<TensorEvaluator<const TensorForcedEvalOp<Expr>, Dev> > {\n  static inline auto getTuple(cl::sycl::handler& cgh, const TensorEvaluator<const TensorForcedEvalOp<Expr>, Dev> eval)\n  -> decltype(AccessorConstructor::template getAccessor<cl::sycl::access::mode::read>(cgh, eval)){\n    return AccessorConstructor::template getAccessor<cl::sycl::access::mode::read>(cgh, eval);\n  }\n};\n\n/// specialisation of the \\ref ExtractAccessor struct when the node type is TensorForcedEvalOp\ntemplate <typename Expr, typename Dev>\nstruct ExtractAccessor<TensorEvaluator<TensorForcedEvalOp<Expr>, Dev> >\n: ExtractAccessor<TensorEvaluator<const TensorForcedEvalOp<Expr>, Dev> >{};\n\n/// specialisation of the \\ref ExtractAccessor struct when the node type is const TensorEvalToOp\ntemplate <typename Expr, typename Dev>\nstruct ExtractAccessor<TensorEvaluator<const TensorEvalToOp<Expr>, Dev> > {\n  static inline auto getTuple(cl::sycl::handler& cgh,const TensorEvaluator<const TensorEvalToOp<Expr>, Dev> eval)\n  -> decltype(utility::tuple::append(AccessorConstructor::template getAccessor<cl::sycl::access::mode::write>(cgh, eval), AccessorConstructor::getTuple(cgh, eval.impl()))){\n    return utility::tuple::append(AccessorConstructor::template getAccessor<cl::sycl::access::mode::write>(cgh, eval), AccessorConstructor::getTuple(cgh, eval.impl()));\n  }\n};\n\n/// specialisation of the \\ref ExtractAccessor struct when the node type is TensorEvalToOp\ntemplate <typename Expr, typename Dev>\nstruct ExtractAccessor<TensorEvaluator<TensorEvalToOp<Expr>, Dev> >\n: ExtractAccessor<TensorEvaluator<const TensorEvalToOp<Expr>, Dev> >{};\n\n/// specialisation of the \\ref ExtractAccessor struct when the node type is const TensorReductionOp\ntemplate <typename OP, typename Dim, typename Expr, typename Dev>\nstruct ExtractAccessor<TensorEvaluator<const TensorReductionOp<OP, Dim, Expr>, Dev> > {\n  static inline auto getTuple(cl::sycl::handler& cgh, const TensorEvaluator<const TensorReductionOp<OP, Dim, Expr>, Dev> eval)\n  -> decltype(AccessorConstructor::template getAccessor<cl::sycl::access::mode::read>(cgh, eval)){\n    return AccessorConstructor::template getAccessor<cl::sycl::access::mode::read>(cgh, eval);\n  }\n};\n\n/// specialisation of the \\ref ExtractAccessor struct when the node type is TensorReductionOp\ntemplate <typename OP, typename Dim, typename Expr, typename Dev>\nstruct ExtractAccessor<TensorEvaluator<TensorReductionOp<OP, Dim, Expr>, Dev> >\n: ExtractAccessor<TensorEvaluator<const TensorReductionOp<OP, Dim, Expr>, Dev> >{};\n\n/// template deduction for \\ref ExtractAccessor\ntemplate <typename Evaluator>\nauto createTupleOfAccessors(cl::sycl::handler& cgh, const Evaluator& expr)\n-> decltype(ExtractAccessor<Evaluator>::getTuple(cgh, expr)) {\n  return ExtractAccessor<Evaluator>::getTuple(cgh, expr);\n}\n\n} /// namespace TensorSycl\n} /// namespace internal\n} /// namespace Eigen\n#endif  // UNSUPPORTED_EIGEN_CXX11_SRC_TENSOR_TENSORSYCL_EXTRACT_ACCESSOR_HPP\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorSyclExtractFunctors.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Mehdi Goli    Codeplay Software Ltd.\n// Ralph Potter  Codeplay Software Ltd.\n// Luke Iwanski  Codeplay Software Ltd.\n// Contact: <eigen@codeplay.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n/*****************************************************************\n * TensorSyclextractFunctors.h\n *\n * \\brief:\n *  Used to extract all the functors allocated to each node of the expression\n*tree.\n *\n*****************************************************************/\n\n#ifndef UNSUPPORTED_EIGEN_CXX11_SRC_TENSOR_TENSORSYCL_EXTRACT_FUNCTORS_HPP\n#define UNSUPPORTED_EIGEN_CXX11_SRC_TENSOR_TENSORSYCL_EXTRACT_FUNCTORS_HPP\n\nnamespace Eigen {\nnamespace TensorSycl {\nnamespace internal {\n/// \\struct FunctorExtractor:  This struct is used to extract the functors\n/// constructed on\n/// the host-side, to pack them and reuse them in reconstruction of the\n/// expression on the device.\n/// We have to do that as in Eigen the functors are not stateless so we cannot\n/// re-instantiate them on the device.\n/// We have to pass instantiated functors to the device.\n// This struct is used for leafNode (TensorMap) and nodes behaving like leafNode (TensorForcedEval).\ntemplate <typename Evaluator> struct FunctorExtractor{\n  typedef typename Evaluator::Dimensions Dimensions;\n  const Dimensions m_dimensions;\n  const Dimensions& dimensions() const { return m_dimensions; }\n  FunctorExtractor(const Evaluator& expr)\n  : m_dimensions(expr.dimensions()) {}\n\n};\n\n/// specialisation of the \\ref FunctorExtractor struct when the node type is\n/// const TensorCwiseNullaryOp, const TensorCwiseUnaryOp, and const TensorBroadcastingOp\ntemplate <template <class, class> class UnaryCategory, typename OP, typename RHSExpr, typename Dev>\nstruct FunctorExtractor<TensorEvaluator<const UnaryCategory<OP, RHSExpr>, Dev> > {\n  FunctorExtractor<TensorEvaluator<RHSExpr, Dev> > rhsExpr;\n  OP func;\n  FunctorExtractor(const TensorEvaluator<const UnaryCategory<OP, RHSExpr>, Dev>& expr)\n  : rhsExpr(expr.impl()), func(expr.functor()) {}\n};\n/// specialisation of the \\ref FunctorExtractor struct when the node type is\n/// TensorCwiseNullaryOp, TensorCwiseUnaryOp, and TensorBroadcastingOp\ntemplate <template <class, class> class UnaryCategory, typename OP, typename RHSExpr, typename Dev>\nstruct FunctorExtractor<TensorEvaluator<UnaryCategory<OP, RHSExpr>, Dev> >\n: FunctorExtractor<TensorEvaluator<const UnaryCategory<OP, RHSExpr>, Dev> >{};\n\n/// specialisation of the \\ref FunctorExtractor struct when the node type is\n/// const TensorCwiseBinaryOp\ntemplate <template<class, class, class> class BinaryCategory, typename OP, typename LHSExpr, typename RHSExpr, typename Dev>\nstruct FunctorExtractor<TensorEvaluator<const BinaryCategory<OP, LHSExpr, RHSExpr>, Dev> > {\n  FunctorExtractor<TensorEvaluator<LHSExpr, Dev> > lhsExpr;\n  FunctorExtractor<TensorEvaluator<RHSExpr, Dev> > rhsExpr;\n  OP func;\n  FunctorExtractor(const TensorEvaluator<const BinaryCategory<OP, LHSExpr, RHSExpr>, Dev>& expr)\n  : lhsExpr(expr.left_impl()),rhsExpr(expr.right_impl()),func(expr.functor()) {}\n};\n\n/// specialisation of the \\ref FunctorExtractor struct when the node type is\n/// const TensorCwiseBinaryOp\ntemplate <template <class, class, class> class BinaryCategory, typename OP, typename LHSExpr, typename RHSExpr, typename Dev>\nstruct FunctorExtractor<TensorEvaluator<BinaryCategory<OP,  LHSExpr, RHSExpr>, Dev> >\n: FunctorExtractor<TensorEvaluator<const BinaryCategory<OP,  LHSExpr, RHSExpr>, Dev> >{};\n\n/// specialisation of the \\ref FunctorExtractor struct when the node type is\n/// const TensorCwiseTernaryOp\ntemplate <template <class, class, class, class> class TernaryCategory, typename OP, typename Arg1Expr, typename Arg2Expr, typename Arg3Expr,typename Dev>\nstruct FunctorExtractor<TensorEvaluator<const TernaryCategory<OP, Arg1Expr, Arg2Expr, Arg3Expr>, Dev> > {\n  FunctorExtractor<TensorEvaluator<Arg1Expr, Dev> > arg1Expr;\n  FunctorExtractor<TensorEvaluator<Arg2Expr, Dev> > arg2Expr;\n  FunctorExtractor<TensorEvaluator<Arg3Expr, Dev> > arg3Expr;\n  OP func;\n  FunctorExtractor(const TensorEvaluator<const TernaryCategory<OP, Arg1Expr, Arg2Expr, Arg3Expr>, Dev>& expr)\n  : arg1Expr(expr.arg1Impl()), arg2Expr(expr.arg2Impl()), arg3Expr(expr.arg3Impl()), func(expr.functor()) {}\n};\n\n/// specialisation of the \\ref FunctorExtractor struct when the node type is\n/// TensorCwiseTernaryOp\ntemplate <template <class, class, class, class> class TernaryCategory, typename OP, typename Arg1Expr, typename Arg2Expr, typename Arg3Expr, typename Dev>\nstruct FunctorExtractor<TensorEvaluator< TernaryCategory<OP, Arg1Expr, Arg2Expr, Arg3Expr>, Dev> >\n:FunctorExtractor<TensorEvaluator<const TernaryCategory<OP, Arg1Expr, Arg2Expr, Arg3Expr>, Dev> >{};\n\n/// specialisation of the \\ref FunctorExtractor struct when the node type is\n/// const TensorCwiseSelectOp. This is an specialisation without OP so it has to be separated.\ntemplate <typename IfExpr, typename ThenExpr, typename ElseExpr, typename Dev>\nstruct FunctorExtractor< TensorEvaluator<const TensorSelectOp<IfExpr, ThenExpr, ElseExpr>, Dev> > {\n  FunctorExtractor<TensorEvaluator<IfExpr, Dev> > ifExpr;\n  FunctorExtractor<TensorEvaluator<ThenExpr, Dev> > thenExpr;\n  FunctorExtractor<TensorEvaluator<ElseExpr, Dev> > elseExpr;\n  FunctorExtractor(const TensorEvaluator<const TensorSelectOp<IfExpr, ThenExpr, ElseExpr>, Dev>& expr)\n  : ifExpr(expr.cond_impl()), thenExpr(expr.then_impl()), elseExpr(expr.else_impl()) {}\n};\n\n/// specialisation of the \\ref FunctorExtractor struct when the node type is\n/// TensorCwiseSelectOp. This is an specialisation without OP so it has to be separated\ntemplate <typename IfExpr, typename ThenExpr, typename ElseExpr, typename Dev>\nstruct FunctorExtractor<TensorEvaluator<TensorSelectOp<IfExpr, ThenExpr, ElseExpr>, Dev> >\n:FunctorExtractor< TensorEvaluator<const TensorSelectOp<IfExpr, ThenExpr, ElseExpr>, Dev> > {};\n\n/// specialisation of the \\ref FunctorExtractor struct when the node type is\n/// const TensorAssignOp. This is an specialisation without OP so it has to be separated.\ntemplate <typename LHSExpr, typename RHSExpr, typename Dev>\nstruct FunctorExtractor<TensorEvaluator<const TensorAssignOp<LHSExpr, RHSExpr>, Dev> > {\n  FunctorExtractor<TensorEvaluator<LHSExpr, Dev> > lhsExpr;\n  FunctorExtractor<TensorEvaluator<RHSExpr, Dev> > rhsExpr;\n  FunctorExtractor(const TensorEvaluator<const TensorAssignOp<LHSExpr, RHSExpr>, Dev>& expr)\n  : lhsExpr(expr.left_impl()), rhsExpr(expr.right_impl()) {}\n};\n\n/// specialisation of the \\ref FunctorExtractor struct when the node type is\n/// TensorAssignOp. This is an specialisation without OP so it has to be separated.\ntemplate <typename LHSExpr, typename RHSExpr, typename Dev>\nstruct FunctorExtractor<TensorEvaluator<TensorAssignOp<LHSExpr, RHSExpr>, Dev> >\n:FunctorExtractor<TensorEvaluator<const TensorAssignOp<LHSExpr, RHSExpr>, Dev> >{};\n\n\n/// specialisation of the \\ref FunctorExtractor struct when the node type is\n/// const TensorEvalToOp, This is an specialisation without OP so it has to be separated.\ntemplate <typename RHSExpr, typename Dev>\nstruct FunctorExtractor<TensorEvaluator<const TensorEvalToOp<RHSExpr>, Dev> > {\n  FunctorExtractor<TensorEvaluator<RHSExpr, Dev> > rhsExpr;\n  FunctorExtractor(const TensorEvaluator<const TensorEvalToOp<RHSExpr>, Dev>& expr)\n  : rhsExpr(expr.impl()) {}\n};\n\n/// specialisation of the \\ref FunctorExtractor struct when the node type is\n/// TensorEvalToOp. This is a specialisation without OP so it has to be separated.\ntemplate <typename RHSExpr, typename Dev>\nstruct FunctorExtractor<TensorEvaluator<TensorEvalToOp<RHSExpr>, Dev> >\n: FunctorExtractor<TensorEvaluator<const TensorEvalToOp<RHSExpr>, Dev> > {};\n\ntemplate<typename Dim, size_t NumOutputDim> struct DimConstr {\ntemplate<typename InDim>\n  static inline Dim getDim(InDim dims ) {return dims;}\n};\n\ntemplate<typename Dim> struct DimConstr<Dim, 0> {\n  template<typename InDim>\n    static inline Dim getDim(InDim dims ) {return Dim(dims.TotalSize());}\n};\n\ntemplate<typename Op, typename Dims, typename ArgType, template <class> class MakePointer_, typename Device>\nstruct FunctorExtractor<TensorEvaluator<const TensorReductionOp<Op, Dims, ArgType, MakePointer_>, Device>>{\n  typedef TensorEvaluator<const TensorReductionOp<Op, Dims, ArgType, MakePointer_>, Device> Evaluator;\n  typedef typename Eigen::internal::conditional<Evaluator::NumOutputDims==0, DSizes<typename Evaluator::Index, 1>, typename Evaluator::Dimensions >::type Dimensions;\n  const Dimensions m_dimensions;\n  const Dimensions& dimensions() const { return m_dimensions; }\n  FunctorExtractor(const TensorEvaluator<const TensorReductionOp<Op, Dims, ArgType, MakePointer_>, Device>& expr)\n  : m_dimensions(DimConstr<Dimensions, Evaluator::NumOutputDims>::getDim(expr.dimensions())) {}\n};\n\n\ntemplate<typename Op, typename Dims, typename ArgType, template <class> class MakePointer_, typename Device>\nstruct FunctorExtractor<TensorEvaluator<TensorReductionOp<Op, Dims, ArgType, MakePointer_>, Device>>\n: FunctorExtractor<TensorEvaluator<const TensorReductionOp<Op, Dims, ArgType, MakePointer_>, Device>>{};\n/// template deduction function for FunctorExtractor\ntemplate <typename Evaluator>\nauto inline extractFunctors(const Evaluator& evaluator)-> FunctorExtractor<Evaluator> {\n  return FunctorExtractor<Evaluator>(evaluator);\n}\n}  // namespace internal\n}  // namespace TensorSycl\n}  // namespace Eigen\n\n#endif  // UNSUPPORTED_EIGEN_CXX11_SRC_TENSOR_TENSORSYCL_EXTRACT_FUNCTORS_HPP\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorSyclLeafCount.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Mehdi Goli    Codeplay Software Ltd.\n// Ralph Potter  Codeplay Software Ltd.\n// Luke Iwanski  Codeplay Software Ltd.\n// Contact: <eigen@codeplay.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n/*****************************************************************\n * TensorSyclLeafCount.h\n *\n * \\brief:\n *  The leaf count used the pre-order expression tree traverse in order to name\n *  count the number of leaf nodes in the expression\n *\n*****************************************************************/\n\n#ifndef UNSUPPORTED_EIGEN_CXX11_SRC_TENSOR_TENSORSYCL_LEAF_COUNT_HPP\n#define UNSUPPORTED_EIGEN_CXX11_SRC_TENSOR_TENSORSYCL_LEAF_COUNT_HPP\n\nnamespace Eigen {\nnamespace TensorSycl {\nnamespace internal {\n/// \\brief LeafCount used to counting terminal nodes. The total number of\n/// leaf nodes is used by MakePlaceHolderExprHelper to find the order\n/// of the leaf node in a expression tree at compile time.\ntemplate <typename Expr>\nstruct LeafCount;\n\ntemplate<typename... Args> struct CategoryCount;\n\ntemplate<> struct CategoryCount<>\n{\n  static const size_t Count =0;\n};\n\ntemplate<typename Arg, typename... Args>\nstruct CategoryCount<Arg,Args...>{\n  static const size_t Count = LeafCount<Arg>::Count + CategoryCount<Args...>::Count;\n};\n\n/// specialisation of the \\ref LeafCount struct when the node type is const TensorMap\ntemplate <typename PlainObjectType, int Options_, template <class> class MakePointer_>\nstruct LeafCount<const TensorMap<PlainObjectType, Options_, MakePointer_> > {\n  static const size_t Count =1;\n};\n\n/// specialisation of the \\ref LeafCount struct when the node type is TensorMap\ntemplate <typename PlainObjectType, int Options_, template <class> class MakePointer_>\nstruct LeafCount<TensorMap<PlainObjectType, Options_, MakePointer_> > :LeafCount<const TensorMap<PlainObjectType, Options_, MakePointer_> >{};\n\n// const TensorCwiseUnaryOp, const TensorCwiseNullaryOp, const TensorCwiseBinaryOp, const TensorCwiseTernaryOp, and Const TensorBroadcastingOp\ntemplate <template <class, class...> class CategoryExpr, typename OP, typename... RHSExpr>\nstruct LeafCount<const CategoryExpr<OP, RHSExpr...> >: CategoryCount<RHSExpr...> {};\n// TensorCwiseUnaryOp,  TensorCwiseNullaryOp,  TensorCwiseBinaryOp,  TensorCwiseTernaryOp, and  TensorBroadcastingOp\ntemplate <template <class, class...> class CategoryExpr, typename OP, typename... RHSExpr>\nstruct LeafCount<CategoryExpr<OP, RHSExpr...> > :LeafCount<const CategoryExpr<OP, RHSExpr...> >{};\n\n/// specialisation of the \\ref LeafCount struct when the node type is const TensorSelectOp is an exception\ntemplate <typename IfExpr, typename ThenExpr, typename ElseExpr>\nstruct LeafCount<const TensorSelectOp<IfExpr, ThenExpr, ElseExpr> > : CategoryCount<IfExpr, ThenExpr, ElseExpr> {};\n/// specialisation of the \\ref LeafCount struct when the node type is TensorSelectOp\ntemplate <typename IfExpr, typename ThenExpr, typename ElseExpr>\nstruct LeafCount<TensorSelectOp<IfExpr, ThenExpr, ElseExpr> >: LeafCount<const TensorSelectOp<IfExpr, ThenExpr, ElseExpr> > {};\n\n\n/// specialisation of the \\ref LeafCount struct when the node type is const TensorAssignOp\ntemplate <typename LHSExpr, typename RHSExpr>\nstruct LeafCount<const TensorAssignOp<LHSExpr, RHSExpr> >: CategoryCount<LHSExpr,RHSExpr> {};\n\n/// specialisation of the \\ref LeafCount struct when the node type is\n/// TensorAssignOp is an exception. It is not the same as Unary\ntemplate <typename LHSExpr, typename RHSExpr>\nstruct LeafCount<TensorAssignOp<LHSExpr, RHSExpr> > :LeafCount<const TensorAssignOp<LHSExpr, RHSExpr> >{};\n\n/// specialisation of the \\ref LeafCount struct when the node type is const TensorForcedEvalOp\ntemplate <typename Expr>\nstruct LeafCount<const TensorForcedEvalOp<Expr> > {\n    static const size_t Count =1;\n};\n\n/// specialisation of the \\ref LeafCount struct when the node type is TensorForcedEvalOp\ntemplate <typename Expr>\nstruct LeafCount<TensorForcedEvalOp<Expr> >: LeafCount<const TensorForcedEvalOp<Expr> > {};\n\n/// specialisation of the \\ref LeafCount struct when the node type is const TensorEvalToOp\ntemplate <typename Expr>\nstruct LeafCount<const TensorEvalToOp<Expr> > {\n  static const size_t Count = 1 + CategoryCount<Expr>::Count;\n};\n\n/// specialisation of the \\ref LeafCount struct when the node type is const TensorReductionOp\ntemplate <typename OP, typename Dim, typename Expr>\nstruct LeafCount<const TensorReductionOp<OP, Dim, Expr> > {\n    static const size_t Count =1;\n};\n\n/// specialisation of the \\ref LeafCount struct when the node type is TensorReductionOp\ntemplate <typename OP, typename Dim, typename Expr>\nstruct LeafCount<TensorReductionOp<OP, Dim, Expr> >: LeafCount<const TensorReductionOp<OP, Dim, Expr> >{};\n\n/// specialisation of the \\ref LeafCount struct when the node type is TensorEvalToOp\ntemplate <typename Expr>\nstruct LeafCount<TensorEvalToOp<Expr> >: LeafCount<const TensorEvalToOp<Expr> >{};\n\n} /// namespace TensorSycl\n} /// namespace internal\n} /// namespace Eigen\n\n#endif  // UNSUPPORTED_EIGEN_CXX11_SRC_TENSOR_TENSORSYCL_LEAF_COUNT_HPP\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorSyclPlaceHolderExpr.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Mehdi Goli    Codeplay Software Ltd.\n// Ralph Potter  Codeplay Software Ltd.\n// Luke Iwanski  Codeplay Software Ltd.\n// Contact: <eigen@codeplay.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n/*****************************************************************\n * TensorSyclPlaceHolderExpr.h\n *\n * \\brief:\n *  This is the specialisation of the placeholder expression based on the\n * operation type\n *\n*****************************************************************/\n\n#ifndef UNSUPPORTED_EIGEN_CXX11_SRC_TENSOR_TENSORSYCL_PLACEHOLDER_EXPR_HPP\n#define UNSUPPORTED_EIGEN_CXX11_SRC_TENSOR_TENSORSYCL_PLACEHOLDER_EXPR_HPP\n\nnamespace Eigen {\nnamespace TensorSycl {\nnamespace internal {\n\n/// \\struct PlaceHolder\n/// \\brief PlaceHolder is used to replace the \\ref TensorMap in the expression\n/// tree.\n/// PlaceHolder contains the order of the leaf node in the expression tree.\ntemplate <typename Scalar, size_t N>\nstruct PlaceHolder {\n  static constexpr size_t I = N;\n  typedef Scalar Type;\n};\n\n/// \\sttruct PlaceHolderExpression\n/// \\brief it is used to create the PlaceHolder expression. The PlaceHolder\n/// expression is a copy of expression type in which the TensorMap of the has\n/// been replaced with PlaceHolder.\ntemplate <typename Expr, size_t N>\nstruct PlaceHolderExpression;\n\ntemplate<size_t N, typename... Args>\nstruct CalculateIndex;\n\ntemplate<size_t N, typename Arg>\nstruct CalculateIndex<N, Arg>{\n  typedef typename PlaceHolderExpression<Arg, N>::Type ArgType;\n  typedef utility::tuple::Tuple<ArgType> ArgsTuple;\n};\n\ntemplate<size_t N, typename Arg1, typename Arg2>\nstruct CalculateIndex<N, Arg1, Arg2>{\n  static const size_t Arg2LeafCount = LeafCount<Arg2>::Count;\n  typedef typename PlaceHolderExpression<Arg1, N - Arg2LeafCount>::Type Arg1Type;\n  typedef typename PlaceHolderExpression<Arg2, N>::Type Arg2Type;\n  typedef utility::tuple::Tuple<Arg1Type, Arg2Type> ArgsTuple;\n};\n\ntemplate<size_t N, typename Arg1, typename Arg2, typename Arg3>\nstruct CalculateIndex<N, Arg1, Arg2, Arg3> {\n  static const size_t Arg3LeafCount = LeafCount<Arg3>::Count;\n  static const size_t Arg2LeafCount = LeafCount<Arg2>::Count;\n  typedef typename PlaceHolderExpression<Arg1, N - Arg3LeafCount - Arg2LeafCount>::Type Arg1Type;\n  typedef typename PlaceHolderExpression<Arg2, N - Arg3LeafCount>::Type Arg2Type;\n  typedef typename PlaceHolderExpression<Arg3, N>::Type Arg3Type;\n  typedef utility::tuple::Tuple<Arg1Type, Arg2Type, Arg3Type> ArgsTuple;\n};\n\ntemplate<template<class...> class Category , class OP, class TPL>\nstruct CategoryHelper;\n\ntemplate<template<class...> class Category , class OP, class ...T >\nstruct CategoryHelper<Category, OP, utility::tuple::Tuple<T...> > {\n  typedef Category<OP, T... > Type;\n};\n\ntemplate<template<class...> class Category , class ...T >\nstruct CategoryHelper<Category, NoOP, utility::tuple::Tuple<T...> > {\n  typedef Category<T... > Type;\n};\n\n/// specialisation of the \\ref PlaceHolderExpression when the node is\n/// TensorCwiseNullaryOp, TensorCwiseUnaryOp, TensorBroadcastingOp, TensorCwiseBinaryOp,  TensorCwiseTernaryOp\n#define OPEXPRCATEGORY(CVQual)\\\ntemplate <template <class, class... > class Category, typename OP, typename... SubExpr, size_t N>\\\nstruct PlaceHolderExpression<CVQual Category<OP, SubExpr...>, N>{\\\n  typedef CVQual typename CategoryHelper<Category, OP, typename CalculateIndex<N, SubExpr...>::ArgsTuple>::Type Type;\\\n};\n\nOPEXPRCATEGORY(const)\nOPEXPRCATEGORY()\n#undef OPEXPRCATEGORY\n\n/// specialisation of the \\ref PlaceHolderExpression when the node is\n/// TensorCwiseSelectOp\n#define SELECTEXPR(CVQual)\\\ntemplate <typename IfExpr, typename ThenExpr, typename ElseExpr, size_t N>\\\nstruct PlaceHolderExpression<CVQual TensorSelectOp<IfExpr, ThenExpr, ElseExpr>, N> {\\\n  typedef CVQual typename CategoryHelper<TensorSelectOp, NoOP, typename CalculateIndex<N, IfExpr, ThenExpr, ElseExpr>::ArgsTuple>::Type Type;\\\n};\n\nSELECTEXPR(const)\nSELECTEXPR()\n#undef SELECTEXPR\n\n/// specialisation of the \\ref PlaceHolderExpression when the node is\n/// TensorAssignOp\n#define ASSIGNEXPR(CVQual)\\\ntemplate <typename LHSExpr, typename RHSExpr, size_t N>\\\nstruct PlaceHolderExpression<CVQual TensorAssignOp<LHSExpr, RHSExpr>, N> {\\\n  typedef CVQual typename CategoryHelper<TensorAssignOp, NoOP, typename CalculateIndex<N, LHSExpr, RHSExpr>::ArgsTuple>::Type Type;\\\n};\n\nASSIGNEXPR(const)\nASSIGNEXPR()\n#undef ASSIGNEXPR\n\n/// specialisation of the \\ref PlaceHolderExpression when the node is\n/// TensorMap\n#define TENSORMAPEXPR(CVQual)\\\ntemplate <typename Scalar_, int Options_, int Options2_, int NumIndices_, typename IndexType_, template <class> class MakePointer_, size_t N>\\\nstruct PlaceHolderExpression< CVQual TensorMap< Tensor<Scalar_, NumIndices_, Options_, IndexType_>, Options2_, MakePointer_>, N> {\\\n  typedef CVQual PlaceHolder<CVQual TensorMap<Tensor<Scalar_, NumIndices_, Options_, IndexType_>, Options2_, MakePointer_>, N> Type;\\\n};\n\nTENSORMAPEXPR(const)\nTENSORMAPEXPR()\n#undef TENSORMAPEXPR\n\n/// specialisation of the \\ref PlaceHolderExpression when the node is\n/// TensorForcedEvalOp\n#define FORCEDEVAL(CVQual)\\\ntemplate <typename Expr, size_t N>\\\nstruct PlaceHolderExpression<CVQual TensorForcedEvalOp<Expr>, N> {\\\n  typedef CVQual PlaceHolder<CVQual TensorForcedEvalOp<Expr>, N> Type;\\\n};\n\nFORCEDEVAL(const)\nFORCEDEVAL()\n#undef FORCEDEVAL\n\n/// specialisation of the \\ref PlaceHolderExpression when the node is\n/// TensorEvalToOp\n#define EVALTO(CVQual)\\\ntemplate <typename Expr, size_t N>\\\nstruct PlaceHolderExpression<CVQual TensorEvalToOp<Expr>, N> {\\\n  typedef CVQual TensorEvalToOp<typename CalculateIndex <N, Expr>::ArgType> Type;\\\n};\n\nEVALTO(const)\nEVALTO()\n#undef EVALTO\n\n\n/// specialisation of the \\ref PlaceHolderExpression when the node is\n/// TensorReductionOp\n#define SYCLREDUCTION(CVQual)\\\ntemplate <typename OP, typename Dims, typename Expr, size_t N>\\\nstruct PlaceHolderExpression<CVQual TensorReductionOp<OP, Dims, Expr>, N>{\\\n  typedef CVQual PlaceHolder<CVQual TensorReductionOp<OP, Dims,Expr>, N> Type;\\\n};\nSYCLREDUCTION(const)\nSYCLREDUCTION()\n#undef SYCLREDUCTION\n\n/// template deduction for \\ref PlaceHolderExpression struct\ntemplate <typename Expr>\nstruct createPlaceHolderExpression {\n  static const size_t TotalLeaves = LeafCount<Expr>::Count;\n  typedef typename PlaceHolderExpression<Expr, TotalLeaves - 1>::Type Type;\n};\n\n}  // internal\n}  // TensorSycl\n}  // namespace Eigen\n\n#endif  // UNSUPPORTED_EIGEN_CXX11_SRC_TENSOR_TENSORSYCL_PLACEHOLDER_EXPR_HPP\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorSyclRun.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Mehdi Goli    Codeplay Software Ltd.\n// Ralph Potter  Codeplay Software Ltd.\n// Luke Iwanski  Codeplay Software Ltd.\n// Cummins Chris PhD student at The University of Edinburgh.\n// Contact: <eigen@codeplay.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n/*****************************************************************\n * TensorSyclRun.h\n *\n * \\brief:\n * Schedule_kernel invoke an specialised version of kernel struct. The\n * specialisation is based on the data dimension in sycl buffer\n *\n*****************************************************************/\n\n#ifndef UNSUPPORTED_EIGEN_CXX11_SRC_TENSOR_TENSORSYCL_SYCLRUN_HPP\n#define UNSUPPORTED_EIGEN_CXX11_SRC_TENSOR_TENSORSYCL_SYCLRUN_HPP\n\nnamespace Eigen {\nnamespace TensorSycl {\n/// The run function in tensor sycl convert the expression tree to a buffer\n/// based expression tree;\n/// creates the expression tree for the device with accessor to buffers;\n/// construct the kernel and submit it to the sycl queue.\ntemplate <typename Expr, typename Dev>\nvoid run(Expr &expr, Dev &dev) {\n  Eigen::TensorEvaluator<Expr, Dev> evaluator(expr, dev);\n  const bool needs_assign = evaluator.evalSubExprsIfNeeded(NULL);\n  if (needs_assign) {\n    typedef  typename internal::createPlaceHolderExpression<Expr>::Type PlaceHolderExpr;\n    auto functors = internal::extractFunctors(evaluator);\n\n    size_t tileSize =dev.m_queue.get_device(). template get_info<cl::sycl::info::device::max_work_group_size>()/2;\n    dev.m_queue.submit([&](cl::sycl::handler &cgh) {\n\n      // create a tuple of accessors from Evaluator\n      auto tuple_of_accessors = internal::createTupleOfAccessors<decltype(evaluator)>(cgh, evaluator);\n      const auto range = utility::tuple::get<0>(tuple_of_accessors).get_range()[0];\n      size_t GRange=range;\n      if (tileSize>GRange) tileSize=GRange;\n      else if(GRange>tileSize){\n        size_t xMode = GRange % tileSize;\n        if (xMode != 0) GRange += (tileSize - xMode);\n      }\n      // run the kernel\n      cgh.parallel_for<PlaceHolderExpr>( cl::sycl::nd_range<1>(cl::sycl::range<1>(GRange), cl::sycl::range<1>(tileSize)), [=](cl::sycl::nd_item<1> itemID) {\n        typedef  typename internal::ConvertToDeviceExpression<Expr>::Type DevExpr;\n        auto device_expr =internal::createDeviceExpression<DevExpr, PlaceHolderExpr>(functors, tuple_of_accessors);\n        auto device_evaluator = Eigen::TensorEvaluator<decltype(device_expr.expr), Eigen::DefaultDevice>(device_expr.expr, Eigen::DefaultDevice());\n        if (itemID.get_global_linear_id() < range) {\n          device_evaluator.evalScalar(static_cast<int>(itemID.get_global_linear_id()));\n        }\n      });\n    });\n    dev.m_queue.throw_asynchronous();\n  }\n\n  evaluator.cleanup();\n}\n}  // namespace TensorSycl\n}  // namespace Eigen\n\n#endif  // UNSUPPORTED_EIGEN_CXX11_SRC_TENSOR_TENSORSYCL_SYCLRUN_HPP\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorSyclTuple.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Mehdi Goli    Codeplay Software Ltd.\n// Ralph Potter  Codeplay Software Ltd.\n// Luke Iwanski  Codeplay Software Ltd.\n// Contact: <eigen@codeplay.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n/*****************************************************************\n * TensroSyclTuple.h\n *\n * \\brief:\n *  Minimal implementation of std::tuple that can be used inside a SYCL kernel.\n *\n*****************************************************************/\n\n#ifndef UNSUPPORTED_EIGEN_CXX11_SRC_TENSOR_TENSORSYCL_TUPLE_HPP\n#define UNSUPPORTED_EIGEN_CXX11_SRC_TENSOR_TENSORSYCL_TUPLE_HPP\nnamespace utility {\nnamespace tuple {\n/// \\struct StaticIf\n/// \\brief The StaticIf struct is used to statically choose the type based on the\n/// condition.\ntemplate <bool, typename T = void> struct StaticIf;\n/// \\brief specialisation of the \\ref StaticIf when the condition is true\ntemplate <typename T>\nstruct StaticIf<true, T> {\n  typedef T type;\n};\n\n/// \\struct Tuple\n/// \\brief is a fixed-size collection of heterogeneous values\n/// \\ztparam Ts...\t-\tthe types of the elements that the tuple stores.\n/// Empty list is supported.\ntemplate <class... Ts>\nstruct Tuple {};\n\n/// \\brief specialisation of the \\ref Tuple class when the tuple has at least\n/// one element.\n/// \\tparam T : the type of the first element in the tuple.\n/// \\tparam Ts... the rest of the elements in the tuple. Ts... can be empty.\ntemplate <class T, class... Ts>\nstruct Tuple<T, Ts...> {\n  Tuple(T t, Ts... ts) : head(t), tail(ts...) {}\n  T head;\n  Tuple<Ts...> tail;\n};\n\n///\\ struct ElemTypeHolder\n/// \\brief ElemTypeHolder class is used to specify the types of the\n/// elements inside the tuple\n/// \\tparam size_t the number of elements inside the tuple\n/// \\tparam class the tuple class\ntemplate <size_t, class>\nstruct ElemTypeHolder;\n\n/// \\brief specialisation of the \\ref ElemTypeHolder class when the number of\n/// elements inside the tuple is 1\ntemplate <class T, class... Ts>\nstruct ElemTypeHolder<0, Tuple<T, Ts...> > {\n  typedef T type;\n};\n\n/// \\brief specialisation of the \\ref ElemTypeHolder class when the number of\n/// elements inside the tuple is bigger than 1. It recursively calls itself to\n/// detect the type of each element in the tuple\n/// \\tparam T : the type of the first element in the tuple.\n/// \\tparam Ts... the rest of the elements in the tuple. Ts... can be empty.\n/// \\tparam K is the Kth element in the tuple\ntemplate <size_t k, class T, class... Ts>\nstruct ElemTypeHolder<k, Tuple<T, Ts...> > {\n  typedef typename ElemTypeHolder<k - 1, Tuple<Ts...> >::type type;\n};\n\n/// get\n/// \\brief Extracts the first element from the tuple.\n/// K=0 represents the first element of the tuple. The tuple cannot be empty.\n/// \\tparam Ts... are the type of the elements in the tuple.\n/// \\param t is the tuple whose contents to extract\n/// \\return  typename ElemTypeHolder<0, Tuple<Ts...> >::type &>::type\n\n#define TERMINATE_CONDS_TUPLE_GET(CVQual) \\\ntemplate <size_t k, class... Ts> \\\ntypename StaticIf<k == 0, CVQual typename ElemTypeHolder<0, Tuple<Ts...> >::type &>::type \\\nget(CVQual Tuple<Ts...> &t) { \\\n  static_assert(sizeof...(Ts)!=0, \"The requseted value is bigger than the size of the tuple\"); \\\n  return t.head; \\\n}\n\nTERMINATE_CONDS_TUPLE_GET(const)\nTERMINATE_CONDS_TUPLE_GET()\n#undef TERMINATE_CONDS_TUPLE_GET\n/// get\n/// \\brief Extracts the Kth element from the tuple.\n///\\tparam K is an integer value in [0,sizeof...(Types)).\n/// \\tparam T is the (sizeof...(Types) -(K+1)) element in the tuple\n/// \\tparam Ts... are the type of the elements  in the tuple.\n/// \\param t is the tuple whose contents to extract\n/// \\return  typename ElemTypeHolder<K, Tuple<Ts...> >::type &>::type\n#define RECURSIVE_TUPLE_GET(CVQual) \\\ntemplate <size_t k, class T, class... Ts> \\\ntypename StaticIf<k != 0, CVQual typename ElemTypeHolder<k, Tuple<T, Ts...> >::type &>::type \\\nget(CVQual Tuple<T, Ts...> &t) { \\\n  return utility::tuple::get<k - 1>(t.tail); \\\n}\nRECURSIVE_TUPLE_GET(const)\nRECURSIVE_TUPLE_GET()\n#undef RECURSIVE_TUPLE_GET\n\n/// make_tuple\n/// \\brief Creates a tuple object, deducing the target type from the types of\n/// arguments.\n/// \\tparam Args the type of the arguments to construct the tuple from\n/// \\param args zero or more arguments to construct the tuple from\n/// \\return Tuple<Args...>\ntemplate <typename... Args>\nTuple<Args...> make_tuple(Args... args) {\n  return Tuple<Args...>(args...);\n}\n\n/// size\n/// \\brief Provides access to the number of elements in a tuple as a\n/// compile-time constant expression.\n/// \\tparam Args the type of the arguments to construct the tuple from\n/// \\return size_t\ntemplate <typename... Args>\nstatic constexpr size_t size(Tuple<Args...> &) {\n  return sizeof...(Args);\n}\n\n/// \\struct IndexList\n/// \\brief Creates a list of index from the elements in the tuple\n/// \\tparam Is... a list of index from [0 to sizeof...(tuple elements))\ntemplate <size_t... Is>\nstruct IndexList {};\n\n/// \\struct RangeBuilder\n/// \\brief Collects internal details for generating index ranges [MIN, MAX)\n/// Declare primary template for index range builder\n/// \\tparam MIN is the starting index in the tuple\n/// \\tparam N represents sizeof..(elemens)- sizeof...(Is)\n/// \\tparam Is... are the list of generated index so far\ntemplate <size_t MIN, size_t N, size_t... Is>\nstruct RangeBuilder;\n\n/// \\brief base Step: Specialisation of the \\ref RangeBuilder when the\n/// MIN==MAX. In this case the Is... is [0 to sizeof...(tuple elements))\n/// \\tparam MIN is the starting index of the tuple\n/// \\tparam Is is [0 to sizeof...(tuple elements))\ntemplate <size_t MIN, size_t... Is>\nstruct RangeBuilder<MIN, MIN, Is...> {\n  typedef IndexList<Is...> type;\n};\n\n/// Induction step: Specialisation of the RangeBuilder class when N!=MIN\n/// in this case we are recursively subtracting N by one and adding one\n/// index to Is... list until MIN==N\n/// \\tparam MIN is the starting index in the tuple\n/// \\tparam N represents sizeof..(elemens)- sizeof...(Is)\n/// \\tparam Is... are the list of generated index so far\ntemplate <size_t MIN, size_t N, size_t... Is>\nstruct RangeBuilder : public RangeBuilder<MIN, N - 1, N - 1, Is...> {};\n\n/// \\brief IndexRange that returns a [MIN, MAX) index range\n/// \\tparam MIN is the starting index in the tuple\n/// \\tparam MAX is the size of the tuple\ntemplate <size_t MIN, size_t MAX>\nstruct IndexRange: RangeBuilder<MIN, MAX>::type {};\n\n/// append_base\n/// \\brief unpacking the elements of the input tuple t and creating a new tuple\n/// by adding element a at the end of it.\n///\\tparam Args... the type of the elements inside the tuple t\n/// \\tparam T the type of the new element going to be added at the end of tuple\n/// \\tparam I... is the list of index from [0 to sizeof...(t))\n/// \\param t the tuple on which we want to append a.\n/// \\param a the new elements going to be added to the tuple\n/// \\return Tuple<Args..., T>\ntemplate <typename... Args, typename T, size_t... I>\nTuple<Args..., T> append_base(Tuple<Args...> t, T a,IndexList<I...>) {\n  return utility::tuple::make_tuple(get<I>(t)..., a);\n}\n\n/// append\n/// \\brief the deduction function for \\ref append_base that automatically\n/// generate the \\ref IndexRange\n///\\tparam Args... the type of the elements inside the tuple t\n/// \\tparam T the type of the new element going to be added at the end of tuple\n/// \\param t the tuple on which we want to append a.\n/// \\param a the new elements going to be added to the tuple\n/// \\return Tuple<Args..., T>\ntemplate <typename... Args, typename T>\nTuple<Args..., T> append(Tuple<Args...> t, T a) {\n  return utility::tuple::append_base(t, a,  IndexRange<0, sizeof...(Args)>());\n}\n\n/// append_base\n/// \\brief This is a specialisation of \\ref append_base when we want to\n/// concatenate\n/// tuple t2 at the end of the tuple t1. Here we unpack both tuples, generate the\n/// IndexRange for each of them and create an output tuple T that contains both\n/// elements of t1 and t2.\n///\\tparam Args1... the type of the elements inside the tuple t1\n///\\tparam Args2... the type of the elements inside the tuple t2\n/// \\tparam I1... is the list of index from [0 to sizeof...(t1))\n/// \\tparam I2... is the list of index from [0 to sizeof...(t2))\n/// \\param t1 is the tuple on which we want to append t2.\n/// \\param t2 is the tuple that is going to be added on t1.\n/// \\return Tuple<Args1..., Args2...>\ntemplate <typename... Args1, typename... Args2, size_t... I1, size_t... I2>\nTuple<Args1..., Args2...> append_base(Tuple<Args1...> t1, Tuple<Args2...> t2, IndexList<I1...>, IndexList<I2...>) {\n  return utility::tuple::make_tuple(get<I1>(t1)...,get<I2>(t2)...);\n}\n\n/// append\n/// \\brief deduction function for \\ref append_base when we are appending tuple\n/// t1 by tuple t2. In this case the \\ref IndexRange for both tuple are\n/// automatically generated.\n///\\tparam Args1... the type of the elements inside the tuple t1\n///\\tparam Args2... the type of the elements inside the tuple t2\n/// \\param t1 is the tuple on which we want to append t2.\n/// \\param t2 is the tuple that is going to be added on t1.\n/// \\return Tuple<Args1..., Args2...>\ntemplate <typename... Args1, typename... Args2>\nTuple<Args1..., Args2...> append(Tuple<Args1...> t1,Tuple<Args2...> t2) {\n  return utility::tuple::append_base(t1, t2, IndexRange<0, sizeof...(Args1)>(), IndexRange<0, sizeof...(Args2)>());\n}\n}  // tuple\n}  // utility\n#endif  // UNSUPPORTED_EIGEN_CXX11_SRC_TENSOR_TENSORSYCL_TUPLE_HPP\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorTraits.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_TRAITS_H\n#define EIGEN_CXX11_TENSOR_TENSOR_TRAITS_H\n\nnamespace Eigen {\nnamespace internal {\n\n\ntemplate<typename Scalar, int Options>\nclass compute_tensor_flags\n{\n  enum {\n    is_dynamic_size_storage = 1,\n\n    is_aligned =\n    (\n        ((Options&DontAlign)==0) && (\n#if EIGEN_MAX_STATIC_ALIGN_BYTES>0\n            (!is_dynamic_size_storage)\n#else\n            0\n#endif\n            |\n#if EIGEN_MAX_ALIGN_BYTES>0\n            is_dynamic_size_storage\n#else\n            0\n#endif\n      )\n     ),\n    packet_access_bit = packet_traits<Scalar>::Vectorizable && is_aligned ? PacketAccessBit : 0\n  };\n\n  public:\n    enum { ret = packet_access_bit };\n};\n\n\ntemplate<typename Scalar_, int NumIndices_, int Options_, typename IndexType_>\nstruct traits<Tensor<Scalar_, NumIndices_, Options_, IndexType_> >\n{\n  typedef Scalar_ Scalar;\n  typedef Dense StorageKind;\n  typedef IndexType_ Index;\n  static const int NumDimensions = NumIndices_;\n  static const int Layout = Options_ & RowMajor ? RowMajor : ColMajor;\n  enum {\n    Options = Options_,\n    Flags = compute_tensor_flags<Scalar_, Options_>::ret | (is_const<Scalar_>::value ? 0 : LvalueBit)\n  };\n  template <typename T> struct MakePointer {\n    typedef T* Type;\n  };\n};\n\n\ntemplate<typename Scalar_, typename Dimensions, int Options_, typename IndexType_>\nstruct traits<TensorFixedSize<Scalar_, Dimensions, Options_, IndexType_> >\n{\n  typedef Scalar_ Scalar;\n  typedef Dense StorageKind;\n  typedef IndexType_ Index;\n  static const int NumDimensions = array_size<Dimensions>::value;\n  static const int Layout = Options_ & RowMajor ? RowMajor : ColMajor;\n  enum {\n    Options = Options_,\n    Flags = compute_tensor_flags<Scalar_, Options_>::ret | (is_const<Scalar_>::value ? 0: LvalueBit)\n  };\n  template <typename T> struct MakePointer {\n    typedef T* Type;\n  };\n};\n\n\ntemplate<typename PlainObjectType, int Options_, template <class> class MakePointer_>\nstruct traits<TensorMap<PlainObjectType, Options_, MakePointer_> >\n  : public traits<PlainObjectType>\n{\n  typedef traits<PlainObjectType> BaseTraits;\n  typedef typename BaseTraits::Scalar Scalar;\n  typedef typename BaseTraits::StorageKind StorageKind;\n  typedef typename BaseTraits::Index Index;\n  static const int NumDimensions = BaseTraits::NumDimensions;\n  static const int Layout = BaseTraits::Layout;\n  enum {\n    Options = Options_,\n    Flags = BaseTraits::Flags\n  };\n  template <class T> struct MakePointer {\n    // Intermediate typedef to workaround MSVC issue.\n    typedef MakePointer_<T> MakePointerT;\n    typedef typename MakePointerT::Type Type;\n  };\n};\n\ntemplate<typename PlainObjectType>\nstruct traits<TensorRef<PlainObjectType> >\n  : public traits<PlainObjectType>\n{\n  typedef traits<PlainObjectType> BaseTraits;\n  typedef typename BaseTraits::Scalar Scalar;\n  typedef typename BaseTraits::StorageKind StorageKind;\n  typedef typename BaseTraits::Index Index;\n  static const int NumDimensions = BaseTraits::NumDimensions;\n  static const int Layout = BaseTraits::Layout;\n  enum {\n    Options = BaseTraits::Options,\n    Flags = BaseTraits::Flags\n  };\n};\n\n\ntemplate<typename _Scalar, int NumIndices_, int Options, typename IndexType_>\nstruct eval<Tensor<_Scalar, NumIndices_, Options, IndexType_>, Eigen::Dense>\n{\n  typedef const Tensor<_Scalar, NumIndices_, Options, IndexType_>& type;\n};\n\ntemplate<typename _Scalar, int NumIndices_, int Options, typename IndexType_>\nstruct eval<const Tensor<_Scalar, NumIndices_, Options, IndexType_>, Eigen::Dense>\n{\n  typedef const Tensor<_Scalar, NumIndices_, Options, IndexType_>& type;\n};\n\ntemplate<typename Scalar_, typename Dimensions, int Options, typename IndexType_>\nstruct eval<TensorFixedSize<Scalar_, Dimensions, Options, IndexType_>, Eigen::Dense>\n{\n  typedef const TensorFixedSize<Scalar_, Dimensions, Options, IndexType_>& type;\n};\n\ntemplate<typename Scalar_, typename Dimensions, int Options, typename IndexType_>\nstruct eval<const TensorFixedSize<Scalar_, Dimensions, Options, IndexType_>, Eigen::Dense>\n{\n  typedef const TensorFixedSize<Scalar_, Dimensions, Options, IndexType_>& type;\n};\n\ntemplate<typename PlainObjectType, int Options, template <class> class MakePointer>\nstruct eval<TensorMap<PlainObjectType, Options, MakePointer>, Eigen::Dense>\n{\n  typedef const TensorMap<PlainObjectType, Options, MakePointer>& type;\n};\n\ntemplate<typename PlainObjectType, int Options, template <class> class MakePointer>\nstruct eval<const TensorMap<PlainObjectType, Options, MakePointer>, Eigen::Dense>\n{\n  typedef const TensorMap<PlainObjectType, Options, MakePointer>& type;\n};\n\ntemplate<typename PlainObjectType>\nstruct eval<TensorRef<PlainObjectType>, Eigen::Dense>\n{\n  typedef const TensorRef<PlainObjectType>& type;\n};\n\ntemplate<typename PlainObjectType>\nstruct eval<const TensorRef<PlainObjectType>, Eigen::Dense>\n{\n  typedef const TensorRef<PlainObjectType>& type;\n};\n\n// TODO nested<> does not exist anymore in Eigen/Core, and it thus has to be removed in favor of ref_selector.\ntemplate<typename T, int n=1, typename PlainObject = void> struct nested\n{\n  typedef typename ref_selector<T>::type type;\n};\n\ntemplate <typename Scalar_, int NumIndices_, int Options_, typename IndexType_>\nstruct nested<Tensor<Scalar_, NumIndices_, Options_, IndexType_> >\n{\n  typedef const Tensor<Scalar_, NumIndices_, Options_, IndexType_>& type;\n};\n\ntemplate <typename Scalar_, int NumIndices_, int Options_, typename IndexType_>\nstruct nested<const Tensor<Scalar_, NumIndices_, Options_, IndexType_> >\n{\n  typedef const Tensor<Scalar_, NumIndices_, Options_, IndexType_>& type;\n};\n\ntemplate <typename Scalar_, typename Dimensions, int Options, typename IndexType_>\nstruct nested<TensorFixedSize<Scalar_, Dimensions, Options, IndexType_> >\n{\n  typedef const TensorFixedSize<Scalar_, Dimensions, Options, IndexType_>& type;\n};\n\ntemplate <typename Scalar_, typename Dimensions, int Options, typename IndexType_>\nstruct nested<const TensorFixedSize<Scalar_, Dimensions, Options, IndexType_> >\n{\n  typedef const TensorFixedSize<Scalar_, Dimensions, Options, IndexType_>& type;\n};\n\n\ntemplate <typename PlainObjectType, int Options, template <class> class MakePointer>\nstruct nested<TensorMap<PlainObjectType, Options, MakePointer> >\n{\n  typedef const TensorMap<PlainObjectType, Options, MakePointer>& type;\n};\n\ntemplate <typename PlainObjectType, int Options, template <class> class MakePointer>\nstruct nested<const TensorMap<PlainObjectType, Options, MakePointer> >\n{\n  typedef const TensorMap<PlainObjectType, Options, MakePointer>& type;\n};\n\ntemplate <typename PlainObjectType>\nstruct nested<TensorRef<PlainObjectType> >\n{\n  typedef const TensorRef<PlainObjectType>& type;\n};\n\ntemplate <typename PlainObjectType>\nstruct nested<const TensorRef<PlainObjectType> >\n{\n  typedef const TensorRef<PlainObjectType>& type;\n};\n\n}  // end namespace internal\n\n// Convolutional layers take in an input tensor of shape (D, R, C, B), or (D, C,\n// R, B), and convolve it with a set of filters, which can also be presented as\n// a tensor (D, K, K, M), where M is the number of filters, K is the filter\n// size, and each 3-dimensional tensor of size (D, K, K) is a filter. For\n// simplicity we assume that we always use square filters (which is usually the\n// case in images), hence the two Ks in the tensor dimension.  It also takes in\n// a few additional parameters:\n// Stride (S): The convolution stride is the offset between locations where we\n//             apply the filters.  A larger stride means that the output will be\n//             spatially smaller.\n// Padding (P): The padding we apply to the input tensor along the R and C\n//              dimensions.  This is usually used to make sure that the spatial\n//              dimensions of the output matches our intention.\n//\n// Two types of padding are often used:\n//   SAME: The pad value is computed so that the output will have size\n//         R/S and C/S.\n//   VALID: no padding is carried out.\n// When we do padding, the padded values at the padded locations are usually\n// zero.\n//\n// The output dimensions for convolution, when given all the parameters above,\n// are as follows:\n// When Padding = SAME: the output size is (B, R', C', M), where\n//   R' = ceil(float(R) / float(S))\n//   C' = ceil(float(C) / float(S))\n// where ceil is the ceiling function.  The input tensor is padded with 0 as\n// needed.  The number of padded rows and columns are computed as:\n//   Pr = ((R' - 1) * S + K - R) / 2\n//   Pc = ((C' - 1) * S + K - C) / 2\n// when the stride is 1, we have the simplified case R'=R, C'=C, Pr=Pc=(K-1)/2.\n// This is where SAME comes from - the output has the same size as the input has.\n// When Padding = VALID: the output size is computed as\n//   R' = ceil(float(R - K + 1) / float(S))\n//   C' = ceil(float(C - K + 1) / float(S))\n// and the number of padded rows and columns are computed in the same way as in\n// the SAME case.\n// When the stride is 1, we have the simplified case R'=R-K+1, C'=C-K+1, Pr=0,\n// Pc=0.\ntypedef enum {\n  PADDING_VALID = 1,\n  PADDING_SAME = 2\n} PaddingType;\n\n}  // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_TRAITS_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorUInt128.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_UINT128_H\n#define EIGEN_CXX11_TENSOR_TENSOR_UINT128_H\n\nnamespace Eigen {\nnamespace internal {\n\n\ntemplate <uint64_t n>\nstruct static_val {\n  static const uint64_t value = n;\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE operator uint64_t() const { return n; }\n\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE static_val() { }\n\n  template <typename T>\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE static_val(const T& v) {\n    eigen_assert(v == n);\n  }\n};\n\n\ntemplate <typename HIGH = uint64_t, typename LOW = uint64_t>\nstruct TensorUInt128\n{\n  HIGH high;\n  LOW low;\n\n  template<typename OTHER_HIGH, typename OTHER_LOW>\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\n  TensorUInt128(const TensorUInt128<OTHER_HIGH, OTHER_LOW>& other) : high(other.high), low(other.low) {\n    EIGEN_STATIC_ASSERT(sizeof(OTHER_HIGH) <= sizeof(HIGH), YOU_MADE_A_PROGRAMMING_MISTAKE);\n    EIGEN_STATIC_ASSERT(sizeof(OTHER_LOW) <= sizeof(LOW), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  }\n\n  template<typename OTHER_HIGH, typename OTHER_LOW>\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\n  TensorUInt128& operator = (const TensorUInt128<OTHER_HIGH, OTHER_LOW>& other) {\n    EIGEN_STATIC_ASSERT(sizeof(OTHER_HIGH) <= sizeof(HIGH), YOU_MADE_A_PROGRAMMING_MISTAKE);\n    EIGEN_STATIC_ASSERT(sizeof(OTHER_LOW) <= sizeof(LOW), YOU_MADE_A_PROGRAMMING_MISTAKE);\n    high = other.high;\n    low = other.low;\n    return *this;\n  }\n\n  template<typename T>\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\n  explicit TensorUInt128(const T& x) : high(0), low(x) {\n    eigen_assert((static_cast<typename conditional<sizeof(T) == 8, uint64_t, uint32_t>::type>(x) <= NumTraits<uint64_t>::highest()));\n    eigen_assert(x >= 0);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\n  TensorUInt128(HIGH y, LOW x) : high(y), low(x) { }\n\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE operator LOW() const {\n    return low;\n  }\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE LOW lower() const {\n    return low;\n  }\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE HIGH upper() const {\n    return high;\n  }\n};\n\n\ntemplate <typename HL, typename LL, typename HR, typename LR>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nbool operator == (const TensorUInt128<HL, LL>& lhs, const TensorUInt128<HR, LR>& rhs)\n{\n  return (lhs.high == rhs.high) & (lhs.low == rhs.low);\n}\n\ntemplate <typename HL, typename LL, typename HR, typename LR>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nbool operator != (const TensorUInt128<HL, LL>& lhs, const TensorUInt128<HR, LR>& rhs)\n{\n  return (lhs.high != rhs.high) | (lhs.low != rhs.low);\n}\n\ntemplate <typename HL, typename LL, typename HR, typename LR>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nbool operator >= (const TensorUInt128<HL, LL>& lhs, const TensorUInt128<HR, LR>& rhs)\n{\n  if (lhs.high != rhs.high) {\n    return lhs.high > rhs.high;\n  }\n  return lhs.low >= rhs.low;\n}\n\ntemplate <typename HL, typename LL, typename HR, typename LR>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nbool operator < (const TensorUInt128<HL, LL>& lhs, const TensorUInt128<HR, LR>& rhs)\n{\n  if (lhs.high != rhs.high) {\n    return lhs.high < rhs.high;\n  }\n  return lhs.low < rhs.low;\n}\n\ntemplate <typename HL, typename LL, typename HR, typename LR>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nTensorUInt128<uint64_t, uint64_t> operator + (const TensorUInt128<HL, LL>& lhs, const TensorUInt128<HR, LR>& rhs)\n{\n  TensorUInt128<uint64_t, uint64_t> result(lhs.high + rhs.high, lhs.low + rhs.low);\n  if (result.low < rhs.low) {\n    result.high += 1;\n  }\n  return result;\n}\n\ntemplate <typename HL, typename LL, typename HR, typename LR>\nEIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\nTensorUInt128<uint64_t, uint64_t> operator - (const TensorUInt128<HL, LL>& lhs, const TensorUInt128<HR, LR>& rhs)\n{\n  TensorUInt128<uint64_t, uint64_t> result(lhs.high - rhs.high, lhs.low - rhs.low);\n  if (result.low > lhs.low) {\n    result.high -= 1;\n  }\n  return result;\n}\n\n\ntemplate <typename HL, typename LL, typename HR, typename LR>\nstatic EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nTensorUInt128<uint64_t, uint64_t> operator * (const TensorUInt128<HL, LL>& lhs, const TensorUInt128<HR, LR>& rhs)\n{\n  // Split each 128-bit integer into 4 32-bit integers, and then do the\n  // multiplications by hand as follow:\n  //   lhs      a  b  c  d\n  //   rhs      e  f  g  h\n  //           -----------\n  //           ah bh ch dh\n  //           bg cg dg\n  //           cf df\n  //           de\n  // The result is stored in 2 64bit integers, high and low.\n\n  const uint64_t LOW = 0x00000000FFFFFFFFLL;\n  const uint64_t HIGH = 0xFFFFFFFF00000000LL;\n\n  uint64_t d = lhs.low & LOW;\n  uint64_t c = (lhs.low & HIGH) >> 32LL;\n  uint64_t b = lhs.high & LOW;\n  uint64_t a = (lhs.high & HIGH) >> 32LL;\n\n  uint64_t h = rhs.low & LOW;\n  uint64_t g = (rhs.low & HIGH) >> 32LL;\n  uint64_t f = rhs.high & LOW;\n  uint64_t e = (rhs.high & HIGH) >> 32LL;\n\n  // Compute the low 32 bits of low\n  uint64_t acc = d * h;\n  uint64_t low = acc & LOW;\n  //  Compute the high 32 bits of low. Add a carry every time we wrap around\n  acc >>= 32LL;\n  uint64_t carry = 0;\n  uint64_t acc2 = acc + c * h;\n  if (acc2 < acc) {\n    carry++;\n  }\n  acc = acc2 + d * g;\n  if (acc < acc2) {\n    carry++;\n  }\n  low |= (acc << 32LL);\n\n  // Carry forward the high bits of acc to initiate the computation of the\n  // low 32 bits of high\n  acc2 = (acc >> 32LL) | (carry << 32LL);\n  carry = 0;\n\n  acc = acc2 + b * h;\n  if (acc < acc2) {\n    carry++;\n  }\n  acc2 = acc + c * g;\n  if (acc2 < acc) {\n    carry++;\n  }\n  acc = acc2 + d * f;\n  if (acc < acc2) {\n    carry++;\n  }\n  uint64_t high = acc & LOW;\n\n  // Start to compute the high 32 bits of high.\n  acc2 = (acc >> 32LL) | (carry << 32LL);\n\n  acc = acc2 + a * h;\n  acc2 = acc + b * g;\n  acc = acc2 + c * f;\n  acc2 = acc + d * e;\n  high |= (acc2 << 32LL);\n\n  return TensorUInt128<uint64_t, uint64_t>(high, low);\n}\n\ntemplate <typename HL, typename LL, typename HR, typename LR>\nstatic EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nTensorUInt128<uint64_t, uint64_t> operator / (const TensorUInt128<HL, LL>& lhs, const TensorUInt128<HR, LR>& rhs)\n{\n  if (rhs == TensorUInt128<static_val<0>, static_val<1> >(1)) {\n    return TensorUInt128<uint64_t, uint64_t>(lhs.high, lhs.low);\n  } else if (lhs < rhs) {\n    return TensorUInt128<uint64_t, uint64_t>(0);\n  } else {\n    // calculate the biggest power of 2 times rhs that's less than or equal to lhs\n    TensorUInt128<uint64_t, uint64_t> power2(1);\n    TensorUInt128<uint64_t, uint64_t> d(rhs);\n    TensorUInt128<uint64_t, uint64_t> tmp(lhs - d);\n    while (lhs >= d) {\n      tmp = tmp - d;\n      d = d + d;\n      power2 = power2 + power2;\n    }\n\n    tmp = TensorUInt128<uint64_t, uint64_t>(lhs.high, lhs.low);\n    TensorUInt128<uint64_t, uint64_t> result(0);\n    while (power2 != TensorUInt128<static_val<0>, static_val<0> >(0)) {\n      if (tmp >= d) {\n        tmp = tmp - d;\n        result = result + power2;\n      }\n      // Shift right\n      power2 = TensorUInt128<uint64_t, uint64_t>(power2.high >> 1, (power2.low >> 1) | (power2.high << 63));\n      d = TensorUInt128<uint64_t, uint64_t>(d.high >> 1, (d.low >> 1) | (d.high << 63));\n    }\n\n    return result;\n  }\n}\n\n\n}  // namespace internal\n}  // namespace Eigen\n\n\n#endif  // EIGEN_CXX11_TENSOR_TENSOR_UINT128_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorVolumePatch.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n\n#ifndef EIGEN_CXX11_TENSOR_TENSOR_VOLUME_PATCH_H\n#define EIGEN_CXX11_TENSOR_TENSOR_VOLUME_PATCH_H\n\nnamespace Eigen {\n\n/** \\class TensorVolumePatch\n  * \\ingroup CXX11_Tensor_Module\n  *\n  * \\brief Patch extraction specialized for processing of volumetric data.\n  * This assumes that the input has a least 4 dimensions ordered as follows:\n  *  - channels\n  *  - planes\n  *  - rows\n  *  - columns\n  *  - (optional) additional dimensions such as time or batch size.\n  * Calling the volume patch code with patch_planes, patch_rows, and patch_cols\n  * is equivalent to calling the regular patch extraction code with parameters\n  * d, patch_planes, patch_rows, patch_cols, and 1 for all the additional\n  * dimensions.\n  */\nnamespace internal {\ntemplate<DenseIndex Planes, DenseIndex Rows, DenseIndex Cols, typename XprType>\nstruct traits<TensorVolumePatchOp<Planes, Rows, Cols, XprType> > : public traits<XprType>\n{\n  typedef typename internal::remove_const<typename XprType::Scalar>::type Scalar;\n  typedef traits<XprType> XprTraits;\n  typedef typename XprTraits::StorageKind StorageKind;\n  typedef typename XprTraits::Index Index;\n  typedef typename XprType::Nested Nested;\n  typedef typename remove_reference<Nested>::type _Nested;\n  static const int NumDimensions = XprTraits::NumDimensions + 1;\n  static const int Layout = XprTraits::Layout;\n};\n\ntemplate<DenseIndex Planes, DenseIndex Rows, DenseIndex Cols, typename XprType>\nstruct eval<TensorVolumePatchOp<Planes, Rows, Cols, XprType>, Eigen::Dense>\n{\n  typedef const TensorVolumePatchOp<Planes, Rows, Cols, XprType>& type;\n};\n\ntemplate<DenseIndex Planes, DenseIndex Rows, DenseIndex Cols, typename XprType>\nstruct nested<TensorVolumePatchOp<Planes, Rows, Cols, XprType>, 1, typename eval<TensorVolumePatchOp<Planes, Rows, Cols, XprType> >::type>\n{\n  typedef TensorVolumePatchOp<Planes, Rows, Cols, XprType> type;\n};\n\n}  // end namespace internal\n\ntemplate<DenseIndex Planes, DenseIndex Rows, DenseIndex Cols, typename XprType>\nclass TensorVolumePatchOp : public TensorBase<TensorVolumePatchOp<Planes, Rows, Cols, XprType>, ReadOnlyAccessors>\n{\n  public:\n  typedef typename Eigen::internal::traits<TensorVolumePatchOp>::Scalar Scalar;\n  typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename Eigen::internal::nested<TensorVolumePatchOp>::type Nested;\n  typedef typename Eigen::internal::traits<TensorVolumePatchOp>::StorageKind StorageKind;\n  typedef typename Eigen::internal::traits<TensorVolumePatchOp>::Index Index;\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorVolumePatchOp(const XprType& expr, DenseIndex patch_planes, DenseIndex patch_rows, DenseIndex patch_cols,\n                                                            DenseIndex plane_strides, DenseIndex row_strides, DenseIndex col_strides,\n                                                            DenseIndex in_plane_strides, DenseIndex in_row_strides, DenseIndex in_col_strides,\n                                                            DenseIndex plane_inflate_strides, DenseIndex row_inflate_strides, DenseIndex col_inflate_strides,\n                                                            PaddingType padding_type, Scalar padding_value)\n      : m_xpr(expr), m_patch_planes(patch_planes), m_patch_rows(patch_rows), m_patch_cols(patch_cols),\n        m_plane_strides(plane_strides), m_row_strides(row_strides), m_col_strides(col_strides),\n        m_in_plane_strides(in_plane_strides), m_in_row_strides(in_row_strides), m_in_col_strides(in_col_strides),\n        m_plane_inflate_strides(plane_inflate_strides), m_row_inflate_strides(row_inflate_strides), m_col_inflate_strides(col_inflate_strides),\n        m_padding_explicit(false), m_padding_top_z(0), m_padding_bottom_z(0), m_padding_top(0), m_padding_bottom(0), m_padding_left(0), m_padding_right(0),\n        m_padding_type(padding_type), m_padding_value(padding_value) {}\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorVolumePatchOp(const XprType& expr, DenseIndex patch_planes, DenseIndex patch_rows, DenseIndex patch_cols,\n                                                           DenseIndex plane_strides, DenseIndex row_strides, DenseIndex col_strides,\n                                                           DenseIndex in_plane_strides, DenseIndex in_row_strides, DenseIndex in_col_strides,\n                                                           DenseIndex plane_inflate_strides, DenseIndex row_inflate_strides, DenseIndex col_inflate_strides,\n                                                           DenseIndex padding_top_z, DenseIndex padding_bottom_z,\n                                                           DenseIndex padding_top, DenseIndex padding_bottom,\n                                                           DenseIndex padding_left, DenseIndex padding_right,\n                                                           Scalar padding_value)\n      : m_xpr(expr), m_patch_planes(patch_planes), m_patch_rows(patch_rows), m_patch_cols(patch_cols),\n        m_plane_strides(plane_strides), m_row_strides(row_strides), m_col_strides(col_strides),\n        m_in_plane_strides(in_plane_strides), m_in_row_strides(in_row_strides), m_in_col_strides(in_col_strides),\n        m_plane_inflate_strides(plane_inflate_strides), m_row_inflate_strides(row_inflate_strides), m_col_inflate_strides(col_inflate_strides),\n        m_padding_explicit(true), m_padding_top_z(padding_top_z), m_padding_bottom_z(padding_bottom_z), m_padding_top(padding_top), m_padding_bottom(padding_bottom),\n        m_padding_left(padding_left), m_padding_right(padding_right),\n        m_padding_type(PADDING_VALID), m_padding_value(padding_value) {}\n\n    EIGEN_DEVICE_FUNC\n    DenseIndex patch_planes() const { return m_patch_planes; }\n    EIGEN_DEVICE_FUNC\n    DenseIndex patch_rows() const { return m_patch_rows; }\n    EIGEN_DEVICE_FUNC\n    DenseIndex patch_cols() const { return m_patch_cols; }\n    EIGEN_DEVICE_FUNC\n    DenseIndex plane_strides() const { return m_plane_strides; }\n    EIGEN_DEVICE_FUNC\n    DenseIndex row_strides() const { return m_row_strides; }\n    EIGEN_DEVICE_FUNC\n    DenseIndex col_strides() const { return m_col_strides; }\n    EIGEN_DEVICE_FUNC\n    DenseIndex in_plane_strides() const { return m_in_plane_strides; }\n    EIGEN_DEVICE_FUNC\n    DenseIndex in_row_strides() const { return m_in_row_strides; }\n    EIGEN_DEVICE_FUNC\n    DenseIndex in_col_strides() const { return m_in_col_strides; }\n    EIGEN_DEVICE_FUNC\n    DenseIndex plane_inflate_strides() const { return m_plane_inflate_strides; }\n    EIGEN_DEVICE_FUNC\n    DenseIndex row_inflate_strides() const { return m_row_inflate_strides; }\n    EIGEN_DEVICE_FUNC\n    DenseIndex col_inflate_strides() const { return m_col_inflate_strides; }\n    EIGEN_DEVICE_FUNC\n    bool padding_explicit() const { return m_padding_explicit; }\n    EIGEN_DEVICE_FUNC\n    DenseIndex padding_top_z() const { return m_padding_top_z; }\n    EIGEN_DEVICE_FUNC\n    DenseIndex padding_bottom_z() const { return m_padding_bottom_z; }\n    EIGEN_DEVICE_FUNC\n    DenseIndex padding_top() const { return m_padding_top; }\n    EIGEN_DEVICE_FUNC\n    DenseIndex padding_bottom() const { return m_padding_bottom; }\n    EIGEN_DEVICE_FUNC\n    DenseIndex padding_left() const { return m_padding_left; }\n    EIGEN_DEVICE_FUNC\n    DenseIndex padding_right() const { return m_padding_right; }\n    EIGEN_DEVICE_FUNC\n    PaddingType padding_type() const { return m_padding_type; }\n    EIGEN_DEVICE_FUNC\n    Scalar padding_value() const { return m_padding_value; }\n\n    EIGEN_DEVICE_FUNC\n    const typename internal::remove_all<typename XprType::Nested>::type&\n    expression() const { return m_xpr; }\n\n  protected:\n    typename XprType::Nested m_xpr;\n    const DenseIndex m_patch_planes;\n    const DenseIndex m_patch_rows;\n    const DenseIndex m_patch_cols;\n    const DenseIndex m_plane_strides;\n    const DenseIndex m_row_strides;\n    const DenseIndex m_col_strides;\n    const DenseIndex m_in_plane_strides;\n    const DenseIndex m_in_row_strides;\n    const DenseIndex m_in_col_strides;\n    const DenseIndex m_plane_inflate_strides;\n    const DenseIndex m_row_inflate_strides;\n    const DenseIndex m_col_inflate_strides;\n    const bool m_padding_explicit;\n    const DenseIndex m_padding_top_z;\n    const DenseIndex m_padding_bottom_z;\n    const DenseIndex m_padding_top;\n    const DenseIndex m_padding_bottom;\n    const DenseIndex m_padding_left;\n    const DenseIndex m_padding_right;\n    const PaddingType m_padding_type;\n    const Scalar m_padding_value;\n};\n\n\n// Eval as rvalue\ntemplate<DenseIndex Planes, DenseIndex Rows, DenseIndex Cols, typename ArgType, typename Device>\nstruct TensorEvaluator<const TensorVolumePatchOp<Planes, Rows, Cols, ArgType>, Device>\n{\n  typedef TensorVolumePatchOp<Planes, Rows, Cols, ArgType> XprType;\n  typedef typename XprType::Index Index;\n  static const int NumInputDims = internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value;\n  static const int NumDims = NumInputDims + 1;\n  typedef DSizes<Index, NumDims> Dimensions;\n  typedef typename internal::remove_const<typename XprType::Scalar>::type Scalar;\n  typedef typename XprType::CoeffReturnType CoeffReturnType;\n  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;\n  static const int PacketSize = internal::unpacket_traits<PacketReturnType>::size;\n\n  enum {\n    IsAligned = false,\n    PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,\n    BlockAccess = false,\n    Layout = TensorEvaluator<ArgType, Device>::Layout,\n    CoordAccess = false,\n    RawAccess = false\n  };\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)\n      : m_impl(op.expression(), device)\n  {\n    EIGEN_STATIC_ASSERT((NumDims >= 5), YOU_MADE_A_PROGRAMMING_MISTAKE);\n\n    m_paddingValue = op.padding_value();\n\n    const typename TensorEvaluator<ArgType, Device>::Dimensions& input_dims = m_impl.dimensions();\n\n    // Cache a few variables.\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      m_inputDepth = input_dims[0];\n      m_inputPlanes = input_dims[1];\n      m_inputRows = input_dims[2];\n      m_inputCols = input_dims[3];\n    } else {\n      m_inputDepth = input_dims[NumInputDims-1];\n      m_inputPlanes = input_dims[NumInputDims-2];\n      m_inputRows = input_dims[NumInputDims-3];\n      m_inputCols = input_dims[NumInputDims-4];\n    }\n\n    m_plane_strides = op.plane_strides();\n    m_row_strides = op.row_strides();\n    m_col_strides = op.col_strides();\n\n    // Input strides and effective input/patch size\n    m_in_plane_strides = op.in_plane_strides();\n    m_in_row_strides = op.in_row_strides();\n    m_in_col_strides = op.in_col_strides();\n    m_plane_inflate_strides = op.plane_inflate_strides();\n    m_row_inflate_strides = op.row_inflate_strides();\n    m_col_inflate_strides = op.col_inflate_strides();\n\n    // The \"effective\" spatial size after inflating data with zeros.\n    m_input_planes_eff = (m_inputPlanes - 1) * m_plane_inflate_strides + 1;\n    m_input_rows_eff = (m_inputRows - 1) * m_row_inflate_strides + 1;\n    m_input_cols_eff = (m_inputCols - 1) * m_col_inflate_strides + 1;\n    m_patch_planes_eff = op.patch_planes() + (op.patch_planes() - 1) * (m_in_plane_strides - 1);\n    m_patch_rows_eff = op.patch_rows() + (op.patch_rows() - 1) * (m_in_row_strides - 1);\n    m_patch_cols_eff = op.patch_cols() + (op.patch_cols() - 1) * (m_in_col_strides - 1);\n\n    if (op.padding_explicit()) {\n      m_outputPlanes = numext::ceil((m_input_planes_eff + op.padding_top_z() + op.padding_bottom_z() - m_patch_planes_eff + 1.f) / static_cast<float>(m_plane_strides));\n      m_outputRows = numext::ceil((m_input_rows_eff + op.padding_top() + op.padding_bottom() - m_patch_rows_eff + 1.f) / static_cast<float>(m_row_strides));\n      m_outputCols = numext::ceil((m_input_cols_eff + op.padding_left() + op.padding_right() - m_patch_cols_eff + 1.f) / static_cast<float>(m_col_strides));\n      m_planePaddingTop = op.padding_top_z();\n      m_rowPaddingTop = op.padding_top();\n      m_colPaddingLeft = op.padding_left();\n    } else {\n      // Computing padding from the type\n      switch (op.padding_type()) {\n        case PADDING_VALID:\n          m_outputPlanes = numext::ceil((m_input_planes_eff - m_patch_planes_eff + 1.f) / static_cast<float>(m_plane_strides));\n          m_outputRows = numext::ceil((m_input_rows_eff - m_patch_rows_eff + 1.f) / static_cast<float>(m_row_strides));\n          m_outputCols = numext::ceil((m_input_cols_eff - m_patch_cols_eff + 1.f) / static_cast<float>(m_col_strides));\n          m_planePaddingTop = 0;\n          m_rowPaddingTop = 0;\n          m_colPaddingLeft = 0;\n          break;\n        case PADDING_SAME: {\n          m_outputPlanes = numext::ceil(m_input_planes_eff / static_cast<float>(m_plane_strides));\n          m_outputRows = numext::ceil(m_input_rows_eff / static_cast<float>(m_row_strides));\n          m_outputCols = numext::ceil(m_input_cols_eff / static_cast<float>(m_col_strides));\n          const Index dz = m_outputPlanes * m_plane_strides + m_patch_planes_eff - 1 - m_input_planes_eff;\n          const Index dy = m_outputRows * m_row_strides + m_patch_rows_eff - 1 - m_input_rows_eff;\n          const Index dx = m_outputCols * m_col_strides + m_patch_cols_eff - 1 - m_input_cols_eff;\n          m_planePaddingTop = dz - dz / 2;\n          m_rowPaddingTop = dy - dy / 2;\n          m_colPaddingLeft = dx - dx / 2;\n          break;\n        }\n        default:\n          eigen_assert(false && \"unexpected padding\");\n      }\n    }\n    eigen_assert(m_outputRows > 0);\n    eigen_assert(m_outputCols > 0);\n    eigen_assert(m_outputPlanes > 0);\n\n    // Dimensions for result of extraction.\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      // ColMajor\n      // 0: depth\n      // 1: patch_planes\n      // 2: patch_rows\n      // 3: patch_cols\n      // 4: number of patches\n      // 5 and beyond: anything else (such as batch).\n      m_dimensions[0] = input_dims[0];\n      m_dimensions[1] = op.patch_planes();\n      m_dimensions[2] = op.patch_rows();\n      m_dimensions[3] = op.patch_cols();\n      m_dimensions[4] = m_outputPlanes * m_outputRows * m_outputCols;\n      for (int i = 5; i < NumDims; ++i) {\n        m_dimensions[i] = input_dims[i-1];\n      }\n    } else {\n      // RowMajor\n      // NumDims-1: depth\n      // NumDims-2: patch_planes\n      // NumDims-3: patch_rows\n      // NumDims-4: patch_cols\n      // NumDims-5: number of patches\n      // NumDims-6 and beyond: anything else (such as batch).\n      m_dimensions[NumDims-1] = input_dims[NumInputDims-1];\n      m_dimensions[NumDims-2] = op.patch_planes();\n      m_dimensions[NumDims-3] = op.patch_rows();\n      m_dimensions[NumDims-4] = op.patch_cols();\n      m_dimensions[NumDims-5] = m_outputPlanes * m_outputRows * m_outputCols;\n      for (int i = NumDims-6; i >= 0; --i) {\n        m_dimensions[i] = input_dims[i];\n      }\n    }\n\n    // Strides for the output tensor.\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      m_rowStride = m_dimensions[1];\n      m_colStride = m_dimensions[2] * m_rowStride;\n      m_patchStride = m_colStride * m_dimensions[3] * m_dimensions[0];\n      m_otherStride = m_patchStride * m_dimensions[4];\n    } else {\n      m_rowStride = m_dimensions[NumDims-2];\n      m_colStride = m_dimensions[NumDims-3] * m_rowStride;\n      m_patchStride = m_colStride * m_dimensions[NumDims-4] * m_dimensions[NumDims-1];\n      m_otherStride = m_patchStride * m_dimensions[NumDims-5];\n    }\n\n    // Strides for navigating through the input tensor.\n    m_planeInputStride = m_inputDepth;\n    m_rowInputStride = m_inputDepth * m_inputPlanes;\n    m_colInputStride = m_inputDepth * m_inputRows * m_inputPlanes;\n    m_otherInputStride = m_inputDepth * m_inputRows * m_inputCols * m_inputPlanes;\n\n    m_outputPlanesRows = m_outputPlanes * m_outputRows;\n\n    // Fast representations of different variables.\n    m_fastOtherStride = internal::TensorIntDivisor<Index>(m_otherStride);\n    m_fastPatchStride = internal::TensorIntDivisor<Index>(m_patchStride);\n    m_fastColStride = internal::TensorIntDivisor<Index>(m_colStride);\n    m_fastRowStride = internal::TensorIntDivisor<Index>(m_rowStride);\n    m_fastInputRowStride = internal::TensorIntDivisor<Index>(m_row_inflate_strides);\n    m_fastInputColStride = internal::TensorIntDivisor<Index>(m_col_inflate_strides);\n    m_fastInputPlaneStride = internal::TensorIntDivisor<Index>(m_plane_inflate_strides);\n    m_fastInputColsEff = internal::TensorIntDivisor<Index>(m_input_cols_eff);\n    m_fastOutputPlanes = internal::TensorIntDivisor<Index>(m_outputPlanes);\n    m_fastOutputPlanesRows = internal::TensorIntDivisor<Index>(m_outputPlanesRows);\n\n    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {\n      m_fastOutputDepth = internal::TensorIntDivisor<Index>(m_dimensions[0]);\n    } else {\n      m_fastOutputDepth = internal::TensorIntDivisor<Index>(m_dimensions[NumDims-1]);\n    }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(Scalar* /*data*/) {\n    m_impl.evalSubExprsIfNeeded(NULL);\n    return true;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {\n    m_impl.cleanup();\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const\n  {\n    // Patch index corresponding to the passed in index.\n    const Index patchIndex = index / m_fastPatchStride;\n\n    // Spatial offset within the patch. This has to be translated into 3D\n    // coordinates within the patch.\n    const Index patchOffset = (index - patchIndex * m_patchStride) / m_fastOutputDepth;\n\n    // Batch, etc.\n    const Index otherIndex = (NumDims == 5) ? 0 : index / m_fastOtherStride;\n    const Index patch3DIndex = (NumDims == 5) ? patchIndex : (index - otherIndex * m_otherStride) / m_fastPatchStride;\n\n    // Calculate column index in the input original tensor.\n    const Index colIndex = patch3DIndex / m_fastOutputPlanesRows;\n    const Index colOffset = patchOffset / m_fastColStride;\n    const Index inputCol = colIndex * m_col_strides + colOffset * m_in_col_strides - m_colPaddingLeft;\n    const Index origInputCol = (m_col_inflate_strides == 1) ? inputCol : ((inputCol >= 0) ? (inputCol / m_fastInputColStride) : 0);\n    if (inputCol < 0 || inputCol >= m_input_cols_eff ||\n        ((m_col_inflate_strides != 1) && (inputCol != origInputCol * m_col_inflate_strides))) {\n      return Scalar(m_paddingValue);\n    }\n\n    // Calculate row index in the original input tensor.\n    const Index rowIndex = (patch3DIndex - colIndex * m_outputPlanesRows) / m_fastOutputPlanes;\n    const Index rowOffset = (patchOffset - colOffset * m_colStride) / m_fastRowStride;\n    const Index inputRow = rowIndex * m_row_strides + rowOffset * m_in_row_strides - m_rowPaddingTop;\n    const Index origInputRow = (m_row_inflate_strides == 1) ? inputRow : ((inputRow >= 0) ? (inputRow / m_fastInputRowStride) : 0);\n    if (inputRow < 0 || inputRow >= m_input_rows_eff ||\n        ((m_row_inflate_strides != 1) && (inputRow != origInputRow * m_row_inflate_strides))) {\n      return Scalar(m_paddingValue);\n    }\n\n    // Calculate plane index in the original input tensor.\n    const Index planeIndex = (patch3DIndex - m_outputPlanes * (colIndex * m_outputRows + rowIndex));\n    const Index planeOffset = patchOffset - colOffset * m_colStride - rowOffset * m_rowStride;\n    const Index inputPlane = planeIndex * m_plane_strides + planeOffset * m_in_plane_strides - m_planePaddingTop;\n    const Index origInputPlane = (m_plane_inflate_strides == 1) ? inputPlane : ((inputPlane >= 0) ? (inputPlane / m_fastInputPlaneStride) : 0);\n    if (inputPlane < 0 || inputPlane >= m_input_planes_eff ||\n        ((m_plane_inflate_strides != 1) && (inputPlane != origInputPlane * m_plane_inflate_strides))) {\n      return Scalar(m_paddingValue);\n    }\n\n    const int depth_index = static_cast<int>(Layout) == static_cast<int>(ColMajor) ? 0 : NumDims - 1;\n    const Index depth = index - (index / m_fastOutputDepth) * m_dimensions[depth_index];\n\n    const Index inputIndex = depth +\n        origInputRow * m_rowInputStride +\n        origInputCol * m_colInputStride +\n        origInputPlane * m_planeInputStride +\n        otherIndex * m_otherInputStride;\n\n    return m_impl.coeff(inputIndex);\n  }\n\n  template<int LoadMode>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const\n  {\n    EIGEN_STATIC_ASSERT((PacketSize > 1), YOU_MADE_A_PROGRAMMING_MISTAKE)\n    eigen_assert(index+PacketSize-1 < dimensions().TotalSize());\n\n    if (m_in_row_strides != 1 || m_in_col_strides != 1 || m_row_inflate_strides != 1 || m_col_inflate_strides != 1 ||\n        m_in_plane_strides != 1 || m_plane_inflate_strides != 1) {\n      return packetWithPossibleZero(index);\n    }\n\n    const Index indices[2] = {index, index + PacketSize - 1};\n    const Index patchIndex = indices[0] / m_fastPatchStride;\n    if (patchIndex != indices[1] / m_fastPatchStride) {\n      return packetWithPossibleZero(index);\n    }\n    const Index otherIndex = (NumDims == 5) ? 0 : indices[0] / m_fastOtherStride;\n    eigen_assert(otherIndex == indices[1] / m_fastOtherStride);\n\n    // Find the offset of the element wrt the location of the first element.\n    const Index patchOffsets[2] = {(indices[0] - patchIndex * m_patchStride) / m_fastOutputDepth,\n                                   (indices[1] - patchIndex * m_patchStride) / m_fastOutputDepth};\n\n    const Index patch3DIndex = (NumDims == 5) ? patchIndex : (indices[0] - otherIndex * m_otherStride) / m_fastPatchStride;\n    eigen_assert(patch3DIndex == (indices[1] - otherIndex * m_otherStride) / m_fastPatchStride);\n\n    const Index colIndex = patch3DIndex / m_fastOutputPlanesRows;\n    const Index colOffsets[2] = {\n      patchOffsets[0] / m_fastColStride,\n      patchOffsets[1] / m_fastColStride};\n\n    // Calculate col indices in the original input tensor.\n    const Index inputCols[2] = {\n      colIndex * m_col_strides + colOffsets[0] - m_colPaddingLeft,\n      colIndex * m_col_strides + colOffsets[1] - m_colPaddingLeft};\n    if (inputCols[1] < 0 || inputCols[0] >= m_inputCols) {\n      return internal::pset1<PacketReturnType>(Scalar(m_paddingValue));\n    }\n\n    if (inputCols[0] != inputCols[1]) {\n      return packetWithPossibleZero(index);\n    }\n\n    const Index rowIndex = (patch3DIndex - colIndex * m_outputPlanesRows) / m_fastOutputPlanes;\n    const Index rowOffsets[2] = {\n      (patchOffsets[0] - colOffsets[0] * m_colStride) / m_fastRowStride,\n      (patchOffsets[1] - colOffsets[1] * m_colStride) / m_fastRowStride};\n    eigen_assert(rowOffsets[0] <= rowOffsets[1]);\n    // Calculate col indices in the original input tensor.\n    const Index inputRows[2] = {\n      rowIndex * m_row_strides + rowOffsets[0] - m_rowPaddingTop,\n      rowIndex * m_row_strides + rowOffsets[1] - m_rowPaddingTop};\n\n    if (inputRows[1] < 0 || inputRows[0] >= m_inputRows) {\n      return internal::pset1<PacketReturnType>(Scalar(m_paddingValue));\n    }\n\n    if (inputRows[0] != inputRows[1]) {\n      return packetWithPossibleZero(index);\n    }\n\n    const Index planeIndex = (patch3DIndex - m_outputPlanes * (colIndex * m_outputRows + rowIndex));\n    const Index planeOffsets[2] = {\n      patchOffsets[0] - colOffsets[0] * m_colStride - rowOffsets[0] * m_rowStride,\n      patchOffsets[1] - colOffsets[1] * m_colStride - rowOffsets[1] * m_rowStride};\n    eigen_assert(planeOffsets[0] <= planeOffsets[1]);\n    const Index inputPlanes[2] = {\n      planeIndex * m_plane_strides + planeOffsets[0] - m_planePaddingTop,\n      planeIndex * m_plane_strides + planeOffsets[1] - m_planePaddingTop};\n\n    if (inputPlanes[1] < 0 || inputPlanes[0] >= m_inputPlanes) {\n      return internal::pset1<PacketReturnType>(Scalar(m_paddingValue));\n    }\n\n    if (inputPlanes[0] >= 0 && inputPlanes[1] < m_inputPlanes) {\n      // no padding\n      const int depth_index = static_cast<int>(Layout) == static_cast<int>(ColMajor) ? 0 : NumDims - 1;\n      const Index depth = index - (index / m_fastOutputDepth) * m_dimensions[depth_index];\n      const Index inputIndex = depth +\n          inputRows[0] * m_rowInputStride +\n          inputCols[0] * m_colInputStride +\n          m_planeInputStride * inputPlanes[0] +\n          otherIndex * m_otherInputStride;\n      return m_impl.template packet<Unaligned>(inputIndex);\n    }\n\n    return packetWithPossibleZero(index);\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost\n  costPerCoeff(bool vectorized) const {\n    const double compute_cost =\n        10 * TensorOpCost::DivCost<Index>() + 21 * TensorOpCost::MulCost<Index>() +\n        8 * TensorOpCost::AddCost<Index>();\n    return TensorOpCost(0, 0, compute_cost, vectorized, PacketSize);\n  }\n\n  EIGEN_DEVICE_FUNC Scalar* data() const { return NULL; }\n\n  const TensorEvaluator<ArgType, Device>& impl() const { return m_impl; }\n\n  Index planePaddingTop() const { return m_planePaddingTop; }\n  Index rowPaddingTop() const { return m_rowPaddingTop; }\n  Index colPaddingLeft() const { return m_colPaddingLeft; }\n  Index outputPlanes() const { return m_outputPlanes; }\n  Index outputRows() const { return m_outputRows; }\n  Index outputCols() const { return m_outputCols; }\n  Index userPlaneStride() const { return m_plane_strides; }\n  Index userRowStride() const { return m_row_strides; }\n  Index userColStride() const { return m_col_strides; }\n  Index userInPlaneStride() const { return m_in_plane_strides; }\n  Index userInRowStride() const { return m_in_row_strides; }\n  Index userInColStride() const { return m_in_col_strides; }\n  Index planeInflateStride() const { return m_plane_inflate_strides; }\n  Index rowInflateStride() const { return m_row_inflate_strides; }\n  Index colInflateStride() const { return m_col_inflate_strides; }\n\n protected:\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packetWithPossibleZero(Index index) const\n  {\n    EIGEN_ALIGN_MAX typename internal::remove_const<CoeffReturnType>::type values[PacketSize];\n    for (int i = 0; i < PacketSize; ++i) {\n      values[i] = coeff(index+i);\n    }\n    PacketReturnType rslt = internal::pload<PacketReturnType>(values);\n    return rslt;\n  }\n\n  Dimensions m_dimensions;\n\n  // Parameters passed to the costructor.\n  Index m_plane_strides;\n  Index m_row_strides;\n  Index m_col_strides;\n\n  Index m_outputPlanes;\n  Index m_outputRows;\n  Index m_outputCols;\n\n  Index m_planePaddingTop;\n  Index m_rowPaddingTop;\n  Index m_colPaddingLeft;\n\n  Index m_in_plane_strides;\n  Index m_in_row_strides;\n  Index m_in_col_strides;\n\n  Index m_plane_inflate_strides;\n  Index m_row_inflate_strides;\n  Index m_col_inflate_strides;\n\n  // Cached input size.\n  Index m_inputDepth;\n  Index m_inputPlanes;\n  Index m_inputRows;\n  Index m_inputCols;\n\n  // Other cached variables.\n  Index m_outputPlanesRows;\n\n  // Effective input/patch post-inflation size.\n  Index m_input_planes_eff;\n  Index m_input_rows_eff;\n  Index m_input_cols_eff;\n  Index m_patch_planes_eff;\n  Index m_patch_rows_eff;\n  Index m_patch_cols_eff;\n\n  // Strides for the output tensor.\n  Index m_otherStride;\n  Index m_patchStride;\n  Index m_rowStride;\n  Index m_colStride;\n\n  // Strides for the input tensor.\n  Index m_planeInputStride;\n  Index m_rowInputStride;\n  Index m_colInputStride;\n  Index m_otherInputStride;\n\n  internal::TensorIntDivisor<Index> m_fastOtherStride;\n  internal::TensorIntDivisor<Index> m_fastPatchStride;\n  internal::TensorIntDivisor<Index> m_fastColStride;\n  internal::TensorIntDivisor<Index> m_fastRowStride;\n  internal::TensorIntDivisor<Index> m_fastInputPlaneStride;\n  internal::TensorIntDivisor<Index> m_fastInputRowStride;\n  internal::TensorIntDivisor<Index> m_fastInputColStride;\n  internal::TensorIntDivisor<Index> m_fastInputColsEff;\n  internal::TensorIntDivisor<Index> m_fastOutputPlanesRows;\n  internal::TensorIntDivisor<Index> m_fastOutputPlanes;\n  internal::TensorIntDivisor<Index> m_fastOutputDepth;\n\n  Scalar m_paddingValue;\n\n  TensorEvaluator<ArgType, Device> m_impl;\n};\n\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSOR_TENSOR_VOLUME_PATCH_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/TensorSymmetry/DynamicSymmetry.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2013 Christian Seiler <christian@iwakd.de>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSORSYMMETRY_DYNAMICSYMMETRY_H\n#define EIGEN_CXX11_TENSORSYMMETRY_DYNAMICSYMMETRY_H\n\nnamespace Eigen {\n\nclass DynamicSGroup\n{\n  public:\n    inline explicit DynamicSGroup() : m_numIndices(1), m_elements(), m_generators(), m_globalFlags(0) { m_elements.push_back(ge(Generator(0, 0, 0))); }\n    inline DynamicSGroup(const DynamicSGroup& o) : m_numIndices(o.m_numIndices), m_elements(o.m_elements), m_generators(o.m_generators), m_globalFlags(o.m_globalFlags) { }\n    inline DynamicSGroup(DynamicSGroup&& o) : m_numIndices(o.m_numIndices), m_elements(), m_generators(o.m_generators), m_globalFlags(o.m_globalFlags) { std::swap(m_elements, o.m_elements); }\n    inline DynamicSGroup& operator=(const DynamicSGroup& o) { m_numIndices = o.m_numIndices; m_elements = o.m_elements; m_generators = o.m_generators; m_globalFlags = o.m_globalFlags; return *this; }\n    inline DynamicSGroup& operator=(DynamicSGroup&& o) { m_numIndices = o.m_numIndices; std::swap(m_elements, o.m_elements); m_generators = o.m_generators; m_globalFlags = o.m_globalFlags; return *this; }\n\n    void add(int one, int two, int flags = 0);\n\n    template<typename Gen_>\n    inline void add(Gen_) { add(Gen_::One, Gen_::Two, Gen_::Flags); }\n    inline void addSymmetry(int one, int two) { add(one, two, 0); }\n    inline void addAntiSymmetry(int one, int two) { add(one, two, NegationFlag); }\n    inline void addHermiticity(int one, int two) { add(one, two, ConjugationFlag); }\n    inline void addAntiHermiticity(int one, int two) { add(one, two, NegationFlag | ConjugationFlag); }\n\n    template<typename Op, typename RV, typename Index, std::size_t N, typename... Args>\n    inline RV apply(const std::array<Index, N>& idx, RV initial, Args&&... args) const\n    {\n      eigen_assert(N >= m_numIndices && \"Can only apply symmetry group to objects that have at least the required amount of indices.\");\n      for (std::size_t i = 0; i < size(); i++)\n        initial = Op::run(h_permute(i, idx, typename internal::gen_numeric_list<int, N>::type()), m_elements[i].flags, initial, std::forward<Args>(args)...);\n      return initial;\n    }\n\n    template<typename Op, typename RV, typename Index, typename... Args>\n    inline RV apply(const std::vector<Index>& idx, RV initial, Args&&... args) const\n    {\n      eigen_assert(idx.size() >= m_numIndices && \"Can only apply symmetry group to objects that have at least the required amount of indices.\");\n      for (std::size_t i = 0; i < size(); i++)\n        initial = Op::run(h_permute(i, idx), m_elements[i].flags, initial, std::forward<Args>(args)...);\n      return initial;\n    }\n\n    inline int globalFlags() const { return m_globalFlags; }\n    inline std::size_t size() const { return m_elements.size(); }\n\n    template<typename Tensor_, typename... IndexTypes>\n    inline internal::tensor_symmetry_value_setter<Tensor_, DynamicSGroup> operator()(Tensor_& tensor, typename Tensor_::Index firstIndex, IndexTypes... otherIndices) const\n    {\n      static_assert(sizeof...(otherIndices) + 1 == Tensor_::NumIndices, \"Number of indices used to access a tensor coefficient must be equal to the rank of the tensor.\");\n      return operator()(tensor, std::array<typename Tensor_::Index, Tensor_::NumIndices>{{firstIndex, otherIndices...}});\n    }\n\n    template<typename Tensor_>\n    inline internal::tensor_symmetry_value_setter<Tensor_, DynamicSGroup> operator()(Tensor_& tensor, std::array<typename Tensor_::Index, Tensor_::NumIndices> const& indices) const\n    {\n      return internal::tensor_symmetry_value_setter<Tensor_, DynamicSGroup>(tensor, *this, indices);\n    }\n  private:\n    struct GroupElement {\n      std::vector<int> representation;\n      int flags;\n      bool isId() const\n      {\n        for (std::size_t i = 0; i < representation.size(); i++)\n          if (i != (size_t)representation[i])\n            return false;\n        return true;\n      }\n    };\n    struct Generator {\n      int one;\n      int two;\n      int flags;\n      constexpr inline Generator(int one_, int two_, int flags_) : one(one_), two(two_), flags(flags_) {}\n    };\n\n    std::size_t m_numIndices;\n    std::vector<GroupElement> m_elements;\n    std::vector<Generator> m_generators;\n    int m_globalFlags;\n\n    template<typename Index, std::size_t N, int... n>\n    inline std::array<Index, N> h_permute(std::size_t which, const std::array<Index, N>& idx, internal::numeric_list<int, n...>) const\n    {\n      return std::array<Index, N>{{ idx[n >= m_numIndices ? n : m_elements[which].representation[n]]... }};\n    }\n\n    template<typename Index>\n    inline std::vector<Index> h_permute(std::size_t which, std::vector<Index> idx) const\n    {\n      std::vector<Index> result;\n      result.reserve(idx.size());\n      for (auto k : m_elements[which].representation)\n        result.push_back(idx[k]);\n      for (std::size_t i = m_numIndices; i < idx.size(); i++)\n        result.push_back(idx[i]);\n      return result;\n    }\n\n    inline GroupElement ge(Generator const& g) const\n    {\n      GroupElement result;\n      result.representation.reserve(m_numIndices);\n      result.flags = g.flags;\n      for (std::size_t k = 0; k < m_numIndices; k++) {\n        if (k == (std::size_t)g.one)\n          result.representation.push_back(g.two);\n        else if (k == (std::size_t)g.two)\n          result.representation.push_back(g.one);\n        else\n          result.representation.push_back(int(k));\n      }\n      return result;\n    }\n\n    GroupElement mul(GroupElement, GroupElement) const;\n    inline GroupElement mul(Generator g1, GroupElement g2) const\n    {\n      return mul(ge(g1), g2);\n    }\n\n    inline GroupElement mul(GroupElement g1, Generator g2) const\n    {\n      return mul(g1, ge(g2));\n    }\n\n    inline GroupElement mul(Generator g1, Generator g2) const\n    {\n      return mul(ge(g1), ge(g2));\n    }\n\n    inline int findElement(GroupElement e) const\n    {\n      for (auto ee : m_elements) {\n        if (ee.representation == e.representation)\n          return ee.flags ^ e.flags;\n      }\n      return -1;\n    }\n\n    void updateGlobalFlags(int flagDiffOfSameGenerator);\n};\n\n// dynamic symmetry group that auto-adds the template parameters in the constructor\ntemplate<typename... Gen>\nclass DynamicSGroupFromTemplateArgs : public DynamicSGroup\n{\n  public:\n    inline DynamicSGroupFromTemplateArgs() : DynamicSGroup()\n    {\n      add_all(internal::type_list<Gen...>());\n    }\n    inline DynamicSGroupFromTemplateArgs(DynamicSGroupFromTemplateArgs const& other) : DynamicSGroup(other) { }\n    inline DynamicSGroupFromTemplateArgs(DynamicSGroupFromTemplateArgs&& other) : DynamicSGroup(other) { }\n    inline DynamicSGroupFromTemplateArgs<Gen...>& operator=(const DynamicSGroupFromTemplateArgs<Gen...>& o) { DynamicSGroup::operator=(o); return *this; }\n    inline DynamicSGroupFromTemplateArgs<Gen...>& operator=(DynamicSGroupFromTemplateArgs<Gen...>&& o) { DynamicSGroup::operator=(o); return *this; }\n  \n  private:\n    template<typename Gen1, typename... GenNext>\n    inline void add_all(internal::type_list<Gen1, GenNext...>)\n    {\n      add(Gen1());\n      add_all(internal::type_list<GenNext...>());\n    }\n\n    inline void add_all(internal::type_list<>)\n    {\n    }\n};\n\ninline DynamicSGroup::GroupElement DynamicSGroup::mul(GroupElement g1, GroupElement g2) const\n{\n  eigen_internal_assert(g1.representation.size() == m_numIndices);\n  eigen_internal_assert(g2.representation.size() == m_numIndices);\n\n  GroupElement result;\n  result.representation.reserve(m_numIndices);\n  for (std::size_t i = 0; i < m_numIndices; i++) {\n    int v = g2.representation[g1.representation[i]];\n    eigen_assert(v >= 0);\n    result.representation.push_back(v);\n  }\n  result.flags = g1.flags ^ g2.flags;\n  return result;\n}\n\ninline void DynamicSGroup::add(int one, int two, int flags)\n{\n  eigen_assert(one >= 0);\n  eigen_assert(two >= 0);\n  eigen_assert(one != two);\n\n  if ((std::size_t)one >= m_numIndices || (std::size_t)two >= m_numIndices) {\n    std::size_t newNumIndices = (one > two) ? one : two + 1;\n    for (auto& gelem : m_elements) {\n      gelem.representation.reserve(newNumIndices);\n      for (std::size_t i = m_numIndices; i < newNumIndices; i++)\n        gelem.representation.push_back(i);\n    }\n    m_numIndices = newNumIndices;\n  }\n\n  Generator g{one, two, flags};\n  GroupElement e = ge(g);\n\n  /* special case for first generator */\n  if (m_elements.size() == 1) {\n    while (!e.isId()) {\n      m_elements.push_back(e);\n      e = mul(e, g);\n    }\n\n    if (e.flags > 0)\n      updateGlobalFlags(e.flags);\n\n    // only add in case we didn't have identity\n    if (m_elements.size() > 1)\n      m_generators.push_back(g);\n    return;\n  }\n\n  int p = findElement(e);\n  if (p >= 0) {\n    updateGlobalFlags(p);\n    return;\n  }\n\n  std::size_t coset_order = m_elements.size();\n  m_elements.push_back(e);\n  for (std::size_t i = 1; i < coset_order; i++)\n    m_elements.push_back(mul(m_elements[i], e));\n  m_generators.push_back(g);\n\n  std::size_t coset_rep = coset_order;\n  do {\n    for (auto g : m_generators) {\n      e = mul(m_elements[coset_rep], g);\n      p = findElement(e);\n      if (p < 0) {\n        // element not yet in group\n        m_elements.push_back(e);\n        for (std::size_t i = 1; i < coset_order; i++)\n          m_elements.push_back(mul(m_elements[i], e));\n      } else if (p > 0) {\n        updateGlobalFlags(p);\n      }\n    }\n    coset_rep += coset_order;\n  } while (coset_rep < m_elements.size());\n}\n\ninline void DynamicSGroup::updateGlobalFlags(int flagDiffOfSameGenerator)\n{\n    switch (flagDiffOfSameGenerator) {\n      case 0:\n      default:\n        // nothing happened\n        break;\n      case NegationFlag:\n        // every element is it's own negative => whole tensor is zero\n        m_globalFlags |= GlobalZeroFlag;\n        break;\n      case ConjugationFlag:\n        // every element is it's own conjugate => whole tensor is real\n        m_globalFlags |= GlobalRealFlag;\n        break;\n      case (NegationFlag | ConjugationFlag):\n        // every element is it's own negative conjugate => whole tensor is imaginary\n        m_globalFlags |= GlobalImagFlag;\n        break;\n      /* NOTE:\n       *   since GlobalZeroFlag == GlobalRealFlag | GlobalImagFlag, if one generator\n       *   causes the tensor to be real and the next one to be imaginary, this will\n       *   trivially give the correct result\n       */\n    }\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSORSYMMETRY_DYNAMICSYMMETRY_H\n\n/*\n * kate: space-indent on; indent-width 2; mixedindent off; indent-mode cstyle;\n */\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/TensorSymmetry/StaticSymmetry.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2013 Christian Seiler <christian@iwakd.de>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSORSYMMETRY_STATICSYMMETRY_H\n#define EIGEN_CXX11_TENSORSYMMETRY_STATICSYMMETRY_H\n\nnamespace Eigen {\n\nnamespace internal {\n\ntemplate<typename list> struct tensor_static_symgroup_permutate;\n\ntemplate<int... nn>\nstruct tensor_static_symgroup_permutate<numeric_list<int, nn...>>\n{\n  constexpr static std::size_t N = sizeof...(nn);\n\n  template<typename T>\n  constexpr static inline std::array<T, N> run(const std::array<T, N>& indices)\n  {\n    return {{indices[nn]...}};\n  }\n};\n\ntemplate<typename indices_, int flags_>\nstruct tensor_static_symgroup_element\n{\n  typedef indices_ indices;\n  constexpr static int flags = flags_;\n};\n\ntemplate<typename Gen, int N>\nstruct tensor_static_symgroup_element_ctor\n{\n  typedef tensor_static_symgroup_element<\n    typename gen_numeric_list_swapped_pair<int, N, Gen::One, Gen::Two>::type,\n    Gen::Flags\n  > type;\n};\n\ntemplate<int N>\nstruct tensor_static_symgroup_identity_ctor\n{\n  typedef tensor_static_symgroup_element<\n    typename gen_numeric_list<int, N>::type,\n    0\n  > type;\n};\n\ntemplate<typename iib>\nstruct tensor_static_symgroup_multiply_helper\n{\n  template<int... iia>\n  constexpr static inline numeric_list<int, get<iia, iib>::value...> helper(numeric_list<int, iia...>) {\n    return numeric_list<int, get<iia, iib>::value...>();\n  }\n};\n\ntemplate<typename A, typename B>\nstruct tensor_static_symgroup_multiply\n{\n  private:\n    typedef typename A::indices iia;\n    typedef typename B::indices iib;\n    constexpr static int ffa = A::flags;\n    constexpr static int ffb = B::flags;\n  \n  public:\n    static_assert(iia::count == iib::count, \"Cannot multiply symmetry elements with different number of indices.\");\n\n    typedef tensor_static_symgroup_element<\n      decltype(tensor_static_symgroup_multiply_helper<iib>::helper(iia())),\n      ffa ^ ffb\n    > type;\n};\n\ntemplate<typename A, typename B>\nstruct tensor_static_symgroup_equality\n{\n    typedef typename A::indices iia;\n    typedef typename B::indices iib;\n    constexpr static int ffa = A::flags;\n    constexpr static int ffb = B::flags;\n    static_assert(iia::count == iib::count, \"Cannot compare symmetry elements with different number of indices.\");\n\n    constexpr static bool value = is_same<iia, iib>::value;\n\n  private:\n    /* this should be zero if they are identical, or else the tensor\n     * will be forced to be pure real, pure imaginary or even pure zero\n     */\n    constexpr static int flags_cmp_ = ffa ^ ffb;\n\n    /* either they are not equal, then we don't care whether the flags\n     * match, or they are equal, and then we have to check\n     */\n    constexpr static bool is_zero      = value && flags_cmp_ == NegationFlag;\n    constexpr static bool is_real      = value && flags_cmp_ == ConjugationFlag;\n    constexpr static bool is_imag      = value && flags_cmp_ == (NegationFlag | ConjugationFlag);\n\n  public:\n    constexpr static int global_flags = \n      (is_real ? GlobalRealFlag : 0) |\n      (is_imag ? GlobalImagFlag : 0) |\n      (is_zero ? GlobalZeroFlag : 0);\n};\n\ntemplate<std::size_t NumIndices, typename... Gen>\nstruct tensor_static_symgroup\n{\n  typedef StaticSGroup<Gen...> type;\n  constexpr static std::size_t size = type::static_size;\n};\n\ntemplate<typename Index, std::size_t N, int... ii, int... jj>\nconstexpr static inline std::array<Index, N> tensor_static_symgroup_index_permute(std::array<Index, N> idx, internal::numeric_list<int, ii...>, internal::numeric_list<int, jj...>)\n{\n  return {{ idx[ii]..., idx[jj]... }};\n}\n\ntemplate<typename Index, int... ii>\nstatic inline std::vector<Index> tensor_static_symgroup_index_permute(std::vector<Index> idx, internal::numeric_list<int, ii...>)\n{\n  std::vector<Index> result{{ idx[ii]... }};\n  std::size_t target_size = idx.size();\n  for (std::size_t i = result.size(); i < target_size; i++)\n    result.push_back(idx[i]);\n  return result;\n}\n\ntemplate<typename T> struct tensor_static_symgroup_do_apply;\n\ntemplate<typename first, typename... next>\nstruct tensor_static_symgroup_do_apply<internal::type_list<first, next...>>\n{\n  template<typename Op, typename RV, std::size_t SGNumIndices, typename Index, std::size_t NumIndices, typename... Args>\n  static inline RV run(const std::array<Index, NumIndices>& idx, RV initial, Args&&... args)\n  {\n    static_assert(NumIndices >= SGNumIndices, \"Can only apply symmetry group to objects that have at least the required amount of indices.\");\n    typedef typename internal::gen_numeric_list<int, NumIndices - SGNumIndices, SGNumIndices>::type remaining_indices;\n    initial = Op::run(tensor_static_symgroup_index_permute(idx, typename first::indices(), remaining_indices()), first::flags, initial, std::forward<Args>(args)...);\n    return tensor_static_symgroup_do_apply<internal::type_list<next...>>::template run<Op, RV, SGNumIndices>(idx, initial, args...);\n  }\n\n  template<typename Op, typename RV, std::size_t SGNumIndices, typename Index, typename... Args>\n  static inline RV run(const std::vector<Index>& idx, RV initial, Args&&... args)\n  {\n    eigen_assert(idx.size() >= SGNumIndices && \"Can only apply symmetry group to objects that have at least the required amount of indices.\");\n    initial = Op::run(tensor_static_symgroup_index_permute(idx, typename first::indices()), first::flags, initial, std::forward<Args>(args)...);\n    return tensor_static_symgroup_do_apply<internal::type_list<next...>>::template run<Op, RV, SGNumIndices>(idx, initial, args...);\n  }\n};\n\ntemplate<EIGEN_TPL_PP_SPEC_HACK_DEF(typename, empty)>\nstruct tensor_static_symgroup_do_apply<internal::type_list<EIGEN_TPL_PP_SPEC_HACK_USE(empty)>>\n{\n  template<typename Op, typename RV, std::size_t SGNumIndices, typename Index, std::size_t NumIndices, typename... Args>\n  static inline RV run(const std::array<Index, NumIndices>&, RV initial, Args&&...)\n  {\n    // do nothing\n    return initial;\n  }\n\n  template<typename Op, typename RV, std::size_t SGNumIndices, typename Index, typename... Args>\n  static inline RV run(const std::vector<Index>&, RV initial, Args&&...)\n  {\n    // do nothing\n    return initial;\n  }\n};\n\n} // end namespace internal\n\ntemplate<typename... Gen>\nclass StaticSGroup\n{\n    constexpr static std::size_t NumIndices = internal::tensor_symmetry_num_indices<Gen...>::value;\n    typedef internal::group_theory::enumerate_group_elements<\n      internal::tensor_static_symgroup_multiply,\n      internal::tensor_static_symgroup_equality,\n      typename internal::tensor_static_symgroup_identity_ctor<NumIndices>::type,\n      internal::type_list<typename internal::tensor_static_symgroup_element_ctor<Gen, NumIndices>::type...>\n    > group_elements;\n    typedef typename group_elements::type ge;\n  public:\n    constexpr inline StaticSGroup() {}\n    constexpr inline StaticSGroup(const StaticSGroup<Gen...>&) {}\n    constexpr inline StaticSGroup(StaticSGroup<Gen...>&&) {}\n\n    template<typename Op, typename RV, typename Index, std::size_t N, typename... Args>\n    static inline RV apply(const std::array<Index, N>& idx, RV initial, Args&&... args)\n    {\n      return internal::tensor_static_symgroup_do_apply<ge>::template run<Op, RV, NumIndices>(idx, initial, args...);\n    }\n\n    template<typename Op, typename RV, typename Index, typename... Args>\n    static inline RV apply(const std::vector<Index>& idx, RV initial, Args&&... args)\n    {\n      eigen_assert(idx.size() == NumIndices);\n      return internal::tensor_static_symgroup_do_apply<ge>::template run<Op, RV, NumIndices>(idx, initial, args...);\n    }\n\n    constexpr static std::size_t static_size = ge::count;\n\n    constexpr static inline std::size_t size() {\n      return ge::count;\n    }\n    constexpr static inline int globalFlags() { return group_elements::global_flags; }\n\n    template<typename Tensor_, typename... IndexTypes>\n    inline internal::tensor_symmetry_value_setter<Tensor_, StaticSGroup<Gen...>> operator()(Tensor_& tensor, typename Tensor_::Index firstIndex, IndexTypes... otherIndices) const\n    {\n      static_assert(sizeof...(otherIndices) + 1 == Tensor_::NumIndices, \"Number of indices used to access a tensor coefficient must be equal to the rank of the tensor.\");\n      return operator()(tensor, std::array<typename Tensor_::Index, Tensor_::NumIndices>{{firstIndex, otherIndices...}});\n    }\n\n    template<typename Tensor_>\n    inline internal::tensor_symmetry_value_setter<Tensor_, StaticSGroup<Gen...>> operator()(Tensor_& tensor, std::array<typename Tensor_::Index, Tensor_::NumIndices> const& indices) const\n    {\n      return internal::tensor_symmetry_value_setter<Tensor_, StaticSGroup<Gen...>>(tensor, *this, indices);\n    }\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSORSYMMETRY_STATICSYMMETRY_H\n\n/*\n * kate: space-indent on; indent-width 2; mixedindent off; indent-mode cstyle;\n */\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/TensorSymmetry/Symmetry.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2013 Christian Seiler <christian@iwakd.de>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSORSYMMETRY_SYMMETRY_H\n#define EIGEN_CXX11_TENSORSYMMETRY_SYMMETRY_H\n\nnamespace Eigen {\n\nenum {\n  NegationFlag           = 0x01,\n  ConjugationFlag        = 0x02\n};\n\nenum {\n  GlobalRealFlag         = 0x01,\n  GlobalImagFlag         = 0x02,\n  GlobalZeroFlag         = 0x03\n};\n\nnamespace internal {\n\ntemplate<std::size_t NumIndices, typename... Sym>                   struct tensor_symmetry_pre_analysis;\ntemplate<std::size_t NumIndices, typename... Sym>                   struct tensor_static_symgroup;\ntemplate<bool instantiate, std::size_t NumIndices, typename... Sym> struct tensor_static_symgroup_if;\ntemplate<typename Tensor_> struct tensor_symmetry_calculate_flags;\ntemplate<typename Tensor_> struct tensor_symmetry_assign_value;\ntemplate<typename... Sym> struct tensor_symmetry_num_indices;\n\n} // end namespace internal\n\ntemplate<int One_, int Two_>\nstruct Symmetry\n{\n  static_assert(One_ != Two_, \"Symmetries must cover distinct indices.\");\n  constexpr static int One = One_;\n  constexpr static int Two = Two_;\n  constexpr static int Flags = 0;\n};\n\ntemplate<int One_, int Two_>\nstruct AntiSymmetry\n{\n  static_assert(One_ != Two_, \"Symmetries must cover distinct indices.\");\n  constexpr static int One = One_;\n  constexpr static int Two = Two_;\n  constexpr static int Flags = NegationFlag;\n};\n\ntemplate<int One_, int Two_>\nstruct Hermiticity\n{\n  static_assert(One_ != Two_, \"Symmetries must cover distinct indices.\");\n  constexpr static int One = One_;\n  constexpr static int Two = Two_;\n  constexpr static int Flags = ConjugationFlag;\n};\n\ntemplate<int One_, int Two_>\nstruct AntiHermiticity\n{\n  static_assert(One_ != Two_, \"Symmetries must cover distinct indices.\");\n  constexpr static int One = One_;\n  constexpr static int Two = Two_;\n  constexpr static int Flags = ConjugationFlag | NegationFlag;\n};\n\n/** \\class DynamicSGroup\n  * \\ingroup TensorSymmetry_Module\n  *\n  * \\brief Dynamic symmetry group\n  *\n  * The %DynamicSGroup class represents a symmetry group that need not be known at\n  * compile time. It is useful if one wants to support arbitrary run-time defineable\n  * symmetries for tensors, but it is also instantiated if a symmetry group is defined\n  * at compile time that would be either too large for the compiler to reasonably\n  * generate (using templates to calculate this at compile time is very inefficient)\n  * or that the compiler could generate the group but that it wouldn't make sense to\n  * unroll the loop for setting coefficients anymore.\n  */\nclass DynamicSGroup;\n\n/** \\internal\n  *\n  * \\class DynamicSGroupFromTemplateArgs\n  * \\ingroup TensorSymmetry_Module\n  *\n  * \\brief Dynamic symmetry group, initialized from template arguments\n  *\n  * This class is a child class of DynamicSGroup. It uses the template arguments\n  * specified to initialize itself.\n  */\ntemplate<typename... Gen>\nclass DynamicSGroupFromTemplateArgs;\n\n/** \\class StaticSGroup\n  * \\ingroup TensorSymmetry_Module\n  *\n  * \\brief Static symmetry group\n  *\n  * This class represents a symmetry group that is known and resolved completely\n  * at compile time. Ideally, no run-time penalty is incurred compared to the\n  * manual unrolling of the symmetry.\n  *\n  * <b><i>CAUTION:</i></b>\n  *\n  * Do not use this class directly for large symmetry groups. The compiler\n  * may run into a limit, or segfault or in the very least will take a very,\n  * very, very long time to compile the code. Use the SGroup class instead\n  * if you want a static group. That class contains logic that will\n  * automatically select the DynamicSGroup class instead if the symmetry\n  * group becomes too large. (In that case, unrolling may not even be\n  * beneficial.)\n  */\ntemplate<typename... Gen>\nclass StaticSGroup;\n\n/** \\class SGroup\n  * \\ingroup TensorSymmetry_Module\n  *\n  * \\brief Symmetry group, initialized from template arguments\n  *\n  * This class represents a symmetry group whose generators are already\n  * known at compile time. It may or may not be resolved at compile time,\n  * depending on the estimated size of the group.\n  *\n  * \\sa StaticSGroup\n  * \\sa DynamicSGroup\n  */\ntemplate<typename... Gen>\nclass SGroup : public internal::tensor_symmetry_pre_analysis<internal::tensor_symmetry_num_indices<Gen...>::value, Gen...>::root_type\n{\n  public:\n    constexpr static std::size_t NumIndices = internal::tensor_symmetry_num_indices<Gen...>::value;\n    typedef typename internal::tensor_symmetry_pre_analysis<NumIndices, Gen...>::root_type Base;\n\n    // make standard constructors + assignment operators public\n    inline SGroup() : Base() { }\n    inline SGroup(const SGroup<Gen...>& other) : Base(other) { }\n    inline SGroup(SGroup<Gen...>&& other) : Base(other) { }\n    inline SGroup<Gen...>& operator=(const SGroup<Gen...>& other) { Base::operator=(other); return *this; }\n    inline SGroup<Gen...>& operator=(SGroup<Gen...>&& other) { Base::operator=(other); return *this; }\n\n    // all else is defined in the base class\n};\n\nnamespace internal {\n\ntemplate<typename... Sym> struct tensor_symmetry_num_indices\n{\n  constexpr static std::size_t value = 1;\n};\n\ntemplate<int One_, int Two_, typename... Sym> struct tensor_symmetry_num_indices<Symmetry<One_, Two_>, Sym...>\n{\nprivate:\n  constexpr static std::size_t One = static_cast<std::size_t>(One_);\n  constexpr static std::size_t Two = static_cast<std::size_t>(Two_);\n  constexpr static std::size_t Three = tensor_symmetry_num_indices<Sym...>::value;\n\n  // don't use std::max, since it's not constexpr until C++14...\n  constexpr static std::size_t maxOneTwoPlusOne = ((One > Two) ? One : Two) + 1;\npublic:\n  constexpr static std::size_t value = (maxOneTwoPlusOne > Three) ? maxOneTwoPlusOne : Three;\n};\n\ntemplate<int One_, int Two_, typename... Sym> struct tensor_symmetry_num_indices<AntiSymmetry<One_, Two_>, Sym...>\n  : public tensor_symmetry_num_indices<Symmetry<One_, Two_>, Sym...> {};\ntemplate<int One_, int Two_, typename... Sym> struct tensor_symmetry_num_indices<Hermiticity<One_, Two_>, Sym...>\n  : public tensor_symmetry_num_indices<Symmetry<One_, Two_>, Sym...> {};\ntemplate<int One_, int Two_, typename... Sym> struct tensor_symmetry_num_indices<AntiHermiticity<One_, Two_>, Sym...>\n  : public tensor_symmetry_num_indices<Symmetry<One_, Two_>, Sym...> {};\n\n/** \\internal\n  *\n  * \\class tensor_symmetry_pre_analysis\n  * \\ingroup TensorSymmetry_Module\n  *\n  * \\brief Pre-select whether to use a static or dynamic symmetry group\n  *\n  * When a symmetry group could in principle be determined at compile time,\n  * this template implements the logic whether to actually do that or whether\n  * to rather defer that to runtime.\n  *\n  * The logic is as follows:\n  * <dl>\n  * <dt><b>No generators (trivial symmetry):</b></dt>\n  * <dd>Use a trivial static group. Ideally, this has no performance impact\n  *     compared to not using symmetry at all. In practice, this might not\n  *     be the case.</dd>\n  * <dt><b>More than 4 generators:</b></dt>\n  * <dd>Calculate the group at run time, it is likely far too large for the\n  *     compiler to be able to properly generate it in a realistic time.</dd>\n  * <dt><b>Up to and including 4 generators:</b></dt>\n  * <dd>Actually enumerate all group elements, but then check how many there\n  *     are. If there are more than 16, it is unlikely that unrolling the\n  *     loop (as is done in the static compile-time case) is sensible, so\n  *     use a dynamic group instead. If there are at most 16 elements, actually\n  *     use that static group. Note that the largest group with 4 generators\n  *     still compiles with reasonable resources.</dd>\n  * </dl>\n  *\n  * Note: Example compile time performance with g++-4.6 on an Intenl Core i5-3470\n  *       with 16 GiB RAM (all generators non-redundant and the subgroups don't\n  *       factorize):\n  *\n  *          # Generators          -O0 -ggdb               -O2\n  *          -------------------------------------------------------------------\n  *          1                 0.5 s  /   250 MiB     0.45s /   230 MiB\n  *          2                 0.5 s  /   260 MiB     0.5 s /   250 MiB\n  *          3                 0.65s  /   310 MiB     0.62s /   310 MiB\n  *          4                 2.2 s  /   860 MiB     1.7 s /   770 MiB\n  *          5               130   s  / 13000 MiB   120   s / 11000 MiB\n  *\n  * It is clear that everything is still very efficient up to 4 generators, then\n  * the memory and CPU requirements become unreasonable. Thus we only instantiate\n  * the template group theory logic if the number of generators supplied is 4 or\n  * lower, otherwise this will be forced to be done during runtime, where the\n  * algorithm is reasonably fast.\n  */\ntemplate<std::size_t NumIndices>\nstruct tensor_symmetry_pre_analysis<NumIndices>\n{\n  typedef StaticSGroup<> root_type;\n};\n\ntemplate<std::size_t NumIndices, typename Gen_, typename... Gens_>\nstruct tensor_symmetry_pre_analysis<NumIndices, Gen_, Gens_...>\n{\n  constexpr static std::size_t max_static_generators = 4;\n  constexpr static std::size_t max_static_elements = 16;\n  typedef tensor_static_symgroup_if<(sizeof...(Gens_) + 1 <= max_static_generators), NumIndices, Gen_, Gens_...> helper;\n  constexpr static std::size_t possible_size = helper::size;\n\n  typedef typename conditional<\n    possible_size == 0 || possible_size >= max_static_elements,\n    DynamicSGroupFromTemplateArgs<Gen_, Gens_...>,\n    typename helper::type\n  >::type root_type;\n};\n\ntemplate<bool instantiate, std::size_t NumIndices, typename... Gens>\nstruct tensor_static_symgroup_if\n{\n  constexpr static std::size_t size = 0;\n  typedef void type;\n};\n\ntemplate<std::size_t NumIndices, typename... Gens>\nstruct tensor_static_symgroup_if<true, NumIndices, Gens...> : tensor_static_symgroup<NumIndices, Gens...> {};\n\ntemplate<typename Tensor_>\nstruct tensor_symmetry_assign_value\n{\n  typedef typename Tensor_::Index Index;\n  typedef typename Tensor_::Scalar Scalar;\n  constexpr static std::size_t NumIndices = Tensor_::NumIndices;\n\n  static inline int run(const std::array<Index, NumIndices>& transformed_indices, int transformation_flags, int dummy, Tensor_& tensor, const Scalar& value_)\n  {\n    Scalar value(value_);\n    if (transformation_flags & ConjugationFlag)\n      value = numext::conj(value);\n    if (transformation_flags & NegationFlag)\n      value = -value;\n    tensor.coeffRef(transformed_indices) = value;\n    return dummy;\n  }\n};\n\ntemplate<typename Tensor_>\nstruct tensor_symmetry_calculate_flags\n{\n  typedef typename Tensor_::Index Index;\n  constexpr static std::size_t NumIndices = Tensor_::NumIndices;\n\n  static inline int run(const std::array<Index, NumIndices>& transformed_indices, int transform_flags, int current_flags, const std::array<Index, NumIndices>& orig_indices)\n  {\n    if (transformed_indices == orig_indices) {\n      if (transform_flags & (ConjugationFlag | NegationFlag))\n        return current_flags | GlobalImagFlag; // anti-hermitian diagonal\n      else if (transform_flags & ConjugationFlag)\n        return current_flags | GlobalRealFlag; // hermitian diagonal\n      else if (transform_flags & NegationFlag)\n        return current_flags | GlobalZeroFlag; // anti-symmetric diagonal\n    }\n    return current_flags;\n  }\n};\n\ntemplate<typename Tensor_, typename Symmetry_, int Flags = 0>\nclass tensor_symmetry_value_setter\n{\n  public:\n    typedef typename Tensor_::Index Index;\n    typedef typename Tensor_::Scalar Scalar;\n    constexpr static std::size_t NumIndices = Tensor_::NumIndices;\n\n    inline tensor_symmetry_value_setter(Tensor_& tensor, Symmetry_ const& symmetry, std::array<Index, NumIndices> const& indices)\n      : m_tensor(tensor), m_symmetry(symmetry), m_indices(indices) { }\n\n    inline tensor_symmetry_value_setter<Tensor_, Symmetry_, Flags>& operator=(Scalar const& value)\n    {\n      doAssign(value);\n      return *this;\n    }\n  private:\n    Tensor_& m_tensor;\n    Symmetry_ m_symmetry;\n    std::array<Index, NumIndices> m_indices;\n\n    inline void doAssign(Scalar const& value)\n    {\n      #ifdef EIGEN_TENSOR_SYMMETRY_CHECK_VALUES\n        int value_flags = m_symmetry.template apply<internal::tensor_symmetry_calculate_flags<Tensor_>, int>(m_indices, m_symmetry.globalFlags(), m_indices);\n        if (value_flags & GlobalRealFlag)\n          eigen_assert(numext::imag(value) == 0);\n        if (value_flags & GlobalImagFlag)\n          eigen_assert(numext::real(value) == 0);\n      #endif\n      m_symmetry.template apply<internal::tensor_symmetry_assign_value<Tensor_>, int>(m_indices, 0, m_tensor, value);\n    }\n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSORSYMMETRY_SYMMETRY_H\n\n/*\n * kate: space-indent on; indent-width 2; mixedindent off; indent-mode cstyle;\n */\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/TensorSymmetry/util/TemplateGroupTheory.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2013 Christian Seiler <christian@iwakd.de>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_TENSORSYMMETRY_TEMPLATEGROUPTHEORY_H\n#define EIGEN_CXX11_TENSORSYMMETRY_TEMPLATEGROUPTHEORY_H\n\nnamespace Eigen {\n\nnamespace internal {\n\nnamespace group_theory {\n\n/** \\internal\n  * \\file CXX11/Tensor/util/TemplateGroupTheory.h\n  * This file contains C++ templates that implement group theory algorithms.\n  *\n  * The algorithms allow for a compile-time analysis of finite groups.\n  *\n  * Currently only Dimino's algorithm is implemented, which returns a list\n  * of all elements in a group given a set of (possibly redundant) generators.\n  * (One could also do that with the so-called orbital algorithm, but that\n  * is much more expensive and usually has no advantages.)\n  */\n\n/**********************************************************************\n *                \"Ok kid, here is where it gets complicated.\"\n *                         - Amelia Pond in the \"Doctor Who\" episode\n *                           \"The Big Bang\"\n *\n * Dimino's algorithm\n * ==================\n *\n * The following is Dimino's algorithm in sequential form:\n *\n * Input: identity element, list of generators, equality check,\n *        multiplication operation\n * Output: list of group elements\n *\n * 1. add identity element\n * 2. remove identities from list of generators\n * 3. add all powers of first generator that aren't the\n *    identity element\n * 4. go through all remaining generators:\n *        a. if generator is already in the list of elements\n *                -> do nothing\n *        b. otherwise\n *                i.   remember current # of elements\n *                     (i.e. the size of the current subgroup)\n *                ii.  add all current elements (which includes\n *                     the identity) each multiplied from right\n *                     with the current generator to the group\n *                iii. add all remaining cosets that are generated\n *                     by products of the new generator with itself\n *                     and all other generators seen so far\n *\n * In functional form, this is implemented as a long set of recursive\n * templates that have a complicated relationship.\n *\n * The main interface for Dimino's algorithm is the template\n * enumerate_group_elements. All lists are implemented as variadic\n * type_list<typename...> and numeric_list<typename = int, int...>\n * templates.\n *\n * 'Calling' templates is usually done via typedefs.\n *\n * This algorithm is an extended version of the basic version. The\n * extension consists in the fact that each group element has a set\n * of flags associated with it. Multiplication of two group elements\n * with each other results in a group element whose flags are the\n * XOR of the flags of the previous elements. Each time the algorithm\n * notices that a group element it just calculated is already in the\n * list of current elements, the flags of both will be compared and\n * added to the so-called 'global flags' of the group.\n *\n * The rationale behind this extension is that this allows not only\n * for the description of symmetries between tensor indices, but\n * also allows for the description of hermiticity, antisymmetry and\n * antihermiticity. Negation and conjugation each are specific bit\n * in the flags value and if two different ways to reach a group\n * element lead to two different flags, this poses a constraint on\n * the allowed values of the resulting tensor. For example, if a\n * group element is reach both with and without the conjugation\n * flags, it is clear that the resulting tensor has to be real.\n *\n * Note that this flag mechanism is quite generic and may have other\n * uses beyond tensor properties.\n *\n * IMPORTANT: \n *     This algorithm assumes the group to be finite. If you try to\n *     run it with a group that's infinite, the algorithm will only\n *     terminate once you hit a compiler limit (max template depth).\n *     Also note that trying to use this implementation to create a\n *     very large group will probably either make you hit the same\n *     limit, cause the compiler to segfault or at the very least\n *     take a *really* long time (hours, days, weeks - sic!) to\n *     compile. It is not recommended to plug in more than 4\n *     generators, unless they are independent of each other.\n */\n\n/** \\internal\n  *\n  * \\class strip_identities\n  * \\ingroup CXX11_TensorSymmetry_Module\n  *\n  * \\brief Cleanse a list of group elements of the identity element\n  *\n  * This template is used to make a first pass through all initial\n  * generators of Dimino's algorithm and remove the identity\n  * elements.\n  *\n  * \\sa enumerate_group_elements\n  */\ntemplate<template<typename, typename> class Equality, typename id, typename L> struct strip_identities;\n\ntemplate<\n  template<typename, typename> class Equality,\n  typename id,\n  typename t,\n  typename... ts\n>\nstruct strip_identities<Equality, id, type_list<t, ts...>>\n{\n  typedef typename conditional<\n    Equality<id, t>::value,\n    typename strip_identities<Equality, id, type_list<ts...>>::type,\n    typename concat<type_list<t>, typename strip_identities<Equality, id, type_list<ts...>>::type>::type\n  >::type type;\n  constexpr static int global_flags = Equality<id, t>::global_flags | strip_identities<Equality, id, type_list<ts...>>::global_flags;\n};\n\ntemplate<\n  template<typename, typename> class Equality,\n  typename id\n  EIGEN_TPL_PP_SPEC_HACK_DEFC(typename, ts)\n>\nstruct strip_identities<Equality, id, type_list<EIGEN_TPL_PP_SPEC_HACK_USE(ts)>>\n{\n  typedef type_list<> type;\n  constexpr static int global_flags = 0;\n};\n\n/** \\internal\n  *\n  * \\class dimino_first_step_elements_helper \n  * \\ingroup CXX11_TensorSymmetry_Module\n  *\n  * \\brief Recursive template that adds powers of the first generator to the list of group elements\n  *\n  * This template calls itself recursively to add powers of the first\n  * generator to the list of group elements. It stops if it reaches\n  * the identity element again.\n  *\n  * \\sa enumerate_group_elements, dimino_first_step_elements\n  */\ntemplate<\n  template<typename, typename> class Multiply,\n  template<typename, typename> class Equality,\n  typename id,\n  typename g,\n  typename current_element,\n  typename elements,\n  bool dont_add_current_element   // = false\n>\nstruct dimino_first_step_elements_helper :\n  public dimino_first_step_elements_helper<\n    Multiply,\n    Equality,\n    id,\n    g,\n    typename Multiply<current_element, g>::type,\n    typename concat<elements, type_list<current_element>>::type,\n    Equality<typename Multiply<current_element, g>::type, id>::value\n  > {};\n\ntemplate<\n  template<typename, typename> class Multiply,\n  template<typename, typename> class Equality,\n  typename id,\n  typename g,\n  typename current_element,\n  typename elements\n>\nstruct dimino_first_step_elements_helper<Multiply, Equality, id, g, current_element, elements, true>\n{\n  typedef elements type;\n  constexpr static int global_flags = Equality<current_element, id>::global_flags;\n};\n\n/** \\internal\n  *\n  * \\class dimino_first_step_elements\n  * \\ingroup CXX11_TensorSymmetry_Module\n  *\n  * \\brief Add all powers of the first generator to the list of group elements\n  *\n  * This template takes the first non-identity generator and generates the initial\n  * list of elements which consists of all powers of that generator. For a group\n  * with just one generated, it would be enumerated after this.\n  *\n  * \\sa enumerate_group_elements\n  */\ntemplate<\n  template<typename, typename> class Multiply,\n  template<typename, typename> class Equality,\n  typename id,\n  typename generators\n>\nstruct dimino_first_step_elements\n{\n  typedef typename get<0, generators>::type first_generator;\n  typedef typename skip<1, generators>::type next_generators;\n  typedef type_list<first_generator> generators_done;\n\n  typedef dimino_first_step_elements_helper<\n    Multiply,\n    Equality,\n    id,\n    first_generator,\n    first_generator,\n    type_list<id>,\n    false\n  > helper;\n  typedef typename helper::type type;\n  constexpr static int global_flags = helper::global_flags;\n};\n\n/** \\internal\n  *\n  * \\class dimino_get_coset_elements\n  * \\ingroup CXX11_TensorSymmetry_Module\n  *\n  * \\brief Generate all elements of a specific coset\n  *\n  * This template generates all the elements of a specific coset by\n  * multiplying all elements in the given subgroup with the new\n  * coset representative. Note that the first element of the\n  * subgroup is always the identity element, so the first element of\n  * ther result of this template is going to be the coset\n  * representative itself.\n  *\n  * Note that this template accepts an additional boolean parameter\n  * that specifies whether to actually generate the coset (true) or\n  * just return an empty list (false).\n  *\n  * \\sa enumerate_group_elements, dimino_add_cosets_for_rep\n  */\ntemplate<\n  template<typename, typename> class Multiply,\n  typename sub_group_elements,\n  typename new_coset_rep,\n  bool generate_coset      // = true\n>\nstruct dimino_get_coset_elements\n{\n  typedef typename apply_op_from_right<Multiply, new_coset_rep, sub_group_elements>::type type;\n};\n\ntemplate<\n  template<typename, typename> class Multiply,\n  typename sub_group_elements,\n  typename new_coset_rep\n>\nstruct dimino_get_coset_elements<Multiply, sub_group_elements, new_coset_rep, false>\n{\n  typedef type_list<> type;\n};\n\n/** \\internal\n  *\n  * \\class dimino_add_cosets_for_rep\n  * \\ingroup CXX11_TensorSymmetry_Module\n  *\n  * \\brief Recursive template for adding coset spaces\n  *\n  * This template multiplies the coset representative with a generator\n  * from the list of previous generators. If the new element is not in\n  * the group already, it adds the corresponding coset. Finally it\n  * proceeds to call itself with the next generator from the list.\n  *\n  * \\sa enumerate_group_elements, dimino_add_all_coset_spaces\n  */\ntemplate<\n  template<typename, typename> class Multiply,\n  template<typename, typename> class Equality,\n  typename id,\n  typename sub_group_elements,\n  typename elements,\n  typename generators,\n  typename rep_element,\n  int sub_group_size\n>\nstruct dimino_add_cosets_for_rep;\n\ntemplate<\n  template<typename, typename> class Multiply,\n  template<typename, typename> class Equality,\n  typename id,\n  typename sub_group_elements,\n  typename elements,\n  typename g,\n  typename... gs,\n  typename rep_element,\n  int sub_group_size\n>\nstruct dimino_add_cosets_for_rep<Multiply, Equality, id, sub_group_elements, elements, type_list<g, gs...>, rep_element, sub_group_size>\n{\n  typedef typename Multiply<rep_element, g>::type new_coset_rep;\n  typedef contained_in_list_gf<Equality, new_coset_rep, elements> _cil;\n  constexpr static bool add_coset = !_cil::value;\n\n  typedef typename dimino_get_coset_elements<\n    Multiply,\n    sub_group_elements,\n    new_coset_rep,\n    add_coset\n  >::type coset_elements;\n\n  typedef dimino_add_cosets_for_rep<\n    Multiply,\n    Equality,\n    id,\n    sub_group_elements,\n    typename concat<elements, coset_elements>::type,\n    type_list<gs...>,\n    rep_element,\n    sub_group_size\n  > _helper;\n\n  typedef typename _helper::type type;\n  constexpr static int global_flags = _cil::global_flags | _helper::global_flags;\n\n  /* Note that we don't have to update global flags here, since\n   * we will only add these elements if they are not part of\n   * the group already. But that only happens if the coset rep\n   * is not already in the group, so the check for the coset rep\n   * will catch this.\n   */\n};\n\ntemplate<\n  template<typename, typename> class Multiply,\n  template<typename, typename> class Equality,\n  typename id,\n  typename sub_group_elements,\n  typename elements\n  EIGEN_TPL_PP_SPEC_HACK_DEFC(typename, empty),\n  typename rep_element,\n  int sub_group_size\n>\nstruct dimino_add_cosets_for_rep<Multiply, Equality, id, sub_group_elements, elements, type_list<EIGEN_TPL_PP_SPEC_HACK_USE(empty)>, rep_element, sub_group_size>\n{\n  typedef elements type;\n  constexpr static int global_flags = 0;\n};\n\n/** \\internal\n  *\n  * \\class dimino_add_all_coset_spaces\n  * \\ingroup CXX11_TensorSymmetry_Module\n  *\n  * \\brief Recursive template for adding all coset spaces for a new generator\n  *\n  * This template tries to go through the list of generators (with\n  * the help of the dimino_add_cosets_for_rep template) as long as\n  * it still finds elements that are not part of the group and add\n  * the corresponding cosets.\n  *\n  * \\sa enumerate_group_elements, dimino_add_cosets_for_rep\n  */\ntemplate<\n  template<typename, typename> class Multiply,\n  template<typename, typename> class Equality,\n  typename id,\n  typename sub_group_elements,\n  typename elements,\n  typename generators,\n  int sub_group_size,\n  int rep_pos,\n  bool stop_condition        // = false\n>\nstruct dimino_add_all_coset_spaces\n{\n  typedef typename get<rep_pos, elements>::type rep_element;\n  typedef dimino_add_cosets_for_rep<\n    Multiply,\n    Equality,\n    id,\n    sub_group_elements,\n    elements,\n    generators,\n    rep_element,\n    sub_group_elements::count\n  > _ac4r;\n  typedef typename _ac4r::type new_elements;\n  \n  constexpr static int new_rep_pos = rep_pos + sub_group_elements::count;\n  constexpr static bool new_stop_condition = new_rep_pos >= new_elements::count;\n\n  typedef dimino_add_all_coset_spaces<\n    Multiply,\n    Equality,\n    id,\n    sub_group_elements,\n    new_elements,\n    generators,\n    sub_group_size,\n    new_rep_pos,\n    new_stop_condition\n  > _helper;\n\n  typedef typename _helper::type type;\n  constexpr static int global_flags = _helper::global_flags | _ac4r::global_flags;\n};\n\ntemplate<\n  template<typename, typename> class Multiply,\n  template<typename, typename> class Equality,\n  typename id,\n  typename sub_group_elements,\n  typename elements,\n  typename generators,\n  int sub_group_size,\n  int rep_pos\n>\nstruct dimino_add_all_coset_spaces<Multiply, Equality, id, sub_group_elements, elements, generators, sub_group_size, rep_pos, true>\n{\n  typedef elements type;\n  constexpr static int global_flags = 0;\n};\n\n/** \\internal\n  *\n  * \\class dimino_add_generator\n  * \\ingroup CXX11_TensorSymmetry_Module\n  *\n  * \\brief Enlarge the group by adding a new generator.\n  *\n  * It accepts a boolean parameter that determines if the generator is redundant,\n  * i.e. was already seen in the group. In that case, it reduces to a no-op.\n  *\n  * \\sa enumerate_group_elements, dimino_add_all_coset_spaces\n  */\ntemplate<\n  template<typename, typename> class Multiply,\n  template<typename, typename> class Equality,\n  typename id,\n  typename elements,\n  typename generators_done,\n  typename current_generator,\n  bool redundant          // = false\n>\nstruct dimino_add_generator\n{\n  /* this template is only called if the generator is not redundant\n   * => all elements of the group multiplied with the new generator\n   *    are going to be new elements of the most trivial coset space\n   */\n  typedef typename apply_op_from_right<Multiply, current_generator, elements>::type multiplied_elements;\n  typedef typename concat<elements, multiplied_elements>::type new_elements;\n\n  constexpr static int rep_pos = elements::count;\n\n  typedef dimino_add_all_coset_spaces<\n    Multiply,\n    Equality,\n    id,\n    elements, // elements of previous subgroup\n    new_elements,\n    typename concat<generators_done, type_list<current_generator>>::type,\n    elements::count, // size of previous subgroup\n    rep_pos,\n    false // don't stop (because rep_pos >= new_elements::count is always false at this point)\n  > _helper;\n  typedef typename _helper::type type;\n  constexpr static int global_flags = _helper::global_flags;\n};\n\ntemplate<\n  template<typename, typename> class Multiply,\n  template<typename, typename> class Equality,\n  typename id,\n  typename elements,\n  typename generators_done,\n  typename current_generator\n>\nstruct dimino_add_generator<Multiply, Equality, id, elements, generators_done, current_generator, true>\n{\n  // redundant case\n  typedef elements type;\n  constexpr static int global_flags = 0;\n};\n\n/** \\internal\n  *\n  * \\class dimino_add_remaining_generators\n  * \\ingroup CXX11_TensorSymmetry_Module\n  *\n  * \\brief Recursive template that adds all remaining generators to a group\n  *\n  * Loop through the list of generators that remain and successively\n  * add them to the group.\n  *\n  * \\sa enumerate_group_elements, dimino_add_generator\n  */\ntemplate<\n  template<typename, typename> class Multiply,\n  template<typename, typename> class Equality,\n  typename id,\n  typename generators_done,\n  typename remaining_generators,\n  typename elements\n>\nstruct dimino_add_remaining_generators\n{\n  typedef typename get<0, remaining_generators>::type first_generator;\n  typedef typename skip<1, remaining_generators>::type next_generators;\n\n  typedef contained_in_list_gf<Equality, first_generator, elements> _cil;\n\n  typedef dimino_add_generator<\n    Multiply,\n    Equality,\n    id,\n    elements,\n    generators_done,\n    first_generator,\n    _cil::value\n  > _helper;\n\n  typedef typename _helper::type new_elements;\n\n  typedef dimino_add_remaining_generators<\n    Multiply,\n    Equality,\n    id,\n    typename concat<generators_done, type_list<first_generator>>::type,\n    next_generators,\n    new_elements\n  > _next_iter;\n\n  typedef typename _next_iter::type type;\n  constexpr static int global_flags =\n    _cil::global_flags |\n    _helper::global_flags |\n    _next_iter::global_flags;\n};\n\ntemplate<\n  template<typename, typename> class Multiply,\n  template<typename, typename> class Equality,\n  typename id,\n  typename generators_done,\n  typename elements\n>\nstruct dimino_add_remaining_generators<Multiply, Equality, id, generators_done, type_list<>, elements>\n{\n  typedef elements type;\n  constexpr static int global_flags = 0;\n};\n\n/** \\internal\n  *\n  * \\class enumerate_group_elements_noid\n  * \\ingroup CXX11_TensorSymmetry_Module\n  *\n  * \\brief Helper template that implements group element enumeration\n  *\n  * This is a helper template that implements the actual enumeration\n  * of group elements. This has been split so that the list of\n  * generators can be cleansed of the identity element before\n  * performing the actual operation.\n  *\n  * \\sa enumerate_group_elements\n  */\ntemplate<\n  template<typename, typename> class Multiply,\n  template<typename, typename> class Equality,\n  typename id,\n  typename generators,\n  int initial_global_flags = 0\n>\nstruct enumerate_group_elements_noid\n{\n  typedef dimino_first_step_elements<Multiply, Equality, id, generators> first_step;\n  typedef typename first_step::type first_step_elements;\n\n  typedef dimino_add_remaining_generators<\n    Multiply,\n    Equality,\n    id,\n    typename first_step::generators_done,\n    typename first_step::next_generators, // remaining_generators\n    typename first_step::type // first_step elements\n  > _helper;\n\n  typedef typename _helper::type type;\n  constexpr static int global_flags =\n    initial_global_flags |\n    first_step::global_flags |\n    _helper::global_flags;\n};\n\n// in case when no generators are specified\ntemplate<\n  template<typename, typename> class Multiply,\n  template<typename, typename> class Equality,\n  typename id,\n  int initial_global_flags\n>\nstruct enumerate_group_elements_noid<Multiply, Equality, id, type_list<>, initial_global_flags>\n{\n  typedef type_list<id> type;\n  constexpr static int global_flags = initial_global_flags;\n};\n\n/** \\internal\n  *\n  * \\class enumerate_group_elements\n  * \\ingroup CXX11_TensorSymmetry_Module\n  *\n  * \\brief Enumerate all elements in a finite group\n  *\n  * This template enumerates all elements in a finite group. It accepts\n  * the following template parameters:\n  *\n  * \\tparam Multiply      The multiplication operation that multiplies two group elements\n  *                       with each other.\n  * \\tparam Equality      The equality check operation that checks if two group elements\n  *                       are equal to another.\n  * \\tparam id            The identity element\n  * \\tparam _generators   A list of (possibly redundant) generators of the group\n  */\ntemplate<\n  template<typename, typename> class Multiply,\n  template<typename, typename> class Equality,\n  typename id,\n  typename _generators\n>\nstruct enumerate_group_elements\n  : public enumerate_group_elements_noid<\n      Multiply,\n      Equality,\n      id,\n      typename strip_identities<Equality, id, _generators>::type,\n      strip_identities<Equality, id, _generators>::global_flags\n    >\n{\n};\n\n} // end namespace group_theory\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11_TENSORSYMMETRY_TEMPLATEGROUPTHEORY_H\n\n/*\n * kate: space-indent on; indent-width 2; mixedindent off; indent-mode cstyle;\n */\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/ThreadPool/EventCount.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Dmitry Vyukov <dvyukov@google.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_THREADPOOL_EVENTCOUNT_H_\n#define EIGEN_CXX11_THREADPOOL_EVENTCOUNT_H_\n\nnamespace Eigen {\n\n// EventCount allows to wait for arbitrary predicates in non-blocking\n// algorithms. Think of condition variable, but wait predicate does not need to\n// be protected by a mutex. Usage:\n// Waiting thread does:\n//\n//   if (predicate)\n//     return act();\n//   EventCount::Waiter& w = waiters[my_index];\n//   ec.Prewait(&w);\n//   if (predicate) {\n//     ec.CancelWait(&w);\n//     return act();\n//   }\n//   ec.CommitWait(&w);\n//\n// Notifying thread does:\n//\n//   predicate = true;\n//   ec.Notify(true);\n//\n// Notify is cheap if there are no waiting threads. Prewait/CommitWait are not\n// cheap, but they are executed only if the preceeding predicate check has\n// failed.\n//\n// Algorihtm outline:\n// There are two main variables: predicate (managed by user) and state_.\n// Operation closely resembles Dekker mutual algorithm:\n// https://en.wikipedia.org/wiki/Dekker%27s_algorithm\n// Waiting thread sets state_ then checks predicate, Notifying thread sets\n// predicate then checks state_. Due to seq_cst fences in between these\n// operations it is guaranteed than either waiter will see predicate change\n// and won't block, or notifying thread will see state_ change and will unblock\n// the waiter, or both. But it can't happen that both threads don't see each\n// other changes, which would lead to deadlock.\nclass EventCount {\n public:\n  class Waiter;\n\n  EventCount(MaxSizeVector<Waiter>& waiters) : waiters_(waiters) {\n    eigen_assert(waiters.size() < (1 << kWaiterBits) - 1);\n    // Initialize epoch to something close to overflow to test overflow.\n    state_ = kStackMask | (kEpochMask - kEpochInc * waiters.size() * 2);\n  }\n\n  ~EventCount() {\n    // Ensure there are no waiters.\n    eigen_assert((state_.load() & (kStackMask | kWaiterMask)) == kStackMask);\n  }\n\n  // Prewait prepares for waiting.\n  // After calling this function the thread must re-check the wait predicate\n  // and call either CancelWait or CommitWait passing the same Waiter object.\n  void Prewait(Waiter* w) {\n    w->epoch = state_.fetch_add(kWaiterInc, std::memory_order_relaxed);\n    std::atomic_thread_fence(std::memory_order_seq_cst);\n  }\n\n  // CommitWait commits waiting.\n  void CommitWait(Waiter* w) {\n    w->state = Waiter::kNotSignaled;\n    // Modification epoch of this waiter.\n    uint64_t epoch =\n        (w->epoch & kEpochMask) +\n        (((w->epoch & kWaiterMask) >> kWaiterShift) << kEpochShift);\n    uint64_t state = state_.load(std::memory_order_seq_cst);\n    for (;;) {\n      if (int64_t((state & kEpochMask) - epoch) < 0) {\n        // The preceeding waiter has not decided on its fate. Wait until it\n        // calls either CancelWait or CommitWait, or is notified.\n        EIGEN_THREAD_YIELD();\n        state = state_.load(std::memory_order_seq_cst);\n        continue;\n      }\n      // We've already been notified.\n      if (int64_t((state & kEpochMask) - epoch) > 0) return;\n      // Remove this thread from prewait counter and add it to the waiter list.\n      eigen_assert((state & kWaiterMask) != 0);\n      uint64_t newstate = state - kWaiterInc + kEpochInc;\n      newstate = (newstate & ~kStackMask) | (w - &waiters_[0]);\n      if ((state & kStackMask) == kStackMask)\n        w->next.store(nullptr, std::memory_order_relaxed);\n      else\n        w->next.store(&waiters_[state & kStackMask], std::memory_order_relaxed);\n      if (state_.compare_exchange_weak(state, newstate,\n                                       std::memory_order_release))\n        break;\n    }\n    Park(w);\n  }\n\n  // CancelWait cancels effects of the previous Prewait call.\n  void CancelWait(Waiter* w) {\n    uint64_t epoch =\n        (w->epoch & kEpochMask) +\n        (((w->epoch & kWaiterMask) >> kWaiterShift) << kEpochShift);\n    uint64_t state = state_.load(std::memory_order_relaxed);\n    for (;;) {\n      if (int64_t((state & kEpochMask) - epoch) < 0) {\n        // The preceeding waiter has not decided on its fate. Wait until it\n        // calls either CancelWait or CommitWait, or is notified.\n        EIGEN_THREAD_YIELD();\n        state = state_.load(std::memory_order_relaxed);\n        continue;\n      }\n      // We've already been notified.\n      if (int64_t((state & kEpochMask) - epoch) > 0) return;\n      // Remove this thread from prewait counter.\n      eigen_assert((state & kWaiterMask) != 0);\n      if (state_.compare_exchange_weak(state, state - kWaiterInc + kEpochInc,\n                                       std::memory_order_relaxed))\n        return;\n    }\n  }\n\n  // Notify wakes one or all waiting threads.\n  // Must be called after changing the associated wait predicate.\n  void Notify(bool all) {\n    std::atomic_thread_fence(std::memory_order_seq_cst);\n    uint64_t state = state_.load(std::memory_order_acquire);\n    for (;;) {\n      // Easy case: no waiters.\n      if ((state & kStackMask) == kStackMask && (state & kWaiterMask) == 0)\n        return;\n      uint64_t waiters = (state & kWaiterMask) >> kWaiterShift;\n      uint64_t newstate;\n      if (all) {\n        // Reset prewait counter and empty wait list.\n        newstate = (state & kEpochMask) + (kEpochInc * waiters) + kStackMask;\n      } else if (waiters) {\n        // There is a thread in pre-wait state, unblock it.\n        newstate = state + kEpochInc - kWaiterInc;\n      } else {\n        // Pop a waiter from list and unpark it.\n        Waiter* w = &waiters_[state & kStackMask];\n        Waiter* wnext = w->next.load(std::memory_order_relaxed);\n        uint64_t next = kStackMask;\n        if (wnext != nullptr) next = wnext - &waiters_[0];\n        // Note: we don't add kEpochInc here. ABA problem on the lock-free stack\n        // can't happen because a waiter is re-pushed onto the stack only after\n        // it was in the pre-wait state which inevitably leads to epoch\n        // increment.\n        newstate = (state & kEpochMask) + next;\n      }\n      if (state_.compare_exchange_weak(state, newstate,\n                                       std::memory_order_acquire)) {\n        if (!all && waiters) return;  // unblocked pre-wait thread\n        if ((state & kStackMask) == kStackMask) return;\n        Waiter* w = &waiters_[state & kStackMask];\n        if (!all) w->next.store(nullptr, std::memory_order_relaxed);\n        Unpark(w);\n        return;\n      }\n    }\n  }\n\n  class Waiter {\n    friend class EventCount;\n    // Align to 128 byte boundary to prevent false sharing with other Waiter objects in the same vector.\n    EIGEN_ALIGN_TO_BOUNDARY(128) std::atomic<Waiter*> next;\n    std::mutex mu;\n    std::condition_variable cv;\n    uint64_t epoch;\n    unsigned state;\n    enum {\n      kNotSignaled,\n      kWaiting,\n      kSignaled,\n    };\n  };\n\n private:\n  // State_ layout:\n  // - low kStackBits is a stack of waiters committed wait.\n  // - next kWaiterBits is count of waiters in prewait state.\n  // - next kEpochBits is modification counter.\n  static const uint64_t kStackBits = 16;\n  static const uint64_t kStackMask = (1ull << kStackBits) - 1;\n  static const uint64_t kWaiterBits = 16;\n  static const uint64_t kWaiterShift = 16;\n  static const uint64_t kWaiterMask = ((1ull << kWaiterBits) - 1)\n                                      << kWaiterShift;\n  static const uint64_t kWaiterInc = 1ull << kWaiterBits;\n  static const uint64_t kEpochBits = 32;\n  static const uint64_t kEpochShift = 32;\n  static const uint64_t kEpochMask = ((1ull << kEpochBits) - 1) << kEpochShift;\n  static const uint64_t kEpochInc = 1ull << kEpochShift;\n  std::atomic<uint64_t> state_;\n  MaxSizeVector<Waiter>& waiters_;\n\n  void Park(Waiter* w) {\n    std::unique_lock<std::mutex> lock(w->mu);\n    while (w->state != Waiter::kSignaled) {\n      w->state = Waiter::kWaiting;\n      w->cv.wait(lock);\n    }\n  }\n\n  void Unpark(Waiter* waiters) {\n    Waiter* next = nullptr;\n    for (Waiter* w = waiters; w; w = next) {\n      next = w->next.load(std::memory_order_relaxed);\n      unsigned state;\n      {\n        std::unique_lock<std::mutex> lock(w->mu);\n        state = w->state;\n        w->state = Waiter::kSignaled;\n      }\n      // Avoid notifying if it wasn't waiting.\n      if (state == Waiter::kWaiting) w->cv.notify_one();\n    }\n  }\n\n  EventCount(const EventCount&) = delete;\n  void operator=(const EventCount&) = delete;\n};\n\n}  // namespace Eigen\n\n#endif  // EIGEN_CXX11_THREADPOOL_EVENTCOUNT_H_\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/ThreadPool/NonBlockingThreadPool.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Dmitry Vyukov <dvyukov@google.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_THREADPOOL_NONBLOCKING_THREAD_POOL_H\n#define EIGEN_CXX11_THREADPOOL_NONBLOCKING_THREAD_POOL_H\n\n\nnamespace Eigen {\n\ntemplate <typename Environment>\nclass NonBlockingThreadPoolTempl : public Eigen::ThreadPoolInterface {\n public:\n  typedef typename Environment::Task Task;\n  typedef RunQueue<Task, 1024> Queue;\n\n  NonBlockingThreadPoolTempl(int num_threads, Environment env = Environment())\n      : env_(env),\n        threads_(num_threads),\n        queues_(num_threads),\n        coprimes_(num_threads),\n        waiters_(num_threads),\n        blocked_(0),\n        spinning_(0),\n        done_(false),\n        ec_(waiters_) {\n    waiters_.resize(num_threads);\n\n    // Calculate coprimes of num_threads.\n    // Coprimes are used for a random walk over all threads in Steal\n    // and NonEmptyQueueIndex. Iteration is based on the fact that if we take\n    // a walk starting thread index t and calculate num_threads - 1 subsequent\n    // indices as (t + coprime) % num_threads, we will cover all threads without\n    // repetitions (effectively getting a presudo-random permutation of thread\n    // indices).\n    for (int i = 1; i <= num_threads; i++) {\n      unsigned a = i;\n      unsigned b = num_threads;\n      // If GCD(a, b) == 1, then a and b are coprimes.\n      while (b != 0) {\n        unsigned tmp = a;\n        a = b;\n        b = tmp % b;\n      }\n      if (a == 1) {\n        coprimes_.push_back(i);\n      }\n    }\n    for (int i = 0; i < num_threads; i++) {\n      queues_.push_back(new Queue());\n    }\n    for (int i = 0; i < num_threads; i++) {\n      threads_.push_back(env_.CreateThread([this, i]() { WorkerLoop(i); }));\n    }\n  }\n\n  ~NonBlockingThreadPoolTempl() {\n    done_ = true;\n    // Now if all threads block without work, they will start exiting.\n    // But note that threads can continue to work arbitrary long,\n    // block, submit new work, unblock and otherwise live full life.\n    ec_.Notify(true);\n\n    // Join threads explicitly to avoid destruction order issues.\n    for (size_t i = 0; i < threads_.size(); i++) delete threads_[i];\n    for (size_t i = 0; i < threads_.size(); i++) delete queues_[i];\n  }\n\n  void Schedule(std::function<void()> fn) {\n    Task t = env_.CreateTask(std::move(fn));\n    PerThread* pt = GetPerThread();\n    if (pt->pool == this) {\n      // Worker thread of this pool, push onto the thread's queue.\n      Queue* q = queues_[pt->thread_id];\n      t = q->PushFront(std::move(t));\n    } else {\n      // A free-standing thread (or worker of another pool), push onto a random\n      // queue.\n      Queue* q = queues_[Rand(&pt->rand) % queues_.size()];\n      t = q->PushBack(std::move(t));\n    }\n    // Note: below we touch this after making w available to worker threads.\n    // Strictly speaking, this can lead to a racy-use-after-free. Consider that\n    // Schedule is called from a thread that is neither main thread nor a worker\n    // thread of this pool. Then, execution of w directly or indirectly\n    // completes overall computations, which in turn leads to destruction of\n    // this. We expect that such scenario is prevented by program, that is,\n    // this is kept alive while any threads can potentially be in Schedule.\n    if (!t.f)\n      ec_.Notify(false);\n    else\n      env_.ExecuteTask(t);  // Push failed, execute directly.\n  }\n\n  int NumThreads() const final {\n    return static_cast<int>(threads_.size());\n  }\n\n  int CurrentThreadId() const final {\n    const PerThread* pt =\n        const_cast<NonBlockingThreadPoolTempl*>(this)->GetPerThread();\n    if (pt->pool == this) {\n      return pt->thread_id;\n    } else {\n      return -1;\n    }\n  }\n\n private:\n  typedef typename Environment::EnvThread Thread;\n\n  struct PerThread {\n    constexpr PerThread() : pool(NULL), rand(0), thread_id(-1) { }\n    NonBlockingThreadPoolTempl* pool;  // Parent pool, or null for normal threads.\n    uint64_t rand;  // Random generator state.\n    int thread_id;  // Worker thread index in pool.\n  };\n\n  Environment env_;\n  MaxSizeVector<Thread*> threads_;\n  MaxSizeVector<Queue*> queues_;\n  MaxSizeVector<unsigned> coprimes_;\n  MaxSizeVector<EventCount::Waiter> waiters_;\n  std::atomic<unsigned> blocked_;\n  std::atomic<bool> spinning_;\n  std::atomic<bool> done_;\n  EventCount ec_;\n\n  // Main worker thread loop.\n  void WorkerLoop(int thread_id) {\n    PerThread* pt = GetPerThread();\n    pt->pool = this;\n    pt->rand = std::hash<std::thread::id>()(std::this_thread::get_id());\n    pt->thread_id = thread_id;\n    Queue* q = queues_[thread_id];\n    EventCount::Waiter* waiter = &waiters_[thread_id];\n    for (;;) {\n      Task t = q->PopFront();\n      if (!t.f) {\n        t = Steal();\n        if (!t.f) {\n          // Leave one thread spinning. This reduces latency.\n          // TODO(dvyukov): 1000 iterations is based on fair dice roll, tune it.\n          // Also, the time it takes to attempt to steal work 1000 times depends\n          // on the size of the thread pool. However the speed at which the user\n          // of the thread pool submit tasks is independent of the size of the\n          // pool. Consider a time based limit instead.\n          if (!spinning_ && !spinning_.exchange(true)) {\n            for (int i = 0; i < 1000 && !t.f; i++) {\n              t = Steal();\n            }\n            spinning_ = false;\n          }\n          if (!t.f) {\n            if (!WaitForWork(waiter, &t)) {\n              return;\n            }\n          }\n        }\n      }\n      if (t.f) {\n        env_.ExecuteTask(t);\n      }\n    }\n  }\n\n  // Steal tries to steal work from other worker threads in best-effort manner.\n  Task Steal() {\n    PerThread* pt = GetPerThread();\n    const size_t size = queues_.size();\n    unsigned r = Rand(&pt->rand);\n    unsigned inc = coprimes_[r % coprimes_.size()];\n    unsigned victim = r % size;\n    for (unsigned i = 0; i < size; i++) {\n      Task t = queues_[victim]->PopBack();\n      if (t.f) {\n        return t;\n      }\n      victim += inc;\n      if (victim >= size) {\n        victim -= size;\n      }\n    }\n    return Task();\n  }\n\n  // WaitForWork blocks until new work is available (returns true), or if it is\n  // time to exit (returns false). Can optionally return a task to execute in t\n  // (in such case t.f != nullptr on return).\n  bool WaitForWork(EventCount::Waiter* waiter, Task* t) {\n    eigen_assert(!t->f);\n    // We already did best-effort emptiness check in Steal, so prepare for\n    // blocking.\n    ec_.Prewait(waiter);\n    // Now do a reliable emptiness check.\n    int victim = NonEmptyQueueIndex();\n    if (victim != -1) {\n      ec_.CancelWait(waiter);\n      *t = queues_[victim]->PopBack();\n      return true;\n    }\n    // Number of blocked threads is used as termination condition.\n    // If we are shutting down and all worker threads blocked without work,\n    // that's we are done.\n    blocked_++;\n    if (done_ && blocked_ == threads_.size()) {\n      ec_.CancelWait(waiter);\n      // Almost done, but need to re-check queues.\n      // Consider that all queues are empty and all worker threads are preempted\n      // right after incrementing blocked_ above. Now a free-standing thread\n      // submits work and calls destructor (which sets done_). If we don't\n      // re-check queues, we will exit leaving the work unexecuted.\n      if (NonEmptyQueueIndex() != -1) {\n        // Note: we must not pop from queues before we decrement blocked_,\n        // otherwise the following scenario is possible. Consider that instead\n        // of checking for emptiness we popped the only element from queues.\n        // Now other worker threads can start exiting, which is bad if the\n        // work item submits other work. So we just check emptiness here,\n        // which ensures that all worker threads exit at the same time.\n        blocked_--;\n        return true;\n      }\n      // Reached stable termination state.\n      ec_.Notify(true);\n      return false;\n    }\n    ec_.CommitWait(waiter);\n    blocked_--;\n    return true;\n  }\n\n  int NonEmptyQueueIndex() {\n    PerThread* pt = GetPerThread();\n    const size_t size = queues_.size();\n    unsigned r = Rand(&pt->rand);\n    unsigned inc = coprimes_[r % coprimes_.size()];\n    unsigned victim = r % size;\n    for (unsigned i = 0; i < size; i++) {\n      if (!queues_[victim]->Empty()) {\n        return victim;\n      }\n      victim += inc;\n      if (victim >= size) {\n        victim -= size;\n      }\n    }\n    return -1;\n  }\n\n  static EIGEN_STRONG_INLINE PerThread* GetPerThread() {\n    EIGEN_THREAD_LOCAL PerThread per_thread_;\n    PerThread* pt = &per_thread_;\n    return pt;\n  }\n\n  static EIGEN_STRONG_INLINE unsigned Rand(uint64_t* state) {\n    uint64_t current = *state;\n    // Update the internal state\n    *state = current * 6364136223846793005ULL + 0xda3e39cb94b95bdbULL;\n    // Generate the random output (using the PCG-XSH-RS scheme)\n    return static_cast<unsigned>((current ^ (current >> 22)) >> (22 + (current >> 61)));\n  }\n};\n\ntypedef NonBlockingThreadPoolTempl<StlThreadEnvironment> NonBlockingThreadPool;\n\n}  // namespace Eigen\n\n#endif  // EIGEN_CXX11_THREADPOOL_NONBLOCKING_THREAD_POOL_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/ThreadPool/RunQueue.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Dmitry Vyukov <dvyukov@google.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_THREADPOOL_RUNQUEUE_H_\n#define EIGEN_CXX11_THREADPOOL_RUNQUEUE_H_\n\n\nnamespace Eigen {\n\n// RunQueue is a fixed-size, partially non-blocking deque or Work items.\n// Operations on front of the queue must be done by a single thread (owner),\n// operations on back of the queue can be done by multiple threads concurrently.\n//\n// Algorithm outline:\n// All remote threads operating on the queue back are serialized by a mutex.\n// This ensures that at most two threads access state: owner and one remote\n// thread (Size aside). The algorithm ensures that the occupied region of the\n// underlying array is logically continuous (can wraparound, but no stray\n// occupied elements). Owner operates on one end of this region, remote thread\n// operates on the other end. Synchronization between these threads\n// (potential consumption of the last element and take up of the last empty\n// element) happens by means of state variable in each element. States are:\n// empty, busy (in process of insertion of removal) and ready. Threads claim\n// elements (empty->busy and ready->busy transitions) by means of a CAS\n// operation. The finishing transition (busy->empty and busy->ready) are done\n// with plain store as the element is exclusively owned by the current thread.\n//\n// Note: we could permit only pointers as elements, then we would not need\n// separate state variable as null/non-null pointer value would serve as state,\n// but that would require malloc/free per operation for large, complex values\n// (and this is designed to store std::function<()>).\ntemplate <typename Work, unsigned kSize>\nclass RunQueue {\n public:\n  RunQueue() : front_(0), back_(0) {\n    // require power-of-two for fast masking\n    eigen_assert((kSize & (kSize - 1)) == 0);\n    eigen_assert(kSize > 2);            // why would you do this?\n    eigen_assert(kSize <= (64 << 10));  // leave enough space for counter\n    for (unsigned i = 0; i < kSize; i++)\n      array_[i].state.store(kEmpty, std::memory_order_relaxed);\n  }\n\n  ~RunQueue() { eigen_assert(Size() == 0); }\n\n  // PushFront inserts w at the beginning of the queue.\n  // If queue is full returns w, otherwise returns default-constructed Work.\n  Work PushFront(Work w) {\n    unsigned front = front_.load(std::memory_order_relaxed);\n    Elem* e = &array_[front & kMask];\n    uint8_t s = e->state.load(std::memory_order_relaxed);\n    if (s != kEmpty ||\n        !e->state.compare_exchange_strong(s, kBusy, std::memory_order_acquire))\n      return w;\n    front_.store(front + 1 + (kSize << 1), std::memory_order_relaxed);\n    e->w = std::move(w);\n    e->state.store(kReady, std::memory_order_release);\n    return Work();\n  }\n\n  // PopFront removes and returns the first element in the queue.\n  // If the queue was empty returns default-constructed Work.\n  Work PopFront() {\n    unsigned front = front_.load(std::memory_order_relaxed);\n    Elem* e = &array_[(front - 1) & kMask];\n    uint8_t s = e->state.load(std::memory_order_relaxed);\n    if (s != kReady ||\n        !e->state.compare_exchange_strong(s, kBusy, std::memory_order_acquire))\n      return Work();\n    Work w = std::move(e->w);\n    e->state.store(kEmpty, std::memory_order_release);\n    front = ((front - 1) & kMask2) | (front & ~kMask2);\n    front_.store(front, std::memory_order_relaxed);\n    return w;\n  }\n\n  // PushBack adds w at the end of the queue.\n  // If queue is full returns w, otherwise returns default-constructed Work.\n  Work PushBack(Work w) {\n    std::unique_lock<std::mutex> lock(mutex_);\n    unsigned back = back_.load(std::memory_order_relaxed);\n    Elem* e = &array_[(back - 1) & kMask];\n    uint8_t s = e->state.load(std::memory_order_relaxed);\n    if (s != kEmpty ||\n        !e->state.compare_exchange_strong(s, kBusy, std::memory_order_acquire))\n      return w;\n    back = ((back - 1) & kMask2) | (back & ~kMask2);\n    back_.store(back, std::memory_order_relaxed);\n    e->w = std::move(w);\n    e->state.store(kReady, std::memory_order_release);\n    return Work();\n  }\n\n  // PopBack removes and returns the last elements in the queue.\n  // Can fail spuriously.\n  Work PopBack() {\n    if (Empty()) return Work();\n    std::unique_lock<std::mutex> lock(mutex_, std::try_to_lock);\n    if (!lock) return Work();\n    unsigned back = back_.load(std::memory_order_relaxed);\n    Elem* e = &array_[back & kMask];\n    uint8_t s = e->state.load(std::memory_order_relaxed);\n    if (s != kReady ||\n        !e->state.compare_exchange_strong(s, kBusy, std::memory_order_acquire))\n      return Work();\n    Work w = std::move(e->w);\n    e->state.store(kEmpty, std::memory_order_release);\n    back_.store(back + 1 + (kSize << 1), std::memory_order_relaxed);\n    return w;\n  }\n\n  // PopBackHalf removes and returns half last elements in the queue.\n  // Returns number of elements removed. But can also fail spuriously.\n  unsigned PopBackHalf(std::vector<Work>* result) {\n    if (Empty()) return 0;\n    std::unique_lock<std::mutex> lock(mutex_, std::try_to_lock);\n    if (!lock) return 0;\n    unsigned back = back_.load(std::memory_order_relaxed);\n    unsigned size = Size();\n    unsigned mid = back;\n    if (size > 1) mid = back + (size - 1) / 2;\n    unsigned n = 0;\n    unsigned start = 0;\n    for (; static_cast<int>(mid - back) >= 0; mid--) {\n      Elem* e = &array_[mid & kMask];\n      uint8_t s = e->state.load(std::memory_order_relaxed);\n      if (n == 0) {\n        if (s != kReady ||\n            !e->state.compare_exchange_strong(s, kBusy,\n                                              std::memory_order_acquire))\n          continue;\n        start = mid;\n      } else {\n        // Note: no need to store temporal kBusy, we exclusively own these\n        // elements.\n        eigen_assert(s == kReady);\n      }\n      result->push_back(std::move(e->w));\n      e->state.store(kEmpty, std::memory_order_release);\n      n++;\n    }\n    if (n != 0)\n      back_.store(start + 1 + (kSize << 1), std::memory_order_relaxed);\n    return n;\n  }\n\n  // Size returns current queue size.\n  // Can be called by any thread at any time.\n  unsigned Size() const {\n    // Emptiness plays critical role in thread pool blocking. So we go to great\n    // effort to not produce false positives (claim non-empty queue as empty).\n    for (;;) {\n      // Capture a consistent snapshot of front/tail.\n      unsigned front = front_.load(std::memory_order_acquire);\n      unsigned back = back_.load(std::memory_order_acquire);\n      unsigned front1 = front_.load(std::memory_order_relaxed);\n      if (front != front1) continue;\n      int size = (front & kMask2) - (back & kMask2);\n      // Fix overflow.\n      if (size < 0) size += 2 * kSize;\n      // Order of modification in push/pop is crafted to make the queue look\n      // larger than it is during concurrent modifications. E.g. pop can\n      // decrement size before the corresponding push has incremented it.\n      // So the computed size can be up to kSize + 1, fix it.\n      if (size > static_cast<int>(kSize)) size = kSize;\n      return size;\n    }\n  }\n\n  // Empty tests whether container is empty.\n  // Can be called by any thread at any time.\n  bool Empty() const { return Size() == 0; }\n\n private:\n  static const unsigned kMask = kSize - 1;\n  static const unsigned kMask2 = (kSize << 1) - 1;\n  struct Elem {\n    std::atomic<uint8_t> state;\n    Work w;\n  };\n  enum {\n    kEmpty,\n    kBusy,\n    kReady,\n  };\n  std::mutex mutex_;\n  // Low log(kSize) + 1 bits in front_ and back_ contain rolling index of\n  // front/back, repsectively. The remaining bits contain modification counters\n  // that are incremented on Push operations. This allows us to (1) distinguish\n  // between empty and full conditions (if we would use log(kSize) bits for\n  // position, these conditions would be indistinguishable); (2) obtain\n  // consistent snapshot of front_/back_ for Size operation using the\n  // modification counters.\n  std::atomic<unsigned> front_;\n  std::atomic<unsigned> back_;\n  Elem array_[kSize];\n\n  RunQueue(const RunQueue&) = delete;\n  void operator=(const RunQueue&) = delete;\n};\n\n}  // namespace Eigen\n\n#endif  // EIGEN_CXX11_THREADPOOL_RUNQUEUE_H_\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/ThreadPool/SimpleThreadPool.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_THREADPOOL_SIMPLE_THREAD_POOL_H\n#define EIGEN_CXX11_THREADPOOL_SIMPLE_THREAD_POOL_H\n\nnamespace Eigen {\n\n// The implementation of the ThreadPool type ensures that the Schedule method\n// runs the functions it is provided in FIFO order when the scheduling is done\n// by a single thread.\n// Environment provides a way to create threads and also allows to intercept\n// task submission and execution.\ntemplate <typename Environment>\nclass SimpleThreadPoolTempl : public ThreadPoolInterface {\n public:\n  // Construct a pool that contains \"num_threads\" threads.\n  explicit SimpleThreadPoolTempl(int num_threads, Environment env = Environment())\n      : env_(env), threads_(num_threads), waiters_(num_threads) {\n    for (int i = 0; i < num_threads; i++) {\n      threads_.push_back(env.CreateThread([this, i]() { WorkerLoop(i); }));\n    }\n  }\n\n  // Wait until all scheduled work has finished and then destroy the\n  // set of threads.\n  ~SimpleThreadPoolTempl() {\n    {\n      // Wait for all work to get done.\n      std::unique_lock<std::mutex> l(mu_);\n      while (!pending_.empty()) {\n        empty_.wait(l);\n      }\n      exiting_ = true;\n\n      // Wakeup all waiters.\n      for (auto w : waiters_) {\n        w->ready = true;\n        w->task.f = nullptr;\n        w->cv.notify_one();\n      }\n    }\n\n    // Wait for threads to finish.\n    for (auto t : threads_) {\n      delete t;\n    }\n  }\n\n  // Schedule fn() for execution in the pool of threads. The functions are\n  // executed in the order in which they are scheduled.\n  void Schedule(std::function<void()> fn) final {\n    Task t = env_.CreateTask(std::move(fn));\n    std::unique_lock<std::mutex> l(mu_);\n    if (waiters_.empty()) {\n      pending_.push_back(std::move(t));\n    } else {\n      Waiter* w = waiters_.back();\n      waiters_.pop_back();\n      w->ready = true;\n      w->task = std::move(t);\n      w->cv.notify_one();\n    }\n  }\n\n  int NumThreads() const final {\n    return static_cast<int>(threads_.size());\n  }\n\n  int CurrentThreadId() const final {\n    const PerThread* pt = this->GetPerThread();\n    if (pt->pool == this) {\n      return pt->thread_id;\n    } else {\n      return -1;\n    }\n  }\n\n protected:\n  void WorkerLoop(int thread_id) {\n    std::unique_lock<std::mutex> l(mu_);\n    PerThread* pt = GetPerThread();\n    pt->pool = this;\n    pt->thread_id = thread_id;\n    Waiter w;\n    Task t;\n    while (!exiting_) {\n      if (pending_.empty()) {\n        // Wait for work to be assigned to me\n        w.ready = false;\n        waiters_.push_back(&w);\n        while (!w.ready) {\n          w.cv.wait(l);\n        }\n        t = w.task;\n        w.task.f = nullptr;\n      } else {\n        // Pick up pending work\n        t = std::move(pending_.front());\n        pending_.pop_front();\n        if (pending_.empty()) {\n          empty_.notify_all();\n        }\n      }\n      if (t.f) {\n        mu_.unlock();\n        env_.ExecuteTask(t);\n        t.f = nullptr;\n        mu_.lock();\n      }\n    }\n  }\n\n private:\n  typedef typename Environment::Task Task;\n  typedef typename Environment::EnvThread Thread;\n\n  struct Waiter {\n    std::condition_variable cv;\n    Task task;\n    bool ready;\n  };\n\n  struct PerThread {\n    constexpr PerThread() : pool(NULL), thread_id(-1) { }\n    SimpleThreadPoolTempl* pool;  // Parent pool, or null for normal threads.\n    int thread_id;                // Worker thread index in pool.\n  };\n\n  Environment env_;\n  std::mutex mu_;\n  MaxSizeVector<Thread*> threads_;  // All threads\n  MaxSizeVector<Waiter*> waiters_;  // Stack of waiting threads.\n  std::deque<Task> pending_;        // Queue of pending work\n  std::condition_variable empty_;   // Signaled on pending_.empty()\n  bool exiting_ = false;\n\n  PerThread* GetPerThread() const {\n    EIGEN_THREAD_LOCAL PerThread per_thread;\n    return &per_thread;\n  }\n};\n\ntypedef SimpleThreadPoolTempl<StlThreadEnvironment> SimpleThreadPool;\n\n}  // namespace Eigen\n\n#endif  // EIGEN_CXX11_THREADPOOL_SIMPLE_THREAD_POOL_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/ThreadPool/ThreadEnvironment.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_THREADPOOL_THREAD_ENVIRONMENT_H\n#define EIGEN_CXX11_THREADPOOL_THREAD_ENVIRONMENT_H\n\nnamespace Eigen {\n\nstruct StlThreadEnvironment {\n  struct Task {\n    std::function<void()> f;\n  };\n\n  // EnvThread constructor must start the thread,\n  // destructor must join the thread.\n  class EnvThread {\n   public:\n    EnvThread(std::function<void()> f) : thr_(std::move(f)) {}\n    ~EnvThread() { thr_.join(); }\n\n   private:\n    std::thread thr_;\n  };\n\n  EnvThread* CreateThread(std::function<void()> f) { return new EnvThread(std::move(f)); }\n  Task CreateTask(std::function<void()> f) { return Task{std::move(f)}; }\n  void ExecuteTask(const Task& t) { t.f(); }\n};\n\n}  // namespace Eigen\n\n#endif  // EIGEN_CXX11_THREADPOOL_THREAD_ENVIRONMENT_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/ThreadPool/ThreadLocal.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_THREADPOOL_THREAD_LOCAL_H\n#define EIGEN_CXX11_THREADPOOL_THREAD_LOCAL_H\n\n// Try to come up with a portable implementation of thread local variables\n#if EIGEN_COMP_GNUC && EIGEN_GNUC_AT_MOST(4, 7)\n#define EIGEN_THREAD_LOCAL static __thread\n#elif EIGEN_COMP_CLANG\n#define EIGEN_THREAD_LOCAL static __thread\n#else\n#define EIGEN_THREAD_LOCAL static thread_local\n#endif\n\n#endif  // EIGEN_CXX11_THREADPOOL_THREAD_LOCAL_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/ThreadPool/ThreadPoolInterface.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_THREADPOOL_THREAD_POOL_INTERFACE_H\n#define EIGEN_CXX11_THREADPOOL_THREAD_POOL_INTERFACE_H\n\nnamespace Eigen {\n\n// This defines an interface that ThreadPoolDevice can take to use\n// custom thread pools underneath.\nclass ThreadPoolInterface {\n public:\n  virtual void Schedule(std::function<void()> fn) = 0;\n\n  // Returns the number of threads in the pool.\n  virtual int NumThreads() const = 0;\n\n  // Returns a logical thread index between 0 and NumThreads() - 1 if called\n  // from one of the threads in the pool. Returns -1 otherwise.\n  virtual int CurrentThreadId() const = 0;\n\n  virtual ~ThreadPoolInterface() {}\n};\n\n}  // namespace Eigen\n\n#endif  // EIGEN_CXX11_THREADPOOL_THREAD_POOL_INTERFACE_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/ThreadPool/ThreadYield.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11_THREADPOOL_THREAD_YIELD_H\n#define EIGEN_CXX11_THREADPOOL_THREAD_YIELD_H\n\n// Try to come up with a portable way to yield\n#if EIGEN_COMP_GNUC && EIGEN_GNUC_AT_MOST(4, 7)\n#define EIGEN_THREAD_YIELD() sched_yield()\n#else\n#define EIGEN_THREAD_YIELD() std::this_thread::yield()\n#endif\n\n#endif  // EIGEN_CXX11_THREADPOOL_THREAD_YIELD_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/util/CXX11Meta.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2013 Christian Seiler <christian@iwakd.de>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11META_H\n#define EIGEN_CXX11META_H\n\n#include <vector>\n#include \"EmulateArray.h\"\n\n// Emulate the cxx11 functionality that we need if the compiler doesn't support it.\n// Visual studio 2015 doesn't advertise itself as cxx11 compliant, although it\n// supports enough of the standard for our needs\n#if __cplusplus > 199711L || EIGEN_COMP_MSVC >= 1900\n\n#include \"CXX11Workarounds.h\"\n\nnamespace Eigen {\n\nnamespace internal {\n\n/** \\internal\n  * \\file CXX11/util/CXX11Meta.h\n  * This file contains generic metaprogramming classes which are not specifically related to Eigen.\n  * This file expands upon Core/util/Meta.h and adds support for C++11 specific features.\n  */\n\ntemplate<typename... tt>\nstruct type_list { constexpr static int count = sizeof...(tt); };\n\ntemplate<typename t, typename... tt>\nstruct type_list<t, tt...> { constexpr static int count = sizeof...(tt) + 1; typedef t first_type; };\n\ntemplate<typename T, T... nn>\nstruct numeric_list { constexpr static std::size_t count = sizeof...(nn); };\n\ntemplate<typename T, T n, T... nn>\nstruct numeric_list<T, n, nn...> { constexpr static std::size_t count = sizeof...(nn) + 1; constexpr static T first_value = n; };\n\n/* numeric list constructors\n *\n * equivalencies:\n *     constructor                                              result\n *     typename gen_numeric_list<int, 5>::type                  numeric_list<int, 0,1,2,3,4>\n *     typename gen_numeric_list_reversed<int, 5>::type         numeric_list<int, 4,3,2,1,0>\n *     typename gen_numeric_list_swapped_pair<int, 5,1,2>::type numeric_list<int, 0,2,1,3,4>\n *     typename gen_numeric_list_repeated<int, 0, 5>::type      numeric_list<int, 0,0,0,0,0>\n */\n\ntemplate<typename T, std::size_t n, T start = 0, T... ii> struct gen_numeric_list                     : gen_numeric_list<T, n-1, start, start + n-1, ii...> {};\ntemplate<typename T, T start, T... ii>                    struct gen_numeric_list<T, 0, start, ii...> { typedef numeric_list<T, ii...> type; };\n\ntemplate<typename T, std::size_t n, T start = 0, T... ii> struct gen_numeric_list_reversed                     : gen_numeric_list_reversed<T, n-1, start, ii..., start + n-1> {};\ntemplate<typename T, T start, T... ii>                    struct gen_numeric_list_reversed<T, 0, start, ii...> { typedef numeric_list<T, ii...> type; };\n\ntemplate<typename T, std::size_t n, T a, T b, T start = 0, T... ii> struct gen_numeric_list_swapped_pair                           : gen_numeric_list_swapped_pair<T, n-1, a, b, start, (start + n-1) == a ? b : ((start + n-1) == b ? a : (start + n-1)), ii...> {};\ntemplate<typename T, T a, T b, T start, T... ii>                    struct gen_numeric_list_swapped_pair<T, 0, a, b, start, ii...> { typedef numeric_list<T, ii...> type; };\n\ntemplate<typename T, std::size_t n, T V, T... nn> struct gen_numeric_list_repeated                 : gen_numeric_list_repeated<T, n-1, V, V, nn...> {};\ntemplate<typename T, T V, T... nn>                struct gen_numeric_list_repeated<T, 0, V, nn...> { typedef numeric_list<T, nn...> type; };\n\n/* list manipulation: concatenate */\n\ntemplate<class a, class b> struct concat;\n\ntemplate<typename... as, typename... bs> struct concat<type_list<as...>,       type_list<bs...>>        { typedef type_list<as..., bs...> type; };\ntemplate<typename T, T... as, T... bs>   struct concat<numeric_list<T, as...>, numeric_list<T, bs...> > { typedef numeric_list<T, as..., bs...> type; };\n\ntemplate<typename... p> struct mconcat;\ntemplate<typename a>                             struct mconcat<a>           { typedef a type; };\ntemplate<typename a, typename b>                 struct mconcat<a, b>        : concat<a, b> {};\ntemplate<typename a, typename b, typename... cs> struct mconcat<a, b, cs...> : concat<a, typename mconcat<b, cs...>::type> {};\n\n/* list manipulation: extract slices */\n\ntemplate<int n, typename x> struct take;\ntemplate<int n, typename a, typename... as> struct take<n, type_list<a, as...>> : concat<type_list<a>, typename take<n-1, type_list<as...>>::type> {};\ntemplate<int n>                             struct take<n, type_list<>>         { typedef type_list<> type; };\ntemplate<typename a, typename... as>        struct take<0, type_list<a, as...>> { typedef type_list<> type; };\ntemplate<>                                  struct take<0, type_list<>>         { typedef type_list<> type; };\n\ntemplate<typename T, int n, T a, T... as> struct take<n, numeric_list<T, a, as...>> : concat<numeric_list<T, a>, typename take<n-1, numeric_list<T, as...>>::type> {};\ntemplate<typename T, int n>               struct take<n, numeric_list<T>>           { typedef numeric_list<T> type; };\ntemplate<typename T, T a, T... as>        struct take<0, numeric_list<T, a, as...>> { typedef numeric_list<T> type; };\ntemplate<typename T>                      struct take<0, numeric_list<T>>           { typedef numeric_list<T> type; };\n\ntemplate<typename T, int n, T... ii>      struct h_skip_helper_numeric;\ntemplate<typename T, int n, T i, T... ii> struct h_skip_helper_numeric<T, n, i, ii...> : h_skip_helper_numeric<T, n-1, ii...> {};\ntemplate<typename T, T i, T... ii>        struct h_skip_helper_numeric<T, 0, i, ii...> { typedef numeric_list<T, i, ii...> type; };\ntemplate<typename T, int n>               struct h_skip_helper_numeric<T, n>           { typedef numeric_list<T> type; };\ntemplate<typename T>                      struct h_skip_helper_numeric<T, 0>           { typedef numeric_list<T> type; };\n\ntemplate<int n, typename... tt>             struct h_skip_helper_type;\ntemplate<int n, typename t, typename... tt> struct h_skip_helper_type<n, t, tt...> : h_skip_helper_type<n-1, tt...> {};\ntemplate<typename t, typename... tt>        struct h_skip_helper_type<0, t, tt...> { typedef type_list<t, tt...> type; };\ntemplate<int n>                             struct h_skip_helper_type<n>           { typedef type_list<> type; };\ntemplate<>                                  struct h_skip_helper_type<0>           { typedef type_list<> type; };\n\ntemplate<int n>\nstruct h_skip {\n  template<typename T, T... ii>\n  constexpr static inline typename h_skip_helper_numeric<T, n, ii...>::type helper(numeric_list<T, ii...>) { return typename h_skip_helper_numeric<T, n, ii...>::type(); }\n  template<typename... tt>\n  constexpr static inline typename h_skip_helper_type<n, tt...>::type helper(type_list<tt...>) { return typename h_skip_helper_type<n, tt...>::type(); }\n};\n\ntemplate<int n, typename a> struct skip { typedef decltype(h_skip<n>::helper(a())) type; };\n\ntemplate<int start, int count, typename a> struct slice : take<count, typename skip<start, a>::type> {};\n\n/* list manipulation: retrieve single element from list */\n\ntemplate<int n, typename x> struct get;\n\ntemplate<int n, typename a, typename... as>               struct get<n, type_list<a, as...>>   : get<n-1, type_list<as...>> {};\ntemplate<typename a, typename... as>                      struct get<0, type_list<a, as...>>   { typedef a type; };\n\ntemplate<typename T, int n, T a, T... as>                        struct get<n, numeric_list<T, a, as...>>   : get<n-1, numeric_list<T, as...>> {};\ntemplate<typename T, T a, T... as>                               struct get<0, numeric_list<T, a, as...>>   { constexpr static T value = a; };\n\n/* always get type, regardless of dummy; good for parameter pack expansion */\n\ntemplate<typename T, T dummy, typename t> struct id_numeric  { typedef t type; };\ntemplate<typename dummy, typename t>      struct id_type     { typedef t type; };\n\n/* equality checking, flagged version */\n\ntemplate<typename a, typename b> struct is_same_gf : is_same<a, b> { constexpr static int global_flags = 0; };\n\n/* apply_op to list */\n\ntemplate<\n  bool from_left, // false\n  template<typename, typename> class op,\n  typename additional_param,\n  typename... values\n>\nstruct h_apply_op_helper                                        { typedef type_list<typename op<values, additional_param>::type...> type; };\ntemplate<\n  template<typename, typename> class op,\n  typename additional_param,\n  typename... values\n>\nstruct h_apply_op_helper<true, op, additional_param, values...> { typedef type_list<typename op<additional_param, values>::type...> type; };\n\ntemplate<\n  bool from_left,\n  template<typename, typename> class op,\n  typename additional_param\n>\nstruct h_apply_op\n{\n  template<typename... values>\n  constexpr static typename h_apply_op_helper<from_left, op, additional_param, values...>::type helper(type_list<values...>)\n  { return typename h_apply_op_helper<from_left, op, additional_param, values...>::type(); }\n};\n\ntemplate<\n  template<typename, typename> class op,\n  typename additional_param,\n  typename a\n>\nstruct apply_op_from_left { typedef decltype(h_apply_op<true, op, additional_param>::helper(a())) type; };\n\ntemplate<\n  template<typename, typename> class op,\n  typename additional_param,\n  typename a\n>\nstruct apply_op_from_right { typedef decltype(h_apply_op<false, op, additional_param>::helper(a())) type; };\n\n/* see if an element is in a list */\n\ntemplate<\n  template<typename, typename> class test,\n  typename check_against,\n  typename h_list,\n  bool last_check_positive = false\n>\nstruct contained_in_list;\n\ntemplate<\n  template<typename, typename> class test,\n  typename check_against,\n  typename h_list\n>\nstruct contained_in_list<test, check_against, h_list, true>\n{\n  constexpr static bool value = true;\n};\n\ntemplate<\n  template<typename, typename> class test,\n  typename check_against,\n  typename a,\n  typename... as\n>\nstruct contained_in_list<test, check_against, type_list<a, as...>, false> : contained_in_list<test, check_against, type_list<as...>, test<check_against, a>::value> {};\n\ntemplate<\n  template<typename, typename> class test,\n  typename check_against\n  EIGEN_TPL_PP_SPEC_HACK_DEFC(typename, empty)\n>\nstruct contained_in_list<test, check_against, type_list<EIGEN_TPL_PP_SPEC_HACK_USE(empty)>, false> { constexpr static bool value = false; };\n\n/* see if an element is in a list and check for global flags */\n\ntemplate<\n  template<typename, typename> class test,\n  typename check_against,\n  typename h_list,\n  int default_flags = 0,\n  bool last_check_positive = false,\n  int last_check_flags = default_flags\n>\nstruct contained_in_list_gf;\n\ntemplate<\n  template<typename, typename> class test,\n  typename check_against,\n  typename h_list,\n  int default_flags,\n  int last_check_flags\n>\nstruct contained_in_list_gf<test, check_against, h_list, default_flags, true, last_check_flags>\n{\n  constexpr static bool value = true;\n  constexpr static int global_flags = last_check_flags;\n};\n\ntemplate<\n  template<typename, typename> class test,\n  typename check_against,\n  typename a,\n  typename... as,\n  int default_flags,\n  int last_check_flags\n>\nstruct contained_in_list_gf<test, check_against, type_list<a, as...>, default_flags, false, last_check_flags> : contained_in_list_gf<test, check_against, type_list<as...>, default_flags, test<check_against, a>::value, test<check_against, a>::global_flags> {};\n\ntemplate<\n  template<typename, typename> class test,\n  typename check_against\n  EIGEN_TPL_PP_SPEC_HACK_DEFC(typename, empty),\n  int default_flags,\n  int last_check_flags\n>\nstruct contained_in_list_gf<test, check_against, type_list<EIGEN_TPL_PP_SPEC_HACK_USE(empty)>, default_flags, false, last_check_flags> { constexpr static bool value = false; constexpr static int global_flags = default_flags; };\n\n/* generic reductions */\n\ntemplate<\n  typename Reducer,\n  typename... Ts\n> struct reduce;\n\ntemplate<\n  typename Reducer\n> struct reduce<Reducer>\n{\n  constexpr static inline int run() { return Reducer::Identity; }\n};\n\ntemplate<\n  typename Reducer,\n  typename A\n> struct reduce<Reducer, A>\n{\n  constexpr static inline A run(A a) { return a; }\n};\n\ntemplate<\n  typename Reducer,\n  typename A,\n  typename... Ts\n> struct reduce<Reducer, A, Ts...>\n{\n  constexpr static inline auto run(A a, Ts... ts) -> decltype(Reducer::run(a, reduce<Reducer, Ts...>::run(ts...))) {\n    return Reducer::run(a, reduce<Reducer, Ts...>::run(ts...));\n  }\n};\n\n/* generic binary operations */\n\nstruct sum_op           {\n  template<typename A, typename B> EIGEN_DEVICE_FUNC constexpr static inline auto run(A a, B b) -> decltype(a + b)   { return a + b;   }\n  static constexpr int Identity = 0;\n};\nstruct product_op       {\n  template<typename A, typename B> EIGEN_DEVICE_FUNC constexpr static inline auto run(A a, B b) -> decltype(a * b)   { return a * b;   }\n  static constexpr int Identity = 1;\n};\n\nstruct logical_and_op   { template<typename A, typename B> constexpr static inline auto run(A a, B b) -> decltype(a && b)  { return a && b;  } };\nstruct logical_or_op    { template<typename A, typename B> constexpr static inline auto run(A a, B b) -> decltype(a || b)  { return a || b;  } };\n\nstruct equal_op         { template<typename A, typename B> constexpr static inline auto run(A a, B b) -> decltype(a == b)  { return a == b;  } };\nstruct not_equal_op     { template<typename A, typename B> constexpr static inline auto run(A a, B b) -> decltype(a != b)  { return a != b;  } };\nstruct lesser_op        { template<typename A, typename B> constexpr static inline auto run(A a, B b) -> decltype(a < b)   { return a < b;   } };\nstruct lesser_equal_op  { template<typename A, typename B> constexpr static inline auto run(A a, B b) -> decltype(a <= b)  { return a <= b;  } };\nstruct greater_op       { template<typename A, typename B> constexpr static inline auto run(A a, B b) -> decltype(a > b)   { return a > b;   } };\nstruct greater_equal_op { template<typename A, typename B> constexpr static inline auto run(A a, B b) -> decltype(a >= b)  { return a >= b;  } };\n\n/* generic unary operations */\n\nstruct not_op                { template<typename A> constexpr static inline auto run(A a) -> decltype(!a)      { return !a;      } };\nstruct negation_op           { template<typename A> constexpr static inline auto run(A a) -> decltype(-a)      { return -a;      } };\nstruct greater_equal_zero_op { template<typename A> constexpr static inline auto run(A a) -> decltype(a >= 0)  { return a >= 0;  } };\n\n\n/* reductions for lists */\n\n// using auto -> return value spec makes ICC 13.0 and 13.1 crash here, so we have to hack it\n// together in front... (13.0 doesn't work with array_prod/array_reduce/... anyway, but 13.1\n// does...\ntemplate<typename... Ts>\nconstexpr inline decltype(reduce<product_op, Ts...>::run((*((Ts*)0))...)) arg_prod(Ts... ts)\n{\n  return reduce<product_op, Ts...>::run(ts...);\n}\n\ntemplate<typename... Ts>\nconstexpr inline decltype(reduce<sum_op, Ts...>::run((*((Ts*)0))...)) arg_sum(Ts... ts)\n{\n  return reduce<sum_op, Ts...>::run(ts...);\n}\n\n/* reverse arrays */\n\ntemplate<typename Array, int... n>\nconstexpr inline Array h_array_reverse(Array arr, numeric_list<int, n...>)\n{\n  return {{array_get<sizeof...(n) - n - 1>(arr)...}};\n}\n\ntemplate<typename T, std::size_t N>\nconstexpr inline array<T, N> array_reverse(array<T, N> arr)\n{\n  return h_array_reverse(arr, typename gen_numeric_list<int, N>::type());\n}\n\n\n/* generic array reductions */\n\n// can't reuse standard reduce() interface above because Intel's Compiler\n// *really* doesn't like it, so we just reimplement the stuff\n// (start from N - 1 and work down to 0 because specialization for\n// n == N - 1 also doesn't work in Intel's compiler, so it goes into\n// an infinite loop)\ntemplate<typename Reducer, typename T, std::size_t N, std::size_t n = N - 1>\nstruct h_array_reduce {\n  EIGEN_DEVICE_FUNC constexpr static inline auto run(array<T, N> arr, T identity) -> decltype(Reducer::run(h_array_reduce<Reducer, T, N, n - 1>::run(arr, identity), array_get<n>(arr)))\n  {\n    return Reducer::run(h_array_reduce<Reducer, T, N, n - 1>::run(arr, identity), array_get<n>(arr));\n  }\n};\n\ntemplate<typename Reducer, typename T, std::size_t N>\nstruct h_array_reduce<Reducer, T, N, 0>\n{\n  EIGEN_DEVICE_FUNC constexpr static inline T run(const array<T, N>& arr, T)\n  {\n    return array_get<0>(arr);\n  }\n};\n\ntemplate<typename Reducer, typename T>\nstruct h_array_reduce<Reducer, T, 0>\n{\n  EIGEN_DEVICE_FUNC constexpr static inline T run(const array<T, 0>&, T identity)\n  {\n    return identity;\n  }\n};\n\ntemplate<typename Reducer, typename T, std::size_t N>\nEIGEN_DEVICE_FUNC constexpr inline auto array_reduce(const array<T, N>& arr, T identity) -> decltype(h_array_reduce<Reducer, T, N>::run(arr, identity))\n{\n  return h_array_reduce<Reducer, T, N>::run(arr, identity);\n}\n\n/* standard array reductions */\n\ntemplate<typename T, std::size_t N>\nEIGEN_DEVICE_FUNC constexpr inline auto array_sum(const array<T, N>& arr) -> decltype(array_reduce<sum_op, T, N>(arr, static_cast<T>(0)))\n{\n  return array_reduce<sum_op, T, N>(arr, static_cast<T>(0));\n}\n\ntemplate<typename T, std::size_t N>\nEIGEN_DEVICE_FUNC constexpr inline auto array_prod(const array<T, N>& arr) -> decltype(array_reduce<product_op, T, N>(arr, static_cast<T>(1)))\n{\n  return array_reduce<product_op, T, N>(arr, static_cast<T>(1));\n}\n\ntemplate<typename t>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE t array_prod(const std::vector<t>& a) {\n  eigen_assert(a.size() > 0);\n  t prod = 1;\n  for (size_t i = 0; i < a.size(); ++i) { prod *= a[i]; }\n  return prod;\n}\n\n/* zip an array */\n\ntemplate<typename Op, typename A, typename B, std::size_t N, int... n>\nconstexpr inline array<decltype(Op::run(A(), B())),N> h_array_zip(array<A, N> a, array<B, N> b, numeric_list<int, n...>)\n{\n  return array<decltype(Op::run(A(), B())),N>{{ Op::run(array_get<n>(a), array_get<n>(b))... }};\n}\n\ntemplate<typename Op, typename A, typename B, std::size_t N>\nconstexpr inline array<decltype(Op::run(A(), B())),N> array_zip(array<A, N> a, array<B, N> b)\n{\n  return h_array_zip<Op>(a, b, typename gen_numeric_list<int, N>::type());\n}\n\n/* zip an array and reduce the result */\n\ntemplate<typename Reducer, typename Op, typename A, typename B, std::size_t N, int... n>\nconstexpr inline auto h_array_zip_and_reduce(array<A, N> a, array<B, N> b, numeric_list<int, n...>) -> decltype(reduce<Reducer, typename id_numeric<int,n,decltype(Op::run(A(), B()))>::type...>::run(Op::run(array_get<n>(a), array_get<n>(b))...))\n{\n  return reduce<Reducer, typename id_numeric<int,n,decltype(Op::run(A(), B()))>::type...>::run(Op::run(array_get<n>(a), array_get<n>(b))...);\n}\n\ntemplate<typename Reducer, typename Op, typename A, typename B, std::size_t N>\nconstexpr inline auto array_zip_and_reduce(array<A, N> a, array<B, N> b) -> decltype(h_array_zip_and_reduce<Reducer, Op, A, B, N>(a, b, typename gen_numeric_list<int, N>::type()))\n{\n  return h_array_zip_and_reduce<Reducer, Op, A, B, N>(a, b, typename gen_numeric_list<int, N>::type());\n}\n\n/* apply stuff to an array */\n\ntemplate<typename Op, typename A, std::size_t N, int... n>\nconstexpr inline array<decltype(Op::run(A())),N> h_array_apply(array<A, N> a, numeric_list<int, n...>)\n{\n  return array<decltype(Op::run(A())),N>{{ Op::run(array_get<n>(a))... }};\n}\n\ntemplate<typename Op, typename A, std::size_t N>\nconstexpr inline array<decltype(Op::run(A())),N> array_apply(array<A, N> a)\n{\n  return h_array_apply<Op>(a, typename gen_numeric_list<int, N>::type());\n}\n\n/* apply stuff to an array and reduce */\n\ntemplate<typename Reducer, typename Op, typename A, std::size_t N, int... n>\nconstexpr inline auto h_array_apply_and_reduce(array<A, N> arr, numeric_list<int, n...>) -> decltype(reduce<Reducer, typename id_numeric<int,n,decltype(Op::run(A()))>::type...>::run(Op::run(array_get<n>(arr))...))\n{\n  return reduce<Reducer, typename id_numeric<int,n,decltype(Op::run(A()))>::type...>::run(Op::run(array_get<n>(arr))...);\n}\n\ntemplate<typename Reducer, typename Op, typename A, std::size_t N>\nconstexpr inline auto array_apply_and_reduce(array<A, N> a) -> decltype(h_array_apply_and_reduce<Reducer, Op, A, N>(a, typename gen_numeric_list<int, N>::type()))\n{\n  return h_array_apply_and_reduce<Reducer, Op, A, N>(a, typename gen_numeric_list<int, N>::type());\n}\n\n/* repeat a value n times (and make an array out of it\n * usage:\n *   array<int, 16> = repeat<16>(42);\n */\n\ntemplate<int n>\nstruct h_repeat\n{\n  template<typename t, int... ii>\n  constexpr static inline array<t, n> run(t v, numeric_list<int, ii...>)\n  {\n    return {{ typename id_numeric<int, ii, t>::type(v)... }};\n  }\n};\n\ntemplate<int n, typename t>\nconstexpr array<t, n> repeat(t v) { return h_repeat<n>::run(v, typename gen_numeric_list<int, n>::type()); }\n\n/* instantiate a class by a C-style array */\ntemplate<class InstType, typename ArrType, std::size_t N, bool Reverse, typename... Ps>\nstruct h_instantiate_by_c_array;\n\ntemplate<class InstType, typename ArrType, std::size_t N, typename... Ps>\nstruct h_instantiate_by_c_array<InstType, ArrType, N, false, Ps...>\n{\n  static InstType run(ArrType* arr, Ps... args)\n  {\n    return h_instantiate_by_c_array<InstType, ArrType, N - 1, false, Ps..., ArrType>::run(arr + 1, args..., arr[0]);\n  }\n};\n\ntemplate<class InstType, typename ArrType, std::size_t N, typename... Ps>\nstruct h_instantiate_by_c_array<InstType, ArrType, N, true, Ps...>\n{\n  static InstType run(ArrType* arr, Ps... args)\n  {\n    return h_instantiate_by_c_array<InstType, ArrType, N - 1, false, ArrType, Ps...>::run(arr + 1, arr[0], args...);\n  }\n};\n\ntemplate<class InstType, typename ArrType, typename... Ps>\nstruct h_instantiate_by_c_array<InstType, ArrType, 0, false, Ps...>\n{\n  static InstType run(ArrType* arr, Ps... args)\n  {\n    (void)arr;\n    return InstType(args...);\n  }\n};\n\ntemplate<class InstType, typename ArrType, typename... Ps>\nstruct h_instantiate_by_c_array<InstType, ArrType, 0, true, Ps...>\n{\n  static InstType run(ArrType* arr, Ps... args)\n  {\n    (void)arr;\n    return InstType(args...);\n  }\n};\n\ntemplate<class InstType, typename ArrType, std::size_t N, bool Reverse = false>\nInstType instantiate_by_c_array(ArrType* arr)\n{\n  return h_instantiate_by_c_array<InstType, ArrType, N, Reverse>::run(arr);\n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#else // Non C++11, fallback to emulation mode\n\n#include \"EmulateCXX11Meta.h\"\n\n#endif\n\n#endif // EIGEN_CXX11META_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/util/CXX11Workarounds.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2013 Christian Seiler <christian@iwakd.de>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CXX11WORKAROUNDS_H\n#define EIGEN_CXX11WORKAROUNDS_H\n\n/* COMPATIBILITY CHECKS\n * (so users of compilers that are too old get some realistic error messages)\n */\n#if defined(__INTEL_COMPILER) && (__INTEL_COMPILER < 1310)\n#error Intel Compiler only supports required C++ features since version 13.1.\n// note that most stuff in principle works with 13.0 but when combining\n// some features, at some point 13.0 will just fail with an internal assertion\n#elif defined(__GNUC__) && !defined(__clang__) && !defined(__INTEL_COMPILER) && (__GNUC__ < 4 || (__GNUC__ == 4 && __GNUC_MINOR__ < 6))\n// G++ < 4.6 by default will continue processing the source files - even if we use #error to make\n// it error out. For this reason, we use the pragma to make sure G++ aborts at the first error\n// it sees. Unfortunately, that is still not our #error directive, but at least the output is\n// short enough the user has a chance to see that the compiler version is not sufficient for\n// the funky template mojo we use.\n#pragma GCC diagnostic error \"-Wfatal-errors\"\n#error GNU C++ Compiler (g++) only supports required C++ features since version 4.6.\n#endif\n\n/* Check that the compiler at least claims to support C++11. It might not be sufficient\n * because the compiler may not implement it correctly, but at least we'll know.\n * On the other hand, visual studio still doesn't claim to support C++11 although it's\n * compliant enugh for our purpose.\n */\n#if (__cplusplus <= 199711L) && (EIGEN_COMP_MSVC < 1900)\n#if defined(__GNUC__) && !defined(__clang__) && !defined(__INTEL_COMPILER)\n#pragma GCC diagnostic error \"-Wfatal-errors\"\n#endif\n#error This library needs at least a C++11 compliant compiler. If you use g++/clang, please enable the -std=c++11 compiler flag. (-std=c++0x on older versions.)\n#endif\n\nnamespace Eigen {\n\nnamespace internal {\n\n/* std::get is only constexpr in C++14, not yet in C++11\n */\n\n\ntemplate<std::size_t I, class T> constexpr inline T&       array_get(std::vector<T>&       a) { return a[I]; }\ntemplate<std::size_t I, class T> constexpr inline T&&      array_get(std::vector<T>&&      a) { return a[I]; }\ntemplate<std::size_t I, class T> constexpr inline T const& array_get(std::vector<T> const& a) { return a[I]; }\n\n/* Suppose you have a template of the form\n * template<typename T> struct X;\n * And you want to specialize it in such a way:\n *    template<typename S1, typename... SN> struct X<Foo<S1, SN...>> { ::: };\n *    template<>                            struct X<Foo<>>          { ::: };\n * This will work in Intel's compiler 13.0, but only to some extent in g++ 4.6, since\n * g++ can only match templates called with parameter packs if the number of template\n * arguments is not a fixed size (so inside the first specialization, referencing\n * X<Foo<Sn...>> will fail in g++). On the other hand, g++ will accept the following:\n *    template<typename S...> struct X<Foo<S...>> { ::: }:\n * as an additional (!) specialization, which will then only match the empty case.\n * But Intel's compiler 13.0 won't accept that, it will only accept the empty syntax,\n * so we have to create a workaround for this.\n */\n#if defined(__GNUC__) && !defined(__INTEL_COMPILER)\n#define EIGEN_TPL_PP_SPEC_HACK_DEF(mt, n)    mt... n\n#define EIGEN_TPL_PP_SPEC_HACK_DEFC(mt, n)   , EIGEN_TPL_PP_SPEC_HACK_DEF(mt, n)\n#define EIGEN_TPL_PP_SPEC_HACK_USE(n)        n...\n#define EIGEN_TPL_PP_SPEC_HACK_USEC(n)       , n...\n#else\n#define EIGEN_TPL_PP_SPEC_HACK_DEF(mt, n)\n#define EIGEN_TPL_PP_SPEC_HACK_DEFC(mt, n)\n#define EIGEN_TPL_PP_SPEC_HACK_USE(n)\n#define EIGEN_TPL_PP_SPEC_HACK_USEC(n)\n#endif\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_CXX11WORKAROUNDS_H\n\n/*\n * kate: space-indent on; indent-width 2; mixedindent off; indent-mode cstyle;\n */\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/util/EmulateArray.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_EMULATE_ARRAY_H\n#define EIGEN_EMULATE_ARRAY_H\n\n\n\n// The array class is only available starting with cxx11. Emulate our own here\n// if needed. Beware, msvc still doesn't advertise itself as a c++11 compiler!\n// Moreover, CUDA doesn't support the STL containers, so we use our own instead.\n#if (__cplusplus <= 199711L && EIGEN_COMP_MSVC < 1900) || defined(__CUDACC__) || defined(EIGEN_AVOID_STL_ARRAY)\n\nnamespace Eigen {\ntemplate <typename T, size_t n> class array {\n public:\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE T& operator[] (size_t index) { return values[index]; }\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE const T& operator[] (size_t index) const { return values[index]; }\n\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE T& front() { return values[0]; }\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE const T& front() const { return values[0]; }\n\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE T& back() { return values[n-1]; }\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE const T& back() const { return values[n-1]; }\n\n  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE\n  static std::size_t size() { return n; }\n\n  T values[n];\n\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE array() { }\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE array(const T& v) {\n    EIGEN_STATIC_ASSERT(n==1, YOU_MADE_A_PROGRAMMING_MISTAKE)\n    values[0] = v;\n  }\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE array(const T& v1, const T& v2) {\n    EIGEN_STATIC_ASSERT(n==2, YOU_MADE_A_PROGRAMMING_MISTAKE)\n    values[0] = v1;\n    values[1] = v2;\n  }\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE array(const T& v1, const T& v2, const T& v3) {\n    EIGEN_STATIC_ASSERT(n==3, YOU_MADE_A_PROGRAMMING_MISTAKE)\n    values[0] = v1;\n    values[1] = v2;\n    values[2] = v3;\n  }\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE array(const T& v1, const T& v2, const T& v3,\n                            const T& v4) {\n    EIGEN_STATIC_ASSERT(n==4, YOU_MADE_A_PROGRAMMING_MISTAKE)\n    values[0] = v1;\n    values[1] = v2;\n    values[2] = v3;\n    values[3] = v4;\n  }\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE array(const T& v1, const T& v2, const T& v3, const T& v4,\n                            const T& v5) {\n    EIGEN_STATIC_ASSERT(n==5, YOU_MADE_A_PROGRAMMING_MISTAKE)\n    values[0] = v1;\n    values[1] = v2;\n    values[2] = v3;\n    values[3] = v4;\n    values[4] = v5;\n  }\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE array(const T& v1, const T& v2, const T& v3, const T& v4,\n                            const T& v5, const T& v6) {\n    EIGEN_STATIC_ASSERT(n==6, YOU_MADE_A_PROGRAMMING_MISTAKE)\n    values[0] = v1;\n    values[1] = v2;\n    values[2] = v3;\n    values[3] = v4;\n    values[4] = v5;\n    values[5] = v6;\n  }\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE array(const T& v1, const T& v2, const T& v3, const T& v4,\n                            const T& v5, const T& v6, const T& v7) {\n    EIGEN_STATIC_ASSERT(n==7, YOU_MADE_A_PROGRAMMING_MISTAKE)\n    values[0] = v1;\n    values[1] = v2;\n    values[2] = v3;\n    values[3] = v4;\n    values[4] = v5;\n    values[5] = v6;\n    values[6] = v7;\n  }\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE array(\n      const T& v1, const T& v2, const T& v3, const T& v4,\n      const T& v5, const T& v6, const T& v7, const T& v8) {\n    EIGEN_STATIC_ASSERT(n==8, YOU_MADE_A_PROGRAMMING_MISTAKE)\n    values[0] = v1;\n    values[1] = v2;\n    values[2] = v3;\n    values[3] = v4;\n    values[4] = v5;\n    values[5] = v6;\n    values[6] = v7;\n    values[7] = v8;\n  }\n\n#if EIGEN_HAS_VARIADIC_TEMPLATES\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE array(std::initializer_list<T> l) {\n    eigen_assert(l.size() == n);\n    internal::smart_copy(l.begin(), l.end(), values);\n  }\n#endif\n};\n\n\n// Specialize array for zero size\ntemplate <typename T> class array<T, 0> {\n public:\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE T& operator[] (size_t) {\n    eigen_assert(false && \"Can't index a zero size array\");\n    return dummy;\n  }\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE const T& operator[] (size_t) const {\n    eigen_assert(false && \"Can't index a zero size array\");\n    return dummy;\n  }\n\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE T& front() {\n    eigen_assert(false && \"Can't index a zero size array\");\n    return dummy;\n  }\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE const T& front() const {\n    eigen_assert(false && \"Can't index a zero size array\");\n    return dummy;\n  }\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE T& back() {\n    eigen_assert(false && \"Can't index a zero size array\");\n    return dummy;\n  }\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE const T& back() const {\n    eigen_assert(false && \"Can't index a zero size array\");\n    return dummy;\n  }\n\n  static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE std::size_t size() { return 0; }\n\n  EIGEN_DEVICE_FUNC\n  EIGEN_STRONG_INLINE array() : dummy() { }\n\n#if EIGEN_HAS_VARIADIC_TEMPLATES\n  EIGEN_DEVICE_FUNC array(std::initializer_list<T> l) : dummy() {\n    eigen_assert(l.size() == 0);\n  }\n#endif\n\n private:\n  T dummy;\n};\n\n// Comparison operator\n// Todo: implement !=, <, <=, >,  and >=\ntemplate<class T, std::size_t N>\nEIGEN_DEVICE_FUNC bool operator==(const array<T,N>& lhs, const array<T,N>& rhs) {\n  for (std::size_t i = 0; i < N; ++i) {\n    if (lhs[i] != rhs[i]) {\n      return false;\n    }\n  }\n  return true;\n}\n\n\nnamespace internal {\ntemplate<std::size_t I, class T, std::size_t N>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T& array_get(array<T,N>& a) {\n  return a[I];\n}\ntemplate<std::size_t I, class T, std::size_t N>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const T& array_get(const array<T,N>& a) {\n  return a[I];\n}\n\ntemplate <typename T> struct array_size;\ntemplate<class T, std::size_t N> struct array_size<array<T,N> > {\n  static const size_t value = N;\n};\ntemplate <typename T> struct array_size;\ntemplate<class T, std::size_t N> struct array_size<array<T,N>& > {\n  static const size_t value = N;\n};\ntemplate <typename T> struct array_size;\ntemplate<class T, std::size_t N> struct array_size<const array<T,N> > {\n  static const size_t value = N;\n};\ntemplate <typename T> struct array_size;\ntemplate<class T, std::size_t N> struct array_size<const array<T,N>& > {\n  static const size_t value = N;\n};\n\n}  // end namespace internal\n}  // end namespace Eigen\n\n#else\n\n// The compiler supports c++11, and we're not targetting cuda: use std::array as Eigen::array\n#include <array>\nnamespace Eigen {\n\ntemplate <typename T, std::size_t N> using array = std::array<T, N>;\n\nnamespace internal {\n/* std::get is only constexpr in C++14, not yet in C++11\n *     - libstdc++ from version 4.7 onwards has it nevertheless,\n *                                          so use that\n *     - libstdc++ older versions: use _M_instance directly\n *     - libc++ all versions so far: use __elems_ directly\n *     - all other libs: use std::get to be portable, but\n *                       this may not be constexpr\n */\n#if defined(__GLIBCXX__) && __GLIBCXX__ < 20120322\n#define STD_GET_ARR_HACK             a._M_instance[I]\n#elif defined(_LIBCPP_VERSION)\n#define STD_GET_ARR_HACK             a.__elems_[I]\n#else\n#define STD_GET_ARR_HACK             std::template get<I, T, N>(a)\n#endif\n\ntemplate<std::size_t I, class T, std::size_t N> constexpr inline T&       array_get(std::array<T,N>&       a) { return (T&)       STD_GET_ARR_HACK; }\ntemplate<std::size_t I, class T, std::size_t N> constexpr inline T&&      array_get(std::array<T,N>&&      a) { return (T&&)      STD_GET_ARR_HACK; }\ntemplate<std::size_t I, class T, std::size_t N> constexpr inline T const& array_get(std::array<T,N> const& a) { return (T const&) STD_GET_ARR_HACK; }\n\n#undef STD_GET_ARR_HACK\n\ntemplate <typename T> struct array_size;\ntemplate<class T, std::size_t N> struct array_size<const std::array<T,N> > {\n  static const size_t value = N;\n};\ntemplate <typename T> struct array_size;\ntemplate<class T, std::size_t N> struct array_size<std::array<T,N> > {\n  static const size_t value = N;\n};\n}  // end namespace internal\n}  // end namespace Eigen\n\n#endif\n\n#endif  // EIGEN_EMULATE_ARRAY_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/util/EmulateCXX11Meta.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_EMULATE_CXX11_META_H\n#define EIGEN_EMULATE_CXX11_META_H\n\n\n\nnamespace Eigen {\n\nnamespace internal {\n\n/** \\internal\n  * \\file CXX11/util/EmulateCXX11Meta.h\n  * This file emulates a subset of the functionality provided by CXXMeta.h for\n  * compilers that don't yet support cxx11 such as nvcc.\n  */\n\nstruct empty_list { static const std::size_t count = 0; };\n\ntemplate<typename T, typename Tail=empty_list> struct type_list {\n  typedef T HeadType;\n  typedef Tail TailType;\n  static const T head;\n  static const Tail tail;\n  static const std::size_t count = 1 + Tail::count;\n};\n\nstruct null_type { };\n\ntemplate<typename T1 = null_type, typename T2 = null_type, typename T3 = null_type,\n         typename T4 = null_type, typename T5 = null_type, typename T6 = null_type,\n         typename T7 = null_type, typename T8 = null_type>\nstruct make_type_list {\n  typedef typename make_type_list<T2, T3, T4, T5, T6, T7, T8>::type tailresult;\n\n  typedef type_list<T1, tailresult> type;\n};\n\ntemplate<> struct make_type_list<> {\n  typedef empty_list type;\n};\n\n\ntemplate <std::size_t index, class TList> struct get_type;\n\ntemplate <class Head, class Tail>\nstruct get_type<0, type_list<Head, Tail> >\n{\n  typedef Head type;\n};\n\ntemplate <std::size_t i, class Head, class Tail>\nstruct get_type<i, type_list<Head, Tail> >\n{\n  typedef typename get_type<i-1, Tail>::type type;\n};\n\n\n/* numeric list */\ntemplate <typename T, T n>\nstruct type2val {\n  typedef T type;\n  static const T value = n;\n};\n\n\ntemplate<typename T, size_t n, T V> struct gen_numeric_list_repeated;\n\ntemplate<typename T, T V> struct gen_numeric_list_repeated<T, 1, V> {\n  typedef typename make_type_list<type2val<T, V> >::type type;\n};\n\ntemplate<typename T, T V> struct gen_numeric_list_repeated<T, 2, V> {\n  typedef typename make_type_list<type2val<T, V>, type2val<T, V> >::type type;\n};\n\ntemplate<typename T, T V> struct gen_numeric_list_repeated<T, 3, V> {\n  typedef typename make_type_list<type2val<T, V>, type2val<T, V>, type2val<T, V> >::type type;\n};\n\ntemplate<typename T, T V> struct gen_numeric_list_repeated<T, 4, V> {\n  typedef typename make_type_list<type2val<T, V>, type2val<T, V>, type2val<T, V>, type2val<T, V> >::type type;\n};\n\ntemplate<typename T, T V> struct gen_numeric_list_repeated<T, 5, V> {\n  typedef typename make_type_list<type2val<T, V>, type2val<T, V>, type2val<T, V>, type2val<T, V>, type2val<T, V> >::type type;\n};\n\ntemplate<typename T, T V> struct gen_numeric_list_repeated<T, 6, V> {\n  typedef typename make_type_list<type2val<T, V>, type2val<T, V>, type2val<T, V>,\n                                  type2val<T, V>, type2val<T, V>, type2val<T, V> >::type type;\n};\n\ntemplate<typename T, T V> struct gen_numeric_list_repeated<T, 7, V> {\n  typedef typename make_type_list<type2val<T, V>, type2val<T, V>, type2val<T, V>,\n                                  type2val<T, V>, type2val<T, V>, type2val<T, V>,\n                                  type2val<T, V> >::type type;\n};\n\ntemplate<typename T, T V> struct gen_numeric_list_repeated<T, 8, V> {\n  typedef typename make_type_list<type2val<T, V>, type2val<T, V>, type2val<T, V>,\n                                  type2val<T, V>, type2val<T, V>, type2val<T, V>,\n                                  type2val<T, V>, type2val<T, V> >::type type;\n};\n\n\ntemplate <std::size_t index, class NList> struct get;\n\ntemplate <std::size_t i>\nstruct get<i, empty_list>\n{\n  get() { eigen_assert(false && \"index overflow\"); }\n  typedef void type;\n  static const char value = '\\0';\n};\n\ntemplate <std::size_t i, class Head>\nstruct get<i, type_list<Head, empty_list> >\n{\n  get() { eigen_assert(false && \"index overflow\"); }\n  typedef void type;\n  static const char value = '\\0';\n};\n\ntemplate <class Head>\nstruct get<0, type_list<Head, empty_list> >\n{\n  typedef typename Head::type type;\n  static const type value = Head::value;\n};\n\ntemplate <class Head, class Tail>\nstruct get<0, type_list<Head, Tail> >\n{\n  typedef typename Head::type type;\n  static const type value = Head::value;\n};\n\ntemplate <std::size_t i, class Head, class Tail>\nstruct get<i, type_list<Head, Tail> >\n{\n  typedef typename Tail::HeadType::type type;\n  static const type value = get<i-1, Tail>::value;\n};\n\n\ntemplate <class NList> struct arg_prod {\n  static const typename NList::HeadType::type value = get<0, NList>::value * arg_prod<typename NList::TailType>::value;\n};\ntemplate <> struct arg_prod<empty_list> {\n  static const int value = 1;\n};\n\n\ntemplate<int n, typename t>\narray<t, n> repeat(t v) {\n  array<t, n> array;\n  array.fill(v);\n  return array;\n}\n\ntemplate<std::size_t I, class Head, class Tail>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename Head::type array_get(type_list<Head, Tail>&) {\n  return get<I, type_list<Head, Tail> >::value;\n}\ntemplate<std::size_t I, class Head, class Tail>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename Head::type array_get(const type_list<Head, Tail>&) {\n  return get<I, type_list<Head, Tail> >::value;\n}\n\ntemplate <class NList>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename NList::HeadType::type array_prod(const NList&) {\n  return arg_prod<NList>::value;\n}\n\ntemplate<typename t, std::size_t n>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE t array_prod(const array<t, n>& a) {\n  t prod = 1;\n  for (size_t i = 0; i < n; ++i) { prod *= a[i]; }\n  return prod;\n}\ntemplate<typename t>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE t array_prod(const array<t, 0>& /*a*/) {\n  return 0;\n}\n\ntemplate<typename t>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE t array_prod(const std::vector<t>& a) {\n  eigen_assert(a.size() > 0);\n  t prod = 1;\n  for (size_t i = 0; i < a.size(); ++i) { prod *= a[i]; }\n  return prod;\n}\n\n\ntemplate<std::size_t I, class T>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T& array_get(std::vector<T>& a) {\n  return a[I];\n}\ntemplate<std::size_t I, class T>\nEIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const T& array_get(const std::vector<T>& a) {\n  return a[I];\n}\n\nstruct sum_op {\n  template<typename A, typename B> static inline bool run(A a, B b) { return a + b; }\n};\nstruct product_op {\n  template<typename A, typename B> static inline bool run(A a, B b) { return a * b; }\n};\n\nstruct logical_and_op {\n  template<typename A, typename B> static inline bool run(A a, B b) { return a && b; }\n};\nstruct logical_or_op {\n  template<typename A, typename B> static inline bool run(A a, B b) { return a || b; }\n};\n\nstruct equal_op {\n  template<typename A, typename B> static inline bool run(A a, B b) { return a == b; }\n};\nstruct not_equal_op {\n  template<typename A, typename B> static inline bool run(A a, B b) { return a != b; }\n};\nstruct lesser_op {\n  template<typename A, typename B> static inline bool run(A a, B b) { return a < b; }\n};\nstruct lesser_equal_op {\n  template<typename A, typename B> static inline bool run(A a, B b) { return a <= b; }\n};\n\nstruct greater_op {\n  template<typename A, typename B> static inline bool run(A a, B b) { return a > b; }\n};\nstruct greater_equal_op {\n  template<typename A, typename B> static inline bool run(A a, B b) { return a >= b; }\n};\n\nstruct not_op {\n  template<typename A> static inline bool run(A a) { return !a; }\n};\nstruct negation_op {\n  template<typename A> static inline bool run(A a) { return -a; }\n};\nstruct greater_equal_zero_op {\n  template<typename A> static inline bool run(A a) { return a >= 0; }\n};\n\n\ntemplate<typename Reducer, typename Op, typename A, std::size_t N>\nstruct ArrayApplyAndReduce {\n  static inline bool run(const array<A, N>& a) {\n    EIGEN_STATIC_ASSERT(N >= 2, YOU_MADE_A_PROGRAMMING_MISTAKE);\n    bool result = Reducer::run(Op::run(a[0]), Op::run(a[1]));\n    for (size_t i = 2; i < N; ++i) {\n      result = Reducer::run(result, Op::run(a[i]));\n    }\n    return result;\n  }\n};\n\ntemplate<typename Reducer, typename Op, typename A>\nstruct ArrayApplyAndReduce<Reducer, Op, A, 1>  {\n  static inline bool run(const array<A, 1>& a) {\n    return Op::run(a[0]);\n  }\n};\n\ntemplate<typename Reducer, typename Op, typename A, std::size_t N>\ninline bool array_apply_and_reduce(const array<A, N>& a) {\n  return ArrayApplyAndReduce<Reducer, Op, A, N>::run(a);\n}\n\ntemplate<typename Reducer, typename Op, typename A, typename B, std::size_t N>\nstruct ArrayZipAndReduce {\n  static inline bool run(const array<A, N>& a, const array<B, N>& b) {\n    EIGEN_STATIC_ASSERT(N >= 2, YOU_MADE_A_PROGRAMMING_MISTAKE);\n    bool result = Reducer::run(Op::run(a[0], b[0]), Op::run(a[1], b[1]));\n    for (size_t i = 2; i < N; ++i) {\n      result = Reducer::run(result, Op::run(a[i], b[i]));\n    }\n    return result;\n  }\n};\n\ntemplate<typename Reducer, typename Op, typename A, typename B>\nstruct ArrayZipAndReduce<Reducer, Op, A, B, 1> {\n  static inline bool run(const array<A, 1>& a, const array<B, 1>& b) {\n    return Op::run(a[0], b[0]);\n  }\n};\n\ntemplate<typename Reducer, typename Op, typename A, typename B, std::size_t N>\ninline bool array_zip_and_reduce(const array<A, N>& a, const array<B, N>& b) {\n  return ArrayZipAndReduce<Reducer, Op, A, B, N>::run(a, b);\n}\n\n}  // end namespace internal\n\n}  // end namespace Eigen\n\n\n\n#endif  // EIGEN_EMULATE_CXX11_META_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/CXX11/src/util/MaxSizeVector.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_FIXEDSIZEVECTOR_H\n#define EIGEN_FIXEDSIZEVECTOR_H\n\nnamespace Eigen {\n\n/** \\class MaxSizeVector\n  * \\ingroup Core\n  *\n  * \\brief The MaxSizeVector class.\n  *\n  * The %MaxSizeVector provides a subset of std::vector functionality.\n  *\n  * The goal is to provide basic std::vector operations when using\n  * std::vector is not an option (e.g. on GPU or when compiling using\n  * FMA/AVX, as this can cause either compilation failures or illegal\n  * instruction failures).\n  *\n  * Beware: The constructors are not API compatible with these of\n  * std::vector.\n  */\ntemplate <typename T>\nclass MaxSizeVector {\n public:\n  // Construct a new MaxSizeVector, reserve n elements.\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  explicit MaxSizeVector(size_t n)\n      : reserve_(n), size_(0),\n        data_(static_cast<T*>(internal::aligned_malloc(n * sizeof(T)))) {\n    for (size_t i = 0; i < n; ++i) { new (&data_[i]) T; }\n  }\n\n  // Construct a new MaxSizeVector, reserve and resize to n.\n  // Copy the init value to all elements.\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  MaxSizeVector(size_t n, const T& init)\n      : reserve_(n), size_(n),\n        data_(static_cast<T*>(internal::aligned_malloc(n * sizeof(T)))) {\n    for (size_t i = 0; i < n; ++i) { new (&data_[i]) T(init); }\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  ~MaxSizeVector() {\n    for (size_t i = 0; i < size_; ++i) {\n      data_[i].~T();\n    }\n    internal::aligned_free(data_);\n  }\n\n  void resize(size_t n) {\n    eigen_assert(n <= reserve_);\n    for (size_t i = size_; i < n; ++i) {\n      new (&data_[i]) T;\n    }\n    for (size_t i = n; i < size_; ++i) {\n      data_[i].~T();\n    }\n    size_ = n;\n  }\n\n  // Append new elements (up to reserved size).\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  void push_back(const T& t) {\n    eigen_assert(size_ < reserve_);\n    data_[size_++] = t;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  const T& operator[] (size_t i) const {\n    eigen_assert(i < size_);\n    return data_[i];\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  T& operator[] (size_t i) {\n    eigen_assert(i < size_);\n    return data_[i];\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  T& back() {\n    eigen_assert(size_ > 0);\n    return data_[size_ - 1];\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  const T& back() const {\n    eigen_assert(size_ > 0);\n    return data_[size_ - 1];\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  void pop_back() {\n    // NOTE: This does not destroy the value at the end the way\n    // std::vector's version of pop_back() does.  That happens when\n    // the Vector is destroyed.\n    eigen_assert(size_ > 0);\n    size_--;\n  }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  size_t size() const { return size_; }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  bool empty() const { return size_ == 0; }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  T* data() { return data_; }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  const T* data() const { return data_; }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  T* begin() { return data_; }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  T* end() { return data_ + size_; }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  const T* begin() const { return data_; }\n\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\n  const T* end() const { return data_ + size_; }\n\n private:\n  size_t reserve_;\n  size_t size_;\n  T* data_;\n};\n\n}  // namespace Eigen\n\n#endif  // EIGEN_FIXEDSIZEVECTOR_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/EulerAngles",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Tal Hadad <tal_hd@hotmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_EULERANGLES_MODULE_H\n#define EIGEN_EULERANGLES_MODULE_H\n\n\n#include \"Eigen/Core\"\n#include \"Eigen/Geometry\"\n\n#include \"Eigen/src/Core/util/DisableStupidWarnings.h\"\n\nnamespace Eigen {\n\n/**\n  * \\defgroup EulerAngles_Module EulerAngles module\n  * \\brief This module provides generic euler angles rotation.\n  *\n  * Euler angles are a way to represent 3D rotation.\n  *\n  * In order to use this module in your code, include this header:\n  * \\code\n  * #include <unsupported/Eigen/EulerAngles>\n  * \\endcode\n  *\n  * See \\ref EulerAngles for more information.\n  *\n  */\n\n}\n\n#include \"src/EulerAngles/EulerSystem.h\"\n#include \"src/EulerAngles/EulerAngles.h\"\n\n#include \"Eigen/src/Core/util/ReenableStupidWarnings.h\"\n\n#endif // EIGEN_EULERANGLES_MODULE_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/FFT",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra. \n//\n// Copyright (C) 2009 Mark Borgerding mark a borgerding net\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_FFT_H\n#define EIGEN_FFT_H\n\n#include <complex>\n#include <vector>\n#include <map>\n#include <Eigen/Core>\n\n\n/**\n  * \\defgroup FFT_Module Fast Fourier Transform module\n  *\n  * \\code\n  * #include <unsupported/Eigen/FFT>\n  * \\endcode\n  *\n  * This module provides Fast Fourier transformation, with a configurable backend\n  * implementation.\n  *\n  * The default implementation is based on kissfft. It is a small, free, and\n  * reasonably efficient default.\n  *\n  * There are currently two implementation backend:\n  *\n  * - fftw (http://www.fftw.org) : faster, GPL -- incompatible with Eigen in LGPL form, bigger code size.\n  * - MKL (http://en.wikipedia.org/wiki/Math_Kernel_Library) : fastest, commercial -- may be incompatible with Eigen in GPL form.\n  *\n  * \\section FFTDesign Design\n  *\n  * The following design decisions were made concerning scaling and\n  * half-spectrum for real FFT.\n  *\n  * The intent is to facilitate generic programming and ease migrating code\n  * from  Matlab/octave.\n  * We think the default behavior of Eigen/FFT should favor correctness and\n  * generality over speed. Of course, the caller should be able to \"opt-out\" from this\n  * behavior and get the speed increase if they want it.\n  *\n  * 1) %Scaling:\n  * Other libraries (FFTW,IMKL,KISSFFT)  do not perform scaling, so there\n  * is a constant gain incurred after the forward&inverse transforms , so \n  * IFFT(FFT(x)) = Kx;  this is done to avoid a vector-by-value multiply.  \n  * The downside is that algorithms that worked correctly in Matlab/octave \n  * don't behave the same way once implemented in C++.\n  *\n  * How Eigen/FFT differs: invertible scaling is performed so IFFT( FFT(x) ) = x. \n  *\n  * 2) Real FFT half-spectrum\n  * Other libraries use only half the frequency spectrum (plus one extra \n  * sample for the Nyquist bin) for a real FFT, the other half is the \n  * conjugate-symmetric of the first half.  This saves them a copy and some \n  * memory.  The downside is the caller needs to have special logic for the \n  * number of bins in complex vs real.\n  *\n  * How Eigen/FFT differs: The full spectrum is returned from the forward \n  * transform.  This facilitates generic template programming by obviating \n  * separate specializations for real vs complex.  On the inverse\n  * transform, only half the spectrum is actually used if the output type is real.\n  */\n \n\n#ifdef EIGEN_FFTW_DEFAULT\n// FFTW: faster, GPL -- incompatible with Eigen in LGPL form, bigger code size\n#  include <fftw3.h>\n#  include \"src/FFT/ei_fftw_impl.h\"\n   namespace Eigen {\n     //template <typename T> typedef struct internal::fftw_impl  default_fft_impl; this does not work\n     template <typename T> struct default_fft_impl : public internal::fftw_impl<T> {};\n   }\n#elif defined EIGEN_MKL_DEFAULT\n// TODO \n// intel Math Kernel Library: fastest, commercial -- may be incompatible with Eigen in GPL form\n#  include \"src/FFT/ei_imklfft_impl.h\"\n   namespace Eigen {\n     template <typename T> struct default_fft_impl : public internal::imklfft_impl {};\n   }\n#else\n// internal::kissfft_impl:  small, free, reasonably efficient default, derived from kissfft\n//\n# include \"src/FFT/ei_kissfft_impl.h\"\n  namespace Eigen {\n     template <typename T> \n       struct default_fft_impl : public internal::kissfft_impl<T> {};\n  }\n#endif\n\nnamespace Eigen {\n\n \n// \ntemplate<typename T_SrcMat,typename T_FftIfc> struct fft_fwd_proxy;\ntemplate<typename T_SrcMat,typename T_FftIfc> struct fft_inv_proxy;\n\nnamespace internal {\ntemplate<typename T_SrcMat,typename T_FftIfc>\nstruct traits< fft_fwd_proxy<T_SrcMat,T_FftIfc> >\n{\n  typedef typename T_SrcMat::PlainObject ReturnType;\n};\ntemplate<typename T_SrcMat,typename T_FftIfc>\nstruct traits< fft_inv_proxy<T_SrcMat,T_FftIfc> >\n{\n  typedef typename T_SrcMat::PlainObject ReturnType;\n};\n}\n\ntemplate<typename T_SrcMat,typename T_FftIfc> \nstruct fft_fwd_proxy\n : public ReturnByValue<fft_fwd_proxy<T_SrcMat,T_FftIfc> >\n{\n  typedef DenseIndex Index;\n\n  fft_fwd_proxy(const T_SrcMat& src,T_FftIfc & fft, Index nfft) : m_src(src),m_ifc(fft), m_nfft(nfft) {}\n\n  template<typename T_DestMat> void evalTo(T_DestMat& dst) const;\n\n  Index rows() const { return m_src.rows(); }\n  Index cols() const { return m_src.cols(); }\nprotected:\n  const T_SrcMat & m_src;\n  T_FftIfc & m_ifc;\n  Index m_nfft;\nprivate:\n  fft_fwd_proxy& operator=(const fft_fwd_proxy&);\n};\n\ntemplate<typename T_SrcMat,typename T_FftIfc> \nstruct fft_inv_proxy\n : public ReturnByValue<fft_inv_proxy<T_SrcMat,T_FftIfc> >\n{\n  typedef DenseIndex Index;\n\n  fft_inv_proxy(const T_SrcMat& src,T_FftIfc & fft, Index nfft) : m_src(src),m_ifc(fft), m_nfft(nfft) {}\n\n  template<typename T_DestMat> void evalTo(T_DestMat& dst) const;\n\n  Index rows() const { return m_src.rows(); }\n  Index cols() const { return m_src.cols(); }\nprotected:\n  const T_SrcMat & m_src;\n  T_FftIfc & m_ifc;\n  Index m_nfft;\nprivate:\n  fft_inv_proxy& operator=(const fft_inv_proxy&);\n};\n\n\ntemplate <typename T_Scalar,\n         typename T_Impl=default_fft_impl<T_Scalar> >\nclass FFT\n{\n  public:\n    typedef T_Impl impl_type;\n    typedef DenseIndex Index;\n    typedef typename impl_type::Scalar Scalar;\n    typedef typename impl_type::Complex Complex;\n\n    enum Flag {\n      Default=0, // goof proof\n      Unscaled=1,\n      HalfSpectrum=2,\n      // SomeOtherSpeedOptimization=4\n      Speedy=32767\n    };\n\n    FFT( const impl_type & impl=impl_type() , Flag flags=Default ) :m_impl(impl),m_flag(flags) { }\n\n    inline\n    bool HasFlag(Flag f) const { return (m_flag & (int)f) == f;}\n\n    inline\n    void SetFlag(Flag f) { m_flag |= (int)f;}\n\n    inline\n    void ClearFlag(Flag f) { m_flag &= (~(int)f);}\n\n    inline\n    void fwd( Complex * dst, const Scalar * src, Index nfft)\n    {\n        m_impl.fwd(dst,src,static_cast<int>(nfft));\n        if ( HasFlag(HalfSpectrum) == false)\n          ReflectSpectrum(dst,nfft);\n    }\n\n    inline\n    void fwd( Complex * dst, const Complex * src, Index nfft)\n    {\n        m_impl.fwd(dst,src,static_cast<int>(nfft));\n    }\n\n    /*\n    inline \n    void fwd2(Complex * dst, const Complex * src, int n0,int n1)\n    {\n      m_impl.fwd2(dst,src,n0,n1);\n    }\n    */\n\n    template <typename _Input>\n    inline\n    void fwd( std::vector<Complex> & dst, const std::vector<_Input> & src) \n    {\n      if ( NumTraits<_Input>::IsComplex == 0 && HasFlag(HalfSpectrum) )\n        dst.resize( (src.size()>>1)+1); // half the bins + Nyquist bin\n      else\n        dst.resize(src.size());\n      fwd(&dst[0],&src[0],src.size());\n    }\n\n    template<typename InputDerived, typename ComplexDerived>\n    inline\n    void fwd( MatrixBase<ComplexDerived> & dst, const MatrixBase<InputDerived> & src, Index nfft=-1)\n    {\n      typedef typename ComplexDerived::Scalar dst_type;\n      typedef typename InputDerived::Scalar src_type;\n      EIGEN_STATIC_ASSERT_VECTOR_ONLY(InputDerived)\n      EIGEN_STATIC_ASSERT_VECTOR_ONLY(ComplexDerived)\n      EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(ComplexDerived,InputDerived) // size at compile-time\n      EIGEN_STATIC_ASSERT((internal::is_same<dst_type, Complex>::value),\n            YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)\n      EIGEN_STATIC_ASSERT(int(InputDerived::Flags)&int(ComplexDerived::Flags)&DirectAccessBit,\n            THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_WITH_DIRECT_MEMORY_ACCESS_SUCH_AS_MAP_OR_PLAIN_MATRICES)\n\n      if (nfft<1)\n        nfft = src.size();\n\n      if ( NumTraits< src_type >::IsComplex == 0 && HasFlag(HalfSpectrum) )\n        dst.derived().resize( (nfft>>1)+1);\n      else\n        dst.derived().resize(nfft);\n\n      if ( src.innerStride() != 1 || src.size() < nfft ) {\n        Matrix<src_type,1,Dynamic> tmp;\n        if (src.size()<nfft) {\n          tmp.setZero(nfft);\n          tmp.block(0,0,src.size(),1 ) = src;\n        }else{\n          tmp = src;\n        }\n        fwd( &dst[0],&tmp[0],nfft );\n      }else{\n        fwd( &dst[0],&src[0],nfft );\n      }\n    }\n \n    template<typename InputDerived>\n    inline\n    fft_fwd_proxy< MatrixBase<InputDerived>, FFT<T_Scalar,T_Impl> >\n    fwd( const MatrixBase<InputDerived> & src, Index nfft=-1)\n    {\n      return fft_fwd_proxy< MatrixBase<InputDerived> ,FFT<T_Scalar,T_Impl> >( src, *this,nfft );\n    }\n\n    template<typename InputDerived>\n    inline\n    fft_inv_proxy< MatrixBase<InputDerived>, FFT<T_Scalar,T_Impl> >\n    inv( const MatrixBase<InputDerived> & src, Index nfft=-1)\n    {\n      return  fft_inv_proxy< MatrixBase<InputDerived> ,FFT<T_Scalar,T_Impl> >( src, *this,nfft );\n    }\n\n    inline\n    void inv( Complex * dst, const Complex * src, Index nfft)\n    {\n      m_impl.inv( dst,src,static_cast<int>(nfft) );\n      if ( HasFlag( Unscaled ) == false)\n        scale(dst,Scalar(1./nfft),nfft); // scale the time series\n    }\n\n    inline\n    void inv( Scalar * dst, const Complex * src, Index nfft)\n    {\n      m_impl.inv( dst,src,static_cast<int>(nfft) );\n      if ( HasFlag( Unscaled ) == false)\n        scale(dst,Scalar(1./nfft),nfft); // scale the time series\n    }\n\n    template<typename OutputDerived, typename ComplexDerived>\n    inline\n    void inv( MatrixBase<OutputDerived> & dst, const MatrixBase<ComplexDerived> & src, Index nfft=-1)\n    {\n      typedef typename ComplexDerived::Scalar src_type;\n      typedef typename OutputDerived::Scalar dst_type;\n      const bool realfft= (NumTraits<dst_type>::IsComplex == 0);\n      EIGEN_STATIC_ASSERT_VECTOR_ONLY(OutputDerived)\n      EIGEN_STATIC_ASSERT_VECTOR_ONLY(ComplexDerived)\n      EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(ComplexDerived,OutputDerived) // size at compile-time\n      EIGEN_STATIC_ASSERT((internal::is_same<src_type, Complex>::value),\n            YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)\n      EIGEN_STATIC_ASSERT(int(OutputDerived::Flags)&int(ComplexDerived::Flags)&DirectAccessBit,\n            THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_WITH_DIRECT_MEMORY_ACCESS_SUCH_AS_MAP_OR_PLAIN_MATRICES)\n\n      if (nfft<1) { //automatic FFT size determination\n        if ( realfft && HasFlag(HalfSpectrum) ) \n          nfft = 2*(src.size()-1); //assume even fft size\n        else\n          nfft = src.size();\n      }\n      dst.derived().resize( nfft );\n\n      // check for nfft that does not fit the input data size\n      Index resize_input= ( realfft && HasFlag(HalfSpectrum) )\n        ? ( (nfft/2+1) - src.size() )\n        : ( nfft - src.size() );\n\n      if ( src.innerStride() != 1 || resize_input ) {\n        // if the vector is strided, then we need to copy it to a packed temporary\n        Matrix<src_type,1,Dynamic> tmp;\n        if ( resize_input ) {\n          size_t ncopy = (std::min)(src.size(),src.size() + resize_input);\n          tmp.setZero(src.size() + resize_input);\n          if ( realfft && HasFlag(HalfSpectrum) ) {\n            // pad at the Nyquist bin\n            tmp.head(ncopy) = src.head(ncopy);\n            tmp(ncopy-1) = real(tmp(ncopy-1)); // enforce real-only Nyquist bin\n          }else{\n            size_t nhead,ntail;\n            nhead = 1+ncopy/2-1; // range  [0:pi)\n            ntail = ncopy/2-1;   // range (-pi:0)\n            tmp.head(nhead) = src.head(nhead);\n            tmp.tail(ntail) = src.tail(ntail);\n            if (resize_input<0) { //shrinking -- create the Nyquist bin as the average of the two bins that fold into it\n              tmp(nhead) = ( src(nfft/2) + src( src.size() - nfft/2 ) )*src_type(.5);\n            }else{ // expanding -- split the old Nyquist bin into two halves\n              tmp(nhead) = src(nhead) * src_type(.5);\n              tmp(tmp.size()-nhead) = tmp(nhead);\n            }\n          }\n        }else{\n          tmp = src;\n        }\n        inv( &dst[0],&tmp[0], nfft);\n      }else{\n        inv( &dst[0],&src[0], nfft);\n      }\n    }\n\n    template <typename _Output>\n    inline\n    void inv( std::vector<_Output> & dst, const std::vector<Complex> & src,Index nfft=-1)\n    {\n      if (nfft<1)\n        nfft = ( NumTraits<_Output>::IsComplex == 0 && HasFlag(HalfSpectrum) ) ? 2*(src.size()-1) : src.size();\n      dst.resize( nfft );\n      inv( &dst[0],&src[0],nfft);\n    }\n\n\n    /*\n    // TODO: multi-dimensional FFTs\n    inline \n    void inv2(Complex * dst, const Complex * src, int n0,int n1)\n    {\n      m_impl.inv2(dst,src,n0,n1);\n      if ( HasFlag( Unscaled ) == false)\n          scale(dst,1./(n0*n1),n0*n1);\n    }\n  */\n\n    inline\n    impl_type & impl() {return m_impl;}\n  private:\n\n    template <typename T_Data>\n    inline\n    void scale(T_Data * x,Scalar s,Index nx)\n    {\n#if 1\n      for (int k=0;k<nx;++k)\n        *x++ *= s;\n#else\n      if ( ((ptrdiff_t)x) & 15 )\n        Matrix<T_Data, Dynamic, 1>::Map(x,nx) *= s;\n      else\n        Matrix<T_Data, Dynamic, 1>::MapAligned(x,nx) *= s;\n         //Matrix<T_Data, Dynamic, Dynamic>::Map(x,nx) * s;\n#endif  \n    }\n\n    inline\n    void ReflectSpectrum(Complex * freq, Index nfft)\n    {\n      // create the implicit right-half spectrum (conjugate-mirror of the left-half)\n      Index nhbins=(nfft>>1)+1;\n      for (Index k=nhbins;k < nfft; ++k )\n        freq[k] = conj(freq[nfft-k]);\n    }\n\n    impl_type m_impl;\n    int m_flag;\n};\n\ntemplate<typename T_SrcMat,typename T_FftIfc> \ntemplate<typename T_DestMat> inline \nvoid fft_fwd_proxy<T_SrcMat,T_FftIfc>::evalTo(T_DestMat& dst) const\n{\n    m_ifc.fwd( dst, m_src, m_nfft);\n}\n\ntemplate<typename T_SrcMat,typename T_FftIfc> \ntemplate<typename T_DestMat> inline \nvoid fft_inv_proxy<T_SrcMat,T_FftIfc>::evalTo(T_DestMat& dst) const\n{\n    m_ifc.inv( dst, m_src, m_nfft);\n}\n\n}\n#endif\n/* vim: set filetype=cpp et sw=2 ts=2 ai: */\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/IterativeSolvers",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <g.gael@free.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_ITERATIVE_SOLVERS_MODULE_H\n#define EIGEN_ITERATIVE_SOLVERS_MODULE_H\n\n#include <Eigen/Sparse>\n\n/**\n  * \\defgroup IterativeSolvers_Module Iterative solvers module\n  * This module aims to provide various iterative linear and non linear solver algorithms.\n  * It currently provides:\n  *  - a constrained conjugate gradient\n  *  - a Householder GMRES implementation\n  * \\code\n  * #include <unsupported/Eigen/IterativeSolvers>\n  * \\endcode\n  */\n//@{\n\n#ifndef EIGEN_MPL2_ONLY\n#include \"src/IterativeSolvers/IterationController.h\"\n#include \"src/IterativeSolvers/ConstrainedConjGrad.h\"\n#endif\n\n#include \"src/IterativeSolvers/IncompleteLU.h\"\n#include \"../../Eigen/Jacobi\"\n#include \"../../Eigen/Householder\"\n#include \"src/IterativeSolvers/GMRES.h\"\n#include \"src/IterativeSolvers/DGMRES.h\"\n//#include \"src/IterativeSolvers/SSORPreconditioner.h\"\n#include \"src/IterativeSolvers/MINRES.h\"\n\n//@}\n\n#endif // EIGEN_ITERATIVE_SOLVERS_MODULE_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/KroneckerProduct",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_KRONECKER_PRODUCT_MODULE_H\n#define EIGEN_KRONECKER_PRODUCT_MODULE_H\n\n#include \"../../Eigen/Core\"\n\n#include \"../../Eigen/src/Core/util/DisableStupidWarnings.h\"\n\n#include \"../../Eigen/src/SparseCore/SparseUtil.h\"\n\nnamespace Eigen {\n\n/**\n  * \\defgroup KroneckerProduct_Module KroneckerProduct module\n  *\n  * This module contains an experimental Kronecker product implementation.\n  *\n  * \\code\n  * #include <Eigen/KroneckerProduct>\n  * \\endcode\n  */\n\n} // namespace Eigen\n\n#include \"src/KroneckerProduct/KroneckerTensorProduct.h\"\n\n#include \"../../Eigen/src/Core/util/ReenableStupidWarnings.h\"\n\n#endif // EIGEN_KRONECKER_PRODUCT_MODULE_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/LevenbergMarquardt",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_LEVENBERGMARQUARDT_MODULE\n#define EIGEN_LEVENBERGMARQUARDT_MODULE\n\n// #include <vector>\n\n#include <Eigen/Core>\n#include <Eigen/Jacobi>\n#include <Eigen/QR>\n#include <unsupported/Eigen/NumericalDiff> \n\n#include <Eigen/SparseQR>\n\n/**\n  * \\defgroup LevenbergMarquardt_Module Levenberg-Marquardt module\n  *\n  * \\code\n  * #include </Eigen/LevenbergMarquardt>\n  * \\endcode\n  *\n  * \n  */\n\n#include \"Eigen/SparseCore\"\n#ifndef EIGEN_PARSED_BY_DOXYGEN\n\n#include \"src/LevenbergMarquardt/LMqrsolv.h\"\n#include \"src/LevenbergMarquardt/LMcovar.h\"\n#include \"src/LevenbergMarquardt/LMpar.h\"\n\n#endif\n\n#include \"src/LevenbergMarquardt/LevenbergMarquardt.h\"\n#include \"src/LevenbergMarquardt/LMonestep.h\"\n\n\n#endif // EIGEN_LEVENBERGMARQUARDT_MODULE\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/MPRealSupport",
    "content": "// This file is part of a joint effort between Eigen, a lightweight C++ template library\n// for linear algebra, and MPFR C++, a C++ interface to MPFR library (http://www.holoborodko.com/pavel/)\n//\n// Copyright (C) 2010-2012 Pavel Holoborodko <pavel@holoborodko.com>\n// Copyright (C) 2010 Konstantin Holoborodko <konstantin@holoborodko.com>\n// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_MPREALSUPPORT_MODULE_H\n#define EIGEN_MPREALSUPPORT_MODULE_H\n\n#include <Eigen/Core>\n#include <mpreal.h>\n\nnamespace Eigen {\n  \n/**\n  * \\defgroup MPRealSupport_Module MPFRC++ Support module\n  * \\code\n  * #include <Eigen/MPRealSupport>\n  * \\endcode\n  *\n  * This module provides support for multi precision floating point numbers\n  * via the <a href=\"http://www.holoborodko.com/pavel/mpfr\">MPFR C++</a>\n  * library which itself is built upon <a href=\"http://www.mpfr.org/\">MPFR</a>/<a href=\"http://gmplib.org/\">GMP</a>.\n  *\n  * \\warning MPFR C++ is licensed under the GPL.\n  *\n  * You can find a copy of MPFR C++ that is known to be compatible in the unsupported/test/mpreal folder.\n  *\n  * Here is an example:\n  *\n\\code\n#include <iostream>\n#include <Eigen/MPRealSupport>\n#include <Eigen/LU>\nusing namespace mpfr;\nusing namespace Eigen;\nint main()\n{\n  // set precision to 256 bits (double has only 53 bits)\n  mpreal::set_default_prec(256);\n  // Declare matrix and vector types with multi-precision scalar type\n  typedef Matrix<mpreal,Dynamic,Dynamic>  MatrixXmp;\n  typedef Matrix<mpreal,Dynamic,1>        VectorXmp;\n\n  MatrixXmp A = MatrixXmp::Random(100,100);\n  VectorXmp b = VectorXmp::Random(100);\n\n  // Solve Ax=b using LU\n  VectorXmp x = A.lu().solve(b);\n  std::cout << \"relative error: \" << (A*x - b).norm() / b.norm() << std::endl;\n  return 0;\n}\n\\endcode\n  *\n  */\n\t\n  template<> struct NumTraits<mpfr::mpreal>\n    : GenericNumTraits<mpfr::mpreal>\n  {\n    enum {\n      IsInteger = 0,\n      IsSigned = 1,\n      IsComplex = 0,\n      RequireInitialization = 1,\n      ReadCost = HugeCost,\n      AddCost  = HugeCost,\n      MulCost  = HugeCost\n    };\n\n    typedef mpfr::mpreal Real;\n    typedef mpfr::mpreal NonInteger;\n    \n    static inline Real highest  (long Precision = mpfr::mpreal::get_default_prec()) { return  mpfr::maxval(Precision); }\n    static inline Real lowest   (long Precision = mpfr::mpreal::get_default_prec()) { return -mpfr::maxval(Precision); }\n\n    // Constants\n    static inline Real Pi      (long Precision = mpfr::mpreal::get_default_prec())  { return mpfr::const_pi(Precision);        }\n    static inline Real Euler   (long Precision = mpfr::mpreal::get_default_prec())  { return mpfr::const_euler(Precision);     }\n    static inline Real Log2    (long Precision = mpfr::mpreal::get_default_prec())  { return mpfr::const_log2(Precision);      }\n    static inline Real Catalan (long Precision = mpfr::mpreal::get_default_prec())  { return mpfr::const_catalan(Precision);   }\n\n    static inline Real epsilon (long Precision = mpfr::mpreal::get_default_prec())  { return mpfr::machine_epsilon(Precision); }\n    static inline Real epsilon (const Real& x)                                      { return mpfr::machine_epsilon(x); }\n\n#ifdef MPREAL_HAVE_DYNAMIC_STD_NUMERIC_LIMITS\n    static inline int digits10 (long Precision = mpfr::mpreal::get_default_prec())  { return std::numeric_limits<Real>::digits10(Precision); }\n    static inline int digits10 (const Real& x)                                      { return std::numeric_limits<Real>::digits10(x); }\n#endif\n\n    static inline Real dummy_precision()\n    {\n      mpfr_prec_t weak_prec = ((mpfr::mpreal::get_default_prec()-1) * 90) / 100;\n      return mpfr::machine_epsilon(weak_prec);\n    }\n  };\n\n  namespace internal {\n\n  template<> inline mpfr::mpreal random<mpfr::mpreal>()\n  {\n    return mpfr::random();\n  }\n\n  template<> inline mpfr::mpreal random<mpfr::mpreal>(const mpfr::mpreal& a, const mpfr::mpreal& b)\n  {\n    return a + (b-a) * random<mpfr::mpreal>();\n  }\n\n  inline bool isMuchSmallerThan(const mpfr::mpreal& a, const mpfr::mpreal& b, const mpfr::mpreal& eps)\n  {\n    return mpfr::abs(a) <= mpfr::abs(b) * eps;\n  }\n\n  inline bool isApprox(const mpfr::mpreal& a, const mpfr::mpreal& b, const mpfr::mpreal& eps)\n  {\n    return mpfr::isEqualFuzzy(a,b,eps);\n  }\n\n  inline bool isApproxOrLessThan(const mpfr::mpreal& a, const mpfr::mpreal& b, const mpfr::mpreal& eps)\n  {\n    return a <= b || mpfr::isEqualFuzzy(a,b,eps);\n  }\n\n  template<> inline long double cast<mpfr::mpreal,long double>(const mpfr::mpreal& x)\n  { return x.toLDouble(); }\n\n  template<> inline double cast<mpfr::mpreal,double>(const mpfr::mpreal& x)\n  { return x.toDouble(); }\n\n  template<> inline long cast<mpfr::mpreal,long>(const mpfr::mpreal& x)\n  { return x.toLong(); }\n\n  template<> inline int cast<mpfr::mpreal,int>(const mpfr::mpreal& x)\n  { return int(x.toLong()); }\n\n  // Specialize GEBP kernel and traits for mpreal (no need for peeling, nor complicated stuff)\n  // This also permits to directly call mpfr's routines and avoid many temporaries produced by mpreal\n    template<>\n    class gebp_traits<mpfr::mpreal, mpfr::mpreal, false, false>\n    {\n    public:\n      typedef mpfr::mpreal ResScalar;\n      enum {\n        Vectorizable = false,\n        LhsPacketSize = 1,\n        RhsPacketSize = 1,\n        ResPacketSize = 1,\n        NumberOfRegisters = 1,\n        nr = 1,\n        mr = 1,\n        LhsProgress = 1,\n        RhsProgress = 1\n      };\n      typedef ResScalar LhsPacket;\n      typedef ResScalar RhsPacket;\n      typedef ResScalar ResPacket;\n      \n    };\n\n\n\n    template<typename Index, typename DataMapper, bool ConjugateLhs, bool ConjugateRhs>\n    struct gebp_kernel<mpfr::mpreal,mpfr::mpreal,Index,DataMapper,1,1,ConjugateLhs,ConjugateRhs>\n    {\n      typedef mpfr::mpreal mpreal;\n\n      EIGEN_DONT_INLINE\n      void operator()(const DataMapper& res, const mpreal* blockA, const mpreal* blockB, \n                      Index rows, Index depth, Index cols, const mpreal& alpha,\n                      Index strideA=-1, Index strideB=-1, Index offsetA=0, Index offsetB=0)\n      {\n        if(rows==0 || cols==0 || depth==0)\n          return;\n\n        mpreal  acc1(0,mpfr_get_prec(blockA[0].mpfr_srcptr())),\n                tmp (0,mpfr_get_prec(blockA[0].mpfr_srcptr()));\n\n        if(strideA==-1) strideA = depth;\n        if(strideB==-1) strideB = depth;\n\n        for(Index i=0; i<rows; ++i)\n        {\n          for(Index j=0; j<cols; ++j)\n          {\n            const mpreal *A = blockA + i*strideA + offsetA;\n            const mpreal *B = blockB + j*strideB + offsetB;\n            \n            acc1 = 0;\n            for(Index k=0; k<depth; k++)\n            {\n              mpfr_mul(tmp.mpfr_ptr(), A[k].mpfr_srcptr(), B[k].mpfr_srcptr(), mpreal::get_default_rnd());\n              mpfr_add(acc1.mpfr_ptr(), acc1.mpfr_ptr(), tmp.mpfr_ptr(),  mpreal::get_default_rnd());\n            }\n            \n            mpfr_mul(acc1.mpfr_ptr(), acc1.mpfr_srcptr(), alpha.mpfr_srcptr(), mpreal::get_default_rnd());\n            mpfr_add(res(i,j).mpfr_ptr(), res(i,j).mpfr_srcptr(), acc1.mpfr_srcptr(),  mpreal::get_default_rnd());\n          }\n        }\n      }\n    };\n  } // end namespace internal\n}\n\n#endif // EIGEN_MPREALSUPPORT_MODULE_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/MatrixFunctions",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Jitse Niesen <jitse@maths.leeds.ac.uk>\n// Copyright (C) 2012 Chen-Pang He <jdh8@ms63.hinet.net>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_MATRIX_FUNCTIONS\n#define EIGEN_MATRIX_FUNCTIONS\n\n#include <cfloat>\n#include <list>\n\n#include <Eigen/Core>\n#include <Eigen/LU>\n#include <Eigen/Eigenvalues>\n\n/**\n  * \\defgroup MatrixFunctions_Module Matrix functions module\n  * \\brief This module aims to provide various methods for the computation of\n  * matrix functions. \n  *\n  * To use this module, add \n  * \\code\n  * #include <unsupported/Eigen/MatrixFunctions>\n  * \\endcode\n  * at the start of your source file.\n  *\n  * This module defines the following MatrixBase methods.\n  *  - \\ref matrixbase_cos \"MatrixBase::cos()\", for computing the matrix cosine\n  *  - \\ref matrixbase_cosh \"MatrixBase::cosh()\", for computing the matrix hyperbolic cosine\n  *  - \\ref matrixbase_exp \"MatrixBase::exp()\", for computing the matrix exponential\n  *  - \\ref matrixbase_log \"MatrixBase::log()\", for computing the matrix logarithm\n  *  - \\ref matrixbase_pow \"MatrixBase::pow()\", for computing the matrix power\n  *  - \\ref matrixbase_matrixfunction \"MatrixBase::matrixFunction()\", for computing general matrix functions\n  *  - \\ref matrixbase_sin \"MatrixBase::sin()\", for computing the matrix sine\n  *  - \\ref matrixbase_sinh \"MatrixBase::sinh()\", for computing the matrix hyperbolic sine\n  *  - \\ref matrixbase_sqrt \"MatrixBase::sqrt()\", for computing the matrix square root\n  *\n  * These methods are the main entry points to this module. \n  *\n  * %Matrix functions are defined as follows.  Suppose that \\f$ f \\f$\n  * is an entire function (that is, a function on the complex plane\n  * that is everywhere complex differentiable).  Then its Taylor\n  * series\n  * \\f[ f(0) + f'(0) x + \\frac{f''(0)}{2} x^2 + \\frac{f'''(0)}{3!} x^3 + \\cdots \\f]\n  * converges to \\f$ f(x) \\f$. In this case, we can define the matrix\n  * function by the same series:\n  * \\f[ f(M) = f(0) + f'(0) M + \\frac{f''(0)}{2} M^2 + \\frac{f'''(0)}{3!} M^3 + \\cdots \\f]\n  *\n  */\n\n#include \"src/MatrixFunctions/MatrixExponential.h\"\n#include \"src/MatrixFunctions/MatrixFunction.h\"\n#include \"src/MatrixFunctions/MatrixSquareRoot.h\"\n#include \"src/MatrixFunctions/MatrixLogarithm.h\"\n#include \"src/MatrixFunctions/MatrixPower.h\"\n\n\n/** \n\\page matrixbaseextra_page\n\\ingroup MatrixFunctions_Module\n\n\\section matrixbaseextra MatrixBase methods defined in the MatrixFunctions module\n\nThe remainder of the page documents the following MatrixBase methods\nwhich are defined in the MatrixFunctions module.\n\n\n\n\\subsection matrixbase_cos MatrixBase::cos()\n\nCompute the matrix cosine.\n\n\\code\nconst MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::cos() const\n\\endcode\n\n\\param[in]  M  a square matrix.\n\\returns  expression representing \\f$ \\cos(M) \\f$.\n\nThis function computes the matrix cosine. Use ArrayBase::cos() for computing the entry-wise cosine.\n\nThe implementation calls \\ref matrixbase_matrixfunction \"matrixFunction()\" with StdStemFunctions::cos().\n\n\\sa \\ref matrixbase_sin \"sin()\" for an example.\n\n\n\n\\subsection matrixbase_cosh MatrixBase::cosh()\n\nCompute the matrix hyberbolic cosine.\n\n\\code\nconst MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::cosh() const\n\\endcode\n\n\\param[in]  M  a square matrix.\n\\returns  expression representing \\f$ \\cosh(M) \\f$\n\nThis function calls \\ref matrixbase_matrixfunction \"matrixFunction()\" with StdStemFunctions::cosh().\n\n\\sa \\ref matrixbase_sinh \"sinh()\" for an example.\n\n\n\n\\subsection matrixbase_exp MatrixBase::exp()\n\nCompute the matrix exponential.\n\n\\code\nconst MatrixExponentialReturnValue<Derived> MatrixBase<Derived>::exp() const\n\\endcode\n\n\\param[in]  M  matrix whose exponential is to be computed.\n\\returns    expression representing the matrix exponential of \\p M.\n\nThe matrix exponential of \\f$ M \\f$ is defined by\n\\f[ \\exp(M) = \\sum_{k=0}^\\infty \\frac{M^k}{k!}. \\f]\nThe matrix exponential can be used to solve linear ordinary\ndifferential equations: the solution of \\f$ y' = My \\f$ with the\ninitial condition \\f$ y(0) = y_0 \\f$ is given by\n\\f$ y(t) = \\exp(M) y_0 \\f$.\n\nThe matrix exponential is different from applying the exp function to all the entries in the matrix.\nUse ArrayBase::exp() if you want to do the latter.\n\nThe cost of the computation is approximately \\f$ 20 n^3 \\f$ for\nmatrices of size \\f$ n \\f$. The number 20 depends weakly on the\nnorm of the matrix.\n\nThe matrix exponential is computed using the scaling-and-squaring\nmethod combined with Pad&eacute; approximation. The matrix is first\nrescaled, then the exponential of the reduced matrix is computed\napproximant, and then the rescaling is undone by repeated\nsquaring. The degree of the Pad&eacute; approximant is chosen such\nthat the approximation error is less than the round-off\nerror. However, errors may accumulate during the squaring phase.\n\nDetails of the algorithm can be found in: Nicholas J. Higham, \"The\nscaling and squaring method for the matrix exponential revisited,\"\n<em>SIAM J. %Matrix Anal. Applic.</em>, <b>26</b>:1179&ndash;1193,\n2005.\n\nExample: The following program checks that\n\\f[ \\exp \\left[ \\begin{array}{ccc}\n      0 & \\frac14\\pi & 0 \\\\\n      -\\frac14\\pi & 0 & 0 \\\\\n      0 & 0 & 0\n    \\end{array} \\right] = \\left[ \\begin{array}{ccc}\n      \\frac12\\sqrt2 & -\\frac12\\sqrt2 & 0 \\\\\n      \\frac12\\sqrt2 & \\frac12\\sqrt2 & 0 \\\\\n      0 & 0 & 1\n    \\end{array} \\right]. \\f]\nThis corresponds to a rotation of \\f$ \\frac14\\pi \\f$ radians around\nthe z-axis.\n\n\\include MatrixExponential.cpp\nOutput: \\verbinclude MatrixExponential.out\n\n\\note \\p M has to be a matrix of \\c float, \\c double, \\c long double\n\\c complex<float>, \\c complex<double>, or \\c complex<long double> .\n\n\n\\subsection matrixbase_log MatrixBase::log()\n\nCompute the matrix logarithm.\n\n\\code\nconst MatrixLogarithmReturnValue<Derived> MatrixBase<Derived>::log() const\n\\endcode\n\n\\param[in]  M  invertible matrix whose logarithm is to be computed.\n\\returns    expression representing the matrix logarithm root of \\p M.\n\nThe matrix logarithm of \\f$ M \\f$ is a matrix \\f$ X \\f$ such that \n\\f$ \\exp(X) = M \\f$ where exp denotes the matrix exponential. As for\nthe scalar logarithm, the equation \\f$ \\exp(X) = M \\f$ may have\nmultiple solutions; this function returns a matrix whose eigenvalues\nhave imaginary part in the interval \\f$ (-\\pi,\\pi] \\f$.\n\nThe matrix logarithm is different from applying the log function to all the entries in the matrix.\nUse ArrayBase::log() if you want to do the latter.\n\nIn the real case, the matrix \\f$ M \\f$ should be invertible and\nit should have no eigenvalues which are real and negative (pairs of\ncomplex conjugate eigenvalues are allowed). In the complex case, it\nonly needs to be invertible.\n\nThis function computes the matrix logarithm using the Schur-Parlett\nalgorithm as implemented by MatrixBase::matrixFunction(). The\nlogarithm of an atomic block is computed by MatrixLogarithmAtomic,\nwhich uses direct computation for 1-by-1 and 2-by-2 blocks and an\ninverse scaling-and-squaring algorithm for bigger blocks, with the\nsquare roots computed by MatrixBase::sqrt().\n\nDetails of the algorithm can be found in Section 11.6.2 of:\nNicholas J. Higham,\n<em>Functions of Matrices: Theory and Computation</em>,\nSIAM 2008. ISBN 978-0-898716-46-7.\n\nExample: The following program checks that\n\\f[ \\log \\left[ \\begin{array}{ccc} \n      \\frac12\\sqrt2 & -\\frac12\\sqrt2 & 0 \\\\\n      \\frac12\\sqrt2 & \\frac12\\sqrt2 & 0 \\\\\n      0 & 0 & 1\n    \\end{array} \\right] = \\left[ \\begin{array}{ccc}\n      0 & \\frac14\\pi & 0 \\\\ \n      -\\frac14\\pi & 0 & 0 \\\\\n      0 & 0 & 0 \n    \\end{array} \\right]. \\f]\nThis corresponds to a rotation of \\f$ \\frac14\\pi \\f$ radians around\nthe z-axis. This is the inverse of the example used in the\ndocumentation of \\ref matrixbase_exp \"exp()\".\n\n\\include MatrixLogarithm.cpp\nOutput: \\verbinclude MatrixLogarithm.out\n\n\\note \\p M has to be a matrix of \\c float, \\c double, <tt>long\ndouble</tt>, \\c complex<float>, \\c complex<double>, or \\c complex<long\ndouble> .\n\n\\sa MatrixBase::exp(), MatrixBase::matrixFunction(), \n    class MatrixLogarithmAtomic, MatrixBase::sqrt().\n\n\n\\subsection matrixbase_pow MatrixBase::pow()\n\nCompute the matrix raised to arbitrary real power.\n\n\\code\nconst MatrixPowerReturnValue<Derived> MatrixBase<Derived>::pow(RealScalar p) const\n\\endcode\n\n\\param[in]  M  base of the matrix power, should be a square matrix.\n\\param[in]  p  exponent of the matrix power.\n\nThe matrix power \\f$ M^p \\f$ is defined as \\f$ \\exp(p \\log(M)) \\f$,\nwhere exp denotes the matrix exponential, and log denotes the matrix\nlogarithm. This is different from raising all the entries in the matrix\nto the p-th power. Use ArrayBase::pow() if you want to do the latter.\n\nIf \\p p is complex, the scalar type of \\p M should be the type of \\p\np . \\f$ M^p \\f$ simply evaluates into \\f$ \\exp(p \\log(M)) \\f$.\nTherefore, the matrix \\f$ M \\f$ should meet the conditions to be an\nargument of matrix logarithm.\n\nIf \\p p is real, it is casted into the real scalar type of \\p M. Then\nthis function computes the matrix power using the Schur-Pad&eacute;\nalgorithm as implemented by class MatrixPower. The exponent is split\ninto integral part and fractional part, where the fractional part is\nin the interval \\f$ (-1, 1) \\f$. The main diagonal and the first\nsuper-diagonal is directly computed.\n\nIf \\p M is singular with a semisimple zero eigenvalue and \\p p is\npositive, the Schur factor \\f$ T \\f$ is reordered with Givens\nrotations, i.e.\n\n\\f[ T = \\left[ \\begin{array}{cc}\n      T_1 & T_2 \\\\\n      0   & 0\n    \\end{array} \\right] \\f]\n\nwhere \\f$ T_1 \\f$ is invertible. Then \\f$ T^p \\f$ is given by\n\n\\f[ T^p = \\left[ \\begin{array}{cc}\n      T_1^p & T_1^{-1} T_1^p T_2 \\\\\n      0     & 0\n    \\end{array}. \\right] \\f]\n\n\\warning Fractional power of a matrix with a non-semisimple zero\neigenvalue is not well-defined. We introduce an assertion failure\nagainst inaccurate result, e.g. \\code\n#include <unsupported/Eigen/MatrixFunctions>\n#include <iostream>\n\nint main()\n{\n  Eigen::Matrix4d A;\n  A << 0, 0, 2, 3,\n       0, 0, 4, 5,\n       0, 0, 6, 7,\n       0, 0, 8, 9;\n  std::cout << A.pow(0.37) << std::endl;\n  \n  // The 1 makes eigenvalue 0 non-semisimple.\n  A.coeffRef(0, 1) = 1;\n\n  // This fails if EIGEN_NO_DEBUG is undefined.\n  std::cout << A.pow(0.37) << std::endl;\n\n  return 0;\n}\n\\endcode\n\nDetails of the algorithm can be found in: Nicholas J. Higham and\nLijing Lin, \"A Schur-Pad&eacute; algorithm for fractional powers of a\nmatrix,\" <em>SIAM J. %Matrix Anal. Applic.</em>,\n<b>32(3)</b>:1056&ndash;1078, 2011.\n\nExample: The following program checks that\n\\f[ \\left[ \\begin{array}{ccc}\n      \\cos1 & -\\sin1 & 0 \\\\\n      \\sin1 & \\cos1 & 0 \\\\\n      0 & 0 & 1\n    \\end{array} \\right]^{\\frac14\\pi} = \\left[ \\begin{array}{ccc}\n      \\frac12\\sqrt2 & -\\frac12\\sqrt2 & 0 \\\\\n      \\frac12\\sqrt2 & \\frac12\\sqrt2 & 0 \\\\\n      0 & 0 & 1\n    \\end{array} \\right]. \\f]\nThis corresponds to \\f$ \\frac14\\pi \\f$ rotations of 1 radian around\nthe z-axis.\n\n\\include MatrixPower.cpp\nOutput: \\verbinclude MatrixPower.out\n\nMatrixBase::pow() is user-friendly. However, there are some\ncircumstances under which you should use class MatrixPower directly.\nMatrixPower can save the result of Schur decomposition, so it's\nbetter for computing various powers for the same matrix.\n\nExample:\n\\include MatrixPower_optimal.cpp\nOutput: \\verbinclude MatrixPower_optimal.out\n\n\\note \\p M has to be a matrix of \\c float, \\c double, <tt>long\ndouble</tt>, \\c complex<float>, \\c complex<double>, or \\c complex<long\ndouble> .\n\n\\sa MatrixBase::exp(), MatrixBase::log(), class MatrixPower.\n\n\n\\subsection matrixbase_matrixfunction MatrixBase::matrixFunction()\n\nCompute a matrix function.\n\n\\code\nconst MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::matrixFunction(typename internal::stem_function<typename internal::traits<Derived>::Scalar>::type f) const\n\\endcode\n\n\\param[in]  M  argument of matrix function, should be a square matrix.\n\\param[in]  f  an entire function; \\c f(x,n) should compute the n-th\nderivative of f at x.\n\\returns  expression representing \\p f applied to \\p M.\n\nSuppose that \\p M is a matrix whose entries have type \\c Scalar. \nThen, the second argument, \\p f, should be a function with prototype\n\\code \nComplexScalar f(ComplexScalar, int) \n\\endcode\nwhere \\c ComplexScalar = \\c std::complex<Scalar> if \\c Scalar is\nreal (e.g., \\c float or \\c double) and \\c ComplexScalar =\n\\c Scalar if \\c Scalar is complex. The return value of \\c f(x,n)\nshould be \\f$ f^{(n)}(x) \\f$, the n-th derivative of f at x.\n\nThis routine uses the algorithm described in:\nPhilip Davies and Nicholas J. Higham, \n\"A Schur-Parlett algorithm for computing matrix functions\", \n<em>SIAM J. %Matrix Anal. Applic.</em>, <b>25</b>:464&ndash;485, 2003.\n\nThe actual work is done by the MatrixFunction class.\n\nExample: The following program checks that\n\\f[ \\exp \\left[ \\begin{array}{ccc} \n      0 & \\frac14\\pi & 0 \\\\ \n      -\\frac14\\pi & 0 & 0 \\\\\n      0 & 0 & 0 \n    \\end{array} \\right] = \\left[ \\begin{array}{ccc}\n      \\frac12\\sqrt2 & -\\frac12\\sqrt2 & 0 \\\\\n      \\frac12\\sqrt2 & \\frac12\\sqrt2 & 0 \\\\\n      0 & 0 & 1\n    \\end{array} \\right]. \\f]\nThis corresponds to a rotation of \\f$ \\frac14\\pi \\f$ radians around\nthe z-axis. This is the same example as used in the documentation\nof \\ref matrixbase_exp \"exp()\".\n\n\\include MatrixFunction.cpp\nOutput: \\verbinclude MatrixFunction.out\n\nNote that the function \\c expfn is defined for complex numbers \n\\c x, even though the matrix \\c A is over the reals. Instead of\n\\c expfn, we could also have used StdStemFunctions::exp:\n\\code\nA.matrixFunction(StdStemFunctions<std::complex<double> >::exp, &B);\n\\endcode\n\n\n\n\\subsection matrixbase_sin MatrixBase::sin()\n\nCompute the matrix sine.\n\n\\code\nconst MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::sin() const\n\\endcode\n\n\\param[in]  M  a square matrix.\n\\returns  expression representing \\f$ \\sin(M) \\f$.\n\nThis function computes the matrix sine. Use ArrayBase::sin() for computing the entry-wise sine.\n\nThe implementation calls \\ref matrixbase_matrixfunction \"matrixFunction()\" with StdStemFunctions::sin().\n\nExample: \\include MatrixSine.cpp\nOutput: \\verbinclude MatrixSine.out\n\n\n\n\\subsection matrixbase_sinh MatrixBase::sinh()\n\nCompute the matrix hyperbolic sine.\n\n\\code\nMatrixFunctionReturnValue<Derived> MatrixBase<Derived>::sinh() const\n\\endcode\n\n\\param[in]  M  a square matrix.\n\\returns  expression representing \\f$ \\sinh(M) \\f$\n\nThis function calls \\ref matrixbase_matrixfunction \"matrixFunction()\" with StdStemFunctions::sinh().\n\nExample: \\include MatrixSinh.cpp\nOutput: \\verbinclude MatrixSinh.out\n\n\n\\subsection matrixbase_sqrt MatrixBase::sqrt()\n\nCompute the matrix square root.\n\n\\code\nconst MatrixSquareRootReturnValue<Derived> MatrixBase<Derived>::sqrt() const\n\\endcode\n\n\\param[in]  M  invertible matrix whose square root is to be computed.\n\\returns    expression representing the matrix square root of \\p M.\n\nThe matrix square root of \\f$ M \\f$ is the matrix \\f$ M^{1/2} \\f$\nwhose square is the original matrix; so if \\f$ S = M^{1/2} \\f$ then\n\\f$ S^2 = M \\f$. This is different from taking the square root of all\nthe entries in the matrix; use ArrayBase::sqrt() if you want to do the\nlatter.\n\nIn the <b>real case</b>, the matrix \\f$ M \\f$ should be invertible and\nit should have no eigenvalues which are real and negative (pairs of\ncomplex conjugate eigenvalues are allowed). In that case, the matrix\nhas a square root which is also real, and this is the square root\ncomputed by this function. \n\nThe matrix square root is computed by first reducing the matrix to\nquasi-triangular form with the real Schur decomposition. The square\nroot of the quasi-triangular matrix can then be computed directly. The\ncost is approximately \\f$ 25 n^3 \\f$ real flops for the real Schur\ndecomposition and \\f$ 3\\frac13 n^3 \\f$ real flops for the remainder\n(though the computation time in practice is likely more than this\nindicates).\n\nDetails of the algorithm can be found in: Nicholas J. Highan,\n\"Computing real square roots of a real matrix\", <em>Linear Algebra\nAppl.</em>, 88/89:405&ndash;430, 1987.\n\nIf the matrix is <b>positive-definite symmetric</b>, then the square\nroot is also positive-definite symmetric. In this case, it is best to\nuse SelfAdjointEigenSolver::operatorSqrt() to compute it.\n\nIn the <b>complex case</b>, the matrix \\f$ M \\f$ should be invertible;\nthis is a restriction of the algorithm. The square root computed by\nthis algorithm is the one whose eigenvalues have an argument in the\ninterval \\f$ (-\\frac12\\pi, \\frac12\\pi] \\f$. This is the usual branch\ncut.\n\nThe computation is the same as in the real case, except that the\ncomplex Schur decomposition is used to reduce the matrix to a\ntriangular matrix. The theoretical cost is the same. Details are in:\n&Aring;ke Bj&ouml;rck and Sven Hammarling, \"A Schur method for the\nsquare root of a matrix\", <em>Linear Algebra Appl.</em>,\n52/53:127&ndash;140, 1983.\n\nExample: The following program checks that the square root of\n\\f[ \\left[ \\begin{array}{cc} \n              \\cos(\\frac13\\pi) & -\\sin(\\frac13\\pi) \\\\\n              \\sin(\\frac13\\pi) & \\cos(\\frac13\\pi)\n    \\end{array} \\right], \\f]\ncorresponding to a rotation over 60 degrees, is a rotation over 30 degrees:\n\\f[ \\left[ \\begin{array}{cc} \n              \\cos(\\frac16\\pi) & -\\sin(\\frac16\\pi) \\\\\n              \\sin(\\frac16\\pi) & \\cos(\\frac16\\pi)\n    \\end{array} \\right]. \\f]\n\n\\include MatrixSquareRoot.cpp\nOutput: \\verbinclude MatrixSquareRoot.out\n\n\\sa class RealSchur, class ComplexSchur, class MatrixSquareRoot,\n    SelfAdjointEigenSolver::operatorSqrt().\n\n*/\n\n#endif // EIGEN_MATRIX_FUNCTIONS\n\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/MoreVectorization",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_MOREVECTORIZATION_MODULE_H\n#define EIGEN_MOREVECTORIZATION_MODULE_H\n\n#include <Eigen/Core>\n\nnamespace Eigen {\n\n/**\n  * \\defgroup MoreVectorization More vectorization module\n  */\n\n}\n\n#include \"src/MoreVectorization/MathFunctions.h\"\n\n#endif // EIGEN_MOREVECTORIZATION_MODULE_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/NonLinearOptimization",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_NONLINEAROPTIMIZATION_MODULE\n#define EIGEN_NONLINEAROPTIMIZATION_MODULE\n\n#include <vector>\n\n#include <Eigen/Core>\n#include <Eigen/Jacobi>\n#include <Eigen/QR>\n#include <unsupported/Eigen/NumericalDiff>\n\n/**\n  * \\defgroup NonLinearOptimization_Module Non linear optimization module\n  *\n  * \\code\n  * #include <unsupported/Eigen/NonLinearOptimization>\n  * \\endcode\n  *\n  * This module provides implementation of two important algorithms in non linear\n  * optimization. In both cases, we consider a system of non linear functions. Of\n  * course, this should work, and even work very well if those functions are\n  * actually linear. But if this is so, you should probably better use other\n  * methods more fitted to this special case.\n  *\n  * One algorithm allows to find an extremum of such a system (Levenberg\n  * Marquardt algorithm) and the second one is used to find \n  * a zero for the system (Powell hybrid \"dogleg\" method).\n  *\n  * This code is a port of minpack (http://en.wikipedia.org/wiki/MINPACK).\n  * Minpack is a very famous, old, robust and well-reknown package, written in \n  * fortran. Those implementations have been carefully tuned, tested, and used\n  * for several decades.\n  *\n  * The original fortran code was automatically translated using f2c (http://en.wikipedia.org/wiki/F2c) in C,\n  * then c++, and then cleaned by several different authors.\n  * The last one of those cleanings being our starting point : \n  * http://devernay.free.fr/hacks/cminpack.html\n  * \n  * Finally, we ported this code to Eigen, creating classes and API\n  * coherent with Eigen. When possible, we switched to Eigen\n  * implementation, such as most linear algebra (vectors, matrices, stable norms).\n  *\n  * Doing so, we were very careful to check the tests we setup at the very\n  * beginning, which ensure that the same results are found.\n  *\n  * \\section Tests Tests\n  * \n  * The tests are placed in the file unsupported/test/NonLinear.cpp.\n  * \n  * There are two kinds of tests : those that come from examples bundled with cminpack.\n  * They guaranty we get the same results as the original algorithms (value for 'x',\n  * for the number of evaluations of the function, and for the number of evaluations\n  * of the jacobian if ever).\n  * \n  * Other tests were added by myself at the very beginning of the \n  * process and check the results for levenberg-marquardt using the reference data \n  * on http://www.itl.nist.gov/div898/strd/nls/nls_main.shtml. Since then i've \n  * carefully checked that the same results were obtained when modifiying the \n  * code. Please note that we do not always get the exact same decimals as they do,\n  * but this is ok : they use 128bits float, and we do the tests using the C type 'double',\n  * which is 64 bits on most platforms (x86 and amd64, at least).\n  * I've performed those tests on several other implementations of levenberg-marquardt, and\n  * (c)minpack performs VERY well compared to those, both in accuracy and speed.\n  * \n  * The documentation for running the tests is on the wiki\n  * http://eigen.tuxfamily.org/index.php?title=Tests\n  * \n  * \\section API API : overview of methods\n  * \n  * Both algorithms can use either the jacobian (provided by the user) or compute \n  * an approximation by themselves (actually using Eigen \\ref NumericalDiff_Module).\n  * The part of API referring to the latter use 'NumericalDiff' in the method names\n  * (exemple: LevenbergMarquardt.minimizeNumericalDiff() ) \n  * \n  * The methods LevenbergMarquardt.lmder1()/lmdif1()/lmstr1() and \n  * HybridNonLinearSolver.hybrj1()/hybrd1() are specific methods from the original \n  * minpack package that you probably should NOT use until you are porting a code that\n  *  was previously using minpack. They just define a 'simple' API with default values \n  * for some parameters.\n  * \n  * All algorithms are provided using Two APIs :\n  *     - one where the user inits the algorithm, and uses '*OneStep()' as much as he wants : \n  * this way the caller have control over the steps\n  *     - one where the user just calls a method (optimize() or solve()) which will \n  * handle the loop: init + loop until a stop condition is met. Those are provided for\n  *  convenience.\n  * \n  * As an example, the method LevenbergMarquardt::minimize() is \n  * implemented as follow : \n  * \\code\n  * Status LevenbergMarquardt<FunctorType,Scalar>::minimize(FVectorType  &x, const int mode)\n  * {\n  *     Status status = minimizeInit(x, mode);\n  *     do {\n  *         status = minimizeOneStep(x, mode);\n  *     } while (status==Running);\n  *     return status;\n  * }\n  * \\endcode\n  * \n  * \\section examples Examples\n  * \n  * The easiest way to understand how to use this module is by looking at the many examples in the file\n  * unsupported/test/NonLinearOptimization.cpp.\n  */\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\n\n#include \"src/NonLinearOptimization/qrsolv.h\"\n#include \"src/NonLinearOptimization/r1updt.h\"\n#include \"src/NonLinearOptimization/r1mpyq.h\"\n#include \"src/NonLinearOptimization/rwupdt.h\"\n#include \"src/NonLinearOptimization/fdjac1.h\"\n#include \"src/NonLinearOptimization/lmpar.h\"\n#include \"src/NonLinearOptimization/dogleg.h\"\n#include \"src/NonLinearOptimization/covar.h\"\n\n#include \"src/NonLinearOptimization/chkder.h\"\n\n#endif\n\n#include \"src/NonLinearOptimization/HybridNonLinearSolver.h\"\n#include \"src/NonLinearOptimization/LevenbergMarquardt.h\"\n\n\n#endif // EIGEN_NONLINEAROPTIMIZATION_MODULE\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/NumericalDiff",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_NUMERICALDIFF_MODULE\n#define EIGEN_NUMERICALDIFF_MODULE\n\n#include <Eigen/Core>\n\nnamespace Eigen {\n\n/**\n  * \\defgroup NumericalDiff_Module Numerical differentiation module\n  *\n  * \\code\n  * #include <unsupported/Eigen/NumericalDiff>\n  * \\endcode\n  *\n  * See http://en.wikipedia.org/wiki/Numerical_differentiation\n  *\n  * Warning : this should NOT be confused with automatic differentiation, which\n  * is a different method and has its own module in Eigen : \\ref\n  * AutoDiff_Module.\n  *\n  * Currently only \"Forward\" and \"Central\" schemes are implemented. Those\n  * are basic methods, and there exist some more elaborated way of\n  * computing such approximates. They are implemented using both\n  * proprietary and free software, and usually requires linking to an\n  * external library. It is very easy for you to write a functor\n  * using such software, and the purpose is quite orthogonal to what we\n  * want to achieve with Eigen.\n  *\n  * This is why we will not provide wrappers for every great numerical\n  * differentiation software that exist, but should rather stick with those\n  * basic ones, that still are useful for testing.\n  *\n  * Also, the \\ref NonLinearOptimization_Module needs this in order to\n  * provide full features compatibility with the original (c)minpack\n  * package.\n  *\n  */\n}\n\n//@{\n\n#include \"src/NumericalDiff/NumericalDiff.h\"\n\n//@}\n\n\n#endif // EIGEN_NUMERICALDIFF_MODULE\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/OpenGLSupport",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_OPENGL_MODULE\n#define EIGEN_OPENGL_MODULE\n\n#include <Eigen/Geometry>\n\n#if defined(__APPLE_CC__)\n  #include <OpenGL/gl.h>\n#else\n  #include <GL/gl.h>\n#endif\n\nnamespace Eigen {\n\n/**\n  * \\defgroup OpenGLSUpport_Module OpenGL Support module\n  *\n  * This module provides wrapper functions for a couple of OpenGL functions\n  * which simplify the way to pass Eigen's object to openGL.\n  * Here is an exmaple:\n  * \n  * \\code\n  * // You need to add path_to_eigen/unsupported to your include path.\n  * #include <Eigen/OpenGLSupport>\n  * // ...\n  * Vector3f x, y;\n  * Matrix3f rot;\n  * \n  * glVertex(y + x * rot);\n  * \n  * Quaternion q;\n  * glRotate(q);\n  * \n  * // ...\n  * \\endcode\n  *\n  */\n//@{\n\n#define EIGEN_GL_FUNC_DECLARATION(FUNC)                                                                             \\\nnamespace internal {                                                                                                \\\n  template< typename XprType,                                                                                       \\\n            typename Scalar = typename XprType::Scalar,                                                             \\\n            int Rows = XprType::RowsAtCompileTime,                                                                  \\\n            int Cols = XprType::ColsAtCompileTime,                                                                  \\\n            bool IsGLCompatible = bool(internal::evaluator<XprType>::Flags&LinearAccessBit)                         \\\n                              && bool(XprType::Flags&DirectAccessBit)                                               \\\n                              && (XprType::IsVectorAtCompileTime || (XprType::Flags&RowMajorBit)==0)>               \\\n  struct EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl);                                                                      \\\n                                                                                                                    \\\n  template<typename XprType, typename Scalar, int Rows, int Cols>                                                   \\\n  struct EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl)<XprType,Scalar,Rows,Cols,false> {                                     \\\n    inline static void run(const XprType& p) {                                                                      \\\n      EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl)<typename plain_matrix_type_column_major<XprType>::type>::run(p); }       \\\n  };                                                                                                                \\\n}                                                                                                                   \\\n                                                                                                                    \\\ntemplate<typename Derived> inline void FUNC(const Eigen::DenseBase<Derived>& p) {                                   \\\n  EIGEN_CAT(EIGEN_CAT(internal::gl_,FUNC),_impl)<Derived>::run(p.derived());                                        \\\n}\n\n\n#define EIGEN_GL_FUNC_SPECIALIZATION_MAT(FUNC,SCALAR,ROWS,COLS,SUFFIX)                                              \\\nnamespace internal {                                                                                                \\\n  template< typename XprType> struct EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl)<XprType, SCALAR, ROWS, COLS, true> {      \\\n    inline static void run(const XprType& p) { FUNC##SUFFIX(p.data()); }                                            \\\n  };                                                                                                                \\\n}\n\n  \n#define EIGEN_GL_FUNC_SPECIALIZATION_VEC(FUNC,SCALAR,SIZE,SUFFIX)                                                   \\\nnamespace internal {                                                                                                \\\n  template< typename XprType> struct EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl)<XprType, SCALAR, SIZE, 1, true> {         \\\n    inline static void run(const XprType& p) { FUNC##SUFFIX(p.data()); }                                            \\\n  };                                                                                                                \\\n  template< typename XprType> struct EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl)<XprType, SCALAR, 1, SIZE, true> {         \\\n    inline static void run(const XprType& p) { FUNC##SUFFIX(p.data()); }                                            \\\n  };                                                                                                                \\\n}\n\n  \nEIGEN_GL_FUNC_DECLARATION       (glVertex)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,int,    2,2iv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,short,  2,2sv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,float,  2,2fv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,double, 2,2dv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,int,    3,3iv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,short,  3,3sv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,float,  3,3fv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,double, 3,3dv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,int,    4,4iv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,short,  4,4sv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,float,  4,4fv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,double, 4,4dv)\n\nEIGEN_GL_FUNC_DECLARATION       (glTexCoord)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,int,    2,2iv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,short,  2,2sv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,float,  2,2fv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,double, 2,2dv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,int,    3,3iv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,short,  3,3sv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,float,  3,3fv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,double, 3,3dv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,int,    4,4iv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,short,  4,4sv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,float,  4,4fv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,double, 4,4dv)\n\nEIGEN_GL_FUNC_DECLARATION       (glColor)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,int,    2,2iv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,short,  2,2sv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,float,  2,2fv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,double, 2,2dv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,int,    3,3iv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,short,  3,3sv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,float,  3,3fv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,double, 3,3dv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,int,    4,4iv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,short,  4,4sv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,float,  4,4fv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,double, 4,4dv)\n\nEIGEN_GL_FUNC_DECLARATION       (glNormal)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glNormal,int,    3,3iv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glNormal,short,  3,3sv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glNormal,float,  3,3fv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glNormal,double, 3,3dv)\n\ninline void glScale2fv(const float*  v) { glScalef(v[0], v[1], 1.f);  }\ninline void glScale2dv(const double* v) { glScaled(v[0], v[1], 1.0);  }\ninline void glScale3fv(const float*  v) { glScalef(v[0], v[1], v[2]); }\ninline void glScale3dv(const double* v) { glScaled(v[0], v[1], v[2]); }\n\nEIGEN_GL_FUNC_DECLARATION       (glScale)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glScale,float,  2,2fv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glScale,double, 2,2dv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glScale,float,  3,3fv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glScale,double, 3,3dv)\n\ntemplate<typename Scalar> void glScale(const UniformScaling<Scalar>& s)  { glScale(Matrix<Scalar,3,1>::Constant(s.factor())); }\n\ninline void glTranslate2fv(const float*  v) { glTranslatef(v[0], v[1], 0.f);  }\ninline void glTranslate2dv(const double* v) { glTranslated(v[0], v[1], 0.0);  }\ninline void glTranslate3fv(const float*  v) { glTranslatef(v[0], v[1], v[2]); }\ninline void glTranslate3dv(const double* v) { glTranslated(v[0], v[1], v[2]); }\n\nEIGEN_GL_FUNC_DECLARATION       (glTranslate)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glTranslate,float,  2,2fv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glTranslate,double, 2,2dv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glTranslate,float,  3,3fv)\nEIGEN_GL_FUNC_SPECIALIZATION_VEC(glTranslate,double, 3,3dv)\n\ntemplate<typename Scalar> void glTranslate(const Translation<Scalar,2>& t)  { glTranslate(t.vector()); }\ntemplate<typename Scalar> void glTranslate(const Translation<Scalar,3>& t)  { glTranslate(t.vector()); }\n\nEIGEN_GL_FUNC_DECLARATION       (glMultMatrix)\nEIGEN_GL_FUNC_SPECIALIZATION_MAT(glMultMatrix,float,  4,4,f)\nEIGEN_GL_FUNC_SPECIALIZATION_MAT(glMultMatrix,double, 4,4,d)\n\ntemplate<typename Scalar> void glMultMatrix(const Transform<Scalar,3,Affine>& t)        { glMultMatrix(t.matrix()); }\ntemplate<typename Scalar> void glMultMatrix(const Transform<Scalar,3,Projective>& t)    { glMultMatrix(t.matrix()); }\ntemplate<typename Scalar> void glMultMatrix(const Transform<Scalar,3,AffineCompact>& t) { glMultMatrix(Transform<Scalar,3,Affine>(t).matrix()); }\n\nEIGEN_GL_FUNC_DECLARATION       (glLoadMatrix)\nEIGEN_GL_FUNC_SPECIALIZATION_MAT(glLoadMatrix,float,  4,4,f)\nEIGEN_GL_FUNC_SPECIALIZATION_MAT(glLoadMatrix,double, 4,4,d)\n\ntemplate<typename Scalar> void glLoadMatrix(const Transform<Scalar,3,Affine>& t)        { glLoadMatrix(t.matrix()); }\ntemplate<typename Scalar> void glLoadMatrix(const Transform<Scalar,3,Projective>& t)    { glLoadMatrix(t.matrix()); }\ntemplate<typename Scalar> void glLoadMatrix(const Transform<Scalar,3,AffineCompact>& t) { glLoadMatrix(Transform<Scalar,3,Affine>(t).matrix()); }\n\ninline void glRotate(const Rotation2D<float>& rot)\n{\n  glRotatef(rot.angle()*180.f/float(EIGEN_PI), 0.f, 0.f, 1.f);\n}\ninline void glRotate(const Rotation2D<double>& rot)\n{\n  glRotated(rot.angle()*180.0/EIGEN_PI, 0.0, 0.0, 1.0);\n}\n\ntemplate<typename Derived> void glRotate(const RotationBase<Derived,3>& rot)\n{  \n  Transform<typename Derived::Scalar,3,Projective> tr(rot);\n  glMultMatrix(tr.matrix());\n}\n\n#define EIGEN_GL_MAKE_CONST_const const\n#define EIGEN_GL_MAKE_CONST__ \n#define EIGEN_GL_EVAL(X) X\n\n#define EIGEN_GL_FUNC1_DECLARATION(FUNC,ARG1,CONST)                                                                             \\\nnamespace internal {                                                                                                            \\\n  template< typename XprType,                                                                                                   \\\n            typename Scalar = typename XprType::Scalar,                                                                         \\\n            int Rows = XprType::RowsAtCompileTime,                                                                              \\\n            int Cols = XprType::ColsAtCompileTime,                                                                              \\\n            bool IsGLCompatible = bool(internal::evaluator<XprType>::Flags&LinearAccessBit)                                     \\\n                              && bool(XprType::Flags&DirectAccessBit)                                                           \\\n                              && (XprType::IsVectorAtCompileTime || (XprType::Flags&RowMajorBit)==0)>                           \\\n  struct EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl);                                                                                  \\\n                                                                                                                                \\\n  template<typename XprType, typename Scalar, int Rows, int Cols>                                                               \\\n  struct EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl)<XprType,Scalar,Rows,Cols,false> {                                                 \\\n    inline static void run(ARG1 a,EIGEN_GL_EVAL(EIGEN_GL_MAKE_CONST_##CONST) XprType& p) {                                      \\\n      EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl)<typename plain_matrix_type_column_major<XprType>::type>::run(a,p); }                 \\\n  };                                                                                                                            \\\n}                                                                                                                               \\\n                                                                                                                                \\\ntemplate<typename Derived> inline void FUNC(ARG1 a,EIGEN_GL_EVAL(EIGEN_GL_MAKE_CONST_##CONST) Eigen::DenseBase<Derived>& p) {   \\\n  EIGEN_CAT(EIGEN_CAT(internal::gl_,FUNC),_impl)<Derived>::run(a,p.derived());                                                  \\\n}\n\n\n#define EIGEN_GL_FUNC1_SPECIALIZATION_MAT(FUNC,ARG1,CONST,SCALAR,ROWS,COLS,SUFFIX)                                              \\\nnamespace internal {                                                                                                            \\\n  template< typename XprType> struct EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl)<XprType, SCALAR, ROWS, COLS, true> {                  \\\n    inline static void run(ARG1 a, EIGEN_GL_EVAL(EIGEN_GL_MAKE_CONST_##CONST) XprType& p) { FUNC##SUFFIX(a,p.data()); }         \\\n  }; \\\n}\n\n  \n#define EIGEN_GL_FUNC1_SPECIALIZATION_VEC(FUNC,ARG1,CONST,SCALAR,SIZE,SUFFIX)                                                   \\\nnamespace internal {                                                                                                            \\\n  template< typename XprType> struct EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl)<XprType, SCALAR, SIZE, 1, true> {                     \\\n    inline static void run(ARG1 a, EIGEN_GL_EVAL(EIGEN_GL_MAKE_CONST_##CONST) XprType& p) { FUNC##SUFFIX(a,p.data()); }         \\\n  };                                                                                                                            \\\n  template< typename XprType> struct EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl)<XprType, SCALAR, 1, SIZE, true> {                     \\\n    inline static void run(ARG1 a, EIGEN_GL_EVAL(EIGEN_GL_MAKE_CONST_##CONST) XprType& p) { FUNC##SUFFIX(a,p.data()); }         \\\n  };                                                                                                                            \\\n}\n\nEIGEN_GL_FUNC1_DECLARATION       (glGet,GLenum,_)\nEIGEN_GL_FUNC1_SPECIALIZATION_MAT(glGet,GLenum,_,float,  4,4,Floatv)\nEIGEN_GL_FUNC1_SPECIALIZATION_MAT(glGet,GLenum,_,double, 4,4,Doublev)\n\n// glUniform API\n\n#ifdef GL_VERSION_2_0\n\ninline void glUniform2fv_ei  (GLint loc, const float* v)         { glUniform2fv(loc,1,v); }\ninline void glUniform2iv_ei  (GLint loc, const int* v)           { glUniform2iv(loc,1,v); }\n\ninline void glUniform3fv_ei  (GLint loc, const float* v)         { glUniform3fv(loc,1,v); }\ninline void glUniform3iv_ei  (GLint loc, const int* v)           { glUniform3iv(loc,1,v); }\n\ninline void glUniform4fv_ei  (GLint loc, const float* v)         { glUniform4fv(loc,1,v); }\ninline void glUniform4iv_ei  (GLint loc, const int* v)           { glUniform4iv(loc,1,v); }\n\ninline void glUniformMatrix2fv_ei  (GLint loc, const float* v)         { glUniformMatrix2fv(loc,1,false,v); }\ninline void glUniformMatrix3fv_ei  (GLint loc, const float* v)         { glUniformMatrix3fv(loc,1,false,v); }\ninline void glUniformMatrix4fv_ei  (GLint loc, const float* v)         { glUniformMatrix4fv(loc,1,false,v); }\n\n\nEIGEN_GL_FUNC1_DECLARATION       (glUniform,GLint,const)\nEIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,float,        2,2fv_ei)\nEIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,int,          2,2iv_ei)\nEIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,float,        3,3fv_ei)\nEIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,int,          3,3iv_ei)\nEIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,float,        4,4fv_ei)\nEIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,int,          4,4iv_ei)\n\nEIGEN_GL_FUNC1_SPECIALIZATION_MAT(glUniform,GLint,const,float,        2,2,Matrix2fv_ei)\nEIGEN_GL_FUNC1_SPECIALIZATION_MAT(glUniform,GLint,const,float,        3,3,Matrix3fv_ei)\nEIGEN_GL_FUNC1_SPECIALIZATION_MAT(glUniform,GLint,const,float,        4,4,Matrix4fv_ei)\n\n#endif\n\n#ifdef GL_VERSION_2_1\n\ninline void glUniformMatrix2x3fv_ei(GLint loc, const float* v)         { glUniformMatrix2x3fv(loc,1,false,v); }\ninline void glUniformMatrix3x2fv_ei(GLint loc, const float* v)         { glUniformMatrix3x2fv(loc,1,false,v); }\ninline void glUniformMatrix2x4fv_ei(GLint loc, const float* v)         { glUniformMatrix2x4fv(loc,1,false,v); }\ninline void glUniformMatrix4x2fv_ei(GLint loc, const float* v)         { glUniformMatrix4x2fv(loc,1,false,v); }\ninline void glUniformMatrix3x4fv_ei(GLint loc, const float* v)         { glUniformMatrix3x4fv(loc,1,false,v); }\ninline void glUniformMatrix4x3fv_ei(GLint loc, const float* v)         { glUniformMatrix4x3fv(loc,1,false,v); }\n\nEIGEN_GL_FUNC1_SPECIALIZATION_MAT(glUniform,GLint,const,float,        2,3,Matrix2x3fv_ei)\nEIGEN_GL_FUNC1_SPECIALIZATION_MAT(glUniform,GLint,const,float,        3,2,Matrix3x2fv_ei)\nEIGEN_GL_FUNC1_SPECIALIZATION_MAT(glUniform,GLint,const,float,        2,4,Matrix2x4fv_ei)\nEIGEN_GL_FUNC1_SPECIALIZATION_MAT(glUniform,GLint,const,float,        4,2,Matrix4x2fv_ei)\nEIGEN_GL_FUNC1_SPECIALIZATION_MAT(glUniform,GLint,const,float,        3,4,Matrix3x4fv_ei)\nEIGEN_GL_FUNC1_SPECIALIZATION_MAT(glUniform,GLint,const,float,        4,3,Matrix4x3fv_ei)\n\n#endif\n\n#ifdef GL_VERSION_3_0\n\ninline void glUniform2uiv_ei (GLint loc, const unsigned int* v)  { glUniform2uiv(loc,1,v); }\ninline void glUniform3uiv_ei (GLint loc, const unsigned int* v)  { glUniform3uiv(loc,1,v); }\ninline void glUniform4uiv_ei (GLint loc, const unsigned int* v)  { glUniform4uiv(loc,1,v); }\n\nEIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,unsigned int, 2,2uiv_ei)\nEIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,unsigned int, 3,3uiv_ei)\nEIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,unsigned int, 4,4uiv_ei)\n\n#endif\n\n#ifdef GL_ARB_gpu_shader_fp64\ninline void glUniform2dv_ei  (GLint loc, const double* v)        { glUniform2dv(loc,1,v); }\ninline void glUniform3dv_ei  (GLint loc, const double* v)        { glUniform3dv(loc,1,v); }\ninline void glUniform4dv_ei  (GLint loc, const double* v)        { glUniform4dv(loc,1,v); }\n\nEIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,double,       2,2dv_ei)\nEIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,double,       3,3dv_ei)\nEIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,double,       4,4dv_ei)\n#endif\n\n\n//@}\n\n}\n\n#endif // EIGEN_OPENGL_MODULE\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/Polynomials",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_POLYNOMIALS_MODULE_H\n#define EIGEN_POLYNOMIALS_MODULE_H\n\n#include <Eigen/Core>\n\n#include <Eigen/src/Core/util/DisableStupidWarnings.h>\n\n#include <Eigen/Eigenvalues>\n\n// Note that EIGEN_HIDE_HEAVY_CODE has to be defined per module\n#if (defined EIGEN_EXTERN_INSTANTIATIONS) && (EIGEN_EXTERN_INSTANTIATIONS>=2)\n  #ifndef EIGEN_HIDE_HEAVY_CODE\n  #define EIGEN_HIDE_HEAVY_CODE\n  #endif\n#elif defined EIGEN_HIDE_HEAVY_CODE\n  #undef EIGEN_HIDE_HEAVY_CODE\n#endif\n\n/**\n  * \\defgroup Polynomials_Module Polynomials module\n  * \\brief This module provides a QR based polynomial solver.\n\t*\n  * To use this module, add\n  * \\code\n  * #include <unsupported/Eigen/Polynomials>\n  * \\endcode\n\t* at the start of your source file.\n  */\n\n#include \"src/Polynomials/PolynomialUtils.h\"\n#include \"src/Polynomials/Companion.h\"\n#include \"src/Polynomials/PolynomialSolver.h\"\n\n/**\n\t\\page polynomials Polynomials defines functions for dealing with polynomials\n\tand a QR based polynomial solver.\n\t\\ingroup Polynomials_Module\n\n\tThe remainder of the page documents first the functions for evaluating, computing\n\tpolynomials, computing estimates about polynomials and next the QR based polynomial\n\tsolver.\n\n\t\\section polynomialUtils convenient functions to deal with polynomials\n\t\\subsection roots_to_monicPolynomial\n\tThe function\n\t\\code\n\tvoid roots_to_monicPolynomial( const RootVector& rv, Polynomial& poly )\n\t\\endcode\n\tcomputes the coefficients \\f$ a_i \\f$ of\n\n\t\\f$ p(x) = a_0 + a_{1}x + ... + a_{n-1}x^{n-1} + x^n \\f$\n\n\twhere \\f$ p \\f$ is known through its roots i.e. \\f$ p(x) = (x-r_1)(x-r_2)...(x-r_n) \\f$.\n\n\t\\subsection poly_eval\n\tThe function\n\t\\code\n\tT poly_eval( const Polynomials& poly, const T& x )\n\t\\endcode\n\tevaluates a polynomial at a given point using stabilized H&ouml;rner method.\n\n\tThe following code: first computes the coefficients in the monomial basis of the monic polynomial that has the provided roots;\n\tthen, it evaluates the computed polynomial, using a stabilized H&ouml;rner method.\n\n\t\\include PolynomialUtils1.cpp\n  Output: \\verbinclude PolynomialUtils1.out\n\n\t\\subsection Cauchy bounds\n\tThe function\n\t\\code\n\tReal cauchy_max_bound( const Polynomial& poly )\n\t\\endcode\n\tprovides a maximum bound (the Cauchy one: \\f$C(p)\\f$) for the absolute value of a root of the given polynomial i.e.\n\t\\f$ \\forall r_i \\f$ root of \\f$ p(x) = \\sum_{k=0}^d a_k x^k \\f$,\n\t\\f$ |r_i| \\le C(p) = \\sum_{k=0}^{d} \\left | \\frac{a_k}{a_d} \\right | \\f$\n\tThe leading coefficient \\f$ p \\f$: should be non zero \\f$a_d \\neq 0\\f$.\n\n\n\tThe function\n\t\\code\n\tReal cauchy_min_bound( const Polynomial& poly )\n\t\\endcode\n\tprovides a minimum bound (the Cauchy one: \\f$c(p)\\f$) for the absolute value of a non zero root of the given polynomial i.e.\n\t\\f$ \\forall r_i \\neq 0 \\f$ root of \\f$ p(x) = \\sum_{k=0}^d a_k x^k \\f$,\n\t\\f$ |r_i| \\ge c(p) = \\left( \\sum_{k=0}^{d} \\left | \\frac{a_k}{a_0} \\right | \\right)^{-1} \\f$\n\n\n\n\n\t\\section QR polynomial solver class\n\tComputes the complex roots of a polynomial by computing the eigenvalues of the associated companion matrix with the QR algorithm.\n\t\n\tThe roots of \\f$ p(x) = a_0 + a_1 x + a_2 x^2 + a_{3} x^3 + x^4 \\f$ are the eigenvalues of\n\t\\f$\n\t\\left [\n\t\\begin{array}{cccc}\n\t0 & 0 &  0 & a_0 \\\\\n\t1 & 0 &  0 & a_1 \\\\\n\t0 & 1 &  0 & a_2 \\\\\n\t0 & 0 &  1 & a_3\n\t\\end{array} \\right ]\n\t\\f$\n\n\tHowever, the QR algorithm is not guaranteed to converge when there are several eigenvalues with same modulus.\n\n\tTherefore the current polynomial solver is guaranteed to provide a correct result only when the complex roots \\f$r_1,r_2,...,r_d\\f$ have distinct moduli i.e.\n\t\n\t\\f$ \\forall i,j \\in [1;d],~ \\| r_i \\| \\neq \\| r_j \\| \\f$.\n\n\tWith 32bit (float) floating types this problem shows up frequently.\n  However, almost always, correct accuracy is reached even in these cases for 64bit\n  (double) floating types and small polynomial degree (<20).\n\n\t\\include PolynomialSolver1.cpp\n\t\n\tIn the above example:\n\t\n\t-# a simple use of the polynomial solver is shown;\n\t-# the accuracy problem with the QR algorithm is presented: a polynomial with almost conjugate roots is provided to the solver.\n\tThose roots have almost same module therefore the QR algorithm failed to converge: the accuracy\n\tof the last root is bad;\n\t-# a simple way to circumvent the problem is shown: use doubles instead of floats.\n\n  Output: \\verbinclude PolynomialSolver1.out\n*/\n\n#include <Eigen/src/Core/util/ReenableStupidWarnings.h>\n\n#endif // EIGEN_POLYNOMIALS_MODULE_H\n/* vim: set filetype=cpp et sw=2 ts=2 ai: */\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/Skyline",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SKYLINE_MODULE_H\n#define EIGEN_SKYLINE_MODULE_H\n\n\n#include \"Eigen/Core\"\n\n#include \"Eigen/src/Core/util/DisableStupidWarnings.h\"\n\n#include <map>\n#include <cstdlib>\n#include <cstring>\n#include <algorithm>\n\n/**\n *  \\defgroup Skyline_Module Skyline module\n *\n *\n *\n *\n */\n\n#include \"src/Skyline/SkylineUtil.h\"\n#include \"src/Skyline/SkylineMatrixBase.h\"\n#include \"src/Skyline/SkylineStorage.h\"\n#include \"src/Skyline/SkylineMatrix.h\"\n#include \"src/Skyline/SkylineInplaceLU.h\"\n#include \"src/Skyline/SkylineProduct.h\"\n\n#include \"Eigen/src/Core/util/ReenableStupidWarnings.h\"\n\n#endif // EIGEN_SKYLINE_MODULE_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/SparseExtra",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <g.gael@free.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSE_EXTRA_MODULE_H\n#define EIGEN_SPARSE_EXTRA_MODULE_H\n\n#include \"../../Eigen/Sparse\"\n\n#include \"../../Eigen/src/Core/util/DisableStupidWarnings.h\"\n\n#include <vector>\n#include <map>\n#include <cstdlib>\n#include <cstring>\n#include <algorithm>\n#include <fstream>\n#include <sstream>\n\n#ifdef EIGEN_GOOGLEHASH_SUPPORT\n  #include <google/dense_hash_map>\n#endif\n\n/**\n  * \\defgroup SparseExtra_Module SparseExtra module\n  *\n  * This module contains some experimental features extending the sparse module.\n  *\n  * \\code\n  * #include <Eigen/SparseExtra>\n  * \\endcode\n  */\n\n\n#include \"src/SparseExtra/DynamicSparseMatrix.h\"\n#include \"src/SparseExtra/BlockOfDynamicSparseMatrix.h\"\n#include \"src/SparseExtra/RandomSetter.h\"\n\n#include \"src/SparseExtra/MarketIO.h\"\n\n#if !defined(_WIN32)\n#include <dirent.h>\n#include \"src/SparseExtra/MatrixMarketIterator.h\"\n#endif\n\n#include \"../../Eigen/src/Core/util/ReenableStupidWarnings.h\"\n\n#endif // EIGEN_SPARSE_EXTRA_MODULE_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/SpecialFunctions",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Gael Guennebaud <g.gael@free.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPECIALFUNCTIONS_MODULE\n#define EIGEN_SPECIALFUNCTIONS_MODULE\n\n#include <math.h>\n\n#include \"../../Eigen/Core\"\n\n#include \"../../Eigen/src/Core/util/DisableStupidWarnings.h\"\n\nnamespace Eigen {\n\n/**\n  * \\defgroup SpecialFunctions_Module Special math functions module\n  *\n  * This module features additional coefficient-wise math functions available\n  * within the numext:: namespace for the scalar version, and as method and/or free\n  * functions of Array. Those include:\n  *\n  * - erf\n  * - erfc\n  * - lgamma\n  * - igamma\n  * - igammac\n  * - digamma\n  * - polygamma\n  * - zeta\n  * - betainc\n  *\n  * \\code\n  * #include <unsupported/Eigen/SpecialFunctions>\n  * \\endcode\n  */\n//@{\n\n}\n\n#include \"src/SpecialFunctions/SpecialFunctionsImpl.h\"\n#include \"src/SpecialFunctions/SpecialFunctionsPacketMath.h\"\n#include \"src/SpecialFunctions/SpecialFunctionsHalf.h\"\n#include \"src/SpecialFunctions/SpecialFunctionsFunctors.h\"\n#include \"src/SpecialFunctions/SpecialFunctionsArrayAPI.h\"\n\n#if defined EIGEN_VECTORIZE_CUDA\n  #include \"src/SpecialFunctions/arch/CUDA/CudaSpecialFunctions.h\"\n#endif\n\nnamespace Eigen {\n//@}\n}\n\n\n#include \"../../Eigen/src/Core/util/ReenableStupidWarnings.h\"\n\n#endif // EIGEN_SPECIALFUNCTIONS_MODULE\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/Splines",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 20010-2011 Hauke Heibel <hauke.heibel@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPLINES_MODULE_H\n#define EIGEN_SPLINES_MODULE_H\n\nnamespace Eigen \n{\n/**\n  * \\defgroup Splines_Module Spline and spline fitting module\n  *\n  * This module provides a simple multi-dimensional spline class while\n  * offering most basic functionality to fit a spline to point sets.\n  *\n  * \\code\n  * #include <unsupported/Eigen/Splines>\n  * \\endcode\n  */\n}\n\n#include \"src/Splines/SplineFwd.h\"\n#include \"src/Splines/Spline.h\"\n#include \"src/Splines/SplineFitting.h\"\n\n#endif // EIGEN_SPLINES_MODULE_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/AutoDiff/AutoDiffJacobian.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_AUTODIFF_JACOBIAN_H\n#define EIGEN_AUTODIFF_JACOBIAN_H\n\nnamespace Eigen\n{\n\ntemplate<typename Functor> class AutoDiffJacobian : public Functor\n{\npublic:\n  AutoDiffJacobian() : Functor() {}\n  AutoDiffJacobian(const Functor& f) : Functor(f) {}\n\n  // forward constructors\n#if EIGEN_HAS_VARIADIC_TEMPLATES\n  template<typename... T>\n  AutoDiffJacobian(const T& ...Values) : Functor(Values...) {}\n#else\n  template<typename T0>\n  AutoDiffJacobian(const T0& a0) : Functor(a0) {}\n  template<typename T0, typename T1>\n  AutoDiffJacobian(const T0& a0, const T1& a1) : Functor(a0, a1) {}\n  template<typename T0, typename T1, typename T2>\n  AutoDiffJacobian(const T0& a0, const T1& a1, const T2& a2) : Functor(a0, a1, a2) {}\n#endif\n\n  typedef typename Functor::InputType InputType;\n  typedef typename Functor::ValueType ValueType;\n  typedef typename ValueType::Scalar Scalar;\n\n  enum {\n    InputsAtCompileTime = InputType::RowsAtCompileTime,\n    ValuesAtCompileTime = ValueType::RowsAtCompileTime\n  };\n\n  typedef Matrix<Scalar, ValuesAtCompileTime, InputsAtCompileTime> JacobianType;\n  typedef typename JacobianType::Index Index;\n\n  typedef Matrix<Scalar, InputsAtCompileTime, 1> DerivativeType;\n  typedef AutoDiffScalar<DerivativeType> ActiveScalar;\n\n  typedef Matrix<ActiveScalar, InputsAtCompileTime, 1> ActiveInput;\n  typedef Matrix<ActiveScalar, ValuesAtCompileTime, 1> ActiveValue;\n\n#if EIGEN_HAS_VARIADIC_TEMPLATES\n  // Some compilers don't accept variadic parameters after a default parameter,\n  // i.e., we can't just write _jac=0 but we need to overload operator():\n  EIGEN_STRONG_INLINE\n  void operator() (const InputType& x, ValueType* v) const\n  {\n      this->operator()(x, v, 0);\n  }\n  template<typename... ParamsType>\n  void operator() (const InputType& x, ValueType* v, JacobianType* _jac,\n                   const ParamsType&... Params) const\n#else\n  void operator() (const InputType& x, ValueType* v, JacobianType* _jac=0) const\n#endif\n  {\n    eigen_assert(v!=0);\n\n    if (!_jac)\n    {\n#if EIGEN_HAS_VARIADIC_TEMPLATES\n      Functor::operator()(x, v, Params...);\n#else\n      Functor::operator()(x, v);\n#endif\n      return;\n    }\n\n    JacobianType& jac = *_jac;\n\n    ActiveInput ax = x.template cast<ActiveScalar>();\n    ActiveValue av(jac.rows());\n\n    if(InputsAtCompileTime==Dynamic)\n      for (Index j=0; j<jac.rows(); j++)\n        av[j].derivatives().resize(x.rows());\n\n    for (Index i=0; i<jac.cols(); i++)\n      ax[i].derivatives() = DerivativeType::Unit(x.rows(),i);\n\n#if EIGEN_HAS_VARIADIC_TEMPLATES\n    Functor::operator()(ax, &av, Params...);\n#else\n    Functor::operator()(ax, &av);\n#endif\n\n    for (Index i=0; i<jac.rows(); i++)\n    {\n      (*v)[i] = av[i].value();\n      jac.row(i) = av[i].derivatives();\n    }\n  }\n};\n\n}\n\n#endif // EIGEN_AUTODIFF_JACOBIAN_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_AUTODIFF_SCALAR_H\n#define EIGEN_AUTODIFF_SCALAR_H\n\nnamespace Eigen {\n\nnamespace internal {\n\ntemplate<typename A, typename B>\nstruct make_coherent_impl {\n  static void run(A&, B&) {}\n};\n\n// resize a to match b is a.size()==0, and conversely.\ntemplate<typename A, typename B>\nvoid make_coherent(const A& a, const B&b)\n{\n  make_coherent_impl<A,B>::run(a.const_cast_derived(), b.const_cast_derived());\n}\n\ntemplate<typename _DerType, bool Enable> struct auto_diff_special_op;\n\n} // end namespace internal\n\ntemplate<typename _DerType> class AutoDiffScalar;\n\ntemplate<typename NewDerType>\ninline AutoDiffScalar<NewDerType> MakeAutoDiffScalar(const typename NewDerType::Scalar& value, const NewDerType &der) {\n  return AutoDiffScalar<NewDerType>(value,der);\n}\n\n/** \\class AutoDiffScalar\n  * \\brief A scalar type replacement with automatic differentation capability\n  *\n  * \\param _DerType the vector type used to store/represent the derivatives. The base scalar type\n  *                 as well as the number of derivatives to compute are determined from this type.\n  *                 Typical choices include, e.g., \\c Vector4f for 4 derivatives, or \\c VectorXf\n  *                 if the number of derivatives is not known at compile time, and/or, the number\n  *                 of derivatives is large.\n  *                 Note that _DerType can also be a reference (e.g., \\c VectorXf&) to wrap a\n  *                 existing vector into an AutoDiffScalar.\n  *                 Finally, _DerType can also be any Eigen compatible expression.\n  *\n  * This class represents a scalar value while tracking its respective derivatives using Eigen's expression\n  * template mechanism.\n  *\n  * It supports the following list of global math function:\n  *  - std::abs, std::sqrt, std::pow, std::exp, std::log, std::sin, std::cos,\n  *  - internal::abs, internal::sqrt, numext::pow, internal::exp, internal::log, internal::sin, internal::cos,\n  *  - internal::conj, internal::real, internal::imag, numext::abs2.\n  *\n  * AutoDiffScalar can be used as the scalar type of an Eigen::Matrix object. However,\n  * in that case, the expression template mechanism only occurs at the top Matrix level,\n  * while derivatives are computed right away.\n  *\n  */\n\ntemplate<typename _DerType>\nclass AutoDiffScalar\n  : public internal::auto_diff_special_op\n            <_DerType, !internal::is_same<typename internal::traits<typename internal::remove_all<_DerType>::type>::Scalar,\n                                          typename NumTraits<typename internal::traits<typename internal::remove_all<_DerType>::type>::Scalar>::Real>::value>\n{\n  public:\n    typedef internal::auto_diff_special_op\n            <_DerType, !internal::is_same<typename internal::traits<typename internal::remove_all<_DerType>::type>::Scalar,\n                       typename NumTraits<typename internal::traits<typename internal::remove_all<_DerType>::type>::Scalar>::Real>::value> Base;\n    typedef typename internal::remove_all<_DerType>::type DerType;\n    typedef typename internal::traits<DerType>::Scalar Scalar;\n    typedef typename NumTraits<Scalar>::Real Real;\n\n    using Base::operator+;\n    using Base::operator*;\n\n    /** Default constructor without any initialization. */\n    AutoDiffScalar() {}\n\n    /** Constructs an active scalar from its \\a value,\n        and initializes the \\a nbDer derivatives such that it corresponds to the \\a derNumber -th variable */\n    AutoDiffScalar(const Scalar& value, int nbDer, int derNumber)\n      : m_value(value), m_derivatives(DerType::Zero(nbDer))\n    {\n      m_derivatives.coeffRef(derNumber) = Scalar(1);\n    }\n\n    /** Conversion from a scalar constant to an active scalar.\n      * The derivatives are set to zero. */\n    /*explicit*/ AutoDiffScalar(const Real& value)\n      : m_value(value)\n    {\n      if(m_derivatives.size()>0)\n        m_derivatives.setZero();\n    }\n\n    /** Constructs an active scalar from its \\a value and derivatives \\a der */\n    AutoDiffScalar(const Scalar& value, const DerType& der)\n      : m_value(value), m_derivatives(der)\n    {}\n\n    template<typename OtherDerType>\n    AutoDiffScalar(const AutoDiffScalar<OtherDerType>& other\n#ifndef EIGEN_PARSED_BY_DOXYGEN\n    , typename internal::enable_if<\n            internal::is_same<Scalar, typename internal::traits<typename internal::remove_all<OtherDerType>::type>::Scalar>::value\n        &&  internal::is_convertible<OtherDerType,DerType>::value , void*>::type = 0\n#endif\n    )\n      : m_value(other.value()), m_derivatives(other.derivatives())\n    {}\n\n    friend  std::ostream & operator << (std::ostream & s, const AutoDiffScalar& a)\n    {\n      return s << a.value();\n    }\n\n    AutoDiffScalar(const AutoDiffScalar& other)\n      : m_value(other.value()), m_derivatives(other.derivatives())\n    {}\n\n    template<typename OtherDerType>\n    inline AutoDiffScalar& operator=(const AutoDiffScalar<OtherDerType>& other)\n    {\n      m_value = other.value();\n      m_derivatives = other.derivatives();\n      return *this;\n    }\n\n    inline AutoDiffScalar& operator=(const AutoDiffScalar& other)\n    {\n      m_value = other.value();\n      m_derivatives = other.derivatives();\n      return *this;\n    }\n\n    inline AutoDiffScalar& operator=(const Scalar& other)\n    {\n      m_value = other;\n      if(m_derivatives.size()>0)\n        m_derivatives.setZero();\n      return *this;\n    }\n\n//     inline operator const Scalar& () const { return m_value; }\n//     inline operator Scalar& () { return m_value; }\n\n    inline const Scalar& value() const { return m_value; }\n    inline Scalar& value() { return m_value; }\n\n    inline const DerType& derivatives() const { return m_derivatives; }\n    inline DerType& derivatives() { return m_derivatives; }\n\n    inline bool operator< (const Scalar& other) const  { return m_value <  other; }\n    inline bool operator<=(const Scalar& other) const  { return m_value <= other; }\n    inline bool operator> (const Scalar& other) const  { return m_value >  other; }\n    inline bool operator>=(const Scalar& other) const  { return m_value >= other; }\n    inline bool operator==(const Scalar& other) const  { return m_value == other; }\n    inline bool operator!=(const Scalar& other) const  { return m_value != other; }\n\n    friend inline bool operator< (const Scalar& a, const AutoDiffScalar& b) { return a <  b.value(); }\n    friend inline bool operator<=(const Scalar& a, const AutoDiffScalar& b) { return a <= b.value(); }\n    friend inline bool operator> (const Scalar& a, const AutoDiffScalar& b) { return a >  b.value(); }\n    friend inline bool operator>=(const Scalar& a, const AutoDiffScalar& b) { return a >= b.value(); }\n    friend inline bool operator==(const Scalar& a, const AutoDiffScalar& b) { return a == b.value(); }\n    friend inline bool operator!=(const Scalar& a, const AutoDiffScalar& b) { return a != b.value(); }\n\n    template<typename OtherDerType> inline bool operator< (const AutoDiffScalar<OtherDerType>& b) const  { return m_value <  b.value(); }\n    template<typename OtherDerType> inline bool operator<=(const AutoDiffScalar<OtherDerType>& b) const  { return m_value <= b.value(); }\n    template<typename OtherDerType> inline bool operator> (const AutoDiffScalar<OtherDerType>& b) const  { return m_value >  b.value(); }\n    template<typename OtherDerType> inline bool operator>=(const AutoDiffScalar<OtherDerType>& b) const  { return m_value >= b.value(); }\n    template<typename OtherDerType> inline bool operator==(const AutoDiffScalar<OtherDerType>& b) const  { return m_value == b.value(); }\n    template<typename OtherDerType> inline bool operator!=(const AutoDiffScalar<OtherDerType>& b) const  { return m_value != b.value(); }\n\n    inline const AutoDiffScalar<DerType&> operator+(const Scalar& other) const\n    {\n      return AutoDiffScalar<DerType&>(m_value + other, m_derivatives);\n    }\n\n    friend inline const AutoDiffScalar<DerType&> operator+(const Scalar& a, const AutoDiffScalar& b)\n    {\n      return AutoDiffScalar<DerType&>(a + b.value(), b.derivatives());\n    }\n\n//     inline const AutoDiffScalar<DerType&> operator+(const Real& other) const\n//     {\n//       return AutoDiffScalar<DerType&>(m_value + other, m_derivatives);\n//     }\n\n//     friend inline const AutoDiffScalar<DerType&> operator+(const Real& a, const AutoDiffScalar& b)\n//     {\n//       return AutoDiffScalar<DerType&>(a + b.value(), b.derivatives());\n//     }\n\n    inline AutoDiffScalar& operator+=(const Scalar& other)\n    {\n      value() += other;\n      return *this;\n    }\n\n    template<typename OtherDerType>\n    inline const AutoDiffScalar<CwiseBinaryOp<internal::scalar_sum_op<Scalar>,const DerType,const typename internal::remove_all<OtherDerType>::type> >\n    operator+(const AutoDiffScalar<OtherDerType>& other) const\n    {\n      internal::make_coherent(m_derivatives, other.derivatives());\n      return AutoDiffScalar<CwiseBinaryOp<internal::scalar_sum_op<Scalar>,const DerType,const typename internal::remove_all<OtherDerType>::type> >(\n        m_value + other.value(),\n        m_derivatives + other.derivatives());\n    }\n\n    template<typename OtherDerType>\n    inline AutoDiffScalar&\n    operator+=(const AutoDiffScalar<OtherDerType>& other)\n    {\n      (*this) = (*this) + other;\n      return *this;\n    }\n\n    inline const AutoDiffScalar<DerType&> operator-(const Scalar& b) const\n    {\n      return AutoDiffScalar<DerType&>(m_value - b, m_derivatives);\n    }\n\n    friend inline const AutoDiffScalar<CwiseUnaryOp<internal::scalar_opposite_op<Scalar>, const DerType> >\n    operator-(const Scalar& a, const AutoDiffScalar& b)\n    {\n      return AutoDiffScalar<CwiseUnaryOp<internal::scalar_opposite_op<Scalar>, const DerType> >\n            (a - b.value(), -b.derivatives());\n    }\n\n    inline AutoDiffScalar& operator-=(const Scalar& other)\n    {\n      value() -= other;\n      return *this;\n    }\n\n    template<typename OtherDerType>\n    inline const AutoDiffScalar<CwiseBinaryOp<internal::scalar_difference_op<Scalar>, const DerType,const typename internal::remove_all<OtherDerType>::type> >\n    operator-(const AutoDiffScalar<OtherDerType>& other) const\n    {\n      internal::make_coherent(m_derivatives, other.derivatives());\n      return AutoDiffScalar<CwiseBinaryOp<internal::scalar_difference_op<Scalar>, const DerType,const typename internal::remove_all<OtherDerType>::type> >(\n        m_value - other.value(),\n        m_derivatives - other.derivatives());\n    }\n\n    template<typename OtherDerType>\n    inline AutoDiffScalar&\n    operator-=(const AutoDiffScalar<OtherDerType>& other)\n    {\n      *this = *this - other;\n      return *this;\n    }\n\n    inline const AutoDiffScalar<CwiseUnaryOp<internal::scalar_opposite_op<Scalar>, const DerType> >\n    operator-() const\n    {\n      return AutoDiffScalar<CwiseUnaryOp<internal::scalar_opposite_op<Scalar>, const DerType> >(\n        -m_value,\n        -m_derivatives);\n    }\n\n    inline const AutoDiffScalar<EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product) >\n    operator*(const Scalar& other) const\n    {\n      return MakeAutoDiffScalar(m_value * other, m_derivatives * other);\n    }\n\n    friend inline const AutoDiffScalar<EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product) >\n    operator*(const Scalar& other, const AutoDiffScalar& a)\n    {\n      return MakeAutoDiffScalar(a.value() * other, a.derivatives() * other);\n    }\n\n//     inline const AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type >\n//     operator*(const Real& other) const\n//     {\n//       return AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type >(\n//         m_value * other,\n//         (m_derivatives * other));\n//     }\n//\n//     friend inline const AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type >\n//     operator*(const Real& other, const AutoDiffScalar& a)\n//     {\n//       return AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type >(\n//         a.value() * other,\n//         a.derivatives() * other);\n//     }\n\n    inline const AutoDiffScalar<EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product) >\n    operator/(const Scalar& other) const\n    {\n      return MakeAutoDiffScalar(m_value / other, (m_derivatives * (Scalar(1)/other)));\n    }\n\n    friend inline const AutoDiffScalar<EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product) >\n    operator/(const Scalar& other, const AutoDiffScalar& a)\n    {\n      return MakeAutoDiffScalar(other / a.value(), a.derivatives() * (Scalar(-other) / (a.value()*a.value())));\n    }\n\n//     inline const AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type >\n//     operator/(const Real& other) const\n//     {\n//       return AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type >(\n//         m_value / other,\n//         (m_derivatives * (Real(1)/other)));\n//     }\n//\n//     friend inline const AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type >\n//     operator/(const Real& other, const AutoDiffScalar& a)\n//     {\n//       return AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type >(\n//         other / a.value(),\n//         a.derivatives() * (-Real(1)/other));\n//     }\n\n    template<typename OtherDerType>\n    inline const AutoDiffScalar<EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(\n        CwiseBinaryOp<internal::scalar_difference_op<Scalar> EIGEN_COMMA\n          const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product) EIGEN_COMMA\n          const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(typename internal::remove_all<OtherDerType>::type,Scalar,product) >,Scalar,product) >\n    operator/(const AutoDiffScalar<OtherDerType>& other) const\n    {\n      internal::make_coherent(m_derivatives, other.derivatives());\n      return MakeAutoDiffScalar(\n        m_value / other.value(),\n          ((m_derivatives * other.value()) - (other.derivatives() * m_value))\n        * (Scalar(1)/(other.value()*other.value())));\n    }\n\n    template<typename OtherDerType>\n    inline const AutoDiffScalar<CwiseBinaryOp<internal::scalar_sum_op<Scalar>,\n        const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product),\n        const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(typename internal::remove_all<OtherDerType>::type,Scalar,product) > >\n    operator*(const AutoDiffScalar<OtherDerType>& other) const\n    {\n      internal::make_coherent(m_derivatives, other.derivatives());\n      return MakeAutoDiffScalar(\n        m_value * other.value(),\n        (m_derivatives * other.value()) + (other.derivatives() * m_value));\n    }\n\n    inline AutoDiffScalar& operator*=(const Scalar& other)\n    {\n      *this = *this * other;\n      return *this;\n    }\n\n    template<typename OtherDerType>\n    inline AutoDiffScalar& operator*=(const AutoDiffScalar<OtherDerType>& other)\n    {\n      *this = *this * other;\n      return *this;\n    }\n\n    inline AutoDiffScalar& operator/=(const Scalar& other)\n    {\n      *this = *this / other;\n      return *this;\n    }\n\n    template<typename OtherDerType>\n    inline AutoDiffScalar& operator/=(const AutoDiffScalar<OtherDerType>& other)\n    {\n      *this = *this / other;\n      return *this;\n    }\n\n  protected:\n    Scalar m_value;\n    DerType m_derivatives;\n\n};\n\nnamespace internal {\n\ntemplate<typename _DerType>\nstruct auto_diff_special_op<_DerType, true>\n//   : auto_diff_scalar_op<_DerType, typename NumTraits<Scalar>::Real,\n//                            is_same<Scalar,typename NumTraits<Scalar>::Real>::value>\n{\n  typedef typename remove_all<_DerType>::type DerType;\n  typedef typename traits<DerType>::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real Real;\n\n//   typedef auto_diff_scalar_op<_DerType, typename NumTraits<Scalar>::Real,\n//                            is_same<Scalar,typename NumTraits<Scalar>::Real>::value> Base;\n\n//   using Base::operator+;\n//   using Base::operator+=;\n//   using Base::operator-;\n//   using Base::operator-=;\n//   using Base::operator*;\n//   using Base::operator*=;\n\n  const AutoDiffScalar<_DerType>& derived() const { return *static_cast<const AutoDiffScalar<_DerType>*>(this); }\n  AutoDiffScalar<_DerType>& derived() { return *static_cast<AutoDiffScalar<_DerType>*>(this); }\n\n\n  inline const AutoDiffScalar<DerType&> operator+(const Real& other) const\n  {\n    return AutoDiffScalar<DerType&>(derived().value() + other, derived().derivatives());\n  }\n\n  friend inline const AutoDiffScalar<DerType&> operator+(const Real& a, const AutoDiffScalar<_DerType>& b)\n  {\n    return AutoDiffScalar<DerType&>(a + b.value(), b.derivatives());\n  }\n\n  inline AutoDiffScalar<_DerType>& operator+=(const Real& other)\n  {\n    derived().value() += other;\n    return derived();\n  }\n\n\n  inline const AutoDiffScalar<typename CwiseUnaryOp<bind2nd_op<scalar_product_op<Scalar,Real> >, DerType>::Type >\n  operator*(const Real& other) const\n  {\n    return AutoDiffScalar<typename CwiseUnaryOp<bind2nd_op<scalar_product_op<Scalar,Real> >, DerType>::Type >(\n      derived().value() * other,\n      derived().derivatives() * other);\n  }\n\n  friend inline const AutoDiffScalar<typename CwiseUnaryOp<bind1st_op<scalar_product_op<Real,Scalar> >, DerType>::Type >\n  operator*(const Real& other, const AutoDiffScalar<_DerType>& a)\n  {\n    return AutoDiffScalar<typename CwiseUnaryOp<bind1st_op<scalar_product_op<Real,Scalar> >, DerType>::Type >(\n      a.value() * other,\n      a.derivatives() * other);\n  }\n\n  inline AutoDiffScalar<_DerType>& operator*=(const Scalar& other)\n  {\n    *this = *this * other;\n    return derived();\n  }\n};\n\ntemplate<typename _DerType>\nstruct auto_diff_special_op<_DerType, false>\n{\n  void operator*() const;\n  void operator-() const;\n  void operator+() const;\n};\n\ntemplate<typename A_Scalar, int A_Rows, int A_Cols, int A_Options, int A_MaxRows, int A_MaxCols, typename B>\nstruct make_coherent_impl<Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols>, B> {\n  typedef Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols> A;\n  static void run(A& a, B& b) {\n    if((A_Rows==Dynamic || A_Cols==Dynamic) && (a.size()==0))\n    {\n      a.resize(b.size());\n      a.setZero();\n    }\n  }\n};\n\ntemplate<typename A, typename B_Scalar, int B_Rows, int B_Cols, int B_Options, int B_MaxRows, int B_MaxCols>\nstruct make_coherent_impl<A, Matrix<B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols> > {\n  typedef Matrix<B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols> B;\n  static void run(A& a, B& b) {\n    if((B_Rows==Dynamic || B_Cols==Dynamic) && (b.size()==0))\n    {\n      b.resize(a.size());\n      b.setZero();\n    }\n  }\n};\n\ntemplate<typename A_Scalar, int A_Rows, int A_Cols, int A_Options, int A_MaxRows, int A_MaxCols,\n         typename B_Scalar, int B_Rows, int B_Cols, int B_Options, int B_MaxRows, int B_MaxCols>\nstruct make_coherent_impl<Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols>,\n                             Matrix<B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols> > {\n  typedef Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols> A;\n  typedef Matrix<B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols> B;\n  static void run(A& a, B& b) {\n    if((A_Rows==Dynamic || A_Cols==Dynamic) && (a.size()==0))\n    {\n      a.resize(b.size());\n      a.setZero();\n    }\n    else if((B_Rows==Dynamic || B_Cols==Dynamic) && (b.size()==0))\n    {\n      b.resize(a.size());\n      b.setZero();\n    }\n  }\n};\n\n} // end namespace internal\n\ntemplate<typename DerType, typename BinOp>\nstruct ScalarBinaryOpTraits<AutoDiffScalar<DerType>,typename DerType::Scalar,BinOp>\n{\n  typedef AutoDiffScalar<DerType> ReturnType;\n};\n\ntemplate<typename DerType, typename BinOp>\nstruct ScalarBinaryOpTraits<typename DerType::Scalar,AutoDiffScalar<DerType>, BinOp>\n{\n  typedef AutoDiffScalar<DerType> ReturnType;\n};\n\n\n// The following is an attempt to let Eigen's known about expression template, but that's more tricky!\n\n// template<typename DerType, typename BinOp>\n// struct ScalarBinaryOpTraits<AutoDiffScalar<DerType>,AutoDiffScalar<DerType>, BinOp>\n// {\n//   enum { Defined = 1 };\n//   typedef AutoDiffScalar<typename DerType::PlainObject> ReturnType;\n// };\n//\n// template<typename DerType1,typename DerType2, typename BinOp>\n// struct ScalarBinaryOpTraits<AutoDiffScalar<DerType1>,AutoDiffScalar<DerType2>, BinOp>\n// {\n//   enum { Defined = 1 };//internal::is_same<typename DerType1::Scalar,typename DerType2::Scalar>::value };\n//   typedef AutoDiffScalar<typename DerType1::PlainObject> ReturnType;\n// };\n\n#define EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(FUNC,CODE) \\\n  template<typename DerType> \\\n  inline const Eigen::AutoDiffScalar< \\\n  EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(typename Eigen::internal::remove_all<DerType>::type, typename Eigen::internal::traits<typename Eigen::internal::remove_all<DerType>::type>::Scalar, product) > \\\n  FUNC(const Eigen::AutoDiffScalar<DerType>& x) { \\\n    using namespace Eigen; \\\n    EIGEN_UNUSED typedef typename Eigen::internal::traits<typename Eigen::internal::remove_all<DerType>::type>::Scalar Scalar; \\\n    CODE; \\\n  }\n\ntemplate<typename DerType>\ninline const AutoDiffScalar<DerType>& conj(const AutoDiffScalar<DerType>& x)  { return x; }\ntemplate<typename DerType>\ninline const AutoDiffScalar<DerType>& real(const AutoDiffScalar<DerType>& x)  { return x; }\ntemplate<typename DerType>\ninline typename DerType::Scalar imag(const AutoDiffScalar<DerType>&)    { return 0.; }\ntemplate<typename DerType, typename T>\ninline AutoDiffScalar<typename Eigen::internal::remove_all<DerType>::type::PlainObject> (min)(const AutoDiffScalar<DerType>& x, const T& y) {\n  typedef AutoDiffScalar<typename Eigen::internal::remove_all<DerType>::type::PlainObject> ADS;\n  return (x <= y ? ADS(x) : ADS(y));\n}\ntemplate<typename DerType, typename T>\ninline AutoDiffScalar<typename Eigen::internal::remove_all<DerType>::type::PlainObject> (max)(const AutoDiffScalar<DerType>& x, const T& y) {\n  typedef AutoDiffScalar<typename Eigen::internal::remove_all<DerType>::type::PlainObject> ADS;\n  return (x >= y ? ADS(x) : ADS(y));\n}\ntemplate<typename DerType, typename T>\ninline AutoDiffScalar<typename Eigen::internal::remove_all<DerType>::type::PlainObject> (min)(const T& x, const AutoDiffScalar<DerType>& y) {\n  typedef AutoDiffScalar<typename Eigen::internal::remove_all<DerType>::type::PlainObject> ADS;\n  return (x < y ? ADS(x) : ADS(y));\n}\ntemplate<typename DerType, typename T>\ninline AutoDiffScalar<typename Eigen::internal::remove_all<DerType>::type::PlainObject> (max)(const T& x, const AutoDiffScalar<DerType>& y) {\n  typedef AutoDiffScalar<typename Eigen::internal::remove_all<DerType>::type::PlainObject> ADS;\n  return (x > y ? ADS(x) : ADS(y));\n}\ntemplate<typename DerType>\ninline AutoDiffScalar<typename Eigen::internal::remove_all<DerType>::type::PlainObject> (min)(const AutoDiffScalar<DerType>& x, const AutoDiffScalar<DerType>& y) {\n  return (x.value() < y.value() ? x : y);\n}\ntemplate<typename DerType>\ninline AutoDiffScalar<typename Eigen::internal::remove_all<DerType>::type::PlainObject> (max)(const AutoDiffScalar<DerType>& x, const AutoDiffScalar<DerType>& y) {\n  return (x.value() >= y.value() ? x : y);\n}\n\n\nEIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(abs,\n  using std::abs;\n  return Eigen::MakeAutoDiffScalar(abs(x.value()), x.derivatives() * (x.value()<0 ? -1 : 1) );)\n\nEIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(abs2,\n  using numext::abs2;\n  return Eigen::MakeAutoDiffScalar(abs2(x.value()), x.derivatives() * (Scalar(2)*x.value()));)\n\nEIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(sqrt,\n  using std::sqrt;\n  Scalar sqrtx = sqrt(x.value());\n  return Eigen::MakeAutoDiffScalar(sqrtx,x.derivatives() * (Scalar(0.5) / sqrtx));)\n\nEIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(cos,\n  using std::cos;\n  using std::sin;\n  return Eigen::MakeAutoDiffScalar(cos(x.value()), x.derivatives() * (-sin(x.value())));)\n\nEIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(sin,\n  using std::sin;\n  using std::cos;\n  return Eigen::MakeAutoDiffScalar(sin(x.value()),x.derivatives() * cos(x.value()));)\n\nEIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(exp,\n  using std::exp;\n  Scalar expx = exp(x.value());\n  return Eigen::MakeAutoDiffScalar(expx,x.derivatives() * expx);)\n\nEIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(log,\n  using std::log;\n  return Eigen::MakeAutoDiffScalar(log(x.value()),x.derivatives() * (Scalar(1)/x.value()));)\n\ntemplate<typename DerType>\ninline const Eigen::AutoDiffScalar<\nEIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(typename internal::remove_all<DerType>::type,typename internal::traits<typename internal::remove_all<DerType>::type>::Scalar,product) >\npow(const Eigen::AutoDiffScalar<DerType> &x, const typename internal::traits<typename internal::remove_all<DerType>::type>::Scalar &y)\n{\n  using namespace Eigen;\n  using std::pow;\n  return Eigen::MakeAutoDiffScalar(pow(x.value(),y), x.derivatives() * (y * pow(x.value(),y-1)));\n}\n\n\ntemplate<typename DerTypeA,typename DerTypeB>\ninline const AutoDiffScalar<Matrix<typename internal::traits<typename internal::remove_all<DerTypeA>::type>::Scalar,Dynamic,1> >\natan2(const AutoDiffScalar<DerTypeA>& a, const AutoDiffScalar<DerTypeB>& b)\n{\n  using std::atan2;\n  typedef typename internal::traits<typename internal::remove_all<DerTypeA>::type>::Scalar Scalar;\n  typedef AutoDiffScalar<Matrix<Scalar,Dynamic,1> > PlainADS;\n  PlainADS ret;\n  ret.value() = atan2(a.value(), b.value());\n  \n  Scalar squared_hypot = a.value() * a.value() + b.value() * b.value();\n  \n  // if (squared_hypot==0) the derivation is undefined and the following results in a NaN:\n  ret.derivatives() = (a.derivatives() * b.value() - a.value() * b.derivatives()) / squared_hypot;\n\n  return ret;\n}\n\nEIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(tan,\n  using std::tan;\n  using std::cos;\n  return Eigen::MakeAutoDiffScalar(tan(x.value()),x.derivatives() * (Scalar(1)/numext::abs2(cos(x.value()))));)\n\nEIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(asin,\n  using std::sqrt;\n  using std::asin;\n  return Eigen::MakeAutoDiffScalar(asin(x.value()),x.derivatives() * (Scalar(1)/sqrt(1-numext::abs2(x.value()))));)\n  \nEIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(acos,\n  using std::sqrt;\n  using std::acos;\n  return Eigen::MakeAutoDiffScalar(acos(x.value()),x.derivatives() * (Scalar(-1)/sqrt(1-numext::abs2(x.value()))));)\n\nEIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(tanh,\n  using std::cosh;\n  using std::tanh;\n  return Eigen::MakeAutoDiffScalar(tanh(x.value()),x.derivatives() * (Scalar(1)/numext::abs2(cosh(x.value()))));)\n\nEIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(sinh,\n  using std::sinh;\n  using std::cosh;\n  return Eigen::MakeAutoDiffScalar(sinh(x.value()),x.derivatives() * cosh(x.value()));)\n\nEIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(cosh,\n  using std::sinh;\n  using std::cosh;\n  return Eigen::MakeAutoDiffScalar(cosh(x.value()),x.derivatives() * sinh(x.value()));)\n\n#undef EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY\n\ntemplate<typename DerType> struct NumTraits<AutoDiffScalar<DerType> >\n  : NumTraits< typename NumTraits<typename internal::remove_all<DerType>::type::Scalar>::Real >\n{\n  typedef typename internal::remove_all<DerType>::type DerTypeCleaned;\n  typedef AutoDiffScalar<Matrix<typename NumTraits<typename DerTypeCleaned::Scalar>::Real,DerTypeCleaned::RowsAtCompileTime,DerTypeCleaned::ColsAtCompileTime,\n                                0, DerTypeCleaned::MaxRowsAtCompileTime, DerTypeCleaned::MaxColsAtCompileTime> > Real;\n  typedef AutoDiffScalar<DerType> NonInteger;\n  typedef AutoDiffScalar<DerType> Nested;\n  typedef typename NumTraits<typename DerTypeCleaned::Scalar>::Literal Literal;\n  enum{\n    RequireInitialization = 1\n  };\n};\n\n}\n\nnamespace std {\ntemplate <typename T>\nclass numeric_limits<Eigen::AutoDiffScalar<T> >\n  : public numeric_limits<typename T::Scalar> {};\n\n}  // namespace std\n\n#endif // EIGEN_AUTODIFF_SCALAR_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/AutoDiff/AutoDiffVector.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_AUTODIFF_VECTOR_H\n#define EIGEN_AUTODIFF_VECTOR_H\n\nnamespace Eigen {\n\n/* \\class AutoDiffScalar\n  * \\brief A scalar type replacement with automatic differentation capability\n  *\n  * \\param DerType the vector type used to store/represent the derivatives (e.g. Vector3f)\n  *\n  * This class represents a scalar value while tracking its respective derivatives.\n  *\n  * It supports the following list of global math function:\n  *  - std::abs, std::sqrt, std::pow, std::exp, std::log, std::sin, std::cos,\n  *  - internal::abs, internal::sqrt, numext::pow, internal::exp, internal::log, internal::sin, internal::cos,\n  *  - internal::conj, internal::real, internal::imag, numext::abs2.\n  *\n  * AutoDiffScalar can be used as the scalar type of an Eigen::Matrix object. However,\n  * in that case, the expression template mechanism only occurs at the top Matrix level,\n  * while derivatives are computed right away.\n  *\n  */\ntemplate<typename ValueType, typename JacobianType>\nclass AutoDiffVector\n{\n  public:\n    //typedef typename internal::traits<ValueType>::Scalar Scalar;\n    typedef typename internal::traits<ValueType>::Scalar BaseScalar;\n    typedef AutoDiffScalar<Matrix<BaseScalar,JacobianType::RowsAtCompileTime,1> > ActiveScalar;\n    typedef ActiveScalar Scalar;\n    typedef AutoDiffScalar<typename JacobianType::ColXpr> CoeffType;\n    typedef typename JacobianType::Index Index;\n\n    inline AutoDiffVector() {}\n\n    inline AutoDiffVector(const ValueType& values)\n      : m_values(values)\n    {\n      m_jacobian.setZero();\n    }\n\n\n    CoeffType operator[] (Index i) { return CoeffType(m_values[i], m_jacobian.col(i)); }\n    const CoeffType operator[] (Index i) const { return CoeffType(m_values[i], m_jacobian.col(i)); }\n\n    CoeffType operator() (Index i) { return CoeffType(m_values[i], m_jacobian.col(i)); }\n    const CoeffType operator() (Index i) const { return CoeffType(m_values[i], m_jacobian.col(i)); }\n\n    CoeffType coeffRef(Index i) { return CoeffType(m_values[i], m_jacobian.col(i)); }\n    const CoeffType coeffRef(Index i) const { return CoeffType(m_values[i], m_jacobian.col(i)); }\n\n    Index size() const { return m_values.size(); }\n\n    // FIXME here we could return an expression of the sum\n    Scalar sum() const { /*std::cerr << \"sum \\n\\n\";*/ /*std::cerr << m_jacobian.rowwise().sum() << \"\\n\\n\";*/ return Scalar(m_values.sum(), m_jacobian.rowwise().sum()); }\n\n\n    inline AutoDiffVector(const ValueType& values, const JacobianType& jac)\n      : m_values(values), m_jacobian(jac)\n    {}\n\n    template<typename OtherValueType, typename OtherJacobianType>\n    inline AutoDiffVector(const AutoDiffVector<OtherValueType, OtherJacobianType>& other)\n      : m_values(other.values()), m_jacobian(other.jacobian())\n    {}\n\n    inline AutoDiffVector(const AutoDiffVector& other)\n      : m_values(other.values()), m_jacobian(other.jacobian())\n    {}\n\n    template<typename OtherValueType, typename OtherJacobianType>\n    inline AutoDiffVector& operator=(const AutoDiffVector<OtherValueType, OtherJacobianType>& other)\n    {\n      m_values = other.values();\n      m_jacobian = other.jacobian();\n      return *this;\n    }\n\n    inline AutoDiffVector& operator=(const AutoDiffVector& other)\n    {\n      m_values = other.values();\n      m_jacobian = other.jacobian();\n      return *this;\n    }\n\n    inline const ValueType& values() const { return m_values; }\n    inline ValueType& values() { return m_values; }\n\n    inline const JacobianType& jacobian() const { return m_jacobian; }\n    inline JacobianType& jacobian() { return m_jacobian; }\n\n    template<typename OtherValueType,typename OtherJacobianType>\n    inline const AutoDiffVector<\n      typename MakeCwiseBinaryOp<internal::scalar_sum_op<BaseScalar>,ValueType,OtherValueType>::Type,\n      typename MakeCwiseBinaryOp<internal::scalar_sum_op<BaseScalar>,JacobianType,OtherJacobianType>::Type >\n    operator+(const AutoDiffVector<OtherValueType,OtherJacobianType>& other) const\n    {\n      return AutoDiffVector<\n      typename MakeCwiseBinaryOp<internal::scalar_sum_op<BaseScalar>,ValueType,OtherValueType>::Type,\n      typename MakeCwiseBinaryOp<internal::scalar_sum_op<BaseScalar>,JacobianType,OtherJacobianType>::Type >(\n        m_values + other.values(),\n        m_jacobian + other.jacobian());\n    }\n\n    template<typename OtherValueType, typename OtherJacobianType>\n    inline AutoDiffVector&\n    operator+=(const AutoDiffVector<OtherValueType,OtherJacobianType>& other)\n    {\n      m_values += other.values();\n      m_jacobian += other.jacobian();\n      return *this;\n    }\n\n    template<typename OtherValueType,typename OtherJacobianType>\n    inline const AutoDiffVector<\n      typename MakeCwiseBinaryOp<internal::scalar_difference_op<Scalar>,ValueType,OtherValueType>::Type,\n      typename MakeCwiseBinaryOp<internal::scalar_difference_op<Scalar>,JacobianType,OtherJacobianType>::Type >\n    operator-(const AutoDiffVector<OtherValueType,OtherJacobianType>& other) const\n    {\n      return AutoDiffVector<\n        typename MakeCwiseBinaryOp<internal::scalar_difference_op<Scalar>,ValueType,OtherValueType>::Type,\n        typename MakeCwiseBinaryOp<internal::scalar_difference_op<Scalar>,JacobianType,OtherJacobianType>::Type >(\n          m_values - other.values(),\n          m_jacobian - other.jacobian());\n    }\n\n    template<typename OtherValueType, typename OtherJacobianType>\n    inline AutoDiffVector&\n    operator-=(const AutoDiffVector<OtherValueType,OtherJacobianType>& other)\n    {\n      m_values -= other.values();\n      m_jacobian -= other.jacobian();\n      return *this;\n    }\n\n    inline const AutoDiffVector<\n      typename MakeCwiseUnaryOp<internal::scalar_opposite_op<Scalar>, ValueType>::Type,\n      typename MakeCwiseUnaryOp<internal::scalar_opposite_op<Scalar>, JacobianType>::Type >\n    operator-() const\n    {\n      return AutoDiffVector<\n        typename MakeCwiseUnaryOp<internal::scalar_opposite_op<Scalar>, ValueType>::Type,\n        typename MakeCwiseUnaryOp<internal::scalar_opposite_op<Scalar>, JacobianType>::Type >(\n          -m_values,\n          -m_jacobian);\n    }\n\n    inline const AutoDiffVector<\n      typename MakeCwiseUnaryOp<internal::scalar_multiple_op<Scalar>, ValueType>::Type,\n      typename MakeCwiseUnaryOp<internal::scalar_multiple_op<Scalar>, JacobianType>::Type>\n    operator*(const BaseScalar& other) const\n    {\n      return AutoDiffVector<\n        typename MakeCwiseUnaryOp<internal::scalar_multiple_op<Scalar>, ValueType>::Type,\n        typename MakeCwiseUnaryOp<internal::scalar_multiple_op<Scalar>, JacobianType>::Type >(\n          m_values * other,\n          m_jacobian * other);\n    }\n\n    friend inline const AutoDiffVector<\n      typename MakeCwiseUnaryOp<internal::scalar_multiple_op<Scalar>, ValueType>::Type,\n      typename MakeCwiseUnaryOp<internal::scalar_multiple_op<Scalar>, JacobianType>::Type >\n    operator*(const Scalar& other, const AutoDiffVector& v)\n    {\n      return AutoDiffVector<\n        typename MakeCwiseUnaryOp<internal::scalar_multiple_op<Scalar>, ValueType>::Type,\n        typename MakeCwiseUnaryOp<internal::scalar_multiple_op<Scalar>, JacobianType>::Type >(\n          v.values() * other,\n          v.jacobian() * other);\n    }\n\n//     template<typename OtherValueType,typename OtherJacobianType>\n//     inline const AutoDiffVector<\n//       CwiseBinaryOp<internal::scalar_multiple_op<Scalar>, ValueType, OtherValueType>\n//       CwiseBinaryOp<internal::scalar_sum_op<Scalar>,\n//         CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, JacobianType>,\n//         CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, OtherJacobianType> > >\n//     operator*(const AutoDiffVector<OtherValueType,OtherJacobianType>& other) const\n//     {\n//       return AutoDiffVector<\n//         CwiseBinaryOp<internal::scalar_multiple_op<Scalar>, ValueType, OtherValueType>\n//         CwiseBinaryOp<internal::scalar_sum_op<Scalar>,\n//           CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, JacobianType>,\n//           CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, OtherJacobianType> > >(\n//             m_values.cwise() * other.values(),\n//             (m_jacobian * other.values()) + (m_values * other.jacobian()));\n//     }\n\n    inline AutoDiffVector& operator*=(const Scalar& other)\n    {\n      m_values *= other;\n      m_jacobian *= other;\n      return *this;\n    }\n\n    template<typename OtherValueType,typename OtherJacobianType>\n    inline AutoDiffVector& operator*=(const AutoDiffVector<OtherValueType,OtherJacobianType>& other)\n    {\n      *this = *this * other;\n      return *this;\n    }\n\n  protected:\n    ValueType m_values;\n    JacobianType m_jacobian;\n\n};\n\n}\n\n#endif // EIGEN_AUTODIFF_VECTOR_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/BVH/BVAlgorithms.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Ilya Baran <ibaran@mit.edu>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_BVALGORITHMS_H\n#define EIGEN_BVALGORITHMS_H\n\nnamespace Eigen { \n\nnamespace internal {\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\ntemplate<typename BVH, typename Intersector>\nbool intersect_helper(const BVH &tree, Intersector &intersector, typename BVH::Index root)\n{\n  typedef typename BVH::Index Index;\n  typedef typename BVH::VolumeIterator VolIter;\n  typedef typename BVH::ObjectIterator ObjIter;\n\n  VolIter vBegin = VolIter(), vEnd = VolIter();\n  ObjIter oBegin = ObjIter(), oEnd = ObjIter();\n\n  std::vector<Index> todo(1, root);\n\n  while(!todo.empty()) {\n    tree.getChildren(todo.back(), vBegin, vEnd, oBegin, oEnd);\n    todo.pop_back();\n\n    for(; vBegin != vEnd; ++vBegin) //go through child volumes\n      if(intersector.intersectVolume(tree.getVolume(*vBegin)))\n        todo.push_back(*vBegin);\n\n    for(; oBegin != oEnd; ++oBegin) //go through child objects\n      if(intersector.intersectObject(*oBegin))\n        return true; //intersector said to stop query\n  }\n  return false;\n}\n#endif //not EIGEN_PARSED_BY_DOXYGEN\n\ntemplate<typename Volume1, typename Object1, typename Object2, typename Intersector>\nstruct intersector_helper1\n{\n  intersector_helper1(const Object2 &inStored, Intersector &in) : stored(inStored), intersector(in) {}\n  bool intersectVolume(const Volume1 &vol) { return intersector.intersectVolumeObject(vol, stored); }\n  bool intersectObject(const Object1 &obj) { return intersector.intersectObjectObject(obj, stored); }\n  Object2 stored;\n  Intersector &intersector;\nprivate:\n  intersector_helper1& operator=(const intersector_helper1&);\n};\n\ntemplate<typename Volume2, typename Object2, typename Object1, typename Intersector>\nstruct intersector_helper2\n{\n  intersector_helper2(const Object1 &inStored, Intersector &in) : stored(inStored), intersector(in) {}\n  bool intersectVolume(const Volume2 &vol) { return intersector.intersectObjectVolume(stored, vol); }\n  bool intersectObject(const Object2 &obj) { return intersector.intersectObjectObject(stored, obj); }\n  Object1 stored;\n  Intersector &intersector;\nprivate:\n  intersector_helper2& operator=(const intersector_helper2&);\n};\n\n} // end namespace internal\n\n/**  Given a BVH, runs the query encapsulated by \\a intersector.\n  *  The Intersector type must provide the following members: \\code\n     bool intersectVolume(const BVH::Volume &volume) //returns true if volume intersects the query\n     bool intersectObject(const BVH::Object &object) //returns true if the search should terminate immediately\n  \\endcode\n  */\ntemplate<typename BVH, typename Intersector>\nvoid BVIntersect(const BVH &tree, Intersector &intersector)\n{\n  internal::intersect_helper(tree, intersector, tree.getRootIndex());\n}\n\n/**  Given two BVH's, runs the query on their Cartesian product encapsulated by \\a intersector.\n  *  The Intersector type must provide the following members: \\code\n     bool intersectVolumeVolume(const BVH1::Volume &v1, const BVH2::Volume &v2) //returns true if product of volumes intersects the query\n     bool intersectVolumeObject(const BVH1::Volume &v1, const BVH2::Object &o2) //returns true if the volume-object product intersects the query\n     bool intersectObjectVolume(const BVH1::Object &o1, const BVH2::Volume &v2) //returns true if the volume-object product intersects the query\n     bool intersectObjectObject(const BVH1::Object &o1, const BVH2::Object &o2) //returns true if the search should terminate immediately\n  \\endcode\n  */\ntemplate<typename BVH1, typename BVH2, typename Intersector>\nvoid BVIntersect(const BVH1 &tree1, const BVH2 &tree2, Intersector &intersector) //TODO: tandem descent when it makes sense\n{\n  typedef typename BVH1::Index Index1;\n  typedef typename BVH2::Index Index2;\n  typedef internal::intersector_helper1<typename BVH1::Volume, typename BVH1::Object, typename BVH2::Object, Intersector> Helper1;\n  typedef internal::intersector_helper2<typename BVH2::Volume, typename BVH2::Object, typename BVH1::Object, Intersector> Helper2;\n  typedef typename BVH1::VolumeIterator VolIter1;\n  typedef typename BVH1::ObjectIterator ObjIter1;\n  typedef typename BVH2::VolumeIterator VolIter2;\n  typedef typename BVH2::ObjectIterator ObjIter2;\n\n  VolIter1 vBegin1 = VolIter1(), vEnd1 = VolIter1();\n  ObjIter1 oBegin1 = ObjIter1(), oEnd1 = ObjIter1();\n  VolIter2 vBegin2 = VolIter2(), vEnd2 = VolIter2(), vCur2 = VolIter2();\n  ObjIter2 oBegin2 = ObjIter2(), oEnd2 = ObjIter2(), oCur2 = ObjIter2();\n\n  std::vector<std::pair<Index1, Index2> > todo(1, std::make_pair(tree1.getRootIndex(), tree2.getRootIndex()));\n\n  while(!todo.empty()) {\n    tree1.getChildren(todo.back().first, vBegin1, vEnd1, oBegin1, oEnd1);\n    tree2.getChildren(todo.back().second, vBegin2, vEnd2, oBegin2, oEnd2);\n    todo.pop_back();\n\n    for(; vBegin1 != vEnd1; ++vBegin1) { //go through child volumes of first tree\n      const typename BVH1::Volume &vol1 = tree1.getVolume(*vBegin1);\n      for(vCur2 = vBegin2; vCur2 != vEnd2; ++vCur2) { //go through child volumes of second tree\n        if(intersector.intersectVolumeVolume(vol1, tree2.getVolume(*vCur2)))\n          todo.push_back(std::make_pair(*vBegin1, *vCur2));\n      }\n\n      for(oCur2 = oBegin2; oCur2 != oEnd2; ++oCur2) {//go through child objects of second tree\n        Helper1 helper(*oCur2, intersector);\n        if(internal::intersect_helper(tree1, helper, *vBegin1))\n          return; //intersector said to stop query\n      }\n    }\n\n    for(; oBegin1 != oEnd1; ++oBegin1) { //go through child objects of first tree\n      for(vCur2 = vBegin2; vCur2 != vEnd2; ++vCur2) { //go through child volumes of second tree\n        Helper2 helper(*oBegin1, intersector);\n        if(internal::intersect_helper(tree2, helper, *vCur2))\n          return; //intersector said to stop query\n      }\n\n      for(oCur2 = oBegin2; oCur2 != oEnd2; ++oCur2) {//go through child objects of second tree\n        if(intersector.intersectObjectObject(*oBegin1, *oCur2))\n          return; //intersector said to stop query\n      }\n    }\n  }\n}\n\nnamespace internal {\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\ntemplate<typename BVH, typename Minimizer>\ntypename Minimizer::Scalar minimize_helper(const BVH &tree, Minimizer &minimizer, typename BVH::Index root, typename Minimizer::Scalar minimum)\n{\n  typedef typename Minimizer::Scalar Scalar;\n  typedef typename BVH::Index Index;\n  typedef std::pair<Scalar, Index> QueueElement; //first element is priority\n  typedef typename BVH::VolumeIterator VolIter;\n  typedef typename BVH::ObjectIterator ObjIter;\n\n  VolIter vBegin = VolIter(), vEnd = VolIter();\n  ObjIter oBegin = ObjIter(), oEnd = ObjIter();\n  std::priority_queue<QueueElement, std::vector<QueueElement>, std::greater<QueueElement> > todo; //smallest is at the top\n\n  todo.push(std::make_pair(Scalar(), root));\n\n  while(!todo.empty()) {\n    tree.getChildren(todo.top().second, vBegin, vEnd, oBegin, oEnd);\n    todo.pop();\n\n    for(; oBegin != oEnd; ++oBegin) //go through child objects\n      minimum = (std::min)(minimum, minimizer.minimumOnObject(*oBegin));\n\n    for(; vBegin != vEnd; ++vBegin) { //go through child volumes\n      Scalar val = minimizer.minimumOnVolume(tree.getVolume(*vBegin));\n      if(val < minimum)\n        todo.push(std::make_pair(val, *vBegin));\n    }\n  }\n\n  return minimum;\n}\n#endif //not EIGEN_PARSED_BY_DOXYGEN\n\n\ntemplate<typename Volume1, typename Object1, typename Object2, typename Minimizer>\nstruct minimizer_helper1\n{\n  typedef typename Minimizer::Scalar Scalar;\n  minimizer_helper1(const Object2 &inStored, Minimizer &m) : stored(inStored), minimizer(m) {}\n  Scalar minimumOnVolume(const Volume1 &vol) { return minimizer.minimumOnVolumeObject(vol, stored); }\n  Scalar minimumOnObject(const Object1 &obj) { return minimizer.minimumOnObjectObject(obj, stored); }\n  Object2 stored;\n  Minimizer &minimizer;\nprivate:\n  minimizer_helper1& operator=(const minimizer_helper1&);\n};\n\ntemplate<typename Volume2, typename Object2, typename Object1, typename Minimizer>\nstruct minimizer_helper2\n{\n  typedef typename Minimizer::Scalar Scalar;\n  minimizer_helper2(const Object1 &inStored, Minimizer &m) : stored(inStored), minimizer(m) {}\n  Scalar minimumOnVolume(const Volume2 &vol) { return minimizer.minimumOnObjectVolume(stored, vol); }\n  Scalar minimumOnObject(const Object2 &obj) { return minimizer.minimumOnObjectObject(stored, obj); }\n  Object1 stored;\n  Minimizer &minimizer;\nprivate:\n  minimizer_helper2& operator=(const minimizer_helper2&);\n};\n\n} // end namespace internal\n\n/**  Given a BVH, runs the query encapsulated by \\a minimizer.\n  *  \\returns the minimum value.\n  *  The Minimizer type must provide the following members: \\code\n     typedef Scalar //the numeric type of what is being minimized--not necessarily the Scalar type of the BVH (if it has one)\n     Scalar minimumOnVolume(const BVH::Volume &volume)\n     Scalar minimumOnObject(const BVH::Object &object)\n  \\endcode\n  */\ntemplate<typename BVH, typename Minimizer>\ntypename Minimizer::Scalar BVMinimize(const BVH &tree, Minimizer &minimizer)\n{\n  return internal::minimize_helper(tree, minimizer, tree.getRootIndex(), (std::numeric_limits<typename Minimizer::Scalar>::max)());\n}\n\n/**  Given two BVH's, runs the query on their cartesian product encapsulated by \\a minimizer.\n  *  \\returns the minimum value.\n  *  The Minimizer type must provide the following members: \\code\n     typedef Scalar //the numeric type of what is being minimized--not necessarily the Scalar type of the BVH (if it has one)\n     Scalar minimumOnVolumeVolume(const BVH1::Volume &v1, const BVH2::Volume &v2)\n     Scalar minimumOnVolumeObject(const BVH1::Volume &v1, const BVH2::Object &o2)\n     Scalar minimumOnObjectVolume(const BVH1::Object &o1, const BVH2::Volume &v2)\n     Scalar minimumOnObjectObject(const BVH1::Object &o1, const BVH2::Object &o2)\n  \\endcode\n  */\ntemplate<typename BVH1, typename BVH2, typename Minimizer>\ntypename Minimizer::Scalar BVMinimize(const BVH1 &tree1, const BVH2 &tree2, Minimizer &minimizer)\n{\n  typedef typename Minimizer::Scalar Scalar;\n  typedef typename BVH1::Index Index1;\n  typedef typename BVH2::Index Index2;\n  typedef internal::minimizer_helper1<typename BVH1::Volume, typename BVH1::Object, typename BVH2::Object, Minimizer> Helper1;\n  typedef internal::minimizer_helper2<typename BVH2::Volume, typename BVH2::Object, typename BVH1::Object, Minimizer> Helper2;\n  typedef std::pair<Scalar, std::pair<Index1, Index2> > QueueElement; //first element is priority\n  typedef typename BVH1::VolumeIterator VolIter1;\n  typedef typename BVH1::ObjectIterator ObjIter1;\n  typedef typename BVH2::VolumeIterator VolIter2;\n  typedef typename BVH2::ObjectIterator ObjIter2;\n\n  VolIter1 vBegin1 = VolIter1(), vEnd1 = VolIter1();\n  ObjIter1 oBegin1 = ObjIter1(), oEnd1 = ObjIter1();\n  VolIter2 vBegin2 = VolIter2(), vEnd2 = VolIter2(), vCur2 = VolIter2();\n  ObjIter2 oBegin2 = ObjIter2(), oEnd2 = ObjIter2(), oCur2 = ObjIter2();\n  std::priority_queue<QueueElement, std::vector<QueueElement>, std::greater<QueueElement> > todo; //smallest is at the top\n\n  Scalar minimum = (std::numeric_limits<Scalar>::max)();\n  todo.push(std::make_pair(Scalar(), std::make_pair(tree1.getRootIndex(), tree2.getRootIndex())));\n\n  while(!todo.empty()) {\n    tree1.getChildren(todo.top().second.first, vBegin1, vEnd1, oBegin1, oEnd1);\n    tree2.getChildren(todo.top().second.second, vBegin2, vEnd2, oBegin2, oEnd2);\n    todo.pop();\n\n    for(; oBegin1 != oEnd1; ++oBegin1) { //go through child objects of first tree\n      for(oCur2 = oBegin2; oCur2 != oEnd2; ++oCur2) {//go through child objects of second tree\n        minimum = (std::min)(minimum, minimizer.minimumOnObjectObject(*oBegin1, *oCur2));\n      }\n\n      for(vCur2 = vBegin2; vCur2 != vEnd2; ++vCur2) { //go through child volumes of second tree\n        Helper2 helper(*oBegin1, minimizer);\n        minimum = (std::min)(minimum, internal::minimize_helper(tree2, helper, *vCur2, minimum));\n      }\n    }\n\n    for(; vBegin1 != vEnd1; ++vBegin1) { //go through child volumes of first tree\n      const typename BVH1::Volume &vol1 = tree1.getVolume(*vBegin1);\n\n      for(oCur2 = oBegin2; oCur2 != oEnd2; ++oCur2) {//go through child objects of second tree\n        Helper1 helper(*oCur2, minimizer);\n        minimum = (std::min)(minimum, internal::minimize_helper(tree1, helper, *vBegin1, minimum));\n      }\n\n      for(vCur2 = vBegin2; vCur2 != vEnd2; ++vCur2) { //go through child volumes of second tree\n        Scalar val = minimizer.minimumOnVolumeVolume(vol1, tree2.getVolume(*vCur2));\n        if(val < minimum)\n          todo.push(std::make_pair(val, std::make_pair(*vBegin1, *vCur2)));\n      }\n    }\n  }\n  return minimum;\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_BVALGORITHMS_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/BVH/KdBVH.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Ilya Baran <ibaran@mit.edu>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef KDBVH_H_INCLUDED\n#define KDBVH_H_INCLUDED\n\nnamespace Eigen { \n\nnamespace internal {\n\n//internal pair class for the BVH--used instead of std::pair because of alignment\ntemplate<typename Scalar, int Dim>\nstruct vector_int_pair\n{\nEIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(Scalar, Dim)\n  typedef Matrix<Scalar, Dim, 1> VectorType;\n\n  vector_int_pair(const VectorType &v, int i) : first(v), second(i) {}\n\n  VectorType first;\n  int second;\n};\n\n//these templates help the tree initializer get the bounding boxes either from a provided\n//iterator range or using bounding_box in a unified way\ntemplate<typename ObjectList, typename VolumeList, typename BoxIter>\nstruct get_boxes_helper {\n  void operator()(const ObjectList &objects, BoxIter boxBegin, BoxIter boxEnd, VolumeList &outBoxes)\n  {\n    outBoxes.insert(outBoxes.end(), boxBegin, boxEnd);\n    eigen_assert(outBoxes.size() == objects.size());\n  }\n};\n\ntemplate<typename ObjectList, typename VolumeList>\nstruct get_boxes_helper<ObjectList, VolumeList, int> {\n  void operator()(const ObjectList &objects, int, int, VolumeList &outBoxes)\n  {\n    outBoxes.reserve(objects.size());\n    for(int i = 0; i < (int)objects.size(); ++i)\n      outBoxes.push_back(bounding_box(objects[i]));\n  }\n};\n\n} // end namespace internal\n\n\n/** \\class KdBVH\n *  \\brief A simple bounding volume hierarchy based on AlignedBox\n *\n *  \\param _Scalar The underlying scalar type of the bounding boxes\n *  \\param _Dim The dimension of the space in which the hierarchy lives\n *  \\param _Object The object type that lives in the hierarchy.  It must have value semantics.  Either bounding_box(_Object) must\n *                 be defined and return an AlignedBox<_Scalar, _Dim> or bounding boxes must be provided to the tree initializer.\n *\n *  This class provides a simple (as opposed to optimized) implementation of a bounding volume hierarchy analogous to a Kd-tree.\n *  Given a sequence of objects, it computes their bounding boxes, constructs a Kd-tree of their centers\n *  and builds a BVH with the structure of that Kd-tree.  When the elements of the tree are too expensive to be copied around,\n *  it is useful for _Object to be a pointer.\n */\ntemplate<typename _Scalar, int _Dim, typename _Object> class KdBVH\n{\npublic:\n  enum { Dim = _Dim };\n  typedef _Object Object;\n  typedef std::vector<Object, aligned_allocator<Object> > ObjectList;\n  typedef _Scalar Scalar;\n  typedef AlignedBox<Scalar, Dim> Volume;\n  typedef std::vector<Volume, aligned_allocator<Volume> > VolumeList;\n  typedef int Index;\n  typedef const int *VolumeIterator; //the iterators are just pointers into the tree's vectors\n  typedef const Object *ObjectIterator;\n\n  KdBVH() {}\n\n  /** Given an iterator range over \\a Object references, constructs the BVH.  Requires that bounding_box(Object) return a Volume. */\n  template<typename Iter> KdBVH(Iter begin, Iter end) { init(begin, end, 0, 0); } //int is recognized by init as not being an iterator type\n\n  /** Given an iterator range over \\a Object references and an iterator range over their bounding boxes, constructs the BVH */\n  template<typename OIter, typename BIter> KdBVH(OIter begin, OIter end, BIter boxBegin, BIter boxEnd) { init(begin, end, boxBegin, boxEnd); }\n\n  /** Given an iterator range over \\a Object references, constructs the BVH, overwriting whatever is in there currently.\n    * Requires that bounding_box(Object) return a Volume. */\n  template<typename Iter> void init(Iter begin, Iter end) { init(begin, end, 0, 0); }\n\n  /** Given an iterator range over \\a Object references and an iterator range over their bounding boxes,\n    * constructs the BVH, overwriting whatever is in there currently. */\n  template<typename OIter, typename BIter> void init(OIter begin, OIter end, BIter boxBegin, BIter boxEnd)\n  {\n    objects.clear();\n    boxes.clear();\n    children.clear();\n\n    objects.insert(objects.end(), begin, end);\n    int n = static_cast<int>(objects.size());\n\n    if(n < 2)\n      return; //if we have at most one object, we don't need any internal nodes\n\n    VolumeList objBoxes;\n    VIPairList objCenters;\n\n    //compute the bounding boxes depending on BIter type\n    internal::get_boxes_helper<ObjectList, VolumeList, BIter>()(objects, boxBegin, boxEnd, objBoxes);\n\n    objCenters.reserve(n);\n    boxes.reserve(n - 1);\n    children.reserve(2 * n - 2);\n\n    for(int i = 0; i < n; ++i)\n      objCenters.push_back(VIPair(objBoxes[i].center(), i));\n\n    build(objCenters, 0, n, objBoxes, 0); //the recursive part of the algorithm\n\n    ObjectList tmp(n);\n    tmp.swap(objects);\n    for(int i = 0; i < n; ++i)\n      objects[i] = tmp[objCenters[i].second];\n  }\n\n  /** \\returns the index of the root of the hierarchy */\n  inline Index getRootIndex() const { return (int)boxes.size() - 1; }\n\n  /** Given an \\a index of a node, on exit, \\a outVBegin and \\a outVEnd range over the indices of the volume children of the node\n    * and \\a outOBegin and \\a outOEnd range over the object children of the node */\n  EIGEN_STRONG_INLINE void getChildren(Index index, VolumeIterator &outVBegin, VolumeIterator &outVEnd,\n                                       ObjectIterator &outOBegin, ObjectIterator &outOEnd) const\n  { //inlining this function should open lots of optimization opportunities to the compiler\n    if(index < 0) {\n      outVBegin = outVEnd;\n      if(!objects.empty())\n        outOBegin = &(objects[0]);\n      outOEnd = outOBegin + objects.size(); //output all objects--necessary when the tree has only one object\n      return;\n    }\n\n    int numBoxes = static_cast<int>(boxes.size());\n\n    int idx = index * 2;\n    if(children[idx + 1] < numBoxes) { //second index is always bigger\n      outVBegin = &(children[idx]);\n      outVEnd = outVBegin + 2;\n      outOBegin = outOEnd;\n    }\n    else if(children[idx] >= numBoxes) { //if both children are objects\n      outVBegin = outVEnd;\n      outOBegin = &(objects[children[idx] - numBoxes]);\n      outOEnd = outOBegin + 2;\n    } else { //if the first child is a volume and the second is an object\n      outVBegin = &(children[idx]);\n      outVEnd = outVBegin + 1;\n      outOBegin = &(objects[children[idx + 1] - numBoxes]);\n      outOEnd = outOBegin + 1;\n    }\n  }\n\n  /** \\returns the bounding box of the node at \\a index */\n  inline const Volume &getVolume(Index index) const\n  {\n    return boxes[index];\n  }\n\nprivate:\n  typedef internal::vector_int_pair<Scalar, Dim> VIPair;\n  typedef std::vector<VIPair, aligned_allocator<VIPair> > VIPairList;\n  typedef Matrix<Scalar, Dim, 1> VectorType;\n  struct VectorComparator //compares vectors, or, more specificall, VIPairs along a particular dimension\n  {\n    VectorComparator(int inDim) : dim(inDim) {}\n    inline bool operator()(const VIPair &v1, const VIPair &v2) const { return v1.first[dim] < v2.first[dim]; }\n    int dim;\n  };\n\n  //Build the part of the tree between objects[from] and objects[to] (not including objects[to]).\n  //This routine partitions the objCenters in [from, to) along the dimension dim, recursively constructs\n  //the two halves, and adds their parent node.  TODO: a cache-friendlier layout\n  void build(VIPairList &objCenters, int from, int to, const VolumeList &objBoxes, int dim)\n  {\n    eigen_assert(to - from > 1);\n    if(to - from == 2) {\n      boxes.push_back(objBoxes[objCenters[from].second].merged(objBoxes[objCenters[from + 1].second]));\n      children.push_back(from + (int)objects.size() - 1); //there are objects.size() - 1 tree nodes\n      children.push_back(from + (int)objects.size());\n    }\n    else if(to - from == 3) {\n      int mid = from + 2;\n      std::nth_element(objCenters.begin() + from, objCenters.begin() + mid,\n                        objCenters.begin() + to, VectorComparator(dim)); //partition\n      build(objCenters, from, mid, objBoxes, (dim + 1) % Dim);\n      int idx1 = (int)boxes.size() - 1;\n      boxes.push_back(boxes[idx1].merged(objBoxes[objCenters[mid].second]));\n      children.push_back(idx1);\n      children.push_back(mid + (int)objects.size() - 1);\n    }\n    else {\n      int mid = from + (to - from) / 2;\n      nth_element(objCenters.begin() + from, objCenters.begin() + mid,\n                  objCenters.begin() + to, VectorComparator(dim)); //partition\n      build(objCenters, from, mid, objBoxes, (dim + 1) % Dim);\n      int idx1 = (int)boxes.size() - 1;\n      build(objCenters, mid, to, objBoxes, (dim + 1) % Dim);\n      int idx2 = (int)boxes.size() - 1;\n      boxes.push_back(boxes[idx1].merged(boxes[idx2]));\n      children.push_back(idx1);\n      children.push_back(idx2);\n    }\n  }\n\n  std::vector<int> children; //children of x are children[2x] and children[2x+1], indices bigger than boxes.size() index into objects.\n  VolumeList boxes;\n  ObjectList objects;\n};\n\n} // end namespace Eigen\n\n#endif //KDBVH_H_INCLUDED\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/Eigenvalues/ArpackSelfAdjointEigenSolver.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 David Harmon <dharmon@gmail.com>\n//\n// Eigen is free software; you can redistribute it and/or\n// modify it under the terms of the GNU Lesser General Public\n// License as published by the Free Software Foundation; either\n// version 3 of the License, or (at your option) any later version.\n//\n// Alternatively, you can redistribute it and/or\n// modify it under the terms of the GNU General Public License as\n// published by the Free Software Foundation; either version 2 of\n// the License, or (at your option) any later version.\n//\n// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY\n// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS\n// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the\n// GNU General Public License for more details.\n//\n// You should have received a copy of the GNU Lesser General Public\n// License and a copy of the GNU General Public License along with\n// Eigen. If not, see <http://www.gnu.org/licenses/>.\n\n#ifndef EIGEN_ARPACKGENERALIZEDSELFADJOINTEIGENSOLVER_H\n#define EIGEN_ARPACKGENERALIZEDSELFADJOINTEIGENSOLVER_H\n\n#include <Eigen/Dense>\n\nnamespace Eigen { \n\nnamespace internal {\n  template<typename Scalar, typename RealScalar> struct arpack_wrapper;\n  template<typename MatrixSolver, typename MatrixType, typename Scalar, bool BisSPD> struct OP;\n}\n\n\n\ntemplate<typename MatrixType, typename MatrixSolver=SimplicialLLT<MatrixType>, bool BisSPD=false>\nclass ArpackGeneralizedSelfAdjointEigenSolver\n{\npublic:\n  //typedef typename MatrixSolver::MatrixType MatrixType;\n\n  /** \\brief Scalar type for matrices of type \\p MatrixType. */\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename MatrixType::Index Index;\n\n  /** \\brief Real scalar type for \\p MatrixType.\n   *\n   * This is just \\c Scalar if #Scalar is real (e.g., \\c float or\n   * \\c Scalar), and the type of the real part of \\c Scalar if #Scalar is\n   * complex.\n   */\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n\n  /** \\brief Type for vector of eigenvalues as returned by eigenvalues().\n   *\n   * This is a column vector with entries of type #RealScalar.\n   * The length of the vector is the size of \\p nbrEigenvalues.\n   */\n  typedef typename internal::plain_col_type<MatrixType, RealScalar>::type RealVectorType;\n\n  /** \\brief Default constructor.\n   *\n   * The default constructor is for cases in which the user intends to\n   * perform decompositions via compute().\n   *\n   */\n  ArpackGeneralizedSelfAdjointEigenSolver()\n   : m_eivec(),\n     m_eivalues(),\n     m_isInitialized(false),\n     m_eigenvectorsOk(false),\n     m_nbrConverged(0),\n     m_nbrIterations(0)\n  { }\n\n  /** \\brief Constructor; computes generalized eigenvalues of given matrix with respect to another matrix.\n   *\n   * \\param[in] A Self-adjoint matrix whose eigenvalues / eigenvectors will\n   *    computed. By default, the upper triangular part is used, but can be changed\n   *    through the template parameter.\n   * \\param[in] B Self-adjoint matrix for the generalized eigenvalue problem.\n   * \\param[in] nbrEigenvalues The number of eigenvalues / eigenvectors to compute.\n   *    Must be less than the size of the input matrix, or an error is returned.\n   * \\param[in] eigs_sigma String containing either \"LM\", \"SM\", \"LA\", or \"SA\", with\n   *    respective meanings to find the largest magnitude , smallest magnitude,\n   *    largest algebraic, or smallest algebraic eigenvalues. Alternatively, this\n   *    value can contain floating point value in string form, in which case the\n   *    eigenvalues closest to this value will be found.\n   * \\param[in]  options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly.\n   * \\param[in] tol What tolerance to find the eigenvalues to. Default is 0, which\n   *    means machine precision.\n   *\n   * This constructor calls compute(const MatrixType&, const MatrixType&, Index, string, int, RealScalar)\n   * to compute the eigenvalues of the matrix \\p A with respect to \\p B. The eigenvectors are computed if\n   * \\p options equals #ComputeEigenvectors.\n   *\n   */\n  ArpackGeneralizedSelfAdjointEigenSolver(const MatrixType& A, const MatrixType& B,\n                                          Index nbrEigenvalues, std::string eigs_sigma=\"LM\",\n                               int options=ComputeEigenvectors, RealScalar tol=0.0)\n    : m_eivec(),\n      m_eivalues(),\n      m_isInitialized(false),\n      m_eigenvectorsOk(false),\n      m_nbrConverged(0),\n      m_nbrIterations(0)\n  {\n    compute(A, B, nbrEigenvalues, eigs_sigma, options, tol);\n  }\n\n  /** \\brief Constructor; computes eigenvalues of given matrix.\n   *\n   * \\param[in] A Self-adjoint matrix whose eigenvalues / eigenvectors will\n   *    computed. By default, the upper triangular part is used, but can be changed\n   *    through the template parameter.\n   * \\param[in] nbrEigenvalues The number of eigenvalues / eigenvectors to compute.\n   *    Must be less than the size of the input matrix, or an error is returned.\n   * \\param[in] eigs_sigma String containing either \"LM\", \"SM\", \"LA\", or \"SA\", with\n   *    respective meanings to find the largest magnitude , smallest magnitude,\n   *    largest algebraic, or smallest algebraic eigenvalues. Alternatively, this\n   *    value can contain floating point value in string form, in which case the\n   *    eigenvalues closest to this value will be found.\n   * \\param[in]  options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly.\n   * \\param[in] tol What tolerance to find the eigenvalues to. Default is 0, which\n   *    means machine precision.\n   *\n   * This constructor calls compute(const MatrixType&, Index, string, int, RealScalar)\n   * to compute the eigenvalues of the matrix \\p A. The eigenvectors are computed if\n   * \\p options equals #ComputeEigenvectors.\n   *\n   */\n\n  ArpackGeneralizedSelfAdjointEigenSolver(const MatrixType& A,\n                                          Index nbrEigenvalues, std::string eigs_sigma=\"LM\",\n                               int options=ComputeEigenvectors, RealScalar tol=0.0)\n    : m_eivec(),\n      m_eivalues(),\n      m_isInitialized(false),\n      m_eigenvectorsOk(false),\n      m_nbrConverged(0),\n      m_nbrIterations(0)\n  {\n    compute(A, nbrEigenvalues, eigs_sigma, options, tol);\n  }\n\n\n  /** \\brief Computes generalized eigenvalues / eigenvectors of given matrix using the external ARPACK library.\n   *\n   * \\param[in]  A  Selfadjoint matrix whose eigendecomposition is to be computed.\n   * \\param[in]  B  Selfadjoint matrix for generalized eigenvalues.\n   * \\param[in] nbrEigenvalues The number of eigenvalues / eigenvectors to compute.\n   *    Must be less than the size of the input matrix, or an error is returned.\n   * \\param[in] eigs_sigma String containing either \"LM\", \"SM\", \"LA\", or \"SA\", with\n   *    respective meanings to find the largest magnitude , smallest magnitude,\n   *    largest algebraic, or smallest algebraic eigenvalues. Alternatively, this\n   *    value can contain floating point value in string form, in which case the\n   *    eigenvalues closest to this value will be found.\n   * \\param[in]  options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly.\n   * \\param[in] tol What tolerance to find the eigenvalues to. Default is 0, which\n   *    means machine precision.\n   *\n   * \\returns    Reference to \\c *this\n   *\n   * This function computes the generalized eigenvalues of \\p A with respect to \\p B using ARPACK.  The eigenvalues()\n   * function can be used to retrieve them.  If \\p options equals #ComputeEigenvectors,\n   * then the eigenvectors are also computed and can be retrieved by\n   * calling eigenvectors().\n   *\n   */\n  ArpackGeneralizedSelfAdjointEigenSolver& compute(const MatrixType& A, const MatrixType& B,\n                                                   Index nbrEigenvalues, std::string eigs_sigma=\"LM\",\n                                        int options=ComputeEigenvectors, RealScalar tol=0.0);\n  \n  /** \\brief Computes eigenvalues / eigenvectors of given matrix using the external ARPACK library.\n   *\n   * \\param[in]  A  Selfadjoint matrix whose eigendecomposition is to be computed.\n   * \\param[in] nbrEigenvalues The number of eigenvalues / eigenvectors to compute.\n   *    Must be less than the size of the input matrix, or an error is returned.\n   * \\param[in] eigs_sigma String containing either \"LM\", \"SM\", \"LA\", or \"SA\", with\n   *    respective meanings to find the largest magnitude , smallest magnitude,\n   *    largest algebraic, or smallest algebraic eigenvalues. Alternatively, this\n   *    value can contain floating point value in string form, in which case the\n   *    eigenvalues closest to this value will be found.\n   * \\param[in]  options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly.\n   * \\param[in] tol What tolerance to find the eigenvalues to. Default is 0, which\n   *    means machine precision.\n   *\n   * \\returns    Reference to \\c *this\n   *\n   * This function computes the eigenvalues of \\p A using ARPACK.  The eigenvalues()\n   * function can be used to retrieve them.  If \\p options equals #ComputeEigenvectors,\n   * then the eigenvectors are also computed and can be retrieved by\n   * calling eigenvectors().\n   *\n   */\n  ArpackGeneralizedSelfAdjointEigenSolver& compute(const MatrixType& A,\n                                                   Index nbrEigenvalues, std::string eigs_sigma=\"LM\",\n                                        int options=ComputeEigenvectors, RealScalar tol=0.0);\n\n\n  /** \\brief Returns the eigenvectors of given matrix.\n   *\n   * \\returns  A const reference to the matrix whose columns are the eigenvectors.\n   *\n   * \\pre The eigenvectors have been computed before.\n   *\n   * Column \\f$ k \\f$ of the returned matrix is an eigenvector corresponding\n   * to eigenvalue number \\f$ k \\f$ as returned by eigenvalues().  The\n   * eigenvectors are normalized to have (Euclidean) norm equal to one. If\n   * this object was used to solve the eigenproblem for the selfadjoint\n   * matrix \\f$ A \\f$, then the matrix returned by this function is the\n   * matrix \\f$ V \\f$ in the eigendecomposition \\f$ A V = D V \\f$.\n   * For the generalized eigenproblem, the matrix returned is the solution \\f$ A V = D B V \\f$\n   *\n   * Example: \\include SelfAdjointEigenSolver_eigenvectors.cpp\n   * Output: \\verbinclude SelfAdjointEigenSolver_eigenvectors.out\n   *\n   * \\sa eigenvalues()\n   */\n  const Matrix<Scalar, Dynamic, Dynamic>& eigenvectors() const\n  {\n    eigen_assert(m_isInitialized && \"ArpackGeneralizedSelfAdjointEigenSolver is not initialized.\");\n    eigen_assert(m_eigenvectorsOk && \"The eigenvectors have not been computed together with the eigenvalues.\");\n    return m_eivec;\n  }\n\n  /** \\brief Returns the eigenvalues of given matrix.\n   *\n   * \\returns A const reference to the column vector containing the eigenvalues.\n   *\n   * \\pre The eigenvalues have been computed before.\n   *\n   * The eigenvalues are repeated according to their algebraic multiplicity,\n   * so there are as many eigenvalues as rows in the matrix. The eigenvalues\n   * are sorted in increasing order.\n   *\n   * Example: \\include SelfAdjointEigenSolver_eigenvalues.cpp\n   * Output: \\verbinclude SelfAdjointEigenSolver_eigenvalues.out\n   *\n   * \\sa eigenvectors(), MatrixBase::eigenvalues()\n   */\n  const Matrix<Scalar, Dynamic, 1>& eigenvalues() const\n  {\n    eigen_assert(m_isInitialized && \"ArpackGeneralizedSelfAdjointEigenSolver is not initialized.\");\n    return m_eivalues;\n  }\n\n  /** \\brief Computes the positive-definite square root of the matrix.\n   *\n   * \\returns the positive-definite square root of the matrix\n   *\n   * \\pre The eigenvalues and eigenvectors of a positive-definite matrix\n   * have been computed before.\n   *\n   * The square root of a positive-definite matrix \\f$ A \\f$ is the\n   * positive-definite matrix whose square equals \\f$ A \\f$. This function\n   * uses the eigendecomposition \\f$ A = V D V^{-1} \\f$ to compute the\n   * square root as \\f$ A^{1/2} = V D^{1/2} V^{-1} \\f$.\n   *\n   * Example: \\include SelfAdjointEigenSolver_operatorSqrt.cpp\n   * Output: \\verbinclude SelfAdjointEigenSolver_operatorSqrt.out\n   *\n   * \\sa operatorInverseSqrt(),\n   *     \\ref MatrixFunctions_Module \"MatrixFunctions Module\"\n   */\n  Matrix<Scalar, Dynamic, Dynamic> operatorSqrt() const\n  {\n    eigen_assert(m_isInitialized && \"SelfAdjointEigenSolver is not initialized.\");\n    eigen_assert(m_eigenvectorsOk && \"The eigenvectors have not been computed together with the eigenvalues.\");\n    return m_eivec * m_eivalues.cwiseSqrt().asDiagonal() * m_eivec.adjoint();\n  }\n\n  /** \\brief Computes the inverse square root of the matrix.\n   *\n   * \\returns the inverse positive-definite square root of the matrix\n   *\n   * \\pre The eigenvalues and eigenvectors of a positive-definite matrix\n   * have been computed before.\n   *\n   * This function uses the eigendecomposition \\f$ A = V D V^{-1} \\f$ to\n   * compute the inverse square root as \\f$ V D^{-1/2} V^{-1} \\f$. This is\n   * cheaper than first computing the square root with operatorSqrt() and\n   * then its inverse with MatrixBase::inverse().\n   *\n   * Example: \\include SelfAdjointEigenSolver_operatorInverseSqrt.cpp\n   * Output: \\verbinclude SelfAdjointEigenSolver_operatorInverseSqrt.out\n   *\n   * \\sa operatorSqrt(), MatrixBase::inverse(),\n   *     \\ref MatrixFunctions_Module \"MatrixFunctions Module\"\n   */\n  Matrix<Scalar, Dynamic, Dynamic> operatorInverseSqrt() const\n  {\n    eigen_assert(m_isInitialized && \"SelfAdjointEigenSolver is not initialized.\");\n    eigen_assert(m_eigenvectorsOk && \"The eigenvectors have not been computed together with the eigenvalues.\");\n    return m_eivec * m_eivalues.cwiseInverse().cwiseSqrt().asDiagonal() * m_eivec.adjoint();\n  }\n\n  /** \\brief Reports whether previous computation was successful.\n   *\n   * \\returns \\c Success if computation was succesful, \\c NoConvergence otherwise.\n   */\n  ComputationInfo info() const\n  {\n    eigen_assert(m_isInitialized && \"ArpackGeneralizedSelfAdjointEigenSolver is not initialized.\");\n    return m_info;\n  }\n\n  size_t getNbrConvergedEigenValues() const\n  { return m_nbrConverged; }\n\n  size_t getNbrIterations() const\n  { return m_nbrIterations; }\n\nprotected:\n  Matrix<Scalar, Dynamic, Dynamic> m_eivec;\n  Matrix<Scalar, Dynamic, 1> m_eivalues;\n  ComputationInfo m_info;\n  bool m_isInitialized;\n  bool m_eigenvectorsOk;\n\n  size_t m_nbrConverged;\n  size_t m_nbrIterations;\n};\n\n\n\n\n\ntemplate<typename MatrixType, typename MatrixSolver, bool BisSPD>\nArpackGeneralizedSelfAdjointEigenSolver<MatrixType, MatrixSolver, BisSPD>&\n    ArpackGeneralizedSelfAdjointEigenSolver<MatrixType, MatrixSolver, BisSPD>\n::compute(const MatrixType& A, Index nbrEigenvalues,\n          std::string eigs_sigma, int options, RealScalar tol)\n{\n    MatrixType B(0,0);\n    compute(A, B, nbrEigenvalues, eigs_sigma, options, tol);\n    \n    return *this;\n}\n\n\ntemplate<typename MatrixType, typename MatrixSolver, bool BisSPD>\nArpackGeneralizedSelfAdjointEigenSolver<MatrixType, MatrixSolver, BisSPD>&\n    ArpackGeneralizedSelfAdjointEigenSolver<MatrixType, MatrixSolver, BisSPD>\n::compute(const MatrixType& A, const MatrixType& B, Index nbrEigenvalues,\n          std::string eigs_sigma, int options, RealScalar tol)\n{\n  eigen_assert(A.cols() == A.rows());\n  eigen_assert(B.cols() == B.rows());\n  eigen_assert(B.rows() == 0 || A.cols() == B.rows());\n  eigen_assert((options &~ (EigVecMask | GenEigMask)) == 0\n            && (options & EigVecMask) != EigVecMask\n            && \"invalid option parameter\");\n\n  bool isBempty = (B.rows() == 0) || (B.cols() == 0);\n\n  // For clarity, all parameters match their ARPACK name\n  //\n  // Always 0 on the first call\n  //\n  int ido = 0;\n\n  int n = (int)A.cols();\n\n  // User options: \"LA\", \"SA\", \"SM\", \"LM\", \"BE\"\n  //\n  char whch[3] = \"LM\";\n    \n  // Specifies the shift if iparam[6] = { 3, 4, 5 }, not used if iparam[6] = { 1, 2 }\n  //\n  RealScalar sigma = 0.0;\n\n  if (eigs_sigma.length() >= 2 && isalpha(eigs_sigma[0]) && isalpha(eigs_sigma[1]))\n  {\n      eigs_sigma[0] = toupper(eigs_sigma[0]);\n      eigs_sigma[1] = toupper(eigs_sigma[1]);\n\n      // In the following special case we're going to invert the problem, since solving\n      // for larger magnitude is much much faster\n      // i.e., if 'SM' is specified, we're going to really use 'LM', the default\n      //\n      if (eigs_sigma.substr(0,2) != \"SM\")\n      {\n          whch[0] = eigs_sigma[0];\n          whch[1] = eigs_sigma[1];\n      }\n  }\n  else\n  {\n      eigen_assert(false && \"Specifying clustered eigenvalues is not yet supported!\");\n\n      // If it's not scalar values, then the user may be explicitly\n      // specifying the sigma value to cluster the evs around\n      //\n      sigma = atof(eigs_sigma.c_str());\n\n      // If atof fails, it returns 0.0, which is a fine default\n      //\n  }\n\n  // \"I\" means normal eigenvalue problem, \"G\" means generalized\n  //\n  char bmat[2] = \"I\";\n  if (eigs_sigma.substr(0,2) == \"SM\" || !(isalpha(eigs_sigma[0]) && isalpha(eigs_sigma[1])) || (!isBempty && !BisSPD))\n      bmat[0] = 'G';\n\n  // Now we determine the mode to use\n  //\n  int mode = (bmat[0] == 'G') + 1;\n  if (eigs_sigma.substr(0,2) == \"SM\" || !(isalpha(eigs_sigma[0]) && isalpha(eigs_sigma[1])))\n  {\n      // We're going to use shift-and-invert mode, and basically find\n      // the largest eigenvalues of the inverse operator\n      //\n      mode = 3;\n  }\n\n  // The user-specified number of eigenvalues/vectors to compute\n  //\n  int nev = (int)nbrEigenvalues;\n\n  // Allocate space for ARPACK to store the residual\n  //\n  Scalar *resid = new Scalar[n];\n\n  // Number of Lanczos vectors, must satisfy nev < ncv <= n\n  // Note that this indicates that nev != n, and we cannot compute\n  // all eigenvalues of a mtrix\n  //\n  int ncv = std::min(std::max(2*nev, 20), n);\n\n  // The working n x ncv matrix, also store the final eigenvectors (if computed)\n  //\n  Scalar *v = new Scalar[n*ncv];\n  int ldv = n;\n\n  // Working space\n  //\n  Scalar *workd = new Scalar[3*n];\n  int lworkl = ncv*ncv+8*ncv; // Must be at least this length\n  Scalar *workl = new Scalar[lworkl];\n\n  int *iparam= new int[11];\n  iparam[0] = 1; // 1 means we let ARPACK perform the shifts, 0 means we'd have to do it\n  iparam[2] = std::max(300, (int)std::ceil(2*n/std::max(ncv,1)));\n  iparam[6] = mode; // The mode, 1 is standard ev problem, 2 for generalized ev, 3 for shift-and-invert\n\n  // Used during reverse communicate to notify where arrays start\n  //\n  int *ipntr = new int[11]; \n\n  // Error codes are returned in here, initial value of 0 indicates a random initial\n  // residual vector is used, any other values means resid contains the initial residual\n  // vector, possibly from a previous run\n  //\n  int info = 0;\n\n  Scalar scale = 1.0;\n  //if (!isBempty)\n  //{\n  //Scalar scale = B.norm() / std::sqrt(n);\n  //scale = std::pow(2, std::floor(std::log(scale+1)));\n  ////M /= scale;\n  //for (size_t i=0; i<(size_t)B.outerSize(); i++)\n  //    for (typename MatrixType::InnerIterator it(B, i); it; ++it)\n  //        it.valueRef() /= scale;\n  //}\n\n  MatrixSolver OP;\n  if (mode == 1 || mode == 2)\n  {\n      if (!isBempty)\n          OP.compute(B);\n  }\n  else if (mode == 3)\n  {\n      if (sigma == 0.0)\n      {\n          OP.compute(A);\n      }\n      else\n      {\n          // Note: We will never enter here because sigma must be 0.0\n          //\n          if (isBempty)\n          {\n            MatrixType AminusSigmaB(A);\n            for (Index i=0; i<A.rows(); ++i)\n                AminusSigmaB.coeffRef(i,i) -= sigma;\n            \n            OP.compute(AminusSigmaB);\n          }\n          else\n          {\n              MatrixType AminusSigmaB = A - sigma * B;\n              OP.compute(AminusSigmaB);\n          }\n      }\n  }\n \n  if (!(mode == 1 && isBempty) && !(mode == 2 && isBempty) && OP.info() != Success)\n      std::cout << \"Error factoring matrix\" << std::endl;\n\n  do\n  {\n    internal::arpack_wrapper<Scalar, RealScalar>::saupd(&ido, bmat, &n, whch, &nev, &tol, resid, \n                                                        &ncv, v, &ldv, iparam, ipntr, workd, workl,\n                                                        &lworkl, &info);\n\n    if (ido == -1 || ido == 1)\n    {\n      Scalar *in  = workd + ipntr[0] - 1;\n      Scalar *out = workd + ipntr[1] - 1;\n\n      if (ido == 1 && mode != 2)\n      {\n          Scalar *out2 = workd + ipntr[2] - 1;\n          if (isBempty || mode == 1)\n            Matrix<Scalar, Dynamic, 1>::Map(out2, n) = Matrix<Scalar, Dynamic, 1>::Map(in, n);\n          else\n            Matrix<Scalar, Dynamic, 1>::Map(out2, n) = B * Matrix<Scalar, Dynamic, 1>::Map(in, n);\n          \n          in = workd + ipntr[2] - 1;\n      }\n\n      if (mode == 1)\n      {\n        if (isBempty)\n        {\n          // OP = A\n          //\n          Matrix<Scalar, Dynamic, 1>::Map(out, n) = A * Matrix<Scalar, Dynamic, 1>::Map(in, n);\n        }\n        else\n        {\n          // OP = L^{-1}AL^{-T}\n          //\n          internal::OP<MatrixSolver, MatrixType, Scalar, BisSPD>::applyOP(OP, A, n, in, out);\n        }\n      }\n      else if (mode == 2)\n      {\n        if (ido == 1)\n          Matrix<Scalar, Dynamic, 1>::Map(in, n)  = A * Matrix<Scalar, Dynamic, 1>::Map(in, n);\n        \n        // OP = B^{-1} A\n        //\n        Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.solve(Matrix<Scalar, Dynamic, 1>::Map(in, n));\n      }\n      else if (mode == 3)\n      {\n        // OP = (A-\\sigmaB)B (\\sigma could be 0, and B could be I)\n        // The B * in is already computed and stored at in if ido == 1\n        //\n        if (ido == 1 || isBempty)\n          Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.solve(Matrix<Scalar, Dynamic, 1>::Map(in, n));\n        else\n          Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.solve(B * Matrix<Scalar, Dynamic, 1>::Map(in, n));\n      }\n    }\n    else if (ido == 2)\n    {\n      Scalar *in  = workd + ipntr[0] - 1;\n      Scalar *out = workd + ipntr[1] - 1;\n\n      if (isBempty || mode == 1)\n        Matrix<Scalar, Dynamic, 1>::Map(out, n) = Matrix<Scalar, Dynamic, 1>::Map(in, n);\n      else\n        Matrix<Scalar, Dynamic, 1>::Map(out, n) = B * Matrix<Scalar, Dynamic, 1>::Map(in, n);\n    }\n  } while (ido != 99);\n\n  if (info == 1)\n    m_info = NoConvergence;\n  else if (info == 3)\n    m_info = NumericalIssue;\n  else if (info < 0)\n    m_info = InvalidInput;\n  else if (info != 0)\n    eigen_assert(false && \"Unknown ARPACK return value!\");\n  else\n  {\n    // Do we compute eigenvectors or not?\n    //\n    int rvec = (options & ComputeEigenvectors) == ComputeEigenvectors;\n\n    // \"A\" means \"All\", use \"S\" to choose specific eigenvalues (not yet supported in ARPACK))\n    //\n    char howmny[2] = \"A\"; \n\n    // if howmny == \"S\", specifies the eigenvalues to compute (not implemented in ARPACK)\n    //\n    int *select = new int[ncv];\n\n    // Final eigenvalues\n    //\n    m_eivalues.resize(nev, 1);\n\n    internal::arpack_wrapper<Scalar, RealScalar>::seupd(&rvec, howmny, select, m_eivalues.data(), v, &ldv,\n                                                        &sigma, bmat, &n, whch, &nev, &tol, resid, &ncv,\n                                                        v, &ldv, iparam, ipntr, workd, workl, &lworkl, &info);\n\n    if (info == -14)\n      m_info = NoConvergence;\n    else if (info != 0)\n      m_info = InvalidInput;\n    else\n    {\n      if (rvec)\n      {\n        m_eivec.resize(A.rows(), nev);\n        for (int i=0; i<nev; i++)\n          for (int j=0; j<n; j++)\n            m_eivec(j,i) = v[i*n+j] / scale;\n      \n        if (mode == 1 && !isBempty && BisSPD)\n          internal::OP<MatrixSolver, MatrixType, Scalar, BisSPD>::project(OP, n, nev, m_eivec.data());\n\n        m_eigenvectorsOk = true;\n      }\n\n      m_nbrIterations = iparam[2];\n      m_nbrConverged  = iparam[4];\n\n      m_info = Success;\n    }\n\n    delete[] select;\n  }\n\n  delete[] v;\n  delete[] iparam;\n  delete[] ipntr;\n  delete[] workd;\n  delete[] workl;\n  delete[] resid;\n\n  m_isInitialized = true;\n\n  return *this;\n}\n\n\n// Single precision\n//\nextern \"C\" void ssaupd_(int *ido, char *bmat, int *n, char *which,\n    int *nev, float *tol, float *resid, int *ncv,\n    float *v, int *ldv, int *iparam, int *ipntr,\n    float *workd, float *workl, int *lworkl,\n    int *info);\n\nextern \"C\" void sseupd_(int *rvec, char *All, int *select, float *d,\n    float *z, int *ldz, float *sigma, \n    char *bmat, int *n, char *which, int *nev,\n    float *tol, float *resid, int *ncv, float *v,\n    int *ldv, int *iparam, int *ipntr, float *workd,\n    float *workl, int *lworkl, int *ierr);\n\n// Double precision\n//\nextern \"C\" void dsaupd_(int *ido, char *bmat, int *n, char *which,\n    int *nev, double *tol, double *resid, int *ncv,\n    double *v, int *ldv, int *iparam, int *ipntr,\n    double *workd, double *workl, int *lworkl,\n    int *info);\n\nextern \"C\" void dseupd_(int *rvec, char *All, int *select, double *d,\n    double *z, int *ldz, double *sigma, \n    char *bmat, int *n, char *which, int *nev,\n    double *tol, double *resid, int *ncv, double *v,\n    int *ldv, int *iparam, int *ipntr, double *workd,\n    double *workl, int *lworkl, int *ierr);\n\n\nnamespace internal {\n\ntemplate<typename Scalar, typename RealScalar> struct arpack_wrapper\n{\n  static inline void saupd(int *ido, char *bmat, int *n, char *which,\n      int *nev, RealScalar *tol, Scalar *resid, int *ncv,\n      Scalar *v, int *ldv, int *iparam, int *ipntr,\n      Scalar *workd, Scalar *workl, int *lworkl, int *info)\n  { \n    EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsComplex, NUMERIC_TYPE_MUST_BE_REAL)\n  }\n\n  static inline void seupd(int *rvec, char *All, int *select, Scalar *d,\n      Scalar *z, int *ldz, RealScalar *sigma,\n      char *bmat, int *n, char *which, int *nev,\n      RealScalar *tol, Scalar *resid, int *ncv, Scalar *v,\n      int *ldv, int *iparam, int *ipntr, Scalar *workd,\n      Scalar *workl, int *lworkl, int *ierr)\n  {\n    EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsComplex, NUMERIC_TYPE_MUST_BE_REAL)\n  }\n};\n\ntemplate <> struct arpack_wrapper<float, float>\n{\n  static inline void saupd(int *ido, char *bmat, int *n, char *which,\n      int *nev, float *tol, float *resid, int *ncv,\n      float *v, int *ldv, int *iparam, int *ipntr,\n      float *workd, float *workl, int *lworkl, int *info)\n  {\n    ssaupd_(ido, bmat, n, which, nev, tol, resid, ncv, v, ldv, iparam, ipntr, workd, workl, lworkl, info);\n  }\n\n  static inline void seupd(int *rvec, char *All, int *select, float *d,\n      float *z, int *ldz, float *sigma,\n      char *bmat, int *n, char *which, int *nev,\n      float *tol, float *resid, int *ncv, float *v,\n      int *ldv, int *iparam, int *ipntr, float *workd,\n      float *workl, int *lworkl, int *ierr)\n  {\n    sseupd_(rvec, All, select, d, z, ldz, sigma, bmat, n, which, nev, tol, resid, ncv, v, ldv, iparam, ipntr,\n        workd, workl, lworkl, ierr);\n  }\n};\n\ntemplate <> struct arpack_wrapper<double, double>\n{\n  static inline void saupd(int *ido, char *bmat, int *n, char *which,\n      int *nev, double *tol, double *resid, int *ncv,\n      double *v, int *ldv, int *iparam, int *ipntr,\n      double *workd, double *workl, int *lworkl, int *info)\n  {\n    dsaupd_(ido, bmat, n, which, nev, tol, resid, ncv, v, ldv, iparam, ipntr, workd, workl, lworkl, info);\n  }\n\n  static inline void seupd(int *rvec, char *All, int *select, double *d,\n      double *z, int *ldz, double *sigma,\n      char *bmat, int *n, char *which, int *nev,\n      double *tol, double *resid, int *ncv, double *v,\n      int *ldv, int *iparam, int *ipntr, double *workd,\n      double *workl, int *lworkl, int *ierr)\n  {\n    dseupd_(rvec, All, select, d, v, ldv, sigma, bmat, n, which, nev, tol, resid, ncv, v, ldv, iparam, ipntr,\n        workd, workl, lworkl, ierr);\n  }\n};\n\n\ntemplate<typename MatrixSolver, typename MatrixType, typename Scalar, bool BisSPD>\nstruct OP\n{\n    static inline void applyOP(MatrixSolver &OP, const MatrixType &A, int n, Scalar *in, Scalar *out);\n    static inline void project(MatrixSolver &OP, int n, int k, Scalar *vecs);\n};\n\ntemplate<typename MatrixSolver, typename MatrixType, typename Scalar>\nstruct OP<MatrixSolver, MatrixType, Scalar, true>\n{\n  static inline void applyOP(MatrixSolver &OP, const MatrixType &A, int n, Scalar *in, Scalar *out)\n{\n    // OP = L^{-1} A L^{-T}  (B = LL^T)\n    //\n    // First solve L^T out = in\n    //\n    Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.matrixU().solve(Matrix<Scalar, Dynamic, 1>::Map(in, n));\n    Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.permutationPinv() * Matrix<Scalar, Dynamic, 1>::Map(out, n);\n\n    // Then compute out = A out\n    //\n    Matrix<Scalar, Dynamic, 1>::Map(out, n) = A * Matrix<Scalar, Dynamic, 1>::Map(out, n);\n\n    // Then solve L out = out\n    //\n    Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.permutationP() * Matrix<Scalar, Dynamic, 1>::Map(out, n);\n    Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.matrixL().solve(Matrix<Scalar, Dynamic, 1>::Map(out, n));\n}\n\n  static inline void project(MatrixSolver &OP, int n, int k, Scalar *vecs)\n{\n    // Solve L^T out = in\n    //\n    Matrix<Scalar, Dynamic, Dynamic>::Map(vecs, n, k) = OP.matrixU().solve(Matrix<Scalar, Dynamic, Dynamic>::Map(vecs, n, k));\n    Matrix<Scalar, Dynamic, Dynamic>::Map(vecs, n, k) = OP.permutationPinv() * Matrix<Scalar, Dynamic, Dynamic>::Map(vecs, n, k);\n}\n\n};\n\ntemplate<typename MatrixSolver, typename MatrixType, typename Scalar>\nstruct OP<MatrixSolver, MatrixType, Scalar, false>\n{\n  static inline void applyOP(MatrixSolver &OP, const MatrixType &A, int n, Scalar *in, Scalar *out)\n{\n    eigen_assert(false && \"Should never be in here...\");\n}\n\n  static inline void project(MatrixSolver &OP, int n, int k, Scalar *vecs)\n{\n    eigen_assert(false && \"Should never be in here...\");\n}\n\n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_ARPACKSELFADJOINTEIGENSOLVER_H\n\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/EulerAngles/CMakeLists.txt",
    "content": "FILE(GLOB Eigen_EulerAngles_SRCS \"*.h\")\n\nINSTALL(FILES\n  ${Eigen_EulerAngles_SRCS}\n  DESTINATION ${INCLUDE_INSTALL_DIR}/unsupported/Eigen/src/EulerAngles COMPONENT Devel\n  )\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/EulerAngles/EulerAngles.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Tal Hadad <tal_hd@hotmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_EULERANGLESCLASS_H// TODO: Fix previous \"EIGEN_EULERANGLES_H\" definition?\n#define EIGEN_EULERANGLESCLASS_H\n\nnamespace Eigen\n{\n  /*template<typename Other,\n         int OtherRows=Other::RowsAtCompileTime,\n         int OtherCols=Other::ColsAtCompileTime>\n  struct ei_eulerangles_assign_impl;*/\n\n  /** \\class EulerAngles\n    *\n    * \\ingroup EulerAngles_Module\n    *\n    * \\brief Represents a rotation in a 3 dimensional space as three Euler angles.\n    *\n    * Euler rotation is a set of three rotation of three angles over three fixed axes, defined by the EulerSystem given as a template parameter.\n    * \n    * Here is how intrinsic Euler angles works:\n    *  - first, rotate the axes system over the alpha axis in angle alpha\n    *  - then, rotate the axes system over the beta axis(which was rotated in the first stage) in angle beta\n    *  - then, rotate the axes system over the gamma axis(which was rotated in the two stages above) in angle gamma\n    *\n    * \\note This class support only intrinsic Euler angles for simplicity,\n    *  see EulerSystem how to easily overcome this for extrinsic systems.\n    *\n    * ### Rotation representation and conversions ###\n    *\n    * It has been proved(see Wikipedia link below) that every rotation can be represented\n    *  by Euler angles, but there is no singular representation (e.g. unlike rotation matrices).\n    * Therefore, you can convert from Eigen rotation and to them\n    *  (including rotation matrices, which is not called \"rotations\" by Eigen design).\n    *\n    * Euler angles usually used for:\n    *  - convenient human representation of rotation, especially in interactive GUI.\n    *  - gimbal systems and robotics\n    *  - efficient encoding(i.e. 3 floats only) of rotation for network protocols.\n    *\n    * However, Euler angles are slow comparing to quaternion or matrices,\n    *  because their unnatural math definition, although it's simple for human.\n    * To overcome this, this class provide easy movement from the math friendly representation\n    *  to the human friendly representation, and vise-versa.\n    *\n    * All the user need to do is a safe simple C++ type conversion,\n    *  and this class take care for the math.\n    * Additionally, some axes related computation is done in compile time.\n    *\n    * #### Euler angles ranges in conversions ####\n    *\n    * When converting some rotation to Euler angles, there are some ways you can guarantee\n    *  the Euler angles ranges.\n    *\n    * #### implicit ranges ####\n    * When using implicit ranges, all angles are guarantee to be in the range [-PI, +PI],\n    *  unless you convert from some other Euler angles.\n    * In this case, the range is __undefined__ (might be even less than -PI or greater than +2*PI).\n    * \\sa EulerAngles(const MatrixBase<Derived>&)\n    * \\sa EulerAngles(const RotationBase<Derived, 3>&)\n    *\n    * #### explicit ranges ####\n    * When using explicit ranges, all angles are guarantee to be in the range you choose.\n    * In the range Boolean parameter, you're been ask whether you prefer the positive range or not:\n    * - _true_ - force the range between [0, +2*PI]\n    * - _false_ - force the range between [-PI, +PI]\n    *\n    * ##### compile time ranges #####\n    * This is when you have compile time ranges and you prefer to\n    *  use template parameter. (e.g. for performance)\n    * \\sa FromRotation()\n    *\n    * ##### run-time time ranges #####\n    * Run-time ranges are also supported.\n    * \\sa EulerAngles(const MatrixBase<Derived>&, bool, bool, bool)\n    * \\sa EulerAngles(const RotationBase<Derived, 3>&, bool, bool, bool)\n    *\n    * ### Convenient user typedefs ###\n    *\n    * Convenient typedefs for EulerAngles exist for float and double scalar,\n    *  in a form of EulerAngles{A}{B}{C}{scalar},\n    *  e.g. \\ref EulerAnglesXYZd, \\ref EulerAnglesZYZf.\n    *\n    * Only for positive axes{+x,+y,+z} Euler systems are have convenient typedef.\n    * If you need negative axes{-x,-y,-z}, it is recommended to create you own typedef with\n    *  a word that represent what you need.\n    *\n    * ### Example ###\n    *\n    * \\include EulerAngles.cpp\n    * Output: \\verbinclude EulerAngles.out\n    *\n    * ### Additional reading ###\n    *\n    * If you're want to get more idea about how Euler system work in Eigen see EulerSystem.\n    *\n    * More information about Euler angles: https://en.wikipedia.org/wiki/Euler_angles\n    *\n    * \\tparam _Scalar the scalar type, i.e., the type of the angles.\n    *\n    * \\tparam _System the EulerSystem to use, which represents the axes of rotation.\n    */\n  template <typename _Scalar, class _System>\n  class EulerAngles : public RotationBase<EulerAngles<_Scalar, _System>, 3>\n  {\n    public:\n      /** the scalar type of the angles */\n      typedef _Scalar Scalar;\n      \n      /** the EulerSystem to use, which represents the axes of rotation. */\n      typedef _System System;\n    \n      typedef Matrix<Scalar,3,3> Matrix3; /*!< the equivalent rotation matrix type */\n      typedef Matrix<Scalar,3,1> Vector3; /*!< the equivalent 3 dimension vector type */\n      typedef Quaternion<Scalar> QuaternionType; /*!< the equivalent quaternion type */\n      typedef AngleAxis<Scalar> AngleAxisType; /*!< the equivalent angle-axis type */\n      \n      /** \\returns the axis vector of the first (alpha) rotation */\n      static Vector3 AlphaAxisVector() {\n        const Vector3& u = Vector3::Unit(System::AlphaAxisAbs - 1);\n        return System::IsAlphaOpposite ? -u : u;\n      }\n      \n      /** \\returns the axis vector of the second (beta) rotation */\n      static Vector3 BetaAxisVector() {\n        const Vector3& u = Vector3::Unit(System::BetaAxisAbs - 1);\n        return System::IsBetaOpposite ? -u : u;\n      }\n      \n      /** \\returns the axis vector of the third (gamma) rotation */\n      static Vector3 GammaAxisVector() {\n        const Vector3& u = Vector3::Unit(System::GammaAxisAbs - 1);\n        return System::IsGammaOpposite ? -u : u;\n      }\n\n    private:\n      Vector3 m_angles;\n\n    public:\n      /** Default constructor without initialization. */\n      EulerAngles() {}\n      /** Constructs and initialize Euler angles(\\p alpha, \\p beta, \\p gamma). */\n      EulerAngles(const Scalar& alpha, const Scalar& beta, const Scalar& gamma) :\n        m_angles(alpha, beta, gamma) {}\n      \n      /** Constructs and initialize Euler angles from a 3x3 rotation matrix \\p m.\n        *\n        * \\note All angles will be in the range [-PI, PI].\n      */\n      template<typename Derived>\n      EulerAngles(const MatrixBase<Derived>& m) { *this = m; }\n      \n      /** Constructs and initialize Euler angles from a 3x3 rotation matrix \\p m,\n        *  with options to choose for each angle the requested range.\n        *\n        * If positive range is true, then the specified angle will be in the range [0, +2*PI].\n        * Otherwise, the specified angle will be in the range [-PI, +PI].\n        *\n        * \\param m The 3x3 rotation matrix to convert\n        * \\param positiveRangeAlpha If true, alpha will be in [0, 2*PI]. Otherwise, in [-PI, +PI].\n        * \\param positiveRangeBeta If true, beta will be in [0, 2*PI]. Otherwise, in [-PI, +PI].\n        * \\param positiveRangeGamma If true, gamma will be in [0, 2*PI]. Otherwise, in [-PI, +PI].\n      */\n      template<typename Derived>\n      EulerAngles(\n        const MatrixBase<Derived>& m,\n        bool positiveRangeAlpha,\n        bool positiveRangeBeta,\n        bool positiveRangeGamma) {\n        \n        System::CalcEulerAngles(*this, m, positiveRangeAlpha, positiveRangeBeta, positiveRangeGamma);\n      }\n      \n      /** Constructs and initialize Euler angles from a rotation \\p rot.\n        *\n        * \\note All angles will be in the range [-PI, PI], unless \\p rot is an EulerAngles.\n        *  If rot is an EulerAngles, expected EulerAngles range is __undefined__.\n        *  (Use other functions here for enforcing range if this effect is desired)\n      */\n      template<typename Derived>\n      EulerAngles(const RotationBase<Derived, 3>& rot) { *this = rot; }\n      \n      /** Constructs and initialize Euler angles from a rotation \\p rot,\n        *  with options to choose for each angle the requested range.\n        *\n        * If positive range is true, then the specified angle will be in the range [0, +2*PI].\n        * Otherwise, the specified angle will be in the range [-PI, +PI].\n        *\n        * \\param rot The 3x3 rotation matrix to convert\n        * \\param positiveRangeAlpha If true, alpha will be in [0, 2*PI]. Otherwise, in [-PI, +PI].\n        * \\param positiveRangeBeta If true, beta will be in [0, 2*PI]. Otherwise, in [-PI, +PI].\n        * \\param positiveRangeGamma If true, gamma will be in [0, 2*PI]. Otherwise, in [-PI, +PI].\n      */\n      template<typename Derived>\n      EulerAngles(\n        const RotationBase<Derived, 3>& rot,\n        bool positiveRangeAlpha,\n        bool positiveRangeBeta,\n        bool positiveRangeGamma) {\n        \n        System::CalcEulerAngles(*this, rot.toRotationMatrix(), positiveRangeAlpha, positiveRangeBeta, positiveRangeGamma);\n      }\n\n      /** \\returns The angle values stored in a vector (alpha, beta, gamma). */\n      const Vector3& angles() const { return m_angles; }\n      /** \\returns A read-write reference to the angle values stored in a vector (alpha, beta, gamma). */\n      Vector3& angles() { return m_angles; }\n\n      /** \\returns The value of the first angle. */\n      Scalar alpha() const { return m_angles[0]; }\n      /** \\returns A read-write reference to the angle of the first angle. */\n      Scalar& alpha() { return m_angles[0]; }\n\n      /** \\returns The value of the second angle. */\n      Scalar beta() const { return m_angles[1]; }\n      /** \\returns A read-write reference to the angle of the second angle. */\n      Scalar& beta() { return m_angles[1]; }\n\n      /** \\returns The value of the third angle. */\n      Scalar gamma() const { return m_angles[2]; }\n      /** \\returns A read-write reference to the angle of the third angle. */\n      Scalar& gamma() { return m_angles[2]; }\n\n      /** \\returns The Euler angles rotation inverse (which is as same as the negative),\n        *  (-alpha, -beta, -gamma).\n      */\n      EulerAngles inverse() const\n      {\n        EulerAngles res;\n        res.m_angles = -m_angles;\n        return res;\n      }\n\n      /** \\returns The Euler angles rotation negative (which is as same as the inverse),\n        *  (-alpha, -beta, -gamma).\n      */\n      EulerAngles operator -() const\n      {\n        return inverse();\n      }\n      \n      /** Constructs and initialize Euler angles from a 3x3 rotation matrix \\p m,\n        *  with options to choose for each angle the requested range (__only in compile time__).\n        *\n        * If positive range is true, then the specified angle will be in the range [0, +2*PI].\n        * Otherwise, the specified angle will be in the range [-PI, +PI].\n        *\n        * \\param m The 3x3 rotation matrix to convert\n        * \\tparam positiveRangeAlpha If true, alpha will be in [0, 2*PI]. Otherwise, in [-PI, +PI].\n        * \\tparam positiveRangeBeta If true, beta will be in [0, 2*PI]. Otherwise, in [-PI, +PI].\n        * \\tparam positiveRangeGamma If true, gamma will be in [0, 2*PI]. Otherwise, in [-PI, +PI].\n        */\n      template<\n        bool PositiveRangeAlpha,\n        bool PositiveRangeBeta,\n        bool PositiveRangeGamma,\n        typename Derived>\n      static EulerAngles FromRotation(const MatrixBase<Derived>& m)\n      {\n        EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived, 3, 3)\n        \n        EulerAngles e;\n        System::template CalcEulerAngles<\n          PositiveRangeAlpha, PositiveRangeBeta, PositiveRangeGamma, _Scalar>(e, m);\n        return e;\n      }\n      \n      /** Constructs and initialize Euler angles from a rotation \\p rot,\n        *  with options to choose for each angle the requested range (__only in compile time__).\n        *\n        * If positive range is true, then the specified angle will be in the range [0, +2*PI].\n        * Otherwise, the specified angle will be in the range [-PI, +PI].\n        *\n        * \\param rot The 3x3 rotation matrix to convert\n        * \\tparam positiveRangeAlpha If true, alpha will be in [0, 2*PI]. Otherwise, in [-PI, +PI].\n        * \\tparam positiveRangeBeta If true, beta will be in [0, 2*PI]. Otherwise, in [-PI, +PI].\n        * \\tparam positiveRangeGamma If true, gamma will be in [0, 2*PI]. Otherwise, in [-PI, +PI].\n      */\n      template<\n        bool PositiveRangeAlpha,\n        bool PositiveRangeBeta,\n        bool PositiveRangeGamma,\n        typename Derived>\n      static EulerAngles FromRotation(const RotationBase<Derived, 3>& rot)\n      {\n        return FromRotation<PositiveRangeAlpha, PositiveRangeBeta, PositiveRangeGamma>(rot.toRotationMatrix());\n      }\n      \n      /*EulerAngles& fromQuaternion(const QuaternionType& q)\n      {\n        // TODO: Implement it in a faster way for quaternions\n        // According to http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToEuler/\n        //  we can compute only the needed matrix cells and then convert to euler angles. (see ZYX example below)\n        // Currently we compute all matrix cells from quaternion.\n\n        // Special case only for ZYX\n        //Scalar y2 = q.y() * q.y();\n        //m_angles[0] = std::atan2(2*(q.w()*q.z() + q.x()*q.y()), (1 - 2*(y2 + q.z()*q.z())));\n        //m_angles[1] = std::asin( 2*(q.w()*q.y() - q.z()*q.x()));\n        //m_angles[2] = std::atan2(2*(q.w()*q.x() + q.y()*q.z()), (1 - 2*(q.x()*q.x() + y2)));\n      }*/\n      \n      /** Set \\c *this from a rotation matrix(i.e. pure orthogonal matrix with determinant of +1). */\n      template<typename Derived>\n      EulerAngles& operator=(const MatrixBase<Derived>& m) {\n        EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived, 3, 3)\n        \n        System::CalcEulerAngles(*this, m);\n        return *this;\n      }\n\n      // TODO: Assign and construct from another EulerAngles (with different system)\n      \n      /** Set \\c *this from a rotation. */\n      template<typename Derived>\n      EulerAngles& operator=(const RotationBase<Derived, 3>& rot) {\n        System::CalcEulerAngles(*this, rot.toRotationMatrix());\n        return *this;\n      }\n      \n      // TODO: Support isApprox function\n\n      /** \\returns an equivalent 3x3 rotation matrix. */\n      Matrix3 toRotationMatrix() const\n      {\n        return static_cast<QuaternionType>(*this).toRotationMatrix();\n      }\n\n      /** Convert the Euler angles to quaternion. */\n      operator QuaternionType() const\n      {\n        return\n          AngleAxisType(alpha(), AlphaAxisVector()) *\n          AngleAxisType(beta(), BetaAxisVector())   *\n          AngleAxisType(gamma(), GammaAxisVector());\n      }\n      \n      friend std::ostream& operator<<(std::ostream& s, const EulerAngles<Scalar, System>& eulerAngles)\n      {\n        s << eulerAngles.angles().transpose();\n        return s;\n      }\n  };\n\n#define EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(AXES, SCALAR_TYPE, SCALAR_POSTFIX) \\\n  /** \\ingroup EulerAngles_Module */ \\\n  typedef EulerAngles<SCALAR_TYPE, EulerSystem##AXES> EulerAngles##AXES##SCALAR_POSTFIX;\n\n#define EIGEN_EULER_ANGLES_TYPEDEFS(SCALAR_TYPE, SCALAR_POSTFIX) \\\n  EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(XYZ, SCALAR_TYPE, SCALAR_POSTFIX) \\\n  EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(XYX, SCALAR_TYPE, SCALAR_POSTFIX) \\\n  EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(XZY, SCALAR_TYPE, SCALAR_POSTFIX) \\\n  EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(XZX, SCALAR_TYPE, SCALAR_POSTFIX) \\\n \\\n  EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(YZX, SCALAR_TYPE, SCALAR_POSTFIX) \\\n  EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(YZY, SCALAR_TYPE, SCALAR_POSTFIX) \\\n  EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(YXZ, SCALAR_TYPE, SCALAR_POSTFIX) \\\n  EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(YXY, SCALAR_TYPE, SCALAR_POSTFIX) \\\n \\\n  EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(ZXY, SCALAR_TYPE, SCALAR_POSTFIX) \\\n  EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(ZXZ, SCALAR_TYPE, SCALAR_POSTFIX) \\\n  EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(ZYX, SCALAR_TYPE, SCALAR_POSTFIX) \\\n  EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(ZYZ, SCALAR_TYPE, SCALAR_POSTFIX)\n\nEIGEN_EULER_ANGLES_TYPEDEFS(float, f)\nEIGEN_EULER_ANGLES_TYPEDEFS(double, d)\n\n  namespace internal\n  {\n    template<typename _Scalar, class _System>\n    struct traits<EulerAngles<_Scalar, _System> >\n    {\n      typedef _Scalar Scalar;\n    };\n  }\n  \n}\n\n#endif // EIGEN_EULERANGLESCLASS_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/EulerAngles/EulerSystem.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Tal Hadad <tal_hd@hotmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_EULERSYSTEM_H\n#define EIGEN_EULERSYSTEM_H\n\nnamespace Eigen\n{\n  // Forward declerations\n  template <typename _Scalar, class _System>\n  class EulerAngles;\n  \n  namespace internal\n  {\n    // TODO: Check if already exists on the rest API\n    template <int Num, bool IsPositive = (Num > 0)>\n    struct Abs\n    {\n      enum { value = Num };\n    };\n  \n    template <int Num>\n    struct Abs<Num, false>\n    {\n      enum { value = -Num };\n    };\n\n    template <int Axis>\n    struct IsValidAxis\n    {\n      enum { value = Axis != 0 && Abs<Axis>::value <= 3 };\n    };\n  }\n  \n  #define EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT(COND,MSG) typedef char static_assertion_##MSG[(COND)?1:-1]\n  \n  /** \\brief Representation of a fixed signed rotation axis for EulerSystem.\n    *\n    * \\ingroup EulerAngles_Module\n    *\n    * Values here represent:\n    *  - The axis of the rotation: X, Y or Z.\n    *  - The sign (i.e. direction of the rotation along the axis): positive(+) or negative(-)\n    *\n    * Therefore, this could express all the axes {+X,+Y,+Z,-X,-Y,-Z}\n    *\n    * For positive axis, use +EULER_{axis}, and for negative axis use -EULER_{axis}.\n    */\n  enum EulerAxis\n  {\n    EULER_X = 1, /*!< the X axis */\n    EULER_Y = 2, /*!< the Y axis */\n    EULER_Z = 3  /*!< the Z axis */\n  };\n  \n  /** \\class EulerSystem\n    *\n    * \\ingroup EulerAngles_Module\n    *\n    * \\brief Represents a fixed Euler rotation system.\n    *\n    * This meta-class goal is to represent the Euler system in compilation time, for EulerAngles.\n    *\n    * You can use this class to get two things:\n    *  - Build an Euler system, and then pass it as a template parameter to EulerAngles.\n    *  - Query some compile time data about an Euler system. (e.g. Whether it's tait bryan)\n    *\n    * Euler rotation is a set of three rotation on fixed axes. (see \\ref EulerAngles)\n    * This meta-class store constantly those signed axes. (see \\ref EulerAxis)\n    *\n    * ### Types of Euler systems ###\n    *\n    * All and only valid 3 dimension Euler rotation over standard\n    *  signed axes{+X,+Y,+Z,-X,-Y,-Z} are supported:\n    *  - all axes X, Y, Z in each valid order (see below what order is valid)\n    *  - rotation over the axis is supported both over the positive and negative directions.\n    *  - both tait bryan and proper/classic Euler angles (i.e. the opposite).\n    *\n    * Since EulerSystem support both positive and negative directions,\n    *  you may call this rotation distinction in other names:\n    *  - _right handed_ or _left handed_\n    *  - _counterclockwise_ or _clockwise_\n    *\n    * Notice all axed combination are valid, and would trigger a static assertion.\n    * Same unsigned axes can't be neighbors, e.g. {X,X,Y} is invalid.\n    * This yield two and only two classes:\n    *  - _tait bryan_ - all unsigned axes are distinct, e.g. {X,Y,Z}\n    *  - _proper/classic Euler angles_ - The first and the third unsigned axes is equal,\n    *     and the second is different, e.g. {X,Y,X}\n    *\n    * ### Intrinsic vs extrinsic Euler systems ###\n    *\n    * Only intrinsic Euler systems are supported for simplicity.\n    *  If you want to use extrinsic Euler systems,\n    *   just use the equal intrinsic opposite order for axes and angles.\n    *  I.e axes (A,B,C) becomes (C,B,A), and angles (a,b,c) becomes (c,b,a).\n    *\n    * ### Convenient user typedefs ###\n    *\n    * Convenient typedefs for EulerSystem exist (only for positive axes Euler systems),\n    *  in a form of EulerSystem{A}{B}{C}, e.g. \\ref EulerSystemXYZ.\n    *\n    * ### Additional reading ###\n    *\n    * More information about Euler angles: https://en.wikipedia.org/wiki/Euler_angles\n    *\n    * \\tparam _AlphaAxis the first fixed EulerAxis\n    *\n    * \\tparam _AlphaAxis the second fixed EulerAxis\n    *\n    * \\tparam _AlphaAxis the third fixed EulerAxis\n    */\n  template <int _AlphaAxis, int _BetaAxis, int _GammaAxis>\n  class EulerSystem\n  {\n    public:\n    // It's defined this way and not as enum, because I think\n    //  that enum is not guerantee to support negative numbers\n    \n    /** The first rotation axis */\n    static const int AlphaAxis = _AlphaAxis;\n    \n    /** The second rotation axis */\n    static const int BetaAxis = _BetaAxis;\n    \n    /** The third rotation axis */\n    static const int GammaAxis = _GammaAxis;\n\n    enum\n    {\n      AlphaAxisAbs = internal::Abs<AlphaAxis>::value, /*!< the first rotation axis unsigned */\n      BetaAxisAbs = internal::Abs<BetaAxis>::value, /*!< the second rotation axis unsigned */\n      GammaAxisAbs = internal::Abs<GammaAxis>::value, /*!< the third rotation axis unsigned */\n      \n      IsAlphaOpposite = (AlphaAxis < 0) ? 1 : 0, /*!< weather alpha axis is negative */\n      IsBetaOpposite = (BetaAxis < 0) ? 1 : 0, /*!< weather beta axis is negative */\n      IsGammaOpposite = (GammaAxis < 0) ? 1 : 0, /*!< weather gamma axis is negative */\n      \n      IsOdd = ((AlphaAxisAbs)%3 == (BetaAxisAbs - 1)%3) ? 0 : 1, /*!< weather the Euler system is odd */\n      IsEven = IsOdd ? 0 : 1, /*!< weather the Euler system is even */\n\n      IsTaitBryan = ((unsigned)AlphaAxisAbs != (unsigned)GammaAxisAbs) ? 1 : 0 /*!< weather the Euler system is tait bryan */\n    };\n    \n    private:\n    \n    EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT(internal::IsValidAxis<AlphaAxis>::value,\n      ALPHA_AXIS_IS_INVALID);\n      \n    EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT(internal::IsValidAxis<BetaAxis>::value,\n      BETA_AXIS_IS_INVALID);\n      \n    EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT(internal::IsValidAxis<GammaAxis>::value,\n      GAMMA_AXIS_IS_INVALID);\n      \n    EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT((unsigned)AlphaAxisAbs != (unsigned)BetaAxisAbs,\n      ALPHA_AXIS_CANT_BE_EQUAL_TO_BETA_AXIS);\n      \n    EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT((unsigned)BetaAxisAbs != (unsigned)GammaAxisAbs,\n      BETA_AXIS_CANT_BE_EQUAL_TO_GAMMA_AXIS);\n\n    enum\n    {\n      // I, J, K are the pivot indexes permutation for the rotation matrix, that match this Euler system. \n      // They are used in this class converters.\n      // They are always different from each other, and their possible values are: 0, 1, or 2.\n      I = AlphaAxisAbs - 1,\n      J = (AlphaAxisAbs - 1 + 1 + IsOdd)%3,\n      K = (AlphaAxisAbs - 1 + 2 - IsOdd)%3\n    };\n    \n    // TODO: Get @mat parameter in form that avoids double evaluation.\n    template <typename Derived>\n    static void CalcEulerAngles_imp(Matrix<typename MatrixBase<Derived>::Scalar, 3, 1>& res, const MatrixBase<Derived>& mat, internal::true_type /*isTaitBryan*/)\n    {\n      using std::atan2;\n      using std::sin;\n      using std::cos;\n      \n      typedef typename Derived::Scalar Scalar;\n      typedef Matrix<Scalar,2,1> Vector2;\n      \n      res[0] = atan2(mat(J,K), mat(K,K));\n      Scalar c2 = Vector2(mat(I,I), mat(I,J)).norm();\n      if((IsOdd && res[0]<Scalar(0)) || ((!IsOdd) && res[0]>Scalar(0))) {\n        if(res[0] > Scalar(0)) {\n          res[0] -= Scalar(EIGEN_PI);\n        }\n        else {\n          res[0] += Scalar(EIGEN_PI);\n        }\n        res[1] = atan2(-mat(I,K), -c2);\n      }\n      else\n        res[1] = atan2(-mat(I,K), c2);\n      Scalar s1 = sin(res[0]);\n      Scalar c1 = cos(res[0]);\n      res[2] = atan2(s1*mat(K,I)-c1*mat(J,I), c1*mat(J,J) - s1 * mat(K,J));\n    }\n\n    template <typename Derived>\n    static void CalcEulerAngles_imp(Matrix<typename MatrixBase<Derived>::Scalar,3,1>& res, const MatrixBase<Derived>& mat, internal::false_type /*isTaitBryan*/)\n    {\n      using std::atan2;\n      using std::sin;\n      using std::cos;\n\n      typedef typename Derived::Scalar Scalar;\n      typedef Matrix<Scalar,2,1> Vector2;\n      \n      res[0] = atan2(mat(J,I), mat(K,I));\n      if((IsOdd && res[0]<Scalar(0)) || ((!IsOdd) && res[0]>Scalar(0)))\n      {\n        if(res[0] > Scalar(0)) {\n          res[0] -= Scalar(EIGEN_PI);\n        }\n        else {\n          res[0] += Scalar(EIGEN_PI);\n        }\n        Scalar s2 = Vector2(mat(J,I), mat(K,I)).norm();\n        res[1] = -atan2(s2, mat(I,I));\n      }\n      else\n      {\n        Scalar s2 = Vector2(mat(J,I), mat(K,I)).norm();\n        res[1] = atan2(s2, mat(I,I));\n      }\n\n      // With a=(0,1,0), we have i=0; j=1; k=2, and after computing the first two angles,\n      // we can compute their respective rotation, and apply its inverse to M. Since the result must\n      // be a rotation around x, we have:\n      //\n      //  c2  s1.s2 c1.s2                   1  0   0 \n      //  0   c1    -s1       *    M    =   0  c3  s3\n      //  -s2 s1.c2 c1.c2                   0 -s3  c3\n      //\n      //  Thus:  m11.c1 - m21.s1 = c3  &   m12.c1 - m22.s1 = s3\n\n      Scalar s1 = sin(res[0]);\n      Scalar c1 = cos(res[0]);\n      res[2] = atan2(c1*mat(J,K)-s1*mat(K,K), c1*mat(J,J) - s1 * mat(K,J));\n    }\n    \n    template<typename Scalar>\n    static void CalcEulerAngles(\n      EulerAngles<Scalar, EulerSystem>& res,\n      const typename EulerAngles<Scalar, EulerSystem>::Matrix3& mat)\n    {\n      CalcEulerAngles(res, mat, false, false, false);\n    }\n    \n    template<\n      bool PositiveRangeAlpha,\n      bool PositiveRangeBeta,\n      bool PositiveRangeGamma,\n      typename Scalar>\n    static void CalcEulerAngles(\n      EulerAngles<Scalar, EulerSystem>& res,\n      const typename EulerAngles<Scalar, EulerSystem>::Matrix3& mat)\n    {\n      CalcEulerAngles(res, mat, PositiveRangeAlpha, PositiveRangeBeta, PositiveRangeGamma);\n    }\n    \n    template<typename Scalar>\n    static void CalcEulerAngles(\n      EulerAngles<Scalar, EulerSystem>& res,\n      const typename EulerAngles<Scalar, EulerSystem>::Matrix3& mat,\n      bool PositiveRangeAlpha,\n      bool PositiveRangeBeta,\n      bool PositiveRangeGamma)\n    {\n      CalcEulerAngles_imp(\n        res.angles(), mat,\n        typename internal::conditional<IsTaitBryan, internal::true_type, internal::false_type>::type());\n\n      if (IsAlphaOpposite == IsOdd)\n        res.alpha() = -res.alpha();\n        \n      if (IsBetaOpposite == IsOdd)\n        res.beta() = -res.beta();\n        \n      if (IsGammaOpposite == IsOdd)\n        res.gamma() = -res.gamma();\n      \n      // Saturate results to the requested range\n      if (PositiveRangeAlpha && (res.alpha() < 0))\n        res.alpha() += Scalar(2 * EIGEN_PI);\n      \n      if (PositiveRangeBeta && (res.beta() < 0))\n        res.beta() += Scalar(2 * EIGEN_PI);\n      \n      if (PositiveRangeGamma && (res.gamma() < 0))\n        res.gamma() += Scalar(2 * EIGEN_PI);\n    }\n    \n    template <typename _Scalar, class _System>\n    friend class Eigen::EulerAngles;\n  };\n\n#define EIGEN_EULER_SYSTEM_TYPEDEF(A, B, C) \\\n  /** \\ingroup EulerAngles_Module */ \\\n  typedef EulerSystem<EULER_##A, EULER_##B, EULER_##C> EulerSystem##A##B##C;\n  \n  EIGEN_EULER_SYSTEM_TYPEDEF(X,Y,Z)\n  EIGEN_EULER_SYSTEM_TYPEDEF(X,Y,X)\n  EIGEN_EULER_SYSTEM_TYPEDEF(X,Z,Y)\n  EIGEN_EULER_SYSTEM_TYPEDEF(X,Z,X)\n  \n  EIGEN_EULER_SYSTEM_TYPEDEF(Y,Z,X)\n  EIGEN_EULER_SYSTEM_TYPEDEF(Y,Z,Y)\n  EIGEN_EULER_SYSTEM_TYPEDEF(Y,X,Z)\n  EIGEN_EULER_SYSTEM_TYPEDEF(Y,X,Y)\n  \n  EIGEN_EULER_SYSTEM_TYPEDEF(Z,X,Y)\n  EIGEN_EULER_SYSTEM_TYPEDEF(Z,X,Z)\n  EIGEN_EULER_SYSTEM_TYPEDEF(Z,Y,X)\n  EIGEN_EULER_SYSTEM_TYPEDEF(Z,Y,Z)\n}\n\n#endif // EIGEN_EULERSYSTEM_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/FFT/ei_fftw_impl.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra. \n//\n// Copyright (C) 2009 Mark Borgerding mark a borgerding net\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\nnamespace Eigen { \n\nnamespace internal {\n\n  // FFTW uses non-const arguments\n  // so we must use ugly const_cast calls for all the args it uses\n  //\n  // This should be safe as long as \n  // 1. we use FFTW_ESTIMATE for all our planning\n  //       see the FFTW docs section 4.3.2 \"Planner Flags\"\n  // 2. fftw_complex is compatible with std::complex\n  //    This assumes std::complex<T> layout is array of size 2 with real,imag\n  template <typename T> \n  inline \n  T * fftw_cast(const T* p)\n  { \n      return const_cast<T*>( p); \n  }\n\n  inline \n  fftw_complex * fftw_cast( const std::complex<double> * p)\n  {\n      return const_cast<fftw_complex*>( reinterpret_cast<const fftw_complex*>(p) ); \n  }\n\n  inline \n  fftwf_complex * fftw_cast( const std::complex<float> * p)\n  { \n      return const_cast<fftwf_complex*>( reinterpret_cast<const fftwf_complex*>(p) ); \n  }\n\n  inline \n  fftwl_complex * fftw_cast( const std::complex<long double> * p)\n  { \n      return const_cast<fftwl_complex*>( reinterpret_cast<const fftwl_complex*>(p) ); \n  }\n\n  template <typename T> \n  struct fftw_plan {};\n\n  template <> \n  struct fftw_plan<float>\n  {\n      typedef float scalar_type;\n      typedef fftwf_complex complex_type;\n      fftwf_plan m_plan;\n      fftw_plan() :m_plan(NULL) {}\n      ~fftw_plan() {if (m_plan) fftwf_destroy_plan(m_plan);}\n\n      inline\n      void fwd(complex_type * dst,complex_type * src,int nfft) {\n          if (m_plan==NULL) m_plan = fftwf_plan_dft_1d(nfft,src,dst, FFTW_FORWARD, FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);\n          fftwf_execute_dft( m_plan, src,dst);\n      }\n      inline\n      void inv(complex_type * dst,complex_type * src,int nfft) {\n          if (m_plan==NULL) m_plan = fftwf_plan_dft_1d(nfft,src,dst, FFTW_BACKWARD , FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);\n          fftwf_execute_dft( m_plan, src,dst);\n      }\n      inline\n      void fwd(complex_type * dst,scalar_type * src,int nfft) {\n          if (m_plan==NULL) m_plan = fftwf_plan_dft_r2c_1d(nfft,src,dst,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);\n          fftwf_execute_dft_r2c( m_plan,src,dst);\n      }\n      inline\n      void inv(scalar_type * dst,complex_type * src,int nfft) {\n          if (m_plan==NULL)\n              m_plan = fftwf_plan_dft_c2r_1d(nfft,src,dst,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);\n          fftwf_execute_dft_c2r( m_plan, src,dst);\n      }\n\n      inline \n      void fwd2( complex_type * dst,complex_type * src,int n0,int n1) {\n          if (m_plan==NULL) m_plan = fftwf_plan_dft_2d(n0,n1,src,dst,FFTW_FORWARD,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);\n          fftwf_execute_dft( m_plan, src,dst);\n      }\n      inline \n      void inv2( complex_type * dst,complex_type * src,int n0,int n1) {\n          if (m_plan==NULL) m_plan = fftwf_plan_dft_2d(n0,n1,src,dst,FFTW_BACKWARD,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);\n          fftwf_execute_dft( m_plan, src,dst);\n      }\n\n  };\n  template <> \n  struct fftw_plan<double>\n  {\n      typedef double scalar_type;\n      typedef fftw_complex complex_type;\n      ::fftw_plan m_plan;\n      fftw_plan() :m_plan(NULL) {}\n      ~fftw_plan() {if (m_plan) fftw_destroy_plan(m_plan);}\n\n      inline\n      void fwd(complex_type * dst,complex_type * src,int nfft) {\n          if (m_plan==NULL) m_plan = fftw_plan_dft_1d(nfft,src,dst, FFTW_FORWARD, FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);\n          fftw_execute_dft( m_plan, src,dst);\n      }\n      inline\n      void inv(complex_type * dst,complex_type * src,int nfft) {\n          if (m_plan==NULL) m_plan = fftw_plan_dft_1d(nfft,src,dst, FFTW_BACKWARD , FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);\n          fftw_execute_dft( m_plan, src,dst);\n      }\n      inline\n      void fwd(complex_type * dst,scalar_type * src,int nfft) {\n          if (m_plan==NULL) m_plan = fftw_plan_dft_r2c_1d(nfft,src,dst,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);\n          fftw_execute_dft_r2c( m_plan,src,dst);\n      }\n      inline\n      void inv(scalar_type * dst,complex_type * src,int nfft) {\n          if (m_plan==NULL)\n              m_plan = fftw_plan_dft_c2r_1d(nfft,src,dst,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);\n          fftw_execute_dft_c2r( m_plan, src,dst);\n      }\n      inline \n      void fwd2( complex_type * dst,complex_type * src,int n0,int n1) {\n          if (m_plan==NULL) m_plan = fftw_plan_dft_2d(n0,n1,src,dst,FFTW_FORWARD,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);\n          fftw_execute_dft( m_plan, src,dst);\n      }\n      inline \n      void inv2( complex_type * dst,complex_type * src,int n0,int n1) {\n          if (m_plan==NULL) m_plan = fftw_plan_dft_2d(n0,n1,src,dst,FFTW_BACKWARD,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);\n          fftw_execute_dft( m_plan, src,dst);\n      }\n  };\n  template <> \n  struct fftw_plan<long double>\n  {\n      typedef long double scalar_type;\n      typedef fftwl_complex complex_type;\n      fftwl_plan m_plan;\n      fftw_plan() :m_plan(NULL) {}\n      ~fftw_plan() {if (m_plan) fftwl_destroy_plan(m_plan);}\n\n      inline\n      void fwd(complex_type * dst,complex_type * src,int nfft) {\n          if (m_plan==NULL) m_plan = fftwl_plan_dft_1d(nfft,src,dst, FFTW_FORWARD, FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);\n          fftwl_execute_dft( m_plan, src,dst);\n      }\n      inline\n      void inv(complex_type * dst,complex_type * src,int nfft) {\n          if (m_plan==NULL) m_plan = fftwl_plan_dft_1d(nfft,src,dst, FFTW_BACKWARD , FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);\n          fftwl_execute_dft( m_plan, src,dst);\n      }\n      inline\n      void fwd(complex_type * dst,scalar_type * src,int nfft) {\n          if (m_plan==NULL) m_plan = fftwl_plan_dft_r2c_1d(nfft,src,dst,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);\n          fftwl_execute_dft_r2c( m_plan,src,dst);\n      }\n      inline\n      void inv(scalar_type * dst,complex_type * src,int nfft) {\n          if (m_plan==NULL)\n              m_plan = fftwl_plan_dft_c2r_1d(nfft,src,dst,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);\n          fftwl_execute_dft_c2r( m_plan, src,dst);\n      }\n      inline \n      void fwd2( complex_type * dst,complex_type * src,int n0,int n1) {\n          if (m_plan==NULL) m_plan = fftwl_plan_dft_2d(n0,n1,src,dst,FFTW_FORWARD,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);\n          fftwl_execute_dft( m_plan, src,dst);\n      }\n      inline \n      void inv2( complex_type * dst,complex_type * src,int n0,int n1) {\n          if (m_plan==NULL) m_plan = fftwl_plan_dft_2d(n0,n1,src,dst,FFTW_BACKWARD,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);\n          fftwl_execute_dft( m_plan, src,dst);\n      }\n  };\n\n  template <typename _Scalar>\n  struct fftw_impl\n  {\n      typedef _Scalar Scalar;\n      typedef std::complex<Scalar> Complex;\n\n      inline\n      void clear() \n      {\n        m_plans.clear();\n      }\n\n      // complex-to-complex forward FFT\n      inline\n      void fwd( Complex * dst,const Complex *src,int nfft)\n      {\n        get_plan(nfft,false,dst,src).fwd(fftw_cast(dst), fftw_cast(src),nfft );\n      }\n\n      // real-to-complex forward FFT\n      inline\n      void fwd( Complex * dst,const Scalar * src,int nfft) \n      {\n          get_plan(nfft,false,dst,src).fwd(fftw_cast(dst), fftw_cast(src) ,nfft);\n      }\n\n      // 2-d complex-to-complex\n      inline\n      void fwd2(Complex * dst, const Complex * src, int n0,int n1)\n      {\n          get_plan(n0,n1,false,dst,src).fwd2(fftw_cast(dst), fftw_cast(src) ,n0,n1);\n      }\n\n      // inverse complex-to-complex\n      inline\n      void inv(Complex * dst,const Complex  *src,int nfft)\n      {\n        get_plan(nfft,true,dst,src).inv(fftw_cast(dst), fftw_cast(src),nfft );\n      }\n\n      // half-complex to scalar\n      inline\n      void inv( Scalar * dst,const Complex * src,int nfft) \n      {\n        get_plan(nfft,true,dst,src).inv(fftw_cast(dst), fftw_cast(src),nfft );\n      }\n\n      // 2-d complex-to-complex\n      inline\n      void inv2(Complex * dst, const Complex * src, int n0,int n1)\n      {\n        get_plan(n0,n1,true,dst,src).inv2(fftw_cast(dst), fftw_cast(src) ,n0,n1);\n      }\n\n\n  protected:\n      typedef fftw_plan<Scalar> PlanData;\n\n      typedef std::map<int64_t,PlanData> PlanMap;\n\n      PlanMap m_plans;\n\n      inline\n      PlanData & get_plan(int nfft,bool inverse,void * dst,const void * src)\n      {\n          bool inplace = (dst==src);\n          bool aligned = ( (reinterpret_cast<size_t>(src)&15) | (reinterpret_cast<size_t>(dst)&15) ) == 0;\n          int64_t key = ( (nfft<<3 ) | (inverse<<2) | (inplace<<1) | aligned ) << 1;\n          return m_plans[key];\n      }\n\n      inline\n      PlanData & get_plan(int n0,int n1,bool inverse,void * dst,const void * src)\n      {\n          bool inplace = (dst==src);\n          bool aligned = ( (reinterpret_cast<size_t>(src)&15) | (reinterpret_cast<size_t>(dst)&15) ) == 0;\n          int64_t key = ( ( (((int64_t)n0) << 30)|(n1<<3 ) | (inverse<<2) | (inplace<<1) | aligned ) << 1 ) + 1;\n          return m_plans[key];\n      }\n  };\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n/* vim: set filetype=cpp et sw=2 ts=2 ai: */\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/FFT/ei_kissfft_impl.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Mark Borgerding mark a borgerding net\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\nnamespace Eigen { \n\nnamespace internal {\n\n  // This FFT implementation was derived from kissfft http:sourceforge.net/projects/kissfft\n  // Copyright 2003-2009 Mark Borgerding\n\ntemplate <typename _Scalar>\nstruct kiss_cpx_fft\n{\n  typedef _Scalar Scalar;\n  typedef std::complex<Scalar> Complex;\n  std::vector<Complex> m_twiddles;\n  std::vector<int> m_stageRadix;\n  std::vector<int> m_stageRemainder;\n  std::vector<Complex> m_scratchBuf;\n  bool m_inverse;\n\n  inline\n    void make_twiddles(int nfft,bool inverse)\n    {\n      using std::acos;\n      m_inverse = inverse;\n      m_twiddles.resize(nfft);\n      Scalar phinc =  (inverse?2:-2)* acos( (Scalar) -1)  / nfft;\n      for (int i=0;i<nfft;++i)\n        m_twiddles[i] = exp( Complex(0,i*phinc) );\n    }\n\n  void factorize(int nfft)\n  {\n    //start factoring out 4's, then 2's, then 3,5,7,9,...\n    int n= nfft;\n    int p=4;\n    do {\n      while (n % p) {\n        switch (p) {\n          case 4: p = 2; break;\n          case 2: p = 3; break;\n          default: p += 2; break;\n        }\n        if (p*p>n)\n          p=n;// impossible to have a factor > sqrt(n)\n      }\n      n /= p;\n      m_stageRadix.push_back(p);\n      m_stageRemainder.push_back(n);\n      if ( p > 5 )\n        m_scratchBuf.resize(p); // scratchbuf will be needed in bfly_generic\n    }while(n>1);\n  }\n\n  template <typename _Src>\n    inline\n    void work( int stage,Complex * xout, const _Src * xin, size_t fstride,size_t in_stride)\n    {\n      int p = m_stageRadix[stage];\n      int m = m_stageRemainder[stage];\n      Complex * Fout_beg = xout;\n      Complex * Fout_end = xout + p*m;\n\n      if (m>1) {\n        do{\n          // recursive call:\n          // DFT of size m*p performed by doing\n          // p instances of smaller DFTs of size m, \n          // each one takes a decimated version of the input\n          work(stage+1, xout , xin, fstride*p,in_stride);\n          xin += fstride*in_stride;\n        }while( (xout += m) != Fout_end );\n      }else{\n        do{\n          *xout = *xin;\n          xin += fstride*in_stride;\n        }while(++xout != Fout_end );\n      }\n      xout=Fout_beg;\n\n      // recombine the p smaller DFTs \n      switch (p) {\n        case 2: bfly2(xout,fstride,m); break;\n        case 3: bfly3(xout,fstride,m); break;\n        case 4: bfly4(xout,fstride,m); break;\n        case 5: bfly5(xout,fstride,m); break;\n        default: bfly_generic(xout,fstride,m,p); break;\n      }\n    }\n\n  inline\n    void bfly2( Complex * Fout, const size_t fstride, int m)\n    {\n      for (int k=0;k<m;++k) {\n        Complex t = Fout[m+k] * m_twiddles[k*fstride];\n        Fout[m+k] = Fout[k] - t;\n        Fout[k] += t;\n      }\n    }\n\n  inline\n    void bfly4( Complex * Fout, const size_t fstride, const size_t m)\n    {\n      Complex scratch[6];\n      int negative_if_inverse = m_inverse * -2 +1;\n      for (size_t k=0;k<m;++k) {\n        scratch[0] = Fout[k+m] * m_twiddles[k*fstride];\n        scratch[1] = Fout[k+2*m] * m_twiddles[k*fstride*2];\n        scratch[2] = Fout[k+3*m] * m_twiddles[k*fstride*3];\n        scratch[5] = Fout[k] - scratch[1];\n\n        Fout[k] += scratch[1];\n        scratch[3] = scratch[0] + scratch[2];\n        scratch[4] = scratch[0] - scratch[2];\n        scratch[4] = Complex( scratch[4].imag()*negative_if_inverse , -scratch[4].real()* negative_if_inverse );\n\n        Fout[k+2*m]  = Fout[k] - scratch[3];\n        Fout[k] += scratch[3];\n        Fout[k+m] = scratch[5] + scratch[4];\n        Fout[k+3*m] = scratch[5] - scratch[4];\n      }\n    }\n\n  inline\n    void bfly3( Complex * Fout, const size_t fstride, const size_t m)\n    {\n      size_t k=m;\n      const size_t m2 = 2*m;\n      Complex *tw1,*tw2;\n      Complex scratch[5];\n      Complex epi3;\n      epi3 = m_twiddles[fstride*m];\n\n      tw1=tw2=&m_twiddles[0];\n\n      do{\n        scratch[1]=Fout[m] * *tw1;\n        scratch[2]=Fout[m2] * *tw2;\n\n        scratch[3]=scratch[1]+scratch[2];\n        scratch[0]=scratch[1]-scratch[2];\n        tw1 += fstride;\n        tw2 += fstride*2;\n        Fout[m] = Complex( Fout->real() - Scalar(.5)*scratch[3].real() , Fout->imag() - Scalar(.5)*scratch[3].imag() );\n        scratch[0] *= epi3.imag();\n        *Fout += scratch[3];\n        Fout[m2] = Complex(  Fout[m].real() + scratch[0].imag() , Fout[m].imag() - scratch[0].real() );\n        Fout[m] += Complex( -scratch[0].imag(),scratch[0].real() );\n        ++Fout;\n      }while(--k);\n    }\n\n  inline\n    void bfly5( Complex * Fout, const size_t fstride, const size_t m)\n    {\n      Complex *Fout0,*Fout1,*Fout2,*Fout3,*Fout4;\n      size_t u;\n      Complex scratch[13];\n      Complex * twiddles = &m_twiddles[0];\n      Complex *tw;\n      Complex ya,yb;\n      ya = twiddles[fstride*m];\n      yb = twiddles[fstride*2*m];\n\n      Fout0=Fout;\n      Fout1=Fout0+m;\n      Fout2=Fout0+2*m;\n      Fout3=Fout0+3*m;\n      Fout4=Fout0+4*m;\n\n      tw=twiddles;\n      for ( u=0; u<m; ++u ) {\n        scratch[0] = *Fout0;\n\n        scratch[1]  = *Fout1 * tw[u*fstride];\n        scratch[2]  = *Fout2 * tw[2*u*fstride];\n        scratch[3]  = *Fout3 * tw[3*u*fstride];\n        scratch[4]  = *Fout4 * tw[4*u*fstride];\n\n        scratch[7] = scratch[1] + scratch[4];\n        scratch[10] = scratch[1] - scratch[4];\n        scratch[8] = scratch[2] + scratch[3];\n        scratch[9] = scratch[2] - scratch[3];\n\n        *Fout0 +=  scratch[7];\n        *Fout0 +=  scratch[8];\n\n        scratch[5] = scratch[0] + Complex(\n            (scratch[7].real()*ya.real() ) + (scratch[8].real() *yb.real() ),\n            (scratch[7].imag()*ya.real()) + (scratch[8].imag()*yb.real())\n            );\n\n        scratch[6] = Complex(\n            (scratch[10].imag()*ya.imag()) + (scratch[9].imag()*yb.imag()),\n            -(scratch[10].real()*ya.imag()) - (scratch[9].real()*yb.imag())\n            );\n\n        *Fout1 = scratch[5] - scratch[6];\n        *Fout4 = scratch[5] + scratch[6];\n\n        scratch[11] = scratch[0] +\n          Complex(\n              (scratch[7].real()*yb.real()) + (scratch[8].real()*ya.real()),\n              (scratch[7].imag()*yb.real()) + (scratch[8].imag()*ya.real())\n              );\n\n        scratch[12] = Complex(\n            -(scratch[10].imag()*yb.imag()) + (scratch[9].imag()*ya.imag()),\n            (scratch[10].real()*yb.imag()) - (scratch[9].real()*ya.imag())\n            );\n\n        *Fout2=scratch[11]+scratch[12];\n        *Fout3=scratch[11]-scratch[12];\n\n        ++Fout0;++Fout1;++Fout2;++Fout3;++Fout4;\n      }\n    }\n\n  /* perform the butterfly for one stage of a mixed radix FFT */\n  inline\n    void bfly_generic(\n        Complex * Fout,\n        const size_t fstride,\n        int m,\n        int p\n        )\n    {\n      int u,k,q1,q;\n      Complex * twiddles = &m_twiddles[0];\n      Complex t;\n      int Norig = static_cast<int>(m_twiddles.size());\n      Complex * scratchbuf = &m_scratchBuf[0];\n\n      for ( u=0; u<m; ++u ) {\n        k=u;\n        for ( q1=0 ; q1<p ; ++q1 ) {\n          scratchbuf[q1] = Fout[ k  ];\n          k += m;\n        }\n\n        k=u;\n        for ( q1=0 ; q1<p ; ++q1 ) {\n          int twidx=0;\n          Fout[ k ] = scratchbuf[0];\n          for (q=1;q<p;++q ) {\n            twidx += static_cast<int>(fstride) * k;\n            if (twidx>=Norig) twidx-=Norig;\n            t=scratchbuf[q] * twiddles[twidx];\n            Fout[ k ] += t;\n          }\n          k += m;\n        }\n      }\n    }\n};\n\ntemplate <typename _Scalar>\nstruct kissfft_impl\n{\n  typedef _Scalar Scalar;\n  typedef std::complex<Scalar> Complex;\n\n  void clear() \n  {\n    m_plans.clear();\n    m_realTwiddles.clear();\n  }\n\n  inline\n    void fwd( Complex * dst,const Complex *src,int nfft)\n    {\n      get_plan(nfft,false).work(0, dst, src, 1,1);\n    }\n\n  inline\n    void fwd2( Complex * dst,const Complex *src,int n0,int n1)\n    {\n        EIGEN_UNUSED_VARIABLE(dst);\n        EIGEN_UNUSED_VARIABLE(src);\n        EIGEN_UNUSED_VARIABLE(n0);\n        EIGEN_UNUSED_VARIABLE(n1);\n    }\n\n  inline\n    void inv2( Complex * dst,const Complex *src,int n0,int n1)\n    {\n        EIGEN_UNUSED_VARIABLE(dst);\n        EIGEN_UNUSED_VARIABLE(src);\n        EIGEN_UNUSED_VARIABLE(n0);\n        EIGEN_UNUSED_VARIABLE(n1);\n    }\n\n  // real-to-complex forward FFT\n  // perform two FFTs of src even and src odd\n  // then twiddle to recombine them into the half-spectrum format\n  // then fill in the conjugate symmetric half\n  inline\n    void fwd( Complex * dst,const Scalar * src,int nfft) \n    {\n      if ( nfft&3  ) {\n        // use generic mode for odd\n        m_tmpBuf1.resize(nfft);\n        get_plan(nfft,false).work(0, &m_tmpBuf1[0], src, 1,1);\n        std::copy(m_tmpBuf1.begin(),m_tmpBuf1.begin()+(nfft>>1)+1,dst );\n      }else{\n        int ncfft = nfft>>1;\n        int ncfft2 = nfft>>2;\n        Complex * rtw = real_twiddles(ncfft2);\n\n        // use optimized mode for even real\n        fwd( dst, reinterpret_cast<const Complex*> (src), ncfft);\n        Complex dc = dst[0].real() +  dst[0].imag();\n        Complex nyquist = dst[0].real() -  dst[0].imag();\n        int k;\n        for ( k=1;k <= ncfft2 ; ++k ) {\n          Complex fpk = dst[k];\n          Complex fpnk = conj(dst[ncfft-k]);\n          Complex f1k = fpk + fpnk;\n          Complex f2k = fpk - fpnk;\n          Complex tw= f2k * rtw[k-1];\n          dst[k] =  (f1k + tw) * Scalar(.5);\n          dst[ncfft-k] =  conj(f1k -tw)*Scalar(.5);\n        }\n        dst[0] = dc;\n        dst[ncfft] = nyquist;\n      }\n    }\n\n  // inverse complex-to-complex\n  inline\n    void inv(Complex * dst,const Complex  *src,int nfft)\n    {\n      get_plan(nfft,true).work(0, dst, src, 1,1);\n    }\n\n  // half-complex to scalar\n  inline\n    void inv( Scalar * dst,const Complex * src,int nfft) \n    {\n      if (nfft&3) {\n        m_tmpBuf1.resize(nfft);\n        m_tmpBuf2.resize(nfft);\n        std::copy(src,src+(nfft>>1)+1,m_tmpBuf1.begin() );\n        for (int k=1;k<(nfft>>1)+1;++k)\n          m_tmpBuf1[nfft-k] = conj(m_tmpBuf1[k]);\n        inv(&m_tmpBuf2[0],&m_tmpBuf1[0],nfft);\n        for (int k=0;k<nfft;++k)\n          dst[k] = m_tmpBuf2[k].real();\n      }else{\n        // optimized version for multiple of 4\n        int ncfft = nfft>>1;\n        int ncfft2 = nfft>>2;\n        Complex * rtw = real_twiddles(ncfft2);\n        m_tmpBuf1.resize(ncfft);\n        m_tmpBuf1[0] = Complex( src[0].real() + src[ncfft].real(), src[0].real() - src[ncfft].real() );\n        for (int k = 1; k <= ncfft / 2; ++k) {\n          Complex fk = src[k];\n          Complex fnkc = conj(src[ncfft-k]);\n          Complex fek = fk + fnkc;\n          Complex tmp = fk - fnkc;\n          Complex fok = tmp * conj(rtw[k-1]);\n          m_tmpBuf1[k] = fek + fok;\n          m_tmpBuf1[ncfft-k] = conj(fek - fok);\n        }\n        get_plan(ncfft,true).work(0, reinterpret_cast<Complex*>(dst), &m_tmpBuf1[0], 1,1);\n      }\n    }\n\n  protected:\n  typedef kiss_cpx_fft<Scalar> PlanData;\n  typedef std::map<int,PlanData> PlanMap;\n\n  PlanMap m_plans;\n  std::map<int, std::vector<Complex> > m_realTwiddles;\n  std::vector<Complex> m_tmpBuf1;\n  std::vector<Complex> m_tmpBuf2;\n\n  inline\n    int PlanKey(int nfft, bool isinverse) const { return (nfft<<1) | int(isinverse); }\n\n  inline\n    PlanData & get_plan(int nfft, bool inverse)\n    {\n      // TODO look for PlanKey(nfft, ! inverse) and conjugate the twiddles\n      PlanData & pd = m_plans[ PlanKey(nfft,inverse) ];\n      if ( pd.m_twiddles.size() == 0 ) {\n        pd.make_twiddles(nfft,inverse);\n        pd.factorize(nfft);\n      }\n      return pd;\n    }\n\n  inline\n    Complex * real_twiddles(int ncfft2)\n    {\n      using std::acos;\n      std::vector<Complex> & twidref = m_realTwiddles[ncfft2];// creates new if not there\n      if ( (int)twidref.size() != ncfft2 ) {\n        twidref.resize(ncfft2);\n        int ncfft= ncfft2<<1;\n        Scalar pi =  acos( Scalar(-1) );\n        for (int k=1;k<=ncfft2;++k) \n          twidref[k-1] = exp( Complex(0,-pi * (Scalar(k) / ncfft + Scalar(.5)) ) );\n      }\n      return &twidref[0];\n    }\n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n/* vim: set filetype=cpp et sw=2 ts=2 ai: */\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/IterativeSolvers/ConstrainedConjGrad.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n\n/* NOTE The functions of this file have been adapted from the GMM++ library */\n\n//========================================================================\n//\n// Copyright (C) 2002-2007 Yves Renard\n//\n// This file is a part of GETFEM++\n//\n// Getfem++ is free software; you can redistribute it and/or modify\n// it under the terms of the GNU Lesser General Public License as\n// published by the Free Software Foundation; version 2.1 of the License.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU Lesser General Public License for more details.\n// You should have received a copy of the GNU Lesser General Public\n// License along with this program; if not, write to the Free Software\n// Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301,\n// USA.\n//\n//========================================================================\n\n#include \"../../../../Eigen/src/Core/util/NonMPL2.h\"\n\n#ifndef EIGEN_CONSTRAINEDCG_H\n#define EIGEN_CONSTRAINEDCG_H\n\n#include <Eigen/Core>\n\nnamespace Eigen { \n\nnamespace internal {\n\n/** \\ingroup IterativeSolvers_Module\n  * Compute the pseudo inverse of the non-square matrix C such that\n  * \\f$ CINV = (C * C^T)^{-1} * C \\f$ based on a conjugate gradient method.\n  *\n  * This function is internally used by constrained_cg.\n  */\ntemplate <typename CMatrix, typename CINVMatrix>\nvoid pseudo_inverse(const CMatrix &C, CINVMatrix &CINV)\n{\n  // optimisable : copie de la ligne, precalcul de C * trans(C).\n  typedef typename CMatrix::Scalar Scalar;\n  typedef typename CMatrix::Index Index;\n  // FIXME use sparse vectors ?\n  typedef Matrix<Scalar,Dynamic,1> TmpVec;\n\n  Index rows = C.rows(), cols = C.cols();\n\n  TmpVec d(rows), e(rows), l(cols), p(rows), q(rows), r(rows);\n  Scalar rho, rho_1, alpha;\n  d.setZero();\n\n  typedef Triplet<double> T;\n  std::vector<T> tripletList;\n    \n  for (Index i = 0; i < rows; ++i)\n  {\n    d[i] = 1.0;\n    rho = 1.0;\n    e.setZero();\n    r = d;\n    p = d;\n\n    while (rho >= 1e-38)\n    { /* conjugate gradient to compute e             */\n      /* which is the i-th row of inv(C * trans(C))  */\n      l = C.transpose() * p;\n      q = C * l;\n      alpha = rho / p.dot(q);\n      e +=  alpha * p;\n      r += -alpha * q;\n      rho_1 = rho;\n      rho = r.dot(r);\n      p = (rho/rho_1) * p + r;\n    }\n\n    l = C.transpose() * e; // l is the i-th row of CINV\n    // FIXME add a generic \"prune/filter\" expression for both dense and sparse object to sparse\n    for (Index j=0; j<l.size(); ++j)\n      if (l[j]<1e-15)\n\ttripletList.push_back(T(i,j,l(j)));\n\n\t\n    d[i] = 0.0;\n  }\n  CINV.setFromTriplets(tripletList.begin(), tripletList.end());\n}\n\n\n\n/** \\ingroup IterativeSolvers_Module\n  * Constrained conjugate gradient\n  *\n  * Computes the minimum of \\f$ 1/2((Ax).x) - bx \\f$ under the contraint \\f$ Cx \\le f \\f$\n  */\ntemplate<typename TMatrix, typename CMatrix,\n         typename VectorX, typename VectorB, typename VectorF>\nvoid constrained_cg(const TMatrix& A, const CMatrix& C, VectorX& x,\n                       const VectorB& b, const VectorF& f, IterationController &iter)\n{\n  using std::sqrt;\n  typedef typename TMatrix::Scalar Scalar;\n  typedef typename TMatrix::Index Index;\n  typedef Matrix<Scalar,Dynamic,1>  TmpVec;\n\n  Scalar rho = 1.0, rho_1, lambda, gamma;\n  Index xSize = x.size();\n  TmpVec  p(xSize), q(xSize), q2(xSize),\n          r(xSize), old_z(xSize), z(xSize),\n          memox(xSize);\n  std::vector<bool> satured(C.rows());\n  p.setZero();\n  iter.setRhsNorm(sqrt(b.dot(b))); // gael vect_sp(PS, b, b)\n  if (iter.rhsNorm() == 0.0) iter.setRhsNorm(1.0);\n\n  SparseMatrix<Scalar,RowMajor> CINV(C.rows(), C.cols());\n  pseudo_inverse(C, CINV);\n\n  while(true)\n  {\n    // computation of residual\n    old_z = z;\n    memox = x;\n    r = b;\n    r += A * -x;\n    z = r;\n    bool transition = false;\n    for (Index i = 0; i < C.rows(); ++i)\n    {\n      Scalar al = C.row(i).dot(x) - f.coeff(i);\n      if (al >= -1.0E-15)\n      {\n        if (!satured[i])\n        {\n          satured[i] = true;\n          transition = true;\n        }\n        Scalar bb = CINV.row(i).dot(z);\n        if (bb > 0.0)\n          // FIXME: we should allow that: z += -bb * C.row(i);\n          for (typename CMatrix::InnerIterator it(C,i); it; ++it)\n            z.coeffRef(it.index()) -= bb*it.value();\n      }\n      else\n        satured[i] = false;\n    }\n\n    // descent direction\n    rho_1 = rho;\n    rho = r.dot(z);\n\n    if (iter.finished(rho)) break;\n\n    if (iter.noiseLevel() > 0 && transition) std::cerr << \"CCG: transition\\n\";\n    if (transition || iter.first()) gamma = 0.0;\n    else gamma = (std::max)(0.0, (rho - old_z.dot(z)) / rho_1);\n    p = z + gamma*p;\n\n    ++iter;\n    // one dimensionnal optimization\n    q = A * p;\n    lambda = rho / q.dot(p);\n    for (Index i = 0; i < C.rows(); ++i)\n    {\n      if (!satured[i])\n      {\n        Scalar bb = C.row(i).dot(p) - f[i];\n        if (bb > 0.0)\n          lambda = (std::min)(lambda, (f.coeff(i)-C.row(i).dot(x)) / bb);\n      }\n    }\n    x += lambda * p;\n    memox -= x;\n  }\n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_CONSTRAINEDCG_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/IterativeSolvers/DGMRES.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_DGMRES_H\n#define EIGEN_DGMRES_H\n\n#include <Eigen/Eigenvalues>\n\nnamespace Eigen { \n  \ntemplate< typename _MatrixType,\n          typename _Preconditioner = DiagonalPreconditioner<typename _MatrixType::Scalar> >\nclass DGMRES;\n\nnamespace internal {\n\ntemplate< typename _MatrixType, typename _Preconditioner>\nstruct traits<DGMRES<_MatrixType,_Preconditioner> >\n{\n  typedef _MatrixType MatrixType;\n  typedef _Preconditioner Preconditioner;\n};\n\n/** \\brief Computes a permutation vector to have a sorted sequence\n  * \\param vec The vector to reorder.\n  * \\param perm gives the sorted sequence on output. Must be initialized with 0..n-1\n  * \\param ncut Put  the ncut smallest elements at the end of the vector\n  * WARNING This is an expensive sort, so should be used only \n  * for small size vectors\n  * TODO Use modified QuickSplit or std::nth_element to get the smallest values \n  */\ntemplate <typename VectorType, typename IndexType>\nvoid sortWithPermutation (VectorType& vec, IndexType& perm, typename IndexType::Scalar& ncut)\n{\n  eigen_assert(vec.size() == perm.size());\n  bool flag; \n  for (Index k  = 0; k < ncut; k++)\n  {\n    flag = false;\n    for (Index j = 0; j < vec.size()-1; j++)\n    {\n      if ( vec(perm(j)) < vec(perm(j+1)) )\n      {\n        std::swap(perm(j),perm(j+1)); \n        flag = true;\n      }\n      if (!flag) break; // The vector is in sorted order\n    }\n  }\n}\n\n}\n/**\n * \\ingroup IterativeLInearSolvers_Module\n * \\brief A Restarted GMRES with deflation.\n * This class implements a modification of the GMRES solver for\n * sparse linear systems. The basis is built with modified \n * Gram-Schmidt. At each restart, a few approximated eigenvectors\n * corresponding to the smallest eigenvalues are used to build a\n * preconditioner for the next cycle. This preconditioner \n * for deflation can be combined with any other preconditioner, \n * the IncompleteLUT for instance. The preconditioner is applied \n * at right of the matrix and the combination is multiplicative.\n * \n * \\tparam _MatrixType the type of the sparse matrix A, can be a dense or a sparse matrix.\n * \\tparam _Preconditioner the type of the preconditioner. Default is DiagonalPreconditioner\n * Typical usage :\n * \\code\n * SparseMatrix<double> A;\n * VectorXd x, b; \n * //Fill A and b ...\n * DGMRES<SparseMatrix<double> > solver;\n * solver.set_restart(30); // Set restarting value\n * solver.setEigenv(1); // Set the number of eigenvalues to deflate\n * solver.compute(A);\n * x = solver.solve(b);\n * \\endcode\n * \n * DGMRES can also be used in a matrix-free context, see the following \\link MatrixfreeSolverExample example \\endlink.\n *\n * References :\n * [1] D. NUENTSA WAKAM and F. PACULL, Memory Efficient Hybrid\n *  Algebraic Solvers for Linear Systems Arising from Compressible\n *  Flows, Computers and Fluids, In Press,\n *  http://dx.doi.org/10.1016/j.compfluid.2012.03.023   \n * [2] K. Burrage and J. Erhel, On the performance of various \n * adaptive preconditioned GMRES strategies, 5(1998), 101-121.\n * [3] J. Erhel, K. Burrage and B. Pohl, Restarted GMRES \n *  preconditioned by deflation,J. Computational and Applied\n *  Mathematics, 69(1996), 303-318. \n\n * \n */\ntemplate< typename _MatrixType, typename _Preconditioner>\nclass DGMRES : public IterativeSolverBase<DGMRES<_MatrixType,_Preconditioner> >\n{\n    typedef IterativeSolverBase<DGMRES> Base;\n    using Base::matrix;\n    using Base::m_error;\n    using Base::m_iterations;\n    using Base::m_info;\n    using Base::m_isInitialized;\n    using Base::m_tolerance; \n  public:\n    using Base::_solve_impl;\n    typedef _MatrixType MatrixType;\n    typedef typename MatrixType::Scalar Scalar;\n    typedef typename MatrixType::StorageIndex StorageIndex;\n    typedef typename MatrixType::RealScalar RealScalar;\n    typedef _Preconditioner Preconditioner;\n    typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix; \n    typedef Matrix<RealScalar,Dynamic,Dynamic> DenseRealMatrix; \n    typedef Matrix<Scalar,Dynamic,1> DenseVector;\n    typedef Matrix<RealScalar,Dynamic,1> DenseRealVector; \n    typedef Matrix<std::complex<RealScalar>, Dynamic, 1> ComplexVector;\n \n    \n  /** Default constructor. */\n  DGMRES() : Base(),m_restart(30),m_neig(0),m_r(0),m_maxNeig(5),m_isDeflAllocated(false),m_isDeflInitialized(false) {}\n\n  /** Initialize the solver with matrix \\a A for further \\c Ax=b solving.\n    * \n    * This constructor is a shortcut for the default constructor followed\n    * by a call to compute().\n    * \n    * \\warning this class stores a reference to the matrix A as well as some\n    * precomputed values that depend on it. Therefore, if \\a A is changed\n    * this class becomes invalid. Call compute() to update it with the new\n    * matrix A, or modify a copy of A.\n    */\n  template<typename MatrixDerived>\n  explicit DGMRES(const EigenBase<MatrixDerived>& A) : Base(A.derived()), m_restart(30),m_neig(0),m_r(0),m_maxNeig(5),m_isDeflAllocated(false),m_isDeflInitialized(false) {}\n\n  ~DGMRES() {}\n  \n  /** \\internal */\n  template<typename Rhs,typename Dest>\n  void _solve_with_guess_impl(const Rhs& b, Dest& x) const\n  {    \n    bool failed = false;\n    for(Index j=0; j<b.cols(); ++j)\n    {\n      m_iterations = Base::maxIterations();\n      m_error = Base::m_tolerance;\n      \n      typename Dest::ColXpr xj(x,j);\n      dgmres(matrix(), b.col(j), xj, Base::m_preconditioner);\n    }\n    m_info = failed ? NumericalIssue\n           : m_error <= Base::m_tolerance ? Success\n           : NoConvergence;\n    m_isInitialized = true;\n  }\n\n  /** \\internal */\n  template<typename Rhs,typename Dest>\n  void _solve_impl(const Rhs& b, MatrixBase<Dest>& x) const\n  {\n    x = b;\n    _solve_with_guess_impl(b,x.derived());\n  }\n  /** \n   * Get the restart value\n    */\n  Index restart() { return m_restart; }\n  \n  /** \n   * Set the restart value (default is 30)  \n   */\n  Index set_restart(const Index restart) { m_restart=restart; }\n  \n  /** \n   * Set the number of eigenvalues to deflate at each restart \n   */\n  void setEigenv(const Index neig) \n  {\n    m_neig = neig;\n    if (neig+1 > m_maxNeig) m_maxNeig = neig+1; // To allow for complex conjugates\n  }\n  \n  /** \n   * Get the size of the deflation subspace size\n   */ \n  Index deflSize() {return m_r; }\n  \n  /**\n   * Set the maximum size of the deflation subspace\n   */\n  void setMaxEigenv(const Index maxNeig) { m_maxNeig = maxNeig; }\n  \n  protected:\n    // DGMRES algorithm \n    template<typename Rhs, typename Dest>\n    void dgmres(const MatrixType& mat,const Rhs& rhs, Dest& x, const Preconditioner& precond) const;\n    // Perform one cycle of GMRES\n    template<typename Dest>\n    Index dgmresCycle(const MatrixType& mat, const Preconditioner& precond, Dest& x, DenseVector& r0, RealScalar& beta, const RealScalar& normRhs, Index& nbIts) const; \n    // Compute data to use for deflation \n    Index dgmresComputeDeflationData(const MatrixType& mat, const Preconditioner& precond, const Index& it, StorageIndex& neig) const;\n    // Apply deflation to a vector\n    template<typename RhsType, typename DestType>\n    Index dgmresApplyDeflation(const RhsType& In, DestType& Out) const; \n    ComplexVector schurValues(const ComplexSchur<DenseMatrix>& schurofH) const;\n    ComplexVector schurValues(const RealSchur<DenseMatrix>& schurofH) const;\n    // Init data for deflation\n    void dgmresInitDeflation(Index& rows) const; \n    mutable DenseMatrix m_V; // Krylov basis vectors\n    mutable DenseMatrix m_H; // Hessenberg matrix \n    mutable DenseMatrix m_Hes; // Initial hessenberg matrix wihout Givens rotations applied\n    mutable Index m_restart; // Maximum size of the Krylov subspace\n    mutable DenseMatrix m_U; // Vectors that form the basis of the invariant subspace \n    mutable DenseMatrix m_MU; // matrix operator applied to m_U (for next cycles)\n    mutable DenseMatrix m_T; /* T=U^T*M^{-1}*A*U */\n    mutable PartialPivLU<DenseMatrix> m_luT; // LU factorization of m_T\n    mutable StorageIndex m_neig; //Number of eigenvalues to extract at each restart\n    mutable Index m_r; // Current number of deflated eigenvalues, size of m_U\n    mutable Index m_maxNeig; // Maximum number of eigenvalues to deflate\n    mutable RealScalar m_lambdaN; //Modulus of the largest eigenvalue of A\n    mutable bool m_isDeflAllocated;\n    mutable bool m_isDeflInitialized;\n    \n    //Adaptive strategy \n    mutable RealScalar m_smv; // Smaller multiple of the remaining number of steps allowed\n    mutable bool m_force; // Force the use of deflation at each restart\n    \n}; \n/** \n * \\brief Perform several cycles of restarted GMRES with modified Gram Schmidt, \n * \n * A right preconditioner is used combined with deflation.\n * \n */\ntemplate< typename _MatrixType, typename _Preconditioner>\ntemplate<typename Rhs, typename Dest>\nvoid DGMRES<_MatrixType, _Preconditioner>::dgmres(const MatrixType& mat,const Rhs& rhs, Dest& x,\n              const Preconditioner& precond) const\n{\n  //Initialization\n  Index n = mat.rows(); \n  DenseVector r0(n); \n  Index nbIts = 0; \n  m_H.resize(m_restart+1, m_restart);\n  m_Hes.resize(m_restart, m_restart);\n  m_V.resize(n,m_restart+1);\n  //Initial residual vector and intial norm\n  x = precond.solve(x);\n  r0 = rhs - mat * x; \n  RealScalar beta = r0.norm(); \n  RealScalar normRhs = rhs.norm();\n  m_error = beta/normRhs; \n  if(m_error < m_tolerance)\n    m_info = Success; \n  else\n    m_info = NoConvergence;\n  \n  // Iterative process\n  while (nbIts < m_iterations && m_info == NoConvergence)\n  {\n    dgmresCycle(mat, precond, x, r0, beta, normRhs, nbIts); \n    \n    // Compute the new residual vector for the restart \n    if (nbIts < m_iterations && m_info == NoConvergence)\n      r0 = rhs - mat * x; \n  }\n} \n\n/**\n * \\brief Perform one restart cycle of DGMRES\n * \\param mat The coefficient matrix\n * \\param precond The preconditioner\n * \\param x the new approximated solution\n * \\param r0 The initial residual vector\n * \\param beta The norm of the residual computed so far\n * \\param normRhs The norm of the right hand side vector\n * \\param nbIts The number of iterations\n */\ntemplate< typename _MatrixType, typename _Preconditioner>\ntemplate<typename Dest>\nIndex DGMRES<_MatrixType, _Preconditioner>::dgmresCycle(const MatrixType& mat, const Preconditioner& precond, Dest& x, DenseVector& r0, RealScalar& beta, const RealScalar& normRhs, Index& nbIts) const\n{\n  //Initialization \n  DenseVector g(m_restart+1); // Right hand side of the least square problem\n  g.setZero();  \n  g(0) = Scalar(beta); \n  m_V.col(0) = r0/beta; \n  m_info = NoConvergence; \n  std::vector<JacobiRotation<Scalar> >gr(m_restart); // Givens rotations\n  Index it = 0; // Number of inner iterations \n  Index n = mat.rows();\n  DenseVector tv1(n), tv2(n);  //Temporary vectors\n  while (m_info == NoConvergence && it < m_restart && nbIts < m_iterations)\n  {    \n    // Apply preconditioner(s) at right\n    if (m_isDeflInitialized )\n    {\n      dgmresApplyDeflation(m_V.col(it), tv1); // Deflation\n      tv2 = precond.solve(tv1); \n    }\n    else\n    {\n      tv2 = precond.solve(m_V.col(it)); // User's selected preconditioner\n    }\n    tv1 = mat * tv2; \n   \n    // Orthogonalize it with the previous basis in the basis using modified Gram-Schmidt\n    Scalar coef; \n    for (Index i = 0; i <= it; ++i)\n    { \n      coef = tv1.dot(m_V.col(i));\n      tv1 = tv1 - coef * m_V.col(i); \n      m_H(i,it) = coef; \n      m_Hes(i,it) = coef; \n    }\n    // Normalize the vector \n    coef = tv1.norm(); \n    m_V.col(it+1) = tv1/coef;\n    m_H(it+1, it) = coef;\n//     m_Hes(it+1,it) = coef; \n    \n    // FIXME Check for happy breakdown \n    \n    // Update Hessenberg matrix with Givens rotations\n    for (Index i = 1; i <= it; ++i) \n    {\n      m_H.col(it).applyOnTheLeft(i-1,i,gr[i-1].adjoint());\n    }\n    // Compute the new plane rotation \n    gr[it].makeGivens(m_H(it, it), m_H(it+1,it)); \n    // Apply the new rotation\n    m_H.col(it).applyOnTheLeft(it,it+1,gr[it].adjoint());\n    g.applyOnTheLeft(it,it+1, gr[it].adjoint()); \n    \n    beta = std::abs(g(it+1));\n    m_error = beta/normRhs; \n    // std::cerr << nbIts << \" Relative Residual Norm \" << m_error << std::endl;\n    it++; nbIts++; \n    \n    if (m_error < m_tolerance)\n    {\n      // The method has converged\n      m_info = Success;\n      break;\n    }\n  }\n  \n  // Compute the new coefficients by solving the least square problem\n//   it++;\n  //FIXME  Check first if the matrix is singular ... zero diagonal\n  DenseVector nrs(m_restart); \n  nrs = m_H.topLeftCorner(it,it).template triangularView<Upper>().solve(g.head(it)); \n  \n  // Form the new solution\n  if (m_isDeflInitialized)\n  {\n    tv1 = m_V.leftCols(it) * nrs; \n    dgmresApplyDeflation(tv1, tv2); \n    x = x + precond.solve(tv2);\n  }\n  else\n    x = x + precond.solve(m_V.leftCols(it) * nrs); \n  \n  // Go for a new cycle and compute data for deflation\n  if(nbIts < m_iterations && m_info == NoConvergence && m_neig > 0 && (m_r+m_neig) < m_maxNeig)\n    dgmresComputeDeflationData(mat, precond, it, m_neig); \n  return 0; \n  \n}\n\n\ntemplate< typename _MatrixType, typename _Preconditioner>\nvoid DGMRES<_MatrixType, _Preconditioner>::dgmresInitDeflation(Index& rows) const\n{\n  m_U.resize(rows, m_maxNeig);\n  m_MU.resize(rows, m_maxNeig); \n  m_T.resize(m_maxNeig, m_maxNeig);\n  m_lambdaN = 0.0; \n  m_isDeflAllocated = true; \n}\n\ntemplate< typename _MatrixType, typename _Preconditioner>\ninline typename DGMRES<_MatrixType, _Preconditioner>::ComplexVector DGMRES<_MatrixType, _Preconditioner>::schurValues(const ComplexSchur<DenseMatrix>& schurofH) const\n{\n  return schurofH.matrixT().diagonal();\n}\n\ntemplate< typename _MatrixType, typename _Preconditioner>\ninline typename DGMRES<_MatrixType, _Preconditioner>::ComplexVector DGMRES<_MatrixType, _Preconditioner>::schurValues(const RealSchur<DenseMatrix>& schurofH) const\n{\n  typedef typename MatrixType::Index Index;\n  const DenseMatrix& T = schurofH.matrixT();\n  Index it = T.rows();\n  ComplexVector eig(it);\n  Index j = 0;\n  while (j < it-1)\n  {\n    if (T(j+1,j) ==Scalar(0))\n    {\n      eig(j) = std::complex<RealScalar>(T(j,j),RealScalar(0)); \n      j++; \n    }\n    else\n    {\n      eig(j) = std::complex<RealScalar>(T(j,j),T(j+1,j)); \n      eig(j+1) = std::complex<RealScalar>(T(j,j+1),T(j+1,j+1));\n      j++;\n    }\n  }\n  if (j < it-1) eig(j) = std::complex<RealScalar>(T(j,j),RealScalar(0));\n  return eig;\n}\n\ntemplate< typename _MatrixType, typename _Preconditioner>\nIndex DGMRES<_MatrixType, _Preconditioner>::dgmresComputeDeflationData(const MatrixType& mat, const Preconditioner& precond, const Index& it, StorageIndex& neig) const\n{\n  // First, find the Schur form of the Hessenberg matrix H\n  typename internal::conditional<NumTraits<Scalar>::IsComplex, ComplexSchur<DenseMatrix>, RealSchur<DenseMatrix> >::type schurofH; \n  bool computeU = true;\n  DenseMatrix matrixQ(it,it); \n  matrixQ.setIdentity();\n  schurofH.computeFromHessenberg(m_Hes.topLeftCorner(it,it), matrixQ, computeU); \n  \n  ComplexVector eig(it);\n  Matrix<StorageIndex,Dynamic,1>perm(it);\n  eig = this->schurValues(schurofH);\n  \n  // Reorder the absolute values of Schur values\n  DenseRealVector modulEig(it); \n  for (Index j=0; j<it; ++j) modulEig(j) = std::abs(eig(j)); \n  perm.setLinSpaced(it,0,internal::convert_index<StorageIndex>(it-1));\n  internal::sortWithPermutation(modulEig, perm, neig);\n  \n  if (!m_lambdaN)\n  {\n    m_lambdaN = (std::max)(modulEig.maxCoeff(), m_lambdaN);\n  }\n  //Count the real number of extracted eigenvalues (with complex conjugates)\n  Index nbrEig = 0; \n  while (nbrEig < neig)\n  {\n    if(eig(perm(it-nbrEig-1)).imag() == RealScalar(0)) nbrEig++; \n    else nbrEig += 2; \n  }\n  // Extract the  Schur vectors corresponding to the smallest Ritz values\n  DenseMatrix Sr(it, nbrEig); \n  Sr.setZero();\n  for (Index j = 0; j < nbrEig; j++)\n  {\n    Sr.col(j) = schurofH.matrixU().col(perm(it-j-1));\n  }\n  \n  // Form the Schur vectors of the initial matrix using the Krylov basis\n  DenseMatrix X; \n  X = m_V.leftCols(it) * Sr;\n  if (m_r)\n  {\n   // Orthogonalize X against m_U using modified Gram-Schmidt\n   for (Index j = 0; j < nbrEig; j++)\n     for (Index k =0; k < m_r; k++)\n      X.col(j) = X.col(j) - (m_U.col(k).dot(X.col(j)))*m_U.col(k); \n  }\n  \n  // Compute m_MX = A * M^-1 * X\n  Index m = m_V.rows();\n  if (!m_isDeflAllocated) \n    dgmresInitDeflation(m); \n  DenseMatrix MX(m, nbrEig);\n  DenseVector tv1(m);\n  for (Index j = 0; j < nbrEig; j++)\n  {\n    tv1 = mat * X.col(j);\n    MX.col(j) = precond.solve(tv1);\n  }\n  \n  //Update m_T = [U'MU U'MX; X'MU X'MX]\n  m_T.block(m_r, m_r, nbrEig, nbrEig) = X.transpose() * MX; \n  if(m_r)\n  {\n    m_T.block(0, m_r, m_r, nbrEig) = m_U.leftCols(m_r).transpose() * MX; \n    m_T.block(m_r, 0, nbrEig, m_r) = X.transpose() * m_MU.leftCols(m_r);\n  }\n  \n  // Save X into m_U and m_MX in m_MU\n  for (Index j = 0; j < nbrEig; j++) m_U.col(m_r+j) = X.col(j);\n  for (Index j = 0; j < nbrEig; j++) m_MU.col(m_r+j) = MX.col(j);\n  // Increase the size of the invariant subspace\n  m_r += nbrEig; \n  \n  // Factorize m_T into m_luT\n  m_luT.compute(m_T.topLeftCorner(m_r, m_r));\n  \n  //FIXME CHeck if the factorization was correctly done (nonsingular matrix)\n  m_isDeflInitialized = true;\n  return 0; \n}\ntemplate<typename _MatrixType, typename _Preconditioner>\ntemplate<typename RhsType, typename DestType>\nIndex DGMRES<_MatrixType, _Preconditioner>::dgmresApplyDeflation(const RhsType &x, DestType &y) const\n{\n  DenseVector x1 = m_U.leftCols(m_r).transpose() * x; \n  y = x + m_U.leftCols(m_r) * ( m_lambdaN * m_luT.solve(x1) - x1);\n  return 0; \n}\n\n} // end namespace Eigen\n#endif \n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/IterativeSolvers/GMRES.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2011 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2012, 2014 Kolja Brix <brix@igpm.rwth-aaachen.de>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_GMRES_H\n#define EIGEN_GMRES_H\n\nnamespace Eigen {\n\nnamespace internal {\n\n/**\n* Generalized Minimal Residual Algorithm based on the\n* Arnoldi algorithm implemented with Householder reflections.\n*\n* Parameters:\n*  \\param mat       matrix of linear system of equations\n*  \\param Rhs       right hand side vector of linear system of equations\n*  \\param x         on input: initial guess, on output: solution\n*  \\param precond   preconditioner used\n*  \\param iters     on input: maximum number of iterations to perform\n*                   on output: number of iterations performed\n*  \\param restart   number of iterations for a restart\n*  \\param tol_error on input: relative residual tolerance\n*                   on output: residuum achieved\n*\n* \\sa IterativeMethods::bicgstab()\n*\n*\n* For references, please see:\n*\n* Saad, Y. and Schultz, M. H.\n* GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems.\n* SIAM J.Sci.Stat.Comp. 7, 1986, pp. 856 - 869.\n*\n* Saad, Y.\n* Iterative Methods for Sparse Linear Systems.\n* Society for Industrial and Applied Mathematics, Philadelphia, 2003.\n*\n* Walker, H. F.\n* Implementations of the GMRES method.\n* Comput.Phys.Comm. 53, 1989, pp. 311 - 320.\n*\n* Walker, H. F.\n* Implementation of the GMRES Method using Householder Transformations.\n* SIAM J.Sci.Stat.Comp. 9, 1988, pp. 152 - 163.\n*\n*/\ntemplate<typename MatrixType, typename Rhs, typename Dest, typename Preconditioner>\nbool gmres(const MatrixType & mat, const Rhs & rhs, Dest & x, const Preconditioner & precond,\n    Index &iters, const Index &restart, typename Dest::RealScalar & tol_error) {\n\n  using std::sqrt;\n  using std::abs;\n\n  typedef typename Dest::RealScalar RealScalar;\n  typedef typename Dest::Scalar Scalar;\n  typedef Matrix < Scalar, Dynamic, 1 > VectorType;\n  typedef Matrix < Scalar, Dynamic, Dynamic, ColMajor> FMatrixType;\n\n  RealScalar tol = tol_error;\n  const Index maxIters = iters;\n  iters = 0;\n\n  const Index m = mat.rows();\n\n  // residual and preconditioned residual\n  VectorType p0 = rhs - mat*x;\n  VectorType r0 = precond.solve(p0);\n\n  const RealScalar r0Norm = r0.norm();\n\n  // is initial guess already good enough?\n  if(r0Norm == 0)\n  {\n    tol_error = 0;\n    return true;\n  }\n\n  // storage for Hessenberg matrix and Householder data\n  FMatrixType H   = FMatrixType::Zero(m, restart + 1);\n  VectorType w    = VectorType::Zero(restart + 1);\n  VectorType tau  = VectorType::Zero(restart + 1);\n\n  // storage for Jacobi rotations\n  std::vector < JacobiRotation < Scalar > > G(restart);\n  \n  // storage for temporaries\n  VectorType t(m), v(m), workspace(m), x_new(m);\n\n  // generate first Householder vector\n  Ref<VectorType> H0_tail = H.col(0).tail(m - 1);\n  RealScalar beta;\n  r0.makeHouseholder(H0_tail, tau.coeffRef(0), beta);\n  w(0) = Scalar(beta);\n  \n  for (Index k = 1; k <= restart; ++k)\n  {\n    ++iters;\n\n    v = VectorType::Unit(m, k - 1);\n\n    // apply Householder reflections H_{1} ... H_{k-1} to v\n    // TODO: use a HouseholderSequence\n    for (Index i = k - 1; i >= 0; --i) {\n      v.tail(m - i).applyHouseholderOnTheLeft(H.col(i).tail(m - i - 1), tau.coeffRef(i), workspace.data());\n    }\n\n    // apply matrix M to v:  v = mat * v;\n    t.noalias() = mat * v;\n    v = precond.solve(t);\n\n    // apply Householder reflections H_{k-1} ... H_{1} to v\n    // TODO: use a HouseholderSequence\n    for (Index i = 0; i < k; ++i) {\n      v.tail(m - i).applyHouseholderOnTheLeft(H.col(i).tail(m - i - 1), tau.coeffRef(i), workspace.data());\n    }\n\n    if (v.tail(m - k).norm() != 0.0)\n    {\n      if (k <= restart)\n      {\n        // generate new Householder vector\n        Ref<VectorType> Hk_tail = H.col(k).tail(m - k - 1);\n        v.tail(m - k).makeHouseholder(Hk_tail, tau.coeffRef(k), beta);\n\n        // apply Householder reflection H_{k} to v\n        v.tail(m - k).applyHouseholderOnTheLeft(Hk_tail, tau.coeffRef(k), workspace.data());\n      }\n    }\n\n    if (k > 1)\n    {\n      for (Index i = 0; i < k - 1; ++i)\n      {\n        // apply old Givens rotations to v\n        v.applyOnTheLeft(i, i + 1, G[i].adjoint());\n      }\n    }\n\n    if (k<m && v(k) != (Scalar) 0)\n    {\n      // determine next Givens rotation\n      G[k - 1].makeGivens(v(k - 1), v(k));\n\n      // apply Givens rotation to v and w\n      v.applyOnTheLeft(k - 1, k, G[k - 1].adjoint());\n      w.applyOnTheLeft(k - 1, k, G[k - 1].adjoint());\n    }\n\n    // insert coefficients into upper matrix triangle\n    H.col(k-1).head(k) = v.head(k);\n\n    tol_error = abs(w(k)) / r0Norm;\n    bool stop = (k==m || tol_error < tol || iters == maxIters);\n\n    if (stop || k == restart)\n    {\n      // solve upper triangular system\n      Ref<VectorType> y = w.head(k);\n      H.topLeftCorner(k, k).template triangularView <Upper>().solveInPlace(y);\n\n      // use Horner-like scheme to calculate solution vector\n      x_new.setZero();\n      for (Index i = k - 1; i >= 0; --i)\n      {\n        x_new(i) += y(i);\n        // apply Householder reflection H_{i} to x_new\n        x_new.tail(m - i).applyHouseholderOnTheLeft(H.col(i).tail(m - i - 1), tau.coeffRef(i), workspace.data());\n      }\n\n      x += x_new;\n\n      if(stop)\n      {\n        return true;\n      }\n      else\n      {\n        k=0;\n\n        // reset data for restart\n        p0.noalias() = rhs - mat*x;\n        r0 = precond.solve(p0);\n\n        // clear Hessenberg matrix and Householder data\n        H.setZero();\n        w.setZero();\n        tau.setZero();\n\n        // generate first Householder vector\n        r0.makeHouseholder(H0_tail, tau.coeffRef(0), beta);\n        w(0) = Scalar(beta);\n      }\n    }\n  }\n\n  return false;\n\n}\n\n}\n\ntemplate< typename _MatrixType,\n          typename _Preconditioner = DiagonalPreconditioner<typename _MatrixType::Scalar> >\nclass GMRES;\n\nnamespace internal {\n\ntemplate< typename _MatrixType, typename _Preconditioner>\nstruct traits<GMRES<_MatrixType,_Preconditioner> >\n{\n  typedef _MatrixType MatrixType;\n  typedef _Preconditioner Preconditioner;\n};\n\n}\n\n/** \\ingroup IterativeLinearSolvers_Module\n  * \\brief A GMRES solver for sparse square problems\n  *\n  * This class allows to solve for A.x = b sparse linear problems using a generalized minimal\n  * residual method. The vectors x and b can be either dense or sparse.\n  *\n  * \\tparam _MatrixType the type of the sparse matrix A, can be a dense or a sparse matrix.\n  * \\tparam _Preconditioner the type of the preconditioner. Default is DiagonalPreconditioner\n  *\n  * The maximal number of iterations and tolerance value can be controlled via the setMaxIterations()\n  * and setTolerance() methods. The defaults are the size of the problem for the maximal number of iterations\n  * and NumTraits<Scalar>::epsilon() for the tolerance.\n  *\n  * This class can be used as the direct solver classes. Here is a typical usage example:\n  * \\code\n  * int n = 10000;\n  * VectorXd x(n), b(n);\n  * SparseMatrix<double> A(n,n);\n  * // fill A and b\n  * GMRES<SparseMatrix<double> > solver(A);\n  * x = solver.solve(b);\n  * std::cout << \"#iterations:     \" << solver.iterations() << std::endl;\n  * std::cout << \"estimated error: \" << solver.error()      << std::endl;\n  * // update b, and solve again\n  * x = solver.solve(b);\n  * \\endcode\n  *\n  * By default the iterations start with x=0 as an initial guess of the solution.\n  * One can control the start using the solveWithGuess() method.\n  * \n  * GMRES can also be used in a matrix-free context, see the following \\link MatrixfreeSolverExample example \\endlink.\n  *\n  * \\sa class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner\n  */\ntemplate< typename _MatrixType, typename _Preconditioner>\nclass GMRES : public IterativeSolverBase<GMRES<_MatrixType,_Preconditioner> >\n{\n  typedef IterativeSolverBase<GMRES> Base;\n  using Base::matrix;\n  using Base::m_error;\n  using Base::m_iterations;\n  using Base::m_info;\n  using Base::m_isInitialized;\n\nprivate:\n  Index m_restart;\n\npublic:\n  using Base::_solve_impl;\n  typedef _MatrixType MatrixType;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename MatrixType::RealScalar RealScalar;\n  typedef _Preconditioner Preconditioner;\n\npublic:\n\n  /** Default constructor. */\n  GMRES() : Base(), m_restart(30) {}\n\n  /** Initialize the solver with matrix \\a A for further \\c Ax=b solving.\n    *\n    * This constructor is a shortcut for the default constructor followed\n    * by a call to compute().\n    *\n    * \\warning this class stores a reference to the matrix A as well as some\n    * precomputed values that depend on it. Therefore, if \\a A is changed\n    * this class becomes invalid. Call compute() to update it with the new\n    * matrix A, or modify a copy of A.\n    */\n  template<typename MatrixDerived>\n  explicit GMRES(const EigenBase<MatrixDerived>& A) : Base(A.derived()), m_restart(30) {}\n\n  ~GMRES() {}\n\n  /** Get the number of iterations after that a restart is performed.\n    */\n  Index get_restart() { return m_restart; }\n\n  /** Set the number of iterations after that a restart is performed.\n    *  \\param restart   number of iterations for a restarti, default is 30.\n    */\n  void set_restart(const Index restart) { m_restart=restart; }\n\n  /** \\internal */\n  template<typename Rhs,typename Dest>\n  void _solve_with_guess_impl(const Rhs& b, Dest& x) const\n  {\n    bool failed = false;\n    for(Index j=0; j<b.cols(); ++j)\n    {\n      m_iterations = Base::maxIterations();\n      m_error = Base::m_tolerance;\n\n      typename Dest::ColXpr xj(x,j);\n      if(!internal::gmres(matrix(), b.col(j), xj, Base::m_preconditioner, m_iterations, m_restart, m_error))\n        failed = true;\n    }\n    m_info = failed ? NumericalIssue\n          : m_error <= Base::m_tolerance ? Success\n          : NoConvergence;\n    m_isInitialized = true;\n  }\n\n  /** \\internal */\n  template<typename Rhs,typename Dest>\n  void _solve_impl(const Rhs& b, MatrixBase<Dest> &x) const\n  {\n    x = b;\n    if(x.squaredNorm() == 0) return; // Check Zero right hand side\n    _solve_with_guess_impl(b,x.derived());\n  }\n\nprotected:\n\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_GMRES_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/IterativeSolvers/IncompleteLU.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2011 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_INCOMPLETE_LU_H\n#define EIGEN_INCOMPLETE_LU_H\n\nnamespace Eigen { \n\ntemplate <typename _Scalar>\nclass IncompleteLU : public SparseSolverBase<IncompleteLU<_Scalar> >\n{\n  protected:\n    typedef SparseSolverBase<IncompleteLU<_Scalar> > Base;\n    using Base::m_isInitialized;\n    \n    typedef _Scalar Scalar;\n    typedef Matrix<Scalar,Dynamic,1> Vector;\n    typedef typename Vector::Index Index;\n    typedef SparseMatrix<Scalar,RowMajor> FactorType;\n\n  public:\n    typedef Matrix<Scalar,Dynamic,Dynamic> MatrixType;\n\n    IncompleteLU() {}\n\n    template<typename MatrixType>\n    IncompleteLU(const MatrixType& mat)\n    {\n      compute(mat);\n    }\n\n    Index rows() const { return m_lu.rows(); }\n    Index cols() const { return m_lu.cols(); }\n\n    template<typename MatrixType>\n    IncompleteLU& compute(const MatrixType& mat)\n    {\n      m_lu = mat;\n      int size = mat.cols();\n      Vector diag(size);\n      for(int i=0; i<size; ++i)\n      {\n        typename FactorType::InnerIterator k_it(m_lu,i);\n        for(; k_it && k_it.index()<i; ++k_it)\n        {\n          int k = k_it.index();\n          k_it.valueRef() /= diag(k);\n\n          typename FactorType::InnerIterator j_it(k_it);\n          typename FactorType::InnerIterator kj_it(m_lu, k);\n          while(kj_it && kj_it.index()<=k) ++kj_it;\n          for(++j_it; j_it; )\n          {\n            if(kj_it.index()==j_it.index())\n            {\n              j_it.valueRef() -= k_it.value() * kj_it.value();\n              ++j_it;\n              ++kj_it;\n            }\n            else if(kj_it.index()<j_it.index()) ++kj_it;\n            else                                ++j_it;\n          }\n        }\n        if(k_it && k_it.index()==i) diag(i) = k_it.value();\n        else                        diag(i) = 1;\n      }\n      m_isInitialized = true;\n      return *this;\n    }\n\n    template<typename Rhs, typename Dest>\n    void _solve_impl(const Rhs& b, Dest& x) const\n    {\n      x = m_lu.template triangularView<UnitLower>().solve(b);\n      x = m_lu.template triangularView<Upper>().solve(x);\n    }\n\n  protected:\n    FactorType m_lu;\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_INCOMPLETE_LU_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/IterativeSolvers/IterationController.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n\n/* NOTE The class IterationController has been adapted from the iteration\n *      class of the GMM++ and ITL libraries.\n */\n\n//=======================================================================\n// Copyright (C) 1997-2001\n// Authors: Andrew Lumsdaine <lums@osl.iu.edu> \n//          Lie-Quan Lee     <llee@osl.iu.edu>\n//\n// This file is part of the Iterative Template Library\n//\n// You should have received a copy of the License Agreement for the\n// Iterative Template Library along with the software;  see the\n// file LICENSE.  \n//\n// Permission to modify the code and to distribute modified code is\n// granted, provided the text of this NOTICE is retained, a notice that\n// the code was modified is included with the above COPYRIGHT NOTICE and\n// with the COPYRIGHT NOTICE in the LICENSE file, and that the LICENSE\n// file is distributed with the modified code.\n//\n// LICENSOR MAKES NO REPRESENTATIONS OR WARRANTIES, EXPRESS OR IMPLIED.\n// By way of example, but not limitation, Licensor MAKES NO\n// REPRESENTATIONS OR WARRANTIES OF MERCHANTABILITY OR FITNESS FOR ANY\n// PARTICULAR PURPOSE OR THAT THE USE OF THE LICENSED SOFTWARE COMPONENTS\n// OR DOCUMENTATION WILL NOT INFRINGE ANY PATENTS, COPYRIGHTS, TRADEMARKS\n// OR OTHER RIGHTS.\n//=======================================================================\n\n//========================================================================\n//\n// Copyright (C) 2002-2007 Yves Renard\n//\n// This file is a part of GETFEM++\n//\n// Getfem++ is free software; you can redistribute it and/or modify\n// it under the terms of the GNU Lesser General Public License as\n// published by the Free Software Foundation; version 2.1 of the License.\n//\n// This program is distributed in the hope that it will be useful,\n// but WITHOUT ANY WARRANTY; without even the implied warranty of\n// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n// GNU Lesser General Public License for more details.\n// You should have received a copy of the GNU Lesser General Public\n// License along with this program; if not, write to the Free Software\n// Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301,\n// USA.\n//\n//========================================================================\n\n#include \"../../../../Eigen/src/Core/util/NonMPL2.h\"\n\n#ifndef EIGEN_ITERATION_CONTROLLER_H\n#define EIGEN_ITERATION_CONTROLLER_H\n\nnamespace Eigen { \n\n/** \\ingroup IterativeSolvers_Module\n  * \\class IterationController\n  *\n  * \\brief Controls the iterations of the iterative solvers\n  *\n  * This class has been adapted from the iteration class of GMM++ and ITL libraries.\n  *\n  */\nclass IterationController\n{\n  protected :\n    double m_rhsn;        ///< Right hand side norm\n    size_t m_maxiter;     ///< Max. number of iterations\n    int m_noise;          ///< if noise > 0 iterations are printed\n    double m_resmax;      ///< maximum residual\n    double m_resminreach, m_resadd;\n    size_t m_nit;         ///< iteration number\n    double m_res;         ///< last computed residual\n    bool m_written;\n    void (*m_callback)(const IterationController&);\n  public :\n\n    void init()\n    {\n      m_nit = 0; m_res = 0.0; m_written = false;\n      m_resminreach = 1E50; m_resadd = 0.0;\n      m_callback = 0;\n    }\n\n    IterationController(double r = 1.0E-8, int noi = 0, size_t mit = size_t(-1))\n      : m_rhsn(1.0), m_maxiter(mit), m_noise(noi), m_resmax(r) { init(); }\n\n    void operator ++(int) { m_nit++; m_written = false; m_resadd += m_res; }\n    void operator ++() { (*this)++; }\n\n    bool first() { return m_nit == 0; }\n\n    /* get/set the \"noisyness\" (verbosity) of the solvers */\n    int noiseLevel() const { return m_noise; }\n    void setNoiseLevel(int n) { m_noise = n; }\n    void reduceNoiseLevel() { if (m_noise > 0) m_noise--; }\n\n    double maxResidual() const { return m_resmax; }\n    void setMaxResidual(double r) { m_resmax = r; }\n\n    double residual() const { return m_res; }\n\n    /* change the user-definable callback, called after each iteration */\n    void setCallback(void (*t)(const IterationController&))\n    {\n      m_callback = t;\n    }\n\n    size_t iteration() const { return m_nit; }\n    void setIteration(size_t i) { m_nit = i; }\n\n    size_t maxIterarions() const { return m_maxiter; }\n    void setMaxIterations(size_t i) { m_maxiter = i; }\n\n    double rhsNorm() const { return m_rhsn; }\n    void setRhsNorm(double r) { m_rhsn = r; }\n\n    bool converged() const { return m_res <= m_rhsn * m_resmax; }\n    bool converged(double nr)\n    {\n      using std::abs;\n      m_res = abs(nr); \n      m_resminreach = (std::min)(m_resminreach, m_res);\n      return converged();\n    }\n    template<typename VectorType> bool converged(const VectorType &v)\n    { return converged(v.squaredNorm()); }\n\n    bool finished(double nr)\n    {\n      if (m_callback) m_callback(*this);\n      if (m_noise > 0 && !m_written)\n      {\n        converged(nr);\n        m_written = true;\n      }\n      return (m_nit >= m_maxiter || converged(nr));\n    }\n    template <typename VectorType>\n    bool finished(const MatrixBase<VectorType> &v)\n    { return finished(double(v.squaredNorm())); }\n\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_ITERATION_CONTROLLER_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/IterativeSolvers/MINRES.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Giacomo Po <gpo@ucla.edu>\n// Copyright (C) 2011-2014 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n\n#ifndef EIGEN_MINRES_H_\n#define EIGEN_MINRES_H_\n\n\nnamespace Eigen {\n    \n    namespace internal {\n        \n        /** \\internal Low-level MINRES algorithm\n         * \\param mat The matrix A\n         * \\param rhs The right hand side vector b\n         * \\param x On input and initial solution, on output the computed solution.\n         * \\param precond A right preconditioner being able to efficiently solve for an\n         *                approximation of Ax=b (regardless of b)\n         * \\param iters On input the max number of iteration, on output the number of performed iterations.\n         * \\param tol_error On input the tolerance error, on output an estimation of the relative error.\n         */\n        template<typename MatrixType, typename Rhs, typename Dest, typename Preconditioner>\n        EIGEN_DONT_INLINE\n        void minres(const MatrixType& mat, const Rhs& rhs, Dest& x,\n                    const Preconditioner& precond, Index& iters,\n                    typename Dest::RealScalar& tol_error)\n        {\n            using std::sqrt;\n            typedef typename Dest::RealScalar RealScalar;\n            typedef typename Dest::Scalar Scalar;\n            typedef Matrix<Scalar,Dynamic,1> VectorType;\n\n            // Check for zero rhs\n            const RealScalar rhsNorm2(rhs.squaredNorm());\n            if(rhsNorm2 == 0)\n            {\n                x.setZero();\n                iters = 0;\n                tol_error = 0;\n                return;\n            }\n            \n            // initialize\n            const Index maxIters(iters);  // initialize maxIters to iters\n            const Index N(mat.cols());    // the size of the matrix\n            const RealScalar threshold2(tol_error*tol_error*rhsNorm2); // convergence threshold (compared to residualNorm2)\n            \n            // Initialize preconditioned Lanczos\n            VectorType v_old(N); // will be initialized inside loop\n            VectorType v( VectorType::Zero(N) ); //initialize v\n            VectorType v_new(rhs-mat*x); //initialize v_new\n            RealScalar residualNorm2(v_new.squaredNorm());\n            VectorType w(N); // will be initialized inside loop\n            VectorType w_new(precond.solve(v_new)); // initialize w_new\n//            RealScalar beta; // will be initialized inside loop\n            RealScalar beta_new2(v_new.dot(w_new));\n            eigen_assert(beta_new2 >= 0.0 && \"PRECONDITIONER IS NOT POSITIVE DEFINITE\");\n            RealScalar beta_new(sqrt(beta_new2));\n            const RealScalar beta_one(beta_new);\n            v_new /= beta_new;\n            w_new /= beta_new;\n            // Initialize other variables\n            RealScalar c(1.0); // the cosine of the Givens rotation\n            RealScalar c_old(1.0);\n            RealScalar s(0.0); // the sine of the Givens rotation\n            RealScalar s_old(0.0); // the sine of the Givens rotation\n            VectorType p_oold(N); // will be initialized in loop\n            VectorType p_old(VectorType::Zero(N)); // initialize p_old=0\n            VectorType p(p_old); // initialize p=0\n            RealScalar eta(1.0);\n                        \n            iters = 0; // reset iters\n            while ( iters < maxIters )\n            {\n                // Preconditioned Lanczos\n                /* Note that there are 4 variants on the Lanczos algorithm. These are\n                 * described in Paige, C. C. (1972). Computational variants of\n                 * the Lanczos method for the eigenproblem. IMA Journal of Applied\n                 * Mathematics, 10(3), 373–381. The current implementation corresponds \n                 * to the case A(2,7) in the paper. It also corresponds to \n                 * algorithm 6.14 in Y. Saad, Iterative Methods ￼￼￼for Sparse Linear\n                 * Systems, 2003 p.173. For the preconditioned version see \n                 * A. Greenbaum, Iterative Methods for Solving Linear Systems, SIAM (1987).\n                 */\n                const RealScalar beta(beta_new);\n                v_old = v; // update: at first time step, this makes v_old = 0 so value of beta doesn't matter\n//                const VectorType v_old(v); // NOT SURE IF CREATING v_old EVERY ITERATION IS EFFICIENT\n                v = v_new; // update\n                w = w_new; // update\n//                const VectorType w(w_new); // NOT SURE IF CREATING w EVERY ITERATION IS EFFICIENT\n                v_new.noalias() = mat*w - beta*v_old; // compute v_new\n                const RealScalar alpha = v_new.dot(w);\n                v_new -= alpha*v; // overwrite v_new\n                w_new = precond.solve(v_new); // overwrite w_new\n                beta_new2 = v_new.dot(w_new); // compute beta_new\n                eigen_assert(beta_new2 >= 0.0 && \"PRECONDITIONER IS NOT POSITIVE DEFINITE\");\n                beta_new = sqrt(beta_new2); // compute beta_new\n                v_new /= beta_new; // overwrite v_new for next iteration\n                w_new /= beta_new; // overwrite w_new for next iteration\n                \n                // Givens rotation\n                const RealScalar r2 =s*alpha+c*c_old*beta; // s, s_old, c and c_old are still from previous iteration\n                const RealScalar r3 =s_old*beta; // s, s_old, c and c_old are still from previous iteration\n                const RealScalar r1_hat=c*alpha-c_old*s*beta;\n                const RealScalar r1 =sqrt( std::pow(r1_hat,2) + std::pow(beta_new,2) );\n                c_old = c; // store for next iteration\n                s_old = s; // store for next iteration\n                c=r1_hat/r1; // new cosine\n                s=beta_new/r1; // new sine\n                \n                // Update solution\n                p_oold = p_old;\n//                const VectorType p_oold(p_old); // NOT SURE IF CREATING p_oold EVERY ITERATION IS EFFICIENT\n                p_old = p;\n                p.noalias()=(w-r2*p_old-r3*p_oold) /r1; // IS NOALIAS REQUIRED?\n                x += beta_one*c*eta*p;\n                \n                /* Update the squared residual. Note that this is the estimated residual.\n                The real residual |Ax-b|^2 may be slightly larger */\n                residualNorm2 *= s*s;\n                \n                if ( residualNorm2 < threshold2)\n                {\n                    break;\n                }\n                \n                eta=-s*eta; // update eta\n                iters++; // increment iteration number (for output purposes)\n            }\n            \n            /* Compute error. Note that this is the estimated error. The real \n             error |Ax-b|/|b| may be slightly larger */\n            tol_error = std::sqrt(residualNorm2 / rhsNorm2);\n        }\n        \n    }\n    \n    template< typename _MatrixType, int _UpLo=Lower,\n    typename _Preconditioner = IdentityPreconditioner>\n    class MINRES;\n    \n    namespace internal {\n        \n        template< typename _MatrixType, int _UpLo, typename _Preconditioner>\n        struct traits<MINRES<_MatrixType,_UpLo,_Preconditioner> >\n        {\n            typedef _MatrixType MatrixType;\n            typedef _Preconditioner Preconditioner;\n        };\n        \n    }\n    \n    /** \\ingroup IterativeLinearSolvers_Module\n     * \\brief A minimal residual solver for sparse symmetric problems\n     *\n     * This class allows to solve for A.x = b sparse linear problems using the MINRES algorithm\n     * of Paige and Saunders (1975). The sparse matrix A must be symmetric (possibly indefinite).\n     * The vectors x and b can be either dense or sparse.\n     *\n     * \\tparam _MatrixType the type of the sparse matrix A, can be a dense or a sparse matrix.\n     * \\tparam _UpLo the triangular part that will be used for the computations. It can be Lower,\n     *               Upper, or Lower|Upper in which the full matrix entries will be considered. Default is Lower.\n     * \\tparam _Preconditioner the type of the preconditioner. Default is DiagonalPreconditioner\n     *\n     * The maximal number of iterations and tolerance value can be controlled via the setMaxIterations()\n     * and setTolerance() methods. The defaults are the size of the problem for the maximal number of iterations\n     * and NumTraits<Scalar>::epsilon() for the tolerance.\n     *\n     * This class can be used as the direct solver classes. Here is a typical usage example:\n     * \\code\n     * int n = 10000;\n     * VectorXd x(n), b(n);\n     * SparseMatrix<double> A(n,n);\n     * // fill A and b\n     * MINRES<SparseMatrix<double> > mr;\n     * mr.compute(A);\n     * x = mr.solve(b);\n     * std::cout << \"#iterations:     \" << mr.iterations() << std::endl;\n     * std::cout << \"estimated error: \" << mr.error()      << std::endl;\n     * // update b, and solve again\n     * x = mr.solve(b);\n     * \\endcode\n     *\n     * By default the iterations start with x=0 as an initial guess of the solution.\n     * One can control the start using the solveWithGuess() method.\n     *\n     * MINRES can also be used in a matrix-free context, see the following \\link MatrixfreeSolverExample example \\endlink.\n     *\n     * \\sa class ConjugateGradient, BiCGSTAB, SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner\n     */\n    template< typename _MatrixType, int _UpLo, typename _Preconditioner>\n    class MINRES : public IterativeSolverBase<MINRES<_MatrixType,_UpLo,_Preconditioner> >\n    {\n        \n        typedef IterativeSolverBase<MINRES> Base;\n        using Base::matrix;\n        using Base::m_error;\n        using Base::m_iterations;\n        using Base::m_info;\n        using Base::m_isInitialized;\n    public:\n        using Base::_solve_impl;\n        typedef _MatrixType MatrixType;\n        typedef typename MatrixType::Scalar Scalar;\n        typedef typename MatrixType::RealScalar RealScalar;\n        typedef _Preconditioner Preconditioner;\n        \n        enum {UpLo = _UpLo};\n        \n    public:\n        \n        /** Default constructor. */\n        MINRES() : Base() {}\n        \n        /** Initialize the solver with matrix \\a A for further \\c Ax=b solving.\n         *\n         * This constructor is a shortcut for the default constructor followed\n         * by a call to compute().\n         *\n         * \\warning this class stores a reference to the matrix A as well as some\n         * precomputed values that depend on it. Therefore, if \\a A is changed\n         * this class becomes invalid. Call compute() to update it with the new\n         * matrix A, or modify a copy of A.\n         */\n        template<typename MatrixDerived>\n        explicit MINRES(const EigenBase<MatrixDerived>& A) : Base(A.derived()) {}\n        \n        /** Destructor. */\n        ~MINRES(){}\n\n        /** \\internal */\n        template<typename Rhs,typename Dest>\n        void _solve_with_guess_impl(const Rhs& b, Dest& x) const\n        {\n            typedef typename Base::MatrixWrapper MatrixWrapper;\n            typedef typename Base::ActualMatrixType ActualMatrixType;\n            enum {\n              TransposeInput  =   (!MatrixWrapper::MatrixFree)\n                              &&  (UpLo==(Lower|Upper))\n                              &&  (!MatrixType::IsRowMajor)\n                              &&  (!NumTraits<Scalar>::IsComplex)\n            };\n            typedef typename internal::conditional<TransposeInput,Transpose<const ActualMatrixType>, ActualMatrixType const&>::type RowMajorWrapper;\n            EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(MatrixWrapper::MatrixFree,UpLo==(Lower|Upper)),MATRIX_FREE_CONJUGATE_GRADIENT_IS_COMPATIBLE_WITH_UPPER_UNION_LOWER_MODE_ONLY);\n            typedef typename internal::conditional<UpLo==(Lower|Upper),\n                                                  RowMajorWrapper,\n                                                  typename MatrixWrapper::template ConstSelfAdjointViewReturnType<UpLo>::Type\n                                            >::type SelfAdjointWrapper;\n\n            m_iterations = Base::maxIterations();\n            m_error = Base::m_tolerance;\n            RowMajorWrapper row_mat(matrix());\n            for(int j=0; j<b.cols(); ++j)\n            {\n                m_iterations = Base::maxIterations();\n                m_error = Base::m_tolerance;\n                \n                typename Dest::ColXpr xj(x,j);\n                internal::minres(SelfAdjointWrapper(row_mat), b.col(j), xj,\n                                 Base::m_preconditioner, m_iterations, m_error);\n            }\n            \n            m_isInitialized = true;\n            m_info = m_error <= Base::m_tolerance ? Success : NoConvergence;\n        }\n        \n        /** \\internal */\n        template<typename Rhs,typename Dest>\n        void _solve_impl(const Rhs& b, MatrixBase<Dest> &x) const\n        {\n            x.setZero();\n            _solve_with_guess_impl(b,x.derived());\n        }\n        \n    protected:\n        \n    };\n\n} // end namespace Eigen\n\n#endif // EIGEN_MINRES_H\n\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/IterativeSolvers/Scaling.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Desire NUENTSA WAKAM <desire.nuentsa_wakam@inria.fr\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_ITERSCALING_H\n#define EIGEN_ITERSCALING_H\n\nnamespace Eigen {\n\n/**\n  * \\ingroup IterativeSolvers_Module\n  * \\brief iterative scaling algorithm to equilibrate rows and column norms in matrices\n  * \n  * This class can be used as a preprocessing tool to accelerate the convergence of iterative methods \n  * \n  * This feature is  useful to limit the pivoting amount during LU/ILU factorization\n  * The  scaling strategy as presented here preserves the symmetry of the problem\n  * NOTE It is assumed that the matrix does not have empty row or column, \n  * \n  * Example with key steps \n  * \\code\n  * VectorXd x(n), b(n);\n  * SparseMatrix<double> A;\n  * // fill A and b;\n  * IterScaling<SparseMatrix<double> > scal; \n  * // Compute the left and right scaling vectors. The matrix is equilibrated at output\n  * scal.computeRef(A); \n  * // Scale the right hand side\n  * b = scal.LeftScaling().cwiseProduct(b); \n  * // Now, solve the equilibrated linear system with any available solver\n  * \n  * // Scale back the computed solution\n  * x = scal.RightScaling().cwiseProduct(x); \n  * \\endcode\n  * \n  * \\tparam _MatrixType the type of the matrix. It should be a real square sparsematrix\n  * \n  * References : D. Ruiz and B. Ucar, A Symmetry Preserving Algorithm for Matrix Scaling, INRIA Research report RR-7552\n  * \n  * \\sa \\ref IncompleteLUT \n  */\ntemplate<typename _MatrixType>\nclass IterScaling\n{\n  public:\n    typedef _MatrixType MatrixType; \n    typedef typename MatrixType::Scalar Scalar;\n    typedef typename MatrixType::Index Index;\n    \n  public:\n    IterScaling() { init(); }\n    \n    IterScaling(const MatrixType& matrix)\n    {\n      init();\n      compute(matrix);\n    }\n    \n    ~IterScaling() { }\n    \n    /** \n     * Compute the left and right diagonal matrices to scale the input matrix @p mat\n     * \n     * FIXME This algorithm will be modified such that the diagonal elements are permuted on the diagonal. \n     * \n     * \\sa LeftScaling() RightScaling()\n     */\n    void compute (const MatrixType& mat)\n    {\n      using std::abs;\n      int m = mat.rows(); \n      int n = mat.cols();\n      eigen_assert((m>0 && m == n) && \"Please give a non - empty matrix\");\n      m_left.resize(m); \n      m_right.resize(n);\n      m_left.setOnes();\n      m_right.setOnes();\n      m_matrix = mat;\n      VectorXd Dr, Dc, DrRes, DcRes; // Temporary Left and right scaling vectors\n      Dr.resize(m); Dc.resize(n);\n      DrRes.resize(m); DcRes.resize(n);\n      double EpsRow = 1.0, EpsCol = 1.0;\n      int its = 0; \n      do\n      { // Iterate until the infinite norm of each row and column is approximately 1\n        // Get the maximum value in each row and column\n        Dr.setZero(); Dc.setZero();\n        for (int k=0; k<m_matrix.outerSize(); ++k)\n        {\n          for (typename MatrixType::InnerIterator it(m_matrix, k); it; ++it)\n          {\n            if ( Dr(it.row()) < abs(it.value()) )\n              Dr(it.row()) = abs(it.value());\n            \n            if ( Dc(it.col()) < abs(it.value()) )\n              Dc(it.col()) = abs(it.value());\n          }\n        }\n        for (int i = 0; i < m; ++i) \n        {\n          Dr(i) = std::sqrt(Dr(i));\n          Dc(i) = std::sqrt(Dc(i));\n        }\n        // Save the scaling factors \n        for (int i = 0; i < m; ++i) \n        {\n          m_left(i) /= Dr(i);\n          m_right(i) /= Dc(i);\n        }\n        // Scale the rows and the columns of the matrix\n        DrRes.setZero(); DcRes.setZero(); \n        for (int k=0; k<m_matrix.outerSize(); ++k)\n        {\n          for (typename MatrixType::InnerIterator it(m_matrix, k); it; ++it)\n          {\n            it.valueRef() = it.value()/( Dr(it.row()) * Dc(it.col()) );\n            // Accumulate the norms of the row and column vectors   \n            if ( DrRes(it.row()) < abs(it.value()) )\n              DrRes(it.row()) = abs(it.value());\n            \n            if ( DcRes(it.col()) < abs(it.value()) )\n              DcRes(it.col()) = abs(it.value());\n          }\n        }  \n        DrRes.array() = (1-DrRes.array()).abs();\n        EpsRow = DrRes.maxCoeff();\n        DcRes.array() = (1-DcRes.array()).abs();\n        EpsCol = DcRes.maxCoeff();\n        its++;\n      }while ( (EpsRow >m_tol || EpsCol > m_tol) && (its < m_maxits) );\n      m_isInitialized = true;\n    }\n    /** Compute the left and right vectors to scale the vectors\n     * the input matrix is scaled with the computed vectors at output\n     * \n     * \\sa compute()\n     */\n    void computeRef (MatrixType& mat)\n    {\n      compute (mat);\n      mat = m_matrix;\n    }\n    /** Get the vector to scale the rows of the matrix \n     */\n    VectorXd& LeftScaling()\n    {\n      return m_left;\n    }\n    \n    /** Get the vector to scale the columns of the matrix \n     */\n    VectorXd& RightScaling()\n    {\n      return m_right;\n    }\n    \n    /** Set the tolerance for the convergence of the iterative scaling algorithm\n     */\n    void setTolerance(double tol)\n    {\n      m_tol = tol; \n    }\n      \n  protected:\n    \n    void init()\n    {\n      m_tol = 1e-10;\n      m_maxits = 5;\n      m_isInitialized = false;\n    }\n    \n    MatrixType m_matrix;\n    mutable ComputationInfo m_info; \n    bool m_isInitialized; \n    VectorXd m_left; // Left scaling vector\n    VectorXd m_right; // m_right scaling vector\n    double m_tol; \n    int m_maxits; // Maximum number of iterations allowed\n};\n}\n#endif\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/KroneckerProduct/KroneckerTensorProduct.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2011 Kolja Brix <brix@igpm.rwth-aachen.de>\n// Copyright (C) 2011 Andreas Platen <andiplaten@gmx.de>\n// Copyright (C) 2012 Chen-Pang He <jdh8@ms63.hinet.net>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef KRONECKER_TENSOR_PRODUCT_H\n#define KRONECKER_TENSOR_PRODUCT_H\n\nnamespace Eigen {\n\n/*!\n * \\ingroup KroneckerProduct_Module\n *\n * \\brief The base class of dense and sparse Kronecker product.\n *\n * \\tparam Derived is the derived type.\n */\ntemplate<typename Derived>\nclass KroneckerProductBase : public ReturnByValue<Derived>\n{\n  private:\n    typedef typename internal::traits<Derived> Traits;\n    typedef typename Traits::Scalar Scalar;\n\n  protected:\n    typedef typename Traits::Lhs Lhs;\n    typedef typename Traits::Rhs Rhs;\n\n  public:\n    /*! \\brief Constructor. */\n    KroneckerProductBase(const Lhs& A, const Rhs& B)\n      : m_A(A), m_B(B)\n    {}\n\n    inline Index rows() const { return m_A.rows() * m_B.rows(); }\n    inline Index cols() const { return m_A.cols() * m_B.cols(); }\n\n    /*!\n     * This overrides ReturnByValue::coeff because this function is\n     * efficient enough.\n     */\n    Scalar coeff(Index row, Index col) const\n    {\n      return m_A.coeff(row / m_B.rows(), col / m_B.cols()) *\n             m_B.coeff(row % m_B.rows(), col % m_B.cols());\n    }\n\n    /*!\n     * This overrides ReturnByValue::coeff because this function is\n     * efficient enough.\n     */\n    Scalar coeff(Index i) const\n    {\n      EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);\n      return m_A.coeff(i / m_A.size()) * m_B.coeff(i % m_A.size());\n    }\n\n  protected:\n    typename Lhs::Nested m_A;\n    typename Rhs::Nested m_B;\n};\n\n/*!\n * \\ingroup KroneckerProduct_Module\n *\n * \\brief Kronecker tensor product helper class for dense matrices\n *\n * This class is the return value of kroneckerProduct(MatrixBase,\n * MatrixBase). Use the function rather than construct this class\n * directly to avoid specifying template prarameters.\n *\n * \\tparam Lhs  Type of the left-hand side, a matrix expression.\n * \\tparam Rhs  Type of the rignt-hand side, a matrix expression.\n */\ntemplate<typename Lhs, typename Rhs>\nclass KroneckerProduct : public KroneckerProductBase<KroneckerProduct<Lhs,Rhs> >\n{\n  private:\n    typedef KroneckerProductBase<KroneckerProduct> Base;\n    using Base::m_A;\n    using Base::m_B;\n\n  public:\n    /*! \\brief Constructor. */\n    KroneckerProduct(const Lhs& A, const Rhs& B)\n      : Base(A, B)\n    {}\n\n    /*! \\brief Evaluate the Kronecker tensor product. */\n    template<typename Dest> void evalTo(Dest& dst) const;\n};\n\n/*!\n * \\ingroup KroneckerProduct_Module\n *\n * \\brief Kronecker tensor product helper class for sparse matrices\n *\n * If at least one of the operands is a sparse matrix expression,\n * then this class is returned and evaluates into a sparse matrix.\n *\n * This class is the return value of kroneckerProduct(EigenBase,\n * EigenBase). Use the function rather than construct this class\n * directly to avoid specifying template prarameters.\n *\n * \\tparam Lhs  Type of the left-hand side, a matrix expression.\n * \\tparam Rhs  Type of the rignt-hand side, a matrix expression.\n */\ntemplate<typename Lhs, typename Rhs>\nclass KroneckerProductSparse : public KroneckerProductBase<KroneckerProductSparse<Lhs,Rhs> >\n{\n  private:\n    typedef KroneckerProductBase<KroneckerProductSparse> Base;\n    using Base::m_A;\n    using Base::m_B;\n\n  public:\n    /*! \\brief Constructor. */\n    KroneckerProductSparse(const Lhs& A, const Rhs& B)\n      : Base(A, B)\n    {}\n\n    /*! \\brief Evaluate the Kronecker tensor product. */\n    template<typename Dest> void evalTo(Dest& dst) const;\n};\n\ntemplate<typename Lhs, typename Rhs>\ntemplate<typename Dest>\nvoid KroneckerProduct<Lhs,Rhs>::evalTo(Dest& dst) const\n{\n  const int BlockRows = Rhs::RowsAtCompileTime,\n            BlockCols = Rhs::ColsAtCompileTime;\n  const Index Br = m_B.rows(),\n              Bc = m_B.cols();\n  for (Index i=0; i < m_A.rows(); ++i)\n    for (Index j=0; j < m_A.cols(); ++j)\n      Block<Dest,BlockRows,BlockCols>(dst,i*Br,j*Bc,Br,Bc) = m_A.coeff(i,j) * m_B;\n}\n\ntemplate<typename Lhs, typename Rhs>\ntemplate<typename Dest>\nvoid KroneckerProductSparse<Lhs,Rhs>::evalTo(Dest& dst) const\n{\n  Index Br = m_B.rows(), Bc = m_B.cols();\n  dst.resize(this->rows(), this->cols());\n  dst.resizeNonZeros(0);\n  \n  // 1 - evaluate the operands if needed:\n  typedef typename internal::nested_eval<Lhs,Dynamic>::type Lhs1;\n  typedef typename internal::remove_all<Lhs1>::type Lhs1Cleaned;\n  const Lhs1 lhs1(m_A);\n  typedef typename internal::nested_eval<Rhs,Dynamic>::type Rhs1;\n  typedef typename internal::remove_all<Rhs1>::type Rhs1Cleaned;\n  const Rhs1 rhs1(m_B);\n    \n  // 2 - construct respective iterators\n  typedef Eigen::InnerIterator<Lhs1Cleaned> LhsInnerIterator;\n  typedef Eigen::InnerIterator<Rhs1Cleaned> RhsInnerIterator;\n  \n  // compute number of non-zeros per innervectors of dst\n  {\n    // TODO VectorXi is not necessarily big enough!\n    VectorXi nnzA = VectorXi::Zero(Dest::IsRowMajor ? m_A.rows() : m_A.cols());\n    for (Index kA=0; kA < m_A.outerSize(); ++kA)\n      for (LhsInnerIterator itA(lhs1,kA); itA; ++itA)\n        nnzA(Dest::IsRowMajor ? itA.row() : itA.col())++;\n      \n    VectorXi nnzB = VectorXi::Zero(Dest::IsRowMajor ? m_B.rows() : m_B.cols());\n    for (Index kB=0; kB < m_B.outerSize(); ++kB)\n      for (RhsInnerIterator itB(rhs1,kB); itB; ++itB)\n        nnzB(Dest::IsRowMajor ? itB.row() : itB.col())++;\n    \n    Matrix<int,Dynamic,Dynamic,ColMajor> nnzAB = nnzB * nnzA.transpose();\n    dst.reserve(VectorXi::Map(nnzAB.data(), nnzAB.size()));\n  }\n\n  for (Index kA=0; kA < m_A.outerSize(); ++kA)\n  {\n    for (Index kB=0; kB < m_B.outerSize(); ++kB)\n    {\n      for (LhsInnerIterator itA(lhs1,kA); itA; ++itA)\n      {\n        for (RhsInnerIterator itB(rhs1,kB); itB; ++itB)\n        {\n          Index i = itA.row() * Br + itB.row(),\n                j = itA.col() * Bc + itB.col();\n          dst.insert(i,j) = itA.value() * itB.value();\n        }\n      }\n    }\n  }\n}\n\nnamespace internal {\n\ntemplate<typename _Lhs, typename _Rhs>\nstruct traits<KroneckerProduct<_Lhs,_Rhs> >\n{\n  typedef typename remove_all<_Lhs>::type Lhs;\n  typedef typename remove_all<_Rhs>::type Rhs;\n  typedef typename ScalarBinaryOpTraits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType Scalar;\n  typedef typename promote_index_type<typename Lhs::StorageIndex, typename Rhs::StorageIndex>::type StorageIndex;\n\n  enum {\n    Rows = size_at_compile_time<traits<Lhs>::RowsAtCompileTime, traits<Rhs>::RowsAtCompileTime>::ret,\n    Cols = size_at_compile_time<traits<Lhs>::ColsAtCompileTime, traits<Rhs>::ColsAtCompileTime>::ret,\n    MaxRows = size_at_compile_time<traits<Lhs>::MaxRowsAtCompileTime, traits<Rhs>::MaxRowsAtCompileTime>::ret,\n    MaxCols = size_at_compile_time<traits<Lhs>::MaxColsAtCompileTime, traits<Rhs>::MaxColsAtCompileTime>::ret\n  };\n\n  typedef Matrix<Scalar,Rows,Cols> ReturnType;\n};\n\ntemplate<typename _Lhs, typename _Rhs>\nstruct traits<KroneckerProductSparse<_Lhs,_Rhs> >\n{\n  typedef MatrixXpr XprKind;\n  typedef typename remove_all<_Lhs>::type Lhs;\n  typedef typename remove_all<_Rhs>::type Rhs;\n  typedef typename ScalarBinaryOpTraits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType Scalar;\n  typedef typename cwise_promote_storage_type<typename traits<Lhs>::StorageKind, typename traits<Rhs>::StorageKind, scalar_product_op<typename Lhs::Scalar, typename Rhs::Scalar> >::ret StorageKind;\n  typedef typename promote_index_type<typename Lhs::StorageIndex, typename Rhs::StorageIndex>::type StorageIndex;\n\n  enum {\n    LhsFlags = Lhs::Flags,\n    RhsFlags = Rhs::Flags,\n\n    RowsAtCompileTime = size_at_compile_time<traits<Lhs>::RowsAtCompileTime, traits<Rhs>::RowsAtCompileTime>::ret,\n    ColsAtCompileTime = size_at_compile_time<traits<Lhs>::ColsAtCompileTime, traits<Rhs>::ColsAtCompileTime>::ret,\n    MaxRowsAtCompileTime = size_at_compile_time<traits<Lhs>::MaxRowsAtCompileTime, traits<Rhs>::MaxRowsAtCompileTime>::ret,\n    MaxColsAtCompileTime = size_at_compile_time<traits<Lhs>::MaxColsAtCompileTime, traits<Rhs>::MaxColsAtCompileTime>::ret,\n\n    EvalToRowMajor = (LhsFlags & RhsFlags & RowMajorBit),\n    RemovedBits = ~(EvalToRowMajor ? 0 : RowMajorBit),\n\n    Flags = ((LhsFlags | RhsFlags) & HereditaryBits & RemovedBits)\n          | EvalBeforeNestingBit,\n    CoeffReadCost = HugeCost\n  };\n\n  typedef SparseMatrix<Scalar, 0, StorageIndex> ReturnType;\n};\n\n} // end namespace internal\n\n/*!\n * \\ingroup KroneckerProduct_Module\n *\n * Computes Kronecker tensor product of two dense matrices\n *\n * \\warning If you want to replace a matrix by its Kronecker product\n *          with some matrix, do \\b NOT do this:\n * \\code\n * A = kroneckerProduct(A,B); // bug!!! caused by aliasing effect\n * \\endcode\n * instead, use eval() to work around this:\n * \\code\n * A = kroneckerProduct(A,B).eval();\n * \\endcode\n *\n * \\param a  Dense matrix a\n * \\param b  Dense matrix b\n * \\return   Kronecker tensor product of a and b\n */\ntemplate<typename A, typename B>\nKroneckerProduct<A,B> kroneckerProduct(const MatrixBase<A>& a, const MatrixBase<B>& b)\n{\n  return KroneckerProduct<A, B>(a.derived(), b.derived());\n}\n\n/*!\n * \\ingroup KroneckerProduct_Module\n *\n * Computes Kronecker tensor product of two matrices, at least one of\n * which is sparse\n *\n * \\warning If you want to replace a matrix by its Kronecker product\n *          with some matrix, do \\b NOT do this:\n * \\code\n * A = kroneckerProduct(A,B); // bug!!! caused by aliasing effect\n * \\endcode\n * instead, use eval() to work around this:\n * \\code\n * A = kroneckerProduct(A,B).eval();\n * \\endcode\n *\n * \\param a  Dense/sparse matrix a\n * \\param b  Dense/sparse matrix b\n * \\return   Kronecker tensor product of a and b, stored in a sparse\n *           matrix\n */\ntemplate<typename A, typename B>\nKroneckerProductSparse<A,B> kroneckerProduct(const EigenBase<A>& a, const EigenBase<B>& b)\n{\n  return KroneckerProductSparse<A,B>(a.derived(), b.derived());\n}\n\n} // end namespace Eigen\n\n#endif // KRONECKER_TENSOR_PRODUCT_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/LevenbergMarquardt/CopyrightMINPACK.txt",
    "content": "Minpack Copyright Notice (1999) University of Chicago.  All rights reserved\n\nRedistribution and use in source and binary forms, with or\nwithout modification, are permitted provided that the\nfollowing conditions are met:\n\n1. Redistributions of source code must retain the above\ncopyright notice, this list of conditions and the following\ndisclaimer.\n\n2. Redistributions in binary form must reproduce the above\ncopyright notice, this list of conditions and the following\ndisclaimer in the documentation and/or other materials\nprovided with the distribution.\n\n3. The end-user documentation included with the\nredistribution, if any, must include the following\nacknowledgment:\n\n   \"This product includes software developed by the\n   University of Chicago, as Operator of Argonne National\n   Laboratory.\n\nAlternately, this acknowledgment may appear in the software\nitself, if and wherever such third-party acknowledgments\nnormally appear.\n\n4. WARRANTY DISCLAIMER. THE SOFTWARE IS SUPPLIED \"AS IS\"\nWITHOUT WARRANTY OF ANY KIND. THE COPYRIGHT HOLDER, THE\nUNITED STATES, THE UNITED STATES DEPARTMENT OF ENERGY, AND\nTHEIR EMPLOYEES: (1) DISCLAIM ANY WARRANTIES, EXPRESS OR\nIMPLIED, INCLUDING BUT NOT LIMITED TO ANY IMPLIED WARRANTIES\nOF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE\nOR NON-INFRINGEMENT, (2) DO NOT ASSUME ANY LEGAL LIABILITY\nOR RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS, OR\nUSEFULNESS OF THE SOFTWARE, (3) DO NOT REPRESENT THAT USE OF\nTHE SOFTWARE WOULD NOT INFRINGE PRIVATELY OWNED RIGHTS, (4)\nDO NOT WARRANT THAT THE SOFTWARE WILL FUNCTION\nUNINTERRUPTED, THAT IT IS ERROR-FREE OR THAT ANY ERRORS WILL\nBE CORRECTED.\n\n5. LIMITATION OF LIABILITY. IN NO EVENT WILL THE COPYRIGHT\nHOLDER, THE UNITED STATES, THE UNITED STATES DEPARTMENT OF\nENERGY, OR THEIR EMPLOYEES: BE LIABLE FOR ANY INDIRECT,\nINCIDENTAL, CONSEQUENTIAL, SPECIAL OR PUNITIVE DAMAGES OF\nANY KIND OR NATURE, INCLUDING BUT NOT LIMITED TO LOSS OF\nPROFITS OR LOSS OF DATA, FOR ANY REASON WHATSOEVER, WHETHER\nSUCH LIABILITY IS ASSERTED ON THE BASIS OF CONTRACT, TORT\n(INCLUDING NEGLIGENCE OR STRICT LIABILITY), OR OTHERWISE,\nEVEN IF ANY OF SAID PARTIES HAS BEEN WARNED OF THE\nPOSSIBILITY OF SUCH LOSS OR DAMAGES.\n\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/LevenbergMarquardt/LMcovar.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// This code initially comes from MINPACK whose original authors are:\n// Copyright Jorge More - Argonne National Laboratory\n// Copyright Burt Garbow - Argonne National Laboratory\n// Copyright Ken Hillstrom - Argonne National Laboratory\n//\n// This Source Code Form is subject to the terms of the Minpack license\n// (a BSD-like license) described in the campaigned CopyrightMINPACK.txt file.\n\n#ifndef EIGEN_LMCOVAR_H\n#define EIGEN_LMCOVAR_H\n\nnamespace Eigen { \n\nnamespace internal {\n\ntemplate <typename Scalar>\nvoid covar(\n        Matrix< Scalar, Dynamic, Dynamic > &r,\n        const VectorXi& ipvt,\n        Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon()) )\n{\n    using std::abs;\n    /* Local variables */\n    Index i, j, k, l, ii, jj;\n    bool sing;\n    Scalar temp;\n\n    /* Function Body */\n    const Index n = r.cols();\n    const Scalar tolr = tol * abs(r(0,0));\n    Matrix< Scalar, Dynamic, 1 > wa(n);\n    eigen_assert(ipvt.size()==n);\n\n    /* form the inverse of r in the full upper triangle of r. */\n    l = -1;\n    for (k = 0; k < n; ++k)\n        if (abs(r(k,k)) > tolr) {\n            r(k,k) = 1. / r(k,k);\n            for (j = 0; j <= k-1; ++j) {\n                temp = r(k,k) * r(j,k);\n                r(j,k) = 0.;\n                r.col(k).head(j+1) -= r.col(j).head(j+1) * temp;\n            }\n            l = k;\n        }\n\n    /* form the full upper triangle of the inverse of (r transpose)*r */\n    /* in the full upper triangle of r. */\n    for (k = 0; k <= l; ++k) {\n        for (j = 0; j <= k-1; ++j)\n            r.col(j).head(j+1) += r.col(k).head(j+1) * r(j,k);\n        r.col(k).head(k+1) *= r(k,k);\n    }\n\n    /* form the full lower triangle of the covariance matrix */\n    /* in the strict lower triangle of r and in wa. */\n    for (j = 0; j < n; ++j) {\n        jj = ipvt[j];\n        sing = j > l;\n        for (i = 0; i <= j; ++i) {\n            if (sing)\n                r(i,j) = 0.;\n            ii = ipvt[i];\n            if (ii > jj)\n                r(ii,jj) = r(i,j);\n            if (ii < jj)\n                r(jj,ii) = r(i,j);\n        }\n        wa[jj] = r(j,j);\n    }\n\n    /* symmetrize the covariance matrix in r. */\n    r.topLeftCorner(n,n).template triangularView<StrictlyUpper>() = r.topLeftCorner(n,n).transpose();\n    r.diagonal() = wa;\n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_LMCOVAR_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/LevenbergMarquardt/LMonestep.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>\n//\n// This code initially comes from MINPACK whose original authors are:\n// Copyright Jorge More - Argonne National Laboratory\n// Copyright Burt Garbow - Argonne National Laboratory\n// Copyright Ken Hillstrom - Argonne National Laboratory\n//\n// This Source Code Form is subject to the terms of the Minpack license\n// (a BSD-like license) described in the campaigned CopyrightMINPACK.txt file.\n\n#ifndef EIGEN_LMONESTEP_H\n#define EIGEN_LMONESTEP_H\n\nnamespace Eigen {\n\ntemplate<typename FunctorType>\nLevenbergMarquardtSpace::Status\nLevenbergMarquardt<FunctorType>::minimizeOneStep(FVectorType  &x)\n{\n  using std::abs;\n  using std::sqrt;\n  RealScalar temp, temp1,temp2; \n  RealScalar ratio; \n  RealScalar pnorm, xnorm, fnorm1, actred, dirder, prered;\n  eigen_assert(x.size()==n); // check the caller is not cheating us\n\n  temp = 0.0; xnorm = 0.0;\n  /* calculate the jacobian matrix. */\n  Index df_ret = m_functor.df(x, m_fjac);\n  if (df_ret<0)\n      return LevenbergMarquardtSpace::UserAsked;\n  if (df_ret>0)\n      // numerical diff, we evaluated the function df_ret times\n      m_nfev += df_ret;\n  else m_njev++;\n\n  /* compute the qr factorization of the jacobian. */\n  for (int j = 0; j < x.size(); ++j)\n    m_wa2(j) = m_fjac.col(j).blueNorm();\n  QRSolver qrfac(m_fjac);\n  if(qrfac.info() != Success) {\n    m_info = NumericalIssue;\n    return LevenbergMarquardtSpace::ImproperInputParameters;\n  }\n  // Make a copy of the first factor with the associated permutation\n  m_rfactor = qrfac.matrixR();\n  m_permutation = (qrfac.colsPermutation());\n\n  /* on the first iteration and if external scaling is not used, scale according */\n  /* to the norms of the columns of the initial jacobian. */\n  if (m_iter == 1) {\n      if (!m_useExternalScaling)\n          for (Index j = 0; j < n; ++j)\n              m_diag[j] = (m_wa2[j]==0.)? 1. : m_wa2[j];\n\n      /* on the first iteration, calculate the norm of the scaled x */\n      /* and initialize the step bound m_delta. */\n      xnorm = m_diag.cwiseProduct(x).stableNorm();\n      m_delta = m_factor * xnorm;\n      if (m_delta == 0.)\n          m_delta = m_factor;\n  }\n\n  /* form (q transpose)*m_fvec and store the first n components in */\n  /* m_qtf. */\n  m_wa4 = m_fvec;\n  m_wa4 = qrfac.matrixQ().adjoint() * m_fvec; \n  m_qtf = m_wa4.head(n);\n\n  /* compute the norm of the scaled gradient. */\n  m_gnorm = 0.;\n  if (m_fnorm != 0.)\n      for (Index j = 0; j < n; ++j)\n          if (m_wa2[m_permutation.indices()[j]] != 0.)\n              m_gnorm = (std::max)(m_gnorm, abs( m_rfactor.col(j).head(j+1).dot(m_qtf.head(j+1)/m_fnorm) / m_wa2[m_permutation.indices()[j]]));\n\n  /* test for convergence of the gradient norm. */\n  if (m_gnorm <= m_gtol) {\n    m_info = Success;\n    return LevenbergMarquardtSpace::CosinusTooSmall;\n  }\n\n  /* rescale if necessary. */\n  if (!m_useExternalScaling)\n      m_diag = m_diag.cwiseMax(m_wa2);\n\n  do {\n    /* determine the levenberg-marquardt parameter. */\n    internal::lmpar2(qrfac, m_diag, m_qtf, m_delta, m_par, m_wa1);\n\n    /* store the direction p and x + p. calculate the norm of p. */\n    m_wa1 = -m_wa1;\n    m_wa2 = x + m_wa1;\n    pnorm = m_diag.cwiseProduct(m_wa1).stableNorm();\n\n    /* on the first iteration, adjust the initial step bound. */\n    if (m_iter == 1)\n        m_delta = (std::min)(m_delta,pnorm);\n\n    /* evaluate the function at x + p and calculate its norm. */\n    if ( m_functor(m_wa2, m_wa4) < 0)\n        return LevenbergMarquardtSpace::UserAsked;\n    ++m_nfev;\n    fnorm1 = m_wa4.stableNorm();\n\n    /* compute the scaled actual reduction. */\n    actred = -1.;\n    if (Scalar(.1) * fnorm1 < m_fnorm)\n        actred = 1. - numext::abs2(fnorm1 / m_fnorm);\n\n    /* compute the scaled predicted reduction and */\n    /* the scaled directional derivative. */\n    m_wa3 = m_rfactor.template triangularView<Upper>() * (m_permutation.inverse() *m_wa1);\n    temp1 = numext::abs2(m_wa3.stableNorm() / m_fnorm);\n    temp2 = numext::abs2(sqrt(m_par) * pnorm / m_fnorm);\n    prered = temp1 + temp2 / Scalar(.5);\n    dirder = -(temp1 + temp2);\n\n    /* compute the ratio of the actual to the predicted */\n    /* reduction. */\n    ratio = 0.;\n    if (prered != 0.)\n        ratio = actred / prered;\n\n    /* update the step bound. */\n    if (ratio <= Scalar(.25)) {\n        if (actred >= 0.)\n            temp = RealScalar(.5);\n        if (actred < 0.)\n            temp = RealScalar(.5) * dirder / (dirder + RealScalar(.5) * actred);\n        if (RealScalar(.1) * fnorm1 >= m_fnorm || temp < RealScalar(.1))\n            temp = Scalar(.1);\n        /* Computing MIN */\n        m_delta = temp * (std::min)(m_delta, pnorm / RealScalar(.1));\n        m_par /= temp;\n    } else if (!(m_par != 0. && ratio < RealScalar(.75))) {\n        m_delta = pnorm / RealScalar(.5);\n        m_par = RealScalar(.5) * m_par;\n    }\n\n    /* test for successful iteration. */\n    if (ratio >= RealScalar(1e-4)) {\n        /* successful iteration. update x, m_fvec, and their norms. */\n        x = m_wa2;\n        m_wa2 = m_diag.cwiseProduct(x);\n        m_fvec = m_wa4;\n        xnorm = m_wa2.stableNorm();\n        m_fnorm = fnorm1;\n        ++m_iter;\n    }\n\n    /* tests for convergence. */\n    if (abs(actred) <= m_ftol && prered <= m_ftol && Scalar(.5) * ratio <= 1. && m_delta <= m_xtol * xnorm)\n    {\n       m_info = Success;\n      return LevenbergMarquardtSpace::RelativeErrorAndReductionTooSmall;\n    }\n    if (abs(actred) <= m_ftol && prered <= m_ftol && Scalar(.5) * ratio <= 1.) \n    {\n      m_info = Success;\n      return LevenbergMarquardtSpace::RelativeReductionTooSmall;\n    }\n    if (m_delta <= m_xtol * xnorm)\n    {\n      m_info = Success;\n      return LevenbergMarquardtSpace::RelativeErrorTooSmall;\n    }\n\n    /* tests for termination and stringent tolerances. */\n    if (m_nfev >= m_maxfev) \n    {\n      m_info = NoConvergence;\n      return LevenbergMarquardtSpace::TooManyFunctionEvaluation;\n    }\n    if (abs(actred) <= NumTraits<Scalar>::epsilon() && prered <= NumTraits<Scalar>::epsilon() && Scalar(.5) * ratio <= 1.)\n    {\n      m_info = Success;\n      return LevenbergMarquardtSpace::FtolTooSmall;\n    }\n    if (m_delta <= NumTraits<Scalar>::epsilon() * xnorm) \n    {\n      m_info = Success;\n      return LevenbergMarquardtSpace::XtolTooSmall;\n    }\n    if (m_gnorm <= NumTraits<Scalar>::epsilon())\n    {\n      m_info = Success;\n      return LevenbergMarquardtSpace::GtolTooSmall;\n    }\n\n  } while (ratio < Scalar(1e-4));\n\n  return LevenbergMarquardtSpace::Running;\n}\n\n  \n} // end namespace Eigen\n\n#endif // EIGEN_LMONESTEP_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/LevenbergMarquardt/LMpar.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// This code initially comes from MINPACK whose original authors are:\n// Copyright Jorge More - Argonne National Laboratory\n// Copyright Burt Garbow - Argonne National Laboratory\n// Copyright Ken Hillstrom - Argonne National Laboratory\n//\n// This Source Code Form is subject to the terms of the Minpack license\n// (a BSD-like license) described in the campaigned CopyrightMINPACK.txt file.\n\n#ifndef EIGEN_LMPAR_H\n#define EIGEN_LMPAR_H\n\nnamespace Eigen {\n\nnamespace internal {\n  \n  template <typename QRSolver, typename VectorType>\n    void lmpar2(\n    const QRSolver &qr,\n    const VectorType  &diag,\n    const VectorType  &qtb,\n    typename VectorType::Scalar m_delta,\n    typename VectorType::Scalar &par,\n    VectorType  &x)\n\n  {\n    using std::sqrt;\n    using std::abs;\n    typedef typename QRSolver::MatrixType MatrixType;\n    typedef typename QRSolver::Scalar Scalar;\n//    typedef typename QRSolver::StorageIndex StorageIndex;\n\n    /* Local variables */\n    Index j;\n    Scalar fp;\n    Scalar parc, parl;\n    Index iter;\n    Scalar temp, paru;\n    Scalar gnorm;\n    Scalar dxnorm;\n    \n    // Make a copy of the triangular factor. \n    // This copy is modified during call the qrsolv\n    MatrixType s;\n    s = qr.matrixR();\n\n    /* Function Body */\n    const Scalar dwarf = (std::numeric_limits<Scalar>::min)();\n    const Index n = qr.matrixR().cols();\n    eigen_assert(n==diag.size());\n    eigen_assert(n==qtb.size());\n\n    VectorType  wa1, wa2;\n\n    /* compute and store in x the gauss-newton direction. if the */\n    /* jacobian is rank-deficient, obtain a least squares solution. */\n\n    //    const Index rank = qr.nonzeroPivots(); // exactly double(0.)\n    const Index rank = qr.rank(); // use a threshold\n    wa1 = qtb;\n    wa1.tail(n-rank).setZero();\n    //FIXME There is no solve in place for sparse triangularView\n    wa1.head(rank) = s.topLeftCorner(rank,rank).template triangularView<Upper>().solve(qtb.head(rank));\n\n    x = qr.colsPermutation()*wa1;\n\n    /* initialize the iteration counter. */\n    /* evaluate the function at the origin, and test */\n    /* for acceptance of the gauss-newton direction. */\n    iter = 0;\n    wa2 = diag.cwiseProduct(x);\n    dxnorm = wa2.blueNorm();\n    fp = dxnorm - m_delta;\n    if (fp <= Scalar(0.1) * m_delta) {\n      par = 0;\n      return;\n    }\n\n    /* if the jacobian is not rank deficient, the newton */\n    /* step provides a lower bound, parl, for the zero of */\n    /* the function. otherwise set this bound to zero. */\n    parl = 0.;\n    if (rank==n) {\n      wa1 = qr.colsPermutation().inverse() *  diag.cwiseProduct(wa2)/dxnorm;\n      s.topLeftCorner(n,n).transpose().template triangularView<Lower>().solveInPlace(wa1);\n      temp = wa1.blueNorm();\n      parl = fp / m_delta / temp / temp;\n    }\n\n    /* calculate an upper bound, paru, for the zero of the function. */\n    for (j = 0; j < n; ++j)\n      wa1[j] = s.col(j).head(j+1).dot(qtb.head(j+1)) / diag[qr.colsPermutation().indices()(j)];\n\n    gnorm = wa1.stableNorm();\n    paru = gnorm / m_delta;\n    if (paru == 0.)\n      paru = dwarf / (std::min)(m_delta,Scalar(0.1));\n\n    /* if the input par lies outside of the interval (parl,paru), */\n    /* set par to the closer endpoint. */\n    par = (std::max)(par,parl);\n    par = (std::min)(par,paru);\n    if (par == 0.)\n      par = gnorm / dxnorm;\n\n    /* beginning of an iteration. */\n    while (true) {\n      ++iter;\n\n      /* evaluate the function at the current value of par. */\n      if (par == 0.)\n        par = (std::max)(dwarf,Scalar(.001) * paru); /* Computing MAX */\n      wa1 = sqrt(par)* diag;\n\n      VectorType sdiag(n);\n      lmqrsolv(s, qr.colsPermutation(), wa1, qtb, x, sdiag);\n\n      wa2 = diag.cwiseProduct(x);\n      dxnorm = wa2.blueNorm();\n      temp = fp;\n      fp = dxnorm - m_delta;\n\n      /* if the function is small enough, accept the current value */\n      /* of par. also test for the exceptional cases where parl */\n      /* is zero or the number of iterations has reached 10. */\n      if (abs(fp) <= Scalar(0.1) * m_delta || (parl == 0. && fp <= temp && temp < 0.) || iter == 10)\n        break;\n\n      /* compute the newton correction. */\n      wa1 = qr.colsPermutation().inverse() * diag.cwiseProduct(wa2/dxnorm);\n      // we could almost use this here, but the diagonal is outside qr, in sdiag[]\n      for (j = 0; j < n; ++j) {\n        wa1[j] /= sdiag[j];\n        temp = wa1[j];\n        for (Index i = j+1; i < n; ++i)\n          wa1[i] -= s.coeff(i,j) * temp;\n      }\n      temp = wa1.blueNorm();\n      parc = fp / m_delta / temp / temp;\n\n      /* depending on the sign of the function, update parl or paru. */\n      if (fp > 0.)\n        parl = (std::max)(parl,par);\n      if (fp < 0.)\n        paru = (std::min)(paru,par);\n\n      /* compute an improved estimate for par. */\n      par = (std::max)(parl,par+parc);\n    }\n    if (iter == 0)\n      par = 0.;\n    return;\n  }\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_LMPAR_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/LevenbergMarquardt/LMqrsolv.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>\n// Copyright (C) 2012 Desire Nuentsa <desire.nuentsa_wakam@inria.fr>\n//\n// This code initially comes from MINPACK whose original authors are:\n// Copyright Jorge More - Argonne National Laboratory\n// Copyright Burt Garbow - Argonne National Laboratory\n// Copyright Ken Hillstrom - Argonne National Laboratory\n//\n// This Source Code Form is subject to the terms of the Minpack license\n// (a BSD-like license) described in the campaigned CopyrightMINPACK.txt file.\n\n#ifndef EIGEN_LMQRSOLV_H\n#define EIGEN_LMQRSOLV_H\n\nnamespace Eigen { \n\nnamespace internal {\n\ntemplate <typename Scalar,int Rows, int Cols, typename PermIndex>\nvoid lmqrsolv(\n  Matrix<Scalar,Rows,Cols> &s,\n  const PermutationMatrix<Dynamic,Dynamic,PermIndex> &iPerm,\n  const Matrix<Scalar,Dynamic,1> &diag,\n  const Matrix<Scalar,Dynamic,1> &qtb,\n  Matrix<Scalar,Dynamic,1> &x,\n  Matrix<Scalar,Dynamic,1> &sdiag)\n{\n    /* Local variables */\n    Index i, j, k;\n    Scalar temp;\n    Index n = s.cols();\n    Matrix<Scalar,Dynamic,1>  wa(n);\n    JacobiRotation<Scalar> givens;\n\n    /* Function Body */\n    // the following will only change the lower triangular part of s, including\n    // the diagonal, though the diagonal is restored afterward\n\n    /*     copy r and (q transpose)*b to preserve input and initialize s. */\n    /*     in particular, save the diagonal elements of r in x. */\n    x = s.diagonal();\n    wa = qtb;\n    \n   \n    s.topLeftCorner(n,n).template triangularView<StrictlyLower>() = s.topLeftCorner(n,n).transpose();\n    /*     eliminate the diagonal matrix d using a givens rotation. */\n    for (j = 0; j < n; ++j) {\n\n        /*        prepare the row of d to be eliminated, locating the */\n        /*        diagonal element using p from the qr factorization. */\n        const PermIndex l = iPerm.indices()(j);\n        if (diag[l] == 0.)\n            break;\n        sdiag.tail(n-j).setZero();\n        sdiag[j] = diag[l];\n\n        /*        the transformations to eliminate the row of d */\n        /*        modify only a single element of (q transpose)*b */\n        /*        beyond the first n, which is initially zero. */\n        Scalar qtbpj = 0.;\n        for (k = j; k < n; ++k) {\n            /*           determine a givens rotation which eliminates the */\n            /*           appropriate element in the current row of d. */\n            givens.makeGivens(-s(k,k), sdiag[k]);\n\n            /*           compute the modified diagonal element of r and */\n            /*           the modified element of ((q transpose)*b,0). */\n            s(k,k) = givens.c() * s(k,k) + givens.s() * sdiag[k];\n            temp = givens.c() * wa[k] + givens.s() * qtbpj;\n            qtbpj = -givens.s() * wa[k] + givens.c() * qtbpj;\n            wa[k] = temp;\n\n            /*           accumulate the tranformation in the row of s. */\n            for (i = k+1; i<n; ++i) {\n                temp = givens.c() * s(i,k) + givens.s() * sdiag[i];\n                sdiag[i] = -givens.s() * s(i,k) + givens.c() * sdiag[i];\n                s(i,k) = temp;\n            }\n        }\n    }\n  \n    /*     solve the triangular system for z. if the system is */\n    /*     singular, then obtain a least squares solution. */\n    Index nsing;\n    for(nsing=0; nsing<n && sdiag[nsing]!=0; nsing++) {}\n\n    wa.tail(n-nsing).setZero();\n    s.topLeftCorner(nsing, nsing).transpose().template triangularView<Upper>().solveInPlace(wa.head(nsing));\n  \n    // restore\n    sdiag = s.diagonal();\n    s.diagonal() = x;\n\n    /* permute the components of z back to components of x. */\n    x = iPerm * wa; \n}\n\ntemplate <typename Scalar, int _Options, typename Index>\nvoid lmqrsolv(\n  SparseMatrix<Scalar,_Options,Index> &s,\n  const PermutationMatrix<Dynamic,Dynamic> &iPerm,\n  const Matrix<Scalar,Dynamic,1> &diag,\n  const Matrix<Scalar,Dynamic,1> &qtb,\n  Matrix<Scalar,Dynamic,1> &x,\n  Matrix<Scalar,Dynamic,1> &sdiag)\n{\n  /* Local variables */\n  typedef SparseMatrix<Scalar,RowMajor,Index> FactorType;\n    Index i, j, k, l;\n    Scalar temp;\n    Index n = s.cols();\n    Matrix<Scalar,Dynamic,1>  wa(n);\n    JacobiRotation<Scalar> givens;\n\n    /* Function Body */\n    // the following will only change the lower triangular part of s, including\n    // the diagonal, though the diagonal is restored afterward\n\n    /*     copy r and (q transpose)*b to preserve input and initialize R. */\n    wa = qtb;\n    FactorType R(s);\n    // Eliminate the diagonal matrix d using a givens rotation\n    for (j = 0; j < n; ++j)\n    {\n      // Prepare the row of d to be eliminated, locating the \n      // diagonal element using p from the qr factorization\n      l = iPerm.indices()(j);\n      if (diag(l) == Scalar(0)) \n        break; \n      sdiag.tail(n-j).setZero();\n      sdiag[j] = diag[l];\n      // the transformations to eliminate the row of d\n      // modify only a single element of (q transpose)*b\n      // beyond the first n, which is initially zero. \n      \n      Scalar qtbpj = 0; \n      // Browse the nonzero elements of row j of the upper triangular s\n      for (k = j; k < n; ++k)\n      {\n        typename FactorType::InnerIterator itk(R,k);\n        for (; itk; ++itk){\n          if (itk.index() < k) continue;\n          else break;\n        }\n        //At this point, we have the diagonal element R(k,k)\n        // Determine a givens rotation which eliminates \n        // the appropriate element in the current row of d\n        givens.makeGivens(-itk.value(), sdiag(k));\n        \n        // Compute the modified diagonal element of r and \n        // the modified element of ((q transpose)*b,0).\n        itk.valueRef() = givens.c() * itk.value() + givens.s() * sdiag(k);\n        temp = givens.c() * wa(k) + givens.s() * qtbpj; \n        qtbpj = -givens.s() * wa(k) + givens.c() * qtbpj;\n        wa(k) = temp;\n        \n        // Accumulate the transformation in the remaining k row/column of R\n        for (++itk; itk; ++itk)\n        {\n          i = itk.index();\n          temp = givens.c() *  itk.value() + givens.s() * sdiag(i);\n          sdiag(i) = -givens.s() * itk.value() + givens.c() * sdiag(i);\n          itk.valueRef() = temp;\n        }\n      }\n    }\n    \n    // Solve the triangular system for z. If the system is \n    // singular, then obtain a least squares solution\n    Index nsing;\n    for(nsing = 0; nsing<n && sdiag(nsing) !=0; nsing++) {}\n    \n    wa.tail(n-nsing).setZero();\n//     x = wa; \n    wa.head(nsing) = R.topLeftCorner(nsing,nsing).template triangularView<Upper>().solve/*InPlace*/(wa.head(nsing));\n    \n    sdiag = R.diagonal();\n    // Permute the components of z back to components of x\n    x = iPerm * wa; \n}\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_LMQRSOLV_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/LevenbergMarquardt/LevenbergMarquardt.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>\n// Copyright (C) 2012 Desire Nuentsa <desire.nuentsa_wakam@inria.fr>\n//\n// The algorithm of this class initially comes from MINPACK whose original authors are:\n// Copyright Jorge More - Argonne National Laboratory\n// Copyright Burt Garbow - Argonne National Laboratory\n// Copyright Ken Hillstrom - Argonne National Laboratory\n//\n// This Source Code Form is subject to the terms of the Minpack license\n// (a BSD-like license) described in the campaigned CopyrightMINPACK.txt file.\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_LEVENBERGMARQUARDT_H\n#define EIGEN_LEVENBERGMARQUARDT_H\n\n\nnamespace Eigen {\nnamespace LevenbergMarquardtSpace {\n    enum Status {\n        NotStarted = -2,\n        Running = -1,\n        ImproperInputParameters = 0,\n        RelativeReductionTooSmall = 1,\n        RelativeErrorTooSmall = 2,\n        RelativeErrorAndReductionTooSmall = 3,\n        CosinusTooSmall = 4,\n        TooManyFunctionEvaluation = 5,\n        FtolTooSmall = 6,\n        XtolTooSmall = 7,\n        GtolTooSmall = 8,\n        UserAsked = 9\n    };\n}\n\ntemplate <typename _Scalar, int NX=Dynamic, int NY=Dynamic>\nstruct DenseFunctor\n{\n  typedef _Scalar Scalar;\n  enum {\n    InputsAtCompileTime = NX,\n    ValuesAtCompileTime = NY\n  };\n  typedef Matrix<Scalar,InputsAtCompileTime,1> InputType;\n  typedef Matrix<Scalar,ValuesAtCompileTime,1> ValueType;\n  typedef Matrix<Scalar,ValuesAtCompileTime,InputsAtCompileTime> JacobianType;\n  typedef ColPivHouseholderQR<JacobianType> QRSolver;\n  const int m_inputs, m_values;\n\n  DenseFunctor() : m_inputs(InputsAtCompileTime), m_values(ValuesAtCompileTime) {}\n  DenseFunctor(int inputs, int values) : m_inputs(inputs), m_values(values) {}\n\n  int inputs() const { return m_inputs; }\n  int values() const { return m_values; }\n\n  //int operator()(const InputType &x, ValueType& fvec) { }\n  // should be defined in derived classes\n  \n  //int df(const InputType &x, JacobianType& fjac) { }\n  // should be defined in derived classes\n};\n\ntemplate <typename _Scalar, typename _Index>\nstruct SparseFunctor\n{\n  typedef _Scalar Scalar;\n  typedef _Index Index;\n  typedef Matrix<Scalar,Dynamic,1> InputType;\n  typedef Matrix<Scalar,Dynamic,1> ValueType;\n  typedef SparseMatrix<Scalar, ColMajor, Index> JacobianType;\n  typedef SparseQR<JacobianType, COLAMDOrdering<int> > QRSolver;\n  enum {\n    InputsAtCompileTime = Dynamic,\n    ValuesAtCompileTime = Dynamic\n  };\n  \n  SparseFunctor(int inputs, int values) : m_inputs(inputs), m_values(values) {}\n\n  int inputs() const { return m_inputs; }\n  int values() const { return m_values; }\n  \n  const int m_inputs, m_values;\n  //int operator()(const InputType &x, ValueType& fvec) { }\n  // to be defined in the functor\n  \n  //int df(const InputType &x, JacobianType& fjac) { }\n  // to be defined in the functor if no automatic differentiation\n  \n};\nnamespace internal {\ntemplate <typename QRSolver, typename VectorType>\nvoid lmpar2(const QRSolver &qr, const VectorType  &diag, const VectorType  &qtb,\n\t    typename VectorType::Scalar m_delta, typename VectorType::Scalar &par,\n\t    VectorType  &x);\n    }\n/**\n  * \\ingroup NonLinearOptimization_Module\n  * \\brief Performs non linear optimization over a non-linear function,\n  * using a variant of the Levenberg Marquardt algorithm.\n  *\n  * Check wikipedia for more information.\n  * http://en.wikipedia.org/wiki/Levenberg%E2%80%93Marquardt_algorithm\n  */\ntemplate<typename _FunctorType>\nclass LevenbergMarquardt : internal::no_assignment_operator\n{\n  public:\n    typedef _FunctorType FunctorType;\n    typedef typename FunctorType::QRSolver QRSolver;\n    typedef typename FunctorType::JacobianType JacobianType;\n    typedef typename JacobianType::Scalar Scalar;\n    typedef typename JacobianType::RealScalar RealScalar; \n    typedef typename QRSolver::StorageIndex PermIndex;\n    typedef Matrix<Scalar,Dynamic,1> FVectorType;\n    typedef PermutationMatrix<Dynamic,Dynamic> PermutationType;\n  public:\n    LevenbergMarquardt(FunctorType& functor) \n    : m_functor(functor),m_nfev(0),m_njev(0),m_fnorm(0.0),m_gnorm(0),\n      m_isInitialized(false),m_info(InvalidInput)\n    {\n      resetParameters();\n      m_useExternalScaling=false; \n    }\n    \n    LevenbergMarquardtSpace::Status minimize(FVectorType &x);\n    LevenbergMarquardtSpace::Status minimizeInit(FVectorType &x);\n    LevenbergMarquardtSpace::Status minimizeOneStep(FVectorType &x);\n    LevenbergMarquardtSpace::Status lmder1(\n      FVectorType  &x, \n      const Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon())\n    );\n    static LevenbergMarquardtSpace::Status lmdif1(\n            FunctorType &functor,\n            FVectorType  &x,\n            Index *nfev,\n            const Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon())\n            );\n    \n    /** Sets the default parameters */\n    void resetParameters() \n    {\n      using std::sqrt;        \n\n      m_factor = 100.; \n      m_maxfev = 400; \n      m_ftol = sqrt(NumTraits<RealScalar>::epsilon());\n      m_xtol = sqrt(NumTraits<RealScalar>::epsilon());\n      m_gtol = 0. ; \n      m_epsfcn = 0. ;\n    }\n    \n    /** Sets the tolerance for the norm of the solution vector*/\n    void setXtol(RealScalar xtol) { m_xtol = xtol; }\n    \n    /** Sets the tolerance for the norm of the vector function*/\n    void setFtol(RealScalar ftol) { m_ftol = ftol; }\n    \n    /** Sets the tolerance for the norm of the gradient of the error vector*/\n    void setGtol(RealScalar gtol) { m_gtol = gtol; }\n    \n    /** Sets the step bound for the diagonal shift */\n    void setFactor(RealScalar factor) { m_factor = factor; }    \n    \n    /** Sets the error precision  */\n    void setEpsilon (RealScalar epsfcn) { m_epsfcn = epsfcn; }\n    \n    /** Sets the maximum number of function evaluation */\n    void setMaxfev(Index maxfev) {m_maxfev = maxfev; }\n    \n    /** Use an external Scaling. If set to true, pass a nonzero diagonal to diag() */\n    void setExternalScaling(bool value) {m_useExternalScaling  = value; }\n    \n    /** \\returns the tolerance for the norm of the solution vector */\n    RealScalar xtol() const {return m_xtol; }\n    \n    /** \\returns the tolerance for the norm of the vector function */\n    RealScalar ftol() const {return m_ftol; }\n    \n    /** \\returns the tolerance for the norm of the gradient of the error vector */\n    RealScalar gtol() const {return m_gtol; }\n    \n    /** \\returns the step bound for the diagonal shift */\n    RealScalar factor() const {return m_factor; }\n    \n    /** \\returns the error precision */\n    RealScalar epsilon() const {return m_epsfcn; }\n    \n    /** \\returns the maximum number of function evaluation */\n    Index maxfev() const {return m_maxfev; }\n    \n    /** \\returns a reference to the diagonal of the jacobian */\n    FVectorType& diag() {return m_diag; }\n    \n    /** \\returns the number of iterations performed */\n    Index iterations() { return m_iter; }\n    \n    /** \\returns the number of functions evaluation */\n    Index nfev() { return m_nfev; }\n    \n    /** \\returns the number of jacobian evaluation */\n    Index njev() { return m_njev; }\n    \n    /** \\returns the norm of current vector function */\n    RealScalar fnorm() {return m_fnorm; }\n    \n    /** \\returns the norm of the gradient of the error */\n    RealScalar gnorm() {return m_gnorm; }\n    \n    /** \\returns the LevenbergMarquardt parameter */\n    RealScalar lm_param(void) { return m_par; }\n    \n    /** \\returns a reference to the  current vector function \n     */\n    FVectorType& fvec() {return m_fvec; }\n    \n    /** \\returns a reference to the matrix where the current Jacobian matrix is stored\n     */\n    JacobianType& jacobian() {return m_fjac; }\n    \n    /** \\returns a reference to the triangular matrix R from the QR of the jacobian matrix.\n     * \\sa jacobian()\n     */\n    JacobianType& matrixR() {return m_rfactor; }\n    \n    /** the permutation used in the QR factorization\n     */\n    PermutationType permutation() {return m_permutation; }\n    \n    /** \n     * \\brief Reports whether the minimization was successful\n     * \\returns \\c Success if the minimization was succesful,\n     *         \\c NumericalIssue if a numerical problem arises during the \n     *          minimization process, for exemple during the QR factorization\n     *         \\c NoConvergence if the minimization did not converge after \n     *          the maximum number of function evaluation allowed\n     *          \\c InvalidInput if the input matrix is invalid\n     */\n    ComputationInfo info() const\n    {\n      \n      return m_info;\n    }\n  private:\n    JacobianType m_fjac; \n    JacobianType m_rfactor; // The triangular matrix R from the QR of the jacobian matrix m_fjac\n    FunctorType &m_functor;\n    FVectorType m_fvec, m_qtf, m_diag; \n    Index n;\n    Index m; \n    Index m_nfev;\n    Index m_njev; \n    RealScalar m_fnorm; // Norm of the current vector function\n    RealScalar m_gnorm; //Norm of the gradient of the error \n    RealScalar m_factor; //\n    Index m_maxfev; // Maximum number of function evaluation\n    RealScalar m_ftol; //Tolerance in the norm of the vector function\n    RealScalar m_xtol; // \n    RealScalar m_gtol; //tolerance of the norm of the error gradient\n    RealScalar m_epsfcn; //\n    Index m_iter; // Number of iterations performed\n    RealScalar m_delta;\n    bool m_useExternalScaling;\n    PermutationType m_permutation;\n    FVectorType m_wa1, m_wa2, m_wa3, m_wa4; //Temporary vectors\n    RealScalar m_par;\n    bool m_isInitialized; // Check whether the minimization step has been called\n    ComputationInfo m_info; \n};\n\ntemplate<typename FunctorType>\nLevenbergMarquardtSpace::Status\nLevenbergMarquardt<FunctorType>::minimize(FVectorType  &x)\n{\n    LevenbergMarquardtSpace::Status status = minimizeInit(x);\n    if (status==LevenbergMarquardtSpace::ImproperInputParameters) {\n      m_isInitialized = true;\n      return status;\n    }\n    do {\n//       std::cout << \" uv \" << x.transpose() << \"\\n\";\n        status = minimizeOneStep(x);\n    } while (status==LevenbergMarquardtSpace::Running);\n     m_isInitialized = true;\n     return status;\n}\n\ntemplate<typename FunctorType>\nLevenbergMarquardtSpace::Status\nLevenbergMarquardt<FunctorType>::minimizeInit(FVectorType  &x)\n{\n    n = x.size();\n    m = m_functor.values();\n\n    m_wa1.resize(n); m_wa2.resize(n); m_wa3.resize(n);\n    m_wa4.resize(m);\n    m_fvec.resize(m);\n    //FIXME Sparse Case : Allocate space for the jacobian\n    m_fjac.resize(m, n);\n//     m_fjac.reserve(VectorXi::Constant(n,5)); // FIXME Find a better alternative\n    if (!m_useExternalScaling)\n        m_diag.resize(n);\n    eigen_assert( (!m_useExternalScaling || m_diag.size()==n) && \"When m_useExternalScaling is set, the caller must provide a valid 'm_diag'\");\n    m_qtf.resize(n);\n\n    /* Function Body */\n    m_nfev = 0;\n    m_njev = 0;\n\n    /*     check the input parameters for errors. */\n    if (n <= 0 || m < n || m_ftol < 0. || m_xtol < 0. || m_gtol < 0. || m_maxfev <= 0 || m_factor <= 0.){\n      m_info = InvalidInput;\n      return LevenbergMarquardtSpace::ImproperInputParameters;\n    }\n\n    if (m_useExternalScaling)\n        for (Index j = 0; j < n; ++j)\n            if (m_diag[j] <= 0.) \n            {\n              m_info = InvalidInput;\n              return LevenbergMarquardtSpace::ImproperInputParameters;\n            }\n\n    /*     evaluate the function at the starting point */\n    /*     and calculate its norm. */\n    m_nfev = 1;\n    if ( m_functor(x, m_fvec) < 0)\n        return LevenbergMarquardtSpace::UserAsked;\n    m_fnorm = m_fvec.stableNorm();\n\n    /*     initialize levenberg-marquardt parameter and iteration counter. */\n    m_par = 0.;\n    m_iter = 1;\n\n    return LevenbergMarquardtSpace::NotStarted;\n}\n\ntemplate<typename FunctorType>\nLevenbergMarquardtSpace::Status\nLevenbergMarquardt<FunctorType>::lmder1(\n        FVectorType  &x,\n        const Scalar tol\n        )\n{\n    n = x.size();\n    m = m_functor.values();\n\n    /* check the input parameters for errors. */\n    if (n <= 0 || m < n || tol < 0.)\n        return LevenbergMarquardtSpace::ImproperInputParameters;\n\n    resetParameters();\n    m_ftol = tol;\n    m_xtol = tol;\n    m_maxfev = 100*(n+1);\n\n    return minimize(x);\n}\n\n\ntemplate<typename FunctorType>\nLevenbergMarquardtSpace::Status\nLevenbergMarquardt<FunctorType>::lmdif1(\n        FunctorType &functor,\n        FVectorType  &x,\n        Index *nfev,\n        const Scalar tol\n        )\n{\n    Index n = x.size();\n    Index m = functor.values();\n\n    /* check the input parameters for errors. */\n    if (n <= 0 || m < n || tol < 0.)\n        return LevenbergMarquardtSpace::ImproperInputParameters;\n\n    NumericalDiff<FunctorType> numDiff(functor);\n    // embedded LevenbergMarquardt\n    LevenbergMarquardt<NumericalDiff<FunctorType> > lm(numDiff);\n    lm.setFtol(tol);\n    lm.setXtol(tol);\n    lm.setMaxfev(200*(n+1));\n\n    LevenbergMarquardtSpace::Status info = LevenbergMarquardtSpace::Status(lm.minimize(x));\n    if (nfev)\n        * nfev = lm.nfev();\n    return info;\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_LEVENBERGMARQUARDT_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/MatrixFunctions/MatrixExponential.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009, 2010, 2013 Jitse Niesen <jitse@maths.leeds.ac.uk>\n// Copyright (C) 2011, 2013 Chen-Pang He <jdh8@ms63.hinet.net>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_MATRIX_EXPONENTIAL\n#define EIGEN_MATRIX_EXPONENTIAL\n\n#include \"StemFunction.h\"\n\nnamespace Eigen {\nnamespace internal {\n\n/** \\brief Scaling operator.\n *\n * This struct is used by CwiseUnaryOp to scale a matrix by \\f$ 2^{-s} \\f$.\n */\ntemplate <typename RealScalar>\nstruct MatrixExponentialScalingOp\n{\n  /** \\brief Constructor.\n   *\n   * \\param[in] squarings  The integer \\f$ s \\f$ in this document.\n   */\n  MatrixExponentialScalingOp(int squarings) : m_squarings(squarings) { }\n\n\n  /** \\brief Scale a matrix coefficient.\n   *\n   * \\param[in,out] x  The scalar to be scaled, becoming \\f$ 2^{-s} x \\f$.\n   */\n  inline const RealScalar operator() (const RealScalar& x) const\n  {\n    using std::ldexp;\n    return ldexp(x, -m_squarings);\n  }\n\n  typedef std::complex<RealScalar> ComplexScalar;\n\n  /** \\brief Scale a matrix coefficient.\n   *\n   * \\param[in,out] x  The scalar to be scaled, becoming \\f$ 2^{-s} x \\f$.\n   */\n  inline const ComplexScalar operator() (const ComplexScalar& x) const\n  {\n    using std::ldexp;\n    return ComplexScalar(ldexp(x.real(), -m_squarings), ldexp(x.imag(), -m_squarings));\n  }\n\n  private:\n    int m_squarings;\n};\n\n/** \\brief Compute the (3,3)-Pad&eacute; approximant to the exponential.\n *\n *  After exit, \\f$ (V+U)(V-U)^{-1} \\f$ is the Pad&eacute;\n *  approximant of \\f$ \\exp(A) \\f$ around \\f$ A = 0 \\f$.\n */\ntemplate <typename MatA, typename MatU, typename MatV>\nvoid matrix_exp_pade3(const MatA& A, MatU& U, MatV& V)\n{\n  typedef typename MatA::PlainObject MatrixType;\n  typedef typename NumTraits<typename traits<MatA>::Scalar>::Real RealScalar;\n  const RealScalar b[] = {120.L, 60.L, 12.L, 1.L};\n  const MatrixType A2 = A * A;\n  const MatrixType tmp = b[3] * A2 + b[1] * MatrixType::Identity(A.rows(), A.cols());\n  U.noalias() = A * tmp;\n  V = b[2] * A2 + b[0] * MatrixType::Identity(A.rows(), A.cols());\n}\n\n/** \\brief Compute the (5,5)-Pad&eacute; approximant to the exponential.\n *\n *  After exit, \\f$ (V+U)(V-U)^{-1} \\f$ is the Pad&eacute;\n *  approximant of \\f$ \\exp(A) \\f$ around \\f$ A = 0 \\f$.\n */\ntemplate <typename MatA, typename MatU, typename MatV>\nvoid matrix_exp_pade5(const MatA& A, MatU& U, MatV& V)\n{\n  typedef typename MatA::PlainObject MatrixType;\n  typedef typename NumTraits<typename traits<MatrixType>::Scalar>::Real RealScalar;\n  const RealScalar b[] = {30240.L, 15120.L, 3360.L, 420.L, 30.L, 1.L};\n  const MatrixType A2 = A * A;\n  const MatrixType A4 = A2 * A2;\n  const MatrixType tmp = b[5] * A4 + b[3] * A2 + b[1] * MatrixType::Identity(A.rows(), A.cols());\n  U.noalias() = A * tmp;\n  V = b[4] * A4 + b[2] * A2 + b[0] * MatrixType::Identity(A.rows(), A.cols());\n}\n\n/** \\brief Compute the (7,7)-Pad&eacute; approximant to the exponential.\n *\n *  After exit, \\f$ (V+U)(V-U)^{-1} \\f$ is the Pad&eacute;\n *  approximant of \\f$ \\exp(A) \\f$ around \\f$ A = 0 \\f$.\n */\ntemplate <typename MatA, typename MatU, typename MatV>\nvoid matrix_exp_pade7(const MatA& A, MatU& U, MatV& V)\n{\n  typedef typename MatA::PlainObject MatrixType;\n  typedef typename NumTraits<typename traits<MatrixType>::Scalar>::Real RealScalar;\n  const RealScalar b[] = {17297280.L, 8648640.L, 1995840.L, 277200.L, 25200.L, 1512.L, 56.L, 1.L};\n  const MatrixType A2 = A * A;\n  const MatrixType A4 = A2 * A2;\n  const MatrixType A6 = A4 * A2;\n  const MatrixType tmp = b[7] * A6 + b[5] * A4 + b[3] * A2 \n    + b[1] * MatrixType::Identity(A.rows(), A.cols());\n  U.noalias() = A * tmp;\n  V = b[6] * A6 + b[4] * A4 + b[2] * A2 + b[0] * MatrixType::Identity(A.rows(), A.cols());\n\n}\n\n/** \\brief Compute the (9,9)-Pad&eacute; approximant to the exponential.\n *\n *  After exit, \\f$ (V+U)(V-U)^{-1} \\f$ is the Pad&eacute;\n *  approximant of \\f$ \\exp(A) \\f$ around \\f$ A = 0 \\f$.\n */\ntemplate <typename MatA, typename MatU, typename MatV>\nvoid matrix_exp_pade9(const MatA& A, MatU& U, MatV& V)\n{\n  typedef typename MatA::PlainObject MatrixType;\n  typedef typename NumTraits<typename traits<MatrixType>::Scalar>::Real RealScalar;\n  const RealScalar b[] = {17643225600.L, 8821612800.L, 2075673600.L, 302702400.L, 30270240.L,\n                          2162160.L, 110880.L, 3960.L, 90.L, 1.L};\n  const MatrixType A2 = A * A;\n  const MatrixType A4 = A2 * A2;\n  const MatrixType A6 = A4 * A2;\n  const MatrixType A8 = A6 * A2;\n  const MatrixType tmp = b[9] * A8 + b[7] * A6 + b[5] * A4 + b[3] * A2 \n    + b[1] * MatrixType::Identity(A.rows(), A.cols());\n  U.noalias() = A * tmp;\n  V = b[8] * A8 + b[6] * A6 + b[4] * A4 + b[2] * A2 + b[0] * MatrixType::Identity(A.rows(), A.cols());\n}\n\n/** \\brief Compute the (13,13)-Pad&eacute; approximant to the exponential.\n *\n *  After exit, \\f$ (V+U)(V-U)^{-1} \\f$ is the Pad&eacute;\n *  approximant of \\f$ \\exp(A) \\f$ around \\f$ A = 0 \\f$.\n */\ntemplate <typename MatA, typename MatU, typename MatV>\nvoid matrix_exp_pade13(const MatA& A, MatU& U, MatV& V)\n{\n  typedef typename MatA::PlainObject MatrixType;\n  typedef typename NumTraits<typename traits<MatrixType>::Scalar>::Real RealScalar;\n  const RealScalar b[] = {64764752532480000.L, 32382376266240000.L, 7771770303897600.L,\n                          1187353796428800.L, 129060195264000.L, 10559470521600.L, 670442572800.L,\n                          33522128640.L, 1323241920.L, 40840800.L, 960960.L, 16380.L, 182.L, 1.L};\n  const MatrixType A2 = A * A;\n  const MatrixType A4 = A2 * A2;\n  const MatrixType A6 = A4 * A2;\n  V = b[13] * A6 + b[11] * A4 + b[9] * A2; // used for temporary storage\n  MatrixType tmp = A6 * V;\n  tmp += b[7] * A6 + b[5] * A4 + b[3] * A2 + b[1] * MatrixType::Identity(A.rows(), A.cols());\n  U.noalias() = A * tmp;\n  tmp = b[12] * A6 + b[10] * A4 + b[8] * A2;\n  V.noalias() = A6 * tmp;\n  V += b[6] * A6 + b[4] * A4 + b[2] * A2 + b[0] * MatrixType::Identity(A.rows(), A.cols());\n}\n\n/** \\brief Compute the (17,17)-Pad&eacute; approximant to the exponential.\n *\n *  After exit, \\f$ (V+U)(V-U)^{-1} \\f$ is the Pad&eacute;\n *  approximant of \\f$ \\exp(A) \\f$ around \\f$ A = 0 \\f$.\n *\n *  This function activates only if your long double is double-double or quadruple.\n */\n#if LDBL_MANT_DIG > 64\ntemplate <typename MatA, typename MatU, typename MatV>\nvoid matrix_exp_pade17(const MatA& A, MatU& U, MatV& V)\n{\n  typedef typename MatA::PlainObject MatrixType;\n  typedef typename NumTraits<typename traits<MatrixType>::Scalar>::Real RealScalar;\n  const RealScalar b[] = {830034394580628357120000.L, 415017197290314178560000.L,\n                          100610229646136770560000.L, 15720348382208870400000.L,\n                          1774878043152614400000.L, 153822763739893248000.L, 10608466464820224000.L,\n                          595373117923584000.L, 27563570274240000.L, 1060137318240000.L,\n                          33924394183680.L, 899510451840.L, 19554575040.L, 341863200.L, 4651200.L,\n                          46512.L, 306.L, 1.L};\n  const MatrixType A2 = A * A;\n  const MatrixType A4 = A2 * A2;\n  const MatrixType A6 = A4 * A2;\n  const MatrixType A8 = A4 * A4;\n  V = b[17] * A8 + b[15] * A6 + b[13] * A4 + b[11] * A2; // used for temporary storage\n  MatrixType tmp = A8 * V;\n  tmp += b[9] * A8 + b[7] * A6 + b[5] * A4 + b[3] * A2 \n    + b[1] * MatrixType::Identity(A.rows(), A.cols());\n  U.noalias() = A * tmp;\n  tmp = b[16] * A8 + b[14] * A6 + b[12] * A4 + b[10] * A2;\n  V.noalias() = tmp * A8;\n  V += b[8] * A8 + b[6] * A6 + b[4] * A4 + b[2] * A2 \n    + b[0] * MatrixType::Identity(A.rows(), A.cols());\n}\n#endif\n\ntemplate <typename MatrixType, typename RealScalar = typename NumTraits<typename traits<MatrixType>::Scalar>::Real>\nstruct matrix_exp_computeUV\n{\n  /** \\brief Compute Pad&eacute; approximant to the exponential.\n    *\n    * Computes \\c U, \\c V and \\c squarings such that \\f$ (V+U)(V-U)^{-1} \\f$ is a Pad&eacute;\n    * approximant of \\f$ \\exp(2^{-\\mbox{squarings}}M) \\f$ around \\f$ M = 0 \\f$, where \\f$ M \\f$\n    * denotes the matrix \\c arg. The degree of the Pad&eacute; approximant and the value of squarings\n    * are chosen such that the approximation error is no more than the round-off error.\n    */\n  static void run(const MatrixType& arg, MatrixType& U, MatrixType& V, int& squarings);\n};\n\ntemplate <typename MatrixType>\nstruct matrix_exp_computeUV<MatrixType, float>\n{\n  template <typename ArgType>\n  static void run(const ArgType& arg, MatrixType& U, MatrixType& V, int& squarings)\n  {\n    using std::frexp;\n    using std::pow;\n    const float l1norm = arg.cwiseAbs().colwise().sum().maxCoeff();\n    squarings = 0;\n    if (l1norm < 4.258730016922831e-001f) {\n      matrix_exp_pade3(arg, U, V);\n    } else if (l1norm < 1.880152677804762e+000f) {\n      matrix_exp_pade5(arg, U, V);\n    } else {\n      const float maxnorm = 3.925724783138660f;\n      frexp(l1norm / maxnorm, &squarings);\n      if (squarings < 0) squarings = 0;\n      MatrixType A = arg.unaryExpr(MatrixExponentialScalingOp<float>(squarings));\n      matrix_exp_pade7(A, U, V);\n    }\n  }\n};\n\ntemplate <typename MatrixType>\nstruct matrix_exp_computeUV<MatrixType, double>\n{\n  template <typename ArgType>\n  static void run(const ArgType& arg, MatrixType& U, MatrixType& V, int& squarings)\n  {\n    using std::frexp;\n    using std::pow;\n    const double l1norm = arg.cwiseAbs().colwise().sum().maxCoeff();\n    squarings = 0;\n    if (l1norm < 1.495585217958292e-002) {\n      matrix_exp_pade3(arg, U, V);\n    } else if (l1norm < 2.539398330063230e-001) {\n      matrix_exp_pade5(arg, U, V);\n    } else if (l1norm < 9.504178996162932e-001) {\n      matrix_exp_pade7(arg, U, V);\n    } else if (l1norm < 2.097847961257068e+000) {\n      matrix_exp_pade9(arg, U, V);\n    } else {\n      const double maxnorm = 5.371920351148152;\n      frexp(l1norm / maxnorm, &squarings);\n      if (squarings < 0) squarings = 0;\n      MatrixType A = arg.unaryExpr(MatrixExponentialScalingOp<double>(squarings));\n      matrix_exp_pade13(A, U, V);\n    }\n  }\n};\n  \ntemplate <typename MatrixType>\nstruct matrix_exp_computeUV<MatrixType, long double>\n{\n  template <typename ArgType>\n  static void run(const ArgType& arg, MatrixType& U, MatrixType& V, int& squarings)\n  {\n#if   LDBL_MANT_DIG == 53   // double precision\n    matrix_exp_computeUV<MatrixType, double>::run(arg, U, V, squarings);\n  \n#else\n  \n    using std::frexp;\n    using std::pow;\n    const long double l1norm = arg.cwiseAbs().colwise().sum().maxCoeff();\n    squarings = 0;\n  \n#if LDBL_MANT_DIG <= 64   // extended precision\n  \n    if (l1norm < 4.1968497232266989671e-003L) {\n      matrix_exp_pade3(arg, U, V);\n    } else if (l1norm < 1.1848116734693823091e-001L) {\n      matrix_exp_pade5(arg, U, V);\n    } else if (l1norm < 5.5170388480686700274e-001L) {\n      matrix_exp_pade7(arg, U, V);\n    } else if (l1norm < 1.3759868875587845383e+000L) {\n      matrix_exp_pade9(arg, U, V);\n    } else {\n      const long double maxnorm = 4.0246098906697353063L;\n      frexp(l1norm / maxnorm, &squarings);\n      if (squarings < 0) squarings = 0;\n      MatrixType A = arg.unaryExpr(MatrixExponentialScalingOp<long double>(squarings));\n      matrix_exp_pade13(A, U, V);\n    }\n  \n#elif LDBL_MANT_DIG <= 106  // double-double\n  \n    if (l1norm < 3.2787892205607026992947488108213e-005L) {\n      matrix_exp_pade3(arg, U, V);\n    } else if (l1norm < 6.4467025060072760084130906076332e-003L) {\n      matrix_exp_pade5(arg, U, V);\n    } else if (l1norm < 6.8988028496595374751374122881143e-002L) {\n      matrix_exp_pade7(arg, U, V);\n    } else if (l1norm < 2.7339737518502231741495857201670e-001L) {\n      matrix_exp_pade9(arg, U, V);\n    } else if (l1norm < 1.3203382096514474905666448850278e+000L) {\n      matrix_exp_pade13(arg, U, V);\n    } else {\n      const long double maxnorm = 3.2579440895405400856599663723517L;\n      frexp(l1norm / maxnorm, &squarings);\n      if (squarings < 0) squarings = 0;\n      MatrixType A = arg.unaryExpr(MatrixExponentialScalingOp<long double>(squarings));\n      matrix_exp_pade17(A, U, V);\n    }\n  \n#elif LDBL_MANT_DIG <= 112  // quadruple precison\n  \n    if (l1norm < 1.639394610288918690547467954466970e-005L) {\n      matrix_exp_pade3(arg, U, V);\n    } else if (l1norm < 4.253237712165275566025884344433009e-003L) {\n      matrix_exp_pade5(arg, U, V);\n    } else if (l1norm < 5.125804063165764409885122032933142e-002L) {\n      matrix_exp_pade7(arg, U, V);\n    } else if (l1norm < 2.170000765161155195453205651889853e-001L) {\n      matrix_exp_pade9(arg, U, V);\n    } else if (l1norm < 1.125358383453143065081397882891878e+000L) {\n      matrix_exp_pade13(arg, U, V);\n    } else {\n      const long double maxnorm = 2.884233277829519311757165057717815L;\n      frexp(l1norm / maxnorm, &squarings);\n      if (squarings < 0) squarings = 0;\n      MatrixType A = arg.unaryExpr(MatrixExponentialScalingOp<long double>(squarings));\n      matrix_exp_pade17(A, U, V);\n    }\n  \n#else\n  \n    // this case should be handled in compute()\n    eigen_assert(false && \"Bug in MatrixExponential\"); \n  \n#endif\n#endif  // LDBL_MANT_DIG\n  }\n};\n\ntemplate<typename T> struct is_exp_known_type : false_type {};\ntemplate<> struct is_exp_known_type<float> : true_type {};\ntemplate<> struct is_exp_known_type<double> : true_type {};\n#if LDBL_MANT_DIG <= 112\ntemplate<> struct is_exp_known_type<long double> : true_type {};\n#endif\n\ntemplate <typename ArgType, typename ResultType>\nvoid matrix_exp_compute(const ArgType& arg, ResultType &result, true_type) // natively supported scalar type\n{\n  typedef typename ArgType::PlainObject MatrixType;\n  MatrixType U, V;\n  int squarings;\n  matrix_exp_computeUV<MatrixType>::run(arg, U, V, squarings); // Pade approximant is (U+V) / (-U+V)\n  MatrixType numer = U + V;\n  MatrixType denom = -U + V;\n  result = denom.partialPivLu().solve(numer);\n  for (int i=0; i<squarings; i++)\n    result *= result;   // undo scaling by repeated squaring\n}\n\n\n/* Computes the matrix exponential\n *\n * \\param arg    argument of matrix exponential (should be plain object)\n * \\param result variable in which result will be stored\n */\ntemplate <typename ArgType, typename ResultType>\nvoid matrix_exp_compute(const ArgType& arg, ResultType &result, false_type) // default\n{\n  typedef typename ArgType::PlainObject MatrixType;\n  typedef typename traits<MatrixType>::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  typedef typename std::complex<RealScalar> ComplexScalar;\n  result = arg.matrixFunction(internal::stem_function_exp<ComplexScalar>);\n}\n\n} // end namespace Eigen::internal\n\n/** \\ingroup MatrixFunctions_Module\n  *\n  * \\brief Proxy for the matrix exponential of some matrix (expression).\n  *\n  * \\tparam Derived  Type of the argument to the matrix exponential.\n  *\n  * This class holds the argument to the matrix exponential until it is assigned or evaluated for\n  * some other reason (so the argument should not be changed in the meantime). It is the return type\n  * of MatrixBase::exp() and most of the time this is the only way it is used.\n  */\ntemplate<typename Derived> struct MatrixExponentialReturnValue\n: public ReturnByValue<MatrixExponentialReturnValue<Derived> >\n{\n    typedef typename Derived::Index Index;\n  public:\n    /** \\brief Constructor.\n      *\n      * \\param src %Matrix (expression) forming the argument of the matrix exponential.\n      */\n    MatrixExponentialReturnValue(const Derived& src) : m_src(src) { }\n\n    /** \\brief Compute the matrix exponential.\n      *\n      * \\param result the matrix exponential of \\p src in the constructor.\n      */\n    template <typename ResultType>\n    inline void evalTo(ResultType& result) const\n    {\n      const typename internal::nested_eval<Derived, 10>::type tmp(m_src);\n      internal::matrix_exp_compute(tmp, result, internal::is_exp_known_type<typename Derived::Scalar>());\n    }\n\n    Index rows() const { return m_src.rows(); }\n    Index cols() const { return m_src.cols(); }\n\n  protected:\n    const typename internal::ref_selector<Derived>::type m_src;\n};\n\nnamespace internal {\ntemplate<typename Derived>\nstruct traits<MatrixExponentialReturnValue<Derived> >\n{\n  typedef typename Derived::PlainObject ReturnType;\n};\n}\n\ntemplate <typename Derived>\nconst MatrixExponentialReturnValue<Derived> MatrixBase<Derived>::exp() const\n{\n  eigen_assert(rows() == cols());\n  return MatrixExponentialReturnValue<Derived>(derived());\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_MATRIX_EXPONENTIAL\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009-2011, 2013 Jitse Niesen <jitse@maths.leeds.ac.uk>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_MATRIX_FUNCTION\n#define EIGEN_MATRIX_FUNCTION\n\n#include \"StemFunction.h\"\n\n\nnamespace Eigen { \n\nnamespace internal {\n\n/** \\brief Maximum distance allowed between eigenvalues to be considered \"close\". */\nstatic const float matrix_function_separation = 0.1f;\n\n/** \\ingroup MatrixFunctions_Module\n  * \\class MatrixFunctionAtomic\n  * \\brief Helper class for computing matrix functions of atomic matrices.\n  *\n  * Here, an atomic matrix is a triangular matrix whose diagonal entries are close to each other.\n  */\ntemplate <typename MatrixType>\nclass MatrixFunctionAtomic \n{\n  public:\n\n    typedef typename MatrixType::Scalar Scalar;\n    typedef typename stem_function<Scalar>::type StemFunction;\n\n    /** \\brief Constructor\n      * \\param[in]  f  matrix function to compute.\n      */\n    MatrixFunctionAtomic(StemFunction f) : m_f(f) { }\n\n    /** \\brief Compute matrix function of atomic matrix\n      * \\param[in]  A  argument of matrix function, should be upper triangular and atomic\n      * \\returns  f(A), the matrix function evaluated at the given matrix\n      */\n    MatrixType compute(const MatrixType& A);\n\n  private:\n    StemFunction* m_f;\n};\n\ntemplate <typename MatrixType>\ntypename NumTraits<typename MatrixType::Scalar>::Real matrix_function_compute_mu(const MatrixType& A)\n{\n  typedef typename plain_col_type<MatrixType>::type VectorType;\n  typename MatrixType::Index rows = A.rows();\n  const MatrixType N = MatrixType::Identity(rows, rows) - A;\n  VectorType e = VectorType::Ones(rows);\n  N.template triangularView<Upper>().solveInPlace(e);\n  return e.cwiseAbs().maxCoeff();\n}\n\ntemplate <typename MatrixType>\nMatrixType MatrixFunctionAtomic<MatrixType>::compute(const MatrixType& A)\n{\n  // TODO: Use that A is upper triangular\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  typedef typename MatrixType::Index Index;\n  Index rows = A.rows();\n  Scalar avgEival = A.trace() / Scalar(RealScalar(rows));\n  MatrixType Ashifted = A - avgEival * MatrixType::Identity(rows, rows);\n  RealScalar mu = matrix_function_compute_mu(Ashifted);\n  MatrixType F = m_f(avgEival, 0) * MatrixType::Identity(rows, rows);\n  MatrixType P = Ashifted;\n  MatrixType Fincr;\n  for (Index s = 1; s < 1.1 * rows + 10; s++) { // upper limit is fairly arbitrary\n    Fincr = m_f(avgEival, static_cast<int>(s)) * P;\n    F += Fincr;\n    P = Scalar(RealScalar(1.0/(s + 1))) * P * Ashifted;\n\n    // test whether Taylor series converged\n    const RealScalar F_norm = F.cwiseAbs().rowwise().sum().maxCoeff();\n    const RealScalar Fincr_norm = Fincr.cwiseAbs().rowwise().sum().maxCoeff();\n    if (Fincr_norm < NumTraits<Scalar>::epsilon() * F_norm) {\n      RealScalar delta = 0;\n      RealScalar rfactorial = 1;\n      for (Index r = 0; r < rows; r++) {\n        RealScalar mx = 0;\n        for (Index i = 0; i < rows; i++)\n          mx = (std::max)(mx, std::abs(m_f(Ashifted(i, i) + avgEival, static_cast<int>(s+r))));\n        if (r != 0)\n          rfactorial *= RealScalar(r);\n        delta = (std::max)(delta, mx / rfactorial);\n      }\n      const RealScalar P_norm = P.cwiseAbs().rowwise().sum().maxCoeff();\n      if (mu * delta * P_norm < NumTraits<Scalar>::epsilon() * F_norm) // series converged\n        break;\n    }\n  }\n  return F;\n}\n\n/** \\brief Find cluster in \\p clusters containing some value \n  * \\param[in] key Value to find\n  * \\returns Iterator to cluster containing \\p key, or \\c clusters.end() if no cluster in \\p m_clusters\n  * contains \\p key.\n  */\ntemplate <typename Index, typename ListOfClusters>\ntypename ListOfClusters::iterator matrix_function_find_cluster(Index key, ListOfClusters& clusters)\n{\n  typename std::list<Index>::iterator j;\n  for (typename ListOfClusters::iterator i = clusters.begin(); i != clusters.end(); ++i) {\n    j = std::find(i->begin(), i->end(), key);\n    if (j != i->end())\n      return i;\n  }\n  return clusters.end();\n}\n\n/** \\brief Partition eigenvalues in clusters of ei'vals close to each other\n  * \n  * \\param[in]  eivals    Eigenvalues\n  * \\param[out] clusters  Resulting partition of eigenvalues\n  *\n  * The partition satisfies the following two properties:\n  * # Any eigenvalue in a certain cluster is at most matrix_function_separation() away from another eigenvalue\n  *   in the same cluster.\n  * # The distance between two eigenvalues in different clusters is more than matrix_function_separation().  \n  * The implementation follows Algorithm 4.1 in the paper of Davies and Higham.\n  */\ntemplate <typename EivalsType, typename Cluster>\nvoid matrix_function_partition_eigenvalues(const EivalsType& eivals, std::list<Cluster>& clusters)\n{\n  typedef typename EivalsType::Index Index;\n  typedef typename EivalsType::RealScalar RealScalar;\n  for (Index i=0; i<eivals.rows(); ++i) {\n    // Find cluster containing i-th ei'val, adding a new cluster if necessary\n    typename std::list<Cluster>::iterator qi = matrix_function_find_cluster(i, clusters);\n    if (qi == clusters.end()) {\n      Cluster l;\n      l.push_back(i);\n      clusters.push_back(l);\n      qi = clusters.end();\n      --qi;\n    }\n\n    // Look for other element to add to the set\n    for (Index j=i+1; j<eivals.rows(); ++j) {\n      if (abs(eivals(j) - eivals(i)) <= RealScalar(matrix_function_separation)\n          && std::find(qi->begin(), qi->end(), j) == qi->end()) {\n        typename std::list<Cluster>::iterator qj = matrix_function_find_cluster(j, clusters);\n        if (qj == clusters.end()) {\n          qi->push_back(j);\n        } else {\n          qi->insert(qi->end(), qj->begin(), qj->end());\n          clusters.erase(qj);\n        }\n      }\n    }\n  }\n}\n\n/** \\brief Compute size of each cluster given a partitioning */\ntemplate <typename ListOfClusters, typename Index>\nvoid matrix_function_compute_cluster_size(const ListOfClusters& clusters, Matrix<Index, Dynamic, 1>& clusterSize)\n{\n  const Index numClusters = static_cast<Index>(clusters.size());\n  clusterSize.setZero(numClusters);\n  Index clusterIndex = 0;\n  for (typename ListOfClusters::const_iterator cluster = clusters.begin(); cluster != clusters.end(); ++cluster) {\n    clusterSize[clusterIndex] = cluster->size();\n    ++clusterIndex;\n  }\n}\n\n/** \\brief Compute start of each block using clusterSize */\ntemplate <typename VectorType>\nvoid matrix_function_compute_block_start(const VectorType& clusterSize, VectorType& blockStart)\n{\n  blockStart.resize(clusterSize.rows());\n  blockStart(0) = 0;\n  for (typename VectorType::Index i = 1; i < clusterSize.rows(); i++) {\n    blockStart(i) = blockStart(i-1) + clusterSize(i-1);\n  }\n}\n\n/** \\brief Compute mapping of eigenvalue indices to cluster indices */\ntemplate <typename EivalsType, typename ListOfClusters, typename VectorType>\nvoid matrix_function_compute_map(const EivalsType& eivals, const ListOfClusters& clusters, VectorType& eivalToCluster)\n{\n  typedef typename EivalsType::Index Index;\n  eivalToCluster.resize(eivals.rows());\n  Index clusterIndex = 0;\n  for (typename ListOfClusters::const_iterator cluster = clusters.begin(); cluster != clusters.end(); ++cluster) {\n    for (Index i = 0; i < eivals.rows(); ++i) {\n      if (std::find(cluster->begin(), cluster->end(), i) != cluster->end()) {\n        eivalToCluster[i] = clusterIndex;\n      }\n    }\n    ++clusterIndex;\n  }\n}\n\n/** \\brief Compute permutation which groups ei'vals in same cluster together */\ntemplate <typename DynVectorType, typename VectorType>\nvoid matrix_function_compute_permutation(const DynVectorType& blockStart, const DynVectorType& eivalToCluster, VectorType& permutation)\n{\n  typedef typename VectorType::Index Index;\n  DynVectorType indexNextEntry = blockStart;\n  permutation.resize(eivalToCluster.rows());\n  for (Index i = 0; i < eivalToCluster.rows(); i++) {\n    Index cluster = eivalToCluster[i];\n    permutation[i] = indexNextEntry[cluster];\n    ++indexNextEntry[cluster];\n  }\n}  \n\n/** \\brief Permute Schur decomposition in U and T according to permutation */\ntemplate <typename VectorType, typename MatrixType>\nvoid matrix_function_permute_schur(VectorType& permutation, MatrixType& U, MatrixType& T)\n{\n  typedef typename VectorType::Index Index;\n  for (Index i = 0; i < permutation.rows() - 1; i++) {\n    Index j;\n    for (j = i; j < permutation.rows(); j++) {\n      if (permutation(j) == i) break;\n    }\n    eigen_assert(permutation(j) == i);\n    for (Index k = j-1; k >= i; k--) {\n      JacobiRotation<typename MatrixType::Scalar> rotation;\n      rotation.makeGivens(T(k, k+1), T(k+1, k+1) - T(k, k));\n      T.applyOnTheLeft(k, k+1, rotation.adjoint());\n      T.applyOnTheRight(k, k+1, rotation);\n      U.applyOnTheRight(k, k+1, rotation);\n      std::swap(permutation.coeffRef(k), permutation.coeffRef(k+1));\n    }\n  }\n}\n\n/** \\brief Compute block diagonal part of matrix function.\n  *\n  * This routine computes the matrix function applied to the block diagonal part of \\p T (which should be\n  * upper triangular), with the blocking given by \\p blockStart and \\p clusterSize. The matrix function of\n  * each diagonal block is computed by \\p atomic. The off-diagonal parts of \\p fT are set to zero.\n  */\ntemplate <typename MatrixType, typename AtomicType, typename VectorType>\nvoid matrix_function_compute_block_atomic(const MatrixType& T, AtomicType& atomic, const VectorType& blockStart, const VectorType& clusterSize, MatrixType& fT)\n{ \n  fT.setZero(T.rows(), T.cols());\n  for (typename VectorType::Index i = 0; i < clusterSize.rows(); ++i) {\n    fT.block(blockStart(i), blockStart(i), clusterSize(i), clusterSize(i))\n      = atomic.compute(T.block(blockStart(i), blockStart(i), clusterSize(i), clusterSize(i)));\n  }\n}\n\n/** \\brief Solve a triangular Sylvester equation AX + XB = C \n  *\n  * \\param[in]  A  the matrix A; should be square and upper triangular\n  * \\param[in]  B  the matrix B; should be square and upper triangular\n  * \\param[in]  C  the matrix C; should have correct size.\n  *\n  * \\returns the solution X.\n  *\n  * If A is m-by-m and B is n-by-n, then both C and X are m-by-n.  The (i,j)-th component of the Sylvester\n  * equation is\n  * \\f[ \n  *     \\sum_{k=i}^m A_{ik} X_{kj} + \\sum_{k=1}^j X_{ik} B_{kj} = C_{ij}. \n  * \\f]\n  * This can be re-arranged to yield:\n  * \\f[ \n  *     X_{ij} = \\frac{1}{A_{ii} + B_{jj}} \\Bigl( C_{ij}\n  *     - \\sum_{k=i+1}^m A_{ik} X_{kj} - \\sum_{k=1}^{j-1} X_{ik} B_{kj} \\Bigr).\n  * \\f]\n  * It is assumed that A and B are such that the numerator is never zero (otherwise the Sylvester equation\n  * does not have a unique solution). In that case, these equations can be evaluated in the order \n  * \\f$ i=m,\\ldots,1 \\f$ and \\f$ j=1,\\ldots,n \\f$.\n  */\ntemplate <typename MatrixType>\nMatrixType matrix_function_solve_triangular_sylvester(const MatrixType& A, const MatrixType& B, const MatrixType& C)\n{\n  eigen_assert(A.rows() == A.cols());\n  eigen_assert(A.isUpperTriangular());\n  eigen_assert(B.rows() == B.cols());\n  eigen_assert(B.isUpperTriangular());\n  eigen_assert(C.rows() == A.rows());\n  eigen_assert(C.cols() == B.rows());\n\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n\n  Index m = A.rows();\n  Index n = B.rows();\n  MatrixType X(m, n);\n\n  for (Index i = m - 1; i >= 0; --i) {\n    for (Index j = 0; j < n; ++j) {\n\n      // Compute AX = \\sum_{k=i+1}^m A_{ik} X_{kj}\n      Scalar AX;\n      if (i == m - 1) {\n\tAX = 0; \n      } else {\n\tMatrix<Scalar,1,1> AXmatrix = A.row(i).tail(m-1-i) * X.col(j).tail(m-1-i);\n\tAX = AXmatrix(0,0);\n      }\n\n      // Compute XB = \\sum_{k=1}^{j-1} X_{ik} B_{kj}\n      Scalar XB;\n      if (j == 0) {\n\tXB = 0; \n      } else {\n\tMatrix<Scalar,1,1> XBmatrix = X.row(i).head(j) * B.col(j).head(j);\n\tXB = XBmatrix(0,0);\n      }\n\n      X(i,j) = (C(i,j) - AX - XB) / (A(i,i) + B(j,j));\n    }\n  }\n  return X;\n}\n\n/** \\brief Compute part of matrix function above block diagonal.\n  *\n  * This routine completes the computation of \\p fT, denoting a matrix function applied to the triangular\n  * matrix \\p T. It assumes that the block diagonal part of \\p fT has already been computed. The part below\n  * the diagonal is zero, because \\p T is upper triangular.\n  */\ntemplate <typename MatrixType, typename VectorType>\nvoid matrix_function_compute_above_diagonal(const MatrixType& T, const VectorType& blockStart, const VectorType& clusterSize, MatrixType& fT)\n{ \n  typedef internal::traits<MatrixType> Traits;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename MatrixType::Index Index;\n  static const int RowsAtCompileTime = Traits::RowsAtCompileTime;\n  static const int ColsAtCompileTime = Traits::ColsAtCompileTime;\n  static const int Options = MatrixType::Options;\n  typedef Matrix<Scalar, Dynamic, Dynamic, Options, RowsAtCompileTime, ColsAtCompileTime> DynMatrixType;\n\n  for (Index k = 1; k < clusterSize.rows(); k++) {\n    for (Index i = 0; i < clusterSize.rows() - k; i++) {\n      // compute (i, i+k) block\n      DynMatrixType A = T.block(blockStart(i), blockStart(i), clusterSize(i), clusterSize(i));\n      DynMatrixType B = -T.block(blockStart(i+k), blockStart(i+k), clusterSize(i+k), clusterSize(i+k));\n      DynMatrixType C = fT.block(blockStart(i), blockStart(i), clusterSize(i), clusterSize(i))\n        * T.block(blockStart(i), blockStart(i+k), clusterSize(i), clusterSize(i+k));\n      C -= T.block(blockStart(i), blockStart(i+k), clusterSize(i), clusterSize(i+k))\n        * fT.block(blockStart(i+k), blockStart(i+k), clusterSize(i+k), clusterSize(i+k));\n      for (Index m = i + 1; m < i + k; m++) {\n        C += fT.block(blockStart(i), blockStart(m), clusterSize(i), clusterSize(m))\n          * T.block(blockStart(m), blockStart(i+k), clusterSize(m), clusterSize(i+k));\n        C -= T.block(blockStart(i), blockStart(m), clusterSize(i), clusterSize(m))\n          * fT.block(blockStart(m), blockStart(i+k), clusterSize(m), clusterSize(i+k));\n      }\n      fT.block(blockStart(i), blockStart(i+k), clusterSize(i), clusterSize(i+k))\n        = matrix_function_solve_triangular_sylvester(A, B, C);\n    }\n  }\n}\n\n/** \\ingroup MatrixFunctions_Module\n  * \\brief Class for computing matrix functions.\n  * \\tparam  MatrixType  type of the argument of the matrix function,\n  *                      expected to be an instantiation of the Matrix class template.\n  * \\tparam  AtomicType  type for computing matrix function of atomic blocks.\n  * \\tparam  IsComplex   used internally to select correct specialization.\n  *\n  * This class implements the Schur-Parlett algorithm for computing matrix functions. The spectrum of the\n  * matrix is divided in clustered of eigenvalues that lies close together. This class delegates the\n  * computation of the matrix function on every block corresponding to these clusters to an object of type\n  * \\p AtomicType and uses these results to compute the matrix function of the whole matrix. The class\n  * \\p AtomicType should have a \\p compute() member function for computing the matrix function of a block.\n  *\n  * \\sa class MatrixFunctionAtomic, class MatrixLogarithmAtomic\n  */\ntemplate <typename MatrixType, int IsComplex = NumTraits<typename internal::traits<MatrixType>::Scalar>::IsComplex>\nstruct matrix_function_compute\n{  \n    /** \\brief Compute the matrix function.\n      *\n      * \\param[in]  A       argument of matrix function, should be a square matrix.\n      * \\param[in]  atomic  class for computing matrix function of atomic blocks.\n      * \\param[out] result  the function \\p f applied to \\p A, as\n      * specified in the constructor.\n      *\n      * See MatrixBase::matrixFunction() for details on how this computation\n      * is implemented.\n      */\n    template <typename AtomicType, typename ResultType> \n    static void run(const MatrixType& A, AtomicType& atomic, ResultType &result);    \n};\n\n/** \\internal \\ingroup MatrixFunctions_Module \n  * \\brief Partial specialization of MatrixFunction for real matrices\n  *\n  * This converts the real matrix to a complex matrix, compute the matrix function of that matrix, and then\n  * converts the result back to a real matrix.\n  */\ntemplate <typename MatrixType>\nstruct matrix_function_compute<MatrixType, 0>\n{  \n  template <typename MatA, typename AtomicType, typename ResultType>\n  static void run(const MatA& A, AtomicType& atomic, ResultType &result)\n  {\n    typedef internal::traits<MatrixType> Traits;\n    typedef typename Traits::Scalar Scalar;\n    static const int Rows = Traits::RowsAtCompileTime, Cols = Traits::ColsAtCompileTime;\n    static const int MaxRows = Traits::MaxRowsAtCompileTime, MaxCols = Traits::MaxColsAtCompileTime;\n\n    typedef std::complex<Scalar> ComplexScalar;\n    typedef Matrix<ComplexScalar, Rows, Cols, 0, MaxRows, MaxCols> ComplexMatrix;\n\n    ComplexMatrix CA = A.template cast<ComplexScalar>();\n    ComplexMatrix Cresult;\n    matrix_function_compute<ComplexMatrix>::run(CA, atomic, Cresult);\n    result = Cresult.real();\n  }\n};\n\n/** \\internal \\ingroup MatrixFunctions_Module \n  * \\brief Partial specialization of MatrixFunction for complex matrices\n  */\ntemplate <typename MatrixType>\nstruct matrix_function_compute<MatrixType, 1>\n{\n  template <typename MatA, typename AtomicType, typename ResultType>\n  static void run(const MatA& A, AtomicType& atomic, ResultType &result)\n  {\n    typedef internal::traits<MatrixType> Traits;\n    \n    // compute Schur decomposition of A\n    const ComplexSchur<MatrixType> schurOfA(A);  \n    MatrixType T = schurOfA.matrixT();\n    MatrixType U = schurOfA.matrixU();\n\n    // partition eigenvalues into clusters of ei'vals \"close\" to each other\n    std::list<std::list<Index> > clusters; \n    matrix_function_partition_eigenvalues(T.diagonal(), clusters);\n\n    // compute size of each cluster\n    Matrix<Index, Dynamic, 1> clusterSize;\n    matrix_function_compute_cluster_size(clusters, clusterSize);\n\n    // blockStart[i] is row index at which block corresponding to i-th cluster starts \n    Matrix<Index, Dynamic, 1> blockStart; \n    matrix_function_compute_block_start(clusterSize, blockStart);\n\n    // compute map so that eivalToCluster[i] = j means that i-th ei'val is in j-th cluster \n    Matrix<Index, Dynamic, 1> eivalToCluster;\n    matrix_function_compute_map(T.diagonal(), clusters, eivalToCluster);\n\n    // compute permutation which groups ei'vals in same cluster together \n    Matrix<Index, Traits::RowsAtCompileTime, 1> permutation;\n    matrix_function_compute_permutation(blockStart, eivalToCluster, permutation);\n\n    // permute Schur decomposition\n    matrix_function_permute_schur(permutation, U, T);\n\n    // compute result\n    MatrixType fT; // matrix function applied to T\n    matrix_function_compute_block_atomic(T, atomic, blockStart, clusterSize, fT);\n    matrix_function_compute_above_diagonal(T, blockStart, clusterSize, fT);\n    result = U * (fT.template triangularView<Upper>() * U.adjoint());\n  }\n};\n\n} // end of namespace internal\n\n/** \\ingroup MatrixFunctions_Module\n  *\n  * \\brief Proxy for the matrix function of some matrix (expression).\n  *\n  * \\tparam Derived  Type of the argument to the matrix function.\n  *\n  * This class holds the argument to the matrix function until it is assigned or evaluated for some other\n  * reason (so the argument should not be changed in the meantime). It is the return type of\n  * matrixBase::matrixFunction() and related functions and most of the time this is the only way it is used.\n  */\ntemplate<typename Derived> class MatrixFunctionReturnValue\n: public ReturnByValue<MatrixFunctionReturnValue<Derived> >\n{\n  public:\n    typedef typename Derived::Scalar Scalar;\n    typedef typename Derived::Index Index;\n    typedef typename internal::stem_function<Scalar>::type StemFunction;\n\n  protected:\n    typedef typename internal::ref_selector<Derived>::type DerivedNested;\n\n  public:\n\n    /** \\brief Constructor.\n      *\n      * \\param[in] A  %Matrix (expression) forming the argument of the matrix function.\n      * \\param[in] f  Stem function for matrix function under consideration.\n      */\n    MatrixFunctionReturnValue(const Derived& A, StemFunction f) : m_A(A), m_f(f) { }\n\n    /** \\brief Compute the matrix function.\n      *\n      * \\param[out] result \\p f applied to \\p A, where \\p f and \\p A are as in the constructor.\n      */\n    template <typename ResultType>\n    inline void evalTo(ResultType& result) const\n    {\n      typedef typename internal::nested_eval<Derived, 10>::type NestedEvalType;\n      typedef typename internal::remove_all<NestedEvalType>::type NestedEvalTypeClean;\n      typedef internal::traits<NestedEvalTypeClean> Traits;\n      static const int RowsAtCompileTime = Traits::RowsAtCompileTime;\n      static const int ColsAtCompileTime = Traits::ColsAtCompileTime;\n      typedef std::complex<typename NumTraits<Scalar>::Real> ComplexScalar;\n      typedef Matrix<ComplexScalar, Dynamic, Dynamic, 0, RowsAtCompileTime, ColsAtCompileTime> DynMatrixType;\n\n      typedef internal::MatrixFunctionAtomic<DynMatrixType> AtomicType;\n      AtomicType atomic(m_f);\n\n      internal::matrix_function_compute<typename NestedEvalTypeClean::PlainObject>::run(m_A, atomic, result);\n    }\n\n    Index rows() const { return m_A.rows(); }\n    Index cols() const { return m_A.cols(); }\n\n  private:\n    const DerivedNested m_A;\n    StemFunction *m_f;\n};\n\nnamespace internal {\ntemplate<typename Derived>\nstruct traits<MatrixFunctionReturnValue<Derived> >\n{\n  typedef typename Derived::PlainObject ReturnType;\n};\n}\n\n\n/********** MatrixBase methods **********/\n\n\ntemplate <typename Derived>\nconst MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::matrixFunction(typename internal::stem_function<typename internal::traits<Derived>::Scalar>::type f) const\n{\n  eigen_assert(rows() == cols());\n  return MatrixFunctionReturnValue<Derived>(derived(), f);\n}\n\ntemplate <typename Derived>\nconst MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::sin() const\n{\n  eigen_assert(rows() == cols());\n  typedef typename internal::stem_function<Scalar>::ComplexScalar ComplexScalar;\n  return MatrixFunctionReturnValue<Derived>(derived(), internal::stem_function_sin<ComplexScalar>);\n}\n\ntemplate <typename Derived>\nconst MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::cos() const\n{\n  eigen_assert(rows() == cols());\n  typedef typename internal::stem_function<Scalar>::ComplexScalar ComplexScalar;\n  return MatrixFunctionReturnValue<Derived>(derived(), internal::stem_function_cos<ComplexScalar>);\n}\n\ntemplate <typename Derived>\nconst MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::sinh() const\n{\n  eigen_assert(rows() == cols());\n  typedef typename internal::stem_function<Scalar>::ComplexScalar ComplexScalar;\n  return MatrixFunctionReturnValue<Derived>(derived(), internal::stem_function_sinh<ComplexScalar>);\n}\n\ntemplate <typename Derived>\nconst MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::cosh() const\n{\n  eigen_assert(rows() == cols());\n  typedef typename internal::stem_function<Scalar>::ComplexScalar ComplexScalar;\n  return MatrixFunctionReturnValue<Derived>(derived(), internal::stem_function_cosh<ComplexScalar>);\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_MATRIX_FUNCTION\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/MatrixFunctions/MatrixLogarithm.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2011, 2013 Jitse Niesen <jitse@maths.leeds.ac.uk>\n// Copyright (C) 2011 Chen-Pang He <jdh8@ms63.hinet.net>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_MATRIX_LOGARITHM\n#define EIGEN_MATRIX_LOGARITHM\n\nnamespace Eigen { \n\nnamespace internal { \n\ntemplate <typename Scalar>\nstruct matrix_log_min_pade_degree \n{\n  static const int value = 3;\n};\n\ntemplate <typename Scalar>\nstruct matrix_log_max_pade_degree \n{\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  static const int value = std::numeric_limits<RealScalar>::digits<= 24?  5:  // single precision\n                           std::numeric_limits<RealScalar>::digits<= 53?  7:  // double precision\n                           std::numeric_limits<RealScalar>::digits<= 64?  8:  // extended precision\n                           std::numeric_limits<RealScalar>::digits<=106? 10:  // double-double\n                                                                         11;  // quadruple precision\n};\n\n/** \\brief Compute logarithm of 2x2 triangular matrix. */\ntemplate <typename MatrixType>\nvoid matrix_log_compute_2x2(const MatrixType& A, MatrixType& result)\n{\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename MatrixType::RealScalar RealScalar;\n  using std::abs;\n  using std::ceil;\n  using std::imag;\n  using std::log;\n\n  Scalar logA00 = log(A(0,0));\n  Scalar logA11 = log(A(1,1));\n\n  result(0,0) = logA00;\n  result(1,0) = Scalar(0);\n  result(1,1) = logA11;\n\n  Scalar y = A(1,1) - A(0,0);\n  if (y==Scalar(0))\n  {\n    result(0,1) = A(0,1) / A(0,0);\n  }\n  else if ((abs(A(0,0)) < RealScalar(0.5)*abs(A(1,1))) || (abs(A(0,0)) > 2*abs(A(1,1))))\n  {\n    result(0,1) = A(0,1) * (logA11 - logA00) / y;\n  }\n  else\n  {\n    // computation in previous branch is inaccurate if A(1,1) \\approx A(0,0)\n    int unwindingNumber = static_cast<int>(ceil((imag(logA11 - logA00) - RealScalar(EIGEN_PI)) / RealScalar(2*EIGEN_PI)));\n    result(0,1) = A(0,1) * (numext::log1p(y/A(0,0)) + Scalar(0,2*EIGEN_PI*unwindingNumber)) / y;\n  }\n}\n\n/* \\brief Get suitable degree for Pade approximation. (specialized for RealScalar = float) */\ninline int matrix_log_get_pade_degree(float normTminusI)\n{\n  const float maxNormForPade[] = { 2.5111573934555054e-1 /* degree = 3 */ , 4.0535837411880493e-1,\n            5.3149729967117310e-1 };\n  const int minPadeDegree = matrix_log_min_pade_degree<float>::value;\n  const int maxPadeDegree = matrix_log_max_pade_degree<float>::value;\n  int degree = minPadeDegree;\n  for (; degree <= maxPadeDegree; ++degree) \n    if (normTminusI <= maxNormForPade[degree - minPadeDegree])\n      break;\n  return degree;\n}\n\n/* \\brief Get suitable degree for Pade approximation. (specialized for RealScalar = double) */\ninline int matrix_log_get_pade_degree(double normTminusI)\n{\n  const double maxNormForPade[] = { 1.6206284795015624e-2 /* degree = 3 */ , 5.3873532631381171e-2,\n            1.1352802267628681e-1, 1.8662860613541288e-1, 2.642960831111435e-1 };\n  const int minPadeDegree = matrix_log_min_pade_degree<double>::value;\n  const int maxPadeDegree = matrix_log_max_pade_degree<double>::value;\n  int degree = minPadeDegree;\n  for (; degree <= maxPadeDegree; ++degree)\n    if (normTminusI <= maxNormForPade[degree - minPadeDegree])\n      break;\n  return degree;\n}\n\n/* \\brief Get suitable degree for Pade approximation. (specialized for RealScalar = long double) */\ninline int matrix_log_get_pade_degree(long double normTminusI)\n{\n#if   LDBL_MANT_DIG == 53         // double precision\n  const long double maxNormForPade[] = { 1.6206284795015624e-2L /* degree = 3 */ , 5.3873532631381171e-2L,\n            1.1352802267628681e-1L, 1.8662860613541288e-1L, 2.642960831111435e-1L };\n#elif LDBL_MANT_DIG <= 64         // extended precision\n  const long double maxNormForPade[] = { 5.48256690357782863103e-3L /* degree = 3 */, 2.34559162387971167321e-2L,\n            5.84603923897347449857e-2L, 1.08486423756725170223e-1L, 1.68385767881294446649e-1L,\n            2.32777776523703892094e-1L };\n#elif LDBL_MANT_DIG <= 106        // double-double\n  const long double maxNormForPade[] = { 8.58970550342939562202529664318890e-5L /* degree = 3 */,\n            9.34074328446359654039446552677759e-4L, 4.26117194647672175773064114582860e-3L,\n            1.21546224740281848743149666560464e-2L, 2.61100544998339436713088248557444e-2L,\n            4.66170074627052749243018566390567e-2L, 7.32585144444135027565872014932387e-2L,\n            1.05026503471351080481093652651105e-1L };\n#else                             // quadruple precision\n  const long double maxNormForPade[] = { 4.7419931187193005048501568167858103e-5L /* degree = 3 */,\n            5.8853168473544560470387769480192666e-4L, 2.9216120366601315391789493628113520e-3L,\n            8.8415758124319434347116734705174308e-3L, 1.9850836029449446668518049562565291e-2L,\n            3.6688019729653446926585242192447447e-2L, 5.9290962294020186998954055264528393e-2L,\n            8.6998436081634343903250580992127677e-2L, 1.1880960220216759245467951592883642e-1L };\n#endif\n  const int minPadeDegree = matrix_log_min_pade_degree<long double>::value;\n  const int maxPadeDegree = matrix_log_max_pade_degree<long double>::value;\n  int degree = minPadeDegree;\n  for (; degree <= maxPadeDegree; ++degree)\n    if (normTminusI <= maxNormForPade[degree - minPadeDegree])\n      break;\n  return degree;\n}\n\n/* \\brief Compute Pade approximation to matrix logarithm */\ntemplate <typename MatrixType>\nvoid matrix_log_compute_pade(MatrixType& result, const MatrixType& T, int degree)\n{\n  typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;\n  const int minPadeDegree = 3;\n  const int maxPadeDegree = 11;\n  assert(degree >= minPadeDegree && degree <= maxPadeDegree);\n\n  const RealScalar nodes[][maxPadeDegree] = { \n    { 0.1127016653792583114820734600217600L, 0.5000000000000000000000000000000000L,  // degree 3\n      0.8872983346207416885179265399782400L }, \n    { 0.0694318442029737123880267555535953L, 0.3300094782075718675986671204483777L,  // degree 4\n      0.6699905217924281324013328795516223L, 0.9305681557970262876119732444464048L },\n    { 0.0469100770306680036011865608503035L, 0.2307653449471584544818427896498956L,  // degree 5\n      0.5000000000000000000000000000000000L, 0.7692346550528415455181572103501044L,\n      0.9530899229693319963988134391496965L },\n    { 0.0337652428984239860938492227530027L, 0.1693953067668677431693002024900473L,  // degree 6\n      0.3806904069584015456847491391596440L, 0.6193095930415984543152508608403560L,\n      0.8306046932331322568306997975099527L, 0.9662347571015760139061507772469973L },\n    { 0.0254460438286207377369051579760744L, 0.1292344072003027800680676133596058L,  // degree 7\n      0.2970774243113014165466967939615193L, 0.5000000000000000000000000000000000L,\n      0.7029225756886985834533032060384807L, 0.8707655927996972199319323866403942L,\n      0.9745539561713792622630948420239256L },\n    { 0.0198550717512318841582195657152635L, 0.1016667612931866302042230317620848L,  // degree 8\n      0.2372337950418355070911304754053768L, 0.4082826787521750975302619288199080L,\n      0.5917173212478249024697380711800920L, 0.7627662049581644929088695245946232L,\n      0.8983332387068133697957769682379152L, 0.9801449282487681158417804342847365L },\n    { 0.0159198802461869550822118985481636L, 0.0819844463366821028502851059651326L,  // degree 9\n      0.1933142836497048013456489803292629L, 0.3378732882980955354807309926783317L,\n      0.5000000000000000000000000000000000L, 0.6621267117019044645192690073216683L,\n      0.8066857163502951986543510196707371L, 0.9180155536633178971497148940348674L,\n      0.9840801197538130449177881014518364L },\n    { 0.0130467357414141399610179939577740L, 0.0674683166555077446339516557882535L,  // degree 10\n      0.1602952158504877968828363174425632L, 0.2833023029353764046003670284171079L,\n      0.4255628305091843945575869994351400L, 0.5744371694908156054424130005648600L,\n      0.7166976970646235953996329715828921L, 0.8397047841495122031171636825574368L,\n      0.9325316833444922553660483442117465L, 0.9869532642585858600389820060422260L },\n    { 0.0108856709269715035980309994385713L, 0.0564687001159523504624211153480364L,  // degree 11\n      0.1349239972129753379532918739844233L, 0.2404519353965940920371371652706952L,\n      0.3652284220238275138342340072995692L, 0.5000000000000000000000000000000000L,\n      0.6347715779761724861657659927004308L, 0.7595480646034059079628628347293048L,\n      0.8650760027870246620467081260155767L, 0.9435312998840476495375788846519636L,\n      0.9891143290730284964019690005614287L } };\n\n  const RealScalar weights[][maxPadeDegree] = { \n    { 0.2777777777777777777777777777777778L, 0.4444444444444444444444444444444444L,  // degree 3\n      0.2777777777777777777777777777777778L },\n    { 0.1739274225687269286865319746109997L, 0.3260725774312730713134680253890003L,  // degree 4\n      0.3260725774312730713134680253890003L, 0.1739274225687269286865319746109997L },\n    { 0.1184634425280945437571320203599587L, 0.2393143352496832340206457574178191L,  // degree 5\n      0.2844444444444444444444444444444444L, 0.2393143352496832340206457574178191L,\n      0.1184634425280945437571320203599587L },\n    { 0.0856622461895851725201480710863665L, 0.1803807865240693037849167569188581L,  // degree 6\n      0.2339569672863455236949351719947755L, 0.2339569672863455236949351719947755L,\n      0.1803807865240693037849167569188581L, 0.0856622461895851725201480710863665L },\n    { 0.0647424830844348466353057163395410L, 0.1398526957446383339507338857118898L,  // degree 7\n      0.1909150252525594724751848877444876L, 0.2089795918367346938775510204081633L,\n      0.1909150252525594724751848877444876L, 0.1398526957446383339507338857118898L,\n      0.0647424830844348466353057163395410L },\n    { 0.0506142681451881295762656771549811L, 0.1111905172266872352721779972131204L,  // degree 8\n      0.1568533229389436436689811009933007L, 0.1813418916891809914825752246385978L,\n      0.1813418916891809914825752246385978L, 0.1568533229389436436689811009933007L,\n      0.1111905172266872352721779972131204L, 0.0506142681451881295762656771549811L },\n    { 0.0406371941807872059859460790552618L, 0.0903240803474287020292360156214564L,  // degree 9\n      0.1303053482014677311593714347093164L, 0.1561735385200014200343152032922218L,\n      0.1651196775006298815822625346434870L, 0.1561735385200014200343152032922218L,\n      0.1303053482014677311593714347093164L, 0.0903240803474287020292360156214564L,\n      0.0406371941807872059859460790552618L },\n    { 0.0333356721543440687967844049466659L, 0.0747256745752902965728881698288487L,  // degree 10\n      0.1095431812579910219977674671140816L, 0.1346333596549981775456134607847347L,\n      0.1477621123573764350869464973256692L, 0.1477621123573764350869464973256692L,\n      0.1346333596549981775456134607847347L, 0.1095431812579910219977674671140816L,\n      0.0747256745752902965728881698288487L, 0.0333356721543440687967844049466659L },\n    { 0.0278342835580868332413768602212743L, 0.0627901847324523123173471496119701L,  // degree 11\n      0.0931451054638671257130488207158280L, 0.1165968822959952399592618524215876L,\n      0.1314022722551233310903444349452546L, 0.1364625433889503153572417641681711L,\n      0.1314022722551233310903444349452546L, 0.1165968822959952399592618524215876L,\n      0.0931451054638671257130488207158280L, 0.0627901847324523123173471496119701L,\n      0.0278342835580868332413768602212743L } };\n\n  MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows());\n  result.setZero(T.rows(), T.rows());\n  for (int k = 0; k < degree; ++k) {\n    RealScalar weight = weights[degree-minPadeDegree][k];\n    RealScalar node = nodes[degree-minPadeDegree][k];\n    result += weight * (MatrixType::Identity(T.rows(), T.rows()) + node * TminusI)\n                       .template triangularView<Upper>().solve(TminusI);\n  }\n} \n\n/** \\brief Compute logarithm of triangular matrices with size > 2. \n  * \\details This uses a inverse scale-and-square algorithm. */\ntemplate <typename MatrixType>\nvoid matrix_log_compute_big(const MatrixType& A, MatrixType& result)\n{\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  using std::pow;\n\n  int numberOfSquareRoots = 0;\n  int numberOfExtraSquareRoots = 0;\n  int degree;\n  MatrixType T = A, sqrtT;\n\n  int maxPadeDegree = matrix_log_max_pade_degree<Scalar>::value;\n  const RealScalar maxNormForPade = maxPadeDegree<= 5? 5.3149729967117310e-1L:                    // single precision\n                                    maxPadeDegree<= 7? 2.6429608311114350e-1L:                    // double precision\n                                    maxPadeDegree<= 8? 2.32777776523703892094e-1L:                // extended precision\n                                    maxPadeDegree<=10? 1.05026503471351080481093652651105e-1L:    // double-double\n                                                       1.1880960220216759245467951592883642e-1L;  // quadruple precision\n\n  while (true) {\n    RealScalar normTminusI = (T - MatrixType::Identity(T.rows(), T.rows())).cwiseAbs().colwise().sum().maxCoeff();\n    if (normTminusI < maxNormForPade) {\n      degree = matrix_log_get_pade_degree(normTminusI);\n      int degree2 = matrix_log_get_pade_degree(normTminusI / RealScalar(2));\n      if ((degree - degree2 <= 1) || (numberOfExtraSquareRoots == 1)) \n        break;\n      ++numberOfExtraSquareRoots;\n    }\n    matrix_sqrt_triangular(T, sqrtT);\n    T = sqrtT.template triangularView<Upper>();\n    ++numberOfSquareRoots;\n  }\n\n  matrix_log_compute_pade(result, T, degree);\n  result *= pow(RealScalar(2), numberOfSquareRoots);\n}\n\n/** \\ingroup MatrixFunctions_Module\n  * \\class MatrixLogarithmAtomic\n  * \\brief Helper class for computing matrix logarithm of atomic matrices.\n  *\n  * Here, an atomic matrix is a triangular matrix whose diagonal entries are close to each other.\n  *\n  * \\sa class MatrixFunctionAtomic, MatrixBase::log()\n  */\ntemplate <typename MatrixType>\nclass MatrixLogarithmAtomic\n{\npublic:\n  /** \\brief Compute matrix logarithm of atomic matrix\n    * \\param[in]  A  argument of matrix logarithm, should be upper triangular and atomic\n    * \\returns  The logarithm of \\p A.\n    */\n  MatrixType compute(const MatrixType& A);\n};\n\ntemplate <typename MatrixType>\nMatrixType MatrixLogarithmAtomic<MatrixType>::compute(const MatrixType& A)\n{\n  using std::log;\n  MatrixType result(A.rows(), A.rows());\n  if (A.rows() == 1)\n    result(0,0) = log(A(0,0));\n  else if (A.rows() == 2)\n    matrix_log_compute_2x2(A, result);\n  else\n    matrix_log_compute_big(A, result);\n  return result;\n}\n\n} // end of namespace internal\n\n/** \\ingroup MatrixFunctions_Module\n  *\n  * \\brief Proxy for the matrix logarithm of some matrix (expression).\n  *\n  * \\tparam Derived  Type of the argument to the matrix function.\n  *\n  * This class holds the argument to the matrix function until it is\n  * assigned or evaluated for some other reason (so the argument\n  * should not be changed in the meantime). It is the return type of\n  * MatrixBase::log() and most of the time this is the only way it\n  * is used.\n  */\ntemplate<typename Derived> class MatrixLogarithmReturnValue\n: public ReturnByValue<MatrixLogarithmReturnValue<Derived> >\n{\npublic:\n  typedef typename Derived::Scalar Scalar;\n  typedef typename Derived::Index Index;\n\nprotected:\n  typedef typename internal::ref_selector<Derived>::type DerivedNested;\n\npublic:\n\n  /** \\brief Constructor.\n    *\n    * \\param[in]  A  %Matrix (expression) forming the argument of the matrix logarithm.\n    */\n  explicit MatrixLogarithmReturnValue(const Derived& A) : m_A(A) { }\n  \n  /** \\brief Compute the matrix logarithm.\n    *\n    * \\param[out]  result  Logarithm of \\p A, where \\A is as specified in the constructor.\n    */\n  template <typename ResultType>\n  inline void evalTo(ResultType& result) const\n  {\n    typedef typename internal::nested_eval<Derived, 10>::type DerivedEvalType;\n    typedef typename internal::remove_all<DerivedEvalType>::type DerivedEvalTypeClean;\n    typedef internal::traits<DerivedEvalTypeClean> Traits;\n    static const int RowsAtCompileTime = Traits::RowsAtCompileTime;\n    static const int ColsAtCompileTime = Traits::ColsAtCompileTime;\n    typedef std::complex<typename NumTraits<Scalar>::Real> ComplexScalar;\n    typedef Matrix<ComplexScalar, Dynamic, Dynamic, 0, RowsAtCompileTime, ColsAtCompileTime> DynMatrixType;\n    typedef internal::MatrixLogarithmAtomic<DynMatrixType> AtomicType;\n    AtomicType atomic;\n    \n    internal::matrix_function_compute<typename DerivedEvalTypeClean::PlainObject>::run(m_A, atomic, result);\n  }\n\n  Index rows() const { return m_A.rows(); }\n  Index cols() const { return m_A.cols(); }\n  \nprivate:\n  const DerivedNested m_A;\n};\n\nnamespace internal {\n  template<typename Derived>\n  struct traits<MatrixLogarithmReturnValue<Derived> >\n  {\n    typedef typename Derived::PlainObject ReturnType;\n  };\n}\n\n\n/********** MatrixBase method **********/\n\n\ntemplate <typename Derived>\nconst MatrixLogarithmReturnValue<Derived> MatrixBase<Derived>::log() const\n{\n  eigen_assert(rows() == cols());\n  return MatrixLogarithmReturnValue<Derived>(derived());\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_MATRIX_LOGARITHM\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/MatrixFunctions/MatrixPower.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012, 2013 Chen-Pang He <jdh8@ms63.hinet.net>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_MATRIX_POWER\n#define EIGEN_MATRIX_POWER\n\nnamespace Eigen {\n\ntemplate<typename MatrixType> class MatrixPower;\n\n/**\n * \\ingroup MatrixFunctions_Module\n *\n * \\brief Proxy for the matrix power of some matrix.\n *\n * \\tparam MatrixType  type of the base, a matrix.\n *\n * This class holds the arguments to the matrix power until it is\n * assigned or evaluated for some other reason (so the argument\n * should not be changed in the meantime). It is the return type of\n * MatrixPower::operator() and related functions and most of the\n * time this is the only way it is used.\n */\n/* TODO This class is only used by MatrixPower, so it should be nested\n * into MatrixPower, like MatrixPower::ReturnValue. However, my\n * compiler complained about unused template parameter in the\n * following declaration in namespace internal.\n *\n * template<typename MatrixType>\n * struct traits<MatrixPower<MatrixType>::ReturnValue>;\n */\ntemplate<typename MatrixType>\nclass MatrixPowerParenthesesReturnValue : public ReturnByValue< MatrixPowerParenthesesReturnValue<MatrixType> >\n{\n  public:\n    typedef typename MatrixType::RealScalar RealScalar;\n    typedef typename MatrixType::Index Index;\n\n    /**\n     * \\brief Constructor.\n     *\n     * \\param[in] pow  %MatrixPower storing the base.\n     * \\param[in] p    scalar, the exponent of the matrix power.\n     */\n    MatrixPowerParenthesesReturnValue(MatrixPower<MatrixType>& pow, RealScalar p) : m_pow(pow), m_p(p)\n    { }\n\n    /**\n     * \\brief Compute the matrix power.\n     *\n     * \\param[out] result\n     */\n    template<typename ResultType>\n    inline void evalTo(ResultType& res) const\n    { m_pow.compute(res, m_p); }\n\n    Index rows() const { return m_pow.rows(); }\n    Index cols() const { return m_pow.cols(); }\n\n  private:\n    MatrixPower<MatrixType>& m_pow;\n    const RealScalar m_p;\n};\n\n/**\n * \\ingroup MatrixFunctions_Module\n *\n * \\brief Class for computing matrix powers.\n *\n * \\tparam MatrixType  type of the base, expected to be an instantiation\n * of the Matrix class template.\n *\n * This class is capable of computing triangular real/complex matrices\n * raised to a power in the interval \\f$ (-1, 1) \\f$.\n *\n * \\note Currently this class is only used by MatrixPower. One may\n * insist that this be nested into MatrixPower. This class is here to\n * faciliate future development of triangular matrix functions.\n */\ntemplate<typename MatrixType>\nclass MatrixPowerAtomic : internal::noncopyable\n{\n  private:\n    enum {\n      RowsAtCompileTime = MatrixType::RowsAtCompileTime,\n      MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime\n    };\n    typedef typename MatrixType::Scalar Scalar;\n    typedef typename MatrixType::RealScalar RealScalar;\n    typedef std::complex<RealScalar> ComplexScalar;\n    typedef typename MatrixType::Index Index;\n    typedef Block<MatrixType,Dynamic,Dynamic> ResultType;\n\n    const MatrixType& m_A;\n    RealScalar m_p;\n\n    void computePade(int degree, const MatrixType& IminusT, ResultType& res) const;\n    void compute2x2(ResultType& res, RealScalar p) const;\n    void computeBig(ResultType& res) const;\n    static int getPadeDegree(float normIminusT);\n    static int getPadeDegree(double normIminusT);\n    static int getPadeDegree(long double normIminusT);\n    static ComplexScalar computeSuperDiag(const ComplexScalar&, const ComplexScalar&, RealScalar p);\n    static RealScalar computeSuperDiag(RealScalar, RealScalar, RealScalar p);\n\n  public:\n    /**\n     * \\brief Constructor.\n     *\n     * \\param[in] T  the base of the matrix power.\n     * \\param[in] p  the exponent of the matrix power, should be in\n     * \\f$ (-1, 1) \\f$.\n     *\n     * The class stores a reference to T, so it should not be changed\n     * (or destroyed) before evaluation. Only the upper triangular\n     * part of T is read.\n     */\n    MatrixPowerAtomic(const MatrixType& T, RealScalar p);\n    \n    /**\n     * \\brief Compute the matrix power.\n     *\n     * \\param[out] res  \\f$ A^p \\f$ where A and p are specified in the\n     * constructor.\n     */\n    void compute(ResultType& res) const;\n};\n\ntemplate<typename MatrixType>\nMatrixPowerAtomic<MatrixType>::MatrixPowerAtomic(const MatrixType& T, RealScalar p) :\n  m_A(T), m_p(p)\n{\n  eigen_assert(T.rows() == T.cols());\n  eigen_assert(p > -1 && p < 1);\n}\n\ntemplate<typename MatrixType>\nvoid MatrixPowerAtomic<MatrixType>::compute(ResultType& res) const\n{\n  using std::pow;\n  switch (m_A.rows()) {\n    case 0:\n      break;\n    case 1:\n      res(0,0) = pow(m_A(0,0), m_p);\n      break;\n    case 2:\n      compute2x2(res, m_p);\n      break;\n    default:\n      computeBig(res);\n  }\n}\n\ntemplate<typename MatrixType>\nvoid MatrixPowerAtomic<MatrixType>::computePade(int degree, const MatrixType& IminusT, ResultType& res) const\n{\n  int i = 2*degree;\n  res = (m_p-degree) / (2*i-2) * IminusT;\n\n  for (--i; i; --i) {\n    res = (MatrixType::Identity(IminusT.rows(), IminusT.cols()) + res).template triangularView<Upper>()\n\t.solve((i==1 ? -m_p : i&1 ? (-m_p-i/2)/(2*i) : (m_p-i/2)/(2*i-2)) * IminusT).eval();\n  }\n  res += MatrixType::Identity(IminusT.rows(), IminusT.cols());\n}\n\n// This function assumes that res has the correct size (see bug 614)\ntemplate<typename MatrixType>\nvoid MatrixPowerAtomic<MatrixType>::compute2x2(ResultType& res, RealScalar p) const\n{\n  using std::abs;\n  using std::pow;\n  res.coeffRef(0,0) = pow(m_A.coeff(0,0), p);\n\n  for (Index i=1; i < m_A.cols(); ++i) {\n    res.coeffRef(i,i) = pow(m_A.coeff(i,i), p);\n    if (m_A.coeff(i-1,i-1) == m_A.coeff(i,i))\n      res.coeffRef(i-1,i) = p * pow(m_A.coeff(i,i), p-1);\n    else if (2*abs(m_A.coeff(i-1,i-1)) < abs(m_A.coeff(i,i)) || 2*abs(m_A.coeff(i,i)) < abs(m_A.coeff(i-1,i-1)))\n      res.coeffRef(i-1,i) = (res.coeff(i,i)-res.coeff(i-1,i-1)) / (m_A.coeff(i,i)-m_A.coeff(i-1,i-1));\n    else\n      res.coeffRef(i-1,i) = computeSuperDiag(m_A.coeff(i,i), m_A.coeff(i-1,i-1), p);\n    res.coeffRef(i-1,i) *= m_A.coeff(i-1,i);\n  }\n}\n\ntemplate<typename MatrixType>\nvoid MatrixPowerAtomic<MatrixType>::computeBig(ResultType& res) const\n{\n  using std::ldexp;\n  const int digits = std::numeric_limits<RealScalar>::digits;\n  const RealScalar maxNormForPade = digits <=  24? 4.3386528e-1L                            // single precision\n                                  : digits <=  53? 2.789358995219730e-1L                    // double precision\n                                  : digits <=  64? 2.4471944416607995472e-1L                // extended precision\n                                  : digits <= 106? 1.1016843812851143391275867258512e-1L    // double-double\n                                  :                9.134603732914548552537150753385375e-2L; // quadruple precision\n  MatrixType IminusT, sqrtT, T = m_A.template triangularView<Upper>();\n  RealScalar normIminusT;\n  int degree, degree2, numberOfSquareRoots = 0;\n  bool hasExtraSquareRoot = false;\n\n  for (Index i=0; i < m_A.cols(); ++i)\n    eigen_assert(m_A(i,i) != RealScalar(0));\n\n  while (true) {\n    IminusT = MatrixType::Identity(m_A.rows(), m_A.cols()) - T;\n    normIminusT = IminusT.cwiseAbs().colwise().sum().maxCoeff();\n    if (normIminusT < maxNormForPade) {\n      degree = getPadeDegree(normIminusT);\n      degree2 = getPadeDegree(normIminusT/2);\n      if (degree - degree2 <= 1 || hasExtraSquareRoot)\n\tbreak;\n      hasExtraSquareRoot = true;\n    }\n    matrix_sqrt_triangular(T, sqrtT);\n    T = sqrtT.template triangularView<Upper>();\n    ++numberOfSquareRoots;\n  }\n  computePade(degree, IminusT, res);\n\n  for (; numberOfSquareRoots; --numberOfSquareRoots) {\n    compute2x2(res, ldexp(m_p, -numberOfSquareRoots));\n    res = res.template triangularView<Upper>() * res;\n  }\n  compute2x2(res, m_p);\n}\n  \ntemplate<typename MatrixType>\ninline int MatrixPowerAtomic<MatrixType>::getPadeDegree(float normIminusT)\n{\n  const float maxNormForPade[] = { 2.8064004e-1f /* degree = 3 */ , 4.3386528e-1f };\n  int degree = 3;\n  for (; degree <= 4; ++degree)\n    if (normIminusT <= maxNormForPade[degree - 3])\n      break;\n  return degree;\n}\n\ntemplate<typename MatrixType>\ninline int MatrixPowerAtomic<MatrixType>::getPadeDegree(double normIminusT)\n{\n  const double maxNormForPade[] = { 1.884160592658218e-2 /* degree = 3 */ , 6.038881904059573e-2, 1.239917516308172e-1,\n      1.999045567181744e-1, 2.789358995219730e-1 };\n  int degree = 3;\n  for (; degree <= 7; ++degree)\n    if (normIminusT <= maxNormForPade[degree - 3])\n      break;\n  return degree;\n}\n\ntemplate<typename MatrixType>\ninline int MatrixPowerAtomic<MatrixType>::getPadeDegree(long double normIminusT)\n{\n#if   LDBL_MANT_DIG == 53\n  const int maxPadeDegree = 7;\n  const double maxNormForPade[] = { 1.884160592658218e-2L /* degree = 3 */ , 6.038881904059573e-2L, 1.239917516308172e-1L,\n      1.999045567181744e-1L, 2.789358995219730e-1L };\n#elif LDBL_MANT_DIG <= 64\n  const int maxPadeDegree = 8;\n  const long double maxNormForPade[] = { 6.3854693117491799460e-3L /* degree = 3 */ , 2.6394893435456973676e-2L,\n      6.4216043030404063729e-2L, 1.1701165502926694307e-1L, 1.7904284231268670284e-1L, 2.4471944416607995472e-1L };\n#elif LDBL_MANT_DIG <= 106\n  const int maxPadeDegree = 10;\n  const double maxNormForPade[] = { 1.0007161601787493236741409687186e-4L /* degree = 3 */ ,\n      1.0007161601787493236741409687186e-3L, 4.7069769360887572939882574746264e-3L, 1.3220386624169159689406653101695e-2L,\n      2.8063482381631737920612944054906e-2L, 4.9625993951953473052385361085058e-2L, 7.7367040706027886224557538328171e-2L,\n      1.1016843812851143391275867258512e-1L };\n#else\n  const int maxPadeDegree = 10;\n  const double maxNormForPade[] = { 5.524506147036624377378713555116378e-5L /* degree = 3 */ ,\n      6.640600568157479679823602193345995e-4L, 3.227716520106894279249709728084626e-3L,\n      9.619593944683432960546978734646284e-3L, 2.134595382433742403911124458161147e-2L,\n      3.908166513900489428442993794761185e-2L, 6.266780814639442865832535460550138e-2L,\n      9.134603732914548552537150753385375e-2L };\n#endif\n  int degree = 3;\n  for (; degree <= maxPadeDegree; ++degree)\n    if (normIminusT <= maxNormForPade[degree - 3])\n      break;\n  return degree;\n}\n\ntemplate<typename MatrixType>\ninline typename MatrixPowerAtomic<MatrixType>::ComplexScalar\nMatrixPowerAtomic<MatrixType>::computeSuperDiag(const ComplexScalar& curr, const ComplexScalar& prev, RealScalar p)\n{\n  using std::ceil;\n  using std::exp;\n  using std::log;\n  using std::sinh;\n\n  ComplexScalar logCurr = log(curr);\n  ComplexScalar logPrev = log(prev);\n  int unwindingNumber = ceil((numext::imag(logCurr - logPrev) - RealScalar(EIGEN_PI)) / RealScalar(2*EIGEN_PI));\n  ComplexScalar w = numext::log1p((curr-prev)/prev)/RealScalar(2) + ComplexScalar(0, EIGEN_PI*unwindingNumber);\n  return RealScalar(2) * exp(RealScalar(0.5) * p * (logCurr + logPrev)) * sinh(p * w) / (curr - prev);\n}\n\ntemplate<typename MatrixType>\ninline typename MatrixPowerAtomic<MatrixType>::RealScalar\nMatrixPowerAtomic<MatrixType>::computeSuperDiag(RealScalar curr, RealScalar prev, RealScalar p)\n{\n  using std::exp;\n  using std::log;\n  using std::sinh;\n\n  RealScalar w = numext::log1p((curr-prev)/prev)/RealScalar(2);\n  return 2 * exp(p * (log(curr) + log(prev)) / 2) * sinh(p * w) / (curr - prev);\n}\n\n/**\n * \\ingroup MatrixFunctions_Module\n *\n * \\brief Class for computing matrix powers.\n *\n * \\tparam MatrixType  type of the base, expected to be an instantiation\n * of the Matrix class template.\n *\n * This class is capable of computing real/complex matrices raised to\n * an arbitrary real power. Meanwhile, it saves the result of Schur\n * decomposition if an non-integral power has even been calculated.\n * Therefore, if you want to compute multiple (>= 2) matrix powers\n * for the same matrix, using the class directly is more efficient than\n * calling MatrixBase::pow().\n *\n * Example:\n * \\include MatrixPower_optimal.cpp\n * Output: \\verbinclude MatrixPower_optimal.out\n */\ntemplate<typename MatrixType>\nclass MatrixPower : internal::noncopyable\n{\n  private:\n    typedef typename MatrixType::Scalar Scalar;\n    typedef typename MatrixType::RealScalar RealScalar;\n    typedef typename MatrixType::Index Index;\n\n  public:\n    /**\n     * \\brief Constructor.\n     *\n     * \\param[in] A  the base of the matrix power.\n     *\n     * The class stores a reference to A, so it should not be changed\n     * (or destroyed) before evaluation.\n     */\n    explicit MatrixPower(const MatrixType& A) :\n      m_A(A),\n      m_conditionNumber(0),\n      m_rank(A.cols()),\n      m_nulls(0)\n    { eigen_assert(A.rows() == A.cols()); }\n\n    /**\n     * \\brief Returns the matrix power.\n     *\n     * \\param[in] p  exponent, a real scalar.\n     * \\return The expression \\f$ A^p \\f$, where A is specified in the\n     * constructor.\n     */\n    const MatrixPowerParenthesesReturnValue<MatrixType> operator()(RealScalar p)\n    { return MatrixPowerParenthesesReturnValue<MatrixType>(*this, p); }\n\n    /**\n     * \\brief Compute the matrix power.\n     *\n     * \\param[in]  p    exponent, a real scalar.\n     * \\param[out] res  \\f$ A^p \\f$ where A is specified in the\n     * constructor.\n     */\n    template<typename ResultType>\n    void compute(ResultType& res, RealScalar p);\n    \n    Index rows() const { return m_A.rows(); }\n    Index cols() const { return m_A.cols(); }\n\n  private:\n    typedef std::complex<RealScalar> ComplexScalar;\n    typedef Matrix<ComplexScalar, Dynamic, Dynamic, 0,\n              MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime> ComplexMatrix;\n\n    /** \\brief Reference to the base of matrix power. */\n    typename MatrixType::Nested m_A;\n\n    /** \\brief Temporary storage. */\n    MatrixType m_tmp;\n\n    /** \\brief Store the result of Schur decomposition. */\n    ComplexMatrix m_T, m_U;\n    \n    /** \\brief Store fractional power of m_T. */\n    ComplexMatrix m_fT;\n\n    /**\n     * \\brief Condition number of m_A.\n     *\n     * It is initialized as 0 to avoid performing unnecessary Schur\n     * decomposition, which is the bottleneck.\n     */\n    RealScalar m_conditionNumber;\n\n    /** \\brief Rank of m_A. */\n    Index m_rank;\n    \n    /** \\brief Rank deficiency of m_A. */\n    Index m_nulls;\n\n    /**\n     * \\brief Split p into integral part and fractional part.\n     *\n     * \\param[in]  p        The exponent.\n     * \\param[out] p        The fractional part ranging in \\f$ (-1, 1) \\f$.\n     * \\param[out] intpart  The integral part.\n     *\n     * Only if the fractional part is nonzero, it calls initialize().\n     */\n    void split(RealScalar& p, RealScalar& intpart);\n\n    /** \\brief Perform Schur decomposition for fractional power. */\n    void initialize();\n\n    template<typename ResultType>\n    void computeIntPower(ResultType& res, RealScalar p);\n\n    template<typename ResultType>\n    void computeFracPower(ResultType& res, RealScalar p);\n\n    template<int Rows, int Cols, int Options, int MaxRows, int MaxCols>\n    static void revertSchur(\n        Matrix<ComplexScalar, Rows, Cols, Options, MaxRows, MaxCols>& res,\n        const ComplexMatrix& T,\n        const ComplexMatrix& U);\n\n    template<int Rows, int Cols, int Options, int MaxRows, int MaxCols>\n    static void revertSchur(\n        Matrix<RealScalar, Rows, Cols, Options, MaxRows, MaxCols>& res,\n        const ComplexMatrix& T,\n        const ComplexMatrix& U);\n};\n\ntemplate<typename MatrixType>\ntemplate<typename ResultType>\nvoid MatrixPower<MatrixType>::compute(ResultType& res, RealScalar p)\n{\n  using std::pow;\n  switch (cols()) {\n    case 0:\n      break;\n    case 1:\n      res(0,0) = pow(m_A.coeff(0,0), p);\n      break;\n    default:\n      RealScalar intpart;\n      split(p, intpart);\n\n      res = MatrixType::Identity(rows(), cols());\n      computeIntPower(res, intpart);\n      if (p) computeFracPower(res, p);\n  }\n}\n\ntemplate<typename MatrixType>\nvoid MatrixPower<MatrixType>::split(RealScalar& p, RealScalar& intpart)\n{\n  using std::floor;\n  using std::pow;\n\n  intpart = floor(p);\n  p -= intpart;\n\n  // Perform Schur decomposition if it is not yet performed and the power is\n  // not an integer.\n  if (!m_conditionNumber && p)\n    initialize();\n\n  // Choose the more stable of intpart = floor(p) and intpart = ceil(p).\n  if (p > RealScalar(0.5) && p > (1-p) * pow(m_conditionNumber, p)) {\n    --p;\n    ++intpart;\n  }\n}\n\ntemplate<typename MatrixType>\nvoid MatrixPower<MatrixType>::initialize()\n{\n  const ComplexSchur<MatrixType> schurOfA(m_A);\n  JacobiRotation<ComplexScalar> rot;\n  ComplexScalar eigenvalue;\n\n  m_fT.resizeLike(m_A);\n  m_T = schurOfA.matrixT();\n  m_U = schurOfA.matrixU();\n  m_conditionNumber = m_T.diagonal().array().abs().maxCoeff() / m_T.diagonal().array().abs().minCoeff();\n\n  // Move zero eigenvalues to the bottom right corner.\n  for (Index i = cols()-1; i>=0; --i) {\n    if (m_rank <= 2)\n      return;\n    if (m_T.coeff(i,i) == RealScalar(0)) {\n      for (Index j=i+1; j < m_rank; ++j) {\n        eigenvalue = m_T.coeff(j,j);\n        rot.makeGivens(m_T.coeff(j-1,j), eigenvalue);\n        m_T.applyOnTheRight(j-1, j, rot);\n        m_T.applyOnTheLeft(j-1, j, rot.adjoint());\n        m_T.coeffRef(j-1,j-1) = eigenvalue;\n        m_T.coeffRef(j,j) = RealScalar(0);\n        m_U.applyOnTheRight(j-1, j, rot);\n      }\n      --m_rank;\n    }\n  }\n\n  m_nulls = rows() - m_rank;\n  if (m_nulls) {\n    eigen_assert(m_T.bottomRightCorner(m_nulls, m_nulls).isZero()\n        && \"Base of matrix power should be invertible or with a semisimple zero eigenvalue.\");\n    m_fT.bottomRows(m_nulls).fill(RealScalar(0));\n  }\n}\n\ntemplate<typename MatrixType>\ntemplate<typename ResultType>\nvoid MatrixPower<MatrixType>::computeIntPower(ResultType& res, RealScalar p)\n{\n  using std::abs;\n  using std::fmod;\n  RealScalar pp = abs(p);\n\n  if (p<0) \n    m_tmp = m_A.inverse();\n  else     \n    m_tmp = m_A;\n\n  while (true) {\n    if (fmod(pp, 2) >= 1)\n      res = m_tmp * res;\n    pp /= 2;\n    if (pp < 1)\n      break;\n    m_tmp *= m_tmp;\n  }\n}\n\ntemplate<typename MatrixType>\ntemplate<typename ResultType>\nvoid MatrixPower<MatrixType>::computeFracPower(ResultType& res, RealScalar p)\n{\n  Block<ComplexMatrix,Dynamic,Dynamic> blockTp(m_fT, 0, 0, m_rank, m_rank);\n  eigen_assert(m_conditionNumber);\n  eigen_assert(m_rank + m_nulls == rows());\n\n  MatrixPowerAtomic<ComplexMatrix>(m_T.topLeftCorner(m_rank, m_rank), p).compute(blockTp);\n  if (m_nulls) {\n    m_fT.topRightCorner(m_rank, m_nulls) = m_T.topLeftCorner(m_rank, m_rank).template triangularView<Upper>()\n        .solve(blockTp * m_T.topRightCorner(m_rank, m_nulls));\n  }\n  revertSchur(m_tmp, m_fT, m_U);\n  res = m_tmp * res;\n}\n\ntemplate<typename MatrixType>\ntemplate<int Rows, int Cols, int Options, int MaxRows, int MaxCols>\ninline void MatrixPower<MatrixType>::revertSchur(\n    Matrix<ComplexScalar, Rows, Cols, Options, MaxRows, MaxCols>& res,\n    const ComplexMatrix& T,\n    const ComplexMatrix& U)\n{ res.noalias() = U * (T.template triangularView<Upper>() * U.adjoint()); }\n\ntemplate<typename MatrixType>\ntemplate<int Rows, int Cols, int Options, int MaxRows, int MaxCols>\ninline void MatrixPower<MatrixType>::revertSchur(\n    Matrix<RealScalar, Rows, Cols, Options, MaxRows, MaxCols>& res,\n    const ComplexMatrix& T,\n    const ComplexMatrix& U)\n{ res.noalias() = (U * (T.template triangularView<Upper>() * U.adjoint())).real(); }\n\n/**\n * \\ingroup MatrixFunctions_Module\n *\n * \\brief Proxy for the matrix power of some matrix (expression).\n *\n * \\tparam Derived  type of the base, a matrix (expression).\n *\n * This class holds the arguments to the matrix power until it is\n * assigned or evaluated for some other reason (so the argument\n * should not be changed in the meantime). It is the return type of\n * MatrixBase::pow() and related functions and most of the\n * time this is the only way it is used.\n */\ntemplate<typename Derived>\nclass MatrixPowerReturnValue : public ReturnByValue< MatrixPowerReturnValue<Derived> >\n{\n  public:\n    typedef typename Derived::PlainObject PlainObject;\n    typedef typename Derived::RealScalar RealScalar;\n    typedef typename Derived::Index Index;\n\n    /**\n     * \\brief Constructor.\n     *\n     * \\param[in] A  %Matrix (expression), the base of the matrix power.\n     * \\param[in] p  real scalar, the exponent of the matrix power.\n     */\n    MatrixPowerReturnValue(const Derived& A, RealScalar p) : m_A(A), m_p(p)\n    { }\n\n    /**\n     * \\brief Compute the matrix power.\n     *\n     * \\param[out] result  \\f$ A^p \\f$ where \\p A and \\p p are as in the\n     * constructor.\n     */\n    template<typename ResultType>\n    inline void evalTo(ResultType& res) const\n    { MatrixPower<PlainObject>(m_A.eval()).compute(res, m_p); }\n\n    Index rows() const { return m_A.rows(); }\n    Index cols() const { return m_A.cols(); }\n\n  private:\n    const Derived& m_A;\n    const RealScalar m_p;\n};\n\n/**\n * \\ingroup MatrixFunctions_Module\n *\n * \\brief Proxy for the matrix power of some matrix (expression).\n *\n * \\tparam Derived  type of the base, a matrix (expression).\n *\n * This class holds the arguments to the matrix power until it is\n * assigned or evaluated for some other reason (so the argument\n * should not be changed in the meantime). It is the return type of\n * MatrixBase::pow() and related functions and most of the\n * time this is the only way it is used.\n */\ntemplate<typename Derived>\nclass MatrixComplexPowerReturnValue : public ReturnByValue< MatrixComplexPowerReturnValue<Derived> >\n{\n  public:\n    typedef typename Derived::PlainObject PlainObject;\n    typedef typename std::complex<typename Derived::RealScalar> ComplexScalar;\n    typedef typename Derived::Index Index;\n\n    /**\n     * \\brief Constructor.\n     *\n     * \\param[in] A  %Matrix (expression), the base of the matrix power.\n     * \\param[in] p  complex scalar, the exponent of the matrix power.\n     */\n    MatrixComplexPowerReturnValue(const Derived& A, const ComplexScalar& p) : m_A(A), m_p(p)\n    { }\n\n    /**\n     * \\brief Compute the matrix power.\n     *\n     * Because \\p p is complex, \\f$ A^p \\f$ is simply evaluated as \\f$\n     * \\exp(p \\log(A)) \\f$.\n     *\n     * \\param[out] result  \\f$ A^p \\f$ where \\p A and \\p p are as in the\n     * constructor.\n     */\n    template<typename ResultType>\n    inline void evalTo(ResultType& res) const\n    { res = (m_p * m_A.log()).exp(); }\n\n    Index rows() const { return m_A.rows(); }\n    Index cols() const { return m_A.cols(); }\n\n  private:\n    const Derived& m_A;\n    const ComplexScalar m_p;\n};\n\nnamespace internal {\n\ntemplate<typename MatrixPowerType>\nstruct traits< MatrixPowerParenthesesReturnValue<MatrixPowerType> >\n{ typedef typename MatrixPowerType::PlainObject ReturnType; };\n\ntemplate<typename Derived>\nstruct traits< MatrixPowerReturnValue<Derived> >\n{ typedef typename Derived::PlainObject ReturnType; };\n\ntemplate<typename Derived>\nstruct traits< MatrixComplexPowerReturnValue<Derived> >\n{ typedef typename Derived::PlainObject ReturnType; };\n\n}\n\ntemplate<typename Derived>\nconst MatrixPowerReturnValue<Derived> MatrixBase<Derived>::pow(const RealScalar& p) const\n{ return MatrixPowerReturnValue<Derived>(derived(), p); }\n\ntemplate<typename Derived>\nconst MatrixComplexPowerReturnValue<Derived> MatrixBase<Derived>::pow(const std::complex<RealScalar>& p) const\n{ return MatrixComplexPowerReturnValue<Derived>(derived(), p); }\n\n} // namespace Eigen\n\n#endif // EIGEN_MATRIX_POWER\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/MatrixFunctions/MatrixSquareRoot.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2011, 2013 Jitse Niesen <jitse@maths.leeds.ac.uk>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_MATRIX_SQUARE_ROOT\n#define EIGEN_MATRIX_SQUARE_ROOT\n\nnamespace Eigen { \n\nnamespace internal {\n\n// pre:  T.block(i,i,2,2) has complex conjugate eigenvalues\n// post: sqrtT.block(i,i,2,2) is square root of T.block(i,i,2,2)\ntemplate <typename MatrixType, typename ResultType>\nvoid matrix_sqrt_quasi_triangular_2x2_diagonal_block(const MatrixType& T, typename MatrixType::Index i, ResultType& sqrtT)\n{\n  // TODO: This case (2-by-2 blocks with complex conjugate eigenvalues) is probably hidden somewhere\n  //       in EigenSolver. If we expose it, we could call it directly from here.\n  typedef typename traits<MatrixType>::Scalar Scalar;\n  Matrix<Scalar,2,2> block = T.template block<2,2>(i,i);\n  EigenSolver<Matrix<Scalar,2,2> > es(block);\n  sqrtT.template block<2,2>(i,i)\n    = (es.eigenvectors() * es.eigenvalues().cwiseSqrt().asDiagonal() * es.eigenvectors().inverse()).real();\n}\n\n// pre:  block structure of T is such that (i,j) is a 1x1 block,\n//       all blocks of sqrtT to left of and below (i,j) are correct\n// post: sqrtT(i,j) has the correct value\ntemplate <typename MatrixType, typename ResultType>\nvoid matrix_sqrt_quasi_triangular_1x1_off_diagonal_block(const MatrixType& T, typename MatrixType::Index i, typename MatrixType::Index j, ResultType& sqrtT)\n{\n  typedef typename traits<MatrixType>::Scalar Scalar;\n  Scalar tmp = (sqrtT.row(i).segment(i+1,j-i-1) * sqrtT.col(j).segment(i+1,j-i-1)).value();\n  sqrtT.coeffRef(i,j) = (T.coeff(i,j) - tmp) / (sqrtT.coeff(i,i) + sqrtT.coeff(j,j));\n}\n\n// similar to compute1x1offDiagonalBlock()\ntemplate <typename MatrixType, typename ResultType>\nvoid matrix_sqrt_quasi_triangular_1x2_off_diagonal_block(const MatrixType& T, typename MatrixType::Index i, typename MatrixType::Index j, ResultType& sqrtT)\n{\n  typedef typename traits<MatrixType>::Scalar Scalar;\n  Matrix<Scalar,1,2> rhs = T.template block<1,2>(i,j);\n  if (j-i > 1)\n    rhs -= sqrtT.block(i, i+1, 1, j-i-1) * sqrtT.block(i+1, j, j-i-1, 2);\n  Matrix<Scalar,2,2> A = sqrtT.coeff(i,i) * Matrix<Scalar,2,2>::Identity();\n  A += sqrtT.template block<2,2>(j,j).transpose();\n  sqrtT.template block<1,2>(i,j).transpose() = A.fullPivLu().solve(rhs.transpose());\n}\n\n// similar to compute1x1offDiagonalBlock()\ntemplate <typename MatrixType, typename ResultType>\nvoid matrix_sqrt_quasi_triangular_2x1_off_diagonal_block(const MatrixType& T, typename MatrixType::Index i, typename MatrixType::Index j, ResultType& sqrtT)\n{\n  typedef typename traits<MatrixType>::Scalar Scalar;\n  Matrix<Scalar,2,1> rhs = T.template block<2,1>(i,j);\n  if (j-i > 2)\n    rhs -= sqrtT.block(i, i+2, 2, j-i-2) * sqrtT.block(i+2, j, j-i-2, 1);\n  Matrix<Scalar,2,2> A = sqrtT.coeff(j,j) * Matrix<Scalar,2,2>::Identity();\n  A += sqrtT.template block<2,2>(i,i);\n  sqrtT.template block<2,1>(i,j) = A.fullPivLu().solve(rhs);\n}\n\n// solves the equation A X + X B = C where all matrices are 2-by-2\ntemplate <typename MatrixType>\nvoid matrix_sqrt_quasi_triangular_solve_auxiliary_equation(MatrixType& X, const MatrixType& A, const MatrixType& B, const MatrixType& C)\n{\n  typedef typename traits<MatrixType>::Scalar Scalar;\n  Matrix<Scalar,4,4> coeffMatrix = Matrix<Scalar,4,4>::Zero();\n  coeffMatrix.coeffRef(0,0) = A.coeff(0,0) + B.coeff(0,0);\n  coeffMatrix.coeffRef(1,1) = A.coeff(0,0) + B.coeff(1,1);\n  coeffMatrix.coeffRef(2,2) = A.coeff(1,1) + B.coeff(0,0);\n  coeffMatrix.coeffRef(3,3) = A.coeff(1,1) + B.coeff(1,1);\n  coeffMatrix.coeffRef(0,1) = B.coeff(1,0);\n  coeffMatrix.coeffRef(0,2) = A.coeff(0,1);\n  coeffMatrix.coeffRef(1,0) = B.coeff(0,1);\n  coeffMatrix.coeffRef(1,3) = A.coeff(0,1);\n  coeffMatrix.coeffRef(2,0) = A.coeff(1,0);\n  coeffMatrix.coeffRef(2,3) = B.coeff(1,0);\n  coeffMatrix.coeffRef(3,1) = A.coeff(1,0);\n  coeffMatrix.coeffRef(3,2) = B.coeff(0,1);\n\n  Matrix<Scalar,4,1> rhs;\n  rhs.coeffRef(0) = C.coeff(0,0);\n  rhs.coeffRef(1) = C.coeff(0,1);\n  rhs.coeffRef(2) = C.coeff(1,0);\n  rhs.coeffRef(3) = C.coeff(1,1);\n\n  Matrix<Scalar,4,1> result;\n  result = coeffMatrix.fullPivLu().solve(rhs);\n\n  X.coeffRef(0,0) = result.coeff(0);\n  X.coeffRef(0,1) = result.coeff(1);\n  X.coeffRef(1,0) = result.coeff(2);\n  X.coeffRef(1,1) = result.coeff(3);\n}\n\n// similar to compute1x1offDiagonalBlock()\ntemplate <typename MatrixType, typename ResultType>\nvoid matrix_sqrt_quasi_triangular_2x2_off_diagonal_block(const MatrixType& T, typename MatrixType::Index i, typename MatrixType::Index j, ResultType& sqrtT)\n{\n  typedef typename traits<MatrixType>::Scalar Scalar;\n  Matrix<Scalar,2,2> A = sqrtT.template block<2,2>(i,i);\n  Matrix<Scalar,2,2> B = sqrtT.template block<2,2>(j,j);\n  Matrix<Scalar,2,2> C = T.template block<2,2>(i,j);\n  if (j-i > 2)\n    C -= sqrtT.block(i, i+2, 2, j-i-2) * sqrtT.block(i+2, j, j-i-2, 2);\n  Matrix<Scalar,2,2> X;\n  matrix_sqrt_quasi_triangular_solve_auxiliary_equation(X, A, B, C);\n  sqrtT.template block<2,2>(i,j) = X;\n}\n\n// pre:  T is quasi-upper-triangular and sqrtT is a zero matrix of the same size\n// post: the diagonal blocks of sqrtT are the square roots of the diagonal blocks of T\ntemplate <typename MatrixType, typename ResultType>\nvoid matrix_sqrt_quasi_triangular_diagonal(const MatrixType& T, ResultType& sqrtT)\n{\n  using std::sqrt;\n  typedef typename MatrixType::Index Index;\n  const Index size = T.rows();\n  for (Index i = 0; i < size; i++) {\n    if (i == size - 1 || T.coeff(i+1, i) == 0) {\n      eigen_assert(T(i,i) >= 0);\n      sqrtT.coeffRef(i,i) = sqrt(T.coeff(i,i));\n    }\n    else {\n      matrix_sqrt_quasi_triangular_2x2_diagonal_block(T, i, sqrtT);\n      ++i;\n    }\n  }\n}\n\n// pre:  T is quasi-upper-triangular and diagonal blocks of sqrtT are square root of diagonal blocks of T.\n// post: sqrtT is the square root of T.\ntemplate <typename MatrixType, typename ResultType>\nvoid matrix_sqrt_quasi_triangular_off_diagonal(const MatrixType& T, ResultType& sqrtT)\n{\n  typedef typename MatrixType::Index Index;\n  const Index size = T.rows();\n  for (Index j = 1; j < size; j++) {\n      if (T.coeff(j, j-1) != 0)  // if T(j-1:j, j-1:j) is a 2-by-2 block\n\tcontinue;\n    for (Index i = j-1; i >= 0; i--) {\n      if (i > 0 && T.coeff(i, i-1) != 0)  // if T(i-1:i, i-1:i) is a 2-by-2 block\n\tcontinue;\n      bool iBlockIs2x2 = (i < size - 1) && (T.coeff(i+1, i) != 0);\n      bool jBlockIs2x2 = (j < size - 1) && (T.coeff(j+1, j) != 0);\n      if (iBlockIs2x2 && jBlockIs2x2) \n        matrix_sqrt_quasi_triangular_2x2_off_diagonal_block(T, i, j, sqrtT);\n      else if (iBlockIs2x2 && !jBlockIs2x2) \n        matrix_sqrt_quasi_triangular_2x1_off_diagonal_block(T, i, j, sqrtT);\n      else if (!iBlockIs2x2 && jBlockIs2x2) \n        matrix_sqrt_quasi_triangular_1x2_off_diagonal_block(T, i, j, sqrtT);\n      else if (!iBlockIs2x2 && !jBlockIs2x2) \n        matrix_sqrt_quasi_triangular_1x1_off_diagonal_block(T, i, j, sqrtT);\n    }\n  }\n}\n\n} // end of namespace internal\n\n/** \\ingroup MatrixFunctions_Module\n  * \\brief Compute matrix square root of quasi-triangular matrix.\n  *\n  * \\tparam  MatrixType  type of \\p arg, the argument of matrix square root,\n  *                      expected to be an instantiation of the Matrix class template.\n  * \\tparam  ResultType  type of \\p result, where result is to be stored.\n  * \\param[in]  arg      argument of matrix square root.\n  * \\param[out] result   matrix square root of upper Hessenberg part of \\p arg.\n  *\n  * This function computes the square root of the upper quasi-triangular matrix stored in the upper\n  * Hessenberg part of \\p arg.  Only the upper Hessenberg part of \\p result is updated, the rest is\n  * not touched.  See MatrixBase::sqrt() for details on how this computation is implemented.\n  *\n  * \\sa MatrixSquareRoot, MatrixSquareRootQuasiTriangular\n  */\ntemplate <typename MatrixType, typename ResultType> \nvoid matrix_sqrt_quasi_triangular(const MatrixType &arg, ResultType &result)\n{\n  eigen_assert(arg.rows() == arg.cols());\n  result.resize(arg.rows(), arg.cols());\n  internal::matrix_sqrt_quasi_triangular_diagonal(arg, result);\n  internal::matrix_sqrt_quasi_triangular_off_diagonal(arg, result);\n}\n\n\n/** \\ingroup MatrixFunctions_Module\n  * \\brief Compute matrix square root of triangular matrix.\n  *\n  * \\tparam  MatrixType  type of \\p arg, the argument of matrix square root,\n  *                      expected to be an instantiation of the Matrix class template.\n  * \\tparam  ResultType  type of \\p result, where result is to be stored.\n  * \\param[in]  arg      argument of matrix square root.\n  * \\param[out] result   matrix square root of upper triangular part of \\p arg.\n  *\n  * Only the upper triangular part (including the diagonal) of \\p result is updated, the rest is not\n  * touched.  See MatrixBase::sqrt() for details on how this computation is implemented.\n  *\n  * \\sa MatrixSquareRoot, MatrixSquareRootQuasiTriangular\n  */\ntemplate <typename MatrixType, typename ResultType> \nvoid matrix_sqrt_triangular(const MatrixType &arg, ResultType &result)\n{\n  using std::sqrt;\n  typedef typename MatrixType::Index Index;\n      typedef typename MatrixType::Scalar Scalar;\n\n  eigen_assert(arg.rows() == arg.cols());\n\n  // Compute square root of arg and store it in upper triangular part of result\n  // This uses that the square root of triangular matrices can be computed directly.\n  result.resize(arg.rows(), arg.cols());\n  for (Index i = 0; i < arg.rows(); i++) {\n    result.coeffRef(i,i) = sqrt(arg.coeff(i,i));\n  }\n  for (Index j = 1; j < arg.cols(); j++) {\n    for (Index i = j-1; i >= 0; i--) {\n      // if i = j-1, then segment has length 0 so tmp = 0\n      Scalar tmp = (result.row(i).segment(i+1,j-i-1) * result.col(j).segment(i+1,j-i-1)).value();\n      // denominator may be zero if original matrix is singular\n      result.coeffRef(i,j) = (arg.coeff(i,j) - tmp) / (result.coeff(i,i) + result.coeff(j,j));\n    }\n  }\n}\n\n\nnamespace internal {\n\n/** \\ingroup MatrixFunctions_Module\n  * \\brief Helper struct for computing matrix square roots of general matrices.\n  * \\tparam  MatrixType  type of the argument of the matrix square root,\n  *                      expected to be an instantiation of the Matrix class template.\n  *\n  * \\sa MatrixSquareRootTriangular, MatrixSquareRootQuasiTriangular, MatrixBase::sqrt()\n  */\ntemplate <typename MatrixType, int IsComplex = NumTraits<typename internal::traits<MatrixType>::Scalar>::IsComplex>\nstruct matrix_sqrt_compute\n{\n  /** \\brief Compute the matrix square root\n    *\n    * \\param[in]  arg     matrix whose square root is to be computed.\n    * \\param[out] result  square root of \\p arg.\n    *\n    * See MatrixBase::sqrt() for details on how this computation is implemented.\n    */\n  template <typename ResultType> static void run(const MatrixType &arg, ResultType &result);    \n};\n\n\n// ********** Partial specialization for real matrices **********\n\ntemplate <typename MatrixType>\nstruct matrix_sqrt_compute<MatrixType, 0>\n{\n  template <typename ResultType>\n  static void run(const MatrixType &arg, ResultType &result)\n  {\n    eigen_assert(arg.rows() == arg.cols());\n\n    // Compute Schur decomposition of arg\n    const RealSchur<MatrixType> schurOfA(arg);  \n    const MatrixType& T = schurOfA.matrixT();\n    const MatrixType& U = schurOfA.matrixU();\n    \n    // Compute square root of T\n    MatrixType sqrtT = MatrixType::Zero(arg.rows(), arg.cols());\n    matrix_sqrt_quasi_triangular(T, sqrtT);\n    \n    // Compute square root of arg\n    result = U * sqrtT * U.adjoint();\n  }\n};\n\n\n// ********** Partial specialization for complex matrices **********\n\ntemplate <typename MatrixType>\nstruct matrix_sqrt_compute<MatrixType, 1>\n{\n  template <typename ResultType>\n  static void run(const MatrixType &arg, ResultType &result)\n  {\n    eigen_assert(arg.rows() == arg.cols());\n\n    // Compute Schur decomposition of arg\n    const ComplexSchur<MatrixType> schurOfA(arg);  \n    const MatrixType& T = schurOfA.matrixT();\n    const MatrixType& U = schurOfA.matrixU();\n    \n    // Compute square root of T\n    MatrixType sqrtT;\n    matrix_sqrt_triangular(T, sqrtT);\n    \n    // Compute square root of arg\n    result = U * (sqrtT.template triangularView<Upper>() * U.adjoint());\n  }\n};\n\n} // end namespace internal\n\n/** \\ingroup MatrixFunctions_Module\n  *\n  * \\brief Proxy for the matrix square root of some matrix (expression).\n  *\n  * \\tparam Derived  Type of the argument to the matrix square root.\n  *\n  * This class holds the argument to the matrix square root until it\n  * is assigned or evaluated for some other reason (so the argument\n  * should not be changed in the meantime). It is the return type of\n  * MatrixBase::sqrt() and most of the time this is the only way it is\n  * used.\n  */\ntemplate<typename Derived> class MatrixSquareRootReturnValue\n: public ReturnByValue<MatrixSquareRootReturnValue<Derived> >\n{\n  protected:\n    typedef typename Derived::Index Index;\n    typedef typename internal::ref_selector<Derived>::type DerivedNested;\n\n  public:\n    /** \\brief Constructor.\n      *\n      * \\param[in]  src  %Matrix (expression) forming the argument of the\n      * matrix square root.\n      */\n    explicit MatrixSquareRootReturnValue(const Derived& src) : m_src(src) { }\n\n    /** \\brief Compute the matrix square root.\n      *\n      * \\param[out]  result  the matrix square root of \\p src in the\n      * constructor.\n      */\n    template <typename ResultType>\n    inline void evalTo(ResultType& result) const\n    {\n      typedef typename internal::nested_eval<Derived, 10>::type DerivedEvalType;\n      typedef typename internal::remove_all<DerivedEvalType>::type DerivedEvalTypeClean;\n      DerivedEvalType tmp(m_src);\n      internal::matrix_sqrt_compute<DerivedEvalTypeClean>::run(tmp, result);\n    }\n\n    Index rows() const { return m_src.rows(); }\n    Index cols() const { return m_src.cols(); }\n\n  protected:\n    const DerivedNested m_src;\n};\n\nnamespace internal {\ntemplate<typename Derived>\nstruct traits<MatrixSquareRootReturnValue<Derived> >\n{\n  typedef typename Derived::PlainObject ReturnType;\n};\n}\n\ntemplate <typename Derived>\nconst MatrixSquareRootReturnValue<Derived> MatrixBase<Derived>::sqrt() const\n{\n  eigen_assert(rows() == cols());\n  return MatrixSquareRootReturnValue<Derived>(derived());\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_MATRIX_FUNCTION\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/MatrixFunctions/StemFunction.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2010, 2013 Jitse Niesen <jitse@maths.leeds.ac.uk>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_STEM_FUNCTION\n#define EIGEN_STEM_FUNCTION\n\nnamespace Eigen { \n\nnamespace internal {\n\n/** \\brief The exponential function (and its derivatives). */\ntemplate <typename Scalar>\nScalar stem_function_exp(Scalar x, int)\n{\n  using std::exp;\n  return exp(x);\n}\n\n/** \\brief Cosine (and its derivatives). */\ntemplate <typename Scalar>\nScalar stem_function_cos(Scalar x, int n)\n{\n  using std::cos;\n  using std::sin;\n  Scalar res;\n\n  switch (n % 4) {\n  case 0: \n    res = std::cos(x);\n    break;\n  case 1:\n    res = -std::sin(x);\n    break;\n  case 2:\n    res = -std::cos(x);\n    break;\n  case 3:\n    res = std::sin(x);\n    break;\n  }\n  return res;\n}\n\n/** \\brief Sine (and its derivatives). */\ntemplate <typename Scalar>\nScalar stem_function_sin(Scalar x, int n)\n{\n  using std::cos;\n  using std::sin;\n  Scalar res;\n\n  switch (n % 4) {\n  case 0:\n    res = std::sin(x);\n    break;\n  case 1:\n    res = std::cos(x);\n    break;\n  case 2:\n    res = -std::sin(x);\n    break;\n  case 3:\n    res = -std::cos(x);\n    break;\n  }\n  return res;\n}\n\n/** \\brief Hyperbolic cosine (and its derivatives). */\ntemplate <typename Scalar>\nScalar stem_function_cosh(Scalar x, int n)\n{\n  using std::cosh;\n  using std::sinh;\n  Scalar res;\n  \n  switch (n % 2) {\n  case 0:\n    res = std::cosh(x);\n    break;\n  case 1:\n    res = std::sinh(x);\n    break;\n  }\n  return res;\n}\n\t\n/** \\brief Hyperbolic sine (and its derivatives). */\ntemplate <typename Scalar>\nScalar stem_function_sinh(Scalar x, int n)\n{\n  using std::cosh;\n  using std::sinh;\n  Scalar res;\n  \n  switch (n % 2) {\n  case 0:\n    res = std::sinh(x);\n    break;\n  case 1:\n    res = std::cosh(x);\n    break;\n  }\n  return res;\n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_STEM_FUNCTION\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/MoreVectorization/MathFunctions.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Rohit Garg <rpg.314@gmail.com>\n// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_MOREVECTORIZATION_MATHFUNCTIONS_H\n#define EIGEN_MOREVECTORIZATION_MATHFUNCTIONS_H\n\nnamespace Eigen { \n\nnamespace internal {\n\n/** \\internal \\returns the arcsin of \\a a (coeff-wise) */\ntemplate<typename Packet> inline static Packet pasin(Packet a) { return std::asin(a); }\n\n#ifdef EIGEN_VECTORIZE_SSE\n\ntemplate<> EIGEN_DONT_INLINE Packet4f pasin(Packet4f x)\n{\n  _EIGEN_DECLARE_CONST_Packet4f(half, 0.5);\n  _EIGEN_DECLARE_CONST_Packet4f(minus_half, -0.5);\n  _EIGEN_DECLARE_CONST_Packet4f(3half, 1.5);\n\n  _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(sign_mask, 0x80000000);\n\n  _EIGEN_DECLARE_CONST_Packet4f(pi, 3.141592654);\n  _EIGEN_DECLARE_CONST_Packet4f(pi_over_2, 3.141592654*0.5);\n\n  _EIGEN_DECLARE_CONST_Packet4f(asin1, 4.2163199048E-2);\n  _EIGEN_DECLARE_CONST_Packet4f(asin2, 2.4181311049E-2);\n  _EIGEN_DECLARE_CONST_Packet4f(asin3, 4.5470025998E-2);\n  _EIGEN_DECLARE_CONST_Packet4f(asin4, 7.4953002686E-2);\n  _EIGEN_DECLARE_CONST_Packet4f(asin5, 1.6666752422E-1);\n\n  Packet4f a = pabs(x);//got the absolute value\n\n  Packet4f sign_bit= _mm_and_ps(x, p4f_sign_mask);//extracted the sign bit\n\n  Packet4f z1,z2;//will need them during computation    \n\n\n//will compute the two branches for asin\n//so first compare with half\n\n  Packet4f branch_mask= _mm_cmpgt_ps(a, p4f_half);//this is to select which branch to take\n//both will be taken, and finally results will be merged\n//the branch for values >0.5\n\n    {\n//the core series expansion \n    z1=pmadd(p4f_minus_half,a,p4f_half);\n    Packet4f x1=psqrt(z1);\n    Packet4f s1=pmadd(p4f_asin1, z1, p4f_asin2);\n    Packet4f s2=pmadd(s1, z1, p4f_asin3);\n    Packet4f s3=pmadd(s2,z1, p4f_asin4);\n    Packet4f s4=pmadd(s3,z1, p4f_asin5);\n    Packet4f temp=pmul(s4,z1);//not really a madd but a mul by z so that the next term can be a madd\n    z1=pmadd(temp,x1,x1);\n    z1=padd(z1,z1);\n    z1=psub(p4f_pi_over_2,z1);\n    }\n\n    {\n//the core series expansion \n    Packet4f x2=a;\n    z2=pmul(x2,x2);\n    Packet4f s1=pmadd(p4f_asin1, z2, p4f_asin2);\n    Packet4f s2=pmadd(s1, z2, p4f_asin3);\n    Packet4f s3=pmadd(s2,z2, p4f_asin4);\n    Packet4f s4=pmadd(s3,z2, p4f_asin5);\n    Packet4f temp=pmul(s4,z2);//not really a madd but a mul by z so that the next term can be a madd\n    z2=pmadd(temp,x2,x2);\n    }\n\n/* select the correct result from the two branch evaluations */\n  z1  = _mm_and_ps(branch_mask, z1);\n  z2  = _mm_andnot_ps(branch_mask, z2);\n  Packet4f z  = _mm_or_ps(z1,z2);\n\n/* update the sign */\n  return _mm_xor_ps(z, sign_bit);\n}\n\n#endif // EIGEN_VECTORIZE_SSE\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_MOREVECTORIZATION_MATHFUNCTIONS_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/NonLinearOptimization/HybridNonLinearSolver.h",
    "content": "// -*- coding: utf-8\n// vim: set fileencoding=utf-8\n\n// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_HYBRIDNONLINEARSOLVER_H\n#define EIGEN_HYBRIDNONLINEARSOLVER_H\n\nnamespace Eigen { \n\nnamespace HybridNonLinearSolverSpace { \n    enum Status {\n        Running = -1,\n        ImproperInputParameters = 0,\n        RelativeErrorTooSmall = 1,\n        TooManyFunctionEvaluation = 2,\n        TolTooSmall = 3,\n        NotMakingProgressJacobian = 4,\n        NotMakingProgressIterations = 5,\n        UserAsked = 6\n    };\n}\n\n/**\n  * \\ingroup NonLinearOptimization_Module\n  * \\brief Finds a zero of a system of n\n  * nonlinear functions in n variables by a modification of the Powell\n  * hybrid method (\"dogleg\").\n  *\n  * The user must provide a subroutine which calculates the\n  * functions. The Jacobian is either provided by the user, or approximated\n  * using a forward-difference method.\n  *\n  */\ntemplate<typename FunctorType, typename Scalar=double>\nclass HybridNonLinearSolver\n{\npublic:\n    typedef DenseIndex Index;\n\n    HybridNonLinearSolver(FunctorType &_functor)\n        : functor(_functor) { nfev=njev=iter = 0;  fnorm= 0.; useExternalScaling=false;}\n\n    struct Parameters {\n        Parameters()\n            : factor(Scalar(100.))\n            , maxfev(1000)\n            , xtol(std::sqrt(NumTraits<Scalar>::epsilon()))\n            , nb_of_subdiagonals(-1)\n            , nb_of_superdiagonals(-1)\n            , epsfcn(Scalar(0.)) {}\n        Scalar factor;\n        Index maxfev;   // maximum number of function evaluation\n        Scalar xtol;\n        Index nb_of_subdiagonals;\n        Index nb_of_superdiagonals;\n        Scalar epsfcn;\n    };\n    typedef Matrix< Scalar, Dynamic, 1 > FVectorType;\n    typedef Matrix< Scalar, Dynamic, Dynamic > JacobianType;\n    /* TODO: if eigen provides a triangular storage, use it here */\n    typedef Matrix< Scalar, Dynamic, Dynamic > UpperTriangularType;\n\n    HybridNonLinearSolverSpace::Status hybrj1(\n            FVectorType  &x,\n            const Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon())\n            );\n\n    HybridNonLinearSolverSpace::Status solveInit(FVectorType  &x);\n    HybridNonLinearSolverSpace::Status solveOneStep(FVectorType  &x);\n    HybridNonLinearSolverSpace::Status solve(FVectorType  &x);\n\n    HybridNonLinearSolverSpace::Status hybrd1(\n            FVectorType  &x,\n            const Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon())\n            );\n\n    HybridNonLinearSolverSpace::Status solveNumericalDiffInit(FVectorType  &x);\n    HybridNonLinearSolverSpace::Status solveNumericalDiffOneStep(FVectorType  &x);\n    HybridNonLinearSolverSpace::Status solveNumericalDiff(FVectorType  &x);\n\n    void resetParameters(void) { parameters = Parameters(); }\n    Parameters parameters;\n    FVectorType  fvec, qtf, diag;\n    JacobianType fjac;\n    UpperTriangularType R;\n    Index nfev;\n    Index njev;\n    Index iter;\n    Scalar fnorm;\n    bool useExternalScaling; \nprivate:\n    FunctorType &functor;\n    Index n;\n    Scalar sum;\n    bool sing;\n    Scalar temp;\n    Scalar delta;\n    bool jeval;\n    Index ncsuc;\n    Scalar ratio;\n    Scalar pnorm, xnorm, fnorm1;\n    Index nslow1, nslow2;\n    Index ncfail;\n    Scalar actred, prered;\n    FVectorType wa1, wa2, wa3, wa4;\n\n    HybridNonLinearSolver& operator=(const HybridNonLinearSolver&);\n};\n\n\n\ntemplate<typename FunctorType, typename Scalar>\nHybridNonLinearSolverSpace::Status\nHybridNonLinearSolver<FunctorType,Scalar>::hybrj1(\n        FVectorType  &x,\n        const Scalar tol\n        )\n{\n    n = x.size();\n\n    /* check the input parameters for errors. */\n    if (n <= 0 || tol < 0.)\n        return HybridNonLinearSolverSpace::ImproperInputParameters;\n\n    resetParameters();\n    parameters.maxfev = 100*(n+1);\n    parameters.xtol = tol;\n    diag.setConstant(n, 1.);\n    useExternalScaling = true;\n    return solve(x);\n}\n\ntemplate<typename FunctorType, typename Scalar>\nHybridNonLinearSolverSpace::Status\nHybridNonLinearSolver<FunctorType,Scalar>::solveInit(FVectorType  &x)\n{\n    n = x.size();\n\n    wa1.resize(n); wa2.resize(n); wa3.resize(n); wa4.resize(n);\n    fvec.resize(n);\n    qtf.resize(n);\n    fjac.resize(n, n);\n    if (!useExternalScaling)\n        diag.resize(n);\n    eigen_assert( (!useExternalScaling || diag.size()==n) && \"When useExternalScaling is set, the caller must provide a valid 'diag'\");\n\n    /* Function Body */\n    nfev = 0;\n    njev = 0;\n\n    /*     check the input parameters for errors. */\n    if (n <= 0 || parameters.xtol < 0. || parameters.maxfev <= 0 || parameters.factor <= 0. )\n        return HybridNonLinearSolverSpace::ImproperInputParameters;\n    if (useExternalScaling)\n        for (Index j = 0; j < n; ++j)\n            if (diag[j] <= 0.)\n                return HybridNonLinearSolverSpace::ImproperInputParameters;\n\n    /*     evaluate the function at the starting point */\n    /*     and calculate its norm. */\n    nfev = 1;\n    if ( functor(x, fvec) < 0)\n        return HybridNonLinearSolverSpace::UserAsked;\n    fnorm = fvec.stableNorm();\n\n    /*     initialize iteration counter and monitors. */\n    iter = 1;\n    ncsuc = 0;\n    ncfail = 0;\n    nslow1 = 0;\n    nslow2 = 0;\n\n    return HybridNonLinearSolverSpace::Running;\n}\n\ntemplate<typename FunctorType, typename Scalar>\nHybridNonLinearSolverSpace::Status\nHybridNonLinearSolver<FunctorType,Scalar>::solveOneStep(FVectorType  &x)\n{\n    using std::abs;\n    \n    eigen_assert(x.size()==n); // check the caller is not cheating us\n\n    Index j;\n    std::vector<JacobiRotation<Scalar> > v_givens(n), w_givens(n);\n\n    jeval = true;\n\n    /* calculate the jacobian matrix. */\n    if ( functor.df(x, fjac) < 0)\n        return HybridNonLinearSolverSpace::UserAsked;\n    ++njev;\n\n    wa2 = fjac.colwise().blueNorm();\n\n    /* on the first iteration and if external scaling is not used, scale according */\n    /* to the norms of the columns of the initial jacobian. */\n    if (iter == 1) {\n        if (!useExternalScaling)\n            for (j = 0; j < n; ++j)\n                diag[j] = (wa2[j]==0.) ? 1. : wa2[j];\n\n        /* on the first iteration, calculate the norm of the scaled x */\n        /* and initialize the step bound delta. */\n        xnorm = diag.cwiseProduct(x).stableNorm();\n        delta = parameters.factor * xnorm;\n        if (delta == 0.)\n            delta = parameters.factor;\n    }\n\n    /* compute the qr factorization of the jacobian. */\n    HouseholderQR<JacobianType> qrfac(fjac); // no pivoting:\n\n    /* copy the triangular factor of the qr factorization into r. */\n    R = qrfac.matrixQR();\n\n    /* accumulate the orthogonal factor in fjac. */\n    fjac = qrfac.householderQ();\n\n    /* form (q transpose)*fvec and store in qtf. */\n    qtf = fjac.transpose() * fvec;\n\n    /* rescale if necessary. */\n    if (!useExternalScaling)\n        diag = diag.cwiseMax(wa2);\n\n    while (true) {\n        /* determine the direction p. */\n        internal::dogleg<Scalar>(R, diag, qtf, delta, wa1);\n\n        /* store the direction p and x + p. calculate the norm of p. */\n        wa1 = -wa1;\n        wa2 = x + wa1;\n        pnorm = diag.cwiseProduct(wa1).stableNorm();\n\n        /* on the first iteration, adjust the initial step bound. */\n        if (iter == 1)\n            delta = (std::min)(delta,pnorm);\n\n        /* evaluate the function at x + p and calculate its norm. */\n        if ( functor(wa2, wa4) < 0)\n            return HybridNonLinearSolverSpace::UserAsked;\n        ++nfev;\n        fnorm1 = wa4.stableNorm();\n\n        /* compute the scaled actual reduction. */\n        actred = -1.;\n        if (fnorm1 < fnorm) /* Computing 2nd power */\n            actred = 1. - numext::abs2(fnorm1 / fnorm);\n\n        /* compute the scaled predicted reduction. */\n        wa3 = R.template triangularView<Upper>()*wa1 + qtf;\n        temp = wa3.stableNorm();\n        prered = 0.;\n        if (temp < fnorm) /* Computing 2nd power */\n            prered = 1. - numext::abs2(temp / fnorm);\n\n        /* compute the ratio of the actual to the predicted reduction. */\n        ratio = 0.;\n        if (prered > 0.)\n            ratio = actred / prered;\n\n        /* update the step bound. */\n        if (ratio < Scalar(.1)) {\n            ncsuc = 0;\n            ++ncfail;\n            delta = Scalar(.5) * delta;\n        } else {\n            ncfail = 0;\n            ++ncsuc;\n            if (ratio >= Scalar(.5) || ncsuc > 1)\n                delta = (std::max)(delta, pnorm / Scalar(.5));\n            if (abs(ratio - 1.) <= Scalar(.1)) {\n                delta = pnorm / Scalar(.5);\n            }\n        }\n\n        /* test for successful iteration. */\n        if (ratio >= Scalar(1e-4)) {\n            /* successful iteration. update x, fvec, and their norms. */\n            x = wa2;\n            wa2 = diag.cwiseProduct(x);\n            fvec = wa4;\n            xnorm = wa2.stableNorm();\n            fnorm = fnorm1;\n            ++iter;\n        }\n\n        /* determine the progress of the iteration. */\n        ++nslow1;\n        if (actred >= Scalar(.001))\n            nslow1 = 0;\n        if (jeval)\n            ++nslow2;\n        if (actred >= Scalar(.1))\n            nslow2 = 0;\n\n        /* test for convergence. */\n        if (delta <= parameters.xtol * xnorm || fnorm == 0.)\n            return HybridNonLinearSolverSpace::RelativeErrorTooSmall;\n\n        /* tests for termination and stringent tolerances. */\n        if (nfev >= parameters.maxfev)\n            return HybridNonLinearSolverSpace::TooManyFunctionEvaluation;\n        if (Scalar(.1) * (std::max)(Scalar(.1) * delta, pnorm) <= NumTraits<Scalar>::epsilon() * xnorm)\n            return HybridNonLinearSolverSpace::TolTooSmall;\n        if (nslow2 == 5)\n            return HybridNonLinearSolverSpace::NotMakingProgressJacobian;\n        if (nslow1 == 10)\n            return HybridNonLinearSolverSpace::NotMakingProgressIterations;\n\n        /* criterion for recalculating jacobian. */\n        if (ncfail == 2)\n            break; // leave inner loop and go for the next outer loop iteration\n\n        /* calculate the rank one modification to the jacobian */\n        /* and update qtf if necessary. */\n        wa1 = diag.cwiseProduct( diag.cwiseProduct(wa1)/pnorm );\n        wa2 = fjac.transpose() * wa4;\n        if (ratio >= Scalar(1e-4))\n            qtf = wa2;\n        wa2 = (wa2-wa3)/pnorm;\n\n        /* compute the qr factorization of the updated jacobian. */\n        internal::r1updt<Scalar>(R, wa1, v_givens, w_givens, wa2, wa3, &sing);\n        internal::r1mpyq<Scalar>(n, n, fjac.data(), v_givens, w_givens);\n        internal::r1mpyq<Scalar>(1, n, qtf.data(), v_givens, w_givens);\n\n        jeval = false;\n    }\n    return HybridNonLinearSolverSpace::Running;\n}\n\ntemplate<typename FunctorType, typename Scalar>\nHybridNonLinearSolverSpace::Status\nHybridNonLinearSolver<FunctorType,Scalar>::solve(FVectorType  &x)\n{\n    HybridNonLinearSolverSpace::Status status = solveInit(x);\n    if (status==HybridNonLinearSolverSpace::ImproperInputParameters)\n        return status;\n    while (status==HybridNonLinearSolverSpace::Running)\n        status = solveOneStep(x);\n    return status;\n}\n\n\n\ntemplate<typename FunctorType, typename Scalar>\nHybridNonLinearSolverSpace::Status\nHybridNonLinearSolver<FunctorType,Scalar>::hybrd1(\n        FVectorType  &x,\n        const Scalar tol\n        )\n{\n    n = x.size();\n\n    /* check the input parameters for errors. */\n    if (n <= 0 || tol < 0.)\n        return HybridNonLinearSolverSpace::ImproperInputParameters;\n\n    resetParameters();\n    parameters.maxfev = 200*(n+1);\n    parameters.xtol = tol;\n\n    diag.setConstant(n, 1.);\n    useExternalScaling = true;\n    return solveNumericalDiff(x);\n}\n\ntemplate<typename FunctorType, typename Scalar>\nHybridNonLinearSolverSpace::Status\nHybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiffInit(FVectorType  &x)\n{\n    n = x.size();\n\n    if (parameters.nb_of_subdiagonals<0) parameters.nb_of_subdiagonals= n-1;\n    if (parameters.nb_of_superdiagonals<0) parameters.nb_of_superdiagonals= n-1;\n\n    wa1.resize(n); wa2.resize(n); wa3.resize(n); wa4.resize(n);\n    qtf.resize(n);\n    fjac.resize(n, n);\n    fvec.resize(n);\n    if (!useExternalScaling)\n        diag.resize(n);\n    eigen_assert( (!useExternalScaling || diag.size()==n) && \"When useExternalScaling is set, the caller must provide a valid 'diag'\");\n\n    /* Function Body */\n    nfev = 0;\n    njev = 0;\n\n    /*     check the input parameters for errors. */\n    if (n <= 0 || parameters.xtol < 0. || parameters.maxfev <= 0 || parameters.nb_of_subdiagonals< 0 || parameters.nb_of_superdiagonals< 0 || parameters.factor <= 0. )\n        return HybridNonLinearSolverSpace::ImproperInputParameters;\n    if (useExternalScaling)\n        for (Index j = 0; j < n; ++j)\n            if (diag[j] <= 0.)\n                return HybridNonLinearSolverSpace::ImproperInputParameters;\n\n    /*     evaluate the function at the starting point */\n    /*     and calculate its norm. */\n    nfev = 1;\n    if ( functor(x, fvec) < 0)\n        return HybridNonLinearSolverSpace::UserAsked;\n    fnorm = fvec.stableNorm();\n\n    /*     initialize iteration counter and monitors. */\n    iter = 1;\n    ncsuc = 0;\n    ncfail = 0;\n    nslow1 = 0;\n    nslow2 = 0;\n\n    return HybridNonLinearSolverSpace::Running;\n}\n\ntemplate<typename FunctorType, typename Scalar>\nHybridNonLinearSolverSpace::Status\nHybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiffOneStep(FVectorType  &x)\n{\n    using std::sqrt;\n    using std::abs;\n    \n    assert(x.size()==n); // check the caller is not cheating us\n\n    Index j;\n    std::vector<JacobiRotation<Scalar> > v_givens(n), w_givens(n);\n\n    jeval = true;\n    if (parameters.nb_of_subdiagonals<0) parameters.nb_of_subdiagonals= n-1;\n    if (parameters.nb_of_superdiagonals<0) parameters.nb_of_superdiagonals= n-1;\n\n    /* calculate the jacobian matrix. */\n    if (internal::fdjac1(functor, x, fvec, fjac, parameters.nb_of_subdiagonals, parameters.nb_of_superdiagonals, parameters.epsfcn) <0)\n        return HybridNonLinearSolverSpace::UserAsked;\n    nfev += (std::min)(parameters.nb_of_subdiagonals+parameters.nb_of_superdiagonals+ 1, n);\n\n    wa2 = fjac.colwise().blueNorm();\n\n    /* on the first iteration and if external scaling is not used, scale according */\n    /* to the norms of the columns of the initial jacobian. */\n    if (iter == 1) {\n        if (!useExternalScaling)\n            for (j = 0; j < n; ++j)\n                diag[j] = (wa2[j]==0.) ? 1. : wa2[j];\n\n        /* on the first iteration, calculate the norm of the scaled x */\n        /* and initialize the step bound delta. */\n        xnorm = diag.cwiseProduct(x).stableNorm();\n        delta = parameters.factor * xnorm;\n        if (delta == 0.)\n            delta = parameters.factor;\n    }\n\n    /* compute the qr factorization of the jacobian. */\n    HouseholderQR<JacobianType> qrfac(fjac); // no pivoting:\n\n    /* copy the triangular factor of the qr factorization into r. */\n    R = qrfac.matrixQR();\n\n    /* accumulate the orthogonal factor in fjac. */\n    fjac = qrfac.householderQ();\n\n    /* form (q transpose)*fvec and store in qtf. */\n    qtf = fjac.transpose() * fvec;\n\n    /* rescale if necessary. */\n    if (!useExternalScaling)\n        diag = diag.cwiseMax(wa2);\n\n    while (true) {\n        /* determine the direction p. */\n        internal::dogleg<Scalar>(R, diag, qtf, delta, wa1);\n\n        /* store the direction p and x + p. calculate the norm of p. */\n        wa1 = -wa1;\n        wa2 = x + wa1;\n        pnorm = diag.cwiseProduct(wa1).stableNorm();\n\n        /* on the first iteration, adjust the initial step bound. */\n        if (iter == 1)\n            delta = (std::min)(delta,pnorm);\n\n        /* evaluate the function at x + p and calculate its norm. */\n        if ( functor(wa2, wa4) < 0)\n            return HybridNonLinearSolverSpace::UserAsked;\n        ++nfev;\n        fnorm1 = wa4.stableNorm();\n\n        /* compute the scaled actual reduction. */\n        actred = -1.;\n        if (fnorm1 < fnorm) /* Computing 2nd power */\n            actred = 1. - numext::abs2(fnorm1 / fnorm);\n\n        /* compute the scaled predicted reduction. */\n        wa3 = R.template triangularView<Upper>()*wa1 + qtf;\n        temp = wa3.stableNorm();\n        prered = 0.;\n        if (temp < fnorm) /* Computing 2nd power */\n            prered = 1. - numext::abs2(temp / fnorm);\n\n        /* compute the ratio of the actual to the predicted reduction. */\n        ratio = 0.;\n        if (prered > 0.)\n            ratio = actred / prered;\n\n        /* update the step bound. */\n        if (ratio < Scalar(.1)) {\n            ncsuc = 0;\n            ++ncfail;\n            delta = Scalar(.5) * delta;\n        } else {\n            ncfail = 0;\n            ++ncsuc;\n            if (ratio >= Scalar(.5) || ncsuc > 1)\n                delta = (std::max)(delta, pnorm / Scalar(.5));\n            if (abs(ratio - 1.) <= Scalar(.1)) {\n                delta = pnorm / Scalar(.5);\n            }\n        }\n\n        /* test for successful iteration. */\n        if (ratio >= Scalar(1e-4)) {\n            /* successful iteration. update x, fvec, and their norms. */\n            x = wa2;\n            wa2 = diag.cwiseProduct(x);\n            fvec = wa4;\n            xnorm = wa2.stableNorm();\n            fnorm = fnorm1;\n            ++iter;\n        }\n\n        /* determine the progress of the iteration. */\n        ++nslow1;\n        if (actred >= Scalar(.001))\n            nslow1 = 0;\n        if (jeval)\n            ++nslow2;\n        if (actred >= Scalar(.1))\n            nslow2 = 0;\n\n        /* test for convergence. */\n        if (delta <= parameters.xtol * xnorm || fnorm == 0.)\n            return HybridNonLinearSolverSpace::RelativeErrorTooSmall;\n\n        /* tests for termination and stringent tolerances. */\n        if (nfev >= parameters.maxfev)\n            return HybridNonLinearSolverSpace::TooManyFunctionEvaluation;\n        if (Scalar(.1) * (std::max)(Scalar(.1) * delta, pnorm) <= NumTraits<Scalar>::epsilon() * xnorm)\n            return HybridNonLinearSolverSpace::TolTooSmall;\n        if (nslow2 == 5)\n            return HybridNonLinearSolverSpace::NotMakingProgressJacobian;\n        if (nslow1 == 10)\n            return HybridNonLinearSolverSpace::NotMakingProgressIterations;\n\n        /* criterion for recalculating jacobian. */\n        if (ncfail == 2)\n            break; // leave inner loop and go for the next outer loop iteration\n\n        /* calculate the rank one modification to the jacobian */\n        /* and update qtf if necessary. */\n        wa1 = diag.cwiseProduct( diag.cwiseProduct(wa1)/pnorm );\n        wa2 = fjac.transpose() * wa4;\n        if (ratio >= Scalar(1e-4))\n            qtf = wa2;\n        wa2 = (wa2-wa3)/pnorm;\n\n        /* compute the qr factorization of the updated jacobian. */\n        internal::r1updt<Scalar>(R, wa1, v_givens, w_givens, wa2, wa3, &sing);\n        internal::r1mpyq<Scalar>(n, n, fjac.data(), v_givens, w_givens);\n        internal::r1mpyq<Scalar>(1, n, qtf.data(), v_givens, w_givens);\n\n        jeval = false;\n    }\n    return HybridNonLinearSolverSpace::Running;\n}\n\ntemplate<typename FunctorType, typename Scalar>\nHybridNonLinearSolverSpace::Status\nHybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiff(FVectorType  &x)\n{\n    HybridNonLinearSolverSpace::Status status = solveNumericalDiffInit(x);\n    if (status==HybridNonLinearSolverSpace::ImproperInputParameters)\n        return status;\n    while (status==HybridNonLinearSolverSpace::Running)\n        status = solveNumericalDiffOneStep(x);\n    return status;\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_HYBRIDNONLINEARSOLVER_H\n\n//vim: ai ts=4 sts=4 et sw=4\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/NonLinearOptimization/LevenbergMarquardt.h",
    "content": "// -*- coding: utf-8\n// vim: set fileencoding=utf-8\n\n// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_LEVENBERGMARQUARDT__H\n#define EIGEN_LEVENBERGMARQUARDT__H\n\nnamespace Eigen { \n\nnamespace LevenbergMarquardtSpace {\n    enum Status {\n        NotStarted = -2,\n        Running = -1,\n        ImproperInputParameters = 0,\n        RelativeReductionTooSmall = 1,\n        RelativeErrorTooSmall = 2,\n        RelativeErrorAndReductionTooSmall = 3,\n        CosinusTooSmall = 4,\n        TooManyFunctionEvaluation = 5,\n        FtolTooSmall = 6,\n        XtolTooSmall = 7,\n        GtolTooSmall = 8,\n        UserAsked = 9\n    };\n}\n\n\n\n/**\n  * \\ingroup NonLinearOptimization_Module\n  * \\brief Performs non linear optimization over a non-linear function,\n  * using a variant of the Levenberg Marquardt algorithm.\n  *\n  * Check wikipedia for more information.\n  * http://en.wikipedia.org/wiki/Levenberg%E2%80%93Marquardt_algorithm\n  */\ntemplate<typename FunctorType, typename Scalar=double>\nclass LevenbergMarquardt\n{\n    static Scalar sqrt_epsilon()\n    {\n      using std::sqrt;\n      return sqrt(NumTraits<Scalar>::epsilon());\n    }\n    \npublic:\n    LevenbergMarquardt(FunctorType &_functor)\n        : functor(_functor) { nfev = njev = iter = 0;  fnorm = gnorm = 0.; useExternalScaling=false; }\n\n    typedef DenseIndex Index;\n    \n    struct Parameters {\n        Parameters()\n            : factor(Scalar(100.))\n            , maxfev(400)\n            , ftol(sqrt_epsilon())\n            , xtol(sqrt_epsilon())\n            , gtol(Scalar(0.))\n            , epsfcn(Scalar(0.)) {}\n        Scalar factor;\n        Index maxfev;   // maximum number of function evaluation\n        Scalar ftol;\n        Scalar xtol;\n        Scalar gtol;\n        Scalar epsfcn;\n    };\n\n    typedef Matrix< Scalar, Dynamic, 1 > FVectorType;\n    typedef Matrix< Scalar, Dynamic, Dynamic > JacobianType;\n\n    LevenbergMarquardtSpace::Status lmder1(\n            FVectorType &x,\n            const Scalar tol = sqrt_epsilon()\n            );\n\n    LevenbergMarquardtSpace::Status minimize(FVectorType &x);\n    LevenbergMarquardtSpace::Status minimizeInit(FVectorType &x);\n    LevenbergMarquardtSpace::Status minimizeOneStep(FVectorType &x);\n\n    static LevenbergMarquardtSpace::Status lmdif1(\n            FunctorType &functor,\n            FVectorType &x,\n            Index *nfev,\n            const Scalar tol = sqrt_epsilon()\n            );\n\n    LevenbergMarquardtSpace::Status lmstr1(\n            FVectorType  &x,\n            const Scalar tol = sqrt_epsilon()\n            );\n\n    LevenbergMarquardtSpace::Status minimizeOptimumStorage(FVectorType  &x);\n    LevenbergMarquardtSpace::Status minimizeOptimumStorageInit(FVectorType  &x);\n    LevenbergMarquardtSpace::Status minimizeOptimumStorageOneStep(FVectorType  &x);\n\n    void resetParameters(void) { parameters = Parameters(); }\n\n    Parameters parameters;\n    FVectorType  fvec, qtf, diag;\n    JacobianType fjac;\n    PermutationMatrix<Dynamic,Dynamic> permutation;\n    Index nfev;\n    Index njev;\n    Index iter;\n    Scalar fnorm, gnorm;\n    bool useExternalScaling; \n\n    Scalar lm_param(void) { return par; }\nprivate:\n    \n    FunctorType &functor;\n    Index n;\n    Index m;\n    FVectorType wa1, wa2, wa3, wa4;\n\n    Scalar par, sum;\n    Scalar temp, temp1, temp2;\n    Scalar delta;\n    Scalar ratio;\n    Scalar pnorm, xnorm, fnorm1, actred, dirder, prered;\n\n    LevenbergMarquardt& operator=(const LevenbergMarquardt&);\n};\n\ntemplate<typename FunctorType, typename Scalar>\nLevenbergMarquardtSpace::Status\nLevenbergMarquardt<FunctorType,Scalar>::lmder1(\n        FVectorType  &x,\n        const Scalar tol\n        )\n{\n    n = x.size();\n    m = functor.values();\n\n    /* check the input parameters for errors. */\n    if (n <= 0 || m < n || tol < 0.)\n        return LevenbergMarquardtSpace::ImproperInputParameters;\n\n    resetParameters();\n    parameters.ftol = tol;\n    parameters.xtol = tol;\n    parameters.maxfev = 100*(n+1);\n\n    return minimize(x);\n}\n\n\ntemplate<typename FunctorType, typename Scalar>\nLevenbergMarquardtSpace::Status\nLevenbergMarquardt<FunctorType,Scalar>::minimize(FVectorType  &x)\n{\n    LevenbergMarquardtSpace::Status status = minimizeInit(x);\n    if (status==LevenbergMarquardtSpace::ImproperInputParameters)\n        return status;\n    do {\n        status = minimizeOneStep(x);\n    } while (status==LevenbergMarquardtSpace::Running);\n    return status;\n}\n\ntemplate<typename FunctorType, typename Scalar>\nLevenbergMarquardtSpace::Status\nLevenbergMarquardt<FunctorType,Scalar>::minimizeInit(FVectorType  &x)\n{\n    n = x.size();\n    m = functor.values();\n\n    wa1.resize(n); wa2.resize(n); wa3.resize(n);\n    wa4.resize(m);\n    fvec.resize(m);\n    fjac.resize(m, n);\n    if (!useExternalScaling)\n        diag.resize(n);\n    eigen_assert( (!useExternalScaling || diag.size()==n) && \"When useExternalScaling is set, the caller must provide a valid 'diag'\");\n    qtf.resize(n);\n\n    /* Function Body */\n    nfev = 0;\n    njev = 0;\n\n    /*     check the input parameters for errors. */\n    if (n <= 0 || m < n || parameters.ftol < 0. || parameters.xtol < 0. || parameters.gtol < 0. || parameters.maxfev <= 0 || parameters.factor <= 0.)\n        return LevenbergMarquardtSpace::ImproperInputParameters;\n\n    if (useExternalScaling)\n        for (Index j = 0; j < n; ++j)\n            if (diag[j] <= 0.)\n                return LevenbergMarquardtSpace::ImproperInputParameters;\n\n    /*     evaluate the function at the starting point */\n    /*     and calculate its norm. */\n    nfev = 1;\n    if ( functor(x, fvec) < 0)\n        return LevenbergMarquardtSpace::UserAsked;\n    fnorm = fvec.stableNorm();\n\n    /*     initialize levenberg-marquardt parameter and iteration counter. */\n    par = 0.;\n    iter = 1;\n\n    return LevenbergMarquardtSpace::NotStarted;\n}\n\ntemplate<typename FunctorType, typename Scalar>\nLevenbergMarquardtSpace::Status\nLevenbergMarquardt<FunctorType,Scalar>::minimizeOneStep(FVectorType  &x)\n{\n    using std::abs;\n    using std::sqrt;\n\n    eigen_assert(x.size()==n); // check the caller is not cheating us\n\n    /* calculate the jacobian matrix. */\n    Index df_ret = functor.df(x, fjac);\n    if (df_ret<0)\n        return LevenbergMarquardtSpace::UserAsked;\n    if (df_ret>0)\n        // numerical diff, we evaluated the function df_ret times\n        nfev += df_ret;\n    else njev++;\n\n    /* compute the qr factorization of the jacobian. */\n    wa2 = fjac.colwise().blueNorm();\n    ColPivHouseholderQR<JacobianType> qrfac(fjac);\n    fjac = qrfac.matrixQR();\n    permutation = qrfac.colsPermutation();\n\n    /* on the first iteration and if external scaling is not used, scale according */\n    /* to the norms of the columns of the initial jacobian. */\n    if (iter == 1) {\n        if (!useExternalScaling)\n            for (Index j = 0; j < n; ++j)\n                diag[j] = (wa2[j]==0.)? 1. : wa2[j];\n\n        /* on the first iteration, calculate the norm of the scaled x */\n        /* and initialize the step bound delta. */\n        xnorm = diag.cwiseProduct(x).stableNorm();\n        delta = parameters.factor * xnorm;\n        if (delta == 0.)\n            delta = parameters.factor;\n    }\n\n    /* form (q transpose)*fvec and store the first n components in */\n    /* qtf. */\n    wa4 = fvec;\n    wa4.applyOnTheLeft(qrfac.householderQ().adjoint());\n    qtf = wa4.head(n);\n\n    /* compute the norm of the scaled gradient. */\n    gnorm = 0.;\n    if (fnorm != 0.)\n        for (Index j = 0; j < n; ++j)\n            if (wa2[permutation.indices()[j]] != 0.)\n                gnorm = (std::max)(gnorm, abs( fjac.col(j).head(j+1).dot(qtf.head(j+1)/fnorm) / wa2[permutation.indices()[j]]));\n\n    /* test for convergence of the gradient norm. */\n    if (gnorm <= parameters.gtol)\n        return LevenbergMarquardtSpace::CosinusTooSmall;\n\n    /* rescale if necessary. */\n    if (!useExternalScaling)\n        diag = diag.cwiseMax(wa2);\n\n    do {\n\n        /* determine the levenberg-marquardt parameter. */\n        internal::lmpar2<Scalar>(qrfac, diag, qtf, delta, par, wa1);\n\n        /* store the direction p and x + p. calculate the norm of p. */\n        wa1 = -wa1;\n        wa2 = x + wa1;\n        pnorm = diag.cwiseProduct(wa1).stableNorm();\n\n        /* on the first iteration, adjust the initial step bound. */\n        if (iter == 1)\n            delta = (std::min)(delta,pnorm);\n\n        /* evaluate the function at x + p and calculate its norm. */\n        if ( functor(wa2, wa4) < 0)\n            return LevenbergMarquardtSpace::UserAsked;\n        ++nfev;\n        fnorm1 = wa4.stableNorm();\n\n        /* compute the scaled actual reduction. */\n        actred = -1.;\n        if (Scalar(.1) * fnorm1 < fnorm)\n            actred = 1. - numext::abs2(fnorm1 / fnorm);\n\n        /* compute the scaled predicted reduction and */\n        /* the scaled directional derivative. */\n        wa3 = fjac.template triangularView<Upper>() * (qrfac.colsPermutation().inverse() *wa1);\n        temp1 = numext::abs2(wa3.stableNorm() / fnorm);\n        temp2 = numext::abs2(sqrt(par) * pnorm / fnorm);\n        prered = temp1 + temp2 / Scalar(.5);\n        dirder = -(temp1 + temp2);\n\n        /* compute the ratio of the actual to the predicted */\n        /* reduction. */\n        ratio = 0.;\n        if (prered != 0.)\n            ratio = actred / prered;\n\n        /* update the step bound. */\n        if (ratio <= Scalar(.25)) {\n            if (actred >= 0.)\n                temp = Scalar(.5);\n            if (actred < 0.)\n                temp = Scalar(.5) * dirder / (dirder + Scalar(.5) * actred);\n            if (Scalar(.1) * fnorm1 >= fnorm || temp < Scalar(.1))\n                temp = Scalar(.1);\n            /* Computing MIN */\n            delta = temp * (std::min)(delta, pnorm / Scalar(.1));\n            par /= temp;\n        } else if (!(par != 0. && ratio < Scalar(.75))) {\n            delta = pnorm / Scalar(.5);\n            par = Scalar(.5) * par;\n        }\n\n        /* test for successful iteration. */\n        if (ratio >= Scalar(1e-4)) {\n            /* successful iteration. update x, fvec, and their norms. */\n            x = wa2;\n            wa2 = diag.cwiseProduct(x);\n            fvec = wa4;\n            xnorm = wa2.stableNorm();\n            fnorm = fnorm1;\n            ++iter;\n        }\n\n        /* tests for convergence. */\n        if (abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1. && delta <= parameters.xtol * xnorm)\n            return LevenbergMarquardtSpace::RelativeErrorAndReductionTooSmall;\n        if (abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1.)\n            return LevenbergMarquardtSpace::RelativeReductionTooSmall;\n        if (delta <= parameters.xtol * xnorm)\n            return LevenbergMarquardtSpace::RelativeErrorTooSmall;\n\n        /* tests for termination and stringent tolerances. */\n        if (nfev >= parameters.maxfev)\n            return LevenbergMarquardtSpace::TooManyFunctionEvaluation;\n        if (abs(actred) <= NumTraits<Scalar>::epsilon() && prered <= NumTraits<Scalar>::epsilon() && Scalar(.5) * ratio <= 1.)\n            return LevenbergMarquardtSpace::FtolTooSmall;\n        if (delta <= NumTraits<Scalar>::epsilon() * xnorm)\n            return LevenbergMarquardtSpace::XtolTooSmall;\n        if (gnorm <= NumTraits<Scalar>::epsilon())\n            return LevenbergMarquardtSpace::GtolTooSmall;\n\n    } while (ratio < Scalar(1e-4));\n\n    return LevenbergMarquardtSpace::Running;\n}\n\ntemplate<typename FunctorType, typename Scalar>\nLevenbergMarquardtSpace::Status\nLevenbergMarquardt<FunctorType,Scalar>::lmstr1(\n        FVectorType  &x,\n        const Scalar tol\n        )\n{\n    n = x.size();\n    m = functor.values();\n\n    /* check the input parameters for errors. */\n    if (n <= 0 || m < n || tol < 0.)\n        return LevenbergMarquardtSpace::ImproperInputParameters;\n\n    resetParameters();\n    parameters.ftol = tol;\n    parameters.xtol = tol;\n    parameters.maxfev = 100*(n+1);\n\n    return minimizeOptimumStorage(x);\n}\n\ntemplate<typename FunctorType, typename Scalar>\nLevenbergMarquardtSpace::Status\nLevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageInit(FVectorType  &x)\n{\n    n = x.size();\n    m = functor.values();\n\n    wa1.resize(n); wa2.resize(n); wa3.resize(n);\n    wa4.resize(m);\n    fvec.resize(m);\n    // Only R is stored in fjac. Q is only used to compute 'qtf', which is\n    // Q.transpose()*rhs. qtf will be updated using givens rotation,\n    // instead of storing them in Q.\n    // The purpose it to only use a nxn matrix, instead of mxn here, so\n    // that we can handle cases where m>>n :\n    fjac.resize(n, n);\n    if (!useExternalScaling)\n        diag.resize(n);\n    eigen_assert( (!useExternalScaling || diag.size()==n) && \"When useExternalScaling is set, the caller must provide a valid 'diag'\");\n    qtf.resize(n);\n\n    /* Function Body */\n    nfev = 0;\n    njev = 0;\n\n    /*     check the input parameters for errors. */\n    if (n <= 0 || m < n || parameters.ftol < 0. || parameters.xtol < 0. || parameters.gtol < 0. || parameters.maxfev <= 0 || parameters.factor <= 0.)\n        return LevenbergMarquardtSpace::ImproperInputParameters;\n\n    if (useExternalScaling)\n        for (Index j = 0; j < n; ++j)\n            if (diag[j] <= 0.)\n                return LevenbergMarquardtSpace::ImproperInputParameters;\n\n    /*     evaluate the function at the starting point */\n    /*     and calculate its norm. */\n    nfev = 1;\n    if ( functor(x, fvec) < 0)\n        return LevenbergMarquardtSpace::UserAsked;\n    fnorm = fvec.stableNorm();\n\n    /*     initialize levenberg-marquardt parameter and iteration counter. */\n    par = 0.;\n    iter = 1;\n\n    return LevenbergMarquardtSpace::NotStarted;\n}\n\n\ntemplate<typename FunctorType, typename Scalar>\nLevenbergMarquardtSpace::Status\nLevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageOneStep(FVectorType  &x)\n{\n    using std::abs;\n    using std::sqrt;\n    \n    eigen_assert(x.size()==n); // check the caller is not cheating us\n\n    Index i, j;\n    bool sing;\n\n    /* compute the qr factorization of the jacobian matrix */\n    /* calculated one row at a time, while simultaneously */\n    /* forming (q transpose)*fvec and storing the first */\n    /* n components in qtf. */\n    qtf.fill(0.);\n    fjac.fill(0.);\n    Index rownb = 2;\n    for (i = 0; i < m; ++i) {\n        if (functor.df(x, wa3, rownb) < 0) return LevenbergMarquardtSpace::UserAsked;\n        internal::rwupdt<Scalar>(fjac, wa3, qtf, fvec[i]);\n        ++rownb;\n    }\n    ++njev;\n\n    /* if the jacobian is rank deficient, call qrfac to */\n    /* reorder its columns and update the components of qtf. */\n    sing = false;\n    for (j = 0; j < n; ++j) {\n        if (fjac(j,j) == 0.)\n            sing = true;\n        wa2[j] = fjac.col(j).head(j).stableNorm();\n    }\n    permutation.setIdentity(n);\n    if (sing) {\n        wa2 = fjac.colwise().blueNorm();\n        // TODO We have no unit test covering this code path, do not modify\n        // until it is carefully tested\n        ColPivHouseholderQR<JacobianType> qrfac(fjac);\n        fjac = qrfac.matrixQR();\n        wa1 = fjac.diagonal();\n        fjac.diagonal() = qrfac.hCoeffs();\n        permutation = qrfac.colsPermutation();\n        // TODO : avoid this:\n        for(Index ii=0; ii< fjac.cols(); ii++) fjac.col(ii).segment(ii+1, fjac.rows()-ii-1) *= fjac(ii,ii); // rescale vectors\n\n        for (j = 0; j < n; ++j) {\n            if (fjac(j,j) != 0.) {\n                sum = 0.;\n                for (i = j; i < n; ++i)\n                    sum += fjac(i,j) * qtf[i];\n                temp = -sum / fjac(j,j);\n                for (i = j; i < n; ++i)\n                    qtf[i] += fjac(i,j) * temp;\n            }\n            fjac(j,j) = wa1[j];\n        }\n    }\n\n    /* on the first iteration and if external scaling is not used, scale according */\n    /* to the norms of the columns of the initial jacobian. */\n    if (iter == 1) {\n        if (!useExternalScaling)\n            for (j = 0; j < n; ++j)\n                diag[j] = (wa2[j]==0.)? 1. : wa2[j];\n\n        /* on the first iteration, calculate the norm of the scaled x */\n        /* and initialize the step bound delta. */\n        xnorm = diag.cwiseProduct(x).stableNorm();\n        delta = parameters.factor * xnorm;\n        if (delta == 0.)\n            delta = parameters.factor;\n    }\n\n    /* compute the norm of the scaled gradient. */\n    gnorm = 0.;\n    if (fnorm != 0.)\n        for (j = 0; j < n; ++j)\n            if (wa2[permutation.indices()[j]] != 0.)\n                gnorm = (std::max)(gnorm, abs( fjac.col(j).head(j+1).dot(qtf.head(j+1)/fnorm) / wa2[permutation.indices()[j]]));\n\n    /* test for convergence of the gradient norm. */\n    if (gnorm <= parameters.gtol)\n        return LevenbergMarquardtSpace::CosinusTooSmall;\n\n    /* rescale if necessary. */\n    if (!useExternalScaling)\n        diag = diag.cwiseMax(wa2);\n\n    do {\n\n        /* determine the levenberg-marquardt parameter. */\n        internal::lmpar<Scalar>(fjac, permutation.indices(), diag, qtf, delta, par, wa1);\n\n        /* store the direction p and x + p. calculate the norm of p. */\n        wa1 = -wa1;\n        wa2 = x + wa1;\n        pnorm = diag.cwiseProduct(wa1).stableNorm();\n\n        /* on the first iteration, adjust the initial step bound. */\n        if (iter == 1)\n            delta = (std::min)(delta,pnorm);\n\n        /* evaluate the function at x + p and calculate its norm. */\n        if ( functor(wa2, wa4) < 0)\n            return LevenbergMarquardtSpace::UserAsked;\n        ++nfev;\n        fnorm1 = wa4.stableNorm();\n\n        /* compute the scaled actual reduction. */\n        actred = -1.;\n        if (Scalar(.1) * fnorm1 < fnorm)\n            actred = 1. - numext::abs2(fnorm1 / fnorm);\n\n        /* compute the scaled predicted reduction and */\n        /* the scaled directional derivative. */\n        wa3 = fjac.topLeftCorner(n,n).template triangularView<Upper>() * (permutation.inverse() * wa1);\n        temp1 = numext::abs2(wa3.stableNorm() / fnorm);\n        temp2 = numext::abs2(sqrt(par) * pnorm / fnorm);\n        prered = temp1 + temp2 / Scalar(.5);\n        dirder = -(temp1 + temp2);\n\n        /* compute the ratio of the actual to the predicted */\n        /* reduction. */\n        ratio = 0.;\n        if (prered != 0.)\n            ratio = actred / prered;\n\n        /* update the step bound. */\n        if (ratio <= Scalar(.25)) {\n            if (actred >= 0.)\n                temp = Scalar(.5);\n            if (actred < 0.)\n                temp = Scalar(.5) * dirder / (dirder + Scalar(.5) * actred);\n            if (Scalar(.1) * fnorm1 >= fnorm || temp < Scalar(.1))\n                temp = Scalar(.1);\n            /* Computing MIN */\n            delta = temp * (std::min)(delta, pnorm / Scalar(.1));\n            par /= temp;\n        } else if (!(par != 0. && ratio < Scalar(.75))) {\n            delta = pnorm / Scalar(.5);\n            par = Scalar(.5) * par;\n        }\n\n        /* test for successful iteration. */\n        if (ratio >= Scalar(1e-4)) {\n            /* successful iteration. update x, fvec, and their norms. */\n            x = wa2;\n            wa2 = diag.cwiseProduct(x);\n            fvec = wa4;\n            xnorm = wa2.stableNorm();\n            fnorm = fnorm1;\n            ++iter;\n        }\n\n        /* tests for convergence. */\n        if (abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1. && delta <= parameters.xtol * xnorm)\n            return LevenbergMarquardtSpace::RelativeErrorAndReductionTooSmall;\n        if (abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1.)\n            return LevenbergMarquardtSpace::RelativeReductionTooSmall;\n        if (delta <= parameters.xtol * xnorm)\n            return LevenbergMarquardtSpace::RelativeErrorTooSmall;\n\n        /* tests for termination and stringent tolerances. */\n        if (nfev >= parameters.maxfev)\n            return LevenbergMarquardtSpace::TooManyFunctionEvaluation;\n        if (abs(actred) <= NumTraits<Scalar>::epsilon() && prered <= NumTraits<Scalar>::epsilon() && Scalar(.5) * ratio <= 1.)\n            return LevenbergMarquardtSpace::FtolTooSmall;\n        if (delta <= NumTraits<Scalar>::epsilon() * xnorm)\n            return LevenbergMarquardtSpace::XtolTooSmall;\n        if (gnorm <= NumTraits<Scalar>::epsilon())\n            return LevenbergMarquardtSpace::GtolTooSmall;\n\n    } while (ratio < Scalar(1e-4));\n\n    return LevenbergMarquardtSpace::Running;\n}\n\ntemplate<typename FunctorType, typename Scalar>\nLevenbergMarquardtSpace::Status\nLevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorage(FVectorType  &x)\n{\n    LevenbergMarquardtSpace::Status status = minimizeOptimumStorageInit(x);\n    if (status==LevenbergMarquardtSpace::ImproperInputParameters)\n        return status;\n    do {\n        status = minimizeOptimumStorageOneStep(x);\n    } while (status==LevenbergMarquardtSpace::Running);\n    return status;\n}\n\ntemplate<typename FunctorType, typename Scalar>\nLevenbergMarquardtSpace::Status\nLevenbergMarquardt<FunctorType,Scalar>::lmdif1(\n        FunctorType &functor,\n        FVectorType  &x,\n        Index *nfev,\n        const Scalar tol\n        )\n{\n    Index n = x.size();\n    Index m = functor.values();\n\n    /* check the input parameters for errors. */\n    if (n <= 0 || m < n || tol < 0.)\n        return LevenbergMarquardtSpace::ImproperInputParameters;\n\n    NumericalDiff<FunctorType> numDiff(functor);\n    // embedded LevenbergMarquardt\n    LevenbergMarquardt<NumericalDiff<FunctorType>, Scalar > lm(numDiff);\n    lm.parameters.ftol = tol;\n    lm.parameters.xtol = tol;\n    lm.parameters.maxfev = 200*(n+1);\n\n    LevenbergMarquardtSpace::Status info = LevenbergMarquardtSpace::Status(lm.minimize(x));\n    if (nfev)\n        * nfev = lm.nfev;\n    return info;\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_LEVENBERGMARQUARDT__H\n\n//vim: ai ts=4 sts=4 et sw=4\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/NonLinearOptimization/chkder.h",
    "content": "#define chkder_log10e 0.43429448190325182765\n#define chkder_factor 100.\n\nnamespace Eigen { \n\nnamespace internal {\n\ntemplate<typename Scalar>\nvoid chkder(\n        const Matrix< Scalar, Dynamic, 1 >  &x,\n        const Matrix< Scalar, Dynamic, 1 >  &fvec,\n        const Matrix< Scalar, Dynamic, Dynamic > &fjac,\n        Matrix< Scalar, Dynamic, 1 >  &xp,\n        const Matrix< Scalar, Dynamic, 1 >  &fvecp,\n        int mode,\n        Matrix< Scalar, Dynamic, 1 >  &err\n        )\n{\n    using std::sqrt;\n    using std::abs;\n    using std::log;\n    \n    typedef DenseIndex Index;\n\n    const Scalar eps = sqrt(NumTraits<Scalar>::epsilon());\n    const Scalar epsf = chkder_factor * NumTraits<Scalar>::epsilon();\n    const Scalar epslog = chkder_log10e * log(eps);\n    Scalar temp;\n\n    const Index m = fvec.size(), n = x.size();\n\n    if (mode != 2) {\n        /* mode = 1. */\n        xp.resize(n);\n        for (Index j = 0; j < n; ++j) {\n            temp = eps * abs(x[j]);\n            if (temp == 0.)\n                temp = eps;\n            xp[j] = x[j] + temp;\n        }\n    }\n    else {\n        /* mode = 2. */\n        err.setZero(m); \n        for (Index j = 0; j < n; ++j) {\n            temp = abs(x[j]);\n            if (temp == 0.)\n                temp = 1.;\n            err += temp * fjac.col(j);\n        }\n        for (Index i = 0; i < m; ++i) {\n            temp = 1.;\n            if (fvec[i] != 0. && fvecp[i] != 0. && abs(fvecp[i] - fvec[i]) >= epsf * abs(fvec[i]))\n                temp = eps * abs((fvecp[i] - fvec[i]) / eps - err[i]) / (abs(fvec[i]) + abs(fvecp[i]));\n            err[i] = 1.;\n            if (temp > NumTraits<Scalar>::epsilon() && temp < eps)\n                err[i] = (chkder_log10e * log(temp) - epslog) / epslog;\n            if (temp >= eps)\n                err[i] = 0.;\n        }\n    }\n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/NonLinearOptimization/covar.h",
    "content": "namespace Eigen { \n\nnamespace internal {\n\ntemplate <typename Scalar>\nvoid covar(\n        Matrix< Scalar, Dynamic, Dynamic > &r,\n        const VectorXi &ipvt,\n        Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon()) )\n{\n    using std::abs;\n    typedef DenseIndex Index;\n\n    /* Local variables */\n    Index i, j, k, l, ii, jj;\n    bool sing;\n    Scalar temp;\n\n    /* Function Body */\n    const Index n = r.cols();\n    const Scalar tolr = tol * abs(r(0,0));\n    Matrix< Scalar, Dynamic, 1 > wa(n);\n    eigen_assert(ipvt.size()==n);\n\n    /* form the inverse of r in the full upper triangle of r. */\n    l = -1;\n    for (k = 0; k < n; ++k)\n        if (abs(r(k,k)) > tolr) {\n            r(k,k) = 1. / r(k,k);\n            for (j = 0; j <= k-1; ++j) {\n                temp = r(k,k) * r(j,k);\n                r(j,k) = 0.;\n                r.col(k).head(j+1) -= r.col(j).head(j+1) * temp;\n            }\n            l = k;\n        }\n\n    /* form the full upper triangle of the inverse of (r transpose)*r */\n    /* in the full upper triangle of r. */\n    for (k = 0; k <= l; ++k) {\n        for (j = 0; j <= k-1; ++j)\n            r.col(j).head(j+1) += r.col(k).head(j+1) * r(j,k);\n        r.col(k).head(k+1) *= r(k,k);\n    }\n\n    /* form the full lower triangle of the covariance matrix */\n    /* in the strict lower triangle of r and in wa. */\n    for (j = 0; j < n; ++j) {\n        jj = ipvt[j];\n        sing = j > l;\n        for (i = 0; i <= j; ++i) {\n            if (sing)\n                r(i,j) = 0.;\n            ii = ipvt[i];\n            if (ii > jj)\n                r(ii,jj) = r(i,j);\n            if (ii < jj)\n                r(jj,ii) = r(i,j);\n        }\n        wa[jj] = r(j,j);\n    }\n\n    /* symmetrize the covariance matrix in r. */\n    r.topLeftCorner(n,n).template triangularView<StrictlyUpper>() = r.topLeftCorner(n,n).transpose();\n    r.diagonal() = wa;\n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/NonLinearOptimization/dogleg.h",
    "content": "namespace Eigen { \n\nnamespace internal {\n\ntemplate <typename Scalar>\nvoid dogleg(\n        const Matrix< Scalar, Dynamic, Dynamic >  &qrfac,\n        const Matrix< Scalar, Dynamic, 1 >  &diag,\n        const Matrix< Scalar, Dynamic, 1 >  &qtb,\n        Scalar delta,\n        Matrix< Scalar, Dynamic, 1 >  &x)\n{\n    using std::abs;\n    using std::sqrt;\n    \n    typedef DenseIndex Index;\n\n    /* Local variables */\n    Index i, j;\n    Scalar sum, temp, alpha, bnorm;\n    Scalar gnorm, qnorm;\n    Scalar sgnorm;\n\n    /* Function Body */\n    const Scalar epsmch = NumTraits<Scalar>::epsilon();\n    const Index n = qrfac.cols();\n    eigen_assert(n==qtb.size());\n    eigen_assert(n==x.size());\n    eigen_assert(n==diag.size());\n    Matrix< Scalar, Dynamic, 1 >  wa1(n), wa2(n);\n\n    /* first, calculate the gauss-newton direction. */\n    for (j = n-1; j >=0; --j) {\n        temp = qrfac(j,j);\n        if (temp == 0.) {\n            temp = epsmch * qrfac.col(j).head(j+1).maxCoeff();\n            if (temp == 0.)\n                temp = epsmch;\n        }\n        if (j==n-1)\n            x[j] = qtb[j] / temp;\n        else\n            x[j] = (qtb[j] - qrfac.row(j).tail(n-j-1).dot(x.tail(n-j-1))) / temp;\n    }\n\n    /* test whether the gauss-newton direction is acceptable. */\n    qnorm = diag.cwiseProduct(x).stableNorm();\n    if (qnorm <= delta)\n        return;\n\n    // TODO : this path is not tested by Eigen unit tests\n\n    /* the gauss-newton direction is not acceptable. */\n    /* next, calculate the scaled gradient direction. */\n\n    wa1.fill(0.);\n    for (j = 0; j < n; ++j) {\n        wa1.tail(n-j) += qrfac.row(j).tail(n-j) * qtb[j];\n        wa1[j] /= diag[j];\n    }\n\n    /* calculate the norm of the scaled gradient and test for */\n    /* the special case in which the scaled gradient is zero. */\n    gnorm = wa1.stableNorm();\n    sgnorm = 0.;\n    alpha = delta / qnorm;\n    if (gnorm == 0.)\n        goto algo_end;\n\n    /* calculate the point along the scaled gradient */\n    /* at which the quadratic is minimized. */\n    wa1.array() /= (diag*gnorm).array();\n    // TODO : once unit tests cover this part,:\n    // wa2 = qrfac.template triangularView<Upper>() * wa1;\n    for (j = 0; j < n; ++j) {\n        sum = 0.;\n        for (i = j; i < n; ++i) {\n            sum += qrfac(j,i) * wa1[i];\n        }\n        wa2[j] = sum;\n    }\n    temp = wa2.stableNorm();\n    sgnorm = gnorm / temp / temp;\n\n    /* test whether the scaled gradient direction is acceptable. */\n    alpha = 0.;\n    if (sgnorm >= delta)\n        goto algo_end;\n\n    /* the scaled gradient direction is not acceptable. */\n    /* finally, calculate the point along the dogleg */\n    /* at which the quadratic is minimized. */\n    bnorm = qtb.stableNorm();\n    temp = bnorm / gnorm * (bnorm / qnorm) * (sgnorm / delta);\n    temp = temp - delta / qnorm * numext::abs2(sgnorm / delta) + sqrt(numext::abs2(temp - delta / qnorm) + (1.-numext::abs2(delta / qnorm)) * (1.-numext::abs2(sgnorm / delta)));\n    alpha = delta / qnorm * (1. - numext::abs2(sgnorm / delta)) / temp;\nalgo_end:\n\n    /* form appropriate convex combination of the gauss-newton */\n    /* direction and the scaled gradient direction. */\n    temp = (1.-alpha) * (std::min)(sgnorm,delta);\n    x = temp * wa1 + alpha * x;\n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/NonLinearOptimization/fdjac1.h",
    "content": "namespace Eigen { \n\nnamespace internal {\n\ntemplate<typename FunctorType, typename Scalar>\nDenseIndex fdjac1(\n        const FunctorType &Functor,\n        Matrix< Scalar, Dynamic, 1 >  &x,\n        Matrix< Scalar, Dynamic, 1 >  &fvec,\n        Matrix< Scalar, Dynamic, Dynamic > &fjac,\n        DenseIndex ml, DenseIndex mu,\n        Scalar epsfcn)\n{\n    using std::sqrt;\n    using std::abs;\n    \n    typedef DenseIndex Index;\n\n    /* Local variables */\n    Scalar h;\n    Index j, k;\n    Scalar eps, temp;\n    Index msum;\n    int iflag;\n    Index start, length;\n\n    /* Function Body */\n    const Scalar epsmch = NumTraits<Scalar>::epsilon();\n    const Index n = x.size();\n    eigen_assert(fvec.size()==n);\n    Matrix< Scalar, Dynamic, 1 >  wa1(n);\n    Matrix< Scalar, Dynamic, 1 >  wa2(n);\n\n    eps = sqrt((std::max)(epsfcn,epsmch));\n    msum = ml + mu + 1;\n    if (msum >= n) {\n        /* computation of dense approximate jacobian. */\n        for (j = 0; j < n; ++j) {\n            temp = x[j];\n            h = eps * abs(temp);\n            if (h == 0.)\n                h = eps;\n            x[j] = temp + h;\n            iflag = Functor(x, wa1);\n            if (iflag < 0)\n                return iflag;\n            x[j] = temp;\n            fjac.col(j) = (wa1-fvec)/h;\n        }\n\n    }else {\n        /* computation of banded approximate jacobian. */\n        for (k = 0; k < msum; ++k) {\n            for (j = k; (msum<0) ? (j>n): (j<n); j += msum) {\n                wa2[j] = x[j];\n                h = eps * abs(wa2[j]);\n                if (h == 0.) h = eps;\n                x[j] = wa2[j] + h;\n            }\n            iflag = Functor(x, wa1);\n            if (iflag < 0)\n                return iflag;\n            for (j = k; (msum<0) ? (j>n): (j<n); j += msum) {\n                x[j] = wa2[j];\n                h = eps * abs(wa2[j]);\n                if (h == 0.) h = eps;\n                fjac.col(j).setZero();\n                start = std::max<Index>(0,j-mu);\n                length = (std::min)(n-1, j+ml) - start + 1;\n                fjac.col(j).segment(start, length) = ( wa1.segment(start, length)-fvec.segment(start, length))/h;\n            }\n        }\n    }\n    return 0;\n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/NonLinearOptimization/lmpar.h",
    "content": "namespace Eigen { \n\nnamespace internal {\n\ntemplate <typename Scalar>\nvoid lmpar(\n        Matrix< Scalar, Dynamic, Dynamic > &r,\n        const VectorXi &ipvt,\n        const Matrix< Scalar, Dynamic, 1 >  &diag,\n        const Matrix< Scalar, Dynamic, 1 >  &qtb,\n        Scalar delta,\n        Scalar &par,\n        Matrix< Scalar, Dynamic, 1 >  &x)\n{\n    using std::abs;\n    using std::sqrt;\n    typedef DenseIndex Index;\n\n    /* Local variables */\n    Index i, j, l;\n    Scalar fp;\n    Scalar parc, parl;\n    Index iter;\n    Scalar temp, paru;\n    Scalar gnorm;\n    Scalar dxnorm;\n\n\n    /* Function Body */\n    const Scalar dwarf = (std::numeric_limits<Scalar>::min)();\n    const Index n = r.cols();\n    eigen_assert(n==diag.size());\n    eigen_assert(n==qtb.size());\n    eigen_assert(n==x.size());\n\n    Matrix< Scalar, Dynamic, 1 >  wa1, wa2;\n\n    /* compute and store in x the gauss-newton direction. if the */\n    /* jacobian is rank-deficient, obtain a least squares solution. */\n    Index nsing = n-1;\n    wa1 = qtb;\n    for (j = 0; j < n; ++j) {\n        if (r(j,j) == 0. && nsing == n-1)\n            nsing = j - 1;\n        if (nsing < n-1)\n            wa1[j] = 0.;\n    }\n    for (j = nsing; j>=0; --j) {\n        wa1[j] /= r(j,j);\n        temp = wa1[j];\n        for (i = 0; i < j ; ++i)\n            wa1[i] -= r(i,j) * temp;\n    }\n\n    for (j = 0; j < n; ++j)\n        x[ipvt[j]] = wa1[j];\n\n    /* initialize the iteration counter. */\n    /* evaluate the function at the origin, and test */\n    /* for acceptance of the gauss-newton direction. */\n    iter = 0;\n    wa2 = diag.cwiseProduct(x);\n    dxnorm = wa2.blueNorm();\n    fp = dxnorm - delta;\n    if (fp <= Scalar(0.1) * delta) {\n        par = 0;\n        return;\n    }\n\n    /* if the jacobian is not rank deficient, the newton */\n    /* step provides a lower bound, parl, for the zero of */\n    /* the function. otherwise set this bound to zero. */\n    parl = 0.;\n    if (nsing >= n-1) {\n        for (j = 0; j < n; ++j) {\n            l = ipvt[j];\n            wa1[j] = diag[l] * (wa2[l] / dxnorm);\n        }\n        // it's actually a triangularView.solveInplace(), though in a weird\n        // way:\n        for (j = 0; j < n; ++j) {\n            Scalar sum = 0.;\n            for (i = 0; i < j; ++i)\n                sum += r(i,j) * wa1[i];\n            wa1[j] = (wa1[j] - sum) / r(j,j);\n        }\n        temp = wa1.blueNorm();\n        parl = fp / delta / temp / temp;\n    }\n\n    /* calculate an upper bound, paru, for the zero of the function. */\n    for (j = 0; j < n; ++j)\n        wa1[j] = r.col(j).head(j+1).dot(qtb.head(j+1)) / diag[ipvt[j]];\n\n    gnorm = wa1.stableNorm();\n    paru = gnorm / delta;\n    if (paru == 0.)\n        paru = dwarf / (std::min)(delta,Scalar(0.1));\n\n    /* if the input par lies outside of the interval (parl,paru), */\n    /* set par to the closer endpoint. */\n    par = (std::max)(par,parl);\n    par = (std::min)(par,paru);\n    if (par == 0.)\n        par = gnorm / dxnorm;\n\n    /* beginning of an iteration. */\n    while (true) {\n        ++iter;\n\n        /* evaluate the function at the current value of par. */\n        if (par == 0.)\n            par = (std::max)(dwarf,Scalar(.001) * paru); /* Computing MAX */\n        wa1 = sqrt(par)* diag;\n\n        Matrix< Scalar, Dynamic, 1 > sdiag(n);\n        qrsolv<Scalar>(r, ipvt, wa1, qtb, x, sdiag);\n\n        wa2 = diag.cwiseProduct(x);\n        dxnorm = wa2.blueNorm();\n        temp = fp;\n        fp = dxnorm - delta;\n\n        /* if the function is small enough, accept the current value */\n        /* of par. also test for the exceptional cases where parl */\n        /* is zero or the number of iterations has reached 10. */\n        if (abs(fp) <= Scalar(0.1) * delta || (parl == 0. && fp <= temp && temp < 0.) || iter == 10)\n            break;\n\n        /* compute the newton correction. */\n        for (j = 0; j < n; ++j) {\n            l = ipvt[j];\n            wa1[j] = diag[l] * (wa2[l] / dxnorm);\n        }\n        for (j = 0; j < n; ++j) {\n            wa1[j] /= sdiag[j];\n            temp = wa1[j];\n            for (i = j+1; i < n; ++i)\n                wa1[i] -= r(i,j) * temp;\n        }\n        temp = wa1.blueNorm();\n        parc = fp / delta / temp / temp;\n\n        /* depending on the sign of the function, update parl or paru. */\n        if (fp > 0.)\n            parl = (std::max)(parl,par);\n        if (fp < 0.)\n            paru = (std::min)(paru,par);\n\n        /* compute an improved estimate for par. */\n        /* Computing MAX */\n        par = (std::max)(parl,par+parc);\n\n        /* end of an iteration. */\n    }\n\n    /* termination. */\n    if (iter == 0)\n        par = 0.;\n    return;\n}\n\ntemplate <typename Scalar>\nvoid lmpar2(\n        const ColPivHouseholderQR<Matrix< Scalar, Dynamic, Dynamic> > &qr,\n        const Matrix< Scalar, Dynamic, 1 >  &diag,\n        const Matrix< Scalar, Dynamic, 1 >  &qtb,\n        Scalar delta,\n        Scalar &par,\n        Matrix< Scalar, Dynamic, 1 >  &x)\n\n{\n    using std::sqrt;\n    using std::abs;\n    typedef DenseIndex Index;\n\n    /* Local variables */\n    Index j;\n    Scalar fp;\n    Scalar parc, parl;\n    Index iter;\n    Scalar temp, paru;\n    Scalar gnorm;\n    Scalar dxnorm;\n\n\n    /* Function Body */\n    const Scalar dwarf = (std::numeric_limits<Scalar>::min)();\n    const Index n = qr.matrixQR().cols();\n    eigen_assert(n==diag.size());\n    eigen_assert(n==qtb.size());\n\n    Matrix< Scalar, Dynamic, 1 >  wa1, wa2;\n\n    /* compute and store in x the gauss-newton direction. if the */\n    /* jacobian is rank-deficient, obtain a least squares solution. */\n\n//    const Index rank = qr.nonzeroPivots(); // exactly double(0.)\n    const Index rank = qr.rank(); // use a threshold\n    wa1 = qtb;\n    wa1.tail(n-rank).setZero();\n    qr.matrixQR().topLeftCorner(rank, rank).template triangularView<Upper>().solveInPlace(wa1.head(rank));\n\n    x = qr.colsPermutation()*wa1;\n\n    /* initialize the iteration counter. */\n    /* evaluate the function at the origin, and test */\n    /* for acceptance of the gauss-newton direction. */\n    iter = 0;\n    wa2 = diag.cwiseProduct(x);\n    dxnorm = wa2.blueNorm();\n    fp = dxnorm - delta;\n    if (fp <= Scalar(0.1) * delta) {\n        par = 0;\n        return;\n    }\n\n    /* if the jacobian is not rank deficient, the newton */\n    /* step provides a lower bound, parl, for the zero of */\n    /* the function. otherwise set this bound to zero. */\n    parl = 0.;\n    if (rank==n) {\n        wa1 = qr.colsPermutation().inverse() *  diag.cwiseProduct(wa2)/dxnorm;\n        qr.matrixQR().topLeftCorner(n, n).transpose().template triangularView<Lower>().solveInPlace(wa1);\n        temp = wa1.blueNorm();\n        parl = fp / delta / temp / temp;\n    }\n\n    /* calculate an upper bound, paru, for the zero of the function. */\n    for (j = 0; j < n; ++j)\n        wa1[j] = qr.matrixQR().col(j).head(j+1).dot(qtb.head(j+1)) / diag[qr.colsPermutation().indices()(j)];\n\n    gnorm = wa1.stableNorm();\n    paru = gnorm / delta;\n    if (paru == 0.)\n        paru = dwarf / (std::min)(delta,Scalar(0.1));\n\n    /* if the input par lies outside of the interval (parl,paru), */\n    /* set par to the closer endpoint. */\n    par = (std::max)(par,parl);\n    par = (std::min)(par,paru);\n    if (par == 0.)\n        par = gnorm / dxnorm;\n\n    /* beginning of an iteration. */\n    Matrix< Scalar, Dynamic, Dynamic > s = qr.matrixQR();\n    while (true) {\n        ++iter;\n\n        /* evaluate the function at the current value of par. */\n        if (par == 0.)\n            par = (std::max)(dwarf,Scalar(.001) * paru); /* Computing MAX */\n        wa1 = sqrt(par)* diag;\n\n        Matrix< Scalar, Dynamic, 1 > sdiag(n);\n        qrsolv<Scalar>(s, qr.colsPermutation().indices(), wa1, qtb, x, sdiag);\n\n        wa2 = diag.cwiseProduct(x);\n        dxnorm = wa2.blueNorm();\n        temp = fp;\n        fp = dxnorm - delta;\n\n        /* if the function is small enough, accept the current value */\n        /* of par. also test for the exceptional cases where parl */\n        /* is zero or the number of iterations has reached 10. */\n        if (abs(fp) <= Scalar(0.1) * delta || (parl == 0. && fp <= temp && temp < 0.) || iter == 10)\n            break;\n\n        /* compute the newton correction. */\n        wa1 = qr.colsPermutation().inverse() * diag.cwiseProduct(wa2/dxnorm);\n        // we could almost use this here, but the diagonal is outside qr, in sdiag[]\n        // qr.matrixQR().topLeftCorner(n, n).transpose().template triangularView<Lower>().solveInPlace(wa1);\n        for (j = 0; j < n; ++j) {\n            wa1[j] /= sdiag[j];\n            temp = wa1[j];\n            for (Index i = j+1; i < n; ++i)\n                wa1[i] -= s(i,j) * temp;\n        }\n        temp = wa1.blueNorm();\n        parc = fp / delta / temp / temp;\n\n        /* depending on the sign of the function, update parl or paru. */\n        if (fp > 0.)\n            parl = (std::max)(parl,par);\n        if (fp < 0.)\n            paru = (std::min)(paru,par);\n\n        /* compute an improved estimate for par. */\n        par = (std::max)(parl,par+parc);\n    }\n    if (iter == 0)\n        par = 0.;\n    return;\n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/NonLinearOptimization/qrsolv.h",
    "content": "namespace Eigen { \n\nnamespace internal {\n\n// TODO : once qrsolv2 is removed, use ColPivHouseholderQR or PermutationMatrix instead of ipvt\ntemplate <typename Scalar>\nvoid qrsolv(\n        Matrix< Scalar, Dynamic, Dynamic > &s,\n        // TODO : use a PermutationMatrix once lmpar is no more:\n        const VectorXi &ipvt,\n        const Matrix< Scalar, Dynamic, 1 >  &diag,\n        const Matrix< Scalar, Dynamic, 1 >  &qtb,\n        Matrix< Scalar, Dynamic, 1 >  &x,\n        Matrix< Scalar, Dynamic, 1 >  &sdiag)\n\n{\n    typedef DenseIndex Index;\n\n    /* Local variables */\n    Index i, j, k, l;\n    Scalar temp;\n    Index n = s.cols();\n    Matrix< Scalar, Dynamic, 1 >  wa(n);\n    JacobiRotation<Scalar> givens;\n\n    /* Function Body */\n    // the following will only change the lower triangular part of s, including\n    // the diagonal, though the diagonal is restored afterward\n\n    /*     copy r and (q transpose)*b to preserve input and initialize s. */\n    /*     in particular, save the diagonal elements of r in x. */\n    x = s.diagonal();\n    wa = qtb;\n\n    s.topLeftCorner(n,n).template triangularView<StrictlyLower>() = s.topLeftCorner(n,n).transpose();\n\n    /*     eliminate the diagonal matrix d using a givens rotation. */\n    for (j = 0; j < n; ++j) {\n\n        /*        prepare the row of d to be eliminated, locating the */\n        /*        diagonal element using p from the qr factorization. */\n        l = ipvt[j];\n        if (diag[l] == 0.)\n            break;\n        sdiag.tail(n-j).setZero();\n        sdiag[j] = diag[l];\n\n        /*        the transformations to eliminate the row of d */\n        /*        modify only a single element of (q transpose)*b */\n        /*        beyond the first n, which is initially zero. */\n        Scalar qtbpj = 0.;\n        for (k = j; k < n; ++k) {\n            /*           determine a givens rotation which eliminates the */\n            /*           appropriate element in the current row of d. */\n            givens.makeGivens(-s(k,k), sdiag[k]);\n\n            /*           compute the modified diagonal element of r and */\n            /*           the modified element of ((q transpose)*b,0). */\n            s(k,k) = givens.c() * s(k,k) + givens.s() * sdiag[k];\n            temp = givens.c() * wa[k] + givens.s() * qtbpj;\n            qtbpj = -givens.s() * wa[k] + givens.c() * qtbpj;\n            wa[k] = temp;\n\n            /*           accumulate the tranformation in the row of s. */\n            for (i = k+1; i<n; ++i) {\n                temp = givens.c() * s(i,k) + givens.s() * sdiag[i];\n                sdiag[i] = -givens.s() * s(i,k) + givens.c() * sdiag[i];\n                s(i,k) = temp;\n            }\n        }\n    }\n\n    /*     solve the triangular system for z. if the system is */\n    /*     singular, then obtain a least squares solution. */\n    Index nsing;\n    for(nsing=0; nsing<n && sdiag[nsing]!=0; nsing++) {}\n\n    wa.tail(n-nsing).setZero();\n    s.topLeftCorner(nsing, nsing).transpose().template triangularView<Upper>().solveInPlace(wa.head(nsing));\n\n    // restore\n    sdiag = s.diagonal();\n    s.diagonal() = x;\n\n    /*     permute the components of z back to components of x. */\n    for (j = 0; j < n; ++j) x[ipvt[j]] = wa[j];\n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/NonLinearOptimization/r1mpyq.h",
    "content": "namespace Eigen { \n\nnamespace internal {\n\n// TODO : move this to GivensQR once there's such a thing in Eigen\n\ntemplate <typename Scalar>\nvoid r1mpyq(DenseIndex m, DenseIndex n, Scalar *a, const std::vector<JacobiRotation<Scalar> > &v_givens, const std::vector<JacobiRotation<Scalar> > &w_givens)\n{\n    typedef DenseIndex Index;\n\n    /*     apply the first set of givens rotations to a. */\n    for (Index j = n-2; j>=0; --j)\n        for (Index i = 0; i<m; ++i) {\n            Scalar temp = v_givens[j].c() * a[i+m*j] - v_givens[j].s() * a[i+m*(n-1)];\n            a[i+m*(n-1)] = v_givens[j].s() * a[i+m*j] + v_givens[j].c() * a[i+m*(n-1)];\n            a[i+m*j] = temp;\n        }\n    /*     apply the second set of givens rotations to a. */\n    for (Index j = 0; j<n-1; ++j)\n        for (Index i = 0; i<m; ++i) {\n            Scalar temp = w_givens[j].c() * a[i+m*j] + w_givens[j].s() * a[i+m*(n-1)];\n            a[i+m*(n-1)] = -w_givens[j].s() * a[i+m*j] + w_givens[j].c() * a[i+m*(n-1)];\n            a[i+m*j] = temp;\n        }\n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/NonLinearOptimization/r1updt.h",
    "content": "namespace Eigen { \n\nnamespace internal {\n\ntemplate <typename Scalar>\nvoid r1updt(\n        Matrix< Scalar, Dynamic, Dynamic > &s,\n        const Matrix< Scalar, Dynamic, 1> &u,\n        std::vector<JacobiRotation<Scalar> > &v_givens,\n        std::vector<JacobiRotation<Scalar> > &w_givens,\n        Matrix< Scalar, Dynamic, 1> &v,\n        Matrix< Scalar, Dynamic, 1> &w,\n        bool *sing)\n{\n    typedef DenseIndex Index;\n    const JacobiRotation<Scalar> IdentityRotation = JacobiRotation<Scalar>(1,0);\n\n    /* Local variables */\n    const Index m = s.rows();\n    const Index n = s.cols();\n    Index i, j=1;\n    Scalar temp;\n    JacobiRotation<Scalar> givens;\n\n    // r1updt had a broader usecase, but we dont use it here. And, more\n    // importantly, we can not test it.\n    eigen_assert(m==n);\n    eigen_assert(u.size()==m);\n    eigen_assert(v.size()==n);\n    eigen_assert(w.size()==n);\n\n    /* move the nontrivial part of the last column of s into w. */\n    w[n-1] = s(n-1,n-1);\n\n    /* rotate the vector v into a multiple of the n-th unit vector */\n    /* in such a way that a spike is introduced into w. */\n    for (j=n-2; j>=0; --j) {\n        w[j] = 0.;\n        if (v[j] != 0.) {\n            /* determine a givens rotation which eliminates the */\n            /* j-th element of v. */\n            givens.makeGivens(-v[n-1], v[j]);\n\n            /* apply the transformation to v and store the information */\n            /* necessary to recover the givens rotation. */\n            v[n-1] = givens.s() * v[j] + givens.c() * v[n-1];\n            v_givens[j] = givens;\n\n            /* apply the transformation to s and extend the spike in w. */\n            for (i = j; i < m; ++i) {\n                temp = givens.c() * s(j,i) - givens.s() * w[i];\n                w[i] = givens.s() * s(j,i) + givens.c() * w[i];\n                s(j,i) = temp;\n            }\n        } else\n            v_givens[j] = IdentityRotation;\n    }\n\n    /* add the spike from the rank 1 update to w. */\n    w += v[n-1] * u;\n\n    /* eliminate the spike. */\n    *sing = false;\n    for (j = 0; j < n-1; ++j) {\n        if (w[j] != 0.) {\n            /* determine a givens rotation which eliminates the */\n            /* j-th element of the spike. */\n            givens.makeGivens(-s(j,j), w[j]);\n\n            /* apply the transformation to s and reduce the spike in w. */\n            for (i = j; i < m; ++i) {\n                temp = givens.c() * s(j,i) + givens.s() * w[i];\n                w[i] = -givens.s() * s(j,i) + givens.c() * w[i];\n                s(j,i) = temp;\n            }\n\n            /* store the information necessary to recover the */\n            /* givens rotation. */\n            w_givens[j] = givens;\n        } else\n            v_givens[j] = IdentityRotation;\n\n        /* test for zero diagonal elements in the output s. */\n        if (s(j,j) == 0.) {\n            *sing = true;\n        }\n    }\n    /* move w back into the last column of the output s. */\n    s(n-1,n-1) = w[n-1];\n\n    if (s(j,j) == 0.) {\n        *sing = true;\n    }\n    return;\n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/NonLinearOptimization/rwupdt.h",
    "content": "namespace Eigen { \n\nnamespace internal {\n\ntemplate <typename Scalar>\nvoid rwupdt(\n        Matrix< Scalar, Dynamic, Dynamic >  &r,\n        const Matrix< Scalar, Dynamic, 1>  &w,\n        Matrix< Scalar, Dynamic, 1>  &b,\n        Scalar alpha)\n{\n    typedef DenseIndex Index;\n\n    const Index n = r.cols();\n    eigen_assert(r.rows()>=n);\n    std::vector<JacobiRotation<Scalar> > givens(n);\n\n    /* Local variables */\n    Scalar temp, rowj;\n\n    /* Function Body */\n    for (Index j = 0; j < n; ++j) {\n        rowj = w[j];\n\n        /* apply the previous transformations to */\n        /* r(i,j), i=0,1,...,j-1, and to w(j). */\n        for (Index i = 0; i < j; ++i) {\n            temp = givens[i].c() * r(i,j) + givens[i].s() * rowj;\n            rowj = -givens[i].s() * r(i,j) + givens[i].c() * rowj;\n            r(i,j) = temp;\n        }\n\n        /* determine a givens rotation which eliminates w(j). */\n        givens[j].makeGivens(-r(j,j), rowj);\n\n        if (rowj == 0.)\n            continue; // givens[j] is identity\n\n        /* apply the current transformation to r(j,j), b(j), and alpha. */\n        r(j,j) = givens[j].c() * r(j,j) + givens[j].s() * rowj;\n        temp = givens[j].c() * b[j] + givens[j].s() * alpha;\n        alpha = -givens[j].s() * b[j] + givens[j].c() * alpha;\n        b[j] = temp;\n    }\n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/NumericalDiff/NumericalDiff.h",
    "content": "// -*- coding: utf-8\n// vim: set fileencoding=utf-8\n\n// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_NUMERICAL_DIFF_H\n#define EIGEN_NUMERICAL_DIFF_H\n\nnamespace Eigen { \n\nenum NumericalDiffMode {\n    Forward,\n    Central\n};\n\n\n/**\n  * This class allows you to add a method df() to your functor, which will \n  * use numerical differentiation to compute an approximate of the\n  * derivative for the functor. Of course, if you have an analytical form\n  * for the derivative, you should rather implement df() by yourself.\n  *\n  * More information on\n  * http://en.wikipedia.org/wiki/Numerical_differentiation\n  *\n  * Currently only \"Forward\" and \"Central\" scheme are implemented.\n  */\ntemplate<typename _Functor, NumericalDiffMode mode=Forward>\nclass NumericalDiff : public _Functor\n{\npublic:\n    typedef _Functor Functor;\n    typedef typename Functor::Scalar Scalar;\n    typedef typename Functor::InputType InputType;\n    typedef typename Functor::ValueType ValueType;\n    typedef typename Functor::JacobianType JacobianType;\n\n    NumericalDiff(Scalar _epsfcn=0.) : Functor(), epsfcn(_epsfcn) {}\n    NumericalDiff(const Functor& f, Scalar _epsfcn=0.) : Functor(f), epsfcn(_epsfcn) {}\n\n    // forward constructors\n    template<typename T0>\n        NumericalDiff(const T0& a0) : Functor(a0), epsfcn(0) {}\n    template<typename T0, typename T1>\n        NumericalDiff(const T0& a0, const T1& a1) : Functor(a0, a1), epsfcn(0) {}\n    template<typename T0, typename T1, typename T2>\n        NumericalDiff(const T0& a0, const T1& a1, const T2& a2) : Functor(a0, a1, a2), epsfcn(0) {}\n\n    enum {\n        InputsAtCompileTime = Functor::InputsAtCompileTime,\n        ValuesAtCompileTime = Functor::ValuesAtCompileTime\n    };\n\n    /**\n      * return the number of evaluation of functor\n     */\n    int df(const InputType& _x, JacobianType &jac) const\n    {\n        using std::sqrt;\n        using std::abs;\n        /* Local variables */\n        Scalar h;\n        int nfev=0;\n        const typename InputType::Index n = _x.size();\n        const Scalar eps = sqrt(((std::max)(epsfcn,NumTraits<Scalar>::epsilon() )));\n        ValueType val1, val2;\n        InputType x = _x;\n        // TODO : we should do this only if the size is not already known\n        val1.resize(Functor::values());\n        val2.resize(Functor::values());\n\n        // initialization\n        switch(mode) {\n            case Forward:\n                // compute f(x)\n                Functor::operator()(x, val1); nfev++;\n                break;\n            case Central:\n                // do nothing\n                break;\n            default:\n                eigen_assert(false);\n        };\n\n        // Function Body\n        for (int j = 0; j < n; ++j) {\n            h = eps * abs(x[j]);\n            if (h == 0.) {\n                h = eps;\n            }\n            switch(mode) {\n                case Forward:\n                    x[j] += h;\n                    Functor::operator()(x, val2);\n                    nfev++;\n                    x[j] = _x[j];\n                    jac.col(j) = (val2-val1)/h;\n                    break;\n                case Central:\n                    x[j] += h;\n                    Functor::operator()(x, val2); nfev++;\n                    x[j] -= 2*h;\n                    Functor::operator()(x, val1); nfev++;\n                    x[j] = _x[j];\n                    jac.col(j) = (val2-val1)/(2*h);\n                    break;\n                default:\n                    eigen_assert(false);\n            };\n        }\n        return nfev;\n    }\nprivate:\n    Scalar epsfcn;\n\n    NumericalDiff& operator=(const NumericalDiff&);\n};\n\n} // end namespace Eigen\n\n//vim: ai ts=4 sts=4 et sw=4\n#endif // EIGEN_NUMERICAL_DIFF_H\n\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/Polynomials/Companion.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2010 Manuel Yguel <manuel.yguel@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_COMPANION_H\n#define EIGEN_COMPANION_H\n\n// This file requires the user to include\n// * Eigen/Core\n// * Eigen/src/PolynomialSolver.h\n\nnamespace Eigen { \n\nnamespace internal {\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\n\ntemplate <typename T>\nT radix(){ return 2; }\n\ntemplate <typename T>\nT radix2(){ return radix<T>()*radix<T>(); }\n\ntemplate<int Size>\nstruct decrement_if_fixed_size\n{\n  enum {\n    ret = (Size == Dynamic) ? Dynamic : Size-1 };\n};\n\n#endif\n\ntemplate< typename _Scalar, int _Deg >\nclass companion\n{\n  public:\n    EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Deg==Dynamic ? Dynamic : _Deg)\n\n    enum {\n      Deg = _Deg,\n      Deg_1=decrement_if_fixed_size<Deg>::ret\n    };\n\n    typedef _Scalar                                Scalar;\n    typedef typename NumTraits<Scalar>::Real       RealScalar;\n    typedef Matrix<Scalar, Deg, 1>                 RightColumn;\n    //typedef DiagonalMatrix< Scalar, Deg_1, Deg_1 > BottomLeftDiagonal;\n    typedef Matrix<Scalar, Deg_1, 1>               BottomLeftDiagonal;\n\n    typedef Matrix<Scalar, Deg, Deg>               DenseCompanionMatrixType;\n    typedef Matrix< Scalar, _Deg, Deg_1 >          LeftBlock;\n    typedef Matrix< Scalar, Deg_1, Deg_1 >         BottomLeftBlock;\n    typedef Matrix< Scalar, 1, Deg_1 >             LeftBlockFirstRow;\n\n    typedef DenseIndex Index;\n\n  public:\n    EIGEN_STRONG_INLINE const _Scalar operator()(Index row, Index col ) const\n    {\n      if( m_bl_diag.rows() > col )\n      {\n        if( 0 < row ){ return m_bl_diag[col]; }\n        else{ return 0; }\n      }\n      else{ return m_monic[row]; }\n    }\n\n  public:\n    template<typename VectorType>\n    void setPolynomial( const VectorType& poly )\n    {\n      const Index deg = poly.size()-1;\n      m_monic = -1/poly[deg] * poly.head(deg);\n      //m_bl_diag.setIdentity( deg-1 );\n      m_bl_diag.setOnes(deg-1);\n    }\n\n    template<typename VectorType>\n    companion( const VectorType& poly ){\n      setPolynomial( poly ); }\n\n  public:\n    DenseCompanionMatrixType denseMatrix() const\n    {\n      const Index deg   = m_monic.size();\n      const Index deg_1 = deg-1;\n      DenseCompanionMatrixType companion(deg,deg);\n      companion <<\n        ( LeftBlock(deg,deg_1)\n          << LeftBlockFirstRow::Zero(1,deg_1),\n          BottomLeftBlock::Identity(deg-1,deg-1)*m_bl_diag.asDiagonal() ).finished()\n        , m_monic;\n      return companion;\n    }\n\n\n\n  protected:\n    /** Helper function for the balancing algorithm.\n     * \\returns true if the row and the column, having colNorm and rowNorm\n     * as norms, are balanced, false otherwise.\n     * colB and rowB are repectively the multipliers for\n     * the column and the row in order to balance them.\n     * */\n    bool balanced( Scalar colNorm, Scalar rowNorm,\n        bool& isBalanced, Scalar& colB, Scalar& rowB );\n\n    /** Helper function for the balancing algorithm.\n     * \\returns true if the row and the column, having colNorm and rowNorm\n     * as norms, are balanced, false otherwise.\n     * colB and rowB are repectively the multipliers for\n     * the column and the row in order to balance them.\n     * */\n    bool balancedR( Scalar colNorm, Scalar rowNorm,\n        bool& isBalanced, Scalar& colB, Scalar& rowB );\n\n  public:\n    /**\n     * Balancing algorithm from B. N. PARLETT and C. REINSCH (1969)\n     * \"Balancing a matrix for calculation of eigenvalues and eigenvectors\"\n     * adapted to the case of companion matrices.\n     * A matrix with non zero row and non zero column is balanced\n     * for a certain norm if the i-th row and the i-th column\n     * have same norm for all i.\n     */\n    void balance();\n\n  protected:\n      RightColumn                m_monic;\n      BottomLeftDiagonal         m_bl_diag;\n};\n\n\n\ntemplate< typename _Scalar, int _Deg >\ninline\nbool companion<_Scalar,_Deg>::balanced( Scalar colNorm, Scalar rowNorm,\n    bool& isBalanced, Scalar& colB, Scalar& rowB )\n{\n  if( Scalar(0) == colNorm || Scalar(0) == rowNorm ){ return true; }\n  else\n  {\n    //To find the balancing coefficients, if the radix is 2,\n    //one finds \\f$ \\sigma \\f$ such that\n    // \\f$ 2^{2\\sigma-1} < rowNorm / colNorm \\le 2^{2\\sigma+1} \\f$\n    // then the balancing coefficient for the row is \\f$ 1/2^{\\sigma} \\f$\n    // and the balancing coefficient for the column is \\f$ 2^{\\sigma} \\f$\n    rowB = rowNorm / radix<Scalar>();\n    colB = Scalar(1);\n    const Scalar s = colNorm + rowNorm;\n\n    while (colNorm < rowB)\n    {\n      colB *= radix<Scalar>();\n      colNorm *= radix2<Scalar>();\n    }\n\n    rowB = rowNorm * radix<Scalar>();\n\n    while (colNorm >= rowB)\n    {\n      colB /= radix<Scalar>();\n      colNorm /= radix2<Scalar>();\n    }\n\n    //This line is used to avoid insubstantial balancing\n    if ((rowNorm + colNorm) < Scalar(0.95) * s * colB)\n    {\n      isBalanced = false;\n      rowB = Scalar(1) / colB;\n      return false;\n    }\n    else{\n      return true; }\n  }\n}\n\ntemplate< typename _Scalar, int _Deg >\ninline\nbool companion<_Scalar,_Deg>::balancedR( Scalar colNorm, Scalar rowNorm,\n    bool& isBalanced, Scalar& colB, Scalar& rowB )\n{\n  if( Scalar(0) == colNorm || Scalar(0) == rowNorm ){ return true; }\n  else\n  {\n    /**\n     * Set the norm of the column and the row to the geometric mean\n     * of the row and column norm\n     */\n    const _Scalar q = colNorm/rowNorm;\n    if( !isApprox( q, _Scalar(1) ) )\n    {\n      rowB = sqrt( colNorm/rowNorm );\n      colB = Scalar(1)/rowB;\n\n      isBalanced = false;\n      return false;\n    }\n    else{\n      return true; }\n  }\n}\n\n\ntemplate< typename _Scalar, int _Deg >\nvoid companion<_Scalar,_Deg>::balance()\n{\n  using std::abs;\n  EIGEN_STATIC_ASSERT( Deg == Dynamic || 1 < Deg, YOU_MADE_A_PROGRAMMING_MISTAKE );\n  const Index deg   = m_monic.size();\n  const Index deg_1 = deg-1;\n\n  bool hasConverged=false;\n  while( !hasConverged )\n  {\n    hasConverged = true;\n    Scalar colNorm,rowNorm;\n    Scalar colB,rowB;\n\n    //First row, first column excluding the diagonal\n    //==============================================\n    colNorm = abs(m_bl_diag[0]);\n    rowNorm = abs(m_monic[0]);\n\n    //Compute balancing of the row and the column\n    if( !balanced( colNorm, rowNorm, hasConverged, colB, rowB ) )\n    {\n      m_bl_diag[0] *= colB;\n      m_monic[0] *= rowB;\n    }\n\n    //Middle rows and columns excluding the diagonal\n    //==============================================\n    for( Index i=1; i<deg_1; ++i )\n    {\n      // column norm, excluding the diagonal\n      colNorm = abs(m_bl_diag[i]);\n\n      // row norm, excluding the diagonal\n      rowNorm = abs(m_bl_diag[i-1]) + abs(m_monic[i]);\n\n      //Compute balancing of the row and the column\n      if( !balanced( colNorm, rowNorm, hasConverged, colB, rowB ) )\n      {\n        m_bl_diag[i]   *= colB;\n        m_bl_diag[i-1] *= rowB;\n        m_monic[i]     *= rowB;\n      }\n    }\n\n    //Last row, last column excluding the diagonal\n    //============================================\n    const Index ebl = m_bl_diag.size()-1;\n    VectorBlock<RightColumn,Deg_1> headMonic( m_monic, 0, deg_1 );\n    colNorm = headMonic.array().abs().sum();\n    rowNorm = abs( m_bl_diag[ebl] );\n\n    //Compute balancing of the row and the column\n    if( !balanced( colNorm, rowNorm, hasConverged, colB, rowB ) )\n    {\n      headMonic      *= colB;\n      m_bl_diag[ebl] *= rowB;\n    }\n  }\n}\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_COMPANION_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/Polynomials/PolynomialSolver.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2010 Manuel Yguel <manuel.yguel@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_POLYNOMIAL_SOLVER_H\n#define EIGEN_POLYNOMIAL_SOLVER_H\n\nnamespace Eigen { \n\n/** \\ingroup Polynomials_Module\n *  \\class PolynomialSolverBase.\n *\n * \\brief Defined to be inherited by polynomial solvers: it provides\n * convenient methods such as\n *  - real roots,\n *  - greatest, smallest complex roots,\n *  - real roots with greatest, smallest absolute real value,\n *  - greatest, smallest real roots.\n *\n * It stores the set of roots as a vector of complexes.\n *\n */\ntemplate< typename _Scalar, int _Deg >\nclass PolynomialSolverBase\n{\n  public:\n    EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Deg==Dynamic ? Dynamic : _Deg)\n\n    typedef _Scalar                             Scalar;\n    typedef typename NumTraits<Scalar>::Real    RealScalar;\n    typedef std::complex<RealScalar>            RootType;\n    typedef Matrix<RootType,_Deg,1>             RootsType;\n\n    typedef DenseIndex Index;\n\n  protected:\n    template< typename OtherPolynomial >\n    inline void setPolynomial( const OtherPolynomial& poly ){\n      m_roots.resize(poly.size()-1); }\n\n  public:\n    template< typename OtherPolynomial >\n    inline PolynomialSolverBase( const OtherPolynomial& poly ){\n      setPolynomial( poly() ); }\n\n    inline PolynomialSolverBase(){}\n\n  public:\n    /** \\returns the complex roots of the polynomial */\n    inline const RootsType& roots() const { return m_roots; }\n\n  public:\n    /** Clear and fills the back insertion sequence with the real roots of the polynomial\n     * i.e. the real part of the complex roots that have an imaginary part which\n     * absolute value is smaller than absImaginaryThreshold.\n     * absImaginaryThreshold takes the dummy_precision associated\n     * with the _Scalar template parameter of the PolynomialSolver class as the default value.\n     *\n     * \\param[out] bi_seq : the back insertion sequence (stl concept)\n     * \\param[in]  absImaginaryThreshold : the maximum bound of the imaginary part of a complex\n     *  number that is considered as real.\n     * */\n    template<typename Stl_back_insertion_sequence>\n    inline void realRoots( Stl_back_insertion_sequence& bi_seq,\n        const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const\n    {\n      using std::abs;\n      bi_seq.clear();\n      for(Index i=0; i<m_roots.size(); ++i )\n      {\n        if( abs( m_roots[i].imag() ) < absImaginaryThreshold ){\n          bi_seq.push_back( m_roots[i].real() ); }\n      }\n    }\n\n  protected:\n    template<typename squaredNormBinaryPredicate>\n    inline const RootType& selectComplexRoot_withRespectToNorm( squaredNormBinaryPredicate& pred ) const\n    {\n      Index res=0;\n      RealScalar norm2 = numext::abs2( m_roots[0] );\n      for( Index i=1; i<m_roots.size(); ++i )\n      {\n        const RealScalar currNorm2 = numext::abs2( m_roots[i] );\n        if( pred( currNorm2, norm2 ) ){\n          res=i; norm2=currNorm2; }\n      }\n      return m_roots[res];\n    }\n\n  public:\n    /**\n     * \\returns the complex root with greatest norm.\n     */\n    inline const RootType& greatestRoot() const\n    {\n      std::greater<Scalar> greater;\n      return selectComplexRoot_withRespectToNorm( greater );\n    }\n\n    /**\n     * \\returns the complex root with smallest norm.\n     */\n    inline const RootType& smallestRoot() const\n    {\n      std::less<Scalar> less;\n      return selectComplexRoot_withRespectToNorm( less );\n    }\n\n  protected:\n    template<typename squaredRealPartBinaryPredicate>\n    inline const RealScalar& selectRealRoot_withRespectToAbsRealPart(\n        squaredRealPartBinaryPredicate& pred,\n        bool& hasArealRoot,\n        const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const\n    {\n      using std::abs;\n      hasArealRoot = false;\n      Index res=0;\n      RealScalar abs2(0);\n\n      for( Index i=0; i<m_roots.size(); ++i )\n      {\n        if( abs( m_roots[i].imag() ) < absImaginaryThreshold )\n        {\n          if( !hasArealRoot )\n          {\n            hasArealRoot = true;\n            res = i;\n            abs2 = m_roots[i].real() * m_roots[i].real();\n          }\n          else\n          {\n            const RealScalar currAbs2 = m_roots[i].real() * m_roots[i].real();\n            if( pred( currAbs2, abs2 ) )\n            {\n              abs2 = currAbs2;\n              res = i;\n            }\n          }\n        }\n        else\n        {\n          if( abs( m_roots[i].imag() ) < abs( m_roots[res].imag() ) ){\n            res = i; }\n        }\n      }\n      return numext::real_ref(m_roots[res]);\n    }\n\n\n    template<typename RealPartBinaryPredicate>\n    inline const RealScalar& selectRealRoot_withRespectToRealPart(\n        RealPartBinaryPredicate& pred,\n        bool& hasArealRoot,\n        const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const\n    {\n      using std::abs;\n      hasArealRoot = false;\n      Index res=0;\n      RealScalar val(0);\n\n      for( Index i=0; i<m_roots.size(); ++i )\n      {\n        if( abs( m_roots[i].imag() ) < absImaginaryThreshold )\n        {\n          if( !hasArealRoot )\n          {\n            hasArealRoot = true;\n            res = i;\n            val = m_roots[i].real();\n          }\n          else\n          {\n            const RealScalar curr = m_roots[i].real();\n            if( pred( curr, val ) )\n            {\n              val = curr;\n              res = i;\n            }\n          }\n        }\n        else\n        {\n          if( abs( m_roots[i].imag() ) < abs( m_roots[res].imag() ) ){\n            res = i; }\n        }\n      }\n      return numext::real_ref(m_roots[res]);\n    }\n\n  public:\n    /**\n     * \\returns a real root with greatest absolute magnitude.\n     * A real root is defined as the real part of a complex root with absolute imaginary\n     * part smallest than absImaginaryThreshold.\n     * absImaginaryThreshold takes the dummy_precision associated\n     * with the _Scalar template parameter of the PolynomialSolver class as the default value.\n     * If no real root is found the boolean hasArealRoot is set to false and the real part of\n     * the root with smallest absolute imaginary part is returned instead.\n     *\n     * \\param[out] hasArealRoot : boolean true if a real root is found according to the\n     *  absImaginaryThreshold criterion, false otherwise.\n     * \\param[in] absImaginaryThreshold : threshold on the absolute imaginary part to decide\n     *  whether or not a root is real.\n     */\n    inline const RealScalar& absGreatestRealRoot(\n        bool& hasArealRoot,\n        const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const\n    {\n      std::greater<Scalar> greater;\n      return selectRealRoot_withRespectToAbsRealPart( greater, hasArealRoot, absImaginaryThreshold );\n    }\n\n\n    /**\n     * \\returns a real root with smallest absolute magnitude.\n     * A real root is defined as the real part of a complex root with absolute imaginary\n     * part smallest than absImaginaryThreshold.\n     * absImaginaryThreshold takes the dummy_precision associated\n     * with the _Scalar template parameter of the PolynomialSolver class as the default value.\n     * If no real root is found the boolean hasArealRoot is set to false and the real part of\n     * the root with smallest absolute imaginary part is returned instead.\n     *\n     * \\param[out] hasArealRoot : boolean true if a real root is found according to the\n     *  absImaginaryThreshold criterion, false otherwise.\n     * \\param[in] absImaginaryThreshold : threshold on the absolute imaginary part to decide\n     *  whether or not a root is real.\n     */\n    inline const RealScalar& absSmallestRealRoot(\n        bool& hasArealRoot,\n        const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const\n    {\n      std::less<Scalar> less;\n      return selectRealRoot_withRespectToAbsRealPart( less, hasArealRoot, absImaginaryThreshold );\n    }\n\n\n    /**\n     * \\returns the real root with greatest value.\n     * A real root is defined as the real part of a complex root with absolute imaginary\n     * part smallest than absImaginaryThreshold.\n     * absImaginaryThreshold takes the dummy_precision associated\n     * with the _Scalar template parameter of the PolynomialSolver class as the default value.\n     * If no real root is found the boolean hasArealRoot is set to false and the real part of\n     * the root with smallest absolute imaginary part is returned instead.\n     *\n     * \\param[out] hasArealRoot : boolean true if a real root is found according to the\n     *  absImaginaryThreshold criterion, false otherwise.\n     * \\param[in] absImaginaryThreshold : threshold on the absolute imaginary part to decide\n     *  whether or not a root is real.\n     */\n    inline const RealScalar& greatestRealRoot(\n        bool& hasArealRoot,\n        const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const\n    {\n      std::greater<Scalar> greater;\n      return selectRealRoot_withRespectToRealPart( greater, hasArealRoot, absImaginaryThreshold );\n    }\n\n\n    /**\n     * \\returns the real root with smallest value.\n     * A real root is defined as the real part of a complex root with absolute imaginary\n     * part smallest than absImaginaryThreshold.\n     * absImaginaryThreshold takes the dummy_precision associated\n     * with the _Scalar template parameter of the PolynomialSolver class as the default value.\n     * If no real root is found the boolean hasArealRoot is set to false and the real part of\n     * the root with smallest absolute imaginary part is returned instead.\n     *\n     * \\param[out] hasArealRoot : boolean true if a real root is found according to the\n     *  absImaginaryThreshold criterion, false otherwise.\n     * \\param[in] absImaginaryThreshold : threshold on the absolute imaginary part to decide\n     *  whether or not a root is real.\n     */\n    inline const RealScalar& smallestRealRoot(\n        bool& hasArealRoot,\n        const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const\n    {\n      std::less<Scalar> less;\n      return selectRealRoot_withRespectToRealPart( less, hasArealRoot, absImaginaryThreshold );\n    }\n\n  protected:\n    RootsType               m_roots;\n};\n\n#define EIGEN_POLYNOMIAL_SOLVER_BASE_INHERITED_TYPES( BASE )  \\\n  typedef typename BASE::Scalar                 Scalar;       \\\n  typedef typename BASE::RealScalar             RealScalar;   \\\n  typedef typename BASE::RootType               RootType;     \\\n  typedef typename BASE::RootsType              RootsType;\n\n\n\n/** \\ingroup Polynomials_Module\n  *\n  * \\class PolynomialSolver\n  *\n  * \\brief A polynomial solver\n  *\n  * Computes the complex roots of a real polynomial.\n  *\n  * \\param _Scalar the scalar type, i.e., the type of the polynomial coefficients\n  * \\param _Deg the degree of the polynomial, can be a compile time value or Dynamic.\n  *             Notice that the number of polynomial coefficients is _Deg+1.\n  *\n  * This class implements a polynomial solver and provides convenient methods such as\n  * - real roots,\n  * - greatest, smallest complex roots,\n  * - real roots with greatest, smallest absolute real value.\n  * - greatest, smallest real roots.\n  *\n  * WARNING: this polynomial solver is experimental, part of the unsupported Eigen modules.\n  *\n  *\n  * Currently a QR algorithm is used to compute the eigenvalues of the companion matrix of\n  * the polynomial to compute its roots.\n  * This supposes that the complex moduli of the roots are all distinct: e.g. there should\n  * be no multiple roots or conjugate roots for instance.\n  * With 32bit (float) floating types this problem shows up frequently.\n  * However, almost always, correct accuracy is reached even in these cases for 64bit\n  * (double) floating types and small polynomial degree (<20).\n  */\ntemplate< typename _Scalar, int _Deg >\nclass PolynomialSolver : public PolynomialSolverBase<_Scalar,_Deg>\n{\n  public:\n    EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Deg==Dynamic ? Dynamic : _Deg)\n\n    typedef PolynomialSolverBase<_Scalar,_Deg>    PS_Base;\n    EIGEN_POLYNOMIAL_SOLVER_BASE_INHERITED_TYPES( PS_Base )\n\n    typedef Matrix<Scalar,_Deg,_Deg>                 CompanionMatrixType;\n    typedef EigenSolver<CompanionMatrixType>         EigenSolverType;\n\n  public:\n    /** Computes the complex roots of a new polynomial. */\n    template< typename OtherPolynomial >\n    void compute( const OtherPolynomial& poly )\n    {\n      eigen_assert( Scalar(0) != poly[poly.size()-1] );\n      eigen_assert( poly.size() > 1 );\n      if(poly.size() >  2 )\n      {\n        internal::companion<Scalar,_Deg> companion( poly );\n        companion.balance();\n        m_eigenSolver.compute( companion.denseMatrix() );\n        m_roots = m_eigenSolver.eigenvalues();\n      }\n      else if(poly.size () == 2)\n      {\n        m_roots.resize(1);\n        m_roots[0] = -poly[0]/poly[1];\n      }\n    }\n\n  public:\n    template< typename OtherPolynomial >\n    inline PolynomialSolver( const OtherPolynomial& poly ){\n      compute( poly ); }\n\n    inline PolynomialSolver(){}\n\n  protected:\n    using                   PS_Base::m_roots;\n    EigenSolverType         m_eigenSolver;\n};\n\n\ntemplate< typename _Scalar >\nclass PolynomialSolver<_Scalar,1> : public PolynomialSolverBase<_Scalar,1>\n{\n  public:\n    typedef PolynomialSolverBase<_Scalar,1>    PS_Base;\n    EIGEN_POLYNOMIAL_SOLVER_BASE_INHERITED_TYPES( PS_Base )\n\n  public:\n    /** Computes the complex roots of a new polynomial. */\n    template< typename OtherPolynomial >\n    void compute( const OtherPolynomial& poly )\n    {\n      eigen_assert( poly.size() == 2 );\n      eigen_assert( Scalar(0) != poly[1] );\n      m_roots[0] = -poly[0]/poly[1];\n    }\n\n  public:\n    template< typename OtherPolynomial >\n    inline PolynomialSolver( const OtherPolynomial& poly ){\n      compute( poly ); }\n\n    inline PolynomialSolver(){}\n\n  protected:\n    using                   PS_Base::m_roots;\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_POLYNOMIAL_SOLVER_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/Polynomials/PolynomialUtils.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2010 Manuel Yguel <manuel.yguel@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_POLYNOMIAL_UTILS_H\n#define EIGEN_POLYNOMIAL_UTILS_H\n\nnamespace Eigen { \n\n/** \\ingroup Polynomials_Module\n * \\returns the evaluation of the polynomial at x using Horner algorithm.\n *\n * \\param[in] poly : the vector of coefficients of the polynomial ordered\n *  by degrees i.e. poly[i] is the coefficient of degree i of the polynomial\n *  e.g. \\f$ 1 + 3x^2 \\f$ is stored as a vector \\f$ [ 1, 0, 3 ] \\f$.\n * \\param[in] x : the value to evaluate the polynomial at.\n *\n * <i><b>Note for stability:</b></i>\n *  <dd> \\f$ |x| \\le 1 \\f$ </dd>\n */\ntemplate <typename Polynomials, typename T>\ninline\nT poly_eval_horner( const Polynomials& poly, const T& x )\n{\n  T val=poly[poly.size()-1];\n  for(DenseIndex i=poly.size()-2; i>=0; --i ){\n    val = val*x + poly[i]; }\n  return val;\n}\n\n/** \\ingroup Polynomials_Module\n * \\returns the evaluation of the polynomial at x using stabilized Horner algorithm.\n *\n * \\param[in] poly : the vector of coefficients of the polynomial ordered\n *  by degrees i.e. poly[i] is the coefficient of degree i of the polynomial\n *  e.g. \\f$ 1 + 3x^2 \\f$ is stored as a vector \\f$ [ 1, 0, 3 ] \\f$.\n * \\param[in] x : the value to evaluate the polynomial at.\n */\ntemplate <typename Polynomials, typename T>\ninline\nT poly_eval( const Polynomials& poly, const T& x )\n{\n  typedef typename NumTraits<T>::Real Real;\n\n  if( numext::abs2( x ) <= Real(1) ){\n    return poly_eval_horner( poly, x ); }\n  else\n  {\n    T val=poly[0];\n    T inv_x = T(1)/x;\n    for( DenseIndex i=1; i<poly.size(); ++i ){\n      val = val*inv_x + poly[i]; }\n\n    return numext::pow(x,(T)(poly.size()-1)) * val;\n  }\n}\n\n/** \\ingroup Polynomials_Module\n * \\returns a maximum bound for the absolute value of any root of the polynomial.\n *\n * \\param[in] poly : the vector of coefficients of the polynomial ordered\n *  by degrees i.e. poly[i] is the coefficient of degree i of the polynomial\n *  e.g. \\f$ 1 + 3x^2 \\f$ is stored as a vector \\f$ [ 1, 0, 3 ] \\f$.\n *\n *  <i><b>Precondition:</b></i>\n *  <dd> the leading coefficient of the input polynomial poly must be non zero </dd>\n */\ntemplate <typename Polynomial>\ninline\ntypename NumTraits<typename Polynomial::Scalar>::Real cauchy_max_bound( const Polynomial& poly )\n{\n  using std::abs;\n  typedef typename Polynomial::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real Real;\n\n  eigen_assert( Scalar(0) != poly[poly.size()-1] );\n  const Scalar inv_leading_coeff = Scalar(1)/poly[poly.size()-1];\n  Real cb(0);\n\n  for( DenseIndex i=0; i<poly.size()-1; ++i ){\n    cb += abs(poly[i]*inv_leading_coeff); }\n  return cb + Real(1);\n}\n\n/** \\ingroup Polynomials_Module\n * \\returns a minimum bound for the absolute value of any non zero root of the polynomial.\n * \\param[in] poly : the vector of coefficients of the polynomial ordered\n *  by degrees i.e. poly[i] is the coefficient of degree i of the polynomial\n *  e.g. \\f$ 1 + 3x^2 \\f$ is stored as a vector \\f$ [ 1, 0, 3 ] \\f$.\n */\ntemplate <typename Polynomial>\ninline\ntypename NumTraits<typename Polynomial::Scalar>::Real cauchy_min_bound( const Polynomial& poly )\n{\n  using std::abs;\n  typedef typename Polynomial::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real Real;\n\n  DenseIndex i=0;\n  while( i<poly.size()-1 && Scalar(0) == poly(i) ){ ++i; }\n  if( poly.size()-1 == i ){\n    return Real(1); }\n\n  const Scalar inv_min_coeff = Scalar(1)/poly[i];\n  Real cb(1);\n  for( DenseIndex j=i+1; j<poly.size(); ++j ){\n    cb += abs(poly[j]*inv_min_coeff); }\n  return Real(1)/cb;\n}\n\n/** \\ingroup Polynomials_Module\n * Given the roots of a polynomial compute the coefficients in the\n * monomial basis of the monic polynomial with same roots and minimal degree.\n * If RootVector is a vector of complexes, Polynomial should also be a vector\n * of complexes.\n * \\param[in] rv : a vector containing the roots of a polynomial.\n * \\param[out] poly : the vector of coefficients of the polynomial ordered\n *  by degrees i.e. poly[i] is the coefficient of degree i of the polynomial\n *  e.g. \\f$ 3 + x^2 \\f$ is stored as a vector \\f$ [ 3, 0, 1 ] \\f$.\n */\ntemplate <typename RootVector, typename Polynomial>\nvoid roots_to_monicPolynomial( const RootVector& rv, Polynomial& poly )\n{\n\n  typedef typename Polynomial::Scalar Scalar;\n\n  poly.setZero( rv.size()+1 );\n  poly[0] = -rv[0]; poly[1] = Scalar(1);\n  for( DenseIndex i=1; i< rv.size(); ++i )\n  {\n    for( DenseIndex j=i+1; j>0; --j ){ poly[j] = poly[j-1] - rv[i]*poly[j]; }\n    poly[0] = -rv[i]*poly[0];\n  }\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_POLYNOMIAL_UTILS_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/Skyline/SkylineInplaceLU.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Guillaume Saupin <guillaume.saupin@cea.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SKYLINEINPLACELU_H\n#define EIGEN_SKYLINEINPLACELU_H\n\nnamespace Eigen { \n\n/** \\ingroup Skyline_Module\n *\n * \\class SkylineInplaceLU\n *\n * \\brief Inplace LU decomposition of a skyline matrix and associated features\n *\n * \\param MatrixType the type of the matrix of which we are computing the LU factorization\n *\n */\ntemplate<typename MatrixType>\nclass SkylineInplaceLU {\nprotected:\n    typedef typename MatrixType::Scalar Scalar;\n    typedef typename MatrixType::Index Index;\n    \n    typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;\n\npublic:\n\n    /** Creates a LU object and compute the respective factorization of \\a matrix using\n     * flags \\a flags. */\n    SkylineInplaceLU(MatrixType& matrix, int flags = 0)\n    : /*m_matrix(matrix.rows(), matrix.cols()),*/ m_flags(flags), m_status(0), m_lu(matrix) {\n        m_precision = RealScalar(0.1) * Eigen::dummy_precision<RealScalar > ();\n        m_lu.IsRowMajor ? computeRowMajor() : compute();\n    }\n\n    /** Sets the relative threshold value used to prune zero coefficients during the decomposition.\n     *\n     * Setting a value greater than zero speeds up computation, and yields to an imcomplete\n     * factorization with fewer non zero coefficients. Such approximate factors are especially\n     * useful to initialize an iterative solver.\n     *\n     * Note that the exact meaning of this parameter might depends on the actual\n     * backend. Moreover, not all backends support this feature.\n     *\n     * \\sa precision() */\n    void setPrecision(RealScalar v) {\n        m_precision = v;\n    }\n\n    /** \\returns the current precision.\n     *\n     * \\sa setPrecision() */\n    RealScalar precision() const {\n        return m_precision;\n    }\n\n    /** Sets the flags. Possible values are:\n     *  - CompleteFactorization\n     *  - IncompleteFactorization\n     *  - MemoryEfficient\n     *  - one of the ordering methods\n     *  - etc...\n     *\n     * \\sa flags() */\n    void setFlags(int f) {\n        m_flags = f;\n    }\n\n    /** \\returns the current flags */\n    int flags() const {\n        return m_flags;\n    }\n\n    void setOrderingMethod(int m) {\n        m_flags = m;\n    }\n\n    int orderingMethod() const {\n        return m_flags;\n    }\n\n    /** Computes/re-computes the LU factorization */\n    void compute();\n    void computeRowMajor();\n\n    /** \\returns the lower triangular matrix L */\n    //inline const MatrixType& matrixL() const { return m_matrixL; }\n\n    /** \\returns the upper triangular matrix U */\n    //inline const MatrixType& matrixU() const { return m_matrixU; }\n\n    template<typename BDerived, typename XDerived>\n    bool solve(const MatrixBase<BDerived> &b, MatrixBase<XDerived>* x,\n            const int transposed = 0) const;\n\n    /** \\returns true if the factorization succeeded */\n    inline bool succeeded(void) const {\n        return m_succeeded;\n    }\n\nprotected:\n    RealScalar m_precision;\n    int m_flags;\n    mutable int m_status;\n    bool m_succeeded;\n    MatrixType& m_lu;\n};\n\n/** Computes / recomputes the in place LU decomposition of the SkylineInplaceLU.\n * using the default algorithm.\n */\ntemplate<typename MatrixType>\n//template<typename _Scalar>\nvoid SkylineInplaceLU<MatrixType>::compute() {\n    const size_t rows = m_lu.rows();\n    const size_t cols = m_lu.cols();\n\n    eigen_assert(rows == cols && \"We do not (yet) support rectangular LU.\");\n    eigen_assert(!m_lu.IsRowMajor && \"LU decomposition does not work with rowMajor Storage\");\n\n    for (Index row = 0; row < rows; row++) {\n        const double pivot = m_lu.coeffDiag(row);\n\n        //Lower matrix Columns update\n        const Index& col = row;\n        for (typename MatrixType::InnerLowerIterator lIt(m_lu, col); lIt; ++lIt) {\n            lIt.valueRef() /= pivot;\n        }\n\n        //Upper matrix update -> contiguous memory access\n        typename MatrixType::InnerLowerIterator lIt(m_lu, col);\n        for (Index rrow = row + 1; rrow < m_lu.rows(); rrow++) {\n            typename MatrixType::InnerUpperIterator uItPivot(m_lu, row);\n            typename MatrixType::InnerUpperIterator uIt(m_lu, rrow);\n            const double coef = lIt.value();\n\n            uItPivot += (rrow - row - 1);\n\n            //update upper part  -> contiguous memory access\n            for (++uItPivot; uIt && uItPivot;) {\n                uIt.valueRef() -= uItPivot.value() * coef;\n\n                ++uIt;\n                ++uItPivot;\n            }\n            ++lIt;\n        }\n\n        //Upper matrix update -> non contiguous memory access\n        typename MatrixType::InnerLowerIterator lIt3(m_lu, col);\n        for (Index rrow = row + 1; rrow < m_lu.rows(); rrow++) {\n            typename MatrixType::InnerUpperIterator uItPivot(m_lu, row);\n            const double coef = lIt3.value();\n\n            //update lower part ->  non contiguous memory access\n            for (Index i = 0; i < rrow - row - 1; i++) {\n                m_lu.coeffRefLower(rrow, row + i + 1) -= uItPivot.value() * coef;\n                ++uItPivot;\n            }\n            ++lIt3;\n        }\n        //update diag -> contiguous\n        typename MatrixType::InnerLowerIterator lIt2(m_lu, col);\n        for (Index rrow = row + 1; rrow < m_lu.rows(); rrow++) {\n\n            typename MatrixType::InnerUpperIterator uItPivot(m_lu, row);\n            typename MatrixType::InnerUpperIterator uIt(m_lu, rrow);\n            const double coef = lIt2.value();\n\n            uItPivot += (rrow - row - 1);\n            m_lu.coeffRefDiag(rrow) -= uItPivot.value() * coef;\n            ++lIt2;\n        }\n    }\n}\n\ntemplate<typename MatrixType>\nvoid SkylineInplaceLU<MatrixType>::computeRowMajor() {\n    const size_t rows = m_lu.rows();\n    const size_t cols = m_lu.cols();\n\n    eigen_assert(rows == cols && \"We do not (yet) support rectangular LU.\");\n    eigen_assert(m_lu.IsRowMajor && \"You're trying to apply rowMajor decomposition on a ColMajor matrix !\");\n\n    for (Index row = 0; row < rows; row++) {\n        typename MatrixType::InnerLowerIterator llIt(m_lu, row);\n\n\n        for (Index col = llIt.col(); col < row; col++) {\n            if (m_lu.coeffExistLower(row, col)) {\n                const double diag = m_lu.coeffDiag(col);\n\n                typename MatrixType::InnerLowerIterator lIt(m_lu, row);\n                typename MatrixType::InnerUpperIterator uIt(m_lu, col);\n\n\n                const Index offset = lIt.col() - uIt.row();\n\n\n                Index stop = offset > 0 ? col - lIt.col() : col - uIt.row();\n\n                //#define VECTORIZE\n#ifdef VECTORIZE\n                Map<VectorXd > rowVal(lIt.valuePtr() + (offset > 0 ? 0 : -offset), stop);\n                Map<VectorXd > colVal(uIt.valuePtr() + (offset > 0 ? offset : 0), stop);\n\n\n                Scalar newCoeff = m_lu.coeffLower(row, col) - rowVal.dot(colVal);\n#else\n                if (offset > 0) //Skip zero value of lIt\n                    uIt += offset;\n                else //Skip zero values of uIt\n                    lIt += -offset;\n                Scalar newCoeff = m_lu.coeffLower(row, col);\n\n                for (Index k = 0; k < stop; ++k) {\n                    const Scalar tmp = newCoeff;\n                    newCoeff = tmp - lIt.value() * uIt.value();\n                    ++lIt;\n                    ++uIt;\n                }\n#endif\n\n                m_lu.coeffRefLower(row, col) = newCoeff / diag;\n            }\n        }\n\n        //Upper matrix update\n        const Index col = row;\n        typename MatrixType::InnerUpperIterator uuIt(m_lu, col);\n        for (Index rrow = uuIt.row(); rrow < col; rrow++) {\n\n            typename MatrixType::InnerLowerIterator lIt(m_lu, rrow);\n            typename MatrixType::InnerUpperIterator uIt(m_lu, col);\n            const Index offset = lIt.col() - uIt.row();\n\n            Index stop = offset > 0 ? rrow - lIt.col() : rrow - uIt.row();\n\n#ifdef VECTORIZE\n            Map<VectorXd > rowVal(lIt.valuePtr() + (offset > 0 ? 0 : -offset), stop);\n            Map<VectorXd > colVal(uIt.valuePtr() + (offset > 0 ? offset : 0), stop);\n\n            Scalar newCoeff = m_lu.coeffUpper(rrow, col) - rowVal.dot(colVal);\n#else\n            if (offset > 0) //Skip zero value of lIt\n                uIt += offset;\n            else //Skip zero values of uIt\n                lIt += -offset;\n            Scalar newCoeff = m_lu.coeffUpper(rrow, col);\n            for (Index k = 0; k < stop; ++k) {\n                const Scalar tmp = newCoeff;\n                newCoeff = tmp - lIt.value() * uIt.value();\n\n                ++lIt;\n                ++uIt;\n            }\n#endif\n            m_lu.coeffRefUpper(rrow, col) = newCoeff;\n        }\n\n\n        //Diag matrix update\n        typename MatrixType::InnerLowerIterator lIt(m_lu, row);\n        typename MatrixType::InnerUpperIterator uIt(m_lu, row);\n\n        const Index offset = lIt.col() - uIt.row();\n\n\n        Index stop = offset > 0 ? lIt.size() : uIt.size();\n#ifdef VECTORIZE\n        Map<VectorXd > rowVal(lIt.valuePtr() + (offset > 0 ? 0 : -offset), stop);\n        Map<VectorXd > colVal(uIt.valuePtr() + (offset > 0 ? offset : 0), stop);\n        Scalar newCoeff = m_lu.coeffDiag(row) - rowVal.dot(colVal);\n#else\n        if (offset > 0) //Skip zero value of lIt\n            uIt += offset;\n        else //Skip zero values of uIt\n            lIt += -offset;\n        Scalar newCoeff = m_lu.coeffDiag(row);\n        for (Index k = 0; k < stop; ++k) {\n            const Scalar tmp = newCoeff;\n            newCoeff = tmp - lIt.value() * uIt.value();\n            ++lIt;\n            ++uIt;\n        }\n#endif\n        m_lu.coeffRefDiag(row) = newCoeff;\n    }\n}\n\n/** Computes *x = U^-1 L^-1 b\n *\n * If \\a transpose is set to SvTranspose or SvAdjoint, the solution\n * of the transposed/adjoint system is computed instead.\n *\n * Not all backends implement the solution of the transposed or\n * adjoint system.\n */\ntemplate<typename MatrixType>\ntemplate<typename BDerived, typename XDerived>\nbool SkylineInplaceLU<MatrixType>::solve(const MatrixBase<BDerived> &b, MatrixBase<XDerived>* x, const int transposed) const {\n    const size_t rows = m_lu.rows();\n    const size_t cols = m_lu.cols();\n\n\n    for (Index row = 0; row < rows; row++) {\n        x->coeffRef(row) = b.coeff(row);\n        Scalar newVal = x->coeff(row);\n        typename MatrixType::InnerLowerIterator lIt(m_lu, row);\n\n        Index col = lIt.col();\n        while (lIt.col() < row) {\n\n            newVal -= x->coeff(col++) * lIt.value();\n            ++lIt;\n        }\n\n        x->coeffRef(row) = newVal;\n    }\n\n\n    for (Index col = rows - 1; col > 0; col--) {\n        x->coeffRef(col) = x->coeff(col) / m_lu.coeffDiag(col);\n\n        const Scalar x_col = x->coeff(col);\n\n        typename MatrixType::InnerUpperIterator uIt(m_lu, col);\n        uIt += uIt.size()-1;\n\n\n        while (uIt) {\n            x->coeffRef(uIt.row()) -= x_col * uIt.value();\n            //TODO : introduce --operator\n            uIt += -1;\n        }\n\n\n    }\n    x->coeffRef(0) = x->coeff(0) / m_lu.coeffDiag(0);\n\n    return true;\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_SKYLINELU_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/Skyline/SkylineMatrix.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Guillaume Saupin <guillaume.saupin@cea.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SKYLINEMATRIX_H\n#define EIGEN_SKYLINEMATRIX_H\n\n#include \"SkylineStorage.h\"\n#include \"SkylineMatrixBase.h\"\n\nnamespace Eigen { \n\n/** \\ingroup Skyline_Module\n *\n * \\class SkylineMatrix\n *\n * \\brief The main skyline matrix class\n *\n * This class implements a skyline matrix using the very uncommon storage\n * scheme.\n *\n * \\param _Scalar the scalar type, i.e. the type of the coefficients\n * \\param _Options Union of bit flags controlling the storage scheme. Currently the only possibility\n *                 is RowMajor. The default is 0 which means column-major.\n *\n *\n */\nnamespace internal {\ntemplate<typename _Scalar, int _Options>\nstruct traits<SkylineMatrix<_Scalar, _Options> > {\n    typedef _Scalar Scalar;\n    typedef Sparse StorageKind;\n\n    enum {\n        RowsAtCompileTime = Dynamic,\n        ColsAtCompileTime = Dynamic,\n        MaxRowsAtCompileTime = Dynamic,\n        MaxColsAtCompileTime = Dynamic,\n        Flags = SkylineBit | _Options,\n        CoeffReadCost = NumTraits<Scalar>::ReadCost,\n    };\n};\n}\n\ntemplate<typename _Scalar, int _Options>\nclass SkylineMatrix\n: public SkylineMatrixBase<SkylineMatrix<_Scalar, _Options> > {\npublic:\n    EIGEN_SKYLINE_GENERIC_PUBLIC_INTERFACE(SkylineMatrix)\n    EIGEN_SKYLINE_INHERIT_ASSIGNMENT_OPERATOR(SkylineMatrix, +=)\n    EIGEN_SKYLINE_INHERIT_ASSIGNMENT_OPERATOR(SkylineMatrix, -=)\n\n    using Base::IsRowMajor;\n\nprotected:\n\n    typedef SkylineMatrix<Scalar, (Flags&~RowMajorBit) | (IsRowMajor ? RowMajorBit : 0) > TransposedSkylineMatrix;\n\n    Index m_outerSize;\n    Index m_innerSize;\n\npublic:\n    Index* m_colStartIndex;\n    Index* m_rowStartIndex;\n    SkylineStorage<Scalar> m_data;\n\npublic:\n\n    inline Index rows() const {\n        return IsRowMajor ? m_outerSize : m_innerSize;\n    }\n\n    inline Index cols() const {\n        return IsRowMajor ? m_innerSize : m_outerSize;\n    }\n\n    inline Index innerSize() const {\n        return m_innerSize;\n    }\n\n    inline Index outerSize() const {\n        return m_outerSize;\n    }\n\n    inline Index upperNonZeros() const {\n        return m_data.upperSize();\n    }\n\n    inline Index lowerNonZeros() const {\n        return m_data.lowerSize();\n    }\n\n    inline Index upperNonZeros(Index j) const {\n        return m_colStartIndex[j + 1] - m_colStartIndex[j];\n    }\n\n    inline Index lowerNonZeros(Index j) const {\n        return m_rowStartIndex[j + 1] - m_rowStartIndex[j];\n    }\n\n    inline const Scalar* _diagPtr() const {\n        return &m_data.diag(0);\n    }\n\n    inline Scalar* _diagPtr() {\n        return &m_data.diag(0);\n    }\n\n    inline const Scalar* _upperPtr() const {\n        return &m_data.upper(0);\n    }\n\n    inline Scalar* _upperPtr() {\n        return &m_data.upper(0);\n    }\n\n    inline const Scalar* _lowerPtr() const {\n        return &m_data.lower(0);\n    }\n\n    inline Scalar* _lowerPtr() {\n        return &m_data.lower(0);\n    }\n\n    inline const Index* _upperProfilePtr() const {\n        return &m_data.upperProfile(0);\n    }\n\n    inline Index* _upperProfilePtr() {\n        return &m_data.upperProfile(0);\n    }\n\n    inline const Index* _lowerProfilePtr() const {\n        return &m_data.lowerProfile(0);\n    }\n\n    inline Index* _lowerProfilePtr() {\n        return &m_data.lowerProfile(0);\n    }\n\n    inline Scalar coeff(Index row, Index col) const {\n        const Index outer = IsRowMajor ? row : col;\n        const Index inner = IsRowMajor ? col : row;\n\n        eigen_assert(outer < outerSize());\n        eigen_assert(inner < innerSize());\n\n        if (outer == inner)\n            return this->m_data.diag(outer);\n\n        if (IsRowMajor) {\n            if (inner > outer) //upper matrix\n            {\n                const Index minOuterIndex = inner - m_data.upperProfile(inner);\n                if (outer >= minOuterIndex)\n                    return this->m_data.upper(m_colStartIndex[inner] + outer - (inner - m_data.upperProfile(inner)));\n                else\n                    return Scalar(0);\n            }\n            if (inner < outer) //lower matrix\n            {\n                const Index minInnerIndex = outer - m_data.lowerProfile(outer);\n                if (inner >= minInnerIndex)\n                    return this->m_data.lower(m_rowStartIndex[outer] + inner - (outer - m_data.lowerProfile(outer)));\n                else\n                    return Scalar(0);\n            }\n            return m_data.upper(m_colStartIndex[inner] + outer - inner);\n        } else {\n            if (outer > inner) //upper matrix\n            {\n                const Index maxOuterIndex = inner + m_data.upperProfile(inner);\n                if (outer <= maxOuterIndex)\n                    return this->m_data.upper(m_colStartIndex[inner] + (outer - inner));\n                else\n                    return Scalar(0);\n            }\n            if (outer < inner) //lower matrix\n            {\n                const Index maxInnerIndex = outer + m_data.lowerProfile(outer);\n\n                if (inner <= maxInnerIndex)\n                    return this->m_data.lower(m_rowStartIndex[outer] + (inner - outer));\n                else\n                    return Scalar(0);\n            }\n        }\n    }\n\n    inline Scalar& coeffRef(Index row, Index col) {\n        const Index outer = IsRowMajor ? row : col;\n        const Index inner = IsRowMajor ? col : row;\n\n        eigen_assert(outer < outerSize());\n        eigen_assert(inner < innerSize());\n\n        if (outer == inner)\n            return this->m_data.diag(outer);\n\n        if (IsRowMajor) {\n            if (col > row) //upper matrix\n            {\n                const Index minOuterIndex = inner - m_data.upperProfile(inner);\n                eigen_assert(outer >= minOuterIndex && \"you try to acces a coeff that do not exist in the storage\");\n                return this->m_data.upper(m_colStartIndex[inner] + outer - (inner - m_data.upperProfile(inner)));\n            }\n            if (col < row) //lower matrix\n            {\n                const Index minInnerIndex = outer - m_data.lowerProfile(outer);\n                eigen_assert(inner >= minInnerIndex && \"you try to acces a coeff that do not exist in the storage\");\n                return this->m_data.lower(m_rowStartIndex[outer] + inner - (outer - m_data.lowerProfile(outer)));\n            }\n        } else {\n            if (outer > inner) //upper matrix\n            {\n                const Index maxOuterIndex = inner + m_data.upperProfile(inner);\n                eigen_assert(outer <= maxOuterIndex && \"you try to acces a coeff that do not exist in the storage\");\n                return this->m_data.upper(m_colStartIndex[inner] + (outer - inner));\n            }\n            if (outer < inner) //lower matrix\n            {\n                const Index maxInnerIndex = outer + m_data.lowerProfile(outer);\n                eigen_assert(inner <= maxInnerIndex && \"you try to acces a coeff that do not exist in the storage\");\n                return this->m_data.lower(m_rowStartIndex[outer] + (inner - outer));\n            }\n        }\n    }\n\n    inline Scalar coeffDiag(Index idx) const {\n        eigen_assert(idx < outerSize());\n        eigen_assert(idx < innerSize());\n        return this->m_data.diag(idx);\n    }\n\n    inline Scalar coeffLower(Index row, Index col) const {\n        const Index outer = IsRowMajor ? row : col;\n        const Index inner = IsRowMajor ? col : row;\n\n        eigen_assert(outer < outerSize());\n        eigen_assert(inner < innerSize());\n        eigen_assert(inner != outer);\n\n        if (IsRowMajor) {\n            const Index minInnerIndex = outer - m_data.lowerProfile(outer);\n            if (inner >= minInnerIndex)\n                return this->m_data.lower(m_rowStartIndex[outer] + inner - (outer - m_data.lowerProfile(outer)));\n            else\n                return Scalar(0);\n\n        } else {\n            const Index maxInnerIndex = outer + m_data.lowerProfile(outer);\n            if (inner <= maxInnerIndex)\n                return this->m_data.lower(m_rowStartIndex[outer] + (inner - outer));\n            else\n                return Scalar(0);\n        }\n    }\n\n    inline Scalar coeffUpper(Index row, Index col) const {\n        const Index outer = IsRowMajor ? row : col;\n        const Index inner = IsRowMajor ? col : row;\n\n        eigen_assert(outer < outerSize());\n        eigen_assert(inner < innerSize());\n        eigen_assert(inner != outer);\n\n        if (IsRowMajor) {\n            const Index minOuterIndex = inner - m_data.upperProfile(inner);\n            if (outer >= minOuterIndex)\n                return this->m_data.upper(m_colStartIndex[inner] + outer - (inner - m_data.upperProfile(inner)));\n            else\n                return Scalar(0);\n        } else {\n            const Index maxOuterIndex = inner + m_data.upperProfile(inner);\n            if (outer <= maxOuterIndex)\n                return this->m_data.upper(m_colStartIndex[inner] + (outer - inner));\n            else\n                return Scalar(0);\n        }\n    }\n\n    inline Scalar& coeffRefDiag(Index idx) {\n        eigen_assert(idx < outerSize());\n        eigen_assert(idx < innerSize());\n        return this->m_data.diag(idx);\n    }\n\n    inline Scalar& coeffRefLower(Index row, Index col) {\n        const Index outer = IsRowMajor ? row : col;\n        const Index inner = IsRowMajor ? col : row;\n\n        eigen_assert(outer < outerSize());\n        eigen_assert(inner < innerSize());\n        eigen_assert(inner != outer);\n\n        if (IsRowMajor) {\n            const Index minInnerIndex = outer - m_data.lowerProfile(outer);\n            eigen_assert(inner >= minInnerIndex && \"you try to acces a coeff that do not exist in the storage\");\n            return this->m_data.lower(m_rowStartIndex[outer] + inner - (outer - m_data.lowerProfile(outer)));\n        } else {\n            const Index maxInnerIndex = outer + m_data.lowerProfile(outer);\n            eigen_assert(inner <= maxInnerIndex && \"you try to acces a coeff that do not exist in the storage\");\n            return this->m_data.lower(m_rowStartIndex[outer] + (inner - outer));\n        }\n    }\n\n    inline bool coeffExistLower(Index row, Index col) {\n        const Index outer = IsRowMajor ? row : col;\n        const Index inner = IsRowMajor ? col : row;\n\n        eigen_assert(outer < outerSize());\n        eigen_assert(inner < innerSize());\n        eigen_assert(inner != outer);\n\n        if (IsRowMajor) {\n            const Index minInnerIndex = outer - m_data.lowerProfile(outer);\n            return inner >= minInnerIndex;\n        } else {\n            const Index maxInnerIndex = outer + m_data.lowerProfile(outer);\n            return inner <= maxInnerIndex;\n        }\n    }\n\n    inline Scalar& coeffRefUpper(Index row, Index col) {\n        const Index outer = IsRowMajor ? row : col;\n        const Index inner = IsRowMajor ? col : row;\n\n        eigen_assert(outer < outerSize());\n        eigen_assert(inner < innerSize());\n        eigen_assert(inner != outer);\n\n        if (IsRowMajor) {\n            const Index minOuterIndex = inner - m_data.upperProfile(inner);\n            eigen_assert(outer >= minOuterIndex && \"you try to acces a coeff that do not exist in the storage\");\n            return this->m_data.upper(m_colStartIndex[inner] + outer - (inner - m_data.upperProfile(inner)));\n        } else {\n            const Index maxOuterIndex = inner + m_data.upperProfile(inner);\n            eigen_assert(outer <= maxOuterIndex && \"you try to acces a coeff that do not exist in the storage\");\n            return this->m_data.upper(m_colStartIndex[inner] + (outer - inner));\n        }\n    }\n\n    inline bool coeffExistUpper(Index row, Index col) {\n        const Index outer = IsRowMajor ? row : col;\n        const Index inner = IsRowMajor ? col : row;\n\n        eigen_assert(outer < outerSize());\n        eigen_assert(inner < innerSize());\n        eigen_assert(inner != outer);\n\n        if (IsRowMajor) {\n            const Index minOuterIndex = inner - m_data.upperProfile(inner);\n            return outer >= minOuterIndex;\n        } else {\n            const Index maxOuterIndex = inner + m_data.upperProfile(inner);\n            return outer <= maxOuterIndex;\n        }\n    }\n\n\nprotected:\n\npublic:\n    class InnerUpperIterator;\n    class InnerLowerIterator;\n\n    class OuterUpperIterator;\n    class OuterLowerIterator;\n\n    /** Removes all non zeros */\n    inline void setZero() {\n        m_data.clear();\n        memset(m_colStartIndex, 0, (m_outerSize + 1) * sizeof (Index));\n        memset(m_rowStartIndex, 0, (m_outerSize + 1) * sizeof (Index));\n    }\n\n    /** \\returns the number of non zero coefficients */\n    inline Index nonZeros() const {\n        return m_data.diagSize() + m_data.upperSize() + m_data.lowerSize();\n    }\n\n    /** Preallocates \\a reserveSize non zeros */\n    inline void reserve(Index reserveSize, Index reserveUpperSize, Index reserveLowerSize) {\n        m_data.reserve(reserveSize, reserveUpperSize, reserveLowerSize);\n    }\n\n    /** \\returns a reference to a novel non zero coefficient with coordinates \\a row x \\a col.\n\n     *\n     * \\warning This function can be extremely slow if the non zero coefficients\n     * are not inserted in a coherent order.\n     *\n     * After an insertion session, you should call the finalize() function.\n     */\n    EIGEN_DONT_INLINE Scalar & insert(Index row, Index col) {\n        const Index outer = IsRowMajor ? row : col;\n        const Index inner = IsRowMajor ? col : row;\n\n        eigen_assert(outer < outerSize());\n        eigen_assert(inner < innerSize());\n\n        if (outer == inner)\n            return m_data.diag(col);\n\n        if (IsRowMajor) {\n            if (outer < inner) //upper matrix\n            {\n                Index minOuterIndex = 0;\n                minOuterIndex = inner - m_data.upperProfile(inner);\n\n                if (outer < minOuterIndex) //The value does not yet exist\n                {\n                    const Index previousProfile = m_data.upperProfile(inner);\n\n                    m_data.upperProfile(inner) = inner - outer;\n\n\n                    const Index bandIncrement = m_data.upperProfile(inner) - previousProfile;\n                    //shift data stored after this new one\n                    const Index stop = m_colStartIndex[cols()];\n                    const Index start = m_colStartIndex[inner];\n\n\n                    for (Index innerIdx = stop; innerIdx >= start; innerIdx--) {\n                        m_data.upper(innerIdx + bandIncrement) = m_data.upper(innerIdx);\n                    }\n\n                    for (Index innerIdx = cols(); innerIdx > inner; innerIdx--) {\n                        m_colStartIndex[innerIdx] += bandIncrement;\n                    }\n\n                    //zeros new data\n                    memset(this->_upperPtr() + start, 0, (bandIncrement - 1) * sizeof (Scalar));\n\n                    return m_data.upper(m_colStartIndex[inner]);\n                } else {\n                    return m_data.upper(m_colStartIndex[inner] + outer - (inner - m_data.upperProfile(inner)));\n                }\n            }\n\n            if (outer > inner) //lower matrix\n            {\n                const Index minInnerIndex = outer - m_data.lowerProfile(outer);\n                if (inner < minInnerIndex) //The value does not yet exist\n                {\n                    const Index previousProfile = m_data.lowerProfile(outer);\n                    m_data.lowerProfile(outer) = outer - inner;\n\n                    const Index bandIncrement = m_data.lowerProfile(outer) - previousProfile;\n                    //shift data stored after this new one\n                    const Index stop = m_rowStartIndex[rows()];\n                    const Index start = m_rowStartIndex[outer];\n\n\n                    for (Index innerIdx = stop; innerIdx >= start; innerIdx--) {\n                        m_data.lower(innerIdx + bandIncrement) = m_data.lower(innerIdx);\n                    }\n\n                    for (Index innerIdx = rows(); innerIdx > outer; innerIdx--) {\n                        m_rowStartIndex[innerIdx] += bandIncrement;\n                    }\n\n                    //zeros new data\n                    memset(this->_lowerPtr() + start, 0, (bandIncrement - 1) * sizeof (Scalar));\n                    return m_data.lower(m_rowStartIndex[outer]);\n                } else {\n                    return m_data.lower(m_rowStartIndex[outer] + inner - (outer - m_data.lowerProfile(outer)));\n                }\n            }\n        } else {\n            if (outer > inner) //upper matrix\n            {\n                const Index maxOuterIndex = inner + m_data.upperProfile(inner);\n                if (outer > maxOuterIndex) //The value does not yet exist\n                {\n                    const Index previousProfile = m_data.upperProfile(inner);\n                    m_data.upperProfile(inner) = outer - inner;\n\n                    const Index bandIncrement = m_data.upperProfile(inner) - previousProfile;\n                    //shift data stored after this new one\n                    const Index stop = m_rowStartIndex[rows()];\n                    const Index start = m_rowStartIndex[inner + 1];\n\n                    for (Index innerIdx = stop; innerIdx >= start; innerIdx--) {\n                        m_data.upper(innerIdx + bandIncrement) = m_data.upper(innerIdx);\n                    }\n\n                    for (Index innerIdx = inner + 1; innerIdx < outerSize() + 1; innerIdx++) {\n                        m_rowStartIndex[innerIdx] += bandIncrement;\n                    }\n                    memset(this->_upperPtr() + m_rowStartIndex[inner] + previousProfile + 1, 0, (bandIncrement - 1) * sizeof (Scalar));\n                    return m_data.upper(m_rowStartIndex[inner] + m_data.upperProfile(inner));\n                } else {\n                    return m_data.upper(m_rowStartIndex[inner] + (outer - inner));\n                }\n            }\n\n            if (outer < inner) //lower matrix\n            {\n                const Index maxInnerIndex = outer + m_data.lowerProfile(outer);\n                if (inner > maxInnerIndex) //The value does not yet exist\n                {\n                    const Index previousProfile = m_data.lowerProfile(outer);\n                    m_data.lowerProfile(outer) = inner - outer;\n\n                    const Index bandIncrement = m_data.lowerProfile(outer) - previousProfile;\n                    //shift data stored after this new one\n                    const Index stop = m_colStartIndex[cols()];\n                    const Index start = m_colStartIndex[outer + 1];\n\n                    for (Index innerIdx = stop; innerIdx >= start; innerIdx--) {\n                        m_data.lower(innerIdx + bandIncrement) = m_data.lower(innerIdx);\n                    }\n\n                    for (Index innerIdx = outer + 1; innerIdx < outerSize() + 1; innerIdx++) {\n                        m_colStartIndex[innerIdx] += bandIncrement;\n                    }\n                    memset(this->_lowerPtr() + m_colStartIndex[outer] + previousProfile + 1, 0, (bandIncrement - 1) * sizeof (Scalar));\n                    return m_data.lower(m_colStartIndex[outer] + m_data.lowerProfile(outer));\n                } else {\n                    return m_data.lower(m_colStartIndex[outer] + (inner - outer));\n                }\n            }\n        }\n    }\n\n    /** Must be called after inserting a set of non zero entries.\n     */\n    inline void finalize() {\n        if (IsRowMajor) {\n            if (rows() > cols())\n                m_data.resize(cols(), cols(), rows(), m_colStartIndex[cols()] + 1, m_rowStartIndex[rows()] + 1);\n            else\n                m_data.resize(rows(), cols(), rows(), m_colStartIndex[cols()] + 1, m_rowStartIndex[rows()] + 1);\n\n            //            eigen_assert(rows() == cols() && \"memory reorganisatrion only works with suare matrix\");\n            //\n            //            Scalar* newArray = new Scalar[m_colStartIndex[cols()] + 1 + m_rowStartIndex[rows()] + 1];\n            //            Index dataIdx = 0;\n            //            for (Index row = 0; row < rows(); row++) {\n            //\n            //                const Index nbLowerElts = m_rowStartIndex[row + 1] - m_rowStartIndex[row];\n            //                //                std::cout << \"nbLowerElts\" << nbLowerElts << std::endl;\n            //                memcpy(newArray + dataIdx, m_data.m_lower + m_rowStartIndex[row], nbLowerElts * sizeof (Scalar));\n            //                m_rowStartIndex[row] = dataIdx;\n            //                dataIdx += nbLowerElts;\n            //\n            //                const Index nbUpperElts = m_colStartIndex[row + 1] - m_colStartIndex[row];\n            //                memcpy(newArray + dataIdx, m_data.m_upper + m_colStartIndex[row], nbUpperElts * sizeof (Scalar));\n            //                m_colStartIndex[row] = dataIdx;\n            //                dataIdx += nbUpperElts;\n            //\n            //\n            //            }\n            //            //todo : don't access m_data profile directly : add an accessor from SkylineMatrix\n            //            m_rowStartIndex[rows()] = m_rowStartIndex[rows()-1] + m_data.lowerProfile(rows()-1);\n            //            m_colStartIndex[cols()] = m_colStartIndex[cols()-1] + m_data.upperProfile(cols()-1);\n            //\n            //            delete[] m_data.m_lower;\n            //            delete[] m_data.m_upper;\n            //\n            //            m_data.m_lower = newArray;\n            //            m_data.m_upper = newArray;\n        } else {\n            if (rows() > cols())\n                m_data.resize(cols(), rows(), cols(), m_rowStartIndex[cols()] + 1, m_colStartIndex[cols()] + 1);\n            else\n                m_data.resize(rows(), rows(), cols(), m_rowStartIndex[rows()] + 1, m_colStartIndex[rows()] + 1);\n        }\n    }\n\n    inline void squeeze() {\n        finalize();\n        m_data.squeeze();\n    }\n\n    void prune(Scalar reference, RealScalar epsilon = dummy_precision<RealScalar > ()) {\n        //TODO\n    }\n\n    /** Resizes the matrix to a \\a rows x \\a cols matrix and initializes it to zero\n     * \\sa resizeNonZeros(Index), reserve(), setZero()\n     */\n    void resize(size_t rows, size_t cols) {\n        const Index diagSize = rows > cols ? cols : rows;\n        m_innerSize = IsRowMajor ? cols : rows;\n\n        eigen_assert(rows == cols && \"Skyline matrix must be square matrix\");\n\n        if (diagSize % 2) { // diagSize is odd\n            const Index k = (diagSize - 1) / 2;\n\n            m_data.resize(diagSize, IsRowMajor ? cols : rows, IsRowMajor ? rows : cols,\n                    2 * k * k + k + 1,\n                    2 * k * k + k + 1);\n\n        } else // diagSize is even\n        {\n            const Index k = diagSize / 2;\n            m_data.resize(diagSize, IsRowMajor ? cols : rows, IsRowMajor ? rows : cols,\n                    2 * k * k - k + 1,\n                    2 * k * k - k + 1);\n        }\n\n        if (m_colStartIndex && m_rowStartIndex) {\n            delete[] m_colStartIndex;\n            delete[] m_rowStartIndex;\n        }\n        m_colStartIndex = new Index [cols + 1];\n        m_rowStartIndex = new Index [rows + 1];\n        m_outerSize = diagSize;\n\n        m_data.reset();\n        m_data.clear();\n\n        m_outerSize = diagSize;\n        memset(m_colStartIndex, 0, (cols + 1) * sizeof (Index));\n        memset(m_rowStartIndex, 0, (rows + 1) * sizeof (Index));\n    }\n\n    void resizeNonZeros(Index size) {\n        m_data.resize(size);\n    }\n\n    inline SkylineMatrix()\n    : m_outerSize(-1), m_innerSize(0), m_colStartIndex(0), m_rowStartIndex(0) {\n        resize(0, 0);\n    }\n\n    inline SkylineMatrix(size_t rows, size_t cols)\n    : m_outerSize(0), m_innerSize(0), m_colStartIndex(0), m_rowStartIndex(0) {\n        resize(rows, cols);\n    }\n\n    template<typename OtherDerived>\n    inline SkylineMatrix(const SkylineMatrixBase<OtherDerived>& other)\n    : m_outerSize(0), m_innerSize(0), m_colStartIndex(0), m_rowStartIndex(0) {\n        *this = other.derived();\n    }\n\n    inline SkylineMatrix(const SkylineMatrix & other)\n    : Base(), m_outerSize(0), m_innerSize(0), m_colStartIndex(0), m_rowStartIndex(0) {\n        *this = other.derived();\n    }\n\n    inline void swap(SkylineMatrix & other) {\n        //EIGEN_DBG_SKYLINE(std::cout << \"SkylineMatrix:: swap\\n\");\n        std::swap(m_colStartIndex, other.m_colStartIndex);\n        std::swap(m_rowStartIndex, other.m_rowStartIndex);\n        std::swap(m_innerSize, other.m_innerSize);\n        std::swap(m_outerSize, other.m_outerSize);\n        m_data.swap(other.m_data);\n    }\n\n    inline SkylineMatrix & operator=(const SkylineMatrix & other) {\n        std::cout << \"SkylineMatrix& operator=(const SkylineMatrix& other)\\n\";\n        if (other.isRValue()) {\n            swap(other.const_cast_derived());\n        } else {\n            resize(other.rows(), other.cols());\n            memcpy(m_colStartIndex, other.m_colStartIndex, (m_outerSize + 1) * sizeof (Index));\n            memcpy(m_rowStartIndex, other.m_rowStartIndex, (m_outerSize + 1) * sizeof (Index));\n            m_data = other.m_data;\n        }\n        return *this;\n    }\n\n    template<typename OtherDerived>\n            inline SkylineMatrix & operator=(const SkylineMatrixBase<OtherDerived>& other) {\n        const bool needToTranspose = (Flags & RowMajorBit) != (OtherDerived::Flags & RowMajorBit);\n        if (needToTranspose) {\n            //         TODO\n            //            return *this;\n        } else {\n            // there is no special optimization\n            return SkylineMatrixBase<SkylineMatrix>::operator=(other.derived());\n        }\n    }\n\n    friend std::ostream & operator <<(std::ostream & s, const SkylineMatrix & m) {\n\n        EIGEN_DBG_SKYLINE(\n        std::cout << \"upper elements : \" << std::endl;\n        for (Index i = 0; i < m.m_data.upperSize(); i++)\n            std::cout << m.m_data.upper(i) << \"\\t\";\n        std::cout << std::endl;\n        std::cout << \"upper profile : \" << std::endl;\n        for (Index i = 0; i < m.m_data.upperProfileSize(); i++)\n            std::cout << m.m_data.upperProfile(i) << \"\\t\";\n        std::cout << std::endl;\n        std::cout << \"lower startIdx : \" << std::endl;\n        for (Index i = 0; i < m.m_data.upperProfileSize(); i++)\n            std::cout << (IsRowMajor ? m.m_colStartIndex[i] : m.m_rowStartIndex[i]) << \"\\t\";\n        std::cout << std::endl;\n\n\n        std::cout << \"lower elements : \" << std::endl;\n        for (Index i = 0; i < m.m_data.lowerSize(); i++)\n            std::cout << m.m_data.lower(i) << \"\\t\";\n        std::cout << std::endl;\n        std::cout << \"lower profile : \" << std::endl;\n        for (Index i = 0; i < m.m_data.lowerProfileSize(); i++)\n            std::cout << m.m_data.lowerProfile(i) << \"\\t\";\n        std::cout << std::endl;\n        std::cout << \"lower startIdx : \" << std::endl;\n        for (Index i = 0; i < m.m_data.lowerProfileSize(); i++)\n            std::cout << (IsRowMajor ? m.m_rowStartIndex[i] : m.m_colStartIndex[i]) << \"\\t\";\n        std::cout << std::endl;\n        );\n        for (Index rowIdx = 0; rowIdx < m.rows(); rowIdx++) {\n            for (Index colIdx = 0; colIdx < m.cols(); colIdx++) {\n                s << m.coeff(rowIdx, colIdx) << \"\\t\";\n            }\n            s << std::endl;\n        }\n        return s;\n    }\n\n    /** Destructor */\n    inline ~SkylineMatrix() {\n        delete[] m_colStartIndex;\n        delete[] m_rowStartIndex;\n    }\n\n    /** Overloaded for performance */\n    Scalar sum() const;\n};\n\ntemplate<typename Scalar, int _Options>\nclass SkylineMatrix<Scalar, _Options>::InnerUpperIterator {\npublic:\n\n    InnerUpperIterator(const SkylineMatrix& mat, Index outer)\n    : m_matrix(mat), m_outer(outer),\n    m_id(_Options == RowMajor ? mat.m_colStartIndex[outer] : mat.m_rowStartIndex[outer] + 1),\n    m_start(m_id),\n    m_end(_Options == RowMajor ? mat.m_colStartIndex[outer + 1] : mat.m_rowStartIndex[outer + 1] + 1) {\n    }\n\n    inline InnerUpperIterator & operator++() {\n        m_id++;\n        return *this;\n    }\n\n    inline InnerUpperIterator & operator+=(Index shift) {\n        m_id += shift;\n        return *this;\n    }\n\n    inline Scalar value() const {\n        return m_matrix.m_data.upper(m_id);\n    }\n\n    inline Scalar* valuePtr() {\n        return const_cast<Scalar*> (&(m_matrix.m_data.upper(m_id)));\n    }\n\n    inline Scalar& valueRef() {\n        return const_cast<Scalar&> (m_matrix.m_data.upper(m_id));\n    }\n\n    inline Index index() const {\n        return IsRowMajor ? m_outer - m_matrix.m_data.upperProfile(m_outer) + (m_id - m_start) :\n                m_outer + (m_id - m_start) + 1;\n    }\n\n    inline Index row() const {\n        return IsRowMajor ? index() : m_outer;\n    }\n\n    inline Index col() const {\n        return IsRowMajor ? m_outer : index();\n    }\n\n    inline size_t size() const {\n        return m_matrix.m_data.upperProfile(m_outer);\n    }\n\n    inline operator bool() const {\n        return (m_id < m_end) && (m_id >= m_start);\n    }\n\nprotected:\n    const SkylineMatrix& m_matrix;\n    const Index m_outer;\n    Index m_id;\n    const Index m_start;\n    const Index m_end;\n};\n\ntemplate<typename Scalar, int _Options>\nclass SkylineMatrix<Scalar, _Options>::InnerLowerIterator {\npublic:\n\n    InnerLowerIterator(const SkylineMatrix& mat, Index outer)\n    : m_matrix(mat),\n    m_outer(outer),\n    m_id(_Options == RowMajor ? mat.m_rowStartIndex[outer] : mat.m_colStartIndex[outer] + 1),\n    m_start(m_id),\n    m_end(_Options == RowMajor ? mat.m_rowStartIndex[outer + 1] : mat.m_colStartIndex[outer + 1] + 1) {\n    }\n\n    inline InnerLowerIterator & operator++() {\n        m_id++;\n        return *this;\n    }\n\n    inline InnerLowerIterator & operator+=(Index shift) {\n        m_id += shift;\n        return *this;\n    }\n\n    inline Scalar value() const {\n        return m_matrix.m_data.lower(m_id);\n    }\n\n    inline Scalar* valuePtr() {\n        return const_cast<Scalar*> (&(m_matrix.m_data.lower(m_id)));\n    }\n\n    inline Scalar& valueRef() {\n        return const_cast<Scalar&> (m_matrix.m_data.lower(m_id));\n    }\n\n    inline Index index() const {\n        return IsRowMajor ? m_outer - m_matrix.m_data.lowerProfile(m_outer) + (m_id - m_start) :\n                m_outer + (m_id - m_start) + 1;\n        ;\n    }\n\n    inline Index row() const {\n        return IsRowMajor ? m_outer : index();\n    }\n\n    inline Index col() const {\n        return IsRowMajor ? index() : m_outer;\n    }\n\n    inline size_t size() const {\n        return m_matrix.m_data.lowerProfile(m_outer);\n    }\n\n    inline operator bool() const {\n        return (m_id < m_end) && (m_id >= m_start);\n    }\n\nprotected:\n    const SkylineMatrix& m_matrix;\n    const Index m_outer;\n    Index m_id;\n    const Index m_start;\n    const Index m_end;\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_SkylineMatrix_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/Skyline/SkylineMatrixBase.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Guillaume Saupin <guillaume.saupin@cea.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SKYLINEMATRIXBASE_H\n#define EIGEN_SKYLINEMATRIXBASE_H\n\n#include \"SkylineUtil.h\"\n\nnamespace Eigen { \n\n/** \\ingroup Skyline_Module\n *\n * \\class SkylineMatrixBase\n *\n * \\brief Base class of any skyline matrices or skyline expressions\n *\n * \\param Derived\n *\n */\ntemplate<typename Derived> class SkylineMatrixBase : public EigenBase<Derived> {\npublic:\n\n    typedef typename internal::traits<Derived>::Scalar Scalar;\n    typedef typename internal::traits<Derived>::StorageKind StorageKind;\n    typedef typename internal::index<StorageKind>::type Index;\n\n    enum {\n        RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,\n        /**< The number of rows at compile-time. This is just a copy of the value provided\n         * by the \\a Derived type. If a value is not known at compile-time,\n         * it is set to the \\a Dynamic constant.\n         * \\sa MatrixBase::rows(), MatrixBase::cols(), ColsAtCompileTime, SizeAtCompileTime */\n\n        ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,\n        /**< The number of columns at compile-time. This is just a copy of the value provided\n         * by the \\a Derived type. If a value is not known at compile-time,\n         * it is set to the \\a Dynamic constant.\n         * \\sa MatrixBase::rows(), MatrixBase::cols(), RowsAtCompileTime, SizeAtCompileTime */\n\n\n        SizeAtCompileTime = (internal::size_at_compile_time<internal::traits<Derived>::RowsAtCompileTime,\n        internal::traits<Derived>::ColsAtCompileTime>::ret),\n        /**< This is equal to the number of coefficients, i.e. the number of\n         * rows times the number of columns, or to \\a Dynamic if this is not\n         * known at compile-time. \\sa RowsAtCompileTime, ColsAtCompileTime */\n\n        MaxRowsAtCompileTime = RowsAtCompileTime,\n        MaxColsAtCompileTime = ColsAtCompileTime,\n\n        MaxSizeAtCompileTime = (internal::size_at_compile_time<MaxRowsAtCompileTime,\n        MaxColsAtCompileTime>::ret),\n\n        IsVectorAtCompileTime = RowsAtCompileTime == 1 || ColsAtCompileTime == 1,\n        /**< This is set to true if either the number of rows or the number of\n         * columns is known at compile-time to be equal to 1. Indeed, in that case,\n         * we are dealing with a column-vector (if there is only one column) or with\n         * a row-vector (if there is only one row). */\n\n        Flags = internal::traits<Derived>::Flags,\n        /**< This stores expression \\ref flags flags which may or may not be inherited by new expressions\n         * constructed from this one. See the \\ref flags \"list of flags\".\n         */\n\n        CoeffReadCost = internal::traits<Derived>::CoeffReadCost,\n        /**< This is a rough measure of how expensive it is to read one coefficient from\n         * this expression.\n         */\n\n        IsRowMajor = Flags & RowMajorBit ? 1 : 0\n    };\n\n#ifndef EIGEN_PARSED_BY_DOXYGEN\n    /** This is the \"real scalar\" type; if the \\a Scalar type is already real numbers\n     * (e.g. int, float or double) then \\a RealScalar is just the same as \\a Scalar. If\n     * \\a Scalar is \\a std::complex<T> then RealScalar is \\a T.\n     *\n     * \\sa class NumTraits\n     */\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n\n    /** type of the equivalent square matrix */\n    typedef Matrix<Scalar, EIGEN_SIZE_MAX(RowsAtCompileTime, ColsAtCompileTime),\n                           EIGEN_SIZE_MAX(RowsAtCompileTime, ColsAtCompileTime) > SquareMatrixType;\n\n    inline const Derived& derived() const {\n        return *static_cast<const Derived*> (this);\n    }\n\n    inline Derived& derived() {\n        return *static_cast<Derived*> (this);\n    }\n\n    inline Derived& const_cast_derived() const {\n        return *static_cast<Derived*> (const_cast<SkylineMatrixBase*> (this));\n    }\n#endif // not EIGEN_PARSED_BY_DOXYGEN\n\n    /** \\returns the number of rows. \\sa cols(), RowsAtCompileTime */\n    inline Index rows() const {\n        return derived().rows();\n    }\n\n    /** \\returns the number of columns. \\sa rows(), ColsAtCompileTime*/\n    inline Index cols() const {\n        return derived().cols();\n    }\n\n    /** \\returns the number of coefficients, which is \\a rows()*cols().\n     * \\sa rows(), cols(), SizeAtCompileTime. */\n    inline Index size() const {\n        return rows() * cols();\n    }\n\n    /** \\returns the number of nonzero coefficients which is in practice the number\n     * of stored coefficients. */\n    inline Index nonZeros() const {\n        return derived().nonZeros();\n    }\n\n    /** \\returns the size of the storage major dimension,\n     * i.e., the number of columns for a columns major matrix, and the number of rows otherwise */\n    Index outerSize() const {\n        return (int(Flags) & RowMajorBit) ? this->rows() : this->cols();\n    }\n\n    /** \\returns the size of the inner dimension according to the storage order,\n     * i.e., the number of rows for a columns major matrix, and the number of cols otherwise */\n    Index innerSize() const {\n        return (int(Flags) & RowMajorBit) ? this->cols() : this->rows();\n    }\n\n    bool isRValue() const {\n        return m_isRValue;\n    }\n\n    Derived& markAsRValue() {\n        m_isRValue = true;\n        return derived();\n    }\n\n    SkylineMatrixBase() : m_isRValue(false) {\n        /* TODO check flags */\n    }\n\n    inline Derived & operator=(const Derived& other) {\n        this->operator=<Derived > (other);\n        return derived();\n    }\n\n    template<typename OtherDerived>\n    inline void assignGeneric(const OtherDerived& other) {\n        derived().resize(other.rows(), other.cols());\n        for (Index row = 0; row < rows(); row++)\n            for (Index col = 0; col < cols(); col++) {\n                if (other.coeff(row, col) != Scalar(0))\n                    derived().insert(row, col) = other.coeff(row, col);\n            }\n        derived().finalize();\n    }\n\n    template<typename OtherDerived>\n            inline Derived & operator=(const SkylineMatrixBase<OtherDerived>& other) {\n        //TODO\n    }\n\n    template<typename Lhs, typename Rhs>\n            inline Derived & operator=(const SkylineProduct<Lhs, Rhs, SkylineTimeSkylineProduct>& product);\n\n    friend std::ostream & operator <<(std::ostream & s, const SkylineMatrixBase& m) {\n        s << m.derived();\n        return s;\n    }\n\n    template<typename OtherDerived>\n    const typename SkylineProductReturnType<Derived, OtherDerived>::Type\n    operator*(const MatrixBase<OtherDerived> &other) const;\n\n    /** \\internal use operator= */\n    template<typename DenseDerived>\n    void evalTo(MatrixBase<DenseDerived>& dst) const {\n        dst.setZero();\n        for (Index i = 0; i < rows(); i++)\n            for (Index j = 0; j < rows(); j++)\n                dst(i, j) = derived().coeff(i, j);\n    }\n\n    Matrix<Scalar, RowsAtCompileTime, ColsAtCompileTime> toDense() const {\n        return derived();\n    }\n\n    /** \\returns the matrix or vector obtained by evaluating this expression.\n     *\n     * Notice that in the case of a plain matrix or vector (not an expression) this function just returns\n     * a const reference, in order to avoid a useless copy.\n     */\n    EIGEN_STRONG_INLINE const typename internal::eval<Derived, IsSkyline>::type eval() const {\n        return typename internal::eval<Derived>::type(derived());\n    }\n\nprotected:\n    bool m_isRValue;\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_SkylineMatrixBase_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/Skyline/SkylineProduct.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Guillaume Saupin <guillaume.saupin@cea.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SKYLINEPRODUCT_H\n#define EIGEN_SKYLINEPRODUCT_H\n\nnamespace Eigen { \n\ntemplate<typename Lhs, typename Rhs, int ProductMode>\nstruct SkylineProductReturnType {\n    typedef const typename internal::nested_eval<Lhs, Rhs::RowsAtCompileTime>::type LhsNested;\n    typedef const typename internal::nested_eval<Rhs, Lhs::RowsAtCompileTime>::type RhsNested;\n\n    typedef SkylineProduct<LhsNested, RhsNested, ProductMode> Type;\n};\n\ntemplate<typename LhsNested, typename RhsNested, int ProductMode>\nstruct internal::traits<SkylineProduct<LhsNested, RhsNested, ProductMode> > {\n    // clean the nested types:\n    typedef typename internal::remove_all<LhsNested>::type _LhsNested;\n    typedef typename internal::remove_all<RhsNested>::type _RhsNested;\n    typedef typename _LhsNested::Scalar Scalar;\n\n    enum {\n        LhsCoeffReadCost = _LhsNested::CoeffReadCost,\n        RhsCoeffReadCost = _RhsNested::CoeffReadCost,\n        LhsFlags = _LhsNested::Flags,\n        RhsFlags = _RhsNested::Flags,\n\n        RowsAtCompileTime = _LhsNested::RowsAtCompileTime,\n        ColsAtCompileTime = _RhsNested::ColsAtCompileTime,\n        InnerSize = EIGEN_SIZE_MIN_PREFER_FIXED(_LhsNested::ColsAtCompileTime, _RhsNested::RowsAtCompileTime),\n\n        MaxRowsAtCompileTime = _LhsNested::MaxRowsAtCompileTime,\n        MaxColsAtCompileTime = _RhsNested::MaxColsAtCompileTime,\n\n        EvalToRowMajor = (RhsFlags & LhsFlags & RowMajorBit),\n        ResultIsSkyline = ProductMode == SkylineTimeSkylineProduct,\n\n        RemovedBits = ~((EvalToRowMajor ? 0 : RowMajorBit) | (ResultIsSkyline ? 0 : SkylineBit)),\n\n        Flags = (int(LhsFlags | RhsFlags) & HereditaryBits & RemovedBits)\n        | EvalBeforeAssigningBit\n        | EvalBeforeNestingBit,\n\n        CoeffReadCost = HugeCost\n    };\n\n    typedef typename internal::conditional<ResultIsSkyline,\n            SkylineMatrixBase<SkylineProduct<LhsNested, RhsNested, ProductMode> >,\n            MatrixBase<SkylineProduct<LhsNested, RhsNested, ProductMode> > >::type Base;\n};\n\nnamespace internal {\ntemplate<typename LhsNested, typename RhsNested, int ProductMode>\nclass SkylineProduct : no_assignment_operator,\npublic traits<SkylineProduct<LhsNested, RhsNested, ProductMode> >::Base {\npublic:\n\n    EIGEN_GENERIC_PUBLIC_INTERFACE(SkylineProduct)\n\nprivate:\n\n    typedef typename traits<SkylineProduct>::_LhsNested _LhsNested;\n    typedef typename traits<SkylineProduct>::_RhsNested _RhsNested;\n\npublic:\n\n    template<typename Lhs, typename Rhs>\n    EIGEN_STRONG_INLINE SkylineProduct(const Lhs& lhs, const Rhs& rhs)\n    : m_lhs(lhs), m_rhs(rhs) {\n        eigen_assert(lhs.cols() == rhs.rows());\n\n        enum {\n            ProductIsValid = _LhsNested::ColsAtCompileTime == Dynamic\n            || _RhsNested::RowsAtCompileTime == Dynamic\n            || int(_LhsNested::ColsAtCompileTime) == int(_RhsNested::RowsAtCompileTime),\n            AreVectors = _LhsNested::IsVectorAtCompileTime && _RhsNested::IsVectorAtCompileTime,\n            SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(_LhsNested, _RhsNested)\n        };\n        // note to the lost user:\n        //    * for a dot product use: v1.dot(v2)\n        //    * for a coeff-wise product use: v1.cwise()*v2\n        EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes),\n                INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)\n                EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),\n                INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)\n                EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)\n    }\n\n    EIGEN_STRONG_INLINE Index rows() const {\n        return m_lhs.rows();\n    }\n\n    EIGEN_STRONG_INLINE Index cols() const {\n        return m_rhs.cols();\n    }\n\n    EIGEN_STRONG_INLINE const _LhsNested& lhs() const {\n        return m_lhs;\n    }\n\n    EIGEN_STRONG_INLINE const _RhsNested& rhs() const {\n        return m_rhs;\n    }\n\nprotected:\n    LhsNested m_lhs;\n    RhsNested m_rhs;\n};\n\n// dense = skyline * dense\n// Note that here we force no inlining and separate the setZero() because GCC messes up otherwise\n\ntemplate<typename Lhs, typename Rhs, typename Dest>\nEIGEN_DONT_INLINE void skyline_row_major_time_dense_product(const Lhs& lhs, const Rhs& rhs, Dest& dst) {\n    typedef typename remove_all<Lhs>::type _Lhs;\n    typedef typename remove_all<Rhs>::type _Rhs;\n    typedef typename traits<Lhs>::Scalar Scalar;\n\n    enum {\n        LhsIsRowMajor = (_Lhs::Flags & RowMajorBit) == RowMajorBit,\n        LhsIsSelfAdjoint = (_Lhs::Flags & SelfAdjointBit) == SelfAdjointBit,\n        ProcessFirstHalf = LhsIsSelfAdjoint\n        && (((_Lhs::Flags & (UpperTriangularBit | LowerTriangularBit)) == 0)\n        || ((_Lhs::Flags & UpperTriangularBit) && !LhsIsRowMajor)\n        || ((_Lhs::Flags & LowerTriangularBit) && LhsIsRowMajor)),\n        ProcessSecondHalf = LhsIsSelfAdjoint && (!ProcessFirstHalf)\n    };\n\n    //Use matrix diagonal part <- Improvement : use inner iterator on dense matrix.\n    for (Index col = 0; col < rhs.cols(); col++) {\n        for (Index row = 0; row < lhs.rows(); row++) {\n            dst(row, col) = lhs.coeffDiag(row) * rhs(row, col);\n        }\n    }\n    //Use matrix lower triangular part\n    for (Index row = 0; row < lhs.rows(); row++) {\n        typename _Lhs::InnerLowerIterator lIt(lhs, row);\n        const Index stop = lIt.col() + lIt.size();\n        for (Index col = 0; col < rhs.cols(); col++) {\n\n            Index k = lIt.col();\n            Scalar tmp = 0;\n            while (k < stop) {\n                tmp +=\n                        lIt.value() *\n                        rhs(k++, col);\n                ++lIt;\n            }\n            dst(row, col) += tmp;\n            lIt += -lIt.size();\n        }\n\n    }\n\n    //Use matrix upper triangular part\n    for (Index lhscol = 0; lhscol < lhs.cols(); lhscol++) {\n        typename _Lhs::InnerUpperIterator uIt(lhs, lhscol);\n        const Index stop = uIt.size() + uIt.row();\n        for (Index rhscol = 0; rhscol < rhs.cols(); rhscol++) {\n\n\n            const Scalar rhsCoeff = rhs.coeff(lhscol, rhscol);\n            Index k = uIt.row();\n            while (k < stop) {\n                dst(k++, rhscol) +=\n                        uIt.value() *\n                        rhsCoeff;\n                ++uIt;\n            }\n            uIt += -uIt.size();\n        }\n    }\n\n}\n\ntemplate<typename Lhs, typename Rhs, typename Dest>\nEIGEN_DONT_INLINE void skyline_col_major_time_dense_product(const Lhs& lhs, const Rhs& rhs, Dest& dst) {\n    typedef typename remove_all<Lhs>::type _Lhs;\n    typedef typename remove_all<Rhs>::type _Rhs;\n    typedef typename traits<Lhs>::Scalar Scalar;\n\n    enum {\n        LhsIsRowMajor = (_Lhs::Flags & RowMajorBit) == RowMajorBit,\n        LhsIsSelfAdjoint = (_Lhs::Flags & SelfAdjointBit) == SelfAdjointBit,\n        ProcessFirstHalf = LhsIsSelfAdjoint\n        && (((_Lhs::Flags & (UpperTriangularBit | LowerTriangularBit)) == 0)\n        || ((_Lhs::Flags & UpperTriangularBit) && !LhsIsRowMajor)\n        || ((_Lhs::Flags & LowerTriangularBit) && LhsIsRowMajor)),\n        ProcessSecondHalf = LhsIsSelfAdjoint && (!ProcessFirstHalf)\n    };\n\n    //Use matrix diagonal part <- Improvement : use inner iterator on dense matrix.\n    for (Index col = 0; col < rhs.cols(); col++) {\n        for (Index row = 0; row < lhs.rows(); row++) {\n            dst(row, col) = lhs.coeffDiag(row) * rhs(row, col);\n        }\n    }\n\n    //Use matrix upper triangular part\n    for (Index row = 0; row < lhs.rows(); row++) {\n        typename _Lhs::InnerUpperIterator uIt(lhs, row);\n        const Index stop = uIt.col() + uIt.size();\n        for (Index col = 0; col < rhs.cols(); col++) {\n\n            Index k = uIt.col();\n            Scalar tmp = 0;\n            while (k < stop) {\n                tmp +=\n                        uIt.value() *\n                        rhs(k++, col);\n                ++uIt;\n            }\n\n\n            dst(row, col) += tmp;\n            uIt += -uIt.size();\n        }\n    }\n\n    //Use matrix lower triangular part\n    for (Index lhscol = 0; lhscol < lhs.cols(); lhscol++) {\n        typename _Lhs::InnerLowerIterator lIt(lhs, lhscol);\n        const Index stop = lIt.size() + lIt.row();\n        for (Index rhscol = 0; rhscol < rhs.cols(); rhscol++) {\n\n            const Scalar rhsCoeff = rhs.coeff(lhscol, rhscol);\n            Index k = lIt.row();\n            while (k < stop) {\n                dst(k++, rhscol) +=\n                        lIt.value() *\n                        rhsCoeff;\n                ++lIt;\n            }\n            lIt += -lIt.size();\n        }\n    }\n\n}\n\ntemplate<typename Lhs, typename Rhs, typename ResultType,\n        int LhsStorageOrder = traits<Lhs>::Flags&RowMajorBit>\n        struct skyline_product_selector;\n\ntemplate<typename Lhs, typename Rhs, typename ResultType>\nstruct skyline_product_selector<Lhs, Rhs, ResultType, RowMajor> {\n    typedef typename traits<typename remove_all<Lhs>::type>::Scalar Scalar;\n\n    static void run(const Lhs& lhs, const Rhs& rhs, ResultType & res) {\n        skyline_row_major_time_dense_product<Lhs, Rhs, ResultType > (lhs, rhs, res);\n    }\n};\n\ntemplate<typename Lhs, typename Rhs, typename ResultType>\nstruct skyline_product_selector<Lhs, Rhs, ResultType, ColMajor> {\n    typedef typename traits<typename remove_all<Lhs>::type>::Scalar Scalar;\n\n    static void run(const Lhs& lhs, const Rhs& rhs, ResultType & res) {\n        skyline_col_major_time_dense_product<Lhs, Rhs, ResultType > (lhs, rhs, res);\n    }\n};\n\n} // end namespace internal\n\n// template<typename Derived>\n// template<typename Lhs, typename Rhs >\n// Derived & MatrixBase<Derived>::lazyAssign(const SkylineProduct<Lhs, Rhs, SkylineTimeDenseProduct>& product) {\n//     typedef typename internal::remove_all<Lhs>::type _Lhs;\n//     internal::skyline_product_selector<typename internal::remove_all<Lhs>::type,\n//             typename internal::remove_all<Rhs>::type,\n//             Derived>::run(product.lhs(), product.rhs(), derived());\n// \n//     return derived();\n// }\n\n// skyline * dense\n\ntemplate<typename Derived>\ntemplate<typename OtherDerived >\nEIGEN_STRONG_INLINE const typename SkylineProductReturnType<Derived, OtherDerived>::Type\nSkylineMatrixBase<Derived>::operator*(const MatrixBase<OtherDerived> &other) const {\n\n    return typename SkylineProductReturnType<Derived, OtherDerived>::Type(derived(), other.derived());\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_SKYLINEPRODUCT_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/Skyline/SkylineStorage.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Guillaume Saupin <guillaume.saupin@cea.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SKYLINE_STORAGE_H\n#define EIGEN_SKYLINE_STORAGE_H\n\nnamespace Eigen { \n\n/** Stores a skyline set of values in three structures :\n * The diagonal elements\n * The upper elements\n * The lower elements\n *\n */\ntemplate<typename Scalar>\nclass SkylineStorage {\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n    typedef SparseIndex Index;\npublic:\n\n    SkylineStorage()\n    : m_diag(0),\n    m_lower(0),\n    m_upper(0),\n    m_lowerProfile(0),\n    m_upperProfile(0),\n    m_diagSize(0),\n    m_upperSize(0),\n    m_lowerSize(0),\n    m_upperProfileSize(0),\n    m_lowerProfileSize(0),\n    m_allocatedSize(0) {\n    }\n\n    SkylineStorage(const SkylineStorage& other)\n    : m_diag(0),\n    m_lower(0),\n    m_upper(0),\n    m_lowerProfile(0),\n    m_upperProfile(0),\n    m_diagSize(0),\n    m_upperSize(0),\n    m_lowerSize(0),\n    m_upperProfileSize(0),\n    m_lowerProfileSize(0),\n    m_allocatedSize(0) {\n        *this = other;\n    }\n\n    SkylineStorage & operator=(const SkylineStorage& other) {\n        resize(other.diagSize(), other.m_upperProfileSize, other.m_lowerProfileSize, other.upperSize(), other.lowerSize());\n        memcpy(m_diag, other.m_diag, m_diagSize * sizeof (Scalar));\n        memcpy(m_upper, other.m_upper, other.upperSize() * sizeof (Scalar));\n        memcpy(m_lower, other.m_lower, other.lowerSize() * sizeof (Scalar));\n        memcpy(m_upperProfile, other.m_upperProfile, m_upperProfileSize * sizeof (Index));\n        memcpy(m_lowerProfile, other.m_lowerProfile, m_lowerProfileSize * sizeof (Index));\n        return *this;\n    }\n\n    void swap(SkylineStorage& other) {\n        std::swap(m_diag, other.m_diag);\n        std::swap(m_upper, other.m_upper);\n        std::swap(m_lower, other.m_lower);\n        std::swap(m_upperProfile, other.m_upperProfile);\n        std::swap(m_lowerProfile, other.m_lowerProfile);\n        std::swap(m_diagSize, other.m_diagSize);\n        std::swap(m_upperSize, other.m_upperSize);\n        std::swap(m_lowerSize, other.m_lowerSize);\n        std::swap(m_allocatedSize, other.m_allocatedSize);\n    }\n\n    ~SkylineStorage() {\n        delete[] m_diag;\n        delete[] m_upper;\n        if (m_upper != m_lower)\n            delete[] m_lower;\n        delete[] m_upperProfile;\n        delete[] m_lowerProfile;\n    }\n\n    void reserve(Index size, Index upperProfileSize, Index lowerProfileSize, Index upperSize, Index lowerSize) {\n        Index newAllocatedSize = size + upperSize + lowerSize;\n        if (newAllocatedSize > m_allocatedSize)\n            reallocate(size, upperProfileSize, lowerProfileSize, upperSize, lowerSize);\n    }\n\n    void squeeze() {\n        if (m_allocatedSize > m_diagSize + m_upperSize + m_lowerSize)\n            reallocate(m_diagSize, m_upperProfileSize, m_lowerProfileSize, m_upperSize, m_lowerSize);\n    }\n\n    void resize(Index diagSize, Index upperProfileSize, Index lowerProfileSize, Index upperSize, Index lowerSize, float reserveSizeFactor = 0) {\n        if (m_allocatedSize < diagSize + upperSize + lowerSize)\n            reallocate(diagSize, upperProfileSize, lowerProfileSize, upperSize + Index(reserveSizeFactor * upperSize), lowerSize + Index(reserveSizeFactor * lowerSize));\n        m_diagSize = diagSize;\n        m_upperSize = upperSize;\n        m_lowerSize = lowerSize;\n        m_upperProfileSize = upperProfileSize;\n        m_lowerProfileSize = lowerProfileSize;\n    }\n\n    inline Index diagSize() const {\n        return m_diagSize;\n    }\n\n    inline Index upperSize() const {\n        return m_upperSize;\n    }\n\n    inline Index lowerSize() const {\n        return m_lowerSize;\n    }\n\n    inline Index upperProfileSize() const {\n        return m_upperProfileSize;\n    }\n\n    inline Index lowerProfileSize() const {\n        return m_lowerProfileSize;\n    }\n\n    inline Index allocatedSize() const {\n        return m_allocatedSize;\n    }\n\n    inline void clear() {\n        m_diagSize = 0;\n    }\n\n    inline Scalar& diag(Index i) {\n        return m_diag[i];\n    }\n\n    inline const Scalar& diag(Index i) const {\n        return m_diag[i];\n    }\n\n    inline Scalar& upper(Index i) {\n        return m_upper[i];\n    }\n\n    inline const Scalar& upper(Index i) const {\n        return m_upper[i];\n    }\n\n    inline Scalar& lower(Index i) {\n        return m_lower[i];\n    }\n\n    inline const Scalar& lower(Index i) const {\n        return m_lower[i];\n    }\n\n    inline Index& upperProfile(Index i) {\n        return m_upperProfile[i];\n    }\n\n    inline const Index& upperProfile(Index i) const {\n        return m_upperProfile[i];\n    }\n\n    inline Index& lowerProfile(Index i) {\n        return m_lowerProfile[i];\n    }\n\n    inline const Index& lowerProfile(Index i) const {\n        return m_lowerProfile[i];\n    }\n\n    static SkylineStorage Map(Index* upperProfile, Index* lowerProfile, Scalar* diag, Scalar* upper, Scalar* lower, Index size, Index upperSize, Index lowerSize) {\n        SkylineStorage res;\n        res.m_upperProfile = upperProfile;\n        res.m_lowerProfile = lowerProfile;\n        res.m_diag = diag;\n        res.m_upper = upper;\n        res.m_lower = lower;\n        res.m_allocatedSize = res.m_diagSize = size;\n        res.m_upperSize = upperSize;\n        res.m_lowerSize = lowerSize;\n        return res;\n    }\n\n    inline void reset() {\n        memset(m_diag, 0, m_diagSize * sizeof (Scalar));\n        memset(m_upper, 0, m_upperSize * sizeof (Scalar));\n        memset(m_lower, 0, m_lowerSize * sizeof (Scalar));\n        memset(m_upperProfile, 0, m_diagSize * sizeof (Index));\n        memset(m_lowerProfile, 0, m_diagSize * sizeof (Index));\n    }\n\n    void prune(Scalar reference, RealScalar epsilon = dummy_precision<RealScalar>()) {\n        //TODO\n    }\n\nprotected:\n\n    inline void reallocate(Index diagSize, Index upperProfileSize, Index lowerProfileSize, Index upperSize, Index lowerSize) {\n\n        Scalar* diag = new Scalar[diagSize];\n        Scalar* upper = new Scalar[upperSize];\n        Scalar* lower = new Scalar[lowerSize];\n        Index* upperProfile = new Index[upperProfileSize];\n        Index* lowerProfile = new Index[lowerProfileSize];\n\n        Index copyDiagSize = (std::min)(diagSize, m_diagSize);\n        Index copyUpperSize = (std::min)(upperSize, m_upperSize);\n        Index copyLowerSize = (std::min)(lowerSize, m_lowerSize);\n        Index copyUpperProfileSize = (std::min)(upperProfileSize, m_upperProfileSize);\n        Index copyLowerProfileSize = (std::min)(lowerProfileSize, m_lowerProfileSize);\n\n        // copy\n        memcpy(diag, m_diag, copyDiagSize * sizeof (Scalar));\n        memcpy(upper, m_upper, copyUpperSize * sizeof (Scalar));\n        memcpy(lower, m_lower, copyLowerSize * sizeof (Scalar));\n        memcpy(upperProfile, m_upperProfile, copyUpperProfileSize * sizeof (Index));\n        memcpy(lowerProfile, m_lowerProfile, copyLowerProfileSize * sizeof (Index));\n\n\n\n        // delete old stuff\n        delete[] m_diag;\n        delete[] m_upper;\n        delete[] m_lower;\n        delete[] m_upperProfile;\n        delete[] m_lowerProfile;\n        m_diag = diag;\n        m_upper = upper;\n        m_lower = lower;\n        m_upperProfile = upperProfile;\n        m_lowerProfile = lowerProfile;\n        m_allocatedSize = diagSize + upperSize + lowerSize;\n        m_upperSize = upperSize;\n        m_lowerSize = lowerSize;\n    }\n\npublic:\n    Scalar* m_diag;\n    Scalar* m_upper;\n    Scalar* m_lower;\n    Index* m_upperProfile;\n    Index* m_lowerProfile;\n    Index m_diagSize;\n    Index m_upperSize;\n    Index m_lowerSize;\n    Index m_upperProfileSize;\n    Index m_lowerProfileSize;\n    Index m_allocatedSize;\n\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_COMPRESSED_STORAGE_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/Skyline/SkylineUtil.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Guillaume Saupin <guillaume.saupin@cea.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SKYLINEUTIL_H\n#define EIGEN_SKYLINEUTIL_H\n\nnamespace Eigen { \n\n#ifdef NDEBUG\n#define EIGEN_DBG_SKYLINE(X)\n#else\n#define EIGEN_DBG_SKYLINE(X) X\n#endif\n\nconst unsigned int SkylineBit = 0x1200;\ntemplate<typename Lhs, typename Rhs, int ProductMode> class SkylineProduct;\nenum AdditionalProductEvaluationMode {SkylineTimeDenseProduct, SkylineTimeSkylineProduct, DenseTimeSkylineProduct};\nenum {IsSkyline = SkylineBit};\n\n\n#define EIGEN_SKYLINE_INHERIT_ASSIGNMENT_OPERATOR(Derived, Op) \\\ntemplate<typename OtherDerived> \\\nEIGEN_STRONG_INLINE Derived& operator Op(const Eigen::SkylineMatrixBase<OtherDerived>& other) \\\n{ \\\n  return Base::operator Op(other.derived()); \\\n} \\\nEIGEN_STRONG_INLINE Derived& operator Op(const Derived& other) \\\n{ \\\n  return Base::operator Op(other); \\\n}\n\n#define EIGEN_SKYLINE_INHERIT_SCALAR_ASSIGNMENT_OPERATOR(Derived, Op) \\\ntemplate<typename Other> \\\nEIGEN_STRONG_INLINE Derived& operator Op(const Other& scalar) \\\n{ \\\n  return Base::operator Op(scalar); \\\n}\n\n#define EIGEN_SKYLINE_INHERIT_ASSIGNMENT_OPERATORS(Derived) \\\n  EIGEN_SKYLINE_INHERIT_ASSIGNMENT_OPERATOR(Derived, =) \\\n  EIGEN_SKYLINE_INHERIT_ASSIGNMENT_OPERATOR(Derived, +=) \\\n  EIGEN_SKYLINE_INHERIT_ASSIGNMENT_OPERATOR(Derived, -=) \\\n  EIGEN_SKYLINE_INHERIT_SCALAR_ASSIGNMENT_OPERATOR(Derived, *=) \\\n  EIGEN_SKYLINE_INHERIT_SCALAR_ASSIGNMENT_OPERATOR(Derived, /=)\n\n#define _EIGEN_SKYLINE_GENERIC_PUBLIC_INTERFACE(Derived, BaseClass) \\\n  typedef BaseClass Base; \\\n  typedef typename Eigen::internal::traits<Derived>::Scalar Scalar; \\\n  typedef typename Eigen::NumTraits<Scalar>::Real RealScalar; \\\n  typedef typename Eigen::internal::traits<Derived>::StorageKind StorageKind; \\\n  typedef typename Eigen::internal::index<StorageKind>::type Index; \\\n  enum {  Flags = Eigen::internal::traits<Derived>::Flags, };\n\n#define EIGEN_SKYLINE_GENERIC_PUBLIC_INTERFACE(Derived) \\\n  _EIGEN_SKYLINE_GENERIC_PUBLIC_INTERFACE(Derived, Eigen::SkylineMatrixBase<Derived>)\n\ntemplate<typename Derived> class SkylineMatrixBase;\ntemplate<typename _Scalar, int _Flags = 0> class SkylineMatrix;\ntemplate<typename _Scalar, int _Flags = 0> class DynamicSkylineMatrix;\ntemplate<typename _Scalar, int _Flags = 0> class SkylineVector;\ntemplate<typename _Scalar, int _Flags = 0> class MappedSkylineMatrix;\n\nnamespace internal {\n\ntemplate<typename Lhs, typename Rhs> struct skyline_product_mode;\ntemplate<typename Lhs, typename Rhs, int ProductMode = skyline_product_mode<Lhs,Rhs>::value> struct SkylineProductReturnType;\n\ntemplate<typename T> class eval<T,IsSkyline>\n{\n    typedef typename traits<T>::Scalar _Scalar;\n    enum {\n          _Flags = traits<T>::Flags\n    };\n\n  public:\n    typedef SkylineMatrix<_Scalar, _Flags> type;\n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_SKYLINEUTIL_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/SparseExtra/BlockOfDynamicSparseMatrix.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSE_BLOCKFORDYNAMICMATRIX_H\n#define EIGEN_SPARSE_BLOCKFORDYNAMICMATRIX_H\n\nnamespace Eigen { \n\n#if 0\n\n// NOTE Have to be reimplemented as a specialization of BlockImpl< DynamicSparseMatrix<_Scalar, _Options, _Index>, ... >\n// See SparseBlock.h for an example\n\n\n/***************************************************************************\n* specialisation for DynamicSparseMatrix\n***************************************************************************/\n\ntemplate<typename _Scalar, int _Options, typename _Index, int Size>\nclass SparseInnerVectorSet<DynamicSparseMatrix<_Scalar, _Options, _Index>, Size>\n  : public SparseMatrixBase<SparseInnerVectorSet<DynamicSparseMatrix<_Scalar, _Options, _Index>, Size> >\n{\n    typedef DynamicSparseMatrix<_Scalar, _Options, _Index> MatrixType;\n  public:\n\n    enum { IsRowMajor = internal::traits<SparseInnerVectorSet>::IsRowMajor };\n\n    EIGEN_SPARSE_PUBLIC_INTERFACE(SparseInnerVectorSet)\n    class InnerIterator: public MatrixType::InnerIterator\n    {\n      public:\n        inline InnerIterator(const SparseInnerVectorSet& xpr, Index outer)\n          : MatrixType::InnerIterator(xpr.m_matrix, xpr.m_outerStart + outer), m_outer(outer)\n        {}\n        inline Index row() const { return IsRowMajor ? m_outer : this->index(); }\n        inline Index col() const { return IsRowMajor ? this->index() : m_outer; }\n      protected:\n        Index m_outer;\n    };\n\n    inline SparseInnerVectorSet(const MatrixType& matrix, Index outerStart, Index outerSize)\n      : m_matrix(matrix), m_outerStart(outerStart), m_outerSize(outerSize)\n    {\n      eigen_assert( (outerStart>=0) && ((outerStart+outerSize)<=matrix.outerSize()) );\n    }\n\n    inline SparseInnerVectorSet(const MatrixType& matrix, Index outer)\n      : m_matrix(matrix), m_outerStart(outer), m_outerSize(Size)\n    {\n      eigen_assert(Size!=Dynamic);\n      eigen_assert( (outer>=0) && (outer<matrix.outerSize()) );\n    }\n\n    template<typename OtherDerived>\n    inline SparseInnerVectorSet& operator=(const SparseMatrixBase<OtherDerived>& other)\n    {\n      if (IsRowMajor != ((OtherDerived::Flags&RowMajorBit)==RowMajorBit))\n      {\n        // need to transpose => perform a block evaluation followed by a big swap\n        DynamicSparseMatrix<Scalar,IsRowMajor?RowMajorBit:0> aux(other);\n        *this = aux.markAsRValue();\n      }\n      else\n      {\n        // evaluate/copy vector per vector\n        for (Index j=0; j<m_outerSize.value(); ++j)\n        {\n          SparseVector<Scalar,IsRowMajor ? RowMajorBit : 0> aux(other.innerVector(j));\n          m_matrix.const_cast_derived()._data()[m_outerStart+j].swap(aux._data());\n        }\n      }\n      return *this;\n    }\n\n    inline SparseInnerVectorSet& operator=(const SparseInnerVectorSet& other)\n    {\n      return operator=<SparseInnerVectorSet>(other);\n    }\n\n    Index nonZeros() const\n    {\n      Index count = 0;\n      for (Index j=0; j<m_outerSize.value(); ++j)\n        count += m_matrix._data()[m_outerStart+j].size();\n      return count;\n    }\n\n    const Scalar& lastCoeff() const\n    {\n      EIGEN_STATIC_ASSERT_VECTOR_ONLY(SparseInnerVectorSet);\n      eigen_assert(m_matrix.data()[m_outerStart].size()>0);\n      return m_matrix.data()[m_outerStart].vale(m_matrix.data()[m_outerStart].size()-1);\n    }\n\n//     template<typename Sparse>\n//     inline SparseInnerVectorSet& operator=(const SparseMatrixBase<OtherDerived>& other)\n//     {\n//       return *this;\n//     }\n\n    EIGEN_STRONG_INLINE Index rows() const { return IsRowMajor ? m_outerSize.value() : m_matrix.rows(); }\n    EIGEN_STRONG_INLINE Index cols() const { return IsRowMajor ? m_matrix.cols() : m_outerSize.value(); }\n\n  protected:\n\n    const typename MatrixType::Nested m_matrix;\n    Index m_outerStart;\n    const internal::variable_if_dynamic<Index, Size> m_outerSize;\n\n};\n\n#endif\n\n} // end namespace Eigen\n\n#endif // EIGEN_SPARSE_BLOCKFORDYNAMICMATRIX_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/SparseExtra/BlockSparseMatrix.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2013 Desire Nuentsa <desire.nuentsa_wakam@inria.fr>\n// Copyright (C) 2013 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSEBLOCKMATRIX_H\n#define EIGEN_SPARSEBLOCKMATRIX_H\n\nnamespace Eigen { \n/** \\ingroup SparseCore_Module\n  *\n  * \\class BlockSparseMatrix\n  *\n  * \\brief A versatile sparse matrix representation where each element is a block\n  *\n  * This class provides routines to manipulate block sparse matrices stored in a\n  * BSR-like representation. There are two main types :\n  *\n  * 1. All blocks have the same number of rows and columns, called block size\n  * in the following. In this case, if this block size is known at compile time,\n  * it can be given as a template parameter like\n  * \\code\n  * BlockSparseMatrix<Scalar, 3, ColMajor> bmat(b_rows, b_cols);\n  * \\endcode\n  * Here, bmat is a b_rows x b_cols block sparse matrix\n  * where each coefficient is a 3x3 dense matrix.\n  * If the block size is fixed but will be given at runtime,\n  * \\code\n  * BlockSparseMatrix<Scalar, Dynamic, ColMajor> bmat(b_rows, b_cols);\n  * bmat.setBlockSize(block_size);\n  * \\endcode\n  *\n  * 2. The second case is for variable-block sparse matrices.\n  * Here each block has its own dimensions. The only restriction is that all the blocks\n  * in a row (resp. a column) should have the same number of rows (resp. of columns).\n  * It is thus required in this case to describe the layout of the matrix by calling\n  * setBlockLayout(rowBlocks, colBlocks).\n  *\n  * In any of the previous case, the matrix can be filled by calling setFromTriplets().\n  * A regular sparse matrix can be converted to a block sparse matrix and vice versa.\n  * It is obviously required to describe the block layout beforehand by calling either\n  * setBlockSize() for fixed-size blocks or setBlockLayout for variable-size blocks.\n  *\n  * \\tparam _Scalar The Scalar type\n  * \\tparam _BlockAtCompileTime The block layout option. It takes the following values\n  * Dynamic : block size known at runtime\n  * a numeric number : fixed-size block known at compile time\n  */\ntemplate<typename _Scalar, int _BlockAtCompileTime=Dynamic, int _Options=ColMajor, typename _StorageIndex=int> class BlockSparseMatrix;\n\ntemplate<typename BlockSparseMatrixT> class BlockSparseMatrixView;\n\nnamespace internal {\ntemplate<typename _Scalar, int _BlockAtCompileTime, int _Options, typename _Index>\nstruct traits<BlockSparseMatrix<_Scalar,_BlockAtCompileTime,_Options, _Index> >\n{\n  typedef _Scalar Scalar;\n  typedef _Index Index;\n  typedef Sparse StorageKind; // FIXME Where is it used ??\n  typedef MatrixXpr XprKind;\n  enum {\n    RowsAtCompileTime = Dynamic,\n    ColsAtCompileTime = Dynamic,\n    MaxRowsAtCompileTime = Dynamic,\n    MaxColsAtCompileTime = Dynamic,\n    BlockSize = _BlockAtCompileTime,\n    Flags = _Options | NestByRefBit | LvalueBit,\n    CoeffReadCost = NumTraits<Scalar>::ReadCost,\n    SupportedAccessPatterns = InnerRandomAccessPattern\n  };\n};\ntemplate<typename BlockSparseMatrixT>\nstruct traits<BlockSparseMatrixView<BlockSparseMatrixT> >\n{\n  typedef Ref<Matrix<typename BlockSparseMatrixT::Scalar, BlockSparseMatrixT::BlockSize, BlockSparseMatrixT::BlockSize> > Scalar;\n  typedef Ref<Matrix<typename BlockSparseMatrixT::RealScalar, BlockSparseMatrixT::BlockSize, BlockSparseMatrixT::BlockSize> > RealScalar;\n\n};\n\n// Function object to sort a triplet list\ntemplate<typename Iterator, bool IsColMajor>\nstruct TripletComp\n{\n  typedef typename Iterator::value_type Triplet;\n  bool operator()(const Triplet& a, const Triplet& b)\n  { if(IsColMajor)\n      return ((a.col() == b.col() && a.row() < b.row()) || (a.col() < b.col()));\n    else\n      return ((a.row() == b.row() && a.col() < b.col()) || (a.row() < b.row()));\n  }\n};\n} // end namespace internal\n\n\n/* Proxy to view the block sparse matrix as a regular sparse matrix */\ntemplate<typename BlockSparseMatrixT>\nclass BlockSparseMatrixView : public SparseMatrixBase<BlockSparseMatrixT>\n{\n  public:\n    typedef Ref<typename BlockSparseMatrixT::BlockScalar> Scalar;\n    typedef Ref<typename BlockSparseMatrixT::BlockRealScalar> RealScalar;\n    typedef typename BlockSparseMatrixT::Index Index;\n    typedef  BlockSparseMatrixT Nested;\n    enum {\n      Flags = BlockSparseMatrixT::Options,\n      Options = BlockSparseMatrixT::Options,\n      RowsAtCompileTime = BlockSparseMatrixT::RowsAtCompileTime,\n      ColsAtCompileTime = BlockSparseMatrixT::ColsAtCompileTime,\n      MaxColsAtCompileTime = BlockSparseMatrixT::MaxColsAtCompileTime,\n      MaxRowsAtCompileTime = BlockSparseMatrixT::MaxRowsAtCompileTime\n    };\n  public:\n    BlockSparseMatrixView(const BlockSparseMatrixT& spblockmat)\n     : m_spblockmat(spblockmat)\n    {}\n\n    Index outerSize() const\n    {\n      return (Flags&RowMajorBit) == 1 ? this->rows() : this->cols();\n    }\n    Index cols() const\n    {\n      return m_spblockmat.blockCols();\n    }\n    Index rows() const\n    {\n      return m_spblockmat.blockRows();\n    }\n    Scalar coeff(Index row, Index col)\n    {\n      return m_spblockmat.coeff(row, col);\n    }\n    Scalar coeffRef(Index row, Index col)\n    {\n      return m_spblockmat.coeffRef(row, col);\n    }\n    // Wrapper to iterate over all blocks\n    class InnerIterator : public BlockSparseMatrixT::BlockInnerIterator\n    {\n      public:\n      InnerIterator(const BlockSparseMatrixView& mat, Index outer)\n          : BlockSparseMatrixT::BlockInnerIterator(mat.m_spblockmat, outer)\n      {}\n\n    };\n\n  protected:\n    const BlockSparseMatrixT& m_spblockmat;\n};\n\n// Proxy to view a regular vector as a block vector\ntemplate<typename BlockSparseMatrixT, typename VectorType>\nclass BlockVectorView\n{\n  public:\n    enum {\n      BlockSize = BlockSparseMatrixT::BlockSize,\n      ColsAtCompileTime = VectorType::ColsAtCompileTime,\n      RowsAtCompileTime = VectorType::RowsAtCompileTime,\n      Flags = VectorType::Flags\n    };\n    typedef Ref<const Matrix<typename BlockSparseMatrixT::Scalar, (RowsAtCompileTime==1)? 1 : BlockSize, (ColsAtCompileTime==1)? 1 : BlockSize> >Scalar;\n    typedef typename BlockSparseMatrixT::Index Index;\n  public:\n    BlockVectorView(const BlockSparseMatrixT& spblockmat, const VectorType& vec)\n    : m_spblockmat(spblockmat),m_vec(vec)\n    { }\n    inline Index cols() const\n    {\n      return m_vec.cols();\n    }\n    inline Index size() const\n    {\n      return m_spblockmat.blockRows();\n    }\n    inline Scalar coeff(Index bi) const\n    {\n      Index startRow = m_spblockmat.blockRowsIndex(bi);\n      Index rowSize = m_spblockmat.blockRowsIndex(bi+1) - startRow;\n      return m_vec.middleRows(startRow, rowSize);\n    }\n    inline Scalar coeff(Index bi, Index j) const\n    {\n      Index startRow = m_spblockmat.blockRowsIndex(bi);\n      Index rowSize = m_spblockmat.blockRowsIndex(bi+1) - startRow;\n      return m_vec.block(startRow, j, rowSize, 1);\n    }\n  protected:\n    const BlockSparseMatrixT& m_spblockmat;\n    const VectorType& m_vec;\n};\n\ntemplate<typename VectorType, typename Index> class BlockVectorReturn;\n\n\n// Proxy to view a regular vector as a block vector\ntemplate<typename BlockSparseMatrixT, typename VectorType>\nclass BlockVectorReturn\n{\n  public:\n    enum {\n      ColsAtCompileTime = VectorType::ColsAtCompileTime,\n      RowsAtCompileTime = VectorType::RowsAtCompileTime,\n      Flags = VectorType::Flags\n    };\n    typedef Ref<Matrix<typename VectorType::Scalar, RowsAtCompileTime, ColsAtCompileTime> > Scalar;\n    typedef typename BlockSparseMatrixT::Index Index;\n  public:\n    BlockVectorReturn(const BlockSparseMatrixT& spblockmat, VectorType& vec)\n    : m_spblockmat(spblockmat),m_vec(vec)\n    { }\n    inline Index size() const\n    {\n      return m_spblockmat.blockRows();\n    }\n    inline Scalar coeffRef(Index bi)\n    {\n      Index startRow = m_spblockmat.blockRowsIndex(bi);\n      Index rowSize = m_spblockmat.blockRowsIndex(bi+1) - startRow;\n      return m_vec.middleRows(startRow, rowSize);\n    }\n    inline Scalar coeffRef(Index bi, Index j)\n    {\n      Index startRow = m_spblockmat.blockRowsIndex(bi);\n      Index rowSize = m_spblockmat.blockRowsIndex(bi+1) - startRow;\n      return m_vec.block(startRow, j, rowSize, 1);\n    }\n\n  protected:\n    const BlockSparseMatrixT& m_spblockmat;\n    VectorType& m_vec;\n};\n\n// Block version of the sparse dense product\ntemplate<typename Lhs, typename Rhs>\nclass BlockSparseTimeDenseProduct;\n\nnamespace internal {\n\ntemplate<typename BlockSparseMatrixT, typename VecType>\nstruct traits<BlockSparseTimeDenseProduct<BlockSparseMatrixT, VecType> >\n{\n  typedef Dense StorageKind;\n  typedef MatrixXpr XprKind;\n  typedef typename BlockSparseMatrixT::Scalar Scalar;\n  typedef typename BlockSparseMatrixT::Index Index;\n  enum {\n    RowsAtCompileTime = Dynamic,\n    ColsAtCompileTime = Dynamic,\n    MaxRowsAtCompileTime = Dynamic,\n    MaxColsAtCompileTime = Dynamic,\n    Flags = 0,\n    CoeffReadCost = internal::traits<BlockSparseMatrixT>::CoeffReadCost\n  };\n};\n} // end namespace internal\n\ntemplate<typename Lhs, typename Rhs>\nclass BlockSparseTimeDenseProduct\n  : public ProductBase<BlockSparseTimeDenseProduct<Lhs,Rhs>, Lhs, Rhs>\n{\n  public:\n    EIGEN_PRODUCT_PUBLIC_INTERFACE(BlockSparseTimeDenseProduct)\n\n    BlockSparseTimeDenseProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs)\n    {}\n\n    template<typename Dest> void scaleAndAddTo(Dest& dest, const typename Rhs::Scalar& alpha) const\n    {\n      BlockVectorReturn<Lhs,Dest> tmpDest(m_lhs, dest);\n      internal::sparse_time_dense_product( BlockSparseMatrixView<Lhs>(m_lhs),  BlockVectorView<Lhs, Rhs>(m_lhs, m_rhs), tmpDest, alpha);\n    }\n\n  private:\n    BlockSparseTimeDenseProduct& operator=(const BlockSparseTimeDenseProduct&);\n};\n\ntemplate<typename _Scalar, int _BlockAtCompileTime, int _Options, typename _StorageIndex>\nclass BlockSparseMatrix : public SparseMatrixBase<BlockSparseMatrix<_Scalar,_BlockAtCompileTime, _Options,_StorageIndex> >\n{\n  public:\n    typedef _Scalar Scalar;\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n    typedef _StorageIndex StorageIndex;\n    typedef typename internal::ref_selector<BlockSparseMatrix<_Scalar, _BlockAtCompileTime, _Options, _StorageIndex> >::type Nested;\n\n    enum {\n      Options = _Options,\n      Flags = Options,\n      BlockSize=_BlockAtCompileTime,\n      RowsAtCompileTime = Dynamic,\n      ColsAtCompileTime = Dynamic,\n      MaxRowsAtCompileTime = Dynamic,\n      MaxColsAtCompileTime = Dynamic,\n      IsVectorAtCompileTime = 0,\n      IsColMajor = Flags&RowMajorBit ? 0 : 1\n    };\n    typedef Matrix<Scalar, _BlockAtCompileTime, _BlockAtCompileTime,IsColMajor ? ColMajor : RowMajor> BlockScalar;\n    typedef Matrix<RealScalar, _BlockAtCompileTime, _BlockAtCompileTime,IsColMajor ? ColMajor : RowMajor> BlockRealScalar;\n    typedef typename internal::conditional<_BlockAtCompileTime==Dynamic, Scalar, BlockScalar>::type BlockScalarReturnType;\n    typedef BlockSparseMatrix<Scalar, BlockSize, IsColMajor ? ColMajor : RowMajor, StorageIndex> PlainObject;\n  public:\n    // Default constructor\n    BlockSparseMatrix()\n    : m_innerBSize(0),m_outerBSize(0),m_innerOffset(0),m_outerOffset(0),\n      m_nonzerosblocks(0),m_values(0),m_blockPtr(0),m_indices(0),\n      m_outerIndex(0),m_blockSize(BlockSize)\n    { }\n\n\n    /**\n     * \\brief Construct and resize\n     *\n     */\n    BlockSparseMatrix(Index brow, Index bcol)\n      : m_innerBSize(IsColMajor ? brow : bcol),\n        m_outerBSize(IsColMajor ? bcol : brow),\n        m_innerOffset(0),m_outerOffset(0),m_nonzerosblocks(0),\n        m_values(0),m_blockPtr(0),m_indices(0),\n        m_outerIndex(0),m_blockSize(BlockSize)\n    { }\n\n    /**\n     * \\brief Copy-constructor\n     */\n    BlockSparseMatrix(const BlockSparseMatrix& other)\n      : m_innerBSize(other.m_innerBSize),m_outerBSize(other.m_outerBSize),\n        m_nonzerosblocks(other.m_nonzerosblocks),m_nonzeros(other.m_nonzeros),\n        m_blockPtr(0),m_blockSize(other.m_blockSize)\n    {\n      // should we allow copying between variable-size blocks and fixed-size blocks ??\n      eigen_assert(m_blockSize == BlockSize && \" CAN NOT COPY BETWEEN FIXED-SIZE AND VARIABLE-SIZE BLOCKS\");\n\n      std::copy(other.m_innerOffset, other.m_innerOffset+m_innerBSize+1, m_innerOffset);\n      std::copy(other.m_outerOffset, other.m_outerOffset+m_outerBSize+1, m_outerOffset);\n      std::copy(other.m_values, other.m_values+m_nonzeros, m_values);\n\n      if(m_blockSize != Dynamic)\n        std::copy(other.m_blockPtr, other.m_blockPtr+m_nonzerosblocks, m_blockPtr);\n\n      std::copy(other.m_indices, other.m_indices+m_nonzerosblocks, m_indices);\n      std::copy(other.m_outerIndex, other.m_outerIndex+m_outerBSize, m_outerIndex);\n    }\n\n    friend void swap(BlockSparseMatrix& first, BlockSparseMatrix& second)\n    {\n      std::swap(first.m_innerBSize, second.m_innerBSize);\n      std::swap(first.m_outerBSize, second.m_outerBSize);\n      std::swap(first.m_innerOffset, second.m_innerOffset);\n      std::swap(first.m_outerOffset, second.m_outerOffset);\n      std::swap(first.m_nonzerosblocks, second.m_nonzerosblocks);\n      std::swap(first.m_nonzeros, second.m_nonzeros);\n      std::swap(first.m_values, second.m_values);\n      std::swap(first.m_blockPtr, second.m_blockPtr);\n      std::swap(first.m_indices, second.m_indices);\n      std::swap(first.m_outerIndex, second.m_outerIndex);\n      std::swap(first.m_BlockSize, second.m_blockSize);\n    }\n\n    BlockSparseMatrix& operator=(BlockSparseMatrix other)\n    {\n      //Copy-and-swap paradigm ... avoid leaked data if thrown\n      swap(*this, other);\n      return *this;\n    }\n\n    // Destructor\n    ~BlockSparseMatrix()\n    {\n      delete[] m_outerIndex;\n      delete[] m_innerOffset;\n      delete[] m_outerOffset;\n      delete[] m_indices;\n      delete[] m_blockPtr;\n      delete[] m_values;\n    }\n\n\n    /**\n      * \\brief Constructor from a sparse matrix\n      *\n      */\n    template<typename MatrixType>\n    inline BlockSparseMatrix(const MatrixType& spmat) : m_blockSize(BlockSize)\n    {\n      EIGEN_STATIC_ASSERT((m_blockSize != Dynamic), THIS_METHOD_IS_ONLY_FOR_FIXED_SIZE);\n\n      *this = spmat;\n    }\n\n    /**\n      * \\brief Assignment from a sparse matrix with the same storage order\n      *\n      * Convert from a sparse matrix to block sparse matrix.\n      * \\warning Before calling this function, tt is necessary to call\n      * either setBlockLayout() (matrices with variable-size blocks)\n      * or setBlockSize() (for fixed-size blocks).\n      */\n    template<typename MatrixType>\n    inline BlockSparseMatrix& operator=(const MatrixType& spmat)\n    {\n      eigen_assert((m_innerBSize != 0 && m_outerBSize != 0)\n                   && \"Trying to assign to a zero-size matrix, call resize() first\");\n      eigen_assert(((MatrixType::Options&RowMajorBit) != IsColMajor) && \"Wrong storage order\");\n      typedef SparseMatrix<bool,MatrixType::Options,typename MatrixType::Index> MatrixPatternType;\n      MatrixPatternType  blockPattern(blockRows(), blockCols());\n      m_nonzeros = 0;\n\n      // First, compute the number of nonzero blocks and their locations\n      for(StorageIndex bj = 0; bj < m_outerBSize; ++bj)\n      {\n        // Browse each outer block and compute the structure\n        std::vector<bool> nzblocksFlag(m_innerBSize,false);  // Record the existing blocks\n        blockPattern.startVec(bj);\n        for(StorageIndex j = blockOuterIndex(bj); j < blockOuterIndex(bj+1); ++j)\n        {\n          typename MatrixType::InnerIterator it_spmat(spmat, j);\n          for(; it_spmat; ++it_spmat)\n          {\n            StorageIndex bi = innerToBlock(it_spmat.index()); // Index of the current nonzero block\n            if(!nzblocksFlag[bi])\n            {\n              // Save the index of this nonzero block\n              nzblocksFlag[bi] = true;\n              blockPattern.insertBackByOuterInnerUnordered(bj, bi) = true;\n              // Compute the total number of nonzeros (including explicit zeros in blocks)\n              m_nonzeros += blockOuterSize(bj) * blockInnerSize(bi);\n            }\n          }\n        } // end current outer block\n      }\n      blockPattern.finalize();\n\n      // Allocate the internal arrays\n      setBlockStructure(blockPattern);\n\n      for(StorageIndex nz = 0; nz < m_nonzeros; ++nz) m_values[nz] = Scalar(0);\n      for(StorageIndex bj = 0; bj < m_outerBSize; ++bj)\n      {\n        // Now copy the values\n        for(StorageIndex j = blockOuterIndex(bj); j < blockOuterIndex(bj+1); ++j)\n        {\n          // Browse the outer block column by column (for column-major matrices)\n          typename MatrixType::InnerIterator it_spmat(spmat, j);\n          for(; it_spmat; ++it_spmat)\n          {\n            StorageIndex idx = 0; // Position of this block in the column block\n            StorageIndex bi = innerToBlock(it_spmat.index()); // Index of the current nonzero block\n            // Go to the inner block where this element belongs to\n            while(bi > m_indices[m_outerIndex[bj]+idx]) ++idx; // Not expensive for ordered blocks\n            StorageIndex idxVal;// Get the right position in the array of values for this element\n            if(m_blockSize == Dynamic)\n            {\n              // Offset from all blocks before ...\n              idxVal =  m_blockPtr[m_outerIndex[bj]+idx];\n              // ... and offset inside the block\n              idxVal += (j - blockOuterIndex(bj)) * blockOuterSize(bj) + it_spmat.index() - m_innerOffset[bi];\n            }\n            else\n            {\n              // All blocks before\n              idxVal = (m_outerIndex[bj] + idx) * m_blockSize * m_blockSize;\n              // inside the block\n              idxVal += (j - blockOuterIndex(bj)) * m_blockSize + (it_spmat.index()%m_blockSize);\n            }\n            // Insert the value\n            m_values[idxVal] = it_spmat.value();\n          } // end of this column\n        } // end of this block\n      } // end of this outer block\n\n      return *this;\n    }\n\n    /**\n      * \\brief Set the nonzero block pattern of the matrix\n      *\n      * Given a sparse matrix describing the nonzero block pattern,\n      * this function prepares the internal pointers for values.\n      * After calling this function, any *nonzero* block (bi, bj) can be set\n      * with a simple call to coeffRef(bi,bj).\n      *\n      *\n      * \\warning Before calling this function, tt is necessary to call\n      * either setBlockLayout() (matrices with variable-size blocks)\n      * or setBlockSize() (for fixed-size blocks).\n      *\n      * \\param blockPattern Sparse matrix of boolean elements describing the block structure\n      *\n      * \\sa setBlockLayout() \\sa setBlockSize()\n      */\n    template<typename MatrixType>\n    void setBlockStructure(const MatrixType& blockPattern)\n    {\n      resize(blockPattern.rows(), blockPattern.cols());\n      reserve(blockPattern.nonZeros());\n\n      // Browse the block pattern and set up the various pointers\n      m_outerIndex[0] = 0;\n      if(m_blockSize == Dynamic) m_blockPtr[0] = 0;\n      for(StorageIndex nz = 0; nz < m_nonzeros; ++nz) m_values[nz] = Scalar(0);\n      for(StorageIndex bj = 0; bj < m_outerBSize; ++bj)\n      {\n        //Browse each outer block\n\n        //First, copy and save the indices of nonzero blocks\n        //FIXME : find a way to avoid this ...\n        std::vector<int> nzBlockIdx;\n        typename MatrixType::InnerIterator it(blockPattern, bj);\n        for(; it; ++it)\n        {\n          nzBlockIdx.push_back(it.index());\n        }\n        std::sort(nzBlockIdx.begin(), nzBlockIdx.end());\n\n        // Now, fill block indices and (eventually) pointers to blocks\n        for(StorageIndex idx = 0; idx < nzBlockIdx.size(); ++idx)\n        {\n          StorageIndex offset = m_outerIndex[bj]+idx; // offset in m_indices\n          m_indices[offset] = nzBlockIdx[idx];\n          if(m_blockSize == Dynamic)\n            m_blockPtr[offset] = m_blockPtr[offset-1] + blockInnerSize(nzBlockIdx[idx]) * blockOuterSize(bj);\n          // There is no blockPtr for fixed-size blocks... not needed !???\n        }\n        // Save the pointer to the next outer block\n        m_outerIndex[bj+1] = m_outerIndex[bj] + nzBlockIdx.size();\n      }\n    }\n\n    /**\n      * \\brief Set the number of rows and columns blocks\n      */\n    inline void resize(Index brow, Index bcol)\n    {\n      m_innerBSize = IsColMajor ? brow : bcol;\n      m_outerBSize = IsColMajor ? bcol : brow;\n    }\n\n    /**\n      * \\brief set the block size at runtime for fixed-size block layout\n      *\n      * Call this only for fixed-size blocks\n      */\n    inline void setBlockSize(Index blockSize)\n    {\n      m_blockSize = blockSize;\n    }\n\n    /**\n      * \\brief Set the row and column block layouts,\n      *\n      * This function set the size of each row and column block.\n      * So this function should be used only for blocks with variable size.\n      * \\param rowBlocks : Number of rows per row block\n      * \\param colBlocks : Number of columns per column block\n      * \\sa resize(), setBlockSize()\n      */\n    inline void setBlockLayout(const VectorXi& rowBlocks, const VectorXi& colBlocks)\n    {\n      const VectorXi& innerBlocks = IsColMajor ? rowBlocks : colBlocks;\n      const VectorXi& outerBlocks = IsColMajor ? colBlocks : rowBlocks;\n      eigen_assert(m_innerBSize == innerBlocks.size() && \"CHECK THE NUMBER OF ROW OR COLUMN BLOCKS\");\n      eigen_assert(m_outerBSize == outerBlocks.size() && \"CHECK THE NUMBER OF ROW OR COLUMN BLOCKS\");\n      m_outerBSize = outerBlocks.size();\n      //  starting index of blocks... cumulative sums\n      m_innerOffset = new StorageIndex[m_innerBSize+1];\n      m_outerOffset = new StorageIndex[m_outerBSize+1];\n      m_innerOffset[0] = 0;\n      m_outerOffset[0] = 0;\n      std::partial_sum(&innerBlocks[0], &innerBlocks[m_innerBSize-1]+1, &m_innerOffset[1]);\n      std::partial_sum(&outerBlocks[0], &outerBlocks[m_outerBSize-1]+1, &m_outerOffset[1]);\n\n      // Compute the total number of nonzeros\n      m_nonzeros = 0;\n      for(StorageIndex bj = 0; bj < m_outerBSize; ++bj)\n        for(StorageIndex bi = 0; bi < m_innerBSize; ++bi)\n          m_nonzeros += outerBlocks[bj] * innerBlocks[bi];\n\n    }\n\n    /**\n      * \\brief Allocate the internal array of pointers to blocks and their inner indices\n      *\n      * \\note For fixed-size blocks, call setBlockSize() to set the block.\n      * And For variable-size blocks, call setBlockLayout() before using this function\n      *\n      * \\param nonzerosblocks Number of nonzero blocks. The total number of nonzeros is\n      * is computed in setBlockLayout() for variable-size blocks\n      * \\sa setBlockSize()\n      */\n    inline void reserve(const Index nonzerosblocks)\n    {\n      eigen_assert((m_innerBSize != 0 && m_outerBSize != 0) &&\n          \"TRYING TO RESERVE ZERO-SIZE MATRICES, CALL resize() first\");\n\n      //FIXME Should free if already allocated\n      m_outerIndex = new StorageIndex[m_outerBSize+1];\n\n      m_nonzerosblocks = nonzerosblocks;\n      if(m_blockSize != Dynamic)\n      {\n        m_nonzeros = nonzerosblocks * (m_blockSize * m_blockSize);\n        m_blockPtr = 0;\n      }\n      else\n      {\n        // m_nonzeros  is already computed in setBlockLayout()\n        m_blockPtr = new StorageIndex[m_nonzerosblocks+1];\n      }\n      m_indices = new StorageIndex[m_nonzerosblocks+1];\n      m_values = new Scalar[m_nonzeros];\n    }\n\n\n    /**\n      * \\brief Fill values in a matrix  from a triplet list.\n      *\n      * Each triplet item has a block stored in an Eigen dense matrix.\n      * The InputIterator class should provide the functions row(), col() and value()\n      *\n      * \\note For fixed-size blocks, call setBlockSize() before this function.\n      *\n      * FIXME Do not accept duplicates\n      */\n    template<typename InputIterator>\n    void setFromTriplets(const InputIterator& begin, const InputIterator& end)\n    {\n      eigen_assert((m_innerBSize!=0 && m_outerBSize !=0) && \"ZERO BLOCKS, PLEASE CALL resize() before\");\n\n      /* First, sort the triplet list\n        * FIXME This can be unnecessarily expensive since only the inner indices have to be sorted\n        * The best approach is like in SparseMatrix::setFromTriplets()\n        */\n      internal::TripletComp<InputIterator, IsColMajor> tripletcomp;\n      std::sort(begin, end, tripletcomp);\n\n      /* Count the number of rows and column blocks,\n       * and the number of nonzero blocks per outer dimension\n       */\n      VectorXi rowBlocks(m_innerBSize); // Size of each block row\n      VectorXi colBlocks(m_outerBSize); // Size of each block column\n      rowBlocks.setZero(); colBlocks.setZero();\n      VectorXi nzblock_outer(m_outerBSize); // Number of nz blocks per outer vector\n      VectorXi nz_outer(m_outerBSize); // Number of nz per outer vector...for variable-size blocks\n      nzblock_outer.setZero();\n      nz_outer.setZero();\n      for(InputIterator it(begin); it !=end; ++it)\n      {\n        eigen_assert(it->row() >= 0 && it->row() < this->blockRows() && it->col() >= 0 && it->col() < this->blockCols());\n        eigen_assert((it->value().rows() == it->value().cols() && (it->value().rows() == m_blockSize))\n                     || (m_blockSize == Dynamic));\n\n        if(m_blockSize == Dynamic)\n        {\n          eigen_assert((rowBlocks[it->row()] == 0 || rowBlocks[it->row()] == it->value().rows()) &&\n              \"NON CORRESPONDING SIZES FOR ROW BLOCKS\");\n          eigen_assert((colBlocks[it->col()] == 0 || colBlocks[it->col()] == it->value().cols()) &&\n              \"NON CORRESPONDING SIZES FOR COLUMN BLOCKS\");\n          rowBlocks[it->row()] =it->value().rows();\n          colBlocks[it->col()] = it->value().cols();\n        }\n        nz_outer(IsColMajor ? it->col() : it->row()) += it->value().rows() * it->value().cols();\n        nzblock_outer(IsColMajor ? it->col() : it->row())++;\n      }\n      // Allocate member arrays\n      if(m_blockSize == Dynamic) setBlockLayout(rowBlocks, colBlocks);\n      StorageIndex nzblocks = nzblock_outer.sum();\n      reserve(nzblocks);\n\n       // Temporary markers\n      VectorXi block_id(m_outerBSize); // To be used as a block marker during insertion\n\n      // Setup outer index pointers and markers\n      m_outerIndex[0] = 0;\n      if (m_blockSize == Dynamic)  m_blockPtr[0] =  0;\n      for(StorageIndex bj = 0; bj < m_outerBSize; ++bj)\n      {\n        m_outerIndex[bj+1] = m_outerIndex[bj] + nzblock_outer(bj);\n        block_id(bj) = m_outerIndex[bj];\n        if(m_blockSize==Dynamic)\n        {\n          m_blockPtr[m_outerIndex[bj+1]] = m_blockPtr[m_outerIndex[bj]] + nz_outer(bj);\n        }\n      }\n\n      // Fill the matrix\n      for(InputIterator it(begin); it!=end; ++it)\n      {\n        StorageIndex outer = IsColMajor ? it->col() : it->row();\n        StorageIndex inner = IsColMajor ? it->row() : it->col();\n        m_indices[block_id(outer)] = inner;\n        StorageIndex block_size = it->value().rows()*it->value().cols();\n        StorageIndex nz_marker = blockPtr(block_id[outer]);\n        memcpy(&(m_values[nz_marker]), it->value().data(), block_size * sizeof(Scalar));\n        if(m_blockSize == Dynamic)\n        {\n          m_blockPtr[block_id(outer)+1] = m_blockPtr[block_id(outer)] + block_size;\n        }\n        block_id(outer)++;\n      }\n\n      // An alternative when the outer indices are sorted...no need to use an array of markers\n//      for(Index bcol = 0; bcol < m_outerBSize; ++bcol)\n//      {\n//      Index id = 0, id_nz = 0, id_nzblock = 0;\n//      for(InputIterator it(begin); it!=end; ++it)\n//      {\n//        while (id<bcol) // one pass should do the job unless there are empty columns\n//        {\n//          id++;\n//          m_outerIndex[id+1]=m_outerIndex[id];\n//        }\n//        m_outerIndex[id+1] += 1;\n//        m_indices[id_nzblock]=brow;\n//        Index block_size = it->value().rows()*it->value().cols();\n//        m_blockPtr[id_nzblock+1] = m_blockPtr[id_nzblock] + block_size;\n//        id_nzblock++;\n//        memcpy(&(m_values[id_nz]),it->value().data(), block_size*sizeof(Scalar));\n//        id_nz += block_size;\n//      }\n//      while(id < m_outerBSize-1) // Empty columns at the end\n//      {\n//        id++;\n//        m_outerIndex[id+1]=m_outerIndex[id];\n//      }\n//      }\n    }\n\n\n    /**\n      * \\returns the number of rows\n      */\n    inline Index rows() const\n    {\n//      return blockRows();\n      return (IsColMajor ? innerSize() : outerSize());\n    }\n\n    /**\n      * \\returns the number of cols\n      */\n    inline Index cols() const\n    {\n//      return blockCols();\n      return (IsColMajor ? outerSize() : innerSize());\n    }\n\n    inline Index innerSize() const\n    {\n      if(m_blockSize == Dynamic) return m_innerOffset[m_innerBSize];\n      else return  (m_innerBSize * m_blockSize) ;\n    }\n\n    inline Index outerSize() const\n    {\n      if(m_blockSize == Dynamic) return m_outerOffset[m_outerBSize];\n      else return  (m_outerBSize * m_blockSize) ;\n    }\n    /** \\returns the number of rows grouped by blocks */\n    inline Index blockRows() const\n    {\n      return (IsColMajor ? m_innerBSize : m_outerBSize);\n    }\n    /** \\returns the number of columns grouped by blocks */\n    inline Index blockCols() const\n    {\n      return (IsColMajor ? m_outerBSize : m_innerBSize);\n    }\n\n    inline Index outerBlocks() const { return m_outerBSize; }\n    inline Index innerBlocks() const { return m_innerBSize; }\n\n    /** \\returns the block index where outer belongs to */\n    inline Index outerToBlock(Index outer) const\n    {\n      eigen_assert(outer < outerSize() && \"OUTER INDEX OUT OF BOUNDS\");\n\n      if(m_blockSize != Dynamic)\n        return (outer / m_blockSize); // Integer division\n\n      StorageIndex b_outer = 0;\n      while(m_outerOffset[b_outer] <= outer) ++b_outer;\n      return b_outer - 1;\n    }\n    /** \\returns  the block index where inner belongs to */\n    inline Index innerToBlock(Index inner) const\n    {\n      eigen_assert(inner < innerSize() && \"OUTER INDEX OUT OF BOUNDS\");\n\n      if(m_blockSize != Dynamic)\n        return (inner / m_blockSize); // Integer division\n\n      StorageIndex b_inner = 0;\n      while(m_innerOffset[b_inner] <= inner) ++b_inner;\n      return b_inner - 1;\n    }\n\n    /**\n      *\\returns a reference to the (i,j) block as an Eigen Dense Matrix\n      */\n    Ref<BlockScalar> coeffRef(Index brow, Index bcol)\n    {\n      eigen_assert(brow < blockRows() && \"BLOCK ROW INDEX OUT OF BOUNDS\");\n      eigen_assert(bcol < blockCols() && \"BLOCK nzblocksFlagCOLUMN OUT OF BOUNDS\");\n\n      StorageIndex rsize = IsColMajor ? blockInnerSize(brow): blockOuterSize(bcol);\n      StorageIndex csize = IsColMajor ? blockOuterSize(bcol) : blockInnerSize(brow);\n      StorageIndex inner = IsColMajor ? brow : bcol;\n      StorageIndex outer = IsColMajor ? bcol : brow;\n      StorageIndex offset = m_outerIndex[outer];\n      while(offset < m_outerIndex[outer+1] && m_indices[offset] != inner)\n        offset++;\n      if(m_indices[offset] == inner)\n      {\n        return Map<BlockScalar>(&(m_values[blockPtr(offset)]), rsize, csize);\n      }\n      else\n      {\n        //FIXME the block does not exist, Insert it !!!!!!!!!\n        eigen_assert(\"DYNAMIC INSERTION IS NOT YET SUPPORTED\");\n      }\n    }\n\n    /**\n      * \\returns the value of the (i,j) block as an Eigen Dense Matrix\n      */\n    Map<const BlockScalar> coeff(Index brow, Index bcol) const\n    {\n      eigen_assert(brow < blockRows() && \"BLOCK ROW INDEX OUT OF BOUNDS\");\n      eigen_assert(bcol < blockCols() && \"BLOCK COLUMN OUT OF BOUNDS\");\n\n      StorageIndex rsize = IsColMajor ? blockInnerSize(brow): blockOuterSize(bcol);\n      StorageIndex csize = IsColMajor ? blockOuterSize(bcol) : blockInnerSize(brow);\n      StorageIndex inner = IsColMajor ? brow : bcol;\n      StorageIndex outer = IsColMajor ? bcol : brow;\n      StorageIndex offset = m_outerIndex[outer];\n      while(offset < m_outerIndex[outer+1] && m_indices[offset] != inner) offset++;\n      if(m_indices[offset] == inner)\n      {\n        return Map<const BlockScalar> (&(m_values[blockPtr(offset)]), rsize, csize);\n      }\n      else\n//        return BlockScalar::Zero(rsize, csize);\n        eigen_assert(\"NOT YET SUPPORTED\");\n    }\n\n    // Block Matrix times vector product\n    template<typename VecType>\n    BlockSparseTimeDenseProduct<BlockSparseMatrix, VecType> operator*(const VecType& lhs) const\n    {\n      return BlockSparseTimeDenseProduct<BlockSparseMatrix, VecType>(*this, lhs);\n    }\n\n    /** \\returns the number of nonzero blocks */\n    inline Index nonZerosBlocks() const { return m_nonzerosblocks; }\n    /** \\returns the total number of nonzero elements, including eventual explicit zeros in blocks */\n    inline Index nonZeros() const { return m_nonzeros; }\n\n    inline BlockScalarReturnType *valuePtr() {return static_cast<BlockScalarReturnType *>(m_values);}\n//    inline Scalar *valuePtr(){ return m_values; }\n    inline StorageIndex *innerIndexPtr() {return m_indices; }\n    inline const StorageIndex *innerIndexPtr() const {return m_indices; }\n    inline StorageIndex *outerIndexPtr() {return m_outerIndex; }\n    inline const StorageIndex* outerIndexPtr() const {return m_outerIndex; }\n\n    /** \\brief for compatibility purposes with the SparseMatrix class */\n    inline bool isCompressed() const {return true;}\n    /**\n      * \\returns the starting index of the bi row block\n      */\n    inline Index blockRowsIndex(Index bi) const\n    {\n      return IsColMajor ? blockInnerIndex(bi) : blockOuterIndex(bi);\n    }\n\n    /**\n      * \\returns the starting index of the bj col block\n      */\n    inline Index blockColsIndex(Index bj) const\n    {\n      return IsColMajor ? blockOuterIndex(bj) : blockInnerIndex(bj);\n    }\n\n    inline Index blockOuterIndex(Index bj) const\n    {\n      return (m_blockSize == Dynamic) ? m_outerOffset[bj] : (bj * m_blockSize);\n    }\n    inline Index blockInnerIndex(Index bi) const\n    {\n      return (m_blockSize == Dynamic) ? m_innerOffset[bi] : (bi * m_blockSize);\n    }\n\n    // Not needed ???\n    inline Index blockInnerSize(Index bi) const\n    {\n      return (m_blockSize == Dynamic) ? (m_innerOffset[bi+1] - m_innerOffset[bi]) : m_blockSize;\n    }\n    inline Index blockOuterSize(Index bj) const\n    {\n      return (m_blockSize == Dynamic) ? (m_outerOffset[bj+1]- m_outerOffset[bj]) : m_blockSize;\n    }\n\n    /**\n      * \\brief Browse the matrix by outer index\n      */\n    class InnerIterator; // Browse column by column\n\n    /**\n      * \\brief Browse the matrix by block outer index\n      */\n    class BlockInnerIterator; // Browse block by block\n\n    friend std::ostream & operator << (std::ostream & s, const BlockSparseMatrix& m)\n    {\n      for (StorageIndex j = 0; j < m.outerBlocks(); ++j)\n      {\n        BlockInnerIterator itb(m, j);\n        for(; itb; ++itb)\n        {\n          s << \"(\"<<itb.row() << \", \" << itb.col() << \")\\n\";\n          s << itb.value() <<\"\\n\";\n        }\n      }\n      s << std::endl;\n      return s;\n    }\n\n    /**\n      * \\returns the starting position of the block <id> in the array of values\n      */\n    Index blockPtr(Index id) const\n    {\n      if(m_blockSize == Dynamic) return m_blockPtr[id];\n      else return id * m_blockSize * m_blockSize;\n      //return blockDynIdx(id, typename internal::conditional<(BlockSize==Dynamic), internal::true_type, internal::false_type>::type());\n    }\n\n\n  protected:\n//    inline Index blockDynIdx(Index id, internal::true_type) const\n//    {\n//      return m_blockPtr[id];\n//    }\n//    inline Index blockDynIdx(Index id, internal::false_type) const\n//    {\n//      return id * BlockSize * BlockSize;\n//    }\n\n    // To be implemented\n    // Insert a block at a particular location... need to make a room for that\n    Map<BlockScalar> insert(Index brow, Index bcol);\n\n    Index m_innerBSize; // Number of block rows\n    Index m_outerBSize; // Number of block columns\n    StorageIndex *m_innerOffset; // Starting index of each inner block (size m_innerBSize+1)\n    StorageIndex *m_outerOffset; // Starting index of each outer block (size m_outerBSize+1)\n    Index m_nonzerosblocks; // Total nonzeros blocks (lower than  m_innerBSize x m_outerBSize)\n    Index m_nonzeros; // Total nonzeros elements\n    Scalar *m_values; //Values stored block column after block column (size m_nonzeros)\n    StorageIndex *m_blockPtr; // Pointer to the beginning of each block in m_values, size m_nonzeroblocks ... null for fixed-size blocks\n    StorageIndex *m_indices; //Inner block indices, size m_nonzerosblocks ... OK\n    StorageIndex *m_outerIndex; // Starting pointer of each block column in m_indices (size m_outerBSize)... OK\n    Index m_blockSize; // Size of a block for fixed-size blocks, otherwise -1\n};\n\ntemplate<typename _Scalar, int _BlockAtCompileTime, int _Options, typename _StorageIndex>\nclass BlockSparseMatrix<_Scalar, _BlockAtCompileTime, _Options, _StorageIndex>::BlockInnerIterator\n{\n  public:\n\n    enum{\n      Flags = _Options\n    };\n\n    BlockInnerIterator(const BlockSparseMatrix& mat, const Index outer)\n    : m_mat(mat),m_outer(outer),\n      m_id(mat.m_outerIndex[outer]),\n      m_end(mat.m_outerIndex[outer+1])\n    {\n    }\n\n    inline BlockInnerIterator& operator++() {m_id++; return *this; }\n\n    inline const Map<const BlockScalar> value() const\n    {\n      return Map<const BlockScalar>(&(m_mat.m_values[m_mat.blockPtr(m_id)]),\n          rows(),cols());\n    }\n    inline Map<BlockScalar> valueRef()\n    {\n      return Map<BlockScalar>(&(m_mat.m_values[m_mat.blockPtr(m_id)]),\n          rows(),cols());\n    }\n    // Block inner index\n    inline Index index() const {return m_mat.m_indices[m_id]; }\n    inline Index outer() const { return m_outer; }\n    // block row index\n    inline Index row() const  {return index(); }\n    // block column index\n    inline Index col() const {return outer(); }\n    // FIXME Number of rows in the current block\n    inline Index rows() const { return (m_mat.m_blockSize==Dynamic) ? (m_mat.m_innerOffset[index()+1] - m_mat.m_innerOffset[index()]) : m_mat.m_blockSize; }\n    // Number of columns in the current block ...\n    inline Index cols() const { return (m_mat.m_blockSize==Dynamic) ? (m_mat.m_outerOffset[m_outer+1]-m_mat.m_outerOffset[m_outer]) : m_mat.m_blockSize;}\n    inline operator bool() const { return (m_id < m_end); }\n\n  protected:\n    const BlockSparseMatrix<_Scalar, _BlockAtCompileTime, _Options, StorageIndex>& m_mat;\n    const Index m_outer;\n    Index m_id;\n    Index m_end;\n};\n\ntemplate<typename _Scalar, int _BlockAtCompileTime, int _Options, typename _StorageIndex>\nclass BlockSparseMatrix<_Scalar, _BlockAtCompileTime, _Options, _StorageIndex>::InnerIterator\n{\n  public:\n    InnerIterator(const BlockSparseMatrix& mat, Index outer)\n    : m_mat(mat),m_outerB(mat.outerToBlock(outer)),m_outer(outer),\n      itb(mat, mat.outerToBlock(outer)),\n      m_offset(outer - mat.blockOuterIndex(m_outerB))\n     {\n        if (itb)\n        {\n          m_id = m_mat.blockInnerIndex(itb.index());\n          m_start = m_id;\n          m_end = m_mat.blockInnerIndex(itb.index()+1);\n        }\n     }\n    inline InnerIterator& operator++()\n    {\n      m_id++;\n      if (m_id >= m_end)\n      {\n        ++itb;\n        if (itb)\n        {\n          m_id = m_mat.blockInnerIndex(itb.index());\n          m_start = m_id;\n          m_end = m_mat.blockInnerIndex(itb.index()+1);\n        }\n      }\n      return *this;\n    }\n    inline const Scalar& value() const\n    {\n      return itb.value().coeff(m_id - m_start, m_offset);\n    }\n    inline Scalar& valueRef()\n    {\n      return itb.valueRef().coeff(m_id - m_start, m_offset);\n    }\n    inline Index index() const { return m_id; }\n    inline Index outer() const {return m_outer; }\n    inline Index col() const {return outer(); }\n    inline Index row() const { return index();}\n    inline operator bool() const\n    {\n      return itb;\n    }\n  protected:\n    const BlockSparseMatrix& m_mat;\n    const Index m_outer;\n    const Index m_outerB;\n    BlockInnerIterator itb; // Iterator through the blocks\n    const Index m_offset; // Position of this column in the block\n    Index m_start; // starting inner index of this block\n    Index m_id; // current inner index in the block\n    Index m_end; // starting inner index of the next block\n\n};\n} // end namespace Eigen\n\n#endif // EIGEN_SPARSEBLOCKMATRIX_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/SparseExtra/DynamicSparseMatrix.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_DYNAMIC_SPARSEMATRIX_H\n#define EIGEN_DYNAMIC_SPARSEMATRIX_H\n\nnamespace Eigen { \n\n/** \\deprecated use a SparseMatrix in an uncompressed mode\n  *\n  * \\class DynamicSparseMatrix\n  *\n  * \\brief A sparse matrix class designed for matrix assembly purpose\n  *\n  * \\param _Scalar the scalar type, i.e. the type of the coefficients\n  *\n  * Unlike SparseMatrix, this class provides a much higher degree of flexibility. In particular, it allows\n  * random read/write accesses in log(rho*outer_size) where \\c rho is the probability that a coefficient is\n  * nonzero and outer_size is the number of columns if the matrix is column-major and the number of rows\n  * otherwise.\n  *\n  * Internally, the data are stored as a std::vector of compressed vector. The performances of random writes might\n  * decrease as the number of nonzeros per inner-vector increase. In practice, we observed very good performance\n  * till about 100 nonzeros/vector, and the performance remains relatively good till 500 nonzeros/vectors.\n  *\n  * \\see SparseMatrix\n  */\n\nnamespace internal {\ntemplate<typename _Scalar, int _Options, typename _StorageIndex>\nstruct traits<DynamicSparseMatrix<_Scalar, _Options, _StorageIndex> >\n{\n  typedef _Scalar Scalar;\n  typedef _StorageIndex StorageIndex;\n  typedef Sparse StorageKind;\n  typedef MatrixXpr XprKind;\n  enum {\n    RowsAtCompileTime = Dynamic,\n    ColsAtCompileTime = Dynamic,\n    MaxRowsAtCompileTime = Dynamic,\n    MaxColsAtCompileTime = Dynamic,\n    Flags = _Options | NestByRefBit | LvalueBit,\n    CoeffReadCost = NumTraits<Scalar>::ReadCost,\n    SupportedAccessPatterns = OuterRandomAccessPattern\n  };\n};\n}\n\ntemplate<typename _Scalar, int _Options, typename _StorageIndex>\n class  DynamicSparseMatrix\n  : public SparseMatrixBase<DynamicSparseMatrix<_Scalar, _Options, _StorageIndex> >\n{\n    typedef SparseMatrixBase<DynamicSparseMatrix> Base;\n    using Base::convert_index;\n  public:\n    EIGEN_SPARSE_PUBLIC_INTERFACE(DynamicSparseMatrix)\n    // FIXME: why are these operator already alvailable ???\n    // EIGEN_SPARSE_INHERIT_ASSIGNMENT_OPERATOR(DynamicSparseMatrix, +=)\n    // EIGEN_SPARSE_INHERIT_ASSIGNMENT_OPERATOR(DynamicSparseMatrix, -=)\n    typedef MappedSparseMatrix<Scalar,Flags> Map;\n    using Base::IsRowMajor;\n    using Base::operator=;\n    enum {\n      Options = _Options\n    };\n\n  protected:\n\n    typedef DynamicSparseMatrix<Scalar,(Flags&~RowMajorBit)|(IsRowMajor?RowMajorBit:0), StorageIndex> TransposedSparseMatrix;\n\n    Index m_innerSize;\n    std::vector<internal::CompressedStorage<Scalar,StorageIndex> > m_data;\n\n  public:\n\n    inline Index rows() const { return IsRowMajor ? outerSize() : m_innerSize; }\n    inline Index cols() const { return IsRowMajor ? m_innerSize : outerSize(); }\n    inline Index innerSize() const { return m_innerSize; }\n    inline Index outerSize() const { return convert_index(m_data.size()); }\n    inline Index innerNonZeros(Index j) const { return m_data[j].size(); }\n\n    std::vector<internal::CompressedStorage<Scalar,StorageIndex> >& _data() { return m_data; }\n    const std::vector<internal::CompressedStorage<Scalar,StorageIndex> >& _data() const { return m_data; }\n\n    /** \\returns the coefficient value at given position \\a row, \\a col\n      * This operation involes a log(rho*outer_size) binary search.\n      */\n    inline Scalar coeff(Index row, Index col) const\n    {\n      const Index outer = IsRowMajor ? row : col;\n      const Index inner = IsRowMajor ? col : row;\n      return m_data[outer].at(inner);\n    }\n\n    /** \\returns a reference to the coefficient value at given position \\a row, \\a col\n      * This operation involes a log(rho*outer_size) binary search. If the coefficient does not\n      * exist yet, then a sorted insertion into a sequential buffer is performed.\n      */\n    inline Scalar& coeffRef(Index row, Index col)\n    {\n      const Index outer = IsRowMajor ? row : col;\n      const Index inner = IsRowMajor ? col : row;\n      return m_data[outer].atWithInsertion(inner);\n    }\n\n    class InnerIterator;\n    class ReverseInnerIterator;\n\n    void setZero()\n    {\n      for (Index j=0; j<outerSize(); ++j)\n        m_data[j].clear();\n    }\n\n    /** \\returns the number of non zero coefficients */\n    Index nonZeros() const\n    {\n      Index res = 0;\n      for (Index j=0; j<outerSize(); ++j)\n        res += m_data[j].size();\n      return res;\n    }\n\n\n\n    void reserve(Index reserveSize = 1000)\n    {\n      if (outerSize()>0)\n      {\n        Index reserveSizePerVector = (std::max)(reserveSize/outerSize(),Index(4));\n        for (Index j=0; j<outerSize(); ++j)\n        {\n          m_data[j].reserve(reserveSizePerVector);\n        }\n      }\n    }\n\n    /** Does nothing: provided for compatibility with SparseMatrix */\n    inline void startVec(Index /*outer*/) {}\n\n    /** \\returns a reference to the non zero coefficient at position \\a row, \\a col assuming that:\n      * - the nonzero does not already exist\n      * - the new coefficient is the last one of the given inner vector.\n      *\n      * \\sa insert, insertBackByOuterInner */\n    inline Scalar& insertBack(Index row, Index col)\n    {\n      return insertBackByOuterInner(IsRowMajor?row:col, IsRowMajor?col:row);\n    }\n\n    /** \\sa insertBack */\n    inline Scalar& insertBackByOuterInner(Index outer, Index inner)\n    {\n      eigen_assert(outer<Index(m_data.size()) && inner<m_innerSize && \"out of range\");\n      eigen_assert(((m_data[outer].size()==0) || (m_data[outer].index(m_data[outer].size()-1)<inner))\n                && \"wrong sorted insertion\");\n      m_data[outer].append(0, inner);\n      return m_data[outer].value(m_data[outer].size()-1);\n    }\n\n    inline Scalar& insert(Index row, Index col)\n    {\n      const Index outer = IsRowMajor ? row : col;\n      const Index inner = IsRowMajor ? col : row;\n\n      Index startId = 0;\n      Index id = static_cast<Index>(m_data[outer].size()) - 1;\n      m_data[outer].resize(id+2,1);\n\n      while ( (id >= startId) && (m_data[outer].index(id) > inner) )\n      {\n        m_data[outer].index(id+1) = m_data[outer].index(id);\n        m_data[outer].value(id+1) = m_data[outer].value(id);\n        --id;\n      }\n      m_data[outer].index(id+1) = inner;\n      m_data[outer].value(id+1) = 0;\n      return m_data[outer].value(id+1);\n    }\n\n    /** Does nothing: provided for compatibility with SparseMatrix */\n    inline void finalize() {}\n\n    /** Suppress all nonzeros which are smaller than \\a reference under the tolerence \\a epsilon */\n    void prune(Scalar reference, RealScalar epsilon = NumTraits<RealScalar>::dummy_precision())\n    {\n      for (Index j=0; j<outerSize(); ++j)\n        m_data[j].prune(reference,epsilon);\n    }\n\n    /** Resize the matrix without preserving the data (the matrix is set to zero)\n      */\n    void resize(Index rows, Index cols)\n    {\n      const Index outerSize = IsRowMajor ? rows : cols;\n      m_innerSize = convert_index(IsRowMajor ? cols : rows);\n      setZero();\n      if (Index(m_data.size()) != outerSize)\n      {\n        m_data.resize(outerSize);\n      }\n    }\n\n    void resizeAndKeepData(Index rows, Index cols)\n    {\n      const Index outerSize = IsRowMajor ? rows : cols;\n      const Index innerSize = IsRowMajor ? cols : rows;\n      if (m_innerSize>innerSize)\n      {\n        // remove all coefficients with innerCoord>=innerSize\n        // TODO\n        //std::cerr << \"not implemented yet\\n\";\n        exit(2);\n      }\n      if (m_data.size() != outerSize)\n      {\n        m_data.resize(outerSize);\n      }\n    }\n\n    /** The class DynamicSparseMatrix is deprectaed */\n    EIGEN_DEPRECATED inline DynamicSparseMatrix()\n      : m_innerSize(0), m_data(0)\n    {\n      eigen_assert(innerSize()==0 && outerSize()==0);\n    }\n\n    /** The class DynamicSparseMatrix is deprectaed */\n    EIGEN_DEPRECATED inline DynamicSparseMatrix(Index rows, Index cols)\n      : m_innerSize(0)\n    {\n      resize(rows, cols);\n    }\n\n    /** The class DynamicSparseMatrix is deprectaed */\n    template<typename OtherDerived>\n    EIGEN_DEPRECATED explicit inline DynamicSparseMatrix(const SparseMatrixBase<OtherDerived>& other)\n      : m_innerSize(0)\n    {\n    Base::operator=(other.derived());\n    }\n\n    inline DynamicSparseMatrix(const DynamicSparseMatrix& other)\n      : Base(), m_innerSize(0)\n    {\n      *this = other.derived();\n    }\n\n    inline void swap(DynamicSparseMatrix& other)\n    {\n      //EIGEN_DBG_SPARSE(std::cout << \"SparseMatrix:: swap\\n\");\n      std::swap(m_innerSize, other.m_innerSize);\n      //std::swap(m_outerSize, other.m_outerSize);\n      m_data.swap(other.m_data);\n    }\n\n    inline DynamicSparseMatrix& operator=(const DynamicSparseMatrix& other)\n    {\n      if (other.isRValue())\n      {\n        swap(other.const_cast_derived());\n      }\n      else\n      {\n        resize(other.rows(), other.cols());\n        m_data = other.m_data;\n      }\n      return *this;\n    }\n\n    /** Destructor */\n    inline ~DynamicSparseMatrix() {}\n\n  public:\n\n    /** \\deprecated\n      * Set the matrix to zero and reserve the memory for \\a reserveSize nonzero coefficients. */\n    EIGEN_DEPRECATED void startFill(Index reserveSize = 1000)\n    {\n      setZero();\n      reserve(reserveSize);\n    }\n\n    /** \\deprecated use insert()\n      * inserts a nonzero coefficient at given coordinates \\a row, \\a col and returns its reference assuming that:\n      *  1 - the coefficient does not exist yet\n      *  2 - this the coefficient with greater inner coordinate for the given outer coordinate.\n      * In other words, assuming \\c *this is column-major, then there must not exists any nonzero coefficient of coordinates\n      * \\c i \\c x \\a col such that \\c i >= \\a row. Otherwise the matrix is invalid.\n      *\n      * \\see fillrand(), coeffRef()\n      */\n    EIGEN_DEPRECATED Scalar& fill(Index row, Index col)\n    {\n      const Index outer = IsRowMajor ? row : col;\n      const Index inner = IsRowMajor ? col : row;\n      return insertBack(outer,inner);\n    }\n\n    /** \\deprecated use insert()\n      * Like fill() but with random inner coordinates.\n      * Compared to the generic coeffRef(), the unique limitation is that we assume\n      * the coefficient does not exist yet.\n      */\n    EIGEN_DEPRECATED Scalar& fillrand(Index row, Index col)\n    {\n      return insert(row,col);\n    }\n\n    /** \\deprecated use finalize()\n      * Does nothing. Provided for compatibility with SparseMatrix. */\n    EIGEN_DEPRECATED void endFill() {}\n    \n#   ifdef EIGEN_DYNAMICSPARSEMATRIX_PLUGIN\n#     include EIGEN_DYNAMICSPARSEMATRIX_PLUGIN\n#   endif\n };\n\ntemplate<typename Scalar, int _Options, typename _StorageIndex>\nclass DynamicSparseMatrix<Scalar,_Options,_StorageIndex>::InnerIterator : public SparseVector<Scalar,_Options,_StorageIndex>::InnerIterator\n{\n    typedef typename SparseVector<Scalar,_Options,_StorageIndex>::InnerIterator Base;\n  public:\n    InnerIterator(const DynamicSparseMatrix& mat, Index outer)\n      : Base(mat.m_data[outer]), m_outer(outer)\n    {}\n\n    inline Index row() const { return IsRowMajor ? m_outer : Base::index(); }\n    inline Index col() const { return IsRowMajor ? Base::index() : m_outer; }\n    inline Index outer() const { return m_outer; }\n\n  protected:\n    const Index m_outer;\n};\n\ntemplate<typename Scalar, int _Options, typename _StorageIndex>\nclass DynamicSparseMatrix<Scalar,_Options,_StorageIndex>::ReverseInnerIterator : public SparseVector<Scalar,_Options,_StorageIndex>::ReverseInnerIterator\n{\n    typedef typename SparseVector<Scalar,_Options,_StorageIndex>::ReverseInnerIterator Base;\n  public:\n    ReverseInnerIterator(const DynamicSparseMatrix& mat, Index outer)\n      : Base(mat.m_data[outer]), m_outer(outer)\n    {}\n\n    inline Index row() const { return IsRowMajor ? m_outer : Base::index(); }\n    inline Index col() const { return IsRowMajor ? Base::index() : m_outer; }\n    inline Index outer() const { return m_outer; }\n\n  protected:\n    const Index m_outer;\n};\n\nnamespace internal {\n\ntemplate<typename _Scalar, int _Options, typename _StorageIndex>\nstruct evaluator<DynamicSparseMatrix<_Scalar,_Options,_StorageIndex> >\n  : evaluator_base<DynamicSparseMatrix<_Scalar,_Options,_StorageIndex> >\n{\n  typedef _Scalar Scalar;\n  typedef DynamicSparseMatrix<_Scalar,_Options,_StorageIndex> SparseMatrixType;\n  typedef typename SparseMatrixType::InnerIterator InnerIterator;\n  typedef typename SparseMatrixType::ReverseInnerIterator ReverseInnerIterator;\n  \n  enum {\n    CoeffReadCost = NumTraits<_Scalar>::ReadCost,\n    Flags = SparseMatrixType::Flags\n  };\n  \n  evaluator() : m_matrix(0) {}\n  evaluator(const SparseMatrixType &mat) : m_matrix(&mat) {}\n  \n  operator SparseMatrixType&() { return m_matrix->const_cast_derived(); }\n  operator const SparseMatrixType&() const { return *m_matrix; }\n  \n  Scalar coeff(Index row, Index col) const { return m_matrix->coeff(row,col); }\n  \n  Index nonZerosEstimate() const { return m_matrix->nonZeros(); }\n\n  const SparseMatrixType *m_matrix;\n};\n\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_DYNAMIC_SPARSEMATRIX_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/SparseExtra/MarketIO.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2011 Gael Guennebaud <gael.guennebaud@inria.fr>\n// Copyright (C) 2012 Desire NUENTSA WAKAM <desire.nuentsa_wakam@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPARSE_MARKET_IO_H\n#define EIGEN_SPARSE_MARKET_IO_H\n\n#include <iostream>\n\nnamespace Eigen { \n\nnamespace internal \n{\n  template <typename Scalar>\n  inline bool GetMarketLine (std::stringstream& line, Index& M, Index& N, Index& i, Index& j, Scalar& value)\n  {\n    line >> i >> j >> value;\n    i--;\n    j--;\n    if(i>=0 && j>=0 && i<M && j<N)\n    {\n      return true; \n    }\n    else\n      return false;\n  }\n  template <typename Scalar>\n  inline bool GetMarketLine (std::stringstream& line, Index& M, Index& N, Index& i, Index& j, std::complex<Scalar>& value)\n  {\n    Scalar valR, valI;\n    line >> i >> j >> valR >> valI;\n    i--;\n    j--;\n    if(i>=0 && j>=0 && i<M && j<N)\n    {\n      value = std::complex<Scalar>(valR, valI);\n      return true; \n    }\n    else\n      return false;\n  }\n\n  template <typename RealScalar>\n  inline void  GetVectorElt (const std::string& line, RealScalar& val)\n  {\n    std::istringstream newline(line);\n    newline >> val;  \n  }\n\n  template <typename RealScalar>\n  inline void GetVectorElt (const std::string& line, std::complex<RealScalar>& val)\n  {\n    RealScalar valR, valI; \n    std::istringstream newline(line);\n    newline >> valR >> valI; \n    val = std::complex<RealScalar>(valR, valI);\n  }\n  \n  template<typename Scalar>\n  inline void putMarketHeader(std::string& header,int sym)\n  {\n    header= \"%%MatrixMarket matrix coordinate \";\n    if(internal::is_same<Scalar, std::complex<float> >::value || internal::is_same<Scalar, std::complex<double> >::value)\n    {\n      header += \" complex\"; \n      if(sym == Symmetric) header += \" symmetric\";\n      else if (sym == SelfAdjoint) header += \" Hermitian\";\n      else header += \" general\";\n    }\n    else\n    {\n      header += \" real\"; \n      if(sym == Symmetric) header += \" symmetric\";\n      else header += \" general\";\n    }\n  }\n\n  template<typename Scalar>\n  inline void PutMatrixElt(Scalar value, int row, int col, std::ofstream& out)\n  {\n    out << row << \" \"<< col << \" \" << value << \"\\n\";\n  }\n  template<typename Scalar>\n  inline void PutMatrixElt(std::complex<Scalar> value, int row, int col, std::ofstream& out)\n  {\n    out << row << \" \" << col << \" \" << value.real() << \" \" << value.imag() << \"\\n\";\n  }\n\n\n  template<typename Scalar>\n  inline void putVectorElt(Scalar value, std::ofstream& out)\n  {\n    out << value << \"\\n\"; \n  }\n  template<typename Scalar>\n  inline void putVectorElt(std::complex<Scalar> value, std::ofstream& out)\n  {\n    out << value.real << \" \" << value.imag()<< \"\\n\"; \n  }\n\n} // end namepsace internal\n\ninline bool getMarketHeader(const std::string& filename, int& sym, bool& iscomplex, bool& isvector)\n{\n  sym = 0; \n  iscomplex = false;\n  isvector = false;\n  std::ifstream in(filename.c_str(),std::ios::in);\n  if(!in)\n    return false;\n  \n  std::string line; \n  // The matrix header is always the first line in the file \n  std::getline(in, line); eigen_assert(in.good());\n  \n  std::stringstream fmtline(line); \n  std::string substr[5];\n  fmtline>> substr[0] >> substr[1] >> substr[2] >> substr[3] >> substr[4];\n  if(substr[2].compare(\"array\") == 0) isvector = true;\n  if(substr[3].compare(\"complex\") == 0) iscomplex = true;\n  if(substr[4].compare(\"symmetric\") == 0) sym = Symmetric;\n  else if (substr[4].compare(\"Hermitian\") == 0) sym = SelfAdjoint;\n  \n  return true;\n}\n  \ntemplate<typename SparseMatrixType>\nbool loadMarket(SparseMatrixType& mat, const std::string& filename)\n{\n  typedef typename SparseMatrixType::Scalar Scalar;\n  typedef typename SparseMatrixType::Index Index;\n  std::ifstream input(filename.c_str(),std::ios::in);\n  if(!input)\n    return false;\n  \n  const int maxBuffersize = 2048;\n  char buffer[maxBuffersize];\n  \n  bool readsizes = false;\n\n  typedef Triplet<Scalar,Index> T;\n  std::vector<T> elements;\n  \n  Index M(-1), N(-1), NNZ(-1);\n  Index count = 0;\n  while(input.getline(buffer, maxBuffersize))\n  {\n    // skip comments   \n    //NOTE An appropriate test should be done on the header to get the  symmetry\n    if(buffer[0]=='%')\n      continue;\n    \n    std::stringstream line(buffer);\n    \n    if(!readsizes)\n    {\n      line >> M >> N >> NNZ;\n      if(M > 0 && N > 0 && NNZ > 0) \n      {\n        readsizes = true;\n        //std::cout << \"sizes: \" << M << \",\" << N << \",\" << NNZ << \"\\n\";\n        mat.resize(M,N);\n        mat.reserve(NNZ);\n      }\n    }\n    else\n    { \n      Index i(-1), j(-1);\n      Scalar value; \n      if( internal::GetMarketLine(line, M, N, i, j, value) ) \n      {\n        ++ count;\n        elements.push_back(T(i,j,value));\n      }\n      else \n        std::cerr << \"Invalid read: \" << i << \",\" << j << \"\\n\";        \n    }\n  }\n  mat.setFromTriplets(elements.begin(), elements.end());\n  if(count!=NNZ)\n    std::cerr << count << \"!=\" << NNZ << \"\\n\";\n  \n  input.close();\n  return true;\n}\n\ntemplate<typename VectorType>\nbool loadMarketVector(VectorType& vec, const std::string& filename)\n{\n   typedef typename VectorType::Scalar Scalar;\n  std::ifstream in(filename.c_str(), std::ios::in);\n  if(!in)\n    return false;\n  \n  std::string line; \n  int n(0), col(0); \n  do \n  { // Skip comments\n    std::getline(in, line); eigen_assert(in.good());\n  } while (line[0] == '%');\n  std::istringstream newline(line);\n  newline  >> n >> col; \n  eigen_assert(n>0 && col>0);\n  vec.resize(n);\n  int i = 0; \n  Scalar value; \n  while ( std::getline(in, line) && (i < n) ){\n    internal::GetVectorElt(line, value); \n    vec(i++) = value; \n  }\n  in.close();\n  if (i!=n){\n    std::cerr<< \"Unable to read all elements from file \" << filename << \"\\n\";\n    return false;\n  }\n  return true;\n}\n\ntemplate<typename SparseMatrixType>\nbool saveMarket(const SparseMatrixType& mat, const std::string& filename, int sym = 0)\n{\n  typedef typename SparseMatrixType::Scalar Scalar;\n  std::ofstream out(filename.c_str(),std::ios::out);\n  if(!out)\n    return false;\n  \n  out.flags(std::ios_base::scientific);\n  out.precision(64);\n  std::string header; \n  internal::putMarketHeader<Scalar>(header, sym); \n  out << header << std::endl; \n  out << mat.rows() << \" \" << mat.cols() << \" \" << mat.nonZeros() << \"\\n\";\n  int count = 0;\n  for(int j=0; j<mat.outerSize(); ++j)\n    for(typename SparseMatrixType::InnerIterator it(mat,j); it; ++it)\n    {\n      ++ count;\n      internal::PutMatrixElt(it.value(), it.row()+1, it.col()+1, out);\n      // out << it.row()+1 << \" \" << it.col()+1 << \" \" << it.value() << \"\\n\";\n    }\n  out.close();\n  return true;\n}\n\ntemplate<typename VectorType>\nbool saveMarketVector (const VectorType& vec, const std::string& filename)\n{\n typedef typename VectorType::Scalar Scalar; \n std::ofstream out(filename.c_str(),std::ios::out);\n  if(!out)\n    return false;\n  \n  out.flags(std::ios_base::scientific);\n  out.precision(64);\n  if(internal::is_same<Scalar, std::complex<float> >::value || internal::is_same<Scalar, std::complex<double> >::value)\n      out << \"%%MatrixMarket matrix array complex general\\n\"; \n  else\n    out << \"%%MatrixMarket matrix array real general\\n\"; \n  out << vec.size() << \" \"<< 1 << \"\\n\";\n  for (int i=0; i < vec.size(); i++){\n    internal::putVectorElt(vec(i), out); \n  }\n  out.close();\n  return true; \n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_SPARSE_MARKET_IO_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/SparseExtra/MatrixMarketIterator.h",
    "content": "\n// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Desire NUENTSA WAKAM <desire.nuentsa_wakam@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_BROWSE_MATRICES_H\n#define EIGEN_BROWSE_MATRICES_H\n\nnamespace Eigen {\n\nenum {\n  SPD = 0x100,\n  NonSymmetric = 0x0\n}; \n\n/** \n * @brief Iterator to browse matrices from a specified folder\n * \n * This is used to load all the matrices from a folder. \n * The matrices should be in Matrix Market format\n * It is assumed that the matrices are named as matname.mtx\n * and matname_SPD.mtx if the matrix is Symmetric and positive definite (or Hermitian)\n * The right hand side vectors are loaded as well, if they exist.\n * They should be named as matname_b.mtx. \n * Note that the right hand side for a SPD matrix is named as matname_SPD_b.mtx\n * \n * Sometimes a reference solution is available. In this case, it should be named as matname_x.mtx\n * \n * Sample code\n * \\code\n * \n * \\endcode\n * \n * \\tparam Scalar The scalar type \n */\ntemplate <typename Scalar>\nclass MatrixMarketIterator \n{\n    typedef typename NumTraits<Scalar>::Real RealScalar;\n  public:\n    typedef Matrix<Scalar,Dynamic,1> VectorType; \n    typedef SparseMatrix<Scalar,ColMajor> MatrixType; \n  \n  public:\n    MatrixMarketIterator(const std::string &folder)\n      : m_sym(0), m_isvalid(false), m_matIsLoaded(false), m_hasRhs(false), m_hasrefX(false), m_folder(folder)\n    {\n      m_folder_id = opendir(folder.c_str());\n      if(m_folder_id)\n        Getnextvalidmatrix();\n    }\n    \n    ~MatrixMarketIterator()\n    {\n      if (m_folder_id) closedir(m_folder_id); \n    }\n    \n    inline MatrixMarketIterator& operator++()\n    {\n      m_matIsLoaded = false;\n      m_hasrefX = false;\n      m_hasRhs = false;\n      Getnextvalidmatrix();\n      return *this;\n    }\n    inline operator bool() const { return m_isvalid;}\n    \n    /** Return the sparse matrix corresponding to the current file */\n    inline MatrixType& matrix() \n    { \n      // Read the matrix\n      if (m_matIsLoaded) return m_mat;\n      \n      std::string matrix_file = m_folder + \"/\" + m_matname + \".mtx\";\n      if ( !loadMarket(m_mat, matrix_file)) \n      {\n        std::cerr << \"Warning loadMarket failed when loading \\\"\" << matrix_file << \"\\\"\" << std::endl;\n        m_matIsLoaded = false;\n        return m_mat;\n      }\n      m_matIsLoaded = true; \n\n      if (m_sym != NonSymmetric) \n      {\n        // Check whether we need to restore a full matrix:\n        RealScalar diag_norm  = m_mat.diagonal().norm();\n        RealScalar lower_norm = m_mat.template triangularView<Lower>().norm();\n        RealScalar upper_norm = m_mat.template triangularView<Upper>().norm();\n        if(lower_norm>diag_norm && upper_norm==diag_norm)\n        {\n          // only the lower part is stored\n          MatrixType tmp(m_mat);\n          m_mat = tmp.template selfadjointView<Lower>();\n        }\n        else if(upper_norm>diag_norm && lower_norm==diag_norm)\n        {\n          // only the upper part is stored\n          MatrixType tmp(m_mat);\n          m_mat = tmp.template selfadjointView<Upper>();\n        }\n      }\n      return m_mat; \n    }\n    \n    /** Return the right hand side corresponding to the current matrix. \n     * If the rhs file is not provided, a random rhs is generated\n     */\n    inline VectorType& rhs() \n    { \n       // Get the right hand side\n      if (m_hasRhs) return m_rhs;\n      \n      std::string rhs_file;\n      rhs_file = m_folder + \"/\" + m_matname + \"_b.mtx\"; // The pattern is matname_b.mtx\n      m_hasRhs = Fileexists(rhs_file);\n      if (m_hasRhs)\n      {\n        m_rhs.resize(m_mat.cols());\n        m_hasRhs = loadMarketVector(m_rhs, rhs_file);\n      }\n      if (!m_hasRhs)\n      {\n        // Generate a random right hand side\n        if (!m_matIsLoaded) this->matrix(); \n        m_refX.resize(m_mat.cols());\n        m_refX.setRandom();\n        m_rhs = m_mat * m_refX;\n        m_hasrefX = true;\n        m_hasRhs = true;\n      }\n      return m_rhs; \n    }\n    \n    /** Return a reference solution\n     * If it is not provided and if the right hand side is not available\n     * then refX is randomly generated such that A*refX = b \n     * where A and b are the matrix and the rhs. \n     * Note that when a rhs is provided, refX is not available \n     */\n    inline VectorType& refX() \n    { \n      // Check if a reference solution is provided\n      if (m_hasrefX) return m_refX;\n      \n      std::string lhs_file;\n      lhs_file = m_folder + \"/\" + m_matname + \"_x.mtx\"; \n      m_hasrefX = Fileexists(lhs_file);\n      if (m_hasrefX)\n      {\n        m_refX.resize(m_mat.cols());\n        m_hasrefX = loadMarketVector(m_refX, lhs_file);\n      }\n      else\n        m_refX.resize(0);\n      return m_refX; \n    }\n    \n    inline std::string& matname() { return m_matname; }\n    \n    inline int sym() { return m_sym; }\n    \n    bool hasRhs() {return m_hasRhs; }\n    bool hasrefX() {return m_hasrefX; }\n    bool isFolderValid() { return bool(m_folder_id); }\n    \n  protected:\n    \n    inline bool Fileexists(std::string file)\n    {\n      std::ifstream file_id(file.c_str());\n      if (!file_id.good() ) \n      {\n        return false;\n      }\n      else \n      {\n        file_id.close();\n        return true;\n      }\n    }\n    \n    void Getnextvalidmatrix( )\n    {\n      m_isvalid = false;\n      // Here, we return with the next valid matrix in the folder\n      while ( (m_curs_id = readdir(m_folder_id)) != NULL) {\n        m_isvalid = false;\n        std::string curfile;\n        curfile = m_folder + \"/\" + m_curs_id->d_name;\n        // Discard if it is a folder\n        if (m_curs_id->d_type == DT_DIR) continue; //FIXME This may not be available on non BSD systems\n//         struct stat st_buf; \n//         stat (curfile.c_str(), &st_buf);\n//         if (S_ISDIR(st_buf.st_mode)) continue;\n        \n        // Determine from the header if it is a matrix or a right hand side \n        bool isvector,iscomplex=false;\n        if(!getMarketHeader(curfile,m_sym,iscomplex,isvector)) continue;\n        if(isvector) continue;\n        if (!iscomplex)\n        {\n          if(internal::is_same<Scalar, std::complex<float> >::value || internal::is_same<Scalar, std::complex<double> >::value)\n            continue; \n        }\n        if (iscomplex)\n        {\n          if(internal::is_same<Scalar, float>::value || internal::is_same<Scalar, double>::value)\n            continue; \n        }\n        \n        \n        // Get the matrix name\n        std::string filename = m_curs_id->d_name;\n        m_matname = filename.substr(0, filename.length()-4); \n        \n        // Find if the matrix is SPD \n        size_t found = m_matname.find(\"SPD\");\n        if( (found!=std::string::npos) && (m_sym != NonSymmetric) )\n          m_sym = SPD;\n       \n        m_isvalid = true;\n        break; \n      }\n    }\n    int m_sym; // Symmetry of the matrix\n    MatrixType m_mat; // Current matrix  \n    VectorType m_rhs;  // Current vector\n    VectorType m_refX; // The reference solution, if exists\n    std::string m_matname; // Matrix Name\n    bool m_isvalid; \n    bool m_matIsLoaded; // Determine if the matrix has already been loaded from the file\n    bool m_hasRhs; // The right hand side exists\n    bool m_hasrefX; // A reference solution is provided\n    std::string m_folder;\n    DIR * m_folder_id;\n    struct dirent *m_curs_id; \n    \n};\n\n} // end namespace Eigen\n\n#endif\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/SparseExtra/RandomSetter.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_RANDOMSETTER_H\n#define EIGEN_RANDOMSETTER_H\n\nnamespace Eigen { \n\n/** Represents a std::map\n  *\n  * \\see RandomSetter\n  */\ntemplate<typename Scalar> struct StdMapTraits\n{\n  typedef int KeyType;\n  typedef std::map<KeyType,Scalar> Type;\n  enum {\n    IsSorted = 1\n  };\n\n  static void setInvalidKey(Type&, const KeyType&) {}\n};\n\n#ifdef EIGEN_UNORDERED_MAP_SUPPORT\n/** Represents a std::unordered_map\n  *\n  * To use it you need to both define EIGEN_UNORDERED_MAP_SUPPORT and include the unordered_map header file\n  * yourself making sure that unordered_map is defined in the std namespace.\n  *\n  * For instance, with current version of gcc you can either enable C++0x standard (-std=c++0x) or do:\n  * \\code\n  * #include <tr1/unordered_map>\n  * #define EIGEN_UNORDERED_MAP_SUPPORT\n  * namespace std {\n  *   using std::tr1::unordered_map;\n  * }\n  * \\endcode\n  *\n  * \\see RandomSetter\n  */\ntemplate<typename Scalar> struct StdUnorderedMapTraits\n{\n  typedef int KeyType;\n  typedef std::unordered_map<KeyType,Scalar> Type;\n  enum {\n    IsSorted = 0\n  };\n\n  static void setInvalidKey(Type&, const KeyType&) {}\n};\n#endif // EIGEN_UNORDERED_MAP_SUPPORT\n\n#ifdef _DENSE_HASH_MAP_H_\n/** Represents a google::dense_hash_map\n  *\n  * \\see RandomSetter\n  */\ntemplate<typename Scalar> struct GoogleDenseHashMapTraits\n{\n  typedef int KeyType;\n  typedef google::dense_hash_map<KeyType,Scalar> Type;\n  enum {\n    IsSorted = 0\n  };\n\n  static void setInvalidKey(Type& map, const KeyType& k)\n  { map.set_empty_key(k); }\n};\n#endif\n\n#ifdef _SPARSE_HASH_MAP_H_\n/** Represents a google::sparse_hash_map\n  *\n  * \\see RandomSetter\n  */\ntemplate<typename Scalar> struct GoogleSparseHashMapTraits\n{\n  typedef int KeyType;\n  typedef google::sparse_hash_map<KeyType,Scalar> Type;\n  enum {\n    IsSorted = 0\n  };\n\n  static void setInvalidKey(Type&, const KeyType&) {}\n};\n#endif\n\n/** \\class RandomSetter\n  *\n  * \\brief The RandomSetter is a wrapper object allowing to set/update a sparse matrix with random access\n  *\n  * \\tparam SparseMatrixType the type of the sparse matrix we are updating\n  * \\tparam MapTraits a traits class representing the map implementation used for the temporary sparse storage.\n  *                  Its default value depends on the system.\n  * \\tparam OuterPacketBits defines the number of rows (or columns) manage by a single map object\n  *                        as a power of two exponent.\n  *\n  * This class temporarily represents a sparse matrix object using a generic map implementation allowing for\n  * efficient random access. The conversion from the compressed representation to a hash_map object is performed\n  * in the RandomSetter constructor, while the sparse matrix is updated back at destruction time. This strategy\n  * suggest the use of nested blocks as in this example:\n  *\n  * \\code\n  * SparseMatrix<double> m(rows,cols);\n  * {\n  *   RandomSetter<SparseMatrix<double> > w(m);\n  *   // don't use m but w instead with read/write random access to the coefficients:\n  *   for(;;)\n  *     w(rand(),rand()) = rand;\n  * }\n  * // when w is deleted, the data are copied back to m\n  * // and m is ready to use.\n  * \\endcode\n  *\n  * Since hash_map objects are not fully sorted, representing a full matrix as a single hash_map would\n  * involve a big and costly sort to update the compressed matrix back. To overcome this issue, a RandomSetter\n  * use multiple hash_map, each representing 2^OuterPacketBits columns or rows according to the storage order.\n  * To reach optimal performance, this value should be adjusted according to the average number of nonzeros\n  * per rows/columns.\n  *\n  * The possible values for the template parameter MapTraits are:\n  *  - \\b StdMapTraits: corresponds to std::map. (does not perform very well)\n  *  - \\b GnuHashMapTraits: corresponds to __gnu_cxx::hash_map (available only with GCC)\n  *  - \\b GoogleDenseHashMapTraits: corresponds to google::dense_hash_map (best efficiency, reasonable memory consumption)\n  *  - \\b GoogleSparseHashMapTraits: corresponds to google::sparse_hash_map (best memory consumption, relatively good performance)\n  *\n  * The default map implementation depends on the availability, and the preferred order is:\n  * GoogleSparseHashMapTraits, GnuHashMapTraits, and finally StdMapTraits.\n  *\n  * For performance and memory consumption reasons it is highly recommended to use one of\n  * the Google's hash_map implementation. To enable the support for them, you have two options:\n  *  - \\#include <google/dense_hash_map> yourself \\b before Eigen/Sparse header\n  *  - define EIGEN_GOOGLEHASH_SUPPORT\n  * In the later case the inclusion of <google/dense_hash_map> is made for you.\n  *\n  * \\see http://code.google.com/p/google-sparsehash/\n  */\ntemplate<typename SparseMatrixType,\n         template <typename T> class MapTraits =\n#if defined _DENSE_HASH_MAP_H_\n          GoogleDenseHashMapTraits\n#elif defined _HASH_MAP\n          GnuHashMapTraits\n#else\n          StdMapTraits\n#endif\n         ,int OuterPacketBits = 6>\nclass RandomSetter\n{\n    typedef typename SparseMatrixType::Scalar Scalar;\n    typedef typename SparseMatrixType::StorageIndex StorageIndex;\n\n    struct ScalarWrapper\n    {\n      ScalarWrapper() : value(0) {}\n      Scalar value;\n    };\n    typedef typename MapTraits<ScalarWrapper>::KeyType KeyType;\n    typedef typename MapTraits<ScalarWrapper>::Type HashMapType;\n    static const int OuterPacketMask = (1 << OuterPacketBits) - 1;\n    enum {\n      SwapStorage = 1 - MapTraits<ScalarWrapper>::IsSorted,\n      TargetRowMajor = (SparseMatrixType::Flags & RowMajorBit) ? 1 : 0,\n      SetterRowMajor = SwapStorage ? 1-TargetRowMajor : TargetRowMajor\n    };\n\n  public:\n\n    /** Constructs a random setter object from the sparse matrix \\a target\n      *\n      * Note that the initial value of \\a target are imported. If you want to re-set\n      * a sparse matrix from scratch, then you must set it to zero first using the\n      * setZero() function.\n      */\n    inline RandomSetter(SparseMatrixType& target)\n      : mp_target(&target)\n    {\n      const Index outerSize = SwapStorage ? target.innerSize() : target.outerSize();\n      const Index innerSize = SwapStorage ? target.outerSize() : target.innerSize();\n      m_outerPackets = outerSize >> OuterPacketBits;\n      if (outerSize&OuterPacketMask)\n        m_outerPackets += 1;\n      m_hashmaps = new HashMapType[m_outerPackets];\n      // compute number of bits needed to store inner indices\n      Index aux = innerSize - 1;\n      m_keyBitsOffset = 0;\n      while (aux)\n      {\n        ++m_keyBitsOffset;\n        aux = aux >> 1;\n      }\n      KeyType ik = (1<<(OuterPacketBits+m_keyBitsOffset));\n      for (Index k=0; k<m_outerPackets; ++k)\n        MapTraits<ScalarWrapper>::setInvalidKey(m_hashmaps[k],ik);\n\n      // insert current coeffs\n      for (Index j=0; j<mp_target->outerSize(); ++j)\n        for (typename SparseMatrixType::InnerIterator it(*mp_target,j); it; ++it)\n          (*this)(TargetRowMajor?j:it.index(), TargetRowMajor?it.index():j) = it.value();\n    }\n\n    /** Destructor updating back the sparse matrix target */\n    ~RandomSetter()\n    {\n      KeyType keyBitsMask = (1<<m_keyBitsOffset)-1;\n      if (!SwapStorage) // also means the map is sorted\n      {\n        mp_target->setZero();\n        mp_target->makeCompressed();\n        mp_target->reserve(nonZeros());\n        Index prevOuter = -1;\n        for (Index k=0; k<m_outerPackets; ++k)\n        {\n          const Index outerOffset = (1<<OuterPacketBits) * k;\n          typename HashMapType::iterator end = m_hashmaps[k].end();\n          for (typename HashMapType::iterator it = m_hashmaps[k].begin(); it!=end; ++it)\n          {\n            const Index outer = (it->first >> m_keyBitsOffset) + outerOffset;\n            const Index inner = it->first & keyBitsMask;\n            if (prevOuter!=outer)\n            {\n              for (Index j=prevOuter+1;j<=outer;++j)\n                mp_target->startVec(j);\n              prevOuter = outer;\n            }\n            mp_target->insertBackByOuterInner(outer, inner) = it->second.value;\n          }\n        }\n        mp_target->finalize();\n      }\n      else\n      {\n        VectorXi positions(mp_target->outerSize());\n        positions.setZero();\n        // pass 1\n        for (Index k=0; k<m_outerPackets; ++k)\n        {\n          typename HashMapType::iterator end = m_hashmaps[k].end();\n          for (typename HashMapType::iterator it = m_hashmaps[k].begin(); it!=end; ++it)\n          {\n            const Index outer = it->first & keyBitsMask;\n            ++positions[outer];\n          }\n        }\n        // prefix sum\n        Index count = 0;\n        for (Index j=0; j<mp_target->outerSize(); ++j)\n        {\n          Index tmp = positions[j];\n          mp_target->outerIndexPtr()[j] = count;\n          positions[j] = count;\n          count += tmp;\n        }\n        mp_target->makeCompressed();\n        mp_target->outerIndexPtr()[mp_target->outerSize()] = count;\n        mp_target->resizeNonZeros(count);\n        // pass 2\n        for (Index k=0; k<m_outerPackets; ++k)\n        {\n          const Index outerOffset = (1<<OuterPacketBits) * k;\n          typename HashMapType::iterator end = m_hashmaps[k].end();\n          for (typename HashMapType::iterator it = m_hashmaps[k].begin(); it!=end; ++it)\n          {\n            const Index inner = (it->first >> m_keyBitsOffset) + outerOffset;\n            const Index outer = it->first & keyBitsMask;\n            // sorted insertion\n            // Note that we have to deal with at most 2^OuterPacketBits unsorted coefficients,\n            // moreover those 2^OuterPacketBits coeffs are likely to be sparse, an so only a\n            // small fraction of them have to be sorted, whence the following simple procedure:\n            Index posStart = mp_target->outerIndexPtr()[outer];\n            Index i = (positions[outer]++) - 1;\n            while ( (i >= posStart) && (mp_target->innerIndexPtr()[i] > inner) )\n            {\n              mp_target->valuePtr()[i+1] = mp_target->valuePtr()[i];\n              mp_target->innerIndexPtr()[i+1] = mp_target->innerIndexPtr()[i];\n              --i;\n            }\n            mp_target->innerIndexPtr()[i+1] = inner;\n            mp_target->valuePtr()[i+1] = it->second.value;\n          }\n        }\n      }\n      delete[] m_hashmaps;\n    }\n\n    /** \\returns a reference to the coefficient at given coordinates \\a row, \\a col */\n    Scalar& operator() (Index row, Index col)\n    {\n      const Index outer = SetterRowMajor ? row : col;\n      const Index inner = SetterRowMajor ? col : row;\n      const Index outerMajor = outer >> OuterPacketBits; // index of the packet/map\n      const Index outerMinor = outer & OuterPacketMask;  // index of the inner vector in the packet\n      const KeyType key = internal::convert_index<KeyType>((outerMinor<<m_keyBitsOffset) | inner);\n      return m_hashmaps[outerMajor][key].value;\n    }\n\n    /** \\returns the number of non zero coefficients\n      *\n      * \\note According to the underlying map/hash_map implementation,\n      * this function might be quite expensive.\n      */\n    Index nonZeros() const\n    {\n      Index nz = 0;\n      for (Index k=0; k<m_outerPackets; ++k)\n        nz += static_cast<Index>(m_hashmaps[k].size());\n      return nz;\n    }\n\n\n  protected:\n\n    HashMapType* m_hashmaps;\n    SparseMatrixType* mp_target;\n    Index m_outerPackets;\n    unsigned char m_keyBitsOffset;\n};\n\n} // end namespace Eigen\n\n#endif // EIGEN_RANDOMSETTER_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsArrayAPI.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n\n#ifndef EIGEN_SPECIALFUNCTIONS_ARRAYAPI_H\n#define EIGEN_SPECIALFUNCTIONS_ARRAYAPI_H\n\nnamespace Eigen {\n\n/** \\cpp11 \\returns an expression of the coefficient-wise igamma(\\a a, \\a x) to the given arrays.\n  *\n  * This function computes the coefficient-wise incomplete gamma function.\n  *\n  * \\note This function supports only float and double scalar types in c++11 mode. To support other scalar types,\n  * or float/double in non c++11 mode, the user has to provide implementations of igammac(T,T) for any scalar\n  * type T to be supported.\n  *\n  * \\sa Eigen::igammac(), Eigen::lgamma()\n  */\ntemplate<typename Derived,typename ExponentDerived>\ninline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_igamma_op<typename Derived::Scalar>, const Derived, const ExponentDerived>\nigamma(const Eigen::ArrayBase<Derived>& a, const Eigen::ArrayBase<ExponentDerived>& x)\n{\n  return Eigen::CwiseBinaryOp<Eigen::internal::scalar_igamma_op<typename Derived::Scalar>, const Derived, const ExponentDerived>(\n    a.derived(),\n    x.derived()\n  );\n}\n\n/** \\cpp11 \\returns an expression of the coefficient-wise igammac(\\a a, \\a x) to the given arrays.\n  *\n  * This function computes the coefficient-wise complementary incomplete gamma function.\n  *\n  * \\note This function supports only float and double scalar types in c++11 mode. To support other scalar types,\n  * or float/double in non c++11 mode, the user has to provide implementations of igammac(T,T) for any scalar\n  * type T to be supported.\n  *\n  * \\sa Eigen::igamma(), Eigen::lgamma()\n  */\ntemplate<typename Derived,typename ExponentDerived>\ninline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_igammac_op<typename Derived::Scalar>, const Derived, const ExponentDerived>\nigammac(const Eigen::ArrayBase<Derived>& a, const Eigen::ArrayBase<ExponentDerived>& x)\n{\n  return Eigen::CwiseBinaryOp<Eigen::internal::scalar_igammac_op<typename Derived::Scalar>, const Derived, const ExponentDerived>(\n    a.derived(),\n    x.derived()\n  );\n}\n\n/** \\cpp11 \\returns an expression of the coefficient-wise polygamma(\\a n, \\a x) to the given arrays.\n  *\n  * It returns the \\a n -th derivative of the digamma(psi) evaluated at \\c x.\n  *\n  * \\note This function supports only float and double scalar types in c++11 mode. To support other scalar types,\n  * or float/double in non c++11 mode, the user has to provide implementations of polygamma(T,T) for any scalar\n  * type T to be supported.\n  *\n  * \\sa Eigen::digamma()\n  */\n// * \\warning Be careful with the order of the parameters: x.polygamma(n) is equivalent to polygamma(n,x)\n// * \\sa ArrayBase::polygamma()\ntemplate<typename DerivedN,typename DerivedX>\ninline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_polygamma_op<typename DerivedX::Scalar>, const DerivedN, const DerivedX>\npolygamma(const Eigen::ArrayBase<DerivedN>& n, const Eigen::ArrayBase<DerivedX>& x)\n{\n  return Eigen::CwiseBinaryOp<Eigen::internal::scalar_polygamma_op<typename DerivedX::Scalar>, const DerivedN, const DerivedX>(\n    n.derived(),\n    x.derived()\n  );\n}\n\n/** \\cpp11 \\returns an expression of the coefficient-wise betainc(\\a x, \\a a, \\a b) to the given arrays.\n  *\n  * This function computes the regularized incomplete beta function (integral).\n  *\n  * \\note This function supports only float and double scalar types in c++11 mode. To support other scalar types,\n  * or float/double in non c++11 mode, the user has to provide implementations of betainc(T,T,T) for any scalar\n  * type T to be supported.\n  *\n  * \\sa Eigen::betainc(), Eigen::lgamma()\n  */\ntemplate<typename ArgADerived, typename ArgBDerived, typename ArgXDerived>\ninline const Eigen::CwiseTernaryOp<Eigen::internal::scalar_betainc_op<typename ArgXDerived::Scalar>, const ArgADerived, const ArgBDerived, const ArgXDerived>\nbetainc(const Eigen::ArrayBase<ArgADerived>& a, const Eigen::ArrayBase<ArgBDerived>& b, const Eigen::ArrayBase<ArgXDerived>& x)\n{\n  return Eigen::CwiseTernaryOp<Eigen::internal::scalar_betainc_op<typename ArgXDerived::Scalar>, const ArgADerived, const ArgBDerived, const ArgXDerived>(\n    a.derived(),\n    b.derived(),\n    x.derived()\n  );\n}\n\n\n/** \\returns an expression of the coefficient-wise zeta(\\a x, \\a q) to the given arrays.\n  *\n  * It returns the Riemann zeta function of two arguments \\a x and \\a q:\n  *\n  * \\param x is the exposent, it must be > 1\n  * \\param q is the shift, it must be > 0\n  *\n  * \\note This function supports only float and double scalar types. To support other scalar types, the user has\n  * to provide implementations of zeta(T,T) for any scalar type T to be supported.\n  *\n  * \\sa ArrayBase::zeta()\n  */\ntemplate<typename DerivedX,typename DerivedQ>\ninline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_zeta_op<typename DerivedX::Scalar>, const DerivedX, const DerivedQ>\nzeta(const Eigen::ArrayBase<DerivedX>& x, const Eigen::ArrayBase<DerivedQ>& q)\n{\n  return Eigen::CwiseBinaryOp<Eigen::internal::scalar_zeta_op<typename DerivedX::Scalar>, const DerivedX, const DerivedQ>(\n    x.derived(),\n    q.derived()\n  );\n}\n\n} // end namespace Eigen\n\n#endif // EIGEN_SPECIALFUNCTIONS_ARRAYAPI_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsFunctors.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Eugene Brevdo <ebrevdo@gmail.com>\n// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPECIALFUNCTIONS_FUNCTORS_H\n#define EIGEN_SPECIALFUNCTIONS_FUNCTORS_H\n\nnamespace Eigen {\n\nnamespace internal {\n\n\n/** \\internal\n  * \\brief Template functor to compute the incomplete gamma function igamma(a, x)\n  *\n  * \\sa class CwiseBinaryOp, Cwise::igamma\n  */\ntemplate<typename Scalar> struct scalar_igamma_op : binary_op_base<Scalar,Scalar>\n{\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_igamma_op)\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& x) const {\n    using numext::igamma; return igamma(a, x);\n  }\n  template<typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& x) const {\n    return internal::pigamma(a, x);\n  }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_igamma_op<Scalar> > {\n  enum {\n    // Guesstimate\n    Cost = 20 * NumTraits<Scalar>::MulCost + 10 * NumTraits<Scalar>::AddCost,\n    PacketAccess = packet_traits<Scalar>::HasIGamma\n  };\n};\n\n\n/** \\internal\n  * \\brief Template functor to compute the complementary incomplete gamma function igammac(a, x)\n  *\n  * \\sa class CwiseBinaryOp, Cwise::igammac\n  */\ntemplate<typename Scalar> struct scalar_igammac_op : binary_op_base<Scalar,Scalar>\n{\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_igammac_op)\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& x) const {\n    using numext::igammac; return igammac(a, x);\n  }\n  template<typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& x) const\n  {\n    return internal::pigammac(a, x);\n  }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_igammac_op<Scalar> > {\n  enum {\n    // Guesstimate\n    Cost = 20 * NumTraits<Scalar>::MulCost + 10 * NumTraits<Scalar>::AddCost,\n    PacketAccess = packet_traits<Scalar>::HasIGammac\n  };\n};\n\n\n/** \\internal\n  * \\brief Template functor to compute the incomplete beta integral betainc(a, b, x)\n  *\n  */\ntemplate<typename Scalar> struct scalar_betainc_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_betainc_op)\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& x, const Scalar& a, const Scalar& b) const {\n    using numext::betainc; return betainc(x, a, b);\n  }\n  template<typename Packet>\n  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& x, const Packet& a, const Packet& b) const\n  {\n    return internal::pbetainc(x, a, b);\n  }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_betainc_op<Scalar> > {\n  enum {\n    // Guesstimate\n    Cost = 400 * NumTraits<Scalar>::MulCost + 400 * NumTraits<Scalar>::AddCost,\n    PacketAccess = packet_traits<Scalar>::HasBetaInc\n  };\n};\n\n\n/** \\internal\n * \\brief Template functor to compute the natural log of the absolute\n * value of Gamma of a scalar\n * \\sa class CwiseUnaryOp, Cwise::lgamma()\n */\ntemplate<typename Scalar> struct scalar_lgamma_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_lgamma_op)\n  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const {\n    using numext::lgamma; return lgamma(a);\n  }\n  typedef typename packet_traits<Scalar>::type Packet;\n  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::plgamma(a); }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_lgamma_op<Scalar> >\n{\n  enum {\n    // Guesstimate\n    Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost,\n    PacketAccess = packet_traits<Scalar>::HasLGamma\n  };\n};\n\n/** \\internal\n * \\brief Template functor to compute psi, the derivative of lgamma of a scalar.\n * \\sa class CwiseUnaryOp, Cwise::digamma()\n */\ntemplate<typename Scalar> struct scalar_digamma_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_digamma_op)\n  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const {\n    using numext::digamma; return digamma(a);\n  }\n  typedef typename packet_traits<Scalar>::type Packet;\n  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pdigamma(a); }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_digamma_op<Scalar> >\n{\n  enum {\n    // Guesstimate\n    Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost,\n    PacketAccess = packet_traits<Scalar>::HasDiGamma\n  };\n};\n\n/** \\internal\n * \\brief Template functor to compute the Riemann Zeta function of two arguments.\n * \\sa class CwiseUnaryOp, Cwise::zeta()\n */\ntemplate<typename Scalar> struct scalar_zeta_op {\n    EIGEN_EMPTY_STRUCT_CTOR(scalar_zeta_op)\n    EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& x, const Scalar& q) const {\n        using numext::zeta; return zeta(x, q);\n    }\n    typedef typename packet_traits<Scalar>::type Packet;\n    EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& x, const Packet& q) const { return internal::pzeta(x, q); }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_zeta_op<Scalar> >\n{\n    enum {\n        // Guesstimate\n        Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost,\n        PacketAccess = packet_traits<Scalar>::HasZeta\n    };\n};\n\n/** \\internal\n * \\brief Template functor to compute the polygamma function.\n * \\sa class CwiseUnaryOp, Cwise::polygamma()\n */\ntemplate<typename Scalar> struct scalar_polygamma_op {\n    EIGEN_EMPTY_STRUCT_CTOR(scalar_polygamma_op)\n    EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& n, const Scalar& x) const {\n        using numext::polygamma; return polygamma(n, x);\n    }\n    typedef typename packet_traits<Scalar>::type Packet;\n    EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& n, const Packet& x) const { return internal::ppolygamma(n, x); }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_polygamma_op<Scalar> >\n{\n    enum {\n        // Guesstimate\n        Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost,\n        PacketAccess = packet_traits<Scalar>::HasPolygamma\n    };\n};\n\n/** \\internal\n * \\brief Template functor to compute the Gauss error function of a\n * scalar\n * \\sa class CwiseUnaryOp, Cwise::erf()\n */\ntemplate<typename Scalar> struct scalar_erf_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_erf_op)\n  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const {\n    using numext::erf; return erf(a);\n  }\n  typedef typename packet_traits<Scalar>::type Packet;\n  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::perf(a); }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_erf_op<Scalar> >\n{\n  enum {\n    // Guesstimate\n    Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost,\n    PacketAccess = packet_traits<Scalar>::HasErf\n  };\n};\n\n/** \\internal\n * \\brief Template functor to compute the Complementary Error Function\n * of a scalar\n * \\sa class CwiseUnaryOp, Cwise::erfc()\n */\ntemplate<typename Scalar> struct scalar_erfc_op {\n  EIGEN_EMPTY_STRUCT_CTOR(scalar_erfc_op)\n  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const {\n    using numext::erfc; return erfc(a);\n  }\n  typedef typename packet_traits<Scalar>::type Packet;\n  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::perfc(a); }\n};\ntemplate<typename Scalar>\nstruct functor_traits<scalar_erfc_op<Scalar> >\n{\n  enum {\n    // Guesstimate\n    Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost,\n    PacketAccess = packet_traits<Scalar>::HasErfc\n  };\n};\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_SPECIALFUNCTIONS_FUNCTORS_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsHalf.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPECIALFUNCTIONS_HALF_H\n#define EIGEN_SPECIALFUNCTIONS_HALF_H\n\nnamespace Eigen {\nnamespace numext {\n\n#if EIGEN_HAS_C99_MATH\ntemplate<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half lgamma(const Eigen::half& a) {\n  return Eigen::half(Eigen::numext::lgamma(static_cast<float>(a)));\n}\ntemplate<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half digamma(const Eigen::half& a) {\n  return Eigen::half(Eigen::numext::digamma(static_cast<float>(a)));\n}\ntemplate<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half zeta(const Eigen::half& x, const Eigen::half& q) {\n  return Eigen::half(Eigen::numext::zeta(static_cast<float>(x), static_cast<float>(q)));\n}\ntemplate<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half polygamma(const Eigen::half& n, const Eigen::half& x) {\n  return Eigen::half(Eigen::numext::polygamma(static_cast<float>(n), static_cast<float>(x)));\n}\ntemplate<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half erf(const Eigen::half& a) {\n  return Eigen::half(Eigen::numext::erf(static_cast<float>(a)));\n}\ntemplate<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half erfc(const Eigen::half& a) {\n  return Eigen::half(Eigen::numext::erfc(static_cast<float>(a)));\n}\ntemplate<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half igamma(const Eigen::half& a, const Eigen::half& x) {\n  return Eigen::half(Eigen::numext::igamma(static_cast<float>(a), static_cast<float>(x)));\n}\ntemplate<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half igammac(const Eigen::half& a, const Eigen::half& x) {\n  return Eigen::half(Eigen::numext::igammac(static_cast<float>(a), static_cast<float>(x)));\n}\ntemplate<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half betainc(const Eigen::half& a, const Eigen::half& b, const Eigen::half& x) {\n  return Eigen::half(Eigen::numext::betainc(static_cast<float>(a), static_cast<float>(b), static_cast<float>(x)));\n}\n#endif\n\n}  // end namespace numext\n}  // end namespace Eigen\n\n#endif  // EIGEN_SPECIALFUNCTIONS_HALF_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsImpl.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Eugene Brevdo <ebrevdo@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPECIAL_FUNCTIONS_H\n#define EIGEN_SPECIAL_FUNCTIONS_H\n\nnamespace Eigen {\nnamespace internal {\n\n//  Parts of this code are based on the Cephes Math Library.\n//\n//  Cephes Math Library Release 2.8:  June, 2000\n//  Copyright 1984, 1987, 1992, 2000 by Stephen L. Moshier\n//\n//  Permission has been kindly provided by the original author\n//  to incorporate the Cephes software into the Eigen codebase:\n//\n//    From: Stephen Moshier\n//    To: Eugene Brevdo\n//    Subject: Re: Permission to wrap several cephes functions in Eigen\n//\n//    Hello Eugene,\n//\n//    Thank you for writing.\n//\n//    If your licensing is similar to BSD, the formal way that has been\n//    handled is simply to add a statement to the effect that you are incorporating\n//    the Cephes software by permission of the author.\n//\n//    Good luck with your project,\n//    Steve\n\nnamespace cephes {\n\n/* polevl (modified for Eigen)\n *\n *      Evaluate polynomial\n *\n *\n *\n * SYNOPSIS:\n *\n * int N;\n * Scalar x, y, coef[N+1];\n *\n * y = polevl<decltype(x), N>( x, coef);\n *\n *\n *\n * DESCRIPTION:\n *\n * Evaluates polynomial of degree N:\n *\n *                     2          N\n * y  =  C  + C x + C x  +...+ C x\n *        0    1     2          N\n *\n * Coefficients are stored in reverse order:\n *\n * coef[0] = C  , ..., coef[N] = C  .\n *            N                   0\n *\n *  The function p1evl() assumes that coef[N] = 1.0 and is\n * omitted from the array.  Its calling arguments are\n * otherwise the same as polevl().\n *\n *\n * The Eigen implementation is templatized.  For best speed, store\n * coef as a const array (constexpr), e.g.\n *\n * const double coef[] = {1.0, 2.0, 3.0, ...};\n *\n */\ntemplate <typename Scalar, int N>\nstruct polevl {\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE Scalar run(const Scalar x, const Scalar coef[]) {\n    EIGEN_STATIC_ASSERT((N > 0), YOU_MADE_A_PROGRAMMING_MISTAKE);\n\n    return polevl<Scalar, N - 1>::run(x, coef) * x + coef[N];\n  }\n};\n\ntemplate <typename Scalar>\nstruct polevl<Scalar, 0> {\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE Scalar run(const Scalar, const Scalar coef[]) {\n    return coef[0];\n  }\n};\n\n}  // end namespace cephes\n\n/****************************************************************************\n * Implementation of lgamma, requires C++11/C99                             *\n ****************************************************************************/\n\ntemplate <typename Scalar>\nstruct lgamma_impl {\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE Scalar run(const Scalar) {\n    EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),\n                        THIS_TYPE_IS_NOT_SUPPORTED);\n    return Scalar(0);\n  }\n};\n\ntemplate <typename Scalar>\nstruct lgamma_retval {\n  typedef Scalar type;\n};\n\n#if EIGEN_HAS_C99_MATH\ntemplate <>\nstruct lgamma_impl<float> {\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE float run(float x) {\n#if !defined(__CUDA_ARCH__) && (defined(_BSD_SOURCE) || defined(_SVID_SOURCE)) && !defined(__APPLE__)\n    int signgam;\n    return ::lgammaf_r(x, &signgam);\n#else\n    return ::lgammaf(x);\n#endif\n  }\n};\n\ntemplate <>\nstruct lgamma_impl<double> {\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE double run(double x) {\n#if !defined(__CUDA_ARCH__) && (defined(_BSD_SOURCE) || defined(_SVID_SOURCE)) && !defined(__APPLE__)\n    int signgam;\n    return ::lgamma_r(x, &signgam);\n#else\n    return ::lgamma(x);\n#endif\n  }\n};\n#endif\n\n/****************************************************************************\n * Implementation of digamma (psi), based on Cephes                         *\n ****************************************************************************/\n\ntemplate <typename Scalar>\nstruct digamma_retval {\n  typedef Scalar type;\n};\n\n/*\n *\n * Polynomial evaluation helper for the Psi (digamma) function.\n *\n * digamma_impl_maybe_poly::run(s) evaluates the asymptotic Psi expansion for\n * input Scalar s, assuming s is above 10.0.\n *\n * If s is above a certain threshold for the given Scalar type, zero\n * is returned.  Otherwise the polynomial is evaluated with enough\n * coefficients for results matching Scalar machine precision.\n *\n *\n */\ntemplate <typename Scalar>\nstruct digamma_impl_maybe_poly {\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE Scalar run(const Scalar) {\n    EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),\n                        THIS_TYPE_IS_NOT_SUPPORTED);\n    return Scalar(0);\n  }\n};\n\n\ntemplate <>\nstruct digamma_impl_maybe_poly<float> {\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE float run(const float s) {\n    const float A[] = {\n      -4.16666666666666666667E-3f,\n      3.96825396825396825397E-3f,\n      -8.33333333333333333333E-3f,\n      8.33333333333333333333E-2f\n    };\n\n    float z;\n    if (s < 1.0e8f) {\n      z = 1.0f / (s * s);\n      return z * cephes::polevl<float, 3>::run(z, A);\n    } else return 0.0f;\n  }\n};\n\ntemplate <>\nstruct digamma_impl_maybe_poly<double> {\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE double run(const double s) {\n    const double A[] = {\n      8.33333333333333333333E-2,\n      -2.10927960927960927961E-2,\n      7.57575757575757575758E-3,\n      -4.16666666666666666667E-3,\n      3.96825396825396825397E-3,\n      -8.33333333333333333333E-3,\n      8.33333333333333333333E-2\n    };\n\n    double z;\n    if (s < 1.0e17) {\n      z = 1.0 / (s * s);\n      return z * cephes::polevl<double, 6>::run(z, A);\n    }\n    else return 0.0;\n  }\n};\n\ntemplate <typename Scalar>\nstruct digamma_impl {\n  EIGEN_DEVICE_FUNC\n  static Scalar run(Scalar x) {\n    /*\n     *\n     *     Psi (digamma) function (modified for Eigen)\n     *\n     *\n     * SYNOPSIS:\n     *\n     * double x, y, psi();\n     *\n     * y = psi( x );\n     *\n     *\n     * DESCRIPTION:\n     *\n     *              d      -\n     *   psi(x)  =  -- ln | (x)\n     *              dx\n     *\n     * is the logarithmic derivative of the gamma function.\n     * For integer x,\n     *                   n-1\n     *                    -\n     * psi(n) = -EUL  +   >  1/k.\n     *                    -\n     *                   k=1\n     *\n     * If x is negative, it is transformed to a positive argument by the\n     * reflection formula  psi(1-x) = psi(x) + pi cot(pi x).\n     * For general positive x, the argument is made greater than 10\n     * using the recurrence  psi(x+1) = psi(x) + 1/x.\n     * Then the following asymptotic expansion is applied:\n     *\n     *                           inf.   B\n     *                            -      2k\n     * psi(x) = log(x) - 1/2x -   >   -------\n     *                            -        2k\n     *                           k=1   2k x\n     *\n     * where the B2k are Bernoulli numbers.\n     *\n     * ACCURACY (float):\n     *    Relative error (except absolute when |psi| < 1):\n     * arithmetic   domain     # trials      peak         rms\n     *    IEEE      0,30        30000       1.3e-15     1.4e-16\n     *    IEEE      -30,0       40000       1.5e-15     2.2e-16\n     *\n     * ACCURACY (double):\n     *    Absolute error,  relative when |psi| > 1 :\n     * arithmetic   domain     # trials      peak         rms\n     *    IEEE      -33,0        30000      8.2e-7      1.2e-7\n     *    IEEE      0,33        100000      7.3e-7      7.7e-8\n     *\n     * ERROR MESSAGES:\n     *     message         condition      value returned\n     * psi singularity    x integer <=0      INFINITY\n     */\n\n    Scalar p, q, nz, s, w, y;\n    bool negative = false;\n\n    const Scalar maxnum = NumTraits<Scalar>::infinity();\n    const Scalar m_pi = Scalar(EIGEN_PI);\n\n    const Scalar zero = Scalar(0);\n    const Scalar one = Scalar(1);\n    const Scalar half = Scalar(0.5);\n    nz = zero;\n\n    if (x <= zero) {\n      negative = true;\n      q = x;\n      p = numext::floor(q);\n      if (p == q) {\n        return maxnum;\n      }\n      /* Remove the zeros of tan(m_pi x)\n       * by subtracting the nearest integer from x\n       */\n      nz = q - p;\n      if (nz != half) {\n        if (nz > half) {\n          p += one;\n          nz = q - p;\n        }\n        nz = m_pi / numext::tan(m_pi * nz);\n      }\n      else {\n        nz = zero;\n      }\n      x = one - x;\n    }\n\n    /* use the recurrence psi(x+1) = psi(x) + 1/x. */\n    s = x;\n    w = zero;\n    while (s < Scalar(10)) {\n      w += one / s;\n      s += one;\n    }\n\n    y = digamma_impl_maybe_poly<Scalar>::run(s);\n\n    y = numext::log(s) - (half / s) - y - w;\n\n    return (negative) ? y - nz : y;\n  }\n};\n\n/****************************************************************************\n * Implementation of erf, requires C++11/C99                                *\n ****************************************************************************/\n\ntemplate <typename Scalar>\nstruct erf_impl {\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE Scalar run(const Scalar) {\n    EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),\n                        THIS_TYPE_IS_NOT_SUPPORTED);\n    return Scalar(0);\n  }\n};\n\ntemplate <typename Scalar>\nstruct erf_retval {\n  typedef Scalar type;\n};\n\n#if EIGEN_HAS_C99_MATH\ntemplate <>\nstruct erf_impl<float> {\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE float run(float x) { return ::erff(x); }\n};\n\ntemplate <>\nstruct erf_impl<double> {\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE double run(double x) { return ::erf(x); }\n};\n#endif  // EIGEN_HAS_C99_MATH\n\n/***************************************************************************\n* Implementation of erfc, requires C++11/C99                               *\n****************************************************************************/\n\ntemplate <typename Scalar>\nstruct erfc_impl {\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE Scalar run(const Scalar) {\n    EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),\n                        THIS_TYPE_IS_NOT_SUPPORTED);\n    return Scalar(0);\n  }\n};\n\ntemplate <typename Scalar>\nstruct erfc_retval {\n  typedef Scalar type;\n};\n\n#if EIGEN_HAS_C99_MATH\ntemplate <>\nstruct erfc_impl<float> {\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE float run(const float x) { return ::erfcf(x); }\n};\n\ntemplate <>\nstruct erfc_impl<double> {\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE double run(const double x) { return ::erfc(x); }\n};\n#endif  // EIGEN_HAS_C99_MATH\n\n/**************************************************************************************************************\n * Implementation of igammac (complemented incomplete gamma integral), based on Cephes but requires C++11/C99 *\n **************************************************************************************************************/\n\ntemplate <typename Scalar>\nstruct igammac_retval {\n  typedef Scalar type;\n};\n\n// NOTE: cephes_helper is also used to implement zeta\ntemplate <typename Scalar>\nstruct cephes_helper {\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE Scalar machep() { assert(false && \"machep not supported for this type\"); return 0.0; }\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE Scalar big() { assert(false && \"big not supported for this type\"); return 0.0; }\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE Scalar biginv() { assert(false && \"biginv not supported for this type\"); return 0.0; }\n};\n\ntemplate <>\nstruct cephes_helper<float> {\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE float machep() {\n    return NumTraits<float>::epsilon() / 2;  // 1.0 - machep == 1.0\n  }\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE float big() {\n    // use epsneg (1.0 - epsneg == 1.0)\n    return 1.0f / (NumTraits<float>::epsilon() / 2);\n  }\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE float biginv() {\n    // epsneg\n    return machep();\n  }\n};\n\ntemplate <>\nstruct cephes_helper<double> {\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE double machep() {\n    return NumTraits<double>::epsilon() / 2;  // 1.0 - machep == 1.0\n  }\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE double big() {\n    return 1.0 / NumTraits<double>::epsilon();\n  }\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE double biginv() {\n    // inverse of eps\n    return NumTraits<double>::epsilon();\n  }\n};\n\n#if !EIGEN_HAS_C99_MATH\n\ntemplate <typename Scalar>\nstruct igammac_impl {\n  EIGEN_DEVICE_FUNC\n  static Scalar run(Scalar a, Scalar x) {\n    EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),\n                        THIS_TYPE_IS_NOT_SUPPORTED);\n    return Scalar(0);\n  }\n};\n\n#else\n\ntemplate <typename Scalar> struct igamma_impl;  // predeclare igamma_impl\n\ntemplate <typename Scalar>\nstruct igammac_impl {\n  EIGEN_DEVICE_FUNC\n  static Scalar run(Scalar a, Scalar x) {\n    /*  igamc()\n     *\n     *\tIncomplete gamma integral (modified for Eigen)\n     *\n     *\n     *\n     * SYNOPSIS:\n     *\n     * double a, x, y, igamc();\n     *\n     * y = igamc( a, x );\n     *\n     * DESCRIPTION:\n     *\n     * The function is defined by\n     *\n     *\n     *  igamc(a,x)   =   1 - igam(a,x)\n     *\n     *                            inf.\n     *                              -\n     *                     1       | |  -t  a-1\n     *               =   -----     |   e   t   dt.\n     *                    -      | |\n     *                   | (a)    -\n     *                             x\n     *\n     *\n     * In this implementation both arguments must be positive.\n     * The integral is evaluated by either a power series or\n     * continued fraction expansion, depending on the relative\n     * values of a and x.\n     *\n     * ACCURACY (float):\n     *\n     *                      Relative error:\n     * arithmetic   domain     # trials      peak         rms\n     *    IEEE      0,30        30000       7.8e-6      5.9e-7\n     *\n     *\n     * ACCURACY (double):\n     *\n     * Tested at random a, x.\n     *                a         x                      Relative error:\n     * arithmetic   domain   domain     # trials      peak         rms\n     *    IEEE     0.5,100   0,100      200000       1.9e-14     1.7e-15\n     *    IEEE     0.01,0.5  0,100      200000       1.4e-13     1.6e-15\n     *\n     */\n    /*\n      Cephes Math Library Release 2.2: June, 1992\n      Copyright 1985, 1987, 1992 by Stephen L. Moshier\n      Direct inquiries to 30 Frost Street, Cambridge, MA 02140\n    */\n    const Scalar zero = 0;\n    const Scalar one = 1;\n    const Scalar nan = NumTraits<Scalar>::quiet_NaN();\n\n    if ((x < zero) || (a <= zero)) {\n      // domain error\n      return nan;\n    }\n\n    if ((x < one) || (x < a)) {\n      /* The checks above ensure that we meet the preconditions for\n       * igamma_impl::Impl(), so call it, rather than igamma_impl::Run().\n       * Calling Run() would also work, but in that case the compiler may not be\n       * able to prove that igammac_impl::Run and igamma_impl::Run are not\n       * mutually recursive.  This leads to worse code, particularly on\n       * platforms like nvptx, where recursion is allowed only begrudgingly.\n       */\n      return (one - igamma_impl<Scalar>::Impl(a, x));\n    }\n\n    return Impl(a, x);\n  }\n\n private:\n  /* igamma_impl calls igammac_impl::Impl. */\n  friend struct igamma_impl<Scalar>;\n\n  /* Actually computes igamc(a, x).\n   *\n   * Preconditions:\n   *   a > 0\n   *   x >= 1\n   *   x >= a\n   */\n  EIGEN_DEVICE_FUNC static Scalar Impl(Scalar a, Scalar x) {\n    const Scalar zero = 0;\n    const Scalar one = 1;\n    const Scalar two = 2;\n    const Scalar machep = cephes_helper<Scalar>::machep();\n    const Scalar maxlog = numext::log(NumTraits<Scalar>::highest());\n    const Scalar big = cephes_helper<Scalar>::big();\n    const Scalar biginv = cephes_helper<Scalar>::biginv();\n    const Scalar inf = NumTraits<Scalar>::infinity();\n\n    Scalar ans, ax, c, yc, r, t, y, z;\n    Scalar pk, pkm1, pkm2, qk, qkm1, qkm2;\n\n    if (x == inf) return zero;  // std::isinf crashes on CUDA\n\n    /* Compute  x**a * exp(-x) / gamma(a)  */\n    ax = a * numext::log(x) - x - lgamma_impl<Scalar>::run(a);\n    if (ax < -maxlog) {  // underflow\n      return zero;\n    }\n    ax = numext::exp(ax);\n\n    // continued fraction\n    y = one - a;\n    z = x + y + one;\n    c = zero;\n    pkm2 = one;\n    qkm2 = x;\n    pkm1 = x + one;\n    qkm1 = z * x;\n    ans = pkm1 / qkm1;\n\n    while (true) {\n      c += one;\n      y += one;\n      z += two;\n      yc = y * c;\n      pk = pkm1 * z - pkm2 * yc;\n      qk = qkm1 * z - qkm2 * yc;\n      if (qk != zero) {\n        r = pk / qk;\n        t = numext::abs((ans - r) / r);\n        ans = r;\n      } else {\n        t = one;\n      }\n      pkm2 = pkm1;\n      pkm1 = pk;\n      qkm2 = qkm1;\n      qkm1 = qk;\n      if (numext::abs(pk) > big) {\n        pkm2 *= biginv;\n        pkm1 *= biginv;\n        qkm2 *= biginv;\n        qkm1 *= biginv;\n      }\n      if (t <= machep) {\n        break;\n      }\n    }\n\n    return (ans * ax);\n  }\n};\n\n#endif  // EIGEN_HAS_C99_MATH\n\n/************************************************************************************************\n * Implementation of igamma (incomplete gamma integral), based on Cephes but requires C++11/C99 *\n ************************************************************************************************/\n\ntemplate <typename Scalar>\nstruct igamma_retval {\n  typedef Scalar type;\n};\n\n#if !EIGEN_HAS_C99_MATH\n\ntemplate <typename Scalar>\nstruct igamma_impl {\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE Scalar run(Scalar a, Scalar x) {\n    EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),\n                        THIS_TYPE_IS_NOT_SUPPORTED);\n    return Scalar(0);\n  }\n};\n\n#else\n\ntemplate <typename Scalar>\nstruct igamma_impl {\n  EIGEN_DEVICE_FUNC\n  static Scalar run(Scalar a, Scalar x) {\n    /*\tigam()\n     *\tIncomplete gamma integral\n     *\n     *\n     *\n     * SYNOPSIS:\n     *\n     * double a, x, y, igam();\n     *\n     * y = igam( a, x );\n     *\n     * DESCRIPTION:\n     *\n     * The function is defined by\n     *\n     *                           x\n     *                            -\n     *                   1       | |  -t  a-1\n     *  igam(a,x)  =   -----     |   e   t   dt.\n     *                  -      | |\n     *                 | (a)    -\n     *                           0\n     *\n     *\n     * In this implementation both arguments must be positive.\n     * The integral is evaluated by either a power series or\n     * continued fraction expansion, depending on the relative\n     * values of a and x.\n     *\n     * ACCURACY (double):\n     *\n     *                      Relative error:\n     * arithmetic   domain     # trials      peak         rms\n     *    IEEE      0,30       200000       3.6e-14     2.9e-15\n     *    IEEE      0,100      300000       9.9e-14     1.5e-14\n     *\n     *\n     * ACCURACY (float):\n     *\n     *                      Relative error:\n     * arithmetic   domain     # trials      peak         rms\n     *    IEEE      0,30        20000       7.8e-6      5.9e-7\n     *\n     */\n    /*\n      Cephes Math Library Release 2.2: June, 1992\n      Copyright 1985, 1987, 1992 by Stephen L. Moshier\n      Direct inquiries to 30 Frost Street, Cambridge, MA 02140\n    */\n\n\n    /* left tail of incomplete gamma function:\n     *\n     *          inf.      k\n     *   a  -x   -       x\n     *  x  e     >   ----------\n     *           -     -\n     *          k=0   | (a+k+1)\n     *\n     */\n    const Scalar zero = 0;\n    const Scalar one = 1;\n    const Scalar nan = NumTraits<Scalar>::quiet_NaN();\n\n    if (x == zero) return zero;\n\n    if ((x < zero) || (a <= zero)) {  // domain error\n      return nan;\n    }\n\n    if ((x > one) && (x > a)) {\n      /* The checks above ensure that we meet the preconditions for\n       * igammac_impl::Impl(), so call it, rather than igammac_impl::Run().\n       * Calling Run() would also work, but in that case the compiler may not be\n       * able to prove that igammac_impl::Run and igamma_impl::Run are not\n       * mutually recursive.  This leads to worse code, particularly on\n       * platforms like nvptx, where recursion is allowed only begrudgingly.\n       */\n      return (one - igammac_impl<Scalar>::Impl(a, x));\n    }\n\n    return Impl(a, x);\n  }\n\n private:\n  /* igammac_impl calls igamma_impl::Impl. */\n  friend struct igammac_impl<Scalar>;\n\n  /* Actually computes igam(a, x).\n   *\n   * Preconditions:\n   *   x > 0\n   *   a > 0\n   *   !(x > 1 && x > a)\n   */\n  EIGEN_DEVICE_FUNC static Scalar Impl(Scalar a, Scalar x) {\n    const Scalar zero = 0;\n    const Scalar one = 1;\n    const Scalar machep = cephes_helper<Scalar>::machep();\n    const Scalar maxlog = numext::log(NumTraits<Scalar>::highest());\n\n    Scalar ans, ax, c, r;\n\n    /* Compute  x**a * exp(-x) / gamma(a)  */\n    ax = a * numext::log(x) - x - lgamma_impl<Scalar>::run(a);\n    if (ax < -maxlog) {\n      // underflow\n      return zero;\n    }\n    ax = numext::exp(ax);\n\n    /* power series */\n    r = a;\n    c = one;\n    ans = one;\n\n    while (true) {\n      r += one;\n      c *= x/r;\n      ans += c;\n      if (c/ans <= machep) {\n        break;\n      }\n    }\n\n    return (ans * ax / a);\n  }\n};\n\n#endif  // EIGEN_HAS_C99_MATH\n\n/*****************************************************************************\n * Implementation of Riemann zeta function of two arguments, based on Cephes *\n *****************************************************************************/\n\ntemplate <typename Scalar>\nstruct zeta_retval {\n    typedef Scalar type;\n};\n\ntemplate <typename Scalar>\nstruct zeta_impl_series {\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE Scalar run(const Scalar) {\n    EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),\n                        THIS_TYPE_IS_NOT_SUPPORTED);\n    return Scalar(0);\n  }\n};\n\ntemplate <>\nstruct zeta_impl_series<float> {\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE bool run(float& a, float& b, float& s, const float x, const float machep) {\n    int i = 0;\n    while(i < 9)\n    {\n        i += 1;\n        a += 1.0f;\n        b = numext::pow( a, -x );\n        s += b;\n        if( numext::abs(b/s) < machep )\n            return true;\n    }\n\n    //Return whether we are done\n    return false;\n  }\n};\n\ntemplate <>\nstruct zeta_impl_series<double> {\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE bool run(double& a, double& b, double& s, const double x, const double machep) {\n    int i = 0;\n    while( (i < 9) || (a <= 9.0) )\n    {\n        i += 1;\n        a += 1.0;\n        b = numext::pow( a, -x );\n        s += b;\n        if( numext::abs(b/s) < machep )\n            return true;\n    }\n\n    //Return whether we are done\n    return false;\n  }\n};\n\ntemplate <typename Scalar>\nstruct zeta_impl {\n    EIGEN_DEVICE_FUNC\n    static Scalar run(Scalar x, Scalar q) {\n        /*\t\t\t\t\t\t\tzeta.c\n         *\n         *\tRiemann zeta function of two arguments\n         *\n         *\n         *\n         * SYNOPSIS:\n         *\n         * double x, q, y, zeta();\n         *\n         * y = zeta( x, q );\n         *\n         *\n         *\n         * DESCRIPTION:\n         *\n         *\n         *\n         *                 inf.\n         *                  -        -x\n         *   zeta(x,q)  =   >   (k+q)\n         *                  -\n         *                 k=0\n         *\n         * where x > 1 and q is not a negative integer or zero.\n         * The Euler-Maclaurin summation formula is used to obtain\n         * the expansion\n         *\n         *                n\n         *                -       -x\n         * zeta(x,q)  =   >  (k+q)\n         *                -\n         *               k=1\n         *\n         *           1-x                 inf.  B   x(x+1)...(x+2j)\n         *      (n+q)           1         -     2j\n         *  +  ---------  -  -------  +   >    --------------------\n         *        x-1              x      -                   x+2j+1\n         *                   2(n+q)      j=1       (2j)! (n+q)\n         *\n         * where the B2j are Bernoulli numbers.  Note that (see zetac.c)\n         * zeta(x,1) = zetac(x) + 1.\n         *\n         *\n         *\n         * ACCURACY:\n         *\n         * Relative error for single precision:\n         * arithmetic   domain     # trials      peak         rms\n         *    IEEE      0,25        10000       6.9e-7      1.0e-7\n         *\n         * Large arguments may produce underflow in powf(), in which\n         * case the results are inaccurate.\n         *\n         * REFERENCE:\n         *\n         * Gradshteyn, I. S., and I. M. Ryzhik, Tables of Integrals,\n         * Series, and Products, p. 1073; Academic Press, 1980.\n         *\n         */\n\n        int i;\n        Scalar p, r, a, b, k, s, t, w;\n\n        const Scalar A[] = {\n            Scalar(12.0),\n            Scalar(-720.0),\n            Scalar(30240.0),\n            Scalar(-1209600.0),\n            Scalar(47900160.0),\n            Scalar(-1.8924375803183791606e9), /*1.307674368e12/691*/\n            Scalar(7.47242496e10),\n            Scalar(-2.950130727918164224e12), /*1.067062284288e16/3617*/\n            Scalar(1.1646782814350067249e14), /*5.109094217170944e18/43867*/\n            Scalar(-4.5979787224074726105e15), /*8.028576626982912e20/174611*/\n            Scalar(1.8152105401943546773e17), /*1.5511210043330985984e23/854513*/\n            Scalar(-7.1661652561756670113e18) /*1.6938241367317436694528e27/236364091*/\n            };\n\n        const Scalar maxnum = NumTraits<Scalar>::infinity();\n        const Scalar zero = 0.0, half = 0.5, one = 1.0;\n        const Scalar machep = cephes_helper<Scalar>::machep();\n        const Scalar nan = NumTraits<Scalar>::quiet_NaN();\n\n        if( x == one )\n            return maxnum;\n\n        if( x < one )\n        {\n            return nan;\n        }\n\n        if( q <= zero )\n        {\n            if(q == numext::floor(q))\n            {\n                return maxnum;\n            }\n            p = x;\n            r = numext::floor(p);\n            if (p != r)\n                return nan;\n        }\n\n        /* Permit negative q but continue sum until n+q > +9 .\n         * This case should be handled by a reflection formula.\n         * If q<0 and x is an integer, there is a relation to\n         * the polygamma function.\n         */\n        s = numext::pow( q, -x );\n        a = q;\n        b = zero;\n        // Run the summation in a helper function that is specific to the floating precision\n        if (zeta_impl_series<Scalar>::run(a, b, s, x, machep)) {\n            return s;\n        }\n\n        w = a;\n        s += b*w/(x-one);\n        s -= half * b;\n        a = one;\n        k = zero;\n        for( i=0; i<12; i++ )\n        {\n            a *= x + k;\n            b /= w;\n            t = a*b/A[i];\n            s = s + t;\n            t = numext::abs(t/s);\n            if( t < machep ) {\n              break;\n            }\n            k += one;\n            a *= x + k;\n            b /= w;\n            k += one;\n        }\n        return s;\n  }\n};\n\n/****************************************************************************\n * Implementation of polygamma function, requires C++11/C99                 *\n ****************************************************************************/\n\ntemplate <typename Scalar>\nstruct polygamma_retval {\n    typedef Scalar type;\n};\n\n#if !EIGEN_HAS_C99_MATH\n\ntemplate <typename Scalar>\nstruct polygamma_impl {\n    EIGEN_DEVICE_FUNC\n    static EIGEN_STRONG_INLINE Scalar run(Scalar n, Scalar x) {\n        EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),\n                            THIS_TYPE_IS_NOT_SUPPORTED);\n        return Scalar(0);\n    }\n};\n\n#else\n\ntemplate <typename Scalar>\nstruct polygamma_impl {\n    EIGEN_DEVICE_FUNC\n    static Scalar run(Scalar n, Scalar x) {\n        Scalar zero = 0.0, one = 1.0;\n        Scalar nplus = n + one;\n        const Scalar nan = NumTraits<Scalar>::quiet_NaN();\n\n        // Check that n is an integer\n        if (numext::floor(n) != n) {\n            return nan;\n        }\n        // Just return the digamma function for n = 1\n        else if (n == zero) {\n            return digamma_impl<Scalar>::run(x);\n        }\n        // Use the same implementation as scipy\n        else {\n            Scalar factorial = numext::exp(lgamma_impl<Scalar>::run(nplus));\n            return numext::pow(-one, nplus) * factorial * zeta_impl<Scalar>::run(nplus, x);\n        }\n  }\n};\n\n#endif  // EIGEN_HAS_C99_MATH\n\n/************************************************************************************************\n * Implementation of betainc (incomplete beta integral), based on Cephes but requires C++11/C99 *\n ************************************************************************************************/\n\ntemplate <typename Scalar>\nstruct betainc_retval {\n  typedef Scalar type;\n};\n\n#if !EIGEN_HAS_C99_MATH\n\ntemplate <typename Scalar>\nstruct betainc_impl {\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE Scalar run(Scalar a, Scalar b, Scalar x) {\n    EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),\n                        THIS_TYPE_IS_NOT_SUPPORTED);\n    return Scalar(0);\n  }\n};\n\n#else\n\ntemplate <typename Scalar>\nstruct betainc_impl {\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE Scalar run(Scalar, Scalar, Scalar) {\n    /*\tbetaincf.c\n     *\n     *\tIncomplete beta integral\n     *\n     *\n     * SYNOPSIS:\n     *\n     * float a, b, x, y, betaincf();\n     *\n     * y = betaincf( a, b, x );\n     *\n     *\n     * DESCRIPTION:\n     *\n     * Returns incomplete beta integral of the arguments, evaluated\n     * from zero to x.  The function is defined as\n     *\n     *                  x\n     *     -            -\n     *    | (a+b)      | |  a-1     b-1\n     *  -----------    |   t   (1-t)   dt.\n     *   -     -     | |\n     *  | (a) | (b)   -\n     *                 0\n     *\n     * The domain of definition is 0 <= x <= 1.  In this\n     * implementation a and b are restricted to positive values.\n     * The integral from x to 1 may be obtained by the symmetry\n     * relation\n     *\n     *    1 - betainc( a, b, x )  =  betainc( b, a, 1-x ).\n     *\n     * The integral is evaluated by a continued fraction expansion.\n     * If a < 1, the function calls itself recursively after a\n     * transformation to increase a to a+1.\n     *\n     * ACCURACY (float):\n     *\n     * Tested at random points (a,b,x) with a and b in the indicated\n     * interval and x between 0 and 1.\n     *\n     * arithmetic   domain     # trials      peak         rms\n     * Relative error:\n     *    IEEE       0,30       10000       3.7e-5      5.1e-6\n     *    IEEE       0,100      10000       1.7e-4      2.5e-5\n     * The useful domain for relative error is limited by underflow\n     * of the single precision exponential function.\n     * Absolute error:\n     *    IEEE       0,30      100000       2.2e-5      9.6e-7\n     *    IEEE       0,100      10000       6.5e-5      3.7e-6\n     *\n     * Larger errors may occur for extreme ratios of a and b.\n     *\n     * ACCURACY (double):\n     * arithmetic   domain     # trials      peak         rms\n     *    IEEE      0,5         10000       6.9e-15     4.5e-16\n     *    IEEE      0,85       250000       2.2e-13     1.7e-14\n     *    IEEE      0,1000      30000       5.3e-12     6.3e-13\n     *    IEEE      0,10000    250000       9.3e-11     7.1e-12\n     *    IEEE      0,100000    10000       8.7e-10     4.8e-11\n     * Outputs smaller than the IEEE gradual underflow threshold\n     * were excluded from these statistics.\n     *\n     * ERROR MESSAGES:\n     *   message         condition      value returned\n     * incbet domain      x<0, x>1          nan\n     * incbet underflow                     nan\n     */\n\n    EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),\n                        THIS_TYPE_IS_NOT_SUPPORTED);\n    return Scalar(0);\n  }\n};\n\n/* Continued fraction expansion #1 for incomplete beta integral (small_branch = True)\n * Continued fraction expansion #2 for incomplete beta integral (small_branch = False)\n */\ntemplate <typename Scalar>\nstruct incbeta_cfe {\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE Scalar run(Scalar a, Scalar b, Scalar x, bool small_branch) {\n    EIGEN_STATIC_ASSERT((internal::is_same<Scalar, float>::value ||\n                         internal::is_same<Scalar, double>::value),\n                        THIS_TYPE_IS_NOT_SUPPORTED);\n    const Scalar big = cephes_helper<Scalar>::big();\n    const Scalar machep = cephes_helper<Scalar>::machep();\n    const Scalar biginv = cephes_helper<Scalar>::biginv();\n\n    const Scalar zero = 0;\n    const Scalar one = 1;\n    const Scalar two = 2;\n\n    Scalar xk, pk, pkm1, pkm2, qk, qkm1, qkm2;\n    Scalar k1, k2, k3, k4, k5, k6, k7, k8, k26update;\n    Scalar ans;\n    int n;\n\n    const int num_iters = (internal::is_same<Scalar, float>::value) ? 100 : 300;\n    const Scalar thresh =\n        (internal::is_same<Scalar, float>::value) ? machep : Scalar(3) * machep;\n    Scalar r = (internal::is_same<Scalar, float>::value) ? zero : one;\n\n    if (small_branch) {\n      k1 = a;\n      k2 = a + b;\n      k3 = a;\n      k4 = a + one;\n      k5 = one;\n      k6 = b - one;\n      k7 = k4;\n      k8 = a + two;\n      k26update = one;\n    } else {\n      k1 = a;\n      k2 = b - one;\n      k3 = a;\n      k4 = a + one;\n      k5 = one;\n      k6 = a + b;\n      k7 = a + one;\n      k8 = a + two;\n      k26update = -one;\n      x = x / (one - x);\n    }\n\n    pkm2 = zero;\n    qkm2 = one;\n    pkm1 = one;\n    qkm1 = one;\n    ans = one;\n    n = 0;\n\n    do {\n      xk = -(x * k1 * k2) / (k3 * k4);\n      pk = pkm1 + pkm2 * xk;\n      qk = qkm1 + qkm2 * xk;\n      pkm2 = pkm1;\n      pkm1 = pk;\n      qkm2 = qkm1;\n      qkm1 = qk;\n\n      xk = (x * k5 * k6) / (k7 * k8);\n      pk = pkm1 + pkm2 * xk;\n      qk = qkm1 + qkm2 * xk;\n      pkm2 = pkm1;\n      pkm1 = pk;\n      qkm2 = qkm1;\n      qkm1 = qk;\n\n      if (qk != zero) {\n        r = pk / qk;\n        if (numext::abs(ans - r) < numext::abs(r) * thresh) {\n          return r;\n        }\n        ans = r;\n      }\n\n      k1 += one;\n      k2 += k26update;\n      k3 += two;\n      k4 += two;\n      k5 += one;\n      k6 -= k26update;\n      k7 += two;\n      k8 += two;\n\n      if ((numext::abs(qk) + numext::abs(pk)) > big) {\n        pkm2 *= biginv;\n        pkm1 *= biginv;\n        qkm2 *= biginv;\n        qkm1 *= biginv;\n      }\n      if ((numext::abs(qk) < biginv) || (numext::abs(pk) < biginv)) {\n        pkm2 *= big;\n        pkm1 *= big;\n        qkm2 *= big;\n        qkm1 *= big;\n      }\n    } while (++n < num_iters);\n\n    return ans;\n  }\n};\n\n/* Helper functions depending on the Scalar type */\ntemplate <typename Scalar>\nstruct betainc_helper {};\n\ntemplate <>\nstruct betainc_helper<float> {\n  /* Core implementation, assumes a large (> 1.0) */\n  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE float incbsa(float aa, float bb,\n                                                            float xx) {\n    float ans, a, b, t, x, onemx;\n    bool reversed_a_b = false;\n\n    onemx = 1.0f - xx;\n\n    /* see if x is greater than the mean */\n    if (xx > (aa / (aa + bb))) {\n      reversed_a_b = true;\n      a = bb;\n      b = aa;\n      t = xx;\n      x = onemx;\n    } else {\n      a = aa;\n      b = bb;\n      t = onemx;\n      x = xx;\n    }\n\n    /* Choose expansion for optimal convergence */\n    if (b > 10.0f) {\n      if (numext::abs(b * x / a) < 0.3f) {\n        t = betainc_helper<float>::incbps(a, b, x);\n        if (reversed_a_b) t = 1.0f - t;\n        return t;\n      }\n    }\n\n    ans = x * (a + b - 2.0f) / (a - 1.0f);\n    if (ans < 1.0f) {\n      ans = incbeta_cfe<float>::run(a, b, x, true /* small_branch */);\n      t = b * numext::log(t);\n    } else {\n      ans = incbeta_cfe<float>::run(a, b, x, false /* small_branch */);\n      t = (b - 1.0f) * numext::log(t);\n    }\n\n    t += a * numext::log(x) + lgamma_impl<float>::run(a + b) -\n         lgamma_impl<float>::run(a) - lgamma_impl<float>::run(b);\n    t += numext::log(ans / a);\n    t = numext::exp(t);\n\n    if (reversed_a_b) t = 1.0f - t;\n    return t;\n  }\n\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE float incbps(float a, float b, float x) {\n    float t, u, y, s;\n    const float machep = cephes_helper<float>::machep();\n\n    y = a * numext::log(x) + (b - 1.0f) * numext::log1p(-x) - numext::log(a);\n    y -= lgamma_impl<float>::run(a) + lgamma_impl<float>::run(b);\n    y += lgamma_impl<float>::run(a + b);\n\n    t = x / (1.0f - x);\n    s = 0.0f;\n    u = 1.0f;\n    do {\n      b -= 1.0f;\n      if (b == 0.0f) {\n        break;\n      }\n      a += 1.0f;\n      u *= t * b / a;\n      s += u;\n    } while (numext::abs(u) > machep);\n\n    return numext::exp(y) * (1.0f + s);\n  }\n};\n\ntemplate <>\nstruct betainc_impl<float> {\n  EIGEN_DEVICE_FUNC\n  static float run(float a, float b, float x) {\n    const float nan = NumTraits<float>::quiet_NaN();\n    float ans, t;\n\n    if (a <= 0.0f) return nan;\n    if (b <= 0.0f) return nan;\n    if ((x <= 0.0f) || (x >= 1.0f)) {\n      if (x == 0.0f) return 0.0f;\n      if (x == 1.0f) return 1.0f;\n      // mtherr(\"betaincf\", DOMAIN);\n      return nan;\n    }\n\n    /* transformation for small aa */\n    if (a <= 1.0f) {\n      ans = betainc_helper<float>::incbsa(a + 1.0f, b, x);\n      t = a * numext::log(x) + b * numext::log1p(-x) +\n          lgamma_impl<float>::run(a + b) - lgamma_impl<float>::run(a + 1.0f) -\n          lgamma_impl<float>::run(b);\n      return (ans + numext::exp(t));\n    } else {\n      return betainc_helper<float>::incbsa(a, b, x);\n    }\n  }\n};\n\ntemplate <>\nstruct betainc_helper<double> {\n  EIGEN_DEVICE_FUNC\n  static EIGEN_STRONG_INLINE double incbps(double a, double b, double x) {\n    const double machep = cephes_helper<double>::machep();\n\n    double s, t, u, v, n, t1, z, ai;\n\n    ai = 1.0 / a;\n    u = (1.0 - b) * x;\n    v = u / (a + 1.0);\n    t1 = v;\n    t = u;\n    n = 2.0;\n    s = 0.0;\n    z = machep * ai;\n    while (numext::abs(v) > z) {\n      u = (n - b) * x / n;\n      t *= u;\n      v = t / (a + n);\n      s += v;\n      n += 1.0;\n    }\n    s += t1;\n    s += ai;\n\n    u = a * numext::log(x);\n    // TODO: gamma() is not directly implemented in Eigen.\n    /*\n    if ((a + b) < maxgam && numext::abs(u) < maxlog) {\n      t = gamma(a + b) / (gamma(a) * gamma(b));\n      s = s * t * pow(x, a);\n    } else {\n    */\n    t = lgamma_impl<double>::run(a + b) - lgamma_impl<double>::run(a) -\n        lgamma_impl<double>::run(b) + u + numext::log(s);\n    return s = numext::exp(t);\n  }\n};\n\ntemplate <>\nstruct betainc_impl<double> {\n  EIGEN_DEVICE_FUNC\n  static double run(double aa, double bb, double xx) {\n    const double nan = NumTraits<double>::quiet_NaN();\n    const double machep = cephes_helper<double>::machep();\n    // const double maxgam = 171.624376956302725;\n\n    double a, b, t, x, xc, w, y;\n    bool reversed_a_b = false;\n\n    if (aa <= 0.0 || bb <= 0.0) {\n      return nan;  // goto domerr;\n    }\n\n    if ((xx <= 0.0) || (xx >= 1.0)) {\n      if (xx == 0.0) return (0.0);\n      if (xx == 1.0) return (1.0);\n      // mtherr(\"incbet\", DOMAIN);\n      return nan;\n    }\n\n    if ((bb * xx) <= 1.0 && xx <= 0.95) {\n      return betainc_helper<double>::incbps(aa, bb, xx);\n    }\n\n    w = 1.0 - xx;\n\n    /* Reverse a and b if x is greater than the mean. */\n    if (xx > (aa / (aa + bb))) {\n      reversed_a_b = true;\n      a = bb;\n      b = aa;\n      xc = xx;\n      x = w;\n    } else {\n      a = aa;\n      b = bb;\n      xc = w;\n      x = xx;\n    }\n\n    if (reversed_a_b && (b * x) <= 1.0 && x <= 0.95) {\n      t = betainc_helper<double>::incbps(a, b, x);\n      if (t <= machep) {\n        t = 1.0 - machep;\n      } else {\n        t = 1.0 - t;\n      }\n      return t;\n    }\n\n    /* Choose expansion for better convergence. */\n    y = x * (a + b - 2.0) - (a - 1.0);\n    if (y < 0.0) {\n      w = incbeta_cfe<double>::run(a, b, x, true /* small_branch */);\n    } else {\n      w = incbeta_cfe<double>::run(a, b, x, false /* small_branch */) / xc;\n    }\n\n    /* Multiply w by the factor\n         a      b   _             _     _\n        x  (1-x)   | (a+b) / ( a | (a) | (b) ) .   */\n\n    y = a * numext::log(x);\n    t = b * numext::log(xc);\n    // TODO: gamma is not directly implemented in Eigen.\n    /*\n    if ((a + b) < maxgam && numext::abs(y) < maxlog && numext::abs(t) < maxlog)\n    {\n      t = pow(xc, b);\n      t *= pow(x, a);\n      t /= a;\n      t *= w;\n      t *= gamma(a + b) / (gamma(a) * gamma(b));\n    } else {\n    */\n    /* Resort to logarithms.  */\n    y += t + lgamma_impl<double>::run(a + b) - lgamma_impl<double>::run(a) -\n         lgamma_impl<double>::run(b);\n    y += numext::log(w / a);\n    t = numext::exp(y);\n\n    /* } */\n    // done:\n\n    if (reversed_a_b) {\n      if (t <= machep) {\n        t = 1.0 - machep;\n      } else {\n        t = 1.0 - t;\n      }\n    }\n    return t;\n  }\n};\n\n#endif  // EIGEN_HAS_C99_MATH\n\n}  // end namespace internal\n\nnamespace numext {\n\ntemplate <typename Scalar>\nEIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(lgamma, Scalar)\n    lgamma(const Scalar& x) {\n  return EIGEN_MATHFUNC_IMPL(lgamma, Scalar)::run(x);\n}\n\ntemplate <typename Scalar>\nEIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(digamma, Scalar)\n    digamma(const Scalar& x) {\n  return EIGEN_MATHFUNC_IMPL(digamma, Scalar)::run(x);\n}\n\ntemplate <typename Scalar>\nEIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(zeta, Scalar)\nzeta(const Scalar& x, const Scalar& q) {\n    return EIGEN_MATHFUNC_IMPL(zeta, Scalar)::run(x, q);\n}\n\ntemplate <typename Scalar>\nEIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(polygamma, Scalar)\npolygamma(const Scalar& n, const Scalar& x) {\n    return EIGEN_MATHFUNC_IMPL(polygamma, Scalar)::run(n, x);\n}\n\ntemplate <typename Scalar>\nEIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(erf, Scalar)\n    erf(const Scalar& x) {\n  return EIGEN_MATHFUNC_IMPL(erf, Scalar)::run(x);\n}\n\ntemplate <typename Scalar>\nEIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(erfc, Scalar)\n    erfc(const Scalar& x) {\n  return EIGEN_MATHFUNC_IMPL(erfc, Scalar)::run(x);\n}\n\ntemplate <typename Scalar>\nEIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(igamma, Scalar)\n    igamma(const Scalar& a, const Scalar& x) {\n  return EIGEN_MATHFUNC_IMPL(igamma, Scalar)::run(a, x);\n}\n\ntemplate <typename Scalar>\nEIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(igammac, Scalar)\n    igammac(const Scalar& a, const Scalar& x) {\n  return EIGEN_MATHFUNC_IMPL(igammac, Scalar)::run(a, x);\n}\n\ntemplate <typename Scalar>\nEIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(betainc, Scalar)\n    betainc(const Scalar& a, const Scalar& b, const Scalar& x) {\n  return EIGEN_MATHFUNC_IMPL(betainc, Scalar)::run(a, b, x);\n}\n\n}  // end namespace numext\n\n\n}  // end namespace Eigen\n\n#endif  // EIGEN_SPECIAL_FUNCTIONS_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsPacketMath.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPECIALFUNCTIONS_PACKETMATH_H\n#define EIGEN_SPECIALFUNCTIONS_PACKETMATH_H\n\nnamespace Eigen {\n\nnamespace internal {\n\n/** \\internal \\returns the ln(|gamma(\\a a)|) (coeff-wise) */\ntemplate<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS\nPacket plgamma(const Packet& a) { using numext::lgamma; return lgamma(a); }\n\n/** \\internal \\returns the derivative of lgamma, psi(\\a a) (coeff-wise) */\ntemplate<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS\nPacket pdigamma(const Packet& a) { using numext::digamma; return digamma(a); }\n\n/** \\internal \\returns the zeta function of two arguments (coeff-wise) */\ntemplate<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS\nPacket pzeta(const Packet& x, const Packet& q) { using numext::zeta; return zeta(x, q); }\n\n/** \\internal \\returns the polygamma function (coeff-wise) */\ntemplate<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS\nPacket ppolygamma(const Packet& n, const Packet& x) { using numext::polygamma; return polygamma(n, x); }\n\n/** \\internal \\returns the erf(\\a a) (coeff-wise) */\ntemplate<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS\nPacket perf(const Packet& a) { using numext::erf; return erf(a); }\n\n/** \\internal \\returns the erfc(\\a a) (coeff-wise) */\ntemplate<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS\nPacket perfc(const Packet& a) { using numext::erfc; return erfc(a); }\n\n/** \\internal \\returns the incomplete gamma function igamma(\\a a, \\a x) */\ntemplate<typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nPacket pigamma(const Packet& a, const Packet& x) { using numext::igamma; return igamma(a, x); }\n\n/** \\internal \\returns the complementary incomplete gamma function igammac(\\a a, \\a x) */\ntemplate<typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nPacket pigammac(const Packet& a, const Packet& x) { using numext::igammac; return igammac(a, x); }\n\n/** \\internal \\returns the complementary incomplete gamma function betainc(\\a a, \\a b, \\a x) */\ntemplate<typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nPacket pbetainc(const Packet& a, const Packet& b,const Packet& x) { using numext::betainc; return betainc(a, b, x); }\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_SPECIALFUNCTIONS_PACKETMATH_H\n\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/SpecialFunctions/arch/CUDA/CudaSpecialFunctions.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_CUDA_SPECIALFUNCTIONS_H\n#define EIGEN_CUDA_SPECIALFUNCTIONS_H\n\nnamespace Eigen {\n\nnamespace internal {\n\n// Make sure this is only available when targeting a GPU: we don't want to\n// introduce conflicts between these packet_traits definitions and the ones\n// we'll use on the host side (SSE, AVX, ...)\n#if defined(__CUDACC__) && defined(EIGEN_USE_GPU)\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nfloat4 plgamma<float4>(const float4& a)\n{\n  return make_float4(lgammaf(a.x), lgammaf(a.y), lgammaf(a.z), lgammaf(a.w));\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\ndouble2 plgamma<double2>(const double2& a)\n{\n  using numext::lgamma;\n  return make_double2(lgamma(a.x), lgamma(a.y));\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nfloat4 pdigamma<float4>(const float4& a)\n{\n  using numext::digamma;\n  return make_float4(digamma(a.x), digamma(a.y), digamma(a.z), digamma(a.w));\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\ndouble2 pdigamma<double2>(const double2& a)\n{\n  using numext::digamma;\n  return make_double2(digamma(a.x), digamma(a.y));\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nfloat4 pzeta<float4>(const float4& x, const float4& q)\n{\n    using numext::zeta;\n    return make_float4(zeta(x.x, q.x), zeta(x.y, q.y), zeta(x.z, q.z), zeta(x.w, q.w));\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\ndouble2 pzeta<double2>(const double2& x, const double2& q)\n{\n    using numext::zeta;\n    return make_double2(zeta(x.x, q.x), zeta(x.y, q.y));\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nfloat4 ppolygamma<float4>(const float4& n, const float4& x)\n{\n    using numext::polygamma;\n    return make_float4(polygamma(n.x, x.x), polygamma(n.y, x.y), polygamma(n.z, x.z), polygamma(n.w, x.w));\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\ndouble2 ppolygamma<double2>(const double2& n, const double2& x)\n{\n    using numext::polygamma;\n    return make_double2(polygamma(n.x, x.x), polygamma(n.y, x.y));\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nfloat4 perf<float4>(const float4& a)\n{\n  return make_float4(erff(a.x), erff(a.y), erff(a.z), erff(a.w));\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\ndouble2 perf<double2>(const double2& a)\n{\n  using numext::erf;\n  return make_double2(erf(a.x), erf(a.y));\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nfloat4 perfc<float4>(const float4& a)\n{\n  using numext::erfc;\n  return make_float4(erfc(a.x), erfc(a.y), erfc(a.z), erfc(a.w));\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\ndouble2 perfc<double2>(const double2& a)\n{\n  using numext::erfc;\n  return make_double2(erfc(a.x), erfc(a.y));\n}\n\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nfloat4 pigamma<float4>(const float4& a, const float4& x)\n{\n  using numext::igamma;\n  return make_float4(\n      igamma(a.x, x.x),\n      igamma(a.y, x.y),\n      igamma(a.z, x.z),\n      igamma(a.w, x.w));\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\ndouble2 pigamma<double2>(const double2& a, const double2& x)\n{\n  using numext::igamma;\n  return make_double2(igamma(a.x, x.x), igamma(a.y, x.y));\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nfloat4 pigammac<float4>(const float4& a, const float4& x)\n{\n  using numext::igammac;\n  return make_float4(\n      igammac(a.x, x.x),\n      igammac(a.y, x.y),\n      igammac(a.z, x.z),\n      igammac(a.w, x.w));\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\ndouble2 pigammac<double2>(const double2& a, const double2& x)\n{\n  using numext::igammac;\n  return make_double2(igammac(a.x, x.x), igammac(a.y, x.y));\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\nfloat4 pbetainc<float4>(const float4& a, const float4& b, const float4& x)\n{\n  using numext::betainc;\n  return make_float4(\n      betainc(a.x, b.x, x.x),\n      betainc(a.y, b.y, x.y),\n      betainc(a.z, b.z, x.z),\n      betainc(a.w, b.w, x.w));\n}\n\ntemplate<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE\ndouble2 pbetainc<double2>(const double2& a, const double2& b, const double2& x)\n{\n  using numext::betainc;\n  return make_double2(betainc(a.x, b.x, x.x), betainc(a.y, b.y, x.y));\n}\n\n#endif\n\n} // end namespace internal\n\n} // end namespace Eigen\n\n#endif // EIGEN_CUDA_SPECIALFUNCTIONS_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/Splines/Spline.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 20010-2011 Hauke Heibel <hauke.heibel@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPLINE_H\n#define EIGEN_SPLINE_H\n\n#include \"SplineFwd.h\"\n\nnamespace Eigen\n{\n    /**\n     * \\ingroup Splines_Module\n     * \\class Spline\n     * \\brief A class representing multi-dimensional spline curves.\n     *\n     * The class represents B-splines with non-uniform knot vectors. Each control\n     * point of the B-spline is associated with a basis function\n     * \\f{align*}\n     *   C(u) & = \\sum_{i=0}^{n}N_{i,p}(u)P_i\n     * \\f}\n     *\n     * \\tparam _Scalar The underlying data type (typically float or double)\n     * \\tparam _Dim The curve dimension (e.g. 2 or 3)\n     * \\tparam _Degree Per default set to Dynamic; could be set to the actual desired\n     *                degree for optimization purposes (would result in stack allocation\n     *                of several temporary variables).\n     **/\n  template <typename _Scalar, int _Dim, int _Degree>\n  class Spline\n  {\n  public:\n    typedef _Scalar Scalar; /*!< The spline curve's scalar type. */\n    enum { Dimension = _Dim /*!< The spline curve's dimension. */ };\n    enum { Degree = _Degree /*!< The spline curve's degree. */ };\n\n    /** \\brief The point type the spline is representing. */\n    typedef typename SplineTraits<Spline>::PointType PointType;\n    \n    /** \\brief The data type used to store knot vectors. */\n    typedef typename SplineTraits<Spline>::KnotVectorType KnotVectorType;\n\n    /** \\brief The data type used to store parameter vectors. */\n    typedef typename SplineTraits<Spline>::ParameterVectorType ParameterVectorType;\n    \n    /** \\brief The data type used to store non-zero basis functions. */\n    typedef typename SplineTraits<Spline>::BasisVectorType BasisVectorType;\n\n    /** \\brief The data type used to store the values of the basis function derivatives. */\n    typedef typename SplineTraits<Spline>::BasisDerivativeType BasisDerivativeType;\n    \n    /** \\brief The data type representing the spline's control points. */\n    typedef typename SplineTraits<Spline>::ControlPointVectorType ControlPointVectorType;\n    \n    /**\n    * \\brief Creates a (constant) zero spline.\n    * For Splines with dynamic degree, the resulting degree will be 0.\n    **/\n    Spline() \n    : m_knots(1, (Degree==Dynamic ? 2 : 2*Degree+2))\n    , m_ctrls(ControlPointVectorType::Zero(Dimension,(Degree==Dynamic ? 1 : Degree+1))) \n    {\n      // in theory this code can go to the initializer list but it will get pretty\n      // much unreadable ...\n      enum { MinDegree = (Degree==Dynamic ? 0 : Degree) };\n      m_knots.template segment<MinDegree+1>(0) = Array<Scalar,1,MinDegree+1>::Zero();\n      m_knots.template segment<MinDegree+1>(MinDegree+1) = Array<Scalar,1,MinDegree+1>::Ones();\n    }\n\n    /**\n    * \\brief Creates a spline from a knot vector and control points.\n    * \\param knots The spline's knot vector.\n    * \\param ctrls The spline's control point vector.\n    **/\n    template <typename OtherVectorType, typename OtherArrayType>\n    Spline(const OtherVectorType& knots, const OtherArrayType& ctrls) : m_knots(knots), m_ctrls(ctrls) {}\n\n    /**\n    * \\brief Copy constructor for splines.\n    * \\param spline The input spline.\n    **/\n    template <int OtherDegree>\n    Spline(const Spline<Scalar, Dimension, OtherDegree>& spline) : \n    m_knots(spline.knots()), m_ctrls(spline.ctrls()) {}\n\n    /**\n     * \\brief Returns the knots of the underlying spline.\n     **/\n    const KnotVectorType& knots() const { return m_knots; }\n    \n    /**\n     * \\brief Returns the ctrls of the underlying spline.\n     **/    \n    const ControlPointVectorType& ctrls() const { return m_ctrls; }\n\n    /**\n     * \\brief Returns the spline value at a given site \\f$u\\f$.\n     *\n     * The function returns\n     * \\f{align*}\n     *   C(u) & = \\sum_{i=0}^{n}N_{i,p}P_i\n     * \\f}\n     *\n     * \\param u Parameter \\f$u \\in [0;1]\\f$ at which the spline is evaluated.\n     * \\return The spline value at the given location \\f$u\\f$.\n     **/\n    PointType operator()(Scalar u) const;\n\n    /**\n     * \\brief Evaluation of spline derivatives of up-to given order.\n     *\n     * The function returns\n     * \\f{align*}\n     *   \\frac{d^i}{du^i}C(u) & = \\sum_{i=0}^{n} \\frac{d^i}{du^i} N_{i,p}(u)P_i\n     * \\f}\n     * for i ranging between 0 and order.\n     *\n     * \\param u Parameter \\f$u \\in [0;1]\\f$ at which the spline derivative is evaluated.\n     * \\param order The order up to which the derivatives are computed.\n     **/\n    typename SplineTraits<Spline>::DerivativeType\n      derivatives(Scalar u, DenseIndex order) const;\n\n    /**\n     * \\copydoc Spline::derivatives\n     * Using the template version of this function is more efficieent since\n     * temporary objects are allocated on the stack whenever this is possible.\n     **/    \n    template <int DerivativeOrder>\n    typename SplineTraits<Spline,DerivativeOrder>::DerivativeType\n      derivatives(Scalar u, DenseIndex order = DerivativeOrder) const;\n\n    /**\n     * \\brief Computes the non-zero basis functions at the given site.\n     *\n     * Splines have local support and a point from their image is defined\n     * by exactly \\f$p+1\\f$ control points \\f$P_i\\f$ where \\f$p\\f$ is the\n     * spline degree.\n     *\n     * This function computes the \\f$p+1\\f$ non-zero basis function values\n     * for a given parameter value \\f$u\\f$. It returns\n     * \\f{align*}{\n     *   N_{i,p}(u), \\hdots, N_{i+p+1,p}(u)\n     * \\f}\n     *\n     * \\param u Parameter \\f$u \\in [0;1]\\f$ at which the non-zero basis functions \n     *          are computed.\n     **/\n    typename SplineTraits<Spline>::BasisVectorType\n      basisFunctions(Scalar u) const;\n\n    /**\n     * \\brief Computes the non-zero spline basis function derivatives up to given order.\n     *\n     * The function computes\n     * \\f{align*}{\n     *   \\frac{d^i}{du^i} N_{i,p}(u), \\hdots, \\frac{d^i}{du^i} N_{i+p+1,p}(u)\n     * \\f}\n     * with i ranging from 0 up to the specified order.\n     *\n     * \\param u Parameter \\f$u \\in [0;1]\\f$ at which the non-zero basis function\n     *          derivatives are computed.\n     * \\param order The order up to which the basis function derivatives are computes.\n     **/\n    typename SplineTraits<Spline>::BasisDerivativeType\n      basisFunctionDerivatives(Scalar u, DenseIndex order) const;\n\n    /**\n     * \\copydoc Spline::basisFunctionDerivatives\n     * Using the template version of this function is more efficieent since\n     * temporary objects are allocated on the stack whenever this is possible.\n     **/    \n    template <int DerivativeOrder>\n    typename SplineTraits<Spline,DerivativeOrder>::BasisDerivativeType\n      basisFunctionDerivatives(Scalar u, DenseIndex order = DerivativeOrder) const;\n\n    /**\n     * \\brief Returns the spline degree.\n     **/ \n    DenseIndex degree() const;\n\n    /** \n     * \\brief Returns the span within the knot vector in which u is falling.\n     * \\param u The site for which the span is determined.\n     **/\n    DenseIndex span(Scalar u) const;\n\n    /**\n     * \\brief Computes the spang within the provided knot vector in which u is falling.\n     **/\n    static DenseIndex Span(typename SplineTraits<Spline>::Scalar u, DenseIndex degree, const typename SplineTraits<Spline>::KnotVectorType& knots);\n    \n    /**\n     * \\brief Returns the spline's non-zero basis functions.\n     *\n     * The function computes and returns\n     * \\f{align*}{\n     *   N_{i,p}(u), \\hdots, N_{i+p+1,p}(u)\n     * \\f}\n     *\n     * \\param u The site at which the basis functions are computed.\n     * \\param degree The degree of the underlying spline.\n     * \\param knots The underlying spline's knot vector.\n     **/\n    static BasisVectorType BasisFunctions(Scalar u, DenseIndex degree, const KnotVectorType& knots);\n\n    /**\n     * \\copydoc Spline::basisFunctionDerivatives\n     * \\param degree The degree of the underlying spline\n     * \\param knots The underlying spline's knot vector.\n     **/    \n    static BasisDerivativeType BasisFunctionDerivatives(\n      const Scalar u, const DenseIndex order, const DenseIndex degree, const KnotVectorType& knots);\n\n  private:\n    KnotVectorType m_knots; /*!< Knot vector. */\n    ControlPointVectorType  m_ctrls; /*!< Control points. */\n\n    template <typename DerivativeType>\n    static void BasisFunctionDerivativesImpl(\n      const typename Spline<_Scalar, _Dim, _Degree>::Scalar u,\n      const DenseIndex order,\n      const DenseIndex p, \n      const typename Spline<_Scalar, _Dim, _Degree>::KnotVectorType& U,\n      DerivativeType& N_);\n  };\n\n  template <typename _Scalar, int _Dim, int _Degree>\n  DenseIndex Spline<_Scalar, _Dim, _Degree>::Span(\n    typename SplineTraits< Spline<_Scalar, _Dim, _Degree> >::Scalar u,\n    DenseIndex degree,\n    const typename SplineTraits< Spline<_Scalar, _Dim, _Degree> >::KnotVectorType& knots)\n  {\n    // Piegl & Tiller, \"The NURBS Book\", A2.1 (p. 68)\n    if (u <= knots(0)) return degree;\n    const Scalar* pos = std::upper_bound(knots.data()+degree-1, knots.data()+knots.size()-degree-1, u);\n    return static_cast<DenseIndex>( std::distance(knots.data(), pos) - 1 );\n  }\n\n  template <typename _Scalar, int _Dim, int _Degree>\n  typename Spline<_Scalar, _Dim, _Degree>::BasisVectorType\n    Spline<_Scalar, _Dim, _Degree>::BasisFunctions(\n    typename Spline<_Scalar, _Dim, _Degree>::Scalar u,\n    DenseIndex degree,\n    const typename Spline<_Scalar, _Dim, _Degree>::KnotVectorType& knots)\n  {\n    typedef typename Spline<_Scalar, _Dim, _Degree>::BasisVectorType BasisVectorType;\n\n    const DenseIndex p = degree;\n    const DenseIndex i = Spline::Span(u, degree, knots);\n\n    const KnotVectorType& U = knots;\n\n    BasisVectorType left(p+1); left(0) = Scalar(0);\n    BasisVectorType right(p+1); right(0) = Scalar(0);        \n\n    VectorBlock<BasisVectorType,Degree>(left,1,p) = u - VectorBlock<const KnotVectorType,Degree>(U,i+1-p,p).reverse();\n    VectorBlock<BasisVectorType,Degree>(right,1,p) = VectorBlock<const KnotVectorType,Degree>(U,i+1,p) - u;\n\n    BasisVectorType N(1,p+1);\n    N(0) = Scalar(1);\n    for (DenseIndex j=1; j<=p; ++j)\n    {\n      Scalar saved = Scalar(0);\n      for (DenseIndex r=0; r<j; r++)\n      {\n        const Scalar tmp = N(r)/(right(r+1)+left(j-r));\n        N[r] = saved + right(r+1)*tmp;\n        saved = left(j-r)*tmp;\n      }\n      N(j) = saved;\n    }\n    return N;\n  }\n\n  template <typename _Scalar, int _Dim, int _Degree>\n  DenseIndex Spline<_Scalar, _Dim, _Degree>::degree() const\n  {\n    if (_Degree == Dynamic)\n      return m_knots.size() - m_ctrls.cols() - 1;\n    else\n      return _Degree;\n  }\n\n  template <typename _Scalar, int _Dim, int _Degree>\n  DenseIndex Spline<_Scalar, _Dim, _Degree>::span(Scalar u) const\n  {\n    return Spline::Span(u, degree(), knots());\n  }\n\n  template <typename _Scalar, int _Dim, int _Degree>\n  typename Spline<_Scalar, _Dim, _Degree>::PointType Spline<_Scalar, _Dim, _Degree>::operator()(Scalar u) const\n  {\n    enum { Order = SplineTraits<Spline>::OrderAtCompileTime };\n\n    const DenseIndex span = this->span(u);\n    const DenseIndex p = degree();\n    const BasisVectorType basis_funcs = basisFunctions(u);\n\n    const Replicate<BasisVectorType,Dimension,1> ctrl_weights(basis_funcs);\n    const Block<const ControlPointVectorType,Dimension,Order> ctrl_pts(ctrls(),0,span-p,Dimension,p+1);\n    return (ctrl_weights * ctrl_pts).rowwise().sum();\n  }\n\n  /* --------------------------------------------------------------------------------------------- */\n\n  template <typename SplineType, typename DerivativeType>\n  void derivativesImpl(const SplineType& spline, typename SplineType::Scalar u, DenseIndex order, DerivativeType& der)\n  {    \n    enum { Dimension = SplineTraits<SplineType>::Dimension };\n    enum { Order = SplineTraits<SplineType>::OrderAtCompileTime };\n    enum { DerivativeOrder = DerivativeType::ColsAtCompileTime };\n\n    typedef typename SplineTraits<SplineType>::ControlPointVectorType ControlPointVectorType;\n    typedef typename SplineTraits<SplineType,DerivativeOrder>::BasisDerivativeType BasisDerivativeType;\n    typedef typename BasisDerivativeType::ConstRowXpr BasisDerivativeRowXpr;    \n\n    const DenseIndex p = spline.degree();\n    const DenseIndex span = spline.span(u);\n\n    const DenseIndex n = (std::min)(p, order);\n\n    der.resize(Dimension,n+1);\n\n    // Retrieve the basis function derivatives up to the desired order...    \n    const BasisDerivativeType basis_func_ders = spline.template basisFunctionDerivatives<DerivativeOrder>(u, n+1);\n\n    // ... and perform the linear combinations of the control points.\n    for (DenseIndex der_order=0; der_order<n+1; ++der_order)\n    {\n      const Replicate<BasisDerivativeRowXpr,Dimension,1> ctrl_weights( basis_func_ders.row(der_order) );\n      const Block<const ControlPointVectorType,Dimension,Order> ctrl_pts(spline.ctrls(),0,span-p,Dimension,p+1);\n      der.col(der_order) = (ctrl_weights * ctrl_pts).rowwise().sum();\n    }\n  }\n\n  template <typename _Scalar, int _Dim, int _Degree>\n  typename SplineTraits< Spline<_Scalar, _Dim, _Degree> >::DerivativeType\n    Spline<_Scalar, _Dim, _Degree>::derivatives(Scalar u, DenseIndex order) const\n  {\n    typename SplineTraits< Spline >::DerivativeType res;\n    derivativesImpl(*this, u, order, res);\n    return res;\n  }\n\n  template <typename _Scalar, int _Dim, int _Degree>\n  template <int DerivativeOrder>\n  typename SplineTraits< Spline<_Scalar, _Dim, _Degree>, DerivativeOrder >::DerivativeType\n    Spline<_Scalar, _Dim, _Degree>::derivatives(Scalar u, DenseIndex order) const\n  {\n    typename SplineTraits< Spline, DerivativeOrder >::DerivativeType res;\n    derivativesImpl(*this, u, order, res);\n    return res;\n  }\n\n  template <typename _Scalar, int _Dim, int _Degree>\n  typename SplineTraits< Spline<_Scalar, _Dim, _Degree> >::BasisVectorType\n    Spline<_Scalar, _Dim, _Degree>::basisFunctions(Scalar u) const\n  {\n    return Spline::BasisFunctions(u, degree(), knots());\n  }\n\n  /* --------------------------------------------------------------------------------------------- */\n  \n  \n  template <typename _Scalar, int _Dim, int _Degree>\n  template <typename DerivativeType>\n  void Spline<_Scalar, _Dim, _Degree>::BasisFunctionDerivativesImpl(\n    const typename Spline<_Scalar, _Dim, _Degree>::Scalar u,\n    const DenseIndex order,\n    const DenseIndex p, \n    const typename Spline<_Scalar, _Dim, _Degree>::KnotVectorType& U,\n    DerivativeType& N_)\n  {\n    typedef Spline<_Scalar, _Dim, _Degree> SplineType;\n    enum { Order = SplineTraits<SplineType>::OrderAtCompileTime };\n\n    typedef typename SplineTraits<SplineType>::Scalar Scalar;\n    typedef typename SplineTraits<SplineType>::BasisVectorType BasisVectorType;\n  \n    const DenseIndex span = SplineType::Span(u, p, U);\n\n    const DenseIndex n = (std::min)(p, order);\n\n    N_.resize(n+1, p+1);\n\n    BasisVectorType left = BasisVectorType::Zero(p+1);\n    BasisVectorType right = BasisVectorType::Zero(p+1);\n\n    Matrix<Scalar,Order,Order> ndu(p+1,p+1);\n\n    Scalar saved, temp; // FIXME These were double instead of Scalar. Was there a reason for that?\n\n    ndu(0,0) = 1.0;\n\n    DenseIndex j;\n    for (j=1; j<=p; ++j)\n    {\n      left[j] = u-U[span+1-j];\n      right[j] = U[span+j]-u;\n      saved = 0.0;\n\n      for (DenseIndex r=0; r<j; ++r)\n      {\n        /* Lower triangle */\n        ndu(j,r) = right[r+1]+left[j-r];\n        temp = ndu(r,j-1)/ndu(j,r);\n        /* Upper triangle */\n        ndu(r,j) = static_cast<Scalar>(saved+right[r+1] * temp);\n        saved = left[j-r] * temp;\n      }\n\n      ndu(j,j) = static_cast<Scalar>(saved);\n    }\n\n    for (j = p; j>=0; --j) \n      N_(0,j) = ndu(j,p);\n\n    // Compute the derivatives\n    DerivativeType a(n+1,p+1);\n    DenseIndex r=0;\n    for (; r<=p; ++r)\n    {\n      DenseIndex s1,s2;\n      s1 = 0; s2 = 1; // alternate rows in array a\n      a(0,0) = 1.0;\n\n      // Compute the k-th derivative\n      for (DenseIndex k=1; k<=static_cast<DenseIndex>(n); ++k)\n      {\n        Scalar d = 0.0;\n        DenseIndex rk,pk,j1,j2;\n        rk = r-k; pk = p-k;\n\n        if (r>=k)\n        {\n          a(s2,0) = a(s1,0)/ndu(pk+1,rk);\n          d = a(s2,0)*ndu(rk,pk);\n        }\n\n        if (rk>=-1) j1 = 1;\n        else        j1 = -rk;\n\n        if (r-1 <= pk) j2 = k-1;\n        else           j2 = p-r;\n\n        for (j=j1; j<=j2; ++j)\n        {\n          a(s2,j) = (a(s1,j)-a(s1,j-1))/ndu(pk+1,rk+j);\n          d += a(s2,j)*ndu(rk+j,pk);\n        }\n\n        if (r<=pk)\n        {\n          a(s2,k) = -a(s1,k-1)/ndu(pk+1,r);\n          d += a(s2,k)*ndu(r,pk);\n        }\n\n        N_(k,r) = static_cast<Scalar>(d);\n        j = s1; s1 = s2; s2 = j; // Switch rows\n      }\n    }\n\n    /* Multiply through by the correct factors */\n    /* (Eq. [2.9])                             */\n    r = p;\n    for (DenseIndex k=1; k<=static_cast<DenseIndex>(n); ++k)\n    {\n      for (j=p; j>=0; --j) N_(k,j) *= r;\n      r *= p-k;\n    }\n  }\n\n  template <typename _Scalar, int _Dim, int _Degree>\n  typename SplineTraits< Spline<_Scalar, _Dim, _Degree> >::BasisDerivativeType\n    Spline<_Scalar, _Dim, _Degree>::basisFunctionDerivatives(Scalar u, DenseIndex order) const\n  {\n    typename SplineTraits<Spline<_Scalar, _Dim, _Degree> >::BasisDerivativeType der;\n    BasisFunctionDerivativesImpl(u, order, degree(), knots(), der);\n    return der;\n  }\n\n  template <typename _Scalar, int _Dim, int _Degree>\n  template <int DerivativeOrder>\n  typename SplineTraits< Spline<_Scalar, _Dim, _Degree>, DerivativeOrder >::BasisDerivativeType\n    Spline<_Scalar, _Dim, _Degree>::basisFunctionDerivatives(Scalar u, DenseIndex order) const\n  {\n    typename SplineTraits< Spline<_Scalar, _Dim, _Degree>, DerivativeOrder >::BasisDerivativeType der;\n    BasisFunctionDerivativesImpl(u, order, degree(), knots(), der);\n    return der;\n  }\n\n  template <typename _Scalar, int _Dim, int _Degree>\n  typename SplineTraits<Spline<_Scalar, _Dim, _Degree> >::BasisDerivativeType\n  Spline<_Scalar, _Dim, _Degree>::BasisFunctionDerivatives(\n    const typename Spline<_Scalar, _Dim, _Degree>::Scalar u,\n    const DenseIndex order,\n    const DenseIndex degree,\n    const typename Spline<_Scalar, _Dim, _Degree>::KnotVectorType& knots)\n  {\n    typename SplineTraits<Spline>::BasisDerivativeType der;\n    BasisFunctionDerivativesImpl(u, order, degree, knots, der);\n    return der;\n  }\n}\n\n#endif // EIGEN_SPLINE_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/Splines/SplineFitting.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 20010-2011 Hauke Heibel <hauke.heibel@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPLINE_FITTING_H\n#define EIGEN_SPLINE_FITTING_H\n\n#include <algorithm>\n#include <functional>\n#include <numeric>\n#include <vector>\n\n#include \"SplineFwd.h\"\n\n#include <Eigen/LU>\n#include <Eigen/QR>\n\nnamespace Eigen\n{\n  /**\n   * \\brief Computes knot averages.\n   * \\ingroup Splines_Module\n   *\n   * The knots are computed as\n   * \\f{align*}\n   *  u_0 & = \\hdots = u_p = 0 \\\\\n   *  u_{m-p} & = \\hdots = u_{m} = 1 \\\\\n   *  u_{j+p} & = \\frac{1}{p}\\sum_{i=j}^{j+p-1}\\bar{u}_i \\quad\\quad j=1,\\hdots,n-p\n   * \\f}\n   * where \\f$p\\f$ is the degree and \\f$m+1\\f$ the number knots\n   * of the desired interpolating spline.\n   *\n   * \\param[in] parameters The input parameters. During interpolation one for each data point.\n   * \\param[in] degree The spline degree which is used during the interpolation.\n   * \\param[out] knots The output knot vector.\n   *\n   * \\sa Les Piegl and Wayne Tiller, The NURBS book (2nd ed.), 1997, 9.2.1 Global Curve Interpolation to Point Data\n   **/\n  template <typename KnotVectorType>\n  void KnotAveraging(const KnotVectorType& parameters, DenseIndex degree, KnotVectorType& knots)\n  {\n    knots.resize(parameters.size()+degree+1);      \n\n    for (DenseIndex j=1; j<parameters.size()-degree; ++j)\n      knots(j+degree) = parameters.segment(j,degree).mean();\n\n    knots.segment(0,degree+1) = KnotVectorType::Zero(degree+1);\n    knots.segment(knots.size()-degree-1,degree+1) = KnotVectorType::Ones(degree+1);\n  }\n\n  /**\n   * \\brief Computes knot averages when derivative constraints are present.\n   * Note that this is a technical interpretation of the referenced article\n   * since the algorithm contained therein is incorrect as written.\n   * \\ingroup Splines_Module\n   *\n   * \\param[in] parameters The parameters at which the interpolation B-Spline\n   *            will intersect the given interpolation points. The parameters\n   *            are assumed to be a non-decreasing sequence.\n   * \\param[in] degree The degree of the interpolating B-Spline. This must be\n   *            greater than zero.\n   * \\param[in] derivativeIndices The indices corresponding to parameters at\n   *            which there are derivative constraints. The indices are assumed\n   *            to be a non-decreasing sequence.\n   * \\param[out] knots The calculated knot vector. These will be returned as a\n   *             non-decreasing sequence\n   *\n   * \\sa Les A. Piegl, Khairan Rajab, Volha Smarodzinana. 2008.\n   * Curve interpolation with directional constraints for engineering design. \n   * Engineering with Computers\n   **/\n  template <typename KnotVectorType, typename ParameterVectorType, typename IndexArray>\n  void KnotAveragingWithDerivatives(const ParameterVectorType& parameters,\n                                    const unsigned int degree,\n                                    const IndexArray& derivativeIndices,\n                                    KnotVectorType& knots)\n  {\n    typedef typename ParameterVectorType::Scalar Scalar;\n\n    DenseIndex numParameters = parameters.size();\n    DenseIndex numDerivatives = derivativeIndices.size();\n\n    if (numDerivatives < 1)\n    {\n      KnotAveraging(parameters, degree, knots);\n      return;\n    }\n\n    DenseIndex startIndex;\n    DenseIndex endIndex;\n  \n    DenseIndex numInternalDerivatives = numDerivatives;\n    \n    if (derivativeIndices[0] == 0)\n    {\n      startIndex = 0;\n      --numInternalDerivatives;\n    }\n    else\n    {\n      startIndex = 1;\n    }\n    if (derivativeIndices[numDerivatives - 1] == numParameters - 1)\n    {\n      endIndex = numParameters - degree;\n      --numInternalDerivatives;\n    }\n    else\n    {\n      endIndex = numParameters - degree - 1;\n    }\n\n    // There are (endIndex - startIndex + 1) knots obtained from the averaging\n    // and 2 for the first and last parameters.\n    DenseIndex numAverageKnots = endIndex - startIndex + 3;\n    KnotVectorType averageKnots(numAverageKnots);\n    averageKnots[0] = parameters[0];\n\n    int newKnotIndex = 0;\n    for (DenseIndex i = startIndex; i <= endIndex; ++i)\n      averageKnots[++newKnotIndex] = parameters.segment(i, degree).mean();\n    averageKnots[++newKnotIndex] = parameters[numParameters - 1];\n\n    newKnotIndex = -1;\n  \n    ParameterVectorType temporaryParameters(numParameters + 1);\n    KnotVectorType derivativeKnots(numInternalDerivatives);\n    for (DenseIndex i = 0; i < numAverageKnots - 1; ++i)\n    {\n      temporaryParameters[0] = averageKnots[i];\n      ParameterVectorType parameterIndices(numParameters);\n      int temporaryParameterIndex = 1;\n      for (DenseIndex j = 0; j < numParameters; ++j)\n      {\n        Scalar parameter = parameters[j];\n        if (parameter >= averageKnots[i] && parameter < averageKnots[i + 1])\n        {\n          parameterIndices[temporaryParameterIndex] = j;\n          temporaryParameters[temporaryParameterIndex++] = parameter;\n        }\n      }\n      temporaryParameters[temporaryParameterIndex] = averageKnots[i + 1];\n\n      for (int j = 0; j <= temporaryParameterIndex - 2; ++j)\n      {\n        for (DenseIndex k = 0; k < derivativeIndices.size(); ++k)\n        {\n          if (parameterIndices[j + 1] == derivativeIndices[k]\n              && parameterIndices[j + 1] != 0\n              && parameterIndices[j + 1] != numParameters - 1)\n          {\n            derivativeKnots[++newKnotIndex] = temporaryParameters.segment(j, 3).mean();\n            break;\n          }\n        }\n      }\n    }\n    \n    KnotVectorType temporaryKnots(averageKnots.size() + derivativeKnots.size());\n\n    std::merge(averageKnots.data(), averageKnots.data() + averageKnots.size(),\n               derivativeKnots.data(), derivativeKnots.data() + derivativeKnots.size(),\n               temporaryKnots.data());\n\n    // Number of knots (one for each point and derivative) plus spline order.\n    DenseIndex numKnots = numParameters + numDerivatives + degree + 1;\n    knots.resize(numKnots);\n\n    knots.head(degree).fill(temporaryKnots[0]);\n    knots.tail(degree).fill(temporaryKnots.template tail<1>()[0]);\n    knots.segment(degree, temporaryKnots.size()) = temporaryKnots;\n  }\n\n  /**\n   * \\brief Computes chord length parameters which are required for spline interpolation.\n   * \\ingroup Splines_Module\n   *\n   * \\param[in] pts The data points to which a spline should be fit.\n   * \\param[out] chord_lengths The resulting chord lenggth vector.\n   *\n   * \\sa Les Piegl and Wayne Tiller, The NURBS book (2nd ed.), 1997, 9.2.1 Global Curve Interpolation to Point Data\n   **/   \n  template <typename PointArrayType, typename KnotVectorType>\n  void ChordLengths(const PointArrayType& pts, KnotVectorType& chord_lengths)\n  {\n    typedef typename KnotVectorType::Scalar Scalar;\n\n    const DenseIndex n = pts.cols();\n\n    // 1. compute the column-wise norms\n    chord_lengths.resize(pts.cols());\n    chord_lengths[0] = 0;\n    chord_lengths.rightCols(n-1) = (pts.array().leftCols(n-1) - pts.array().rightCols(n-1)).matrix().colwise().norm();\n\n    // 2. compute the partial sums\n    std::partial_sum(chord_lengths.data(), chord_lengths.data()+n, chord_lengths.data());\n\n    // 3. normalize the data\n    chord_lengths /= chord_lengths(n-1);\n    chord_lengths(n-1) = Scalar(1);\n  }\n\n  /**\n   * \\brief Spline fitting methods.\n   * \\ingroup Splines_Module\n   **/     \n  template <typename SplineType>\n  struct SplineFitting\n  {\n    typedef typename SplineType::KnotVectorType KnotVectorType;\n    typedef typename SplineType::ParameterVectorType ParameterVectorType;\n\n    /**\n     * \\brief Fits an interpolating Spline to the given data points.\n     *\n     * \\param pts The points for which an interpolating spline will be computed.\n     * \\param degree The degree of the interpolating spline.\n     *\n     * \\returns A spline interpolating the initially provided points.\n     **/\n    template <typename PointArrayType>\n    static SplineType Interpolate(const PointArrayType& pts, DenseIndex degree);\n\n    /**\n     * \\brief Fits an interpolating Spline to the given data points.\n     *\n     * \\param pts The points for which an interpolating spline will be computed.\n     * \\param degree The degree of the interpolating spline.\n     * \\param knot_parameters The knot parameters for the interpolation.\n     *\n     * \\returns A spline interpolating the initially provided points.\n     **/\n    template <typename PointArrayType>\n    static SplineType Interpolate(const PointArrayType& pts, DenseIndex degree, const KnotVectorType& knot_parameters);\n\n    /**\n     * \\brief Fits an interpolating spline to the given data points and\n     * derivatives.\n     * \n     * \\param points The points for which an interpolating spline will be computed.\n     * \\param derivatives The desired derivatives of the interpolating spline at interpolation\n     *                    points.\n     * \\param derivativeIndices An array indicating which point each derivative belongs to. This\n     *                          must be the same size as @a derivatives.\n     * \\param degree The degree of the interpolating spline.\n     *\n     * \\returns A spline interpolating @a points with @a derivatives at those points.\n     *\n     * \\sa Les A. Piegl, Khairan Rajab, Volha Smarodzinana. 2008.\n     * Curve interpolation with directional constraints for engineering design. \n     * Engineering with Computers\n     **/\n    template <typename PointArrayType, typename IndexArray>\n    static SplineType InterpolateWithDerivatives(const PointArrayType& points,\n                                                 const PointArrayType& derivatives,\n                                                 const IndexArray& derivativeIndices,\n                                                 const unsigned int degree);\n\n    /**\n     * \\brief Fits an interpolating spline to the given data points and derivatives.\n     * \n     * \\param points The points for which an interpolating spline will be computed.\n     * \\param derivatives The desired derivatives of the interpolating spline at interpolation points.\n     * \\param derivativeIndices An array indicating which point each derivative belongs to. This\n     *                          must be the same size as @a derivatives.\n     * \\param degree The degree of the interpolating spline.\n     * \\param parameters The parameters corresponding to the interpolation points.\n     *\n     * \\returns A spline interpolating @a points with @a derivatives at those points.\n     *\n     * \\sa Les A. Piegl, Khairan Rajab, Volha Smarodzinana. 2008.\n     * Curve interpolation with directional constraints for engineering design. \n     * Engineering with Computers\n     */\n    template <typename PointArrayType, typename IndexArray>\n    static SplineType InterpolateWithDerivatives(const PointArrayType& points,\n                                                 const PointArrayType& derivatives,\n                                                 const IndexArray& derivativeIndices,\n                                                 const unsigned int degree,\n                                                 const ParameterVectorType& parameters);\n  };\n\n  template <typename SplineType>\n  template <typename PointArrayType>\n  SplineType SplineFitting<SplineType>::Interpolate(const PointArrayType& pts, DenseIndex degree, const KnotVectorType& knot_parameters)\n  {\n    typedef typename SplineType::KnotVectorType::Scalar Scalar;      \n    typedef typename SplineType::ControlPointVectorType ControlPointVectorType;      \n\n    typedef Matrix<Scalar,Dynamic,Dynamic> MatrixType;\n\n    KnotVectorType knots;\n    KnotAveraging(knot_parameters, degree, knots);\n\n    DenseIndex n = pts.cols();\n    MatrixType A = MatrixType::Zero(n,n);\n    for (DenseIndex i=1; i<n-1; ++i)\n    {\n      const DenseIndex span = SplineType::Span(knot_parameters[i], degree, knots);\n\n      // The segment call should somehow be told the spline order at compile time.\n      A.row(i).segment(span-degree, degree+1) = SplineType::BasisFunctions(knot_parameters[i], degree, knots);\n    }\n    A(0,0) = 1.0;\n    A(n-1,n-1) = 1.0;\n\n    HouseholderQR<MatrixType> qr(A);\n\n    // Here, we are creating a temporary due to an Eigen issue.\n    ControlPointVectorType ctrls = qr.solve(MatrixType(pts.transpose())).transpose();\n\n    return SplineType(knots, ctrls);\n  }\n\n  template <typename SplineType>\n  template <typename PointArrayType>\n  SplineType SplineFitting<SplineType>::Interpolate(const PointArrayType& pts, DenseIndex degree)\n  {\n    KnotVectorType chord_lengths; // knot parameters\n    ChordLengths(pts, chord_lengths);\n    return Interpolate(pts, degree, chord_lengths);\n  }\n  \n  template <typename SplineType>\n  template <typename PointArrayType, typename IndexArray>\n  SplineType \n  SplineFitting<SplineType>::InterpolateWithDerivatives(const PointArrayType& points,\n                                                        const PointArrayType& derivatives,\n                                                        const IndexArray& derivativeIndices,\n                                                        const unsigned int degree,\n                                                        const ParameterVectorType& parameters)\n  {\n    typedef typename SplineType::KnotVectorType::Scalar Scalar;      \n    typedef typename SplineType::ControlPointVectorType ControlPointVectorType;\n\n    typedef Matrix<Scalar, Dynamic, Dynamic> MatrixType;\n\n    const DenseIndex n = points.cols() + derivatives.cols();\n    \n    KnotVectorType knots;\n\n    KnotAveragingWithDerivatives(parameters, degree, derivativeIndices, knots);\n    \n    // fill matrix\n    MatrixType A = MatrixType::Zero(n, n);\n\n    // Use these dimensions for quicker populating, then transpose for solving.\n    MatrixType b(points.rows(), n);\n\n    DenseIndex startRow;\n    DenseIndex derivativeStart;\n\n    // End derivatives.\n    if (derivativeIndices[0] == 0)\n    {\n      A.template block<1, 2>(1, 0) << -1, 1;\n      \n      Scalar y = (knots(degree + 1) - knots(0)) / degree;\n      b.col(1) = y*derivatives.col(0);\n      \n      startRow = 2;\n      derivativeStart = 1;\n    }\n    else\n    {\n      startRow = 1;\n      derivativeStart = 0;\n    }\n    if (derivativeIndices[derivatives.cols() - 1] == points.cols() - 1)\n    {\n      A.template block<1, 2>(n - 2, n - 2) << -1, 1;\n\n      Scalar y = (knots(knots.size() - 1) - knots(knots.size() - (degree + 2))) / degree;\n      b.col(b.cols() - 2) = y*derivatives.col(derivatives.cols() - 1);\n    }\n    \n    DenseIndex row = startRow;\n    DenseIndex derivativeIndex = derivativeStart;\n    for (DenseIndex i = 1; i < parameters.size() - 1; ++i)\n    {\n      const DenseIndex span = SplineType::Span(parameters[i], degree, knots);\n\n      if (derivativeIndices[derivativeIndex] == i)\n      {\n        A.block(row, span - degree, 2, degree + 1)\n          = SplineType::BasisFunctionDerivatives(parameters[i], 1, degree, knots);\n\n        b.col(row++) = points.col(i);\n        b.col(row++) = derivatives.col(derivativeIndex++);\n      }\n      else\n      {\n        A.row(row++).segment(span - degree, degree + 1)\n          = SplineType::BasisFunctions(parameters[i], degree, knots);\n      }\n    }\n    b.col(0) = points.col(0);\n    b.col(b.cols() - 1) = points.col(points.cols() - 1);\n    A(0,0) = 1;\n    A(n - 1, n - 1) = 1;\n    \n    // Solve\n    FullPivLU<MatrixType> lu(A);\n    ControlPointVectorType controlPoints = lu.solve(MatrixType(b.transpose())).transpose();\n\n    SplineType spline(knots, controlPoints);\n    \n    return spline;\n  }\n  \n  template <typename SplineType>\n  template <typename PointArrayType, typename IndexArray>\n  SplineType\n  SplineFitting<SplineType>::InterpolateWithDerivatives(const PointArrayType& points,\n                                                        const PointArrayType& derivatives,\n                                                        const IndexArray& derivativeIndices,\n                                                        const unsigned int degree)\n  {\n    ParameterVectorType parameters;\n    ChordLengths(points, parameters);\n    return InterpolateWithDerivatives(points, derivatives, derivativeIndices, degree, parameters);\n  }\n}\n\n#endif // EIGEN_SPLINE_FITTING_H\n"
  },
  {
    "path": "include/eigen3/unsupported/Eigen/src/Splines/SplineFwd.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 20010-2011 Hauke Heibel <hauke.heibel@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifndef EIGEN_SPLINES_FWD_H\n#define EIGEN_SPLINES_FWD_H\n\n#include <Eigen/Core>\n\nnamespace Eigen\n{\n    template <typename Scalar, int Dim, int Degree = Dynamic> class Spline;\n\n    template < typename SplineType, int DerivativeOrder = Dynamic > struct SplineTraits {};\n\n    /**\n     * \\ingroup Splines_Module\n     * \\brief Compile-time attributes of the Spline class for Dynamic degree.\n     **/\n    template <typename _Scalar, int _Dim, int _Degree>\n    struct SplineTraits< Spline<_Scalar, _Dim, _Degree>, Dynamic >\n    {\n      typedef _Scalar Scalar; /*!< The spline curve's scalar type. */\n      enum { Dimension = _Dim /*!< The spline curve's dimension. */ };\n      enum { Degree = _Degree /*!< The spline curve's degree. */ };\n\n      enum { OrderAtCompileTime = _Degree==Dynamic ? Dynamic : _Degree+1 /*!< The spline curve's order at compile-time. */ };\n      enum { NumOfDerivativesAtCompileTime = OrderAtCompileTime /*!< The number of derivatives defined for the current spline. */ };\n      \n      enum { DerivativeMemoryLayout = Dimension==1 ? RowMajor : ColMajor /*!< The derivative type's memory layout. */ };\n\n      /** \\brief The data type used to store non-zero basis functions. */\n      typedef Array<Scalar,1,OrderAtCompileTime> BasisVectorType;\n\n      /** \\brief The data type used to store the values of the basis function derivatives. */\n      typedef Array<Scalar,Dynamic,Dynamic,RowMajor,NumOfDerivativesAtCompileTime,OrderAtCompileTime> BasisDerivativeType;\n      \n      /** \\brief The data type used to store the spline's derivative values. */\n      typedef Array<Scalar,Dimension,Dynamic,DerivativeMemoryLayout,Dimension,NumOfDerivativesAtCompileTime> DerivativeType;\n\n      /** \\brief The point type the spline is representing. */\n      typedef Array<Scalar,Dimension,1> PointType;\n      \n      /** \\brief The data type used to store knot vectors. */\n      typedef Array<Scalar,1,Dynamic> KnotVectorType;\n\n      /** \\brief The data type used to store parameter vectors. */\n      typedef Array<Scalar,1,Dynamic> ParameterVectorType;\n      \n      /** \\brief The data type representing the spline's control points. */\n      typedef Array<Scalar,Dimension,Dynamic> ControlPointVectorType;\n    };\n\n    /**\n     * \\ingroup Splines_Module\n     * \\brief Compile-time attributes of the Spline class for fixed degree.\n     *\n     * The traits class inherits all attributes from the SplineTraits of Dynamic degree.\n     **/\n    template < typename _Scalar, int _Dim, int _Degree, int _DerivativeOrder >\n    struct SplineTraits< Spline<_Scalar, _Dim, _Degree>, _DerivativeOrder > : public SplineTraits< Spline<_Scalar, _Dim, _Degree> >\n    {\n      enum { OrderAtCompileTime = _Degree==Dynamic ? Dynamic : _Degree+1 /*!< The spline curve's order at compile-time. */ };\n      enum { NumOfDerivativesAtCompileTime = _DerivativeOrder==Dynamic ? Dynamic : _DerivativeOrder+1 /*!< The number of derivatives defined for the current spline. */ };\n      \n      enum { DerivativeMemoryLayout = _Dim==1 ? RowMajor : ColMajor /*!< The derivative type's memory layout. */ };\n\n      /** \\brief The data type used to store the values of the basis function derivatives. */\n      typedef Array<_Scalar,Dynamic,Dynamic,RowMajor,NumOfDerivativesAtCompileTime,OrderAtCompileTime> BasisDerivativeType;\n      \n      /** \\brief The data type used to store the spline's derivative values. */      \n      typedef Array<_Scalar,_Dim,Dynamic,DerivativeMemoryLayout,_Dim,NumOfDerivativesAtCompileTime> DerivativeType;\n    };\n\n    /** \\brief 2D float B-spline with dynamic degree. */\n    typedef Spline<float,2> Spline2f;\n    \n    /** \\brief 3D float B-spline with dynamic degree. */\n    typedef Spline<float,3> Spline3f;\n\n    /** \\brief 2D double B-spline with dynamic degree. */\n    typedef Spline<double,2> Spline2d;\n    \n    /** \\brief 3D double B-spline with dynamic degree. */\n    typedef Spline<double,3> Spline3d;\n}\n\n#endif // EIGEN_SPLINES_FWD_H\n"
  },
  {
    "path": "include/eigen3/unsupported/README.txt",
    "content": "This directory contains contributions from various users.\nThey are provided \"as is\", without any support. Nevertheless,\nmost of them are subject to be included in Eigen in the future.\n\nIn order to use an unsupported module you have to do either:\n\n - add the path_to_eigen/unsupported directory to your include path and do:\n   #include <Eigen/ModuleHeader>\n\n - or directly do:\n   #include <unsupported/Eigen/ModuleHeader>\n\n\nIf you are interested in contributing to one of them, or have other stuff\nyou would like to share, feel free to contact us:\nhttp://eigen.tuxfamily.org/index.php?title=Main_Page#Mailing_list\n\nAny kind of contributions are much appreciated, even very preliminary ones.\nHowever, it:\n - must rely on Eigen,\n - must be highly related to math,\n - should have some general purpose in the sense that it could\n   potentially become an offical Eigen module (or be merged into another one).\n\nIn doubt feel free to contact us. For instance, if your addons is very too specific\nbut it shows an interesting way of using Eigen, then it could be a nice demo.\n\n\nThis directory is organized as follow:\n\nunsupported/Eigen/ModuleHeader1\nunsupported/Eigen/ModuleHeader2\nunsupported/Eigen/...\nunsupported/Eigen/src/Module1/SourceFile1.h\nunsupported/Eigen/src/Module1/SourceFile2.h\nunsupported/Eigen/src/Module1/...\nunsupported/Eigen/src/Module2/SourceFile1.h\nunsupported/Eigen/src/Module2/SourceFile2.h\nunsupported/Eigen/src/Module2/...\nunsupported/Eigen/src/...\nunsupported/doc/snippets/.cpp   <- code snippets for the doc\nunsupported/doc/examples/.cpp   <- examples for the doc\nunsupported/doc/TutorialModule1.dox\nunsupported/doc/TutorialModule2.dox\nunsupported/doc/...\nunsupported/test/.cpp           <- unit test files\n\nThe documentation is generated at the same time than the main Eigen documentation.\nThe .html files are generated in: build_dir/doc/html/unsupported/\n\n"
  },
  {
    "path": "include/eigen3/unsupported/bench/bench_svd.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2013 Gauthier Brun <brun.gauthier@gmail.com>\n// Copyright (C) 2013 Nicolas Carre <nicolas.carre@ensimag.fr>\n// Copyright (C) 2013 Jean Ceccato <jean.ceccato@ensimag.fr>\n// Copyright (C) 2013 Pierre Zoppitelli <pierre.zoppitelli@ensimag.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/\n\n// Bench to compare the efficiency of SVD algorithms\n\n#include <iostream>\n#include <bench/BenchTimer.h>\n#include <unsupported/Eigen/SVD>\n\n\nusing namespace Eigen;\nusing namespace std;\n\n// number of computations of each algorithm before the print of the time\n#ifndef REPEAT\n#define REPEAT 10\n#endif\n\n// number of tests of the same type\n#ifndef NUMBER_SAMPLE\n#define NUMBER_SAMPLE 2\n#endif\n\ntemplate<typename MatrixType>\nvoid bench_svd(const MatrixType& a = MatrixType())\n{\n  MatrixType m = MatrixType::Random(a.rows(), a.cols());\n  BenchTimer timerJacobi;\n  BenchTimer timerBDC;\n  timerJacobi.reset();\n  timerBDC.reset();\n\n  cout << \" Only compute Singular Values\" <<endl;\n  for (int k=1; k<=NUMBER_SAMPLE; ++k)\n  {\n    timerBDC.start();\n    for (int i=0; i<REPEAT; ++i) \n    {\n      BDCSVD<MatrixType> bdc_matrix(m);\n    }\n    timerBDC.stop();\n    \n    timerJacobi.start();\n    for (int i=0; i<REPEAT; ++i) \n    {\n      JacobiSVD<MatrixType> jacobi_matrix(m);\n    }\n    timerJacobi.stop();\n\n\n    cout << \"Sample \" << k << \" : \" << REPEAT << \" computations :  Jacobi : \" << fixed << timerJacobi.value() << \"s \";\n    cout << \" || \" << \" BDC : \" << timerBDC.value() << \"s \" <<endl <<endl;\n      \n    if (timerBDC.value() >= timerJacobi.value())  \n      cout << \"KO : BDC is \" <<  timerJacobi.value() / timerBDC.value() << \"  times faster than Jacobi\" <<endl;\n    else \n      cout << \"OK : BDC is \" << timerJacobi.value() / timerBDC.value() << \"  times faster than Jacobi\"  <<endl;\n      \n  }\n  cout << \"       =================\" <<endl;\n  std::cout<< std::endl;\n  timerJacobi.reset();\n  timerBDC.reset();\n  cout << \" Computes rotaion matrix\" <<endl;\n  for (int k=1; k<=NUMBER_SAMPLE; ++k)\n  {\n    timerBDC.start();\n    for (int i=0; i<REPEAT; ++i) \n    {\n      BDCSVD<MatrixType> bdc_matrix(m, ComputeFullU|ComputeFullV);\n    }\n    timerBDC.stop();\n    \n    timerJacobi.start();\n    for (int i=0; i<REPEAT; ++i) \n    {\n      JacobiSVD<MatrixType> jacobi_matrix(m, ComputeFullU|ComputeFullV);\n    }\n    timerJacobi.stop();\n\n\n    cout << \"Sample \" << k << \" : \" << REPEAT << \" computations :  Jacobi : \" << fixed << timerJacobi.value() << \"s \";\n    cout << \" || \" << \" BDC : \" << timerBDC.value() << \"s \" <<endl <<endl;\n      \n    if (timerBDC.value() >= timerJacobi.value())  \n      cout << \"KO : BDC is \" <<  timerJacobi.value() / timerBDC.value() << \"  times faster than Jacobi\" <<endl;\n    else \n      cout << \"OK : BDC is \" << timerJacobi.value() / timerBDC.value() << \"  times faster than Jacobi\"  <<endl;\n      \n  }\n  std::cout<< std::endl;\n}\n\n\n\nint main(int argc, char* argv[])\n{\n  std::cout<< std::endl;\n\n  std::cout<<\"On a (Dynamic, Dynamic) (6, 6) Matrix\" <<std::endl;\n  bench_svd<Matrix<double,Dynamic,Dynamic> >(Matrix<double,Dynamic,Dynamic>(6, 6));\n  \n  std::cout<<\"On a (Dynamic, Dynamic) (32, 32) Matrix\" <<std::endl;\n  bench_svd<Matrix<double,Dynamic,Dynamic> >(Matrix<double,Dynamic,Dynamic>(32, 32));\n\n  //std::cout<<\"On a (Dynamic, Dynamic) (128, 128) Matrix\" <<std::endl;\n  //bench_svd<Matrix<double,Dynamic,Dynamic> >(Matrix<double,Dynamic,Dynamic>(128, 128));\n\n  std::cout<<\"On a (Dynamic, Dynamic) (160, 160) Matrix\" <<std::endl;\n  bench_svd<Matrix<double,Dynamic,Dynamic> >(Matrix<double,Dynamic,Dynamic>(160, 160));\n  \n  std::cout<< \"--------------------------------------------------------------------\"<< std::endl;\n           \n}\n"
  },
  {
    "path": "include/eigen3/unsupported/doc/CMakeLists.txt",
    "content": "set_directory_properties(PROPERTIES EXCLUDE_FROM_ALL TRUE)\n\nadd_subdirectory(examples)\nadd_subdirectory(snippets)\n"
  },
  {
    "path": "include/eigen3/unsupported/doc/Overview.dox",
    "content": "/// \\brief Namespace containing all symbols from the %Eigen library.\nnamespace Eigen {\n\n/** \\mainpage %Eigen's unsupported modules\n\nThis is the API documentation for %Eigen's unsupported modules.\n\nThese modules are contributions from various users. They are provided \"as is\", without any support.\n\nClick on the \\e Modules tab at the top of this page to get a list of all unsupported modules.\n\nDon't miss the <a href=\"../index.html\">official Eigen documentation</a>.\n\n*/\n\n/*\n\n\\defgroup Unsupported_modules Unsupported modules\n\nThe unsupported modules are contributions from various users. They are\nprovided \"as is\", without any support. Nevertheless, some of them are\nsubject to be included in %Eigen in the future.\n\n*/\n\n/// \\internal \\brief Namespace containing low-level routines from the %Eigen library.\nnamespace internal {}\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/doc/eigendoxy_layout.xml.in",
    "content": "<?xml version=\"1.0\"?>\n<doxygenlayout version=\"1.0\">\n  <!-- Navigation index tabs for HTML output -->\n  <navindex>\n    <tab type=\"user\" url=\"index.html\" title=\"Overview\" />\n    <tab type=\"modules\" visible=\"yes\" title=\"Unsupported Modules\" intro=\"\"/>\n<!--     <tab type=\"mainpage\" visible=\"yes\" title=\"\"/> -->\n    <tab type=\"classlist\" visible=\"yes\" title=\"\" intro=\"\"/>\n<!--     <tab type=\"classmembers\" visible=\"yes\" title=\"\" intro=\"\"/> -->\n  </navindex>\n\n  <!-- Layout definition for a class page -->\n  <class>\n    <briefdescription visible=\"no\"/>\n    <includes visible=\"$SHOW_INCLUDE_FILES\"/>\n    <detaileddescription title=\"\"/>\n    <inheritancegraph visible=\"$CLASS_GRAPH\"/>\n    <collaborationgraph visible=\"$COLLABORATION_GRAPH\"/>\n    <allmemberslink visible=\"yes\"/>\n    <memberdecl>\n      <nestedclasses visible=\"yes\" title=\"\"/>\n      <publictypes title=\"\"/>\n      <publicslots title=\"\"/>\n      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  },
  {
    "path": "include/eigen3/unsupported/doc/examples/BVH_Example.cpp",
    "content": "#include <Eigen/StdVector>\n#include <unsupported/Eigen/BVH>\n#include <iostream>\n\nusing namespace Eigen;\ntypedef AlignedBox<double, 2> Box2d;\n\nnamespace Eigen {\n  Box2d bounding_box(const Vector2d &v) { return Box2d(v, v); } //compute the bounding box of a single point\n}\n\nstruct PointPointMinimizer //how to compute squared distances between points and rectangles\n{\n  PointPointMinimizer() : calls(0) {}\n  typedef double Scalar;\n\n  double minimumOnVolumeVolume(const Box2d &r1, const Box2d &r2) { ++calls; return r1.squaredExteriorDistance(r2); }\n  double minimumOnVolumeObject(const Box2d &r, const Vector2d &v) { ++calls; return r.squaredExteriorDistance(v); }\n  double minimumOnObjectVolume(const Vector2d &v, const Box2d &r) { ++calls; return r.squaredExteriorDistance(v); }\n  double minimumOnObjectObject(const Vector2d &v1, const Vector2d &v2) { ++calls; return (v1 - v2).squaredNorm(); }\n\n  int calls;\n};\n\nint main()\n{\n  typedef std::vector<Vector2d, aligned_allocator<Vector2d> > StdVectorOfVector2d;\n  StdVectorOfVector2d redPoints, bluePoints;\n  for(int i = 0; i < 100; ++i) { //initialize random set of red points and blue points\n    redPoints.push_back(Vector2d::Random());\n    bluePoints.push_back(Vector2d::Random());\n  }\n\n  PointPointMinimizer minimizer;\n  double minDistSq = std::numeric_limits<double>::max();\n\n  //brute force to find closest red-blue pair\n  for(int i = 0; i < (int)redPoints.size(); ++i)\n    for(int j = 0; j < (int)bluePoints.size(); ++j)\n      minDistSq = std::min(minDistSq, minimizer.minimumOnObjectObject(redPoints[i], bluePoints[j]));\n  std::cout << \"Brute force distance = \" << sqrt(minDistSq) << \", calls = \" << minimizer.calls << std::endl;\n\n  //using BVH to find closest red-blue pair\n  minimizer.calls = 0;\n  KdBVH<double, 2, Vector2d> redTree(redPoints.begin(), redPoints.end()), blueTree(bluePoints.begin(), bluePoints.end()); //construct the trees\n  minDistSq = BVMinimize(redTree, blueTree, minimizer); //actual BVH minimization call\n  std::cout << \"BVH distance         = \" << sqrt(minDistSq) << \", calls = \" << minimizer.calls << std::endl;\n\n  return 0;\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/doc/examples/CMakeLists.txt",
    "content": "FILE(GLOB examples_SRCS \"*.cpp\")\n\nADD_CUSTOM_TARGET(unsupported_examples)\n\nINCLUDE_DIRECTORIES(../../../unsupported ../../../unsupported/test)\n\nFOREACH(example_src ${examples_SRCS})\n  GET_FILENAME_COMPONENT(example ${example_src} NAME_WE)\n  ADD_EXECUTABLE(example_${example} ${example_src})\n  if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO)\n    target_link_libraries(example_${example} ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO})\n  endif()\n  ADD_CUSTOM_COMMAND(\n    TARGET example_${example}\n    POST_BUILD\n    COMMAND example_${example}\n    ARGS >${CMAKE_CURRENT_BINARY_DIR}/${example}.out\n  )\n  ADD_DEPENDENCIES(unsupported_examples example_${example})\nENDFOREACH(example_src)\n"
  },
  {
    "path": "include/eigen3/unsupported/doc/examples/EulerAngles.cpp",
    "content": "#include <unsupported/Eigen/EulerAngles>\n#include <iostream>\n\nusing namespace Eigen;\n\nint main()\n{\n  // A common Euler system by many armies around the world,\n  //  where the first one is the azimuth(the angle from the north -\n  //   the same angle that is show in compass)\n  //  and the second one is elevation(the angle from the horizon)\n  //  and the third one is roll(the angle between the horizontal body\n  //   direction and the plane ground surface)\n  // Keep remembering we're using radian angles here!\n  typedef EulerSystem<-EULER_Z, EULER_Y, EULER_X> MyArmySystem;\n  typedef EulerAngles<double, MyArmySystem> MyArmyAngles;\n  \n  MyArmyAngles vehicleAngles(\n    3.14/*PI*/ / 2, /* heading to east, notice that this angle is counter-clockwise */\n    -0.3, /* going down from a mountain */\n    0.1); /* slightly rolled to the right */\n  \n  // Some Euler angles representation that our plane use.\n  EulerAnglesZYZd planeAngles(0.78474, 0.5271, -0.513794);\n  \n  MyArmyAngles planeAnglesInMyArmyAngles = MyArmyAngles::FromRotation<true, false, false>(planeAngles);\n  \n  std::cout << \"vehicle angles(MyArmy):     \" << vehicleAngles << std::endl;\n  std::cout << \"plane angles(ZYZ):        \" << planeAngles << std::endl;\n  std::cout << \"plane angles(MyArmy):     \" << planeAnglesInMyArmyAngles << std::endl;\n  \n  // Now lets rotate the plane a little bit\n  std::cout << \"==========================================================\\n\";\n  std::cout << \"rotating plane now!\\n\";\n  std::cout << \"==========================================================\\n\";\n  \n  Quaterniond planeRotated = AngleAxisd(-0.342, Vector3d::UnitY()) * planeAngles;\n  \n  planeAngles = planeRotated;\n  planeAnglesInMyArmyAngles = MyArmyAngles::FromRotation<true, false, false>(planeRotated);\n  \n  std::cout << \"new plane angles(ZYZ):     \" << planeAngles << std::endl;\n  std::cout << \"new plane angles(MyArmy): \" << planeAnglesInMyArmyAngles << std::endl;\n  \n  return 0;\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/doc/examples/FFT.cpp",
    "content": "//  To use the simple FFT implementation\n//  g++ -o demofft -I.. -Wall -O3 FFT.cpp \n\n//  To use the FFTW implementation\n//  g++ -o demofft -I.. -DUSE_FFTW -Wall -O3 FFT.cpp -lfftw3 -lfftw3f -lfftw3l\n\n#ifdef USE_FFTW\n#include <fftw3.h>\n#endif\n\n#include <vector>\n#include <complex>\n#include <algorithm>\n#include <iterator>\n#include <iostream>\n#include <Eigen/Core>\n#include <unsupported/Eigen/FFT>\n\nusing namespace std;\nusing namespace Eigen;\n\ntemplate <typename T>\nT mag2(T a)\n{\n    return a*a;\n}\ntemplate <typename T>\nT mag2(std::complex<T> a)\n{\n    return norm(a);\n}\n\ntemplate <typename T>\nT mag2(const std::vector<T> & vec)\n{\n    T out=0;\n    for (size_t k=0;k<vec.size();++k)\n        out += mag2(vec[k]);\n    return out;\n}\n\ntemplate <typename T>\nT mag2(const std::vector<std::complex<T> > & vec)\n{\n    T out=0;\n    for (size_t k=0;k<vec.size();++k)\n        out += mag2(vec[k]);\n    return out;\n}\n\ntemplate <typename T>\nvector<T> operator-(const vector<T> & a,const vector<T> & b )\n{\n    vector<T> c(a);\n    for (size_t k=0;k<b.size();++k) \n        c[k] -= b[k];\n    return c;\n}\n\ntemplate <typename T>\nvoid RandomFill(std::vector<T> & vec)\n{\n    for (size_t k=0;k<vec.size();++k)\n        vec[k] = T( rand() )/T(RAND_MAX) - .5;\n}\n\ntemplate <typename T>\nvoid RandomFill(std::vector<std::complex<T> > & vec)\n{\n    for (size_t k=0;k<vec.size();++k)\n        vec[k] = std::complex<T> ( T( rand() )/T(RAND_MAX) - .5, T( rand() )/T(RAND_MAX) - .5);\n}\n\ntemplate <typename T_time,typename T_freq>\nvoid fwd_inv(size_t nfft)\n{\n    typedef typename NumTraits<T_freq>::Real Scalar;\n    vector<T_time> timebuf(nfft);\n    RandomFill(timebuf);\n\n    vector<T_freq> freqbuf;\n    static FFT<Scalar> fft;\n    fft.fwd(freqbuf,timebuf);\n\n    vector<T_time> timebuf2;\n    fft.inv(timebuf2,freqbuf);\n\n    long double rmse = mag2(timebuf - timebuf2) / mag2(timebuf);\n    cout << \"roundtrip rmse: \" << rmse << endl;\n}\n\ntemplate <typename T_scalar>\nvoid two_demos(int nfft)\n{\n    cout << \"     scalar \";\n    fwd_inv<T_scalar,std::complex<T_scalar> >(nfft);\n    cout << \"    complex \";\n    fwd_inv<std::complex<T_scalar>,std::complex<T_scalar> >(nfft);\n}\n\nvoid demo_all_types(int nfft)\n{\n    cout << \"nfft=\" << nfft << endl;\n    cout << \"   float\" << endl;\n    two_demos<float>(nfft);\n    cout << \"   double\" << endl;\n    two_demos<double>(nfft);\n    cout << \"   long double\" << endl;\n    two_demos<long double>(nfft);\n}\n\nint main()\n{\n    demo_all_types( 2*3*4*5*7 );\n    demo_all_types( 2*9*16*25 );\n    demo_all_types( 1024 );\n    return 0;\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/doc/examples/MatrixExponential.cpp",
    "content": "#include <unsupported/Eigen/MatrixFunctions>\n#include <iostream>\n\nusing namespace Eigen;\n\nint main()\n{\n  const double pi = std::acos(-1.0);\n\n  MatrixXd A(3,3);\n  A << 0,    -pi/4, 0,\n       pi/4, 0,     0,\n       0,    0,     0;\n  std::cout << \"The matrix A is:\\n\" << A << \"\\n\\n\";\n  std::cout << \"The matrix exponential of A is:\\n\" << A.exp() << \"\\n\\n\";\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/doc/examples/MatrixFunction.cpp",
    "content": "#include <unsupported/Eigen/MatrixFunctions>\n#include <iostream>\n\nusing namespace Eigen;\n\nstd::complex<double> expfn(std::complex<double> x, int)\n{\n  return std::exp(x);\n}\n\nint main()\n{\n  const double pi = std::acos(-1.0);\n\n  MatrixXd A(3,3);\n  A << 0,    -pi/4, 0,\n       pi/4, 0,     0,\n       0,    0,     0;\n\n  std::cout << \"The matrix A is:\\n\" << A << \"\\n\\n\";\n  std::cout << \"The matrix exponential of A is:\\n\" \n            << A.matrixFunction(expfn) << \"\\n\\n\";\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/doc/examples/MatrixLogarithm.cpp",
    "content": "#include <unsupported/Eigen/MatrixFunctions>\n#include <iostream>\n\nusing namespace Eigen;\n\nint main()\n{\n  using std::sqrt;\n  MatrixXd A(3,3);\n  A << 0.5*sqrt(2), -0.5*sqrt(2), 0,\n       0.5*sqrt(2),  0.5*sqrt(2), 0,\n       0,            0,           1;\n  std::cout << \"The matrix A is:\\n\" << A << \"\\n\\n\";\n  std::cout << \"The matrix logarithm of A is:\\n\" << A.log() << \"\\n\";\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/doc/examples/MatrixPower.cpp",
    "content": "#include <unsupported/Eigen/MatrixFunctions>\n#include <iostream>\n\nusing namespace Eigen;\n\nint main()\n{\n  const double pi = std::acos(-1.0);\n  Matrix3d A;\n  A << cos(1), -sin(1), 0,\n       sin(1),  cos(1), 0,\n\t   0 ,      0 , 1;\n  std::cout << \"The matrix A is:\\n\" << A << \"\\n\\n\"\n\t       \"The matrix power A^(pi/4) is:\\n\" << A.pow(pi/4) << std::endl;\n  return 0;\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/doc/examples/MatrixPower_optimal.cpp",
    "content": "#include <unsupported/Eigen/MatrixFunctions>\n#include <iostream>\n\nusing namespace Eigen;\n\nint main()\n{\n  Matrix4cd A = Matrix4cd::Random();\n  MatrixPower<Matrix4cd> Apow(A);\n\n  std::cout << \"The matrix A is:\\n\" << A << \"\\n\\n\"\n\t       \"A^3.1 is:\\n\" << Apow(3.1) << \"\\n\\n\"\n\t       \"A^3.3 is:\\n\" << Apow(3.3) << \"\\n\\n\"\n\t       \"A^3.7 is:\\n\" << Apow(3.7) << \"\\n\\n\"\n\t       \"A^3.9 is:\\n\" << Apow(3.9) << std::endl;\n  return 0;\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/doc/examples/MatrixSine.cpp",
    "content": "#include <unsupported/Eigen/MatrixFunctions>\n#include <iostream>\n\nusing namespace Eigen;\n\nint main()\n{\n  MatrixXd A = MatrixXd::Random(3,3);\n  std::cout << \"A = \\n\" << A << \"\\n\\n\";\n\n  MatrixXd sinA = A.sin();\n  std::cout << \"sin(A) = \\n\" << sinA << \"\\n\\n\";\n\n  MatrixXd cosA = A.cos();\n  std::cout << \"cos(A) = \\n\" << cosA << \"\\n\\n\";\n  \n  // The matrix functions satisfy sin^2(A) + cos^2(A) = I, \n  // like the scalar functions.\n  std::cout << \"sin^2(A) + cos^2(A) = \\n\" << sinA*sinA + cosA*cosA << \"\\n\\n\";\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/doc/examples/MatrixSinh.cpp",
    "content": "#include <unsupported/Eigen/MatrixFunctions>\n#include <iostream>\n\nusing namespace Eigen;\n\nint main()\n{\n  MatrixXf A = MatrixXf::Random(3,3);\n  std::cout << \"A = \\n\" << A << \"\\n\\n\";\n\n  MatrixXf sinhA = A.sinh();\n  std::cout << \"sinh(A) = \\n\" << sinhA << \"\\n\\n\";\n\n  MatrixXf coshA = A.cosh();\n  std::cout << \"cosh(A) = \\n\" << coshA << \"\\n\\n\";\n  \n  // The matrix functions satisfy cosh^2(A) - sinh^2(A) = I, \n  // like the scalar functions.\n  std::cout << \"cosh^2(A) - sinh^2(A) = \\n\" << coshA*coshA - sinhA*sinhA << \"\\n\\n\";\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/doc/examples/MatrixSquareRoot.cpp",
    "content": "#include <unsupported/Eigen/MatrixFunctions>\n#include <iostream>\n\nusing namespace Eigen;\n\nint main()\n{\n  const double pi = std::acos(-1.0);\n\n  MatrixXd A(2,2);\n  A << cos(pi/3), -sin(pi/3), \n       sin(pi/3),  cos(pi/3);\n  std::cout << \"The matrix A is:\\n\" << A << \"\\n\\n\";\n  std::cout << \"The matrix square root of A is:\\n\" << A.sqrt() << \"\\n\\n\";\n  std::cout << \"The square of the last matrix is:\\n\" << A.sqrt() * A.sqrt() << \"\\n\";\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/doc/examples/PolynomialSolver1.cpp",
    "content": "#include <unsupported/Eigen/Polynomials>\n#include <vector>\n#include <iostream>\n\nusing namespace Eigen;\nusing namespace std;\n\nint main()\n{\n  typedef Matrix<double,5,1> Vector5d;\n\n  Vector5d roots = Vector5d::Random();\n  cout << \"Roots: \" << roots.transpose() << endl;\n  Eigen::Matrix<double,6,1> polynomial;\n  roots_to_monicPolynomial( roots, polynomial );\n\n  PolynomialSolver<double,5> psolve( polynomial );\n  cout << \"Complex roots: \" << psolve.roots().transpose() << endl;\n\n  std::vector<double> realRoots;\n  psolve.realRoots( realRoots );\n  Map<Vector5d> mapRR( &realRoots[0] );\n  cout << \"Real roots: \" << mapRR.transpose() << endl;\n\n  cout << endl;\n  cout << \"Illustration of the convergence problem with the QR algorithm: \" << endl;\n  cout << \"---------------------------------------------------------------\" << endl;\n  Eigen::Matrix<float,7,1> hardCase_polynomial;\n  hardCase_polynomial <<\n  -0.957, 0.9219, 0.3516, 0.9453, -0.4023, -0.5508, -0.03125;\n  cout << \"Hard case polynomial defined by floats: \" << hardCase_polynomial.transpose() << endl;\n  PolynomialSolver<float,6> psolvef( hardCase_polynomial );\n  cout << \"Complex roots: \" << psolvef.roots().transpose() << endl;\n  Eigen::Matrix<float,6,1> evals;\n  for( int i=0; i<6; ++i ){ evals[i] = std::abs( poly_eval( hardCase_polynomial, psolvef.roots()[i] ) ); }\n  cout << \"Norms of the evaluations of the polynomial at the roots: \" << evals.transpose() << endl << endl;\n\n  cout << \"Using double's almost always solves the problem for small degrees: \" << endl;\n  cout << \"-------------------------------------------------------------------\" << endl;\n  PolynomialSolver<double,6> psolve6d( hardCase_polynomial.cast<double>() );\n  cout << \"Complex roots: \" << psolve6d.roots().transpose() << endl;\n  for( int i=0; i<6; ++i )\n  {\n    std::complex<float> castedRoot( psolve6d.roots()[i].real(), psolve6d.roots()[i].imag() );\n    evals[i] = std::abs( poly_eval( hardCase_polynomial, castedRoot ) );\n  }\n  cout << \"Norms of the evaluations of the polynomial at the roots: \" << evals.transpose() << endl << endl;\n\n  cout.precision(10);\n  cout << \"The last root in float then in double: \" << psolvef.roots()[5] << \"\\t\" << psolve6d.roots()[5] << endl;\n  std::complex<float> castedRoot( psolve6d.roots()[5].real(), psolve6d.roots()[5].imag() );\n  cout << \"Norm of the difference: \" << std::abs( psolvef.roots()[5] - castedRoot ) << endl;\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/doc/examples/PolynomialUtils1.cpp",
    "content": "#include <unsupported/Eigen/Polynomials>\n#include <iostream>\n\nusing namespace Eigen;\nusing namespace std;\n\nint main()\n{\n  Vector4d roots = Vector4d::Random();\n  cout << \"Roots: \" << roots.transpose() << endl;\n  Eigen::Matrix<double,5,1> polynomial;\n  roots_to_monicPolynomial( roots, polynomial );\n  cout << \"Polynomial: \";\n  for( int i=0; i<4; ++i ){ cout << polynomial[i] << \".x^\" << i << \"+ \"; }\n  cout << polynomial[4] << \".x^4\" << endl;\n  Vector4d evaluation;\n  for( int i=0; i<4; ++i ){\n    evaluation[i] = poly_eval( polynomial, roots[i] ); }\n  cout << \"Evaluation of the polynomial at the roots: \" << evaluation.transpose();\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/doc/snippets/CMakeLists.txt",
    "content": "FILE(GLOB snippets_SRCS \"*.cpp\")\n\nADD_CUSTOM_TARGET(unsupported_snippets)\n\nFOREACH(snippet_src ${snippets_SRCS})\n  GET_FILENAME_COMPONENT(snippet ${snippet_src} NAME_WE)\n  SET(compile_snippet_target compile_${snippet})\n  SET(compile_snippet_src ${compile_snippet_target}.cpp)\n  FILE(READ ${snippet_src} snippet_source_code)\n  CONFIGURE_FILE(${PROJECT_SOURCE_DIR}/doc/snippets/compile_snippet.cpp.in\n                 ${CMAKE_CURRENT_BINARY_DIR}/${compile_snippet_src})\n  ADD_EXECUTABLE(${compile_snippet_target}\n                 ${CMAKE_CURRENT_BINARY_DIR}/${compile_snippet_src})\n  if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO)\n    target_link_libraries(${compile_snippet_target} ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO})\n  endif()\n  ADD_CUSTOM_COMMAND(\n    TARGET ${compile_snippet_target}\n    POST_BUILD\n    COMMAND ${compile_snippet_target}\n    ARGS >${CMAKE_CURRENT_BINARY_DIR}/${snippet}.out\n  )\n  ADD_DEPENDENCIES(unsupported_snippets ${compile_snippet_target})\n  set_source_files_properties(${CMAKE_CURRENT_BINARY_DIR}/${compile_snippet_src}\n                              PROPERTIES OBJECT_DEPENDS ${snippet_src})\nENDFOREACH(snippet_src)\n"
  },
  {
    "path": "include/eigen3/unsupported/test/BVH.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Ilya Baran <ibaran@mit.edu>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <Eigen/StdVector>\n#include <Eigen/Geometry>\n#include <unsupported/Eigen/BVH>\n\nnamespace Eigen {\n\ntemplate<typename Scalar, int Dim> AlignedBox<Scalar, Dim> bounding_box(const Matrix<Scalar, Dim, 1> &v) { return AlignedBox<Scalar, Dim>(v); }\n\n}\n\n\ntemplate<int Dim>\nstruct Ball\n{\nEIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(double, Dim)\n\n  typedef Matrix<double, Dim, 1> VectorType;\n\n  Ball() {}\n  Ball(const VectorType &c, double r) : center(c), radius(r) {}\n\n  VectorType center;\n  double radius;\n};\ntemplate<int Dim> AlignedBox<double, Dim> bounding_box(const Ball<Dim> &b)\n{ return AlignedBox<double, Dim>(b.center.array() - b.radius, b.center.array() + b.radius); }\n\ninline double SQR(double x) { return x * x; }\n\ntemplate<int Dim>\nstruct BallPointStuff //this class provides functions to be both an intersector and a minimizer, both for a ball and a point and for two trees\n{\n  typedef double Scalar;\n  typedef Matrix<double, Dim, 1> VectorType;\n  typedef Ball<Dim> BallType;\n  typedef AlignedBox<double, Dim> BoxType;\n\n  BallPointStuff() : calls(0), count(0) {}\n  BallPointStuff(const VectorType &inP) : p(inP), calls(0), count(0) {}\n\n\n  bool intersectVolume(const BoxType &r) { ++calls; return r.contains(p); }\n  bool intersectObject(const BallType &b) {\n    ++calls;\n    if((b.center - p).squaredNorm() < SQR(b.radius))\n      ++count;\n    return false; //continue\n  }\n\n  bool intersectVolumeVolume(const BoxType &r1, const BoxType &r2) { ++calls; return !(r1.intersection(r2)).isNull(); }\n  bool intersectVolumeObject(const BoxType &r, const BallType &b) { ++calls; return r.squaredExteriorDistance(b.center) < SQR(b.radius); }\n  bool intersectObjectVolume(const BallType &b, const BoxType &r) { ++calls; return r.squaredExteriorDistance(b.center) < SQR(b.radius); }\n  bool intersectObjectObject(const BallType &b1, const BallType &b2){\n    ++calls;\n    if((b1.center - b2.center).norm() < b1.radius + b2.radius)\n      ++count;\n    return false;\n  }\n  bool intersectVolumeObject(const BoxType &r, const VectorType &v) { ++calls; return r.contains(v); }\n  bool intersectObjectObject(const BallType &b, const VectorType &v){\n    ++calls;\n    if((b.center - v).squaredNorm() < SQR(b.radius))\n      ++count;\n    return false;\n  }\n\n  double minimumOnVolume(const BoxType &r) { ++calls; return r.squaredExteriorDistance(p); }\n  double minimumOnObject(const BallType &b) { ++calls; return (std::max)(0., (b.center - p).squaredNorm() - SQR(b.radius)); }\n  double minimumOnVolumeVolume(const BoxType &r1, const BoxType &r2) { ++calls; return r1.squaredExteriorDistance(r2); }\n  double minimumOnVolumeObject(const BoxType &r, const BallType &b) { ++calls; return SQR((std::max)(0., r.exteriorDistance(b.center) - b.radius)); }\n  double minimumOnObjectVolume(const BallType &b, const BoxType &r) { ++calls; return SQR((std::max)(0., r.exteriorDistance(b.center) - b.radius)); }\n  double minimumOnObjectObject(const BallType &b1, const BallType &b2){ ++calls; return SQR((std::max)(0., (b1.center - b2.center).norm() - b1.radius - b2.radius)); }\n  double minimumOnVolumeObject(const BoxType &r, const VectorType &v) { ++calls; return r.squaredExteriorDistance(v); }\n  double minimumOnObjectObject(const BallType &b, const VectorType &v){ ++calls; return SQR((std::max)(0., (b.center - v).norm() - b.radius)); }\n\n  VectorType p;\n  int calls;\n  int count;\n};\n\n\ntemplate<int Dim>\nstruct TreeTest\n{\n  typedef Matrix<double, Dim, 1> VectorType;\n  typedef std::vector<VectorType, aligned_allocator<VectorType> > VectorTypeList;\n  typedef Ball<Dim> BallType;\n  typedef std::vector<BallType, aligned_allocator<BallType> > BallTypeList;\n  typedef AlignedBox<double, Dim> BoxType;\n\n  void testIntersect1()\n  {\n    BallTypeList b;\n    for(int i = 0; i < 500; ++i) {\n        b.push_back(BallType(VectorType::Random(), 0.5 * internal::random(0., 1.)));\n    }\n    KdBVH<double, Dim, BallType> tree(b.begin(), b.end());\n\n    VectorType pt = VectorType::Random();\n    BallPointStuff<Dim> i1(pt), i2(pt);\n\n    for(int i = 0; i < (int)b.size(); ++i)\n      i1.intersectObject(b[i]);\n\n    BVIntersect(tree, i2);\n\n    VERIFY(i1.count == i2.count);\n  }\n\n  void testMinimize1()\n  {\n    BallTypeList b;\n    for(int i = 0; i < 500; ++i) {\n        b.push_back(BallType(VectorType::Random(), 0.01 * internal::random(0., 1.)));\n    }\n    KdBVH<double, Dim, BallType> tree(b.begin(), b.end());\n\n    VectorType pt = VectorType::Random();\n    BallPointStuff<Dim> i1(pt), i2(pt);\n\n    double m1 = (std::numeric_limits<double>::max)(), m2 = m1;\n\n    for(int i = 0; i < (int)b.size(); ++i)\n      m1 = (std::min)(m1, i1.minimumOnObject(b[i]));\n\n    m2 = BVMinimize(tree, i2);\n\n    VERIFY_IS_APPROX(m1, m2);\n  }\n\n  void testIntersect2()\n  {\n    BallTypeList b;\n    VectorTypeList v;\n\n    for(int i = 0; i < 50; ++i) {\n        b.push_back(BallType(VectorType::Random(), 0.5 * internal::random(0., 1.)));\n        for(int j = 0; j < 3; ++j)\n            v.push_back(VectorType::Random());\n    }\n\n    KdBVH<double, Dim, BallType> tree(b.begin(), b.end());\n    KdBVH<double, Dim, VectorType> vTree(v.begin(), v.end());\n\n    BallPointStuff<Dim> i1, i2;\n\n    for(int i = 0; i < (int)b.size(); ++i)\n        for(int j = 0; j < (int)v.size(); ++j)\n            i1.intersectObjectObject(b[i], v[j]);\n\n    BVIntersect(tree, vTree, i2);\n\n    VERIFY(i1.count == i2.count);\n  }\n\n  void testMinimize2()\n  {\n    BallTypeList b;\n    VectorTypeList v;\n\n    for(int i = 0; i < 50; ++i) {\n        b.push_back(BallType(VectorType::Random(), 1e-7 + 1e-6 * internal::random(0., 1.)));\n        for(int j = 0; j < 3; ++j)\n            v.push_back(VectorType::Random());\n    }\n\n    KdBVH<double, Dim, BallType> tree(b.begin(), b.end());\n    KdBVH<double, Dim, VectorType> vTree(v.begin(), v.end());\n\n    BallPointStuff<Dim> i1, i2;\n\n    double m1 = (std::numeric_limits<double>::max)(), m2 = m1;\n\n    for(int i = 0; i < (int)b.size(); ++i)\n        for(int j = 0; j < (int)v.size(); ++j)\n            m1 = (std::min)(m1, i1.minimumOnObjectObject(b[i], v[j]));\n\n    m2 = BVMinimize(tree, vTree, i2);\n\n    VERIFY_IS_APPROX(m1, m2);\n  }\n};\n\n\nvoid test_BVH()\n{\n  for(int i = 0; i < g_repeat; i++) {\n#ifdef EIGEN_TEST_PART_1\n    TreeTest<2> test2;\n    CALL_SUBTEST(test2.testIntersect1());\n    CALL_SUBTEST(test2.testMinimize1());\n    CALL_SUBTEST(test2.testIntersect2());\n    CALL_SUBTEST(test2.testMinimize2());\n#endif\n\n#ifdef EIGEN_TEST_PART_2\n    TreeTest<3> test3;\n    CALL_SUBTEST(test3.testIntersect1());\n    CALL_SUBTEST(test3.testMinimize1());\n    CALL_SUBTEST(test3.testIntersect2());\n    CALL_SUBTEST(test3.testMinimize2());\n#endif\n\n#ifdef EIGEN_TEST_PART_3\n    TreeTest<4> test4;\n    CALL_SUBTEST(test4.testIntersect1());\n    CALL_SUBTEST(test4.testMinimize1());\n    CALL_SUBTEST(test4.testIntersect2());\n    CALL_SUBTEST(test4.testMinimize2());\n#endif\n  }\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/CMakeLists.txt",
    "content": "# generate split test header file only if it does not yet exist\n# in order to prevent a rebuild everytime cmake is configured\nif(NOT EXISTS ${CMAKE_CURRENT_BINARY_DIR}/split_test_helper.h)\n  file(WRITE ${CMAKE_CURRENT_BINARY_DIR}/split_test_helper.h \"\")\n  foreach(i RANGE 1 999)\n    file(APPEND ${CMAKE_CURRENT_BINARY_DIR}/split_test_helper.h\n      \"#ifdef EIGEN_TEST_PART_${i}\\n\"\n      \"#define CALL_SUBTEST_${i}(FUNC) CALL_SUBTEST(FUNC)\\n\"\n      \"#else\\n\"\n      \"#define CALL_SUBTEST_${i}(FUNC)\\n\"\n      \"#endif\\n\\n\"\n    )\n  endforeach()\nendif()\n\nset_property(GLOBAL PROPERTY EIGEN_CURRENT_SUBPROJECT \"Unsupported\")\nadd_custom_target(BuildUnsupported)\n\ninclude_directories(../../test ../../unsupported ../../Eigen\n                    ${CMAKE_CURRENT_BINARY_DIR}/../../test)\n\nfind_package (Threads)\n\nfind_package(GoogleHash)\nif(GOOGLEHASH_FOUND)\n  add_definitions(\"-DEIGEN_GOOGLEHASH_SUPPORT\")\n  include_directories(${GOOGLEHASH_INCLUDES})\n  ei_add_property(EIGEN_TESTED_BACKENDS  \"GoogleHash, \")\nelse(GOOGLEHASH_FOUND)\n  ei_add_property(EIGEN_MISSING_BACKENDS  \"GoogleHash, \")\nendif(GOOGLEHASH_FOUND)\n\n\nfind_package(Adolc)\nif(ADOLC_FOUND)\n  include_directories(${ADOLC_INCLUDES})\n  ei_add_property(EIGEN_TESTED_BACKENDS \"Adolc, \")\n  if(EIGEN_TEST_CXX11)\n    ei_add_test(forward_adolc \"\" ${ADOLC_LIBRARIES})\n  else()\n    message(STATUS \"Adolc found, but tests require C++11 mode\")\n  endif()\nelse(ADOLC_FOUND)\n  ei_add_property(EIGEN_MISSING_BACKENDS \"Adolc, \")\nendif(ADOLC_FOUND)\n\n# this test seems to never have been successful on x87, so is considered to contain a FP-related bug.\n# see thread: \"non-linear optimization test summary\"\nei_add_test(NonLinearOptimization)\n\nei_add_test(NumericalDiff)\nei_add_test(autodiff_scalar)\nei_add_test(autodiff)\n\nif (NOT CMAKE_CXX_COMPILER MATCHES \"clang\\\\+\\\\+$\")\nei_add_test(BVH)\nendif()\n\nei_add_test(matrix_exponential)\nei_add_test(matrix_function)\nei_add_test(matrix_power)\nei_add_test(matrix_square_root)\nei_add_test(alignedvector3)\n\nei_add_test(FFT)\n\nei_add_test(EulerAngles)\n\nfind_package(MPFR 2.3.0)\nfind_package(GMP)\nif(MPFR_FOUND AND EIGEN_COMPILER_SUPPORT_CXX11)\n  include_directories(${MPFR_INCLUDES} ./mpreal)\n  ei_add_property(EIGEN_TESTED_BACKENDS \"MPFR C++, \")\n  set(EIGEN_MPFR_TEST_LIBRARIES ${MPFR_LIBRARIES} ${GMP_LIBRARIES})\n ei_add_test(mpreal_support \"-std=c++11\" \"${EIGEN_MPFR_TEST_LIBRARIES}\" )\nelse()\n  ei_add_property(EIGEN_MISSING_BACKENDS \"MPFR C++, \")\nendif()\n\nei_add_test(sparse_extra   \"\" \"\")\n\nfind_package(FFTW)\nif(FFTW_FOUND)\n  ei_add_property(EIGEN_TESTED_BACKENDS \"fftw, \")\n  include_directories( ${FFTW_INCLUDES} )\n  if(FFTWL_LIB)\n    ei_add_test(FFTW  \"-DEIGEN_FFTW_DEFAULT -DEIGEN_HAS_FFTWL\" \"${FFTW_LIBRARIES}\" )\n  else()\n    ei_add_test(FFTW  \"-DEIGEN_FFTW_DEFAULT\" \"${FFTW_LIBRARIES}\" )\n  endif()\nelse()\n  ei_add_property(EIGEN_MISSING_BACKENDS \"fftw, \")\nendif()\n\noption(EIGEN_TEST_NO_OPENGL \"Disable OpenGL support in unit tests\" OFF)\nif(NOT EIGEN_TEST_NO_OPENGL)\n  find_package(OpenGL)\n  find_package(GLUT)\n  find_package(GLEW)\n  if(OPENGL_FOUND AND GLUT_FOUND AND GLEW_FOUND)\n    include_directories(${OPENGL_INCLUDE_DIR} ${GLUT_INCLUDE_DIR} ${GLEW_INCLUDE_DIRS})\n    ei_add_property(EIGEN_TESTED_BACKENDS \"OpenGL, \")\n    set(EIGEN_GL_LIB ${GLUT_LIBRARIES} ${GLEW_LIBRARIES} ${OPENGL_LIBRARIES})\n    ei_add_test(openglsupport  \"\" \"${EIGEN_GL_LIB}\" )\n  else()\n    ei_add_property(EIGEN_MISSING_BACKENDS \"OpenGL, \")\n  endif()\nelse()\n    ei_add_property(EIGEN_MISSING_BACKENDS \"OpenGL, \")\nendif()\n\nei_add_test(polynomialsolver)\nei_add_test(polynomialutils)\nei_add_test(splines)\nei_add_test(gmres)\nei_add_test(minres)\nei_add_test(levenberg_marquardt)\nei_add_test(kronecker_product)\nei_add_test(special_functions)\n\n# TODO: The following test names are prefixed with the cxx11 string, since historically\n# the tests depended on c++11. This isn't the case anymore so we ought to rename them.\n# FIXME: Old versions of MSVC fail to compile this code, so we just disable these tests\n# when using visual studio. We should make the check more strict to enable the tests for\n# newer versions of MSVC.\nif (NOT CMAKE_CXX_COMPILER_ID STREQUAL \"MSVC\")\nei_add_test(cxx11_tensor_dimension)\nei_add_test(cxx11_tensor_map)\nei_add_test(cxx11_tensor_assign)\nei_add_test(cxx11_tensor_comparisons)\nei_add_test(cxx11_tensor_forced_eval)\nei_add_test(cxx11_tensor_math)\nei_add_test(cxx11_tensor_const)\nei_add_test(cxx11_tensor_intdiv)\nei_add_test(cxx11_tensor_casts)\nei_add_test(cxx11_tensor_empty)\nei_add_test(cxx11_tensor_sugar)\nei_add_test(cxx11_tensor_roundings)\nei_add_test(cxx11_tensor_layout_swap)\nei_add_test(cxx11_tensor_io)\nif(\"${CMAKE_SIZEOF_VOID_P}\" EQUAL \"8\")\n  # This test requires __uint128_t which is only available on 64bit systems\n  ei_add_test(cxx11_tensor_uint128)\nendif()\nendif()\n\nif(EIGEN_TEST_CXX11)\n  if(EIGEN_TEST_SYCL)\n    ei_add_test_sycl(cxx11_tensor_sycl \"-std=c++11\")\n    ei_add_test_sycl(cxx11_tensor_forced_eval_sycl \"-std=c++11\")\n    ei_add_test_sycl(cxx11_tensor_broadcast_sycl \"-std=c++11\")\n    ei_add_test_sycl(cxx11_tensor_device_sycl \"-std=c++11\")\n    ei_add_test_sycl(cxx11_tensor_reduction_sycl \"-std=c++11\")\n  endif(EIGEN_TEST_SYCL)\n  # It should be safe to always run these tests as there is some fallback code for\n  # older compiler that don't support cxx11.\n  set(CMAKE_CXX_STANDARD 11)\n\n  ei_add_test(cxx11_eventcount \"-pthread\" \"${CMAKE_THREAD_LIBS_INIT}\")\n  ei_add_test(cxx11_runqueue \"-pthread\" \"${CMAKE_THREAD_LIBS_INIT}\")\n  ei_add_test(cxx11_non_blocking_thread_pool \"-pthread\" \"${CMAKE_THREAD_LIBS_INIT}\")\n\n  ei_add_test(cxx11_meta)\n  ei_add_test(cxx11_tensor_simple)\n#  ei_add_test(cxx11_tensor_symmetry)\n  ei_add_test(cxx11_tensor_index_list)\n  ei_add_test(cxx11_tensor_mixed_indices)\n  ei_add_test(cxx11_tensor_contraction)\n  ei_add_test(cxx11_tensor_convolution)\n  ei_add_test(cxx11_tensor_expr)\n  ei_add_test(cxx11_tensor_fixed_size)\n  ei_add_test(cxx11_tensor_of_const_values)\n  ei_add_test(cxx11_tensor_of_complex)\n  ei_add_test(cxx11_tensor_of_strings)\n  ei_add_test(cxx11_tensor_lvalue)\n  ei_add_test(cxx11_tensor_broadcasting)\n  ei_add_test(cxx11_tensor_chipping)\n  ei_add_test(cxx11_tensor_concatenation)\n  ei_add_test(cxx11_tensor_inflation)\n  ei_add_test(cxx11_tensor_morphing)\n  ei_add_test(cxx11_tensor_padding)\n  ei_add_test(cxx11_tensor_patch)\n  ei_add_test(cxx11_tensor_image_patch)\n  ei_add_test(cxx11_tensor_volume_patch)\n  ei_add_test(cxx11_tensor_reduction)\n  ei_add_test(cxx11_tensor_argmax)\n  ei_add_test(cxx11_tensor_shuffling)\n  ei_add_test(cxx11_tensor_striding)\n  ei_add_test(cxx11_tensor_notification \"-pthread\" \"${CMAKE_THREAD_LIBS_INIT}\")\n  ei_add_test(cxx11_tensor_thread_pool \"-pthread\" \"${CMAKE_THREAD_LIBS_INIT}\")\n  ei_add_test(cxx11_tensor_ref)\n  ei_add_test(cxx11_tensor_random)\n  ei_add_test(cxx11_tensor_generator)\n  ei_add_test(cxx11_tensor_custom_op)\n  ei_add_test(cxx11_tensor_custom_index)\n  ei_add_test(cxx11_tensor_fft)\n  ei_add_test(cxx11_tensor_ifft)\n  ei_add_test(cxx11_tensor_scan)\n\nendif()\n\n# These tests needs nvcc\nfind_package(CUDA 7.0)\nif(CUDA_FOUND AND EIGEN_TEST_CUDA)\n  # Make sure to compile without the -pedantic, -Wundef, -Wnon-virtual-dtor\n  # and -fno-check-new flags since they trigger thousands of compilation warnings\n  # in the CUDA runtime\n  # Also remove -ansi that is incompatible with std=c++11.\n  string(REPLACE \"-pedantic\" \"\" CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS}\")\n  string(REPLACE \"-Wundef\" \"\" CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS}\")\n  string(REPLACE \"-Wnon-virtual-dtor\" \"\" CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS}\")\n  string(REPLACE \"-fno-check-new\" \"\" CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS}\")\n  string(REPLACE \"-ansi\" \"\" CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS}\")\n\n  message(STATUS \"Flags used to compile cuda code: \" ${CMAKE_CXX_FLAGS})\n\n  if(\"${CMAKE_CXX_COMPILER_ID}\" STREQUAL \"Clang\")\n    set(CUDA_NVCC_FLAGS \"-ccbin ${CMAKE_C_COMPILER}\" CACHE STRING \"nvcc flags\" FORCE)\n  endif()\n  if(EIGEN_TEST_CUDA_CLANG)\n   set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} -std=c++11 --cuda-gpu-arch=sm_${EIGEN_CUDA_COMPUTE_ARCH}\")\n  endif()\n\n  set(EIGEN_CUDA_RELAXED_CONSTEXPR \"--expt-relaxed-constexpr\")\n  if (${CUDA_VERSION} STREQUAL \"7.0\")\n    set(EIGEN_CUDA_RELAXED_CONSTEXPR \"--relaxed-constexpr\")\n  endif()\n\n  if( (NOT EIGEN_TEST_CXX11) OR (CMAKE_VERSION VERSION_LESS 3.3))\n    set(EIGEN_CUDA_CXX11_FLAG \"-std=c++11\")\n  else()\n    # otherwise the flag has already been added because of the above set(CMAKE_CXX_STANDARD 11)\n    set(EIGEN_CUDA_CXX11_FLAG \"\")\n  endif()\n\n  set(CUDA_NVCC_FLAGS  \"${EIGEN_CUDA_CXX11_FLAG} ${EIGEN_CUDA_RELAXED_CONSTEXPR} -arch compute_${EIGEN_CUDA_COMPUTE_ARCH} -Xcudafe \\\"--display_error_number\\\" ${CUDA_NVCC_FLAGS}\")\n  cuda_include_directories(\"${CMAKE_CURRENT_BINARY_DIR}\" \"${CUDA_TOOLKIT_ROOT_DIR}/include\")\n  set(EIGEN_ADD_TEST_FILENAME_EXTENSION \"cu\")\n\n  ei_add_test(cxx11_tensor_complex_cuda)\n  ei_add_test(cxx11_tensor_complex_cwise_ops_cuda)\n  ei_add_test(cxx11_tensor_reduction_cuda)\n  ei_add_test(cxx11_tensor_argmax_cuda)\n  ei_add_test(cxx11_tensor_cast_float16_cuda)\n  ei_add_test(cxx11_tensor_scan_cuda)\n\n  # Contractions require arch 3.0 or higher\n  if (${EIGEN_CUDA_COMPUTE_ARCH} GREATER 29)\n    ei_add_test(cxx11_tensor_device)\n    ei_add_test(cxx11_tensor_cuda)\n    ei_add_test(cxx11_tensor_contract_cuda)\n    ei_add_test(cxx11_tensor_of_float16_cuda)\n  endif()\n\n  # The random number generation code requires arch 3.5 or greater.\n  if (${EIGEN_CUDA_COMPUTE_ARCH} GREATER 34)\n    ei_add_test(cxx11_tensor_random_cuda)\n  endif()\n\n\n  unset(EIGEN_ADD_TEST_FILENAME_EXTENSION)\nendif()\n"
  },
  {
    "path": "include/eigen3/unsupported/test/EulerAngles.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Tal Hadad <tal_hd@hotmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <unsupported/Eigen/EulerAngles>\n\nusing namespace Eigen;\n\ntemplate<typename EulerSystem, typename Scalar>\nvoid verify_euler_ranged(const Matrix<Scalar,3,1>& ea,\n  bool positiveRangeAlpha, bool positiveRangeBeta, bool positiveRangeGamma)\n{\n  typedef EulerAngles<Scalar, EulerSystem> EulerAnglesType;\n  typedef Matrix<Scalar,3,3> Matrix3;\n  typedef Matrix<Scalar,3,1> Vector3;\n  typedef Quaternion<Scalar> QuaternionType;\n  typedef AngleAxis<Scalar> AngleAxisType;\n  using std::abs;\n  \n  Scalar alphaRangeStart, alphaRangeEnd;\n  Scalar betaRangeStart, betaRangeEnd;\n  Scalar gammaRangeStart, gammaRangeEnd;\n  \n  if (positiveRangeAlpha)\n  {\n    alphaRangeStart = Scalar(0);\n    alphaRangeEnd = Scalar(2 * EIGEN_PI);\n  }\n  else\n  {\n    alphaRangeStart = -Scalar(EIGEN_PI);\n    alphaRangeEnd = Scalar(EIGEN_PI);\n  }\n  \n  if (positiveRangeBeta)\n  {\n    betaRangeStart = Scalar(0);\n    betaRangeEnd = Scalar(2 * EIGEN_PI);\n  }\n  else\n  {\n    betaRangeStart = -Scalar(EIGEN_PI);\n    betaRangeEnd = Scalar(EIGEN_PI);\n  }\n  \n  if (positiveRangeGamma)\n  {\n    gammaRangeStart = Scalar(0);\n    gammaRangeEnd = Scalar(2 * EIGEN_PI);\n  }\n  else\n  {\n    gammaRangeStart = -Scalar(EIGEN_PI);\n    gammaRangeEnd = Scalar(EIGEN_PI);\n  }\n  \n  const int i = EulerSystem::AlphaAxisAbs - 1;\n  const int j = EulerSystem::BetaAxisAbs - 1;\n  const int k = EulerSystem::GammaAxisAbs - 1;\n  \n  const int iFactor = EulerSystem::IsAlphaOpposite ? -1 : 1;\n  const int jFactor = EulerSystem::IsBetaOpposite ? -1 : 1;\n  const int kFactor = EulerSystem::IsGammaOpposite ? -1 : 1;\n  \n  const Vector3 I = EulerAnglesType::AlphaAxisVector();\n  const Vector3 J = EulerAnglesType::BetaAxisVector();\n  const Vector3 K = EulerAnglesType::GammaAxisVector();\n  \n  EulerAnglesType e(ea[0], ea[1], ea[2]);\n  \n  Matrix3 m(e);\n  Vector3 eabis = EulerAnglesType(m, positiveRangeAlpha, positiveRangeBeta, positiveRangeGamma).angles();\n  \n  // Check that eabis in range\n  VERIFY(alphaRangeStart <= eabis[0] && eabis[0] <= alphaRangeEnd);\n  VERIFY(betaRangeStart <= eabis[1] && eabis[1] <= betaRangeEnd);\n  VERIFY(gammaRangeStart <= eabis[2] && eabis[2] <= gammaRangeEnd);\n  \n  Vector3 eabis2 = m.eulerAngles(i, j, k);\n  \n  // Invert the relevant axes\n  eabis2[0] *= iFactor;\n  eabis2[1] *= jFactor;\n  eabis2[2] *= kFactor;\n  \n  // Saturate the angles to the correct range\n  if (positiveRangeAlpha && (eabis2[0] < 0))\n    eabis2[0] += Scalar(2 * EIGEN_PI);\n  if (positiveRangeBeta && (eabis2[1] < 0))\n    eabis2[1] += Scalar(2 * EIGEN_PI);\n  if (positiveRangeGamma && (eabis2[2] < 0))\n    eabis2[2] += Scalar(2 * EIGEN_PI);\n  \n  VERIFY_IS_APPROX(eabis, eabis2);// Verify that our estimation is the same as m.eulerAngles() is\n  \n  Matrix3 mbis(AngleAxisType(eabis[0], I) * AngleAxisType(eabis[1], J) * AngleAxisType(eabis[2], K));\n  VERIFY_IS_APPROX(m,  mbis);\n  \n  // Tests that are only relevant for no possitive range\n  if (!(positiveRangeAlpha || positiveRangeBeta || positiveRangeGamma))\n  {\n    /* If I==K, and ea[1]==0, then there no unique solution. */ \n    /* The remark apply in the case where I!=K, and |ea[1]| is close to pi/2. */ \n    if( (i!=k || ea[1]!=0) && (i==k || !internal::isApprox(abs(ea[1]),Scalar(EIGEN_PI/2),test_precision<Scalar>())) ) \n      VERIFY((ea-eabis).norm() <= test_precision<Scalar>());\n    \n    // approx_or_less_than does not work for 0\n    VERIFY(0 < eabis[0] || test_isMuchSmallerThan(eabis[0], Scalar(1)));\n  }\n  \n  // Quaternions\n  QuaternionType q(e);\n  eabis = EulerAnglesType(q, positiveRangeAlpha, positiveRangeBeta, positiveRangeGamma).angles();\n  VERIFY_IS_APPROX(eabis, eabis2);// Verify that the euler angles are still the same\n}\n\ntemplate<typename EulerSystem, typename Scalar>\nvoid verify_euler(const Matrix<Scalar,3,1>& ea)\n{\n  verify_euler_ranged<EulerSystem>(ea, false, false, false);\n  verify_euler_ranged<EulerSystem>(ea, false, false, true);\n  verify_euler_ranged<EulerSystem>(ea, false, true, false);\n  verify_euler_ranged<EulerSystem>(ea, false, true, true);\n  verify_euler_ranged<EulerSystem>(ea, true, false, false);\n  verify_euler_ranged<EulerSystem>(ea, true, false, true);\n  verify_euler_ranged<EulerSystem>(ea, true, true, false);\n  verify_euler_ranged<EulerSystem>(ea, true, true, true);\n}\n\ntemplate<typename Scalar> void check_all_var(const Matrix<Scalar,3,1>& ea)\n{\n  verify_euler<EulerSystemXYZ>(ea);\n  verify_euler<EulerSystemXYX>(ea);\n  verify_euler<EulerSystemXZY>(ea);\n  verify_euler<EulerSystemXZX>(ea);\n  \n  verify_euler<EulerSystemYZX>(ea);\n  verify_euler<EulerSystemYZY>(ea);\n  verify_euler<EulerSystemYXZ>(ea);\n  verify_euler<EulerSystemYXY>(ea);\n  \n  verify_euler<EulerSystemZXY>(ea);\n  verify_euler<EulerSystemZXZ>(ea);\n  verify_euler<EulerSystemZYX>(ea);\n  verify_euler<EulerSystemZYZ>(ea);\n}\n\ntemplate<typename Scalar> void eulerangles()\n{\n  typedef Matrix<Scalar,3,3> Matrix3;\n  typedef Matrix<Scalar,3,1> Vector3;\n  typedef Array<Scalar,3,1> Array3;\n  typedef Quaternion<Scalar> Quaternionx;\n  typedef AngleAxis<Scalar> AngleAxisType;\n\n  Scalar a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI));\n  Quaternionx q1;\n  q1 = AngleAxisType(a, Vector3::Random().normalized());\n  Matrix3 m;\n  m = q1;\n  \n  Vector3 ea = m.eulerAngles(0,1,2);\n  check_all_var(ea);\n  ea = m.eulerAngles(0,1,0);\n  check_all_var(ea);\n  \n  // Check with purely random Quaternion:\n  q1.coeffs() = Quaternionx::Coefficients::Random().normalized();\n  m = q1;\n  ea = m.eulerAngles(0,1,2);\n  check_all_var(ea);\n  ea = m.eulerAngles(0,1,0);\n  check_all_var(ea);\n  \n  // Check with random angles in range [0:pi]x[-pi:pi]x[-pi:pi].\n  ea = (Array3::Random() + Array3(1,0,0))*Scalar(EIGEN_PI)*Array3(0.5,1,1);\n  check_all_var(ea);\n  \n  ea[2] = ea[0] = internal::random<Scalar>(0,Scalar(EIGEN_PI));\n  check_all_var(ea);\n  \n  ea[0] = ea[1] = internal::random<Scalar>(0,Scalar(EIGEN_PI));\n  check_all_var(ea);\n  \n  ea[1] = 0;\n  check_all_var(ea);\n  \n  ea.head(2).setZero();\n  check_all_var(ea);\n  \n  ea.setZero();\n  check_all_var(ea);\n}\n\nvoid test_EulerAngles()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( eulerangles<float>() );\n    CALL_SUBTEST_2( eulerangles<double>() );\n  }\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/FFT.cpp",
    "content": "#define test_FFTW test_FFT\n#include \"FFTW.cpp\"\n"
  },
  {
    "path": "include/eigen3/unsupported/test/FFTW.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Mark Borgerding mark a borgerding net\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <unsupported/Eigen/FFT>\n\ntemplate <typename T> \nstd::complex<T> RandomCpx() { return std::complex<T>( (T)(rand()/(T)RAND_MAX - .5), (T)(rand()/(T)RAND_MAX - .5) ); }\n\nusing namespace std;\nusing namespace Eigen;\n\n\ntemplate < typename T>\ncomplex<long double>  promote(complex<T> x) { return complex<long double>((long double)x.real(),(long double)x.imag()); }\n\ncomplex<long double>  promote(float x) { return complex<long double>((long double)x); }\ncomplex<long double>  promote(double x) { return complex<long double>((long double)x); }\ncomplex<long double>  promote(long double x) { return complex<long double>((long double)x); }\n    \n\n    template <typename VT1,typename VT2>\n    long double fft_rmse( const VT1 & fftbuf,const VT2 & timebuf)\n    {\n        long double totalpower=0;\n        long double difpower=0;\n        long double pi = acos((long double)-1 );\n        for (size_t k0=0;k0<(size_t)fftbuf.size();++k0) {\n            complex<long double> acc = 0;\n            long double phinc = (long double)(-2.)*k0* pi / timebuf.size();\n            for (size_t k1=0;k1<(size_t)timebuf.size();++k1) {\n                acc +=  promote( timebuf[k1] ) * exp( complex<long double>(0,k1*phinc) );\n            }\n            totalpower += numext::abs2(acc);\n            complex<long double> x = promote(fftbuf[k0]); \n            complex<long double> dif = acc - x;\n            difpower += numext::abs2(dif);\n            //cerr << k0 << \"\\t\" << acc << \"\\t\" <<  x << \"\\t\" << sqrt(numext::abs2(dif)) << endl;\n        }\n        cerr << \"rmse:\" << sqrt(difpower/totalpower) << endl;\n        return sqrt(difpower/totalpower);\n    }\n\n    template <typename VT1,typename VT2>\n    long double dif_rmse( const VT1 buf1,const VT2 buf2)\n    {\n        long double totalpower=0;\n        long double difpower=0;\n        size_t n = (min)( buf1.size(),buf2.size() );\n        for (size_t k=0;k<n;++k) {\n            totalpower += (long double)((numext::abs2( buf1[k] ) + numext::abs2(buf2[k]) )/2);\n            difpower += (long double)(numext::abs2(buf1[k] - buf2[k]));\n        }\n        return sqrt(difpower/totalpower);\n    }\n\nenum { StdVectorContainer, EigenVectorContainer };\n\ntemplate<int Container, typename Scalar> struct VectorType;\n\ntemplate<typename Scalar> struct VectorType<StdVectorContainer,Scalar>\n{\n  typedef vector<Scalar> type;\n};\n\ntemplate<typename Scalar> struct VectorType<EigenVectorContainer,Scalar>\n{\n  typedef Matrix<Scalar,Dynamic,1> type;\n};\n\ntemplate <int Container, typename T>\nvoid test_scalar_generic(int nfft)\n{\n    typedef typename FFT<T>::Complex Complex;\n    typedef typename FFT<T>::Scalar Scalar;\n    typedef typename VectorType<Container,Scalar>::type ScalarVector;\n    typedef typename VectorType<Container,Complex>::type ComplexVector;\n\n    FFT<T> fft;\n    ScalarVector tbuf(nfft);\n    ComplexVector freqBuf;\n    for (int k=0;k<nfft;++k)\n        tbuf[k]= (T)( rand()/(double)RAND_MAX - .5);\n\n    // make sure it DOESN'T give the right full spectrum answer\n    // if we've asked for half-spectrum\n    fft.SetFlag(fft.HalfSpectrum );\n    fft.fwd( freqBuf,tbuf);\n    VERIFY((size_t)freqBuf.size() == (size_t)( (nfft>>1)+1) );\n    VERIFY( T(fft_rmse(freqBuf,tbuf)) < test_precision<T>()  );// gross check\n\n    fft.ClearFlag(fft.HalfSpectrum );\n    fft.fwd( freqBuf,tbuf);\n    VERIFY( (size_t)freqBuf.size() == (size_t)nfft);\n    VERIFY( T(fft_rmse(freqBuf,tbuf)) < test_precision<T>()  );// gross check\n\n    if (nfft&1)\n        return; // odd FFTs get the wrong size inverse FFT\n\n    ScalarVector tbuf2;\n    fft.inv( tbuf2 , freqBuf);\n    VERIFY( T(dif_rmse(tbuf,tbuf2)) < test_precision<T>()  );// gross check\n\n\n    // verify that the Unscaled flag takes effect\n    ScalarVector tbuf3;\n    fft.SetFlag(fft.Unscaled);\n\n    fft.inv( tbuf3 , freqBuf);\n\n    for (int k=0;k<nfft;++k)\n        tbuf3[k] *= T(1./nfft);\n\n\n    //for (size_t i=0;i<(size_t) tbuf.size();++i)\n    //    cout << \"freqBuf=\" << freqBuf[i] << \" in2=\" << tbuf3[i] << \" -  in=\" << tbuf[i] << \" => \" << (tbuf3[i] - tbuf[i] ) <<  endl;\n\n    VERIFY( T(dif_rmse(tbuf,tbuf3)) < test_precision<T>()  );// gross check\n\n    // verify that ClearFlag works\n    fft.ClearFlag(fft.Unscaled);\n    fft.inv( tbuf2 , freqBuf);\n    VERIFY( T(dif_rmse(tbuf,tbuf2)) < test_precision<T>()  );// gross check\n}\n\ntemplate <typename T>\nvoid test_scalar(int nfft)\n{\n  test_scalar_generic<StdVectorContainer,T>(nfft);\n  //test_scalar_generic<EigenVectorContainer,T>(nfft);\n}\n\n\ntemplate <int Container, typename T>\nvoid test_complex_generic(int nfft)\n{\n    typedef typename FFT<T>::Complex Complex;\n    typedef typename VectorType<Container,Complex>::type ComplexVector;\n\n    FFT<T> fft;\n\n    ComplexVector inbuf(nfft);\n    ComplexVector outbuf;\n    ComplexVector buf3;\n    for (int k=0;k<nfft;++k)\n        inbuf[k]= Complex( (T)(rand()/(double)RAND_MAX - .5), (T)(rand()/(double)RAND_MAX - .5) );\n    fft.fwd( outbuf , inbuf);\n\n    VERIFY( T(fft_rmse(outbuf,inbuf)) < test_precision<T>()  );// gross check\n    fft.inv( buf3 , outbuf);\n\n    VERIFY( T(dif_rmse(inbuf,buf3)) < test_precision<T>()  );// gross check\n\n    // verify that the Unscaled flag takes effect\n    ComplexVector buf4;\n    fft.SetFlag(fft.Unscaled);\n    fft.inv( buf4 , outbuf);\n    for (int k=0;k<nfft;++k)\n        buf4[k] *= T(1./nfft);\n    VERIFY( T(dif_rmse(inbuf,buf4)) < test_precision<T>()  );// gross check\n\n    // verify that ClearFlag works\n    fft.ClearFlag(fft.Unscaled);\n    fft.inv( buf3 , outbuf);\n    VERIFY( T(dif_rmse(inbuf,buf3)) < test_precision<T>()  );// gross check\n}\n\ntemplate <typename T>\nvoid test_complex(int nfft)\n{\n  test_complex_generic<StdVectorContainer,T>(nfft);\n  test_complex_generic<EigenVectorContainer,T>(nfft);\n}\n/*\ntemplate <typename T,int nrows,int ncols>\nvoid test_complex2d()\n{\n    typedef typename Eigen::FFT<T>::Complex Complex;\n    FFT<T> fft;\n    Eigen::Matrix<Complex,nrows,ncols> src,src2,dst,dst2;\n\n    src = Eigen::Matrix<Complex,nrows,ncols>::Random();\n    //src =  Eigen::Matrix<Complex,nrows,ncols>::Identity();\n\n    for (int k=0;k<ncols;k++) {\n        Eigen::Matrix<Complex,nrows,1> tmpOut;\n        fft.fwd( tmpOut,src.col(k) );\n        dst2.col(k) = tmpOut;\n    }\n\n    for (int k=0;k<nrows;k++) {\n        Eigen::Matrix<Complex,1,ncols> tmpOut;\n        fft.fwd( tmpOut,  dst2.row(k) );\n        dst2.row(k) = tmpOut;\n    }\n\n    fft.fwd2(dst.data(),src.data(),ncols,nrows);\n    fft.inv2(src2.data(),dst.data(),ncols,nrows);\n    VERIFY( (src-src2).norm() < test_precision<T>() );\n    VERIFY( (dst-dst2).norm() < test_precision<T>() );\n}\n*/\n\n\nvoid test_return_by_value(int len)\n{\n    VectorXf in;\n    VectorXf in1;\n    in.setRandom( len );\n    VectorXcf out1,out2;\n    FFT<float> fft;\n\n    fft.SetFlag(fft.HalfSpectrum );\n\n    fft.fwd(out1,in);\n    out2 = fft.fwd(in);\n    VERIFY( (out1-out2).norm() < test_precision<float>() );\n    in1 = fft.inv(out1);\n    VERIFY( (in1-in).norm() < test_precision<float>() );\n}\n\nvoid test_FFTW()\n{\n  CALL_SUBTEST( test_return_by_value(32) );\n  //CALL_SUBTEST( ( test_complex2d<float,4,8> () ) ); CALL_SUBTEST( ( test_complex2d<double,4,8> () ) );\n  //CALL_SUBTEST( ( test_complex2d<long double,4,8> () ) );\n  CALL_SUBTEST( test_complex<float>(32) ); CALL_SUBTEST( test_complex<double>(32) ); \n  CALL_SUBTEST( test_complex<float>(256) ); CALL_SUBTEST( test_complex<double>(256) ); \n  CALL_SUBTEST( test_complex<float>(3*8) ); CALL_SUBTEST( test_complex<double>(3*8) ); \n  CALL_SUBTEST( test_complex<float>(5*32) ); CALL_SUBTEST( test_complex<double>(5*32) ); \n  CALL_SUBTEST( test_complex<float>(2*3*4) ); CALL_SUBTEST( test_complex<double>(2*3*4) ); \n  CALL_SUBTEST( test_complex<float>(2*3*4*5) ); CALL_SUBTEST( test_complex<double>(2*3*4*5) ); \n  CALL_SUBTEST( test_complex<float>(2*3*4*5*7) ); CALL_SUBTEST( test_complex<double>(2*3*4*5*7) ); \n\n  CALL_SUBTEST( test_scalar<float>(32) ); CALL_SUBTEST( test_scalar<double>(32) ); \n  CALL_SUBTEST( test_scalar<float>(45) ); CALL_SUBTEST( test_scalar<double>(45) ); \n  CALL_SUBTEST( test_scalar<float>(50) ); CALL_SUBTEST( test_scalar<double>(50) ); \n  CALL_SUBTEST( test_scalar<float>(256) ); CALL_SUBTEST( test_scalar<double>(256) ); \n  CALL_SUBTEST( test_scalar<float>(2*3*4*5*7) ); CALL_SUBTEST( test_scalar<double>(2*3*4*5*7) ); \n  \n  #ifdef EIGEN_HAS_FFTWL\n  CALL_SUBTEST( test_complex<long double>(32) );\n  CALL_SUBTEST( test_complex<long double>(256) );\n  CALL_SUBTEST( test_complex<long double>(3*8) );\n  CALL_SUBTEST( test_complex<long double>(5*32) );\n  CALL_SUBTEST( test_complex<long double>(2*3*4) );\n  CALL_SUBTEST( test_complex<long double>(2*3*4*5) );\n  CALL_SUBTEST( test_complex<long double>(2*3*4*5*7) );\n  \n  CALL_SUBTEST( test_scalar<long double>(32) );\n  CALL_SUBTEST( test_scalar<long double>(45) );\n  CALL_SUBTEST( test_scalar<long double>(50) );\n  CALL_SUBTEST( test_scalar<long double>(256) );\n  CALL_SUBTEST( test_scalar<long double>(2*3*4*5*7) );\n  #endif\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/NonLinearOptimization.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>\n\n#include <stdio.h>\n\n#include \"main.h\"\n#include <unsupported/Eigen/NonLinearOptimization>\n\n// This disables some useless Warnings on MSVC.\n// It is intended to be done for this test only.\n#include <Eigen/src/Core/util/DisableStupidWarnings.h>\n\n// tolerance for chekcing number of iterations\n#define LM_EVAL_COUNT_TOL 4/3\n\nint fcn_chkder(const VectorXd &x, VectorXd &fvec, MatrixXd &fjac, int iflag)\n{\n    /*      subroutine fcn for chkder example. */\n\n    int i;\n    assert(15 ==  fvec.size());\n    assert(3 ==  x.size());\n    double tmp1, tmp2, tmp3, tmp4;\n    static const double y[15]={1.4e-1, 1.8e-1, 2.2e-1, 2.5e-1, 2.9e-1, 3.2e-1, 3.5e-1,\n        3.9e-1, 3.7e-1, 5.8e-1, 7.3e-1, 9.6e-1, 1.34, 2.1, 4.39};\n\n\n    if (iflag == 0)\n        return 0;\n\n    if (iflag != 2)\n        for (i=0; i<15; i++) {\n            tmp1 = i+1;\n            tmp2 = 16-i-1;\n            tmp3 = tmp1;\n            if (i >= 8) tmp3 = tmp2;\n            fvec[i] = y[i] - (x[0] + tmp1/(x[1]*tmp2 + x[2]*tmp3));\n        }\n    else {\n        for (i = 0; i < 15; i++) {\n            tmp1 = i+1;\n            tmp2 = 16-i-1;\n\n            /* error introduced into next statement for illustration. */\n            /* corrected statement should read    tmp3 = tmp1 . */\n\n            tmp3 = tmp2;\n            if (i >= 8) tmp3 = tmp2;\n            tmp4 = (x[1]*tmp2 + x[2]*tmp3); tmp4=tmp4*tmp4;\n            fjac(i,0) = -1.;\n            fjac(i,1) = tmp1*tmp2/tmp4;\n            fjac(i,2) = tmp1*tmp3/tmp4;\n        }\n    }\n    return 0;\n}\n\n\nvoid testChkder()\n{\n  const int m=15, n=3;\n  VectorXd x(n), fvec(m), xp, fvecp(m), err;\n  MatrixXd fjac(m,n);\n  VectorXi ipvt;\n\n  /*      the following values should be suitable for */\n  /*      checking the jacobian matrix. */\n  x << 9.2e-1, 1.3e-1, 5.4e-1;\n\n  internal::chkder(x, fvec, fjac, xp, fvecp, 1, err);\n  fcn_chkder(x, fvec, fjac, 1);\n  fcn_chkder(x, fvec, fjac, 2);\n  fcn_chkder(xp, fvecp, fjac, 1);\n  internal::chkder(x, fvec, fjac, xp, fvecp, 2, err);\n\n  fvecp -= fvec;\n\n  // check those\n  VectorXd fvec_ref(m), fvecp_ref(m), err_ref(m);\n  fvec_ref <<\n      -1.181606, -1.429655, -1.606344,\n      -1.745269, -1.840654, -1.921586,\n      -1.984141, -2.022537, -2.468977,\n      -2.827562, -3.473582, -4.437612,\n      -6.047662, -9.267761, -18.91806;\n  fvecp_ref <<\n      -7.724666e-09, -3.432406e-09, -2.034843e-10,\n      2.313685e-09,  4.331078e-09,  5.984096e-09,\n      7.363281e-09,   8.53147e-09,  1.488591e-08,\n      2.33585e-08,  3.522012e-08,  5.301255e-08,\n      8.26666e-08,  1.419747e-07,   3.19899e-07;\n  err_ref <<\n      0.1141397,  0.09943516,  0.09674474,\n      0.09980447,  0.1073116, 0.1220445,\n      0.1526814, 1, 1,\n      1, 1, 1,\n      1, 1, 1;\n\n  VERIFY_IS_APPROX(fvec, fvec_ref);\n  VERIFY_IS_APPROX(fvecp, fvecp_ref);\n  VERIFY_IS_APPROX(err, err_ref);\n}\n\n// Generic functor\ntemplate<typename _Scalar, int NX=Dynamic, int NY=Dynamic>\nstruct Functor\n{\n  typedef _Scalar Scalar;\n  enum {\n    InputsAtCompileTime = NX,\n    ValuesAtCompileTime = NY\n  };\n  typedef Matrix<Scalar,InputsAtCompileTime,1> InputType;\n  typedef Matrix<Scalar,ValuesAtCompileTime,1> ValueType;\n  typedef Matrix<Scalar,ValuesAtCompileTime,InputsAtCompileTime> JacobianType;\n\n  const int m_inputs, m_values;\n\n  Functor() : m_inputs(InputsAtCompileTime), m_values(ValuesAtCompileTime) {}\n  Functor(int inputs, int values) : m_inputs(inputs), m_values(values) {}\n\n  int inputs() const { return m_inputs; }\n  int values() const { return m_values; }\n\n  // you should define that in the subclass :\n//  void operator() (const InputType& x, ValueType* v, JacobianType* _j=0) const;\n};\n\nstruct lmder_functor : Functor<double>\n{\n    lmder_functor(void): Functor<double>(3,15) {}\n    int operator()(const VectorXd &x, VectorXd &fvec) const\n    {\n        double tmp1, tmp2, tmp3;\n        static const double y[15] = {1.4e-1, 1.8e-1, 2.2e-1, 2.5e-1, 2.9e-1, 3.2e-1, 3.5e-1,\n            3.9e-1, 3.7e-1, 5.8e-1, 7.3e-1, 9.6e-1, 1.34, 2.1, 4.39};\n\n        for (int i = 0; i < values(); i++)\n        {\n            tmp1 = i+1;\n            tmp2 = 16 - i - 1;\n            tmp3 = (i>=8)? tmp2 : tmp1;\n            fvec[i] = y[i] - (x[0] + tmp1/(x[1]*tmp2 + x[2]*tmp3));\n        }\n        return 0;\n    }\n\n    int df(const VectorXd &x, MatrixXd &fjac) const\n    {\n        double tmp1, tmp2, tmp3, tmp4;\n        for (int i = 0; i < values(); i++)\n        {\n            tmp1 = i+1;\n            tmp2 = 16 - i - 1;\n            tmp3 = (i>=8)? tmp2 : tmp1;\n            tmp4 = (x[1]*tmp2 + x[2]*tmp3); tmp4 = tmp4*tmp4;\n            fjac(i,0) = -1;\n            fjac(i,1) = tmp1*tmp2/tmp4;\n            fjac(i,2) = tmp1*tmp3/tmp4;\n        }\n        return 0;\n    }\n};\n\nvoid testLmder1()\n{\n  int n=3, info;\n\n  VectorXd x;\n\n  /* the following starting values provide a rough fit. */\n  x.setConstant(n, 1.);\n\n  // do the computation\n  lmder_functor functor;\n  LevenbergMarquardt<lmder_functor> lm(functor);\n  info = lm.lmder1(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev, 6);\n  VERIFY_IS_EQUAL(lm.njev, 5);\n\n  // check norm\n  VERIFY_IS_APPROX(lm.fvec.blueNorm(), 0.09063596);\n\n  // check x\n  VectorXd x_ref(n);\n  x_ref << 0.08241058, 1.133037, 2.343695;\n  VERIFY_IS_APPROX(x, x_ref);\n}\n\nvoid testLmder()\n{\n  const int m=15, n=3;\n  int info;\n  double fnorm, covfac;\n  VectorXd x;\n\n  /* the following starting values provide a rough fit. */\n  x.setConstant(n, 1.);\n\n  // do the computation\n  lmder_functor functor;\n  LevenbergMarquardt<lmder_functor> lm(functor);\n  info = lm.minimize(x);\n\n  // check return values\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev, 6);\n  VERIFY_IS_EQUAL(lm.njev, 5);\n\n  // check norm\n  fnorm = lm.fvec.blueNorm();\n  VERIFY_IS_APPROX(fnorm, 0.09063596);\n\n  // check x\n  VectorXd x_ref(n);\n  x_ref << 0.08241058, 1.133037, 2.343695;\n  VERIFY_IS_APPROX(x, x_ref);\n\n  // check covariance\n  covfac = fnorm*fnorm/(m-n);\n  internal::covar(lm.fjac, lm.permutation.indices()); // TODO : move this as a function of lm\n\n  MatrixXd cov_ref(n,n);\n  cov_ref <<\n      0.0001531202,   0.002869941,  -0.002656662,\n      0.002869941,    0.09480935,   -0.09098995,\n      -0.002656662,   -0.09098995,    0.08778727;\n\n//  std::cout << fjac*covfac << std::endl;\n\n  MatrixXd cov;\n  cov =  covfac*lm.fjac.topLeftCorner<n,n>();\n  VERIFY_IS_APPROX( cov, cov_ref);\n  // TODO: why isn't this allowed ? :\n  // VERIFY_IS_APPROX( covfac*fjac.topLeftCorner<n,n>() , cov_ref);\n}\n\nstruct hybrj_functor : Functor<double>\n{\n    hybrj_functor(void) : Functor<double>(9,9) {}\n\n    int operator()(const VectorXd &x, VectorXd &fvec)\n    {\n        double temp, temp1, temp2;\n        const VectorXd::Index n = x.size();\n        assert(fvec.size()==n);\n        for (VectorXd::Index k = 0; k < n; k++)\n        {\n            temp = (3. - 2.*x[k])*x[k];\n            temp1 = 0.;\n            if (k) temp1 = x[k-1];\n            temp2 = 0.;\n            if (k != n-1) temp2 = x[k+1];\n            fvec[k] = temp - temp1 - 2.*temp2 + 1.;\n        }\n        return 0;\n    }\n    int df(const VectorXd &x, MatrixXd &fjac)\n    {\n        const VectorXd::Index n = x.size();\n        assert(fjac.rows()==n);\n        assert(fjac.cols()==n);\n        for (VectorXd::Index k = 0; k < n; k++)\n        {\n            for (VectorXd::Index j = 0; j < n; j++)\n                fjac(k,j) = 0.;\n            fjac(k,k) = 3.- 4.*x[k];\n            if (k) fjac(k,k-1) = -1.;\n            if (k != n-1) fjac(k,k+1) = -2.;\n        }\n        return 0;\n    }\n};\n\n\nvoid testHybrj1()\n{\n  const int n=9;\n  int info;\n  VectorXd x(n);\n\n  /* the following starting values provide a rough fit. */\n  x.setConstant(n, -1.);\n\n  // do the computation\n  hybrj_functor functor;\n  HybridNonLinearSolver<hybrj_functor> solver(functor);\n  info = solver.hybrj1(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(solver.nfev, 11);\n  VERIFY_IS_EQUAL(solver.njev, 1);\n\n  // check norm\n  VERIFY_IS_APPROX(solver.fvec.blueNorm(), 1.192636e-08);\n\n\n// check x\n  VectorXd x_ref(n);\n  x_ref <<\n     -0.5706545,    -0.6816283,    -0.7017325,\n     -0.7042129,     -0.701369,    -0.6918656,\n     -0.665792,    -0.5960342,    -0.4164121;\n  VERIFY_IS_APPROX(x, x_ref);\n}\n\nvoid testHybrj()\n{\n  const int n=9;\n  int info;\n  VectorXd x(n);\n\n  /* the following starting values provide a rough fit. */\n  x.setConstant(n, -1.);\n\n\n  // do the computation\n  hybrj_functor functor;\n  HybridNonLinearSolver<hybrj_functor> solver(functor);\n  solver.diag.setConstant(n, 1.);\n  solver.useExternalScaling = true;\n  info = solver.solve(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(solver.nfev, 11);\n  VERIFY_IS_EQUAL(solver.njev, 1);\n\n  // check norm\n  VERIFY_IS_APPROX(solver.fvec.blueNorm(), 1.192636e-08);\n\n\n// check x\n  VectorXd x_ref(n);\n  x_ref <<\n     -0.5706545,    -0.6816283,    -0.7017325,\n     -0.7042129,     -0.701369,    -0.6918656,\n     -0.665792,    -0.5960342,    -0.4164121;\n  VERIFY_IS_APPROX(x, x_ref);\n\n}\n\nstruct hybrd_functor : Functor<double>\n{\n    hybrd_functor(void) : Functor<double>(9,9) {}\n    int operator()(const VectorXd &x, VectorXd &fvec) const\n    {\n        double temp, temp1, temp2;\n        const VectorXd::Index n = x.size();\n\n        assert(fvec.size()==n);\n        for (VectorXd::Index k=0; k < n; k++)\n        {\n            temp = (3. - 2.*x[k])*x[k];\n            temp1 = 0.;\n            if (k) temp1 = x[k-1];\n            temp2 = 0.;\n            if (k != n-1) temp2 = x[k+1];\n            fvec[k] = temp - temp1 - 2.*temp2 + 1.;\n        }\n        return 0;\n    }\n};\n\nvoid testHybrd1()\n{\n  int n=9, info;\n  VectorXd x(n);\n\n  /* the following starting values provide a rough solution. */\n  x.setConstant(n, -1.);\n\n  // do the computation\n  hybrd_functor functor;\n  HybridNonLinearSolver<hybrd_functor> solver(functor);\n  info = solver.hybrd1(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(solver.nfev, 20);\n\n  // check norm\n  VERIFY_IS_APPROX(solver.fvec.blueNorm(), 1.192636e-08);\n\n  // check x\n  VectorXd x_ref(n);\n  x_ref << -0.5706545, -0.6816283, -0.7017325, -0.7042129, -0.701369, -0.6918656, -0.665792, -0.5960342, -0.4164121;\n  VERIFY_IS_APPROX(x, x_ref);\n}\n\nvoid testHybrd()\n{\n  const int n=9;\n  int info;\n  VectorXd x;\n\n  /* the following starting values provide a rough fit. */\n  x.setConstant(n, -1.);\n\n  // do the computation\n  hybrd_functor functor;\n  HybridNonLinearSolver<hybrd_functor> solver(functor);\n  solver.parameters.nb_of_subdiagonals = 1;\n  solver.parameters.nb_of_superdiagonals = 1;\n  solver.diag.setConstant(n, 1.);\n  solver.useExternalScaling = true;\n  info = solver.solveNumericalDiff(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(solver.nfev, 14);\n\n  // check norm\n  VERIFY_IS_APPROX(solver.fvec.blueNorm(), 1.192636e-08);\n\n  // check x\n  VectorXd x_ref(n);\n  x_ref <<\n      -0.5706545,    -0.6816283,    -0.7017325,\n      -0.7042129,     -0.701369,    -0.6918656,\n      -0.665792,    -0.5960342,    -0.4164121;\n  VERIFY_IS_APPROX(x, x_ref);\n}\n\nstruct lmstr_functor : Functor<double>\n{\n    lmstr_functor(void) : Functor<double>(3,15) {}\n    int operator()(const VectorXd &x, VectorXd &fvec)\n    {\n        /*  subroutine fcn for lmstr1 example. */\n        double tmp1, tmp2, tmp3;\n        static const double y[15]={1.4e-1, 1.8e-1, 2.2e-1, 2.5e-1, 2.9e-1, 3.2e-1, 3.5e-1,\n            3.9e-1, 3.7e-1, 5.8e-1, 7.3e-1, 9.6e-1, 1.34, 2.1, 4.39};\n\n        assert(15==fvec.size());\n        assert(3==x.size());\n\n        for (int i=0; i<15; i++)\n        {\n            tmp1 = i+1;\n            tmp2 = 16 - i - 1;\n            tmp3 = (i>=8)? tmp2 : tmp1;\n            fvec[i] = y[i] - (x[0] + tmp1/(x[1]*tmp2 + x[2]*tmp3));\n        }\n        return 0;\n    }\n    int df(const VectorXd &x, VectorXd &jac_row, VectorXd::Index rownb)\n    {\n        assert(x.size()==3);\n        assert(jac_row.size()==x.size());\n        double tmp1, tmp2, tmp3, tmp4;\n\n        VectorXd::Index i = rownb-2;\n        tmp1 = i+1;\n        tmp2 = 16 - i - 1;\n        tmp3 = (i>=8)? tmp2 : tmp1;\n        tmp4 = (x[1]*tmp2 + x[2]*tmp3); tmp4 = tmp4*tmp4;\n        jac_row[0] = -1;\n        jac_row[1] = tmp1*tmp2/tmp4;\n        jac_row[2] = tmp1*tmp3/tmp4;\n        return 0;\n    }\n};\n\nvoid testLmstr1()\n{\n  const int n=3;\n  int info;\n\n  VectorXd x(n);\n\n  /* the following starting values provide a rough fit. */\n  x.setConstant(n, 1.);\n\n  // do the computation\n  lmstr_functor functor;\n  LevenbergMarquardt<lmstr_functor> lm(functor);\n  info = lm.lmstr1(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev, 6);\n  VERIFY_IS_EQUAL(lm.njev, 5);\n\n  // check norm\n  VERIFY_IS_APPROX(lm.fvec.blueNorm(), 0.09063596);\n\n  // check x\n  VectorXd x_ref(n);\n  x_ref << 0.08241058, 1.133037, 2.343695 ;\n  VERIFY_IS_APPROX(x, x_ref);\n}\n\nvoid testLmstr()\n{\n  const int n=3;\n  int info;\n  double fnorm;\n  VectorXd x(n);\n\n  /* the following starting values provide a rough fit. */\n  x.setConstant(n, 1.);\n\n  // do the computation\n  lmstr_functor functor;\n  LevenbergMarquardt<lmstr_functor> lm(functor);\n  info = lm.minimizeOptimumStorage(x);\n\n  // check return values\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev, 6);\n  VERIFY_IS_EQUAL(lm.njev, 5);\n\n  // check norm\n  fnorm = lm.fvec.blueNorm();\n  VERIFY_IS_APPROX(fnorm, 0.09063596);\n\n  // check x\n  VectorXd x_ref(n);\n  x_ref << 0.08241058, 1.133037, 2.343695;\n  VERIFY_IS_APPROX(x, x_ref);\n\n}\n\nstruct lmdif_functor : Functor<double>\n{\n    lmdif_functor(void) : Functor<double>(3,15) {}\n    int operator()(const VectorXd &x, VectorXd &fvec) const\n    {\n        int i;\n        double tmp1,tmp2,tmp3;\n        static const double y[15]={1.4e-1,1.8e-1,2.2e-1,2.5e-1,2.9e-1,3.2e-1,3.5e-1,3.9e-1,\n            3.7e-1,5.8e-1,7.3e-1,9.6e-1,1.34e0,2.1e0,4.39e0};\n\n        assert(x.size()==3);\n        assert(fvec.size()==15);\n        for (i=0; i<15; i++)\n        {\n            tmp1 = i+1;\n            tmp2 = 15 - i;\n            tmp3 = tmp1;\n\n            if (i >= 8) tmp3 = tmp2;\n            fvec[i] = y[i] - (x[0] + tmp1/(x[1]*tmp2 + x[2]*tmp3));\n        }\n        return 0;\n    }\n};\n\nvoid testLmdif1()\n{\n  const int n=3;\n  int info;\n\n  VectorXd x(n), fvec(15);\n\n  /* the following starting values provide a rough fit. */\n  x.setConstant(n, 1.);\n\n  // do the computation\n  lmdif_functor functor;\n  DenseIndex nfev;\n  info = LevenbergMarquardt<lmdif_functor>::lmdif1(functor, x, &nfev);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(nfev, 26);\n\n  // check norm\n  functor(x, fvec);\n  VERIFY_IS_APPROX(fvec.blueNorm(), 0.09063596);\n\n  // check x\n  VectorXd x_ref(n);\n  x_ref << 0.0824106, 1.1330366, 2.3436947;\n  VERIFY_IS_APPROX(x, x_ref);\n\n}\n\nvoid testLmdif()\n{\n  const int m=15, n=3;\n  int info;\n  double fnorm, covfac;\n  VectorXd x(n);\n\n  /* the following starting values provide a rough fit. */\n  x.setConstant(n, 1.);\n\n  // do the computation\n  lmdif_functor functor;\n  NumericalDiff<lmdif_functor> numDiff(functor);\n  LevenbergMarquardt<NumericalDiff<lmdif_functor> > lm(numDiff);\n  info = lm.minimize(x);\n\n  // check return values\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev, 26);\n\n  // check norm\n  fnorm = lm.fvec.blueNorm();\n  VERIFY_IS_APPROX(fnorm, 0.09063596);\n\n  // check x\n  VectorXd x_ref(n);\n  x_ref << 0.08241058, 1.133037, 2.343695;\n  VERIFY_IS_APPROX(x, x_ref);\n\n  // check covariance\n  covfac = fnorm*fnorm/(m-n);\n  internal::covar(lm.fjac, lm.permutation.indices()); // TODO : move this as a function of lm\n\n  MatrixXd cov_ref(n,n);\n  cov_ref <<\n      0.0001531202,   0.002869942,  -0.002656662,\n      0.002869942,    0.09480937,   -0.09098997,\n      -0.002656662,   -0.09098997,    0.08778729;\n\n//  std::cout << fjac*covfac << std::endl;\n\n  MatrixXd cov;\n  cov =  covfac*lm.fjac.topLeftCorner<n,n>();\n  VERIFY_IS_APPROX( cov, cov_ref);\n  // TODO: why isn't this allowed ? :\n  // VERIFY_IS_APPROX( covfac*fjac.topLeftCorner<n,n>() , cov_ref);\n}\n\nstruct chwirut2_functor : Functor<double>\n{\n    chwirut2_functor(void) : Functor<double>(3,54) {}\n    static const double m_x[54];\n    static const double m_y[54];\n    int operator()(const VectorXd &b, VectorXd &fvec)\n    {\n        int i;\n\n        assert(b.size()==3);\n        assert(fvec.size()==54);\n        for(i=0; i<54; i++) {\n            double x = m_x[i];\n            fvec[i] = exp(-b[0]*x)/(b[1]+b[2]*x) - m_y[i];\n        }\n        return 0;\n    }\n    int df(const VectorXd &b, MatrixXd &fjac)\n    {\n        assert(b.size()==3);\n        assert(fjac.rows()==54);\n        assert(fjac.cols()==3);\n        for(int i=0; i<54; i++) {\n            double x = m_x[i];\n            double factor = 1./(b[1]+b[2]*x);\n            double e = exp(-b[0]*x);\n            fjac(i,0) = -x*e*factor;\n            fjac(i,1) = -e*factor*factor;\n            fjac(i,2) = -x*e*factor*factor;\n        }\n        return 0;\n    }\n};\nconst double chwirut2_functor::m_x[54] = { 0.500E0, 1.000E0, 1.750E0, 3.750E0, 5.750E0, 0.875E0, 2.250E0, 3.250E0, 5.250E0, 0.750E0, 1.750E0, 2.750E0, 4.750E0, 0.625E0, 1.250E0, 2.250E0, 4.250E0, .500E0, 3.000E0, .750E0, 3.000E0, 1.500E0, 6.000E0, 3.000E0, 6.000E0, 1.500E0, 3.000E0, .500E0, 2.000E0, 4.000E0, .750E0, 2.000E0, 5.000E0, .750E0, 2.250E0, 3.750E0, 5.750E0, 3.000E0, .750E0, 2.500E0, 4.000E0, .750E0, 2.500E0, 4.000E0, .750E0, 2.500E0, 4.000E0, .500E0, 6.000E0, 3.000E0, .500E0, 2.750E0, .500E0, 1.750E0};\nconst double chwirut2_functor::m_y[54] = { 92.9000E0 ,57.1000E0 ,31.0500E0 ,11.5875E0 ,8.0250E0 ,63.6000E0 ,21.4000E0 ,14.2500E0 ,8.4750E0 ,63.8000E0 ,26.8000E0 ,16.4625E0 ,7.1250E0 ,67.3000E0 ,41.0000E0 ,21.1500E0 ,8.1750E0 ,81.5000E0 ,13.1200E0 ,59.9000E0 ,14.6200E0 ,32.9000E0 ,5.4400E0 ,12.5600E0 ,5.4400E0 ,32.0000E0 ,13.9500E0 ,75.8000E0 ,20.0000E0 ,10.4200E0 ,59.5000E0 ,21.6700E0 ,8.5500E0 ,62.0000E0 ,20.2000E0 ,7.7600E0 ,3.7500E0 ,11.8100E0 ,54.7000E0 ,23.7000E0 ,11.5500E0 ,61.3000E0 ,17.7000E0 ,8.7400E0 ,59.2000E0 ,16.3000E0 ,8.6200E0 ,81.0000E0 ,4.8700E0 ,14.6200E0 ,81.7000E0 ,17.1700E0 ,81.3000E0 ,28.9000E0  };\n\n// http://www.itl.nist.gov/div898/strd/nls/data/chwirut2.shtml\nvoid testNistChwirut2(void)\n{\n  const int n=3;\n  int info;\n\n  VectorXd x(n);\n\n  /*\n   * First try\n   */\n  x<< 0.1, 0.01, 0.02;\n  // do the computation\n  chwirut2_functor functor;\n  LevenbergMarquardt<chwirut2_functor> lm(functor);\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev, 10);\n  VERIFY_IS_EQUAL(lm.njev, 8);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.1304802941E+02);\n  // check x\n  VERIFY_IS_APPROX(x[0], 1.6657666537E-01);\n  VERIFY_IS_APPROX(x[1], 5.1653291286E-03);\n  VERIFY_IS_APPROX(x[2], 1.2150007096E-02);\n\n  /*\n   * Second try\n   */\n  x<< 0.15, 0.008, 0.010;\n  // do the computation\n  lm.resetParameters();\n  lm.parameters.ftol = 1.E6*NumTraits<double>::epsilon();\n  lm.parameters.xtol = 1.E6*NumTraits<double>::epsilon();\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev, 7);\n  VERIFY_IS_EQUAL(lm.njev, 6);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.1304802941E+02);\n  // check x\n  VERIFY_IS_APPROX(x[0], 1.6657666537E-01);\n  VERIFY_IS_APPROX(x[1], 5.1653291286E-03);\n  VERIFY_IS_APPROX(x[2], 1.2150007096E-02);\n}\n\n\nstruct misra1a_functor : Functor<double>\n{\n    misra1a_functor(void) : Functor<double>(2,14) {}\n    static const double m_x[14];\n    static const double m_y[14];\n    int operator()(const VectorXd &b, VectorXd &fvec)\n    {\n        assert(b.size()==2);\n        assert(fvec.size()==14);\n        for(int i=0; i<14; i++) {\n            fvec[i] = b[0]*(1.-exp(-b[1]*m_x[i])) - m_y[i] ;\n        }\n        return 0;\n    }\n    int df(const VectorXd &b, MatrixXd &fjac)\n    {\n        assert(b.size()==2);\n        assert(fjac.rows()==14);\n        assert(fjac.cols()==2);\n        for(int i=0; i<14; i++) {\n            fjac(i,0) = (1.-exp(-b[1]*m_x[i]));\n            fjac(i,1) = (b[0]*m_x[i]*exp(-b[1]*m_x[i]));\n        }\n        return 0;\n    }\n};\nconst double misra1a_functor::m_x[14] = { 77.6E0, 114.9E0, 141.1E0, 190.8E0, 239.9E0, 289.0E0, 332.8E0, 378.4E0, 434.8E0, 477.3E0, 536.8E0, 593.1E0, 689.1E0, 760.0E0};\nconst double misra1a_functor::m_y[14] = { 10.07E0, 14.73E0, 17.94E0, 23.93E0, 29.61E0, 35.18E0, 40.02E0, 44.82E0, 50.76E0, 55.05E0, 61.01E0, 66.40E0, 75.47E0, 81.78E0};\n\n// http://www.itl.nist.gov/div898/strd/nls/data/misra1a.shtml\nvoid testNistMisra1a(void)\n{\n  const int n=2;\n  int info;\n\n  VectorXd x(n);\n\n  /*\n   * First try\n   */\n  x<< 500., 0.0001;\n  // do the computation\n  misra1a_functor functor;\n  LevenbergMarquardt<misra1a_functor> lm(functor);\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev, 19);\n  VERIFY_IS_EQUAL(lm.njev, 15);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.2455138894E-01);\n  // check x\n  VERIFY_IS_APPROX(x[0], 2.3894212918E+02);\n  VERIFY_IS_APPROX(x[1], 5.5015643181E-04);\n\n  /*\n   * Second try\n   */\n  x<< 250., 0.0005;\n  // do the computation\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev, 5);\n  VERIFY_IS_EQUAL(lm.njev, 4);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.2455138894E-01);\n  // check x\n  VERIFY_IS_APPROX(x[0], 2.3894212918E+02);\n  VERIFY_IS_APPROX(x[1], 5.5015643181E-04);\n}\n\nstruct hahn1_functor : Functor<double>\n{\n    hahn1_functor(void) : Functor<double>(7,236) {}\n    static const double m_x[236];\n    int operator()(const VectorXd &b, VectorXd &fvec)\n    {\n        static const double m_y[236] = { .591E0 , 1.547E0 , 2.902E0 , 2.894E0 , 4.703E0 , 6.307E0 , 7.03E0  , 7.898E0 , 9.470E0 , 9.484E0 , 10.072E0 , 10.163E0 , 11.615E0 , 12.005E0 , 12.478E0 , 12.982E0 , 12.970E0 , 13.926E0 , 14.452E0 , 14.404E0 , 15.190E0 , 15.550E0 , 15.528E0 , 15.499E0 , 16.131E0 , 16.438E0 , 16.387E0 , 16.549E0 , 16.872E0 , 16.830E0 , 16.926E0 , 16.907E0 , 16.966E0 , 17.060E0 , 17.122E0 , 17.311E0 , 17.355E0 , 17.668E0 , 17.767E0 , 17.803E0 , 17.765E0 , 17.768E0 , 17.736E0 , 17.858E0 , 17.877E0 , 17.912E0 , 18.046E0 , 18.085E0 , 18.291E0 , 18.357E0 , 18.426E0 , 18.584E0 , 18.610E0 , 18.870E0 , 18.795E0 , 19.111E0 , .367E0 , .796E0 , 0.892E0 , 1.903E0 , 2.150E0 , 3.697E0 , 5.870E0 , 6.421E0 , 7.422E0 , 9.944E0 , 11.023E0 , 11.87E0  , 12.786E0 , 14.067E0 , 13.974E0 , 14.462E0 , 14.464E0 , 15.381E0 , 15.483E0 , 15.59E0  , 16.075E0 , 16.347E0 , 16.181E0 , 16.915E0 , 17.003E0 , 16.978E0 , 17.756E0 , 17.808E0 , 17.868E0 , 18.481E0 , 18.486E0 , 19.090E0 , 16.062E0 , 16.337E0 , 16.345E0 ,\n        16.388E0 , 17.159E0 , 17.116E0 , 17.164E0 , 17.123E0 , 17.979E0 , 17.974E0 , 18.007E0 , 17.993E0 , 18.523E0 , 18.669E0 , 18.617E0 , 19.371E0 , 19.330E0 , 0.080E0 , 0.248E0 , 1.089E0 , 1.418E0 , 2.278E0 , 3.624E0 , 4.574E0 , 5.556E0 , 7.267E0 , 7.695E0 , 9.136E0 , 9.959E0 , 9.957E0 , 11.600E0 , 13.138E0 , 13.564E0 , 13.871E0 , 13.994E0 , 14.947E0 , 15.473E0 , 15.379E0 , 15.455E0 , 15.908E0 , 16.114E0 , 17.071E0 , 17.135E0 , 17.282E0 , 17.368E0 , 17.483E0 , 17.764E0 , 18.185E0 , 18.271E0 , 18.236E0 , 18.237E0 , 18.523E0 , 18.627E0 , 18.665E0 , 19.086E0 , 0.214E0 , 0.943E0 , 1.429E0 , 2.241E0 , 2.951E0 , 3.782E0 , 4.757E0 , 5.602E0 , 7.169E0 , 8.920E0 , 10.055E0 , 12.035E0 , 12.861E0 , 13.436E0 , 14.167E0 , 14.755E0 , 15.168E0 , 15.651E0 , 15.746E0 , 16.216E0 , 16.445E0 , 16.965E0 , 17.121E0 , 17.206E0 , 17.250E0 , 17.339E0 , 17.793E0 , 18.123E0 , 18.49E0  , 18.566E0 , 18.645E0 , 18.706E0 , 18.924E0 , 19.1E0   , 0.375E0 , 0.471E0 , 1.504E0 , 2.204E0 , 2.813E0 , 4.765E0 , 9.835E0 , 10.040E0 , 11.946E0 , 12.596E0 , \n13.303E0 , 13.922E0 , 14.440E0 , 14.951E0 , 15.627E0 , 15.639E0 , 15.814E0 , 16.315E0 , 16.334E0 , 16.430E0 , 16.423E0 , 17.024E0 , 17.009E0 , 17.165E0 , 17.134E0 , 17.349E0 , 17.576E0 , 17.848E0 , 18.090E0 , 18.276E0 , 18.404E0 , 18.519E0 , 19.133E0 , 19.074E0 , 19.239E0 , 19.280E0 , 19.101E0 , 19.398E0 , 19.252E0 , 19.89E0  , 20.007E0 , 19.929E0 , 19.268E0 , 19.324E0 , 20.049E0 , 20.107E0 , 20.062E0 , 20.065E0 , 19.286E0 , 19.972E0 , 20.088E0 , 20.743E0 , 20.83E0  , 20.935E0 , 21.035E0 , 20.93E0  , 21.074E0 , 21.085E0 , 20.935E0 };\n\n        //        int called=0; printf(\"call hahn1_functor with  iflag=%d, called=%d\\n\", iflag, called); if (iflag==1) called++;\n\n        assert(b.size()==7);\n        assert(fvec.size()==236);\n        for(int i=0; i<236; i++) {\n            double x=m_x[i], xx=x*x, xxx=xx*x;\n            fvec[i] = (b[0]+b[1]*x+b[2]*xx+b[3]*xxx) / (1.+b[4]*x+b[5]*xx+b[6]*xxx) - m_y[i];\n        }\n        return 0;\n    }\n\n    int df(const VectorXd &b, MatrixXd &fjac)\n    {\n        assert(b.size()==7);\n        assert(fjac.rows()==236);\n        assert(fjac.cols()==7);\n        for(int i=0; i<236; i++) {\n            double x=m_x[i], xx=x*x, xxx=xx*x;\n            double fact = 1./(1.+b[4]*x+b[5]*xx+b[6]*xxx);\n            fjac(i,0) = 1.*fact;\n            fjac(i,1) = x*fact;\n            fjac(i,2) = xx*fact;\n            fjac(i,3) = xxx*fact;\n            fact = - (b[0]+b[1]*x+b[2]*xx+b[3]*xxx) * fact * fact;\n            fjac(i,4) = x*fact;\n            fjac(i,5) = xx*fact;\n            fjac(i,6) = xxx*fact;\n        }\n        return 0;\n    }\n};\nconst double hahn1_functor::m_x[236] = { 24.41E0 , 34.82E0 , 44.09E0 , 45.07E0 , 54.98E0 , 65.51E0 , 70.53E0 , 75.70E0 , 89.57E0 , 91.14E0 , 96.40E0 , 97.19E0 , 114.26E0 , 120.25E0 , 127.08E0 , 133.55E0 , 133.61E0 , 158.67E0 , 172.74E0 , 171.31E0 , 202.14E0 , 220.55E0 , 221.05E0 , 221.39E0 , 250.99E0 , 268.99E0 , 271.80E0 , 271.97E0 , 321.31E0 , 321.69E0 , 330.14E0 , 333.03E0 , 333.47E0 , 340.77E0 , 345.65E0 , 373.11E0 , 373.79E0 , 411.82E0 , 419.51E0 , 421.59E0 , 422.02E0 , 422.47E0 , 422.61E0 , 441.75E0 , 447.41E0 , 448.7E0  , 472.89E0 , 476.69E0 , 522.47E0 , 522.62E0 , 524.43E0 , 546.75E0 , 549.53E0 , 575.29E0 , 576.00E0 , 625.55E0 , 20.15E0 , 28.78E0 , 29.57E0 , 37.41E0 , 39.12E0 , 50.24E0 , 61.38E0 , 66.25E0 , 73.42E0 , 95.52E0 , 107.32E0 , 122.04E0 , 134.03E0 , 163.19E0 , 163.48E0 , 175.70E0 , 179.86E0 , 211.27E0 , 217.78E0 , 219.14E0 , 262.52E0 , 268.01E0 , 268.62E0 , 336.25E0 , 337.23E0 , 339.33E0 , 427.38E0 , 428.58E0 , 432.68E0 , 528.99E0 , 531.08E0 , 628.34E0 , 253.24E0 , 273.13E0 , 273.66E0 ,\n282.10E0 , 346.62E0 , 347.19E0 , 348.78E0 , 351.18E0 , 450.10E0 , 450.35E0 , 451.92E0 , 455.56E0 , 552.22E0 , 553.56E0 , 555.74E0 , 652.59E0 , 656.20E0 , 14.13E0 , 20.41E0 , 31.30E0 , 33.84E0 , 39.70E0 , 48.83E0 , 54.50E0 , 60.41E0 , 72.77E0 , 75.25E0 , 86.84E0 , 94.88E0 , 96.40E0 , 117.37E0 , 139.08E0 , 147.73E0 , 158.63E0 , 161.84E0 , 192.11E0 , 206.76E0 , 209.07E0 , 213.32E0 , 226.44E0 , 237.12E0 , 330.90E0 , 358.72E0 , 370.77E0 , 372.72E0 , 396.24E0 , 416.59E0 , 484.02E0 , 495.47E0 , 514.78E0 , 515.65E0 , 519.47E0 , 544.47E0 , 560.11E0 , 620.77E0 , 18.97E0 , 28.93E0 , 33.91E0 , 40.03E0 , 44.66E0 , 49.87E0 , 55.16E0 , 60.90E0 , 72.08E0 , 85.15E0 , 97.06E0 , 119.63E0 , 133.27E0 , 143.84E0 , 161.91E0 , 180.67E0 , 198.44E0 , 226.86E0 , 229.65E0 , 258.27E0 , 273.77E0 , 339.15E0 , 350.13E0 , 362.75E0 , 371.03E0 , 393.32E0 , 448.53E0 , 473.78E0 , 511.12E0 , 524.70E0 , 548.75E0 , 551.64E0 , 574.02E0 , 623.86E0 , 21.46E0 , 24.33E0 , 33.43E0 , 39.22E0 , 44.18E0 , 55.02E0 , 94.33E0 , 96.44E0 , 118.82E0 , 128.48E0 ,\n141.94E0 , 156.92E0 , 171.65E0 , 190.00E0 , 223.26E0 , 223.88E0 , 231.50E0 , 265.05E0 , 269.44E0 , 271.78E0 , 273.46E0 , 334.61E0 , 339.79E0 , 349.52E0 , 358.18E0 , 377.98E0 , 394.77E0 , 429.66E0 , 468.22E0 , 487.27E0 , 519.54E0 , 523.03E0 , 612.99E0 , 638.59E0 , 641.36E0 , 622.05E0 , 631.50E0 , 663.97E0 , 646.9E0  , 748.29E0 , 749.21E0 , 750.14E0 , 647.04E0 , 646.89E0 , 746.9E0  , 748.43E0 , 747.35E0 , 749.27E0 , 647.61E0 , 747.78E0 , 750.51E0 , 851.37E0 , 845.97E0 , 847.54E0 , 849.93E0 , 851.61E0 , 849.75E0 , 850.98E0 , 848.23E0};\n\n// http://www.itl.nist.gov/div898/strd/nls/data/hahn1.shtml\nvoid testNistHahn1(void)\n{\n  const int  n=7;\n  int info;\n\n  VectorXd x(n);\n\n  /*\n   * First try\n   */\n  x<< 10., -1., .05, -.00001, -.05, .001, -.000001;\n  // do the computation\n  hahn1_functor functor;\n  LevenbergMarquardt<hahn1_functor> lm(functor);\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev, 11);\n  VERIFY_IS_EQUAL(lm.njev, 10);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.5324382854E+00);\n  // check x\n  VERIFY_IS_APPROX(x[0], 1.0776351733E+00);\n  VERIFY_IS_APPROX(x[1],-1.2269296921E-01);\n  VERIFY_IS_APPROX(x[2], 4.0863750610E-03);\n  VERIFY_IS_APPROX(x[3],-1.426264e-06); // shoulde be : -1.4262662514E-06\n  VERIFY_IS_APPROX(x[4],-5.7609940901E-03);\n  VERIFY_IS_APPROX(x[5], 2.4053735503E-04);\n  VERIFY_IS_APPROX(x[6],-1.2314450199E-07);\n\n  /*\n   * Second try\n   */\n  x<< .1, -.1, .005, -.000001, -.005, .0001, -.0000001;\n  // do the computation\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev, 11);\n  VERIFY_IS_EQUAL(lm.njev, 10);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.5324382854E+00);\n  // check x\n  VERIFY_IS_APPROX(x[0], 1.077640); // should be :  1.0776351733E+00\n  VERIFY_IS_APPROX(x[1], -0.1226933); // should be : -1.2269296921E-01\n  VERIFY_IS_APPROX(x[2], 0.004086383); // should be : 4.0863750610E-03\n  VERIFY_IS_APPROX(x[3], -1.426277e-06); // shoulde be : -1.4262662514E-06\n  VERIFY_IS_APPROX(x[4],-5.7609940901E-03);\n  VERIFY_IS_APPROX(x[5], 0.00024053772); // should be : 2.4053735503E-04\n  VERIFY_IS_APPROX(x[6], -1.231450e-07); // should be : -1.2314450199E-07\n\n}\n\nstruct misra1d_functor : Functor<double>\n{\n    misra1d_functor(void) : Functor<double>(2,14) {}\n    static const double x[14];\n    static const double y[14];\n    int operator()(const VectorXd &b, VectorXd &fvec)\n    {\n        assert(b.size()==2);\n        assert(fvec.size()==14);\n        for(int i=0; i<14; i++) {\n            fvec[i] = b[0]*b[1]*x[i]/(1.+b[1]*x[i]) - y[i];\n        }\n        return 0;\n    }\n    int df(const VectorXd &b, MatrixXd &fjac)\n    {\n        assert(b.size()==2);\n        assert(fjac.rows()==14);\n        assert(fjac.cols()==2);\n        for(int i=0; i<14; i++) {\n            double den = 1.+b[1]*x[i];\n            fjac(i,0) = b[1]*x[i] / den;\n            fjac(i,1) = b[0]*x[i]*(den-b[1]*x[i])/den/den;\n        }\n        return 0;\n    }\n};\nconst double misra1d_functor::x[14] = { 77.6E0, 114.9E0, 141.1E0, 190.8E0, 239.9E0, 289.0E0, 332.8E0, 378.4E0, 434.8E0, 477.3E0, 536.8E0, 593.1E0, 689.1E0, 760.0E0};\nconst double misra1d_functor::y[14] = { 10.07E0, 14.73E0, 17.94E0, 23.93E0, 29.61E0, 35.18E0, 40.02E0, 44.82E0, 50.76E0, 55.05E0, 61.01E0, 66.40E0, 75.47E0, 81.78E0};\n\n// http://www.itl.nist.gov/div898/strd/nls/data/misra1d.shtml\nvoid testNistMisra1d(void)\n{\n  const int n=2;\n  int info;\n\n  VectorXd x(n);\n\n  /*\n   * First try\n   */\n  x<< 500., 0.0001;\n  // do the computation\n  misra1d_functor functor;\n  LevenbergMarquardt<misra1d_functor> lm(functor);\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 3);\n  VERIFY_IS_EQUAL(lm.nfev, 9);\n  VERIFY_IS_EQUAL(lm.njev, 7);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.6419295283E-02);\n  // check x\n  VERIFY_IS_APPROX(x[0], 4.3736970754E+02);\n  VERIFY_IS_APPROX(x[1], 3.0227324449E-04);\n\n  /*\n   * Second try\n   */\n  x<< 450., 0.0003;\n  // do the computation\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev, 4);\n  VERIFY_IS_EQUAL(lm.njev, 3);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.6419295283E-02);\n  // check x\n  VERIFY_IS_APPROX(x[0], 4.3736970754E+02);\n  VERIFY_IS_APPROX(x[1], 3.0227324449E-04);\n}\n\n\nstruct lanczos1_functor : Functor<double>\n{\n    lanczos1_functor(void) : Functor<double>(6,24) {}\n    static const double x[24];\n    static const double y[24];\n    int operator()(const VectorXd &b, VectorXd &fvec)\n    {\n        assert(b.size()==6);\n        assert(fvec.size()==24);\n        for(int i=0; i<24; i++)\n            fvec[i] = b[0]*exp(-b[1]*x[i]) + b[2]*exp(-b[3]*x[i]) + b[4]*exp(-b[5]*x[i])  - y[i];\n        return 0;\n    }\n    int df(const VectorXd &b, MatrixXd &fjac)\n    {\n        assert(b.size()==6);\n        assert(fjac.rows()==24);\n        assert(fjac.cols()==6);\n        for(int i=0; i<24; i++) {\n            fjac(i,0) = exp(-b[1]*x[i]);\n            fjac(i,1) = -b[0]*x[i]*exp(-b[1]*x[i]);\n            fjac(i,2) = exp(-b[3]*x[i]);\n            fjac(i,3) = -b[2]*x[i]*exp(-b[3]*x[i]);\n            fjac(i,4) = exp(-b[5]*x[i]);\n            fjac(i,5) = -b[4]*x[i]*exp(-b[5]*x[i]);\n        }\n        return 0;\n    }\n};\nconst double lanczos1_functor::x[24] = { 0.000000000000E+00, 5.000000000000E-02, 1.000000000000E-01, 1.500000000000E-01, 2.000000000000E-01, 2.500000000000E-01, 3.000000000000E-01, 3.500000000000E-01, 4.000000000000E-01, 4.500000000000E-01, 5.000000000000E-01, 5.500000000000E-01, 6.000000000000E-01, 6.500000000000E-01, 7.000000000000E-01, 7.500000000000E-01, 8.000000000000E-01, 8.500000000000E-01, 9.000000000000E-01, 9.500000000000E-01, 1.000000000000E+00, 1.050000000000E+00, 1.100000000000E+00, 1.150000000000E+00 };\nconst double lanczos1_functor::y[24] = { 2.513400000000E+00 ,2.044333373291E+00 ,1.668404436564E+00 ,1.366418021208E+00 ,1.123232487372E+00 ,9.268897180037E-01 ,7.679338563728E-01 ,6.388775523106E-01 ,5.337835317402E-01 ,4.479363617347E-01 ,3.775847884350E-01 ,3.197393199326E-01 ,2.720130773746E-01 ,2.324965529032E-01 ,1.996589546065E-01 ,1.722704126914E-01 ,1.493405660168E-01 ,1.300700206922E-01 ,1.138119324644E-01 ,1.000415587559E-01 ,8.833209084540E-02 ,7.833544019350E-02 ,6.976693743449E-02 ,6.239312536719E-02 };\n\n// http://www.itl.nist.gov/div898/strd/nls/data/lanczos1.shtml\nvoid testNistLanczos1(void)\n{\n  const int n=6;\n  int info;\n\n  VectorXd x(n);\n\n  /*\n   * First try\n   */\n  x<< 1.2, 0.3, 5.6, 5.5, 6.5, 7.6;\n  // do the computation\n  lanczos1_functor functor;\n  LevenbergMarquardt<lanczos1_functor> lm(functor);\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 2);\n  VERIFY_IS_EQUAL(lm.nfev, 79);\n  VERIFY_IS_EQUAL(lm.njev, 72);\n  // check norm^2\n  std::cout.precision(30);\n  std::cout << lm.fvec.squaredNorm() << \"\\n\";\n  VERIFY(lm.fvec.squaredNorm() <= 1.4307867721E-25);\n  // check x\n  VERIFY_IS_APPROX(x[0], 9.5100000027E-02);\n  VERIFY_IS_APPROX(x[1], 1.0000000001E+00);\n  VERIFY_IS_APPROX(x[2], 8.6070000013E-01);\n  VERIFY_IS_APPROX(x[3], 3.0000000002E+00);\n  VERIFY_IS_APPROX(x[4], 1.5575999998E+00);\n  VERIFY_IS_APPROX(x[5], 5.0000000001E+00);\n\n  /*\n   * Second try\n   */\n  x<< 0.5, 0.7, 3.6, 4.2, 4., 6.3;\n  // do the computation\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 2);\n  VERIFY_IS_EQUAL(lm.nfev, 9);\n  VERIFY_IS_EQUAL(lm.njev, 8);\n  // check norm^2\n  VERIFY(lm.fvec.squaredNorm() <= 1.4307867721E-25);\n  // check x\n  VERIFY_IS_APPROX(x[0], 9.5100000027E-02);\n  VERIFY_IS_APPROX(x[1], 1.0000000001E+00);\n  VERIFY_IS_APPROX(x[2], 8.6070000013E-01);\n  VERIFY_IS_APPROX(x[3], 3.0000000002E+00);\n  VERIFY_IS_APPROX(x[4], 1.5575999998E+00);\n  VERIFY_IS_APPROX(x[5], 5.0000000001E+00);\n\n}\n\nstruct rat42_functor : Functor<double>\n{\n    rat42_functor(void) : Functor<double>(3,9) {}\n    static const double x[9];\n    static const double y[9];\n    int operator()(const VectorXd &b, VectorXd &fvec)\n    {\n        assert(b.size()==3);\n        assert(fvec.size()==9);\n        for(int i=0; i<9; i++) {\n            fvec[i] = b[0] / (1.+exp(b[1]-b[2]*x[i])) - y[i];\n        }\n        return 0;\n    }\n\n    int df(const VectorXd &b, MatrixXd &fjac)\n    {\n        assert(b.size()==3);\n        assert(fjac.rows()==9);\n        assert(fjac.cols()==3);\n        for(int i=0; i<9; i++) {\n            double e = exp(b[1]-b[2]*x[i]);\n            fjac(i,0) = 1./(1.+e);\n            fjac(i,1) = -b[0]*e/(1.+e)/(1.+e);\n            fjac(i,2) = +b[0]*e*x[i]/(1.+e)/(1.+e);\n        }\n        return 0;\n    }\n};\nconst double rat42_functor::x[9] = { 9.000E0, 14.000E0, 21.000E0, 28.000E0, 42.000E0, 57.000E0, 63.000E0, 70.000E0, 79.000E0 };\nconst double rat42_functor::y[9] = { 8.930E0 ,10.800E0 ,18.590E0 ,22.330E0 ,39.350E0 ,56.110E0 ,61.730E0 ,64.620E0 ,67.080E0 };\n\n// http://www.itl.nist.gov/div898/strd/nls/data/ratkowsky2.shtml\nvoid testNistRat42(void)\n{\n  const int n=3;\n  int info;\n\n  VectorXd x(n);\n\n  /*\n   * First try\n   */\n  x<< 100., 1., 0.1;\n  // do the computation\n  rat42_functor functor;\n  LevenbergMarquardt<rat42_functor> lm(functor);\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev, 10);\n  VERIFY_IS_EQUAL(lm.njev, 8);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 8.0565229338E+00);\n  // check x\n  VERIFY_IS_APPROX(x[0], 7.2462237576E+01);\n  VERIFY_IS_APPROX(x[1], 2.6180768402E+00);\n  VERIFY_IS_APPROX(x[2], 6.7359200066E-02);\n\n  /*\n   * Second try\n   */\n  x<< 75., 2.5, 0.07;\n  // do the computation\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev, 6);\n  VERIFY_IS_EQUAL(lm.njev, 5);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 8.0565229338E+00);\n  // check x\n  VERIFY_IS_APPROX(x[0], 7.2462237576E+01);\n  VERIFY_IS_APPROX(x[1], 2.6180768402E+00);\n  VERIFY_IS_APPROX(x[2], 6.7359200066E-02);\n}\n\nstruct MGH10_functor : Functor<double>\n{\n    MGH10_functor(void) : Functor<double>(3,16) {}\n    static const double x[16];\n    static const double y[16];\n    int operator()(const VectorXd &b, VectorXd &fvec)\n    {\n        assert(b.size()==3);\n        assert(fvec.size()==16);\n        for(int i=0; i<16; i++)\n            fvec[i] =  b[0] * exp(b[1]/(x[i]+b[2])) - y[i];\n        return 0;\n    }\n    int df(const VectorXd &b, MatrixXd &fjac)\n    {\n        assert(b.size()==3);\n        assert(fjac.rows()==16);\n        assert(fjac.cols()==3);\n        for(int i=0; i<16; i++) {\n            double factor = 1./(x[i]+b[2]);\n            double e = exp(b[1]*factor);\n            fjac(i,0) = e;\n            fjac(i,1) = b[0]*factor*e;\n            fjac(i,2) = -b[1]*b[0]*factor*factor*e;\n        }\n        return 0;\n    }\n};\nconst double MGH10_functor::x[16] = { 5.000000E+01, 5.500000E+01, 6.000000E+01, 6.500000E+01, 7.000000E+01, 7.500000E+01, 8.000000E+01, 8.500000E+01, 9.000000E+01, 9.500000E+01, 1.000000E+02, 1.050000E+02, 1.100000E+02, 1.150000E+02, 1.200000E+02, 1.250000E+02 };\nconst double MGH10_functor::y[16] = { 3.478000E+04, 2.861000E+04, 2.365000E+04, 1.963000E+04, 1.637000E+04, 1.372000E+04, 1.154000E+04, 9.744000E+03, 8.261000E+03, 7.030000E+03, 6.005000E+03, 5.147000E+03, 4.427000E+03, 3.820000E+03, 3.307000E+03, 2.872000E+03 };\n\n// http://www.itl.nist.gov/div898/strd/nls/data/mgh10.shtml\nvoid testNistMGH10(void)\n{\n  const int n=3;\n  int info;\n\n  VectorXd x(n);\n\n  /*\n   * First try\n   */\n  x<< 2., 400000., 25000.;\n  // do the computation\n  MGH10_functor functor;\n  LevenbergMarquardt<MGH10_functor> lm(functor);\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 2); \n  VERIFY_IS_EQUAL(lm.nfev, 284 ); \n  VERIFY_IS_EQUAL(lm.njev, 249 ); \n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 8.7945855171E+01);\n  // check x\n  VERIFY_IS_APPROX(x[0], 5.6096364710E-03);\n  VERIFY_IS_APPROX(x[1], 6.1813463463E+03);\n  VERIFY_IS_APPROX(x[2], 3.4522363462E+02);\n\n  /*\n   * Second try\n   */\n  x<< 0.02, 4000., 250.;\n  // do the computation\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 3);\n  VERIFY_IS_EQUAL(lm.nfev, 126);\n  VERIFY_IS_EQUAL(lm.njev, 116);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 8.7945855171E+01);\n  // check x\n  VERIFY_IS_APPROX(x[0], 5.6096364710E-03);\n  VERIFY_IS_APPROX(x[1], 6.1813463463E+03);\n  VERIFY_IS_APPROX(x[2], 3.4522363462E+02);\n}\n\n\nstruct BoxBOD_functor : Functor<double>\n{\n    BoxBOD_functor(void) : Functor<double>(2,6) {}\n    static const double x[6];\n    int operator()(const VectorXd &b, VectorXd &fvec)\n    {\n        static const double y[6] = { 109., 149., 149., 191., 213., 224. };\n        assert(b.size()==2);\n        assert(fvec.size()==6);\n        for(int i=0; i<6; i++)\n            fvec[i] =  b[0]*(1.-exp(-b[1]*x[i])) - y[i];\n        return 0;\n    }\n    int df(const VectorXd &b, MatrixXd &fjac)\n    {\n        assert(b.size()==2);\n        assert(fjac.rows()==6);\n        assert(fjac.cols()==2);\n        for(int i=0; i<6; i++) {\n            double e = exp(-b[1]*x[i]);\n            fjac(i,0) = 1.-e;\n            fjac(i,1) = b[0]*x[i]*e;\n        }\n        return 0;\n    }\n};\nconst double BoxBOD_functor::x[6] = { 1., 2., 3., 5., 7., 10. };\n\n// http://www.itl.nist.gov/div898/strd/nls/data/boxbod.shtml\nvoid testNistBoxBOD(void)\n{\n  const int n=2;\n  int info;\n\n  VectorXd x(n);\n\n  /*\n   * First try\n   */\n  x<< 1., 1.;\n  // do the computation\n  BoxBOD_functor functor;\n  LevenbergMarquardt<BoxBOD_functor> lm(functor);\n  lm.parameters.ftol = 1.E6*NumTraits<double>::epsilon();\n  lm.parameters.xtol = 1.E6*NumTraits<double>::epsilon();\n  lm.parameters.factor = 10.;\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY(lm.nfev < 31); // 31\n  VERIFY(lm.njev < 25); // 25\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.1680088766E+03);\n  // check x\n  VERIFY_IS_APPROX(x[0], 2.1380940889E+02);\n  VERIFY_IS_APPROX(x[1], 5.4723748542E-01);\n\n  /*\n   * Second try\n   */\n  x<< 100., 0.75;\n  // do the computation\n  lm.resetParameters();\n  lm.parameters.ftol = NumTraits<double>::epsilon();\n  lm.parameters.xtol = NumTraits<double>::epsilon();\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1); \n  VERIFY_IS_EQUAL(lm.nfev, 15 ); \n  VERIFY_IS_EQUAL(lm.njev, 14 ); \n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.1680088766E+03);\n  // check x\n  VERIFY_IS_APPROX(x[0], 2.1380940889E+02);\n  VERIFY_IS_APPROX(x[1], 5.4723748542E-01);\n}\n\nstruct MGH17_functor : Functor<double>\n{\n    MGH17_functor(void) : Functor<double>(5,33) {}\n    static const double x[33];\n    static const double y[33];\n    int operator()(const VectorXd &b, VectorXd &fvec)\n    {\n        assert(b.size()==5);\n        assert(fvec.size()==33);\n        for(int i=0; i<33; i++)\n            fvec[i] =  b[0] + b[1]*exp(-b[3]*x[i]) +  b[2]*exp(-b[4]*x[i]) - y[i];\n        return 0;\n    }\n    int df(const VectorXd &b, MatrixXd &fjac)\n    {\n        assert(b.size()==5);\n        assert(fjac.rows()==33);\n        assert(fjac.cols()==5);\n        for(int i=0; i<33; i++) {\n            fjac(i,0) = 1.;\n            fjac(i,1) = exp(-b[3]*x[i]);\n            fjac(i,2) = exp(-b[4]*x[i]);\n            fjac(i,3) = -x[i]*b[1]*exp(-b[3]*x[i]);\n            fjac(i,4) = -x[i]*b[2]*exp(-b[4]*x[i]);\n        }\n        return 0;\n    }\n};\nconst double MGH17_functor::x[33] = { 0.000000E+00, 1.000000E+01, 2.000000E+01, 3.000000E+01, 4.000000E+01, 5.000000E+01, 6.000000E+01, 7.000000E+01, 8.000000E+01, 9.000000E+01, 1.000000E+02, 1.100000E+02, 1.200000E+02, 1.300000E+02, 1.400000E+02, 1.500000E+02, 1.600000E+02, 1.700000E+02, 1.800000E+02, 1.900000E+02, 2.000000E+02, 2.100000E+02, 2.200000E+02, 2.300000E+02, 2.400000E+02, 2.500000E+02, 2.600000E+02, 2.700000E+02, 2.800000E+02, 2.900000E+02, 3.000000E+02, 3.100000E+02, 3.200000E+02 };\nconst double MGH17_functor::y[33] = { 8.440000E-01, 9.080000E-01, 9.320000E-01, 9.360000E-01, 9.250000E-01, 9.080000E-01, 8.810000E-01, 8.500000E-01, 8.180000E-01, 7.840000E-01, 7.510000E-01, 7.180000E-01, 6.850000E-01, 6.580000E-01, 6.280000E-01, 6.030000E-01, 5.800000E-01, 5.580000E-01, 5.380000E-01, 5.220000E-01, 5.060000E-01, 4.900000E-01, 4.780000E-01, 4.670000E-01, 4.570000E-01, 4.480000E-01, 4.380000E-01, 4.310000E-01, 4.240000E-01, 4.200000E-01, 4.140000E-01, 4.110000E-01, 4.060000E-01 };\n\n// http://www.itl.nist.gov/div898/strd/nls/data/mgh17.shtml\nvoid testNistMGH17(void)\n{\n  const int n=5;\n  int info;\n\n  VectorXd x(n);\n\n  /*\n   * First try\n   */\n  x<< 50., 150., -100., 1., 2.;\n  // do the computation\n  MGH17_functor functor;\n  LevenbergMarquardt<MGH17_functor> lm(functor);\n  lm.parameters.ftol = NumTraits<double>::epsilon();\n  lm.parameters.xtol = NumTraits<double>::epsilon();\n  lm.parameters.maxfev = 1000;\n  info = lm.minimize(x);\n\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.4648946975E-05);\n  // check x\n  VERIFY_IS_APPROX(x[0], 3.7541005211E-01);\n  VERIFY_IS_APPROX(x[1], 1.9358469127E+00);\n  VERIFY_IS_APPROX(x[2], -1.4646871366E+00);\n  VERIFY_IS_APPROX(x[3], 1.2867534640E-02);\n  VERIFY_IS_APPROX(x[4], 2.2122699662E-02);\n  \n  // check return value\n  VERIFY_IS_EQUAL(info, 2); \n  ++g_test_level;\n  VERIFY_IS_EQUAL(lm.nfev, 602);  // 602\n  VERIFY_IS_EQUAL(lm.njev, 545);  // 545\n  --g_test_level;\n  VERIFY(lm.nfev < 602 * LM_EVAL_COUNT_TOL);\n  VERIFY(lm.njev < 545 * LM_EVAL_COUNT_TOL);\n\n  /*\n   * Second try\n   */\n  x<< 0.5  ,1.5  ,-1   ,0.01 ,0.02;\n  // do the computation\n  lm.resetParameters();\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev, 18);\n  VERIFY_IS_EQUAL(lm.njev, 15);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.4648946975E-05);\n  // check x\n  VERIFY_IS_APPROX(x[0], 3.7541005211E-01);\n  VERIFY_IS_APPROX(x[1], 1.9358469127E+00);\n  VERIFY_IS_APPROX(x[2], -1.4646871366E+00);\n  VERIFY_IS_APPROX(x[3], 1.2867534640E-02);\n  VERIFY_IS_APPROX(x[4], 2.2122699662E-02);\n}\n\nstruct MGH09_functor : Functor<double>\n{\n    MGH09_functor(void) : Functor<double>(4,11) {}\n    static const double _x[11];\n    static const double y[11];\n    int operator()(const VectorXd &b, VectorXd &fvec)\n    {\n        assert(b.size()==4);\n        assert(fvec.size()==11);\n        for(int i=0; i<11; i++) {\n            double x = _x[i], xx=x*x;\n            fvec[i] = b[0]*(xx+x*b[1])/(xx+x*b[2]+b[3]) - y[i];\n        }\n        return 0;\n    }\n    int df(const VectorXd &b, MatrixXd &fjac)\n    {\n        assert(b.size()==4);\n        assert(fjac.rows()==11);\n        assert(fjac.cols()==4);\n        for(int i=0; i<11; i++) {\n            double x = _x[i], xx=x*x;\n            double factor = 1./(xx+x*b[2]+b[3]);\n            fjac(i,0) = (xx+x*b[1]) * factor;\n            fjac(i,1) = b[0]*x* factor;\n            fjac(i,2) = - b[0]*(xx+x*b[1]) * x * factor * factor;\n            fjac(i,3) = - b[0]*(xx+x*b[1]) * factor * factor;\n        }\n        return 0;\n    }\n};\nconst double MGH09_functor::_x[11] = { 4., 2., 1., 5.E-1 , 2.5E-01, 1.670000E-01, 1.250000E-01,  1.E-01, 8.330000E-02, 7.140000E-02, 6.250000E-02 };\nconst double MGH09_functor::y[11] = { 1.957000E-01, 1.947000E-01, 1.735000E-01, 1.600000E-01, 8.440000E-02, 6.270000E-02, 4.560000E-02, 3.420000E-02, 3.230000E-02, 2.350000E-02, 2.460000E-02 };\n\n// http://www.itl.nist.gov/div898/strd/nls/data/mgh09.shtml\nvoid testNistMGH09(void)\n{\n  const int n=4;\n  int info;\n\n  VectorXd x(n);\n\n  /*\n   * First try\n   */\n  x<< 25., 39, 41.5, 39.;\n  // do the computation\n  MGH09_functor functor;\n  LevenbergMarquardt<MGH09_functor> lm(functor);\n  lm.parameters.maxfev = 1000;\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1); \n  VERIFY_IS_EQUAL(lm.nfev, 490 ); \n  VERIFY_IS_EQUAL(lm.njev, 376 ); \n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 3.0750560385E-04);\n  // check x\n  VERIFY_IS_APPROX(x[0], 0.1928077089); // should be 1.9280693458E-01\n  VERIFY_IS_APPROX(x[1], 0.19126423573); // should be 1.9128232873E-01\n  VERIFY_IS_APPROX(x[2], 0.12305309914); // should be 1.2305650693E-01\n  VERIFY_IS_APPROX(x[3], 0.13605395375); // should be 1.3606233068E-01\n\n  /*\n   * Second try\n   */\n  x<< 0.25, 0.39, 0.415, 0.39;\n  // do the computation\n  lm.resetParameters();\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev, 18);\n  VERIFY_IS_EQUAL(lm.njev, 16);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 3.0750560385E-04);\n  // check x\n  VERIFY_IS_APPROX(x[0], 0.19280781); // should be 1.9280693458E-01\n  VERIFY_IS_APPROX(x[1], 0.19126265); // should be 1.9128232873E-01\n  VERIFY_IS_APPROX(x[2], 0.12305280); // should be 1.2305650693E-01\n  VERIFY_IS_APPROX(x[3], 0.13605322); // should be 1.3606233068E-01\n}\n\n\n\nstruct Bennett5_functor : Functor<double>\n{\n    Bennett5_functor(void) : Functor<double>(3,154) {}\n    static const double x[154];\n    static const double y[154];\n    int operator()(const VectorXd &b, VectorXd &fvec)\n    {\n        assert(b.size()==3);\n        assert(fvec.size()==154);\n        for(int i=0; i<154; i++)\n            fvec[i] = b[0]* pow(b[1]+x[i],-1./b[2]) - y[i];\n        return 0;\n    }\n    int df(const VectorXd &b, MatrixXd &fjac)\n    {\n        assert(b.size()==3);\n        assert(fjac.rows()==154);\n        assert(fjac.cols()==3);\n        for(int i=0; i<154; i++) {\n            double e = pow(b[1]+x[i],-1./b[2]);\n            fjac(i,0) = e;\n            fjac(i,1) = - b[0]*e/b[2]/(b[1]+x[i]);\n            fjac(i,2) = b[0]*e*log(b[1]+x[i])/b[2]/b[2];\n        }\n        return 0;\n    }\n};\nconst double Bennett5_functor::x[154] = { 7.447168E0, 8.102586E0, 8.452547E0, 8.711278E0, 8.916774E0, 9.087155E0, 9.232590E0, 9.359535E0, 9.472166E0, 9.573384E0, 9.665293E0, 9.749461E0, 9.827092E0, 9.899128E0, 9.966321E0, 10.029280E0, 10.088510E0, 10.144430E0, 10.197380E0, 10.247670E0, 10.295560E0, 10.341250E0, 10.384950E0, 10.426820E0, 10.467000E0, 10.505640E0, 10.542830E0, 10.578690E0, 10.613310E0, 10.646780E0, 10.679150E0, 10.710520E0, 10.740920E0, 10.770440E0, 10.799100E0, 10.826970E0, 10.854080E0, 10.880470E0, 10.906190E0, 10.931260E0, 10.955720E0, 10.979590E0, 11.002910E0, 11.025700E0, 11.047980E0, 11.069770E0, 11.091100E0, 11.111980E0, 11.132440E0, 11.152480E0, 11.172130E0, 11.191410E0, 11.210310E0, 11.228870E0, 11.247090E0, 11.264980E0, 11.282560E0, 11.299840E0, 11.316820E0, 11.333520E0, 11.349940E0, 11.366100E0, 11.382000E0, 11.397660E0, 11.413070E0, 11.428240E0, 11.443200E0, 11.457930E0, 11.472440E0, 11.486750E0, 11.500860E0, 11.514770E0, 11.528490E0, 11.542020E0, 11.555380E0, 11.568550E0,\n11.581560E0, 11.594420E0, 11.607121E0, 11.619640E0, 11.632000E0, 11.644210E0, 11.656280E0, 11.668200E0, 11.679980E0, 11.691620E0, 11.703130E0, 11.714510E0, 11.725760E0, 11.736880E0, 11.747890E0, 11.758780E0, 11.769550E0, 11.780200E0, 11.790730E0, 11.801160E0, 11.811480E0, 11.821700E0, 11.831810E0, 11.841820E0, 11.851730E0, 11.861550E0, 11.871270E0, 11.880890E0, 11.890420E0, 11.899870E0, 11.909220E0, 11.918490E0, 11.927680E0, 11.936780E0, 11.945790E0, 11.954730E0, 11.963590E0, 11.972370E0, 11.981070E0, 11.989700E0, 11.998260E0, 12.006740E0, 12.015150E0, 12.023490E0, 12.031760E0, 12.039970E0, 12.048100E0, 12.056170E0, 12.064180E0, 12.072120E0, 12.080010E0, 12.087820E0, 12.095580E0, 12.103280E0, 12.110920E0, 12.118500E0, 12.126030E0, 12.133500E0, 12.140910E0, 12.148270E0, 12.155570E0, 12.162830E0, 12.170030E0, 12.177170E0, 12.184270E0, 12.191320E0, 12.198320E0, 12.205270E0, 12.212170E0, 12.219030E0, 12.225840E0, 12.232600E0, 12.239320E0, 12.245990E0, 12.252620E0, 12.259200E0, 12.265750E0, 12.272240E0 };\nconst double Bennett5_functor::y[154] = { -34.834702E0 ,-34.393200E0 ,-34.152901E0 ,-33.979099E0 ,-33.845901E0 ,-33.732899E0 ,-33.640301E0 ,-33.559200E0 ,-33.486801E0 ,-33.423100E0 ,-33.365101E0 ,-33.313000E0 ,-33.260899E0 ,-33.217400E0 ,-33.176899E0 ,-33.139198E0 ,-33.101601E0 ,-33.066799E0 ,-33.035000E0 ,-33.003101E0 ,-32.971298E0 ,-32.942299E0 ,-32.916302E0 ,-32.890202E0 ,-32.864101E0 ,-32.841000E0 ,-32.817799E0 ,-32.797501E0 ,-32.774300E0 ,-32.757000E0 ,-32.733799E0 ,-32.716400E0 ,-32.699100E0 ,-32.678799E0 ,-32.661400E0 ,-32.644001E0 ,-32.626701E0 ,-32.612202E0 ,-32.597698E0 ,-32.583199E0 ,-32.568699E0 ,-32.554298E0 ,-32.539799E0 ,-32.525299E0 ,-32.510799E0 ,-32.499199E0 ,-32.487598E0 ,-32.473202E0 ,-32.461601E0 ,-32.435501E0 ,-32.435501E0 ,-32.426800E0 ,-32.412300E0 ,-32.400799E0 ,-32.392101E0 ,-32.380501E0 ,-32.366001E0 ,-32.357300E0 ,-32.348598E0 ,-32.339901E0 ,-32.328400E0 ,-32.319698E0 ,-32.311001E0 ,-32.299400E0 ,-32.290699E0 ,-32.282001E0 ,-32.273300E0 ,-32.264599E0 ,-32.256001E0 ,-32.247299E0\n,-32.238602E0 ,-32.229900E0 ,-32.224098E0 ,-32.215401E0 ,-32.203800E0 ,-32.198002E0 ,-32.189400E0 ,-32.183601E0 ,-32.174900E0 ,-32.169102E0 ,-32.163300E0 ,-32.154598E0 ,-32.145901E0 ,-32.140099E0 ,-32.131401E0 ,-32.125599E0 ,-32.119801E0 ,-32.111198E0 ,-32.105400E0 ,-32.096699E0 ,-32.090900E0 ,-32.088001E0 ,-32.079300E0 ,-32.073502E0 ,-32.067699E0 ,-32.061901E0 ,-32.056099E0 ,-32.050301E0 ,-32.044498E0 ,-32.038799E0 ,-32.033001E0 ,-32.027199E0 ,-32.024300E0 ,-32.018501E0 ,-32.012699E0 ,-32.004002E0 ,-32.001099E0 ,-31.995300E0 ,-31.989500E0 ,-31.983700E0 ,-31.977900E0 ,-31.972099E0 ,-31.969299E0 ,-31.963501E0 ,-31.957701E0 ,-31.951900E0 ,-31.946100E0 ,-31.940300E0 ,-31.937401E0 ,-31.931601E0 ,-31.925800E0 ,-31.922899E0 ,-31.917101E0 ,-31.911301E0 ,-31.908400E0 ,-31.902599E0 ,-31.896900E0 ,-31.893999E0 ,-31.888201E0 ,-31.885300E0 ,-31.882401E0 ,-31.876600E0 ,-31.873699E0 ,-31.867901E0 ,-31.862101E0 ,-31.859200E0 ,-31.856300E0 ,-31.850500E0 ,-31.844700E0 ,-31.841801E0 ,-31.838900E0 ,-31.833099E0 ,-31.830200E0 ,\n-31.827299E0 ,-31.821600E0 ,-31.818701E0 ,-31.812901E0 ,-31.809999E0 ,-31.807100E0 ,-31.801300E0 ,-31.798401E0 ,-31.795500E0 ,-31.789700E0 ,-31.786800E0 };\n\n// http://www.itl.nist.gov/div898/strd/nls/data/bennett5.shtml\nvoid testNistBennett5(void)\n{\n  const int  n=3;\n  int info;\n\n  VectorXd x(n);\n\n  /*\n   * First try\n   */\n  x<< -2000., 50., 0.8;\n  // do the computation\n  Bennett5_functor functor;\n  LevenbergMarquardt<Bennett5_functor> lm(functor);\n  lm.parameters.maxfev = 1000;\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev, 758);\n  VERIFY_IS_EQUAL(lm.njev, 744);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.2404744073E-04);\n  // check x\n  VERIFY_IS_APPROX(x[0], -2.5235058043E+03);\n  VERIFY_IS_APPROX(x[1], 4.6736564644E+01);\n  VERIFY_IS_APPROX(x[2], 9.3218483193E-01);\n  /*\n   * Second try\n   */\n  x<< -1500., 45., 0.85;\n  // do the computation\n  lm.resetParameters();\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev, 203);\n  VERIFY_IS_EQUAL(lm.njev, 192);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.2404744073E-04);\n  // check x\n  VERIFY_IS_APPROX(x[0], -2523.3007865); // should be -2.5235058043E+03\n  VERIFY_IS_APPROX(x[1], 46.735705771); // should be 4.6736564644E+01);\n  VERIFY_IS_APPROX(x[2], 0.93219881891); // should be 9.3218483193E-01);\n}\n\nstruct thurber_functor : Functor<double>\n{\n    thurber_functor(void) : Functor<double>(7,37) {}\n    static const double _x[37];\n    static const double _y[37];\n    int operator()(const VectorXd &b, VectorXd &fvec)\n    {\n        //        int called=0; printf(\"call hahn1_functor with  iflag=%d, called=%d\\n\", iflag, called); if (iflag==1) called++;\n        assert(b.size()==7);\n        assert(fvec.size()==37);\n        for(int i=0; i<37; i++) {\n            double x=_x[i], xx=x*x, xxx=xx*x;\n            fvec[i] = (b[0]+b[1]*x+b[2]*xx+b[3]*xxx) / (1.+b[4]*x+b[5]*xx+b[6]*xxx) - _y[i];\n        }\n        return 0;\n    }\n    int df(const VectorXd &b, MatrixXd &fjac)\n    {\n        assert(b.size()==7);\n        assert(fjac.rows()==37);\n        assert(fjac.cols()==7);\n        for(int i=0; i<37; i++) {\n            double x=_x[i], xx=x*x, xxx=xx*x;\n            double fact = 1./(1.+b[4]*x+b[5]*xx+b[6]*xxx);\n            fjac(i,0) = 1.*fact;\n            fjac(i,1) = x*fact;\n            fjac(i,2) = xx*fact;\n            fjac(i,3) = xxx*fact;\n            fact = - (b[0]+b[1]*x+b[2]*xx+b[3]*xxx) * fact * fact;\n            fjac(i,4) = x*fact;\n            fjac(i,5) = xx*fact;\n            fjac(i,6) = xxx*fact;\n        }\n        return 0;\n    }\n};\nconst double thurber_functor::_x[37] = { -3.067E0, -2.981E0, -2.921E0, -2.912E0, -2.840E0, -2.797E0, -2.702E0, -2.699E0, -2.633E0, -2.481E0, -2.363E0, -2.322E0, -1.501E0, -1.460E0, -1.274E0, -1.212E0, -1.100E0, -1.046E0, -0.915E0, -0.714E0, -0.566E0, -0.545E0, -0.400E0, -0.309E0, -0.109E0, -0.103E0, 0.010E0, 0.119E0, 0.377E0, 0.790E0, 0.963E0, 1.006E0, 1.115E0, 1.572E0, 1.841E0, 2.047E0, 2.200E0 };\nconst double thurber_functor::_y[37] = { 80.574E0, 84.248E0, 87.264E0, 87.195E0, 89.076E0, 89.608E0, 89.868E0, 90.101E0, 92.405E0, 95.854E0, 100.696E0, 101.060E0, 401.672E0, 390.724E0, 567.534E0, 635.316E0, 733.054E0, 759.087E0, 894.206E0, 990.785E0, 1090.109E0, 1080.914E0, 1122.643E0, 1178.351E0, 1260.531E0, 1273.514E0, 1288.339E0, 1327.543E0, 1353.863E0, 1414.509E0, 1425.208E0, 1421.384E0, 1442.962E0, 1464.350E0, 1468.705E0, 1447.894E0, 1457.628E0};\n\n// http://www.itl.nist.gov/div898/strd/nls/data/thurber.shtml\nvoid testNistThurber(void)\n{\n  const int n=7;\n  int info;\n\n  VectorXd x(n);\n\n  /*\n   * First try\n   */\n  x<< 1000 ,1000 ,400 ,40 ,0.7,0.3,0.0 ;\n  // do the computation\n  thurber_functor functor;\n  LevenbergMarquardt<thurber_functor> lm(functor);\n  lm.parameters.ftol = 1.E4*NumTraits<double>::epsilon();\n  lm.parameters.xtol = 1.E4*NumTraits<double>::epsilon();\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev, 39);\n  VERIFY_IS_EQUAL(lm.njev, 36);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.6427082397E+03);\n  // check x\n  VERIFY_IS_APPROX(x[0], 1.2881396800E+03);\n  VERIFY_IS_APPROX(x[1], 1.4910792535E+03);\n  VERIFY_IS_APPROX(x[2], 5.8323836877E+02);\n  VERIFY_IS_APPROX(x[3], 7.5416644291E+01);\n  VERIFY_IS_APPROX(x[4], 9.6629502864E-01);\n  VERIFY_IS_APPROX(x[5], 3.9797285797E-01);\n  VERIFY_IS_APPROX(x[6], 4.9727297349E-02);\n\n  /*\n   * Second try\n   */\n  x<< 1300 ,1500 ,500  ,75   ,1    ,0.4  ,0.05  ;\n  // do the computation\n  lm.resetParameters();\n  lm.parameters.ftol = 1.E4*NumTraits<double>::epsilon();\n  lm.parameters.xtol = 1.E4*NumTraits<double>::epsilon();\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev, 29);\n  VERIFY_IS_EQUAL(lm.njev, 28);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.6427082397E+03);\n  // check x\n  VERIFY_IS_APPROX(x[0], 1.2881396800E+03);\n  VERIFY_IS_APPROX(x[1], 1.4910792535E+03);\n  VERIFY_IS_APPROX(x[2], 5.8323836877E+02);\n  VERIFY_IS_APPROX(x[3], 7.5416644291E+01);\n  VERIFY_IS_APPROX(x[4], 9.6629502864E-01);\n  VERIFY_IS_APPROX(x[5], 3.9797285797E-01);\n  VERIFY_IS_APPROX(x[6], 4.9727297349E-02);\n}\n\nstruct rat43_functor : Functor<double>\n{\n    rat43_functor(void) : Functor<double>(4,15) {}\n    static const double x[15];\n    static const double y[15];\n    int operator()(const VectorXd &b, VectorXd &fvec)\n    {\n        assert(b.size()==4);\n        assert(fvec.size()==15);\n        for(int i=0; i<15; i++)\n            fvec[i] = b[0] * pow(1.+exp(b[1]-b[2]*x[i]),-1./b[3]) - y[i];\n        return 0;\n    }\n    int df(const VectorXd &b, MatrixXd &fjac)\n    {\n        assert(b.size()==4);\n        assert(fjac.rows()==15);\n        assert(fjac.cols()==4);\n        for(int i=0; i<15; i++) {\n            double e = exp(b[1]-b[2]*x[i]);\n            double power = -1./b[3];\n            fjac(i,0) = pow(1.+e, power);\n            fjac(i,1) = power*b[0]*e*pow(1.+e, power-1.);\n            fjac(i,2) = -power*b[0]*e*x[i]*pow(1.+e, power-1.);\n            fjac(i,3) = b[0]*power*power*log(1.+e)*pow(1.+e, power);\n        }\n        return 0;\n    }\n};\nconst double rat43_functor::x[15] = { 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14., 15. };\nconst double rat43_functor::y[15] = { 16.08, 33.83, 65.80, 97.20, 191.55, 326.20, 386.87, 520.53, 590.03, 651.92, 724.93, 699.56, 689.96, 637.56, 717.41 };\n\n// http://www.itl.nist.gov/div898/strd/nls/data/ratkowsky3.shtml\nvoid testNistRat43(void)\n{\n  const int n=4;\n  int info;\n\n  VectorXd x(n);\n\n  /*\n   * First try\n   */\n  x<< 100., 10., 1., 1.;\n  // do the computation\n  rat43_functor functor;\n  LevenbergMarquardt<rat43_functor> lm(functor);\n  lm.parameters.ftol = 1.E6*NumTraits<double>::epsilon();\n  lm.parameters.xtol = 1.E6*NumTraits<double>::epsilon();\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev, 27);\n  VERIFY_IS_EQUAL(lm.njev, 20);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 8.7864049080E+03);\n  // check x\n  VERIFY_IS_APPROX(x[0], 6.9964151270E+02);\n  VERIFY_IS_APPROX(x[1], 5.2771253025E+00);\n  VERIFY_IS_APPROX(x[2], 7.5962938329E-01);\n  VERIFY_IS_APPROX(x[3], 1.2792483859E+00);\n\n  /*\n   * Second try\n   */\n  x<< 700., 5., 0.75, 1.3;\n  // do the computation\n  lm.resetParameters();\n  lm.parameters.ftol = 1.E5*NumTraits<double>::epsilon();\n  lm.parameters.xtol = 1.E5*NumTraits<double>::epsilon();\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev, 9);\n  VERIFY_IS_EQUAL(lm.njev, 8);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 8.7864049080E+03);\n  // check x\n  VERIFY_IS_APPROX(x[0], 6.9964151270E+02);\n  VERIFY_IS_APPROX(x[1], 5.2771253025E+00);\n  VERIFY_IS_APPROX(x[2], 7.5962938329E-01);\n  VERIFY_IS_APPROX(x[3], 1.2792483859E+00);\n}\n\n\n\nstruct eckerle4_functor : Functor<double>\n{\n    eckerle4_functor(void) : Functor<double>(3,35) {}\n    static const double x[35];\n    static const double y[35];\n    int operator()(const VectorXd &b, VectorXd &fvec)\n    {\n        assert(b.size()==3);\n        assert(fvec.size()==35);\n        for(int i=0; i<35; i++)\n            fvec[i] = b[0]/b[1] * exp(-0.5*(x[i]-b[2])*(x[i]-b[2])/(b[1]*b[1])) - y[i];\n        return 0;\n    }\n    int df(const VectorXd &b, MatrixXd &fjac)\n    {\n        assert(b.size()==3);\n        assert(fjac.rows()==35);\n        assert(fjac.cols()==3);\n        for(int i=0; i<35; i++) {\n            double b12 = b[1]*b[1];\n            double e = exp(-0.5*(x[i]-b[2])*(x[i]-b[2])/b12);\n            fjac(i,0) = e / b[1];\n            fjac(i,1) = ((x[i]-b[2])*(x[i]-b[2])/b12-1.) * b[0]*e/b12;\n            fjac(i,2) = (x[i]-b[2])*e*b[0]/b[1]/b12;\n        }\n        return 0;\n    }\n};\nconst double eckerle4_functor::x[35] = { 400.0, 405.0, 410.0, 415.0, 420.0, 425.0, 430.0, 435.0, 436.5, 438.0, 439.5, 441.0, 442.5, 444.0, 445.5, 447.0, 448.5, 450.0, 451.5, 453.0, 454.5, 456.0, 457.5, 459.0, 460.5, 462.0, 463.5, 465.0, 470.0, 475.0, 480.0, 485.0, 490.0, 495.0, 500.0};\nconst double eckerle4_functor::y[35] = { 0.0001575, 0.0001699, 0.0002350, 0.0003102, 0.0004917, 0.0008710, 0.0017418, 0.0046400, 0.0065895, 0.0097302, 0.0149002, 0.0237310, 0.0401683, 0.0712559, 0.1264458, 0.2073413, 0.2902366, 0.3445623, 0.3698049, 0.3668534, 0.3106727, 0.2078154, 0.1164354, 0.0616764, 0.0337200, 0.0194023, 0.0117831, 0.0074357, 0.0022732, 0.0008800, 0.0004579, 0.0002345, 0.0001586, 0.0001143, 0.0000710 };\n\n// http://www.itl.nist.gov/div898/strd/nls/data/eckerle4.shtml\nvoid testNistEckerle4(void)\n{\n  const int n=3;\n  int info;\n\n  VectorXd x(n);\n\n  /*\n   * First try\n   */\n  x<< 1., 10., 500.;\n  // do the computation\n  eckerle4_functor functor;\n  LevenbergMarquardt<eckerle4_functor> lm(functor);\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev, 18);\n  VERIFY_IS_EQUAL(lm.njev, 15);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.4635887487E-03);\n  // check x\n  VERIFY_IS_APPROX(x[0], 1.5543827178);\n  VERIFY_IS_APPROX(x[1], 4.0888321754);\n  VERIFY_IS_APPROX(x[2], 4.5154121844E+02);\n\n  /*\n   * Second try\n   */\n  x<< 1.5, 5., 450.;\n  // do the computation\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev, 7);\n  VERIFY_IS_EQUAL(lm.njev, 6);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.4635887487E-03);\n  // check x\n  VERIFY_IS_APPROX(x[0], 1.5543827178);\n  VERIFY_IS_APPROX(x[1], 4.0888321754);\n  VERIFY_IS_APPROX(x[2], 4.5154121844E+02);\n}\n\nvoid test_NonLinearOptimization()\n{\n    // Tests using the examples provided by (c)minpack\n    CALL_SUBTEST/*_1*/(testChkder());\n    CALL_SUBTEST/*_1*/(testLmder1());\n    CALL_SUBTEST/*_1*/(testLmder());\n    CALL_SUBTEST/*_2*/(testHybrj1());\n    CALL_SUBTEST/*_2*/(testHybrj());\n    CALL_SUBTEST/*_2*/(testHybrd1());\n    CALL_SUBTEST/*_2*/(testHybrd());\n    CALL_SUBTEST/*_3*/(testLmstr1());\n    CALL_SUBTEST/*_3*/(testLmstr());\n    CALL_SUBTEST/*_3*/(testLmdif1());\n    CALL_SUBTEST/*_3*/(testLmdif());\n\n    // NIST tests, level of difficulty = \"Lower\"\n    CALL_SUBTEST/*_4*/(testNistMisra1a());\n    CALL_SUBTEST/*_4*/(testNistChwirut2());\n\n    // NIST tests, level of difficulty = \"Average\"\n    CALL_SUBTEST/*_5*/(testNistHahn1());\n    CALL_SUBTEST/*_6*/(testNistMisra1d());\n    CALL_SUBTEST/*_7*/(testNistMGH17());\n    CALL_SUBTEST/*_8*/(testNistLanczos1());\n\n//     // NIST tests, level of difficulty = \"Higher\"\n    CALL_SUBTEST/*_9*/(testNistRat42());\n//     CALL_SUBTEST/*_10*/(testNistMGH10());\n    CALL_SUBTEST/*_11*/(testNistBoxBOD());\n//     CALL_SUBTEST/*_12*/(testNistMGH09());\n    CALL_SUBTEST/*_13*/(testNistBennett5());\n    CALL_SUBTEST/*_14*/(testNistThurber());\n    CALL_SUBTEST/*_15*/(testNistRat43());\n    CALL_SUBTEST/*_16*/(testNistEckerle4());\n}\n\n/*\n * Can be useful for debugging...\n  printf(\"info, nfev : %d, %d\\n\", info, lm.nfev);\n  printf(\"info, nfev, njev : %d, %d, %d\\n\", info, solver.nfev, solver.njev);\n  printf(\"info, nfev : %d, %d\\n\", info, solver.nfev);\n  printf(\"x[0] : %.32g\\n\", x[0]);\n  printf(\"x[1] : %.32g\\n\", x[1]);\n  printf(\"x[2] : %.32g\\n\", x[2]);\n  printf(\"x[3] : %.32g\\n\", x[3]);\n  printf(\"fvec.blueNorm() : %.32g\\n\", solver.fvec.blueNorm());\n  printf(\"fvec.blueNorm() : %.32g\\n\", lm.fvec.blueNorm());\n\n  printf(\"info, nfev, njev : %d, %d, %d\\n\", info, lm.nfev, lm.njev);\n  printf(\"fvec.squaredNorm() : %.13g\\n\", lm.fvec.squaredNorm());\n  std::cout << x << std::endl;\n  std::cout.precision(9);\n  std::cout << x[0] << std::endl;\n  std::cout << x[1] << std::endl;\n  std::cout << x[2] << std::endl;\n  std::cout << x[3] << std::endl;\n*/\n\n"
  },
  {
    "path": "include/eigen3/unsupported/test/NumericalDiff.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>\n\n#include <stdio.h>\n\n#include \"main.h\"\n#include <unsupported/Eigen/NumericalDiff>\n    \n// Generic functor\ntemplate<typename _Scalar, int NX=Dynamic, int NY=Dynamic>\nstruct Functor\n{\n  typedef _Scalar Scalar;\n  enum {\n    InputsAtCompileTime = NX,\n    ValuesAtCompileTime = NY\n  };\n  typedef Matrix<Scalar,InputsAtCompileTime,1> InputType;\n  typedef Matrix<Scalar,ValuesAtCompileTime,1> ValueType;\n  typedef Matrix<Scalar,ValuesAtCompileTime,InputsAtCompileTime> JacobianType;\n  \n  int m_inputs, m_values;\n  \n  Functor() : m_inputs(InputsAtCompileTime), m_values(ValuesAtCompileTime) {}\n  Functor(int inputs, int values) : m_inputs(inputs), m_values(values) {}\n  \n  int inputs() const { return m_inputs; }\n  int values() const { return m_values; }\n\n};\n\nstruct my_functor : Functor<double>\n{\n    my_functor(void): Functor<double>(3,15) {}\n    int operator()(const VectorXd &x, VectorXd &fvec) const\n    {\n        double tmp1, tmp2, tmp3;\n        double y[15] = {1.4e-1, 1.8e-1, 2.2e-1, 2.5e-1, 2.9e-1, 3.2e-1, 3.5e-1,\n            3.9e-1, 3.7e-1, 5.8e-1, 7.3e-1, 9.6e-1, 1.34, 2.1, 4.39};\n\n        for (int i = 0; i < values(); i++)\n        {\n            tmp1 = i+1;\n            tmp2 = 16 - i - 1;\n            tmp3 = (i>=8)? tmp2 : tmp1;\n            fvec[i] = y[i] - (x[0] + tmp1/(x[1]*tmp2 + x[2]*tmp3));\n        }\n        return 0;\n    }\n\n    int actual_df(const VectorXd &x, MatrixXd &fjac) const\n    {\n        double tmp1, tmp2, tmp3, tmp4;\n        for (int i = 0; i < values(); i++)\n        {\n            tmp1 = i+1;\n            tmp2 = 16 - i - 1;\n            tmp3 = (i>=8)? tmp2 : tmp1;\n            tmp4 = (x[1]*tmp2 + x[2]*tmp3); tmp4 = tmp4*tmp4;\n            fjac(i,0) = -1;\n            fjac(i,1) = tmp1*tmp2/tmp4;\n            fjac(i,2) = tmp1*tmp3/tmp4;\n        }\n        return 0;\n    }\n};\n\nvoid test_forward()\n{\n    VectorXd x(3);\n    MatrixXd jac(15,3);\n    MatrixXd actual_jac(15,3);\n    my_functor functor;\n\n    x << 0.082, 1.13, 2.35;\n\n    // real one \n    functor.actual_df(x, actual_jac);\n//    std::cout << actual_jac << std::endl << std::endl;\n\n    // using NumericalDiff\n    NumericalDiff<my_functor> numDiff(functor);\n    numDiff.df(x, jac);\n//    std::cout << jac << std::endl;\n\n    VERIFY_IS_APPROX(jac, actual_jac);\n}\n\nvoid test_central()\n{\n    VectorXd x(3);\n    MatrixXd jac(15,3);\n    MatrixXd actual_jac(15,3);\n    my_functor functor;\n\n    x << 0.082, 1.13, 2.35;\n\n    // real one \n    functor.actual_df(x, actual_jac);\n\n    // using NumericalDiff\n    NumericalDiff<my_functor,Central> numDiff(functor);\n    numDiff.df(x, jac);\n\n    VERIFY_IS_APPROX(jac, actual_jac);\n}\n\nvoid test_NumericalDiff()\n{\n    CALL_SUBTEST(test_forward());\n    CALL_SUBTEST(test_central());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/alignedvector3.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Gael Guennebaud <g.gael@free.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <unsupported/Eigen/AlignedVector3>\n\nnamespace Eigen {\n\ntemplate<typename T,typename Derived>\nT test_relative_error(const AlignedVector3<T> &a, const MatrixBase<Derived> &b)\n{\n  return test_relative_error(a.coeffs().template head<3>(), b);\n}\n\n}\n\ntemplate<typename Scalar>\nvoid alignedvector3()\n{\n  Scalar s1 = internal::random<Scalar>();\n  Scalar s2 = internal::random<Scalar>();\n  typedef Matrix<Scalar,3,1> RefType;\n  typedef Matrix<Scalar,3,3> Mat33;\n  typedef AlignedVector3<Scalar> FastType;\n  RefType  r1(RefType::Random()), r2(RefType::Random()), r3(RefType::Random()),\n           r4(RefType::Random()), r5(RefType::Random());\n  FastType f1(r1), f2(r2), f3(r3), f4(r4), f5(r5);\n  Mat33 m1(Mat33::Random());\n  \n  VERIFY_IS_APPROX(f1,r1);\n  VERIFY_IS_APPROX(f4,r4);\n\n  VERIFY_IS_APPROX(f4+f1,r4+r1);\n  VERIFY_IS_APPROX(f4-f1,r4-r1);\n  VERIFY_IS_APPROX(f4+f1-f2,r4+r1-r2);\n  VERIFY_IS_APPROX(f4+=f3,r4+=r3);\n  VERIFY_IS_APPROX(f4-=f5,r4-=r5);\n  VERIFY_IS_APPROX(f4-=f5+f1,r4-=r5+r1);\n  VERIFY_IS_APPROX(f5+f1-s1*f2,r5+r1-s1*r2);\n  VERIFY_IS_APPROX(f5+f1/s2-s1*f2,r5+r1/s2-s1*r2);\n  \n  VERIFY_IS_APPROX(m1*f4,m1*r4);\n  VERIFY_IS_APPROX(f4.transpose()*m1,r4.transpose()*m1);\n  \n  VERIFY_IS_APPROX(f2.dot(f3),r2.dot(r3));\n  VERIFY_IS_APPROX(f2.cross(f3),r2.cross(r3));\n  VERIFY_IS_APPROX(f2.norm(),r2.norm());\n\n  VERIFY_IS_APPROX(f2.normalized(),r2.normalized());\n\n  VERIFY_IS_APPROX((f2+f1).normalized(),(r2+r1).normalized());\n  \n  f2.normalize();\n  r2.normalize();\n  VERIFY_IS_APPROX(f2,r2);\n  \n  {\n    FastType f6 = RefType::Zero();\n    FastType f7 = FastType::Zero();\n    VERIFY_IS_APPROX(f6,f7);\n    f6 = r4+r1;\n    VERIFY_IS_APPROX(f6,r4+r1);\n    f6 -= Scalar(2)*r4;\n    VERIFY_IS_APPROX(f6,r1-r4);\n  }\n  \n  std::stringstream ss1, ss2;\n  ss1 << f1;\n  ss2 << r1;\n  VERIFY(ss1.str()==ss2.str());\n}\n\nvoid test_alignedvector3()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST( alignedvector3<float>() );\n  }\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/autodiff.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Gael Guennebaud <g.gael@free.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <unsupported/Eigen/AutoDiff>\n\ntemplate<typename Scalar>\nEIGEN_DONT_INLINE Scalar foo(const Scalar& x, const Scalar& y)\n{\n  using namespace std;\n//   return x+std::sin(y);\n  EIGEN_ASM_COMMENT(\"mybegin\");\n  // pow(float, int) promotes to pow(double, double)\n  return x*2 - 1 + static_cast<Scalar>(pow(1+x,2)) + 2*sqrt(y*y+0) - 4 * sin(0+x) + 2 * cos(y+0) - exp(Scalar(-0.5)*x*x+0);\n  //return x+2*y*x;//x*2 -std::pow(x,2);//(2*y/x);// - y*2;\n  EIGEN_ASM_COMMENT(\"myend\");\n}\n\ntemplate<typename Vector>\nEIGEN_DONT_INLINE typename Vector::Scalar foo(const Vector& p)\n{\n  typedef typename Vector::Scalar Scalar;\n  return (p-Vector(Scalar(-1),Scalar(1.))).norm() + (p.array() * p.array()).sum() + p.dot(p);\n}\n\ntemplate<typename _Scalar, int NX=Dynamic, int NY=Dynamic>\nstruct TestFunc1\n{\n  typedef _Scalar Scalar;\n  enum {\n    InputsAtCompileTime = NX,\n    ValuesAtCompileTime = NY\n  };\n  typedef Matrix<Scalar,InputsAtCompileTime,1> InputType;\n  typedef Matrix<Scalar,ValuesAtCompileTime,1> ValueType;\n  typedef Matrix<Scalar,ValuesAtCompileTime,InputsAtCompileTime> JacobianType;\n\n  int m_inputs, m_values;\n\n  TestFunc1() : m_inputs(InputsAtCompileTime), m_values(ValuesAtCompileTime) {}\n  TestFunc1(int inputs, int values) : m_inputs(inputs), m_values(values) {}\n\n  int inputs() const { return m_inputs; }\n  int values() const { return m_values; }\n\n  template<typename T>\n  void operator() (const Matrix<T,InputsAtCompileTime,1>& x, Matrix<T,ValuesAtCompileTime,1>* _v) const\n  {\n    Matrix<T,ValuesAtCompileTime,1>& v = *_v;\n\n    v[0] = 2 * x[0] * x[0] + x[0] * x[1];\n    v[1] = 3 * x[1] * x[0] + 0.5 * x[1] * x[1];\n    if(inputs()>2)\n    {\n      v[0] += 0.5 * x[2];\n      v[1] += x[2];\n    }\n    if(values()>2)\n    {\n      v[2] = 3 * x[1] * x[0] * x[0];\n    }\n    if (inputs()>2 && values()>2)\n      v[2] *= x[2];\n  }\n\n  void operator() (const InputType& x, ValueType* v, JacobianType* _j) const\n  {\n    (*this)(x, v);\n\n    if(_j)\n    {\n      JacobianType& j = *_j;\n\n      j(0,0) = 4 * x[0] + x[1];\n      j(1,0) = 3 * x[1];\n\n      j(0,1) = x[0];\n      j(1,1) = 3 * x[0] + 2 * 0.5 * x[1];\n\n      if (inputs()>2)\n      {\n        j(0,2) = 0.5;\n        j(1,2) = 1;\n      }\n      if(values()>2)\n      {\n        j(2,0) = 3 * x[1] * 2 * x[0];\n        j(2,1) = 3 * x[0] * x[0];\n      }\n      if (inputs()>2 && values()>2)\n      {\n        j(2,0) *= x[2];\n        j(2,1) *= x[2];\n\n        j(2,2) = 3 * x[1] * x[0] * x[0];\n        j(2,2) = 3 * x[1] * x[0] * x[0];\n      }\n    }\n  }\n};\n\n\n#if EIGEN_HAS_VARIADIC_TEMPLATES\n/* Test functor for the C++11 features. */\ntemplate <typename Scalar>\nstruct integratorFunctor\n{\n    typedef Matrix<Scalar, 2, 1> InputType;\n    typedef Matrix<Scalar, 2, 1> ValueType;\n\n    /*\n     * Implementation starts here.\n     */\n    integratorFunctor(const Scalar gain) : _gain(gain) {}\n    integratorFunctor(const integratorFunctor& f) : _gain(f._gain) {}\n    const Scalar _gain;\n\n    template <typename T1, typename T2>\n    void operator() (const T1 &input, T2 *output, const Scalar dt) const\n    {\n        T2 &o = *output;\n\n        /* Integrator to test the AD. */\n        o[0] = input[0] + input[1] * dt * _gain;\n        o[1] = input[1] * _gain;\n    }\n\n    /* Only needed for the test */\n    template <typename T1, typename T2, typename T3>\n    void operator() (const T1 &input, T2 *output, T3 *jacobian, const Scalar dt) const\n    {\n        T2 &o = *output;\n\n        /* Integrator to test the AD. */\n        o[0] = input[0] + input[1] * dt * _gain;\n        o[1] = input[1] * _gain;\n\n        if (jacobian)\n        {\n            T3 &j = *jacobian;\n\n            j(0, 0) = 1;\n            j(0, 1) = dt * _gain;\n            j(1, 0) = 0;\n            j(1, 1) = _gain;\n        }\n    }\n\n};\n\ntemplate<typename Func> void forward_jacobian_cpp11(const Func& f)\n{\n    typedef typename Func::ValueType::Scalar Scalar;\n    typedef typename Func::ValueType ValueType;\n    typedef typename Func::InputType InputType;\n    typedef typename AutoDiffJacobian<Func>::JacobianType JacobianType;\n\n    InputType x = InputType::Random(InputType::RowsAtCompileTime);\n    ValueType y, yref;\n    JacobianType j, jref;\n\n    const Scalar dt = internal::random<double>();\n\n    jref.setZero();\n    yref.setZero();\n    f(x, &yref, &jref, dt);\n\n    //std::cerr << \"y, yref, jref: \" << \"\\n\";\n    //std::cerr << y.transpose() << \"\\n\\n\";\n    //std::cerr << yref << \"\\n\\n\";\n    //std::cerr << jref << \"\\n\\n\";\n\n    AutoDiffJacobian<Func> autoj(f);\n    autoj(x, &y, &j, dt);\n\n    //std::cerr << \"y j (via autodiff): \" << \"\\n\";\n    //std::cerr << y.transpose() << \"\\n\\n\";\n    //std::cerr << j << \"\\n\\n\";\n\n    VERIFY_IS_APPROX(y, yref);\n    VERIFY_IS_APPROX(j, jref);\n}\n#endif\n\ntemplate<typename Func> void forward_jacobian(const Func& f)\n{\n    typename Func::InputType x = Func::InputType::Random(f.inputs());\n    typename Func::ValueType y(f.values()), yref(f.values());\n    typename Func::JacobianType j(f.values(),f.inputs()), jref(f.values(),f.inputs());\n\n    jref.setZero();\n    yref.setZero();\n    f(x,&yref,&jref);\n//     std::cerr << y.transpose() << \"\\n\\n\";;\n//     std::cerr << j << \"\\n\\n\";;\n\n    j.setZero();\n    y.setZero();\n    AutoDiffJacobian<Func> autoj(f);\n    autoj(x, &y, &j);\n//     std::cerr << y.transpose() << \"\\n\\n\";;\n//     std::cerr << j << \"\\n\\n\";;\n\n    VERIFY_IS_APPROX(y, yref);\n    VERIFY_IS_APPROX(j, jref);\n}\n\n// TODO also check actual derivatives!\ntemplate <int>\nvoid test_autodiff_scalar()\n{\n  Vector2f p = Vector2f::Random();\n  typedef AutoDiffScalar<Vector2f> AD;\n  AD ax(p.x(),Vector2f::UnitX());\n  AD ay(p.y(),Vector2f::UnitY());\n  AD res = foo<AD>(ax,ay);\n  VERIFY_IS_APPROX(res.value(), foo(p.x(),p.y()));\n}\n\n\n// TODO also check actual derivatives!\ntemplate <int>\nvoid test_autodiff_vector()\n{\n  Vector2f p = Vector2f::Random();\n  typedef AutoDiffScalar<Vector2f> AD;\n  typedef Matrix<AD,2,1> VectorAD;\n  VectorAD ap = p.cast<AD>();\n  ap.x().derivatives() = Vector2f::UnitX();\n  ap.y().derivatives() = Vector2f::UnitY();\n\n  AD res = foo<VectorAD>(ap);\n  VERIFY_IS_APPROX(res.value(), foo(p));\n}\n\ntemplate <int>\nvoid test_autodiff_jacobian()\n{\n  CALL_SUBTEST(( forward_jacobian(TestFunc1<double,2,2>()) ));\n  CALL_SUBTEST(( forward_jacobian(TestFunc1<double,2,3>()) ));\n  CALL_SUBTEST(( forward_jacobian(TestFunc1<double,3,2>()) ));\n  CALL_SUBTEST(( forward_jacobian(TestFunc1<double,3,3>()) ));\n  CALL_SUBTEST(( forward_jacobian(TestFunc1<double>(3,3)) ));\n#if EIGEN_HAS_VARIADIC_TEMPLATES\n  CALL_SUBTEST(( forward_jacobian_cpp11(integratorFunctor<double>(10)) ));\n#endif\n}\n\n\ntemplate <int>\nvoid test_autodiff_hessian()\n{\n  typedef AutoDiffScalar<VectorXd> AD;\n  typedef Matrix<AD,Eigen::Dynamic,1> VectorAD;\n  typedef AutoDiffScalar<VectorAD> ADD;\n  typedef Matrix<ADD,Eigen::Dynamic,1> VectorADD;\n  VectorADD x(2);\n  double s1 = internal::random<double>(), s2 = internal::random<double>(), s3 = internal::random<double>(), s4 = internal::random<double>();\n  x(0).value()=s1;\n  x(1).value()=s2;\n\n  //set unit vectors for the derivative directions (partial derivatives of the input vector)\n  x(0).derivatives().resize(2);\n  x(0).derivatives().setZero();\n  x(0).derivatives()(0)= 1;\n  x(1).derivatives().resize(2);\n  x(1).derivatives().setZero();\n  x(1).derivatives()(1)=1;\n\n  //repeat partial derivatives for the inner AutoDiffScalar\n  x(0).value().derivatives() = VectorXd::Unit(2,0);\n  x(1).value().derivatives() = VectorXd::Unit(2,1);\n\n  //set the hessian matrix to zero\n  for(int idx=0; idx<2; idx++) {\n      x(0).derivatives()(idx).derivatives()  = VectorXd::Zero(2);\n      x(1).derivatives()(idx).derivatives()  = VectorXd::Zero(2);\n  }\n\n  ADD y = sin(AD(s3)*x(0) + AD(s4)*x(1));\n\n  VERIFY_IS_APPROX(y.value().derivatives()(0), y.derivatives()(0).value());\n  VERIFY_IS_APPROX(y.value().derivatives()(1), y.derivatives()(1).value());\n  VERIFY_IS_APPROX(y.value().derivatives()(0), s3*std::cos(s1*s3+s2*s4));\n  VERIFY_IS_APPROX(y.value().derivatives()(1), s4*std::cos(s1*s3+s2*s4));\n  VERIFY_IS_APPROX(y.derivatives()(0).derivatives(), -std::sin(s1*s3+s2*s4)*Vector2d(s3*s3,s4*s3));\n  VERIFY_IS_APPROX(y.derivatives()(1).derivatives(),  -std::sin(s1*s3+s2*s4)*Vector2d(s3*s4,s4*s4));\n\n  ADD z = x(0)*x(1);\n  VERIFY_IS_APPROX(z.derivatives()(0).derivatives(), Vector2d(0,1));\n  VERIFY_IS_APPROX(z.derivatives()(1).derivatives(), Vector2d(1,0));\n}\n\ndouble bug_1222() {\n  typedef Eigen::AutoDiffScalar<Eigen::Vector3d> AD;\n  const double _cv1_3 = 1.0;\n  const AD chi_3 = 1.0;\n  // this line did not work, because operator+ returns ADS<DerType&>, which then cannot be converted to ADS<DerType>\n  const AD denom = chi_3 + _cv1_3;\n  return denom.value();\n}\n\n#ifdef EIGEN_TEST_PART_5\n\ndouble bug_1223() {\n  using std::min;\n  typedef Eigen::AutoDiffScalar<Eigen::Vector3d> AD;\n\n  const double _cv1_3 = 1.0;\n  const AD chi_3 = 1.0;\n  const AD denom = 1.0;\n\n  // failed because implementation of min attempts to construct ADS<DerType&> via constructor AutoDiffScalar(const Real& value)\n  // without initializing m_derivatives (which is a reference in this case)\n  #define EIGEN_TEST_SPACE\n  const AD t = min EIGEN_TEST_SPACE (denom / chi_3, 1.0);\n\n  const AD t2 = min EIGEN_TEST_SPACE (denom / (chi_3 * _cv1_3), 1.0);\n\n  return t.value() + t2.value();\n}\n\n// regression test for some compilation issues with specializations of ScalarBinaryOpTraits\nvoid bug_1260() {\n  Matrix4d A = Matrix4d::Ones();\n  Vector4d v = Vector4d::Ones();\n  A*v;\n}\n\n// check a compilation issue with numext::max\ndouble bug_1261() {\n  typedef AutoDiffScalar<Matrix2d> AD;\n  typedef Matrix<AD,2,1> VectorAD;\n\n  VectorAD v(0.,0.);\n  const AD maxVal = v.maxCoeff();\n  const AD minVal = v.minCoeff();\n  return maxVal.value() + minVal.value();\n}\n\ndouble bug_1264() {\n  typedef AutoDiffScalar<Vector2d> AD;\n  const AD s = 0.;\n  const Matrix<AD, 3, 1> v1(0.,0.,0.);\n  const Matrix<AD, 3, 1> v2 = (s + 3.0) * v1;\n  return v2(0).value();\n}\n\n#endif\n\nvoid test_autodiff()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( test_autodiff_scalar<1>() );\n    CALL_SUBTEST_2( test_autodiff_vector<1>() );\n    CALL_SUBTEST_3( test_autodiff_jacobian<1>() );\n    CALL_SUBTEST_4( test_autodiff_hessian<1>() );\n  }\n\n  CALL_SUBTEST_5( bug_1222() );\n  CALL_SUBTEST_5( bug_1223() );\n  CALL_SUBTEST_5( bug_1260() );\n  CALL_SUBTEST_5( bug_1261() );\n}\n\n"
  },
  {
    "path": "include/eigen3/unsupported/test/autodiff_scalar.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2013 Christoph Hertzberg <chtz@informatik.uni-bremen.de>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <unsupported/Eigen/AutoDiff>\n\n/*\n * In this file scalar derivations are tested for correctness.\n * TODO add more tests!\n */\n\ntemplate<typename Scalar> void check_atan2()\n{\n  typedef Matrix<Scalar, 1, 1> Deriv1;\n  typedef AutoDiffScalar<Deriv1> AD;\n  \n  AD x(internal::random<Scalar>(-3.0, 3.0), Deriv1::UnitX());\n  \n  using std::exp;\n  Scalar r = exp(internal::random<Scalar>(-10, 10));\n  \n  AD s = sin(x), c = cos(x);\n  AD res = atan2(r*s, r*c);\n  \n  VERIFY_IS_APPROX(res.value(), x.value());\n  VERIFY_IS_APPROX(res.derivatives(), x.derivatives());\n\n  res = atan2(r*s+0, r*c+0);\n  VERIFY_IS_APPROX(res.value(), x.value());\n  VERIFY_IS_APPROX(res.derivatives(), x.derivatives());\n}\n\ntemplate<typename Scalar> void check_hyperbolic_functions()\n{\n  using std::sinh;\n  using std::cosh;\n  using std::tanh;\n  typedef Matrix<Scalar, 1, 1> Deriv1;\n  typedef AutoDiffScalar<Deriv1> AD;\n  Deriv1 p = Deriv1::Random();\n  AD val(p.x(),Deriv1::UnitX());\n\n  Scalar cosh_px = std::cosh(p.x());\n  AD res1 = tanh(val);\n  VERIFY_IS_APPROX(res1.value(), std::tanh(p.x()));\n  VERIFY_IS_APPROX(res1.derivatives().x(), Scalar(1.0) / (cosh_px * cosh_px));\n\n  AD res2 = sinh(val);\n  VERIFY_IS_APPROX(res2.value(), std::sinh(p.x()));\n  VERIFY_IS_APPROX(res2.derivatives().x(), cosh_px);\n\n  AD res3 = cosh(val);\n  VERIFY_IS_APPROX(res3.value(), cosh_px);\n  VERIFY_IS_APPROX(res3.derivatives().x(), std::sinh(p.x()));\n\n  // Check constant values.\n  const Scalar sample_point = Scalar(1) / Scalar(3); \n  val = AD(sample_point,Deriv1::UnitX());\n  res1 = tanh(val);\n  VERIFY_IS_APPROX(res1.derivatives().x(), Scalar(0.896629559604914));\n\n  res2 = sinh(val);\n  VERIFY_IS_APPROX(res2.derivatives().x(), Scalar(1.056071867829939));\n\n  res3 = cosh(val);\n  VERIFY_IS_APPROX(res3.derivatives().x(), Scalar(0.339540557256150));\n}\n\ntemplate <typename Scalar>\nvoid check_limits_specialization()\n{\n  typedef Eigen::Matrix<Scalar, 1, 1> Deriv;\n  typedef Eigen::AutoDiffScalar<Deriv> AD;\n\n  typedef std::numeric_limits<AD> A;\n  typedef std::numeric_limits<Scalar> B;\n\n  // workaround \"unsed typedef\" warning:\n  VERIFY(!bool(internal::is_same<B, A>::value));\n\n#if EIGEN_HAS_CXX11\n  VERIFY(bool(std::is_base_of<B, A>::value));\n#endif\n}\n\nvoid test_autodiff_scalar()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1( check_atan2<float>() );\n    CALL_SUBTEST_2( check_atan2<double>() );\n    CALL_SUBTEST_3( check_hyperbolic_functions<float>() );\n    CALL_SUBTEST_4( check_hyperbolic_functions<double>() );\n    CALL_SUBTEST_5( check_limits_specialization<double>());\n  }\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_eventcount.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Dmitry Vyukov <dvyukov@google.com>\n// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define EIGEN_USE_THREADS\n#include \"main.h\"\n#include <Eigen/CXX11/ThreadPool>\n\n// Visual studio doesn't implement a rand_r() function since its\n// implementation of rand() is already thread safe\nint rand_reentrant(unsigned int* s) {\n#ifdef EIGEN_COMP_MSVC_STRICT\n  EIGEN_UNUSED_VARIABLE(s);\n  return rand();\n#else\n  return rand_r(s);\n#endif\n}\n\nstatic void test_basic_eventcount()\n{\n  MaxSizeVector<EventCount::Waiter> waiters(1);\n  waiters.resize(1);\n  EventCount ec(waiters);\n  EventCount::Waiter& w = waiters[0];\n  ec.Notify(false);\n  ec.Prewait(&w);\n  ec.Notify(true);\n  ec.CommitWait(&w);\n  ec.Prewait(&w);\n  ec.CancelWait(&w);\n}\n\n// Fake bounded counter-based queue.\nstruct TestQueue {\n  std::atomic<int> val_;\n  static const int kQueueSize = 10;\n\n  TestQueue() : val_() {}\n\n  ~TestQueue() { VERIFY_IS_EQUAL(val_.load(), 0); }\n\n  bool Push() {\n    int val = val_.load(std::memory_order_relaxed);\n    for (;;) {\n      VERIFY_GE(val, 0);\n      VERIFY_LE(val, kQueueSize);\n      if (val == kQueueSize) return false;\n      if (val_.compare_exchange_weak(val, val + 1, std::memory_order_relaxed))\n        return true;\n    }\n  }\n\n  bool Pop() {\n    int val = val_.load(std::memory_order_relaxed);\n    for (;;) {\n      VERIFY_GE(val, 0);\n      VERIFY_LE(val, kQueueSize);\n      if (val == 0) return false;\n      if (val_.compare_exchange_weak(val, val - 1, std::memory_order_relaxed))\n        return true;\n    }\n  }\n\n  bool Empty() { return val_.load(std::memory_order_relaxed) == 0; }\n};\n\nconst int TestQueue::kQueueSize;\n\n// A number of producers send messages to a set of consumers using a set of\n// fake queues. Ensure that it does not crash, consumers don't deadlock and\n// number of blocked and unblocked threads match.\nstatic void test_stress_eventcount()\n{\n  const int kThreads = std::thread::hardware_concurrency();\n  static const int kEvents = 1 << 16;\n  static const int kQueues = 10;\n\n  MaxSizeVector<EventCount::Waiter> waiters(kThreads);\n  waiters.resize(kThreads);\n  EventCount ec(waiters);\n  TestQueue queues[kQueues];\n\n  std::vector<std::unique_ptr<std::thread>> producers;\n  for (int i = 0; i < kThreads; i++) {\n    producers.emplace_back(new std::thread([&ec, &queues]() {\n      unsigned int rnd = static_cast<unsigned int>(std::hash<std::thread::id>()(std::this_thread::get_id()));\n      for (int j = 0; j < kEvents; j++) {\n        unsigned idx = rand_reentrant(&rnd) % kQueues;\n        if (queues[idx].Push()) {\n          ec.Notify(false);\n          continue;\n        }\n        EIGEN_THREAD_YIELD();\n        j--;\n      }\n    }));\n  }\n\n  std::vector<std::unique_ptr<std::thread>> consumers;\n  for (int i = 0; i < kThreads; i++) {\n    consumers.emplace_back(new std::thread([&ec, &queues, &waiters, i]() {\n      EventCount::Waiter& w = waiters[i];\n      unsigned int rnd = static_cast<unsigned int>(std::hash<std::thread::id>()(std::this_thread::get_id()));\n      for (int j = 0; j < kEvents; j++) {\n        unsigned idx = rand_reentrant(&rnd) % kQueues;\n        if (queues[idx].Pop()) continue;\n        j--;\n        ec.Prewait(&w);\n        bool empty = true;\n        for (int q = 0; q < kQueues; q++) {\n          if (!queues[q].Empty()) {\n            empty = false;\n            break;\n          }\n        }\n        if (!empty) {\n          ec.CancelWait(&w);\n          continue;\n        }\n        ec.CommitWait(&w);\n      }\n    }));\n  }\n\n  for (int i = 0; i < kThreads; i++) {\n    producers[i]->join();\n    consumers[i]->join();\n  }\n}\n\nvoid test_cxx11_eventcount()\n{\n  CALL_SUBTEST(test_basic_eventcount());\n  CALL_SUBTEST(test_stress_eventcount());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_meta.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2013 Christian Seiler <christian@iwakd.de>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <array>\n#include <Eigen/CXX11/src/util/CXX11Meta.h>\n\nusing Eigen::internal::is_same;\nusing Eigen::internal::type_list;\nusing Eigen::internal::numeric_list;\nusing Eigen::internal::gen_numeric_list;\nusing Eigen::internal::gen_numeric_list_reversed;\nusing Eigen::internal::gen_numeric_list_swapped_pair;\nusing Eigen::internal::gen_numeric_list_repeated;\nusing Eigen::internal::concat;\nusing Eigen::internal::mconcat;\nusing Eigen::internal::take;\nusing Eigen::internal::skip;\nusing Eigen::internal::slice;\nusing Eigen::internal::get;\nusing Eigen::internal::id_numeric;\nusing Eigen::internal::id_type;\nusing Eigen::internal::is_same_gf;\nusing Eigen::internal::apply_op_from_left;\nusing Eigen::internal::apply_op_from_right;\nusing Eigen::internal::contained_in_list;\nusing Eigen::internal::contained_in_list_gf;\nusing Eigen::internal::arg_prod;\nusing Eigen::internal::arg_sum;\nusing Eigen::internal::sum_op;\nusing Eigen::internal::product_op;\nusing Eigen::internal::array_reverse;\nusing Eigen::internal::array_sum;\nusing Eigen::internal::array_prod;\nusing Eigen::internal::array_reduce;\nusing Eigen::internal::array_zip;\nusing Eigen::internal::array_zip_and_reduce;\nusing Eigen::internal::array_apply;\nusing Eigen::internal::array_apply_and_reduce;\nusing Eigen::internal::repeat;\nusing Eigen::internal::instantiate_by_c_array;\n\nstruct dummy_a {};\nstruct dummy_b {};\nstruct dummy_c {};\nstruct dummy_d {};\nstruct dummy_e {};\n\n// dummy operation for testing apply\ntemplate<typename A, typename B> struct dummy_op;\ntemplate<> struct dummy_op<dummy_a, dummy_b> { typedef dummy_c type; };\ntemplate<> struct dummy_op<dummy_b, dummy_a> { typedef dummy_d type; };\ntemplate<> struct dummy_op<dummy_b, dummy_c> { typedef dummy_a type; };\ntemplate<> struct dummy_op<dummy_c, dummy_b> { typedef dummy_d type; };\ntemplate<> struct dummy_op<dummy_c, dummy_a> { typedef dummy_b type; };\ntemplate<> struct dummy_op<dummy_a, dummy_c> { typedef dummy_d type; };\ntemplate<> struct dummy_op<dummy_a, dummy_a> { typedef dummy_e type; };\ntemplate<> struct dummy_op<dummy_b, dummy_b> { typedef dummy_e type; };\ntemplate<> struct dummy_op<dummy_c, dummy_c> { typedef dummy_e type; };\n\ntemplate<typename A, typename B> struct dummy_test { constexpr static bool value = false; constexpr static int global_flags = 0; };\ntemplate<> struct dummy_test<dummy_a, dummy_a>     { constexpr static bool value = true;  constexpr static int global_flags = 1; };\ntemplate<> struct dummy_test<dummy_b, dummy_b>     { constexpr static bool value = true;  constexpr static int global_flags = 2; };\ntemplate<> struct dummy_test<dummy_c, dummy_c>     { constexpr static bool value = true;  constexpr static int global_flags = 4; };\n\nstruct times2_op { template<typename A> static A run(A v) { return v * 2; } };\n\nstruct dummy_inst\n{\n  int c;\n\n  dummy_inst() : c(0) {}\n  explicit dummy_inst(int) : c(1) {}\n  dummy_inst(int, int) : c(2) {}\n  dummy_inst(int, int, int) : c(3) {}\n  dummy_inst(int, int, int, int) : c(4) {}\n  dummy_inst(int, int, int, int, int) : c(5) {}\n};\n\nstatic void test_gen_numeric_list()\n{\n  VERIFY((is_same<typename gen_numeric_list<int, 0>::type, numeric_list<int>>::value));\n  VERIFY((is_same<typename gen_numeric_list<int, 1>::type, numeric_list<int, 0>>::value));\n  VERIFY((is_same<typename gen_numeric_list<int, 2>::type, numeric_list<int, 0, 1>>::value));\n  VERIFY((is_same<typename gen_numeric_list<int, 5>::type, numeric_list<int, 0, 1, 2, 3, 4>>::value));\n  VERIFY((is_same<typename gen_numeric_list<int, 10>::type, numeric_list<int, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9>>::value));\n\n  VERIFY((is_same<typename gen_numeric_list<int, 0, 42>::type, numeric_list<int>>::value));\n  VERIFY((is_same<typename gen_numeric_list<int, 1, 42>::type, numeric_list<int, 42>>::value));\n  VERIFY((is_same<typename gen_numeric_list<int, 2, 42>::type, numeric_list<int, 42, 43>>::value));\n  VERIFY((is_same<typename gen_numeric_list<int, 5, 42>::type, numeric_list<int, 42, 43, 44, 45, 46>>::value));\n  VERIFY((is_same<typename gen_numeric_list<int, 10, 42>::type, numeric_list<int, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51>>::value));\n\n  VERIFY((is_same<typename gen_numeric_list_reversed<int, 0>::type, numeric_list<int>>::value));\n  VERIFY((is_same<typename gen_numeric_list_reversed<int, 1>::type, numeric_list<int, 0>>::value));\n  VERIFY((is_same<typename gen_numeric_list_reversed<int, 2>::type, numeric_list<int, 1, 0>>::value));\n  VERIFY((is_same<typename gen_numeric_list_reversed<int, 5>::type, numeric_list<int, 4, 3, 2, 1, 0>>::value));\n  VERIFY((is_same<typename gen_numeric_list_reversed<int, 10>::type, numeric_list<int, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0>>::value));\n\n  VERIFY((is_same<typename gen_numeric_list_reversed<int, 0, 42>::type, numeric_list<int>>::value));\n  VERIFY((is_same<typename gen_numeric_list_reversed<int, 1, 42>::type, numeric_list<int, 42>>::value));\n  VERIFY((is_same<typename gen_numeric_list_reversed<int, 2, 42>::type, numeric_list<int, 43, 42>>::value));\n  VERIFY((is_same<typename gen_numeric_list_reversed<int, 5, 42>::type, numeric_list<int, 46, 45, 44, 43, 42>>::value));\n  VERIFY((is_same<typename gen_numeric_list_reversed<int, 10, 42>::type, numeric_list<int, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42>>::value));\n\n  VERIFY((is_same<typename gen_numeric_list_swapped_pair<int, 0, 2, 3>::type, numeric_list<int>>::value));\n  VERIFY((is_same<typename gen_numeric_list_swapped_pair<int, 1, 2, 3>::type, numeric_list<int, 0>>::value));\n  VERIFY((is_same<typename gen_numeric_list_swapped_pair<int, 2, 2, 3>::type, numeric_list<int, 0, 1>>::value));\n  VERIFY((is_same<typename gen_numeric_list_swapped_pair<int, 5, 2, 3>::type, numeric_list<int, 0, 1, 3, 2, 4>>::value));\n  VERIFY((is_same<typename gen_numeric_list_swapped_pair<int, 10, 2, 3>::type, numeric_list<int, 0, 1, 3, 2, 4, 5, 6, 7, 8, 9>>::value));\n\n  VERIFY((is_same<typename gen_numeric_list_swapped_pair<int, 0, 44, 45, 42>::type, numeric_list<int>>::value));\n  VERIFY((is_same<typename gen_numeric_list_swapped_pair<int, 1, 44, 45, 42>::type, numeric_list<int, 42>>::value));\n  VERIFY((is_same<typename gen_numeric_list_swapped_pair<int, 2, 44, 45, 42>::type, numeric_list<int, 42, 43>>::value));\n  VERIFY((is_same<typename gen_numeric_list_swapped_pair<int, 5, 44, 45, 42>::type, numeric_list<int, 42, 43, 45, 44, 46>>::value));\n  VERIFY((is_same<typename gen_numeric_list_swapped_pair<int, 10, 44, 45, 42>::type, numeric_list<int, 42, 43, 45, 44, 46, 47, 48, 49, 50, 51>>::value));\n\n  VERIFY((is_same<typename gen_numeric_list_repeated<int, 0, 0>::type, numeric_list<int>>::value));\n  VERIFY((is_same<typename gen_numeric_list_repeated<int, 1, 0>::type, numeric_list<int, 0>>::value));\n  VERIFY((is_same<typename gen_numeric_list_repeated<int, 2, 0>::type, numeric_list<int, 0, 0>>::value));\n  VERIFY((is_same<typename gen_numeric_list_repeated<int, 5, 0>::type, numeric_list<int, 0, 0, 0, 0, 0>>::value));\n  VERIFY((is_same<typename gen_numeric_list_repeated<int, 10, 0>::type, numeric_list<int, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0>>::value));\n}\n\nstatic void test_concat()\n{\n  VERIFY((is_same<typename concat<type_list<dummy_a, dummy_a>, type_list<>>::type, type_list<dummy_a, dummy_a>>::value));\n  VERIFY((is_same<typename concat<type_list<>, type_list<dummy_a, dummy_a>>::type, type_list<dummy_a, dummy_a>>::value));\n  VERIFY((is_same<typename concat<type_list<dummy_a, dummy_a>, type_list<dummy_a, dummy_a>>::type, type_list<dummy_a, dummy_a, dummy_a, dummy_a>>::value));\n  VERIFY((is_same<typename concat<type_list<dummy_a, dummy_a>, type_list<dummy_b, dummy_c>>::type, type_list<dummy_a, dummy_a, dummy_b, dummy_c>>::value));\n  VERIFY((is_same<typename concat<type_list<dummy_a>, type_list<dummy_b, dummy_c>>::type, type_list<dummy_a, dummy_b, dummy_c>>::value));\n\n  VERIFY((is_same<typename concat<numeric_list<int, 0, 0>, numeric_list<int>>::type, numeric_list<int, 0, 0>>::value));\n  VERIFY((is_same<typename concat<numeric_list<int>, numeric_list<int, 0, 0>>::type, numeric_list<int, 0, 0>>::value));\n  VERIFY((is_same<typename concat<numeric_list<int, 0, 0>, numeric_list<int, 0, 0>>::type, numeric_list<int, 0, 0, 0, 0>>::value));\n  VERIFY((is_same<typename concat<numeric_list<int, 0, 0>, numeric_list<int, 1, 2>>::type, numeric_list<int, 0, 0, 1, 2>>::value));\n  VERIFY((is_same<typename concat<numeric_list<int, 0>, numeric_list<int, 1, 2>>::type, numeric_list<int, 0, 1, 2>>::value));\n\n  VERIFY((is_same<typename mconcat<type_list<dummy_a>>::type, type_list<dummy_a>>::value));\n  VERIFY((is_same<typename mconcat<type_list<dummy_a>, type_list<dummy_b>>::type, type_list<dummy_a, dummy_b>>::value));\n  VERIFY((is_same<typename mconcat<type_list<dummy_a>, type_list<dummy_b>, type_list<dummy_c>>::type, type_list<dummy_a, dummy_b, dummy_c>>::value));\n  VERIFY((is_same<typename mconcat<type_list<dummy_a>, type_list<dummy_b, dummy_c>>::type, type_list<dummy_a, dummy_b, dummy_c>>::value));\n  VERIFY((is_same<typename mconcat<type_list<dummy_a, dummy_b>, type_list<dummy_c>>::type, type_list<dummy_a, dummy_b, dummy_c>>::value));\n\n  VERIFY((is_same<typename mconcat<numeric_list<int, 0>>::type, numeric_list<int, 0>>::value));\n  VERIFY((is_same<typename mconcat<numeric_list<int, 0>, numeric_list<int, 1>>::type, numeric_list<int, 0, 1>>::value));\n  VERIFY((is_same<typename mconcat<numeric_list<int, 0>, numeric_list<int, 1>, numeric_list<int, 2>>::type, numeric_list<int, 0, 1, 2>>::value));\n  VERIFY((is_same<typename mconcat<numeric_list<int, 0>, numeric_list<int, 1, 2>>::type, numeric_list<int, 0, 1, 2>>::value));\n  VERIFY((is_same<typename mconcat<numeric_list<int, 0, 1>, numeric_list<int, 2>>::type, numeric_list<int, 0, 1, 2>>::value));\n}\n\nstatic void test_slice()\n{\n  typedef type_list<dummy_a, dummy_a, dummy_b, dummy_b, dummy_c, dummy_c> tl;\n  typedef numeric_list<int, 0, 1, 2, 3, 4, 5> il;\n\n  VERIFY((is_same<typename take<0, tl>::type, type_list<>>::value));\n  VERIFY((is_same<typename take<1, tl>::type, type_list<dummy_a>>::value));\n  VERIFY((is_same<typename take<2, tl>::type, type_list<dummy_a, dummy_a>>::value));\n  VERIFY((is_same<typename take<3, tl>::type, type_list<dummy_a, dummy_a, dummy_b>>::value));\n  VERIFY((is_same<typename take<4, tl>::type, type_list<dummy_a, dummy_a, dummy_b, dummy_b>>::value));\n  VERIFY((is_same<typename take<5, tl>::type, type_list<dummy_a, dummy_a, dummy_b, dummy_b, dummy_c>>::value));\n  VERIFY((is_same<typename take<6, tl>::type, type_list<dummy_a, dummy_a, dummy_b, dummy_b, dummy_c, dummy_c>>::value));\n\n  VERIFY((is_same<typename take<0, il>::type, numeric_list<int>>::value));\n  VERIFY((is_same<typename take<1, il>::type, numeric_list<int, 0>>::value));\n  VERIFY((is_same<typename take<2, il>::type, numeric_list<int, 0, 1>>::value));\n  VERIFY((is_same<typename take<3, il>::type, numeric_list<int, 0, 1, 2>>::value));\n  VERIFY((is_same<typename take<4, il>::type, numeric_list<int, 0, 1, 2, 3>>::value));\n  VERIFY((is_same<typename take<5, il>::type, numeric_list<int, 0, 1, 2, 3, 4>>::value));\n  VERIFY((is_same<typename take<6, il>::type, numeric_list<int, 0, 1, 2, 3, 4, 5>>::value));\n  \n  VERIFY((is_same<typename skip<0, tl>::type, type_list<dummy_a, dummy_a, dummy_b, dummy_b, dummy_c, dummy_c>>::value));\n  VERIFY((is_same<typename skip<1, tl>::type, type_list<dummy_a, dummy_b, dummy_b, dummy_c, dummy_c>>::value));\n  VERIFY((is_same<typename skip<2, tl>::type, type_list<dummy_b, dummy_b, dummy_c, dummy_c>>::value));\n  VERIFY((is_same<typename skip<3, tl>::type, type_list<dummy_b, dummy_c, dummy_c>>::value));\n  VERIFY((is_same<typename skip<4, tl>::type, type_list<dummy_c, dummy_c>>::value));\n  VERIFY((is_same<typename skip<5, tl>::type, type_list<dummy_c>>::value));\n  VERIFY((is_same<typename skip<6, tl>::type, type_list<>>::value));\n\n  VERIFY((is_same<typename skip<0, il>::type, numeric_list<int, 0, 1, 2, 3, 4, 5>>::value));\n  VERIFY((is_same<typename skip<1, il>::type, numeric_list<int, 1, 2, 3, 4, 5>>::value));\n  VERIFY((is_same<typename skip<2, il>::type, numeric_list<int, 2, 3, 4, 5>>::value));\n  VERIFY((is_same<typename skip<3, il>::type, numeric_list<int, 3, 4, 5>>::value));\n  VERIFY((is_same<typename skip<4, il>::type, numeric_list<int, 4, 5>>::value));\n  VERIFY((is_same<typename skip<5, il>::type, numeric_list<int, 5>>::value));\n  VERIFY((is_same<typename skip<6, il>::type, numeric_list<int>>::value));\n\n  VERIFY((is_same<typename slice<0, 3, tl>::type, typename take<3, tl>::type>::value));\n  VERIFY((is_same<typename slice<0, 3, il>::type, typename take<3, il>::type>::value));\n  VERIFY((is_same<typename slice<1, 3, tl>::type, type_list<dummy_a, dummy_b, dummy_b>>::value));\n  VERIFY((is_same<typename slice<1, 3, il>::type, numeric_list<int, 1, 2, 3>>::value));\n}\n\nstatic void test_get()\n{\n  typedef type_list<dummy_a, dummy_a, dummy_b, dummy_b, dummy_c, dummy_c> tl;\n  typedef numeric_list<int, 4, 8, 15, 16, 23, 42> il;\n\n  VERIFY((is_same<typename get<0, tl>::type, dummy_a>::value));\n  VERIFY((is_same<typename get<1, tl>::type, dummy_a>::value));\n  VERIFY((is_same<typename get<2, tl>::type, dummy_b>::value));\n  VERIFY((is_same<typename get<3, tl>::type, dummy_b>::value));\n  VERIFY((is_same<typename get<4, tl>::type, dummy_c>::value));\n  VERIFY((is_same<typename get<5, tl>::type, dummy_c>::value));\n\n  VERIFY_IS_EQUAL(((int)get<0, il>::value), 4);\n  VERIFY_IS_EQUAL(((int)get<1, il>::value), 8);\n  VERIFY_IS_EQUAL(((int)get<2, il>::value), 15);\n  VERIFY_IS_EQUAL(((int)get<3, il>::value), 16);\n  VERIFY_IS_EQUAL(((int)get<4, il>::value), 23);\n  VERIFY_IS_EQUAL(((int)get<5, il>::value), 42);\n}\n\nstatic void test_id_helper(dummy_a a, dummy_a b, dummy_a c)\n{\n  (void)a;\n  (void)b;\n  (void)c;\n}\n\ntemplate<int... ii>\nstatic void test_id_numeric()\n{\n  test_id_helper(typename id_numeric<int, ii, dummy_a>::type()...);\n}\n\ntemplate<typename... tt>\nstatic void test_id_type()\n{\n  test_id_helper(typename id_type<tt, dummy_a>::type()...);\n}\n\nstatic void test_id()\n{\n  // don't call VERIFY here, just assume it works if it compiles\n  // (otherwise it will complain that it can't find the function)\n  test_id_numeric<1, 4, 6>();\n  test_id_type<dummy_a, dummy_b, dummy_c>();\n}\n\nstatic void test_is_same_gf()\n{\n  VERIFY((!is_same_gf<dummy_a, dummy_b>::value));\n  VERIFY((!!is_same_gf<dummy_a, dummy_a>::value));\n  VERIFY_IS_EQUAL((!!is_same_gf<dummy_a, dummy_b>::global_flags), false);\n  VERIFY_IS_EQUAL((!!is_same_gf<dummy_a, dummy_a>::global_flags), false);\n}\n\nstatic void test_apply_op()\n{\n  typedef type_list<dummy_a, dummy_b, dummy_c> tl;\n  VERIFY((!!is_same<typename apply_op_from_left<dummy_op, dummy_a, tl>::type, type_list<dummy_e, dummy_c, dummy_d>>::value));\n  VERIFY((!!is_same<typename apply_op_from_right<dummy_op, dummy_a, tl>::type, type_list<dummy_e, dummy_d, dummy_b>>::value));\n}\n\nstatic void test_contained_in_list()\n{\n  typedef type_list<dummy_a, dummy_b, dummy_c> tl;\n\n  VERIFY((!!contained_in_list<is_same, dummy_a, tl>::value));\n  VERIFY((!!contained_in_list<is_same, dummy_b, tl>::value));\n  VERIFY((!!contained_in_list<is_same, dummy_c, tl>::value));\n  VERIFY((!contained_in_list<is_same, dummy_d, tl>::value));\n  VERIFY((!contained_in_list<is_same, dummy_e, tl>::value));\n\n  VERIFY((!!contained_in_list_gf<dummy_test, dummy_a, tl>::value));\n  VERIFY((!!contained_in_list_gf<dummy_test, dummy_b, tl>::value));\n  VERIFY((!!contained_in_list_gf<dummy_test, dummy_c, tl>::value));\n  VERIFY((!contained_in_list_gf<dummy_test, dummy_d, tl>::value));\n  VERIFY((!contained_in_list_gf<dummy_test, dummy_e, tl>::value));\n\n  VERIFY_IS_EQUAL(((int)contained_in_list_gf<dummy_test, dummy_a, tl>::global_flags), 1);\n  VERIFY_IS_EQUAL(((int)contained_in_list_gf<dummy_test, dummy_b, tl>::global_flags), 2);\n  VERIFY_IS_EQUAL(((int)contained_in_list_gf<dummy_test, dummy_c, tl>::global_flags), 4);\n  VERIFY_IS_EQUAL(((int)contained_in_list_gf<dummy_test, dummy_d, tl>::global_flags), 0);\n  VERIFY_IS_EQUAL(((int)contained_in_list_gf<dummy_test, dummy_e, tl>::global_flags), 0);\n}\n\nstatic void test_arg_reductions()\n{\n  VERIFY_IS_EQUAL(arg_sum(1,2,3,4), 10);\n  VERIFY_IS_EQUAL(arg_prod(1,2,3,4), 24);\n  VERIFY_IS_APPROX(arg_sum(0.5, 2, 5), 7.5);\n  VERIFY_IS_APPROX(arg_prod(0.5, 2, 5), 5.0);\n}\n\nstatic void test_array_reverse_and_reduce()\n{\n  array<int, 6> a{{4, 8, 15, 16, 23, 42}};\n  array<int, 6> b{{42, 23, 16, 15, 8, 4}};\n\n  // there is no operator<< for std::array, so VERIFY_IS_EQUAL will\n  // not compile\n  VERIFY((array_reverse(a) == b));\n  VERIFY((array_reverse(b) == a));\n  VERIFY_IS_EQUAL((array_sum(a)), 108);\n  VERIFY_IS_EQUAL((array_sum(b)), 108);\n  VERIFY_IS_EQUAL((array_prod(a)), 7418880);\n  VERIFY_IS_EQUAL((array_prod(b)), 7418880);\n}\n\nstatic void test_array_zip_and_apply()\n{\n  array<int, 6> a{{4, 8, 15, 16, 23, 42}};\n  array<int, 6> b{{0, 1, 2, 3, 4, 5}};\n  array<int, 6> c{{4, 9, 17, 19, 27, 47}};\n  array<int, 6> d{{0, 8, 30, 48, 92, 210}};\n  array<int, 6> e{{0, 2, 4, 6, 8, 10}};\n\n  VERIFY((array_zip<sum_op>(a, b) == c));\n  VERIFY((array_zip<product_op>(a, b) == d));\n  VERIFY((array_apply<times2_op>(b) == e));\n  VERIFY_IS_EQUAL((array_apply_and_reduce<sum_op, times2_op>(a)), 216);\n  VERIFY_IS_EQUAL((array_apply_and_reduce<sum_op, times2_op>(b)), 30);\n  VERIFY_IS_EQUAL((array_zip_and_reduce<product_op, sum_op>(a, b)), 14755932);\n  VERIFY_IS_EQUAL((array_zip_and_reduce<sum_op, product_op>(a, b)), 388);\n}\n\nstatic void test_array_misc()\n{\n  array<int, 3> a3{{1, 1, 1}};\n  array<int, 6> a6{{2, 2, 2, 2, 2, 2}};\n  VERIFY((repeat<3, int>(1) == a3));\n  VERIFY((repeat<6, int>(2) == a6));\n\n  int data[5] = { 0, 1, 2, 3, 4 };\n  VERIFY_IS_EQUAL((instantiate_by_c_array<dummy_inst, int, 0>(data).c), 0);\n  VERIFY_IS_EQUAL((instantiate_by_c_array<dummy_inst, int, 1>(data).c), 1);\n  VERIFY_IS_EQUAL((instantiate_by_c_array<dummy_inst, int, 2>(data).c), 2);\n  VERIFY_IS_EQUAL((instantiate_by_c_array<dummy_inst, int, 3>(data).c), 3);\n  VERIFY_IS_EQUAL((instantiate_by_c_array<dummy_inst, int, 4>(data).c), 4);\n  VERIFY_IS_EQUAL((instantiate_by_c_array<dummy_inst, int, 5>(data).c), 5);\n}\n\nvoid test_cxx11_meta()\n{\n  CALL_SUBTEST(test_gen_numeric_list());\n  CALL_SUBTEST(test_concat());\n  CALL_SUBTEST(test_slice());\n  CALL_SUBTEST(test_get());\n  CALL_SUBTEST(test_id());\n  CALL_SUBTEST(test_is_same_gf());\n  CALL_SUBTEST(test_apply_op());\n  CALL_SUBTEST(test_contained_in_list());\n  CALL_SUBTEST(test_arg_reductions());\n  CALL_SUBTEST(test_array_reverse_and_reduce());\n  CALL_SUBTEST(test_array_zip_and_apply());\n  CALL_SUBTEST(test_array_misc());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_non_blocking_thread_pool.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Dmitry Vyukov <dvyukov@google.com>\n// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define EIGEN_USE_THREADS\n#include \"main.h\"\n#include \"Eigen/CXX11/ThreadPool\"\n\nstatic void test_create_destroy_empty_pool()\n{\n  // Just create and destroy the pool. This will wind up and tear down worker\n  // threads. Ensure there are no issues in that logic.\n  for (int i = 0; i < 16; ++i) {\n    NonBlockingThreadPool tp(i);\n  }\n}\n\n\nstatic void test_parallelism()\n{\n  // Test we never-ever fail to match available tasks with idle threads.\n  const int kThreads = 16;  // code below expects that this is a multiple of 4\n  NonBlockingThreadPool tp(kThreads);\n  VERIFY_IS_EQUAL(tp.NumThreads(), kThreads);\n  VERIFY_IS_EQUAL(tp.CurrentThreadId(), -1);\n  for (int iter = 0; iter < 100; ++iter) {\n    std::atomic<int> running(0);\n    std::atomic<int> done(0);\n    std::atomic<int> phase(0);\n    // Schedule kThreads tasks and ensure that they all are running.\n    for (int i = 0; i < kThreads; ++i) {\n      tp.Schedule([&]() {\n        const int thread_id = tp.CurrentThreadId();\n        VERIFY_GE(thread_id, 0);\n        VERIFY_LE(thread_id, kThreads - 1);\n        running++;\n        while (phase < 1) {\n        }\n        done++;\n      });\n    }\n    while (running != kThreads) {\n    }\n    running = 0;\n    phase = 1;\n    // Now, while the previous tasks exit, schedule another kThreads tasks and\n    // ensure that they are running.\n    for (int i = 0; i < kThreads; ++i) {\n      tp.Schedule([&, i]() {\n        running++;\n        while (phase < 2) {\n        }\n        // When all tasks are running, half of tasks exit, quarter of tasks\n        // continue running and quarter of tasks schedule another 2 tasks each.\n        // Concurrently main thread schedules another quarter of tasks.\n        // This gives us another kThreads tasks and we ensure that they all\n        // are running.\n        if (i < kThreads / 2) {\n        } else if (i < 3 * kThreads / 4) {\n          running++;\n          while (phase < 3) {\n          }\n          done++;\n        } else {\n          for (int j = 0; j < 2; ++j) {\n            tp.Schedule([&]() {\n              running++;\n              while (phase < 3) {\n              }\n              done++;\n            });\n          }\n        }\n        done++;\n      });\n    }\n    while (running != kThreads) {\n    }\n    running = 0;\n    phase = 2;\n    for (int i = 0; i < kThreads / 4; ++i) {\n      tp.Schedule([&]() {\n        running++;\n        while (phase < 3) {\n        }\n        done++;\n      });\n    }\n    while (running != kThreads) {\n    }\n    phase = 3;\n    while (done != 3 * kThreads) {\n    }\n  }\n}\n\nvoid test_cxx11_non_blocking_thread_pool()\n{\n  CALL_SUBTEST(test_create_destroy_empty_pool());\n  CALL_SUBTEST(test_parallelism());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_runqueue.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Dmitry Vyukov <dvyukov@google.com>\n// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define EIGEN_USE_THREADS\n#include <cstdlib>\n#include \"main.h\"\n#include <Eigen/CXX11/ThreadPool>\n\n\n// Visual studio doesn't implement a rand_r() function since its\n// implementation of rand() is already thread safe\nint rand_reentrant(unsigned int* s) {\n#ifdef EIGEN_COMP_MSVC_STRICT\n  EIGEN_UNUSED_VARIABLE(s);\n  return rand();\n#else\n  return rand_r(s);\n#endif\n}\n\nvoid test_basic_runqueue()\n{\n  RunQueue<int, 4> q;\n  // Check empty state.\n  VERIFY(q.Empty());\n  VERIFY_IS_EQUAL(0u, q.Size());\n  VERIFY_IS_EQUAL(0, q.PopFront());\n  std::vector<int> stolen;\n  VERIFY_IS_EQUAL(0u, q.PopBackHalf(&stolen));\n  VERIFY_IS_EQUAL(0u, stolen.size());\n  // Push one front, pop one front.\n  VERIFY_IS_EQUAL(0, q.PushFront(1));\n  VERIFY_IS_EQUAL(1u, q.Size());\n  VERIFY_IS_EQUAL(1, q.PopFront());\n  VERIFY_IS_EQUAL(0u, q.Size());\n  // Push front to overflow.\n  VERIFY_IS_EQUAL(0, q.PushFront(2));\n  VERIFY_IS_EQUAL(1u, q.Size());\n  VERIFY_IS_EQUAL(0, q.PushFront(3));\n  VERIFY_IS_EQUAL(2u, q.Size());\n  VERIFY_IS_EQUAL(0, q.PushFront(4));\n  VERIFY_IS_EQUAL(3u, q.Size());\n  VERIFY_IS_EQUAL(0, q.PushFront(5));\n  VERIFY_IS_EQUAL(4u, q.Size());\n  VERIFY_IS_EQUAL(6, q.PushFront(6));\n  VERIFY_IS_EQUAL(4u, q.Size());\n  VERIFY_IS_EQUAL(5, q.PopFront());\n  VERIFY_IS_EQUAL(3u, q.Size());\n  VERIFY_IS_EQUAL(4, q.PopFront());\n  VERIFY_IS_EQUAL(2u, q.Size());\n  VERIFY_IS_EQUAL(3, q.PopFront());\n  VERIFY_IS_EQUAL(1u, q.Size());\n  VERIFY_IS_EQUAL(2, q.PopFront());\n  VERIFY_IS_EQUAL(0u, q.Size());\n  VERIFY_IS_EQUAL(0, q.PopFront());\n  // Push one back, pop one back.\n  VERIFY_IS_EQUAL(0, q.PushBack(7));\n  VERIFY_IS_EQUAL(1u, q.Size());\n  VERIFY_IS_EQUAL(1u, q.PopBackHalf(&stolen));\n  VERIFY_IS_EQUAL(1u, stolen.size());\n  VERIFY_IS_EQUAL(7, stolen[0]);\n  VERIFY_IS_EQUAL(0u, q.Size());\n  stolen.clear();\n  // Push back to overflow.\n  VERIFY_IS_EQUAL(0, q.PushBack(8));\n  VERIFY_IS_EQUAL(1u, q.Size());\n  VERIFY_IS_EQUAL(0, q.PushBack(9));\n  VERIFY_IS_EQUAL(2u, q.Size());\n  VERIFY_IS_EQUAL(0, q.PushBack(10));\n  VERIFY_IS_EQUAL(3u, q.Size());\n  VERIFY_IS_EQUAL(0, q.PushBack(11));\n  VERIFY_IS_EQUAL(4u, q.Size());\n  VERIFY_IS_EQUAL(12, q.PushBack(12));\n  VERIFY_IS_EQUAL(4u, q.Size());\n  // Pop back in halves.\n  VERIFY_IS_EQUAL(2u, q.PopBackHalf(&stolen));\n  VERIFY_IS_EQUAL(2u, stolen.size());\n  VERIFY_IS_EQUAL(10, stolen[0]);\n  VERIFY_IS_EQUAL(11, stolen[1]);\n  VERIFY_IS_EQUAL(2u, q.Size());\n  stolen.clear();\n  VERIFY_IS_EQUAL(1u, q.PopBackHalf(&stolen));\n  VERIFY_IS_EQUAL(1u, stolen.size());\n  VERIFY_IS_EQUAL(9, stolen[0]);\n  VERIFY_IS_EQUAL(1u, q.Size());\n  stolen.clear();\n  VERIFY_IS_EQUAL(1u, q.PopBackHalf(&stolen));\n  VERIFY_IS_EQUAL(1u, stolen.size());\n  VERIFY_IS_EQUAL(8, stolen[0]);\n  stolen.clear();\n  VERIFY_IS_EQUAL(0u, q.PopBackHalf(&stolen));\n  VERIFY_IS_EQUAL(0u, stolen.size());\n  // Empty again.\n  VERIFY(q.Empty());\n  VERIFY_IS_EQUAL(0u, q.Size());\n  VERIFY_IS_EQUAL(0, q.PushFront(1));\n  VERIFY_IS_EQUAL(0, q.PushFront(2));\n  VERIFY_IS_EQUAL(0, q.PushFront(3));\n  VERIFY_IS_EQUAL(1, q.PopBack());\n  VERIFY_IS_EQUAL(2, q.PopBack());\n  VERIFY_IS_EQUAL(3, q.PopBack());\n  VERIFY(q.Empty());\n  VERIFY_IS_EQUAL(0u, q.Size());\n}\n\n// Empty tests that the queue is not claimed to be empty when is is in fact not.\n// Emptiness property is crucial part of thread pool blocking scheme,\n// so we go to great effort to ensure this property. We create a queue with\n// 1 element and then push 1 element (either front or back at random) and pop\n// 1 element (either front or back at random). So queue always contains at least\n// 1 element, but otherwise changes chaotically. Another thread constantly tests\n// that the queue is not claimed to be empty.\nvoid test_empty_runqueue()\n{\n  RunQueue<int, 4> q;\n  q.PushFront(1);\n  std::atomic<bool> done(false);\n  std::thread mutator([&q, &done]() {\n    unsigned rnd = 0;\n    std::vector<int> stolen;\n    for (int i = 0; i < 1 << 18; i++) {\n      if (rand_reentrant(&rnd) % 2)\n        VERIFY_IS_EQUAL(0, q.PushFront(1));\n      else\n        VERIFY_IS_EQUAL(0, q.PushBack(1));\n      if (rand_reentrant(&rnd) % 2)\n        VERIFY_IS_EQUAL(1, q.PopFront());\n      else {\n        for (;;) {\n          if (q.PopBackHalf(&stolen) == 1) {\n            stolen.clear();\n            break;\n          }\n          VERIFY_IS_EQUAL(0u, stolen.size());\n        }\n      }\n    }\n    done = true;\n  });\n  while (!done) {\n    VERIFY(!q.Empty());\n    int size = q.Size();\n    VERIFY_GE(size, 1);\n    VERIFY_LE(size, 2);\n  }\n  VERIFY_IS_EQUAL(1, q.PopFront());\n  mutator.join();\n}\n\n// Stress is a chaotic random test.\n// One thread (owner) calls PushFront/PopFront, other threads call PushBack/\n// PopBack. Ensure that we don't crash, deadlock, and all sanity checks pass.\nvoid test_stress_runqueue()\n{\n  static const int kEvents = 1 << 18;\n  RunQueue<int, 8> q;\n  std::atomic<int> total(0);\n  std::vector<std::unique_ptr<std::thread>> threads;\n  threads.emplace_back(new std::thread([&q, &total]() {\n    int sum = 0;\n    int pushed = 1;\n    int popped = 1;\n    while (pushed < kEvents || popped < kEvents) {\n      if (pushed < kEvents) {\n        if (q.PushFront(pushed) == 0) {\n          sum += pushed;\n          pushed++;\n        }\n      }\n      if (popped < kEvents) {\n        int v = q.PopFront();\n        if (v != 0) {\n          sum -= v;\n          popped++;\n        }\n      }\n    }\n    total += sum;\n  }));\n  for (int i = 0; i < 2; i++) {\n    threads.emplace_back(new std::thread([&q, &total]() {\n      int sum = 0;\n      for (int j = 1; j < kEvents; j++) {\n        if (q.PushBack(j) == 0) {\n          sum += j;\n          continue;\n        }\n        EIGEN_THREAD_YIELD();\n        j--;\n      }\n      total += sum;\n    }));\n    threads.emplace_back(new std::thread([&q, &total]() {\n      int sum = 0;\n      std::vector<int> stolen;\n      for (int j = 1; j < kEvents;) {\n        if (q.PopBackHalf(&stolen) == 0) {\n          EIGEN_THREAD_YIELD();\n          continue;\n        }\n        while (stolen.size() && j < kEvents) {\n          int v = stolen.back();\n          stolen.pop_back();\n          VERIFY_IS_NOT_EQUAL(v, 0);\n          sum += v;\n          j++;\n        }\n      }\n      while (stolen.size()) {\n        int v = stolen.back();\n        stolen.pop_back();\n        VERIFY_IS_NOT_EQUAL(v, 0);\n        while ((v = q.PushBack(v)) != 0) EIGEN_THREAD_YIELD();\n      }\n      total -= sum;\n    }));\n  }\n  for (size_t i = 0; i < threads.size(); i++) threads[i]->join();\n  VERIFY(q.Empty());\n  VERIFY(total.load() == 0);\n}\n\nvoid test_cxx11_runqueue()\n{\n  CALL_SUBTEST_1(test_basic_runqueue());\n  CALL_SUBTEST_2(test_empty_runqueue());\n  CALL_SUBTEST_3(test_stress_runqueue());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_argmax.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Eugene Brevdo <ebrevdo@google.com>\n//                    Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\nusing Eigen::array;\nusing Eigen::Tuple;\n\ntemplate <int DataLayout>\nstatic void test_simple_index_tuples()\n{\n  Tensor<float, 4, DataLayout> tensor(2,3,5,7);\n  tensor.setRandom();\n  tensor = (tensor + tensor.constant(0.5)).log();\n\n  Tensor<Tuple<DenseIndex, float>, 4, DataLayout> index_tuples(2,3,5,7);\n  index_tuples = tensor.index_tuples();\n\n  for (DenseIndex n = 0; n < 2*3*5*7; ++n) {\n    const Tuple<DenseIndex, float>& v = index_tuples.coeff(n);\n    VERIFY_IS_EQUAL(v.first, n);\n    VERIFY_IS_EQUAL(v.second, tensor.coeff(n));\n  }\n}\n\ntemplate <int DataLayout>\nstatic void test_index_tuples_dim()\n{\n  Tensor<float, 4, DataLayout> tensor(2,3,5,7);\n  tensor.setRandom();\n  tensor = (tensor + tensor.constant(0.5)).log();\n\n  Tensor<Tuple<DenseIndex, float>, 4, DataLayout> index_tuples(2,3,5,7);\n\n  index_tuples = tensor.index_tuples();\n\n  for (Eigen::DenseIndex n = 0; n < tensor.size(); ++n) {\n    const Tuple<DenseIndex, float>& v = index_tuples(n); //(i, j, k, l);\n    VERIFY_IS_EQUAL(v.first, n);\n    VERIFY_IS_EQUAL(v.second, tensor(n));\n  }\n}\n\ntemplate <int DataLayout>\nstatic void test_argmax_tuple_reducer()\n{\n  Tensor<float, 4, DataLayout> tensor(2,3,5,7);\n  tensor.setRandom();\n  tensor = (tensor + tensor.constant(0.5)).log();\n\n  Tensor<Tuple<DenseIndex, float>, 4, DataLayout> index_tuples(2,3,5,7);\n  index_tuples = tensor.index_tuples();\n\n  Tensor<Tuple<DenseIndex, float>, 0, DataLayout> reduced;\n  DimensionList<DenseIndex, 4> dims;\n  reduced = index_tuples.reduce(\n      dims, internal::ArgMaxTupleReducer<Tuple<DenseIndex, float> >());\n\n  Tensor<float, 0, DataLayout> maxi = tensor.maximum();\n\n  VERIFY_IS_EQUAL(maxi(), reduced(0).second);\n\n  array<DenseIndex, 3> reduce_dims;\n  for (int d = 0; d < 3; ++d) reduce_dims[d] = d;\n  Tensor<Tuple<DenseIndex, float>, 1, DataLayout> reduced_by_dims(7);\n  reduced_by_dims = index_tuples.reduce(\n      reduce_dims, internal::ArgMaxTupleReducer<Tuple<DenseIndex, float> >());\n\n  Tensor<float, 1, DataLayout> max_by_dims = tensor.maximum(reduce_dims);\n\n  for (int l = 0; l < 7; ++l) {\n    VERIFY_IS_EQUAL(max_by_dims(l), reduced_by_dims(l).second);\n  }\n}\n\ntemplate <int DataLayout>\nstatic void test_argmin_tuple_reducer()\n{\n  Tensor<float, 4, DataLayout> tensor(2,3,5,7);\n  tensor.setRandom();\n  tensor = (tensor + tensor.constant(0.5)).log();\n\n  Tensor<Tuple<DenseIndex, float>, 4, DataLayout> index_tuples(2,3,5,7);\n  index_tuples = tensor.index_tuples();\n\n  Tensor<Tuple<DenseIndex, float>, 0, DataLayout> reduced;\n  DimensionList<DenseIndex, 4> dims;\n  reduced = index_tuples.reduce(\n      dims, internal::ArgMinTupleReducer<Tuple<DenseIndex, float> >());\n\n  Tensor<float, 0, DataLayout> mini = tensor.minimum();\n\n  VERIFY_IS_EQUAL(mini(), reduced(0).second);\n\n  array<DenseIndex, 3> reduce_dims;\n  for (int d = 0; d < 3; ++d) reduce_dims[d] = d;\n  Tensor<Tuple<DenseIndex, float>, 1, DataLayout> reduced_by_dims(7);\n  reduced_by_dims = index_tuples.reduce(\n      reduce_dims, internal::ArgMinTupleReducer<Tuple<DenseIndex, float> >());\n\n  Tensor<float, 1, DataLayout> min_by_dims = tensor.minimum(reduce_dims);\n\n  for (int l = 0; l < 7; ++l) {\n    VERIFY_IS_EQUAL(min_by_dims(l), reduced_by_dims(l).second);\n  }\n}\n\ntemplate <int DataLayout>\nstatic void test_simple_argmax()\n{\n  Tensor<float, 4, DataLayout> tensor(2,3,5,7);\n  tensor.setRandom();\n  tensor = (tensor + tensor.constant(0.5)).log();\n  tensor(0,0,0,0) = 10.0;\n\n  Tensor<DenseIndex, 0, DataLayout> tensor_argmax;\n\n  tensor_argmax = tensor.argmax();\n\n  VERIFY_IS_EQUAL(tensor_argmax(0), 0);\n\n  tensor(1,2,4,6) = 20.0;\n\n  tensor_argmax = tensor.argmax();\n\n  VERIFY_IS_EQUAL(tensor_argmax(0), 2*3*5*7 - 1);\n}\n\ntemplate <int DataLayout>\nstatic void test_simple_argmin()\n{\n  Tensor<float, 4, DataLayout> tensor(2,3,5,7);\n  tensor.setRandom();\n  tensor = (tensor + tensor.constant(0.5)).log();\n  tensor(0,0,0,0) = -10.0;\n\n  Tensor<DenseIndex, 0, DataLayout> tensor_argmin;\n\n  tensor_argmin = tensor.argmin();\n\n  VERIFY_IS_EQUAL(tensor_argmin(0), 0);\n\n  tensor(1,2,4,6) = -20.0;\n\n  tensor_argmin = tensor.argmin();\n\n  VERIFY_IS_EQUAL(tensor_argmin(0), 2*3*5*7 - 1);\n}\n\ntemplate <int DataLayout>\nstatic void test_argmax_dim()\n{\n  Tensor<float, 4, DataLayout> tensor(2,3,5,7);\n  std::vector<int> dims {2, 3, 5, 7};\n\n  for (int dim = 0; dim < 4; ++dim) {\n    tensor.setRandom();\n    tensor = (tensor + tensor.constant(0.5)).log();\n\n    Tensor<DenseIndex, 3, DataLayout> tensor_argmax;\n    array<DenseIndex, 4> ix;\n    for (int i = 0; i < 2; ++i) {\n      for (int j = 0; j < 3; ++j) {\n        for (int k = 0; k < 5; ++k) {\n          for (int l = 0; l < 7; ++l) {\n            ix[0] = i; ix[1] = j; ix[2] = k; ix[3] = l;\n            if (ix[dim] != 0) continue;\n            // suppose dim == 1, then for all i, k, l, set tensor(i, 0, k, l) = 10.0\n            tensor(ix) = 10.0;\n          }\n        }\n      }\n    }\n\n    tensor_argmax = tensor.argmax(dim);\n\n    VERIFY_IS_EQUAL(tensor_argmax.size(),\n                    ptrdiff_t(2*3*5*7 / tensor.dimension(dim)));\n    for (ptrdiff_t n = 0; n < tensor_argmax.size(); ++n) {\n      // Expect max to be in the first index of the reduced dimension\n      VERIFY_IS_EQUAL(tensor_argmax.data()[n], 0);\n    }\n\n    for (int i = 0; i < 2; ++i) {\n      for (int j = 0; j < 3; ++j) {\n        for (int k = 0; k < 5; ++k) {\n          for (int l = 0; l < 7; ++l) {\n            ix[0] = i; ix[1] = j; ix[2] = k; ix[3] = l;\n            if (ix[dim] != tensor.dimension(dim) - 1) continue;\n            // suppose dim == 1, then for all i, k, l, set tensor(i, 2, k, l) = 20.0\n            tensor(ix) = 20.0;\n          }\n        }\n      }\n    }\n\n    tensor_argmax = tensor.argmax(dim);\n\n    VERIFY_IS_EQUAL(tensor_argmax.size(),\n                    ptrdiff_t(2*3*5*7 / tensor.dimension(dim)));\n    for (ptrdiff_t n = 0; n < tensor_argmax.size(); ++n) {\n      // Expect max to be in the last index of the reduced dimension\n      VERIFY_IS_EQUAL(tensor_argmax.data()[n], tensor.dimension(dim) - 1);\n    }\n  }\n}\n\ntemplate <int DataLayout>\nstatic void test_argmin_dim()\n{\n  Tensor<float, 4, DataLayout> tensor(2,3,5,7);\n  std::vector<int> dims {2, 3, 5, 7};\n\n  for (int dim = 0; dim < 4; ++dim) {\n    tensor.setRandom();\n    tensor = (tensor + tensor.constant(0.5)).log();\n\n    Tensor<DenseIndex, 3, DataLayout> tensor_argmin;\n    array<DenseIndex, 4> ix;\n    for (int i = 0; i < 2; ++i) {\n      for (int j = 0; j < 3; ++j) {\n        for (int k = 0; k < 5; ++k) {\n          for (int l = 0; l < 7; ++l) {\n            ix[0] = i; ix[1] = j; ix[2] = k; ix[3] = l;\n            if (ix[dim] != 0) continue;\n            // suppose dim == 1, then for all i, k, l, set tensor(i, 0, k, l) = -10.0\n            tensor(ix) = -10.0;\n          }\n        }\n      }\n    }\n\n    tensor_argmin = tensor.argmin(dim);\n\n    VERIFY_IS_EQUAL(tensor_argmin.size(),\n                    ptrdiff_t(2*3*5*7 / tensor.dimension(dim)));\n    for (ptrdiff_t n = 0; n < tensor_argmin.size(); ++n) {\n      // Expect min to be in the first index of the reduced dimension\n      VERIFY_IS_EQUAL(tensor_argmin.data()[n], 0);\n    }\n\n    for (int i = 0; i < 2; ++i) {\n      for (int j = 0; j < 3; ++j) {\n        for (int k = 0; k < 5; ++k) {\n          for (int l = 0; l < 7; ++l) {\n            ix[0] = i; ix[1] = j; ix[2] = k; ix[3] = l;\n            if (ix[dim] != tensor.dimension(dim) - 1) continue;\n            // suppose dim == 1, then for all i, k, l, set tensor(i, 2, k, l) = -20.0\n            tensor(ix) = -20.0;\n          }\n        }\n      }\n    }\n\n    tensor_argmin = tensor.argmin(dim);\n\n    VERIFY_IS_EQUAL(tensor_argmin.size(),\n                    ptrdiff_t(2*3*5*7 / tensor.dimension(dim)));\n    for (ptrdiff_t n = 0; n < tensor_argmin.size(); ++n) {\n      // Expect min to be in the last index of the reduced dimension\n      VERIFY_IS_EQUAL(tensor_argmin.data()[n], tensor.dimension(dim) - 1);\n    }\n  }\n}\n\nvoid test_cxx11_tensor_argmax()\n{\n  CALL_SUBTEST(test_simple_index_tuples<RowMajor>());\n  CALL_SUBTEST(test_simple_index_tuples<ColMajor>());\n  CALL_SUBTEST(test_index_tuples_dim<RowMajor>());\n  CALL_SUBTEST(test_index_tuples_dim<ColMajor>());\n  CALL_SUBTEST(test_argmax_tuple_reducer<RowMajor>());\n  CALL_SUBTEST(test_argmax_tuple_reducer<ColMajor>());\n  CALL_SUBTEST(test_argmin_tuple_reducer<RowMajor>());\n  CALL_SUBTEST(test_argmin_tuple_reducer<ColMajor>());\n  CALL_SUBTEST(test_simple_argmax<RowMajor>());\n  CALL_SUBTEST(test_simple_argmax<ColMajor>());\n  CALL_SUBTEST(test_simple_argmin<RowMajor>());\n  CALL_SUBTEST(test_simple_argmin<ColMajor>());\n  CALL_SUBTEST(test_argmax_dim<RowMajor>());\n  CALL_SUBTEST(test_argmax_dim<ColMajor>());\n  CALL_SUBTEST(test_argmin_dim<RowMajor>());\n  CALL_SUBTEST(test_argmin_dim<ColMajor>());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_argmax_cuda.cu",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n\n#define EIGEN_TEST_NO_LONGDOUBLE\n#define EIGEN_TEST_FUNC cxx11_tensor_cuda\n#define EIGEN_USE_GPU\n\n#include \"main.h\"\n#include <unsupported/Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\n\ntemplate <int Layout>\nvoid test_cuda_simple_argmax()\n{\n  Tensor<double, 3, Layout> in(Eigen::array<DenseIndex, 3>(72,53,97));\n  Tensor<DenseIndex, 1, Layout> out_max(Eigen::array<DenseIndex, 1>(1));\n  Tensor<DenseIndex, 1, Layout> out_min(Eigen::array<DenseIndex, 1>(1));\n  in.setRandom();\n  in *= in.constant(100.0);\n  in(0, 0, 0) = -1000.0;\n  in(71, 52, 96) = 1000.0;\n\n  std::size_t in_bytes = in.size() * sizeof(double);\n  std::size_t out_bytes = out_max.size() * sizeof(DenseIndex);\n\n  double* d_in;\n  DenseIndex* d_out_max;\n  DenseIndex* d_out_min;\n  cudaMalloc((void**)(&d_in), in_bytes);\n  cudaMalloc((void**)(&d_out_max), out_bytes);\n  cudaMalloc((void**)(&d_out_min), out_bytes);\n\n  cudaMemcpy(d_in, in.data(), in_bytes, cudaMemcpyHostToDevice);\n\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n\n  Eigen::TensorMap<Eigen::Tensor<double, 3, Layout>, Aligned > gpu_in(d_in, Eigen::array<DenseIndex, 3>(72,53,97));\n  Eigen::TensorMap<Eigen::Tensor<DenseIndex, 1, Layout>, Aligned > gpu_out_max(d_out_max, Eigen::array<DenseIndex, 1>(1));\n  Eigen::TensorMap<Eigen::Tensor<DenseIndex, 1, Layout>, Aligned > gpu_out_min(d_out_min, Eigen::array<DenseIndex, 1>(1));\n\n  gpu_out_max.device(gpu_device) = gpu_in.argmax();\n  gpu_out_min.device(gpu_device) = gpu_in.argmin();\n\n  assert(cudaMemcpyAsync(out_max.data(), d_out_max, out_bytes, cudaMemcpyDeviceToHost, gpu_device.stream()) == cudaSuccess);\n  assert(cudaMemcpyAsync(out_min.data(), d_out_min, out_bytes, cudaMemcpyDeviceToHost, gpu_device.stream()) == cudaSuccess);\n  assert(cudaStreamSynchronize(gpu_device.stream()) == cudaSuccess);\n\n  VERIFY_IS_EQUAL(out_max(Eigen::array<DenseIndex, 1>(0)), 72*53*97 - 1);\n  VERIFY_IS_EQUAL(out_min(Eigen::array<DenseIndex, 1>(0)), 0);\n\n  cudaFree(d_in);\n  cudaFree(d_out_max);\n  cudaFree(d_out_min);\n}\n\ntemplate <int DataLayout>\nvoid test_cuda_argmax_dim()\n{\n  Tensor<float, 4, DataLayout> tensor(2,3,5,7);\n  std::vector<int> dims;\n  dims.push_back(2); dims.push_back(3); dims.push_back(5); dims.push_back(7);\n\n  for (int dim = 0; dim < 4; ++dim) {\n    tensor.setRandom();\n    tensor = (tensor + tensor.constant(0.5)).log();\n\n    array<DenseIndex, 3> out_shape;\n    for (int d = 0; d < 3; ++d) out_shape[d] = (d < dim) ? dims[d] : dims[d+1];\n\n    Tensor<DenseIndex, 3, DataLayout> tensor_arg(out_shape);\n\n    array<DenseIndex, 4> ix;\n    for (int i = 0; i < 2; ++i) {\n      for (int j = 0; j < 3; ++j) {\n        for (int k = 0; k < 5; ++k) {\n          for (int l = 0; l < 7; ++l) {\n            ix[0] = i; ix[1] = j; ix[2] = k; ix[3] = l;\n            if (ix[dim] != 0) continue;\n            // suppose dim == 1, then for all i, k, l, set tensor(i, 0, k, l) = 10.0\n            tensor(ix) = 10.0;\n          }\n        }\n      }\n    }\n\n    std::size_t in_bytes = tensor.size() * sizeof(float);\n    std::size_t out_bytes = tensor_arg.size() * sizeof(DenseIndex);\n\n    float* d_in;\n    DenseIndex* d_out;\n    cudaMalloc((void**)(&d_in), in_bytes);\n    cudaMalloc((void**)(&d_out), out_bytes);\n\n    cudaMemcpy(d_in, tensor.data(), in_bytes, cudaMemcpyHostToDevice);\n\n    Eigen::CudaStreamDevice stream;\n    Eigen::GpuDevice gpu_device(&stream);\n\n    Eigen::TensorMap<Eigen::Tensor<float, 4, DataLayout>, Aligned > gpu_in(d_in, Eigen::array<DenseIndex, 4>(2, 3, 5, 7));\n    Eigen::TensorMap<Eigen::Tensor<DenseIndex, 3, DataLayout>, Aligned > gpu_out(d_out, out_shape);\n\n    gpu_out.device(gpu_device) = gpu_in.argmax(dim);\n\n    assert(cudaMemcpyAsync(tensor_arg.data(), d_out, out_bytes, cudaMemcpyDeviceToHost, gpu_device.stream()) == cudaSuccess);\n    assert(cudaStreamSynchronize(gpu_device.stream()) == cudaSuccess);\n\n    VERIFY_IS_EQUAL(tensor_arg.size(),\n                    size_t(2*3*5*7 / tensor.dimension(dim)));\n\n    for (DenseIndex n = 0; n < tensor_arg.size(); ++n) {\n      // Expect max to be in the first index of the reduced dimension\n      VERIFY_IS_EQUAL(tensor_arg.data()[n], 0);\n    }\n\n    for (int i = 0; i < 2; ++i) {\n      for (int j = 0; j < 3; ++j) {\n        for (int k = 0; k < 5; ++k) {\n          for (int l = 0; l < 7; ++l) {\n            ix[0] = i; ix[1] = j; ix[2] = k; ix[3] = l;\n            if (ix[dim] != tensor.dimension(dim) - 1) continue;\n            // suppose dim == 1, then for all i, k, l, set tensor(i, 2, k, l) = 20.0\n            tensor(ix) = 20.0;\n          }\n        }\n      }\n    }\n\n    cudaMemcpy(d_in, tensor.data(), in_bytes, cudaMemcpyHostToDevice);\n\n    gpu_out.device(gpu_device) = gpu_in.argmax(dim);\n\n    assert(cudaMemcpyAsync(tensor_arg.data(), d_out, out_bytes, cudaMemcpyDeviceToHost, gpu_device.stream()) == cudaSuccess);\n    assert(cudaStreamSynchronize(gpu_device.stream()) == cudaSuccess);\n\n    for (DenseIndex n = 0; n < tensor_arg.size(); ++n) {\n      // Expect max to be in the last index of the reduced dimension\n      VERIFY_IS_EQUAL(tensor_arg.data()[n], tensor.dimension(dim) - 1);\n    }\n\n    cudaFree(d_in);\n    cudaFree(d_out);\n  }\n}\n\ntemplate <int DataLayout>\nvoid test_cuda_argmin_dim()\n{\n  Tensor<float, 4, DataLayout> tensor(2,3,5,7);\n  std::vector<int> dims;\n  dims.push_back(2); dims.push_back(3); dims.push_back(5); dims.push_back(7);\n\n  for (int dim = 0; dim < 4; ++dim) {\n    tensor.setRandom();\n    tensor = (tensor + tensor.constant(0.5)).log();\n\n    array<DenseIndex, 3> out_shape;\n    for (int d = 0; d < 3; ++d) out_shape[d] = (d < dim) ? dims[d] : dims[d+1];\n\n    Tensor<DenseIndex, 3, DataLayout> tensor_arg(out_shape);\n\n    array<DenseIndex, 4> ix;\n    for (int i = 0; i < 2; ++i) {\n      for (int j = 0; j < 3; ++j) {\n        for (int k = 0; k < 5; ++k) {\n          for (int l = 0; l < 7; ++l) {\n            ix[0] = i; ix[1] = j; ix[2] = k; ix[3] = l;\n            if (ix[dim] != 0) continue;\n            // suppose dim == 1, then for all i, k, l, set tensor(i, 0, k, l) = 10.0\n            tensor(ix) = -10.0;\n          }\n        }\n      }\n    }\n\n    std::size_t in_bytes = tensor.size() * sizeof(float);\n    std::size_t out_bytes = tensor_arg.size() * sizeof(DenseIndex);\n\n    float* d_in;\n    DenseIndex* d_out;\n    cudaMalloc((void**)(&d_in), in_bytes);\n    cudaMalloc((void**)(&d_out), out_bytes);\n\n    cudaMemcpy(d_in, tensor.data(), in_bytes, cudaMemcpyHostToDevice);\n\n    Eigen::CudaStreamDevice stream;\n    Eigen::GpuDevice gpu_device(&stream);\n\n    Eigen::TensorMap<Eigen::Tensor<float, 4, DataLayout>, Aligned > gpu_in(d_in, Eigen::array<DenseIndex, 4>(2, 3, 5, 7));\n    Eigen::TensorMap<Eigen::Tensor<DenseIndex, 3, DataLayout>, Aligned > gpu_out(d_out, out_shape);\n\n    gpu_out.device(gpu_device) = gpu_in.argmin(dim);\n\n    assert(cudaMemcpyAsync(tensor_arg.data(), d_out, out_bytes, cudaMemcpyDeviceToHost, gpu_device.stream()) == cudaSuccess);\n    assert(cudaStreamSynchronize(gpu_device.stream()) == cudaSuccess);\n\n    VERIFY_IS_EQUAL(tensor_arg.size(),\n                    2*3*5*7 / tensor.dimension(dim));\n\n    for (DenseIndex n = 0; n < tensor_arg.size(); ++n) {\n      // Expect min to be in the first index of the reduced dimension\n      VERIFY_IS_EQUAL(tensor_arg.data()[n], 0);\n    }\n\n    for (int i = 0; i < 2; ++i) {\n      for (int j = 0; j < 3; ++j) {\n        for (int k = 0; k < 5; ++k) {\n          for (int l = 0; l < 7; ++l) {\n            ix[0] = i; ix[1] = j; ix[2] = k; ix[3] = l;\n            if (ix[dim] != tensor.dimension(dim) - 1) continue;\n            // suppose dim == 1, then for all i, k, l, set tensor(i, 2, k, l) = 20.0\n            tensor(ix) = -20.0;\n          }\n        }\n      }\n    }\n\n    cudaMemcpy(d_in, tensor.data(), in_bytes, cudaMemcpyHostToDevice);\n\n    gpu_out.device(gpu_device) = gpu_in.argmin(dim);\n\n    assert(cudaMemcpyAsync(tensor_arg.data(), d_out, out_bytes, cudaMemcpyDeviceToHost, gpu_device.stream()) == cudaSuccess);\n    assert(cudaStreamSynchronize(gpu_device.stream()) == cudaSuccess);\n\n    for (DenseIndex n = 0; n < tensor_arg.size(); ++n) {\n      // Expect max to be in the last index of the reduced dimension\n      VERIFY_IS_EQUAL(tensor_arg.data()[n], tensor.dimension(dim) - 1);\n    }\n\n    cudaFree(d_in);\n    cudaFree(d_out);\n  }\n}\n\nvoid test_cxx11_tensor_cuda()\n{\n  CALL_SUBTEST_1(test_cuda_simple_argmax<RowMajor>());\n  CALL_SUBTEST_1(test_cuda_simple_argmax<ColMajor>());\n  CALL_SUBTEST_2(test_cuda_argmax_dim<RowMajor>());\n  CALL_SUBTEST_2(test_cuda_argmax_dim<ColMajor>());\n  CALL_SUBTEST_3(test_cuda_argmin_dim<RowMajor>());\n  CALL_SUBTEST_3(test_cuda_argmin_dim<ColMajor>());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_assign.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\nusing Eigen::RowMajor;\n\nstatic void test_1d()\n{\n  Tensor<int, 1> vec1(6);\n  Tensor<int, 1, RowMajor> vec2(6);\n  vec1(0) = 4;  vec2(0) = 0;\n  vec1(1) = 8;  vec2(1) = 1;\n  vec1(2) = 15; vec2(2) = 2;\n  vec1(3) = 16; vec2(3) = 3;\n  vec1(4) = 23; vec2(4) = 4;\n  vec1(5) = 42; vec2(5) = 5;\n\n  int col_major[6];\n  int row_major[6];\n  memset(col_major, 0, 6*sizeof(int));\n  memset(row_major, 0, 6*sizeof(int));\n  TensorMap<Tensor<int, 1> > vec3(col_major, 6);\n  TensorMap<Tensor<int, 1, RowMajor> > vec4(row_major, 6);\n\n  vec3 = vec1;\n  vec4 = vec2;\n\n  VERIFY_IS_EQUAL(vec3(0), 4);\n  VERIFY_IS_EQUAL(vec3(1), 8);\n  VERIFY_IS_EQUAL(vec3(2), 15);\n  VERIFY_IS_EQUAL(vec3(3), 16);\n  VERIFY_IS_EQUAL(vec3(4), 23);\n  VERIFY_IS_EQUAL(vec3(5), 42);\n\n  VERIFY_IS_EQUAL(vec4(0), 0);\n  VERIFY_IS_EQUAL(vec4(1), 1);\n  VERIFY_IS_EQUAL(vec4(2), 2);\n  VERIFY_IS_EQUAL(vec4(3), 3);\n  VERIFY_IS_EQUAL(vec4(4), 4);\n  VERIFY_IS_EQUAL(vec4(5), 5);\n\n  vec1.setZero();\n  vec2.setZero();\n  vec1 = vec3;\n  vec2 = vec4;\n\n  VERIFY_IS_EQUAL(vec1(0), 4);\n  VERIFY_IS_EQUAL(vec1(1), 8);\n  VERIFY_IS_EQUAL(vec1(2), 15);\n  VERIFY_IS_EQUAL(vec1(3), 16);\n  VERIFY_IS_EQUAL(vec1(4), 23);\n  VERIFY_IS_EQUAL(vec1(5), 42);\n\n  VERIFY_IS_EQUAL(vec2(0), 0);\n  VERIFY_IS_EQUAL(vec2(1), 1);\n  VERIFY_IS_EQUAL(vec2(2), 2);\n  VERIFY_IS_EQUAL(vec2(3), 3);\n  VERIFY_IS_EQUAL(vec2(4), 4);\n  VERIFY_IS_EQUAL(vec2(5), 5);\n}\n\nstatic void test_2d()\n{\n  Tensor<int, 2> mat1(2,3);\n  Tensor<int, 2, RowMajor> mat2(2,3);\n\n  mat1(0,0) = 0;\n  mat1(0,1) = 1;\n  mat1(0,2) = 2;\n  mat1(1,0) = 3;\n  mat1(1,1) = 4;\n  mat1(1,2) = 5;\n\n  mat2(0,0) = 0;\n  mat2(0,1) = 1;\n  mat2(0,2) = 2;\n  mat2(1,0) = 3;\n  mat2(1,1) = 4;\n  mat2(1,2) = 5;\n\n  int col_major[6];\n  int row_major[6];\n  memset(col_major, 0, 6*sizeof(int));\n  memset(row_major, 0, 6*sizeof(int));\n  TensorMap<Tensor<int, 2> > mat3(row_major, 2, 3);\n  TensorMap<Tensor<int, 2, RowMajor> > mat4(col_major, 2, 3);\n\n  mat3 = mat1;\n  mat4 = mat2;\n\n  VERIFY_IS_EQUAL(mat3(0,0), 0);\n  VERIFY_IS_EQUAL(mat3(0,1), 1);\n  VERIFY_IS_EQUAL(mat3(0,2), 2);\n  VERIFY_IS_EQUAL(mat3(1,0), 3);\n  VERIFY_IS_EQUAL(mat3(1,1), 4);\n  VERIFY_IS_EQUAL(mat3(1,2), 5);\n\n  VERIFY_IS_EQUAL(mat4(0,0), 0);\n  VERIFY_IS_EQUAL(mat4(0,1), 1);\n  VERIFY_IS_EQUAL(mat4(0,2), 2);\n  VERIFY_IS_EQUAL(mat4(1,0), 3);\n  VERIFY_IS_EQUAL(mat4(1,1), 4);\n  VERIFY_IS_EQUAL(mat4(1,2), 5);\n\n  mat1.setZero();\n  mat2.setZero();\n  mat1 = mat3;\n  mat2 = mat4;\n\n  VERIFY_IS_EQUAL(mat1(0,0), 0);\n  VERIFY_IS_EQUAL(mat1(0,1), 1);\n  VERIFY_IS_EQUAL(mat1(0,2), 2);\n  VERIFY_IS_EQUAL(mat1(1,0), 3);\n  VERIFY_IS_EQUAL(mat1(1,1), 4);\n  VERIFY_IS_EQUAL(mat1(1,2), 5);\n\n  VERIFY_IS_EQUAL(mat2(0,0), 0);\n  VERIFY_IS_EQUAL(mat2(0,1), 1);\n  VERIFY_IS_EQUAL(mat2(0,2), 2);\n  VERIFY_IS_EQUAL(mat2(1,0), 3);\n  VERIFY_IS_EQUAL(mat2(1,1), 4);\n  VERIFY_IS_EQUAL(mat2(1,2), 5);\n}\n\nstatic void test_3d()\n{\n  Tensor<int, 3> mat1(2,3,7);\n  Tensor<int, 3, RowMajor> mat2(2,3,7);\n\n  int val = 0;\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        mat1(i,j,k) = val;\n        mat2(i,j,k) = val;\n        val++;\n      }\n    }\n  }\n\n  int col_major[2*3*7];\n  int row_major[2*3*7];\n  memset(col_major, 0, 2*3*7*sizeof(int));\n  memset(row_major, 0, 2*3*7*sizeof(int));\n  TensorMap<Tensor<int, 3> > mat3(col_major, 2, 3, 7);\n  TensorMap<Tensor<int, 3, RowMajor> > mat4(row_major, 2, 3, 7);\n\n  mat3 = mat1;\n  mat4 = mat2;\n\n  val = 0;\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        VERIFY_IS_EQUAL(mat3(i,j,k), val);\n        VERIFY_IS_EQUAL(mat4(i,j,k), val);\n        val++;\n      }\n    }\n  }\n\n  mat1.setZero();\n  mat2.setZero();\n  mat1 = mat3;\n  mat2 = mat4;\n\n  val = 0;\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        VERIFY_IS_EQUAL(mat1(i,j,k), val);\n        VERIFY_IS_EQUAL(mat2(i,j,k), val);\n        val++;\n      }\n    }\n  }\n}\n\nstatic void test_same_type()\n{\n  Tensor<int, 1> orig_tensor(5);\n  Tensor<int, 1> dest_tensor(5);\n  orig_tensor.setRandom();\n  dest_tensor.setRandom();\n  int* orig_data = orig_tensor.data();\n  int* dest_data = dest_tensor.data();\n  dest_tensor = orig_tensor;\n  VERIFY_IS_EQUAL(orig_tensor.data(), orig_data);\n  VERIFY_IS_EQUAL(dest_tensor.data(), dest_data);\n  for (int i = 0; i < 5; ++i) {\n    VERIFY_IS_EQUAL(dest_tensor(i), orig_tensor(i));\n  }\n\n  TensorFixedSize<int, Sizes<5> > orig_array;\n  TensorFixedSize<int, Sizes<5> > dest_array;\n  orig_array.setRandom();\n  dest_array.setRandom();\n  orig_data = orig_array.data();\n  dest_data = dest_array.data();\n  dest_array = orig_array;\n  VERIFY_IS_EQUAL(orig_array.data(), orig_data);\n  VERIFY_IS_EQUAL(dest_array.data(), dest_data);\n  for (int i = 0; i < 5; ++i) {\n    VERIFY_IS_EQUAL(dest_array(i), orig_array(i));\n  }\n\n  int orig[5] = {1, 2, 3, 4, 5};\n  int dest[5] = {6, 7, 8, 9, 10};\n  TensorMap<Tensor<int, 1> > orig_map(orig, 5);\n  TensorMap<Tensor<int, 1> > dest_map(dest, 5);\n  orig_data = orig_map.data();\n  dest_data = dest_map.data();\n  dest_map = orig_map;\n  VERIFY_IS_EQUAL(orig_map.data(), orig_data);\n  VERIFY_IS_EQUAL(dest_map.data(), dest_data);\n  for (int i = 0; i < 5; ++i) {\n    VERIFY_IS_EQUAL(dest[i], i+1);\n  }\n}\n\nstatic void test_auto_resize()\n{\n  Tensor<int, 1> tensor1;\n  Tensor<int, 1> tensor2(3);\n  Tensor<int, 1> tensor3(5);\n  Tensor<int, 1> tensor4(7);\n\n  Tensor<int, 1> new_tensor(5);\n  new_tensor.setRandom();\n\n  tensor1 = tensor2 = tensor3 = tensor4 = new_tensor;\n\n  VERIFY_IS_EQUAL(tensor1.dimension(0), new_tensor.dimension(0));\n  VERIFY_IS_EQUAL(tensor2.dimension(0), new_tensor.dimension(0));\n  VERIFY_IS_EQUAL(tensor3.dimension(0), new_tensor.dimension(0));\n  VERIFY_IS_EQUAL(tensor4.dimension(0), new_tensor.dimension(0));\n  for (int i = 0; i < new_tensor.dimension(0); ++i) {\n    VERIFY_IS_EQUAL(tensor1(i), new_tensor(i));\n    VERIFY_IS_EQUAL(tensor2(i), new_tensor(i));\n    VERIFY_IS_EQUAL(tensor3(i), new_tensor(i));\n    VERIFY_IS_EQUAL(tensor4(i), new_tensor(i));\n  }\n}\n\n\nstatic void test_compound_assign()\n{\n  Tensor<int, 1> start_tensor(10);\n  Tensor<int, 1> offset_tensor(10);\n  start_tensor.setRandom();\n  offset_tensor.setRandom();\n\n  Tensor<int, 1> tensor = start_tensor;\n  tensor += offset_tensor;\n  for (int i = 0; i < 10; ++i) {\n    VERIFY_IS_EQUAL(tensor(i), start_tensor(i) + offset_tensor(i));\n  }\n\n  tensor = start_tensor;\n  tensor -= offset_tensor;\n  for (int i = 0; i < 10; ++i) {\n    VERIFY_IS_EQUAL(tensor(i), start_tensor(i) - offset_tensor(i));\n  }\n\n  tensor = start_tensor;\n  tensor *= offset_tensor;\n  for (int i = 0; i < 10; ++i) {\n    VERIFY_IS_EQUAL(tensor(i), start_tensor(i) * offset_tensor(i));\n  }\n\n  tensor = start_tensor;\n  tensor /= offset_tensor;\n  for (int i = 0; i < 10; ++i) {\n    VERIFY_IS_EQUAL(tensor(i), start_tensor(i) / offset_tensor(i));\n  }\n}\n\nstatic void test_std_initializers_tensor() {\n#if EIGEN_HAS_VARIADIC_TEMPLATES\n  Tensor<int, 1> a(3);\n  a.setValues({0, 1, 2});\n  VERIFY_IS_EQUAL(a(0), 0);\n  VERIFY_IS_EQUAL(a(1), 1);\n  VERIFY_IS_EQUAL(a(2), 2);\n\n  // It fills the top-left slice.\n  a.setValues({10, 20});\n  VERIFY_IS_EQUAL(a(0), 10);\n  VERIFY_IS_EQUAL(a(1), 20);\n  VERIFY_IS_EQUAL(a(2), 2);\n\n  // Chaining.\n  Tensor<int, 1> a2(3);\n  a2 = a.setValues({100, 200, 300});\n  VERIFY_IS_EQUAL(a(0), 100);\n  VERIFY_IS_EQUAL(a(1), 200);\n  VERIFY_IS_EQUAL(a(2), 300);\n  VERIFY_IS_EQUAL(a2(0), 100);\n  VERIFY_IS_EQUAL(a2(1), 200);\n  VERIFY_IS_EQUAL(a2(2), 300);\n\n  Tensor<int, 2> b(2, 3);\n  b.setValues({{0, 1, 2}, {3, 4, 5}});\n  VERIFY_IS_EQUAL(b(0, 0), 0);\n  VERIFY_IS_EQUAL(b(0, 1), 1);\n  VERIFY_IS_EQUAL(b(0, 2), 2);\n  VERIFY_IS_EQUAL(b(1, 0), 3);\n  VERIFY_IS_EQUAL(b(1, 1), 4);\n  VERIFY_IS_EQUAL(b(1, 2), 5);\n\n  // It fills the top-left slice.\n  b.setValues({{10, 20}, {30}});\n  VERIFY_IS_EQUAL(b(0, 0), 10);\n  VERIFY_IS_EQUAL(b(0, 1), 20);\n  VERIFY_IS_EQUAL(b(0, 2), 2);\n  VERIFY_IS_EQUAL(b(1, 0), 30);\n  VERIFY_IS_EQUAL(b(1, 1), 4);\n  VERIFY_IS_EQUAL(b(1, 2), 5);\n\n  Eigen::Tensor<int, 3> c(3, 2, 4);\n  c.setValues({{{0, 1, 2, 3}, {4, 5, 6, 7}},\n               {{10, 11, 12, 13}, {14, 15, 16, 17}},\n               {{20, 21, 22, 23}, {24, 25, 26, 27}}});\n  VERIFY_IS_EQUAL(c(0, 0, 0), 0);\n  VERIFY_IS_EQUAL(c(0, 0, 1), 1);\n  VERIFY_IS_EQUAL(c(0, 0, 2), 2);\n  VERIFY_IS_EQUAL(c(0, 0, 3), 3);\n  VERIFY_IS_EQUAL(c(0, 1, 0), 4);\n  VERIFY_IS_EQUAL(c(0, 1, 1), 5);\n  VERIFY_IS_EQUAL(c(0, 1, 2), 6);\n  VERIFY_IS_EQUAL(c(0, 1, 3), 7);\n  VERIFY_IS_EQUAL(c(1, 0, 0), 10);\n  VERIFY_IS_EQUAL(c(1, 0, 1), 11);\n  VERIFY_IS_EQUAL(c(1, 0, 2), 12);\n  VERIFY_IS_EQUAL(c(1, 0, 3), 13);\n  VERIFY_IS_EQUAL(c(1, 1, 0), 14);\n  VERIFY_IS_EQUAL(c(1, 1, 1), 15);\n  VERIFY_IS_EQUAL(c(1, 1, 2), 16);\n  VERIFY_IS_EQUAL(c(1, 1, 3), 17);\n  VERIFY_IS_EQUAL(c(2, 0, 0), 20);\n  VERIFY_IS_EQUAL(c(2, 0, 1), 21);\n  VERIFY_IS_EQUAL(c(2, 0, 2), 22);\n  VERIFY_IS_EQUAL(c(2, 0, 3), 23);\n  VERIFY_IS_EQUAL(c(2, 1, 0), 24);\n  VERIFY_IS_EQUAL(c(2, 1, 1), 25);\n  VERIFY_IS_EQUAL(c(2, 1, 2), 26);\n  VERIFY_IS_EQUAL(c(2, 1, 3), 27);\n#endif  // EIGEN_HAS_VARIADIC_TEMPLATES\n}\n\nvoid test_cxx11_tensor_assign()\n{\n  CALL_SUBTEST(test_1d());\n  CALL_SUBTEST(test_2d());\n  CALL_SUBTEST(test_3d());\n  CALL_SUBTEST(test_same_type());\n  CALL_SUBTEST(test_auto_resize());\n  CALL_SUBTEST(test_compound_assign());\n  CALL_SUBTEST(test_std_initializers_tensor());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_broadcast_sycl.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016\n// Mehdi Goli    Codeplay Software Ltd.\n// Ralph Potter  Codeplay Software Ltd.\n// Luke Iwanski  Codeplay Software Ltd.\n// Contact: <eigen@codeplay.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define EIGEN_TEST_NO_LONGDOUBLE\n#define EIGEN_TEST_NO_COMPLEX\n#define EIGEN_TEST_FUNC cxx11_tensor_broadcast_sycl\n#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int\n#define EIGEN_USE_SYCL\n\n#include \"main.h\"\n#include <unsupported/Eigen/CXX11/Tensor>\n\nusing Eigen::array;\nusing Eigen::SyclDevice;\nusing Eigen::Tensor;\nusing Eigen::TensorMap;\n\nstatic void test_broadcast_sycl(const Eigen::SyclDevice &sycl_device){\n\n  // BROADCAST test:\n  array<int, 4> in_range   = {{2, 3, 5, 7}};\n  array<int, 4> broadcasts = {{2, 3, 1, 4}};\n  array<int, 4> out_range;  // = in_range * broadcasts\n  for (size_t i = 0; i < out_range.size(); ++i)\n    out_range[i] = in_range[i] * broadcasts[i];\n\n  Tensor<float, 4>  input(in_range);\n  Tensor<float, 4> out(out_range);\n\n  for (size_t i = 0; i < in_range.size(); ++i)\n    VERIFY_IS_EQUAL(out.dimension(i), out_range[i]);\n\n\n  for (int i = 0; i < input.size(); ++i)\n    input(i) = static_cast<float>(i);\n\n  float * gpu_in_data  = static_cast<float*>(sycl_device.allocate(input.dimensions().TotalSize()*sizeof(float)));\n  float * gpu_out_data  = static_cast<float*>(sycl_device.allocate(out.dimensions().TotalSize()*sizeof(float)));\n\n  TensorMap<Tensor<float, 4>>  gpu_in(gpu_in_data, in_range);\n  TensorMap<Tensor<float, 4>> gpu_out(gpu_out_data, out_range);\n  sycl_device.memcpyHostToDevice(gpu_in_data, input.data(),(input.dimensions().TotalSize())*sizeof(float));\n  gpu_out.device(sycl_device) = gpu_in.broadcast(broadcasts);\n  sycl_device.memcpyDeviceToHost(out.data(), gpu_out_data,(out.dimensions().TotalSize())*sizeof(float));\n\n  for (int i = 0; i < 4; ++i) {\n    for (int j = 0; j < 9; ++j) {\n      for (int k = 0; k < 5; ++k) {\n        for (int l = 0; l < 28; ++l) {\n          VERIFY_IS_APPROX(input(i%2,j%3,k%5,l%7), out(i,j,k,l));\n        }\n      }\n    }\n  }\n  printf(\"Broadcast Test Passed\\n\");\n  sycl_device.deallocate(gpu_in_data);\n  sycl_device.deallocate(gpu_out_data);\n}\n\nvoid test_cxx11_tensor_broadcast_sycl() {\n  cl::sycl::gpu_selector s;\n  Eigen::SyclDevice sycl_device(s);\n  CALL_SUBTEST(test_broadcast_sycl(sycl_device));\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_broadcasting.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\n\ntemplate <int DataLayout>\nstatic void test_simple_broadcasting()\n{\n  Tensor<float, 4, DataLayout> tensor(2,3,5,7);\n  tensor.setRandom();\n  array<ptrdiff_t, 4> broadcasts;\n  broadcasts[0] = 1;\n  broadcasts[1] = 1;\n  broadcasts[2] = 1;\n  broadcasts[3] = 1;\n\n  Tensor<float, 4, DataLayout> no_broadcast;\n  no_broadcast = tensor.broadcast(broadcasts);\n\n  VERIFY_IS_EQUAL(no_broadcast.dimension(0), 2);\n  VERIFY_IS_EQUAL(no_broadcast.dimension(1), 3);\n  VERIFY_IS_EQUAL(no_broadcast.dimension(2), 5);\n  VERIFY_IS_EQUAL(no_broadcast.dimension(3), 7);\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 5; ++k) {\n        for (int l = 0; l < 7; ++l) {\n          VERIFY_IS_EQUAL(tensor(i,j,k,l), no_broadcast(i,j,k,l));\n        }\n      }\n    }\n  }\n\n  broadcasts[0] = 2;\n  broadcasts[1] = 3;\n  broadcasts[2] = 1;\n  broadcasts[3] = 4;\n  Tensor<float, 4, DataLayout> broadcast;\n  broadcast = tensor.broadcast(broadcasts);\n\n  VERIFY_IS_EQUAL(broadcast.dimension(0), 4);\n  VERIFY_IS_EQUAL(broadcast.dimension(1), 9);\n  VERIFY_IS_EQUAL(broadcast.dimension(2), 5);\n  VERIFY_IS_EQUAL(broadcast.dimension(3), 28);\n\n  for (int i = 0; i < 4; ++i) {\n    for (int j = 0; j < 9; ++j) {\n      for (int k = 0; k < 5; ++k) {\n        for (int l = 0; l < 28; ++l) {\n          VERIFY_IS_EQUAL(tensor(i%2,j%3,k%5,l%7), broadcast(i,j,k,l));\n        }\n      }\n    }\n  }\n}\n\n\ntemplate <int DataLayout>\nstatic void test_vectorized_broadcasting()\n{\n  Tensor<float, 3, DataLayout> tensor(8,3,5);\n  tensor.setRandom();\n  array<ptrdiff_t, 3> broadcasts;\n  broadcasts[0] = 2;\n  broadcasts[1] = 3;\n  broadcasts[2] = 4;\n\n  Tensor<float, 3, DataLayout> broadcast;\n  broadcast = tensor.broadcast(broadcasts);\n\n  VERIFY_IS_EQUAL(broadcast.dimension(0), 16);\n  VERIFY_IS_EQUAL(broadcast.dimension(1), 9);\n  VERIFY_IS_EQUAL(broadcast.dimension(2), 20);\n\n  for (int i = 0; i < 16; ++i) {\n    for (int j = 0; j < 9; ++j) {\n      for (int k = 0; k < 20; ++k) {\n        VERIFY_IS_EQUAL(tensor(i%8,j%3,k%5), broadcast(i,j,k));\n      }\n    }\n  }\n\n  tensor.resize(11,3,5);\n  tensor.setRandom();\n  broadcast = tensor.broadcast(broadcasts);\n\n  VERIFY_IS_EQUAL(broadcast.dimension(0), 22);\n  VERIFY_IS_EQUAL(broadcast.dimension(1), 9);\n  VERIFY_IS_EQUAL(broadcast.dimension(2), 20);\n\n  for (int i = 0; i < 22; ++i) {\n    for (int j = 0; j < 9; ++j) {\n      for (int k = 0; k < 20; ++k) {\n        VERIFY_IS_EQUAL(tensor(i%11,j%3,k%5), broadcast(i,j,k));\n      }\n    }\n  }\n}\n\n\ntemplate <int DataLayout>\nstatic void test_static_broadcasting()\n{\n  Tensor<float, 3, DataLayout> tensor(8,3,5);\n  tensor.setRandom();\n\n#if EIGEN_HAS_CONSTEXPR\n  Eigen::IndexList<Eigen::type2index<2>, Eigen::type2index<3>, Eigen::type2index<4>> broadcasts;\n#else\n  Eigen::array<int, 3> broadcasts;\n  broadcasts[0] = 2;\n  broadcasts[1] = 3;\n  broadcasts[2] = 4;\n#endif\n\n  Tensor<float, 3, DataLayout> broadcast;\n  broadcast = tensor.broadcast(broadcasts);\n\n  VERIFY_IS_EQUAL(broadcast.dimension(0), 16);\n  VERIFY_IS_EQUAL(broadcast.dimension(1), 9);\n  VERIFY_IS_EQUAL(broadcast.dimension(2), 20);\n\n  for (int i = 0; i < 16; ++i) {\n    for (int j = 0; j < 9; ++j) {\n      for (int k = 0; k < 20; ++k) {\n        VERIFY_IS_EQUAL(tensor(i%8,j%3,k%5), broadcast(i,j,k));\n      }\n    }\n  }\n\n  tensor.resize(11,3,5);\n  tensor.setRandom();\n  broadcast = tensor.broadcast(broadcasts);\n\n  VERIFY_IS_EQUAL(broadcast.dimension(0), 22);\n  VERIFY_IS_EQUAL(broadcast.dimension(1), 9);\n  VERIFY_IS_EQUAL(broadcast.dimension(2), 20);\n\n  for (int i = 0; i < 22; ++i) {\n    for (int j = 0; j < 9; ++j) {\n      for (int k = 0; k < 20; ++k) {\n        VERIFY_IS_EQUAL(tensor(i%11,j%3,k%5), broadcast(i,j,k));\n      }\n    }\n  }\n}\n\n\ntemplate <int DataLayout>\nstatic void test_fixed_size_broadcasting()\n{\n  // Need to add a [] operator to the Size class for this to work\n#if 0\n  Tensor<float, 1, DataLayout> t1(10);\n  t1.setRandom();\n  TensorFixedSize<float, Sizes<1>, DataLayout> t2;\n  t2 = t2.constant(20.0f);\n\n  Tensor<float, 1, DataLayout> t3 = t1 + t2.broadcast(Eigen::array<int, 1>{{10}});\n  for (int i = 0; i < 10; ++i) {\n    VERIFY_IS_APPROX(t3(i), t1(i) + t2(0));\n  }\n\n  TensorMap<TensorFixedSize<float, Sizes<1>, DataLayout> > t4(t2.data(), {{1}});\n  Tensor<float, 1, DataLayout> t5 = t1 + t4.broadcast(Eigen::array<int, 1>{{10}});\n  for (int i = 0; i < 10; ++i) {\n    VERIFY_IS_APPROX(t5(i), t1(i) + t2(0));\n  }\n#endif\n}\n\n\nvoid test_cxx11_tensor_broadcasting()\n{\n  CALL_SUBTEST(test_simple_broadcasting<ColMajor>());\n  CALL_SUBTEST(test_simple_broadcasting<RowMajor>());\n  CALL_SUBTEST(test_vectorized_broadcasting<ColMajor>());\n  CALL_SUBTEST(test_vectorized_broadcasting<RowMajor>());\n  CALL_SUBTEST(test_static_broadcasting<ColMajor>());\n  CALL_SUBTEST(test_static_broadcasting<RowMajor>());\n  CALL_SUBTEST(test_fixed_size_broadcasting<ColMajor>());\n  CALL_SUBTEST(test_fixed_size_broadcasting<RowMajor>());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_cast_float16_cuda.cu",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define EIGEN_TEST_NO_LONGDOUBLE\n#define EIGEN_TEST_NO_COMPLEX\n#define EIGEN_TEST_FUNC cxx11_tensor_cast_float16_cuda\n#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int\n#define EIGEN_USE_GPU\n\n#include \"main.h\"\n#include <unsupported/Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\n\nvoid test_cuda_conversion() {\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n  int num_elem = 101;\n\n  Tensor<float, 1> floats(num_elem);\n  floats.setRandom();\n\n  float* d_float = (float*)gpu_device.allocate(num_elem * sizeof(float));\n  Eigen::half* d_half = (Eigen::half*)gpu_device.allocate(num_elem * sizeof(Eigen::half));\n  float* d_conv = (float*)gpu_device.allocate(num_elem * sizeof(float));\n\n  Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_float(\n      d_float, num_elem);\n  Eigen::TensorMap<Eigen::Tensor<Eigen::half, 1>, Eigen::Aligned> gpu_half(\n      d_half, num_elem);\n  Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_conv(\n      d_conv, num_elem);\n\n  gpu_device.memcpyHostToDevice(d_float, floats.data(), num_elem*sizeof(float));\n\n  gpu_half.device(gpu_device) = gpu_float.cast<Eigen::half>();\n  gpu_conv.device(gpu_device) = gpu_half.cast<float>();\n\n  Tensor<float, 1> initial(num_elem);\n  Tensor<float, 1> final(num_elem);\n  gpu_device.memcpyDeviceToHost(initial.data(), d_float, num_elem*sizeof(float));\n  gpu_device.memcpyDeviceToHost(final.data(), d_conv, num_elem*sizeof(float));\n  gpu_device.synchronize();\n\n  for (int i = 0; i < num_elem; ++i) {\n    VERIFY_IS_APPROX(initial(i), final(i));\n  }\n\n  gpu_device.deallocate(d_float);\n  gpu_device.deallocate(d_half);\n  gpu_device.deallocate(d_conv);\n}\n\n\nvoid test_fallback_conversion() {\n  int num_elem = 101;\n  Tensor<float, 1> floats(num_elem);\n  floats.setRandom();\n\n  Eigen::Tensor<Eigen::half, 1> halfs = floats.cast<Eigen::half>();\n  Eigen::Tensor<float, 1> conv = halfs.cast<float>();\n\n  for (int i = 0; i < num_elem; ++i) {\n    VERIFY_IS_APPROX(floats(i), conv(i));\n  }\n}\n\n\nvoid test_cxx11_tensor_cast_float16_cuda()\n{\n  CALL_SUBTEST(test_cuda_conversion());\n  CALL_SUBTEST(test_fallback_conversion());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_casts.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\nusing Eigen::array;\n\nstatic void test_simple_cast()\n{\n  Tensor<float, 2> ftensor(20,30);\n  ftensor = ftensor.random() * 100.f;\n  Tensor<char, 2> chartensor(20,30);\n  chartensor.setRandom();\n  Tensor<std::complex<float>, 2> cplextensor(20,30);\n  cplextensor.setRandom();\n\n  chartensor = ftensor.cast<char>();\n  cplextensor = ftensor.cast<std::complex<float> >();\n\n  for (int i = 0; i < 20; ++i) {\n    for (int j = 0; j < 30; ++j) {\n      VERIFY_IS_EQUAL(chartensor(i,j), static_cast<char>(ftensor(i,j)));\n      VERIFY_IS_EQUAL(cplextensor(i,j), static_cast<std::complex<float> >(ftensor(i,j)));\n    }\n  }\n}\n\n\nstatic void test_vectorized_cast()\n{\n  Tensor<int, 2> itensor(20,30);\n  itensor = itensor.random() / 1000;\n  Tensor<float, 2> ftensor(20,30);\n  ftensor.setRandom();\n  Tensor<double, 2> dtensor(20,30);\n  dtensor.setRandom();\n\n  ftensor = itensor.cast<float>();\n  dtensor = itensor.cast<double>();\n\n  for (int i = 0; i < 20; ++i) {\n    for (int j = 0; j < 30; ++j) {\n      VERIFY_IS_EQUAL(itensor(i,j), static_cast<int>(ftensor(i,j)));\n      VERIFY_IS_EQUAL(dtensor(i,j), static_cast<double>(ftensor(i,j)));\n    }\n  }\n}\n\n\nstatic void test_float_to_int_cast()\n{\n  Tensor<float, 2> ftensor(20,30);\n  ftensor = ftensor.random() * 1000.0f;\n  Tensor<double, 2> dtensor(20,30);\n  dtensor = dtensor.random() * 1000.0;\n\n  Tensor<int, 2> i1tensor = ftensor.cast<int>();\n  Tensor<int, 2> i2tensor = dtensor.cast<int>();\n\n  for (int i = 0; i < 20; ++i) {\n    for (int j = 0; j < 30; ++j) {\n      VERIFY_IS_EQUAL(i1tensor(i,j), static_cast<int>(ftensor(i,j)));\n      VERIFY_IS_EQUAL(i2tensor(i,j), static_cast<int>(dtensor(i,j)));\n    }\n  }\n}\n\n\nstatic void test_big_to_small_type_cast()\n{\n  Tensor<double, 2> dtensor(20, 30);\n  dtensor.setRandom();\n  Tensor<float, 2> ftensor(20, 30);\n  ftensor = dtensor.cast<float>();\n\n  for (int i = 0; i < 20; ++i) {\n    for (int j = 0; j < 30; ++j) {\n      VERIFY_IS_APPROX(dtensor(i,j), static_cast<double>(ftensor(i,j)));\n    }\n  }\n}\n\n\nstatic void test_small_to_big_type_cast()\n{\n  Tensor<float, 2> ftensor(20, 30);\n  ftensor.setRandom();\n  Tensor<double, 2> dtensor(20, 30);\n  dtensor = ftensor.cast<double>();\n\n  for (int i = 0; i < 20; ++i) {\n    for (int j = 0; j < 30; ++j) {\n      VERIFY_IS_APPROX(dtensor(i,j), static_cast<double>(ftensor(i,j)));\n    }\n  }\n}\n\n\nvoid test_cxx11_tensor_casts()\n{\n   CALL_SUBTEST(test_simple_cast());\n   CALL_SUBTEST(test_vectorized_cast());\n   CALL_SUBTEST(test_float_to_int_cast());\n   CALL_SUBTEST(test_big_to_small_type_cast());\n   CALL_SUBTEST(test_small_to_big_type_cast());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_chipping.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\n\ntemplate<int DataLayout>\nstatic void test_simple_chip()\n{\n  Tensor<float, 5, DataLayout> tensor(2,3,5,7,11);\n  tensor.setRandom();\n\n  Tensor<float, 4, DataLayout> chip1;\n  chip1 = tensor.template chip<0>(1);\n\n  VERIFY_IS_EQUAL(chip1.dimension(0), 3);\n  VERIFY_IS_EQUAL(chip1.dimension(1), 5);\n  VERIFY_IS_EQUAL(chip1.dimension(2), 7);\n  VERIFY_IS_EQUAL(chip1.dimension(3), 11);\n\n  for (int i = 0; i < 3; ++i) {\n    for (int j = 0; j < 5; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        for (int l = 0; l < 11; ++l) {\n          VERIFY_IS_EQUAL(chip1(i,j,k,l), tensor(1,i,j,k,l));\n        }\n      }\n    }\n  }\n\n  Tensor<float, 4, DataLayout> chip2 = tensor.template chip<1>(1);\n  VERIFY_IS_EQUAL(chip2.dimension(0), 2);\n  VERIFY_IS_EQUAL(chip2.dimension(1), 5);\n  VERIFY_IS_EQUAL(chip2.dimension(2), 7);\n  VERIFY_IS_EQUAL(chip2.dimension(3), 11);\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        for (int l = 0; l < 11; ++l) {\n          VERIFY_IS_EQUAL(chip2(i,j,k,l), tensor(i,1,j,k,l));\n        }\n      }\n    }\n  }\n\n  Tensor<float, 4, DataLayout> chip3 = tensor.template chip<2>(2);\n  VERIFY_IS_EQUAL(chip3.dimension(0), 2);\n  VERIFY_IS_EQUAL(chip3.dimension(1), 3);\n  VERIFY_IS_EQUAL(chip3.dimension(2), 7);\n  VERIFY_IS_EQUAL(chip3.dimension(3), 11);\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        for (int l = 0; l < 11; ++l) {\n          VERIFY_IS_EQUAL(chip3(i,j,k,l), tensor(i,j,2,k,l));\n        }\n      }\n    }\n  }\n\n  Tensor<float, 4, DataLayout> chip4(tensor.template chip<3>(5));\n  VERIFY_IS_EQUAL(chip4.dimension(0), 2);\n  VERIFY_IS_EQUAL(chip4.dimension(1), 3);\n  VERIFY_IS_EQUAL(chip4.dimension(2), 5);\n  VERIFY_IS_EQUAL(chip4.dimension(3), 11);\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 5; ++k) {\n        for (int l = 0; l < 7; ++l) {\n          VERIFY_IS_EQUAL(chip4(i,j,k,l), tensor(i,j,k,5,l));\n        }\n      }\n    }\n  }\n\n  Tensor<float, 4, DataLayout> chip5(tensor.template chip<4>(7));\n  VERIFY_IS_EQUAL(chip5.dimension(0), 2);\n  VERIFY_IS_EQUAL(chip5.dimension(1), 3);\n  VERIFY_IS_EQUAL(chip5.dimension(2), 5);\n  VERIFY_IS_EQUAL(chip5.dimension(3), 7);\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 5; ++k) {\n        for (int l = 0; l < 7; ++l) {\n          VERIFY_IS_EQUAL(chip5(i,j,k,l), tensor(i,j,k,l,7));\n        }\n      }\n    }\n  }\n}\n\ntemplate<int DataLayout>\nstatic void test_dynamic_chip()\n{\n  Tensor<float, 5, DataLayout> tensor(2,3,5,7,11);\n  tensor.setRandom();\n\n  Tensor<float, 4, DataLayout> chip1;\n  chip1 = tensor.chip(1, 0);\n  VERIFY_IS_EQUAL(chip1.dimension(0), 3);\n  VERIFY_IS_EQUAL(chip1.dimension(1), 5);\n  VERIFY_IS_EQUAL(chip1.dimension(2), 7);\n  VERIFY_IS_EQUAL(chip1.dimension(3), 11);\n  for (int i = 0; i < 3; ++i) {\n    for (int j = 0; j < 5; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        for (int l = 0; l < 11; ++l) {\n          VERIFY_IS_EQUAL(chip1(i,j,k,l), tensor(1,i,j,k,l));\n        }\n      }\n    }\n  }\n\n  Tensor<float, 4, DataLayout> chip2 = tensor.chip(1, 1);\n  VERIFY_IS_EQUAL(chip2.dimension(0), 2);\n  VERIFY_IS_EQUAL(chip2.dimension(1), 5);\n  VERIFY_IS_EQUAL(chip2.dimension(2), 7);\n  VERIFY_IS_EQUAL(chip2.dimension(3), 11);\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        for (int l = 0; l < 11; ++l) {\n          VERIFY_IS_EQUAL(chip2(i,j,k,l), tensor(i,1,j,k,l));\n        }\n      }\n    }\n  }\n\n  Tensor<float, 4, DataLayout> chip3 = tensor.chip(2, 2);\n  VERIFY_IS_EQUAL(chip3.dimension(0), 2);\n  VERIFY_IS_EQUAL(chip3.dimension(1), 3);\n  VERIFY_IS_EQUAL(chip3.dimension(2), 7);\n  VERIFY_IS_EQUAL(chip3.dimension(3), 11);\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        for (int l = 0; l < 11; ++l) {\n          VERIFY_IS_EQUAL(chip3(i,j,k,l), tensor(i,j,2,k,l));\n        }\n      }\n    }\n  }\n\n  Tensor<float, 4, DataLayout> chip4(tensor.chip(5, 3));\n  VERIFY_IS_EQUAL(chip4.dimension(0), 2);\n  VERIFY_IS_EQUAL(chip4.dimension(1), 3);\n  VERIFY_IS_EQUAL(chip4.dimension(2), 5);\n  VERIFY_IS_EQUAL(chip4.dimension(3), 11);\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 5; ++k) {\n        for (int l = 0; l < 7; ++l) {\n          VERIFY_IS_EQUAL(chip4(i,j,k,l), tensor(i,j,k,5,l));\n        }\n      }\n    }\n  }\n\n  Tensor<float, 4, DataLayout> chip5(tensor.chip(7, 4));\n  VERIFY_IS_EQUAL(chip5.dimension(0), 2);\n  VERIFY_IS_EQUAL(chip5.dimension(1), 3);\n  VERIFY_IS_EQUAL(chip5.dimension(2), 5);\n  VERIFY_IS_EQUAL(chip5.dimension(3), 7);\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 5; ++k) {\n        for (int l = 0; l < 7; ++l) {\n          VERIFY_IS_EQUAL(chip5(i,j,k,l), tensor(i,j,k,l,7));\n        }\n      }\n    }\n  }\n}\n\ntemplate<int DataLayout>\nstatic void test_chip_in_expr() {\n  Tensor<float, 5, DataLayout> input1(2,3,5,7,11);\n  input1.setRandom();\n  Tensor<float, 4, DataLayout> input2(3,5,7,11);\n  input2.setRandom();\n\n  Tensor<float, 4, DataLayout> result = input1.template chip<0>(0) + input2;\n  for (int i = 0; i < 3; ++i) {\n    for (int j = 0; j < 5; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        for (int l = 0; l < 11; ++l) {\n          float expected = input1(0,i,j,k,l) + input2(i,j,k,l);\n          VERIFY_IS_EQUAL(result(i,j,k,l), expected);\n        }\n      }\n    }\n  }\n\n  Tensor<float, 3, DataLayout> input3(3,7,11);\n  input3.setRandom();\n  Tensor<float, 3, DataLayout> result2 = input1.template chip<0>(0).template chip<1>(2) + input3;\n  for (int i = 0; i < 3; ++i) {\n    for (int j = 0; j < 7; ++j) {\n      for (int k = 0; k < 11; ++k) {\n        float expected = input1(0,i,2,j,k) + input3(i,j,k);\n        VERIFY_IS_EQUAL(result2(i,j,k), expected);\n      }\n    }\n  }\n}\n\ntemplate<int DataLayout>\nstatic void test_chip_as_lvalue()\n{\n  Tensor<float, 5, DataLayout> input1(2,3,5,7,11);\n  input1.setRandom();\n\n  Tensor<float, 4, DataLayout> input2(3,5,7,11);\n  input2.setRandom();\n  Tensor<float, 5, DataLayout> tensor = input1;\n  tensor.template chip<0>(1) = input2;\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 5; ++k) {\n        for (int l = 0; l < 7; ++l) {\n          for (int m = 0; m < 11; ++m) {\n            if (i != 1) {\n              VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input1(i,j,k,l,m));\n            } else {\n              VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input2(j,k,l,m));\n            }\n          }\n        }\n      }\n    }\n  }\n\n  Tensor<float, 4, DataLayout> input3(2,5,7,11);\n  input3.setRandom();\n  tensor = input1;\n  tensor.template chip<1>(1) = input3;\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 5; ++k) {\n        for (int l = 0; l < 7; ++l) {\n          for (int m = 0; m < 11; ++m) {\n            if (j != 1) {\n              VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input1(i,j,k,l,m));\n            } else {\n              VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input3(i,k,l,m));\n            }\n          }\n        }\n      }\n    }\n  }\n\n  Tensor<float, 4, DataLayout> input4(2,3,7,11);\n  input4.setRandom();\n  tensor = input1;\n  tensor.template chip<2>(3) = input4;\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 5; ++k) {\n        for (int l = 0; l < 7; ++l) {\n          for (int m = 0; m < 11; ++m) {\n            if (k != 3) {\n              VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input1(i,j,k,l,m));\n            } else {\n              VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input4(i,j,l,m));\n            }\n          }\n        }\n      }\n    }\n  }\n\n  Tensor<float, 4, DataLayout> input5(2,3,5,11);\n  input5.setRandom();\n  tensor = input1;\n  tensor.template chip<3>(4) = input5;\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 5; ++k) {\n        for (int l = 0; l < 7; ++l) {\n          for (int m = 0; m < 11; ++m) {\n            if (l != 4) {\n              VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input1(i,j,k,l,m));\n            } else {\n              VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input5(i,j,k,m));\n            }\n          }\n        }\n      }\n    }\n  }\n\n  Tensor<float, 4, DataLayout> input6(2,3,5,7);\n  input6.setRandom();\n  tensor = input1;\n  tensor.template chip<4>(5) = input6;\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 5; ++k) {\n        for (int l = 0; l < 7; ++l) {\n          for (int m = 0; m < 11; ++m) {\n            if (m != 5) {\n              VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input1(i,j,k,l,m));\n            } else {\n              VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input6(i,j,k,l));\n            }\n          }\n        }\n      }\n    }\n  }\n\n  Tensor<float, 5, DataLayout> input7(2,3,5,7,11);\n  input7.setRandom();\n  tensor = input1;\n  tensor.chip(0, 0) = input7.chip(0, 0);\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 5; ++k) {\n        for (int l = 0; l < 7; ++l) {\n          for (int m = 0; m < 11; ++m) {\n            if (i != 0) {\n              VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input1(i,j,k,l,m));\n            } else {\n              VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input7(i,j,k,l,m));\n            }\n          }\n        }\n      }\n    }\n  }\n}\n\nstatic void test_chip_raw_data_col_major()\n{\n  Tensor<float, 5, ColMajor> tensor(2,3,5,7,11);\n  tensor.setRandom();\n\n  typedef TensorEvaluator<decltype(tensor.chip<4>(3)), DefaultDevice> Evaluator4;\n  auto chip = Evaluator4(tensor.chip<4>(3), DefaultDevice());\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 5; ++k) {\n        for (int l = 0; l < 7; ++l) {\n          int chip_index = i + 2 * (j + 3 * (k + 5 * l));\n          VERIFY_IS_EQUAL(chip.data()[chip_index], tensor(i,j,k,l,3));\n        }\n      }\n    }\n  }\n\n  typedef TensorEvaluator<decltype(tensor.chip<0>(0)), DefaultDevice> Evaluator0;\n  auto chip0 = Evaluator0(tensor.chip<0>(0), DefaultDevice());\n  VERIFY_IS_EQUAL(chip0.data(), static_cast<float*>(0));\n\n  typedef TensorEvaluator<decltype(tensor.chip<1>(0)), DefaultDevice> Evaluator1;\n  auto chip1 = Evaluator1(tensor.chip<1>(0), DefaultDevice());\n  VERIFY_IS_EQUAL(chip1.data(), static_cast<float*>(0));\n\n  typedef TensorEvaluator<decltype(tensor.chip<2>(0)), DefaultDevice> Evaluator2;\n  auto chip2 = Evaluator2(tensor.chip<2>(0), DefaultDevice());\n  VERIFY_IS_EQUAL(chip2.data(), static_cast<float*>(0));\n\n  typedef TensorEvaluator<decltype(tensor.chip<3>(0)), DefaultDevice> Evaluator3;\n  auto chip3 = Evaluator3(tensor.chip<3>(0), DefaultDevice());\n  VERIFY_IS_EQUAL(chip3.data(), static_cast<float*>(0));\n}\n\nstatic void test_chip_raw_data_row_major()\n{\n  Tensor<float, 5, RowMajor> tensor(11,7,5,3,2);\n  tensor.setRandom();\n\n  typedef TensorEvaluator<decltype(tensor.chip<0>(3)), DefaultDevice> Evaluator0;\n  auto chip = Evaluator0(tensor.chip<0>(3), DefaultDevice());\n  for (int i = 0; i < 7; ++i) {\n    for (int j = 0; j < 5; ++j) {\n      for (int k = 0; k < 3; ++k) {\n        for (int l = 0; l < 2; ++l) {\n          int chip_index = l + 2 * (k + 3 * (j + 5 * i));\n          VERIFY_IS_EQUAL(chip.data()[chip_index], tensor(3,i,j,k,l));\n        }\n      }\n    }\n  }\n\n  typedef TensorEvaluator<decltype(tensor.chip<1>(0)), DefaultDevice> Evaluator1;\n  auto chip1 = Evaluator1(tensor.chip<1>(0), DefaultDevice());\n  VERIFY_IS_EQUAL(chip1.data(), static_cast<float*>(0));\n\n  typedef TensorEvaluator<decltype(tensor.chip<2>(0)), DefaultDevice> Evaluator2;\n  auto chip2 = Evaluator2(tensor.chip<2>(0), DefaultDevice());\n  VERIFY_IS_EQUAL(chip2.data(), static_cast<float*>(0));\n\n  typedef TensorEvaluator<decltype(tensor.chip<3>(0)), DefaultDevice> Evaluator3;\n  auto chip3 = Evaluator3(tensor.chip<3>(0), DefaultDevice());\n  VERIFY_IS_EQUAL(chip3.data(), static_cast<float*>(0));\n\n  typedef TensorEvaluator<decltype(tensor.chip<4>(0)), DefaultDevice> Evaluator4;\n  auto chip4 = Evaluator4(tensor.chip<4>(0), DefaultDevice());\n  VERIFY_IS_EQUAL(chip4.data(), static_cast<float*>(0));\n}\n\nvoid test_cxx11_tensor_chipping()\n{\n  CALL_SUBTEST(test_simple_chip<ColMajor>());\n  CALL_SUBTEST(test_simple_chip<RowMajor>());\n  CALL_SUBTEST(test_dynamic_chip<ColMajor>());\n  CALL_SUBTEST(test_dynamic_chip<RowMajor>());\n  CALL_SUBTEST(test_chip_in_expr<ColMajor>());\n  CALL_SUBTEST(test_chip_in_expr<RowMajor>());\n  CALL_SUBTEST(test_chip_as_lvalue<ColMajor>());\n  CALL_SUBTEST(test_chip_as_lvalue<RowMajor>());\n  CALL_SUBTEST(test_chip_raw_data_col_major());\n  CALL_SUBTEST(test_chip_raw_data_row_major());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_comparisons.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\nusing Eigen::RowMajor;\n\nstatic void test_orderings()\n{\n  Tensor<float, 3> mat1(2,3,7);\n  Tensor<float, 3> mat2(2,3,7);\n  Tensor<bool, 3> lt(2,3,7);\n  Tensor<bool, 3> le(2,3,7);\n  Tensor<bool, 3> gt(2,3,7);\n  Tensor<bool, 3> ge(2,3,7);\n\n  mat1.setRandom();\n  mat2.setRandom();\n\n  lt = mat1 < mat2;\n  le = mat1 <= mat2;\n  gt = mat1 > mat2;\n  ge = mat1 >= mat2;\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        VERIFY_IS_EQUAL(lt(i,j,k), mat1(i,j,k) < mat2(i,j,k));\n        VERIFY_IS_EQUAL(le(i,j,k), mat1(i,j,k) <= mat2(i,j,k));\n        VERIFY_IS_EQUAL(gt(i,j,k), mat1(i,j,k) > mat2(i,j,k));\n        VERIFY_IS_EQUAL(ge(i,j,k), mat1(i,j,k) >= mat2(i,j,k));\n      }\n    }\n  }\n}\n\n\nstatic void test_equality()\n{\n  Tensor<float, 3> mat1(2,3,7);\n  Tensor<float, 3> mat2(2,3,7);\n\n  mat1.setRandom();\n  mat2.setRandom();\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        if (internal::random<bool>()) {\n          mat2(i,j,k) = mat1(i,j,k);\n        }\n      }\n    }\n  }\n\n  Tensor<bool, 3> eq(2,3,7);\n  Tensor<bool, 3> ne(2,3,7);\n  eq = (mat1 == mat2);\n  ne = (mat1 != mat2);\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        VERIFY_IS_EQUAL(eq(i,j,k), mat1(i,j,k) == mat2(i,j,k));\n        VERIFY_IS_EQUAL(ne(i,j,k), mat1(i,j,k) != mat2(i,j,k));\n      }\n    }\n  }\n}\n\n\nvoid test_cxx11_tensor_comparisons()\n{\n  CALL_SUBTEST(test_orderings());\n  CALL_SUBTEST(test_equality());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_complex_cuda.cu",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define EIGEN_TEST_NO_LONGDOUBLE\n#define EIGEN_TEST_FUNC cxx11_tensor_complex\n#define EIGEN_USE_GPU\n\n#include \"main.h\"\n#include <unsupported/Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\n\nvoid test_cuda_nullary() {\n  Tensor<std::complex<float>, 1, 0, int> in1(2);\n  Tensor<std::complex<float>, 1, 0, int> in2(2);\n  in1.setRandom();\n  in2.setRandom();\n\n  std::size_t float_bytes = in1.size() * sizeof(float);\n  std::size_t complex_bytes = in1.size() * sizeof(std::complex<float>);\n\n  std::complex<float>* d_in1;\n  std::complex<float>* d_in2;\n  float* d_out2;\n  cudaMalloc((void**)(&d_in1), complex_bytes);\n  cudaMalloc((void**)(&d_in2), complex_bytes);\n  cudaMalloc((void**)(&d_out2), float_bytes);\n  cudaMemcpy(d_in1, in1.data(), complex_bytes, cudaMemcpyHostToDevice);\n  cudaMemcpy(d_in2, in2.data(), complex_bytes, cudaMemcpyHostToDevice);\n\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n\n  Eigen::TensorMap<Eigen::Tensor<std::complex<float>, 1, 0, int>, Eigen::Aligned> gpu_in1(\n      d_in1, 2);\n  Eigen::TensorMap<Eigen::Tensor<std::complex<float>, 1, 0, int>, Eigen::Aligned> gpu_in2(\n      d_in2, 2);\n  Eigen::TensorMap<Eigen::Tensor<float, 1, 0, int>, Eigen::Aligned> gpu_out2(\n      d_out2, 2);\n\n  gpu_in1.device(gpu_device) = gpu_in1.constant(std::complex<float>(3.14f, 2.7f));\n  gpu_out2.device(gpu_device) = gpu_in2.abs();\n\n  Tensor<std::complex<float>, 1, 0, int> new1(2);\n  Tensor<float, 1, 0, int> new2(2);\n\n  assert(cudaMemcpyAsync(new1.data(), d_in1, complex_bytes, cudaMemcpyDeviceToHost,\n                         gpu_device.stream()) == cudaSuccess);\n  assert(cudaMemcpyAsync(new2.data(), d_out2, float_bytes, cudaMemcpyDeviceToHost,\n                         gpu_device.stream()) == cudaSuccess);\n\n  assert(cudaStreamSynchronize(gpu_device.stream()) == cudaSuccess);\n\n  for (int i = 0; i < 2; ++i) {\n    VERIFY_IS_APPROX(new1(i), std::complex<float>(3.14f, 2.7f));\n    VERIFY_IS_APPROX(new2(i), std::abs(in2(i)));\n  }\n\n  cudaFree(d_in1);\n  cudaFree(d_in2);\n  cudaFree(d_out2);\n}\n\n\nstatic void test_cuda_sum_reductions() {\n\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n\n  const int num_rows = internal::random<int>(1024, 5*1024);\n  const int num_cols = internal::random<int>(1024, 5*1024);\n\n  Tensor<std::complex<float>, 2> in(num_rows, num_cols);\n  in.setRandom();\n\n  Tensor<std::complex<float>, 0> full_redux;\n  full_redux = in.sum();\n\n  std::size_t in_bytes = in.size() * sizeof(std::complex<float>);\n  std::size_t out_bytes = full_redux.size() * sizeof(std::complex<float>);\n  std::complex<float>* gpu_in_ptr = static_cast<std::complex<float>*>(gpu_device.allocate(in_bytes));\n  std::complex<float>* gpu_out_ptr = static_cast<std::complex<float>*>(gpu_device.allocate(out_bytes));\n  gpu_device.memcpyHostToDevice(gpu_in_ptr, in.data(), in_bytes);\n\n  TensorMap<Tensor<std::complex<float>, 2> > in_gpu(gpu_in_ptr, num_rows, num_cols);\n  TensorMap<Tensor<std::complex<float>, 0> > out_gpu(gpu_out_ptr);\n\n  out_gpu.device(gpu_device) = in_gpu.sum();\n\n  Tensor<std::complex<float>, 0> full_redux_gpu;\n  gpu_device.memcpyDeviceToHost(full_redux_gpu.data(), gpu_out_ptr, out_bytes);\n  gpu_device.synchronize();\n\n  // Check that the CPU and GPU reductions return the same result.\n  VERIFY_IS_APPROX(full_redux(), full_redux_gpu());\n\n  gpu_device.deallocate(gpu_in_ptr);\n  gpu_device.deallocate(gpu_out_ptr);\n}\n\n\nstatic void test_cuda_product_reductions() {\n\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n\n  const int num_rows = internal::random<int>(1024, 5*1024);\n  const int num_cols = internal::random<int>(1024, 5*1024);\n\n  Tensor<std::complex<float>, 2> in(num_rows, num_cols);\n  in.setRandom();\n\n  Tensor<std::complex<float>, 0> full_redux;\n  full_redux = in.prod();\n\n  std::size_t in_bytes = in.size() * sizeof(std::complex<float>);\n  std::size_t out_bytes = full_redux.size() * sizeof(std::complex<float>);\n  std::complex<float>* gpu_in_ptr = static_cast<std::complex<float>*>(gpu_device.allocate(in_bytes));\n  std::complex<float>* gpu_out_ptr = static_cast<std::complex<float>*>(gpu_device.allocate(out_bytes));\n  gpu_device.memcpyHostToDevice(gpu_in_ptr, in.data(), in_bytes);\n\n  TensorMap<Tensor<std::complex<float>, 2> > in_gpu(gpu_in_ptr, num_rows, num_cols);\n  TensorMap<Tensor<std::complex<float>, 0> > out_gpu(gpu_out_ptr);\n\n  out_gpu.device(gpu_device) = in_gpu.prod();\n\n  Tensor<std::complex<float>, 0> full_redux_gpu;\n  gpu_device.memcpyDeviceToHost(full_redux_gpu.data(), gpu_out_ptr, out_bytes);\n  gpu_device.synchronize();\n\n  // Check that the CPU and GPU reductions return the same result.\n  VERIFY_IS_APPROX(full_redux(), full_redux_gpu());\n\n  gpu_device.deallocate(gpu_in_ptr);\n  gpu_device.deallocate(gpu_out_ptr);\n}\n\n\nvoid test_cxx11_tensor_complex()\n{\n  CALL_SUBTEST(test_cuda_nullary());\n  CALL_SUBTEST(test_cuda_sum_reductions());\n  CALL_SUBTEST(test_cuda_product_reductions());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_complex_cwise_ops_cuda.cu",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define EIGEN_TEST_NO_LONGDOUBLE\n#define EIGEN_TEST_FUNC cxx11_tensor_complex_cwise_ops\n#define EIGEN_USE_GPU\n\n#include \"main.h\"\n#include <unsupported/Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\n\ntemplate<typename T>\nvoid test_cuda_complex_cwise_ops() {\n  const int kNumItems = 2;\n  std::size_t complex_bytes = kNumItems * sizeof(std::complex<T>);\n\n  std::complex<T>* d_in1;\n  std::complex<T>* d_in2;\n  std::complex<T>* d_out;\n  cudaMalloc((void**)(&d_in1), complex_bytes);\n  cudaMalloc((void**)(&d_in2), complex_bytes);\n  cudaMalloc((void**)(&d_out), complex_bytes);\n\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n\n  Eigen::TensorMap<Eigen::Tensor<std::complex<T>, 1, 0, int>, Eigen::Aligned> gpu_in1(\n      d_in1, kNumItems);\n  Eigen::TensorMap<Eigen::Tensor<std::complex<T>, 1, 0, int>, Eigen::Aligned> gpu_in2(\n      d_in2, kNumItems);\n  Eigen::TensorMap<Eigen::Tensor<std::complex<T>, 1, 0, int>, Eigen::Aligned> gpu_out(\n      d_out, kNumItems);\n\n  const std::complex<T> a(3.14f, 2.7f);\n  const std::complex<T> b(-10.6f, 1.4f);\n\n  gpu_in1.device(gpu_device) = gpu_in1.constant(a);\n  gpu_in2.device(gpu_device) = gpu_in2.constant(b);\n\n  enum CwiseOp {\n    Add = 0,\n    Sub,\n    Mul,\n    Div\n  };\n\n  Tensor<std::complex<T>, 1, 0, int> actual(kNumItems);\n  for (int op = Add; op <= Div; op++) {\n    std::complex<T> expected;\n    switch (static_cast<CwiseOp>(op)) {\n      case Add:\n        gpu_out.device(gpu_device) = gpu_in1 + gpu_in2;\n        expected = a + b;\n        break;\n      case Sub:\n        gpu_out.device(gpu_device) = gpu_in1 - gpu_in2;\n        expected = a - b;\n        break;\n      case Mul:\n        gpu_out.device(gpu_device) = gpu_in1 * gpu_in2;\n        expected = a * b;\n        break;\n      case Div:\n        gpu_out.device(gpu_device) = gpu_in1 / gpu_in2;\n        expected = a / b;\n        break;\n    }\n    assert(cudaMemcpyAsync(actual.data(), d_out, complex_bytes, cudaMemcpyDeviceToHost,\n                           gpu_device.stream()) == cudaSuccess);\n    assert(cudaStreamSynchronize(gpu_device.stream()) == cudaSuccess);\n\n    for (int i = 0; i < kNumItems; ++i) {\n      VERIFY_IS_APPROX(actual(i), expected);\n    }\n  }\n\n  cudaFree(d_in1);\n  cudaFree(d_in2);\n  cudaFree(d_out);\n}\n\n\nvoid test_cxx11_tensor_complex_cwise_ops()\n{\n  CALL_SUBTEST(test_cuda_complex_cwise_ops<float>());\n  CALL_SUBTEST(test_cuda_complex_cwise_ops<double>());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_concatenation.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\n\ntemplate<int DataLayout>\nstatic void test_dimension_failures()\n{\n  Tensor<int, 3, DataLayout> left(2, 3, 1);\n  Tensor<int, 3, DataLayout> right(3, 3, 1);\n  left.setRandom();\n  right.setRandom();\n\n  // Okay; other dimensions are equal.\n  Tensor<int, 3, DataLayout> concatenation = left.concatenate(right, 0);\n\n  // Dimension mismatches.\n  VERIFY_RAISES_ASSERT(concatenation = left.concatenate(right, 1));\n  VERIFY_RAISES_ASSERT(concatenation = left.concatenate(right, 2));\n\n  // Axis > NumDims or < 0.\n  VERIFY_RAISES_ASSERT(concatenation = left.concatenate(right, 3));\n  VERIFY_RAISES_ASSERT(concatenation = left.concatenate(right, -1));\n}\n\ntemplate<int DataLayout>\nstatic void test_static_dimension_failure()\n{\n  Tensor<int, 2, DataLayout> left(2, 3);\n  Tensor<int, 3, DataLayout> right(2, 3, 1);\n\n#ifdef CXX11_TENSOR_CONCATENATION_STATIC_DIMENSION_FAILURE\n  // Technically compatible, but we static assert that the inputs have same\n  // NumDims.\n  Tensor<int, 3, DataLayout> concatenation = left.concatenate(right, 0);\n#endif\n\n  // This can be worked around in this case.\n  Tensor<int, 3, DataLayout> concatenation = left\n      .reshape(Tensor<int, 3>::Dimensions(2, 3, 1))\n      .concatenate(right, 0);\n  Tensor<int, 2, DataLayout> alternative = left\n      .concatenate(right.reshape(Tensor<int, 2>::Dimensions{{{2, 3}}}), 0);\n}\n\ntemplate<int DataLayout>\nstatic void test_simple_concatenation()\n{\n  Tensor<int, 3, DataLayout> left(2, 3, 1);\n  Tensor<int, 3, DataLayout> right(2, 3, 1);\n  left.setRandom();\n  right.setRandom();\n\n  Tensor<int, 3, DataLayout> concatenation = left.concatenate(right, 0);\n  VERIFY_IS_EQUAL(concatenation.dimension(0), 4);\n  VERIFY_IS_EQUAL(concatenation.dimension(1), 3);\n  VERIFY_IS_EQUAL(concatenation.dimension(2), 1);\n  for (int j = 0; j < 3; ++j) {\n    for (int i = 0; i < 2; ++i) {\n      VERIFY_IS_EQUAL(concatenation(i, j, 0), left(i, j, 0));\n    }\n    for (int i = 2; i < 4; ++i) {\n      VERIFY_IS_EQUAL(concatenation(i, j, 0), right(i - 2, j, 0));\n    }\n  }\n\n  concatenation = left.concatenate(right, 1);\n  VERIFY_IS_EQUAL(concatenation.dimension(0), 2);\n  VERIFY_IS_EQUAL(concatenation.dimension(1), 6);\n  VERIFY_IS_EQUAL(concatenation.dimension(2), 1);\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      VERIFY_IS_EQUAL(concatenation(i, j, 0), left(i, j, 0));\n    }\n    for (int j = 3; j < 6; ++j) {\n      VERIFY_IS_EQUAL(concatenation(i, j, 0), right(i, j - 3, 0));\n    }\n  }\n\n  concatenation = left.concatenate(right, 2);\n  VERIFY_IS_EQUAL(concatenation.dimension(0), 2);\n  VERIFY_IS_EQUAL(concatenation.dimension(1), 3);\n  VERIFY_IS_EQUAL(concatenation.dimension(2), 2);\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      VERIFY_IS_EQUAL(concatenation(i, j, 0), left(i, j, 0));\n      VERIFY_IS_EQUAL(concatenation(i, j, 1), right(i, j, 0));\n    }\n  }\n}\n\n\n// TODO(phli): Add test once we have a real vectorized implementation.\n// static void test_vectorized_concatenation() {}\n\nstatic void test_concatenation_as_lvalue()\n{\n  Tensor<int, 2> t1(2, 3);\n  Tensor<int, 2> t2(2, 3);\n  t1.setRandom();\n  t2.setRandom();\n\n  Tensor<int, 2> result(4, 3);\n  result.setRandom();\n  t1.concatenate(t2, 0) = result;\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      VERIFY_IS_EQUAL(t1(i, j), result(i, j));\n      VERIFY_IS_EQUAL(t2(i, j), result(i+2, j));\n    }\n  }\n}\n\n\nvoid test_cxx11_tensor_concatenation()\n{\n   CALL_SUBTEST(test_dimension_failures<ColMajor>());\n   CALL_SUBTEST(test_dimension_failures<RowMajor>());\n   CALL_SUBTEST(test_static_dimension_failure<ColMajor>());\n   CALL_SUBTEST(test_static_dimension_failure<RowMajor>());\n   CALL_SUBTEST(test_simple_concatenation<ColMajor>());\n   CALL_SUBTEST(test_simple_concatenation<RowMajor>());\n   // CALL_SUBTEST(test_vectorized_concatenation());\n   CALL_SUBTEST(test_concatenation_as_lvalue());\n\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_const.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\nusing Eigen::Tensor;\n\n\nstatic void test_simple_assign()\n{\n  Tensor<int, 3> random(2,3,7);\n  random.setRandom();\n\n  TensorMap<Tensor<const int, 3> > constant(random.data(), 2, 3, 7);\n  Tensor<int, 3> result(2,3,7);\n  result = constant;\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        VERIFY_IS_EQUAL((result(i,j,k)), random(i,j,k));\n      }\n    }\n  }\n}\n\n\nstatic void test_assign_of_const_tensor()\n{\n  Tensor<int, 3> random(2,3,7);\n  random.setRandom();\n\n  TensorMap<Tensor<const int, 3> > constant1(random.data(), 2, 3, 7);\n  TensorMap<const Tensor<int, 3> > constant2(random.data(), 2, 3, 7);\n  const TensorMap<Tensor<int, 3> > constant3(random.data(), 2, 3, 7);\n\n  Tensor<int, 2> result1 = constant1.chip(0, 2);\n  Tensor<int, 2> result2 = constant2.chip(0, 2);\n  Tensor<int, 2> result3 = constant3.chip(0, 2);\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      VERIFY_IS_EQUAL((result1(i,j)), random(i,j,0));\n      VERIFY_IS_EQUAL((result2(i,j)), random(i,j,0));\n      VERIFY_IS_EQUAL((result3(i,j)), random(i,j,0));\n    }\n  }\n}\n\n\nvoid test_cxx11_tensor_const()\n{\n  CALL_SUBTEST(test_simple_assign());\n  CALL_SUBTEST(test_assign_of_const_tensor());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_contract_cuda.cu",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n// Copyright (C) 2014 Navdeep Jaitly <ndjaitly@google.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define EIGEN_TEST_NO_LONGDOUBLE\n#define EIGEN_TEST_NO_COMPLEX\n#define EIGEN_TEST_FUNC cxx11_tensor_cuda\n#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int\n#define EIGEN_USE_GPU\n\n#include \"main.h\"\n#include <unsupported/Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\ntypedef Tensor<float, 1>::DimensionPair DimPair;\n\ntemplate<int DataLayout>\nvoid test_cuda_contraction(int m_size, int k_size, int n_size)\n{\n  std::cout << \"Testing for (\" << m_size << \",\" << k_size << \",\" << n_size << \")\" << std::endl;\n  // with these dimensions, the output has 300 * 140 elements, which is\n  // more than 30 * 1024, which is the number of threads in blocks on\n  // a 15 SM GK110 GPU\n  Tensor<float, 2, DataLayout> t_left(m_size, k_size);\n  Tensor<float, 2, DataLayout> t_right(k_size, n_size);\n  Tensor<float, 2, DataLayout> t_result(m_size, n_size);\n  Tensor<float, 2, DataLayout> t_result_gpu(m_size, n_size);\n  Eigen::array<DimPair, 1> dims(DimPair(1, 0));\n\n  t_left.setRandom();\n  t_right.setRandom();\n\n  std::size_t t_left_bytes = t_left.size()  * sizeof(float);\n  std::size_t t_right_bytes = t_right.size() * sizeof(float);\n  std::size_t t_result_bytes = t_result.size() * sizeof(float);\n\n  float* d_t_left;\n  float* d_t_right;\n  float* d_t_result;\n\n  cudaMalloc((void**)(&d_t_left), t_left_bytes);\n  cudaMalloc((void**)(&d_t_right), t_right_bytes);\n  cudaMalloc((void**)(&d_t_result), t_result_bytes);\n\n  cudaMemcpy(d_t_left, t_left.data(), t_left_bytes, cudaMemcpyHostToDevice);\n  cudaMemcpy(d_t_right, t_right.data(), t_right_bytes, cudaMemcpyHostToDevice);\n\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n\n  Eigen::TensorMap<Eigen::Tensor<float, 2, DataLayout> >\n      gpu_t_left(d_t_left, Eigen::array<int, 2>(m_size, k_size));\n  Eigen::TensorMap<Eigen::Tensor<float, 2, DataLayout> >\n      gpu_t_right(d_t_right, Eigen::array<int, 2>(k_size, n_size));\n  Eigen::TensorMap<Eigen::Tensor<float, 2, DataLayout> >\n      gpu_t_result(d_t_result, Eigen::array<int, 2>(m_size, n_size));\n\n\n  gpu_t_result.device(gpu_device) = gpu_t_left.contract(gpu_t_right, dims);\n  t_result = t_left.contract(t_right, dims);\n\n  cudaMemcpy(t_result_gpu.data(), d_t_result, t_result_bytes, cudaMemcpyDeviceToHost);\n  for (DenseIndex i = 0; i < t_result.size(); i++) {\n    if (fabs(t_result(i) - t_result_gpu(i)) < 1e-4f) {\n      continue;\n    }\n    if (Eigen::internal::isApprox(t_result(i), t_result_gpu(i), 1e-4f)) {\n      continue;\n    }\n    std::cout << \"mismatch detected at index \" << i << \": \" << t_result(i)\n              << \" vs \" <<  t_result_gpu(i) << std::endl;\n    assert(false);\n  }\n\n  cudaFree((void*)d_t_left);\n  cudaFree((void*)d_t_right);\n  cudaFree((void*)d_t_result);\n}\n\n\ntemplate<int DataLayout>\nvoid test_scalar(int m_size, int k_size, int n_size)\n{\n  std::cout << \"Testing for (\" << m_size << \",\" << k_size << \",\" << n_size << \")\" << std::endl;\n  // with these dimensions, the output has 300 * 140 elements, which is\n  // more than 30 * 1024, which is the number of threads in blocks on\n  // a 15 SM GK110 GPU\n  Tensor<float, 2, DataLayout> t_left(m_size, k_size);\n  Tensor<float, 2, DataLayout> t_right(k_size, n_size);\n  Tensor<float, 0, DataLayout> t_result;\n  Tensor<float, 0, DataLayout> t_result_gpu;\n  Eigen::array<DimPair, 2> dims(DimPair(0, 0), DimPair(1, 1));\n\n  t_left.setRandom();\n  t_right.setRandom();\n\n  std::size_t t_left_bytes = t_left.size()  * sizeof(float);\n  std::size_t t_right_bytes = t_right.size() * sizeof(float);\n  std::size_t t_result_bytes = sizeof(float);\n\n  float* d_t_left;\n  float* d_t_right;\n  float* d_t_result;\n\n  cudaMalloc((void**)(&d_t_left), t_left_bytes);\n  cudaMalloc((void**)(&d_t_right), t_right_bytes);\n  cudaMalloc((void**)(&d_t_result), t_result_bytes);\n\n  cudaMemcpy(d_t_left, t_left.data(), t_left_bytes, cudaMemcpyHostToDevice);\n  cudaMemcpy(d_t_right, t_right.data(), t_right_bytes, cudaMemcpyHostToDevice);\n\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n\n  Eigen::TensorMap<Eigen::Tensor<float, 2, DataLayout> >\n      gpu_t_left(d_t_left, m_size, k_size);\n  Eigen::TensorMap<Eigen::Tensor<float, 2, DataLayout> >\n      gpu_t_right(d_t_right, k_size, n_size);\n  Eigen::TensorMap<Eigen::Tensor<float, 0, DataLayout> >\n      gpu_t_result(d_t_result);\n\n  gpu_t_result.device(gpu_device) = gpu_t_left.contract(gpu_t_right, dims);\n  t_result = t_left.contract(t_right, dims);\n\n  cudaMemcpy(t_result_gpu.data(), d_t_result, t_result_bytes, cudaMemcpyDeviceToHost);\n  if (fabs(t_result() - t_result_gpu()) > 1e-4f &&\n      !Eigen::internal::isApprox(t_result(), t_result_gpu(), 1e-4f)) {\n    std::cout << \"mismatch detected: \" << t_result()\n              << \" vs \" <<  t_result_gpu() << std::endl;\n    assert(false);\n  }\n\n  cudaFree((void*)d_t_left);\n  cudaFree((void*)d_t_right);\n  cudaFree((void*)d_t_result);\n}\n\n\ntemplate<int DataLayout>\nvoid test_cuda_contraction_m() {\n  for (int k = 32; k < 256; k++) {\n    test_cuda_contraction<ColMajor>(k, 128, 128);\n    test_cuda_contraction<RowMajor>(k, 128, 128);\n  }\n}\n\ntemplate<int DataLayout>\nvoid test_cuda_contraction_k() {\n  for (int k = 32; k < 256; k++) {\n    test_cuda_contraction<ColMajor>(128, k, 128);\n    test_cuda_contraction<RowMajor>(128, k, 128);\n  }\n}\n\ntemplate<int DataLayout>\nvoid test_cuda_contraction_n() {\n  for (int k = 32; k < 256; k++) {\n    test_cuda_contraction<ColMajor>(128, 128, k);\n    test_cuda_contraction<RowMajor>(128, 128, k);\n  }\n}\n\n\ntemplate<int DataLayout>\nvoid test_cuda_contraction_sizes() {\n  int m_sizes[] = { 31,  39,   63,   64,   65,\n                   127, 129,  255,  257 , 511,\n                   512, 513, 1023, 1024, 1025};\n\n  int n_sizes[] = { 31,  39,   63,   64,   65,\n                   127, 129,  255,  257,  511,\n                   512, 513, 1023, 1024, 1025};\n\n  int k_sizes[] = {  31,   39,  63,  64,   65,\n                     95,   96, 127, 129,  255,\n                    257,  511, 512, 513, 1023,\n                   1024, 1025};\n\n  for (int i = 0; i < 15; i++) {\n    for (int j = 0; j < 15; j++) {\n      for (int k = 0; k < 17; k++) {\n        test_cuda_contraction<DataLayout>(m_sizes[i], n_sizes[j], k_sizes[k]);\n      }\n    }\n  }\n}\n\nvoid test_cxx11_tensor_cuda()\n{\n  CALL_SUBTEST_1(test_cuda_contraction<ColMajor>(128, 128, 128));\n  CALL_SUBTEST_1(test_cuda_contraction<RowMajor>(128, 128, 128));\n\n  CALL_SUBTEST_1(test_scalar<ColMajor>(128, 128, 128));\n  CALL_SUBTEST_1(test_scalar<RowMajor>(128, 128, 128));\n\n  CALL_SUBTEST_2(test_cuda_contraction_m<ColMajor>());\n  CALL_SUBTEST_3(test_cuda_contraction_m<RowMajor>());\n\n  CALL_SUBTEST_4(test_cuda_contraction_k<ColMajor>());\n  CALL_SUBTEST_5(test_cuda_contraction_k<RowMajor>());\n\n  CALL_SUBTEST_6(test_cuda_contraction_n<ColMajor>());\n  CALL_SUBTEST_7(test_cuda_contraction_n<RowMajor>());\n\n  CALL_SUBTEST_8(test_cuda_contraction_sizes<ColMajor>());\n  CALL_SUBTEST_9(test_cuda_contraction_sizes<RowMajor>());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_contraction.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::DefaultDevice;\nusing Eigen::Tensor;\n\ntypedef Tensor<float, 1>::DimensionPair DimPair;\n\ntemplate<int DataLayout>\nstatic void test_evals()\n{\n  Tensor<float, 2, DataLayout> mat1(2, 3);\n  Tensor<float, 2, DataLayout> mat2(2, 3);\n  Tensor<float, 2, DataLayout> mat3(3, 2);\n\n  mat1.setRandom();\n  mat2.setRandom();\n  mat3.setRandom();\n\n  Tensor<float, 2, DataLayout> mat4(3,3);\n  mat4.setZero();\n  Eigen::array<DimPair, 1> dims3 = {{DimPair(0, 0)}};\n  typedef TensorEvaluator<decltype(mat1.contract(mat2, dims3)), DefaultDevice> Evaluator;\n  Evaluator eval(mat1.contract(mat2, dims3), DefaultDevice());\n  eval.evalTo(mat4.data());\n  EIGEN_STATIC_ASSERT(Evaluator::NumDims==2ul, YOU_MADE_A_PROGRAMMING_MISTAKE);\n  VERIFY_IS_EQUAL(eval.dimensions()[0], 3);\n  VERIFY_IS_EQUAL(eval.dimensions()[1], 3);\n\n  VERIFY_IS_APPROX(mat4(0,0), mat1(0,0)*mat2(0,0) + mat1(1,0)*mat2(1,0));\n  VERIFY_IS_APPROX(mat4(0,1), mat1(0,0)*mat2(0,1) + mat1(1,0)*mat2(1,1));\n  VERIFY_IS_APPROX(mat4(0,2), mat1(0,0)*mat2(0,2) + mat1(1,0)*mat2(1,2));\n  VERIFY_IS_APPROX(mat4(1,0), mat1(0,1)*mat2(0,0) + mat1(1,1)*mat2(1,0));\n  VERIFY_IS_APPROX(mat4(1,1), mat1(0,1)*mat2(0,1) + mat1(1,1)*mat2(1,1));\n  VERIFY_IS_APPROX(mat4(1,2), mat1(0,1)*mat2(0,2) + mat1(1,1)*mat2(1,2));\n  VERIFY_IS_APPROX(mat4(2,0), mat1(0,2)*mat2(0,0) + mat1(1,2)*mat2(1,0));\n  VERIFY_IS_APPROX(mat4(2,1), mat1(0,2)*mat2(0,1) + mat1(1,2)*mat2(1,1));\n  VERIFY_IS_APPROX(mat4(2,2), mat1(0,2)*mat2(0,2) + mat1(1,2)*mat2(1,2));\n\n  Tensor<float, 2, DataLayout> mat5(2,2);\n  mat5.setZero();\n  Eigen::array<DimPair, 1> dims4 = {{DimPair(1, 1)}};\n  typedef TensorEvaluator<decltype(mat1.contract(mat2, dims4)), DefaultDevice> Evaluator2;\n  Evaluator2 eval2(mat1.contract(mat2, dims4), DefaultDevice());\n  eval2.evalTo(mat5.data());\n  EIGEN_STATIC_ASSERT(Evaluator2::NumDims==2ul, YOU_MADE_A_PROGRAMMING_MISTAKE);\n  VERIFY_IS_EQUAL(eval2.dimensions()[0], 2);\n  VERIFY_IS_EQUAL(eval2.dimensions()[1], 2);\n\n  VERIFY_IS_APPROX(mat5(0,0), mat1(0,0)*mat2(0,0) + mat1(0,1)*mat2(0,1) + mat1(0,2)*mat2(0,2));\n  VERIFY_IS_APPROX(mat5(0,1), mat1(0,0)*mat2(1,0) + mat1(0,1)*mat2(1,1) + mat1(0,2)*mat2(1,2));\n  VERIFY_IS_APPROX(mat5(1,0), mat1(1,0)*mat2(0,0) + mat1(1,1)*mat2(0,1) + mat1(1,2)*mat2(0,2));\n  VERIFY_IS_APPROX(mat5(1,1), mat1(1,0)*mat2(1,0) + mat1(1,1)*mat2(1,1) + mat1(1,2)*mat2(1,2));\n\n  Tensor<float, 2, DataLayout> mat6(2,2);\n  mat6.setZero();\n  Eigen::array<DimPair, 1> dims6 = {{DimPair(1, 0)}};\n  typedef TensorEvaluator<decltype(mat1.contract(mat3, dims6)), DefaultDevice> Evaluator3;\n  Evaluator3 eval3(mat1.contract(mat3, dims6), DefaultDevice());\n  eval3.evalTo(mat6.data());\n  EIGEN_STATIC_ASSERT(Evaluator3::NumDims==2ul, YOU_MADE_A_PROGRAMMING_MISTAKE);\n  VERIFY_IS_EQUAL(eval3.dimensions()[0], 2);\n  VERIFY_IS_EQUAL(eval3.dimensions()[1], 2);\n\n  VERIFY_IS_APPROX(mat6(0,0), mat1(0,0)*mat3(0,0) + mat1(0,1)*mat3(1,0) + mat1(0,2)*mat3(2,0));\n  VERIFY_IS_APPROX(mat6(0,1), mat1(0,0)*mat3(0,1) + mat1(0,1)*mat3(1,1) + mat1(0,2)*mat3(2,1));\n  VERIFY_IS_APPROX(mat6(1,0), mat1(1,0)*mat3(0,0) + mat1(1,1)*mat3(1,0) + mat1(1,2)*mat3(2,0));\n  VERIFY_IS_APPROX(mat6(1,1), mat1(1,0)*mat3(0,1) + mat1(1,1)*mat3(1,1) + mat1(1,2)*mat3(2,1));\n}\n\ntemplate<int DataLayout>\nstatic void test_scalar()\n{\n  Tensor<float, 1, DataLayout> vec1({6});\n  Tensor<float, 1, DataLayout> vec2({6});\n\n  vec1.setRandom();\n  vec2.setRandom();\n\n  Eigen::array<DimPair, 1> dims = {{DimPair(0, 0)}};\n  Tensor<float, 0, DataLayout> scalar = vec1.contract(vec2, dims);\n\n  float expected = 0.0f;\n  for (int i = 0; i < 6; ++i) {\n    expected += vec1(i) * vec2(i);\n  }\n  VERIFY_IS_APPROX(scalar(), expected);\n}\n\ntemplate<int DataLayout>\nstatic void test_multidims()\n{\n  Tensor<float, 3, DataLayout> mat1(2, 2, 2);\n  Tensor<float, 4, DataLayout> mat2(2, 2, 2, 2);\n\n  mat1.setRandom();\n  mat2.setRandom();\n\n  Tensor<float, 3, DataLayout> mat3(2, 2, 2);\n  mat3.setZero();\n  Eigen::array<DimPair, 2> dims = {{DimPair(1, 2), DimPair(2, 3)}};\n  typedef TensorEvaluator<decltype(mat1.contract(mat2, dims)), DefaultDevice> Evaluator;\n  Evaluator eval(mat1.contract(mat2, dims), DefaultDevice());\n  eval.evalTo(mat3.data());\n  EIGEN_STATIC_ASSERT(Evaluator::NumDims==3ul, YOU_MADE_A_PROGRAMMING_MISTAKE);\n  VERIFY_IS_EQUAL(eval.dimensions()[0], 2);\n  VERIFY_IS_EQUAL(eval.dimensions()[1], 2);\n  VERIFY_IS_EQUAL(eval.dimensions()[2], 2);\n\n  VERIFY_IS_APPROX(mat3(0,0,0), mat1(0,0,0)*mat2(0,0,0,0) + mat1(0,1,0)*mat2(0,0,1,0) +\n                                mat1(0,0,1)*mat2(0,0,0,1) + mat1(0,1,1)*mat2(0,0,1,1));\n  VERIFY_IS_APPROX(mat3(0,0,1), mat1(0,0,0)*mat2(0,1,0,0) + mat1(0,1,0)*mat2(0,1,1,0) +\n                                mat1(0,0,1)*mat2(0,1,0,1) + mat1(0,1,1)*mat2(0,1,1,1));\n  VERIFY_IS_APPROX(mat3(0,1,0), mat1(0,0,0)*mat2(1,0,0,0) + mat1(0,1,0)*mat2(1,0,1,0) +\n                                mat1(0,0,1)*mat2(1,0,0,1) + mat1(0,1,1)*mat2(1,0,1,1));\n  VERIFY_IS_APPROX(mat3(0,1,1), mat1(0,0,0)*mat2(1,1,0,0) + mat1(0,1,0)*mat2(1,1,1,0) +\n                                mat1(0,0,1)*mat2(1,1,0,1) + mat1(0,1,1)*mat2(1,1,1,1));\n  VERIFY_IS_APPROX(mat3(1,0,0), mat1(1,0,0)*mat2(0,0,0,0) + mat1(1,1,0)*mat2(0,0,1,0) +\n                                mat1(1,0,1)*mat2(0,0,0,1) + mat1(1,1,1)*mat2(0,0,1,1));\n  VERIFY_IS_APPROX(mat3(1,0,1), mat1(1,0,0)*mat2(0,1,0,0) + mat1(1,1,0)*mat2(0,1,1,0) +\n                                mat1(1,0,1)*mat2(0,1,0,1) + mat1(1,1,1)*mat2(0,1,1,1));\n  VERIFY_IS_APPROX(mat3(1,1,0), mat1(1,0,0)*mat2(1,0,0,0) + mat1(1,1,0)*mat2(1,0,1,0) +\n                                mat1(1,0,1)*mat2(1,0,0,1) + mat1(1,1,1)*mat2(1,0,1,1));\n  VERIFY_IS_APPROX(mat3(1,1,1), mat1(1,0,0)*mat2(1,1,0,0) + mat1(1,1,0)*mat2(1,1,1,0) +\n                                mat1(1,0,1)*mat2(1,1,0,1) + mat1(1,1,1)*mat2(1,1,1,1));\n\n  Tensor<float, 2, DataLayout> mat4(2, 2);\n  Tensor<float, 3, DataLayout> mat5(2, 2, 2);\n\n  mat4.setRandom();\n  mat5.setRandom();\n\n  Tensor<float, 1, DataLayout> mat6(2);\n  mat6.setZero();\n  Eigen::array<DimPair, 2> dims2({{DimPair(0, 1), DimPair(1, 0)}});\n  typedef TensorEvaluator<decltype(mat4.contract(mat5, dims2)), DefaultDevice> Evaluator2;\n  Evaluator2 eval2(mat4.contract(mat5, dims2), DefaultDevice());\n  eval2.evalTo(mat6.data());\n  EIGEN_STATIC_ASSERT(Evaluator2::NumDims==1ul, YOU_MADE_A_PROGRAMMING_MISTAKE);\n  VERIFY_IS_EQUAL(eval2.dimensions()[0], 2);\n\n  VERIFY_IS_APPROX(mat6(0), mat4(0,0)*mat5(0,0,0) + mat4(1,0)*mat5(0,1,0) +\n                   mat4(0,1)*mat5(1,0,0) + mat4(1,1)*mat5(1,1,0));\n  VERIFY_IS_APPROX(mat6(1), mat4(0,0)*mat5(0,0,1) + mat4(1,0)*mat5(0,1,1) +\n                   mat4(0,1)*mat5(1,0,1) + mat4(1,1)*mat5(1,1,1));\n}\n\ntemplate<int DataLayout>\nstatic void test_holes() {\n  Tensor<float, 4, DataLayout> t1(2, 5, 7, 3);\n  Tensor<float, 5, DataLayout> t2(2, 7, 11, 13, 3);\n  t1.setRandom();\n  t2.setRandom();\n\n  Eigen::array<DimPair, 2> dims = {{DimPair(0, 0), DimPair(3, 4)}};\n  Tensor<float, 5, DataLayout> result = t1.contract(t2, dims);\n  VERIFY_IS_EQUAL(result.dimension(0), 5);\n  VERIFY_IS_EQUAL(result.dimension(1), 7);\n  VERIFY_IS_EQUAL(result.dimension(2), 7);\n  VERIFY_IS_EQUAL(result.dimension(3), 11);\n  VERIFY_IS_EQUAL(result.dimension(4), 13);\n\n  for (int i = 0; i < 5; ++i) {\n    for (int j = 0; j < 5; ++j) {\n      for (int k = 0; k < 5; ++k) {\n        for (int l = 0; l < 5; ++l) {\n          for (int m = 0; m < 5; ++m) {\n            VERIFY_IS_APPROX(result(i, j, k, l, m),\n                             t1(0, i, j, 0) * t2(0, k, l, m, 0) +\n                             t1(1, i, j, 0) * t2(1, k, l, m, 0) +\n                             t1(0, i, j, 1) * t2(0, k, l, m, 1) +\n                             t1(1, i, j, 1) * t2(1, k, l, m, 1) +\n                             t1(0, i, j, 2) * t2(0, k, l, m, 2) +\n                             t1(1, i, j, 2) * t2(1, k, l, m, 2));\n          }\n        }\n      }\n    }\n  }\n}\n\ntemplate<int DataLayout>\nstatic void test_full_redux()\n{\n  Tensor<float, 2, DataLayout> t1(2, 2);\n  Tensor<float, 3, DataLayout> t2(2, 2, 2);\n  t1.setRandom();\n  t2.setRandom();\n\n  Eigen::array<DimPair, 2> dims = {{DimPair(0, 0), DimPair(1, 1)}};\n  Tensor<float, 1, DataLayout> result = t1.contract(t2, dims);\n  VERIFY_IS_EQUAL(result.dimension(0), 2);\n  VERIFY_IS_APPROX(result(0), t1(0, 0) * t2(0, 0, 0) +  t1(1, 0) * t2(1, 0, 0)\n                            + t1(0, 1) * t2(0, 1, 0) +  t1(1, 1) * t2(1, 1, 0));\n  VERIFY_IS_APPROX(result(1), t1(0, 0) * t2(0, 0, 1) +  t1(1, 0) * t2(1, 0, 1)\n                            + t1(0, 1) * t2(0, 1, 1) +  t1(1, 1) * t2(1, 1, 1));\n\n  dims[0] = DimPair(1, 0);\n  dims[1] = DimPair(2, 1);\n  result = t2.contract(t1, dims);\n  VERIFY_IS_EQUAL(result.dimension(0), 2);\n  VERIFY_IS_APPROX(result(0), t1(0, 0) * t2(0, 0, 0) +  t1(1, 0) * t2(0, 1, 0)\n                            + t1(0, 1) * t2(0, 0, 1) +  t1(1, 1) * t2(0, 1, 1));\n  VERIFY_IS_APPROX(result(1), t1(0, 0) * t2(1, 0, 0) +  t1(1, 0) * t2(1, 1, 0)\n                            + t1(0, 1) * t2(1, 0, 1) +  t1(1, 1) * t2(1, 1, 1));\n}\n\ntemplate<int DataLayout>\nstatic void test_contraction_of_contraction()\n{\n  Tensor<float, 2, DataLayout> t1(2, 2);\n  Tensor<float, 2, DataLayout> t2(2, 2);\n  Tensor<float, 2, DataLayout> t3(2, 2);\n  Tensor<float, 2, DataLayout> t4(2, 2);\n  t1.setRandom();\n  t2.setRandom();\n  t3.setRandom();\n  t4.setRandom();\n\n  Eigen::array<DimPair, 1> dims = {{DimPair(1, 0)}};\n  auto contract1 = t1.contract(t2, dims);\n  auto diff = t3 - contract1;\n  auto contract2 = t1.contract(t4, dims);\n  Tensor<float, 2, DataLayout> result = contract2.contract(diff, dims);\n\n  VERIFY_IS_EQUAL(result.dimension(0), 2);\n  VERIFY_IS_EQUAL(result.dimension(1), 2);\n\n  Eigen::Map<Eigen::Matrix<float, Dynamic, Dynamic, DataLayout>>\n      m1(t1.data(), 2, 2), m2(t2.data(), 2, 2), m3(t3.data(), 2, 2),\n      m4(t4.data(), 2, 2);\n  Eigen::Matrix<float, Dynamic, Dynamic, DataLayout>\n      expected = (m1 * m4) * (m3 - m1 * m2);\n\n  VERIFY_IS_APPROX(result(0, 0), expected(0, 0));\n  VERIFY_IS_APPROX(result(0, 1), expected(0, 1));\n  VERIFY_IS_APPROX(result(1, 0), expected(1, 0));\n  VERIFY_IS_APPROX(result(1, 1), expected(1, 1));\n}\n\ntemplate<int DataLayout>\nstatic void test_expr()\n{\n  Tensor<float, 2, DataLayout> mat1(2, 3);\n  Tensor<float, 2, DataLayout> mat2(3, 2);\n  mat1.setRandom();\n  mat2.setRandom();\n\n  Tensor<float, 2, DataLayout> mat3(2,2);\n\n  Eigen::array<DimPair, 1> dims = {{DimPair(1, 0)}};\n  mat3 = mat1.contract(mat2, dims);\n\n  VERIFY_IS_APPROX(mat3(0,0), mat1(0,0)*mat2(0,0) + mat1(0,1)*mat2(1,0) + mat1(0,2)*mat2(2,0));\n  VERIFY_IS_APPROX(mat3(0,1), mat1(0,0)*mat2(0,1) + mat1(0,1)*mat2(1,1) + mat1(0,2)*mat2(2,1));\n  VERIFY_IS_APPROX(mat3(1,0), mat1(1,0)*mat2(0,0) + mat1(1,1)*mat2(1,0) + mat1(1,2)*mat2(2,0));\n  VERIFY_IS_APPROX(mat3(1,1), mat1(1,0)*mat2(0,1) + mat1(1,1)*mat2(1,1) + mat1(1,2)*mat2(2,1));\n}\n\ntemplate<int DataLayout>\nstatic void test_out_of_order_contraction()\n{\n  Tensor<float, 3, DataLayout> mat1(2, 2, 2);\n  Tensor<float, 3, DataLayout> mat2(2, 2, 2);\n\n  mat1.setRandom();\n  mat2.setRandom();\n\n  Tensor<float, 2, DataLayout> mat3(2, 2);\n\n  Eigen::array<DimPair, 2> dims = {{DimPair(2, 0), DimPair(0, 2)}};\n  mat3 = mat1.contract(mat2, dims);\n\n  VERIFY_IS_APPROX(mat3(0, 0),\n                   mat1(0,0,0)*mat2(0,0,0) + mat1(1,0,0)*mat2(0,0,1) +\n                   mat1(0,0,1)*mat2(1,0,0) + mat1(1,0,1)*mat2(1,0,1));\n  VERIFY_IS_APPROX(mat3(1, 0),\n                   mat1(0,1,0)*mat2(0,0,0) + mat1(1,1,0)*mat2(0,0,1) +\n                   mat1(0,1,1)*mat2(1,0,0) + mat1(1,1,1)*mat2(1,0,1));\n  VERIFY_IS_APPROX(mat3(0, 1),\n                   mat1(0,0,0)*mat2(0,1,0) + mat1(1,0,0)*mat2(0,1,1) +\n                   mat1(0,0,1)*mat2(1,1,0) + mat1(1,0,1)*mat2(1,1,1));\n  VERIFY_IS_APPROX(mat3(1, 1),\n                   mat1(0,1,0)*mat2(0,1,0) + mat1(1,1,0)*mat2(0,1,1) +\n                   mat1(0,1,1)*mat2(1,1,0) + mat1(1,1,1)*mat2(1,1,1));\n\n  Eigen::array<DimPair, 2> dims2 = {{DimPair(0, 2), DimPair(2, 0)}};\n  mat3 = mat1.contract(mat2, dims2);\n\n  VERIFY_IS_APPROX(mat3(0, 0),\n                   mat1(0,0,0)*mat2(0,0,0) + mat1(1,0,0)*mat2(0,0,1) +\n                   mat1(0,0,1)*mat2(1,0,0) + mat1(1,0,1)*mat2(1,0,1));\n  VERIFY_IS_APPROX(mat3(1, 0),\n                   mat1(0,1,0)*mat2(0,0,0) + mat1(1,1,0)*mat2(0,0,1) +\n                   mat1(0,1,1)*mat2(1,0,0) + mat1(1,1,1)*mat2(1,0,1));\n  VERIFY_IS_APPROX(mat3(0, 1),\n                   mat1(0,0,0)*mat2(0,1,0) + mat1(1,0,0)*mat2(0,1,1) +\n                   mat1(0,0,1)*mat2(1,1,0) + mat1(1,0,1)*mat2(1,1,1));\n  VERIFY_IS_APPROX(mat3(1, 1),\n                   mat1(0,1,0)*mat2(0,1,0) + mat1(1,1,0)*mat2(0,1,1) +\n                   mat1(0,1,1)*mat2(1,1,0) + mat1(1,1,1)*mat2(1,1,1));\n\n}\n\ntemplate<int DataLayout>\nstatic void test_consistency()\n{\n  // this does something like testing (A*B)^T = (B^T * A^T)\n\n  Tensor<float, 3, DataLayout> mat1(4, 3, 5);\n  Tensor<float, 5, DataLayout> mat2(3, 2, 1, 5, 4);\n  mat1.setRandom();\n  mat2.setRandom();\n\n  Tensor<float, 4, DataLayout> mat3(5, 2, 1, 5);\n  Tensor<float, 4, DataLayout> mat4(2, 1, 5, 5);\n\n  // contract on dimensions of size 4 and 3\n  Eigen::array<DimPair, 2> dims1 = {{DimPair(0, 4), DimPair(1, 0)}};\n  Eigen::array<DimPair, 2> dims2 = {{DimPair(4, 0), DimPair(0, 1)}};\n\n  mat3 = mat1.contract(mat2, dims1);\n  mat4 = mat2.contract(mat1, dims2);\n\n  // check that these are equal except for ordering of dimensions\n  if (DataLayout == ColMajor) {\n    for (size_t i = 0; i < 5; i++) {\n      for (size_t j = 0; j < 10; j++) {\n        VERIFY_IS_APPROX(mat3.data()[i + 5 * j], mat4.data()[j + 10 * i]);\n      }\n    }\n  } else {\n    // Row major\n    for (size_t i = 0; i < 5; i++) {\n      for (size_t j = 0; j < 10; j++) {\n        VERIFY_IS_APPROX(mat3.data()[10 * i + j], mat4.data()[i + 5 * j]);\n      }\n    }\n  }\n}\n\ntemplate<int DataLayout>\nstatic void test_large_contraction()\n{\n  Tensor<float, 4, DataLayout> t_left(30, 50, 8, 31);\n  Tensor<float, 5, DataLayout> t_right(8, 31, 7, 20, 10);\n  Tensor<float, 5, DataLayout> t_result(30, 50, 7, 20, 10);\n\n  t_left.setRandom();\n  t_right.setRandom();\n\n  // Add a little offset so that the results won't be close to zero.\n  t_left += t_left.constant(1.0f);\n  t_right += t_right.constant(1.0f);\n\n  typedef Map<Eigen::Matrix<float, Dynamic, Dynamic, DataLayout>> MapXf;\n  MapXf m_left(t_left.data(), 1500, 248);\n  MapXf m_right(t_right.data(), 248, 1400);\n  Eigen::Matrix<float, Dynamic, Dynamic, DataLayout> m_result(1500, 1400);\n\n  // this contraction should be equivalent to a single matrix multiplication\n  Eigen::array<DimPair, 2> dims = {{DimPair(2, 0), DimPair(3, 1)}};\n\n  // compute results by separate methods\n  t_result = t_left.contract(t_right, dims);\n  m_result = m_left * m_right;\n\n  for (int i = 0; i < t_result.dimensions().TotalSize(); i++) {\n    VERIFY(&t_result.data()[i] != &m_result.data()[i]);\n    VERIFY_IS_APPROX(t_result.data()[i], m_result.data()[i]);\n  }\n}\n\ntemplate<int DataLayout>\nstatic void test_matrix_vector()\n{\n  Tensor<float, 2, DataLayout> t_left(30, 50);\n  Tensor<float, 1, DataLayout> t_right(50);\n  Tensor<float, 1, DataLayout> t_result(30);\n\n  t_left.setRandom();\n  t_right.setRandom();\n\n  typedef Map<Eigen::Matrix<float, Dynamic, Dynamic, DataLayout>> MapXf;\n  MapXf m_left(t_left.data(), 30, 50);\n  MapXf m_right(t_right.data(), 50, 1);\n  Eigen::Matrix<float, Dynamic, Dynamic, DataLayout> m_result(30, 1);\n\n  // this contraction should be equivalent to a single matrix multiplication\n  Eigen::array<DimPair, 1> dims{{DimPair(1, 0)}};\n\n  // compute results by separate methods\n  t_result = t_left.contract(t_right, dims);\n  m_result = m_left * m_right;\n\n  for (int i = 0; i < t_result.dimensions().TotalSize(); i++) {\n    VERIFY(internal::isApprox(t_result(i), m_result(i, 0), 1));\n  }\n}\n\n\ntemplate<int DataLayout>\nstatic void test_tensor_vector()\n{\n  Tensor<float, 3, DataLayout> t_left(7, 13, 17);\n  Tensor<float, 2, DataLayout> t_right(1, 7);\n\n  t_left.setRandom();\n  t_right.setRandom();\n\n  typedef typename Tensor<float, 1, DataLayout>::DimensionPair DimensionPair;\n  Eigen::array<DimensionPair, 1> dim_pair01{{{0, 1}}};\n  Tensor<float, 3, DataLayout> t_result = t_left.contract(t_right, dim_pair01);\n\n  typedef Map<Eigen::Matrix<float, Dynamic, Dynamic, DataLayout>> MapXf;\n  MapXf m_left(t_left.data(), 7, 13*17);\n  MapXf m_right(t_right.data(), 1, 7);\n  Eigen::Matrix<float, Dynamic, Dynamic, DataLayout> m_result = m_left.transpose() * m_right.transpose();\n\n  for (int i = 0; i < t_result.dimensions().TotalSize(); i++) {\n    VERIFY(internal::isApprox(t_result(i), m_result(i, 0), 1));\n  }\n}\n\n\ntemplate<int DataLayout>\nstatic void test_small_blocking_factors()\n{\n  Tensor<float, 4, DataLayout> t_left(30, 5, 3, 31);\n  Tensor<float, 5, DataLayout> t_right(3, 31, 7, 20, 1);\n  t_left.setRandom();\n  t_right.setRandom();\n\n  // Add a little offset so that the results won't be close to zero.\n  t_left += t_left.constant(1.0f);\n  t_right += t_right.constant(1.0f);\n\n  // Force the cache sizes, which results in smaller blocking factors.\n  Eigen::setCpuCacheSizes(896, 1920, 2944);\n\n  // this contraction should be equivalent to a single matrix multiplication\n  Eigen::array<DimPair, 2> dims = {{DimPair(2, 0), DimPair(3, 1)}};\n  Tensor<float, 5, DataLayout> t_result;\n  t_result = t_left.contract(t_right, dims);\n\n  // compute result using a simple eigen matrix product\n  Map<Eigen::Matrix<float, Dynamic, Dynamic, DataLayout>> m_left(t_left.data(), 150, 93);\n  Map<Eigen::Matrix<float, Dynamic, Dynamic, DataLayout>> m_right(t_right.data(), 93, 140);\n  Eigen::Matrix<float, Dynamic, Dynamic, DataLayout> m_result = m_left * m_right;\n\n  for (int i = 0; i < t_result.dimensions().TotalSize(); i++) {\n    VERIFY_IS_APPROX(t_result.data()[i], m_result.data()[i]);\n  }\n}\n\ntemplate<int DataLayout>\nstatic void test_tensor_product()\n{\n  Tensor<float, 2, DataLayout> mat1(2, 3);\n  Tensor<float, 2, DataLayout> mat2(4, 1);\n  mat1.setRandom();\n  mat2.setRandom();\n\n  Tensor<float, 4, DataLayout> result = mat1.contract(mat2, Eigen::array<DimPair, 0>{{}});\n\n  VERIFY_IS_EQUAL(result.dimension(0), 2);\n  VERIFY_IS_EQUAL(result.dimension(1), 3);\n  VERIFY_IS_EQUAL(result.dimension(2), 4);\n  VERIFY_IS_EQUAL(result.dimension(3), 1);\n  for (int i = 0; i < result.dimension(0); ++i) {\n    for (int j = 0; j < result.dimension(1); ++j) {\n      for (int k = 0; k < result.dimension(2); ++k) {\n        for (int l = 0; l < result.dimension(3); ++l) {\n\t\t\tVERIFY_IS_APPROX(result(i, j, k, l), mat1(i, j) * mat2(k, l) );\n        }\n      }\n    }\n  }\n}\n\n\ntemplate<int DataLayout>\nstatic void test_const_inputs()\n{\n  Tensor<float, 2, DataLayout> in1(2, 3);\n  Tensor<float, 2, DataLayout> in2(3, 2);\n  in1.setRandom();\n  in2.setRandom();\n\n  TensorMap<Tensor<const float, 2, DataLayout> > mat1(in1.data(), 2, 3);\n  TensorMap<Tensor<const float, 2, DataLayout> > mat2(in2.data(), 3, 2);\n  Tensor<float, 2, DataLayout> mat3(2,2);\n\n  Eigen::array<DimPair, 1> dims = {{DimPair(1, 0)}};\n  mat3 = mat1.contract(mat2, dims);\n\n  VERIFY_IS_APPROX(mat3(0,0), mat1(0,0)*mat2(0,0) + mat1(0,1)*mat2(1,0) + mat1(0,2)*mat2(2,0));\n  VERIFY_IS_APPROX(mat3(0,1), mat1(0,0)*mat2(0,1) + mat1(0,1)*mat2(1,1) + mat1(0,2)*mat2(2,1));\n  VERIFY_IS_APPROX(mat3(1,0), mat1(1,0)*mat2(0,0) + mat1(1,1)*mat2(1,0) + mat1(1,2)*mat2(2,0));\n  VERIFY_IS_APPROX(mat3(1,1), mat1(1,0)*mat2(0,1) + mat1(1,1)*mat2(1,1) + mat1(1,2)*mat2(2,1));\n}\n\nvoid test_cxx11_tensor_contraction()\n{\n  CALL_SUBTEST(test_evals<ColMajor>());\n  CALL_SUBTEST(test_evals<RowMajor>());\n  CALL_SUBTEST(test_scalar<ColMajor>());\n  CALL_SUBTEST(test_scalar<RowMajor>());\n  CALL_SUBTEST(test_multidims<ColMajor>());\n  CALL_SUBTEST(test_multidims<RowMajor>());\n  CALL_SUBTEST(test_holes<ColMajor>());\n  CALL_SUBTEST(test_holes<RowMajor>());\n  CALL_SUBTEST(test_full_redux<ColMajor>());\n  CALL_SUBTEST(test_full_redux<RowMajor>());\n  CALL_SUBTEST(test_contraction_of_contraction<ColMajor>());\n  CALL_SUBTEST(test_contraction_of_contraction<RowMajor>());\n  CALL_SUBTEST(test_expr<ColMajor>());\n  CALL_SUBTEST(test_expr<RowMajor>());\n  CALL_SUBTEST(test_out_of_order_contraction<ColMajor>());\n  CALL_SUBTEST(test_out_of_order_contraction<RowMajor>());\n  CALL_SUBTEST(test_consistency<ColMajor>());\n  CALL_SUBTEST(test_consistency<RowMajor>());\n  CALL_SUBTEST(test_large_contraction<ColMajor>());\n  CALL_SUBTEST(test_large_contraction<RowMajor>());\n  CALL_SUBTEST(test_matrix_vector<ColMajor>());\n  CALL_SUBTEST(test_matrix_vector<RowMajor>());\n  CALL_SUBTEST(test_tensor_vector<ColMajor>());\n  CALL_SUBTEST(test_tensor_vector<RowMajor>());\n  CALL_SUBTEST(test_small_blocking_factors<ColMajor>());\n  CALL_SUBTEST(test_small_blocking_factors<RowMajor>());\n  CALL_SUBTEST(test_tensor_product<ColMajor>());\n  CALL_SUBTEST(test_tensor_product<RowMajor>());\n  CALL_SUBTEST(test_const_inputs<ColMajor>());\n  CALL_SUBTEST(test_const_inputs<RowMajor>());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_convolution.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\nusing Eigen::DefaultDevice;\n\ntemplate <int DataLayout>\nstatic void test_evals()\n{\n  Tensor<float, 2, DataLayout> input(3, 3);\n  Tensor<float, 1, DataLayout> kernel(2);\n\n  input.setRandom();\n  kernel.setRandom();\n\n  Tensor<float, 2, DataLayout> result(2,3);\n  result.setZero();\n  Eigen::array<Tensor<float, 2>::Index, 1> dims3{{0}};\n\n  typedef TensorEvaluator<decltype(input.convolve(kernel, dims3)), DefaultDevice> Evaluator;\n  Evaluator eval(input.convolve(kernel, dims3), DefaultDevice());\n  eval.evalTo(result.data());\n  EIGEN_STATIC_ASSERT(Evaluator::NumDims==2ul, YOU_MADE_A_PROGRAMMING_MISTAKE);\n  VERIFY_IS_EQUAL(eval.dimensions()[0], 2);\n  VERIFY_IS_EQUAL(eval.dimensions()[1], 3);\n\n  VERIFY_IS_APPROX(result(0,0), input(0,0)*kernel(0) + input(1,0)*kernel(1));  // index 0\n  VERIFY_IS_APPROX(result(0,1), input(0,1)*kernel(0) + input(1,1)*kernel(1));  // index 2\n  VERIFY_IS_APPROX(result(0,2), input(0,2)*kernel(0) + input(1,2)*kernel(1));  // index 4\n  VERIFY_IS_APPROX(result(1,0), input(1,0)*kernel(0) + input(2,0)*kernel(1));  // index 1\n  VERIFY_IS_APPROX(result(1,1), input(1,1)*kernel(0) + input(2,1)*kernel(1));  // index 3\n  VERIFY_IS_APPROX(result(1,2), input(1,2)*kernel(0) + input(2,2)*kernel(1));  // index 5\n}\n\ntemplate <int DataLayout>\nstatic void test_expr()\n{\n  Tensor<float, 2, DataLayout> input(3, 3);\n  Tensor<float, 2, DataLayout> kernel(2, 2);\n  input.setRandom();\n  kernel.setRandom();\n\n  Tensor<float, 2, DataLayout> result(2,2);\n  Eigen::array<ptrdiff_t, 2> dims;\n  dims[0] = 0;\n  dims[1] = 1;\n  result = input.convolve(kernel, dims);\n\n  VERIFY_IS_APPROX(result(0,0), input(0,0)*kernel(0,0) + input(0,1)*kernel(0,1) +\n                                input(1,0)*kernel(1,0) + input(1,1)*kernel(1,1));\n  VERIFY_IS_APPROX(result(0,1), input(0,1)*kernel(0,0) + input(0,2)*kernel(0,1) +\n                                input(1,1)*kernel(1,0) + input(1,2)*kernel(1,1));\n  VERIFY_IS_APPROX(result(1,0), input(1,0)*kernel(0,0) + input(1,1)*kernel(0,1) +\n                                input(2,0)*kernel(1,0) + input(2,1)*kernel(1,1));\n  VERIFY_IS_APPROX(result(1,1), input(1,1)*kernel(0,0) + input(1,2)*kernel(0,1) +\n                                input(2,1)*kernel(1,0) + input(2,2)*kernel(1,1));\n}\n\ntemplate <int DataLayout>\nstatic void test_modes() {\n  Tensor<float, 1, DataLayout> input(3);\n  Tensor<float, 1, DataLayout> kernel(3);\n  input(0) = 1.0f;\n  input(1) = 2.0f;\n  input(2) = 3.0f;\n  kernel(0) = 0.5f;\n  kernel(1) = 1.0f;\n  kernel(2) = 0.0f;\n\n  Eigen::array<ptrdiff_t, 1> dims;\n  dims[0] = 0;\n  Eigen::array<std::pair<ptrdiff_t, ptrdiff_t>, 1> padding;\n\n  // Emulate VALID mode (as defined in\n  // http://docs.scipy.org/doc/numpy/reference/generated/numpy.convolve.html).\n  padding[0] = std::make_pair(0, 0);\n  Tensor<float, 1, DataLayout> valid(1);\n  valid = input.pad(padding).convolve(kernel, dims);\n  VERIFY_IS_EQUAL(valid.dimension(0), 1);\n  VERIFY_IS_APPROX(valid(0), 2.5f);\n\n  // Emulate SAME mode (as defined in\n  // http://docs.scipy.org/doc/numpy/reference/generated/numpy.convolve.html).\n  padding[0] = std::make_pair(1, 1);\n  Tensor<float, 1, DataLayout> same(3);\n  same = input.pad(padding).convolve(kernel, dims);\n  VERIFY_IS_EQUAL(same.dimension(0), 3);\n  VERIFY_IS_APPROX(same(0), 1.0f);\n  VERIFY_IS_APPROX(same(1), 2.5f);\n  VERIFY_IS_APPROX(same(2), 4.0f);\n\n  // Emulate FULL mode (as defined in\n  // http://docs.scipy.org/doc/numpy/reference/generated/numpy.convolve.html).\n  padding[0] = std::make_pair(2, 2);\n  Tensor<float, 1, DataLayout> full(5);\n  full = input.pad(padding).convolve(kernel, dims);\n  VERIFY_IS_EQUAL(full.dimension(0), 5);\n  VERIFY_IS_APPROX(full(0), 0.0f);\n  VERIFY_IS_APPROX(full(1), 1.0f);\n  VERIFY_IS_APPROX(full(2), 2.5f);\n  VERIFY_IS_APPROX(full(3), 4.0f);\n  VERIFY_IS_APPROX(full(4), 1.5f);\n}\n\ntemplate <int DataLayout>\nstatic void test_strides() {\n  Tensor<float, 1, DataLayout> input(13);\n  Tensor<float, 1, DataLayout> kernel(3);\n  input.setRandom();\n  kernel.setRandom();\n\n  Eigen::array<ptrdiff_t, 1> dims;\n  dims[0] = 0;\n  Eigen::array<ptrdiff_t, 1> stride_of_3;\n  stride_of_3[0] = 3;\n  Eigen::array<ptrdiff_t, 1> stride_of_2;\n  stride_of_2[0] = 2;\n\n  Tensor<float, 1, DataLayout> result;\n  result = input.stride(stride_of_3).convolve(kernel, dims).stride(stride_of_2);\n\n  VERIFY_IS_EQUAL(result.dimension(0), 2);\n  VERIFY_IS_APPROX(result(0), (input(0)*kernel(0) + input(3)*kernel(1) +\n                               input(6)*kernel(2)));\n  VERIFY_IS_APPROX(result(1), (input(6)*kernel(0) + input(9)*kernel(1) +\n                               input(12)*kernel(2)));\n}\n\nvoid test_cxx11_tensor_convolution()\n{\n  CALL_SUBTEST(test_evals<ColMajor>());\n  CALL_SUBTEST(test_evals<RowMajor>());\n  CALL_SUBTEST(test_expr<ColMajor>());\n  CALL_SUBTEST(test_expr<RowMajor>());\n  CALL_SUBTEST(test_modes<ColMajor>());\n  CALL_SUBTEST(test_modes<RowMajor>());\n  CALL_SUBTEST(test_strides<ColMajor>());\n  CALL_SUBTEST(test_strides<RowMajor>());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_cuda.cu",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define EIGEN_TEST_NO_LONGDOUBLE\n#define EIGEN_TEST_NO_COMPLEX\n#define EIGEN_TEST_FUNC cxx11_tensor_cuda\n#define EIGEN_USE_GPU\n\n#include \"main.h\"\n#include <unsupported/Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\n\nvoid test_cuda_nullary() {\n  Tensor<float, 1, 0, int> in1(2);\n  Tensor<float, 1, 0, int> in2(2);\n  in1.setRandom();\n  in2.setRandom();\n\n  std::size_t tensor_bytes = in1.size() * sizeof(float);\n\n  float* d_in1;\n  float* d_in2;\n  cudaMalloc((void**)(&d_in1), tensor_bytes);\n  cudaMalloc((void**)(&d_in2), tensor_bytes);\n  cudaMemcpy(d_in1, in1.data(), tensor_bytes, cudaMemcpyHostToDevice);\n  cudaMemcpy(d_in2, in2.data(), tensor_bytes, cudaMemcpyHostToDevice);\n\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n\n  Eigen::TensorMap<Eigen::Tensor<float, 1, 0, int>, Eigen::Aligned> gpu_in1(\n      d_in1, 2);\n  Eigen::TensorMap<Eigen::Tensor<float, 1, 0, int>, Eigen::Aligned> gpu_in2(\n      d_in2, 2);\n\n  gpu_in1.device(gpu_device) = gpu_in1.constant(3.14f);\n  gpu_in2.device(gpu_device) = gpu_in2.random();\n\n  Tensor<float, 1, 0, int> new1(2);\n  Tensor<float, 1, 0, int> new2(2);\n\n  assert(cudaMemcpyAsync(new1.data(), d_in1, tensor_bytes, cudaMemcpyDeviceToHost,\n                         gpu_device.stream()) == cudaSuccess);\n  assert(cudaMemcpyAsync(new2.data(), d_in2, tensor_bytes, cudaMemcpyDeviceToHost,\n                         gpu_device.stream()) == cudaSuccess);\n\n  assert(cudaStreamSynchronize(gpu_device.stream()) == cudaSuccess);\n\n  for (int i = 0; i < 2; ++i) {\n    VERIFY_IS_APPROX(new1(i), 3.14f);\n    VERIFY_IS_NOT_EQUAL(new2(i), in2(i));\n  }\n\n  cudaFree(d_in1);\n  cudaFree(d_in2);\n}\n\nvoid test_cuda_elementwise_small() {\n  Tensor<float, 1> in1(Eigen::array<Eigen::DenseIndex, 1>(2));\n  Tensor<float, 1> in2(Eigen::array<Eigen::DenseIndex, 1>(2));\n  Tensor<float, 1> out(Eigen::array<Eigen::DenseIndex, 1>(2));\n  in1.setRandom();\n  in2.setRandom();\n\n  std::size_t in1_bytes = in1.size() * sizeof(float);\n  std::size_t in2_bytes = in2.size() * sizeof(float);\n  std::size_t out_bytes = out.size() * sizeof(float);\n\n  float* d_in1;\n  float* d_in2;\n  float* d_out;\n  cudaMalloc((void**)(&d_in1), in1_bytes);\n  cudaMalloc((void**)(&d_in2), in2_bytes);\n  cudaMalloc((void**)(&d_out), out_bytes);\n\n  cudaMemcpy(d_in1, in1.data(), in1_bytes, cudaMemcpyHostToDevice);\n  cudaMemcpy(d_in2, in2.data(), in2_bytes, cudaMemcpyHostToDevice);\n\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n\n  Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_in1(\n      d_in1, Eigen::array<Eigen::DenseIndex, 1>(2));\n  Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_in2(\n      d_in2, Eigen::array<Eigen::DenseIndex, 1>(2));\n  Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_out(\n      d_out, Eigen::array<Eigen::DenseIndex, 1>(2));\n\n  gpu_out.device(gpu_device) = gpu_in1 + gpu_in2;\n\n  assert(cudaMemcpyAsync(out.data(), d_out, out_bytes, cudaMemcpyDeviceToHost,\n                         gpu_device.stream()) == cudaSuccess);\n  assert(cudaStreamSynchronize(gpu_device.stream()) == cudaSuccess);\n\n  for (int i = 0; i < 2; ++i) {\n    VERIFY_IS_APPROX(\n        out(Eigen::array<Eigen::DenseIndex, 1>(i)),\n        in1(Eigen::array<Eigen::DenseIndex, 1>(i)) + in2(Eigen::array<Eigen::DenseIndex, 1>(i)));\n  }\n\n  cudaFree(d_in1);\n  cudaFree(d_in2);\n  cudaFree(d_out);\n}\n\nvoid test_cuda_elementwise()\n{\n  Tensor<float, 3> in1(Eigen::array<Eigen::DenseIndex, 3>(72,53,97));\n  Tensor<float, 3> in2(Eigen::array<Eigen::DenseIndex, 3>(72,53,97));\n  Tensor<float, 3> in3(Eigen::array<Eigen::DenseIndex, 3>(72,53,97));\n  Tensor<float, 3> out(Eigen::array<Eigen::DenseIndex, 3>(72,53,97));\n  in1.setRandom();\n  in2.setRandom();\n  in3.setRandom();\n\n  std::size_t in1_bytes = in1.size() * sizeof(float);\n  std::size_t in2_bytes = in2.size() * sizeof(float);\n  std::size_t in3_bytes = in3.size() * sizeof(float);\n  std::size_t out_bytes = out.size() * sizeof(float);\n\n  float* d_in1;\n  float* d_in2;\n  float* d_in3;\n  float* d_out;\n  cudaMalloc((void**)(&d_in1), in1_bytes);\n  cudaMalloc((void**)(&d_in2), in2_bytes);\n  cudaMalloc((void**)(&d_in3), in3_bytes);\n  cudaMalloc((void**)(&d_out), out_bytes);\n\n  cudaMemcpy(d_in1, in1.data(), in1_bytes, cudaMemcpyHostToDevice);\n  cudaMemcpy(d_in2, in2.data(), in2_bytes, cudaMemcpyHostToDevice);\n  cudaMemcpy(d_in3, in3.data(), in3_bytes, cudaMemcpyHostToDevice);\n\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n\n  Eigen::TensorMap<Eigen::Tensor<float, 3> > gpu_in1(d_in1, Eigen::array<Eigen::DenseIndex, 3>(72,53,97));\n  Eigen::TensorMap<Eigen::Tensor<float, 3> > gpu_in2(d_in2, Eigen::array<Eigen::DenseIndex, 3>(72,53,97));\n  Eigen::TensorMap<Eigen::Tensor<float, 3> > gpu_in3(d_in3, Eigen::array<Eigen::DenseIndex, 3>(72,53,97));\n  Eigen::TensorMap<Eigen::Tensor<float, 3> > gpu_out(d_out, Eigen::array<Eigen::DenseIndex, 3>(72,53,97));\n\n  gpu_out.device(gpu_device) = gpu_in1 + gpu_in2 * gpu_in3;\n\n  assert(cudaMemcpyAsync(out.data(), d_out, out_bytes, cudaMemcpyDeviceToHost, gpu_device.stream()) == cudaSuccess);\n  assert(cudaStreamSynchronize(gpu_device.stream()) == cudaSuccess);\n\n  for (int i = 0; i < 72; ++i) {\n    for (int j = 0; j < 53; ++j) {\n      for (int k = 0; k < 97; ++k) {\n        VERIFY_IS_APPROX(out(Eigen::array<Eigen::DenseIndex, 3>(i,j,k)), in1(Eigen::array<Eigen::DenseIndex, 3>(i,j,k)) + in2(Eigen::array<Eigen::DenseIndex, 3>(i,j,k)) * in3(Eigen::array<Eigen::DenseIndex, 3>(i,j,k)));\n      }\n    }\n  }\n\n  cudaFree(d_in1);\n  cudaFree(d_in2);\n  cudaFree(d_in3);\n  cudaFree(d_out);\n}\n\nvoid test_cuda_props() {\n  Tensor<float, 1> in1(200);\n  Tensor<bool, 1> out(200);\n  in1.setRandom();\n\n  std::size_t in1_bytes = in1.size() * sizeof(float);\n  std::size_t out_bytes = out.size() * sizeof(bool);\n\n  float* d_in1;\n  bool* d_out;\n  cudaMalloc((void**)(&d_in1), in1_bytes);\n  cudaMalloc((void**)(&d_out), out_bytes);\n\n  cudaMemcpy(d_in1, in1.data(), in1_bytes, cudaMemcpyHostToDevice);\n\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n\n  Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_in1(\n      d_in1, 200);\n  Eigen::TensorMap<Eigen::Tensor<bool, 1>, Eigen::Aligned> gpu_out(\n      d_out, 200);\n\n  gpu_out.device(gpu_device) = (gpu_in1.isnan)();\n\n  assert(cudaMemcpyAsync(out.data(), d_out, out_bytes, cudaMemcpyDeviceToHost,\n                         gpu_device.stream()) == cudaSuccess);\n  assert(cudaStreamSynchronize(gpu_device.stream()) == cudaSuccess);\n\n  for (int i = 0; i < 200; ++i) {\n    VERIFY_IS_EQUAL(out(i), (std::isnan)(in1(i)));\n  }\n\n  cudaFree(d_in1);\n  cudaFree(d_out);\n}\n\nvoid test_cuda_reduction()\n{\n  Tensor<float, 4> in1(72,53,97,113);\n  Tensor<float, 2> out(72,97);\n  in1.setRandom();\n\n  std::size_t in1_bytes = in1.size() * sizeof(float);\n  std::size_t out_bytes = out.size() * sizeof(float);\n\n  float* d_in1;\n  float* d_out;\n  cudaMalloc((void**)(&d_in1), in1_bytes);\n  cudaMalloc((void**)(&d_out), out_bytes);\n\n  cudaMemcpy(d_in1, in1.data(), in1_bytes, cudaMemcpyHostToDevice);\n\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n\n  Eigen::TensorMap<Eigen::Tensor<float, 4> > gpu_in1(d_in1, 72,53,97,113);\n  Eigen::TensorMap<Eigen::Tensor<float, 2> > gpu_out(d_out, 72,97);\n\n  array<Eigen::DenseIndex, 2> reduction_axis;\n  reduction_axis[0] = 1;\n  reduction_axis[1] = 3;\n\n  gpu_out.device(gpu_device) = gpu_in1.maximum(reduction_axis);\n\n  assert(cudaMemcpyAsync(out.data(), d_out, out_bytes, cudaMemcpyDeviceToHost, gpu_device.stream()) == cudaSuccess);\n  assert(cudaStreamSynchronize(gpu_device.stream()) == cudaSuccess);\n\n  for (int i = 0; i < 72; ++i) {\n    for (int j = 0; j < 97; ++j) {\n      float expected = 0;\n      for (int k = 0; k < 53; ++k) {\n        for (int l = 0; l < 113; ++l) {\n          expected =\n              std::max<float>(expected, in1(i, k, j, l));\n        }\n      }\n      VERIFY_IS_APPROX(out(i,j), expected);\n    }\n  }\n\n  cudaFree(d_in1);\n  cudaFree(d_out);\n}\n\ntemplate<int DataLayout>\nvoid test_cuda_contraction()\n{\n  // with these dimensions, the output has 300 * 140 elements, which is\n  // more than 30 * 1024, which is the number of threads in blocks on\n  // a 15 SM GK110 GPU\n  Tensor<float, 4, DataLayout> t_left(6, 50, 3, 31);\n  Tensor<float, 5, DataLayout> t_right(Eigen::array<Eigen::DenseIndex, 5>(3, 31, 7, 20, 1));\n  Tensor<float, 5, DataLayout> t_result(Eigen::array<Eigen::DenseIndex, 5>(6, 50, 7, 20, 1));\n\n  t_left.setRandom();\n  t_right.setRandom();\n\n  std::size_t t_left_bytes = t_left.size()  * sizeof(float);\n  std::size_t t_right_bytes = t_right.size() * sizeof(float);\n  std::size_t t_result_bytes = t_result.size() * sizeof(float);\n\n  float* d_t_left;\n  float* d_t_right;\n  float* d_t_result;\n\n  cudaMalloc((void**)(&d_t_left), t_left_bytes);\n  cudaMalloc((void**)(&d_t_right), t_right_bytes);\n  cudaMalloc((void**)(&d_t_result), t_result_bytes);\n\n  cudaMemcpy(d_t_left, t_left.data(), t_left_bytes, cudaMemcpyHostToDevice);\n  cudaMemcpy(d_t_right, t_right.data(), t_right_bytes, cudaMemcpyHostToDevice);\n\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n\n  Eigen::TensorMap<Eigen::Tensor<float, 4, DataLayout> > gpu_t_left(d_t_left, 6, 50, 3, 31);\n  Eigen::TensorMap<Eigen::Tensor<float, 5, DataLayout> > gpu_t_right(d_t_right, 3, 31, 7, 20, 1);\n  Eigen::TensorMap<Eigen::Tensor<float, 5, DataLayout> > gpu_t_result(d_t_result, 6, 50, 7, 20, 1);\n\n  typedef Eigen::Map<Eigen::Matrix<float, Dynamic, Dynamic, DataLayout> > MapXf;\n  MapXf m_left(t_left.data(), 300, 93);\n  MapXf m_right(t_right.data(), 93, 140);\n  Eigen::Matrix<float, Dynamic, Dynamic, DataLayout> m_result(300, 140);\n\n  typedef Tensor<float, 1>::DimensionPair DimPair;\n  Eigen::array<DimPair, 2> dims;\n  dims[0] = DimPair(2, 0);\n  dims[1] = DimPair(3, 1);\n\n  m_result = m_left * m_right;\n  gpu_t_result.device(gpu_device) = gpu_t_left.contract(gpu_t_right, dims);\n\n  cudaMemcpy(t_result.data(), d_t_result, t_result_bytes, cudaMemcpyDeviceToHost);\n\n  for (DenseIndex i = 0; i < t_result.size(); i++) {\n    if (fabs(t_result.data()[i] - m_result.data()[i]) >= 1e-4f) {\n      std::cout << \"mismatch detected at index \" << i << \": \" << t_result.data()[i] << \" vs \" <<  m_result.data()[i] << std::endl;\n      assert(false);\n    }\n  }\n\n  cudaFree(d_t_left);\n  cudaFree(d_t_right);\n  cudaFree(d_t_result);\n}\n\ntemplate<int DataLayout>\nvoid test_cuda_convolution_1d()\n{\n  Tensor<float, 4, DataLayout> input(74,37,11,137);\n  Tensor<float, 1, DataLayout> kernel(4);\n  Tensor<float, 4, DataLayout> out(74,34,11,137);\n  input = input.constant(10.0f) + input.random();\n  kernel = kernel.constant(7.0f) + kernel.random();\n\n  std::size_t input_bytes = input.size() * sizeof(float);\n  std::size_t kernel_bytes = kernel.size() * sizeof(float);\n  std::size_t out_bytes = out.size() * sizeof(float);\n\n  float* d_input;\n  float* d_kernel;\n  float* d_out;\n  cudaMalloc((void**)(&d_input), input_bytes);\n  cudaMalloc((void**)(&d_kernel), kernel_bytes);\n  cudaMalloc((void**)(&d_out), out_bytes);\n\n  cudaMemcpy(d_input, input.data(), input_bytes, cudaMemcpyHostToDevice);\n  cudaMemcpy(d_kernel, kernel.data(), kernel_bytes, cudaMemcpyHostToDevice);\n\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n\n  Eigen::TensorMap<Eigen::Tensor<float, 4, DataLayout> > gpu_input(d_input, 74,37,11,137);\n  Eigen::TensorMap<Eigen::Tensor<float, 1, DataLayout> > gpu_kernel(d_kernel, 4);\n  Eigen::TensorMap<Eigen::Tensor<float, 4, DataLayout> > gpu_out(d_out, 74,34,11,137);\n\n  Eigen::array<Eigen::DenseIndex, 1> dims(1);\n  gpu_out.device(gpu_device) = gpu_input.convolve(gpu_kernel, dims);\n\n  assert(cudaMemcpyAsync(out.data(), d_out, out_bytes, cudaMemcpyDeviceToHost, gpu_device.stream()) == cudaSuccess);\n  assert(cudaStreamSynchronize(gpu_device.stream()) == cudaSuccess);\n\n  for (int i = 0; i < 74; ++i) {\n    for (int j = 0; j < 34; ++j) {\n      for (int k = 0; k < 11; ++k) {\n        for (int l = 0; l < 137; ++l) {\n          const float result = out(i,j,k,l);\n          const float expected = input(i,j+0,k,l) * kernel(0) + input(i,j+1,k,l) * kernel(1) +\n                                 input(i,j+2,k,l) * kernel(2) + input(i,j+3,k,l) * kernel(3);\n          VERIFY_IS_APPROX(result, expected);\n        }\n      }\n    }\n  }\n\n  cudaFree(d_input);\n  cudaFree(d_kernel);\n  cudaFree(d_out);\n}\n\nvoid test_cuda_convolution_inner_dim_col_major_1d()\n{\n  Tensor<float, 4, ColMajor> input(74,9,11,7);\n  Tensor<float, 1, ColMajor> kernel(4);\n  Tensor<float, 4, ColMajor> out(71,9,11,7);\n  input = input.constant(10.0f) + input.random();\n  kernel = kernel.constant(7.0f) + kernel.random();\n\n  std::size_t input_bytes = input.size() * sizeof(float);\n  std::size_t kernel_bytes = kernel.size() * sizeof(float);\n  std::size_t out_bytes = out.size() * sizeof(float);\n\n  float* d_input;\n  float* d_kernel;\n  float* d_out;\n  cudaMalloc((void**)(&d_input), input_bytes);\n  cudaMalloc((void**)(&d_kernel), kernel_bytes);\n  cudaMalloc((void**)(&d_out), out_bytes);\n\n  cudaMemcpy(d_input, input.data(), input_bytes, cudaMemcpyHostToDevice);\n  cudaMemcpy(d_kernel, kernel.data(), kernel_bytes, cudaMemcpyHostToDevice);\n\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n\n  Eigen::TensorMap<Eigen::Tensor<float, 4, ColMajor> > gpu_input(d_input,74,9,11,7);\n  Eigen::TensorMap<Eigen::Tensor<float, 1, ColMajor> > gpu_kernel(d_kernel,4);\n  Eigen::TensorMap<Eigen::Tensor<float, 4, ColMajor> > gpu_out(d_out,71,9,11,7);\n\n  Eigen::array<Eigen::DenseIndex, 1> dims(0);\n  gpu_out.device(gpu_device) = gpu_input.convolve(gpu_kernel, dims);\n\n  assert(cudaMemcpyAsync(out.data(), d_out, out_bytes, cudaMemcpyDeviceToHost, gpu_device.stream()) == cudaSuccess);\n  assert(cudaStreamSynchronize(gpu_device.stream()) == cudaSuccess);\n\n  for (int i = 0; i < 71; ++i) {\n    for (int j = 0; j < 9; ++j) {\n      for (int k = 0; k < 11; ++k) {\n        for (int l = 0; l < 7; ++l) {\n          const float result = out(i,j,k,l);\n          const float expected = input(i+0,j,k,l) * kernel(0) + input(i+1,j,k,l) * kernel(1) +\n                                 input(i+2,j,k,l) * kernel(2) + input(i+3,j,k,l) * kernel(3);\n          VERIFY_IS_APPROX(result, expected);\n        }\n      }\n    }\n  }\n\n  cudaFree(d_input);\n  cudaFree(d_kernel);\n  cudaFree(d_out);\n}\n\nvoid test_cuda_convolution_inner_dim_row_major_1d()\n{\n  Tensor<float, 4, RowMajor> input(7,9,11,74);\n  Tensor<float, 1, RowMajor> kernel(4);\n  Tensor<float, 4, RowMajor> out(7,9,11,71);\n  input = input.constant(10.0f) + input.random();\n  kernel = kernel.constant(7.0f) + kernel.random();\n\n  std::size_t input_bytes = input.size() * sizeof(float);\n  std::size_t kernel_bytes = kernel.size() * sizeof(float);\n  std::size_t out_bytes = out.size() * sizeof(float);\n\n  float* d_input;\n  float* d_kernel;\n  float* d_out;\n  cudaMalloc((void**)(&d_input), input_bytes);\n  cudaMalloc((void**)(&d_kernel), kernel_bytes);\n  cudaMalloc((void**)(&d_out), out_bytes);\n\n  cudaMemcpy(d_input, input.data(), input_bytes, cudaMemcpyHostToDevice);\n  cudaMemcpy(d_kernel, kernel.data(), kernel_bytes, cudaMemcpyHostToDevice);\n\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n\n  Eigen::TensorMap<Eigen::Tensor<float, 4, RowMajor> > gpu_input(d_input, 7,9,11,74);\n  Eigen::TensorMap<Eigen::Tensor<float, 1, RowMajor> > gpu_kernel(d_kernel, 4);\n  Eigen::TensorMap<Eigen::Tensor<float, 4, RowMajor> > gpu_out(d_out, 7,9,11,71);\n\n  Eigen::array<Eigen::DenseIndex, 1> dims(3);\n  gpu_out.device(gpu_device) = gpu_input.convolve(gpu_kernel, dims);\n\n  assert(cudaMemcpyAsync(out.data(), d_out, out_bytes, cudaMemcpyDeviceToHost, gpu_device.stream()) == cudaSuccess);\n  assert(cudaStreamSynchronize(gpu_device.stream()) == cudaSuccess);\n\n  for (int i = 0; i < 7; ++i) {\n    for (int j = 0; j < 9; ++j) {\n      for (int k = 0; k < 11; ++k) {\n        for (int l = 0; l < 71; ++l) {\n          const float result = out(i,j,k,l);\n          const float expected = input(i,j,k,l+0) * kernel(0) + input(i,j,k,l+1) * kernel(1) +\n                                 input(i,j,k,l+2) * kernel(2) + input(i,j,k,l+3) * kernel(3);\n          VERIFY_IS_APPROX(result, expected);\n        }\n      }\n    }\n  }\n\n  cudaFree(d_input);\n  cudaFree(d_kernel);\n  cudaFree(d_out);\n}\n\ntemplate<int DataLayout>\nvoid test_cuda_convolution_2d()\n{\n  Tensor<float, 4, DataLayout> input(74,37,11,137);\n  Tensor<float, 2, DataLayout> kernel(3,4);\n  Tensor<float, 4, DataLayout> out(74,35,8,137);\n  input = input.constant(10.0f) + input.random();\n  kernel = kernel.constant(7.0f) + kernel.random();\n\n  std::size_t input_bytes = input.size() * sizeof(float);\n  std::size_t kernel_bytes = kernel.size() * sizeof(float);\n  std::size_t out_bytes = out.size() * sizeof(float);\n\n  float* d_input;\n  float* d_kernel;\n  float* d_out;\n  cudaMalloc((void**)(&d_input), input_bytes);\n  cudaMalloc((void**)(&d_kernel), kernel_bytes);\n  cudaMalloc((void**)(&d_out), out_bytes);\n\n  cudaMemcpy(d_input, input.data(), input_bytes, cudaMemcpyHostToDevice);\n  cudaMemcpy(d_kernel, kernel.data(), kernel_bytes, cudaMemcpyHostToDevice);\n\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n\n  Eigen::TensorMap<Eigen::Tensor<float, 4, DataLayout> > gpu_input(d_input,74,37,11,137);\n  Eigen::TensorMap<Eigen::Tensor<float, 2, DataLayout> > gpu_kernel(d_kernel,3,4);\n  Eigen::TensorMap<Eigen::Tensor<float, 4, DataLayout> > gpu_out(d_out,74,35,8,137);\n\n  Eigen::array<Eigen::DenseIndex, 2> dims(1,2);\n  gpu_out.device(gpu_device) = gpu_input.convolve(gpu_kernel, dims);\n\n  assert(cudaMemcpyAsync(out.data(), d_out, out_bytes, cudaMemcpyDeviceToHost, gpu_device.stream()) == cudaSuccess);\n  assert(cudaStreamSynchronize(gpu_device.stream()) == cudaSuccess);\n\n  for (int i = 0; i < 74; ++i) {\n    for (int j = 0; j < 35; ++j) {\n      for (int k = 0; k < 8; ++k) {\n        for (int l = 0; l < 137; ++l) {\n          const float result = out(i,j,k,l);\n          const float expected = input(i,j+0,k+0,l) * kernel(0,0) +\n                                 input(i,j+1,k+0,l) * kernel(1,0) +\n                                 input(i,j+2,k+0,l) * kernel(2,0) +\n                                 input(i,j+0,k+1,l) * kernel(0,1) +\n                                 input(i,j+1,k+1,l) * kernel(1,1) +\n                                 input(i,j+2,k+1,l) * kernel(2,1) +\n                                 input(i,j+0,k+2,l) * kernel(0,2) +\n                                 input(i,j+1,k+2,l) * kernel(1,2) +\n                                 input(i,j+2,k+2,l) * kernel(2,2) +\n                                 input(i,j+0,k+3,l) * kernel(0,3) +\n                                 input(i,j+1,k+3,l) * kernel(1,3) +\n                                 input(i,j+2,k+3,l) * kernel(2,3);\n          VERIFY_IS_APPROX(result, expected);\n        }\n      }\n    }\n  }\n\n  cudaFree(d_input);\n  cudaFree(d_kernel);\n  cudaFree(d_out);\n}\n\ntemplate<int DataLayout>\nvoid test_cuda_convolution_3d()\n{\n  Tensor<float, 5, DataLayout> input(Eigen::array<Eigen::DenseIndex, 5>(74,37,11,137,17));\n  Tensor<float, 3, DataLayout> kernel(3,4,2);\n  Tensor<float, 5, DataLayout> out(Eigen::array<Eigen::DenseIndex, 5>(74,35,8,136,17));\n  input = input.constant(10.0f) + input.random();\n  kernel = kernel.constant(7.0f) + kernel.random();\n\n  std::size_t input_bytes = input.size() * sizeof(float);\n  std::size_t kernel_bytes = kernel.size() * sizeof(float);\n  std::size_t out_bytes = out.size() * sizeof(float);\n\n  float* d_input;\n  float* d_kernel;\n  float* d_out;\n  cudaMalloc((void**)(&d_input), input_bytes);\n  cudaMalloc((void**)(&d_kernel), kernel_bytes);\n  cudaMalloc((void**)(&d_out), out_bytes);\n\n  cudaMemcpy(d_input, input.data(), input_bytes, cudaMemcpyHostToDevice);\n  cudaMemcpy(d_kernel, kernel.data(), kernel_bytes, cudaMemcpyHostToDevice);\n\n  Eigen::CudaStreamDevice stream;    \n  Eigen::GpuDevice gpu_device(&stream);\n\n  Eigen::TensorMap<Eigen::Tensor<float, 5, DataLayout> > gpu_input(d_input,74,37,11,137,17);\n  Eigen::TensorMap<Eigen::Tensor<float, 3, DataLayout> > gpu_kernel(d_kernel,3,4,2);\n  Eigen::TensorMap<Eigen::Tensor<float, 5, DataLayout> > gpu_out(d_out,74,35,8,136,17);\n\n  Eigen::array<Eigen::DenseIndex, 3> dims(1,2,3);\n  gpu_out.device(gpu_device) = gpu_input.convolve(gpu_kernel, dims);\n\n  assert(cudaMemcpyAsync(out.data(), d_out, out_bytes, cudaMemcpyDeviceToHost, gpu_device.stream()) == cudaSuccess);\n  assert(cudaStreamSynchronize(gpu_device.stream()) == cudaSuccess);\n\n  for (int i = 0; i < 74; ++i) {\n    for (int j = 0; j < 35; ++j) {\n      for (int k = 0; k < 8; ++k) {\n        for (int l = 0; l < 136; ++l) {\n          for (int m = 0; m < 17; ++m) {\n            const float result = out(i,j,k,l,m);\n            const float expected = input(i,j+0,k+0,l+0,m) * kernel(0,0,0) +\n                                   input(i,j+1,k+0,l+0,m) * kernel(1,0,0) +\n                                   input(i,j+2,k+0,l+0,m) * kernel(2,0,0) +\n                                   input(i,j+0,k+1,l+0,m) * kernel(0,1,0) +\n                                   input(i,j+1,k+1,l+0,m) * kernel(1,1,0) +\n                                   input(i,j+2,k+1,l+0,m) * kernel(2,1,0) +\n                                   input(i,j+0,k+2,l+0,m) * kernel(0,2,0) +\n                                   input(i,j+1,k+2,l+0,m) * kernel(1,2,0) +\n                                   input(i,j+2,k+2,l+0,m) * kernel(2,2,0) +\n                                   input(i,j+0,k+3,l+0,m) * kernel(0,3,0) +\n                                   input(i,j+1,k+3,l+0,m) * kernel(1,3,0) +\n                                   input(i,j+2,k+3,l+0,m) * kernel(2,3,0) +\n                                   input(i,j+0,k+0,l+1,m) * kernel(0,0,1) +\n                                   input(i,j+1,k+0,l+1,m) * kernel(1,0,1) +\n                                   input(i,j+2,k+0,l+1,m) * kernel(2,0,1) +\n                                   input(i,j+0,k+1,l+1,m) * kernel(0,1,1) +\n                                   input(i,j+1,k+1,l+1,m) * kernel(1,1,1) +\n                                   input(i,j+2,k+1,l+1,m) * kernel(2,1,1) +\n                                   input(i,j+0,k+2,l+1,m) * kernel(0,2,1) +\n                                   input(i,j+1,k+2,l+1,m) * kernel(1,2,1) +\n                                   input(i,j+2,k+2,l+1,m) * kernel(2,2,1) +\n                                   input(i,j+0,k+3,l+1,m) * kernel(0,3,1) +\n                                   input(i,j+1,k+3,l+1,m) * kernel(1,3,1) +\n                                   input(i,j+2,k+3,l+1,m) * kernel(2,3,1);\n            VERIFY_IS_APPROX(result, expected);\n          }\n        }\n      }\n    }\n  }\n\n  cudaFree(d_input);\n  cudaFree(d_kernel);\n  cudaFree(d_out);\n}\n\n\ntemplate <typename Scalar>\nvoid test_cuda_lgamma(const Scalar stddev)\n{\n  Tensor<Scalar, 2> in(72,97);\n  in.setRandom();\n  in *= in.constant(stddev);\n  Tensor<Scalar, 2> out(72,97);\n  out.setZero();\n\n  std::size_t bytes = in.size() * sizeof(Scalar);\n\n  Scalar* d_in;\n  Scalar* d_out;\n  cudaMalloc((void**)(&d_in), bytes);\n  cudaMalloc((void**)(&d_out), bytes);\n\n  cudaMemcpy(d_in, in.data(), bytes, cudaMemcpyHostToDevice);\n\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n\n  Eigen::TensorMap<Eigen::Tensor<Scalar, 2> > gpu_in(d_in, 72, 97);\n  Eigen::TensorMap<Eigen::Tensor<Scalar, 2> > gpu_out(d_out, 72, 97);\n\n  gpu_out.device(gpu_device) = gpu_in.lgamma();\n\n  assert(cudaMemcpyAsync(out.data(), d_out, bytes, cudaMemcpyDeviceToHost, gpu_device.stream()) == cudaSuccess);\n  assert(cudaStreamSynchronize(gpu_device.stream()) == cudaSuccess);\n\n  for (int i = 0; i < 72; ++i) {\n    for (int j = 0; j < 97; ++j) {\n      VERIFY_IS_APPROX(out(i,j), (std::lgamma)(in(i,j)));\n    }\n  }\n\n  cudaFree(d_in);\n  cudaFree(d_out);\n}\n\ntemplate <typename Scalar>\nvoid test_cuda_digamma()\n{\n  Tensor<Scalar, 1> in(7);\n  Tensor<Scalar, 1> out(7);\n  Tensor<Scalar, 1> expected_out(7);\n  out.setZero();\n\n  in(0) = Scalar(1);\n  in(1) = Scalar(1.5);\n  in(2) = Scalar(4);\n  in(3) = Scalar(-10.5);\n  in(4) = Scalar(10000.5);\n  in(5) = Scalar(0);\n  in(6) = Scalar(-1);\n\n  expected_out(0) = Scalar(-0.5772156649015329);\n  expected_out(1) = Scalar(0.03648997397857645);\n  expected_out(2) = Scalar(1.2561176684318);\n  expected_out(3) = Scalar(2.398239129535781);\n  expected_out(4) = Scalar(9.210340372392849);\n  expected_out(5) = std::numeric_limits<Scalar>::infinity();\n  expected_out(6) = std::numeric_limits<Scalar>::infinity();\n\n  std::size_t bytes = in.size() * sizeof(Scalar);\n\n  Scalar* d_in;\n  Scalar* d_out;\n  cudaMalloc((void**)(&d_in), bytes);\n  cudaMalloc((void**)(&d_out), bytes);\n\n  cudaMemcpy(d_in, in.data(), bytes, cudaMemcpyHostToDevice);\n\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n\n  Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_in(d_in, 7);\n  Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_out(d_out, 7);\n\n  gpu_out.device(gpu_device) = gpu_in.digamma();\n\n  assert(cudaMemcpyAsync(out.data(), d_out, bytes, cudaMemcpyDeviceToHost, gpu_device.stream()) == cudaSuccess);\n  assert(cudaStreamSynchronize(gpu_device.stream()) == cudaSuccess);\n\n  for (int i = 0; i < 5; ++i) {\n    VERIFY_IS_APPROX(out(i), expected_out(i));\n  }\n  for (int i = 5; i < 7; ++i) {\n    VERIFY_IS_EQUAL(out(i), expected_out(i));\n  }\n\n  cudaFree(d_in);\n  cudaFree(d_out);\n}\n\ntemplate <typename Scalar>\nvoid test_cuda_zeta()\n{\n  Tensor<Scalar, 1> in_x(6);\n  Tensor<Scalar, 1> in_q(6);\n  Tensor<Scalar, 1> out(6);\n  Tensor<Scalar, 1> expected_out(6);\n  out.setZero();\n\n  in_x(0) = Scalar(1);\n  in_x(1) = Scalar(1.5);\n  in_x(2) = Scalar(4);\n  in_x(3) = Scalar(-10.5);\n  in_x(4) = Scalar(10000.5);\n  in_x(5) = Scalar(3);\n  \n  in_q(0) = Scalar(1.2345);\n  in_q(1) = Scalar(2);\n  in_q(2) = Scalar(1.5);\n  in_q(3) = Scalar(3);\n  in_q(4) = Scalar(1.0001);\n  in_q(5) = Scalar(-2.5);\n\n  expected_out(0) = std::numeric_limits<Scalar>::infinity();\n  expected_out(1) = Scalar(1.61237534869);\n  expected_out(2) = Scalar(0.234848505667);\n  expected_out(3) = Scalar(1.03086757337e-5);\n  expected_out(4) = Scalar(0.367879440865);\n  expected_out(5) = Scalar(0.054102025820864097);\n\n  std::size_t bytes = in_x.size() * sizeof(Scalar);\n\n  Scalar* d_in_x;\n  Scalar* d_in_q;\n  Scalar* d_out;\n  cudaMalloc((void**)(&d_in_x), bytes);\n  cudaMalloc((void**)(&d_in_q), bytes);\n  cudaMalloc((void**)(&d_out), bytes);\n\n  cudaMemcpy(d_in_x, in_x.data(), bytes, cudaMemcpyHostToDevice);\n  cudaMemcpy(d_in_q, in_q.data(), bytes, cudaMemcpyHostToDevice);\n  \n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n\n  Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_in_x(d_in_x, 6);\n  Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_in_q(d_in_q, 6);\n  Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_out(d_out, 6);\n\n  gpu_out.device(gpu_device) = gpu_in_x.zeta(gpu_in_q);\n\n  assert(cudaMemcpyAsync(out.data(), d_out, bytes, cudaMemcpyDeviceToHost, gpu_device.stream()) == cudaSuccess);\n  assert(cudaStreamSynchronize(gpu_device.stream()) == cudaSuccess);\n\n  VERIFY_IS_EQUAL(out(0), expected_out(0));\n  VERIFY((std::isnan)(out(3)));\n\n  for (int i = 1; i < 6; ++i) {\n    if (i != 3) {\n      VERIFY_IS_APPROX(out(i), expected_out(i));\n    }\n  }\n\n  cudaFree(d_in_x);\n  cudaFree(d_in_q);\n  cudaFree(d_out);\n}\n\ntemplate <typename Scalar>\nvoid test_cuda_polygamma()\n{\n  Tensor<Scalar, 1> in_x(7);\n  Tensor<Scalar, 1> in_n(7);\n  Tensor<Scalar, 1> out(7);\n  Tensor<Scalar, 1> expected_out(7);\n  out.setZero();\n\n  in_n(0) = Scalar(1);\n  in_n(1) = Scalar(1);\n  in_n(2) = Scalar(1);\n  in_n(3) = Scalar(17);\n  in_n(4) = Scalar(31);\n  in_n(5) = Scalar(28);\n  in_n(6) = Scalar(8);\n  \n  in_x(0) = Scalar(2);\n  in_x(1) = Scalar(3);\n  in_x(2) = Scalar(25.5);\n  in_x(3) = Scalar(4.7);\n  in_x(4) = Scalar(11.8);\n  in_x(5) = Scalar(17.7);\n  in_x(6) = Scalar(30.2);\n\n  expected_out(0) = Scalar(0.644934066848);\n  expected_out(1) = Scalar(0.394934066848);\n  expected_out(2) = Scalar(0.0399946696496);\n  expected_out(3) = Scalar(293.334565435);\n  expected_out(4) = Scalar(0.445487887616);\n  expected_out(5) = Scalar(-2.47810300902e-07);\n  expected_out(6) = Scalar(-8.29668781082e-09);\n\n  std::size_t bytes = in_x.size() * sizeof(Scalar);\n\n  Scalar* d_in_x;\n  Scalar* d_in_n;\n  Scalar* d_out;\n  cudaMalloc((void**)(&d_in_x), bytes);\n  cudaMalloc((void**)(&d_in_n), bytes);\n  cudaMalloc((void**)(&d_out), bytes);\n\n  cudaMemcpy(d_in_x, in_x.data(), bytes, cudaMemcpyHostToDevice);\n  cudaMemcpy(d_in_n, in_n.data(), bytes, cudaMemcpyHostToDevice);\n  \n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n\n  Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_in_x(d_in_x, 7);\n  Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_in_n(d_in_n, 7);\n  Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_out(d_out, 7);\n\n  gpu_out.device(gpu_device) = gpu_in_n.polygamma(gpu_in_x);\n\n  assert(cudaMemcpyAsync(out.data(), d_out, bytes, cudaMemcpyDeviceToHost, gpu_device.stream()) == cudaSuccess);\n  assert(cudaStreamSynchronize(gpu_device.stream()) == cudaSuccess);\n\n  for (int i = 0; i < 7; ++i) {\n    VERIFY_IS_APPROX(out(i), expected_out(i));\n  }\n\n  cudaFree(d_in_x);\n  cudaFree(d_in_n);\n  cudaFree(d_out);\n}\n\ntemplate <typename Scalar>\nvoid test_cuda_igamma()\n{\n  Tensor<Scalar, 2> a(6, 6);\n  Tensor<Scalar, 2> x(6, 6);\n  Tensor<Scalar, 2> out(6, 6);\n  out.setZero();\n\n  Scalar a_s[] = {Scalar(0), Scalar(1), Scalar(1.5), Scalar(4), Scalar(0.0001), Scalar(1000.5)};\n  Scalar x_s[] = {Scalar(0), Scalar(1), Scalar(1.5), Scalar(4), Scalar(0.0001), Scalar(1000.5)};\n\n  for (int i = 0; i < 6; ++i) {\n    for (int j = 0; j < 6; ++j) {\n      a(i, j) = a_s[i];\n      x(i, j) = x_s[j];\n    }\n  }\n\n  Scalar nan = std::numeric_limits<Scalar>::quiet_NaN();\n  Scalar igamma_s[][6] = {{0.0, nan, nan, nan, nan, nan},\n                          {0.0, 0.6321205588285578, 0.7768698398515702,\n                           0.9816843611112658, 9.999500016666262e-05, 1.0},\n                          {0.0, 0.4275932955291202, 0.608374823728911,\n                           0.9539882943107686, 7.522076445089201e-07, 1.0},\n                          {0.0, 0.01898815687615381, 0.06564245437845008,\n                           0.5665298796332909, 4.166333347221828e-18, 1.0},\n                          {0.0, 0.9999780593618628, 0.9999899967080838,\n                           0.9999996219837988, 0.9991370418689945, 1.0},\n                          {0.0, 0.0, 0.0, 0.0, 0.0, 0.5042041932513908}};\n\n\n\n  std::size_t bytes = a.size() * sizeof(Scalar);\n\n  Scalar* d_a;\n  Scalar* d_x;\n  Scalar* d_out;\n  assert(cudaMalloc((void**)(&d_a), bytes) == cudaSuccess);\n  assert(cudaMalloc((void**)(&d_x), bytes) == cudaSuccess);\n  assert(cudaMalloc((void**)(&d_out), bytes) == cudaSuccess);\n\n  cudaMemcpy(d_a, a.data(), bytes, cudaMemcpyHostToDevice);\n  cudaMemcpy(d_x, x.data(), bytes, cudaMemcpyHostToDevice);\n\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n\n  Eigen::TensorMap<Eigen::Tensor<Scalar, 2> > gpu_a(d_a, 6, 6);\n  Eigen::TensorMap<Eigen::Tensor<Scalar, 2> > gpu_x(d_x, 6, 6);\n  Eigen::TensorMap<Eigen::Tensor<Scalar, 2> > gpu_out(d_out, 6, 6);\n\n  gpu_out.device(gpu_device) = gpu_a.igamma(gpu_x);\n\n  assert(cudaMemcpyAsync(out.data(), d_out, bytes, cudaMemcpyDeviceToHost, gpu_device.stream()) == cudaSuccess);\n  assert(cudaStreamSynchronize(gpu_device.stream()) == cudaSuccess);\n\n  for (int i = 0; i < 6; ++i) {\n    for (int j = 0; j < 6; ++j) {\n      if ((std::isnan)(igamma_s[i][j])) {\n        VERIFY((std::isnan)(out(i, j)));\n      } else {\n        VERIFY_IS_APPROX(out(i, j), igamma_s[i][j]);\n      }\n    }\n  }\n\n  cudaFree(d_a);\n  cudaFree(d_x);\n  cudaFree(d_out);\n}\n\ntemplate <typename Scalar>\nvoid test_cuda_igammac()\n{\n  Tensor<Scalar, 2> a(6, 6);\n  Tensor<Scalar, 2> x(6, 6);\n  Tensor<Scalar, 2> out(6, 6);\n  out.setZero();\n\n  Scalar a_s[] = {Scalar(0), Scalar(1), Scalar(1.5), Scalar(4), Scalar(0.0001), Scalar(1000.5)};\n  Scalar x_s[] = {Scalar(0), Scalar(1), Scalar(1.5), Scalar(4), Scalar(0.0001), Scalar(1000.5)};\n\n  for (int i = 0; i < 6; ++i) {\n    for (int j = 0; j < 6; ++j) {\n      a(i, j) = a_s[i];\n      x(i, j) = x_s[j];\n    }\n  }\n\n  Scalar nan = std::numeric_limits<Scalar>::quiet_NaN();\n  Scalar igammac_s[][6] = {{nan, nan, nan, nan, nan, nan},\n                           {1.0, 0.36787944117144233, 0.22313016014842982,\n                            0.018315638888734182, 0.9999000049998333, 0.0},\n                           {1.0, 0.5724067044708798, 0.3916251762710878,\n                            0.04601170568923136, 0.9999992477923555, 0.0},\n                           {1.0, 0.9810118431238462, 0.9343575456215499,\n                            0.4334701203667089, 1.0, 0.0},\n                           {1.0, 2.1940638138146658e-05, 1.0003291916285e-05,\n                            3.7801620118431334e-07, 0.0008629581310054535,\n                            0.0},\n                           {1.0, 1.0, 1.0, 1.0, 1.0, 0.49579580674813944}};\n\n  std::size_t bytes = a.size() * sizeof(Scalar);\n\n  Scalar* d_a;\n  Scalar* d_x;\n  Scalar* d_out;\n  cudaMalloc((void**)(&d_a), bytes);\n  cudaMalloc((void**)(&d_x), bytes);\n  cudaMalloc((void**)(&d_out), bytes);\n\n  cudaMemcpy(d_a, a.data(), bytes, cudaMemcpyHostToDevice);\n  cudaMemcpy(d_x, x.data(), bytes, cudaMemcpyHostToDevice);\n\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n\n  Eigen::TensorMap<Eigen::Tensor<Scalar, 2> > gpu_a(d_a, 6, 6);\n  Eigen::TensorMap<Eigen::Tensor<Scalar, 2> > gpu_x(d_x, 6, 6);\n  Eigen::TensorMap<Eigen::Tensor<Scalar, 2> > gpu_out(d_out, 6, 6);\n\n  gpu_out.device(gpu_device) = gpu_a.igammac(gpu_x);\n\n  assert(cudaMemcpyAsync(out.data(), d_out, bytes, cudaMemcpyDeviceToHost, gpu_device.stream()) == cudaSuccess);\n  assert(cudaStreamSynchronize(gpu_device.stream()) == cudaSuccess);\n\n  for (int i = 0; i < 6; ++i) {\n    for (int j = 0; j < 6; ++j) {\n      if ((std::isnan)(igammac_s[i][j])) {\n        VERIFY((std::isnan)(out(i, j)));\n      } else {\n        VERIFY_IS_APPROX(out(i, j), igammac_s[i][j]);\n      }\n    }\n  }\n\n  cudaFree(d_a);\n  cudaFree(d_x);\n  cudaFree(d_out);\n}\n\ntemplate <typename Scalar>\nvoid test_cuda_erf(const Scalar stddev)\n{\n  Tensor<Scalar, 2> in(72,97);\n  in.setRandom();\n  in *= in.constant(stddev);\n  Tensor<Scalar, 2> out(72,97);\n  out.setZero();\n\n  std::size_t bytes = in.size() * sizeof(Scalar);\n\n  Scalar* d_in;\n  Scalar* d_out;\n  assert(cudaMalloc((void**)(&d_in), bytes) == cudaSuccess);\n  assert(cudaMalloc((void**)(&d_out), bytes) == cudaSuccess);\n\n  cudaMemcpy(d_in, in.data(), bytes, cudaMemcpyHostToDevice);\n\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n\n  Eigen::TensorMap<Eigen::Tensor<Scalar, 2> > gpu_in(d_in, 72, 97);\n  Eigen::TensorMap<Eigen::Tensor<Scalar, 2> > gpu_out(d_out, 72, 97);\n\n  gpu_out.device(gpu_device) = gpu_in.erf();\n\n  assert(cudaMemcpyAsync(out.data(), d_out, bytes, cudaMemcpyDeviceToHost, gpu_device.stream()) == cudaSuccess);\n  assert(cudaStreamSynchronize(gpu_device.stream()) == cudaSuccess);\n\n  for (int i = 0; i < 72; ++i) {\n    for (int j = 0; j < 97; ++j) {\n      VERIFY_IS_APPROX(out(i,j), (std::erf)(in(i,j)));\n    }\n  }\n\n  cudaFree(d_in);\n  cudaFree(d_out);\n}\n\ntemplate <typename Scalar>\nvoid test_cuda_erfc(const Scalar stddev)\n{\n  Tensor<Scalar, 2> in(72,97);\n  in.setRandom();\n  in *= in.constant(stddev);\n  Tensor<Scalar, 2> out(72,97);\n  out.setZero();\n\n  std::size_t bytes = in.size() * sizeof(Scalar);\n\n  Scalar* d_in;\n  Scalar* d_out;\n  cudaMalloc((void**)(&d_in), bytes);\n  cudaMalloc((void**)(&d_out), bytes);\n\n  cudaMemcpy(d_in, in.data(), bytes, cudaMemcpyHostToDevice);\n\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n\n  Eigen::TensorMap<Eigen::Tensor<Scalar, 2> > gpu_in(d_in, 72, 97);\n  Eigen::TensorMap<Eigen::Tensor<Scalar, 2> > gpu_out(d_out, 72, 97);\n\n  gpu_out.device(gpu_device) = gpu_in.erfc();\n\n  assert(cudaMemcpyAsync(out.data(), d_out, bytes, cudaMemcpyDeviceToHost, gpu_device.stream()) == cudaSuccess);\n  assert(cudaStreamSynchronize(gpu_device.stream()) == cudaSuccess);\n\n  for (int i = 0; i < 72; ++i) {\n    for (int j = 0; j < 97; ++j) {\n      VERIFY_IS_APPROX(out(i,j), (std::erfc)(in(i,j)));\n    }\n  }\n\n  cudaFree(d_in);\n  cudaFree(d_out);\n}\n\ntemplate <typename Scalar>\nvoid test_cuda_betainc()\n{\n  Tensor<Scalar, 1> in_x(125);\n  Tensor<Scalar, 1> in_a(125);\n  Tensor<Scalar, 1> in_b(125);\n  Tensor<Scalar, 1> out(125);\n  Tensor<Scalar, 1> expected_out(125);\n  out.setZero();\n\n  Scalar nan = std::numeric_limits<Scalar>::quiet_NaN();\n\n  Array<Scalar, 1, Dynamic> x(125);\n  Array<Scalar, 1, Dynamic> a(125);\n  Array<Scalar, 1, Dynamic> b(125);\n  Array<Scalar, 1, Dynamic> v(125);\n\n  a << 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,\n      0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,\n      0.03062277660168379, 0.03062277660168379, 0.03062277660168379,\n      0.03062277660168379, 0.03062277660168379, 0.03062277660168379,\n      0.03062277660168379, 0.03062277660168379, 0.03062277660168379,\n      0.03062277660168379, 0.03062277660168379, 0.03062277660168379,\n      0.03062277660168379, 0.03062277660168379, 0.03062277660168379,\n      0.03062277660168379, 0.03062277660168379, 0.03062277660168379,\n      0.03062277660168379, 0.03062277660168379, 0.03062277660168379,\n      0.03062277660168379, 0.03062277660168379, 0.03062277660168379,\n      0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999,\n      0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999,\n      0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 31.62177660168379,\n      31.62177660168379, 31.62177660168379, 31.62177660168379,\n      31.62177660168379, 31.62177660168379, 31.62177660168379,\n      31.62177660168379, 31.62177660168379, 31.62177660168379,\n      31.62177660168379, 31.62177660168379, 31.62177660168379,\n      31.62177660168379, 31.62177660168379, 31.62177660168379,\n      31.62177660168379, 31.62177660168379, 31.62177660168379,\n      31.62177660168379, 31.62177660168379, 31.62177660168379,\n      31.62177660168379, 31.62177660168379, 31.62177660168379, 999.999, 999.999,\n      999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999,\n      999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999,\n      999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999;\n\n  b << 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379, 0.03062277660168379,\n      0.03062277660168379, 0.03062277660168379, 0.03062277660168379, 0.999,\n      0.999, 0.999, 0.999, 0.999, 31.62177660168379, 31.62177660168379,\n      31.62177660168379, 31.62177660168379, 31.62177660168379, 999.999, 999.999,\n      999.999, 999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379,\n      0.03062277660168379, 0.03062277660168379, 0.03062277660168379,\n      0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999, 31.62177660168379,\n      31.62177660168379, 31.62177660168379, 31.62177660168379,\n      31.62177660168379, 999.999, 999.999, 999.999, 999.999, 999.999, 0.0, 0.0,\n      0.0, 0.0, 0.0, 0.03062277660168379, 0.03062277660168379,\n      0.03062277660168379, 0.03062277660168379, 0.03062277660168379, 0.999,\n      0.999, 0.999, 0.999, 0.999, 31.62177660168379, 31.62177660168379,\n      31.62177660168379, 31.62177660168379, 31.62177660168379, 999.999, 999.999,\n      999.999, 999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379,\n      0.03062277660168379, 0.03062277660168379, 0.03062277660168379,\n      0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999, 31.62177660168379,\n      31.62177660168379, 31.62177660168379, 31.62177660168379,\n      31.62177660168379, 999.999, 999.999, 999.999, 999.999, 999.999, 0.0, 0.0,\n      0.0, 0.0, 0.0, 0.03062277660168379, 0.03062277660168379,\n      0.03062277660168379, 0.03062277660168379, 0.03062277660168379, 0.999,\n      0.999, 0.999, 0.999, 0.999, 31.62177660168379, 31.62177660168379,\n      31.62177660168379, 31.62177660168379, 31.62177660168379, 999.999, 999.999,\n      999.999, 999.999, 999.999;\n\n  x << -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8,\n      1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5,\n      0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2,\n      0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1,\n      0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1,\n      -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8,\n      1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5,\n      0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2,\n      0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1;\n\n  v << nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,\n      nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,\n      nan, nan, 0.47972119876364683, 0.5, 0.5202788012363533, nan, nan,\n      0.9518683957740043, 0.9789663010413743, 0.9931729188073435, nan, nan,\n      0.999995949033062, 0.9999999999993698, 0.9999999999999999, nan, nan,\n      0.9999999999999999, 0.9999999999999999, 0.9999999999999999, nan, nan, nan,\n      nan, nan, nan, nan, 0.006827081192655869, 0.0210336989586256,\n      0.04813160422599567, nan, nan, 0.20014344256217678, 0.5000000000000001,\n      0.7998565574378232, nan, nan, 0.9991401428435834, 0.999999999698403,\n      0.9999999999999999, nan, nan, 0.9999999999999999, 0.9999999999999999,\n      0.9999999999999999, nan, nan, nan, nan, nan, nan, nan,\n      1.0646600232370887e-25, 6.301722877826246e-13, 4.050966937974938e-06, nan,\n      nan, 7.864342668429763e-23, 3.015969667594166e-10, 0.0008598571564165444,\n      nan, nan, 6.031987710123844e-08, 0.5000000000000007, 0.9999999396801229,\n      nan, nan, 0.9999999999999999, 0.9999999999999999, 0.9999999999999999, nan,\n      nan, nan, nan, nan, nan, nan, 0.0, 7.029920380986636e-306,\n      2.2450728208591345e-101, nan, nan, 0.0, 9.275871147869727e-302,\n      1.2232913026152827e-97, nan, nan, 0.0, 3.0891393081932924e-252,\n      2.9303043666183996e-60, nan, nan, 2.248913486879199e-196,\n      0.5000000000004947, 0.9999999999999999, nan;\n\n  for (int i = 0; i < 125; ++i) {\n    in_x(i) = x(i);\n    in_a(i) = a(i);\n    in_b(i) = b(i);\n    expected_out(i) = v(i);\n  }\n\n  std::size_t bytes = in_x.size() * sizeof(Scalar);\n\n  Scalar* d_in_x;\n  Scalar* d_in_a;\n  Scalar* d_in_b;\n  Scalar* d_out;\n  cudaMalloc((void**)(&d_in_x), bytes);\n  cudaMalloc((void**)(&d_in_a), bytes);\n  cudaMalloc((void**)(&d_in_b), bytes);\n  cudaMalloc((void**)(&d_out), bytes);\n\n  cudaMemcpy(d_in_x, in_x.data(), bytes, cudaMemcpyHostToDevice);\n  cudaMemcpy(d_in_a, in_a.data(), bytes, cudaMemcpyHostToDevice);\n  cudaMemcpy(d_in_b, in_b.data(), bytes, cudaMemcpyHostToDevice);\n\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n\n  Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_in_x(d_in_x, 125);\n  Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_in_a(d_in_a, 125);\n  Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_in_b(d_in_b, 125);\n  Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_out(d_out, 125);\n\n  gpu_out.device(gpu_device) = betainc(gpu_in_a, gpu_in_b, gpu_in_x);\n\n  assert(cudaMemcpyAsync(out.data(), d_out, bytes, cudaMemcpyDeviceToHost, gpu_device.stream()) == cudaSuccess);\n  assert(cudaStreamSynchronize(gpu_device.stream()) == cudaSuccess);\n\n  for (int i = 1; i < 125; ++i) {\n    if ((std::isnan)(expected_out(i))) {\n      VERIFY((std::isnan)(out(i)));\n    } else {\n      VERIFY_IS_APPROX(out(i), expected_out(i));\n    }\n  }\n\n  cudaFree(d_in_x);\n  cudaFree(d_in_a);\n  cudaFree(d_in_b);\n  cudaFree(d_out);\n}\n\n\nvoid test_cxx11_tensor_cuda()\n{\n  CALL_SUBTEST_1(test_cuda_nullary());\n  CALL_SUBTEST_1(test_cuda_elementwise_small());\n  CALL_SUBTEST_1(test_cuda_elementwise());\n  CALL_SUBTEST_1(test_cuda_props());\n  CALL_SUBTEST_1(test_cuda_reduction());\n  CALL_SUBTEST_2(test_cuda_contraction<ColMajor>());\n  CALL_SUBTEST_2(test_cuda_contraction<RowMajor>());\n  CALL_SUBTEST_3(test_cuda_convolution_1d<ColMajor>());\n  CALL_SUBTEST_3(test_cuda_convolution_1d<RowMajor>());\n  CALL_SUBTEST_3(test_cuda_convolution_inner_dim_col_major_1d());\n  CALL_SUBTEST_3(test_cuda_convolution_inner_dim_row_major_1d());\n  CALL_SUBTEST_3(test_cuda_convolution_2d<ColMajor>());\n  CALL_SUBTEST_3(test_cuda_convolution_2d<RowMajor>());\n  CALL_SUBTEST_3(test_cuda_convolution_3d<ColMajor>());\n  CALL_SUBTEST_3(test_cuda_convolution_3d<RowMajor>());\n\n#if __cplusplus > 199711L\n  // std::erf, std::erfc, and so on where only added in c++11. We use them\n  // as a golden reference to validate the results produced by Eigen. Therefore\n  // we can only run these tests if we use a c++11 compiler.\n  CALL_SUBTEST_4(test_cuda_lgamma<float>(1.0f));\n  CALL_SUBTEST_4(test_cuda_lgamma<float>(100.0f));\n  CALL_SUBTEST_4(test_cuda_lgamma<float>(0.01f));\n  CALL_SUBTEST_4(test_cuda_lgamma<float>(0.001f));\n\n  CALL_SUBTEST_4(test_cuda_lgamma<double>(1.0));\n  CALL_SUBTEST_4(test_cuda_lgamma<double>(100.0));\n  CALL_SUBTEST_4(test_cuda_lgamma<double>(0.01));\n  CALL_SUBTEST_4(test_cuda_lgamma<double>(0.001));\n\n  CALL_SUBTEST_4(test_cuda_erf<float>(1.0f));\n  CALL_SUBTEST_4(test_cuda_erf<float>(100.0f));\n  CALL_SUBTEST_4(test_cuda_erf<float>(0.01f));\n  CALL_SUBTEST_4(test_cuda_erf<float>(0.001f));\n\n  CALL_SUBTEST_4(test_cuda_erfc<float>(1.0f));\n  // CALL_SUBTEST(test_cuda_erfc<float>(100.0f));\n  CALL_SUBTEST_4(test_cuda_erfc<float>(5.0f)); // CUDA erfc lacks precision for large inputs\n  CALL_SUBTEST_4(test_cuda_erfc<float>(0.01f));\n  CALL_SUBTEST_4(test_cuda_erfc<float>(0.001f));\n\n  CALL_SUBTEST_4(test_cuda_erf<double>(1.0));\n  CALL_SUBTEST_4(test_cuda_erf<double>(100.0));\n  CALL_SUBTEST_4(test_cuda_erf<double>(0.01));\n  CALL_SUBTEST_4(test_cuda_erf<double>(0.001));\n\n  CALL_SUBTEST_4(test_cuda_erfc<double>(1.0));\n  // CALL_SUBTEST(test_cuda_erfc<double>(100.0));\n  CALL_SUBTEST_4(test_cuda_erfc<double>(5.0)); // CUDA erfc lacks precision for large inputs\n  CALL_SUBTEST_4(test_cuda_erfc<double>(0.01));\n  CALL_SUBTEST_4(test_cuda_erfc<double>(0.001));\n\n  CALL_SUBTEST_5(test_cuda_digamma<float>());\n  CALL_SUBTEST_5(test_cuda_digamma<double>());\n\n  CALL_SUBTEST_5(test_cuda_polygamma<float>());\n  CALL_SUBTEST_5(test_cuda_polygamma<double>());\n\n  CALL_SUBTEST_5(test_cuda_zeta<float>());\n  CALL_SUBTEST_5(test_cuda_zeta<double>());\n\n  CALL_SUBTEST_5(test_cuda_igamma<float>());\n  CALL_SUBTEST_5(test_cuda_igammac<float>());\n\n  CALL_SUBTEST_5(test_cuda_igamma<double>());\n  CALL_SUBTEST_5(test_cuda_igammac<double>());\n\n  CALL_SUBTEST_6(test_cuda_betainc<float>());\n  CALL_SUBTEST_6(test_cuda_betainc<double>());\n#endif\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_custom_index.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <limits>\n#include <map>\n\n#include <Eigen/Dense>\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\n\n\ntemplate <int DataLayout>\nstatic void test_map_as_index()\n{\n#ifdef EIGEN_HAS_SFINAE\n  Tensor<float, 4, DataLayout> tensor(2, 3, 5, 7);\n  tensor.setRandom();\n\n  using NormalIndex = DSizes<ptrdiff_t, 4>;\n  using CustomIndex = std::map<ptrdiff_t, ptrdiff_t>;\n  CustomIndex coeffC;\n  coeffC[0] = 1;\n  coeffC[1] = 2;\n  coeffC[2] = 4;\n  coeffC[3] = 1;\n  NormalIndex coeff(1,2,4,1);\n\n  VERIFY_IS_EQUAL(tensor.coeff(coeffC), tensor.coeff(coeff));\n  VERIFY_IS_EQUAL(tensor.coeffRef(coeffC), tensor.coeffRef(coeff));\n#endif\n}\n\n\ntemplate <int DataLayout>\nstatic void test_matrix_as_index()\n{\n#ifdef EIGEN_HAS_SFINAE\n  Tensor<float, 4, DataLayout> tensor(2, 3, 5, 7);\n  tensor.setRandom();\n\n  using NormalIndex = DSizes<ptrdiff_t, 4>;\n  using CustomIndex = Matrix<unsigned int, 4, 1>;\n  CustomIndex coeffC(1,2,4,1);\n  NormalIndex coeff(1,2,4,1);\n\n  VERIFY_IS_EQUAL(tensor.coeff(coeffC), tensor.coeff(coeff));\n  VERIFY_IS_EQUAL(tensor.coeffRef(coeffC), tensor.coeffRef(coeff));\n#endif\n}\n\n\ntemplate <int DataLayout>\nstatic void test_varlist_as_index()\n{\n#ifdef EIGEN_HAS_SFINAE\n  Tensor<float, 4, DataLayout> tensor(2, 3, 5, 7);\n  tensor.setRandom();\n\n  DSizes<ptrdiff_t, 4> coeff(1,2,4,1);\n\n  VERIFY_IS_EQUAL(tensor.coeff({1,2,4,1}), tensor.coeff(coeff));\n  VERIFY_IS_EQUAL(tensor.coeffRef({1,2,4,1}), tensor.coeffRef(coeff));\n#endif\n}\n\n\ntemplate <int DataLayout>\nstatic void test_sizes_as_index()\n{\n#ifdef EIGEN_HAS_SFINAE\n  Tensor<float, 4, DataLayout> tensor(2, 3, 5, 7);\n  tensor.setRandom();\n\n  DSizes<ptrdiff_t, 4> coeff(1,2,4,1);\n  Sizes<1,2,4,1> coeffC;\n\n  VERIFY_IS_EQUAL(tensor.coeff(coeffC), tensor.coeff(coeff));\n  VERIFY_IS_EQUAL(tensor.coeffRef(coeffC), tensor.coeffRef(coeff));\n#endif\n}\n\n\nvoid test_cxx11_tensor_custom_index() {\n  test_map_as_index<ColMajor>();\n  test_map_as_index<RowMajor>();\n  test_matrix_as_index<ColMajor>();\n  test_matrix_as_index<RowMajor>();\n  test_varlist_as_index<ColMajor>();\n  test_varlist_as_index<RowMajor>();\n  test_sizes_as_index<ColMajor>();\n  test_sizes_as_index<RowMajor>();\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_custom_op.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\n\n\nstruct InsertZeros {\n  DSizes<DenseIndex, 2> dimensions(const Tensor<float, 2>& input) const {\n    DSizes<DenseIndex, 2> result;\n    result[0] = input.dimension(0) * 2;\n    result[1] = input.dimension(1) * 2;\n    return result;\n  }\n\n  template <typename Output, typename Device>\n  void eval(const Tensor<float, 2>& input, Output& output, const Device& device) const\n  {\n    array<DenseIndex, 2> strides;\n    strides[0] = 2;\n    strides[1] = 2;\n    output.stride(strides).device(device) = input;\n\n    Eigen::DSizes<DenseIndex, 2> offsets(1,1);\n    Eigen::DSizes<DenseIndex, 2> extents(output.dimension(0)-1, output.dimension(1)-1);\n    output.slice(offsets, extents).stride(strides).device(device) = input.constant(0.0f);\n  }\n};\n\nstatic void test_custom_unary_op()\n{\n  Tensor<float, 2> tensor(3,5);\n  tensor.setRandom();\n\n  Tensor<float, 2> result = tensor.customOp(InsertZeros());\n  VERIFY_IS_EQUAL(result.dimension(0), 6);\n  VERIFY_IS_EQUAL(result.dimension(1), 10);\n\n  for (int i = 0; i < 6; i+=2) {\n    for (int j = 0; j < 10; j+=2) {\n      VERIFY_IS_EQUAL(result(i, j), tensor(i/2, j/2));\n    }\n  }\n  for (int i = 1; i < 6; i+=2) {\n    for (int j = 1; j < 10; j+=2) {\n      VERIFY_IS_EQUAL(result(i, j), 0);\n    }\n  }\n}\n\n\nstruct BatchMatMul {\n  DSizes<DenseIndex, 3> dimensions(const Tensor<float, 3>& input1, const Tensor<float, 3>& input2) const {\n    DSizes<DenseIndex, 3> result;\n    result[0] = input1.dimension(0);\n    result[1] = input2.dimension(1);\n    result[2] = input2.dimension(2);\n    return result;\n  }\n\n  template <typename Output, typename Device>\n  void eval(const Tensor<float, 3>& input1, const Tensor<float, 3>& input2,\n            Output& output, const Device& device) const\n  {\n    typedef Tensor<float, 3>::DimensionPair DimPair;\n    array<DimPair, 1> dims;\n    dims[0] = DimPair(1, 0);\n    for (int i = 0; i < output.dimension(2); ++i) {\n      output.template chip<2>(i).device(device) = input1.chip<2>(i).contract(input2.chip<2>(i), dims);\n    }\n  }\n};\n\n\nstatic void test_custom_binary_op()\n{\n  Tensor<float, 3> tensor1(2,3,5);\n  tensor1.setRandom();\n  Tensor<float, 3> tensor2(3,7,5);\n  tensor2.setRandom();\n\n  Tensor<float, 3> result = tensor1.customOp(tensor2, BatchMatMul());\n  for (int i = 0; i < 5; ++i) {\n    typedef Tensor<float, 3>::DimensionPair DimPair;\n    array<DimPair, 1> dims;\n    dims[0] = DimPair(1, 0);\n    Tensor<float, 2> reference = tensor1.chip<2>(i).contract(tensor2.chip<2>(i), dims);\n    TensorRef<Tensor<float, 2> > val = result.chip<2>(i);\n    for (int j = 0; j < 2; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        VERIFY_IS_APPROX(val(j, k), reference(j, k));\n      }\n    }\n  }\n}\n\n\nvoid test_cxx11_tensor_custom_op()\n{\n  CALL_SUBTEST(test_custom_unary_op());\n  CALL_SUBTEST(test_custom_binary_op());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_device.cu",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define EIGEN_TEST_NO_LONGDOUBLE\n#define EIGEN_TEST_NO_COMPLEX\n#define EIGEN_TEST_FUNC cxx11_tensor_device\n#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int\n#define EIGEN_USE_GPU\n\n#include \"main.h\"\n#include <unsupported/Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\nusing Eigen::RowMajor;\n\n// Context for evaluation on cpu\nstruct CPUContext {\n  CPUContext(const Eigen::Tensor<float, 3>& in1, Eigen::Tensor<float, 3>& in2, Eigen::Tensor<float, 3>& out) : in1_(in1), in2_(in2), out_(out), kernel_1d_(2), kernel_2d_(2,2), kernel_3d_(2,2,2) {\n    kernel_1d_(0) = 3.14f;\n    kernel_1d_(1) = 2.7f;\n\n    kernel_2d_(0,0) = 3.14f;\n    kernel_2d_(1,0) = 2.7f;\n    kernel_2d_(0,1) = 0.2f;\n    kernel_2d_(1,1) = 7.0f;\n\n    kernel_3d_(0,0,0) = 3.14f;\n    kernel_3d_(0,1,0) = 2.7f;\n    kernel_3d_(0,0,1) = 0.2f;\n    kernel_3d_(0,1,1) = 7.0f;\n    kernel_3d_(1,0,0) = -1.0f;\n    kernel_3d_(1,1,0) = -0.3f;\n    kernel_3d_(1,0,1) = -0.7f;\n    kernel_3d_(1,1,1) = -0.5f;\n  }\n\n  const Eigen::DefaultDevice& device() const { return cpu_device_; }\n\n  const Eigen::Tensor<float, 3>& in1() const { return in1_; }\n  const Eigen::Tensor<float, 3>& in2() const { return in2_; }\n  Eigen::Tensor<float, 3>& out() { return out_; }\n  const Eigen::Tensor<float, 1>& kernel1d() const { return kernel_1d_; }\n  const Eigen::Tensor<float, 2>& kernel2d() const { return kernel_2d_; }\n  const Eigen::Tensor<float, 3>& kernel3d() const { return kernel_3d_; }\n\n private:\n  const Eigen::Tensor<float, 3>& in1_;\n  const Eigen::Tensor<float, 3>& in2_;\n  Eigen::Tensor<float, 3>& out_;\n\n  Eigen::Tensor<float, 1> kernel_1d_;\n  Eigen::Tensor<float, 2> kernel_2d_;\n  Eigen::Tensor<float, 3> kernel_3d_;\n\n  Eigen::DefaultDevice cpu_device_;\n};\n\n\n// Context for evaluation on GPU\nstruct GPUContext {\n  GPUContext(const Eigen::TensorMap<Eigen::Tensor<float, 3> >& in1, Eigen::TensorMap<Eigen::Tensor<float, 3> >& in2, Eigen::TensorMap<Eigen::Tensor<float, 3> >& out) : in1_(in1), in2_(in2), out_(out), gpu_device_(&stream_) {\n    assert(cudaMalloc((void**)(&kernel_1d_), 2*sizeof(float)) == cudaSuccess);\n    float kernel_1d_val[] = {3.14f, 2.7f};\n    assert(cudaMemcpy(kernel_1d_, kernel_1d_val, 2*sizeof(float), cudaMemcpyHostToDevice) == cudaSuccess);\n\n    assert(cudaMalloc((void**)(&kernel_2d_), 4*sizeof(float)) == cudaSuccess);\n    float kernel_2d_val[] = {3.14f, 2.7f, 0.2f, 7.0f};\n    assert(cudaMemcpy(kernel_2d_, kernel_2d_val, 4*sizeof(float), cudaMemcpyHostToDevice) == cudaSuccess);\n\n    assert(cudaMalloc((void**)(&kernel_3d_), 8*sizeof(float)) == cudaSuccess);\n    float kernel_3d_val[] = {3.14f, -1.0f, 2.7f, -0.3f, 0.2f, -0.7f, 7.0f, -0.5f};\n    assert(cudaMemcpy(kernel_3d_, kernel_3d_val, 8*sizeof(float), cudaMemcpyHostToDevice) == cudaSuccess);\n  }\n  ~GPUContext() {\n    assert(cudaFree(kernel_1d_) == cudaSuccess);\n    assert(cudaFree(kernel_2d_) == cudaSuccess);\n    assert(cudaFree(kernel_3d_) == cudaSuccess);\n  }\n\n  const Eigen::GpuDevice& device() const { return gpu_device_; }\n\n  const Eigen::TensorMap<Eigen::Tensor<float, 3> >& in1() const { return in1_; }\n  const Eigen::TensorMap<Eigen::Tensor<float, 3> >& in2() const { return in2_; }\n  Eigen::TensorMap<Eigen::Tensor<float, 3> >& out() { return out_; }\n  Eigen::TensorMap<Eigen::Tensor<float, 1> > kernel1d() const { return Eigen::TensorMap<Eigen::Tensor<float, 1> >(kernel_1d_, 2); }\n  Eigen::TensorMap<Eigen::Tensor<float, 2> > kernel2d() const { return Eigen::TensorMap<Eigen::Tensor<float, 2> >(kernel_2d_, 2, 2); }\n  Eigen::TensorMap<Eigen::Tensor<float, 3> > kernel3d() const { return Eigen::TensorMap<Eigen::Tensor<float, 3> >(kernel_3d_, 2, 2, 2); }\n\n private:\n  const Eigen::TensorMap<Eigen::Tensor<float, 3> >& in1_;\n  const Eigen::TensorMap<Eigen::Tensor<float, 3> >& in2_;\n  Eigen::TensorMap<Eigen::Tensor<float, 3> >& out_;\n\n  float* kernel_1d_;\n  float* kernel_2d_;\n  float* kernel_3d_;\n\n  Eigen::CudaStreamDevice stream_;\n  Eigen::GpuDevice gpu_device_;\n};\n\n\n// The actual expression to evaluate\ntemplate <typename Context>\nvoid test_contextual_eval(Context* context)\n{\n  context->out().device(context->device()) = context->in1() + context->in2() * 3.14f + context->in1().constant(2.718f);\n}\n\ntemplate <typename Context>\nvoid test_forced_contextual_eval(Context* context)\n{\n  context->out().device(context->device()) = (context->in1() + context->in2()).eval() * 3.14f + context->in1().constant(2.718f);\n}\n\ntemplate <typename Context>\nvoid test_compound_assignment(Context* context)\n{\n  context->out().device(context->device()) = context->in1().constant(2.718f);\n  context->out().device(context->device()) += context->in1() + context->in2() * 3.14f;\n}\n\n\ntemplate <typename Context>\nvoid test_contraction(Context* context)\n{\n  Eigen::array<std::pair<int, int>, 2> dims;\n  dims[0] = std::make_pair(1, 1);\n  dims[1] = std::make_pair(2, 2);\n\n  Eigen::array<int, 2> shape(40, 50*70);\n\n  Eigen::DSizes<int, 2> indices(0,0);\n  Eigen::DSizes<int, 2> sizes(40,40);\n\n  context->out().reshape(shape).slice(indices, sizes).device(context->device()) = context->in1().contract(context->in2(), dims);\n}\n\n\ntemplate <typename Context>\nvoid test_1d_convolution(Context* context)\n{\n  Eigen::DSizes<int, 3> indices(0,0,0);\n  Eigen::DSizes<int, 3> sizes(40,49,70);\n\n  Eigen::array<int, 1> dims(1);\n  context->out().slice(indices, sizes).device(context->device()) = context->in1().convolve(context->kernel1d(), dims);\n}\n\ntemplate <typename Context>\nvoid test_2d_convolution(Context* context)\n{\n  Eigen::DSizes<int, 3> indices(0,0,0);\n  Eigen::DSizes<int, 3> sizes(40,49,69);\n\n  Eigen::array<int, 2> dims(1,2);\n  context->out().slice(indices, sizes).device(context->device()) = context->in1().convolve(context->kernel2d(), dims);\n}\n\ntemplate <typename Context>\nvoid test_3d_convolution(Context* context)\n{\n  Eigen::DSizes<int, 3> indices(0,0,0);\n  Eigen::DSizes<int, 3> sizes(39,49,69);\n\n  Eigen::array<int, 3> dims(0,1,2);\n  context->out().slice(indices, sizes).device(context->device()) = context->in1().convolve(context->kernel3d(), dims);\n}\n\n\nvoid test_cpu() {\n  Eigen::Tensor<float, 3> in1(40,50,70);\n  Eigen::Tensor<float, 3> in2(40,50,70);\n  Eigen::Tensor<float, 3> out(40,50,70);\n\n  in1 = in1.random() + in1.constant(10.0f);\n  in2 = in2.random() + in2.constant(10.0f);\n\n  CPUContext context(in1, in2, out);\n  test_contextual_eval(&context);\n  for (int i = 0; i < 40; ++i) {\n    for (int j = 0; j < 50; ++j) {\n      for (int k = 0; k < 70; ++k) {\n        VERIFY_IS_APPROX(out(i,j,k), in1(i,j,k) + in2(i,j,k) * 3.14f + 2.718f);\n      }\n    }\n  }\n\n  test_forced_contextual_eval(&context);\n  for (int i = 0; i < 40; ++i) {\n    for (int j = 0; j < 50; ++j) {\n      for (int k = 0; k < 70; ++k) {\n        VERIFY_IS_APPROX(out(i,j,k), (in1(i,j,k) + in2(i,j,k)) * 3.14f + 2.718f);\n      }\n    }\n  }\n\n  test_compound_assignment(&context);\n  for (int i = 0; i < 40; ++i) {\n    for (int j = 0; j < 50; ++j) {\n      for (int k = 0; k < 70; ++k) {\n        VERIFY_IS_APPROX(out(i,j,k), in1(i,j,k) + in2(i,j,k) * 3.14f + 2.718f);\n      }\n    }\n  }\n\n  test_contraction(&context);\n  for (int i = 0; i < 40; ++i) {\n    for (int j = 0; j < 40; ++j) {\n      const float result = out(i,j,0);\n      float expected = 0;\n      for (int k = 0; k < 50; ++k) {\n        for (int l = 0; l < 70; ++l) {\n          expected += in1(i, k, l) * in2(j, k, l);\n        }\n      }\n      VERIFY_IS_APPROX(expected, result);\n    }\n  }\n\n  test_1d_convolution(&context);\n  for (int i = 0; i < 40; ++i) {\n    for (int j = 0; j < 49; ++j) {\n      for (int k = 0; k < 70; ++k) {\n        VERIFY_IS_APPROX(out(i,j,k), (in1(i,j,k) * 3.14f + in1(i,j+1,k) * 2.7f));\n      }\n    }\n  }\n\n  test_2d_convolution(&context);\n  for (int i = 0; i < 40; ++i) {\n    for (int j = 0; j < 49; ++j) {\n      for (int k = 0; k < 69; ++k) {\n        const float result = out(i,j,k);\n        const float expected = (in1(i,j,k) * 3.14f + in1(i,j+1,k) * 2.7f) +\n                               (in1(i,j,k+1) * 0.2f + in1(i,j+1,k+1) * 7.0f);\n        if (fabs(expected) < 1e-4f && fabs(result) < 1e-4f) {\n          continue;\n        }\n        VERIFY_IS_APPROX(expected, result);\n      }\n    }\n  }\n\n  test_3d_convolution(&context);\n  for (int i = 0; i < 39; ++i) {\n    for (int j = 0; j < 49; ++j) {\n      for (int k = 0; k < 69; ++k) {\n        const float result = out(i,j,k);\n        const float expected = (in1(i,j,k) * 3.14f + in1(i,j+1,k) * 2.7f +\n                                in1(i,j,k+1) * 0.2f + in1(i,j+1,k+1) * 7.0f) +\n                               (in1(i+1,j,k) * -1.0f + in1(i+1,j+1,k) * -0.3f +\n                                in1(i+1,j,k+1) * -0.7f + in1(i+1,j+1,k+1) * -0.5f);\n        if (fabs(expected) < 1e-4f && fabs(result) < 1e-4f) {\n          continue;\n        }\n        VERIFY_IS_APPROX(expected, result);\n      }\n    }\n  }\n}\n\nvoid test_gpu() {\n  Eigen::Tensor<float, 3> in1(40,50,70);\n  Eigen::Tensor<float, 3> in2(40,50,70);\n  Eigen::Tensor<float, 3> out(40,50,70);\n  in1 = in1.random() + in1.constant(10.0f);\n  in2 = in2.random() + in2.constant(10.0f);\n\n  std::size_t in1_bytes = in1.size() * sizeof(float);\n  std::size_t in2_bytes = in2.size() * sizeof(float);\n  std::size_t out_bytes = out.size() * sizeof(float);\n\n  float* d_in1;\n  float* d_in2;\n  float* d_out;\n  cudaMalloc((void**)(&d_in1), in1_bytes);\n  cudaMalloc((void**)(&d_in2), in2_bytes);\n  cudaMalloc((void**)(&d_out), out_bytes);\n\n  cudaMemcpy(d_in1, in1.data(), in1_bytes, cudaMemcpyHostToDevice);\n  cudaMemcpy(d_in2, in2.data(), in2_bytes, cudaMemcpyHostToDevice);\n\n  Eigen::TensorMap<Eigen::Tensor<float, 3> > gpu_in1(d_in1, 40,50,70);\n  Eigen::TensorMap<Eigen::Tensor<float, 3> > gpu_in2(d_in2, 40,50,70);\n  Eigen::TensorMap<Eigen::Tensor<float, 3> > gpu_out(d_out, 40,50,70);\n\n  GPUContext context(gpu_in1, gpu_in2, gpu_out);\n  test_contextual_eval(&context);\n  assert(cudaMemcpy(out.data(), d_out, out_bytes, cudaMemcpyDeviceToHost) == cudaSuccess);\n  for (int i = 0; i < 40; ++i) {\n    for (int j = 0; j < 50; ++j) {\n      for (int k = 0; k < 70; ++k) {\n        VERIFY_IS_APPROX(out(i,j,k), in1(i,j,k) + in2(i,j,k) * 3.14f + 2.718f);\n      }\n    }\n  }\n\n  test_forced_contextual_eval(&context);\n  assert(cudaMemcpy(out.data(), d_out, out_bytes, cudaMemcpyDeviceToHost) == cudaSuccess);\n  for (int i = 0; i < 40; ++i) {\n    for (int j = 0; j < 50; ++j) {\n      for (int k = 0; k < 70; ++k) {\n        VERIFY_IS_APPROX(out(i,j,k), (in1(i,j,k) + in2(i,j,k)) * 3.14f + 2.718f);\n      }\n    }\n  }\n\n  test_compound_assignment(&context);\n  assert(cudaMemcpy(out.data(), d_out, out_bytes, cudaMemcpyDeviceToHost) == cudaSuccess);\n  for (int i = 0; i < 40; ++i) {\n    for (int j = 0; j < 50; ++j) {\n      for (int k = 0; k < 70; ++k) {\n        VERIFY_IS_APPROX(out(i,j,k), in1(i,j,k) + in2(i,j,k) * 3.14f + 2.718f);\n      }\n    }\n  }\n\n  test_contraction(&context);\n  assert(cudaMemcpy(out.data(), d_out, out_bytes, cudaMemcpyDeviceToHost) == cudaSuccess);\n  for (int i = 0; i < 40; ++i) {\n    for (int j = 0; j < 40; ++j) {\n      const float result = out(i,j,0);\n      float expected = 0;\n      for (int k = 0; k < 50; ++k) {\n        for (int l = 0; l < 70; ++l) {\n          expected += in1(i, k, l) * in2(j, k, l);\n        }\n      }\n      VERIFY_IS_APPROX(expected, result);\n    }\n  }\n\n  test_1d_convolution(&context);\n  assert(cudaMemcpyAsync(out.data(), d_out, out_bytes, cudaMemcpyDeviceToHost, context.device().stream()) == cudaSuccess);\n  assert(cudaStreamSynchronize(context.device().stream()) == cudaSuccess);\n  for (int i = 0; i < 40; ++i) {\n    for (int j = 0; j < 49; ++j) {\n      for (int k = 0; k < 70; ++k) {\n        VERIFY_IS_APPROX(out(i,j,k), (in1(i,j,k) * 3.14f + in1(i,j+1,k) * 2.7f));\n      }\n    }\n  }\n\n  test_2d_convolution(&context);\n  assert(cudaMemcpyAsync(out.data(), d_out, out_bytes, cudaMemcpyDeviceToHost, context.device().stream()) == cudaSuccess);\n  assert(cudaStreamSynchronize(context.device().stream()) == cudaSuccess);\n  for (int i = 0; i < 40; ++i) {\n    for (int j = 0; j < 49; ++j) {\n      for (int k = 0; k < 69; ++k) {\n        const float result = out(i,j,k);\n        const float expected = (in1(i,j,k) * 3.14f + in1(i,j+1,k) * 2.7f +\n                                in1(i,j,k+1) * 0.2f + in1(i,j+1,k+1) * 7.0f);\n        VERIFY_IS_APPROX(expected, result);\n      }\n    }\n  }\n\n  test_3d_convolution(&context);\n  assert(cudaMemcpyAsync(out.data(), d_out, out_bytes, cudaMemcpyDeviceToHost, context.device().stream()) == cudaSuccess);\n  assert(cudaStreamSynchronize(context.device().stream()) == cudaSuccess);\n  for (int i = 0; i < 39; ++i) {\n    for (int j = 0; j < 49; ++j) {\n      for (int k = 0; k < 69; ++k) {\n       const float result = out(i,j,k);\n        const float expected = (in1(i,j,k) * 3.14f + in1(i,j+1,k) * 2.7f +\n                                in1(i,j,k+1) * 0.2f + in1(i,j+1,k+1) * 7.0f +\n                                in1(i+1,j,k) * -1.0f + in1(i+1,j+1,k) * -0.3f +\n                                in1(i+1,j,k+1) * -0.7f + in1(i+1,j+1,k+1) * -0.5f);\n        VERIFY_IS_APPROX(expected, result);\n      }\n    }\n  }\n}\n\n\nvoid test_cxx11_tensor_device()\n{\n  CALL_SUBTEST_1(test_cpu());\n  CALL_SUBTEST_2(test_gpu());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_device_sycl.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016\n// Mehdi Goli    Codeplay Software Ltd.\n// Ralph Potter  Codeplay Software Ltd.\n// Luke Iwanski  Codeplay Software Ltd.\n// Contact: <eigen@codeplay.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define EIGEN_TEST_NO_LONGDOUBLE\n#define EIGEN_TEST_NO_COMPLEX\n#define EIGEN_TEST_FUNC cxx11_tensor_device_sycl\n#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int\n#define EIGEN_USE_SYCL\n\n#include \"main.h\"\n#include <unsupported/Eigen/CXX11/Tensor>\n\nvoid test_device_sycl(const Eigen::SyclDevice &sycl_device) {\n  std::cout <<\"Helo from ComputeCpp: the requested device exists and the device name is : \"\n    << sycl_device.m_queue.get_device(). template get_info<cl::sycl::info::device::name>() <<std::endl;;\n}\nvoid test_cxx11_tensor_device_sycl() {\n  cl::sycl::gpu_selector s;\n  Eigen::SyclDevice sycl_device(s);\n  CALL_SUBTEST(test_device_sycl(sycl_device));\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_dimension.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\n\n\nstatic void test_dynamic_size()\n{\n  Eigen::DSizes<int, 3> dimensions(2,3,7);\n\n  VERIFY_IS_EQUAL((int)Eigen::internal::array_get<0>(dimensions), 2);\n  VERIFY_IS_EQUAL((int)Eigen::internal::array_get<1>(dimensions), 3);\n  VERIFY_IS_EQUAL((int)Eigen::internal::array_get<2>(dimensions), 7);\n  VERIFY_IS_EQUAL((int)dimensions.TotalSize(), 2*3*7);\n  VERIFY_IS_EQUAL((int)dimensions[0], 2);\n  VERIFY_IS_EQUAL((int)dimensions[1], 3);\n  VERIFY_IS_EQUAL((int)dimensions[2], 7);\n}\n\nstatic void test_fixed_size()\n{\n  Eigen::Sizes<2,3,7> dimensions;\n\n  VERIFY_IS_EQUAL((int)Eigen::internal::array_get<0>(dimensions), 2);\n  VERIFY_IS_EQUAL((int)Eigen::internal::array_get<1>(dimensions), 3);\n  VERIFY_IS_EQUAL((int)Eigen::internal::array_get<2>(dimensions), 7);\n  VERIFY_IS_EQUAL((int)dimensions.TotalSize(), 2*3*7);\n}\n\nstatic void test_match()\n{\n  Eigen::DSizes<unsigned int, 3> dyn((unsigned int)2,(unsigned int)3,(unsigned int)7);\n  Eigen::Sizes<2,3,7> stat;\n  VERIFY_IS_EQUAL(Eigen::dimensions_match(dyn, stat), true);\n\n  Eigen::DSizes<int, 3> dyn1(2,3,7);\n  Eigen::DSizes<int, 2> dyn2(2,3);\n  VERIFY_IS_EQUAL(Eigen::dimensions_match(dyn1, dyn2), false);\n}\n\nstatic void test_rank_zero()\n{\n  Eigen::Sizes<> scalar;\n  VERIFY_IS_EQUAL((int)scalar.TotalSize(), 1);\n  VERIFY_IS_EQUAL((int)scalar.rank(), 0);\n  VERIFY_IS_EQUAL((int)internal::array_prod(scalar), 1);\n\n  Eigen::DSizes<ptrdiff_t, 0> dscalar;\n  VERIFY_IS_EQUAL((int)dscalar.TotalSize(), 1);\n  VERIFY_IS_EQUAL((int)dscalar.rank(), 0);\n}\n\nvoid test_cxx11_tensor_dimension()\n{\n  CALL_SUBTEST(test_dynamic_size());\n  CALL_SUBTEST(test_fixed_size());\n  CALL_SUBTEST(test_match());\n  CALL_SUBTEST(test_rank_zero());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_empty.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\n\nstatic void test_empty_tensor()\n{\n  Tensor<float, 2> source;\n  Tensor<float, 2> tgt1 = source;\n  Tensor<float, 2> tgt2(source);\n  Tensor<float, 2> tgt3;\n  tgt3 = tgt1;\n  tgt3 = tgt2;\n}\n\nstatic void test_empty_fixed_size_tensor()\n{\n  TensorFixedSize<float, Sizes<0> > source;\n  TensorFixedSize<float, Sizes<0> > tgt1 = source;\n  TensorFixedSize<float, Sizes<0> > tgt2(source);\n  TensorFixedSize<float, Sizes<0> > tgt3;\n  tgt3 = tgt1;\n  tgt3 = tgt2;\n}\n\n\nvoid test_cxx11_tensor_empty()\n{\n   CALL_SUBTEST(test_empty_tensor());\n   CALL_SUBTEST(test_empty_fixed_size_tensor());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_expr.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\nusing Eigen::RowMajor;\n\nstatic void test_1d()\n{\n  Tensor<float, 1> vec1(6);\n  Tensor<float, 1, RowMajor> vec2(6);\n\n  vec1(0) = 4.0;  vec2(0) = 0.0;\n  vec1(1) = 8.0;  vec2(1) = 1.0;\n  vec1(2) = 15.0; vec2(2) = 2.0;\n  vec1(3) = 16.0; vec2(3) = 3.0;\n  vec1(4) = 23.0; vec2(4) = 4.0;\n  vec1(5) = 42.0; vec2(5) = 5.0;\n\n  float data3[6];\n  TensorMap<Tensor<float, 1>> vec3(data3, 6);\n  vec3 = vec1.sqrt();\n  float data4[6];\n  TensorMap<Tensor<float, 1, RowMajor>> vec4(data4, 6);\n  vec4 = vec2.square();\n  float data5[6];\n  TensorMap<Tensor<float, 1, RowMajor>> vec5(data5, 6);\n  vec5 = vec2.cube();\n\n  VERIFY_IS_APPROX(vec3(0), sqrtf(4.0));\n  VERIFY_IS_APPROX(vec3(1), sqrtf(8.0));\n  VERIFY_IS_APPROX(vec3(2), sqrtf(15.0));\n  VERIFY_IS_APPROX(vec3(3), sqrtf(16.0));\n  VERIFY_IS_APPROX(vec3(4), sqrtf(23.0));\n  VERIFY_IS_APPROX(vec3(5), sqrtf(42.0));\n\n  VERIFY_IS_APPROX(vec4(0), 0.0f);\n  VERIFY_IS_APPROX(vec4(1), 1.0f);\n  VERIFY_IS_APPROX(vec4(2), 2.0f * 2.0f);\n  VERIFY_IS_APPROX(vec4(3), 3.0f * 3.0f);\n  VERIFY_IS_APPROX(vec4(4), 4.0f * 4.0f);\n  VERIFY_IS_APPROX(vec4(5), 5.0f * 5.0f);\n\n  VERIFY_IS_APPROX(vec5(0), 0.0f);\n  VERIFY_IS_APPROX(vec5(1), 1.0f);\n  VERIFY_IS_APPROX(vec5(2), 2.0f * 2.0f * 2.0f);\n  VERIFY_IS_APPROX(vec5(3), 3.0f * 3.0f * 3.0f);\n  VERIFY_IS_APPROX(vec5(4), 4.0f * 4.0f * 4.0f);\n  VERIFY_IS_APPROX(vec5(5), 5.0f * 5.0f * 5.0f);\n\n  vec3 = vec1 + vec2;\n  VERIFY_IS_APPROX(vec3(0), 4.0f + 0.0f);\n  VERIFY_IS_APPROX(vec3(1), 8.0f + 1.0f);\n  VERIFY_IS_APPROX(vec3(2), 15.0f + 2.0f);\n  VERIFY_IS_APPROX(vec3(3), 16.0f + 3.0f);\n  VERIFY_IS_APPROX(vec3(4), 23.0f + 4.0f);\n  VERIFY_IS_APPROX(vec3(5), 42.0f + 5.0f);\n}\n\nstatic void test_2d()\n{\n  float data1[6];\n  TensorMap<Tensor<float, 2>> mat1(data1, 2, 3);\n  float data2[6];\n  TensorMap<Tensor<float, 2, RowMajor>> mat2(data2, 2, 3);\n\n  mat1(0,0) = 0.0;\n  mat1(0,1) = 1.0;\n  mat1(0,2) = 2.0;\n  mat1(1,0) = 3.0;\n  mat1(1,1) = 4.0;\n  mat1(1,2) = 5.0;\n\n  mat2(0,0) = -0.0;\n  mat2(0,1) = -1.0;\n  mat2(0,2) = -2.0;\n  mat2(1,0) = -3.0;\n  mat2(1,1) = -4.0;\n  mat2(1,2) = -5.0;\n\n  Tensor<float, 2> mat3(2,3);\n  Tensor<float, 2, RowMajor> mat4(2,3);\n  mat3 = mat1.abs();\n  mat4 = mat2.abs();\n\n  VERIFY_IS_APPROX(mat3(0,0), 0.0f);\n  VERIFY_IS_APPROX(mat3(0,1), 1.0f);\n  VERIFY_IS_APPROX(mat3(0,2), 2.0f);\n  VERIFY_IS_APPROX(mat3(1,0), 3.0f);\n  VERIFY_IS_APPROX(mat3(1,1), 4.0f);\n  VERIFY_IS_APPROX(mat3(1,2), 5.0f);\n\n  VERIFY_IS_APPROX(mat4(0,0), 0.0f);\n  VERIFY_IS_APPROX(mat4(0,1), 1.0f);\n  VERIFY_IS_APPROX(mat4(0,2), 2.0f);\n  VERIFY_IS_APPROX(mat4(1,0), 3.0f);\n  VERIFY_IS_APPROX(mat4(1,1), 4.0f);\n  VERIFY_IS_APPROX(mat4(1,2), 5.0f);\n}\n\nstatic void test_3d()\n{\n  Tensor<float, 3> mat1(2,3,7);\n  Tensor<float, 3, RowMajor> mat2(2,3,7);\n\n  float val = 1.0f;\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        mat1(i,j,k) = val;\n        mat2(i,j,k) = val;\n        val += 1.0f;\n      }\n    }\n  }\n\n  Tensor<float, 3> mat3(2,3,7);\n  mat3 = mat1 + mat1;\n  Tensor<float, 3, RowMajor> mat4(2,3,7);\n  mat4 = mat2 * 3.14f;\n  Tensor<float, 3> mat5(2,3,7);\n  mat5 = mat1.inverse().log();\n  Tensor<float, 3, RowMajor> mat6(2,3,7);\n  mat6 = mat2.pow(0.5f) * 3.14f;\n  Tensor<float, 3> mat7(2,3,7);\n  mat7 = mat1.cwiseMax(mat5 * 2.0f).exp();\n  Tensor<float, 3, RowMajor> mat8(2,3,7);\n  mat8 = (-mat2).exp() * 3.14f;\n  Tensor<float, 3, RowMajor> mat9(2,3,7);\n  mat9 = mat2 + 3.14f;\n  Tensor<float, 3, RowMajor> mat10(2,3,7);\n  mat10 = mat2 - 3.14f;\n  Tensor<float, 3, RowMajor> mat11(2,3,7);\n  mat11 = mat2 / 3.14f;\n\n  val = 1.0f;\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        VERIFY_IS_APPROX(mat3(i,j,k), val + val);\n        VERIFY_IS_APPROX(mat4(i,j,k), val * 3.14f);\n        VERIFY_IS_APPROX(mat5(i,j,k), logf(1.0f/val));\n        VERIFY_IS_APPROX(mat6(i,j,k), sqrtf(val) * 3.14f);\n        VERIFY_IS_APPROX(mat7(i,j,k), expf((std::max)(val, mat5(i,j,k) * 2.0f)));\n        VERIFY_IS_APPROX(mat8(i,j,k), expf(-val) * 3.14f);\n        VERIFY_IS_APPROX(mat9(i,j,k), val + 3.14f);\n        VERIFY_IS_APPROX(mat10(i,j,k), val - 3.14f);\n        VERIFY_IS_APPROX(mat11(i,j,k), val / 3.14f);\n        val += 1.0f;\n      }\n    }\n  }\n}\n\nstatic void test_constants()\n{\n  Tensor<float, 3> mat1(2,3,7);\n  Tensor<float, 3> mat2(2,3,7);\n  Tensor<float, 3> mat3(2,3,7);\n\n  float val = 1.0f;\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        mat1(i,j,k) = val;\n        val += 1.0f;\n      }\n    }\n  }\n  mat2 = mat1.constant(3.14f);\n  mat3 = mat1.cwiseMax(7.3f).exp();\n\n  val = 1.0f;\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        VERIFY_IS_APPROX(mat2(i,j,k), 3.14f);\n        VERIFY_IS_APPROX(mat3(i,j,k), expf((std::max)(val, 7.3f)));\n        val += 1.0f;\n      }\n    }\n  }\n}\n\nstatic void test_boolean()\n{\n  Tensor<int, 1> vec(6);\n  std::copy_n(std::begin({0, 1, 2, 3, 4, 5}), 6, vec.data());\n\n  // Test ||.\n  Tensor<bool, 1> bool1 = vec < vec.constant(1) || vec > vec.constant(4);\n  VERIFY_IS_EQUAL(bool1[0], true);\n  VERIFY_IS_EQUAL(bool1[1], false);\n  VERIFY_IS_EQUAL(bool1[2], false);\n  VERIFY_IS_EQUAL(bool1[3], false);\n  VERIFY_IS_EQUAL(bool1[4], false);\n  VERIFY_IS_EQUAL(bool1[5], true);\n\n  // Test &&, including cast of operand vec.\n  Tensor<bool, 1> bool2 = vec.cast<bool>() && vec < vec.constant(4);\n  VERIFY_IS_EQUAL(bool2[0], false);\n  VERIFY_IS_EQUAL(bool2[1], true);\n  VERIFY_IS_EQUAL(bool2[2], true);\n  VERIFY_IS_EQUAL(bool2[3], true);\n  VERIFY_IS_EQUAL(bool2[4], false);\n  VERIFY_IS_EQUAL(bool2[5], false);\n\n  // Compilation tests:\n  // Test Tensor<bool> against results of cast or comparison; verifies that\n  // CoeffReturnType is set to match Op return type of bool for Unary and Binary\n  // Ops.\n  Tensor<bool, 1> bool3 = vec.cast<bool>() && bool2;\n  bool3 = vec < vec.constant(4) && bool2;\n}\n\nstatic void test_functors()\n{\n  Tensor<float, 3> mat1(2,3,7);\n  Tensor<float, 3> mat2(2,3,7);\n  Tensor<float, 3> mat3(2,3,7);\n\n  float val = 1.0f;\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        mat1(i,j,k) = val;\n        val += 1.0f;\n      }\n    }\n  }\n  mat2 = mat1.inverse().unaryExpr(&asinf);\n  mat3 = mat1.unaryExpr(&tanhf);\n\n  val = 1.0f;\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        VERIFY_IS_APPROX(mat2(i,j,k), asinf(1.0f / mat1(i,j,k)));\n        VERIFY_IS_APPROX(mat3(i,j,k), tanhf(mat1(i,j,k)));\n        val += 1.0f;\n      }\n    }\n  }\n}\n\nstatic void test_type_casting()\n{\n  Tensor<bool, 3> mat1(2,3,7);\n  Tensor<float, 3> mat2(2,3,7);\n  Tensor<double, 3> mat3(2,3,7);\n  mat1.setRandom();\n  mat2.setRandom();\n\n  mat3 = mat1.cast<double>();\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        VERIFY_IS_APPROX(mat3(i,j,k), mat1(i,j,k) ? 1.0 : 0.0);\n      }\n    }\n  }\n\n  mat3 = mat2.cast<double>();\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        VERIFY_IS_APPROX(mat3(i,j,k), static_cast<double>(mat2(i,j,k)));\n      }\n    }\n  }\n}\n\nstatic void test_select()\n{\n  Tensor<float, 3> selector(2,3,7);\n  Tensor<float, 3> mat1(2,3,7);\n  Tensor<float, 3> mat2(2,3,7);\n  Tensor<float, 3> result(2,3,7);\n\n  selector.setRandom();\n  mat1.setRandom();\n  mat2.setRandom();\n  result = (selector > selector.constant(0.5f)).select(mat1, mat2);\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        VERIFY_IS_APPROX(result(i,j,k), (selector(i,j,k) > 0.5f) ? mat1(i,j,k) : mat2(i,j,k));\n      }\n    }\n  }\n}\n\n\nvoid test_cxx11_tensor_expr()\n{\n  CALL_SUBTEST(test_1d());\n  CALL_SUBTEST(test_2d());\n  CALL_SUBTEST(test_3d());\n  CALL_SUBTEST(test_constants());\n  CALL_SUBTEST(test_boolean());\n  CALL_SUBTEST(test_functors());\n  CALL_SUBTEST(test_type_casting());\n  CALL_SUBTEST(test_select());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_fft.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Jianwei Cui <thucjw@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\n\ntemplate <int DataLayout>\nstatic void test_fft_2D_golden() {\n  Tensor<float, 2, DataLayout> input(2, 3);\n  input(0, 0) = 1;\n  input(0, 1) = 2;\n  input(0, 2) = 3;\n  input(1, 0) = 4;\n  input(1, 1) = 5;\n  input(1, 2) = 6;\n\n  array<ptrdiff_t, 2> fft;\n  fft[0] = 0;\n  fft[1] = 1;\n\n  Tensor<std::complex<float>, 2, DataLayout> output = input.template fft<Eigen::BothParts, Eigen::FFT_FORWARD>(fft);\n\n  std::complex<float> output_golden[6]; // in ColMajor order\n  output_golden[0] = std::complex<float>(21, 0);\n  output_golden[1] = std::complex<float>(-9, 0);\n  output_golden[2] = std::complex<float>(-3, 1.73205);\n  output_golden[3] = std::complex<float>( 0, 0);\n  output_golden[4] = std::complex<float>(-3, -1.73205);\n  output_golden[5] = std::complex<float>(0 ,0);\n\n  std::complex<float> c_offset = std::complex<float>(1.0, 1.0);\n\n  if (DataLayout == ColMajor) {\n    VERIFY_IS_APPROX(output(0) + c_offset, output_golden[0] + c_offset);\n    VERIFY_IS_APPROX(output(1) + c_offset, output_golden[1] + c_offset);\n    VERIFY_IS_APPROX(output(2) + c_offset, output_golden[2] + c_offset);\n    VERIFY_IS_APPROX(output(3) + c_offset, output_golden[3] + c_offset);\n    VERIFY_IS_APPROX(output(4) + c_offset, output_golden[4] + c_offset);\n    VERIFY_IS_APPROX(output(5) + c_offset, output_golden[5] + c_offset);\n  }\n  else {\n    VERIFY_IS_APPROX(output(0)+ c_offset, output_golden[0]+ c_offset);\n    VERIFY_IS_APPROX(output(1)+ c_offset, output_golden[2]+ c_offset);\n    VERIFY_IS_APPROX(output(2)+ c_offset, output_golden[4]+ c_offset);\n    VERIFY_IS_APPROX(output(3)+ c_offset, output_golden[1]+ c_offset);\n    VERIFY_IS_APPROX(output(4)+ c_offset, output_golden[3]+ c_offset);\n    VERIFY_IS_APPROX(output(5)+ c_offset, output_golden[5]+ c_offset);\n  }\n}\n\nstatic void test_fft_complex_input_golden() {\n  Tensor<std::complex<float>, 1, ColMajor> input(5);\n  input(0) = std::complex<float>(1, 1);\n  input(1) = std::complex<float>(2, 2);\n  input(2) = std::complex<float>(3, 3);\n  input(3) = std::complex<float>(4, 4);\n  input(4) = std::complex<float>(5, 5);\n\n  array<ptrdiff_t, 1> fft;\n  fft[0] = 0;\n\n  Tensor<std::complex<float>, 1, ColMajor> forward_output_both_parts = input.fft<BothParts, FFT_FORWARD>(fft);\n  Tensor<std::complex<float>, 1, ColMajor> reverse_output_both_parts = input.fft<BothParts, FFT_REVERSE>(fft);\n\n  Tensor<float, 1, ColMajor> forward_output_real_part = input.fft<RealPart, FFT_FORWARD>(fft);\n  Tensor<float, 1, ColMajor> reverse_output_real_part = input.fft<RealPart, FFT_REVERSE>(fft);\n\n  Tensor<float, 1, ColMajor> forward_output_imag_part = input.fft<ImagPart, FFT_FORWARD>(fft);\n  Tensor<float, 1, ColMajor> reverse_output_imag_part = input.fft<ImagPart, FFT_REVERSE>(fft);\n\n  VERIFY_IS_EQUAL(forward_output_both_parts.dimension(0), input.dimension(0));\n  VERIFY_IS_EQUAL(reverse_output_both_parts.dimension(0), input.dimension(0));\n\n  VERIFY_IS_EQUAL(forward_output_real_part.dimension(0), input.dimension(0));\n  VERIFY_IS_EQUAL(reverse_output_real_part.dimension(0), input.dimension(0));\n\n  VERIFY_IS_EQUAL(forward_output_imag_part.dimension(0), input.dimension(0));\n  VERIFY_IS_EQUAL(reverse_output_imag_part.dimension(0), input.dimension(0));\n\n  std::complex<float> forward_golden_result[5];\n  std::complex<float> reverse_golden_result[5];\n\n  forward_golden_result[0] = std::complex<float>(15.000000000000000,+15.000000000000000);\n  forward_golden_result[1] = std::complex<float>(-5.940954801177935, +0.940954801177934);\n  forward_golden_result[2] = std::complex<float>(-3.312299240582266, -1.687700759417735);\n  forward_golden_result[3] = std::complex<float>(-1.687700759417735, -3.312299240582266);\n  forward_golden_result[4] = std::complex<float>( 0.940954801177934, -5.940954801177935);\n\n  reverse_golden_result[0] = std::complex<float>( 3.000000000000000, + 3.000000000000000);\n  reverse_golden_result[1] = std::complex<float>( 0.188190960235587, - 1.188190960235587);\n  reverse_golden_result[2] = std::complex<float>(-0.337540151883547, - 0.662459848116453);\n  reverse_golden_result[3] = std::complex<float>(-0.662459848116453, - 0.337540151883547);\n  reverse_golden_result[4] = std::complex<float>(-1.188190960235587, + 0.188190960235587);\n\n  for(int i = 0; i < 5; ++i) {\n    VERIFY_IS_APPROX(forward_output_both_parts(i), forward_golden_result[i]);\n    VERIFY_IS_APPROX(forward_output_real_part(i), forward_golden_result[i].real());\n    VERIFY_IS_APPROX(forward_output_imag_part(i), forward_golden_result[i].imag());\n  }\n\n  for(int i = 0; i < 5; ++i) {\n    VERIFY_IS_APPROX(reverse_output_both_parts(i), reverse_golden_result[i]);\n    VERIFY_IS_APPROX(reverse_output_real_part(i), reverse_golden_result[i].real());\n    VERIFY_IS_APPROX(reverse_output_imag_part(i), reverse_golden_result[i].imag());\n  }\n}\n\nstatic void test_fft_real_input_golden() {\n  Tensor<float, 1, ColMajor> input(5);\n  input(0) = 1.0;\n  input(1) = 2.0;\n  input(2) = 3.0;\n  input(3) = 4.0;\n  input(4) = 5.0;\n\n  array<ptrdiff_t, 1> fft;\n  fft[0] = 0;\n\n  Tensor<std::complex<float>, 1, ColMajor> forward_output_both_parts = input.fft<BothParts, FFT_FORWARD>(fft);\n  Tensor<std::complex<float>, 1, ColMajor> reverse_output_both_parts = input.fft<BothParts, FFT_REVERSE>(fft);\n\n  Tensor<float, 1, ColMajor> forward_output_real_part = input.fft<RealPart, FFT_FORWARD>(fft);\n  Tensor<float, 1, ColMajor> reverse_output_real_part = input.fft<RealPart, FFT_REVERSE>(fft);\n\n  Tensor<float, 1, ColMajor> forward_output_imag_part = input.fft<ImagPart, FFT_FORWARD>(fft);\n  Tensor<float, 1, ColMajor> reverse_output_imag_part = input.fft<ImagPart, FFT_REVERSE>(fft);\n\n  VERIFY_IS_EQUAL(forward_output_both_parts.dimension(0), input.dimension(0));\n  VERIFY_IS_EQUAL(reverse_output_both_parts.dimension(0), input.dimension(0));\n\n  VERIFY_IS_EQUAL(forward_output_real_part.dimension(0), input.dimension(0));\n  VERIFY_IS_EQUAL(reverse_output_real_part.dimension(0), input.dimension(0));\n\n  VERIFY_IS_EQUAL(forward_output_imag_part.dimension(0), input.dimension(0));\n  VERIFY_IS_EQUAL(reverse_output_imag_part.dimension(0), input.dimension(0));\n\n  std::complex<float> forward_golden_result[5];\n  std::complex<float> reverse_golden_result[5];\n\n\n  forward_golden_result[0] = std::complex<float>(  15, 0);\n  forward_golden_result[1] = std::complex<float>(-2.5, +3.44095480117793);\n  forward_golden_result[2] = std::complex<float>(-2.5, +0.81229924058227);\n  forward_golden_result[3] = std::complex<float>(-2.5, -0.81229924058227);\n  forward_golden_result[4] = std::complex<float>(-2.5, -3.44095480117793);\n\n  reverse_golden_result[0] = std::complex<float>( 3.0, 0);\n  reverse_golden_result[1] = std::complex<float>(-0.5, -0.688190960235587);\n  reverse_golden_result[2] = std::complex<float>(-0.5, -0.162459848116453);\n  reverse_golden_result[3] = std::complex<float>(-0.5, +0.162459848116453);\n  reverse_golden_result[4] = std::complex<float>(-0.5, +0.688190960235587);\n\n  std::complex<float> c_offset(1.0, 1.0);\n  float r_offset = 1.0;\n\n  for(int i = 0; i < 5; ++i) {\n    VERIFY_IS_APPROX(forward_output_both_parts(i) + c_offset, forward_golden_result[i] + c_offset);\n    VERIFY_IS_APPROX(forward_output_real_part(i)  + r_offset, forward_golden_result[i].real() + r_offset);\n    VERIFY_IS_APPROX(forward_output_imag_part(i)  + r_offset, forward_golden_result[i].imag() + r_offset);\n  }\n\n  for(int i = 0; i < 5; ++i) {\n    VERIFY_IS_APPROX(reverse_output_both_parts(i) + c_offset, reverse_golden_result[i] + c_offset);\n    VERIFY_IS_APPROX(reverse_output_real_part(i)  + r_offset, reverse_golden_result[i].real() + r_offset);\n    VERIFY_IS_APPROX(reverse_output_imag_part(i)  + r_offset, reverse_golden_result[i].imag() + r_offset);\n  }\n}\n\n\ntemplate <int DataLayout, typename RealScalar, bool isComplexInput, int FFTResultType, int FFTDirection, int TensorRank>\nstatic void test_fft_real_input_energy() {\n\n  Eigen::DSizes<ptrdiff_t, TensorRank> dimensions;\n  ptrdiff_t total_size = 1;\n  for (int i = 0; i < TensorRank; ++i) {\n    dimensions[i] = rand() % 20 + 1;\n    total_size *= dimensions[i];\n  }\n  const DSizes<ptrdiff_t, TensorRank> arr = dimensions;\n\n  typedef typename internal::conditional<isComplexInput == true, std::complex<RealScalar>, RealScalar>::type InputScalar;\n\n  Tensor<InputScalar, TensorRank, DataLayout> input;\n  input.resize(arr);\n  input.setRandom();\n\n  array<ptrdiff_t, TensorRank> fft;\n  for (int i = 0; i < TensorRank; ++i) {\n    fft[i] = i;\n  }\n\n  typedef typename internal::conditional<FFTResultType == Eigen::BothParts, std::complex<RealScalar>, RealScalar>::type OutputScalar;\n  Tensor<OutputScalar, TensorRank, DataLayout> output;\n  output = input.template fft<FFTResultType, FFTDirection>(fft);\n\n  for (int i = 0; i < TensorRank; ++i) {\n    VERIFY_IS_EQUAL(output.dimension(i), input.dimension(i));\n  }\n\n  RealScalar energy_original = 0.0;\n  RealScalar energy_after_fft = 0.0;\n\n  for (int i = 0; i < total_size; ++i) {\n    energy_original += numext::abs2(input(i));\n  }\n\n  for (int i = 0; i < total_size; ++i) {\n    energy_after_fft += numext::abs2(output(i));\n  }\n\n  if(FFTDirection == FFT_FORWARD) {\n    VERIFY_IS_APPROX(energy_original, energy_after_fft / total_size);\n  }\n  else {\n    VERIFY_IS_APPROX(energy_original, energy_after_fft * total_size);\n  }\n}\n\nvoid test_cxx11_tensor_fft() {\n    test_fft_complex_input_golden();\n    test_fft_real_input_golden();\n\n    test_fft_2D_golden<ColMajor>();\n    test_fft_2D_golden<RowMajor>();\n\n    test_fft_real_input_energy<ColMajor, float,  true,  Eigen::BothParts, FFT_FORWARD, 1>();\n    test_fft_real_input_energy<ColMajor, double, true,  Eigen::BothParts, FFT_FORWARD, 1>();\n    test_fft_real_input_energy<ColMajor, float,  false,  Eigen::BothParts, FFT_FORWARD, 1>();\n    test_fft_real_input_energy<ColMajor, double, false,  Eigen::BothParts, FFT_FORWARD, 1>();\n\n    test_fft_real_input_energy<ColMajor, float,  true,  Eigen::BothParts, FFT_FORWARD, 2>();\n    test_fft_real_input_energy<ColMajor, double, true,  Eigen::BothParts, FFT_FORWARD, 2>();\n    test_fft_real_input_energy<ColMajor, float,  false,  Eigen::BothParts, FFT_FORWARD, 2>();\n    test_fft_real_input_energy<ColMajor, double, false,  Eigen::BothParts, FFT_FORWARD, 2>();\n\n    test_fft_real_input_energy<ColMajor, float,  true,  Eigen::BothParts, FFT_FORWARD, 3>();\n    test_fft_real_input_energy<ColMajor, double, true,  Eigen::BothParts, FFT_FORWARD, 3>();\n    test_fft_real_input_energy<ColMajor, float,  false,  Eigen::BothParts, FFT_FORWARD, 3>();\n    test_fft_real_input_energy<ColMajor, double, false,  Eigen::BothParts, FFT_FORWARD, 3>();\n\n    test_fft_real_input_energy<ColMajor, float,  true,  Eigen::BothParts, FFT_FORWARD, 4>();\n    test_fft_real_input_energy<ColMajor, double, true,  Eigen::BothParts, FFT_FORWARD, 4>();\n    test_fft_real_input_energy<ColMajor, float,  false,  Eigen::BothParts, FFT_FORWARD, 4>();\n    test_fft_real_input_energy<ColMajor, double, false,  Eigen::BothParts, FFT_FORWARD, 4>();\n\n    test_fft_real_input_energy<RowMajor, float,  true,  Eigen::BothParts, FFT_FORWARD, 1>();\n    test_fft_real_input_energy<RowMajor, double, true,  Eigen::BothParts, FFT_FORWARD, 1>();\n    test_fft_real_input_energy<RowMajor, float,  false,  Eigen::BothParts, FFT_FORWARD, 1>();\n    test_fft_real_input_energy<RowMajor, double, false,  Eigen::BothParts, FFT_FORWARD, 1>();\n\n    test_fft_real_input_energy<RowMajor, float,  true,  Eigen::BothParts, FFT_FORWARD, 2>();\n    test_fft_real_input_energy<RowMajor, double, true,  Eigen::BothParts, FFT_FORWARD, 2>();\n    test_fft_real_input_energy<RowMajor, float,  false,  Eigen::BothParts, FFT_FORWARD, 2>();\n    test_fft_real_input_energy<RowMajor, double, false,  Eigen::BothParts, FFT_FORWARD, 2>();\n\n    test_fft_real_input_energy<RowMajor, float,  true,  Eigen::BothParts, FFT_FORWARD, 3>();\n    test_fft_real_input_energy<RowMajor, double, true,  Eigen::BothParts, FFT_FORWARD, 3>();\n    test_fft_real_input_energy<RowMajor, float,  false,  Eigen::BothParts, FFT_FORWARD, 3>();\n    test_fft_real_input_energy<RowMajor, double, false,  Eigen::BothParts, FFT_FORWARD, 3>();\n\n    test_fft_real_input_energy<RowMajor, float,  true,  Eigen::BothParts, FFT_FORWARD, 4>();\n    test_fft_real_input_energy<RowMajor, double, true,  Eigen::BothParts, FFT_FORWARD, 4>();\n    test_fft_real_input_energy<RowMajor, float,  false,  Eigen::BothParts, FFT_FORWARD, 4>();\n    test_fft_real_input_energy<RowMajor, double, false,  Eigen::BothParts, FFT_FORWARD, 4>();\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_fixed_size.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\nusing Eigen::RowMajor;\n\n\nstatic void test_0d()\n{\n  TensorFixedSize<float, Sizes<> > scalar1;\n  TensorFixedSize<float, Sizes<>, RowMajor> scalar2;\n  VERIFY_IS_EQUAL(scalar1.rank(), 0);\n  VERIFY_IS_EQUAL(scalar1.size(), 1);\n  VERIFY_IS_EQUAL(array_prod(scalar1.dimensions()), 1);\n\n  scalar1() = 7.0;\n  scalar2() = 13.0;\n\n  // Test against shallow copy.\n  TensorFixedSize<float, Sizes<> > copy = scalar1;\n  VERIFY_IS_NOT_EQUAL(scalar1.data(), copy.data());\n  VERIFY_IS_APPROX(scalar1(), copy());\n  copy = scalar1;\n  VERIFY_IS_NOT_EQUAL(scalar1.data(), copy.data());\n  VERIFY_IS_APPROX(scalar1(), copy());\n\n  TensorFixedSize<float, Sizes<> > scalar3 = scalar1.sqrt();\n  TensorFixedSize<float, Sizes<>, RowMajor> scalar4 = scalar2.sqrt();\n  VERIFY_IS_EQUAL(scalar3.rank(), 0);\n  VERIFY_IS_APPROX(scalar3(), sqrtf(7.0));\n  VERIFY_IS_APPROX(scalar4(), sqrtf(13.0));\n\n  scalar3 = scalar1 + scalar2;\n  VERIFY_IS_APPROX(scalar3(), 7.0f + 13.0f);\n}\n\nstatic void test_1d()\n{\n  TensorFixedSize<float, Sizes<6> > vec1;\n  TensorFixedSize<float, Sizes<6>, RowMajor> vec2;\n\n  VERIFY_IS_EQUAL((vec1.size()), 6);\n  //  VERIFY_IS_EQUAL((vec1.dimensions()[0]), 6);\n  //  VERIFY_IS_EQUAL((vec1.dimension(0)), 6);\n\n  vec1(0) = 4.0;  vec2(0) = 0.0;\n  vec1(1) = 8.0;  vec2(1) = 1.0;\n  vec1(2) = 15.0; vec2(2) = 2.0;\n  vec1(3) = 16.0; vec2(3) = 3.0;\n  vec1(4) = 23.0; vec2(4) = 4.0;\n  vec1(5) = 42.0; vec2(5) = 5.0;\n\n  // Test against shallow copy.\n  TensorFixedSize<float, Sizes<6> > copy = vec1;\n  VERIFY_IS_NOT_EQUAL(vec1.data(), copy.data());\n  for (int i = 0; i < 6; ++i) {\n    VERIFY_IS_APPROX(vec1(i), copy(i));\n  }\n  copy = vec1;\n  VERIFY_IS_NOT_EQUAL(vec1.data(), copy.data());\n  for (int i = 0; i < 6; ++i) {\n    VERIFY_IS_APPROX(vec1(i), copy(i));\n  }\n\n  TensorFixedSize<float, Sizes<6> > vec3 = vec1.sqrt();\n  TensorFixedSize<float, Sizes<6>, RowMajor> vec4 = vec2.sqrt();\n\n  VERIFY_IS_EQUAL((vec3.size()), 6);\n  VERIFY_IS_EQUAL(vec3.rank(), 1);\n  //  VERIFY_IS_EQUAL((vec3.dimensions()[0]), 6);\n  //  VERIFY_IS_EQUAL((vec3.dimension(0)), 6);\n\n  VERIFY_IS_APPROX(vec3(0), sqrtf(4.0));\n  VERIFY_IS_APPROX(vec3(1), sqrtf(8.0));\n  VERIFY_IS_APPROX(vec3(2), sqrtf(15.0));\n  VERIFY_IS_APPROX(vec3(3), sqrtf(16.0));\n  VERIFY_IS_APPROX(vec3(4), sqrtf(23.0));\n  VERIFY_IS_APPROX(vec3(5), sqrtf(42.0));\n\n  VERIFY_IS_APPROX(vec4(0), sqrtf(0.0));\n  VERIFY_IS_APPROX(vec4(1), sqrtf(1.0));\n  VERIFY_IS_APPROX(vec4(2), sqrtf(2.0));\n  VERIFY_IS_APPROX(vec4(3), sqrtf(3.0));\n  VERIFY_IS_APPROX(vec4(4), sqrtf(4.0));\n  VERIFY_IS_APPROX(vec4(5), sqrtf(5.0));\n\n  vec3 = vec1 + vec2;\n  VERIFY_IS_APPROX(vec3(0), 4.0f + 0.0f);\n  VERIFY_IS_APPROX(vec3(1), 8.0f + 1.0f);\n  VERIFY_IS_APPROX(vec3(2), 15.0f + 2.0f);\n  VERIFY_IS_APPROX(vec3(3), 16.0f + 3.0f);\n  VERIFY_IS_APPROX(vec3(4), 23.0f + 4.0f);\n  VERIFY_IS_APPROX(vec3(5), 42.0f + 5.0f);\n}\n\nstatic void test_tensor_map()\n{\n  TensorFixedSize<float, Sizes<6> > vec1;\n  TensorFixedSize<float, Sizes<6>, RowMajor> vec2;\n\n  vec1(0) = 4.0;  vec2(0) = 0.0;\n  vec1(1) = 8.0;  vec2(1) = 1.0;\n  vec1(2) = 15.0; vec2(2) = 2.0;\n  vec1(3) = 16.0; vec2(3) = 3.0;\n  vec1(4) = 23.0; vec2(4) = 4.0;\n  vec1(5) = 42.0; vec2(5) = 5.0;\n\n  float data3[6];\n  TensorMap<TensorFixedSize<float, Sizes<6> > > vec3(data3, 6);\n  vec3 = vec1.sqrt() + vec2;\n\n  VERIFY_IS_APPROX(vec3(0), sqrtf(4.0));\n  VERIFY_IS_APPROX(vec3(1), sqrtf(8.0) + 1.0f);\n  VERIFY_IS_APPROX(vec3(2), sqrtf(15.0) + 2.0f);\n  VERIFY_IS_APPROX(vec3(3), sqrtf(16.0) + 3.0f);\n  VERIFY_IS_APPROX(vec3(4), sqrtf(23.0) + 4.0f);\n  VERIFY_IS_APPROX(vec3(5), sqrtf(42.0) + 5.0f);\n}\n\nstatic void test_2d()\n{\n  float data1[6];\n  TensorMap<TensorFixedSize<float, Sizes<2, 3> > > mat1(data1,2,3);\n  float data2[6];\n  TensorMap<TensorFixedSize<float, Sizes<2, 3>, RowMajor> > mat2(data2,2,3);\n\n  VERIFY_IS_EQUAL((mat1.size()), 2*3);\n  VERIFY_IS_EQUAL(mat1.rank(), 2);\n  //  VERIFY_IS_EQUAL((mat1.dimension(0)), 2);\n  //  VERIFY_IS_EQUAL((mat1.dimension(1)), 3);\n\n  mat1(0,0) = 0.0;\n  mat1(0,1) = 1.0;\n  mat1(0,2) = 2.0;\n  mat1(1,0) = 3.0;\n  mat1(1,1) = 4.0;\n  mat1(1,2) = 5.0;\n\n  mat2(0,0) = -0.0;\n  mat2(0,1) = -1.0;\n  mat2(0,2) = -2.0;\n  mat2(1,0) = -3.0;\n  mat2(1,1) = -4.0;\n  mat2(1,2) = -5.0;\n\n  TensorFixedSize<float, Sizes<2, 3> > mat3;\n  TensorFixedSize<float, Sizes<2, 3>, RowMajor> mat4;\n  mat3 = mat1.abs();\n  mat4 = mat2.abs();\n\n  VERIFY_IS_EQUAL((mat3.size()), 2*3);\n    //  VERIFY_IS_EQUAL((mat3.dimension(0)), 2);\n    //  VERIFY_IS_EQUAL((mat3.dimension(1)), 3);\n\n  VERIFY_IS_APPROX(mat3(0,0), 0.0f);\n  VERIFY_IS_APPROX(mat3(0,1), 1.0f);\n  VERIFY_IS_APPROX(mat3(0,2), 2.0f);\n  VERIFY_IS_APPROX(mat3(1,0), 3.0f);\n  VERIFY_IS_APPROX(mat3(1,1), 4.0f);\n  VERIFY_IS_APPROX(mat3(1,2), 5.0f);\n\n  VERIFY_IS_APPROX(mat4(0,0), 0.0f);\n  VERIFY_IS_APPROX(mat4(0,1), 1.0f);\n  VERIFY_IS_APPROX(mat4(0,2), 2.0f);\n  VERIFY_IS_APPROX(mat4(1,0), 3.0f);\n  VERIFY_IS_APPROX(mat4(1,1), 4.0f);\n  VERIFY_IS_APPROX(mat4(1,2), 5.0f);\n}\n\nstatic void test_3d()\n{\n  TensorFixedSize<float, Sizes<2, 3, 7> > mat1;\n  TensorFixedSize<float, Sizes<2, 3, 7>, RowMajor> mat2;\n\n  VERIFY_IS_EQUAL((mat1.size()), 2*3*7);\n  VERIFY_IS_EQUAL(mat1.rank(), 3);\n  //  VERIFY_IS_EQUAL((mat1.dimension(0)), 2);\n  //  VERIFY_IS_EQUAL((mat1.dimension(1)), 3);\n  //  VERIFY_IS_EQUAL((mat1.dimension(2)), 7);\n\n  float val = 0.0f;\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        mat1(i,j,k) = val;\n        mat2(i,j,k) = val;\n        val += 1.0f;\n      }\n    }\n  }\n\n  TensorFixedSize<float, Sizes<2, 3, 7> > mat3;\n  mat3 = mat1.sqrt();\n  TensorFixedSize<float, Sizes<2, 3, 7>, RowMajor> mat4;\n  mat4 = mat2.sqrt();\n\n  VERIFY_IS_EQUAL((mat3.size()), 2*3*7);\n  //  VERIFY_IS_EQUAL((mat3.dimension(0)), 2);\n  //  VERIFY_IS_EQUAL((mat3.dimension(1)), 3);\n  //  VERIFY_IS_EQUAL((mat3.dimension(2)), 7);\n\n\n  val = 0.0f;\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        VERIFY_IS_APPROX(mat3(i,j,k), sqrtf(val));\n        VERIFY_IS_APPROX(mat4(i,j,k), sqrtf(val));\n        val += 1.0f;\n      }\n    }\n  }\n}\n\n\nstatic void test_array()\n{\n  TensorFixedSize<float, Sizes<2, 3, 7> > mat1;\n  float val = 0.0f;\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        mat1(i,j,k) = val;\n        val += 1.0f;\n      }\n    }\n  }\n\n  TensorFixedSize<float, Sizes<2, 3, 7> > mat3;\n  mat3 = mat1.pow(3.5f);\n\n  val = 0.0f;\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        VERIFY_IS_APPROX(mat3(i,j,k), powf(val, 3.5f));\n        val += 1.0f;\n      }\n    }\n  }\n}\n\nvoid test_cxx11_tensor_fixed_size()\n{\n  CALL_SUBTEST(test_0d());\n  CALL_SUBTEST(test_1d());\n  CALL_SUBTEST(test_tensor_map());\n  CALL_SUBTEST(test_2d());\n  CALL_SUBTEST(test_3d());\n  CALL_SUBTEST(test_array());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_forced_eval.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/Core>\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::MatrixXf;\nusing Eigen::Tensor;\n\nstatic void test_simple()\n{\n  MatrixXf m1(3,3);\n  MatrixXf m2(3,3);\n  m1.setRandom();\n  m2.setRandom();\n\n  TensorMap<Tensor<float, 2> > mat1(m1.data(), 3,3);\n  TensorMap<Tensor<float, 2> > mat2(m2.data(), 3,3);\n\n  Tensor<float, 2> mat3(3,3);\n  mat3 = mat1;\n\n  typedef Tensor<float, 1>::DimensionPair DimPair;\n  Eigen::array<DimPair, 1> dims;\n  dims[0] = DimPair(1, 0);\n\n  mat3 = mat3.contract(mat2, dims).eval();\n\n  VERIFY_IS_APPROX(mat3(0, 0), (m1*m2).eval()(0,0));\n  VERIFY_IS_APPROX(mat3(0, 1), (m1*m2).eval()(0,1));\n  VERIFY_IS_APPROX(mat3(0, 2), (m1*m2).eval()(0,2));\n  VERIFY_IS_APPROX(mat3(1, 0), (m1*m2).eval()(1,0));\n  VERIFY_IS_APPROX(mat3(1, 1), (m1*m2).eval()(1,1));\n  VERIFY_IS_APPROX(mat3(1, 2), (m1*m2).eval()(1,2));\n  VERIFY_IS_APPROX(mat3(2, 0), (m1*m2).eval()(2,0));\n  VERIFY_IS_APPROX(mat3(2, 1), (m1*m2).eval()(2,1));\n  VERIFY_IS_APPROX(mat3(2, 2), (m1*m2).eval()(2,2));\n}\n\n\nstatic void test_const()\n{\n  MatrixXf input(3,3);\n  input.setRandom();\n  MatrixXf output = input;\n  output.rowwise() -= input.colwise().maxCoeff();\n\n  Eigen::array<int, 1> depth_dim;\n  depth_dim[0] = 0;\n  Tensor<float, 2>::Dimensions dims2d;\n  dims2d[0] = 1;\n  dims2d[1] = 3;\n  Eigen::array<int, 2> bcast;\n  bcast[0] = 3;\n  bcast[1] = 1;\n  const TensorMap<Tensor<const float, 2> > input_tensor(input.data(), 3, 3);\n  Tensor<float, 2> output_tensor= (input_tensor - input_tensor.maximum(depth_dim).eval().reshape(dims2d).broadcast(bcast));\n\n  for (int i = 0; i < 3; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      VERIFY_IS_APPROX(output(i, j), output_tensor(i, j));\n    }\n  }\n}\n\n\nvoid test_cxx11_tensor_forced_eval()\n{\n  CALL_SUBTEST(test_simple());\n  CALL_SUBTEST(test_const());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_forced_eval_sycl.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016\n// Mehdi Goli    Codeplay Software Ltd.\n// Ralph Potter  Codeplay Software Ltd.\n// Luke Iwanski  Codeplay Software Ltd.\n// Contact: <eigen@codeplay.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define EIGEN_TEST_NO_LONGDOUBLE\n#define EIGEN_TEST_NO_COMPLEX\n#define EIGEN_TEST_FUNC cxx11_tensor_forced_eval_sycl\n#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int\n#define EIGEN_USE_SYCL\n\n#include \"main.h\"\n#include <unsupported/Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\n\nvoid test_forced_eval_sycl(const Eigen::SyclDevice &sycl_device) {\n\n  int sizeDim1 = 100;\n  int sizeDim2 = 200;\n  int sizeDim3 = 200;\n  Eigen::array<int, 3> tensorRange = {{sizeDim1, sizeDim2, sizeDim3}};\n  Eigen::Tensor<float, 3> in1(tensorRange);\n  Eigen::Tensor<float, 3> in2(tensorRange);\n  Eigen::Tensor<float, 3> out(tensorRange);\n\n  float * gpu_in1_data  = static_cast<float*>(sycl_device.allocate(in1.dimensions().TotalSize()*sizeof(float)));\n  float * gpu_in2_data  = static_cast<float*>(sycl_device.allocate(in2.dimensions().TotalSize()*sizeof(float)));\n  float * gpu_out_data =  static_cast<float*>(sycl_device.allocate(out.dimensions().TotalSize()*sizeof(float)));\n\n  in1 = in1.random() + in1.constant(10.0f);\n  in2 = in2.random() + in2.constant(10.0f);\n\n  // creating TensorMap from tensor\n  Eigen::TensorMap<Eigen::Tensor<float, 3>> gpu_in1(gpu_in1_data, tensorRange);\n  Eigen::TensorMap<Eigen::Tensor<float, 3>> gpu_in2(gpu_in2_data, tensorRange);\n  Eigen::TensorMap<Eigen::Tensor<float, 3>> gpu_out(gpu_out_data, tensorRange);\n  sycl_device.memcpyHostToDevice(gpu_in1_data, in1.data(),(in1.dimensions().TotalSize())*sizeof(float));\n  sycl_device.memcpyHostToDevice(gpu_in2_data, in2.data(),(in1.dimensions().TotalSize())*sizeof(float));\n  /// c=(a+b)*b\n  gpu_out.device(sycl_device) =(gpu_in1 + gpu_in2).eval() * gpu_in2;\n  sycl_device.memcpyDeviceToHost(out.data(), gpu_out_data,(out.dimensions().TotalSize())*sizeof(float));\n  for (int i = 0; i < sizeDim1; ++i) {\n    for (int j = 0; j < sizeDim2; ++j) {\n      for (int k = 0; k < sizeDim3; ++k) {\n        VERIFY_IS_APPROX(out(i, j, k),\n                         (in1(i, j, k) + in2(i, j, k)) * in2(i, j, k));\n      }\n    }\n  }\n  printf(\"(a+b)*b Test Passed\\n\");\n  sycl_device.deallocate(gpu_in1_data);\n  sycl_device.deallocate(gpu_in2_data);\n  sycl_device.deallocate(gpu_out_data);\n\n}\n\nvoid test_cxx11_tensor_forced_eval_sycl() {\n  cl::sycl::gpu_selector s;\n  Eigen::SyclDevice sycl_device(s);\n  CALL_SUBTEST(test_forced_eval_sycl(sycl_device));\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_generator.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\nstruct Generator1D {\n  Generator1D() { }\n\n  float operator()(const array<Eigen::DenseIndex, 1>& coordinates) const {\n    return coordinates[0];\n  }\n};\n\ntemplate <int DataLayout>\nstatic void test_1D()\n{\n  Tensor<float, 1> vec(6);\n  Tensor<float, 1> result = vec.generate(Generator1D());\n\n  for (int i = 0; i < 6; ++i) {\n    VERIFY_IS_EQUAL(result(i), i);\n  }\n}\n\n\nstruct Generator2D {\n  Generator2D() { }\n\n  float operator()(const array<Eigen::DenseIndex, 2>& coordinates) const {\n    return 3 * coordinates[0] + 11 * coordinates[1];\n  }\n};\n\ntemplate <int DataLayout>\nstatic void test_2D()\n{\n  Tensor<float, 2> matrix(5, 7);\n  Tensor<float, 2> result = matrix.generate(Generator2D());\n\n  for (int i = 0; i < 5; ++i) {\n    for (int j = 0; j < 5; ++j) {\n      VERIFY_IS_EQUAL(result(i, j), 3*i + 11*j);\n    }\n  }\n}\n\n\ntemplate <int DataLayout>\nstatic void test_gaussian()\n{\n  int rows = 32;\n  int cols = 48;\n  array<float, 2> means;\n  means[0] = rows / 2.0f;\n  means[1] = cols / 2.0f;\n  array<float, 2> std_devs;\n  std_devs[0] = 3.14f;\n  std_devs[1] = 2.7f;\n  internal::GaussianGenerator<float, Eigen::DenseIndex, 2> gaussian_gen(means, std_devs);\n\n  Tensor<float, 2> matrix(rows, cols);\n  Tensor<float, 2> result = matrix.generate(gaussian_gen);\n\n  for (int i = 0; i < rows; ++i) {\n    for (int j = 0; j < cols; ++j) {\n      float g_rows = powf(rows/2.0f - i, 2) / (3.14f * 3.14f) * 0.5f;\n      float g_cols = powf(cols/2.0f - j, 2) / (2.7f * 2.7f) * 0.5f;\n      float gaussian = expf(-g_rows - g_cols);\n      VERIFY_IS_EQUAL(result(i, j), gaussian);\n    }\n  }\n}\n\n\nvoid test_cxx11_tensor_generator()\n{\n  CALL_SUBTEST(test_1D<ColMajor>());\n  CALL_SUBTEST(test_1D<RowMajor>());\n  CALL_SUBTEST(test_2D<ColMajor>());\n  CALL_SUBTEST(test_2D<RowMajor>());\n  CALL_SUBTEST(test_gaussian<ColMajor>());\n  CALL_SUBTEST(test_gaussian<RowMajor>());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_ifft.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Jianwei Cui <thucjw@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <complex>\n#include <cmath>\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\n\ntemplate <int DataLayout>\nstatic void test_1D_fft_ifft_invariant(int sequence_length) {\n  Tensor<double, 1, DataLayout> tensor(sequence_length);\n  tensor.setRandom();\n\n  array<int, 1> fft;\n  fft[0] = 0;\n\n  Tensor<std::complex<double>, 1, DataLayout> tensor_after_fft;\n  Tensor<std::complex<double>, 1, DataLayout> tensor_after_fft_ifft;\n\n  tensor_after_fft = tensor.template fft<Eigen::BothParts, Eigen::FFT_FORWARD>(fft);\n  tensor_after_fft_ifft = tensor_after_fft.template fft<Eigen::BothParts, Eigen::FFT_REVERSE>(fft);\n\n  VERIFY_IS_EQUAL(tensor_after_fft.dimension(0), sequence_length);\n  VERIFY_IS_EQUAL(tensor_after_fft_ifft.dimension(0), sequence_length);\n\n  for (int i = 0; i < sequence_length; ++i) {\n    VERIFY_IS_APPROX(static_cast<float>(tensor(i)), static_cast<float>(std::real(tensor_after_fft_ifft(i))));\n  }\n}\n\ntemplate <int DataLayout>\nstatic void test_2D_fft_ifft_invariant(int dim0, int dim1) {\n  Tensor<double, 2, DataLayout> tensor(dim0, dim1);\n  tensor.setRandom();\n\n  array<int, 2> fft;\n  fft[0] = 0;\n  fft[1] = 1;\n\n  Tensor<std::complex<double>, 2, DataLayout> tensor_after_fft;\n  Tensor<std::complex<double>, 2, DataLayout> tensor_after_fft_ifft;\n\n  tensor_after_fft = tensor.template fft<Eigen::BothParts, Eigen::FFT_FORWARD>(fft);\n  tensor_after_fft_ifft = tensor_after_fft.template fft<Eigen::BothParts, Eigen::FFT_REVERSE>(fft);\n\n  VERIFY_IS_EQUAL(tensor_after_fft.dimension(0), dim0);\n  VERIFY_IS_EQUAL(tensor_after_fft.dimension(1), dim1);\n  VERIFY_IS_EQUAL(tensor_after_fft_ifft.dimension(0), dim0);\n  VERIFY_IS_EQUAL(tensor_after_fft_ifft.dimension(1), dim1);\n\n  for (int i = 0; i < dim0; ++i) {\n    for (int j = 0; j < dim1; ++j) {\n      //std::cout << \"[\" << i << \"][\" << j << \"]\" <<  \"  Original data: \" << tensor(i,j) << \" Transformed data:\" << tensor_after_fft_ifft(i,j) << std::endl;\n      VERIFY_IS_APPROX(static_cast<float>(tensor(i,j)), static_cast<float>(std::real(tensor_after_fft_ifft(i,j))));\n    }\n  }\n}\n\ntemplate <int DataLayout>\nstatic void test_3D_fft_ifft_invariant(int dim0, int dim1, int dim2) {\n  Tensor<double, 3, DataLayout> tensor(dim0, dim1, dim2);\n  tensor.setRandom();\n\n  array<int, 3> fft;\n  fft[0] = 0;\n  fft[1] = 1;\n  fft[2] = 2;\n\n  Tensor<std::complex<double>, 3, DataLayout> tensor_after_fft;\n  Tensor<std::complex<double>, 3, DataLayout> tensor_after_fft_ifft;\n\n  tensor_after_fft = tensor.template fft<Eigen::BothParts, Eigen::FFT_FORWARD>(fft);\n  tensor_after_fft_ifft = tensor_after_fft.template fft<Eigen::BothParts, Eigen::FFT_REVERSE>(fft);\n\n  VERIFY_IS_EQUAL(tensor_after_fft.dimension(0), dim0);\n  VERIFY_IS_EQUAL(tensor_after_fft.dimension(1), dim1);\n  VERIFY_IS_EQUAL(tensor_after_fft.dimension(2), dim2);\n  VERIFY_IS_EQUAL(tensor_after_fft_ifft.dimension(0), dim0);\n  VERIFY_IS_EQUAL(tensor_after_fft_ifft.dimension(1), dim1);\n  VERIFY_IS_EQUAL(tensor_after_fft_ifft.dimension(2), dim2);\n\n  for (int i = 0; i < dim0; ++i) {\n    for (int j = 0; j < dim1; ++j) {\n      for (int k = 0; k < dim2; ++k) {\n        VERIFY_IS_APPROX(static_cast<float>(tensor(i,j,k)), static_cast<float>(std::real(tensor_after_fft_ifft(i,j,k))));\n      }\n    }\n  }\n}\n\ntemplate <int DataLayout>\nstatic void test_sub_fft_ifft_invariant(int dim0, int dim1, int dim2, int dim3) {\n  Tensor<double, 4, DataLayout> tensor(dim0, dim1, dim2, dim3);\n  tensor.setRandom();\n\n  array<int, 2> fft;\n  fft[0] = 2;\n  fft[1] = 0;\n\n  Tensor<std::complex<double>, 4, DataLayout> tensor_after_fft;\n  Tensor<double, 4, DataLayout> tensor_after_fft_ifft;\n\n  tensor_after_fft = tensor.template fft<Eigen::BothParts, Eigen::FFT_FORWARD>(fft);\n  tensor_after_fft_ifft = tensor_after_fft.template fft<Eigen::RealPart, Eigen::FFT_REVERSE>(fft);\n\n  VERIFY_IS_EQUAL(tensor_after_fft.dimension(0), dim0);\n  VERIFY_IS_EQUAL(tensor_after_fft.dimension(1), dim1);\n  VERIFY_IS_EQUAL(tensor_after_fft.dimension(2), dim2);\n  VERIFY_IS_EQUAL(tensor_after_fft.dimension(3), dim3);\n  VERIFY_IS_EQUAL(tensor_after_fft_ifft.dimension(0), dim0);\n  VERIFY_IS_EQUAL(tensor_after_fft_ifft.dimension(1), dim1);\n  VERIFY_IS_EQUAL(tensor_after_fft_ifft.dimension(2), dim2);\n  VERIFY_IS_EQUAL(tensor_after_fft_ifft.dimension(3), dim3);\n\n  for (int i = 0; i < dim0; ++i) {\n    for (int j = 0; j < dim1; ++j) {\n      for (int k = 0; k < dim2; ++k) {\n        for (int l = 0; l < dim3; ++l) {\n          VERIFY_IS_APPROX(static_cast<float>(tensor(i,j,k,l)), static_cast<float>(tensor_after_fft_ifft(i,j,k,l)));\n        }\n      }\n    }\n  }\n}\n\nvoid test_cxx11_tensor_ifft() {\n  CALL_SUBTEST(test_1D_fft_ifft_invariant<ColMajor>(4));\n  CALL_SUBTEST(test_1D_fft_ifft_invariant<ColMajor>(16));\n  CALL_SUBTEST(test_1D_fft_ifft_invariant<ColMajor>(32));\n  CALL_SUBTEST(test_1D_fft_ifft_invariant<ColMajor>(1024*1024));\n\n  CALL_SUBTEST(test_2D_fft_ifft_invariant<ColMajor>(4,4));\n  CALL_SUBTEST(test_2D_fft_ifft_invariant<ColMajor>(8,16));\n  CALL_SUBTEST(test_2D_fft_ifft_invariant<ColMajor>(16,32));\n  CALL_SUBTEST(test_2D_fft_ifft_invariant<ColMajor>(1024,1024));\n\n  CALL_SUBTEST(test_3D_fft_ifft_invariant<ColMajor>(4,4,4));\n  CALL_SUBTEST(test_3D_fft_ifft_invariant<ColMajor>(8,16,32));\n  CALL_SUBTEST(test_3D_fft_ifft_invariant<ColMajor>(16,4,8));\n  CALL_SUBTEST(test_3D_fft_ifft_invariant<ColMajor>(256,256,256));\n\n  CALL_SUBTEST(test_sub_fft_ifft_invariant<ColMajor>(4,4,4,4));\n  CALL_SUBTEST(test_sub_fft_ifft_invariant<ColMajor>(8,16,32,64));\n  CALL_SUBTEST(test_sub_fft_ifft_invariant<ColMajor>(16,4,8,12));\n  CALL_SUBTEST(test_sub_fft_ifft_invariant<ColMajor>(64,64,64,64));\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_image_patch.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\n\nvoid test_simple_patch()\n{\n  Tensor<float, 4> tensor(2,3,5,7);\n  tensor.setRandom();\n  Tensor<float, 4, RowMajor> tensor_row_major = tensor.swap_layout();\n  VERIFY_IS_EQUAL(tensor.dimension(0), tensor_row_major.dimension(3));\n  VERIFY_IS_EQUAL(tensor.dimension(1), tensor_row_major.dimension(2));\n  VERIFY_IS_EQUAL(tensor.dimension(2), tensor_row_major.dimension(1));\n  VERIFY_IS_EQUAL(tensor.dimension(3), tensor_row_major.dimension(0));\n\n  // Single pixel patch: ColMajor\n  Tensor<float, 5> single_pixel_patch;\n  single_pixel_patch = tensor.extract_image_patches(1, 1);\n  VERIFY_IS_EQUAL(single_pixel_patch.dimension(0), 2);\n  VERIFY_IS_EQUAL(single_pixel_patch.dimension(1), 1);\n  VERIFY_IS_EQUAL(single_pixel_patch.dimension(2), 1);\n  VERIFY_IS_EQUAL(single_pixel_patch.dimension(3), 3*5);\n  VERIFY_IS_EQUAL(single_pixel_patch.dimension(4), 7);\n\n  // Single pixel patch: RowMajor\n  Tensor<float, 5, RowMajor> single_pixel_patch_row_major;\n  single_pixel_patch_row_major = tensor_row_major.extract_image_patches(1, 1);\n  VERIFY_IS_EQUAL(single_pixel_patch_row_major.dimension(0), 7);\n  VERIFY_IS_EQUAL(single_pixel_patch_row_major.dimension(1), 3*5);\n  VERIFY_IS_EQUAL(single_pixel_patch_row_major.dimension(2), 1);\n  VERIFY_IS_EQUAL(single_pixel_patch_row_major.dimension(3), 1);\n  VERIFY_IS_EQUAL(single_pixel_patch_row_major.dimension(4), 2);\n\n  for (int i = 0; i < tensor.size(); ++i) {\n    // ColMajor\n    if (tensor.data()[i] != single_pixel_patch.data()[i]) {\n      std::cout << \"Mismatch detected at index \" << i << \" : \"\n           << tensor.data()[i] << \" vs \" << single_pixel_patch.data()[i]\n           << std::endl;\n    }\n    VERIFY_IS_EQUAL(single_pixel_patch.data()[i], tensor.data()[i]);\n    // RowMajor\n    if (tensor_row_major.data()[i] != single_pixel_patch_row_major.data()[i]) {\n      std::cout << \"Mismatch detected at index \" << i << \" : \"\n           << tensor.data()[i] << \" vs \"\n           << single_pixel_patch_row_major.data()[i] << std::endl;\n    }\n    VERIFY_IS_EQUAL(single_pixel_patch_row_major.data()[i],\n                    tensor_row_major.data()[i]);\n    VERIFY_IS_EQUAL(tensor.data()[i], tensor_row_major.data()[i]);\n    VERIFY_IS_EQUAL(single_pixel_patch.data()[i],\n                    single_pixel_patch_row_major.data()[i]);\n  }\n\n  // Entire image patch: ColMajor\n  Tensor<float, 5> entire_image_patch;\n  entire_image_patch = tensor.extract_image_patches(3, 5);\n  VERIFY_IS_EQUAL(entire_image_patch.dimension(0), 2);\n  VERIFY_IS_EQUAL(entire_image_patch.dimension(1), 3);\n  VERIFY_IS_EQUAL(entire_image_patch.dimension(2), 5);\n  VERIFY_IS_EQUAL(entire_image_patch.dimension(3), 3*5);\n  VERIFY_IS_EQUAL(entire_image_patch.dimension(4), 7);\n\n  // Entire image patch: RowMajor\n  Tensor<float, 5, RowMajor> entire_image_patch_row_major;\n  entire_image_patch_row_major = tensor_row_major.extract_image_patches(3, 5);\n  VERIFY_IS_EQUAL(entire_image_patch_row_major.dimension(0), 7);\n  VERIFY_IS_EQUAL(entire_image_patch_row_major.dimension(1), 3*5);\n  VERIFY_IS_EQUAL(entire_image_patch_row_major.dimension(2), 5);\n  VERIFY_IS_EQUAL(entire_image_patch_row_major.dimension(3), 3);\n  VERIFY_IS_EQUAL(entire_image_patch_row_major.dimension(4), 2);\n\n  for (int i = 0; i < 3; ++i) {\n    for (int j = 0; j < 5; ++j) {\n      int patchId = i+3*j;\n      for (int r = 0; r < 3; ++r) {\n        for (int c = 0; c < 5; ++c) {\n          for (int d = 0; d < 2; ++d) {\n            for (int b = 0; b < 7; ++b) {\n              float expected = 0.0f;\n              float expected_row_major = 0.0f;\n              if (r-1+i >= 0 && c-2+j >= 0 && r-1+i < 3 && c-2+j < 5) {\n                expected = tensor(d, r-1+i, c-2+j, b);\n                expected_row_major = tensor_row_major(b, c-2+j, r-1+i, d);\n              }\n              // ColMajor\n              if (entire_image_patch(d, r, c, patchId, b) != expected) {\n                std::cout << \"Mismatch detected at index i=\" << i << \" j=\" << j << \" r=\" << r << \" c=\" << c << \" d=\" << d << \" b=\" << b << std::endl;\n              }\n              VERIFY_IS_EQUAL(entire_image_patch(d, r, c, patchId, b), expected);\n              // RowMajor\n              if (entire_image_patch_row_major(b, patchId, c, r, d) !=\n                  expected_row_major) {\n                std::cout << \"Mismatch detected at index i=\" << i << \" j=\" << j\n                     << \" r=\" << r << \" c=\" << c << \" d=\" << d << \" b=\" << b\n                     << std::endl;\n              }\n              VERIFY_IS_EQUAL(entire_image_patch_row_major(b, patchId, c, r, d),\n                              expected_row_major);\n              // Check that ColMajor and RowMajor agree.\n              VERIFY_IS_EQUAL(expected, expected_row_major);\n            }\n          }\n        }\n      }\n    }\n  }\n\n  // 2D patch: ColMajor\n  Tensor<float, 5> twod_patch;\n  twod_patch = tensor.extract_image_patches(2, 2);\n  VERIFY_IS_EQUAL(twod_patch.dimension(0), 2);\n  VERIFY_IS_EQUAL(twod_patch.dimension(1), 2);\n  VERIFY_IS_EQUAL(twod_patch.dimension(2), 2);\n  VERIFY_IS_EQUAL(twod_patch.dimension(3), 3*5);\n  VERIFY_IS_EQUAL(twod_patch.dimension(4), 7);\n\n  // 2D patch: RowMajor\n  Tensor<float, 5, RowMajor> twod_patch_row_major;\n  twod_patch_row_major = tensor_row_major.extract_image_patches(2, 2);\n  VERIFY_IS_EQUAL(twod_patch_row_major.dimension(0), 7);\n  VERIFY_IS_EQUAL(twod_patch_row_major.dimension(1), 3*5);\n  VERIFY_IS_EQUAL(twod_patch_row_major.dimension(2), 2);\n  VERIFY_IS_EQUAL(twod_patch_row_major.dimension(3), 2);\n  VERIFY_IS_EQUAL(twod_patch_row_major.dimension(4), 2);\n\n\n  // Based on the calculation described in TensorTraits.h, padding happens to be 0.\n  int row_padding = 0;\n  int col_padding = 0;\n  int stride = 1;\n\n  for (int i = 0; i < 3; ++i) {\n    for (int j = 0; j < 5; ++j) {\n      int patchId = i+3*j;\n      for (int r = 0; r < 2; ++r) {\n        for (int c = 0; c < 2; ++c) {\n          for (int d = 0; d < 2; ++d) {\n            for (int b = 0; b < 7; ++b) {\n              float expected = 0.0f;\n              float expected_row_major = 0.0f;\n              int row_offset = r*stride + i - row_padding;\n              int col_offset = c*stride + j - col_padding;\n              // ColMajor\n              if (row_offset >= 0 && col_offset >= 0 && row_offset < tensor.dimension(1) && col_offset < tensor.dimension(2)) {\n                expected = tensor(d, row_offset, col_offset, b);\n              }\n              if (twod_patch(d, r, c, patchId, b) != expected) {\n                std::cout << \"Mismatch detected at index i=\" << i << \" j=\" << j << \" r=\" << r << \" c=\" << c << \" d=\" << d << \" b=\" << b << std::endl;\n              }\n              VERIFY_IS_EQUAL(twod_patch(d, r, c, patchId, b), expected);\n\n              // RowMajor\n              if (row_offset >= 0 && col_offset >= 0 && row_offset < tensor_row_major.dimension(2) && col_offset < tensor_row_major.dimension(1)) {\n                expected_row_major = tensor_row_major(b, col_offset, row_offset, d);\n\n              }\n              if (twod_patch_row_major(b, patchId, c, r, d) != expected_row_major) {\n                std::cout << \"Mismatch detected at index i=\" << i << \" j=\" << j << \" r=\" << r << \" c=\" << c << \" d=\" << d << \" b=\" << b << std::endl;\n              }\n              VERIFY_IS_EQUAL(twod_patch_row_major(b, patchId, c, r, d), expected_row_major);\n              // Check that ColMajor and RowMajor agree.\n              VERIFY_IS_EQUAL(expected, expected_row_major);\n            }\n          }\n        }\n      }\n    }\n  }\n}\n\n// Verifies VALID padding (no padding) with incrementing values.\nvoid test_patch_padding_valid()\n{\n  int input_depth = 3;\n  int input_rows = 3;\n  int input_cols = 3;\n  int input_batches = 1;\n  int ksize = 2;  // Corresponds to the Rows and Cols for tensor.extract_image_patches<>.\n  int stride = 2;  // Only same stride is supported.\n  Tensor<float, 4> tensor(input_depth, input_rows, input_cols, input_batches);\n  // Initializes tensor with incrementing numbers.\n  for (int i = 0; i < tensor.size(); ++i) {\n    tensor.data()[i] = i + 1;\n  }\n  // ColMajor\n  Tensor<float, 5> result = tensor.extract_image_patches(ksize, ksize, stride, stride, 1, 1, PADDING_VALID);\n\n  VERIFY_IS_EQUAL(result.dimension(0), input_depth);  // depth\n  VERIFY_IS_EQUAL(result.dimension(1), ksize);  // kernel rows\n  VERIFY_IS_EQUAL(result.dimension(2), ksize);  // kernel cols\n  VERIFY_IS_EQUAL(result.dimension(3), 1);  // number of patches\n  VERIFY_IS_EQUAL(result.dimension(4), input_batches);  // number of batches\n\n  // RowMajor\n  Tensor<float, 4, RowMajor> tensor_row_major = tensor.swap_layout();\n  VERIFY_IS_EQUAL(tensor.dimension(0), tensor_row_major.dimension(3));\n  VERIFY_IS_EQUAL(tensor.dimension(1), tensor_row_major.dimension(2));\n  VERIFY_IS_EQUAL(tensor.dimension(2), tensor_row_major.dimension(1));\n  VERIFY_IS_EQUAL(tensor.dimension(3), tensor_row_major.dimension(0));\n\n  Tensor<float, 5, RowMajor> result_row_major = tensor_row_major.extract_image_patches(ksize, ksize, stride, stride, 1, 1, PADDING_VALID);\n  VERIFY_IS_EQUAL(result.dimension(0), result_row_major.dimension(4));\n  VERIFY_IS_EQUAL(result.dimension(1), result_row_major.dimension(3));\n  VERIFY_IS_EQUAL(result.dimension(2), result_row_major.dimension(2));\n  VERIFY_IS_EQUAL(result.dimension(3), result_row_major.dimension(1));\n  VERIFY_IS_EQUAL(result.dimension(4), result_row_major.dimension(0));\n\n  // No padding is carried out.\n  int row_padding = 0;\n  int col_padding = 0;\n\n  for (int i = 0; (i+stride+ksize-1) < input_rows; i += stride) {  // input rows\n    for (int j = 0; (j+stride+ksize-1) < input_cols; j += stride) {  // input cols\n      int patchId = i+input_rows*j;\n      for (int r = 0; r < ksize; ++r) {  // patch rows\n        for (int c = 0; c < ksize; ++c) {  // patch cols\n          for (int d = 0; d < input_depth; ++d) {  // depth\n            for (int b = 0; b < input_batches; ++b) {  // batch\n              float expected = 0.0f;\n              float expected_row_major = 0.0f;\n              int row_offset = r + i - row_padding;\n              int col_offset = c + j - col_padding;\n              if (row_offset >= 0 && col_offset >= 0 && row_offset < input_rows && col_offset < input_cols) {\n                expected = tensor(d, row_offset, col_offset, b);\n                expected_row_major = tensor_row_major(b, col_offset, row_offset, d);\n              }\n              // ColMajor\n              if (result(d, r, c, patchId, b) != expected) {\n                std::cout << \"Mismatch detected at index i=\" << i << \" j=\" << j << \" r=\" << r << \" c=\" << c << \" d=\" << d << \" b=\" << b << std::endl;\n              }\n              VERIFY_IS_EQUAL(result(d, r, c, patchId, b), expected);\n              // RowMajor\n              if (result_row_major(b, patchId, c, r, d) != expected_row_major) {\n                std::cout << \"Mismatch detected at index i=\" << i << \" j=\" << j << \" r=\" << r << \" c=\" << c << \" d=\" << d << \" b=\" << b << std::endl;\n              }\n              VERIFY_IS_EQUAL(result_row_major(b, patchId, c, r, d), expected_row_major);\n              // Check that ColMajor and RowMajor agree.\n              VERIFY_IS_EQUAL(expected, expected_row_major);\n            }\n          }\n        }\n      }\n    }\n  }\n}\n\n// Verifies VALID padding (no padding) with the same value.\nvoid test_patch_padding_valid_same_value()\n{\n  int input_depth = 1;\n  int input_rows = 5;\n  int input_cols = 5;\n  int input_batches = 2;\n  int ksize = 3;  // Corresponds to the Rows and Cols for tensor.extract_image_patches<>.\n  int stride = 2;  // Only same stride is supported.\n  // ColMajor\n  Tensor<float, 4> tensor(input_depth, input_rows, input_cols, input_batches);\n  tensor = tensor.constant(11.0f);\n  Tensor<float, 5> result = tensor.extract_image_patches(ksize, ksize, stride, stride, 1, 1, PADDING_VALID);\n\n  VERIFY_IS_EQUAL(result.dimension(0), input_depth);  // depth\n  VERIFY_IS_EQUAL(result.dimension(1), ksize);  // kernel rows\n  VERIFY_IS_EQUAL(result.dimension(2), ksize);  // kernel cols\n  VERIFY_IS_EQUAL(result.dimension(3), 4);  // number of patches\n  VERIFY_IS_EQUAL(result.dimension(4), input_batches);  // number of batches\n\n  // RowMajor\n  Tensor<float, 4, RowMajor> tensor_row_major = tensor.swap_layout();\n  VERIFY_IS_EQUAL(tensor.dimension(0), tensor_row_major.dimension(3));\n  VERIFY_IS_EQUAL(tensor.dimension(1), tensor_row_major.dimension(2));\n  VERIFY_IS_EQUAL(tensor.dimension(2), tensor_row_major.dimension(1));\n  VERIFY_IS_EQUAL(tensor.dimension(3), tensor_row_major.dimension(0));\n\n  Tensor<float, 5, RowMajor> result_row_major = tensor_row_major.extract_image_patches(ksize, ksize, stride, stride, 1, 1, PADDING_VALID);\n  VERIFY_IS_EQUAL(result.dimension(0), result_row_major.dimension(4));\n  VERIFY_IS_EQUAL(result.dimension(1), result_row_major.dimension(3));\n  VERIFY_IS_EQUAL(result.dimension(2), result_row_major.dimension(2));\n  VERIFY_IS_EQUAL(result.dimension(3), result_row_major.dimension(1));\n  VERIFY_IS_EQUAL(result.dimension(4), result_row_major.dimension(0));\n\n  // No padding is carried out.\n  int row_padding = 0;\n  int col_padding = 0;\n\n  for (int i = 0; (i+stride+ksize-1) <= input_rows; i += stride) {  // input rows\n    for (int j = 0; (j+stride+ksize-1) <= input_cols; j += stride) {  // input cols\n      int patchId = i+input_rows*j;\n      for (int r = 0; r < ksize; ++r) {  // patch rows\n        for (int c = 0; c < ksize; ++c) {  // patch cols\n          for (int d = 0; d < input_depth; ++d) {  // depth\n            for (int b = 0; b < input_batches; ++b) {  // batch\n              float expected = 0.0f;\n              float expected_row_major = 0.0f;\n              int row_offset = r + i - row_padding;\n              int col_offset = c + j - col_padding;\n              if (row_offset >= 0 && col_offset >= 0 && row_offset < input_rows && col_offset < input_cols) {\n                expected = tensor(d, row_offset, col_offset, b);\n                expected_row_major = tensor_row_major(b, col_offset, row_offset, d);\n              }\n              // ColMajor\n              if (result(d, r, c, patchId, b) != expected) {\n                std::cout << \"Mismatch detected at index i=\" << i << \" j=\" << j << \" r=\" << r << \" c=\" << c << \" d=\" << d << \" b=\" << b << std::endl;\n              }\n              VERIFY_IS_EQUAL(result(d, r, c, patchId, b), expected);\n              // RowMajor\n              if (result_row_major(b, patchId, c, r, d) != expected_row_major) {\n                std::cout << \"Mismatch detected at index i=\" << i << \" j=\" << j << \" r=\" << r << \" c=\" << c << \" d=\" << d << \" b=\" << b << std::endl;\n              }\n              VERIFY_IS_EQUAL(result_row_major(b, patchId, c, r, d), expected_row_major);\n              // Check that ColMajor and RowMajor agree.\n              VERIFY_IS_EQUAL(expected, expected_row_major);\n            }\n          }\n        }\n      }\n    }\n  }\n}\n\n// Verifies SAME padding.\nvoid test_patch_padding_same()\n{\n  int input_depth = 3;\n  int input_rows = 4;\n  int input_cols = 2;\n  int input_batches = 1;\n  int ksize = 2;  // Corresponds to the Rows and Cols for tensor.extract_image_patches<>.\n  int stride = 2;  // Only same stride is supported.\n  // ColMajor\n  Tensor<float, 4> tensor(input_depth, input_rows, input_cols, input_batches);\n  // Initializes tensor with incrementing numbers.\n  for (int i = 0; i < tensor.size(); ++i) {\n    tensor.data()[i] = i + 1;\n  }\n  Tensor<float, 5> result = tensor.extract_image_patches(ksize, ksize, stride, stride, PADDING_SAME);\n\n  VERIFY_IS_EQUAL(result.dimension(0), input_depth);  // depth\n  VERIFY_IS_EQUAL(result.dimension(1), ksize);  // kernel rows\n  VERIFY_IS_EQUAL(result.dimension(2), ksize);  // kernel cols\n  VERIFY_IS_EQUAL(result.dimension(3), 2);  // number of patches\n  VERIFY_IS_EQUAL(result.dimension(4), input_batches);  // number of batches\n\n  // RowMajor\n  Tensor<float, 4, RowMajor> tensor_row_major = tensor.swap_layout();\n  VERIFY_IS_EQUAL(tensor.dimension(0), tensor_row_major.dimension(3));\n  VERIFY_IS_EQUAL(tensor.dimension(1), tensor_row_major.dimension(2));\n  VERIFY_IS_EQUAL(tensor.dimension(2), tensor_row_major.dimension(1));\n  VERIFY_IS_EQUAL(tensor.dimension(3), tensor_row_major.dimension(0));\n\n  Tensor<float, 5, RowMajor> result_row_major = tensor_row_major.extract_image_patches(ksize, ksize, stride, stride, PADDING_SAME);\n  VERIFY_IS_EQUAL(result.dimension(0), result_row_major.dimension(4));\n  VERIFY_IS_EQUAL(result.dimension(1), result_row_major.dimension(3));\n  VERIFY_IS_EQUAL(result.dimension(2), result_row_major.dimension(2));\n  VERIFY_IS_EQUAL(result.dimension(3), result_row_major.dimension(1));\n  VERIFY_IS_EQUAL(result.dimension(4), result_row_major.dimension(0));\n\n  // Based on the calculation described in TensorTraits.h, padding happens to be\n  // 0.\n  int row_padding = 0;\n  int col_padding = 0;\n\n  for (int i = 0; (i+stride+ksize-1) <= input_rows; i += stride) {  // input rows\n    for (int j = 0; (j+stride+ksize-1) <= input_cols; j += stride) {  // input cols\n      int patchId = i+input_rows*j;\n      for (int r = 0; r < ksize; ++r) {  // patch rows\n        for (int c = 0; c < ksize; ++c) {  // patch cols\n          for (int d = 0; d < input_depth; ++d) {  // depth\n            for (int b = 0; b < input_batches; ++b) {  // batch\n              float expected = 0.0f;\n              float expected_row_major = 0.0f;\n              int row_offset = r*stride + i - row_padding;\n              int col_offset = c*stride + j - col_padding;\n              if (row_offset >= 0 && col_offset >= 0 && row_offset < input_rows && col_offset < input_cols) {\n                expected = tensor(d, row_offset, col_offset, b);\n                expected_row_major = tensor_row_major(b, col_offset, row_offset, d);\n              }\n              // ColMajor\n              if (result(d, r, c, patchId, b) != expected) {\n                std::cout << \"Mismatch detected at index i=\" << i << \" j=\" << j << \" r=\" << r << \" c=\" << c << \" d=\" << d << \" b=\" << b << std::endl;\n              }\n              VERIFY_IS_EQUAL(result(d, r, c, patchId, b), expected);\n              // RowMajor\n              if (result_row_major(b, patchId, c, r, d) != expected_row_major) {\n                std::cout << \"Mismatch detected at index i=\" << i << \" j=\" << j << \" r=\" << r << \" c=\" << c << \" d=\" << d << \" b=\" << b << std::endl;\n              }\n              VERIFY_IS_EQUAL(result_row_major(b, patchId, c, r, d), expected_row_major);\n              // Check that ColMajor and RowMajor agree.\n              VERIFY_IS_EQUAL(expected, expected_row_major);\n            }\n          }\n        }\n      }\n    }\n  }\n}\n\nvoid test_patch_no_extra_dim()\n{\n  Tensor<float, 3> tensor(2,3,5);\n  tensor.setRandom();\n  Tensor<float, 3, RowMajor> tensor_row_major = tensor.swap_layout();\n  VERIFY_IS_EQUAL(tensor.dimension(0), tensor_row_major.dimension(2));\n  VERIFY_IS_EQUAL(tensor.dimension(1), tensor_row_major.dimension(1));\n  VERIFY_IS_EQUAL(tensor.dimension(2), tensor_row_major.dimension(0));\n\n  // Single pixel patch: ColMajor\n  Tensor<float, 4> single_pixel_patch;\n  single_pixel_patch = tensor.extract_image_patches(1, 1);\n  VERIFY_IS_EQUAL(single_pixel_patch.dimension(0), 2);\n  VERIFY_IS_EQUAL(single_pixel_patch.dimension(1), 1);\n  VERIFY_IS_EQUAL(single_pixel_patch.dimension(2), 1);\n  VERIFY_IS_EQUAL(single_pixel_patch.dimension(3), 3*5);\n\n  // Single pixel patch: RowMajor\n  Tensor<float, 4, RowMajor> single_pixel_patch_row_major;\n  single_pixel_patch_row_major = tensor_row_major.extract_image_patches(1, 1);\n  VERIFY_IS_EQUAL(single_pixel_patch_row_major.dimension(0), 3*5);\n  VERIFY_IS_EQUAL(single_pixel_patch_row_major.dimension(1), 1);\n  VERIFY_IS_EQUAL(single_pixel_patch_row_major.dimension(2), 1);\n  VERIFY_IS_EQUAL(single_pixel_patch_row_major.dimension(3), 2);\n\n  for (int i = 0; i < tensor.size(); ++i) {\n    // ColMajor\n    if (tensor.data()[i] != single_pixel_patch.data()[i]) {\n      std::cout << \"Mismatch detected at index \" << i << \" : \" << tensor.data()[i] << \" vs \" << single_pixel_patch.data()[i] << std::endl;\n    }\n    VERIFY_IS_EQUAL(single_pixel_patch.data()[i], tensor.data()[i]);\n    // RowMajor\n    if (tensor_row_major.data()[i] != single_pixel_patch_row_major.data()[i]) {\n      std::cout << \"Mismatch detected at index \" << i << \" : \"\n           << tensor.data()[i] << \" vs \"\n           << single_pixel_patch_row_major.data()[i] << std::endl;\n    }\n    VERIFY_IS_EQUAL(single_pixel_patch_row_major.data()[i],\n                    tensor_row_major.data()[i]);\n    VERIFY_IS_EQUAL(tensor.data()[i], tensor_row_major.data()[i]);\n    VERIFY_IS_EQUAL(single_pixel_patch.data()[i],\n                    single_pixel_patch_row_major.data()[i]);\n  }\n\n  // Entire image patch: ColMajor\n  Tensor<float, 4> entire_image_patch;\n  entire_image_patch = tensor.extract_image_patches(3, 5);\n  VERIFY_IS_EQUAL(entire_image_patch.dimension(0), 2);\n  VERIFY_IS_EQUAL(entire_image_patch.dimension(1), 3);\n  VERIFY_IS_EQUAL(entire_image_patch.dimension(2), 5);\n  VERIFY_IS_EQUAL(entire_image_patch.dimension(3), 3*5);\n\n  // Entire image patch: RowMajor\n  Tensor<float, 4, RowMajor> entire_image_patch_row_major;\n  entire_image_patch_row_major = tensor_row_major.extract_image_patches(3, 5);\n  VERIFY_IS_EQUAL(entire_image_patch_row_major.dimension(0), 3*5);\n  VERIFY_IS_EQUAL(entire_image_patch_row_major.dimension(1), 5);\n  VERIFY_IS_EQUAL(entire_image_patch_row_major.dimension(2), 3);\n  VERIFY_IS_EQUAL(entire_image_patch_row_major.dimension(3), 2);\n\n  for (int i = 0; i < 3; ++i) {\n    for (int j = 0; j < 5; ++j) {\n      int patchId = i+3*j;\n      for (int r = 0; r < 3; ++r) {\n        for (int c = 0; c < 5; ++c) {\n          for (int d = 0; d < 2; ++d) {\n            float expected = 0.0f;\n            float expected_row_major = 0.0f;\n            if (r-1+i >= 0 && c-2+j >= 0 && r-1+i < 3 && c-2+j < 5) {\n              expected = tensor(d, r-1+i, c-2+j);\n              expected_row_major = tensor_row_major(c-2+j, r-1+i, d);\n            }\n            // ColMajor\n            if (entire_image_patch(d, r, c, patchId) != expected) {\n              std::cout << \"Mismatch detected at index i=\" << i << \" j=\" << j << \" r=\" << r << \" c=\" << c << \" d=\" << d << std::endl;\n            }\n            VERIFY_IS_EQUAL(entire_image_patch(d, r, c, patchId), expected);\n            // RowMajor\n            if (entire_image_patch_row_major(patchId, c, r, d) !=\n                expected_row_major) {\n              std::cout << \"Mismatch detected at index i=\" << i << \" j=\" << j << \" r=\" << r << \" c=\" << c << \" d=\" << d << std::endl;\n            }\n            VERIFY_IS_EQUAL(entire_image_patch_row_major(patchId, c, r, d),\n                            expected_row_major);\n            // Check that ColMajor and RowMajor agree.\n            VERIFY_IS_EQUAL(expected, expected_row_major);\n          }\n        }\n      }\n    }\n  }\n\n  // 2D patch: ColMajor\n  Tensor<float, 4> twod_patch;\n  twod_patch = tensor.extract_image_patches(2, 2);\n  VERIFY_IS_EQUAL(twod_patch.dimension(0), 2);\n  VERIFY_IS_EQUAL(twod_patch.dimension(1), 2);\n  VERIFY_IS_EQUAL(twod_patch.dimension(2), 2);\n  VERIFY_IS_EQUAL(twod_patch.dimension(3), 3*5);\n\n  // 2D patch: RowMajor\n  Tensor<float, 4, RowMajor> twod_patch_row_major;\n  twod_patch_row_major = tensor_row_major.extract_image_patches(2, 2);\n  VERIFY_IS_EQUAL(twod_patch_row_major.dimension(0), 3*5);\n  VERIFY_IS_EQUAL(twod_patch_row_major.dimension(1), 2);\n  VERIFY_IS_EQUAL(twod_patch_row_major.dimension(2), 2);\n  VERIFY_IS_EQUAL(twod_patch_row_major.dimension(3), 2);\n\n  // Based on the calculation described in TensorTraits.h, padding happens to be 0.\n  int row_padding = 0;\n  int col_padding = 0;\n  int stride = 1;\n\n  for (int i = 0; i < 3; ++i) {\n    for (int j = 0; j < 5; ++j) {\n      int patchId = i+3*j;\n      for (int r = 0; r < 2; ++r) {\n        for (int c = 0; c < 2; ++c) {\n          for (int d = 0; d < 2; ++d) {\n            float expected = 0.0f;\n            float expected_row_major = 0.0f;\n            int row_offset = r*stride + i - row_padding;\n            int col_offset = c*stride + j - col_padding;\n            // ColMajor\n            if (row_offset >= 0 && col_offset >= 0 && row_offset < tensor.dimension(1) && col_offset < tensor.dimension(2)) {\n              expected = tensor(d, row_offset, col_offset);\n            }\n            if (twod_patch(d, r, c, patchId) != expected) {\n              std::cout << \"Mismatch detected at index i=\" << i << \" j=\" << j << \" r=\" << r << \" c=\" << c << \" d=\" << d << std::endl;\n            }\n            VERIFY_IS_EQUAL(twod_patch(d, r, c, patchId), expected);\n            // RowMajor\n            if (row_offset >= 0 && col_offset >= 0 && row_offset < tensor_row_major.dimension(1) && col_offset < tensor_row_major.dimension(0)) {\n              expected_row_major = tensor_row_major(col_offset, row_offset, d);\n            }\n            if (twod_patch_row_major(patchId, c, r, d) != expected_row_major) {\n              std::cout << \"Mismatch detected at index i=\" << i << \" j=\" << j << \" r=\" << r << \" c=\" << c << \" d=\" << d << std::endl;\n            }\n            VERIFY_IS_EQUAL(twod_patch_row_major(patchId, c, r, d), expected_row_major);\n            // Check that ColMajor and RowMajor agree.\n            VERIFY_IS_EQUAL(expected, expected_row_major);\n          }\n        }\n      }\n    }\n  }\n}\n\nvoid test_imagenet_patches()\n{\n  // Test the code on typical configurations used by the 'imagenet' benchmarks at\n  // https://github.com/soumith/convnet-benchmarks\n  // ColMajor\n  Tensor<float, 4> l_in(3, 128, 128, 16);\n  l_in.setRandom();\n  Tensor<float, 5> l_out = l_in.extract_image_patches(11, 11);\n  VERIFY_IS_EQUAL(l_out.dimension(0), 3);\n  VERIFY_IS_EQUAL(l_out.dimension(1), 11);\n  VERIFY_IS_EQUAL(l_out.dimension(2), 11);\n  VERIFY_IS_EQUAL(l_out.dimension(3), 128*128);\n  VERIFY_IS_EQUAL(l_out.dimension(4), 16);\n\n  // RowMajor\n  Tensor<float, 5, RowMajor> l_out_row_major = l_in.swap_layout().extract_image_patches(11, 11);\n  VERIFY_IS_EQUAL(l_out_row_major.dimension(0), 16);\n  VERIFY_IS_EQUAL(l_out_row_major.dimension(1), 128*128);\n  VERIFY_IS_EQUAL(l_out_row_major.dimension(2), 11);\n  VERIFY_IS_EQUAL(l_out_row_major.dimension(3), 11);\n  VERIFY_IS_EQUAL(l_out_row_major.dimension(4), 3);\n\n  for (int b = 0; b < 16; ++b) {\n    for (int i = 0; i < 128; ++i) {\n      for (int j = 0; j < 128; ++j) {\n        int patchId = i+128*j;\n        for (int c = 0; c < 11; ++c) {\n          for (int r = 0; r < 11; ++r) {\n            for (int d = 0; d < 3; ++d) {\n              float expected = 0.0f;\n              if (r-5+i >= 0 && c-5+j >= 0 && r-5+i < 128 && c-5+j < 128) {\n                expected = l_in(d, r-5+i, c-5+j, b);\n              }\n              // ColMajor\n              if (l_out(d, r, c, patchId, b) != expected) {\n                std::cout << \"Mismatch detected at index i=\" << i << \" j=\" << j << \" r=\" << r << \" c=\" << c << \" d=\" << d << \" b=\" << b << std::endl;\n              }\n              VERIFY_IS_EQUAL(l_out(d, r, c, patchId, b), expected);\n              // RowMajor\n              if (l_out_row_major(b, patchId, c, r, d) !=\n                  expected) {\n                std::cout << \"Mismatch detected at index i=\" << i << \" j=\" << j\n                     << \" r=\" << r << \" c=\" << c << \" d=\" << d << \" b=\" << b\n                     << std::endl;\n              }\n              VERIFY_IS_EQUAL(l_out_row_major(b, patchId, c, r, d),\n                              expected);\n            }\n          }\n        }\n      }\n    }\n  }\n\n  // ColMajor\n  l_in.resize(16, 64, 64, 32);\n  l_in.setRandom();\n  l_out = l_in.extract_image_patches(9, 9);\n  VERIFY_IS_EQUAL(l_out.dimension(0), 16);\n  VERIFY_IS_EQUAL(l_out.dimension(1), 9);\n  VERIFY_IS_EQUAL(l_out.dimension(2), 9);\n  VERIFY_IS_EQUAL(l_out.dimension(3), 64*64);\n  VERIFY_IS_EQUAL(l_out.dimension(4), 32);\n\n  // RowMajor\n  l_out_row_major = l_in.swap_layout().extract_image_patches(9, 9);\n  VERIFY_IS_EQUAL(l_out_row_major.dimension(0), 32);\n  VERIFY_IS_EQUAL(l_out_row_major.dimension(1), 64*64);\n  VERIFY_IS_EQUAL(l_out_row_major.dimension(2), 9);\n  VERIFY_IS_EQUAL(l_out_row_major.dimension(3), 9);\n  VERIFY_IS_EQUAL(l_out_row_major.dimension(4), 16);\n\n  for (int b = 0; b < 32; ++b) {\n    for (int i = 0; i < 64; ++i) {\n      for (int j = 0; j < 64; ++j) {\n        int patchId = i+64*j;\n        for (int c = 0; c < 9; ++c) {\n          for (int r = 0; r < 9; ++r) {\n            for (int d = 0; d < 16; ++d) {\n              float expected = 0.0f;\n              if (r-4+i >= 0 && c-4+j >= 0 && r-4+i < 64 && c-4+j < 64) {\n                expected = l_in(d, r-4+i, c-4+j, b);\n              }\n              // ColMajor\n              if (l_out(d, r, c, patchId, b) != expected) {\n                std::cout << \"Mismatch detected at index i=\" << i << \" j=\" << j << \" r=\" << r << \" c=\" << c << \" d=\" << d << \" b=\" << b << std::endl;\n              }\n              VERIFY_IS_EQUAL(l_out(d, r, c, patchId, b), expected);\n              // RowMajor\n              if (l_out_row_major(b, patchId, c, r, d) != expected) {\n                std::cout << \"Mismatch detected at index i=\" << i << \" j=\" << j << \" r=\" << r << \" c=\" << c << \" d=\" << d << \" b=\" << b << std::endl;\n              }\n              VERIFY_IS_EQUAL(l_out_row_major(b, patchId, c, r, d), expected);\n            }\n          }\n        }\n      }\n    }\n  }\n\n  // ColMajor\n  l_in.resize(32, 16, 16, 32);\n  l_in.setRandom();\n  l_out = l_in.extract_image_patches(7, 7);\n  VERIFY_IS_EQUAL(l_out.dimension(0), 32);\n  VERIFY_IS_EQUAL(l_out.dimension(1), 7);\n  VERIFY_IS_EQUAL(l_out.dimension(2), 7);\n  VERIFY_IS_EQUAL(l_out.dimension(3), 16*16);\n  VERIFY_IS_EQUAL(l_out.dimension(4), 32);\n\n  // RowMajor\n  l_out_row_major = l_in.swap_layout().extract_image_patches(7, 7);\n  VERIFY_IS_EQUAL(l_out_row_major.dimension(0), 32);\n  VERIFY_IS_EQUAL(l_out_row_major.dimension(1), 16*16);\n  VERIFY_IS_EQUAL(l_out_row_major.dimension(2), 7);\n  VERIFY_IS_EQUAL(l_out_row_major.dimension(3), 7);\n  VERIFY_IS_EQUAL(l_out_row_major.dimension(4), 32);\n\n  for (int b = 0; b < 32; ++b) {\n    for (int i = 0; i < 16; ++i) {\n      for (int j = 0; j < 16; ++j) {\n        int patchId = i+16*j;\n        for (int c = 0; c < 7; ++c) {\n          for (int r = 0; r < 7; ++r) {\n            for (int d = 0; d < 32; ++d) {\n              float expected = 0.0f;\n              if (r-3+i >= 0 && c-3+j >= 0 && r-3+i < 16 && c-3+j < 16) {\n                expected = l_in(d, r-3+i, c-3+j, b);\n              }\n              // ColMajor\n              if (l_out(d, r, c, patchId, b) != expected) {\n                std::cout << \"Mismatch detected at index i=\" << i << \" j=\" << j << \" r=\" << r << \" c=\" << c << \" d=\" << d << \" b=\" << b << std::endl;\n              }\n              VERIFY_IS_EQUAL(l_out(d, r, c, patchId, b), expected);\n              // RowMajor\n              if (l_out_row_major(b, patchId, c, r, d) != expected) {\n                std::cout << \"Mismatch detected at index i=\" << i << \" j=\" << j << \" r=\" << r << \" c=\" << c << \" d=\" << d << \" b=\" << b << std::endl;\n              }\n              VERIFY_IS_EQUAL(l_out_row_major(b, patchId, c, r, d), expected);\n            }\n          }\n        }\n      }\n    }\n  }\n\n  // ColMajor\n  l_in.resize(64, 13, 13, 32);\n  l_in.setRandom();\n  l_out = l_in.extract_image_patches(3, 3);\n  VERIFY_IS_EQUAL(l_out.dimension(0), 64);\n  VERIFY_IS_EQUAL(l_out.dimension(1), 3);\n  VERIFY_IS_EQUAL(l_out.dimension(2), 3);\n  VERIFY_IS_EQUAL(l_out.dimension(3), 13*13);\n  VERIFY_IS_EQUAL(l_out.dimension(4), 32);\n\n  // RowMajor\n  l_out_row_major = l_in.swap_layout().extract_image_patches(3, 3);\n  VERIFY_IS_EQUAL(l_out_row_major.dimension(0), 32);\n  VERIFY_IS_EQUAL(l_out_row_major.dimension(1), 13*13);\n  VERIFY_IS_EQUAL(l_out_row_major.dimension(2), 3);\n  VERIFY_IS_EQUAL(l_out_row_major.dimension(3), 3);\n  VERIFY_IS_EQUAL(l_out_row_major.dimension(4), 64);\n\n  for (int b = 0; b < 32; ++b) {\n    for (int i = 0; i < 13; ++i) {\n      for (int j = 0; j < 13; ++j) {\n        int patchId = i+13*j;\n        for (int c = 0; c < 3; ++c) {\n          for (int r = 0; r < 3; ++r) {\n            for (int d = 0; d < 64; ++d) {\n              float expected = 0.0f;\n              if (r-1+i >= 0 && c-1+j >= 0 && r-1+i < 13 && c-1+j < 13) {\n                expected = l_in(d, r-1+i, c-1+j, b);\n              }\n              // ColMajor\n              if (l_out(d, r, c, patchId, b) != expected) {\n                std::cout << \"Mismatch detected at index i=\" << i << \" j=\" << j << \" r=\" << r << \" c=\" << c << \" d=\" << d << \" b=\" << b << std::endl;\n              }\n              VERIFY_IS_EQUAL(l_out(d, r, c, patchId, b), expected);\n              // RowMajor\n              if (l_out_row_major(b, patchId, c, r, d) != expected) {\n                std::cout << \"Mismatch detected at index i=\" << i << \" j=\" << j << \" r=\" << r << \" c=\" << c << \" d=\" << d << \" b=\" << b << std::endl;\n              }\n              VERIFY_IS_EQUAL(l_out_row_major(b, patchId, c, r, d), expected);\n            }\n          }\n        }\n      }\n    }\n  }\n}\n\nvoid test_cxx11_tensor_image_patch()\n{\n  CALL_SUBTEST_1(test_simple_patch());\n  CALL_SUBTEST_2(test_patch_no_extra_dim());\n  CALL_SUBTEST_3(test_patch_padding_valid());\n  CALL_SUBTEST_4(test_patch_padding_valid_same_value());\n  CALL_SUBTEST_5(test_patch_padding_same());\n  CALL_SUBTEST_6(test_imagenet_patches());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_index_list.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\n#ifdef EIGEN_HAS_INDEX_LIST\n\nstatic void test_static_index_list()\n{\n  Tensor<float, 4> tensor(2,3,5,7);\n  tensor.setRandom();\n\n  constexpr auto reduction_axis = make_index_list(0, 1, 2);\n  VERIFY_IS_EQUAL(internal::array_get<0>(reduction_axis), 0);\n  VERIFY_IS_EQUAL(internal::array_get<1>(reduction_axis), 1);\n  VERIFY_IS_EQUAL(internal::array_get<2>(reduction_axis), 2);\n  VERIFY_IS_EQUAL(static_cast<DenseIndex>(reduction_axis[0]), 0);\n  VERIFY_IS_EQUAL(static_cast<DenseIndex>(reduction_axis[1]), 1);\n  VERIFY_IS_EQUAL(static_cast<DenseIndex>(reduction_axis[2]), 2);\n\n  EIGEN_STATIC_ASSERT((internal::array_get<0>(reduction_axis) == 0), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((internal::array_get<1>(reduction_axis) == 1), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((internal::array_get<2>(reduction_axis) == 2), YOU_MADE_A_PROGRAMMING_MISTAKE);\n\n  Tensor<float, 1> result = tensor.sum(reduction_axis);\n  for (int i = 0; i < result.size(); ++i) {\n    float expected = 0.0f;\n    for (int j = 0; j < 2; ++j) {\n      for (int k = 0; k < 3; ++k) {\n        for (int l = 0; l < 5; ++l) {\n          expected += tensor(j,k,l,i);\n        }\n      }\n    }\n    VERIFY_IS_APPROX(result(i), expected);\n  }\n}\n\n\nstatic void test_type2index_list()\n{\n  Tensor<float, 5> tensor(2,3,5,7,11);\n  tensor.setRandom();\n  tensor += tensor.constant(10.0f);\n\n  typedef Eigen::IndexList<Eigen::type2index<0>> Dims0;\n  typedef Eigen::IndexList<Eigen::type2index<0>, Eigen::type2index<1>> Dims1;\n  typedef Eigen::IndexList<Eigen::type2index<0>, Eigen::type2index<1>, Eigen::type2index<2>> Dims2;\n  typedef Eigen::IndexList<Eigen::type2index<0>, Eigen::type2index<1>, Eigen::type2index<2>, Eigen::type2index<3>> Dims3;\n  typedef Eigen::IndexList<Eigen::type2index<0>, Eigen::type2index<1>, Eigen::type2index<2>, Eigen::type2index<3>, Eigen::type2index<4>> Dims4;\n\n#if 0\n  EIGEN_STATIC_ASSERT((internal::indices_statically_known_to_increase<Dims0>() == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((internal::indices_statically_known_to_increase<Dims1>() == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((internal::indices_statically_known_to_increase<Dims2>() == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((internal::indices_statically_known_to_increase<Dims3>() == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((internal::indices_statically_known_to_increase<Dims4>() == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n#endif\n\n  EIGEN_STATIC_ASSERT((internal::are_inner_most_dims<Dims0, 1, ColMajor>::value == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((internal::are_inner_most_dims<Dims1, 2, ColMajor>::value == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((internal::are_inner_most_dims<Dims2, 3, ColMajor>::value == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((internal::are_inner_most_dims<Dims3, 4, ColMajor>::value == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((internal::are_inner_most_dims<Dims4, 5, ColMajor>::value == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n\n  EIGEN_STATIC_ASSERT((internal::are_inner_most_dims<Dims0, 1, RowMajor>::value == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((internal::are_inner_most_dims<Dims1, 2, RowMajor>::value == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((internal::are_inner_most_dims<Dims2, 3, RowMajor>::value == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((internal::are_inner_most_dims<Dims3, 4, RowMajor>::value == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((internal::are_inner_most_dims<Dims4, 5, RowMajor>::value == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n\n  const Dims0 reduction_axis0;\n  Tensor<float, 4> result0 = tensor.sum(reduction_axis0);\n  for (int m = 0; m < 11; ++m) {\n    for (int l = 0; l < 7; ++l) {\n      for (int k = 0; k < 5; ++k) {\n        for (int j = 0; j < 3; ++j) {\n          float expected = 0.0f;\n          for (int i = 0; i < 2; ++i) {\n            expected += tensor(i,j,k,l,m);\n          }\n          VERIFY_IS_APPROX(result0(j,k,l,m), expected);\n        }\n      }\n    }\n  }\n\n  const Dims1 reduction_axis1;\n  Tensor<float, 3> result1 = tensor.sum(reduction_axis1);\n  for (int m = 0; m < 11; ++m) {\n    for (int l = 0; l < 7; ++l) {\n      for (int k = 0; k < 5; ++k) {\n        float expected = 0.0f;\n        for (int j = 0; j < 3; ++j) {\n          for (int i = 0; i < 2; ++i) {\n            expected += tensor(i,j,k,l,m);\n          }\n        }\n        VERIFY_IS_APPROX(result1(k,l,m), expected);\n      }\n    }\n  }\n\n  const Dims2 reduction_axis2;\n  Tensor<float, 2> result2 = tensor.sum(reduction_axis2);\n  for (int m = 0; m < 11; ++m) {\n    for (int l = 0; l < 7; ++l) {\n      float expected = 0.0f;\n      for (int k = 0; k < 5; ++k) {\n        for (int j = 0; j < 3; ++j) {\n          for (int i = 0; i < 2; ++i) {\n            expected += tensor(i,j,k,l,m);\n          }\n        }\n      }\n      VERIFY_IS_APPROX(result2(l,m), expected);\n    }\n  }\n\n  const Dims3 reduction_axis3;\n  Tensor<float, 1> result3 = tensor.sum(reduction_axis3);\n  for (int m = 0; m < 11; ++m) {\n    float expected = 0.0f;\n    for (int l = 0; l < 7; ++l) {\n      for (int k = 0; k < 5; ++k) {\n        for (int j = 0; j < 3; ++j) {\n          for (int i = 0; i < 2; ++i) {\n            expected += tensor(i,j,k,l,m);\n          }\n        }\n      }\n    }\n    VERIFY_IS_APPROX(result3(m), expected);\n  }\n\n  const Dims4 reduction_axis4;\n  Tensor<float, 0> result4 = tensor.sum(reduction_axis4);\n  float expected = 0.0f;\n  for (int m = 0; m < 11; ++m) {\n    for (int l = 0; l < 7; ++l) {\n      for (int k = 0; k < 5; ++k) {\n        for (int j = 0; j < 3; ++j) {\n          for (int i = 0; i < 2; ++i) {\n            expected += tensor(i,j,k,l,m);\n          }\n        }\n      }\n    }\n  }\n  VERIFY_IS_APPROX(result4(), expected);\n}\n\n\nstatic void test_type2indexpair_list()\n{\n  Tensor<float, 5> tensor(2,3,5,7,11);\n  tensor.setRandom();\n  tensor += tensor.constant(10.0f);\n\n  typedef Eigen::IndexPairList<Eigen::type2indexpair<0,10>> Dims0;\n  typedef Eigen::IndexPairList<Eigen::type2indexpair<0,10>, Eigen::type2indexpair<1,11>, Eigen::type2indexpair<2,12>> Dims2_a;\n  typedef Eigen::IndexPairList<Eigen::type2indexpair<0,10>, Eigen::IndexPair<DenseIndex>, Eigen::type2indexpair<2,12>> Dims2_b;\n  typedef Eigen::IndexPairList<Eigen::IndexPair<DenseIndex>, Eigen::type2indexpair<1,11>, Eigen::IndexPair<DenseIndex>> Dims2_c;\n\n  Dims0 d0;\n  Dims2_a d2_a;\n\n  Dims2_b d2_b;\n  d2_b.set(1, Eigen::IndexPair<DenseIndex>(1,11));\n\n  Dims2_c d2_c;\n  d2_c.set(0, Eigen::IndexPair<DenseIndex>(Eigen::IndexPair<DenseIndex>(0,10)));\n  d2_c.set(1, Eigen::IndexPair<DenseIndex>(1,11));  // setting type2indexpair to correct value.\n  d2_c.set(2, Eigen::IndexPair<DenseIndex>(2,12));\n\n  VERIFY_IS_EQUAL(d2_a[0].first, 0);\n  VERIFY_IS_EQUAL(d2_a[0].second, 10);\n  VERIFY_IS_EQUAL(d2_a[1].first, 1);\n  VERIFY_IS_EQUAL(d2_a[1].second, 11);\n  VERIFY_IS_EQUAL(d2_a[2].first, 2);\n  VERIFY_IS_EQUAL(d2_a[2].second, 12);\n\n  VERIFY_IS_EQUAL(d2_b[0].first, 0);\n  VERIFY_IS_EQUAL(d2_b[0].second, 10);\n  VERIFY_IS_EQUAL(d2_b[1].first, 1);\n  VERIFY_IS_EQUAL(d2_b[1].second, 11);\n  VERIFY_IS_EQUAL(d2_b[2].first, 2);\n  VERIFY_IS_EQUAL(d2_b[2].second, 12);\n\n  VERIFY_IS_EQUAL(d2_c[0].first, 0);\n  VERIFY_IS_EQUAL(d2_c[0].second, 10);\n  VERIFY_IS_EQUAL(d2_c[1].first, 1);\n  VERIFY_IS_EQUAL(d2_c[1].second, 11);\n  VERIFY_IS_EQUAL(d2_c[2].first, 2);\n  VERIFY_IS_EQUAL(d2_c[2].second, 12);\n\n  EIGEN_STATIC_ASSERT((d2_a.value_known_statically(0) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((d2_a.value_known_statically(1) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((d2_a.value_known_statically(2) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n\n  EIGEN_STATIC_ASSERT((d2_b.value_known_statically(0) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((d2_b.value_known_statically(1) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((d2_b.value_known_statically(2) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n\n  EIGEN_STATIC_ASSERT((d2_c.value_known_statically(0) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((d2_c.value_known_statically(1) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((d2_c.value_known_statically(2) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);\n\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims0>(0, 0) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims0>(0, 1) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);\n\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_a>(0, 0) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_a>(0, 1) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_a>(1, 1) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_a>(1, 2) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_a>(2, 2) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_a>(2, 3) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);\n\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_b>(0, 0) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_b>(0, 1) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_b>(1, 1) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_b>(1, 2) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_b>(2, 2) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_b>(2, 3) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);\n\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_c>(0, 0) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_c>(0, 1) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_c>(1, 1) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_c>(1, 2) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_c>(2, 2) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_c>(2, 3) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);\n\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims0>(0, 10) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims0>(0, 11) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);\n\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_a>(0, 10) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_a>(0, 11) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_a>(1, 11) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_a>(1, 12) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_a>(2, 12) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_a>(2, 13) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);\n\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_b>(0, 10) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_b>(0, 11) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_b>(1, 11) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_b>(1, 12) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_b>(2, 12) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_b>(2, 13) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);\n\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_c>(0, 10) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_c>(0, 11) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_c>(1, 11) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_c>(1, 12) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_c>(2, 12) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_c>(2, 13) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);\n}\n\n\nstatic void test_dynamic_index_list()\n{\n  Tensor<float, 4> tensor(2,3,5,7);\n  tensor.setRandom();\n\n  int dim1 = 2;\n  int dim2 = 1;\n  int dim3 = 0;\n\n  auto reduction_axis = make_index_list(dim1, dim2, dim3);\n\n  VERIFY_IS_EQUAL(internal::array_get<0>(reduction_axis), 2);\n  VERIFY_IS_EQUAL(internal::array_get<1>(reduction_axis), 1);\n  VERIFY_IS_EQUAL(internal::array_get<2>(reduction_axis), 0);\n  VERIFY_IS_EQUAL(static_cast<DenseIndex>(reduction_axis[0]), 2);\n  VERIFY_IS_EQUAL(static_cast<DenseIndex>(reduction_axis[1]), 1);\n  VERIFY_IS_EQUAL(static_cast<DenseIndex>(reduction_axis[2]), 0);\n\n  Tensor<float, 1> result = tensor.sum(reduction_axis);\n  for (int i = 0; i < result.size(); ++i) {\n    float expected = 0.0f;\n    for (int j = 0; j < 2; ++j) {\n      for (int k = 0; k < 3; ++k) {\n        for (int l = 0; l < 5; ++l) {\n          expected += tensor(j,k,l,i);\n        }\n      }\n    }\n    VERIFY_IS_APPROX(result(i), expected);\n  }\n}\n\nstatic void test_mixed_index_list()\n{\n  Tensor<float, 4> tensor(2,3,5,7);\n  tensor.setRandom();\n\n  int dim2 = 1;\n  int dim4 = 3;\n\n  auto reduction_axis = make_index_list(0, dim2, 2, dim4);\n\n  VERIFY_IS_EQUAL(internal::array_get<0>(reduction_axis), 0);\n  VERIFY_IS_EQUAL(internal::array_get<1>(reduction_axis), 1);\n  VERIFY_IS_EQUAL(internal::array_get<2>(reduction_axis), 2);\n  VERIFY_IS_EQUAL(internal::array_get<3>(reduction_axis), 3);\n  VERIFY_IS_EQUAL(static_cast<DenseIndex>(reduction_axis[0]), 0);\n  VERIFY_IS_EQUAL(static_cast<DenseIndex>(reduction_axis[1]), 1);\n  VERIFY_IS_EQUAL(static_cast<DenseIndex>(reduction_axis[2]), 2);\n  VERIFY_IS_EQUAL(static_cast<DenseIndex>(reduction_axis[3]), 3);\n\n  typedef IndexList<type2index<0>, int, type2index<2>, int> ReductionIndices;\n  ReductionIndices reduction_indices;\n  reduction_indices.set(1, 1);\n  reduction_indices.set(3, 3);\n  EIGEN_STATIC_ASSERT((internal::array_get<0>(reduction_indices) == 0), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((internal::array_get<2>(reduction_indices) == 2), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((internal::index_known_statically<ReductionIndices>(0) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((internal::index_known_statically<ReductionIndices>(2) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((internal::index_statically_eq<ReductionIndices>(0, 0) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((internal::index_statically_eq<ReductionIndices>(2, 2) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n#if 0\n  EIGEN_STATIC_ASSERT((internal::all_indices_known_statically<ReductionIndices>() == false), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((internal::indices_statically_known_to_increase<ReductionIndices>() == false), YOU_MADE_A_PROGRAMMING_MISTAKE);\n#endif\n\n  typedef IndexList<type2index<0>, type2index<1>, type2index<2>, type2index<3>> ReductionList;\n  ReductionList reduction_list;\n  EIGEN_STATIC_ASSERT((internal::index_statically_eq<ReductionList>(0, 0) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((internal::index_statically_eq<ReductionList>(1, 1) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((internal::index_statically_eq<ReductionList>(2, 2) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((internal::index_statically_eq<ReductionList>(3, 3) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n#if 0\n  EIGEN_STATIC_ASSERT((internal::all_indices_known_statically<ReductionList>() == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((internal::indices_statically_known_to_increase<ReductionList>() == true), YOU_MADE_A_PROGRAMMING_MISTAKE);\n#endif\n\n  Tensor<float, 0> result1 = tensor.sum(reduction_axis);\n  Tensor<float, 0> result2 = tensor.sum(reduction_indices);\n  Tensor<float, 0> result3 = tensor.sum(reduction_list);\n\n  float expected = 0.0f;\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 5; ++k) {\n        for (int l = 0; l < 7; ++l) {\n          expected += tensor(i,j,k,l);\n        }\n      }\n    }\n  }\n  VERIFY_IS_APPROX(result1(), expected);\n  VERIFY_IS_APPROX(result2(), expected);\n  VERIFY_IS_APPROX(result3(), expected);\n}\n\n\nstatic void test_dim_check()\n{\n  Eigen::IndexList<Eigen::type2index<1>, int> dim1;\n  dim1.set(1, 2);\n  Eigen::IndexList<Eigen::type2index<1>, int> dim2;\n  dim2.set(1, 2);\n  VERIFY(dimensions_match(dim1, dim2));\n}\n\n\n#endif\n\nvoid test_cxx11_tensor_index_list()\n{\n#ifdef EIGEN_HAS_INDEX_LIST\n  CALL_SUBTEST(test_static_index_list());\n  CALL_SUBTEST(test_type2index_list());\n  CALL_SUBTEST(test_type2indexpair_list());\n  CALL_SUBTEST(test_dynamic_index_list());\n  CALL_SUBTEST(test_mixed_index_list());\n  CALL_SUBTEST(test_dim_check());\n#endif\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_inflation.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Ke Yang <yangke@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\n\ntemplate<int DataLayout>\nstatic void test_simple_inflation()\n{\n  Tensor<float, 4, DataLayout> tensor(2,3,5,7);\n  tensor.setRandom();\n  array<ptrdiff_t, 4> strides;\n\n  strides[0] = 1;\n  strides[1] = 1;\n  strides[2] = 1;\n  strides[3] = 1;\n\n  Tensor<float, 4, DataLayout> no_stride;\n  no_stride = tensor.inflate(strides);\n\n  VERIFY_IS_EQUAL(no_stride.dimension(0), 2);\n  VERIFY_IS_EQUAL(no_stride.dimension(1), 3);\n  VERIFY_IS_EQUAL(no_stride.dimension(2), 5);\n  VERIFY_IS_EQUAL(no_stride.dimension(3), 7);\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 5; ++k) {\n        for (int l = 0; l < 7; ++l) {\n          VERIFY_IS_EQUAL(tensor(i,j,k,l), no_stride(i,j,k,l));\n        }\n      }\n    }\n  }\n\n  strides[0] = 2;\n  strides[1] = 4;\n  strides[2] = 2;\n  strides[3] = 3;\n  Tensor<float, 4, DataLayout> inflated;\n  inflated = tensor.inflate(strides);\n\n  VERIFY_IS_EQUAL(inflated.dimension(0), 3);\n  VERIFY_IS_EQUAL(inflated.dimension(1), 9);\n  VERIFY_IS_EQUAL(inflated.dimension(2), 9);\n  VERIFY_IS_EQUAL(inflated.dimension(3), 19);\n\n  for (int i = 0; i < 3; ++i) {\n    for (int j = 0; j < 9; ++j) {\n      for (int k = 0; k < 9; ++k) {\n        for (int l = 0; l < 19; ++l) {\n          if (i % 2 == 0 &&\n              j % 4 == 0 &&\n              k % 2 == 0 &&\n              l % 3 == 0) {\n            VERIFY_IS_EQUAL(inflated(i,j,k,l),\n                            tensor(i/2, j/4, k/2, l/3));\n          } else {\n            VERIFY_IS_EQUAL(0, inflated(i,j,k,l));\n          }\n        }\n      }\n    }\n  }\n}\n\nvoid test_cxx11_tensor_inflation()\n{\n  CALL_SUBTEST(test_simple_inflation<ColMajor>());\n  CALL_SUBTEST(test_simple_inflation<RowMajor>());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_intdiv.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014-2015 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\n\nvoid test_signed_32bit()\n{\n  // Divide by one\n  const Eigen::internal::TensorIntDivisor<int32_t, false> div_by_one(1);\n\n  for (int32_t j = 0; j < 25000; ++j) {\n    const int32_t fast_div = j / div_by_one;\n    const int32_t slow_div = j / 1;\n    VERIFY_IS_EQUAL(fast_div, slow_div);\n  }\n\n  // Standard divide by 2 or more\n  for (int32_t i = 2; i < 25000; ++i) {\n    const Eigen::internal::TensorIntDivisor<int32_t, false> div(i);\n\n    for (int32_t j = 0; j < 25000; ++j) {\n      const int32_t fast_div = j / div;\n      const int32_t slow_div = j / i;\n      VERIFY_IS_EQUAL(fast_div, slow_div);\n    }\n  }\n\n  // Optimized divide by 2 or more\n  for (int32_t i = 2; i < 25000; ++i) {\n    const Eigen::internal::TensorIntDivisor<int32_t, true> div(i);\n\n    for (int32_t j = 0; j < 25000; ++j) {\n      const int32_t fast_div = j / div;\n      const int32_t slow_div = j / i;\n      VERIFY_IS_EQUAL(fast_div, slow_div);\n    }\n  }\n}\n\n\nvoid test_unsigned_32bit()\n{\n  for (uint32_t i = 1; i < 25000; ++i) {\n    const Eigen::internal::TensorIntDivisor<uint32_t> div(i);\n\n    for (uint32_t j = 0; j < 25000; ++j) {\n      const uint32_t fast_div = j / div;\n      const uint32_t slow_div = j / i;\n      VERIFY_IS_EQUAL(fast_div, slow_div);\n    }\n  }\n}\n\n\nvoid test_signed_64bit()\n{\n  for (int64_t i = 1; i < 25000; ++i) {\n    const Eigen::internal::TensorIntDivisor<int64_t> div(i);\n\n    for (int64_t j = 0; j < 25000; ++j) {\n      const int64_t fast_div = j / div;\n      const int64_t slow_div = j / i;\n      VERIFY_IS_EQUAL(fast_div, slow_div);\n    }\n  }\n}\n\n\nvoid test_unsigned_64bit()\n{\n  for (uint64_t i = 1; i < 25000; ++i) {\n    const Eigen::internal::TensorIntDivisor<uint64_t> div(i);\n\n    for (uint64_t j = 0; j < 25000; ++j) {\n      const uint64_t fast_div = j / div;\n      const uint64_t slow_div = j / i;\n      VERIFY_IS_EQUAL(fast_div, slow_div);\n    }\n  }\n}\n\nvoid test_powers_32bit() {\n  for (int expon = 1; expon < 31; expon++) {\n    int32_t div = (1 << expon);\n    for (int num_expon = 0; num_expon < 32; num_expon++) {\n      int32_t start_num = (1 << num_expon) - 100;\n      int32_t end_num = (1 << num_expon) + 100;\n      if (start_num < 0)\n        start_num = 0;\n      for (int32_t num = start_num; num < end_num; num++) {\n        Eigen::internal::TensorIntDivisor<int32_t> divider =\n          Eigen::internal::TensorIntDivisor<int32_t>(div);\n        int32_t result = num/div;\n        int32_t result_op = divider.divide(num);\n        VERIFY_IS_EQUAL(result_op, result);\n      }\n    }\n  }\n}\n\nvoid test_powers_64bit() {\n  for (int expon = 0; expon < 63; expon++) {\n    int64_t div = (1ull << expon);\n    for (int num_expon = 0; num_expon < 63; num_expon++) {\n      int64_t start_num = (1ull << num_expon) - 10;\n      int64_t end_num = (1ull << num_expon) + 10;\n      if (start_num < 0)\n        start_num = 0;\n      for (int64_t num = start_num; num < end_num; num++) {\n        Eigen::internal::TensorIntDivisor<int64_t> divider(div);\n        int64_t result = num/div;\n        int64_t result_op = divider.divide(num);\n        VERIFY_IS_EQUAL(result_op, result);\n      }\n    }\n  }\n}\n\nvoid test_specific() {\n  // A particular combination that was previously failing\n  int64_t div = 209715200;\n  int64_t num = 3238002688ll;\n  Eigen::internal::TensorIntDivisor<int64_t> divider(div);\n  int64_t result = num/div;\n  int64_t result_op = divider.divide(num);\n  VERIFY_IS_EQUAL(result, result_op);\n}\n\nvoid test_cxx11_tensor_intdiv()\n{\n  CALL_SUBTEST_1(test_signed_32bit());\n  CALL_SUBTEST_2(test_unsigned_32bit());\n  CALL_SUBTEST_3(test_signed_64bit());\n  CALL_SUBTEST_4(test_unsigned_64bit());\n  CALL_SUBTEST_5(test_powers_32bit());\n  CALL_SUBTEST_6(test_powers_64bit());\n  CALL_SUBTEST_7(test_specific());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_io.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <sstream>\n#include <string>\n#include <Eigen/CXX11/Tensor>\n\n\ntemplate<int DataLayout>\nstatic void test_output_0d()\n{\n  Tensor<int, 0, DataLayout> tensor;\n  tensor() = 123;\n\n  std::stringstream os;\n  os << tensor;\n\n  std::string expected(\"123\");\n  VERIFY_IS_EQUAL(std::string(os.str()), expected);\n}\n\n\ntemplate<int DataLayout>\nstatic void test_output_1d()\n{\n  Tensor<int, 1, DataLayout> tensor(5);\n  for (int i = 0; i < 5; ++i) {\n    tensor(i) = i;\n  }\n\n  std::stringstream os;\n  os << tensor;\n\n  std::string expected(\"0\\n1\\n2\\n3\\n4\");\n  VERIFY_IS_EQUAL(std::string(os.str()), expected);\n\n  Eigen::Tensor<double,1,DataLayout> empty_tensor(0);\n  std::stringstream empty_os;\n  empty_os << empty_tensor;\n  std::string empty_string;\n  VERIFY_IS_EQUAL(std::string(empty_os.str()), empty_string);\n}\n\n\ntemplate<int DataLayout>\nstatic void test_output_2d()\n{\n  Tensor<int, 2, DataLayout> tensor(5, 3);\n  for (int i = 0; i < 5; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      tensor(i, j) = i*j;\n    }\n  }\n\n  std::stringstream os;\n  os << tensor;\n\n  std::string expected(\"0  0  0\\n0  1  2\\n0  2  4\\n0  3  6\\n0  4  8\");\n  VERIFY_IS_EQUAL(std::string(os.str()), expected);\n}\n\n\ntemplate<int DataLayout>\nstatic void test_output_expr()\n{\n  Tensor<int, 1, DataLayout> tensor1(5);\n  Tensor<int, 1, DataLayout> tensor2(5);\n  for (int i = 0; i < 5; ++i) {\n    tensor1(i) = i;\n    tensor2(i) = 7;\n  }\n\n  std::stringstream os;\n  os << tensor1 + tensor2;\n\n  std::string expected(\" 7\\n 8\\n 9\\n10\\n11\");\n  VERIFY_IS_EQUAL(std::string(os.str()), expected);\n}\n\n\ntemplate<int DataLayout>\nstatic void test_output_string()\n{\n  Tensor<std::string, 2, DataLayout> tensor(5, 3);\n  tensor.setConstant(std::string(\"foo\"));\n\n  std::cout << tensor << std::endl;\n\n  std::stringstream os;\n  os << tensor;\n\n  std::string expected(\"foo  foo  foo\\nfoo  foo  foo\\nfoo  foo  foo\\nfoo  foo  foo\\nfoo  foo  foo\");\n  VERIFY_IS_EQUAL(std::string(os.str()), expected);\n}\n\n\ntemplate<int DataLayout>\nstatic void test_output_const()\n{\n  Tensor<int, 1, DataLayout> tensor(5);\n  for (int i = 0; i < 5; ++i) {\n    tensor(i) = i;\n  }\n\n  TensorMap<Tensor<const int, 1, DataLayout> > tensor_map(tensor.data(), 5);\n\n  std::stringstream os;\n  os << tensor_map;\n\n  std::string expected(\"0\\n1\\n2\\n3\\n4\");\n  VERIFY_IS_EQUAL(std::string(os.str()), expected);\n}\n\n\nvoid test_cxx11_tensor_io()\n{\n  CALL_SUBTEST(test_output_0d<ColMajor>());\n  CALL_SUBTEST(test_output_0d<RowMajor>());\n  CALL_SUBTEST(test_output_1d<ColMajor>());\n  CALL_SUBTEST(test_output_1d<RowMajor>());\n  CALL_SUBTEST(test_output_2d<ColMajor>());\n  CALL_SUBTEST(test_output_2d<RowMajor>());\n  CALL_SUBTEST(test_output_expr<ColMajor>());\n  CALL_SUBTEST(test_output_expr<RowMajor>());\n  CALL_SUBTEST(test_output_string<ColMajor>());\n  CALL_SUBTEST(test_output_string<RowMajor>());\n  CALL_SUBTEST(test_output_const<ColMajor>());\n  CALL_SUBTEST(test_output_const<RowMajor>());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_layout_swap.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\n\nstatic void test_simple_swap()\n{\n  Tensor<float, 3, ColMajor> tensor(2,3,7);\n  tensor.setRandom();\n\n  Tensor<float, 3, RowMajor> tensor2 = tensor.swap_layout();\n  VERIFY_IS_EQUAL(tensor.dimension(0), tensor2.dimension(2));\n  VERIFY_IS_EQUAL(tensor.dimension(1), tensor2.dimension(1));\n  VERIFY_IS_EQUAL(tensor.dimension(2), tensor2.dimension(0));\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        VERIFY_IS_EQUAL(tensor(i,j,k), tensor2(k,j,i));\n      }\n    }\n  }\n}\n\n\nstatic void test_swap_as_lvalue()\n{\n  Tensor<float, 3, ColMajor> tensor(2,3,7);\n  tensor.setRandom();\n\n  Tensor<float, 3, RowMajor> tensor2(7,3,2);\n  tensor2.swap_layout() = tensor;\n  VERIFY_IS_EQUAL(tensor.dimension(0), tensor2.dimension(2));\n  VERIFY_IS_EQUAL(tensor.dimension(1), tensor2.dimension(1));\n  VERIFY_IS_EQUAL(tensor.dimension(2), tensor2.dimension(0));\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        VERIFY_IS_EQUAL(tensor(i,j,k), tensor2(k,j,i));\n      }\n    }\n  }\n}\n\n\nvoid test_cxx11_tensor_layout_swap()\n{\n  CALL_SUBTEST(test_simple_swap());\n  CALL_SUBTEST(test_swap_as_lvalue());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_lvalue.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\nusing Eigen::RowMajor;\n\n\nstatic void test_compound_assignment()\n{\n  Tensor<float, 3> mat1(2,3,7);\n  Tensor<float, 3> mat2(2,3,7);\n  Tensor<float, 3> mat3(2,3,7);\n\n  mat1.setRandom();\n  mat2.setRandom();\n  mat3 = mat1;\n  mat3 += mat2;\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        VERIFY_IS_APPROX(mat3(i,j,k), mat1(i,j,k) + mat2(i,j,k));\n      }\n    }\n  }\n}\n\n\nvoid test_cxx11_tensor_lvalue()\n{\n  CALL_SUBTEST(test_compound_assignment());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_map.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\nusing Eigen::RowMajor;\n\nstatic void test_0d()\n{\n  Tensor<int, 0> scalar1;\n  Tensor<int, 0, RowMajor> scalar2;\n\n  TensorMap<Tensor<const int, 0> > scalar3(scalar1.data());\n  TensorMap<Tensor<const int, 0, RowMajor> > scalar4(scalar2.data());\n\n  scalar1() = 7;\n  scalar2() = 13;\n\n  VERIFY_IS_EQUAL(scalar1.rank(), 0);\n  VERIFY_IS_EQUAL(scalar1.size(), 1);\n\n  VERIFY_IS_EQUAL(scalar3(), 7);\n  VERIFY_IS_EQUAL(scalar4(), 13);\n}\n\nstatic void test_1d()\n{\n  Tensor<int, 1> vec1(6);\n  Tensor<int, 1, RowMajor> vec2(6);\n\n  TensorMap<Tensor<const int, 1> > vec3(vec1.data(), 6);\n  TensorMap<Tensor<const int, 1, RowMajor> > vec4(vec2.data(), 6);\n\n  vec1(0) = 4;  vec2(0) = 0;\n  vec1(1) = 8;  vec2(1) = 1;\n  vec1(2) = 15; vec2(2) = 2;\n  vec1(3) = 16; vec2(3) = 3;\n  vec1(4) = 23; vec2(4) = 4;\n  vec1(5) = 42; vec2(5) = 5;\n\n  VERIFY_IS_EQUAL(vec1.rank(), 1);\n  VERIFY_IS_EQUAL(vec1.size(), 6);\n  VERIFY_IS_EQUAL(vec1.dimension(0), 6);\n\n  VERIFY_IS_EQUAL(vec3(0), 4);\n  VERIFY_IS_EQUAL(vec3(1), 8);\n  VERIFY_IS_EQUAL(vec3(2), 15);\n  VERIFY_IS_EQUAL(vec3(3), 16);\n  VERIFY_IS_EQUAL(vec3(4), 23);\n  VERIFY_IS_EQUAL(vec3(5), 42);\n\n  VERIFY_IS_EQUAL(vec4(0), 0);\n  VERIFY_IS_EQUAL(vec4(1), 1);\n  VERIFY_IS_EQUAL(vec4(2), 2);\n  VERIFY_IS_EQUAL(vec4(3), 3);\n  VERIFY_IS_EQUAL(vec4(4), 4);\n  VERIFY_IS_EQUAL(vec4(5), 5);\n}\n\nstatic void test_2d()\n{\n  Tensor<int, 2> mat1(2,3);\n  Tensor<int, 2, RowMajor> mat2(2,3);\n\n  mat1(0,0) = 0;\n  mat1(0,1) = 1;\n  mat1(0,2) = 2;\n  mat1(1,0) = 3;\n  mat1(1,1) = 4;\n  mat1(1,2) = 5;\n\n  mat2(0,0) = 0;\n  mat2(0,1) = 1;\n  mat2(0,2) = 2;\n  mat2(1,0) = 3;\n  mat2(1,1) = 4;\n  mat2(1,2) = 5;\n\n  TensorMap<Tensor<const int, 2> > mat3(mat1.data(), 2, 3);\n  TensorMap<Tensor<const int, 2, RowMajor> > mat4(mat2.data(), 2, 3);\n\n  VERIFY_IS_EQUAL(mat3.rank(), 2);\n  VERIFY_IS_EQUAL(mat3.size(), 6);\n  VERIFY_IS_EQUAL(mat3.dimension(0), 2);\n  VERIFY_IS_EQUAL(mat3.dimension(1), 3);\n\n  VERIFY_IS_EQUAL(mat4.rank(), 2);\n  VERIFY_IS_EQUAL(mat4.size(), 6);\n  VERIFY_IS_EQUAL(mat4.dimension(0), 2);\n  VERIFY_IS_EQUAL(mat4.dimension(1), 3);\n\n  VERIFY_IS_EQUAL(mat3(0,0), 0);\n  VERIFY_IS_EQUAL(mat3(0,1), 1);\n  VERIFY_IS_EQUAL(mat3(0,2), 2);\n  VERIFY_IS_EQUAL(mat3(1,0), 3);\n  VERIFY_IS_EQUAL(mat3(1,1), 4);\n  VERIFY_IS_EQUAL(mat3(1,2), 5);\n\n  VERIFY_IS_EQUAL(mat4(0,0), 0);\n  VERIFY_IS_EQUAL(mat4(0,1), 1);\n  VERIFY_IS_EQUAL(mat4(0,2), 2);\n  VERIFY_IS_EQUAL(mat4(1,0), 3);\n  VERIFY_IS_EQUAL(mat4(1,1), 4);\n  VERIFY_IS_EQUAL(mat4(1,2), 5);\n}\n\nstatic void test_3d()\n{\n  Tensor<int, 3> mat1(2,3,7);\n  Tensor<int, 3, RowMajor> mat2(2,3,7);\n\n  int val = 0;\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        mat1(i,j,k) = val;\n        mat2(i,j,k) = val;\n        val++;\n      }\n    }\n  }\n\n  TensorMap<Tensor<const int, 3> > mat3(mat1.data(), 2, 3, 7);\n  TensorMap<Tensor<const int, 3, RowMajor> > mat4(mat2.data(), 2, 3, 7);\n\n  VERIFY_IS_EQUAL(mat3.rank(), 3);\n  VERIFY_IS_EQUAL(mat3.size(), 2*3*7);\n  VERIFY_IS_EQUAL(mat3.dimension(0), 2);\n  VERIFY_IS_EQUAL(mat3.dimension(1), 3);\n  VERIFY_IS_EQUAL(mat3.dimension(2), 7);\n\n  VERIFY_IS_EQUAL(mat4.rank(), 3);\n  VERIFY_IS_EQUAL(mat4.size(), 2*3*7);\n  VERIFY_IS_EQUAL(mat4.dimension(0), 2);\n  VERIFY_IS_EQUAL(mat4.dimension(1), 3);\n  VERIFY_IS_EQUAL(mat4.dimension(2), 7);\n\n  val = 0;\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        VERIFY_IS_EQUAL(mat3(i,j,k), val);\n        VERIFY_IS_EQUAL(mat4(i,j,k), val);\n        val++;\n      }\n    }\n  }\n}\n\n\nstatic void test_from_tensor()\n{\n  Tensor<int, 3> mat1(2,3,7);\n  Tensor<int, 3, RowMajor> mat2(2,3,7);\n\n  int val = 0;\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        mat1(i,j,k) = val;\n        mat2(i,j,k) = val;\n        val++;\n      }\n    }\n  }\n\n  TensorMap<Tensor<int, 3> > mat3(mat1);\n  TensorMap<Tensor<int, 3, RowMajor> > mat4(mat2);\n\n  VERIFY_IS_EQUAL(mat3.rank(), 3);\n  VERIFY_IS_EQUAL(mat3.size(), 2*3*7);\n  VERIFY_IS_EQUAL(mat3.dimension(0), 2);\n  VERIFY_IS_EQUAL(mat3.dimension(1), 3);\n  VERIFY_IS_EQUAL(mat3.dimension(2), 7);\n\n  VERIFY_IS_EQUAL(mat4.rank(), 3);\n  VERIFY_IS_EQUAL(mat4.size(), 2*3*7);\n  VERIFY_IS_EQUAL(mat4.dimension(0), 2);\n  VERIFY_IS_EQUAL(mat4.dimension(1), 3);\n  VERIFY_IS_EQUAL(mat4.dimension(2), 7);\n\n  val = 0;\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        VERIFY_IS_EQUAL(mat3(i,j,k), val);\n        VERIFY_IS_EQUAL(mat4(i,j,k), val);\n        val++;\n      }\n    }\n  }\n\n  TensorFixedSize<int, Sizes<2,3,7> > mat5;\n\n  val = 0;\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        array<ptrdiff_t, 3> coords;\n        coords[0] = i;\n        coords[1] = j;\n        coords[2] = k;\n        mat5(coords) = val;\n        val++;\n      }\n    }\n  }\n\n  TensorMap<TensorFixedSize<int, Sizes<2,3,7> > > mat6(mat5);\n\n  VERIFY_IS_EQUAL(mat6.rank(), 3);\n  VERIFY_IS_EQUAL(mat6.size(), 2*3*7);\n  VERIFY_IS_EQUAL(mat6.dimension(0), 2);\n  VERIFY_IS_EQUAL(mat6.dimension(1), 3);\n  VERIFY_IS_EQUAL(mat6.dimension(2), 7);\n\n  val = 0;\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        VERIFY_IS_EQUAL(mat6(i,j,k), val);\n        val++;\n      }\n    }\n  }\n}\n\n\nstatic int f(const TensorMap<Tensor<int, 3> >& tensor) {\n  //  Size<0> empty;\n  EIGEN_STATIC_ASSERT((internal::array_size<Sizes<> >::value == 0), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  EIGEN_STATIC_ASSERT((internal::array_size<DSizes<int, 0> >::value == 0), YOU_MADE_A_PROGRAMMING_MISTAKE);\n  Tensor<int, 0> result = tensor.sum();\n  return result();\n}\n\nstatic void test_casting()\n{\n  Tensor<int, 3> tensor(2,3,7);\n\n  int val = 0;\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        tensor(i,j,k) = val;\n        val++;\n      }\n    }\n  }\n\n  TensorMap<Tensor<int, 3> > map(tensor);\n  int sum1 = f(map);\n  int sum2 = f(tensor);\n\n  VERIFY_IS_EQUAL(sum1, sum2);\n  VERIFY_IS_EQUAL(sum1, 861);\n}\n\nvoid test_cxx11_tensor_map()\n{\n  CALL_SUBTEST(test_0d());\n  CALL_SUBTEST(test_1d());\n  CALL_SUBTEST(test_2d());\n  CALL_SUBTEST(test_3d());\n\n  CALL_SUBTEST(test_from_tensor());\n  CALL_SUBTEST(test_casting());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_math.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\nusing Eigen::RowMajor;\n\nstatic void test_tanh()\n{\n  Tensor<float, 1> vec1(6);\n  vec1.setRandom();\n\n  Tensor<float, 1> vec2 = vec1.tanh();\n\n  for (int i = 0; i < 6; ++i) {\n    VERIFY_IS_APPROX(vec2(i), tanhf(vec1(i)));\n  }\n}\n\nstatic void test_sigmoid()\n{\n  Tensor<float, 1> vec1(6);\n  vec1.setRandom();\n\n  Tensor<float, 1> vec2 = vec1.sigmoid();\n\n  for (int i = 0; i < 6; ++i) {\n    VERIFY_IS_APPROX(vec2(i), 1.0f / (1.0f + std::exp(-vec1(i))));\n  }\n}\n\n\nvoid test_cxx11_tensor_math()\n{\n  CALL_SUBTEST(test_tanh());\n  CALL_SUBTEST(test_sigmoid());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_mixed_indices.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\n\nstatic void test_simple()\n{\n  Tensor<float, 1, ColMajor> vec1(6);\n  Tensor<float, 1, ColMajor, int> vec2(6);\n\n  vec1(0) = 4.0;  vec2(0) = 0.0;\n  vec1(1) = 8.0;  vec2(1) = 1.0;\n  vec1(2) = 15.0; vec2(2) = 2.0;\n  vec1(3) = 16.0; vec2(3) = 3.0;\n  vec1(4) = 23.0; vec2(4) = 4.0;\n  vec1(5) = 42.0; vec2(5) = 5.0;\n\n  float data3[6];\n  TensorMap<Tensor<float, 1, ColMajor>> vec3(data3, 6);\n  vec3 = vec1.sqrt();\n  float data4[6];\n  TensorMap<Tensor<float, 1, ColMajor, int>> vec4(data4, 6);\n  vec4 = vec2.square();\n\n  VERIFY_IS_APPROX(vec3(0), sqrtf(4.0));\n  VERIFY_IS_APPROX(vec3(1), sqrtf(8.0));\n  VERIFY_IS_APPROX(vec3(2), sqrtf(15.0));\n  VERIFY_IS_APPROX(vec3(3), sqrtf(16.0));\n  VERIFY_IS_APPROX(vec3(4), sqrtf(23.0));\n  VERIFY_IS_APPROX(vec3(5), sqrtf(42.0));\n\n  VERIFY_IS_APPROX(vec4(0), 0.0f);\n  VERIFY_IS_APPROX(vec4(1), 1.0f);\n  VERIFY_IS_APPROX(vec4(2), 2.0f * 2.0f);\n  VERIFY_IS_APPROX(vec4(3), 3.0f * 3.0f);\n  VERIFY_IS_APPROX(vec4(4), 4.0f * 4.0f);\n  VERIFY_IS_APPROX(vec4(5), 5.0f * 5.0f);\n}\n\n\nvoid test_cxx11_tensor_mixed_indices()\n{\n  CALL_SUBTEST(test_simple());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_morphing.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\n\ntemplate<typename>\nstatic void test_simple_reshape()\n{\n  Tensor<float, 5> tensor1(2,3,1,7,1);\n  tensor1.setRandom();\n\n  Tensor<float, 3> tensor2(2,3,7);\n  Tensor<float, 2> tensor3(6,7);\n  Tensor<float, 2> tensor4(2,21);\n\n  Tensor<float, 3>::Dimensions dim1(2,3,7);\n  tensor2 = tensor1.reshape(dim1);\n  Tensor<float, 2>::Dimensions dim2(6,7);\n  tensor3 = tensor1.reshape(dim2);\n  Tensor<float, 2>::Dimensions dim3(2,21);\n  tensor4 = tensor1.reshape(dim1).reshape(dim3);\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        VERIFY_IS_EQUAL(tensor1(i,j,0,k,0), tensor2(i,j,k));\n        VERIFY_IS_EQUAL(tensor1(i,j,0,k,0), tensor3(i+2*j,k));\n        VERIFY_IS_EQUAL(tensor1(i,j,0,k,0), tensor4(i,j+3*k));\n      }\n    }\n  }\n}\n\ntemplate<typename>\nstatic void test_reshape_in_expr() {\n  MatrixXf m1(2,3*5*7*11);\n  MatrixXf m2(3*5*7*11,13);\n  m1.setRandom();\n  m2.setRandom();\n  MatrixXf m3 = m1 * m2;\n\n  TensorMap<Tensor<float, 5>> tensor1(m1.data(), 2,3,5,7,11);\n  TensorMap<Tensor<float, 5>> tensor2(m2.data(), 3,5,7,11,13);\n  Tensor<float, 2>::Dimensions newDims1(2,3*5*7*11);\n  Tensor<float, 2>::Dimensions newDims2(3*5*7*11,13);\n  typedef Tensor<float, 1>::DimensionPair DimPair;\n  array<DimPair, 1> contract_along{{DimPair(1, 0)}};\n  Tensor<float, 2> tensor3(2,13);\n  tensor3 = tensor1.reshape(newDims1).contract(tensor2.reshape(newDims2), contract_along);\n\n  Map<MatrixXf> res(tensor3.data(), 2, 13);\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 13; ++j) {\n      VERIFY_IS_APPROX(res(i,j), m3(i,j));\n    }\n  }\n}\n\ntemplate<typename>\nstatic void test_reshape_as_lvalue()\n{\n  Tensor<float, 3> tensor(2,3,7);\n  tensor.setRandom();\n\n  Tensor<float, 2> tensor2d(6,7);\n  Tensor<float, 3>::Dimensions dim(2,3,7);\n  tensor2d.reshape(dim) = tensor;\n\n  float scratch[2*3*1*7*1];\n  TensorMap<Tensor<float, 5>> tensor5d(scratch, 2,3,1,7,1);\n  tensor5d.reshape(dim).device(Eigen::DefaultDevice()) = tensor;\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        VERIFY_IS_EQUAL(tensor2d(i+2*j,k), tensor(i,j,k));\n        VERIFY_IS_EQUAL(tensor5d(i,j,0,k,0), tensor(i,j,k));\n      }\n    }\n  }\n}\n\ntemplate<int DataLayout>\nstatic void test_simple_slice()\n{\n  Tensor<float, 5, DataLayout> tensor(2,3,5,7,11);\n  tensor.setRandom();\n\n  Tensor<float, 5, DataLayout> slice1(1,1,1,1,1);\n  Eigen::DSizes<ptrdiff_t, 5> indices(1,2,3,4,5);\n  Eigen::DSizes<ptrdiff_t, 5> sizes(1,1,1,1,1);\n  slice1 = tensor.slice(indices, sizes);\n  VERIFY_IS_EQUAL(slice1(0,0,0,0,0), tensor(1,2,3,4,5));\n\n  Tensor<float, 5, DataLayout> slice2(1,1,2,2,3);\n  Eigen::DSizes<ptrdiff_t, 5> indices2(1,1,3,4,5);\n  Eigen::DSizes<ptrdiff_t, 5> sizes2(1,1,2,2,3);\n  slice2 = tensor.slice(indices2, sizes2);\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 2; ++j) {\n      for (int k = 0; k < 3; ++k) {\n        VERIFY_IS_EQUAL(slice2(0,0,i,j,k), tensor(1,1,3+i,4+j,5+k));\n      }\n    }\n  }\n}\n\ntemplate<typename=void>\nstatic void test_const_slice()\n{\n  const float b[1] = {42};\n  TensorMap<Tensor<const float, 1> > m(b, 1);\n  DSizes<DenseIndex, 1> offsets;\n  offsets[0] = 0;\n  TensorRef<Tensor<const float, 1> > slice_ref(m.slice(offsets, m.dimensions()));\n  VERIFY_IS_EQUAL(slice_ref(0), 42);\n}\n\ntemplate<int DataLayout>\nstatic void test_slice_in_expr() {\n  typedef Matrix<float, Dynamic, Dynamic, DataLayout> Mtx;\n  Mtx m1(7,7);\n  Mtx m2(3,3);\n  m1.setRandom();\n  m2.setRandom();\n\n  Mtx m3 = m1.block(1, 2, 3, 3) * m2.block(0, 2, 3, 1);\n\n  TensorMap<Tensor<float, 2, DataLayout>> tensor1(m1.data(), 7, 7);\n  TensorMap<Tensor<float, 2, DataLayout>> tensor2(m2.data(), 3, 3);\n  Tensor<float, 2, DataLayout> tensor3(3,1);\n  typedef Tensor<float, 1>::DimensionPair DimPair;\n  array<DimPair, 1> contract_along{{DimPair(1, 0)}};\n\n  Eigen::DSizes<ptrdiff_t, 2> indices1(1,2);\n  Eigen::DSizes<ptrdiff_t, 2> sizes1(3,3);\n  Eigen::DSizes<ptrdiff_t, 2> indices2(0,2);\n  Eigen::DSizes<ptrdiff_t, 2> sizes2(3,1);\n  tensor3 = tensor1.slice(indices1, sizes1).contract(tensor2.slice(indices2, sizes2), contract_along);\n\n  Map<Mtx> res(tensor3.data(), 3, 1);\n  for (int i = 0; i < 3; ++i) {\n    for (int j = 0; j < 1; ++j) {\n      VERIFY_IS_APPROX(res(i,j), m3(i,j));\n    }\n  }\n\n  // Take an arbitrary slice of an arbitrarily sized tensor.\n  TensorMap<Tensor<const float, 2, DataLayout>> tensor4(m1.data(), 7, 7);\n  Tensor<float, 1, DataLayout> tensor6 = tensor4.reshape(DSizes<ptrdiff_t, 1>(7*7)).exp().slice(DSizes<ptrdiff_t, 1>(0), DSizes<ptrdiff_t, 1>(35));\n  for (int i = 0; i < 35; ++i) {\n    VERIFY_IS_APPROX(tensor6(i), expf(tensor4.data()[i]));\n  }\n}\n\ntemplate<int DataLayout>\nstatic void test_slice_as_lvalue()\n{\n  Tensor<float, 3, DataLayout> tensor1(2,2,7);\n  tensor1.setRandom();\n  Tensor<float, 3, DataLayout> tensor2(2,2,7);\n  tensor2.setRandom();\n  Tensor<float, 3, DataLayout> tensor3(4,3,5);\n  tensor3.setRandom();\n  Tensor<float, 3, DataLayout> tensor4(4,3,2);\n  tensor4.setRandom();\n  Tensor<float, 3, DataLayout> tensor5(10,13,12);\n  tensor5.setRandom();\n\n  Tensor<float, 3, DataLayout> result(4,5,7);\n  Eigen::DSizes<ptrdiff_t, 3> sizes12(2,2,7);\n  Eigen::DSizes<ptrdiff_t, 3> first_slice(0,0,0);\n  result.slice(first_slice, sizes12) = tensor1;\n  Eigen::DSizes<ptrdiff_t, 3> second_slice(2,0,0);\n  result.slice(second_slice, sizes12).device(Eigen::DefaultDevice()) = tensor2;\n\n  Eigen::DSizes<ptrdiff_t, 3> sizes3(4,3,5);\n  Eigen::DSizes<ptrdiff_t, 3> third_slice(0,2,0);\n  result.slice(third_slice, sizes3) = tensor3;\n\n  Eigen::DSizes<ptrdiff_t, 3> sizes4(4,3,2);\n  Eigen::DSizes<ptrdiff_t, 3> fourth_slice(0,2,5);\n  result.slice(fourth_slice, sizes4) = tensor4;\n\n  for (int j = 0; j < 2; ++j) {\n    for (int k = 0; k < 7; ++k) {\n      for (int i = 0; i < 2; ++i) {\n        VERIFY_IS_EQUAL(result(i,j,k), tensor1(i,j,k));\n        VERIFY_IS_EQUAL(result(i+2,j,k), tensor2(i,j,k));\n      }\n    }\n  }\n  for (int i = 0; i < 4; ++i) {\n    for (int j = 2; j < 5; ++j) {\n      for (int k = 0; k < 5; ++k) {\n        VERIFY_IS_EQUAL(result(i,j,k), tensor3(i,j-2,k));\n      }\n      for (int k = 5; k < 7; ++k) {\n        VERIFY_IS_EQUAL(result(i,j,k), tensor4(i,j-2,k-5));\n      }\n    }\n  }\n\n  Eigen::DSizes<ptrdiff_t, 3> sizes5(4,5,7);\n  Eigen::DSizes<ptrdiff_t, 3> fifth_slice(0,0,0);\n  result.slice(fifth_slice, sizes5) = tensor5.slice(fifth_slice, sizes5);\n  for (int i = 0; i < 4; ++i) {\n    for (int j = 2; j < 5; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        VERIFY_IS_EQUAL(result(i,j,k), tensor5(i,j,k));\n      }\n    }\n  }\n}\n\ntemplate<int DataLayout>\nstatic void test_slice_raw_data()\n{\n  Tensor<float, 4, DataLayout> tensor(3,5,7,11);\n  tensor.setRandom();\n\n  Eigen::DSizes<ptrdiff_t, 4> offsets(1,2,3,4);\n  Eigen::DSizes<ptrdiff_t, 4> extents(1,1,1,1);\n  typedef TensorEvaluator<decltype(tensor.slice(offsets, extents)), DefaultDevice> SliceEvaluator;\n  auto slice1 = SliceEvaluator(tensor.slice(offsets, extents), DefaultDevice());\n  VERIFY_IS_EQUAL(slice1.dimensions().TotalSize(), 1);\n  VERIFY_IS_EQUAL(slice1.data()[0], tensor(1,2,3,4));\n\n  if (DataLayout == ColMajor) {\n    extents = Eigen::DSizes<ptrdiff_t, 4>(2,1,1,1);\n    auto slice2 = SliceEvaluator(tensor.slice(offsets, extents), DefaultDevice());\n    VERIFY_IS_EQUAL(slice2.dimensions().TotalSize(), 2);\n    VERIFY_IS_EQUAL(slice2.data()[0], tensor(1,2,3,4));\n    VERIFY_IS_EQUAL(slice2.data()[1], tensor(2,2,3,4));\n  } else {\n    extents = Eigen::DSizes<ptrdiff_t, 4>(1,1,1,2);\n    auto slice2 = SliceEvaluator(tensor.slice(offsets, extents), DefaultDevice());\n    VERIFY_IS_EQUAL(slice2.dimensions().TotalSize(), 2);\n    VERIFY_IS_EQUAL(slice2.data()[0], tensor(1,2,3,4));\n    VERIFY_IS_EQUAL(slice2.data()[1], tensor(1,2,3,5));\n  }\n\n  extents = Eigen::DSizes<ptrdiff_t, 4>(1,2,1,1);\n  auto slice3 = SliceEvaluator(tensor.slice(offsets, extents), DefaultDevice());\n  VERIFY_IS_EQUAL(slice3.dimensions().TotalSize(), 2);\n  VERIFY_IS_EQUAL(slice3.data(), static_cast<float*>(0));\n\n  if (DataLayout == ColMajor) {\n    offsets = Eigen::DSizes<ptrdiff_t, 4>(0,2,3,4);\n    extents = Eigen::DSizes<ptrdiff_t, 4>(3,2,1,1);\n    auto slice4 = SliceEvaluator(tensor.slice(offsets, extents), DefaultDevice());\n    VERIFY_IS_EQUAL(slice4.dimensions().TotalSize(), 6);\n    for (int i = 0; i < 3; ++i) {\n      for (int j = 0; j < 2; ++j) {\n        VERIFY_IS_EQUAL(slice4.data()[i+3*j], tensor(i,2+j,3,4));\n      }\n    }\n  } else {\n    offsets = Eigen::DSizes<ptrdiff_t, 4>(1,2,3,0);\n    extents = Eigen::DSizes<ptrdiff_t, 4>(1,1,2,11);\n    auto slice4 = SliceEvaluator(tensor.slice(offsets, extents), DefaultDevice());\n    VERIFY_IS_EQUAL(slice4.dimensions().TotalSize(), 22);\n    for (int l = 0; l < 11; ++l) {\n      for (int k = 0; k < 2; ++k) {\n        VERIFY_IS_EQUAL(slice4.data()[l+11*k], tensor(1,2,3+k,l));\n      }\n    }\n  }\n\n  if (DataLayout == ColMajor) {\n    offsets = Eigen::DSizes<ptrdiff_t, 4>(0,0,0,4);\n    extents = Eigen::DSizes<ptrdiff_t, 4>(3,5,7,2);\n    auto slice5 = SliceEvaluator(tensor.slice(offsets, extents), DefaultDevice());\n    VERIFY_IS_EQUAL(slice5.dimensions().TotalSize(), 210);\n    for (int i = 0; i < 3; ++i) {\n      for (int j = 0; j < 5; ++j) {\n        for (int k = 0; k < 7; ++k) {\n          for (int l = 0; l < 2; ++l) {\n            int slice_index = i + 3 * (j + 5 * (k + 7 * l));\n            VERIFY_IS_EQUAL(slice5.data()[slice_index], tensor(i,j,k,l+4));\n          }\n        }\n      }\n    }\n  } else {\n    offsets = Eigen::DSizes<ptrdiff_t, 4>(1,0,0,0);\n    extents = Eigen::DSizes<ptrdiff_t, 4>(2,5,7,11);\n    auto slice5 = SliceEvaluator(tensor.slice(offsets, extents), DefaultDevice());\n    VERIFY_IS_EQUAL(slice5.dimensions().TotalSize(), 770);\n    for (int l = 0; l < 11; ++l) {\n      for (int k = 0; k < 7; ++k) {\n        for (int j = 0; j < 5; ++j) {\n          for (int i = 0; i < 2; ++i) {\n            int slice_index = l + 11 * (k + 7 * (j + 5 * i));\n            VERIFY_IS_EQUAL(slice5.data()[slice_index], tensor(i+1,j,k,l));\n          }\n        }\n      }\n    }\n\n  }\n\n  offsets = Eigen::DSizes<ptrdiff_t, 4>(0,0,0,0);\n  extents = Eigen::DSizes<ptrdiff_t, 4>(3,5,7,11);\n  auto slice6 = SliceEvaluator(tensor.slice(offsets, extents), DefaultDevice());\n  VERIFY_IS_EQUAL(slice6.dimensions().TotalSize(), 3*5*7*11);\n  VERIFY_IS_EQUAL(slice6.data(), tensor.data());\n}\n\n\ntemplate<int DataLayout>\nstatic void test_strided_slice()\n{\n  typedef Tensor<float, 5, DataLayout> Tensor5f;\n  typedef Eigen::DSizes<Eigen::DenseIndex, 5> Index5;\n  typedef Tensor<float, 2, DataLayout> Tensor2f;\n  typedef Eigen::DSizes<Eigen::DenseIndex, 2> Index2;\n  Tensor<float, 5, DataLayout> tensor(2,3,5,7,11);\n  Tensor<float, 2, DataLayout> tensor2(7,11);\n  tensor.setRandom();\n  tensor2.setRandom();\n\n  if (true) {\n    Tensor2f slice(2,3);\n    Index2 strides(-2,-1);\n    Index2 indicesStart(5,7);\n    Index2 indicesStop(0,4);\n    slice = tensor2.stridedSlice(indicesStart, indicesStop, strides);\n    for (int j = 0; j < 2; ++j) {\n      for (int k = 0; k < 3; ++k) {\n        VERIFY_IS_EQUAL(slice(j,k), tensor2(5-2*j,7-k));\n      }\n    }\n  }\n\n  if(true) {\n    Tensor2f slice(0,1);\n    Index2 strides(1,1);\n    Index2 indicesStart(5,4);\n    Index2 indicesStop(5,5);\n    slice = tensor2.stridedSlice(indicesStart, indicesStop, strides);\n  }\n\n  if(true) { // test clamped degenerate interavls\n    Tensor2f slice(7,11);\n    Index2 strides(1,-1);\n    Index2 indicesStart(-3,20); // should become 0,10\n    Index2 indicesStop(20,-11); // should become 11, -1\n    slice = tensor2.stridedSlice(indicesStart, indicesStop, strides);\n    for (int j = 0; j < 7; ++j) {\n      for (int k = 0; k < 11; ++k) {\n        VERIFY_IS_EQUAL(slice(j,k), tensor2(j,10-k));\n      }\n    }\n  }\n\n  if(true) {\n    Tensor5f slice1(1,1,1,1,1);\n    Eigen::DSizes<Eigen::DenseIndex, 5> indicesStart(1, 2, 3, 4, 5);\n    Eigen::DSizes<Eigen::DenseIndex, 5> indicesStop(2, 3, 4, 5, 6);\n    Eigen::DSizes<Eigen::DenseIndex, 5> strides(1, 1, 1, 1, 1);\n    slice1 = tensor.stridedSlice(indicesStart, indicesStop, strides);\n    VERIFY_IS_EQUAL(slice1(0,0,0,0,0), tensor(1,2,3,4,5));\n  }\n\n  if(true) {\n    Tensor5f slice(1,1,2,2,3);\n    Index5 start(1, 1, 3, 4, 5);\n    Index5 stop(2, 2, 5, 6, 8);\n    Index5 strides(1, 1, 1, 1, 1);\n    slice = tensor.stridedSlice(start, stop, strides);\n    for (int i = 0; i < 2; ++i) {\n      for (int j = 0; j < 2; ++j) {\n        for (int k = 0; k < 3; ++k) {\n          VERIFY_IS_EQUAL(slice(0,0,i,j,k), tensor(1,1,3+i,4+j,5+k));\n        }\n      }\n    }\n  }\n\n  if(true) {\n    Tensor5f slice(1,1,2,2,3);\n    Index5 strides3(1, 1, -2, 1, -1);\n    Index5 indices3Start(1, 1, 4, 4, 7);\n    Index5 indices3Stop(2, 2, 0, 6, 4);\n    slice = tensor.stridedSlice(indices3Start, indices3Stop, strides3);\n    for (int i = 0; i < 2; ++i) {\n      for (int j = 0; j < 2; ++j) {\n        for (int k = 0; k < 3; ++k) {\n          VERIFY_IS_EQUAL(slice(0,0,i,j,k), tensor(1,1,4-2*i,4+j,7-k));\n        }\n      }\n    }\n  }\n\n  if(false) { // tests degenerate interval\n    Tensor5f slice(1,1,2,2,3);\n    Index5 strides3(1, 1, 2, 1, 1);\n    Index5 indices3Start(1, 1, 4, 4, 7);\n    Index5 indices3Stop(2, 2, 0, 6, 4);\n    slice = tensor.stridedSlice(indices3Start, indices3Stop, strides3);\n  }\n}\n\ntemplate<int DataLayout>\nstatic void test_strided_slice_write()\n{\n  typedef Tensor<float, 2, DataLayout> Tensor2f;\n  typedef Eigen::DSizes<Eigen::DenseIndex, 2> Index2;\n\n  Tensor<float, 2, DataLayout> tensor(7,11),tensor2(7,11);\n  tensor.setRandom();\n  tensor2=tensor;\n  Tensor2f slice(2,3);\n\n  slice.setRandom();\n\n  Index2 strides(1,1);\n  Index2 indicesStart(3,4);\n  Index2 indicesStop(5,7);\n  Index2 lengths(2,3);\n\n  tensor.slice(indicesStart,lengths)=slice;\n  tensor2.stridedSlice(indicesStart,indicesStop,strides)=slice;\n\n  for(int i=0;i<7;i++) for(int j=0;j<11;j++){\n    VERIFY_IS_EQUAL(tensor(i,j), tensor2(i,j));\n  }\n}\n\n\ntemplate<int DataLayout>\nstatic void test_composition()\n{\n  Eigen::Tensor<float, 2, DataLayout> matrix(7, 11);\n  matrix.setRandom();\n\n  const DSizes<ptrdiff_t, 3> newDims(1, 1, 11);\n  Eigen::Tensor<float, 3, DataLayout> tensor =\n      matrix.slice(DSizes<ptrdiff_t, 2>(2, 0), DSizes<ptrdiff_t, 2>(1, 11)).reshape(newDims);\n\n  VERIFY_IS_EQUAL(tensor.dimensions().TotalSize(), 11);\n  VERIFY_IS_EQUAL(tensor.dimension(0), 1);\n  VERIFY_IS_EQUAL(tensor.dimension(1), 1);\n  VERIFY_IS_EQUAL(tensor.dimension(2), 11);\n  for (int i = 0; i < 11; ++i) {\n    VERIFY_IS_EQUAL(tensor(0,0,i), matrix(2,i));\n  }\n}\n\n\nvoid test_cxx11_tensor_morphing()\n{\n  CALL_SUBTEST_1(test_simple_reshape<void>());\n  CALL_SUBTEST_1(test_reshape_in_expr<void>());\n  CALL_SUBTEST_1(test_reshape_as_lvalue<void>());\n\n  CALL_SUBTEST_1(test_simple_slice<ColMajor>());\n  CALL_SUBTEST_1(test_simple_slice<RowMajor>());\n  CALL_SUBTEST_1(test_const_slice());\n  CALL_SUBTEST_2(test_slice_in_expr<ColMajor>());\n  CALL_SUBTEST_3(test_slice_in_expr<RowMajor>());\n  CALL_SUBTEST_4(test_slice_as_lvalue<ColMajor>());\n  CALL_SUBTEST_4(test_slice_as_lvalue<RowMajor>());\n  CALL_SUBTEST_5(test_slice_raw_data<ColMajor>());\n  CALL_SUBTEST_5(test_slice_raw_data<RowMajor>());\n\n  CALL_SUBTEST_6(test_strided_slice_write<ColMajor>());\n  CALL_SUBTEST_6(test_strided_slice<ColMajor>());\n  CALL_SUBTEST_6(test_strided_slice_write<RowMajor>());\n  CALL_SUBTEST_6(test_strided_slice<RowMajor>());\n\n  CALL_SUBTEST_7(test_composition<ColMajor>());\n  CALL_SUBTEST_7(test_composition<RowMajor>());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_notification.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Vijay Vasudevan <vrv@google.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define EIGEN_USE_THREADS\n\n#include <stdlib.h>\n#include \"main.h\"\n#include <Eigen/CXX11/Tensor>\n\n#if EIGEN_OS_WIN || EIGEN_OS_WIN64\n#include <windows.h>\nvoid sleep(int seconds) {\n  Sleep(seconds*1000);\n}\n#else\n#include <unistd.h>\n#endif\n\n\nnamespace {\n\nvoid WaitAndAdd(Eigen::Notification* n, int* counter) {\n  n->Wait();\n  *counter = *counter + 1;\n}\n\n}  // namespace\n\nstatic void test_notification_single()\n{\n  ThreadPool thread_pool(1);\n\n  int counter = 0;\n  Eigen::Notification n;\n  std::function<void()> func = std::bind(&WaitAndAdd, &n, &counter);\n  thread_pool.Schedule(func);\n  sleep(1);\n\n  // The thread should be waiting for the notification.\n  VERIFY_IS_EQUAL(counter, 0);\n\n  // Unblock the thread\n  n.Notify();\n\n  sleep(1);\n\n  // Verify the counter has been incremented\n  VERIFY_IS_EQUAL(counter, 1);\n}\n\n// Like test_notification_single() but enqueues multiple threads to\n// validate that all threads get notified by Notify().\nstatic void test_notification_multiple()\n{\n  ThreadPool thread_pool(1);\n\n  int counter = 0;\n  Eigen::Notification n;\n  std::function<void()> func = std::bind(&WaitAndAdd, &n, &counter);\n  thread_pool.Schedule(func);\n  thread_pool.Schedule(func);\n  thread_pool.Schedule(func);\n  thread_pool.Schedule(func);\n  sleep(1);\n  VERIFY_IS_EQUAL(counter, 0);\n  n.Notify();\n  sleep(1);\n  VERIFY_IS_EQUAL(counter, 4);\n}\n\nvoid test_cxx11_tensor_notification()\n{\n  CALL_SUBTEST(test_notification_single());\n  CALL_SUBTEST(test_notification_multiple());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_of_complex.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\nusing Eigen::TensorMap;\n\n\n\nstatic void test_additions()\n{\n  Tensor<std::complex<float>, 1> data1(3);\n  Tensor<std::complex<float>, 1> data2(3);\n  for (int i = 0; i < 3; ++i) {\n    data1(i) = std::complex<float>(i, -i);\n    data2(i) = std::complex<float>(i, 7 * i);\n  }\n\n  Tensor<std::complex<float>, 1> sum = data1 + data2;\n  for (int i = 0; i < 3; ++i) {\n    VERIFY_IS_EQUAL(sum(i),  std::complex<float>(2*i, 6*i));\n  }\n}\n\n\nstatic void test_abs()\n{\n  Tensor<std::complex<float>, 1> data1(3);\n  Tensor<std::complex<double>, 1> data2(3);\n  data1.setRandom();\n  data2.setRandom();\n\n  Tensor<float, 1> abs1 = data1.abs();\n  Tensor<double, 1> abs2 = data2.abs();\n  for (int i = 0; i < 3; ++i) {\n    VERIFY_IS_APPROX(abs1(i), std::abs(data1(i)));\n    VERIFY_IS_APPROX(abs2(i), std::abs(data2(i)));\n  }\n}\n\n\nstatic void test_conjugate()\n{\n  Tensor<std::complex<float>, 1> data1(3);\n  Tensor<std::complex<double>, 1> data2(3);\n  Tensor<int, 1> data3(3);\n  data1.setRandom();\n  data2.setRandom();\n  data3.setRandom();\n\n  Tensor<std::complex<float>, 1> conj1 = data1.conjugate();\n  Tensor<std::complex<double>, 1> conj2 = data2.conjugate();\n  Tensor<int, 1> conj3 = data3.conjugate();\n  for (int i = 0; i < 3; ++i) {\n    VERIFY_IS_APPROX(conj1(i), std::conj(data1(i)));\n    VERIFY_IS_APPROX(conj2(i), std::conj(data2(i)));\n    VERIFY_IS_APPROX(conj3(i), data3(i));\n  }\n}\n\nstatic void test_contractions()\n{\n  Tensor<std::complex<float>, 4> t_left(30, 50, 8, 31);\n  Tensor<std::complex<float>, 5> t_right(8, 31, 7, 20, 10);\n  Tensor<std::complex<float>, 5> t_result(30, 50, 7, 20, 10);\n\n  t_left.setRandom();\n  t_right.setRandom();\n\n  typedef Map<Matrix<std::complex<float>, Dynamic, Dynamic>> MapXcf;\n  MapXcf m_left(t_left.data(), 1500, 248);\n  MapXcf m_right(t_right.data(), 248, 1400);\n  Matrix<std::complex<float>, Dynamic, Dynamic> m_result(1500, 1400);\n\n  // This contraction should be equivalent to a regular matrix multiplication\n  typedef Tensor<float, 1>::DimensionPair DimPair;\n  Eigen::array<DimPair, 2> dims;\n  dims[0] = DimPair(2, 0);\n  dims[1] = DimPair(3, 1);\n  t_result = t_left.contract(t_right, dims);\n  m_result = m_left * m_right;\n  for (int i = 0; i < t_result.dimensions().TotalSize(); i++) {\n    VERIFY_IS_APPROX(t_result.data()[i], m_result.data()[i]);\n  }\n}\n\n\nvoid test_cxx11_tensor_of_complex()\n{\n  CALL_SUBTEST(test_additions());\n  CALL_SUBTEST(test_abs());\n  CALL_SUBTEST(test_conjugate());\n  CALL_SUBTEST(test_contractions());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_of_const_values.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\nusing Eigen::RowMajor;\n\nstatic void test_assign()\n{\n  float data1[6];\n  TensorMap<Tensor<const float, 2>> mat1(data1, 2, 3);\n  float data2[6];\n  const TensorMap<Tensor<float, 2>> mat2(data2, 2, 3);\n\n  for (int i = 0; i < 6; ++i) {\n    data1[i] = i;\n    data2[i] = -i;\n  }\n\n  Tensor<float, 2> rslt1;\n  rslt1 = mat1;\n  Tensor<float, 2> rslt2;\n  rslt2 = mat2;\n\n  Tensor<float, 2> rslt3 = mat1;\n  Tensor<float, 2> rslt4 = mat2;\n\n  Tensor<float, 2> rslt5(mat1);\n  Tensor<float, 2> rslt6(mat2);\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      VERIFY_IS_APPROX(rslt1(i,j), static_cast<float>(i + 2*j));\n      VERIFY_IS_APPROX(rslt2(i,j), static_cast<float>(-i - 2*j));\n      VERIFY_IS_APPROX(rslt3(i,j), static_cast<float>(i + 2*j));\n      VERIFY_IS_APPROX(rslt4(i,j), static_cast<float>(-i - 2*j));\n      VERIFY_IS_APPROX(rslt5(i,j), static_cast<float>(i + 2*j));\n      VERIFY_IS_APPROX(rslt6(i,j), static_cast<float>(-i - 2*j));\n    }\n  }\n}\n\n\nstatic void test_plus()\n{\n  float data1[6];\n  TensorMap<Tensor<const float, 2>> mat1(data1, 2, 3);\n  float data2[6];\n  TensorMap<Tensor<float, 2>> mat2(data2, 2, 3);\n\n  for (int i = 0; i < 6; ++i) {\n    data1[i] = i;\n    data2[i] = -i;\n  }\n\n  Tensor<float, 2> sum1;\n  sum1 = mat1 + mat2;\n  Tensor<float, 2> sum2;\n  sum2 = mat2 + mat1;\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      VERIFY_IS_APPROX(sum1(i,j), 0.0f);\n      VERIFY_IS_APPROX(sum2(i,j), 0.0f);\n    }\n  }\n}\n\n\nstatic void test_plus_equal()\n{\n  float data1[6];\n  TensorMap<Tensor<const float, 2>> mat1(data1, 2, 3);\n  float data2[6];\n  TensorMap<Tensor<float, 2>> mat2(data2, 2, 3);\n\n  for (int i = 0; i < 6; ++i) {\n    data1[i] = i;\n    data2[i] = -i;\n  }\n  mat2 += mat1;\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      VERIFY_IS_APPROX(mat2(i,j), 0.0f);\n    }\n  }\n}\n\n\nvoid test_cxx11_tensor_of_const_values()\n{\n  CALL_SUBTEST(test_assign());\n  CALL_SUBTEST(test_plus());\n  CALL_SUBTEST(test_plus_equal());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_of_float16_cuda.cu",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define EIGEN_TEST_NO_LONGDOUBLE\n#define EIGEN_TEST_NO_COMPLEX\n#define EIGEN_TEST_FUNC cxx11_tensor_of_float16_cuda\n#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int\n#define EIGEN_USE_GPU\n\n#include \"main.h\"\n#include <unsupported/Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\n\ntemplate<typename>\nvoid test_cuda_numext() {\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n  int num_elem = 101;\n\n  float* d_float = (float*)gpu_device.allocate(num_elem * sizeof(float));\n  bool* d_res_half = (bool*)gpu_device.allocate(num_elem * sizeof(bool));\n  bool* d_res_float = (bool*)gpu_device.allocate(num_elem * sizeof(bool));\n\n  Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_float(\n      d_float, num_elem);\n  Eigen::TensorMap<Eigen::Tensor<bool, 1>, Eigen::Aligned> gpu_res_half(\n      d_res_half, num_elem);\n  Eigen::TensorMap<Eigen::Tensor<bool, 1>, Eigen::Aligned> gpu_res_float(\n      d_res_float, num_elem);\n\n  gpu_float.device(gpu_device) = gpu_float.random() - gpu_float.constant(0.5f);\n  gpu_res_float.device(gpu_device) = gpu_float.unaryExpr(Eigen::internal::scalar_isnan_op<float>());\n  gpu_res_half.device(gpu_device) = gpu_float.cast<Eigen::half>().unaryExpr(Eigen::internal::scalar_isnan_op<Eigen::half>());\n\n  Tensor<bool, 1> half_prec(num_elem);\n  Tensor<bool, 1> full_prec(num_elem);\n  gpu_device.memcpyDeviceToHost(half_prec.data(), d_res_half, num_elem*sizeof(bool));\n  gpu_device.memcpyDeviceToHost(full_prec.data(), d_res_float, num_elem*sizeof(bool));\n  gpu_device.synchronize();\n\n  for (int i = 0; i < num_elem; ++i) {\n    std::cout << \"Checking numext \" << i << std::endl;\n    VERIFY_IS_EQUAL(full_prec(i), half_prec(i));\n  }\n\n  gpu_device.deallocate(d_float);\n  gpu_device.deallocate(d_res_half);\n  gpu_device.deallocate(d_res_float);\n}\n\n\n#ifdef EIGEN_HAS_CUDA_FP16\n\ntemplate<typename>\nvoid test_cuda_conversion() {\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n  int num_elem = 101;\n  \n  float* d_float = (float*)gpu_device.allocate(num_elem * sizeof(float));\n  Eigen::half* d_half = (Eigen::half*)gpu_device.allocate(num_elem * sizeof(Eigen::half));\n  float* d_conv = (float*)gpu_device.allocate(num_elem * sizeof(float));\n\n  Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_float(\n      d_float, num_elem);\n  Eigen::TensorMap<Eigen::Tensor<Eigen::half, 1>, Eigen::Aligned> gpu_half(\n      d_half, num_elem);\n  Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_conv(\n      d_conv, num_elem);\n\n  gpu_float.device(gpu_device) = gpu_float.random();\n  gpu_half.device(gpu_device) = gpu_float.cast<Eigen::half>();\n  gpu_conv.device(gpu_device) = gpu_half.cast<float>();\n\n  Tensor<float, 1> initial(num_elem);\n  Tensor<float, 1> final(num_elem);\n  gpu_device.memcpyDeviceToHost(initial.data(), d_float, num_elem*sizeof(float));\n  gpu_device.memcpyDeviceToHost(final.data(), d_conv, num_elem*sizeof(float));\n\n  for (int i = 0; i < num_elem; ++i) {\n    VERIFY_IS_APPROX(initial(i), final(i));\n  }\n\n  gpu_device.deallocate(d_float);\n  gpu_device.deallocate(d_half);\n  gpu_device.deallocate(d_conv);\n}\n\ntemplate<typename>\nvoid test_cuda_unary() {\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n  int num_elem = 101;\n\n  float* d_float = (float*)gpu_device.allocate(num_elem * sizeof(float));\n  float* d_res_half = (float*)gpu_device.allocate(num_elem * sizeof(float));\n  float* d_res_float = (float*)gpu_device.allocate(num_elem * sizeof(float));\n\n  Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_float(\n      d_float, num_elem);\n  Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_res_half(\n      d_res_half, num_elem);\n  Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_res_float(\n      d_res_float, num_elem);\n\n  gpu_float.device(gpu_device) = gpu_float.random() - gpu_float.constant(0.5f);\n  gpu_res_float.device(gpu_device) = gpu_float.abs();\n  gpu_res_half.device(gpu_device) = gpu_float.cast<Eigen::half>().abs().cast<float>();\n\n  Tensor<float, 1> half_prec(num_elem);\n  Tensor<float, 1> full_prec(num_elem);\n  gpu_device.memcpyDeviceToHost(half_prec.data(), d_res_half, num_elem*sizeof(float));\n  gpu_device.memcpyDeviceToHost(full_prec.data(), d_res_float, num_elem*sizeof(float));\n  gpu_device.synchronize();\n\n  for (int i = 0; i < num_elem; ++i) {\n    std::cout << \"Checking unary \" << i << std::endl;\n    VERIFY_IS_APPROX(full_prec(i), half_prec(i));\n  }\n\n  gpu_device.deallocate(d_float);\n  gpu_device.deallocate(d_res_half);\n  gpu_device.deallocate(d_res_float);\n}\n\ntemplate<typename>\nvoid test_cuda_elementwise() {\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n  int num_elem = 101;\n\n  float* d_float1 = (float*)gpu_device.allocate(num_elem * sizeof(float));\n  float* d_float2 = (float*)gpu_device.allocate(num_elem * sizeof(float));\n  float* d_res_half = (float*)gpu_device.allocate(num_elem * sizeof(float));\n  float* d_res_float = (float*)gpu_device.allocate(num_elem * sizeof(float));\n\n  Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_float1(\n      d_float1, num_elem);\n  Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_float2(\n      d_float2, num_elem);\n  Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_res_half(\n      d_res_half, num_elem);\n  Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_res_float(\n      d_res_float, num_elem);\n\n  gpu_float1.device(gpu_device) = gpu_float1.random();\n  gpu_float2.device(gpu_device) = gpu_float2.random();\n  gpu_res_float.device(gpu_device) = (gpu_float1 + gpu_float2) * gpu_float1;\n  gpu_res_half.device(gpu_device) = ((gpu_float1.cast<Eigen::half>() + gpu_float2.cast<Eigen::half>()) * gpu_float1.cast<Eigen::half>()).cast<float>();\n\n  Tensor<float, 1> half_prec(num_elem);\n  Tensor<float, 1> full_prec(num_elem);\n  gpu_device.memcpyDeviceToHost(half_prec.data(), d_res_half, num_elem*sizeof(float));\n  gpu_device.memcpyDeviceToHost(full_prec.data(), d_res_float, num_elem*sizeof(float));\n  gpu_device.synchronize();\n\n  for (int i = 0; i < num_elem; ++i) {\n    std::cout << \"Checking elemwise \" << i << \": full prec = \" << full_prec(i) << \" vs half prec = \" << half_prec(i) << std::endl;\n    VERIFY_IS_APPROX(static_cast<Eigen::half>(full_prec(i)), static_cast<Eigen::half>(half_prec(i)));\n  }\n\n  gpu_device.deallocate(d_float1);\n  gpu_device.deallocate(d_float2);\n  gpu_device.deallocate(d_res_half);\n  gpu_device.deallocate(d_res_float);\n}\n\ntemplate<typename>\nvoid test_cuda_trancendental() {\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n  int num_elem = 101;\n\n  float* d_float1 = (float*)gpu_device.allocate(num_elem * sizeof(float));\n  float* d_float2 = (float*)gpu_device.allocate(num_elem * sizeof(float));\n  float* d_float3 = (float*)gpu_device.allocate(num_elem * sizeof(float));\n  Eigen::half* d_res1_half = (Eigen::half*)gpu_device.allocate(num_elem * sizeof(Eigen::half));\n  Eigen::half* d_res1_float = (Eigen::half*)gpu_device.allocate(num_elem * sizeof(Eigen::half));\n  Eigen::half* d_res2_half = (Eigen::half*)gpu_device.allocate(num_elem * sizeof(Eigen::half));\n  Eigen::half* d_res2_float = (Eigen::half*)gpu_device.allocate(num_elem * sizeof(Eigen::half));\n  Eigen::half* d_res3_half = (Eigen::half*)gpu_device.allocate(num_elem * sizeof(Eigen::half));\n  Eigen::half* d_res3_float = (Eigen::half*)gpu_device.allocate(num_elem * sizeof(Eigen::half));\n\n  Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_float1(d_float1, num_elem);\n  Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_float2(d_float2, num_elem);\n  Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_float3(d_float3, num_elem);\n  Eigen::TensorMap<Eigen::Tensor<Eigen::half, 1>, Eigen::Aligned> gpu_res1_half(d_res1_half, num_elem);\n  Eigen::TensorMap<Eigen::Tensor<Eigen::half, 1>, Eigen::Aligned> gpu_res1_float(d_res1_float, num_elem);\n  Eigen::TensorMap<Eigen::Tensor<Eigen::half, 1>, Eigen::Aligned> gpu_res2_half(d_res2_half, num_elem);\n  Eigen::TensorMap<Eigen::Tensor<Eigen::half, 1>, Eigen::Aligned> gpu_res2_float(d_res2_float, num_elem);\n  Eigen::TensorMap<Eigen::Tensor<Eigen::half, 1>, Eigen::Aligned> gpu_res3_half(d_res3_half, num_elem);\n  Eigen::TensorMap<Eigen::Tensor<Eigen::half, 1>, Eigen::Aligned> gpu_res3_float(d_res3_float, num_elem);\n\n  gpu_float1.device(gpu_device) = gpu_float1.random() - gpu_float1.constant(0.5f);\n  gpu_float2.device(gpu_device) = gpu_float2.random() + gpu_float1.constant(0.5f);\n  gpu_float3.device(gpu_device) = gpu_float3.random();\n  gpu_res1_float.device(gpu_device) = gpu_float1.exp().cast<Eigen::half>();\n  gpu_res2_float.device(gpu_device) = gpu_float2.log().cast<Eigen::half>();\n  gpu_res3_float.device(gpu_device) = gpu_float3.log1p().cast<Eigen::half>();\n\n  gpu_res1_half.device(gpu_device) = gpu_float1.cast<Eigen::half>();\n  gpu_res1_half.device(gpu_device) = gpu_res1_half.exp();\n\n  gpu_res2_half.device(gpu_device) = gpu_float2.cast<Eigen::half>();\n  gpu_res2_half.device(gpu_device) = gpu_res2_half.log();\n\n  gpu_res3_half.device(gpu_device) = gpu_float3.cast<Eigen::half>();\n  gpu_res3_half.device(gpu_device) = gpu_res3_half.log1p();\n\n  Tensor<float, 1> input1(num_elem);\n  Tensor<Eigen::half, 1> half_prec1(num_elem);\n  Tensor<Eigen::half, 1> full_prec1(num_elem);\n  Tensor<float, 1> input2(num_elem);\n  Tensor<Eigen::half, 1> half_prec2(num_elem);\n  Tensor<Eigen::half, 1> full_prec2(num_elem);\n  Tensor<float, 1> input3(num_elem);\n  Tensor<Eigen::half, 1> half_prec3(num_elem);\n  Tensor<Eigen::half, 1> full_prec3(num_elem);\n  gpu_device.memcpyDeviceToHost(input1.data(), d_float1, num_elem*sizeof(float));\n  gpu_device.memcpyDeviceToHost(input2.data(), d_float2, num_elem*sizeof(float));\n  gpu_device.memcpyDeviceToHost(input3.data(), d_float3, num_elem*sizeof(float));\n  gpu_device.memcpyDeviceToHost(half_prec1.data(), d_res1_half, num_elem*sizeof(Eigen::half));\n  gpu_device.memcpyDeviceToHost(full_prec1.data(), d_res1_float, num_elem*sizeof(Eigen::half));\n  gpu_device.memcpyDeviceToHost(half_prec2.data(), d_res2_half, num_elem*sizeof(Eigen::half));\n  gpu_device.memcpyDeviceToHost(full_prec2.data(), d_res2_float, num_elem*sizeof(Eigen::half));\n  gpu_device.memcpyDeviceToHost(half_prec3.data(), d_res3_half, num_elem*sizeof(Eigen::half));\n  gpu_device.memcpyDeviceToHost(full_prec3.data(), d_res3_float, num_elem*sizeof(Eigen::half));\n  gpu_device.synchronize();\n\n  for (int i = 0; i < num_elem; ++i) {\n    std::cout << \"Checking elemwise exp \" << i << \" input = \" << input1(i) << \" full = \" << full_prec1(i) << \" half = \" << half_prec1(i) << std::endl;\n    VERIFY_IS_APPROX(full_prec1(i), half_prec1(i));\n  }\n  for (int i = 0; i < num_elem; ++i) {\n    std::cout << \"Checking elemwise log \" << i << \" input = \" << input2(i) << \" full = \" << full_prec2(i) << \" half = \" << half_prec2(i) << std::endl;\n    if(std::abs(input2(i)-1.f)<0.05f) // log lacks accurary nearby 1\n      VERIFY_IS_APPROX(full_prec2(i)+Eigen::half(0.1f), half_prec2(i)+Eigen::half(0.1f));\n    else\n      VERIFY_IS_APPROX(full_prec2(i), half_prec2(i));\n  }\n  for (int i = 0; i < num_elem; ++i) {\n    std::cout << \"Checking elemwise plog1 \" << i << \" input = \" << input3(i) << \" full = \" << full_prec3(i) << \" half = \" << half_prec3(i) << std::endl;\n    VERIFY_IS_APPROX(full_prec3(i), half_prec3(i));\n  }\n  gpu_device.deallocate(d_float1);\n  gpu_device.deallocate(d_float2);\n  gpu_device.deallocate(d_float3);\n  gpu_device.deallocate(d_res1_half);\n  gpu_device.deallocate(d_res1_float);\n  gpu_device.deallocate(d_res2_half);\n  gpu_device.deallocate(d_res2_float);\n  gpu_device.deallocate(d_res3_float);\n  gpu_device.deallocate(d_res3_half);\n}\n\ntemplate<typename>\nvoid test_cuda_contractions() {\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n  int rows = 23;\n  int cols = 23;\n  int num_elem = rows*cols;\n\n  float* d_float1 = (float*)gpu_device.allocate(num_elem * sizeof(float));\n  float* d_float2 = (float*)gpu_device.allocate(num_elem * sizeof(float));\n  Eigen::half* d_res_half = (Eigen::half*)gpu_device.allocate(num_elem * sizeof(Eigen::half));\n  Eigen::half* d_res_float = (Eigen::half*)gpu_device.allocate(num_elem * sizeof(Eigen::half));\n\n  Eigen::TensorMap<Eigen::Tensor<float, 2>, Eigen::Aligned> gpu_float1(\n      d_float1, rows, cols);\n  Eigen::TensorMap<Eigen::Tensor<float, 2>, Eigen::Aligned> gpu_float2(\n      d_float2, rows, cols);\n  Eigen::TensorMap<Eigen::Tensor<Eigen::half, 2>, Eigen::Aligned> gpu_res_half(\n      d_res_half, rows, cols);\n  Eigen::TensorMap<Eigen::Tensor<Eigen::half, 2>, Eigen::Aligned> gpu_res_float(\n      d_res_float, rows, cols);\n\n  gpu_float1.device(gpu_device) = gpu_float1.random() - gpu_float1.constant(0.5f);\n  gpu_float2.device(gpu_device) = gpu_float2.random() - gpu_float2.constant(0.5f);\n\n  typedef Tensor<float, 2>::DimensionPair DimPair;\n  Eigen::array<DimPair, 1> dims(DimPair(1, 0));\n  gpu_res_float.device(gpu_device) = gpu_float1.contract(gpu_float2, dims).cast<Eigen::half>();\n  gpu_res_half.device(gpu_device) = gpu_float1.cast<Eigen::half>().contract(gpu_float2.cast<Eigen::half>(), dims);\n\n  Tensor<Eigen::half, 2> half_prec(rows, cols);\n  Tensor<Eigen::half, 2> full_prec(rows, cols);\n  gpu_device.memcpyDeviceToHost(half_prec.data(), d_res_half, num_elem*sizeof(Eigen::half));\n  gpu_device.memcpyDeviceToHost(full_prec.data(), d_res_float, num_elem*sizeof(Eigen::half));\n  gpu_device.synchronize();\n\n  for (int i = 0; i < rows; ++i) {\n    for (int j = 0; j < cols; ++j) {\n      std::cout << \"Checking contract \" << i << \" \" << j << full_prec(i, j) << \" \" << half_prec(i, j) << std::endl;\n      if (numext::abs(full_prec(i, j) - half_prec(i, j)) > Eigen::half(1e-2f)) {\n        VERIFY_IS_APPROX(full_prec(i, j), half_prec(i, j));\n      }\n    }\n  }\n\n  gpu_device.deallocate(d_float1);\n  gpu_device.deallocate(d_float2);\n  gpu_device.deallocate(d_res_half);\n  gpu_device.deallocate(d_res_float);\n}\n\ntemplate<typename>\nvoid test_cuda_reductions(int size1, int size2, int redux) {\n\n   std::cout << \"Reducing \" << size1 << \" by \" << size2\n             << \" tensor along dim \" << redux << std::endl; \n\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n  int num_elem = size1*size2;\n  int result_size = (redux == 1 ? size1 : size2);\n\n  float* d_float1 = (float*)gpu_device.allocate(num_elem * sizeof(float));\n  float* d_float2 = (float*)gpu_device.allocate(num_elem * sizeof(float));\n  Eigen::half* d_res_half = (Eigen::half*)gpu_device.allocate(result_size * sizeof(Eigen::half));\n  Eigen::half* d_res_float = (Eigen::half*)gpu_device.allocate(result_size * sizeof(Eigen::half));\n\n  Eigen::TensorMap<Eigen::Tensor<float, 2>, Eigen::Aligned> gpu_float1(\n      d_float1, size1, size2);\n  Eigen::TensorMap<Eigen::Tensor<float, 2>, Eigen::Aligned> gpu_float2(\n      d_float2, size1, size2);\n  Eigen::TensorMap<Eigen::Tensor<Eigen::half, 1>, Eigen::Aligned> gpu_res_half(\n      d_res_half, result_size);\n  Eigen::TensorMap<Eigen::Tensor<Eigen::half, 1>, Eigen::Aligned> gpu_res_float(\n      d_res_float, result_size);\n\n  gpu_float1.device(gpu_device) = gpu_float1.random() * 2.0f;\n  gpu_float2.device(gpu_device) = gpu_float2.random() * 2.0f;\n\n  Eigen::array<int, 1> redux_dim = {{redux}};\n  gpu_res_float.device(gpu_device) = gpu_float1.sum(redux_dim).cast<Eigen::half>();\n  gpu_res_half.device(gpu_device) = gpu_float1.cast<Eigen::half>().sum(redux_dim);\n\n  Tensor<Eigen::half, 1> half_prec(result_size);\n  Tensor<Eigen::half, 1> full_prec(result_size);\n  gpu_device.memcpyDeviceToHost(half_prec.data(), d_res_half, result_size*sizeof(Eigen::half));\n  gpu_device.memcpyDeviceToHost(full_prec.data(), d_res_float, result_size*sizeof(Eigen::half));\n  gpu_device.synchronize();\n\n  for (int i = 0; i < result_size; ++i) {\n    std::cout << \"EXPECTED \" << full_prec(i) << \" GOT \" << half_prec(i) << std::endl;\n    VERIFY_IS_APPROX(full_prec(i), half_prec(i));\n  }\n\n  gpu_device.deallocate(d_float1);\n  gpu_device.deallocate(d_float2);\n  gpu_device.deallocate(d_res_half);\n  gpu_device.deallocate(d_res_float);\n}\n\ntemplate<typename>\nvoid test_cuda_reductions() {\n  test_cuda_reductions<void>(13, 13, 0);\n  test_cuda_reductions<void>(13, 13, 1);\n\n  test_cuda_reductions<void>(35, 36, 0);\n  test_cuda_reductions<void>(35, 36, 1);\n\n  test_cuda_reductions<void>(36, 35, 0);\n  test_cuda_reductions<void>(36, 35, 1);\n}\n\ntemplate<typename>\nvoid test_cuda_full_reductions() {\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n  int size = 13;\n  int num_elem = size*size;\n\n  float* d_float1 = (float*)gpu_device.allocate(num_elem * sizeof(float));\n  float* d_float2 = (float*)gpu_device.allocate(num_elem * sizeof(float));\n  Eigen::half* d_res_half = (Eigen::half*)gpu_device.allocate(1 * sizeof(Eigen::half));\n  Eigen::half* d_res_float = (Eigen::half*)gpu_device.allocate(1 * sizeof(Eigen::half));\n\n  Eigen::TensorMap<Eigen::Tensor<float, 2>, Eigen::Aligned> gpu_float1(\n      d_float1, size, size);\n  Eigen::TensorMap<Eigen::Tensor<float, 2>, Eigen::Aligned> gpu_float2(\n      d_float2, size, size);\n  Eigen::TensorMap<Eigen::Tensor<Eigen::half, 0>, Eigen::Aligned> gpu_res_half(\n      d_res_half);\n  Eigen::TensorMap<Eigen::Tensor<Eigen::half, 0>, Eigen::Aligned> gpu_res_float(\n      d_res_float);\n\n  gpu_float1.device(gpu_device) = gpu_float1.random();\n  gpu_float2.device(gpu_device) = gpu_float2.random();\n\n  gpu_res_float.device(gpu_device) = gpu_float1.sum().cast<Eigen::half>();\n  gpu_res_half.device(gpu_device) = gpu_float1.cast<Eigen::half>().sum();\n\n  Tensor<Eigen::half, 0> half_prec;\n  Tensor<Eigen::half, 0> full_prec;\n  gpu_device.memcpyDeviceToHost(half_prec.data(), d_res_half, sizeof(Eigen::half));\n  gpu_device.memcpyDeviceToHost(full_prec.data(), d_res_float, sizeof(Eigen::half));\n  gpu_device.synchronize();\n\n  VERIFY_IS_APPROX(full_prec(), half_prec());\n\n  gpu_res_float.device(gpu_device) = gpu_float1.maximum().cast<Eigen::half>();\n  gpu_res_half.device(gpu_device) = gpu_float1.cast<Eigen::half>().maximum();\n  gpu_device.memcpyDeviceToHost(half_prec.data(), d_res_half, sizeof(Eigen::half));\n  gpu_device.memcpyDeviceToHost(full_prec.data(), d_res_float, sizeof(Eigen::half));\n  gpu_device.synchronize();\n\n  VERIFY_IS_APPROX(full_prec(), half_prec());\n\n  gpu_device.deallocate(d_float1);\n  gpu_device.deallocate(d_float2);\n  gpu_device.deallocate(d_res_half);\n  gpu_device.deallocate(d_res_float);\n}\n\ntemplate<typename>\nvoid test_cuda_forced_evals() {\n\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n  int num_elem = 101;\n\n  float* d_float = (float*)gpu_device.allocate(num_elem * sizeof(float));\n  float* d_res_half1 = (float*)gpu_device.allocate(num_elem * sizeof(float));\n  float* d_res_half2 = (float*)gpu_device.allocate(num_elem * sizeof(float));\n  float* d_res_float = (float*)gpu_device.allocate(num_elem * sizeof(float));\n\n  Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_float(\n      d_float, num_elem);\n  Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_res_half1(\n      d_res_half1, num_elem);\n Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Unaligned> gpu_res_half2(\n      d_res_half2, num_elem);\n  Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_res_float(\n      d_res_float, num_elem);\n\n  Eigen::array<int, 1> no_bcast;\n  no_bcast[0] = 1;\n\n  gpu_float.device(gpu_device) = gpu_float.random() - gpu_float.constant(0.5f);\n  gpu_res_float.device(gpu_device) = gpu_float.abs();\n  gpu_res_half1.device(gpu_device) = gpu_float.cast<Eigen::half>().abs().eval().cast<float>();\n  gpu_res_half2.device(gpu_device) = gpu_float.cast<Eigen::half>().abs().broadcast(no_bcast).eval().cast<float>();\n\n  Tensor<float, 1> half_prec1(num_elem);\n  Tensor<float, 1> half_prec2(num_elem);\n  Tensor<float, 1> full_prec(num_elem);\n  gpu_device.memcpyDeviceToHost(half_prec1.data(), d_res_half1, num_elem*sizeof(float));\n  gpu_device.memcpyDeviceToHost(half_prec2.data(), d_res_half1, num_elem*sizeof(float));\n  gpu_device.memcpyDeviceToHost(full_prec.data(), d_res_float, num_elem*sizeof(float));\n  gpu_device.synchronize();\n\n  for (int i = 0; i < num_elem; ++i) {\n    std::cout << \"Checking forced eval \" << i << full_prec(i) << \" vs \" << half_prec1(i) << \" vs \" << half_prec2(i) << std::endl;\n    VERIFY_IS_APPROX(full_prec(i), half_prec1(i));\n    VERIFY_IS_APPROX(full_prec(i), half_prec2(i));\n  }\n\n  gpu_device.deallocate(d_float);\n  gpu_device.deallocate(d_res_half1);\n  gpu_device.deallocate(d_res_half2);\n  gpu_device.deallocate(d_res_float);\n}\n#endif\n\n\nvoid test_cxx11_tensor_of_float16_cuda()\n{\n  CALL_SUBTEST_1(test_cuda_numext<void>());\n\n#ifdef EIGEN_HAS_CUDA_FP16\n  CALL_SUBTEST_1(test_cuda_conversion<void>());\n  CALL_SUBTEST_1(test_cuda_unary<void>());\n  CALL_SUBTEST_1(test_cuda_elementwise<void>());\n  CALL_SUBTEST_1(test_cuda_trancendental<void>());\n  CALL_SUBTEST_2(test_cuda_contractions<void>());\n  CALL_SUBTEST_3(test_cuda_reductions<void>());\n  CALL_SUBTEST_4(test_cuda_full_reductions<void>());\n  CALL_SUBTEST_5(test_cuda_forced_evals<void>());\n#else\n  std::cout << \"Half floats are not supported by this version of cuda: skipping the test\" << std::endl;\n#endif\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_of_strings.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\nusing Eigen::TensorMap;\n\nstatic void test_assign()\n{\n  std::string data1[6];\n  TensorMap<Tensor<std::string, 2>> mat1(data1, 2, 3);\n  std::string data2[6];\n  const TensorMap<Tensor<const std::string, 2>> mat2(data2, 2, 3);\n\n  for (int i = 0; i < 6; ++i) {\n    std::ostringstream s1;\n    s1 << \"abc\" << i*3;\n    data1[i] = s1.str();\n    std::ostringstream s2;\n    s2 << \"def\" << i*5;\n    data2[i] = s2.str();\n  }\n\n  Tensor<std::string, 2> rslt1;\n  rslt1 = mat1;\n  Tensor<std::string, 2> rslt2;\n  rslt2 = mat2;\n\n  Tensor<std::string, 2> rslt3 = mat1;\n  Tensor<std::string, 2> rslt4 = mat2;\n\n  Tensor<std::string, 2> rslt5(mat1);\n  Tensor<std::string, 2> rslt6(mat2);\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      VERIFY_IS_EQUAL(rslt1(i,j), data1[i+2*j]);\n      VERIFY_IS_EQUAL(rslt2(i,j), data2[i+2*j]);\n      VERIFY_IS_EQUAL(rslt3(i,j), data1[i+2*j]);\n      VERIFY_IS_EQUAL(rslt4(i,j), data2[i+2*j]);\n      VERIFY_IS_EQUAL(rslt5(i,j), data1[i+2*j]);\n      VERIFY_IS_EQUAL(rslt6(i,j), data2[i+2*j]);\n    }\n  }\n}\n\n\nstatic void test_concat()\n{\n  Tensor<std::string, 2> t1(2, 3);\n  Tensor<std::string, 2> t2(2, 3);\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      std::ostringstream s1;\n      s1 << \"abc\" << i + j*2;\n      t1(i, j) = s1.str();\n      std::ostringstream s2;\n      s2 << \"def\" << i*5 + j*32;\n      t2(i, j) = s2.str();\n    }\n  }\n\n  Tensor<std::string, 2> result = t1.concatenate(t2, 1);\n  VERIFY_IS_EQUAL(result.dimension(0), 2);\n  VERIFY_IS_EQUAL(result.dimension(1), 6);\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      VERIFY_IS_EQUAL(result(i, j),   t1(i, j));\n      VERIFY_IS_EQUAL(result(i, j+3), t2(i, j));\n    }\n  }\n}\n\n\nstatic void test_slices()\n{\n  Tensor<std::string, 2> data(2, 6);\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      std::ostringstream s1;\n      s1 << \"abc\" << i + j*2;\n      data(i, j) = s1.str();\n    }\n  }\n\n  const Eigen::DSizes<ptrdiff_t, 2> half_size(2, 3);\n  const Eigen::DSizes<ptrdiff_t, 2> first_half(0, 0);\n  const Eigen::DSizes<ptrdiff_t, 2> second_half(0, 3);\n\n  Tensor<std::string, 2> t1 = data.slice(first_half, half_size);\n  Tensor<std::string, 2> t2 = data.slice(second_half, half_size);\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      VERIFY_IS_EQUAL(data(i, j),   t1(i, j));\n      VERIFY_IS_EQUAL(data(i, j+3), t2(i, j));\n    }\n  }\n}\n\n\nstatic void test_additions()\n{\n  Tensor<std::string, 1> data1(3);\n  Tensor<std::string, 1> data2(3);\n  for (int i = 0; i < 3; ++i) {\n    data1(i) = \"abc\";\n    std::ostringstream s1;\n    s1 << i;\n    data2(i) = s1.str();\n  }\n\n  Tensor<std::string, 1> sum = data1 + data2;\n  for (int i = 0; i < 3; ++i) {\n    std::ostringstream concat;\n    concat << \"abc\" << i;\n    std::string expected = concat.str();\n    VERIFY_IS_EQUAL(sum(i), expected);\n  }\n}\n\n\nstatic void test_initialization()\n{\n  Tensor<std::string, 2> a(2, 3);\n  a.setConstant(std::string(\"foo\"));\n  for (int i = 0; i < 2*3; ++i) {\n    VERIFY_IS_EQUAL(a(i), std::string(\"foo\"));\n  }\n}\n\n\nvoid test_cxx11_tensor_of_strings()\n{\n  // Beware: none of this is likely to ever work on a GPU.\n  CALL_SUBTEST(test_assign());\n  CALL_SUBTEST(test_concat());\n  CALL_SUBTEST(test_slices());\n  CALL_SUBTEST(test_additions());\n  CALL_SUBTEST(test_initialization());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_padding.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\n\ntemplate<int DataLayout>\nstatic void test_simple_padding()\n{\n  Tensor<float, 4, DataLayout> tensor(2,3,5,7);\n  tensor.setRandom();\n\n  array<std::pair<ptrdiff_t, ptrdiff_t>, 4> paddings;\n  paddings[0] = std::make_pair(0, 0);\n  paddings[1] = std::make_pair(2, 1);\n  paddings[2] = std::make_pair(3, 4);\n  paddings[3] = std::make_pair(0, 0);\n\n  Tensor<float, 4, DataLayout> padded;\n  padded = tensor.pad(paddings);\n\n  VERIFY_IS_EQUAL(padded.dimension(0), 2+0);\n  VERIFY_IS_EQUAL(padded.dimension(1), 3+3);\n  VERIFY_IS_EQUAL(padded.dimension(2), 5+7);\n  VERIFY_IS_EQUAL(padded.dimension(3), 7+0);\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 6; ++j) {\n      for (int k = 0; k < 12; ++k) {\n        for (int l = 0; l < 7; ++l) {\n          if (j >= 2 && j < 5 && k >= 3 && k < 8) {\n            VERIFY_IS_EQUAL(padded(i,j,k,l), tensor(i,j-2,k-3,l));\n          } else {\n            VERIFY_IS_EQUAL(padded(i,j,k,l), 0.0f);\n          }\n        }\n      }\n    }\n  }\n}\n\ntemplate<int DataLayout>\nstatic void test_padded_expr()\n{\n  Tensor<float, 4, DataLayout> tensor(2,3,5,7);\n  tensor.setRandom();\n\n  array<std::pair<ptrdiff_t, ptrdiff_t>, 4> paddings;\n  paddings[0] = std::make_pair(0, 0);\n  paddings[1] = std::make_pair(2, 1);\n  paddings[2] = std::make_pair(3, 4);\n  paddings[3] = std::make_pair(0, 0);\n\n  Eigen::DSizes<ptrdiff_t, 2> reshape_dims;\n  reshape_dims[0] = 12;\n  reshape_dims[1] = 84;\n\n  Tensor<float, 2, DataLayout> result;\n  result = tensor.pad(paddings).reshape(reshape_dims);\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 6; ++j) {\n      for (int k = 0; k < 12; ++k) {\n        for (int l = 0; l < 7; ++l) {\n          const float result_value = DataLayout == ColMajor ?\n              result(i+2*j,k+12*l) : result(j+6*i,l+7*k);\n          if (j >= 2 && j < 5 && k >= 3 && k < 8) {\n            VERIFY_IS_EQUAL(result_value, tensor(i,j-2,k-3,l));\n          } else {\n            VERIFY_IS_EQUAL(result_value, 0.0f);\n          }\n        }\n      }\n    }\n  }\n}\n\nvoid test_cxx11_tensor_padding()\n{\n  CALL_SUBTEST(test_simple_padding<ColMajor>());\n  CALL_SUBTEST(test_simple_padding<RowMajor>());\n  CALL_SUBTEST(test_padded_expr<ColMajor>());\n  CALL_SUBTEST(test_padded_expr<RowMajor>());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_patch.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\n\ntemplate<int DataLayout>\nstatic void test_simple_patch()\n{\n  Tensor<float, 4, DataLayout> tensor(2,3,5,7);\n  tensor.setRandom();\n  array<ptrdiff_t, 4> patch_dims;\n\n  patch_dims[0] = 1;\n  patch_dims[1] = 1;\n  patch_dims[2] = 1;\n  patch_dims[3] = 1;\n\n  Tensor<float, 5, DataLayout> no_patch;\n  no_patch = tensor.extract_patches(patch_dims);\n\n  if (DataLayout == ColMajor) {\n    VERIFY_IS_EQUAL(no_patch.dimension(0), 1);\n    VERIFY_IS_EQUAL(no_patch.dimension(1), 1);\n    VERIFY_IS_EQUAL(no_patch.dimension(2), 1);\n    VERIFY_IS_EQUAL(no_patch.dimension(3), 1);\n    VERIFY_IS_EQUAL(no_patch.dimension(4), tensor.size());\n  } else {\n    VERIFY_IS_EQUAL(no_patch.dimension(0), tensor.size());\n    VERIFY_IS_EQUAL(no_patch.dimension(1), 1);\n    VERIFY_IS_EQUAL(no_patch.dimension(2), 1);\n    VERIFY_IS_EQUAL(no_patch.dimension(3), 1);\n    VERIFY_IS_EQUAL(no_patch.dimension(4), 1);\n  }\n\n  for (int i = 0; i < tensor.size(); ++i) {\n    VERIFY_IS_EQUAL(tensor.data()[i], no_patch.data()[i]);\n  }\n\n  patch_dims[0] = 2;\n  patch_dims[1] = 3;\n  patch_dims[2] = 5;\n  patch_dims[3] = 7;\n  Tensor<float, 5, DataLayout> single_patch;\n  single_patch = tensor.extract_patches(patch_dims);\n\n  if (DataLayout == ColMajor) {\n    VERIFY_IS_EQUAL(single_patch.dimension(0), 2);\n    VERIFY_IS_EQUAL(single_patch.dimension(1), 3);\n    VERIFY_IS_EQUAL(single_patch.dimension(2), 5);\n    VERIFY_IS_EQUAL(single_patch.dimension(3), 7);\n    VERIFY_IS_EQUAL(single_patch.dimension(4), 1);\n  } else {\n    VERIFY_IS_EQUAL(single_patch.dimension(0), 1);\n    VERIFY_IS_EQUAL(single_patch.dimension(1), 2);\n    VERIFY_IS_EQUAL(single_patch.dimension(2), 3);\n    VERIFY_IS_EQUAL(single_patch.dimension(3), 5);\n    VERIFY_IS_EQUAL(single_patch.dimension(4), 7);\n  }\n\n  for (int i = 0; i < tensor.size(); ++i) {\n    VERIFY_IS_EQUAL(tensor.data()[i], single_patch.data()[i]);\n  }\n\n  patch_dims[0] = 1;\n  patch_dims[1] = 2;\n  patch_dims[2] = 2;\n  patch_dims[3] = 1;\n  Tensor<float, 5, DataLayout> twod_patch;\n  twod_patch = tensor.extract_patches(patch_dims);\n\n  if (DataLayout == ColMajor) {\n    VERIFY_IS_EQUAL(twod_patch.dimension(0), 1);\n    VERIFY_IS_EQUAL(twod_patch.dimension(1), 2);\n    VERIFY_IS_EQUAL(twod_patch.dimension(2), 2);\n    VERIFY_IS_EQUAL(twod_patch.dimension(3), 1);\n    VERIFY_IS_EQUAL(twod_patch.dimension(4), 2*2*4*7);\n  } else {\n    VERIFY_IS_EQUAL(twod_patch.dimension(0), 2*2*4*7);\n    VERIFY_IS_EQUAL(twod_patch.dimension(1), 1);\n    VERIFY_IS_EQUAL(twod_patch.dimension(2), 2);\n    VERIFY_IS_EQUAL(twod_patch.dimension(3), 2);\n    VERIFY_IS_EQUAL(twod_patch.dimension(4), 1);\n  }\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 2; ++j) {\n      for (int k = 0; k < 4; ++k) {\n        for (int l = 0; l < 7; ++l) {\n          int patch_loc;\n          if (DataLayout == ColMajor) {\n            patch_loc = i + 2 * (j + 2 * (k + 4 * l));\n          } else {\n            patch_loc = l + 7 * (k + 4 * (j + 2 * i));\n          }\n          for (int x = 0; x < 2; ++x) {\n            for (int y = 0; y < 2; ++y) {\n              if (DataLayout == ColMajor) {\n                VERIFY_IS_EQUAL(tensor(i,j+x,k+y,l), twod_patch(0,x,y,0,patch_loc));\n              } else {\n                VERIFY_IS_EQUAL(tensor(i,j+x,k+y,l), twod_patch(patch_loc,0,x,y,0));\n              }\n            }\n          }\n        }\n      }\n    }\n  }\n\n  patch_dims[0] = 1;\n  patch_dims[1] = 2;\n  patch_dims[2] = 3;\n  patch_dims[3] = 5;\n  Tensor<float, 5, DataLayout> threed_patch;\n  threed_patch = tensor.extract_patches(patch_dims);\n\n  if (DataLayout == ColMajor) {\n    VERIFY_IS_EQUAL(threed_patch.dimension(0), 1);\n    VERIFY_IS_EQUAL(threed_patch.dimension(1), 2);\n    VERIFY_IS_EQUAL(threed_patch.dimension(2), 3);\n    VERIFY_IS_EQUAL(threed_patch.dimension(3), 5);\n    VERIFY_IS_EQUAL(threed_patch.dimension(4), 2*2*3*3);\n  } else {\n    VERIFY_IS_EQUAL(threed_patch.dimension(0), 2*2*3*3);\n    VERIFY_IS_EQUAL(threed_patch.dimension(1), 1);\n    VERIFY_IS_EQUAL(threed_patch.dimension(2), 2);\n    VERIFY_IS_EQUAL(threed_patch.dimension(3), 3);\n    VERIFY_IS_EQUAL(threed_patch.dimension(4), 5);\n  }\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 2; ++j) {\n      for (int k = 0; k < 3; ++k) {\n        for (int l = 0; l < 3; ++l) {\n          int patch_loc;\n          if (DataLayout == ColMajor) {\n            patch_loc = i + 2 * (j + 2 * (k + 3 * l));\n          } else {\n            patch_loc = l + 3 * (k + 3 * (j + 2 * i));\n          }\n          for (int x = 0; x < 2; ++x) {\n            for (int y = 0; y < 3; ++y) {\n              for (int z = 0; z < 5; ++z) {\n                if (DataLayout == ColMajor) {\n                  VERIFY_IS_EQUAL(tensor(i,j+x,k+y,l+z), threed_patch(0,x,y,z,patch_loc));\n                } else {\n                  VERIFY_IS_EQUAL(tensor(i,j+x,k+y,l+z), threed_patch(patch_loc,0,x,y,z));\n                }\n              }\n            }\n          }\n        }\n      }\n    }\n  }\n}\n\nvoid test_cxx11_tensor_patch()\n{\n   CALL_SUBTEST(test_simple_patch<ColMajor>());\n   CALL_SUBTEST(test_simple_patch<RowMajor>());\n   //   CALL_SUBTEST(test_expr_shuffling());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_random.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\nstatic void test_default()\n{\n  Tensor<float, 1> vec(6);\n  vec.setRandom();\n\n  // Fixme: we should check that the generated numbers follow a uniform\n  // distribution instead.\n  for (int i = 1; i < 6; ++i) {\n    VERIFY_IS_NOT_EQUAL(vec(i), vec(i-1));\n  }\n}\n\nstatic void test_normal()\n{\n  Tensor<float, 1> vec(6);\n  vec.setRandom<Eigen::internal::NormalRandomGenerator<float>>();\n\n  // Fixme: we should check that the generated numbers follow a gaussian\n  // distribution instead.\n  for (int i = 1; i < 6; ++i) {\n    VERIFY_IS_NOT_EQUAL(vec(i), vec(i-1));\n  }\n}\n\n\nstruct MyGenerator {\n  MyGenerator() { }\n  MyGenerator(const MyGenerator&) { }\n\n  // Return a random value to be used.  \"element_location\" is the\n  // location of the entry to set in the tensor, it can typically\n  // be ignored.\n  int operator()(Eigen::DenseIndex element_location, Eigen::DenseIndex /*unused*/ = 0) const {\n    return static_cast<int>(3 * element_location);\n  }\n\n  // Same as above but generates several numbers at a time.\n  internal::packet_traits<int>::type packetOp(\n      Eigen::DenseIndex packet_location, Eigen::DenseIndex /*unused*/ = 0) const {\n    const int packetSize = internal::packet_traits<int>::size;\n    EIGEN_ALIGN_MAX int values[packetSize];\n    for (int i = 0; i < packetSize; ++i) {\n      values[i] = static_cast<int>(3 * (packet_location + i));\n    }\n    return internal::pload<typename internal::packet_traits<int>::type>(values);\n  }\n};\n\n\nstatic void test_custom()\n{\n  Tensor<int, 1> vec(6);\n  vec.setRandom<MyGenerator>();\n\n  for (int i = 0; i < 6; ++i) {\n    VERIFY_IS_EQUAL(vec(i), 3*i);\n  }\n}\n\nvoid test_cxx11_tensor_random()\n{\n  CALL_SUBTEST(test_default());\n  CALL_SUBTEST(test_normal());\n  CALL_SUBTEST(test_custom());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_random_cuda.cu",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define EIGEN_TEST_NO_LONGDOUBLE\n#define EIGEN_TEST_NO_COMPLEX\n#define EIGEN_TEST_FUNC cxx11_tensor_random_cuda\n#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int\n#define EIGEN_USE_GPU\n\n#include \"main.h\"\n#include <Eigen/CXX11/Tensor>\n\n\nvoid test_cuda_random_uniform()\n{\n  Tensor<float, 2> out(72,97);\n  out.setZero();\n\n  std::size_t out_bytes = out.size() * sizeof(float);\n\n  float* d_out;\n  cudaMalloc((void**)(&d_out), out_bytes);\n\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n\n  Eigen::TensorMap<Eigen::Tensor<float, 2> > gpu_out(d_out, 72,97);\n\n  gpu_out.device(gpu_device) = gpu_out.random();\n\n  assert(cudaMemcpyAsync(out.data(), d_out, out_bytes, cudaMemcpyDeviceToHost, gpu_device.stream()) == cudaSuccess);\n  assert(cudaStreamSynchronize(gpu_device.stream()) == cudaSuccess);\n\n  // For now we just check thes code doesn't crash.\n  // TODO: come up with a valid test of randomness\n}\n\n\nvoid test_cuda_random_normal()\n{\n  Tensor<float, 2> out(72,97);\n  out.setZero();\n\n  std::size_t out_bytes = out.size() * sizeof(float);\n\n  float* d_out;\n  cudaMalloc((void**)(&d_out), out_bytes);\n\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n\n  Eigen::TensorMap<Eigen::Tensor<float, 2> > gpu_out(d_out, 72,97);\n\n  Eigen::internal::NormalRandomGenerator<float> gen(true);\n  gpu_out.device(gpu_device) = gpu_out.random(gen);\n\n  assert(cudaMemcpyAsync(out.data(), d_out, out_bytes, cudaMemcpyDeviceToHost, gpu_device.stream()) == cudaSuccess);\n  assert(cudaStreamSynchronize(gpu_device.stream()) == cudaSuccess);\n}\n\nstatic void test_complex()\n{\n  Tensor<std::complex<float>, 1> vec(6);\n  vec.setRandom();\n\n  // Fixme: we should check that the generated numbers follow a uniform\n  // distribution instead.\n  for (int i = 1; i < 6; ++i) {\n    VERIFY_IS_NOT_EQUAL(vec(i), vec(i-1));\n  }\n}\n\n\nvoid test_cxx11_tensor_random_cuda()\n{\n  CALL_SUBTEST(test_cuda_random_uniform());\n  CALL_SUBTEST(test_cuda_random_normal());\n  CALL_SUBTEST(test_complex());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_reduction.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <limits>\n#include <numeric>\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\n\ntemplate <int DataLayout>\nstatic void test_trivial_reductions() {\n  {\n    Tensor<float, 0, DataLayout> tensor;\n    tensor.setRandom();\n    array<ptrdiff_t, 0> reduction_axis;\n\n    Tensor<float, 0, DataLayout> result = tensor.sum(reduction_axis);\n    VERIFY_IS_EQUAL(result(), tensor());\n  }\n\n  {\n    Tensor<float, 1, DataLayout> tensor(7);\n    tensor.setRandom();\n    array<ptrdiff_t, 0> reduction_axis;\n\n    Tensor<float, 1, DataLayout> result = tensor.sum(reduction_axis);\n    VERIFY_IS_EQUAL(result.dimension(0), 7);\n    for (int i = 0; i < 7; ++i) {\n      VERIFY_IS_EQUAL(result(i), tensor(i));\n    }\n  }\n\n  {\n    Tensor<float, 2, DataLayout> tensor(2, 3);\n    tensor.setRandom();\n    array<ptrdiff_t, 0> reduction_axis;\n\n    Tensor<float, 2, DataLayout> result = tensor.sum(reduction_axis);\n    VERIFY_IS_EQUAL(result.dimension(0), 2);\n    VERIFY_IS_EQUAL(result.dimension(1), 3);\n    for (int i = 0; i < 2; ++i) {\n      for (int j = 0; j < 3; ++j) {\n        VERIFY_IS_EQUAL(result(i, j), tensor(i, j));\n      }\n    }\n  }\n}\n\ntemplate <int DataLayout>\nstatic void test_simple_reductions() {\n  Tensor<float, 4, DataLayout> tensor(2, 3, 5, 7);\n  tensor.setRandom();\n  array<ptrdiff_t, 2> reduction_axis2;\n  reduction_axis2[0] = 1;\n  reduction_axis2[1] = 3;\n\n  Tensor<float, 2, DataLayout> result = tensor.sum(reduction_axis2);\n  VERIFY_IS_EQUAL(result.dimension(0), 2);\n  VERIFY_IS_EQUAL(result.dimension(1), 5);\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 5; ++j) {\n      float sum = 0.0f;\n      for (int k = 0; k < 3; ++k) {\n        for (int l = 0; l < 7; ++l) {\n          sum += tensor(i, k, j, l);\n        }\n      }\n      VERIFY_IS_APPROX(result(i, j), sum);\n    }\n  }\n\n  {\n    Tensor<float, 0, DataLayout> sum1 = tensor.sum();\n    VERIFY_IS_EQUAL(sum1.rank(), 0);\n\n    array<ptrdiff_t, 4> reduction_axis4;\n    reduction_axis4[0] = 0;\n    reduction_axis4[1] = 1;\n    reduction_axis4[2] = 2;\n    reduction_axis4[3] = 3;\n    Tensor<float, 0, DataLayout> sum2 = tensor.sum(reduction_axis4);\n    VERIFY_IS_EQUAL(sum2.rank(), 0);\n\n    VERIFY_IS_APPROX(sum1(), sum2());\n  }\n\n  reduction_axis2[0] = 0;\n  reduction_axis2[1] = 2;\n  result = tensor.prod(reduction_axis2);\n  VERIFY_IS_EQUAL(result.dimension(0), 3);\n  VERIFY_IS_EQUAL(result.dimension(1), 7);\n  for (int i = 0; i < 3; ++i) {\n    for (int j = 0; j < 7; ++j) {\n      float prod = 1.0f;\n      for (int k = 0; k < 2; ++k) {\n        for (int l = 0; l < 5; ++l) {\n          prod *= tensor(k, i, l, j);\n        }\n      }\n      VERIFY_IS_APPROX(result(i, j), prod);\n    }\n  }\n\n  {\n    Tensor<float, 0, DataLayout> prod1 = tensor.prod();\n    VERIFY_IS_EQUAL(prod1.rank(), 0);\n\n    array<ptrdiff_t, 4> reduction_axis4;\n    reduction_axis4[0] = 0;\n    reduction_axis4[1] = 1;\n    reduction_axis4[2] = 2;\n    reduction_axis4[3] = 3;\n    Tensor<float, 0, DataLayout> prod2 = tensor.prod(reduction_axis4);\n    VERIFY_IS_EQUAL(prod2.rank(), 0);\n\n    VERIFY_IS_APPROX(prod1(), prod2());\n  }\n\n  reduction_axis2[0] = 0;\n  reduction_axis2[1] = 2;\n  result = tensor.maximum(reduction_axis2);\n  VERIFY_IS_EQUAL(result.dimension(0), 3);\n  VERIFY_IS_EQUAL(result.dimension(1), 7);\n  for (int i = 0; i < 3; ++i) {\n    for (int j = 0; j < 7; ++j) {\n      float max_val = std::numeric_limits<float>::lowest();\n      for (int k = 0; k < 2; ++k) {\n        for (int l = 0; l < 5; ++l) {\n          max_val = (std::max)(max_val, tensor(k, i, l, j));\n        }\n      }\n      VERIFY_IS_APPROX(result(i, j), max_val);\n    }\n  }\n\n  {\n    Tensor<float, 0, DataLayout> max1 = tensor.maximum();\n    VERIFY_IS_EQUAL(max1.rank(), 0);\n\n    array<ptrdiff_t, 4> reduction_axis4;\n    reduction_axis4[0] = 0;\n    reduction_axis4[1] = 1;\n    reduction_axis4[2] = 2;\n    reduction_axis4[3] = 3;\n    Tensor<float, 0, DataLayout> max2 = tensor.maximum(reduction_axis4);\n    VERIFY_IS_EQUAL(max2.rank(), 0);\n\n    VERIFY_IS_APPROX(max1(), max2());\n  }\n\n  reduction_axis2[0] = 0;\n  reduction_axis2[1] = 1;\n  result = tensor.minimum(reduction_axis2);\n  VERIFY_IS_EQUAL(result.dimension(0), 5);\n  VERIFY_IS_EQUAL(result.dimension(1), 7);\n  for (int i = 0; i < 5; ++i) {\n    for (int j = 0; j < 7; ++j) {\n      float min_val = (std::numeric_limits<float>::max)();\n      for (int k = 0; k < 2; ++k) {\n        for (int l = 0; l < 3; ++l) {\n          min_val = (std::min)(min_val, tensor(k, l, i, j));\n        }\n      }\n      VERIFY_IS_APPROX(result(i, j), min_val);\n    }\n  }\n\n  {\n    Tensor<float, 0, DataLayout> min1 = tensor.minimum();\n    VERIFY_IS_EQUAL(min1.rank(), 0);\n\n    array<ptrdiff_t, 4> reduction_axis4;\n    reduction_axis4[0] = 0;\n    reduction_axis4[1] = 1;\n    reduction_axis4[2] = 2;\n    reduction_axis4[3] = 3;\n    Tensor<float, 0, DataLayout> min2 = tensor.minimum(reduction_axis4);\n    VERIFY_IS_EQUAL(min2.rank(), 0);\n\n    VERIFY_IS_APPROX(min1(), min2());\n  }\n\n  reduction_axis2[0] = 0;\n  reduction_axis2[1] = 1;\n  result = tensor.mean(reduction_axis2);\n  VERIFY_IS_EQUAL(result.dimension(0), 5);\n  VERIFY_IS_EQUAL(result.dimension(1), 7);\n  for (int i = 0; i < 5; ++i) {\n    for (int j = 0; j < 7; ++j) {\n      float sum = 0.0f;\n      int count = 0;\n      for (int k = 0; k < 2; ++k) {\n        for (int l = 0; l < 3; ++l) {\n          sum += tensor(k, l, i, j);\n          ++count;\n        }\n      }\n      VERIFY_IS_APPROX(result(i, j), sum / count);\n    }\n  }\n\n  {\n    Tensor<float, 0, DataLayout> mean1 = tensor.mean();\n    VERIFY_IS_EQUAL(mean1.rank(), 0);\n\n    array<ptrdiff_t, 4> reduction_axis4;\n    reduction_axis4[0] = 0;\n    reduction_axis4[1] = 1;\n    reduction_axis4[2] = 2;\n    reduction_axis4[3] = 3;\n    Tensor<float, 0, DataLayout> mean2 = tensor.mean(reduction_axis4);\n    VERIFY_IS_EQUAL(mean2.rank(), 0);\n\n    VERIFY_IS_APPROX(mean1(), mean2());\n  }\n\n  {\n    Tensor<int, 1> ints(10);\n    std::iota(ints.data(), ints.data() + ints.dimension(0), 0);\n\n    TensorFixedSize<bool, Sizes<> > all;\n    all = ints.all();\n    VERIFY(!all());\n    all = (ints >= ints.constant(0)).all();\n    VERIFY(all());\n\n    TensorFixedSize<bool, Sizes<> > any;\n    any = (ints > ints.constant(10)).any();\n    VERIFY(!any());\n    any = (ints < ints.constant(1)).any();\n    VERIFY(any());\n  }\n}\n\n\ntemplate <int DataLayout>\nstatic void test_reductions_in_expr() {\n  Tensor<float, 4, DataLayout> tensor(2, 3, 5, 7);\n  tensor.setRandom();\n  array<ptrdiff_t, 2> reduction_axis2;\n  reduction_axis2[0] = 1;\n  reduction_axis2[1] = 3;\n\n  Tensor<float, 2, DataLayout> result(2, 5);\n  result = result.constant(1.0f) - tensor.sum(reduction_axis2);\n  VERIFY_IS_EQUAL(result.dimension(0), 2);\n  VERIFY_IS_EQUAL(result.dimension(1), 5);\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 5; ++j) {\n      float sum = 0.0f;\n      for (int k = 0; k < 3; ++k) {\n        for (int l = 0; l < 7; ++l) {\n          sum += tensor(i, k, j, l);\n        }\n      }\n      VERIFY_IS_APPROX(result(i, j), 1.0f - sum);\n    }\n  }\n}\n\n\ntemplate <int DataLayout>\nstatic void test_full_reductions() {\n  Tensor<float, 2, DataLayout> tensor(2, 3);\n  tensor.setRandom();\n  array<ptrdiff_t, 2> reduction_axis;\n  reduction_axis[0] = 0;\n  reduction_axis[1] = 1;\n\n  Tensor<float, 0, DataLayout> result = tensor.sum(reduction_axis);\n  VERIFY_IS_EQUAL(result.rank(), 0);\n\n  float sum = 0.0f;\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      sum += tensor(i, j);\n    }\n  }\n  VERIFY_IS_APPROX(result(0), sum);\n\n  result = tensor.square().sum(reduction_axis).sqrt();\n  VERIFY_IS_EQUAL(result.rank(), 0);\n\n  sum = 0.0f;\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      sum += tensor(i, j) * tensor(i, j);\n    }\n  }\n  VERIFY_IS_APPROX(result(), sqrtf(sum));\n}\n\nstruct UserReducer {\n  static const bool PacketAccess = false;\n  UserReducer(float offset) : offset_(offset) {}\n  void reduce(const float val, float* accum) { *accum += val * val; }\n  float initialize() const { return 0; }\n  float finalize(const float accum) const { return 1.0f / (accum + offset_); }\n\n private:\n  const float offset_;\n};\n\ntemplate <int DataLayout>\nstatic void test_user_defined_reductions() {\n  Tensor<float, 2, DataLayout> tensor(5, 7);\n  tensor.setRandom();\n  array<ptrdiff_t, 1> reduction_axis;\n  reduction_axis[0] = 1;\n\n  UserReducer reducer(10.0f);\n  Tensor<float, 1, DataLayout> result = tensor.reduce(reduction_axis, reducer);\n  VERIFY_IS_EQUAL(result.dimension(0), 5);\n  for (int i = 0; i < 5; ++i) {\n    float expected = 10.0f;\n    for (int j = 0; j < 7; ++j) {\n      expected += tensor(i, j) * tensor(i, j);\n    }\n    expected = 1.0f / expected;\n    VERIFY_IS_APPROX(result(i), expected);\n  }\n}\n\ntemplate <int DataLayout>\nstatic void test_tensor_maps() {\n  int inputs[2 * 3 * 5 * 7];\n  TensorMap<Tensor<int, 4, DataLayout> > tensor_map(inputs, 2, 3, 5, 7);\n  TensorMap<Tensor<const int, 4, DataLayout> > tensor_map_const(inputs, 2, 3, 5,\n                                                                7);\n  const TensorMap<Tensor<const int, 4, DataLayout> > tensor_map_const_const(\n      inputs, 2, 3, 5, 7);\n\n  tensor_map.setRandom();\n  array<ptrdiff_t, 2> reduction_axis;\n  reduction_axis[0] = 1;\n  reduction_axis[1] = 3;\n\n  Tensor<int, 2, DataLayout> result = tensor_map.sum(reduction_axis);\n  Tensor<int, 2, DataLayout> result2 = tensor_map_const.sum(reduction_axis);\n  Tensor<int, 2, DataLayout> result3 =\n      tensor_map_const_const.sum(reduction_axis);\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 5; ++j) {\n      int sum = 0;\n      for (int k = 0; k < 3; ++k) {\n        for (int l = 0; l < 7; ++l) {\n          sum += tensor_map(i, k, j, l);\n        }\n      }\n      VERIFY_IS_EQUAL(result(i, j), sum);\n      VERIFY_IS_EQUAL(result2(i, j), sum);\n      VERIFY_IS_EQUAL(result3(i, j), sum);\n    }\n  }\n}\n\ntemplate <int DataLayout>\nstatic void test_static_dims() {\n  Tensor<float, 4, DataLayout> in(72, 53, 97, 113);\n  Tensor<float, 2, DataLayout> out(72, 97);\n  in.setRandom();\n\n#if !EIGEN_HAS_CONSTEXPR \n  array<int, 2> reduction_axis;\n  reduction_axis[0] = 1;\n  reduction_axis[1] = 3;\n#else\n  Eigen::IndexList<Eigen::type2index<1>, Eigen::type2index<3> > reduction_axis;\n#endif\n\n  out = in.maximum(reduction_axis);\n\n  for (int i = 0; i < 72; ++i) {\n    for (int j = 0; j < 97; ++j) {\n      float expected = -1e10f;\n      for (int k = 0; k < 53; ++k) {\n        for (int l = 0; l < 113; ++l) {\n          expected = (std::max)(expected, in(i, k, j, l));\n        }\n      }\n      VERIFY_IS_APPROX(out(i, j), expected);\n    }\n  }\n}\n\ntemplate <int DataLayout>\nstatic void test_innermost_last_dims() {\n  Tensor<float, 4, DataLayout> in(72, 53, 97, 113);\n  Tensor<float, 2, DataLayout> out(97, 113);\n  in.setRandom();\n\n// Reduce on the innermost dimensions.\n#if !EIGEN_HAS_CONSTEXPR\n  array<int, 2> reduction_axis;\n  reduction_axis[0] = 0;\n  reduction_axis[1] = 1;\n#else\n  // This triggers the use of packets for ColMajor.\n  Eigen::IndexList<Eigen::type2index<0>, Eigen::type2index<1> > reduction_axis;\n#endif\n\n  out = in.maximum(reduction_axis);\n\n  for (int i = 0; i < 97; ++i) {\n    for (int j = 0; j < 113; ++j) {\n      float expected = -1e10f;\n      for (int k = 0; k < 53; ++k) {\n        for (int l = 0; l < 72; ++l) {\n          expected = (std::max)(expected, in(l, k, i, j));\n        }\n      }\n      VERIFY_IS_APPROX(out(i, j), expected);\n    }\n  }\n}\n\ntemplate <int DataLayout>\nstatic void test_innermost_first_dims() {\n  Tensor<float, 4, DataLayout> in(72, 53, 97, 113);\n  Tensor<float, 2, DataLayout> out(72, 53);\n  in.setRandom();\n\n// Reduce on the innermost dimensions.\n#if !EIGEN_HAS_CONSTEXPR\n  array<int, 2> reduction_axis;\n  reduction_axis[0] = 2;\n  reduction_axis[1] = 3;\n#else\n  // This triggers the use of packets for RowMajor.\n  Eigen::IndexList<Eigen::type2index<2>, Eigen::type2index<3>> reduction_axis;\n#endif\n\n  out = in.maximum(reduction_axis);\n\n  for (int i = 0; i < 72; ++i) {\n    for (int j = 0; j < 53; ++j) {\n      float expected = -1e10f;\n      for (int k = 0; k < 97; ++k) {\n        for (int l = 0; l < 113; ++l) {\n          expected = (std::max)(expected, in(i, j, k, l));\n        }\n      }\n      VERIFY_IS_APPROX(out(i, j), expected);\n    }\n  }\n}\n\ntemplate <int DataLayout>\nstatic void test_reduce_middle_dims() {\n  Tensor<float, 4, DataLayout> in(72, 53, 97, 113);\n  Tensor<float, 2, DataLayout> out(72, 53);\n  in.setRandom();\n\n// Reduce on the innermost dimensions.\n#if !EIGEN_HAS_CONSTEXPR\n  array<int, 2> reduction_axis;\n  reduction_axis[0] = 1;\n  reduction_axis[1] = 2;\n#else\n  // This triggers the use of packets for RowMajor.\n  Eigen::IndexList<Eigen::type2index<1>, Eigen::type2index<2>> reduction_axis;\n#endif\n\n  out = in.maximum(reduction_axis);\n\n  for (int i = 0; i < 72; ++i) {\n    for (int j = 0; j < 113; ++j) {\n      float expected = -1e10f;\n      for (int k = 0; k < 53; ++k) {\n        for (int l = 0; l < 97; ++l) {\n          expected = (std::max)(expected, in(i, k, l, j));\n        }\n      }\n      VERIFY_IS_APPROX(out(i, j), expected);\n    }\n  }\n}\n\nvoid test_cxx11_tensor_reduction() {\n  CALL_SUBTEST(test_trivial_reductions<ColMajor>());\n  CALL_SUBTEST(test_trivial_reductions<RowMajor>());\n  CALL_SUBTEST(test_simple_reductions<ColMajor>());\n  CALL_SUBTEST(test_simple_reductions<RowMajor>());\n  CALL_SUBTEST(test_reductions_in_expr<ColMajor>());\n  CALL_SUBTEST(test_reductions_in_expr<RowMajor>());\n  CALL_SUBTEST(test_full_reductions<ColMajor>());\n  CALL_SUBTEST(test_full_reductions<RowMajor>());\n  CALL_SUBTEST(test_user_defined_reductions<ColMajor>());\n  CALL_SUBTEST(test_user_defined_reductions<RowMajor>());\n  CALL_SUBTEST(test_tensor_maps<ColMajor>());\n  CALL_SUBTEST(test_tensor_maps<RowMajor>());\n  CALL_SUBTEST(test_static_dims<ColMajor>());\n  CALL_SUBTEST(test_static_dims<RowMajor>());\n  CALL_SUBTEST(test_innermost_last_dims<ColMajor>());\n  CALL_SUBTEST(test_innermost_last_dims<RowMajor>());\n  CALL_SUBTEST(test_innermost_first_dims<ColMajor>());\n  CALL_SUBTEST(test_innermost_first_dims<RowMajor>());\n  CALL_SUBTEST(test_reduce_middle_dims<ColMajor>());\n  CALL_SUBTEST(test_reduce_middle_dims<RowMajor>());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_reduction_cuda.cu",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define EIGEN_TEST_NO_LONGDOUBLE\n#define EIGEN_TEST_NO_COMPLEX\n#define EIGEN_TEST_FUNC cxx11_tensor_reduction_cuda\n#define EIGEN_USE_GPU\n\n#include \"main.h\"\n#include <unsupported/Eigen/CXX11/Tensor>\n\n\ntemplate<typename Type, int DataLayout>\nstatic void test_full_reductions() {\n\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n\n  const int num_rows = internal::random<int>(1024, 5*1024);\n  const int num_cols = internal::random<int>(1024, 5*1024);\n\n  Tensor<Type, 2, DataLayout> in(num_rows, num_cols);\n  in.setRandom();\n\n  Tensor<Type, 0, DataLayout> full_redux;\n  full_redux = in.sum();\n\n  std::size_t in_bytes = in.size() * sizeof(Type);\n  std::size_t out_bytes = full_redux.size() * sizeof(Type);\n  Type* gpu_in_ptr = static_cast<Type*>(gpu_device.allocate(in_bytes));\n  Type* gpu_out_ptr = static_cast<Type*>(gpu_device.allocate(out_bytes));\n  gpu_device.memcpyHostToDevice(gpu_in_ptr, in.data(), in_bytes);\n\n  TensorMap<Tensor<Type, 2, DataLayout> > in_gpu(gpu_in_ptr, num_rows, num_cols);\n  TensorMap<Tensor<Type, 0, DataLayout> > out_gpu(gpu_out_ptr);\n\n  out_gpu.device(gpu_device) = in_gpu.sum();\n\n  Tensor<Type, 0, DataLayout> full_redux_gpu;\n  gpu_device.memcpyDeviceToHost(full_redux_gpu.data(), gpu_out_ptr, out_bytes);\n  gpu_device.synchronize();\n\n  // Check that the CPU and GPU reductions return the same result.\n  VERIFY_IS_APPROX(full_redux(), full_redux_gpu());\n\n  gpu_device.deallocate(gpu_in_ptr);\n  gpu_device.deallocate(gpu_out_ptr);\n}\n\ntemplate<typename Type, int DataLayout>\nstatic void test_first_dim_reductions() {\n  int dim_x = 33;\n  int dim_y = 1;\n  int dim_z = 128;\n\n  Tensor<Type, 3, DataLayout> in(dim_x, dim_y, dim_z);\n  in.setRandom();\n\n  Eigen::array<int, 1> red_axis;\n  red_axis[0] = 0;\n  Tensor<Type, 2, DataLayout> redux = in.sum(red_axis);\n\n  // Create device\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice dev(&stream);\n  \n  // Create data(T)\n  Type* in_data = (Type*)dev.allocate(dim_x*dim_y*dim_z*sizeof(Type));\n  Type* out_data = (Type*)dev.allocate(dim_z*dim_y*sizeof(Type));\n  Eigen::TensorMap<Eigen::Tensor<Type, 3, DataLayout> > gpu_in(in_data, dim_x, dim_y, dim_z);\n  Eigen::TensorMap<Eigen::Tensor<Type, 2, DataLayout> > gpu_out(out_data, dim_y, dim_z);\n  \n  // Perform operation\n  dev.memcpyHostToDevice(in_data, in.data(), in.size()*sizeof(Type));\n  gpu_out.device(dev) = gpu_in.sum(red_axis);\n  gpu_out.device(dev) += gpu_in.sum(red_axis);\n  Tensor<Type, 2, DataLayout> redux_gpu(dim_y, dim_z);\n  dev.memcpyDeviceToHost(redux_gpu.data(), out_data, gpu_out.size()*sizeof(Type));\n  dev.synchronize();\n\n  // Check that the CPU and GPU reductions return the same result.\n  for (int i = 0; i < gpu_out.size(); ++i) {\n    VERIFY_IS_APPROX(2*redux(i), redux_gpu(i));\n  }\n\n  dev.deallocate(in_data);\n  dev.deallocate(out_data);\n}\n\ntemplate<typename Type, int DataLayout>\nstatic void test_last_dim_reductions() {\n  int dim_x = 128;\n  int dim_y = 1;\n  int dim_z = 33;\n\n  Tensor<Type, 3, DataLayout> in(dim_x, dim_y, dim_z);\n  in.setRandom();\n\n  Eigen::array<int, 1> red_axis;\n  red_axis[0] = 2;\n  Tensor<Type, 2, DataLayout> redux = in.sum(red_axis);\n\n  // Create device\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice dev(&stream);\n  \n  // Create data\n  Type* in_data = (Type*)dev.allocate(dim_x*dim_y*dim_z*sizeof(Type));\n  Type* out_data = (Type*)dev.allocate(dim_x*dim_y*sizeof(Type));\n  Eigen::TensorMap<Eigen::Tensor<Type, 3, DataLayout> > gpu_in(in_data, dim_x, dim_y, dim_z);\n  Eigen::TensorMap<Eigen::Tensor<Type, 2, DataLayout> > gpu_out(out_data, dim_x, dim_y);\n  \n  // Perform operation\n  dev.memcpyHostToDevice(in_data, in.data(), in.size()*sizeof(Type));\n  gpu_out.device(dev) = gpu_in.sum(red_axis);\n  gpu_out.device(dev) += gpu_in.sum(red_axis);\n  Tensor<Type, 2, DataLayout> redux_gpu(dim_x, dim_y);\n  dev.memcpyDeviceToHost(redux_gpu.data(), out_data, gpu_out.size()*sizeof(Type));\n  dev.synchronize();\n\n  // Check that the CPU and GPU reductions return the same result.\n  for (int i = 0; i < gpu_out.size(); ++i) {\n    VERIFY_IS_APPROX(2*redux(i), redux_gpu(i));\n  }\n\n  dev.deallocate(in_data);\n  dev.deallocate(out_data);\n}\n\n\nvoid test_cxx11_tensor_reduction_cuda() {\n  CALL_SUBTEST_1((test_full_reductions<float, ColMajor>()));\n  CALL_SUBTEST_1((test_full_reductions<double, ColMajor>()));\n  CALL_SUBTEST_2((test_full_reductions<float, RowMajor>()));\n  CALL_SUBTEST_2((test_full_reductions<double, RowMajor>()));\n  \n  CALL_SUBTEST_3((test_first_dim_reductions<float, ColMajor>()));\n  CALL_SUBTEST_3((test_first_dim_reductions<double, ColMajor>()));\n  CALL_SUBTEST_4((test_first_dim_reductions<float, RowMajor>()));\n// Outer reductions of doubles aren't supported just yet.  \t\t\t\t\t      \n//  CALL_SUBTEST_4((test_first_dim_reductions<double, RowMajor>()))\n\n  CALL_SUBTEST_5((test_last_dim_reductions<float, ColMajor>()));\n// Outer reductions of doubles aren't supported just yet.  \t\t\t\t\t      \n//  CALL_SUBTEST_5((test_last_dim_reductions<double, ColMajor>()));\n  CALL_SUBTEST_6((test_last_dim_reductions<float, RowMajor>()));\n  CALL_SUBTEST_6((test_last_dim_reductions<double, RowMajor>()));\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_reduction_sycl.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015\n// Mehdi Goli    Codeplay Software Ltd.\n// Ralph Potter  Codeplay Software Ltd.\n// Luke Iwanski  Codeplay Software Ltd.\n// Contact: <eigen@codeplay.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define EIGEN_TEST_NO_LONGDOUBLE\n#define EIGEN_TEST_NO_COMPLEX\n#define EIGEN_TEST_FUNC cxx11_tensor_reduction_sycl\n#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int\n#define EIGEN_USE_SYCL\n\n#include \"main.h\"\n#include <unsupported/Eigen/CXX11/Tensor>\n\n\n\nstatic void test_full_reductions_sycl(const Eigen::SyclDevice&  sycl_device) {\n\n  const int num_rows = 452;\n  const int num_cols = 765;\n  array<int, 2> tensorRange = {{num_rows, num_cols}};\n\n  Tensor<float, 2> in(tensorRange);\n  Tensor<float, 0> full_redux;\n  Tensor<float, 0> full_redux_gpu;\n\n  in.setRandom();\n\n  full_redux = in.sum();\n\n  float* gpu_in_data = static_cast<float*>(sycl_device.allocate(in.dimensions().TotalSize()*sizeof(float)));\n  float* gpu_out_data =(float*)sycl_device.allocate(sizeof(float));\n\n  TensorMap<Tensor<float, 2> >  in_gpu(gpu_in_data, tensorRange);\n  TensorMap<Tensor<float, 0> >  out_gpu(gpu_out_data);\n\n  sycl_device.memcpyHostToDevice(gpu_in_data, in.data(),(in.dimensions().TotalSize())*sizeof(float));\n  out_gpu.device(sycl_device) = in_gpu.sum();\n  sycl_device.memcpyDeviceToHost(full_redux_gpu.data(), gpu_out_data, sizeof(float));\n  // Check that the CPU and GPU reductions return the same result.\n  VERIFY_IS_APPROX(full_redux_gpu(), full_redux());\n\n  sycl_device.deallocate(gpu_in_data);\n  sycl_device.deallocate(gpu_out_data);\n}\n\nstatic void test_first_dim_reductions_sycl(const Eigen::SyclDevice& sycl_device) {\n\n  int dim_x = 145;\n  int dim_y = 1;\n  int dim_z = 67;\n\n  array<int, 3> tensorRange = {{dim_x, dim_y, dim_z}};\n  Eigen::array<int, 1> red_axis;\n  red_axis[0] = 0;\n  array<int, 2> reduced_tensorRange = {{dim_y, dim_z}};\n\n  Tensor<float, 3> in(tensorRange);\n  Tensor<float, 2> redux(reduced_tensorRange);\n  Tensor<float, 2> redux_gpu(reduced_tensorRange);\n\n  in.setRandom();\n\n  redux= in.sum(red_axis);\n\n  float* gpu_in_data = static_cast<float*>(sycl_device.allocate(in.dimensions().TotalSize()*sizeof(float)));\n  float* gpu_out_data = static_cast<float*>(sycl_device.allocate(redux_gpu.dimensions().TotalSize()*sizeof(float)));\n\n  TensorMap<Tensor<float, 3> >  in_gpu(gpu_in_data, tensorRange);\n  TensorMap<Tensor<float, 2> >  out_gpu(gpu_out_data, reduced_tensorRange);\n\n  sycl_device.memcpyHostToDevice(gpu_in_data, in.data(),(in.dimensions().TotalSize())*sizeof(float));\n  out_gpu.device(sycl_device) = in_gpu.sum(red_axis);\n  sycl_device.memcpyDeviceToHost(redux_gpu.data(), gpu_out_data, redux_gpu.dimensions().TotalSize()*sizeof(float));\n\n  // Check that the CPU and GPU reductions return the same result.\n  for(int j=0; j<reduced_tensorRange[0]; j++ )\n    for(int k=0; k<reduced_tensorRange[1]; k++ )\n      VERIFY_IS_APPROX(redux_gpu(j,k), redux(j,k));\n\n  sycl_device.deallocate(gpu_in_data);\n  sycl_device.deallocate(gpu_out_data);\n}\n\nstatic void test_last_dim_reductions_sycl(const Eigen::SyclDevice &sycl_device) {\n\n  int dim_x = 567;\n  int dim_y = 1;\n  int dim_z = 47;\n\n  array<int, 3> tensorRange = {{dim_x, dim_y, dim_z}};\n  Eigen::array<int, 1> red_axis;\n  red_axis[0] = 2;\n  array<int, 2> reduced_tensorRange = {{dim_x, dim_y}};\n\n  Tensor<float, 3> in(tensorRange);\n  Tensor<float, 2> redux(reduced_tensorRange);\n  Tensor<float, 2> redux_gpu(reduced_tensorRange);\n\n  in.setRandom();\n\n  redux= in.sum(red_axis);\n\n  float* gpu_in_data = static_cast<float*>(sycl_device.allocate(in.dimensions().TotalSize()*sizeof(float)));\n  float* gpu_out_data = static_cast<float*>(sycl_device.allocate(redux_gpu.dimensions().TotalSize()*sizeof(float)));\n\n  TensorMap<Tensor<float, 3> >  in_gpu(gpu_in_data, tensorRange);\n  TensorMap<Tensor<float, 2> >  out_gpu(gpu_out_data, reduced_tensorRange);\n\n  sycl_device.memcpyHostToDevice(gpu_in_data, in.data(),(in.dimensions().TotalSize())*sizeof(float));\n  out_gpu.device(sycl_device) = in_gpu.sum(red_axis);\n  sycl_device.memcpyDeviceToHost(redux_gpu.data(), gpu_out_data, redux_gpu.dimensions().TotalSize()*sizeof(float));\n  // Check that the CPU and GPU reductions return the same result.\n  for(int j=0; j<reduced_tensorRange[0]; j++ )\n    for(int k=0; k<reduced_tensorRange[1]; k++ )\n      VERIFY_IS_APPROX(redux_gpu(j,k), redux(j,k));\n\n  sycl_device.deallocate(gpu_in_data);\n  sycl_device.deallocate(gpu_out_data);\n\n}\n\nvoid test_cxx11_tensor_reduction_sycl() {\n  cl::sycl::gpu_selector s;\n  Eigen::SyclDevice sycl_device(s);\n  CALL_SUBTEST((test_full_reductions_sycl(sycl_device)));\n  CALL_SUBTEST((test_first_dim_reductions_sycl(sycl_device)));\n  CALL_SUBTEST((test_last_dim_reductions_sycl(sycl_device)));\n\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_ref.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\nusing Eigen::RowMajor;\n\nstatic void test_simple_lvalue_ref()\n{\n  Tensor<int, 1> input(6);\n  input.setRandom();\n\n  TensorRef<Tensor<int, 1>> ref3(input);\n  TensorRef<Tensor<int, 1>> ref4 = input;\n\n  VERIFY_IS_EQUAL(ref3.data(), input.data());\n  VERIFY_IS_EQUAL(ref4.data(), input.data());\n\n  for (int i = 0; i < 6; ++i) {\n    VERIFY_IS_EQUAL(ref3(i), input(i));\n    VERIFY_IS_EQUAL(ref4(i), input(i));\n  }\n\n  for (int i = 0; i < 6; ++i) {\n    ref3.coeffRef(i) = i;\n  }\n  for (int i = 0; i < 6; ++i) {\n    VERIFY_IS_EQUAL(input(i), i);\n  }\n  for (int i = 0; i < 6; ++i) {\n    ref4.coeffRef(i) = -i * 2;\n  }\n  for (int i = 0; i < 6; ++i) {\n    VERIFY_IS_EQUAL(input(i), -i*2);\n  }\n}\n\n\nstatic void test_simple_rvalue_ref()\n{\n  Tensor<int, 1> input1(6);\n  input1.setRandom();\n  Tensor<int, 1> input2(6);\n  input2.setRandom();\n\n  TensorRef<Tensor<int, 1>> ref3(input1 + input2);\n  TensorRef<Tensor<int, 1>> ref4 = input1 + input2;\n\n  VERIFY_IS_NOT_EQUAL(ref3.data(), input1.data());\n  VERIFY_IS_NOT_EQUAL(ref4.data(), input1.data());\n  VERIFY_IS_NOT_EQUAL(ref3.data(), input2.data());\n  VERIFY_IS_NOT_EQUAL(ref4.data(), input2.data());\n\n  for (int i = 0; i < 6; ++i) {\n    VERIFY_IS_EQUAL(ref3(i), input1(i) + input2(i));\n    VERIFY_IS_EQUAL(ref4(i), input1(i) + input2(i));\n  }\n}\n\n\nstatic void test_multiple_dims()\n{\n  Tensor<float, 3> input(3,5,7);\n  input.setRandom();\n\n  TensorRef<Tensor<float, 3>> ref(input);\n  VERIFY_IS_EQUAL(ref.data(), input.data());\n  VERIFY_IS_EQUAL(ref.dimension(0), 3);\n  VERIFY_IS_EQUAL(ref.dimension(1), 5);\n  VERIFY_IS_EQUAL(ref.dimension(2), 7);\n\n  for (int i = 0; i < 3; ++i) {\n    for (int j = 0; j < 5; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        VERIFY_IS_EQUAL(ref(i,j,k), input(i,j,k));\n      }\n    }\n  }\n}\n\n\nstatic void test_slice()\n{\n  Tensor<float, 5> tensor(2,3,5,7,11);\n  tensor.setRandom();\n\n  Eigen::DSizes<ptrdiff_t, 5> indices(1,2,3,4,5);\n  Eigen::DSizes<ptrdiff_t, 5> sizes(1,1,1,1,1);\n  TensorRef<Tensor<float, 5>> slice = tensor.slice(indices, sizes);\n  VERIFY_IS_EQUAL(slice(0,0,0,0,0), tensor(1,2,3,4,5));\n\n  Eigen::DSizes<ptrdiff_t, 5> indices2(1,1,3,4,5);\n  Eigen::DSizes<ptrdiff_t, 5> sizes2(1,1,2,2,3);\n  slice = tensor.slice(indices2, sizes2);\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 2; ++j) {\n      for (int k = 0; k < 3; ++k) {\n        VERIFY_IS_EQUAL(slice(0,0,i,j,k), tensor(1,1,3+i,4+j,5+k));\n      }\n    }\n  }\n\n  Eigen::DSizes<ptrdiff_t, 5> indices3(0,0,0,0,0);\n  Eigen::DSizes<ptrdiff_t, 5> sizes3(2,3,1,1,1);\n  slice = tensor.slice(indices3, sizes3);\n  VERIFY_IS_EQUAL(slice.data(), tensor.data());\n}\n\n\nstatic void test_ref_of_ref()\n{\n  Tensor<float, 3> input(3,5,7);\n  input.setRandom();\n\n  TensorRef<Tensor<float, 3>> ref(input);\n  TensorRef<Tensor<float, 3>> ref_of_ref(ref);\n  TensorRef<Tensor<float, 3>> ref_of_ref2;\n  ref_of_ref2 = ref;\n\n  VERIFY_IS_EQUAL(ref_of_ref.data(), input.data());\n  VERIFY_IS_EQUAL(ref_of_ref.dimension(0), 3);\n  VERIFY_IS_EQUAL(ref_of_ref.dimension(1), 5);\n  VERIFY_IS_EQUAL(ref_of_ref.dimension(2), 7);\n\n  VERIFY_IS_EQUAL(ref_of_ref2.data(), input.data());\n  VERIFY_IS_EQUAL(ref_of_ref2.dimension(0), 3);\n  VERIFY_IS_EQUAL(ref_of_ref2.dimension(1), 5);\n  VERIFY_IS_EQUAL(ref_of_ref2.dimension(2), 7);\n\n  for (int i = 0; i < 3; ++i) {\n    for (int j = 0; j < 5; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        VERIFY_IS_EQUAL(ref_of_ref(i,j,k), input(i,j,k));\n        VERIFY_IS_EQUAL(ref_of_ref2(i,j,k), input(i,j,k));\n     }\n    }\n  }\n}\n\n\nstatic void test_ref_in_expr()\n{\n  Tensor<float, 3> input(3,5,7);\n  input.setRandom();\n  TensorRef<Tensor<float, 3>> input_ref(input);\n\n  Tensor<float, 3> result(3,5,7);\n  result.setRandom();\n  TensorRef<Tensor<float, 3>> result_ref(result);\n\n  Tensor<float, 3> bias(3,5,7);\n  bias.setRandom();\n\n  result_ref = input_ref + bias;\n  for (int i = 0; i < 3; ++i) {\n    for (int j = 0; j < 5; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        VERIFY_IS_EQUAL(result_ref(i,j,k), input(i,j,k) + bias(i,j,k));\n        VERIFY_IS_NOT_EQUAL(result(i,j,k), input(i,j,k) + bias(i,j,k));\n      }\n    }\n  }\n\n  result = result_ref;\n  for (int i = 0; i < 3; ++i) {\n    for (int j = 0; j < 5; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        VERIFY_IS_EQUAL(result(i,j,k), input(i,j,k) + bias(i,j,k));\n      }\n    }\n  }\n}\n\n\nstatic void test_coeff_ref()\n{\n  Tensor<float, 5> tensor(2,3,5,7,11);\n  tensor.setRandom();\n  Tensor<float, 5> original = tensor;\n\n  TensorRef<Tensor<float, 4>> slice = tensor.chip(7, 4);\n  slice.coeffRef(0, 0, 0, 0) = 1.0f;\n  slice.coeffRef(1, 0, 0, 0) += 2.0f;\n\n  VERIFY_IS_EQUAL(tensor(0,0,0,0,7), 1.0f);\n  VERIFY_IS_EQUAL(tensor(1,0,0,0,7), original(1,0,0,0,7) + 2.0f);\n}\n\n\nstatic void test_nested_ops_with_ref()\n{\n  Tensor<float, 4> t(2, 3, 5, 7);\n  t.setRandom();\n  TensorMap<Tensor<const float, 4> > m(t.data(), 2, 3, 5, 7);\n  array<std::pair<ptrdiff_t, ptrdiff_t>, 4> paddings;\n  paddings[0] = std::make_pair(0, 0);\n  paddings[1] = std::make_pair(2, 1);\n  paddings[2] = std::make_pair(3, 4);\n  paddings[3] = std::make_pair(0, 0);\n  DSizes<Eigen::DenseIndex, 4> shuffle_dims(0, 1, 2, 3);\n  TensorRef<Tensor<const float, 4> > ref(m.pad(paddings));\n  array<std::pair<ptrdiff_t, ptrdiff_t>, 4> trivial;\n  trivial[0] = std::make_pair(0, 0);\n  trivial[1] = std::make_pair(0, 0);\n  trivial[2] = std::make_pair(0, 0);\n  trivial[3] = std::make_pair(0, 0);\n  Tensor<float, 4> padded = ref.shuffle(shuffle_dims).pad(trivial);\n  VERIFY_IS_EQUAL(padded.dimension(0), 2+0);\n  VERIFY_IS_EQUAL(padded.dimension(1), 3+3);\n  VERIFY_IS_EQUAL(padded.dimension(2), 5+7);\n  VERIFY_IS_EQUAL(padded.dimension(3), 7+0);\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 6; ++j) {\n      for (int k = 0; k < 12; ++k) {\n        for (int l = 0; l < 7; ++l) {\n          if (j >= 2 && j < 5 && k >= 3 && k < 8) {\n            VERIFY_IS_EQUAL(padded(i,j,k,l), t(i,j-2,k-3,l));\n          } else {\n            VERIFY_IS_EQUAL(padded(i,j,k,l), 0.0f);\n          }\n        }\n      }\n    }\n  }\n}\n\n\nvoid test_cxx11_tensor_ref()\n{\n  CALL_SUBTEST(test_simple_lvalue_ref());\n  CALL_SUBTEST(test_simple_rvalue_ref());\n  CALL_SUBTEST(test_multiple_dims());\n  CALL_SUBTEST(test_slice());\n  CALL_SUBTEST(test_ref_of_ref());\n  CALL_SUBTEST(test_ref_in_expr());\n  CALL_SUBTEST(test_coeff_ref());\n  CALL_SUBTEST(test_nested_ops_with_ref());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_reverse.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Navdeep Jaitly <ndjaitly@google.com and\n//                    Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\nusing Eigen::array;\n\ntemplate <int DataLayout>\nstatic void test_simple_reverse()\n{\n  Tensor<float, 4, DataLayout> tensor(2,3,5,7);\n  tensor.setRandom();\n\n  array<bool, 4> dim_rev;\n  dim_rev[0] = false;\n  dim_rev[1] = true;\n  dim_rev[2] = true;\n  dim_rev[3] = false;\n\n  Tensor<float, 4, DataLayout> reversed_tensor;\n  reversed_tensor = tensor.reverse(dim_rev);\n\n  VERIFY_IS_EQUAL(reversed_tensor.dimension(0), 2);\n  VERIFY_IS_EQUAL(reversed_tensor.dimension(1), 3);\n  VERIFY_IS_EQUAL(reversed_tensor.dimension(2), 5);\n  VERIFY_IS_EQUAL(reversed_tensor.dimension(3), 7);\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 5; ++k) {\n        for (int l = 0; l < 7; ++l) {\n          VERIFY_IS_EQUAL(tensor(i,j,k,l), reversed_tensor(i,2-j,4-k,l));\n        }\n      }\n    }\n  }\n\n  dim_rev[0] = true;\n  dim_rev[1] = false;\n  dim_rev[2] = false;\n  dim_rev[3] = false;\n\n  reversed_tensor = tensor.reverse(dim_rev);\n\n  VERIFY_IS_EQUAL(reversed_tensor.dimension(0), 2);\n  VERIFY_IS_EQUAL(reversed_tensor.dimension(1), 3);\n  VERIFY_IS_EQUAL(reversed_tensor.dimension(2), 5);\n  VERIFY_IS_EQUAL(reversed_tensor.dimension(3), 7);\n\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 5; ++k) {\n        for (int l = 0; l < 7; ++l) {\n          VERIFY_IS_EQUAL(tensor(i,j,k,l), reversed_tensor(1-i,j,k,l));\n        }\n      }\n    }\n  }\n\n  dim_rev[0] = true;\n  dim_rev[1] = false;\n  dim_rev[2] = false;\n  dim_rev[3] = true;\n\n  reversed_tensor = tensor.reverse(dim_rev);\n\n  VERIFY_IS_EQUAL(reversed_tensor.dimension(0), 2);\n  VERIFY_IS_EQUAL(reversed_tensor.dimension(1), 3);\n  VERIFY_IS_EQUAL(reversed_tensor.dimension(2), 5);\n  VERIFY_IS_EQUAL(reversed_tensor.dimension(3), 7);\n\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 5; ++k) {\n        for (int l = 0; l < 7; ++l) {\n          VERIFY_IS_EQUAL(tensor(i,j,k,l), reversed_tensor(1-i,j,k,6-l));\n        }\n      }\n    }\n  }\n}\n\n\ntemplate <int DataLayout>\nstatic void test_expr_reverse(bool LValue)\n{\n  Tensor<float, 4, DataLayout> tensor(2,3,5,7);\n  tensor.setRandom();\n\n  array<bool, 4> dim_rev;\n  dim_rev[0] = false;\n  dim_rev[1] = true;\n  dim_rev[2] = false;\n  dim_rev[3] = true;\n\n  Tensor<float, 4, DataLayout> expected(2, 3, 5, 7);\n  if (LValue) {\n    expected.reverse(dim_rev) = tensor;\n  } else {\n    expected = tensor.reverse(dim_rev);\n  }\n\n  Tensor<float, 4, DataLayout> result(2,3,5,7);\n\n  array<ptrdiff_t, 4> src_slice_dim;\n  src_slice_dim[0] = 2;\n  src_slice_dim[1] = 3;\n  src_slice_dim[2] = 1;\n  src_slice_dim[3] = 7;\n  array<ptrdiff_t, 4> src_slice_start;\n  src_slice_start[0] = 0;\n  src_slice_start[1] = 0;\n  src_slice_start[2] = 0;\n  src_slice_start[3] = 0;\n  array<ptrdiff_t, 4> dst_slice_dim = src_slice_dim;\n  array<ptrdiff_t, 4> dst_slice_start = src_slice_start;\n\n  for (int i = 0; i < 5; ++i) {\n    if (LValue) {\n      result.slice(dst_slice_start, dst_slice_dim).reverse(dim_rev) =\n          tensor.slice(src_slice_start, src_slice_dim);\n    } else {\n      result.slice(dst_slice_start, dst_slice_dim) =\n          tensor.slice(src_slice_start, src_slice_dim).reverse(dim_rev);\n    }\n    src_slice_start[2] += 1;\n    dst_slice_start[2] += 1;\n  }\n\n  VERIFY_IS_EQUAL(result.dimension(0), 2);\n  VERIFY_IS_EQUAL(result.dimension(1), 3);\n  VERIFY_IS_EQUAL(result.dimension(2), 5);\n  VERIFY_IS_EQUAL(result.dimension(3), 7);\n\n  for (int i = 0; i < expected.dimension(0); ++i) {\n    for (int j = 0; j < expected.dimension(1); ++j) {\n      for (int k = 0; k < expected.dimension(2); ++k) {\n        for (int l = 0; l < expected.dimension(3); ++l) {\n          VERIFY_IS_EQUAL(result(i,j,k,l), expected(i,j,k,l));\n        }\n      }\n    }\n  }\n\n  dst_slice_start[2] = 0;\n  result.setRandom();\n  for (int i = 0; i < 5; ++i) {\n     if (LValue) {\n       result.slice(dst_slice_start, dst_slice_dim).reverse(dim_rev) =\n           tensor.slice(dst_slice_start, dst_slice_dim);\n     } else {\n       result.slice(dst_slice_start, dst_slice_dim) =\n           tensor.reverse(dim_rev).slice(dst_slice_start, dst_slice_dim);\n     }\n    dst_slice_start[2] += 1;\n  }\n\n  for (int i = 0; i < expected.dimension(0); ++i) {\n    for (int j = 0; j < expected.dimension(1); ++j) {\n      for (int k = 0; k < expected.dimension(2); ++k) {\n        for (int l = 0; l < expected.dimension(3); ++l) {\n          VERIFY_IS_EQUAL(result(i,j,k,l), expected(i,j,k,l));\n        }\n      }\n    }\n  }\n}\n\n\nvoid test_cxx11_tensor_reverse()\n{\n  CALL_SUBTEST(test_simple_reverse<ColMajor>());\n  CALL_SUBTEST(test_simple_reverse<RowMajor>());\n  CALL_SUBTEST(test_expr_reverse<ColMajor>(true));\n  CALL_SUBTEST(test_expr_reverse<RowMajor>(true));\n  CALL_SUBTEST(test_expr_reverse<ColMajor>(false));\n  CALL_SUBTEST(test_expr_reverse<RowMajor>(false));\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_roundings.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\n\nstatic void test_float_rounding()\n{\n  Tensor<float, 2> ftensor(20,30);\n  ftensor = ftensor.random() * 100.f;\n\n  Tensor<float, 2> result = ftensor.round();\n\n  for (int i = 0; i < 20; ++i) {\n    for (int j = 0; j < 30; ++j) {\n      VERIFY_IS_EQUAL(result(i,j), numext::round(ftensor(i,j)));\n    }\n  }\n}\n\nstatic void test_float_flooring()\n{\n  Tensor<float, 2> ftensor(20,30);\n  ftensor = ftensor.random() * 100.f;\n\n  Tensor<float, 2> result = ftensor.floor();\n\n  for (int i = 0; i < 20; ++i) {\n    for (int j = 0; j < 30; ++j) {\n      VERIFY_IS_EQUAL(result(i,j), numext::floor(ftensor(i,j)));\n    }\n  }\n}\n\nstatic void test_float_ceiling()\n{\n  Tensor<float, 2> ftensor(20,30);\n  ftensor = ftensor.random() * 100.f;\n\n  Tensor<float, 2> result = ftensor.ceil();\n\n  for (int i = 0; i < 20; ++i) {\n    for (int j = 0; j < 30; ++j) {\n      VERIFY_IS_EQUAL(result(i,j), numext::ceil(ftensor(i,j)));\n    }\n  }\n}\n\nvoid test_cxx11_tensor_roundings()\n{\n   CALL_SUBTEST(test_float_rounding());\n   CALL_SUBTEST(test_float_ceiling());\n   CALL_SUBTEST(test_float_flooring());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_scan.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Igor Babuschkin <igor@babuschk.in>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <limits>\n#include <numeric>\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\n\ntemplate <int DataLayout, typename Type=float, bool Exclusive = false>\nstatic void test_1d_scan()\n{\n  int size = 50;\n  Tensor<Type, 1, DataLayout> tensor(size);\n  tensor.setRandom();\n  Tensor<Type, 1, DataLayout> result = tensor.cumsum(0, Exclusive);\n\n  VERIFY_IS_EQUAL(tensor.dimension(0), result.dimension(0));\n\n  float accum = 0;\n  for (int i = 0; i < size; i++) {\n    if (Exclusive) {\n      VERIFY_IS_EQUAL(result(i), accum);\n      accum += tensor(i);\n    } else {\n      accum += tensor(i);\n      VERIFY_IS_EQUAL(result(i), accum);\n    }\n  }\n\n  accum = 1;\n  result = tensor.cumprod(0, Exclusive);\n  for (int i = 0; i < size; i++) {\n    if (Exclusive) {\n      VERIFY_IS_EQUAL(result(i), accum);\n      accum *= tensor(i);\n    } else {\n      accum *= tensor(i);\n      VERIFY_IS_EQUAL(result(i), accum);\n    }\n  }\n}\n\ntemplate <int DataLayout, typename Type=float>\nstatic void test_4d_scan()\n{\n  int size = 5;\n  Tensor<Type, 4, DataLayout> tensor(size, size, size, size);\n  tensor.setRandom();\n\n  Tensor<Type, 4, DataLayout> result(size, size, size, size);\n\n  result = tensor.cumsum(0);\n  float accum = 0;\n  for (int i = 0; i < size; i++) {\n    accum += tensor(i, 1, 2, 3);\n    VERIFY_IS_EQUAL(result(i, 1, 2, 3), accum);\n  }\n  result = tensor.cumsum(1);\n  accum = 0;\n  for (int i = 0; i < size; i++) {\n    accum += tensor(1, i, 2, 3);\n    VERIFY_IS_EQUAL(result(1, i, 2, 3), accum);\n  }\n  result = tensor.cumsum(2);\n  accum = 0;\n  for (int i = 0; i < size; i++) {\n    accum += tensor(1, 2, i, 3);\n    VERIFY_IS_EQUAL(result(1, 2, i, 3), accum);\n  }\n  result = tensor.cumsum(3);\n  accum = 0;\n  for (int i = 0; i < size; i++) {\n    accum += tensor(1, 2, 3, i);\n    VERIFY_IS_EQUAL(result(1, 2, 3, i), accum);\n  }\n}\n\ntemplate <int DataLayout>\nstatic void test_tensor_maps() {\n  int inputs[20];\n  TensorMap<Tensor<int, 1, DataLayout> > tensor_map(inputs, 20);\n  tensor_map.setRandom();\n\n  Tensor<int, 1, DataLayout> result = tensor_map.cumsum(0);\n\n  int accum = 0;\n  for (int i = 0; i < 20; ++i) {\n    accum += tensor_map(i);\n    VERIFY_IS_EQUAL(result(i), accum);\n  }\n}\n\nvoid test_cxx11_tensor_scan() {\n  CALL_SUBTEST((test_1d_scan<ColMajor, float, true>()));\n  CALL_SUBTEST((test_1d_scan<ColMajor, float, false>()));\n  CALL_SUBTEST((test_1d_scan<RowMajor, float, true>()));\n  CALL_SUBTEST((test_1d_scan<RowMajor, float, false>()));\n  CALL_SUBTEST(test_4d_scan<ColMajor>());\n  CALL_SUBTEST(test_4d_scan<RowMajor>());\n  CALL_SUBTEST(test_tensor_maps<ColMajor>());\n  CALL_SUBTEST(test_tensor_maps<RowMajor>());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_scan_cuda.cu",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define EIGEN_TEST_NO_LONGDOUBLE\n#define EIGEN_TEST_NO_COMPLEX\n#define EIGEN_TEST_FUNC cxx11_tensor_scan_cuda\n#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int\n#define EIGEN_USE_GPU\n\n#include \"main.h\"\n#include <unsupported/Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\ntypedef Tensor<float, 1>::DimensionPair DimPair;\n\ntemplate<int DataLayout>\nvoid test_cuda_cumsum(int m_size, int k_size, int n_size)\n{\n  std::cout << \"Testing for (\" << m_size << \",\" << k_size << \",\" << n_size << \")\" << std::endl;\n  Tensor<float, 3, DataLayout> t_input(m_size, k_size, n_size);\n  Tensor<float, 3, DataLayout> t_result(m_size, k_size, n_size);\n  Tensor<float, 3, DataLayout> t_result_gpu(m_size, k_size, n_size);\n\n  t_input.setRandom();\n\n  std::size_t t_input_bytes = t_input.size()  * sizeof(float);\n  std::size_t t_result_bytes = t_result.size() * sizeof(float);\n\n  float* d_t_input;\n  float* d_t_result;\n\n  cudaMalloc((void**)(&d_t_input), t_input_bytes);\n  cudaMalloc((void**)(&d_t_result), t_result_bytes);\n\n  cudaMemcpy(d_t_input, t_input.data(), t_input_bytes, cudaMemcpyHostToDevice);\n\n  Eigen::CudaStreamDevice stream;\n  Eigen::GpuDevice gpu_device(&stream);\n\n  Eigen::TensorMap<Eigen::Tensor<float, 3, DataLayout> >\n      gpu_t_input(d_t_input, Eigen::array<int, 3>(m_size, k_size, n_size));\n  Eigen::TensorMap<Eigen::Tensor<float, 3, DataLayout> >\n      gpu_t_result(d_t_result, Eigen::array<int, 3>(m_size, k_size, n_size));\n\n  gpu_t_result.device(gpu_device) = gpu_t_input.cumsum(1);\n  t_result = t_input.cumsum(1);\n\n  cudaMemcpy(t_result_gpu.data(), d_t_result, t_result_bytes, cudaMemcpyDeviceToHost);\n  for (DenseIndex i = 0; i < t_result.size(); i++) {\n    if (fabs(t_result(i) - t_result_gpu(i)) < 1e-4f) {\n      continue;\n    }\n    if (Eigen::internal::isApprox(t_result(i), t_result_gpu(i), 1e-4f)) {\n      continue;\n    }\n    std::cout << \"mismatch detected at index \" << i << \": \" << t_result(i)\n              << \" vs \" <<  t_result_gpu(i) << std::endl;\n    assert(false);\n  }\n\n  cudaFree((void*)d_t_input);\n  cudaFree((void*)d_t_result);\n}\n\n\nvoid test_cxx11_tensor_scan_cuda()\n{\n  CALL_SUBTEST_1(test_cuda_cumsum<ColMajor>(128, 128, 128));\n  CALL_SUBTEST_2(test_cuda_cumsum<RowMajor>(128, 128, 128));\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_shuffling.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\nusing Eigen::array;\n\ntemplate <int DataLayout>\nstatic void test_simple_shuffling()\n{\n  Tensor<float, 4, DataLayout> tensor(2,3,5,7);\n  tensor.setRandom();\n  array<ptrdiff_t, 4> shuffles;\n  shuffles[0] = 0;\n  shuffles[1] = 1;\n  shuffles[2] = 2;\n  shuffles[3] = 3;\n\n  Tensor<float, 4, DataLayout> no_shuffle;\n  no_shuffle = tensor.shuffle(shuffles);\n\n  VERIFY_IS_EQUAL(no_shuffle.dimension(0), 2);\n  VERIFY_IS_EQUAL(no_shuffle.dimension(1), 3);\n  VERIFY_IS_EQUAL(no_shuffle.dimension(2), 5);\n  VERIFY_IS_EQUAL(no_shuffle.dimension(3), 7);\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 5; ++k) {\n        for (int l = 0; l < 7; ++l) {\n          VERIFY_IS_EQUAL(tensor(i,j,k,l), no_shuffle(i,j,k,l));\n        }\n      }\n    }\n  }\n\n  shuffles[0] = 2;\n  shuffles[1] = 3;\n  shuffles[2] = 1;\n  shuffles[3] = 0;\n  Tensor<float, 4, DataLayout> shuffle;\n  shuffle = tensor.shuffle(shuffles);\n\n  VERIFY_IS_EQUAL(shuffle.dimension(0), 5);\n  VERIFY_IS_EQUAL(shuffle.dimension(1), 7);\n  VERIFY_IS_EQUAL(shuffle.dimension(2), 3);\n  VERIFY_IS_EQUAL(shuffle.dimension(3), 2);\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 5; ++k) {\n        for (int l = 0; l < 7; ++l) {\n          VERIFY_IS_EQUAL(tensor(i,j,k,l), shuffle(k,l,j,i));\n        }\n      }\n    }\n  }\n}\n\n\ntemplate <int DataLayout>\nstatic void test_expr_shuffling()\n{\n  Tensor<float, 4, DataLayout> tensor(2,3,5,7);\n  tensor.setRandom();\n\n  array<ptrdiff_t, 4> shuffles;\n  shuffles[0] = 2;\n  shuffles[1] = 3;\n  shuffles[2] = 1;\n  shuffles[3] = 0;\n  Tensor<float, 4, DataLayout> expected;\n  expected = tensor.shuffle(shuffles);\n\n  Tensor<float, 4, DataLayout> result(5,7,3,2);\n\n  array<int, 4> src_slice_dim{{2,3,1,7}};\n  array<int, 4> src_slice_start{{0,0,0,0}};\n  array<int, 4> dst_slice_dim{{1,7,3,2}};\n  array<int, 4> dst_slice_start{{0,0,0,0}};\n\n  for (int i = 0; i < 5; ++i) {\n    result.slice(dst_slice_start, dst_slice_dim) =\n        tensor.slice(src_slice_start, src_slice_dim).shuffle(shuffles);\n    src_slice_start[2] += 1;\n    dst_slice_start[0] += 1;\n  }\n\n  VERIFY_IS_EQUAL(result.dimension(0), 5);\n  VERIFY_IS_EQUAL(result.dimension(1), 7);\n  VERIFY_IS_EQUAL(result.dimension(2), 3);\n  VERIFY_IS_EQUAL(result.dimension(3), 2);\n\n  for (int i = 0; i < expected.dimension(0); ++i) {\n    for (int j = 0; j < expected.dimension(1); ++j) {\n      for (int k = 0; k < expected.dimension(2); ++k) {\n        for (int l = 0; l < expected.dimension(3); ++l) {\n          VERIFY_IS_EQUAL(result(i,j,k,l), expected(i,j,k,l));\n        }\n      }\n    }\n  }\n\n  dst_slice_start[0] = 0;\n  result.setRandom();\n  for (int i = 0; i < 5; ++i) {\n    result.slice(dst_slice_start, dst_slice_dim) =\n        tensor.shuffle(shuffles).slice(dst_slice_start, dst_slice_dim);\n    dst_slice_start[0] += 1;\n  }\n\n  for (int i = 0; i < expected.dimension(0); ++i) {\n    for (int j = 0; j < expected.dimension(1); ++j) {\n      for (int k = 0; k < expected.dimension(2); ++k) {\n        for (int l = 0; l < expected.dimension(3); ++l) {\n          VERIFY_IS_EQUAL(result(i,j,k,l), expected(i,j,k,l));\n        }\n      }\n    }\n  }\n}\n\n\ntemplate <int DataLayout>\nstatic void test_shuffling_as_value()\n{\n  Tensor<float, 4, DataLayout> tensor(2,3,5,7);\n  tensor.setRandom();\n  array<ptrdiff_t, 4> shuffles;\n  shuffles[2] = 0;\n  shuffles[3] = 1;\n  shuffles[1] = 2;\n  shuffles[0] = 3;\n  Tensor<float, 4, DataLayout> shuffle(5,7,3,2);\n  shuffle.shuffle(shuffles) = tensor;\n\n  VERIFY_IS_EQUAL(shuffle.dimension(0), 5);\n  VERIFY_IS_EQUAL(shuffle.dimension(1), 7);\n  VERIFY_IS_EQUAL(shuffle.dimension(2), 3);\n  VERIFY_IS_EQUAL(shuffle.dimension(3), 2);\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 5; ++k) {\n        for (int l = 0; l < 7; ++l) {\n          VERIFY_IS_EQUAL(tensor(i,j,k,l), shuffle(k,l,j,i));\n        }\n      }\n    }\n  }\n\n  array<ptrdiff_t, 4> no_shuffle;\n  no_shuffle[0] = 0;\n  no_shuffle[1] = 1;\n  no_shuffle[2] = 2;\n  no_shuffle[3] = 3;\n  Tensor<float, 4, DataLayout> shuffle2(5,7,3,2);\n  shuffle2.shuffle(shuffles) = tensor.shuffle(no_shuffle);\n  for (int i = 0; i < 5; ++i) {\n    for (int j = 0; j < 7; ++j) {\n      for (int k = 0; k < 3; ++k) {\n        for (int l = 0; l < 2; ++l) {\n          VERIFY_IS_EQUAL(shuffle2(i,j,k,l), shuffle(i,j,k,l));\n        }\n      }\n    }\n  }\n}\n\n\ntemplate <int DataLayout>\nstatic void test_shuffle_unshuffle()\n{\n  Tensor<float, 4, DataLayout> tensor(2,3,5,7);\n  tensor.setRandom();\n\n  // Choose a random permutation.\n  array<ptrdiff_t, 4> shuffles;\n  for (int i = 0; i < 4; ++i) {\n    shuffles[i] = i;\n  }\n  array<ptrdiff_t, 4> shuffles_inverse;\n  for (int i = 0; i < 4; ++i) {\n    const ptrdiff_t index = internal::random<ptrdiff_t>(i, 3);\n    shuffles_inverse[shuffles[index]] = i;\n    std::swap(shuffles[i], shuffles[index]);\n  }\n\n  Tensor<float, 4, DataLayout> shuffle;\n  shuffle = tensor.shuffle(shuffles).shuffle(shuffles_inverse);\n\n  VERIFY_IS_EQUAL(shuffle.dimension(0), 2);\n  VERIFY_IS_EQUAL(shuffle.dimension(1), 3);\n  VERIFY_IS_EQUAL(shuffle.dimension(2), 5);\n  VERIFY_IS_EQUAL(shuffle.dimension(3), 7);\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 5; ++k) {\n        for (int l = 0; l < 7; ++l) {\n          VERIFY_IS_EQUAL(tensor(i,j,k,l), shuffle(i,j,k,l));\n        }\n      }\n    }\n  }\n}\n\n\nvoid test_cxx11_tensor_shuffling()\n{\n  CALL_SUBTEST(test_simple_shuffling<ColMajor>());\n  CALL_SUBTEST(test_simple_shuffling<RowMajor>());\n  CALL_SUBTEST(test_expr_shuffling<ColMajor>());\n  CALL_SUBTEST(test_expr_shuffling<RowMajor>());\n  CALL_SUBTEST(test_shuffling_as_value<ColMajor>());\n  CALL_SUBTEST(test_shuffling_as_value<RowMajor>());\n  CALL_SUBTEST(test_shuffle_unshuffle<ColMajor>());\n  CALL_SUBTEST(test_shuffle_unshuffle<RowMajor>());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_simple.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2013 Christian Seiler <christian@iwakd.de>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\nusing Eigen::RowMajor;\n\nstatic void test_0d()\n{\n  Tensor<int, 0> scalar1;\n  Tensor<int, 0, RowMajor> scalar2;\n  Tensor<int, 0> scalar3;\n  Tensor<int, 0, RowMajor> scalar4;\n\n  scalar3.resize();\n  scalar4.resize();\n\n  scalar1() = 7;\n  scalar2() = 13;\n  scalar3.setValues(17);\n  scalar4.setZero();\n\n  VERIFY_IS_EQUAL(scalar1.rank(), 0);\n  VERIFY_IS_EQUAL(scalar1.size(), 1);\n\n  VERIFY_IS_EQUAL(scalar1(), 7);\n  VERIFY_IS_EQUAL(scalar2(), 13);\n  VERIFY_IS_EQUAL(scalar3(), 17);\n  VERIFY_IS_EQUAL(scalar4(), 0);\n\n  Tensor<int, 0> scalar5(scalar1);\n\n  VERIFY_IS_EQUAL(scalar5(), 7);\n  VERIFY_IS_EQUAL(scalar5.data()[0], 7);\n}\n\nstatic void test_1d()\n{\n  Tensor<int, 1> vec1(6);\n  Tensor<int, 1, RowMajor> vec2(6);\n  Tensor<int, 1> vec3;\n  Tensor<int, 1, RowMajor> vec4;\n\n  vec3.resize(6);\n  vec4.resize(6);\n\n  vec1(0) = 4;  vec2(0) = 0; vec3(0) = 5;\n  vec1(1) = 8;  vec2(1) = 1; vec3(1) = 4;\n  vec1(2) = 15; vec2(2) = 2; vec3(2) = 3;\n  vec1(3) = 16; vec2(3) = 3; vec3(3) = 2;\n  vec1(4) = 23; vec2(4) = 4; vec3(4) = 1;\n  vec1(5) = 42; vec2(5) = 5; vec3(5) = 0;\n  vec4.setZero();\n\n  VERIFY_IS_EQUAL((vec1.rank()), 1);\n  VERIFY_IS_EQUAL((vec1.size()), 6);\n  VERIFY_IS_EQUAL((vec1.dimensions()[0]), 6);\n\n  VERIFY_IS_EQUAL((vec1[0]), 4);\n  VERIFY_IS_EQUAL((vec1[1]), 8);\n  VERIFY_IS_EQUAL((vec1[2]), 15);\n  VERIFY_IS_EQUAL((vec1[3]), 16);\n  VERIFY_IS_EQUAL((vec1[4]), 23);\n  VERIFY_IS_EQUAL((vec1[5]), 42);\n\n  VERIFY_IS_EQUAL((vec2[0]), 0);\n  VERIFY_IS_EQUAL((vec2[1]), 1);\n  VERIFY_IS_EQUAL((vec2[2]), 2);\n  VERIFY_IS_EQUAL((vec2[3]), 3);\n  VERIFY_IS_EQUAL((vec2[4]), 4);\n  VERIFY_IS_EQUAL((vec2[5]), 5);\n\n  VERIFY_IS_EQUAL((vec3[0]), 5);\n  VERIFY_IS_EQUAL((vec3[1]), 4);\n  VERIFY_IS_EQUAL((vec3[2]), 3);\n  VERIFY_IS_EQUAL((vec3[3]), 2);\n  VERIFY_IS_EQUAL((vec3[4]), 1);\n  VERIFY_IS_EQUAL((vec3[5]), 0);\n\n  VERIFY_IS_EQUAL((vec4[0]), 0);\n  VERIFY_IS_EQUAL((vec4[1]), 0);\n  VERIFY_IS_EQUAL((vec4[2]), 0);\n  VERIFY_IS_EQUAL((vec4[3]), 0);\n  VERIFY_IS_EQUAL((vec4[4]), 0);\n  VERIFY_IS_EQUAL((vec4[5]), 0);\n\n  Tensor<int, 1> vec5(vec1);\n\n  VERIFY_IS_EQUAL((vec5(0)), 4);\n  VERIFY_IS_EQUAL((vec5(1)), 8);\n  VERIFY_IS_EQUAL((vec5(2)), 15);\n  VERIFY_IS_EQUAL((vec5(3)), 16);\n  VERIFY_IS_EQUAL((vec5(4)), 23);\n  VERIFY_IS_EQUAL((vec5(5)), 42);\n\n  VERIFY_IS_EQUAL((vec5.data()[0]), 4);\n  VERIFY_IS_EQUAL((vec5.data()[1]), 8);\n  VERIFY_IS_EQUAL((vec5.data()[2]), 15);\n  VERIFY_IS_EQUAL((vec5.data()[3]), 16);\n  VERIFY_IS_EQUAL((vec5.data()[4]), 23);\n  VERIFY_IS_EQUAL((vec5.data()[5]), 42);\n}\n\nstatic void test_2d()\n{\n  Tensor<int, 2> mat1(2,3);\n  Tensor<int, 2, RowMajor> mat2(2,3);\n\n  mat1(0,0) = 0;\n  mat1(0,1) = 1;\n  mat1(0,2) = 2;\n  mat1(1,0) = 3;\n  mat1(1,1) = 4;\n  mat1(1,2) = 5;\n\n  mat2(0,0) = 0;\n  mat2(0,1) = 1;\n  mat2(0,2) = 2;\n  mat2(1,0) = 3;\n  mat2(1,1) = 4;\n  mat2(1,2) = 5;\n\n  VERIFY_IS_EQUAL((mat1.rank()), 2);\n  VERIFY_IS_EQUAL((mat1.size()), 6);\n  VERIFY_IS_EQUAL((mat1.dimensions()[0]), 2);\n  VERIFY_IS_EQUAL((mat1.dimensions()[1]), 3);\n\n  VERIFY_IS_EQUAL((mat2.rank()), 2);\n  VERIFY_IS_EQUAL((mat2.size()), 6);\n  VERIFY_IS_EQUAL((mat2.dimensions()[0]), 2);\n  VERIFY_IS_EQUAL((mat2.dimensions()[1]), 3);\n\n  VERIFY_IS_EQUAL((mat1.data()[0]), 0);\n  VERIFY_IS_EQUAL((mat1.data()[1]), 3);\n  VERIFY_IS_EQUAL((mat1.data()[2]), 1);\n  VERIFY_IS_EQUAL((mat1.data()[3]), 4);\n  VERIFY_IS_EQUAL((mat1.data()[4]), 2);\n  VERIFY_IS_EQUAL((mat1.data()[5]), 5);\n\n  VERIFY_IS_EQUAL((mat2.data()[0]), 0);\n  VERIFY_IS_EQUAL((mat2.data()[1]), 1);\n  VERIFY_IS_EQUAL((mat2.data()[2]), 2);\n  VERIFY_IS_EQUAL((mat2.data()[3]), 3);\n  VERIFY_IS_EQUAL((mat2.data()[4]), 4);\n  VERIFY_IS_EQUAL((mat2.data()[5]), 5);\n}\n\nstatic void test_3d()\n{\n  Tensor<int, 3> epsilon(3,3,3);\n  epsilon.setZero();\n  epsilon(0,1,2) = epsilon(2,0,1) = epsilon(1,2,0) = 1;\n  epsilon(2,1,0) = epsilon(0,2,1) = epsilon(1,0,2) = -1;\n\n  VERIFY_IS_EQUAL((epsilon.size()), 27);\n  VERIFY_IS_EQUAL((epsilon.dimensions()[0]), 3);\n  VERIFY_IS_EQUAL((epsilon.dimensions()[1]), 3);\n  VERIFY_IS_EQUAL((epsilon.dimensions()[2]), 3);\n\n  VERIFY_IS_EQUAL((epsilon(0,0,0)), 0);\n  VERIFY_IS_EQUAL((epsilon(0,0,1)), 0);\n  VERIFY_IS_EQUAL((epsilon(0,0,2)), 0);\n  VERIFY_IS_EQUAL((epsilon(0,1,0)), 0);\n  VERIFY_IS_EQUAL((epsilon(0,1,1)), 0);\n  VERIFY_IS_EQUAL((epsilon(0,2,0)), 0);\n  VERIFY_IS_EQUAL((epsilon(0,2,2)), 0);\n  VERIFY_IS_EQUAL((epsilon(1,0,0)), 0);\n  VERIFY_IS_EQUAL((epsilon(1,0,1)), 0);\n  VERIFY_IS_EQUAL((epsilon(1,1,0)), 0);\n  VERIFY_IS_EQUAL((epsilon(1,1,1)), 0);\n  VERIFY_IS_EQUAL((epsilon(1,1,2)), 0);\n  VERIFY_IS_EQUAL((epsilon(1,2,1)), 0);\n  VERIFY_IS_EQUAL((epsilon(1,2,2)), 0);\n  VERIFY_IS_EQUAL((epsilon(2,0,0)), 0);\n  VERIFY_IS_EQUAL((epsilon(2,0,2)), 0);\n  VERIFY_IS_EQUAL((epsilon(2,1,1)), 0);\n  VERIFY_IS_EQUAL((epsilon(2,1,2)), 0);\n  VERIFY_IS_EQUAL((epsilon(2,2,0)), 0);\n  VERIFY_IS_EQUAL((epsilon(2,2,1)), 0);\n  VERIFY_IS_EQUAL((epsilon(2,2,2)), 0);\n\n  VERIFY_IS_EQUAL((epsilon(0,1,2)), 1);\n  VERIFY_IS_EQUAL((epsilon(2,0,1)), 1);\n  VERIFY_IS_EQUAL((epsilon(1,2,0)), 1);\n  VERIFY_IS_EQUAL((epsilon(2,1,0)), -1);\n  VERIFY_IS_EQUAL((epsilon(0,2,1)), -1);\n  VERIFY_IS_EQUAL((epsilon(1,0,2)), -1);\n\n  array<Eigen::DenseIndex, 3> dims;\n  dims[0] = 2;\n  dims[1] = 3;\n  dims[2] = 4;\n  Tensor<int, 3> t1(dims);\n  Tensor<int, 3, RowMajor> t2(dims);\n\n  VERIFY_IS_EQUAL((t1.size()), 24);\n  VERIFY_IS_EQUAL((t1.dimensions()[0]), 2);\n  VERIFY_IS_EQUAL((t1.dimensions()[1]), 3);\n  VERIFY_IS_EQUAL((t1.dimensions()[2]), 4);\n\n  VERIFY_IS_EQUAL((t2.size()), 24);\n  VERIFY_IS_EQUAL((t2.dimensions()[0]), 2);\n  VERIFY_IS_EQUAL((t2.dimensions()[1]), 3);\n  VERIFY_IS_EQUAL((t2.dimensions()[2]), 4);\n\n  for (int i = 0; i < 2; i++) {\n    for (int j = 0; j < 3; j++) {\n      for (int k = 0; k < 4; k++) {\n        t1(i, j, k) = 100 * i + 10 * j + k;\n        t2(i, j, k) = 100 * i + 10 * j + k;\n      }\n    }\n  }\n\n  VERIFY_IS_EQUAL((t1.data()[0]),    0);\n  VERIFY_IS_EQUAL((t1.data()[1]),  100);\n  VERIFY_IS_EQUAL((t1.data()[2]),   10);\n  VERIFY_IS_EQUAL((t1.data()[3]),  110);\n  VERIFY_IS_EQUAL((t1.data()[4]),   20);\n  VERIFY_IS_EQUAL((t1.data()[5]),  120);\n  VERIFY_IS_EQUAL((t1.data()[6]),    1);\n  VERIFY_IS_EQUAL((t1.data()[7]),  101);\n  VERIFY_IS_EQUAL((t1.data()[8]),   11);\n  VERIFY_IS_EQUAL((t1.data()[9]),  111);\n  VERIFY_IS_EQUAL((t1.data()[10]),  21);\n  VERIFY_IS_EQUAL((t1.data()[11]), 121);\n  VERIFY_IS_EQUAL((t1.data()[12]),   2);\n  VERIFY_IS_EQUAL((t1.data()[13]), 102);\n  VERIFY_IS_EQUAL((t1.data()[14]),  12);\n  VERIFY_IS_EQUAL((t1.data()[15]), 112);\n  VERIFY_IS_EQUAL((t1.data()[16]),  22);\n  VERIFY_IS_EQUAL((t1.data()[17]), 122);\n  VERIFY_IS_EQUAL((t1.data()[18]),   3);\n  VERIFY_IS_EQUAL((t1.data()[19]), 103);\n  VERIFY_IS_EQUAL((t1.data()[20]),  13);\n  VERIFY_IS_EQUAL((t1.data()[21]), 113);\n  VERIFY_IS_EQUAL((t1.data()[22]),  23);\n  VERIFY_IS_EQUAL((t1.data()[23]), 123);\n\n  VERIFY_IS_EQUAL((t2.data()[0]),    0);\n  VERIFY_IS_EQUAL((t2.data()[1]),    1);\n  VERIFY_IS_EQUAL((t2.data()[2]),    2);\n  VERIFY_IS_EQUAL((t2.data()[3]),    3);\n  VERIFY_IS_EQUAL((t2.data()[4]),   10);\n  VERIFY_IS_EQUAL((t2.data()[5]),   11);\n  VERIFY_IS_EQUAL((t2.data()[6]),   12);\n  VERIFY_IS_EQUAL((t2.data()[7]),   13);\n  VERIFY_IS_EQUAL((t2.data()[8]),   20);\n  VERIFY_IS_EQUAL((t2.data()[9]),   21);\n  VERIFY_IS_EQUAL((t2.data()[10]),  22);\n  VERIFY_IS_EQUAL((t2.data()[11]),  23);\n  VERIFY_IS_EQUAL((t2.data()[12]), 100);\n  VERIFY_IS_EQUAL((t2.data()[13]), 101);\n  VERIFY_IS_EQUAL((t2.data()[14]), 102);\n  VERIFY_IS_EQUAL((t2.data()[15]), 103);\n  VERIFY_IS_EQUAL((t2.data()[16]), 110);\n  VERIFY_IS_EQUAL((t2.data()[17]), 111);\n  VERIFY_IS_EQUAL((t2.data()[18]), 112);\n  VERIFY_IS_EQUAL((t2.data()[19]), 113);\n  VERIFY_IS_EQUAL((t2.data()[20]), 120);\n  VERIFY_IS_EQUAL((t2.data()[21]), 121);\n  VERIFY_IS_EQUAL((t2.data()[22]), 122);\n  VERIFY_IS_EQUAL((t2.data()[23]), 123);\n}\n\nstatic void test_simple_assign()\n{\n  Tensor<int, 3> epsilon(3,3,3);\n  epsilon.setZero();\n  epsilon(0,1,2) = epsilon(2,0,1) = epsilon(1,2,0) = 1;\n  epsilon(2,1,0) = epsilon(0,2,1) = epsilon(1,0,2) = -1;\n\n  Tensor<int, 3> e2(3,3,3);\n  e2.setZero();\n  VERIFY_IS_EQUAL((e2(1,2,0)), 0);\n\n  e2 = epsilon;\n  VERIFY_IS_EQUAL((e2(1,2,0)), 1);\n  VERIFY_IS_EQUAL((e2(0,1,2)), 1);\n  VERIFY_IS_EQUAL((e2(2,0,1)), 1);\n  VERIFY_IS_EQUAL((e2(2,1,0)), -1);\n  VERIFY_IS_EQUAL((e2(0,2,1)), -1);\n  VERIFY_IS_EQUAL((e2(1,0,2)), -1);\n}\n\nstatic void test_resize()\n{\n  Tensor<int, 3> epsilon;\n  epsilon.resize(2,3,7);\n  VERIFY_IS_EQUAL(epsilon.dimension(0), 2);\n  VERIFY_IS_EQUAL(epsilon.dimension(1), 3);\n  VERIFY_IS_EQUAL(epsilon.dimension(2), 7);\n  VERIFY_IS_EQUAL(epsilon.size(), 2*3*7);\n\n  const int* old_data = epsilon.data();\n  epsilon.resize(3,2,7);\n  VERIFY_IS_EQUAL(epsilon.dimension(0), 3);\n  VERIFY_IS_EQUAL(epsilon.dimension(1), 2);\n  VERIFY_IS_EQUAL(epsilon.dimension(2), 7);\n  VERIFY_IS_EQUAL(epsilon.size(), 2*3*7);\n  VERIFY_IS_EQUAL(epsilon.data(), old_data);\n\n  epsilon.resize(3,5,7);\n  VERIFY_IS_EQUAL(epsilon.dimension(0), 3);\n  VERIFY_IS_EQUAL(epsilon.dimension(1), 5);\n  VERIFY_IS_EQUAL(epsilon.dimension(2), 7);\n  VERIFY_IS_EQUAL(epsilon.size(), 3*5*7);\n}\n\nvoid test_cxx11_tensor_simple()\n{\n  CALL_SUBTEST(test_0d());\n  CALL_SUBTEST(test_1d());\n  CALL_SUBTEST(test_2d());\n  CALL_SUBTEST(test_3d());\n  CALL_SUBTEST(test_simple_assign());\n  CALL_SUBTEST(test_resize());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_striding.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\n\ntemplate<int DataLayout>\nstatic void test_simple_striding()\n{\n  Tensor<float, 4, DataLayout> tensor(2,3,5,7);\n  tensor.setRandom();\n  array<ptrdiff_t, 4> strides;\n  strides[0] = 1;\n  strides[1] = 1;\n  strides[2] = 1;\n  strides[3] = 1;\n\n  Tensor<float, 4, DataLayout> no_stride;\n  no_stride = tensor.stride(strides);\n\n  VERIFY_IS_EQUAL(no_stride.dimension(0), 2);\n  VERIFY_IS_EQUAL(no_stride.dimension(1), 3);\n  VERIFY_IS_EQUAL(no_stride.dimension(2), 5);\n  VERIFY_IS_EQUAL(no_stride.dimension(3), 7);\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 5; ++k) {\n        for (int l = 0; l < 7; ++l) {\n          VERIFY_IS_EQUAL(tensor(i,j,k,l), no_stride(i,j,k,l));\n        }\n      }\n    }\n  }\n\n  strides[0] = 2;\n  strides[1] = 4;\n  strides[2] = 2;\n  strides[3] = 3;\n  Tensor<float, 4, DataLayout> stride;\n  stride = tensor.stride(strides);\n\n  VERIFY_IS_EQUAL(stride.dimension(0), 1);\n  VERIFY_IS_EQUAL(stride.dimension(1), 1);\n  VERIFY_IS_EQUAL(stride.dimension(2), 3);\n  VERIFY_IS_EQUAL(stride.dimension(3), 3);\n\n  for (int i = 0; i < 1; ++i) {\n    for (int j = 0; j < 1; ++j) {\n      for (int k = 0; k < 3; ++k) {\n        for (int l = 0; l < 3; ++l) {\n          VERIFY_IS_EQUAL(tensor(2*i,4*j,2*k,3*l), stride(i,j,k,l));\n        }\n      }\n    }\n  }\n}\n\n\ntemplate<int DataLayout>\nstatic void test_striding_as_lvalue()\n{\n  Tensor<float, 4, DataLayout> tensor(2,3,5,7);\n  tensor.setRandom();\n  array<ptrdiff_t, 4> strides;\n  strides[0] = 2;\n  strides[1] = 4;\n  strides[2] = 2;\n  strides[3] = 3;\n\n  Tensor<float, 4, DataLayout> result(3, 12, 10, 21);\n  result.stride(strides) = tensor;\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 5; ++k) {\n        for (int l = 0; l < 7; ++l) {\n          VERIFY_IS_EQUAL(tensor(i,j,k,l), result(2*i,4*j,2*k,3*l));\n        }\n      }\n    }\n  }\n\n  array<ptrdiff_t, 4> no_strides;\n  no_strides[0] = 1;\n  no_strides[1] = 1;\n  no_strides[2] = 1;\n  no_strides[3] = 1;\n  Tensor<float, 4, DataLayout> result2(3, 12, 10, 21);\n  result2.stride(strides) = tensor.stride(no_strides);\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 5; ++k) {\n        for (int l = 0; l < 7; ++l) {\n          VERIFY_IS_EQUAL(tensor(i,j,k,l), result2(2*i,4*j,2*k,3*l));\n        }\n      }\n    }\n  }\n}\n\n\nvoid test_cxx11_tensor_striding()\n{\n  CALL_SUBTEST(test_simple_striding<ColMajor>());\n  CALL_SUBTEST(test_simple_striding<RowMajor>());\n  CALL_SUBTEST(test_striding_as_lvalue<ColMajor>());\n  CALL_SUBTEST(test_striding_as_lvalue<RowMajor>());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_sugar.cpp",
    "content": "#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\nusing Eigen::RowMajor;\n\nstatic void test_comparison_sugar() {\n  // we already trust comparisons between tensors, we're simply checking that\n  // the sugared versions are doing the same thing\n  Tensor<int, 3> t(6, 7, 5);\n\n  t.setRandom();\n  // make sure we have at least one value == 0\n  t(0,0,0) = 0;\n\n  Tensor<bool,0> b;\n\n#define TEST_TENSOR_EQUAL(e1, e2) \\\n  b = ((e1) == (e2)).all();       \\\n  VERIFY(b())\n\n#define TEST_OP(op) TEST_TENSOR_EQUAL(t op 0, t op t.constant(0))\n\n  TEST_OP(==);\n  TEST_OP(!=);\n  TEST_OP(<=);\n  TEST_OP(>=);\n  TEST_OP(<);\n  TEST_OP(>);\n#undef TEST_OP\n#undef TEST_TENSOR_EQUAL\n}\n\n\nstatic void test_scalar_sugar_add_mul() {\n  Tensor<float, 3> A(6, 7, 5);\n  Tensor<float, 3> B(6, 7, 5);\n  A.setRandom();\n  B.setRandom();\n\n  const float alpha = 0.43f;\n  const float beta = 0.21f;\n  const float gamma = 0.14f;\n\n  Tensor<float, 3> R = A.constant(gamma) + A * A.constant(alpha) + B * B.constant(beta);\n  Tensor<float, 3> S = A * alpha + B * beta + gamma;\n  Tensor<float, 3> T = gamma + alpha * A + beta * B;\n\n  for (int i = 0; i < 6*7*5; ++i) {\n    VERIFY_IS_APPROX(R(i), S(i));\n    VERIFY_IS_APPROX(R(i), T(i));\n  }\n}\n\nstatic void test_scalar_sugar_sub_div() {\n  Tensor<float, 3> A(6, 7, 5);\n  Tensor<float, 3> B(6, 7, 5);\n  A.setRandom();\n  B.setRandom();\n\n  const float alpha = 0.43f;\n  const float beta = 0.21f;\n  const float gamma = 0.14f;\n  const float delta = 0.32f;\n\n  Tensor<float, 3> R = A.constant(gamma) - A / A.constant(alpha)\n      - B.constant(beta) / B - A.constant(delta);\n  Tensor<float, 3> S = gamma - A / alpha - beta / B - delta;\n\n  for (int i = 0; i < 6*7*5; ++i) {\n    VERIFY_IS_APPROX(R(i), S(i));\n  }\n}\n\nvoid test_cxx11_tensor_sugar()\n{\n  CALL_SUBTEST(test_comparison_sugar());\n  CALL_SUBTEST(test_scalar_sugar_add_mul());\n  CALL_SUBTEST(test_scalar_sugar_sub_div());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_sycl.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016\n// Mehdi Goli    Codeplay Software Ltd.\n// Ralph Potter  Codeplay Software Ltd.\n// Luke Iwanski  Codeplay Software Ltd.\n// Contact: <eigen@codeplay.com>\n// Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n\n#define EIGEN_TEST_NO_LONGDOUBLE\n#define EIGEN_TEST_NO_COMPLEX\n#define EIGEN_TEST_FUNC cxx11_tensor_sycl\n#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int\n#define EIGEN_USE_SYCL\n\n#include \"main.h\"\n#include <unsupported/Eigen/CXX11/Tensor>\n\nusing Eigen::array;\nusing Eigen::SyclDevice;\nusing Eigen::Tensor;\nusing Eigen::TensorMap;\n\nvoid test_sycl_cpu(const Eigen::SyclDevice &sycl_device) {\n\n  int sizeDim1 = 100;\n  int sizeDim2 = 100;\n  int sizeDim3 = 100;\n  array<int, 3> tensorRange = {{sizeDim1, sizeDim2, sizeDim3}};\n  Tensor<float, 3> in1(tensorRange);\n  Tensor<float, 3> in2(tensorRange);\n  Tensor<float, 3> in3(tensorRange);\n  Tensor<float, 3> out(tensorRange);\n\n  in2 = in2.random();\n  in3 = in3.random();\n\n  float * gpu_in1_data  = static_cast<float*>(sycl_device.allocate(in1.dimensions().TotalSize()*sizeof(float)));\n  float * gpu_in2_data  = static_cast<float*>(sycl_device.allocate(in2.dimensions().TotalSize()*sizeof(float)));\n  float * gpu_in3_data  = static_cast<float*>(sycl_device.allocate(in3.dimensions().TotalSize()*sizeof(float)));\n  float * gpu_out_data =  static_cast<float*>(sycl_device.allocate(out.dimensions().TotalSize()*sizeof(float)));\n\n  TensorMap<Tensor<float, 3>> gpu_in1(gpu_in1_data, tensorRange);\n  TensorMap<Tensor<float, 3>> gpu_in2(gpu_in2_data, tensorRange);\n  TensorMap<Tensor<float, 3>> gpu_in3(gpu_in3_data, tensorRange);\n  TensorMap<Tensor<float, 3>> gpu_out(gpu_out_data, tensorRange);\n\n  /// a=1.2f\n  gpu_in1.device(sycl_device) = gpu_in1.constant(1.2f);\n  sycl_device.memcpyDeviceToHost(in1.data(), gpu_in1_data ,(in1.dimensions().TotalSize())*sizeof(float));\n  for (int i = 0; i < sizeDim1; ++i) {\n    for (int j = 0; j < sizeDim2; ++j) {\n      for (int k = 0; k < sizeDim3; ++k) {\n        VERIFY_IS_APPROX(in1(i,j,k), 1.2f);\n      }\n    }\n  }\n  printf(\"a=1.2f Test passed\\n\");\n\n  /// a=b*1.2f\n  gpu_out.device(sycl_device) = gpu_in1 * 1.2f;\n  sycl_device.memcpyDeviceToHost(out.data(), gpu_out_data ,(out.dimensions().TotalSize())*sizeof(float));\n  for (int i = 0; i < sizeDim1; ++i) {\n    for (int j = 0; j < sizeDim2; ++j) {\n      for (int k = 0; k < sizeDim3; ++k) {\n        VERIFY_IS_APPROX(out(i,j,k),\n                         in1(i,j,k) * 1.2f);\n      }\n    }\n  }\n  printf(\"a=b*1.2f Test Passed\\n\");\n\n  /// c=a*b\n  sycl_device.memcpyHostToDevice(gpu_in2_data, in2.data(),(in2.dimensions().TotalSize())*sizeof(float));\n  gpu_out.device(sycl_device) = gpu_in1 * gpu_in2;\n  sycl_device.memcpyDeviceToHost(out.data(), gpu_out_data,(out.dimensions().TotalSize())*sizeof(float));\n  for (int i = 0; i < sizeDim1; ++i) {\n    for (int j = 0; j < sizeDim2; ++j) {\n      for (int k = 0; k < sizeDim3; ++k) {\n        VERIFY_IS_APPROX(out(i,j,k),\n                         in1(i,j,k) *\n                             in2(i,j,k));\n      }\n    }\n  }\n  printf(\"c=a*b Test Passed\\n\");\n\n  /// c=a+b\n  gpu_out.device(sycl_device) = gpu_in1 + gpu_in2;\n  sycl_device.memcpyDeviceToHost(out.data(), gpu_out_data,(out.dimensions().TotalSize())*sizeof(float));\n  for (int i = 0; i < sizeDim1; ++i) {\n    for (int j = 0; j < sizeDim2; ++j) {\n      for (int k = 0; k < sizeDim3; ++k) {\n        VERIFY_IS_APPROX(out(i,j,k),\n                         in1(i,j,k) +\n                             in2(i,j,k));\n      }\n    }\n  }\n  printf(\"c=a+b Test Passed\\n\");\n\n  /// c=a*a\n  gpu_out.device(sycl_device) = gpu_in1 * gpu_in1;\n  sycl_device.memcpyDeviceToHost(out.data(), gpu_out_data,(out.dimensions().TotalSize())*sizeof(float));\n  for (int i = 0; i < sizeDim1; ++i) {\n    for (int j = 0; j < sizeDim2; ++j) {\n      for (int k = 0; k < sizeDim3; ++k) {\n        VERIFY_IS_APPROX(out(i,j,k),\n                         in1(i,j,k) *\n                             in1(i,j,k));\n      }\n    }\n  }\n  printf(\"c= a*a Test Passed\\n\");\n\n  //a*3.14f + b*2.7f\n  gpu_out.device(sycl_device) =  gpu_in1 * gpu_in1.constant(3.14f) + gpu_in2 * gpu_in2.constant(2.7f);\n  sycl_device.memcpyDeviceToHost(out.data(),gpu_out_data,(out.dimensions().TotalSize())*sizeof(float));\n  for (int i = 0; i < sizeDim1; ++i) {\n    for (int j = 0; j < sizeDim2; ++j) {\n      for (int k = 0; k < sizeDim3; ++k) {\n        VERIFY_IS_APPROX(out(i,j,k),\n                         in1(i,j,k) * 3.14f\n                       + in2(i,j,k) * 2.7f);\n      }\n    }\n  }\n  printf(\"a*3.14f + b*2.7f Test Passed\\n\");\n\n  ///d= (a>0.5? b:c)\n  sycl_device.memcpyHostToDevice(gpu_in3_data, in3.data(),(in3.dimensions().TotalSize())*sizeof(float));\n  gpu_out.device(sycl_device) =(gpu_in1 > gpu_in1.constant(0.5f)).select(gpu_in2, gpu_in3);\n  sycl_device.memcpyDeviceToHost(out.data(), gpu_out_data,(out.dimensions().TotalSize())*sizeof(float));\n  for (int i = 0; i < sizeDim1; ++i) {\n    for (int j = 0; j < sizeDim2; ++j) {\n      for (int k = 0; k < sizeDim3; ++k) {\n        VERIFY_IS_APPROX(out(i, j, k), (in1(i, j, k) > 0.5f)\n                                                ? in2(i, j, k)\n                                                : in3(i, j, k));\n      }\n    }\n  }\n  printf(\"d= (a>0.5? b:c) Test Passed\\n\");\n  sycl_device.deallocate(gpu_in1_data);\n  sycl_device.deallocate(gpu_in2_data);\n  sycl_device.deallocate(gpu_in3_data);\n  sycl_device.deallocate(gpu_out_data);\n}\nvoid test_cxx11_tensor_sycl() {\n  cl::sycl::gpu_selector s;\n  Eigen::SyclDevice sycl_device(s);\n  CALL_SUBTEST(test_sycl_cpu(sycl_device));\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_symmetry.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2013 Christian Seiler <christian@iwakd.de>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n#include <Eigen/CXX11/TensorSymmetry>\n\n#include <map>\n#include <set>\n\nusing Eigen::Tensor;\nusing Eigen::SGroup;\nusing Eigen::DynamicSGroup;\nusing Eigen::StaticSGroup;\nusing Eigen::Symmetry;\nusing Eigen::AntiSymmetry;\nusing Eigen::Hermiticity;\nusing Eigen::AntiHermiticity;\n\nusing Eigen::NegationFlag;\nusing Eigen::ConjugationFlag;\nusing Eigen::GlobalZeroFlag;\nusing Eigen::GlobalRealFlag;\nusing Eigen::GlobalImagFlag;\n\n// helper function to determine if the compiler intantiated a static\n// or dynamic symmetry group\ntemplate<typename... Sym>\nbool isDynGroup(StaticSGroup<Sym...> const& dummy)\n{\n  (void)dummy;\n  return false;\n}\n\nbool isDynGroup(DynamicSGroup const& dummy)\n{\n  (void)dummy;\n  return true;\n}\n\n// helper class for checking that the symmetry groups are correct\nstruct checkIdx {\n  template<typename ArrType>\n  static inline int doCheck_(ArrType e, int flags, int dummy, std::set<uint64_t>& found, std::map<uint64_t, int> const& expected)\n  {\n    // use decimal representation of value\n    uint64_t value = e[0];\n    for (std::size_t i = 1; i < e.size(); i++)\n      value = value * 10 + e[i];\n\n    // we want to make sure that we find each element\n    auto it = expected.find(value);\n    VERIFY((it != expected.end()));\n    VERIFY_IS_EQUAL(it->second, flags);\n\n    // we want to make sure we only have each element once;\n    // set::insert returns true for the second part of the pair\n    // if the element was really inserted and not already there\n    auto p = found.insert(value);\n    VERIFY((p.second));\n\n    return dummy;\n  }\n\n  static inline int run(std::vector<int> e, int flags, int dummy, std::set<uint64_t>& found, std::map<uint64_t, int> const& expected)\n  {\n    return doCheck_(e, flags, dummy, found, expected);\n  }\n\n  template<std::size_t N>\n  static inline int run(std::array<int, N> e, int flags, int dummy, std::set<uint64_t>& found, std::map<uint64_t, int> const& expected)\n  {\n    return doCheck_(e, flags, dummy, found, expected);\n  }\n};\n\nstatic void test_symgroups_static()\n{\n  std::array<int, 7> identity{{0,1,2,3,4,5,6}};\n\n  // Simple static symmetry group\n  StaticSGroup<\n    AntiSymmetry<0,1>,\n    Hermiticity<0,2>\n  > group;\n\n  std::set<uint64_t> found;\n  std::map<uint64_t, int> expected;\n  expected[ 123456] = 0;\n  expected[1023456] = NegationFlag;\n  expected[2103456] = ConjugationFlag;\n  expected[1203456] = ConjugationFlag | NegationFlag;\n  expected[2013456] = ConjugationFlag | NegationFlag;\n  expected[ 213456] = ConjugationFlag;\n\n  VERIFY_IS_EQUAL(group.size(), 6u);\n  VERIFY_IS_EQUAL(group.globalFlags(), GlobalImagFlag);\n  group.apply<checkIdx, int>(identity, 0, found, expected);\n  VERIFY_IS_EQUAL(found.size(), 6u);\n}\n\nstatic void test_symgroups_dynamic()\n{\n  std::vector<int> identity;\n  for (int i = 0; i <= 6; i++)\n    identity.push_back(i);\n\n  // Simple dynamic symmetry group\n  DynamicSGroup group;\n  group.add(0,1,NegationFlag);\n  group.add(0,2,ConjugationFlag);\n\n  VERIFY_IS_EQUAL(group.size(), 6u);\n  VERIFY_IS_EQUAL(group.globalFlags(), GlobalImagFlag);\n\n  std::set<uint64_t> found;\n  std::map<uint64_t, int> expected;\n  expected[ 123456] = 0;\n  expected[1023456] = NegationFlag;\n  expected[2103456] = ConjugationFlag;\n  expected[1203456] = ConjugationFlag | NegationFlag;\n  expected[2013456] = ConjugationFlag | NegationFlag;\n  expected[ 213456] = ConjugationFlag;\n\n  VERIFY_IS_EQUAL(group.size(), 6u);\n  VERIFY_IS_EQUAL(group.globalFlags(), GlobalImagFlag);\n  group.apply<checkIdx, int>(identity, 0, found, expected);\n  VERIFY_IS_EQUAL(found.size(), 6u);\n}\n\nstatic void test_symgroups_selection()\n{\n  std::array<int, 7> identity7{{0,1,2,3,4,5,6}};\n  std::array<int, 10> identity10{{0,1,2,3,4,5,6,7,8,9}};\n\n  {\n    // Do the same test as in test_symgroups_static but\n    // require selection via SGroup\n    SGroup<\n      AntiSymmetry<0,1>,\n      Hermiticity<0,2>\n    > group;\n\n    std::set<uint64_t> found;\n    std::map<uint64_t, int> expected;\n    expected[ 123456] = 0;\n    expected[1023456] = NegationFlag;\n    expected[2103456] = ConjugationFlag;\n    expected[1203456] = ConjugationFlag | NegationFlag;\n    expected[2013456] = ConjugationFlag | NegationFlag;\n    expected[ 213456] = ConjugationFlag;\n\n    VERIFY(!isDynGroup(group));\n    VERIFY_IS_EQUAL(group.size(), 6u);\n    VERIFY_IS_EQUAL(group.globalFlags(), GlobalImagFlag);\n    group.apply<checkIdx, int>(identity7, 0, found, expected);\n    VERIFY_IS_EQUAL(found.size(), 6u);\n  }\n\n  {\n    // simple factorizing group: 5 generators, 2^5 = 32 elements\n    // selection should make this dynamic, although static group\n    // can still be reasonably generated\n    SGroup<\n      Symmetry<0,1>,\n      Symmetry<2,3>,\n      Symmetry<4,5>,\n      Symmetry<6,7>,\n      Symmetry<8,9>\n    > group;\n\n    std::set<uint64_t> found;\n    std::map<uint64_t, int> expected;\n    expected[ 123456789] = 0; expected[ 123456798] = 0; expected[ 123457689] = 0; expected[ 123457698] = 0;\n    expected[ 123546789] = 0; expected[ 123546798] = 0; expected[ 123547689] = 0; expected[ 123547698] = 0;\n    expected[ 132456789] = 0; expected[ 132456798] = 0; expected[ 132457689] = 0; expected[ 132457698] = 0;\n    expected[ 132546789] = 0; expected[ 132546798] = 0; expected[ 132547689] = 0; expected[ 132547698] = 0;\n    expected[1023456789] = 0; expected[1023456798] = 0; expected[1023457689] = 0; expected[1023457698] = 0;\n    expected[1023546789] = 0; expected[1023546798] = 0; expected[1023547689] = 0; expected[1023547698] = 0;\n    expected[1032456789] = 0; expected[1032456798] = 0; expected[1032457689] = 0; expected[1032457698] = 0;\n    expected[1032546789] = 0; expected[1032546798] = 0; expected[1032547689] = 0; expected[1032547698] = 0;\n\n    VERIFY(isDynGroup(group));\n    VERIFY_IS_EQUAL(group.size(), 32u);\n    VERIFY_IS_EQUAL(group.globalFlags(), 0);\n    group.apply<checkIdx, int>(identity10, 0, found, expected);\n    VERIFY_IS_EQUAL(found.size(), 32u);\n\n    // no verify that we could also generate a static group\n    // with these generators\n    found.clear();\n    StaticSGroup<\n      Symmetry<0,1>,\n      Symmetry<2,3>,\n      Symmetry<4,5>,\n      Symmetry<6,7>,\n      Symmetry<8,9>\n    > group_static;\n    VERIFY_IS_EQUAL(group_static.size(), 32u);\n    VERIFY_IS_EQUAL(group_static.globalFlags(), 0);\n    group_static.apply<checkIdx, int>(identity10, 0, found, expected);\n    VERIFY_IS_EQUAL(found.size(), 32u);\n  }\n\n  {\n    // try to create a HUGE group\n    SGroup<\n      Symmetry<0,1>,\n      Symmetry<1,2>,\n      Symmetry<2,3>,\n      Symmetry<3,4>,\n      Symmetry<4,5>,\n      Symmetry<5,6>\n    > group;\n\n    std::set<uint64_t> found;\n    uint64_t pre_expected[5040] = {\n       123456, 1023456,  213456, 2013456, 1203456, 2103456,  132456, 1032456,  312456, 3012456, 1302456, 3102456,\n       231456, 2031456,  321456, 3021456, 2301456, 3201456, 1230456, 2130456, 1320456, 3120456, 2310456, 3210456,\n       124356, 1024356,  214356, 2014356, 1204356, 2104356,  142356, 1042356,  412356, 4012356, 1402356, 4102356,\n       241356, 2041356,  421356, 4021356, 2401356, 4201356, 1240356, 2140356, 1420356, 4120356, 2410356, 4210356,\n       134256, 1034256,  314256, 3014256, 1304256, 3104256,  143256, 1043256,  413256, 4013256, 1403256, 4103256,\n       341256, 3041256,  431256, 4031256, 3401256, 4301256, 1340256, 3140256, 1430256, 4130256, 3410256, 4310256,\n       234156, 2034156,  324156, 3024156, 2304156, 3204156,  243156, 2043156,  423156, 4023156, 2403156, 4203156,\n       342156, 3042156,  432156, 4032156, 3402156, 4302156, 2340156, 3240156, 2430156, 4230156, 3420156, 4320156,\n      1234056, 2134056, 1324056, 3124056, 2314056, 3214056, 1243056, 2143056, 1423056, 4123056, 2413056, 4213056,\n      1342056, 3142056, 1432056, 4132056, 3412056, 4312056, 2341056, 3241056, 2431056, 4231056, 3421056, 4321056,\n       123546, 1023546,  213546, 2013546, 1203546, 2103546,  132546, 1032546,  312546, 3012546, 1302546, 3102546,\n       231546, 2031546,  321546, 3021546, 2301546, 3201546, 1230546, 2130546, 1320546, 3120546, 2310546, 3210546,\n       125346, 1025346,  215346, 2015346, 1205346, 2105346,  152346, 1052346,  512346, 5012346, 1502346, 5102346,\n       251346, 2051346,  521346, 5021346, 2501346, 5201346, 1250346, 2150346, 1520346, 5120346, 2510346, 5210346,\n       135246, 1035246,  315246, 3015246, 1305246, 3105246,  153246, 1053246,  513246, 5013246, 1503246, 5103246,\n       351246, 3051246,  531246, 5031246, 3501246, 5301246, 1350246, 3150246, 1530246, 5130246, 3510246, 5310246,\n       235146, 2035146,  325146, 3025146, 2305146, 3205146,  253146, 2053146,  523146, 5023146, 2503146, 5203146,\n       352146, 3052146,  532146, 5032146, 3502146, 5302146, 2350146, 3250146, 2530146, 5230146, 3520146, 5320146,\n      1235046, 2135046, 1325046, 3125046, 2315046, 3215046, 1253046, 2153046, 1523046, 5123046, 2513046, 5213046,\n      1352046, 3152046, 1532046, 5132046, 3512046, 5312046, 2351046, 3251046, 2531046, 5231046, 3521046, 5321046,\n       124536, 1024536,  214536, 2014536, 1204536, 2104536,  142536, 1042536,  412536, 4012536, 1402536, 4102536,\n       241536, 2041536,  421536, 4021536, 2401536, 4201536, 1240536, 2140536, 1420536, 4120536, 2410536, 4210536,\n       125436, 1025436,  215436, 2015436, 1205436, 2105436,  152436, 1052436,  512436, 5012436, 1502436, 5102436,\n       251436, 2051436,  521436, 5021436, 2501436, 5201436, 1250436, 2150436, 1520436, 5120436, 2510436, 5210436,\n       145236, 1045236,  415236, 4015236, 1405236, 4105236,  154236, 1054236,  514236, 5014236, 1504236, 5104236,\n       451236, 4051236,  541236, 5041236, 4501236, 5401236, 1450236, 4150236, 1540236, 5140236, 4510236, 5410236,\n       245136, 2045136,  425136, 4025136, 2405136, 4205136,  254136, 2054136,  524136, 5024136, 2504136, 5204136,\n       452136, 4052136,  542136, 5042136, 4502136, 5402136, 2450136, 4250136, 2540136, 5240136, 4520136, 5420136,\n      1245036, 2145036, 1425036, 4125036, 2415036, 4215036, 1254036, 2154036, 1524036, 5124036, 2514036, 5214036,\n      1452036, 4152036, 1542036, 5142036, 4512036, 5412036, 2451036, 4251036, 2541036, 5241036, 4521036, 5421036,\n       134526, 1034526,  314526, 3014526, 1304526, 3104526,  143526, 1043526,  413526, 4013526, 1403526, 4103526,\n       341526, 3041526,  431526, 4031526, 3401526, 4301526, 1340526, 3140526, 1430526, 4130526, 3410526, 4310526,\n       135426, 1035426,  315426, 3015426, 1305426, 3105426,  153426, 1053426,  513426, 5013426, 1503426, 5103426,\n       351426, 3051426,  531426, 5031426, 3501426, 5301426, 1350426, 3150426, 1530426, 5130426, 3510426, 5310426,\n       145326, 1045326,  415326, 4015326, 1405326, 4105326,  154326, 1054326,  514326, 5014326, 1504326, 5104326,\n       451326, 4051326,  541326, 5041326, 4501326, 5401326, 1450326, 4150326, 1540326, 5140326, 4510326, 5410326,\n       345126, 3045126,  435126, 4035126, 3405126, 4305126,  354126, 3054126,  534126, 5034126, 3504126, 5304126,\n       453126, 4053126,  543126, 5043126, 4503126, 5403126, 3450126, 4350126, 3540126, 5340126, 4530126, 5430126,\n      1345026, 3145026, 1435026, 4135026, 3415026, 4315026, 1354026, 3154026, 1534026, 5134026, 3514026, 5314026,\n      1453026, 4153026, 1543026, 5143026, 4513026, 5413026, 3451026, 4351026, 3541026, 5341026, 4531026, 5431026,\n       234516, 2034516,  324516, 3024516, 2304516, 3204516,  243516, 2043516,  423516, 4023516, 2403516, 4203516,\n       342516, 3042516,  432516, 4032516, 3402516, 4302516, 2340516, 3240516, 2430516, 4230516, 3420516, 4320516,\n       235416, 2035416,  325416, 3025416, 2305416, 3205416,  253416, 2053416,  523416, 5023416, 2503416, 5203416,\n       352416, 3052416,  532416, 5032416, 3502416, 5302416, 2350416, 3250416, 2530416, 5230416, 3520416, 5320416,\n       245316, 2045316,  425316, 4025316, 2405316, 4205316,  254316, 2054316,  524316, 5024316, 2504316, 5204316,\n       452316, 4052316,  542316, 5042316, 4502316, 5402316, 2450316, 4250316, 2540316, 5240316, 4520316, 5420316,\n       345216, 3045216,  435216, 4035216, 3405216, 4305216,  354216, 3054216,  534216, 5034216, 3504216, 5304216,\n       453216, 4053216,  543216, 5043216, 4503216, 5403216, 3450216, 4350216, 3540216, 5340216, 4530216, 5430216,\n      2345016, 3245016, 2435016, 4235016, 3425016, 4325016, 2354016, 3254016, 2534016, 5234016, 3524016, 5324016,\n      2453016, 4253016, 2543016, 5243016, 4523016, 5423016, 3452016, 4352016, 3542016, 5342016, 4532016, 5432016,\n      1234506, 2134506, 1324506, 3124506, 2314506, 3214506, 1243506, 2143506, 1423506, 4123506, 2413506, 4213506,\n      1342506, 3142506, 1432506, 4132506, 3412506, 4312506, 2341506, 3241506, 2431506, 4231506, 3421506, 4321506,\n      1235406, 2135406, 1325406, 3125406, 2315406, 3215406, 1253406, 2153406, 1523406, 5123406, 2513406, 5213406,\n      1352406, 3152406, 1532406, 5132406, 3512406, 5312406, 2351406, 3251406, 2531406, 5231406, 3521406, 5321406,\n      1245306, 2145306, 1425306, 4125306, 2415306, 4215306, 1254306, 2154306, 1524306, 5124306, 2514306, 5214306,\n      1452306, 4152306, 1542306, 5142306, 4512306, 5412306, 2451306, 4251306, 2541306, 5241306, 4521306, 5421306,\n      1345206, 3145206, 1435206, 4135206, 3415206, 4315206, 1354206, 3154206, 1534206, 5134206, 3514206, 5314206,\n      1453206, 4153206, 1543206, 5143206, 4513206, 5413206, 3451206, 4351206, 3541206, 5341206, 4531206, 5431206,\n      2345106, 3245106, 2435106, 4235106, 3425106, 4325106, 2354106, 3254106, 2534106, 5234106, 3524106, 5324106,\n      2453106, 4253106, 2543106, 5243106, 4523106, 5423106, 3452106, 4352106, 3542106, 5342106, 4532106, 5432106,\n       123465, 1023465,  213465, 2013465, 1203465, 2103465,  132465, 1032465,  312465, 3012465, 1302465, 3102465,\n       231465, 2031465,  321465, 3021465, 2301465, 3201465, 1230465, 2130465, 1320465, 3120465, 2310465, 3210465,\n       124365, 1024365,  214365, 2014365, 1204365, 2104365,  142365, 1042365,  412365, 4012365, 1402365, 4102365,\n       241365, 2041365,  421365, 4021365, 2401365, 4201365, 1240365, 2140365, 1420365, 4120365, 2410365, 4210365,\n       134265, 1034265,  314265, 3014265, 1304265, 3104265,  143265, 1043265,  413265, 4013265, 1403265, 4103265,\n       341265, 3041265,  431265, 4031265, 3401265, 4301265, 1340265, 3140265, 1430265, 4130265, 3410265, 4310265,\n       234165, 2034165,  324165, 3024165, 2304165, 3204165,  243165, 2043165,  423165, 4023165, 2403165, 4203165,\n       342165, 3042165,  432165, 4032165, 3402165, 4302165, 2340165, 3240165, 2430165, 4230165, 3420165, 4320165,\n      1234065, 2134065, 1324065, 3124065, 2314065, 3214065, 1243065, 2143065, 1423065, 4123065, 2413065, 4213065,\n      1342065, 3142065, 1432065, 4132065, 3412065, 4312065, 2341065, 3241065, 2431065, 4231065, 3421065, 4321065,\n       123645, 1023645,  213645, 2013645, 1203645, 2103645,  132645, 1032645,  312645, 3012645, 1302645, 3102645,\n       231645, 2031645,  321645, 3021645, 2301645, 3201645, 1230645, 2130645, 1320645, 3120645, 2310645, 3210645,\n       126345, 1026345,  216345, 2016345, 1206345, 2106345,  162345, 1062345,  612345, 6012345, 1602345, 6102345,\n       261345, 2061345,  621345, 6021345, 2601345, 6201345, 1260345, 2160345, 1620345, 6120345, 2610345, 6210345,\n       136245, 1036245,  316245, 3016245, 1306245, 3106245,  163245, 1063245,  613245, 6013245, 1603245, 6103245,\n       361245, 3061245,  631245, 6031245, 3601245, 6301245, 1360245, 3160245, 1630245, 6130245, 3610245, 6310245,\n       236145, 2036145,  326145, 3026145, 2306145, 3206145,  263145, 2063145,  623145, 6023145, 2603145, 6203145,\n       362145, 3062145,  632145, 6032145, 3602145, 6302145, 2360145, 3260145, 2630145, 6230145, 3620145, 6320145,\n      1236045, 2136045, 1326045, 3126045, 2316045, 3216045, 1263045, 2163045, 1623045, 6123045, 2613045, 6213045,\n      1362045, 3162045, 1632045, 6132045, 3612045, 6312045, 2361045, 3261045, 2631045, 6231045, 3621045, 6321045,\n       124635, 1024635,  214635, 2014635, 1204635, 2104635,  142635, 1042635,  412635, 4012635, 1402635, 4102635,\n       241635, 2041635,  421635, 4021635, 2401635, 4201635, 1240635, 2140635, 1420635, 4120635, 2410635, 4210635,\n       126435, 1026435,  216435, 2016435, 1206435, 2106435,  162435, 1062435,  612435, 6012435, 1602435, 6102435,\n       261435, 2061435,  621435, 6021435, 2601435, 6201435, 1260435, 2160435, 1620435, 6120435, 2610435, 6210435,\n       146235, 1046235,  416235, 4016235, 1406235, 4106235,  164235, 1064235,  614235, 6014235, 1604235, 6104235,\n       461235, 4061235,  641235, 6041235, 4601235, 6401235, 1460235, 4160235, 1640235, 6140235, 4610235, 6410235,\n       246135, 2046135,  426135, 4026135, 2406135, 4206135,  264135, 2064135,  624135, 6024135, 2604135, 6204135,\n       462135, 4062135,  642135, 6042135, 4602135, 6402135, 2460135, 4260135, 2640135, 6240135, 4620135, 6420135,\n      1246035, 2146035, 1426035, 4126035, 2416035, 4216035, 1264035, 2164035, 1624035, 6124035, 2614035, 6214035,\n      1462035, 4162035, 1642035, 6142035, 4612035, 6412035, 2461035, 4261035, 2641035, 6241035, 4621035, 6421035,\n       134625, 1034625,  314625, 3014625, 1304625, 3104625,  143625, 1043625,  413625, 4013625, 1403625, 4103625,\n       341625, 3041625,  431625, 4031625, 3401625, 4301625, 1340625, 3140625, 1430625, 4130625, 3410625, 4310625,\n       136425, 1036425,  316425, 3016425, 1306425, 3106425,  163425, 1063425,  613425, 6013425, 1603425, 6103425,\n       361425, 3061425,  631425, 6031425, 3601425, 6301425, 1360425, 3160425, 1630425, 6130425, 3610425, 6310425,\n       146325, 1046325,  416325, 4016325, 1406325, 4106325,  164325, 1064325,  614325, 6014325, 1604325, 6104325,\n       461325, 4061325,  641325, 6041325, 4601325, 6401325, 1460325, 4160325, 1640325, 6140325, 4610325, 6410325,\n       346125, 3046125,  436125, 4036125, 3406125, 4306125,  364125, 3064125,  634125, 6034125, 3604125, 6304125,\n       463125, 4063125,  643125, 6043125, 4603125, 6403125, 3460125, 4360125, 3640125, 6340125, 4630125, 6430125,\n      1346025, 3146025, 1436025, 4136025, 3416025, 4316025, 1364025, 3164025, 1634025, 6134025, 3614025, 6314025,\n      1463025, 4163025, 1643025, 6143025, 4613025, 6413025, 3461025, 4361025, 3641025, 6341025, 4631025, 6431025,\n       234615, 2034615,  324615, 3024615, 2304615, 3204615,  243615, 2043615,  423615, 4023615, 2403615, 4203615,\n       342615, 3042615,  432615, 4032615, 3402615, 4302615, 2340615, 3240615, 2430615, 4230615, 3420615, 4320615,\n       236415, 2036415,  326415, 3026415, 2306415, 3206415,  263415, 2063415,  623415, 6023415, 2603415, 6203415,\n       362415, 3062415,  632415, 6032415, 3602415, 6302415, 2360415, 3260415, 2630415, 6230415, 3620415, 6320415,\n       246315, 2046315,  426315, 4026315, 2406315, 4206315,  264315, 2064315,  624315, 6024315, 2604315, 6204315,\n       462315, 4062315,  642315, 6042315, 4602315, 6402315, 2460315, 4260315, 2640315, 6240315, 4620315, 6420315,\n       346215, 3046215,  436215, 4036215, 3406215, 4306215,  364215, 3064215,  634215, 6034215, 3604215, 6304215,\n       463215, 4063215,  643215, 6043215, 4603215, 6403215, 3460215, 4360215, 3640215, 6340215, 4630215, 6430215,\n      2346015, 3246015, 2436015, 4236015, 3426015, 4326015, 2364015, 3264015, 2634015, 6234015, 3624015, 6324015,\n      2463015, 4263015, 2643015, 6243015, 4623015, 6423015, 3462015, 4362015, 3642015, 6342015, 4632015, 6432015,\n      1234605, 2134605, 1324605, 3124605, 2314605, 3214605, 1243605, 2143605, 1423605, 4123605, 2413605, 4213605,\n      1342605, 3142605, 1432605, 4132605, 3412605, 4312605, 2341605, 3241605, 2431605, 4231605, 3421605, 4321605,\n      1236405, 2136405, 1326405, 3126405, 2316405, 3216405, 1263405, 2163405, 1623405, 6123405, 2613405, 6213405,\n      1362405, 3162405, 1632405, 6132405, 3612405, 6312405, 2361405, 3261405, 2631405, 6231405, 3621405, 6321405,\n      1246305, 2146305, 1426305, 4126305, 2416305, 4216305, 1264305, 2164305, 1624305, 6124305, 2614305, 6214305,\n      1462305, 4162305, 1642305, 6142305, 4612305, 6412305, 2461305, 4261305, 2641305, 6241305, 4621305, 6421305,\n      1346205, 3146205, 1436205, 4136205, 3416205, 4316205, 1364205, 3164205, 1634205, 6134205, 3614205, 6314205,\n      1463205, 4163205, 1643205, 6143205, 4613205, 6413205, 3461205, 4361205, 3641205, 6341205, 4631205, 6431205,\n      2346105, 3246105, 2436105, 4236105, 3426105, 4326105, 2364105, 3264105, 2634105, 6234105, 3624105, 6324105,\n      2463105, 4263105, 2643105, 6243105, 4623105, 6423105, 3462105, 4362105, 3642105, 6342105, 4632105, 6432105,\n       123564, 1023564,  213564, 2013564, 1203564, 2103564,  132564, 1032564,  312564, 3012564, 1302564, 3102564,\n       231564, 2031564,  321564, 3021564, 2301564, 3201564, 1230564, 2130564, 1320564, 3120564, 2310564, 3210564,\n       125364, 1025364,  215364, 2015364, 1205364, 2105364,  152364, 1052364,  512364, 5012364, 1502364, 5102364,\n       251364, 2051364,  521364, 5021364, 2501364, 5201364, 1250364, 2150364, 1520364, 5120364, 2510364, 5210364,\n       135264, 1035264,  315264, 3015264, 1305264, 3105264,  153264, 1053264,  513264, 5013264, 1503264, 5103264,\n       351264, 3051264,  531264, 5031264, 3501264, 5301264, 1350264, 3150264, 1530264, 5130264, 3510264, 5310264,\n       235164, 2035164,  325164, 3025164, 2305164, 3205164,  253164, 2053164,  523164, 5023164, 2503164, 5203164,\n       352164, 3052164,  532164, 5032164, 3502164, 5302164, 2350164, 3250164, 2530164, 5230164, 3520164, 5320164,\n      1235064, 2135064, 1325064, 3125064, 2315064, 3215064, 1253064, 2153064, 1523064, 5123064, 2513064, 5213064,\n      1352064, 3152064, 1532064, 5132064, 3512064, 5312064, 2351064, 3251064, 2531064, 5231064, 3521064, 5321064,\n       123654, 1023654,  213654, 2013654, 1203654, 2103654,  132654, 1032654,  312654, 3012654, 1302654, 3102654,\n       231654, 2031654,  321654, 3021654, 2301654, 3201654, 1230654, 2130654, 1320654, 3120654, 2310654, 3210654,\n       126354, 1026354,  216354, 2016354, 1206354, 2106354,  162354, 1062354,  612354, 6012354, 1602354, 6102354,\n       261354, 2061354,  621354, 6021354, 2601354, 6201354, 1260354, 2160354, 1620354, 6120354, 2610354, 6210354,\n       136254, 1036254,  316254, 3016254, 1306254, 3106254,  163254, 1063254,  613254, 6013254, 1603254, 6103254,\n       361254, 3061254,  631254, 6031254, 3601254, 6301254, 1360254, 3160254, 1630254, 6130254, 3610254, 6310254,\n       236154, 2036154,  326154, 3026154, 2306154, 3206154,  263154, 2063154,  623154, 6023154, 2603154, 6203154,\n       362154, 3062154,  632154, 6032154, 3602154, 6302154, 2360154, 3260154, 2630154, 6230154, 3620154, 6320154,\n      1236054, 2136054, 1326054, 3126054, 2316054, 3216054, 1263054, 2163054, 1623054, 6123054, 2613054, 6213054,\n      1362054, 3162054, 1632054, 6132054, 3612054, 6312054, 2361054, 3261054, 2631054, 6231054, 3621054, 6321054,\n       125634, 1025634,  215634, 2015634, 1205634, 2105634,  152634, 1052634,  512634, 5012634, 1502634, 5102634,\n       251634, 2051634,  521634, 5021634, 2501634, 5201634, 1250634, 2150634, 1520634, 5120634, 2510634, 5210634,\n       126534, 1026534,  216534, 2016534, 1206534, 2106534,  162534, 1062534,  612534, 6012534, 1602534, 6102534,\n       261534, 2061534,  621534, 6021534, 2601534, 6201534, 1260534, 2160534, 1620534, 6120534, 2610534, 6210534,\n       156234, 1056234,  516234, 5016234, 1506234, 5106234,  165234, 1065234,  615234, 6015234, 1605234, 6105234,\n       561234, 5061234,  651234, 6051234, 5601234, 6501234, 1560234, 5160234, 1650234, 6150234, 5610234, 6510234,\n       256134, 2056134,  526134, 5026134, 2506134, 5206134,  265134, 2065134,  625134, 6025134, 2605134, 6205134,\n       562134, 5062134,  652134, 6052134, 5602134, 6502134, 2560134, 5260134, 2650134, 6250134, 5620134, 6520134,\n      1256034, 2156034, 1526034, 5126034, 2516034, 5216034, 1265034, 2165034, 1625034, 6125034, 2615034, 6215034,\n      1562034, 5162034, 1652034, 6152034, 5612034, 6512034, 2561034, 5261034, 2651034, 6251034, 5621034, 6521034,\n       135624, 1035624,  315624, 3015624, 1305624, 3105624,  153624, 1053624,  513624, 5013624, 1503624, 5103624,\n       351624, 3051624,  531624, 5031624, 3501624, 5301624, 1350624, 3150624, 1530624, 5130624, 3510624, 5310624,\n       136524, 1036524,  316524, 3016524, 1306524, 3106524,  163524, 1063524,  613524, 6013524, 1603524, 6103524,\n       361524, 3061524,  631524, 6031524, 3601524, 6301524, 1360524, 3160524, 1630524, 6130524, 3610524, 6310524,\n       156324, 1056324,  516324, 5016324, 1506324, 5106324,  165324, 1065324,  615324, 6015324, 1605324, 6105324,\n       561324, 5061324,  651324, 6051324, 5601324, 6501324, 1560324, 5160324, 1650324, 6150324, 5610324, 6510324,\n       356124, 3056124,  536124, 5036124, 3506124, 5306124,  365124, 3065124,  635124, 6035124, 3605124, 6305124,\n       563124, 5063124,  653124, 6053124, 5603124, 6503124, 3560124, 5360124, 3650124, 6350124, 5630124, 6530124,\n      1356024, 3156024, 1536024, 5136024, 3516024, 5316024, 1365024, 3165024, 1635024, 6135024, 3615024, 6315024,\n      1563024, 5163024, 1653024, 6153024, 5613024, 6513024, 3561024, 5361024, 3651024, 6351024, 5631024, 6531024,\n       235614, 2035614,  325614, 3025614, 2305614, 3205614,  253614, 2053614,  523614, 5023614, 2503614, 5203614,\n       352614, 3052614,  532614, 5032614, 3502614, 5302614, 2350614, 3250614, 2530614, 5230614, 3520614, 5320614,\n       236514, 2036514,  326514, 3026514, 2306514, 3206514,  263514, 2063514,  623514, 6023514, 2603514, 6203514,\n       362514, 3062514,  632514, 6032514, 3602514, 6302514, 2360514, 3260514, 2630514, 6230514, 3620514, 6320514,\n       256314, 2056314,  526314, 5026314, 2506314, 5206314,  265314, 2065314,  625314, 6025314, 2605314, 6205314,\n       562314, 5062314,  652314, 6052314, 5602314, 6502314, 2560314, 5260314, 2650314, 6250314, 5620314, 6520314,\n       356214, 3056214,  536214, 5036214, 3506214, 5306214,  365214, 3065214,  635214, 6035214, 3605214, 6305214,\n       563214, 5063214,  653214, 6053214, 5603214, 6503214, 3560214, 5360214, 3650214, 6350214, 5630214, 6530214,\n      2356014, 3256014, 2536014, 5236014, 3526014, 5326014, 2365014, 3265014, 2635014, 6235014, 3625014, 6325014,\n      2563014, 5263014, 2653014, 6253014, 5623014, 6523014, 3562014, 5362014, 3652014, 6352014, 5632014, 6532014,\n      1235604, 2135604, 1325604, 3125604, 2315604, 3215604, 1253604, 2153604, 1523604, 5123604, 2513604, 5213604,\n      1352604, 3152604, 1532604, 5132604, 3512604, 5312604, 2351604, 3251604, 2531604, 5231604, 3521604, 5321604,\n      1236504, 2136504, 1326504, 3126504, 2316504, 3216504, 1263504, 2163504, 1623504, 6123504, 2613504, 6213504,\n      1362504, 3162504, 1632504, 6132504, 3612504, 6312504, 2361504, 3261504, 2631504, 6231504, 3621504, 6321504,\n      1256304, 2156304, 1526304, 5126304, 2516304, 5216304, 1265304, 2165304, 1625304, 6125304, 2615304, 6215304,\n      1562304, 5162304, 1652304, 6152304, 5612304, 6512304, 2561304, 5261304, 2651304, 6251304, 5621304, 6521304,\n      1356204, 3156204, 1536204, 5136204, 3516204, 5316204, 1365204, 3165204, 1635204, 6135204, 3615204, 6315204,\n      1563204, 5163204, 1653204, 6153204, 5613204, 6513204, 3561204, 5361204, 3651204, 6351204, 5631204, 6531204,\n      2356104, 3256104, 2536104, 5236104, 3526104, 5326104, 2365104, 3265104, 2635104, 6235104, 3625104, 6325104,\n      2563104, 5263104, 2653104, 6253104, 5623104, 6523104, 3562104, 5362104, 3652104, 6352104, 5632104, 6532104,\n       124563, 1024563,  214563, 2014563, 1204563, 2104563,  142563, 1042563,  412563, 4012563, 1402563, 4102563,\n       241563, 2041563,  421563, 4021563, 2401563, 4201563, 1240563, 2140563, 1420563, 4120563, 2410563, 4210563,\n       125463, 1025463,  215463, 2015463, 1205463, 2105463,  152463, 1052463,  512463, 5012463, 1502463, 5102463,\n       251463, 2051463,  521463, 5021463, 2501463, 5201463, 1250463, 2150463, 1520463, 5120463, 2510463, 5210463,\n       145263, 1045263,  415263, 4015263, 1405263, 4105263,  154263, 1054263,  514263, 5014263, 1504263, 5104263,\n       451263, 4051263,  541263, 5041263, 4501263, 5401263, 1450263, 4150263, 1540263, 5140263, 4510263, 5410263,\n       245163, 2045163,  425163, 4025163, 2405163, 4205163,  254163, 2054163,  524163, 5024163, 2504163, 5204163,\n       452163, 4052163,  542163, 5042163, 4502163, 5402163, 2450163, 4250163, 2540163, 5240163, 4520163, 5420163,\n      1245063, 2145063, 1425063, 4125063, 2415063, 4215063, 1254063, 2154063, 1524063, 5124063, 2514063, 5214063,\n      1452063, 4152063, 1542063, 5142063, 4512063, 5412063, 2451063, 4251063, 2541063, 5241063, 4521063, 5421063,\n       124653, 1024653,  214653, 2014653, 1204653, 2104653,  142653, 1042653,  412653, 4012653, 1402653, 4102653,\n       241653, 2041653,  421653, 4021653, 2401653, 4201653, 1240653, 2140653, 1420653, 4120653, 2410653, 4210653,\n       126453, 1026453,  216453, 2016453, 1206453, 2106453,  162453, 1062453,  612453, 6012453, 1602453, 6102453,\n       261453, 2061453,  621453, 6021453, 2601453, 6201453, 1260453, 2160453, 1620453, 6120453, 2610453, 6210453,\n       146253, 1046253,  416253, 4016253, 1406253, 4106253,  164253, 1064253,  614253, 6014253, 1604253, 6104253,\n       461253, 4061253,  641253, 6041253, 4601253, 6401253, 1460253, 4160253, 1640253, 6140253, 4610253, 6410253,\n       246153, 2046153,  426153, 4026153, 2406153, 4206153,  264153, 2064153,  624153, 6024153, 2604153, 6204153,\n       462153, 4062153,  642153, 6042153, 4602153, 6402153, 2460153, 4260153, 2640153, 6240153, 4620153, 6420153,\n      1246053, 2146053, 1426053, 4126053, 2416053, 4216053, 1264053, 2164053, 1624053, 6124053, 2614053, 6214053,\n      1462053, 4162053, 1642053, 6142053, 4612053, 6412053, 2461053, 4261053, 2641053, 6241053, 4621053, 6421053,\n       125643, 1025643,  215643, 2015643, 1205643, 2105643,  152643, 1052643,  512643, 5012643, 1502643, 5102643,\n       251643, 2051643,  521643, 5021643, 2501643, 5201643, 1250643, 2150643, 1520643, 5120643, 2510643, 5210643,\n       126543, 1026543,  216543, 2016543, 1206543, 2106543,  162543, 1062543,  612543, 6012543, 1602543, 6102543,\n       261543, 2061543,  621543, 6021543, 2601543, 6201543, 1260543, 2160543, 1620543, 6120543, 2610543, 6210543,\n       156243, 1056243,  516243, 5016243, 1506243, 5106243,  165243, 1065243,  615243, 6015243, 1605243, 6105243,\n       561243, 5061243,  651243, 6051243, 5601243, 6501243, 1560243, 5160243, 1650243, 6150243, 5610243, 6510243,\n       256143, 2056143,  526143, 5026143, 2506143, 5206143,  265143, 2065143,  625143, 6025143, 2605143, 6205143,\n       562143, 5062143,  652143, 6052143, 5602143, 6502143, 2560143, 5260143, 2650143, 6250143, 5620143, 6520143,\n      1256043, 2156043, 1526043, 5126043, 2516043, 5216043, 1265043, 2165043, 1625043, 6125043, 2615043, 6215043,\n      1562043, 5162043, 1652043, 6152043, 5612043, 6512043, 2561043, 5261043, 2651043, 6251043, 5621043, 6521043,\n       145623, 1045623,  415623, 4015623, 1405623, 4105623,  154623, 1054623,  514623, 5014623, 1504623, 5104623,\n       451623, 4051623,  541623, 5041623, 4501623, 5401623, 1450623, 4150623, 1540623, 5140623, 4510623, 5410623,\n       146523, 1046523,  416523, 4016523, 1406523, 4106523,  164523, 1064523,  614523, 6014523, 1604523, 6104523,\n       461523, 4061523,  641523, 6041523, 4601523, 6401523, 1460523, 4160523, 1640523, 6140523, 4610523, 6410523,\n       156423, 1056423,  516423, 5016423, 1506423, 5106423,  165423, 1065423,  615423, 6015423, 1605423, 6105423,\n       561423, 5061423,  651423, 6051423, 5601423, 6501423, 1560423, 5160423, 1650423, 6150423, 5610423, 6510423,\n       456123, 4056123,  546123, 5046123, 4506123, 5406123,  465123, 4065123,  645123, 6045123, 4605123, 6405123,\n       564123, 5064123,  654123, 6054123, 5604123, 6504123, 4560123, 5460123, 4650123, 6450123, 5640123, 6540123,\n      1456023, 4156023, 1546023, 5146023, 4516023, 5416023, 1465023, 4165023, 1645023, 6145023, 4615023, 6415023,\n      1564023, 5164023, 1654023, 6154023, 5614023, 6514023, 4561023, 5461023, 4651023, 6451023, 5641023, 6541023,\n       245613, 2045613,  425613, 4025613, 2405613, 4205613,  254613, 2054613,  524613, 5024613, 2504613, 5204613,\n       452613, 4052613,  542613, 5042613, 4502613, 5402613, 2450613, 4250613, 2540613, 5240613, 4520613, 5420613,\n       246513, 2046513,  426513, 4026513, 2406513, 4206513,  264513, 2064513,  624513, 6024513, 2604513, 6204513,\n       462513, 4062513,  642513, 6042513, 4602513, 6402513, 2460513, 4260513, 2640513, 6240513, 4620513, 6420513,\n       256413, 2056413,  526413, 5026413, 2506413, 5206413,  265413, 2065413,  625413, 6025413, 2605413, 6205413,\n       562413, 5062413,  652413, 6052413, 5602413, 6502413, 2560413, 5260413, 2650413, 6250413, 5620413, 6520413,\n       456213, 4056213,  546213, 5046213, 4506213, 5406213,  465213, 4065213,  645213, 6045213, 4605213, 6405213,\n       564213, 5064213,  654213, 6054213, 5604213, 6504213, 4560213, 5460213, 4650213, 6450213, 5640213, 6540213,\n      2456013, 4256013, 2546013, 5246013, 4526013, 5426013, 2465013, 4265013, 2645013, 6245013, 4625013, 6425013,\n      2564013, 5264013, 2654013, 6254013, 5624013, 6524013, 4562013, 5462013, 4652013, 6452013, 5642013, 6542013,\n      1245603, 2145603, 1425603, 4125603, 2415603, 4215603, 1254603, 2154603, 1524603, 5124603, 2514603, 5214603,\n      1452603, 4152603, 1542603, 5142603, 4512603, 5412603, 2451603, 4251603, 2541603, 5241603, 4521603, 5421603,\n      1246503, 2146503, 1426503, 4126503, 2416503, 4216503, 1264503, 2164503, 1624503, 6124503, 2614503, 6214503,\n      1462503, 4162503, 1642503, 6142503, 4612503, 6412503, 2461503, 4261503, 2641503, 6241503, 4621503, 6421503,\n      1256403, 2156403, 1526403, 5126403, 2516403, 5216403, 1265403, 2165403, 1625403, 6125403, 2615403, 6215403,\n      1562403, 5162403, 1652403, 6152403, 5612403, 6512403, 2561403, 5261403, 2651403, 6251403, 5621403, 6521403,\n      1456203, 4156203, 1546203, 5146203, 4516203, 5416203, 1465203, 4165203, 1645203, 6145203, 4615203, 6415203,\n      1564203, 5164203, 1654203, 6154203, 5614203, 6514203, 4561203, 5461203, 4651203, 6451203, 5641203, 6541203,\n      2456103, 4256103, 2546103, 5246103, 4526103, 5426103, 2465103, 4265103, 2645103, 6245103, 4625103, 6425103,\n      2564103, 5264103, 2654103, 6254103, 5624103, 6524103, 4562103, 5462103, 4652103, 6452103, 5642103, 6542103,\n       134562, 1034562,  314562, 3014562, 1304562, 3104562,  143562, 1043562,  413562, 4013562, 1403562, 4103562,\n       341562, 3041562,  431562, 4031562, 3401562, 4301562, 1340562, 3140562, 1430562, 4130562, 3410562, 4310562,\n       135462, 1035462,  315462, 3015462, 1305462, 3105462,  153462, 1053462,  513462, 5013462, 1503462, 5103462,\n       351462, 3051462,  531462, 5031462, 3501462, 5301462, 1350462, 3150462, 1530462, 5130462, 3510462, 5310462,\n       145362, 1045362,  415362, 4015362, 1405362, 4105362,  154362, 1054362,  514362, 5014362, 1504362, 5104362,\n       451362, 4051362,  541362, 5041362, 4501362, 5401362, 1450362, 4150362, 1540362, 5140362, 4510362, 5410362,\n       345162, 3045162,  435162, 4035162, 3405162, 4305162,  354162, 3054162,  534162, 5034162, 3504162, 5304162,\n       453162, 4053162,  543162, 5043162, 4503162, 5403162, 3450162, 4350162, 3540162, 5340162, 4530162, 5430162,\n      1345062, 3145062, 1435062, 4135062, 3415062, 4315062, 1354062, 3154062, 1534062, 5134062, 3514062, 5314062,\n      1453062, 4153062, 1543062, 5143062, 4513062, 5413062, 3451062, 4351062, 3541062, 5341062, 4531062, 5431062,\n       134652, 1034652,  314652, 3014652, 1304652, 3104652,  143652, 1043652,  413652, 4013652, 1403652, 4103652,\n       341652, 3041652,  431652, 4031652, 3401652, 4301652, 1340652, 3140652, 1430652, 4130652, 3410652, 4310652,\n       136452, 1036452,  316452, 3016452, 1306452, 3106452,  163452, 1063452,  613452, 6013452, 1603452, 6103452,\n       361452, 3061452,  631452, 6031452, 3601452, 6301452, 1360452, 3160452, 1630452, 6130452, 3610452, 6310452,\n       146352, 1046352,  416352, 4016352, 1406352, 4106352,  164352, 1064352,  614352, 6014352, 1604352, 6104352,\n       461352, 4061352,  641352, 6041352, 4601352, 6401352, 1460352, 4160352, 1640352, 6140352, 4610352, 6410352,\n       346152, 3046152,  436152, 4036152, 3406152, 4306152,  364152, 3064152,  634152, 6034152, 3604152, 6304152,\n       463152, 4063152,  643152, 6043152, 4603152, 6403152, 3460152, 4360152, 3640152, 6340152, 4630152, 6430152,\n      1346052, 3146052, 1436052, 4136052, 3416052, 4316052, 1364052, 3164052, 1634052, 6134052, 3614052, 6314052,\n      1463052, 4163052, 1643052, 6143052, 4613052, 6413052, 3461052, 4361052, 3641052, 6341052, 4631052, 6431052,\n       135642, 1035642,  315642, 3015642, 1305642, 3105642,  153642, 1053642,  513642, 5013642, 1503642, 5103642,\n       351642, 3051642,  531642, 5031642, 3501642, 5301642, 1350642, 3150642, 1530642, 5130642, 3510642, 5310642,\n       136542, 1036542,  316542, 3016542, 1306542, 3106542,  163542, 1063542,  613542, 6013542, 1603542, 6103542,\n       361542, 3061542,  631542, 6031542, 3601542, 6301542, 1360542, 3160542, 1630542, 6130542, 3610542, 6310542,\n       156342, 1056342,  516342, 5016342, 1506342, 5106342,  165342, 1065342,  615342, 6015342, 1605342, 6105342,\n       561342, 5061342,  651342, 6051342, 5601342, 6501342, 1560342, 5160342, 1650342, 6150342, 5610342, 6510342,\n       356142, 3056142,  536142, 5036142, 3506142, 5306142,  365142, 3065142,  635142, 6035142, 3605142, 6305142,\n       563142, 5063142,  653142, 6053142, 5603142, 6503142, 3560142, 5360142, 3650142, 6350142, 5630142, 6530142,\n      1356042, 3156042, 1536042, 5136042, 3516042, 5316042, 1365042, 3165042, 1635042, 6135042, 3615042, 6315042,\n      1563042, 5163042, 1653042, 6153042, 5613042, 6513042, 3561042, 5361042, 3651042, 6351042, 5631042, 6531042,\n       145632, 1045632,  415632, 4015632, 1405632, 4105632,  154632, 1054632,  514632, 5014632, 1504632, 5104632,\n       451632, 4051632,  541632, 5041632, 4501632, 5401632, 1450632, 4150632, 1540632, 5140632, 4510632, 5410632,\n       146532, 1046532,  416532, 4016532, 1406532, 4106532,  164532, 1064532,  614532, 6014532, 1604532, 6104532,\n       461532, 4061532,  641532, 6041532, 4601532, 6401532, 1460532, 4160532, 1640532, 6140532, 4610532, 6410532,\n       156432, 1056432,  516432, 5016432, 1506432, 5106432,  165432, 1065432,  615432, 6015432, 1605432, 6105432,\n       561432, 5061432,  651432, 6051432, 5601432, 6501432, 1560432, 5160432, 1650432, 6150432, 5610432, 6510432,\n       456132, 4056132,  546132, 5046132, 4506132, 5406132,  465132, 4065132,  645132, 6045132, 4605132, 6405132,\n       564132, 5064132,  654132, 6054132, 5604132, 6504132, 4560132, 5460132, 4650132, 6450132, 5640132, 6540132,\n      1456032, 4156032, 1546032, 5146032, 4516032, 5416032, 1465032, 4165032, 1645032, 6145032, 4615032, 6415032,\n      1564032, 5164032, 1654032, 6154032, 5614032, 6514032, 4561032, 5461032, 4651032, 6451032, 5641032, 6541032,\n       345612, 3045612,  435612, 4035612, 3405612, 4305612,  354612, 3054612,  534612, 5034612, 3504612, 5304612,\n       453612, 4053612,  543612, 5043612, 4503612, 5403612, 3450612, 4350612, 3540612, 5340612, 4530612, 5430612,\n       346512, 3046512,  436512, 4036512, 3406512, 4306512,  364512, 3064512,  634512, 6034512, 3604512, 6304512,\n       463512, 4063512,  643512, 6043512, 4603512, 6403512, 3460512, 4360512, 3640512, 6340512, 4630512, 6430512,\n       356412, 3056412,  536412, 5036412, 3506412, 5306412,  365412, 3065412,  635412, 6035412, 3605412, 6305412,\n       563412, 5063412,  653412, 6053412, 5603412, 6503412, 3560412, 5360412, 3650412, 6350412, 5630412, 6530412,\n       456312, 4056312,  546312, 5046312, 4506312, 5406312,  465312, 4065312,  645312, 6045312, 4605312, 6405312,\n       564312, 5064312,  654312, 6054312, 5604312, 6504312, 4560312, 5460312, 4650312, 6450312, 5640312, 6540312,\n      3456012, 4356012, 3546012, 5346012, 4536012, 5436012, 3465012, 4365012, 3645012, 6345012, 4635012, 6435012,\n      3564012, 5364012, 3654012, 6354012, 5634012, 6534012, 4563012, 5463012, 4653012, 6453012, 5643012, 6543012,\n      1345602, 3145602, 1435602, 4135602, 3415602, 4315602, 1354602, 3154602, 1534602, 5134602, 3514602, 5314602,\n      1453602, 4153602, 1543602, 5143602, 4513602, 5413602, 3451602, 4351602, 3541602, 5341602, 4531602, 5431602,\n      1346502, 3146502, 1436502, 4136502, 3416502, 4316502, 1364502, 3164502, 1634502, 6134502, 3614502, 6314502,\n      1463502, 4163502, 1643502, 6143502, 4613502, 6413502, 3461502, 4361502, 3641502, 6341502, 4631502, 6431502,\n      1356402, 3156402, 1536402, 5136402, 3516402, 5316402, 1365402, 3165402, 1635402, 6135402, 3615402, 6315402,\n      1563402, 5163402, 1653402, 6153402, 5613402, 6513402, 3561402, 5361402, 3651402, 6351402, 5631402, 6531402,\n      1456302, 4156302, 1546302, 5146302, 4516302, 5416302, 1465302, 4165302, 1645302, 6145302, 4615302, 6415302,\n      1564302, 5164302, 1654302, 6154302, 5614302, 6514302, 4561302, 5461302, 4651302, 6451302, 5641302, 6541302,\n      3456102, 4356102, 3546102, 5346102, 4536102, 5436102, 3465102, 4365102, 3645102, 6345102, 4635102, 6435102,\n      3564102, 5364102, 3654102, 6354102, 5634102, 6534102, 4563102, 5463102, 4653102, 6453102, 5643102, 6543102,\n       234561, 2034561,  324561, 3024561, 2304561, 3204561,  243561, 2043561,  423561, 4023561, 2403561, 4203561,\n       342561, 3042561,  432561, 4032561, 3402561, 4302561, 2340561, 3240561, 2430561, 4230561, 3420561, 4320561,\n       235461, 2035461,  325461, 3025461, 2305461, 3205461,  253461, 2053461,  523461, 5023461, 2503461, 5203461,\n       352461, 3052461,  532461, 5032461, 3502461, 5302461, 2350461, 3250461, 2530461, 5230461, 3520461, 5320461,\n       245361, 2045361,  425361, 4025361, 2405361, 4205361,  254361, 2054361,  524361, 5024361, 2504361, 5204361,\n       452361, 4052361,  542361, 5042361, 4502361, 5402361, 2450361, 4250361, 2540361, 5240361, 4520361, 5420361,\n       345261, 3045261,  435261, 4035261, 3405261, 4305261,  354261, 3054261,  534261, 5034261, 3504261, 5304261,\n       453261, 4053261,  543261, 5043261, 4503261, 5403261, 3450261, 4350261, 3540261, 5340261, 4530261, 5430261,\n      2345061, 3245061, 2435061, 4235061, 3425061, 4325061, 2354061, 3254061, 2534061, 5234061, 3524061, 5324061,\n      2453061, 4253061, 2543061, 5243061, 4523061, 5423061, 3452061, 4352061, 3542061, 5342061, 4532061, 5432061,\n       234651, 2034651,  324651, 3024651, 2304651, 3204651,  243651, 2043651,  423651, 4023651, 2403651, 4203651,\n       342651, 3042651,  432651, 4032651, 3402651, 4302651, 2340651, 3240651, 2430651, 4230651, 3420651, 4320651,\n       236451, 2036451,  326451, 3026451, 2306451, 3206451,  263451, 2063451,  623451, 6023451, 2603451, 6203451,\n       362451, 3062451,  632451, 6032451, 3602451, 6302451, 2360451, 3260451, 2630451, 6230451, 3620451, 6320451,\n       246351, 2046351,  426351, 4026351, 2406351, 4206351,  264351, 2064351,  624351, 6024351, 2604351, 6204351,\n       462351, 4062351,  642351, 6042351, 4602351, 6402351, 2460351, 4260351, 2640351, 6240351, 4620351, 6420351,\n       346251, 3046251,  436251, 4036251, 3406251, 4306251,  364251, 3064251,  634251, 6034251, 3604251, 6304251,\n       463251, 4063251,  643251, 6043251, 4603251, 6403251, 3460251, 4360251, 3640251, 6340251, 4630251, 6430251,\n      2346051, 3246051, 2436051, 4236051, 3426051, 4326051, 2364051, 3264051, 2634051, 6234051, 3624051, 6324051,\n      2463051, 4263051, 2643051, 6243051, 4623051, 6423051, 3462051, 4362051, 3642051, 6342051, 4632051, 6432051,\n       235641, 2035641,  325641, 3025641, 2305641, 3205641,  253641, 2053641,  523641, 5023641, 2503641, 5203641,\n       352641, 3052641,  532641, 5032641, 3502641, 5302641, 2350641, 3250641, 2530641, 5230641, 3520641, 5320641,\n       236541, 2036541,  326541, 3026541, 2306541, 3206541,  263541, 2063541,  623541, 6023541, 2603541, 6203541,\n       362541, 3062541,  632541, 6032541, 3602541, 6302541, 2360541, 3260541, 2630541, 6230541, 3620541, 6320541,\n       256341, 2056341,  526341, 5026341, 2506341, 5206341,  265341, 2065341,  625341, 6025341, 2605341, 6205341,\n       562341, 5062341,  652341, 6052341, 5602341, 6502341, 2560341, 5260341, 2650341, 6250341, 5620341, 6520341,\n       356241, 3056241,  536241, 5036241, 3506241, 5306241,  365241, 3065241,  635241, 6035241, 3605241, 6305241,\n       563241, 5063241,  653241, 6053241, 5603241, 6503241, 3560241, 5360241, 3650241, 6350241, 5630241, 6530241,\n      2356041, 3256041, 2536041, 5236041, 3526041, 5326041, 2365041, 3265041, 2635041, 6235041, 3625041, 6325041,\n      2563041, 5263041, 2653041, 6253041, 5623041, 6523041, 3562041, 5362041, 3652041, 6352041, 5632041, 6532041,\n       245631, 2045631,  425631, 4025631, 2405631, 4205631,  254631, 2054631,  524631, 5024631, 2504631, 5204631,\n       452631, 4052631,  542631, 5042631, 4502631, 5402631, 2450631, 4250631, 2540631, 5240631, 4520631, 5420631,\n       246531, 2046531,  426531, 4026531, 2406531, 4206531,  264531, 2064531,  624531, 6024531, 2604531, 6204531,\n       462531, 4062531,  642531, 6042531, 4602531, 6402531, 2460531, 4260531, 2640531, 6240531, 4620531, 6420531,\n       256431, 2056431,  526431, 5026431, 2506431, 5206431,  265431, 2065431,  625431, 6025431, 2605431, 6205431,\n       562431, 5062431,  652431, 6052431, 5602431, 6502431, 2560431, 5260431, 2650431, 6250431, 5620431, 6520431,\n       456231, 4056231,  546231, 5046231, 4506231, 5406231,  465231, 4065231,  645231, 6045231, 4605231, 6405231,\n       564231, 5064231,  654231, 6054231, 5604231, 6504231, 4560231, 5460231, 4650231, 6450231, 5640231, 6540231,\n      2456031, 4256031, 2546031, 5246031, 4526031, 5426031, 2465031, 4265031, 2645031, 6245031, 4625031, 6425031,\n      2564031, 5264031, 2654031, 6254031, 5624031, 6524031, 4562031, 5462031, 4652031, 6452031, 5642031, 6542031,\n       345621, 3045621,  435621, 4035621, 3405621, 4305621,  354621, 3054621,  534621, 5034621, 3504621, 5304621,\n       453621, 4053621,  543621, 5043621, 4503621, 5403621, 3450621, 4350621, 3540621, 5340621, 4530621, 5430621,\n       346521, 3046521,  436521, 4036521, 3406521, 4306521,  364521, 3064521,  634521, 6034521, 3604521, 6304521,\n       463521, 4063521,  643521, 6043521, 4603521, 6403521, 3460521, 4360521, 3640521, 6340521, 4630521, 6430521,\n       356421, 3056421,  536421, 5036421, 3506421, 5306421,  365421, 3065421,  635421, 6035421, 3605421, 6305421,\n       563421, 5063421,  653421, 6053421, 5603421, 6503421, 3560421, 5360421, 3650421, 6350421, 5630421, 6530421,\n       456321, 4056321,  546321, 5046321, 4506321, 5406321,  465321, 4065321,  645321, 6045321, 4605321, 6405321,\n       564321, 5064321,  654321, 6054321, 5604321, 6504321, 4560321, 5460321, 4650321, 6450321, 5640321, 6540321,\n      3456021, 4356021, 3546021, 5346021, 4536021, 5436021, 3465021, 4365021, 3645021, 6345021, 4635021, 6435021,\n      3564021, 5364021, 3654021, 6354021, 5634021, 6534021, 4563021, 5463021, 4653021, 6453021, 5643021, 6543021,\n      2345601, 3245601, 2435601, 4235601, 3425601, 4325601, 2354601, 3254601, 2534601, 5234601, 3524601, 5324601,\n      2453601, 4253601, 2543601, 5243601, 4523601, 5423601, 3452601, 4352601, 3542601, 5342601, 4532601, 5432601,\n      2346501, 3246501, 2436501, 4236501, 3426501, 4326501, 2364501, 3264501, 2634501, 6234501, 3624501, 6324501,\n      2463501, 4263501, 2643501, 6243501, 4623501, 6423501, 3462501, 4362501, 3642501, 6342501, 4632501, 6432501,\n      2356401, 3256401, 2536401, 5236401, 3526401, 5326401, 2365401, 3265401, 2635401, 6235401, 3625401, 6325401,\n      2563401, 5263401, 2653401, 6253401, 5623401, 6523401, 3562401, 5362401, 3652401, 6352401, 5632401, 6532401,\n      2456301, 4256301, 2546301, 5246301, 4526301, 5426301, 2465301, 4265301, 2645301, 6245301, 4625301, 6425301,\n      2564301, 5264301, 2654301, 6254301, 5624301, 6524301, 4562301, 5462301, 4652301, 6452301, 5642301, 6542301,\n      3456201, 4356201, 3546201, 5346201, 4536201, 5436201, 3465201, 4365201, 3645201, 6345201, 4635201, 6435201,\n      3564201, 5364201, 3654201, 6354201, 5634201, 6534201, 4563201, 5463201, 4653201, 6453201, 5643201, 6543201,\n      1234560, 2134560, 1324560, 3124560, 2314560, 3214560, 1243560, 2143560, 1423560, 4123560, 2413560, 4213560,\n      1342560, 3142560, 1432560, 4132560, 3412560, 4312560, 2341560, 3241560, 2431560, 4231560, 3421560, 4321560,\n      1235460, 2135460, 1325460, 3125460, 2315460, 3215460, 1253460, 2153460, 1523460, 5123460, 2513460, 5213460,\n      1352460, 3152460, 1532460, 5132460, 3512460, 5312460, 2351460, 3251460, 2531460, 5231460, 3521460, 5321460,\n      1245360, 2145360, 1425360, 4125360, 2415360, 4215360, 1254360, 2154360, 1524360, 5124360, 2514360, 5214360,\n      1452360, 4152360, 1542360, 5142360, 4512360, 5412360, 2451360, 4251360, 2541360, 5241360, 4521360, 5421360,\n      1345260, 3145260, 1435260, 4135260, 3415260, 4315260, 1354260, 3154260, 1534260, 5134260, 3514260, 5314260,\n      1453260, 4153260, 1543260, 5143260, 4513260, 5413260, 3451260, 4351260, 3541260, 5341260, 4531260, 5431260,\n      2345160, 3245160, 2435160, 4235160, 3425160, 4325160, 2354160, 3254160, 2534160, 5234160, 3524160, 5324160,\n      2453160, 4253160, 2543160, 5243160, 4523160, 5423160, 3452160, 4352160, 3542160, 5342160, 4532160, 5432160,\n      1234650, 2134650, 1324650, 3124650, 2314650, 3214650, 1243650, 2143650, 1423650, 4123650, 2413650, 4213650,\n      1342650, 3142650, 1432650, 4132650, 3412650, 4312650, 2341650, 3241650, 2431650, 4231650, 3421650, 4321650,\n      1236450, 2136450, 1326450, 3126450, 2316450, 3216450, 1263450, 2163450, 1623450, 6123450, 2613450, 6213450,\n      1362450, 3162450, 1632450, 6132450, 3612450, 6312450, 2361450, 3261450, 2631450, 6231450, 3621450, 6321450,\n      1246350, 2146350, 1426350, 4126350, 2416350, 4216350, 1264350, 2164350, 1624350, 6124350, 2614350, 6214350,\n      1462350, 4162350, 1642350, 6142350, 4612350, 6412350, 2461350, 4261350, 2641350, 6241350, 4621350, 6421350,\n      1346250, 3146250, 1436250, 4136250, 3416250, 4316250, 1364250, 3164250, 1634250, 6134250, 3614250, 6314250,\n      1463250, 4163250, 1643250, 6143250, 4613250, 6413250, 3461250, 4361250, 3641250, 6341250, 4631250, 6431250,\n      2346150, 3246150, 2436150, 4236150, 3426150, 4326150, 2364150, 3264150, 2634150, 6234150, 3624150, 6324150,\n      2463150, 4263150, 2643150, 6243150, 4623150, 6423150, 3462150, 4362150, 3642150, 6342150, 4632150, 6432150,\n      1235640, 2135640, 1325640, 3125640, 2315640, 3215640, 1253640, 2153640, 1523640, 5123640, 2513640, 5213640,\n      1352640, 3152640, 1532640, 5132640, 3512640, 5312640, 2351640, 3251640, 2531640, 5231640, 3521640, 5321640,\n      1236540, 2136540, 1326540, 3126540, 2316540, 3216540, 1263540, 2163540, 1623540, 6123540, 2613540, 6213540,\n      1362540, 3162540, 1632540, 6132540, 3612540, 6312540, 2361540, 3261540, 2631540, 6231540, 3621540, 6321540,\n      1256340, 2156340, 1526340, 5126340, 2516340, 5216340, 1265340, 2165340, 1625340, 6125340, 2615340, 6215340,\n      1562340, 5162340, 1652340, 6152340, 5612340, 6512340, 2561340, 5261340, 2651340, 6251340, 5621340, 6521340,\n      1356240, 3156240, 1536240, 5136240, 3516240, 5316240, 1365240, 3165240, 1635240, 6135240, 3615240, 6315240,\n      1563240, 5163240, 1653240, 6153240, 5613240, 6513240, 3561240, 5361240, 3651240, 6351240, 5631240, 6531240,\n      2356140, 3256140, 2536140, 5236140, 3526140, 5326140, 2365140, 3265140, 2635140, 6235140, 3625140, 6325140,\n      2563140, 5263140, 2653140, 6253140, 5623140, 6523140, 3562140, 5362140, 3652140, 6352140, 5632140, 6532140,\n      1245630, 2145630, 1425630, 4125630, 2415630, 4215630, 1254630, 2154630, 1524630, 5124630, 2514630, 5214630,\n      1452630, 4152630, 1542630, 5142630, 4512630, 5412630, 2451630, 4251630, 2541630, 5241630, 4521630, 5421630,\n      1246530, 2146530, 1426530, 4126530, 2416530, 4216530, 1264530, 2164530, 1624530, 6124530, 2614530, 6214530,\n      1462530, 4162530, 1642530, 6142530, 4612530, 6412530, 2461530, 4261530, 2641530, 6241530, 4621530, 6421530,\n      1256430, 2156430, 1526430, 5126430, 2516430, 5216430, 1265430, 2165430, 1625430, 6125430, 2615430, 6215430,\n      1562430, 5162430, 1652430, 6152430, 5612430, 6512430, 2561430, 5261430, 2651430, 6251430, 5621430, 6521430,\n      1456230, 4156230, 1546230, 5146230, 4516230, 5416230, 1465230, 4165230, 1645230, 6145230, 4615230, 6415230,\n      1564230, 5164230, 1654230, 6154230, 5614230, 6514230, 4561230, 5461230, 4651230, 6451230, 5641230, 6541230,\n      2456130, 4256130, 2546130, 5246130, 4526130, 5426130, 2465130, 4265130, 2645130, 6245130, 4625130, 6425130,\n      2564130, 5264130, 2654130, 6254130, 5624130, 6524130, 4562130, 5462130, 4652130, 6452130, 5642130, 6542130,\n      1345620, 3145620, 1435620, 4135620, 3415620, 4315620, 1354620, 3154620, 1534620, 5134620, 3514620, 5314620,\n      1453620, 4153620, 1543620, 5143620, 4513620, 5413620, 3451620, 4351620, 3541620, 5341620, 4531620, 5431620,\n      1346520, 3146520, 1436520, 4136520, 3416520, 4316520, 1364520, 3164520, 1634520, 6134520, 3614520, 6314520,\n      1463520, 4163520, 1643520, 6143520, 4613520, 6413520, 3461520, 4361520, 3641520, 6341520, 4631520, 6431520,\n      1356420, 3156420, 1536420, 5136420, 3516420, 5316420, 1365420, 3165420, 1635420, 6135420, 3615420, 6315420,\n      1563420, 5163420, 1653420, 6153420, 5613420, 6513420, 3561420, 5361420, 3651420, 6351420, 5631420, 6531420,\n      1456320, 4156320, 1546320, 5146320, 4516320, 5416320, 1465320, 4165320, 1645320, 6145320, 4615320, 6415320,\n      1564320, 5164320, 1654320, 6154320, 5614320, 6514320, 4561320, 5461320, 4651320, 6451320, 5641320, 6541320,\n      3456120, 4356120, 3546120, 5346120, 4536120, 5436120, 3465120, 4365120, 3645120, 6345120, 4635120, 6435120,\n      3564120, 5364120, 3654120, 6354120, 5634120, 6534120, 4563120, 5463120, 4653120, 6453120, 5643120, 6543120,\n      2345610, 3245610, 2435610, 4235610, 3425610, 4325610, 2354610, 3254610, 2534610, 5234610, 3524610, 5324610,\n      2453610, 4253610, 2543610, 5243610, 4523610, 5423610, 3452610, 4352610, 3542610, 5342610, 4532610, 5432610,\n      2346510, 3246510, 2436510, 4236510, 3426510, 4326510, 2364510, 3264510, 2634510, 6234510, 3624510, 6324510,\n      2463510, 4263510, 2643510, 6243510, 4623510, 6423510, 3462510, 4362510, 3642510, 6342510, 4632510, 6432510,\n      2356410, 3256410, 2536410, 5236410, 3526410, 5326410, 2365410, 3265410, 2635410, 6235410, 3625410, 6325410,\n      2563410, 5263410, 2653410, 6253410, 5623410, 6523410, 3562410, 5362410, 3652410, 6352410, 5632410, 6532410,\n      2456310, 4256310, 2546310, 5246310, 4526310, 5426310, 2465310, 4265310, 2645310, 6245310, 4625310, 6425310,\n      2564310, 5264310, 2654310, 6254310, 5624310, 6524310, 4562310, 5462310, 4652310, 6452310, 5642310, 6542310,\n      3456210, 4356210, 3546210, 5346210, 4536210, 5436210, 3465210, 4365210, 3645210, 6345210, 4635210, 6435210,\n      3564210, 5364210, 3654210, 6354210, 5634210, 6534210, 4563210, 5463210, 4653210, 6453210, 5643210, 6543210\n    };\n    std::map<uint64_t, int> expected;\n    for (std::size_t i = 0; i < 5040; i++)\n      expected[pre_expected[i]] = 0; // flags are 0, everything is symmetric here\n\n    VERIFY(isDynGroup(group));\n    VERIFY_IS_EQUAL(group.size(), 5040u);\n    VERIFY_IS_EQUAL(group.globalFlags(), 0);\n    group.apply<checkIdx, int>(identity7, 0, found, expected);\n    VERIFY_IS_EQUAL(found.size(), 5040u);\n  }\n}\n\nstatic void test_tensor_epsilon()\n{\n  SGroup<AntiSymmetry<0,1>, AntiSymmetry<1,2>> sym;\n  Tensor<int, 3> epsilon(3,3,3);\n\n  epsilon.setZero();\n  sym(epsilon, 0, 1, 2) = 1;\n\n  for (int i = 0; i < 3; i++) {\n    for (int j = 0; j < 3; j++) {\n      for (int k = 0; k < 3; k++) {\n        VERIFY_IS_EQUAL((epsilon(i,j,k)), (- (j - i) * (k - j) * (i - k) / 2) );\n      }\n    }\n  }\n}\n\nstatic void test_tensor_sym()\n{\n  SGroup<Symmetry<0,1>, Symmetry<2,3>> sym;\n  Tensor<int, 4> t(10,10,10,10);\n\n  t.setZero();\n\n  for (int l = 0; l < 10; l++) {\n    for (int k = l; k < 10; k++) {\n      for (int j = 0; j < 10; j++) {\n        for (int i = j; i < 10; i++) {\n          sym(t, i, j, k, l) = (i + j) * (k + l);\n        }\n      }\n    }\n  }\n\n  for (int l = 0; l < 10; l++) {\n    for (int k = 0; k < 10; k++) {\n      for (int j = 0; j < 10; j++) {\n        for (int i = 0; i < 10; i++) {\n          VERIFY_IS_EQUAL((t(i, j, k, l)), ((i + j) * (k + l)));\n        }\n      }\n    }\n  }\n\n}\n\nstatic void test_tensor_asym()\n{\n  SGroup<AntiSymmetry<0,1>, AntiSymmetry<2,3>> sym;\n  Tensor<int, 4> t(10,10,10,10);\n\n  t.setZero();\n\n  for (int l = 0; l < 10; l++) {\n    for (int k = l + 1; k < 10; k++) {\n      for (int j = 0; j < 10; j++) {\n        for (int i = j + 1; i < 10; i++) {\n          sym(t, i, j, k, l) = ((i * j) + (k * l));\n        }\n      }\n    }\n  }\n\n  for (int l = 0; l < 10; l++) {\n    for (int k = 0; k < 10; k++) {\n      for (int j = 0; j < 10; j++) {\n        for (int i = 0; i < 10; i++) {\n          if (i < j && k < l)\n            VERIFY_IS_EQUAL((t(i, j, k, l)), (((i * j) + (k * l))));\n          else if (i > j && k > l)\n            VERIFY_IS_EQUAL((t(i, j, k, l)), (((i * j) + (k * l))));\n          else if (i < j && k > l)\n            VERIFY_IS_EQUAL((t(i, j, k, l)), (- ((i * j) + (k * l))));\n          else if (i > j && k < l)\n            VERIFY_IS_EQUAL((t(i, j, k, l)), (- ((i * j) + (k * l))));\n          else\n            VERIFY_IS_EQUAL((t(i, j, k, l)), 0);\n        }\n      }\n    }\n  }\n}\n\nstatic void test_tensor_dynsym()\n{\n  DynamicSGroup sym;\n  sym.addSymmetry(0,1);\n  sym.addSymmetry(2,3);\n  Tensor<int, 4> t(10,10,10,10);\n\n  t.setZero();\n\n  for (int l = 0; l < 10; l++) {\n    for (int k = l; k < 10; k++) {\n      for (int j = 0; j < 10; j++) {\n        for (int i = j; i < 10; i++) {\n          sym(t, i, j, k, l) = (i + j) * (k + l);\n        }\n      }\n    }\n  }\n\n  for (int l = 0; l < 10; l++) {\n    for (int k = 0; k < 10; k++) {\n      for (int j = 0; j < 10; j++) {\n        for (int i = 0; i < 10; i++) {\n          VERIFY_IS_EQUAL((t(i, j, k, l)), ((i + j) * (k + l)));\n        }\n      }\n    }\n  }\n}\n\nstatic void test_tensor_randacc()\n{\n  SGroup<Symmetry<0,1>, Symmetry<2,3>> sym;\n  Tensor<int, 4> t(10,10,10,10);\n\n  t.setZero();\n\n  // set elements 1 million times, that way we access the\n  // entire matrix\n  for (int n = 0; n < 1000000; n++) {\n    int i = rand() % 10;\n    int j = rand() % 10;\n    int k = rand() % 10;\n    int l = rand() % 10;\n    // only access those indices in a given order\n    if (i < j)\n      std::swap(i, j);\n    if (k < l)\n      std::swap(k, l);\n    sym(t, i, j, k, l) = (i + j) * (k + l);\n  }\n\n  for (int l = 0; l < 10; l++) {\n    for (int k = 0; k < 10; k++) {\n      for (int j = 0; j < 10; j++) {\n        for (int i = 0; i < 10; i++) {\n          VERIFY_IS_EQUAL((t(i, j, k, l)), ((i + j) * (k + l)));\n        }\n      }\n    }\n  }\n}\n\nvoid test_cxx11_tensor_symmetry()\n{\n  CALL_SUBTEST(test_symgroups_static());\n  CALL_SUBTEST(test_symgroups_dynamic());\n  CALL_SUBTEST(test_symgroups_selection());\n  CALL_SUBTEST(test_tensor_epsilon());\n  CALL_SUBTEST(test_tensor_sym());\n  CALL_SUBTEST(test_tensor_asym());\n  CALL_SUBTEST(test_tensor_dynsym());\n  CALL_SUBTEST(test_tensor_randacc());\n}\n\n/*\n * kate: space-indent on; indent-width 2; mixedindent off; indent-mode cstyle;\n */\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_thread_pool.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#define EIGEN_USE_THREADS\n\n\n#include \"main.h\"\n#include <iostream>\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\n\n\nvoid test_multithread_elementwise()\n{\n  Tensor<float, 3> in1(2,3,7);\n  Tensor<float, 3> in2(2,3,7);\n  Tensor<float, 3> out(2,3,7);\n\n  in1.setRandom();\n  in2.setRandom();\n\n  Eigen::ThreadPool tp(internal::random<int>(3, 11));\n  Eigen::ThreadPoolDevice thread_pool_device(&tp, internal::random<int>(3, 11));\n  out.device(thread_pool_device) = in1 + in2 * 3.14f;\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        VERIFY_IS_APPROX(out(i,j,k), in1(i,j,k) + in2(i,j,k) * 3.14f);\n      }\n    }\n  }\n}\n\n\nvoid test_multithread_compound_assignment()\n{\n  Tensor<float, 3> in1(2,3,7);\n  Tensor<float, 3> in2(2,3,7);\n  Tensor<float, 3> out(2,3,7);\n\n  in1.setRandom();\n  in2.setRandom();\n\n  Eigen::ThreadPool tp(internal::random<int>(3, 11));\n  Eigen::ThreadPoolDevice thread_pool_device(&tp, internal::random<int>(3, 11));\n  out.device(thread_pool_device) = in1;\n  out.device(thread_pool_device) += in2 * 3.14f;\n\n  for (int i = 0; i < 2; ++i) {\n    for (int j = 0; j < 3; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        VERIFY_IS_APPROX(out(i,j,k), in1(i,j,k) + in2(i,j,k) * 3.14f);\n      }\n    }\n  }\n}\n\ntemplate<int DataLayout>\nvoid test_multithread_contraction()\n{\n  Tensor<float, 4, DataLayout> t_left(30, 50, 37, 31);\n  Tensor<float, 5, DataLayout> t_right(37, 31, 70, 2, 10);\n  Tensor<float, 5, DataLayout> t_result(30, 50, 70, 2, 10);\n\n  t_left.setRandom();\n  t_right.setRandom();\n\n  // this contraction should be equivalent to a single matrix multiplication\n  typedef Tensor<float, 1>::DimensionPair DimPair;\n  Eigen::array<DimPair, 2> dims({{DimPair(2, 0), DimPair(3, 1)}});\n\n  typedef Map<Matrix<float, Dynamic, Dynamic, DataLayout>> MapXf;\n  MapXf m_left(t_left.data(), 1500, 1147);\n  MapXf m_right(t_right.data(), 1147, 1400);\n  Matrix<float, Dynamic, Dynamic, DataLayout> m_result(1500, 1400);\n\n  Eigen::ThreadPool tp(4);\n  Eigen::ThreadPoolDevice thread_pool_device(&tp, 4);\n\n  // compute results by separate methods\n  t_result.device(thread_pool_device) = t_left.contract(t_right, dims);\n  m_result = m_left * m_right;\n\n for (ptrdiff_t i = 0; i < t_result.size(); i++) {\n    VERIFY(&t_result.data()[i] != &m_result.data()[i]);\n    if (fabsf(t_result(i) - m_result(i)) < 1e-4f) {\n      continue;\n    }\n    if (Eigen::internal::isApprox(t_result(i), m_result(i), 1e-4f)) {\n      continue;\n    }\n    std::cout << \"mismatch detected at index \" << i << \": \" << t_result(i)\n              << \" vs \" <<  m_result(i) << std::endl;\n    assert(false);\n  }\n}\n\ntemplate<int DataLayout>\nvoid test_contraction_corner_cases()\n{\n  Tensor<float, 2, DataLayout> t_left(32, 500);\n  Tensor<float, 2, DataLayout> t_right(32, 28*28);\n  Tensor<float, 2, DataLayout> t_result(500, 28*28);\n\n  t_left = (t_left.constant(-0.5f) + t_left.random()) * 2.0f;\n  t_right = (t_right.constant(-0.6f) + t_right.random()) * 2.0f;\n  t_result = t_result.constant(NAN);\n\n  // this contraction should be equivalent to a single matrix multiplication\n  typedef Tensor<float, 1>::DimensionPair DimPair;\n  Eigen::array<DimPair, 1> dims{{DimPair(0, 0)}};\n\n  typedef Map<Matrix<float, Dynamic, Dynamic, DataLayout>> MapXf;\n  MapXf m_left(t_left.data(), 32, 500);\n  MapXf m_right(t_right.data(), 32, 28*28);\n  Matrix<float, Dynamic, Dynamic, DataLayout> m_result(500, 28*28);\n\n  Eigen::ThreadPool tp(12);\n  Eigen::ThreadPoolDevice thread_pool_device(&tp, 12);\n\n  // compute results by separate methods\n  t_result.device(thread_pool_device) = t_left.contract(t_right, dims);\n  m_result = m_left.transpose() * m_right;\n\n  for (ptrdiff_t i = 0; i < t_result.size(); i++) {\n    assert(!(numext::isnan)(t_result.data()[i]));\n    if (fabsf(t_result.data()[i] - m_result.data()[i]) >= 1e-4f) {\n      std::cout << \"mismatch detected at index \" << i << \" : \" << t_result.data()[i] << \" vs \" <<  m_result.data()[i] << std::endl;\n      assert(false);\n    }\n  }\n\n  t_left.resize(32, 1);\n  t_left = (t_left.constant(-0.5f) + t_left.random()) * 2.0f;\n  t_result.resize (1, 28*28);\n  t_result = t_result.constant(NAN);\n  t_result.device(thread_pool_device) = t_left.contract(t_right, dims);\n  new(&m_left) MapXf(t_left.data(), 32, 1);\n  m_result = m_left.transpose() * m_right;\n  for (ptrdiff_t i = 0; i < t_result.size(); i++) {\n    assert(!(numext::isnan)(t_result.data()[i]));\n    if (fabsf(t_result.data()[i] - m_result.data()[i]) >= 1e-4f) {\n      std::cout << \"mismatch detected: \" << t_result.data()[i] << \" vs \" <<  m_result.data()[i] << std::endl;\n      assert(false);\n    }\n  }\n\n  t_left.resize(32, 500);\n  t_right.resize(32, 4);\n  t_left = (t_left.constant(-0.5f) + t_left.random()) * 2.0f;\n  t_right = (t_right.constant(-0.6f) + t_right.random()) * 2.0f;\n  t_result.resize (500, 4);\n  t_result = t_result.constant(NAN);\n  t_result.device(thread_pool_device) = t_left.contract(t_right, dims);\n  new(&m_left) MapXf(t_left.data(), 32, 500);\n  new(&m_right) MapXf(t_right.data(), 32, 4);\n  m_result = m_left.transpose() * m_right;\n  for (ptrdiff_t i = 0; i < t_result.size(); i++) {\n    assert(!(numext::isnan)(t_result.data()[i]));\n    if (fabsf(t_result.data()[i] - m_result.data()[i]) >= 1e-4f) {\n      std::cout << \"mismatch detected: \" << t_result.data()[i] << \" vs \" <<  m_result.data()[i] << std::endl;\n      assert(false);\n    }\n  }\n\n  t_left.resize(32, 1);\n  t_right.resize(32, 4);\n  t_left = (t_left.constant(-0.5f) + t_left.random()) * 2.0f;\n  t_right = (t_right.constant(-0.6f) + t_right.random()) * 2.0f;\n  t_result.resize (1, 4);\n  t_result = t_result.constant(NAN);\n  t_result.device(thread_pool_device) = t_left.contract(t_right, dims);\n  new(&m_left) MapXf(t_left.data(), 32, 1);\n  new(&m_right) MapXf(t_right.data(), 32, 4);\n  m_result = m_left.transpose() * m_right;\n  for (ptrdiff_t i = 0; i < t_result.size(); i++) {\n    assert(!(numext::isnan)(t_result.data()[i]));\n    if (fabsf(t_result.data()[i] - m_result.data()[i]) >= 1e-4f) {\n      std::cout << \"mismatch detected: \" << t_result.data()[i] << \" vs \" <<  m_result.data()[i] << std::endl;\n      assert(false);\n    }\n  }\n}\n\ntemplate<int DataLayout>\nvoid test_multithread_contraction_agrees_with_singlethread() {\n  int contract_size = internal::random<int>(1, 5000);\n\n  Tensor<float, 3, DataLayout> left(internal::random<int>(1, 80),\n                                    contract_size,\n                                    internal::random<int>(1, 100));\n\n  Tensor<float, 4, DataLayout> right(internal::random<int>(1, 25),\n                                     internal::random<int>(1, 37),\n                                     contract_size,\n                                     internal::random<int>(1, 51));\n\n  left.setRandom();\n  right.setRandom();\n\n  // add constants to shift values away from 0 for more precision\n  left += left.constant(1.5f);\n  right += right.constant(1.5f);\n\n  typedef Tensor<float, 1>::DimensionPair DimPair;\n  Eigen::array<DimPair, 1> dims({{DimPair(1, 2)}});\n\n  Eigen::ThreadPool tp(internal::random<int>(2, 11));\n  Eigen::ThreadPoolDevice thread_pool_device(&tp, internal::random<int>(2, 11));\n\n  Tensor<float, 5, DataLayout> st_result;\n  st_result = left.contract(right, dims);\n\n  Tensor<float, 5, DataLayout> tp_result(st_result.dimensions());\n  tp_result.device(thread_pool_device) = left.contract(right, dims);\n\n  VERIFY(dimensions_match(st_result.dimensions(), tp_result.dimensions()));\n  for (ptrdiff_t i = 0; i < st_result.size(); i++) {\n    // if both of the values are very small, then do nothing (because the test will fail\n    // due to numerical precision issues when values are small)\n    if (numext::abs(st_result.data()[i] - tp_result.data()[i]) >= 1e-4f) {\n      VERIFY_IS_APPROX(st_result.data()[i], tp_result.data()[i]);\n    }\n  }\n}\n\n\ntemplate<int DataLayout>\nvoid test_full_contraction() {\n  int contract_size1 = internal::random<int>(1, 500);\n  int contract_size2 = internal::random<int>(1, 500);\n\n  Tensor<float, 2, DataLayout> left(contract_size1,\n                                    contract_size2);\n  Tensor<float, 2, DataLayout> right(contract_size1,\n                                    contract_size2);\n  left.setRandom();\n  right.setRandom();\n\n  // add constants to shift values away from 0 for more precision\n  left += left.constant(1.5f);\n  right += right.constant(1.5f);\n\n  typedef Tensor<float, 2>::DimensionPair DimPair;\n  Eigen::array<DimPair, 2> dims({{DimPair(0, 0), DimPair(1, 1)}});\n\n  Eigen::ThreadPool tp(internal::random<int>(2, 11));\n  Eigen::ThreadPoolDevice thread_pool_device(&tp, internal::random<int>(2, 11));\n\n  Tensor<float, 0, DataLayout> st_result;\n  st_result = left.contract(right, dims);\n\n  Tensor<float, 0, DataLayout> tp_result;\n  tp_result.device(thread_pool_device) = left.contract(right, dims);\n\n  VERIFY(dimensions_match(st_result.dimensions(), tp_result.dimensions()));\n  // if both of the values are very small, then do nothing (because the test will fail\n  // due to numerical precision issues when values are small)\n  if (numext::abs(st_result() - tp_result()) >= 1e-4f) {\n    VERIFY_IS_APPROX(st_result(), tp_result());\n  }\n}\n\ntemplate<int DataLayout>\nvoid test_multithreaded_reductions() {\n  const int num_threads = internal::random<int>(3, 11);\n  ThreadPool thread_pool(num_threads);\n  Eigen::ThreadPoolDevice thread_pool_device(&thread_pool, num_threads);\n\n  const int num_rows = internal::random<int>(13, 732);\n  const int num_cols = internal::random<int>(13, 732);\n  Tensor<float, 2, DataLayout> t1(num_rows, num_cols);\n  t1.setRandom();\n\n  Tensor<float, 0, DataLayout> full_redux;\n  full_redux = t1.sum();\n\n  Tensor<float, 0, DataLayout> full_redux_tp;\n  full_redux_tp.device(thread_pool_device) = t1.sum();\n\n  // Check that the single threaded and the multi threaded reductions return\n  // the same result.\n  VERIFY_IS_APPROX(full_redux(), full_redux_tp());\n}\n\n\nvoid test_memcpy() {\n\n  for (int i = 0; i < 5; ++i) {\n    const int num_threads = internal::random<int>(3, 11);\n    Eigen::ThreadPool tp(num_threads);\n    Eigen::ThreadPoolDevice thread_pool_device(&tp, num_threads);\n\n    const int size = internal::random<int>(13, 7632);\n    Tensor<float, 1> t1(size);\n    t1.setRandom();\n    std::vector<float> result(size);\n    thread_pool_device.memcpy(&result[0], t1.data(), size*sizeof(float));\n    for (int j = 0; j < size; j++) {\n      VERIFY_IS_EQUAL(t1(j), result[j]);\n    }\n  }\n}\n\n\nvoid test_multithread_random()\n{\n  Eigen::ThreadPool tp(2);\n  Eigen::ThreadPoolDevice device(&tp, 2);\n  Tensor<float, 1> t(1 << 20);\n  t.device(device) = t.random<Eigen::internal::NormalRandomGenerator<float>>();\n}\n\ntemplate<int DataLayout>\nvoid test_multithread_shuffle()\n{\n  Tensor<float, 4, DataLayout> tensor(17,5,7,11);\n  tensor.setRandom();\n\n  const int num_threads = internal::random<int>(2, 11);\n  ThreadPool threads(num_threads);\n  Eigen::ThreadPoolDevice device(&threads, num_threads);\n\n  Tensor<float, 4, DataLayout> shuffle(7,5,11,17);\n  array<ptrdiff_t, 4> shuffles = {{2,1,3,0}};\n  shuffle.device(device) = tensor.shuffle(shuffles);\n\n  for (int i = 0; i < 17; ++i) {\n    for (int j = 0; j < 5; ++j) {\n      for (int k = 0; k < 7; ++k) {\n        for (int l = 0; l < 11; ++l) {\n          VERIFY_IS_EQUAL(tensor(i,j,k,l), shuffle(k,j,l,i));\n        }\n      }\n    }\n  }\n}\n\n\nvoid test_cxx11_tensor_thread_pool()\n{\n  CALL_SUBTEST_1(test_multithread_elementwise());\n  CALL_SUBTEST_1(test_multithread_compound_assignment());\n\n  CALL_SUBTEST_2(test_multithread_contraction<ColMajor>());\n  CALL_SUBTEST_2(test_multithread_contraction<RowMajor>());\n\n  CALL_SUBTEST_3(test_multithread_contraction_agrees_with_singlethread<ColMajor>());\n  CALL_SUBTEST_3(test_multithread_contraction_agrees_with_singlethread<RowMajor>());\n\n  // Exercise various cases that have been problematic in the past.\n  CALL_SUBTEST_4(test_contraction_corner_cases<ColMajor>());\n  CALL_SUBTEST_4(test_contraction_corner_cases<RowMajor>());\n\n  CALL_SUBTEST_4(test_full_contraction<ColMajor>());\n  CALL_SUBTEST_4(test_full_contraction<RowMajor>());\n\n  CALL_SUBTEST_5(test_multithreaded_reductions<ColMajor>());\n  CALL_SUBTEST_5(test_multithreaded_reductions<RowMajor>());\n\n  CALL_SUBTEST_6(test_memcpy());\n  CALL_SUBTEST_6(test_multithread_random());\n  CALL_SUBTEST_6(test_multithread_shuffle<ColMajor>());\n  CALL_SUBTEST_6(test_multithread_shuffle<RowMajor>());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_uint128.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2015 Benoit Steiner <benoit.steiner.goog@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\n\n#if EIGEN_COMP_MSVC\n#define EIGEN_NO_INT128\n#else\ntypedef __uint128_t uint128_t;\n#endif\n\n// Only run the test on compilers that support 128bit integers natively\n#ifndef EIGEN_NO_INT128\n\nusing Eigen::internal::TensorUInt128;\nusing Eigen::internal::static_val;\n\nvoid VERIFY_EQUAL(TensorUInt128<uint64_t, uint64_t> actual, uint128_t expected) {\n  bool matchl = actual.lower() == static_cast<uint64_t>(expected);\n  bool matchh = actual.upper() == static_cast<uint64_t>(expected >> 64);\n  if (!matchl || !matchh) {\n    const char* testname = g_test_stack.back().c_str();\n    std::cerr << \"Test \" << testname << \" failed in \" << __FILE__\n              << \" (\" << __LINE__ << \")\"\n              << std::endl;\n    abort();\n  }\n}\n\n\nvoid test_add() {\n  uint64_t incr = internal::random<uint64_t>(1, 9999999999);\n  for (uint64_t i1 = 0; i1 < 100; ++i1) {\n    for (uint64_t i2 = 1; i2 < 100 * incr; i2 += incr) {\n      TensorUInt128<uint64_t, uint64_t> i(i1, i2);\n      uint128_t a = (static_cast<uint128_t>(i1) << 64) + static_cast<uint128_t>(i2);\n      for (uint64_t j1 = 0; j1 < 100; ++j1) {\n        for (uint64_t j2 = 1; j2 < 100 * incr; j2 += incr) {\n          TensorUInt128<uint64_t, uint64_t> j(j1, j2);\n          uint128_t b = (static_cast<uint128_t>(j1) << 64) + static_cast<uint128_t>(j2);\n          TensorUInt128<uint64_t, uint64_t> actual = i + j;\n          uint128_t expected = a + b;\n          VERIFY_EQUAL(actual, expected);\n        }\n      }\n    }\n  }\n}\n\nvoid test_sub() {\n  uint64_t incr = internal::random<uint64_t>(1, 9999999999);\n  for (uint64_t i1 = 0; i1 < 100; ++i1) {\n    for (uint64_t i2 = 1; i2 < 100 * incr; i2 += incr) {\n      TensorUInt128<uint64_t, uint64_t> i(i1, i2);\n      uint128_t a = (static_cast<uint128_t>(i1) << 64) + static_cast<uint128_t>(i2);\n      for (uint64_t j1 = 0; j1 < 100; ++j1) {\n        for (uint64_t j2 = 1; j2 < 100 * incr; j2 += incr) {\n          TensorUInt128<uint64_t, uint64_t> j(j1, j2);\n          uint128_t b = (static_cast<uint128_t>(j1) << 64) + static_cast<uint128_t>(j2);\n          TensorUInt128<uint64_t, uint64_t> actual = i - j;\n          uint128_t expected = a - b;\n          VERIFY_EQUAL(actual, expected);\n        }\n      }\n    }\n  }\n}\n\nvoid test_mul() {\n  uint64_t incr = internal::random<uint64_t>(1, 9999999999);\n  for (uint64_t i1 = 0; i1 < 100; ++i1) {\n    for (uint64_t i2 = 1; i2 < 100 * incr; i2 += incr) {\n      TensorUInt128<uint64_t, uint64_t> i(i1, i2);\n      uint128_t a = (static_cast<uint128_t>(i1) << 64) + static_cast<uint128_t>(i2);\n      for (uint64_t j1 = 0; j1 < 100; ++j1) {\n        for (uint64_t j2 = 1; j2 < 100 * incr; j2 += incr) {\n          TensorUInt128<uint64_t, uint64_t> j(j1, j2);\n          uint128_t b = (static_cast<uint128_t>(j1) << 64) + static_cast<uint128_t>(j2);\n          TensorUInt128<uint64_t, uint64_t> actual = i * j;\n          uint128_t expected = a * b;\n          VERIFY_EQUAL(actual, expected);\n        }\n      }\n    }\n  }\n}\n\nvoid test_div() {\n  uint64_t incr = internal::random<uint64_t>(1, 9999999999);\n  for (uint64_t i1 = 0; i1 < 100; ++i1) {\n    for (uint64_t i2 = 1; i2 < 100 * incr; i2 += incr) {\n      TensorUInt128<uint64_t, uint64_t> i(i1, i2);\n      uint128_t a = (static_cast<uint128_t>(i1) << 64) + static_cast<uint128_t>(i2);\n      for (uint64_t j1 = 0; j1 < 100; ++j1) {\n        for (uint64_t j2 = 1; j2 < 100 * incr; j2 += incr) {\n          TensorUInt128<uint64_t, uint64_t> j(j1, j2);\n          uint128_t b = (static_cast<uint128_t>(j1) << 64) + static_cast<uint128_t>(j2);\n          TensorUInt128<uint64_t, uint64_t> actual = i / j;\n          uint128_t expected = a / b;\n          VERIFY_EQUAL(actual, expected);\n        }\n      }\n    }\n  }\n}\n\nvoid test_misc1() {\n  uint64_t incr = internal::random<uint64_t>(1, 9999999999);\n  for (uint64_t i2 = 1; i2 < 100 * incr; i2 += incr) {\n    TensorUInt128<static_val<0>, uint64_t> i(0, i2);\n    uint128_t a = static_cast<uint128_t>(i2);\n    for (uint64_t j2 = 1; j2 < 100 * incr; j2 += incr) {\n      TensorUInt128<static_val<0>, uint64_t> j(0, j2);\n      uint128_t b = static_cast<uint128_t>(j2);\n      uint64_t actual = (i * j).upper();\n      uint64_t expected = (a * b) >> 64;\n      VERIFY_IS_EQUAL(actual, expected);\n    }\n  }\n}\n\nvoid test_misc2() {\n  int64_t incr = internal::random<int64_t>(1, 100);\n  for (int64_t log_div = 0; log_div < 63; ++log_div) {\n    for (int64_t divider = 1; divider <= 1000000 * incr; divider += incr) {\n      uint64_t expected = (static_cast<uint128_t>(1) << (64+log_div)) / static_cast<uint128_t>(divider) - (static_cast<uint128_t>(1) << 64) + 1;\n      uint64_t shift = 1ULL << log_div;\n\n      TensorUInt128<uint64_t, uint64_t> result = (TensorUInt128<uint64_t, static_val<0> >(shift, 0) / TensorUInt128<static_val<0>, uint64_t>(divider) - TensorUInt128<static_val<1>, static_val<0> >(1, 0) + TensorUInt128<static_val<0>, static_val<1> >(1));\n      uint64_t actual = static_cast<uint64_t>(result);\n      VERIFY_IS_EQUAL(actual, expected);\n    }\n  }\n}\n#endif\n\n\nvoid test_cxx11_tensor_uint128()\n{\n#ifdef EIGEN_NO_INT128\n  // Skip the test on compilers that don't support 128bit integers natively\n  return;\n#else\n  CALL_SUBTEST_1(test_add());\n  CALL_SUBTEST_2(test_sub());\n  CALL_SUBTEST_3(test_mul());\n  CALL_SUBTEST_4(test_div());\n  CALL_SUBTEST_5(test_misc1());\n  CALL_SUBTEST_6(test_misc2());\n#endif\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/cxx11_tensor_volume_patch.cpp",
    "content": "#include \"main.h\"\n\n#include <Eigen/CXX11/Tensor>\n\nusing Eigen::Tensor;\n\nstatic void test_single_voxel_patch()\n{\n  Tensor<float, 5> tensor(4,2,3,5,7);\n  tensor.setRandom();\n  Tensor<float, 5, RowMajor> tensor_row_major = tensor.swap_layout();\n\n  Tensor<float, 6> single_voxel_patch;\n  single_voxel_patch = tensor.extract_volume_patches(1, 1, 1);\n  VERIFY_IS_EQUAL(single_voxel_patch.dimension(0), 4);\n  VERIFY_IS_EQUAL(single_voxel_patch.dimension(1), 1);\n  VERIFY_IS_EQUAL(single_voxel_patch.dimension(2), 1);\n  VERIFY_IS_EQUAL(single_voxel_patch.dimension(3), 1);\n  VERIFY_IS_EQUAL(single_voxel_patch.dimension(4), 2 * 3 * 5);\n  VERIFY_IS_EQUAL(single_voxel_patch.dimension(5), 7);\n\n  Tensor<float, 6, RowMajor> single_voxel_patch_row_major;\n  single_voxel_patch_row_major = tensor_row_major.extract_volume_patches(1, 1, 1);\n  VERIFY_IS_EQUAL(single_voxel_patch_row_major.dimension(0), 7);\n  VERIFY_IS_EQUAL(single_voxel_patch_row_major.dimension(1), 2 * 3 * 5);\n  VERIFY_IS_EQUAL(single_voxel_patch_row_major.dimension(2), 1);\n  VERIFY_IS_EQUAL(single_voxel_patch_row_major.dimension(3), 1);\n  VERIFY_IS_EQUAL(single_voxel_patch_row_major.dimension(4), 1);\n  VERIFY_IS_EQUAL(single_voxel_patch_row_major.dimension(5), 4);\n\n  for (int i = 0; i < tensor.size(); ++i) {\n    VERIFY_IS_EQUAL(tensor.data()[i], single_voxel_patch.data()[i]);\n    VERIFY_IS_EQUAL(tensor_row_major.data()[i], single_voxel_patch_row_major.data()[i]);\n    VERIFY_IS_EQUAL(tensor.data()[i], tensor_row_major.data()[i]);\n  }\n}\n\n\nstatic void test_entire_volume_patch()\n{\n  const int depth = 4;\n  const int patch_z = 2;\n  const int patch_y = 3;\n  const int patch_x = 5;\n  const int batch = 7;\n\n  Tensor<float, 5> tensor(depth, patch_z, patch_y, patch_x, batch);\n  tensor.setRandom();\n  Tensor<float, 5, RowMajor> tensor_row_major = tensor.swap_layout();\n\n  Tensor<float, 6> entire_volume_patch;\n  entire_volume_patch = tensor.extract_volume_patches(patch_z, patch_y, patch_x);\n  VERIFY_IS_EQUAL(entire_volume_patch.dimension(0), depth);\n  VERIFY_IS_EQUAL(entire_volume_patch.dimension(1), patch_z);\n  VERIFY_IS_EQUAL(entire_volume_patch.dimension(2), patch_y);\n  VERIFY_IS_EQUAL(entire_volume_patch.dimension(3), patch_x);\n  VERIFY_IS_EQUAL(entire_volume_patch.dimension(4), patch_z * patch_y * patch_x);\n  VERIFY_IS_EQUAL(entire_volume_patch.dimension(5), batch);\n\n  Tensor<float, 6, RowMajor> entire_volume_patch_row_major;\n  entire_volume_patch_row_major = tensor_row_major.extract_volume_patches(patch_z, patch_y, patch_x);\n  VERIFY_IS_EQUAL(entire_volume_patch_row_major.dimension(0), batch);\n  VERIFY_IS_EQUAL(entire_volume_patch_row_major.dimension(1), patch_z * patch_y * patch_x);\n  VERIFY_IS_EQUAL(entire_volume_patch_row_major.dimension(2), patch_x);\n  VERIFY_IS_EQUAL(entire_volume_patch_row_major.dimension(3), patch_y);\n  VERIFY_IS_EQUAL(entire_volume_patch_row_major.dimension(4), patch_z);\n  VERIFY_IS_EQUAL(entire_volume_patch_row_major.dimension(5), depth);\n\n  const int dz = patch_z - 1;\n  const int dy = patch_y - 1;\n  const int dx = patch_x - 1;\n\n  const int forward_pad_z = dz - dz / 2;\n  const int forward_pad_y = dy - dy / 2;\n  const int forward_pad_x = dx - dx / 2;\n\n  for (int pz = 0; pz < patch_z; pz++) {\n    for (int py = 0; py < patch_y; py++) {\n      for (int px = 0; px < patch_x; px++) {\n        const int patchId = pz + patch_z * (py + px * patch_y);\n        for (int z = 0; z < patch_z; z++) {\n          for (int y = 0; y < patch_y; y++) {\n            for (int x = 0; x < patch_x; x++) {\n              for (int b = 0; b < batch; b++) {\n                for (int d = 0; d < depth; d++) {\n                  float expected = 0.0f;\n                  float expected_row_major = 0.0f;\n                  const int eff_z = z - forward_pad_z + pz;\n                  const int eff_y = y - forward_pad_y + py;\n                  const int eff_x = x - forward_pad_x + px;\n                  if (eff_z >= 0 && eff_y >= 0 && eff_x >= 0 &&\n                      eff_z < patch_z && eff_y < patch_y && eff_x < patch_x) {\n                    expected = tensor(d, eff_z, eff_y, eff_x, b);\n                    expected_row_major = tensor_row_major(b, eff_x, eff_y, eff_z, d);\n                  }\n                  VERIFY_IS_EQUAL(entire_volume_patch(d, z, y, x, patchId, b), expected);\n                  VERIFY_IS_EQUAL(entire_volume_patch_row_major(b, patchId, x, y, z, d), expected_row_major);\n                }\n              }\n            }\n          }\n        }\n      }\n    }\n  }\n}\n\nvoid test_cxx11_tensor_volume_patch()\n{\n  CALL_SUBTEST(test_single_voxel_patch());\n  CALL_SUBTEST(test_entire_volume_patch());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/dgmres.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2011 Gael Guennebaud <g.gael@free.fr>\n// Copyright (C) 2012 desire Nuentsa <desire.nuentsa_wakam@inria.fr\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"../../test/sparse_solver.h\"\n#include <Eigen/src/IterativeSolvers/DGMRES.h>\n\ntemplate<typename T> void test_dgmres_T()\n{\n  DGMRES<SparseMatrix<T>, DiagonalPreconditioner<T> > dgmres_colmajor_diag;\n  DGMRES<SparseMatrix<T>, IdentityPreconditioner    > dgmres_colmajor_I;\n  DGMRES<SparseMatrix<T>, IncompleteLUT<T> >           dgmres_colmajor_ilut;\n  //GMRES<SparseMatrix<T>, SSORPreconditioner<T> >     dgmres_colmajor_ssor;\n\n  CALL_SUBTEST( check_sparse_square_solving(dgmres_colmajor_diag)  );\n//   CALL_SUBTEST( check_sparse_square_solving(dgmres_colmajor_I)     );\n  CALL_SUBTEST( check_sparse_square_solving(dgmres_colmajor_ilut)     );\n  //CALL_SUBTEST( check_sparse_square_solving(dgmres_colmajor_ssor)     );\n}\n\nvoid test_dgmres()\n{\n  CALL_SUBTEST_1(test_dgmres_T<double>());\n  CALL_SUBTEST_2(test_dgmres_T<std::complex<double> >());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/forward_adolc.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <Eigen/Dense>\n\n#define NUMBER_DIRECTIONS 16\n#include <unsupported/Eigen/AdolcForward>\n\ntemplate<typename Vector>\nEIGEN_DONT_INLINE typename Vector::Scalar foo(const Vector& p)\n{\n  typedef typename Vector::Scalar Scalar;\n  return (p-Vector(Scalar(-1),Scalar(1.))).norm() + (p.array().sqrt().abs() * p.array().sin()).sum() + p.dot(p);\n}\n\ntemplate<typename _Scalar, int NX=Dynamic, int NY=Dynamic>\nstruct TestFunc1\n{\n  typedef _Scalar Scalar;\n  enum {\n    InputsAtCompileTime = NX,\n    ValuesAtCompileTime = NY\n  };\n  typedef Matrix<Scalar,InputsAtCompileTime,1> InputType;\n  typedef Matrix<Scalar,ValuesAtCompileTime,1> ValueType;\n  typedef Matrix<Scalar,ValuesAtCompileTime,InputsAtCompileTime> JacobianType;\n\n  int m_inputs, m_values;\n\n  TestFunc1() : m_inputs(InputsAtCompileTime), m_values(ValuesAtCompileTime) {}\n  TestFunc1(int inputs, int values) : m_inputs(inputs), m_values(values) {}\n\n  int inputs() const { return m_inputs; }\n  int values() const { return m_values; }\n\n  template<typename T>\n  void operator() (const Matrix<T,InputsAtCompileTime,1>& x, Matrix<T,ValuesAtCompileTime,1>* _v) const\n  {\n    Matrix<T,ValuesAtCompileTime,1>& v = *_v;\n\n    v[0] = 2 * x[0] * x[0] + x[0] * x[1];\n    v[1] = 3 * x[1] * x[0] + 0.5 * x[1] * x[1];\n    if(inputs()>2)\n    {\n      v[0] += 0.5 * x[2];\n      v[1] += x[2];\n    }\n    if(values()>2)\n    {\n      v[2] = 3 * x[1] * x[0] * x[0];\n    }\n    if (inputs()>2 && values()>2)\n      v[2] *= x[2];\n  }\n\n  void operator() (const InputType& x, ValueType* v, JacobianType* _j) const\n  {\n    (*this)(x, v);\n\n    if(_j)\n    {\n      JacobianType& j = *_j;\n\n      j(0,0) = 4 * x[0] + x[1];\n      j(1,0) = 3 * x[1];\n\n      j(0,1) = x[0];\n      j(1,1) = 3 * x[0] + 2 * 0.5 * x[1];\n\n      if (inputs()>2)\n      {\n        j(0,2) = 0.5;\n        j(1,2) = 1;\n      }\n      if(values()>2)\n      {\n        j(2,0) = 3 * x[1] * 2 * x[0];\n        j(2,1) = 3 * x[0] * x[0];\n      }\n      if (inputs()>2 && values()>2)\n      {\n        j(2,0) *= x[2];\n        j(2,1) *= x[2];\n\n        j(2,2) = 3 * x[1] * x[0] * x[0];\n        j(2,2) = 3 * x[1] * x[0] * x[0];\n      }\n    }\n  }\n};\n\ntemplate<typename Func> void adolc_forward_jacobian(const Func& f)\n{\n    typename Func::InputType x = Func::InputType::Random(f.inputs());\n    typename Func::ValueType y(f.values()), yref(f.values());\n    typename Func::JacobianType j(f.values(),f.inputs()), jref(f.values(),f.inputs());\n\n    jref.setZero();\n    yref.setZero();\n    f(x,&yref,&jref);\n//     std::cerr << y.transpose() << \"\\n\\n\";;\n//     std::cerr << j << \"\\n\\n\";;\n\n    j.setZero();\n    y.setZero();\n    AdolcForwardJacobian<Func> autoj(f);\n    autoj(x, &y, &j);\n//     std::cerr << y.transpose() << \"\\n\\n\";;\n//     std::cerr << j << \"\\n\\n\";;\n\n    VERIFY_IS_APPROX(y, yref);\n    VERIFY_IS_APPROX(j, jref);\n}\n\nvoid test_forward_adolc()\n{\n  adtl::setNumDir(NUMBER_DIRECTIONS);\n\n  for(int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST(( adolc_forward_jacobian(TestFunc1<double,2,2>()) ));\n    CALL_SUBTEST(( adolc_forward_jacobian(TestFunc1<double,2,3>()) ));\n    CALL_SUBTEST(( adolc_forward_jacobian(TestFunc1<double,3,2>()) ));\n    CALL_SUBTEST(( adolc_forward_jacobian(TestFunc1<double,3,3>()) ));\n    CALL_SUBTEST(( adolc_forward_jacobian(TestFunc1<double>(3,3)) ));\n  }\n\n  {\n    // simple instanciation tests\n    Matrix<adtl::adouble,2,1> x;\n    foo(x);\n    Matrix<adtl::adouble,Dynamic,Dynamic> A(4,4);;\n    A.selfadjointView<Lower>().eigenvalues();\n  }\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/gmres.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2011 Gael Guennebaud <g.gael@free.fr>\n// Copyright (C) 2012 Kolja Brix <brix@igpm.rwth-aaachen.de>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"../../test/sparse_solver.h\"\n#include <Eigen/IterativeSolvers>\n\ntemplate<typename T> void test_gmres_T()\n{\n  GMRES<SparseMatrix<T>, DiagonalPreconditioner<T> > gmres_colmajor_diag;\n  GMRES<SparseMatrix<T>, IdentityPreconditioner    > gmres_colmajor_I;\n  GMRES<SparseMatrix<T>, IncompleteLUT<T> >           gmres_colmajor_ilut;\n  //GMRES<SparseMatrix<T>, SSORPreconditioner<T> >     gmres_colmajor_ssor;\n\n  CALL_SUBTEST( check_sparse_square_solving(gmres_colmajor_diag)  );\n//   CALL_SUBTEST( check_sparse_square_solving(gmres_colmajor_I)     );\n  CALL_SUBTEST( check_sparse_square_solving(gmres_colmajor_ilut)     );\n  //CALL_SUBTEST( check_sparse_square_solving(gmres_colmajor_ssor)     );\n}\n\nvoid test_gmres()\n{\n  CALL_SUBTEST_1(test_gmres_T<double>());\n  CALL_SUBTEST_2(test_gmres_T<std::complex<double> >());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/kronecker_product.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2011 Kolja Brix <brix@igpm.rwth-aachen.de>\n// Copyright (C) 2011 Andreas Platen <andiplaten@gmx.de>\n// Copyright (C) 2012 Chen-Pang He <jdh8@ms63.hinet.net>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#ifdef EIGEN_TEST_PART_1\n\n#include \"sparse.h\"\n#include <Eigen/SparseExtra>\n#include <Eigen/KroneckerProduct>\n\ntemplate<typename MatrixType>\nvoid check_dimension(const MatrixType& ab, const int rows,  const int cols)\n{\n  VERIFY_IS_EQUAL(ab.rows(), rows);\n  VERIFY_IS_EQUAL(ab.cols(), cols);\n}\n\n\ntemplate<typename MatrixType>\nvoid check_kronecker_product(const MatrixType& ab)\n{\n  VERIFY_IS_EQUAL(ab.rows(), 6);\n  VERIFY_IS_EQUAL(ab.cols(), 6);\n  VERIFY_IS_EQUAL(ab.nonZeros(),  36);\n  VERIFY_IS_APPROX(ab.coeff(0,0), -0.4017367630386106);\n  VERIFY_IS_APPROX(ab.coeff(0,1),  0.1056863433932735);\n  VERIFY_IS_APPROX(ab.coeff(0,2), -0.7255206194554212);\n  VERIFY_IS_APPROX(ab.coeff(0,3),  0.1908653336744706);\n  VERIFY_IS_APPROX(ab.coeff(0,4),  0.350864567234111);\n  VERIFY_IS_APPROX(ab.coeff(0,5), -0.0923032108308013);\n  VERIFY_IS_APPROX(ab.coeff(1,0),  0.415417514804677);\n  VERIFY_IS_APPROX(ab.coeff(1,1), -0.2369227701722048);\n  VERIFY_IS_APPROX(ab.coeff(1,2),  0.7502275131458511);\n  VERIFY_IS_APPROX(ab.coeff(1,3), -0.4278731019742696);\n  VERIFY_IS_APPROX(ab.coeff(1,4), -0.3628129162264507);\n  VERIFY_IS_APPROX(ab.coeff(1,5),  0.2069210808481275);\n  VERIFY_IS_APPROX(ab.coeff(2,0),  0.05465890160863986);\n  VERIFY_IS_APPROX(ab.coeff(2,1), -0.2634092511419858);\n  VERIFY_IS_APPROX(ab.coeff(2,2),  0.09871180285793758);\n  VERIFY_IS_APPROX(ab.coeff(2,3), -0.4757066334017702);\n  VERIFY_IS_APPROX(ab.coeff(2,4), -0.04773740823058334);\n  VERIFY_IS_APPROX(ab.coeff(2,5),  0.2300535609645254);\n  VERIFY_IS_APPROX(ab.coeff(3,0), -0.8172945853260133);\n  VERIFY_IS_APPROX(ab.coeff(3,1),  0.2150086428359221);\n  VERIFY_IS_APPROX(ab.coeff(3,2),  0.5825113847292743);\n  VERIFY_IS_APPROX(ab.coeff(3,3), -0.1532433770097174);\n  VERIFY_IS_APPROX(ab.coeff(3,4), -0.329383387282399);\n  VERIFY_IS_APPROX(ab.coeff(3,5),  0.08665207912033064);\n  VERIFY_IS_APPROX(ab.coeff(4,0),  0.8451267514863225);\n  VERIFY_IS_APPROX(ab.coeff(4,1), -0.481996458918977);\n  VERIFY_IS_APPROX(ab.coeff(4,2), -0.6023482390791535);\n  VERIFY_IS_APPROX(ab.coeff(4,3),  0.3435339347164565);\n  VERIFY_IS_APPROX(ab.coeff(4,4),  0.3406002157428891);\n  VERIFY_IS_APPROX(ab.coeff(4,5), -0.1942526344200915);\n  VERIFY_IS_APPROX(ab.coeff(5,0),  0.1111982482925399);\n  VERIFY_IS_APPROX(ab.coeff(5,1), -0.5358806424754169);\n  VERIFY_IS_APPROX(ab.coeff(5,2), -0.07925446559335647);\n  VERIFY_IS_APPROX(ab.coeff(5,3),  0.3819388757769038);\n  VERIFY_IS_APPROX(ab.coeff(5,4),  0.04481475387219876);\n  VERIFY_IS_APPROX(ab.coeff(5,5), -0.2159688616158057);\n}\n\n\ntemplate<typename MatrixType>\nvoid check_sparse_kronecker_product(const MatrixType& ab)\n{\n  VERIFY_IS_EQUAL(ab.rows(), 12);\n  VERIFY_IS_EQUAL(ab.cols(), 10);\n  VERIFY_IS_EQUAL(ab.nonZeros(), 3*2);\n  VERIFY_IS_APPROX(ab.coeff(3,0), -0.04);\n  VERIFY_IS_APPROX(ab.coeff(5,1),  0.05);\n  VERIFY_IS_APPROX(ab.coeff(0,6), -0.08);\n  VERIFY_IS_APPROX(ab.coeff(2,7),  0.10);\n  VERIFY_IS_APPROX(ab.coeff(6,8),  0.12);\n  VERIFY_IS_APPROX(ab.coeff(8,9), -0.15);\n}\n\n\nvoid test_kronecker_product()\n{\n  // DM = dense matrix; SM = sparse matrix\n\n  Matrix<double, 2, 3> DM_a;\n  SparseMatrix<double> SM_a(2,3);\n  SM_a.insert(0,0) = DM_a.coeffRef(0,0) = -0.4461540300782201;\n  SM_a.insert(0,1) = DM_a.coeffRef(0,1) = -0.8057364375283049;\n  SM_a.insert(0,2) = DM_a.coeffRef(0,2) =  0.3896572459516341;\n  SM_a.insert(1,0) = DM_a.coeffRef(1,0) = -0.9076572187376921;\n  SM_a.insert(1,1) = DM_a.coeffRef(1,1) =  0.6469156566545853;\n  SM_a.insert(1,2) = DM_a.coeffRef(1,2) = -0.3658010398782789;\n \n  MatrixXd             DM_b(3,2);\n  SparseMatrix<double> SM_b(3,2);\n  SM_b.insert(0,0) = DM_b.coeffRef(0,0) =  0.9004440976767099;\n  SM_b.insert(0,1) = DM_b.coeffRef(0,1) = -0.2368830858139832;\n  SM_b.insert(1,0) = DM_b.coeffRef(1,0) = -0.9311078389941825;\n  SM_b.insert(1,1) = DM_b.coeffRef(1,1) =  0.5310335762980047;\n  SM_b.insert(2,0) = DM_b.coeffRef(2,0) = -0.1225112806872035;\n  SM_b.insert(2,1) = DM_b.coeffRef(2,1) =  0.5903998022741264;\n\n  SparseMatrix<double,RowMajor> SM_row_a(SM_a), SM_row_b(SM_b);\n\n  // test DM_fixedSize = kroneckerProduct(DM_block,DM)\n  Matrix<double, 6, 6> DM_fix_ab = kroneckerProduct(DM_a.topLeftCorner<2,3>(),DM_b);\n\n  CALL_SUBTEST(check_kronecker_product(DM_fix_ab));\n  CALL_SUBTEST(check_kronecker_product(kroneckerProduct(DM_a.topLeftCorner<2,3>(),DM_b)));\n\n  for(int i=0;i<DM_fix_ab.rows();++i)\n    for(int j=0;j<DM_fix_ab.cols();++j)\n       VERIFY_IS_APPROX(kroneckerProduct(DM_a,DM_b).coeff(i,j), DM_fix_ab(i,j));\n\n  // test DM_block = kroneckerProduct(DM,DM)\n  MatrixXd DM_block_ab(10,15);\n  DM_block_ab.block<6,6>(2,5) = kroneckerProduct(DM_a,DM_b);\n  CALL_SUBTEST(check_kronecker_product(DM_block_ab.block<6,6>(2,5)));\n\n  // test DM = kroneckerProduct(DM,DM)\n  MatrixXd DM_ab = kroneckerProduct(DM_a,DM_b);\n  CALL_SUBTEST(check_kronecker_product(DM_ab));\n  CALL_SUBTEST(check_kronecker_product(kroneckerProduct(DM_a,DM_b)));\n\n  // test SM = kroneckerProduct(SM,DM)\n  SparseMatrix<double> SM_ab = kroneckerProduct(SM_a,DM_b);\n  CALL_SUBTEST(check_kronecker_product(SM_ab));\n  SparseMatrix<double,RowMajor> SM_ab2 = kroneckerProduct(SM_a,DM_b);\n  CALL_SUBTEST(check_kronecker_product(SM_ab2));\n  CALL_SUBTEST(check_kronecker_product(kroneckerProduct(SM_a,DM_b)));\n\n  // test SM = kroneckerProduct(DM,SM)\n  SM_ab.setZero();\n  SM_ab.insert(0,0)=37.0;\n  SM_ab = kroneckerProduct(DM_a,SM_b);\n  CALL_SUBTEST(check_kronecker_product(SM_ab));\n  SM_ab2.setZero();\n  SM_ab2.insert(0,0)=37.0;\n  SM_ab2 = kroneckerProduct(DM_a,SM_b);\n  CALL_SUBTEST(check_kronecker_product(SM_ab2));\n  CALL_SUBTEST(check_kronecker_product(kroneckerProduct(DM_a,SM_b)));\n\n  // test SM = kroneckerProduct(SM,SM)\n  SM_ab.resize(2,33);\n  SM_ab.insert(0,0)=37.0;\n  SM_ab = kroneckerProduct(SM_a,SM_b);\n  CALL_SUBTEST(check_kronecker_product(SM_ab));\n  SM_ab2.resize(5,11);\n  SM_ab2.insert(0,0)=37.0;\n  SM_ab2 = kroneckerProduct(SM_a,SM_b);\n  CALL_SUBTEST(check_kronecker_product(SM_ab2));\n  CALL_SUBTEST(check_kronecker_product(kroneckerProduct(SM_a,SM_b)));\n\n  // test SM = kroneckerProduct(SM,SM) with sparse pattern\n  SM_a.resize(4,5);\n  SM_b.resize(3,2);\n  SM_a.resizeNonZeros(0);\n  SM_b.resizeNonZeros(0);\n  SM_a.insert(1,0) = -0.1;\n  SM_a.insert(0,3) = -0.2;\n  SM_a.insert(2,4) =  0.3;\n  SM_a.finalize();\n  \n  SM_b.insert(0,0) =  0.4;\n  SM_b.insert(2,1) = -0.5;\n  SM_b.finalize();\n  SM_ab.resize(1,1);\n  SM_ab.insert(0,0)=37.0;\n  SM_ab = kroneckerProduct(SM_a,SM_b);\n  CALL_SUBTEST(check_sparse_kronecker_product(SM_ab));\n\n  // test dimension of result of DM = kroneckerProduct(DM,DM)\n  MatrixXd DM_a2(2,1);\n  MatrixXd DM_b2(5,4);\n  MatrixXd DM_ab2 = kroneckerProduct(DM_a2,DM_b2);\n  CALL_SUBTEST(check_dimension(DM_ab2,2*5,1*4));\n  DM_a2.resize(10,9);\n  DM_b2.resize(4,8);\n  DM_ab2 = kroneckerProduct(DM_a2,DM_b2);\n  CALL_SUBTEST(check_dimension(DM_ab2,10*4,9*8));\n  \n  for(int i = 0; i < g_repeat; i++)\n  {\n    double density = Eigen::internal::random<double>(0.01,0.5);\n    int ra = Eigen::internal::random<int>(1,50);\n    int ca = Eigen::internal::random<int>(1,50);\n    int rb = Eigen::internal::random<int>(1,50);\n    int cb = Eigen::internal::random<int>(1,50);\n    SparseMatrix<float,ColMajor> sA(ra,ca), sB(rb,cb), sC;\n    SparseMatrix<float,RowMajor> sC2;\n    MatrixXf dA(ra,ca), dB(rb,cb), dC;\n    initSparse(density, dA, sA);\n    initSparse(density, dB, sB);\n    \n    sC = kroneckerProduct(sA,sB);\n    dC = kroneckerProduct(dA,dB);\n    VERIFY_IS_APPROX(MatrixXf(sC),dC);\n    \n    sC = kroneckerProduct(sA.transpose(),sB);\n    dC = kroneckerProduct(dA.transpose(),dB);\n    VERIFY_IS_APPROX(MatrixXf(sC),dC);\n    \n    sC = kroneckerProduct(sA.transpose(),sB.transpose());\n    dC = kroneckerProduct(dA.transpose(),dB.transpose());\n    VERIFY_IS_APPROX(MatrixXf(sC),dC);\n    \n    sC = kroneckerProduct(sA,sB.transpose());\n    dC = kroneckerProduct(dA,dB.transpose());\n    VERIFY_IS_APPROX(MatrixXf(sC),dC);\n    \n    sC2 = kroneckerProduct(sA,sB);\n    dC = kroneckerProduct(dA,dB);\n    VERIFY_IS_APPROX(MatrixXf(sC2),dC);\n    \n    sC2 = kroneckerProduct(dA,sB);\n    dC = kroneckerProduct(dA,dB);\n    VERIFY_IS_APPROX(MatrixXf(sC2),dC);\n    \n    sC2 = kroneckerProduct(sA,dB);\n    dC = kroneckerProduct(dA,dB);\n    VERIFY_IS_APPROX(MatrixXf(sC2),dC);\n    \n    sC2 = kroneckerProduct(2*sA,sB);\n    dC = kroneckerProduct(2*dA,dB);\n    VERIFY_IS_APPROX(MatrixXf(sC2),dC);\n  }\n}\n\n#endif\n\n#ifdef EIGEN_TEST_PART_2\n\n// simply check that for a dense kronecker product, sparse module is not needed\n\n#include \"main.h\"\n#include <Eigen/KroneckerProduct>\n\nvoid test_kronecker_product()\n{\n  MatrixXd a(2,2), b(3,3), c;\n  a.setRandom();\n  b.setRandom();\n  c = kroneckerProduct(a,b);\n  VERIFY_IS_APPROX(c.block(3,3,3,3), a(1,1)*b);\n}\n\n#endif\n"
  },
  {
    "path": "include/eigen3/unsupported/test/levenberg_marquardt.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>\n// Copyright (C) 2012 desire Nuentsa <desire.nuentsa_wakam@inria.fr\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n\n// FIXME: These tests all check for hard-coded values. Ideally, parameters and start estimates should be randomized.\n\n\n#include <stdio.h>\n\n#include \"main.h\"\n#include <unsupported/Eigen/LevenbergMarquardt>\n\n// This disables some useless Warnings on MSVC.\n// It is intended to be done for this test only.\n#include <Eigen/src/Core/util/DisableStupidWarnings.h>\n\nusing std::sqrt;\n\n// tolerance for chekcing number of iterations\n#define LM_EVAL_COUNT_TOL 4/3\n\nstruct lmder_functor : DenseFunctor<double>\n{\n    lmder_functor(void): DenseFunctor<double>(3,15) {}\n    int operator()(const VectorXd &x, VectorXd &fvec) const\n    {\n        double tmp1, tmp2, tmp3;\n        static const double y[15] = {1.4e-1, 1.8e-1, 2.2e-1, 2.5e-1, 2.9e-1, 3.2e-1, 3.5e-1,\n            3.9e-1, 3.7e-1, 5.8e-1, 7.3e-1, 9.6e-1, 1.34, 2.1, 4.39};\n\n        for (int i = 0; i < values(); i++)\n        {\n            tmp1 = i+1;\n            tmp2 = 16 - i - 1;\n            tmp3 = (i>=8)? tmp2 : tmp1;\n            fvec[i] = y[i] - (x[0] + tmp1/(x[1]*tmp2 + x[2]*tmp3));\n        }\n        return 0;\n    }\n\n    int df(const VectorXd &x, MatrixXd &fjac) const\n    {\n        double tmp1, tmp2, tmp3, tmp4;\n        for (int i = 0; i < values(); i++)\n        {\n            tmp1 = i+1;\n            tmp2 = 16 - i - 1;\n            tmp3 = (i>=8)? tmp2 : tmp1;\n            tmp4 = (x[1]*tmp2 + x[2]*tmp3); tmp4 = tmp4*tmp4;\n            fjac(i,0) = -1;\n            fjac(i,1) = tmp1*tmp2/tmp4;\n            fjac(i,2) = tmp1*tmp3/tmp4;\n        }\n        return 0;\n    }\n};\n\nvoid testLmder1()\n{\n  int n=3, info;\n\n  VectorXd x;\n\n  /* the following starting values provide a rough fit. */\n  x.setConstant(n, 1.);\n\n  // do the computation\n  lmder_functor functor;\n  LevenbergMarquardt<lmder_functor> lm(functor);\n  info = lm.lmder1(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev(), 6);\n  VERIFY_IS_EQUAL(lm.njev(), 5);\n\n  // check norm\n  VERIFY_IS_APPROX(lm.fvec().blueNorm(), 0.09063596);\n\n  // check x\n  VectorXd x_ref(n);\n  x_ref << 0.08241058, 1.133037, 2.343695;\n  VERIFY_IS_APPROX(x, x_ref);\n}\n\nvoid testLmder()\n{\n  const int m=15, n=3;\n  int info;\n  double fnorm, covfac;\n  VectorXd x;\n\n  /* the following starting values provide a rough fit. */\n  x.setConstant(n, 1.);\n\n  // do the computation\n  lmder_functor functor;\n  LevenbergMarquardt<lmder_functor> lm(functor);\n  info = lm.minimize(x);\n\n  // check return values\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev(), 6);\n  VERIFY_IS_EQUAL(lm.njev(), 5);\n\n  // check norm\n  fnorm = lm.fvec().blueNorm();\n  VERIFY_IS_APPROX(fnorm, 0.09063596);\n\n  // check x\n  VectorXd x_ref(n);\n  x_ref << 0.08241058, 1.133037, 2.343695;\n  VERIFY_IS_APPROX(x, x_ref);\n\n  // check covariance\n  covfac = fnorm*fnorm/(m-n);\n  internal::covar(lm.matrixR(), lm.permutation().indices()); // TODO : move this as a function of lm\n\n  MatrixXd cov_ref(n,n);\n  cov_ref <<\n      0.0001531202,   0.002869941,  -0.002656662,\n      0.002869941,    0.09480935,   -0.09098995,\n      -0.002656662,   -0.09098995,    0.08778727;\n\n//  std::cout << fjac*covfac << std::endl;\n\n  MatrixXd cov;\n  cov =  covfac*lm.matrixR().topLeftCorner<n,n>();\n  VERIFY_IS_APPROX( cov, cov_ref);\n  // TODO: why isn't this allowed ? :\n  // VERIFY_IS_APPROX( covfac*fjac.topLeftCorner<n,n>() , cov_ref);\n}\n\nstruct lmdif_functor : DenseFunctor<double>\n{\n    lmdif_functor(void) : DenseFunctor<double>(3,15) {}\n    int operator()(const VectorXd &x, VectorXd &fvec) const\n    {\n        int i;\n        double tmp1,tmp2,tmp3;\n        static const double y[15]={1.4e-1,1.8e-1,2.2e-1,2.5e-1,2.9e-1,3.2e-1,3.5e-1,3.9e-1,\n            3.7e-1,5.8e-1,7.3e-1,9.6e-1,1.34e0,2.1e0,4.39e0};\n\n        assert(x.size()==3);\n        assert(fvec.size()==15);\n        for (i=0; i<15; i++)\n        {\n            tmp1 = i+1;\n            tmp2 = 15 - i;\n            tmp3 = tmp1;\n\n            if (i >= 8) tmp3 = tmp2;\n            fvec[i] = y[i] - (x[0] + tmp1/(x[1]*tmp2 + x[2]*tmp3));\n        }\n        return 0;\n    }\n};\n\nvoid testLmdif1()\n{\n  const int n=3;\n  int info;\n\n  VectorXd x(n), fvec(15);\n\n  /* the following starting values provide a rough fit. */\n  x.setConstant(n, 1.);\n\n  // do the computation\n  lmdif_functor functor;\n  DenseIndex nfev;\n  info = LevenbergMarquardt<lmdif_functor>::lmdif1(functor, x, &nfev);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n//   VERIFY_IS_EQUAL(nfev, 26);\n\n  // check norm\n  functor(x, fvec);\n  VERIFY_IS_APPROX(fvec.blueNorm(), 0.09063596);\n\n  // check x\n  VectorXd x_ref(n);\n  x_ref << 0.0824106, 1.1330366, 2.3436947;\n  VERIFY_IS_APPROX(x, x_ref);\n\n}\n\nvoid testLmdif()\n{\n  const int m=15, n=3;\n  int info;\n  double fnorm, covfac;\n  VectorXd x(n);\n\n  /* the following starting values provide a rough fit. */\n  x.setConstant(n, 1.);\n\n  // do the computation\n  lmdif_functor functor;\n  NumericalDiff<lmdif_functor> numDiff(functor);\n  LevenbergMarquardt<NumericalDiff<lmdif_functor> > lm(numDiff);\n  info = lm.minimize(x);\n\n  // check return values\n  VERIFY_IS_EQUAL(info, 1);\n//   VERIFY_IS_EQUAL(lm.nfev(), 26);\n\n  // check norm\n  fnorm = lm.fvec().blueNorm();\n  VERIFY_IS_APPROX(fnorm, 0.09063596);\n\n  // check x\n  VectorXd x_ref(n);\n  x_ref << 0.08241058, 1.133037, 2.343695;\n  VERIFY_IS_APPROX(x, x_ref);\n\n  // check covariance\n  covfac = fnorm*fnorm/(m-n);\n  internal::covar(lm.matrixR(), lm.permutation().indices()); // TODO : move this as a function of lm\n\n  MatrixXd cov_ref(n,n);\n  cov_ref <<\n      0.0001531202,   0.002869942,  -0.002656662,\n      0.002869942,    0.09480937,   -0.09098997,\n      -0.002656662,   -0.09098997,    0.08778729;\n\n//  std::cout << fjac*covfac << std::endl;\n\n  MatrixXd cov;\n  cov =  covfac*lm.matrixR().topLeftCorner<n,n>();\n  VERIFY_IS_APPROX( cov, cov_ref);\n  // TODO: why isn't this allowed ? :\n  // VERIFY_IS_APPROX( covfac*fjac.topLeftCorner<n,n>() , cov_ref);\n}\n\nstruct chwirut2_functor : DenseFunctor<double>\n{\n    chwirut2_functor(void) : DenseFunctor<double>(3,54) {}\n    static const double m_x[54];\n    static const double m_y[54];\n    int operator()(const VectorXd &b, VectorXd &fvec)\n    {\n        int i;\n\n        assert(b.size()==3);\n        assert(fvec.size()==54);\n        for(i=0; i<54; i++) {\n            double x = m_x[i];\n            fvec[i] = exp(-b[0]*x)/(b[1]+b[2]*x) - m_y[i];\n        }\n        return 0;\n    }\n    int df(const VectorXd &b, MatrixXd &fjac)\n    {\n        assert(b.size()==3);\n        assert(fjac.rows()==54);\n        assert(fjac.cols()==3);\n        for(int i=0; i<54; i++) {\n            double x = m_x[i];\n            double factor = 1./(b[1]+b[2]*x);\n            double e = exp(-b[0]*x);\n            fjac(i,0) = -x*e*factor;\n            fjac(i,1) = -e*factor*factor;\n            fjac(i,2) = -x*e*factor*factor;\n        }\n        return 0;\n    }\n};\nconst double chwirut2_functor::m_x[54] = { 0.500E0, 1.000E0, 1.750E0, 3.750E0, 5.750E0, 0.875E0, 2.250E0, 3.250E0, 5.250E0, 0.750E0, 1.750E0, 2.750E0, 4.750E0, 0.625E0, 1.250E0, 2.250E0, 4.250E0, .500E0, 3.000E0, .750E0, 3.000E0, 1.500E0, 6.000E0, 3.000E0, 6.000E0, 1.500E0, 3.000E0, .500E0, 2.000E0, 4.000E0, .750E0, 2.000E0, 5.000E0, .750E0, 2.250E0, 3.750E0, 5.750E0, 3.000E0, .750E0, 2.500E0, 4.000E0, .750E0, 2.500E0, 4.000E0, .750E0, 2.500E0, 4.000E0, .500E0, 6.000E0, 3.000E0, .500E0, 2.750E0, .500E0, 1.750E0};\nconst double chwirut2_functor::m_y[54] = { 92.9000E0 ,57.1000E0 ,31.0500E0 ,11.5875E0 ,8.0250E0 ,63.6000E0 ,21.4000E0 ,14.2500E0 ,8.4750E0 ,63.8000E0 ,26.8000E0 ,16.4625E0 ,7.1250E0 ,67.3000E0 ,41.0000E0 ,21.1500E0 ,8.1750E0 ,81.5000E0 ,13.1200E0 ,59.9000E0 ,14.6200E0 ,32.9000E0 ,5.4400E0 ,12.5600E0 ,5.4400E0 ,32.0000E0 ,13.9500E0 ,75.8000E0 ,20.0000E0 ,10.4200E0 ,59.5000E0 ,21.6700E0 ,8.5500E0 ,62.0000E0 ,20.2000E0 ,7.7600E0 ,3.7500E0 ,11.8100E0 ,54.7000E0 ,23.7000E0 ,11.5500E0 ,61.3000E0 ,17.7000E0 ,8.7400E0 ,59.2000E0 ,16.3000E0 ,8.6200E0 ,81.0000E0 ,4.8700E0 ,14.6200E0 ,81.7000E0 ,17.1700E0 ,81.3000E0 ,28.9000E0  };\n\n// http://www.itl.nist.gov/div898/strd/nls/data/chwirut2.shtml\nvoid testNistChwirut2(void)\n{\n  const int n=3;\n  LevenbergMarquardtSpace::Status info;\n\n  VectorXd x(n);\n\n  /*\n   * First try\n   */\n  x<< 0.1, 0.01, 0.02;\n  // do the computation\n  chwirut2_functor functor;\n  LevenbergMarquardt<chwirut2_functor> lm(functor);\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n//   VERIFY_IS_EQUAL(lm.nfev(), 10);\n  VERIFY_IS_EQUAL(lm.njev(), 8);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 5.1304802941E+02);\n  // check x\n  VERIFY_IS_APPROX(x[0], 1.6657666537E-01);\n  VERIFY_IS_APPROX(x[1], 5.1653291286E-03);\n  VERIFY_IS_APPROX(x[2], 1.2150007096E-02);\n\n  /*\n   * Second try\n   */\n  x<< 0.15, 0.008, 0.010;\n  // do the computation\n  lm.resetParameters();\n  lm.setFtol(1.E6*NumTraits<double>::epsilon());\n  lm.setXtol(1.E6*NumTraits<double>::epsilon());\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n//   VERIFY_IS_EQUAL(lm.nfev(), 7);\n  VERIFY_IS_EQUAL(lm.njev(), 6);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 5.1304802941E+02);\n  // check x\n  VERIFY_IS_APPROX(x[0], 1.6657666537E-01);\n  VERIFY_IS_APPROX(x[1], 5.1653291286E-03);\n  VERIFY_IS_APPROX(x[2], 1.2150007096E-02);\n}\n\n\nstruct misra1a_functor : DenseFunctor<double>\n{\n    misra1a_functor(void) : DenseFunctor<double>(2,14) {}\n    static const double m_x[14];\n    static const double m_y[14];\n    int operator()(const VectorXd &b, VectorXd &fvec)\n    {\n        assert(b.size()==2);\n        assert(fvec.size()==14);\n        for(int i=0; i<14; i++) {\n            fvec[i] = b[0]*(1.-exp(-b[1]*m_x[i])) - m_y[i] ;\n        }\n        return 0;\n    }\n    int df(const VectorXd &b, MatrixXd &fjac)\n    {\n        assert(b.size()==2);\n        assert(fjac.rows()==14);\n        assert(fjac.cols()==2);\n        for(int i=0; i<14; i++) {\n            fjac(i,0) = (1.-exp(-b[1]*m_x[i]));\n            fjac(i,1) = (b[0]*m_x[i]*exp(-b[1]*m_x[i]));\n        }\n        return 0;\n    }\n};\nconst double misra1a_functor::m_x[14] = { 77.6E0, 114.9E0, 141.1E0, 190.8E0, 239.9E0, 289.0E0, 332.8E0, 378.4E0, 434.8E0, 477.3E0, 536.8E0, 593.1E0, 689.1E0, 760.0E0};\nconst double misra1a_functor::m_y[14] = { 10.07E0, 14.73E0, 17.94E0, 23.93E0, 29.61E0, 35.18E0, 40.02E0, 44.82E0, 50.76E0, 55.05E0, 61.01E0, 66.40E0, 75.47E0, 81.78E0};\n\n// http://www.itl.nist.gov/div898/strd/nls/data/misra1a.shtml\nvoid testNistMisra1a(void)\n{\n  const int n=2;\n  int info;\n\n  VectorXd x(n);\n\n  /*\n   * First try\n   */\n  x<< 500., 0.0001;\n  // do the computation\n  misra1a_functor functor;\n  LevenbergMarquardt<misra1a_functor> lm(functor);\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev(), 19);\n  VERIFY_IS_EQUAL(lm.njev(), 15);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 1.2455138894E-01);\n  // check x\n  VERIFY_IS_APPROX(x[0], 2.3894212918E+02);\n  VERIFY_IS_APPROX(x[1], 5.5015643181E-04);\n\n  /*\n   * Second try\n   */\n  x<< 250., 0.0005;\n  // do the computation\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev(), 5);\n  VERIFY_IS_EQUAL(lm.njev(), 4);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 1.2455138894E-01);\n  // check x\n  VERIFY_IS_APPROX(x[0], 2.3894212918E+02);\n  VERIFY_IS_APPROX(x[1], 5.5015643181E-04);\n}\n\nstruct hahn1_functor : DenseFunctor<double>\n{\n    hahn1_functor(void) : DenseFunctor<double>(7,236) {}\n    static const double m_x[236];\n    int operator()(const VectorXd &b, VectorXd &fvec)\n    {\n        static const double m_y[236] = { .591E0 , 1.547E0 , 2.902E0 , 2.894E0 , 4.703E0 , 6.307E0 , 7.03E0  , 7.898E0 , 9.470E0 , 9.484E0 , 10.072E0 , 10.163E0 , 11.615E0 , 12.005E0 , 12.478E0 , 12.982E0 , 12.970E0 , 13.926E0 , 14.452E0 , 14.404E0 , 15.190E0 , 15.550E0 , 15.528E0 , 15.499E0 , 16.131E0 , 16.438E0 , 16.387E0 , 16.549E0 , 16.872E0 , 16.830E0 , 16.926E0 , 16.907E0 , 16.966E0 , 17.060E0 , 17.122E0 , 17.311E0 , 17.355E0 , 17.668E0 , 17.767E0 , 17.803E0 , 17.765E0 , 17.768E0 , 17.736E0 , 17.858E0 , 17.877E0 , 17.912E0 , 18.046E0 , 18.085E0 , 18.291E0 , 18.357E0 , 18.426E0 , 18.584E0 , 18.610E0 , 18.870E0 , 18.795E0 , 19.111E0 , .367E0 , .796E0 , 0.892E0 , 1.903E0 , 2.150E0 , 3.697E0 , 5.870E0 , 6.421E0 , 7.422E0 , 9.944E0 , 11.023E0 , 11.87E0  , 12.786E0 , 14.067E0 , 13.974E0 , 14.462E0 , 14.464E0 , 15.381E0 , 15.483E0 , 15.59E0  , 16.075E0 , 16.347E0 , 16.181E0 , 16.915E0 , 17.003E0 , 16.978E0 , 17.756E0 , 17.808E0 , 17.868E0 , 18.481E0 , 18.486E0 , 19.090E0 , 16.062E0 , 16.337E0 , 16.345E0 ,\n        16.388E0 , 17.159E0 , 17.116E0 , 17.164E0 , 17.123E0 , 17.979E0 , 17.974E0 , 18.007E0 , 17.993E0 , 18.523E0 , 18.669E0 , 18.617E0 , 19.371E0 , 19.330E0 , 0.080E0 , 0.248E0 , 1.089E0 , 1.418E0 , 2.278E0 , 3.624E0 , 4.574E0 , 5.556E0 , 7.267E0 , 7.695E0 , 9.136E0 , 9.959E0 , 9.957E0 , 11.600E0 , 13.138E0 , 13.564E0 , 13.871E0 , 13.994E0 , 14.947E0 , 15.473E0 , 15.379E0 , 15.455E0 , 15.908E0 , 16.114E0 , 17.071E0 , 17.135E0 , 17.282E0 , 17.368E0 , 17.483E0 , 17.764E0 , 18.185E0 , 18.271E0 , 18.236E0 , 18.237E0 , 18.523E0 , 18.627E0 , 18.665E0 , 19.086E0 , 0.214E0 , 0.943E0 , 1.429E0 , 2.241E0 , 2.951E0 , 3.782E0 , 4.757E0 , 5.602E0 , 7.169E0 , 8.920E0 , 10.055E0 , 12.035E0 , 12.861E0 , 13.436E0 , 14.167E0 , 14.755E0 , 15.168E0 , 15.651E0 , 15.746E0 , 16.216E0 , 16.445E0 , 16.965E0 , 17.121E0 , 17.206E0 , 17.250E0 , 17.339E0 , 17.793E0 , 18.123E0 , 18.49E0  , 18.566E0 , 18.645E0 , 18.706E0 , 18.924E0 , 19.1E0   , 0.375E0 , 0.471E0 , 1.504E0 , 2.204E0 , 2.813E0 , 4.765E0 , 9.835E0 , 10.040E0 , 11.946E0 , \n12.596E0 , \n13.303E0 , 13.922E0 , 14.440E0 , 14.951E0 , 15.627E0 , 15.639E0 , 15.814E0 , 16.315E0 , 16.334E0 , 16.430E0 , 16.423E0 , 17.024E0 , 17.009E0 , 17.165E0 , 17.134E0 , 17.349E0 , 17.576E0 , 17.848E0 , 18.090E0 , 18.276E0 , 18.404E0 , 18.519E0 , 19.133E0 , 19.074E0 , 19.239E0 , 19.280E0 , 19.101E0 , 19.398E0 , 19.252E0 , 19.89E0  , 20.007E0 , 19.929E0 , 19.268E0 , 19.324E0 , 20.049E0 , 20.107E0 , 20.062E0 , 20.065E0 , 19.286E0 , 19.972E0 , 20.088E0 , 20.743E0 , 20.83E0  , 20.935E0 , 21.035E0 , 20.93E0  , 21.074E0 , 21.085E0 , 20.935E0 };\n\n        //        int called=0; printf(\"call hahn1_functor with  iflag=%d, called=%d\\n\", iflag, called); if (iflag==1) called++;\n\n        assert(b.size()==7);\n        assert(fvec.size()==236);\n        for(int i=0; i<236; i++) {\n            double x=m_x[i], xx=x*x, xxx=xx*x;\n            fvec[i] = (b[0]+b[1]*x+b[2]*xx+b[3]*xxx) / (1.+b[4]*x+b[5]*xx+b[6]*xxx) - m_y[i];\n        }\n        return 0;\n    }\n\n    int df(const VectorXd &b, MatrixXd &fjac)\n    {\n        assert(b.size()==7);\n        assert(fjac.rows()==236);\n        assert(fjac.cols()==7);\n        for(int i=0; i<236; i++) {\n            double x=m_x[i], xx=x*x, xxx=xx*x;\n            double fact = 1./(1.+b[4]*x+b[5]*xx+b[6]*xxx);\n            fjac(i,0) = 1.*fact;\n            fjac(i,1) = x*fact;\n            fjac(i,2) = xx*fact;\n            fjac(i,3) = xxx*fact;\n            fact = - (b[0]+b[1]*x+b[2]*xx+b[3]*xxx) * fact * fact;\n            fjac(i,4) = x*fact;\n            fjac(i,5) = xx*fact;\n            fjac(i,6) = xxx*fact;\n        }\n        return 0;\n    }\n};\nconst double hahn1_functor::m_x[236] = { 24.41E0 , 34.82E0 , 44.09E0 , 45.07E0 , 54.98E0 , 65.51E0 , 70.53E0 , 75.70E0 , 89.57E0 , 91.14E0 , 96.40E0 , 97.19E0 , 114.26E0 , 120.25E0 , 127.08E0 , 133.55E0 , 133.61E0 , 158.67E0 , 172.74E0 , 171.31E0 , 202.14E0 , 220.55E0 , 221.05E0 , 221.39E0 , 250.99E0 , 268.99E0 , 271.80E0 , 271.97E0 , 321.31E0 , 321.69E0 , 330.14E0 , 333.03E0 , 333.47E0 , 340.77E0 , 345.65E0 , 373.11E0 , 373.79E0 , 411.82E0 , 419.51E0 , 421.59E0 , 422.02E0 , 422.47E0 , 422.61E0 , 441.75E0 , 447.41E0 , 448.7E0  , 472.89E0 , 476.69E0 , 522.47E0 , 522.62E0 , 524.43E0 , 546.75E0 , 549.53E0 , 575.29E0 , 576.00E0 , 625.55E0 , 20.15E0 , 28.78E0 , 29.57E0 , 37.41E0 , 39.12E0 , 50.24E0 , 61.38E0 , 66.25E0 , 73.42E0 , 95.52E0 , 107.32E0 , 122.04E0 , 134.03E0 , 163.19E0 , 163.48E0 , 175.70E0 , 179.86E0 , 211.27E0 , 217.78E0 , 219.14E0 , 262.52E0 , 268.01E0 , 268.62E0 , 336.25E0 , 337.23E0 , 339.33E0 , 427.38E0 , 428.58E0 , 432.68E0 , 528.99E0 , 531.08E0 , 628.34E0 , 253.24E0 , 273.13E0 , 273.66E0 ,\n282.10E0 , 346.62E0 , 347.19E0 , 348.78E0 , 351.18E0 , 450.10E0 , 450.35E0 , 451.92E0 , 455.56E0 , 552.22E0 , 553.56E0 , 555.74E0 , 652.59E0 , 656.20E0 , 14.13E0 , 20.41E0 , 31.30E0 , 33.84E0 , 39.70E0 , 48.83E0 , 54.50E0 , 60.41E0 , 72.77E0 , 75.25E0 , 86.84E0 , 94.88E0 , 96.40E0 , 117.37E0 , 139.08E0 , 147.73E0 , 158.63E0 , 161.84E0 , 192.11E0 , 206.76E0 , 209.07E0 , 213.32E0 , 226.44E0 , 237.12E0 , 330.90E0 , 358.72E0 , 370.77E0 , 372.72E0 , 396.24E0 , 416.59E0 , 484.02E0 , 495.47E0 , 514.78E0 , 515.65E0 , 519.47E0 , 544.47E0 , 560.11E0 , 620.77E0 , 18.97E0 , 28.93E0 , 33.91E0 , 40.03E0 , 44.66E0 , 49.87E0 , 55.16E0 , 60.90E0 , 72.08E0 , 85.15E0 , 97.06E0 , 119.63E0 , 133.27E0 , 143.84E0 , 161.91E0 , 180.67E0 , 198.44E0 , 226.86E0 , 229.65E0 , 258.27E0 , 273.77E0 , 339.15E0 , 350.13E0 , 362.75E0 , 371.03E0 , 393.32E0 , 448.53E0 , 473.78E0 , 511.12E0 , 524.70E0 , 548.75E0 , 551.64E0 , 574.02E0 , 623.86E0 , 21.46E0 , 24.33E0 , 33.43E0 , 39.22E0 , 44.18E0 , 55.02E0 , 94.33E0 , 96.44E0 , 118.82E0 , 128.48E0 ,\n141.94E0 , 156.92E0 , 171.65E0 , 190.00E0 , 223.26E0 , 223.88E0 , 231.50E0 , 265.05E0 , 269.44E0 , 271.78E0 , 273.46E0 , 334.61E0 , 339.79E0 , 349.52E0 , 358.18E0 , 377.98E0 , 394.77E0 , 429.66E0 , 468.22E0 , 487.27E0 , 519.54E0 , 523.03E0 , 612.99E0 , 638.59E0 , 641.36E0 , 622.05E0 , 631.50E0 , 663.97E0 , 646.9E0  , 748.29E0 , 749.21E0 , 750.14E0 , 647.04E0 , 646.89E0 , 746.9E0  , 748.43E0 , 747.35E0 , 749.27E0 , 647.61E0 , 747.78E0 , 750.51E0 , 851.37E0 , 845.97E0 , 847.54E0 , 849.93E0 , 851.61E0 , 849.75E0 , 850.98E0 , 848.23E0};\n\n// http://www.itl.nist.gov/div898/strd/nls/data/hahn1.shtml\nvoid testNistHahn1(void)\n{\n  const int  n=7;\n  int info;\n\n  VectorXd x(n);\n\n  /*\n   * First try\n   */\n  x<< 10., -1., .05, -.00001, -.05, .001, -.000001;\n  // do the computation\n  hahn1_functor functor;\n  LevenbergMarquardt<hahn1_functor> lm(functor);\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev(), 11);\n  VERIFY_IS_EQUAL(lm.njev(), 10);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 1.5324382854E+00);\n  // check x\n  VERIFY_IS_APPROX(x[0], 1.0776351733E+00);\n  VERIFY_IS_APPROX(x[1],-1.2269296921E-01);\n  VERIFY_IS_APPROX(x[2], 4.0863750610E-03);\n  VERIFY_IS_APPROX(x[3],-1.426264e-06); // shoulde be : -1.4262662514E-06\n  VERIFY_IS_APPROX(x[4],-5.7609940901E-03);\n  VERIFY_IS_APPROX(x[5], 2.4053735503E-04);\n  VERIFY_IS_APPROX(x[6],-1.2314450199E-07);\n\n  /*\n   * Second try\n   */\n  x<< .1, -.1, .005, -.000001, -.005, .0001, -.0000001;\n  // do the computation\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n//   VERIFY_IS_EQUAL(lm.nfev(), 11);\n  VERIFY_IS_EQUAL(lm.njev(), 10);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 1.5324382854E+00);\n  // check x\n  VERIFY_IS_APPROX(x[0], 1.077640); // should be :  1.0776351733E+00\n  VERIFY_IS_APPROX(x[1], -0.1226933); // should be : -1.2269296921E-01\n  VERIFY_IS_APPROX(x[2], 0.004086383); // should be : 4.0863750610E-03\n  VERIFY_IS_APPROX(x[3], -1.426277e-06); // shoulde be : -1.4262662514E-06\n  VERIFY_IS_APPROX(x[4],-5.7609940901E-03);\n  VERIFY_IS_APPROX(x[5], 0.00024053772); // should be : 2.4053735503E-04\n  VERIFY_IS_APPROX(x[6], -1.231450e-07); // should be : -1.2314450199E-07\n\n}\n\nstruct misra1d_functor : DenseFunctor<double>\n{\n    misra1d_functor(void) : DenseFunctor<double>(2,14) {}\n    static const double x[14];\n    static const double y[14];\n    int operator()(const VectorXd &b, VectorXd &fvec)\n    {\n        assert(b.size()==2);\n        assert(fvec.size()==14);\n        for(int i=0; i<14; i++) {\n            fvec[i] = b[0]*b[1]*x[i]/(1.+b[1]*x[i]) - y[i];\n        }\n        return 0;\n    }\n    int df(const VectorXd &b, MatrixXd &fjac)\n    {\n        assert(b.size()==2);\n        assert(fjac.rows()==14);\n        assert(fjac.cols()==2);\n        for(int i=0; i<14; i++) {\n            double den = 1.+b[1]*x[i];\n            fjac(i,0) = b[1]*x[i] / den;\n            fjac(i,1) = b[0]*x[i]*(den-b[1]*x[i])/den/den;\n        }\n        return 0;\n    }\n};\nconst double misra1d_functor::x[14] = { 77.6E0, 114.9E0, 141.1E0, 190.8E0, 239.9E0, 289.0E0, 332.8E0, 378.4E0, 434.8E0, 477.3E0, 536.8E0, 593.1E0, 689.1E0, 760.0E0};\nconst double misra1d_functor::y[14] = { 10.07E0, 14.73E0, 17.94E0, 23.93E0, 29.61E0, 35.18E0, 40.02E0, 44.82E0, 50.76E0, 55.05E0, 61.01E0, 66.40E0, 75.47E0, 81.78E0};\n\n// http://www.itl.nist.gov/div898/strd/nls/data/misra1d.shtml\nvoid testNistMisra1d(void)\n{\n  const int n=2;\n  int info;\n\n  VectorXd x(n);\n\n  /*\n   * First try\n   */\n  x<< 500., 0.0001;\n  // do the computation\n  misra1d_functor functor;\n  LevenbergMarquardt<misra1d_functor> lm(functor);\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev(), 9);\n  VERIFY_IS_EQUAL(lm.njev(), 7);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 5.6419295283E-02);\n  // check x\n  VERIFY_IS_APPROX(x[0], 4.3736970754E+02);\n  VERIFY_IS_APPROX(x[1], 3.0227324449E-04);\n\n  /*\n   * Second try\n   */\n  x<< 450., 0.0003;\n  // do the computation\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev(), 4);\n  VERIFY_IS_EQUAL(lm.njev(), 3);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 5.6419295283E-02);\n  // check x\n  VERIFY_IS_APPROX(x[0], 4.3736970754E+02);\n  VERIFY_IS_APPROX(x[1], 3.0227324449E-04);\n}\n\n\nstruct lanczos1_functor : DenseFunctor<double>\n{\n    lanczos1_functor(void) : DenseFunctor<double>(6,24) {}\n    static const double x[24];\n    static const double y[24];\n    int operator()(const VectorXd &b, VectorXd &fvec)\n    {\n        assert(b.size()==6);\n        assert(fvec.size()==24);\n        for(int i=0; i<24; i++)\n            fvec[i] = b[0]*exp(-b[1]*x[i]) + b[2]*exp(-b[3]*x[i]) + b[4]*exp(-b[5]*x[i])  - y[i];\n        return 0;\n    }\n    int df(const VectorXd &b, MatrixXd &fjac)\n    {\n        assert(b.size()==6);\n        assert(fjac.rows()==24);\n        assert(fjac.cols()==6);\n        for(int i=0; i<24; i++) {\n            fjac(i,0) = exp(-b[1]*x[i]);\n            fjac(i,1) = -b[0]*x[i]*exp(-b[1]*x[i]);\n            fjac(i,2) = exp(-b[3]*x[i]);\n            fjac(i,3) = -b[2]*x[i]*exp(-b[3]*x[i]);\n            fjac(i,4) = exp(-b[5]*x[i]);\n            fjac(i,5) = -b[4]*x[i]*exp(-b[5]*x[i]);\n        }\n        return 0;\n    }\n};\nconst double lanczos1_functor::x[24] = { 0.000000000000E+00, 5.000000000000E-02, 1.000000000000E-01, 1.500000000000E-01, 2.000000000000E-01, 2.500000000000E-01, 3.000000000000E-01, 3.500000000000E-01, 4.000000000000E-01, 4.500000000000E-01, 5.000000000000E-01, 5.500000000000E-01, 6.000000000000E-01, 6.500000000000E-01, 7.000000000000E-01, 7.500000000000E-01, 8.000000000000E-01, 8.500000000000E-01, 9.000000000000E-01, 9.500000000000E-01, 1.000000000000E+00, 1.050000000000E+00, 1.100000000000E+00, 1.150000000000E+00 };\nconst double lanczos1_functor::y[24] = { 2.513400000000E+00 ,2.044333373291E+00 ,1.668404436564E+00 ,1.366418021208E+00 ,1.123232487372E+00 ,9.268897180037E-01 ,7.679338563728E-01 ,6.388775523106E-01 ,5.337835317402E-01 ,4.479363617347E-01 ,3.775847884350E-01 ,3.197393199326E-01 ,2.720130773746E-01 ,2.324965529032E-01 ,1.996589546065E-01 ,1.722704126914E-01 ,1.493405660168E-01 ,1.300700206922E-01 ,1.138119324644E-01 ,1.000415587559E-01 ,8.833209084540E-02 ,7.833544019350E-02 ,6.976693743449E-02 ,6.239312536719E-02 };\n\n// http://www.itl.nist.gov/div898/strd/nls/data/lanczos1.shtml\nvoid testNistLanczos1(void)\n{\n  const int n=6;\n  LevenbergMarquardtSpace::Status info;\n\n  VectorXd x(n);\n\n  /*\n   * First try\n   */\n  x<< 1.2, 0.3, 5.6, 5.5, 6.5, 7.6;\n  // do the computation\n  lanczos1_functor functor;\n  LevenbergMarquardt<lanczos1_functor> lm(functor);\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, LevenbergMarquardtSpace::RelativeErrorTooSmall);\n  VERIFY_IS_EQUAL(lm.nfev(), 79);\n  VERIFY_IS_EQUAL(lm.njev(), 72);\n  // check norm^2\n  VERIFY(lm.fvec().squaredNorm() <= 1.4307867721E-25);\n  // check x\n  VERIFY_IS_APPROX(x[0], 9.5100000027E-02);\n  VERIFY_IS_APPROX(x[1], 1.0000000001E+00);\n  VERIFY_IS_APPROX(x[2], 8.6070000013E-01);\n  VERIFY_IS_APPROX(x[3], 3.0000000002E+00);\n  VERIFY_IS_APPROX(x[4], 1.5575999998E+00);\n  VERIFY_IS_APPROX(x[5], 5.0000000001E+00);\n\n  /*\n   * Second try\n   */\n  x<< 0.5, 0.7, 3.6, 4.2, 4., 6.3;\n  // do the computation\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, LevenbergMarquardtSpace::RelativeErrorTooSmall);\n  VERIFY_IS_EQUAL(lm.nfev(), 9);\n  VERIFY_IS_EQUAL(lm.njev(), 8);\n  // check norm^2\n  VERIFY(lm.fvec().squaredNorm() <= 1.4307867721E-25);\n  // check x\n  VERIFY_IS_APPROX(x[0], 9.5100000027E-02);\n  VERIFY_IS_APPROX(x[1], 1.0000000001E+00);\n  VERIFY_IS_APPROX(x[2], 8.6070000013E-01);\n  VERIFY_IS_APPROX(x[3], 3.0000000002E+00);\n  VERIFY_IS_APPROX(x[4], 1.5575999998E+00);\n  VERIFY_IS_APPROX(x[5], 5.0000000001E+00);\n\n}\n\nstruct rat42_functor : DenseFunctor<double>\n{\n    rat42_functor(void) : DenseFunctor<double>(3,9) {}\n    static const double x[9];\n    static const double y[9];\n    int operator()(const VectorXd &b, VectorXd &fvec)\n    {\n        assert(b.size()==3);\n        assert(fvec.size()==9);\n        for(int i=0; i<9; i++) {\n            fvec[i] = b[0] / (1.+exp(b[1]-b[2]*x[i])) - y[i];\n        }\n        return 0;\n    }\n\n    int df(const VectorXd &b, MatrixXd &fjac)\n    {\n        assert(b.size()==3);\n        assert(fjac.rows()==9);\n        assert(fjac.cols()==3);\n        for(int i=0; i<9; i++) {\n            double e = exp(b[1]-b[2]*x[i]);\n            fjac(i,0) = 1./(1.+e);\n            fjac(i,1) = -b[0]*e/(1.+e)/(1.+e);\n            fjac(i,2) = +b[0]*e*x[i]/(1.+e)/(1.+e);\n        }\n        return 0;\n    }\n};\nconst double rat42_functor::x[9] = { 9.000E0, 14.000E0, 21.000E0, 28.000E0, 42.000E0, 57.000E0, 63.000E0, 70.000E0, 79.000E0 };\nconst double rat42_functor::y[9] = { 8.930E0 ,10.800E0 ,18.590E0 ,22.330E0 ,39.350E0 ,56.110E0 ,61.730E0 ,64.620E0 ,67.080E0 };\n\n// http://www.itl.nist.gov/div898/strd/nls/data/ratkowsky2.shtml\nvoid testNistRat42(void)\n{\n  const int n=3;\n  LevenbergMarquardtSpace::Status info;\n\n  VectorXd x(n);\n\n  /*\n   * First try\n   */\n  x<< 100., 1., 0.1;\n  // do the computation\n  rat42_functor functor;\n  LevenbergMarquardt<rat42_functor> lm(functor);\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, LevenbergMarquardtSpace::RelativeReductionTooSmall);\n  VERIFY_IS_EQUAL(lm.nfev(), 10);\n  VERIFY_IS_EQUAL(lm.njev(), 8);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 8.0565229338E+00);\n  // check x\n  VERIFY_IS_APPROX(x[0], 7.2462237576E+01);\n  VERIFY_IS_APPROX(x[1], 2.6180768402E+00);\n  VERIFY_IS_APPROX(x[2], 6.7359200066E-02);\n\n  /*\n   * Second try\n   */\n  x<< 75., 2.5, 0.07;\n  // do the computation\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, LevenbergMarquardtSpace::RelativeReductionTooSmall);\n  VERIFY_IS_EQUAL(lm.nfev(), 6);\n  VERIFY_IS_EQUAL(lm.njev(), 5);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 8.0565229338E+00);\n  // check x\n  VERIFY_IS_APPROX(x[0], 7.2462237576E+01);\n  VERIFY_IS_APPROX(x[1], 2.6180768402E+00);\n  VERIFY_IS_APPROX(x[2], 6.7359200066E-02);\n}\n\nstruct MGH10_functor : DenseFunctor<double>\n{\n    MGH10_functor(void) : DenseFunctor<double>(3,16) {}\n    static const double x[16];\n    static const double y[16];\n    int operator()(const VectorXd &b, VectorXd &fvec)\n    {\n        assert(b.size()==3);\n        assert(fvec.size()==16);\n        for(int i=0; i<16; i++)\n            fvec[i] =  b[0] * exp(b[1]/(x[i]+b[2])) - y[i];\n        return 0;\n    }\n    int df(const VectorXd &b, MatrixXd &fjac)\n    {\n        assert(b.size()==3);\n        assert(fjac.rows()==16);\n        assert(fjac.cols()==3);\n        for(int i=0; i<16; i++) {\n            double factor = 1./(x[i]+b[2]);\n            double e = exp(b[1]*factor);\n            fjac(i,0) = e;\n            fjac(i,1) = b[0]*factor*e;\n            fjac(i,2) = -b[1]*b[0]*factor*factor*e;\n        }\n        return 0;\n    }\n};\nconst double MGH10_functor::x[16] = { 5.000000E+01, 5.500000E+01, 6.000000E+01, 6.500000E+01, 7.000000E+01, 7.500000E+01, 8.000000E+01, 8.500000E+01, 9.000000E+01, 9.500000E+01, 1.000000E+02, 1.050000E+02, 1.100000E+02, 1.150000E+02, 1.200000E+02, 1.250000E+02 };\nconst double MGH10_functor::y[16] = { 3.478000E+04, 2.861000E+04, 2.365000E+04, 1.963000E+04, 1.637000E+04, 1.372000E+04, 1.154000E+04, 9.744000E+03, 8.261000E+03, 7.030000E+03, 6.005000E+03, 5.147000E+03, 4.427000E+03, 3.820000E+03, 3.307000E+03, 2.872000E+03 };\n\n// http://www.itl.nist.gov/div898/strd/nls/data/mgh10.shtml\nvoid testNistMGH10(void)\n{\n  const int n=3;\n  LevenbergMarquardtSpace::Status info;\n\n  VectorXd x(n);\n\n  /*\n   * First try\n   */\n  x<< 2., 400000., 25000.;\n  // do the computation\n  MGH10_functor functor;\n  LevenbergMarquardt<MGH10_functor> lm(functor);\n  info = lm.minimize(x);\n  ++g_test_level;\n  VERIFY_IS_EQUAL(info, LevenbergMarquardtSpace::RelativeReductionTooSmall);\n  --g_test_level;\n  // was: VERIFY_IS_EQUAL(info, 1);\n\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 8.7945855171E+01);\n  // check x\n  VERIFY_IS_APPROX(x[0], 5.6096364710E-03);\n  VERIFY_IS_APPROX(x[1], 6.1813463463E+03);\n  VERIFY_IS_APPROX(x[2], 3.4522363462E+02);\n  \n  // check return value\n\n  ++g_test_level;\n  VERIFY_IS_EQUAL(lm.nfev(), 284 );\n  VERIFY_IS_EQUAL(lm.njev(), 249 );\n  --g_test_level;\n  VERIFY(lm.nfev() < 284 * LM_EVAL_COUNT_TOL);\n  VERIFY(lm.njev() < 249 * LM_EVAL_COUNT_TOL);\n\n  /*\n   * Second try\n   */\n  x<< 0.02, 4000., 250.;\n  // do the computation\n  info = lm.minimize(x);\n  ++g_test_level;\n  VERIFY_IS_EQUAL(info, LevenbergMarquardtSpace::RelativeReductionTooSmall);\n  // was: VERIFY_IS_EQUAL(info, 1);\n  --g_test_level;\n\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 8.7945855171E+01);\n  // check x\n  VERIFY_IS_APPROX(x[0], 5.6096364710E-03);\n  VERIFY_IS_APPROX(x[1], 6.1813463463E+03);\n  VERIFY_IS_APPROX(x[2], 3.4522363462E+02);\n  \n  // check return value\n  ++g_test_level;\n  VERIFY_IS_EQUAL(lm.nfev(), 126);\n  VERIFY_IS_EQUAL(lm.njev(), 116);\n  --g_test_level;\n  VERIFY(lm.nfev() < 126 * LM_EVAL_COUNT_TOL);\n  VERIFY(lm.njev() < 116 * LM_EVAL_COUNT_TOL);\n}\n\n\nstruct BoxBOD_functor : DenseFunctor<double>\n{\n    BoxBOD_functor(void) : DenseFunctor<double>(2,6) {}\n    static const double x[6];\n    int operator()(const VectorXd &b, VectorXd &fvec)\n    {\n        static const double y[6] = { 109., 149., 149., 191., 213., 224. };\n        assert(b.size()==2);\n        assert(fvec.size()==6);\n        for(int i=0; i<6; i++)\n            fvec[i] =  b[0]*(1.-exp(-b[1]*x[i])) - y[i];\n        return 0;\n    }\n    int df(const VectorXd &b, MatrixXd &fjac)\n    {\n        assert(b.size()==2);\n        assert(fjac.rows()==6);\n        assert(fjac.cols()==2);\n        for(int i=0; i<6; i++) {\n            double e = exp(-b[1]*x[i]);\n            fjac(i,0) = 1.-e;\n            fjac(i,1) = b[0]*x[i]*e;\n        }\n        return 0;\n    }\n};\nconst double BoxBOD_functor::x[6] = { 1., 2., 3., 5., 7., 10. };\n\n// http://www.itl.nist.gov/div898/strd/nls/data/boxbod.shtml\nvoid testNistBoxBOD(void)\n{\n  const int n=2;\n  int info;\n\n  VectorXd x(n);\n\n  /*\n   * First try\n   */\n  x<< 1., 1.;\n  // do the computation\n  BoxBOD_functor functor;\n  LevenbergMarquardt<BoxBOD_functor> lm(functor);\n  lm.setFtol(1.E6*NumTraits<double>::epsilon());\n  lm.setXtol(1.E6*NumTraits<double>::epsilon());\n  lm.setFactor(10);\n  info = lm.minimize(x);\n\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 1.1680088766E+03);\n  // check x\n  VERIFY_IS_APPROX(x[0], 2.1380940889E+02);\n  VERIFY_IS_APPROX(x[1], 5.4723748542E-01);\n  \n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY(lm.nfev() < 31); // 31\n  VERIFY(lm.njev() < 25); // 25\n\n  /*\n   * Second try\n   */\n  x<< 100., 0.75;\n  // do the computation\n  lm.resetParameters();\n  lm.setFtol(NumTraits<double>::epsilon());\n  lm.setXtol( NumTraits<double>::epsilon());\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1); \n  ++g_test_level;\n  VERIFY_IS_EQUAL(lm.nfev(), 16 );\n  VERIFY_IS_EQUAL(lm.njev(), 15 );\n  --g_test_level;\n  VERIFY(lm.nfev() < 16 * LM_EVAL_COUNT_TOL);\n  VERIFY(lm.njev() < 15 * LM_EVAL_COUNT_TOL);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 1.1680088766E+03);\n  // check x\n  VERIFY_IS_APPROX(x[0], 2.1380940889E+02);\n  VERIFY_IS_APPROX(x[1], 5.4723748542E-01);\n}\n\nstruct MGH17_functor : DenseFunctor<double>\n{\n    MGH17_functor(void) : DenseFunctor<double>(5,33) {}\n    static const double x[33];\n    static const double y[33];\n    int operator()(const VectorXd &b, VectorXd &fvec)\n    {\n        assert(b.size()==5);\n        assert(fvec.size()==33);\n        for(int i=0; i<33; i++)\n            fvec[i] =  b[0] + b[1]*exp(-b[3]*x[i]) +  b[2]*exp(-b[4]*x[i]) - y[i];\n        return 0;\n    }\n    int df(const VectorXd &b, MatrixXd &fjac)\n    {\n        assert(b.size()==5);\n        assert(fjac.rows()==33);\n        assert(fjac.cols()==5);\n        for(int i=0; i<33; i++) {\n            fjac(i,0) = 1.;\n            fjac(i,1) = exp(-b[3]*x[i]);\n            fjac(i,2) = exp(-b[4]*x[i]);\n            fjac(i,3) = -x[i]*b[1]*exp(-b[3]*x[i]);\n            fjac(i,4) = -x[i]*b[2]*exp(-b[4]*x[i]);\n        }\n        return 0;\n    }\n};\nconst double MGH17_functor::x[33] = { 0.000000E+00, 1.000000E+01, 2.000000E+01, 3.000000E+01, 4.000000E+01, 5.000000E+01, 6.000000E+01, 7.000000E+01, 8.000000E+01, 9.000000E+01, 1.000000E+02, 1.100000E+02, 1.200000E+02, 1.300000E+02, 1.400000E+02, 1.500000E+02, 1.600000E+02, 1.700000E+02, 1.800000E+02, 1.900000E+02, 2.000000E+02, 2.100000E+02, 2.200000E+02, 2.300000E+02, 2.400000E+02, 2.500000E+02, 2.600000E+02, 2.700000E+02, 2.800000E+02, 2.900000E+02, 3.000000E+02, 3.100000E+02, 3.200000E+02 };\nconst double MGH17_functor::y[33] = { 8.440000E-01, 9.080000E-01, 9.320000E-01, 9.360000E-01, 9.250000E-01, 9.080000E-01, 8.810000E-01, 8.500000E-01, 8.180000E-01, 7.840000E-01, 7.510000E-01, 7.180000E-01, 6.850000E-01, 6.580000E-01, 6.280000E-01, 6.030000E-01, 5.800000E-01, 5.580000E-01, 5.380000E-01, 5.220000E-01, 5.060000E-01, 4.900000E-01, 4.780000E-01, 4.670000E-01, 4.570000E-01, 4.480000E-01, 4.380000E-01, 4.310000E-01, 4.240000E-01, 4.200000E-01, 4.140000E-01, 4.110000E-01, 4.060000E-01 };\n\n// http://www.itl.nist.gov/div898/strd/nls/data/mgh17.shtml\nvoid testNistMGH17(void)\n{\n  const int n=5;\n  int info;\n\n  VectorXd x(n);\n\n  /*\n   * First try\n   */\n  x<< 50., 150., -100., 1., 2.;\n  // do the computation\n  MGH17_functor functor;\n  LevenbergMarquardt<MGH17_functor> lm(functor);\n  lm.setFtol(NumTraits<double>::epsilon());\n  lm.setXtol(NumTraits<double>::epsilon());\n  lm.setMaxfev(1000);\n  info = lm.minimize(x);\n\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 5.4648946975E-05);\n  // check x\n  VERIFY_IS_APPROX(x[0], 3.7541005211E-01);\n  VERIFY_IS_APPROX(x[1], 1.9358469127E+00);\n  VERIFY_IS_APPROX(x[2], -1.4646871366E+00);\n  VERIFY_IS_APPROX(x[3], 1.2867534640E-02);\n  VERIFY_IS_APPROX(x[4], 2.2122699662E-02);\n  \n    // check return value\n//   VERIFY_IS_EQUAL(info, 2);  //FIXME Use (lm.info() == Success)\n  VERIFY(lm.nfev() < 700 ); // 602\n  VERIFY(lm.njev() < 600 ); // 545\n\n  /*\n   * Second try\n   */\n  x<< 0.5  ,1.5  ,-1   ,0.01 ,0.02;\n  // do the computation\n  lm.resetParameters();\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev(), 18);\n  VERIFY_IS_EQUAL(lm.njev(), 15);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 5.4648946975E-05);\n  // check x\n  VERIFY_IS_APPROX(x[0], 3.7541005211E-01);\n  VERIFY_IS_APPROX(x[1], 1.9358469127E+00);\n  VERIFY_IS_APPROX(x[2], -1.4646871366E+00);\n  VERIFY_IS_APPROX(x[3], 1.2867534640E-02);\n  VERIFY_IS_APPROX(x[4], 2.2122699662E-02);\n}\n\nstruct MGH09_functor : DenseFunctor<double>\n{\n    MGH09_functor(void) : DenseFunctor<double>(4,11) {}\n    static const double _x[11];\n    static const double y[11];\n    int operator()(const VectorXd &b, VectorXd &fvec)\n    {\n        assert(b.size()==4);\n        assert(fvec.size()==11);\n        for(int i=0; i<11; i++) {\n            double x = _x[i], xx=x*x;\n            fvec[i] = b[0]*(xx+x*b[1])/(xx+x*b[2]+b[3]) - y[i];\n        }\n        return 0;\n    }\n    int df(const VectorXd &b, MatrixXd &fjac)\n    {\n        assert(b.size()==4);\n        assert(fjac.rows()==11);\n        assert(fjac.cols()==4);\n        for(int i=0; i<11; i++) {\n            double x = _x[i], xx=x*x;\n            double factor = 1./(xx+x*b[2]+b[3]);\n            fjac(i,0) = (xx+x*b[1]) * factor;\n            fjac(i,1) = b[0]*x* factor;\n            fjac(i,2) = - b[0]*(xx+x*b[1]) * x * factor * factor;\n            fjac(i,3) = - b[0]*(xx+x*b[1]) * factor * factor;\n        }\n        return 0;\n    }\n};\nconst double MGH09_functor::_x[11] = { 4., 2., 1., 5.E-1 , 2.5E-01, 1.670000E-01, 1.250000E-01,  1.E-01, 8.330000E-02, 7.140000E-02, 6.250000E-02 };\nconst double MGH09_functor::y[11] = { 1.957000E-01, 1.947000E-01, 1.735000E-01, 1.600000E-01, 8.440000E-02, 6.270000E-02, 4.560000E-02, 3.420000E-02, 3.230000E-02, 2.350000E-02, 2.460000E-02 };\n\n// http://www.itl.nist.gov/div898/strd/nls/data/mgh09.shtml\nvoid testNistMGH09(void)\n{\n  const int n=4;\n  int info;\n\n  VectorXd x(n);\n\n  /*\n   * First try\n   */\n  x<< 25., 39, 41.5, 39.;\n  // do the computation\n  MGH09_functor functor;\n  LevenbergMarquardt<MGH09_functor> lm(functor);\n  lm.setMaxfev(1000);\n  info = lm.minimize(x);\n\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 3.0750560385E-04);\n  // check x\n  VERIFY_IS_APPROX(x[0], 0.1928077089); // should be 1.9280693458E-01\n  VERIFY_IS_APPROX(x[1], 0.19126423573); // should be 1.9128232873E-01\n  VERIFY_IS_APPROX(x[2], 0.12305309914); // should be 1.2305650693E-01\n  VERIFY_IS_APPROX(x[3], 0.13605395375); // should be 1.3606233068E-01\n  // check return value\n  VERIFY_IS_EQUAL(info, 1); \n  VERIFY(lm.nfev() < 510 ); // 490\n  VERIFY(lm.njev() < 400 ); // 376\n\n  /*\n   * Second try\n   */\n  x<< 0.25, 0.39, 0.415, 0.39;\n  // do the computation\n  lm.resetParameters();\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev(), 18);\n  VERIFY_IS_EQUAL(lm.njev(), 16);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 3.0750560385E-04);\n  // check x\n  VERIFY_IS_APPROX(x[0], 0.19280781); // should be 1.9280693458E-01\n  VERIFY_IS_APPROX(x[1], 0.19126265); // should be 1.9128232873E-01\n  VERIFY_IS_APPROX(x[2], 0.12305280); // should be 1.2305650693E-01\n  VERIFY_IS_APPROX(x[3], 0.13605322); // should be 1.3606233068E-01\n}\n\n\n\nstruct Bennett5_functor : DenseFunctor<double>\n{\n    Bennett5_functor(void) : DenseFunctor<double>(3,154) {}\n    static const double x[154];\n    static const double y[154];\n    int operator()(const VectorXd &b, VectorXd &fvec)\n    {\n        assert(b.size()==3);\n        assert(fvec.size()==154);\n        for(int i=0; i<154; i++)\n            fvec[i] = b[0]* pow(b[1]+x[i],-1./b[2]) - y[i];\n        return 0;\n    }\n    int df(const VectorXd &b, MatrixXd &fjac)\n    {\n        assert(b.size()==3);\n        assert(fjac.rows()==154);\n        assert(fjac.cols()==3);\n        for(int i=0; i<154; i++) {\n            double e = pow(b[1]+x[i],-1./b[2]);\n            fjac(i,0) = e;\n            fjac(i,1) = - b[0]*e/b[2]/(b[1]+x[i]);\n            fjac(i,2) = b[0]*e*log(b[1]+x[i])/b[2]/b[2];\n        }\n        return 0;\n    }\n};\nconst double Bennett5_functor::x[154] = { 7.447168E0, 8.102586E0, 8.452547E0, 8.711278E0, 8.916774E0, 9.087155E0, 9.232590E0, 9.359535E0, 9.472166E0, 9.573384E0, 9.665293E0, 9.749461E0, 9.827092E0, 9.899128E0, 9.966321E0, 10.029280E0, 10.088510E0, 10.144430E0, 10.197380E0, 10.247670E0, 10.295560E0, 10.341250E0, 10.384950E0, 10.426820E0, 10.467000E0, 10.505640E0, 10.542830E0, 10.578690E0, 10.613310E0, 10.646780E0, 10.679150E0, 10.710520E0, 10.740920E0, 10.770440E0, 10.799100E0, 10.826970E0, 10.854080E0, 10.880470E0, 10.906190E0, 10.931260E0, 10.955720E0, 10.979590E0, 11.002910E0, 11.025700E0, 11.047980E0, 11.069770E0, 11.091100E0, 11.111980E0, 11.132440E0, 11.152480E0, 11.172130E0, 11.191410E0, 11.210310E0, 11.228870E0, 11.247090E0, 11.264980E0, 11.282560E0, 11.299840E0, 11.316820E0, 11.333520E0, 11.349940E0, 11.366100E0, 11.382000E0, 11.397660E0, 11.413070E0, 11.428240E0, 11.443200E0, 11.457930E0, 11.472440E0, 11.486750E0, 11.500860E0, 11.514770E0, 11.528490E0, 11.542020E0, 11.555380E0, 11.568550E0,\n11.581560E0, 11.594420E0, 11.607121E0, 11.619640E0, 11.632000E0, 11.644210E0, 11.656280E0, 11.668200E0, 11.679980E0, 11.691620E0, 11.703130E0, 11.714510E0, 11.725760E0, 11.736880E0, 11.747890E0, 11.758780E0, 11.769550E0, 11.780200E0, 11.790730E0, 11.801160E0, 11.811480E0, 11.821700E0, 11.831810E0, 11.841820E0, 11.851730E0, 11.861550E0, 11.871270E0, 11.880890E0, 11.890420E0, 11.899870E0, 11.909220E0, 11.918490E0, 11.927680E0, 11.936780E0, 11.945790E0, 11.954730E0, 11.963590E0, 11.972370E0, 11.981070E0, 11.989700E0, 11.998260E0, 12.006740E0, 12.015150E0, 12.023490E0, 12.031760E0, 12.039970E0, 12.048100E0, 12.056170E0, 12.064180E0, 12.072120E0, 12.080010E0, 12.087820E0, 12.095580E0, 12.103280E0, 12.110920E0, 12.118500E0, 12.126030E0, 12.133500E0, 12.140910E0, 12.148270E0, 12.155570E0, 12.162830E0, 12.170030E0, 12.177170E0, 12.184270E0, 12.191320E0, 12.198320E0, 12.205270E0, 12.212170E0, 12.219030E0, 12.225840E0, 12.232600E0, 12.239320E0, 12.245990E0, 12.252620E0, 12.259200E0, 12.265750E0, 12.272240E0 };\nconst double Bennett5_functor::y[154] = { -34.834702E0 ,-34.393200E0 ,-34.152901E0 ,-33.979099E0 ,-33.845901E0 ,-33.732899E0 ,-33.640301E0 ,-33.559200E0 ,-33.486801E0 ,-33.423100E0 ,-33.365101E0 ,-33.313000E0 ,-33.260899E0 ,-33.217400E0 ,-33.176899E0 ,-33.139198E0 ,-33.101601E0 ,-33.066799E0 ,-33.035000E0 ,-33.003101E0 ,-32.971298E0 ,-32.942299E0 ,-32.916302E0 ,-32.890202E0 ,-32.864101E0 ,-32.841000E0 ,-32.817799E0 ,-32.797501E0 ,-32.774300E0 ,-32.757000E0 ,-32.733799E0 ,-32.716400E0 ,-32.699100E0 ,-32.678799E0 ,-32.661400E0 ,-32.644001E0 ,-32.626701E0 ,-32.612202E0 ,-32.597698E0 ,-32.583199E0 ,-32.568699E0 ,-32.554298E0 ,-32.539799E0 ,-32.525299E0 ,-32.510799E0 ,-32.499199E0 ,-32.487598E0 ,-32.473202E0 ,-32.461601E0 ,-32.435501E0 ,-32.435501E0 ,-32.426800E0 ,-32.412300E0 ,-32.400799E0 ,-32.392101E0 ,-32.380501E0 ,-32.366001E0 ,-32.357300E0 ,-32.348598E0 ,-32.339901E0 ,-32.328400E0 ,-32.319698E0 ,-32.311001E0 ,-32.299400E0 ,-32.290699E0 ,-32.282001E0 ,-32.273300E0 ,-32.264599E0 ,-32.256001E0 ,-32.247299E0\n,-32.238602E0 ,-32.229900E0 ,-32.224098E0 ,-32.215401E0 ,-32.203800E0 ,-32.198002E0 ,-32.189400E0 ,-32.183601E0 ,-32.174900E0 ,-32.169102E0 ,-32.163300E0 ,-32.154598E0 ,-32.145901E0 ,-32.140099E0 ,-32.131401E0 ,-32.125599E0 ,-32.119801E0 ,-32.111198E0 ,-32.105400E0 ,-32.096699E0 ,-32.090900E0 ,-32.088001E0 ,-32.079300E0 ,-32.073502E0 ,-32.067699E0 ,-32.061901E0 ,-32.056099E0 ,-32.050301E0 ,-32.044498E0 ,-32.038799E0 ,-32.033001E0 ,-32.027199E0 ,-32.024300E0 ,-32.018501E0 ,-32.012699E0 ,-32.004002E0 ,-32.001099E0 ,-31.995300E0 ,-31.989500E0 ,-31.983700E0 ,-31.977900E0 ,-31.972099E0 ,-31.969299E0 ,-31.963501E0 ,-31.957701E0 ,-31.951900E0 ,-31.946100E0 ,-31.940300E0 ,-31.937401E0 ,-31.931601E0 ,-31.925800E0 ,-31.922899E0 ,-31.917101E0 ,-31.911301E0 ,-31.908400E0 ,-31.902599E0 ,-31.896900E0 ,-31.893999E0 ,-31.888201E0 ,-31.885300E0 ,-31.882401E0 ,-31.876600E0 ,-31.873699E0 ,-31.867901E0 ,-31.862101E0 ,-31.859200E0 ,-31.856300E0 ,-31.850500E0 ,-31.844700E0 ,-31.841801E0 ,-31.838900E0 ,-31.833099E0 ,-31.830200E0 ,\n-31.827299E0 ,-31.821600E0 ,-31.818701E0 ,-31.812901E0 ,-31.809999E0 ,-31.807100E0 ,-31.801300E0 ,-31.798401E0 ,-31.795500E0 ,-31.789700E0 ,-31.786800E0 };\n\n// http://www.itl.nist.gov/div898/strd/nls/data/bennett5.shtml\nvoid testNistBennett5(void)\n{\n  const int  n=3;\n  int info;\n\n  VectorXd x(n);\n\n  /*\n   * First try\n   */\n  x<< -2000., 50., 0.8;\n  // do the computation\n  Bennett5_functor functor;\n  LevenbergMarquardt<Bennett5_functor> lm(functor);\n  lm.setMaxfev(1000);\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev(), 758);\n  VERIFY_IS_EQUAL(lm.njev(), 744);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 5.2404744073E-04);\n  // check x\n  VERIFY_IS_APPROX(x[0], -2.5235058043E+03);\n  VERIFY_IS_APPROX(x[1], 4.6736564644E+01);\n  VERIFY_IS_APPROX(x[2], 9.3218483193E-01);\n  /*\n   * Second try\n   */\n  x<< -1500., 45., 0.85;\n  // do the computation\n  lm.resetParameters();\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev(), 203);\n  VERIFY_IS_EQUAL(lm.njev(), 192);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 5.2404744073E-04);\n  // check x\n  VERIFY_IS_APPROX(x[0], -2523.3007865); // should be -2.5235058043E+03\n  VERIFY_IS_APPROX(x[1], 46.735705771); // should be 4.6736564644E+01);\n  VERIFY_IS_APPROX(x[2], 0.93219881891); // should be 9.3218483193E-01);\n}\n\nstruct thurber_functor : DenseFunctor<double>\n{\n    thurber_functor(void) : DenseFunctor<double>(7,37) {}\n    static const double _x[37];\n    static const double _y[37];\n    int operator()(const VectorXd &b, VectorXd &fvec)\n    {\n        //        int called=0; printf(\"call hahn1_functor with  iflag=%d, called=%d\\n\", iflag, called); if (iflag==1) called++;\n        assert(b.size()==7);\n        assert(fvec.size()==37);\n        for(int i=0; i<37; i++) {\n            double x=_x[i], xx=x*x, xxx=xx*x;\n            fvec[i] = (b[0]+b[1]*x+b[2]*xx+b[3]*xxx) / (1.+b[4]*x+b[5]*xx+b[6]*xxx) - _y[i];\n        }\n        return 0;\n    }\n    int df(const VectorXd &b, MatrixXd &fjac)\n    {\n        assert(b.size()==7);\n        assert(fjac.rows()==37);\n        assert(fjac.cols()==7);\n        for(int i=0; i<37; i++) {\n            double x=_x[i], xx=x*x, xxx=xx*x;\n            double fact = 1./(1.+b[4]*x+b[5]*xx+b[6]*xxx);\n            fjac(i,0) = 1.*fact;\n            fjac(i,1) = x*fact;\n            fjac(i,2) = xx*fact;\n            fjac(i,3) = xxx*fact;\n            fact = - (b[0]+b[1]*x+b[2]*xx+b[3]*xxx) * fact * fact;\n            fjac(i,4) = x*fact;\n            fjac(i,5) = xx*fact;\n            fjac(i,6) = xxx*fact;\n        }\n        return 0;\n    }\n};\nconst double thurber_functor::_x[37] = { -3.067E0, -2.981E0, -2.921E0, -2.912E0, -2.840E0, -2.797E0, -2.702E0, -2.699E0, -2.633E0, -2.481E0, -2.363E0, -2.322E0, -1.501E0, -1.460E0, -1.274E0, -1.212E0, -1.100E0, -1.046E0, -0.915E0, -0.714E0, -0.566E0, -0.545E0, -0.400E0, -0.309E0, -0.109E0, -0.103E0, 0.010E0, 0.119E0, 0.377E0, 0.790E0, 0.963E0, 1.006E0, 1.115E0, 1.572E0, 1.841E0, 2.047E0, 2.200E0 };\nconst double thurber_functor::_y[37] = { 80.574E0, 84.248E0, 87.264E0, 87.195E0, 89.076E0, 89.608E0, 89.868E0, 90.101E0, 92.405E0, 95.854E0, 100.696E0, 101.060E0, 401.672E0, 390.724E0, 567.534E0, 635.316E0, 733.054E0, 759.087E0, 894.206E0, 990.785E0, 1090.109E0, 1080.914E0, 1122.643E0, 1178.351E0, 1260.531E0, 1273.514E0, 1288.339E0, 1327.543E0, 1353.863E0, 1414.509E0, 1425.208E0, 1421.384E0, 1442.962E0, 1464.350E0, 1468.705E0, 1447.894E0, 1457.628E0};\n\n// http://www.itl.nist.gov/div898/strd/nls/data/thurber.shtml\nvoid testNistThurber(void)\n{\n  const int n=7;\n  int info;\n\n  VectorXd x(n);\n\n  /*\n   * First try\n   */\n  x<< 1000 ,1000 ,400 ,40 ,0.7,0.3,0.0 ;\n  // do the computation\n  thurber_functor functor;\n  LevenbergMarquardt<thurber_functor> lm(functor);\n  lm.setFtol(1.E4*NumTraits<double>::epsilon());\n  lm.setXtol(1.E4*NumTraits<double>::epsilon());\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev(), 39);\n  VERIFY_IS_EQUAL(lm.njev(), 36);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 5.6427082397E+03);\n  // check x\n  VERIFY_IS_APPROX(x[0], 1.2881396800E+03);\n  VERIFY_IS_APPROX(x[1], 1.4910792535E+03);\n  VERIFY_IS_APPROX(x[2], 5.8323836877E+02);\n  VERIFY_IS_APPROX(x[3], 7.5416644291E+01);\n  VERIFY_IS_APPROX(x[4], 9.6629502864E-01);\n  VERIFY_IS_APPROX(x[5], 3.9797285797E-01);\n  VERIFY_IS_APPROX(x[6], 4.9727297349E-02);\n\n  /*\n   * Second try\n   */\n  x<< 1300 ,1500 ,500  ,75   ,1    ,0.4  ,0.05  ;\n  // do the computation\n  lm.resetParameters();\n  lm.setFtol(1.E4*NumTraits<double>::epsilon());\n  lm.setXtol(1.E4*NumTraits<double>::epsilon());\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev(), 29);\n  VERIFY_IS_EQUAL(lm.njev(), 28);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 5.6427082397E+03);\n  // check x\n  VERIFY_IS_APPROX(x[0], 1.2881396800E+03);\n  VERIFY_IS_APPROX(x[1], 1.4910792535E+03);\n  VERIFY_IS_APPROX(x[2], 5.8323836877E+02);\n  VERIFY_IS_APPROX(x[3], 7.5416644291E+01);\n  VERIFY_IS_APPROX(x[4], 9.6629502864E-01);\n  VERIFY_IS_APPROX(x[5], 3.9797285797E-01);\n  VERIFY_IS_APPROX(x[6], 4.9727297349E-02);\n}\n\nstruct rat43_functor : DenseFunctor<double>\n{\n    rat43_functor(void) : DenseFunctor<double>(4,15) {}\n    static const double x[15];\n    static const double y[15];\n    int operator()(const VectorXd &b, VectorXd &fvec)\n    {\n        assert(b.size()==4);\n        assert(fvec.size()==15);\n        for(int i=0; i<15; i++)\n            fvec[i] = b[0] * pow(1.+exp(b[1]-b[2]*x[i]),-1./b[3]) - y[i];\n        return 0;\n    }\n    int df(const VectorXd &b, MatrixXd &fjac)\n    {\n        assert(b.size()==4);\n        assert(fjac.rows()==15);\n        assert(fjac.cols()==4);\n        for(int i=0; i<15; i++) {\n            double e = exp(b[1]-b[2]*x[i]);\n            double power = -1./b[3];\n            fjac(i,0) = pow(1.+e, power);\n            fjac(i,1) = power*b[0]*e*pow(1.+e, power-1.);\n            fjac(i,2) = -power*b[0]*e*x[i]*pow(1.+e, power-1.);\n            fjac(i,3) = b[0]*power*power*log(1.+e)*pow(1.+e, power);\n        }\n        return 0;\n    }\n};\nconst double rat43_functor::x[15] = { 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14., 15. };\nconst double rat43_functor::y[15] = { 16.08, 33.83, 65.80, 97.20, 191.55, 326.20, 386.87, 520.53, 590.03, 651.92, 724.93, 699.56, 689.96, 637.56, 717.41 };\n\n// http://www.itl.nist.gov/div898/strd/nls/data/ratkowsky3.shtml\nvoid testNistRat43(void)\n{\n  const int n=4;\n  int info;\n\n  VectorXd x(n);\n\n  /*\n   * First try\n   */\n  x<< 100., 10., 1., 1.;\n  // do the computation\n  rat43_functor functor;\n  LevenbergMarquardt<rat43_functor> lm(functor);\n  lm.setFtol(1.E6*NumTraits<double>::epsilon());\n  lm.setXtol(1.E6*NumTraits<double>::epsilon());\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev(), 27);\n  VERIFY_IS_EQUAL(lm.njev(), 20);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 8.7864049080E+03);\n  // check x\n  VERIFY_IS_APPROX(x[0], 6.9964151270E+02);\n  VERIFY_IS_APPROX(x[1], 5.2771253025E+00);\n  VERIFY_IS_APPROX(x[2], 7.5962938329E-01);\n  VERIFY_IS_APPROX(x[3], 1.2792483859E+00);\n\n  /*\n   * Second try\n   */\n  x<< 700., 5., 0.75, 1.3;\n  // do the computation\n  lm.resetParameters();\n  lm.setFtol(1.E5*NumTraits<double>::epsilon());\n  lm.setXtol(1.E5*NumTraits<double>::epsilon());\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev(), 9);\n  VERIFY_IS_EQUAL(lm.njev(), 8);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 8.7864049080E+03);\n  // check x\n  VERIFY_IS_APPROX(x[0], 6.9964151270E+02);\n  VERIFY_IS_APPROX(x[1], 5.2771253025E+00);\n  VERIFY_IS_APPROX(x[2], 7.5962938329E-01);\n  VERIFY_IS_APPROX(x[3], 1.2792483859E+00);\n}\n\n\n\nstruct eckerle4_functor : DenseFunctor<double>\n{\n    eckerle4_functor(void) : DenseFunctor<double>(3,35) {}\n    static const double x[35];\n    static const double y[35];\n    int operator()(const VectorXd &b, VectorXd &fvec)\n    {\n        assert(b.size()==3);\n        assert(fvec.size()==35);\n        for(int i=0; i<35; i++)\n            fvec[i] = b[0]/b[1] * exp(-0.5*(x[i]-b[2])*(x[i]-b[2])/(b[1]*b[1])) - y[i];\n        return 0;\n    }\n    int df(const VectorXd &b, MatrixXd &fjac)\n    {\n        assert(b.size()==3);\n        assert(fjac.rows()==35);\n        assert(fjac.cols()==3);\n        for(int i=0; i<35; i++) {\n            double b12 = b[1]*b[1];\n            double e = exp(-0.5*(x[i]-b[2])*(x[i]-b[2])/b12);\n            fjac(i,0) = e / b[1];\n            fjac(i,1) = ((x[i]-b[2])*(x[i]-b[2])/b12-1.) * b[0]*e/b12;\n            fjac(i,2) = (x[i]-b[2])*e*b[0]/b[1]/b12;\n        }\n        return 0;\n    }\n};\nconst double eckerle4_functor::x[35] = { 400.0, 405.0, 410.0, 415.0, 420.0, 425.0, 430.0, 435.0, 436.5, 438.0, 439.5, 441.0, 442.5, 444.0, 445.5, 447.0, 448.5, 450.0, 451.5, 453.0, 454.5, 456.0, 457.5, 459.0, 460.5, 462.0, 463.5, 465.0, 470.0, 475.0, 480.0, 485.0, 490.0, 495.0, 500.0};\nconst double eckerle4_functor::y[35] = { 0.0001575, 0.0001699, 0.0002350, 0.0003102, 0.0004917, 0.0008710, 0.0017418, 0.0046400, 0.0065895, 0.0097302, 0.0149002, 0.0237310, 0.0401683, 0.0712559, 0.1264458, 0.2073413, 0.2902366, 0.3445623, 0.3698049, 0.3668534, 0.3106727, 0.2078154, 0.1164354, 0.0616764, 0.0337200, 0.0194023, 0.0117831, 0.0074357, 0.0022732, 0.0008800, 0.0004579, 0.0002345, 0.0001586, 0.0001143, 0.0000710 };\n\n// http://www.itl.nist.gov/div898/strd/nls/data/eckerle4.shtml\nvoid testNistEckerle4(void)\n{\n  const int n=3;\n  int info;\n\n  VectorXd x(n);\n\n  /*\n   * First try\n   */\n  x<< 1., 10., 500.;\n  // do the computation\n  eckerle4_functor functor;\n  LevenbergMarquardt<eckerle4_functor> lm(functor);\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev(), 18);\n  VERIFY_IS_EQUAL(lm.njev(), 15);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 1.4635887487E-03);\n  // check x\n  VERIFY_IS_APPROX(x[0], 1.5543827178);\n  VERIFY_IS_APPROX(x[1], 4.0888321754);\n  VERIFY_IS_APPROX(x[2], 4.5154121844E+02);\n\n  /*\n   * Second try\n   */\n  x<< 1.5, 5., 450.;\n  // do the computation\n  info = lm.minimize(x);\n\n  // check return value\n  VERIFY_IS_EQUAL(info, 1);\n  VERIFY_IS_EQUAL(lm.nfev(), 7);\n  VERIFY_IS_EQUAL(lm.njev(), 6);\n  // check norm^2\n  VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 1.4635887487E-03);\n  // check x\n  VERIFY_IS_APPROX(x[0], 1.5543827178);\n  VERIFY_IS_APPROX(x[1], 4.0888321754);\n  VERIFY_IS_APPROX(x[2], 4.5154121844E+02);\n}\n\nvoid test_levenberg_marquardt()\n{\n    // Tests using the examples provided by (c)minpack\n    CALL_SUBTEST(testLmder1());\n    CALL_SUBTEST(testLmder());\n    CALL_SUBTEST(testLmdif1());\n//     CALL_SUBTEST(testLmstr1());\n//     CALL_SUBTEST(testLmstr());\n    CALL_SUBTEST(testLmdif());\n\n    // NIST tests, level of difficulty = \"Lower\"\n    CALL_SUBTEST(testNistMisra1a());\n    CALL_SUBTEST(testNistChwirut2());\n\n    // NIST tests, level of difficulty = \"Average\"\n    CALL_SUBTEST(testNistHahn1());\n    CALL_SUBTEST(testNistMisra1d());\n    CALL_SUBTEST(testNistMGH17());\n    CALL_SUBTEST(testNistLanczos1());\n\n//     // NIST tests, level of difficulty = \"Higher\"\n    CALL_SUBTEST(testNistRat42());\n    CALL_SUBTEST(testNistMGH10());\n    CALL_SUBTEST(testNistBoxBOD());\n//     CALL_SUBTEST(testNistMGH09());\n    CALL_SUBTEST(testNistBennett5());\n    CALL_SUBTEST(testNistThurber());\n    CALL_SUBTEST(testNistRat43());\n    CALL_SUBTEST(testNistEckerle4());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/matrix_exponential.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009 Jitse Niesen <jitse@maths.leeds.ac.uk>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"matrix_functions.h\"\n\ndouble binom(int n, int k)\n{\n  double res = 1;\n  for (int i=0; i<k; i++)\n    res = res * (n-k+i+1) / (i+1);\n  return res;\n}\n\ntemplate <typename T>\nT expfn(T x, int)\n{\n  return std::exp(x);\n}\n\ntemplate <typename T>\nvoid test2dRotation(double tol)\n{\n  Matrix<T,2,2> A, B, C;\n  T angle;\n\n  A << 0, 1, -1, 0;\n  for (int i=0; i<=20; i++)\n  {\n    angle = static_cast<T>(pow(10, i / 5. - 2));\n    B << std::cos(angle), std::sin(angle), -std::sin(angle), std::cos(angle);\n\n    C = (angle*A).matrixFunction(expfn);\n    std::cout << \"test2dRotation: i = \" << i << \"   error funm = \" << relerr(C, B);\n    VERIFY(C.isApprox(B, static_cast<T>(tol)));\n\n    C = (angle*A).exp();\n    std::cout << \"   error expm = \" << relerr(C, B) << \"\\n\";\n    VERIFY(C.isApprox(B, static_cast<T>(tol)));\n  }\n}\n\ntemplate <typename T>\nvoid test2dHyperbolicRotation(double tol)\n{\n  Matrix<std::complex<T>,2,2> A, B, C;\n  std::complex<T> imagUnit(0,1);\n  T angle, ch, sh;\n\n  for (int i=0; i<=20; i++)\n  {\n    angle = static_cast<T>((i-10) / 2.0);\n    ch = std::cosh(angle);\n    sh = std::sinh(angle);\n    A << 0, angle*imagUnit, -angle*imagUnit, 0;\n    B << ch, sh*imagUnit, -sh*imagUnit, ch;\n\n    C = A.matrixFunction(expfn);\n    std::cout << \"test2dHyperbolicRotation: i = \" << i << \"   error funm = \" << relerr(C, B);\n    VERIFY(C.isApprox(B, static_cast<T>(tol)));\n\n    C = A.exp();\n    std::cout << \"   error expm = \" << relerr(C, B) << \"\\n\";\n    VERIFY(C.isApprox(B, static_cast<T>(tol)));\n  }\n}\n\ntemplate <typename T>\nvoid testPascal(double tol)\n{\n  for (int size=1; size<20; size++)\n  {\n    Matrix<T,Dynamic,Dynamic> A(size,size), B(size,size), C(size,size);\n    A.setZero();\n    for (int i=0; i<size-1; i++)\n      A(i+1,i) = static_cast<T>(i+1);\n    B.setZero();\n    for (int i=0; i<size; i++)\n      for (int j=0; j<=i; j++)\n    B(i,j) = static_cast<T>(binom(i,j));\n\n    C = A.matrixFunction(expfn);\n    std::cout << \"testPascal: size = \" << size << \"   error funm = \" << relerr(C, B);\n    VERIFY(C.isApprox(B, static_cast<T>(tol)));\n\n    C = A.exp();\n    std::cout << \"   error expm = \" << relerr(C, B) << \"\\n\";\n    VERIFY(C.isApprox(B, static_cast<T>(tol)));\n  }\n}\n\ntemplate<typename MatrixType>\nvoid randomTest(const MatrixType& m, double tol)\n{\n  /* this test covers the following files:\n     Inverse.h\n  */\n  typename MatrixType::Index rows = m.rows();\n  typename MatrixType::Index cols = m.cols();\n  MatrixType m1(rows, cols), m2(rows, cols), identity = MatrixType::Identity(rows, cols);\n\n  typedef typename NumTraits<typename internal::traits<MatrixType>::Scalar>::Real RealScalar;\n\n  for(int i = 0; i < g_repeat; i++) {\n    m1 = MatrixType::Random(rows, cols);\n\n    m2 = m1.matrixFunction(expfn) * (-m1).matrixFunction(expfn);\n    std::cout << \"randomTest: error funm = \" << relerr(identity, m2);\n    VERIFY(identity.isApprox(m2, static_cast<RealScalar>(tol)));\n\n    m2 = m1.exp() * (-m1).exp();\n    std::cout << \"   error expm = \" << relerr(identity, m2) << \"\\n\";\n    VERIFY(identity.isApprox(m2, static_cast<RealScalar>(tol)));\n  }\n}\n\nvoid test_matrix_exponential()\n{\n  CALL_SUBTEST_2(test2dRotation<double>(1e-13));\n  CALL_SUBTEST_1(test2dRotation<float>(2e-5));  // was 1e-5, relaxed for clang 2.8 / linux / x86-64\n  CALL_SUBTEST_8(test2dRotation<long double>(1e-13)); \n  CALL_SUBTEST_2(test2dHyperbolicRotation<double>(1e-14));\n  CALL_SUBTEST_1(test2dHyperbolicRotation<float>(1e-5));\n  CALL_SUBTEST_8(test2dHyperbolicRotation<long double>(1e-14));\n  CALL_SUBTEST_6(testPascal<float>(1e-6));\n  CALL_SUBTEST_5(testPascal<double>(1e-15));\n  CALL_SUBTEST_2(randomTest(Matrix2d(), 1e-13));\n  CALL_SUBTEST_7(randomTest(Matrix<double,3,3,RowMajor>(), 1e-13));\n  CALL_SUBTEST_3(randomTest(Matrix4cd(), 1e-13));\n  CALL_SUBTEST_4(randomTest(MatrixXd(8,8), 1e-13));\n  CALL_SUBTEST_1(randomTest(Matrix2f(), 1e-4));\n  CALL_SUBTEST_5(randomTest(Matrix3cf(), 1e-4));\n  CALL_SUBTEST_1(randomTest(Matrix4f(), 1e-4));\n  CALL_SUBTEST_6(randomTest(MatrixXf(8,8), 1e-4));\n  CALL_SUBTEST_9(randomTest(Matrix<long double,Dynamic,Dynamic>(7,7), 1e-13));\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/matrix_function.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <unsupported/Eigen/MatrixFunctions>\n\n// Variant of VERIFY_IS_APPROX which uses absolute error instead of\n// relative error.\n#define VERIFY_IS_APPROX_ABS(a, b) VERIFY(test_isApprox_abs(a, b))\n\ntemplate<typename Type1, typename Type2>\ninline bool test_isApprox_abs(const Type1& a, const Type2& b)\n{\n  return ((a-b).array().abs() < test_precision<typename Type1::RealScalar>()).all();\n}\n\n\n// Returns a matrix with eigenvalues clustered around 0, 1 and 2.\ntemplate<typename MatrixType>\nMatrixType randomMatrixWithRealEivals(const typename MatrixType::Index size)\n{\n  typedef typename MatrixType::Index Index;\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename MatrixType::RealScalar RealScalar;\n  MatrixType diag = MatrixType::Zero(size, size);\n  for (Index i = 0; i < size; ++i) {\n    diag(i, i) = Scalar(RealScalar(internal::random<int>(0,2)))\n      + internal::random<Scalar>() * Scalar(RealScalar(0.01));\n  }\n  MatrixType A = MatrixType::Random(size, size);\n  HouseholderQR<MatrixType> QRofA(A);\n  return QRofA.householderQ().inverse() * diag * QRofA.householderQ();\n}\n\ntemplate <typename MatrixType, int IsComplex = NumTraits<typename internal::traits<MatrixType>::Scalar>::IsComplex>\nstruct randomMatrixWithImagEivals\n{\n  // Returns a matrix with eigenvalues clustered around 0 and +/- i.\n  static MatrixType run(const typename MatrixType::Index size);\n};\n\n// Partial specialization for real matrices\ntemplate<typename MatrixType>\nstruct randomMatrixWithImagEivals<MatrixType, 0>\n{\n  static MatrixType run(const typename MatrixType::Index size)\n  {\n    typedef typename MatrixType::Index Index;\n    typedef typename MatrixType::Scalar Scalar;\n    MatrixType diag = MatrixType::Zero(size, size);\n    Index i = 0;\n    while (i < size) {\n      Index randomInt = internal::random<Index>(-1, 1);\n      if (randomInt == 0 || i == size-1) {\n        diag(i, i) = internal::random<Scalar>() * Scalar(0.01);\n        ++i;\n      } else {\n        Scalar alpha = Scalar(randomInt) + internal::random<Scalar>() * Scalar(0.01);\n        diag(i, i+1) = alpha;\n        diag(i+1, i) = -alpha;\n        i += 2;\n      }\n    }\n    MatrixType A = MatrixType::Random(size, size);\n    HouseholderQR<MatrixType> QRofA(A);\n    return QRofA.householderQ().inverse() * diag * QRofA.householderQ();\n  }\n};\n\n// Partial specialization for complex matrices\ntemplate<typename MatrixType>\nstruct randomMatrixWithImagEivals<MatrixType, 1>\n{\n  static MatrixType run(const typename MatrixType::Index size)\n  {\n    typedef typename MatrixType::Index Index;\n    typedef typename MatrixType::Scalar Scalar;\n    typedef typename MatrixType::RealScalar RealScalar;\n    const Scalar imagUnit(0, 1);\n    MatrixType diag = MatrixType::Zero(size, size);\n    for (Index i = 0; i < size; ++i) {\n      diag(i, i) = Scalar(RealScalar(internal::random<Index>(-1, 1))) * imagUnit\n        + internal::random<Scalar>() * Scalar(RealScalar(0.01));\n    }\n    MatrixType A = MatrixType::Random(size, size);\n    HouseholderQR<MatrixType> QRofA(A);\n    return QRofA.householderQ().inverse() * diag * QRofA.householderQ();\n  }\n};\n\n\ntemplate<typename MatrixType>\nvoid testMatrixExponential(const MatrixType& A)\n{\n  typedef typename internal::traits<MatrixType>::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  typedef std::complex<RealScalar> ComplexScalar;\n\n  VERIFY_IS_APPROX(A.exp(), A.matrixFunction(internal::stem_function_exp<ComplexScalar>));\n}\n\ntemplate<typename MatrixType>\nvoid testMatrixLogarithm(const MatrixType& A)\n{\n  typedef typename internal::traits<MatrixType>::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n\n  MatrixType scaledA;\n  RealScalar maxImagPartOfSpectrum = A.eigenvalues().imag().cwiseAbs().maxCoeff();\n  if (maxImagPartOfSpectrum >= RealScalar(0.9L * EIGEN_PI))\n    scaledA = A * RealScalar(0.9L * EIGEN_PI) / maxImagPartOfSpectrum;\n  else\n    scaledA = A;\n\n  // identity X.exp().log() = X only holds if Im(lambda) < pi for all eigenvalues of X\n  MatrixType expA = scaledA.exp();\n  MatrixType logExpA = expA.log();\n  VERIFY_IS_APPROX(logExpA, scaledA);\n}\n\ntemplate<typename MatrixType>\nvoid testHyperbolicFunctions(const MatrixType& A)\n{\n  // Need to use absolute error because of possible cancellation when\n  // adding/subtracting expA and expmA.\n  VERIFY_IS_APPROX_ABS(A.sinh(), (A.exp() - (-A).exp()) / 2);\n  VERIFY_IS_APPROX_ABS(A.cosh(), (A.exp() + (-A).exp()) / 2);\n}\n\ntemplate<typename MatrixType>\nvoid testGonioFunctions(const MatrixType& A)\n{\n  typedef typename MatrixType::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n  typedef std::complex<RealScalar> ComplexScalar;\n  typedef Matrix<ComplexScalar, MatrixType::RowsAtCompileTime, \n                 MatrixType::ColsAtCompileTime, MatrixType::Options> ComplexMatrix;\n\n  ComplexScalar imagUnit(0,1);\n  ComplexScalar two(2,0);\n\n  ComplexMatrix Ac = A.template cast<ComplexScalar>();\n  \n  ComplexMatrix exp_iA = (imagUnit * Ac).exp();\n  ComplexMatrix exp_miA = (-imagUnit * Ac).exp();\n  \n  ComplexMatrix sinAc = A.sin().template cast<ComplexScalar>();\n  VERIFY_IS_APPROX_ABS(sinAc, (exp_iA - exp_miA) / (two*imagUnit));\n  \n  ComplexMatrix cosAc = A.cos().template cast<ComplexScalar>();\n  VERIFY_IS_APPROX_ABS(cosAc, (exp_iA + exp_miA) / 2);\n}\n\ntemplate<typename MatrixType>\nvoid testMatrix(const MatrixType& A)\n{\n  testMatrixExponential(A);\n  testMatrixLogarithm(A);\n  testHyperbolicFunctions(A);\n  testGonioFunctions(A);\n}\n\ntemplate<typename MatrixType>\nvoid testMatrixType(const MatrixType& m)\n{\n  // Matrices with clustered eigenvalue lead to different code paths\n  // in MatrixFunction.h and are thus useful for testing.\n  typedef typename MatrixType::Index Index;\n\n  const Index size = m.rows();\n  for (int i = 0; i < g_repeat; i++) {\n    testMatrix(MatrixType::Random(size, size).eval());\n    testMatrix(randomMatrixWithRealEivals<MatrixType>(size));\n    testMatrix(randomMatrixWithImagEivals<MatrixType>::run(size));\n  }\n}\n\nvoid test_matrix_function()\n{\n  CALL_SUBTEST_1(testMatrixType(Matrix<float,1,1>()));\n  CALL_SUBTEST_2(testMatrixType(Matrix3cf()));\n  CALL_SUBTEST_3(testMatrixType(MatrixXf(8,8)));\n  CALL_SUBTEST_4(testMatrixType(Matrix2d()));\n  CALL_SUBTEST_5(testMatrixType(Matrix<double,5,5,RowMajor>()));\n  CALL_SUBTEST_6(testMatrixType(Matrix4cd()));\n  CALL_SUBTEST_7(testMatrixType(MatrixXd(13,13)));\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/matrix_functions.h",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2009-2011 Jitse Niesen <jitse@maths.leeds.ac.uk>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <unsupported/Eigen/MatrixFunctions>\n\n// For complex matrices, any matrix is fine.\ntemplate<typename MatrixType, int IsComplex = NumTraits<typename internal::traits<MatrixType>::Scalar>::IsComplex>\nstruct processTriangularMatrix\n{\n  static void run(MatrixType&, MatrixType&, const MatrixType&)\n  { }\n};\n\n// For real matrices, make sure none of the eigenvalues are negative.\ntemplate<typename MatrixType>\nstruct processTriangularMatrix<MatrixType,0>\n{\n  static void run(MatrixType& m, MatrixType& T, const MatrixType& U)\n  {\n    const Index size = m.cols();\n\n    for (Index i=0; i < size; ++i) {\n      if (i == size - 1 || T.coeff(i+1,i) == 0)\n        T.coeffRef(i,i) = std::abs(T.coeff(i,i));\n      else\n        ++i;\n    }\n    m = U * T * U.transpose();\n  }\n};\n\ntemplate <typename MatrixType, int IsComplex = NumTraits<typename internal::traits<MatrixType>::Scalar>::IsComplex>\nstruct generateTestMatrix;\n\ntemplate <typename MatrixType>\nstruct generateTestMatrix<MatrixType,0>\n{\n  static void run(MatrixType& result, typename MatrixType::Index size)\n  {\n    result = MatrixType::Random(size, size);\n    RealSchur<MatrixType> schur(result);\n    MatrixType T = schur.matrixT();\n    processTriangularMatrix<MatrixType>::run(result, T, schur.matrixU());\n  }\n};\n\ntemplate <typename MatrixType>\nstruct generateTestMatrix<MatrixType,1>\n{\n  static void run(MatrixType& result, typename MatrixType::Index size)\n  {\n    result = MatrixType::Random(size, size);\n  }\n};\n\ntemplate <typename Derived, typename OtherDerived>\ntypename Derived::RealScalar relerr(const MatrixBase<Derived>& A, const MatrixBase<OtherDerived>& B)\n{\n  return std::sqrt((A - B).cwiseAbs2().sum() / (std::min)(A.cwiseAbs2().sum(), B.cwiseAbs2().sum()));\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/matrix_power.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012, 2013 Chen-Pang He <jdh8@ms63.hinet.net>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"matrix_functions.h\"\n\ntemplate<typename T>\nvoid test2dRotation(const T& tol)\n{\n  Matrix<T,2,2> A, B, C;\n  T angle, c, s;\n\n  A << 0, 1, -1, 0;\n  MatrixPower<Matrix<T,2,2> > Apow(A);\n\n  for (int i=0; i<=20; ++i) {\n    angle = std::pow(T(10), (i-10) / T(5.));\n    c = std::cos(angle);\n    s = std::sin(angle);\n    B << c, s, -s, c;\n\n    C = Apow(std::ldexp(angle,1) / T(EIGEN_PI));\n    std::cout << \"test2dRotation: i = \" << i << \"   error powerm = \" << relerr(C,B) << '\\n';\n    VERIFY(C.isApprox(B, tol));\n  }\n}\n\ntemplate<typename T>\nvoid test2dHyperbolicRotation(const T& tol)\n{\n  Matrix<std::complex<T>,2,2> A, B, C;\n  T angle, ch = std::cosh((T)1);\n  std::complex<T> ish(0, std::sinh((T)1));\n\n  A << ch, ish, -ish, ch;\n  MatrixPower<Matrix<std::complex<T>,2,2> > Apow(A);\n\n  for (int i=0; i<=20; ++i) {\n    angle = std::ldexp(static_cast<T>(i-10), -1);\n    ch = std::cosh(angle);\n    ish = std::complex<T>(0, std::sinh(angle));\n    B << ch, ish, -ish, ch;\n\n    C = Apow(angle);\n    std::cout << \"test2dHyperbolicRotation: i = \" << i << \"   error powerm = \" << relerr(C,B) << '\\n';\n    VERIFY(C.isApprox(B, tol));\n  }\n}\n\ntemplate<typename T>\nvoid test3dRotation(const T& tol)\n{\n  Matrix<T,3,1> v;\n  T angle;\n\n  for (int i=0; i<=20; ++i) {\n    v = Matrix<T,3,1>::Random();\n    v.normalize();\n    angle = std::pow(T(10), (i-10) / T(5.));\n    VERIFY(AngleAxis<T>(angle, v).matrix().isApprox(AngleAxis<T>(1,v).matrix().pow(angle), tol));\n  }\n}\n\ntemplate<typename MatrixType>\nvoid testGeneral(const MatrixType& m, const typename MatrixType::RealScalar& tol)\n{\n  typedef typename MatrixType::RealScalar RealScalar;\n  MatrixType m1, m2, m3, m4, m5;\n  RealScalar x, y;\n\n  for (int i=0; i < g_repeat; ++i) {\n    generateTestMatrix<MatrixType>::run(m1, m.rows());\n    MatrixPower<MatrixType> mpow(m1);\n\n    x = internal::random<RealScalar>();\n    y = internal::random<RealScalar>();\n    m2 = mpow(x);\n    m3 = mpow(y);\n\n    m4 = mpow(x+y);\n    m5.noalias() = m2 * m3;\n    VERIFY(m4.isApprox(m5, tol));\n\n    m4 = mpow(x*y);\n    m5 = m2.pow(y);\n    VERIFY(m4.isApprox(m5, tol));\n\n    m4 = (std::abs(x) * m1).pow(y);\n    m5 = std::pow(std::abs(x), y) * m3;\n    VERIFY(m4.isApprox(m5, tol));\n  }\n}\n\ntemplate<typename MatrixType>\nvoid testSingular(const MatrixType& m_const, const typename MatrixType::RealScalar& tol)\n{\n  // we need to pass by reference in order to prevent errors with\n  // MSVC for aligned data types ...\n  MatrixType& m = const_cast<MatrixType&>(m_const);\n\n  const int IsComplex = NumTraits<typename internal::traits<MatrixType>::Scalar>::IsComplex;\n  typedef typename internal::conditional<IsComplex, TriangularView<MatrixType,Upper>, const MatrixType&>::type TriangularType;\n  typename internal::conditional< IsComplex, ComplexSchur<MatrixType>, RealSchur<MatrixType> >::type schur;\n  MatrixType T;\n\n  for (int i=0; i < g_repeat; ++i) {\n    m.setRandom();\n    m.col(0).fill(0);\n\n    schur.compute(m);\n    T = schur.matrixT();\n    const MatrixType& U = schur.matrixU();\n    processTriangularMatrix<MatrixType>::run(m, T, U);\n    MatrixPower<MatrixType> mpow(m);\n\n    T = T.sqrt();\n    VERIFY(mpow(0.5L).isApprox(U * (TriangularType(T) * U.adjoint()), tol));\n\n    T = T.sqrt();\n    VERIFY(mpow(0.25L).isApprox(U * (TriangularType(T) * U.adjoint()), tol));\n\n    T = T.sqrt();\n    VERIFY(mpow(0.125L).isApprox(U * (TriangularType(T) * U.adjoint()), tol));\n  }\n}\n\ntemplate<typename MatrixType>\nvoid testLogThenExp(const MatrixType& m_const, const typename MatrixType::RealScalar& tol)\n{\n  // we need to pass by reference in order to prevent errors with\n  // MSVC for aligned data types ...\n  MatrixType& m = const_cast<MatrixType&>(m_const);\n\n  typedef typename MatrixType::Scalar Scalar;\n  Scalar x;\n\n  for (int i=0; i < g_repeat; ++i) {\n    generateTestMatrix<MatrixType>::run(m, m.rows());\n    x = internal::random<Scalar>();\n    VERIFY(m.pow(x).isApprox((x * m.log()).exp(), tol));\n  }\n}\n\ntypedef Matrix<double,3,3,RowMajor>         Matrix3dRowMajor;\ntypedef Matrix<long double,3,3>             Matrix3e;\ntypedef Matrix<long double,Dynamic,Dynamic> MatrixXe;\n \nvoid test_matrix_power()\n{\n  CALL_SUBTEST_2(test2dRotation<double>(1e-13));\n  CALL_SUBTEST_1(test2dRotation<float>(2e-5));  // was 1e-5, relaxed for clang 2.8 / linux / x86-64\n  CALL_SUBTEST_9(test2dRotation<long double>(1e-13L));\n  CALL_SUBTEST_2(test2dHyperbolicRotation<double>(1e-14));\n  CALL_SUBTEST_1(test2dHyperbolicRotation<float>(1e-5));\n  CALL_SUBTEST_9(test2dHyperbolicRotation<long double>(1e-14L));\n\n  CALL_SUBTEST_10(test3dRotation<double>(1e-13));\n  CALL_SUBTEST_11(test3dRotation<float>(1e-5));\n  CALL_SUBTEST_12(test3dRotation<long double>(1e-13L));\n\n  CALL_SUBTEST_2(testGeneral(Matrix2d(),         1e-13));\n  CALL_SUBTEST_7(testGeneral(Matrix3dRowMajor(), 1e-13));\n  CALL_SUBTEST_3(testGeneral(Matrix4cd(),        1e-13));\n  CALL_SUBTEST_4(testGeneral(MatrixXd(8,8),      2e-12));\n  CALL_SUBTEST_1(testGeneral(Matrix2f(),         1e-4));\n  CALL_SUBTEST_5(testGeneral(Matrix3cf(),        1e-4));\n  CALL_SUBTEST_8(testGeneral(Matrix4f(),         1e-4));\n  CALL_SUBTEST_6(testGeneral(MatrixXf(2,2),      1e-3)); // see bug 614\n  CALL_SUBTEST_9(testGeneral(MatrixXe(7,7),      1e-13L));\n  CALL_SUBTEST_10(testGeneral(Matrix3d(),        1e-13));\n  CALL_SUBTEST_11(testGeneral(Matrix3f(),        1e-4));\n  CALL_SUBTEST_12(testGeneral(Matrix3e(),        1e-13L));\n\n  CALL_SUBTEST_2(testSingular(Matrix2d(),         1e-13));\n  CALL_SUBTEST_7(testSingular(Matrix3dRowMajor(), 1e-13));\n  CALL_SUBTEST_3(testSingular(Matrix4cd(),        1e-13));\n  CALL_SUBTEST_4(testSingular(MatrixXd(8,8),      2e-12));\n  CALL_SUBTEST_1(testSingular(Matrix2f(),         1e-4));\n  CALL_SUBTEST_5(testSingular(Matrix3cf(),        1e-4));\n  CALL_SUBTEST_8(testSingular(Matrix4f(),         1e-4));\n  CALL_SUBTEST_6(testSingular(MatrixXf(2,2),      1e-3));\n  CALL_SUBTEST_9(testSingular(MatrixXe(7,7),      1e-13L));\n  CALL_SUBTEST_10(testSingular(Matrix3d(),        1e-13));\n  CALL_SUBTEST_11(testSingular(Matrix3f(),        1e-4));\n  CALL_SUBTEST_12(testSingular(Matrix3e(),        1e-13L));\n\n  CALL_SUBTEST_2(testLogThenExp(Matrix2d(),         1e-13));\n  CALL_SUBTEST_7(testLogThenExp(Matrix3dRowMajor(), 1e-13));\n  CALL_SUBTEST_3(testLogThenExp(Matrix4cd(),        1e-13));\n  CALL_SUBTEST_4(testLogThenExp(MatrixXd(8,8),      2e-12));\n  CALL_SUBTEST_1(testLogThenExp(Matrix2f(),         1e-4));\n  CALL_SUBTEST_5(testLogThenExp(Matrix3cf(),        1e-4));\n  CALL_SUBTEST_8(testLogThenExp(Matrix4f(),         1e-4));\n  CALL_SUBTEST_6(testLogThenExp(MatrixXf(2,2),      1e-3));\n  CALL_SUBTEST_9(testLogThenExp(MatrixXe(7,7),      1e-13L));\n  CALL_SUBTEST_10(testLogThenExp(Matrix3d(),        1e-13));\n  CALL_SUBTEST_11(testLogThenExp(Matrix3f(),        1e-4));\n  CALL_SUBTEST_12(testLogThenExp(Matrix3e(),        1e-13L));\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/matrix_square_root.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2011 Jitse Niesen <jitse@maths.leeds.ac.uk>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"matrix_functions.h\"\n\ntemplate<typename MatrixType>\nvoid testMatrixSqrt(const MatrixType& m)\n{\n  MatrixType A;\n  generateTestMatrix<MatrixType>::run(A, m.rows());\n  MatrixType sqrtA = A.sqrt();\n  VERIFY_IS_APPROX(sqrtA * sqrtA, A);\n}\n\nvoid test_matrix_square_root()\n{\n  for (int i = 0; i < g_repeat; i++) {\n    CALL_SUBTEST_1(testMatrixSqrt(Matrix3cf()));\n    CALL_SUBTEST_2(testMatrixSqrt(MatrixXcd(12,12)));\n    CALL_SUBTEST_3(testMatrixSqrt(Matrix4f()));\n    CALL_SUBTEST_4(testMatrixSqrt(Matrix<double,Dynamic,Dynamic,RowMajor>(9, 9)));\n    CALL_SUBTEST_5(testMatrixSqrt(Matrix<float,1,1>()));\n    CALL_SUBTEST_5(testMatrixSqrt(Matrix<std::complex<float>,1,1>()));\n  }\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/minres.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2012 Giacomo Po <gpo@ucla.edu>\n// Copyright (C) 2011 Gael Guennebaud <g.gael@free.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n#include <cmath>\n\n#include \"../../test/sparse_solver.h\"\n#include <Eigen/IterativeSolvers>\n\ntemplate<typename T> void test_minres_T()\n{\n  // Identity preconditioner\n  MINRES<SparseMatrix<T>, Lower, IdentityPreconditioner    > minres_colmajor_lower_I;\n  MINRES<SparseMatrix<T>, Upper, IdentityPreconditioner    > minres_colmajor_upper_I;\n\n  // Diagonal preconditioner\n  MINRES<SparseMatrix<T>, Lower, DiagonalPreconditioner<T> > minres_colmajor_lower_diag;\n  MINRES<SparseMatrix<T>, Upper, DiagonalPreconditioner<T> > minres_colmajor_upper_diag;\n  MINRES<SparseMatrix<T>, Lower|Upper, DiagonalPreconditioner<T> > minres_colmajor_uplo_diag;\n  \n  // call tests for SPD matrix\n  CALL_SUBTEST( check_sparse_spd_solving(minres_colmajor_lower_I) );\n  CALL_SUBTEST( check_sparse_spd_solving(minres_colmajor_upper_I) );\n    \n  CALL_SUBTEST( check_sparse_spd_solving(minres_colmajor_lower_diag)  );\n  CALL_SUBTEST( check_sparse_spd_solving(minres_colmajor_upper_diag)  );\n  CALL_SUBTEST( check_sparse_spd_solving(minres_colmajor_uplo_diag)  );\n    \n  // TO DO: symmetric semi-definite matrix\n  // TO DO: symmetric indefinite matrix\n\n}\n\nvoid test_minres()\n{\n  CALL_SUBTEST_1(test_minres_T<double>());\n//  CALL_SUBTEST_2(test_minres_T<std::compex<double> >());\n\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/mpreal/mpreal.h",
    "content": "/*\n    MPFR C++: Multi-precision floating point number class for C++.\n    Based on MPFR library:    http://mpfr.org\n\n    Project homepage:    http://www.holoborodko.com/pavel/mpfr\n    Contact e-mail:      pavel@holoborodko.com\n\n    Copyright (c) 2008-2015 Pavel Holoborodko\n\n    Contributors:\n    Dmitriy Gubanov, Konstantin Holoborodko, Brian Gladman,\n    Helmut Jarausch, Fokko Beekhof, Ulrich Mutze, Heinz van Saanen,\n    Pere Constans, Peter van Hoof, Gael Guennebaud, Tsai Chia Cheng,\n    Alexei Zubanov, Jauhien Piatlicki, Victor Berger, John Westwood,\n    Petr Aleksandrov, Orion Poplawski, Charles Karney, Arash Partow,\n    Rodney James, Jorge Leitao.\n\n    Licensing:\n    (A) MPFR C++ is under GNU General Public License (\"GPL\").\n\n    (B) Non-free licenses may also be purchased from the author, for users who\n        do not want their programs protected by the GPL.\n\n        The non-free licenses are for users that wish to use MPFR C++ in\n        their products but are unwilling to release their software\n        under the GPL (which would require them to release source code\n        and allow free redistribution).\n\n        Such users can purchase an unlimited-use license from the author.\n        Contact us for more details.\n\n    GNU General Public License (\"GPL\") copyright permissions statement:\n    **************************************************************************\n    This program is free software: you can redistribute it and/or modify\n    it under the terms of the GNU General Public License as published by\n    the Free Software Foundation, either version 3 of the License, or\n    (at your option) any later version.\n\n    This program is distributed in the hope that it will be useful,\n    but WITHOUT ANY WARRANTY; without even the implied warranty of\n    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n    GNU General Public License for more details.\n\n    You should have received a copy of the GNU General Public License\n    along with this program.  If not, see <http://www.gnu.org/licenses/>.\n*/\n\n#ifndef __MPREAL_H__\n#define __MPREAL_H__\n\n#include <string>\n#include <iostream>\n#include <sstream>\n#include <stdexcept>\n#include <cfloat>\n#include <cmath>\n#include <cstring>\n#include <limits>\n#include <complex>\n#include <algorithm>\n\n// Options\n#define MPREAL_HAVE_MSVC_DEBUGVIEW              // Enable Debugger Visualizer for \"Debug\" builds in MSVC.\n#define MPREAL_HAVE_DYNAMIC_STD_NUMERIC_LIMITS  // Enable extended std::numeric_limits<mpfr::mpreal> specialization.\n                                                // Meaning that \"digits\", \"round_style\" and similar members are defined as functions, not constants.\n                                                // See std::numeric_limits<mpfr::mpreal> at the end of the file for more information.\n\n// Library version\n#define MPREAL_VERSION_MAJOR 3\n#define MPREAL_VERSION_MINOR 6\n#define MPREAL_VERSION_PATCHLEVEL 2\n#define MPREAL_VERSION_STRING \"3.6.2\"\n\n// Detect compiler using signatures from http://predef.sourceforge.net/\n#if defined(__GNUC__)\n    #define IsInf(x) (isinf)(x)                 // GNU C++/Intel ICC compiler on Linux\n#elif defined(_MSC_VER)                         // Microsoft Visual C++\n    #define IsInf(x) (!_finite(x))\n#else\n    #define IsInf(x) (std::isinf)(x)              // GNU C/C++ (and/or other compilers), just hope for C99 conformance\n#endif\n\n// A Clang feature extension to determine compiler features.\n#ifndef __has_feature\n    #define __has_feature(x) 0\n#endif\n\n// Detect support for r-value references (move semantic). Borrowed from Eigen.\n#if (__has_feature(cxx_rvalue_references) || \\\n       defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103L || \\\n      (defined(_MSC_VER) && _MSC_VER >= 1600))\n\n    #define MPREAL_HAVE_MOVE_SUPPORT\n\n    // Use fields in mpfr_t structure to check if it was initialized / set dummy initialization\n    #define mpfr_is_initialized(x)      (0 != (x)->_mpfr_d)\n    #define mpfr_set_uninitialized(x)   ((x)->_mpfr_d = 0 )\n#endif\n\n// Detect support for explicit converters.\n#if (__has_feature(cxx_explicit_conversions) || \\\n       (defined(__GXX_EXPERIMENTAL_CXX0X__) && __GNUC_MINOR__ >= 5) || __cplusplus >= 201103L || \\\n       (defined(_MSC_VER) && _MSC_VER >= 1800))\n\n    #define MPREAL_HAVE_EXPLICIT_CONVERTERS\n#endif\n\n#define MPFR_USE_INTMAX_T   // Enable 64-bit integer types - should be defined before mpfr.h\n\n#if defined(MPREAL_HAVE_MSVC_DEBUGVIEW) && defined(_MSC_VER) && defined(_DEBUG)\n    #define MPREAL_MSVC_DEBUGVIEW_CODE     DebugView = toString();\n    #define MPREAL_MSVC_DEBUGVIEW_DATA     std::string DebugView;\n#else\n    #define MPREAL_MSVC_DEBUGVIEW_CODE\n    #define MPREAL_MSVC_DEBUGVIEW_DATA\n#endif\n\n#include <mpfr.h>\n\n#if (MPFR_VERSION < MPFR_VERSION_NUM(3,0,0))\n    #include <cstdlib>                          // Needed for random()\n#endif\n\n// Less important options\n#define MPREAL_DOUBLE_BITS_OVERFLOW -1          // Triggers overflow exception during conversion to double if mpreal\n                                                // cannot fit in MPREAL_DOUBLE_BITS_OVERFLOW bits\n                                                // = -1 disables overflow checks (default)\n\n// Fast replacement for mpfr_set_zero(x, +1):\n// (a) uses low-level data members, might not be compatible with new versions of MPFR\n// (b) sign is not set, add (x)->_mpfr_sign = 1;\n#define mpfr_set_zero_fast(x)  ((x)->_mpfr_exp = __MPFR_EXP_ZERO)\n\n#if defined(__GNUC__)\n  #define MPREAL_PERMISSIVE_EXPR __extension__\n#else\n  #define MPREAL_PERMISSIVE_EXPR\n#endif\n\nnamespace mpfr {\n\nclass mpreal {\nprivate:\n    mpfr_t mp;\n\npublic:\n\n    // Get default rounding mode & precision\n    inline static mp_rnd_t   get_default_rnd()    {    return (mp_rnd_t)(mpfr_get_default_rounding_mode());       }\n    inline static mp_prec_t  get_default_prec()   {    return mpfr_get_default_prec();                            }\n\n    // Constructors && type conversions\n    mpreal();\n    mpreal(const mpreal& u);\n    mpreal(const mpf_t u);\n    mpreal(const mpz_t u,                  mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd());\n    mpreal(const mpq_t u,                  mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd());\n    mpreal(const double u,                 mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd());\n    mpreal(const long double u,            mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd());\n    mpreal(const unsigned long long int u, mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd());\n    mpreal(const long long int u,          mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd());\n    mpreal(const unsigned long int u,      mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd());\n    mpreal(const unsigned int u,           mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd());\n    mpreal(const long int u,               mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd());\n    mpreal(const int u,                    mp_prec_t prec = mpreal::get_default_prec(), mp_rnd_t mode = mpreal::get_default_rnd());\n\n    // Construct mpreal from mpfr_t structure.\n    // shared = true allows to avoid deep copy, so that mpreal and 'u' share the same data & pointers.\n    mpreal(const mpfr_t  u, bool shared = false);\n\n    mpreal(const char* s,             mp_prec_t prec = mpreal::get_default_prec(), int base = 10, mp_rnd_t mode = mpreal::get_default_rnd());\n    mpreal(const std::string& s,      mp_prec_t prec = mpreal::get_default_prec(), int base = 10, mp_rnd_t mode = mpreal::get_default_rnd());\n\n    ~mpreal();\n\n#ifdef MPREAL_HAVE_MOVE_SUPPORT\n    mpreal& operator=(mpreal&& v);\n    mpreal(mpreal&& u);\n#endif\n\n    // Operations\n    // =\n    // +, -, *, /, ++, --, <<, >>\n    // *=, +=, -=, /=,\n    // <, >, ==, <=, >=\n\n    // =\n    mpreal& operator=(const mpreal& v);\n    mpreal& operator=(const mpf_t v);\n    mpreal& operator=(const mpz_t v);\n    mpreal& operator=(const mpq_t v);\n    mpreal& operator=(const long double v);\n    mpreal& operator=(const double v);\n    mpreal& operator=(const unsigned long int v);\n    mpreal& operator=(const unsigned long long int v);\n    mpreal& operator=(const long long int v);\n    mpreal& operator=(const unsigned int v);\n    mpreal& operator=(const long int v);\n    mpreal& operator=(const int v);\n    mpreal& operator=(const char* s);\n    mpreal& operator=(const std::string& s);\n    template <typename real_t> mpreal& operator= (const std::complex<real_t>& z);\n\n    // +\n    mpreal& operator+=(const mpreal& v);\n    mpreal& operator+=(const mpf_t v);\n    mpreal& operator+=(const mpz_t v);\n    mpreal& operator+=(const mpq_t v);\n    mpreal& operator+=(const long double u);\n    mpreal& operator+=(const double u);\n    mpreal& operator+=(const unsigned long int u);\n    mpreal& operator+=(const unsigned int u);\n    mpreal& operator+=(const long int u);\n    mpreal& operator+=(const int u);\n\n    mpreal& operator+=(const long long int  u);\n    mpreal& operator+=(const unsigned long long int u);\n    mpreal& operator-=(const long long int  u);\n    mpreal& operator-=(const unsigned long long int u);\n    mpreal& operator*=(const long long int  u);\n    mpreal& operator*=(const unsigned long long int u);\n    mpreal& operator/=(const long long int  u);\n    mpreal& operator/=(const unsigned long long int u);\n\n    const mpreal operator+() const;\n    mpreal& operator++ ();\n    const mpreal  operator++ (int);\n\n    // -\n    mpreal& operator-=(const mpreal& v);\n    mpreal& operator-=(const mpz_t v);\n    mpreal& operator-=(const mpq_t v);\n    mpreal& operator-=(const long double u);\n    mpreal& operator-=(const double u);\n    mpreal& operator-=(const unsigned long int u);\n    mpreal& operator-=(const unsigned int u);\n    mpreal& operator-=(const long int u);\n    mpreal& operator-=(const int u);\n    const mpreal operator-() const;\n    friend const mpreal operator-(const unsigned long int b, const mpreal& a);\n    friend const mpreal operator-(const unsigned int b,      const mpreal& a);\n    friend const mpreal operator-(const long int b,          const mpreal& a);\n    friend const mpreal operator-(const int b,               const mpreal& a);\n    friend const mpreal operator-(const double b,            const mpreal& a);\n    mpreal& operator-- ();\n    const mpreal  operator-- (int);\n\n    // *\n    mpreal& operator*=(const mpreal& v);\n    mpreal& operator*=(const mpz_t v);\n    mpreal& operator*=(const mpq_t v);\n    mpreal& operator*=(const long double v);\n    mpreal& operator*=(const double v);\n    mpreal& operator*=(const unsigned long int v);\n    mpreal& operator*=(const unsigned int v);\n    mpreal& operator*=(const long int v);\n    mpreal& operator*=(const int v);\n\n    // /\n    mpreal& operator/=(const mpreal& v);\n    mpreal& operator/=(const mpz_t v);\n    mpreal& operator/=(const mpq_t v);\n    mpreal& operator/=(const long double v);\n    mpreal& operator/=(const double v);\n    mpreal& operator/=(const unsigned long int v);\n    mpreal& operator/=(const unsigned int v);\n    mpreal& operator/=(const long int v);\n    mpreal& operator/=(const int v);\n    friend const mpreal operator/(const unsigned long int b, const mpreal& a);\n    friend const mpreal operator/(const unsigned int b,      const mpreal& a);\n    friend const mpreal operator/(const long int b,          const mpreal& a);\n    friend const mpreal operator/(const int b,               const mpreal& a);\n    friend const mpreal operator/(const double b,            const mpreal& a);\n\n    //<<= Fast Multiplication by 2^u\n    mpreal& operator<<=(const unsigned long int u);\n    mpreal& operator<<=(const unsigned int u);\n    mpreal& operator<<=(const long int u);\n    mpreal& operator<<=(const int u);\n\n    //>>= Fast Division by 2^u\n    mpreal& operator>>=(const unsigned long int u);\n    mpreal& operator>>=(const unsigned int u);\n    mpreal& operator>>=(const long int u);\n    mpreal& operator>>=(const int u);\n\n    // Type Conversion operators\n    bool               toBool      (                        )    const;\n    long               toLong      (mp_rnd_t mode = GMP_RNDZ)    const;\n    unsigned long      toULong     (mp_rnd_t mode = GMP_RNDZ)    const;\n    long long          toLLong     (mp_rnd_t mode = GMP_RNDZ)    const;\n    unsigned long long toULLong    (mp_rnd_t mode = GMP_RNDZ)    const;\n    float              toFloat     (mp_rnd_t mode = GMP_RNDN)    const;\n    double             toDouble    (mp_rnd_t mode = GMP_RNDN)    const;\n    long double        toLDouble   (mp_rnd_t mode = GMP_RNDN)    const;\n\n#if defined (MPREAL_HAVE_EXPLICIT_CONVERTERS)\n    explicit operator bool               () const { return toBool();                 }\n    explicit operator int                () const { return int(toLong());            }\n    explicit operator long               () const { return toLong();                 }\n    explicit operator long long          () const { return toLLong();                }\n    explicit operator unsigned           () const { return unsigned(toULong());      }\n    explicit operator unsigned long      () const { return toULong();                }\n    explicit operator unsigned long long () const { return toULLong();               }\n    explicit operator float              () const { return toFloat();                }\n    explicit operator double             () const { return toDouble();               }\n    explicit operator long double        () const { return toLDouble();              }\n#endif\n\n    // Get raw pointers so that mpreal can be directly used in raw mpfr_* functions\n    ::mpfr_ptr    mpfr_ptr();\n    ::mpfr_srcptr mpfr_ptr()    const;\n    ::mpfr_srcptr mpfr_srcptr() const;\n\n    // Convert mpreal to string with n significant digits in base b\n    // n = -1 -> convert with the maximum available digits\n    std::string toString(int n = -1, int b = 10, mp_rnd_t mode = mpreal::get_default_rnd()) const;\n\n#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))\n    std::string toString(const std::string& format) const;\n#endif\n\n    std::ostream& output(std::ostream& os) const;\n\n    // Math Functions\n    friend const mpreal sqr (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal sqrt(const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal sqrt(const unsigned long int v, mp_rnd_t rnd_mode);\n    friend const mpreal cbrt(const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal root(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode);\n    friend const mpreal pow (const mpreal& a, const mpreal& b, mp_rnd_t rnd_mode);\n    friend const mpreal pow (const mpreal& a, const mpz_t b, mp_rnd_t rnd_mode);\n    friend const mpreal pow (const mpreal& a, const unsigned long int b, mp_rnd_t rnd_mode);\n    friend const mpreal pow (const mpreal& a, const long int b, mp_rnd_t rnd_mode);\n    friend const mpreal pow (const unsigned long int a, const mpreal& b, mp_rnd_t rnd_mode);\n    friend const mpreal pow (const unsigned long int a, const unsigned long int b, mp_rnd_t rnd_mode);\n    friend const mpreal fabs(const mpreal& v, mp_rnd_t rnd_mode);\n\n    friend const mpreal abs(const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal dim(const mpreal& a, const mpreal& b, mp_rnd_t rnd_mode);\n    friend inline const mpreal mul_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode);\n    friend inline const mpreal mul_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode);\n    friend inline const mpreal div_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode);\n    friend inline const mpreal div_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode);\n    friend int cmpabs(const mpreal& a,const mpreal& b);\n\n    friend const mpreal log  (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal log2 (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal logb (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal log10(const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal exp  (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal exp2 (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal exp10(const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal log1p(const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal expm1(const mpreal& v, mp_rnd_t rnd_mode);\n\n    friend const mpreal cos(const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal sin(const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal tan(const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal sec(const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal csc(const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal cot(const mpreal& v, mp_rnd_t rnd_mode);\n    friend int sin_cos(mpreal& s, mpreal& c, const mpreal& v, mp_rnd_t rnd_mode);\n\n    friend const mpreal acos  (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal asin  (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal atan  (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal atan2 (const mpreal& y, const mpreal& x, mp_rnd_t rnd_mode);\n    friend const mpreal acot  (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal asec  (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal acsc  (const mpreal& v, mp_rnd_t rnd_mode);\n\n    friend const mpreal cosh  (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal sinh  (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal tanh  (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal sech  (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal csch  (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal coth  (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal acosh (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal asinh (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal atanh (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal acoth (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal asech (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal acsch (const mpreal& v, mp_rnd_t rnd_mode);\n\n    friend const mpreal hypot (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode);\n\n    friend const mpreal fac_ui (unsigned long int v,  mp_prec_t prec, mp_rnd_t rnd_mode);\n    friend const mpreal eint   (const mpreal& v, mp_rnd_t rnd_mode);\n\n    friend const mpreal gamma    (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal tgamma   (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal lngamma  (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal lgamma   (const mpreal& v, int *signp, mp_rnd_t rnd_mode);\n    friend const mpreal zeta     (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal erf      (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal erfc     (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal besselj0 (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal besselj1 (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal besseljn (long n, const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal bessely0 (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal bessely1 (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal besselyn (long n, const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal fma      (const mpreal& v1, const mpreal& v2, const mpreal& v3, mp_rnd_t rnd_mode);\n    friend const mpreal fms      (const mpreal& v1, const mpreal& v2, const mpreal& v3, mp_rnd_t rnd_mode);\n    friend const mpreal agm      (const mpreal& v1, const mpreal& v2, mp_rnd_t rnd_mode);\n    friend const mpreal sum      (const mpreal tab[], const unsigned long int n, int& status, mp_rnd_t rnd_mode);\n    friend int sgn(const mpreal& v); // returns -1 or +1\n\n// MPFR 2.4.0 Specifics\n#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))\n    friend int          sinh_cosh   (mpreal& s, mpreal& c, const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal li2         (const mpreal& v,                       mp_rnd_t rnd_mode);\n    friend const mpreal fmod        (const mpreal& x, const mpreal& y,      mp_rnd_t rnd_mode);\n    friend const mpreal rec_sqrt    (const mpreal& v,                       mp_rnd_t rnd_mode);\n\n    // MATLAB's semantic equivalents\n    friend const mpreal rem (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode); // Remainder after division\n    friend const mpreal mod (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode); // Modulus after division\n#endif\n\n#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,0,0))\n    friend const mpreal digamma (const mpreal& v,        mp_rnd_t rnd_mode);\n    friend const mpreal ai      (const mpreal& v,        mp_rnd_t rnd_mode);\n    friend const mpreal urandom (gmp_randstate_t& state, mp_rnd_t rnd_mode);     // use gmp_randinit_default() to init state, gmp_randclear() to clear\n#endif\n\n#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,1,0))\n    friend const mpreal grandom (gmp_randstate_t& state, mp_rnd_t rnd_mode);     // use gmp_randinit_default() to init state, gmp_randclear() to clear\n    friend const mpreal grandom (unsigned int seed);\n#endif\n\n    // Uniformly distributed random number generation in [0,1] using\n    // Mersenne-Twister algorithm by default.\n    // Use parameter to setup seed, e.g.: random((unsigned)time(NULL))\n    // Check urandom() for more precise control.\n    friend const mpreal random(unsigned int seed);\n\n    // Splits mpreal value into fractional and integer parts.\n    // Returns fractional part and stores integer part in n.\n    friend const mpreal modf(const mpreal& v, mpreal& n);\n\n    // Constants\n    // don't forget to call mpfr_free_cache() for every thread where you are using const-functions\n    friend const mpreal const_log2      (mp_prec_t prec, mp_rnd_t rnd_mode);\n    friend const mpreal const_pi        (mp_prec_t prec, mp_rnd_t rnd_mode);\n    friend const mpreal const_euler     (mp_prec_t prec, mp_rnd_t rnd_mode);\n    friend const mpreal const_catalan   (mp_prec_t prec, mp_rnd_t rnd_mode);\n\n    // returns +inf iff sign>=0 otherwise -inf\n    friend const mpreal const_infinity(int sign, mp_prec_t prec);\n\n    // Output/ Input\n    friend std::ostream& operator<<(std::ostream& os, const mpreal& v);\n    friend std::istream& operator>>(std::istream& is, mpreal& v);\n\n    // Integer Related Functions\n    friend const mpreal rint (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal ceil (const mpreal& v);\n    friend const mpreal floor(const mpreal& v);\n    friend const mpreal round(const mpreal& v);\n    friend const mpreal trunc(const mpreal& v);\n    friend const mpreal rint_ceil   (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal rint_floor  (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal rint_round  (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal rint_trunc  (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal frac        (const mpreal& v, mp_rnd_t rnd_mode);\n    friend const mpreal remainder   (         const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode);\n    friend const mpreal remquo      (long* q, const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode);\n\n    // Miscellaneous Functions\n    friend const mpreal nexttoward (const mpreal& x, const mpreal& y);\n    friend const mpreal nextabove  (const mpreal& x);\n    friend const mpreal nextbelow  (const mpreal& x);\n\n    // use gmp_randinit_default() to init state, gmp_randclear() to clear\n    friend const mpreal urandomb (gmp_randstate_t& state);\n\n// MPFR < 2.4.2 Specifics\n#if (MPFR_VERSION <= MPFR_VERSION_NUM(2,4,2))\n    friend const mpreal random2 (mp_size_t size, mp_exp_t exp);\n#endif\n\n    // Instance Checkers\n    friend bool (isnan)    (const mpreal& v);\n    friend bool (isinf)    (const mpreal& v);\n    friend bool (isfinite) (const mpreal& v);\n\n    friend bool isnum    (const mpreal& v);\n    friend bool iszero   (const mpreal& v);\n    friend bool isint    (const mpreal& v);\n\n#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,0,0))\n    friend bool isregular(const mpreal& v);\n#endif\n\n    // Set/Get instance properties\n    inline mp_prec_t    get_prec() const;\n    inline void         set_prec(mp_prec_t prec, mp_rnd_t rnd_mode = get_default_rnd());    // Change precision with rounding mode\n\n    // Aliases for get_prec(), set_prec() - needed for compatibility with std::complex<mpreal> interface\n    inline mpreal&      setPrecision(int Precision, mp_rnd_t RoundingMode = get_default_rnd());\n    inline int          getPrecision() const;\n\n    // Set mpreal to +/- inf, NaN, +/-0\n    mpreal&        setInf  (int Sign = +1);\n    mpreal&        setNan  ();\n    mpreal&        setZero (int Sign = +1);\n    mpreal&        setSign (int Sign, mp_rnd_t RoundingMode = get_default_rnd());\n\n    //Exponent\n    mp_exp_t get_exp();\n    int set_exp(mp_exp_t e);\n    int check_range  (int t, mp_rnd_t rnd_mode = get_default_rnd());\n    int subnormalize (int t, mp_rnd_t rnd_mode = get_default_rnd());\n\n    // Inexact conversion from float\n    inline bool fits_in_bits(double x, int n);\n\n    // Set/Get global properties\n    static void            set_default_prec(mp_prec_t prec);\n    static void            set_default_rnd(mp_rnd_t rnd_mode);\n\n    static mp_exp_t  get_emin (void);\n    static mp_exp_t  get_emax (void);\n    static mp_exp_t  get_emin_min (void);\n    static mp_exp_t  get_emin_max (void);\n    static mp_exp_t  get_emax_min (void);\n    static mp_exp_t  get_emax_max (void);\n    static int       set_emin (mp_exp_t exp);\n    static int       set_emax (mp_exp_t exp);\n\n    // Efficient swapping of two mpreal values - needed for std algorithms\n    friend void swap(mpreal& x, mpreal& y);\n\n    friend const mpreal fmax(const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode);\n    friend const mpreal fmin(const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode);\n\nprivate:\n    // Human friendly Debug Preview in Visual Studio.\n    // Put one of these lines:\n    //\n    // mpfr::mpreal=<DebugView>                              ; Show value only\n    // mpfr::mpreal=<DebugView>, <mp[0]._mpfr_prec,u>bits    ; Show value & precision\n    //\n    // at the beginning of\n    // [Visual Studio Installation Folder]\\Common7\\Packages\\Debugger\\autoexp.dat\n    MPREAL_MSVC_DEBUGVIEW_DATA\n\n    // \"Smart\" resources deallocation. Checks if instance initialized before deletion.\n    void clear(::mpfr_ptr);\n};\n\n//////////////////////////////////////////////////////////////////////////\n// Exceptions\nclass conversion_overflow : public std::exception {\npublic:\n    std::string why() { return \"inexact conversion from floating point\"; }\n};\n\n//////////////////////////////////////////////////////////////////////////\n// Constructors & converters\n// Default constructor: creates mp number and initializes it to 0.\ninline mpreal::mpreal()\n{\n    mpfr_init2(mpfr_ptr(), mpreal::get_default_prec());\n    mpfr_set_zero_fast(mpfr_ptr());\n\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n}\n\ninline mpreal::mpreal(const mpreal& u)\n{\n    mpfr_init2(mpfr_ptr(),mpfr_get_prec(u.mpfr_srcptr()));\n    mpfr_set  (mpfr_ptr(),u.mpfr_srcptr(),mpreal::get_default_rnd());\n\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n}\n\n#ifdef MPREAL_HAVE_MOVE_SUPPORT\ninline mpreal::mpreal(mpreal&& other)\n{\n    mpfr_set_uninitialized(mpfr_ptr());     // make sure \"other\" holds no pointer to actual data\n    mpfr_swap(mpfr_ptr(), other.mpfr_ptr());\n\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n}\n\ninline mpreal& mpreal::operator=(mpreal&& other)\n{\n    mpfr_swap(mpfr_ptr(), other.mpfr_ptr());\n\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n#endif\n\ninline mpreal::mpreal(const mpfr_t  u, bool shared)\n{\n    if(shared)\n    {\n        std::memcpy(mpfr_ptr(), u, sizeof(mpfr_t));\n    }\n    else\n    {\n        mpfr_init2(mpfr_ptr(), mpfr_get_prec(u));\n        mpfr_set  (mpfr_ptr(), u, mpreal::get_default_rnd());\n    }\n\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n}\n\ninline mpreal::mpreal(const mpf_t u)\n{\n    mpfr_init2(mpfr_ptr(),(mp_prec_t) mpf_get_prec(u)); // (gmp: mp_bitcnt_t) unsigned long -> long (mpfr: mp_prec_t)\n    mpfr_set_f(mpfr_ptr(),u,mpreal::get_default_rnd());\n\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n}\n\ninline mpreal::mpreal(const mpz_t u, mp_prec_t prec, mp_rnd_t mode)\n{\n    mpfr_init2(mpfr_ptr(), prec);\n    mpfr_set_z(mpfr_ptr(), u, mode);\n\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n}\n\ninline mpreal::mpreal(const mpq_t u, mp_prec_t prec, mp_rnd_t mode)\n{\n    mpfr_init2(mpfr_ptr(), prec);\n    mpfr_set_q(mpfr_ptr(), u, mode);\n\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n}\n\ninline mpreal::mpreal(const double u, mp_prec_t prec, mp_rnd_t mode)\n{\n     mpfr_init2(mpfr_ptr(), prec);\n\n#if (MPREAL_DOUBLE_BITS_OVERFLOW > -1)\n  if(fits_in_bits(u, MPREAL_DOUBLE_BITS_OVERFLOW))\n  {\n    mpfr_set_d(mpfr_ptr(), u, mode);\n  }else\n    throw conversion_overflow();\n#else\n  mpfr_set_d(mpfr_ptr(), u, mode);\n#endif\n\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n}\n\ninline mpreal::mpreal(const long double u, mp_prec_t prec, mp_rnd_t mode)\n{\n    mpfr_init2 (mpfr_ptr(), prec);\n    mpfr_set_ld(mpfr_ptr(), u, mode);\n\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n}\n\ninline mpreal::mpreal(const unsigned long long int u, mp_prec_t prec, mp_rnd_t mode)\n{\n    mpfr_init2 (mpfr_ptr(), prec);\n    mpfr_set_uj(mpfr_ptr(), u, mode);\n\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n}\n\ninline mpreal::mpreal(const long long int u, mp_prec_t prec, mp_rnd_t mode)\n{\n    mpfr_init2 (mpfr_ptr(), prec);\n    mpfr_set_sj(mpfr_ptr(), u, mode);\n\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n}\n\ninline mpreal::mpreal(const unsigned long int u, mp_prec_t prec, mp_rnd_t mode)\n{\n    mpfr_init2 (mpfr_ptr(), prec);\n    mpfr_set_ui(mpfr_ptr(), u, mode);\n\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n}\n\ninline mpreal::mpreal(const unsigned int u, mp_prec_t prec, mp_rnd_t mode)\n{\n    mpfr_init2 (mpfr_ptr(), prec);\n    mpfr_set_ui(mpfr_ptr(), u, mode);\n\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n}\n\ninline mpreal::mpreal(const long int u, mp_prec_t prec, mp_rnd_t mode)\n{\n    mpfr_init2 (mpfr_ptr(), prec);\n    mpfr_set_si(mpfr_ptr(), u, mode);\n\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n}\n\ninline mpreal::mpreal(const int u, mp_prec_t prec, mp_rnd_t mode)\n{\n    mpfr_init2 (mpfr_ptr(), prec);\n    mpfr_set_si(mpfr_ptr(), u, mode);\n\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n}\n\ninline mpreal::mpreal(const char* s, mp_prec_t prec, int base, mp_rnd_t mode)\n{\n    mpfr_init2  (mpfr_ptr(), prec);\n    mpfr_set_str(mpfr_ptr(), s, base, mode);\n\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n}\n\ninline mpreal::mpreal(const std::string& s, mp_prec_t prec, int base, mp_rnd_t mode)\n{\n    mpfr_init2  (mpfr_ptr(), prec);\n    mpfr_set_str(mpfr_ptr(), s.c_str(), base, mode);\n\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n}\n\ninline void mpreal::clear(::mpfr_ptr x)\n{\n#ifdef MPREAL_HAVE_MOVE_SUPPORT\n    if(mpfr_is_initialized(x))\n#endif\n    mpfr_clear(x);\n}\n\ninline mpreal::~mpreal()\n{\n    clear(mpfr_ptr());\n}\n\n// internal namespace needed for template magic\nnamespace internal{\n\n    // Use SFINAE to restrict arithmetic operations instantiation only for numeric types\n    // This is needed for smooth integration with libraries based on expression templates, like Eigen.\n    // TODO: Do the same for boolean operators.\n    template <typename ArgumentType> struct result_type {};\n\n    template <> struct result_type<mpreal>              {typedef mpreal type;};\n    template <> struct result_type<mpz_t>               {typedef mpreal type;};\n    template <> struct result_type<mpq_t>               {typedef mpreal type;};\n    template <> struct result_type<long double>         {typedef mpreal type;};\n    template <> struct result_type<double>              {typedef mpreal type;};\n    template <> struct result_type<unsigned long int>   {typedef mpreal type;};\n    template <> struct result_type<unsigned int>        {typedef mpreal type;};\n    template <> struct result_type<long int>            {typedef mpreal type;};\n    template <> struct result_type<int>                 {typedef mpreal type;};\n    template <> struct result_type<long long>           {typedef mpreal type;};\n    template <> struct result_type<unsigned long long>  {typedef mpreal type;};\n}\n\n// + Addition\ntemplate <typename Rhs>\ninline const typename internal::result_type<Rhs>::type\n    operator+(const mpreal& lhs, const Rhs& rhs){ return mpreal(lhs) += rhs;    }\n\ntemplate <typename Lhs>\ninline const typename internal::result_type<Lhs>::type\n    operator+(const Lhs& lhs, const mpreal& rhs){ return mpreal(rhs) += lhs;    }\n\n// - Subtraction\ntemplate <typename Rhs>\ninline const typename internal::result_type<Rhs>::type\n    operator-(const mpreal& lhs, const Rhs& rhs){ return mpreal(lhs) -= rhs;    }\n\ntemplate <typename Lhs>\ninline const typename internal::result_type<Lhs>::type\n    operator-(const Lhs& lhs, const mpreal& rhs){ return mpreal(lhs) -= rhs;    }\n\n// * Multiplication\ntemplate <typename Rhs>\ninline const typename internal::result_type<Rhs>::type\n    operator*(const mpreal& lhs, const Rhs& rhs){ return mpreal(lhs) *= rhs;    }\n\ntemplate <typename Lhs>\ninline const typename internal::result_type<Lhs>::type\n    operator*(const Lhs& lhs, const mpreal& rhs){ return mpreal(rhs) *= lhs;    }\n\n// / Division\ntemplate <typename Rhs>\ninline const typename internal::result_type<Rhs>::type\n    operator/(const mpreal& lhs, const Rhs& rhs){ return mpreal(lhs) /= rhs;    }\n\ntemplate <typename Lhs>\ninline const typename internal::result_type<Lhs>::type\n    operator/(const Lhs& lhs, const mpreal& rhs){ return mpreal(lhs) /= rhs;    }\n\n//////////////////////////////////////////////////////////////////////////\n// sqrt\nconst mpreal sqrt(const unsigned int v, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal sqrt(const long int v, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal sqrt(const int v, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal sqrt(const long double v, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal sqrt(const double v, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\n\n// abs\ninline const mpreal abs(const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd());\n\n//////////////////////////////////////////////////////////////////////////\n// pow\nconst mpreal pow(const mpreal& a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal pow(const mpreal& a, const int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal pow(const mpreal& a, const long double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal pow(const mpreal& a, const double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\n\nconst mpreal pow(const unsigned int a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal pow(const long int a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal pow(const int a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal pow(const long double a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal pow(const double a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\n\nconst mpreal pow(const unsigned long int a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal pow(const unsigned long int a, const long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal pow(const unsigned long int a, const int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal pow(const unsigned long int a, const long double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal pow(const unsigned long int a, const double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\n\nconst mpreal pow(const unsigned int a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal pow(const unsigned int a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal pow(const unsigned int a, const long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal pow(const unsigned int a, const int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal pow(const unsigned int a, const long double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal pow(const unsigned int a, const double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\n\nconst mpreal pow(const long int a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal pow(const long int a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal pow(const long int a, const long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal pow(const long int a, const int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal pow(const long int a, const long double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal pow(const long int a, const double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\n\nconst mpreal pow(const int a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal pow(const int a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal pow(const int a, const long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal pow(const int a, const int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal pow(const int a, const long double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal pow(const int a, const double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\n\nconst mpreal pow(const long double a, const long double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal pow(const long double a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal pow(const long double a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal pow(const long double a, const long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal pow(const long double a, const int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\n\nconst mpreal pow(const double a, const double b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal pow(const double a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal pow(const double a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal pow(const double a, const long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\nconst mpreal pow(const double a, const int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\n\ninline const mpreal mul_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\ninline const mpreal mul_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\ninline const mpreal div_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\ninline const mpreal div_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode = mpreal::get_default_rnd());\n\n//////////////////////////////////////////////////////////////////////////\n// Estimate machine epsilon for the given precision\n// Returns smallest eps such that 1.0 + eps != 1.0\ninline mpreal machine_epsilon(mp_prec_t prec = mpreal::get_default_prec());\n\n// Returns smallest eps such that x + eps != x (relative machine epsilon)\ninline mpreal machine_epsilon(const mpreal& x);\n\n// Gives max & min values for the required precision,\n// minval is 'safe' meaning 1 / minval does not overflow\n// maxval is 'safe' meaning 1 / maxval does not underflow\ninline mpreal minval(mp_prec_t prec = mpreal::get_default_prec());\ninline mpreal maxval(mp_prec_t prec = mpreal::get_default_prec());\n\n// 'Dirty' equality check 1: |a-b| < min{|a|,|b|} * eps\ninline bool isEqualFuzzy(const mpreal& a, const mpreal& b, const mpreal& eps);\n\n// 'Dirty' equality check 2: |a-b| < min{|a|,|b|} * eps( min{|a|,|b|} )\ninline bool isEqualFuzzy(const mpreal& a, const mpreal& b);\n\n// 'Bitwise' equality check\n//  maxUlps - a and b can be apart by maxUlps binary numbers.\ninline bool isEqualUlps(const mpreal& a, const mpreal& b, int maxUlps);\n\n//////////////////////////////////////////////////////////////////////////\n// Convert precision in 'bits' to decimal digits and vice versa.\n//    bits   = ceil(digits*log[2](10))\n//    digits = floor(bits*log[10](2))\n\ninline mp_prec_t digits2bits(int d);\ninline int       bits2digits(mp_prec_t b);\n\n//////////////////////////////////////////////////////////////////////////\n// min, max\nconst mpreal (max)(const mpreal& x, const mpreal& y);\nconst mpreal (min)(const mpreal& x, const mpreal& y);\n\n//////////////////////////////////////////////////////////////////////////\n// Implementation\n//////////////////////////////////////////////////////////////////////////\n\n//////////////////////////////////////////////////////////////////////////\n// Operators - Assignment\ninline mpreal& mpreal::operator=(const mpreal& v)\n{\n    if (this != &v)\n    {\n    mp_prec_t tp = mpfr_get_prec(  mpfr_srcptr());\n    mp_prec_t vp = mpfr_get_prec(v.mpfr_srcptr());\n\n    if(tp != vp){\n      clear(mpfr_ptr());\n      mpfr_init2(mpfr_ptr(), vp);\n    }\n\n        mpfr_set(mpfr_ptr(), v.mpfr_srcptr(), mpreal::get_default_rnd());\n\n        MPREAL_MSVC_DEBUGVIEW_CODE;\n    }\n    return *this;\n}\n\ninline mpreal& mpreal::operator=(const mpf_t v)\n{\n    mpfr_set_f(mpfr_ptr(), v, mpreal::get_default_rnd());\n\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator=(const mpz_t v)\n{\n    mpfr_set_z(mpfr_ptr(), v, mpreal::get_default_rnd());\n\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator=(const mpq_t v)\n{\n    mpfr_set_q(mpfr_ptr(), v, mpreal::get_default_rnd());\n\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator=(const long double v)\n{\n    mpfr_set_ld(mpfr_ptr(), v, mpreal::get_default_rnd());\n\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator=(const double v)\n{\n#if (MPREAL_DOUBLE_BITS_OVERFLOW > -1)\n  if(fits_in_bits(v, MPREAL_DOUBLE_BITS_OVERFLOW))\n  {\n    mpfr_set_d(mpfr_ptr(),v,mpreal::get_default_rnd());\n  }else\n    throw conversion_overflow();\n#else\n  mpfr_set_d(mpfr_ptr(),v,mpreal::get_default_rnd());\n#endif\n\n  MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator=(const unsigned long int v)\n{\n    mpfr_set_ui(mpfr_ptr(), v, mpreal::get_default_rnd());\n\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator=(const unsigned int v)\n{\n    mpfr_set_ui(mpfr_ptr(), v, mpreal::get_default_rnd());\n\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator=(const unsigned long long int v)\n{\n    mpfr_set_uj(mpfr_ptr(), v, mpreal::get_default_rnd());\n\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator=(const long long int v)\n{\n    mpfr_set_sj(mpfr_ptr(), v, mpreal::get_default_rnd());\n\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator=(const long int v)\n{\n    mpfr_set_si(mpfr_ptr(), v, mpreal::get_default_rnd());\n\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator=(const int v)\n{\n    mpfr_set_si(mpfr_ptr(), v, mpreal::get_default_rnd());\n\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator=(const char* s)\n{\n    // Use other converters for more precise control on base & precision & rounding:\n    //\n    //        mpreal(const char* s,        mp_prec_t prec, int base, mp_rnd_t mode)\n    //        mpreal(const std::string& s,mp_prec_t prec, int base, mp_rnd_t mode)\n    //\n    // Here we assume base = 10 and we use precision of target variable.\n\n    mpfr_t t;\n\n    mpfr_init2(t, mpfr_get_prec(mpfr_srcptr()));\n\n    if(0 == mpfr_set_str(t, s, 10, mpreal::get_default_rnd()))\n    {\n        mpfr_set(mpfr_ptr(), t, mpreal::get_default_rnd());\n        MPREAL_MSVC_DEBUGVIEW_CODE;\n    }\n\n    clear(t);\n    return *this;\n}\n\ninline mpreal& mpreal::operator=(const std::string& s)\n{\n    // Use other converters for more precise control on base & precision & rounding:\n    //\n    //        mpreal(const char* s,        mp_prec_t prec, int base, mp_rnd_t mode)\n    //        mpreal(const std::string& s,mp_prec_t prec, int base, mp_rnd_t mode)\n    //\n    // Here we assume base = 10 and we use precision of target variable.\n\n    mpfr_t t;\n\n    mpfr_init2(t, mpfr_get_prec(mpfr_srcptr()));\n\n    if(0 == mpfr_set_str(t, s.c_str(), 10, mpreal::get_default_rnd()))\n    {\n        mpfr_set(mpfr_ptr(), t, mpreal::get_default_rnd());\n        MPREAL_MSVC_DEBUGVIEW_CODE;\n    }\n\n    clear(t);\n    return *this;\n}\n\ntemplate <typename real_t>\ninline mpreal& mpreal::operator= (const std::complex<real_t>& z)\n{\n    return *this = z.real();\n}\n\n//////////////////////////////////////////////////////////////////////////\n// + Addition\ninline mpreal& mpreal::operator+=(const mpreal& v)\n{\n    mpfr_add(mpfr_ptr(), mpfr_srcptr(), v.mpfr_srcptr(), mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator+=(const mpf_t u)\n{\n    *this += mpreal(u);\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator+=(const mpz_t u)\n{\n    mpfr_add_z(mpfr_ptr(),mpfr_srcptr(),u,mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator+=(const mpq_t u)\n{\n    mpfr_add_q(mpfr_ptr(),mpfr_srcptr(),u,mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator+= (const long double u)\n{\n    *this += mpreal(u);\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator+= (const double u)\n{\n#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))\n    mpfr_add_d(mpfr_ptr(),mpfr_srcptr(),u,mpreal::get_default_rnd());\n#else\n    *this += mpreal(u);\n#endif\n\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator+=(const unsigned long int u)\n{\n    mpfr_add_ui(mpfr_ptr(),mpfr_srcptr(),u,mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator+=(const unsigned int u)\n{\n    mpfr_add_ui(mpfr_ptr(),mpfr_srcptr(),u,mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator+=(const long int u)\n{\n    mpfr_add_si(mpfr_ptr(),mpfr_srcptr(),u,mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator+=(const int u)\n{\n    mpfr_add_si(mpfr_ptr(),mpfr_srcptr(),u,mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator+=(const long long int u)         {    *this += mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this;    }\ninline mpreal& mpreal::operator+=(const unsigned long long int u){    *this += mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this;    }\ninline mpreal& mpreal::operator-=(const long long int  u)        {    *this -= mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this;    }\ninline mpreal& mpreal::operator-=(const unsigned long long int u){    *this -= mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this;    }\ninline mpreal& mpreal::operator*=(const long long int  u)        {    *this *= mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this;    }\ninline mpreal& mpreal::operator*=(const unsigned long long int u){    *this *= mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this;    }\ninline mpreal& mpreal::operator/=(const long long int  u)        {    *this /= mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this;    }\ninline mpreal& mpreal::operator/=(const unsigned long long int u){    *this /= mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this;    }\n\ninline const mpreal mpreal::operator+()const    {    return mpreal(*this); }\n\ninline const mpreal operator+(const mpreal& a, const mpreal& b)\n{\n  mpreal c(0, (std::max)(mpfr_get_prec(a.mpfr_ptr()), mpfr_get_prec(b.mpfr_ptr())));\n  mpfr_add(c.mpfr_ptr(), a.mpfr_srcptr(), b.mpfr_srcptr(), mpreal::get_default_rnd());\n  return c;\n}\n\ninline mpreal& mpreal::operator++()\n{\n    return *this += 1;\n}\n\ninline const mpreal mpreal::operator++ (int)\n{\n    mpreal x(*this);\n    *this += 1;\n    return x;\n}\n\ninline mpreal& mpreal::operator--()\n{\n    return *this -= 1;\n}\n\ninline const mpreal mpreal::operator-- (int)\n{\n    mpreal x(*this);\n    *this -= 1;\n    return x;\n}\n\n//////////////////////////////////////////////////////////////////////////\n// - Subtraction\ninline mpreal& mpreal::operator-=(const mpreal& v)\n{\n    mpfr_sub(mpfr_ptr(),mpfr_srcptr(),v.mpfr_srcptr(),mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator-=(const mpz_t v)\n{\n    mpfr_sub_z(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator-=(const mpq_t v)\n{\n    mpfr_sub_q(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator-=(const long double v)\n{\n    *this -= mpreal(v);\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator-=(const double v)\n{\n#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))\n    mpfr_sub_d(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd());\n#else\n    *this -= mpreal(v);\n#endif\n\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator-=(const unsigned long int v)\n{\n    mpfr_sub_ui(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator-=(const unsigned int v)\n{\n    mpfr_sub_ui(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator-=(const long int v)\n{\n    mpfr_sub_si(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator-=(const int v)\n{\n    mpfr_sub_si(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline const mpreal mpreal::operator-()const\n{\n    mpreal u(*this);\n    mpfr_neg(u.mpfr_ptr(),u.mpfr_srcptr(),mpreal::get_default_rnd());\n    return u;\n}\n\ninline const mpreal operator-(const mpreal& a, const mpreal& b)\n{\n  mpreal c(0, (std::max)(mpfr_get_prec(a.mpfr_ptr()), mpfr_get_prec(b.mpfr_ptr())));\n  mpfr_sub(c.mpfr_ptr(), a.mpfr_srcptr(), b.mpfr_srcptr(), mpreal::get_default_rnd());\n  return c;\n}\n\ninline const mpreal operator-(const double  b, const mpreal& a)\n{\n#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))\n    mpreal x(0, mpfr_get_prec(a.mpfr_ptr()));\n    mpfr_d_sub(x.mpfr_ptr(), b, a.mpfr_srcptr(), mpreal::get_default_rnd());\n    return x;\n#else\n    mpreal x(b, mpfr_get_prec(a.mpfr_ptr()));\n    x -= a;\n    return x;\n#endif\n}\n\ninline const mpreal operator-(const unsigned long int b, const mpreal& a)\n{\n    mpreal x(0, mpfr_get_prec(a.mpfr_ptr()));\n    mpfr_ui_sub(x.mpfr_ptr(), b, a.mpfr_srcptr(), mpreal::get_default_rnd());\n    return x;\n}\n\ninline const mpreal operator-(const unsigned int b, const mpreal& a)\n{\n    mpreal x(0, mpfr_get_prec(a.mpfr_ptr()));\n    mpfr_ui_sub(x.mpfr_ptr(), b, a.mpfr_srcptr(), mpreal::get_default_rnd());\n    return x;\n}\n\ninline const mpreal operator-(const long int b, const mpreal& a)\n{\n    mpreal x(0, mpfr_get_prec(a.mpfr_ptr()));\n    mpfr_si_sub(x.mpfr_ptr(), b, a.mpfr_srcptr(), mpreal::get_default_rnd());\n    return x;\n}\n\ninline const mpreal operator-(const int b, const mpreal& a)\n{\n    mpreal x(0, mpfr_get_prec(a.mpfr_ptr()));\n    mpfr_si_sub(x.mpfr_ptr(), b, a.mpfr_srcptr(), mpreal::get_default_rnd());\n    return x;\n}\n\n//////////////////////////////////////////////////////////////////////////\n// * Multiplication\ninline mpreal& mpreal::operator*= (const mpreal& v)\n{\n    mpfr_mul(mpfr_ptr(),mpfr_srcptr(),v.mpfr_srcptr(),mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator*=(const mpz_t v)\n{\n    mpfr_mul_z(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator*=(const mpq_t v)\n{\n    mpfr_mul_q(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator*=(const long double v)\n{\n    *this *= mpreal(v);\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator*=(const double v)\n{\n#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))\n    mpfr_mul_d(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd());\n#else\n    *this *= mpreal(v);\n#endif\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator*=(const unsigned long int v)\n{\n    mpfr_mul_ui(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator*=(const unsigned int v)\n{\n    mpfr_mul_ui(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator*=(const long int v)\n{\n    mpfr_mul_si(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator*=(const int v)\n{\n    mpfr_mul_si(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline const mpreal operator*(const mpreal& a, const mpreal& b)\n{\n  mpreal c(0, (std::max)(mpfr_get_prec(a.mpfr_ptr()), mpfr_get_prec(b.mpfr_ptr())));\n  mpfr_mul(c.mpfr_ptr(), a.mpfr_srcptr(), b.mpfr_srcptr(), mpreal::get_default_rnd());\n  return c;\n}\n\n//////////////////////////////////////////////////////////////////////////\n// / Division\ninline mpreal& mpreal::operator/=(const mpreal& v)\n{\n    mpfr_div(mpfr_ptr(),mpfr_srcptr(),v.mpfr_srcptr(),mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator/=(const mpz_t v)\n{\n    mpfr_div_z(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator/=(const mpq_t v)\n{\n    mpfr_div_q(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator/=(const long double v)\n{\n    *this /= mpreal(v);\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator/=(const double v)\n{\n#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))\n    mpfr_div_d(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd());\n#else\n    *this /= mpreal(v);\n#endif\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator/=(const unsigned long int v)\n{\n    mpfr_div_ui(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator/=(const unsigned int v)\n{\n    mpfr_div_ui(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator/=(const long int v)\n{\n    mpfr_div_si(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator/=(const int v)\n{\n    mpfr_div_si(mpfr_ptr(),mpfr_srcptr(),v,mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline const mpreal operator/(const mpreal& a, const mpreal& b)\n{\n  mpreal c(0, (std::max)(mpfr_get_prec(a.mpfr_srcptr()), mpfr_get_prec(b.mpfr_srcptr())));\n  mpfr_div(c.mpfr_ptr(), a.mpfr_srcptr(), b.mpfr_srcptr(), mpreal::get_default_rnd());\n  return c;\n}\n\ninline const mpreal operator/(const unsigned long int b, const mpreal& a)\n{\n    mpreal x(0, mpfr_get_prec(a.mpfr_srcptr()));\n    mpfr_ui_div(x.mpfr_ptr(), b, a.mpfr_srcptr(), mpreal::get_default_rnd());\n    return x;\n}\n\ninline const mpreal operator/(const unsigned int b, const mpreal& a)\n{\n    mpreal x(0, mpfr_get_prec(a.mpfr_srcptr()));\n    mpfr_ui_div(x.mpfr_ptr(), b, a.mpfr_srcptr(), mpreal::get_default_rnd());\n    return x;\n}\n\ninline const mpreal operator/(const long int b, const mpreal& a)\n{\n    mpreal x(0, mpfr_get_prec(a.mpfr_srcptr()));\n    mpfr_si_div(x.mpfr_ptr(), b, a.mpfr_srcptr(), mpreal::get_default_rnd());\n    return x;\n}\n\ninline const mpreal operator/(const int b, const mpreal& a)\n{\n    mpreal x(0, mpfr_get_prec(a.mpfr_srcptr()));\n    mpfr_si_div(x.mpfr_ptr(), b, a.mpfr_srcptr(), mpreal::get_default_rnd());\n    return x;\n}\n\ninline const mpreal operator/(const double  b, const mpreal& a)\n{\n#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))\n    mpreal x(0, mpfr_get_prec(a.mpfr_srcptr()));\n    mpfr_d_div(x.mpfr_ptr(), b, a.mpfr_srcptr(), mpreal::get_default_rnd());\n    return x;\n#else\n    mpreal x(0, mpfr_get_prec(a.mpfr_ptr()));\n    x /= a;\n    return x;\n#endif\n}\n\n//////////////////////////////////////////////////////////////////////////\n// Shifts operators - Multiplication/Division by power of 2\ninline mpreal& mpreal::operator<<=(const unsigned long int u)\n{\n    mpfr_mul_2ui(mpfr_ptr(),mpfr_srcptr(),u,mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator<<=(const unsigned int u)\n{\n    mpfr_mul_2ui(mpfr_ptr(),mpfr_srcptr(),static_cast<unsigned long int>(u),mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator<<=(const long int u)\n{\n    mpfr_mul_2si(mpfr_ptr(),mpfr_srcptr(),u,mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator<<=(const int u)\n{\n    mpfr_mul_2si(mpfr_ptr(),mpfr_srcptr(),static_cast<long int>(u),mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator>>=(const unsigned long int u)\n{\n    mpfr_div_2ui(mpfr_ptr(),mpfr_srcptr(),u,mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator>>=(const unsigned int u)\n{\n    mpfr_div_2ui(mpfr_ptr(),mpfr_srcptr(),static_cast<unsigned long int>(u),mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator>>=(const long int u)\n{\n    mpfr_div_2si(mpfr_ptr(),mpfr_srcptr(),u,mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::operator>>=(const int u)\n{\n    mpfr_div_2si(mpfr_ptr(),mpfr_srcptr(),static_cast<long int>(u),mpreal::get_default_rnd());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline const mpreal operator<<(const mpreal& v, const unsigned long int k)\n{\n    return mul_2ui(v,k);\n}\n\ninline const mpreal operator<<(const mpreal& v, const unsigned int k)\n{\n    return mul_2ui(v,static_cast<unsigned long int>(k));\n}\n\ninline const mpreal operator<<(const mpreal& v, const long int k)\n{\n    return mul_2si(v,k);\n}\n\ninline const mpreal operator<<(const mpreal& v, const int k)\n{\n    return mul_2si(v,static_cast<long int>(k));\n}\n\ninline const mpreal operator>>(const mpreal& v, const unsigned long int k)\n{\n    return div_2ui(v,k);\n}\n\ninline const mpreal operator>>(const mpreal& v, const long int k)\n{\n    return div_2si(v,k);\n}\n\ninline const mpreal operator>>(const mpreal& v, const unsigned int k)\n{\n    return div_2ui(v,static_cast<unsigned long int>(k));\n}\n\ninline const mpreal operator>>(const mpreal& v, const int k)\n{\n    return div_2si(v,static_cast<long int>(k));\n}\n\n// mul_2ui\ninline const mpreal mul_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode)\n{\n    mpreal x(v);\n    mpfr_mul_2ui(x.mpfr_ptr(),v.mpfr_srcptr(),k,rnd_mode);\n    return x;\n}\n\n// mul_2si\ninline const mpreal mul_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode)\n{\n    mpreal x(v);\n    mpfr_mul_2si(x.mpfr_ptr(),v.mpfr_srcptr(),k,rnd_mode);\n    return x;\n}\n\ninline const mpreal div_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode)\n{\n    mpreal x(v);\n    mpfr_div_2ui(x.mpfr_ptr(),v.mpfr_srcptr(),k,rnd_mode);\n    return x;\n}\n\ninline const mpreal div_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode)\n{\n    mpreal x(v);\n    mpfr_div_2si(x.mpfr_ptr(),v.mpfr_srcptr(),k,rnd_mode);\n    return x;\n}\n\n//////////////////////////////////////////////////////////////////////////\n//Relational operators\n\n// WARNING:\n//\n// Please note that following checks for double-NaN are guaranteed to work only in IEEE math mode:\n//\n// isnan(b) =  (b != b)\n// isnan(b) = !(b == b)  (we use in code below)\n//\n// Be cautions if you use compiler options which break strict IEEE compliance (e.g. -ffast-math in GCC).\n// Use std::isnan instead (C++11).\n\ninline bool operator >  (const mpreal& a, const mpreal& b           ){  return (mpfr_greater_p(a.mpfr_srcptr(),b.mpfr_srcptr()) != 0 );            }\ninline bool operator >  (const mpreal& a, const unsigned long int b ){  return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_ui(a.mpfr_srcptr(),b) > 0 );                 }\ninline bool operator >  (const mpreal& a, const unsigned int b      ){  return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_ui(a.mpfr_srcptr(),b) > 0 );                 }\ninline bool operator >  (const mpreal& a, const long int b          ){  return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_si(a.mpfr_srcptr(),b) > 0 );                 }\ninline bool operator >  (const mpreal& a, const int b               ){  return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_si(a.mpfr_srcptr(),b) > 0 );                 }\ninline bool operator >  (const mpreal& a, const long double b       ){  return !isnan EIGEN_NOT_A_MACRO (a) && (b == b) && (mpfr_cmp_ld(a.mpfr_srcptr(),b) > 0 );    }\ninline bool operator >  (const mpreal& a, const double b            ){  return !isnan EIGEN_NOT_A_MACRO (a) && (b == b) && (mpfr_cmp_d (a.mpfr_srcptr(),b) > 0 );    }\n\ninline bool operator >= (const mpreal& a, const mpreal& b           ){  return (mpfr_greaterequal_p(a.mpfr_srcptr(),b.mpfr_srcptr()) != 0 );       }\ninline bool operator >= (const mpreal& a, const unsigned long int b ){  return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_ui(a.mpfr_srcptr(),b) >= 0 );                }\n// inline bool operator >= (const mpreal& a, const unsigned int b      ){  return !isnan EIGEN_NOT_A_MACRO (isnan()a) && (mpfr_cmp_ui(a.mpfr_srcptr(),b) >= 0 );                }\ninline bool operator >= (const mpreal& a, const long int b          ){  return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_si(a.mpfr_srcptr(),b) >= 0 );                }\ninline bool operator >= (const mpreal& a, const int b               ){  return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_si(a.mpfr_srcptr(),b) >= 0 );                }\ninline bool operator >= (const mpreal& a, const long double b       ){  return !isnan EIGEN_NOT_A_MACRO (a) && (b == b) && (mpfr_cmp_ld(a.mpfr_srcptr(),b) >= 0 );   }\ninline bool operator >= (const mpreal& a, const double b            ){  return !isnan EIGEN_NOT_A_MACRO (a) && (b == b) && (mpfr_cmp_d (a.mpfr_srcptr(),b) >= 0 );   }\n\ninline bool operator <  (const mpreal& a, const mpreal& b           ){  return (mpfr_less_p(a.mpfr_srcptr(),b.mpfr_srcptr()) != 0 );               }\ninline bool operator <  (const mpreal& a, const unsigned long int b ){  return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_ui(a.mpfr_srcptr(),b) < 0 );                 }\ninline bool operator <  (const mpreal& a, const unsigned int b      ){  return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_ui(a.mpfr_srcptr(),b) < 0 );                 }\ninline bool operator <  (const mpreal& a, const long int b          ){  return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_si(a.mpfr_srcptr(),b) < 0 );                 }\ninline bool operator <  (const mpreal& a, const int b               ){  return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_si(a.mpfr_srcptr(),b) < 0 );                 }\ninline bool operator <  (const mpreal& a, const long double b       ){  return !isnan EIGEN_NOT_A_MACRO (a) && (b == b) && (mpfr_cmp_ld(a.mpfr_srcptr(),b) < 0 );    }\ninline bool operator <  (const mpreal& a, const double b            ){  return !isnan EIGEN_NOT_A_MACRO (a) && (b == b) && (mpfr_cmp_d (a.mpfr_srcptr(),b) < 0 );    }\n\ninline bool operator <= (const mpreal& a, const mpreal& b           ){  return (mpfr_lessequal_p(a.mpfr_srcptr(),b.mpfr_srcptr()) != 0 );          }\ninline bool operator <= (const mpreal& a, const unsigned long int b ){  return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_ui(a.mpfr_srcptr(),b) <= 0 );                }\ninline bool operator <= (const mpreal& a, const unsigned int b      ){  return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_ui(a.mpfr_srcptr(),b) <= 0 );                }\ninline bool operator <= (const mpreal& a, const long int b          ){  return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_si(a.mpfr_srcptr(),b) <= 0 );                }\ninline bool operator <= (const mpreal& a, const int b               ){  return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_si(a.mpfr_srcptr(),b) <= 0 );                }\ninline bool operator <= (const mpreal& a, const long double b       ){  return !isnan EIGEN_NOT_A_MACRO (a) && (b == b) && (mpfr_cmp_ld(a.mpfr_srcptr(),b) <= 0 );   }\ninline bool operator <= (const mpreal& a, const double b            ){  return !isnan EIGEN_NOT_A_MACRO (a) && (b == b) && (mpfr_cmp_d (a.mpfr_srcptr(),b) <= 0 );   }\n\ninline bool operator == (const mpreal& a, const mpreal& b           ){  return (mpfr_equal_p(a.mpfr_srcptr(),b.mpfr_srcptr()) != 0 );              }\ninline bool operator == (const mpreal& a, const unsigned long int b ){  return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_ui(a.mpfr_srcptr(),b) == 0 );                }\ninline bool operator == (const mpreal& a, const unsigned int b      ){  return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_ui(a.mpfr_srcptr(),b) == 0 );                }\ninline bool operator == (const mpreal& a, const long int b          ){  return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_si(a.mpfr_srcptr(),b) == 0 );                }\ninline bool operator == (const mpreal& a, const int b               ){  return !isnan EIGEN_NOT_A_MACRO (a) && (mpfr_cmp_si(a.mpfr_srcptr(),b) == 0 );                }\ninline bool operator == (const mpreal& a, const long double b       ){  return !isnan EIGEN_NOT_A_MACRO (a) && (b == b) && (mpfr_cmp_ld(a.mpfr_srcptr(),b) == 0 );   }\ninline bool operator == (const mpreal& a, const double b            ){  return !isnan EIGEN_NOT_A_MACRO (a) && (b == b) && (mpfr_cmp_d (a.mpfr_srcptr(),b) == 0 );   }\n\ninline bool operator != (const mpreal& a, const mpreal& b           ){  return !(a == b);  }\ninline bool operator != (const mpreal& a, const unsigned long int b ){  return !(a == b);  }\ninline bool operator != (const mpreal& a, const unsigned int b      ){  return !(a == b);  }\ninline bool operator != (const mpreal& a, const long int b          ){  return !(a == b);  }\ninline bool operator != (const mpreal& a, const int b               ){  return !(a == b);  }\ninline bool operator != (const mpreal& a, const long double b       ){  return !(a == b);  }\ninline bool operator != (const mpreal& a, const double b            ){  return !(a == b);  }\n\ninline bool (isnan)    (const mpreal& op){    return (mpfr_nan_p    (op.mpfr_srcptr()) != 0 );    }\ninline bool (isinf)    (const mpreal& op){    return (mpfr_inf_p    (op.mpfr_srcptr()) != 0 );    }\ninline bool (isfinite) (const mpreal& op){    return (mpfr_number_p (op.mpfr_srcptr()) != 0 );    }\ninline bool iszero   (const mpreal& op){    return (mpfr_zero_p   (op.mpfr_srcptr()) != 0 );    }\ninline bool isint    (const mpreal& op){    return (mpfr_integer_p(op.mpfr_srcptr()) != 0 );    }\n\n#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,0,0))\ninline bool isregular(const mpreal& op){    return (mpfr_regular_p(op.mpfr_srcptr()));}\n#endif\n\n//////////////////////////////////////////////////////////////////////////\n// Type Converters\ninline bool               mpreal::toBool   (             )  const    {    return  mpfr_zero_p (mpfr_srcptr()) == 0;     }\ninline long               mpreal::toLong   (mp_rnd_t mode)  const    {    return  mpfr_get_si (mpfr_srcptr(), mode);    }\ninline unsigned long      mpreal::toULong  (mp_rnd_t mode)  const    {    return  mpfr_get_ui (mpfr_srcptr(), mode);    }\ninline float              mpreal::toFloat  (mp_rnd_t mode)  const    {    return  mpfr_get_flt(mpfr_srcptr(), mode);    }\ninline double             mpreal::toDouble (mp_rnd_t mode)  const    {    return  mpfr_get_d  (mpfr_srcptr(), mode);    }\ninline long double        mpreal::toLDouble(mp_rnd_t mode)  const    {    return  mpfr_get_ld (mpfr_srcptr(), mode);    }\ninline long long          mpreal::toLLong  (mp_rnd_t mode)  const    {    return  mpfr_get_sj (mpfr_srcptr(), mode);    }\ninline unsigned long long mpreal::toULLong (mp_rnd_t mode)  const    {    return  mpfr_get_uj (mpfr_srcptr(), mode);    }\n\ninline ::mpfr_ptr     mpreal::mpfr_ptr()             { return mp; }\ninline ::mpfr_srcptr  mpreal::mpfr_ptr()    const    { return mp; }\ninline ::mpfr_srcptr  mpreal::mpfr_srcptr() const    { return mp; }\n\ntemplate <class T>\ninline std::string toString(T t, std::ios_base & (*f)(std::ios_base&))\n{\n    std::ostringstream oss;\n    oss << f << t;\n    return oss.str();\n}\n\n#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))\n\ninline std::string mpreal::toString(const std::string& format) const\n{\n    char *s = NULL;\n    std::string out;\n\n    if( !format.empty() )\n    {\n        if(!(mpfr_asprintf(&s, format.c_str(), mpfr_srcptr()) < 0))\n        {\n            out = std::string(s);\n\n            mpfr_free_str(s);\n        }\n    }\n\n    return out;\n}\n\n#endif\n\ninline std::string mpreal::toString(int n, int b, mp_rnd_t mode) const\n{\n    // TODO: Add extended format specification (f, e, rounding mode) as it done in output operator\n    (void)b;\n    (void)mode;\n\n#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))\n\n    std::ostringstream format;\n\n    int digits = (n >= 0) ? n : 1 + bits2digits(mpfr_get_prec(mpfr_srcptr()));\n\n    format << \"%.\" << digits << \"RNg\";\n\n    return toString(format.str());\n\n#else\n\n    char *s, *ns = NULL;\n    size_t slen, nslen;\n    mp_exp_t exp;\n    std::string out;\n\n    if(mpfr_inf_p(mp))\n    {\n        if(mpfr_sgn(mp)>0) return \"+Inf\";\n        else               return \"-Inf\";\n    }\n\n    if(mpfr_zero_p(mp)) return \"0\";\n    if(mpfr_nan_p(mp))  return \"NaN\";\n\n    s  = mpfr_get_str(NULL, &exp, b, 0, mp, mode);\n    ns = mpfr_get_str(NULL, &exp, b, (std::max)(0,n), mp, mode);\n\n    if(s!=NULL && ns!=NULL)\n    {\n        slen  = strlen(s);\n        nslen = strlen(ns);\n        if(nslen<=slen)\n        {\n            mpfr_free_str(s);\n            s = ns;\n            slen = nslen;\n        }\n        else {\n            mpfr_free_str(ns);\n        }\n\n        // Make human eye-friendly formatting if possible\n        if (exp>0 && static_cast<size_t>(exp)<slen)\n        {\n            if(s[0]=='-')\n            {\n                // Remove zeros starting from right end\n                char* ptr = s+slen-1;\n                while (*ptr=='0' && ptr>s+exp) ptr--;\n\n                if(ptr==s+exp) out = std::string(s,exp+1);\n                else           out = std::string(s,exp+1)+'.'+std::string(s+exp+1,ptr-(s+exp+1)+1);\n\n                //out = string(s,exp+1)+'.'+string(s+exp+1);\n            }\n            else\n            {\n                // Remove zeros starting from right end\n                char* ptr = s+slen-1;\n                while (*ptr=='0' && ptr>s+exp-1) ptr--;\n\n                if(ptr==s+exp-1) out = std::string(s,exp);\n                else             out = std::string(s,exp)+'.'+std::string(s+exp,ptr-(s+exp)+1);\n\n                //out = string(s,exp)+'.'+string(s+exp);\n            }\n\n        }else{ // exp<0 || exp>slen\n            if(s[0]=='-')\n            {\n                // Remove zeros starting from right end\n                char* ptr = s+slen-1;\n                while (*ptr=='0' && ptr>s+1) ptr--;\n\n                if(ptr==s+1) out = std::string(s,2);\n                else         out = std::string(s,2)+'.'+std::string(s+2,ptr-(s+2)+1);\n\n                //out = string(s,2)+'.'+string(s+2);\n            }\n            else\n            {\n                // Remove zeros starting from right end\n                char* ptr = s+slen-1;\n                while (*ptr=='0' && ptr>s) ptr--;\n\n                if(ptr==s) out = std::string(s,1);\n                else       out = std::string(s,1)+'.'+std::string(s+1,ptr-(s+1)+1);\n\n                //out = string(s,1)+'.'+string(s+1);\n            }\n\n            // Make final string\n            if(--exp)\n            {\n                if(exp>0) out += \"e+\"+mpfr::toString<mp_exp_t>(exp,std::dec);\n                else       out += \"e\"+mpfr::toString<mp_exp_t>(exp,std::dec);\n            }\n        }\n\n        mpfr_free_str(s);\n        return out;\n    }else{\n        return \"conversion error!\";\n    }\n#endif\n}\n\n\n//////////////////////////////////////////////////////////////////////////\n// I/O\ninline std::ostream& mpreal::output(std::ostream& os) const\n{\n    std::ostringstream format;\n    const std::ios::fmtflags flags = os.flags();\n\n    format << ((flags & std::ios::showpos) ? \"%+\" : \"%\");\n    if (os.precision() >= 0)\n        format << '.' << os.precision() << \"R*\"\n               << ((flags & std::ios::floatfield) == std::ios::fixed ? 'f' :\n                   (flags & std::ios::floatfield) == std::ios::scientific ? 'e' :\n                   'g');\n    else\n        format << \"R*e\";\n\n    char *s = NULL;\n    if(!(mpfr_asprintf(&s, format.str().c_str(),\n                        mpfr::mpreal::get_default_rnd(),\n                        mpfr_srcptr())\n        < 0))\n    {\n        os << std::string(s);\n        mpfr_free_str(s);\n    }\n    return os;\n}\n\ninline std::ostream& operator<<(std::ostream& os, const mpreal& v)\n{\n    return v.output(os);\n}\n\ninline std::istream& operator>>(std::istream &is, mpreal& v)\n{\n    // TODO: use cout::hexfloat and other flags to setup base\n    std::string tmp;\n    is >> tmp;\n    mpfr_set_str(v.mpfr_ptr(), tmp.c_str(), 10, mpreal::get_default_rnd());\n    return is;\n}\n\n//////////////////////////////////////////////////////////////////////////\n//     Bits - decimal digits relation\n//        bits   = ceil(digits*log[2](10))\n//        digits = floor(bits*log[10](2))\n\ninline mp_prec_t digits2bits(int d)\n{\n    const double LOG2_10 = 3.3219280948873624;\n\n    return mp_prec_t(std::ceil( d * LOG2_10 ));\n}\n\ninline int bits2digits(mp_prec_t b)\n{\n    const double LOG10_2 = 0.30102999566398119;\n\n    return int(std::floor( b * LOG10_2 ));\n}\n\n//////////////////////////////////////////////////////////////////////////\n// Set/Get number properties\ninline int sgn(const mpreal& op)\n{\n    return mpfr_sgn(op.mpfr_srcptr());\n}\n\ninline mpreal& mpreal::setSign(int sign, mp_rnd_t RoundingMode)\n{\n    mpfr_setsign(mpfr_ptr(), mpfr_srcptr(), (sign < 0 ? 1 : 0), RoundingMode);\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline int mpreal::getPrecision() const\n{\n    return int(mpfr_get_prec(mpfr_srcptr()));\n}\n\ninline mpreal& mpreal::setPrecision(int Precision, mp_rnd_t RoundingMode)\n{\n    mpfr_prec_round(mpfr_ptr(), Precision, RoundingMode);\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::setInf(int sign)\n{\n    mpfr_set_inf(mpfr_ptr(), sign);\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::setNan()\n{\n    mpfr_set_nan(mpfr_ptr());\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mpreal& mpreal::setZero(int sign)\n{\n#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,0,0))\n    mpfr_set_zero(mpfr_ptr(), sign);\n#else\n    mpfr_set_si(mpfr_ptr(), 0, (mpfr_get_default_rounding_mode)());\n    setSign(sign);\n#endif\n\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return *this;\n}\n\ninline mp_prec_t mpreal::get_prec() const\n{\n    return mpfr_get_prec(mpfr_srcptr());\n}\n\ninline void mpreal::set_prec(mp_prec_t prec, mp_rnd_t rnd_mode)\n{\n    mpfr_prec_round(mpfr_ptr(),prec,rnd_mode);\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n}\n\ninline mp_exp_t mpreal::get_exp ()\n{\n    return mpfr_get_exp(mpfr_srcptr());\n}\n\ninline int mpreal::set_exp (mp_exp_t e)\n{\n    int x = mpfr_set_exp(mpfr_ptr(), e);\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return x;\n}\n\ninline const mpreal frexp(const mpreal& x, mp_exp_t* exp, mp_rnd_t mode = mpreal::get_default_rnd())\n{\n    mpreal y(x);\n#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,1,0))\n    mpfr_frexp(exp,y.mpfr_ptr(),x.mpfr_srcptr(),mode);\n#else\n    *exp = mpfr_get_exp(y.mpfr_srcptr());\n    mpfr_set_exp(y.mpfr_ptr(),0);\n#endif\n    return y;\n}\n\ninline const mpreal ldexp(const mpreal& v, mp_exp_t exp)\n{\n    mpreal x(v);\n\n    // rounding is not important since we are just increasing the exponent (= exact operation)\n    mpfr_mul_2si(x.mpfr_ptr(), x.mpfr_srcptr(), exp, mpreal::get_default_rnd());\n    return x;\n}\n\ninline const mpreal scalbn(const mpreal& v, mp_exp_t exp)\n{\n    return ldexp(v, exp);\n}\n\ninline mpreal machine_epsilon(mp_prec_t prec)\n{\n    /* the smallest eps such that 1 + eps != 1 */\n    return machine_epsilon(mpreal(1, prec));\n}\n\ninline mpreal machine_epsilon(const mpreal& x)\n{\n    /* the smallest eps such that x + eps != x */\n    if( x < 0)\n    {\n        return nextabove(-x) + x;\n    }else{\n        return nextabove( x) - x;\n    }\n}\n\n// minval is 'safe' meaning 1 / minval does not overflow\ninline mpreal minval(mp_prec_t prec)\n{\n    /* min = 1/2 * 2^emin = 2^(emin - 1) */\n    return mpreal(1, prec) << mpreal::get_emin()-1;\n}\n\n// maxval is 'safe' meaning 1 / maxval does not underflow\ninline mpreal maxval(mp_prec_t prec)\n{\n    /* max = (1 - eps) * 2^emax, eps is machine epsilon */\n    return (mpreal(1, prec) - machine_epsilon(prec)) << mpreal::get_emax();\n}\n\ninline bool isEqualUlps(const mpreal& a, const mpreal& b, int maxUlps)\n{\n    return abs(a - b) <= machine_epsilon((max)(abs(a), abs(b))) * maxUlps;\n}\n\ninline bool isEqualFuzzy(const mpreal& a, const mpreal& b, const mpreal& eps)\n{\n    return abs(a - b) <= eps;\n}\n\ninline bool isEqualFuzzy(const mpreal& a, const mpreal& b)\n{\n    return isEqualFuzzy(a, b, machine_epsilon((max)(1, (min)(abs(a), abs(b)))));\n}\n\n//////////////////////////////////////////////////////////////////////////\n// C++11 sign functions.\ninline mpreal copysign(const mpreal& x, const  mpreal& y, mp_rnd_t rnd_mode = mpreal::get_default_rnd())\n{\n    mpreal rop(0, mpfr_get_prec(x.mpfr_ptr()));\n    mpfr_setsign(rop.mpfr_ptr(), x.mpfr_srcptr(), mpfr_signbit(y.mpfr_srcptr()), rnd_mode);\n    return rop;\n}\n\ninline bool signbit(const mpreal& x)\n{\n    return mpfr_signbit(x.mpfr_srcptr());\n}\n\ninline const mpreal modf(const mpreal& v, mpreal& n)\n{\n    mpreal f(v);\n\n    // rounding is not important since we are using the same number\n    mpfr_frac (f.mpfr_ptr(),f.mpfr_srcptr(),mpreal::get_default_rnd());\n    mpfr_trunc(n.mpfr_ptr(),v.mpfr_srcptr());\n    return f;\n}\n\ninline int mpreal::check_range (int t, mp_rnd_t rnd_mode)\n{\n    return mpfr_check_range(mpfr_ptr(),t,rnd_mode);\n}\n\ninline int mpreal::subnormalize (int t,mp_rnd_t rnd_mode)\n{\n    int r = mpfr_subnormalize(mpfr_ptr(),t,rnd_mode);\n    MPREAL_MSVC_DEBUGVIEW_CODE;\n    return r;\n}\n\ninline mp_exp_t mpreal::get_emin (void)\n{\n    return mpfr_get_emin();\n}\n\ninline int mpreal::set_emin (mp_exp_t exp)\n{\n    return mpfr_set_emin(exp);\n}\n\ninline mp_exp_t mpreal::get_emax (void)\n{\n    return mpfr_get_emax();\n}\n\ninline int mpreal::set_emax (mp_exp_t exp)\n{\n    return mpfr_set_emax(exp);\n}\n\ninline mp_exp_t mpreal::get_emin_min (void)\n{\n    return mpfr_get_emin_min();\n}\n\ninline mp_exp_t mpreal::get_emin_max (void)\n{\n    return mpfr_get_emin_max();\n}\n\ninline mp_exp_t mpreal::get_emax_min (void)\n{\n    return mpfr_get_emax_min();\n}\n\ninline mp_exp_t mpreal::get_emax_max (void)\n{\n    return mpfr_get_emax_max();\n}\n\n//////////////////////////////////////////////////////////////////////////\n// Mathematical Functions\n//////////////////////////////////////////////////////////////////////////\n#define MPREAL_UNARY_MATH_FUNCTION_BODY(f)                    \\\n        mpreal y(0, mpfr_get_prec(x.mpfr_srcptr()));          \\\n        mpfr_##f(y.mpfr_ptr(), x.mpfr_srcptr(), r);           \\\n        return y;\n\ninline const mpreal sqr  (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd())\n{   MPREAL_UNARY_MATH_FUNCTION_BODY(sqr );    }\n\ninline const mpreal sqrt (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd())\n{   MPREAL_UNARY_MATH_FUNCTION_BODY(sqrt);    }\n\ninline const mpreal sqrt(const unsigned long int x, mp_rnd_t r)\n{\n    mpreal y;\n    mpfr_sqrt_ui(y.mpfr_ptr(), x, r);\n    return y;\n}\n\ninline const mpreal sqrt(const unsigned int v, mp_rnd_t rnd_mode)\n{\n    return sqrt(static_cast<unsigned long int>(v),rnd_mode);\n}\n\ninline const mpreal sqrt(const long int v, mp_rnd_t rnd_mode)\n{\n    if (v>=0)   return sqrt(static_cast<unsigned long int>(v),rnd_mode);\n    else        return mpreal().setNan(); // NaN\n}\n\ninline const mpreal sqrt(const int v, mp_rnd_t rnd_mode)\n{\n    if (v>=0)   return sqrt(static_cast<unsigned long int>(v),rnd_mode);\n    else        return mpreal().setNan(); // NaN\n}\n\ninline const mpreal root(const mpreal& x, unsigned long int k, mp_rnd_t r = mpreal::get_default_rnd())\n{\n    mpreal y(0, mpfr_get_prec(x.mpfr_srcptr()));\n    mpfr_root(y.mpfr_ptr(), x.mpfr_srcptr(), k, r);\n    return y;\n}\n\ninline const mpreal dim(const mpreal& a, const mpreal& b, mp_rnd_t r = mpreal::get_default_rnd())\n{\n    mpreal y(0, mpfr_get_prec(a.mpfr_srcptr()));\n    mpfr_dim(y.mpfr_ptr(), a.mpfr_srcptr(), b.mpfr_srcptr(), r);\n    return y;\n}\n\ninline int cmpabs(const mpreal& a,const mpreal& b)\n{\n    return mpfr_cmpabs(a.mpfr_ptr(), b.mpfr_srcptr());\n}\n\ninline int sin_cos(mpreal& s, mpreal& c, const mpreal& v, mp_rnd_t rnd_mode = mpreal::get_default_rnd())\n{\n    return mpfr_sin_cos(s.mpfr_ptr(), c.mpfr_ptr(), v.mpfr_srcptr(), rnd_mode);\n}\n\ninline const mpreal sqrt  (const long double v, mp_rnd_t rnd_mode)    {   return sqrt(mpreal(v),rnd_mode);    }\ninline const mpreal sqrt  (const double v, mp_rnd_t rnd_mode)         {   return sqrt(mpreal(v),rnd_mode);    }\n\ninline const mpreal cbrt  (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(cbrt );    }\ninline const mpreal fabs  (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(abs  );    }\ninline const mpreal abs   (const mpreal& x, mp_rnd_t r)                             {   MPREAL_UNARY_MATH_FUNCTION_BODY(abs  );    }\ninline const mpreal log   (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(log  );    }\ninline const mpreal log2  (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(log2 );    }\ninline const mpreal log10 (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(log10);    }\ninline const mpreal exp   (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(exp  );    }\ninline const mpreal exp2  (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(exp2 );    }\ninline const mpreal exp10 (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(exp10);    }\ninline const mpreal cos   (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(cos  );    }\ninline const mpreal sin   (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(sin  );    }\ninline const mpreal tan   (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(tan  );    }\ninline const mpreal sec   (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(sec  );    }\ninline const mpreal csc   (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(csc  );    }\ninline const mpreal cot   (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(cot  );    }\ninline const mpreal acos  (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(acos );    }\ninline const mpreal asin  (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(asin );    }\ninline const mpreal atan  (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(atan );    }\n\ninline const mpreal logb  (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   return log2 (abs(x),r);                    }\n\ninline const mpreal acot  (const mpreal& v, mp_rnd_t r = mpreal::get_default_rnd()) {   return atan (1/v, r);                      }\ninline const mpreal asec  (const mpreal& v, mp_rnd_t r = mpreal::get_default_rnd()) {   return acos (1/v, r);                      }\ninline const mpreal acsc  (const mpreal& v, mp_rnd_t r = mpreal::get_default_rnd()) {   return asin (1/v, r);                      }\ninline const mpreal acoth (const mpreal& v, mp_rnd_t r = mpreal::get_default_rnd()) {   return atanh(1/v, r);                      }\ninline const mpreal asech (const mpreal& v, mp_rnd_t r = mpreal::get_default_rnd()) {   return acosh(1/v, r);                      }\ninline const mpreal acsch (const mpreal& v, mp_rnd_t r = mpreal::get_default_rnd()) {   return asinh(1/v, r);                      }\n\ninline const mpreal cosh  (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(cosh );    }\ninline const mpreal sinh  (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(sinh );    }\ninline const mpreal tanh  (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(tanh );    }\ninline const mpreal sech  (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(sech );    }\ninline const mpreal csch  (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(csch );    }\ninline const mpreal coth  (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(coth );    }\ninline const mpreal acosh (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(acosh);    }\ninline const mpreal asinh (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(asinh);    }\ninline const mpreal atanh (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(atanh);    }\n\ninline const mpreal log1p   (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(log1p  );    }\ninline const mpreal expm1   (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(expm1  );    }\ninline const mpreal eint    (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(eint   );    }\ninline const mpreal gamma   (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(gamma  );    }\ninline const mpreal tgamma  (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(gamma  );    }\ninline const mpreal lngamma (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(lngamma);    }\ninline const mpreal zeta    (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(zeta   );    }\ninline const mpreal erf     (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(erf    );    }\ninline const mpreal erfc    (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(erfc   );    }\ninline const mpreal besselj0(const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(j0     );    }\ninline const mpreal besselj1(const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(j1     );    }\ninline const mpreal bessely0(const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(y0     );    }\ninline const mpreal bessely1(const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(y1     );    }\n\ninline const mpreal atan2 (const mpreal& y, const mpreal& x, mp_rnd_t rnd_mode = mpreal::get_default_rnd())\n{\n    mpreal a(0,(std::max)(y.getPrecision(), x.getPrecision()));\n    mpfr_atan2(a.mpfr_ptr(), y.mpfr_srcptr(), x.mpfr_srcptr(), rnd_mode);\n    return a;\n}\n\ninline const mpreal hypot (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::get_default_rnd())\n{\n    mpreal a(0,(std::max)(y.getPrecision(), x.getPrecision()));\n    mpfr_hypot(a.mpfr_ptr(), x.mpfr_srcptr(), y.mpfr_srcptr(), rnd_mode);\n    return a;\n}\n\ninline const mpreal remainder (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::get_default_rnd())\n{\n    mpreal a(0,(std::max)(y.getPrecision(), x.getPrecision()));\n    mpfr_remainder(a.mpfr_ptr(), x.mpfr_srcptr(), y.mpfr_srcptr(), rnd_mode);\n    return a;\n}\n\ninline const mpreal remquo (long* q, const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::get_default_rnd())\n{\n    mpreal a(0,(std::max)(y.getPrecision(), x.getPrecision()));\n    mpfr_remquo(a.mpfr_ptr(),q, x.mpfr_srcptr(), y.mpfr_srcptr(), rnd_mode);\n    return a;\n}\n\ninline const mpreal fac_ui (unsigned long int v, mp_prec_t prec     = mpreal::get_default_prec(),\n                                           mp_rnd_t  rnd_mode = mpreal::get_default_rnd())\n{\n    mpreal x(0, prec);\n    mpfr_fac_ui(x.mpfr_ptr(),v,rnd_mode);\n    return x;\n}\n\n\ninline const mpreal lgamma (const mpreal& v, int *signp = 0, mp_rnd_t rnd_mode = mpreal::get_default_rnd())\n{\n    mpreal x(v);\n    int tsignp;\n\n    if(signp)   mpfr_lgamma(x.mpfr_ptr(),  signp,v.mpfr_srcptr(),rnd_mode);\n    else        mpfr_lgamma(x.mpfr_ptr(),&tsignp,v.mpfr_srcptr(),rnd_mode);\n\n    return x;\n}\n\n\ninline const mpreal besseljn (long n, const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd())\n{\n    mpreal  y(0, x.getPrecision());\n    mpfr_jn(y.mpfr_ptr(), n, x.mpfr_srcptr(), r);\n    return y;\n}\n\ninline const mpreal besselyn (long n, const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd())\n{\n    mpreal  y(0, x.getPrecision());\n    mpfr_yn(y.mpfr_ptr(), n, x.mpfr_srcptr(), r);\n    return y;\n}\n\ninline const mpreal fma (const mpreal& v1, const mpreal& v2, const mpreal& v3, mp_rnd_t rnd_mode = mpreal::get_default_rnd())\n{\n    mpreal a;\n    mp_prec_t p1, p2, p3;\n\n    p1 = v1.get_prec();\n    p2 = v2.get_prec();\n    p3 = v3.get_prec();\n\n    a.set_prec(p3>p2?(p3>p1?p3:p1):(p2>p1?p2:p1));\n\n    mpfr_fma(a.mp,v1.mp,v2.mp,v3.mp,rnd_mode);\n    return a;\n}\n\ninline const mpreal fms (const mpreal& v1, const mpreal& v2, const mpreal& v3, mp_rnd_t rnd_mode = mpreal::get_default_rnd())\n{\n    mpreal a;\n    mp_prec_t p1, p2, p3;\n\n    p1 = v1.get_prec();\n    p2 = v2.get_prec();\n    p3 = v3.get_prec();\n\n    a.set_prec(p3>p2?(p3>p1?p3:p1):(p2>p1?p2:p1));\n\n    mpfr_fms(a.mp,v1.mp,v2.mp,v3.mp,rnd_mode);\n    return a;\n}\n\ninline const mpreal agm (const mpreal& v1, const mpreal& v2, mp_rnd_t rnd_mode = mpreal::get_default_rnd())\n{\n    mpreal a;\n    mp_prec_t p1, p2;\n\n    p1 = v1.get_prec();\n    p2 = v2.get_prec();\n\n    a.set_prec(p1>p2?p1:p2);\n\n    mpfr_agm(a.mp, v1.mp, v2.mp, rnd_mode);\n\n    return a;\n}\n\ninline const mpreal sum (const mpreal tab[], const unsigned long int n, int& status, mp_rnd_t mode = mpreal::get_default_rnd())\n{\n    mpfr_srcptr *p = new mpfr_srcptr[n];\n\n    for (unsigned long int  i = 0; i < n; i++)\n        p[i] = tab[i].mpfr_srcptr();\n\n    mpreal x;\n    status = mpfr_sum(x.mpfr_ptr(), (mpfr_ptr*)p, n, mode);\n\n    delete [] p;\n    return x;\n}\n\n//////////////////////////////////////////////////////////////////////////\n// MPFR 2.4.0 Specifics\n#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))\n\ninline int sinh_cosh(mpreal& s, mpreal& c, const mpreal& v, mp_rnd_t rnd_mode = mpreal::get_default_rnd())\n{\n    return mpfr_sinh_cosh(s.mp,c.mp,v.mp,rnd_mode);\n}\n\ninline const mpreal li2 (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd())\n{\n    MPREAL_UNARY_MATH_FUNCTION_BODY(li2);\n}\n\ninline const mpreal rem (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::get_default_rnd())\n{\n    /*  R = rem(X,Y) if Y != 0, returns X - n * Y where n = trunc(X/Y). */\n    return fmod(x, y, rnd_mode);\n}\n\ninline const mpreal mod (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::get_default_rnd())\n{\n    (void)rnd_mode;\n\n    /*\n\n    m = mod(x,y) if y != 0, returns x - n*y where n = floor(x/y)\n\n    The following are true by convention:\n    - mod(x,0) is x\n    - mod(x,x) is 0\n    - mod(x,y) for x != y and y != 0 has the same sign as y.\n\n    */\n\n    if(iszero(y)) return x;\n    if(x == y) return 0;\n\n    mpreal m = x - floor(x / y) * y;\n\n    m.setSign(sgn(y)); // make sure result has the same sign as Y\n\n    return m;\n}\n\ninline const mpreal fmod (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::get_default_rnd())\n{\n    mpreal a;\n    mp_prec_t yp, xp;\n\n    yp = y.get_prec();\n    xp = x.get_prec();\n\n    a.set_prec(yp>xp?yp:xp);\n\n    mpfr_fmod(a.mp, x.mp, y.mp, rnd_mode);\n\n    return a;\n}\n\ninline const mpreal rec_sqrt(const mpreal& v, mp_rnd_t rnd_mode = mpreal::get_default_rnd())\n{\n    mpreal x(v);\n    mpfr_rec_sqrt(x.mp,v.mp,rnd_mode);\n    return x;\n}\n#endif //  MPFR 2.4.0 Specifics\n\n//////////////////////////////////////////////////////////////////////////\n// MPFR 3.0.0 Specifics\n#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,0,0))\ninline const mpreal digamma (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(digamma);     }\ninline const mpreal ai      (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(ai);          }\n#endif // MPFR 3.0.0 Specifics\n\n//////////////////////////////////////////////////////////////////////////\n// Constants\ninline const mpreal const_log2 (mp_prec_t p = mpreal::get_default_prec(), mp_rnd_t r = mpreal::get_default_rnd())\n{\n    mpreal x(0, p);\n    mpfr_const_log2(x.mpfr_ptr(), r);\n    return x;\n}\n\ninline const mpreal const_pi (mp_prec_t p = mpreal::get_default_prec(), mp_rnd_t r = mpreal::get_default_rnd())\n{\n    mpreal x(0, p);\n    mpfr_const_pi(x.mpfr_ptr(), r);\n    return x;\n}\n\ninline const mpreal const_euler (mp_prec_t p = mpreal::get_default_prec(), mp_rnd_t r = mpreal::get_default_rnd())\n{\n    mpreal x(0, p);\n    mpfr_const_euler(x.mpfr_ptr(), r);\n    return x;\n}\n\ninline const mpreal const_catalan (mp_prec_t p = mpreal::get_default_prec(), mp_rnd_t r = mpreal::get_default_rnd())\n{\n    mpreal x(0, p);\n    mpfr_const_catalan(x.mpfr_ptr(), r);\n    return x;\n}\n\ninline const mpreal const_infinity (int sign = 1, mp_prec_t p = mpreal::get_default_prec())\n{\n    mpreal x(0, p);\n    mpfr_set_inf(x.mpfr_ptr(), sign);\n    return x;\n}\n\n//////////////////////////////////////////////////////////////////////////\n// Integer Related Functions\ninline const mpreal ceil(const mpreal& v)\n{\n    mpreal x(v);\n    mpfr_ceil(x.mp,v.mp);\n    return x;\n}\n\ninline const mpreal floor(const mpreal& v)\n{\n    mpreal x(v);\n    mpfr_floor(x.mp,v.mp);\n    return x;\n}\n\ninline const mpreal round(const mpreal& v)\n{\n    mpreal x(v);\n    mpfr_round(x.mp,v.mp);\n    return x;\n}\n\ninline const mpreal trunc(const mpreal& v)\n{\n    mpreal x(v);\n    mpfr_trunc(x.mp,v.mp);\n    return x;\n}\n\ninline const mpreal rint       (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(rint      );     }\ninline const mpreal rint_ceil  (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(rint_ceil );     }\ninline const mpreal rint_floor (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(rint_floor);     }\ninline const mpreal rint_round (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(rint_round);     }\ninline const mpreal rint_trunc (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(rint_trunc);     }\ninline const mpreal frac       (const mpreal& x, mp_rnd_t r = mpreal::get_default_rnd()) {   MPREAL_UNARY_MATH_FUNCTION_BODY(frac      );     }\n\n//////////////////////////////////////////////////////////////////////////\n// Miscellaneous Functions\ninline void         swap (mpreal& a, mpreal& b)            {    mpfr_swap(a.mp,b.mp);   }\ninline const mpreal (max)(const mpreal& x, const mpreal& y){    return (x>y?x:y);       }\ninline const mpreal (min)(const mpreal& x, const mpreal& y){    return (x<y?x:y);       }\n\ninline const mpreal fmax(const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::get_default_rnd())\n{\n    mpreal a;\n    mpfr_max(a.mp,x.mp,y.mp,rnd_mode);\n    return a;\n}\n\ninline const mpreal fmin(const mpreal& x, const mpreal& y,  mp_rnd_t rnd_mode = mpreal::get_default_rnd())\n{\n    mpreal a;\n    mpfr_min(a.mp,x.mp,y.mp,rnd_mode);\n    return a;\n}\n\ninline const mpreal nexttoward (const mpreal& x, const mpreal& y)\n{\n    mpreal a(x);\n    mpfr_nexttoward(a.mp,y.mp);\n    return a;\n}\n\ninline const mpreal nextabove  (const mpreal& x)\n{\n    mpreal a(x);\n    mpfr_nextabove(a.mp);\n    return a;\n}\n\ninline const mpreal nextbelow  (const mpreal& x)\n{\n    mpreal a(x);\n    mpfr_nextbelow(a.mp);\n    return a;\n}\n\ninline const mpreal urandomb (gmp_randstate_t& state)\n{\n    mpreal x;\n    mpfr_urandomb(x.mpfr_ptr(),state);\n    return x;\n}\n\n#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,0,0))\ninline const mpreal urandom (gmp_randstate_t& state, mp_rnd_t rnd_mode = mpreal::get_default_rnd())\n{\n    mpreal x;\n    mpfr_urandom(x.mpfr_ptr(), state, rnd_mode);\n    return x;\n}\n#endif\n\n#if (MPFR_VERSION <= MPFR_VERSION_NUM(2,4,2))\ninline const mpreal random2 (mp_size_t size, mp_exp_t exp)\n{\n    mpreal x;\n    mpfr_random2(x.mpfr_ptr(),size,exp);\n    return x;\n}\n#endif\n\n// Uniformly distributed random number generation\n// a = random(seed); <- initialization & first random number generation\n// a = random();     <- next random numbers generation\n// seed != 0\ninline const mpreal random(unsigned int seed = 0)\n{\n#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,0,0))\n    static gmp_randstate_t state;\n    static bool initialize = true;\n\n    if(initialize)\n    {\n        gmp_randinit_default(state);\n        gmp_randseed_ui(state,0);\n        initialize = false;\n    }\n\n    if(seed != 0)    gmp_randseed_ui(state,seed);\n\n    return mpfr::urandom(state);\n#else\n    if(seed != 0)    std::srand(seed);\n    return mpfr::mpreal(std::rand()/(double)RAND_MAX);\n#endif\n\n}\n\n#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,1,0))\n\ninline const mpreal grandom (gmp_randstate_t& state, mp_rnd_t rnd_mode = mpreal::get_default_rnd())\n{\n    mpreal x;\n    mpfr_grandom(x.mpfr_ptr(), NULL, state, rnd_mode);\n    return x;\n}\n\ninline const mpreal grandom(unsigned int seed = 0)\n{\n    static gmp_randstate_t state;\n    static bool initialize = true;\n\n    if(initialize)\n    {\n        gmp_randinit_default(state);\n        gmp_randseed_ui(state,0);\n        initialize = false;\n    }\n\n    if(seed != 0) gmp_randseed_ui(state,seed);\n\n    return mpfr::grandom(state);\n}\n#endif\n\n//////////////////////////////////////////////////////////////////////////\n// Set/Get global properties\ninline void mpreal::set_default_prec(mp_prec_t prec)\n{\n    mpfr_set_default_prec(prec);\n}\n\ninline void mpreal::set_default_rnd(mp_rnd_t rnd_mode)\n{\n    mpfr_set_default_rounding_mode(rnd_mode);\n}\n\ninline bool mpreal::fits_in_bits(double x, int n)\n{\n    int i;\n    double t;\n    return IsInf(x) || (std::modf ( std::ldexp ( std::frexp ( x, &i ), n ), &t ) == 0.0);\n}\n\ninline const mpreal pow(const mpreal& a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::get_default_rnd())\n{\n    mpreal x(a);\n    mpfr_pow(x.mp,x.mp,b.mp,rnd_mode);\n    return x;\n}\n\ninline const mpreal pow(const mpreal& a, const mpz_t b, mp_rnd_t rnd_mode = mpreal::get_default_rnd())\n{\n    mpreal x(a);\n    mpfr_pow_z(x.mp,x.mp,b,rnd_mode);\n    return x;\n}\n\ninline const mpreal pow(const mpreal& a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd())\n{\n    mpreal x(a);\n    mpfr_pow_ui(x.mp,x.mp,b,rnd_mode);\n    return x;\n}\n\ninline const mpreal pow(const mpreal& a, const unsigned int b, mp_rnd_t rnd_mode)\n{\n    return pow(a,static_cast<unsigned long int>(b),rnd_mode);\n}\n\ninline const mpreal pow(const mpreal& a, const long int b, mp_rnd_t rnd_mode = mpreal::get_default_rnd())\n{\n    mpreal x(a);\n    mpfr_pow_si(x.mp,x.mp,b,rnd_mode);\n    return x;\n}\n\ninline const mpreal pow(const mpreal& a, const int b, mp_rnd_t rnd_mode)\n{\n    return pow(a,static_cast<long int>(b),rnd_mode);\n}\n\ninline const mpreal pow(const mpreal& a, const long double b, mp_rnd_t rnd_mode)\n{\n    return pow(a,mpreal(b),rnd_mode);\n}\n\ninline const mpreal pow(const mpreal& a, const double b, mp_rnd_t rnd_mode)\n{\n    return pow(a,mpreal(b),rnd_mode);\n}\n\ninline const mpreal pow(const unsigned long int a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::get_default_rnd())\n{\n    mpreal x(a);\n    mpfr_ui_pow(x.mp,a,b.mp,rnd_mode);\n    return x;\n}\n\ninline const mpreal pow(const unsigned int a, const mpreal& b, mp_rnd_t rnd_mode)\n{\n    return pow(static_cast<unsigned long int>(a),b,rnd_mode);\n}\n\ninline const mpreal pow(const long int a, const mpreal& b, mp_rnd_t rnd_mode)\n{\n    if (a>=0)     return pow(static_cast<unsigned long int>(a),b,rnd_mode);\n    else          return pow(mpreal(a),b,rnd_mode);\n}\n\ninline const mpreal pow(const int a, const mpreal& b, mp_rnd_t rnd_mode)\n{\n    if (a>=0)     return pow(static_cast<unsigned long int>(a),b,rnd_mode);\n    else          return pow(mpreal(a),b,rnd_mode);\n}\n\ninline const mpreal pow(const long double a, const mpreal& b, mp_rnd_t rnd_mode)\n{\n    return pow(mpreal(a),b,rnd_mode);\n}\n\ninline const mpreal pow(const double a, const mpreal& b, mp_rnd_t rnd_mode)\n{\n    return pow(mpreal(a),b,rnd_mode);\n}\n\n// pow unsigned long int\ninline const mpreal pow(const unsigned long int a, const unsigned long int b, mp_rnd_t rnd_mode)\n{\n    mpreal x(a);\n    mpfr_ui_pow_ui(x.mp,a,b,rnd_mode);\n    return x;\n}\n\ninline const mpreal pow(const unsigned long int a, const unsigned int b, mp_rnd_t rnd_mode)\n{\n    return pow(a,static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui\n}\n\ninline const mpreal pow(const unsigned long int a, const long int b, mp_rnd_t rnd_mode)\n{\n    if(b>0)    return pow(a,static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui\n    else       return pow(a,mpreal(b),rnd_mode); //mpfr_ui_pow\n}\n\ninline const mpreal pow(const unsigned long int a, const int b, mp_rnd_t rnd_mode)\n{\n    if(b>0)    return pow(a,static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui\n    else       return pow(a,mpreal(b),rnd_mode); //mpfr_ui_pow\n}\n\ninline const mpreal pow(const unsigned long int a, const long double b, mp_rnd_t rnd_mode)\n{\n    return pow(a,mpreal(b),rnd_mode); //mpfr_ui_pow\n}\n\ninline const mpreal pow(const unsigned long int a, const double b, mp_rnd_t rnd_mode)\n{\n    return pow(a,mpreal(b),rnd_mode); //mpfr_ui_pow\n}\n\n// pow unsigned int\ninline const mpreal pow(const unsigned int a, const unsigned long int b, mp_rnd_t rnd_mode)\n{\n    return pow(static_cast<unsigned long int>(a),b,rnd_mode); //mpfr_ui_pow_ui\n}\n\ninline const mpreal pow(const unsigned int a, const unsigned int b, mp_rnd_t rnd_mode)\n{\n    return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui\n}\n\ninline const mpreal pow(const unsigned int a, const long int b, mp_rnd_t rnd_mode)\n{\n    if(b>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui\n    else    return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow\n}\n\ninline const mpreal pow(const unsigned int a, const int b, mp_rnd_t rnd_mode)\n{\n    if(b>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui\n    else    return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow\n}\n\ninline const mpreal pow(const unsigned int a, const long double b, mp_rnd_t rnd_mode)\n{\n    return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow\n}\n\ninline const mpreal pow(const unsigned int a, const double b, mp_rnd_t rnd_mode)\n{\n    return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow\n}\n\n// pow long int\ninline const mpreal pow(const long int a, const unsigned long int b, mp_rnd_t rnd_mode)\n{\n    if (a>0) return pow(static_cast<unsigned long int>(a),b,rnd_mode); //mpfr_ui_pow_ui\n    else     return pow(mpreal(a),b,rnd_mode); //mpfr_pow_ui\n}\n\ninline const mpreal pow(const long int a, const unsigned int b, mp_rnd_t rnd_mode)\n{\n    if (a>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode);  //mpfr_ui_pow_ui\n    else     return pow(mpreal(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_pow_ui\n}\n\ninline const mpreal pow(const long int a, const long int b, mp_rnd_t rnd_mode)\n{\n    if (a>0)\n    {\n        if(b>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui\n        else    return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow\n    }else{\n        return pow(mpreal(a),b,rnd_mode); // mpfr_pow_si\n    }\n}\n\ninline const mpreal pow(const long int a, const int b, mp_rnd_t rnd_mode)\n{\n    if (a>0)\n    {\n        if(b>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui\n        else    return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow\n    }else{\n        return pow(mpreal(a),static_cast<long int>(b),rnd_mode); // mpfr_pow_si\n    }\n}\n\ninline const mpreal pow(const long int a, const long double b, mp_rnd_t rnd_mode)\n{\n    if (a>=0)   return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow\n    else        return pow(mpreal(a),mpreal(b),rnd_mode); //mpfr_pow\n}\n\ninline const mpreal pow(const long int a, const double b, mp_rnd_t rnd_mode)\n{\n    if (a>=0)   return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow\n    else        return pow(mpreal(a),mpreal(b),rnd_mode); //mpfr_pow\n}\n\n// pow int\ninline const mpreal pow(const int a, const unsigned long int b, mp_rnd_t rnd_mode)\n{\n    if (a>0) return pow(static_cast<unsigned long int>(a),b,rnd_mode); //mpfr_ui_pow_ui\n    else     return pow(mpreal(a),b,rnd_mode); //mpfr_pow_ui\n}\n\ninline const mpreal pow(const int a, const unsigned int b, mp_rnd_t rnd_mode)\n{\n    if (a>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode);  //mpfr_ui_pow_ui\n    else     return pow(mpreal(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_pow_ui\n}\n\ninline const mpreal pow(const int a, const long int b, mp_rnd_t rnd_mode)\n{\n    if (a>0)\n    {\n        if(b>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui\n        else    return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow\n    }else{\n        return pow(mpreal(a),b,rnd_mode); // mpfr_pow_si\n    }\n}\n\ninline const mpreal pow(const int a, const int b, mp_rnd_t rnd_mode)\n{\n    if (a>0)\n    {\n        if(b>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui\n        else    return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow\n    }else{\n        return pow(mpreal(a),static_cast<long int>(b),rnd_mode); // mpfr_pow_si\n    }\n}\n\ninline const mpreal pow(const int a, const long double b, mp_rnd_t rnd_mode)\n{\n    if (a>=0)   return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow\n    else        return pow(mpreal(a),mpreal(b),rnd_mode); //mpfr_pow\n}\n\ninline const mpreal pow(const int a, const double b, mp_rnd_t rnd_mode)\n{\n    if (a>=0)   return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow\n    else        return pow(mpreal(a),mpreal(b),rnd_mode); //mpfr_pow\n}\n\n// pow long double\ninline const mpreal pow(const long double a, const long double b, mp_rnd_t rnd_mode)\n{\n    return pow(mpreal(a),mpreal(b),rnd_mode);\n}\n\ninline const mpreal pow(const long double a, const unsigned long int b, mp_rnd_t rnd_mode)\n{\n    return pow(mpreal(a),b,rnd_mode); //mpfr_pow_ui\n}\n\ninline const mpreal pow(const long double a, const unsigned int b, mp_rnd_t rnd_mode)\n{\n    return pow(mpreal(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_pow_ui\n}\n\ninline const mpreal pow(const long double a, const long int b, mp_rnd_t rnd_mode)\n{\n    return pow(mpreal(a),b,rnd_mode); // mpfr_pow_si\n}\n\ninline const mpreal pow(const long double a, const int b, mp_rnd_t rnd_mode)\n{\n    return pow(mpreal(a),static_cast<long int>(b),rnd_mode); // mpfr_pow_si\n}\n\ninline const mpreal pow(const double a, const double b, mp_rnd_t rnd_mode)\n{\n    return pow(mpreal(a),mpreal(b),rnd_mode);\n}\n\ninline const mpreal pow(const double a, const unsigned long int b, mp_rnd_t rnd_mode)\n{\n    return pow(mpreal(a),b,rnd_mode); // mpfr_pow_ui\n}\n\ninline const mpreal pow(const double a, const unsigned int b, mp_rnd_t rnd_mode)\n{\n    return pow(mpreal(a),static_cast<unsigned long int>(b),rnd_mode); // mpfr_pow_ui\n}\n\ninline const mpreal pow(const double a, const long int b, mp_rnd_t rnd_mode)\n{\n    return pow(mpreal(a),b,rnd_mode); // mpfr_pow_si\n}\n\ninline const mpreal pow(const double a, const int b, mp_rnd_t rnd_mode)\n{\n    return pow(mpreal(a),static_cast<long int>(b),rnd_mode); // mpfr_pow_si\n}\n} // End of mpfr namespace\n\n// Explicit specialization of std::swap for mpreal numbers\n// Thus standard algorithms will use efficient version of swap (due to Koenig lookup)\n// Non-throwing swap C++ idiom: http://en.wikibooks.org/wiki/More_C%2B%2B_Idioms/Non-throwing_swap\nnamespace std\n{\n  // we are allowed to extend namespace std with specializations only\n    template <>\n    inline void swap(mpfr::mpreal& x, mpfr::mpreal& y)\n    {\n        return mpfr::swap(x, y);\n    }\n\n    template<>\n    class numeric_limits<mpfr::mpreal>\n    {\n    public:\n        static const bool is_specialized    = true;\n        static const bool is_signed         = true;\n        static const bool is_integer        = false;\n        static const bool is_exact          = false;\n        static const int  radix             = 2;\n\n        static const bool has_infinity      = true;\n        static const bool has_quiet_NaN     = true;\n        static const bool has_signaling_NaN = true;\n\n        static const bool is_iec559         = true;        // = IEEE 754\n        static const bool is_bounded        = true;\n        static const bool is_modulo         = false;\n        static const bool traps             = true;\n        static const bool tinyness_before   = true;\n\n        static const float_denorm_style has_denorm  = denorm_absent;\n\n        inline static mpfr::mpreal (min)    (mp_prec_t precision = mpfr::mpreal::get_default_prec()) {  return  mpfr::minval(precision);  }\n        inline static mpfr::mpreal (max)    (mp_prec_t precision = mpfr::mpreal::get_default_prec()) {  return  mpfr::maxval(precision);  }\n        inline static mpfr::mpreal lowest   (mp_prec_t precision = mpfr::mpreal::get_default_prec()) {  return -mpfr::maxval(precision);  }\n\n        // Returns smallest eps such that 1 + eps != 1 (classic machine epsilon)\n        inline static mpfr::mpreal epsilon(mp_prec_t precision = mpfr::mpreal::get_default_prec()) {  return  mpfr::machine_epsilon(precision); }\n\n        // Returns smallest eps such that x + eps != x (relative machine epsilon)\n        inline static mpfr::mpreal epsilon(const mpfr::mpreal& x) {  return mpfr::machine_epsilon(x);  }\n\n        inline static mpfr::mpreal round_error(mp_prec_t precision = mpfr::mpreal::get_default_prec())\n        {\n            mp_rnd_t r = mpfr::mpreal::get_default_rnd();\n\n            if(r == GMP_RNDN)  return mpfr::mpreal(0.5, precision);\n            else               return mpfr::mpreal(1.0, precision);\n        }\n\n        inline static const mpfr::mpreal infinity()         { return mpfr::const_infinity();     }\n        inline static const mpfr::mpreal quiet_NaN()        { return mpfr::mpreal().setNan();    }\n        inline static const mpfr::mpreal signaling_NaN()    { return mpfr::mpreal().setNan();    }\n        inline static const mpfr::mpreal denorm_min()       { return (min)();                    }\n\n        // Please note, exponent range is not fixed in MPFR\n        static const int min_exponent = MPFR_EMIN_DEFAULT;\n        static const int max_exponent = MPFR_EMAX_DEFAULT;\n        MPREAL_PERMISSIVE_EXPR static const int min_exponent10 = (int) (MPFR_EMIN_DEFAULT * 0.3010299956639811);\n        MPREAL_PERMISSIVE_EXPR static const int max_exponent10 = (int) (MPFR_EMAX_DEFAULT * 0.3010299956639811);\n\n#ifdef MPREAL_HAVE_DYNAMIC_STD_NUMERIC_LIMITS\n\n        // Following members should be constant according to standard, but they can be variable in MPFR\n        // So we define them as functions here.\n        //\n        // This is preferable way for std::numeric_limits<mpfr::mpreal> specialization.\n        // But it is incompatible with standard std::numeric_limits and might not work with other libraries, e.g. boost.\n        // See below for compatible implementation.\n        inline static float_round_style round_style()\n        {\n            mp_rnd_t r = mpfr::mpreal::get_default_rnd();\n\n            switch (r)\n            {\n            case GMP_RNDN: return round_to_nearest;\n            case GMP_RNDZ: return round_toward_zero;\n            case GMP_RNDU: return round_toward_infinity;\n            case GMP_RNDD: return round_toward_neg_infinity;\n            default: return round_indeterminate;\n            }\n        }\n\n        inline static int digits()                        {    return int(mpfr::mpreal::get_default_prec());    }\n        inline static int digits(const mpfr::mpreal& x)   {    return x.getPrecision();                         }\n\n        inline static int digits10(mp_prec_t precision = mpfr::mpreal::get_default_prec())\n        {\n            return mpfr::bits2digits(precision);\n        }\n\n        inline static int digits10(const mpfr::mpreal& x)\n        {\n            return mpfr::bits2digits(x.getPrecision());\n        }\n\n        inline static int max_digits10(mp_prec_t precision = mpfr::mpreal::get_default_prec())\n        {\n            return digits10(precision);\n        }\n#else\n        // Digits and round_style are NOT constants when it comes to mpreal.\n        // If possible, please use functions digits() and round_style() defined above.\n        //\n        // These (default) values are preserved for compatibility with existing libraries, e.g. boost.\n        // Change them accordingly to your application.\n        //\n        // For example, if you use 256 bits of precision uniformly in your program, then:\n        // digits       = 256\n        // digits10     = 77\n        // max_digits10 = 78\n        //\n        // Approximate formula for decimal digits is: digits10 = floor(log10(2) * digits). See bits2digits() for more details.\n\n        static const std::float_round_style round_style = round_to_nearest;\n        static const int digits       = 53;\n        static const int digits10     = 15;\n        static const int max_digits10 = 16;\n#endif\n    };\n\n}\n\n#endif /* __MPREAL_H__ */\n"
  },
  {
    "path": "include/eigen3/unsupported/test/mpreal_support.cpp",
    "content": "#include \"main.h\"\n#include <Eigen/MPRealSupport>\n#include <Eigen/LU>\n#include <Eigen/Eigenvalues>\n#include <sstream>\n\nusing namespace mpfr;\nusing namespace Eigen;\n\nvoid test_mpreal_support()\n{\n  // set precision to 256 bits (double has only 53 bits)\n  mpreal::set_default_prec(256);\n  typedef Matrix<mpreal,Eigen::Dynamic,Eigen::Dynamic> MatrixXmp;\n  typedef Matrix<std::complex<mpreal>,Eigen::Dynamic,Eigen::Dynamic> MatrixXcmp;\n\n  std::cerr << \"epsilon =         \" << NumTraits<mpreal>::epsilon() << \"\\n\";\n  std::cerr << \"dummy_precision = \" << NumTraits<mpreal>::dummy_precision() << \"\\n\";\n  std::cerr << \"highest =         \" << NumTraits<mpreal>::highest() << \"\\n\";\n  std::cerr << \"lowest =          \" << NumTraits<mpreal>::lowest() << \"\\n\";\n  std::cerr << \"digits10 =        \" << NumTraits<mpreal>::digits10() << \"\\n\";\n\n  for(int i = 0; i < g_repeat; i++) {\n    int s = Eigen::internal::random<int>(1,100);\n    MatrixXmp A = MatrixXmp::Random(s,s);\n    MatrixXmp B = MatrixXmp::Random(s,s);\n    MatrixXmp S = A.adjoint() * A;\n    MatrixXmp X;\n    MatrixXcmp Ac = MatrixXcmp::Random(s,s);\n    MatrixXcmp Bc = MatrixXcmp::Random(s,s);\n    MatrixXcmp Sc = Ac.adjoint() * Ac;\n    MatrixXcmp Xc;\n    \n    // Basic stuffs\n    VERIFY_IS_APPROX(A.real(), A);\n    VERIFY(Eigen::internal::isApprox(A.array().abs2().sum(), A.squaredNorm()));\n    VERIFY_IS_APPROX(A.array().exp(),         exp(A.array()));\n    VERIFY_IS_APPROX(A.array().abs2().sqrt(), A.array().abs());\n    VERIFY_IS_APPROX(A.array().sin(),         sin(A.array()));\n    VERIFY_IS_APPROX(A.array().cos(),         cos(A.array()));\n\n    // Cholesky\n    X = S.selfadjointView<Lower>().llt().solve(B);\n    VERIFY_IS_APPROX((S.selfadjointView<Lower>()*X).eval(),B);\n\n    Xc = Sc.selfadjointView<Lower>().llt().solve(Bc);\n    VERIFY_IS_APPROX((Sc.selfadjointView<Lower>()*Xc).eval(),Bc);\n    \n    // partial LU\n    X = A.lu().solve(B);\n    VERIFY_IS_APPROX((A*X).eval(),B);\n\n    // symmetric eigenvalues\n    SelfAdjointEigenSolver<MatrixXmp> eig(S);\n    VERIFY_IS_EQUAL(eig.info(), Success);\n    VERIFY( (S.selfadjointView<Lower>() * eig.eigenvectors()).isApprox(eig.eigenvectors() * eig.eigenvalues().asDiagonal(), NumTraits<mpreal>::dummy_precision()*1e3) );\n  }\n  \n  {\n    MatrixXmp A(8,3); A.setRandom();\n    // test output (interesting things happen in this code)\n    std::stringstream stream;\n    stream << A;\n  }\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/openglsupport.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include <main.h>\n#include <iostream>\n#include <GL/glew.h>\n#include <Eigen/OpenGLSupport>\n#include <GL/glut.h>\nusing namespace Eigen;\n\n\n\n\n#define VERIFY_MATRIX(CODE,REF) { \\\n    glLoadIdentity(); \\\n    CODE; \\\n    Matrix<float,4,4,ColMajor> m; m.setZero(); \\\n    glGet(GL_MODELVIEW_MATRIX, m); \\\n    if(!(REF).cast<float>().isApprox(m)) { \\\n      std::cerr << \"Expected:\\n\" << ((REF).cast<float>()) << \"\\n\" << \"got\\n\" << m << \"\\n\\n\"; \\\n    } \\\n    VERIFY_IS_APPROX((REF).cast<float>(), m); \\\n  }\n\n#define VERIFY_UNIFORM(SUFFIX,NAME,TYPE) { \\\n    TYPE value; value.setRandom(); \\\n    TYPE data; \\\n    int loc = glGetUniformLocation(prg_id, #NAME); \\\n    VERIFY((loc!=-1) && \"uniform not found\"); \\\n    glUniform(loc,value); \\\n    EIGEN_CAT(glGetUniform,SUFFIX)(prg_id,loc,data.data()); \\\n    if(!value.isApprox(data)) { \\\n      std::cerr << \"Expected:\\n\" << value << \"\\n\" << \"got\\n\" << data << \"\\n\\n\"; \\\n    } \\\n    VERIFY_IS_APPROX(value, data); \\\n  }\n  \n#define VERIFY_UNIFORMi(NAME,TYPE) { \\\n    TYPE value = TYPE::Random().eval().cast<float>().cast<TYPE::Scalar>(); \\\n    TYPE data; \\\n    int loc = glGetUniformLocation(prg_id, #NAME); \\\n    VERIFY((loc!=-1) && \"uniform not found\"); \\\n    glUniform(loc,value); \\\n    glGetUniformiv(prg_id,loc,(GLint*)data.data()); \\\n    if(!value.isApprox(data)) { \\\n      std::cerr << \"Expected:\\n\" << value << \"\\n\" << \"got\\n\" << data << \"\\n\\n\"; \\\n    } \\\n    VERIFY_IS_APPROX(value, data); \\\n  }\n  \nvoid printInfoLog(GLuint objectID)\n{\n    int infologLength, charsWritten;\n    GLchar *infoLog;\n    glGetProgramiv(objectID,GL_INFO_LOG_LENGTH, &infologLength);\n    if(infologLength > 0)\n    {\n        infoLog = new GLchar[infologLength];\n        glGetProgramInfoLog(objectID, infologLength, &charsWritten, infoLog);\n        if (charsWritten>0)\n          std::cerr << \"Shader info : \\n\" << infoLog << std::endl;\n        delete[] infoLog;\n    }\n}\n\nGLint createShader(const char* vtx, const char* frg)\n{\n  GLint prg_id = glCreateProgram();\n  GLint vtx_id = glCreateShader(GL_VERTEX_SHADER);\n  GLint frg_id = glCreateShader(GL_FRAGMENT_SHADER);\n  GLint ok;\n  \n  glShaderSource(vtx_id, 1, &vtx, 0);\n  glCompileShader(vtx_id);\n  glGetShaderiv(vtx_id,GL_COMPILE_STATUS,&ok);\n  if(!ok)\n  {\n    std::cerr << \"vtx compilation failed\\n\";\n  }\n  \n  glShaderSource(frg_id, 1, &frg, 0);\n  glCompileShader(frg_id);\n  glGetShaderiv(frg_id,GL_COMPILE_STATUS,&ok);\n  if(!ok)\n  {\n    std::cerr << \"frg compilation failed\\n\";\n  }\n  \n  glAttachShader(prg_id, vtx_id);\n  glAttachShader(prg_id, frg_id);\n  glLinkProgram(prg_id);\n  glGetProgramiv(prg_id,GL_LINK_STATUS,&ok);\n  if(!ok)\n  {\n    std::cerr << \"linking failed\\n\";\n  }\n  printInfoLog(prg_id);\n  \n  glUseProgram(prg_id);\n  return prg_id;\n}\n\nvoid test_openglsupport()\n{\n  int argc = 0;\n  glutInit(&argc, 0);\n  glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB | GLUT_DEPTH);\n  glutInitWindowPosition (0,0);\n  glutInitWindowSize(10, 10);\n\n  if(glutCreateWindow(\"Eigen\") <= 0)\n  {\n    std::cerr << \"Error: Unable to create GLUT Window.\\n\";\n    exit(1);\n  }\n  \n  glewExperimental = GL_TRUE;\n  if(glewInit() != GLEW_OK)\n  {\n    std::cerr << \"Warning: Failed to initialize GLEW\\n\";\n  }\n\n  Vector3f v3f;\n  Matrix3f rot;\n  glBegin(GL_POINTS);\n  \n  glVertex(v3f);\n  glVertex(2*v3f+v3f);\n  glVertex(rot*v3f);\n  \n  glEnd();\n  \n  // 4x4 matrices\n  Matrix4f mf44; mf44.setRandom();\n  VERIFY_MATRIX(glLoadMatrix(mf44), mf44);\n  VERIFY_MATRIX(glMultMatrix(mf44), mf44);\n  Matrix4d md44; md44.setRandom();\n  VERIFY_MATRIX(glLoadMatrix(md44), md44);\n  VERIFY_MATRIX(glMultMatrix(md44), md44);\n  \n  // Quaternion\n  Quaterniond qd(AngleAxisd(internal::random<double>(), Vector3d::Random()));\n  VERIFY_MATRIX(glRotate(qd), Projective3d(qd).matrix());\n  \n  Quaternionf qf(AngleAxisf(internal::random<double>(), Vector3f::Random()));\n  VERIFY_MATRIX(glRotate(qf), Projective3f(qf).matrix());\n  \n  // 3D Transform\n  Transform<float,3,AffineCompact> acf3; acf3.matrix().setRandom();\n  VERIFY_MATRIX(glLoadMatrix(acf3), Projective3f(acf3).matrix());\n  VERIFY_MATRIX(glMultMatrix(acf3), Projective3f(acf3).matrix());\n  \n  Transform<float,3,Affine> af3(acf3);\n  VERIFY_MATRIX(glLoadMatrix(af3), Projective3f(af3).matrix());\n  VERIFY_MATRIX(glMultMatrix(af3), Projective3f(af3).matrix());\n  \n  Transform<float,3,Projective> pf3; pf3.matrix().setRandom();\n  VERIFY_MATRIX(glLoadMatrix(pf3), Projective3f(pf3).matrix());\n  VERIFY_MATRIX(glMultMatrix(pf3), Projective3f(pf3).matrix());\n  \n  Transform<double,3,AffineCompact> acd3; acd3.matrix().setRandom();\n  VERIFY_MATRIX(glLoadMatrix(acd3), Projective3d(acd3).matrix());\n  VERIFY_MATRIX(glMultMatrix(acd3), Projective3d(acd3).matrix());\n  \n  Transform<double,3,Affine> ad3(acd3);\n  VERIFY_MATRIX(glLoadMatrix(ad3), Projective3d(ad3).matrix());\n  VERIFY_MATRIX(glMultMatrix(ad3), Projective3d(ad3).matrix());\n  \n  Transform<double,3,Projective> pd3; pd3.matrix().setRandom();\n  VERIFY_MATRIX(glLoadMatrix(pd3), Projective3d(pd3).matrix());\n  VERIFY_MATRIX(glMultMatrix(pd3), Projective3d(pd3).matrix());\n  \n  // translations (2D and 3D)\n  {\n    Vector2f vf2; vf2.setRandom(); Vector3f vf23; vf23 << vf2, 0;\n    VERIFY_MATRIX(glTranslate(vf2), Projective3f(Translation3f(vf23)).matrix());\n    Vector2d vd2; vd2.setRandom(); Vector3d vd23; vd23 << vd2, 0;\n    VERIFY_MATRIX(glTranslate(vd2), Projective3d(Translation3d(vd23)).matrix());\n    \n    Vector3f vf3; vf3.setRandom();\n    VERIFY_MATRIX(glTranslate(vf3), Projective3f(Translation3f(vf3)).matrix());\n    Vector3d vd3; vd3.setRandom();\n    VERIFY_MATRIX(glTranslate(vd3), Projective3d(Translation3d(vd3)).matrix());\n    \n    Translation<float,3> tf3; tf3.vector().setRandom();\n    VERIFY_MATRIX(glTranslate(tf3), Projective3f(tf3).matrix());\n    \n    Translation<double,3> td3;  td3.vector().setRandom();\n    VERIFY_MATRIX(glTranslate(td3), Projective3d(td3).matrix());\n  }\n  \n  // scaling (2D and 3D)\n  {\n    Vector2f vf2; vf2.setRandom(); Vector3f vf23; vf23 << vf2, 1;\n    VERIFY_MATRIX(glScale(vf2), Projective3f(Scaling(vf23)).matrix());\n    Vector2d vd2; vd2.setRandom(); Vector3d vd23; vd23 << vd2, 1;\n    VERIFY_MATRIX(glScale(vd2), Projective3d(Scaling(vd23)).matrix());\n    \n    Vector3f vf3; vf3.setRandom();\n    VERIFY_MATRIX(glScale(vf3), Projective3f(Scaling(vf3)).matrix());\n    Vector3d vd3; vd3.setRandom();\n    VERIFY_MATRIX(glScale(vd3), Projective3d(Scaling(vd3)).matrix());\n    \n    UniformScaling<float> usf(internal::random<float>());\n    VERIFY_MATRIX(glScale(usf), Projective3f(usf).matrix());\n    \n    UniformScaling<double> usd(internal::random<double>());\n    VERIFY_MATRIX(glScale(usd), Projective3d(usd).matrix());\n  }\n  \n  // uniform\n  {\n    const char* vtx = \"void main(void) { gl_Position = gl_Vertex; }\\n\";\n    \n    if(GLEW_VERSION_2_0)\n    {\n      #ifdef GL_VERSION_2_0\n      const char* frg = \"\"\n        \"uniform vec2 v2f;\\n\"\n        \"uniform vec3 v3f;\\n\"\n        \"uniform vec4 v4f;\\n\"\n        \"uniform ivec2 v2i;\\n\"\n        \"uniform ivec3 v3i;\\n\"\n        \"uniform ivec4 v4i;\\n\"\n        \"uniform mat2 m2f;\\n\"\n        \"uniform mat3 m3f;\\n\"\n        \"uniform mat4 m4f;\\n\"\n        \"void main(void) { gl_FragColor = vec4(v2f[0]+v3f[0]+v4f[0])+vec4(v2i[0]+v3i[0]+v4i[0])+vec4(m2f[0][0]+m3f[0][0]+m4f[0][0]); }\\n\";\n        \n      GLint prg_id = createShader(vtx,frg);\n      \n      VERIFY_UNIFORM(fv,v2f, Vector2f);\n      VERIFY_UNIFORM(fv,v3f, Vector3f);\n      VERIFY_UNIFORM(fv,v4f, Vector4f);\n      VERIFY_UNIFORMi(v2i, Vector2i);\n      VERIFY_UNIFORMi(v3i, Vector3i);\n      VERIFY_UNIFORMi(v4i, Vector4i);\n      VERIFY_UNIFORM(fv,m2f, Matrix2f);\n      VERIFY_UNIFORM(fv,m3f, Matrix3f);\n      VERIFY_UNIFORM(fv,m4f, Matrix4f);\n      #endif\n    }\n    else\n      std::cerr << \"Warning: opengl 2.0 was not tested\\n\";\n    \n    if(GLEW_VERSION_2_1)\n    {\n      #ifdef GL_VERSION_2_1\n      const char* frg = \"#version 120\\n\"\n        \"uniform mat2x3 m23f;\\n\"\n        \"uniform mat3x2 m32f;\\n\"\n        \"uniform mat2x4 m24f;\\n\"\n        \"uniform mat4x2 m42f;\\n\"\n        \"uniform mat3x4 m34f;\\n\"\n        \"uniform mat4x3 m43f;\\n\"\n        \"void main(void) { gl_FragColor = vec4(m23f[0][0]+m32f[0][0]+m24f[0][0]+m42f[0][0]+m34f[0][0]+m43f[0][0]); }\\n\";\n        \n      GLint prg_id = createShader(vtx,frg);\n      \n      typedef Matrix<float,2,3> Matrix23f;\n      typedef Matrix<float,3,2> Matrix32f;\n      typedef Matrix<float,2,4> Matrix24f;\n      typedef Matrix<float,4,2> Matrix42f;\n      typedef Matrix<float,3,4> Matrix34f;\n      typedef Matrix<float,4,3> Matrix43f;\n      \n      VERIFY_UNIFORM(fv,m23f, Matrix23f);\n      VERIFY_UNIFORM(fv,m32f, Matrix32f);\n      VERIFY_UNIFORM(fv,m24f, Matrix24f);\n      VERIFY_UNIFORM(fv,m42f, Matrix42f);\n      VERIFY_UNIFORM(fv,m34f, Matrix34f);\n      VERIFY_UNIFORM(fv,m43f, Matrix43f);\n      #endif\n    }\n    else\n      std::cerr << \"Warning: opengl 2.1 was not tested\\n\";\n    \n    if(GLEW_VERSION_3_0)\n    {\n      #ifdef GL_VERSION_3_0\n      const char* frg = \"#version 150\\n\"\n        \"uniform uvec2 v2ui;\\n\"\n        \"uniform uvec3 v3ui;\\n\"\n        \"uniform uvec4 v4ui;\\n\"\n        \"out vec4 data;\\n\"\n        \"void main(void) { data = vec4(v2ui[0]+v3ui[0]+v4ui[0]); }\\n\";\n        \n      GLint prg_id = createShader(vtx,frg);\n      \n      typedef Matrix<unsigned int,2,1> Vector2ui;\n      typedef Matrix<unsigned int,3,1> Vector3ui;\n      typedef Matrix<unsigned int,4,1> Vector4ui;\n      \n      VERIFY_UNIFORMi(v2ui, Vector2ui);\n      VERIFY_UNIFORMi(v3ui, Vector3ui);\n      VERIFY_UNIFORMi(v4ui, Vector4ui);\n      #endif\n    }\n    else\n      std::cerr << \"Warning: opengl 3.0 was not tested\\n\";\n    \n    #ifdef GLEW_ARB_gpu_shader_fp64\n    if(GLEW_ARB_gpu_shader_fp64)\n    {\n      #ifdef GL_ARB_gpu_shader_fp64\n      const char* frg = \"#version 150\\n\"\n        \"uniform dvec2 v2d;\\n\"\n        \"uniform dvec3 v3d;\\n\"\n        \"uniform dvec4 v4d;\\n\"\n        \"out vec4 data;\\n\"\n        \"void main(void) { data = vec4(v2d[0]+v3d[0]+v4d[0]); }\\n\";\n        \n      GLint prg_id = createShader(vtx,frg);\n      \n      typedef Vector2d Vector2d;\n      typedef Vector3d Vector3d;\n      typedef Vector4d Vector4d;\n      \n      VERIFY_UNIFORM(dv,v2d, Vector2d);\n      VERIFY_UNIFORM(dv,v3d, Vector3d);\n      VERIFY_UNIFORM(dv,v4d, Vector4d);\n      #endif\n    }\n    else\n      std::cerr << \"Warning: GLEW_ARB_gpu_shader_fp64 was not tested\\n\";\n    #else\n      std::cerr << \"Warning: GLEW_ARB_gpu_shader_fp64 was not tested\\n\";\n    #endif\n  }\n  \n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/polynomialsolver.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2010 Manuel Yguel <manuel.yguel@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <unsupported/Eigen/Polynomials>\n#include <iostream>\n#include <algorithm>\n\nusing namespace std;\n\nnamespace Eigen {\nnamespace internal {\ntemplate<int Size>\nstruct increment_if_fixed_size\n{\n  enum {\n    ret = (Size == Dynamic) ? Dynamic : Size+1\n  };\n};\n}\n}\n\n\ntemplate<int Deg, typename POLYNOMIAL, typename SOLVER>\nbool aux_evalSolver( const POLYNOMIAL& pols, SOLVER& psolve )\n{\n  typedef typename POLYNOMIAL::Index Index;\n  typedef typename POLYNOMIAL::Scalar Scalar;\n\n  typedef typename SOLVER::RootsType    RootsType;\n  typedef Matrix<Scalar,Deg,1>          EvalRootsType;\n\n  const Index deg = pols.size()-1;\n\n  // Test template constructor from coefficient vector\n  SOLVER solve_constr (pols);\n\n  psolve.compute( pols );\n  const RootsType& roots( psolve.roots() );\n  EvalRootsType evr( deg );\n  for( int i=0; i<roots.size(); ++i ){\n    evr[i] = std::abs( poly_eval( pols, roots[i] ) ); }\n\n  bool evalToZero = evr.isZero( test_precision<Scalar>() );\n  if( !evalToZero )\n  {\n    cerr << \"WRONG root: \" << endl;\n    cerr << \"Polynomial: \" << pols.transpose() << endl;\n    cerr << \"Roots found: \" << roots.transpose() << endl;\n    cerr << \"Abs value of the polynomial at the roots: \" << evr.transpose() << endl;\n    cerr << endl;\n  }\n\n  std::vector<Scalar> rootModuli( roots.size() );\n  Map< EvalRootsType > aux( &rootModuli[0], roots.size() );\n  aux = roots.array().abs();\n  std::sort( rootModuli.begin(), rootModuli.end() );\n  bool distinctModuli=true;\n  for( size_t i=1; i<rootModuli.size() && distinctModuli; ++i )\n  {\n    if( internal::isApprox( rootModuli[i], rootModuli[i-1] ) ){\n      distinctModuli = false; }\n  }\n  VERIFY( evalToZero || !distinctModuli );\n\n  return distinctModuli;\n}\n\n\n\n\n\n\n\ntemplate<int Deg, typename POLYNOMIAL>\nvoid evalSolver( const POLYNOMIAL& pols )\n{\n  typedef typename POLYNOMIAL::Scalar Scalar;\n\n  typedef PolynomialSolver<Scalar, Deg >              PolynomialSolverType;\n\n  PolynomialSolverType psolve;\n  aux_evalSolver<Deg, POLYNOMIAL, PolynomialSolverType>( pols, psolve );\n}\n\n\n\n\ntemplate< int Deg, typename POLYNOMIAL, typename ROOTS, typename REAL_ROOTS >\nvoid evalSolverSugarFunction( const POLYNOMIAL& pols, const ROOTS& roots, const REAL_ROOTS& real_roots )\n{\n  using std::sqrt;\n  typedef typename POLYNOMIAL::Scalar Scalar;\n\n  typedef PolynomialSolver<Scalar, Deg >              PolynomialSolverType;\n\n  PolynomialSolverType psolve;\n  if( aux_evalSolver<Deg, POLYNOMIAL, PolynomialSolverType>( pols, psolve ) )\n  {\n    //It is supposed that\n    // 1) the roots found are correct\n    // 2) the roots have distinct moduli\n\n    typedef typename POLYNOMIAL::Scalar                 Scalar;\n    typedef typename REAL_ROOTS::Scalar                 Real;\n\n    //Test realRoots\n    std::vector< Real > calc_realRoots;\n    psolve.realRoots( calc_realRoots );\n    VERIFY( calc_realRoots.size() == (size_t)real_roots.size() );\n\n    const Scalar psPrec = sqrt( test_precision<Scalar>() );\n\n    for( size_t i=0; i<calc_realRoots.size(); ++i )\n    {\n      bool found = false;\n      for( size_t j=0; j<calc_realRoots.size()&& !found; ++j )\n      {\n        if( internal::isApprox( calc_realRoots[i], real_roots[j], psPrec ) ){\n          found = true; }\n      }\n      VERIFY( found );\n    }\n\n    //Test greatestRoot\n    VERIFY( internal::isApprox( roots.array().abs().maxCoeff(),\n          abs( psolve.greatestRoot() ), psPrec ) );\n\n    //Test smallestRoot\n    VERIFY( internal::isApprox( roots.array().abs().minCoeff(),\n          abs( psolve.smallestRoot() ), psPrec ) );\n\n    bool hasRealRoot;\n    //Test absGreatestRealRoot\n    Real r = psolve.absGreatestRealRoot( hasRealRoot );\n    VERIFY( hasRealRoot == (real_roots.size() > 0 ) );\n    if( hasRealRoot ){\n      VERIFY( internal::isApprox( real_roots.array().abs().maxCoeff(), abs(r), psPrec ) );  }\n\n    //Test absSmallestRealRoot\n    r = psolve.absSmallestRealRoot( hasRealRoot );\n    VERIFY( hasRealRoot == (real_roots.size() > 0 ) );\n    if( hasRealRoot ){\n      VERIFY( internal::isApprox( real_roots.array().abs().minCoeff(), abs( r ), psPrec ) ); }\n\n    //Test greatestRealRoot\n    r = psolve.greatestRealRoot( hasRealRoot );\n    VERIFY( hasRealRoot == (real_roots.size() > 0 ) );\n    if( hasRealRoot ){\n      VERIFY( internal::isApprox( real_roots.array().maxCoeff(), r, psPrec ) ); }\n\n    //Test smallestRealRoot\n    r = psolve.smallestRealRoot( hasRealRoot );\n    VERIFY( hasRealRoot == (real_roots.size() > 0 ) );\n    if( hasRealRoot ){\n    VERIFY( internal::isApprox( real_roots.array().minCoeff(), r, psPrec ) ); }\n  }\n}\n\n\ntemplate<typename _Scalar, int _Deg>\nvoid polynomialsolver(int deg)\n{\n  typedef internal::increment_if_fixed_size<_Deg>            Dim;\n  typedef Matrix<_Scalar,Dim::ret,1>                  PolynomialType;\n  typedef Matrix<_Scalar,_Deg,1>                      EvalRootsType;\n\n  cout << \"Standard cases\" << endl;\n  PolynomialType pols = PolynomialType::Random(deg+1);\n  evalSolver<_Deg,PolynomialType>( pols );\n\n  cout << \"Hard cases\" << endl;\n  _Scalar multipleRoot = internal::random<_Scalar>();\n  EvalRootsType allRoots = EvalRootsType::Constant(deg,multipleRoot);\n  roots_to_monicPolynomial( allRoots, pols );\n  evalSolver<_Deg,PolynomialType>( pols );\n\n  cout << \"Test sugar\" << endl;\n  EvalRootsType realRoots = EvalRootsType::Random(deg);\n  roots_to_monicPolynomial( realRoots, pols );\n  evalSolverSugarFunction<_Deg>(\n      pols,\n      realRoots.template cast <\n                    std::complex<\n                         typename NumTraits<_Scalar>::Real\n                         >\n                    >(),\n      realRoots );\n}\n\nvoid test_polynomialsolver()\n{\n  for(int i = 0; i < g_repeat; i++)\n  {\n    CALL_SUBTEST_1( (polynomialsolver<float,1>(1)) );\n    CALL_SUBTEST_2( (polynomialsolver<double,2>(2)) );\n    CALL_SUBTEST_3( (polynomialsolver<double,3>(3)) );\n    CALL_SUBTEST_4( (polynomialsolver<float,4>(4)) );\n    CALL_SUBTEST_5( (polynomialsolver<double,5>(5)) );\n    CALL_SUBTEST_6( (polynomialsolver<float,6>(6)) );\n    CALL_SUBTEST_7( (polynomialsolver<float,7>(7)) );\n    CALL_SUBTEST_8( (polynomialsolver<double,8>(8)) );\n\n    CALL_SUBTEST_9( (polynomialsolver<float,Dynamic>(\n            internal::random<int>(9,13)\n            )) );\n    CALL_SUBTEST_10((polynomialsolver<double,Dynamic>(\n            internal::random<int>(9,13)\n            )) );\n    CALL_SUBTEST_11((polynomialsolver<float,Dynamic>(1)) );\n  }\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/polynomialutils.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2010 Manuel Yguel <manuel.yguel@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include <unsupported/Eigen/Polynomials>\n#include <iostream>\n\nusing namespace std;\n\nnamespace Eigen {\nnamespace internal {\ntemplate<int Size>\nstruct increment_if_fixed_size\n{\n  enum {\n    ret = (Size == Dynamic) ? Dynamic : Size+1\n  };\n};\n}\n}\n\ntemplate<typename _Scalar, int _Deg>\nvoid realRoots_to_monicPolynomial_test(int deg)\n{\n  typedef internal::increment_if_fixed_size<_Deg>            Dim;\n  typedef Matrix<_Scalar,Dim::ret,1>                  PolynomialType;\n  typedef Matrix<_Scalar,_Deg,1>                      EvalRootsType;\n\n  PolynomialType pols(deg+1);\n  EvalRootsType roots = EvalRootsType::Random(deg);\n  roots_to_monicPolynomial( roots, pols );\n\n  EvalRootsType evr( deg );\n  for( int i=0; i<roots.size(); ++i ){\n    evr[i] = std::abs( poly_eval( pols, roots[i] ) ); }\n\n  bool evalToZero = evr.isZero( test_precision<_Scalar>() );\n  if( !evalToZero ){\n    cerr << evr.transpose() << endl; }\n  VERIFY( evalToZero );\n}\n\ntemplate<typename _Scalar> void realRoots_to_monicPolynomial_scalar()\n{\n  CALL_SUBTEST_2( (realRoots_to_monicPolynomial_test<_Scalar,2>(2)) );\n  CALL_SUBTEST_3( (realRoots_to_monicPolynomial_test<_Scalar,3>(3)) );\n  CALL_SUBTEST_4( (realRoots_to_monicPolynomial_test<_Scalar,4>(4)) );\n  CALL_SUBTEST_5( (realRoots_to_monicPolynomial_test<_Scalar,5>(5)) );\n  CALL_SUBTEST_6( (realRoots_to_monicPolynomial_test<_Scalar,6>(6)) );\n  CALL_SUBTEST_7( (realRoots_to_monicPolynomial_test<_Scalar,7>(7)) );\n  CALL_SUBTEST_8( (realRoots_to_monicPolynomial_test<_Scalar,17>(17)) );\n\n  CALL_SUBTEST_9( (realRoots_to_monicPolynomial_test<_Scalar,Dynamic>(\n          internal::random<int>(18,26) )) );\n}\n\n\n\n\ntemplate<typename _Scalar, int _Deg>\nvoid CauchyBounds(int deg)\n{\n  typedef internal::increment_if_fixed_size<_Deg>            Dim;\n  typedef Matrix<_Scalar,Dim::ret,1>                  PolynomialType;\n  typedef Matrix<_Scalar,_Deg,1>                      EvalRootsType;\n\n  PolynomialType pols(deg+1);\n  EvalRootsType roots = EvalRootsType::Random(deg);\n  roots_to_monicPolynomial( roots, pols );\n  _Scalar M = cauchy_max_bound( pols );\n  _Scalar m = cauchy_min_bound( pols );\n  _Scalar Max = roots.array().abs().maxCoeff();\n  _Scalar min = roots.array().abs().minCoeff();\n  bool eval = (M >= Max) && (m <= min);\n  if( !eval )\n  {\n    cerr << \"Roots: \" << roots << endl;\n    cerr << \"Bounds: (\" << m << \", \" << M << \")\" << endl;\n    cerr << \"Min,Max: (\" << min << \", \" << Max << \")\" << endl;\n  }\n  VERIFY( eval );\n}\n\ntemplate<typename _Scalar> void CauchyBounds_scalar()\n{\n  CALL_SUBTEST_2( (CauchyBounds<_Scalar,2>(2)) );\n  CALL_SUBTEST_3( (CauchyBounds<_Scalar,3>(3)) );\n  CALL_SUBTEST_4( (CauchyBounds<_Scalar,4>(4)) );\n  CALL_SUBTEST_5( (CauchyBounds<_Scalar,5>(5)) );\n  CALL_SUBTEST_6( (CauchyBounds<_Scalar,6>(6)) );\n  CALL_SUBTEST_7( (CauchyBounds<_Scalar,7>(7)) );\n  CALL_SUBTEST_8( (CauchyBounds<_Scalar,17>(17)) );\n\n  CALL_SUBTEST_9( (CauchyBounds<_Scalar,Dynamic>(\n          internal::random<int>(18,26) )) );\n}\n\nvoid test_polynomialutils()\n{\n  for(int i = 0; i < g_repeat; i++)\n  {\n    realRoots_to_monicPolynomial_scalar<double>();\n    realRoots_to_monicPolynomial_scalar<float>();\n    CauchyBounds_scalar<double>();\n    CauchyBounds_scalar<float>();\n  }\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/sparse_extra.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2008-2010 Gael Guennebaud <g.gael@free.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n\n// import basic and product tests for deprectaed DynamicSparseMatrix\n#define EIGEN_NO_DEPRECATED_WARNING\n#include \"sparse_basic.cpp\"\n#include \"sparse_product.cpp\"\n#include <Eigen/SparseExtra>\n\ntemplate<typename SetterType,typename DenseType, typename Scalar, int Options>\nbool test_random_setter(SparseMatrix<Scalar,Options>& sm, const DenseType& ref, const std::vector<Vector2i>& nonzeroCoords)\n{\n  {\n    sm.setZero();\n    SetterType w(sm);\n    std::vector<Vector2i> remaining = nonzeroCoords;\n    while(!remaining.empty())\n    {\n      int i = internal::random<int>(0,static_cast<int>(remaining.size())-1);\n      w(remaining[i].x(),remaining[i].y()) = ref.coeff(remaining[i].x(),remaining[i].y());\n      remaining[i] = remaining.back();\n      remaining.pop_back();\n    }\n  }\n  return sm.isApprox(ref);\n}\n\ntemplate<typename SetterType,typename DenseType, typename T>\nbool test_random_setter(DynamicSparseMatrix<T>& sm, const DenseType& ref, const std::vector<Vector2i>& nonzeroCoords)\n{\n  sm.setZero();\n  std::vector<Vector2i> remaining = nonzeroCoords;\n  while(!remaining.empty())\n  {\n    int i = internal::random<int>(0,static_cast<int>(remaining.size())-1);\n    sm.coeffRef(remaining[i].x(),remaining[i].y()) = ref.coeff(remaining[i].x(),remaining[i].y());\n    remaining[i] = remaining.back();\n    remaining.pop_back();\n  }\n  return sm.isApprox(ref);\n}\n\ntemplate<typename SparseMatrixType> void sparse_extra(const SparseMatrixType& ref)\n{\n  const Index rows = ref.rows();\n  const Index cols = ref.cols();\n  typedef typename SparseMatrixType::Scalar Scalar;\n  enum { Flags = SparseMatrixType::Flags };\n\n  double density = (std::max)(8./(rows*cols), 0.01);\n  typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;\n  typedef Matrix<Scalar,Dynamic,1> DenseVector;\n  Scalar eps = 1e-6;\n\n  SparseMatrixType m(rows, cols);\n  DenseMatrix refMat = DenseMatrix::Zero(rows, cols);\n  DenseVector vec1 = DenseVector::Random(rows);\n\n  std::vector<Vector2i> zeroCoords;\n  std::vector<Vector2i> nonzeroCoords;\n  initSparse<Scalar>(density, refMat, m, 0, &zeroCoords, &nonzeroCoords);\n\n  if (zeroCoords.size()==0 || nonzeroCoords.size()==0)\n    return;\n\n  // test coeff and coeffRef\n  for (int i=0; i<(int)zeroCoords.size(); ++i)\n  {\n    VERIFY_IS_MUCH_SMALLER_THAN( m.coeff(zeroCoords[i].x(),zeroCoords[i].y()), eps );\n    if(internal::is_same<SparseMatrixType,SparseMatrix<Scalar,Flags> >::value)\n      VERIFY_RAISES_ASSERT( m.coeffRef(zeroCoords[0].x(),zeroCoords[0].y()) = 5 );\n  }\n  VERIFY_IS_APPROX(m, refMat);\n\n  m.coeffRef(nonzeroCoords[0].x(), nonzeroCoords[0].y()) = Scalar(5);\n  refMat.coeffRef(nonzeroCoords[0].x(), nonzeroCoords[0].y()) = Scalar(5);\n\n  VERIFY_IS_APPROX(m, refMat);\n\n  // random setter\n//   {\n//     m.setZero();\n//     VERIFY_IS_NOT_APPROX(m, refMat);\n//     SparseSetter<SparseMatrixType, RandomAccessPattern> w(m);\n//     std::vector<Vector2i> remaining = nonzeroCoords;\n//     while(!remaining.empty())\n//     {\n//       int i = internal::random<int>(0,remaining.size()-1);\n//       w->coeffRef(remaining[i].x(),remaining[i].y()) = refMat.coeff(remaining[i].x(),remaining[i].y());\n//       remaining[i] = remaining.back();\n//       remaining.pop_back();\n//     }\n//   }\n//   VERIFY_IS_APPROX(m, refMat);\n\n    VERIFY(( test_random_setter<RandomSetter<SparseMatrixType, StdMapTraits> >(m,refMat,nonzeroCoords) ));\n    #ifdef EIGEN_UNORDERED_MAP_SUPPORT\n    VERIFY(( test_random_setter<RandomSetter<SparseMatrixType, StdUnorderedMapTraits> >(m,refMat,nonzeroCoords) ));\n    #endif\n    #ifdef _DENSE_HASH_MAP_H_\n    VERIFY(( test_random_setter<RandomSetter<SparseMatrixType, GoogleDenseHashMapTraits> >(m,refMat,nonzeroCoords) ));\n    #endif\n    #ifdef _SPARSE_HASH_MAP_H_\n    VERIFY(( test_random_setter<RandomSetter<SparseMatrixType, GoogleSparseHashMapTraits> >(m,refMat,nonzeroCoords) ));\n    #endif\n\n\n  // test RandomSetter\n  /*{\n    SparseMatrixType m1(rows,cols), m2(rows,cols);\n    DenseMatrix refM1 = DenseMatrix::Zero(rows, rows);\n    initSparse<Scalar>(density, refM1, m1);\n    {\n      Eigen::RandomSetter<SparseMatrixType > setter(m2);\n      for (int j=0; j<m1.outerSize(); ++j)\n        for (typename SparseMatrixType::InnerIterator i(m1,j); i; ++i)\n          setter(i.index(), j) = i.value();\n    }\n    VERIFY_IS_APPROX(m1, m2);\n  }*/\n\n\n}\n\nvoid test_sparse_extra()\n{\n  for(int i = 0; i < g_repeat; i++) {\n    int s = Eigen::internal::random<int>(1,50);\n    CALL_SUBTEST_1( sparse_extra(SparseMatrix<double>(8, 8)) );\n    CALL_SUBTEST_2( sparse_extra(SparseMatrix<std::complex<double> >(s, s)) );\n    CALL_SUBTEST_1( sparse_extra(SparseMatrix<double>(s, s)) );\n\n    CALL_SUBTEST_3( sparse_extra(DynamicSparseMatrix<double>(s, s)) );\n//    CALL_SUBTEST_3(( sparse_basic(DynamicSparseMatrix<double>(s, s)) ));\n//    CALL_SUBTEST_3(( sparse_basic(DynamicSparseMatrix<double,ColMajor,long int>(s, s)) ));\n\n    CALL_SUBTEST_3( (sparse_product<DynamicSparseMatrix<float, ColMajor> >()) );\n    CALL_SUBTEST_3( (sparse_product<DynamicSparseMatrix<float, RowMajor> >()) );\n  }\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/special_functions.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n#include \"../Eigen/SpecialFunctions\"\n\ntemplate<typename X, typename Y>\nvoid verify_component_wise(const X& x, const Y& y)\n{\n  for(Index i=0; i<x.size(); ++i)\n  {\n    if((numext::isfinite)(y(i)))\n      VERIFY_IS_APPROX( x(i), y(i) );\n    else if((numext::isnan)(y(i)))\n      VERIFY((numext::isnan)(x(i)));\n    else\n      VERIFY_IS_EQUAL( x(i), y(i) );\n  }\n}\n\ntemplate<typename ArrayType> void array_special_functions()\n{\n  using std::abs;\n  using std::sqrt;\n  typedef typename ArrayType::Scalar Scalar;\n  typedef typename NumTraits<Scalar>::Real RealScalar;\n\n  Scalar plusinf = std::numeric_limits<Scalar>::infinity();\n  Scalar nan = std::numeric_limits<Scalar>::quiet_NaN();\n\n  Index rows = internal::random<Index>(1,30);\n  Index cols = 1;\n\n  // API\n  {\n    ArrayType m1 = ArrayType::Random(rows,cols);\n#if EIGEN_HAS_C99_MATH\n    VERIFY_IS_APPROX(m1.lgamma(), lgamma(m1));\n    VERIFY_IS_APPROX(m1.digamma(), digamma(m1));\n    VERIFY_IS_APPROX(m1.erf(), erf(m1));\n    VERIFY_IS_APPROX(m1.erfc(), erfc(m1));\n#endif  // EIGEN_HAS_C99_MATH\n  }\n\n\n#if EIGEN_HAS_C99_MATH\n  // check special functions (comparing against numpy implementation)\n  if (!NumTraits<Scalar>::IsComplex)\n  {\n\n    {\n      ArrayType m1 = ArrayType::Random(rows,cols);\n      ArrayType m2 = ArrayType::Random(rows,cols);\n\n      // Test various propreties of igamma & igammac.  These are normalized\n      // gamma integrals where\n      //   igammac(a, x) = Gamma(a, x) / Gamma(a)\n      //   igamma(a, x) = gamma(a, x) / Gamma(a)\n      // where Gamma and gamma are considered the standard unnormalized\n      // upper and lower incomplete gamma functions, respectively.\n      ArrayType a = m1.abs() + 2;\n      ArrayType x = m2.abs() + 2;\n      ArrayType zero = ArrayType::Zero(rows, cols);\n      ArrayType one = ArrayType::Constant(rows, cols, Scalar(1.0));\n      ArrayType a_m1 = a - one;\n      ArrayType Gamma_a_x = Eigen::igammac(a, x) * a.lgamma().exp();\n      ArrayType Gamma_a_m1_x = Eigen::igammac(a_m1, x) * a_m1.lgamma().exp();\n      ArrayType gamma_a_x = Eigen::igamma(a, x) * a.lgamma().exp();\n      ArrayType gamma_a_m1_x = Eigen::igamma(a_m1, x) * a_m1.lgamma().exp();\n\n      // Gamma(a, 0) == Gamma(a)\n      VERIFY_IS_APPROX(Eigen::igammac(a, zero), one);\n\n      // Gamma(a, x) + gamma(a, x) == Gamma(a)\n      VERIFY_IS_APPROX(Gamma_a_x + gamma_a_x, a.lgamma().exp());\n\n      // Gamma(a, x) == (a - 1) * Gamma(a-1, x) + x^(a-1) * exp(-x)\n      VERIFY_IS_APPROX(Gamma_a_x, (a - 1) * Gamma_a_m1_x + x.pow(a-1) * (-x).exp());\n\n      // gamma(a, x) == (a - 1) * gamma(a-1, x) - x^(a-1) * exp(-x)\n      VERIFY_IS_APPROX(gamma_a_x, (a - 1) * gamma_a_m1_x - x.pow(a-1) * (-x).exp());\n    }\n\n    {\n      // Check exact values of igamma and igammac against a third party calculation.\n      Scalar a_s[] = {Scalar(0), Scalar(1), Scalar(1.5), Scalar(4), Scalar(0.0001), Scalar(1000.5)};\n      Scalar x_s[] = {Scalar(0), Scalar(1), Scalar(1.5), Scalar(4), Scalar(0.0001), Scalar(1000.5)};\n\n      // location i*6+j corresponds to a_s[i], x_s[j].\n      Scalar igamma_s[][6] = {{0.0, nan, nan, nan, nan, nan},\n                              {0.0, 0.6321205588285578, 0.7768698398515702,\n                              0.9816843611112658, 9.999500016666262e-05, 1.0},\n                              {0.0, 0.4275932955291202, 0.608374823728911,\n                              0.9539882943107686, 7.522076445089201e-07, 1.0},\n                              {0.0, 0.01898815687615381, 0.06564245437845008,\n                              0.5665298796332909, 4.166333347221828e-18, 1.0},\n                              {0.0, 0.9999780593618628, 0.9999899967080838,\n                              0.9999996219837988, 0.9991370418689945, 1.0},\n                              {0.0, 0.0, 0.0, 0.0, 0.0, 0.5042041932513908}};\n      Scalar igammac_s[][6] = {{nan, nan, nan, nan, nan, nan},\n                              {1.0, 0.36787944117144233, 0.22313016014842982,\n                                0.018315638888734182, 0.9999000049998333, 0.0},\n                              {1.0, 0.5724067044708798, 0.3916251762710878,\n                                0.04601170568923136, 0.9999992477923555, 0.0},\n                              {1.0, 0.9810118431238462, 0.9343575456215499,\n                                0.4334701203667089, 1.0, 0.0},\n                              {1.0, 2.1940638138146658e-05, 1.0003291916285e-05,\n                                3.7801620118431334e-07, 0.0008629581310054535,\n                                0.0},\n                              {1.0, 1.0, 1.0, 1.0, 1.0, 0.49579580674813944}};\n      for (int i = 0; i < 6; ++i) {\n        for (int j = 0; j < 6; ++j) {\n          if ((std::isnan)(igamma_s[i][j])) {\n            VERIFY((std::isnan)(numext::igamma(a_s[i], x_s[j])));\n          } else {\n            VERIFY_IS_APPROX(numext::igamma(a_s[i], x_s[j]), igamma_s[i][j]);\n          }\n\n          if ((std::isnan)(igammac_s[i][j])) {\n            VERIFY((std::isnan)(numext::igammac(a_s[i], x_s[j])));\n          } else {\n            VERIFY_IS_APPROX(numext::igammac(a_s[i], x_s[j]), igammac_s[i][j]);\n          }\n        }\n      }\n    }\n  }\n#endif  // EIGEN_HAS_C99_MATH\n\n  // Check the zeta function against scipy.special.zeta\n  {\n    ArrayType x(7), q(7), res(7), ref(7);\n    x << 1.5,   4, 10.5, 10000.5,    3, 1,        0.9;\n    q << 2,   1.5,    3,  1.0001, -2.5, 1.2345, 1.2345;\n    ref << 1.61237534869, 0.234848505667, 1.03086757337e-5, 0.367879440865, 0.054102025820864097, plusinf, nan;\n    CALL_SUBTEST( verify_component_wise(ref, ref); );\n    CALL_SUBTEST( res = x.zeta(q); verify_component_wise(res, ref); );\n    CALL_SUBTEST( res = zeta(x,q); verify_component_wise(res, ref); );\n  }\n\n  // digamma\n  {\n    ArrayType x(7), res(7), ref(7);\n    x << 1, 1.5, 4, -10.5, 10000.5, 0, -1;\n    ref << -0.5772156649015329, 0.03648997397857645, 1.2561176684318, 2.398239129535781, 9.210340372392849, plusinf, plusinf;\n    CALL_SUBTEST( verify_component_wise(ref, ref); );\n\n    CALL_SUBTEST( res = x.digamma(); verify_component_wise(res, ref); );\n    CALL_SUBTEST( res = digamma(x);  verify_component_wise(res, ref); );\n  }\n\n\n#if EIGEN_HAS_C99_MATH\n  {\n    ArrayType n(11), x(11), res(11), ref(11);\n    n << 1, 1,    1, 1.5,   17,   31,   28,    8, 42, 147, 170;\n    x << 2, 3, 25.5, 1.5,  4.7, 11.8, 17.7, 30.2, 15.8, 54.1, 64;\n    ref << 0.644934066848, 0.394934066848, 0.0399946696496, nan, 293.334565435, 0.445487887616, -2.47810300902e-07, -8.29668781082e-09, -0.434562276666, 0.567742190178, -0.0108615497927;\n    CALL_SUBTEST( verify_component_wise(ref, ref); );\n\n    if(sizeof(RealScalar)>=8) {  // double\n      // Reason for commented line: http://eigen.tuxfamily.org/bz/show_bug.cgi?id=1232\n      //       CALL_SUBTEST( res = x.polygamma(n); verify_component_wise(res, ref); );\n      CALL_SUBTEST( res = polygamma(n,x);  verify_component_wise(res, ref); );\n    }\n    else {\n      //       CALL_SUBTEST( res = x.polygamma(n); verify_component_wise(res.head(8), ref.head(8)); );\n      CALL_SUBTEST( res = polygamma(n,x); verify_component_wise(res.head(8), ref.head(8)); );\n    }\n  }\n#endif\n\n#if EIGEN_HAS_C99_MATH\n  {\n    // Inputs and ground truth generated with scipy via:\n    //   a = np.logspace(-3, 3, 5) - 1e-3\n    //   b = np.logspace(-3, 3, 5) - 1e-3\n    //   x = np.linspace(-0.1, 1.1, 5)\n    //   (full_a, full_b, full_x) = np.vectorize(lambda a, b, x: (a, b, x))(*np.ix_(a, b, x))\n    //   full_a = full_a.flatten().tolist()  # same for full_b, full_x\n    //   v = scipy.special.betainc(full_a, full_b, full_x).flatten().tolist()\n    //\n    // Note in Eigen, we call betainc with arguments in the order (x, a, b).\n    ArrayType a(125);\n    ArrayType b(125);\n    ArrayType x(125);\n    ArrayType v(125);\n    ArrayType res(125);\n\n    a << 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,\n        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,\n        0.03062277660168379, 0.03062277660168379, 0.03062277660168379,\n        0.03062277660168379, 0.03062277660168379, 0.03062277660168379,\n        0.03062277660168379, 0.03062277660168379, 0.03062277660168379,\n        0.03062277660168379, 0.03062277660168379, 0.03062277660168379,\n        0.03062277660168379, 0.03062277660168379, 0.03062277660168379,\n        0.03062277660168379, 0.03062277660168379, 0.03062277660168379,\n        0.03062277660168379, 0.03062277660168379, 0.03062277660168379,\n        0.03062277660168379, 0.03062277660168379, 0.03062277660168379,\n        0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999,\n        0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999,\n        0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999,\n        31.62177660168379, 31.62177660168379, 31.62177660168379,\n        31.62177660168379, 31.62177660168379, 31.62177660168379,\n        31.62177660168379, 31.62177660168379, 31.62177660168379,\n        31.62177660168379, 31.62177660168379, 31.62177660168379,\n        31.62177660168379, 31.62177660168379, 31.62177660168379,\n        31.62177660168379, 31.62177660168379, 31.62177660168379,\n        31.62177660168379, 31.62177660168379, 31.62177660168379,\n        31.62177660168379, 31.62177660168379, 31.62177660168379,\n        31.62177660168379, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999,\n        999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999,\n        999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999,\n        999.999, 999.999, 999.999;\n\n    b << 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379, 0.03062277660168379,\n        0.03062277660168379, 0.03062277660168379, 0.03062277660168379, 0.999,\n        0.999, 0.999, 0.999, 0.999, 31.62177660168379, 31.62177660168379,\n        31.62177660168379, 31.62177660168379, 31.62177660168379, 999.999,\n        999.999, 999.999, 999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0,\n        0.03062277660168379, 0.03062277660168379, 0.03062277660168379,\n        0.03062277660168379, 0.03062277660168379, 0.999, 0.999, 0.999, 0.999,\n        0.999, 31.62177660168379, 31.62177660168379, 31.62177660168379,\n        31.62177660168379, 31.62177660168379, 999.999, 999.999, 999.999,\n        999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379,\n        0.03062277660168379, 0.03062277660168379, 0.03062277660168379,\n        0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999,\n        31.62177660168379, 31.62177660168379, 31.62177660168379,\n        31.62177660168379, 31.62177660168379, 999.999, 999.999, 999.999,\n        999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379,\n        0.03062277660168379, 0.03062277660168379, 0.03062277660168379,\n        0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999,\n        31.62177660168379, 31.62177660168379, 31.62177660168379,\n        31.62177660168379, 31.62177660168379, 999.999, 999.999, 999.999,\n        999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379,\n        0.03062277660168379, 0.03062277660168379, 0.03062277660168379,\n        0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999,\n        31.62177660168379, 31.62177660168379, 31.62177660168379,\n        31.62177660168379, 31.62177660168379, 999.999, 999.999, 999.999,\n        999.999, 999.999;\n\n    x << -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5,\n        0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2,\n        0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1,\n        0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1,\n        -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8,\n        1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5,\n        0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2,\n        0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1,\n        0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5,\n        0.8, 1.1;\n\n    v << nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,\n        nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,\n        nan, nan, nan, 0.47972119876364683, 0.5, 0.5202788012363533, nan, nan,\n        0.9518683957740043, 0.9789663010413743, 0.9931729188073435, nan, nan,\n        0.999995949033062, 0.9999999999993698, 0.9999999999999999, nan, nan,\n        0.9999999999999999, 0.9999999999999999, 0.9999999999999999, nan, nan,\n        nan, nan, nan, nan, nan, 0.006827081192655869, 0.0210336989586256,\n        0.04813160422599567, nan, nan, 0.20014344256217678, 0.5000000000000001,\n        0.7998565574378232, nan, nan, 0.9991401428435834, 0.999999999698403,\n        0.9999999999999999, nan, nan, 0.9999999999999999, 0.9999999999999999,\n        0.9999999999999999, nan, nan, nan, nan, nan, nan, nan,\n        1.0646600232370887e-25, 6.301722877826246e-13, 4.050966937974938e-06,\n        nan, nan, 7.864342668429763e-23, 3.015969667594166e-10,\n        0.0008598571564165444, nan, nan, 6.031987710123844e-08,\n        0.5000000000000007, 0.9999999396801229, nan, nan, 0.9999999999999999,\n        0.9999999999999999, 0.9999999999999999, nan, nan, nan, nan, nan, nan,\n        nan, 0.0, 7.029920380986636e-306, 2.2450728208591345e-101, nan, nan,\n        0.0, 9.275871147869727e-302, 1.2232913026152827e-97, nan, nan, 0.0,\n        3.0891393081932924e-252, 2.9303043666183996e-60, nan, nan,\n        2.248913486879199e-196, 0.5000000000004947, 0.9999999999999999, nan;\n\n    CALL_SUBTEST(res = betainc(a, b, x);\n                 verify_component_wise(res, v););\n  }\n\n  // Test various properties of betainc\n  {\n    ArrayType m1 = ArrayType::Random(32);\n    ArrayType m2 = ArrayType::Random(32);\n    ArrayType m3 = ArrayType::Random(32);\n    ArrayType one = ArrayType::Constant(32, Scalar(1.0));\n    const Scalar eps = std::numeric_limits<Scalar>::epsilon();\n    ArrayType a = (m1 * 4.0).exp();\n    ArrayType b = (m2 * 4.0).exp();\n    ArrayType x = m3.abs();\n\n    // betainc(a, 1, x) == x**a\n    CALL_SUBTEST(\n        ArrayType test = betainc(a, one, x);\n        ArrayType expected = x.pow(a);\n        verify_component_wise(test, expected););\n\n    // betainc(1, b, x) == 1 - (1 - x)**b\n    CALL_SUBTEST(\n        ArrayType test = betainc(one, b, x);\n        ArrayType expected = one - (one - x).pow(b);\n        verify_component_wise(test, expected););\n\n    // betainc(a, b, x) == 1 - betainc(b, a, 1-x)\n    CALL_SUBTEST(\n        ArrayType test = betainc(a, b, x) + betainc(b, a, one - x);\n        ArrayType expected = one;\n        verify_component_wise(test, expected););\n\n    // betainc(a+1, b, x) = betainc(a, b, x) - x**a * (1 - x)**b / (a * beta(a, b))\n    CALL_SUBTEST(\n        ArrayType num = x.pow(a) * (one - x).pow(b);\n        ArrayType denom = a * (a.lgamma() + b.lgamma() - (a + b).lgamma()).exp();\n        // Add eps to rhs and lhs so that component-wise test doesn't result in\n        // nans when both outputs are zeros.\n        ArrayType expected = betainc(a, b, x) - num / denom + eps;\n        ArrayType test = betainc(a + one, b, x) + eps;\n        if (sizeof(Scalar) >= 8) { // double\n          verify_component_wise(test, expected);\n        } else {\n          // Reason for limited test: http://eigen.tuxfamily.org/bz/show_bug.cgi?id=1232\n          verify_component_wise(test.head(8), expected.head(8));\n        });\n\n    // betainc(a, b+1, x) = betainc(a, b, x) + x**a * (1 - x)**b / (b * beta(a, b))\n    CALL_SUBTEST(\n        // Add eps to rhs and lhs so that component-wise test doesn't result in\n        // nans when both outputs are zeros.\n        ArrayType num = x.pow(a) * (one - x).pow(b);\n        ArrayType denom = b * (a.lgamma() + b.lgamma() - (a + b).lgamma()).exp();\n        ArrayType expected = betainc(a, b, x) + num / denom + eps;\n        ArrayType test = betainc(a, b + one, x) + eps;\n        verify_component_wise(test, expected););\n  }\n#endif\n}\n\nvoid test_special_functions()\n{\n  CALL_SUBTEST_1(array_special_functions<ArrayXf>());\n  CALL_SUBTEST_2(array_special_functions<ArrayXd>());\n}\n"
  },
  {
    "path": "include/eigen3/unsupported/test/splines.cpp",
    "content": "// This file is part of Eigen, a lightweight C++ template library\n// for linear algebra.\n//\n// Copyright (C) 2010-2011 Hauke Heibel <heibel@gmail.com>\n//\n// This Source Code Form is subject to the terms of the Mozilla\n// Public License v. 2.0. If a copy of the MPL was not distributed\n// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.\n\n#include \"main.h\"\n\n#include <unsupported/Eigen/Splines>\n\nnamespace Eigen {\n  \n  // lets do some explicit instantiations and thus\n  // force the compilation of all spline functions...\n  template class Spline<double, 2, Dynamic>;\n  template class Spline<double, 3, Dynamic>;\n\n  template class Spline<double, 2, 2>;\n  template class Spline<double, 2, 3>;\n  template class Spline<double, 2, 4>;\n  template class Spline<double, 2, 5>;\n\n  template class Spline<float, 2, Dynamic>;\n  template class Spline<float, 3, Dynamic>;\n\n  template class Spline<float, 3, 2>;\n  template class Spline<float, 3, 3>;\n  template class Spline<float, 3, 4>;\n  template class Spline<float, 3, 5>;\n\n}\n\nSpline<double, 2, Dynamic> closed_spline2d()\n{\n  RowVectorXd knots(12);\n  knots << 0,\n    0,\n    0,\n    0,\n    0.867193179093898,\n    1.660330955342408,\n    2.605084834823134,\n    3.484154586374428,\n    4.252699478956276,\n    4.252699478956276,\n    4.252699478956276,\n    4.252699478956276;\n\n  MatrixXd ctrls(8,2);\n  ctrls << -0.370967741935484,   0.236842105263158,\n    -0.231401860693277,   0.442245185027632,\n    0.344361228532831,   0.773369994120753,\n    0.828990216203802,   0.106550882647595,\n    0.407270163678382,  -1.043452922172848,\n    -0.488467813584053,  -0.390098582530090,\n    -0.494657189446427,   0.054804824897884,\n    -0.370967741935484,   0.236842105263158;\n  ctrls.transposeInPlace();\n\n  return Spline<double, 2, Dynamic>(knots, ctrls);\n}\n\n/* create a reference spline */\nSpline<double, 3, Dynamic> spline3d()\n{\n  RowVectorXd knots(11);\n  knots << 0,\n    0,\n    0,\n    0.118997681558377,\n    0.162611735194631,\n    0.498364051982143,\n    0.655098003973841,\n    0.679702676853675,\n    1.000000000000000,\n    1.000000000000000,\n    1.000000000000000;\n\n  MatrixXd ctrls(8,3);\n  ctrls <<    0.959743958516081,   0.340385726666133,   0.585267750979777,\n    0.223811939491137,   0.751267059305653,   0.255095115459269,\n    0.505957051665142,   0.699076722656686,   0.890903252535799,\n    0.959291425205444,   0.547215529963803,   0.138624442828679,\n    0.149294005559057,   0.257508254123736,   0.840717255983663,\n    0.254282178971531,   0.814284826068816,   0.243524968724989,\n    0.929263623187228,   0.349983765984809,   0.196595250431208,\n    0.251083857976031,   0.616044676146639,   0.473288848902729;\n  ctrls.transposeInPlace();\n\n  return Spline<double, 3, Dynamic>(knots, ctrls);\n}\n\n/* compares evaluations against known results */\nvoid eval_spline3d()\n{\n  Spline3d spline = spline3d();\n\n  RowVectorXd u(10);\n  u << 0.351659507062997,\n    0.830828627896291,\n    0.585264091152724,\n    0.549723608291140,\n    0.917193663829810,\n    0.285839018820374,\n    0.757200229110721,\n    0.753729094278495,\n    0.380445846975357,\n    0.567821640725221;\n\n  MatrixXd pts(10,3);\n  pts << 0.707620811535916,   0.510258911240815,   0.417485437023409,\n    0.603422256426978,   0.529498282727551,   0.270351549348981,\n    0.228364197569334,   0.423745615677815,   0.637687289287490,\n    0.275556796335168,   0.350856706427970,   0.684295784598905,\n    0.514519311047655,   0.525077224890754,   0.351628308305896,\n    0.724152914315666,   0.574461155457304,   0.469860285484058,\n    0.529365063753288,   0.613328702656816,   0.237837040141739,\n    0.522469395136878,   0.619099658652895,   0.237139665242069,\n    0.677357023849552,   0.480655768435853,   0.422227610314397,\n    0.247046593173758,   0.380604672404750,   0.670065791405019;\n  pts.transposeInPlace();\n\n  for (int i=0; i<u.size(); ++i)\n  {\n    Vector3d pt = spline(u(i));\n    VERIFY( (pt - pts.col(i)).norm() < 1e-14 );\n  }\n}\n\n/* compares evaluations on corner cases */\nvoid eval_spline3d_onbrks()\n{\n  Spline3d spline = spline3d();\n\n  RowVectorXd u = spline.knots();\n\n  MatrixXd pts(11,3);\n  pts <<    0.959743958516081,   0.340385726666133,   0.585267750979777,\n    0.959743958516081,   0.340385726666133,   0.585267750979777,\n    0.959743958516081,   0.340385726666133,   0.585267750979777,\n    0.430282980289940,   0.713074680056118,   0.720373307943349,\n    0.558074875553060,   0.681617921034459,   0.804417124839942,\n    0.407076008291750,   0.349707710518163,   0.617275937419545,\n    0.240037008286602,   0.738739390398014,   0.324554153129411,\n    0.302434111480572,   0.781162443963899,   0.240177089094644,\n    0.251083857976031,   0.616044676146639,   0.473288848902729,\n    0.251083857976031,   0.616044676146639,   0.473288848902729,\n    0.251083857976031,   0.616044676146639,   0.473288848902729;\n  pts.transposeInPlace();\n\n  for (int i=0; i<u.size(); ++i)\n  {\n    Vector3d pt = spline(u(i));\n    VERIFY( (pt - pts.col(i)).norm() < 1e-14 );\n  }\n}\n\nvoid eval_closed_spline2d()\n{\n  Spline2d spline = closed_spline2d();\n\n  RowVectorXd u(12);\n  u << 0,\n    0.332457030395796,\n    0.356467130532952,\n    0.453562180176215,\n    0.648017921874804,\n    0.973770235555003,\n    1.882577647219307,\n    2.289408593930498,\n    3.511951429883045,\n    3.884149321369450,\n    4.236261590369414,\n    4.252699478956276;\n\n  MatrixXd pts(12,2);\n  pts << -0.370967741935484,   0.236842105263158,\n    -0.152576775123250,   0.448975001279334,\n    -0.133417538277668,   0.461615613865667,\n    -0.053199060826740,   0.507630360006299,\n    0.114249591147281,   0.570414135097409,\n    0.377810316891987,   0.560497102875315,\n    0.665052120135908,  -0.157557441109611,\n    0.516006487053228,  -0.559763292174825,\n    -0.379486035348887,  -0.331959640488223,\n    -0.462034726249078,  -0.039105670080824,\n    -0.378730600917982,   0.225127015099919,\n    -0.370967741935484,   0.236842105263158;\n  pts.transposeInPlace();\n\n  for (int i=0; i<u.size(); ++i)\n  {\n    Vector2d pt = spline(u(i));\n    VERIFY( (pt - pts.col(i)).norm() < 1e-14 );\n  }\n}\n\nvoid check_global_interpolation2d()\n{\n  typedef Spline2d::PointType PointType;\n  typedef Spline2d::KnotVectorType KnotVectorType;\n  typedef Spline2d::ControlPointVectorType ControlPointVectorType;\n\n  ControlPointVectorType points = ControlPointVectorType::Random(2,100);\n\n  KnotVectorType chord_lengths; // knot parameters\n  Eigen::ChordLengths(points, chord_lengths);\n\n  // interpolation without knot parameters\n  {\n    const Spline2d spline = SplineFitting<Spline2d>::Interpolate(points,3);  \n\n    for (Eigen::DenseIndex i=0; i<points.cols(); ++i)\n    {\n      PointType pt = spline( chord_lengths(i) );\n      PointType ref = points.col(i);\n      VERIFY( (pt - ref).matrix().norm() < 1e-14 );\n    }\n  }\n\n  // interpolation with given knot parameters\n  {\n    const Spline2d spline = SplineFitting<Spline2d>::Interpolate(points,3,chord_lengths);  \n\n    for (Eigen::DenseIndex i=0; i<points.cols(); ++i)\n    {\n      PointType pt = spline( chord_lengths(i) );\n      PointType ref = points.col(i);\n      VERIFY( (pt - ref).matrix().norm() < 1e-14 );\n    }\n  }\n}\n\nvoid check_global_interpolation_with_derivatives2d()\n{\n  typedef Spline2d::PointType PointType;\n  typedef Spline2d::KnotVectorType KnotVectorType;\n\n  const Eigen::DenseIndex numPoints = 100;\n  const unsigned int dimension = 2;\n  const unsigned int degree = 3;\n\n  ArrayXXd points = ArrayXXd::Random(dimension, numPoints);\n\n  KnotVectorType knots;\n  Eigen::ChordLengths(points, knots);\n\n  ArrayXXd derivatives = ArrayXXd::Random(dimension, numPoints);\n  VectorXd derivativeIndices(numPoints);\n\n  for (Eigen::DenseIndex i = 0; i < numPoints; ++i)\n      derivativeIndices(i) = static_cast<double>(i);\n\n  const Spline2d spline = SplineFitting<Spline2d>::InterpolateWithDerivatives(\n    points, derivatives, derivativeIndices, degree);  \n    \n  for (Eigen::DenseIndex i = 0; i < points.cols(); ++i)\n  {\n    PointType point = spline(knots(i));\n    PointType referencePoint = points.col(i);\n    VERIFY_IS_APPROX(point, referencePoint);\n    PointType derivative = spline.derivatives(knots(i), 1).col(1);\n    PointType referenceDerivative = derivatives.col(i);\n    VERIFY_IS_APPROX(derivative, referenceDerivative);\n  }\n}\n\nvoid test_splines()\n{\n  for (int i = 0; i < g_repeat; ++i)\n  {\n    CALL_SUBTEST( eval_spline3d() );\n    CALL_SUBTEST( eval_spline3d_onbrks() );\n    CALL_SUBTEST( eval_closed_spline2d() );\n    CALL_SUBTEST( check_global_interpolation2d() );\n    CALL_SUBTEST( check_global_interpolation_with_derivatives2d() );\n  }\n}\n"
  },
  {
    "path": "location/CMakeLists.txt",
    "content": "aux_source_directory(. location_src_lists)\nadd_library(Location_location ${location_src_lists})\n\ntarget_link_libraries(\n        Location_location\n        Location_sensor\n        Location_system\n        Location_models\n)"
  },
  {
    "path": "location/Location.cpp",
    "content": "//\n// Created by yangcheng on 2019/1/14.\n//\n\n#include <cmath>\n#include \"Location.h\"\n#include <iostream>\n#include <fstream>\n#include \"../sensor/GPS.h\"\n#include \"../sensor/Accelerometer.h\"\n#include \"../sensor/Gravity.h\"\n#include \"../sensor/Compass.h\"\n#include \"../models/AHRS.h\"\n#include \"../models/StrapdownAHRS.h\"\n#include \"../math/LPF.h\"\n#include \"../models/XgboostDetector.h\"\n\nusing namespace Eigen;\nusing namespace routing;\n\n/**\n * Location 初始化。\n */\nLocation::Location() {\n    // 初始化参数\n    this->status.Init();\n    LPF lpf;\n    lpf.LowPassFilter2ndFactorCal(&status);\n//    LoadStopDetectModel();\n}\n\nLocation::~Location() {\n\n}\n\n/**\n * 定位,计算当前位置\n *\n * @param gyro_data, 陀螺仪原始数据, w(x,y,z)\n * @param acc_data, 加速计原始数据, a(x,y,z)\n * @param mag_data, 地磁计原始数据, m(x,y,z)\n * @param gps_data, GPS原始数据, gps(lng,lat,alt,accuracy,speed,bearing,t)\n * @param g_data, 重力感应数据, g(x,y,z)\n * @param ornt_data, 方向传感器数据, o(roll,pitch,yaw)\n * @param road_data, 道路方向数据,包含距离下个路口距离和当前位置道路方向, 道路类型编码, v(distance, bearing, code)\n * @param status, 状态容器, 包含位置,姿态,速度,参数等信息\n */\nvoid Location::PredictCurrentPosition(Vector3d &gyro_data, Vector3d &acc_data, Vector3d &mag_data, VectorXd &gps_data,\n                                      Vector3d &g_data, Vector3d &ornt_data, Vector3d &road_data) {\n\n    // 记录起始位置和当前位置\n    double start_x = status.position.x;\n    double start_y = status.position.y;\n    double start_lng = status.position.lng;\n    double start_lat = status.position.lat;\n\n    // 行车状态预测\n//    PredictStopStatus(gyro_data, acc_data, mag_data, g_data, ornt_data);\n    // 更新道路状态\n    UpdateRoadType(road_data);\n    // 更新惯性位置,速度\n    Accelerometer accelerometer;\n//    accelerometer.PositionIntegral(&status, final_acc_lpf, status.parameters.t);\n    Quaternions quaternions;\n    // 方向数据修正\n    LPF lpf;\n    Vector3d ornt_filter = lpf.LowPassFilter4Ornt(&status, ornt_data);\n    Vector4d attitude = quaternions.GetQFromEuler(ornt_filter);\n    AutoAdjustMovingFactor();\n    accelerometer.StrapdownUpdateVelocityPosition(&status, acc_data, attitude, g_data);\n\n    // 指南针波动情况\n    Compass compass;\n    bool is_compass_vaild = compass.IsCompassVaild(&status, ornt_data);\n\n    // 判断手机是否摆放发生变化\n    Gravity gravity;\n    bool is_shaking = gravity.IsShaking(&status, g_data);\n\n    // 判断是否以及行走到路口一定范围内\n    bool is_near_cross = status.parameters.dist_from_pre_cross < status.parameters.min_dist_from_pre_cross ||\n                         status.parameters.dist_to_next_cross < status.parameters.min_dist_to_next_cross;\n\n    // 判断是否处于重新规划线路的时间段内\n    bool is_routing = IsRouting(ornt_filter, road_data);\n\n    // 判断指南针跟道路的方向变化是否一直\n//    bool is_same_change = IsRoadCompassSameRange(&status, ornt_filter, road_data);\n\n    // 判断是否偏航\n//    bool is_off_course = IsOffCourse(&status, ornt_filter, road_data);\n\n    // 获取GPS精度\n    GPS gps;\n    // 计算传感器运动距离\n    double end_x = status.position.x;\n    double end_y = status.position.y;\n    double distance = sqrt((end_x - start_x) * (end_x - start_x) + (end_y - start_y) * (end_y - start_y));\n\n    // 判断ins是否走的距离达到限制最大距离\n    bool is_ins_move_not_too_far = status.parameters.ins_dist < status.parameters.max_ins_dist;\n    // 判断是否采用GPS数据\n    bool is_gps_valid = gps.IsGPSValid(&status, &gps_data);\n    status.parameters.is_current_gps_valid = is_gps_valid;\n    if (!is_gps_valid) {\n\n        // 采用惯导更新经纬度\n        double heading_no_limit;\n//        if ((is_shaking || !is_compass_vaild) || (!is_near_cross || is_same_change)) {\n        if ((is_shaking || !is_compass_vaild) || (!is_near_cross && !is_routing)) {\n//        if ((is_shaking || !is_compass_vaild) || !is_near_cross) {\n            // 更新道路方向和方向传感器Z轴方向, 当GPS精度低或不可用一定时间后\n            UpdateZaxisWithRoad(ornt_filter, road_data);\n            heading_no_limit = ornt_filter(2) + status.parameters.diff_road_ornt;\n        } else {\n            if (status.parameters.ins_count >\n                status.parameters.Hz * status.parameters.least_gap_time_for_using_road) {\n                // 当无信号运动超过一定时间,此时用道路差值修正,GPS方向已经比较旧\n                heading_no_limit = ornt_filter(2) + status.parameters.diff_road_ornt;\n            } else {\n                // 当无信号运动还没超过一定时间,此时用GPS方向\n                heading_no_limit = ornt_filter(2) + status.parameters.diff_gps_ornt;\n            }\n        }\n\n        // 限制取值范围\n        double heading;\n        if (heading_no_limit > 360.0) {\n            heading = heading_no_limit - 360.0;\n        } else if (heading_no_limit < 0) {\n            heading = heading_no_limit + 360.0;\n        } else {\n            heading = heading_no_limit;\n        }\n        status.attitude.yaw = heading;\n        if (is_ins_move_not_too_far) {\n            // 计算航向角\n            Vector2d gps_new = gps.CalDestination(start_lng, start_lat, distance, heading);\n            // 更新经纬度\n            status.position.lng = gps_new(0);\n            status.position.lat = gps_new(1);\n            // 更新相关参数\n            status.parameters.ins_count += 1;\n            status.parameters.ins_dist += distance;\n        }\n    } else {\n        // 采用GPS数据更新经纬度和方位角\n        double gps_speed = gps_data(4);\n        double gps_bearing = gps_data(5);\n        status.position.lng = gps_data(0);\n        status.position.lat = gps_data(1);\n        status.position.altitude = gps_data(2);\n        status.attitude.yaw = gps_bearing;\n        gps.UpdateVelocity(&status, gps_speed, gps_bearing);\n        // 更新相关参数值,gps(lng,lat,alt,accuracy,speed,bearing,t)\n        status.parameters.gps_pre_lng = gps_data(0);\n        status.parameters.gps_pre_lat = gps_data(1);\n        status.parameters.gps_pre_altitude = gps_data(2);\n        status.parameters.gps_pre_accuracy = gps_data(3);\n        status.parameters.gps_pre_speed = gps_speed;\n        status.parameters.gps_pre_bearing = gps_bearing;\n        status.parameters.gps_pre_t = gps_data(6);\n        // 时间t影响因子自调整\n//        AutoAdjustTFactor(&status, gps_data, status.parameters.ins_dist);\n        // 更新GPS方向和方向传感器Z轴方向, 当GPS可用且精度高时\n        UpdateZaxisWithGPS(gps_data, ornt_filter);\n        // 更新其他INS变量\n        status.parameters.gps_count += 1;\n        status.parameters.ins_count = 0;\n        status.parameters.ins_dist = 0;\n        status.parameters.move_t_factor = 1.0;\n        // 更新融合定位结果输出\n        status.gnssins.accuracy = gps_data(3);\n        status.gnssins.speed = gps_speed;\n        // 每个x,y,z都是相对与上一个准确的GPS数据。\n        status.position.x = 0.0;\n        status.position.y = 0.0;\n        status.position.z = 0.0;\n    }\n//\n//    std::string log_msg = std::to_string(status.parameters.gps_pre_bearing) + \" \" + std::to_string(ornt_filter(2)) + \" \"\n//                          + std::to_string(status.parameters.diff_gps_ornt) + \" \"\n//                          + std::to_string(status.parameters.diff_road_ornt) + \" \"\n//                          + std::to_string(status.attitude.yaw) + \" \" + std::to_string(road_data(1)) + \" \"\n//                          + std::to_string(road_data(0)) + \" \" + std::to_string(status.parameters.ins_count) + \" \"\n//                          + std::to_string(gps_data(0)) + \" \" + std::to_string(gps_data(1)) + \" \"\n//                          + std::to_string(((is_shaking || !is_compass_vaild) || (!is_near_cross)))\n//                          + \" \" + std::to_string(is_shaking) + \" \" + std::to_string(is_compass_vaild) + \" \"\n//                          + std::to_string(!is_near_cross) + \" \" + std::to_string(status.parameters.dist_to_next_cross)\n//                          + \" \" + std::to_string(status.parameters.dist_from_pre_cross);\n//    Log(log_msg);\n//    std::cout << log_msg << std::endl;\n//    std::cout << status.parameters.gps_pre_bearing << \" \" << ornt_filter(2) << \" \"\n//              << status.parameters.diff_gps_ornt << \" \" << status.parameters.diff_road_ornt\n//              << \" \" << status.attitude.yaw << \" \" << road_data(1) <<\n//              \" \" << road_data(0) << \" \"\n//              << status.parameters.ins_count << \" \" << gps_data(0) << \" \" << gps_data(1)\n//              << \" \" << ((is_shaking || !is_compass_vaild) || (!is_near_cross || is_same_change)) << \" \"\n//              << is_shaking << \" \" << is_same_change << \" \" << !is_near_cross\n//              << \" \" << status.parameters.dist_to_next_cross << \" \"\n//              << status.parameters.dist_from_pre_cross << std::endl;\n\n    // 约定当惯导起作用时,精度返回99.99\n    if (status.parameters.ins_count >\n        status.parameters.Hz * status.parameters.least_gap_time_for_using_road)\n        status.gnssins.accuracy = 99.99;\n    // 更新融合定位的结果，精度沿用GPS信号好时的精度,速度由于加速计计算的是三个方位的速度，故速度还是沿用GPS的速度\n    status.gnssins.lng = status.position.lng;\n    status.gnssins.lat = status.position.lat;\n    status.gnssins.altitude = status.position.altitude;\n    status.gnssins.bearing = status.attitude.yaw;\n\n\n}\n\n/**\n * 设置传感器频率\n * @param f\n */\nvoid Location::SetHz(double f) {\n    this->status.parameters.Hz = f;\n    this->status.parameters.acc_hz = f / 2.0;\n    this->status.parameters.halfT = 1.0 / (f * 2.0);\n    this->status.parameters.t = 1.0 / (f * (this->status.parameters.static_t_factor));\n}\n\n/**\n * 设置模型路径\n * @param model_path\n */\nvoid Location::SetModelPath(std::string model_path) {\n    this->status.parameters.stop_detector_model_path = model_path;\n}\n\n/**\n * 判断文件是否有效\n * @param model_path\n * @return\n */\nbool Location::IsFileVaild(std::string &model_path) {\n    std::ifstream inFile;\n    inFile.open(model_path);\n    if (inFile) {\n        inFile.close();\n        return true;\n    } else {\n        inFile.close();\n        return false;\n    }\n}\n\n/**\n * 加载模型\n */\nvoid Location::LoadStopDetectModel() {\n    std::string model_path = this->status.parameters.stop_detector_model_path;\n    std::string model_name = \"stopDetector.model\";\n    if (model_path.find(model_name) != std::string::npos) {\n        bool is_file_vaild = IsFileVaild(model_path);\n        if (is_file_vaild) {\n            this->stopDetection = std::make_shared<XgboostDetector>(model_path);\n        }\n    } else {\n        std::string model_full_path = model_path + \"/stopDetector.model\";\n        bool is_file_vaild = IsFileVaild(model_full_path);\n        if (is_file_vaild) {\n            this->stopDetection = std::make_shared<XgboostDetector>(model_path);\n        }\n    }\n}\n\n/**\n * 预测行车状态\n *\n * @param gyro_data\n * @param acc_data\n * @param mag_data\n * @param g_data\n * @param ornt_data\n */\nvoid Location::PredictStopStatus(Eigen::Vector3d &gyro_data, Eigen::Vector3d &acc_data, Eigen::Vector3d &mag_data,\n                                 Eigen::Vector3d &g_data, Eigen::Vector3d &ornt_data) {\n\n    static Vector3d pre_ornt_data(-999.0, -999.0, -999.0);\n    static Vector3d pre_mag_data(-999.0, -999.0, -999.0);\n    int total_detect_size = (int) (this->status.parameters.stop_status_window * this->status.parameters.Hz);\n    static int cnt = 0;\n    static VectorXd stop_status_v(total_detect_size);\n\n    Quaternions quaternions;\n    Accelerometer accelerometer;\n\n    if (pre_ornt_data(0) != -999.0 && pre_ornt_data(1) != -999.0 && pre_ornt_data(2) != -999.0) {\n\n        Vector3d ornt_diff = ornt_data - pre_ornt_data;\n        Vector4d q = quaternions.GetQFromEuler(ornt_data);\n        Matrix3d dcm = quaternions.GetDCMFromQ(q);\n\n        Vector3d acc_v = acc_data;\n        Vector3d acc_n = dcm * acc_v;\n        Vector3d acc_v_norm = accelerometer.Normalise(acc_v);\n        Vector3d acc_n_norm = accelerometer.Normalise(acc_n);\n\n        Vector3d g_v = g_data;\n        Vector3d g_n = dcm * g_v;\n        Vector3d g_v_norm = accelerometer.Normalise(g_v);\n        Vector3d g_n_norm = accelerometer.Normalise(g_n);\n        Vector3d a_diff = acc_n - g_n;\n\n        Vector3d gyro_v = gyro_data;\n        Vector3d gyro_v_norm = accelerometer.Normalise(gyro_v);\n\n        Vector3d mag_v_diff = (dcm * mag_data) - (dcm * pre_mag_data);\n        Vector3d mag_v_norm = accelerometer.Normalise(mag_v_diff);\n\n        VectorXd input_data(27);\n        input_data << acc_v_norm(0), acc_v_norm(1), acc_v_norm(2), acc_n_norm(0), acc_n_norm(1), acc_n_norm(2),\n                g_v_norm(0), g_v_norm(1), g_v_norm(2), g_n_norm(0), g_n_norm(1), g_n_norm(2),\n                gyro_v_norm(0), gyro_v_norm(1), gyro_v_norm(2), mag_v_norm(0), mag_v_norm(1), mag_v_norm(2),\n                mag_v_diff(0), mag_v_diff(1), mag_v_diff(2), a_diff(0), a_diff(1), a_diff(2),\n                ornt_diff(0), ornt_diff(1), ornt_diff(2);\n\n        if (this->stopDetection) {\n            bool detect_res = this->stopDetection->IsStopping(input_data);\n            if (cnt < total_detect_size) {\n                stop_status_v(cnt) = detect_res;\n                cnt += 1;\n            } else {\n                // 队列先进先出\n                for (int i = 0; i < total_detect_size - 1; ++i) {\n                    stop_status_v(i) = stop_status_v(i + 1);\n                    stop_status_v(i) = stop_status_v(i + 1);\n                }\n                stop_status_v(total_detect_size - 1) = detect_res;\n                if (stop_status_v.sum() / total_detect_size > 0.5) this->status.parameters.stop_status = 0;\n            }\n\n        }\n\n    } else {\n        pre_ornt_data = ornt_data;\n        pre_mag_data = mag_data;\n    }\n}\n\n/**\n * 获取当前融合定位结果作为输出\n * @return\n */\nGNSSINS Location::GetGNSSINS() {\n    return this->status.gnssins;\n}\n\n\n/**\n * 获取当前位置\n * @return\n */\nPosition Location::GetCurrentPosition() {\n    return this->status.position;\n}\n\n/**\n * 获取当前方位角\n * @return\n */\ndouble Location::GetCurrentBearing() {\n    return this->status.attitude.yaw;\n}\n\n/**\n * 自调节机制, 利用GPS运动距离调整t的放大因子\n *\n * @param gps_data, gps(lng,lat,alt,accuracy,speed,bearing,t)\n * @param ins_distance\n */\nvoid Location::AutoAdjustTFactor(Eigen::VectorXd &gps_data, double ins_distance) {\n\n    static int cnt = 0;\n    static MatrixXd gps_queue(3, 7);\n    static Vector3d ins_move_dist(3);\n\n    if (cnt < 3) {\n        gps_queue.row(cnt) = gps_data;\n        ins_move_dist(cnt) = ins_distance;\n        cnt += 1;\n    } else {\n        GPS gps;\n        double lng1 = gps_queue(0, 0);\n        double lat1 = gps_queue(0, 1);\n        double lng2 = gps_queue(1, 0);\n        double lat2 = gps_queue(1, 1);\n        double lng3 = gps_queue(2, 0);\n        double lat3 = gps_queue(2, 1);\n//        double gps_dist1 = gps_queue(0,4) * ((gps_queue(1, 6) - gps_queue(0, 6)) / 1000.0) + gps_queue(1, 4) * ((gps_queue(2, 6) - gps_queue(1, 6)) / 1000.0);\n        double gps_dist = gps.CalDistance(lng1, lat1, lng2, lat2) + gps.CalDistance(lng2, lat2, lng3, lat3);\n        double ins_dist = ins_move_dist(1) + ins_move_dist(2);\n        double deltaT = (gps_queue(2, 6) - gps_queue(0, 6)) / 1000.0;\n        if (gps_dist != 0.0 && ins_dist != 0.0 && deltaT != 0.0) {\n//            (*status).parameters.move_t_factor *= sqrt(gps_dist / ins_dist);\n            this->status.parameters.move_t_factor = sqrt(gps_dist / ins_dist);\n//            std::string log_msg = std::to_string(gps_dist) + \" \" + std::to_string(gps_dist1) + \" \"\n//                                  + std::to_string(ins_dist) + \" \"\n//                                  + std::to_string(deltaT) + \" \" + std::to_string(sqrt(gps_dist / ins_dist)) + \" \"\n//                                  + std::to_string((*status).parameters.move_t_factor);\n//            std::cout << log_msg << std::endl;\n        }\n\n        // 先进先出\n        gps_queue.row(0) = gps_queue.row(1);\n        gps_queue.row(1) = gps_queue.row(2);\n        gps_queue.row(2) = gps_data;\n        ins_move_dist(0) = ins_move_dist(1);\n        ins_move_dist(1) = ins_move_dist(2);\n        ins_move_dist(2) = ins_distance;\n    }\n}\n\n/**\n * 惯导运动衰减因子,随时间及方位角变化而衰减\n */\nvoid Location::AutoAdjustMovingFactor() {\n    static Vector2d ornt_queue;\n    static int cnt = 0;\n\n    if (cnt <= 1) {\n        ornt_queue(cnt) = this->status.attitude.yaw;\n        cnt += 1;\n    } else {\n        // 更新队列数据\n        ornt_queue(0) = ornt_queue(1);\n        ornt_queue(1) = this->status.attitude.yaw;\n        // 计算角度变化\n        double angle_factor;\n        if (ornt_queue(0) < 90.0 && ornt_queue(1) > 270.0) {\n            angle_factor = ornt_queue(0) + 360.0 - ornt_queue(1);\n        } else if (ornt_queue(1) < 90.0 && ornt_queue(0) > 270.0) {\n            angle_factor = ornt_queue(1) + 360.0 - ornt_queue(0);\n        } else {\n            angle_factor = abs(ornt_queue(1) - ornt_queue(0));\n        }\n\n        int gap_time = int(this->status.parameters.Hz * this->status.parameters.least_gap_time_for_using_road);\n        int ins_move_factor = this->status.parameters.ins_count % int(this->status.parameters.Hz);\n\n        if (this->status.parameters.ins_count > gap_time &&\n            (ins_move_factor == 0 || angle_factor >= this->status.parameters.accepted_max_diff_change_range)) {\n            this->status.parameters.move_t_factor *= this->status.parameters.move_decay;\n        }\n//        std::cout << (*status).parameters.move_t_factor << std::endl;\n    }\n}\n\n/**\n * 方向传感器和GPS,道路方向差值修正\n *\n * @param gps_data, gps(lng,lat,alt,accuracy,speed,bearing,t)\n * @param ornt_data, v(x,y,z)\n * @param road_data, 道路方向数据,包含距离下个路口距离,和当前点的瞬时方向,以及当前道路类型编码, v(distance, heading, code)\n */\nvoid Location::UpdateZaxisWithGPSAndRoad(Eigen::VectorXd &gps_data, Eigen::Vector3d &ornt_data,\n                                         Eigen::Vector3d &road_data) {\n    static MatrixXd gps_queue(this->status.parameters.queue_gps_ornt, 7);\n    static MatrixXd ornt_queue(this->status.parameters.queue_gps_ornt, 3);\n    static MatrixXd road_queue(this->status.parameters.queue_gps_ornt, 3);\n    static int gps_ornt_cnt = 0;\n    static int road_ornt_cnt = 0;\n\n    if (gps_ornt_cnt < this->status.parameters.queue_gps_ornt ||\n        road_ornt_cnt < this->status.parameters.queue_gps_ornt) {\n//    if (gps_ornt_cnt < (*status).parameters.queue_gps_ornt) {\n        // gps方向队列\n        if (gps_ornt_cnt < this->status.parameters.queue_gps_ornt &&\n            gps_data(4) > this->status.parameters.gps_static_speed_threshold) {\n            gps_queue.row(gps_ornt_cnt) = gps_data;\n            ornt_queue.row(gps_ornt_cnt) = ornt_data;\n            gps_ornt_cnt += 1;\n        }\n        // 道路方向队列\n        if (road_ornt_cnt < this->status.parameters.queue_gps_ornt && road_data(0) != 0.0 && road_data(1) != 0.0) {\n            road_queue.row(road_ornt_cnt) = road_data;\n            road_ornt_cnt += 1;\n        }\n    } else {\n        if (gps_data(0) == 0.0 && gps_data(1) == 0.0) {\n            if (this->status.parameters.ins_count >\n                this->status.parameters.Hz * this->status.parameters.least_gap_time_for_using_road) {\n                // 没gps信号, 且超过一定时间后, 采用道路方向做修正\n                VectorXd road_bearing = road_queue.col(1);\n                VectorXd ornt_bearing = ornt_queue.col(2);\n                double diff_road_ornt = (road_bearing - ornt_bearing).mean();\n                // TODO: 当距下个路口一定距离同时方向差别在一定范围内,采用道路方向修正指南针方向\n                this->status.parameters.diff_gps_ornt = diff_road_ornt;\n//                std::cout << road_bearing(0) << \" \" << ornt_bearing(0) << std::endl;\n//                if (road_data(0) != 0.0 && road_data(1) != 0.0) {\n//                    for (int i = 0; i < (*status).parameters.queue_gps_ornt - 1; i++) {\n//                        road_queue.row(i) = road_queue.row(i + 1);\n//                        ornt_queue.row(i) = ornt_queue.row(i + 1);\n//                    }\n//                    road_queue.row((*status).parameters.queue_gps_ornt - 1) = road_data;\n//                    ornt_queue.row((*status).parameters.queue_gps_ornt - 1) = ornt_data;\n//                }\n            } else {\n                // 没信号,但是没有超过一定时间间隔, 仍用当前指南针和上个GPS点修正\n                VectorXd gps_bearing = gps_queue.col(5);\n                VectorXd ornt_bearing = ornt_queue.col(2);\n                double diff_gps_ornt = (gps_bearing - ornt_bearing).mean();\n                this->status.parameters.diff_gps_ornt = diff_gps_ornt;\n//                for (int i = 0; i < (*status).parameters.queue_gps_ornt - 1; i++) {\n//                    ornt_queue.row(i) = ornt_queue.row(i + 1);\n//                }\n//                ornt_queue.row((*status).parameters.queue_gps_ornt - 1) = ornt_data;\n//                // 不用道路信息的时候也要更新道路状态\n//                if (road_data(0) != 0.0 && road_data(1) != 0.0) {\n//                    for (int i = 0; i < (*status).parameters.queue_gps_ornt - 1; i++) {\n//                        road_queue.row(i) = road_queue.row(i + 1);\n//                    }\n//                    road_queue.row((*status).parameters.queue_gps_ornt - 1) = road_data;\n//                }\n            }\n        } else {\n            // 有gps信号时尽量采用gps信号做辅助修正\n            VectorXd gps_bearing = gps_queue.col(5);\n            VectorXd ornt_bearing = ornt_queue.col(2);\n            double diff_gps_ornt = (gps_bearing - ornt_bearing).mean();\n            this->status.parameters.diff_gps_ornt = diff_gps_ornt;\n//            if (gps_data(4) > (*status).parameters.gps_static_speed_threshold) {\n//                for (int i = 0; i < (*status).parameters.queue_gps_ornt - 1; i++) {\n//                    gps_queue.row(i) = gps_queue.row(i + 1);\n//                    ornt_queue.row(i) = ornt_queue.row(i + 1);\n//                }\n//                gps_queue.row((*status).parameters.queue_gps_ornt - 1) = gps_data;\n//                ornt_queue.row((*status).parameters.queue_gps_ornt - 1) = ornt_data;\n//            }\n//            // 不用道路信息的时候也要更新道路状态\n//            if (road_data(0) != 0.0 && road_data(1) != 0.0) {\n//                for (int i = 0; i < (*status).parameters.queue_gps_ornt - 1; i++) {\n//                    road_queue.row(i) = road_queue.row(i + 1);\n//                }\n//                road_queue.row((*status).parameters.queue_gps_ornt - 1) = road_data;\n//            }\n        }\n\n        // 更新GPS数据\n        if (gps_data(0) != 0.0 && gps_data(1) != 0.0 && gps_data(4) > this->status.parameters.gps_static_speed_threshold) {\n            for (int i = 0; i < this->status.parameters.queue_gps_ornt - 1; i++) {\n                gps_queue.row(i) = gps_queue.row(i + 1);\n            }\n            gps_queue.row(this->status.parameters.queue_gps_ornt - 1) = gps_data;\n        }\n\n        // 更新道路数据\n        if (road_data(0) != 0.0 || road_data(1) != 0.0) {\n            for (int i = 0; i < this->status.parameters.queue_gps_ornt - 1; i++) {\n                road_queue.row(i) = road_queue.row(i + 1);\n            }\n            road_queue.row(this->status.parameters.queue_gps_ornt - 1) = road_data;\n        }\n\n        // 更新指南针数据\n        for (int i = 0; i < this->status.parameters.queue_gps_ornt - 1; i++) {\n            ornt_queue.row(i) = ornt_queue.row(i + 1);\n        }\n        ornt_queue.row(this->status.parameters.queue_gps_ornt - 1) = ornt_data;\n\n    }\n//    std::cout << gps_queue(0,5) << \" \" << road_queue(0,1) << \" \" << ornt_queue(0,2) << \" \"\n//              <<  (*status).parameters.diff_gps_ornt << std::endl;\n}\n\n/**\n * 方向传感器和GPS方向差值修正\n *\n * @param gps_data, gps(lng,lat,alt,accuracy,speed,bearing,t)\n * @param ornt_data, v(x,y,z)\n */\nvoid Location::UpdateZaxisWithGPS(Eigen::VectorXd &gps_data, Eigen::Vector3d &ornt_data) {\n    static MatrixXd gps_queue(this->status.parameters.queue_gps_ornt, 7);\n    static MatrixXd ornt_queue(this->status.parameters.queue_gps_ornt, 3);\n    static int gps_ornt_cnt = 0;\n\n    if (gps_ornt_cnt < this->status.parameters.queue_gps_ornt) {\n        // gps方向队列\n        if (gps_data(4) > this->status.parameters.gps_static_speed_threshold) {\n            gps_queue.row(gps_ornt_cnt) = gps_data;\n            ornt_queue.row(gps_ornt_cnt) = ornt_data;\n            gps_ornt_cnt += 1;\n        }\n    } else {\n\n        // 更新GPS数据\n        if (gps_data(4) > this->status.parameters.gps_static_speed_threshold) {\n            for (int i = 0; i < this->status.parameters.queue_gps_ornt - 1; i++) {\n                gps_queue.row(i) = gps_queue.row(i + 1);\n            }\n            gps_queue.row(this->status.parameters.queue_gps_ornt - 1) = gps_data;\n        }\n\n        // 更新指南针数据\n        for (int i = 0; i < this->status.parameters.queue_gps_ornt - 1; i++) {\n            ornt_queue.row(i) = ornt_queue.row(i + 1);\n        }\n        ornt_queue.row(this->status.parameters.queue_gps_ornt - 1) = ornt_data;\n\n        // 有gps信号时尽量采用gps信号做辅助修正\n        VectorXd gps_bearing = gps_queue.col(5);\n        VectorXd ornt_bearing = ornt_queue.col(2);\n        double diff_gps_ornt = (gps_bearing - ornt_bearing).mean();\n        this->status.parameters.diff_gps_ornt = diff_gps_ornt;\n        // 用此时有效的GPS方向更新道路差值\n        this->status.parameters.diff_road_ornt = diff_gps_ornt;\n\n    }\n}\n\n/**\n * 方向传感器和道路方向差值修正\n *\n * @param ornt_data, v(x,y,z)\n * @param road_data, 道路方向数据,包含距离下个路口距离,和当前点的瞬时方向,以及当前道路类型编码, v(distance, heading, code)\n */\nvoid\nLocation::UpdateZaxisWithRoad(Eigen::Vector3d &ornt_data, Eigen::Vector3d &road_data) {\n    static MatrixXd ornt_queue(this->status.parameters.queue_gps_ornt, 3);\n    static MatrixXd road_queue(this->status.parameters.queue_gps_ornt, 3);\n    static int road_ornt_cnt = 0;\n\n    if (road_ornt_cnt < this->status.parameters.queue_gps_ornt) {\n        // 道路方向队列\n        if (road_data(0) != 0.0 || road_data(1) != 0.0) {\n            road_queue.row(road_ornt_cnt) = road_data;\n            road_ornt_cnt += 1;\n        }\n    } else {\n        // 更新道路数据\n        if (road_data(0) != 0.0 || road_data(1) != 0.0) {\n            for (int i = 0; i < this->status.parameters.queue_gps_ornt - 1; i++) {\n                road_queue.row(i) = road_queue.row(i + 1);\n            }\n            road_queue.row(this->status.parameters.queue_gps_ornt - 1) = road_data;\n        }\n\n        // 更新指南针数据\n        for (int i = 0; i < this->status.parameters.queue_gps_ornt - 1; i++) {\n            ornt_queue.row(i) = ornt_queue.row(i + 1);\n        }\n        ornt_queue.row(this->status.parameters.queue_gps_ornt - 1) = ornt_data;\n\n        if (this->status.parameters.ins_count >\n            this->status.parameters.Hz * this->status.parameters.least_gap_time_for_using_road) {\n            // 没gps信号, 且超过一定时间后, 采用道路方向做修正\n            VectorXd road_bearing = road_queue.col(1);\n            VectorXd ornt_bearing = ornt_queue.col(2);\n            double diff_road_ornt = (road_bearing - ornt_bearing).mean();\n            // TODO: 当距下个路口一定距离同时方向差别在一定范围内,采用道路方向修正指南针方向\n            this->status.parameters.diff_road_ornt = diff_road_ornt;\n        } else {\n            // 没信号,但是没有超过一定时间间隔, 仍用当前指南针和上个GPS点修正\n            this->status.parameters.diff_road_ornt = this->status.parameters.diff_gps_ornt;\n        }\n\n    }\n}\n\n/**\n *  判断道路方向变化幅度是否与指南针幅度一致\n *\n * @param ornt_data, v(x,y,z)\n * @param road_data, 道路方向数据,包含距离下个路口距离,和当前点的瞬时方向,以及当前道路类型编码, v(distance, heading, code)\n * @return\n */\nbool Location::IsRoadCompassSameRange(Vector3d &ornt_data, Vector3d &road_data) {\n    static MatrixXd ornt_queue(this->status.parameters.queue_road_ornt_len, 3);\n    static MatrixXd road_queue(this->status.parameters.queue_road_ornt_len, 3);\n    static int road_ornt_cnt = 0;\n\n    bool res = true;\n    if (road_ornt_cnt < this->status.parameters.queue_road_ornt_len) {\n\n        // 道路方向队列\n        if (road_data(0) != 0.0 || road_data(1) != 0.0) {\n            if (road_ornt_cnt == 0) {\n                road_queue.row(road_ornt_cnt) = road_data;\n                ornt_queue.row(road_ornt_cnt) = ornt_data;\n                road_ornt_cnt += 1;\n            } else {\n                if (road_queue(road_ornt_cnt - 1, 1) != road_data(1)\n                    || road_queue(road_ornt_cnt - 1, 0) != road_data(0)) {\n                    road_queue.row(road_ornt_cnt) = road_data;\n                    ornt_queue.row(road_ornt_cnt) = ornt_data;\n                    road_ornt_cnt += 1;\n                }\n            }\n        }\n\n    } else {\n\n        // 更新道路数据\n        if ((road_data(0) != 0.0 || road_data(1) != 0.0) &&\n            (road_queue(road_ornt_cnt - 1, 1) != road_data(1)\n             || road_queue(road_ornt_cnt - 1, 0) != road_data(0))) {\n            for (int i = 0; i < this->status.parameters.queue_road_ornt_len - 1; i++) {\n                road_queue.row(i) = road_queue.row(i + 1);\n            }\n            road_queue.row(this->status.parameters.queue_road_ornt_len - 1) = road_data;\n\n            // 更新指南针数据\n            for (int i = 0; i < this->status.parameters.queue_road_ornt_len - 1; i++) {\n                ornt_queue.row(i) = ornt_queue.row(i + 1);\n            }\n            ornt_queue.row(this->status.parameters.queue_road_ornt_len - 1) = ornt_data;\n        }\n\n        VectorXd road_bearing = road_queue.col(1);\n        VectorXd ornt_bearing = ornt_queue.col(2);\n        VectorXd road_diff(this->status.parameters.queue_road_ornt_len - 1);\n        VectorXd ornt_diff(this->status.parameters.queue_road_ornt_len - 1);\n        LPF lpf;\n        for (int i = 0; i <= (this->status.parameters.queue_road_ornt_len - 2); ++i) {\n            std::string road_flag = lpf.JudgeOrientation(road_bearing(i)) + lpf.JudgeOrientation(road_bearing(i + 1));\n            std::string ornt_flag = lpf.JudgeOrientation(ornt_bearing(i)) + lpf.JudgeOrientation(ornt_bearing(i + 1));\n            // 处理0/360跳点问题\n            if (road_flag == \"14\") {\n                road_diff(i) = road_bearing(i) - (road_bearing(i + 1) + 360.0);\n            } else if (road_flag == \"41\") {\n                road_diff(i) = (road_bearing(i + 1) + 360.0) - road_bearing(i);\n            } else {\n                road_diff(i) = road_bearing(i + 1) - road_bearing(i);\n            }\n            if (ornt_flag == \"14\") {\n                ornt_diff(i) = ornt_bearing(i) - (ornt_bearing(i + 1) + 360.0);\n            } else if (ornt_flag == \"41\") {\n                ornt_diff(i) = (ornt_bearing(i + 1) + 360.0) - ornt_bearing(i);\n            } else {\n                ornt_diff(i) = ornt_bearing(i + 1) - ornt_bearing(i);\n            }\n\n        }\n\n        for (int i = 0; i <= this->status.parameters.queue_road_ornt_len - 2; i++) {\n            if (abs(road_diff(i)) < this->status.parameters.accepted_change_range) {\n                res = res && abs((road_diff(i) - ornt_diff(i))) < this->status.parameters.accepted_change_range;\n            } else {\n                res = res && abs(road_diff(i) - ornt_diff(i)) < this->status.parameters.accepted_max_diff_change_range;\n            }\n//            std::cout << (road_diff(i) < (*status).parameters.accepted_change_range)\n//                      << \" \" << road_diff(i) << \" \" << road_bearing(i) << \" \"  << road_bearing(i + 1)\n//                      << \" \" << ornt_diff(i) << \" \" << ornt_bearing(i) << \" \" << ornt_bearing(i + 1)\n//                      << \" \" << res << std::endl;\n        }\n    }\n    return res;\n}\n\n/**\n * 判断当前是否正处于重新规划中\n *\n * @param status\n * @param ornt_data, v(x,y,z)\n * @param road_data, 道路方向数据,包含距离下个路口距离,和当前点的瞬时方向,以及当前道路类型编码, v(distance, heading, code)\n * @return\n */\nbool Location::IsRouting(Eigen::Vector3d &ornt_data, Eigen::Vector3d &road_data) {\n    static bool routing = false;\n    static int cnt = 0;\n\n    if (road_data(0) == 0.0 && road_data(1) == 0.0) routing = true;\n    if (routing) cnt += 1;\n\n    if (cnt > (this->status.parameters.routing_time * this->status.parameters.Hz)) {\n        cnt = 0;\n        routing = false;\n    }\n    return routing;\n\n}\n\n/**\n * 判断是否偏离航线\n *\n * @param ornt_data, v(x,y,z)\n * @param road_data, 道路方向数据,包含距离下个路口距离,和当前点的瞬时方向,以及当前道路类型编码, v(distance, heading, code)\n * @return\n */\nbool Location::IsOffCourse(Eigen::Vector3d &ornt_data, Eigen::Vector3d &road_data) {\n\n    static VectorXd is_near_cross_queue(this->status.parameters.off_course_data_queue);\n    static VectorXd is_same_change_queue(this->status.parameters.off_course_data_queue);\n    static int cnt = 0;\n    static bool routing = false;\n\n    // 偏航标志\n    bool offCourseFlag = false;\n\n    // 判断是否以及行走到路口一定范围内\n    bool is_near_cross =\n            this->status.parameters.dist_from_pre_cross < this->status.parameters.min_dist_from_pre_cross ||\n            this->status.parameters.dist_to_next_cross < this->status.parameters.min_dist_to_next_cross;\n\n    // 判断指南针跟道路的方向变化是否一直\n    bool is_same_change = IsRoadCompassSameRange(ornt_data, road_data);\n\n    if (cnt < this->status.parameters.off_course_data_queue) {\n        is_near_cross_queue(cnt) = is_near_cross;\n        is_same_change_queue(cnt) = is_same_change;\n        cnt += 1;\n    } else {\n\n        if (is_near_cross_queue(0)) {\n            // 在路口发生偏航的时候\n            bool res = true;\n            // 连续一个窗口内都判断是否偏航\n            for (int i = 0; i < this->status.parameters.off_course_data_queue; ++i) {\n                res = res && is_near_cross_queue(i) && !is_same_change_queue(i);\n            }\n            offCourseFlag = res;\n        }\n\n        // 队列先进先出\n        for (int k = 0; k < this->status.parameters.off_course_data_queue - 1; ++k) {\n            is_near_cross_queue(k) = is_near_cross_queue(k + 1);\n            is_same_change_queue(k) = is_same_change_queue(k + 1);\n        }\n        is_near_cross_queue(this->status.parameters.off_course_data_queue - 1) = is_near_cross;\n        is_same_change_queue(this->status.parameters.off_course_data_queue - 1) = is_same_change;\n\n    }\n\n    // 重新规划,重置flag.\n    if (road_data(0) == 0.0 && road_data(1) == 0.0) routing = true;\n    if (routing && (road_data(0) != 0.0 || road_data(1) != 0.0)) {\n        offCourseFlag = false;\n        routing = false;\n    }\n\n    return offCourseFlag;\n}\n\n/**\n * 更新道路状态\n * @param road_data, v(distance, bearing, code)\n */\nvoid Location::UpdateRoadType(Eigen::Vector3d &road_data) {\n    static double jump_point = 0.0;\n\n    if (road_data(0) != 0.0 || road_data(1) != 0.0) {\n        this->status.parameters.road_type = road_data(2);\n\n        if (road_data(0) > this->status.parameters.dist_to_next_cross) {\n            jump_point = road_data(0);\n            this->status.parameters.dist_from_pre_cross = 0.0;\n        } else {\n            if (jump_point > road_data(0)) {\n                this->status.parameters.dist_from_pre_cross = jump_point - road_data(0);\n            }\n        }\n        this->status.parameters.dist_to_next_cross = road_data(0);\n    } else {\n        jump_point = 0.0;\n        this->status.parameters.road_type = 0.0;\n        this->status.parameters.dist_to_next_cross = 100000.0;\n        this->status.parameters.dist_from_pre_cross = 100000.0;\n    }\n\n}\n\n/**\n * 获取当前输入GPS点状态, 需在调用`PredictCurrentPosition`方法后调用.\n * @return true 为可用, false 不可用\n */\nbool Location::GetCurentGPSStatus() {\n    return status.parameters.is_current_gps_valid;\n}\n\n//Eigen::VectorXd Location::GPSJumpPointCompensate(routing::Status *status, Eigen::VectorXd &gps_bearing_queue) {\n//\n//\n//}"
  },
  {
    "path": "location/Location.h",
    "content": "//\n// Created by yangcheng on 2019/1/14.\n//\n\n#ifndef LOCATION_LOCATION_H\n#define LOCATION_LOCATION_H\n\n#include \"../system/Status.h\"\n#include \"../include/eigen3/Eigen/Dense\"\n#include \"../models/StopDetection.h\"\n#include <memory>\n\nusing LOG_CALLBACK = std::function<void(std::string)>;\n\nclass Location {\n\nprivate:\n\n    // 状态容器\n    routing::Status status;\n    LOG_CALLBACK Log;\n\n    // 无信号时检测行车状态的模型\n    std::shared_ptr<StopDetection> stopDetection;\n\n    // 判断模型文件是否存在或损坏\n    bool IsFileVaild(std::string &model_path);\n    // 加载模型\n    void LoadStopDetectModel();\n    // 预测整个过程中的行车状态0/1\n    void PredictStopStatus(Eigen::Vector3d &gyro_data, Eigen::Vector3d &acc_data, Eigen::Vector3d &mag_data,\n                           Eigen::Vector3d &g_data, Eigen::Vector3d &ornt_data);\n\n    // 获取当前位置\n    routing::Position GetCurrentPosition();\n\n    // 获取当前方位角\n    double GetCurrentBearing();\n\n    // 采样时间自适应\n    void AutoAdjustTFactor(Eigen::VectorXd &gps_data, double ins_distance);\n\n    // 惯导运动衰减因子\n    void AutoAdjustMovingFactor();\n\n    // 方向传感器和GPS方向差值修正\n    void UpdateZaxisWithGPSAndRoad(Eigen::VectorXd &gps_data, Eigen::Vector3d &ornt_data,\n                                   Eigen::Vector3d &road_data);\n\n    // 方向传感器和GPS方向差值修正\n    void UpdateZaxisWithGPS(Eigen::VectorXd &gps_data, Eigen::Vector3d &ornt_data);\n\n    // 方向传感器和道路方向差值修正\n    void UpdateZaxisWithRoad(Eigen::Vector3d &ornt_data, Eigen::Vector3d &road_data);\n\n    // 判断道路方向变化幅度是否与指南针幅度一致\n    bool IsRoadCompassSameRange(Eigen::Vector3d &ornt_data, Eigen::Vector3d &road_data);\n\n    // 判断当前是否正处于重新规划中\n    bool IsRouting(Eigen::Vector3d &ornt_data, Eigen::Vector3d &road_data);\n\n    // 判断是否偏离航道\n    bool IsOffCourse(Eigen::Vector3d &ornt_data, Eigen::Vector3d &road_data);\n\n    // 更新道路类型\n    void UpdateRoadType(Eigen::Vector3d &road_data);\n\npublic:\n\n    Location();\n\n    ~Location();\n    \n    void SetLogCallback(LOG_CALLBACK callback) { Log = callback; }\n    \n    // 定位,计算当前位置\n    void PredictCurrentPosition(Eigen::Vector3d &gyro_data, Eigen::Vector3d &acc_data, Eigen::Vector3d &mag_data,\n                                Eigen::VectorXd &gps_data, Eigen::Vector3d &g_data, Eigen::Vector3d &ornt_data,\n                                Eigen::Vector3d &road_data\n    );\n\n    // 获取当前GPS是否可用\n    bool GetCurentGPSStatus();\n\n    // 获取当前融合定位的输出\n    routing::GNSSINS GetGNSSINS();\n\n    // 设置采样频率\n    void SetHz(double f);\n\n    // 设置解压后的模型路径\n    void SetModelPath(std::string model_path);\n//    Eigen::VectorXd GPSJumpPointCompensate(routing::Status *status, Eigen::VectorXd &gps_bearing_queue);\n\n};\n\n\n#endif //LOCATION_LOCATION_H\n"
  },
  {
    "path": "main.cpp",
    "content": "#include <Eigen/Dense>\n#include \"sensor/GPS.h\"\n#include <iomanip>\n#include \"math/Optimizer.h\"\n#include <iostream>\n#include <fstream>\n#include <cassert>\n#include <string>\n#include \"test/utils/DataFormat.h\"\n#include \"test/TestLocation.h\"\n#include \"test/TestCalibration.h\"\n#include \"config/Config.h\"\n#include \"Location.h\"\n#include \"XgboostDetector.h\"\n#include \"math/Quaternions.h\"\n#include <chrono>\n#include \"TestXgboostDetector.h\"\n\nusing namespace Eigen;\nusing namespace std;\n\nint main() {\n\n//    TestXgboostDetector testXgboostDetector;\n//    testXgboostDetector.TestDetector();\n\n//    using namespace std::chrono;\n//    long long int ms = duration_cast< milliseconds >(\n//            system_clock::now().time_since_epoch()\n//    ).count();\n//    // testing xgboost model.\n//    std::string model_path = \"D:\\\\worksheet\\\\clion\\\\Location\\\\models\\\\xgboost_model.txt\";\n//    StopDetection stopDetection = XgboostDetector(model_path);\n//    Eigen::VectorXd input(27);\n//    input << 0.166704003,0.793647502,0.585092658,-0.836314314,-0.495913423,0.233769642,0.202316318,0.528412458,0.824529188,-0.85625963,-0.222778842,0.466035443,0.221061031,-0.715468667,-0.662749279,0.922008461,0.260256615,0.28664768,3.344844582,0.94415395,1.039894947,2.136208297,-1.528755739,-2.820955601,-0.750271,2.003565,-1.070326;\n//    bool res = stopDetection.IsStopping(input);\n//    long long int ms2 = duration_cast< milliseconds >(\n//            system_clock::now().time_since_epoch()\n//    ).count();\n//    std::cout << \"xgboost detector, current status is stopping: \" << res\n//              << \" using time(ms) \" << ms2 - ms << std::endl;\n\n    // unit test\n//    int data_size = 45461;\n//    MatrixXd gyro2(data_size,3),acc2(data_size,3),mag2(data_size,3), gps2(data_size,7),\n//            g2(data_size,3), ornt2(data_size,3), road_data(data_size,3);\n//    DataFormat dataFormat;\n//    dataFormat.writeCSVs();\n//    std::string file = \"D:\\\\worksheet\\\\clion\\\\Location\\\\test\\\\data\\\\sensor_log\\\\origin_sensors_data_1558592729003.9297.csv\";\n//    dataFormat.readCSV(file, gyro2,acc2,mag2, gps2, g2, ornt2, road_data);\n//    TestLocation testLocation;\n//    testLocation.testLocation(gyro2, acc2, mag2, gps2, g2, ornt2, road_data);\n\n//     checking sensor.\n    Vector3d e(57.221,-0.543, 143.2);\n    Quaternions quaternions;\n    Vector4d q = quaternions.GetQFromEuler(e);\n//    cout << q.transpose() << endl;\n    MatrixXd dcm = quaternions.GetDCMFromQ(q);\n    Vector3d gb(0.041, 8.248, 5.311);\n    Vector3d gn = dcm * gb;\n    cout << \"Using euler rotate the gravity from b frame: [\" << gb.transpose()\n         << \"] to n frame, result is: [\" << gn.transpose() << \"].\" << endl;\n\n\n//     testing work flow.\n    Location location;\n    Vector3d gyro_data_v(0.004263,0.019169,-0.001014);\n    Vector3d mag_data_v(-2.313675,-82.446960,-366.183838);\n    Vector3d acc_data_v(0.105081,0.108075,9.774973);\n    VectorXd gps_data_v(7);\n    gps_data_v << 114.174118,22.283789,0.0,0.0,24.0,0.0,1554348968704.665039;\n    Vector3d g_data_v(0.094139, 0.107857,9.808955);\n    Vector3d ornt_data_v(-0.549866,0.629957,-0.069398);\n    Vector3d road_data(1000.0, 0.0, 0);\n    location.PredictCurrentPosition(gyro_data_v,acc_data_v,mag_data_v,gps_data_v,g_data_v,ornt_data_v, road_data);\n    cout << \"Current predict result: lng \" << location.GetGNSSINS().lng << \", lat \" <<     location.GetGNSSINS().lat << endl;\n    return 0;\n}"
  },
  {
    "path": "math/CMakeLists.txt",
    "content": "aux_source_directory(. math_src_lists)\nadd_library(Location_math ${math_src_lists})"
  },
  {
    "path": "math/Coordinate.cpp",
    "content": "//\n// Created by yangcheng on 2018/12/14.\n//\n\n#include <cmath>\n#include \"Coordinate.h\"\n\nusing namespace std;\n\nCoordinate::Coordinate() {}\n\nCoordinate::~Coordinate() = default;\n\nPoint2D Coordinate::LngLat2Mercator(double lng, double lat) {\n    double x = lng * 20037508.34 / 180.0;\n    double y = log(tan((90.0 + lat) * M_PI / 360.0)) / (M_PI / 180.0);\n    y *= 20037508.34 / 180.0;\n    return {x, y};\n}\n\nPoint2D Coordinate::Mercator2LngLat(double x, double y) {\n    double lng = x / 20037508.34 * 180.0;\n    double lat = y / 20037508.34 * 180.0;\n    lat = 180.0 / M_PI * (2 * atan(exp(lat * M_PI / 180.0)) -  M_PI / 2.0);\n    return {lng, lat};\n}\n\ndouble Coordinate::Deg2Rad(double deg) {\n    return deg * M_PI / 180.0;\n}\n\ndouble Coordinate::Rad2Deg(double rad) {\n    return rad * 180.0 / M_PI;\n}"
  },
  {
    "path": "math/Coordinate.h",
    "content": "//\n// Created by yangcheng on 2018/12/14.\n//\n\n#ifndef LOCATION_COORDINATE_H\n#define LOCATION_COORDINATE_H\n\nstruct Point2D {\n    double lng;\n    double lat;\n\n    Point2D(double _lng, double _lat) : lng(_lng), lat(_lat) {};\n};\n\nstruct Point3D {\n    double lng;\n    double lat;\n    double altitude;\n\n    Point3D(double _lng, double _lat, double _altitude) : lng(_lng), lat(_lat), altitude(_altitude) {};\n};\n\nclass Coordinate {\npublic:\n\n    Coordinate();\n\n    ~Coordinate();\n\n    // 经纬度转墨卡托\n    Point2D LngLat2Mercator(double lng, double lat);\n\n    // 墨卡托转经纬度\n    Point2D Mercator2LngLat(double x, double y);\n\n    // 角度转弧度\n    double Deg2Rad(double deg);\n\n    // 弧度转角度\n    double Rad2Deg(double rad);\n\n};\n\n\n#endif //LOCATION_COORDINATE_H\n"
  },
  {
    "path": "math/KalmanFilter.cpp",
    "content": "//\n// Created by yangcheng on 2018/11/25.\n//\n\n#include \"KalmanFilter.h\"\n#include \"../sensor/GPS.h\"\n\nusing namespace Eigen;\n\n\nKalmanFilter::KalmanFilter(Eigen::Vector4d &init_state) {\n\n    this->x = init_state;\n\n    // 转移矩阵\n    this->F << 1.0, 0.0, 1.0, 0.0,\n            0.0, 1.0, 0.0, 1.0,\n            0.0, 0.0, 1.0, 0.0,\n            0.0, 0.0, 0.0, 1.0;\n\n    // 转移误差\n    this->Q << 0.0, 0.0, 0.0, 0.0,\n            0.0, 0.0, 0.0, 0.0,\n            0.0, 0.0, 0.1, 0.0,\n            0.0, 0.0, 0.0, 0.1;\n\n    // 测量矩阵\n    this->H << 1.0, 0.0, 0.0, 0.0,\n            0.0, 1.0, 0.0, 0.0,\n            0.0,0.0,1.0,0.0,\n            0.0,0.0,0.0,1.0;\n\n    // GPS噪声方差\n    this->R << 0.00001, 0.0, 0.0, 0.0,\n            0.0, 0.00001, 0.0, 0.0,\n            0.0, 0.0, 0.1, 0.0001,\n            0.0, 0.0, 0.0001, 0.1;\n\n\n    // 协方差初始化\n    this->P << 0.00001, 0.0, 0.0, 0.0,\n            0.0, 0.00001, 0.0, 0.0,\n            0.0, 0.0, 0.1, 0.0,\n            0.0, 0.0, 0.0, 0.1;\n}\n\n\nEigen::Vector4d KalmanFilter::PredictState() {\n\n    GPS gps;\n    double lng = this->x(0);\n    double lat = this->x(1);\n    double v_east = this->x(2);\n    double v_north = this->x(3);\n    double east_dist = v_east * this->F(0, 2);\n    double north_dist = v_north * this->F(1, 3);\n    double north_angle = 0.0;\n    double east_angle = 90.0;\n    double new_lat = gps.CalDestination(lng, lat, north_dist, north_angle)(1);\n    double new_lng = gps.CalDestination(lng, lat, east_dist, east_angle)(0);\n\n    Vector4d priori_State(new_lng, new_lat, v_east, v_north);\n    return priori_State;\n}\n\nEigen::Matrix4d KalmanFilter::CalcPrioriCov() {\n    return this->F * this->P * this->F.transpose() + this->Q;\n}\n\nvoid KalmanFilter::UpdateState(Eigen::Vector4d &measure_state) {\n\n    Vector4d prioriState = PredictState();\n    Matrix4d prioriCov = CalcPrioriCov();\n    // TODO: 求逆方法改进\n    Matrix4d k = prioriCov * this->H.transpose() * (this->H * prioriCov * this->H.transpose() + this->R).inverse();\n    Vector4d posteriorState = prioriState + k * (measure_state - this->H * prioriState);\n    Matrix4d posteriorCov = (MatrixXd::Identity(4, 4) - k * this->H) * prioriCov;\n    this->x = posteriorState;\n    this->P = posteriorCov;\n}\n\n\nvoid KalmanFilter::SetF(double deltaT) {\n    this->F(0,2) = deltaT;\n    this->F(1,3) = deltaT;\n}\n\nvoid KalmanFilter::SetPQ(double varS) {\n    this->P(2,2) = varS;\n    this->P(3,3) = varS;\n\n    this->Q(2,2) = varS;\n    this->Q(3,3) = varS;\n}\n\nEigen::Vector4d KalmanFilter::GetState() {\n    return this->x;\n}"
  },
  {
    "path": "math/KalmanFilter.h",
    "content": "//\n// Created by yangcheng on 2018/11/25.\n//\n\n#ifndef LOCATION_KALMANFILTER_H\n#define LOCATION_KALMANFILTER_H\n\n\n#include <Eigen/Dense>\n\n\nclass KalmanFilter {\n\nprivate:\n\n    // t-1时刻状态\n    Eigen::Vector4d x;\n    // 转移矩阵\n    Eigen::Matrix4d F;\n    // 状态转移误差矩阵\n    Eigen::Matrix4d Q;\n    // 测量矩阵\n    Eigen::Matrix4d H;\n    // 测量误差矩阵)\n    Eigen::Matrix4d R;\n    // 协方差矩阵\n    Eigen::Matrix4d P;\n\npublic:\n\n    // 实例化\n    KalmanFilter(Eigen::Vector4d &init_state);\n\n    // 预测过程\n    Eigen::Vector4d PredictState();\n\n    Eigen::Matrix4d CalcPrioriCov();\n\n    // 更新过程\n    void UpdateState(Eigen::Vector4d &measure_state);\n\n    // 由于每次GPS更新间隔并非常数,需手动更新矩阵F\n    void SetF(double deltaT);\n\n    // 过程随着运动不断更新deltas,即速度方差, P和Q\n    void SetPQ(double varS);\n\n    // 获取过滤后的\n    Eigen::Vector4d GetState();\n\n};\n\n\n#endif //LOCATION_KALMANFILTER_H\n"
  },
  {
    "path": "math/LPF.cpp",
    "content": "//\n// Created by yangcheng on 2019/2/26.\n//\n\n#include \"LPF.h\"\n#include \"iostream\"\n#include <string.h>\n\nusing namespace routing;\nusing namespace Eigen;\n\n/**\n * 二级低通滤波参数计算\n * @param status\n */\nvoid LPF::LowPassFilter2ndFactorCal(Status *status) {\n    double a = 1 / (2 * M_PI * status->parameters.acc_hz * status->parameters.t);\n    status->parameters.acc_b0 = 1 / (a * a + 3 * a + 1);\n    status->parameters.acc_a1 = (2 * a * a + 3 * a) / (a * a + 3 * a + 1);\n    status->parameters.acc_a2 = (a * a) / (a * a + 3 * a + 1);\n\n\n    double o = 1 / (2 * M_PI * status->parameters.ornt_hz * status->parameters.t);\n    status->parameters.ornt_b0 = 1 / (o * o + 3 * o + 1);\n    status->parameters.ornt_a1 = (2 * o * o + 3 * o) / (o * o + 3 * o + 1);\n    status->parameters.ornt_a2 = (o * o) / (o * o + 3 * o + 1);\n}\n\n/**\n * 二阶低通滤波\n *\n * @param status\n * @param cur_data\n */\nVector3d LPF::LowPassFilter2nd4ACC(Status *status, Vector3d &cur_data) {\n    Vector3d lpf_acc;\n\n    double b0 = status->parameters.acc_b0;\n    double a1 = status->parameters.acc_a1;\n    double a2 = status->parameters.acc_a2;\n    lpf_acc(0) =\n            cur_data(0) * b0 + status->parameters.sec_last_acc_data(0) * a1 - status->parameters.last_acc_data(0) * a2;\n    lpf_acc(1) =\n            cur_data(1) * b0 + status->parameters.sec_last_acc_data(1) * a1 - status->parameters.last_acc_data(1) * a2;\n    lpf_acc(2) =\n            cur_data(2) * b0 + status->parameters.sec_last_acc_data(2) * a1 - status->parameters.last_acc_data(2) * a2;\n\n    status->parameters.last_acc_data = status->parameters.sec_last_acc_data;\n    status->parameters.sec_last_acc_data = lpf_acc;\n//    std::cout << \"parameter \" << b0 << \" \" <<  a1  << \" \" << a2 << std::endl;\n    return lpf_acc;\n}\n\n\nstd::string LPF::JudgeOrientation(double orientation) {\n    if (orientation <= 90.0) {\n        return \"1\";\n    } else if (orientation > 90.0 && orientation <= 180.0) {\n        return \"2\";\n    } else if (orientation > 180.0 && orientation <= 270.0) {\n        return \"3\";\n    } else {\n        return \"4\";\n    }\n}\n\n/**\n * 指南针360度跳点补偿.\n *\n * @param current\n * @param sec_last\n * @param last\n * @return\n */\nEigen::Vector3d LPF::JumpPointCompensate(double current, double sec_last, double last) {\n    Vector3d lpf_compensate;\n    std::string flag = JudgeOrientation(current) + JudgeOrientation(sec_last) + JudgeOrientation(last);\n\n    if (flag == \"144\") {\n        lpf_compensate(0) = current + 360.0;\n        lpf_compensate(1) = sec_last;\n        lpf_compensate(2) = last;\n    } else if (flag == \"114\") {\n        lpf_compensate(0) = current + 360.0;\n        lpf_compensate(1) = sec_last + 360.0;\n        lpf_compensate(2) = last;\n    } else if (flag == \"141\") {\n        lpf_compensate(0) = current + 360;\n        lpf_compensate(1) = sec_last;\n        lpf_compensate(2) = last;\n    } else if (flag == \"411\") {\n        lpf_compensate(0) = current;\n        lpf_compensate(1) = sec_last + 360.0;\n        lpf_compensate(2) = last + 360.0;\n    } else if (flag == \"441\") {\n        lpf_compensate(0) = current;\n        lpf_compensate(1) = sec_last;\n        lpf_compensate(2) = last + 360.0;\n    } else if (flag == \"414\") {\n        lpf_compensate(0) = current;\n        lpf_compensate(1) = sec_last + 360.0;\n        lpf_compensate(2) = last;\n    } else {\n        lpf_compensate(0) = current;\n        lpf_compensate(1) = sec_last;\n        lpf_compensate(2) = last;\n    }\n    return lpf_compensate;\n}\n\nEigen::Vector3d LPF::LowPassFilter4Ornt(routing::Status *status, Eigen::Vector3d &ornt_data) {\n    Vector3d lpf_ornt;\n\n    double b0 = status->parameters.ornt_b0;\n    double a1 = status->parameters.ornt_a1;\n    double a2 = status->parameters.ornt_a2;\n\n    if((*status).parameters.gps_count == 0){\n        status->parameters.last_ornt_data = ornt_data;\n        status->parameters.sec_last_ornt_data = ornt_data;\n    }\n\n    for(int i = 0; i < 3; ++i){\n        Vector3d lpf_compensate = JumpPointCompensate(ornt_data(i), status->parameters.sec_last_ornt_data(i), status->parameters.last_ornt_data(i));\n        double lpf_filter = lpf_compensate(0) * b0 + lpf_compensate(1) * a1 - lpf_compensate(2) * a2;\n        if(lpf_filter > 360.0){\n            lpf_ornt(i) = lpf_filter - 360.0;\n        }else{\n            lpf_ornt(i) = lpf_filter;\n        }\n    }\n\n//    lpf_ornt(0) = ornt_data(0) * b0 + status->parameters.sec_last_ornt_data(0) * a1 - status->parameters.last_ornt_data(0) * a2;\n//    lpf_ornt(1) = ornt_data(1) * b0 + status->parameters.sec_last_ornt_data(1) * a1 - status->parameters.last_ornt_data(1) * a2;\n//    lpf_ornt(2) = ornt_data(2) * b0 + status->parameters.sec_last_ornt_data(2) * a1 - status->parameters.last_ornt_data(2) * a2;\n\n    status->parameters.last_ornt_data = status->parameters.sec_last_ornt_data;\n    status->parameters.sec_last_ornt_data = lpf_ornt;\n//    std::cout << ornt_data(2) << \" \" << lpf_ornt(2) << std::endl;\n//    std::cout << \"parameter \" << b0 << \" \" <<  a1  << \" \" << a2 << std::endl;\n    return lpf_ornt;\n\n}\n\n// 初始化,计算对应参数\nLPF::LPF() {\n//    LowPassFilter2ndFactorCal(status);\n}\n\nLPF::~LPF() {}"
  },
  {
    "path": "math/LPF.h",
    "content": "//\n// Created by yangcheng on 2019/2/26.\n//\n\n#ifndef LOCATION_LPF_H\n#define LOCATION_LPF_H\n\n#include \"../system/Status.h\"\n#include \"Eigen/Dense\"\n\n\nclass LPF {\npublic:\n\n    LPF();\n    ~LPF();\n//    void LowPassFilter();\n\n    void LowPassFilter2ndFactorCal(routing::Status *status);\n\n    Eigen::Vector3d LowPassFilter2nd4ACC(routing::Status *status, Eigen::Vector3d &cur_data);\n\n    Eigen::Vector3d LowPassFilter4Ornt(routing::Status *status, Eigen::Vector3d &ornt_data);\n\n    Eigen::Vector3d JumpPointCompensate(double current, double sec_last, double last);\n\n    std::string JudgeOrientation(double orientation);\n};\n\n\n#endif //LOCATION_LPF_H\n"
  },
  {
    "path": "math/Optimizer.cpp",
    "content": "//\n// Created by yangcheng on 2019/1/7.\n//\n#include \"iostream\"\n#include \"Optimizer.h\"\n\nusing namespace Eigen;\n\n/**\n * LM(Levenberg-Marquardt)算法, 简化了牛顿法中Hessian矩阵的二阶项, 同时加入了阻尼因子\n *\n * @param input_data, n*3, n组数据,每组3维\n * @param coef 椭圆6参数，用于标定(加速计/地磁计)传感器\n * @param gamma, 初始化阻尼因子用, mu = gamma * max(A), A = Jacobi_t * Jacobi;\n * @param epsilon 迭代精度\n * @param max_iter 最高迭代次数\n */\nvoid\nOptimizer::LevenbergMarquardt(MatrixXd &input_data, double &R, VectorXd *coef, double &gamma, double &epsilon,\n                              int &max_iter) {\n\n    int data_nums = static_cast<int>(input_data.rows());\n    // delta, coef的梯度\n    VectorXd delta(6);\n    // e_k = 1 - (x_k - coef(0))² * coef(3)² - (y_k - coef(1))² * coef(4)² - (z_k - coef(2))² * coef(5)²\n    VectorXd e_k(data_nums);\n    // Hessian矩阵, 忽略牛顿法中的二阶项\n    MatrixXd hessian(6, 6);\n    // 阻尼Hessian矩阵\n    MatrixXd hessian_mu(6, 6);\n    // g向量, Jacobi_t * e_k\n    VectorXd g(6);\n\n    // jacobi矩阵\n    MatrixXd jacobi(data_nums, 6);\n\n    // 初始化算法迭代参数\n    int iter = 0;\n    int v = 2;\n    double mu = 0;\n    bool found = false;\n\n    // LM算法主流程\n    // e_k 计算\n    e_k = EllipticalFx(input_data, coef, R);\n    // 椭球方程的Jacobi矩阵计算\n    jacobi = EllipticalCaliJacobi(input_data, coef, R);\n    // hssian矩阵计算\n    hessian = jacobi.transpose() * jacobi;\n    // 初始计算阻尼\n    mu = gamma * hessian.maxCoeff();\n    // 计算g\n    g = jacobi.transpose() * e_k;\n\n\n    while (!found && iter <= max_iter) {\n\n        iter += 1;\n        //std::cout << iter << std::endl;\n        // hessin矩阵加入阻尼因子\n        hessian_mu = hessian + mu * MatrixXd::Identity(6, 6);\n        // 计算更新步长\n        delta = hessian_mu.inverse() * (-1 * g);\n        // 判断是否退出\n        if (delta.norm() <= epsilon * ((*coef).norm() + epsilon)) {\n            found = true;\n        } else {\n\n            // 计算可能的新参数\n            VectorXd coef_new(6);\n            coef_new(0) = (*coef)(0) + delta(0);\n            coef_new(1) = (*coef)(1) + delta(1);\n            coef_new(2) = (*coef)(2) + delta(2);\n            coef_new(3) = (*coef)(3) + delta(3);\n            coef_new(4) = (*coef)(4) + delta(4);\n            coef_new(5) = (*coef)(5) + delta(5);\n\n            // 计算rho, 为更新阻尼因子做准备\n            double L0_Ldelta = 0.5 * delta.transpose() * (mu * delta - g);\n            // 通用此处原算法只用到一组数据，修改为多组情况下取模\n            double Fx_Fxdelta = e_k.norm() - EllipticalFx(input_data, &coef_new, R).norm();\n//            double Fx_Fxdelta_v = Fx_Fxdelta.mean();\n            // rho\n//            double rho = Fx_Fxdelta_v / L0_Ldelta;\n            double rho = Fx_Fxdelta / L0_Ldelta;\n            // 根据rho大小更新mu\n            if (rho > 0) {\n                (*coef)(0) = coef_new(0);\n                (*coef)(1) = coef_new(1);\n                (*coef)(2) = coef_new(2);\n                (*coef)(3) = coef_new(3);\n                (*coef)(4) = coef_new(4);\n                (*coef)(5) = coef_new(5);\n\n                // 重新计算Jacobi, e_k, hessian, g\n                e_k = EllipticalFx(input_data, coef, R);\n                jacobi = EllipticalCaliJacobi(input_data, coef, R);\n                hessian = jacobi.transpose() * jacobi;\n                g = jacobi.transpose() * e_k;\n\n                if (g.norm() < epsilon) {\n                    found = true;\n                }\n\n                // 更新mu\n                Vector2d temp(1 / 3.0, 1 - (2 * rho - 1) * (2 * rho - 1) * (2 * rho - 1));\n                mu = mu * temp.maxCoeff();\n                v = 2;\n            } else {\n                mu *= v;\n                v *= 2;\n            }\n            std::cout << \"delta.norm() \" << delta.norm() << \" g.norm() \" << g.norm() << \" iter \" << iter << \" found \"\n                      << found\n                      << \" rho \" << rho << std::endl;\n        }\n    }\n}\n\n/**\n * 高斯牛顿法, 简化了牛顿法中Hessian矩阵的二阶项, 在某些情况下不收敛，待验证中。\n *\n * @param input_data, n*3, n组数据,每组3维\n * @param coef 椭圆6参数，用于标定(加速计/地磁计)传感器\n * @param epsilon 迭代精度\n * @param max_iter 最高迭代次数\n */\nvoid Optimizer::GaussNewton(MatrixXd &input_data, double &R, VectorXd *coef, double &epsilon, int &max_iter) {\n\n    int data_nums = static_cast<int>(input_data.rows());\n    // delta, coef的梯度\n    VectorXd delta(6);\n    // e_k = 1 - (x_k - coef(0))² * coef(3)² - (y_k - coef(1))² * coef(4)² - (z_k - coef(2))² * coef(5)²\n    VectorXd e_k(data_nums);\n    // Hessian矩阵, 忽略牛顿法中的二阶项\n    MatrixXd hessian(6, 6);\n    // jacobi矩阵\n    MatrixXd jacobi(data_nums, 6);\n\n    double epsilon_temp = 10.0;\n    int iter = 0;\n\n    while (epsilon_temp > epsilon && iter <= max_iter) {\n        // e_k 计算\n        e_k = EllipticalFx(input_data, coef, R);\n\n        // 椭球方程的Jacobi矩阵计算\n        jacobi = EllipticalCaliJacobi(input_data, coef, R);\n        // hssian矩阵计算\n        hessian = jacobi.transpose() * jacobi;\n        // 计算delta\n        delta = hessian.inverse() * (jacobi.transpose() * e_k);\n\n        // 更新coef\n        (*coef)(0) -= delta(0);\n        (*coef)(1) -= delta(1);\n        (*coef)(2) -= delta(2);\n        (*coef)(3) -= delta(3);\n        (*coef)(4) -= delta(4);\n        (*coef)(5) -= delta(5);\n\n        epsilon_temp = delta.norm();//e_k.cwiseAbs().sum();//delta.sum();\n        iter += 1;\n//        std::cout << \" iter \" << iter << \"\\n jacobi \\n\" << jacobi  << \"\\n hessian \\n\" << hessian  << \"\\n hessian inverse \\n\" << hessian.inverse() << std::endl;\n//        std::cout << \"epsilon \" << epsilon_temp << std::endl;\n    }\n}\n\n/**\n * 椭圆方程的雅可比矩阵计算, 椭球公式如下：\n * e_k = R² - (x_k - coef(0))² * coef(3)² - (y_k - coef(1))² * coef(4)² - (z_k - coef(2))² * coef(5)²\n *\n * @param input_data n*3, n组数据,每组3维\n * @param coef 椭圆6参数，用于标定(加速计/地磁计)传感器\n * @return n*6 的雅可比矩阵\n */\nMatrixXd Optimizer::EllipticalCaliJacobi(MatrixXd &input_data, VectorXd *coef, double &R) {\n\n    int data_nums = static_cast<int>(input_data.rows());\n    MatrixXd jacobiPileUp(data_nums, 6);\n\n    for (int i = 0; i < data_nums; i++) {\n\n        double ex = (input_data(i, 0) - (*coef)(0));\n        double ey = (input_data(i, 1) - (*coef)(1));\n        double ez = (input_data(i, 2) - (*coef)(2));\n        double e = R*R - ex * ex * (*coef)(3) * (*coef)(3)\n                   - ey * ey * (*coef)(4) * (*coef)(4)\n                   - ez * ez * (*coef)(5) * (*coef)(5);\n\n        // 对每个coef求导\n        jacobiPileUp(i, 0) = 2*e* 2 * ex * (*coef)(3) * (*coef)(3);\n        jacobiPileUp(i, 1) = 2*e* 2 * ey * (*coef)(4) * (*coef)(4);\n        jacobiPileUp(i, 2) = 2*e* 2 * ez * (*coef)(5) * (*coef)(5);\n        jacobiPileUp(i, 3) = 2*e* (-2) * (*coef)(3) * ex * ex;\n        jacobiPileUp(i, 4) = 2*e* (-2) * (*coef)(4) * ey * ey;\n        jacobiPileUp(i, 5) = 2*e* (-2) * (*coef)(5) * ez * ez;\n\n    }\n\n    return jacobiPileUp;\n}\n\n/**\n * 计算椭球方程误差, 椭球公式如下：\n * e_k = R² - (x_k - coef(0))² * coef(3)² - (y_k - coef(1))² * coef(4)² - (z_k - coef(2))² * coef(5)²\n *\n * @param input_data n*3, n组数据,每组3维\n * @param coef 椭圆6参数，用于标定(加速计/地磁计)传感器\n * @param R 椭圆半径\n * @return e_k 向量\n */\nVectorXd Optimizer::EllipticalFx(MatrixXd &input_data, VectorXd *coef, double &R) {\n\n    int data_nums = static_cast<int>(input_data.rows());\n    // e_k = R² - (x_k - coef(0))² * coef(3)² - (y_k - coef(1))² * coef(4)² - (z_k - coef(2))² * coef(5)²\n    VectorXd e_k(data_nums);\n\n    for (int i = 0; i < data_nums; i++) {\n        double ex = (input_data(i, 0) - (*coef)(0));\n        double ey = (input_data(i, 1) - (*coef)(1));\n        double ez = (input_data(i, 2) - (*coef)(2));\n\n        double e = R*R - ex * ex * (*coef)(3) * (*coef)(3)\n                   - ey * ey * (*coef)(4) * (*coef)(4)\n                   - ez * ez * (*coef)(5) * (*coef)(5);\n        e_k(i) = e * e;\n    }\n\n    return e_k;\n}"
  },
  {
    "path": "math/Optimizer.h",
    "content": "//\n// Created by yangcheng on 2019/1/7.\n//\n\n#ifndef LOCATION_OPTIMIZER_H\n#define LOCATION_OPTIMIZER_H\n\n#include \"Eigen/Dense\"\n#include \"../system/Status.h\"\n\n// 优化器, 解决标定参数求解问题\nclass Optimizer {\npublic:\n\n    void LevenbergMarquardt(Eigen::MatrixXd &input_data, double &R, Eigen::VectorXd *coef, double &gamma, double &epsilon, int &max_iter);\n\n//    void LevenbergMarquardt(Eigen::MatrixXd &input_data, Parameters *parameters);\n\n    void GaussNewton(Eigen::MatrixXd &input_data, double &R, Eigen::VectorXd *coef, double &epsilon, int &max_iter);\n\n//    void GaussNewton(Eigen::MatrixXd &input_data, Parameters *parameters);\n\n//private:\n\n    Eigen::MatrixXd EllipticalCaliJacobi(Eigen::MatrixXd &input_data, Eigen::VectorXd *coef, double &R);\n\n//    Eigen::MatrixXd EllipticalCaliJacobi(Eigen::MatrixXd &input_data, Parameters *parameters);\n\n    Eigen::VectorXd EllipticalFx(Eigen::MatrixXd &input_data, Eigen::VectorXd *coef, double &R);\n\n//    Eigen::VectorXd EllipticalFx(Eigen::MatrixXd &input_data, Parameters *parameters);\n};\n\n\n#endif //LOCATION_OPTIMIZER_H\n"
  },
  {
    "path": "math/Quaternions.cpp",
    "content": "//\n// Created by yangcheng on 2018/11/27.\n//\n\n#include <cmath>\n#include \"Eigen/Dense\"\n#include \"Quaternions.h\"\n\nusing namespace Eigen;\n\nQuaternions::Quaternions() {};\n\nQuaternions::~Quaternions() = default;\n\n// 归一化.\nVector4d Quaternions::Normalise(Vector4d &q) const {\n    Vector4d normQ;\n    double norm2 = q(0) * q(0) + q(1) * q(1) + q(2) * q(2) + q(3) * q(3);\n    // 如果四元数各项足够接近单位四元数, 则不做任何处理.\n    if (norm2 != 0.0) {\n        double norm = sqrt(norm2);\n        normQ(0) = q(0) / norm;\n        normQ(1) = q(1) / norm;\n        normQ(2) = q(2) / norm;\n        normQ(3) = q(3) / norm;\n    } else {\n        normQ = q;\n    }\n    return normQ;\n}\n\n// 共轭四元数, 实部相同，虚部取反.\nVector4d Quaternions::GetConjugate(Vector4d &q) const {\n    Vector4d conjQ;\n    conjQ(0) = q(0);\n    conjQ(1) = -q(1);\n    conjQ(2) = -q(2);\n    conjQ(3) = -q(3);\n    return conjQ;\n}\n\n// 四元数基本运算, 加.\nVector4d Quaternions::Add(Vector4d &q1, Vector4d &q2) const {\n    Vector4d addRes;\n\n    addRes(0) = q1(0) + q2(0);\n    addRes(1) = q1(1) + q2(1);\n    addRes(2) = q1(2) + q2(2);\n    addRes(3) = q1(3) + q2(3);\n\n    return addRes;\n}\n\n// 四元数基本运算, 点乘.\nVector4d Quaternions::DotMulti(Vector4d &q1, Vector4d &q2) const {\n    Vector4d dotMultiRes;\n\n    dotMultiRes(0) = q1(0) * q2(0);\n    dotMultiRes(1) = q1(1) * q2(1);\n    dotMultiRes(2) = q1(2) * q2(2);\n    dotMultiRes(3) = q1(3) * q2(3);\n\n    return dotMultiRes;\n}\n\n// 四元数基本运算, 叉乘.\nVector4d Quaternions::CrossMulti(Vector4d &q1, Vector4d &q2) const {\n    Vector4d crossMultiRes;\n\n    crossMultiRes(0) = q1(0) * q2(0) - q1(1) * q2(1) - q1(2) * q2(2) - q1(3) * q2(3);\n    crossMultiRes(1) = q1(1) * q2(0) + q1(0) * q2(1) + q1(2) * q2(3) - q1(3) * q2(2);\n    crossMultiRes(2) = q1(2) * q2(0) + q1(0) * q2(2) + q1(3) * q2(1) - q1(1) * q2(3);\n    crossMultiRes(3) = q1(3) * q2(0) + q1(0) * q2(3) + q1(1) * q2(2) - q1(2) * q2(1);\n\n    return crossMultiRes;\n}\n\n// 从欧拉角 v(x, y, z)/v(Roll, Pitch, Yaw) 中获取四元数 Q(q0,q1,q2,q3).\nVector4d Quaternions::GetQFromEuler(Vector3d &euler_angle) const {\n    Vector4d eulerQ;\n\n    double r = (euler_angle(0) * M_PI / 180.0) / 2.0;\n    double p = (euler_angle(1) * M_PI / 180.0) / 2.0;\n    double y = (euler_angle(2) * M_PI / 180.0) / 2.0;\n\n\n    double sinp = sin(p);\n    double siny = sin(y);\n    double sinr = sin(r);\n    double cosp = cos(p);\n    double cosy = cos(y);\n    double cosr = cos(r);\n\n    eulerQ(0) = cosr * cosp * cosy + sinr * sinp * siny;\n    eulerQ(1) = sinr * cosp * cosy - cosr * sinp * siny;\n    eulerQ(2) = cosr * sinp * cosy + sinr * cosp * siny;\n    eulerQ(3) = cosr * cosp * siny - sinr * sinp * cosy;\n\n    return eulerQ;\n}\n\n// 从四元数获取余弦矩阵DCM\nMatrix3d Quaternions::GetDCMFromQ(Vector4d &q) {\n    // b系到地理系n系\n    Matrix3d dcm_b2n;\n\n    dcm_b2n(0, 0) = q(0) * q(0) + q(1) * q(1) - q(2) * q(2) - q(3) * q(3);\n    dcm_b2n(0, 1) = 2 * (q(1) * q(2) - q(0) * q(3));\n    dcm_b2n(0, 2) = 2 * (q(1) * q(3) + q(0) * q(2));\n    dcm_b2n(1, 0) = 2 * (q(1) * q(2) + q(0) * q(3));\n    dcm_b2n(1, 1) = q(0) * q(0) - q(1) * q(1) + q(2) * q(2) - q(3) * q(3);\n    dcm_b2n(1, 2) = 2 * (q(2) * q(3) - q(0) * q(1));\n    dcm_b2n(2, 0) = 2 * (q(1) * q(3) - q(0) * q(2));\n    dcm_b2n(2, 1) = 2 * (q(2) * q(3) + q(0) * q(1));\n    dcm_b2n(2, 2) = q(0) * q(0) - q(1) * q(1) - q(2) * q(2) + q(3) * q(3);\n\n    return dcm_b2n;\n}\n\n// 从余弦矩阵DCM获取四元数\nVector4d Quaternions::GetQfromDCM(Matrix3d &dcm_b2n) {\n\n    Vector4d q;\n    double trace = dcm_b2n(0,0) + dcm_b2n(1,1) + dcm_b2n(2,2); // I removed + 1.0f; see discussion with Ethan\n    if( trace > 0 ) {// I changed M_EPSILON to 0\n        double s = 0.5 / sqrt(trace+ 1.0);\n        q(0) = 0.25 / s;\n        q(1) = ( dcm_b2n(2,1) - dcm_b2n(1,2) ) * s;\n        q(2) = ( dcm_b2n(0,2) - dcm_b2n(2,0) ) * s;\n        q(3) = ( dcm_b2n(1,0) - dcm_b2n(0,1) ) * s;\n    } else {\n        if ( dcm_b2n(0,0) > dcm_b2n(1,1) && dcm_b2n(0,0) > dcm_b2n(2,2) ) {\n            double s = 2.0 * sqrt( 1.0 + dcm_b2n(0,0) - dcm_b2n(1,1) - dcm_b2n(2,2));\n            q(0) = (dcm_b2n(2,1) - dcm_b2n(1,2) ) / s;\n            q(1) = 0.25 * s;\n            q(2) = (dcm_b2n(0,1) + dcm_b2n(1,0) ) / s;\n            q(3) = (dcm_b2n(0,2) + dcm_b2n(2,0) ) / s;\n        } else if (dcm_b2n(1,1) > dcm_b2n(2,2)) {\n            double s = 2.0 * sqrt( 1.0 + dcm_b2n(1,1) - dcm_b2n(0,0) - dcm_b2n(2,2));\n            q(0) = (dcm_b2n(0,2) - dcm_b2n(2,0) ) / s;\n            q(1) = (dcm_b2n(0,1) + dcm_b2n(1,0) ) / s;\n            q(2) = 0.25 * s;\n            q(3) = (dcm_b2n(1,2) + dcm_b2n(2,1)) / s;\n        } else {\n            double s = 2.0 * sqrt( 1.0 + dcm_b2n(2,2) - dcm_b2n(0,0) - dcm_b2n(1,1) );\n            q(0) = (dcm_b2n(1,0) - dcm_b2n(0,1) ) / s;\n            q(1) = (dcm_b2n(0,2) + dcm_b2n(2,0) ) / s;\n            q(2) = (dcm_b2n(1,2) + dcm_b2n(2,1) ) / s;\n            q(3) = 0.25 * s;\n        }\n    }\n\n//    q(0) = 0.5 * sqrt(1.0 + dcm_b2n(0, 0) + dcm_b2n(1, 1) + dcm_b2n(2, 2));\n//    double beta = 1.0 / (4.0 * q(0));\n//    q(1) = beta * (dcm_b2n(2,1) - dcm_b2n(1,2));\n//    q(2) = beta * (dcm_b2n(0,2) - dcm_b2n(2,0));\n//    q(3) = beta * (dcm_b2n(1,0) - dcm_b2n(0,1));\n    return q;\n}\n\nVector3d Quaternions::GetEulerFromQ(Vector4d &q) {\n    Vector3d euler;\n\n    euler(0) = atan2(2.0 * (q(0) * q(1) + q(2) * q(3)), 1 - 2 * (q(1) * q(1) + q(2) * q(2)));\n    euler(1) = asin(2 * (q(0) * q(2) - q(3) * q(1)));\n    euler(2) = atan2(2 * (q(0) * q(3) + q(1) * q(2)), 1 - 2 * (q(2) * q(2) + q(3) * q(3)));\n    return euler;\n}"
  },
  {
    "path": "math/Quaternions.h",
    "content": "//\n// Created by yangcheng on 2018/11/27.\n//\n#include \"Eigen/Dense\"\n\n#ifndef LOCATION_QUATERNION_H\n#define LOCATION_QUATERNION_H\n\n\nclass Quaternions {\npublic:\n\n    Quaternions();\n\n    virtual ~Quaternions();\n\n    // 归一化.\n    Eigen::Vector4d Normalise(Eigen::Vector4d &q) const;\n\n    // 共轭四元数.\n    Eigen::Vector4d GetConjugate(Eigen::Vector4d &q) const;\n\n    // 四元数基本运算，加，点乘，叉乘\n    // Quaternion operator*(const Quaternion &quaternion) const;\n    Eigen::Vector4d Add(Eigen::Vector4d &q1, Eigen::Vector4d &q2) const;\n\n    Eigen::Vector4d DotMulti(Eigen::Vector4d &q1, Eigen::Vector4d &q2) const;\n\n    Eigen::Vector4d CrossMulti(Eigen::Vector4d &q1, Eigen::Vector4d &q2) const;\n\n    // 从欧拉角v(x,y,z)中获取四元数Q(q0,q1,q2,q3).\n    Eigen::Vector4d GetQFromEuler(Eigen::Vector3d &euler_angle) const;\n\n    // 从四元数获取余弦矩阵DCM\n    Eigen::Matrix3d GetDCMFromQ(Eigen::Vector4d &q);\n\n    // 从余弦矩阵DCM获取四元数\n    Eigen::Vector4d GetQfromDCM(Eigen::Matrix3d &dcm_b2n);\n\n    // 从四元数获取欧拉角\n    Eigen::Vector3d GetEulerFromQ(Eigen::Vector4d &q);\n\n};\n\n\n#endif //LOCATION_QUATERNION_H\n"
  },
  {
    "path": "models/AHRS.cpp",
    "content": "//\n// Created by yangcheng on 2018/12/26.\n//\n\n#include \"Eigen/Dense\"\n#include \"../math/Quaternions.h\"\n#include \"../sensor/Accelerometer.h\"\n#include \"../sensor/Magnetometer.h\"\n#include \"AHRS.h\"\n#include \"iostream\"\n\nusing namespace Eigen;\n\n/**\n * 姿态更新(AHRS: attitude and heading reference system)。\n *\n * @param err: 误差积分\n * @param gyro: 陀螺仪数据, 欧拉角\n * @param acc: 加速计数据, 该数据需为重力传感器数据 或者 静止时的加速计数据。\n * @param mag: 地磁感应数据, 注意手机获取到的磁力计数据单位为 μT, 需乘上 10^-3 转成 mT 单位。\n * @param ki: 比例参数\n * @param kp: 积分参数\n * @param halfT: 采样周期的一半\n * @return 返回更新完的四元数数据\n */\nVector4d AHRS::UpdateAttitude(Vector3d *err, Vector4d &q_attitude, Vector3d &gyro, Vector3d &acc, Vector3d &mag, double &ki, double &kp,\n                              double &halfT) const {\n\n    Quaternions quaternions;\n    Accelerometer accelerometer;\n    Magnetometer magnetometer;\n    Vector4d newAttitude;\n\n    // 从欧拉角获取四元数\n//    Vector4d euler_q = quaternions.GetQFromEuler(orientation);\n    Vector4d euler_q = q_attitude;\n\n    // 计算旋转矩阵(b系到n系)\n    Matrix3d b2n = quaternions.GetDCMFromQ(euler_q);\n    Matrix3d n2b = b2n.transpose();\n\n    // 归一化加速计数据和地磁数据\n    Vector3d norm_acc = accelerometer.Normalise(acc);\n    Vector3d norm_mag = magnetometer.Normalise(mag);\n\n    // 计算加速计误差\n//    Vector3d rotate_g = accelerometer.RotateG(n2b);\n//    std::cout << rotate_g.transpose() << std::endl;\n//    Vector3d acc_error = accelerometer.GetAccError(norm_acc, rotate_g);\n    Vector3d acc_error = accelerometer.GetAccError(norm_acc, euler_q);\n\n    // 计算地磁感应误差\n//    Vector3d mag_error = magnetometer.GetMagError(b2n, mag);\n    Vector3d mag_error = magnetometer.GetMagError(euler_q, mag);\n\n    // 计算总误差\n    Vector3d e;\n    e(0) = acc_error(0) + mag_error(0);\n    e(1) = acc_error(1) + mag_error(1);\n    e(2) = acc_error(2) + mag_error(2);\n\n    // 误差积分, 累计部分。\n    (*err)(0) += e(0) * ki * 2.0 * halfT;\n    (*err)(1) += e(1) * ki * 2.0 * halfT;\n    (*err)(2) += e(2) * ki * 2.0 * halfT;\n    // 误差修正, 比例部分。\n    gyro(0) += e(0) * kp + (*err)(0);\n    gyro(1) += e(1) * kp + (*err)(1);\n    gyro(2) += e(2) * kp + (*err)(2);\n\n    // Integrate rate of change of quaternion\n    gyro(0) *= halfT;\t\t// pre-multiply common factors\n    gyro(1) *= halfT;\n    gyro(2) *= halfT;\n    double qa = euler_q(0);\n    double qb = euler_q(1);\n    double qc = euler_q(2);\n    euler_q(0) += (-qb * gyro(0) - qc * gyro(1) - euler_q(3) * gyro(2));\n    euler_q(1) += (qa * gyro(0) + qc * gyro(2) - euler_q(3) * gyro(1));\n    euler_q(2) += (qa * gyro(1) - qb * gyro(2) + euler_q(3) * gyro(0));\n    euler_q(3) += (qa * gyro(2) + qb * gyro(1) - qc * gyro(0));\n\n    // 重新调整旋转四元数, 一阶龙格库塔法更新四元数\n//    euler_q(0) = euler_q(0) + (-euler_q(1) * gyro(0) - euler_q(2) * gyro(1) - euler_q(3) * gyro(2)) * halfT;\n//    euler_q(1) = euler_q(1) + (euler_q(0) * gyro(0) + euler_q(2) * gyro(2) - euler_q(3) * gyro(1)) * halfT;\n//    euler_q(2) = euler_q(2) + (euler_q(0) * gyro(1) - euler_q(1) * gyro(2) + euler_q(3) * gyro(0)) * halfT;\n//    euler_q(3) = euler_q(3) + (euler_q(0) * gyro(2) + euler_q(1) * gyro(1) - euler_q(2) * gyro(0)) * halfT;\n\n\n    newAttitude = quaternions.Normalise(euler_q);\n//    Vector3d eur = quaternions.GetEulerFromQ(newAttitude) * 180.0 / M_PI ;\n//    std::cout << eur.transpose() << std::endl;\n    return newAttitude;\n\n}"
  },
  {
    "path": "models/AHRS.h",
    "content": "//\n// Created by yangcheng on 2018/12/26.\n//\n#include \"Eigen/Dense\"\n\n#ifndef LOCATION_ARHS_H\n#define LOCATION_ARHS_H\n\n\nclass AHRS {\npublic:\n\n    // 姿态更新.\n    Eigen::Vector4d UpdateAttitude(Eigen::Vector3d *err, Eigen::Vector4d &q_attitude, Eigen::Vector3d &gyro,\n                                   Eigen::Vector3d &acc, Eigen::Vector3d &mag,\n                                   double &ki, double &kp, double &halfT) const ;\n\n};\n\n\n#endif //LOCATION_ARHS_H\n"
  },
  {
    "path": "models/CMakeLists.txt",
    "content": "aux_source_directory(. models_src_lists)\nadd_library(Location_models ${models_src_lists})"
  },
  {
    "path": "models/StopDetection.cpp",
    "content": "//\n// Created by yangcheng on 2019/7/1.\n//\n\n#include \"StopDetection.h\"\n\nStopDetection::StopDetection() {};\n\nStopDetection::StopDetection(std::string *model) {};\n\nStopDetection::~StopDetection() {};\n\nbool StopDetection::IsStopping(Eigen::VectorXd &data) const { return false; };"
  },
  {
    "path": "models/StopDetection.h",
    "content": "//\n// Created by yangcheng on 2019/7/1.\n//\n\n#ifndef LOCATION_STOPDETECTION_H\n#define LOCATION_STOPDETECTION_H\n\n#include <Eigen/Dense>\n\nclass StopDetection {\npublic:\n\n    StopDetection();\n    explicit StopDetection(std::string *model);\n    ~StopDetection();\n\n    virtual bool IsStopping(Eigen::VectorXd &data) const;\n};\n\n\n#endif //LOCATION_STOPDETECTION_H\n"
  },
  {
    "path": "models/StrapdownAHRS.cpp",
    "content": "//\n// Created by yangcheng on 2019/3/13.\n//\n\n#include \"StrapdownAHRS.h\"\n#include \"../math/Quaternions.h\"\n\nusing namespace Eigen;\nusing namespace routing;\n\n/**\n * 捷联式姿态更新\n *\n * @param q_attitude, 上衣时刻姿态四元数\n * @param gyro, 陀螺仪旋转角\n * @param acc, 加速计输出\n * @return\n */\nVector4d StrapdownAHRS::StrapdownUpdateAttitude(Vector4d &q_attitude, Vector3d &gyro,  Status *status) {\n\n    // 四元数转方向余弦矩阵\n    Quaternions quaternions;\n    Matrix3d dcm_b2n = quaternions.GetDCMFromQ(q_attitude);\n\n\n    /**\n     * dcm_b2n(t+1) = dcm_b2n(t) * σ\n     * //Ak = I + sinσ/σ * (σ X) + (1 - cosσ)/σ² * (σ X)²\n     * σ = wn_b * deltaT = (w_i_b - dcm_n2b(t) * (wi_n + we_n)) * deltaT\n     */\n\n    // 导航坐标系下的地球自转角速度\n    double cur_lat = (*status).position.lat * M_PI / 180.0;\n    Vector3d wi_n((*status).parameters.we * cos(cur_lat), 0.0, -(*status).parameters.we * sin(cur_lat));\n    // 导航坐标系下的旋转速率\n    double v_east = (*status).velocity.v_y;\n    double v_north = (*status).velocity.v_x;\n    double Rh = (*status).parameters.R + (*status).position.altitude;\n    Vector3d we_n(v_east / Rh, -v_north / Rh, -v_east * tan(cur_lat) / Rh);\n    // 计算载体相对导航系的角速度\n    Matrix3d dcm_n2b = dcm_b2n.transpose();\n    Vector3d wn_b = gyro - dcm_n2b * (wi_n + we_n);\n//    Vector3d wn_b = gyro;\n\n    // 计算载体相对导航系角速率斜对称阵\n    Matrix3d Ob_n;\n    Ob_n(0,0) = 0.0;\n    Ob_n(0,1) = -wn_b(2) * (*status).parameters.t;\n    Ob_n(0,2) = wn_b(1) * (*status).parameters.t;\n    Ob_n(1,0) = wn_b(2) * (*status).parameters.t;\n    Ob_n(1,1) = 0.0;\n    Ob_n(1,2) = -wn_b(0) * (*status).parameters.t;\n    Ob_n(2,0) = -wn_b(1) * (*status).parameters.t;\n    Ob_n(2,1) = wn_b(0) * (*status).parameters.t;\n    Ob_n(2,2) = 0.0;\n    // 计算载体相对导航系角速率斜对称阵平方\n//    Matrix3d Ob_n2;\n//    Vector3d wn_bt = (*status).parameters.t * wn_b;\n//    Ob_n2(0,0) = - (wn_bt(1) * wn_bt(1) + wn_bt(2) * wn_bt(2));\n//    Ob_n2(0,1) = wn_bt(0) * wn_b(1);\n//    Ob_n2(0,2) = wn_bt(0) * wn_b(2);\n//    Ob_n2(1,0) = wn_bt(0) * wn_b(1);\n//    Ob_n2(1,1) = - (wn_bt(0) * wn_bt(0) + wn_bt(2) * wn_bt(2));\n//    Ob_n2(1,2) = wn_bt(1) * wn_b(2);\n//    Ob_n2(2,0) = wn_bt(0) * wn_b(2);\n//    Ob_n2(2,1) =  wn_bt(1) * wn_b(2);\n//    Ob_n2(2,2) =  - (wn_bt(0) * wn_bt(0) + wn_bt(1) * wn_bt(1));\n//    // 计算更新矩阵Ak\n//    double sigma = wn_bt.norm();\n//    Matrix3d Ak = MatrixXd::Identity(3,3) + sin(sigma)/sigma * Ob_n + (1 - cos(sigma)/(sigma*sigma)) * Ob_n2;\n\n    // 更新姿态\n    Matrix3d dcm_b2n_new = dcm_b2n * Ob_n;\n    Vector4d q_attitude_new = quaternions.GetQfromDCM(dcm_b2n_new);\n    Vector4d q_attitude_new_norm = quaternions.Normalise(q_attitude_new);\n    return q_attitude_new_norm;\n}"
  },
  {
    "path": "models/StrapdownAHRS.h",
    "content": "//\n// Created by yangcheng on 2019/3/13.\n//\n\n#ifndef LOCATION_STRAPDOWNAHRS_H\n#define LOCATION_STRAPDOWNAHRS_H\n\n#include \"Eigen/Dense\"\n#include \"../system/Status.h\"\n\n\nclass StrapdownAHRS {\npublic:\n\n    // 捷联式姿态更新.\n    Eigen::Vector4d\n    StrapdownUpdateAttitude(Eigen::Vector4d &q_attitude, Eigen::Vector3d &gyro, routing::Status *status);\n};\n\n\n#endif //LOCATION_STRAPDOWNAHRS_H\n"
  },
  {
    "path": "models/XgboostDetector.cpp",
    "content": "//\n// Created by yangcheng on 2019/7/4.\n//\n\n#include \"XgboostDetector.h\"\n#include \"../utils/Tools.h\"\n#include <fstream>\n#include <iostream>\n\nXgboostDetector::~XgboostDetector() {};\n\n/**\n * xgboost read model and decompress into shared_ptr<XTree>.\n * @param model_path\n */\nXgboostDetector::XgboostDetector(std::string &model_path) {\n    Tools tools;\n    XTree_map_ptr xtree_map_ptr = std::make_shared<std::unordered_map<int, XTree_ptr>>();\n\n    std::ifstream infile(model_path);\n    std::string line;\n    std::getline(infile, line);\n\n    int boost_id = 0;\n    while (std::getline(infile, line)) {\n        if (line.find(\"booster\") != std::string::npos) {\n            boost_id += 1;\n            this->XTrees.push_back(xtree_map_ptr);\n            xtree_map_ptr.reset(new std::unordered_map<int, XTree_ptr>());\n        } else {\n            int node_id = std::stoi(tools.split(line, \":\")[0]);\n            XTree xtree = this->detectTrees(line);\n            XTree_ptr xtree_ptr = std::make_shared<XTree>(xtree);\n//            std::cout.precision(10);\n//            std::cout << \"booster id \" << boost_id\n//                      << \" node id \" << node_id\n//                      << \" feature idx: \" << xtree.feature_idx_\n//                      << \" condition: \" <<  xtree.split_condition_\n//                      << \" yes node \" << xtree.left_node_\n//                      << \" no node \" << xtree.right_node_\n//                      << \" miss node \" << xtree.miss_node_\n//                      << \" leaf weight \" << xtree.leaf_weight_\n//                      << std::endl;\n            xtree_map_ptr->emplace(std::make_pair(node_id, xtree_ptr));\n        }\n    }\n    this->XTrees.push_back(xtree_map_ptr);\n\n}\n\n/**\n * detect tree node and convert it into XTree structure.\n *\n * @param model_line: file read line.\n * @return XTree\n */\nXTree XgboostDetector::detectTrees(std::string &model_line) {\n\n    Tools tools;\n    if (model_line.find(\"leaf\") == std::string::npos) {\n\n        // e.g \"0:[f5<0.999779344] yes=1,no=2,missing=1\" => \"0:[f5<0.999779344]\" \"yes=1,no=2,missing=1\"\n        std::vector<std::string> feature_node = tools.split(model_line, \" \");\n        // e.g \"0:[f5<0.999779344]\" => \"0:[f5\" \"0.999779344]\"\n        std::vector<std::string> feature_s = tools.split(feature_node[0], \"<\");\n\n        // feature idx; e.g \"0:[f5\" => \"0:\" \"f5\"\n        std::string feature_idx_s = tools.split(feature_s[0], \"[\")[1];\n        feature_idx_s.erase(0, 1);\n        int feature_idx = std::stoi(feature_idx_s);\n\n        // split condition; e.g \"0.999779344]\" => 0.999779344\n        std::string split_condition_s = feature_s[1];\n        split_condition_s.pop_back();\n        double split_condition = std::stod(split_condition_s);\n\n        // yes/no/missing\n        std::vector<std::string> node_s = tools.split(feature_node[1], \",\");\n        int yes_node = std::stoi(tools.split(node_s[0], \"=\")[1]);\n        int no_node = std::stoi(tools.split(node_s[1], \"=\")[1]);\n        int missing_node = std::stoi(tools.split(node_s[2], \"=\")[1]);\n        return {feature_idx, split_condition, yes_node, no_node, missing_node};\n\n    } else {\n\n        double leaf_value = std::stof(tools.split(model_line, \"=\")[1]);\n        return {leaf_value};\n\n    }\n\n}\n\n/**\n * predict the vector belong to which class.\n * Note: typedef std::shared_ptr<XTree> XTree_ptr;\n *       typedef std::shared_ptr<std::unordered_map<int, XTree_ptr>> XTree_map_ptr;\n *       std::vector<XTree_map_ptr> XTrees;\n *\n * @param current_input\n * @return\n */\nstd::vector<double> XgboostDetector::predictTrees(std::vector<double> &current_input) const {\n\n    std::vector<double> res{0.0, 0.0};\n    int tag = 0;\n    for (auto &tree_map : this->XTrees) {\n\n        int class_idx = tag % 2;\n        tag += 1;\n\n        int node_id = 0;\n        while (tree_map->find(node_id) != tree_map->end()) {\n\n            XTree_ptr tree = (*tree_map)[node_id];\n\n            if (tree->feature_idx_ == -1) {\n                res[class_idx] += tree->leaf_weight_;\n                break;\n            } else {\n                double feature = current_input[tree->feature_idx_];\n                if (feature != this->missing_feature) {\n                    if (feature < tree->split_condition_) {\n                        node_id = tree->left_node_;\n                    } else {\n                        node_id = tree->right_node_;\n                    }\n                } else {\n                    node_id = tree->miss_node_;\n                }\n            }\n        }\n    }\n    return res;\n}\n\n\n/**\n * predict current data using the xgboost model.\n *\n * @param data, input vector.\n * @return preidct probability vector for each class according to input training class order.\n */\nbool XgboostDetector::IsStopping(Eigen::VectorXd &data) const {\n    std::vector<double> inputs;\n    size_t nums = data.rows();\n    for (std::size_t i = 0; i < nums; ++i) {\n        inputs.push_back(data(i));\n    }\n    std::vector<double> res = this->predictTrees(inputs);\n\n    double stop_exp = exp(res[0]);\n    double move_exp = exp(res[1]);\n    double stop_prob = stop_exp / (stop_exp + move_exp);\n    double move_prob = move_exp / (stop_exp + move_exp);\n    return stop_prob > move_prob;\n}\n\n"
  },
  {
    "path": "models/XgboostDetector.h",
    "content": "//\n// Created by yangcheng on 2019/7/4.\n//\n\n#ifndef LOCATION_XGBOOSTDETECTOR_H\n#define LOCATION_XGBOOSTDETECTOR_H\n\n#include \"StopDetection.h\"\n#include <unordered_map>\n#include <vector>\n#include <memory>\n\nstruct XTree {\n    int feature_idx_;\n    double split_condition_;\n    int left_node_;\n    int right_node_;\n    int miss_node_;\n    double leaf_weight_;\n\n    // tree node\n    XTree(int feature_idx, double split_condition, int left_node, int right_node, int miss_node) :\n            feature_idx_(feature_idx), split_condition_(split_condition), left_node_(left_node),\n            right_node_(right_node), miss_node_(miss_node), leaf_weight_(0.0) {};\n\n    // leaf node\n    XTree(double weight) :\n            feature_idx_(-1), split_condition_(0.0), left_node_(-1),\n            right_node_(-1), miss_node_(-1), leaf_weight_(weight) {};\n\n};\n\nclass XgboostDetector : public StopDetection {\nprivate:\n\n    double missing_feature = 999.0;\n    typedef std::shared_ptr<XTree> XTree_ptr;\n    typedef std::shared_ptr<std::unordered_map<int, XTree_ptr>> XTree_map_ptr;\n    std::vector<XTree_map_ptr> XTrees;\n\n    void decompress();\n\n    XTree detectTrees(std::string &model_line);\n    std::vector<double> predictTrees(std::vector<double> &current_input) const ;\n\npublic:\n\n    explicit XgboostDetector(std::string &model_path);\n\n    ~XgboostDetector();\n\n    bool IsStopping(Eigen::VectorXd &data) const override;\n};\n\n\n#endif //LOCATION_XGBOOSTDETECTOR_H\n"
  },
  {
    "path": "sensor/Accelerometer.cpp",
    "content": "//\n// Created by yangcheng on 2018/11/28.\n//\n\n#include \"Accelerometer.h\"\n#include \"../math/Optimizer.h\"\n#include \"iostream\"\n#include \"../math/LPF.h\"\n\nusing namespace Eigen;\nusing namespace routing;\n\nVector3d Accelerometer::Normalise(Vector3d &a) const {\n    Vector3d normA;\n    double norm2 = a(0) * a(0) + a(1) * a(1) + a(2) * a(2);\n    // 如果四元数各项足够接近单位四元数, 则不做任何处理.\n    if (norm2 != 0.0) {\n        double norm = sqrt(norm2);\n        normA(0) = a(0) / norm;\n        normA(1) = a(1) / norm;\n        normA(2) = a(2) / norm;\n    } else {\n        normA = a;\n    }\n    return normA;\n}\n\n// 通过旋转获取 地理坐标系下重力加速度 转 机体坐标系下的重力加速度.\nVector3d Accelerometer::RotateG(Matrix3d &n2b) const {\n    // b系下坐标\n    Vector3d bg;\n    // 地理坐标系下重力加速度\n    Vector3d g(0, 0, 1);\n    bg = n2b * g;\n    return bg;\n}\n\nVector3d Accelerometer::GetAccError(Vector3d &originA, Vector4d &q) const {\n    double halfvx = q(1) * q(3) - q(0) * q(2);\n    double halfvy = q(0) * q(1) + q(2) * q(3);\n    double halfvz = q(0) * q(0) - 0.5 + q(3) * q(3);\n\n    double halfex = originA(1) * halfvz - originA(2) * halfvy;\n    double halfey = originA(2) * halfvx - originA(0) * halfvz;\n    double halfez = originA(0) * halfvy - originA(1) * halfvx;\n    Vector3d e(halfex,halfey,halfez);\n    return e;\n}\n\n// 加速计向量(originA)叉乘地理重力转b系(rotatedG)误差，用于较正陀螺仪.\nVector3d Accelerometer::GetAccError(Vector3d &originA, Vector3d &rotatedG) const {\n    Vector3d accErr;\n\n    accErr(0) = originA(1) * rotatedG(2) - originA(2) * rotatedG(1);\n    accErr(1) = originA(2) * rotatedG(0) - originA(0) * rotatedG(2);\n    accErr(2) = originA(0) * rotatedG(1) - originA(1) * rotatedG(0);\n\n    return accErr;\n}\n\nvoid Accelerometer::AccCalibration(MatrixXd &input_data, Status *status) {\n    double R = 1.0;\n    double gamma = (*status).parameters.gamma;\n    double epsilon = (*status).parameters.epsilon;\n    int max_step = (*status).parameters.max_step;\n    VectorXd *coef = &(*status).parameters.acc_coef;\n    MatrixXd input_data_format = input_data / (*status).parameters.g;\n    Optimizer optimizer;\n    optimizer.LevenbergMarquardt(input_data_format, R, coef, gamma, epsilon, max_step);\n}\n\n\nvoid Accelerometer::PositionIntegral(Status *status, Vector3d &acc, double t) {\n\n    // 更新位置\n    (*status).position.x += (*status).velocity.v_x * t + 0.5 * acc(0) * t * t;\n    (*status).position.y += (*status).velocity.v_y * t + 0.5 * acc(1) * t * t;\n    (*status).position.z += (*status).velocity.v_z * t + 0.5 * acc(2) * t * t;\n    // 更新速度\n    (*status).velocity.v_x = (*status).velocity.v_x + acc(0) * t;\n    (*status).velocity.v_y = (*status).velocity.v_y + acc(1) * t;\n    (*status).velocity.v_z = (*status).velocity.v_z + acc(2) * t;\n\n}\n\n/**\n * 捷联更新位置速度\n *\n * @param status\n * @param acc, 载体系加速度\n * @param q_attitude, 上一时刻姿态四元数\n */\nvoid Accelerometer::StrapdownUpdateVelocityPosition(Status *status, Vector3d &acc, Vector4d &q_attitude, Vector3d &g_data) {\n\n    Quaternions quaternions;\n\n    /**\n     * ve_n_new = acc_n - (2*wi_n + we_n) X ve_n - gl_n;\n     */\n\n    // 计算导航系加速度\n    Matrix3d dcm_b2n = quaternions.GetDCMFromQ(q_attitude);\n    Vector3d acc_n = dcm_b2n * acc;\n\n    // 导航坐标系下的地球自转角速度\n    double cur_lat = (*status).position.lat * M_PI / 180.0;\n    Vector3d wi_n((*status).parameters.we * cos(cur_lat), 0.0, -(*status).parameters.we * sin(cur_lat));\n    // 导航坐标系下的旋转速率\n    double v_east = (*status).velocity.v_y;\n    double v_north = (*status).velocity.v_x;\n    double v_down = (*status).velocity.v_z;\n    Vector3d ve_n(v_north, v_east, v_down);\n    double Rh = (*status).parameters.R + (*status).position.altitude;\n    Vector3d we_n(v_east / Rh, -v_north / Rh, -v_east * tan(cur_lat) / Rh);\n\n    // 计算导航系下的重力加速计修正向量\n//    Vector3d gn(0.0,0.0,(*status).parameters.g);\n    Vector3d gn = dcm_b2n * g_data;\n    double beta = (*status).parameters.we * (*status).parameters.we * Rh / 2.0;\n    Vector3d wwR(beta * sin(2.0 * cur_lat), 0.0, beta * (1.0 + cos(2.0 * cur_lat)));\n    Vector3d gl_n = gn - wwR;\n\n    // 计算导航系下加速度减去地球旋转影响和重力影响\n    Vector3d acc_n_not_filter = acc_n - (2.0 * wi_n + we_n).cross(ve_n) - gl_n;\n\n//    std::cout << \"acc_n_not_filter \" << acc_n_not_filter.transpose() << std::endl;\n    Vector3d acc_n_real = FilterData(status, acc_n_not_filter);\n//    std::cout << \"acc_n_real \" << acc_n_real.transpose() << std::endl;\n\n    // 速度和位置积分\n    double deltaT = (*status).parameters.t;\n    double v_x_new = v_north + acc_n_real(0) * deltaT;\n    double v_y_new = v_east + acc_n_real(1) * deltaT;\n    double v_z_new = v_down + acc_n_real(2) * deltaT;\n    double x_new = (*status).position.x + (v_north + v_x_new) * deltaT * (*status).parameters.move_t_factor * 0.5;\n    double y_new = (*status).position.y + (v_east + v_y_new) * deltaT * (*status).parameters.move_t_factor * 0.5;\n    double z_new = (*status).position.z + (v_down + v_z_new) * deltaT * (*status).parameters.move_t_factor * 0.5;\n//    double x_new = (v_north + v_x_new) * deltaT * 0.5;\n//    double y_new = (v_east + v_y_new) * deltaT * 0.5;\n//    double z_new = (v_down + v_z_new) * deltaT * 0.5;\n//    std::cout.precision(9);\n//    std::cout << x_new << \" \" << y_new << std::endl;\n//    std::cout << \"acc \" << acc_n_real.transpose() << std::endl;\n//    std::cout << \"v \" << v_x_new << \" \" << v_y_new << \" \" << v_z_new  <<std::endl;\n//    double ov = sqrt(v_x_new*v_x_new+v_y_new*v_y_new);\n//    std::cout << acc_n_not_filter(0) << \" \" << acc_n_not_filter(1) << \" \" << acc_n_not_filter(2)\n//              << \" \" << ov << \" \" << v_x_new << \" \" << v_y_new << \" \" << v_z_new\n//              << \" \" << acc_n_real(0) << \" \" << acc_n_real(1) << \" \" << acc_n_real(2)\n//              << std::endl;\n\n    // 更新速度和位置\n    (*status).velocity.v_x = v_x_new;\n    (*status).velocity.v_y = v_y_new;\n    (*status).velocity.v_z = v_z_new;\n    (*status).position.x = x_new;\n    (*status).position.y = y_new;\n    (*status).position.z = z_new;\n}\n\n/**\n * 加速计数据过滤\n *\n * @param status\n * @param acc_data\n * @return\n */\nVector3d Accelerometer::FilterData(Status *status, Vector3d &acc_data) {\n    LPF lpf;\n    Vector3d filter_acc;\n    filter_acc = lpf.LowPassFilter2nd4ACC(status, acc_data);\n    if(abs(filter_acc(0)) <= (*status).parameters.acc_thres){\n        filter_acc(0) = 0.0;\n    }\n    if(abs(filter_acc(1)) <= (*status).parameters.acc_thres){\n        filter_acc(1) = 0.0;\n    }\n    if(abs(filter_acc(2)) <= (*status).parameters.acc_thres){\n        filter_acc(2) = 0.0;\n    }\n    return  filter_acc;\n}\n\nAccelerometer::Accelerometer() {}\n\nAccelerometer::~Accelerometer() = default;\n"
  },
  {
    "path": "sensor/Accelerometer.h",
    "content": "//\n// Created by yangcheng on 2018/11/28.\n//\n#include \"../math/Quaternions.h\"\n#include \"../system/Status.h\"\n\n\n#ifndef LOCATION_ACCELEROMETER_H\n#define LOCATION_ACCELEROMETER_H\n\n\nclass Accelerometer {\npublic:\n\n    // accelerate data\n//    double x, y, z;\n//    Velocity velocity;\n\n//    Accelerometer(double &x, double &y, double &z, Velocity &velocity);\n    Accelerometer();\n\n    virtual ~Accelerometer();\n\n    // 归一化.\n    Eigen::Vector3d Normalise(Eigen::Vector3d &a) const;\n\n    // 通过旋转获取 地理坐标系下重力加速度 转 机体坐标系下的重力加速度.\n    Eigen::Vector3d RotateG(Eigen::Matrix3d &n2b) const;\n\n    // 加速计向量(originA)叉乘地理重力转b系(rotatedG)误差，用于较正陀螺仪\n    Eigen::Vector3d GetAccError(Eigen::Vector3d &originA, Eigen::Vector3d &rotatedG) const;\n\n    Eigen::Vector3d GetAccError(Eigen::Vector3d &originA, Eigen::Vector4d &q) const;\n\n    // 加速计标定\n    void AccCalibration(Eigen::MatrixXd &input_data, routing::Status *status);\n\n    // rotate the accelerate data into Geo coordinates.\n//    Accelerometer Rotate(const Quaternions &quaternions, const Quaternions &quaternion_inv) const;\n\n//    // format the Accelerate data, correct the error and unit.\n//    void Correct();\n//\n//    // delete the affection from gravity.\n//    void DeleteGravity();\n\n    // position integral.\n    void PositionIntegral(routing::Status *status, Eigen::Vector3d &acc, double t);\n\n    void StrapdownUpdateVelocityPosition(routing::Status *status, Eigen::Vector3d &acc,\n                                         Eigen::Vector4d &q_attitude, Eigen::Vector3d &g_data);\n\n    // 用于加速计过滤数据\n    Eigen::Vector3d FilterData(routing::Status *status, Eigen::Vector3d &acc_data);\n};\n\n\n#endif //LOCATION_ACCELEROMETER_H\n"
  },
  {
    "path": "sensor/CMakeLists.txt",
    "content": "aux_source_directory(. sensor_src_lists)\nadd_library(Location_sensor ${sensor_src_lists})\ntarget_link_libraries(Location_sensor Location_math)"
  },
  {
    "path": "sensor/Compass.cpp",
    "content": "//\n// Created by yangcheng on 2019/4/17.\n//\n\n#include \"Compass.h\"\n#include <iostream>\n\nusing namespace Eigen;\n\nbool Compass::IsCompassVaild(routing::Status *status, Eigen::Vector3d &ornt_data) {\n\n    static VectorXd sin_compass_queue((*status).parameters.compass_queue_len);\n    static VectorXd cos_compass_queue((*status).parameters.compass_queue_len);\n    static int cnt = 0;\n\n    if (cnt < (*status).parameters.compass_queue_len) {\n        sin_compass_queue(cnt) = sin(ornt_data(2) * M_PI / 180.0);\n        cos_compass_queue(cnt) = cos(ornt_data(2) * M_PI / 180.0);\n        cnt += 1;\n        return true;\n    } else {\n        double sin_mean = sin_compass_queue.mean();\n        double cos_mean = cos_compass_queue.mean();\n        double sin_var = (sin_compass_queue.array() - sin_mean).pow(2).sum() / (*status).parameters.compass_queue_len;\n        double cos_var = (cos_compass_queue.array() - cos_mean).pow(2).sum() / (*status).parameters.compass_queue_len;\n//        std::cout << ornt_data(2) << \" \" << sin_var << \" \" << cos_var << std::endl;\n        for (int i = 0; i < (*status).parameters.compass_queue_len - 1; i++) {\n            sin_compass_queue(i) = sin_compass_queue(i + 1);\n            cos_compass_queue(i) = cos_compass_queue(i + 1);\n        }\n        sin_compass_queue((*status).parameters.compass_queue_len - 1) = sin(ornt_data(2) * M_PI / 180.0);\n        cos_compass_queue((*status).parameters.compass_queue_len - 1) = cos(ornt_data(2) * M_PI / 180.0);\n        return sin_var < (*status).parameters.compass_vaild_var_thres && cos_var < (*status).parameters.compass_vaild_var_thres;\n    }\n\n}"
  },
  {
    "path": "sensor/Compass.h",
    "content": "//\n// Created by yangcheng on 2019/4/17.\n//\n\n#ifndef LOCATION_COMPASS_H\n#define LOCATION_COMPASS_H\n\n#include <Eigen/Dense>\n#include \"../system/Status.h\"\n\nclass Compass {\npublic:\n\n    bool IsCompassVaild(routing::Status *status, Eigen::Vector3d &ornt_data);\n};\n\n\n#endif //LOCATION_COMPASS_H\n"
  },
  {
    "path": "sensor/GPS.cpp",
    "content": "//\n// Created by yangcheng on 2018/12/24.\n//\n\n#include <iostream>\n#include \"GPS.h\"\n#include \"../math/KalmanFilter.h\"\n\nusing namespace Eigen;\nusing namespace routing;\n\n/**\n * 给定起点经度,纬度,距离,方向, 计算终点的经纬度.\n *\n * @param startLng 起点经度\n * @param startLat 起点纬度\n * @param distance 距离\n * @param heading 方向（与正北夹角）,角度\n * @return\n */\nEigen::Vector2d GPS::CalDestination(double &startLng, double &startLat, double &distance, double &heading) {\n    Vector2d nextLngLat;\n    double R = 6378.137 * 1000.0;\n    double rad_lng = startLng / 180.0 * M_PI;\n    double rad_lat = startLat / 180.0 * M_PI;\n    double heading_rad = heading / 180.0 * M_PI;\n    double lat = asin(sin(rad_lat) * cos(distance / R) + cos(rad_lat) * sin(distance / R) * cos(heading_rad));\n    double lng = rad_lng + atan2(sin(heading_rad) * sin(distance / R) * cos(rad_lat),\n                                 cos(distance / R) - sin(rad_lat) * sin(lat));\n    nextLngLat(0) = lng / M_PI * 180.0;\n    nextLngLat(1) = lat / M_PI * 180.0;\n    return nextLngLat;\n}\n\n/**\n * 根据GPS速度,方向 计算正北,正东方向速度.\n *\n * @param status\n * @param velocity\n * @param bearing\n */\nvoid GPS::UpdateVelocity(Status *status, double &velocity, double &bearing) {\n    double bearing_rad = bearing / 180.0 * M_PI;\n    double v_north = velocity * cos(bearing_rad);\n    double v_east = velocity * sin(bearing_rad);\n    (*status).velocity.v_x = v_north;\n    (*status).velocity.v_y = v_east;\n}\n\n/**\n * 计算两个经纬度点之间的距离.\n *\n * @param startLng 起点经度\n * @param startLat 起点纬度\n * @param endLng 终点经度\n * @param endLat 终点纬度\n * @return\n */\ndouble GPS::CalDistance(double &startLng, double &startLat, double &endLng, double &endLat) {\n\n    double startLng_rad = startLng / 180.0 * M_PI;\n    double startLat_rad = startLat / 180.0 * M_PI;\n    double endLng_rad = endLng / 180.0 * M_PI;\n    double endLat_rad = endLat / 180.0 * M_PI;\n\n\n    double a = pow(sin((endLat_rad - startLat_rad) / 2.0), 2.0) +\n               cos(startLat_rad) * cos(endLat_rad) * pow(sin((endLng_rad - startLng_rad) / 2.0), 2.0);\n    double c = 2 * asin(sqrt(a));\n    return c * 6378.137 * 1000.0;\n}\n\n/**\n * 计算当前kalman输入所需gps状态\n *\n * @param gps_data\n * @return vector4d(lng,lat,v_east,v_north)\n */\nEigen::Vector4d GPS::CalcState(Eigen::VectorXd &gps_data) {\n    // 根据当前gps角度计算两个分速度\n    double bearing_rad = gps_data(5) / 180.0 * M_PI;\n    double v_north = gps_data(4) * cos(bearing_rad);\n    double v_east = gps_data(4) * sin(bearing_rad);\n\n    Vector4d cur_state(gps_data(0), gps_data(1), v_east, v_north);\n    return cur_state;\n}\n\n/**\n * 判断GPS点是否符合GPS历史轨迹\n *\n * @param status\n * @param gps_data, gps(lng,lat,alt,accuracy,speed,bearing,t)\n * @return\n */\nbool GPS::IsGPSBelongToTrack(routing::Status *status, Eigen::VectorXd &gps_data) {\n\n    bool result = true;\n    static MatrixXd gps_queue((*status).parameters.gps_track_len, 7);\n    static int cnt = 0;\n    static int ignore_in_tunnel = 0;\n    static int ignore_in_common = 0;\n    static double pre_gps_t = 0.0;\n\n    if (cnt < (*status).parameters.gps_track_len) {\n        if (cnt >= 1) {\n            // 初步判断该点是否时间在允许的范围内\n            // TODO: 可以做更进一步判断该点是否合理能被加入数据做滤波轨迹\n            double time_diff1 = (gps_data(6) - gps_queue(cnt - 1, 6)) / 1000.0;\n            if (time_diff1 < (*status).parameters.gps_max_gap_time && time_diff1 != 0.0) {\n                gps_queue.row(cnt) = gps_data;\n                cnt += 1;\n            } else {\n                cnt = 0;\n            }\n        } else {\n            gps_queue.row(cnt) = gps_data;\n            cnt += 1;\n        }\n    } else {\n\n        // 初始化kalman\n        VectorXd init_state = gps_queue.row(0);\n        Vector4d cur_state = CalcState(init_state);\n        KalmanFilter kalmanFilter(cur_state);\n\n        // 滤波计算\n        for (int i = 1; i < (*status).parameters.gps_track_len; ++i) {\n            VectorXd origin_gps = gps_queue.row(i);\n            Vector4d measurement_state = CalcState(origin_gps);\n            double delta_t = (gps_queue(i, 6) - gps_queue(i - 1, 6)) / 1000.0;\n            kalmanFilter.SetF(delta_t);\n            kalmanFilter.UpdateState(measurement_state);\n        }\n\n        // 计算比较当前预测与实际测量的差距\n        double cur_delta_t = (gps_data(6) - gps_queue((*status).parameters.gps_track_len - 1, 6)) / 1000.0;\n        kalmanFilter.SetF(cur_delta_t);\n        VectorXd predict_state = kalmanFilter.PredictState();\n        double start_lng = predict_state(0);\n        double start_lat = predict_state(1);\n        double end_lng = gps_data(0);\n        double end_lat = gps_data(1);\n        double cur_error = CalDistance(start_lng, start_lat, end_lng, end_lat);\n//        double time_diff2 = (gps_data(6) - gps_queue.row((*status).parameters.gps_track_len - 1)(6)) / 1000.0;\n\n//        std::cout << \"cur_error <= (*status).parameters.weak_gps \" << (cur_error <= (*status).parameters.weak_gps)\n//                  << \" \"\n//                  << end_lng << \" \" << end_lat << \" \" << cur_error << \" \"\n//                  << (*status).parameters.road_type << std::endl;\n        if (cur_error <= (*status).parameters.weak_gps) {\n            // 误差在可接受的范围\n            for (int i = 0; i < (*status).parameters.gps_track_len - 1; i++) {\n                gps_queue.row(i) = gps_queue.row(i + 1);\n            }\n            gps_queue.row((*status).parameters.gps_track_len - 1) = gps_data;\n            ignore_in_common = 0;\n            ignore_in_tunnel = 0;\n        } else {\n\n            if(gps_data(6) == pre_gps_t){\n                // 由于status记录的pre gps是可用的pre gps, 故这里需记录一个无论可不可用的pre gps时间戳.\n                result = false;\n            }else{\n                if ((*status).parameters.road_type == 1.0) {\n                    // 误差不可接受, 同时处于隧道状态, 则不考虑时间间隔,同时不拿下个点作为初始了,因为下个点可能是仍在隧道,但有次数限制\n                    if (ignore_in_tunnel < (*status).parameters.max_ignore_in_tunnel) {\n                        ignore_in_tunnel += 1;\n                    } else {\n                        cnt = 0;\n                        ignore_in_tunnel = 0;\n                    }\n                    result = false;\n                } else {\n                    // 误差不可接受,但不处于隧道状态,则不可接受点设置严格一些\n                    if (ignore_in_common < (*status).parameters.max_ignore_in_common) {\n                        ignore_in_common += 1;\n                    } else {\n                        cnt = 0;\n                        ignore_in_common = 0;\n                    }\n                    result = false;//time_diff2 > (*status).parameters.gps_max_gap_time;\n                }\n\n                pre_gps_t = gps_data(6);\n            }\n\n        }\n    }\n    return result;\n}\n\n/**\n * 根据当前输入以及状态判断采用GPS还是INS\n *\n * @param status\n * @param gps_data, GPS原始数据, gps(lng,lat,alt,accuracy,speed,bearing,t)\n * @return gps是否有效\n */\nbool GPS::IsGPSValid(Status *status, VectorXd *gps_data) {\n\n    // 精度是否足够\n    bool is_gps_accuracy = (*gps_data)(3) <= (*status).parameters.weak_gps;\n\n    // gps是否为空\n    bool is_gps_not_null = ((*gps_data)(0) != 0.0 && (*gps_data)(1) != 0.0);\n\n    // gps运动距离是否过大,判断是否相同时间间隔GPS移动与惯导相差不大,用于判断该点是否被采用\n    double start_lng = (*status).position.lng;\n    double start_lat = (*status).position.lat;\n    double end_Lng = (*gps_data)(0);\n    double end_Lat = (*gps_data)(1);\n    double gps_move_dist = CalDistance(start_lng, start_lat, end_Lng, end_Lat);\n    bool is_gps_move_accepted = ceil((*status).parameters.ins_count / 10.0 + 1.0) * gps_move_dist <\n                                ceil((*status).parameters.ins_count / 10.0 + 1.0) *\n                                (*status).parameters.move_distance_threshod;\n\n    // 判断是否当前是导航初始状态\n    bool is_gps_initializing = (*status).parameters.gps_count <= (*status).parameters.gps_init_threshold;\n\n    // 判断当前GPS是否与上个GPS点同个时间戳\n    bool is_gps_not_duplicated = (*gps_data)(6) != (*status).parameters.gps_pre_t;\n\n    // 当GPS速度为0时,方向沿用上个GPS点方向\n//    if ((*gps_data)(4) == 0.0) {\n//        (*gps_data)(5) = (*status).parameters.gps_pre_bearing;\n//    }\n\n    // 低速时GPS方向改用为融合后的方向\n    if((*gps_data)(4) <= (*status).parameters.gps_static_speed_threshold && !is_gps_initializing){\n        (*gps_data)(5) = (*status).gnssins.bearing;\n    }\n\n//    // 利用kalman根据历史轨迹进行滤波估计\n//    bool is_gps_belong_to_track = true;\n//    if (is_gps_accuracy && is_gps_not_null && is_gps_not_duplicated) {\n//        is_gps_belong_to_track = IsGPSBelongToTrack(status, (*gps_data));\n//    }\n\n    // 当GPS在初始状态内时，处理为0.0的情况,gps(lng,lat,alt,accuracy,speed,bearing,t)\n    if (is_gps_initializing && !is_gps_not_null) {\n        (*gps_data)(0) = (*status).parameters.gps_pre_lng;\n        (*gps_data)(1) = (*status).parameters.gps_pre_lat;\n        (*gps_data)(2) = (*status).parameters.gps_pre_altitude;\n        (*gps_data)(3) = (*status).parameters.gps_pre_accuracy;\n        (*gps_data)(4) = (*status).parameters.gps_pre_speed;\n        (*gps_data)(5) = (*status).parameters.gps_pre_bearing;\n        (*gps_data)(6) = (*status).parameters.gps_pre_t;\n    }\n\n    // 当载体处于静止，则无论怎样都采用该GPS\n    bool is_gps_static;\n    if (is_gps_not_null && (*gps_data)(4) <= (*status).parameters.gps_static_speed_threshold) {\n        is_gps_static = true;\n        // 静止时候传感器采用静止因子\n        (*status).parameters.t = 1.0 / ((*status).parameters.Hz * (*status).parameters.static_t_factor);\n    } else {\n        is_gps_static = false;\n        // 运动时候传感器采用运动因子\n//        (*status).parameters.t = 1.0 / ((*status).parameters.Hz * (*status).parameters.move_t_factor);\n    }\n\n    // 利用kalman根据历史轨迹进行滤波估计\n    bool is_gps_belong_to_track = true;\n    if (is_gps_not_null) {\n        is_gps_belong_to_track = IsGPSBelongToTrack(status, (*gps_data));\n    }\n\n    // 当前一个GPS点速度为0,当前GPS数据又为空的的时候,采用前一点的数据,gps(lng,lat,alt,accuracy,speed,bearing,t)\n    bool is_gps_still_static;\n    if (!is_gps_not_null && (*status).parameters.gps_pre_speed <= (*status).parameters.gps_static_speed_threshold) {\n        (*gps_data)(0) = (*status).parameters.gps_pre_lng;\n        (*gps_data)(1) = (*status).parameters.gps_pre_lat;\n        (*gps_data)(2) = (*status).parameters.gps_pre_altitude;\n        (*gps_data)(3) = (*status).parameters.gps_pre_accuracy;\n        (*gps_data)(4) = (*status).parameters.gps_pre_speed;\n        (*gps_data)(5) = (*status).parameters.gps_pre_bearing;\n        (*gps_data)(6) = (*status).parameters.gps_pre_t;\n        is_gps_still_static = true;\n        // 静止时候传感器采用静止因子\n        (*status).parameters.t = 1.0 / ((*status).parameters.Hz * (*status).parameters.static_t_factor);\n    } else {\n        is_gps_still_static = false;\n        // 运动时候传感器采用运动因子\n//        (*status).parameters.t = 1.0 / ((*status).parameters.Hz * (*status).parameters.move_t_factor);\n    }\n\n    return (is_gps_accuracy && is_gps_not_null && is_gps_move_accepted && is_gps_not_duplicated &&\n            is_gps_belong_to_track)\n           || is_gps_initializing || (is_gps_static || is_gps_still_static) && is_gps_belong_to_track;\n}"
  },
  {
    "path": "sensor/GPS.h",
    "content": "//\n// Created by yangcheng on 2018/12/24.\n//\n\n#ifndef LOCATION_GPS_H\n#define LOCATION_GPS_H\n\n#include \"Eigen/Dense\"\n#include \"../system/Status.h\"\n\nclass GPS {\npublic:\n\n    // 给定起点经度,纬度,距离,方向, 计算终点的经纬度.\n    Eigen::Vector2d CalDestination(double &startLng, double &startLat, double &distance, double &heading);\n\n    // 利用GPS速度作为加速计初始速度,根据GPS速度,方向 计算正北,正东方向速度.\n    void UpdateVelocity(routing::Status *status, double &velocity, double &bearing);\n\n    // 计算两个经纬度点之间的距离\n    double CalDistance(double &startLng, double &startLat, double &endLng, double &endLat);\n\n    // 根据当前输入以及状态判断采用GPS还是INS\n    bool IsGPSValid(routing::Status *status,  Eigen::VectorXd *gps_data);\n\n    // 判断GPS点是否符合GPS历史轨迹\n    bool IsGPSBelongToTrack(routing::Status *status, Eigen::VectorXd &gps_data);\n\nprivate:\n    // 计算kalman当前gps所需状态\n    Eigen::Vector4d CalcState(Eigen::VectorXd &gps_data);\n\n\n};\n\n\n#endif //LOCATION_GPS_H\n"
  },
  {
    "path": "sensor/Gravity.cpp",
    "content": "//\n// Created by yangcheng on 2019/4/13.\n//\n\n#include \"Gravity.h\"\n#include <iostream>\n#include <queue>\n\nusing namespace Eigen;\n\nbool Gravity::IsShaking(routing::Status *status, Eigen::Vector3d &g_data) {\n\n    static std::queue<Vector3d> pre_g_data;\n    static int cnt = 0;\n\n\n    if (cnt <= (*status).parameters.Hz) {\n        pre_g_data.push(g_data);\n        cnt += 1;\n//        std::cout << g_data(0) << \" \" << g_data(1) << \" \" << g_data(2) << \" \" << 0 << \" \" << 0 << std::endl;\n        return false;\n    } else {\n        double diff_pre_curent = (g_data - pre_g_data.front()).squaredNorm();\n        pre_g_data.pop();\n        pre_g_data.push(g_data);\n//        std::cout << g_data(0) << \" \" << g_data(1) << \" \" << g_data(2) << \" \" << diff_pre_curent << \" \" << (diff_pre_curent > 0.5) << std::endl;\n        return diff_pre_curent > (*status).parameters.shaking_threshold;\n    }\n\n}"
  },
  {
    "path": "sensor/Gravity.h",
    "content": "//\n// Created by yangcheng on 2019/4/13.\n//\n\n#ifndef LOCATION_GRAVITY_H\n#define LOCATION_GRAVITY_H\n\n#include \"Eigen/Dense\"\n#include \"../system/Status.h\"\n\nclass Gravity {\n\npublic:\n\n    bool IsShaking(routing::Status *status, Eigen::Vector3d &g_data);\n};\n\n\n#endif //LOCATION_GRAVITY_H\n"
  },
  {
    "path": "sensor/Gyroscope.cpp",
    "content": "//\n// Created by yangcheng on 2018/12/13.\n//\n\n#include \"Gyroscope.h\"\n#include <Eigen/Dense>\n#include <cmath>\n\nusing namespace Eigen;\nusing namespace routing;\n\n///**\n// * 从陀螺仪获取姿态旋转矩阵(方向余弦矩阵DCM), b系坐标转g系\n// *\n// * @param gyro, 陀螺仪欧拉角w(x,y,z);\n// * @param deltaT\n// * @return 方向余弦矩阵DCM\n// */\n//Matrix3d Gyroscope::GetDCM(Vector3d &gyro, double &deltaT) {\n//\n//    // 计算deltaT时间内角度变化值，deltaT越小越精确。\n//    double delta_wx = gyro(0) * deltaT;\n//    double delta_wy = gyro(1) * deltaT;\n//    double delta_wz = gyro(2) * deltaT;\n//\n//    double cos_delta_wx = cos(delta_wx);\n//    double sin_delta_wx = sin(delta_wx);\n//    double cos_delta_wy = cos(delta_wy);\n//    double sin_delta_wy = sin(delta_wy);\n//    double cos_delta_wz = cos(delta_wz);\n//    double sin_delta_wz = sin(delta_wz);\n//\n//    // 计算DCM矩阵(z * y * x)。\n//    Matrix3d DCM;\n//    DCM(0, 0) = cos_delta_wy * cos_delta_wz;\n//    DCM(0, 1) = -sin_delta_wz * cos_delta_wx + sin_delta_wx * sin_delta_wy * cos_delta_wz;\n//    DCM(0, 2) = sin_delta_wx * sin_delta_wz + sin_delta_wy * cos_delta_wx * cos_delta_wz;\n//    DCM(1, 0) = sin_delta_wz * cos_delta_wy;\n//    DCM(1, 1) = cos_delta_wx * cos_delta_wz + sin_delta_wx * sin_delta_wy * sin_delta_wz;\n//    DCM(1, 2) = -sin_delta_wx * cos_delta_wz + sin_delta_wy * sin_delta_wz * cos_delta_wx;\n//    DCM(2, 0) = -sin_delta_wy;\n//    DCM(2, 1) = sin_delta_wx * cos_delta_wy;\n//    DCM(2, 2) = cos_delta_wx * cos_delta_wy;\n//\n//    return DCM;\n//}\n\n/**\n * 陀螺仪标定,测量零飘误差.\n *\n * @param input_data, 静止时的陀螺仪数据(建议,n=200);\n * @param parameters , 陀螺仪标定参数 coef(offset_x,offset_y,offset_z);\n */\nvoid Gyroscope::GyroCalibration(MatrixXd &input_data, Status *status) {\n\n    int data_nums = static_cast<int>(input_data.rows());\n    double offset_x = 0;\n    double offset_y = 0;\n    double offset_z = 0;\n\n    // 用于判断陀螺仪是否静止, 若非静止, 标定将会产生较大误差.\n    double x_diff = 0;\n    double y_diff = 0;\n    double z_diff = 0;\n    double gyro_x_init = input_data(0, 0);\n    double gyro_y_init = input_data(0, 1);\n    double gyro_z_init = input_data(0, 2);\n\n    for (int i = 0; i < data_nums; i++) {\n\n        // 计算前后偏差,用以判断是否处于静止.\n        x_diff += input_data(i, 0) - gyro_x_init;\n        y_diff += input_data(i, 1) - gyro_y_init;\n        z_diff += input_data(i, 2) - gyro_z_init;\n        // 重赋x,y,z, 用于计算两两样本前后差\n        gyro_x_init = input_data(i, 0);\n        gyro_y_init = input_data(i, 1);\n        gyro_z_init = input_data(i, 2);\n        // 计算offset\n        offset_x += input_data(i, 0);\n        offset_y += input_data(i, 1);\n        offset_z += input_data(i, 2);\n    }\n\n    // 判断是否静止\n    if (x_diff < data_nums * 0.5 && y_diff < data_nums * 0.5 && z_diff < data_nums * 0.5) {\n        VectorXd gyro_coef(3);\n        gyro_coef(0) = offset_x / data_nums;\n        gyro_coef(1) = offset_y / data_nums;\n        gyro_coef(2) = offset_z / data_nums;\n\n        (*status).parameters.gyro_coef = gyro_coef;\n    }\n}\n\n\n//\n//// 姿态更新。\n//Vector3d Gyroscope::UpdateAttitude(Matrix3d &dcm, Vector3d &state) {\n//\n//    Vector3d newState;\n//    // 旋转更新.\n//    newState = dcm * state;\n//    return newState;\n//}"
  },
  {
    "path": "sensor/Gyroscope.h",
    "content": "//\n// Created by yangcheng on 2018/12/13.\n//\n\n#include <Eigen/Dense>\n#include \"../system/Status.h\"\n\n#ifndef LOCATION_GYROSCOPE_H\n#define LOCATION_GYROSCOPE_H\n\n\nclass Gyroscope {\npublic:\n\n    // 从陀螺仪获取姿态旋转矩阵(方向余弦矩阵DCM), b系坐标转g系\n//    Matrix3d GetDCM(Vector3d &gyro, double &deltaT);\n\n    // 陀螺仪标定\n    void GyroCalibration(Eigen::MatrixXd &input_data, routing::Status *status);\n\n};\n\n\n#endif //LOCATION_GYROSCOPE_H\n"
  },
  {
    "path": "sensor/Magnetometer.cpp",
    "content": "//\n// Created by yangcheng on 2018/12/24.\n//\n\n#include \"cmath\"\n#include \"Magnetometer.h\"\n#include \"../math/Optimizer.h\"\n\nusing namespace Eigen;\nusing namespace routing;\n\nVector3d Magnetometer::Normalise(Vector3d &m) const {\n    Vector3d normM;\n    double norm2 = m(0) * m(0) + m(1) * m(1) + m(2) * m(2);\n    // 如果四元数各项足够接近单位四元数, 则不做任何处理.\n    if (norm2 != 0.0) {\n        double norm = sqrt(norm2);\n        normM(0) = m(0) / norm;\n        normM(1) = m(1) / norm;\n        normM(2) = m(2) / norm;\n    } else {\n        normM = m;\n    }\n    return normM;\n}\n\n\nVector3d Magnetometer::GetMagError(Vector4d &q, Vector3d &originMag) {\n    double hx = 2.0 * (originMag(0) * (0.5 - q(2) * q(2) - q(3) * q(3)) + originMag(1) * (q(1) * q(2) - q(0) * q(3)) +\n                       originMag(2) * (q(1) * q(3) + q(0) * q(2)));\n    double hy = 2.0 * (originMag(0) * (q(1) * q(2) + q(0) * q(3)) + originMag(1) * (0.5 - q(1) * q(1) - q(3) * q(3)) +\n                       originMag(2) * (q(2) * q(3) - q(0) * q(1)));\n    double bx = sqrt(hx * hx + hy * hy);\n    double bz = 2.0f * (originMag(0) * (q(1) * q(3) - q(0) * q(2)) + originMag(1) * (q(2) * q(3) + q(0) * q(1)) +\n                        originMag(2) * (0.5 - q(1) * q(1) - q(2) * q(2)));\n\n\n    double halfwx = bx * (0.5 - q(2) * q(2) - q(3) * q(3)) + bz * (q(1) * q(3) - q(0) * q(2));\n    double halfwy = bx * (q(1) * q(2) - q(0) * q(3)) + bz * (q(0) * q(1) + q(2) * q(3));\n    double halfwz = bx * (q(0) * q(2) + q(1) * q(3)) + bz * (0.5f - q(1) * q(1) - q(2) * q(2));\n\n    double ex = originMag(1) * halfwz - originMag(2) * halfwy;\n    double ey = originMag(2) * halfwx - originMag(0) * halfwz;\n    double ez = originMag(0) * halfwy - originMag(1) * halfwx;\n    Vector3d e(ex, ey, ez);\n\n    return e;\n}\n\n// 地磁感应误差计算\nVector3d Magnetometer::GetMagError(Matrix3d &b2n, Vector3d &originMag) const {\n\n    Vector3d magErr;\n    Vector3d formatMag;\n\n    // 旋转b系下地磁数据到n系.\n    Vector3d rotatedMag = b2n * originMag;\n    // 地理坐标系下的真实地磁数据。\n    formatMag(0) = sqrt(rotatedMag(0) * rotatedMag(0) + rotatedMag(1) * rotatedMag(1));\n    formatMag(1) = 0.0;\n    formatMag(2) = rotatedMag(2);\n    // 转到b系\n    Vector3d realMag = b2n.transpose() * formatMag;\n\n    // 计算误差.\n//    magErr(0) = realMag(1) * originMag(2) - realMag(2) * originMag(1);\n//    magErr(1) = realMag(2) * originMag(0) - realMag(0) * originMag(2);\n//    magErr(2) = realMag(0) * originMag(1) - realMag(1) * originMag(0);\n\n    magErr(0) = realMag(2) * originMag(1) - realMag(1) * originMag(2);\n    magErr(1) = realMag(0) * originMag(2) - realMag(2) * originMag(0);\n    magErr(2) = realMag(1) * originMag(0) - realMag(0) * originMag(1);\n\n    return magErr;\n}\n\nvoid Magnetometer::MagCalibration(MatrixXd &input_data, Status *status) {\n    double mag = (*status).parameters.mag;\n    double gamma = (*status).parameters.gamma;\n    double epsilon = (*status).parameters.epsilon;\n    int max_step = (*status).parameters.max_step;\n    VectorXd *coef = &(*status).parameters.mag_coef;\n    Optimizer optimizer;\n    optimizer.LevenbergMarquardt(input_data, mag, coef, gamma, epsilon, max_step);\n}"
  },
  {
    "path": "sensor/Magnetometer.h",
    "content": "//\n// Created by yangcheng on 2018/12/24.\n//\n\n#include \"../system/Status.h\"\n#include \"Eigen/Dense\"\n\n#ifndef LOCATION_MAGNETOMETER_H\n#define LOCATION_MAGNETOMETER_H\n\n\nclass Magnetometer {\npublic:\n\n    // 归一化.\n    Eigen::Vector3d Normalise(Eigen::Vector3d &m) const;\n\n    // 地磁感应误差计算\n    Eigen::Vector3d GetMagError(Eigen::Matrix3d &b2n, Eigen::Vector3d &originMag) const;\n\n    Eigen::Vector3d GetMagError(Eigen::Vector4d &q, Eigen::Vector3d &originMag);\n\n    // 地磁计标定\n    void MagCalibration(Eigen::MatrixXd &input_data, routing::Status *status);\n};\n\n\n#endif //LOCATION_MAGNETOMETER_H\n"
  },
  {
    "path": "sensor/Sensor.cpp",
    "content": "//\n// Created by yangcheng on 2019/1/13.\n//\n\n#include \"Sensor.h\"\n#include \"../sensor/Gyroscope.h\"\n#include \"../sensor/Accelerometer.h\"\n#include \"../sensor/Magnetometer.h\"\n\nusing namespace Eigen;\nusing namespace routing;\n\n/**\n * 传感器标定入口, 目前包含陀螺仪,地磁计,加速计\n *\n * @param gyro_data,陀螺仪数据, 采样建议: n>=200\n * @param acc_data, 加速计数据, 采样建议: 静止时采集6个轴转向180°各1组数据, 共6组数据\n * @param mag_data, 地磁计数据, 采样建议: 静止时采集6个轴转向180°各1组数据, 共6组数据\n * @param status\n */\nvoid Sensor::Calibrate(MatrixXd &gyro_data, MatrixXd &acc_data, MatrixXd &mag_data, Status *status) {\n\n    // 标定陀螺仪\n    Gyroscope gyroscope;\n    gyroscope.GyroCalibration(gyro_data, status);\n\n    // 标定加速计\n    Accelerometer accelerometer;\n    accelerometer.AccCalibration(acc_data, status);\n\n    // 标定地磁计\n    Magnetometer magnetometer;\n    magnetometer.MagCalibration(mag_data, status);\n}"
  },
  {
    "path": "sensor/Sensor.h",
    "content": "//\n// Created by yangcheng on 2019/1/13.\n//\n\n#include \"../system/Status.h\"\n#include \"Eigen/Dense\"\n\n#ifndef LOCATION_SENSOR_H\n#define LOCATION_SENSOR_H\n\n\nclass Sensor {\npublic:\n\n    void Calibrate(Eigen::MatrixXd &gyro_data,Eigen::MatrixXd &acc_data,Eigen::MatrixXd &mag_data, routing::Status *status);\n\n};\n\n#endif //LOCATION_SENSOR_H\n"
  },
  {
    "path": "system/CMakeLists.txt",
    "content": "aux_source_directory(. system_src_lists)\nadd_library(Location_system ${system_src_lists})"
  },
  {
    "path": "system/Status.cpp",
    "content": "//\n// Created by yangcheng on 2019/1/14.\n//\n\n#include \"Status.h\"\n#include \"../math/Quaternions.h\"\n#include \"../sensor/Gyroscope.h\"\n#include \"../sensor/Accelerometer.h\"\n#include \"../sensor/Magnetometer.h\"\n#include \"Eigen/Dense\"\n\nusing namespace Eigen;\nusing namespace routing;\n\nPosition Status::GetPosition() const {\n    return this->position;\n}\n\nAttitude Status::GetAttitude() const {\n    return this->attitude;\n}\n\nVelocity Status::GetVelocity() const {\n    return this->velocity;\n}\n\nParameters Status::GetParameters() const {\n    return this->parameters;\n}\n\nvoid Status::Init() {\n\n    this->gnssins.lng = 0.0;\n    this->gnssins.lat = 0.0;\n    this->gnssins.altitude = 0.0;\n    this->gnssins.accuracy = 0.0;\n    this->gnssins.speed = 0.0;\n    this->gnssins.bearing = 0.0;\n\n    this->velocity.v_x = 0.0;\n    this->velocity.v_y = 0.0;\n    this->velocity.v_z = 0.0;\n\n    this->position.x = 0.0;\n    this->position.y = 0.0;\n    this->position.z = 0.0;\n    this->position.lng = 0.0;\n    this->position.lat = 0.0;\n    this->position.altitude = 0.0;\n\n    this->attitude.roll = 0.0;\n    this->attitude.pitch = 0.0;\n    this->attitude.yaw = 0.0;\n\n    this->parameters.stop_detector_model_path = \"\";\n    this->parameters.stop_status = 1;\n    this->parameters.stop_status_window = 3;\n\n    Quaternions quaternions;\n    Vector3d init_euler_angle(this->attitude.roll, this->attitude.pitch, this->attitude.yaw);\n    this->attitude.q_attitude = quaternions.GetQFromEuler(init_euler_angle);\n    Vector3d gyro_coef(0.0,0.0,0.0);\n    this->parameters.gyro_coef = gyro_coef;\n    VectorXd acc_coef(6);\n    acc_coef << 0.0,0.0,0.0,1.0,1.0,1.0;\n    this->parameters.acc_coef = acc_coef;\n    VectorXd mag_coef(6);\n    mag_coef << 0.0,0.0,0.0,1.0,1.0,1.0;\n    this->parameters.mag_coef = mag_coef;\n\n    this->parameters.weak_gps = 100;\n    this->parameters.gamma = 1.0;\n    this->parameters.epsilon = 0.000001;\n    this->parameters.max_step = 200;\n\n    this->parameters.acc_a1 = 0.0;\n    this->parameters.acc_a2 = 0.0;\n    this->parameters.acc_b0 = 0.0;\n    this->parameters.acc_hz = 5.0;\n    this->parameters.acc_thres = 0.1;\n    Vector3d acc(0.0,0.0,0.0);\n    this->parameters.last_acc_data = acc;\n    this->parameters.sec_last_acc_data = acc;\n    this->parameters.ornt_hz = 1.5;\n    Vector3d ornt(0.0,0.0,0.0);\n    this->parameters.last_ornt_data = ornt;\n    this->parameters.sec_last_ornt_data = ornt;\n\n    Vector3d err(0.0,0.0,0.0);\n    this->parameters.err = err;\n    this->parameters.ki = 0.1;\n    this->parameters.kp = 1.0;\n    this->parameters.Hz = 20.0;\n    this->parameters.halfT = 1.0 / (this->parameters.Hz * 2.0);\n    this->parameters.static_t_factor = 1.0;\n    this->parameters.move_t_factor = 1.0;\n    this->parameters.t = 1.0 / (this->parameters.Hz * this->parameters.static_t_factor);\n    this->parameters.move_decay = 0.995;\n\n    this->parameters.move_distance_threshod = 500000.0;\n    this->parameters.ins_count = 0;\n    this->parameters.ins_dist = 0.0;\n    this->parameters.max_ins_dist = 1000.0;\n\n    this->parameters.least_gap_time_for_using_road = 2.5;\n    this->parameters.queue_gps_ornt = 1;\n    this->parameters.diff_gps_ornt = 0.0;\n    this->parameters.diff_road_ornt = 0.0;\n    this->parameters.queue_road_ornt_len = 3;\n    this->parameters.accepted_change_range = 8.0;\n    this->parameters.accepted_max_diff_change_range = 12.0;\n    this->parameters.off_course_data_queue = 30;\n    this->parameters.routing_time = 5;\n\n    this->parameters.is_current_gps_valid = true;\n    this->parameters.gps_static_speed_threshold = 2.0;\n    this->parameters.gps_count = 0;\n    this->parameters.gps_init_threshold = 10;\n    this->parameters.gps_pre_lng = 0.0;\n    this->parameters.gps_pre_lat = 0.0;\n    this->parameters.gps_pre_t = 0.0;\n    this->parameters.gps_pre_speed = 0.0;\n    this->parameters.gps_pre_accuracy = 0.0;\n    this->parameters.gps_pre_bearing = 0.0;\n    this->parameters.gps_pre_altitude = 0.0;\n    this->parameters.gps_track_len = 7;\n    this->parameters.gps_max_gap_time = 5;\n\n    this->parameters.shaking_threshold = 0.8;\n    this->parameters.compass_queue_len = 20;\n    this->parameters.compass_vaild_var_thres = 0.085;\n\n    this->parameters.road_type = 0.0;\n    this->parameters.max_ignore_in_common = 3;\n    this->parameters.max_ignore_in_tunnel = 8;\n    this->parameters.min_dist_to_next_cross = 50.0;\n    this->parameters.min_dist_from_pre_cross = 150.0;\n    this->parameters.dist_to_next_cross = 100000.0;\n    this->parameters.dist_from_pre_cross = 100000.0;\n\n    this->parameters.g = 9.805567;\n    this->parameters.mag = 157.44;\n    this->parameters.we = 7.2921158 / 100000.0;\n    this->parameters.R = 6378137.0;\n}"
  },
  {
    "path": "system/Status.h",
    "content": "//\n// Created by yangcheng on 2019/1/14.\n//\n\n#ifndef LOCATION_STATUS_H\n#define LOCATION_STATUS_H\n\n#include \"../include/eigen3/Eigen/Dense\"\n\nnamespace routing {\n\n    // 用于最终输出\n    struct GNSSINS {\n        double lng;\n        double lat;\n        double altitude;\n        double accuracy;\n        double speed;\n        double bearing;\n    };\n\n    struct Position {\n        // x,y,z轴的平面位置坐标\n        double x;\n        double y;\n        double z;\n\n        // 经纬度,海拔\n        double lng;\n        double lat;\n        double altitude;\n    };\n\n    struct Velocity {\n        // x,y,z轴的速度\n        double v_x;\n        double v_y;\n        double v_z;\n    };\n\n    struct Attitude {\n        // 姿态角, 弧度\n        double roll;\n        double pitch;\n        double yaw;\n\n        // 姿态四元数\n        Eigen::Vector4d q_attitude;\n    };\n\n    struct Parameters{\n\n        // 用于无信号时检测行车状态的模型\n        std::string stop_detector_model_path;\n\n        // 停车状态,0停车,1运动\n        int stop_status;\n        // 停车检测窗口\n        int stop_status_window;\n\n        // 弱GPS精度阈值\n        double weak_gps;\n\n        // 陀螺仪标定参数, v(offset_x,offset_y,offset_z)\n        Eigen::VectorXd gyro_coef;\n\n        // 加速计标定参数, v(offset_x,offset_y,offset_z,scale_x,scale_y,scale_z)\n        Eigen::VectorXd acc_coef;\n\n        // 地磁计标定参数, v(offset_x,offset_y,offset_z,scale_x,scale_y,scale_z)\n        Eigen::VectorXd mag_coef;\n\n        // LM算法标定参数, 对加速计和地磁计通用\n        // 初始化阻尼因子用, mu = gamma * max(A), A = Jacobi_t * Jacobi;\n        double gamma;\n        // 迭代精度\n        double epsilon;\n        // 最高迭代次数\n        int max_step;\n\n        // 低通滤波算法参数\n        double acc_a1, acc_a2, acc_b0, ornt_a1, ornt_a2, ornt_b0;\n        // 加速计截至频率\n        double acc_hz, ornt_hz;\n        // 用于平滑数据,t-1 与 t-2 时刻的加速计数都\n        Eigen::Vector3d last_acc_data, last_ornt_data;\n        Eigen::Vector3d sec_last_acc_data, sec_last_ornt_data;\n        // 用于加速计干扰过滤\n        double acc_thres;\n\n        // AHRS算法参数\n        // 误差积分\n        Eigen::Vector3d err;\n        // PID控制算法参数, 比例参数\n        double ki;\n        // PID控制算法参数, 积分参数\n        double kp;\n        // 采用频率\n        double Hz;\n        // 采样频率的一半\n        double halfT;\n        // 采样时间间隔\n        double t;\n        // 采样时间放大因子,分为运动和静止两个\n        double static_t_factor;\n        double move_t_factor;\n        // 惯导运动衰减因子\n        double move_decay;\n\n        // 等间隔时间内GPS的运动距离阈值,用于判断高精度但是漂移的点\n        double move_distance_threshod;\n        // 利用惯导计算位置的次数;\n        int ins_count;\n        // 惯导累计的最大距离限制\n        double max_ins_dist;\n        // 利用惯导计算的距离\n        double ins_dist;\n        // GPS和方向传感器持续较正的队列长度\n        int queue_gps_ornt;\n        // GPS和方向传感器之间的偏差\n        double diff_gps_ornt;\n        // 道路和方向传感器之间的偏差\n        double diff_road_ornt;\n        // 当多长时间没GPS信号后才使用道路方向做指南针修正\n        double least_gap_time_for_using_road;\n        // 指南针与道路方向的变化幅度队列长度\n        int queue_road_ornt_len;\n        // 角度误差波动可接受范围\n        double accepted_change_range;\n        // 当道路方向发生比较大变化时, 与指南针方向变化 的可容许误差范围\n        double accepted_max_diff_change_range;\n        // 判断偏航所需保存的历史数据队列长度\n        int off_course_data_queue;\n        // 重新规划线路后沿用指南针方向的时间\n        int routing_time;\n\n        // 当前输入GPS点是否可用\n        bool is_current_gps_valid;\n        // GPS初始状态计数\n        int gps_count;\n        // 导航GPS初始化后，记录多久后接入ins\n        int gps_init_threshold;\n        // gps静止速度阈值\n        double gps_static_speed_threshold;\n        // gps上一个点,经纬度,时间戳,海拔,精度,速度,方向\n        double gps_pre_lng;\n        double gps_pre_lat;\n        double gps_pre_t;\n        double gps_pre_altitude;\n        double gps_pre_accuracy;\n        double gps_pre_speed;\n        double gps_pre_bearing;\n        // gps轨迹历史信息记录长度\n        int gps_track_len;\n        // gps最大时间间隔,超过这个间隔的GPS都会采用,不做任何舍弃\n        int gps_max_gap_time;\n\n        // 重力判断晃动阈值\n        double shaking_threshold;\n\n        // 指南针方差计算队列长度\n        int compass_queue_len;\n        // 指南针晃动方差阈值\n        double compass_vaild_var_thres;\n\n        /**\n         * 道路类型\n         * 0:正常道路\n         * 1:隧道\n         */\n        double road_type;\n        // 普通情况下判断为误差的最多次数\n        int max_ignore_in_common;\n        // 隧道里判断为误差的最多次数\n        int max_ignore_in_tunnel;\n        // 距路口多少米时开始侧重指南针,在此之前gps可用则用,其次是道路方向\n        double min_dist_to_next_cross;\n        double min_dist_from_pre_cross;\n        // 距下个路口距离\n        double dist_to_next_cross;\n        // 距离上个路口距离\n        double dist_from_pre_cross;\n\n        // 当地重力加速度值\n        double g;\n        // 当地场强模值\n        double mag;\n        // 地球自转角速度\n        double we;\n        // 地球半径\n        double R;\n    };\n\n    class Status {\n    public:\n\n        GNSSINS gnssins;\n        Position position;\n        Velocity velocity;\n        Attitude attitude;\n        Parameters parameters;\n\n        Position GetPosition() const;\n\n        Velocity GetVelocity() const;\n\n        Attitude GetAttitude() const;\n\n        Parameters GetParameters() const;\n\n        void Init();\n\n    };\n\n}\n\n#endif //LOCATION_STATUS_H\n"
  },
  {
    "path": "test/CMakeLists.txt",
    "content": "aux_source_directory(utils sub_src_lists)\naux_source_directory(. src_lists)\nadd_library(Location_test ${src_lists} ${sub_src_lists})\ntarget_link_libraries(Location_test Location_location)\ntarget_link_libraries(Location_test Location_utils)"
  },
  {
    "path": "test/TestCalibration.cpp",
    "content": "//\n// Created by yangcheng on 2019/1/18.\n//\n\n#include \"TestCalibration.h\"\n#include \"../sensor/Sensor.h\"\n#include \"iostream\"\n\nusing namespace Eigen;\nusing namespace routing;\n\nvoid TestCalibration::testCalibration(MatrixXd &gyro_data, MatrixXd &acc_data, MatrixXd &mag_data, Status *status) {\n\n    Vector3d gyro_coef(0.0,0.0,0.0);\n    (*status).parameters.gyro_coef = gyro_coef;\n    VectorXd acc_coef(6);\n    acc_coef << 0.0,0.0,0.0,1.0,1.0,1.0;\n    (*status).parameters.acc_coef = acc_coef;\n    VectorXd mag_coef(6);\n    mag_coef << 0.0,0.0,0.0,1.0,1.0,1.0;\n    (*status).parameters.mag_coef = mag_coef;\n\n    (*status).parameters.gamma = 1.0;\n    (*status).parameters.epsilon = 0.0000000001;\n    (*status).parameters.max_step = 500;\n    Vector3d err(0.0,0.0,0.0);\n    (*status).parameters.err = err;\n    (*status).parameters.ki = 0.0001;\n    (*status).parameters.kp = 300.0;\n    (*status).parameters.halfT = 1 / 20.0;\n    (*status).parameters.g = 9.805567;\n    (*status).parameters.mag = 0.15744;\n\n    Sensor sensor;\n\n    // acc数据调整\n//    MatrixXd acc_data_adj(12, 3);\n    // mag数据调整\n//    MatrixXd mag_data_adj(12, 3);\n\n//    acc_data = acc_data / (*status).parameters.g;\n\n//    for (int i = 0; i < 12; i++) {\n//        // 加速计数据单位为g\n//        acc_data_adj.block(i, 0, 1, 3) = acc_data.block(i * 5, 0, 1, 3) / (*status).parameters.g;\n//        mag_data_adj.block(i, 0, 1, 3) = mag_data.block(i * 5, 0, 1, 3);\n//    }\n\n//    cout << gyro_data << endl;\n//    cout << \"------------------\" << endl;\n//    cout << acc_data << endl;\n//    cout << \"--------------\" << endl;\n//    cout << mag_data << endl;\n    sensor.Calibrate(gyro_data, acc_data, mag_data, status);\n\n}"
  },
  {
    "path": "test/TestCalibration.h",
    "content": "//\n// Created by yangcheng on 2019/1/18.\n//\n\n#ifndef LOCATION_TESTCALIBRATION_H\n#define LOCATION_TESTCALIBRATION_H\n\n#include \"Eigen/Dense\"\n#include \"../system/Status.h\"\n\n\nclass TestCalibration {\npublic:\n    void testCalibration(Eigen::MatrixXd &gyro_data, Eigen::MatrixXd &acc_data, Eigen::MatrixXd &mag_data, routing::Status *status);\n};\n\n\n#endif //LOCATION_TESTCALIBRATION_H\n"
  },
  {
    "path": "test/TestLocation.cpp",
    "content": "//\n// Created by yangcheng on 2019/1/17.\n//\n\n#include \"TestLocation.h\"\n#include \"TestCalibration.h\"\n#include \"iostream\"\n#include \"../sensor/Accelerometer.h\"\n#include \"../sensor/GPS.h\"\n#include \"../math/Quaternions.h\"\n#include \"../test/utils/DataFormat.h\"\nusing namespace Eigen;\nusing namespace routing;\n//using namespace std;\n\nvoid TestLocation::testLocation(MatrixXd &gyro_data, MatrixXd &acc_data, MatrixXd &mag_data, MatrixXd &gps_data, MatrixXd &g_data, MatrixXd &ornt_data, MatrixXd &road_data) {\n\n//    // 初始状态\n//    Quaternions quaternions;\n//    Status status{};\n//    status.Init();\n\n\n    // 包括初始化状态\n    Location location;\n    location.SetHz(20.0);\n//    DataFormat dataFormat;\n//    dataFormat.writeCSV(acc_data, g_data, gyro_data, mag_data, ornt_data, gps_data);\n\n    for(int i = 0; i < gyro_data.rows(); i++){\n//    for(int i = 0; i < 13000; i++){\n//\n        Vector3d gyro_data_v = gyro_data.row(i);\n        Vector3d mag_data_v = mag_data.row(i) / 1000.0;\n        Vector3d acc_data_v = acc_data.row(i);\n        VectorXd gps_data_v = gps_data.row(i);\n        Vector3d g_data_v = g_data.row(i);\n        Vector3d ornt_data_v = ornt_data.row(i);\n        Vector3d road_data_v = road_data.row(i);\n\n\n        location.PredictCurrentPosition(gyro_data_v, acc_data_v, mag_data_v, gps_data_v, g_data_v, ornt_data_v, road_data_v);\n        GNSSINS gnssins = location.GetGNSSINS();\n//\n//\n        std::cout.precision(7);\n//        std::cout << location.status.position.lng << \" \" << location.status.position.lat << std::endl;\n        std::cout << gnssins.lng << \" \" << gnssins.lat << \" \" << gnssins.bearing << std::endl;\n    }\n\n}\n"
  },
  {
    "path": "test/TestLocation.h",
    "content": "//\n// Created by yangcheng on 2019/1/17.\n//\n\n#ifndef LOCATION_TESTLOCATION_H\n#define LOCATION_TESTLOCATION_H\n\n#include \"../location/Location.h\"\n\n\nclass TestLocation {\npublic:\n\n    void testLocation(Eigen::MatrixXd &gyro_data, Eigen::MatrixXd &acc_data, Eigen::MatrixXd &mag_data,\n                      Eigen::MatrixXd &gps_data, Eigen::MatrixXd &g_data, Eigen::MatrixXd &ornt_data,\n                      Eigen::MatrixXd &road_data);\n};\n\n\n#endif //LOCATION_TESTLOCATION_H\n"
  },
  {
    "path": "test/TestXgboostDetector.cpp",
    "content": "//\n// Created by yangcheng on 2019/7/10.\n//\n\n#include \"TestXgboostDetector.h\"\n#include <fstream>\n#include <iostream>\n#include \"../utils/Tools.h\"\n#include \"../models/XgboostDetector.h\"\n//#include \"utils/DataFormat.h\"\n\n\nTestXgboostDetector::TestXgboostDetector() {};\nTestXgboostDetector::~TestXgboostDetector() {};\n\nvoid TestXgboostDetector::TestDetector() {\n\n    std::cout.precision(9);\n    // read data\n    std::string file_name = \"C:\\\\Users\\\\yangcheng\\\\Desktop\\\\validation_data.csv\";\n\n    std::ifstream infile;\n    infile.open(file_name, std::ios::in);\n    long long int rows_cout = std::count(std::istreambuf_iterator<char>(infile),\n                               std::istreambuf_iterator<char>(), '\\n') + 1;\n    infile.close();\n    infile.open(file_name, std::ios::in);\n    Eigen::MatrixXd data(rows_cout, 27);\n\n    std::string s;\n    int i = 0;\n    Tools tools;\n    while (std::getline(infile, s)) {\n\n        std::vector<std::string> s_split = tools.split(s, \",\");\n\n        // data.\n        for(int j = 0; j < 27; ++j){\n            data(i, j) = stod(s_split[j]);\n        }\n        i +=1;\n    }\n    infile.close();\n\n\n    // detector\n    Eigen::VectorXd res(rows_cout);\n    std::string model_path = \"D:\\\\worksheet\\\\clion\\\\Location\\\\models\\\\raw_model.txt\";\n    XgboostDetector xgboostDetector = XgboostDetector(model_path);\n    StopDetection &stopDetection = xgboostDetector;\n    for(int k = 0; k < rows_cout; ++k){\n        Eigen::VectorXd input = data.row(k);\n        bool is_stop = stopDetection.IsStopping(input);\n        res(k) = is_stop;\n        std::cout << is_stop << std::endl;\n    }\n}"
  },
  {
    "path": "test/TestXgboostDetector.h",
    "content": "//\n// Created by yangcheng on 2019/7/10.\n//\n\n#ifndef LOCATION_TESTXGBOOSTDETECTOR_H\n#define LOCATION_TESTXGBOOSTDETECTOR_H\n\nclass TestXgboostDetector {\npublic:\n    TestXgboostDetector();\n    ~TestXgboostDetector();\n\n    void TestDetector();\n};\n\n\n#endif //LOCATION_TESTXGBOOSTDETECTOR_H\n"
  },
  {
    "path": "test/data/EEWalk2.csv",
    "content": "-0.3268,-0.2526,9.9,-0.1337,-0.1165,9.805,0.0195,-0.055,-0.0086,-2.4,22.3,-43.5,0.119729587,0.68,0.78,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,45,2015-10-30 10:13:40:921,1446171220921.0 \n-0.3591,-0.0335,9.8462,-0.1179,-0.0726,9.8057,0.0367,0.0244,0.0415,-2.4,22.1,-43.8,0.115366264,0.53,0.65,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,147,2015-10-30 10:13:41:023,1446171221023.0 \n-0.3412,-0.1233,9.6426,-0.1484,-0.092,9.8051,-0.0452,-0.0134,0.0024,-2.5,21.9,-43.7,0.122871179,0.54,0.87,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,250,2015-10-30 10:13:41:126,1446171221126.0 \n-0.2406,-0.0503,9.6929,-0.1319,-0.1066,9.8052,0.0183,-0.0281,0.011,-2.5,21.9,-43.5,0.120776784,0.65,0.81,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,352,2015-10-30 10:13:41:228,1446171221228.0 \n-0.3519,-0.0431,9.5277,-0.1071,-0.0914,9.8056,0.0428,-0.0367,0.0159,-2.5,21.9,-43.2,0.115715329,0.61,0.67,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,454,2015-10-30 10:13:41:330,1446171221330.0 \n-0.2215,-0.006,9.7624,-0.0754,-0.061,9.8062,0.033,-0.0232,-0.0073,-2.4,22,-43,0.10681415,0.36,0.44,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,555,2015-10-30 10:13:41:431,1446171221431.0 \n-0.261,-0.1089,9.7719,-0.0559,-0.0474,9.8064,0.0232,-0.044,-0.0061,-2.5,21.9,-42.9,0.10262536,0.28,0.33,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,657,2015-10-30 10:13:41:533,1446171221533.0 \n-0.2538,-0.0455,9.6702,-0.0593,-0.0236,9.8064,0.0171,-0.0159,-0.0086,-2.6,21.8,-42.7,0.148003921,0.17,0.35,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,760,2015-10-30 10:13:41:636,1446171221636.0 \n-0.1664,-0.0527,9.7839,-0.0505,-0.0185,9.8065,0.0354,-0.0049,0.0024,-2.8,21.8,-42.9,0.146956723,0.13,0.32,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,862,2015-10-30 10:13:41:738,1446171221738.0 \n-0.1508,0.1209,9.76,-0.0311,-0.0036,9.8066,-0.0024,-0.0415,0.0073,-2.9,21.7,-43,0.141720735,0.02,0.18,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,964,2015-10-30 10:13:41:840,1446171221840.0 \n-0.2478,0.0108,9.6367,-0.0129,-0.0066,9.8066,-0.0037,-0.0024,-0.011,-3.1,21.7,-43.2,0.138230077,0.04,0.08,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,1065,2015-10-30 10:13:41:941,1446171221941.0 \n-0.0982,0.0072,9.7887,0.0127,-0.0017,9.8066,0.0122,-0.0574,-0.0122,-3.1,21.7,-43.3,0.136135682,0.03,0.01,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,1167,2015-10-30 10:13:42:043,1446171222043.0 \n-0.1125,-0.0431,9.5852,0.037,-0.0115,9.8066,-0.0122,-0.044,0.0037,-3.3,21.7,-43.4,0.128630766,0.07,-0.22,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,1269,2015-10-30 10:13:42:145,1446171222145.0 \n-0.0359,0.0347,9.7731,0.0961,-0.0195,9.8062,0.0037,-0.0929,0.0318,-3.4,21.7,-43.3,0.122173048,0.13,-0.42,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,1371,2015-10-30 10:13:42:247,1446171222247.0 \n-0.0622,0.0287,9.7252,0.1225,0.0047,9.8059,0.0318,-0.0024,0.0122,-3.7,21.8,-43.5,0.156032435,0.02,-0.72,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,1473,2015-10-30 10:13:42:349,1446171222349.0 \n0,0.0934,9.8138,0.1,0.0232,9.8061,0.0098,0.0476,0.0073,-3.9,21.8,-43.4,0.157603231,-0.1,-0.65,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,1576,2015-10-30 10:13:42:452,1446171222452.0 \n-0.0742,0.0275,9.663,0.0736,0.0209,9.8064,0,0.0171,0.0086,-3.8,21.6,-43.3,0.164933614,-0.12,-0.43,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,1677,2015-10-30 10:13:42:553,1446171222553.0 \n-0.0718,-0.0215,9.7552,0.0637,0.0168,9.8064,-0.0208,-0.0073,0.0183,-3.7,21.6,-43.4,0.166853476,-0.14,-0.37,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,1779,2015-10-30 10:13:42:655,1446171222655.0 \n-0.0622,0.1018,9.6774,0.0548,0.0323,9.8064,0.0171,0.0147,0.022,-3.6,21.5,-43.8,0.167900674,-0.19,-0.32,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,1881,2015-10-30 10:13:42:757,1446171222757.0 \n-0.0503,0.1365,9.5505,0.043,0.024,9.8065,-0.0012,0.0171,0.0379,-3.5,21.4,-43.6,0.130899694,-0.11,-0.29,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,1984,2015-10-30 10:13:42:860,1446171222860.0 \n-0.0395,0.1891,9.7612,0.0254,0.0383,9.8065,0.0379,0.0024,0.0037,-3.3,21.3,-43.6,0.13543755,-0.22,-0.15,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,2085,2015-10-30 10:13:42:961,1446171222961.0 \n-0.1269,0.1712,9.4954,0.035,0.0323,9.8065,0.0086,0.0098,0.0269,-3.2,21.4,-43.4,0.133866754,-0.19,-0.2,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,2188,2015-10-30 10:13:43:064,1446171223064.0 \n-0.0754,0.1724,9.8186,0.0521,0.0513,9.8064,0.0098,-0.0147,0.0037,-3.3,21.4,-43.4,0.131423293,-0.27,-0.26,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,2290,2015-10-30 10:13:43:166,1446171223166.0 \n-0.0922,0.1401,9.7803,0.0502,0.063,9.8063,0.0086,0.0061,-0.0061,-3.3,21.4,-43.2,0.129852496,-0.37,-0.29,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,2391,2015-10-30 10:13:43:267,1446171223267.0 \n-0.1437,0.158,9.6415,0.0212,0.0501,9.8065,-0.0024,-0.0012,-0.0208,-3.2,21.3,-42.9,0.135961149,-0.3,-0.13,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,2493,2015-10-30 10:13:43:369,1446171223369.0 \n-0.079,0.0563,9.7588,0.0178,0.0298,9.8066,-0.0061,-0.0037,0.0134,-3,21.3,-43,0.137008346,-0.21,-0.11,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,2595,2015-10-30 10:13:43:471,1446171223471.0 \n-0.103,0.0802,9.6618,0.0152,0.0281,9.8066,-0.0098,-0.0049,0.0147,-3.1,21.3,-43.1,0.138055544,-0.16,-0.09,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,2698,2015-10-30 10:13:43:574,1446171223574.0 \n-0.0718,0.0108,9.7001,0.0391,0.0254,9.8065,0.0171,-0.0257,0.0208,-3.2,21.3,-43.6,0.132994089,-0.15,-0.23,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,2800,2015-10-30 10:13:43:676,1446171223676.0 \n-0.0742,0.0898,9.7288,0.0708,0.0421,9.8063,0.0061,-0.011,0.044,-3.3,21.4,-43.8,0.125838239,-0.25,-0.41,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,2901,2015-10-30 10:13:43:777,1446171223777.0 \n-0.0682,0.1125,9.6486,0.0638,0.0556,9.8063,-0.0086,-0.0122,0.0281,-3.3,21.4,-43.7,0.126361838,-0.27,-0.4,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,3004,2015-10-30 10:13:43:880,1446171223880.0 \n-0.012,0.0802,9.8713,0.0859,0.032,9.8062,-0.0195,-0.0269,0.0024,-3.4,21.5,-43.4,0.117984257,-0.19,-0.5,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,3105,2015-10-30 10:13:43:981,1446171223981.0 \n-0.0455,0.1891,9.8162,0.081,0.0444,9.8062,-0.0024,0.0049,0.0232,-3.3,21.5,-43.4,0.118682389,-0.26,-0.47,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,3207,2015-10-30 10:13:44:083,1446171224083.0 \n-0.1006,0.1209,9.5457,0.0464,0.0427,9.8064,-0.0134,0.0269,-0.0037,-3.3,21.4,-43.2,0.13124876,-0.25,-0.27,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,3309,2015-10-30 10:13:44:185,1446171224185.0 \n-0.1018,0.0407,9.5612,0.0311,0.0374,9.8065,0.0024,0.0171,-0.0171,-3.2,21.2,-43.3,0.133168622,-0.21,-0.22,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,3411,2015-10-30 10:13:44:287,1446171224287.0 \n-0.0503,-0.0156,9.827,0.0417,0.0458,9.8065,-0.0159,-0.022,-0.0061,-3.1,21.2,-43.4,0.132121424,-0.27,-0.24,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,3514,2015-10-30 10:13:44:390,1446171224390.0 \n-0.1113,0.1185,9.6678,0.0403,0.0301,9.8065,-0.0037,-0.0012,0.044,-3.1,21.2,-43.5,0.132819556,-0.18,-0.24,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,3616,2015-10-30 10:13:44:492,1446171224492.0 \n-0.1532,0.0515,9.7384,0.031,0.0306,9.8066,-0.0134,-0.0147,0.022,-3.1,21.2,-43.8,0.133866754,-0.21,-0.2,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,16 / 17,3717,2015-10-30 10:13:44:593,1446171224593.0 \n-0.0838,0.1389,9.7624,0.035,0.0421,9.8065,0.0122,-0.0098,0.0073,-3.2,21.3,-44,0.133517688,-0.22,-0.2,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,16 / 17,3819,2015-10-30 10:13:44:695,1446171224695.0 \n-0.1006,0.1915,9.6582,0.0078,0.0453,9.8065,0.0024,0.0122,0.0305,-3.1,21.4,-44,0.138055544,-0.25,-0.07,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,16 / 17,3922,2015-10-30 10:13:44:798,1446171224798.0 \n-0.1065,0.0658,9.8019,0,0.0451,9.8065,0.0049,-0.0269,0.0024,-3.1,21.5,-43.8,0.134390352,-0.26,0,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,16 / 17,4023,2015-10-30 10:13:44:899,1446171224899.0 \n-0.164,0.0766,9.7707,-0.0051,0.0458,9.8065,0.0122,0.0147,0.0183,-3,21.4,-43.5,0.141546202,-0.27,0.03,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,16 / 17,4125,2015-10-30 10:13:45:001,1446171225001.0 \n-0.1616,0.1125,9.7707,-0.0223,0.0443,9.8065,-0.0098,0.0183,-0.0024,-2.9,21.4,-43.7,0.145211394,-0.26,0.13,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,16 / 17,4228,2015-10-30 10:13:45:104,1446171225104.0 \n-0.1652,0.0563,9.7588,-0.0377,0.0307,9.8065,0.0159,0.0257,-0.0049,-2.9,21.5,-43.6,0.142244334,-0.18,0.22,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,16 / 17,4330,2015-10-30 10:13:45:206,1446171225206.0 \n-0.1365,0.1125,9.6546,-0.049,0.0373,9.8065,-0.0073,0.011,-0.0086,-2.8,21.4,-43.8,0.15271631,-0.22,0.34,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,16 / 17,4432,2015-10-30 10:13:45:308,1446171225308.0 \n-0.176,0.0299,9.7552,-0.0341,0.0361,9.8065,-0.0049,-0.0257,-0.0147,-2.7,21.3,-43.5,0.147829388,-0.21,0.2,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,16 / 17,4533,2015-10-30 10:13:45:409,1446171225409.0 \n-0.1772,0.0682,9.7145,-0.0135,0.0412,9.8066,0.011,-0.0208,0.0122,-2.7,21.2,-43.5,0.145036861,-0.27,0.13,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,16 / 17,4636,2015-10-30 10:13:45:512,1446171225512.0 \n-0.1281,0.0658,9.8497,-3.00E-04,0.0505,9.8065,0.0073,-0.0305,-0.0098,-2.8,21.3,-43.3,0.140499005,-0.3,0,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,15 / 17,4738,2015-10-30 10:13:45:614,1446171225614.0 \n-0.1832,0.1532,9.6642,-0.0071,0.0402,9.8066,-0.0159,-0.011,0.0024,-2.9,21.3,-43.3,0.142244334,-0.23,0.04,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,15 / 17,4840,2015-10-30 10:13:45:716,1446171225716.0 \n-0.1113,0.1281,9.6486,-0.0167,0.0439,9.8065,-0.0012,0.0147,0,-2.9,21.3,-42.9,0.143989663,-0.26,0.1,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,15 / 17,4941,2015-10-30 10:13:45:817,1446171225817.0 \n-0.097,0.0766,9.6666,-0.013,0.0504,9.8065,-0.0086,-0.0073,-0.0037,-2.9,21.3,-43.1,0.143640597,-0.26,0.09,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,15 / 17,5043,2015-10-30 10:13:45:919,1446171225919.0 \n-0.0599,0.0922,9.748,0.0063,0.0463,9.8065,-0.011,-0.0281,0.0049,-2.9,21.2,-43.3,0.139277274,-0.27,-0.04,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,15 / 17,5146,2015-10-30 10:13:46:022,1446171226022.0 \n-0.0754,0.1233,9.7169,0.0118,0.045,9.8065,0.011,-0.0086,0.0171,-3,21.3,-43.5,0.138230077,-0.26,-0.07,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,15 / 17,5248,2015-10-30 10:13:46:124,1446171226124.0 \n-0.1101,0.085,9.8162,0.0218,0.0323,9.8066,0.0159,0,-0.0012,-3.1,21.2,-43.8,0.136310215,-0.19,-0.13,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,15 / 17,5349,2015-10-30 10:13:46:225,1446171226225.0 \n-0.1401,0.0802,9.5577,0.0108,0.0288,9.8066,-0.033,0.011,0.0086,-3.2,21.2,-43.8,0.137357412,-0.22,-0.1,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,15 / 17,5451,2015-10-30 10:13:46:327,1446171226327.0 \n-0.0994,0.0048,9.6965,0.0075,0.0232,9.8066,0.0086,-0.0305,0.0183,-3,21.3,-43.6,0.13962634,-0.14,-0.04,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,15 / 17,5553,2015-10-30 10:13:46:429,1446171226429.0 \n-0.1532,0.1676,9.7516,0.0133,0.0387,9.8066,-0.0061,0.0049,0.0037,-3,21.3,-43.5,0.137706478,-0.23,-0.09,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,15 / 17,5655,2015-10-30 10:13:46:531,1446171226531.0 \n-0.1604,0.0251,9.6786,-0.003,0.0259,9.8066,-0.0195,0.0049,-0.0037,-2.9,21.3,-43.6,0.141720735,-0.15,0.02,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,5757,2015-10-30 10:13:46:633,1446171226633.0 \n-0.0958,0.0622,9.7779,-0.0253,0.0227,9.8066,-0.0281,0.0171,0.011,-2.8,21.2,-43.8,0.145211394,-0.19,0.12,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,5859,2015-10-30 10:13:46:735,1446171226735.0 \n-0.1664,0.0718,9.8342,-0.0457,0.0136,9.8065,-0.0379,0.0037,0.0244,-2.8,21.3,-43.6,0.15097098,-0.08,0.27,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,5961,2015-10-30 10:13:46:837,1446171226837.0 \n-0.1137,0.1185,9.8653,-0.0614,0.0135,9.8064,-0.0012,0.0244,0.0086,-2.7,21.3,-43.4,0.15393804,-0.08,0.36,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,6063,2015-10-30 10:13:46:939,1446171226939.0 \n-0.1437,0.0156,9.7049,-0.0689,-9.00E-04,9.8064,-0.033,-0.0012,-0.0171,-2.7,21.4,-43,0.155508836,-0.04,0.4,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,6166,2015-10-30 10:13:47:042,1446171227042.0 \n-0.0706,0.0239,9.7767,-0.0681,-0.0083,9.8064,-0.0037,-0.0281,-0.0403,-2.6,21.4,-43.2,0.156032435,0.05,0.4,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,6268,2015-10-30 10:13:47:144,1446171227144.0 \n-0.2789,-0.0778,9.6163,-0.0716,-0.0323,9.8063,0.0257,0.0037,-0.0012,-2.6,21.4,-43.3,0.156381501,0.12,0.4,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,6370,2015-10-30 10:13:47:246,1446171227246.0 \n-0.1425,0.103,9.8126,-0.0539,-0.0051,9.8065,0.0269,-0.0391,0.0024,-2.8,21.6,-43.4,0.148352986,0.05,0.38,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,6471,2015-10-30 10:13:47:347,1446171227347.0 \n-0.2622,0.0634,9.572,-0.0573,-0.0335,9.8064,-0.0269,-0.0012,0.0012,-2.9,21.6,-43.2,0.147305789,0.13,0.33,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,6573,2015-10-30 10:13:47:449,1446171227449.0 \n-0.2251,0.0575,9.7671,-0.0685,-0.0294,9.8064,-0.0012,0.0037,0.0086,-2.9,21.7,-43.1,0.148527519,0.22,0.35,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,6676,2015-10-30 10:13:47:552,1446171227552.0 \n-0.1856,-0.0144,9.6881,-0.0812,-0.0449,9.8062,-0.0232,0.0183,-0.0061,-2.9,21.8,-43,0.15271631,0.26,0.47,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,16 / 17,6777,2015-10-30 10:13:47:653,1446171227653.0 \n-0.2251,0.0467,9.6151,-0.1018,-0.0528,9.806,0.0244,0.0134,0.0024,-2.8,21.8,-43.1,0.155508836,0.33,0.54,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,16 / 17,6879,2015-10-30 10:13:47:755,1446171227755.0 \n-0.2143,-0.0694,9.6331,-0.0991,-0.0557,9.806,0.0012,0.0244,-0.0147,-2.7,21.8,-43.1,0.155334303,0.3,0.55,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,16 / 17,6982,2015-10-30 10:13:47:858,1446171227858.0 \n-0.1365,-0.006,9.7695,-0.0855,-0.05,9.8062,0.022,-0.0379,-0.0195,-2.6,21.7,-42.7,0.153763507,0.29,0.5,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,16 / 17,7084,2015-10-30 10:13:47:960,1446171227960.0 \n-0.2334,-0.0934,9.6917,-0.0691,-0.0457,9.8063,-0.0122,0.0037,-0.0086,-2.6,21.7,-42.9,0.150447382,0.27,0.4,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,16 / 17,7186,2015-10-30 10:13:48:062,1446171228062.0 \n-0.1903,-0.0359,9.7671,-0.0558,-0.0516,9.8064,0.0024,-0.033,-0.0012,-2.7,21.7,-42.7,0.149400184,0.3,0.37,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,16 / 17,7287,2015-10-30 10:13:48:163,1446171228163.0 \n-0.2813,-0.0419,9.6331,-0.0512,-0.0634,9.8063,-0.0147,0.0086,0.0098,-2.8,21.6,-42.8,0.147305789,0.37,0.3,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,16 / 17,7390,2015-10-30 10:13:48:266,1446171228266.0 \n-0.1832,0.0371,9.8114,-0.0677,-0.0638,9.8062,0.0208,0.0122,0.0098,-2.9,21.6,-42.7,0.149574717,0.38,0.36,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,16 / 17,7492,2015-10-30 10:13:48:368,1446171228368.0 \n-0.1891,0.0323,9.6067,-0.1054,-0.0669,9.8059,-0.0037,0.0367,-0.0086,-3,21.6,-42.8,0.155159771,0.39,0.53,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,16 / 17,7594,2015-10-30 10:13:48:470,1446171228470.0 \n-0.2753,-0.0455,9.5217,-0.1219,-0.0689,9.8057,0.0281,-0.022,-0.0037,-2.9,21.6,-43,0.160046692,0.45,0.66,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,16 / 17,7695,2015-10-30 10:13:48:571,1446171228571.0 \n-0.1425,0.0132,9.9491,-0.1102,-0.0549,9.8059,0.011,0.0012,-0.0037,-2.8,21.7,-43.2,0.158650429,0.32,0.64,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,16 / 17,7798,2015-10-30 10:13:48:674,1446171228674.0 \n-0.3376,-0.0311,9.5205,-0.1203,-0.0869,9.8055,-0.0574,0.0171,0.011,-2.7,21.6,-43.4,0.160395758,0.41,0.68,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,16 / 17,7899,2015-10-30 10:13:48:775,1446171228775.0 \n-0.231,-0.0108,9.7348,-0.1226,-0.0825,9.8055,0.0061,0,0.0159,-2.8,21.7,-43.6,0.162664686,0.48,0.72,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,16 / 17,8002,2015-10-30 10:13:48:878,1446171228878.0 \n-0.1867,-0.0431,9.7659,-0.1126,-0.071,9.8057,-0.0024,-0.033,-0.0086,-2.8,21.7,-43.3,0.16109389,0.41,0.7,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,16 / 17,8103,2015-10-30 10:13:48:979,1446171228979.0 \n-0.2717,0.006,9.7396,-0.1075,-0.0546,9.8059,-0.0281,-0.0098,0.0122,-2.8,21.8,-43.2,0.15812683,0.32,0.63,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,16 / 17,8205,2015-10-30 10:13:49:081,1446171229081.0 \n-0.2011,0.1592,9.8749,-0.1154,-0.0483,9.8059,0.0159,-0.0122,0.0086,-3,21.8,-43.2,0.159523094,0.28,0.67,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,16 / 17,8307,2015-10-30 10:13:49:183,1446171229183.0 \n-0.3675,-0.0467,9.6426,-0.1297,-0.0442,9.8057,0.0171,-0.011,0.0086,-2.9,21.7,-43.4,0.161442956,0.25,0.74,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,16 / 17,8409,2015-10-30 10:13:49:285,1446171229285.0 \n-0.9541,-0.2059,10.088,-0.148,-0.0137,9.8055,0.0159,-0.0134,0.0403,-2.8,21.7,-43.3,0.164759081,0.08,0.86,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,16 / 17,8512,2015-10-30 10:13:49:388,1446171229388.0 \n-1.634,-0.1089,10.094,-0.2859,0.2565,9.7991,0.4496,0.1979,0.766,-2.6,21.5,-43.4,0.172962129,-0.52,1.22,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,16 / 17,8614,2015-10-30 10:13:49:490,1446171229490.0 \n-0.8116,0.6201,9.6558,-0.5094,0.9024,9.7518,0.4374,0.2541,1.609,-1.2,19.9,-43.8,0.13124876,-4.31,2.7,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,8715,2015-10-30 10:13:49:591,1446171229591.0 \n-0.5614,0.7602,8.5748,-0.3636,1.1382,9.7336,0.1747,0.1124,2.0159,2.9,16.2,-44.2,6.255260039,-6.66,3.14,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,8817,2015-10-30 10:13:49:693,1446171229693.0 \n-0.48,0.3759,9.0692,-0.0333,1.0786,9.7471,-0.0623,-0.099,2.1356,5.7,12.8,-45.4,6.002710896,-6.54,1.02,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,8920,2015-10-30 10:13:49:796,1446171229796.0 \n0.753,0.3795,10.5548,0.1822,0.6716,9.7819,-0.4349,0.1955,2.1002,7.6,10.9,-45.4,5.721538354,-3.93,-1.07,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,9021,2015-10-30 10:13:49:897,1446171229897.0 \n0.1915,0.7242,9.1806,-0.0951,0.3535,9.7998,-0.2871,-0.0367,1.8998,11.3,6.7,-44.9,5.396907113,-2.07,0.56,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,9123,2015-10-30 10:13:49:999,1446171229999.0 \n-0.1365,-0.7685,9.7396,-0.0052,-0.133,9.8057,-0.6353,-0.1381,1.7691,12.6,4.9,-44.4,5.086936638,-0.05,0.23,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,9225,2015-10-30 10:13:50:101,1446171230101.0 \n0.8308,-0.255,10.1718,-0.1581,-0.2616,9.8019,-0.1234,0.5082,1.3195,14.2,2.7,-43.9,4.848524662,1.53,0.92,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,9327,2015-10-30 10:13:50:203,1446171230203.0 \n-1.4329,-0.0096,8.7424,-0.7216,-0.1835,9.7783,0.6402,0.0929,0.0745,15.7,0.3,-42.9,4.647986331,1.07,4.22,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,9429,2015-10-30 10:13:50:305,1446171230305.0 \n-0.9529,0.4142,11.5197,-0.5482,0.1239,9.7905,-0.0965,-0.3946,0.3653,16.7,-1.9,-42.5,4.613079746,-0.72,3.2,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,9531,2015-10-30 10:13:50:407,1446171230407.0 \n0.4178,0.4884,8.5557,-0.4094,0.6035,9.7795,0.2468,-0.2981,0.0538,17.2,-3.6,-42.1,4.588645136,-2.86,2.72,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,9634,2015-10-30 10:13:50:510,1446171230510.0 \n1.0355,0.6668,8.4539,-0.0785,0.6689,9.7835,0.259,0.2334,0.3775,16.6,-5.5,-42.7,4.590215933,-3.91,0.46,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,9735,2015-10-30 10:13:50:611,1446171230611.0 \n0.3843,-0.1425,11.746,0.4844,0.5174,9.781,-0.463,-1.1655,-0.0941,15.8,-6.4,-43.2,4.506614662,-3.23,-1.64,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,9837,2015-10-30 10:13:50:713,1446171230713.0 \n-0.3472,0.4908,8.8155,0.059,0.7029,9.7812,0.033,0.5461,-0.3604,14.4,-6.9,-44,4.463505029,-4.07,-1.72,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,9940,2015-10-30 10:13:50:816,1446171230816.0 \n-1.1636,0.1365,9.7683,-0.4275,0.4543,9.7868,-0.3262,0.2847,-0.3054,14.7,-6.6,-43.8,4.351803957,-2.66,2.5,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,10041,2015-10-30 10:13:50:917,1446171230917.0 \n-0.182,-0.0335,10.1131,-0.1513,0.089,9.8051,0.325,0.4203,-0.0953,15.3,-5.7,-43.5,4.341506514,-0.78,1.45,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,10144,2015-10-30 10:13:51:020,1446171231020.0 \n-0.0431,0.103,9.6091,-0.1925,0.4823,9.7929,0.38,-0.0489,-0.0183,16,-5,-42.9,4.501378674,-2.28,0.95,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,10245,2015-10-30 10:13:51:121,1446171231121.0 \n-1.2366,0.1293,9.2608,-0.2494,0.5195,9.7897,0.0599,-0.1869,0.0073,16.2,-4.4,-42.7,4.599117112,-3.04,1.46,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,10348,2015-10-30 10:13:51:224,1446171231224.0 \n0.2286,1.0295,10.2747,-0.0456,0.5742,9.7897,0.0452,0.1002,-0.1466,15.8,-4.8,-42.9,4.557403743,-3.36,0.27,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,10450,2015-10-30 10:13:51:326,1446171231326.0 \n0.152,0.6656,9.6163,0.0895,0.7792,9.7752,0.2786,-0.2676,-0.1014,15.7,-4.9,-43,4.595626453,-4.14,-0.1,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,10551,2015-10-30 10:13:51:427,1446171231427.0 \n-0.4812,0.1724,10.1083,0.0542,0.7941,9.7743,-0.0122,0.0525,-0.0244,15.2,-5.3,-43.1,4.613777878,-4.64,-0.32,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,10653,2015-10-30 10:13:51:529,1446171231529.0 \n0.0575,1.0499,8.503,0.1249,0.9658,9.7582,-0.0037,-0.1026,-0.0147,15.1,-5.6,-43.2,4.59423019,-5.55,-0.53,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,10756,2015-10-30 10:13:51:632,1446171231632.0 \n-0.0766,0.8691,9.8665,0.0312,0.8283,9.7716,-0.1503,0.1258,-0.0684,14.9,-6.1,-43.5,4.574333437,-5.15,-0.43,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,10857,2015-10-30 10:13:51:733,1446171231733.0 \n-0.1688,0.9637,9.256,-0.081,0.7617,9.7767,-0.0709,0.1918,-0.0367,15,-6.1,-43.6,4.539601384,-4.45,0.47,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,10960,2015-10-30 10:13:51:836,1446171231836.0 \n-0.2921,0.7997,9.6235,0.0041,0.7777,9.7758,-0.0501,0.0782,0.0257,15.1,-5.8,-43.2,4.542742977,-4.55,-0.02,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,11061,2015-10-30 10:13:51:937,1446171231937.0 \n-0.1652,0.7614,9.9503,0.0483,0.7454,9.7782,0.0147,-0.0501,0.0452,15.1,-5.6,-43.1,4.535412594,-4.36,-0.28,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,11163,2015-10-30 10:13:52:039,1446171232039.0 \n-0.1269,0.7446,9.7037,0.0695,0.7464,9.778,-0.0037,-0.0354,0.0171,15,-5.6,-43.3,4.536634325,-4.37,-0.41,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,11266,2015-10-30 10:13:52:142,1446171232142.0 \n0.0994,1.0618,9.3506,0.0972,0.7844,9.7747,0.0232,-0.1063,0.0098,14.8,-5.6,-43.6,4.553564018,-4.59,-0.57,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,11367,2015-10-30 10:13:52:243,1446171232243.0 \n-0.1149,1.0786,9.6103,0.1536,0.7996,9.7728,0.0684,-0.0684,0.0342,14.5,-5.7,-43.8,4.559847204,-4.68,-0.9,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,11470,2015-10-30 10:13:52:346,1446171232346.0 \n0.091,1.3647,9.7217,0.1637,0.8405,9.7692,-0.0073,0.0183,0.0831,14.5,-5.8,-43.9,4.568922916,-4.86,-0.98,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,11571,2015-10-30 10:13:52:447,1446171232447.0 \n0.2227,1.4521,9.8043,0.1626,0.8689,9.7667,-0.1307,0.0281,0.0733,14.4,-6,-44,4.570842778,-5.08,-0.95,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,11675,2015-10-30 10:13:52:551,1446171232551.0 \n0.231,1.33,9.73,0.1379,0.8616,9.7678,-0.011,-0.0024,0.1234,14.4,-6.3,-43.8,4.56560679,-5,-0.8,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,11775,2015-10-30 10:13:52:651,1446171232651.0 \n0.4154,1.1923,9.7671,0.1691,0.9472,9.7593,0.1063,0.0061,0.1869,14.3,-6.4,-43.7,4.577649562,-5.22,-0.9,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,11878,2015-10-30 10:13:52:754,1446171232754.0 \n0.237,0.7889,10.471,0.2689,0.9611,9.7557,-0.022,-0.1136,0.0342,14.3,-6.8,-43.9,4.542742977,-5.77,-1.38,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,11980,2015-10-30 10:13:52:856,1446171232856.0 \n0.2346,0.8499,9.6379,0.3598,1.0144,9.7474,0.077,-0.0929,0.099,14,-7.4,-43.7,4.555658414,-5.94,-2.11,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,12082,2015-10-30 10:13:52:958,1446171232958.0 \n-0.0527,0.5638,10.1742,0.4215,0.9622,9.7502,-0.0672,0.0269,0.1051,13.6,-7.8,-43.8,4.483052717,-5.63,-2.48,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,12184,2015-10-30 10:13:53:060,1446171233060.0 \n0.0239,0.8128,9.9491,0.3699,0.9143,9.7569,0.0159,0.055,0.1319,13.4,-7.9,-43.9,4.45163679,-5.35,-2.17,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,12291,2015-10-30 10:13:53:167,1446171233167.0 \n0.0491,0.7973,10.0545,0.3213,0.9223,9.7579,-0.0806,0.1258,0.1014,13.4,-8.2,-44.1,4.450589593,-5.4,-1.89,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,12388,2015-10-30 10:13:53:264,1446171233264.0 \n-0.0383,1.1001,9.3194,0.2473,1.0007,9.7523,0.1442,-0.0941,0.1466,13.5,-8.3,-43.6,4.474151537,-5.66,-1.38,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,12489,2015-10-30 10:13:53:365,1446171233365.0 \n0.0898,1.4653,9.8641,0.334,1.0431,9.7453,-0.0489,-0.0819,-0.0525,13.6,-8.9,-43.3,4.433485366,-6.11,-1.96,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,12591,2015-10-30 10:13:53:467,1446171233467.0 \n0.0132,2.0027,9.0357,0.2779,0.8997,9.7613,-0.1466,0.0428,-0.0916,13.6,-8.8,-43,4.401196775,-5.43,-1.78,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,12693,2015-10-30 10:13:53:569,1446171233569.0 \n-0.0563,1.8854,9.183,0.2701,0.8086,9.7695,-0.0648,-0.0012,-0.1197,13.6,-8.4,-43.5,4.426329516,-4.71,-1.61,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,12795,2015-10-30 10:13:53:671,1446171233671.0 \n-0.3124,1.8938,8.9052,0.2769,0.8429,9.7664,0.0073,-0.055,-0.0757,13.7,-7.5,-43.8,4.503647602,-4.93,-1.62,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,12898,2015-10-30 10:13:53:774,1446171233774.0 \n-0.0215,1.6819,9.1566,0.3288,0.9506,9.7549,0.0806,-0.0696,0.0342,13.7,-7,-44.1,4.522148092,-5.29,-1.79,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,13000,2015-10-30 10:13:53:876,1446171233876.0 \n0.5818,0.3615,9.0585,0.392,1.0613,9.7412,0.0195,-0.1173,-0.0733,13.5,-6.9,-44.2,4.56979558,-6.21,-2.3,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,13102,2015-10-30 10:13:53:978,1446171233978.0 \n0.6321,0.7362,8.5425,0.3384,1.0064,9.749,0.3836,0.0403,0.1295,13.4,-7,-44.3,4.542044845,-5.89,-1.99,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,13203,2015-10-30 10:13:54:079,1446171234079.0 \n1.5299,0.7877,9.663,0.4329,1.0293,9.7429,-0.1173,-0.1784,0.0379,13.3,-7.2,-44.1,4.559323605,-6.21,-2.09,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,13305,2015-10-30 10:13:54:181,1446171234181.0 \n0.7506,1.1732,9.1207,0.4175,0.8929,9.757,-0.0452,0.0354,-0.0819,13.2,-7.2,-44,4.516388505,-5.3,-2.51,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,13407,2015-10-30 10:13:54:283,1446171234283.0 \n0.5698,1.4892,9.4379,0.4467,0.7918,9.7644,-0.1503,-0.044,-0.2016,13.1,-6.9,-43.7,4.484623513,-4.63,-2.62,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,13510,2015-10-30 10:13:54:386,1446171234386.0 \n0.1772,1.5622,9.6678,0.4168,0.7612,9.7682,-0.0452,0.0538,-0.1772,13.1,-6.2,-43.7,4.536983391,-4.39,-2.64,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,13612,2015-10-30 10:13:54:488,1446171234488.0 \n-0.7039,0.2969,11.4958,0.4161,0.8306,9.7626,0.1124,-0.0305,-0.0232,13.1,-5.4,-43.6,4.624773452,-4.86,-2.44,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,13713,2015-10-30 10:13:54:589,1446171234589.0 \n0.9912,1.1097,7.355,0.4107,1.1304,9.7326,-0.2798,-0.496,-0.0049,13.2,-5.3,-43.6,4.68847797,-6.1,-2.23,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,13816,2015-10-30 10:13:54:692,1446171234692.0 \n0.0215,1.3994,7.282,0.5886,1.1381,9.7226,0.3176,0.1564,0.1723,13.1,-5.8,-43.4,4.611334417,-6,-3.12,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,13918,2015-10-30 10:13:54:794,1446171234794.0 \n-0.1137,1.2306,8.9064,0.6694,1.0721,9.7249,-0.1038,-0.055,0.0489,12.8,-6.2,-43.3,4.632103835,-6.41,-3.72,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,14020,2015-10-30 10:13:54:896,1446171234896.0 \n-0.3005,1.5395,9.6031,0.6319,1.0179,9.7332,-0.0721,0.2126,-0.0855,12.2,-6.5,-43.8,4.612207081,-5.96,-3.71,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,14121,2015-10-30 10:13:54:997,1446171234997.0 \n0.0156,1.7071,9.6486,0.5047,1.114,9.7301,-0.0134,0.1869,-0.2053,12.1,-6.4,-44.2,4.639608751,-6.52,-2.97,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,14223,2015-10-30 10:13:55:099,1446171235099.0 \n-0.0455,0.9673,10.1335,0.3568,1.1988,9.7266,0.1613,0.0648,-0.1955,12.4,-6.1,-44.1,4.665788689,-7.02,-2.1,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,14325,2015-10-30 10:13:55:201,1446171235201.0 \n0.7434,-0.2227,9.8893,0.3565,1.162,9.731,-0.3665,-0.0452,-0.3738,12.7,-5.9,-43.8,4.683067449,-7.29,-2.05,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,14427,2015-10-30 10:13:55:303,1446171235303.0 \n0.3292,0.6632,8.3414,0.192,1.0673,9.7465,-0.2053,-0.0403,-0.1857,13,-5.1,-43.3,4.689350634,-6.25,-1.13,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,14530,2015-10-30 10:13:55:406,1446171235406.0 \n0.2502,1.0056,8.7005,0.1231,0.9182,9.7628,-0.0538,0.0916,-0.0819,13.1,-4.4,-43.1,4.709247388,-5.28,-0.84,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,14632,2015-10-30 10:13:55:508,1446171235508.0 \n-0.103,1.1672,8.9388,0.1673,0.8407,9.7691,-0.077,-0.1381,-0.0354,13.6,-3.5,-42.9,4.765097924,-5.03,-0.71,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,14733,2015-10-30 10:13:55:609,1446171235609.0 \n0.2286,1.1468,10.2436,0.2077,0.7667,9.7744,0.0648,-0.0037,0.171,13.7,-3.1,-42.9,4.739267051,-4.55,-1.2,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,14836,2015-10-30 10:13:55:712,1446171235712.0 \n-0.0455,0.8164,11.8597,0.2709,0.8882,9.7626,0.1588,-0.1161,0.2492,13.4,-3,-42.8,4.77382457,-5.2,-1.59,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,14937,2015-10-30 10:13:55:813,1446171235813.0 \n-0.3579,0.243,8.7759,0.3962,1.0853,9.7383,0.1478,0.0257,0.2175,13.1,-3.5,-42.8,4.832816699,-6.41,-2.09,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,15040,2015-10-30 10:13:55:916,1446171235916.0 \n0.2286,0.8906,7.5621,0.6165,1.0088,9.7351,0.1283,-0.182,0.2028,12.4,-4.3,-42.8,4.719021232,-5.54,-3.29,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,15142,2015-10-30 10:13:56:018,1446171236018.0 \n-0.0012,1.1025,9.2799,0.5378,0.8005,9.7591,-0.3262,0.2407,0.0269,12,-4.9,-43,4.605923896,-4.68,-3.15,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,15244,2015-10-30 10:13:56:120,1446171236120.0 \n0.0192,1.5838,8.5281,0.4902,0.8561,9.7569,0.0843,0.259,0.0183,11.6,-4.8,-43.3,4.621806392,-5.01,-2.88,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,15346,2015-10-30 10:13:56:222,1446171236222.0 \n-0.012,1.0786,8.7305,0.3952,1.0141,9.7461,0.1466,0.088,-0.1271,11.8,-5.1,-43.3,4.670152012,-5.94,-2.32,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,15448,2015-10-30 10:13:56:324,1446171236324.0 \n-0.0072,0.51,11.7986,0.47,1.0679,9.737,0.3433,-0.0232,-0.0977,12.1,-5.3,-43.1,4.672770006,-5.98,-2.52,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,15550,2015-10-30 10:13:56:426,1446171236426.0 \n0.6009,-0.2227,11.2025,0.5187,1.1268,9.7279,-0.2468,-0.0134,-0.303,12.2,-5.9,-42.9,4.63541996,-6.6,-3.05,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,15652,2015-10-30 10:13:56:528,1446171236528.0 \n0.17,0.1281,9.104,0.4133,0.8206,9.7635,-0.2712,-0.0049,-0.2236,12.3,-5.7,-43,4.538379654,-4.8,-2.42,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,15753,2015-10-30 10:13:56:629,1446171236629.0 \n0.3256,1.0523,8.2959,0.3581,0.5557,9.7843,-0.1515,0.0721,-0.0953,12.4,-4.7,-42.8,4.539252319,-3.51,-2.23,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,15855,2015-10-30 10:13:56:731,1446171236731.0 \n0.6237,1.2893,9.4523,0.3741,0.489,9.7873,-0.0489,-0.0623,-0.0684,12.7,-3.5,-42.7,4.652349654,-2.86,-2.19,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,15960,2015-10-30 10:13:56:836,1446171236836.0 \n0.2634,0.9421,9.991,0.4311,0.6009,9.7787,0.2053,-0.077,0.0586,12.8,-3,-42.6,4.667708552,-3.16,-2.39,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,16059,2015-10-30 10:13:56:935,1446171236935.0 \n0.2705,0.3998,10.6111,0.5966,0.9724,9.7401,0.4337,-0.1295,0.1686,12.9,-3.2,-42.8,4.756894876,-5,-3.25,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,16161,2015-10-30 10:13:57:037,1446171237037.0 \n0.5842,0.17,8.8454,0.7721,0.9077,9.734,0.5009,0.0037,0.1258,12.6,-4.2,-43.3,4.705582196,-5.31,-4.54,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,16263,2015-10-30 10:13:57:139,1446171237139.0 \n0.1724,0.4657,9.013,0.7458,1.0373,9.7231,-0.1332,0.0379,-0.0049,12.3,-5.1,-43.3,4.690572365,-6.35,-4.45,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,16365,2015-10-30 10:13:57:241,1446171237241.0 \n0.2191,0.9708,8.1008,0.7426,1.0448,9.7225,-0.0208,0.0037,-0.0269,12.3,-5.5,-43.3,4.677482395,-6.07,-4.31,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,16467,2015-10-30 10:13:57:343,1446171237343.0 \n0.5734,1.8208,8.5114,0.7655,1.1185,9.7125,0.0232,-0.1026,-0.0696,12.4,-5.6,-43.3,4.635769026,-6.55,-4.51,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,16570,2015-10-30 10:13:57:446,1446171237446.0 \n0.2406,0.929,11.2204,0.7358,1.208,9.7041,0.0819,0.1038,-0.171,12.6,-5.6,-43.4,4.655142181,-6.89,-4.29,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,16671,2015-10-30 10:13:57:547,1446171237547.0 \n0.9086,0.8823,10.252,0.6829,1.3029,9.6957,-0.0134,0.0342,-0.2468,12.8,-5.8,-43.6,4.698251813,-7.65,-4.14,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,16773,2015-10-30 10:13:57:649,1446171237649.0 \n0.3519,0.1999,10.5381,0.4602,1.0276,9.7418,0.0904,0.0843,-0.0367,13.2,-5.4,-43.5,4.683765581,-6.16,-2.99,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,16876,2015-10-30 10:13:57:752,1446171237752.0 \n0.1305,0.3675,9.8282,0.5166,0.9423,9.7476,-0.2566,-0.1723,-0.055,13.9,-4.6,-43.2,4.65566578,-5.51,-3.03,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,16977,2015-10-30 10:13:57:853,1446171237853.0 \n0.091,0.8906,8.77,0.4929,0.8403,9.7581,-0.0208,0.099,0.0892,14.1,-3.7,-43.3,4.688303437,-4.89,-3,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,17079,2015-10-30 10:13:57:955,1446171237955.0 \n0.3256,1.1085,9.5541,0.5704,0.8642,9.7518,-0.0098,-0.0611,0.2211,14.3,-3.2,-43.3,4.756196745,-5.06,-3.35,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,17181,2015-10-30 10:13:58:057,1446171238057.0 \n0.4717,0.5447,10.9056,0.6492,0.894,9.7442,0.0562,-0.0525,0.259,14.1,-3.1,-43.7,4.767366852,-5.23,-3.81,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,17283,2015-10-30 10:13:58:159,1446171238159.0 \n1.1384,0.8368,9.7659,0.6233,0.9989,9.7357,0.1283,0.1014,0.3433,13.9,-4,-43.8,4.736299991,-5.85,-3.66,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,17386,2015-10-30 10:13:58:262,1446171238262.0 \n0.6009,0.6177,9.6019,0.7862,0.8906,9.7344,0.0501,-0.1564,0.1234,13.7,-4.4,-44,4.706454861,-5.21,-4.62,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,17488,2015-10-30 10:13:58:364,1446171238364.0 \n-0.31,0.5004,8.5006,0.6979,0.8363,9.746,-0.0794,-0.1038,-0.0281,13.5,-4.7,-44.1,4.635070895,-4.89,-4.1,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,17589,2015-10-30 10:13:58:465,1446171238465.0 \n0.0503,1.2737,7.8494,0.6669,0.9294,9.7397,0.2077,0.1295,0.0513,13.5,-4.6,-44,4.646066469,-5.14,-4.04,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,17692,2015-10-30 10:13:58:568,1446171238568.0 \n0.2837,1.415,9.0237,0.5967,1.0085,9.7364,0.1222,0.1576,-0.0794,13.5,-4.5,-44.1,4.72844601,-5.68,-3.77,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,17793,2015-10-30 10:13:58:669,1446171238669.0 \n0.2777,0.6117,10.647,0.6697,1.1158,9.7199,0.43,0.0134,-0.1429,13.6,-4.6,-44.1,4.707502058,-6.53,-3.94,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,17896,2015-10-30 10:13:58:772,1446171238772.0 \n0.4058,-0.3795,12.6055,0.6876,1.0738,9.7234,-0.4838,-0.099,-0.3274,13.5,-4.7,-44.4,4.696506484,-6.29,-4.05,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,17998,2015-10-30 10:13:58:874,1446171238874.0 \n0.3531,0.2239,8.6718,0.6812,0.8229,9.7483,-0.2334,-0.1637,0.0037,13.5,-4.3,-44.4,4.71238898,-5.31,-3.73,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,18100,2015-10-30 10:13:58:976,1446171238976.0 \n0.3376,0.9014,8.5545,0.662,0.7023,9.759,-0.0672,0.0086,-0.0696,13.3,-3.4,-44.5,4.726351614,-4.29,-3.94,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,18202,2015-10-30 10:13:59:078,1446171239078.0 \n0.5387,1.2965,8.7412,0.6593,0.7292,9.7573,0.0538,-0.0696,0.033,13.3,-2.5,-44.6,4.792150527,-4.26,-3.87,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,18304,2015-10-30 10:13:59:180,1446171239180.0 \n0.6644,1.0068,9.7384,0.7262,0.8573,9.7421,0.1527,-0.0208,0.0867,13.1,-2.3,-44.3,4.806811293,-4.72,-4.24,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,18406,2015-10-30 10:13:59:282,1446171239282.0 \n0.4645,0.8188,9.9383,0.8324,1.0311,9.7167,0.2773,0.0147,0.2187,12.9,-3,-44.1,4.80244797,-6.04,-4.9,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,18508,2015-10-30 10:13:59:384,1446171239384.0 \n0.8559,0.1065,11.7711,0.8926,0.9017,9.7242,-0.0342,0.0293,-0.0232,12.6,-3.5,-44.1,4.782376683,-5.6,-5.07,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,18609,2015-10-30 10:13:59:485,1446171239485.0 \n0.2562,0.5303,8.9579,0.9162,0.9453,9.7179,0.0586,-0.0941,0.0696,12.3,-4.2,-44.5,4.720592028,-5.53,-5.39,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,18711,2015-10-30 10:13:59:587,1446171239587.0 \n0.5938,0.899,9.0956,0.9073,0.7444,9.7362,-0.11,-0.0623,0.0684,12.3,-4.2,-44.9,4.678878659,-4.52,-5.29,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,18813,2015-10-30 10:13:59:689,1446171239689.0 \n0.3005,1.3132,9.2129,0.8876,0.7998,9.7336,0.1906,-0.099,0.0635,12.2,-4.1,-45.2,4.686209042,-4.68,-5.21,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,18916,2015-10-30 10:13:59:792,1446171239792.0 \n0.3484,0.9074,10.1047,0.8687,0.9318,9.7236,0.0599,0.1075,-0.0709,12,-4,-45.2,4.717974034,-5.35,-5.23,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,19018,2015-10-30 10:13:59:894,1446171239894.0 \n1.6125,1.0175,9.3374,0.9066,1.2523,9.684,0.38,-0.0354,-0.0354,12,-4.5,-44.9,4.789707066,-6.85,-5.23,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,19119,2015-10-30 10:13:59:995,1446171239995.0 \n-0.0383,-0.2646,12.5935,0.6805,0.9492,9.7369,0.1698,0.2602,-0.0122,12.2,-5,-44.7,4.665963222,-5.56,-4.56,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,19221,2015-10-30 10:14:00:097,1446171240097.0 \n0.7123,0.668,9.5361,0.6324,0.8822,9.7464,-0.0452,0.0183,0.0318,12.6,-4.9,-44.4,4.64257581,-5.16,-3.71,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,19324,2015-10-30 10:14:00:200,1446171240200.0 \n0.2789,0.8128,8.9854,0.5363,0.759,9.7625,-0.1967,0.2016,0.0623,13,-4.2,-44.4,4.670675611,-4.44,-3.14,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,19425,2015-10-30 10:14:00:301,1446171240301.0 \n0.4992,1.2749,8.855,0.4355,0.7388,9.7691,-0.0354,0.0183,0.1454,13.6,-3.8,-44.3,4.66701042,-4.32,-2.55,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,19527,2015-10-30 10:14:00:403,1446171240403.0 \n0.2861,0.7973,10.4722,0.4756,0.7126,9.7692,0.1955,-0.2077,0.2321,13.9,-3.7,-44.2,4.657760175,-4.12,-2.73,36.81401,-119.74732,250.04,336.8658286,0.85,19.35484,,17 / 17,19630,2015-10-30 10:14:00:506,1446171240506.0 \n0.0359,0.5686,9.5864,0.6667,0.9323,9.7394,0.314,-0.0721,0.3042,13.8,-4.4,-44,4.7183231,-5.46,-3.92,36.814037,-119.74742,248.26,336.8658286,3.75,25.806452,,17 / 17,19732,2015-10-30 10:14:00:608,1446171240608.0 \n-0.2083,-0.1173,10.7332,0.8018,0.8351,9.7381,0.1442,-0.0611,0.1759,13.6,-5,-44.3,4.625820649,-4.65,-4.62,36.814037,-119.74742,248.26,336.8658286,3.75,25.806452,,17 / 17,19833,2015-10-30 10:14:00:709,1446171240709.0 \n-0.0383,0.4142,9.0321,0.8118,0.7667,9.7429,-0.3005,0.1918,-0.0489,12.9,-5.7,-44.4,4.554785749,-4.48,-4.76,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,19935,2015-10-30 10:14:00:811,1446171240811.0 \n0.1652,1.0427,9.3087,0.7309,0.6483,9.7579,-0.044,0.0098,0.0525,12.7,-5.8,-44.5,4.523544355,-3.84,-4.38,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,20038,2015-10-30 10:14:00:914,1446171240914.0 \n0.2382,1.4401,9.6019,0.6383,0.7145,9.7597,0.0159,0.0232,-0.0696,12.7,-5.6,-44.3,4.5327946,-4.12,-3.84,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,20140,2015-10-30 10:14:01:016,1446171241016.0 \n-0.1113,0.7733,10.8613,0.5666,0.7992,9.7576,0.1356,0.0367,-0.182,13.1,-5.3,-44.1,4.618315734,-4.67,-3.32,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,20241,2015-10-30 10:14:01:117,1446171241117.0 \n1.421,0.0311,9.3003,0.7286,0.8657,9.7412,-0.6671,-0.066,-0.358,13.2,-5.4,-44,4.660203636,-5.53,-3.82,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,20344,2015-10-30 10:14:01:220,1446171241220.0 \n-0.1664,0.8978,6.5314,0.4761,0.6094,9.7761,0.1136,0.3238,-0.1393,13.4,-4.8,-43.9,4.561592533,-3.56,-2.79,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,20445,2015-10-30 10:14:01:321,1446171241321.0 \n0.5722,0.7614,10.1263,0.5419,0.4754,9.7801,-0.0403,-0.0489,0.0195,13.5,-4.2,-43.7,4.597022717,-2.78,-3.17,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,20547,2015-10-30 10:14:01:423,1446171241423.0 \n-0.0658,0.8212,9.019,0.5458,0.5179,9.7777,0.0037,0.0269,-0.0061,13.6,-3.4,-43.6,4.663694294,-2.91,-3.27,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,20649,2015-10-30 10:14:01:525,1446171241525.0 \n0.4717,0.8224,10.2328,0.5628,0.6229,9.7707,-0.0073,0.011,0.0318,13.7,-2.8,-43.9,4.68673264,-3.42,-3.33,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,20751,2015-10-30 10:14:01:627,1446171241627.0 \n0.4441,0.6835,11.5329,0.67,0.7952,9.7514,0.1527,-0.2505,0.2114,13.5,-3.1,-44,4.741361446,-4.65,-3.93,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,20853,2015-10-30 10:14:01:729,1446171241729.0 \n0.4788,-0.4681,10.9678,0.8772,0.704,9.7419,-0.336,-0.3409,0.2443,13.3,-3.6,-44.3,4.683940114,-4.71,-4.45,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,20956,2015-10-30 10:14:01:832,1446171241832.0 \n0.4657,0.8847,7.8889,0.9797,0.6708,9.7345,0.1637,-0.0428,0.3983,12.7,-4.2,-44.3,4.649906193,-3.92,-5.75,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,21058,2015-10-30 10:14:01:934,1446171241934.0 \n0.6249,0.5327,8.4623,1.0456,0.5016,9.7378,-0.0134,0.0428,0.1796,12.1,-4.8,-44.6,4.550596959,-2.99,-6.09,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,21160,2015-10-30 10:14:02:036,1446171242036.0 \n1.0175,0.9182,8.1702,1.0911,0.5527,9.7301,0.0122,0.0244,-0.0086,11.8,-5,-44.6,4.55722921,-3.09,-6.42,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,21261,2015-10-30 10:14:02:137,1446171242137.0 \n0.6416,0.8224,9.7169,0.9694,0.6288,9.7383,0.1234,0.1466,-0.3543,11.5,-5.2,-44.4,4.565781323,-3.43,-6.04,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,21363,2015-10-30 10:14:02:239,1446171242239.0 \n1.0056,0.31,10.6865,0.8582,0.7091,9.7433,0.0122,0.0672,-0.3897,11.7,-5.2,-44.3,4.593182992,-4.15,-5.03,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,21465,2015-10-30 10:14:02:341,1446171242341.0 \n0.1125,-0.3639,11.4527,0.6708,0.5082,9.7705,-0.16,0.16,-0.2566,12.1,-4.8,-44.1,4.565781323,-3.65,-4.31,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,21568,2015-10-30 10:14:02:444,1446171242444.0 \n0.2741,0.1484,9.7671,0.6087,0.4064,9.7793,-0.1271,0.0147,-0.1136,12.8,-3.7,-43.9,4.572588107,-2.37,-3.56,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,21669,2015-10-30 10:14:02:545,1446171242545.0 \n-0.2729,0.8368,8.0852,0.5638,0.3669,9.7836,-0.0415,0.088,-0.1368,13.1,-2.9,-43.9,4.623551721,-2.14,-3.3,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,21771,2015-10-30 10:14:02:647,1446171242647.0 \n0.1269,0.8595,10.2017,0.5,0.3164,9.7888,-0.055,0.0464,-0.0098,13.5,-1.9,-43.9,4.675213467,-1.85,-2.92,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,21873,2015-10-30 10:14:02:749,1446171242749.0 \n0.2442,0.7171,10.0102,0.3957,0.4532,9.7882,0.1674,0.0941,0.1881,13.7,-1.7,-44,4.699473544,-2.37,-2.47,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,21975,2015-10-30 10:14:02:851,1446171242851.0 \n-0.1915,0.243,9.5696,0.3087,0.6786,9.7783,0.4191,0.193,0.1564,14.1,-2,-43.6,4.778362426,-3.97,-1.81,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,22077,2015-10-30 10:14:02:953,1446171242953.0 \n-0.3962,0.3496,9.1626,0.2924,0.6284,9.7821,0.1393,-0.0806,0.1124,14.6,-2.9,-43.4,4.695982885,-3.67,-1.71,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,22179,2015-10-30 10:14:03:055,1446171243055.0 \n-0.2418,0.4609,9.6007,0.4419,0.5423,9.7817,-0.3091,0.0257,-0.0098,14.7,-3.9,-43.3,4.614825075,-3.17,-2.59,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,22281,2015-10-30 10:14:03:157,1446171243157.0 \n-0.1329,1.2546,8.8562,0.4713,0.5622,9.7792,0.0183,0.0623,0.0684,14.6,-3.9,-43.7,4.620584662,-3.21,-2.75,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,22384,2015-10-30 10:14:03:260,1446171243260.0 \n0.4082,1.8184,9.0692,0.4717,0.6408,9.7743,0.1417,-0.0611,0.0367,14.3,-4,-43.7,4.640306882,-3.75,-2.76,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,22485,2015-10-30 10:14:03:361,1446171243361.0 \n-0.0838,1.0175,10.8362,0.4048,0.6688,9.7754,0.1662,0.0122,-0.1478,14.3,-3.9,-43.4,4.642750343,-3.91,-2.37,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,22587,2015-10-30 10:14:03:463,1446171243463.0 \n0.6285,-0.5195,11.1618,0.5069,0.7812,9.7623,-0.4838,0.0428,-0.4117,14.3,-4.1,-43.2,4.673817204,-4.57,-2.97,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,22689,2015-10-30 10:14:03:565,1446171243565.0 \n0.2155,0.3938,8.0062,0.4302,0.5656,9.7809,0.1112,0.0586,-0.1723,14.4,-3.6,-43.2,4.606796561,-3.15,-2.31,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,22792,2015-10-30 10:14:03:668,1446171243668.0 \n0.0718,0.4094,8.1702,0.5085,0.4196,9.7845,0.0415,-0.0415,-0.066,14.3,-2.6,-43.4,4.636467158,-2.39,-2.97,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,22894,2015-10-30 10:14:03:770,1446171243770.0 \n0.0503,1.0175,8.2217,0.4655,0.4017,9.7874,0.0806,0.0391,0.0599,14.3,-1.5,-43.3,4.758116607,-2.35,-2.72,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,22996,2015-10-30 10:14:03:872,1446171243872.0 \n-0.1616,0.8296,10.2089,0.3899,0.3447,9.7928,-0.1527,0.0709,0.0415,14.3,-1.1,-43.2,4.743630374,-2.01,-2.28,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,23098,2015-10-30 10:14:03:974,1446171243974.0 \n0.2705,0.6033,12.6079,0.4522,0.3793,9.7889,0.1356,-0.077,0.2541,14.4,-1.1,-43.3,4.747993697,-2.11,-2.42,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,23199,2015-10-30 10:14:04:075,1446171244075.0 \n-0.1963,-0.7422,11.394,0.5723,0.3509,9.7836,0.1026,-0.0904,0.2114,14.3,-1.4,-43.1,4.744153973,-2.06,-3.13,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,23302,2015-10-30 10:14:04:178,1446171244178.0 \n0.1712,0.1927,8.8681,0.7076,0.4436,9.771,-0.1295,0.0635,0.0305,13.9,-1.9,-43.5,4.706280328,-2.59,-4.14,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,23403,2015-10-30 10:14:04:279,1446171244279.0 \n0.0886,0.6847,8.7915,0.6335,0.4056,9.7778,0.0452,0.0367,0.0672,13.6,-2.1,-43.8,4.690048766,-2.16,-3.77,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,23505,2015-10-30 10:14:04:381,1446171244381.0 \n0.2682,1.1133,9.0202,0.5936,0.5237,9.7746,0.0208,-0.0037,-0.055,13.5,-2.6,-44.2,4.670675611,-3.06,-3.48,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,23607,2015-10-30 10:14:04:483,1446171244483.0 \n-0.1856,0.5746,9.9491,0.5672,0.5519,9.7747,0.0916,-0.1332,-0.1662,13.5,-2.8,-44,4.678005994,-3.23,-3.32,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,23710,2015-10-30 10:14:04:586,1446171244586.0 \n1.1097,-0.5195,10.9954,0.6855,0.6487,9.7611,0.0892,-0.0929,-0.1405,13.6,-3.1,-44.2,4.703313268,-3.79,-4.02,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,23811,2015-10-30 10:14:04:687,1446171244687.0 \n0.8499,0.5435,7.3933,0.4575,0.4928,9.7836,0.303,0.1026,-0.0977,13.7,-2.6,-44.1,4.661250833,-2.88,-2.68,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,23913,2015-10-30 10:14:04:789,1446171244789.0 \n0.4274,0.2909,9.8414,0.3886,0.3431,9.7929,0.0684,0.1552,-0.1222,13.9,-2.2,-43.8,4.681845718,-2,-2.27,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,24015,2015-10-30 10:14:04:891,1446171244891.0 \n0.1269,0.9673,7.932,0.2581,0.4038,9.7949,0.0415,0.0709,-0.0782,14.5,-1.3,-43.4,4.750786224,-2.18,-1.62,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,24117,2015-10-30 10:14:04:993,1446171244993.0 \n0.0156,0.9218,9.7827,0.3229,0.4059,9.7929,-0.0684,-0.0819,0.0525,14.9,-1.1,-43.2,4.758116607,-2.35,-1.76,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,24219,2015-10-30 10:14:05:095,1446171245095.0 \n0.4405,0.8475,12.1925,0.4679,0.4935,9.783,0.1405,-0.0831,0.2077,15,-1,-43.5,4.778362426,-2.88,-2.74,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,24322,2015-10-30 10:14:05:198,1446171245198.0 \n-0.2286,-0.4489,11.485,0.5243,0.5018,9.7798,-0.088,-0.1759,0.077,14.7,-1.3,-43.5,4.795641186,-3.29,-2.75,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,24424,2015-10-30 10:14:05:300,1446171245300.0 \n0.2813,0.5962,8.0349,0.5963,0.5457,9.7733,0.171,-0.0855,0.1368,14.3,-1.7,-43.6,4.736125458,-3.18,-3.39,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,24525,2015-10-30 10:14:05:401,1446171245401.0 \n-0.2442,0.7386,8.2025,0.5178,0.4076,9.7845,0.0415,0.2382,-0.0086,14,-1.8,-43.6,4.699997143,-2.38,-3.03,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,24628,2015-10-30 10:14:05:504,1446171245504.0 \n-0.0395,1.2246,8.4898,0.4212,0.4986,9.7849,0.182,0.1246,0.1014,14.1,-1.9,-43.8,4.72547895,-2.91,-2.47,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,24729,2015-10-30 10:14:05:605,1446171245605.0 \n-0.1556,0.8727,10.8948,0.3,0.5349,9.7875,-0.0916,0.121,-0.0367,14.3,-2,-43.5,4.732285734,-3.1,-1.75,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,24832,2015-10-30 10:14:05:708,1446171245708.0 \n0.486,0.3819,10.386,0.3656,0.706,9.7744,0.1454,-0.1295,-0.1698,14.7,-2.4,-43.2,4.776093498,-4.13,-2.14,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,24934,2015-10-30 10:14:05:810,1446171245810.0 \n-0.3148,-0.4944,11.9279,0.2963,0.4838,9.7902,0.1674,-0.1063,-0.0965,14.9,-2.4,-42.9,4.739441584,-3.3,-2.01,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,25036,2015-10-30 10:14:05:912,1446171245912.0 \n0.1353,0.1233,9.1423,0.3389,0.5087,9.7876,-0.16,-0.0098,-0.0415,15,-2.1,-43,4.724780818,-2.97,-1.98,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,25137,2015-10-30 10:14:06:013,1446171246013.0 \n-0.4729,0.7614,8.7053,0.3046,0.4159,9.7931,-0.0269,0.0073,0.0134,14.9,-1.3,-42.8,4.761607265,-2.43,-1.78,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,25240,2015-10-30 10:14:06:116,1446171246116.0 \n0.0575,1.3096,8.4611,0.2886,0.45,9.7921,-0.0648,0.0183,0.1552,15,-1.1,-42.7,4.77085751,-2.63,-1.69,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,25341,2015-10-30 10:14:06:217,1446171246217.0 \n-0.0718,0.7566,12.2499,0.398,0.6157,9.7792,0.4386,0.0953,0.303,15,-1.3,-43,4.784471078,-2.96,-1.99,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,25443,2015-10-30 10:14:06:319,1446171246319.0 \n-0.9014,-0.7362,12.3361,0.4369,0.6055,9.7782,-0.3641,-0.1967,0.0941,15.1,-2.3,-43.4,4.748691829,-3.54,-2.56,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,25546,2015-10-30 10:14:06:422,1446171246422.0 \n0.1736,0.7793,8.5234,0.514,0.6922,9.7687,0.1197,-0.2908,0.2334,14.9,-2.9,-43.5,4.711341783,-4.05,-3.01,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,25647,2015-10-30 10:14:06:523,1446171246523.0 \n0.2119,0.8835,8.8753,0.5319,0.5998,9.7738,0.0281,0.0171,0.0586,14.6,-3.6,-43.7,4.634547296,-3.51,-3.11,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,25750,2015-10-30 10:14:06:626,1446171246626.0 \n-0.3148,1.1241,8.6479,0.4452,0.6608,9.7742,0.1124,0.0929,0.0061,14.6,-4,-43.8,4.649208061,-3.86,-2.61,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,25852,2015-10-30 10:14:06:728,1446171246728.0 \n-0.3675,0.9697,9.6462,0.3553,0.7082,9.7746,0.0977,-0.0086,-0.1063,14.7,-4.2,-43.8,4.650778858,-3.91,-2.22,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,25954,2015-10-30 10:14:06:830,1446171246830.0 \n0.7075,0.231,10.6949,0.4005,0.8337,9.7629,-0.0696,-0.1038,-0.11,15,-4.6,-43.2,4.628962242,-4.86,-2.18,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,26056,2015-10-30 10:14:06:932,1446171246932.0 \n-0.1772,-0.0144,10.9247,0.2435,0.6051,9.7849,-0.3567,0.303,-0.1576,15.1,-4.5,-43,4.626518781,-3.5,-1.6,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,26158,2015-10-30 10:14:07:034,1446171247034.0 \n0.012,0.3184,10.0748,0.3933,0.5027,9.7859,-0.2676,-0.2358,-0.0586,15.2,-3.8,-43,4.603654968,-2.94,-2.3,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,26259,2015-10-30 10:14:07:135,1446171247135.0 \n-0.2035,0.8619,8.5712,0.4235,0.4564,9.7869,0.0562,-0.0757,0.0525,15.1,-3.1,-42.8,4.651476989,-2.67,-2.48,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,26362,2015-10-30 10:14:07:238,1446171247238.0 \n0.0898,0.9972,9.5205,0.4527,0.4923,9.7838,0.0782,-0.0232,0.1674,14.9,-2.9,-42.8,4.661250833,-2.89,-2.64,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,26463,2015-10-30 10:14:07:339,1446171247339.0 \n0.0299,0.5004,11.9985,0.5002,0.5838,9.7765,0.1161,-0.0415,0.1429,14.6,-3,-42.8,4.684289179,-3.41,-2.93,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,26565,2015-10-30 10:14:07:441,1446171247441.0 \n-0.1041,-0.7781,13.4482,0.5841,0.5328,9.7747,-0.3176,-0.0037,0.1845,14.5,-3.6,-43.2,4.642226744,-3.77,-3.23,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,26670,2015-10-30 10:14:07:546,1446171247546.0 \n0.097,0.6333,8.0553,0.6483,0.6441,9.764,-0.2053,-0.0721,-0.0183,14.4,-4.3,-43.4,4.639085152,-3.77,-3.8,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,26769,2015-10-30 10:14:07:645,1446171247645.0 \n-0.267,0.4968,8.7293,0.6321,0.3944,9.7783,-0.226,0.0782,-0.0452,14.3,-4.6,-43.7,4.529478475,-2.52,-3.69,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,26871,2015-10-30 10:14:07:747,1446171247747.0 \n0.1006,1.1468,8.7484,0.5869,0.3761,9.7818,0.0171,0.0538,0.0428,14.1,-4.3,-43.9,4.572064509,-2.2,-3.43,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,26973,2015-10-30 10:14:07:849,1446171247849.0 \n0.1281,0.7506,11.3784,0.5578,0.4218,9.7817,0.2712,-0.0061,-0.1503,14.1,-4.2,-43.8,4.573809838,-2.25,-3.29,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,27075,2015-10-30 10:14:07:951,1446171247951.0 \n0.3687,-0.1389,10.252,0.5498,0.6401,9.7703,0.1735,0.0037,-0.1429,14.3,-4.2,-43.9,4.641005014,-3.74,-3.22,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,27178,2015-10-30 10:14:08:054,1446171248054.0 \n0.0419,0.328,10.0066,0.4393,0.578,9.7797,0.1869,0.0232,0.1148,14.4,-4.2,-43.8,4.610287219,-3.12,-2.62,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,27280,2015-10-30 10:14:08:156,1446171248156.0 \n-0.0431,0.2239,9.1913,0.5565,0.4207,9.7818,0.011,0.0709,0.0098,14.4,-4.1,-43.9,4.58288555,-2.46,-3.26,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,27381,2015-10-30 10:14:08:257,1446171248257.0 \n0.1125,0.9864,8.3187,0.5106,0.4212,9.7843,0.0269,-0.011,-0.0122,14.5,-3.8,-43.6,4.588994202,-2.46,-2.99,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,27483,2015-10-30 10:14:08:359,1446171248359.0 \n-0.1065,0.8033,10.4615,0.4777,0.4186,9.7861,-0.0232,0.0635,-0.0195,14.6,-3.6,-43.4,4.582187418,-2.38,-2.92,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,27586,2015-10-30 10:14:08:462,1446171248462.0 \n0.0239,0.5351,11.2791,0.5279,0.6095,9.7734,0.2724,-0.0635,0.1503,14.8,-3.7,-43.2,4.633151032,-3.56,-3.09,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,27687,2015-10-30 10:14:08:563,1446171248563.0 \n0.5734,-0.419,12.0141,0.6616,0.6538,9.7624,-0.0415,-0.0855,0.1087,14.7,-4.2,-43,4.657236576,-4.12,-3.43,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,27790,2015-10-30 10:14:08:666,1446171248666.0 \n-0.0072,0.4944,7.908,0.746,0.7485,9.7495,0.1845,-0.1747,0.077,14.2,-5,-43,4.608716423,-4.38,-4.38,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,27891,2015-10-30 10:14:08:767,1446171248767.0 \n-0.0263,0.8332,8.4491,0.716,0.5651,9.7641,-0.0195,-0.0782,0.0049,14,-5.2,-43.4,4.562639731,-3.3,-4.19,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,27993,2015-10-30 10:14:08:869,1446171248869.0 \n0.0874,1.4353,8.5665,0.6683,0.5349,9.7692,-0.044,0.044,-0.0892,13.9,-5,-43.7,4.558101875,-3.14,-3.96,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,28095,2015-10-30 10:14:08:971,1446171248971.0 \n-0.492,0.4178,11.5053,0.5697,0.5175,9.7764,-0.0684,0.0782,-0.2578,14.1,-4.6,-44,4.549549761,-3.02,-3.33,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,28197,2015-10-30 10:14:09:073,1446171249073.0 \n0.1173,0.7051,10.72,0.5823,0.6948,9.7647,0.2908,-0.088,-0.1344,14.2,-4.2,-44,4.632452901,-3.56,-3.12,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,28300,2015-10-30 10:14:09:176,1446171249176.0 \n-0.0622,-0.4812,12.542,0.6172,0.4636,9.7762,-0.2529,0.0892,-0.2859,14.3,-3.8,-43.7,4.595800986,-2.71,-3.61,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,28401,2015-10-30 10:14:09:277,1446171249277.0 \n0.6345,0.4597,9.2584,0.7023,0.4631,9.7705,-0.1185,-0.044,-0.0965,14.2,-3,-43.6,4.65566578,-2.71,-4.11,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,28503,2015-10-30 10:14:09:379,1446171249379.0 \n-0.2322,0.838,8.9208,0.633,0.3457,9.7801,-0.0721,0.1332,-0.121,14.1,-2.1,-43.7,4.683765581,-2.02,-3.7,36.814037,-119.74742,248.26,336.835366,3.75,25.806452,,17 / 17,28606,2015-10-30 10:14:09:482,1446171249482.0 \n0.1413,1.0499,8.6838,0.6171,0.3757,9.78,0.1075,-0.0672,0.066,14.2,-1.6,-43.7,4.691445029,-2.2,-3.61,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,28708,2015-10-30 10:14:09:584,1446171249584.0 \n0.1796,0.8272,11.1151,0.6359,0.5576,9.7701,0.3861,-0.0892,0.2187,14.2,-1.5,-44,4.798084647,-3.26,-3.72,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,28809,2015-10-30 10:14:09:685,1446171249685.0 \n0.5291,-0.4298,10.5046,0.8162,0.6799,9.7489,-0.0257,-0.1503,0.1515,14.1,-1.9,-43.9,4.788310803,-4.41,-4.14,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,28912,2015-10-30 10:14:09:788,1446171249788.0 \n0.3687,0.8009,7.5848,0.8368,0.6508,9.7492,0.1808,-0.1491,0.1515,13.8,-2.5,-43.6,4.744328506,-3.44,-4.77,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,29014,2015-10-30 10:14:09:890,1446171249890.0 \n-0.0168,0.7709,8.5976,0.7927,0.4875,9.7624,-0.0012,-0.0037,0.0257,13.6,-3.1,-43.5,4.659505504,-2.85,-4.64,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,29116,2015-10-30 10:14:09:992,1446171249992.0 \n-0.0431,1.3731,8.1307,0.7501,0.5651,9.7616,0.0892,0.1148,0.0415,13.5,-3,-43.8,4.672246408,-3.08,-4.43,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,29217,2015-10-30 10:14:10:093,1446171250093.0 \n-0.1065,0.9421,10.0293,0.7519,0.6735,9.7546,0.0904,0.0037,-0.0709,13.5,-3,-43.8,4.695110221,-3.61,-4.54,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,29319,2015-10-30 10:14:10:195,1446171250195.0 \n0.3364,0.6476,10.8397,0.8006,0.839,9.7378,0.1723,-0.1662,-0.0354,13.5,-3.1,-44,4.732983866,-4.5,-4.63,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,29421,2015-10-30 10:14:10:297,1446171250297.0 \n0.6021,0.0826,10.8122,0.7119,0.7364,9.753,0.1173,-0.0195,-0.0098,13.4,-3.5,-43.9,4.730191339,-4.39,-4.38,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,29524,2015-10-30 10:14:10:400,1446171250400.0 \n0.5914,0.4381,10.0137,0.7262,0.6556,9.7577,-0.2957,-0.0623,-0.11,13.5,-3.4,-43.9,4.704884065,-3.83,-4.26,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,29626,2015-10-30 10:14:10:502,1446171250502.0 \n-0.1844,0.814,8.1558,0.5761,0.5174,9.776,-0.1124,0.0696,-0.0159,13.7,-2.9,-43.5,4.665439624,-3.02,-3.37,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,29728,2015-10-30 10:14:10:604,1446171250604.0 \n0.4118,1.0594,9.681,0.503,0.4254,9.7845,-0.0183,0.011,0.1723,14,-2.2,-43.3,4.702091538,-2.49,-2.94,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,29829,2015-10-30 10:14:10:705,1446171250705.0 \n-0.0311,0.6991,10.0975,0.482,0.5003,9.782,0.1002,0.0305,0.171,14.2,-1.9,-43.2,4.714832441,-2.76,-2.73,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,29931,2015-10-30 10:14:10:807,1446171250807.0 \n0.3867,-0.8523,10.9044,0.6624,0.7035,9.7589,0.0293,-0.2737,0.1112,14.4,-2.4,-43.1,4.772428307,-4.11,-3.88,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,30033,2015-10-30 10:14:10:909,1446171250909.0 \n0.1963,0.1149,9.3254,0.8516,0.5661,9.7532,0.3115,-0.1918,0.226,14,-2.9,-43.7,4.682369317,-3.31,-4.99,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,30136,2015-10-30 10:14:11:012,1446171251012.0 \n0.006,0.1317,8.8346,0.9166,0.4292,9.7543,-0.4374,0.0293,-0.0134,13.3,-3.6,-44.2,4.606272962,-2.91,-5.64,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,30237,2015-10-30 10:14:11:113,1446171251113.0 \n0.0982,0.7805,8.5198,0.8315,0.3776,9.764,-0.0232,0.2297,0.055,12.8,-3.6,-44.6,4.580965688,-2.27,-5.37,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,30340,2015-10-30 10:14:11:216,1446171251216.0 \n-0.006,1.3036,9.0573,0.7256,0.4178,9.7708,0,0.1026,-0.1026,12.9,-3.4,-44.4,4.636990757,-2.35,-4.5,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,30442,2015-10-30 10:14:11:318,1446171251318.0 \n0.0024,0.4884,11.6933,0.744,0.4384,9.7686,0.2566,-0.1185,-0.0635,13.2,-3.2,-44.1,4.646241002,-2.56,-4.36,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,30543,2015-10-30 10:14:11:419,1446171251419.0 \n0.4357,-0.8356,12.7587,0.7918,0.5313,9.7602,-0.2847,0.1002,-0.2162,13.4,-3.2,-43.9,4.671373743,-3.11,-4.64,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,30646,2015-10-30 10:14:11:522,1446171251522.0 \n0.6177,-0.0431,6.9791,0.4778,0.3782,9.7877,0.1368,-0.3409,-0.1234,13.7,-2.9,-44,4.630183973,-2.21,-2.79,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,30748,2015-10-30 10:14:11:624,1446171251624.0 \n0.34,0.4298,7.6411,0.5446,0.2883,9.7873,-0.1723,-0.0037,-0.1442,13.9,-2.4,-44,4.672944539,-1.79,-3.1,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,30849,2015-10-30 10:14:11:725,1446171251725.0 \n-0.1724,0.8487,8.0122,0.5436,0.2322,9.7888,0.0281,-0.0208,0.0293,14.3,-1.6,-44.1,4.652873253,-1.36,-3.18,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,30951,2015-10-30 10:14:11:827,1446171251827.0 \n0.2634,0.7949,9.9695,0.7313,0.2346,9.7765,0.0623,-0.1405,0.171,14.2,-1.3,-44.3,4.712563513,-1.34,-3.93,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,31054,2015-10-30 10:14:11:930,1446171251930.0 \n0.2011,0.3029,10.8314,0.9515,0.3934,9.7524,0.1796,0.0794,0.2566,13.6,-1.5,-44.6,4.752880619,-2.3,-5.57,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,31155,2015-10-30 10:14:12:031,1446171252031.0 \n0.6141,0,11.5951,1.0375,0.3812,9.7442,-0.1503,-0.1808,0.3775,13.2,-2.1,-44.6,4.710992717,-2.6,-5.76,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,31257,2015-10-30 10:14:12:133,1446171252133.0 \n0.6883,0.5207,9.1075,1.1495,0.3898,9.7312,-0.0171,-0.0037,0.1808,12.5,-3.3,-44.8,4.648858996,-2.44,-6.85,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,31359,2015-10-30 10:14:12:235,1446171252235.0 \n0.146,0.7817,8.4982,1.0241,0.3293,9.7475,0.0672,0.0574,-0.0367,12.2,-3.9,-45.1,4.561068934,-1.92,-6,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,31461,2015-10-30 10:14:12:337,1446171252337.0 \n0.1796,1.2151,8.1606,0.8729,0.4216,9.7586,0.0208,0.0709,-0.0672,12.2,-4,-45.2,4.576078766,-2.35,-5.23,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,31563,2015-10-30 10:14:12:439,1446171252439.0 \n-0.152,0.3615,11.1103,0.8044,0.5177,9.7599,0.1234,0.0073,-0.2346,12.7,-4,-45.4,4.611683483,-3.03,-4.71,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,31666,2015-10-30 10:14:12:542,1446171252542.0 \n0.7494,0.3867,10.5728,0.884,0.7135,9.7406,0.0635,-0.1442,-0.0501,13,-4.1,-45.1,4.652349654,-3.91,-4.85,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,31768,2015-10-30 10:14:12:644,1446171252644.0 \n0.6117,0.1185,8.758,0.6995,0.5068,9.7685,0.0525,0.1613,-0.0281,13.3,-4.1,-44.6,4.606272962,-2.96,-4.1,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,31870,2015-10-30 10:14:12:746,1446171252746.0 \n0.3304,0.146,9.833,0.5325,0.3391,9.7863,-0.3629,0.1759,-0.0977,13.6,-3.9,-44.2,4.562988796,-2,-3.4,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,31971,2015-10-30 10:14:12:847,1446171252847.0 \n-0.3172,1.0283,8.2265,0.3445,0.3087,9.7957,-0.0586,0.2541,-0.0305,14.2,-3.2,-43.8,4.607843758,-1.8,-2.01,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,32073,2015-10-30 10:14:12:949,1446171252949.0 \n-0.1137,1.1708,9.3362,0.136,0.2961,9.8012,-0.0134,0.3567,0.1051,14.8,-2.8,-43.7,4.612207081,-1.83,-1.24,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,32176,2015-10-30 10:14:13:052,1446171253052.0 \n-0.3867,0.8559,11.0385,0.0102,0.3997,9.7985,0.099,0.0159,0.2162,15.8,-2.7,-43.3,4.630183973,-2.24,0.06,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,32277,2015-10-30 10:14:13:153,1446171253153.0 \n-0.8859,-1.9632,16.6194,0.3146,0.1085,9.801,-0.5889,-0.5534,0.0269,16.2,-2.9,-43,4.604004034,-1.58,-0.94,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,32380,2015-10-30 10:14:13:256,1446171253256.0 \n0.0431,0.6524,7.4747,0.5519,0.3694,9.7841,0.1588,-0.6341,0.2883,16.2,-3.2,-42.8,4.624598919,-1.96,-2.15,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,32482,2015-10-30 10:14:13:358,1446171253358.0 \n0.0886,0.5387,8.6886,0.6783,0.196,9.7812,0.3702,-0.1649,0.0745,15,-3.7,-43.3,4.537856055,-1.15,-3.97,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,32584,2015-10-30 10:14:13:460,1446171253460.0 \n0.0323,1.4162,8.3019,0.5897,0.3912,9.7811,0.0831,0.4704,0.0183,14.4,-4.2,-43.6,4.576253299,-2.29,-3.45,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,32686,2015-10-30 10:14:13:562,1446171253562.0 \n-0.6069,0.7027,10.75,0.2617,0.5188,9.7894,-0.0403,0.1051,-0.2639,14.4,-4.8,-43.4,4.533492732,-3.03,-1.53,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,32787,2015-10-30 10:14:13:663,1446171253663.0 \n0.7721,-0.1305,10.5955,0.4506,0.4687,9.7851,-0.6084,-0.3225,-0.2883,14.9,-4.9,-43.3,4.552167755,-3.15,-1.94,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,32890,2015-10-30 10:14:13:766,1446171253766.0 \n0.5351,0.3065,7.8949,0.4583,0.266,9.7923,0.1662,0.0403,0.1784,15.3,-4.3,-42.9,4.546059103,-1.55,-2.68,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,32992,2015-10-30 10:14:13:868,1446171253868.0 \n0.4489,0.5279,9.0788,0.5435,0.1526,9.7904,-0.0305,0.0415,0.0244,15,-3.6,-43,4.522148092,-0.89,-3.18,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,33093,2015-10-30 10:14:13:969,1446171253969.0 \n-0.4788,0.8942,7.7656,0.2162,0.1275,9.8034,0.0037,0.0501,-0.0183,15,-3.2,-42.9,4.56438506,-0.81,-1.43,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,33196,2015-10-30 10:14:14:072,1446171254072.0 \n-0.0024,0.8739,9.7707,0.2097,0.1113,9.8038,-0.0525,0.0073,0.0391,15.4,-3,-42.8,4.558974539,-0.72,-1.22,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,33298,2015-10-30 10:14:14:174,1446171254174.0 \n-0.4621,0.0934,11.7136,0.2834,0.1813,9.8009,0.1552,-0.1772,0.2382,15.7,-2.9,-42.5,4.568399317,-0.75,-1.28,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,33399,2015-10-30 10:14:14:275,1446171254275.0 \n-0.0994,-1.1001,12.3696,0.483,0.2133,9.7924,-0.3262,-0.3763,0.1918,15.7,-3.2,-42.2,4.596324585,-1.25,-2.82,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,33502,2015-10-30 10:14:14:378,1446171254378.0 \n0.5052,0.8667,7.701,0.8121,0.2214,9.7705,-0.1955,-0.0904,0.0073,14.9,-3.9,-42.6,4.547455366,-1.33,-4.34,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,33603,2015-10-30 10:14:14:479,1446171254479.0 \n-0.1987,0.6716,8.764,0.6872,0.113,9.7819,-0.0147,0.2248,-0.1417,14,-4.5,-43.4,4.508185458,-0.66,-4.02,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,33705,2015-10-30 10:14:14:581,1446171254581.0 \n-0.3124,1.239,7.7859,0.4544,0.2826,9.792,0.1857,0.1564,-0.1588,13.8,-4.6,-43.5,4.468741017,-1.32,-2.94,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,33808,2015-10-30 10:14:14:684,1446171254684.0 \n-0.5447,0.231,10.6506,0.3694,0.3947,9.7917,0.0623,-0.0965,-0.3079,14.5,-4.7,-43.4,4.516912104,-2.31,-2.16,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,33909,2015-10-30 10:14:14:785,1446171254785.0 \n1.2366,-0.3807,11.0612,0.4363,0.4816,9.7851,0.1784,-0.088,-0.2224,14.9,-4.5,-43,4.599291645,-2.81,-2.55,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,34012,2015-10-30 10:14:14:888,1446171254888.0 \n0.231,-0.3089,10.9367,0.3274,0.2429,9.7982,0.1393,0.1319,-0.0941,15.1,-4.2,-43.1,4.547978965,-1.63,-2.49,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,34113,2015-10-30 10:14:14:989,1446171254989.0 \n-0.1341,0.1592,9.7588,0.2967,0.1948,9.8002,-0.0049,0.1222,-0.1833,15.2,-3.4,-43.1,4.587597939,-1.26,-1.92,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,34215,2015-10-30 10:14:15:091,1446171255091.0 \n-0.9254,0.8308,8.2013,0.1423,0.1183,9.8049,-0.1649,0.1637,-0.2297,15.7,-2.5,-42.8,4.630533038,-0.84,-1.05,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,34317,2015-10-30 10:14:15:193,1446171255193.0 \n-0.2286,1.1456,9.4128,0.1384,0.1509,9.8045,0.0428,-0.0183,0.0904,16.1,-2,-42.4,4.624773452,-0.75,-0.8,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,34420,2015-10-30 10:14:15:296,1446171255296.0 \n-0.2921,0.5279,11.5987,0.1265,0.3793,9.7985,0.369,-0.0855,0.2786,16.4,-1.8,-42.1,4.689350634,-2.22,-0.74,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,34522,2015-10-30 10:14:15:398,1446171255398.0 \n0.0694,-0.6416,12.4355,0.3009,0.5095,9.7888,0.0745,-0.1613,0.1564,16.2,-2.3,-42.3,4.734380129,-3.27,-1.43,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,34624,2015-10-30 10:14:15:500,1446171255500.0 \n-0.0144,0.6237,7.9356,0.4343,0.5328,9.7825,0.2089,-0.182,0.1747,15.9,-3.1,-42.4,4.66701042,-3.04,-2.23,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,34725,2015-10-30 10:14:15:601,1446171255601.0 \n-0.1353,0.7446,8.2492,0.4947,0.3554,9.7877,-0.0318,-0.0806,0.0721,15.5,-3.7,-42.6,4.577125963,-2.08,-2.89,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,34828,2015-10-30 10:14:15:704,1446171255704.0 \n-0.2131,1.0618,8.3941,0.4906,0.3757,9.7872,0.215,-0.0403,0.088,15.3,-3.7,-42.9,4.564035994,-1.94,-2.98,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,34930,2015-10-30 10:14:15:806,1446171255806.0 \n-0.5028,0.3603,11.3964,0.5236,0.5221,9.7787,0.1136,-0.0086,-0.1319,15.1,-3.7,-43.1,4.611334417,-3.05,-3.06,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,35032,2015-10-30 10:14:15:908,1446171255908.0 \n0.2693,0.4058,10.076,0.6121,0.7162,9.7613,0.1649,-0.0916,-0.1649,14.9,-3.9,-43.1,4.659505504,-4.18,-3.44,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,35133,2015-10-30 10:14:16:009,1446171256009.0 \n0.261,0.0084,9.2835,0.4024,0.405,9.79,0.2358,0.0635,0.1881,14.9,-3.7,-42.7,4.579045826,-2.37,-2.35,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,35236,2015-10-30 10:14:16:112,1446171256112.0 \n0.1377,-0.1568,9.3422,0.4511,0.2215,9.7938,-0.5437,-0.0183,0.1038,14.9,-3.4,-42.8,4.635594493,-2.29,-2.68,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,35338,2015-10-30 10:14:16:214,1446171256214.0 \n-0.158,0.6201,8.5222,0.4683,-0.0026,9.7955,-0.1454,0.0855,0.1271,15,-2.5,-42.8,4.606622028,-0.24,-2.92,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,35440,2015-10-30 10:14:16:316,1446171256316.0 \n0.1125,0.929,9.3362,0.531,0.022,9.7922,0.0024,0.0684,0.1735,15,-2.2,-43.2,4.602258705,-0.12,-3.09,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,35543,2015-10-30 10:14:16:419,1446171256419.0 \n-0.1736,0.4525,11.734,0.6028,0.3062,9.7833,0.336,-0.1307,0.2004,14.8,-2.4,-43.3,4.645891936,-1.14,-3.21,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,35644,2015-10-30 10:14:16:520,1446171256520.0 \n-1.087,-1.2677,13.3932,0.7473,0.3069,9.7733,-0.3836,-0.3592,0.0342,14.5,-3.4,-43.1,4.61988653,-1.79,-4.37,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,35745,2015-10-30 10:14:16:621,1446171256621.0 \n-0.0299,0.2227,9.3889,0.8848,0.4393,9.7568,-0.1674,-0.2529,0.1063,14.3,-4.2,-43.2,4.588121538,-2.51,-4.55,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,35847,2015-10-30 10:14:16:723,1446171256723.0 \n-0.0563,0.4657,9.2632,0.7902,0.3513,9.7684,-0.0611,0.0098,0.0305,13.8,-5.1,-43.5,4.513945044,-2.05,-4.62,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,35950,2015-10-30 10:14:16:826,1446171256826.0 \n-0.0215,1.0499,8.0062,0.7113,0.4041,9.7725,0.1393,0.0794,0.0183,13.7,-5.4,-43.7,4.520751829,-2.22,-4.21,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,36052,2015-10-30 10:14:16:928,1446171256928.0 \n0.0012,0.5806,10.9319,0.6904,0.4361,9.7726,-0.0232,-0.0012,-0.2162,13.9,-5.7,-43.4,4.473977005,-2.55,-4.04,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,36153,2015-10-30 10:14:17:029,1446171257029.0 \n1.1528,0.164,11.072,0.7964,0.5318,9.7598,-0.2602,-0.0208,-0.3738,14,-5.7,-43.2,4.496840818,-3.03,-4.41,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,36255,2015-10-30 10:14:17:131,1446171257131.0 \n0.3256,0.0766,8.6682,0.5857,0.2773,9.7852,-0.2443,0.2346,-0.1747,14,-5,-43.2,4.486194309,-1.62,-3.43,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,36358,2015-10-30 10:14:17:234,1446171257234.0 \n0.5363,0.2538,9.5385,0.618,0.1676,9.7857,-0.0513,-0.0916,0.0562,14.2,-4.4,-43.1,4.529303942,-1.27,-3.43,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,36459,2015-10-30 10:14:17:335,1446171257335.0 \n-0.0431,0.6213,9.0345,0.647,0.1469,9.7842,0.1173,0.0049,-0.0501,14.3,-3.6,-43.2,4.514468643,-0.86,-3.78,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,36562,2015-10-30 10:14:17:438,1446171257438.0 \n-0.0192,0.4429,10.1371,0.5598,0.2282,9.788,-0.0073,0.0403,-0.1197,14.5,-3.1,-43.2,4.597546316,-1.31,-3.58,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,36663,2015-10-30 10:14:17:539,1446171257539.0 \n-0.0204,0.6883,11.2037,0.6042,0.4009,9.7798,0.1356,-0.11,0.088,14.6,-3.1,-43.5,4.639783284,-2.34,-3.54,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,36766,2015-10-30 10:14:17:642,1446171257642.0 \n-0.5902,-0.6369,13.3992,0.7969,0.301,9.7696,-0.3274,-0.0929,0.1148,14.6,-3.5,-43.4,4.619362931,-1.76,-4.66,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,36868,2015-10-30 10:14:17:744,1446171257744.0 \n-0.1652,0.4022,9.1423,0.9079,0.3889,9.7568,-0.1955,0.0904,-0.0696,14.1,-4,-43.4,4.582012885,-2.27,-5.32,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,36970,2015-10-30 10:14:17:846,1446171257846.0 \n-0.1161,0.5662,8.8286,0.7263,0.3495,9.7735,0.011,0.1124,-0.0819,13.8,-4.2,-43.2,4.563686928,-1.91,-4.58,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,37072,2015-10-30 10:14:17:948,1446171257948.0 \n0.1484,1.3946,8.5736,0.6369,0.4981,9.7733,0.1417,0,-0.011,13.9,-4.5,-43.4,4.601735106,-2.91,-3.73,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,37174,2015-10-30 10:14:18:050,1446171258050.0 \n0.0515,0.9361,10.2951,0.661,0.6124,9.7652,0.0415,-0.0953,-0.237,14.2,-4.8,-43.3,4.561767066,-3.34,-3.73,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,37276,2015-10-30 10:14:18:152,1446171258152.0 \n0.6919,-0.231,10.5979,0.727,0.6747,9.7564,0.0941,-0.0819,-0.2346,14.3,-4.9,-43.4,4.5900414,-3.94,-4.26,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,37378,2015-10-30 10:14:18:254,1446171258254.0 \n0.2993,0.1832,9.2859,0.5883,0.4876,9.7768,0.1283,0.0648,-0.0892,14.4,-4.7,-43.5,4.538903253,-2.85,-3.44,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,37479,2015-10-30 10:14:18:355,1446171258355.0 \n0.0958,0.3831,9.4104,0.5397,0.3142,9.7867,-0.0415,0.088,0.0171,14.4,-3.9,-43.6,4.565432257,-2.06,-3.36,36.81405,-119.747536,249.22,336.835366,3.9,19.35484,281.75,17 / 17,37581,2015-10-30 10:14:18:457,1446171258457.0 \n-0.0491,1.1337,8.6227,0.4618,0.2275,9.7931,-0.1637,0.1185,-0.0257,14.8,-2.9,-43.2,4.59423019,-1.33,-2.7,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,37684,2015-10-30 10:14:18:560,1446171258560.0 \n-0.0335,0.0551,10.8122,0.4632,0.2074,9.7935,-0.1112,0.0672,-0.0037,15,-2.3,-43,4.647462732,-1.21,-2.71,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,37785,2015-10-30 10:14:18:661,1446171258661.0 \n-0.2035,0.4968,10.3633,0.4791,0.4244,9.7857,0.1869,0.0867,0.2712,15.1,-2.3,-42.8,4.6896997,-2.19,-2.94,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,37888,2015-10-30 10:14:18:764,1446171258764.0 \n0.1053,0.2358,9.845,0.572,0.2406,9.787,0.3555,-0.1258,0.3396,15.1,-2.7,-42.6,4.600338842,-1.41,-3.35,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,37989,2015-10-30 10:14:18:865,1446171258865.0 \n0.4549,0.2873,8.8585,0.7825,0.3084,9.7705,-0.0672,-0.2566,0.0806,15,-3.2,-43,4.64135408,-2.33,-4.48,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,38092,2015-10-30 10:14:18:968,1446171258968.0 \n-0.3651,0.4729,8.6993,0.803,0.2569,9.7703,-0.0086,0.0147,-0.0562,14.5,-3.6,-43.6,4.558276407,-1.5,-4.7,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,38193,2015-10-30 10:14:19:069,1446171259069.0 \n0.0204,1.2737,8.1558,0.7677,0.3175,9.7714,0.0147,0.0195,-0.0757,14.3,-3.8,-43.9,4.559149072,-1.76,-4.48,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,38296,2015-10-30 10:14:19:172,1446171259172.0 \n-0.1197,0.5447,12.0608,0.7897,0.368,9.7679,0.0379,-0.1136,-0.2138,14.1,-3.6,-43.7,4.576427832,-2.15,-4.62,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,38397,2015-10-30 10:14:19:273,1446171259273.0 \n0.4453,-0.3831,11.3485,0.7391,0.3146,9.7737,-0.204,0.0867,-0.2651,14.1,-3.5,-43.7,4.6186648,-1.84,-4.32,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,38499,2015-10-30 10:14:19:375,1446171259375.0 \n0.0778,0.1006,8.2384,0.5552,0.2165,9.7885,-0.0757,-0.1002,-0.022,14.2,-2.9,-43.7,4.581838352,-1.12,-3.21,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,38601,2015-10-30 10:14:19:477,1446171259477.0 \n0.2885,0.0946,9.3709,0.6904,0.0774,9.782,-0.1246,-0.1552,-0.0379,14.6,-2.2,-43.3,4.620410129,-0.47,-4,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,38703,2015-10-30 10:14:19:579,1446171259579.0 \n0.1472,0.9577,8.1594,0.7079,0.073,9.7808,0.0403,-0.0073,0.0611,14.9,-1.3,-43.1,4.671897342,-0.37,-4.13,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,38806,2015-10-30 10:14:19:682,1446171259682.0 \n0.2286,0.759,10.0796,0.7082,0.1114,9.7804,0.044,0.0208,0.099,14.6,-1.1,-42.9,4.683416515,-0.65,-4.14,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,38908,2015-10-30 10:14:19:784,1446171259784.0 \n0.0958,0.0168,11.2599,0.7343,0.2058,9.777,0.1454,-0.2187,0.1381,14.5,-1.3,-42.9,4.705582196,-1.2,-4.3,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,39010,2015-10-30 10:14:19:886,1446171259886.0 \n0.0646,-0.4621,10.5034,0.891,0.204,9.764,-0.2199,-0.0293,0.0867,14.1,-1.8,-42.9,4.635594493,-0.84,-5.52,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,39112,2015-10-30 10:14:19:988,1446171259988.0 \n0.4633,0.4729,7.9416,0.9481,0.358,9.7541,-0.0476,-0.0745,0.0391,13.8,-2.4,-43,4.689001568,-2.18,-5.43,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,39213,2015-10-30 10:14:20:089,1446171260089.0 \n-0.0862,0.6812,8.5712,0.9412,0.3371,9.7556,0.1503,0.1173,0.0415,13.4,-3,-43.3,4.620759195,-1.97,-5.51,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,39316,2015-10-30 10:14:20:192,1446171260192.0 \n0.1221,1.6915,8.0062,0.8485,0.558,9.7539,0.2676,0.0489,0.1185,13.6,-3.6,-43.4,4.620759195,-3.26,-4.97,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,39418,2015-10-30 10:14:20:294,1446171260294.0 \n-0.0814,0.7997,11.6286,0.8731,0.6094,9.7487,-0.0147,-0.1295,-0.077,13.7,-4,-43.5,4.633325565,-3.56,-5.12,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,39520,2015-10-30 10:14:20:396,1446171260396.0 \n0.7039,-0.7362,12.9179,0.9934,0.5724,9.7394,-0.5131,0.1002,-0.2761,13.7,-4.5,-43.8,4.651826055,-3.89,-5.89,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,39622,2015-10-30 10:14:20:498,1446171260498.0 \n0.4752,0.1377,8.2492,0.8381,0.5584,9.7548,-0.1075,-0.0648,0.0599,13.7,-4.4,-43.7,4.624249853,-3.26,-4.91,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,39723,2015-10-30 10:14:20:599,1446171260599.0 \n0.401,0.9254,6.9216,0.8124,0.4836,9.761,0.0721,0.0965,0.0953,13.8,-4.2,-43.7,4.605400297,-2.83,-4.76,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,39826,2015-10-30 10:14:20:702,1446171260702.0 \n0.1676,1.1971,7.9847,0.8551,0.4462,9.7591,0.0672,0.0098,0.1943,13.9,-4,-43.3,4.591437663,-2.54,-5.01,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,39928,2015-10-30 10:14:20:804,1446171260804.0 \n0.2442,1.0953,9.8916,0.9358,0.4604,9.751,0.0831,0.1148,0.1332,13.8,-4.1,-43.2,4.599291645,-2.69,-5.48,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,40030,2015-10-30 10:14:20:906,1446171260906.0 \n0.8128,1.1923,11.7974,0.929,0.6416,9.7414,0.1967,-0.1026,0.3262,13.7,-4.4,-43.2,4.62407532,-3.32,-5.39,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,40132,2015-10-30 10:14:21:008,1446171261008.0 \n-0.085,-0.8068,12.7348,1.1091,0.4559,9.7331,-0.3311,-0.1723,0.1857,13.6,-5.2,-43.3,4.549724294,-2.66,-6.5,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,40234,2015-10-30 10:14:21:110,1446171261110.0 \n0.8775,0.4034,8.017,1.1033,0.542,9.7293,-0.3201,0.2114,-0.0428,13.4,-5.8,-43.7,4.509581721,-3.14,-6.44,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,40336,2015-10-30 10:14:21:212,1446171261212.0 \n0.0766,0.6249,8.2887,0.8924,0.3394,9.7601,-0.0855,0.1808,-0.077,13.2,-6.3,-43.9,4.451811323,-1.98,-5.22,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,40437,2015-10-30 10:14:21:313,1446171261313.0 \n0.103,1.2977,8.023,0.7598,0.3579,9.7706,0.0782,0.0037,-0.022,13.4,-6.2,-43.8,4.447971599,-2.09,-4.45,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,40540,2015-10-30 10:14:21:416,1446171261416.0 \n0.7829,1.1169,11.0014,0.5643,0.5293,9.7761,0.1271,0.1393,-0.4875,14,-5.9,-43.4,4.480958322,-2.8,-3.66,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,40642,2015-10-30 10:14:21:518,1446171261518.0 \n0.4585,-0.316,12.1111,0.4425,0.5717,9.78,-0.5058,0.27,-0.4386,14.8,-5.4,-43.2,4.564210527,-3.34,-2.59,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,40744,2015-10-30 10:14:21:620,1446171261620.0 \n0.158,0.4537,8.3318,0.2662,0.4007,9.7948,0.2053,-0.0367,-0.1197,15.4,-4.5,-42.7,4.573635305,-2.34,-1.56,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,40846,2015-10-30 10:14:21:722,1446171261722.0 \n-0.3831,0.8703,7.7117,0.373,0.298,9.795,0.1026,0.0513,-0.0782,15.9,-3.1,-42.5,4.613603345,-1.74,-2.18,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,40947,2015-10-30 10:14:21:823,1446171261823.0 \n-0.5794,1.2031,7.938,0.3547,0.3539,9.7938,0.0965,-0.0061,0.0538,16,-2.2,-42.1,4.675737066,-1.88,-2.06,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,41049,2015-10-30 10:14:21:925,1446171261925.0 \n-0.5962,0.68,10.0197,0.3287,0.3719,9.7941,-0.0428,0.0159,0.1478,15.8,-2,-42,4.687779838,-2.17,-1.92,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,41152,2015-10-30 10:14:22:028,1446171262028.0 \n-0.1592,0.3903,10.3645,0.3831,0.5403,9.7843,0.3445,-0.0257,0.4068,15.8,-2.3,-41.8,4.728271477,-3.16,-2.24,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,41253,2015-10-30 10:14:22:129,1446171262129.0 \n-0.2406,-0.7506,12.6019,0.5267,0.4292,9.7831,0.0538,-0.1283,0.3348,15.8,-3,-42.2,4.658458306,-2.82,-2.75,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,41356,2015-10-30 10:14:22:232,1446171262232.0 \n-0.0251,0.486,8.3282,0.6411,0.4645,9.7746,0.0318,-0.1368,0.1747,15.5,-4.1,-42.6,4.60557483,-2.71,-3.75,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,41457,2015-10-30 10:14:22:333,1446171262333.0 \n-0.1927,0.8176,8.4036,0.5716,0.3222,9.7847,0.0269,-0.0134,0.033,15.2,-4.6,-43,4.509581721,-1.91,-3.36,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,41559,2015-10-30 10:14:22:435,1446171262435.0 \n-0.3292,1.5455,8.7484,0.5733,0.3695,9.7829,-0.066,-0.0586,-0.0819,15.1,-4.6,-42.9,4.520926361,-2.21,-3.25,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,41661,2015-10-30 10:14:22:537,1446171262537.0 \n-1.0618,0.334,12.5145,0.5912,0.4585,9.7781,0.0208,-0.0538,-0.1026,15,-4.3,-42.7,4.59719725,-2.68,-3.46,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,41764,2015-10-30 10:14:22:640,1446171262640.0 \n1.4162,-0.2083,11.3306,0.7177,0.4709,9.769,-0.0305,-0.259,0.0073,15,-4.3,-42.5,4.610636285,-3.05,-3.83,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,41865,2015-10-30 10:14:22:741,1446171262741.0 \n0.7195,0.3807,7.6004,0.6114,0.3429,9.7816,0.2101,-0.0012,0.0855,14.8,-3.8,-42.3,4.567701185,-2,-3.58,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,41967,2015-10-30 10:14:22:843,1446171262843.0 \n0.3567,0.7015,7.683,0.6157,0.2261,9.7847,-0.0892,0.1161,-0.077,14.8,-3.6,-42.4,4.540648582,-1.32,-3.6,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,42069,2015-10-30 10:14:22:945,1446171262945.0 \n-0.1077,0.5997,8.0888,0.5255,0.1401,9.7916,-0.0599,0.0586,-0.0672,15,-3,-42.3,4.573286239,-0.82,-3.07,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,42171,2015-10-30 10:14:23:047,1446171263047.0 \n-0.2622,0.3555,10.6638,0.5268,0.1056,9.7919,0.0098,0.0391,0.1491,15,-2.7,-42.4,4.565083192,-0.62,-3.08,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,42274,2015-10-30 10:14:23:150,1446171263150.0 \n-0.3783,0.589,10.8589,0.5535,0.2685,9.7873,-0.0061,-0.204,0.2297,15.2,-2.7,-42.6,4.606622028,-1.57,-3.24,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,42376,2015-10-30 10:14:23:252,1446171263252.0 \n-0.1149,0.073,8.7759,0.6351,0.0158,9.7861,-0.4765,0.1222,0.0819,14.9,-3,-43,4.545360971,0.1,-4.35,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,42478,2015-10-30 10:14:23:354,1446171263354.0 \n-0.4752,-0.0108,9.3027,0.673,-0.0081,9.7835,-0.1552,0.022,0.2456,14.8,-3.4,-43.3,4.555832946,-0.22,-4.04,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,42579,2015-10-30 10:14:23:455,1446171263455.0 \n-0.2071,0.5351,9.2105,0.6241,0.0072,9.7868,0.0904,0.1967,0.1649,14.6,-3.6,-43.1,4.491779363,-0.04,-3.65,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,42681,2015-10-30 10:14:23:557,1446171263557.0 \n-0.3675,1.1456,8.9483,0.4621,0.1747,9.7942,0.0709,-0.0171,-0.0012,14.9,-4.3,-42.8,4.523718888,-1.02,-2.7,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,42784,2015-10-30 10:14:23:660,1446171263660.0 \n-0.2993,1.0858,10.9283,0.594,0.298,9.7841,0.2309,-0.2236,0.0806,15,-4.8,-42.6,4.483576315,-1.31,-3.12,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,42885,2015-10-30 10:14:23:761,1446171263761.0 \n-0.5794,-1.4988,12.1781,0.7979,0.2277,9.7715,-0.3238,0.1063,-0.1356,14.7,-5.5,-43,4.497189884,-1.33,-4.67,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,42987,2015-10-30 10:14:23:863,1446171263863.0 \n0.68,0.0874,8.6862,0.679,0.2912,9.7788,-0.1552,-0.1002,0.0904,14.5,-5.7,-43.2,4.453382119,-1.7,-3.97,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,43089,2015-10-30 10:14:23:965,1446171263965.0 \n0.4238,0.8523,8.272,0.6901,0.1693,9.7809,-0.0623,0.0354,0.0538,14.3,-5.7,-43,4.411319684,-0.99,-4.04,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,43192,2015-10-30 10:14:24:068,1446171264068.0 \n0.5746,1.3156,7.9775,0.5721,0.103,9.7894,0.0086,0.0134,0.066,14.5,-5.6,-42.9,4.404861966,-0.6,-3.38,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,43294,2015-10-30 10:14:24:170,1446171264170.0 \n0.5746,0.5674,10.1801,0.546,0.1412,9.7904,0.2309,-0.0733,0.0538,14.7,-5.5,-42.6,4.46472676,-0.83,-3.19,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,43396,2015-10-30 10:14:24:272,1446171264272.0 \n0.5578,-0.0826,10.0987,0.6013,0.3698,9.7812,0.2688,-0.0147,0.1246,14.8,-5.6,-42.6,4.466995688,-2.16,-3.52,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,43497,2015-10-30 10:14:24:373,1446171264373.0 \n0.3579,0.6967,8.4491,0.7786,0.2339,9.7729,0.2211,0.1148,0.1515,14.7,-6,-42.4,4.444131874,-1.37,-4.55,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,43599,2015-10-30 10:14:24:475,1446171264475.0 \n-0.8248,0.0072,8.7652,0.7873,0.1697,9.7735,-0.0843,0.0061,0,14.3,-6.2,-42.5,4.43191457,-1.37,-4.77,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,43701,2015-10-30 10:14:24:577,1446171264577.0 \n-0.3077,0.9852,8.169,0.8026,0.2736,9.7699,0.2407,-0.0073,0.1332,14,-6.1,-43,4.431740037,-1.29,-4.82,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,43804,2015-10-30 10:14:24:680,1446171264680.0 \n-0.0587,0.8751,10.4663,0.8042,0.4062,9.7652,0.0733,0,-0.0098,13.8,-6.3,-43.4,4.472929807,-2.37,-4.71,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,43906,2015-10-30 10:14:24:782,1446171264782.0 \n0.1484,0.3603,10.5764,0.8414,0.5383,9.7556,0.1576,-0.022,-0.0635,13.8,-6.6,-43.6,4.445528138,-2.89,-4.91,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,44007,2015-10-30 10:14:24:883,1446171264883.0 \n0.0287,-0.1496,9.93,0.6792,0.2445,9.78,0.2492,0.2847,0.1784,13.8,-6.8,-43.1,4.37466777,-1.43,-3.97,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,44110,2015-10-30 10:14:24:986,1446171264986.0 \n0.8164,0.3436,9.1949,0.6362,0.2855,9.7818,-0.1808,-0.1319,0.0733,14.1,-6.7,-43.2,4.395262655,-2.1,-3.52,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,44211,2015-10-30 10:14:25:087,1446171265087.0 \n-0.5088,0.5231,8.4288,0.5428,0.0867,9.7912,-0.1491,0.1234,-0.0257,14.5,-6.2,-43.1,4.41044702,-0.75,-3.35,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,44314,2015-10-30 10:14:25:190,1446171265190.0 \n0.4597,1.3563,8.3282,0.4992,0.0954,9.7935,-0.0061,0.0733,0.1307,14.7,-5.9,-42.9,4.397007985,-0.51,-3,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,44416,2015-10-30 10:14:25:292,1446171265292.0 \n-0.3124,0.3508,12.4223,0.5373,0.1624,9.7906,0.1735,-0.1087,0.1417,14.8,-5.7,-42.4,4.413763145,-0.95,-3.14,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,44518,2015-10-30 10:14:25:394,1446171265394.0 \n-0.1472,-0.6955,11.6454,0.6034,0.3289,9.7825,-0.1564,-0.3567,0.1063,14.9,-6.2,-42.1,4.464028628,-2.28,-3,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,44620,2015-10-30 10:14:25:496,1446171265496.0 \n0.2957,0.9278,7.9942,0.6838,0.3777,9.7755,0.0929,-0.2101,0.1381,14.6,-7.3,-42.2,4.418126468,-2.21,-4,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,44721,2015-10-30 10:14:25:597,1446171265597.0 \n-0.2071,0.4537,8.8538,0.692,0.176,9.7806,-0.066,-0.0403,0.0415,14.1,-8.1,-42.7,4.309392456,-1.03,-4.05,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,44823,2015-10-30 10:14:25:699,1446171265699.0 \n0.2741,1.1049,7.847,0.5814,0.2248,9.7868,0.1564,0.2334,0.1466,13.9,-8.1,-42.8,4.303807402,-1.07,-3.58,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,44926,2015-10-30 10:14:25:802,1446171265802.0 \n-0.1353,0.5267,10.6123,0.6246,0.3766,9.7795,0.1417,0.0183,-0.1979,14,-8.3,-42.7,4.347615167,-2.2,-3.65,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,45028,2015-10-30 10:14:25:904,1446171265904.0 \n0.4896,-0.3998,10.2053,0.6523,0.5186,9.7712,-0.4679,-0.0232,-0.2871,14.1,-8.5,-42.6,4.382172686,-3.03,-3.82,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,45129,2015-10-30 10:14:26:005,1446171266005.0 \n0.4345,0.7027,8.2349,0.4507,0.1703,9.7948,-0.1393,0.2798,-0.0134,14.5,-8.3,-42.6,4.307647127,-0.99,-2.63,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,45231,2015-10-30 10:14:26:107,1446171266107.0 \n0.3053,0.1437,10.3274,0.4816,0.0232,9.7948,-0.1429,-0.0672,-0.0134,14.8,-7.7,-42.3,4.283910649,-0.34,-2.73,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,45334,2015-10-30 10:14:26:210,1446171266210.0 \n0.0048,0.9373,8.0182,0.412,0.0253,9.798,0.1662,0.0342,0.0648,15.2,-6.6,-42.1,4.321958827,-0.15,-2.41,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,45435,2015-10-30 10:14:26:311,1446171266311.0 \n-0.4944,0.4214,9.3218,0.3934,0.0142,9.7987,-0.1222,0.0367,-0.0086,15.3,-6.4,-42,4.376936698,-0.3,-2.18,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,45537,2015-10-30 10:14:26:413,1446171266413.0 \n-0.0634,0.5531,9.9719,0.4673,0.2534,9.7922,0.3372,0.0745,0.2969,15.3,-6.4,-41.8,4.429820174,-1.48,-2.73,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,45639,2015-10-30 10:14:26:515,1446171266515.0 \n-0.2777,-0.6512,12.2787,0.5501,0.1251,9.7904,-0.1772,-0.0464,0.1881,15.2,-7,-41.8,4.365242992,-1.06,-3.1,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,45742,2015-10-30 10:14:26:618,1446171266618.0 \n0.4705,0.6524,8.4946,0.759,0.2565,9.7739,-0.1148,0.0525,-0.1124,14.6,-7.6,-42,4.337492257,-1.3,-4.12,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,45844,2015-10-30 10:14:26:720,1446171266720.0 \n-0.1472,0.8009,8.3641,0.6913,0.1818,9.7806,0.0257,0.0452,-0.0574,14.2,-8.2,-42.6,4.310614187,-1.06,-4.04,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,45945,2015-10-30 10:14:26:821,1446171266821.0 \n0.0156,1.1504,7.853,0.595,0.3236,9.7832,0.1344,-0.0257,-0.121,14.1,-8.3,-42.6,4.323704156,-1.66,-3.45,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,46047,2015-10-30 10:14:26:923,1446171266923.0 \n-0.5758,0.3651,11.8094,0.6081,0.419,9.7788,0.1136,0.0281,-0.2077,14.3,-8.3,-42.7,4.355992747,-2.45,-3.56,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,46149,2015-10-30 10:14:27:025,1446171267025.0 \n0.7266,-0.0431,9.7911,0.6577,0.5448,9.7694,0.1833,-0.2162,-0.1393,14.5,-8.4,-42.6,4.398055182,-3.07,-3.58,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,46251,2015-10-30 10:14:27:127,1446171267127.0 \n0.4154,0.4752,7.6614,0.5853,0.2857,9.785,0.2358,-0.0464,0.0721,14.7,-7.8,-42.5,4.341331981,-1.67,-3.42,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,46353,2015-10-30 10:14:27:229,1446171267229.0 \n0.2155,0.5914,9.0728,0.5547,0.1462,9.7899,0.1173,0.0941,0.0892,14.7,-7.3,-42.2,4.357563543,-0.76,-3.34,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,46455,2015-10-30 10:14:27:331,1446171267331.0 \n-0.2993,0.4836,9.3182,0.4362,0.2026,9.7948,-0.0171,0.1197,0,15,-6.7,-42.2,4.355469148,-0.92,-2.76,36.81406,-119.747665,249.31,336.835366,4.2,19.35484,271.5,17 / 17,46558,2015-10-30 10:14:27:434,1446171267434.0 \n-0.2239,0.3519,9.7145,0.3201,0.3631,9.7947,0.0953,0.1796,0.1136,15.3,-6.8,-41.8,4.390375733,-2.12,-1.87,36.814064,-119.74779,247.94,336.835366,4.17,12.903226,274.68,17 / 17,46659,2015-10-30 10:14:27:535,1446171267535.0 \n0.5183,0.8499,8.831,0.3299,0.5523,9.7855,0.0843,0.0709,0.3262,15.7,-7.7,-41.7,4.398404248,-3.23,-1.93,36.814064,-119.74779,247.94,336.835366,4.17,12.903226,274.68,17 / 17,46762,2015-10-30 10:14:27:638,1446171267638.0 \n-0.2861,0.6213,9.5828,0.4319,0.2682,9.7935,0.1857,-0.11,0.2566,15.7,-8.2,-41.7,4.34482264,-1.57,-2.53,36.814064,-119.74779,247.94,336.835366,4.17,12.903226,274.68,17 / 17,46863,2015-10-30 10:14:27:739,1446171267739.0 \n-0.3065,0.5291,9.6415,0.5149,0.2529,9.7899,-0.1625,-0.0806,0.0208,15.5,-8.6,-42.2,4.314104845,-1.81,-3.17,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,46965,2015-10-30 10:14:27:841,1446171267841.0 \n-0.2993,1.2067,8.6203,0.4906,0.2515,9.7911,0.055,0.0489,0.033,15.1,-8.5,-42.5,4.326496683,-1.47,-2.87,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,47067,2015-10-30 10:14:27:943,1446171267943.0 \n-0.3328,1.239,9.9192,0.4425,0.4126,9.788,0.1515,0.0037,-0.1478,14.8,-8.6,-42.4,4.306425396,-2.41,-2.59,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,47170,2015-10-30 10:14:28:046,1446171268046.0 \n-0.0443,0.7003,11.2683,0.4609,0.6607,9.7735,0.2101,-0.0599,-0.1772,14.9,-8.8,-42.4,4.361926867,-3.86,-2.7,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,47271,2015-10-30 10:14:28:147,1446171268147.0 \n-0.2155,-0.2849,10.2316,0.4553,0.7695,9.7658,-0.2187,0.2712,-0.3641,14.9,-9.2,-42.2,4.400149577,-4.74,-3.1,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,47374,2015-10-30 10:14:28:250,1446171268250.0 \n-0.3077,-0.091,9.2117,0.3851,0.6929,9.7746,-0.292,0.066,-0.0794,15.1,-9.1,-42,4.363497663,-4.05,-2.26,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,47476,2015-10-30 10:14:28:352,1446171268352.0 \n-0.0898,0.9146,7.8266,0.2859,0.5147,9.789,-0.022,0.0684,0.1002,15.3,-8.8,-41.6,4.31497751,-3.01,-1.67,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,47577,2015-10-30 10:14:28:453,1446171268453.0 \n0.1317,1.2761,8.5605,0.1698,0.4373,9.7954,0.1772,-0.0183,0.1173,15.6,-8.1,-41.4,4.358261675,-2.56,-0.99,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,47679,2015-10-30 10:14:28:555,1446171268555.0 \n-0.1999,0.8499,10.0568,0.1388,0.6506,9.7841,0.2712,-0.2199,0.1234,15.9,-8,-41.2,4.381998153,-3.33,-0.51,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,47781,2015-10-30 10:14:28:657,1446171268657.0 \n-0.6177,0.0527,9.1985,0.2254,0.8997,9.7627,-0.3372,-0.3201,0.1332,16,-8.6,-41.3,4.412715948,-5.26,-1.32,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,47884,2015-10-30 10:14:28:760,1446171268760.0 \n0.1472,1.1995,8.4013,0.44,0.7478,9.7682,0.066,-0.0538,0.2492,15.4,-9.4,-41.2,4.375016836,-4.37,-2.58,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,47986,2015-10-30 10:14:28:862,1446171268862.0 \n-0.4465,0.6812,8.7472,0.5175,0.5627,9.7768,-0.1136,0.0305,-0.0122,14.8,-9.7,-41.5,4.303458337,-3.61,-3.1,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,48087,2015-10-30 10:14:28:963,1446171268963.0 \n-0.1065,1.6352,8.2277,0.4979,0.5177,9.7803,0.1772,0.0208,0.0037,14.4,-9.4,-42,4.312534049,-3.03,-2.91,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,48189,2015-10-30 10:14:29:065,1446171269065.0 \n-0.2047,1.6592,8.7819,0.4239,0.6643,9.7749,0.077,0.1222,-0.0709,14.3,-9.2,-42.3,4.335572395,-3.71,-2.68,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,48291,2015-10-30 10:14:29:167,1446171269167.0 \n0.1329,1.063,10.3621,0.4889,0.7774,9.7636,0.259,-0.0147,0.055,14.5,-9.1,-42.3,4.390026668,-4.55,-2.87,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,48393,2015-10-30 10:14:29:269,1446171269269.0 \n-0.1353,-0.5698,12.3182,0.5785,0.7289,9.7624,-0.3054,0.3335,-0.1136,14.5,-9.4,-42.2,4.385139746,-4.26,-3.39,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,48495,2015-10-30 10:14:29:371,1446171269371.0 \n-0.0778,0.3783,9.1051,0.3669,0.5199,9.786,-0.0452,0.1319,0.0635,14.4,-9.3,-42.4,4.322831491,-3.54,-2.26,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,48598,2015-10-30 10:14:29:474,1446171269474.0 \n0.2933,1.4533,8.0637,0.3693,0.4437,9.7896,-0.0892,0.1344,0.0831,14.4,-9.1,-42.5,4.296302487,-2.8,-2.44,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,48699,2015-10-30 10:14:29:575,1446171269575.0 \n0.34,1.4246,8.5557,0.3153,0.4772,9.79,0.0648,0.1649,0.1051,14.5,-8.6,-42.8,4.312534049,-2.79,-1.84,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,48802,2015-10-30 10:14:29:678,1446171269678.0 \n-0.073,1.2031,12.1494,0.3126,0.6068,9.7829,0.2175,-0.2248,0.0953,14.6,-8.9,-42.6,4.342030113,-3.55,-1.83,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,48903,2015-10-30 10:14:29:779,1446171269779.0 \n0.1784,-0.6919,12.3445,0.4144,0.6006,9.7795,-0.2321,-0.0953,0.0024,14.6,-9.4,-42.4,4.359832471,-4.03,-2.04,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,49006,2015-10-30 10:14:29:882,1446171269882.0 \n0.067,0.9182,8.1307,0.557,0.6641,9.7683,0.1967,-0.2773,0.1906,14.2,-9.9,-42.2,4.298396882,-3.88,-3.26,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,49108,2015-10-30 10:14:29:984,1446171269984.0 \n-0.0431,0.68,8.9651,0.6603,0.5189,9.7706,-0.0648,-0.0648,-0.044,13.5,-10,-42.5,4.276754799,-3.03,-3.87,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,49209,2015-10-30 10:14:30:085,1446171270085.0 \n-0.0539,1.3827,8.1199,0.6296,0.5483,9.771,0.1368,0.1136,-0.0281,13,-9.9,-43,4.260872303,-3.21,-3.69,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,49312,2015-10-30 10:14:30:188,1446171270188.0 \n-0.2741,0.9529,9.6857,0.5315,0.6967,9.7674,0.055,0.0489,-0.2871,12.8,-9.9,-43,4.285132379,-4.07,-3.11,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,49413,2015-10-30 10:14:30:289,1446171270289.0 \n0.1077,1.0415,10.5608,0.5471,0.8252,9.7565,0.1112,-0.215,-0.1918,12.9,-9.7,-43,4.301189409,-4.42,-3.24,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,49515,2015-10-30 10:14:30:391,1446171270391.0 \n0.3783,-0.2095,11.2504,0.5574,0.6755,9.7675,-0.391,0.314,-0.2578,13.2,-9.7,-42.7,4.282688919,-3.95,-3.27,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,49618,2015-10-30 10:14:30:494,1446171270494.0 \n0.0718,0.5399,7.7979,0.301,0.8288,9.7669,-0.1454,0.1014,-0.2114,13.5,-9.5,-42.9,4.387408674,-5.09,-1.88,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,49720,2015-10-30 10:14:30:596,1446171270596.0 \n-0.4824,0.9661,8.922,0.2279,0.6791,9.7805,-0.022,0.1258,-0.1637,14,-9.1,-42.4,4.325973084,-3.97,-1.33,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,49824,2015-10-30 10:14:30:700,1446171270700.0 \n-0.7183,1.4198,10.0724,0.2125,0.7027,9.7791,-0.1503,-0.1454,-0.0501,14.5,-8.7,-42.2,4.352153023,-4.11,-1.24,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,49924,2015-10-30 10:14:30:800,1446171270800.0 \n-0.2933,1.4856,11.1474,0.334,0.6816,9.7772,-0.0061,-0.1344,0.1258,14.6,-8.3,-42,4.409923421,-4.04,-1.64,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,50025,2015-10-30 10:14:30:901,1446171270901.0 \n0.4369,0.2562,10.8146,0.4739,0.627,9.7751,-0.3531,-0.2297,0.0977,14.4,-8.2,-42.2,4.404687433,-4.1,-2.49,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,50127,2015-10-30 10:14:31:003,1446171271003.0 \n-0.4944,0.9086,8.1977,0.58,0.5497,9.774,0.0733,-0.1185,0.0929,13.7,-8.1,-42.8,4.384092548,-3.21,-3.4,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,50229,2015-10-30 10:14:31:105,1446171271105.0 \n-0.2023,0.3232,9.5984,0.6966,0.4849,9.7699,-0.2065,-0.1112,-0.0037,13.1,-8.2,-43.3,4.358785274,-2.83,-4.08,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,50332,2015-10-30 10:14:31:208,1446171271208.0 \n-0.4705,1.1229,8.2959,0.6268,0.5255,9.7725,0.1258,0.0611,0.1258,12.7,-8.2,-43.9,4.357912609,-2.83,-3.74,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,50433,2015-10-30 10:14:31:309,1446171271309.0 \n-0.4214,1.2186,9.408,0.6138,0.6411,9.7664,0.1674,-0.0892,0.0965,12.5,-8.6,-44.1,4.328765611,-3.49,-3.61,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,50536,2015-10-30 10:14:31:412,1446171271412.0 \n0.5531,0.5974,10.3573,0.6663,0.8606,9.7461,0.3335,-0.0012,0.0391,12.6,-9.4,-43.8,4.398229715,-5.03,-3.91,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,50638,2015-10-30 10:14:31:514,1446171271514.0 \n0.103,-0.7278,12.5743,0.4427,0.6199,9.777,-0.3873,0.4374,-0.1906,12.7,-10.1,-43.9,4.290193834,-4.01,-3.26,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,50739,2015-10-30 10:14:31:615,1446171271615.0 \n-0.0407,-0.0215,10.1155,0.3699,0.3865,9.792,-0.5901,0.0073,-0.0562,13.1,-10.1,-43.9,4.19804045,-2.26,-2.16,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,50841,2015-10-30 10:14:31:717,1446171271717.0 \n0.3388,1.2833,8.5102,0.4377,0.2634,9.7933,0.1002,0.0354,0.11,13.3,-9.5,-44.1,4.231027173,-1.54,-2.61,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,50944,2015-10-30 10:14:31:820,1446171271820.0 \n0.3531,1.4916,9.9695,0.4427,0.3856,9.7891,0.0794,-0.0098,-0.0012,13.5,-8.9,-43.9,4.284259715,-2.25,-2.59,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,51045,2015-10-30 10:14:31:921,1446171271921.0 \n-0.3077,1.0534,10.6063,0.3467,0.5911,9.7827,0.3115,0.0354,0.0867,13.5,-9,-43.9,4.304156468,-2.94,-2.14,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,51147,2015-10-30 10:14:32:023,1446171272023.0 \n-0.9026,-0.7697,12.5241,0.3812,0.6828,9.7754,-0.2272,-0.2211,0.0012,13.5,-9.9,-43.4,4.290891966,-3.99,-2.23,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,51249,2015-10-30 10:14:32:125,1446171272125.0 \n-0.1664,0.5148,9.5146,0.572,0.6911,9.7655,0.1967,-0.1808,0.2566,13.4,-10.2,-43.5,4.276754799,-3.88,-3.08,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,51351,2015-10-30 10:14:32:227,1446171272227.0 \n-0.5447,0.6297,8.9172,0.5214,0.5286,9.7785,-0.1698,-0.055,-0.0293,13.1,-10.6,-43.3,4.201182042,-3.32,-2.97,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,51454,2015-10-30 10:14:32:330,1446171272330.0 \n-0.3196,1.5586,7.5381,0.41,0.56,9.7821,0.1197,0.0318,0.0171,13.1,-10.7,-43.4,4.187743007,-3.27,-2.4,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,51556,2015-10-30 10:14:32:432,1446171272432.0 \n-0.1484,1.0391,9.997,0.4295,0.7158,9.7711,0.1393,-0.0122,-0.077,13.4,-10.9,-42.9,4.225442119,-4.19,-2.52,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,51657,2015-10-30 10:14:32:533,1446171272533.0 \n-0.0323,0.9421,10.0868,0.4837,0.9217,9.7512,0.1002,-0.0965,-0.2285,13.6,-11.3,-42.9,4.291764631,-5.13,-2.74,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,51760,2015-10-30 10:14:32:636,1446171272636.0 \n0.0036,0.2035,10.9547,0.3507,0.6446,9.7792,0.1576,0.1148,-0.022,13.9,-11.4,-42.7,4.227361981,-3.77,-2.05,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,51861,2015-10-30 10:14:32:737,1446171272737.0 \n0,0.6764,9.8904,0.2557,0.5427,9.7883,-0.1234,0.0195,-0.0745,14.4,-10.9,-42.6,4.194026193,-3.17,-1.5,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,51963,2015-10-30 10:14:32:839,1446171272839.0 \n-0.2143,1.4269,8.0625,0.172,0.4741,9.7937,-0.0086,0.0916,-0.0721,14.8,-10.2,-42.5,4.249527663,-2.86,-1.17,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,52066,2015-10-30 10:14:32:942,1446171272942.0 \n-0.3364,1.2725,9.1506,0.1699,0.5691,9.7886,0.0696,0.0354,-0.0281,15.3,-9.7,-41.9,4.264188428,-3.33,-0.99,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,52168,2015-10-30 10:14:33:044,1446171273044.0 \n-0.5243,0.6129,10.0868,0.1644,0.7027,9.7801,0.1222,-0.2663,0.1894,15.4,-9.6,-41.9,4.276929332,-3.8,-0.67,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,52270,2015-10-30 10:14:33:146,1446171273146.0 \n0.3962,-0.753,12.736,0.3641,0.6955,9.7752,-0.0904,-0.1588,0.1662,15.5,-10,-41.6,4.330860006,-4.07,-2.13,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,52371,2015-10-30 10:14:33:247,1446171273247.0 \n0.2777,0.8116,8.2923,0.582,0.4998,9.7766,0.1918,-0.1442,0.259,15.1,-10,-41.7,4.280943589,-2.83,-3.17,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,52474,2015-10-30 10:14:33:350,1446171273350.0 \n-0.3244,0.3555,9.153,0.6214,0.2704,9.7832,-0.0965,-0.0696,-0.0391,14.4,-9.9,-42.1,4.222824125,-1.58,-3.63,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,52576,2015-10-30 10:14:33:452,1446171273452.0 \n-0.2741,0.7159,8.3606,0.5867,0.356,9.7826,0.1246,0.0721,0.0782,13.9,-9.5,-42.5,4.277103865,-1.77,-3.61,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,52677,2015-10-30 10:14:33:553,1446171273553.0 \n-0.152,0.8452,9.7719,0.5546,0.4731,9.7795,0.1136,0.0012,-0.055,13.9,-9.5,-42.8,4.311486851,-2.77,-3.25,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,52779,2015-10-30 10:14:33:655,1446171273655.0 \n0.0646,0.7542,11.7328,0.6229,0.7043,9.7615,0.2981,-0.0159,-0.1442,14,-9.8,-42.5,4.28757584,-3.47,-3.54,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,52881,2015-10-30 10:14:33:757,1446171273757.0 \n-0.6608,-0.2191,11.3473,0.3743,0.599,9.7812,-0.1576,0.1894,-0.1185,14.1,-10.1,-42.4,4.308170726,-4.29,-2.88,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,52983,2015-10-30 10:14:33:859,1446171273859.0 \n0.0455,0.6548,8.8538,0.3445,0.4614,9.7897,-0.1943,-0.044,0.1674,14.6,-9.9,-41.9,4.274660404,-3.27,-1.74,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,53085,2015-10-30 10:14:33:961,1446171273961.0 \n-0.2071,0.7889,9.0908,0.4963,0.3828,9.7866,-0.033,-0.0379,0.0904,14.9,-9.4,-42.3,4.3048546,-2.24,-2.9,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,53188,2015-10-30 10:14:34:064,1446171274064.0 \n0.3196,1.4521,8.8298,0.5207,0.4802,9.781,0.0061,0.1588,0.0684,14.8,-9.2,-42.4,4.327369347,-2.81,-3.05,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,53289,2015-10-30 10:14:34:165,1446171274165.0 \n0.3831,1.0953,10.392,0.4616,0.619,9.7762,0.1833,-0.0232,0.1038,14.6,-9.4,-42.5,4.340459317,-3.3,-2.67,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,53392,2015-10-30 10:14:34:268,1446171274268.0 \n-0.2059,-0.2298,10.7847,0.4194,0.7995,9.765,0.0098,0.0257,0.1148,14.7,-10.3,-41.9,4.337841323,-4.68,-2.46,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,53493,2015-10-30 10:14:34:369,1446171274369.0 \n-0.3759,0.5088,9.8545,0.5147,0.6336,9.7726,0.0232,-0.2578,0.27,14.7,-10.7,-41.6,4.258254309,-3.72,-2.76,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,53596,2015-10-30 10:14:34:472,1446171274472.0 \n-0.1221,0.6464,9.481,0.6857,0.4776,9.771,-0.2871,-0.1222,0.1148,14.2,-11.3,-41.5,4.219508,-2.79,-4.01,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,53697,2015-10-30 10:14:34:573,1446171274573.0 \n-0.595,0.8727,9.5361,0.6906,0.4376,9.7725,-0.0208,0.1112,0.0941,13.8,-11.2,-42,4.221602395,-2.64,-4.21,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,53800,2015-10-30 10:14:34:676,1446171274676.0 \n-0.2011,1.2953,9.2296,0.6579,0.5738,9.7677,0.1478,0.0134,0.1955,13.3,-11.4,-42.5,4.214621078,-3.35,-3.85,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,53902,2015-10-30 10:14:34:778,1446171274778.0 \n-0.0431,0.7554,10.228,0.7423,0.8478,9.7417,0.4215,-0.3054,0.2297,13.2,-12,-42.7,4.23800849,-4.96,-4.36,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,54004,2015-10-30 10:14:34:880,1446171274880.0 \n0.1389,-0.0778,10.738,0.7762,0.8076,9.7425,-0.2676,0.171,-0.0855,12.9,-12.9,-42.6,4.223173191,-5.47,-5.21,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,54106,2015-10-30 10:14:34:982,1446171274982.0 \n-0.0575,0.3065,8.6898,0.7781,0.716,9.7495,-0.1943,0.0391,0.182,12.8,-13.6,-42.5,4.119500633,-4.19,-4.56,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,54208,2015-10-30 10:14:35:084,1446171275084.0 \n0.0886,0.8619,8.4623,0.7655,0.5318,9.7623,-0.0929,0.2285,0.2126,12.6,-13.8,-42.4,4.085641246,-3.11,-4.48,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,54309,2015-10-30 10:14:35:185,1446171275185.0 \n0.2837,1.0379,8.1786,0.6443,0.4701,9.7742,0.0257,0.0513,0.259,12.6,-13.6,-42.2,4.060159439,-2.75,-3.77,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,54411,2015-10-30 10:14:35:287,1446171275287.0 \n1.7573,1.3838,10.4734,0.6286,0.5007,9.7737,0.1466,-0.0403,0.3665,12.6,-13.8,-42.5,4.054399852,-2.66,-3.62,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,54514,2015-10-30 10:14:35:390,1446171275390.0 \n0.9505,1.2857,8.9459,0.4385,0.6792,9.7733,0.0244,-0.0147,-0.0525,12.6,-14.4,-42.4,4.070631414,-3.63,-3.03,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,54615,2015-10-30 10:14:35:491,1446171275491.0 \n0.1053,0.0539,10.4543,0.4473,0.4686,9.7852,-0.3873,0.1869,-0.3091,12.7,-14.9,-42.2,3.994884125,-2.74,-2.62,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,54717,2015-10-30 10:14:35:593,1446171275593.0 \n0.2538,0.6045,9.2273,0.5036,0.41,9.7851,-0.1405,-0.0428,-0.1784,12.9,-14.8,-41.9,4.00413437,-2.7,-3.06,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,54820,2015-10-30 10:14:35:696,1446171275696.0 \n0.1748,0.668,9.4128,0.5467,0.3589,9.7848,0.0024,0.0049,-0.2578,13.1,-13.7,-41.9,4.028743512,-2.1,-3.2,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,54921,2015-10-30 10:14:35:797,1446171275797.0 \n0.4118,1.0798,8.2001,0.3862,0.3807,9.7916,0.1552,0.0929,-0.2871,13.5,-12.6,-42,4.083372318,-2.22,-2.26,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,55024,2015-10-30 10:14:35:900,1446171275900.0 \n-0.0862,0.176,11.5592,0.3425,0.464,9.7897,0.0599,-0.044,-0.3873,14,-12.1,-41.9,4.137128459,-2.71,-2,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,55125,2015-10-30 10:14:36:001,1446171276001.0 \n0.1975,0.2334,11.3749,0.3052,0.4998,9.7891,-0.4154,0.1197,-0.4447,14.7,-11.6,-41.7,4.168020787,-2.92,-1.79,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,55228,2015-10-30 10:14:36:104,1446171276104.0 \n-0.4741,0.5866,9.3122,0.2095,0.3485,9.7982,-0.066,-0.0684,-0.2297,15.2,-10.9,-41.8,4.166973589,-1.92,-1.11,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,55330,2015-10-30 10:14:36:206,1446171276206.0 \n-0.2023,0.9936,8.0721,0.2108,0.2641,9.8008,-0.0733,-0.0269,-0.2346,15.7,-9.5,-41.6,4.278849194,-1.53,-1.42,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,55431,2015-10-30 10:14:36:307,1446171276307.0 \n0.0527,1.3707,8.4743,0.2395,0.3727,9.7966,0.1943,-0.0941,-0.1173,16,-8.4,-41.5,4.33051094,-1.75,-1.16,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,55533,2015-10-30 10:14:36:409,1446171276409.0 \n-0.4118,0.6812,10.2951,0.152,0.5244,9.7914,0.2529,0.1112,-0.0745,16.1,-8.1,-41.4,4.363672196,-2.6,-1.29,36.814064,-119.74779,247.94,336.7213758,4.17,12.903226,274.68,17 / 17,55635,2015-10-30 10:14:36:511,1446171276511.0 \n0.0862,1.0151,9.2799,0.0791,0.8051,9.7732,0.3885,0.1222,0.1332,16.3,-8.3,-41.7,4.441688413,-4.71,-0.46,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,55737,2015-10-30 10:14:36:613,1446171276613.0 \n-0.4657,-0.2119,12.2799,0.2303,0.6473,9.7826,-0.1393,-0.0037,-0.0379,16.4,-8.6,-41.7,4.375191369,-4.21,-1.21,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,55840,2015-10-30 10:14:36:716,1446171276716.0 \n-0.3077,0.3053,9.7348,0.2672,0.5319,9.7886,-0.3433,0.0806,-0.2065,16.3,-8.7,-41.8,4.362275932,-3.72,-1.67,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,55942,2015-10-30 10:14:36:818,1446171276818.0 \n-0.8428,0.5004,8.327,0.1967,0.4071,9.7962,-0.088,0.0476,-0.1723,16.2,-8.4,-41.7,4.359832471,-2.49,-1.09,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,56043,2015-10-30 10:14:36:919,1446171276919.0 \n-0.3448,1.4066,8.8011,0.2429,0.4652,9.7926,0.0452,-0.0586,-0.0012,16.3,-7.7,-41.6,4.369431782,-2.66,-1.33,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,56145,2015-10-30 10:14:37:021,1446171277021.0 \n-0.4705,0.6369,11.6131,0.311,0.55,9.7863,0.1735,-0.0745,-0.0635,16.2,-7.1,-41.5,4.446051737,-3.22,-1.82,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,56247,2015-10-30 10:14:37:123,1446171277123.0 \n-0.0551,-0.0658,10.4854,0.245,0.6311,9.7833,-0.3042,0.2334,-0.1613,16.2,-7.1,-41.7,4.46472676,-3.69,-1.43,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,56350,2015-10-30 10:14:37:226,1446171277226.0 \n-0.103,0.243,8.3246,0.1687,0.4921,9.7928,0.0269,-0.0171,-0.0391,16.3,-7,-41.9,4.429994707,-2.97,-0.88,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,56452,2015-10-30 10:14:37:328,1446171277328.0 \n-0.0323,0.6129,8.8789,0.2394,0.2717,9.8,-0.1747,-0.0147,0.0367,16.4,-6.7,-42,4.381649087,-1.59,-1.4,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,56553,2015-10-30 10:14:37:429,1446171277429.0 \n-0.2897,1.1396,8.1355,0.3134,0.2215,9.7991,0.0721,-0.0733,0.1576,16.4,-5.9,-42.1,4.422315259,-1.18,-1.7,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,56655,2015-10-30 10:14:37:531,1446171277531.0 \n-0.085,0.759,10.4004,0.3764,0.26,9.796,0.0147,-0.0513,0.1393,16.2,-5.8,-42,4.437848689,-1.45,-2.18,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,56758,2015-10-30 10:14:37:634,1446171277634.0 \n0.9062,0.5555,9.8545,0.4108,0.525,9.784,0.2065,-0.055,0.2602,16,-6.3,-41.9,4.502425871,-3.07,-2.4,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,56859,2015-10-30 10:14:37:735,1446171277735.0 \n0.4908,0.3388,8.922,0.5478,0.4434,9.7813,0.5131,0.0305,0.3396,15.5,-7,-41.7,4.416904738,-1.91,-3.46,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,56962,2015-10-30 10:14:37:838,1446171277838.0 \n-0.1305,0.4752,8.5593,0.594,0.4585,9.7779,-0.1698,-0.0086,-0.0183,15.2,-7.6,-41.9,4.395786254,-3.14,-3.48,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,57064,2015-10-30 10:14:37:940,1446171277940.0 \n-0.4262,0.6632,8.9675,0.5662,0.4001,9.7821,0.0024,0.0305,-0.0281,14.7,-7.9,-42.3,4.361752334,-2.23,-3.43,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,57165,2015-10-30 10:14:38:041,1446171278041.0 \n-0.1281,1.2522,9.0154,0.4994,0.5008,9.7811,0.0147,0.0269,-0.1124,14.9,-8.1,-42.5,4.381300021,-2.93,-2.92,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,57267,2015-10-30 10:14:38:143,1446171278143.0 \n-0.1065,0.6608,11.4072,0.5693,0.5793,9.773,0.121,-0.1295,-0.226,15,-8.1,-42.5,4.388281338,-3.03,-3.18,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,57369,2015-10-30 10:14:38:245,1446171278245.0 \n-0.0108,-0.2885,11.0684,0.4822,0.5322,9.7803,-0.2382,0.2615,-0.3384,15.3,-8,-42.1,4.387059608,-3.11,-2.82,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,57472,2015-10-30 10:14:38:348,1446171278348.0 \n0.3915,0.6488,7.7644,0.3212,0.4259,9.7921,-0.3213,-0.0012,-0.1234,15.4,-7.5,-42,4.421442594,-2.85,-2.03,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,57573,2015-10-30 10:14:38:449,1446171278449.0 \n-0.2658,0.8942,8.2384,0.3551,0.1727,9.7987,-0.0757,-0.044,-0.0574,15.9,-6.5,-42.1,4.424584187,-1.14,-2.01,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,57675,2015-10-30 10:14:38:551,1446171278551.0 \n-0.0778,1.1696,8.345,0.3792,0.2715,9.7956,0.1588,-0.0037,0.0794,16.1,-5.7,-42,4.429122043,-1.21,-2.21,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,57777,2015-10-30 10:14:38:653,1446171278653.0 \n-0.4896,0.3903,12.0584,0.3418,0.3709,9.7937,0.0721,-0.0232,0.1185,16.2,-5.5,-42,4.508359991,-1.92,-1.98,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,57879,2015-10-30 10:14:38:755,1446171278755.0 \n-0.0443,0.9373,9.839,0.3337,0.6497,9.7794,0.0183,-0.3433,0.2321,16.2,-5.9,-41.8,4.510628919,-3.39,-1.74,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,57982,2015-10-30 10:14:38:858,1446171278858.0 \n0.2885,0.7638,9.5062,0.5342,0.5668,9.7757,-0.1393,0.0721,0.226,15.9,-7.1,-41.7,4.464901292,-3.31,-3.13,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,58084,2015-10-30 10:14:38:960,1446171278960.0 \n-0.1101,0.7063,8.7424,0.6402,0.5939,9.7677,-0.2346,0.0281,-0.0061,15.3,-8.1,-41.9,4.410970619,-3.47,-3.75,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,58186,2015-10-30 10:14:39:062,1446171279062.0 \n-0.067,1.3012,8.4432,0.6113,0.7135,9.7615,0.2309,0.1246,0.0049,14.9,-8.4,-41.8,4.423362456,-3.77,-3.88,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,58288,2015-10-30 10:14:39:164,1446171279164.0 \n-0.4657,1.0439,9.6726,0.4806,0.8462,9.7582,0.1307,-0.0208,-0.2346,14.9,-9,-42,4.405036499,-4.95,-2.82,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,58390,2015-10-30 10:14:39:266,1446171279266.0 \n0.1915,0.9888,10.6015,0.4605,1.0805,9.7361,0.2969,0.0318,-0.16,15.1,-9.2,-42,4.429471109,-5.57,-2.81,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,58491,2015-10-30 10:14:39:367,1446171279367.0 \n-0.6093,-0.0431,11.4203,0.2267,0.9115,9.7616,-0.4129,0.3763,-0.2517,15.5,-9.4,-41.7,4.443957341,-5.81,-1.78,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,58593,2015-10-30 10:14:39:469,1446171279469.0 \n0.0012,0.1879,10.5967,0.1981,0.6648,9.7821,-0.4789,0.0281,0.0293,16,-8.9,-41.4,4.358261675,-3.89,-1.16,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,58696,2015-10-30 10:14:39:572,1446171279572.0 \n0.1425,1.1384,8.3103,0.2312,0.4957,9.7914,-0.121,-0.0672,0.0599,16.3,-8.2,-41.4,4.386885075,-3.2,-1.33,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,58797,2015-10-30 10:14:39:673,1446171279673.0 \n-0.1185,1.3264,8.6646,0.2635,0.4905,9.7908,-0.0977,-0.0513,-0.0098,16.6,-7.3,-41.8,4.447622533,-2.87,-1.54,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,58899,2015-10-30 10:14:39:775,1446171279775.0 \n-0.1879,1.0594,10.5836,0.3535,0.519,9.7865,0.1833,-0.0049,0.2211,16.6,-6.8,-42.1,4.447098934,-2.72,-2.07,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,59002,2015-10-30 10:14:39:878,1446171279878.0 \n0.2933,-0.334,10.7955,0.4888,0.5611,9.7784,0.1344,-0.0709,0.1393,16.4,-7.1,-42.1,4.465075825,-3.51,-2.28,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,59104,2015-10-30 10:14:39:980,1446171279980.0 \n-0.1724,1.0965,7.9583,0.5115,0.4829,9.7814,0.3519,-0.0391,0.4264,15.9,-7.4,-42.3,4.445528138,-2.82,-2.99,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,59205,2015-10-30 10:14:40:081,1446171280081.0 \n0.0886,0.729,9.4535,0.6771,0.5535,9.7676,-0.204,-0.0831,0.0684,15.3,-8,-42.5,4.4045129,-3.24,-3.97,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,59307,2015-10-30 10:14:40:183,1446171280183.0 \n0.0084,1.2474,8.4671,0.6609,0.5828,9.767,0.1112,0.0916,-0.0452,14.8,-8.3,-42.6,4.412541415,-3.28,-4.17,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,59409,2015-10-30 10:14:40:285,1446171280285.0 \n-0.0539,1.0223,10.7667,0.6462,0.7129,9.7593,0.1038,0.011,-0.1075,14.5,-8.9,-42.6,4.390899332,-4.17,-3.79,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,59511,2015-10-30 10:14:40:387,1446171280387.0 \n0.5399,0.8571,11.2611,0.7061,0.9134,9.7385,0.2407,-0.1271,-0.1808,14.6,-9.1,-42.7,4.43907042,-5.34,-4.15,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,59613,2015-10-30 10:14:40:489,1446171280489.0 \n-0.4513,0.0239,11.0409,0.5848,0.8786,9.7497,0.0037,0.1515,-0.2578,14.8,-9.2,-42.6,4.424409654,-5.14,-3.43,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,59716,2015-10-30 10:14:40:592,1446171280592.0 \n0.0874,0.3771,8.412,0.4368,0.7997,9.7642,-0.1161,0.1674,-0.0941,15.2,-9.1,-42.6,4.41463581,-5.13,-2.54,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,59817,2015-10-30 10:14:40:693,1446171280693.0 \n-0.3448,0.814,7.756,0.3076,0.5801,9.7846,-0.2004,0.2456,-0.0134,15.7,-8.3,-42.5,4.403116637,-3.39,-1.8,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,59919,2015-10-30 10:14:40:795,1446171280795.0 \n0.1544,1.585,7.9787,0.2751,0.4831,9.7909,-0.0464,0.0379,0.1161,16.1,-7.7,-42.6,4.388630404,-2.97,-1.67,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,60022,2015-10-30 10:14:40:898,1446171280898.0 \n-0.2538,0.8631,11.6753,0.3317,0.5166,9.7874,0.0134,-0.0538,0.1613,16.4,-7.3,-42.4,4.431565504,-2.82,-1.6,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,60124,2015-10-30 10:14:41:000,1446171281000.0 \n-0.2562,-0.735,13.131,0.381,0.6129,9.7801,-0.0367,-0.0281,0.2871,16.3,-7.6,-42.3,4.414984876,-3.58,-2.23,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,60226,2015-10-30 10:14:41:102,1446171281102.0 \n0.249,0.7087,7.7081,0.591,0.5214,9.7749,0.314,-0.1967,0.4533,15.8,-8.1,-42.5,4.408178092,-3.05,-3.46,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,60328,2015-10-30 10:14:41:204,1446171281204.0 \n-0.3615,-0.0036,10.0461,0.5972,0.3046,9.7837,-0.0037,0.0379,0.1979,15.2,-8.5,-42.9,4.374144171,-2.33,-3.9,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,60430,2015-10-30 10:14:41:306,1446171281306.0 \n-0.0599,1.4066,7.6327,0.5426,0.3771,9.7844,0.1063,0.2944,0.1344,14.7,-8.7,-43.1,4.310614187,-2.2,-3.17,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,60532,2015-10-30 10:14:41:408,1446171281408.0 \n-0.0239,1.239,9.7276,0.4863,0.5389,9.7797,0.1234,0.0672,-0.1173,14.7,-9.3,-43.4,4.340982916,-3.15,-2.85,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,60634,2015-10-30 10:14:41:510,1446171281510.0 \n-0.1401,0.9565,10.6578,0.5389,0.6699,9.7689,-0.0757,-0.0929,-0.2334,14.9,-9.5,-43.2,4.365766591,-3.72,-3.08,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,60736,2015-10-30 10:14:41:612,1446171281612.0 \n-0.4262,-0.6093,12.1925,0.4589,0.3748,9.7887,-0.4753,0.1429,-0.3519,14.9,-9.5,-43,4.323878689,-2.57,-3.18,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,60838,2015-10-30 10:14:41:714,1446171281714.0 \n-0.0946,0.2717,7.6411,0.3347,0.4385,9.7911,-0.1087,0.1124,-0.0195,15.2,-9.1,-42.8,4.322307893,-2.9,-2.2,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,60940,2015-10-30 10:14:41:816,1446171281816.0 \n-0.4573,1.0116,8.2851,0.3001,0.3792,9.7947,0.0024,0.171,-0.0415,15.6,-8.3,-43,4.360705136,-2.22,-1.76,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,61041,2015-10-30 10:14:41:917,1446171281917.0 \n0.1724,1.2989,8.8957,0.2668,0.428,9.7937,0.0904,-0.0391,0.0171,15.8,-8,-43.2,4.364719393,-2.4,-1.52,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,61143,2015-10-30 10:14:42:019,1446171282019.0 \n-0.3112,0.5662,11.4168,0.1953,0.546,9.7895,0.1185,-0.0489,0.1112,16.1,-8,-43.4,4.378507494,-2.93,-0.99,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,61245,2015-10-30 10:14:42:121,1446171282121.0 \n-0.5327,-0.486,13.2782,0.3024,0.5528,9.7864,-0.3042,-0.2859,0.1381,16.2,-8.5,-43,4.400149577,-3.23,-1.77,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,61348,2015-10-30 10:14:42:224,1446171282224.0 \n-0.1041,0.8499,8.1906,0.4235,0.5877,9.7799,-0.1332,-0.215,0.0195,16.2,-9,-42.4,4.352502089,-3.31,-2.11,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,61450,2015-10-30 10:14:42:326,1446171282326.0 \n-0.5519,0.5662,8.3438,0.3208,0.3902,9.7936,-0.2224,0.3067,-0.0208,15.6,-9.4,-42.1,4.312359516,-2.28,-1.88,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,61552,2015-10-30 10:14:42:428,1446171282428.0 \n-0.1496,1.1277,8.3629,0.3648,0.3399,9.794,0.0244,0.0134,0.0354,15.5,-9.3,-42.1,4.302934738,-1.93,-2.09,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,61654,2015-10-30 10:14:42:530,1446171282530.0 \n-0.3112,0.7913,10.4651,0.3545,0.4438,9.7902,0.1784,0.0415,-0.2651,15.5,-8.9,-42.4,4.31619924,-2.26,-2.19,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,61755,2015-10-30 10:14:42:631,1446171282631.0 \n-0.5842,0.0862,11.133,0.4669,0.587,9.7779,0.182,-0.1222,-0.3348,15.6,-8.8,-42.5,4.355120083,-3.35,-2.18,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,61857,2015-10-30 10:14:42:733,1446171282733.0 \n-0.8092,-0.5806,12.4618,0.2011,0.217,9.8022,-0.5412,0.441,-0.16,15.6,-8.4,-42.4,4.345869837,-1.88,-1.77,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,61960,2015-10-30 10:14:42:836,1446171282836.0 \n0.1077,0.7015,7.938,0.1254,0.2933,9.8015,-0.1075,-0.0672,0.2236,16,-8,-42.1,4.332779868,-1.93,-0.69,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,62062,2015-10-30 10:14:42:938,1446171282938.0 \n-0.1257,0.5818,8.7759,0.1667,0.2368,9.8024,0.0599,-0.0476,0.0012,16.4,-7.3,-42.1,4.365592058,-1.37,-0.81,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,62163,2015-10-30 10:14:43:039,1446171283039.0 \n-0.255,1.1313,8.0481,0.1188,0.3406,9.8,0.121,0.0745,-0.0086,16.7,-7.2,-41.8,4.405734631,-1.99,-0.69,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,62265,2015-10-30 10:14:43:141,1446171283141.0 \n-0.4812,0.4046,11.8716,0.1806,0.3935,9.7971,0.1576,-0.281,0.3079,16.7,-7.4,-41.8,4.421442594,-2.3,-1.06,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,62368,2015-10-30 10:14:43:244,1446171283244.0 \n-0.7661,-0.929,14.0456,0.553,0.3707,9.784,-0.1368,-0.0452,0.2529,16.2,-8.1,-42,4.37466777,-2.17,-3.23,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,62470,2015-10-30 10:14:43:346,1446171283346.0 \n0.2167,1.3288,7.7644,0.6023,0.5512,9.7726,0.3189,-0.1491,0.237,15.6,-8.7,-42.4,4.351803957,-2.91,-3.19,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,62571,2015-10-30 10:14:43:447,1446171283447.0 \n-0.2011,0.4513,9.1566,0.4806,0.4867,9.7828,0.0977,0.1967,-0.1772,14.6,-9.4,-43.1,4.328940144,-2.84,-2.81,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,62674,2015-10-30 10:14:43:550,1446171283550.0 \n-0.3196,1.2833,7.3275,0.3645,0.5978,9.7816,0.1576,0.0269,-0.0672,14.6,-9.6,-43.3,4.279896392,-3.07,-2.3,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,62775,2015-10-30 10:14:43:651,1446171283651.0 \n-0.7614,0.6357,10.7955,0.373,0.7457,9.7711,0.1393,-0.0403,-0.1662,14.9,-9.7,-43.1,4.301363942,-3.82,-1.89,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,62878,2015-10-30 10:14:43:754,1446171283754.0 \n-0.1197,0.516,10.3597,0.4227,0.8859,9.7574,0.0171,-0.1258,-0.2346,15.3,-9.9,-42.9,4.36035607,-5.16,-2.34,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,62979,2015-10-30 10:14:43:855,1446171283855.0 \n-0.1724,0.5674,9.7899,0.2739,0.6231,9.783,-0.0684,-0.0037,-0.1051,15.6,-9.6,-42.4,4.308345259,-3.64,-1.6,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,63081,2015-10-30 10:14:43:957,1446171283957.0 \n0.3112,1.0211,8.3175,0.2919,0.3789,9.795,0.0257,0.121,-0.0195,15.7,-8.6,-42.6,4.310090588,-2.21,-1.71,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,63183,2015-10-30 10:14:44:059,1446171284059.0 \n-0.3926,0.9864,8.7029,0.2249,0.3564,9.7976,-0.0538,0.0428,-0.0745,15.8,-7.6,-42.5,4.3477897,-2.07,-1.39,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,63285,2015-10-30 10:14:44:161,1446171284161.0 \n-0.2454,1.0068,9.7995,0.236,0.4334,9.7942,-0.0098,0.0489,-0.0147,16.1,-7,-42.5,4.418126468,-2.53,-1.38,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,63387,2015-10-30 10:14:44:263,1446171284263.0 \n-0.0886,1.0355,11.06,0.2168,0.5993,9.7859,0.2407,-0.0513,0.1662,16.2,-6.9,-42.1,4.455651047,-3.5,-1.27,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,63489,2015-10-30 10:14:44:365,1446171284365.0 \n-0.4992,-0.9254,13.8768,0.4193,0.3959,9.7897,-0.4484,-0.4423,-0.0293,16.2,-7.3,-42.2,4.454254784,-3.29,-2.02,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,63591,2015-10-30 10:14:44:467,1446171284467.0 \n-0.249,0.8116,8.4599,0.5802,0.4468,9.7793,0.0476,-0.2443,0.0929,15.8,-7.5,-42.8,4.44325921,-2.68,-2.97,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,63694,2015-10-30 10:14:44:570,1446171284570.0 \n-0.1556,0.7338,8.9519,0.5834,0.3139,9.7842,-0.0012,-0.0183,-0.0049,15.4,-7.6,-43.1,4.350582226,-1.89,-3.3,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,63795,2015-10-30 10:14:44:671,1446171284671.0 \n-0.2119,1.1576,8.3091,0.5087,0.3702,9.7864,0.1271,0.0867,0.0195,15,-7.5,-43.2,4.408178092,-2.16,-2.98,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,63897,2015-10-30 10:14:44:773,1446171284773.0 \n-0.3675,0.2682,11.7926,0.4631,0.5559,9.7799,0.1894,-0.0941,-0.0843,14.9,-7.6,-43.1,4.377460297,-2.85,-2.57,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,64000,2015-10-30 10:14:44:876,1446171284876.0 \n0.8859,0.4908,10.7835,0.48,0.7389,9.767,-0.2187,0.1136,-0.2627,15,-7.9,-43,4.434707096,-4.26,-2.65,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,64101,2015-10-30 10:14:44:977,1446171284977.0 \n0.2801,0.7817,8.2444,0.3246,0.5082,9.7881,-0.2847,-0.0208,-0.0904,15.5,-8.1,-43.1,4.395960787,-3.09,-1.9,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,64203,2015-10-30 10:14:45:079,1446171285079.0 \n0.1915,1.1456,7.4077,0.3466,0.28,9.7965,-0.1185,-0.0244,-0.033,15.8,-7.6,-42.6,4.342728245,-1.64,-2.03,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,64306,2015-10-30 10:14:45:182,1446171285182.0 \n-0.4441,0.929,8.8071,0.3348,0.2333,9.7982,0.1515,-0.0586,0.0257,16,-6.8,-42.6,4.376238566,-1.22,-1.94,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,64407,2015-10-30 10:14:45:283,1446171285283.0 \n-0.3089,0.6859,10.3118,0.3285,0.3345,9.7954,0.2615,-0.0415,0.1038,16,-6.2,-42.4,4.454778383,-1.95,-1.92,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,64510,2015-10-30 10:14:45:386,1446171285386.0 \n-0.0658,0.8679,9.505,0.2624,0.7436,9.7749,0.4911,0.1833,0.2517,16.1,-6.4,-42.3,4.52441702,-3.74,-1.72,36.81406,-119.747894,247.38,336.7213758,4.14,19.35484,266.2,17 / 17,64611,2015-10-30 10:14:45:487,1446171285487.0 \n-0.4106,0.2885,9.5864,0.3305,0.6161,9.7817,0.0195,-0.1564,0.1674,16.3,-7.6,-42.3,4.412541415,-3.6,-1.94,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,64714,2015-10-30 10:14:45:590,1446171285590.0 \n-0.5507,0.0227,8.6682,0.4829,0.5504,9.7793,-0.2749,-0.1063,0.0782,16.1,-8.2,-42.4,4.420918995,-3.62,-2.68,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,64816,2015-10-30 10:14:45:692,1446171285692.0 \n-0.1413,1.1672,8.6754,0.5682,0.4101,9.7816,-0.0819,-0.0819,0.0757,15.7,-8.4,-42.9,4.386710542,-2.4,-3.32,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,64918,2015-10-30 10:14:45:794,1446171285794.0 \n-0.0024,1.5646,8.8765,0.5383,0.4319,9.7823,-0.0159,0.0538,-0.0953,15.2,-8.3,-43.1,4.373620573,-2.51,-3.29,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,65020,2015-10-30 10:14:45:896,1446171285896.0 \n-0.1724,1.0582,11.3437,0.5564,0.5423,9.7758,0.3775,0.171,-0.1381,15.1,-7.9,-43.5,4.398229715,-3.17,-3.26,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,65121,2015-10-30 10:14:45:997,1446171285997.0 \n-1.008,-0.6177,12.1745,0.374,0.5242,9.7855,-0.2651,0.2272,-0.2053,15.3,-7.9,-43.1,4.380950955,-3.06,-2.19,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,65224,2015-10-30 10:14:46:100,1446171286100.0 \n0.2825,0.3891,8.9711,0.3607,0.4614,9.7891,-0.1014,-0.1429,-0.088,15.7,-7.4,-42.7,4.435230695,-2.7,-2.11,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,65325,2015-10-30 10:14:46:201,1446171286201.0 \n-0.8464,0.8703,8.6407,0.3313,0.2297,9.7984,-0.1552,0.0098,-0.0819,16.1,-6.5,-42.3,4.431216438,-1.34,-1.94,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,65428,2015-10-30 10:14:46:304,1446171286304.0 \n-0.2825,0.9397,9.335,0.3543,0.268,9.7966,0.1161,0.0831,0.1307,16.4,-5.7,-42.5,4.441339348,-1.57,-2.07,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,65530,2015-10-30 10:14:46:406,1446171286406.0 \n-0.2155,0.3472,10.914,0.2697,0.4377,9.7932,0.2382,0.0757,0.171,16.4,-5.7,-42.6,4.478340328,-2.56,-1.58,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,65631,2015-10-30 10:14:46:507,1446171286507.0 \n0.0108,-0.5866,11.9926,0.3498,0.7263,9.7735,-0.1381,-0.2407,0.1405,16.5,-6.7,-42.6,4.523369822,-4.72,-1.56,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,65734,2015-10-30 10:14:46:610,1446171286610.0 \n0.2933,0.8631,7.9547,0.5449,0.7797,9.7604,0.1307,-0.1918,0.1503,16.1,-7.8,-42.6,4.465424891,-4.56,-3.2,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,65835,2015-10-30 10:14:46:711,1446171286711.0 \n-0.4585,0.3819,8.8933,0.591,0.6195,9.7692,-0.3824,0.0391,-0.0147,15.6,-8.6,-42.8,4.383743482,-3.62,-3.46,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,65937,2015-10-30 10:14:46:813,1446171286813.0 \n0.0311,1.4234,7.8422,0.5775,0.4794,9.7779,0.1161,0.0611,0.0843,15.3,-8.6,-42.8,4.335572395,-2.76,-3.53,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,66039,2015-10-30 10:14:46:915,1446171286915.0 \n-0.0156,1.251,9.9443,0.6007,0.5579,9.7723,0.1014,-0.2089,-0.1759,15.1,-8.4,-42.8,4.404687433,-3.26,-3.52,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,66142,2015-10-30 10:14:47:018,1446171287018.0 \n0.7482,0.8176,10.5524,0.6774,0.8288,9.7481,0.1246,-0.2285,-0.2004,15.1,-8.3,-42.8,4.47013728,-4.85,-3.97,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,66245,2015-10-30 10:14:47:121,1446171287121.0 \n0.2047,0.5806,10.0556,0.5861,0.7292,9.7619,-0.3262,0.3262,-0.1906,15.1,-8.4,-42.8,4.460887035,-4.63,-3.87,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,66345,2015-10-30 10:14:47:221,1446171287221.0 \n0.1233,0.6776,9.4966,0.55,0.6629,9.7687,-0.3763,0.0611,-0.1759,15.2,-8.2,-42.5,4.420744462,-3.88,-3.22,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,66448,2015-10-30 10:14:47:324,1446171287324.0 \n-0.6764,1.0918,8.3809,0.4336,0.4981,9.7844,-0.1271,0.0012,-0.11,15.4,-7.6,-42.2,4.38775774,-3.16,-2.73,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,66550,2015-10-30 10:14:47:426,1446171287426.0 \n-0.1963,1.0846,8.8933,0.4764,0.5221,9.7811,0.1258,-0.0195,0.0452,15.7,-6.7,-42.1,4.452160389,-3.05,-2.79,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,66651,2015-10-30 10:14:47:527,1446171287527.0 \n-0.231,0.7805,12.4211,0.5648,0.6391,9.7695,0.2566,-0.2541,0.2627,15.8,-6.5,-42,4.534190864,-3.74,-3.31,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,66754,2015-10-30 10:14:47:630,1446171287630.0 \n-0.0874,-0.6584,12.6043,0.6166,0.601,9.7688,-0.4728,0.0183,0.1808,15.6,-7.2,-42.2,4.512025182,-4.51,-3.47,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,66856,2015-10-30 10:14:47:732,1446171287732.0 \n0.1293,0.8571,8.7951,0.6448,0.5624,9.7693,0.0855,-0.0916,0.3665,15.6,-7.7,-42.4,4.424584187,-3.49,-3.54,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,66957,2015-10-30 10:14:47:833,1446171287833.0 \n-0.249,0.4932,8.904,0.511,0.3063,9.7885,-0.1686,0.1576,0.0867,15.3,-7.9,-42.5,4.339761185,-1.79,-2.99,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,67060,2015-10-30 10:14:47:936,1446171287936.0 \n-0.3891,1.2641,8.1427,0.4059,0.3671,9.7914,0.1038,0.0953,0.0684,15.4,-7.8,-42.5,4.33766679,-1.86,-2.64,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,67161,2015-10-30 10:14:48:037,1446171288037.0 \n-0.5351,0.3256,12.0021,0.3822,0.485,9.7872,0.1662,-0.0843,-0.1124,15.7,-7.8,-42.1,4.377809363,-2.66,-2.01,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,67264,2015-10-30 10:14:48:140,1446171288140.0 \n0.8667,-0.097,10.9271,0.4717,0.6352,9.7747,0.1063,-0.1698,-0.0843,16,-8.4,-42,4.425282318,-3.71,-2.76,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,67366,2015-10-30 10:14:48:242,1446171288242.0 \n-0.097,-0.0443,11.1977,0.3084,0.4454,9.7917,0.1515,0.0073,0.1026,16.1,-8.3,-41.8,4.373271507,-2.6,-1.8,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,67468,2015-10-30 10:14:48:344,1446171288344.0 \n0.3256,0.6225,8.8573,0.2095,0.3006,9.7998,-0.0086,0.0965,-0.0244,16.2,-8.1,-41.5,4.339237586,-1.88,-1.44,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,67569,2015-10-30 10:14:48:445,1446171288445.0 \n-0.2885,0.9864,8.8406,0.1827,0.2839,9.8008,-0.0367,-0.0195,-0.0476,16.6,-7.4,-41.1,4.388804937,-1.5,-0.98,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,67671,2015-10-30 10:14:48:547,1446171288547.0 \n-0.2885,0.8033,10.0221,0.2009,0.3918,9.7968,0.0415,0.0049,0.0024,16.8,-7.2,-41.3,4.419871798,-2.29,-1.17,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,67773,2015-10-30 10:14:48:649,1446171288649.0 \n-0.7877,0.8571,11.4958,0.2696,0.6768,9.7796,0.4019,0.3702,0.2834,16.8,-7.3,-41.5,4.44448094,-2.88,-1.48,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,67875,2015-10-30 10:14:48:751,1446171288751.0 \n-0.5495,0.0455,10.4842,0.2242,0.6564,9.7821,-0.237,-0.1051,0.1576,16.8,-8.3,-41.3,4.432787234,-4.07,-1.04,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,67978,2015-10-30 10:14:48:854,1446171288854.0 \n-0.0431,0.6931,8.8573,0.4268,0.5643,9.7811,-0.1784,-0.16,-0.0611,16.7,-8.9,-41.4,4.377983896,-3.59,-2.23,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,68079,2015-10-30 10:14:48:955,1446171288955.0 \n-0.8296,1.0475,8.4815,0.3979,0.2958,9.7941,0.1087,-0.0916,0.0941,16.3,-9,-41.6,4.299444079,-1.73,-2.33,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,68182,2015-10-30 10:14:49:058,1446171289058.0 \n-0.4549,0.9948,9.3518,0.4188,0.3709,9.7907,-0.0159,-0.0147,0.0464,15.9,-8.8,-41.9,4.315152043,-2.22,-2.24,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,68284,2015-10-30 10:14:49:160,1446171289160.0 \n-0.3328,0.1508,11.8321,0.4111,0.5443,9.7829,0.0843,-0.0183,-0.1967,15.6,-8.4,-41.7,4.391073865,-2.84,-2.57,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,68386,2015-10-30 10:14:49:262,1446171289262.0 \n-0.5818,-0.9014,11.4251,0.4454,0.5793,9.7794,-0.3592,0.1161,-0.4362,15.7,-8.7,-41.6,4.361577801,-3.39,-2.61,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,68487,2015-10-30 10:14:49:363,1446171289363.0 \n0.17,0.3938,8.3294,0.3048,0.3755,9.7947,-0.2761,0.0342,-0.1038,16,-8.1,-41.4,4.355120083,-2.19,-1.78,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,68589,2015-10-30 10:14:49:465,1446171289465.0 \n0.0192,0.8835,8.0864,0.2822,0.1179,9.8019,-0.1833,-0.0122,-0.0464,16.3,-7.5,-41.2,4.355294615,-0.81,-1.74,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,68692,2015-10-30 10:14:49:568,1446171289568.0 \n-0.1401,1.2366,7.5274,0.3609,0.0803,9.7997,0.077,-0.1429,0.1112,16.4,-6.1,-41.3,4.39910238,-0.47,-2.11,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,68794,2015-10-30 10:14:49:670,1446171289670.0 \n-0.2167,0.5112,11.0672,0.4902,0.0541,9.7942,0.1649,-0.0293,0.1148,16.3,-5.8,-41.6,4.40329117,-0.36,-2.71,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,68896,2015-10-30 10:14:49:772,1446171289772.0 \n-0.3053,0.2155,12.536,0.5592,0.3088,9.7858,0.4362,-0.044,0.2529,16,-5.6,-41.8,4.434707096,-1.09,-3.2,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,68997,2015-10-30 10:14:49:873,1446171289873.0 \n-0.7961,-0.7242,12.7898,0.6346,0.2593,9.7827,-0.1185,0.0452,0.2053,15.4,-6.3,-42,4.441339348,-1.52,-3.71,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,69100,2015-10-30 10:14:49:976,1446171289976.0 \n-0.2478,-0.0407,9.9084,0.8127,0.3235,9.7676,-0.4142,0,-0.1356,14.8,-7.3,-42.5,4.41463581,-1.89,-4.76,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,69202,2015-10-30 10:14:50:078,1446171290078.0 \n-0.0443,0.6776,8.8849,0.7777,0.2013,9.7737,0.0342,0.0354,-0.0122,14.5,-7.7,-43,4.341506514,-1.11,-4.73,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,69303,2015-10-30 10:14:50:179,1446171290179.0 \n0.0359,1.1839,8.7592,0.6866,0.4669,9.7714,0.2236,0.0696,-0.0586,14.3,-7.7,-43.5,4.361926867,-2.38,-4.19,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,69405,2015-10-30 10:14:50:281,1446171290281.0 \n0.2167,0.5698,11.0061,0.6212,0.7477,9.7584,0.3299,0.0733,-0.2065,14.6,-8,-43,4.448844263,-4.37,-3.64,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,69508,2015-10-30 10:14:50:384,1446171290384.0 \n-0.5327,-0.5195,11.5089,0.4592,0.6372,9.7751,-0.5559,0.1429,-0.3286,15,-8.3,-42.6,4.465075825,-4.85,-3.37,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,69610,2015-10-30 10:14:50:486,1446171290486.0 \n0.2658,0.3472,10.2304,0.4858,0.3123,9.7896,-0.2334,-0.1271,-0.0379,15.7,-7.8,-42.1,4.382347219,-2.52,-2.81,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,69711,2015-10-30 10:14:50:587,1446171290587.0 \n0.152,1.069,8.0349,0.4649,0.165,9.7942,-0.1991,-0.0208,-0.0428,15.8,-6.9,-42.2,4.386536009,-1.3,-2.68,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,69814,2015-10-30 10:14:50:690,1446171290690.0 \n-0.0575,1.1708,8.9316,0.4994,0.2099,9.7917,0.0574,0.1723,0.0904,15.9,-5.7,-42.3,4.437150557,-1.23,-2.92,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,69916,2015-10-30 10:14:50:792,1446171290792.0 \n-0.3579,0.3531,11.0289,0.4067,0.4275,9.7889,0.2053,0.0379,0.121,15.8,-5.4,-42.4,4.506614662,-1.82,-2.29,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,70018,2015-10-30 10:14:50:894,1446171290894.0 \n1.0092,-0.814,11.9938,0.4426,0.6658,9.774,-0.0672,-0.2407,0.171,15.9,-6.4,-42.3,4.536110726,-3.89,-2.59,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,70119,2015-10-30 10:14:50:995,1446171290995.0 \n0.4417,0.6225,8.3797,0.4542,0.5546,9.7804,0.0232,0.011,0.1063,15.9,-7.2,-42.2,4.448844263,-2.93,-2.91,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,70224,2015-10-30 10:14:51:100,1446171291100.0 \n-0.0802,0.3891,9.0046,0.5589,0.3705,9.7837,-0.3018,-0.1918,0.0733,15.8,-8,-42.5,4.375016836,-2.17,-3.27,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,70325,2015-10-30 10:14:51:201,1446171291201.0 \n-0.2969,1.2594,8.0924,0.5853,0.4055,9.7808,0.11,0.1332,0.1246,15.3,-7.9,-43.2,4.369780848,-2.37,-3.42,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,70428,2015-10-30 10:14:51:304,1446171291304.0 \n-0.3244,1.2151,9.5026,0.5288,0.5146,9.7788,0.0098,-0.0403,-0.0965,15,-7.9,-43.6,4.393691859,-3.01,-3.1,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,70532,2015-10-30 10:14:51:408,1446171291408.0 \n0.7087,0.6752,10.3789,0.5578,0.636,9.7701,-0.0037,-0.0428,-0.1796,14.8,-8.2,-43.9,4.423886055,-3.72,-3.27,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,70629,2015-10-30 10:14:51:505,1446171291505.0 \n-0.3448,-0.5016,11.4646,0.428,0.4135,9.7886,-0.4032,0.2981,-0.1869,15,-8.2,-44,4.386885075,-2.91,-2.86,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,70731,2015-10-30 10:14:51:607,1446171291607.0 \n-0.3448,-0.5016,11.4646,0.428,0.4135,9.7886,-0.4032,0.2981,-0.1869,15,-8.2,-44,4.386885075,-2.91,-2.86,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,70833,2015-10-30 10:14:51:709,1446171291709.0 \n-0.3196,0.9732,9.4104,0.5145,0.1647,9.7918,-0.0855,-0.0648,0.1979,15.4,-7.1,-43.3,4.362450465,-0.96,-3.01,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,70936,2015-10-30 10:14:51:812,1446171291812.0 \n0.0658,1.1612,9.1542,0.5653,0.1913,9.7885,0.204,-0.0892,0.3286,15.3,-6.9,-42.9,4.359483406,-0.86,-3.07,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,71038,2015-10-30 10:14:51:914,1446171291914.0 \n0.0443,0.5543,12.323,0.6288,0.4808,9.7747,0.1686,0.0635,0.2382,14.6,-7.4,-42.6,4.440990282,-2.81,-3.68,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,71139,2015-10-30 10:14:52:015,1446171292015.0 \n0.1161,-0.3543,10.8062,0.6859,0.6594,9.7604,-0.2859,-0.1503,0.292,14.3,-8.7,-42.5,4.377285764,-4.41,-3.75,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,71241,2015-10-30 10:14:52:117,1446171292117.0 \n0.7195,0.8607,8.4683,0.7672,0.5557,9.7608,-0.4007,0.0977,-0.1124,13.8,-10.4,-43.2,4.298222349,-3.25,-4.49,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,71344,2015-10-30 10:14:52:220,1446171292220.0 \n-0.1173,0.8332,8.7089,0.7028,0.2408,9.7785,-0.1515,-0.022,-0.0367,13.4,-10.9,-43.8,4.159817739,-1.41,-4.11,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,71446,2015-10-30 10:14:52:322,1446171292322.0 \n0.3603,1.4533,8.0936,0.682,0.3114,9.7779,0.1869,-0.0672,-0.0281,13.3,-10.4,-44,4.202752839,-1.44,-3.88,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,71547,2015-10-30 10:14:52:423,1446171292423.0 \n-0.0575,0.2825,11.2719,0.7934,0.4682,9.7633,0.3262,0.0709,-0.2431,13.3,-10.1,-43.5,4.259825105,-2.74,-4.65,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,71650,2015-10-30 10:14:52:526,1446171292526.0 \n-0.0215,-0.7135,11.2647,0.6836,0.6147,9.7635,-0.0024,-0.0379,-0.3348,13.4,-10.1,-43.2,4.306076331,-4,-4.59,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,71751,2015-10-30 10:14:52:627,1446171292627.0 \n0.753,0.8236,8.3091,0.4971,0.5232,9.7801,0.0403,-0.099,0.1649,13.9,-10,-43.3,4.266282824,-3.06,-2.91,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,71853,2015-10-30 10:14:52:729,1446171292729.0 \n0.3974,0.7111,9.6211,0.4475,0.2846,9.7923,0.0073,0.0623,0.1014,14.3,-9.7,-43.2,4.210781353,-1.68,-2.65,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,71955,2015-10-30 10:14:52:831,1446171292831.0 \n0.4609,1.4018,7.9416,0.3845,0.3152,9.794,0.099,0.0599,0.1002,14.9,-9.1,-43.3,4.283037984,-1.84,-2.25,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,72057,2015-10-30 10:14:52:933,1446171292933.0 \n-0.0012,0.5136,10.5333,0.4671,0.354,9.7891,0.16,-0.0721,0.0415,14.9,-9.1,-43.1,4.290891966,-1.9,-2.6,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,72160,2015-10-30 10:14:53:036,1446171293036.0 \n0.1281,0.4477,9.6486,0.4637,0.6462,9.7743,0.1258,0.2224,0.2138,14.7,-9.4,-43.4,4.353723819,-3.43,-3.02,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,72261,2015-10-30 10:14:53:137,1446171293137.0 \n-0.4621,0.1401,9.3589,0.3998,0.4559,9.7879,-0.099,-0.4288,0.182,14.6,-10.1,-43.6,4.268900817,-2.66,-2.34,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,72363,2015-10-30 10:14:53:239,1446171293239.0 \n-0.2095,0.3759,9.4272,0.6019,0.2532,9.7849,-0.2211,0.0281,0.0012,14.3,-10.4,-43.9,4.244291675,-1.87,-3.94,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,72466,2015-10-30 10:14:53:342,1446171293342.0 \n-0.5914,1.1875,8.3486,0.5268,0.1975,9.7905,0.0464,0.1747,-0.0037,14,-10.2,-43.9,4.203101905,-1.15,-3.08,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,72567,2015-10-30 10:14:53:443,1446171293443.0 \n-0.0515,1.1839,9.7624,0.4683,0.3168,9.7903,0.237,0.0464,-0.1038,13.9,-10,-44,4.221602395,-1.85,-2.74,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,72670,2015-10-30 10:14:53:546,1446171293546.0 \n-0.9577,0.7242,11.4431,0.4061,0.5767,9.7813,0.1405,-0.0049,-0.3457,14.2,-10.1,-43.5,4.26907535,-3.37,-2.38,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,72771,2015-10-30 10:14:53:647,1446171293647.0 \n0.0144,-0.0886,9.4128,0.4665,0.7246,9.7687,-0.2615,-0.0721,-0.4484,14.4,-10.4,-43.3,4.312883115,-4.42,-2.52,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,72873,2015-10-30 10:14:53:749,1446171293749.0 \n-0.0383,0.419,7.7824,0.3632,0.3945,9.792,-0.237,-0.0635,-0.0745,14.8,-10,-42.9,4.254414585,-2.5,-2.03,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,72975,2015-10-30 10:14:53:851,1446171293851.0 \n0.1808,1.063,7.9212,0.4334,0.2442,9.794,-0.0354,-0.0916,0.0281,15.1,-9.3,-42.8,4.272216943,-1.47,-2.41,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,73077,2015-10-30 10:14:53:953,1446171293953.0 \n-0.1832,1.1241,8.345,0.3886,0.1801,9.7973,0.1258,0.0403,0,15.3,-8.1,-42.9,4.304156468,-1.05,-2.27,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,73180,2015-10-30 10:14:54:056,1446171294056.0 \n-0.0994,0.5495,10.1766,0.4527,0.3596,9.7896,0.1772,-0.0929,0.1881,15.2,-7.7,-43,4.336619592,-1.83,-2.48,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,73281,2015-10-30 10:14:54:157,1446171294157.0 \n0.3316,0.674,8.7819,0.4271,0.6195,9.7777,-0.3384,-0.1552,0.1759,15,-8.2,-42.9,4.407305427,-3.62,-2.5,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,73384,2015-10-30 10:14:54:260,1446171294260.0 \n0.3591,0.6656,9.2859,0.603,0.3702,9.7811,-0.1234,-0.1124,0.2272,14.5,-9.2,-42.7,4.314279378,-2.16,-3.53,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,73486,2015-10-30 10:14:54:362,1446171294362.0 \n-0.0251,0.6117,8.6886,0.6486,0.2285,9.7825,-0.2517,0.1869,-0.0318,14.1,-9.7,-42.8,4.237310358,-1.73,-4.01,36.81404,-119.74804,249.34,336.7213758,4.12,12.903226,268.28,17 / 17,73588,2015-10-30 10:14:54:464,1446171294464.0 \n-0.2957,1.008,8.5461,0.5779,0.1598,9.7883,0.1148,0.2272,0.0379,13.7,-9.5,-43,4.246037004,-0.93,-3.38,36.814014,-119.74819,252.6,336.7213758,4.53,19.35484,269.22,17 / 17,73689,2015-10-30 10:14:54:565,1446171294565.0 \n-0.1413,0.8906,9.4571,0.4532,0.2636,9.7926,0.0941,0.0391,-0.0635,13.6,-9.2,-43.3,4.255112716,-1.54,-2.65,36.814014,-119.74819,252.6,336.7213758,4.53,19.35484,269.22,17 / 17,73793,2015-10-30 10:14:54:669,1446171294669.0 \n0.9086,0.668,10.7117,0.4819,0.4679,9.7836,0.3653,0.0428,0.1014,13.8,-9.3,-43.2,4.30363287,-2.74,-2.82,36.814014,-119.74819,252.6,336.7213758,4.53,19.35484,269.22,17 / 17,73894,2015-10-30 10:14:54:770,1446171294770.0 \n0.1951,-0.2011,10.1538,0.5203,0.5808,9.7756,-0.4484,0.0757,-0.2346,14,-9.8,-42.9,4.299793145,-3.82,-3.19,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,73996,2015-10-30 10:14:54:872,1446171294872.0 \n-0.267,-0.0814,9.59,0.524,0.3706,9.7856,0.0538,-0.0525,-0.0574,14,-10,-42.9,4.252494722,-2.56,-3.19,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,74098,2015-10-30 10:14:54:974,1446171294974.0 \n0.3208,1.1061,7.7464,0.3927,0.2822,9.7947,0.055,0.2456,0.0586,14.1,-9.8,-42.7,4.208163359,-1.57,-2.7,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,74199,2015-10-30 10:14:55:075,1446171295075.0 \n0.31,1.561,7.9416,0.2652,0.3763,9.7958,0.2346,0.0367,0.0476,14.5,-9.3,-42.6,4.271169745,-1.81,-1.61,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,74302,2015-10-30 10:14:55:178,1446171295178.0 \n0.0072,1.2342,9.5014,0.2671,0.438,9.7932,0.1503,-0.0195,-0.0183,14.8,-9.1,-42.2,4.296127954,-2.56,-1.56,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,74403,2015-10-30 10:14:55:279,1446171295279.0 \n-0.8236,-0.1951,10.5393,0.2676,0.7317,9.7757,0.1637,0.1894,0.2004,15.2,-9.9,-41.9,4.310090588,-4.28,-1.57,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,74505,2015-10-30 10:14:55:381,1446171295381.0 \n0.0706,0.5363,9.9635,0.5475,0.6441,9.7701,0.0147,-0.3067,0.3409,15,-10.6,-42.1,4.257381644,-3.77,-2.6,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,74608,2015-10-30 10:14:55:484,1446171295484.0 \n-0.1879,0.729,8.8597,0.6311,0.4014,9.7781,-0.2297,0.0782,-0.0843,14.2,-11.1,-42.4,4.203101905,-2.35,-3.69,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,74709,2015-10-30 10:14:55:585,1446171295585.0 \n-0.5866,1.2007,8.5605,0.5483,0.2559,9.788,-0.1332,0.1576,-0.0244,13.8,-11,-42.6,4.169067984,-1.5,-3.21,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,74811,2015-10-30 10:14:55:687,1446171295687.0 \n-0.0922,0.6333,9.8797,0.503,0.4264,9.7845,0.2126,0.0513,-0.1026,13.6,-10.4,-43.2,4.245862471,-2.49,-2.94,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,74913,2015-10-30 10:14:55:789,1446171295789.0 \n0.2753,0.3711,10.4543,0.5108,0.6522,9.7716,0.2089,-0.1759,-0.1356,13.8,-10.1,-43.2,4.276580266,-3.29,-3,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,75017,2015-10-30 10:14:55:893,1446171295893.0 \n0.2873,-0.4788,12.7168,0.4804,0.374,9.7877,-0.5962,0.1698,-0.4887,14,-10.2,-42.9,4.262792165,-2.92,-3.02,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,75117,2015-10-30 10:14:55:993,1446171295993.0 \n0.8535,0.1257,9.572,0.4924,0.2223,9.7918,-0.4227,0.1161,-0.055,14.1,-9.9,-42.7,4.229979975,-2.01,-3.04,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,75220,2015-10-30 10:14:56:096,1446171296096.0 \n0.0347,0.7949,8.2073,0.3994,0.1694,9.797,-0.0476,0.022,-0.0586,14.5,-8.9,-42.9,4.253716453,-0.99,-2.33,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,75322,2015-10-30 10:14:56:198,1446171296198.0 \n0.1365,1.1815,9.7767,0.3877,0.2623,9.7955,0.0342,0.0965,-0.099,14.9,-8.3,-42.3,4.320038965,-1.53,-2.27,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,75424,2015-10-30 10:14:56:300,1446171296300.0 \n-0.1712,0.7183,12.9167,0.4435,0.4507,9.7862,0.248,-0.2004,-0.022,15.1,-8.3,-42.3,4.340284784,-2.08,-2.23,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,75526,2015-10-30 10:14:56:402,1446171296402.0 \n-1.2342,-0.8811,12.3756,0.4303,0.6124,9.778,-0.3861,-0.2883,-0.1576,15.1,-8.9,-42.1,4.348836897,-3.58,-2.52,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,75627,2015-10-30 10:14:56:503,1446171296503.0 \n-0.0491,0.5483,8.3653,0.6649,0.4328,9.7745,-0.369,-0.0623,-0.1368,14.8,-9.2,-42.6,4.342030113,-2.9,-3.6,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,75729,2015-10-30 10:14:56:605,1446171296605.0 \n-1.0403,0.3543,9.3111,0.6307,0.2699,9.7826,-0.0757,0.0098,-0.0208,14.4,-9,-42.9,4.274311338,-1.58,-3.69,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,75831,2015-10-30 10:14:56:707,1446171296707.0 \n-0.3041,1.1384,8.169,0.5299,0.3642,9.7855,0.1478,0.0806,0.0403,14,-8.5,-43.3,4.330161874,-1.91,-3.21,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,75934,2015-10-30 10:14:56:810,1446171296810.0 \n-0.1245,0.1772,11.7196,0.4888,0.5052,9.7814,0.1857,-0.0611,-0.2089,14.1,-8.3,-43.8,4.370304447,-2.95,-2.86,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,76036,2015-10-30 10:14:56:912,1446171296912.0 \n1.3659,-0.0347,9.4248,0.4739,0.6286,9.775,0.1112,0.0415,-0.1185,14.3,-8.6,-43.8,4.346218903,-3.73,-2.73,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,76138,2015-10-30 10:14:57:014,1446171297014.0 \n0.9349,0.5303,7.0856,0.3607,0.3294,9.7945,0.2395,0.0696,0.1417,14.6,-8.3,-43.2,4.32632215,-1.72,-2.08,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,76239,2015-10-30 10:14:57:115,1446171297115.0 \n0.1018,0.3926,8.9842,0.4161,0.076,9.7975,-0.066,0.055,0.0892,14.8,-7.8,-43.3,4.294033559,-0.63,-2.6,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,76342,2015-10-30 10:14:57:218,1446171297218.0 \n0.2167,0.9218,9.0046,0.5054,0.0666,9.7934,0.1344,-0.0012,0.0745,14.9,-6.6,-43.7,4.327194814,-0.07,-2.82,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,76444,2015-10-30 10:14:57:320,1446171297320.0 \n-0.0563,0.4286,10.8122,0.5017,0.1481,9.7927,0.0904,-0.0208,-0.0073,14.7,-6.3,-44.5,4.411494217,-0.87,-2.93,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,76545,2015-10-30 10:14:57:421,1446171297421.0 \n-0.0922,0.8272,9.6558,0.5224,0.4569,9.7821,0.3873,-0.0354,0.1307,14.5,-6.5,-44.8,4.489510435,-2.67,-3.06,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,76647,2015-10-30 10:14:57:523,1446171297523.0 \n-0.1532,-0.0431,10.2364,0.7049,0.431,9.7718,0.2248,-0.0183,0.226,14.2,-7.3,-45,4.42598045,-2.52,-4.13,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,76750,2015-10-30 10:14:57:626,1446171297626.0 \n-0.6081,0.2933,8.2468,0.7002,0.4809,9.7698,-0.0293,0.0122,0.0269,14,-7.8,-45.2,4.391422931,-2.97,-4.12,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,76852,2015-10-30 10:14:57:728,1446171297728.0 \n-0.2131,0.7242,8.4695,0.7012,0.4056,9.7731,0.0183,0,0.0195,13.7,-8.2,-45,4.366813788,-2.33,-4.19,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,76954,2015-10-30 10:14:57:830,1446171297830.0 \n-0.0431,1.0774,8.1008,0.6137,0.4493,9.7771,-0.0574,0.1002,-0.0977,13.5,-8.3,-44.9,4.373271507,-2.64,-3.76,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,77055,2015-10-30 10:14:57:931,1446171297931.0 \n0.1317,0.6895,12.7767,0.6305,0.515,9.7728,0.1307,-0.1686,-0.1368,13.6,-8.4,-44.7,4.38775774,-3.01,-3.69,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,77157,2015-10-30 10:14:58:033,1446171298033.0 \n1.0702,-0.2873,10.5429,0.6261,0.7059,9.7612,-0.639,0.0098,-0.4129,13.7,-8.5,-44.4,4.429296576,-4.13,-3.67,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,77259,2015-10-30 10:14:58:135,1446171298135.0 \n0.4633,0.1365,8.837,0.4545,0.3628,9.7894,-0.391,-0.1796,-0.1319,14.1,-7.9,-44,4.332779868,-2.12,-2.66,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,77362,2015-10-30 10:14:58:238,1446171298238.0 \n0.0515,1.1899,7.8458,0.5298,0.1492,9.7912,-0.0354,0.0513,-0.0452,14.2,-6.9,-43.6,4.342553712,-0.87,-3.1,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,77464,2015-10-30 10:14:58:340,1446171298340.0 \n-0.0718,1.0606,8.5258,0.5337,0.1761,9.7905,0.1222,-0.0415,-0.0403,14.5,-6,-43.6,4.420220864,-1.03,-3.12,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,77566,2015-10-30 10:14:58:442,1446171298442.0 \n-0.3891,0.3519,12.3313,0.4644,0.2856,9.7915,0.0794,-0.1283,0.1442,14.6,-5.7,-43.1,4.439244952,-1.67,-2.72,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,77667,2015-10-30 10:14:58:543,1446171298543.0 \n1.002,0.1592,9.1746,0.5429,0.4974,9.779,-0.3567,-0.5889,0.1405,14.6,-6.2,-43.3,4.485321645,-2.73,-3.02,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,77769,2015-10-30 10:14:58:645,1446171298645.0 \n1.1756,1.0463,8.0469,0.7981,0.3365,9.7683,0.1552,0.0379,0.3054,14.2,-7.1,-43.3,4.403814769,-1.97,-4.67,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,77871,2015-10-30 10:14:58:747,1446171298747.0 \n-0.2274,-0.1999,8.819,0.8301,0.227,9.7688,-0.0342,-0.055,-0.0269,13.8,-7.6,-43.5,4.333827066,-1.41,-4.77,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,77973,2015-10-30 10:14:58:849,1446171298849.0 \n0.0419,0.9852,7.3454,0.8174,0.3655,9.7657,0.2382,-0.033,-0.0244,13.2,-7.6,-43.7,4.34482264,-2.14,-4.78,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,78076,2015-10-30 10:14:58:952,1446171298952.0 \n-0.3364,0.7602,9.918,0.7932,0.5213,9.7606,0.0501,0.0269,-0.1686,13.1,-7.7,-43.9,4.368733651,-2.76,-4.73,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,78177,2015-10-30 10:14:59:053,1446171299053.0 \n1.063,-0.1101,10.2256,0.8872,0.7054,9.7409,0.215,-0.1112,-0.193,13.1,-7.8,-43.9,4.410097954,-3.71,-4.94,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,78279,2015-10-30 10:14:59:155,1446171299155.0 \n-0.1712,-0.1377,10.9223,0.5996,0.4981,9.7756,0.1283,0.2639,0.066,13.3,-7.8,-43.6,4.376238566,-3.06,-4.37,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,78382,2015-10-30 10:14:59:258,1446171299258.0 \n0.31,-0.1999,10.343,0.6896,0.2868,9.7782,-0.0354,0.0281,0.204,13.8,-7.4,-43.4,4.393517326,-1.93,-3.92,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,78484,2015-10-30 10:14:59:360,1446171299360.0 \n0.5207,1.1564,8.685,0.6917,0.2811,9.7782,-0.0024,-0.0428,0.1674,14.2,-6.8,-43.3,4.383743482,-1.64,-4.05,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,78586,2015-10-30 10:14:59:462,1446171299462.0 \n0.4669,1.3862,9.5996,0.6951,0.4423,9.772,0.1674,0.0721,0.055,14.2,-6.9,-43.1,4.408701691,-2.25,-4.14,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,78688,2015-10-30 10:14:59:564,1446171299564.0 \n-0.1975,0.674,9.3506,0.6581,0.6873,9.7604,0.54,0.3311,0.2468,14,-7.5,-43,4.477118597,-4.02,-3.86,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,78790,2015-10-30 10:14:59:666,1446171299666.0 \n-0.0479,-0.2646,11.8716,0.6608,0.7965,9.7519,-0.2456,-0.226,0.1625,14,-8.4,-42.7,4.459665305,-5.02,-3.51,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,78892,2015-10-30 10:14:59:768,1446171299768.0 \n0.8691,0.9553,8.1475,0.8288,0.7994,9.7388,-0.2529,-0.0684,-0.0367,13.8,-9.3,-42.6,4.405560098,-4.68,-4.86,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,78993,2015-10-30 10:14:59:869,1446171299869.0 \n-0.018,0.0922,9.3817,0.7406,0.2835,9.7745,-0.2285,0.2602,-0.0586,13.5,-9.4,-42.6,4.3048546,-2.04,-4.58,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,79096,2015-10-30 10:14:59:972,1446171299972.0 \n-0.7458,0.7721,9.0046,0.2825,0.1501,9.8014,0.0501,0.5437,0.1625,13.5,-8.7,-42.7,4.23923022,-1.16,-2.55,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,79197,2015-10-30 10:15:00:073,1446171300073.0 \n0.4298,0.4609,11.309,0.1617,0.074,9.805,-0.044,-0.2944,-0.1136,14.4,-7.7,-42.3,4.230503574,-0.43,-0.94,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,79300,2015-10-30 10:15:00:176,1446171300176.0 \n-0.1389,-0.6033,10.7679,0.213,0.3654,9.7975,-0.4398,0.3286,-0.4276,15,-7.6,-42.1,4.327718413,-2.14,-1.25,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,79402,2015-10-30 10:15:00:278,1446171300278.0 \n0.6668,0.4429,9.0573,-0.0908,0.1764,9.8046,0.066,0.2786,0.1087,15.7,-7.5,-41.6,4.332081736,-1.03,0.53,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,79504,2015-10-30 10:15:00:380,1446171300380.0 \n0.4741,1.4162,7.5633,-0.2911,0.3017,9.7977,-0.0037,0.0513,0.1454,16.5,-7.6,-40.9,4.309741522,-1.76,1.7,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,79605,2015-10-30 10:15:00:481,1446171300481.0 \n-0.4729,1.2809,8.8178,-0.3854,0.3285,9.7936,0.1368,-0.0195,0.0122,17.2,-7.5,-40.5,4.361926867,-1.92,2.25,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,79707,2015-10-30 10:15:00:583,1446171300583.0 \n-1.1289,0.9433,9.9575,-0.3368,0.5484,9.7855,0.1881,0.1772,0.1918,17.6,-7.8,-40.2,4.380950955,-3.21,1.97,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,79810,2015-10-30 10:15:00:686,1446171300686.0 \n-0.5962,1.5407,9.9359,-0.1773,0.788,9.7733,0.3335,-0.2468,0.3567,17.7,-8.4,-40.2,4.417777403,-4.01,1.47,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,79912,2015-10-30 10:15:00:788,1446171300788.0 \n-1.3791,0.1556,10.0257,0.0054,0.3642,9.7999,-0.2199,0.11,0.3213,17.1,-9,-40.4,4.297000618,-2.13,-0.03,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,80013,2015-10-30 10:15:00:889,1446171300889.0 \n-0.7781,0.5399,8.9878,0.1362,0.3293,9.8002,-0.3922,0.2224,-0.0367,16.5,-9.3,-40.3,4.328067479,-2.61,-1.09,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,80115,2015-10-30 10:15:00:991,1446171300991.0 \n-0.7841,0.929,8.5557,0.0587,0.339,9.8006,0.1112,-0.0464,-0.0159,15.9,-9.2,-40.8,4.275707602,-1.98,-0.34,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,80218,2015-10-30 10:15:01:094,1446171301094.0 \n-0.6033,1.3958,8.7628,-0.0169,0.5114,9.7933,0.1796,-0.1014,-0.1918,15.9,-9.2,-41,4.292637295,-2.66,0.17,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,80319,2015-10-30 10:15:01:195,1446171301195.0 \n-0.8547,0.6249,11.9973,0.1315,0.7147,9.7797,0.4972,-0.2786,-0.1613,16.1,-9.3,-41.2,4.364370328,-4.18,-0.77,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,80422,2015-10-30 10:15:01:298,1446171301298.0 \n-0.8056,-0.7386,11.7699,0.2034,0.8362,9.7688,-0.0098,0.3335,-0.1051,15.8,-9.8,-41,4.344299041,-4.89,-1.19,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,80524,2015-10-30 10:15:01:400,1446171301400.0 \n-0.5076,0.5435,9.4523,-0.101,0.6421,9.7851,-0.2969,0.1429,-0.16,15.9,-9.7,-41,4.27500947,-3.75,0.59,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,80626,2015-10-30 10:15:01:502,1446171301502.0 \n-0.4226,1.482,7.0868,-0.307,0.532,9.7874,-0.033,-0.0501,-0.0501,16.3,-9.1,-41,4.279896392,-3.05,1.84,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,80727,2015-10-30 10:15:01:603,1446171301603.0 \n-0.7003,0.759,8.8813,-0.2696,0.581,9.7857,-0.0208,-0.9566,-0.0195,17.3,-8.2,-41.1,4.376936698,-3.4,1.58,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,80829,2015-10-30 10:15:01:705,1446171301705.0 \n-0.9433,0.1915,9.7923,0.0112,0.6013,9.7882,0.077,0.2187,0.4252,17.3,-7.7,-40.9,4.402593038,-3.39,-0.57,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,80932,2015-10-30 10:15:01:808,1446171301808.0 \n-0.3771,-1.233,13.647,0.1071,0.4165,9.7972,-0.1185,-0.5131,0.0806,16.9,-8,-40.8,4.367860986,-2.43,-0.63,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,81034,2015-10-30 10:15:01:910,1446171301910.0 \n0.31,0.9732,8.254,0.1239,0.3547,9.7995,0.1881,-0.2187,0.2456,16.3,-8.1,-40.7,4.317770037,-1.69,-0.43,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,81136,2015-10-30 10:15:02:012,1446171302012.0 \n-0.8296,0.3831,8.7257,-0.0608,0.0515,9.8063,-0.5327,0.3836,-0.1381,15.9,-8.4,-41.1,4.278849194,-0.73,-0.21,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,81238,2015-10-30 10:15:02:114,1446171302114.0 \n-1.0499,0.7075,7.7943,-0.1338,0.1226,9.805,0.1478,0.204,0.1197,15.9,-8.2,-41.2,4.257556177,-0.47,0.47,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,81340,2015-10-30 10:15:02:216,1446171302216.0 \n-0.899,0.7697,9.4056,-0.1356,0.178,9.8041,0.0929,-0.4264,-0.1491,16.2,-8.2,-41.4,4.262268566,-0.9,1.09,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,81442,2015-10-30 10:15:02:318,1446171302318.0 \n-0.0994,0.5614,10.4435,0.1029,0.395,9.7982,0.4215,-0.0061,-0.0232,16.4,-8.2,-41.4,4.343600909,-2.31,-0.6,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,81544,2015-10-30 10:15:02:420,1446171302420.0 \n-0.8871,-0.5327,10.4423,-0.0513,0.3064,9.8017,-0.0195,0.3335,-0.2162,16.3,-8.4,-41.4,4.293859026,-1.16,-0.17,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,81645,2015-10-30 10:15:02:521,1446171302521.0 \n-0.9218,-0.1053,10.1658,-0.0687,0.1156,9.8057,-0.5388,0.2712,-0.2749,16.3,-8.1,-41.5,4.266282824,-0.68,0.4,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,81747,2015-10-30 10:15:02:623,1446171302623.0 \n-0.4058,0.9014,8.1379,-0.1252,0.1414,9.8048,0.0806,-0.0831,-0.0281,16.7,-7.4,-41.4,4.341681047,-0.83,0.73,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,81850,2015-10-30 10:15:02:726,1446171302726.0 \n-0.5064,0.7997,10.1514,-0.1015,0.2181,9.8037,0.0415,0.0183,-0.0232,17.1,-7,-41.3,4.360705136,-1.27,0.59,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,81952,2015-10-30 10:15:02:828,1446171302828.0 \n-3.699,-0.1353,10.6662,0.1144,0.6751,9.7827,0.6304,-1.1912,-0.1307,17.3,-7.1,-41.3,4.436452426,-3.24,0.75,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,82054,2015-10-30 10:15:02:930,1446171302930.0 \n-2.4912,-1.9261,10.6039,0.2534,0.54,9.7885,-0.2089,0.0098,0.4924,16.9,-7.7,-41.3,4.403814769,-3.16,-1.48,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,82155,2015-10-30 10:15:03:031,1446171303031.0 \n0.8942,0.9493,10.4818,0.4513,0.1374,9.7953,0.1051,0.1772,0.6121,16.3,-8.1,-41.7,4.319689899,-0.8,-2.64,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,82258,2015-10-30 10:15:03:134,1446171303134.0 \n-0.3591,1.3719,7.9452,-0.3598,0.7657,9.7701,0.9835,0.27,-0.0684,15.8,-9.1,-41.4,4.335746928,-4.48,2.11,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,82360,2015-10-30 10:15:03:236,1446171303236.0 \n-0.8882,2.9904,8.1403,-0.2057,2.0201,9.5941,0.6976,0.0073,-0.1087,16.8,-12.6,-40,4.445702671,-11.89,1.23,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,82488,2015-10-30 10:15:03:364,1446171303364.0 \n-0.7721,2.8575,11.4036,-0.0447,2.4884,9.4856,0.7318,-0.4704,-0.0782,17.2,-13.8,-39.2,4.49998241,-14.7,0.27,36.814014,-119.74819,252.6,336.5554464,4.53,19.35484,269.22,17 / 17,82563,2015-10-30 10:15:03:439,1446171303439.0 \n0.5303,2.5007,11.3485,0.146,2.7758,9.4045,-0.4105,-0.033,-0.3604,17.1,-15.7,-38.4,4.466472089,-16.79,-0.97,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,82666,2015-10-30 10:15:03:542,1446171303542.0 \n0.8547,3.0227,7.2676,0.1961,2.7418,9.4135,-0.1014,-0.2028,0.0098,16.6,-17.3,-38.2,4.397182517,-16.24,-1.19,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,82768,2015-10-30 10:15:03:644,1446171303644.0 \n-0.0443,2.9999,5.545,0.012,2.2397,9.5475,-0.6194,-0.204,-0.0061,16.5,-17.2,-38.2,4.306948995,-13.93,-0.26,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,82870,2015-10-30 10:15:03:746,1446171303746.0 \n-0.4154,2.1201,7.3957,0.0351,1.4785,9.6945,-0.9297,0.1161,-0.1026,16.6,-15.4,-38.9,4.23085264,-8.67,-0.21,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,82972,2015-10-30 10:15:03:848,1446171303848.0 \n-1.4557,0.4166,11.7795,-0.1916,0.4099,9.7962,-0.9615,0.1393,-0.044,17,-12.2,-39.3,4.205545366,-4.13,0.78,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,83074,2015-10-30 10:15:03:950,1446171303950.0 \n-0.0862,0.7901,9.4631,0.2162,0.3744,9.7971,-0.215,-0.4899,0.1356,17.1,-9.5,-40.4,4.302236606,-2.06,-0.57,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,83176,2015-10-30 10:15:04:052,1446171304052.0 \n-0.2011,0.4645,8.7879,0.4203,0.0322,9.7976,-0.3555,-0.1319,0.1979,16.8,-7.6,-41.1,4.29769875,0.37,-2.49,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,83277,2015-10-30 10:15:04:153,1446171304153.0 \n-0.7075,-0.0192,8.667,0.5075,0.1859,9.7917,-0.2957,0.1283,-0.2309,15.7,-7.1,-42,4.382347219,-1.09,-2.97,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,83380,2015-10-30 10:15:04:256,1446171304256.0 \n-1.0283,0.486,8.4276,0.5041,0.2149,9.7913,0.1246,0.2407,-0.066,15.1,-7.3,-42.2,4.370653513,-1.26,-2.95,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,83483,2015-10-30 10:15:04:359,1446171304359.0 \n-0.1221,1.5131,8.5234,0.3647,0.4839,9.7879,0.2529,-0.0122,-0.0684,15,-7.9,-41.9,4.34901143,-2.34,-2.16,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,83584,2015-10-30 10:15:04:460,1446171304460.0 \n-0.2969,0.1317,11.1785,0.4074,0.4937,9.7857,0.044,-0.0513,-0.336,15.3,-8.2,-41.6,4.372922441,-2.89,-2.38,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,83686,2015-10-30 10:15:04:562,1446171304562.0 \n0.1425,-0.7374,12.0811,0.5411,0.4005,9.7835,-0.2993,-0.0305,-0.2101,15.5,-8,-41.9,4.379903758,-2.34,-3.17,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,83788,2015-10-30 10:15:04:664,1446171304664.0 \n-0.1724,0.4298,9.1016,0.4024,0.1788,9.7968,-0.4264,0.2138,-0.1234,15.4,-7.5,-42.2,4.399625978,-2.05,-2.84,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,83890,2015-10-30 10:15:04:766,1446171304766.0 \n-1.1516,0.4764,8.8969,0.0195,0.0185,9.8066,-0.1197,0.6329,0.011,15.9,-6.3,-42,4.359657939,-0.11,-0.11,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,83993,2015-10-30 10:15:04:869,1446171304869.0 \n0.5076,1.4401,8.0302,-0.2027,0.1827,9.8029,0.2676,0.2712,0.0709,16.5,-5.8,-41.7,4.387059608,-0.6,0.72,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,84096,2015-10-30 10:15:04:972,1446171304972.0 \n-1.5634,-0.243,7.3957,-0.0486,0.3113,9.8016,0.3983,-0.6426,0.8137,17.4,-5.7,-41.3,4.439943084,-1.82,0.28,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,84195,2015-10-30 10:15:05:071,1446171305071.0 \n1.5778,0.1113,11.376,0.4129,0.198,9.796,-0.1991,-0.0892,0.6316,17.2,-6.6,-41.4,4.419697265,-1.84,-2.73,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,84297,2015-10-30 10:15:05:173,1446171305173.0 \n-1.506,-0.3543,9.5565,0.3509,0.3646,9.7936,0.8369,-0.1979,0.8381,16.7,-7.4,-41.7,4.373969638,-0.78,-1.75,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,84399,2015-10-30 10:15:05:275,1446171305275.0 \n-0.8583,0.8775,8.3019,0.3416,0.5193,9.7869,-0.1014,0.16,-0.1491,15.8,-9.2,-41.7,4.341157448,-3.04,-2,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,84502,2015-10-30 10:15:05:378,1446171305378.0 \n-0.3196,1.8244,7.586,0.263,0.6493,9.7816,0.1442,0.1491,-0.0831,15.8,-10.3,-41.4,4.309217923,-3.8,-1.54,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,84604,2015-10-30 10:15:05:480,1446171305480.0 \n-0.3986,1.2414,10.2197,0.252,0.7116,9.7775,0.0134,-0.088,-0.2395,15.8,-11.1,-41.2,4.265584692,-4.05,-1.28,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,84706,2015-10-30 10:15:05:582,1446171305582.0 \n-0.2155,0.3855,11.6765,0.3661,0.7641,9.77,-0.0525,-0.0611,-0.4019,15.9,-11,-41.5,4.287052242,-4.34,-2.06,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,84808,2015-10-30 10:15:05:684,1446171305684.0 \n-0.3915,-0.0144,8.3139,0.2728,0.5876,9.7852,0.1955,0.4239,0.077,16.2,-10.2,-41.3,4.297175151,-3.44,-1.6,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,84909,2015-10-30 10:15:05:785,1446171305785.0 \n-0.5447,0.2263,10.6003,0.024,0.4272,9.7973,-0.4948,0.0342,-0.2187,16.7,-9.4,-41.3,4.323529623,-2.77,-0.17,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,85012,2015-10-30 10:15:05:888,1446171305888.0 \n-0.4812,1.5048,8.8765,0.07,0.7292,9.7792,0.303,-0.0843,0.1051,17.3,-8.4,-40.8,4.434183498,-4.26,-0.41,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,85114,2015-10-30 10:15:05:990,1446171305990.0 \n-0.2729,1.9716,8.4013,0.1652,1.122,9.7409,0.1943,-0.292,0.1087,17.5,-8.7,-40.7,4.465075825,-6.04,-0.61,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,85215,2015-10-30 10:15:06:091,1446171306091.0 \n-0.6524,1.4928,10.5153,0.4824,1.4942,9.6801,0.336,-0.3213,0.2358,16.8,-10.2,-40.9,4.485321645,-7.94,-2.59,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,85318,2015-10-30 10:15:06:194,1446171306194.0 \n-0.0048,0.5327,13.1047,0.715,1.2871,9.6955,-0.5241,-0.2712,0.171,16.3,-11.7,-41.3,4.393691859,-8.23,-3.84,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,85420,2015-10-30 10:15:06:296,1446171306296.0 \n1.1983,2.3774,7.9296,0.6221,1.221,9.7104,-0.5962,0.2651,-0.1576,15.3,-12.8,-41.3,4.307647127,-7.58,-3.98,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,85522,2015-10-30 10:15:06:398,1446171306398.0 \n-0.0778,1.6831,7.7776,0.572,1.0435,9.7342,-0.055,0.1478,-0.2016,14.7,-13.1,-41.4,4.249876729,-6.11,-3.36,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,85624,2015-10-30 10:15:06:500,1446171306500.0 \n0.0694,2.2242,7.7895,0.5423,1.1879,9.7193,0.2847,-0.1161,-0.0648,14.7,-12.6,-41.4,4.2762312,-6.96,-3.19,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,85725,2015-10-30 10:15:06:601,1446171306601.0 \n-0.2897,0.7661,12.5313,0.7088,1.2143,9.7053,0.1368,-0.1955,-0.3445,14.9,-12.4,-41.3,4.332954401,-6.99,-3.81,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,85827,2015-10-30 10:15:06:703,1446171306703.0 \n-0.8332,-0.7003,13.1083,0.6074,1.0803,9.728,-0.628,0.2639,-0.5583,14.9,-12,-41.4,4.306948995,-6.32,-3.57,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,85929,2015-10-30 10:15:06:805,1446171306805.0 \n0.9182,1.4844,7.0749,0.3912,0.9602,9.7517,0.2505,0.1332,0.1906,15.3,-11.2,-41.3,4.306076331,-5.36,-2.38,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,86032,2015-10-30 10:15:06:908,1446171306908.0 \n0.079,1.5443,7.78,0.27,0.5904,9.7851,-0.0024,0.1637,0.1319,15.8,-9.5,-41.7,4.352327556,-3.43,-1.74,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,86133,2015-10-30 10:15:07:009,1446171307009.0 \n-0.3675,1.4724,8.4886,0.2603,0.641,9.7822,0.1319,0.0403,0.1319,16.3,-8.7,-41.5,4.351803957,-3.55,-1.66,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,86235,2015-10-30 10:15:07:111,1446171307111.0 \n-0.729,1.0606,9.8893,0.1829,0.7211,9.7784,0.0305,0.1148,-0.1112,16.6,-8.3,-41.4,4.438721354,-4.22,-1.07,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,86337,2015-10-30 10:15:07:213,1446171307213.0 \n-0.5435,1.2677,10.2615,0.1223,0.9173,9.7629,0.4129,-0.1625,0.3164,16.8,-8.5,-41,4.442561078,-4.49,-0.37,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,86440,2015-10-30 10:15:07:316,1446171307316.0 \n-0.6572,0.1125,9.5122,0.4131,0.7221,9.7713,0.3457,0.0134,0.4178,16.7,-8.9,-40.9,4.401545841,-4.22,-2.42,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,86542,2015-10-30 10:15:07:418,1446171307418.0 \n-0.5207,0.2274,8.9555,0.3502,0.6043,9.7817,-0.5571,0.0745,-0.2382,16.6,-9.1,-40.9,4.411145151,-4.56,-2.18,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,86644,2015-10-30 10:15:07:520,1446171307520.0 \n-0.9361,0.6991,8.3725,0.4409,0.4978,9.7841,0.0733,0.033,-0.0794,16.1,-8.7,-40.9,4.340982916,-2.91,-2.58,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,86746,2015-10-30 10:15:07:622,1446171307622.0 \n-0.4238,0.4992,11.1749,0.5166,0.6548,9.7711,0.0538,-0.2773,-0.2602,15.8,-8.2,-41.4,4.427900312,-3.83,-3.03,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,86847,2015-10-30 10:15:07:723,1446171307723.0 \n0.2646,0.6931,11.303,0.6659,1.0042,9.7323,0.43,-0.099,-0.1515,15.5,-8.1,-41.4,4.481307387,-5.13,-3.87,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,86950,2015-10-30 10:15:07:826,1446171307826.0 \n-0.2741,-0.1556,11.5724,0.6124,0.9281,9.7434,-0.3653,0.1038,-0.4997,15,-8.5,-42,4.484274447,-5.43,-3.6,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,87051,2015-10-30 10:15:07:927,1446171307927.0 \n1.0104,0.814,8.497,0.3651,0.564,9.7836,-0.5852,-0.0367,-0.1429,15.1,-8.1,-41.9,4.419348199,-4.12,-2.18,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,87154,2015-10-30 10:15:08:030,1446171308030.0 \n-0.0718,1.2306,7.9296,0.282,0.2681,9.7989,0.0977,-0.0024,-0.0024,15.8,-6.5,-41.7,4.436801491,-1.57,-1.65,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,87255,2015-10-30 10:15:08:131,1446171308131.0 \n-0.1269,1.4341,8.0433,0.2248,0.3493,9.7978,0.0586,0.1185,-0.0073,16.4,-5.2,-41.5,4.50888359,-2.08,-1.5,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,87357,2015-10-30 10:15:08:233,1446171308233.0 \n-0.5076,0.3388,11.6215,0.2174,0.4305,9.7948,0.0745,-0.1136,0.0086,16.8,-4.4,-41.2,4.589343268,-2.52,-1.27,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,87461,2015-10-30 10:15:08:337,1446171308337.0 \n0.3268,0.4489,9.0525,0.3535,0.6719,9.7772,-0.1796,-0.2627,0.2993,16.8,-4.7,-41.2,4.566479455,-3.26,-1.84,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,87562,2015-10-30 10:15:08:438,1446171308438.0 \n0.4345,1.1516,7.5932,0.3622,0.6381,9.7792,0.259,0.1735,0.3812,16.5,-5.5,-41.3,4.585329011,-3.73,-2.12,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,87664,2015-10-30 10:15:08:540,1446171308540.0 \n-1.142,0.2143,9.0513,0.3012,0.4073,9.7936,-0.4606,0.171,-0.2285,16,-6.3,-41.8,4.493001093,-2.89,-2.11,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,87765,2015-10-30 10:15:08:641,1446171308641.0 \n-0.893,0.996,7.9751,0.2839,0.3949,9.7946,0.2089,0.0367,0.0391,16.2,-6.5,-42.1,4.466297556,-2.31,-1.66,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,87868,2015-10-30 10:15:08:744,1446171308744.0 \n-0.4896,0.8859,9.5672,0.255,0.5177,9.7897,0.0073,-0.3274,-0.2651,16.3,-6.6,-41.8,4.438721354,-3.03,-1.49,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,87969,2015-10-30 10:15:08:845,1446171308845.0 \n0.3244,0.4405,9.2871,0.2472,0.8304,9.7683,0.5339,0.3299,0.1222,16.5,-6.6,-41.6,4.523369822,-4.86,-1.45,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,88071,2015-10-30 10:15:08:947,1446171308947.0 \n-1.0953,-1.2917,12.4295,0.0726,0.678,9.7829,-0.0929,0.3665,-0.0892,16.6,-7.1,-41.6,4.501378674,-4.35,-1.17,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,88174,2015-10-30 10:15:09:050,1446171309050.0 \n-0.1353,0.6273,9.6007,0.0238,0.6568,9.7846,-0.3213,-0.0208,-0.0269,17,-7.5,-41.3,4.469264616,-3.84,-0.14,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,88276,2015-10-30 10:15:09:152,1446171309152.0 \n0.2454,1.2019,8.2337,0.0542,0.3968,9.7985,-0.1808,-0.0257,-0.0257,17.4,-7.5,-41.2,4.429296576,-2.82,-0.14,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,88377,2015-10-30 10:15:09:253,1446171309253.0 \n0.1951,1.3431,9.2416,0.0456,0.3044,9.8018,0.0452,-0.0672,0.0134,17.5,-6.7,-40.8,4.40747996,-1.78,-0.27,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,88479,2015-10-30 10:15:09:355,1446171309355.0 \n-0.5722,0.8487,10.1526,0.1111,0.4578,9.7953,0.3702,-0.4386,0.1979,17.5,-6.2,-41,4.472755274,-2.17,-0.26,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,88581,2015-10-30 10:15:09:457,1446171309457.0 \n0.2119,0.6548,7.671,0.3476,0.9057,9.7585,-0.4618,-0.4545,0.1576,16.8,-6.2,-40.8,4.575031568,-4.89,-1.88,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,88684,2015-10-30 10:15:09:560,1446171309560.0 \n-1.7657,-0.3208,10.568,0.4366,0.5394,9.7821,-0.1295,0.1784,0.2321,16.3,-6.9,-41.2,4.463155963,-3.42,-2.87,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,88786,2015-10-30 10:15:09:662,1446171309662.0 \n-1.2031,-0.0958,10.3753,0.6523,0.202,9.7828,-0.6206,-0.0159,-0.1784,15.3,-7.7,-41.6,4.365417525,-2.2,-3.83,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,88887,2015-10-30 10:15:09:763,1446171309763.0 \n-0.8308,0.8392,8.9854,0.6463,0.2241,9.7828,0.1234,0.1649,-0.0122,14.7,-7.2,-41.9,4.383045351,-1.31,-3.78,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,88990,2015-10-30 10:15:09:866,1446171309866.0 \n-0.2179,1.1133,9.5122,0.5894,0.4146,9.7801,0.1637,-0.0208,-0.0672,14.5,-7.1,-42.2,4.410621553,-2.14,-3.52,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,89092,2015-10-30 10:15:09:968,1446171309968.0 \n0.1185,0.4417,11.1522,0.6832,0.6616,9.7604,0.2871,-0.0623,-0.1051,14.3,-7.1,-42.1,4.445877204,-3.33,-3.99,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,89196,2015-10-30 10:15:10:072,1446171310072.0 \n-0.261,-0.4836,12.1183,0.6716,0.5621,9.7675,-0.6145,0.5327,-0.5046,14.4,-7.8,-42.4,4.389328536,-3.29,-3.93,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,89296,2015-10-30 10:15:10:172,1446171310172.0 \n0.4884,0.9493,7.5238,0.3416,0.4138,9.792,0.0929,0.1442,-0.033,14.6,-7.6,-42.1,4.351803957,-2.48,-1.98,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,89397,2015-10-30 10:15:10:273,1446171310273.0 \n0.0132,0.5818,8.576,0.177,0.1512,9.8039,-0.2236,0.65,-0.3213,15.2,-6.7,-41.9,4.328940144,-0.88,-1.03,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,89499,2015-10-30 10:15:10:375,1446171310375.0 \n-0.6357,0.7781,9.4296,-0.0495,-0.0018,9.8065,-0.1368,-0.369,-0.0831,16.5,-4.9,-41.3,4.422664325,0.01,0.29,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,89601,2015-10-30 10:15:10:477,1446171310477.0 \n-0.559,0.4322,10.3286,0.1233,0.0053,9.8059,0.2114,-0.0379,0.1723,17,-3.9,-41.2,4.488986836,-0.03,-0.72,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,89704,2015-10-30 10:15:10:580,1446171310580.0 \n0.7159,-0.3867,10.5309,0.4959,0.6929,9.7696,0.7343,-0.0965,0.5046,16.7,-4.4,-41.9,4.655491247,-4.05,-2.91,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,89808,2015-10-30 10:15:10:684,1446171310684.0 \n-0.1987,0.0503,9.7181,0.5699,0.3411,9.7841,0.0721,0.2224,0.4423,15.9,-5.2,-42,4.52738408,-2.11,-3.67,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,89908,2015-10-30 10:15:10:784,1446171310784.0 \n-0.8248,-0.3496,9.566,0.6174,0.0851,9.7868,-0.033,-0.1136,-0.011,15,-6.4,-42.4,4.402243972,-0.5,-3.61,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,90009,2015-10-30 10:15:10:885,1446171310885.0 \n-0.6297,0.7003,9.092,0.5994,0.0799,9.788,0.033,0.0538,0.1002,14.6,-6,-42.6,4.401371308,-0.47,-3.5,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,90112,2015-10-30 10:15:10:988,1446171310988.0 \n0.2849,0.7733,10.088,0.7119,0.3401,9.7749,0.0916,-0.1698,0.022,14.6,-5.8,-42.5,4.463330496,-1.99,-4.17,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,90215,2015-10-30 10:15:11:091,1446171311091.0 \n1.0319,0.656,10.3597,0.6541,0.5737,9.768,0.0782,0.1393,-0.1283,14.4,-6.2,-42.4,4.501378674,-3.35,-3.83,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,90316,2015-10-30 10:15:11:192,1446171311192.0 \n-0.5148,-0.4513,10.5213,0.4946,0.3603,9.7875,-0.3922,0.1112,-0.4875,14.5,-6.7,-42.2,4.402243972,-2.11,-2.89,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,90418,2015-10-30 10:15:11:294,1446171311294.0 \n0.9337,0.4609,9.5074,0.434,0.2635,9.7935,-0.3629,-0.0709,-0.0867,14.7,-6.7,-42.2,4.396484386,-2.11,-2.39,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,90519,2015-10-30 10:15:11:395,1446171311395.0 \n0.4286,0.808,8.2025,0.421,0.2149,9.7953,-0.0183,0.0122,0.0476,15.1,-6.2,-41.9,4.417951936,-1.26,-2.46,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,90621,2015-10-30 10:15:11:497,1446171311497.0 \n0.1305,1.0283,8.6179,0.3783,0.3164,9.7942,0.0183,0.1124,-0.0086,15.5,-5.4,-41.7,4.506789194,-1.79,-2.46,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,90723,2015-10-30 10:15:11:599,1446171311599.0 \n-0.0239,0.5219,11.4826,0.4624,0.3513,9.7894,0.0501,-0.2272,0.1698,15.6,-5.3,-41.7,4.505741997,-1.8,-2.25,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,90826,2015-10-30 10:15:11:702,1446171311702.0 \n-0.0898,0.0934,11.3066,0.5828,0.5338,9.7747,-0.2321,-0.1063,0.1833,15.4,-6,-42,4.500506009,-3.12,-3.41,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,90927,2015-10-30 10:15:11:803,1446171311803.0 \n0.8643,0.6764,9.4763,0.729,0.4949,9.767,-0.1405,0,0.0367,15,-6.9,-42.1,4.446051737,-2.89,-4.27,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,91030,2015-10-30 10:15:11:906,1446171311906.0 \n-0.2466,0.3747,9.4092,0.652,0.4203,9.7759,-0.022,0.077,-0.077,14.5,-7.4,-42.2,4.416730205,-2.16,-4.03,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,91133,2015-10-30 10:15:12:009,1446171312009.0 \n-0.1173,1.4269,8.1092,0.4566,0.5583,9.7801,0.1381,0.2615,0.0354,14.3,-7.7,-42.4,4.372573375,-3.26,-2.67,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,91233,2015-10-30 10:15:12:109,1446171312109.0 \n-0.2885,0.6009,10.6051,0.5893,0.7145,9.7628,0.1552,-0.2541,-0.0257,14.6,-7.9,-42.2,4.42179166,-3.98,-2.93,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,91336,2015-10-30 10:15:12:212,1446171312212.0 \n1.6029,0.2442,10.392,0.7189,1.0944,9.7188,0.5571,-0.1173,0.0733,14.6,-8.7,-41.7,4.473802472,-6.41,-4.23,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,91438,2015-10-30 10:15:12:314,1446171312314.0 \n-0.3962,-0.0084,10.0006,0.6302,1.0774,9.7269,0.2468,0.3653,-0.022,14.5,-9.2,-41.6,4.456872778,-5.94,-4.34,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,91540,2015-10-30 10:15:12:416,1446171312416.0 \n-0.103,0.7482,9.6391,0.6413,0.9584,9.7386,-0.2162,0.0684,-0.0843,14.4,-9.8,-41.6,4.370828046,-5.61,-3.77,36.814007,-119.74832,255.46,336.5554464,4.28,12.903226,265.55,17 / 17,91641,2015-10-30 10:15:12:517,1446171312517.0 \n-0.0431,1.5119,8.4982,0.5603,0.8356,9.7549,0.0965,0.0648,0.0538,14.6,-9.2,-41.9,4.407654493,-4.89,-3.29,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,91743,2015-10-30 10:15:12:619,1446171312619.0 \n-0.0204,1.5323,9.6187,0.4782,0.8681,9.7564,-0.0195,0.1332,0.0696,14.9,-9.1,-41.9,4.409923421,-5.08,-2.81,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,91846,2015-10-30 10:15:12:722,1446171312722.0 \n-0.0443,1.5,8.764,0.4871,1.106,9.7319,0.4068,0.1393,0.3299,15,-9.1,-41.6,4.46594849,-6.48,-2.87,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,91947,2015-10-30 10:15:12:823,1446171312823.0 \n-1.0367,-0.6776,13.0903,0.7447,0.75,9.7495,-0.6023,-0.5009,0.044,14.9,-9.5,-41.3,4.431216438,-5.52,-3.84,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,92050,2015-10-30 10:15:12:926,1446171312926.0 \n0.5387,1.1432,8.0182,0.7079,0.517,9.7674,-0.3567,0.1613,0.2407,14.4,-9.4,-41.5,4.326147617,-3.02,-4.15,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,92152,2015-10-30 10:15:13:028,1446171313028.0 \n-0.1676,1.1037,9.9754,0.5419,0.1599,9.7904,-0.0159,-0.1356,0.1588,14.3,-8.5,-42.1,4.289844768,-0.93,-3.17,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,92254,2015-10-30 10:15:13:130,1446171313130.0 \n0.0215,1.3898,9.5972,0.4383,0.4955,9.7843,0.3433,0.0635,-0.0635,14.4,-7.7,-42.2,4.356341813,-2.9,-2.57,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,92355,2015-10-30 10:15:13:231,1446171313231.0 \n-0.7781,0.2514,11.9219,0.4304,0.8591,9.7595,0.336,-0.0611,-0.3176,14.6,-7.6,-41.8,4.4331363,-4.38,-2.5,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,92458,2015-10-30 10:15:13:334,1446171313334.0 \n0.9852,0.3615,11.9028,0.3949,1.06,9.7412,-0.1344,-0.0061,-0.3592,14.8,-8.7,-41.4,4.443608276,-6.21,-2.32,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,92559,2015-10-30 10:15:13:435,1446171313435.0 \n0.3184,0.6081,7.3298,0.1947,1.0168,9.7518,-0.3128,-0.2199,-0.2737,15.2,-9.2,-41.2,4.421617127,-5.95,-1.14,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,92661,2015-10-30 10:15:13:537,1446171313537.0 \n0.0012,1.2342,7.6567,0.2487,0.6704,9.7805,-0.1332,0.0098,0.0831,15.7,-8.9,-41.2,4.373620573,-4.17,-1.55,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,92764,2015-10-30 10:15:13:640,1446171313640.0 \n-0.0575,1.6436,7.9164,0.2916,0.6429,9.7812,0.0745,-0.0843,0.0037,15.9,-7.9,-41.3,4.412192349,-3.76,-1.71,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,92865,2015-10-30 10:15:13:741,1446171313741.0 \n-0.5758,0.7661,10.5309,0.2732,0.6328,9.7824,-0.0367,0.0391,-0.0208,15.9,-7.3,-41.4,4.462806897,-3.7,-1.6,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,92968,2015-10-30 10:15:13:844,1446171313844.0 \n0.2693,0.9254,9.8234,0.2918,0.7466,9.7738,-0.3738,-0.3641,0.0745,16,-7.2,-41.3,4.487066974,-4.33,-1.54,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,93070,2015-10-30 10:15:13:946,1446171313946.0 \n0.1305,1.3743,7.8362,0.3073,0.5361,9.7872,0.0476,0.281,0.2358,15.8,-7.2,-41.5,4.442735611,-3.13,-1.8,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,93171,2015-10-30 10:15:14:047,1446171314047.0 \n-0.99,0.2861,9.2285,0.3175,0.4516,9.7911,-0.3946,0.0024,-0.1295,15.9,-7.4,-41.7,4.427376714,-2.64,-1.86,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,93277,2015-10-30 10:15:14:153,1446171314153.0 \n-0.8966,0.6452,8.9088,0.2433,0.3463,9.7975,0.248,0.0684,0.0831,15.7,-7.1,-42,4.387583207,-1.69,-1.56,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,93375,2015-10-30 10:15:14:251,1446171314251.0 \n-0.5112,1.1265,8.8394,0.1967,0.5326,9.7902,0.16,0.0367,0.011,15.7,-7.2,-41.8,4.430518306,-2.91,-1.14,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,93478,2015-10-30 10:15:14:354,1446171314354.0 \n0.1113,0.0419,11.0038,0.3395,0.6644,9.7782,0.1051,-0.0538,-0.2016,15.6,-7.3,-41.5,4.473278873,-3.88,-1.99,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,93580,2015-10-30 10:15:14:456,1446171314456.0 \n-1.5383,-1.2917,12.208,0.1014,0.3354,9.8004,-0.2443,0.3421,-0.088,15.7,-7.3,-41.4,4.425282318,-2.86,-1.12,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,93682,2015-10-30 10:15:14:558,1446171314558.0 \n1.0558,0.9529,9.8306,0.0373,0.0629,9.8064,-0.1735,-0.0953,0.2871,16.2,-6.6,-41,4.340284784,-1.11,0.14,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,93784,2015-10-30 10:15:14:660,1446171314660.0 \n0.3496,1.561,7.8362,-0.023,-0.0739,9.8063,0.088,0.0391,0.2969,16.8,-5.2,-40.6,4.408003559,0.43,0.13,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,93885,2015-10-30 10:15:14:761,1446171314761.0 \n-0.1772,1.0523,8.3594,-0.0207,-0.0345,9.8066,-0.066,0.0061,-0.022,16.9,-4.8,-40.4,4.421442594,0.09,0.12,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,93988,2015-10-30 10:15:14:864,1446171314864.0 \n-0.5387,0.1281,11.9997,0.0887,0.0213,9.8062,0.2834,-0.1319,0.4056,16.7,-4.6,-40.4,4.436626959,-0.12,-0.52,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,94090,2015-10-30 10:15:14:966,1446171314966.0 \n0.5243,-0.5471,11.8321,0.2396,0.0881,9.8033,-0.1112,-0.2175,0.2908,16.6,-5,-40.6,4.469788214,-0.89,-0.88,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,94192,2015-10-30 10:15:15:068,1446171315068.0 \n0.893,1.2198,7.1132,0.4609,0.2677,9.7922,0.3567,-0.2529,0.3971,16.1,-5.9,-41.3,4.429471109,-1.27,-2.19,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,94293,2015-10-30 10:15:15:169,1446171315169.0 \n-0.6141,-0.0156,9.3051,0.4542,0.0444,9.796,0.0696,0.1442,0.0061,15.5,-6.5,-42,4.406432763,-0.34,-3.06,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,94396,2015-10-30 10:15:15:272,1446171315272.0 \n-0.2789,0.6237,9.4367,0.44,0.1033,9.7962,0.3531,-0.0574,0.0623,15.1,-6.8,-42.3,4.341331981,-0.6,-2.57,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,94498,2015-10-30 10:15:15:374,1446171315374.0 \n-0.571,-0.4764,12.5169,0.5165,0.6141,9.7738,0.3176,-0.2309,-0.2517,14.8,-7.4,-42.3,4.416381139,-2.52,-2.74,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,94618,2015-10-30 10:15:15:494,1446171315494.0 \n1.1253,0.5986,9.1889,0.3921,0.8543,9.7615,-0.3763,0.2162,-0.4606,14.8,-8,-41.7,4.469788214,-5.27,-2.57,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,94701,2015-10-30 10:15:15:577,1446171315577.0 \n-0.6237,0.1053,8.3234,0.0607,0.4728,9.7951,-0.4093,0.0159,-0.0244,15.3,-8.2,-41.3,4.336619592,-2.76,-0.36,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,94804,2015-10-30 10:15:15:680,1446171315680.0 \n-0.5914,0.2286,9.6606,-0.0216,0.1454,9.8055,-0.0721,0.1588,-0.0305,15.8,-7.5,-41,4.35320022,-1.32,-0.19,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,94906,2015-10-30 10:15:15:782,1446171315782.0 \n-0.7183,0.9074,8.758,-0.0139,0.1305,9.8058,0.0464,-0.022,-0.0476,16.6,-5.8,-40.6,4.401022242,-0.76,0.08,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,95009,2015-10-30 10:15:15:885,1446171315885.0 \n-1.3252,0.4094,11.1857,-0.0376,0.2236,9.804,0.0354,-0.1796,-0.0367,16.9,-4.9,-40.4,4.474500603,-1.31,0.22,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,95109,2015-10-30 10:15:15:985,1446171315985.0 \n-0.68,0.5507,9.3182,0.0918,0.5813,9.789,0.6854,-0.0367,0.3726,16.9,-5.1,-40.5,4.520053697,-2.33,-0.48,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,95212,2015-10-30 10:15:16:088,1446171316088.0 \n-1.5131,-1.1803,13.313,0.2522,0.449,9.7931,0.0525,0.0391,0.2089,16.8,-5.8,-40.4,4.48444898,-2.62,-1.49,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,95313,2015-10-30 10:15:16:189,1446171316189.0 \n-1.403,-0.395,9.9647,0.2504,0.203,9.8014,-0.2871,0.099,-0.0183,16.3,-6.7,-40.8,4.365592058,-1.19,-1.46,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,95415,2015-10-30 10:15:16:291,1446171316291.0 \n-1.0391,0.8727,8.9842,0.1621,0.1496,9.8042,-0.0244,0.0757,0.1051,16.1,-6.7,-40.7,4.34901143,-0.86,-1.12,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,95517,2015-10-30 10:15:16:393,1446171316393.0 \n-0.2717,0.4453,9.7205,0.2109,0.4171,9.7955,0.2285,-0.1026,0.0794,15.9,-6.6,-41,4.410097954,-2.44,-1.23,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,95619,2015-10-30 10:15:16:495,1446171316495.0 \n0.152,0.8104,10.9523,0.2629,0.6496,9.7816,0.3824,-0.204,0.0709,15.9,-7,-40.8,4.466123023,-3.8,-1.54,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,95722,2015-10-30 10:15:16:598,1446171316598.0 \n-0.8152,-0.5938,11.631,0.2705,0.4943,9.7904,-0.1295,0.463,-0.0745,15.7,-7.7,-40.9,4.378158429,-2.89,-1.58,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,95824,2015-10-30 10:15:16:700,1446171316700.0 \n0.5076,0.6045,8.412,0.1013,0.4599,9.7953,-0.1796,-0.0098,0.0012,15.9,-7.6,-40.9,4.358087142,-2.69,-0.59,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,95925,2015-10-30 10:15:16:801,1446171316801.0 \n-0.3998,0.6656,9.1494,0.0886,0.2423,9.8033,-0.0489,-0.248,-0.1197,16.1,-6.7,-41.3,4.361752334,-1.42,-0.52,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,96028,2015-10-30 10:15:16:904,1446171316904.0 \n0.1975,1.2354,8.2732,0.1422,0.3324,9.8,0.0562,-0.0745,0.0354,16.5,-6.2,-41.4,4.449542395,-1.79,-0.77,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,96129,2015-10-30 10:15:17:005,1446171317005.0 \n-0.4441,0.4681,9.8174,0.2754,0.4236,9.7936,0.1466,-0.2456,0.1869,16.5,-6,-41.2,4.469439149,-2.25,-1.06,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,96232,2015-10-30 10:15:17:108,1446171317108.0 \n0.0862,-0.3041,12.7539,0.5499,0.4241,9.782,-0.4924,-0.1674,0.1356,15.8,-6.7,-41.2,4.469090083,-3.54,-3.05,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,96334,2015-10-30 10:15:17:210,1446171317210.0 \n-0.1018,0.9349,8.7233,0.5265,0.3065,9.7877,-0.1491,-0.1429,0.2004,15.3,-7,-41.4,4.387932272,-1.81,-2.85,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,96436,2015-10-30 10:15:17:312,1446171317312.0 \n-0.8631,-0.0431,9.7671,0.4717,0.1251,9.7945,-0.1564,0.1381,0.1197,14.7,-7.2,-41.7,4.357389011,-0.86,-3.06,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,96538,2015-10-30 10:15:17:414,1446171317414.0 \n-0.3256,1.2522,8.0038,0.4209,0.2208,9.7951,0.2199,0.0965,0.0501,14.5,-7.1,-41.7,4.365592058,-1.29,-2.46,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,96640,2015-10-30 10:15:17:516,1446171317516.0 \n-0.2011,1.1564,9.505,0.4389,0.4426,9.7868,0.077,-0.0269,-0.0782,14.4,-7.2,-41.7,4.363846729,-1.8,-2.31,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,96743,2015-10-30 10:15:17:619,1446171317619.0 \n2.0279,-0.2682,10.7524,0.4723,0.6315,9.7749,-0.3384,0.1735,-0.474,14.7,-8,-41.2,4.399800511,-3.59,-2.68,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,96845,2015-10-30 10:15:17:721,1446171317721.0 \n0.656,0.5878,7.8063,0.1792,0.385,9.7974,-0.1222,0.336,-0.0916,15,-8,-41.1,4.326671216,-2.25,-1.05,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,96945,2015-10-30 10:15:17:821,1446171317821.0 \n-0.6153,-0.0862,10.5309,0.166,0.1246,9.8045,-0.1246,0.0892,-0.0941,15.3,-7.4,-41.1,4.332081736,-0.96,-1.13,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,97049,2015-10-30 10:15:17:925,1446171317925.0 \n-0.3998,1.0319,8.3749,0.0923,0.141,9.8052,-0.0342,0.0782,-0.0635,15.8,-6.6,-40.9,4.339412119,-0.82,-0.54,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,97152,2015-10-30 10:15:18:028,1446171318028.0 \n-0.6357,0.6883,9.6869,0.1437,0.1969,9.8036,-0.0171,-0.0623,-0.011,16.2,-5.7,-40.7,4.409923421,-1.15,-0.84,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,97251,2015-10-30 10:15:18:127,1446171318127.0 \n-0.6608,0.5267,11.6825,0.2875,0.4182,9.7935,0.4398,0.0733,0.4447,16.1,-5.6,-40.5,4.441339348,-1.76,-1.74,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,97354,2015-10-30 10:15:18:230,1446171318230.0 \n-0.808,-0.6656,11.5173,0.436,0.2957,9.7925,0.0183,-0.1979,0.3519,15.8,-6.3,-40.8,4.449891461,-1.73,-2.55,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,97456,2015-10-30 10:15:18:332,1446171318332.0 \n0.3651,0.3591,8.7376,0.5801,0.2841,9.7854,-0.1197,-0.0599,0.0489,15.3,-6.9,-41.1,4.388804937,-1.66,-3.39,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,97560,2015-10-30 10:15:18:436,1446171318436.0 \n-0.504,0.5243,7.9009,0.3399,0.0352,9.8007,-0.3225,0.3531,-0.16,15,-7.1,-41.4,4.320737096,-0.27,-2.09,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,97661,2015-10-30 10:15:18:537,1446171318537.0 \n-0.51,0.7506,8.4072,0.3245,0.0173,9.8013,-0.0867,0.0709,-0.0134,15,-7.1,-41.4,4.313930312,-0.15,-1.94,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,97764,2015-10-30 10:15:18:640,1446171318640.0 \n-0.3496,0.3699,11.1199,0.2121,0.1768,9.8028,0.1393,0.0244,-0.1674,15.2,-6.5,-41.2,4.392295596,-1.03,-1.24,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,97864,2015-10-30 10:15:18:740,1446171318740.0 \n-0.5004,-1.0858,13.3154,0.2205,0.3681,9.7973,-0.1503,-0.2175,-0.2676,15.8,-6.7,-41.3,4.399625978,-2.15,-1.29,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,97965,2015-10-30 10:15:18:841,1446171318841.0 \n0.6297,0.2406,7.8087,0.2078,0.1246,9.8037,0.0342,-0.2822,0.0098,16.1,-6.2,-41.5,4.390899332,-0.69,-0.76,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,98068,2015-10-30 10:15:18:944,1446171318944.0 \n-0.1448,0.6512,7.9559,-0.0077,-0.1596,9.8053,-0.121,0.1393,0.0049,16.2,-5.3,-41.4,4.371351645,0.93,0.04,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,98169,2015-10-30 10:15:19:045,1446171319045.0 \n-0.5531,0.5315,8.3845,0.1083,-0.1022,9.8055,0.1539,-0.226,0.0257,16.3,-4.4,-41,4.439943084,0.78,-0.42,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,98272,2015-10-30 10:15:19:148,1446171319148.0 \n-0.1125,0.7254,9.5253,0.0789,-0.0581,9.8062,0.0831,0.0782,0.1075,16.4,-4.2,-40.7,4.458269041,0.34,-0.46,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,98373,2015-10-30 10:15:19:249,1446171319249.0 \n0.0036,0.2885,10.0568,0.2929,0.1426,9.8012,0.0867,-0.0794,0.2285,16.2,-4.4,-40.5,4.515690374,-0.83,-1.71,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,98479,2015-10-30 10:15:19:355,1446171319355.0 \n-1.5479,-1.2055,10.3525,0.4106,0.0572,9.7979,-0.1857,-0.0977,-0.0611,15.8,-5,-40.9,4.446749868,-0.26,-2.4,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,98578,2015-10-30 10:15:19:454,1446171319454.0 \n-0.5088,-0.2562,8.9711,0.4576,-0.0351,9.7959,-0.2883,0.0611,-0.1173,15.2,-5.4,-41.5,4.44151388,-0.41,-2.78,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,98680,2015-10-30 10:15:19:556,1446171319556.0 \n0.0048,0.5686,8.5485,0.479,-0.0072,9.7949,0.0428,0.1527,-0.0293,14.9,-5.6,-41.9,4.372049776,0.04,-2.8,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,98781,2015-10-30 10:15:19:657,1446171319657.0 \n0.1006,0.5219,9.8509,0.4378,0.1195,9.7961,0.1038,-0.1002,-0.099,14.8,-5.8,-42.2,4.387234141,-0.48,-2.44,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,98883,2015-10-30 10:15:19:759,1446171319759.0 \n-0.5052,0.1018,11.9303,0.5469,0.353,9.785,0.3824,-0.1234,-0.0134,14.9,-6.1,-42.1,4.428598444,-1.38,-2.99,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,98986,2015-10-30 10:15:19:862,1446171319862.0 \n0.012,-0.097,10.1203,0.4473,0.2888,9.7922,-0.43,0.2798,-0.3323,14.8,-6.8,-42.3,4.423362456,-2.56,-3.24,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,99088,2015-10-30 10:15:19:964,1446171319964.0 \n-0.0431,-0.2286,10.7009,0.5101,0.0564,9.7932,-0.3592,0.0611,-0.0929,14.7,-6.5,-42.2,4.388455871,-0.33,-2.98,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,99190,2015-10-30 10:15:20:066,1446171320066.0 \n0.2813,0.9529,7.8123,0.3237,-0.0565,9.8011,-0.0342,0.3299,0.1271,14.9,-5.9,-42.3,4.348487831,0.33,-1.89,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,99291,2015-10-30 10:15:20:167,1446171320167.0 \n0.4812,0.8583,9.9036,0.324,0.0881,9.8009,0.2175,-0.1662,0.171,15.3,-5,-42.1,4.417951936,-0.11,-1.7,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,99393,2015-10-30 10:15:20:269,1446171320269.0 \n0.3065,0.1425,11.4994,0.3995,0.4369,9.7888,0.6646,-0.2505,0.0342,15.5,-5.2,-41.9,4.493524692,-1.55,-1.96,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,99497,2015-10-30 10:15:20:373,1446171320373.0 \n-0.5531,-0.401,11.6717,0.5068,0.7636,9.7637,0.1772,-0.1136,0.0171,15.5,-6.8,-41.5,4.502600404,-4.47,-2.97,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,99598,2015-10-30 10:15:20:474,1446171320474.0 \n0.0084,0.8547,8.1846,0.5986,0.7045,9.763,0.1869,-0.1405,0.1173,15.3,-7.7,-41.6,4.424933253,-3.98,-3.23,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,99699,2015-10-30 10:15:20:575,1446171320575.0 \n-0.1484,1.0391,8.2983,0.5339,0.4283,9.7827,-0.1845,-0.0183,0.2309,15,-8.6,-41.8,4.332779868,-2.89,-3.23,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,99802,2015-10-30 10:15:20:678,1446171320678.0 \n-0.4202,1.0618,8.9423,0.6572,0.4432,9.7746,-0.0403,0.066,0.0367,14.5,-8.1,-42.1,4.379729225,-2.59,-3.85,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,99903,2015-10-30 10:15:20:779,1446171320779.0 \n-0.085,1.0546,10.8924,0.3062,0.5401,9.787,0.1271,0.1491,-0.1014,14.6,-7.9,-42.1,4.376064034,-3.16,-1.79,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,100006,2015-10-30 10:15:20:882,1446171320882.0 \n1.4641,0.814,11.3042,0.4742,0.6713,9.7722,-0.0586,-0.1148,-0.6011,14.6,-7.8,-41.9,4.410272487,-3.8,-2.5,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,100108,2015-10-30 10:15:20:984,1446171320984.0 \n-0.6381,-0.3448,8.7209,0.288,0.5218,9.7885,0.4313,-0.0562,0.0525,15.3,-7.4,-41.5,4.422489792,-3.05,-1.69,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,100210,2015-10-30 10:15:21:086,1446171321086.0 \n-0.0407,0.2334,8.8777,0.5425,0.5711,9.775,-0.3335,-0.5168,-0.3067,15.5,-6.5,-41,4.514643176,-3.34,-3.18,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,100311,2015-10-30 10:15:21:187,1446171321187.0 \n-0.5231,0.7494,8.5114,0.1927,0.4319,9.7952,0.0098,0.3152,-0.0501,15.7,-5.6,-41,4.468391951,-2.42,-1.69,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,100413,2015-10-30 10:15:21:289,1446171321289.0 \n-1.4078,0.1173,10.2987,-0.118,0.3603,9.7993,-0.1649,0.2871,0.1344,16.3,-4.9,-40.8,4.491430297,-2.11,0.69,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,100515,2015-10-30 10:15:21:391,1446171321391.0 \n-0.595,1.0295,10.4004,-0.352,0.3892,9.7926,0.1784,0.2749,0.3836,17,-4.6,-40.5,4.480783789,-1.83,1.86,36.814014,-119.74844,257.42,336.5554464,4.18,12.903226,271.05,17 / 17,100618,2015-10-30 10:15:21:494,1446171321494.0 \n-1.1648,-0.0455,9.9994,0.0631,0.2596,9.803,-0.3348,0.5131,0.1967,17.7,-4.8,-40.1,4.499633345,-1.52,-0.37,36.814014,-119.74857,258.83,336.5554464,4.39,12.903226,271.47,17 / 17,100720,2015-10-30 10:15:21:596,1446171321596.0 \n-0.8116,0.4022,8.3989,0.1009,0.2768,9.8022,-0.1356,0.1051,0.0428,17.7,-5,-40.4,4.49282656,-1.4,-0.03,36.814014,-119.74857,258.83,336.5554464,4.39,12.903226,271.47,17 / 17,100822,2015-10-30 10:15:21:698,1446171321698.0 \n-1.093,0.7745,8.7915,0.0585,0.1698,9.805,0.193,0.0513,0.2334,17.3,-5.2,-40.8,4.463679562,-0.9,-0.22,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,100924,2015-10-30 10:15:21:800,1446171321800.0 \n-0.2095,1.1001,9.4463,0.1397,0.3494,9.7994,0.16,-0.1319,0.1173,16.9,-5.5,-40.9,4.513421446,-2.04,-0.82,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,101026,2015-10-30 10:15:21:902,1446171321902.0 \n-1.0642,0.0012,12.3553,0.213,0.5346,9.7898,0.3958,0.1295,-0.0379,16.8,-5.9,-40.8,4.480958322,-2.46,-1.47,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,101129,2015-10-30 10:15:22:005,1446171322005.0 \n-0.1736,-0.3771,10.6913,0.123,0.5786,9.7888,-0.2969,0.325,-0.2615,16.6,-6.7,-41,4.456523712,-3.38,-0.72,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,101231,2015-10-30 10:15:22:107,1446171322107.0 \n-0.2825,-0.0204,8.6084,0.2655,0.4191,9.7941,-0.0794,-0.4655,-0.1625,16.6,-6.8,-41.1,4.429296576,-2.69,-0.66,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,101331,2015-10-30 10:15:22:207,1446171322207.0 \n0.1856,0.5914,8.7053,0.4543,0.2233,9.7936,-0.2676,-0.0574,-0.1319,16.3,-6.1,-41.2,4.435405228,-1.3,-2.66,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,101433,2015-10-30 10:15:22:309,1446171322309.0 \n0.1006,0.8356,8.5437,0.4211,0.1202,9.7969,-0.0648,0.022,-0.088,16.1,-5.3,-41.3,4.465773957,-0.73,-2.6,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,101536,2015-10-30 10:15:22:412,1446171322412.0 \n-0.1472,0.4226,10.7308,0.4005,0.121,9.7977,0.0916,-0.0073,0.0586,15.7,-4.6,-41.7,4.464028628,-0.71,-2.34,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,101645,2015-10-30 10:15:22:521,1446171322521.0 \n0.3663,0.4645,9.1854,0.7193,0.502,9.7673,0.3067,-0.3054,0.2211,15.3,-4.5,-41.6,4.607145626,-2.93,-4.21,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,101739,2015-10-30 10:15:22:615,1446171322615.0 \n-0.8978,-0.832,10.5225,0.8513,0.3027,9.7649,0.1674,-0.2407,0.4056,15,-5,-42,4.509232655,-1.69,-4.8,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,101841,2015-10-30 10:15:22:717,1446171322717.0 \n-0.0455,0.4393,9.2416,0.9833,0.2125,9.7549,-0.2089,-0.1161,0.0147,14,-5.8,-42.4,4.437150557,-1.24,-5.76,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,101945,2015-10-30 10:15:22:821,1446171322821.0 \n-0.0706,0.7386,9.1004,0.9058,0.0881,9.7643,-0.1454,0.0476,-0.1393,13.6,-5.8,-42.7,4.416381139,-0.62,-5.71,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,102046,2015-10-30 10:15:22:922,1446171322922.0 \n-0.2179,0.7362,10.1789,0.789,0.1773,9.7733,0.0171,0.0855,-0.0696,13.4,-5.4,-43,4.456698245,-0.91,-4.86,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,102147,2015-10-30 10:15:23:023,1446171323023.0 \n0.0359,0.4621,9.7779,0.7194,0.4623,9.7693,0.0403,0.1197,-0.1845,13.8,-5.1,-43,4.537681522,-2.7,-4.21,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,102250,2015-10-30 10:15:23:126,1446171323126.0 \n-0.6871,-1.5191,14.0683,0.6274,0.2055,9.7844,-0.5864,0.1185,-0.2871,14.2,-5.1,-43,4.470835412,-1.2,-3.67,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,102351,2015-10-30 10:15:23:227,1446171323227.0 \n0.1951,-0.4501,11.1929,0.4533,0.0469,9.7961,-0.5534,-0.1319,-0.1234,14.8,-4.9,-43.2,4.436801491,-0.27,-2.65,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,102454,2015-10-30 10:15:23:330,1446171323330.0 \n0.0395,0.9122,7.3909,0.3126,-0.0285,9.8016,-0.0305,-0.0513,0.0501,15.3,-4.5,-43.4,4.468741017,0.13,-1.98,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,102556,2015-10-30 10:15:23:432,1446171323432.0 \n0.2538,0.595,10.0521,0.3722,6.00E-04,9.7996,0.0635,-0.066,0.0709,15.7,-4,-43.3,4.489335902,0,-2.18,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,102657,2015-10-30 10:15:23:533,1446171323533.0 \n0.1676,0.2837,10.8218,0.3315,0.1604,9.7997,0.3225,-0.0391,0.1845,15.9,-3.8,-43.5,4.500331476,-0.36,-1.79,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,102759,2015-10-30 10:15:23:635,1446171323635.0 \n0.097,-0.8511,12.6007,0.5169,0.2503,9.7898,-0.3971,-0.2847,-0.1161,16,-4.5,-43.8,4.555309348,-1.46,-3.02,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,102861,2015-10-30 10:15:23:737,1446171323737.0 \n-0.0419,0.3292,8.4336,0.7785,0.2907,9.7714,-0.0489,-0.0819,-0.1772,15.6,-5,-43.8,4.522671691,-1.7,-4.56,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,102964,2015-10-30 10:15:23:840,1446171323840.0 \n-0.6057,0.34,7.9176,0.689,0.2081,9.7802,-0.0648,0.1307,-0.2443,15.2,-5.2,-44,4.495095489,-1.33,-4.13,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,103066,2015-10-30 10:15:23:942,1446171323942.0 \n0.5746,1.3803,8.5413,0.6211,0.3115,9.782,0.2162,-0.0855,-0.0024,14.8,-5.1,-44.1,4.510628919,-1.82,-3.63,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,103167,2015-10-30 10:15:24:043,1446171324043.0 \n-0.3029,0.5351,10.1957,0.497,0.4457,9.7839,0.0501,0.1491,-0.2615,14.9,-5.2,-44.2,4.53453993,-2.47,-3.27,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,103270,2015-10-30 10:15:24:146,1446171324146.0 \n0.0718,-1.069,11.989,0.4633,0.2921,9.7913,-0.3763,-0.0379,-0.2443,15.2,-5.1,-44.1,4.498237081,-1.71,-2.71,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,103371,2015-10-30 10:15:24:247,1446171324247.0 \n0.6273,0.7733,8.5006,0.3337,0.2529,9.7977,0.281,-0.0586,0.259,15.7,-4.7,-44.1,4.477991262,-1.12,-1.81,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,103473,2015-10-30 10:15:24:349,1446171324349.0 \n-0.2849,-0.0156,9.9252,0.4253,-0.0521,9.7973,-0.0904,0.1161,-0.0819,16.1,-4,-43.7,4.48026019,0.3,-2.49,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,103575,2015-10-30 10:15:24:451,1446171324451.0 \n-0.1808,0.917,7.9356,0.356,-0.0201,9.8002,0.0379,0.022,0.0024,16.2,-3.3,-43.4,4.534365397,0.21,-2.05,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,103677,2015-10-30 10:15:24:553,1446171324553.0 \n-0.1113,0.4286,10.1981,0.42,0.0797,9.7973,-0.0562,-0.0134,-0.0525,15.9,-3.1,-43.5,4.567875718,-0.55,-2.46,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,103780,2015-10-30 10:15:24:656,1446171324656.0 \n-0.0132,0.5507,11.8166,0.5028,0.2905,9.7894,0.4911,0.0037,0.3335,15.8,-3.1,-43.8,4.584281813,-0.89,-2.75,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,103881,2015-10-30 10:15:24:757,1446171324757.0 \n-1.7669,-1.6652,12.9131,0.732,0.1784,9.7777,0.1075,0.2101,0.3286,15.4,-4,-43.9,4.554785749,-1.44,-4.48,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,103984,2015-10-30 10:15:24:860,1446171324860.0 \n-0.1616,0.4334,9.2237,0.845,0.1626,9.7688,-0.1503,-0.2566,0.1246,14.7,-4.7,-44.3,4.487066974,-0.95,-4.94,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,104085,2015-10-30 10:15:24:961,1446171324961.0 \n0.1736,0.9493,9.2775,0.8265,-0.0144,9.7717,-0.0086,-0.0464,0.1002,14.2,-4.8,-44.5,4.4331363,0.08,-4.83,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,104187,2015-10-30 10:15:25:063,1446171325063.0 \n-0.316,0.7805,9.5349,0.6478,0.147,9.7841,0.0648,0.2505,-0.0953,13.9,-4.7,-44.8,4.461585167,-0.86,-3.79,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,104289,2015-10-30 10:15:25:165,1446171325165.0 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\n0.1065,0.2382,8.5078,0.2006,0.0103,9.8046,-0.0867,0.1478,-0.1222,15.6,-4.1,-42.1,4.4903831,-0.21,-1.46,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,104800,2015-10-30 10:15:25:676,1446171325676.0 \n-0.3687,0.0958,9.924,0.094,-0.0552,9.806,0.0159,-0.0122,0.1527,16,-3.6,-41.9,4.459665305,0.32,-0.55,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,104901,2015-10-30 10:15:25:777,1446171325777.0 \n-0.9242,0.0622,10.5884,0.1637,-0.0323,9.8052,0.1026,-0.1173,0.215,16.2,-3.5,-41.9,4.516388505,0.39,-0.74,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,105003,2015-10-30 10:15:25:879,1446171325879.0 \n-0.0515,0.237,9.7121,0.3704,-0.1913,9.7978,0.16,-0.0709,0.1979,16.1,-3.3,-41.7,4.483750848,1.45,-1.92,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,105106,2015-10-30 10:15:25:982,1446171325982.0 \n-0.4393,0.0108,7.6914,0.4965,-0.0471,9.794,0.0195,0.1283,-0.2028,15.6,-3.5,-42.1,4.537506989,0.28,-2.9,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,105207,2015-10-30 10:15:26:083,1446171326083.0 \n-0.7374,0.158,8.5976,0.3945,-0.0663,9.7985,0.2138,-0.0037,0,15.2,-3.5,-42.4,4.510977985,0.57,-2.36,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,105310,2015-10-30 10:15:26:186,1446171326186.0 \n-0.4286,0.158,9.7241,0.4083,0.0982,9.7977,0.1796,-0.0183,0.0391,15.1,-3.8,-42.5,4.501378674,-0.57,-2.39,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,105412,2015-10-30 10:15:26:288,1446171326288.0 \n-0.7865,-0.1113,11.2863,0.3186,0.2591,9.798,0.1979,0.1491,0.0782,15.1,-3.9,-42.4,4.524766086,-1.19,-2.11,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,105514,2015-10-30 10:15:26:390,1446171326390.0 \n-0.413,-0.5148,12.566,0.0719,0.0422,9.8063,0.0464,0.2847,0.0354,15.6,-4.3,-42.1,4.482354585,-0.25,-0.42,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,105616,2015-10-30 10:15:26:492,1446171326492.0 \n0.1628,0.0742,8.5054,-0.0721,0.1152,9.8057,-0.0024,0.0171,0.077,16.2,-4.3,-41.7,4.502425871,-0.9,0.44,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,105717,2015-10-30 10:15:26:593,1446171326593.0 \n-0.5698,0.3783,7.6148,-0.1062,0.0504,9.8059,-0.1393,-0.0269,0.0929,17.1,-4.3,-41.2,4.48741604,-0.29,0.62,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,105820,2015-10-30 10:15:26:696,1446171326696.0 \n-0.0539,0.9732,8.4252,0.0517,-0.0414,9.8064,-0.0867,-0.1307,0.171,17.3,-4.2,-41.2,4.47729313,0.12,-0.08,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,105922,2015-10-30 10:15:26:798,1446171326798.0 \n-0.0551,-0.0443,13.2866,0.2731,0.0382,9.8028,0.1161,-0.2859,0.292,16.8,-4.5,-41.6,4.504171201,-0.22,-1.6,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,106024,2015-10-30 10:15:26:900,1446171326900.0 \n-0.9732,-1.3994,13.2687,0.4541,0.1593,9.7948,-0.2297,-0.3409,0.1454,16,-5.5,-42,4.475373268,-0.93,-2.65,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,106126,2015-10-30 10:15:27:002,1446171327002.0 \n0.3388,0.8236,7.8398,0.5445,0.1422,9.7905,-0.0476,-0.1381,0.0965,15.4,-6.1,-42.3,4.4045129,-0.78,-2.91,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,106229,2015-10-30 10:15:27:105,1446171327105.0 \n-0.1437,0.4872,8.1475,0.5477,-0.0412,9.7913,-0.1051,-0.0061,-0.0684,14.8,-6.6,-42.5,4.319864432,0.24,-3.2,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,106330,2015-10-30 10:15:27:206,1446171327206.0 \n-0.1784,0.8464,8.108,0.4604,-0.0471,9.7957,0.1075,0.1319,-0.011,14.5,-6.3,-42.5,4.359657939,0.44,-2.96,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,106431,2015-10-30 10:15:27:307,1446171327307.0 \n-0.7805,-0.2921,12.1841,0.419,-0.009,9.7977,0.0049,-0.0635,-0.1503,14.8,-5.8,-42.4,4.366988321,0.05,-2.45,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,106534,2015-10-30 10:15:27:410,1446171327410.0 \n0.5614,-0.2394,10.1778,0.2281,0.0197,9.804,-0.4105,0.2773,-0.3629,15,-5.5,-42.3,4.43732509,-0.56,-1.76,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,106635,2015-10-30 10:15:27:511,1446171327511.0 \n0.1197,-0.2119,8.6598,-0.0628,-0.3018,9.8018,-0.3482,0.3567,-0.2199,15.8,-4.8,-41.9,4.331907203,1.76,0.37,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,106737,2015-10-30 10:15:27:613,1446171327613.0 \n0.267,-0.1592,10.1311,-0.0107,-0.364,9.7999,-0.16,-0.1197,-0.0061,16.3,-4.2,-41.8,4.388106805,1.75,0.39,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,106839,2015-10-30 10:15:27:715,1446171327715.0 \n-0.7709,0.4908,8.1774,-0.04,-0.3391,9.8007,0.1063,-0.0941,-0.033,17.1,-3.3,-41.3,4.449716928,2.08,0.41,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,106941,2015-10-30 10:15:27:817,1446171327817.0 \n-0.4477,0.3077,8.2971,0.0506,-0.2514,9.8033,-0.044,-0.0538,0.1197,17,-3.1,-41.3,4.483925381,1.47,-0.3,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,107043,2015-10-30 10:15:27:919,1446171327919.0 \n-0.4908,-0.6357,12.8628,0.1334,-0.2634,9.8022,0.1283,-0.1979,0.2822,16.8,-3.1,-41.4,4.48322725,1.54,-0.78,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,107146,2015-10-30 10:15:28:022,1446171328022.0 \n-0.7709,-2.2901,16.3704,0.5821,-0.407,9.7809,-0.5327,-0.4447,-0.1161,16.2,-3.6,-42,4.435579761,1.52,-2.67,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,107248,2015-10-30 10:15:28:124,1446171328124.0 \n0.4357,0.6452,7.4711,0.6269,-0.2089,9.7844,-0.1759,0.1552,-0.0733,15.4,-3.8,-42.7,4.442910144,1.22,-3.67,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,107356,2015-10-30 10:15:28:232,1446171328232.0 \n-0.4357,0.2047,8.6598,0.485,-0.3344,9.7889,-0.0403,0.0831,-0.1258,15,-4,-43,4.408876223,1.9,-2.99,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,107456,2015-10-30 10:15:28:332,1446171328332.0 \n-0.17,0.7266,8.6036,0.4095,-0.1763,9.7965,0.1637,0.0354,-0.1124,14.8,-4,-43.1,4.435928827,1.03,-2.39,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,107554,2015-10-30 10:15:28:430,1446171328430.0 \n-0.6788,-0.2263,12.0524,0.4261,-0.0918,9.797,0.1527,-0.0513,-0.1918,15,-4.1,-42.8,4.457221844,0.54,-2.49,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,107655,2015-10-30 10:15:28:531,1446171328531.0 \n-0.5519,-1.8579,13.696,0.4693,-0.1954,9.7935,-0.0904,-0.044,-0.2077,15.2,-3.9,-42.3,4.475547801,0.13,-2.7,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,107758,2015-10-30 10:15:28:634,1446171328634.0 \n0.073,-0.4262,7.586,0.2248,-0.1375,9.8031,0.5424,0.0611,0.2651,15.5,-3.6,-42.3,4.416032073,1.66,-1.44,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,107860,2015-10-30 10:15:28:736,1446171328736.0 \n0.7566,0.4106,7.4268,0.2933,-0.223,9.7997,-0.2663,0.1319,-0.1478,16,-3.1,-42.5,4.487590573,1.3,-1.71,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,107961,2015-10-30 10:15:28:837,1446171328837.0 \n0.0778,0.4884,8.0313,0.3596,-0.4258,9.7908,0.0159,0.0269,-0.0794,16.3,-2.4,-42.8,4.497189884,2.49,-2.1,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,108063,2015-10-30 10:15:28:939,1446171328939.0 \n-0.2945,-0.0431,10.5596,0.4248,-0.4615,9.7866,-0.1087,-0.1002,-0.1136,16.2,-1.9,-43.2,4.489335902,2.71,-2.19,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,108165,2015-10-30 10:15:29:041,1446171329041.0 \n0.4645,-0.2634,12.536,0.5617,-0.2692,9.7868,0.2443,0,0.1222,16.1,-1.5,-43.1,4.578173161,2.03,-3.28,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,108268,2015-10-30 10:15:29:144,1446171329144.0 \n-0.4429,-0.9816,10.4902,0.6761,-0.3834,9.7758,-0.2737,-0.1564,-0.0305,15.6,-1.5,-43.2,4.574158904,2.24,-3.96,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,108370,2015-10-30 10:15:29:246,1446171329246.0 \n-0.1317,-0.4381,9.4463,0.8678,-0.4991,9.7554,-0.2162,-0.2138,0.011,15.2,-1.9,-43.4,4.496666285,2.92,-5.08,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,108471,2015-10-30 10:15:29:347,1446171329347.0 \n-0.2322,0.1101,8.6634,0.8518,-0.568,9.7531,-0.0061,0.0941,-0.0623,14.8,-1.8,-43.6,4.480434723,3.32,-5.15,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,108573,2015-10-30 10:15:29:449,1446171329449.0 \n0.0156,0.3855,9.1087,0.7575,-0.4186,9.7684,0.1393,0.0672,-0.1454,14.6,-1.6,-43.9,4.50713826,2.45,-4.43,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,108676,2015-10-30 10:15:29:552,1446171329552.0 \n-0.012,-0.51,12.8712,0.8418,-0.2495,9.7673,0.2053,-0.1368,-0.2443,14.6,-1.5,-43.8,4.580965688,1.97,-4.82,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,108777,2015-10-30 10:15:29:653,1446171329653.0 \n0.2658,-1.0942,11.9195,0.6356,-0.2909,9.7817,-0.2957,0.4728,-0.2834,14.9,-1.7,-43.7,4.551644156,1.34,-4.59,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,108881,2015-10-30 10:15:29:757,1446171329757.0 \n-0.2382,-0.2274,7.7752,0.3646,-0.2513,9.7966,-0.0379,0.0501,-0.0208,15.4,-1.5,-43.5,4.58707434,1.49,-2.27,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,108984,2015-10-30 10:15:29:860,1446171329860.0 \n-0.2011,0.4202,7.1646,0.2305,-0.3335,9.7983,-0.088,0.2786,-0.0012,16.3,-1.1,-42.5,4.571191844,1.95,-1.35,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,109083,2015-10-30 10:15:29:959,1446171329959.0 \n0.0204,0.4788,7.7129,0.2132,-0.3499,9.7981,0.0684,-0.1075,0.0929,17.2,-0.6,-41.8,4.574507969,2.04,-1.25,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,109185,2015-10-30 10:15:30:061,1446171330061.0 \n-0.2981,-1.0211,12.3469,0.3549,-0.4284,9.7909,0.1796,-0.1906,0.1527,17.3,-0.6,-41.6,4.561941599,2.5,-2.08,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,109288,2015-10-30 10:15:30:164,1446171330164.0 \n-0.2909,-2.132,13.8481,0.5939,-0.4007,9.7804,-0.4496,-0.474,0.0098,17,-1,-42.2,4.576427832,2.34,-3.47,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,109389,2015-10-30 10:15:30:265,1446171330265.0 \n0.1221,-0.0311,8.7376,0.679,-0.4438,9.773,0.2529,0.033,0.4826,16.4,-1.2,-42.5,4.548502564,2.98,-3.97,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,109492,2015-10-30 10:15:30:368,1446171330368.0 \n-0.0419,-0.1867,8.4898,0.7939,-0.4915,9.7621,-0.1943,0.1246,-0.0757,15.6,-1.9,-43.3,4.505392931,2.87,-4.65,36.814014,-119.74857,258.83,336.4767745,4.39,12.903226,271.47,17 / 17,109593,2015-10-30 10:15:30:469,1446171330469.0 \n-0.0994,0.5004,8.3199,0.6892,-0.4398,9.7725,0.1588,0.1393,-0.1686,15.2,-2.1,-43.8,4.490208567,2.85,-4.29,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,109695,2015-10-30 10:15:30:571,1446171330571.0 \n-0.7661,-0.6237,11.0097,0.6745,-0.2967,9.7789,0.1234,-0.033,-0.1979,15.2,-2.2,-44,4.531223804,1.73,-3.95,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,109798,2015-10-30 10:15:30:674,1446171330674.0 \n0.3579,-0.0431,10.7859,0.6719,-0.0573,9.7834,0.215,0.0464,-0.0721,15.3,-2.5,-43.8,4.587947005,0.33,-3.93,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,109899,2015-10-30 10:15:30:775,1446171330775.0 \n-0.0443,-0.7877,11.552,0.3947,-0.251,9.7955,0.0342,0.3005,-0.1051,15.5,-2.6,-43.6,4.500331476,1.24,-2.95,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,110001,2015-10-30 10:15:30:877,1446171330877.0 \n-0.0646,-0.431,9.3901,0.3521,-0.3349,9.7946,0.0257,0.11,0.0538,16.1,-2.4,-43,4.518308368,1.96,-2.06,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,110104,2015-10-30 10:15:30:980,1446171330980.0 \n-0.4944,0.2179,8.6766,0.3305,-0.3772,9.7938,-0.0782,-0.0599,-0.0379,16.6,-1.6,-42.4,4.519704631,2.2,-1.93,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,110206,2015-10-30 10:15:31:082,1446171331082.0 \n0.6668,0.6404,9.3841,0.5264,-0.2956,9.788,-0.0024,-0.182,0.0476,16.7,-1.4,-42.2,4.591612196,1.81,-2.69,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,110309,2015-10-30 10:15:31:185,1446171331185.0 \n-0.1053,-0.0431,10.5967,0.6305,-0.2307,9.7836,0.2615,-0.0415,0.2468,16.2,-1.6,-42.4,4.555134815,1.35,-3.69,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,110410,2015-10-30 10:15:31:286,1446171331286.0 \n-0.9457,-2.2254,15.8676,0.9667,-0.3945,9.7509,-0.5498,-0.6451,-0.044,15.7,-2.1,-42.7,4.551818689,1.64,-4.96,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,110511,2015-10-30 10:15:31:387,1446171331387.0 \n-0.0036,0.0132,8.114,1.0378,-0.182,9.7499,0.0965,-0.1332,0.0574,14.8,-2.7,-43,4.52144996,1.06,-6.08,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,110614,2015-10-30 10:15:31:490,1446171331490.0 \n-0.3723,0.0994,8.6036,0.8883,-0.2612,9.7628,0.1405,0.0794,-0.0623,14.3,-3,-43.3,4.486194309,1.53,-5.2,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,110715,2015-10-30 10:15:31:591,1446171331591.0 \n0.0814,0.6536,7.6579,0.7349,-0.019,9.7791,0.2798,0.1588,0.0159,14.1,-3.2,-43.2,4.525289685,0.39,-4.53,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,110818,2015-10-30 10:15:31:694,1446171331694.0 \n-0.5842,-0.2837,12.2811,0.7455,0.0591,9.7781,0.1405,-0.2334,-0.1393,14.4,-3.7,-42.9,4.498237081,-0.35,-4.36,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,110919,2015-10-30 10:15:31:795,1446171331795.0 \n0.261,-1.5383,13.4494,0.7572,0.0618,9.7772,-0.8247,0.1515,-0.3164,14.7,-3.9,-42.4,4.509581721,-0.36,-4.43,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,111022,2015-10-30 10:15:31:898,1446171331898.0 \n0.3543,0.3555,7.4651,0.4764,-0.1843,9.7933,0.2431,0.3201,0.1955,14.9,-3.5,-42,4.482005519,1.47,-3.14,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,111124,2015-10-30 10:15:32:000,1446171332000.0 \n0.4848,0.3005,7.9942,0.525,-0.2403,9.7896,-0.0098,0.1747,-0.0733,15.2,-2.8,-42,4.490557632,1.33,-3.49,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,111225,2015-10-30 10:15:32:101,1446171332101.0 \n-0.0299,0.6812,7.8877,0.4837,-0.1631,9.7934,0.1478,0.0037,-0.0232,15.4,-2.1,-42,4.545535504,1.21,-2.82,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,111327,2015-10-30 10:15:32:203,1446171332203.0 \n-0.0587,-0.1317,11.1247,0.5434,-0.0806,9.7913,0.1649,-0.3482,0.3274,15.6,-2.3,-42.1,4.585329011,0.47,-3.18,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,111430,2015-10-30 10:15:32:306,1446171332306.0 \n0.4573,0.4381,9.7073,0.8361,0.1274,9.7701,0.281,-0.1784,0.3567,15.4,-2.7,-42.1,4.579743957,-0.74,-4.89,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,111531,2015-10-30 10:15:32:407,1446171332407.0 \n-1.0403,-1.3515,13.3596,1.0428,-0.2313,9.7483,-0.6243,-0.595,0.0024,14.9,-3.3,-42.1,4.540299516,0.55,-6.22,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,111634,2015-10-30 10:15:32:510,1446171332510.0 \n-0.4513,-0.2502,8.8502,0.8708,-0.3044,9.7632,-0.1698,0.3873,-0.0012,14.1,-3.8,-42.6,4.42301339,1.78,-5.1,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,111736,2015-10-30 10:15:32:612,1446171332612.0 \n-0.3771,0.3639,8.6036,0.6523,-0.3184,9.7797,0.0635,0.1417,0.0843,14.2,-3.6,-42.6,4.401196775,2,-4.01,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,111838,2015-10-30 10:15:32:714,1446171332714.0 \n-0.5986,0.3998,11.0002,0.5149,-0.193,9.7912,0.0428,0.1906,-0.0098,14.8,-3.7,-42.6,4.439244952,1.13,-3.01,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,111939,2015-10-30 10:15:32:815,1446171332815.0 \n-0.4693,0.0156,11.4359,0.3282,-0.0668,9.8009,0.4374,-0.1258,-0.0086,15.2,-3.8,-42.2,4.456872778,0.39,-1.92,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,112041,2015-10-30 10:15:32:917,1446171332917.0 \n-0.5818,-0.9337,10.2173,0.5322,-0.0546,9.792,-0.088,0.4704,0.1283,16.1,-4.6,-41.4,4.432961767,0.32,-3.11,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,112144,2015-10-30 10:15:33:020,1446171333020.0 \n-0.3424,-0.5686,9.0597,0.3717,-0.2747,9.7958,-0.3409,0.0342,0.0086,16.4,-4.6,-41.1,4.379554692,1.26,-1.46,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,112246,2015-10-30 10:15:33:122,1446171333122.0 \n0.3053,0.2562,7.2305,0.7423,-0.3585,9.7719,-0.2395,-0.1051,0.1173,15.8,-4.3,-41.5,4.434008965,2.1,-4.34,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,112348,2015-10-30 10:15:33:224,1446171333224.0 \n1.1109,1.3707,7.5214,0.6857,-0.4918,9.7703,-0.1955,-0.1991,-0.0806,15.4,-4,-42,4.397531583,2.7,-4.38,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,112450,2015-10-30 10:15:33:326,1446171333326.0 \n0.7075,0.1748,12.2631,0.9721,-0.5042,9.7453,0.2382,-0.3897,0.099,14.4,-3.8,-42.8,4.38775774,2.95,-5.7,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,112552,2015-10-30 10:15:33:428,1446171333428.0 \n2.2063,-0.8475,13.1801,1.5123,-0.1535,9.6881,-0.43,-0.7025,-0.2822,13.6,-4.2,-43.2,4.501204141,0.3,-7.72,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,112653,2015-10-30 10:15:33:529,1446171333529.0 \n0.0802,0.5052,6.9384,1.4114,0.0357,9.7045,0.0367,-0.0208,-0.1124,12.1,-4.8,-44,4.452160389,-0.21,-8.28,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,112755,2015-10-30 10:15:33:631,1446171333631.0 \n-0.0395,-0.1915,9.1842,1.3897,-0.169,9.7062,-0.369,-0.0183,-0.1222,11.4,-5.5,-44.1,4.410621553,0.57,-8.54,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,112857,2015-10-30 10:15:33:733,1446171333733.0 \n0.5124,1.1073,7.0856,1.2817,-0.052,9.7224,0.3629,0.0428,0.1197,11.3,-5.3,-44.1,4.408527158,0.3,-7.51,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,112959,2015-10-30 10:15:33:835,1446171333835.0 \n0.5243,-0.0599,12.8569,1.4559,0.1009,9.6975,0.182,-0.3018,-0.1503,11.5,-5.5,-44.1,4.454254784,-0.33,-8.03,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,113062,2015-10-30 10:15:33:938,1446171333938.0 \n0.9661,-1.3647,12.6665,1.3527,0.2745,9.709,-0.65,0.2309,-0.3042,11.5,-5.8,-44,4.449891461,-1.6,-7.93,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,113165,2015-10-30 10:15:34:041,1446171334041.0 \n1.2079,0.073,7.5848,1.0262,0.0394,9.7527,0.3054,0.5376,0.1381,11.4,-5.6,-43.7,4.353723819,-0.23,-6.01,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,113268,2015-10-30 10:15:34:144,1446171334144.0 \n0.425,-0.1197,9.068,0.8271,-0.0258,9.7717,-0.0525,0.2724,-0.0831,11.9,-5.4,-43.4,4.395611721,0.15,-4.84,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,113368,2015-10-30 10:15:34:244,1446171334244.0 \n-0.1688,0.6057,7.4735,0.6008,-0.1316,9.7873,-0.1319,0.1698,-0.1869,13,-4.7,-43,4.381300021,0.58,-3.74,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,113469,2015-10-30 10:15:34:345,1446171334345.0 \n-0.0383,0.6548,9.3948,0.6418,-0.165,9.7842,0.0049,-0.066,-0.0061,13.9,-3.9,-42.8,4.435579761,1.05,-3.74,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,113573,2015-10-30 10:15:34:449,1446171334449.0 \n0.9278,0.68,9.4116,0.9133,0.092,9.7636,0.6695,-0.2175,0.3702,13.8,-3.6,-42.7,4.513770512,-0.54,-5.34,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,113674,2015-10-30 10:15:34:550,1446171334550.0 \n-0.6632,-1.1073,11.5173,1.1244,-0.139,9.741,0.2162,0.2944,0.3543,13,-3.7,-43,4.460887035,0.81,-6.58,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,113776,2015-10-30 10:15:34:652,1446171334652.0 \n0.4369,0.5567,7.2568,1.0978,-0.0659,9.7448,0.0843,-0.1576,0.1552,12.6,-4.1,-42.9,4.486717908,0.06,-6.26,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,113878,2015-10-30 10:15:34:754,1446171334754.0 \n0.1113,0.3771,9.1734,1.0884,-0.1922,9.7442,0.0391,-0.1063,-0.0721,12.1,-4.1,-43.1,4.43191457,1.12,-6.37,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,113980,2015-10-30 10:15:34:856,1446171334856.0 \n0.1891,0.7266,8.4731,0.9962,-0.0372,9.7559,0.1283,0.0122,-0.1759,12.1,-3.8,-43.1,4.453556652,0.51,-6.09,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,114082,2015-10-30 10:15:34:958,1446171334958.0 \n-0.0814,0.0215,11.2252,1.0552,0.189,9.7479,0.2004,-0.2016,-0.171,12,-3.8,-42.8,4.52144996,-1.1,-6.18,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,114184,2015-10-30 10:15:35:060,1446171335060.0 \n-0.1616,-1.2629,12.2212,0.8924,0.0879,9.7656,-0.4691,0.121,-0.3115,12.3,-3.9,-42.3,4.485845243,-0.51,-5.22,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,114285,2015-10-30 10:15:35:161,1446171335161.0 \n1.2713,0.3639,7.3909,0.7331,-0.0448,9.7791,-0.2688,-0.022,0.0232,12.7,-3.5,-42.1,4.517086637,0.26,-4.29,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,114388,2015-10-30 10:15:35:264,1446171335264.0 \n0.3136,0.5327,8.0661,0.6567,-0.4088,9.7761,-0.3897,0.1515,-0.1246,13.2,-2.6,-41.9,4.422489792,2.39,-3.84,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,114490,2015-10-30 10:15:35:366,1446171335366.0 \n0.0575,0.7482,8.509,0.5746,-0.482,9.7779,0.0159,0.0244,0.0159,13.6,-1,-41.7,4.530700205,2.82,-3.36,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,114592,2015-10-30 10:15:35:468,1446171335468.0 \n-0.5255,-0.6045,12.5779,0.6812,-0.4534,9.7724,0.2627,-0.2004,0.1979,13.7,-0.3,-41.7,4.581140221,3.07,-3.66,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,114694,2015-10-30 10:15:35:570,1446171335570.0 \n1.6448,-0.844,10.8469,0.7855,-0.111,9.7745,-0.2663,-0.4594,0.0635,13.8,-0.5,-41.8,4.685859976,0.65,-4.59,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,114795,2015-10-30 10:15:35:671,1446171335671.0 \n-0.2382,-0.5219,9.3913,0.8681,-0.2302,9.7654,0.2065,0.3555,0.292,13.3,-0.9,-42.2,4.595626453,1.35,-5.08,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,114900,2015-10-30 10:15:35:776,1446171335776.0 \n-0.2514,-0.0096,9.3111,0.8898,-0.2125,9.7639,-0.38,-0.0159,-0.0611,12.9,-1.9,-42.7,4.568224784,0.64,-5.42,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,115017,2015-10-30 10:15:35:893,1446171335893.0 \n-0.5064,0.3795,8.6491,0.8464,-0.2097,9.7678,0.182,0.1466,-0.0281,12.7,-2,-42.9,4.534365397,1.38,-4.99,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,115103,2015-10-30 10:15:35:979,1446171335979.0 \n-0.2634,0.1496,9.0477,0.7789,-0.0685,9.7754,0.0831,0.0183,-0.1417,12.9,-2.2,-42.9,4.572588107,0.39,-4.39,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,115204,2015-10-30 10:15:36:080,1446171336080.0 \n1.1672,-0.4884,11.1414,0.9459,0.0495,9.7608,0.3213,-0.0684,-0.0953,13.1,-1.8,-42.7,4.608018291,-0.29,-5.54,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,115305,2015-10-30 10:15:36:181,1446171336181.0 \n0.3711,-1.1851,11.3569,0.6917,-0.1811,9.7805,-0.281,0.3604,-0.1319,13.1,-1.6,-42.6,4.56560679,0.59,-4.65,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,115408,2015-10-30 10:15:36:284,1446171336284.0 \n-0.1867,-0.2227,9.9802,0.5541,-0.4117,9.7823,-0.3922,0.0367,-0.0318,13.6,-0.7,-42.3,4.547280833,2.41,-3.24,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,115509,2015-10-30 10:15:36:385,1446171336385.0 \n-0.2837,0.5806,8.0936,0.4768,-0.5643,9.7788,-0.0696,0.0806,0,14.1,0,-42,4.565257724,3.3,-2.79,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,115612,2015-10-30 10:15:36:488,1446171336488.0 \n0.0156,0.0192,9.7947,0.5177,-0.4908,9.7807,0.0367,-0.099,-0.0134,14.7,1.1,-41.5,4.64973166,2.95,-2.89,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,115713,2015-10-30 10:15:36:589,1446171336589.0 \n-0.0658,-0.589,11.2958,0.6768,-0.2323,9.7805,0.4362,-0.237,0.292,14.6,1.5,-41.8,4.732809333,2.29,-3.44,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,115816,2015-10-30 10:15:36:692,1446171336692.0 \n0.2047,-0.8571,11.4395,0.7391,-0.0624,9.7786,0.2248,-0.0024,0.369,14.2,0.7,-42.4,4.755498613,0.36,-4.32,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,115918,2015-10-30 10:15:36:794,1446171336794.0 \n0.4154,0.1508,9.0968,0.962,-0.1756,9.7578,0.3641,-0.2016,0.4496,13.7,0,-43.1,4.649557127,1.56,-5.29,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,116019,2015-10-30 10:15:36:895,1446171336895.0 \n0.1856,0.0682,8.1918,0.914,-0.3605,9.7573,-0.1319,0.3372,-0.077,12.9,-0.8,-43.9,4.562988796,2.11,-5.35,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,116122,2015-10-30 10:15:36:998,1446171336998.0 \n-0.1269,0.1891,8.6048,0.7293,-0.2913,9.7752,0.1784,0.0709,-0.0904,12.5,-0.5,-44.2,4.634023697,1.7,-4.27,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,116226,2015-10-30 10:15:37:102,1446171337102.0 \n0.0251,-0.0958,10.2915,0.7627,-0.1257,9.7761,0.1784,-0.0977,-0.0916,12.7,-0.5,-44.2,4.663868827,1.05,-4.22,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,116325,2015-10-30 10:15:37:201,1446171337201.0 \n1.3827,-0.7985,10.9906,0.9488,0.0394,9.7606,0.0024,-0.2211,-0.1894,12.7,-0.4,-44.3,4.722337357,-0.23,-5.55,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,116429,2015-10-30 10:15:37:305,1446171337305.0 \n0.6572,0.1233,7.8602,0.8876,-0.1388,9.7654,0.2676,0.1234,-0.0648,12.3,-0.4,-44.6,4.673817204,0.81,-5.19,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,116530,2015-10-30 10:15:37:406,1446171337406.0 \n0.5578,-0.4561,10.2232,0.8794,-0.1828,9.7654,-0.347,-0.0806,-0.2896,11.9,-0.1,-44.7,4.676958797,0.74,-5.14,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,116631,2015-10-30 10:15:37:507,1446171337507.0 \n-0.3172,0.3998,7.6734,0.7029,-0.2572,9.778,-0.0721,0.0489,-0.1662,11.8,0.4,-44.5,4.643972074,1.39,-4.27,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,116734,2015-10-30 10:15:37:610,1446171337610.0 \n-0.1748,0.1185,10.0137,0.6984,-0.3204,9.7765,-0.1051,0.0098,0.0122,12,1.3,-44.7,4.692841293,1.69,-4.13,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,116836,2015-10-30 10:15:37:712,1446171337712.0 \n-0.0575,0.0479,11.8142,0.7757,-0.1831,9.7742,0.2297,-0.2443,0.215,11.9,1.7,-45,4.764923391,1.55,-4.48,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,116938,2015-10-30 10:15:37:814,1446171337814.0 \n-0.911,-2.3511,13.7379,1.0838,-0.5232,9.7325,-0.4801,-0.0819,-0.1197,11.3,1.7,-45.8,4.688827035,3.06,-6.35,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,117040,2015-10-30 10:15:37:916,1446171337916.0 \n-0.0024,-0.2131,7.3059,0.8445,-0.3703,9.7632,-0.2236,-0.0855,0.0819,10.9,1.6,-46.1,4.724257219,2.32,-4.81,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,117141,2015-10-30 10:15:38:017,1446171338017.0 \n-0.0443,0.2741,8.0325,0.7208,-0.5441,9.765,0.0904,0.0024,0.1637,10.6,1.4,-46.7,4.602782303,3.24,-4.38,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,117243,2015-10-30 10:15:38:119,1446171338119.0 \n-0.0479,0.334,8.5114,0.7653,-0.4986,9.764,0.0574,-0.1368,0.1381,10.7,1.2,-46.8,4.617094003,2.97,-4.34,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,117347,2015-10-30 10:15:38:223,1446171338223.0 \n-0.2035,-0.7398,12.2966,0.8457,-0.5456,9.7549,-0.11,-0.2395,-0.0819,10.7,0.7,-46.9,4.609240022,3.19,-4.95,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,117450,2015-10-30 10:15:38:326,1446171338326.0 \n0.7063,-0.7398,10.1359,0.8162,-0.5995,9.7542,-0.5351,-0.0855,-0.1588,10.5,0.3,-47.2,4.50294947,3.96,-4.81,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,117550,2015-10-30 10:15:38:426,1446171338426.0 \n0.4561,-1.2797,10.0437,0.7224,-0.8386,9.744,0.077,0.2663,0.0513,10.3,0.6,-47.2,4.472755274,5.45,-4.7,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,117652,2015-10-30 10:15:38:528,1446171338528.0 \n0.431,-0.7087,8.5688,0.68,-0.815,9.749,-0.033,0.1136,-0.0953,10.5,0.8,-47.5,4.523893421,4.65,-4.12,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,117753,2015-10-30 10:15:38:629,1446171338629.0 \n0.1939,-0.1544,8.1965,0.6193,-0.7916,9.755,-0.0269,-0.1112,-0.1148,11,0.7,-47.2,4.519181032,4.59,-3.48,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,117856,2015-10-30 10:15:38:732,1446171338732.0 \n0.2394,-0.2478,9.1985,0.6847,-0.7791,9.7516,0.0049,-0.044,-0.077,11.2,0.4,-47.3,4.459141706,4.61,-4.07,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,117958,2015-10-30 10:15:38:834,1446171338834.0 \n-0.0551,-0.3903,11.133,0.7038,-0.6095,9.7624,0.4215,-0.0648,0.2309,11.2,0.1,-47.5,4.481830986,4.16,-4.01,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,118060,2015-10-30 10:15:38:936,1446171338936.0 \n-0.8056,-1.646,13.3812,0.8902,-0.4584,9.7554,-0.1906,0.0648,0.0183,11,-0.9,-48,4.507312793,2.68,-5.21,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,118163,2015-10-30 10:15:39:039,1446171339039.0 \n-0.498,-0.0622,8.2899,0.6682,-0.2883,9.7796,0.4129,0.204,0.2334,10.9,-1.9,-47.8,4.479038459,1.68,-3.91,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,118264,2015-10-30 10:15:39:140,1446171339140.0 \n-0.0443,0.3148,7.9212,0.5994,-0.1634,9.7869,0.1552,0.2358,0.0916,11,-3.5,-47.4,4.446575335,0.95,-3.5,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,118366,2015-10-30 10:15:39:242,1446171339242.0 \n-0.2227,0.8464,8.0278,0.4307,0.0355,9.7971,0.2492,0.1368,0.0843,11.4,-4.3,-46.9,4.407305427,0.21,-2.75,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,118468,2015-10-30 10:15:39:344,1446171339344.0 \n-0.5602,0.7602,9.7983,0.455,0.2018,9.794,0.1723,-0.336,-0.077,12.1,-5.7,-46.4,4.346742502,-0.86,-2.35,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,118570,2015-10-30 10:15:39:446,1446171339446.0 \n-0.17,0.4477,10.9283,0.5684,0.2694,9.7865,-0.0415,-0.1222,-0.1772,12.3,-6.3,-46.1,4.398404248,-1.57,-3.32,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,118671,2015-10-30 10:15:39:547,1446171339547.0 \n0.7578,-0.255,8.8777,0.6556,-0.0869,9.7843,-0.1613,0.0147,-0.0024,12.4,-6.9,-45.9,4.255461782,0.51,-3.83,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,118773,2015-10-30 10:15:39:649,1446171339649.0 \n0.2981,-0.4357,10.3214,0.6937,-0.4283,9.7727,0.0098,0.1051,0.0269,12.2,-6.2,-45.8,4.230678107,2.5,-4.06,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,118876,2015-10-30 10:15:39:752,1446171339752.0 \n0.1089,0.5339,7.7297,0.626,-0.4969,9.774,-0.1454,0.0415,-0.1625,12.4,-4.8,-45.3,4.259301507,2.9,-3.66,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,118978,2015-10-30 10:15:39:854,1446171339854.0 \n-0.3699,-0.103,10.5608,0.7405,-0.5738,9.7618,-0.0757,-0.1002,-0.0574,12.5,-3.6,-45.1,4.332605335,3.24,-4.15,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,119080,2015-10-30 10:15:39:956,1446171339956.0 \n0.395,0.1927,10.6386,0.7755,-0.1926,9.774,0.4924,0.0061,0.4191,12.7,-3.1,-44.5,4.445179072,1.99,-4.48,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,119181,2015-10-30 10:15:40:057,1446171340057.0 \n-0.0491,-1.4521,13.5644,0.908,-0.2144,9.7622,-0.1808,-0.3067,0.0672,12.6,-3.6,-44.4,4.447622533,0.77,-5.1,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,119284,2015-10-30 10:15:40:160,1446171340160.0 \n0.0407,0.0587,8.0493,0.8344,-0.1741,9.7695,0.0134,-0.1368,-0.0073,12.6,-4.7,-44.2,4.392819194,0.68,-4.82,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,119386,2015-10-30 10:15:40:262,1446171340262.0 \n-0.0455,0.4118,8.3749,0.7976,-0.2365,9.7713,0.0929,-0.0464,-0.0501,12.8,-5.3,-44.3,4.362624998,1.38,-4.67,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,119487,2015-10-30 10:15:40:363,1446171340363.0 \n0.1389,0.8918,7.58,0.7452,-0.102,9.7778,0.0489,-0.044,-0.182,13,-5.3,-44.2,4.37047898,1.08,-4.39,36.814014,-119.74869,260.26,336.4767745,4.45,12.903226,274.59,17 / 17,119589,2015-10-30 10:15:40:465,1446171340465.0 \n-0.2502,-0.4082,11.886,0.8959,-0.0331,9.7656,0.0696,-0.3018,-0.2321,13.3,-5.1,-44,4.417951936,0.19,-5.24,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,119691,2015-10-30 10:15:40:567,1446171340567.0 \n0.7781,-1.1193,10.2316,0.9021,-0.1775,9.7635,-0.573,-0.0244,-0.3409,13.3,-5,-43.9,4.431565504,-0.12,-5.33,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,119794,2015-10-30 10:15:40:670,1446171340670.0 \n1.3707,-0.0108,7.4196,0.7597,-0.2929,9.7728,0.0501,-0.1869,0.2138,13.4,-4.1,-43.5,4.400847709,1.71,-4.44,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,119896,2015-10-30 10:15:40:772,1446171340772.0 \n1.0822,-0.1221,9.0597,0.7698,-0.4814,9.7645,-0.2615,0.1319,-0.0892,13.5,-3.6,-43.6,4.390724799,2.54,-4.85,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,119998,2015-10-30 10:15:40:874,1446171340874.0 \n-0.0108,0.3926,7.6195,0.5463,-0.4779,9.7798,-0.0061,0.2199,-0.1491,14.3,-2.6,-43.3,4.413239547,2.79,-3.2,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,120099,2015-10-30 10:15:40:975,1446171340975.0 \n-0.6991,-0.2071,10.2137,0.4923,-0.497,9.7817,0.0794,-0.0599,0.0965,14.7,-2.2,-43.3,4.475722334,2.92,-2.95,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,120201,2015-10-30 10:15:41:077,1446171341077.0 \n-0.2514,0.0874,9.2129,0.531,-0.2046,9.7901,0.4911,-0.0379,0.4239,15.3,-1.9,-42.6,4.547629899,1.2,-3.1,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,120303,2015-10-30 10:15:41:179,1446171341179.0 \n0.1125,-0.0371,9.4619,0.8,-0.3317,9.7683,-0.2688,-0.2065,0.16,15.2,-2.7,-42.6,4.477991262,1.94,-4.68,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,120406,2015-10-30 10:15:41:282,1446171341282.0 \n-0.1293,-0.3436,9.9515,0.9324,-0.2487,9.7591,-0.3213,-0.1833,-0.1527,14.7,-3.5,-42.7,4.514643176,1.03,-5.01,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,120507,2015-10-30 10:15:41:383,1446171341383.0 \n-0.1437,0.1604,9.0668,0.8691,-0.2257,9.7655,0.2676,0.1735,-0.1002,14,-3.9,-43.2,4.44029215,1.32,-5.09,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,120610,2015-10-30 10:15:41:486,1446171341486.0 \n0.1891,0.1089,9.0704,0.707,0.0241,9.7811,0.1808,0.1185,-0.204,14,-4.2,-43.2,4.487939639,-0.14,-4.13,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,120711,2015-10-30 10:15:41:587,1446171341587.0 \n1.4593,0.1999,8.2995,0.6517,0.5041,9.772,0.6402,0.3726,-0.2676,14.3,-4.7,-43,4.545535504,-2.95,-3.82,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,120813,2015-10-30 10:15:41:689,1446171341689.0 \n0.6165,-1.7753,11.7998,0.5434,0.4403,9.7817,-0.6768,0.8968,-0.9603,14.8,-5.2,-42.7,4.5757297,-3.47,-3.89,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,120915,2015-10-30 10:15:41:791,1446171341791.0 \n1.6233,0.0395,10.1191,-0.0262,0.0513,9.8065,-0.226,0.2981,-1.091,16.1,-3.8,-41.6,4.478863926,-0.3,0.15,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,121020,2015-10-30 10:15:41:896,1446171341896.0 \n1.5598,0.7829,8.8729,-0.458,-0.0056,9.7959,0.2981,0.011,-1.5137,18.1,0.4,-39.8,4.710992717,0.03,2.68,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,121120,2015-10-30 10:15:41:996,1446171341996.0 \n-0.2933,0.176,9.5852,-0.6823,0.1048,9.7823,0.193,0.022,-1.6432,19.2,3.7,-39.1,4.974537434,-0.54,3.87,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,121222,2015-10-30 10:15:42:098,1446171342098.0 \n-0.8248,-0.2322,10.2161,-0.5744,0.3524,9.7835,0.3958,-0.1539,-1.6432,18.5,7.3,-39,5.167221783,-1.57,3.54,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,121324,2015-10-30 10:15:42:200,1446171342200.0 \n0.3005,-1.4269,11.9363,-0.6682,0.4979,9.7712,0.2101,-0.1429,-1.3085,17.9,9.9,-38.8,5.378581156,-2.91,3.91,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,121425,2015-10-30 10:15:42:301,1446171342301.0 \n0.0563,-0.8667,8.4408,-0.6705,0.6695,9.7608,0.38,-0.3396,-1.19,16,13.3,-38.7,5.580690283,-3.91,3.93,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,121528,2015-10-30 10:15:42:404,1446171342404.0 \n-1.0762,-0.2885,8.6227,-0.7695,0.4343,9.7668,-0.281,0.1564,-1.3134,14.6,15.2,-38.8,5.670051141,-3,4.33,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,121629,2015-10-30 10:15:42:505,1446171342505.0 \n-1.5131,0.0922,9.1674,-0.648,0.2573,9.7818,-0.1051,-0.1197,-1.102,11.6,18.5,-38.6,5.844758599,-1.5,3.79,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,121731,2015-10-30 10:15:42:607,1446171342607.0 \n-1.4521,-0.2286,8.5126,-0.5563,0.1931,9.789,0.0794,-0.2712,-0.9163,9.9,20.2,-38.6,5.933595858,-1.03,3.58,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,121834,2015-10-30 10:15:42:710,1446171342710.0 \n-0.8643,-0.1496,10.1323,-0.3044,0.2669,9.7983,0.7709,0.033,-0.4459,7,22.5,-38.8,6.047216792,-1.56,1.78,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,121936,2015-10-30 10:15:42:812,1446171342812.0 \n0.1496,0.0946,11.3222,-0.3762,0.5134,9.786,-0.215,-0.0098,-0.8833,5.2,23,-39.5,6.143209901,-3.67,2.07,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,122038,2015-10-30 10:15:42:914,1446171342914.0 \n-0.9708,0.1053,8.7281,-0.4696,0.511,9.7821,0.0819,-0.0916,-0.5143,2.8,23.4,-40,6.242693669,-3.2,2.83,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,122139,2015-10-30 10:15:43:015,1446171343015.0 \n-0.1856,0.9433,7.5262,-0.4043,0.4286,9.7889,-0.1943,-0.0819,-0.2089,1.5,23.6,-40.3,6.269746272,-2.5,2.36,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,122241,2015-10-30 10:15:43:117,1446171343117.0 \n-0.0706,0.9062,9.5924,-0.1889,0.2201,9.8024,-0.1918,-0.2419,-0.1454,0.3,24.4,-39.8,0.040491639,-1.34,1.45,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,122343,2015-10-30 10:15:43:219,1446171343219.0 \n-0.3424,0.1867,13.1873,-0.068,0.283,9.8023,0.1014,-0.2847,0.0391,-0.6,24.8,-39.5,0.048694686,-1.65,0.4,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,122446,2015-10-30 10:15:43:322,1446171343322.0 \n-0.9792,-1.2617,12.6965,0.0482,0.3615,9.7999,-0.2566,-0.3018,-0.1258,-1.2,24.8,-39.4,0.030543262,-2.11,-0.28,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,122548,2015-10-30 10:15:43:424,1446171343424.0 \n-0.1185,0.6321,7.3801,0.144,0.2713,9.8018,-0.2822,-0.11,-0.2285,-1.4,24.5,-39.5,0.01850049,-1.69,-0.76,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,122649,2015-10-30 10:15:43:525,1446171343525.0 \n-0.5267,0.1796,8.2325,-0.0113,0.0759,9.8064,-0.1075,0.3213,-0.1491,-1.7,24.5,-39.8,0.080634211,-0.44,0.07,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,122751,2015-10-30 10:15:43:627,1446171343627.0 \n-0.6165,0.4932,8.2756,-0.0853,0.3033,9.8016,0.0696,0.0171,-0.1442,-1.8,24.4,-39.7,0.091106187,-1.8,0.44,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,122854,2015-10-30 10:15:43:730,1446171343730.0 \n-0.4142,-0.5578,10.6494,-0.1558,0.439,9.7956,0.259,-0.2627,-0.0574,-1.8,23.9,-39.9,0.101927228,-2.57,0.91,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,122955,2015-10-30 10:15:43:831,1446171343831.0 \n1.0223,-0.4776,9.4044,-0.0251,0.6793,9.7831,0.2541,-0.0318,-0.022,-2,23.2,-39.7,0.08709193,-3.78,0.33,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,123057,2015-10-30 10:15:43:933,1446171343933.0 \n-0.1796,0.1125,8.8166,-0.2087,0.3445,9.7984,0.0367,0.1307,-0.0953,-2.6,22.5,-39.9,0.156556034,-2.01,1.22,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,123160,2015-10-30 10:15:44:036,1446171344036.0 \n0.3388,0.5243,8.0302,-0.2035,0.2622,9.801,0.2395,0.1148,-0.0354,-3.2,22.5,-39.4,0.15097098,-1.22,0.92,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,123262,2015-10-30 10:15:44:138,1446171344138.0 \n-0.2358,0.7242,7.8614,-0.3096,0.3471,9.7956,0.0367,0.1332,-0.1185,-3.5,22.8,-39.3,0.167377075,-1.94,1.63,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,123363,2015-10-30 10:15:44:239,1446171344239.0 \n-0.5124,-0.1784,10.5058,-0.2393,0.3187,9.7985,-0.0513,-0.1625,0.0122,-3.8,23,-39.2,0.201410996,-1.86,1.4,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,123466,2015-10-30 10:15:44:342,1446171344342.0 \n-0.2322,-0.4345,9.8904,-0.0351,0.5531,9.791,0.2175,-0.0012,0.259,-4.3,22.6,-39.7,0.162839219,-3.23,0.21,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,123567,2015-10-30 10:15:44:443,1446171344443.0 \n-1.573,-1.4377,10.3932,-0.0225,0.4283,9.7973,0.0452,0.0208,0.2871,-4.6,22.3,-39.8,0.202458193,-2.66,-0.15,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,123670,2015-10-30 10:15:44:546,1446171344546.0 \n-0.8523,-0.0431,8.9579,0.0926,0.3907,9.7984,-0.0855,-0.2993,0.2724,-4.7,22.2,-39.9,0.193557014,-2.28,-0.54,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,123771,2015-10-30 10:15:44:647,1446171344647.0 \n-1.5191,0.3136,9.3529,0.1328,0.2627,9.8022,0.0244,-0.1747,0.4594,-4.5,22.4,-39.8,0.154985238,-1.5,-0.57,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,123875,2015-10-30 10:15:44:751,1446171344751.0 \n-1.6316,0.3974,9.4439,0.3797,0.3725,9.7922,0.0024,-0.4728,0.8613,-4.2,22.5,-39.4,0.101229097,-2.18,-2.22,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,123975,2015-10-30 10:15:44:851,1446171344851.0 \n-0.9098,0.3268,10.744,0.7248,0.4307,9.7703,0.1283,-0.2761,0.7245,-3.9,22.3,-39.2,0.043982297,-2.45,-4.34,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,124077,2015-10-30 10:15:44:953,1446171344953.0 \n-1.0942,-1.1791,13.55,0.6189,0.4133,9.7784,-0.4227,-0.1038,0.2932,-2.9,21.6,-39.5,0.022514747,-2.42,-3.62,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,124180,2015-10-30 10:15:45:056,1446171345056.0 \n0.0012,1.0307,7.8278,0.5281,0.394,9.7845,0.0562,-0.1918,0.6927,-1.9,21.3,-39.6,0.003839724,-1.98,-2.74,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,124282,2015-10-30 10:15:45:158,1446171345158.0 \n-0.2825,0.7566,8.5904,0.6879,0.2611,9.779,-0.0855,-0.2138,0.6842,-0.3,20.7,-39.7,6.156648936,-1.53,-4.02,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,124384,2015-10-30 10:15:45:260,1446171345260.0 \n-0.3508,0.8332,8.2636,0.5669,0.2086,9.788,0.0965,-0.0159,0.7721,1.1,20.1,-39.3,6.12820007,-1.22,-3.31,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,124486,2015-10-30 10:15:45:362,1446171345362.0 \n-0.1377,-0.1245,11.4287,0.584,0.2234,9.7867,0.16,-0.182,1.0629,2.1,19.6,-39.3,6.088755629,-1.11,-3.07,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,124588,2015-10-30 10:15:45:464,1446171345464.0 \n-0.0898,0.1628,8.691,0.4144,0.4387,9.7881,-0.5498,-0.1857,0.7343,3.2,18.8,-39.4,6.03395229,-2.36,-3.3,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,124690,2015-10-30 10:15:45:566,1446171345566.0 \n-0.2586,0.2119,8.4815,0.3194,0.1668,9.8,0.0684,0.4545,1.0104,5.7,17,-39.4,5.892755154,-0.97,-1.87,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,124791,2015-10-30 10:15:45:667,1446171345667.0 \n0.17,0.1867,9.1877,0.2063,-0.0373,9.8044,-0.1051,0.2309,0.6182,7.1,16.1,-39.3,5.811597343,0.03,-1.69,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,124895,2015-10-30 10:15:45:771,1446171345771.0 \n-0.0108,0.6189,8.8226,0.1917,-0.1239,9.804,0.121,-0.0513,0.2957,9.1,15.5,-39.2,5.721363821,0.72,-1.12,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,124996,2015-10-30 10:15:45:872,1446171345872.0 \n-0.6488,0.6081,9.9216,0.1745,-0.0653,9.8049,0.0269,-0.0134,0.0318,10,15.2,-39,5.653121447,0.56,-0.97,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,125098,2015-10-30 10:15:45:974,1446171345974.0 \n0.0323,0.3077,8.7209,0.2916,0.2076,9.8001,0.3005,0.1967,-0.011,10.4,14.7,-39.1,5.653645046,-0.85,-1.98,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,125200,2015-10-30 10:15:46:076,1446171346076.0 \n-1.6221,-1.5347,12.8401,0.3533,-0.012,9.8003,0.1478,0.077,-0.0073,10.1,14.6,-39.3,5.632875628,-0.12,-2.18,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,125302,2015-10-30 10:15:46:178,1446171346178.0 \n-0.5638,-0.498,9.5708,0.2503,-0.0828,9.8031,-0.2602,0.1051,-0.2297,9.7,14.7,-39.5,5.640206011,0.48,-1.46,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,125403,2015-10-30 10:15:46:279,1446171346279.0 \n-0.2622,0.6213,7.2796,0.0194,-0.1342,9.8057,-0.011,0.1319,-0.0672,9.7,15.2,-39.5,5.668131279,0.76,-0.34,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,125506,2015-10-30 10:15:46:382,1446171346382.0 \n-0.6895,0.3903,9.8797,0.0047,-0.0226,9.8066,0.0061,-0.0562,-0.0623,10.1,15.8,-39.1,5.721189288,0.13,-0.03,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,125608,2015-10-30 10:15:46:484,1446171346484.0 \n-0.7769,0.1772,10.5489,0.077,0.2068,9.8042,0.0611,0.2248,0.1588,10.4,16,-39,5.733406593,-1.21,-0.45,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,125711,2015-10-30 10:15:46:587,1446171346587.0 \n-0.644,-0.0227,10.0844,0.0178,0.1062,9.8061,-0.2407,-0.0586,0.0305,10.6,15.7,-39.1,5.689947894,-0.62,-0.1,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,125811,2015-10-30 10:15:46:687,1446171346687.0 \n-0.9158,-0.2897,10.0521,0.1272,-0.0374,9.8058,-0.3164,-0.1222,-0.044,10.6,15.5,-39.3,5.655390375,0.22,-0.74,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,125915,2015-10-30 10:15:46:791,1446171346791.0 \n-1.057,0.2274,8.9926,0.074,-0.0446,9.8063,0.0696,-0.0415,-0.066,10.6,15.7,-39.3,5.663244357,0.26,-0.43,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,126016,2015-10-30 10:15:46:892,1446171346892.0 \n-0.7123,0.723,8.0481,0.0153,0.087,9.8063,0.1796,0.1356,0.0525,10.7,15.7,-39.6,5.688377098,-0.51,-0.09,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,126117,2015-10-30 10:15:46:993,1446171346993.0 \n-1.0187,-0.3124,11.5173,0.0924,0.3503,9.8,0.3836,0.0843,0.0648,10.7,15.6,-39.8,5.691518691,-1.38,-0.57,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,126219,2015-10-30 10:15:47:095,1446171347095.0 \n-1.5071,-1.5526,12.6737,0.0329,0.2137,9.8043,0.0428,0.2847,-0.0269,10.7,15,-40.2,5.671272871,-1.25,-0.19,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,126322,2015-10-30 10:15:47:198,1446171347198.0 \n0.0108,-0.0934,10.0078,-0.0425,0.1,9.806,-0.16,-0.0953,-0.16,10.7,15,-40.5,5.689424296,-1.24,0.42,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,126424,2015-10-30 10:15:47:300,1446171347300.0 \n-0.9876,0.4513,7.4172,-0.2563,-0.0407,9.8032,-0.1637,0.1014,-0.1026,10.7,15.6,-40.4,5.722061953,0.24,1.5,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,126526,2015-10-30 10:15:47:402,1446171347402.0 \n-0.8703,0.5171,9.5565,-0.2877,-0.1486,9.8013,-0.1356,-0.044,0.0843,10.8,16.6,-40.1,5.743180437,0.87,1.68,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,126628,2015-10-30 10:15:47:504,1446171347504.0 \n-0.6656,-0.0778,12.3218,-0.1263,0.0218,9.8058,0.3958,0.0745,0.4142,11,16.8,-39.7,5.724854479,0.52,0.87,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,126730,2015-10-30 10:15:47:606,1446171347606.0 \n-1.7286,-1.646,13.2782,0.0233,0.0132,9.8066,-0.2334,-0.3897,0.1674,11.3,16.2,-39.9,5.678428721,-0.08,-0.14,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,126831,2015-10-30 10:15:47:707,1446171347707.0 \n-0.9146,0.1891,8.4527,-0.0368,-0.009,9.8066,-0.0049,-0.2358,0.3335,11.4,15.8,-40.1,5.686282703,0.05,0.22,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,126934,2015-10-30 10:15:47:810,1446171347810.0 \n-0.1891,0.7853,8.1151,0.0364,-0.1495,9.8054,0.0745,-0.055,0.2676,11.4,15.1,-40.2,5.623974449,0.87,-0.21,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,127036,2015-10-30 10:15:47:912,1446171347912.0 \n-0.5339,0.7386,8.1558,-0.0345,-0.0556,9.8064,0.1234,0.1442,0.1686,11.5,14.9,-40.2,5.596049181,0.56,0.02,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,127138,2015-10-30 10:15:48:014,1446171348014.0 \n-0.3675,-0.2322,11.2312,0.0558,0.1005,9.806,0.2786,-0.1979,0.0379,11.9,14.4,-40.3,5.579468553,-0.59,-0.33,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,127239,2015-10-30 10:15:48:115,1446171348115.0 \n0.1927,-0.2418,10.3597,0.18,0.1685,9.8036,-0.3763,-0.1038,-0.2724,12,14.1,-40.4,5.598143576,-1.48,-0.39,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,127341,2015-10-30 10:15:48:217,1446171348217.0 \n0.929,0.9493,8.0373,0.022,0.1161,9.8059,-0.3286,-0.0049,-0.3848,11.7,13.7,-41,5.587497067,-0.68,-0.13,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,127451,2015-10-30 10:15:48:327,1446171348327.0 \n-0.2119,0.6201,7.2449,-0.091,-0.1775,9.8046,-0.2162,0.2749,-0.314,11.4,14.3,-41,5.607742887,1.04,0.53,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,127546,2015-10-30 10:15:48:422,1446171348422.0 \n-0.4298,0.7889,7.7309,-0.1619,-0.1391,9.8043,0.2602,0.022,-0.0354,11.3,15.1,-40.7,5.651201585,1.23,0.93,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,127648,2015-10-30 10:15:48:524,1446171348524.0 \n-0.7805,-0.3603,12.05,-0.0831,0.0073,9.8063,0.347,-0.2101,0.1943,11.1,15.8,-40.2,5.69623108,-0.04,0.49,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,127750,2015-10-30 10:15:48:626,1446171348626.0 \n-0.0144,0.2634,9.511,-5.00E-04,0.3958,9.7987,0.4569,0.1173,0.3958,11,15.3,-40.4,5.698150942,-2.31,0,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,127852,2015-10-30 10:15:48:728,1446171348728.0 \n-0.5842,-0.2155,10.3525,0.1295,0.2783,9.8018,0.0586,-0.2334,0.3396,10.6,14.4,-40.9,5.632352029,-1.63,-0.76,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,127955,2015-10-30 10:15:48:831,1446171348831.0 \n-0.3484,0.158,8.831,0.1701,0.1293,9.8043,-0.0586,0.0342,0.0257,10.4,13.4,-41.8,5.613153407,-0.94,-1.15,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,128056,2015-10-30 10:15:48:932,1446171348932.0 \n-0.5734,0.5279,8.582,0.1148,0.1676,9.8045,0.0305,0.088,-0.0012,10.2,13.5,-41.9,5.655913974,-0.82,-0.8,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,128158,2015-10-30 10:15:49:034,1446171349034.0 \n-0.577,0.5746,9.7157,0.0749,0.324,9.801,0.121,-0.0073,-0.0024,10.3,13.3,-41.9,5.660626363,-1.89,-0.44,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,128260,2015-10-30 10:15:49:136,1446171349136.0 \n-0.7278,0.1269,10.1059,0.1352,0.5883,9.7881,0.1222,-0.0709,0.0538,10.4,12.9,-42,5.675636195,-3.13,-0.84,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,128362,2015-10-30 10:15:49:238,1446171349238.0 \n-0.2502,-0.1568,10.647,0.057,0.3436,9.8005,-0.0599,0.0843,0.0086,10.4,12.2,-42.5,5.632701095,-2.01,-0.33,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,128464,2015-10-30 10:15:49:340,1446171349340.0 \n0.5351,0.2598,10.0126,0.053,0.1927,9.8046,-0.3555,-0.0977,-0.2639,10.4,12,-42.5,5.631653897,-1.65,-0.1,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,128566,2015-10-30 10:15:49:442,1446171349442.0 \n-0.3615,0.4537,8.0074,-0.1981,-0.0246,9.8046,-0.1197,0.2395,-0.3018,10.5,12.9,-41.9,5.608266485,-0.07,0.76,36.814037,-119.74878,259.4,336.4767745,4.23,12.903226,278.92,17 / 17,128668,2015-10-30 10:15:49:544,1446171349544.0 \n0.2382,0.595,9.6989,-0.3415,-0.0612,9.8005,-0.1222,0.2749,-0.6744,10.9,14.2,-41.6,5.676508859,0.36,2,36.814144,-119.74884,258.68,336.4767745,3.84,12.903226,331.44,17 / 17,128770,2015-10-30 10:15:49:646,1446171349646.0 \n0.6249,0.4884,11.1654,-0.5988,-0.0328,9.7883,0.2175,0.3286,-0.6231,11.1,15.1,-41.1,5.764822519,0.19,3.5,36.814144,-119.74884,258.68,336.4767745,3.84,12.903226,331.44,17 / 17,128872,2015-10-30 10:15:49:748,1446171349748.0 \n-0.9792,-2.1452,13.6984,-0.7076,0.2761,9.7772,-0.4606,0.0782,-1.5259,11.1,15.8,-40.9,5.846503928,-1.61,4.14,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,128973,2015-10-30 10:15:49:849,1446171349849.0 \n-0.7841,-0.5423,7.2472,-0.8412,0.368,9.7636,0.485,-0.3812,-1.179,10.5,16.8,-40.6,5.905146991,-1.23,5.38,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,129076,2015-10-30 10:15:49:952,1446171349952.0 \n-0.8559,-0.3136,8.9807,-0.8272,0.113,9.771,-0.4423,0.1759,-1.1716,8.9,18.1,-40.7,5.993460651,-0.66,4.84,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,129177,2015-10-30 10:15:50:053,1446171350053.0 \n-1.2857,0.0838,8.8933,-0.7405,0.2706,9.7749,0.0489,0.0745,-0.8271,7.1,19.5,-40.8,6.097307742,-1.54,4.21,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,129280,2015-10-30 10:15:50:156,1446171350156.0 \n-1.306,0.51,8.7747,-0.7004,0.396,9.7736,-0.0794,-0.2517,-0.6622,4.5,20.6,-41.4,6.192602719,-2.31,4.1,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,129382,2015-10-30 10:15:50:258,1446171350258.0 \n-1.6843,-0.0407,11.0097,-0.5752,0.3539,9.7834,0.0929,0.0318,-0.5632,2.7,21.2,-41.8,6.25648177,-1.79,3.28,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,129485,2015-10-30 10:15:50:361,1446171350361.0 \n-0.9637,-0.9577,12.7587,-0.4126,0.0671,9.7977,-0.4569,0.0086,-0.5889,0.4,21.6,-41.9,0.077841685,-0.93,2.42,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,129586,2015-10-30 10:15:50:462,1446171350462.0 \n-0.3962,0.0407,9.5972,-0.3588,0.094,9.7996,-0.2248,-0.0318,-0.2065,-1.5,22.5,-41.9,0.107861348,-0.55,2.1,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,129687,2015-10-30 10:15:50:563,1446171350563.0 \n-1.3563,0.3184,7.1682,-0.4716,0.0697,9.7951,-0.0147,0.0049,0.1136,-2.3,22.9,-41.6,0.170693201,-0.41,2.76,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,129790,2015-10-30 10:15:50:666,1446171350666.0 \n-0.844,0.3017,9.1291,-0.4236,0.0896,9.7971,0.0061,-0.0611,0.088,-2.6,23.2,-41.6,0.202981792,-0.52,2.48,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,129891,2015-10-30 10:15:50:767,1446171350767.0 \n-0.6404,-0.4298,12.8377,-0.3128,0.1084,9.8011,0.3103,0.0281,0.259,-2.6,23.3,-41.6,0.185004901,-0.12,1.81,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,129994,2015-10-30 10:15:50:870,1446171350870.0 \n-2.0399,-1.1097,11.655,-0.3755,0.076,9.7992,-0.2993,0.1405,0.1356,-2.3,23,-41.3,0.151843645,-0.44,2.19,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,130097,2015-10-30 10:15:50:973,1446171350973.0 \n-0.3843,0.2765,9.0202,-0.0402,0.1683,9.8051,0.3506,-0.5938,0.2773,-2.2,23,-41.2,0.113620934,-0.82,0.96,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,130198,2015-10-30 10:15:51:074,1446171351074.0 \n-0.9062,0.3041,8.9759,-0.016,0.1082,9.806,-0.044,-0.0574,0.0244,-2.2,22.8,-41.3,0.087964594,-0.63,0.09,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,130300,2015-10-30 10:15:51:176,1446171351176.0 \n-0.9122,0.8212,7.5178,-0.0628,0.2721,9.8027,0.0892,-0.0183,-0.0024,-2.4,22.9,-41.4,0.091455253,-1.11,0.25,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,130401,2015-10-30 10:15:51:277,1446171351277.0 \n-0.9732,-0.0443,11.1306,-0.0282,0.3643,9.7998,0.0489,0.0122,-0.011,-2.6,22.4,-42.1,0.13962634,-1.78,0.38,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,130503,2015-10-30 10:15:51:379,1446171351379.0 \n-0.3424,-0.7482,10.9678,-0.0047,0.2847,9.8025,-0.4423,0.0501,-0.2395,-2.6,22.1,-42.2,0.123045712,-2.42,-0.09,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,130607,2015-10-30 10:15:51:483,1446171351483.0 \n-0.3041,0.243,8.1439,-0.2318,0.0701,9.8037,0.2334,-0.2175,0.1991,-2.6,22.4,-41.9,0.190589954,-0.02,1.7,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,130708,2015-10-30 10:15:51:584,1446171351584.0 \n-0.4992,0.4118,8.3043,-0.3177,-0.0921,9.8011,0.0696,-0.0977,0.1173,-2.1,22.9,-41.2,0.146084058,0.54,1.86,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,130809,2015-10-30 10:15:51:685,1446171351685.0 \n-0.6357,0.4968,8.0385,-0.304,-0.0505,9.8018,0.0452,0.1222,0.0782,-1.7,23.4,-40.6,0.1425934,0.3,1.78,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,130912,2015-10-30 10:15:51:788,1446171351788.0 \n-0.9337,-0.1891,10.404,-0.2689,0.0173,9.8029,0.1307,0.0354,0.1075,-1.2,23.4,-40.4,0.090582588,-0.1,1.57,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,131014,2015-10-30 10:15:51:890,1446171351890.0 \n0.0048,0.2562,10.2029,-0.1941,0.2683,9.8011,0.1808,0.2492,0.2749,-1.1,23.2,-40.2,0.076445421,-0.79,1.15,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,131116,2015-10-30 10:15:51:992,1446171351992.0 \n-0.8799,-0.7302,12.3864,-0.2257,0.185,9.8023,-0.1564,0.0721,0.0819,-0.9,22.7,-40.4,0.077318086,-1.35,1.22,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,131218,2015-10-30 10:15:52:094,1446171352094.0 \n-0.5243,-0.0515,9.0968,-0.0703,0.2798,9.8024,-0.0354,-0.1405,-0.0452,-0.7,22.2,-40.7,0.055850536,-1.63,0.41,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,131319,2015-10-30 10:15:52:195,1446171352195.0 \n-0.6201,0.5794,8.1666,-0.0703,0.2961,9.8019,0.1075,-0.0073,-0.1173,-0.6,22.2,-40.9,0.060388392,-1.45,0.55,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,131422,2015-10-30 10:15:52:298,1446171352298.0 \n-0.7673,0.9278,8.1175,-0.1322,0.5127,9.7923,0.2468,0.066,-0.0391,-0.8,22,-41.1,0.063704518,-2.5,0.72,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,131524,2015-10-30 10:15:52:400,1446171352400.0 \n-0.1257,0.492,9.7217,-0.045,0.6912,9.7822,0.3262,-0.0379,-0.0611,-1.3,21.5,-41.7,0.047822022,-4.04,0.26,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,131626,2015-10-30 10:15:52:502,1446171352502.0 \n-1.2629,-0.6812,11.4012,-0.2163,0.556,9.7885,-0.3567,0.336,-0.3897,-1.5,21.1,-42.1,0.063006386,-3.86,0.68,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,131727,2015-10-30 10:15:52:603,1446171352603.0 \n-0.595,-0.0575,8.9651,-0.2602,0.4742,9.7917,-0.3995,-0.0599,-0.1539,-1.8,21.2,-42.5,0.134564885,-2.77,1.52,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,131830,2015-10-30 10:15:52:706,1446171352706.0 \n-0.5555,0.5997,7.5561,-0.2238,0.2717,9.8003,-0.0171,0.066,0.0269,-1.9,21.6,-42.3,0.12705997,-1.59,1.31,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,131932,2015-10-30 10:15:52:808,1446171352808.0 \n-0.5997,0.814,8.7424,-0.1967,0.2901,9.8004,0.0721,-0.0794,0.099,-1.9,22.3,-42,0.121823982,-1.7,1.15,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,132033,2015-10-30 10:15:52:909,1446171352909.0 \n-0.9996,0.1053,11.5712,-0.1011,0.3632,9.7994,0.2871,-0.1881,0.2077,-2.1,22.6,-41.7,0.108908545,-1.73,0.89,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,132135,2015-10-30 10:15:53:011,1446171353011.0 \n-1.0511,-0.565,11.7424,-0.1272,0.5327,9.7913,0.0672,0.2077,0.1991,-2.2,22.4,-41.7,0.104545222,-3.11,0.74,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,132238,2015-10-30 10:15:53:114,1446171353114.0 \n-0.6153,0.3915,9.2787,-0.0143,0.407,9.7982,-0.0745,-0.1258,0.1124,-2.1,22.2,-41.7,0.090757121,-2.5,0.23,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,132340,2015-10-30 10:15:53:216,1446171353216.0 \n-1.0822,0.1927,9.0202,0.0299,0.1632,9.8052,-0.0696,-0.022,0.0672,-2,22,-41.5,0.080634211,-1.21,-0.21,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,132442,2015-10-30 10:15:53:318,1446171353318.0 \n-0.4465,1.1265,7.7237,0.0618,0.2646,9.8029,0.1564,-0.0452,0.0929,-2,22.3,-41.5,0.07819075,-1.3,-0.29,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,132544,2015-10-30 10:15:53:420,1446171353420.0 \n-0.5243,0.8224,10.3585,0.1386,0.4114,9.797,0.2065,-0.1332,-0.1405,-2.2,22.4,-41.5,0.059864793,-2.4,-0.81,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,132646,2015-10-30 10:15:53:522,1446171353522.0 \n0.996,0.3843,10.0556,0.4554,0.7668,9.766,0.2639,-0.3751,-0.1588,-2.8,21.8,-42.3,0.04118977,-4.48,-2.67,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,132748,2015-10-30 10:15:53:624,1446171353624.0 \n0.1329,0.3711,9.5098,0.6381,0.7399,9.7579,0.0367,-0.171,-0.0562,-3.8,21.2,-42.8,0.044854962,-4.35,-3.87,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,132849,2015-10-30 10:15:53:725,1446171353725.0 \n0.5148,0.7123,8.4252,0.6593,0.5209,9.7706,-0.441,0.1393,-0.1442,-5.5,21,-43.1,0.089709924,-3.04,-3.86,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,132952,2015-10-30 10:15:53:828,1446171353828.0 \n-0.1808,0.6608,8.9998,0.4477,0.4624,9.7855,-0.0489,0.2395,-0.0464,-6,21.2,-43.1,0.16109389,-2.68,-3,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,133054,2015-10-30 10:15:53:930,1446171353930.0 \n0.091,1.0223,9.9742,0.3744,0.538,9.7847,0.121,0.1735,0.1576,-5.9,21.8,-42.9,0.176976386,-3.15,-2.19,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,133155,2015-10-30 10:15:54:031,1446171354031.0 \n0.1592,1.1193,11.1247,0.432,0.8779,9.7577,0.4191,-0.2468,0.27,-5.5,21.8,-43,0.125838239,-4.42,-2.4,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,133261,2015-10-30 10:15:54:137,1446171354137.0 \n-1.0247,-0.4884,11.6071,0.5617,0.6098,9.7715,-0.3592,-0.0599,-0.0269,-5.1,21.2,-43.4,0.106290551,-3.57,-3.29,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,133360,2015-10-30 10:15:54:236,1446171354236.0 \n0.3831,0.6859,7.908,0.6659,0.6301,9.7637,-0.347,0.0929,0.0147,-4.9,20.9,-43.5,0.097389372,-3.68,-3.56,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,133462,2015-10-30 10:15:54:338,1446171354338.0 \n-0.0443,0.8308,8.5856,0.6224,0.4615,9.776,-0.0086,-0.0293,0.0379,-5,21.1,-43.4,0.103323492,-2.57,-3.49,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,133564,2015-10-30 10:15:54:440,1446171354440.0 \n-0.4597,0.814,8.6933,0.5405,0.4862,9.7797,-0.0073,0.0318,-0.1319,-5.1,21.5,-43.4,0.108210414,-2.84,-3.16,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,133666,2015-10-30 10:15:54:542,1446171354542.0 \n-0.7075,0.1832,12.2032,0.6101,0.678,9.7641,0.3152,-0.1368,0.0208,-5.1,21.5,-43.3,0.105766953,-3.33,-3.58,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,133768,2015-10-30 10:15:54:644,1446171354644.0 \n-1.1911,-1.4114,14.036,0.5306,0.4122,9.7836,-0.0354,0.5241,0.0269,-5.4,21.3,-43.5,0.085695666,-3.1,-3.98,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,133870,2015-10-30 10:15:54:746,1446171354746.0 \n0.3148,-0.1724,10.4016,0.4682,0.4539,9.7849,-0.1381,-0.1087,-0.0501,-5.5,21.5,-43.7,0.119729587,-2.65,-2.74,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,133971,2015-10-30 10:15:54:847,1446171354847.0 \n0.1065,0.5866,8.0577,0.4221,0.3488,9.7913,-0.0147,0.1686,-0.0916,-5.6,21.8,-43.3,0.167377075,-2,-2.69,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,134073,2015-10-30 10:15:54:949,1446171354949.0 \n-0.0431,1.1708,8.005,0.3511,0.3819,9.7929,0.0061,0.1197,0.0293,-5.4,22.2,-43,0.145036861,-2.23,-2.05,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,134176,2015-10-30 10:15:55:052,1446171355052.0 \n-0.6536,0.6333,11.5245,0.3656,0.508,9.7867,0.1051,-0.0916,0.0782,-5.3,22.3,-42.8,0.150621914,-2.42,-1.85,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,134278,2015-10-30 10:15:55:154,1446171355154.0 \n-0.103,0.1353,10.7859,0.2735,0.7969,9.7704,0.099,0.16,0.2126,-4.9,21.7,-43.2,0.148178453,-4.66,-1.6,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,134380,2015-10-30 10:15:55:256,1446171355256.0 \n-0.2789,0.2442,9.8641,0.2708,0.6544,9.781,-0.1246,-0.237,0.2065,-4.5,21.1,-43.5,0.106116019,-4.11,-1.92,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,134482,2015-10-30 10:15:55:358,1446171355358.0 \n-0.1305,0.2143,9.153,0.4094,0.623,9.7783,-0.4337,0.0195,-0.1319,-4.3,20.8,-43.6,0.090408055,-3.64,-2.4,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,134584,2015-10-30 10:15:55:460,1446171355460.0 \n-0.2777,0.4525,9.7336,0.5769,0.2511,9.7864,-0.1552,-0.0843,0.0525,-4.3,21.2,-43.2,0.066147979,-1.47,-3.37,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,134685,2015-10-30 10:15:55:561,1446171355561.0 \n-0.1688,0.8368,9.5397,0.5034,0.439,9.7839,0.2407,-0.055,-0.1002,-4.6,21.5,-43.2,0.115540796,-2.16,-3,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,134787,2015-10-30 10:15:55:663,1446171355663.0 \n0.6249,0.6584,10.4028,0.56,0.6781,9.7671,0.0195,-0.0354,-0.1649,-5,21.4,-43.2,0.105243354,-3.96,-3.28,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,134890,2015-10-30 10:15:55:766,1446171355766.0 \n-0.6548,-0.3747,11.157,0.4414,0.5378,9.7819,-0.4178,0.3042,-0.3396,-5.2,21.1,-43.5,0.130201562,-3.14,-2.58,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,134992,2015-10-30 10:15:55:868,1446171355868.0 \n-0.146,-0.0036,10.0616,0.3589,0.365,9.7933,-0.3482,-0.0941,-0.1515,-5.2,20.9,-43.8,0.148527519,-2.13,-2.1,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,135093,2015-10-30 10:15:55:969,1446171355969.0 \n-0.7865,0.6261,8.1666,0.2721,0.333,9.7972,0.099,0.1637,0.0037,-5.2,21.3,-43.7,0.153065375,-1.9,-2,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,135196,2015-10-30 10:15:56:072,1446171356072.0 \n-0.3795,0.6476,9.8581,0.1937,0.4031,9.7964,0.088,0.0733,0.0757,-5,21.6,-43.4,0.172962129,-2.36,-1.13,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,135297,2015-10-30 10:15:56:173,1446171356173.0 \n-0.2107,0.4657,11.8166,0.2286,0.483,9.7921,0.3176,-0.1381,0.2505,-4.9,21.6,-43.4,0.174183859,-2.31,-1.1,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,135399,2015-10-30 10:15:56:275,1446171356275.0 \n-0.4298,-0.3687,12.3301,0.2399,0.4374,9.794,-0.3751,-0.3274,0.3042,-4.5,21.3,-43.6,0.142069801,-3.2,-0.85,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,135502,2015-10-30 10:15:56:378,1446171356378.0 \n0.2993,0.8871,8.1618,0.5789,0.5362,9.7749,0.3128,-0.3482,0.4484,-4.3,21.3,-43.7,0.096342175,-2.62,-2.31,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,135604,2015-10-30 10:15:56:480,1446171356480.0 \n0.1269,1.0391,8.4013,0.6303,0.3847,9.7788,-0.0855,0.0855,0.0501,-4.4,21.2,-44.1,0.05131268,-2.32,-3.68,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,135706,2015-10-30 10:15:56:582,1446171356582.0 \n-0.492,0.9577,8.0266,0.5615,0.5177,9.7769,0.2114,0.077,-0.0428,-4.6,21.1,-43.7,0.10559242,-3.03,-3.29,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,135807,2015-10-30 10:15:56:683,1446171356683.0 \n-0.2143,0.674,11.2097,0.5493,0.7193,9.7648,0.3115,-0.0745,-0.1527,-4.7,20.8,-43.8,0.111177473,-3.75,-3.04,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,135909,2015-10-30 10:15:56:785,1446171356785.0 \n0.48,0.1544,10.0568,0.4678,0.8783,9.756,0.1051,0.1356,-0.1991,-4.6,20,-43.9,0.120253185,-5.14,-2.75,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,136012,2015-10-30 10:15:56:888,1446171356888.0 \n-0.3615,0.3148,9.0058,0.2,0.5557,9.7889,0.1075,0.0782,-0.0073,-4.6,19.8,-43.9,0.16528268,-3.53,-1.59,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,136113,2015-10-30 10:15:56:989,1446171356989.0 \n-0.1161,0.8811,7.3287,0.2275,0.3237,9.7987,-0.0159,0.0965,0.0904,-4.5,20.3,-43.8,0.138055544,-1.89,-1.33,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,136215,2015-10-30 10:15:57:091,1446171357091.0 \n-0.8152,0.8871,8.3498,0.2605,0.2505,9.8,-0.1295,-0.0745,0.0147,-4.4,20.9,-43.5,0.135786616,-1.63,-1.29,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,136318,2015-10-30 10:15:57:194,1446171357194.0 \n-0.583,0.3304,11.3294,0.2591,0.2933,9.7988,0.0733,0.0574,0.1173,-4.4,21.8,-43.1,0.122347581,-1.71,-1.51,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,136420,2015-10-30 10:15:57:296,1446171357296.0 \n0.486,0.5794,8.9543,0.2932,0.615,9.783,0.1478,-0.1063,0.1723,-4.3,21.5,-42.8,0.109432144,-3.6,-1.72,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,136522,2015-10-30 10:15:57:398,1446171357398.0 \n-0.9756,-0.8104,12.2763,0.4528,0.4217,9.7871,-0.3592,0.0513,-0.0403,-4.3,21.2,-43.1,0.087790061,-2.46,-2.65,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,136624,2015-10-30 10:15:57:500,1446171357500.0 \n-0.5926,0.2598,9.086,0.4078,0.4308,9.7887,-0.3457,0.0721,-0.0843,-4.1,20.7,-43.4,0.096167642,-2.52,-2.39,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,136725,2015-10-30 10:15:57:601,1446171357601.0 \n-0.5471,0.838,8.5832,0.441,0.4922,9.7844,0.0892,0.0623,-0.0195,-4.1,20.7,-43.4,0.087440996,-2.75,-2.63,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,136828,2015-10-30 10:15:57:704,1446171357704.0 \n-0.7494,0.9469,9.9862,0.3946,0.6009,9.7803,0.066,0.0049,-0.1772,-4,20.8,-43.3,0.095644043,-3.51,-2.31,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,136930,2015-10-30 10:15:57:806,1446171357806.0 \n-0.5626,1.002,10.6207,0.4069,0.8149,9.7643,0.4264,-0.022,-0.0611,-4.1,20.7,-43.3,0.089709924,-4.77,-2.39,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,137031,2015-10-30 10:15:57:907,1446171357907.0 \n-1.2977,-0.656,12.2547,0.3978,0.8017,9.7657,-0.5718,0.2639,-0.4068,-4.3,20.2,-43.5,0.09546951,-4.69,-2.33,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,137134,2015-10-30 10:15:58:010,1446171358010.0 \n0.5136,0.5614,7.4675,0.2505,0.6007,9.785,-0.4875,0.1295,-0.0232,-4.3,20.1,-43.6,0.12112585,-4.04,-1.55,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,137235,2015-10-30 10:15:58:111,1446171358111.0 \n0.4633,0.899,7.701,0.2112,0.4355,9.7947,-0.0513,-0.0623,0.0819,-4.3,20.3,-43.5,0.139451807,-2.55,-1.24,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,137339,2015-10-30 10:15:58:215,1446171358215.0 \n-0.2035,1.1229,8.9268,0.2011,0.2881,9.8004,-0.0122,0.0501,0.0696,-4.2,21.4,-43.2,0.139102741,-1.68,-1.18,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,137469,2015-10-30 10:15:58:345,1446171358345.0 \n-0.6309,0.401,12.2236,0.2145,0.24,9.8014,0.2199,-0.3323,0.2834,-4.1,22,-42.9,0.131946891,-1.4,-1.25,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,137541,2015-10-30 10:15:58:417,1446171358417.0 \n0.7063,-0.6093,10.1837,0.4109,0.4565,9.7874,0.1906,-0.1368,0.1576,-4.2,22.1,-42.8,0.091106187,-2.67,-2.4,36.814144,-119.74884,258.68,336.4766495,3.84,12.903226,331.44,17 / 17,137643,2015-10-30 10:15:58:519,1446171358519.0 \n-0.1688,0.6081,7.5776,0.4217,0.3986,9.7895,0.3115,-0.0586,0.2419,-4.3,22.2,-42.9,0.090233522,-2.33,-2.47,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,137745,2015-10-30 10:15:58:621,1446171358621.0 \n-0.4908,0.5064,8.7532,0.4486,0.2023,9.7943,-0.011,0.0648,0.0293,-4.4,22.1,-43,0.08831366,-1.18,-2.62,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,137847,2015-10-30 10:15:58:723,1446171358723.0 \n-0.17,1.3348,7.6591,0.4307,0.262,9.7937,0.11,0.0024,-0.0367,-4.2,22.3,-43.2,0.090757121,-1.53,-2.52,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,137949,2015-10-30 10:15:58:825,1446171358825.0 \n-0.7901,0.4597,11.5209,0.4064,0.3103,9.7933,-0.0611,0.0037,-0.1808,-4.3,22.4,-43.1,0.094422313,-1.81,-2.38,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,138052,2015-10-30 10:15:58:928,1446171358928.0 \n0.4142,0.3148,11.1019,0.4129,0.5399,9.7831,0.3665,0.0843,0.0672,-4.5,22.2,-43.1,0.086742864,-2.56,-2.55,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,138160,2015-10-30 10:15:59:036,1446171359036.0 \n-1.4916,-1.3443,12.6785,0.3398,0.3806,9.7934,-0.099,0.2028,-0.2578,-4.9,22,-43.7,0.145385927,-2.22,-1.99,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,138256,2015-10-30 10:15:59:132,1446171359132.0 \n-0.3867,-0.0898,8.3977,0.2805,0.4056,9.7942,-0.0379,-0.0122,-0.0367,-5.1,21.9,-43.9,0.158650429,-2.67,-1.5,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,138357,2015-10-30 10:15:59:233,1446171359233.0 \n-0.5387,1.008,7.0605,0.3089,0.3236,9.7964,-0.0574,0.0831,0.0562,-5.2,22,-44.2,0.152890842,-1.89,-1.81,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,138459,2015-10-30 10:15:59:335,1446171359335.0 \n-0.1951,0.9708,8.679,0.3983,0.2129,9.7962,-0.193,-0.0904,0.121,-5.3,22.2,-43.9,0.145909525,-1.49,-2.08,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,138561,2015-10-30 10:15:59:437,1446171359437.0 \n0.0239,0.5016,12.6402,0.483,0.2481,9.7916,0.4056,0.0538,0.3372,-5.5,22.6,-44.1,0.125663706,-1,-2.6,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,138663,2015-10-30 10:15:59:539,1446171359539.0 \n0.085,-0.2957,11.2132,0.5166,0.2569,9.7897,-0.2578,-0.1112,-0.0721,-5.5,22.5,-44.1,0.113795467,-2.07,-2.85,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,138766,2015-10-30 10:15:59:642,1446171359642.0 \n0.1796,0.5219,8.5102,0.4767,0.3091,9.7902,0.1356,-0.0244,-0.0318,-5.5,22.2,-44.5,0.121474916,-1.81,-2.79,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,138867,2015-10-30 10:15:59:743,1446171359743.0 \n-0.5638,0.2191,8.175,0.4485,0.2357,9.7936,0.1002,-0.0134,-0.066,-5.4,21.6,-44.8,0.126536371,-1.38,-2.62,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,138969,2015-10-30 10:15:59:845,1446171359845.0 \n-0.5411,0.6357,8.2923,0.4274,0.2855,9.7932,0.0232,0.0904,-0.0195,-5.5,21.6,-44.8,0.123743844,-1.55,-2.68,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,139071,2015-10-30 10:15:59:947,1446171359947.0 \n-0.5339,0.2346,11.728,0.4791,0.3988,9.7868,0.0721,-0.2077,-0.0122,-5.7,21.2,-44.9,0.164584548,-2.33,-2.8,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,139174,2015-10-30 10:16:00:050,1446171360050.0 \n0.3795,0.516,10.1119,0.5653,0.5454,9.7751,-0.0122,-0.121,-0.0208,-5.8,20.8,-44.9,0.14678219,-3.1,-3.22,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,139275,2015-10-30 10:16:00:151,1446171360151.0 \n-0.2825,-0.1664,10.8493,0.4373,0.277,9.793,-0.463,0.2908,-0.2272,-6,20.5,-45.1,0.177150919,-1.62,-2.56,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,139377,2015-10-30 10:16:00:253,1446171360253.0 \n-0.158,0.431,8.4743,0.2129,0.2104,9.8021,-0.1393,0.2932,-0.0415,-5.8,20.5,-44.8,0.224798408,-1.23,-1.24,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,139479,2015-10-30 10:16:00:355,1446171360355.0 \n-0.2274,0.9565,7.9727,0.1185,0.1631,9.8046,-0.0538,0.0257,-0.0024,-5.5,20.9,-44.5,0.200538331,-1.01,-0.75,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,139581,2015-10-30 10:16:00:457,1446171360457.0 \n-0.0419,0.8727,9.6654,0.1808,0.2094,9.8027,0.1002,-0.1026,0.1662,-4.9,21.4,-44.2,0.188670092,-1.22,-1.06,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,139684,2015-10-30 10:16:00:560,1446171360560.0 \n-0.1221,1.1516,12.0368,0.2372,0.4026,9.7955,0.2541,-0.1833,0.3714,-4.7,21.3,-44.3,0.170867734,-2.35,-1.39,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,139786,2015-10-30 10:16:00:662,1446171360662.0 \n-1.2019,-0.8104,12.7192,0.3559,0.4798,9.7884,-0.3824,-0.3274,-0.0012,-4.7,20.7,-44.6,0.143989663,-2.8,-2.08,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,139888,2015-10-30 10:16:00:764,1446171360764.0 \n0.2251,0.5016,8.0828,0.6083,0.3317,9.7821,-0.4435,-0.1466,-0.1478,-4.8,20.3,-44.8,0.111352006,-2.43,-3.24,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,139989,2015-10-30 10:16:00:865,1446171360865.0 \n-0.0024,0.5578,8.2337,0.5722,0.1054,9.7894,-0.1112,0.0855,0.0525,-5.2,20.4,-44.4,0.117809725,-0.62,-3.35,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,140091,2015-10-30 10:16:00:967,1446171360967.0 \n-0.0323,0.9002,8.515,0.5581,0.1069,9.7902,0.1491,0.0379,0.0171,-5.6,21,-43.9,0.159523094,-0.44,-3.33,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,140194,2015-10-30 10:16:01:070,1446171361070.0 \n-0.3615,-0.0443,13.3908,0.6921,0.2664,9.7786,0.2419,-0.4215,-0.0538,-5.7,21.2,-43.7,0.128979832,-1.56,-4.05,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,140295,2015-10-30 10:16:01:171,1446171361171.0 \n1.2534,-0.0431,11.1103,0.6509,0.3789,9.7777,-0.0513,0.215,-0.0757,-5.9,20.9,-44,0.122522113,-2.56,-4.12,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,140397,2015-10-30 10:16:01:273,1446171361273.0 \n0.5902,0.8332,7.3969,0.412,0.2927,9.7936,0.1796,0.055,0.1026,-5.8,20.3,-44.1,0.192160751,-1.71,-2.41,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,140499,2015-10-30 10:16:01:375,1446171361375.0 \n0.0886,0.3292,9.0166,0.4246,0.076,9.7972,-0.0904,0.2993,0.0147,-5.6,20.4,-44,0.181863308,-0.62,-2.9,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,140601,2015-10-30 10:16:01:477,1446171361477.0 \n0.097,1.1217,7.3777,0.3719,0.0189,9.7996,-0.0464,-0.0586,0.011,-5.2,20.8,-43.5,0.158301363,-0.11,-2.17,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,140704,2015-10-30 10:16:01:580,1446171361580.0 \n-1.0678,-0.0718,10.9283,0.4286,-0.0483,9.7972,0.0012,-0.1246,0.1087,-5.1,21.1,-43.4,0.155159771,0.17,-2.31,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,140805,2015-10-30 10:16:01:681,1446171361681.0 \n0.9876,-0.9481,12.0895,0.7648,0.0213,9.7768,-0.1967,-0.3702,0.1723,-5.1,21.3,-43.2,0.097912971,-0.49,-3.86,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,140908,2015-10-30 10:16:01:784,1446171361784.0 \n-0.2274,0.4142,7.8949,0.5276,-0.1183,9.7917,0.292,-0.248,0.3714,-5.2,21.4,-43,0.130027029,0.69,-3.08,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,141010,2015-10-30 10:16:01:886,1446171361886.0 \n0.0108,0.2179,9.8378,0.6498,-0.1304,9.7842,-0.3592,-0.0794,0.1906,-4.8,21.2,-43,0.104370689,0.76,-3.8,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,141112,2015-10-30 10:16:01:988,1446171361988.0 \n-0.0551,0.9421,8.1379,0.6955,0.007,9.782,0.0953,0.0904,-0.0538,-4.5,21.2,-42.6,0.03996804,0.14,-4.2,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,141213,2015-10-30 10:16:02:089,1446171362089.0 \n-0.4489,0.4537,10.981,0.6754,0.1424,9.7823,0.1087,-0.1869,-0.2395,-4,20.9,-42.7,0.047472956,-0.83,-3.95,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,141316,2015-10-30 10:16:02:192,1446171362192.0 \n0.2765,-0.1053,11.5724,0.7887,0.4417,9.7649,0.4325,-0.0599,-0.1307,-4.1,20.6,-42.5,0.031939525,-1.61,-4.48,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,141418,2015-10-30 10:16:02:294,1446171362294.0 \n-0.2251,-0.255,10.1933,0.5674,0.4085,9.7817,-0.2468,0.2651,-0.3409,-4.4,19.7,-43.2,0.068940505,-2.39,-3.32,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,141519,2015-10-30 10:16:02:395,1446171362395.0 \n-0.0431,-0.0431,10.3202,0.5071,0.1451,9.7925,-0.1759,-0.0318,-0.0098,-4.4,19.6,-43.3,0.08831366,-1.35,-2.85,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,141621,2015-10-30 10:16:02:497,1446171362497.0 \n-0.0084,1.1971,8.2791,0.4139,0.1199,9.7972,-0.0403,0.0904,0.0122,-4.2,20,-43.2,0.105941486,-0.7,-2.42,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,141723,2015-10-30 10:16:02:599,1446171362599.0 \n0.1652,1.4425,8.2983,0.3222,0.0981,9.8009,-0.0929,0.0696,0.0061,-3.9,20.5,-42.6,0.113795467,-0.64,-2.06,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,141826,2015-10-30 10:16:02:702,1446171362702.0 \n-0.2083,0.5435,11.9495,0.4807,0.2443,9.7918,0.4191,-0.2822,0.1429,-3.5,20.8,-42.2,0.059864793,-0.76,-2.33,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,141928,2015-10-30 10:16:02:804,1446171362804.0 \n-0.267,-0.8464,12.7647,0.6214,0.1743,9.7854,-0.237,-0.1955,-0.0733,-3.5,20.7,-42.2,0.021642083,-1.47,-3.44,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,142030,2015-10-30 10:16:02:906,1446171362906.0 \n0.1688,0.3891,8.7807,0.766,0.2107,9.7744,0.0855,-0.2162,0.237,-3.8,20.5,-42.3,0.048520153,-1.54,-3.98,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,142132,2015-10-30 10:16:03:008,1446171363008.0 \n0.1137,0.4788,9.0477,0.8228,0.0996,9.7716,-0.0024,-0.0843,0.0501,-4.1,20.5,-42.4,0.02565634,-0.59,-4.69,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,142234,2015-10-30 10:16:03:110,1446171363110.0 \n0.0467,1.154,8.5712,0.7385,0.2383,9.7759,0.2053,0.0929,-0.0867,-4.2,20.7,-42.1,0.037350046,-1.39,-4.32,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,142336,2015-10-30 10:16:03:212,1446171363212.0 \n-0.3699,0.3124,12.135,0.76,0.4046,9.7688,0.1258,-0.1515,-0.215,-4.2,20.5,-42.2,0.040317106,-2.07,-4.21,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,142437,2015-10-30 10:16:03:313,1446171363313.0 \n-0.0347,-0.6967,11.959,0.7439,0.57,9.7618,-0.3054,0.0733,-0.3274,-4.3,19.8,-42.7,0.032114058,-3.33,-4.36,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,142540,2015-10-30 10:16:03:416,1446171363416.0 \n0.8679,0.656,8.1989,0.6016,0.4726,9.7768,-0.204,0.0538,-0.0733,-4.3,19.6,-42.9,0.059864793,-2.52,-3.57,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,142642,2015-10-30 10:16:03:518,1446171363518.0 \n0.4166,1.1169,7.3011,0.6254,0.3358,9.7809,0.0159,0.1038,-0.0354,-4.4,19.5,-43,0.058119464,-1.96,-3.66,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,142743,2015-10-30 10:16:03:619,1446171363619.0 \n0.17,1.5945,7.6387,0.5571,0.3056,9.786,0.0867,0.0232,0.0819,-4.2,19.8,-42.9,0.071034901,-1.68,-3.31,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,142847,2015-10-30 10:16:03:723,1446171363723.0 \n-0.2825,0.9206,10.6243,0.5219,0.272,9.789,0.0024,-0.0599,0.0611,-4.1,20,-42.9,0.080285146,-1.59,-3.05,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,142948,2015-10-30 10:16:03:824,1446171363824.0 \n0.0682,-0.0694,11.2013,0.5858,0.4279,9.7798,-0.2089,-0.1405,0.1796,-3.8,20,-42.7,0.064926248,-2.5,-3.43,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,143049,2015-10-30 10:16:03:925,1446171363925.0 \n-0.1664,0.0096,10.1789,0.7969,0.3689,9.7672,0.1588,-0.2553,0.4349,-3.9,20,-42.9,0.036128316,-1.94,-4.29,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,143151,2015-10-30 10:16:04:027,1446171364027.0 \n-0.3926,0.0479,9.3122,0.8593,0.2835,9.7648,-0.2419,0.0244,-0.1014,-3.8,19.7,-43.1,0.01012291,-1.66,-5.03,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,143254,2015-10-30 10:16:04:130,1446171364130.0 \n-0.4262,0.7207,9.1937,0.7518,0.2533,9.7745,0.2456,0.1197,0.0476,-3.8,19.8,-43,0.028099801,-1.25,-4.54,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,143355,2015-10-30 10:16:04:231,1446171364231.0 \n-0.0886,0.5279,10.0928,0.6968,0.4549,9.7713,0.1735,0.0147,-0.0024,-3.6,19.6,-42.8,0.042411501,-2.66,-4.08,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,143458,2015-10-30 10:16:04:334,1446171364334.0 \n0.6835,0.6632,9.8533,0.7821,0.7328,9.7479,0.3445,-0.1246,0.0391,-3.5,19.3,-42.9,6.267651877,-3.64,-4.44,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,143559,2015-10-30 10:16:04:435,1446171364435.0 \n0.2717,0.0946,9.6786,0.7608,0.4556,9.7665,0.1429,0.0965,0.1332,-3.6,18.7,-43.1,0.030892328,-2.66,-4.45,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,143662,2015-10-30 10:16:04:538,1446171364538.0 \n0.4812,0.1496,9.839,0.6363,0.2152,9.7836,-0.4569,0.0403,-0.0623,-3.8,18.7,-43.3,0.053058009,-1.79,-3.88,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,143764,2015-10-30 10:16:04:640,1446171364640.0 \n-0.1113,1.4449,8.4324,0.4363,0.057,9.7968,-0.2358,0.2798,-0.0965,-3.5,19.6,-43,0.053407075,-0.33,-2.55,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,143865,2015-10-30 10:16:04:741,1446171364741.0 \n-0.3531,0.905,11.0816,0.3866,0.0766,9.7987,-0.0806,0.0257,-0.1271,-3,20.5,-42.2,0.062831853,-0.45,-2.26,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,143967,2015-10-30 10:16:04:843,1446171364843.0 \n-0.3938,0.7183,10.7117,0.4652,0.2748,9.7918,0.4313,-0.1723,0.0782,-2.8,20.7,-41.9,0.045204028,-1.61,-2.72,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,144069,2015-10-30 10:16:04:945,1446171364945.0 \n-0.8918,-0.2502,11.1797,0.5796,0.3592,9.7829,-0.0586,-0.3506,0.0574,-2.9,20.3,-42.1,0.023736478,-2.1,-3.39,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,144172,2015-10-30 10:16:05:048,1446171365048.0 \n0.0539,0.2538,8.8071,0.7402,0.3914,9.7708,-0.0623,-0.1686,0.1222,-3.1,19.8,-42.4,0.003665191,-2.32,-3.98,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,144273,2015-10-30 10:16:05:149,1446171365149.0 \n0.0611,1.2151,8.1175,0.6687,0.2861,9.7796,0.044,-0.0244,0.0379,-3.3,19.5,-42.5,0.006981317,-1.61,-3.88,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,144376,2015-10-30 10:16:05:252,1446171365252.0 \n-0.3148,1.166,8.995,0.6155,0.3561,9.7808,0.0696,0.0672,-0.0782,-3.5,19.5,-42.7,0.009075712,-1.87,-3.73,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,144479,2015-10-30 10:16:05:355,1446171365355.0 \n-0.8715,0.3603,11.9471,0.5587,0.5128,9.7773,0.1576,-0.0489,-0.0941,-3.4,19.5,-43,0.02443461,-3,-3.27,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,144579,2015-10-30 10:16:05:455,1446171365455.0 \n0.2215,-0.1317,11.6885,0.5739,0.5717,9.7731,-0.2627,0.2309,-0.2077,-3.4,19.1,-43.1,0.008901179,-3.76,-3.73,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,144682,2015-10-30 10:16:05:558,1446171365558.0 \n0.2442,-0.0599,9.092,0.5015,0.3531,9.7875,-0.2016,0.0305,-0.0354,-3.4,18.8,-43.3,0.038746309,-2.06,-2.93,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,144783,2015-10-30 10:16:05:659,1446171365659.0 \n0.5686,1.1887,7.501,0.4671,0.1293,9.7947,-0.0867,0.0122,0.0929,-3.4,19.2,-42.9,0.048694686,-0.95,-2.71,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,144887,2015-10-30 10:16:05:763,1446171365763.0 \n0.4621,1.1756,8.2373,0.5739,0.0708,9.7896,0.0342,-0.055,-0.0904,-3.3,20.1,-42.5,0.026354472,-0.41,-3.36,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,144987,2015-10-30 10:16:05:863,1446171365863.0 \n-0.067,0.5459,11.5796,0.5582,0.2101,9.7885,0.1246,-0.2798,-0.0281,-3.5,20.7,-42.1,0.027576202,-1.23,-3.26,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,145090,2015-10-30 10:16:05:966,1446171365966.0 \n0.2478,0.1484,10.9535,0.5517,0.3358,9.7854,0.1649,0.237,0.1429,-3.6,20.6,-42.3,0.062133721,-2.01,-3.54,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,145191,2015-10-30 10:16:06:067,1446171366067.0 \n-0.0335,0.2741,9.6546,0.6186,0.3658,9.7803,0.0159,-0.2505,0.0159,-3.6,20.1,-42.6,0.059166662,-2.14,-3.62,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,145293,2015-10-30 10:16:06:169,1446171366169.0 \n-0.844,-0.1006,9.2751,0.6664,0.2308,9.7813,-0.0134,0.2382,-0.0782,-3.9,20,-42.8,0.035430184,-1.43,-4.32,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,145395,2015-10-30 10:16:06:271,1446171366271.0 \n-0.243,1.1504,8.4707,0.6817,0.2526,9.7797,-0.0379,-0.1625,-0.0916,-4.1,20,-42.6,0.05009095,-1.35,-3.92,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,145501,2015-10-30 10:16:06:377,1446171366377.0 \n-0.1053,0.3316,12.1075,0.7635,0.456,9.7662,0.16,-0.2651,-0.1735,-4.8,20.1,-42.5,0.077841685,-2.67,-4.47,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,145600,2015-10-30 10:16:06:476,1446171366476.0 \n0.8487,0.0539,8.764,0.6912,0.6508,9.7606,-0.5046,0.0611,-0.4484,-5.1,19.8,-42.5,0.075572757,-3.7,-4.46,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,145701,2015-10-30 10:16:06:577,1446171366577.0 \n1.0271,0.7757,7.6531,0.5486,0.1985,9.7893,-0.303,0.1038,-0.1503,-5.5,19.7,-42.8,0.109257611,-1.37,-3.58,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,145805,2015-10-30 10:16:06:681,1446171366681.0 \n-0.2334,-0.0862,10.5644,0.5685,-0.1522,9.789,-0.0538,-0.1686,0.0941,-5.6,20.1,-42.5,0.190240888,0.75,-3.07,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,145907,2015-10-30 10:16:06:783,1446171366783.0 \n0.3735,1.2809,8.2851,0.52,-0.1028,9.7923,0.3128,-0.0586,0.1564,-5.6,21.6,-41.6,0.172962129,0.6,-3.04,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,146007,2015-10-30 10:16:06:883,1446171366883.0 \n-0.3998,0.6213,11.1929,0.4523,0.1714,9.7947,0.3018,-0.0648,0.2248,-5.1,21.9,-41,0.135786616,-1,-2.64,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,146109,2015-10-30 10:16:06:985,1446171366985.0 \n0.1927,0.5758,8.9076,0.343,0.644,9.7795,0.6597,0.3067,0.4252,-4.9,21.1,-41.3,0.133866754,-3.42,-2.57,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,146212,2015-10-30 10:16:07:088,1446171367088.0 \n-0.3903,-0.407,10.5429,0.567,0.3594,9.7836,-0.0904,-0.1503,0.3433,-4.2,19.8,-41.9,0.072431164,-2.1,-3.32,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,146317,2015-10-30 10:16:07:193,1446171367193.0 \n-0.0431,0.2478,8.6407,0.5681,0.1416,9.7892,-0.4068,0.1161,0.0574,-3.9,19.5,-42.2,0.068940505,-1.73,-3.45,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,146416,2015-10-30 10:16:07:292,1446171367292.0 \n-0.5543,0.674,8.0349,0.5528,0.0627,9.7909,0.0745,-0.099,0.0342,-3.4,20,-41.9,0.029496064,-0.11,-3.28,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,146517,2015-10-30 10:16:07:393,1446171367393.0 \n-0.4573,1.0235,9.1937,0.5525,0.1916,9.7892,0.0648,-0.0635,-0.0562,-3.3,20.2,-41.9,0.03281219,-0.96,-3.16,36.814247,-119.74885,258.56,336.4766495,3.92,19.35484,3.09,17 / 17,146620,2015-10-30 10:16:07:496,1446171367496.0 \n0.7877,0.3543,12.1218,0.6423,0.3843,9.778,0.077,-0.1112,-0.1784,-3.3,20.1,-42.1,0.011170107,-2.25,-3.76,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,146721,2015-10-30 10:16:07:597,1446171367597.0 \n-1.3958,-1.1552,13.4901,0.4422,0.1955,9.7947,-0.4753,0.4618,-0.4447,-3.6,19.8,-42.4,0.074351026,-1.82,-3.28,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,146824,2015-10-30 10:16:07:700,1446171367700.0 \n0.7673,0.6584,6.7493,0.2394,0.2396,9.8008,-0.3653,0.0073,-0.1625,-3.5,19.7,-42.5,0.086568331,-1.83,-1.57,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,146926,2015-10-30 10:16:07:802,1446171367802.0 \n-0.4274,0.8715,7.3789,0.1403,0.1161,9.805,-0.0061,0.0623,-0.0721,-3.2,20,-42.1,0.116587994,-0.68,-0.82,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,147029,2015-10-30 10:16:07:905,1446171367905.0 \n-0.6249,0.9756,8.7281,0.1934,0.1411,9.8037,0.0195,-0.0489,0.0489,-2.6,20.2,-41.6,0.105068821,-0.82,-1.13,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,147130,2015-10-30 10:16:08:006,1446171368006.0 \n0.1041,0.5578,11.8166,0.4356,0.3865,9.7893,0.3384,-0.369,0.2138,-2.8,20.2,-41.3,0.05427974,-2.26,-2.55,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,147232,2015-10-30 10:16:08:108,1446171368108.0 \n-0.6428,-0.9373,13.6242,0.5016,0.2665,9.7902,-0.5095,-0.3262,0.0391,-3,19.8,-41.4,0.059341195,-2.42,-2.38,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,147334,2015-10-30 10:16:08:210,1446171368210.0 \n0.2933,0.3053,7.9057,0.6504,0.2488,9.7819,-0.1857,-0.0843,0.099,-3.3,19.6,-41.8,0.009773844,-1.45,-3.8,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,147437,2015-10-30 10:16:08:313,1446171368313.0 \n-0.0634,0.4334,7.8709,0.7055,0.1019,9.7807,-0.0855,-0.0159,0.0403,-3.5,19.5,-41.9,0.004886922,-0.48,-3.95,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,147537,2015-10-30 10:16:08:413,1446171368413.0 \n-0.3089,1.0475,8.254,0.6981,0.1881,9.78,0.1784,0.0489,0.0049,-3.6,19.9,-42.1,0.046600291,-0.8,-4.14,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,147640,2015-10-30 10:16:08:516,1446171368516.0 \n-0.0491,0.5231,10.8793,0.8416,0.3189,9.7653,0.1613,-0.3641,-0.1112,-3.8,19.7,-42,0.036826447,-1.63,-4.38,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,147741,2015-10-30 10:16:08:617,1446171368617.0 \n0.8607,-0.0503,11.4598,0.935,0.5472,9.7541,-0.1491,0.3311,-0.3164,-4.4,19.2,-42.3,6.281789044,-3.2,-5.48,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,147844,2015-10-30 10:16:08:720,1446171368720.0 \n0.5507,0.0898,10.0197,0.7373,0.4658,9.7678,0.0342,-0.0037,-0.0073,-4.8,18.9,-42.3,0.079587014,-2.84,-4.51,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,147945,2015-10-30 10:16:08:821,1446171368821.0 \n0.589,1.0475,7.276,0.6528,0.2861,9.7807,-0.0012,0.088,0.088,-5,18.8,-42.4,0.108035881,-1.67,-3.82,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,148047,2015-10-30 10:16:08:923,1446171368923.0 \n0.1592,1.069,8.7245,0.6189,0.152,9.7859,0.0574,0.0819,0.0452,-4.7,19.5,-42.2,0.11274827,-0.89,-3.62,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,148149,2015-10-30 10:16:09:025,1446171369025.0 \n0.0754,1.1013,10.0437,0.4996,0.2724,9.7901,0.11,0.1051,0.0122,-4.4,19.8,-41.9,0.08115781,-1.18,-3.14,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,148252,2015-10-30 10:16:09:128,1446171369128.0 \n-0.0012,0.8583,10.4327,0.4859,0.5355,9.78,0.4093,0.0684,0.1222,-4.2,19.8,-41.7,0.085521133,-3.13,-2.84,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,148354,2015-10-30 10:16:09:230,1446171369230.0 \n-1.1349,-0.8272,12.4307,0.5316,0.4474,9.782,0.0831,-0.0867,0.3885,-3.9,19.4,-41.9,0.087615528,-2.69,-2.94,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,148456,2015-10-30 10:16:09:332,1446171369332.0 \n-0.1113,-0.0012,9.2177,0.7142,0.409,9.7721,-0.1344,-0.2627,0.1185,-3.8,18.8,-42.2,0.044680429,-2.39,-4.18,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,148557,2015-10-30 10:16:09:433,1446171369433.0 \n0.3136,0.9768,8.1463,0.6691,0.2842,9.7797,0.0452,-0.1173,0.0134,-3.7,18.9,-42.1,0.060911991,-1.58,-3.77,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,148659,2015-10-30 10:16:09:535,1446171369535.0 \n0.0706,1.5694,8.6419,0.6193,0.3566,9.7806,0.0195,0.0538,-0.1552,-3.9,19.1,-42.1,0.065100781,-2.08,-3.62,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,148761,2015-10-30 10:16:09:637,1446171369637.0 \n0.0587,0.5734,11.4814,0.6855,0.4117,9.774,0.0244,-0.2138,-0.2566,-3.9,19.1,-42.3,0.062831853,-2.35,-3.67,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,148864,2015-10-30 10:16:09:740,1446171369740.0 \n-0.4381,-0.8416,12.3289,0.7006,0.2701,9.7779,-0.43,0.1429,-0.3677,-4.4,19,-42.7,0.031590459,-2.39,-4.44,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,148965,2015-10-30 10:16:09:841,1446171369841.0 \n0.7386,0.4262,7.7225,0.5467,0.2261,9.7888,-0.1857,0.0501,0.0244,-4.7,19.4,-42.5,0.122173048,-1.23,-3.48,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,149068,2015-10-30 10:16:09:944,1446171369944.0 \n0.3891,0.9697,7.6327,0.5581,0.0053,9.7908,-0.2126,0.0538,-0.1295,-5.1,20.1,-42,0.129154365,-0.03,-3.26,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,149169,2015-10-30 10:16:10:045,1446171370045.0 \n-0.0467,0.9852,9.4128,0.5362,-0.1683,9.7905,-0.0574,-0.0257,-0.0086,-5,21,-41.3,0.134739418,0.98,-3.14,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,149271,2015-10-30 10:16:10:147,1446171370147.0 \n-0.2023,0.3567,11.06,0.4658,-0.1287,9.7947,0.3445,0.0379,0.2065,-5,21.5,-40.9,0.141371669,1.19,-2.78,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,149374,2015-10-30 10:16:10:250,1446171370250.0 \n1.1756,-0.9385,10.3094,0.4634,0.143,9.7947,-0.204,-0.325,0.055,-4.8,21.4,-41,0.140673538,-0.84,-2.71,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,149476,2015-10-30 10:16:10:352,1446171370352.0 \n-0.4405,-0.3627,8.6036,0.6376,0.0357,9.7858,0.1906,0.2004,0.2443,-4.8,21.3,-41.2,0.109432144,-0.21,-3.73,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,149577,2015-10-30 10:16:10:453,1446171370453.0 \n-0.4812,-0.2047,9.7121,0.6984,-0.0758,9.7815,-0.2676,-0.011,0.077,-4.8,20.9,-41.6,0.096342175,0.44,-4.08,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,149680,2015-10-30 10:16:10:556,1446171370556.0 \n0.0646,1.1827,7.4148,0.5796,-0.0359,9.7894,0.2321,0.11,0.0635,-4.9,21.2,-41.8,0.114144533,0.61,-3.59,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,149781,2015-10-30 10:16:10:657,1446171370657.0 \n-0.3543,0.8428,9.1219,0.5381,0.1045,9.7913,0.1319,0.0525,-0.1271,-4.7,21.2,-41.7,0.124791042,-0.32,-3.18,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,149884,2015-10-30 10:16:10:760,1446171370760.0 \n0.0706,0.0958,11.4886,0.6281,0.3274,9.781,0.2285,-0.0305,-0.1393,-4.8,20.7,-41.7,0.102276294,-1.91,-3.67,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,149985,2015-10-30 10:16:10:861,1446171370861.0 \n0.5626,0.2394,9.3529,0.5091,0.1473,9.7923,0.0208,0.1258,-0.0012,-5.1,20.2,-41.5,0.138055544,-0.86,-2.98,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,150088,2015-10-30 10:16:10:964,1446171370964.0 \n0.2897,-0.1879,10.9595,0.5045,-0.0661,9.7934,-0.0538,-0.1845,-0.0269,-5.3,20.1,-41.5,0.15812683,-0.23,-2.49,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,150190,2015-10-30 10:16:11:066,1446171371066.0 \n0.0527,0.8356,8.5569,0.5444,-0.1262,9.7907,-0.1381,-0.0269,-0.0049,-5.5,20.7,-41.4,0.131946891,0.74,-3.18,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,150292,2015-10-30 10:16:11:168,1446171371168.0 \n-0.0479,0.832,9.2356,0.6219,-0.0765,9.7866,-0.0232,-0.0122,-0.077,-5.6,21,-41.5,0.162490153,0.45,-3.64,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,150396,2015-10-30 10:16:11:272,1446171371272.0 \n-0.4238,0.2801,11.5029,0.6071,0.1022,9.7873,0.3225,-0.0171,0.2993,-5.8,21.1,-41.3,0.159697627,-0.6,-3.55,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,150495,2015-10-30 10:16:11:371,1446171371371.0 \n0.1604,-1.1253,13.9546,0.8083,0.0483,9.7732,-0.3018,-0.4325,0.1393,-5.9,20.8,-41.3,0.146607657,-0.97,-3.89,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,150597,2015-10-30 10:16:11:473,1446171371473.0 \n1.2318,1.0582,7.2496,0.8564,0.1747,9.7676,0.1747,-0.0733,0.2175,-6,20.4,-41.1,0.118682389,-0.99,-4.91,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,150700,2015-10-30 10:16:11:576,1446171371576.0 \n-0.0072,0.7135,7.7871,0.7156,0.0827,9.7802,0.0635,-0.044,-0.0415,-5.8,19.9,-41.2,0.146084058,-0.48,-4.18,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,150802,2015-10-30 10:16:11:678,1446171371678.0 \n0.0407,1.0175,7.768,0.667,0.1226,9.7832,0.011,0.1197,-0.0562,-5.7,19.9,-41.2,0.152367244,-0.69,-3.97,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,150904,2015-10-30 10:16:11:780,1446171371780.0 \n-0.6057,-0.0263,12.1015,0.6925,0.093,9.7817,-0.1393,-0.2737,-0.3176,-5.5,19.7,-41.2,0.102276294,-0.54,-4.05,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,151006,2015-10-30 10:16:11:882,1446171371882.0 \n0.334,-0.9936,12.7719,0.8415,0.2092,9.7682,-0.303,-0.0843,-0.3213,-6,19.7,-41.3,0.117286126,-1.22,-4.92,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,151108,2015-10-30 10:16:11:984,1446171371984.0 \n0.6835,0.2897,7.5214,0.6826,0.0096,9.7829,-0.0819,0.314,-0.0757,-6.5,19.8,-41,0.154985238,-0.06,-3.99,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,151210,2015-10-30 10:16:12:086,1446171372086.0 \n0.085,0.0491,8.8693,0.6608,-0.1966,9.7824,-0.3018,-0.0721,-0.1356,-7,20.3,-41.2,0.208915911,0.93,-4.04,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,151311,2015-10-30 10:16:12:187,1446171372187.0 \n-0.3831,0.3938,8.934,0.6291,-0.308,9.7816,0.0415,-0.0819,0.033,-7.1,20.8,-41,0.217642558,1.8,-3.68,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,151414,2015-10-30 10:16:12:290,1446171372290.0 \n-0.2239,0.1808,11.0373,0.6278,-0.315,9.7815,-0.1319,-0.2016,0.0525,-7,21.5,-40.6,0.208043247,1.84,-3.67,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,151515,2015-10-30 10:16:12:391,1446171372391.0 \n0.6847,0.2957,10.8326,0.717,-0.1916,9.7785,0.4704,-0.0159,0.314,-7,21.7,-40.3,0.189019158,1.12,-4.19,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,151618,2015-10-30 10:16:12:494,1446171372494.0 \n-1.6209,-1.8555,12.3349,0.8221,-0.1912,9.7703,-0.27,-0.3115,-0.0171,-6.8,21.3,-40.6,0.173485728,1.12,-4.81,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,151720,2015-10-30 10:16:12:596,1446171372596.0 \n0.3208,0.4393,8.0098,0.876,-0.1556,9.7662,-0.2395,-0.0782,0.0183,-6.7,21,-40.9,0.166853476,0.58,-4.91,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,151822,2015-10-30 10:16:12:698,1446171372698.0 \n0.1269,0.6381,8.6455,0.7601,-0.3027,9.7725,-0.1271,0.1674,0.1368,-6.4,20.8,-41.1,0.141197136,1.77,-4.45,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,151923,2015-10-30 10:16:12:799,1446171372799.0 \n0.3783,1.0319,7.9535,0.6396,-0.1713,9.7843,0.1552,0.11,-0.0745,-6.3,21,-40.9,0.154985238,1.32,-3.99,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,152026,2015-10-30 10:16:12:902,1446171372902.0 \n-0.3496,-0.0132,11.6083,0.6811,0.0943,9.7825,0.3103,-0.1613,-0.1625,-6,20.9,-41,0.157254166,-0.01,-3.71,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,152128,2015-10-30 10:16:13:004,1446171373004.0 \n-0.5136,-1.5287,12.8581,0.7389,0.0667,9.7785,-0.4618,0.2773,-0.3115,-6.2,20.2,-41,0.141720735,-0.39,-4.32,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,152229,2015-10-30 10:16:13:105,1446171373105.0 \n0.6009,-0.0611,8.5425,0.5328,-0.0382,9.7921,0.0513,0.1417,0.0892,-6.4,20,-40.9,0.187448362,0.22,-3.11,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,152331,2015-10-30 10:16:13:207,1446171373207.0 \n0.1209,0.2933,7.6914,0.5045,-0.4189,9.7847,-0.182,0.0684,0.0379,-6.5,20.4,-40.7,0.209788576,2.45,-2.95,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,152435,2015-10-30 10:16:13:311,1446171373311.0 \n0.0371,0.3603,8.8585,0.5852,-0.5396,9.7743,-0.0599,-0.0513,-0.0122,-6.4,21.5,-40,0.183085039,3.08,-3.33,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,152536,2015-10-30 10:16:13:412,1446171373412.0 \n-0.401,-0.0395,10.1382,0.573,-0.5458,9.7747,0.0391,0.0941,0.0525,-6.4,22,-39.7,0.182910506,3.19,-3.36,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,152638,2015-10-30 10:16:13:514,1446171373514.0 \n-0.0144,0.1257,9.8797,0.5671,-0.2766,9.7863,0.2126,0.0574,0.4019,-6.4,22.2,-39.4,0.176976386,1.62,-3.32,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,152740,2015-10-30 10:16:13:616,1446171373616.0 \n0.2957,0.1065,9.9635,0.7413,-0.4913,9.7662,0.2932,0.0782,0.6414,-6.3,22,-39.5,0.150447382,2.87,-4.34,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,152842,2015-10-30 10:16:13:718,1446171373718.0 \n0.3998,0.176,9.2404,0.7952,-0.383,9.7668,-0.0489,-0.1491,0.0318,-6.2,21.8,-39.5,0.136833813,2.24,-4.65,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,152946,2015-10-30 10:16:13:822,1446171373822.0 \n-0.334,0.5734,7.926,0.5588,-0.3988,9.7826,0.0293,-0.0134,-0.11,-5.8,22,-39.7,0.179943446,2.48,-3.31,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,153046,2015-10-30 10:16:13:922,1446171373922.0 \n-0.2981,0.1125,9.924,0.5752,-0.3152,9.7847,0.0721,-0.1491,-0.1405,-5.4,21.9,-39.6,0.12705997,1.84,-3.36,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,153147,2015-10-30 10:16:14:023,1446171374023.0 \n0.2789,-0.2993,11.6298,0.8167,-0.1692,9.7711,-0.2016,0.0733,-0.2896,-5.4,21.7,-40,0.077318086,0.99,-4.78,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,153250,2015-10-30 10:16:14:126,1446171374126.0 \n-0.2035,-1.1313,10.8816,0.8072,-0.5097,9.7601,-0.5571,0.1063,-0.3763,-6.1,21.8,-40.1,0.134215819,2.98,-4.73,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,153352,2015-10-30 10:16:14:228,1446171374228.0 \n0.5567,-0.3077,10.0616,0.6029,-0.6409,9.7671,-0.3824,-0.1381,-0.1063,-6.4,22,-40.2,0.184306769,3.15,-3.31,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,153455,2015-10-30 10:16:14:331,1446171374331.0 \n-0.1269,0.5255,8.1427,0.5783,-0.6149,9.7703,0.0171,-0.0733,-0.0415,-6.5,22.8,-39.6,0.175580123,3.59,-3.39,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,153556,2015-10-30 10:16:14:432,1446171374432.0 \n0.2035,0.7087,8.6503,0.6035,-0.5441,9.7729,0.1234,0.0073,-0.0379,-6.2,23,-39.1,0.170867734,3.18,-3.53,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,153660,2015-10-30 10:16:14:536,1446171374536.0 \n-0.0802,-0.6788,12.9227,0.6329,-0.2319,9.7835,0.595,0.0525,0.2419,-6.1,23,-39.2,0.157254166,2.33,-3.81,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,153759,2015-10-30 10:16:14:635,1446171374635.0 \n-1.1349,-2.2613,14.2862,0.7566,-0.2406,9.7745,-0.4667,-0.1772,-0.0318,-5.9,22.2,-39.7,0.137008346,1.41,-4.43,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,153862,2015-10-30 10:16:14:738,1446171374738.0 \n1.008,0.2969,8.3438,0.8622,-0.3218,9.7634,0.1246,-0.215,0.2443,-6,22,-40.1,0.125838239,1.73,-4.81,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,153963,2015-10-30 10:16:14:839,1446171374839.0 \n-0.3831,0.2466,8.0325,0.6985,-0.5247,9.7677,-0.0098,0.0024,-0.055,-5.8,22,-40.1,0.156730567,3.07,-4.09,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,154066,2015-10-30 10:16:14:942,1446171374942.0 \n-0.4645,0.565,9.1877,0.6482,-0.4446,9.7751,0.0391,-0.0086,-0.1087,-5.6,22.5,-39.6,0.156730567,2.6,-3.79,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,154168,2015-10-30 10:16:15:044,1446171375044.0 \n-0.0371,-0.1939,11.9279,0.7265,-0.3277,9.7742,0.2321,-0.0513,-0.1417,-5.5,22.5,-39.3,0.105766953,2.2,-3.98,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,154269,2015-10-30 10:16:15:145,1446171375145.0 \n0.2286,-1.221,12.2176,0.7853,-0.2443,9.7721,-0.1038,-0.055,-0.2737,-5.7,22.3,-39.4,0.135088484,1.43,-4.59,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,154371,2015-10-30 10:16:15:247,1446171375247.0 \n0.5435,-0.6153,8.2229,0.6577,-0.3244,9.7792,0.1026,0.1307,-0.0611,-6,22.2,-39.3,0.155159771,1.89,-4.04,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,154474,2015-10-30 10:16:15:350,1446171375350.0 \n0.0072,0.5183,7.5405,0.6245,-0.4089,9.7782,-0.033,-0.1845,-0.0134,-6.3,22.4,-39.3,0.170518668,2.39,-3.65,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,154575,2015-10-30 10:16:15:451,1446171375451.0 \n0.2358,0.747,8.6263,0.7251,-0.4049,9.7714,0.0159,-0.0648,0.0049,-6.5,22.7,-39.3,0.144687795,2.49,-4.24,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,154678,2015-10-30 10:16:15:554,1446171375554.0 \n-0.723,-0.1963,12.0512,0.6457,-0.3631,9.7786,0.16,0,-0.0672,-6.6,23,-39.5,0.20228366,2.12,-3.78,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,154779,2015-10-30 10:16:15:655,1446171375655.0 \n0.741,-1.2306,9.821,0.7125,-0.2528,9.7775,-0.5339,-0.4459,-0.1197,-6.6,22.9,-39.6,0.197047673,0.81,-3.6,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,154881,2015-10-30 10:16:15:757,1446171375757.0 \n0.413,0.2634,7.2365,0.6849,-0.3124,9.7777,0.2712,0.2896,0.4691,-6.6,22.9,-39.5,0.193382481,1.83,-4.01,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,154983,2015-10-30 10:16:15:859,1446171375859.0 \n0.1736,0.2526,8.3833,0.7688,-0.5413,9.7615,-0.182,0.0819,0.1283,-6.4,22.9,-39.1,0.139451807,3.16,-4.5,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,155086,2015-10-30 10:16:15:962,1446171375962.0 \n-0.1425,1.0977,8.0768,0.7444,-0.5418,9.7633,0.2297,0.0586,0.1161,-6.1,23.4,-38.8,0.144164196,3.17,-4.36,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,155187,2015-10-30 10:16:16:063,1446171376063.0 \n-0.5016,-0.2753,10.7176,0.7616,-0.2686,9.7733,0.3665,-0.1161,-0.0415,-5.9,23.5,-39.1,0.128107167,1.57,-4.46,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,155289,2015-10-30 10:16:16:165,1446171376165.0 \n0.4525,-0.0958,9.9719,0.7525,0.1043,9.7772,0.4862,0.0977,0.1564,-5.9,23,-39.8,0.123220245,0.23,-4.52,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,155391,2015-10-30 10:16:16:267,1446171376267.0 \n-0.4082,-0.8679,12.1063,0.7357,-0.128,9.7782,-0.4679,0.0257,-0.2382,-6,22.1,-40.4,0.138055544,0.75,-4.3,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,155493,2015-10-30 10:16:16:369,1446171376369.0 \n0.2849,-0.0431,9.9228,0.7135,-0.2336,9.7779,-0.0831,0.0415,-0.0489,-6.1,21.8,-40.4,0.145036861,1.36,-4.17,36.814358,-119.74883,262.36,336.4766495,4.17,19.35484,354.51,17 / 17,155596,2015-10-30 10:16:16:472,1446171376472.0 \n-0.5662,0.559,8.3378,0.5569,-0.3559,9.7844,-0.1662,0.2529,-0.1026,-6,22.2,-39.9,0.179245314,2.08,-3.26,36.814476,-119.748825,264.3,336.4766495,4.41,25.806452,358.53,17 / 17,155697,2015-10-30 10:16:16:573,1446171376573.0 \n0.0491,1.3168,9.2141,0.5023,-0.2334,9.791,0.1417,-0.0318,0.2321,-5.8,22.6,-39.7,0.17837265,1.74,-2.96,36.814476,-119.748825,264.3,336.4766495,4.41,25.806452,358.53,17 / 17,155800,2015-10-30 10:16:16:676,1446171376676.0 \n-0.1365,0.012,10.5046,0.5707,0.072,9.7898,0.507,0.1967,0.1026,-5.2,22.4,-39.7,0.118856922,-0.42,-3.34,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,155903,2015-10-30 10:16:16:779,1446171376779.0 \n-1.0391,-1.9357,14.5998,0.7138,-0.033,9.7806,-0.4337,-0.4679,-0.2602,-5,22,-40.3,0.096865773,-0.43,-4.05,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,156004,2015-10-30 10:16:16:880,1446171376880.0 \n-0.4441,-0.0024,8.0373,0.5636,0.0211,9.7904,-0.0599,0.1026,0.0318,-5,21.5,-40.5,0.121300383,-0.12,-3.29,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,156105,2015-10-30 10:16:16:981,1446171376981.0 \n-0.6608,0.7362,7.8111,0.484,-0.056,9.7945,0.0855,0.055,0.0489,-4.8,21.5,-40.3,0.137881011,0.33,-2.83,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,156207,2015-10-30 10:16:17:083,1446171377083.0 \n-0.3831,0.826,8.6862,0.4704,0.0569,9.7952,0.1136,-0.1491,-0.0916,-4.4,21.5,-40.5,0.093200582,-0.33,-2.75,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,156310,2015-10-30 10:16:17:186,1446171377186.0 \n0.3017,-0.0958,10.8158,0.6294,0.3079,9.7816,0.2639,-0.1723,-0.099,-4.4,21.2,-40.8,0.060911991,-1.8,-3.68,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,156412,2015-10-30 10:16:17:288,1446171377288.0 \n-0.2011,-0.7985,12.481,0.5594,0.2002,9.7886,-0.3616,0.0147,-0.1674,-4.7,20.8,-40.8,0.115366264,-1.78,-3.37,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,156514,2015-10-30 10:16:17:390,1446171377390.0 \n-0.4609,-0.31,9.5756,0.4921,0.094,9.7938,-0.3054,-0.0281,-0.2272,-5,20.6,-41,0.136484748,-0.55,-2.88,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,156619,2015-10-30 10:16:17:495,1446171377495.0 \n-0.662,0.8176,7.5717,0.3677,-0.0506,9.7996,-0.0415,0.2456,0.1002,-5.1,20.9,-41,0.164933614,0.3,-2.15,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,156717,2015-10-30 10:16:17:593,1446171377593.0 \n0.3041,1.2713,8.582,0.4107,0.0488,9.7979,0.2492,-0.0171,0.2162,-4.9,21.4,-41,0.155159771,0.09,-2.41,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,156819,2015-10-30 10:16:17:695,1446171377695.0 \n0.3112,0.577,12.1494,0.4683,0.2092,9.7932,0.38,-0.1222,0.16,-4.7,21.4,-40.8,0.137881011,-1.22,-2.74,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,156921,2015-10-30 10:16:17:797,1446171377797.0 \n-0.0287,-0.0108,10.2532,0.4035,0.384,9.7908,0.0281,0.1319,0.1368,-4.3,21,-40.9,0.102974426,-2.49,-2.3,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,157023,2015-10-30 10:16:17:899,1446171377899.0 \n0.4908,0.9254,8.2205,0.6307,0.2698,9.7826,0.1148,-0.215,0.1796,-4.3,20.5,-41.1,0.061086524,-1.58,-3.69,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,157125,2015-10-30 10:16:18:001,1446171378001.0 \n-0.4022,0.3831,8.9615,0.7256,0.0461,9.7797,-0.1588,-0.0819,-0.0806,-4.6,20.4,-41.4,0.096342175,-0.27,-4.24,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,157228,2015-10-30 10:16:18:104,1446171378104.0 \n-0.2286,1.2725,7.5956,0.636,0.1477,9.7849,0.1649,0.0648,-0.1319,-4.9,20.8,-41.5,0.099309234,-0.48,-4,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,157329,2015-10-30 10:16:18:205,1446171378205.0 \n-0.4693,-0.0467,12.1362,0.6909,0.2747,9.7784,0.0892,-0.2285,-0.3176,-5.1,20.8,-41.8,0.091106187,-1.6,-4.04,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,157432,2015-10-30 10:16:18:308,1446171378308.0 \n0.1065,-1.1492,12.0345,0.6848,0.3365,9.7769,-0.4728,-0.0757,-0.4887,-5.4,20.5,-41.9,0.09128072,-1.97,-4.01,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,157534,2015-10-30 10:16:18:410,1446171378410.0 \n0.8116,0.3771,7.4232,0.5763,0.0269,9.7897,-0.2321,-0.1918,0.0208,-5.7,20.6,-41.8,0.164584548,0.07,-3.42,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,157635,2015-10-30 10:16:18:511,1446171378511.0 \n0.3232,0.8763,6.687,0.6897,-0.2155,9.78,-0.1246,0.0073,-0.0757,-6.3,21.5,-41.5,0.148178453,1.2,-3.96,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,157738,2015-10-30 10:16:18:614,1446171378614.0 \n-0.4537,0.7075,8.5449,0.735,-0.257,9.7757,0.0965,0.0073,-0.0354,-6.4,22.3,-41.3,0.137531945,1.71,-4.35,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,157839,2015-10-30 10:16:18:715,1446171378715.0 \n-0.5303,0.0802,11.0756,0.6401,-0.2411,9.7828,0.1759,-0.0049,0.1454,-6.7,22.9,-40.6,0.191462619,1.59,-3.85,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,157943,2015-10-30 10:16:18:819,1446171378819.0 \n0.3077,0.1125,10.2747,0.6551,-0.0356,9.7847,0.3494,0.0586,0.3128,-6.9,23,-40.5,0.183259571,0.49,-3.99,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,158043,2015-10-30 10:16:18:919,1446171378919.0 \n0.5136,0.3543,8.7736,0.8096,-0.2172,9.7708,0.2724,0.1344,0.4423,-7,22.9,-40.4,0.164759081,1.27,-4.74,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,158145,2015-10-30 10:16:19:021,1446171379021.0 \n-0.1939,0.1772,8.1427,0.819,-0.2276,9.7697,-0.1686,0.1161,0.0452,-6.9,22.6,-40.9,0.159697627,1.33,-4.79,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,158248,2015-10-30 10:16:19:124,1446171379124.0 \n-0.3232,1.0511,7.8709,0.7122,-0.1915,9.7789,0.2407,0.1649,0.0183,-6.7,22.7,-40.9,0.178547182,1.12,-4.17,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,158352,2015-10-30 10:16:19:228,1446171379228.0 \n-0.5291,-0.0455,10.7835,0.6493,-0.0623,9.7849,0.1087,-0.0061,-0.1491,-6.4,22.5,-41,0.142942466,0.36,-3.8,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,158452,2015-10-30 10:16:19:328,1446171379328.0 \n0.668,0.2634,10.7619,0.6221,0.1915,9.785,0.1258,0.1173,-0.0318,-6.3,22.2,-41.1,0.147480322,-1.12,-3.64,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,158554,2015-10-30 10:16:19:430,1446171379430.0 \n-0.2861,-1.0463,12.7431,0.54,0.0107,9.7918,-0.4557,0.1833,-0.3213,-6.3,21.8,-41.7,0.16528268,-0.06,-3.16,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,158655,2015-10-30 10:16:19:531,1446171379531.0 \n0.6416,0.3484,8.1128,0.3653,-0.0234,9.7998,-0.4227,-0.1295,-0.1124,-6.2,21.7,-42.1,0.199665666,0.14,-2.14,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,158758,2015-10-30 10:16:19:634,1446171379634.0 \n-0.018,1.1564,7.1216,0.3926,-0.2793,9.7948,-0.1723,-0.1344,-0.0819,-6,22,-42.2,0.20821778,1.3,-2.3,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,158859,2015-10-30 10:16:19:735,1446171379735.0 \n-0.5052,0.0551,11.1043,0.4586,-0.3178,9.7908,-0.0648,-0.0391,-0.0073,-5.9,22.8,-41.7,0.184132236,1.86,-2.68,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,158962,2015-10-30 10:16:19:838,1446171379838.0 \n-0.6021,0.0491,12.5169,0.4793,-0.1407,9.7939,0.3506,-0.022,0.2944,-6,23,-41.4,0.177325452,1.45,-2.88,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,159063,2015-10-30 10:16:19:939,1446171379939.0 \n-0.838,-0.8847,11.5843,0.5147,-0.0947,9.7927,-0.1552,-0.1197,0.3201,-5.7,22.5,-41.6,0.171914931,0.35,-2.79,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,159165,2015-10-30 10:16:20:041,1446171380041.0 \n-0.5219,-0.0742,8.4312,0.7523,0.0104,9.7777,-0.1478,0.0599,-0.0648,-5.4,21.9,-41.8,0.079761547,-0.06,-4.4,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,159267,2015-10-30 10:16:20:143,1446171380143.0 \n-0.3077,0.6716,8.7544,0.7097,-0.1064,9.7804,0.0696,0.1271,-0.0342,-5.1,21.6,-41.8,0.091804319,0.66,-4.1,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,159370,2015-10-30 10:16:20:246,1446171380246.0 \n-0.1484,1.0822,7.4639,0.617,0.0012,9.7872,0.2346,0.0941,-0.0574,-5.1,21.6,-41.9,0.106290551,-0.01,-3.61,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,159471,2015-10-30 10:16:20:347,1446171380347.0 \n-0.1891,0.2059,10.1275,0.6088,0.2227,9.7852,0.3323,0.0415,-0.1796,-5.1,21.2,-42.3,0.108035881,-1.3,-3.56,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,159573,2015-10-30 10:16:20:449,1446171380449.0 \n-0.2083,-1.1959,12.3601,0.5019,0.0513,9.7937,-0.3506,0.3005,-0.2114,-5.3,20.9,-42.3,0.115889862,-1.14,-3.34,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,159675,2015-10-30 10:16:20:551,1446171380551.0 \n0.0048,-0.1341,9.5289,0.3737,-0.0678,9.7993,-0.1075,0.0281,0.0941,-5.4,21,-42.1,0.162490153,0.4,-2.18,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,159778,2015-10-30 10:16:20:654,1446171380654.0 \n0.3603,1.0918,7.4915,0.4813,-0.2956,9.7904,-0.1429,-0.1026,0.2224,-5.4,21.4,-41.9,0.149225651,1.39,-2.72,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,159880,2015-10-30 10:16:20:756,1446171380756.0 \n0.6584,1.4856,8.6072,0.5325,-0.2735,9.7884,0.011,-0.0147,0.1185,-5.2,22.1,-41.7,0.12950343,1.6,-3.11,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,159982,2015-10-30 10:16:20:858,1446171380858.0 \n-0.4776,0.0431,11.7771,0.464,-0.1593,9.7944,0.1967,0.1258,0.16,-5.1,22.4,-41.5,0.141022604,1.54,-2.83,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,160088,2015-10-30 10:16:20:964,1446171380964.0 \n0.6297,-0.7769,12.153,0.5069,0.0346,9.7935,-0.0855,-0.2517,0.1906,-4.6,22,-41.7,0.14381513,-0.92,-2.34,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,160185,2015-10-30 10:16:21:061,1446171381061.0 \n0.3795,0.8056,7.8266,0.5021,0.0198,9.7938,0.0049,-0.237,0.0819,-4,21.3,-41.9,0.087266463,-0.12,-2.93,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,160287,2015-10-30 10:16:21:163,1446171381163.0 \n-0.2825,0.1185,8.4288,0.4451,-0.2719,9.7928,0.0122,-0.1674,-0.1112,-3.7,21.1,-41.8,0.099134702,1.13,-2.72,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,160390,2015-10-30 10:16:21:266,1446171381266.0 \n-0.6536,0.7566,7.7656,0.4246,-0.1399,9.7965,0.2517,0.1319,0.0159,-3.7,21.5,-41.8,0.10140363,0.82,-2.48,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,160491,2015-10-30 10:16:21:367,1446171381367.0 \n-0.8308,0.2239,11.7926,0.4976,0.0211,9.794,0.2321,-0.1393,-0.2346,-3.8,21.6,-41.7,0.08412487,-0.12,-2.91,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,160594,2015-10-30 10:16:21:470,1446171381470.0 \n0.2406,-0.4573,11.0768,0.4522,0.2119,9.7939,-0.2908,0.1576,-0.3738,-4,21.1,-42.2,0.093724181,-1.24,-2.64,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,160696,2015-10-30 10:16:21:572,1446171381572.0 \n-0.2861,-0.3579,9.505,0.257,-0.0457,9.8032,-0.1943,0.1454,-0.0623,-4.1,21,-42.3,0.130725161,0.07,-1.7,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,160798,2015-10-30 10:16:21:674,1446171381674.0 \n-0.1484,0.4597,7.6555,0.2744,-0.348,9.7966,-0.2358,-0.0195,0.1283,-4,21.4,-42.5,0.14381513,2.03,-1.6,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,160900,2015-10-30 10:16:21:776,1446171381776.0 \n-0.2837,0.9756,8.1858,0.3723,-0.4044,9.7912,0.0745,-0.0464,0.1026,-3.8,22,-42.4,0.122173048,2.36,-2.06,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,161001,2015-10-30 10:16:21:877,1446171381877.0 \n-0.6692,-0.3759,12.1637,0.4108,-0.4218,9.789,-0.1271,-0.0379,-0.1295,-3.8,22.7,-41.9,0.105243354,2.47,-2.4,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,161103,2015-10-30 10:16:21:979,1446171381979.0 \n-0.5327,0.1556,9.827,0.2361,-0.1094,9.8032,0.3421,0.2419,0.4313,-3.6,22.6,-41.7,0.131772359,0.64,-1.38,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,161206,2015-10-30 10:16:22:082,1446171382082.0 \n-1.549,-1.6185,12.1853,0.5306,-0.288,9.788,-0.0525,-0.1405,0.4178,-3.6,22.3,-41.6,0.093026049,1.25,-2.77,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,161307,2015-10-30 10:16:22:183,1446171382183.0 \n-0.6548,-0.2945,8.7819,0.7983,-0.3818,9.7666,-0.1381,0.0953,0.0305,-3.5,22.1,-42,6.26189229,2.23,-4.67,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,161409,2015-10-30 10:16:22:285,1446171382285.0 \n-0.2574,0.5507,8.491,0.7991,-0.3889,9.7663,0.0867,-0.0562,-0.0257,-3.6,22.2,-42,0.027576202,2.27,-4.68,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,161512,2015-10-30 10:16:22:388,1446171382388.0 \n-0.1209,0.2634,9.3709,0.6605,-0.2176,9.782,0.0916,0.0782,-0.2896,-3.9,22.3,-42.2,0.055152404,1.27,-3.86,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,161613,2015-10-30 10:16:22:489,1446171382489.0 \n-0.3555,0.1329,11.6993,0.6741,-0.1109,9.7828,0.1991,0.0672,-0.2309,-3.9,22.1,-42.2,0.05009095,1,-3.99,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,161715,2015-10-30 10:16:22:591,1446171382591.0 \n-0.3819,-1.2737,12.2032,0.5891,-0.2012,9.7869,-0.2419,0.0929,-0.5938,-4.4,21.7,-42.4,0.058817596,0.5,-3.71,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,161818,2015-10-30 10:16:22:694,1446171382694.0 \n0.1784,-0.4214,8.1187,0.5214,-0.3308,9.7872,-0.2615,-0.0049,-0.1857,-4.8,21.8,-42.2,0.131772359,1.38,-3.02,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,161920,2015-10-30 10:16:22:796,1446171382796.0 \n-0.1353,1.0259,7.1718,0.4553,-0.4436,9.786,-0.1442,0.0672,-0.1112,-5.3,22.4,-41.6,0.150447382,2.59,-2.66,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,162022,2015-10-30 10:16:22:898,1446171382898.0 \n0.1425,0.8559,8.321,0.5413,-0.4099,9.7831,0.193,-0.1698,0.0305,-5.3,23,-41.3,0.136833813,2.68,-2.93,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,162126,2015-10-30 10:16:23:002,1446171383002.0 \n-0.2059,-0.0503,12.1518,0.5052,-0.2408,9.7907,0.2993,-0.0134,0.088,-5.4,23.2,-40.9,0.130376095,1.41,-2.95,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,162226,2015-10-30 10:16:23:102,1446171383102.0 \n-0.4968,-1.4257,12.1434,0.3962,0.0319,9.7986,-0.2883,-0.2126,-0.0147,-5.3,22.5,-41.4,0.143291532,-0.19,-2.32,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,162327,2015-10-30 10:16:23:203,1446171383203.0 \n0.0144,-0.2993,9.2476,0.5713,-0.185,9.7882,-0.1674,-0.1991,0.1698,-5.2,22.2,-41.5,0.133866754,0.91,-2.96,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,162429,2015-10-30 10:16:23:305,1446171383305.0 \n0.0096,0.6979,8.6682,0.5293,-0.3793,9.785,-0.1955,0.1429,0.1857,-5.1,22.1,-41.8,0.132994089,2.22,-3.1,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,162531,2015-10-30 10:16:23:407,1446171383407.0 \n0.073,1.2761,7.3849,0.5083,-0.3289,9.7879,0.1686,0.1075,0.1026,-5,22.4,-41.7,0.135961149,1.92,-2.97,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,162634,2015-10-30 10:16:23:510,1446171383510.0 \n-0.1257,0.2334,11.5209,0.5262,-0.213,9.7902,0.1845,-0.121,-0.1723,-4.9,22.8,-41.8,0.132295957,1.5,-2.84,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,162736,2015-10-30 10:16:23:612,1446171383612.0 \n0.8799,-0.6416,10.5417,0.6571,-0.1285,9.7838,0.1185,-0.1967,-0.2334,-4.8,22.7,-41.9,0.105417887,0.47,-3.54,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,162837,2015-10-30 10:16:23:713,1446171383713.0 \n0.4405,-0.4597,9.487,0.5569,-0.457,9.7802,-0.0611,0.1576,-0.3115,-5.5,22.9,-41.9,0.123394778,2.67,-3.26,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,162939,2015-10-30 10:16:23:815,1446171383815.0 \n-0.5016,-0.7362,9.0118,0.4522,-0.5419,9.7812,0.1698,0.0122,-0.0464,-6.1,23.2,-41.5,0.193557014,3.37,-2.75,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,163041,2015-10-30 10:16:23:917,1446171383917.0 \n-0.5411,0.2526,8.5497,0.4911,-0.5648,9.778,-0.1002,-0.0513,-0.11,-6.6,23.9,-40.8,0.224798408,3.3,-2.87,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,163144,2015-10-30 10:16:24:020,1446171384020.0 \n-0.2083,0.7003,8.8681,0.4811,-0.4926,9.7824,0.0379,0.0367,0.0452,-6.8,24.1,-40.6,0.221656815,2.96,-2.89,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,163245,2015-10-30 10:16:24:121,1446171384121.0 \n0.0287,0.6165,9.0656,0.4698,-0.0366,9.7953,0.5791,0.2382,0.3629,-6.9,23.9,-40.6,0.202458193,1.15,-3.12,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,163347,2015-10-30 10:16:24:223,1446171384223.0 \n-0.808,-0.9565,11.5676,0.6283,-0.2449,9.7834,0.1026,0.0953,0.3519,-6.9,23.2,-41.3,0.195825942,1.43,-3.67,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,163450,2015-10-30 10:16:24:326,1446171384326.0 \n0.1484,0.2693,7.9284,0.6577,-0.1542,9.7834,0.077,-0.1307,0.1429,-6.7,22.8,-41.8,0.188321026,0.86,-3.72,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,163552,2015-10-30 10:16:24:428,1446171384428.0 \n-0.5363,0.4513,8.9962,0.6106,-0.2879,9.7834,0.055,-0.0293,-0.0073,-6.5,22.6,-42.3,0.153763507,1.68,-3.57,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,163654,2015-10-30 10:16:24:530,1446171384530.0 \n-0.1832,1.0295,8.0505,0.5111,-0.0953,9.7929,0.088,0.011,-0.1087,-6.3,22.7,-42.1,0.167726141,0.83,-3,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,163755,2015-10-30 10:16:24:631,1446171384631.0 \n-0.067,0.0778,10.665,0.6518,0.0116,9.785,0.1332,-0.3189,-0.1833,-6.3,22.6,-41.9,0.137706478,-0.07,-3.81,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,163858,2015-10-30 10:16:24:734,1446171384734.0 \n-0.3124,-1.5909,13.6817,0.6057,-0.268,9.7843,-0.5864,0.0904,-0.325,-6.5,22.2,-42,0.147131256,0.79,-3.84,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,163960,2015-10-30 10:16:24:836,1446171384836.0 \n0.7709,-0.0527,8.8526,0.4396,-0.2019,9.7947,-0.369,-0.0843,-0.1527,-6.6,22.2,-42,0.237364778,1.18,-2.57,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,164061,2015-10-30 10:16:24:937,1446171384937.0 \n0.1999,0.6668,6.5613,0.3293,-0.3786,9.7938,-0.0159,0.2578,-0.0159,-6.6,22.5,-41.7,0.236492114,2.02,-2.47,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,164163,2015-10-30 10:16:25:039,1446171385039.0 \n-0.3029,0.7207,8.3246,0.3234,-0.446,9.7912,0.0501,0.0037,0.0672,-6.2,23.2,-41.1,0.21659536,2.61,-1.89,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,164266,2015-10-30 10:16:25:142,1446171385142.0 \n-0.431,0.2095,12.5253,0.3693,-0.371,9.7927,0.3018,-0.0965,0.3115,-6.2,23.7,-40.8,0.196000475,2.17,-2.16,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,164368,2015-10-30 10:16:25:244,1446171385244.0 \n-0.3268,-0.9792,11.2097,0.3448,-0.1559,9.7993,-0.3201,-0.2443,0.1808,-6.1,23.6,-40.7,0.192684349,0.91,-2.02,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,164470,2015-10-30 10:16:25:346,1446171385346.0 \n0.7889,0.893,8.4851,0.5611,-0.1979,9.7886,0.2358,-0.2053,0.4716,-5.9,23.1,-41.2,0.163013752,1.16,-3.28,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,164572,2015-10-30 10:16:25:448,1446171385448.0 \n-0.4345,-0.0862,9.6953,0.5669,-0.2471,9.7871,0.1197,0.2236,-0.0721,-5.7,22.8,-41.6,0.148003921,1.36,-3.7,36.814476,-119.748825,264.3,336.579551,4.41,25.806452,358.53,17 / 17,164673,2015-10-30 10:16:25:549,1446171385549.0 \n-0.2191,0.7207,7.8889,0.4896,-0.0578,9.7942,0.2211,-0.0733,-0.1136,-5.6,22.5,-42,0.169646003,0.34,-2.86,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,164776,2015-10-30 10:16:25:652,1446171385652.0 \n-0.504,0.1927,9.8114,0.5982,0.1832,9.7867,0.2211,-0.0721,-0.1417,-5.7,22.1,-42.1,0.163013752,-0.73,-3.12,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,164877,2015-10-30 10:16:25:753,1446171385753.0 \n0.8224,-0.322,10.8816,0.6122,0.2995,9.7829,-0.0855,0.0489,-0.2761,-6.1,21.4,-42.1,0.149923783,-1.75,-3.58,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,164979,2015-10-30 10:16:25:855,1446171385855.0 \n-0.5255,0.085,10.3585,0.2825,0.0028,9.8026,0.1173,0.2309,0.077,-6.3,21.2,-42.2,0.196349541,-0.2,-2.44,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,165081,2015-10-30 10:16:25:957,1446171385957.0 \n-0.2981,0.1257,9.3027,0.1826,-0.1988,9.8029,-0.4019,-0.011,-0.0037,-6.1,21.4,-41.9,0.244869694,0.84,-1.24,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,165187,2015-10-30 10:16:26:063,1446171386063.0 \n-0.7578,0.9996,8.6095,0.0883,-0.2656,9.8027,-0.11,-0.0049,0.0208,-5.5,22.4,-41.4,0.218166156,1.55,-0.52,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,165285,2015-10-30 10:16:26:161,1446171386161.0 \n-0.9864,0.0431,10.805,0.1343,-0.2338,9.8029,0.0757,-0.0953,0.099,-5.2,22.7,-41.2,0.198967535,1.37,-0.79,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,165387,2015-10-30 10:16:26:263,1446171386263.0 \n-0.4657,0.1209,9.9946,0.1203,0.0126,9.8059,0.0403,0.0367,0.3189,-4.9,22.6,-41.1,0.192684349,-0.07,-0.7,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,165489,2015-10-30 10:16:26:365,1446171386365.0 \n-0.9505,-1.3024,12.2212,0.2193,-0.0899,9.8038,-0.1881,-0.1393,0.2407,-4.8,22.4,-41.1,0.186575697,0.53,-1.28,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,165591,2015-10-30 10:16:26:467,1446171386467.0 \n-0.6931,-0.5195,9.5672,0.4213,-0.2787,9.7936,-0.3971,-0.0159,-0.1405,-4.5,22.1,-41.2,0.108908545,0.64,-2.3,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,165693,2015-10-30 10:16:26:569,1446171386569.0 \n-0.5267,0.7673,9.2464,0.4179,-0.3595,9.7911,0.022,-0.099,0.0562,-4.5,22.3,-41.1,0.109257611,2.1,-2.44,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,165796,2015-10-30 10:16:26:672,1446171386672.0 \n0.0227,1.1576,9.1195,0.4572,-0.2013,9.7939,0.1405,-0.0672,-0.0525,-4.7,22.6,-41.2,0.13962634,1.48,-2.67,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,165897,2015-10-30 10:16:26:773,1446171386773.0 \n-0.4884,-0.1496,12.3409,0.5627,-0.0259,9.7905,0.3946,-0.1014,-0.2028,-5,22.6,-41.2,0.114842665,0.15,-3.29,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,166001,2015-10-30 10:16:26:877,1446171386877.0 \n-0.8547,-1.4066,11.9303,0.5231,0.1034,9.7921,-0.3482,0.3299,-0.2627,-5.7,22,-41.5,0.168075207,-0.6,-3.06,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,166102,2015-10-30 10:16:26:978,1446171386978.0 \n0.5124,0.3316,7.2844,0.3057,0.0412,9.8018,0.1173,0.1466,0.0648,-5.9,21.6,-41.3,0.200189265,-0.14,-2.11,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,166204,2015-10-30 10:16:27:080,1446171387080.0 \n0.018,0.9744,7.288,0.26,-0.1708,9.8017,-0.0623,0.0672,0.0342,-5.9,21.7,-41.1,0.221482282,0.82,-1.65,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,166307,2015-10-30 10:16:27:183,1446171387183.0 \n-0.7278,0.3531,9.7145,0.3165,-0.2193,9.7991,-0.1087,-0.0269,0.0147,-5.6,22.3,-40.8,0.218166156,1.28,-1.85,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,166407,2015-10-30 10:16:27:283,1446171387283.0 \n-0.2873,0.2658,12.2164,0.3379,-0.0908,9.8004,0.441,0.1038,0.3531,-5.5,22.7,-40.8,0.161268423,1.12,-1.94,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,166510,2015-10-30 10:16:27:386,1446171387386.0 \n-0.6728,-1.4712,15.0188,0.4596,-0.0686,9.7956,-0.2334,-0.3543,0.1967,-5.4,22.5,-40.9,0.134564885,0.4,-2.69,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,166612,2015-10-30 10:16:27:488,1446171387488.0 \n0.3962,1.0977,7.9942,0.4461,-0.1099,9.7959,0.2859,-0.1161,0.2382,-5.2,22.5,-41.1,0.138055544,0.64,-2.61,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,166714,2015-10-30 10:16:27:590,1446171387590.0 \n-0.5997,0.2981,8.7065,0.4407,-0.1774,9.7951,0.1698,-0.1051,0.0195,-5,22.4,-41.3,0.147305789,1.04,-2.58,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,166815,2015-10-30 10:16:27:691,1446171387691.0 \n-0.4705,1.0271,7.8518,0.4113,0.018,9.798,0.1967,0.1295,0.011,-5,22.5,-41.4,0.136833813,0.4,-2.61,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,166918,2015-10-30 10:16:27:794,1446171387794.0 \n-0.6524,0.267,12.0871,0.4496,0.1497,9.7952,0.0904,-0.226,-0.2321,-4.9,22.2,-41.7,0.134739418,-0.87,-2.63,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,167020,2015-10-30 10:16:27:896,1446171387896.0 \n1.0499,-0.3795,11.0816,0.6427,0.3568,9.7791,-0.237,-0.226,-0.4618,-5.3,21.7,-41.6,0.11100294,-2.14,-3.23,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,167121,2015-10-30 10:16:27:997,1446171387997.0 \n0.3723,0.5411,7.2365,0.3685,0.2901,9.7954,0.0183,0.4924,-0.0721,-6,21.2,-41.6,0.196000475,-1.69,-2.15,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,167224,2015-10-30 10:16:28:100,1446171388100.0 \n-0.1628,0.6309,9.1447,0.4431,0.0955,9.7962,-0.3629,-0.0806,-0.0464,-6.3,21.1,-41.8,0.191462619,-1.25,-2.38,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,167326,2015-10-30 10:16:28:202,1446171388202.0 \n-0.146,1.1277,9.0513,0.5139,-0.166,9.7918,-0.1038,-0.088,-0.0134,-6.4,22,-41.8,0.179419847,0.83,-2.88,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,167427,2015-10-30 10:16:28:303,1446171388303.0 \n-0.4669,0.5447,10.641,0.505,-0.248,9.7905,0.0953,0.0318,0.1991,-6.4,22.8,-41.4,0.174881991,1.45,-2.95,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,167529,2015-10-30 10:16:28:405,1446171388405.0 \n0.2215,0.6764,11.9447,0.6073,-0.0111,9.7878,0.3519,-0.2627,0.3409,-6.5,23.2,-41.2,0.160744824,0.73,-3.28,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,167632,2015-10-30 10:16:28:508,1446171388508.0 \n-0.1269,-1.0403,12.73,0.643,-0.0145,9.7855,-0.4508,-0.3323,0.1686,-6.3,22.7,-41.6,0.139975406,0.08,-3.76,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,167733,2015-10-30 10:16:28:609,1446171388609.0 \n1.5407,0.8248,7.9715,0.8916,-0.0969,9.7656,-0.2981,0.0623,-0.1845,-6.2,22.6,-41.8,0.100880031,0.59,-5.04,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,167835,2015-10-30 10:16:28:711,1446171388711.0 \n0.1772,0.82,8.266,0.7587,-0.2268,9.7746,0.0024,0.1148,-0.0977,-6.1,22.6,-41.9,0.123394778,1.33,-4.44,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,167938,2015-10-30 10:16:28:814,1446171388814.0 \n-0.5064,0.7877,8.4671,0.6141,-0.1094,9.7868,0.2028,0.0782,-0.1759,-6.2,22.9,-41.7,0.143116999,0.98,-3.79,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,168040,2015-10-30 10:16:28:916,1446171388916.0 \n-0.3639,0.158,11.5065,0.6281,0.1216,9.7858,0.4691,-0.0623,-0.0354,-6.1,22.6,-41.6,0.139277274,-0.71,-3.67,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,168142,2015-10-30 10:16:29:018,1446171389018.0 \n-0.0431,-0.753,11.8321,0.5962,0.1157,9.7878,-0.2321,-0.099,-0.2285,-6.2,22.1,-42,0.132295957,-1.56,-3.97,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,168244,2015-10-30 10:16:29:120,1446171389120.0 \n0.4752,-0.0922,8.8621,0.544,-0.039,9.7915,-0.0867,-0.0183,0.1319,-6.2,21.8,-42.2,0.163886417,-0.09,-3.19,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,168346,2015-10-30 10:16:29:222,1446171389222.0 \n-0.2622,0.5997,8.1834,0.4636,-0.194,9.7938,-0.0538,0.0721,0.099,-6.2,22.3,-41.9,0.187099296,1.13,-2.71,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,168447,2015-10-30 10:16:29:323,1446171389323.0 \n0.2789,0.9828,8.4312,0.4508,-0.187,9.7945,0.0147,0.0672,0.1429,-6,22.9,-41.8,0.180990643,1.09,-2.64,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,168549,2015-10-30 10:16:29:425,1446171389425.0 \n-0.1939,0.0527,11.8573,0.4089,-0.1125,9.7975,0.0794,0.0012,0.1234,-5.4,23.2,-41.7,0.143116999,0.66,-2.39,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,168651,2015-10-30 10:16:29:527,1446171389527.0 \n0.2215,0.5626,8.3965,0.3781,0.1638,9.798,0.0171,0.0953,0.2285,-5,22.8,-42.1,0.141546202,-0.96,-2.21,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,168754,2015-10-30 10:16:29:630,1446171389630.0 \n0.5794,0.7805,8.6131,0.5688,-0.066,9.7899,0.1307,-0.1759,0.3494,-4.6,22.3,-42.2,0.117111593,0.39,-3.33,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,168855,2015-10-30 10:16:29:731,1446171389731.0 \n-0.723,-0.176,9.6175,0.6832,-0.1617,9.7815,-0.2321,-0.1344,-0.1002,-4.6,22.1,-42.3,0.094422313,0.63,-4.02,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,168957,2015-10-30 10:16:29:833,1446171389833.0 \n-0.2107,0.6776,8.3258,0.5863,-0.1906,9.7873,0.0293,0.0073,-0.0489,-4.7,22.4,-42.4,0.11397,1.28,-3.52,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,169059,2015-10-30 10:16:29:935,1446171389935.0 \n-0.237,0.9373,8.7807,0.5537,-0.173,9.7895,0.0195,-0.0086,-0.1881,-4.7,22.6,-42.2,0.117286126,1.01,-3.24,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,169163,2015-10-30 10:16:30:039,1446171390039.0 \n-0.4705,-0.4345,11.8932,0.6376,-0.1475,9.7848,0.0794,-0.2285,-0.1368,-4.7,22.8,-42.4,0.100705498,0.86,-3.73,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,169264,2015-10-30 10:16:30:140,1446171390140.0 \n-0.2322,-1.2091,12.6019,0.56,-0.3538,9.7843,-0.4117,0.0916,-0.1405,-5,22.9,-42,0.112399204,1.85,-3.48,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,169366,2015-10-30 10:16:30:242,1446171390242.0 \n0.6165,0.018,7.9069,0.4883,-0.3503,9.7882,-0.3592,-0.1271,-0.0929,-5.1,23,-41.9,0.129677963,1.82,-2.96,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,169468,2015-10-30 10:16:30:344,1446171390344.0 \n-0.3675,0.4669,8.2277,0.5065,-0.5311,9.7792,0.0916,-0.0489,-0.0342,-4.9,23.7,-41.2,0.131423293,3.1,-2.96,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,169570,2015-10-30 10:16:30:446,1446171390446.0 \n-0.1257,0.5782,8.4348,0.5388,-0.4644,9.7808,0.0257,-0.0159,-0.0574,-4.9,24.1,-41,0.123569311,2.71,-3.15,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,169671,2015-10-30 10:16:30:547,1446171390547.0 \n0.1389,-0.0443,11.7974,0.5087,-0.4181,9.7845,0.1478,-0.1075,0.1991,-5,24.3,-40.7,0.1282817,2.44,-2.98,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,169773,2015-10-30 10:16:30:649,1446171390649.0 \n0.7638,-1.5814,10.9547,0.6564,-0.4256,9.7754,-0.551,-0.43,-0.0867,-5,24.2,-40.7,0.113795467,1.72,-3.35,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,169876,2015-10-30 10:16:30:752,1446171390752.0 \n0.1508,0.2921,8.7736,0.637,-0.4772,9.7743,0.259,0.1026,0.2847,-5,24.2,-40.7,0.105417887,2.79,-3.73,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,169977,2015-10-30 10:16:30:853,1446171390853.0 \n-0.3615,0.0383,8.5904,0.7149,-0.4389,9.7707,-0.0098,0.0464,-0.0965,-5.1,24,-40.9,0.089884456,2.57,-4.18,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,170079,2015-10-30 10:16:30:955,1446171390955.0 \n-0.6225,0.6955,7.6531,0.5684,-0.2053,9.788,0.2492,0.077,-0.0024,-5.1,23.9,-41,0.108734012,1.61,-3.49,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,170182,2015-10-30 10:16:31:058,1446171391058.0 \n-0.5028,0.4262,9.0417,0.5587,-0.0781,9.7904,0.1332,0.0195,0.0024,-5.1,23.3,-41.3,0.116587994,0.46,-3.27,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,170283,2015-10-30 10:16:31:159,1446171391159.0 \n0.3986,-0.3376,10.671,0.6978,-0.0744,9.7815,0.0977,-0.0232,0.0904,-5.1,23,-41.4,0.094073247,0.6,-4,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,170386,2015-10-30 10:16:31:262,1446171391262.0 \n0.3519,-0.7745,10.993,0.6374,-0.44,9.776,0.1234,0.2077,0.1991,-5.3,23,-41.4,0.091978852,2.55,-4.25,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,170487,2015-10-30 10:16:31:363,1446171391363.0 \n0.0814,-0.3376,9.4379,0.6235,-0.533,9.7723,0.0672,0.1466,0.0183,-5.2,23.5,-41.4,0.109083078,3.12,-3.65,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,170590,2015-10-30 10:16:31:466,1446171391466.0 \n0.1413,0.6357,7.4819,0.4645,-0.4978,9.783,0.0122,0.1759,-0.0342,-5.1,24,-41.1,0.138579143,2.91,-2.72,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,170692,2015-10-30 10:16:31:568,1446171391568.0 \n0.0275,0.9146,8.4599,0.4047,-0.4536,9.7878,0.033,-0.0415,-0.0061,-4.5,24.2,-41.1,0.104021623,2.65,-2.37,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,170793,2015-10-30 10:16:31:669,1446171391669.0 \n-0.1628,-0.9924,13.8564,0.4978,-0.4076,9.7855,0.5522,0.0476,0.27,-4.3,24.3,-41.2,0.097214839,2.62,-2.57,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,170896,2015-10-30 10:16:31:772,1446171391772.0 \n-1.0415,-2.1739,13.4363,0.5451,-0.208,9.7893,-0.1295,-0.2211,-0.0635,-4.1,24,-41.4,0.07400196,1.22,-3.19,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,171002,2015-10-30 10:16:31:878,1446171391878.0 \n0.1425,-0.2813,8.102,0.6626,-0.092,9.7838,0.0244,-0.1967,-0.1442,-4.3,23.4,-42,0.050963614,0.54,-3.87,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,171100,2015-10-30 10:16:31:976,1446171391976.0 \n-0.1903,-0.0599,7.5022,0.6227,-0.3939,9.7789,-0.2004,0.0782,-0.3018,-4.5,23.2,-41.9,0.057246799,1.99,-3.77,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,171202,2015-10-30 10:16:32:078,1446171392078.0 \n-0.0766,0.9685,7.1611,0.6351,-0.4055,9.7777,0.022,-0.0183,-0.1955,-5,23.4,-41.7,0.109432144,2.69,-3.66,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,171304,2015-10-30 10:16:32:180,1446171392180.0 \n-0.018,0.4357,10.9427,0.7337,-0.3112,9.7742,0.0379,-0.1503,-0.2236,-5.8,24,-41.1,0.127758101,1.82,-4.29,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,171406,2015-10-30 10:16:32:282,1446171392282.0 \n-0.8428,0.82,11.1953,0.5635,0.0265,9.7904,0.3702,0.5901,-0.1026,-6.2,23.9,-41.4,0.126012772,0.5,-4.18,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,171507,2015-10-30 10:16:32:383,1446171392383.0 \n-2.7749,-2.8084,16.4709,0.7046,-0.24,9.7784,-0.2053,0.8467,0.1332,-6.9,23.4,-41.8,0.178547182,1.4,-4.12,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,171610,2015-10-30 10:16:32:486,1446171392486.0 \n0.3555,0.9661,8.7616,0.2104,-0.3717,9.7973,0,0.1772,0.2211,-6.6,23.3,-42.1,0.287630261,1.76,-0.79,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,171712,2015-10-30 10:16:32:588,1446171392588.0 \n-0.662,0.723,7.7069,0.0748,-0.4311,9.7969,-0.0342,0.2602,-0.0232,-6.1,24,-41.7,0.251152879,2.52,-0.44,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,171813,2015-10-30 10:16:32:689,1446171392689.0 \n-0.2286,0.6189,7.7297,0.1156,-0.3569,9.7995,-0.1075,0.237,-0.1368,-5.5,24.5,-41.2,0.189891823,2.09,-0.68,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,171915,2015-10-30 10:16:32:791,1446171392791.0 \n-1.391,-0.9792,12.724,0.1281,-0.4093,9.7973,0.0354,-0.4239,0.0623,-5.2,24.7,-40.8,0.189542757,2.39,-0.75,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,172017,2015-10-30 10:16:32:893,1446171392893.0 \n-0.012,-1.4186,14.0695,0.5357,-0.3948,9.784,-0.4337,-0.5583,0.1674,-5.1,24.4,-41,0.1425934,1.75,-2.42,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,172119,2015-10-30 10:16:32:995,1446171392995.0 \n-0.6093,-0.0431,10.0245,0.6544,-0.384,9.7773,-0.2443,-0.3225,0.0696,-5.3,24.2,-41.6,0.117460659,1.82,-3.16,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,172221,2015-10-30 10:16:33:097,1446171393097.0 \n-0.7781,0.0587,8.3941,0.6002,-0.4033,9.78,0.0415,0.1173,0.0953,-5.6,24.3,-41.9,0.147480322,2.51,-3.69,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,172324,2015-10-30 10:16:33:200,1446171393200.0 \n-0.3304,0.6835,8.1463,0.5612,-0.2056,9.7884,0.2847,-0.0232,0.2162,-5.4,24.3,-42.3,0.111526539,1.2,-3.28,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,172426,2015-10-30 10:16:33:302,1446171393302.0 \n-0.2131,0.0826,12.1434,0.5955,-0.0116,9.7885,0.1515,-0.2053,-0.0281,-5,23.7,-42.6,0.098960169,0.07,-3.48,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,172527,2015-10-30 10:16:33:403,1446171393403.0 \n0.571,-0.668,11.0995,0.614,0.0972,9.7869,0.1881,0.0379,-0.1319,-4.8,22.9,-42.7,0.097738438,-0.57,-3.59,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,172630,2015-10-30 10:16:33:506,1446171393506.0 \n0.4561,0.4322,7.5417,0.2806,-0.0616,9.8024,0.1075,0.1894,0.0354,-4.8,22.5,-42.6,0.158824962,0.31,-1.8,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,172732,2015-10-30 10:16:33:608,1446171393608.0 \n0.2598,0.6871,7.7776,0.2744,-0.3347,9.7971,-0.0098,0.1503,0.0562,-4.6,22.8,-42.4,0.175580123,1.96,-1.6,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,172833,2015-10-30 10:16:33:709,1446171393709.0 \n-0.2586,0.7649,8.6419,0.2842,-0.3552,9.7961,0.1197,-0.1918,-0.0134,-4.5,23.5,-42.2,0.134913951,2.23,-1.32,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,172936,2015-10-30 10:16:33:812,1446171393812.0 \n0.0622,-0.2861,11.7436,0.4375,-0.3936,9.789,-0.1173,-0.1552,-0.0757,-4.6,24.1,-42.1,0.139102741,2.3,-2.56,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,173039,2015-10-30 10:16:33:915,1446171393915.0 \n-0.1927,-0.2777,9.906,0.5175,-0.1357,9.792,0.0904,-0.11,0.182,-4.7,24,-42.1,0.122871179,1.1,-2.91,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,173140,2015-10-30 10:16:34:016,1446171394016.0 \n0.3639,0.5818,7.9021,0.5811,-0.2485,9.7863,0.3213,-0.1674,0.358,-5,23.9,-42.6,0.106988683,1.96,-3.43,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,173241,2015-10-30 10:16:34:117,1446171394117.0 \n-0.0443,0.0706,9.4559,0.6856,-0.2407,9.7797,-0.1051,-0.1112,0.0648,-5.1,23.6,-42.9,0.078888882,1.28,-4.22,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,173343,2015-10-30 10:16:34:219,1446171394219.0 \n-0.6955,0.8775,8.1056,0.5942,-0.1265,9.7878,0.0953,0.1466,0.0354,-4.9,23.4,-42.9,0.100705498,0.88,-3.65,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,173446,2015-10-30 10:16:34:322,1446171394322.0 \n-0.3077,0.9996,9.7851,0.579,-0.0466,9.7894,0.077,0.1405,0.0122,-4.6,22.7,-43.2,0.107163216,0.27,-3.38,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,173547,2015-10-30 10:16:34:423,1446171394423.0 \n-0.4369,0.3148,11.2336,0.6019,0.1453,9.7871,0.336,-0.0538,0.0049,-4.3,22.3,-43.2,0.05969026,-0.85,-3.52,36.814583,-119.74883,266.81,336.579551,4.63,25.806452,5.53,17 / 17,173649,2015-10-30 10:16:34:525,1446171394525.0 \n0.0934,-0.9194,11.9842,0.6023,0.1546,9.7869,-0.3555,0.0452,-0.2456,-4.2,21.6,-43.5,0.059515727,-0.9,-3.52,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,173751,2015-10-30 10:16:34:627,1446171394627.0 \n0.8535,0.7697,7.3346,0.5444,0.2103,9.7893,-0.3152,-0.2138,-0.1576,-4.3,21.4,-43.5,0.073129296,-1.23,-3.18,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,173854,2015-10-30 10:16:34:730,1446171394730.0 \n0.9685,1.6305,8.1199,0.6402,-0.1821,9.784,-0.1576,-0.077,-0.1136,-4.5,21.5,-43.4,0.057770398,0.71,-3.67,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,173956,2015-10-30 10:16:34:832,1446171394832.0 \n-0.0431,1.0558,9.4703,0.6643,-0.2738,9.7803,-0.1148,-0.0037,-0.1857,-4.9,22.4,-42.8,0.099483767,1.6,-3.89,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,174058,2015-10-30 10:16:34:934,1446171394934.0 \n-0.4298,0.0658,11.4778,0.654,-0.2465,9.7817,0.0709,-0.0428,-0.0147,-5.1,23,-42.6,0.104196156,1.68,-3.62,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,174160,2015-10-30 10:16:35:036,1446171395036.0 \n0.1329,-0.9134,11.7627,0.6203,0.0694,9.7868,-0.0037,-0.2211,0.0623,-5.3,23.1,-42.6,0.097040306,-0.41,-3.63,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,174262,2015-10-30 10:16:35:138,1446171395138.0 \n0.0275,-0.7123,9.323,0.7508,0.1385,9.7769,0.1613,-0.0904,0.2688,-5.2,22.7,-43,0.076270888,-0.64,-4.25,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,174364,2015-10-30 10:16:35:240,1446171395240.0 \n-0.5183,-0.2274,9.1063,0.7482,-0.0432,9.778,-0.2505,0.1759,-0.0538,-5,22,-43.6,0.061610123,-0.02,-4.73,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,174466,2015-10-30 10:16:35:342,1446171395342.0 \n-0.674,0.6895,8.2301,0.6931,-0.074,9.7818,0.0086,0.1234,-0.066,-4.9,21.9,-43.8,0.086393798,0.43,-4.05,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,174568,2015-10-30 10:16:35:444,1446171395444.0 \n-0.6321,1.0594,8.4958,0.6058,-0.0628,9.7877,0.1173,0.0305,-0.0819,-4.8,22,-43.8,0.104196156,0.37,-3.54,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,174670,2015-10-30 10:16:35:546,1446171395546.0 \n-0.1137,-0.0611,12.4427,0.7957,0.1134,9.7737,0.1808,-0.3897,-0.0892,-4.7,22,-43.7,0.083077672,-0.29,-4.09,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,174771,2015-10-30 10:16:35:647,1446171395647.0 \n0.4561,-1.0487,11.0049,0.7324,0.3053,9.7745,-0.3213,0.0159,-0.38,-5,21.6,-43.9,0.072605697,-1.78,-4.29,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,174873,2015-10-30 10:16:35:749,1446171395749.0 \n-0.4597,-0.5327,8.4443,0.5475,0.0251,9.7913,-0.0318,0.1112,0.0391,-5.2,21.6,-43.4,0.102276294,-0.04,-3.64,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,174977,2015-10-30 10:16:35:853,1446171395853.0 \n0.5207,0.9912,7.5776,0.5446,-0.043,9.7914,0.0037,0.0428,0.1894,-5.3,21.9,-42.9,0.11274827,0.42,-3.38,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,175077,2015-10-30 10:16:35:953,1446171395953.0 \n0.5818,1.1456,9.0752,0.6109,0.0182,9.7876,0.2285,-0.1637,0.1258,-5,22.3,-42.5,0.107163216,-0.11,-3.57,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,175179,2015-10-30 10:16:36:055,1446171396055.0 \n0.0084,1.1049,9.2249,0.52,0.268,9.7892,0.4142,0.1246,0.088,-4.8,22.1,-42.5,0.118856922,-1.57,-3.04,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,175282,2015-10-30 10:16:36:158,1446171396158.0 \n0.6883,0.6584,9.6163,0.4064,0.7725,9.7677,0.1772,-0.1063,0.0476,-4.5,20.9,-43.1,0.090582588,-4.52,-2.38,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,175386,2015-10-30 10:16:36:262,1446171396262.0 \n-0.1796,-1.0427,12.2068,0.5696,0.6856,9.7661,-0.2321,-0.1637,-0.0892,-4.4,20,-43.8,0.06265732,-4.32,-3.3,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,175486,2015-10-30 10:16:36:362,1446171396362.0 \n0.3496,-0.1951,10.0054,0.4675,0.6573,9.7734,-0.1442,-0.1735,-0.0831,-4.1,19.1,-44.3,0.086219265,-3.84,-2.74,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,175587,2015-10-30 10:16:36:463,1446171396463.0 \n0.3891,-0.328,10.3286,0.4314,0.5374,9.7824,0.0611,-0.0342,-0.4814,-4.1,19.1,-44.4,0.095818576,-3.14,-2.52,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,175690,2015-10-30 10:16:36:566,1446171396566.0 \n0.6357,-0.4082,9.5409,0.31,0.5591,9.7858,0.0525,0.2272,-0.5974,-4.1,19.5,-44,0.115366264,-3.27,-1.81,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,175792,2015-10-30 10:16:36:668,1446171396668.0 \n2.5163,1.1372,6.7301,0.0198,0.8973,9.7655,0.3763,0.4655,-1.1582,-4.4,19.6,-43.9,0.135088484,-4.63,-1.05,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,175894,2015-10-30 10:16:36:770,1446171396770.0 \n1.1432,-0.2957,8.2408,-0.4359,0.7309,9.7697,0.4191,0.2993,-2.1246,-5.4,19.4,-44,0.303512757,-4.27,2.55,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,175998,2015-10-30 10:16:36:874,1446171396874.0 \n1.4018,-0.6488,9.7624,-0.6224,0.8691,9.7482,0.2798,-0.0635,-2.2297,-6.8,19.1,-44.3,0.403520123,-4.83,3.47,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,176098,2015-10-30 10:16:36:974,1446171396974.0 \n0.9996,-0.7578,9.3206,-0.4712,0.9633,9.7478,0.2419,-0.4032,-2.4276,-12.7,16.9,-45.5,0.630587459,-5.57,3.18,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,176200,2015-10-30 10:16:37:076,1446171397076.0 \n-0.8966,-1.3372,8.9423,-0.313,0.8931,9.7609,-0.1332,-0.3433,-2.5119,-18.5,13.9,-45,0.817337689,-5.62,1.9,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,176302,2015-10-30 10:16:37:178,1446171397178.0 \n-1.5287,-0.9661,9.6654,-0.0398,0.8588,9.7689,0.2639,-0.617,-2.3543,-23.8,8.7,-44.7,1.080882406,-5.02,0.23,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,176403,2015-10-30 10:16:37:279,1446171397279.0 \n-2.7366,-1.7765,10.8457,0.2831,0.7501,9.7738,0.099,-0.8161,-1.2523,-26.8,5.6,-45,1.21719262,-4.39,-1.66,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,176507,2015-10-30 10:16:37:383,1446171397383.0 \n-2.053,-0.1604,9.5624,0.5067,0.4897,9.7813,-0.2224,-0.4655,-0.4154,-27.7,5,-43.8,1.295383371,-2.86,-2.97,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,176607,2015-10-30 10:16:37:483,1446171397483.0 \n-1.992,0.8595,9.6031,0.4275,0.1198,9.7966,-0.1625,0.1466,-0.1136,-28.9,3.9,-43.1,1.391201947,-1.1,-2.97,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,176710,2015-10-30 10:16:37:586,1446171397586.0 \n-1.6939,1.2067,9.5565,0.139,0.0273,9.8056,-0.182,0.0965,0.0244,-29.9,3.9,-42.6,1.431519052,-0.16,-0.81,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,176811,2015-10-30 10:16:37:687,1446171397687.0 \n-0.9373,1.4581,10.1167,-0.2424,0.0624,9.8035,0.0049,0.0171,0.0611,-29.9,4.3,-42.7,1.435882376,-0.28,1.31,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,176913,2015-10-30 10:16:37:789,1446171397789.0 \n-1.7693,0.5411,10.6255,-0.3242,0.2248,9.7987,0.0305,-0.0672,0.1417,-29.6,4.8,-42.8,1.383173432,-1.31,1.89,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,177017,2015-10-30 10:16:37:893,1446171397893.0 \n-0.3555,0.4417,11.0289,-0.304,0.3467,9.7958,0.204,0.0147,0.2932,-29.5,5.1,-42.9,1.369036265,-1.63,1.76,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,177118,2015-10-30 10:16:37:994,1446171397994.0 \n-0.6584,-1.063,14.5029,-0.3069,0.0821,9.8015,-0.7196,-0.044,-0.5315,-29.4,5,-43,1.370257996,-1.57,1.69,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,177219,2015-10-30 10:16:38:095,1446171398095.0 \n-0.2693,0.2143,7.5669,-0.4323,0.2822,9.7931,-0.0757,-0.066,-0.4911,-29.4,5.1,-43.1,1.378635576,-1.4,2.59,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,177322,2015-10-30 10:16:38:198,1446171398198.0 \n-0.8104,0.2825,7.9332,-0.5267,0.2828,9.7884,0.1662,0.1808,-0.2981,-29.3,4.4,-43.3,1.406211778,-1.65,3.08,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,177424,2015-10-30 10:16:38:300,1446171398300.0 \n-0.4238,0.7745,8.4599,-0.5166,0.3449,9.787,0.1576,-0.1405,0.0293,-29,3.8,-43.4,1.40394285,-1.78,3.2,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,177525,2015-10-30 10:16:38:401,1446171398401.0 \n-0.4238,0.832,9.1231,-0.3483,0.5203,9.7866,0.1173,-0.1222,0.1087,-28.9,2.5,-43.2,1.408131641,-2.78,2.22,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,177627,2015-10-30 10:16:38:503,1446171398503.0 \n-0.595,-0.1832,10.0066,-0.1511,0.5437,9.7904,-0.1283,-0.0806,0.0806,-29.5,2.1,-43.1,1.425061334,-3.18,0.88,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,177729,2015-10-30 10:16:38:605,1446171398605.0 \n-1.3779,-0.3603,10.1167,-0.0295,0.3006,9.802,-0.2468,0.0501,0.2114,-30.1,2.2,-43.2,1.46118965,-1.76,0.17,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,177832,2015-10-30 10:16:38:708,1446171398708.0 \n-0.2765,-0.1652,9.5337,0.1428,0.2647,9.802,-0.0843,-0.0305,0.3042,-31,3.1,-43,1.434311579,-1.55,-0.83,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,177933,2015-10-30 10:16:38:809,1446171398809.0 \n-0.8571,0.2729,9.2596,0.1916,0.3531,9.7984,0.2773,0.0574,0.2749,-31.3,3.8,-42.8,1.399404994,-1.64,-0.91,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,178037,2015-10-30 10:16:38:913,1446171398913.0 \n-0.5938,0.8404,8.8346,0.1309,0.5856,9.7883,0.2285,0.0513,0.1173,-31.7,4.2,-42.9,1.364149343,-3.42,-0.77,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,178138,2015-10-30 10:16:39:014,1446171399014.0 \n0.1269,0.0718,11.5029,0.2411,0.6837,9.7798,0.1332,-0.2004,-0.0977,-31.7,4.1,-43,1.355248164,-3.74,-1.05,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,178240,2015-10-30 10:16:39:116,1446171399116.0 \n0.4154,-0.6273,11.8166,0.1345,0.6622,9.7833,-0.5938,0.1295,-0.4655,-31.8,3.4,-43.3,1.38422063,-3.87,-0.79,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,178341,2015-10-30 10:16:39:217,1446171399217.0 \n0.4477,0.3256,7.7405,0.0449,0.4018,9.7983,0.0757,0.0476,-0.0709,-31.7,3.2,-43.2,1.422094275,-2.35,-0.26,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,178443,2015-10-30 10:16:39:319,1446171399319.0 \n-0.0168,0.3041,8.9495,0.1125,0.1849,9.8043,-0.0208,0.0611,-0.0916,-31.6,3.2,-43,1.444434489,-1.31,-0.73,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,178545,2015-10-30 10:16:39:421,1446171399421.0 \n-0.3998,0.5495,8.5497,0.0423,0.2047,9.8044,0.0024,0.0672,-0.2077,-31.6,3.5,-42.8,1.417905484,-1.2,-0.25,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,178647,2015-10-30 10:16:39:523,1446171399523.0 \n-0.498,-0.6967,12.2296,-0.038,0.2586,9.8032,0.2236,-0.0782,0.1417,-31.5,3.2,-42.6,1.439023968,-1.51,0.22,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,178750,2015-10-30 10:16:39:626,1446171399626.0 \n-0.0144,-0.0431,9.2668,-0.0673,0.4362,9.7967,0.2053,0.2138,0.325,-31.4,2.9,-43.1,1.415462023,-2.55,0.39,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,178851,2015-10-30 10:16:39:727,1446171399727.0 \n0.146,0.2538,8.4874,0.1263,0.1531,9.8046,0.1759,-0.1222,0.5205,-31.6,3.1,-43.4,1.454382866,-0.89,-0.74,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,178954,2015-10-30 10:16:39:830,1446171399830.0 \n-0.1125,-0.0826,9.8318,0.393,0.1308,9.7979,0.11,0.182,0.1417,-32,3.6,-43.2,1.414763892,-0.99,-2.27,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,179055,2015-10-30 10:16:39:931,1446171399931.0 \n-0.2634,0.8452,8.6095,0.3457,0.3708,9.7935,0.16,-0.1087,0.0929,-32.4,4.5,-42.5,1.369036265,-1.64,-2.09,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,179158,2015-10-30 10:16:40:034,1446171400034.0 \n-0.2981,0.3879,10.5728,0.2832,0.6271,9.7825,0.1808,0.0599,-0.1454,-32.5,4.2,-42.1,1.355248164,-3.67,-1.66,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,179260,2015-10-30 10:16:40:136,1446171400136.0 \n0.3244,-0.0323,10.7835,0.1917,0.8951,9.7638,0.2236,0.0635,-0.1943,-32.4,3.3,-42.3,1.353677368,-5.24,-1.12,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,179362,2015-10-30 10:16:40:238,1446171400238.0 \n-0.5806,-0.6883,11.3928,0.0709,0.6821,9.7826,-0.4398,0.0941,-0.5095,-32.3,1.9,-42.6,1.397310599,-4.61,-0.92,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,179465,2015-10-30 10:16:40:341,1446171400341.0 \n0.2729,0.2586,7.7536,0.1047,0.5788,9.789,-0.3616,-0.2175,-0.2578,-32.1,1.3,-43,1.445830752,-3.98,-0.29,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,179566,2015-10-30 10:16:40:442,1446171400442.0 \n-0.6045,0.8452,7.7824,0.0816,0.4249,9.7971,-0.0513,0.0061,-0.0965,-32.1,0.9,-43.4,1.478642942,-2.55,-0.5,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,179669,2015-10-30 10:16:40:545,1446171400545.0 \n-0.48,0.5351,9.3518,0.0638,0.4934,9.794,-0.0281,0.0684,-0.0159,-32.1,1,-43.5,1.471138027,-2.88,-0.37,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,179769,2015-10-30 10:16:40:645,1446171400645.0 \n-0.0982,-0.1377,12.3385,0.0813,0.5061,9.7932,0.1124,-0.1246,0.1845,-32.2,1.1,-43.4,1.469043631,-2.96,-0.48,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,179872,2015-10-30 10:16:40:748,1446171400748.0 \n-0.844,-1.3898,14.364,0.1591,0.4214,9.7963,-0.5864,-0.3824,0.033,-32.2,1,-43.4,1.479341074,-2.46,-0.93,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,179974,2015-10-30 10:16:40:850,1446171400850.0 \n-0.0156,0.3639,9.0621,0.3258,0.4492,9.7909,0.1112,-0.4435,0.3409,-32.3,1.4,-43.1,1.488242253,-2.1,-0.9,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,180076,2015-10-30 10:16:40:952,1446171400952.0 \n0.0024,0.7937,7.8482,0.3275,0.404,9.7929,-0.1136,0.2248,0.2089,-32.7,2.3,-42.9,1.450543141,-2.36,-1.92,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,180178,2015-10-30 10:16:41:054,1446171401054.0 \n-0.1161,0.9649,7.5178,0.3282,0.5596,9.7852,0.1148,0.0684,0.0745,-33,3,-42.8,1.401848455,-3.08,-2.05,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,180280,2015-10-30 10:16:41:156,1446171401156.0 \n-0.0072,0.5064,11.8118,0.4007,0.6853,9.7745,0.2065,-0.2896,-0.2737,-33.2,3,-42.7,1.378111977,-4.01,-2.35,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,180381,2015-10-30 10:16:41:257,1446171401257.0 \n1.0594,0.3316,10.471,0.5876,0.938,9.744,0.2993,-0.0538,-0.2211,-33.4,2.5,-42.5,1.34128553,-5.46,-3.2,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,180483,2015-10-30 10:16:41:359,1446171401359.0 \n0.3436,0.5088,7.3418,0.3377,0.6015,9.7824,-0.0941,0.4533,-0.2101,-33.8,1.4,-42.4,1.459269788,-3.52,-1.98,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,180585,2015-10-30 10:16:41:461,1446171401461.0 \n0.7434,0.4106,8.3641,0.5398,0.309,9.7869,-0.0599,-0.0538,0.0342,-34,0.8,-42.2,1.495747169,-1.81,-3.16,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,180688,2015-10-30 10:16:41:564,1446171401564.0 \n-0.1532,0.68,8.6933,0.4456,0.3501,9.7903,0.226,0.1967,0.0599,-34,0.9,-42.2,1.493129175,-1.94,-2.97,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,180790,2015-10-30 10:16:41:666,1446171401666.0 \n-0.3041,0.2873,10.5692,0.3416,0.4164,9.7918,-0.0464,0.055,-0.0183,-33.8,1,-42.3,1.48387893,-2.43,-2,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,180892,2015-10-30 10:16:41:768,1446171401768.0 \n-0.4609,0.3316,10.7931,0.3639,0.5123,9.7865,0.5522,0.2724,0.4117,-33.8,1,-42.4,1.470614428,-2.99,-2.13,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,180997,2015-10-30 10:16:41:873,1446171401873.0 \n-0.4286,-0.2538,11.4754,0.3375,0.501,9.788,-0.055,-0.0403,0.3299,-33.4,1,-42.7,1.467996434,-2.93,-1.97,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,181095,2015-10-30 10:16:41:971,1446171401971.0 \n0.5327,0.5339,8.5677,0.6039,0.5562,9.7722,0.1014,-0.43,0.2199,-33.5,1.4,-42.4,1.458746189,-3.25,-2.89,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,181198,2015-10-30 10:16:42:074,1446171402074.0 \n0.0275,0.899,8.3199,0.5509,0.4252,9.7819,0.0244,0.0538,0.1148,-33.8,2.2,-42.1,1.450543141,-2.36,-3.36,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,181300,2015-10-30 10:16:42:176,1446171402176.0 \n0.0634,1.0127,8.6119,0.4744,0.5105,9.7819,0.0305,-0.0953,-0.0599,-34.1,2.7,-42.1,1.407608042,-2.97,-2.77,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,181402,2015-10-30 10:16:42:278,1446171402278.0 \n-0.1269,-0.2574,12.2894,0.5306,0.5337,9.7777,-0.0318,-0.077,-0.1698,-34.2,2.7,-42.1,1.402546587,-3.12,-3.11,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,181504,2015-10-30 10:16:42:380,1446171402380.0 \n1.1684,-0.3879,10.9738,0.3799,0.5658,9.7829,-0.226,0.1368,-0.2419,-34.2,2.3,-42,1.419476281,-3.81,-2.65,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,181609,2015-10-30 10:16:42:485,1446171402485.0 \n-0.3555,-0.4741,11.2611,0.3094,0.4992,9.789,-0.0819,0.2077,-0.0941,-34.1,2.1,-41.9,1.443212758,-2.92,-1.81,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,181709,2015-10-30 10:16:42:585,1446171402585.0 \n0.3938,0.3986,8.8286,0.243,0.3929,9.7958,-0.1161,0.0171,0.0147,-33.8,1.7,-42.5,1.456302728,-2.4,-1.39,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,181811,2015-10-30 10:16:42:687,1446171402687.0 \n0.0742,0.9924,8.345,0.293,0.4594,9.7915,0.1466,-0.0696,0.0428,-33.5,1.6,-43.2,1.450019543,-2.43,-1.58,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,181912,2015-10-30 10:16:42:788,1446171402788.0 \n-0.1341,0.0754,12.0883,0.2983,0.4948,9.7896,0.1784,-0.0134,0.1918,-33.6,1.6,-43.3,1.442340094,-2.89,-1.75,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,182014,2015-10-30 10:16:42:890,1446171402890.0 \n0.1365,0.2095,8.5784,0.3104,0.7661,9.7718,-0.4716,-0.3665,0.1185,-33.7,1.4,-43.1,1.432740783,-4.66,-1.54,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,182115,2015-10-30 10:16:42:991,1446171402991.0 \n0.2789,0.6488,8.8454,0.4365,0.6689,9.7741,0.2944,0.0208,0.4264,-33.8,1.3,-43,1.459793386,-3.34,-2.4,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,182217,2015-10-30 10:16:43:093,1446171403093.0 \n-0.0527,0.3112,8.6119,0.5176,0.5597,9.777,-0.2053,0.1185,0.0599,-34,1.4,-42.5,1.453335668,-3.56,-3.24,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,182319,2015-10-30 10:16:43:195,1446171403195.0 \n-0.6871,0.8188,8.2468,0.3029,0.5773,9.785,0.2382,0.2358,0.1356,-34,1.9,-42.3,1.438151304,-3.06,-2.3,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,182423,2015-10-30 10:16:43:299,1446171403299.0 \n-0.2693,0.5555,10.4603,0.2307,0.6771,9.7805,0.0367,0.0195,-0.0782,-33.8,2.2,-42.5,1.421919742,-3.96,-1.35,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,182524,2015-10-30 10:16:43:400,1446171403400.0 \n0.9361,0.3639,9.6546,0.1569,0.9096,9.7631,0.1979,0.022,-0.1478,-33.2,1.5,-43.1,1.386315025,-5.32,-0.92,36.814655,-119.74884,270.93,336.579551,3.99,12.903226,0.51,17 / 17,182625,2015-10-30 10:16:43:501,1446171403501.0 \n-0.9481,-0.7554,12.4666,0.1327,0.588,9.7881,-0.1344,0.16,-0.1381,-33.1,1,-43.6,1.45822259,-3.44,-0.78,36.814705,-119.74874,277.07,336.579551,4.27,19.35484,89.44,17 / 17,182728,2015-10-30 10:16:43:604,1446171403604.0 \n-0.0335,0.1844,9.1183,0.2014,0.6541,9.7827,-0.1918,0.0709,-0.0281,-32.9,0.4,-43.6,1.478293876,-3.82,-1.18,36.814705,-119.74874,277.07,336.579551,4.27,19.35484,89.44,17 / 17,182829,2015-10-30 10:16:43:705,1446171403705.0 \n-0.2334,0.9469,8.667,0.1788,0.5523,9.7895,-0.0281,-0.0159,-0.0403,-33,0.5,-43.7,1.462236847,-3.23,-1.05,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,182931,2015-10-30 10:16:43:807,1446171403807.0 \n0.0455,1.2151,9.1566,0.1831,0.6569,9.7829,0.0745,0.0293,0.1002,-33,0.5,-43.8,1.45106674,-3.68,-1.11,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,183033,2015-10-30 10:16:43:909,1446171403909.0 \n-0.3112,0.7446,12.5696,0.1432,0.7638,9.7758,0.2602,0.0696,0.2749,-33.1,0.4,-43.8,1.464156709,-4.47,-0.84,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,183136,2015-10-30 10:16:44:012,1446171404012.0 \n0.3615,-0.2598,10.6099,0.0905,0.9122,9.7637,-0.0709,-0.0342,0.2175,-33,0.1,-43.7,1.444958088,-5.34,-0.53,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,183238,2015-10-30 10:16:44:114,1446171404114.0 \n0.1772,1.0511,8.2552,0.2662,0.8289,9.7679,0.2285,-0.2443,0.1845,-32.9,0.2,-43.6,1.45822259,-4.67,-1.13,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,183339,2015-10-30 10:16:44:215,1446171404215.0 \n-0.8787,0.3232,8.7161,0.2318,0.6542,9.7821,-0.0709,-0.0733,-0.0122,-33,0.4,-43.5,1.477246679,-3.93,-1.34,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,183442,2015-10-30 10:16:44:318,1446171404318.0 \n-0.1209,1.5095,7.3346,0.0933,0.5596,9.7902,-0.1258,0.2346,-0.0623,-33.1,1,-43.4,1.464680308,-3.27,-0.55,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,183544,2015-10-30 10:16:44:420,1446171404420.0 \n-0.6141,0.4776,10.9104,0.062,0.5095,9.7932,-0.022,0.0476,-0.1747,-32.8,1.1,-43.7,1.470439895,-2.98,-0.36,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,183646,2015-10-30 10:16:44:522,1446171404522.0 \n-0.3519,0.3484,10.4267,0.1515,0.6343,9.7849,0.0867,-0.1124,0.0012,-32.8,1.1,-43.9,1.45700086,-3.48,-0.84,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,183747,2015-10-30 10:16:44:623,1446171404623.0 \n0.1305,0.3388,9.7612,0.1268,0.4013,9.7976,0.1319,0.0367,0.0562,-32.9,0.9,-44.1,1.484227996,-2.35,-0.74,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,183850,2015-10-30 10:16:44:726,1446171404726.0 \n-0.2969,0.3053,9.7073,0.0096,0.2026,9.8046,-0.4264,0.0904,-0.1454,-32.9,0.9,-44.1,1.497841564,-1.82,-0.24,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,183951,2015-10-30 10:16:44:827,1446171404827.0 \n-0.5291,0.7961,8.1858,-0.0237,0.1511,9.8055,-0.0208,0.0672,-0.0586,-32.7,1,-44.2,1.520181778,-0.88,0.14,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,184058,2015-10-30 10:16:44:934,1446171404934.0 \n-0.3304,0.1592,10.2963,0.0079,0.2278,9.804,0.1381,0.0293,0.1038,-32.4,1.4,-44.4,1.507615408,-1.33,-0.05,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,184156,2015-10-30 10:16:45:032,1446171405032.0 \n-0.7183,0.7877,11.1438,0.0583,0.419,9.7975,0.336,-0.1148,0.2162,-32.4,1.3,-44.1,1.480039206,-2.45,-0.34,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,184257,2015-10-30 10:16:45:133,1446171405133.0 \n-1.4724,-0.6069,11.1019,0.1559,0.3533,9.799,-0.2871,-0.0428,0.1552,-32.4,0.9,-43.8,1.481435469,-2.34,-0.74,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,184361,2015-10-30 10:16:45:237,1446171405237.0 \n-0.1664,0.5136,8.8298,0.3438,0.2586,9.7972,-0.3848,0.0342,-0.0318,-32.5,1.1,-43.5,1.48806772,-2,-1.86,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,184462,2015-10-30 10:16:45:338,1446171405338.0 \n-0.8092,0.747,8.7867,0.2668,0.0807,9.8027,-0.0574,0.0525,0.033,-32.7,1.8,-43.1,1.496794367,-0.47,-1.56,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,184563,2015-10-30 10:16:45:439,1446171405439.0 \n-0.3519,1.1145,8.0613,0.1753,0.2085,9.8029,0.1356,0.1002,0.0367,-32.9,2.4,-43,1.48684599,-0.91,-1.22,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,184666,2015-10-30 10:16:45:542,1446171405542.0 \n-0.7458,0.6225,9.7719,0.1106,0.4287,9.7967,0.3164,0.0293,-0.0171,-32.5,2.3,-43.2,1.461887781,-1.91,-0.69,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,184767,2015-10-30 10:16:45:643,1446171405643.0 \n-0.1844,-0.7003,10.6111,0.0227,0.0687,9.8064,0.2004,0.2786,0.1808,-32.2,1.9,-43.4,1.498714229,-0.4,-0.13,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,184870,2015-10-30 10:16:45:746,1446171405746.0 \n0.2119,-0.267,8.7209,-0.0668,0.0618,9.8062,-0.1344,-0.0916,0.0415,-31.8,1.7,-43.8,1.488416786,-0.88,0.44,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,184972,2015-10-30 10:16:45:848,1446171405848.0 \n-0.3472,0.7314,8.6131,0.0015,-0.0417,9.8066,-0.0965,-0.0513,0.0024,-31.6,2.1,-43.8,1.514247659,0.24,-0.01,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,185074,2015-10-30 10:16:45:950,1446171405950.0 \n-0.2047,0.82,9.3529,0.0897,-0.0042,9.8062,-0.0855,0.0476,-0.1075,-31.5,2.4,-44,1.506219144,0.02,-0.52,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,185175,2015-10-30 10:16:46:051,1446171406051.0 \n-0.5531,0.3112,11.5041,0.0327,0.205,9.8045,0.3531,0.0257,0.0757,-31.6,2.5,-43.3,1.448972345,-1.2,-0.19,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,185277,2015-10-30 10:16:46:153,1446171406153.0 \n-1.0523,-0.9744,11.8274,-0.0265,0.2655,9.803,-0.2834,-0.0122,-0.0293,-31.5,2.1,-43.4,1.459095255,-2,0.19,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,185383,2015-10-30 10:16:46:259,1446171406259.0 \n-0.2107,0.2322,8.8454,0.1458,0.3041,9.8008,-0.088,-0.0867,0.0599,-31.4,1.7,-43.1,1.461015117,-1.78,-0.85,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,185482,2015-10-30 10:16:46:358,1446171406358.0 \n-0.6057,0.2382,9.6019,0.228,0.1119,9.8034,-0.281,-0.16,-0.0782,-31.4,1.7,-43,1.483180798,-0.84,-1.26,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,185584,2015-10-30 10:16:46:460,1446171406460.0 \n-0.6369,0.6201,8.5401,0.2022,0.124,9.8038,0.0428,0.0513,-0.011,-31.6,2,-42.7,1.491383846,-0.62,-1.29,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,185685,2015-10-30 10:16:46:561,1446171406561.0 \n-0.6452,0.0227,11.6598,0.2485,0.1657,9.8021,-0.0599,-0.2883,-0.215,-31.7,2.2,-42.4,1.483006265,-0.97,-1.45,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,185787,2015-10-30 10:16:46:663,1446171406663.0 \n0.0084,-0.8835,12.56,0.3835,0.2385,9.7962,-0.4362,-0.0098,-0.3726,-31.9,1.8,-42.2,1.470614428,-1.39,-2.24,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,185890,2015-10-30 10:16:46:766,1446171406766.0 \n0.2346,-0.2107,9.2368,0.2459,0.1287,9.8027,0.1381,0.0782,0.0855,-31.9,1.6,-42.2,1.495921702,-0.43,-1.43,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,185992,2015-10-30 10:16:46:868,1446171406868.0 \n0.4034,0.7063,6.9372,0.2828,0.0714,9.8023,0.0281,-0.0403,0.0965,-32,1.5,-42.2,1.495747169,-0.42,-1.65,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,186093,2015-10-30 10:16:46:969,1446171406969.0 \n-0.0431,0.577,9.0585,0.3374,-0.033,9.8008,0.0452,0,0.0367,-31.9,1.7,-42.4,1.507789941,0.09,-1.87,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,186196,2015-10-30 10:16:47:072,1446171407072.0 \n-0.1927,0.3256,10.5788,0.2749,-0.011,9.8028,-0.0293,0.088,0.0562,-31.8,2.1,-42.5,1.509186204,0.14,-1.73,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,186298,2015-10-30 10:16:47:174,1446171407174.0 \n-0.0622,0.0275,10.064,0.2753,0.2258,9.8002,0.3372,0.0709,0.226,-31.6,2.3,-42.2,1.4826572,-0.97,-1.59,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,186400,2015-10-30 10:16:47:276,1446171407276.0 \n-0.3699,-0.3077,9.5541,0.3737,0.0805,9.7992,0.2639,-0.011,0.171,-31.5,2.3,-42,1.490860247,-0.47,-2.18,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,186502,2015-10-30 10:16:47:378,1446171407378.0 \n-0.3005,-0.2466,8.9771,0.4883,0.0938,9.794,-0.1637,-0.1894,-0.1283,-31.5,2.4,-41.8,1.475675883,-1.02,-2.68,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,186604,2015-10-30 10:16:47:480,1446171407480.0 \n-0.2825,0.3376,8.5186,0.4456,-0.0362,9.7965,-0.0037,0.066,-0.0586,-31.7,2.4,-41.6,1.509709803,0.21,-2.6,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,186706,2015-10-30 10:16:47:582,1446171407582.0 \n-0.4944,0.6285,10.0185,0.3145,0.0707,9.8014,0.0831,0.0525,-0.1148,-31.7,2.6,-41.5,1.468694566,-0.18,-2.02,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,186808,2015-10-30 10:16:47:684,1446171407684.0 \n0.3639,-0.577,11.1366,0.2472,0.2412,9.8006,-0.1833,0.1124,-0.1857,-31.5,2.3,-42.1,1.469218164,-1.41,-1.45,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,186909,2015-10-30 10:16:47:785,1446171407785.0 \n-0.5267,-0.8296,10.4914,0.023,0.0278,9.8066,-0.2541,0.3238,-0.171,-30.9,2,-42.9,1.50534648,-0.03,-0.2,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,187011,2015-10-30 10:16:47:887,1446171407887.0 \n-0.2107,-0.176,9.5924,0.1659,-0.1656,9.8038,-0.2431,-0.2028,-0.0098,-30.3,1.9,-43.1,1.527686694,0.97,-0.97,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,187114,2015-10-30 10:16:47:990,1446171407990.0 \n-0.4262,0.7314,9.1135,0.2606,-0.2028,9.8011,0.0611,-0.1014,0.1344,-30.1,2.2,-43,1.529082958,1.04,-1.31,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,187216,2015-10-30 10:16:48:092,1446171408092.0 \n-0.5578,0.5423,10.6901,0.2678,-0.1101,9.8024,0.0415,0.0208,0.0904,-30.5,2.8,-42.5,1.483704397,0.64,-1.57,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,187318,2015-10-30 10:16:48:194,1446171408194.0 \n-0.4992,0.17,11.5568,0.2177,0.127,9.8034,0.5253,0.1943,0.2663,-30.7,2.9,-42.4,1.453161135,-0.74,-1.27,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,187420,2015-10-30 10:16:48:296,1446171408296.0 \n-1.0989,-1.1576,11.9147,0.1729,0.2104,9.8029,0,0.0733,0.1674,-30.5,2.6,-42.4,1.430122789,-1.53,-1.07,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,187522,2015-10-30 10:16:48:398,1446171408398.0 \n-0.0946,0.0838,8.1415,0.3141,0.2746,9.7978,0.0709,-0.2309,0.1075,-30.3,2.4,-43,1.452113938,-1.87,-1.64,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,187623,2015-10-30 10:16:48:499,1446171408499.0 \n-0.2897,0.6081,8.2827,0.3098,0.1858,9.8,0.1283,-0.066,-0.0049,-30.2,2.4,-43.3,1.472185224,-1.09,-1.81,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,187725,2015-10-30 10:16:48:601,1446171408601.0 \n-0.4764,1.0606,8.7544,0.2404,0.3068,9.7989,0.0574,0.0415,-0.0831,-30.3,2.5,-43.1,1.421047077,-1.79,-1.41,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,187827,2015-10-30 10:16:48:703,1446171408703.0 \n-0.2634,0.0156,11.558,0.3106,0.3896,9.794,0.1894,-0.1038,-0.1271,-30.3,2.2,-43,1.440769298,-2.28,-1.82,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,187931,2015-10-30 10:16:48:807,1446171408807.0 \n0.249,-0.1472,10.6829,0.4263,0.5566,9.7816,0.16,-0.1356,-0.0696,-30.4,1.3,-42.7,1.446528884,-3.25,-2.5,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,188032,2015-10-30 10:16:48:908,1446171408908.0 \n-0.3029,0.3938,8.5964,0.3442,0.3372,9.7948,-0.0086,0.1222,0.0183,-30.6,0.8,-42.7,1.485624259,-1.97,-2.01,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,188133,2015-10-30 10:16:49:009,1446171409009.0 \n0.0084,1.0187,8.0768,0.2637,0.119,9.8024,-0.088,0.0892,0.0073,-30.6,0.6,-42.9,1.519483647,-0.7,-1.54,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,188235,2015-10-30 10:16:49:111,1446171409111.0 \n-0.31,0.7554,8.3306,0.2163,0.1054,9.8037,0.0794,0.0305,0.0635,-30.5,1,-43.3,1.52384697,-0.48,-1.24,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,188337,2015-10-30 10:16:49:213,1446171409213.0 \n-0.0431,-0.0431,11.1199,0.2161,0.165,9.8029,0.1368,-0.0208,0.2285,-30.1,1.5,-43.6,1.476374014,-0.96,-1.26,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,188439,2015-10-30 10:16:49:315,1446171409315.0 \n0.0156,0.1113,9.0453,0.2192,0.4786,9.7925,-0.0757,-0.1075,0.3323,-30,1.6,-43.7,1.436929573,-2.42,-1.41,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,188542,2015-10-30 10:16:49:418,1446171409418.0 \n-0.1712,0.0431,10.1227,0.2887,0.2463,9.7993,-0.2529,-0.0342,0.3348,-30,1.8,-43.9,1.462236847,-1.44,-1.69,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,188643,2015-10-30 10:16:49:519,1446171409519.0 \n-0.0634,0.2538,8.7209,0.4824,0.1424,9.7937,-0.2529,0.0147,-0.1026,-30.4,2.3,-43.6,1.47550135,-0.83,-2.82,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,188746,2015-10-30 10:16:49:622,1446171409622.0 \n-0.5387,0.4549,8.9256,0.3945,0.0847,9.7983,0.0428,0.2578,-0.1845,-30.6,2.9,-43.4,1.454557399,-0.48,-2.73,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,188847,2015-10-30 10:16:49:723,1446171409723.0 \n-0.7961,-0.0275,11.0612,0.3038,0.1791,9.8003,0.1087,-0.0281,-0.0806,-30.6,3.1,-43.4,1.443212758,-1.05,-1.78,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,188949,2015-10-30 10:16:49:825,1446171409825.0 \n-0.4597,0.4274,9.8964,0.3157,0.4347,9.7919,0.3213,-0.0061,-0.0391,-30.3,2.8,-43.5,1.410749634,-2.11,-1.85,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,189052,2015-10-30 10:16:49:928,1446171409928.0 \n-0.6488,-1.1839,12.7563,0.3238,0.1933,9.7994,-0.3519,0.1784,-0.2993,-30.1,2.1,-43.7,1.449670477,-1.84,-2.14,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,189154,2015-10-30 10:16:50:030,1446171410030.0 \n-0.328,0.3603,8.491,0.1871,0.1666,9.8034,-0.2505,0.022,-0.0635,-30,1.5,-43.8,1.465727506,-1.37,-1.17,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,189256,2015-10-30 10:16:50:132,1446171410132.0 \n-0.1963,0.7949,8.2432,0.1711,0.0457,9.8051,-0.1051,0.022,0.0403,-29.8,1.4,-43.9,1.52384697,-0.48,-1.05,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,189357,2015-10-30 10:16:50:233,1446171410233.0 \n-0.0563,0.7302,9.4332,0.1601,0.0577,9.8052,0.0147,0.0134,0.011,-29.5,1.8,-43.9,1.49103478,-0.34,-0.94,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,189460,2015-10-30 10:16:50:336,1446171410336.0 \n-0.6656,0.0168,11.0397,0.1397,0.1197,9.8049,0.27,-0.1222,0.1918,-29.5,2,-43.9,1.492431043,-0.31,-0.66,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,189561,2015-10-30 10:16:50:437,1446171410437.0 \n-0.2394,-0.7183,11.6717,0.1292,0.2566,9.8024,0.1918,0.1148,0.3067,-29.5,2,-43.9,1.459967919,-1.5,-0.76,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,189663,2015-10-30 10:16:50:539,1446171410539.0 \n0.3759,0.7135,8.855,0.2522,0.2385,9.8005,0.2651,-0.2114,0.2871,-29.5,2.1,-43.8,1.47375602,-0.95,-1.15,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,189765,2015-10-30 10:16:50:641,1446171410641.0 \n-0.4214,0.0599,9.2596,0.3691,0.1161,9.799,-0.1038,0.0098,-0.0733,-29.8,2.2,-43.9,1.474803218,-0.93,-2.16,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,189868,2015-10-30 10:16:50:744,1446171410744.0 \n-0.3376,0.9577,7.7512,0.2274,0.1593,9.8027,0.1038,0.1319,-0.0611,-30,2.6,-43.8,1.442863693,-0.93,-1.33,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,189970,2015-10-30 10:16:50:846,1446171410846.0 \n-0.8918,0.6608,9.7312,0.0748,0.2089,9.8041,-0.0049,0.1417,-0.1845,-30,2.4,-43.9,1.472010691,-1.22,-0.44,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,190072,2015-10-30 10:16:50:948,1446171410948.0 \n-0.1137,0.0527,10.3645,0.1155,0.3717,9.7989,0.215,-0.0012,-0.0941,-29.6,2,-43.8,1.446703417,-2.17,-0.68,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,190174,2015-10-30 10:16:51:050,1446171411050.0 \n-1.0295,-0.9637,12.2176,0.0271,0.0881,9.8062,-0.0073,0.1356,-0.0831,-29.5,1.5,-43.9,1.462062314,-1.44,-0.62,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,190276,2015-10-30 10:16:51:152,1446171411152.0 \n-0.3675,0.0527,9.3254,-0.0035,-0.0592,9.8065,-0.1918,-0.0269,-0.1087,-29.3,1.2,-43.9,1.527861227,-0.32,0.06,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,190377,2015-10-30 10:16:51:253,1446171411253.0 \n-0.6967,0.4405,8.9627,-0.0312,-0.1804,9.8049,-0.0819,0.0648,-0.0452,-29.4,1.4,-44.1,1.561022483,0.93,0.05,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,190479,2015-10-30 10:16:51:355,1446171411355.0 \n-0.5818,0.3041,9.7671,-0.0414,-0.1169,9.8059,0.0049,0.066,0.0904,-29.3,1.9,-44.2,1.520181778,0.68,0.24,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,190581,2015-10-30 10:16:51:457,1446171411457.0 \n-0.0982,-0.0431,11.0301,-0.1063,-0.0404,9.806,0.2224,0.0379,0.2407,-29.3,2.1,-44.3,1.509186204,0.24,0.62,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,190684,2015-10-30 10:16:51:560,1446171411560.0 \n-0.1365,-0.9062,11.4646,-0.0134,0.059,9.8065,-0.3396,-0.3152,0.2101,-29.2,2,-44.4,1.479515607,-0.91,0.6,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,190786,2015-10-30 10:16:51:662,1446171411662.0 \n-0.0706,0.4896,9.2165,0.1196,0.0437,9.8058,0.088,-0.2932,0.0611,-29.3,2.2,-44.4,1.493827307,-0.26,-0.7,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,190887,2015-10-30 10:16:51:763,1446171411763.0 \n-0.3627,0.3148,8.6084,0.2097,-0.019,9.8044,-0.0342,-0.0183,-0.0696,-29.7,2.6,-44.1,1.470788961,0.11,-1.23,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,190991,2015-10-30 10:16:51:867,1446171411867.0 \n-0.504,0.8739,8.2672,0.1802,0.0093,9.805,0.0941,0.0428,-0.1429,-30.1,3,-44.1,1.470963494,0.11,-1.16,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,191091,2015-10-30 10:16:51:967,1446171411967.0 \n-0.923,0.1173,11.9363,0.1019,0.2157,9.8038,0.1527,-0.0195,-0.2529,-30.4,2.5,-44.2,1.437104106,-1.26,-0.6,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,191210,2015-10-30 10:16:52:086,1446171412086.0 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\n-0.5423,0.5974,9.0489,-0.0083,0.1878,9.8048,0.0782,0,0.0293,-30,-0.2,-44.1,1.542871059,-1.09,0.06,36.814705,-119.74874,277.07,336.6579477,4.27,19.35484,89.44,17 / 17,191704,2015-10-30 10:16:52:580,1446171412580.0 \n-1.2689,0.4118,10.161,-0.0653,0.3486,9.8002,0.2749,-0.0012,0.3543,-30,-0.1,-44.4,1.529955622,-1.62,0.34,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,191806,2015-10-30 10:16:52:682,1446171412682.0 \n0.5567,-0.3508,12.8437,0.1002,0.1558,9.8049,-0.3189,0.0684,0.2541,-30.1,-0.1,-44.4,1.52681403,-1.7,-0.27,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,191907,2015-10-30 10:16:52:783,1446171412783.0 \n-0.0874,0.4633,9.1554,0.2437,0.0088,9.8036,-0.259,-0.0244,-0.0147,-30.5,0.6,-43.7,1.524545102,-0.44,-1.27,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,192009,2015-10-30 10:16:52:885,1446171412885.0 \n0.182,0.4094,8.2109,0.2476,-0.086,9.8031,-0.0794,-0.0819,-0.0464,-30.9,1.4,-43.4,1.550201442,0.5,-1.45,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,192112,2015-10-30 10:16:52:988,1446171412988.0 \n-0.5854,1.2294,8.2899,0.2805,0.0125,9.8026,0.0525,-0.1002,-0.1442,-31.4,2.4,-43.1,1.504997414,0.04,-1.48,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,192213,2015-10-30 10:16:53:089,1446171413089.0 \n-1.1253,-0.0994,12.7419,0.3207,0.1508,9.8002,0.1747,-0.0696,-0.2346,-31.8,2.3,-43.1,1.483529864,-0.88,-1.87,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,192316,2015-10-30 10:16:53:192,1446171413192.0 \n1.3958,-0.6907,11.5628,0.3664,0.2714,9.796,0.1723,-0.0831,-0.0831,-31.9,1.6,-42.9,1.456651794,-1.95,-1.99,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,192418,2015-10-30 10:16:53:294,1446171413294.0 \n0.5088,0.2969,6.8139,0.206,0.3767,9.7972,0.4362,0.0977,-0.0012,-32,0.6,-42.8,1.484926128,-2.2,-1.2,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,192519,2015-10-30 10:16:53:395,1446171413395.0 \n0.1425,0.3172,9.2955,0.235,0.2849,9.7997,0.0293,0.0965,-0.0672,-32.1,0.1,-43,1.526115898,-1.8,-1.53,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,192621,2015-10-30 10:16:53:497,1446171413497.0 \n-0.741,0.486,9.0441,0.2554,0.2962,9.7988,-0.0244,-0.0721,-0.1173,-32,0,-43,1.532573616,-1.55,-1.34,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,192723,2015-10-30 10:16:53:599,1446171413599.0 \n0.0407,0.8715,9.1207,0.1472,0.4132,9.7968,0.1735,0.2175,0.1197,-32,-0.5,-43.1,1.51250233,-2.42,-0.86,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,192825,2015-10-30 10:16:53:701,1446171413701.0 \n-0.6249,0.7961,11.3353,0.0762,0.6058,9.7876,0.2431,0.2712,0.2443,-31.8,-0.6,-43.1,1.526639497,-3.18,-0.45,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,192933,2015-10-30 10:16:53:809,1446171413809.0 \n-0.0599,0.2574,9.8928,0.0778,0.3438,9.8003,-0.2028,-0.3311,0.204,-31.5,-0.7,-43.6,1.54356919,-2.39,-0.2,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,193030,2015-10-30 10:16:53:906,1446171413906.0 \n-0.1652,0.3986,9.3913,0.3775,0.1612,9.7981,-0.1845,-0.325,0.0684,-31.7,0.1,-43.3,1.546885316,-0.94,-2.21,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,193132,2015-10-30 10:16:54:008,1446171414008.0 \n-0.6584,0.8068,8.8298,0.3573,-0.0057,9.8001,-0.0415,-0.0782,-0.1295,-32,0.9,-42.9,1.538856801,0.03,-2.09,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,193234,2015-10-30 10:16:54:110,1446171414110.0 \n-0.2059,1.0271,9.645,0.3549,0.0591,9.8,0.1185,0.0757,-0.0599,-32.6,1.9,-42.5,1.499063295,-0.35,-2.07,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,193336,2015-10-30 10:16:54:212,1446171414212.0 \n-0.2239,0.401,11.5365,0.3552,0.2816,9.7962,0.1759,-0.1173,-0.1747,-32.8,2,-42.6,1.474977751,-1.34,-1.91,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,193438,2015-10-30 10:16:54:314,1446171414314.0 \n0.5231,-0.3615,10.9403,0.3414,0.4385,9.7909,0.0049,-0.0464,-0.2639,-32.9,1.2,-42.7,1.47672308,-2.56,-2,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,193539,2015-10-30 10:16:54:415,1446171414415.0 \n0.1808,-0.2239,9.6139,0.2371,0.3607,9.7971,0.0024,-0.044,-0.2089,-32.7,0.5,-42.8,1.489289451,-2.11,-1.39,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,193642,2015-10-30 10:16:54:518,1446171414518.0 \n-0.1233,0.4657,8.3079,0.1948,0.0773,9.8044,-0.4728,0.1051,-0.27,-32.6,-0.3,-42.6,1.552295837,-0.78,-1.2,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,193743,2015-10-30 10:16:54:619,1446171414619.0 \n-0.9649,0.498,9.1303,0.2213,0.0497,9.804,0.0806,-0.0232,0.0269,-32.4,-0.2,-42.8,1.567131135,-0.15,-1.3,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,193846,2015-10-30 10:16:54:722,1446171414722.0 \n-0.2059,0.2969,10.2867,0.222,0.2555,9.8008,0.2456,0.0134,0.2627,-32.4,-0.2,-42.9,1.544267322,-1.08,-1.32,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,193947,2015-10-30 10:16:54:823,1446171414823.0 \n0.006,0.8152,9.6726,0.1758,0.5695,9.7885,0.463,0.0794,0.2871,-32.4,-0.2,-42.8,1.499935959,-2.89,-1.23,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,194050,2015-10-30 10:16:54:926,1446171414926.0 \n-0.7817,-0.4286,10.4196,0.2289,0.2574,9.8006,-0.2859,0.0806,0.2053,-32.5,-0.4,-42.6,1.533795347,-1.5,-1.34,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,194151,2015-10-30 10:16:55:027,1446171415027.0 \n-0.0994,0.3316,9.2572,0.4362,0.1849,9.7952,-0.248,-0.0562,0.033,-32.9,0.2,-42.4,1.544441855,-1.08,-2.55,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,194254,2015-10-30 10:16:55:130,1446171415130.0 \n-0.3711,0.6728,8.8705,0.4473,0.0751,9.7962,0.0232,0.0379,-0.1454,-33.2,0.8,-42.1,1.527512161,-0.45,-2.64,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,194356,2015-10-30 10:16:55:232,1446171415232.0 \n-0.0036,0.7614,8.989,0.4166,0.1845,9.7961,0.1124,0.0049,-0.099,-33.6,1.5,-41.9,1.483529864,-1.08,-2.44,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,194458,2015-10-30 10:16:55:334,1446171415334.0 \n-0.3244,-0.2119,11.8764,0.508,0.3062,9.7887,0.1393,-0.1527,-0.1747,-33.7,1.3,-41.7,1.50237942,-1.57,-2.66,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,194560,2015-10-30 10:16:55:436,1446171415436.0 \n-0.2107,-1.1648,12.821,0.5169,0.1661,9.7916,-0.4643,0.4349,-0.3543,-33.9,0.5,-41.7,1.495049037,-1.8,-3.52,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,194663,2015-10-30 10:16:55:539,1446171415539.0 \n0.2179,0.2143,7.8254,0.359,0.2152,9.7977,0.2737,0.0501,-0.0538,-34,0.2,-42,1.548281579,-0.97,-2.17,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,194763,2015-10-30 10:16:55:639,1446171415639.0 \n0.1915,0.6309,7.9356,0.3314,0.1134,9.8004,0.0012,0.0501,-0.0794,-33.8,0,-42.4,1.555437429,-0.66,-1.94,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,194866,2015-10-30 10:16:55:742,1446171415742.0 \n-0.0096,1.0295,7.9428,0.1837,0.1344,9.804,0.1038,0.121,0.1112,-33.3,-0.1,-42.9,1.552295837,-0.79,-1.07,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,194967,2015-10-30 10:16:55:843,1446171415843.0 \n-0.3268,0.1556,10.7715,0.1355,0.1055,9.8051,0.1637,-0.066,0.2957,-33,-0.2,-42.8,1.556833693,-0.59,-0.79,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,195070,2015-10-30 10:16:55:946,1446171415946.0 \n0.5171,-0.334,10.9595,0.1881,0.3305,9.7993,0.3152,0.0672,0.3702,-32.7,-0.2,-42.9,1.5250687,-1.93,-1.1,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,195173,2015-10-30 10:16:56:049,1446171416049.0 \n-0.5195,-0.0563,9.7887,0.2652,0.1602,9.8018,0.2187,0.0709,0.4924,-32.7,0.1,-42.8,1.551946771,-0.78,-1.75,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,195273,2015-10-30 10:16:56:149,1446171416149.0 \n-0.5279,0.1832,8.9316,0.4283,0.1927,9.7954,-0.2053,0.0721,0.0122,-33,0.8,-42.7,1.510582468,-1.13,-2.5,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,195375,2015-10-30 10:16:56:251,1446171416251.0 \n-0.6225,0.559,8.6443,0.3515,0.0653,9.8001,-0.0611,0.0574,0.0049,-33.3,1.4,-42.6,1.528559359,-0.42,-2.23,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,195477,2015-10-30 10:16:56:353,1446171416353.0 \n0.0515,0.9888,9.1363,0.3088,0.1278,9.801,0.0941,-0.0147,-0.0354,-33.2,1.8,-42.7,1.489638517,-0.75,-1.8,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,195580,2015-10-30 10:16:56:456,1446171416456.0 \n-0.5698,-0.255,12.5097,0.327,0.2139,9.7989,0.2236,0.1429,-0.1808,-33.2,1.8,-42.9,1.482482667,-1.05,-1.67,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,195682,2015-10-30 10:16:56:558,1446171416558.0 \n-0.656,-0.8966,12.1506,0.1941,0.0836,9.8044,-0.2236,-0.0269,-0.1869,-33.1,1.3,-42.8,1.510407935,-1.22,-1.4,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,195784,2015-10-30 10:16:56:660,1446171416660.0 \n0.3687,0.328,7.7644,0.1078,0.0871,9.8057,0.121,-0.0232,-0.0024,-33,1.1,-43,1.537111472,-0.12,-0.64,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,195885,2015-10-30 10:16:56:761,1446171416761.0 \n-0.3268,0.4633,8.1989,0.1304,-0.1296,9.8049,-0.1393,0.0244,-0.1075,-32.7,0.9,-43.3,1.552644903,0.55,-0.72,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,195988,2015-10-30 10:16:56:864,1446171416864.0 \n-0.3065,0.559,9.3494,0.1495,-0.1826,9.8038,0.0892,0.0024,0.1332,-32.5,1.4,-43.4,1.564687674,1.07,-0.87,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,196090,2015-10-30 10:16:56:966,1446171416966.0 \n-0.5878,-0.1748,11.6346,0.1051,-0.0912,9.8057,0.0305,0.0464,0.1271,-32.5,1.7,-42.9,1.524021503,0.7,-0.7,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,196191,2015-10-30 10:16:57:067,1446171417067.0 \n0.0192,-1.2438,10.7751,0.0597,0.249,9.8033,-0.0244,-0.1014,0.2468,-32.6,1.9,-43,1.476548547,-1.46,-0.35,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,196293,2015-10-30 10:16:57:169,1446171417169.0 \n-0.1724,0.1999,8.1798,0.1314,0.1265,9.805,0.2162,-0.2541,0.2981,-32.7,2,-42.9,1.502728486,-0.27,-0.95,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,196395,2015-10-30 10:16:57:271,1446171417271.0 \n-0.1197,0.2789,8.9651,0.302,0.0662,9.8018,-0.1857,-0.0269,-0.0171,-32.9,2.3,-43,1.498365163,-0.39,-1.76,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,196497,2015-10-30 10:16:57:373,1446171417373.0 \n-0.7195,0.3879,9.1638,0.3115,0.079,9.8014,0.0696,0.0721,-0.0318,-33.1,2.6,-42.8,1.470963494,-0.21,-1.92,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,196599,2015-10-30 10:16:57:475,1446171417475.0 \n0.0946,1.0786,9.4547,0.3657,0.2826,9.7958,0.1857,-0.1429,-0.1552,-33.4,2.4,-42.4,1.467821901,-1.65,-2.14,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,196701,2015-10-30 10:16:57:577,1446171417577.0 \n-0.4345,0.3376,11.4778,0.4602,0.5092,9.7826,0.2285,-0.0794,-0.2957,-33.6,2,-42.2,1.451241273,-2.42,-2.73,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,196804,2015-10-30 10:16:57:680,1446171417680.0 \n-0.8811,-0.571,11.3258,0.2688,0.3689,9.796,-0.4191,0.4276,-0.3738,-33.5,0.7,-42.2,1.488940385,-2.16,-1.57,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,196906,2015-10-30 10:16:57:782,1446171417782.0 \n-0.0766,0.2191,9.3841,0.129,0.2678,9.8021,-0.38,-0.1002,-0.11,-33.1,0,-42.5,1.535017077,-1.57,-0.75,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,197008,2015-10-30 10:16:57:884,1446171417884.0 \n-0.2837,0.8583,8.3905,0.1775,0.0624,9.8048,-0.0696,0.0354,0.0183,-32.9,0,-42.9,1.562244213,-0.36,-1.04,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,197110,2015-10-30 10:16:57:986,1446171417986.0 \n-0.2286,0.6249,9.7504,0.216,0.0399,9.8042,0.0293,-0.121,0.0916,-32.9,0.5,-42.7,1.53396988,-0.23,-1.26,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,197211,2015-10-30 10:16:58:087,1446171418087.0 \n-0.4417,-0.1437,11.9554,0.1904,0.1136,9.8041,0.226,0.0538,0.2663,-33,0.9,-42.4,1.533097215,-0.28,-1.19,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,197313,2015-10-30 10:16:58:189,1446171418189.0 \n0.3124,-1.3886,13.0568,0.2566,0.2735,9.7995,-0.6072,-0.4264,-0.0709,-33,1.1,-42.4,1.502030354,-1.6,-1.5,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,197415,2015-10-30 10:16:58:291,1446171418291.0 \n-0.2251,0.7434,7.4196,0.3209,0.082,9.8011,0.1808,0.248,0.3115,-33.2,1.4,-42.5,1.531875484,-0.33,-1.32,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,197518,2015-10-30 10:16:58:394,1446171418394.0 \n-0.3256,0.2071,9.7815,0.4426,-0.0416,9.7966,-0.1234,-0.077,0.0208,-33.4,2.1,-42.6,1.508837138,0.09,-2.48,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,197619,2015-10-30 10:16:58:495,1446171418495.0 \n-0.6476,0.6536,7.9631,0.3941,0.0926,9.7983,0.1796,0.0147,-0.033,-33.8,2.6,-42.3,1.471487092,-0.27,-2.43,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,197721,2015-10-30 10:16:58:597,1446171418597.0 \n-0.4597,0.4142,10.3262,0.3998,0.2175,9.7961,0.0977,0.0122,-0.1051,-33.9,2.6,-42.3,1.448623279,-1.27,-2.34,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,197824,2015-10-30 10:16:58:700,1446171418700.0 \n0.0503,-0.1903,10.5357,0.5837,0.4,9.7811,0.3103,-0.1442,-0.1393,-34.1,2,-42.1,1.450717674,-2.34,-3.42,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,197926,2015-10-30 10:16:58:802,1446171418802.0 \n0.1676,0.0227,8.1654,0.3587,0.253,9.7968,0.1955,0.1613,0.0403,-34,0.9,-42,1.505695546,-1.48,-2.1,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,198028,2015-10-30 10:16:58:904,1446171418904.0 \n0.6321,0.2083,8.6706,0.4101,0.1719,9.7966,-0.2236,-0.1112,0.0476,-34.1,0.6,-41.7,1.516167521,-1,-2.4,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,198130,2015-10-30 10:16:59:006,1446171419006.0 \n0.3089,0.8607,8.2744,0.4956,-0.0531,9.794,-0.0464,-0.0147,-0.0281,-34,1.1,-41.8,1.546885316,0.31,-2.9,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,198232,2015-10-30 10:16:59:108,1446171419108.0 \n0.176,1.0355,9.1686,0.4456,-0.1316,9.7956,-0.1258,0.121,-0.0794,-34.1,1.3,-41.9,1.552295837,0.54,-2.87,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,198335,2015-10-30 10:16:59:211,1446171419211.0 \n0.0778,0.5866,12.3672,0.4406,-0.1011,9.7962,0.3873,0.0977,0.3067,-34.1,1.8,-42.1,1.522450707,0.59,-2.57,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,198437,2015-10-30 10:16:59:313,1446171419313.0 \n0.079,-1.4114,12.5169,0.5608,0.0188,9.7906,-0.1833,-0.358,-0.0354,-34,1.7,-42,1.493303708,-0.66,-2.45,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,198538,2015-10-30 10:16:59:414,1446171419414.0 \n-0.1568,0.2801,9.5086,0.5868,-0.0359,9.789,0.16,-0.2431,0.1417,-34,1.8,-42.1,1.518960048,0.47,-3.2,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,198641,2015-10-30 10:16:59:517,1446171419517.0 \n-0.3316,0.0096,9.2009,0.6042,-0.0651,9.7878,0.1173,-0.0049,0.0171,-34.3,2.1,-41.9,1.518960048,0.49,-3.59,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,198742,2015-10-30 10:16:59:618,1446171419618.0 \n-0.0575,0.8116,7.926,0.4705,0.1539,9.7941,0.2993,0.2285,0.0489,-34.4,2.4,-41.9,1.487020523,-0.9,-2.75,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,198843,2015-10-30 10:16:59:719,1446171419719.0 \n-0.3891,0.0299,9.5792,0.3586,0.3046,9.7954,0.1833,0.0391,-0.1466,-34.3,2.1,-41.9,1.475326817,-1.44,-2.36,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,198946,2015-10-30 10:16:59:822,1446171419822.0 \n1.919,-0.2705,9.979,0.4443,0.6167,9.7772,-0.1503,-0.2199,-0.2382,-34,1.1,-42.1,1.457698991,-3.55,-2.2,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,199047,2015-10-30 10:16:59:923,1446171419923.0 \n0.3567,0.6081,7.6483,0.2457,0.3987,9.7955,-0.1332,-0.2456,-0.055,-33.7,0.3,-42.3,1.51791285,-2.33,-1.44,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,199150,2015-10-30 10:17:00:026,1446171420026.0 \n0.8128,0.8152,8.5796,0.4089,0.0998,9.7976,-0.4423,-0.0929,-0.0464,-33.7,0,-42.5,1.557182759,-0.58,-2.39,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,199251,2015-10-30 10:17:00:127,1446171420127.0 \n-0.3136,0.4082,9.2703,0.5378,-0.0582,9.7917,-0.0208,-0.0464,0.0415,-33.8,0.3,-42.4,1.578999374,0.34,-3.14,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,199357,2015-10-30 10:17:00:233,1446171420233.0 \n0.3352,0.6333,9.809,0.5605,-0.0125,9.7906,0.0586,0.0977,0.077,-34.1,0.9,-42,1.540776664,0.07,-3.47,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,199456,2015-10-30 10:17:00:332,1446171420332.0 \n0.5124,0.838,10.6362,0.4623,0.1073,9.7952,0.1625,0.1271,0.2382,-34.4,1.5,-41.9,1.493478241,-0.63,-2.7,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,199557,2015-10-30 10:17:00:433,1446171420433.0 \n0.5076,-0.5411,11.6227,0.5336,0.2223,9.7896,-0.336,-0.1808,0.0024,-34.3,1.4,-41.8,1.507964474,-1.3,-3.12,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,199660,2015-10-30 10:17:00:536,1446171420536.0 \n0.2394,0.9768,7.8302,0.6535,0.1751,9.7833,-0.1319,-0.1491,-0.0086,-34.4,1.6,-42.1,1.481610002,-1.05,-3.48,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,199762,2015-10-30 10:17:00:638,1446171420638.0 \n-0.4932,0.1137,9.0333,0.6286,-0.0469,9.7864,-0.2566,-0.0049,-0.0965,-34.6,2,-41.8,1.514596725,0.25,-3.82,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,199863,2015-10-30 10:17:00:739,1446171420739.0 \n-0.1329,0.7949,8.0086,0.5376,0.0349,9.7918,0.1442,0.0269,0.0098,-34.8,2.4,-41.7,1.510058869,0.02,-3.19,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,199966,2015-10-30 10:17:00:842,1446171420842.0 \n-0.2921,-0.2526,11.8441,0.5832,0.1588,9.788,0.1503,-0.1161,-0.1576,-34.6,2.5,-41.7,1.463982177,-0.64,-3.24,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,200067,2015-10-30 10:17:00:943,1446171420943.0 \n1.0702,-0.7913,11.2767,0.6327,0.344,9.7802,-0.5486,-0.0073,-0.5009,-34.7,1.8,-42,1.461015117,-2.01,-3.7,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,200170,2015-10-30 10:17:01:046,1446171421046.0 \n-0.0299,0.2993,7.6674,0.4101,0.0658,9.7979,0.1087,0.303,-0.1087,-34.6,1.4,-41.9,1.531875484,-0.38,-2.4,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,200272,2015-10-30 10:17:01:148,1446171421148.0 \n0.4166,0.3208,8.4276,0.5124,-0.0963,9.7928,-0.1442,0.0281,-0.0501,-34.4,0.8,-42.3,1.552819435,0.56,-3,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,200374,2015-10-30 10:17:01:250,1446171421250.0 \n-0.7554,-0.0072,9.657,0.4729,-0.216,9.7929,0.1466,0.0574,0.193,-34.2,0.8,-42.1,1.566956602,1.15,-2.95,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,200476,2015-10-30 10:17:01:352,1446171421352.0 \n-0.2227,0.1305,10.0185,0.407,-0.186,9.7964,-0.0586,0.0513,0.1991,-34.2,1.2,-42.2,1.565385806,1.09,-2.38,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,200577,2015-10-30 10:17:01:453,1446171421453.0 \n0.1425,-0.0491,11.7651,0.4043,-0.1146,9.7976,0.1943,-0.0965,0.485,-34.2,1.6,-41.9,1.530304688,0.92,-2.22,36.814713,-119.74859,278.16,336.6579477,4.28,19.35484,100.93,17 / 17,200680,2015-10-30 10:17:01:556,1446171421556.0 \n0.2251,-0.9194,11.9638,0.4403,-0.0668,9.7965,-0.3348,-0.2272,0.2187,-34,2.2,-42.1,1.517738318,0.39,-2.57,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,200782,2015-10-30 10:17:01:658,1446171421658.0 \n0.6393,0.6608,8.1475,0.7208,-0.0955,9.7797,0.2798,-0.2944,0.54,-34.2,3.3,-41.8,1.489638517,0.6,-3.75,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,200886,2015-10-30 10:17:01:762,1446171421762.0 \n0.1185,0.2023,9.0046,0.7075,-0.2416,9.7781,-0.0892,0.0525,0.0147,-34.5,4.1,-41.9,1.473057889,1.26,-4.24,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,200985,2015-10-30 10:17:01:861,1446171421861.0 \n-0.3124,0.5914,8.9399,0.6392,-0.1741,9.7842,0.0354,-0.0098,-0.0293,-35,4.9,-41.7,1.440594765,1.02,-3.74,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,201088,2015-10-30 10:17:01:964,1446171421964.0 \n-0.1604,-0.2274,11.9794,0.6046,-0.0731,9.7877,0.1967,0.0501,-0.1405,-35,5.1,-41.6,1.427330262,0.43,-3.53,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,201190,2015-10-30 10:17:02:066,1446171422066.0 \n1.4222,-0.8248,10.6614,0.6047,0.1273,9.7872,0.215,-0.0367,-0.1491,-34.8,4.6,-41.8,1.400277659,-0.74,-3.54,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,201298,2015-10-30 10:17:02:174,1446171422174.0 \n0.0946,0.1903,8.7317,0.4136,0.0215,9.7979,0.4985,0.1344,0.1136,-34.7,4.2,-41.7,1.465203907,0.66,-2.68,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,201393,2015-10-30 10:17:02:269,1446171422269.0 \n0.2131,0.2993,9.4379,0.4972,-0.0524,9.7939,-0.0293,0.0269,-0.0965,-34.6,3.5,-42.1,1.456477261,0.31,-2.91,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,201496,2015-10-30 10:17:02:372,1446171422372.0 \n-0.6512,0.5842,9.0692,0.3984,-0.0555,9.7984,-0.0354,0.1405,-0.1417,-34.5,3.3,-42.1,1.487020523,0.4,-2.59,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,201598,2015-10-30 10:17:02:474,1446171422474.0 \n-0.644,0.1413,10.4232,0.28,0.0647,9.8024,-0.0428,0.1148,0.0098,-34.3,2.9,-42.7,1.470963494,-0.34,-1.92,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,201700,2015-10-30 10:17:02:576,1446171422576.0 \n-0.6464,-0.1676,12.0919,0.2405,0.2284,9.801,0.347,0.1173,0.4789,-34,2.7,-42.8,1.458920722,-0.91,-1.44,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,201802,2015-10-30 10:17:02:678,1446171422678.0 \n-1.0151,-0.9529,12.4822,0.3667,0.1733,9.7983,-0.3641,-0.485,0.2187,-33.6,2.7,-43.1,1.454557399,-1.01,-2.14,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,201903,2015-10-30 10:17:02:779,1446171422779.0 \n-0.735,-0.3256,10.1239,0.4601,0.1332,9.7949,-0.2859,-0.3348,-0.0415,-33.5,3.2,-42.9,1.454906464,-0.78,-2.69,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,202011,2015-10-30 10:17:02:887,1446171422887.0 \n-0.0419,1.0475,8.2684,0.4654,-0.0351,9.7955,0.066,-0.0208,0.0953,-33.7,4.1,-42.3,1.45106674,0.2,-2.72,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,202108,2015-10-30 10:17:02:984,1446171422984.0 \n0.2861,1.3946,8.6491,0.5092,0.052,9.7933,0.1381,-0.1051,0.0171,-34,4.7,-42.2,1.407608042,-0.3,-2.98,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,202210,2015-10-30 10:17:03:086,1446171423086.0 \n-0.2885,0.3759,10.4722,0.6271,0.0184,9.7866,-0.0195,-0.2126,-0.3396,-34.1,4.7,-42.2,1.411622299,-0.11,-3.11,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,202318,2015-10-30 10:17:03:194,1446171423194.0 \n0.2358,-0.7578,11.4132,0.639,0.0514,9.7857,-0.3238,-0.0562,-0.4154,-34.5,4,-42.1,1.435882376,-0.3,-3.74,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,202414,2015-10-30 10:17:03:290,1446171423290.0 \n0.1712,-0.0922,8.5186,0.5765,-0.1895,9.7879,-0.0098,-0.1368,-0.1246,-34.8,3.7,-42,1.481086403,1.4,-3.21,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,202516,2015-10-30 10:17:03:392,1446171423392.0 \n0.3543,0.4561,7.349,0.6354,-0.3043,9.7813,-0.1258,-0.0318,-0.0721,-35,3.3,-41.7,1.520356311,1.78,-3.72,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,202617,2015-10-30 10:17:03:493,1446171423493.0 \n-0.5997,0.1963,9.3996,0.6093,-0.3501,9.7814,0.0379,-0.0354,0,-35.1,3.4,-41.9,1.52681403,2.05,-3.56,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,202719,2015-10-30 10:17:03:595,1446171423595.0 \n-0.2502,0.0096,10.4794,0.4511,-0.2307,9.7936,0.1234,0.182,0.1796,-35.1,3.3,-41.8,1.514247659,1.5,-3.01,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,202822,2015-10-30 10:17:03:698,1446171423698.0 \n0.2358,-0.1209,11.2216,0.3947,-0.006,9.7987,0.3213,-0.0257,0.3323,-34.9,3.3,-42,1.493652774,0.58,-2.49,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,202924,2015-10-30 10:17:03:800,1446171423800.0 \n-0.5004,-0.8835,11.3282,0.55,-0.2039,9.7891,-0.1857,0.0293,0.1735,-34.7,3.4,-42,1.506917276,1.19,-3.22,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,203027,2015-10-30 10:17:03:903,1446171423903.0 \n-0.1209,-0.1341,9.3661,0.5884,-0.1182,9.7883,-0.215,0.1319,-0.099,-34.8,3.8,-41.5,1.463982177,0.69,-3.44,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,203130,2015-10-30 10:17:04:006,1446171424006.0 \n-0.3998,0.504,8.1439,0.4695,-0.0975,9.7949,0.0415,0.1881,-0.0745,-34.9,4.1,-41.1,1.461887781,0.55,-3.01,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,203229,2015-10-30 10:17:04:105,1446171424105.0 \n-0.5567,0.5183,9.6031,0.3686,-0.1196,9.799,-0.1442,0.0709,-0.1466,-34.8,4.2,-41.2,1.466949236,0.7,-2.15,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,203331,2015-10-30 10:17:04:207,1446171424207.0 \n-0.4262,0.0168,12.2104,0.5439,-0.0339,9.7915,0.1258,-0.0513,-0.1637,-34.9,4,-41.3,1.461364183,0.54,-3.08,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,203441,2015-10-30 10:17:04:317,1446171424317.0 \n-0.4944,-1.6161,12.797,0.5824,-0.3,9.7847,-0.3286,0.3079,-0.1552,-35.2,3.6,-41.2,1.488416786,1.75,-3.41,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,203536,2015-10-30 10:17:04:412,1446171424412.0 \n0.3531,-0.0108,9.2548,0.5189,-0.2765,9.789,0.1051,-0.0538,0.0367,-35.3,3.5,-41.2,1.493827307,1.97,-3.03,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,203638,2015-10-30 10:17:04:514,1446171424514.0 \n0.6213,-0.0108,9.2404,0.5409,-0.2787,9.7878,-0.1552,-0.1087,-0.1014,-35.5,3.4,-41.2,1.516342054,1.63,-3.16,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,203739,2015-10-30 10:17:04:615,1446171424615.0 \n0.0395,0.419,8.6419,0.5485,-0.3765,9.7841,-0.0403,0.0024,0.0232,-35.8,3.6,-41.2,1.500808624,2.18,-3.19,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,203841,2015-10-30 10:17:04:717,1446171424717.0 \n-0.3196,-0.1149,10.3046,0.5023,-0.3468,9.7876,0.0599,0.0379,0.1649,-35.8,3.7,-41.1,1.502204887,2.24,-2.94,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,203943,2015-10-30 10:17:04:819,1446171424819.0 \n1.3455,-0.996,10.5489,0.5531,-0.2047,9.7889,0.0281,-0.033,0.3409,-35.9,3.9,-41.3,1.478817475,1.2,-3.23,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,204046,2015-10-30 10:17:04:922,1446171424922.0 \n0.4717,0.3795,8.1618,0.7541,-0.2591,9.7742,0.3958,-0.1417,0.3861,-36.3,4.5,-40.8,1.453859267,1.51,-4.41,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,204148,2015-10-30 10:17:05:024,1446171425024.0 \n-0.0012,-0.1688,9.1243,0.7535,-0.2721,9.7739,-0.1735,0.1258,0.0122,-36.6,4.9,-40.5,1.458571656,1.59,-4.41,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,204249,2015-10-30 10:17:05:125,1446171425125.0 \n0.1281,0.911,7.2724,0.6145,-0.2405,9.7844,0.1906,0.1698,0.033,-36.7,5.4,-39.9,1.456128195,1.41,-3.59,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,204352,2015-10-30 10:17:05:228,1446171425228.0 \n0.1832,0.6057,9.2979,0.5783,-0.1354,9.7886,0.0183,-0.011,-0.2053,-36.5,5.3,-40.1,1.439896633,0.79,-3.38,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,204453,2015-10-30 10:17:05:329,1446171425329.0 \n-0.5183,-0.1341,11.5065,0.642,-0.0599,9.7854,0.1332,-0.0269,-0.2162,-36.5,5.1,-40.2,1.435882376,0.66,-3.84,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,204555,2015-10-30 10:17:05:431,1446171425431.0 \n-0.68,-1.4796,14.2575,0.5102,-0.3766,9.7861,-0.6793,0.3213,-0.4081,-36.6,4.7,-40.6,1.463284045,1.69,-3.39,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,204657,2015-10-30 10:17:05:533,1446171425533.0 \n-0.0718,-0.4932,9.6642,0.3191,-0.2357,9.7986,-0.2468,-0.0574,-0.1442,-36.3,4.5,-41,1.456302728,1.38,-1.87,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,204760,2015-10-30 10:17:05:636,1446171425636.0 \n-0.4238,0.0575,8.4192,0.2374,-0.3223,9.7985,0.0513,-0.0244,0.0061,-35.9,4.4,-41.6,1.494350906,1.77,-1.48,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,204862,2015-10-30 10:17:05:738,1446171425738.0 \n-0.334,0.4154,8.9136,0.2461,-0.2677,9.7999,-0.0574,-0.0391,0.1906,-35.4,4.5,-42.2,1.456651794,1.49,-1.45,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,204968,2015-10-30 10:17:05:844,1446171425844.0 \n-0.5112,-0.4118,13.0544,0.392,-0.154,9.7976,0.2346,-0.2285,0.2981,-35.3,4.7,-42.3,1.457524458,1.56,-1.86,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,205066,2015-10-30 10:17:05:942,1446171425942.0 \n0.3855,-1.4605,13.8349,0.548,-0.0068,9.7913,-0.5253,-0.6219,-0.0538,-35.4,4.9,-42.5,1.419476281,0.04,-3.2,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,205168,2015-10-30 10:17:06:044,1446171426044.0 \n-0.0383,0.668,6.8965,0.5816,0.0018,9.7894,-0.0892,-0.0806,0.0293,-35.7,5.3,-42.4,1.422094275,-0.01,-3.4,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,205269,2015-10-30 10:17:06:145,1446171426145.0 \n0.0575,0.5171,8.5054,0.6052,-0.2027,9.7859,-0.2297,0.0281,0.0244,-35.9,5.5,-42.2,1.413018562,0.89,-3.42,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,205372,2015-10-30 10:17:06:248,1446171426248.0 \n0.3328,0.8416,8.3222,0.6479,-0.0916,9.7848,0.2016,0.0208,-0.044,-36,6,-41.8,1.403768317,0.54,-3.79,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,205473,2015-10-30 10:17:06:349,1446171426349.0 \n-0.3304,-0.1425,11.394,0.6869,0.0491,9.7824,0.2639,-0.11,-0.2663,-36.1,5.8,-41.7,1.391551013,-0.01,-3.73,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,205575,2015-10-30 10:17:06:451,1446171426451.0 \n0.5674,-0.4836,10.3992,0.642,0.222,9.7831,0.1124,0.0159,-0.325,-36.2,4.7,-41.6,1.387711288,-1.43,-3.98,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,205677,2015-10-30 10:17:06:553,1446171426553.0 \n-0.1209,-0.2227,10.7045,0.4804,0.0768,9.7946,0.193,0.1283,-0.0599,-36.1,3.8,-41.8,1.449146878,-0.16,-3.04,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,205779,2015-10-30 10:17:06:655,1446171426655.0 \n-0.1975,0.0527,8.254,0.4734,-0.0212,9.7952,0.0049,0.0244,-0.022,-35.8,2.8,-42.2,1.485449726,0.12,-2.77,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,205886,2015-10-30 10:17:06:762,1446171426762.0 \n-0.2729,0.7733,8.8143,0.4691,-0.0831,9.7951,-0.1087,0.0159,-0.0342,-35.5,2.6,-42.4,1.491209313,0.49,-2.74,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,205983,2015-10-30 10:17:06:859,1446171426859.0 \n-0.2921,0.5339,10.319,0.4537,-0.0321,9.7961,0.0049,0.1491,0.1344,-35.7,2.6,-42.5,1.48806772,0.26,-2.93,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,206086,2015-10-30 10:17:06:962,1446171426962.0 \n0.322,1.087,9.4763,0.3973,0.2794,9.7946,0.325,0.0452,0.4325,-35.8,2.7,-42.7,1.44687795,-1.63,-2.32,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,206188,2015-10-30 10:17:07:064,1446171427064.0 \n-0.9577,-1.1732,11.5939,0.5356,0.0249,9.792,-0.6548,-0.4019,-0.1454,-36,2.7,-42.9,1.478293876,-0.15,-3.13,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,206290,2015-10-30 10:17:07:166,1446171427166.0 \n-0.2705,0.267,8.2408,0.5051,0.1218,9.7929,-0.1393,-0.1429,0.0843,-36,3.1,-43,1.465727506,-0.71,-2.95,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,206392,2015-10-30 10:17:07:268,1446171427268.0 \n-0.5543,0.492,8.5114,0.5387,-0.0553,9.7917,-0.0269,0.0562,-0.0159,-36.4,3.8,-43,1.459618853,0.32,-3.15,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,206493,2015-10-30 10:17:07:369,1446171427369.0 \n-0.158,0.8643,8.1379,0.4896,-0.0412,9.7943,-0.0061,-0.0806,-0.11,-36.5,4.4,-43.1,1.458571656,0.24,-2.86,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,206595,2015-10-30 10:17:07:471,1446171427471.0 \n-0.1197,-0.492,10.5129,0.6727,0.0959,9.7831,0.1381,-0.2651,-0.0904,-37.2,4.7,-43,1.422617873,-0.07,-4.04,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,206697,2015-10-30 10:17:07:573,1446171427573.0 \n-0.1101,-1.0894,12.153,0.5599,-0.1317,9.7898,-0.5095,0.4191,-0.2382,-37.6,4.6,-43,1.427504795,-0.05,-3.93,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,206800,2015-10-30 10:17:07:676,1446171427676.0 \n0.4693,-0.1879,9.3733,0.4415,-0.1105,9.7961,-0.2578,-0.0794,-0.0709,-37.9,4.5,-43,1.446703417,0.65,-2.58,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,206901,2015-10-30 10:17:07:777,1446171427777.0 \n0.1532,0.2107,8.3917,0.4243,-0.2539,9.7942,-0.0476,0.0696,-0.0599,-37.9,4.6,-43.3,1.463109512,1.42,-2.6,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,207004,2015-10-30 10:17:07:880,1446171427880.0 \n0.6237,1.3886,8.1056,0.3864,-0.1908,9.7972,0.121,-0.011,-0.0147,-37.7,5.2,-43.8,1.457698991,1.11,-2.26,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,207105,2015-10-30 10:17:07:981,1446171427981.0 \n-0.5722,-0.3627,11.789,0.4037,-0.215,9.796,0.3054,-0.0183,-0.022,-38,5.3,-44.1,1.460666051,1.26,-2.36,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,207207,2015-10-30 10:17:08:083,1446171428083.0 \n0.7314,-1.8399,12.3206,0.438,-0.0859,9.7965,-0.4704,-0.2382,0.0244,-38.1,5.1,-44.2,1.443736357,0.5,-2.56,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,207310,2015-10-30 10:17:08:186,1446171428186.0 \n-0.085,0.8571,7.8362,0.3665,-0.1369,9.7988,0.3702,0.1136,0.3653,-38.2,5.3,-44.1,1.451241273,0.8,-2.14,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,207412,2015-10-30 10:17:08:288,1446171428288.0 \n-0.395,0.1425,9.0812,0.5152,-0.1827,9.7914,-0.121,-0.0232,0.0293,-38.2,5.7,-43.8,1.427504795,1.07,-3.01,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,207514,2015-10-30 10:17:08:390,1446171428390.0 \n-0.3986,0.8607,7.446,0.4442,-0.1148,9.7959,0.0867,0.1307,0.0696,-38.2,6.5,-43.9,1.392947276,0.67,-2.6,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,207616,2015-10-30 10:17:08:492,1446171428492.0 \n-0.7147,0.1592,10.6267,0.388,-0.1672,9.7975,-0.1515,0.0244,-0.1588,-38,6.8,-43.9,1.398881395,0.92,-2.42,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,207717,2015-10-30 10:17:08:593,1446171428593.0 \n-0.3771,0.1293,10.2663,0.3535,-0.0816,9.7999,0.1576,0.0525,0,-37.8,7.1,-44.3,1.390852881,0.48,-2.07,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,207820,2015-10-30 10:17:08:696,1446171428696.0 \n-0.577,-1.3599,11.8333,0.3255,-0.3248,9.7959,-0.4007,0,-0.2822,-37.4,7,-44.5,1.405164581,1.39,-2.16,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,207921,2015-10-30 10:17:08:797,1446171428797.0 \n-0.0431,-0.3292,8.4443,0.3192,-0.4071,9.793,0,-0.0452,-0.055,-36.9,7.1,-44.8,1.421396143,2.04,-1.81,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,208024,2015-10-30 10:17:08:900,1446171428900.0 \n-0.6057,0.3591,8.0493,0.29,-0.4656,9.7913,0.0147,0.1246,-0.0599,-36.5,7.4,-45,1.432915316,2.72,-1.7,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,208125,2015-10-30 10:17:09:001,1446171429001.0 \n-0.0563,0.6381,8.995,0.2583,-0.4334,9.7937,0.0159,0.0342,0.0611,-36.1,7.6,-45.2,1.402372054,2.58,-1.46,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,208227,2015-10-30 10:17:09:103,1446171429103.0 \n-0.6823,-0.3843,13.3369,0.294,-0.2727,9.7984,0.5376,-0.11,0.3225,-35.7,7.8,-45.3,1.390852881,2.05,-1.33,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,208329,2015-10-30 10:17:09:205,1446171429205.0 \n-1.3743,-1.6173,14.2694,0.4285,-0.207,9.7951,-0.2969,-0.38,-0.0733,-35.3,7.3,-45.5,1.390503815,1.21,-2.5,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,208431,2015-10-30 10:17:09:307,1446171429307.0 \n-0.3687,0.4453,7.6195,0.3799,-0.1805,9.7976,-0.0122,-0.2688,-0.0929,-35.1,7.1,-45.5,1.394518072,1.29,-1.97,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,208534,2015-10-30 10:17:09:410,1446171429410.0 \n-0.4956,0.0886,8.5461,0.5799,-0.2811,9.7855,0.1148,-0.1747,-0.0086,-35.2,6.7,-45.4,1.402197521,1.79,-3.1,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,208636,2015-10-30 10:17:09:512,1446171429512.0 \n-0.3879,0.6632,8.1846,0.6262,-0.1549,9.7854,0.1625,-0.0073,-0.0305,-35.4,6.6,-45.2,1.386664091,1.26,-3.69,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,208738,2015-10-30 10:17:09:614,1446171429614.0 \n-0.8835,-0.2753,12.5265,0.6969,-0.0983,9.7814,-0.088,-0.1564,-0.3079,-35.7,5.9,-45.2,1.403419252,0.57,-4.08,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,208840,2015-10-30 10:17:09:716,1446171429716.0 \n0.4118,0.0742,10.6542,0.6583,-0.052,9.7844,-0.2419,-0.0134,-0.2321,-35.9,5,-45.2,1.421047077,0.04,-3.8,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,208944,2015-10-30 10:17:09:820,1446171429820.0 \n-0.0287,-0.5195,9.1842,0.5453,-0.34,9.7856,-0.3726,0.204,-0.1527,-36,3.9,-45.2,1.500110492,1.99,-3.19,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,209043,2015-10-30 10:17:09:919,1446171429919.0 \n0.1257,-0.2873,9.4104,0.5449,-0.482,9.7796,-0.303,0.0122,-0.0122,-36,3.6,-45.1,1.506742743,2.26,-3.19,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,209145,2015-10-30 10:17:10:021,1446171430021.0 \n-0.1089,0.5279,8.1223,0.5096,-0.5451,9.7782,0.1136,0.0501,0.1295,-35.8,4,-45.1,1.53222455,3.3,-3.08,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,209248,2015-10-30 10:17:10:124,1446171430124.0 \n-0.1939,-0.4812,10.8338,0.5103,-0.513,9.7799,0.0379,-0.0305,0.1112,-35.8,4.2,-45.3,1.524894167,3,-2.99,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,209349,2015-10-30 10:17:10:225,1446171430225.0 \n-0.2179,-0.1508,11.1977,0.5422,-0.3454,9.7856,0.3726,-0.0672,0.303,-35.9,4.2,-45.4,1.500808624,2.02,-3.17,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,209451,2015-10-30 10:17:10:327,1446171430327.0 \n0.3029,-0.6273,11.4587,0.5478,-0.4091,9.7828,-0.2724,-0.0684,0.3311,-36.1,4.1,-45.5,1.509884336,2.39,-3.21,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,209554,2015-10-30 10:17:10:430,1446171430430.0 \n0.0347,-0.0706,9.9311,0.6684,-0.3684,9.7769,0.0745,-0.292,0.2285,-36.5,4.3,-45.5,1.503426618,2.15,-3.91,36.8147,-119.74845,279.24,336.6579477,4.06,19.35484,95.45,17 / 17,209655,2015-10-30 10:17:10:531,1446171430531.0 \n-0.2741,0.1724,8.8214,0.6599,-0.3214,9.7791,0.0635,0.1417,0.0195,-37,4.7,-45.3,1.472185224,1.99,-3.87,36.8147,-119.748344,280.85,336.6579477,3.91,19.35484,107.99,17 / 17,209758,2015-10-30 10:17:10:634,1446171430634.0 \n0.2119,0.7302,8.1894,0.6015,-0.1153,9.7875,0.3604,0.1002,0.0415,-37.4,4.9,-45.4,1.450717674,1.08,-3.63,36.8147,-119.748344,280.85,336.6579477,3.91,19.35484,107.99,17 / 17,209859,2015-10-30 10:17:10:735,1446171430735.0 \n-0.1652,-0.3986,11.7807,0.6498,0.015,9.7851,0.3005,0.2334,-0.1539,-37.7,4.6,-45.2,1.426632131,-0.09,-3.8,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,209961,2015-10-30 10:17:10:837,1446171430837.0 \n0.0347,-0.5543,11.248,0.4893,-0.0716,9.7942,-0.248,-0.0183,-0.281,-37.7,3.5,-45.4,1.444783555,-0.62,-3.01,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,210064,2015-10-30 10:17:10:940,1446171430940.0 \n0.255,-0.395,10.1778,0.501,-0.2544,9.7905,0.1368,-0.0819,-0.0318,-37.6,3.1,-45.3,1.525417766,1.68,-2.81,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,210166,2015-10-30 10:17:11:042,1446171431042.0 \n0.7673,0.7721,8.7077,0.4706,-0.3854,9.7878,-0.088,0.0562,-0.0012,-37.3,3,-45.6,1.538507736,2.25,-2.75,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,210268,2015-10-30 10:17:11:144,1446171431144.0 \n-0.0383,0.486,9.7336,0.3962,-0.3402,9.7927,0.1185,-0.077,-0.1368,-37,3.3,-45.7,1.532399083,1.99,-2.32,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,210372,2015-10-30 10:17:11:248,1446171431248.0 \n-0.5914,-0.322,11.6514,0.3518,-0.1753,9.7988,0.2676,0.0415,0.0452,-36.9,3.2,-45.6,1.509884336,1.02,-2.06,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,210475,2015-10-30 10:17:11:351,1446171431351.0 \n-1.0403,-2.0566,16.3763,0.5873,-0.0213,9.789,-0.744,-0.6988,-0.2089,-36.8,2.6,-45.2,1.486322391,0.12,-3.43,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,210573,2015-10-30 10:17:11:449,1446171431449.0 \n-0.5028,0.4369,6.6475,0.4968,-0.0595,9.7939,-0.2749,-0.2297,0.0513,-36.8,2.2,-45,1.521403509,0.35,-2.9,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,210675,2015-10-30 10:17:11:551,1446171431551.0 \n-0.5519,0.5339,8.9723,0.6234,-0.2915,9.7825,-0.1637,-0.0672,0.226,-37,2.4,-44.5,1.55247037,1.7,-3.65,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,210777,2015-10-30 10:17:11:653,1446171431653.0 \n-0.4166,0.9445,8.2648,0.6394,-0.1638,9.7844,0.1979,-0.1588,0.1857,-36.9,3,-44.5,1.513898593,1.3,-3.55,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,210880,2015-10-30 10:17:11:756,1446171431756.0 \n0.2083,0.5483,11.0768,0.7931,0.0487,9.7744,0.2138,-0.1491,-0.16,-37.1,3.3,-44.4,1.482133601,0.02,-4.34,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,210981,2015-10-30 10:17:11:857,1446171431857.0 \n1.6951,0.5614,10.07,0.8401,0.3247,9.7652,0.3421,0.0012,-0.1405,-37.2,2.8,-44.3,1.433962513,-1.9,-4.92,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,211084,2015-10-30 10:17:11:960,1446171431960.0 \n-0.7123,-1.4078,11.9638,0.812,0.1402,9.772,-0.292,-0.0195,-0.4068,-37.4,2,-44.1,1.485449726,-1.04,-4.65,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,211186,2015-10-30 10:17:12:062,1446171432062.0 \n0.4884,0.0922,9.0309,0.8409,-0.0053,9.7705,-0.3384,-0.0586,-0.0305,-37.4,1.1,-43.5,1.541474795,0.03,-4.92,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,211288,2015-10-30 10:17:12:164,1446171432164.0 \n0.0551,0.3711,8.6299,0.8017,-0.1947,9.7719,0.1576,0.2053,0.1686,-37.2,1.1,-43.3,1.568178333,1.14,-4.69,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,211389,2015-10-30 10:17:12:265,1446171432265.0 \n0.0922,0.4393,9.4547,0.6053,-0.1035,9.7874,0.0073,0.1136,0.16,-36.9,1.5,-43.3,1.529257491,0.74,-3.74,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,211491,2015-10-30 10:17:12:367,1446171432367.0 \n-0.3867,0.316,9.7408,0.4492,0.0519,9.7962,0.3067,0.1991,0.325,-36.2,2.1,-44.4,1.504822881,-0.3,-2.63,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,211594,2015-10-30 10:17:12:470,1446171432470.0 \n0.5638,-0.1856,12.0249,0.4432,-0.1244,9.7958,-0.3873,-0.1393,0.1258,-35.6,2.4,-45.1,1.498016097,-0.63,-2.08,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,211695,2015-10-30 10:17:12:571,1446171432571.0 \n0.3184,0.3053,9.4655,0.7028,-0.2196,9.779,0.0476,-0.3861,0.2566,-35.3,3.6,-45.1,1.478293876,1.28,-4.11,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,211797,2015-10-30 10:17:12:673,1446171432673.0 \n-0.2047,0.4334,8.4527,0.7421,-0.252,9.7753,0.0745,0.0684,-0.0525,-35.5,4.3,-45,1.486322391,1.61,-4.41,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,211900,2015-10-30 10:17:12:776,1446171432776.0 \n0.0395,1.0151,8.9986,0.7193,0.0012,9.7802,0.3409,0.0061,-0.1112,-36,4.9,-44.4,1.418778149,-0.01,-4.21,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,212001,2015-10-30 10:17:12:877,1446171432877.0 \n0.3089,0.2957,11.0708,0.7461,0.3436,9.7722,0.4129,-0.0929,-0.1686,-36.2,4.3,-44.6,1.416683754,-1.27,-4.27,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,212104,2015-10-30 10:17:12:980,1446171432980.0 \n-0.7123,-1.6233,13.441,0.6861,0.3834,9.7751,-0.6439,-0.0257,-0.5486,-36,2.6,-45,1.423839604,-2.24,-4.01,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,212206,2015-10-30 10:17:13:082,1446171433082.0 \n1.0259,0.34,8.1235,0.5579,0.2407,9.7878,-0.1527,0.0428,-0.099,-35.8,1.5,-45.3,1.481086403,-1.2,-3.51,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,212310,2015-10-30 10:17:13:186,1446171433186.0 \n0.2634,0.6189,8.5449,0.5142,0.0201,9.7931,-0.2407,0.077,-0.1564,-35.5,0.8,-45.6,1.537111472,-0.12,-3.01,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,212410,2015-10-30 10:17:13:286,1446171433286.0 \n0.2622,1.1911,8.9136,0.6649,0.0758,9.7838,0.2077,-0.0501,-0.0318,-35.6,0.8,-45.4,1.529257491,-0.44,-3.89,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,212511,2015-10-30 10:17:13:387,1446171433387.0 \n0.3747,1.2139,9.1459,0.7355,0.4098,9.7704,0.314,-0.0049,0.0501,-35.8,0.4,-45.2,1.524370569,-1.82,-4.3,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,212614,2015-10-30 10:17:13:490,1446171433490.0 \n1.1157,0.2047,9.9084,0.7065,0.6399,9.7602,-0.1539,-0.0342,0.0599,-36,-0.7,-44.7,1.50656821,-3.74,-4.14,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,212715,2015-10-30 10:17:13:591,1446171433591.0 \n-0.2658,-0.6069,10.0353,0.7411,0.443,9.7686,-0.1063,0.0367,0.1283,-36.1,-1.4,-44.7,1.527337628,-2.91,-4.26,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,212818,2015-10-30 10:17:13:694,1446171433694.0 \n0.407,0.899,7.9116,0.9441,0.3024,9.7564,-0.1588,-0.1833,0.1515,-36.3,-1.6,-44.4,1.587900553,-1.77,-5.53,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,212920,2015-10-30 10:17:13:796,1446171433796.0 \n-0.3029,0.7673,9.4547,0.9652,0.1169,9.7583,0.1417,0.0049,0.0867,-36.6,-1.2,-44.1,1.584584428,-0.66,-5.56,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,213022,2015-10-30 10:17:13:898,1446171433898.0 \n0.1209,1.0511,9.5577,0.9266,0.2622,9.7593,0.1552,0.0183,0.0538,-37.2,-0.4,-43.2,1.537809604,-1.34,-5.48,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,213124,2015-10-30 10:17:14:000,1446171434000.0 \n0.3783,0.2059,11.7902,0.9272,0.3835,9.7552,0.2199,0.1307,0.0281,-37.3,-0.2,-42.7,1.524021503,-1.89,-5.63,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,213225,2015-10-30 10:17:14:101,1446171434101.0 \n-0.6201,-0.9912,11.4371,0.7569,0.2616,9.7739,-0.5608,0.1991,-0.1894,-37.1,-0.6,-42.7,1.564164076,-1.53,-4.43,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,213327,2015-10-30 10:17:14:203,1446171434203.0 \n1.087,0.085,9.1961,0.6779,-0.0725,9.7829,-0.5669,0.0855,-0.044,-36.5,-0.7,-42.9,1.611287965,0.42,-3.96,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,213430,2015-10-30 10:17:14:306,1446171434306.0 \n0.17,0.4441,8.3677,0.5806,-0.4141,9.7807,-0.2737,0.1429,-0.0916,-36.2,-0.1,-42.9,1.620712743,2.1,-3.71,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,213531,2015-10-30 10:17:14:407,1446171434407.0 \n0.5495,0.8272,9.1482,0.4644,-0.4785,9.784,0.0648,0.1368,0.0721,-35.7,1.1,-42.9,1.605528379,2.8,-2.72,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,213633,2015-10-30 10:17:14:509,1446171434509.0 \n-0.0132,-0.17,11.7184,0.282,-0.212,9.8003,0.5315,0.0024,0.1869,-35.3,1.7,-42.9,1.557182759,2.01,-1.66,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,213735,2015-10-30 10:17:14:611,1446171434611.0 \n-0.3627,-0.893,11.6011,0.2506,0.0241,9.8034,0.3677,0.1356,0.2089,-34.7,1.5,-43.4,1.495747169,-0.75,-1.1,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,213838,2015-10-30 10:17:14:714,1446171434714.0 \n-0.1305,-0.3723,10.2927,0.4653,-0.1134,9.7949,0.0354,-0.3714,0.2211,-34.6,1.5,-43.7,1.526988563,0.67,-1.91,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,213940,2015-10-30 10:17:14:816,1446171434816.0 \n-0.3496,0.2741,8.497,0.545,-0.2257,9.7889,-0.1723,0.0599,-0.077,-34.9,1.7,-43.3,1.54112573,1.32,-3.19,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,214042,2015-10-30 10:17:14:918,1446171434918.0 \n-0.5794,0.6261,8.7544,0.5247,-0.2464,9.7895,0.0489,0.0147,-0.055,-35.3,2.3,-43.1,1.548456112,1.62,-3.15,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,214143,2015-10-30 10:17:15:019,1446171435019.0 \n-0.1281,0.1149,10.2987,0.5098,6.00E-04,9.7934,0.2126,-0.0122,-0.0916,-35.6,2.4,-42.7,1.520181778,0.37,-2.96,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,214247,2015-10-30 10:17:15:123,1446171435123.0 \n0.8882,0.4417,10.422,0.4504,0.1096,9.7957,0.0147,-0.0696,-0.1246,-35.7,2,-42.8,1.497492498,-0.64,-2.63,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,214348,2015-10-30 10:17:15:224,1446171435224.0 \n-0.6297,-1.1899,11.9734,0.3784,-0.0874,9.799,0.0195,0.1246,-0.0513,-35.6,1.4,-42.8,1.553168501,0.51,-2.21,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,214450,2015-10-30 10:17:15:326,1446171435326.0 \n-0.6931,-0.3017,9.9407,0.2326,-0.2046,9.8018,-0.2272,0.1319,-0.0672,-35.3,1.1,-42.8,1.568352866,1.2,-1.36,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,214556,2015-10-30 10:17:15:432,1446171435432.0 \n-0.4872,0.6237,8.2684,0.1448,-0.2722,9.8018,-0.0208,-0.0525,0.1588,-35,1.3,-43,1.574810584,1.49,-0.9,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,214654,2015-10-30 10:17:15:530,1446171435530.0 \n-0.3256,0.6237,10.2316,0.16,-0.2283,9.8027,0.1943,-0.0733,0.1723,-34.6,1.8,-43.1,1.541998394,1.33,-0.94,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,214756,2015-10-30 10:17:15:632,1446171435632.0 \n-0.1293,0.1496,10.8852,0.2502,0.2146,9.8011,0.4667,-0.0977,0.3384,-34.6,2.2,-43.2,1.501332223,-0.48,-1.3,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,214857,2015-10-30 10:17:15:733,1446171435733.0 \n-0.8164,-0.9852,12.226,0.3661,0.2179,9.7974,-0.3641,-0.2822,0.0244,-34.9,2,-43,1.481610002,-1.27,-2.14,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,214960,2015-10-30 10:17:15:836,1446171435836.0 \n0.4298,0.4633,8.1295,0.4765,0.1301,9.7942,-0.3983,0.0183,-0.2492,-35.3,2.1,-42.7,1.492081978,-0.76,-2.79,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,215065,2015-10-30 10:17:15:941,1446171435941.0 \n0.0551,0.31,9.1303,0.4397,-0.217,9.7944,-0.3225,0.033,-0.171,-35.7,2.4,-42.1,1.540427598,1.27,-2.57,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,215164,2015-10-30 10:17:16:040,1446171436040.0 \n0.243,1.1121,7.1958,0.3572,-0.0277,9.8001,0.1613,0.0867,-0.0672,-35.8,2.8,-42,1.495572636,0.54,-2.25,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,215266,2015-10-30 10:17:16:142,1446171436142.0 \n-0.3316,-0.1808,11.9794,0.4561,0.0715,9.7958,0.336,-0.0037,-0.2114,-36,2.7,-41.7,1.473581487,-0.42,-2.67,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,215368,2015-10-30 10:17:16:244,1446171436244.0 \n-0.7901,-0.3831,10.7583,0.5075,0.2575,9.7901,-0.3433,0.259,-0.2529,-36.2,1.6,-41.6,1.477770278,-1.5,-2.97,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,215471,2015-10-30 10:17:16:347,1446171436347.0 \n0.2059,-0.0431,9.7695,0.3549,-0.0453,9.8001,-0.2615,0.0171,-0.1368,-36.5,0.9,-41.5,1.547408915,0.26,-2.07,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,215571,2015-10-30 10:17:16:447,1446171436447.0 \n0.3268,0.1317,11.0349,0.354,-0.3276,9.7948,-0.4924,-0.0574,-0.0953,-36.5,0.8,-41.5,1.582839099,1.91,-2.07,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,215674,2015-10-30 10:17:16:550,1446171436550.0 \n0.4908,0.9433,8.594,0.3473,-0.3866,9.7929,0.11,0.2334,0.0672,-36.4,0.9,-41.4,1.590169481,2.26,-2.03,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,215776,2015-10-30 10:17:16:652,1446171436652.0 \n-1.0678,0.1736,11.0325,0.3003,0.1709,9.8006,0.3763,-0.0513,0.1075,-36,1.4,-41.5,1.52087991,-1,-1.76,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,215878,2015-10-30 10:17:16:754,1446171436754.0 \n-0.504,-1.0714,12.4259,0.3968,0.2258,9.796,-0.4191,-0.3128,-0.0965,-35.9,0.9,-41.5,1.499761426,-1.99,-1.94,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,215980,2015-10-30 10:17:16:856,1446171436856.0 \n0.2514,0.2789,8.1295,0.5632,0.171,9.789,-0.2456,-0.1222,-0.1075,-36.1,0.6,-41.1,1.518785515,-1,-3.29,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,216082,2015-10-30 10:17:16:958,1446171436958.0 \n-0.6249,0.1257,9.232,0.5291,-0.0528,9.7922,-0.2101,0.0452,-0.1112,-36.3,0.8,-40.6,1.547408915,0.28,-3.15,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,216183,2015-10-30 10:17:17:059,1446171437059.0 \n-0.4154,0.6788,8.3641,0.4832,0.2369,9.7919,0.2981,0.0037,0.0134,-36.7,1.4,-40.4,1.523672437,-0.89,-2.78,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,216285,2015-10-30 10:17:17:161,1446171437161.0 \n-0.6081,0.4154,10.1143,0.4457,0.4451,9.7864,0.1991,0.1246,-0.0635,-36.8,1.2,-40.4,1.488765852,-2.6,-2.61,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,216387,2015-10-30 10:17:17:263,1446171437263.0 \n0.7961,0.1808,10.9319,0.3935,0.4396,9.7889,-0.5449,0.2712,-0.3751,-36.7,0.7,-40.6,1.488765852,-2.57,-2.3,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,216490,2015-10-30 10:17:17:366,1446171437366.0 \n0.5375,0.6488,7.3741,0.1328,0.203,9.8036,0.11,0.2162,0.0819,-36.3,0.3,-40.7,1.54653625,-1.19,-0.78,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,216592,2015-10-30 10:17:17:468,1446171437468.0 \n-0.1173,-0.006,9.1614,0.1076,-0.1507,9.8049,-0.4203,-0.0122,-0.1381,-36,0.4,-41.1,1.562767812,-0.39,-0.61,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,216693,2015-10-30 10:17:17:569,1446171437569.0 \n-0.5866,0.4022,9.177,0.0622,-0.2489,9.8033,0.1649,0.0476,0.1527,-35.5,1.3,-41.3,1.57515965,1.6,-0.45,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,216795,2015-10-30 10:17:17:671,1446171437671.0 \n-1.0127,0.1329,9.8186,-0.0342,-0.1355,9.8057,0.1271,0.1307,0.1527,-35.2,2.1,-41.4,1.529955622,0.79,0.2,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,216898,2015-10-30 10:17:17:774,1446171437774.0 \n-1.1372,0.7566,9.7755,-0.112,0.2355,9.8032,0.4997,0.2334,0.595,-35,2.5,-41.4,1.473057889,-0.64,0.29,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,216999,2015-10-30 10:17:17:875,1446171437875.0 \n0.1425,-0.2861,10.8242,0.0424,0.1411,9.8055,-0.1393,-0.2443,0.4447,-34.8,2.8,-41.7,1.467647368,-0.82,-0.25,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,217102,2015-10-30 10:17:17:978,1446171437978.0 \n-0.237,-0.2646,9.4439,0.2236,-0.0031,9.8041,-0.1613,-0.1943,0.0855,-34.8,3.3,-41.7,1.479341074,-0.2,-0.92,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,217203,2015-10-30 10:17:18:079,1446171438079.0 \n0.0371,0.3903,8.6191,0.2783,-0.1542,9.8015,-0.1075,0.1014,-0.0122,-35.1,4.2,-41.2,1.472359757,0.9,-1.63,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,217306,2015-10-30 10:17:18:182,1446171438182.0 \n-0.0431,1.136,8.0325,0.1887,-0.0974,9.8044,0.11,-0.2419,-0.1539,-35.3,5.1,-40.8,1.437453172,0.57,-1.1,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,217408,2015-10-30 10:17:18:284,1446171438284.0 \n-0.1592,0.5471,10.7679,0.4542,0.1631,9.7948,0.1881,0.2285,-0.2101,-35.7,4.8,-40.5,1.405513647,-0.95,-2.65,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,217510,2015-10-30 10:17:18:386,1446171438386.0 \n-0.6668,-0.2047,10.9283,0.2698,0.0815,9.8026,-0.3042,0.0867,-0.3714,-35.8,4.2,-40.5,1.431693585,-1.21,-1.78,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,217614,2015-10-30 10:17:18:490,1446171438490.0 \n0.5088,0.2227,8.7029,0.2323,0.0115,9.8039,-0.0562,0.0819,0.121,-35.9,3.5,-40.5,1.455779129,-0.07,-1.36,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,217714,2015-10-30 10:17:18:590,1446171438590.0 \n0.1173,0.7254,8.1702,0.2347,-0.0423,9.8038,0.0037,0.2602,-0.0293,-35.8,3.5,-40.5,1.463458578,0.34,-1.53,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,217815,2015-10-30 10:17:18:691,1446171438691.0 \n0.5674,1.3575,8.5485,0.1938,0.0111,9.8047,0.1381,-0.1527,-0.0244,-35.6,3.7,-40.5,1.456302728,-0.06,-1.13,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,217917,2015-10-30 10:17:18:793,1446171438793.0 \n-0.577,0.0227,11.8824,0.3606,0.2174,9.7976,0.1564,-0.1979,-0.0037,-35.7,3.6,-40.6,1.439023968,-0.83,-1.69,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,218020,2015-10-30 10:17:18:896,1446171438896.0 \n0.8823,-0.6764,12.2571,0.5385,0.3919,9.784,-0.5034,-0.6035,-0.0929,-35.8,3.1,-40.7,1.421396143,-2.93,-2.35,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,218123,2015-10-30 10:17:18:999,1446171438999.0 \n-0.2143,0.2131,9.6283,0.6299,0.2137,9.7841,-0.0049,0.0929,0.3311,-36.1,2.9,-40.3,1.454731932,-1.2,-3.78,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,218223,2015-10-30 10:17:19:099,1446171439099.0 \n0.1125,0.7506,8.1032,0.57,0.104,9.7895,-0.0648,0.0782,0.1063,-36.4,3.3,-40,1.468694566,-0.61,-3.33,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,218326,2015-10-30 10:17:19:202,1446171439202.0 \n-0.0922,1.0379,7.5657,0.5142,0.2748,9.7893,0.3299,0.0709,0.1112,-36.5,3.9,-39.8,1.430122789,-1.07,-3.13,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,218427,2015-10-30 10:17:19:303,1446171439303.0 \n-0.3675,0.6416,11.0468,0.5227,0.4351,9.783,0.193,-0.1527,-0.1014,-36.2,4,-39.8,1.399404994,-2.54,-3.06,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,218529,2015-10-30 10:17:19:405,1446171439405.0 \n0.6237,0.1939,12.3876,0.5612,0.5216,9.7767,-0.0342,0.055,-0.0476,-36.2,3.6,-39.8,1.387711288,-3.05,-3.29,36.8147,-119.748344,280.85,336.7455556,3.91,19.35484,107.99,17 / 17,218631,2015-10-30 10:17:19:507,1446171439507.0 \n-0.0096,-0.4609,9.8581,0.3953,0.4218,9.7896,-0.1527,0.0305,-0.2285,-36.1,3.1,-40.1,1.43256625,-2.47,-2.31,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,218734,2015-10-30 10:17:19:610,1446171439610.0 \n-0.3041,-0.0886,9.2799,0.2901,0.1054,9.8018,-0.1979,0.0354,0.0147,-36,2.8,-40.3,1.462236847,-1.1,-1.74,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,218835,2015-10-30 10:17:19:711,1446171439711.0 \n-0.4501,0.6333,8.5234,0.2641,-0.0898,9.8027,-0.2419,0.0037,-0.0391,-35.6,3.3,-40.7,1.495921702,0.52,-1.54,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,218938,2015-10-30 10:17:19:814,1446171439814.0 \n-0.0084,1.1839,9.2787,0.2868,-0.059,9.8023,0.0342,-0.011,0.0696,-35.5,3.7,-40.7,1.464854841,0.56,-1.74,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,219039,2015-10-30 10:17:19:915,1446171439915.0 \n-0.4489,0.1101,12.0907,0.2486,0.1781,9.8019,0.3922,-0.0843,0.2761,-35.3,4.1,-40.8,1.445656219,-0.39,-1.34,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,219141,2015-10-30 10:17:20:017,1446171440017.0 \n0.8823,0.3352,10.507,0.1942,0.3346,9.799,0.1417,0.1723,0.4826,-35.1,4,-41,1.408131641,-2.24,-1.04,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,219243,2015-10-30 10:17:20:119,1446171440119.0 \n0.8535,1.1492,8.5198,0.397,0.3207,9.7934,0.1772,-0.3067,0.3824,-35,4.2,-40.7,1.410575101,-1.87,-2.32,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,219345,2015-10-30 10:17:20:221,1446171440221.0 \n0.0706,0.8859,7.8865,0.4303,0.0523,9.7971,-0.1735,0.0635,-0.1222,-35.2,4.8,-40.3,1.414938425,-0.31,-2.51,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,219448,2015-10-30 10:17:20:324,1446171440324.0 \n-0.2346,1.1684,8.0804,0.3994,0.0408,9.7984,-0.0904,0.0318,-0.1979,-35.4,5.3,-39.9,1.421396143,-0.01,-2.42,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,219550,2015-10-30 10:17:20:426,1446171440426.0 \n-0.4046,1.1863,8.9076,0.4172,0.1453,9.7967,0.237,-0.2334,-0.237,-35.5,5.4,-39.9,1.403593784,-0.85,-2.44,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,219652,2015-10-30 10:17:20:528,1446171440528.0 \n-0.3974,0.2729,12.0045,0.5619,0.338,9.7847,0.3409,-0.0354,-0.1454,-35.5,5.2,-40.1,1.385616893,-1.58,-2.99,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,219775,2015-10-30 10:17:20:651,1446171440651.0 \n0.3304,0.1939,8.9998,0.3269,0.2148,9.7988,-0.0318,0.0171,0.0293,-35.6,3.8,-40.3,1.431169987,-1.18,-2.11,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,219856,2015-10-30 10:17:20:732,1446171440732.0 \n0.5519,0.8679,7.8027,0.3243,0.0033,9.8013,-0.3018,-0.0037,-0.0293,-35.4,3.3,-40.4,1.481435469,-0.02,-1.89,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,219958,2015-10-30 10:17:20:834,1446171440834.0 \n0.0084,1.069,8.7125,0.3537,-0.1083,9.7997,-0.0562,-0.1955,0.0134,-35.2,3.7,-40.6,1.465552973,0.6,-1.76,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,220060,2015-10-30 10:17:20:936,1446171440936.0 \n0.0539,0.7661,9.2512,0.396,0.0627,9.7985,0.1772,-0.121,0.0147,-35.1,4.1,-40.4,1.451590339,-0.01,-2.19,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,220161,2015-10-30 10:17:21:037,1446171441037.0 \n0.6967,0.8751,9.104,0.53,0.4547,9.7818,0.628,-0.1173,0.1381,-35.4,4.1,-40.3,1.391725546,-2.66,-3.1,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,220264,2015-10-30 10:17:21:140,1446171441140.0 \n-1.7765,-1.7119,13.9259,0.6839,0.2285,9.7801,-0.1222,0.2187,-0.0562,-35.7,3.8,-40.1,1.408480706,-1.92,-4.06,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,220366,2015-10-30 10:17:21:242,1446171441242.0 \n-0.6584,0.3591,8.8597,0.657,0.2233,9.7821,-0.2407,0.0904,0.0159,-36,3.3,-39.7,1.441991028,-1.75,-3.98,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,220467,2015-10-30 10:17:21:343,1446171441343.0 \n-0.1784,0.7207,8.7376,0.6346,0.2477,9.783,0.11,-0.033,0.0562,-36.1,3.3,-39.5,1.45822259,-1.08,-3.75,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,220570,2015-10-30 10:17:21:446,1446171441446.0 \n-0.0204,1.3551,7.9547,0.5044,0.4297,9.7842,0.2077,0.1454,-0.0538,-36,3.4,-39.5,1.430820921,-2.51,-2.95,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,220672,2015-10-30 10:17:21:548,1446171441548.0 \n-1.1349,0.3867,10.8158,0.4852,0.6429,9.7735,0.3176,0.0929,-0.2089,-35.8,2.9,-39.9,1.413542161,-3.25,-3.02,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,220773,2015-10-30 10:17:21:649,1446171441649.0 \n-0.407,-0.3891,11.6574,0.3695,0.3703,9.7927,-0.2407,0.022,0,-35.5,2,-40.1,1.464854841,-2.16,-2.16,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,220876,2015-10-30 10:17:21:752,1446171441752.0 \n0.2646,0.3316,8.5389,0.4095,0.1757,9.7965,-0.2101,-0.0831,0.0232,-35.4,1.7,-40.3,1.477072146,-1.59,-2.14,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,220977,2015-10-30 10:17:21:853,1446171441853.0 \n-0.2753,0.4561,8.8334,0.5145,-0.1811,9.7915,-0.2627,0.0305,0.0403,-35.3,2.1,-39.9,1.524894167,0.67,-3.01,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,221081,2015-10-30 10:17:21:957,1446171441957.0 \n0.1544,0.8727,8.2827,0.5629,-0.1678,9.789,0.022,-0.0342,0.1979,-35.5,3.1,-39.8,1.500983157,0.98,-3.29,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,221182,2015-10-30 10:17:22:058,1446171442058.0 \n0.0527,0.2239,11.4694,0.6057,-0.1257,9.7871,0.0745,-0.0635,0.1991,-35.6,3.8,-39.5,1.471312559,0.9,-3.49,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,221284,2015-10-30 10:17:22:160,1446171442160.0 \n0.1185,-0.7913,11.9124,0.6217,-0.0478,9.7868,-0.2358,-0.2309,0.2358,-35.6,4.3,-39.5,1.444609022,-0.4,-3.16,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,221386,2015-10-30 10:17:22:262,1446171442262.0 \n0.3364,0.5614,9.6678,0.7504,-0.1652,9.7765,0.0831,-0.2272,0.2553,-35.6,4.8,-39.2,1.446179818,1.17,-4.01,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,221487,2015-10-30 10:17:22:363,1446171442363.0 \n-0.231,0.1377,9.845,0.8513,-0.3743,9.7625,0.1222,0.0122,0.0391,-35.8,5.6,-38.4,1.433438915,2.1,-5.04,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,221590,2015-10-30 10:17:22:466,1446171442466.0 \n-0.1113,0.6632,8.6706,0.8186,-0.231,9.7697,0.121,0.0476,-0.0037,-36.1,6.4,-38.1,1.418080017,1.35,-4.79,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,221693,2015-10-30 10:17:22:569,1446171442569.0 \n-0.3567,-0.559,12.0105,0.789,-0.1108,9.7742,0.1197,-0.0782,-0.1442,-36.3,6.4,-37.9,1.407084443,0.81,-4.58,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,221794,2015-10-30 10:17:22:670,1446171442670.0 \n1.5431,0.2227,10.8014,0.763,0.2136,9.7746,0.2358,0.4349,-0.193,-36.2,5.8,-38.2,1.364672942,-1.25,-4.46,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,221896,2015-10-30 10:17:22:772,1446171442772.0 \n-0.2035,-0.2526,10.1682,0.4464,0.2964,9.792,-0.2505,0.0794,-0.325,-35.7,4.5,-38.7,1.390678348,-1.73,-2.61,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,222001,2015-10-30 10:17:22:877,1446171442877.0 \n0.4166,-0.0443,9.1997,0.4069,0.2635,9.7947,-0.171,-0.0305,-0.303,-35.5,4.1,-39.1,1.419476281,-1.54,-2.38,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,222100,2015-10-30 10:17:22:976,1446171442976.0 \n-1.2246,0.1832,8.8454,0.3603,0.0025,9.8,-0.1503,-0.077,-0.1588,-34.7,2.9,-39.7,1.474279619,-0.36,-1.96,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,222203,2015-10-30 10:17:23:079,1446171443079.0 \n-0.4693,0.5507,9.7971,0.4103,0.0114,9.7981,0.0171,-0.1014,0.0965,-34.6,3,-39.7,1.479515607,-0.07,-2.4,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,222303,2015-10-30 10:17:23:179,1446171443179.0 \n-0.1724,0.3579,8.7065,0.3622,0.205,9.7978,0.3592,0.204,0.2749,-34.7,2.8,-39.9,1.455953662,-1.2,-2.12,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,222406,2015-10-30 10:17:23:282,1446171443282.0 \n-1.2306,-1.3755,12.6701,0.3097,0.0139,9.8017,-0.4728,0.0782,0.1112,-34.6,2.9,-40.2,1.463633111,-0.87,-1.91,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,222508,2015-10-30 10:17:23:384,1446171443384.0 \n-0.3316,-0.3915,10.2053,0.4561,0.0035,9.796,-0.4337,-0.1625,-0.0843,-34.5,3.5,-40.5,1.446354351,-0.02,-2.67,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,222609,2015-10-30 10:17:23:485,1446171443485.0 \n0.334,0.7338,8.3127,0.5162,-0.1427,9.792,0.0391,0.0305,0.1283,-34.6,4.1,-40.4,1.467821901,0.83,-3.02,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,222712,2015-10-30 10:17:23:588,1446171443588.0 \n-0.0275,1.2091,8.4611,0.4686,0.0033,9.7954,0.171,0.0305,0.055,-34.7,4.9,-39.9,1.420174412,-0.02,-2.74,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,222813,2015-10-30 10:17:23:689,1446171443689.0 \n0.2011,0.6261,11.7472,0.6264,0.2294,9.7839,0.391,-0.0415,-0.066,-34.8,4.8,-39.6,1.402895653,-0.75,-3.16,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,222916,2015-10-30 10:17:23:792,1446171443792.0 \n0.2693,-0.4872,12.2846,0.6334,0.4354,9.7765,0.1063,-0.1087,-0.088,-34.8,3.7,-39.2,1.381777169,-3.04,-3.82,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,223017,2015-10-30 10:17:23:893,1446171443893.0 \n0.9182,0.4286,8.193,0.4283,0.3512,9.791,0.0672,0.1808,-0.033,-35,3.1,-39.3,1.437976771,-2,-2.8,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,223120,2015-10-30 10:17:23:996,1446171443996.0 \n0.2047,0.4585,7.6854,0.3795,0.0476,9.7992,-0.2395,0.088,-0.1368,-34.8,2.6,-39.6,1.475326817,-0.28,-2.22,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,223221,2015-10-30 10:17:24:097,1446171444097.0 \n-0.5962,0.5602,8.837,0.3504,-0.0976,9.7999,-0.1381,-0.0098,-0.1295,-34.5,2.8,-39.8,1.488591319,0.44,-2.05,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,223328,2015-10-30 10:17:24:204,1446171444204.0 \n-0.0419,1.0475,8.4898,0.3471,-0.0637,9.8003,-0.0623,-0.1087,0.0733,-34.2,2.8,-40.1,1.487020523,0.37,-2.03,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,223426,2015-10-30 10:17:24:302,1446171444302.0 \n0.4202,0.5088,9.7121,0.3285,0.1657,9.7997,0.0147,-0.0257,0.3751,-34.1,3.2,-40.3,1.458048057,-0.97,-1.92,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,223528,2015-10-30 10:17:24:404,1446171444404.0 \n-1.2055,-1.0989,12.1542,0.5156,-0.1174,9.7924,-0.4288,-0.1038,0.2114,-34.3,3.5,-40.4,1.459618853,0.57,-2.61,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,223630,2015-10-30 10:17:24:506,1446171444506.0 \n-0.3053,0.1293,8.4204,0.7678,-0.2461,9.7734,-0.3286,-0.0696,-0.0452,-34.7,4.5,-40.1,1.447750615,1.44,-4.49,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,223732,2015-10-30 10:17:24:608,1446171444608.0 \n-0.5698,0.4202,9.1339,0.807,-0.3583,9.7668,-0.0244,0.1356,-0.0428,-35.2,5.3,-39.7,1.46241138,2.09,-4.72,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,223834,2015-10-30 10:17:24:710,1446171444710.0 \n-0.2155,0.7111,9.0118,0.7536,-0.2051,9.7755,0.1454,-0.1417,-0.1515,-35.7,5.8,-39.3,1.416160155,1.2,-4.41,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,223936,2015-10-30 10:17:24:812,1446171444812.0 \n-0.7937,-0.2047,11.2719,0.7582,0.0249,9.7773,0.4459,0.2224,-0.077,-35.7,5.4,-39.1,1.416683754,-0.15,-4.43,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,224039,2015-10-30 10:17:24:915,1446171444915.0 \n-0.2586,-0.6129,11.1067,0.5422,0.167,9.7902,-0.314,0.3299,-0.2077,-35.4,4.3,-39.3,1.428551993,-0.98,-3.17,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,224140,2015-10-30 10:17:25:016,1446171445016.0 \n0.316,0.1592,8.0122,0.4604,0.0702,9.7956,-0.3714,-0.022,-0.0513,-35.1,3.6,-39.7,1.435882376,-0.68,-2.66,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,224242,2015-10-30 10:17:25:118,1446171445118.0 \n-0.2382,0.8404,8.1187,0.4107,-0.1423,9.797,-0.1442,0.0916,-0.0183,-34.6,3.4,-40.3,1.498888762,0.83,-2.4,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,224343,2015-10-30 10:17:25:219,1446171445219.0 \n-0.0204,1.1073,8.0481,0.4412,-0.2124,9.7944,-0.0244,-0.0757,-0.055,-34.4,3.7,-40.3,1.473406955,1.17,-2.41,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,224447,2015-10-30 10:17:25:323,1446171445323.0 \n-0.6093,-0.2035,12.615,0.3414,-0.0596,9.8005,0.2969,0.1381,0.2224,-34.3,3.9,-40,1.465203907,0.78,-2.27,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,224548,2015-10-30 10:17:25:424,1446171445424.0 \n1.3647,-0.1197,9.3685,0.305,0.2024,9.7998,0.2443,-0.0476,0.3677,-34.1,3.8,-40.1,1.423839604,-1.18,-1.78,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,224650,2015-10-30 10:17:25:526,1446171445526.0 \n0.4238,0.6345,7.8721,0.531,0.0352,9.7922,-0.5034,-0.1784,-0.1466,-34.1,3.6,-40.2,1.44094383,-0.21,-3.1,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,224752,2015-10-30 10:17:25:628,1446171445628.0 \n-0.0658,0.4645,8.5629,0.5003,-0.1221,9.7931,-0.0428,0.022,-0.0147,-34.4,3.7,-40.4,1.462236847,0.71,-2.92,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,224854,2015-10-30 10:17:25:730,1446171445730.0 \n-0.4561,0.7745,7.7488,0.4429,-0.061,9.7965,0.2101,0.1637,-0.0489,-34.6,3.9,-40.3,1.458397123,0.36,-2.59,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,224956,2015-10-30 10:17:25:832,1446171445832.0 \n-1.0534,0.0455,12.1015,0.4175,0.0798,9.7974,0.0293,-0.1625,-0.1808,-34.5,3.6,-40.6,1.43675504,-0.47,-2.44,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,225057,2015-10-30 10:17:25:933,1446171445933.0 \n0.243,0.0419,11.1342,0.418,0.2986,9.7932,0.2602,-0.1588,-0.0183,-34.4,3.2,-40.8,1.451415806,-1.2,-2.23,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,225160,2015-10-30 10:17:26:036,1446171446036.0 \n-0.1472,-0.6991,11.7795,0.3633,0.0587,9.7997,-0.1087,0.0159,-0.1869,-34.3,2.3,-41,1.48684599,-1.01,-1.98,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,225262,2015-10-30 10:17:26:138,1446171446138.0 \n-0.1808,-0.0335,9.6187,0.3644,-0.0793,9.7996,-0.2627,-0.0831,-0.0684,-34.4,2,-40.9,1.513200461,0.17,-2.04,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,225364,2015-10-30 10:17:26:240,1446171446240.0 \n-0.6273,0.7709,8.8538,0.3236,-0.2011,9.7992,-0.2407,-0.0086,-0.1002,-34.2,2.2,-40.8,1.536064275,1.17,-1.89,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,225466,2015-10-30 10:17:26:342,1446171446342.0 \n-0.7506,0.4369,10.1287,0.331,-0.1675,9.7996,0.0489,0.0318,0.0501,-34.1,2.5,-40.6,1.500983157,0.98,-1.93,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,225568,2015-10-30 10:17:26:444,1446171446444.0 \n-0.334,0.5507,11.0373,0.2881,0.1863,9.8006,0.4875,0.1295,0.347,-34.2,2.6,-40.7,1.482482667,0.16,-2.04,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,225669,2015-10-30 10:17:26:545,1446171446545.0 \n-1.3084,-1.5323,13.1262,0.4335,-0.01,9.7971,-0.6451,-0.215,-0.2334,-34.3,2.4,-40.8,1.510058869,0.06,-2.53,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,225772,2015-10-30 10:17:26:648,1446171446648.0 \n-0.2562,0.2478,7.8207,0.4978,-0.0758,9.7937,-0.2321,-0.0501,0.0061,-34.4,2.5,-40.5,1.475675883,-0.07,-2.85,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,225873,2015-10-30 10:17:26:749,1446171446749.0 \n-0.5495,0.5435,8.4084,0.5564,-0.1876,9.7891,0.0525,-0.0745,0.0342,-34.5,3.1,-40.3,1.501506755,1.1,-3.25,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,225978,2015-10-30 10:17:26:854,1446171446854.0 \n-0.4645,0.9936,8.0158,0.5322,-0.077,9.7919,0.2211,0.0843,0.055,-34.6,3.4,-40.1,1.489463984,0.45,-3.11,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,226078,2015-10-30 10:17:26:954,1446171446954.0 \n-0.8224,-0.4381,12.6677,0.534,0.0344,9.792,0.1038,-0.0953,-0.099,-34.6,3.4,-40,1.475152284,-0.2,-3.12,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,226180,2015-10-30 10:17:27:056,1446171447056.0 \n1.148,-0.267,11.4156,0.4762,0.1791,9.7934,-0.4007,0.4081,-0.3677,-34.7,2.9,-40,1.444085423,-1.58,-3.29,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,226281,2015-10-30 10:17:27:157,1446171447157.0 \n0.6333,0.486,7.1754,0.2893,0.1066,9.8018,0.1503,0.1051,0.1271,-34.3,2,-40,1.494350906,-0.7,-1.84,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,226384,2015-10-30 10:17:27:260,1446171447260.0 \n-0.3208,0.2119,7.9763,0.3215,-0.1386,9.8004,-0.1454,0.0415,0.0086,-34.2,2,-40.1,1.521403509,0.54,-1.94,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,226487,2015-10-30 10:17:27:363,1446171447363.0 \n-0.4058,0.7422,8.7927,0.3039,-0.2601,9.7985,0.0745,-0.033,0.1393,-33.8,2.4,-39.9,1.545489053,1.64,-1.73,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,226588,2015-10-30 10:17:27:464,1446171447464.0 \n-0.5195,-0.419,12.0416,0.3082,-0.2133,9.7995,0.2908,-0.0635,0.2004,-33.8,3,-40,1.50656821,1.25,-1.8,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,226689,2015-10-30 10:17:27:565,1446171447565.0 \n-0.0922,0.3986,8.9292,0.282,0.1601,9.8013,0.5424,0.2492,0.3787,-33.8,3.2,-40,1.459618853,-0.94,-1.65,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,226791,2015-10-30 10:17:27:667,1446171447667.0 \n0.0994,0.2131,9.5277,0.3464,0.0923,9.8001,0.0428,-0.0977,0.3751,-33.7,3,-40.1,1.467123769,-0.54,-2.02,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,226895,2015-10-30 10:17:27:771,1446171447771.0 \n0.1341,0.4609,8.7747,0.5894,0.0783,9.7886,-0.3335,0.077,-0.2114,-33.8,3,-40,1.46537844,-0.46,-3.45,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,227015,2015-10-30 10:17:27:891,1446171447891.0 \n-0.9625,0.6919,8.9388,0.5191,-0.1494,9.7918,0.0757,0.1124,-0.1222,-34.2,3.6,-39.9,1.464505775,0.84,-3.21,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,227121,2015-10-30 10:17:27:997,1446171447997.0 \n-0.7961,0.978,9.2057,0.4786,-0.0934,9.7945,0.0782,0.044,-0.1674,-34.4,3.8,-39.7,1.458746189,0.55,-2.8,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,227214,2015-10-30 10:17:28:090,1446171448090.0 \n-0.6716,-0.1616,10.6638,0.5695,0.16,9.7888,0.2224,0.0977,-0.0904,-34.5,3.5,-39.4,1.424537735,-0.93,-3.33,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,227302,2015-10-30 10:17:28:178,1446171448178.0 \n-0.7422,-1.5263,13.5823,0.4702,-0.0249,9.7953,-0.4545,0.1185,-0.2786,-34.5,2.9,-39.3,1.462585913,-0.64,-3.15,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,227403,2015-10-30 10:17:28:279,1446171448279.0 \n0.8332,0.091,8.6479,0.3912,0.2336,9.7961,0.0171,-0.099,0.0281,-34.4,2,-39.9,1.478817475,-1.36,-2.29,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,227506,2015-10-30 10:17:28:382,1446171448382.0 \n-0.1784,0.3496,7.5884,0.3474,0.0365,9.8004,-0.16,0.1014,-0.0171,-34.3,1.7,-40.1,1.498888762,-0.46,-2.33,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,227608,2015-10-30 10:17:28:484,1446171448484.0 \n-0.4992,0.5986,7.6136,0.3367,-0.0073,9.8009,-0.16,0.1014,-0.0171,-34.2,1.7,-40.4,1.504822881,-0.21,-2.03,36.814705,-119.748215,282.93,336.7455556,3.88,25.806452,89.06,17 / 17,227709,2015-10-30 10:17:28:585,1446171448585.0 \n-0.4764,-0.3795,13.1238,0.4935,-0.0406,9.7941,0.0098,-0.1674,0.2089,-34.2,2,-40.2,1.51372406,0.24,-2.88,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,227811,2015-10-30 10:17:28:687,1446171448687.0 \n0.9517,0.5986,8.9842,0.3465,0.2351,9.7977,-0.0648,0.0574,0.3702,-34.2,2.2,-39.8,1.48806772,-0.93,-2.56,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,227913,2015-10-30 10:17:28:789,1446171448789.0 \n0.0395,-0.0898,9.7157,0.4012,0.0637,9.7982,-0.1588,0.0379,0.2749,-34.2,2.6,-39.2,1.470439895,-0.37,-2.34,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,228015,2015-10-30 10:17:28:891,1446171448891.0 \n-0.3807,0.4142,8.7759,0.5354,-0.0918,9.7916,-0.3225,0.1197,-0.0867,-34.5,3,-39,1.470614428,-0.25,-3.43,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,228118,2015-10-30 10:17:28:994,1446171448994.0 \n-0.577,1.2282,8.0194,0.4827,-0.1479,9.7936,0.0623,0.1063,-0.1112,-34.7,3.5,-39,1.468694566,0.86,-2.82,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,228219,2015-10-30 10:17:29:095,1446171449095.0 \n-0.6967,0.8607,9.3434,0.4643,-0.0446,9.7956,0.0941,-0.022,-0.2358,-34.8,3.4,-39.1,1.485973325,0.26,-2.71,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,228321,2015-10-30 10:17:29:197,1446171449197.0 \n-1.1217,-0.3005,12.3744,0.4577,0.1463,9.7949,0.1356,-0.0171,-0.2114,-34.9,2.5,-39,1.471138027,-0.42,-2.88,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,228424,2015-10-30 10:17:29:300,1446171449300.0 \n-0.3807,-1.1863,12.6821,0.4809,0.1978,9.7929,-0.2578,0.0599,-0.259,-35,1.5,-38.6,1.477072146,-1.55,-2.9,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,228526,2015-10-30 10:17:29:402,1446171449402.0 \n-0.3771,-0.0539,8.9759,0.3958,0.1794,9.797,-0.314,0.0244,-0.1246,-35.4,0.2,-38.4,1.539205867,-1.54,-2.36,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,228627,2015-10-30 10:17:29:503,1446171449503.0 \n0.1724,0.6404,7.926,0.4897,0.0375,9.7943,-0.237,-0.1332,-0.0183,-35.8,-0.3,-38.1,1.566258471,-0.22,-2.86,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,228730,2015-10-30 10:17:29:606,1446171449606.0 \n0.2765,0.8739,8.7963,0.5878,-0.0248,9.789,0.0476,-0.0709,0.1173,-36.2,-0.4,-38,1.573763387,0.14,-3.44,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,228831,2015-10-30 10:17:29:707,1446171449707.0 \n0.0682,0.0215,9.973,0.5133,-0.0586,9.793,-0.0501,-0.0098,0.066,-37,-0.3,-37.4,1.577428578,0.34,-3,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,228934,2015-10-30 10:17:29:810,1446171449810.0 \n0.3675,-0.2454,9.6606,0.455,0.0432,9.796,-0.314,-0.0623,0.0513,-37.6,-0.2,-37.1,1.57219259,0.07,-2.94,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,229035,2015-10-30 10:17:29:911,1446171449911.0 \n-0.1281,-0.1389,10.009,0.5035,-0.2527,9.7905,-0.2138,-0.0367,0.2028,-38.8,0,-36.6,1.59784893,1.48,-2.94,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,229139,2015-10-30 10:17:30:015,1446171450015.0 \n-0.3232,-0.1149,9.1602,0.6153,-0.4343,9.7777,-0.1735,0.0391,-0.0159,-39.9,0.3,-35.9,1.612335163,2.32,-3.78,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,229239,2015-10-30 10:17:30:115,1446171450115.0 \n-0.5806,0.0479,8.8825,0.5569,-0.4476,9.7806,0.0941,0.1747,0.0403,-41.7,1.4,-34.2,1.587202422,2.62,-3.26,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,229342,2015-10-30 10:17:30:218,1446171450218.0 \n-0.5926,0.3627,8.9639,0.4554,-0.395,9.7881,0.0452,0.0696,-0.0086,-42.6,2.2,-33.6,1.558579022,2.37,-2.82,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,229447,2015-10-30 10:17:30:323,1446171450323.0 \n-0.8176,-0.7386,12.3852,0.5175,-0.3514,9.7867,0.2077,0.0049,0.099,-43.6,3.3,-32.5,1.528908425,2.05,-3.03,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,229545,2015-10-30 10:17:30:421,1446171450421.0 \n-0.4717,-1.6149,12.7826,0.4391,-0.5344,9.7822,-0.4679,0.3751,-0.1246,-44.1,4.7,-31.8,1.496968899,3.12,-2.57,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,229648,2015-10-30 10:17:30:524,1446171450524.0 \n0.4202,-0.3699,9.0321,0.3637,-0.4249,9.7907,-0.2896,-0.1759,-0.1613,-44,5.8,-31.4,1.464505775,2.5,-2.05,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,229749,2015-10-30 10:17:30:625,1446171450625.0 \n0.0946,0.1688,8.8837,0.4551,-0.5812,9.7788,-0.066,-0.0098,-0.0391,-43.6,7.6,-30.9,1.429948256,3.4,-2.66,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,229851,2015-10-30 10:17:30:727,1446171450727.0 \n0.1425,0.4034,9.0968,0.4698,-0.5429,9.7803,0.0806,-0.0684,-0.0134,-43.2,8.5,-30.4,1.398706863,3.17,-2.75,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,229953,2015-10-30 10:17:30:829,1446171450829.0 \n-0.3567,-0.4956,10.8912,0.4605,-0.4308,9.7864,0.2602,-0.0012,0.0941,-42.6,9.4,-29.6,1.390154749,2.52,-2.69,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,230056,2015-10-30 10:17:30:932,1446171450932.0 \n-0.1975,-0.6752,9.6283,0.4012,-0.1489,9.7973,0.3604,0.1283,0.2615,-42.1,9.9,-29.4,1.345997919,1.3,-2.57,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,230158,2015-10-30 10:17:31:034,1446171451034.0 \n-0.3041,-0.3172,9.5325,0.5716,-0.2164,9.7876,0.0208,-0.2676,0.2431,-41,10.8,-29.7,1.314058394,1.26,-3.34,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,230259,2015-10-30 10:17:31:135,1446171451135.0 \n-0.0431,0.1018,8.8059,0.7257,-0.3028,9.7751,-0.1417,0.1234,-0.1026,-40.1,11.3,-29.9,1.307600676,1.49,-4.3,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,230361,2015-10-30 10:17:31:237,1446171451237.0 \n-0.3508,0.5076,8.5114,0.5616,-0.3751,9.7834,-0.044,0.1625,-0.1283,-38.3,12,-30.1,1.281769803,2.27,-3.62,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,230463,2015-10-30 10:17:31:339,1446171451339.0 \n-0.1245,0.5986,9.1028,0.4847,-0.3091,9.7898,0.0648,0.0782,-0.1576,-37.1,11.8,-30.6,1.272519558,1.96,-2.96,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,230566,2015-10-30 10:17:31:442,1446171451442.0 \n0.097,-0.1018,10.1562,0.5297,-0.1735,9.7908,0.2456,0.1234,-0.0709,-35.5,10.8,-32,1.267458103,1.01,-3.1,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,230667,2015-10-30 10:17:31:543,1446171451543.0 \n-0.5207,-1.5754,13.362,0.4222,-0.455,9.787,-0.1845,0.3311,-0.1112,-34.5,9.3,-33.5,1.347394183,2.66,-2.47,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,230770,2015-10-30 10:17:31:646,1446171451646.0 \n0.486,0.0407,9.3194,0.3934,-0.4225,9.7896,0.0635,-0.0806,-0.0428,-34,8.4,-34.3,1.369734397,2.14,-2.05,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,230871,2015-10-30 10:17:31:747,1446171451747.0 \n-0.2969,0.48,8.8059,0.3742,-0.5806,9.7823,-0.066,0.1588,-0.1918,-33.5,7.4,-34.9,1.418952682,3.39,-2.19,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,230973,2015-10-30 10:17:31:849,1446171451849.0 \n0.1712,0.8464,9.0058,0.3992,-0.4694,9.7873,0.0819,-0.0586,-0.0696,-33.1,6.8,-35.2,1.411447766,3.02,-2.26,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,231076,2015-10-30 10:17:31:952,1446171451952.0 \n-0.2442,-0.5626,11.5975,0.4511,-0.3776,9.789,0.121,-0.0843,-0.0428,-33.2,5.6,-35.5,1.4254104,2.21,-2.64,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,231177,2015-10-30 10:17:32:053,1446171452053.0 \n0.1077,-1.2689,11.212,0.4459,-0.1873,9.7947,-0.0428,-0.1576,0.1772,-33.2,4.4,-35.8,1.466425638,1.09,-2.61,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,231280,2015-10-30 10:17:32:156,1446171452156.0 \n0.0287,0.413,8.3857,0.641,-0.2891,9.7814,0.0098,-0.4398,0.1295,-33.5,3.8,-36,1.480039206,1.79,-3.08,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,231382,2015-10-30 10:17:32:258,1446171452258.0 \n-0.4633,-0.0204,8.7831,0.7031,-0.5042,9.7684,-0.3702,0.044,-0.2334,-33.8,3.6,-35.6,1.506219144,2.95,-4.12,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,231483,2015-10-30 10:17:32:359,1446171452359.0 \n-0.7338,0.3184,8.6538,0.6483,-0.4848,9.7732,0.1222,0.1576,-0.1087,-34.2,3.6,-35.3,1.505521013,2.98,-4.06,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,231586,2015-10-30 10:17:32:462,1446171452462.0 \n-0.5219,0.091,10.1323,0.5648,-0.2819,9.7863,0.11,-0.0281,-0.1881,-34.5,3.2,-35,1.515294857,1.9,-3.38,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,231688,2015-10-30 10:17:32:564,1446171452564.0 \n0.5327,-0.1652,10.5919,0.6173,-0.1003,9.7867,0.022,0.1246,-0.1967,-35,2.1,-35.2,1.521403509,0.59,-3.61,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,231789,2015-10-30 10:17:32:665,1446171452665.0 \n-0.6009,-1.1875,11.2288,0.4009,-0.288,9.7942,-0.3787,0.27,-0.3751,-35,1.2,-35.3,1.568527399,1.45,-2.57,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,231891,2015-10-30 10:17:32:767,1446171452767.0 \n-0.2179,-0.5614,9.8869,0.4315,-0.4226,9.788,-0.3885,-0.0965,-0.2639,-35.2,0.6,-35.5,1.587900553,2.47,-2.52,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,231993,2015-10-30 10:17:32:869,1446171452869.0 \n-0.1377,0.4178,7.2628,0.3538,-0.5457,9.7851,-0.0855,-0.0623,-0.1038,-35.1,0.4,-35.8,1.632231916,3.19,-2.07,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,232096,2015-10-30 10:17:32:972,1446171452972.0 \n-0.2466,0.4166,9.3075,0.3727,-0.5373,9.7848,0.055,0.0171,0.055,-35.2,0.6,-36,1.601863187,3.14,-2.18,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,232198,2015-10-30 10:17:33:074,1446171453074.0 \n-0.3962,-0.6464,12.2284,0.3985,-0.417,9.7897,0.215,-0.1759,0.2272,-35.3,0.7,-35.9,1.594183739,2.75,-2.09,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,232299,2015-10-30 10:17:33:175,1446171453175.0 \n-0.8906,-1.822,14.1773,0.5661,-0.376,9.7831,-0.369,-0.1674,-0.077,-35.5,0.8,-35.7,1.570796327,1.52,-2.72,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,232402,2015-10-30 10:17:33:278,1446171453278.0 \n0.3436,0.3077,8.3582,0.5327,-0.3126,9.7872,0.2321,-0.0476,0.2505,-35.5,1.2,-35.6,1.582839099,2.13,-2.79,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,232503,2015-10-30 10:17:33:379,1446171453379.0 \n-0.0239,0.2682,7.6878,0.5237,-0.4569,9.782,-0.033,0.0428,-0.0684,-35.9,1.8,-35.3,1.562593279,2.67,-3.06,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,232605,2015-10-30 10:17:33:481,1446171453481.0 \n-0.1377,0.4992,8.0098,0.5314,-0.4078,9.7837,0.182,-0.0293,-0.0342,-35.9,2.3,-35.6,1.558404489,2.38,-3.11,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,232707,2015-10-30 10:17:33:583,1446171453583.0 \n-0.6452,-0.0982,10.6638,0.562,-0.3402,9.7846,0.0147,-0.0391,-0.1772,-35.9,2.3,-36.1,1.552819435,2.1,-3.18,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,232809,2015-10-30 10:17:33:685,1446171453685.0 \n0.8954,-0.0814,10.4435,0.6498,-0.029,9.7851,0.2981,-0.0574,-0.1637,-35.9,1.7,-36.9,1.520007246,0.43,-3.7,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,232912,2015-10-30 10:17:33:788,1446171453788.0 \n0.2143,0.176,7.7812,0.389,-0.2098,9.7967,0.2773,0.2358,-0.0525,-35.7,0.8,-37.3,1.565560339,1.23,-2.27,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,233013,2015-10-30 10:17:33:889,1446171453889.0 \n-0.3472,-0.164,9.1267,0.3615,-0.2191,9.7975,-0.0367,0,0.0134,-35.3,0.2,-37.5,1.589645883,0.96,-1.99,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,233116,2015-10-30 10:17:33:992,1446171453992.0 \n-0.5902,0.4812,7.9416,0.332,-0.2581,9.7976,-0.0635,0.0086,0.1698,-34.5,0,-38.1,1.602212253,1.51,-1.94,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,233217,2015-10-30 10:17:34:093,1446171454093.0 \n0.5279,0.5902,10.3322,0.5046,-0.2969,9.7892,-0.0965,-0.1161,0.1148,-34.3,0,-38.4,1.605528379,1.61,-2.83,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,233320,2015-10-30 10:17:34:196,1446171454196.0 \n-0.5171,-0.0898,10.9439,0.4806,-0.2175,9.7925,0.2187,0.2028,0.2749,-34.5,0.6,-38.3,1.566956602,1.27,-2.81,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,233421,2015-10-30 10:17:34:297,1446171454297.0 \n0.4334,-0.6692,11.6167,0.5085,-0.34,9.7876,-0.2883,-0.2676,0.3983,-34.6,1.1,-38.1,1.56922553,1.38,-2.43,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,233524,2015-10-30 10:17:34:400,1446171454400.0 \n0.0084,0.0072,9.068,0.7456,-0.5154,9.7647,-0.1649,-0.1796,0.0403,-34.7,2,-37.9,1.574985117,3.01,-4.37,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,233625,2015-10-30 10:17:34:501,1446171454501.0 \n-0.51,0.656,8.8059,0.6456,-0.603,9.7668,0.1588,-0.0195,0.0073,-35,3.1,-38,1.554739298,3.53,-3.78,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,233727,2015-10-30 10:17:34:603,1446171454603.0 \n-0.8308,0.2263,9.7815,0.5642,-0.3659,9.7836,0.2651,0.0208,0.0244,-35.1,3.4,-37.9,1.532050017,2.48,-3.3,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,233830,2015-10-30 10:17:34:706,1446171454706.0 \n-1.4904,-0.2729,10.6303,0.5105,-0.1324,9.7925,0.2382,0.0147,0.033,-34.9,3.1,-38,1.496270768,0.77,-2.98,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,233933,2015-10-30 10:17:34:809,1446171454809.0 \n0.0036,-1.3084,12.0704,0.5424,-0.0796,9.7913,-0.4936,0.1246,-0.2065,-34.7,2.5,-38,1.474454152,-0.26,-3.02,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,234034,2015-10-30 10:17:34:910,1446171454910.0 \n0.067,-0.1245,8.0493,0.4338,-0.167,9.7956,-0.2834,-0.1539,-0.0513,-34.4,2.1,-38.6,1.530130155,0.98,-2.54,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,234135,2015-10-30 10:17:35:011,1446171455011.0 \n0.0024,0.0563,8.983,0.5326,-0.3835,9.7847,-0.1014,-0.0562,0.011,-34.3,2.2,-38.9,1.554739298,2.08,-3.36,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,234238,2015-10-30 10:17:35:114,1446171455114.0 \n-0.1401,0.498,7.9847,0.457,-0.3252,9.7906,0.2114,0.1613,0.1038,-34.2,2.7,-39.2,1.519309114,1.9,-2.67,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,234339,2015-10-30 10:17:35:215,1446171455215.0 \n0.0551,-0.3041,11.376,0.4054,-0.2071,9.7961,0.2346,-0.1539,0.2663,-34.2,2.8,-39.3,1.504473815,1.21,-2.37,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,234441,2015-10-30 10:17:35:317,1446171455317.0 \n0.9732,-0.1041,8.7676,0.4421,0.0584,9.7965,0.4337,0.0611,0.3616,-34.2,2.7,-39.2,1.465552973,-0.58,-2.48,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,234544,2015-10-30 10:17:35:420,1446171455420.0 \n0.1844,-0.2813,8.8957,0.4765,-0.0516,9.7949,0.0538,-0.0867,0.2285,-34.1,2.5,-38.9,1.484053463,0.3,-2.79,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,234645,2015-10-30 10:17:35:521,1446171455521.0 \n0.0311,-0.2334,8.8526,0.3895,-0.2495,9.7957,-0.0806,0.2334,-0.1112,-34,2.7,-38.6,1.510058869,1.46,-2.28,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,234747,2015-10-30 10:17:35:623,1446171455623.0 \n0.1149,-0.0239,9.4439,0.3113,-0.2331,9.7989,0.1796,0.2199,-0.2896,-33.8,2.9,-38.9,1.512676863,1.57,-2.03,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,234850,2015-10-30 10:17:35:726,1446171455726.0 \n0.1233,-1.0822,10.7129,0.1577,0.051,9.8053,0.4215,0.1918,-0.5412,-33.6,2.4,-39.8,1.504648348,-0.3,-0.92,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,234951,2015-10-30 10:17:35:827,1446171455827.0 \n0.9002,-0.7769,7.9871,0.0993,0.5282,9.7919,0.2407,0.0122,-0.7807,-33.3,1,-40.3,1.47375602,-3.09,-0.58,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,235056,2015-10-30 10:17:35:932,1446171455932.0 \n1.9728,-0.091,8.0601,-0.2559,0.5414,9.7884,0.2761,0.1686,-1.0507,-32.4,-1.8,-41,1.564164076,-3.16,1.5,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,235157,2015-10-30 10:17:36:033,1446171456033.0 \n1.3587,-1.1205,9.6594,-0.4364,0.6687,9.7741,0.2737,0.2651,-1.5553,-31.6,-4.3,-41.3,1.617222085,-3.51,1.76,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,235257,2015-10-30 10:17:36:133,1446171456133.0 \n1.0846,-0.8679,8.1307,-0.8304,0.8738,9.7323,0.4166,0.0965,-2.1649,-27.2,-12.5,-41,1.844114888,-5.11,4.88,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,235360,2015-10-30 10:17:36:236,1446171456236.0 \n-0.0982,-0.8583,9.6606,-0.9882,0.8128,9.7228,0.3348,-0.1857,-2.1087,-23.3,-17.3,-40.5,2.044304153,-4.77,5.9,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,235461,2015-10-30 10:17:36:337,1446171456337.0 \n-1.4222,-1.0523,10.1311,-0.9833,0.8093,9.7236,0.16,-0.2224,-2.116,-18.7,-21.8,-41,2.253220064,-4.73,5.77,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,235564,2015-10-30 10:17:36:440,1446171456440.0 \n-2.2338,-1.579,11.0816,-0.8467,0.8333,9.7344,-0.1955,-0.3299,-1.8851,-15.2,-25,-39.4,2.440842959,-4.87,4.97,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,235666,2015-10-30 10:17:36:542,1446171456542.0 \n-2.1691,-1.3671,9.8474,-0.543,0.6725,9.7685,-0.1442,-0.4142,-1.3158,-12.9,-25.8,-38.4,2.551147768,-4.38,3.78,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,235767,2015-10-30 10:17:36:643,1446171456643.0 \n-1.9381,-0.9062,8.9699,-0.3634,0.5378,9.7851,-0.1759,-0.2431,-0.7624,-11.3,-26.7,-39.3,2.677335073,-3.14,2.13,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,235872,2015-10-30 10:17:36:748,1446171456748.0 \n-2.9305,-1.0056,9.402,-0.356,0.2949,9.7957,-0.1943,0.0244,-0.7831,-9.4,-26.9,-39.4,2.758492883,-1.72,2.08,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,235972,2015-10-30 10:17:36:848,1446171456848.0 \n-2.5462,-0.1927,9.6355,-0.3927,0.0205,9.7988,-0.3115,0.0257,-0.3616,-7.5,-26.4,-39.7,2.821324736,-0.12,2.29,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,236074,2015-10-30 10:17:36:950,1446171456950.0 \n-1.3934,1.0235,9.7468,-0.2022,-0.2244,9.802,-0.2065,-0.0379,-0.1833,-6.8,-25.8,-40.5,2.856929453,1.16,1.21,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,236176,2015-10-30 10:17:37:052,1446171457052.0 \n-1.2318,1.3048,9.0237,-0.1774,-0.2555,9.8017,0.0464,-0.0757,0.0855,-6.5,-24.8,-41.2,2.897770157,1.91,0.78,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,236277,2015-10-30 10:17:37:153,1446171457153.0 \n-1.0319,1.7609,8.3833,-0.2319,-0.1219,9.8031,0.0525,0.0977,0.0061,-6.5,-24.5,-41.5,2.869844889,0.82,1.19,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,236379,2015-10-30 10:17:37:255,1446171457255.0 \n-1.1265,1.0546,9.4966,-0.3035,-0.0564,9.8018,-0.0977,0.0134,-0.1417,-6.8,-24.3,-41,2.812947155,0.33,1.77,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,236483,2015-10-30 10:17:37:359,1446171457359.0 \n-0.0096,0.2753,10.228,-0.2795,-0.105,9.8021,0.2089,0.0073,-0.0367,-6.6,-24.4,-40.6,2.819055808,0.61,1.63,36.814724,-119.74807,286.96,336.7455556,4.33,19.35484,88.4,17 / 17,236583,2015-10-30 10:17:37:459,1446171457459.0 \n-0.6632,-1.0427,12.8293,-0.2504,-0.1667,9.802,-0.3299,0.0024,-0.4814,-6.4,-24.3,-40.3,2.864434368,0.97,1.46,36.8147,-119.74797,290.21,336.7455556,2.37,19.35484,150.27,17 / 17,236685,2015-10-30 10:17:37:561,1446171457561.0 \n-0.923,-0.6788,9.6163,-0.3034,-0.1092,9.8013,-0.066,-0.077,-0.3445,-5.5,-24.4,-40.3,2.891836038,0.64,1.77,36.8147,-119.74797,290.21,336.7455556,2.37,19.35484,150.27,17 / 17,236788,2015-10-30 10:17:37:664,1446171457664.0 \n-0.4597,0.4848,8.4491,-0.2374,-0.0579,9.8036,0.1002,-0.0489,0.0098,-5,-24.5,-40.3,2.893581367,0.4,1.65,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,236889,2015-10-30 10:17:37:765,1446171457765.0 \n-0.1305,1.1277,8.3474,-0.1629,0.1416,9.8043,0.4056,0.0562,0.1649,-4.7,-24.8,-40.1,2.913652653,-0.83,0.95,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,236992,2015-10-30 10:17:37:868,1446171457868.0 \n-1.1372,0.1137,11.4874,-0.2159,0.3516,9.798,0.2077,0.0208,0.27,-4.8,-25.2,-39.9,2.900039085,-1.68,1.25,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,237094,2015-10-30 10:17:37:970,1446171457970.0 \n0.2789,-0.8212,11.8429,-0.1483,0.5294,9.7912,-0.452,-0.3457,0.0513,-5.3,-26,-39.6,2.910336528,-3.09,0.87,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,237196,2015-10-30 10:17:38:072,1446171458072.0 \n-0.0371,1.057,7.7656,-0.004,0.4903,9.7944,0.2957,-0.0098,0.4459,-6,-26.5,-39.1,2.895501229,-2.48,0.15,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,237298,2015-10-30 10:17:38:174,1446171458174.0 \n-0.0239,0.516,8.6359,0.0605,0.4138,9.7977,0.1466,-0.1478,0.1686,-7,-26.9,-38.7,2.880840463,-2.42,-0.35,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,237399,2015-10-30 10:17:38:275,1446171458275.0 \n-0.747,0.7985,7.616,0.0672,0.5738,9.7896,0.1833,-0.0696,-0.0171,-7.6,-26.9,-38.7,2.837905364,-3.35,-0.39,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,237502,2015-10-30 10:17:38:378,1446171458378.0 \n-0.911,-0.0371,10.5872,0.1037,0.7594,9.7767,0.1808,0.0476,-0.0452,-8,-27.2,-38.2,2.830574981,-4.31,-0.4,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,237604,2015-10-30 10:17:38:480,1446171458480.0 \n0.0874,0.4298,9.5397,0.0996,0.8929,9.7654,0.1723,0.0696,-0.0024,-8.3,-27.6,-38.1,2.84366495,-4.99,-0.68,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,237705,2015-10-30 10:17:38:581,1446171458581.0 \n0.0359,0.261,9.5038,0.0595,0.6829,9.7827,0.3726,0.0012,0.1637,-8,-27.9,-37.6,2.847679208,-3.41,-0.34,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,237808,2015-10-30 10:17:38:684,1446171458684.0 \n-0.3184,0.6105,9.6678,0.1419,0.5168,9.792,-0.1552,0.0452,-0.0269,-7.8,-27.9,-37.6,2.86216544,-3.02,-0.83,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,237910,2015-10-30 10:17:38:786,1446171458786.0 \n-0.5519,1.0355,8.1511,0.0765,0.4776,9.7947,-0.0171,0.011,-0.0318,-7.7,-27.3,-37.7,2.844014016,-2.79,-0.45,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,238012,2015-10-30 10:17:38:888,1446171458888.0 \n-1.0104,0.4334,10.3262,0.0428,0.5379,9.7918,0.0538,0.0574,0.0379,-7.7,-27.4,-37.7,2.840523358,-3.11,-0.4,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,238114,2015-10-30 10:17:38:990,1446171458990.0 \n-0.2885,0.6141,8.9567,-0.0421,0.7205,9.7801,0.1087,-0.0403,0.292,-7.8,-27.4,-37.7,2.815390616,-4.21,0.25,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,238215,2015-10-30 10:17:39:091,1446171459091.0 \n-1.2713,-0.7769,12.7,0.1211,0.4691,9.7947,-0.5143,-0.1197,0.0476,-8.1,-27.6,-37.4,2.861292776,-2.74,-0.71,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,238318,2015-10-30 10:17:39:194,1446171459194.0 \n-0.7123,0.0922,9.1243,0.2354,0.3582,9.7973,-0.3213,-0.1662,-0.0012,-8.9,-27.7,-37.2,2.835461903,-2.61,-1.08,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,238420,2015-10-30 10:17:39:296,1446171459296.0 \n-0.7518,0.8475,8.4563,0.313,0.4053,9.7933,0.2871,0.0941,0.1381,-9.8,-27.5,-37.5,2.808060234,-2.37,-1.83,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,238522,2015-10-30 10:17:39:398,1446171459398.0 \n-0.3795,0.996,8.6335,0.3177,0.6129,9.7823,0.1784,-0.0965,-0.0122,-10.5,-27.4,-37.7,2.797413725,-3.38,-1.72,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,238624,2015-10-30 10:17:39:500,1446171459500.0 \n-0.3077,0.2777,10.4244,0.3331,0.6743,9.7778,0.1442,0.0452,-0.0696,-11,-27.6,-37.4,2.778215103,-3.7,-1.99,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,238725,2015-10-30 10:17:39:601,1446171459601.0 \n-0.5531,-0.9134,11.5628,0.3752,0.4314,9.79,-0.2859,0.237,-0.2749,-11.1,-27.9,-37,2.792701336,-2.52,-2.19,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,238828,2015-10-30 10:17:39:704,1446171459704.0 \n-0.0587,-0.2263,8.9998,0.334,0.4402,9.7911,-0.3372,-0.1148,-0.099,-10.9,-27.7,-37.1,2.787116283,-2.57,-1.95,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,238930,2015-10-30 10:17:39:806,1446171459806.0 \n-0.4872,0.6883,7.5872,0.3012,0.213,9.7997,-0.0428,0.1503,0.0538,-10.6,-27.1,-37.2,2.781531229,-1.24,-1.76,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,239032,2015-10-30 10:17:39:908,1446171459908.0 \n-0.0239,0.9493,8.2001,0.3094,0.2189,9.7993,0.0195,-0.0024,0.0794,-10.5,-26.8,-37.3,2.816612347,-1.22,-1.81,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,239134,2015-10-30 10:17:40:010,1446171460010.0 \n-0.7781,-0.4345,12.1566,0.2838,0.22,9.8001,0.0073,0.0134,-0.0073,-10.6,-26.3,-37.1,2.765823266,-1.29,-1.66,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,239236,2015-10-30 10:17:40:112,1446171460112.0 \n-0.3603,-0.9134,12.3086,0.2289,0.2966,9.7995,-0.0745,-0.0794,0.1869,-10.7,-26.2,-37,2.754653158,-1.73,-1.34,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,239337,2015-10-30 10:17:40:213,1446171460213.0 \n-0.2167,0.1867,8.8442,0.3773,0.359,9.7928,0.1747,-0.2382,0.1698,-11.3,-25.9,-36.6,2.77088472,-2.1,-2.21,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,239440,2015-10-30 10:17:40:316,1446171460316.0 \n-0.2801,0.1748,8.9016,0.3709,0.2944,9.7952,0.0648,0.0501,0.0354,-11.8,-25.9,-36.3,2.741214123,-1.75,-2.32,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,239541,2015-10-30 10:17:40:417,1446171460417.0 \n-0.413,0.6345,8.163,0.3301,0.4085,9.7926,0.237,0.1148,0.0733,-12.4,-25.7,-36,2.726553357,-2.39,-1.93,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,239644,2015-10-30 10:17:40:520,1446171460520.0 \n-0.0838,0.8715,8.0505,0.3743,0.6394,9.7786,0.215,0.1222,-0.0049,-12.5,-25.7,-35.9,2.720444705,-2.7,-1.79,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,239746,2015-10-30 10:17:40:622,1446171460622.0 \n0.4369,-0.589,11.8034,0.4223,0.7122,9.7716,-0.3335,0.2395,-0.4875,-12.5,-26.1,-35.5,2.719921106,-4.16,-2.47,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,239847,2015-10-30 10:17:40:723,1446171460723.0 \n0.5662,0.6225,7.1419,0.1266,0.6519,9.7841,0.0061,0.1222,-0.1723,-11.6,-26.1,-35.4,2.686759851,-3.81,-0.74,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,239949,2015-10-30 10:17:40:825,1446171460825.0 \n-0.4549,0.1628,8.9723,0.1236,0.5079,9.7927,-0.1576,-0.0794,-0.259,-10.9,-25.9,-35.2,2.730218549,-3.12,-0.83,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,240051,2015-10-30 10:17:40:927,1446171460927.0 \n-0.8272,0.8679,7.4412,0.0359,0.5469,9.7913,0.0538,-0.044,-0.0379,-10.1,-25.6,-35.2,2.750987967,-3.14,-0.16,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,240153,2015-10-30 10:17:41:029,1446171461029.0 \n-1.0092,0.4334,10.9619,0.0186,0.5302,9.7923,-0.0513,0.022,0.0257,-9.3,-25,-35.2,2.772106451,-3.1,-0.11,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,240255,2015-10-30 10:17:41:131,1446171461131.0 \n-0.5267,0.3639,11.1342,-0.0083,0.6465,9.7853,0.2443,0.0073,0.2651,-9,-24.8,-35.3,2.775073511,-3.3,-0.32,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,240358,2015-10-30 10:17:41:234,1446171461234.0 \n-0.583,0.4274,9.7061,0.0898,0.5381,9.7915,-0.066,-0.0831,0.1686,-9.1,-24.5,-35.4,2.766521397,-3.15,-0.53,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,240471,2015-10-30 10:17:41:347,1446171461347.0 \n-0.8978,-0.1999,9.7995,0.3106,0.6148,9.7824,-0.2456,-0.0086,-0.0806,-9.5,-24.3,-35.3,2.793748534,-3.59,-1.82,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,240562,2015-10-30 10:17:41:438,1446171461438.0 \n-0.5363,0.7817,7.6902,0.2337,0.5479,9.7885,0.0867,0.0757,-0.0501,-9.9,-24.1,-35.4,2.74697371,-3.2,-1.37,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,240663,2015-10-30 10:17:41:539,1446171461539.0 \n-0.9613,0.8128,9.159,0.084,0.5054,9.7933,-0.0183,0.0599,-0.0977,-10,-23.6,-35.4,2.734058273,-2.91,-0.69,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,240766,2015-10-30 10:17:41:642,1446171461642.0 \n-1.1612,0.0922,11.5712,0.201,0.4981,9.7919,0.2847,0.16,0.0281,-9.6,-23.3,-35.5,2.728647753,-2.91,-1.18,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,240867,2015-10-30 10:17:41:743,1446171461743.0 \n-1.1648,-0.7841,12.0357,0.1308,0.5458,9.7906,-0.1906,0.1698,-0.1918,-8.9,-23.2,-35.6,2.755525823,-3.19,-0.77,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,240970,2015-10-30 10:17:41:846,1446171461846.0 \n-0.012,0.0766,8.4036,0.0326,0.4155,9.7978,-0.0098,0.0428,0.0806,-8.3,-23.1,-35.5,2.785021887,-2.87,-0.16,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,241072,2015-10-30 10:17:41:948,1446171461948.0 \n-0.3124,1.057,6.6547,-0.0693,0.3107,9.8015,-0.1478,0.2004,0.1173,-7.7,-22.8,-35.3,2.781182163,-1.82,0.41,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,241174,2015-10-30 10:17:42:050,1446171462050.0 \n-0.7386,0.3855,9.675,-0.0855,0.1179,9.8056,-0.2346,-0.1136,0.0965,-7.4,-22.4,-35.3,2.815216083,-0.69,0.5,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,241275,2015-10-30 10:17:42:151,1446171462151.0 \n-1.1337,-0.1939,12.0105,-0.1698,0.1856,9.8034,0.0024,0.2773,0.2541,-7.4,-21.6,-35.5,2.799159054,-1.08,0.99,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,241377,2015-10-30 10:17:42:253,1446171462253.0 \n0.1353,-1.1468,10.8912,0.0324,0.2611,9.8031,-0.4313,-0.3897,0.0281,-7.6,-21.4,-35.5,2.742610387,-2.26,0.43,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,241480,2015-10-30 10:17:42:356,1446171462356.0 \n-0.3723,0.6273,7.9583,0.0558,0.1968,9.8045,-0.0073,-0.1197,0.1258,-8.1,-21.3,-35.6,2.774549912,-1.15,-0.33,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,241582,2015-10-30 10:17:42:458,1446171462458.0 \n-0.6404,0.0946,8.8202,0.1193,0.0745,9.8056,0.0721,-0.022,0.0464,-8.9,-21.2,-35.8,2.749940769,-0.44,-0.7,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,241683,2015-10-30 10:17:42:559,1446171462559.0 \n-0.7266,0.6117,7.5561,0.0644,0.1493,9.8053,0.182,0.1234,0.0941,-9.1,-21.2,-35.9,2.736676267,-0.87,-0.38,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,241786,2015-10-30 10:17:42:662,1446171462662.0 \n-1.0127,0.2646,9.6079,0.0772,0.2067,9.8042,-0.022,-0.2419,-0.1258,-8.9,-21.3,-36.1,2.727600555,-1.27,-0.2,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,241888,2015-10-30 10:17:42:764,1446171462764.0 \n-0.3244,-0.3783,11.6262,0.1117,0.2886,9.8018,0.1588,0.077,-0.0269,-8.7,-21.5,-36,2.743308518,-1.27,-0.8,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,241989,2015-10-30 10:17:42:865,1446171462865.0 \n-0.2023,-0.5028,11.8573,-0.0062,0.1757,9.8051,-0.3738,0.1136,-0.2358,-8.5,-21.7,-36,2.782229361,-1.03,0.04,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,242091,2015-10-30 10:17:42:967,1446171462967.0 \n-0.6536,-0.2729,10.2963,-0.0264,0.0284,9.8066,-0.3213,-0.1784,-0.1368,-8,-21.5,-36.2,2.771931918,-0.17,0.15,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,242194,2015-10-30 10:17:43:070,1446171463070.0 \n-0.7494,0.5806,8.0792,-0.0467,-0.0127,9.8065,0.0538,-0.0623,0.0037,-7.5,-21.3,-36.9,2.812947155,0.07,0.27,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,242295,2015-10-30 10:17:43:171,1446171463171.0 \n-0.1425,0.9756,8.9615,0.0049,0.0943,9.8062,0.1283,-0.0305,0.0354,-7.1,-21,-37.2,2.814517952,-0.41,0.05,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,242398,2015-10-30 10:17:43:274,1446171463274.0 \n-0.559,-0.2095,11.4718,0.0557,0.2125,9.8042,0.2224,-0.088,0.0709,-7.1,-21.1,-37,2.816437814,-0.88,-0.17,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,242499,2015-10-30 10:17:43:375,1446171463375.0 \n-0.8068,-1.3048,13.8888,0.1653,0.2863,9.8011,-0.4105,-0.2089,-0.0745,-7.1,-21.5,-36.7,2.831622178,-1.67,-0.97,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,242601,2015-10-30 10:17:43:477,1446171463477.0 \n-0.164,0.577,8.9842,0.2434,0.213,9.8013,0.1539,-0.1014,0.2395,-7.2,-21.6,-36.7,2.85797665,-0.91,-1.18,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,242703,2015-10-30 10:17:43:579,1446171463579.0 \n-0.5962,0.2753,8.9962,0.3297,0.0856,9.8007,-0.1564,-0.0696,-0.0183,-7.6,-21.6,-36.7,2.836334567,-0.48,-1.8,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,242806,2015-10-30 10:17:43:682,1446171463682.0 \n-1.0259,0.498,8.9388,0.2524,0.1936,9.8015,0.2553,0.0929,0.0257,-7.8,-21.5,-37,2.819928472,-0.79,-1.81,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,242908,2015-10-30 10:17:43:784,1446171463784.0 \n-0.8691,-0.103,11.1654,0.138,0.3488,9.7995,0.1686,-0.0648,-0.0819,-7.7,-21.6,-37.2,2.794446665,-2.04,-0.81,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,243010,2015-10-30 10:17:43:886,1446171463886.0 \n0.5495,-0.1496,10.1993,0.0697,0.5921,9.7885,0.2932,0.1381,0.0476,-7.2,-22.1,-37.2,2.812423557,-3.46,-0.41,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,243111,2015-10-30 10:17:43:987,1446171463987.0 \n-0.492,-0.2813,10.5237,-0.1012,0.3839,9.7986,0.0305,0.1527,0.0318,-6.7,-22.5,-37.1,2.804220509,-2.24,0.32,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,243213,2015-10-30 10:17:44:089,1446171464089.0 \n-0.656,-0.0096,9.754,-0.0034,0.1817,9.805,-0.27,-0.2114,-0.0867,-5.9,-22.5,-37.5,2.866528763,-1.06,0.02,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,243315,2015-10-30 10:17:44:191,1446171464191.0 \n-0.9816,0.4645,8.8358,0.0313,0.0201,9.8066,-0.0892,0.0183,0.0379,-5.6,-22.1,-37.7,2.879618733,-0.12,-0.18,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,243418,2015-10-30 10:17:44:294,1446171464294.0 \n-0.7757,0.0802,10.9212,0.0799,0.0664,9.8061,-0.0305,-0.0293,0.1319,-5.5,-21.5,-38,2.919237707,-0.39,-0.47,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,243520,2015-10-30 10:17:44:396,1446171464396.0 \n-0.8607,0.1341,11.9387,0.0588,0.3157,9.8014,0.4643,0.1539,0.4557,-5.8,-21.3,-38.2,2.871939284,-1.1,-0.6,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,243622,2015-10-30 10:17:44:498,1446171464498.0 \n-1.7214,-1.1576,12.1829,0.1345,0.2591,9.8023,-0.3763,-0.2749,0.0391,-6.4,-21.7,-37.8,2.886250984,-1.51,-0.79,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,243723,2015-10-30 10:17:44:599,1446171464599.0 \n-0.4513,0.5974,8.8454,0.3174,0.2625,9.798,-0.0305,-0.2944,0.1271,-6.9,-22,-37.8,2.861292776,-1.67,-1.49,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,243826,2015-10-30 10:17:44:702,1446171464702.0 \n-0.3077,0.5662,8.2935,0.3066,0.2135,9.7995,0.1246,-0.0159,-0.0476,-7.6,-22.3,-37.4,2.82935325,-1.25,-1.79,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,243927,2015-10-30 10:17:44:803,1446171464803.0 \n-0.5375,0.6716,8.8011,0.221,0.4127,9.7955,0.0367,-0.0024,-0.1539,-7.9,-22.6,-37.2,2.818881275,-2.41,-1.29,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,244030,2015-10-30 10:17:44:906,1446171464906.0 \n-0.4681,0.1844,11.746,0.2507,0.5084,9.7903,0.1833,-0.077,-0.1808,-7.8,-23,-36.8,2.82097567,-2.62,-1.45,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,244132,2015-10-30 10:17:45:008,1446171465008.0 \n-0.4058,-0.1006,10.8397,0.1025,0.5691,9.7896,-0.1784,0.2663,-0.3225,-7,-23.8,-36.1,2.847504675,-3.33,-0.6,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,244234,2015-10-30 10:17:45:110,1446171465110.0 \n-0.2981,0.9601,7.7608,-0.2218,0.3707,9.7971,-0.1784,-0.0391,-0.1503,-6.3,-24,-36,2.851867998,-2.18,1.19,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,244335,2015-10-30 10:17:45:211,1446171465211.0 \n-0.6476,0.2682,9.3649,-0.1068,0.0615,9.8059,-0.3714,-0.2114,-0.281,-5.3,-23.5,-36.3,2.909114797,-0.36,0.62,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,244437,2015-10-30 10:17:45:313,1446171465313.0 \n-1.0427,0.5878,8.6802,-0.1369,0.1283,9.8049,0.1625,-0.0501,-0.0061,-4.9,-22.9,-36.4,2.902482546,-0.46,0.85,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,244540,2015-10-30 10:17:45:416,1446171465416.0 \n-0.7793,0.3747,10.5177,-0.161,0.2346,9.8025,0.2602,0.0232,0.1906,-4.7,-22.4,-36,2.882934858,-1.37,0.94,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,244641,2015-10-30 10:17:45:517,1446171465517.0 \n-0.7673,0.5471,11.1318,-0.1719,0.5258,9.791,0.3641,-0.0012,0.259,-4.9,-22.5,-35.3,2.876302607,-2.39,0.95,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,244743,2015-10-30 10:17:45:619,1446171465619.0 \n-1.4257,-0.5207,10.6243,-0.1006,0.4619,9.7953,-0.1466,-0.0147,0.1417,-5.2,-23,-34.1,2.897246558,-2.77,0.54,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,244846,2015-10-30 10:17:45:722,1446171465722.0 \n0.0455,0.7087,8.2947,0.0958,0.5069,9.7931,-0.3238,-0.0611,-0.077,-5.5,-23.2,-33,2.914525318,-3.27,-0.22,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,244947,2015-10-30 10:17:45:823,1446171465823.0 \n-0.8188,0.723,9.3362,0.0747,0.4162,9.7975,0.1466,0.077,-0.1038,-5.9,-23,-32,2.883982056,-2.32,-0.51,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,245050,2015-10-30 10:17:45:926,1446171465926.0 \n-0.4932,1.2725,8.5916,0.0262,0.571,9.79,0.1918,0.0024,-0.1038,-5.9,-22.6,-32.2,2.868274093,-3.34,-0.15,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,245152,2015-10-30 10:17:46:028,1446171466028.0 \n-0.9074,0.5902,10.5728,0.1193,0.7241,9.7792,0.3005,0.0892,-0.2553,-5.2,-22.1,-32.3,2.910336528,-4.23,-0.7,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,245254,2015-10-30 10:17:46:130,1446171466130.0 \n-0.5543,-0.3747,11.0061,-0.0801,0.7125,9.7804,-0.4655,0.2761,-0.4288,-4.2,-22.1,-32.2,2.934422071,-4.88,0.06,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,245355,2015-10-30 10:17:46:231,1446171466231.0 \n0.2298,0.9421,7.9057,-0.2427,0.6994,9.7787,0.2688,0.1234,0.1796,-2.6,-22,-32.4,2.951002699,-4.09,1.42,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,245457,2015-10-30 10:17:46:333,1446171466333.0 \n-0.2717,1.0235,7.8853,-0.1857,0.4954,9.7924,-0.1222,0.0745,0.0757,-1.7,-22,-33,3.015230816,-3.11,0.98,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,245560,2015-10-30 10:17:46:436,1446171466436.0 \n-0.4956,0.9457,8.6658,-0.1524,0.4417,9.7955,0.0171,-0.0977,0.0342,-0.8,-21.7,-34.3,3.066892562,-2.58,0.89,36.8147,-119.74797,290.21,336.8387955,2.37,19.35484,150.27,17 / 17,245661,2015-10-30 10:17:46:537,1446171466537.0 \n-0.8739,0.0646,10.7955,-0.103,0.5231,9.7921,0.0745,0.0232,0.0672,-0.5,-21.8,-35.5,3.1216959,-2.67,0.66,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,17 / 17,245764,2015-10-30 10:17:46:640,1446171466640.0 \n-0.8595,0.577,9.262,-0.0698,0.6856,9.7824,-0.0379,0.0648,0.2224,-0.4,-22,-36.2,3.130771612,-4.11,0.34,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,17 / 17,245866,2015-10-30 10:17:46:742,1446171466742.0 \n-0.2705,1.0211,8.6526,-0.0237,0.3191,9.8014,-0.0929,-0.3262,0.4386,-0.6,-22.3,-36.8,3.089232776,-1.86,0.14,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,17 / 17,245968,2015-10-30 10:17:46:844,1446171466844.0 \n-0.6285,0.2095,9.5828,0.1876,0.0848,9.8045,-0.3543,-0.0794,0.1857,-1,-22.3,-37.5,3.128677217,-1.09,-1.12,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,17 / 17,246069,2015-10-30 10:17:46:945,1446171466945.0 \n-0.5974,0.6931,8.1092,0.2543,0.0916,9.8029,0.182,-0.055,0.1759,-1.7,-21.6,-38.8,3.09185077,-0.21,-1.34,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,17 / 17,246172,2015-10-30 10:17:47:048,1446171467048.0 \n-0.0682,0.1844,11.0109,0.3722,0.1985,9.7976,0.1698,-0.1393,0.011,-2,-21.5,-39.7,3.117856176,-1.16,-2.18,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,17 / 17,246273,2015-10-30 10:17:47:149,1446171467149.0 \n-0.2753,-0.1269,10.0305,0.4597,0.4242,9.7867,-0.0244,-0.2395,-0.0061,-1.8,-22,-40,3.135658534,-2.48,-2.69,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,17 / 17,246375,2015-10-30 10:17:47:251,1446171467251.0 \n-0.5662,-0.9924,12.5863,0.545,0.148,9.7904,-0.6035,0.204,-0.2492,-1.4,-23.2,-40.1,3.196221459,-0.86,-3.19,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,17 / 17,246478,2015-10-30 10:17:47:354,1446171467354.0 \n-1.2617,-0.9301,10.1694,0.2753,-0.1675,9.8014,-0.3543,0.1197,-0.4325,-0.7,-24,-40.9,3.147701306,0.98,-1.61,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,17 / 17,246580,2015-10-30 10:17:47:456,1446171467456.0 \n-0.9421,0.1951,7.8482,-0.0052,-0.3059,9.8019,-0.0819,0.1991,-0.0257,-0.2,-24.3,-41.5,3.153460893,1.58,-0.42,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,17 / 17,246681,2015-10-30 10:17:47:557,1446171467557.0 \n-0.6357,0.0455,10.0999,-0.0079,-0.4335,9.7971,-0.193,-0.0489,-0.0525,0.4,-24.4,-42.1,3.14019639,2.53,0.05,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,16 / 17,246785,2015-10-30 10:17:47:661,1446171467661.0 \n-0.4573,-0.2095,11.5053,0.0705,-0.3618,9.7997,0.1906,-0.1527,0.2053,0.5,-24.8,-42,3.183480556,2.47,-0.17,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,16 / 17,246885,2015-10-30 10:17:47:761,1446171467761.0 \n-0.662,-1.4736,12.9323,0.1171,-0.3158,9.8009,-0.3103,-0.2981,0.1503,-0.3,-25.6,-40.9,3.159569545,1.85,-0.68,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,16 / 17,246988,2015-10-30 10:17:47:864,1446171467864.0 \n-0.079,0.176,8.7652,0.1556,-0.3016,9.8008,0.2346,0.0269,0.358,-1.3,-26.3,-40.3,3.128153618,1.76,-0.91,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,16 / 17,247090,2015-10-30 10:17:47:966,1446171467966.0 \n-0.6057,-0.2634,9.2308,0.1494,-0.4683,9.7943,-0.2871,0.077,-0.1332,-3.4,-27,-39.5,3.058340448,2.74,-0.87,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,16 / 17,247191,2015-10-30 10:17:48:067,1446171468067.0 \n-0.4214,0.5399,7.8039,0.0584,-0.3864,9.7989,0.1417,0.099,0.0403,-4.4,-26.9,-39.4,3.01488175,2.49,-0.51,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,16 / 17,247294,2015-10-30 10:17:48:170,1446171468170.0 \n-0.8368,-0.4884,10.9834,0.0391,-0.3235,9.8012,0.0586,-0.1918,-0.2663,-5,-26.7,-39.2,2.97194665,1.89,-0.23,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,16 / 17,247396,2015-10-30 10:17:48:272,1446171468272.0 \n-0.7087,-0.5602,11.1474,0.1373,-0.1079,9.8051,0.314,0.0293,-0.0513,-5.1,-26.8,-38.9,2.984338488,1.39,-0.83,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,16 / 17,247497,2015-10-30 10:17:48:373,1446171468373.0 \n-0.9062,-1.5909,11.7615,0.1095,-0.1628,9.8047,-0.0086,0.2737,-0.1613,-5.2,-27.3,-38,2.977531704,0.95,-0.64,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,16 / 17,247600,2015-10-30 10:17:48:476,1446171468476.0 \n-0.0766,-0.516,9.0489,0.0567,-0.0213,9.8065,-0.2248,-0.1356,-0.0855,-5,-27.8,-37.1,2.972819315,0.12,-0.33,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,14 / 17,247702,2015-10-30 10:17:48:578,1446171468578.0 \n-0.7554,0.1628,8.8526,0.1043,-0.1901,9.8043,-0.2016,0.0415,-0.11,-5,-28,-36.9,2.982593159,1.11,-0.61,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,14 / 17,247803,2015-10-30 10:17:48:679,1446171468679.0 \n-0.079,0.7697,9.2285,0.1589,-0.2409,9.8024,-0.0672,-0.0709,-0.0159,-5.1,-27.7,-37,2.99044714,1.41,-0.93,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,14 / 17,247906,2015-10-30 10:17:48:782,1446171468782.0 \n-0.929,-0.4705,11.9507,0.1624,-0.2219,9.8028,0.2395,-0.1161,0.1576,-5.4,-27.4,-37.1,2.985211153,1.3,-0.95,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,14 / 17,248007,2015-10-30 10:17:48:883,1446171468883.0 \n-0.583,-1.3539,12.3565,0.2385,-0.1024,9.8032,-0.2077,-0.0134,0.121,-5.9,-27.6,-36.6,2.95641322,0.07,-1.15,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,14 / 17,248109,2015-10-30 10:17:48:985,1446171468985.0 \n-0.5866,0.1604,8.7281,0.2595,-0.0771,9.8029,0.11,-0.1417,0.2492,-6.8,-27.8,-36.3,2.931105946,0.45,-1.52,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,14 / 17,248212,2015-10-30 10:17:49:088,1446171469088.0 \n-0.5662,-0.322,9.7935,0.3138,-0.2509,9.7984,-0.0061,-0.0562,0.0098,-7.6,-28,-36.3,2.90928933,1.47,-1.83,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,14 / 17,248314,2015-10-30 10:17:49:190,1446171469190.0 \n-0.5423,0.5974,8.0134,0.165,-0.1451,9.8042,0.1723,0.0916,-0.0012,-8.3,-27.9,-36.4,2.894279499,1.16,-1.19,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,14 / 17,248417,2015-10-30 10:17:49:293,1446171469293.0 \n-0.7793,-0.2334,10.3382,0.1146,-0.0559,9.8058,0.0733,0.0599,-0.1576,-8.7,-28,-36.1,2.846282944,0.33,-0.67,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,14 / 17,248517,2015-10-30 10:17:49:393,1446171469393.0 \n-0.8775,-0.0527,10.0449,0.0738,0.1729,9.8048,0.2615,0.1833,0.0098,-8.8,-28.3,-35.8,2.839825226,-0.68,-0.66,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,14 / 17,248620,2015-10-30 10:17:49:496,1446171469496.0 \n-0.9661,-1.1372,12.2499,0.0114,-0.1029,9.8061,-0.2859,0.2773,-0.1148,-8.9,-28.7,-35.3,2.84541028,0.6,-0.07,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,14 / 17,248721,2015-10-30 10:17:49:597,1446171469597.0 \n0.1269,-0.0898,8.6706,-0.0525,-0.1246,9.8057,-0.1026,-0.0904,-0.0073,-8.8,-28.6,-35.1,2.839127094,0.73,0.31,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,14 / 17,248823,2015-10-30 10:17:49:699,1446171469699.0 \n0.079,0.5267,8.8741,0.0403,-0.359,9.8,-0.1674,0.0415,-0.044,-9,-28,-35.2,2.846981076,1.85,-0.27,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,14 / 17,248925,2015-10-30 10:17:49:801,1446171469801.0 \n-0.1257,0.6883,9.487,0.0799,-0.3342,9.8006,0.0061,0.0098,-0.0024,-9.7,-26.9,-35.6,2.810503694,2.06,-0.45,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,14 / 17,249028,2015-10-30 10:17:49:904,1446171469904.0 \n-0.6823,-0.3029,11.9914,0.0364,-0.1628,9.8052,0.3201,-0.1442,0.1869,-10.7,-26.4,-35.6,2.753780494,0.95,-0.21,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,14 / 17,249129,2015-10-30 10:17:50:005,1446171470005.0 \n0.2107,-0.6261,10.9164,0.0953,0.1054,9.8056,0.1894,0.0489,0.2773,-11.6,-26.1,-34.8,2.714510586,-0.62,-0.56,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,14 / 17,249233,2015-10-30 10:17:50:109,1446171470109.0 \n-0.9864,-0.0898,8.9507,0.1338,-0.0864,9.8054,0.0269,-0.1955,0.3213,-12.2,-25.8,-34.4,2.726902423,0.44,-0.74,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,14 / 17,249333,2015-10-30 10:17:50:209,1446171470209.0 \n-0.6871,-0.3328,10.1514,0.3153,-0.2541,9.7983,-0.0855,-0.0501,0.0513,-13.4,-24.6,-34,2.710670861,1.48,-1.84,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,14 / 17,249435,2015-10-30 10:17:50:311,1446171470311.0 \n-0.7685,0.3424,8.9675,0.2303,-0.2112,9.8017,0.0855,0.1442,0.022,-14,-23.4,-34.2,2.645221014,1.52,-1.76,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,14 / 17,249538,2015-10-30 10:17:50:414,1446171470414.0 \n-0.3675,0.4573,9.0369,0.1422,-0.0091,9.8056,0.1943,0.1405,-0.0342,-14.4,-21.9,-34,2.591639406,0.05,-0.83,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,14 / 17,249640,2015-10-30 10:17:50:516,1446171470516.0 \n-1.0774,-0.3304,11.0792,0.0908,0.1852,9.8045,0.2053,0.0831,-0.0672,-14.3,-21.3,-33.8,2.557954552,-0.71,-0.69,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,1117,249741,2015-10-30 10:17:50:617,1446171470617.0 \n-1.4281,-1.5957,12.2164,0.1099,-0.0239,9.806,-0.3348,-0.1197,-0.3506,-13.6,-20.6,-33,2.567728396,0.14,-0.64,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,1117,249844,2015-10-30 10:17:50:720,1446171470720.0 \n-0.6656,-0.7518,10.0628,-0.0105,-0.1048,9.8061,0.0892,-0.044,0.0024,-12.8,-19.4,-32.6,2.54887884,0.61,0.06,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,1117,249951,2015-10-30 10:17:50:827,1446171470827.0 \n-0.729,-0.413,8.4719,0.1427,-0.3121,9.8006,-0.0782,0.1087,0.1258,-12.4,-18.4,-32.2,2.596351795,1.82,-0.83,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,1117,250050,2015-10-30 10:17:50:926,1446171470926.0 \n0.3903,0.8176,8.4695,0.1908,-0.2828,9.8007,0.0037,-0.0269,0.1014,-12.1,-17.2,-31.9,2.576105976,1.65,-1.12,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,1117,250149,2015-10-30 10:17:51:025,1446171471025.0 \n-0.2981,-0.231,10.4782,0.2261,-0.1992,9.802,0.0916,-0.0318,-0.0538,-12.1,-16.5,-31.6,2.54713351,1.16,-1.32,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,1117,250252,2015-10-30 10:17:51:128,1446171471128.0 \n-0.2119,-0.2334,9.742,0.1299,-0.0617,9.8056,0.2468,0.1613,0.2615,-12.1,-16.2,-31.4,2.535614337,0.84,-1.1,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,1117,250354,2015-10-30 10:17:51:230,1446171471230.0 \n-0.9254,-0.9924,9.9766,0.2473,-0.2558,9.8002,0.2077,0.1454,0.3311,-12.1,-16,-30.8,2.553242163,1.49,-1.45,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,1117,250456,2015-10-30 10:17:51:332,1446171471332.0 \n-0.2502,-0.3208,8.9208,0.2832,-0.2361,9.7997,-0.0232,-0.2187,0.1087,-12.1,-15.8,-30.3,2.547482576,0.99,-1.6,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,1117,250558,2015-10-30 10:17:51:434,1446171471434.0 \n-0.8511,-0.2682,8.7987,0.2155,-0.3113,9.7993,0.0305,0.1417,-0.044,-12.4,-15.3,-29.6,2.523746098,1.82,-1.26,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,1117,250659,2015-10-30 10:17:51:535,1446171471535.0 \n-0.5052,0.2909,8.6514,0.097,-0.2715,9.8024,-0.0415,0.0232,-0.0232,-12.5,-14.7,-29.1,2.503325746,1.54,-0.58,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,1017,250761,2015-10-30 10:17:51:637,1446171471637.0 \n-1.1971,-1.1001,12.2667,0.1944,-0.3004,9.8001,-0.0635,-0.2028,-0.1319,-12.4,-14.2,-28.4,2.485348855,1.76,-1.14,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,1017,250866,2015-10-30 10:17:51:742,1446171471742.0 \n0.929,0.6452,9.1279,0.1943,-0.1871,9.8029,-0.0501,-0.1014,0.0049,-12.5,-13.9,-27.9,2.474702346,1.09,-1.14,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,1017,250965,2015-10-30 10:17:51:841,1446171471841.0 \n0.2454,-0.1197,7.8829,0.1601,-0.4824,9.7935,0.4129,0.0892,0.1796,-12.7,-13.5,-27.3,2.4373523,3.43,-1.24,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,1017,251068,2015-10-30 10:17:51:944,1446171471944.0 \n-0.0551,-0.6117,9.2189,0.2862,-0.5177,9.7888,-0.1038,0.1295,-0.1002,-13,-13,-26.6,2.439446696,3.03,-1.67,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,1017,251171,2015-10-30 10:17:52:047,1446171472047.0 \n-0.7985,-0.0192,8.6694,0.1672,-0.6317,9.7849,-0.1136,0.0672,-0.0672,-13,-12.6,-26.3,2.433512576,3.69,-0.98,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,1017,251272,2015-10-30 10:17:52:148,1446171472148.0 \n-0.5459,-0.3017,10.3214,0.1836,-0.6974,9.7801,-0.0782,0.0354,0.0745,-13.5,-12.2,-25.5,2.403143847,4.08,-1.08,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,1017,251376,2015-10-30 10:17:52:252,1446171472252.0 \n-0.3615,-0.5219,11.1881,0.1903,-0.5396,9.7899,0.43,-0.2382,0.347,-13.8,-12,-25.2,2.353925562,3.68,-0.79,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,1017,251476,2015-10-30 10:17:52:352,1446171472352.0 \n-0.4298,-2.302,12.9622,0.3421,-0.4368,9.7909,-0.0904,-0.1613,0.2468,-14.6,-12.1,-24.4,2.316750049,2.55,-2,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,1017,251578,2015-10-30 10:17:52:454,1446171472454.0 \n-0.2933,-0.9768,7.9009,0.4199,-0.3839,9.7901,0.2358,0.0086,0.3653,-15.2,-12.2,-24.2,2.321113372,2.53,-2.3,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,251680,2015-10-30 10:17:52:556,1446171472556.0 \n-0.1113,-1.646,10.1945,0.5023,-0.3912,9.786,-0.1197,0.1442,0.0574,-16.2,-12.4,-23.3,2.289173847,2.29,-2.94,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,251781,2015-10-30 10:17:52:657,1446171472657.0 \n-0.0706,-1.4952,9.1842,0.326,-0.3786,9.7939,0.1833,0.1772,-0.0073,-16.6,-12.7,-23.2,2.279050937,2.21,-1.91,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,251884,2015-10-30 10:17:52:760,1446171472760.0 \n-0.1544,-1.1516,9.0142,0.2657,-0.2641,9.7995,0.0489,0.0611,-0.1161,-16.6,-13,-22.9,2.265437369,1.55,-1.58,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,251986,2015-10-30 10:17:52:862,1446171472862.0 \n-0.0443,-1.057,9.2416,0.076,-0.2637,9.8028,-0.1026,0.1674,-0.1283,-16,-13.8,-22.6,2.321462438,1.43,-0.93,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,252088,2015-10-30 10:17:52:964,1446171472964.0 \n-0.7159,-0.7362,9.1111,-0.1358,-0.4503,9.7954,-0.0476,-0.0953,0.1442,-15.1,-14.4,-22.3,2.345722515,2.63,0.79,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,252189,2015-10-30 10:17:53:065,1446171473065.0 \n-0.0503,-0.589,10.1969,0.024,-0.5291,9.7923,-0.1393,-0.2492,0.1026,-14.8,-14.5,-22.3,2.363524873,3.09,-0.14,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,252291,2015-10-30 10:17:53:167,1446171473167.0 \n-0.2909,-0.6057,9.754,0.0782,-0.6826,9.7826,-0.1662,-0.1075,-0.0452,-14.8,-14.2,-22.3,2.378709238,3.99,-0.46,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,252393,2015-10-30 10:17:53:269,1446171473269.0 \n-0.3448,-0.6979,10.3777,0.1403,-0.8312,9.7704,-0.0941,-0.0819,-0.0672,-14.9,-14,-22.6,2.390752009,4.64,-0.57,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,252496,2015-10-30 10:17:53:372,1446171473372.0 \n-0.3831,-0.5746,9.5241,0.1219,-0.92,9.7626,-0.0684,0.0489,-0.0195,-15.1,-13.6,-22.9,2.400525853,5.27,-0.73,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,252598,2015-10-30 10:17:53:474,1446171473474.0 \n-0.1484,-0.419,9.5074,0.1296,-0.9737,9.7573,-0.088,-0.044,0.0379,-15.1,-13.5,-23,2.372426052,5.58,-0.72,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,252700,2015-10-30 10:17:53:576,1446171473576.0 \n-0.4956,-0.6716,9.8689,0.1245,-1.0409,9.7505,-0.077,-0.0367,0.0305,-15.2,-13.2,-23,2.37888377,6.09,-0.73,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,252802,2015-10-30 10:17:53:678,1446171473678.0 \n-0.4705,-0.6812,10.0293,0.1068,-1.091,9.7452,-0.0696,-0.0489,0.0586,-15.3,-13,-23.1,2.380803633,6.34,-0.66,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,252904,2015-10-30 10:17:53:780,1446171473780.0 \n-0.3232,-0.7326,9.669,0.0656,-1.0931,9.7453,0.0061,0.0379,0.0977,-15.3,-12.9,-23.5,2.37766204,6.4,-0.39,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,253005,2015-10-30 10:17:53:881,1446171473881.0 \n-0.2634,-0.7338,9.7396,0.0266,-1.0705,9.748,-0.0024,-0.0073,0.1051,-15.4,-12.9,-23.8,2.377138441,6.29,-0.2,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,253110,2015-10-30 10:17:53:986,1446171473986.0 \n-0.2239,-0.8068,9.7049,0.0126,-1.0288,9.7525,0.0098,-0.0134,0.0672,-15.5,-12.7,-23.7,2.372600585,6.07,-0.08,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,253209,2015-10-30 10:17:54:085,1446171474085.0 \n-0.2825,-0.9373,9.7671,0.0051,-1.0208,9.7534,0.0257,0.0073,0.0562,-15.6,-12.7,-23.4,2.335076006,5.97,-0.03,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,253312,2015-10-30 10:17:54:188,1446171474188.0 \n-0.4202,-0.8248,9.9096,-0.0267,-0.9861,9.7569,0.0073,-0.0159,0.0525,-15.6,-12.7,-23.2,2.33053815,5.8,0.14,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,253414,2015-10-30 10:17:54:290,1446171474290.0 \n-0.4417,-0.7961,9.7899,-0.055,-0.9517,9.7602,0.0415,0.0305,0.0147,-15.6,-12.8,-23.1,2.325302162,5.57,0.32,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,253515,2015-10-30 10:17:54:391,1446171474391.0 \n-0.4154,-0.7278,9.6007,-0.1073,-0.9089,9.7638,0.0195,0.0293,0.0147,-15.6,-12.8,-23,2.320066175,5.37,0.53,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,253617,2015-10-30 10:17:54:493,1446171474493.0 \n-0.4884,-0.7207,9.7336,-0.1306,-0.9059,9.7638,0.0269,-0.0147,0.0391,-15.6,-12.8,-22.8,2.316051917,5.3,0.77,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,253720,2015-10-30 10:17:54:596,1446171474596.0 \n-0.3938,-0.6201,9.657,-0.1353,-0.86,9.7679,0.0305,-0.0037,0.0318,-15.5,-12.8,-22.8,2.343977185,5.03,0.79,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,253822,2015-10-30 10:17:54:698,1446171474698.0 \n-0.5112,-0.6895,9.8378,-0.1376,-0.8296,9.7705,-0.0049,-0.022,0.0147,-15.5,-12.8,-22.8,2.34188279,4.87,0.8,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,253924,2015-10-30 10:17:54:800,1446171474800.0 \n-0.6105,-0.6345,9.572,-0.1679,-0.8077,9.7719,0.0403,0.0367,0.0806,-15.6,-12.8,-22.7,2.308372469,4.8,0.88,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,254026,2015-10-30 10:17:54:902,1446171474902.0 \n-0.6608,-0.5351,9.6678,-0.183,-0.7951,9.7727,-0.0269,0.0086,0.1271,-15.8,-12.9,-23,2.304009146,4.65,1.07,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,254127,2015-10-30 10:17:55:003,1446171475003.0 \n-0.3915,-0.4681,10.0473,-0.2209,-0.8072,9.7709,0.0244,0.0134,0.1625,-15.9,-12.8,-23.3,2.302089283,4.72,1.29,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,254229,2015-10-30 10:17:55:105,1446171475105.0 \n-0.3687,-0.4836,9.6438,-0.2675,-0.7693,9.7728,0.0244,0.0513,0.1442,-16.1,-12.7,-23.6,2.29772596,4.5,1.57,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,254331,2015-10-30 10:17:55:207,1446171475207.0 \n-0.2705,-0.6189,10.0006,-0.29,-0.746,9.7739,0.0232,0.0037,0.0757,-16.4,-12.4,-23.2,2.25775792,4.36,1.7,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,254433,2015-10-30 10:17:55:309,1446171475309.0 \n-0.0982,-0.3998,9.6391,-0.3115,-0.6963,9.7769,0.0672,0.0269,0.0354,-16.5,-12.5,-23.2,2.2523474,4.07,1.82,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,254536,2015-10-30 10:17:55:412,1446171475412.0 \n-0.2969,-0.5459,9.3541,-0.3779,-0.6078,9.7805,0.0929,0.1075,-0.1869,-16.5,-12.5,-22.9,2.240479161,3.55,2.21,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,254638,2015-10-30 10:17:55:514,1446171475514.0 \n-0.6668,-0.3962,9.5577,-0.4011,-0.5864,9.7809,0.0232,0.0525,-0.2639,-16.1,-12.7,-23.1,2.272593219,3.43,2.35,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,254740,2015-10-30 10:17:55:616,1446171475616.0 \n-0.8272,-0.504,9.7169,-0.4152,-0.5736,9.7811,0.055,-0.0232,-0.1637,-15.7,-12.9,-22.9,2.271196956,3.45,2.5,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,254841,2015-10-30 10:17:55:717,1446171475717.0 \n-0.7147,-0.3998,9.5457,-0.3622,-0.5052,9.7869,0.0733,-0.0892,-0.1564,-15.3,-13.2,-22.8,2.29947129,3.08,2.25,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,254944,2015-10-30 10:17:55:820,1446171475820.0 \n-0.9026,-0.425,9.3649,-0.3605,-0.5016,9.7872,-0.0171,-0.0269,-0.0929,-15.2,-13.2,-22.7,2.299296757,2.93,2.11,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,255046,2015-10-30 10:17:55:922,1446171475922.0 \n-0.7159,-0.4357,9.9551,-0.2879,-0.5207,9.7886,-0.033,-0.0782,0.1063,-15,-13.4,-22.5,2.305405409,3.04,1.68,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,255149,2015-10-30 10:17:56:025,1446171476025.0 \n-0.6093,-0.3723,9.6786,-0.2725,-0.5139,9.7894,-0.0134,-0.0012,0.1148,-15.2,-13.3,-22.6,2.306976205,3,1.59,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,255258,2015-10-30 10:17:56:134,1446171476134.0 \n-0.6536,-0.4573,9.7659,-0.3011,-0.5213,9.7882,-0.0098,0.0147,0.1381,-15.5,-13.2,-22.6,2.306278074,3.04,1.69,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,255352,2015-10-30 10:17:56:228,1446171476228.0 \n-0.3711,-0.3998,10.0473,-0.3178,-0.5169,9.7879,-0.0122,0.0061,0.1552,-15.8,-13,-22.8,2.273116818,3.02,1.86,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,255454,2015-10-30 10:17:56:330,1446171476330.0 \n-0.2274,-0.1736,9.5684,-0.3305,-0.4803,9.7893,0.0586,0.0171,0.1063,-15.9,-12.9,-22.7,2.269451626,2.81,1.93,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,255556,2015-10-30 10:17:56:432,1446171476432.0 \n-0.3639,-0.2394,9.6558,-0.3253,-0.4116,9.7926,0.0476,-0.0379,0.0586,-16,-13,-22.4,2.263866573,2.41,1.9,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,255657,2015-10-30 10:17:56:533,1446171476533.0 \n-0.3867,-0.2586,9.6403,-0.3048,-0.3754,9.7947,0.0305,-0.0086,0.0464,-16,-13,-22,2.263168441,2.25,1.79,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,255759,2015-10-30 10:17:56:635,1446171476635.0 \n-0.571,-0.2478,9.7312,-0.2996,-0.3649,9.7953,0.0024,-0.0232,0.0782,-16.1,-13,-22.1,2.262121244,2.15,1.78,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,255861,2015-10-30 10:17:56:737,1446171476737.0 \n-0.5088,-0.1568,9.8342,-0.2905,-0.3495,9.7961,0.011,-0.0159,0.0208,-16.2,-13,-22.3,2.261597645,2.04,1.7,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,255965,2015-10-30 10:17:56:841,1446171476841.0 \n-0.5531,-0.176,9.6869,-0.2806,-0.3458,9.7965,0.0452,-0.0257,0.0159,-16.4,-12.9,-22.2,2.262819375,2.1,1.66,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,256069,2015-10-30 10:17:56:945,1446171476945.0 \n-0.5626,-0.1616,9.6187,-0.2727,-0.3123,9.7979,0.0122,-0.0037,-0.0073,-16.5,-12.9,-22,2.259852315,1.83,1.59,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,256168,2015-10-30 10:17:57:044,1446171477044.0 \n-0.5375,-0.255,9.8641,-0.2651,-0.2893,9.7988,0.0171,-0.0122,-0.0257,-16.5,-12.9,-22.1,2.258630585,1.69,1.55,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,256270,2015-10-30 10:17:57:146,1446171477146.0 \n-0.6189,-0.2502,9.6151,-0.3029,-0.2728,9.7982,-0.0183,0.0012,-0.0318,-16.4,-13,-22.5,2.254790861,1.59,1.77,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,256371,2015-10-30 10:17:57:247,1446171477247.0 \n-0.5064,-0.1508,9.5134,-0.3135,-0.3038,9.7969,-0.0391,-0.011,0.022,-16.5,-13,-22.3,2.255488992,1.71,1.84,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,256474,2015-10-30 10:17:57:350,1446171477350.0 \n-0.3663,-0.1724,9.8019,-0.3029,-0.3167,9.7969,-0.0134,0.0195,0.0379,-16.5,-13.1,-22,2.258106986,1.85,1.77,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 17,256575,2015-10-30 10:17:57:451,1446171477451.0 \n-0.3388,-0.1592,9.8916,-0.3326,-0.3075,9.7962,0,0.0232,0.022,-16.6,-13,-22,2.228610922,1.85,1.88,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,256678,2015-10-30 10:17:57:554,1446171477554.0 \n-0.3903,-0.0431,9.4415,-0.3582,-0.2834,9.796,0.0024,0.0012,0.0147,-16.8,-13,-22.2,2.223898533,1.66,2.09,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,256780,2015-10-30 10:17:57:656,1446171477656.0 \n-0.4896,-0.3053,9.8952,-0.3252,-0.304,9.7965,-0.0281,-0.0342,-0.0049,-16.8,-13,-22.3,2.225992928,1.72,1.96,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,256881,2015-10-30 10:17:57:757,1446171477757.0 \n-0.4094,-0.1448,9.5433,-0.3088,-0.3083,9.7969,0.0257,-0.011,0.0159,-16.6,-13.1,-22.6,2.228087323,1.76,1.83,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,256984,2015-10-30 10:17:57:860,1446171477860.0 \n-0.3998,-0.1676,9.8306,-0.2606,-0.3259,9.7978,-0.0293,-0.055,0.0257,-16.6,-13.1,-22.8,2.23210158,1.87,1.61,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,257086,2015-10-30 10:17:57:962,1446171477962.0 \n-0.3663,-0.1257,9.7935,-0.175,-0.2901,9.8008,0.0843,-0.1405,0.0721,-16.7,-12.9,-22.9,2.235941305,1.84,1.23,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,257187,2015-10-30 10:17:58:063,1446171478063.0 \n-0.3472,-0.2274,9.5636,-0.1234,-0.2415,9.8029,0.0562,0.0147,0.0171,-17,-12.9,-22.6,2.235766772,1.41,0.72,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,257289,2015-10-30 10:17:58:165,1446171478165.0 \n-0.1844,-0.1652,9.5026,-0.0253,-0.1746,9.8051,0.0452,-0.1295,-0.0061,-17.1,-12.9,-22.4,2.236290371,1.02,0.15,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,257391,2015-10-30 10:17:58:267,1446171478267.0 \n-0.0431,-0.0443,9.3841,0.0256,-0.1729,9.8051,0.0281,-0.0379,0.0367,-17.4,-13,-22.5,2.239431963,1.01,-0.15,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,257493,2015-10-30 10:17:58:369,1446171478369.0 \n-0.1101,-0.1269,9.9443,0.0246,-0.1981,9.8046,0.0342,-0.0012,0,-17.4,-13,-22.4,2.241177292,1.13,-0.15,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,257596,2015-10-30 10:17:58:472,1446171478472.0 \n-0.103,-0.006,9.5493,0.0065,-0.172,9.8051,0.0208,0.0147,-0.0049,-17.6,-13,-22.4,2.210634031,0.98,-0.07,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,257697,2015-10-30 10:17:58:573,1446171478573.0 \n-0.3065,-0.1628,9.8881,-0.0084,-0.1926,9.8048,0.0086,0.0086,-0.0171,-17.5,-13.1,-22.3,2.238908364,1.13,0.05,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,257800,2015-10-30 10:17:58:676,1446171478676.0 \n-0.2777,-0.0742,9.7659,-0.0484,-0.1818,9.8048,0,0.033,-0.0147,-17.4,-13.1,-22.3,2.236290371,1.08,0.22,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,257902,2015-10-30 10:17:58:778,1446171478778.0 \n-0.3089,-0.0682,9.6522,-0.07,-0.1702,9.8049,0.0122,0.0049,-0.0098,-17.3,-13,-22.3,2.233672377,1.02,0.39,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,258007,2015-10-30 10:17:58:883,1446171478883.0 \n-0.1736,-0.0838,9.7528,-0.0786,-0.1689,9.8049,0.022,0.0037,0.0281,-17.3,-12.9,-22.3,2.232450646,0.99,0.46,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,258106,2015-10-30 10:17:58:982,1446171478982.0 \n-0.1664,-0.0503,9.7037,-0.1103,-0.1648,9.8046,-0.022,0.0183,-0.0171,-17.3,-13,-22.3,2.229832652,0.93,0.62,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,258208,2015-10-30 10:17:59:084,1446171479084.0 \n-0.2837,-0.0658,9.5086,-0.1263,-0.1736,9.8043,0.0208,-0.0098,0.0208,-17.2,-13.1,-22.1,2.228436389,0.93,0.75,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,258310,2015-10-30 10:17:59:186,1446171479186.0 \n-0.3208,-0.1856,9.9431,-0.1083,-0.1779,9.8044,-0.0318,-0.0342,-0.0122,-17.1,-13.2,-21.9,2.231228916,1.04,0.63,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,258411,2015-10-30 10:17:59:287,1446171479287.0 \n-0.3352,-0.0491,9.4427,-0.1256,-0.2073,9.8037,-0.0012,0.0171,0.0464,-17,-13.2,-21.9,2.232450646,1.21,0.73,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,258514,2015-10-30 10:17:59:390,1446171479390.0 \n-0.1496,0.0204,9.7312,-0.1155,-0.2196,9.8035,-0.0147,-0.0257,0.055,-17,-13,-22.2,2.233672377,1.28,0.71,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,258616,2015-10-30 10:17:59:492,1446171479492.0 \n-0.261,-0.0754,9.7241,-0.1027,-0.2032,9.804,0.0122,0.0012,0.0208,-17.1,-12.9,-22.7,2.234021443,1.2,0.63,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,258717,2015-10-30 10:17:59:593,1446171479593.0 \n-0.4214,-0.249,10.1215,-0.0947,-0.2179,9.8038,-0.0073,-0.0195,-0.0012,-17.3,-12.7,-22.8,2.235417706,1.25,0.57,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,258820,2015-10-30 10:17:59:696,1446171479696.0 \n-0.2873,-0.0431,9.6187,-0.0944,-0.2084,9.804,-0.0244,-0.0403,0.0012,-17.4,-12.7,-22.6,2.234021443,1.2,0.61,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,258922,2015-10-30 10:17:59:798,1446171479798.0 \n-0.2538,-0.073,9.5062,-0.0653,-0.2032,9.8043,0.0171,-0.0452,0.0159,-17.3,-12.7,-22.5,2.235592239,1.2,0.44,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,259023,2015-10-30 10:17:59:899,1446171479899.0 \n-0.34,-0.1796,9.7983,-0.0486,-0.2185,9.8041,0.0159,0.0049,0.0171,-17.2,-12.7,-22.1,2.238210233,1.28,0.28,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,259125,2015-10-30 10:18:00:001,1446171480001.0 \n-0.1879,-0.0503,9.5181,-0.0736,-0.1985,9.8044,0,0.011,0.0562,-17.3,-12.8,-22.2,2.236115838,1.18,0.37,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,259228,2015-10-30 10:18:00:104,1446171480104.0 \n-0.0742,-0.1257,9.7097,-0.0726,-0.1993,9.8044,-0.0147,0.0159,-0.0098,-17.5,-12.7,-22.4,2.23506864,1.15,0.42,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,259329,2015-10-30 10:18:00:205,1446171480205.0 \n-0.2502,-0.182,9.7671,-0.086,-0.2122,9.804,-0.0171,-0.0037,0.0037,-17.5,-12.7,-22.7,2.235941305,1.24,0.5,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,259432,2015-10-30 10:18:00:308,1446171480308.0 \n-0.3555,-0.1604,9.8067,-0.0855,-0.217,9.8039,-0.0428,-0.0183,0.0134,-17.4,-12.6,-22.4,2.235766772,1.27,0.5,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,259534,2015-10-30 10:18:00:410,1446171480410.0 \n-0.3077,-0.2047,9.93,-0.0666,-0.2556,9.8031,-0.033,-0.0305,0.0269,-17.4,-12.5,-22.4,2.203129115,1.49,0.39,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,259636,2015-10-30 10:18:00:512,1446171480512.0 \n-0.2897,-0.1772,9.7181,-0.0856,-0.2539,9.803,-0.0024,0.0159,0.0452,-17.5,-12.5,-22.4,2.201907384,1.48,0.5,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,259737,2015-10-30 10:18:00:613,1446171480613.0 \n-0.2574,-0.2562,9.7624,-0.0841,-0.2674,9.8026,-0.0122,-0.0012,0.0452,-17.5,-12.4,-22.6,2.203827246,1.56,0.49,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,259840,2015-10-30 10:18:00:716,1446171480716.0 \n-0.267,-0.2442,9.6247,-0.1088,-0.2792,9.8021,-0.0269,0.0244,0.0403,-17.6,-12.2,-22.3,2.175727446,1.6,0.6,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,259942,2015-10-30 10:18:00:818,1446171480818.0 \n-0.1927,-0.2646,9.9707,-0.1195,-0.3035,9.8012,-0.0232,0.0086,0.0342,-17.6,-12.3,-22.3,2.177123709,1.77,0.7,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,260043,2015-10-30 10:18:00:919,1446171480919.0 \n-0.2191,-0.2071,9.7695,-0.1306,-0.3122,9.8008,0.0122,0.0073,0.0195,-17.6,-12.3,-22.5,2.177647308,1.84,0.75,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,260145,2015-10-30 10:18:01:021,1446171481021.0 \n-0.2957,-0.2442,9.7564,-0.1161,-0.3016,9.8013,-0.0024,-0.0403,-0.0098,-17.7,-12.3,-22.8,2.177472775,1.76,0.73,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,260248,2015-10-30 10:18:01:124,1446171481124.0 \n-0.2598,-0.231,9.6055,-0.0913,-0.2913,9.8019,0.0257,-0.011,0,-17.7,-12.2,-22.9,2.178694505,1.7,0.53,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,260349,2015-10-30 10:18:01:225,1446171481225.0 \n-0.3136,-0.2741,9.6929,-0.0795,-0.272,9.8026,0.0098,-0.0232,-0.0049,-17.7,-12.4,-22.8,2.177647308,1.59,0.48,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,260453,2015-10-30 10:18:01:329,1446171481329.0 \n-0.2729,-0.2634,9.906,-0.0657,-0.2635,9.8029,-0.0293,-0.0318,-0.0134,-17.7,-12.5,-22.7,2.177996374,1.54,0.38,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,260553,2015-10-30 10:18:01:429,1446171481429.0 \n-0.2514,-0.2071,9.6271,-0.0597,-0.266,9.8029,0.0171,-0.0037,0.0244,-17.7,-12.5,-22.7,2.178519972,1.55,0.35,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 15,260656,2015-10-30 10:18:01:532,1446171481532.0 \n-0.2634,-0.1736,9.7863,-0.0556,-0.2588,9.8031,-0.0086,-0.0171,0.0147,-17.8,-12.5,-22.5,2.177298242,1.51,0.32,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 14,260758,2015-10-30 10:18:01:634,1446171481634.0 \n-0.3424,-0.2251,9.8198,-0.0512,-0.2667,9.8029,-0.0171,-0.0049,0.011,-17.8,-12.5,-22.8,2.178869038,1.53,0.29,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 14,260860,2015-10-30 10:18:01:736,1446171481736.0 \n-0.1353,-0.1844,9.8114,-0.0643,-0.2652,9.8029,0.0195,0.0073,0.0342,-18,-12.5,-22.8,2.178694505,1.57,0.36,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 14,260961,2015-10-30 10:18:01:837,1446171481837.0 \n-0.2047,-0.2107,9.8653,-0.0912,-0.2613,9.8027,-0.0232,-0.0024,-0.0073,-17.9,-12.4,-22.8,2.176076511,1.53,0.53,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 14,261063,2015-10-30 10:18:01:939,1446171481939.0 \n-0.1891,-0.1748,9.5146,-0.1035,-0.2566,9.8027,0.0232,0.0134,0.0012,-17.8,-12.4,-22.7,2.175029314,1.5,0.61,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 14,261165,2015-10-30 10:18:02:041,1446171482041.0 \n-0.249,-0.2179,9.6355,-0.1109,-0.2602,9.8026,-0.0122,0.0049,-0.0391,-17.8,-12.4,-22.5,2.174156649,1.52,0.66,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 14,261267,2015-10-30 10:18:02:143,1446171482143.0 \n-0.3651,-0.249,9.8126,-0.1145,-0.2832,9.8019,-0.0134,-0.0037,-0.0257,-17.7,-12.5,-22.4,2.175029314,1.61,0.68,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 14,261369,2015-10-30 10:18:02:245,1446171482245.0 \n-0.2155,-0.1401,9.6415,-0.1127,-0.2932,9.8016,-0.0086,-0.0183,-0.0024,-17.8,-12.5,-22.4,2.176774643,1.71,0.66,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 14,261472,2015-10-30 10:18:02:348,1446171482348.0 \n-0.2239,-0.2107,9.7923,-0.0915,-0.2912,9.8019,-0.0195,-0.0415,-0.0171,-17.8,-12.5,-22.6,2.177647308,1.68,0.59,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 14,261575,2015-10-30 10:18:02:451,1446171482451.0 \n-0.2179,-0.1927,9.7827,-0.0804,-0.2634,9.8028,0.0415,-0.0012,-0.0037,-17.9,-12.3,-22.6,2.176949176,1.54,0.47,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 14,261676,2015-10-30 10:18:02:552,1446171482552.0 \n-0.1856,-0.1006,9.4894,-0.0757,-0.2191,9.8039,0.0452,-0.011,-0.0122,-17.8,-12.4,-22.9,2.174156649,1.34,0.47,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,261778,2015-10-30 10:18:02:654,1446171482654.0 \n-0.2418,-0.1496,9.7348,-0.0534,-0.2048,9.8044,0.0244,-0.0037,0,-17.8,-12.5,-22.7,2.17363305,1.2,0.31,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,261880,2015-10-30 10:18:02:756,1446171482756.0 \n-0.1628,-0.1185,9.5732,-0.0421,-0.1854,9.8048,-0.0037,-0.0367,0.0159,-17.8,-12.6,-22.7,2.209063234,1.1,0.28,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,261981,2015-10-30 10:18:02:857,1446171482857.0 \n-0.0874,-0.0144,9.5624,-0.009,-0.1889,9.8048,-0.0134,-0.0134,0.0208,-18,-12.5,-22.3,2.173109452,1.09,0.14,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,262084,2015-10-30 10:18:02:960,1446171482960.0 \n-0.0754,-0.1018,9.9551,0.0202,-0.2038,9.8045,0.0269,-0.0232,0.0354,-17.9,-12.5,-22.6,2.178519972,1.24,-0.09,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,262186,2015-10-30 10:18:03:062,1446171483062.0 \n-0.0503,-0.0431,9.493,0.0182,-0.1893,9.8048,0.0073,-0.0171,-0.0098,-17.9,-12.6,-22.4,2.212553893,1.11,-0.11,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,262287,2015-10-30 10:18:03:163,1446171483163.0 \n-0.231,-0.237,9.8007,0.0262,-0.1999,9.8046,-0.0257,-0.0159,-0.0269,-18,-12.6,-22.4,2.213950156,1.17,-0.15,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,262390,2015-10-30 10:18:03:266,1446171483266.0 \n-0.2023,-0.2095,9.6714,-0.0029,-0.2382,9.8038,-0.0342,0.0159,0.0061,-17.9,-12.5,-22.3,2.178694505,1.39,0.02,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,262510,2015-10-30 10:18:03:386,1446171483386.0 \n-0.1269,-0.1939,9.6211,-0.0195,-0.2576,9.8032,-0.0098,0.0147,-0.0183,-17.9,-12.5,-22.5,2.179392637,1.49,0.09,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,262594,2015-10-30 10:18:03:470,1446171483470.0 \n-0.2646,-0.328,9.8126,-0.0231,-0.3024,9.802,-0.0086,0,0.0061,-17.7,-12.5,-23,2.183930493,1.77,0.14,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,262696,2015-10-30 10:18:03:572,1446171483572.0 \n-0.231,-0.2263,9.7193,-0.0338,-0.3137,9.8016,-0.0195,0.0086,0.0061,-17.7,-12.5,-23,2.184105026,1.81,0.16,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,262798,2015-10-30 10:18:03:674,1446171483674.0 \n-0.1245,-0.2586,9.9347,-0.0194,-0.3148,9.8016,-0.0049,-0.0159,-0.0012,-17.7,-12.5,-22.9,2.185326756,1.85,0.12,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,262900,2015-10-30 10:18:03:776,1446171483776.0 \n-0.1927,-0.3136,9.7815,-0.0289,-0.2918,9.8023,0.0183,0.0122,-0.0269,-17.7,-12.5,-22.8,2.183057828,1.73,0.17,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,263001,2015-10-30 10:18:03:877,1446171483877.0 \n-0.1377,-0.103,9.2656,-0.0519,-0.2538,9.8032,0.0611,0.0257,-0.0342,-17.7,-12.6,-22.7,2.214124689,1.48,0.3,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,263104,2015-10-30 10:18:03:980,1446171483980.0 \n-0.3077,-0.3376,10.1466,-0.0437,-0.2532,9.8033,-0.0281,-0.0122,-0.1063,-17.7,-12.7,-22.7,2.214124689,1.46,0.28,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,263205,2015-10-30 10:18:04:081,1446171484081.0 \n-0.1939,-0.1185,9.8976,-0.0332,-0.1768,9.805,0.0916,0.0257,-0.1222,-17.6,-13,-22.5,2.208539635,1.03,0.19,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,263307,2015-10-30 10:18:04:183,1446171484183.0 \n-0.2442,0.0012,9.7576,-0.0282,-0.0815,9.8063,0.1014,-0.0574,-0.1442,-17.5,-13.1,-22.4,2.229483586,0.59,0.23,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,263409,2015-10-30 10:18:04:285,1446171484285.0 \n-0.3639,-0.0108,9.5026,-0.0916,-0.0453,9.8061,0.0318,0.0525,-0.1185,-17.1,-13.4,-22,2.221629605,0.26,0.54,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,263511,2015-10-30 10:18:04:387,1446171484387.0 \n-0.4992,-0.0347,9.6367,-0.1729,-0.0423,9.805,-0.0183,0.0709,-0.0367,-16.9,-13.5,-22.1,2.217440815,0.21,0.87,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,263613,2015-10-30 10:18:04:489,1446171484489.0 \n-0.2322,0.2586,9.9228,-0.2047,-0.0653,9.8043,-0.0354,-0.022,0.0061,-16.6,-13.7,-22.3,2.251823801,0.38,1.2,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,263715,2015-10-30 10:18:04:591,1446171484591.0 \n0.3615,0.5136,10.1861,-0.209,-0.0593,9.8042,0.0134,0.0281,-0.0562,-16.5,-13.7,-22.4,2.280098135,0.35,1.22,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,263817,2015-10-30 10:18:04:693,1446171484693.0 \n-0.516,-0.012,9.5636,-0.311,0.0116,9.8017,0.0586,-0.0098,-0.0147,-16.1,-13.9,-22.6,2.266833632,-0.07,1.82,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,263920,2015-10-30 10:18:04:796,1446171484796.0 \n-0.3591,0.0371,9.5217,-0.3048,0.03,9.8019,-0.0037,-0.0171,-0.0147,-15.9,-14,-22.6,2.265786435,-0.18,1.78,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,264022,2015-10-30 10:18:04:898,1446171484898.0 \n-0.3879,0.0802,9.6977,-0.2808,0.0239,9.8026,0.0024,-0.0391,-0.0183,-15.7,-14.1,-22.6,2.26788083,-0.14,1.64,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,264124,2015-10-30 10:18:05:000,1446171485000.0 \n-0.407,0.0946,9.8916,-0.2795,0.001,9.8027,-0.033,0.0232,-0.0513,-15.7,-14,-22.5,2.270324291,-0.07,1.58,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,264226,2015-10-30 10:18:05:102,1446171485102.0 \n-0.5052,0.1401,9.4679,-0.3582,0.0156,9.8001,0.0305,0.0244,-0.0721,-15.6,-13.9,-22.3,2.264564704,-0.09,2.09,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,264327,2015-10-30 10:18:05:203,1446171485203.0 \n-0.6788,0.1951,9.1842,-0.4125,0.0531,9.7978,0.0305,0.0379,-0.0635,-15.4,-14,-22.6,2.286730386,-0.31,2.41,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,264430,2015-10-30 10:18:05:306,1446171485306.0 \n-0.5064,0.1903,9.432,-0.4269,0.0138,9.7973,-0.0208,0.0147,-0.0342,-15.1,-14.1,-22.5,2.289173847,-0.09,2.58,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,264532,2015-10-30 10:18:05:408,1446171485408.0 \n-0.4705,0.1113,9.8402,-0.2951,0.033,9.8022,-0.0574,0.0159,0.0049,-15.1,-14.1,-22.3,2.297900493,-0.19,1.72,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,264637,2015-10-30 10:18:05:513,1446171485513.0 \n-0.5064,0.085,9.7959,-0.2721,0.011,9.8029,-0.0012,0.0305,0.0281,-15.2,-14,-22.4,2.301216619,-0.06,1.59,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,264736,2015-10-30 10:18:05:612,1446171485612.0 \n-0.4286,0.1209,9.7109,-0.2935,0.0203,9.8022,0.0171,0,-0.0024,-15.2,-14,-22.6,2.297900493,-0.12,1.72,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,264839,2015-10-30 10:18:05:715,1446171485715.0 \n-0.419,0.1832,9.4954,-0.3154,0.0413,9.8015,0.0098,-0.011,-0.0147,-15.3,-14.1,-22.7,2.294584368,-0.24,1.85,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,264940,2015-10-30 10:18:05:816,1446171485816.0 \n-0.5303,0.0946,9.736,-0.3163,0.0228,9.8015,-0.0012,-0.0134,-0.0024,-15.3,-14.1,-22.6,2.296155164,-0.13,1.85,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,265043,2015-10-30 10:18:05:919,1446171485919.0 \n-0.3855,0.073,9.7995,-0.2957,0.015,9.8022,-0.0159,-0.0208,0.0098,-15.3,-14.2,-22.6,2.297202361,-0.12,1.77,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,265143,2015-10-30 10:18:06:019,1446171486019.0 \n-0.4824,0.1101,9.8043,-0.2786,0.01,9.8027,-0.0281,-0.0281,-0.0049,-15.3,-14.2,-22.6,2.299820355,-0.06,1.63,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,265245,2015-10-30 10:18:06:121,1446171486121.0 \n-0.3508,0.1101,9.8916,-0.2494,0.0159,9.8035,0.011,-0.0257,0.0073,-15.4,-14.3,-22.9,2.301565685,-0.09,1.46,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,265347,2015-10-30 10:18:06:223,1446171486223.0 \n-0.4357,-0.0419,9.9,-0.2132,0.0447,9.8042,0.0232,-0.0379,-0.0134,-15.3,-14.3,-23.1,2.301740218,-0.26,1.25,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,265450,2015-10-30 10:18:06:326,1446171486326.0 \n-0.4896,0.0096,9.742,-0.2119,0.0546,9.8042,0.0086,-0.0098,-0.0037,-15.4,-14.3,-23,2.301042086,-0.32,1.23,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,265551,2015-10-30 10:18:06:427,1446171486427.0 \n-0.4322,0.1437,9.7719,-0.2315,0.0529,9.8038,-0.0208,0.0281,0.0391,-15.3,-14.3,-22.7,2.299820355,-0.31,1.35,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,265653,2015-10-30 10:18:06:529,1446171486529.0 \n-0.723,0.1209,10.0078,-0.232,0.0572,9.8037,0.1124,-0.1576,0.0489,-15.4,-14.3,-22.5,2.299296757,-0.31,1.48,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 11,265756,2015-10-30 10:18:06:632,1446171486632.0 \n-0.4262,0.3017,9.7659,-0.1562,0.1625,9.8041,0.0916,-0.0159,0.0916,-15.5,-14.3,-22.6,2.296155164,-0.95,0.91,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 11,265857,2015-10-30 10:18:06:733,1446171486733.0 \n-0.2849,0.2394,9.681,-0.1889,0.238,9.8019,0.099,0.0086,0.0916,-15.7,-14.3,-22.4,2.260201381,-1.23,1.09,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 11,265960,2015-10-30 10:18:06:836,1446171486836.0 \n-0.267,0.243,9.6391,-0.2057,0.2649,9.8009,0.0086,0.0293,-0.0147,-15.8,-14.5,-22.4,2.254441795,-1.55,1.2,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 11,266062,2015-10-30 10:18:06:938,1446171486938.0 \n-0.3938,0.1437,9.3446,-0.1841,0.2515,9.8017,0.0012,-0.0757,-0.0733,-15.8,-14.6,-22.4,2.290744643,-1.53,1.16,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 11,266164,2015-10-30 10:18:07:040,1446171487040.0 \n-0.3208,0.2873,10.0114,-0.1645,0.2167,9.8029,-0.0574,-0.0635,0.0134,-15.7,-14.6,-22.7,2.295107966,-1.27,0.96,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 11,266266,2015-10-30 10:18:07:142,1446171487142.0 \n-0.3759,0.2993,9.6678,-0.1369,0.2059,9.8035,0.0024,-0.0208,-0.0086,-15.8,-14.5,-22.5,2.263866573,-1.2,0.8,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 11,266368,2015-10-30 10:18:07:244,1446171487244.0 \n-0.2957,0.2251,9.9323,-0.1302,0.2054,9.8036,-0.0061,-0.0171,-0.0037,-15.8,-14.6,-22.3,2.29947129,-1.2,0.76,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 11,266469,2015-10-30 10:18:07:345,1446171487345.0 \n-0.3077,0.2837,9.675,-0.1598,0.1958,9.8034,-0.011,0.022,0.0147,-15.9,-14.6,-21.9,2.298249559,-1.14,0.93,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 11,266572,2015-10-30 10:18:07:448,1446171487448.0 \n-0.2574,0.3005,9.6917,-0.1681,0.1833,9.8035,-0.0232,0.0122,0.0208,-15.9,-14.5,-22.2,2.263517507,-1.1,0.96,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 11,266673,2015-10-30 10:18:07:549,1446171487549.0 \n-0.2646,0.1772,9.8904,-0.1636,0.1677,9.8039,-0.0134,-0.0195,-0.0122,-16,-14.4,-22,2.265088303,-0.98,0.96,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 11,266776,2015-10-30 10:18:07:652,1446171487652.0 \n-0.3627,0.2622,9.584,-0.1614,0.1607,9.804,0.0024,0.0122,0.0073,-16.1,-14.3,-22.3,2.265786435,-0.94,0.94,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 11,266877,2015-10-30 10:18:07:753,1446171487753.0 \n-0.2035,0.2873,10.2544,-0.1217,0.1858,9.8041,0.0012,-0.0599,-0.0086,-15.9,-14.4,-22.2,2.266484567,-1.09,0.71,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 11,266979,2015-10-30 10:18:07:855,1446171487855.0 \n-0.1999,0.3364,9.6438,-0.114,0.2617,9.8025,0.0476,0.055,-0.044,-16,-14.4,-22.3,2.26072498,-1.53,0.67,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 11,267081,2015-10-30 10:18:07:957,1446171487957.0 \n-0.2897,0.249,9.7659,-0.1461,0.293,9.8012,0.0232,0.0086,-0.0574,-16,-14.5,-22.2,2.257408855,-1.69,0.76,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 11,267183,2015-10-30 10:18:08:059,1446171488059.0 \n-0.6093,0.237,9.3278,-0.1761,0.2845,9.8009,-0.033,0.0501,-0.0806,-15.9,-14.6,-22.1,2.290395577,-1.66,1.03,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 11,267285,2015-10-30 10:18:08:161,1446171488161.0 \n-0.2801,0.2957,10.0173,-0.1427,0.2246,9.803,-0.088,-0.1576,-0.0061,-15.8,-14.7,-21.9,2.297202361,-1.31,0.83,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 11,267388,2015-10-30 10:18:08:264,1446171488264.0 \n0.0287,0.2705,9.9563,0.0357,0.1417,9.8056,-0.0354,-0.0513,-0.1295,-15.7,-14.6,-22.2,2.312735792,-0.88,-0.02,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 11,267491,2015-10-30 10:18:08:367,1446171488367.0 \n-0.2035,0.1927,10.1562,0.04,0.1275,9.8057,0.0024,0.0183,-0.1491,-15.8,-14.6,-22.5,2.317099115,-0.74,-0.23,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 11,267592,2015-10-30 10:18:08:468,1446171488468.0 \n-0.3639,0.0994,10.2699,0.0143,0.1202,9.8059,0.0782,0.055,-0.0953,-15.7,-14.6,-22.4,2.315877384,-0.7,-0.08,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 11,267694,2015-10-30 10:18:08:570,1446171488570.0 \n-0.4429,0.3029,9.5493,-0.0958,0.2189,9.8037,0.0709,0.0073,0.0159,-15.5,-14.8,-22.2,2.335250539,-1.13,0.49,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,267796,2015-10-30 10:18:08:672,1446171488672.0 \n-0.5148,0.2179,9.7659,-0.1196,0.2574,9.8025,0.0428,0.0171,0.0269,-15.1,-14.9,-22.2,2.327745623,-1.5,0.7,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,267897,2015-10-30 10:18:08:773,1446171488773.0 \n-0.3112,0.3089,9.9754,-0.172,0.301,9.8005,0.0305,0.044,0.0672,-15,-15,-22.2,2.322509636,-1.69,0.92,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,268000,2015-10-30 10:18:08:876,1446171488876.0 \n-0.3639,0.4405,9.2823,-0.2617,0.3656,9.7963,0.055,0.1112,0.0513,-15,-15,-22.2,2.309245133,-2.14,1.53,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,268101,2015-10-30 10:18:08:977,1446171488977.0 \n-0.4537,0.4429,9.3278,-0.3308,0.3785,9.7938,0.0061,0.0648,0.0831,-15,-14.9,-21.8,2.304532744,-2.21,1.85,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,268203,2015-10-30 10:18:09:079,1446171489079.0 \n-0.5674,0.3974,9.8665,-0.2888,0.3573,9.7959,-0.066,-0.0586,0.1087,-15,-15,-21.8,2.305929008,-2.16,1.79,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,268306,2015-10-30 10:18:09:182,1446171489182.0 \n-0.2191,0.4621,9.7707,-0.2242,0.3581,9.7975,0.011,-0.0501,0.1075,-15.2,-15,-21.9,2.312386726,-2.09,1.31,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,268407,2015-10-30 10:18:09:283,1446171489283.0 \n-0.2813,0.4393,9.7085,-0.165,0.3706,9.7983,-0.0147,-0.055,0.0354,-15.3,-15,-21.9,2.314132055,-2.21,1.03,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,268509,2015-10-30 10:18:09:385,1446171489385.0 \n-0.3424,0.4022,9.6474,-0.1561,0.3637,9.7987,-0.0024,0.0037,0.0379,-15.7,-14.9,-21.9,2.285334123,-2.13,0.91,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,268612,2015-10-30 10:18:09:488,1446171489488.0 \n-0.4262,0.3388,9.8545,-0.1611,0.3548,9.7989,-0.0159,0.0037,0.0538,-15.8,-14.8,-21.6,2.285857721,-2.07,0.94,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,268713,2015-10-30 10:18:09:589,1446171489589.0 \n-0.2957,0.4357,9.985,-0.1607,0.3426,9.7993,-0.0012,-0.0134,0.0208,-16,-14.7,-22,2.286730386,-2,0.94,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,268815,2015-10-30 10:18:09:691,1446171489691.0 \n-0.1987,0.4776,9.8533,-0.1667,0.3634,9.7985,0.0305,0,0.0122,-16.1,-14.7,-21.7,2.285683188,-2.05,0.98,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,268918,2015-10-30 10:18:09:794,1446171489794.0 \n-0.2885,0.419,9.6235,-0.1776,0.413,9.7963,0.0464,0.0049,-0.0513,-16.1,-14.6,-21.8,2.281494398,-2.33,1.01,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,269020,2015-10-30 10:18:09:896,1446171489896.0 \n-0.4944,0.322,9.7935,-0.1891,0.4227,9.7957,0.0159,-0.0061,-0.055,-16.1,-14.6,-21.8,2.278527338,-2.48,1.09,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,269122,2015-10-30 10:18:09:998,1446171489998.0 \n-0.5471,0.4932,9.5481,-0.1977,0.446,9.7945,0.0367,-0.0024,-0.0208,-16,-14.6,-21.9,2.276083878,-2.61,1.16,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,269224,2015-10-30 10:18:10:100,1446171490100.0 \n-0.4513,0.5638,9.6498,-0.1925,0.4508,9.7944,-0.0098,-0.0367,0.0208,-15.9,-14.7,-21.7,2.275385746,-2.65,1.17,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,269325,2015-10-30 10:18:10:201,1446171490201.0 \n-0.334,0.583,9.6091,-0.1827,0.4565,9.7943,0.011,-0.0037,0.0586,-15.7,-14.8,-21.8,2.27625841,-2.67,1.07,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,269427,2015-10-30 10:18:10:303,1446171490303.0 \n-0.267,0.5758,9.6307,-0.1634,0.462,9.7944,-0.0159,-0.0354,0.0476,-15.7,-14.8,-21.9,2.275909345,-2.74,1,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,269530,2015-10-30 10:18:10:406,1446171490406.0 \n-0.3651,0.5148,9.7695,-0.1556,0.4443,9.7953,-0.0305,-0.0195,0.0428,-15.8,-14.8,-22,2.279050937,-2.6,0.91,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,269634,2015-10-30 10:18:10:510,1446171490510.0 \n-0.328,0.5842,9.6031,-0.1607,0.4297,9.7959,0.0024,0.0122,0.0525,-15.9,-14.8,-21.9,2.279749069,-2.51,0.94,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,269734,2015-10-30 10:18:10:610,1446171490610.0 \n-0.2993,0.4645,9.9156,-0.164,0.4225,9.7962,0.0012,0.0061,0.0367,-16.1,-14.7,-22,2.279923602,-2.49,0.95,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,269836,2015-10-30 10:18:10:712,1446171490712.0 \n-0.267,0.5231,9.7085,-0.1777,0.44,9.7952,0.022,0.0171,0.0257,-16.2,-14.5,-21.9,2.241700891,-2.57,1.04,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,269938,2015-10-30 10:18:10:814,1446171490814.0 \n-0.3292,0.5267,9.5481,-0.1684,0.4485,9.7949,-0.0159,-0.0122,-0.0171,-16.2,-14.5,-21.7,2.241526358,-2.62,0.99,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,270040,2015-10-30 10:18:10:916,1446171490916.0 \n-0.3316,0.5315,9.6462,-0.1501,0.4391,9.7957,-0.0049,-0.0195,0,-16.1,-14.7,-21.6,2.279574536,-2.57,0.89,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,270142,2015-10-30 10:18:11:018,1446171491018.0 \n-0.2909,0.5076,9.8174,-0.1421,0.4314,9.7961,-0.0147,-0.0159,0.0049,-16.2,-14.6,-21.7,2.280447201,-2.55,0.84,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,270244,2015-10-30 10:18:11:120,1446171491120.0 \n-0.2658,0.5219,9.8545,-0.1339,0.438,9.7959,-0.0183,-0.022,-0.0024,-16.2,-14.6,-21.8,2.280970799,-2.56,0.78,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,270345,2015-10-30 10:18:11:221,1446171491221.0 \n-0.0371,0.5614,9.7767,-0.1338,0.4506,9.7954,0.0513,0.0073,-0.0159,-16.2,-14.6,-22,2.281145332,-2.55,0.77,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,270448,2015-10-30 10:18:11:324,1446171491324.0 \n-0.1856,0.6189,9.0525,-0.1441,0.5041,9.7926,-0.0525,-0.033,-0.121,-16.1,-14.7,-21.6,2.274513081,-2.96,0.86,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,270550,2015-10-30 10:18:11:426,1446171491426.0 \n-0.4908,0.3735,10.1957,-0.1002,0.4669,9.795,-0.0208,-0.0733,-0.0941,-16.1,-14.7,-21.6,2.279574536,-2.74,0.67,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,270651,2015-10-30 10:18:11:527,1446171491527.0 \n-0.164,0.5974,9.9359,-0.0659,0.5104,9.7931,0.0379,-0.0208,-0.0782,-16.1,-14.7,-21.5,2.282017997,-2.91,0.42,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,270755,2015-10-30 10:18:11:631,1446171491631.0 \n0.5028,0.729,9.4535,-0.1217,0.5476,9.7906,-0.0367,0.1075,-0.259,-16,-14.9,-21.9,2.272767752,-3.2,0.71,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,270856,2015-10-30 10:18:11:732,1446171491732.0 \n1.16,0.9254,9.5828,-0.1995,0.5557,9.7889,0.0305,0.1002,-0.3567,-15.6,-15,-22.3,2.268578962,-3.16,1.15,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,270958,2015-10-30 10:18:11:834,1446171491834.0 \n1.3707,0.7506,9.3386,-0.1775,0.629,9.7848,0.1393,-0.0318,-0.8858,-14.8,-15.3,-22.5,2.293362637,-3.68,1.04,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,271059,2015-10-30 10:18:11:935,1446171491935.0 \n0.9349,0.2741,9.7719,-0.0894,0.6793,9.7827,0.0843,-0.1772,-1.416,-13.9,-15.5,-22.5,2.32757109,-3.91,0.72,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,271161,2015-10-30 10:18:12:037,1446171492037.0 \n0.2298,-0.0455,9.6403,0.0567,0.691,9.7821,0.0208,-0.2126,-1.5858,-12,-16,-22.2,2.448871473,-4.03,-0.1,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,271263,2015-10-30 10:18:12:139,1446171492139.0 \n0.079,-0.0395,9.4978,0.2015,0.6967,9.7798,0.0037,-0.3115,-1.8094,-10.4,-16.4,-22.2,2.55010057,-4.07,-0.87,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,271366,2015-10-30 10:18:12:242,1446171492242.0 \n-0.1245,-0.6045,10.2783,0.3895,0.6486,9.7774,-0.0635,-0.2688,-2.0036,-7.7,-16.8,-21.9,2.710845394,-3.79,-2.28,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,271468,2015-10-30 10:18:12:344,1446171492344.0 \n-0.0778,-0.8739,10.1466,0.5742,0.721,9.7632,-0.0904,-0.3983,-2.0696,-4.6,-16.7,-22,2.904576941,-4.22,-3.37,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,271569,2015-10-30 10:18:12:445,1446171492445.0 \n-0.1879,-0.9158,9.9826,0.6709,0.7665,9.7536,0.044,-0.2602,-1.9303,-2.3,-16.3,-22.2,3.103369943,-4.36,-3.78,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,271671,2015-10-30 10:18:12:547,1446171492547.0 \n-0.5399,-0.146,8.9232,0.5773,0.754,9.7606,0.0122,0.0635,-1.5369,0.8,-14.7,-22.6,3.318394507,-4.41,-3.39,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,271774,2015-10-30 10:18:12:650,1446171492650.0 \n-0.9673,-0.0455,9.1746,0.418,0.7323,9.7703,-0.1527,-0.0623,-0.9969,2.8,-13.4,-23,3.486644247,-4.45,-2.55,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,271876,2015-10-30 10:18:12:752,1446171492752.0 \n-0.8859,0.5303,9.4667,0.326,0.5563,9.7854,-0.2309,0.033,-0.6439,5,-11.1,-23.4,3.678281399,-3.25,-1.91,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,271977,2015-10-30 10:18:12:853,1446171492853.0 \n-0.7721,0.48,9.7899,0.1885,0.4096,9.7963,-0.0745,-0.0086,-0.2639,6.2,-9.8,-23.7,3.764500664,-2.39,-1.1,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,272080,2015-10-30 10:18:12:956,1446171492956.0 \n-1.3072,-0.3364,11.2109,0.0966,0.1923,9.8043,0.0672,0.1234,0.0159,7,-8.4,-23.5,3.905174201,-1.12,-0.56,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,272181,2015-10-30 10:18:13:057,1446171493057.0 \n-0.1053,0.4896,9.8246,0.0501,0.3211,9.8013,0.088,-0.0208,0.033,7.4,-7.9,-23.3,3.924721889,-1.81,-0.59,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,272284,2015-10-30 10:18:13:160,1446171493160.0 \n-0.3879,-0.0443,9.9168,-0.0153,0.2756,9.8028,-0.1344,-0.0061,-0.1979,7.5,-7.7,-23.2,3.96713339,-1.61,0.09,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,272389,2015-10-30 10:18:13:265,1446171493265.0 \n0.1221,0.1796,9.4248,0.1078,0.2114,9.8038,-0.0733,-0.1283,-0.1173,7.7,-7.6,-23.1,3.967656989,-1.39,-0.18,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,272488,2015-10-30 10:18:13:364,1446171493364.0 \n-0.079,0.2274,9.6343,0.1863,0.1577,9.8036,-0.0611,-0.1014,-0.1881,7.8,-7.4,-23.1,4.046196805,-1.02,-0.97,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,272589,2015-10-30 10:18:13:465,1446171493465.0 \n-0.3196,-0.073,10.0509,0.1728,0.0692,9.8049,-0.0831,-0.0147,-0.281,7.9,-6.9,-23.2,4.029267111,-0.4,-1.01,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,272695,2015-10-30 10:18:13:571,1446171493571.0 \n-0.6297,-0.2263,10.1227,0.1123,0.0825,9.8057,-0.0073,0.044,-0.2272,7.8,-6.4,-23.3,4.099778413,-0.48,-0.66,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 10,272794,2015-10-30 10:18:13:670,1446171493670.0 \n-0.419,0.0658,9.2536,0.069,0.1392,9.8054,0.0757,-0.044,-0.0257,8.1,-5.9,-23.8,4.106410664,-0.81,-0.4,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,272895,2015-10-30 10:18:13:771,1446171493771.0 \n-0.1867,0.1472,9.3829,0.1331,0.1569,9.8045,-0.0293,-0.0721,0.0049,8.3,-5.7,-23.9,4.119500633,-1.04,-0.62,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,272997,2015-10-30 10:18:13:873,1446171493873.0 \n-0.1568,-0.0455,9.8222,0.196,0.1084,9.8041,-0.011,-0.0244,0.0086,8.4,-5.6,-23.7,4.117580771,-0.63,-1.15,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,273100,2015-10-30 10:18:13:976,1446171493976.0 \n-0.0132,0.0814,9.4846,0.2243,0.124,9.8033,-0.0061,-0.0464,-0.0269,8.3,-5.5,-23.8,4.209210557,-0.74,-1.26,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,273202,2015-10-30 10:18:14:078,1446171494078.0 \n-0.0431,0.0718,9.596,0.2417,0.1365,9.8027,0.0195,-0.0073,-0.0696,8.3,-5.6,-23.5,4.126656483,-0.8,-1.41,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,273304,2015-10-30 10:18:14:180,1446171494180.0 \n0.091,0.1018,9.9611,0.2169,0.114,9.8036,-0.0073,0.0391,-0.0806,8.3,-5.4,-23.2,4.204498168,-0.67,-1.27,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,273406,2015-10-30 10:18:14:282,1446171494282.0 \n0.2993,0.2753,9.7624,0.1717,0.1501,9.804,0.0269,0.055,-0.1772,8.3,-5.4,-23.1,4.205894431,-0.82,-1.06,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,273508,2015-10-30 10:18:14:384,1446171494384.0 \n0.6704,0.1712,9.7695,0.1348,0.1866,9.8039,0.0611,0.0916,-0.281,8.3,-5.2,-23.2,4.210432288,-1.09,-0.79,36.814613,-119.74797,287.03,336.8387955,1.82,51.612904,289.44,0 / 12,273609,2015-10-30 10:18:14:485,1446171494485.0 \n0.7673,0.1616,9.4966,0.0537,0.2812,9.8025,0.0757,0.0904,-0.5864,8.7,-4.9,-23.7,4.271344278,-1.64,-0.31,36.814472,-119.74797,284.96,336.8387955,2.16,77.41935,215.07,0 / 12,273711,2015-10-30 10:18:14:587,1446171494587.0 \n0.5363,0.2945,9.7923,0.001,0.3334,9.801,0.0599,0.0574,-0.8748,9.2,-4.1,-23.4,4.369257249,-1.95,-0.01,36.814472,-119.74797,284.96,336.8387955,2.16,77.41935,215.07,914,273813,2015-10-30 10:18:14:689,1446171494689.0 \n0.4022,0.4501,9.4942,-0.0194,0.3994,9.7985,-0.0049,0.0208,-1.0898,9.5,-3.2,-23.4,4.509058123,-2.33,0.01,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,914,273915,2015-10-30 10:18:14:791,1446171494791.0 \n-0.316,0.1173,9.651,0.0013,0.4083,9.7981,0.0305,-0.1161,-1.1594,9.6,-1.7,-23.4,4.608716423,-2.39,-0.01,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,914,274018,2015-10-30 10:18:14:894,1446171494894.0 \n-0.9577,0.2514,9.6319,-0.0596,0.3827,9.799,0.1148,-0.1356,-0.8809,9.7,0.2,-23.8,4.807334892,-2.24,0.35,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,914,274119,2015-10-30 10:18:14:995,1446171494995.0 \n-1.2127,-0.249,10.6674,-0.0597,0.3294,9.8009,-0.0648,-0.0806,-0.5046,9.4,1.6,-24.1,5.03038797,-2.13,0.5,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,914,274221,2015-10-30 10:18:15:097,1446171495097.0 \n-1.0834,0.4322,8.5102,-0.073,0.4326,9.7968,0.1833,-0.0232,-0.3335,9.2,3.5,-24.6,5.237209486,-2.53,0.43,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,914,274324,2015-10-30 10:18:15:200,1446171495200.0 \n-0.9242,0.0263,9.8162,-0.0439,0.2687,9.8029,-0.1087,0.099,-0.5021,8.8,4.4,-24.9,5.203350099,-1.82,0.09,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,914,274425,2015-10-30 10:18:15:301,1446171495301.0 \n-1.4832,0.1915,9.9575,-0.2284,0.0272,9.804,-0.1808,0.0819,-0.2761,8.4,5.7,-24.7,5.40388843,-0.5,1.11,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,914,274528,2015-10-30 10:18:15:404,1446171495404.0 \n-0.9613,0.9122,9.985,-0.2907,-0.0274,9.8023,-0.0733,0.0024,-0.1857,8.2,6.9,-24.7,5.474748798,0.16,1.7,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,914,274629,2015-10-30 10:18:15:505,1446171495505.0 \n-1.0894,0.9254,9.7276,-0.3491,0.0353,9.8004,-0.0073,0.0134,-0.2089,8.2,7.7,-24.7,5.55067062,0.04,1.87,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,274732,2015-10-30 10:18:15:608,1446171495608.0 \n-0.8823,1.2641,9.262,-0.3839,0.1983,9.7971,0.0684,-0.0122,-0.182,8.1,8.6,-25.1,5.647710927,-1.16,2.24,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,274834,2015-10-30 10:18:15:710,1446171495710.0 \n-0.7877,1.2881,9.1889,-0.3574,0.3092,9.7953,0.066,-0.0904,-0.2529,7.9,8.9,-25.3,5.656961172,-1.81,2.09,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,274936,2015-10-30 10:18:15:812,1446171495812.0 \n-0.4202,0.4166,10.07,-0.1979,0.5196,9.7909,0.171,-0.1857,-0.226,7.6,9.3,-25.8,5.655041309,-2.48,1.42,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,275037,2015-10-30 10:18:15:913,1446171495913.0 \n0.571,-0.8212,12.6139,0.0913,0.4651,9.7952,-0.369,-0.4264,-0.6194,7.2,9.5,-26.2,5.73742085,-3.29,0.07,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,275140,2015-10-30 10:18:16:016,1446171496016.0 \n-0.4525,-0.7075,9.7612,-0.002,0.5269,9.7925,-0.022,-0.0929,-0.3225,6.4,10,-27.1,5.800427236,-3.08,0.01,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,275242,2015-10-30 10:18:16:118,1446171496118.0 \n-0.067,-0.2191,9.0597,-0.0861,0.5847,9.7888,0.1466,0.1258,-0.1625,5.9,10.3,-27.5,5.807408553,-3.27,0.13,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,275343,2015-10-30 10:18:16:219,1446171496219.0 \n0.2957,-0.0132,8.2648,-0.1902,0.6611,9.7825,0.2407,0.1503,0.0745,5.3,10.5,-27.7,5.950001953,-3.87,1.11,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,275446,2015-10-30 10:18:16:322,1446171496322.0 \n-0.5459,-0.2502,8.7233,-0.3047,0.7229,9.7752,-0.0806,0.16,0.0428,5.3,10.3,-27.6,5.948256624,-4.28,1.63,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,275548,2015-10-30 10:18:16:424,1446171496424.0 \n-1.6424,-0.3472,10.7188,-0.2315,0.6314,9.7836,-0.0232,-0.0782,0.7453,5.4,9.8,-27.5,5.93970451,-3.85,1.65,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,275650,2015-10-30 10:18:16:526,1446171496526.0 \n-2.1895,-0.7111,9.9323,0.0162,0.686,9.7826,0.0819,-0.3714,1.1619,5.5,8.7,-27.9,5.778087022,-4.01,-0.09,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,275752,2015-10-30 10:18:16:628,1446171496628.0 \n-1.4485,-1.1145,10.4878,0.3704,0.6526,9.7779,0.099,-0.0513,1.8094,5.4,7.7,-27.8,5.731137665,-3.82,-2.17,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,275853,2015-10-30 10:18:16:729,1446171496729.0 \n-0.6117,-0.8356,9.5996,0.4009,0.6119,9.7793,-0.0929,0.2346,1.7226,5.3,5.5,-28,5.611233545,-3.58,-2.35,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,275955,2015-10-30 10:18:16:831,1446171496831.0 \n-0.1472,-0.9313,9.7911,0.2219,0.3854,9.7966,-0.0733,0.2065,1.6994,5.2,3.8,-27.9,5.445601799,-2.55,-1.66,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,276058,2015-10-30 10:18:16:934,1446171496934.0 \n1.0104,-0.1089,8.8406,0.0116,0.3344,9.8009,-0.0354,0.2089,1.3842,5.7,1.8,-28,5.167570849,-1.95,-0.07,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,276160,2015-10-30 10:18:17:036,1446171497036.0 \n1.4078,0.0144,9.566,-0.0645,0.1736,9.8049,-0.2162,-0.0464,0.628,6.2,0.6,-27.6,5.002986301,-1.51,0.39,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,276261,2015-10-30 10:18:17:137,1446171497137.0 \n0.589,0.5231,8.5353,-0.0794,0.0745,9.806,-0.0342,0.1271,0.4215,7,-0.4,-27,4.742757709,-0.44,0.46,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,276364,2015-10-30 10:18:17:240,1446171497240.0 \n-0.7841,0.3496,9.7767,0.0825,-0.1452,9.8052,-0.204,-0.1271,0.0586,7.2,-0.8,-26.7,4.53872872,0.54,-0.29,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,276466,2015-10-30 10:18:17:342,1446171497342.0 \n-0.5746,0.7649,10.1406,0.3227,-0.2159,9.799,-0.0635,-0.0257,-0.0086,7,-0.5,-27,4.637863421,1.26,-1.89,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,276567,2015-10-30 10:18:17:443,1446171497443.0 \n-0.6883,0.917,9.4439,0.2687,-0.1791,9.8013,-0.0073,0.0086,-0.0464,6.8,-0.2,-27.5,4.649208061,1.05,-1.57,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,276671,2015-10-30 10:18:17:547,1446171497547.0 \n-0.5243,0.7841,9.4631,0.1785,-0.0079,9.805,-0.0733,-0.0819,0.0159,6.7,0.3,-27.7,4.715879639,-0.05,-0.94,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,276772,2015-10-30 10:18:17:648,1446171497648.0 \n-0.3196,0.3496,11.2408,0.0862,0.1126,9.8056,0.0709,-0.0953,0.0195,6.8,1,-27.6,4.883082181,-0.5,-0.41,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 14,276873,2015-10-30 10:18:17:749,1446171497749.0 \n0.5758,-0.3926,12.8652,0.0373,0.2716,9.8028,0.0293,-0.099,-0.3323,7.2,1.8,-27.1,5.081351584,-1.59,-0.22,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 14,276976,2015-10-30 10:18:17:852,1446171497852.0 \n0.6476,-0.1939,9.499,-0.0763,0.5196,9.7926,0.3531,0.2859,-0.3592,7.5,2.4,-26.7,5.101946469,-2.68,0.12,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 14,277078,2015-10-30 10:18:17:954,1446171497954.0 \n-0.182,0.1867,7.4172,-0.0744,0.6447,9.7852,0.2724,0.0501,0.0037,8.1,3.4,-26.3,5.255186378,-3.77,0.44,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 14,277180,2015-10-30 10:18:18:056,1446171498056.0 \n-0.0347,0.7386,7.8662,0.2553,0.7224,9.7767,-0.1478,-0.314,-0.1576,8.4,4,-26.3,5.334773392,-4.55,-0.92,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 14,277281,2015-10-30 10:18:18:157,1446171498157.0 \n0.1281,1.0151,7.7764,0.3358,0.6622,9.7785,0.0049,-0.022,-0.0012,8.5,5.1,-26.2,5.318192764,-4.23,-2.06,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 14,277384,2015-10-30 10:18:18:260,1446171498260.0 \n0.4417,0.8906,9.9371,0.5061,0.4274,9.7843,-0.2566,-0.3201,0.2663,8.6,5.8,-26.4,5.339311248,-2.95,-2.41,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 14,277485,2015-10-30 10:18:18:361,1446171498361.0 \n0.1077,0.0922,10.5884,0.4783,0.2605,9.7915,0.0159,0.2407,0.5779,9.1,7,-26.1,5.354844678,-1.52,-2.8,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 14,277588,2015-10-30 10:18:18:464,1446171498464.0 \n-0.4298,-0.4609,11.8609,0.4255,0.034,9.7974,0.2553,0.0098,0.4545,9.9,7.6,-26.1,5.34123111,-0.2,-2.49,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 14,277690,2015-10-30 10:18:18:566,1446171498566.0 \n-0.2131,-0.5387,9.56,0.4319,0.1843,9.7954,0.0684,-0.0684,0.0208,11.2,8,-26.1,5.322207021,-1.08,-2.52,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 14,277791,2015-10-30 10:18:18:667,1446171498667.0 \n-0.668,0.3555,8.3893,0.2911,0.1656,9.8009,0.1527,0.1332,0.1295,12,7.9,-26,5.28695137,-0.76,-1.96,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 14,277894,2015-10-30 10:18:18:770,1446171498770.0 \n-0.6117,0.5207,8.9052,0.3243,0.2672,9.7976,0.0941,-0.1466,0.0977,12.6,7.9,-26,5.272814203,-1.56,-1.9,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 14,277997,2015-10-30 10:18:18:873,1446171498873.0 \n-0.3292,-0.1185,11.7136,0.3827,0.4137,9.7904,0.022,-0.055,-0.1087,13.5,7.7,-25.7,5.255884509,-2.42,-2.24,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 14,278098,2015-10-30 10:18:18:974,1446171498974.0 \n1.0092,0.9708,9.1614,0.2271,0.6261,9.784,0.1478,0.1381,-0.0733,14.3,7.4,-25.3,5.242445474,-3.68,-1.43,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 14,278204,2015-10-30 10:18:19:080,1446171499080.0 \n0.176,0.0287,7.1515,0.0914,0.5612,9.7902,0.2627,0.215,-0.0232,15.1,7.2,-24.8,5.20160477,-2.82,-0.96,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 14,278302,2015-10-30 10:18:19:178,1446171499178.0 \n0.0611,-0.3508,9.068,0.1727,0.4147,9.7964,-0.2822,-0.2028,-0.215,15.7,7,-24.6,5.182929747,-2.99,-0.65,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 14,278403,2015-10-30 10:18:19:279,1446171499279.0 \n-0.1915,0.3196,8.8969,0.1743,0.3576,9.7986,0,-0.0525,0.033,16.6,7,-24.5,5.136154923,-2.09,-1.02,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 14,278507,2015-10-30 10:18:19:383,1446171499383.0 \n0.0287,0.7482,9.8557,0.1887,0.4391,9.795,0.0244,-0.0892,0.1222,17.3,6.6,-24.7,5.146277832,-2.57,-1.1,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 14,278609,2015-10-30 10:18:19:485,1446171499485.0 \n-0.4956,0.2538,11.4431,0.1688,0.5196,9.7914,0.2138,-0.0635,0.2553,17.6,6,-24.6,5.086238506,-2.9,-1.05,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 16,278710,2015-10-30 10:18:19:586,1446171499586.0 \n0.1808,-0.9266,14.2275,0.215,0.5937,9.7863,-0.0806,0.0257,0.16,17.8,4.4,-24.8,4.999844708,-3.47,-1.26,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 16,278811,2015-10-30 10:18:19:687,1446171499687.0 \n0.4094,0.5842,7.4089,0.2675,0.5496,9.7876,0.3348,-0.1148,0.3018,17.7,3.4,-24.8,4.931427802,-2.66,-1.36,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 16,278914,2015-10-30 10:18:19:790,1446171499790.0 \n-0.3783,0.1209,9.2715,0.3869,0.5804,9.7818,-0.0709,-0.1515,0.033,17.8,1.4,-25,4.839972549,-3.39,-2.27,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 16,279017,2015-10-30 10:18:19:893,1446171499893.0 \n-0.3077,0.8679,7.999,0.4856,0.6583,9.7725,0.2077,-0.0464,0.1405,17.5,0.2,-25.1,4.793372258,-3.69,-2.68,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 16,279118,2015-10-30 10:18:19:994,1446171499994.0 \n0.401,0.9254,9.5888,0.472,0.7212,9.7687,0.0831,0.0904,-0.022,16.7,-1.5,-25.3,4.749739026,-3.99,-2.87,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 16,279219,2015-10-30 10:18:20:095,1446171500095.0 \n0.5758,-0.0443,12.7539,0.5806,0.9349,9.7447,0.3995,0.2089,-0.1466,16,-2.5,-25.6,4.717101369,-4.77,-3.53,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 16,279321,2015-10-30 10:18:20:197,1446171500197.0 \n-0.1676,-0.2981,11.5305,0.3227,0.8497,9.7644,-0.4349,0.259,-0.5938,14.9,-3.7,-25.9,4.600862441,-4.97,-1.89,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 16,279423,2015-10-30 10:18:20:299,1446171500299.0 \n0.146,0.5614,6.9827,0.05,0.6762,9.7832,-0.2431,-0.0721,-0.3274,14.5,-4.1,-26,4.583758215,-4.51,-0.08,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 16,279526,2015-10-30 10:18:20:402,1446171500402.0 \n-0.2682,0.2945,8.6251,0.0567,0.5115,9.7931,-0.1906,-0.055,-0.2492,14,-3.8,-25.8,4.53872872,-3.32,-0.51,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 16,279628,2015-10-30 10:18:20:504,1446171500504.0 \n-0.0084,0.9876,9.7923,5.00E-04,0.4201,9.7976,-0.0623,-0.1417,0.1161,13,-2.9,-25.8,4.56857385,-2.46,0,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 16,279730,2015-10-30 10:18:20:606,1446171500606.0 \n-0.3687,0.4082,11.084,0.0591,0.4219,9.7974,0.0648,0.0391,0.1772,12.1,-2.5,-26.1,4.639957816,-2.47,-0.35,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 16,279832,2015-10-30 10:18:20:708,1446171500708.0 \n0.1999,0.0395,8.5605,0.089,0.6363,9.7856,0.1698,0.11,0.2627,10.9,-2.8,-26.3,4.595975519,-3.72,-0.52,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 16,279934,2015-10-30 10:18:20:810,1446171500810.0 \n-0.7242,-0.2382,8.5269,0.1622,0.4393,9.7955,0.3067,-0.1319,0.3971,10,-2.9,-26.8,4.532271002,-2.3,-1.2,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 16,280038,2015-10-30 10:18:20:914,1446171500914.0 \n0.0192,-0.1257,9.6738,0.4058,0.5113,9.7849,-0.0806,-0.2712,-0.0147,8.8,-3,-26.9,4.554611216,-2.99,-2.37,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 16,280137,2015-10-30 10:18:21:013,1446171501013.0 \n-0.5722,0.5722,9.0656,0.3715,0.3617,9.7929,-0.0232,0.0073,0.0794,8.2,-2.5,-27,4.600338842,-2.11,-2.17,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 16,280239,2015-10-30 10:18:21:115,1446171501115.0 \n-0.3065,0.8416,9.5864,0.4267,0.4136,9.7886,0.1344,-0.0061,0.1112,7.7,-1.9,-26.9,4.605400297,-2.18,-2.49,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 16,280346,2015-10-30 10:18:21:222,1446171501222.0 \n-0.0527,0.243,11.497,0.588,0.6023,9.7705,0.2224,-0.3409,-0.1087,7.3,-1.1,-27,4.785518276,-3.52,-3.44,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 16,280444,2015-10-30 10:18:21:320,1446171501320.0 \n0.996,-0.1879,10.258,0.5021,0.6401,9.7728,-0.4801,0.0623,-0.5009,7.3,-0.8,-26.8,4.828278843,-4.25,-2.97,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 16,280545,2015-10-30 10:18:21:421,1446171501421.0 \n0.4884,0.401,7.9476,0.3066,0.418,9.7929,-0.314,-0.1222,-0.1918,7.9,0,-26.9,4.856029578,-2.72,-1.68,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 16,280648,2015-10-30 10:18:21:524,1446171501524.0 \n-0.0347,1.0989,7.9224,0.2879,0.2894,9.7981,0.0049,0.0134,-0.0305,8.6,1.2,-27.5,4.893030558,-1.69,-1.68,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 16,280750,2015-10-30 10:18:21:626,1446171501626.0 \n-0.1879,0.8392,8.418,0.2754,0.3793,9.7954,0.1662,0.0403,0.0489,9.1,2.1,-27.7,5.008745887,-2.04,-1.61,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 16,280851,2015-10-30 10:18:21:727,1446171501727.0 \n-0.3424,0.0263,11.3569,0.231,0.4795,9.7922,0.1881,0.11,0.2602,9.8,2.9,-28,5.10020114,-2.8,-1.35,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 16,280954,2015-10-30 10:18:21:830,1446171501830.0 \n0.7111,0.012,9.5349,0.2358,0.6661,9.7812,-0.4215,-0.2395,0.1124,10.5,2.8,-27.9,5.108055122,-3.89,-1.38,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 16,281055,2015-10-30 10:18:21:931,1446171501931.0 \n0.2442,0.6488,8.6706,0.3041,0.5154,9.7884,0.1613,0.0953,0.3873,11.6,2.5,-27.3,5.042256209,-3.01,-1.78,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 16,281158,2015-10-30 10:18:22:034,1446171502034.0 \n-0.2394,0.1425,8.837,0.3773,0.4352,9.7897,-0.1332,0.077,0.1075,12.2,2.4,-27,4.957956806,-2.77,-2.31,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 16,281260,2015-10-30 10:18:22:136,1446171502136.0 \n-0.3352,1.0355,7.4759,0.3335,0.4432,9.791,0.0929,0.022,0.0342,13,2.5,-26.7,4.998622978,-2.4,-2.04,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 16,281361,2015-10-30 10:18:22:237,1446171502237.0 \n-0.2981,0.8033,9.2189,0.3897,0.5027,9.786,0.0611,-0.0806,-0.0244,13.4,2.5,-26.6,5.007175091,-2.74,-2.21,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 16,281463,2015-10-30 10:18:22:339,1446171502339.0 \n0.5543,0.0874,11.0145,0.465,0.6337,9.7751,0.2492,0.0403,-0.0757,13.9,2.7,-26.9,5.01066575,-3.71,-2.72,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 16,281566,2015-10-30 10:18:22:442,1446171502442.0 \n-0.6129,-1.0463,12.0787,0.264,0.3665,9.7962,-0.2798,0.2187,-0.2993,14.4,2.7,-27.1,4.993561523,-2.87,-2.06,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,281667,2015-10-30 10:18:22:543,1446171502543.0 \n-0.0886,-0.1353,9.6582,0.2852,0.2709,9.7988,-0.1185,-0.0904,-0.1075,15.1,3.4,-27.5,4.944692304,-1.58,-1.67,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,281769,2015-10-30 10:18:22:645,1446171502645.0 \n-0.8188,0.3771,8.8597,0.3121,0.1575,9.8004,-0.1271,0.0049,-0.0672,15.8,4.2,-27.7,4.969650512,-0.92,-1.82,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,281872,2015-10-30 10:18:22:748,1446171502748.0 \n-0.0658,0.911,9.1854,0.2634,0.242,9.8001,0.1136,0.0635,0.0782,16,4.7,-27.9,5.033005964,-1.22,-1.67,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,281974,2015-10-30 10:18:22:850,1446171502850.0 \n-0.5626,0.1209,12.3696,0.1469,0.4123,9.7969,0.215,0.0305,0.1943,16.6,4.6,-27.9,5.052379119,-2.41,-0.86,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,282075,2015-10-30 10:18:22:951,1446171502951.0 \n0.3172,-0.0371,9.9,0.0824,0.5632,9.7901,0.1002,0.1503,0.2749,17.1,4.2,-27.9,5.038765551,-3.72,-0.28,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,282178,2015-10-30 10:18:23:054,1446171503054.0 \n-0.6357,-0.0419,9.5397,0.1596,0.4752,9.7938,0.2822,-0.2651,0.4068,17.6,3.5,-27.9,4.993910589,-2.78,-0.93,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,282280,2015-10-30 10:18:23:156,1446171503156.0 \n-0.1616,0.2849,8.4898,0.4896,0.5017,9.7816,0.011,-0.1161,0.0929,17.9,2.2,-28.5,4.88779457,-3.01,-2.71,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,282382,2015-10-30 10:18:23:258,1446171503258.0 \n-0.559,1.0139,7.8003,0.5513,0.5755,9.7742,0.1319,-0.0122,0.0599,17.7,1.6,-28.9,4.889714432,-3.1,-3.19,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,282483,2015-10-30 10:18:23:359,1446171503359.0 \n-0.1664,0.9661,9.3817,0.5871,0.7133,9.763,0.1747,0.0073,-0.033,17.3,1,-29.4,4.862312763,-3.77,-3.5,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,282586,2015-10-30 10:18:23:462,1446171503462.0 \n0.4537,0.1604,10.8086,0.531,0.8259,9.7574,0.1136,0.033,-0.1747,17,0.5,-30.1,4.895299486,-4.83,-3.11,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,282687,2015-10-30 10:18:23:563,1446171503563.0 \n-0.2945,-0.5291,10.7428,0.3805,0.6785,9.7757,-0.4484,0.3213,-0.4618,16.9,0.4,-30.1,4.823740987,-3.97,-2.23,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,282790,2015-10-30 10:18:23:666,1446171503666.0 \n0.0299,0.0407,10.2687,0.3431,0.2772,9.7967,-0.171,0.0195,-0.2126,17,1,-29.7,4.842765076,-2.62,-1.75,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,282891,2015-10-30 10:18:23:767,1446171503767.0 \n-0.6823,0.4429,8.4862,0.3116,0.1699,9.8002,-0.1038,-0.0171,-0.0733,17,2,-29.2,4.850619057,-0.99,-1.82,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,282994,2015-10-30 10:18:23:870,1446171503870.0 \n0.2705,1.0199,9.7887,0.3278,0.2413,9.7982,0.1454,0.1161,0.2016,17,2.9,-29,4.915545305,-1.41,-1.92,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,283097,2015-10-30 10:18:23:973,1446171503973.0 \n-0.2729,0.4812,10.3406,0.1756,0.4363,9.7954,0.1784,0.1979,0.1381,17,2.8,-28.8,4.940678047,-2.22,-1.33,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,283198,2015-10-30 10:18:24:074,1446171504074.0 \n-0.0204,-0.0503,9.1877,0.0885,0.7027,9.781,0.1979,0.1234,0.2395,17.4,1.8,-28.2,4.938583651,-4.09,-0.6,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,283300,2015-10-30 10:18:24:176,1446171504176.0 \n-0.7793,-0.0766,9.3529,0.204,0.5407,9.7896,0.0379,-0.171,0.3372,17.8,1,-27.7,4.842765076,-2.97,-1.15,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,283401,2015-10-30 10:18:24:277,1446171504277.0 \n-0.2382,0.5686,8.6203,0.4311,0.4251,9.7879,-0.1784,-0.237,0.11,18,0,-27.2,4.771555642,-2.48,-2.52,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,283504,2015-10-30 10:18:24:380,1446171504380.0 \n-0.7075,0.492,9.7624,0.5437,0.3437,9.7855,0.0281,-0.1002,0.0403,17.9,-0.3,-27.1,4.754625948,-1.82,-3.15,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,283605,2015-10-30 10:18:24:481,1446171504481.0 \n-0.0156,0.9768,9.6151,0.5371,0.5406,9.777,0.1686,0.0672,-0.1295,17.7,-1,-27.2,4.726875213,-2.84,-3.28,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,283708,2015-10-30 10:18:24:584,1446171504584.0 \n0.3555,0.1113,10.4339,0.5497,0.7673,9.7611,0.3225,0.1466,-0.2382,17.6,-1.9,-26.8,4.714308843,-4.49,-3.22,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,283809,2015-10-30 10:18:24:685,1446171504685.0 \n-0.3304,-0.8547,11.2743,0.2539,0.6503,9.7818,-0.4875,0.3103,-0.6426,17.7,-2.4,-26.4,4.717275902,-4.74,-2.34,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,283911,2015-10-30 10:18:24:787,1446171504787.0 \n0.0012,-0.0263,9.584,0.1456,0.4225,9.7965,-0.4985,-0.0953,-0.2529,18.1,-2.2,-25.6,4.66404336,-2.47,-0.85,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,284014,2015-10-30 10:18:24:890,1446171504890.0 \n0.158,0.7949,8.0014,0.156,0.1715,9.8039,-0.0648,0.0061,-0.011,18.3,-1.7,-25,4.627391446,-1,-0.91,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,284117,2015-10-30 10:18:24:993,1446171504993.0 \n-0.0886,0.8799,8.6491,0.1629,0.1811,9.8036,0.1222,-0.0452,0.0892,18.4,-1,-24.8,4.679751323,-0.93,-0.86,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,284217,2015-10-30 10:18:25:093,1446171505093.0 \n-0.6883,0.1221,10.5177,0.1041,0.2854,9.8019,0.1955,0.1173,0.1662,18,-1,-24.9,4.697204616,-1.67,-0.61,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,284320,2015-10-30 10:18:25:196,1446171505196.0 \n-0.1389,0.6404,9.4068,0.1157,0.6678,9.7832,-0.022,-0.0672,0.3299,17.6,-1.9,-24.9,4.690572365,-3.69,-0.65,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,284421,2015-10-30 10:18:25:297,1446171505297.0 \n-0.5064,-0.4214,11.1091,0.2787,0.3961,9.7947,-0.3616,-0.1491,0.237,16.9,-2.5,-24.8,4.662298031,-2.6,-1.63,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,284524,2015-10-30 10:18:25:400,1446171505400.0 \n-0.3651,0,8.6562,0.5077,0.28,9.7895,-0.2089,-0.0318,-0.0379,16.1,-3.3,-25.4,4.579394891,-1.64,-2.97,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,284626,2015-10-30 10:18:25:502,1446171505502.0 \n-0.4681,0.4202,9.6929,0.4371,0.2615,9.7934,0.2346,0.0269,-0.0061,15.6,-3.2,-26.1,4.56735212,-1.11,-2.66,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,284727,2015-10-30 10:18:25:603,1446171505603.0 \n-0.6812,0.5471,9.754,0.3479,0.4065,9.792,0.1979,0.1857,-0.0232,15.5,-3,-27,4.600687908,-2.38,-2.03,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,284830,2015-10-30 10:18:25:706,1446171505706.0 \n-1.2043,0.3196,11.0038,0.2186,0.5406,9.7893,0.0709,0.0049,-0.1356,15.6,-2.7,-27.1,4.620584662,-3.16,-1.28,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,284932,2015-10-30 10:18:25:808,1446171505808.0 \n1.0762,0.2622,9.7169,0.1877,0.5838,9.7875,-0.2993,0.0318,-0.2443,15.8,-2.5,-27.2,4.687779838,-3.41,-1.1,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,285033,2015-10-30 10:18:25:909,1446171505909.0 \n-0.0814,-0.0611,8.8585,0.1068,0.3311,9.8005,-0.2798,-0.0086,0.0892,16,-2,-27.4,4.648335397,-2.04,-0.54,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,285136,2015-10-30 10:18:26:012,1446171506012.0 \n0.0599,0.3496,8.9316,0.0915,0.1128,9.8056,-0.1307,0.0049,0.2529,16.6,-1.3,-27.4,4.672420941,-0.66,-0.53,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,285238,2015-10-30 10:18:26:114,1446171506114.0 \n-0.0874,0.9301,8.3234,0.0053,0.1309,9.8058,0.0073,0.2065,0.2028,16.9,-0.7,-27.7,4.675562533,-0.75,-0.36,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,285339,2015-10-30 10:18:26:215,1446171506215.0 \n-0.085,0.7745,9.3242,-0.049,0.1548,9.8053,0.0586,-0.0037,0.1344,17.6,-0.8,-27.7,4.68132212,-0.9,0.29,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,285441,2015-10-30 10:18:26:317,1446171506317.0 \n-0.4298,0.0826,12.5133,0.136,0.2872,9.8015,0.0648,-0.3286,0.1845,17.9,-1.1,-27.8,4.689176101,-1.19,-0.37,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,285544,2015-10-30 10:18:26:420,1446171506420.0 \n-0.7661,-0.9625,12.9251,0.0678,0.3268,9.801,-0.3091,-0.3311,0.1649,18,-1.6,-27.9,4.661774432,-2.21,-0.49,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,285645,2015-10-30 10:18:26:521,1446171506521.0 \n0.492,0.7949,8.3701,0.2628,0.3085,9.7983,-0.1845,-0.2407,-0.1014,18,-2.4,-28.2,4.644844738,-1.54,-1.05,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,285748,2015-10-30 10:18:26:624,1446171506624.0 \n-0.6812,0.1006,9.5936,0.2487,-0.0154,9.8035,-0.0244,-0.1784,-0.2187,18.2,-3,-28.7,4.560894401,-0.3,-1.36,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,285849,2015-10-30 10:18:26:725,1446171506725.0 \n-0.5782,0.7661,8.6503,0.1772,0.0997,9.8045,0.1319,0.2272,-0.0648,18.6,-2.8,-29.5,4.574507969,-0.58,-1.04,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,285952,2015-10-30 10:18:26:828,1446171506828.0 \n-0.8571,-0.0132,10.9068,0.2223,0.2613,9.8006,0.1173,-0.2602,-0.2358,18.8,-2.4,-30.2,4.650953391,-1.53,-1.3,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,286055,2015-10-30 10:18:26:931,1446171506931.0 \n0.5507,-0.2047,11.5197,0.3792,0.4253,9.7901,-0.1833,-0.121,-0.1796,18.8,-2,-31.1,4.67835506,-2.49,-2.22,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,286156,2015-10-30 10:18:27:032,1446171507032.0 \n0.4142,0.0622,10.7811,0.3513,0.3034,9.7957,-0.0696,0.1038,0.1051,18.8,-1.9,-32.4,4.661250833,-1.77,-2.23,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,286258,2015-10-30 10:18:27:134,1446171507134.0 \n-0.2263,-0.2191,10.1335,0.3548,0.1181,9.7995,-0.3775,-0.0867,-0.2859,19,-1.8,-34.2,4.650778858,-1.3,-2.01,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,286360,2015-10-30 10:18:27:236,1446171507236.0 \n-0.5902,0.164,8.4539,0.2216,0.0089,9.8041,0.0086,-0.0269,-0.0318,19.2,-1.6,-35.2,4.616046806,-0.14,-1.34,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,286462,2015-10-30 10:18:27:338,1446171507338.0 \n0.182,0.4693,9.5768,0.2504,0.0334,9.8034,0.0171,-0.0049,0.0476,19.9,-1.3,-36.2,4.670326545,-0.2,-1.46,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,286563,2015-10-30 10:18:27:439,1446171507439.0 \n0.2813,0.0455,9.8186,0.268,0.1531,9.8018,0.171,-0.0831,0.2285,20.1,-1,-36.7,4.683067449,-0.61,-1.41,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 15,286666,2015-10-30 10:18:27:542,1446171507542.0 \n0.073,-0.5578,11.0217,0.4688,0.3761,9.7882,-0.3702,-0.0635,0.0672,20.2,-1.7,-37.4,4.683940114,-2.2,-2.74,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,286767,2015-10-30 10:18:27:643,1446171507643.0 \n0.1401,0.1856,9.1554,0.6147,0.2736,9.7835,-0.0696,-0.3213,-0.0819,20.2,-2.7,-38.5,4.624249853,-1.6,-3.6,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,286869,2015-10-30 10:18:27:745,1446171507745.0 \n-0.067,0.1796,7.6782,0.7448,0.1916,9.7764,-0.121,0.0379,-0.1808,19.8,-3.2,-39.5,4.613603345,-1.12,-4.36,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,286972,2015-10-30 10:18:27:848,1446171507848.0 \n-0.5004,0.3112,9.0668,0.6939,0.0386,9.782,-0.0024,-0.0342,-0.193,19.7,-3,-40.6,4.588470603,-0.23,-4.06,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,287074,2015-10-30 10:18:27:950,1446171507950.0 \n-0.5878,0.5842,9.7061,0.5723,0.0786,9.7896,0.1038,0.1063,-0.0977,19.7,-2.6,-41,4.5900414,-0.32,-3.66,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,287175,2015-10-30 10:18:28:051,1446171508051.0 \n-0.668,0.1101,11.3306,0.5729,0.1727,9.7884,0.1271,-0.1087,-0.1625,20.1,-2.1,-40.8,4.654269516,-1.01,-3.35,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,287278,2015-10-30 10:18:28:154,1446171508154.0 \n1.0834,-0.826,12.2715,0.6779,0.2297,9.7805,-0.3201,-0.0953,-0.2712,20.3,-2.3,-40.5,4.67835506,-1.83,-3.84,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,287380,2015-10-30 10:18:28:256,1446171508256.0 \n0.6404,0.085,7.7704,0.52,0.2596,9.7894,-0.1429,-0.0929,-0.1808,20.4,-2.3,-40.1,4.668581216,-1.52,-3.04,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,287481,2015-10-30 10:18:28:357,1446171508357.0 \n-0.1257,-0.0144,8.9328,0.5032,0.04,9.7937,-0.2358,0.0733,-0.1955,20.5,-2.3,-39.9,4.643099409,-0.58,-3.12,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,287584,2015-10-30 10:18:28:460,1446171508460.0 \n-0.4944,0.3531,8.6993,0.4344,-0.0854,9.7967,-0.088,0.0806,0.0757,20.6,-1.8,-39.8,4.613952411,0.37,-2.65,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,287686,2015-10-30 10:18:28:562,1446171508562.0 \n0.4848,0.5375,10.0856,0.3715,-0.1131,9.799,0.1894,0.1833,0.0904,21.1,-1.3,-39.4,4.648335397,0.66,-2.17,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,287787,2015-10-30 10:18:28:663,1446171508663.0 \n0.3029,0.1137,10.9559,0.2818,0.17,9.8011,0.2627,0.0305,0.1906,21.4,-1.4,-39.1,4.68132212,-0.47,-1.46,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,287890,2015-10-30 10:18:28:766,1446171508766.0 \n-0.3543,-0.6464,12.0452,0.3773,0.1357,9.7984,-0.2101,-0.2981,0.0183,21.8,-2.5,-38.9,4.65688751,-1.07,-1.76,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,287992,2015-10-30 10:18:28:868,1446171508868.0 \n0.2107,0.0239,8.5389,0.5111,0.1946,9.7914,-0.1674,-0.2908,-0.1014,21.8,-3.8,-38.8,4.577824095,-1.14,-2.99,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,288093,2015-10-30 10:18:28:969,1446171508969.0 \n-0.7865,-0.2382,10.7284,0.7248,-0.1611,9.7785,-0.0318,-0.0208,-0.1112,21.6,-4,-39.1,4.528780343,0.94,-4.24,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,288195,2015-10-30 10:18:29:071,1446171509071.0 \n-0.0168,0.6943,9.7049,0.7306,-0.1121,9.7788,0.0965,0,-0.0672,21.3,-3.6,-39.5,4.528780343,0.65,-4.27,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,288297,2015-10-30 10:18:29:173,1446171509173.0 \n-0.2538,0.4561,10.258,0.6285,0.0733,9.7862,0.2627,0.0391,-0.1857,21.3,-3.4,-39.4,4.58410728,0.06,-3.86,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,288399,2015-10-30 10:18:29:275,1446171509275.0 \n0.267,-0.2394,11.248,0.5583,0.2623,9.7872,-0.1185,0.1332,-0.2773,21.6,-3.8,-38.6,4.589343268,-1.53,-3.27,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,288502,2015-10-30 10:18:29:378,1446171509378.0 \n-0.097,-0.3723,10.9654,0.2797,0.0714,9.8024,-0.2517,0.4459,-0.1857,21.9,-4.1,-38,4.552167755,-0.42,-1.63,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,288604,2015-10-30 10:18:29:480,1446171509480.0 \n-0.2514,0.1245,9.08,0.1184,0.1078,9.8053,-0.1234,-0.0098,-0.1014,22.6,-4.2,-37.2,4.565955856,-0.85,-0.68,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,288706,2015-10-30 10:18:29:582,1446171509582.0 \n-0.5028,0.6165,8.6107,0.0856,0.0121,9.8063,-0.0367,0.0489,0.0452,23.1,-4,-36.9,4.544488306,-0.07,-0.5,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,288807,2015-10-30 10:18:29:683,1446171509683.0 \n-0.4022,0.4621,9.2548,0.0683,-0.0111,9.8064,-0.0684,0.0293,0.1332,23.3,-4.2,-36.6,4.540299516,0.06,-0.4,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,288910,2015-10-30 10:18:29:786,1446171509786.0 \n-0.3112,0.3615,11.1282,0.2556,0.2311,9.8006,0.2346,-0.2505,0.3238,22.9,-5,-36.3,4.540124983,-1.35,-1.49,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,289016,2015-10-30 10:18:29:892,1446171509892.0 \n-0.0263,-1.1181,11.9854,0.3927,0.2668,9.7952,-0.3665,-0.2957,0.0684,22.4,-6.2,-36.3,4.510977985,-2.06,-1.87,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,289114,2015-10-30 10:18:29:990,1446171509990.0 \n0.4669,0.6081,9.2261,0.4978,0.2154,9.7916,0.0367,-0.1417,0.1258,21.1,-8.2,-36.9,4.406781828,-1.26,-2.91,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,289216,2015-10-30 10:18:30:092,1446171510092.0 \n-0.1065,0.3567,8.9783,0.4877,0.1286,9.7937,-0.1772,0.1051,-0.0061,20.2,-9.4,-37.3,4.347266101,-1.03,-2.91,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,289318,2015-10-30 10:18:30:194,1446171510194.0 \n-0.2215,0.8356,8.2109,0.4175,0.2107,9.7955,0.1344,0.0464,0.0757,19,-10.2,-37.6,4.292462762,-1.23,-2.44,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,289420,2015-10-30 10:18:30:296,1446171510296.0 \n-0.1963,0.5746,9.3901,0.4268,0.3205,9.7921,0.1918,-0.0855,-0.0794,18.2,-10.7,-37.3,4.248131399,-1.87,-2.5,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,289522,2015-10-30 10:18:30:398,1446171510398.0 \n-0.2885,0.3364,10.3441,0.5274,0.475,9.7809,0.1405,-0.1234,-0.088,17.2,-11.1,-36.9,4.258952441,-2.78,-3.09,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,289623,2015-10-30 10:18:30:499,1446171510499.0 \n-0.3627,-0.8655,11.9902,0.4638,0.1812,9.794,-0.3787,0.1772,-0.1833,16.5,-11.2,-36.7,4.227536514,-1.64,-2.99,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,289726,2015-10-30 10:18:30:602,1446171510602.0 \n0.1712,-0.1736,9.3901,0.4421,0.0919,9.7962,-0.1503,0.0415,-0.1161,15.4,-10.7,-36.5,4.149869362,-0.81,-2.66,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,289828,2015-10-30 10:18:30:704,1446171510704.0 \n-0.6632,0.0036,8.8585,0.4333,-0.0785,9.7968,-0.0709,-0.1283,0.1161,14.5,-9.8,-36.9,4.15807241,0.46,-2.53,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,289930,2015-10-30 10:18:30:806,1446171510806.0 \n0.3112,0.5052,9.3793,0.519,-0.1188,9.7922,-0.0318,-0.0733,0.2248,13.8,-9.3,-37,4.177096499,0.65,-2.92,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,290033,2015-10-30 10:18:30:909,1446171510909.0 \n-0.1939,-0.0802,11.3042,0.5083,-0.0042,9.7935,0.2321,0.0012,0.2651,12.5,-9,-37.1,4.16819532,0.02,-2.97,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,290133,2015-10-30 10:18:31:009,1446171511009.0 \n0.4729,-0.103,8.9974,0.4845,0.3247,9.7893,-0.2798,-0.2456,0.0843,11.7,-9.4,-36.7,4.194026193,-1.76,-2.84,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,290238,2015-10-30 10:18:31:114,1446171511114.0 \n0.5626,0.5531,8.6526,0.5991,0.1704,9.7868,0.044,0.055,0.237,10.3,-10,-36.6,4.059286774,-1,-3.5,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,290338,2015-10-30 10:18:31:214,1446171511214.0 \n-0.2753,0.2191,8.521,0.681,0.0779,9.7827,-0.1857,-0.1796,-0.022,9.4,-10.3,-36.4,4.012337417,-0.78,-3.7,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,290439,2015-10-30 10:18:31:315,1446171511315.0 \n-0.2454,0.4381,8.9004,0.834,0.0487,9.771,0.1222,-0.0562,-0.0208,8.1,-9.7,-36.5,3.976209102,-0.1,-4.78,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,290542,2015-10-30 10:18:31:418,1446171511418.0 \n0.0898,0.9876,8.9639,0.8332,0.1798,9.7695,0.1332,0,-0.0867,7.3,-9.3,-36.2,4.01129022,-0.77,-4.97,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,290644,2015-10-30 10:18:31:520,1446171511520.0 \n0.0431,0.34,11.2372,0.8122,0.3895,9.7652,0.2578,-0.0122,-0.1466,6.6,-8.7,-36.3,4.045673206,-1.81,-4.85,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,290745,2015-10-30 10:18:31:621,1446171511621.0 \n0.1939,-0.8847,12.3146,0.8113,0.4174,9.7641,-0.5864,0.044,-0.4643,5.9,-8,-36.1,4.085815779,-2.44,-4.75,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,290847,2015-10-30 10:18:31:723,1446171511723.0 \n0.1796,0.3472,8.3139,0.6395,0.3065,9.781,0.2749,0.2676,0.0049,5.8,-7.2,-36.3,4.089655503,-1.33,-4.17,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,290950,2015-10-30 10:18:31:826,1446171511826.0 \n-0.3436,0.1975,8.7604,0.6766,0.286,9.7791,0.0122,0.1087,-0.0794,5.9,-5.6,-36,4.186172211,-1.53,-4.33,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,291051,2015-10-30 10:18:31:927,1446171511927.0 \n-0.0215,0.7997,8.6503,0.6126,0.3755,9.7803,0.121,0.1038,0.088,6.5,-4.1,-35.9,4.434183498,-2.19,-3.58,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,291154,2015-10-30 10:18:32:030,1446171512030.0 \n-0.0742,0.7602,9.1638,0.4127,0.4135,9.7892,0.066,0.1772,0.1869,7,-3.5,-35.9,4.53872872,-2.42,-2.41,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,291255,2015-10-30 10:18:32:131,1446171512131.0 \n-0.1401,0.2753,11.0792,0.3489,0.4985,9.7878,0.2248,-0.1063,0.3482,7.8,-3,-36.1,4.565432257,-2.63,-1.9,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,291359,2015-10-30 10:18:32:235,1446171512235.0 \n-0.1903,-0.0646,11.3808,0.5556,0.4411,9.781,0.1442,-0.1014,0.3372,9.2,-3,-35.7,4.58585261,-2.58,-3.25,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,291460,2015-10-30 10:18:32:336,1446171512336.0 \n0.2167,0.583,9.0441,0.736,0.4154,9.7702,-0.2492,-0.248,-0.1539,9.8,-3.2,-36,4.608716423,-2.78,-3.81,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,291561,2015-10-30 10:18:32:437,1446171512437.0 \n-0.5387,0.2478,9.9671,0.7634,0.2827,9.7728,-0.0806,-0.0122,0.0538,10.1,-3,-36.5,4.558101875,-1.65,-4.47,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,291663,2015-10-30 10:18:32:539,1446171512539.0 \n-0.0587,1.0714,7.8733,0.6816,0.4802,9.7711,0.1881,0.0379,0.2236,10.5,-2.9,-37.2,4.61150895,-2.58,-3.99,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,291766,2015-10-30 10:18:32:642,1446171512642.0 \n0.4214,0.7554,10.5105,0.6602,0.6011,9.7659,0.0892,-0.066,-0.0721,11.1,-3,-37.7,4.659505504,-3.51,-3.87,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,291867,2015-10-30 10:18:32:743,1446171512743.0 \n0.7961,-0.1592,10.4615,0.5725,0.6939,9.7653,-0.2297,0.2114,-0.2883,11.8,-3.4,-37.9,4.687256239,-4.06,-3.36,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,291970,2015-10-30 10:18:32:846,1446171512846.0 \n-0.1784,0.431,9.0513,0.3558,0.5276,9.786,-0.0672,0.237,-0.1148,12.4,-3.3,-37.9,4.639434218,-3.08,-2.08,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,292071,2015-10-30 10:18:32:947,1446171512947.0 \n0.4046,0.5495,8.9771,0.4176,0.4052,9.7894,-0.2443,-0.1857,-0.1136,13.4,-2.8,-37.8,4.613254279,-2.37,-2.44,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,292173,2015-10-30 10:18:33:049,1446171513049.0 \n-0.3615,0.8104,8.7831,0.4913,0.2354,9.7915,-0.055,-0.066,-0.0159,14.5,-1.8,-38.2,4.646939133,-1.38,-2.87,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,292276,2015-10-30 10:18:33:152,1446171513152.0 \n0.4238,0.929,10.0353,0.4906,0.2081,9.7922,-0.0562,0,0.0794,14.9,-1.2,-38.4,4.699299011,-1.2,-2.95,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,292379,2015-10-30 10:18:33:255,1446171513255.0 \n0.0227,0.7649,12.469,0.4699,0.3193,9.7902,0.0745,-0.16,0.2065,15.5,-0.8,-39.1,4.726002549,-1.87,-2.75,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,292480,2015-10-30 10:18:33:356,1446171513356.0 \n0.5698,-0.1856,11.3198,0.6253,0.3529,9.7803,-0.1576,-0.2663,0.121,16,-0.9,-39.5,4.746248368,-2.42,-3.06,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,292582,2015-10-30 10:18:33:458,1446171513458.0 \n0.5626,0.8775,8.5186,0.7152,0.4472,9.7703,0.2126,-0.1246,0.3176,16.5,-1.5,-40,4.750786224,-2.61,-4.19,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,292683,2015-10-30 10:18:33:559,1446171513559.0 \n0.0599,0.3783,8.8897,0.7637,0.3884,9.7691,0.0415,0.0379,0.0696,16.7,-1.9,-40.2,4.690746898,-2.32,-4.53,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,292786,2015-10-30 10:18:33:662,1446171513662.0 \n0.1197,0.8511,8.1283,0.6923,0.4697,9.7709,0.0599,0.0782,-0.0733,17.2,-2.1,-40.1,4.701393406,-2.64,-4.19,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,292888,2015-10-30 10:18:33:764,1446171513764.0 \n-0.1808,0.9242,10.726,0.6166,0.5198,9.7734,-0.0696,-0.1234,-0.2224,18.2,-2.1,-39.9,4.715181507,-3.04,-3.61,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,292991,2015-10-30 10:18:33:867,1446171513867.0 \n0.3998,0.5902,11.4431,0.6708,0.5334,9.7691,0.1808,-0.0086,0.0367,19,-1.9,-39.6,4.717101369,-3.12,-3.93,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,293092,2015-10-30 10:18:33:968,1446171513968.0 \n0.0467,-0.1532,10.8445,0.5499,0.3912,9.7834,-0.2419,0.2224,-0.1894,20.3,-1.7,-39.1,4.690223299,-2.29,-3.22,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,293193,2015-10-30 10:18:34:069,1446171514069.0 \n0.6512,0.5088,8.1882,0.5838,0.4279,9.7799,-0.2749,-0.1759,-0.077,21.2,-1.3,-38.9,4.749913559,-2.82,-2.93,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,293296,2015-10-30 10:18:34:172,1446171514172.0 \n-0.2071,0.7626,8.6095,0.6142,0.2773,9.7835,-0.1527,0.0049,-0.0953,22.6,-0.6,-38.7,4.714832441,-1.62,-3.59,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,293397,2015-10-30 10:18:34:273,1446171514273.0 \n0.3543,0.7733,9.2847,0.6193,0.2078,9.7849,-0.0452,0.0367,0.0379,23.3,-0.2,-38.7,4.744503039,-1.25,-3.76,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,293501,2015-10-30 10:18:34:377,1446171514377.0 \n-0.1544,0.7482,9.3721,0.5143,0.2549,9.7898,0.1393,-0.0538,0.1955,24.4,0,-38.7,4.750088092,-1.49,-3.01,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,293606,2015-10-30 10:18:34:482,1446171514482.0 \n-0.0419,0.2526,12.6294,0.5718,0.3243,9.7846,0.0147,-0.0403,0.1747,25.2,-0.2,-38.6,4.757942074,-1.9,-3.34,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,293704,2015-10-30 10:18:34:580,1446171514580.0 \n-0.3232,0.2861,9.3553,0.5272,0.2755,9.7886,0.1869,0.0611,0.1637,26.6,-1.1,-39.1,4.707676591,-1.32,-3.22,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,293806,2015-10-30 10:18:34:682,1446171514682.0 \n-0.1532,-0.0431,8.8538,0.6809,0.308,9.7781,-0.0941,0.182,-0.0941,27.6,-2.4,-39.6,4.686034509,-1.8,-3.98,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,293907,2015-10-30 10:18:34:783,1446171514783.0 \n-0.5148,0.9254,8.2528,0.5451,0.3117,9.7865,0.1038,0.0929,0.0098,28.6,-3.2,-40.4,4.655316714,-1.82,-3.19,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,294010,2015-10-30 10:18:34:886,1446171514886.0 \n-0.2658,0.6213,10.1454,0.4442,0.3467,9.7904,-0.0086,0.1051,-0.0208,29.2,-3.7,-40.6,4.626867847,-1.94,-2.8,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,294111,2015-10-30 10:18:34:987,1446171514987.0 \n-0.328,0.0754,10.6913,0.4439,0.5139,9.7831,0.1686,0.0611,-0.0538,30.5,-4.7,-40.2,4.621980925,-3,-2.6,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,294214,2015-10-30 10:18:35:090,1446171515090.0 \n0.4441,0.0694,10.9726,0.3988,0.416,9.7897,-0.3067,0.1955,-0.1222,31.3,-5.7,-40,4.594753789,-3.15,-2.55,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,294315,2015-10-30 10:18:35:191,1446171515191.0 \n0.6213,0.2789,8.9842,0.3565,0.3296,9.7946,-0.0037,-0.0269,0.0635,32,-6.8,-39.8,4.543790175,-1.93,-2.08,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,294418,2015-10-30 10:18:35:294,1446171515294.0 \n0.1149,0.6153,7.5334,0.2635,0.179,9.8015,-0.1124,0.2724,-0.1124,32.3,-7.3,-39.9,4.527907678,-1.13,-2,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,294520,2015-10-30 10:18:35:396,1446171515396.0 \n-0.4178,0.7266,8.4396,0.1657,0.1406,9.8042,0.0354,0.0476,-0.0122,32.7,-7.5,-39.9,4.522846224,-0.76,-1.12,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,294622,2015-10-30 10:18:35:498,1446171515498.0 \n-0.5519,0.2023,10.4363,0.1142,0.1509,9.8048,0.011,-0.0024,0.0721,33.5,-8.3,-39.5,4.500680542,-0.88,-0.67,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,294723,2015-10-30 10:18:35:599,1446171515599.0 \n0.2382,-0.401,10.3406,0.2668,0.2456,9.7999,-0.1576,-0.5058,0.0147,33.9,-9.2,-39.1,4.486717908,-1.57,-0.89,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,294827,2015-10-30 10:18:35:703,1446171515703.0 \n0.2346,0.5926,8.4396,0.5103,0.2658,9.7898,-0.2957,-0.4911,-0.055,33.3,-11.2,-39.2,4.434358031,-1.55,-2.98,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,294928,2015-10-30 10:18:35:804,1446171515804.0 \n-0.2478,-0.0431,9.0166,0.7531,0.0872,9.7773,-0.0574,-0.0501,-0.1002,32,-12.5,-39.7,4.390375733,-0.51,-4.4,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,295030,2015-10-30 10:18:35:906,1446171515906.0 \n-0.3938,1.0271,7.3263,0.6213,0.1634,9.7856,0.1576,0.0709,-0.0403,30.6,-13.5,-39.8,4.358436208,-0.95,-3.63,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,295132,2015-10-30 10:18:36:008,1446171516008.0 \n-0.4465,0.2789,10.7667,0.6376,0.1452,9.7848,0.0073,-0.0428,-0.1674,29.9,-13.8,-39.4,4.320213497,-0.89,-3.7,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,295234,2015-10-30 10:18:36:110,1446171516110.0 \n0.2969,0.2095,11.7603,0.6678,0.3389,9.778,0.2529,0.0941,-0.16,29,-14.2,-38.5,4.328067479,-1.98,-3.91,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,295335,2015-10-30 10:18:36:211,1446171516211.0 \n-0.6369,-0.5578,10.9475,0.4934,0.3318,9.7886,-0.3213,0.2346,-0.3958,27.7,-14.5,-37.6,4.308868857,-1.94,-2.89,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,295438,2015-10-30 10:18:36:314,1446171516314.0 \n0.3053,-0.0838,9.238,0.5674,0.1684,9.7888,-0.3091,-0.2468,-0.11,26.7,-14.1,-37.1,4.287401308,-1.5,-2.93,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,295539,2015-10-30 10:18:36:415,1446171516415.0 \n-0.182,0.7901,8.509,0.5605,0.0282,9.7906,-0.1515,0.0195,-0.1258,25.4,-13.1,-37.1,4.276405733,-0.57,-3.38,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,295641,2015-10-30 10:18:36:517,1446171516517.0 \n0.0958,1.3216,8.4072,0.5781,0.0039,9.7896,-0.0086,-0.0232,0.044,24.6,-12,-37,4.298745948,-0.16,-3.33,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,295744,2015-10-30 10:18:36:620,1446171516620.0 \n0.0108,0.0575,10.9056,0.5692,0.0498,9.79,0.2358,0.0929,0.1662,23.2,-11.1,-36.9,4.305552732,-0.29,-3.33,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,295845,2015-10-30 10:18:36:721,1446171516721.0 \n0.2239,0.1006,10.1766,0.602,0.2592,9.7847,-0.0684,-0.1845,0.2443,22.2,-10.9,-36.7,4.317420971,-1.52,-3.33,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,295948,2015-10-30 10:18:36:824,1446171516824.0 \n0.7003,1.16,7.7776,0.6761,0.288,9.7791,0.1906,0.0623,0.4239,20.6,-11.2,-36.5,4.309566989,-1.68,-3.95,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,296049,2015-10-30 10:18:36:925,1446171516925.0 \n0.0467,0.3376,8.2516,0.7905,0.1451,9.7737,-0.2297,0.011,-0.1014,18.9,-11.6,-36.7,4.230154508,-0.85,-4.62,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,296152,2015-10-30 10:18:37:028,1446171517028.0 \n-0.419,0.9062,8.3713,0.7428,0.1145,9.7778,0.077,0.0024,-0.0415,18.1,-11.2,-36.9,4.238183023,-0.56,-4.34,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,296254,2015-10-30 10:18:37:130,1446171517130.0 \n0.5255,0.4178,10.2687,0.7591,0.2118,9.7749,0.1307,-0.1026,-0.1869,17,-10.2,-37,4.276405733,-1.24,-4.44,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,296355,2015-10-30 10:18:37:231,1446171517231.0 \n0.4752,0.3053,10.9427,0.7903,0.4881,9.7626,0.3531,0.0648,-0.1869,16.5,-9.4,-36.8,4.350756759,-2.31,-4.73,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,296458,2015-10-30 10:18:37:334,1446171517334.0 \n0.1209,-0.48,10.1981,0.6811,0.363,9.7762,-0.1894,0.1332,-0.2517,16,-8.3,-36.5,4.364021262,-2.12,-3.99,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,296560,2015-10-30 10:18:37:436,1446171517436.0 \n0.3974,-0.2023,10.2376,0.7121,0.245,9.7777,-0.1295,0.0623,-0.0061,15.6,-7.3,-36.8,4.395960787,-1.43,-4.17,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,296661,2015-10-30 10:18:37:537,1446171517537.0 \n-0.5004,0.6237,8.2384,0.6513,0.0436,9.7849,-0.1881,0.0843,-0.0794,15.2,-5.6,-37.4,4.396309853,-0.53,-3.65,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,296764,2015-10-30 10:18:37:640,1446171517640.0 \n0.5662,0.9074,9.4559,0.6979,0.0513,9.7817,0.0012,-0.0061,0.1307,15,-4.4,-37.8,4.498411614,-0.25,-4.07,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,296867,2015-10-30 10:18:37:743,1446171517743.0 \n0.103,0.2358,11.2372,0.6556,0.2042,9.7826,0.3787,0.0538,0.3824,14.6,-3.4,-38.2,4.585678077,-1.19,-3.83,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,296968,2015-10-30 10:18:37:844,1446171517844.0 \n0.2885,-0.2622,10.3813,0.633,0.3492,9.78,0.0391,0.033,0.2688,14.5,-3.3,-38.1,4.619188398,-2.12,-3.7,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,297069,2015-10-30 10:18:37:945,1446171517945.0 \n0.3579,0.8152,8.8717,0.7878,0.3516,9.7686,0.1234,-0.2443,0.38,14.2,-3.3,-38,4.613952411,-2.05,-4.61,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,297171,2015-10-30 10:18:38:047,1446171518047.0 \n-0.255,0.3867,8.9866,0.8963,0.221,9.7631,-0.1637,0.0501,0.044,13.9,-3.4,-37.7,4.588121538,-1.29,-5.25,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,297274,2015-10-30 10:18:38:150,1446171518150.0 \n0.1125,1.2977,7.9368,0.7939,0.2226,9.7719,0.0648,0.0269,0.0415,13.9,-3,-37.7,4.580267556,-1.12,-4.84,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,297378,2015-10-30 10:18:38:254,1446171518254.0 \n0.3292,0.1149,11.4503,0.8195,0.3172,9.7672,0.11,-0.0941,-0.121,14.2,-2.5,-37.3,4.66282163,-1.85,-4.8,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,297478,2015-10-30 10:18:38:354,1446171518354.0 \n1.0211,0.413,10.7117,0.8744,0.5352,9.7529,0.0916,0.022,-0.1906,14.7,-2.1,-36.7,4.709247388,-3.13,-5.12,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,297581,2015-10-30 10:18:38:457,1446171518457.0 \n-0.3795,-1.1349,11.4766,0.7417,0.3673,9.7717,-0.4007,0.303,-0.4777,15.1,-1.8,-36,4.672944539,-2.15,-4.34,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,297681,2015-10-30 10:18:38:557,1446171518557.0 \n0.5064,0.4573,8.7233,0.7198,0.126,9.7794,-0.3506,-0.0721,-0.1686,15.9,-0.6,-34.8,4.701567939,-1.36,-4.15,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,297783,2015-10-30 10:18:38:659,1446171518659.0 \n-0.31,0.6033,9.1303,0.7639,-0.0578,9.7767,-0.1723,-0.0904,-0.1857,16.9,0.9,-33.7,4.753578751,0.34,-4.47,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,297886,2015-10-30 10:18:38:762,1446171518762.0 \n0.2682,0.4106,11.2575,0.7507,-0.1362,9.7769,-0.088,0.1332,0.0061,17.6,2,-33.2,4.788485336,0.8,-4.39,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,297987,2015-10-30 10:18:38:863,1446171518863.0 \n0.7171,0.5914,10.1933,0.5517,0.0311,9.7911,0.2957,0.2236,0.2566,18.1,2.6,-32.5,4.853586117,0.33,-3.42,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,298090,2015-10-30 10:18:38:966,1446171518966.0 \n-0.9565,-0.6201,12.0704,0.5861,0.1932,9.7872,-0.1087,0.0061,-0.011,19.1,2.7,-31.1,4.882907648,-1.13,-3.43,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,298193,2015-10-30 10:18:39:069,1446171519069.0 \n0.243,0.8667,8.5389,0.6646,0.1356,9.7832,0.0183,-0.3519,0.237,19.6,2.3,-30.6,4.821122993,-0.79,-3.89,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,298295,2015-10-30 10:18:39:171,1446171519171.0 \n0.2107,0.4214,7.8841,0.8257,-0.0336,9.7718,-0.1466,-0.0049,0.1918,20.2,1.8,-31.2,4.79651385,0.2,-4.83,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,298395,2015-10-30 10:18:39:271,1446171519271.0 \n-0.2107,1.0666,8.2217,0.8852,-0.0109,9.7666,0.1906,-0.0892,0.1918,20.5,1.5,-31.8,4.789183467,0.33,-5.07,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,298498,2015-10-30 10:18:39:374,1446171519374.0 \n0.249,0.7147,10.7488,0.9319,0.0635,9.7621,0.3054,-0.055,-0.0293,20.7,0.9,-32.4,4.762130864,-0.37,-5.45,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,298600,2015-10-30 10:18:39:476,1446171519476.0 \n1.7023,-0.0946,9.7588,0.8723,0.4289,9.7584,0.0562,0.1344,-0.1564,20.9,-0.2,-33,4.769112181,-2.51,-5.11,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 13,298701,2015-10-30 10:18:39:577,1446171519577.0 \n0.0503,-0.2298,10.1454,0.6677,0.34,9.778,-0.1979,0.2248,-0.2297,21.1,-0.9,-33.2,4.711865382,-1.8,-4.27,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 12,298804,2015-10-30 10:18:39:680,1446171519680.0 \n0.0802,-0.0622,9.5409,0.7173,0.1045,9.7798,-0.347,-0.0916,-0.2297,21.4,-1.1,-33.7,4.684463712,-0.61,-4.19,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 12,298905,2015-10-30 10:18:39:781,1446171519781.0 \n-0.4262,0.753,7.7608,0.5201,-0.006,9.7928,0.1258,0.0953,0.0391,21.7,-0.7,-34,4.669802947,0.05,-3.53,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 12,299007,2015-10-30 10:18:39:883,1446171519883.0 \n-0.2227,0.2107,10.4591,0.5746,0.0771,9.7895,0.1845,-0.033,0.1332,22.2,-0.1,-33.8,4.721115627,-0.37,-3.18,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 12,299110,2015-10-30 10:18:39:986,1446171519986.0 \n-0.4046,-0.0168,10.975,0.6239,0.2969,9.7823,0.2724,-0.0696,0.2651,22.3,-0.2,-33.7,4.753229685,-1.73,-3.65,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 12,299214,2015-10-30 10:18:40:090,1446171520090.0 \n0.7566,0.2478,11.3509,0.7826,0.1708,9.7739,-0.204,0.0929,0.2883,22.2,-0.9,-33.5,4.693713957,-1,-4.58,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 12,299314,2015-10-30 10:18:40:190,1446171520190.0 \n-0.2562,0.1257,8.9531,0.9519,0.1149,9.7597,-0.1051,0.0684,-0.2077,21.6,-1.9,-33.8,4.647811798,-0.67,-5.57,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 12,299418,2015-10-30 10:18:40:294,1446171520294.0 \n-0.182,0.4752,8.5712,0.9492,0.096,9.7601,-0.0293,-0.0599,-0.0709,21.4,-2.2,-34,4.642052212,-0.54,-5.55,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 12,299518,2015-10-30 10:18:40:394,1446171520394.0 \n-0.2765,0.6919,9.3218,0.9929,0.2251,9.7537,0.121,-0.2236,-0.0819,21.2,-2.3,-34,4.660203636,-1.32,-5.81,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 12,299619,2015-10-30 10:18:40:495,1446171520495.0 \n0.4884,0.7554,10.8625,1.2147,0.4499,9.7207,0.1417,-0.16,-0.2175,20.8,-2.4,-34.1,4.683241982,-2.33,-6.74,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,299722,2015-10-30 10:18:40:598,1446171520598.0 \n1.0989,-0.3232,11.1749,1.1899,0.4181,9.7252,-0.0342,0.0342,-0.2065,19.8,-2.7,-34.5,4.658109241,-3.09,-7.34,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,299823,2015-10-30 10:18:40:699,1446171520699.0 \n0.6859,-0.0874,9.165,0.9701,0.2224,9.756,0.0012,0.2382,-0.0403,19.2,-2.4,-35,4.660552702,-1.44,-6.08,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,299926,2015-10-30 10:18:40:802,1446171520802.0 \n0.2837,0.3915,7.6315,0.8291,8.00E-04,9.7715,-0.1637,0.1979,0.1478,18.9,-1.4,-35.5,4.666835887,0,-4.85,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,300028,2015-10-30 10:18:40:904,1446171520904.0 \n-0.3711,0.3543,8.509,0.7475,-0.1575,9.7769,-0.1588,0.0073,0.0501,19,-0.7,-35.6,4.645193804,0.76,-4.32,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,300129,2015-10-30 10:18:41:005,1446171521005.0 \n-0.2574,0.2334,10.5237,0.734,-0.1382,9.7782,-0.0147,0.0134,0.1173,19,-0.3,-35.7,4.688303437,0.87,-4.29,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,300231,2015-10-30 10:18:41:107,1446171521107.0 \n0.2119,0.1389,10.0616,0.6717,0.0576,9.7835,0.2224,0.1698,0.4386,18.5,-0.6,-35.9,4.675213467,-0.34,-3.93,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,300333,2015-10-30 10:18:41:209,1446171521209.0 \n-0.3591,-0.7853,10.5453,0.6707,-0.0095,9.7837,0.033,0.011,0.5669,18.2,-1.3,-36.3,4.664566959,-0.03,-4.09,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,300436,2015-10-30 10:18:41:312,1446171521312.0 \n0.1664,-0.018,8.9687,0.8095,-0.0366,9.7731,-0.0403,-0.237,0.2272,17.8,-2.4,-37.1,4.611159884,0.21,-4.74,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,300538,2015-10-30 10:18:41:414,1446171521414.0 \n-0.4729,0.1317,8.9088,0.7482,-0.1841,9.7763,0.0318,0.0428,0.0929,17.6,-3.1,-37.9,4.537506989,1.08,-4.38,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,300640,2015-10-30 10:18:41:516,1446171521516.0 \n0.2682,0.8487,8.1894,0.66,-0.0527,9.7843,0.1124,-0.1429,-0.0269,17.5,-3.6,-38.4,4.503647602,0.5,-3.68,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,300742,2015-10-30 10:18:41:618,1446171521618.0 \n0.0587,0.0862,10.2615,0.7728,0.1239,9.7754,0.2248,-0.1344,-0.1136,17.3,-4.2,-39.1,4.538030588,-0.72,-4.52,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,300843,2015-10-30 10:18:41:719,1446171521719.0 \n1.1205,-0.4298,10.7452,0.799,0.0329,9.774,-0.6109,0.0562,-0.4911,17.2,-4.9,-39.3,4.497538949,-0.94,-4.63,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,300947,2015-10-30 10:18:41:823,1446171521823.0 \n0.583,-0.2813,8.8478,0.6702,-0.3083,9.7789,-0.2749,-0.0049,-0.0855,16.9,-4.5,-39.6,4.453556652,1.8,-3.92,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,301048,2015-10-30 10:18:41:924,1446171521924.0 \n1.1229,0.267,7.0749,0.5426,-0.6729,9.7685,-0.43,0.0049,-0.1686,17.1,-3.3,-39.7,4.425107786,3.93,-3.18,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,301150,2015-10-30 10:18:42:026,1446171522026.0 \n0.0826,-0.0622,9.7612,0.6135,-0.8804,9.7478,-0.1564,-0.1332,0.055,17.1,-2,-39.8,4.441862946,4.97,-3.39,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,301252,2015-10-30 10:18:42:128,1446171522128.0 \n0.5411,0.0838,10.6769,0.6712,-0.7034,9.7583,0.391,0.1503,0.2602,17,-1.4,-39.7,4.523020757,4.11,-3.93,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,301354,2015-10-30 10:18:42:230,1446171522230.0 \n0.0455,0.1448,9.3122,0.6397,-0.2546,9.7825,0.5119,-0.0757,0.193,16.7,-1.7,-39.4,4.560719868,1.49,-3.74,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,301456,2015-10-30 10:18:42:332,1446171522332.0 \n0.1437,-0.1365,9.6247,0.7226,-0.4184,9.771,-0.1356,-0.0244,0.1515,16.6,-2.9,-39.1,4.484274447,2.45,-4.23,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,301558,2015-10-30 10:18:42:434,1446171522434.0 \n-0.0455,-0.4178,8.9388,0.881,-0.3675,9.7601,-0.1442,-0.1845,0.022,16.5,-3.9,-39.1,4.454254784,2.15,-5.16,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,301659,2015-10-30 10:18:42:535,1446171522535.0 \n-0.2514,0.4274,8.4036,0.8613,-0.3523,9.7624,0.1649,0.1283,0.0232,16,-4.7,-39.3,4.390724799,2.3,-5.23,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,301762,2015-10-30 10:18:42:638,1446171522638.0 \n-0.0108,0.6416,8.6455,0.7674,-0.2387,9.7737,0.1075,0.1197,-0.0831,15.8,-5.3,-39.4,4.408178092,1.52,-4.61,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,301864,2015-10-30 10:18:42:740,1446171522740.0 \n-0.1832,0.0766,9.7731,0.7819,0.0065,9.7754,0.3812,0.1393,-0.0929,15.4,-6.1,-39.2,4.392993727,-0.04,-4.57,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,301966,2015-10-30 10:18:42:842,1446171522842.0 \n0.1257,-0.9301,11.7974,0.6666,-0.0925,9.7835,-0.1857,0.2834,-0.1234,15.2,-6.4,-38.9,4.390026668,-0.04,-4.29,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,302069,2015-10-30 10:18:42:945,1446171522945.0 \n0.9349,-0.1796,8.1283,0.5114,-0.1443,9.7922,-0.3702,0.0745,-0.099,14.6,-6.1,-39.2,4.344299041,0.84,-2.99,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,302169,2015-10-30 10:18:43:045,1446171523045.0 \n-0.2298,-0.2179,8.9974,0.4626,-0.5837,9.7783,-0.4252,-0.0012,-0.0244,14.3,-5,-39.3,4.281816254,3.41,-2.71,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,302272,2015-10-30 10:18:43:148,1446171523148.0 \n0.7518,0.7195,9.1351,0.5455,-0.6421,9.7704,-0.0586,-0.0611,0.1075,14.1,-4.1,-39.7,4.329463742,3.68,-3.11,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,302373,2015-10-30 10:18:43:249,1446171523249.0 \n0.1484,-0.1556,11.3006,0.5825,-0.5401,9.7744,0.3201,0.0428,0.1307,13.5,-3.1,-40,4.40747996,3.16,-3.41,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,302476,2015-10-30 10:18:43:352,1446171523352.0 \n0.7494,-0.5806,10.3633,0.5607,-0.2982,9.7861,0.1833,0.0183,0.1307,13,-3.1,-40.3,4.44448094,1.74,-3.28,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,302577,2015-10-30 10:18:43:453,1446171523453.0 \n0.3484,0.1437,8.436,0.6503,-0.3312,9.7795,0.1136,-0.0709,0.2993,12.3,-3.6,-40.9,4.363148597,1.94,-3.8,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,302682,2015-10-30 10:18:43:558,1446171523558.0 \n0.2023,-0.1329,8.8849,0.8555,-0.4635,9.7583,-0.3176,0.0342,-0.1258,11.9,-4.1,-41.7,4.367162854,2.22,-4.86,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,302782,2015-10-30 10:18:43:658,1446171523658.0 \n-0.3496,0.316,8.2121,0.766,-0.468,9.7655,0.099,0.0208,-0.1417,10.8,-4,-42.6,4.312708582,2.9,-4.7,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,302886,2015-10-30 10:18:43:762,1446171523762.0 \n-0.2502,0.3831,9.0465,0.6557,-0.3292,9.7792,0.1478,0.0831,-0.1271,10.4,-3.9,-43,4.296651553,2.39,-4.08,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,302986,2015-10-30 10:18:43:862,1446171523862.0 \n-0.0192,-0.4345,11.054,0.6768,-0.2292,9.7806,0.1271,0.0929,-0.1173,10,-3.5,-43.4,4.413763145,1.34,-3.96,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,303088,2015-10-30 10:18:43:964,1446171523964.0 \n-0.176,-0.5626,10.5704,0.4898,-0.2818,9.7904,-0.3555,0.3519,-0.3201,9.8,-3.3,-43.7,4.420220864,1.05,-3.43,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,303193,2015-10-30 10:18:44:069,1446171524069.0 \n0.237,-0.7841,10.082,0.5305,-0.5513,9.7768,-0.3335,-0.0208,-0.27,9.8,-2.4,-44.3,4.400673176,2.65,-3.19,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,303293,2015-10-30 10:18:44:169,1446171524169.0 \n-0.8631,-0.0587,9.1854,0.4691,-0.8447,9.7589,-0.3213,-0.1173,-0.1991,10.1,-0.7,-45.1,4.334176131,4.94,-2.75,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,303393,2015-10-30 10:18:44:269,1446171524269.0 \n-0.2682,0.4561,9.7743,0.5433,-0.8115,9.7579,0.2321,-0.077,0.1527,10.3,0.5,-45.2,4.491779363,4.9,-3.16,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,303496,2015-10-30 10:18:44:372,1446171524372.0 \n-0.2274,-0.7314,11.9626,0.5697,-0.511,9.7767,0.4264,-0.0061,0.2615,10.2,1.2,-45,4.608716423,2.99,-3.33,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,303597,2015-10-30 10:18:44:473,1446171524473.0 \n1.0582,-0.2239,9.596,0.4507,-0.0576,9.7961,-0.0024,-0.1234,0.2957,10,0.7,-45.1,4.774522702,0.33,-2.45,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,303700,2015-10-30 10:18:44:576,1446171524576.0 \n0.3675,0.31,8.7089,0.5278,-0.1602,9.7911,-0.0305,-0.121,0.3751,9.8,-0.7,-45.6,4.573460772,0.94,-3.09,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,303801,2015-10-30 10:18:44:677,1446171524677.0 \n-0.7817,-0.7075,9.7839,0.5616,-0.3867,9.7829,-0.3384,-0.0305,-0.0342,9.4,-1.3,-46,4.508010925,1.77,-3.26,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,303903,2015-10-30 10:18:44:779,1446171524779.0 \n-0.3029,0.2298,8.4336,0.5485,-0.381,9.7839,0.1283,0.0586,0,8.8,-1,-46,4.477642196,2.23,-3.21,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,304006,2015-10-30 10:18:44:882,1446171524882.0 \n0.5279,0.6476,9.7719,0.4438,-0.1537,9.7954,0.3042,0.0489,-0.1173,8.6,-0.6,-45.7,4.524940619,1.4,-2.68,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,304109,2015-10-30 10:18:44:985,1446171524985.0 \n-0.4022,-0.0024,10.5812,0.2876,0.0863,9.8021,0.0037,0.0599,-0.2883,8.9,-0.3,-45.3,4.746771967,-0.46,-1.9,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,304223,2015-10-30 10:18:45:099,1446171525099.0 \n-0.2406,-0.6704,11.7926,0.2039,-0.1471,9.8034,-0.4484,0.1747,-0.3812,9.6,0.1,-44.8,4.650953391,0.86,-1.19,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,304312,2015-10-30 10:18:45:188,1446171525188.0 \n-0.0359,-0.1389,8.5353,0.2102,-0.1733,9.8029,-0.3421,-0.0892,-0.3018,10.1,0.8,-44.6,4.76247993,0.58,-1.11,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,304414,2015-10-30 10:18:45:290,1446171525290.0 \n-0.8835,0.2574,8.0313,0.2274,-0.352,9.7977,-0.1955,-0.0721,-0.0428,10.7,2.8,-44.1,4.830722304,2.06,-1.33,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,304517,2015-10-30 10:18:45:393,1446171525393.0 \n-0.0048,0.395,9.0824,0.3639,-0.4176,9.791,0.044,-0.2101,0.1515,10.9,4,-43.9,4.880289654,2.44,-2.13,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,304617,2015-10-30 10:18:45:493,1446171525493.0 \n-0.5028,-0.4298,11.6885,0.385,-0.3095,9.7942,0.1051,-0.0061,0.1613,11.2,5.1,-43.8,4.989896331,1.81,-2.25,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,304719,2015-10-30 10:18:45:595,1446171525595.0 \n0.5136,-0.7039,10.416,0.3892,-0.321,9.7937,-0.3616,-0.4484,0.2016,11.7,5.1,-43.2,5.008396822,1.32,-1.58,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,304822,2015-10-30 10:18:45:698,1446171525698.0 \n0.6165,0.1472,9.4751,0.652,-0.409,9.7764,0.0415,-0.3225,0.5742,12.8,4.9,-42.7,4.914323575,2.39,-3.82,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,304923,2015-10-30 10:18:45:799,1446171525799.0 \n-0.2119,-0.7805,9.432,0.8131,-0.5189,9.7591,-0.259,-0.0476,-0.0916,13.4,4.5,-42.1,4.903677066,2.56,-4.7,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,305025,2015-10-30 10:18:45:901,1446171525901.0 \n-0.231,0.2801,7.4543,0.6022,-0.4662,9.777,0.226,0.4435,-0.1918,14.2,4.3,-41.5,4.838401752,2.72,-3.52,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,305128,2015-10-30 10:18:46:004,1446171526004.0 \n-0.492,0.2322,10.6686,0.4067,-0.2921,9.7939,0.1588,-0.1478,-0.2016,15.9,3.7,-40.2,4.871213942,1.71,-2.38,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,305230,2015-10-30 10:18:46:106,1446171526106.0 \n-0.0646,-0.0395,10.4639,0.5325,-0.0981,9.7917,0.2211,-0.0941,-0.11,17.1,3.1,-39.5,4.839274417,0.88,-2.86,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,305332,2015-10-30 10:18:46:208,1446171526208.0 \n-0.1724,-0.6165,11.1965,0.6119,-0.2985,9.783,-0.2224,0.0574,-0.281,18.5,1.3,-38.9,4.705407663,1.74,-3.58,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,305433,2015-10-30 10:18:46:309,1446171526309.0 \n0.9697,-0.0646,9.3685,0.642,-0.2709,9.7819,-0.2724,-0.0476,-0.3189,18.6,0.1,-38.7,4.66404336,1.58,-3.75,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,305537,2015-10-30 10:18:46:413,1446171526413.0 \n-0.4118,0.4262,7.7524,0.5818,-0.3933,9.7815,-0.0684,0.1686,-0.2859,18.1,-1.2,-38.4,4.590564999,2.3,-3.4,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,305638,2015-10-30 10:18:46:514,1446171526514.0 \n-0.2813,0.5578,8.5353,0.5044,-0.3722,9.7866,-0.044,0.0733,-0.2639,17.6,-2,-38.4,4.545360971,2.13,-3.07,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,305739,2015-10-30 10:18:46:615,1446171526615.0 \n-0.5507,-0.2107,11.0385,0.3413,-0.2845,9.7966,0.2028,-0.1295,0.4056,16.4,-3,-38.5,4.480783789,1.66,-2,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,305844,2015-10-30 10:18:46:720,1446171526720.0 \n1.1456,-0.6979,11.0624,0.4669,-0.1782,9.7939,0.1038,-0.0757,0.3934,15.1,-4,-38.7,4.440815749,0.94,-2.4,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,305944,2015-10-30 10:18:46:820,1446171526820.0 \n0.8499,0.4633,9.1925,0.6509,-0.269,9.7813,0.3519,0.0929,0.5156,12.7,-5.1,-39.1,4.342030113,1.57,-3.81,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,306047,2015-10-30 10:18:46:923,1446171526923.0 \n-0.1808,-0.2346,8.406,0.7501,-0.2076,9.7757,-0.0086,-0.022,-0.0806,9.4,-6.3,-39.6,4.201356575,1.07,-4.34,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,306148,2015-10-30 10:18:47:024,1446171527024.0 \n-0.7518,-0.091,8.418,0.7494,-0.1081,9.7774,0.0867,0.0183,-0.1979,7.4,-6.3,-40,4.132765136,0.96,-4.58,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,306249,2015-10-30 10:18:47:125,1446171527125.0 \n-0.2418,0.2574,9.7061,0.6833,-0.0104,9.7828,-0.0354,-0.0049,-0.1918,5.2,-5.8,-39.5,4.047418535,0.06,-4,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,306351,2015-10-30 10:18:47:227,1446171527227.0 \n1.1684,0.1425,11.072,0.7271,0.0055,9.7797,-0.0831,-0.0586,-0.121,3.4,-4.2,-39.3,4.117755304,-0.03,-4.25,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,306454,2015-10-30 10:18:47:330,1446171527330.0 \n-0.2574,-0.6117,10.2975,0.612,-0.3639,9.7808,0.2419,0.1136,0.0806,2.4,-2.3,-39.5,4.05247999,2.13,-3.58,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,306562,2015-10-30 10:18:47:438,1446171527438.0 \n0.419,-0.5136,9.7983,0.7393,-0.4285,9.7693,-0.2651,-0.2688,0.0367,1.8,-0.1,-40.1,4.37885656,2.5,-4.33,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,306659,2015-10-30 10:18:47:535,1446171527535.0 \n0.0072,0.328,7.4675,0.5908,-0.5987,9.7705,-0.0379,0.1955,0.033,1.7,1.5,-40.5,4.630707571,3.42,-3.79,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,306760,2015-10-30 10:18:47:636,1446171527636.0 \n0.079,0.5854,8.9364,0.5275,-0.6277,9.7723,-0.1662,0.022,0.1185,2.1,3.6,-40.6,5.028991707,3.67,-3.09,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,306861,2015-10-30 10:18:47:737,1446171527737.0 \n-0.8978,-1.1001,12.6605,0.544,-0.5787,9.7744,0.1026,-0.0782,0.1918,2.5,4.6,-40.7,5.100899272,3.97,-3.21,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,306964,2015-10-30 10:18:47:840,1446171527840.0 \n-0.1089,-1.8364,13.6541,0.639,-0.5057,9.7727,-0.2162,-0.4948,0.2004,3.5,5.2,-40.6,5.122366822,2.96,-3.74,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,307066,2015-10-30 10:18:47:942,1446171527942.0 \n0.8487,0.7446,8.2013,0.6544,-0.5223,9.7708,0.0147,-0.2126,0.1014,4,5.4,-40.7,5.086587572,3.31,-3.85,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,307167,2015-10-30 10:18:48:043,1446171528043.0 \n0.1077,-0.2442,8.4803,0.7351,-0.6468,9.7576,-0.2004,0.0159,-0.1161,4.5,5.3,-40.6,4.992165259,3.78,-4.31,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,307269,2015-10-30 10:18:48:145,1446171528145.0 \n0.3783,0.6704,7.8721,0.6596,-0.2943,9.78,0.4081,0.1442,0.0562,4.9,5.2,-40,5.17298137,1.72,-3.86,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,307371,2015-10-30 10:18:48:247,1446171528247.0 \n-0.1245,-0.1317,10.2149,0.6758,-0.0925,9.7829,0.1136,-0.1368,-0.2566,5.3,4.8,-39.9,5.234591493,0.85,-3.83,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,307474,2015-10-30 10:18:48:350,1446171528350.0 \n0.6692,-1.2151,11.4179,0.6557,-0.1032,9.7842,-0.6561,0.0049,-0.3934,5.8,4.4,-39.3,5.108578721,0.6,-3.83,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,307576,2015-10-30 10:18:48:452,1446171528452.0 \n-0.1305,-0.3376,10.1167,0.5397,-0.5033,9.7788,-0.1148,0.1539,-0.0086,6.3,4.7,-39.1,5.037718353,3.24,-3.46,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,307678,2015-10-30 10:18:48:554,1446171528554.0 \n-0.2251,-0.3555,8.855,0.543,-0.6872,9.7675,-0.2896,0.055,-0.1723,7,6.1,-38.6,5.056916975,4.02,-3.18,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,307779,2015-10-30 10:18:48:655,1446171528655.0 \n-0.5447,0.1173,8.4515,0.2894,-0.721,9.7758,0.2456,-0.0061,0.0709,7.8,7.2,-38.1,5.122715888,4.55,-1.76,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,307882,2015-10-30 10:18:48:758,1446171528758.0 \n-0.3579,-0.3998,9.9527,0.1992,-0.5992,9.7863,0.0403,0.1148,0.1332,9.2,7.9,-37.6,5.23860575,3.5,-1.17,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,307986,2015-10-30 10:18:48:862,1446171528862.0 \n-0.3053,0.0634,11.3198,0.2227,-0.3132,9.7991,0.4203,-0.022,0.3506,10.2,7.8,-37.2,5.245412534,2.51,-1.28,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,308086,2015-10-30 10:18:48:962,1446171528962.0 \n-0.7266,-1.3767,12.9287,0.5111,-0.5422,9.7783,-0.0953,0.0073,0.2932,11.4,6.5,-37.3,5.080304387,3.17,-2.99,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,308187,2015-10-30 10:18:49:063,1446171529063.0 \n0.4848,0.2334,7.7608,0.5863,-0.5793,9.772,0.0696,-0.1356,0.1112,11.7,5.7,-37.4,4.994085122,3.04,-3.22,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,308289,2015-10-30 10:18:49:165,1446171529165.0 \n-0.3759,0.1484,8.6574,0.5132,-0.6036,9.7746,0.0855,0.0733,-0.0843,11.7,4.9,-37.8,4.895648552,3.68,-3.06,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,308392,2015-10-30 10:18:49:268,1446171529268.0 \n-0.3328,0.2873,8.3965,0.4138,-0.3687,9.791,0.2187,0.0281,-0.1662,11.7,4.4,-37.8,4.900535474,2.15,-2.42,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,308493,2015-10-30 10:18:49:369,1446171529369.0 \n-0.1006,-0.176,10.8002,0.5656,-0.177,9.7887,0.1943,0.1148,-0.0208,11.7,4,-37.8,4.942946975,1.03,-3.31,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,308596,2015-10-30 10:18:49:472,1446171529472.0 \n-0.4896,-1.7992,12.6701,0.567,-0.2612,9.7868,-0.3421,-0.0379,-0.2932,11.7,3.7,-38.1,4.921304892,1.53,-3.32,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,308698,2015-10-30 10:18:49:574,1446171529574.0 \n1.1133,0.1712,7.616,0.5354,-0.373,9.7849,-0.1429,-0.0037,-0.0892,11.7,3.9,-38.2,4.896346684,2.12,-3.16,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,308799,2015-10-30 10:18:49:675,1446171529675.0 \n-0.2322,0.3651,7.677,0.5297,-0.634,9.7718,-0.1613,0.0562,-0.193,12,4.7,-38.1,4.894077756,3.71,-3.1,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,308902,2015-10-30 10:18:49:778,1446171529778.0 \n-0.1425,0.2263,8.5126,0.5638,-0.6636,9.7679,0.0696,-0.044,-0.0892,12.3,5.7,-38,4.95219722,3.88,-3.3,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,309004,2015-10-30 10:18:49:880,1446171529880.0 \n-0.8882,-1.0762,11.0073,0.5528,-0.666,9.7684,0.0696,-0.0232,0.1381,12.6,6.4,-38,4.933173131,4,-3.22,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,309106,2015-10-30 10:18:49:982,1446171529982.0 \n0.1329,-1.233,11.4419,0.4709,-0.467,9.7842,-0.0379,-0.2786,0.182,13.2,6.7,-38,5.050808322,2.73,-2.76,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,309208,2015-10-30 10:18:50:084,1446171530084.0 \n-0.3041,-0.7434,9.6594,0.7502,-0.5086,9.7647,0.0831,-0.2566,0.4093,13.7,6.4,-38.1,4.960051201,2.78,-4,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,309312,2015-10-30 10:18:50:188,1446171530188.0 \n-0.5028,-0.1353,8.5485,0.7646,-0.6867,9.7527,-0.2443,0.1869,0.2101,14.3,5.5,-38.8,4.921653958,3.53,-4.9,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,309412,2015-10-30 10:18:50:288,1446171530288.0 \n0.0515,0.6536,7.9464,0.6495,-0.6428,9.764,0.3018,0.1515,0.237,14.9,4.9,-38.9,4.854109716,3.76,-3.81,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,309514,2015-10-30 10:18:50:390,1446171530390.0 \n-0.2705,-0.4597,11.0397,0.599,-0.3962,9.7803,0.3201,-0.2773,-0.2028,15.4,4.2,-39.2,4.839274417,2.74,-3.03,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,309616,2015-10-30 10:18:50:492,1446171530492.0 \n1.3467,-0.6536,11.0073,0.5811,-0.1146,9.7887,0.3128,0.1784,-0.1381,16.1,3.2,-39,4.851317189,0.67,-3.4,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,309718,2015-10-30 10:18:50:594,1446171530594.0 \n-0.0323,-0.7266,11.7088,0.5698,-0.2609,9.7866,-0.0476,0.1271,0.0904,16.3,2.9,-38.8,4.82094846,1.52,-3.33,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,309819,2015-10-30 10:18:50:695,1446171530695.0 \n0.2454,0.3555,8.4659,0.4331,-0.4528,9.7866,-0.2663,0.2859,-0.033,16.5,3.4,-38.5,4.797561048,2.14,-2.93,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,309922,2015-10-30 10:18:50:798,1446171530798.0 \n-0.3472,-0.0108,7.665,0.301,-0.533,9.7875,-0.0867,0.077,-0.0293,16.9,4.2,-38.4,4.822868322,3.03,-1.76,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,310025,2015-10-30 10:18:50:901,1446171530901.0 \n0.1592,0.1472,8.9795,0.1776,-0.4721,9.7937,-0.0513,0.1148,0.0562,17.9,5,-38,4.880987786,2.76,-1.04,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,310127,2015-10-30 10:18:51:003,1446171531003.0 \n-0.2155,0.1484,10.3932,0.2446,-0.3518,9.7973,0.1662,-0.1417,0.325,18.8,5.4,-38,4.883256714,2.4,-1.22,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,310227,2015-10-30 10:18:51:103,1446171531103.0 \n-2.1069,-2.1237,13.8325,0.5073,-0.5786,9.7764,-0.4349,-0.4875,-0.1906,20,5.4,-37.7,4.839972549,3.38,-2.97,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,310330,2015-10-30 10:18:51:206,1446171531206.0 \n-0.6225,-0.2107,8.0721,0.6086,-0.5685,9.7712,0.044,-0.325,0.11,21.1,5.3,-37.9,4.834736561,3.32,-3.56,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,310432,2015-10-30 10:18:51:308,1446171531308.0 \n-0.2909,-0.0204,9.4535,0.7085,-0.721,9.7544,0.0428,0.0061,-0.077,21.7,5.3,-38,4.802797036,4.34,-4.22,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,310533,2015-10-30 10:18:51:409,1446171531409.0 \n-0.6464,0.419,8.0409,0.6308,-0.5511,9.7708,0.2529,0.1564,0.0269,22.6,5.1,-37.9,4.827755244,3.22,-3.69,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,310642,2015-10-30 10:18:51:518,1446171531518.0 \n-0.486,-0.3591,12.0129,0.6861,-0.2699,9.7789,0.2517,-0.2016,-0.0208,23.7,4.1,-38.1,4.824788184,1.58,-4.01,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,310738,2015-10-30 10:18:51:614,1446171531614.0 \n0.4788,-1.3563,12.22,0.6095,-0.2166,9.7853,-0.4838,0.0745,-0.2382,24.8,2.7,-37.9,4.792674126,1.27,-3.56,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,310839,2015-10-30 10:18:51:715,1446171531715.0 \n0.9445,0.4453,7.0797,0.3757,-0.4153,9.7906,-0.1173,0.0635,0.1124,25.7,1.3,-37.4,4.693190359,2.43,-2.2,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,310942,2015-10-30 10:18:51:818,1446171531818.0 \n-0.1604,0.0658,8.7041,0.3855,-0.6218,9.7793,-0.2053,-0.1087,-0.1222,26,0.9,-36.9,4.66997748,3.47,-2.48,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,311044,2015-10-30 10:18:51:920,1446171531920.0 \n-0.4034,0.5231,7.7141,0.2893,-0.622,9.7826,0.1063,0.0977,0.0415,26.5,1,-36.1,4.668406683,3.64,-1.69,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,311145,2015-10-30 10:18:52:021,1446171532021.0 \n-0.662,-0.5375,10.7583,0.2268,-0.6197,9.7844,0.0941,-0.0965,0.2077,26.8,0.7,-35.4,4.669802947,3.64,-1.34,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,311248,2015-10-30 10:18:52:124,1446171532124.0 \n0.1592,-1.3204,11.5796,0.1969,-0.4915,9.7923,0.3091,0.2309,0.3592,27.1,0,-34,4.658109241,2.56,-0.97,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,311350,2015-10-30 10:18:52:226,1446171532226.0 \n0.2203,0.4441,8.2349,0.2794,-0.5525,9.7871,0.1576,-0.1869,0.4472,27.2,-1.1,-32.9,4.612032548,3.23,-1.64,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,311452,2015-10-30 10:18:52:328,1446171532328.0 \n-0.6105,-0.6871,9.3302,0.4903,-0.7062,9.7689,-0.2761,-0.0464,-0.182,27,-2,-32.7,4.57276264,3.67,-2.82,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,311554,2015-10-30 10:18:52:430,1446171532430.0 \n-0.34,0.3675,7.1934,0.4012,-0.6528,9.7767,0.1943,0.2358,-0.1014,26.7,-2.5,-32.6,4.568050251,3.82,-2.35,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,311655,2015-10-30 10:18:52:531,1446171532531.0 \n-0.8655,-0.0958,9.1794,0.2967,-0.5173,9.7885,0.1185,0.0525,-0.3103,26.6,-2.6,-32.7,4.546233636,3.02,-1.74,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,311757,2015-10-30 10:18:52:633,1446171532633.0 \n0.6225,-1.5395,11.7543,0.4939,-0.4512,9.7838,-0.0538,-0.1784,-0.3238,26.5,-2.4,-32.8,4.595626453,2.4,-2.46,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,311862,2015-10-30 10:18:52:738,1446171532738.0 \n-0.0862,-0.8009,10.2675,0.2877,-0.6321,9.782,0.1991,0.1368,0.055,26.4,-2.2,-32.9,4.562116132,3.83,-2.26,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,311961,2015-10-30 10:18:52:837,1446171532837.0 \n-0.1856,-0.583,8.7209,0.3479,-0.7467,9.772,-0.3482,-0.1478,-0.1148,26.3,-2,-33.1,4.550596959,4.37,-2.04,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,312064,2015-10-30 10:18:52:940,1446171532940.0 \n-0.334,0.0898,8.5641,0.4028,-0.9024,9.7567,-0.0037,-0.1014,-0.0611,26.1,-1.9,-33.4,4.535063528,5.18,-2.18,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,312165,2015-10-30 10:18:53:041,1446171533041.0 \n-0.486,0.1903,9.5636,0.3921,-0.8557,9.7614,0.0037,0.0073,0.0171,25.5,-2.2,-33.3,4.539077786,5.01,-2.3,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,312267,2015-10-30 10:18:53:143,1446171533143.0 \n-0.5255,-0.492,12.6091,0.4385,-0.7164,9.7706,0.1185,-0.1918,0.1955,24.6,-2.4,-33.4,4.541870312,4.63,-2.67,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,312369,2015-10-30 10:18:53:245,1446171533245.0 \n-1.5814,-1.992,11.4287,0.5928,-0.9082,9.7465,-0.1955,0.0929,-0.0831,23.1,-3.3,-33.5,4.479911124,5.31,-3.48,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,312472,2015-10-30 10:18:53:348,1446171533348.0 \n-0.2514,-0.4764,9.3613,0.5732,-0.8009,9.7571,-0.2114,-0.077,-0.0354,21.9,-3.9,-33.5,4.443957341,4.68,-3.36,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,312573,2015-10-30 10:18:53:449,1446171533449.0 \n-0.7278,-0.3603,8.6526,0.508,-0.8127,9.7597,0.1881,0.0904,-0.0086,21.5,-4,-33.5,4.437150557,4.92,-3.11,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,312676,2015-10-30 10:18:53:552,1446171533552.0 \n-0.7063,-0.0215,9.3637,0.4589,-0.6637,9.7734,0.1124,0.0367,-0.0403,21.4,-4.1,-33.5,4.445702671,3.88,-2.69,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,312777,2015-10-30 10:18:53:653,1446171533653.0 \n-1.4389,-0.395,11.4802,0.6102,-0.4379,9.7778,0.314,-0.1014,0.0757,21.3,-4.3,-33.8,4.466995688,3.09,-3.39,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,312880,2015-10-30 10:18:53:756,1446171533756.0 \n-0.2083,-1.1887,12.5612,0.5897,-0.3424,9.7829,-0.0171,0.215,0.0476,20.8,-5.1,-34.4,4.45163679,2,-3.45,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,312982,2015-10-30 10:18:53:858,1446171533858.0 \n1.0558,-0.3244,7.8542,0.5897,-0.1863,9.7871,0.2395,-0.0257,0.0293,20.3,-5.7,-34.8,4.422664325,0.86,-3.06,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,313083,2015-10-30 10:18:53:959,1446171533959.0 \n0.5243,0.6381,7.0665,0.5203,-0.1467,9.7917,-0.0049,0.2578,-0.0757,19.6,-6,-35.1,4.425456851,0.87,-3.45,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,313185,2015-10-30 10:18:54:061,1446171534061.0 \n-0.2394,0.8248,8.3079,0.5111,-0.1315,9.7924,-0.0354,0.0684,0.0782,19.2,-5.8,-35.3,4.411494217,0.77,-2.99,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,313288,2015-10-30 10:18:54:164,1446171534164.0 \n-0.0072,0.6033,9.5349,0.5051,-0.1068,9.7931,0.1014,0.0171,0.2407,19.2,-5.7,-35.4,4.412192349,0.64,-2.66,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,313390,2015-10-30 10:18:54:266,1446171534266.0 \n0.0658,-0.8009,11.3461,0.5276,-0.0148,9.7924,-0.0195,-0.0476,0.2602,19.2,-5.7,-35.4,4.429994707,0.09,-3.08,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,313492,2015-10-30 10:18:54:368,1446171534368.0 \n0.5495,0.2981,8.7604,0.6966,-0.1037,9.7813,0.0929,-0.2443,0.3604,19.2,-6.2,-35.2,4.424235121,0.61,-4.07,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,313593,2015-10-30 10:18:54:469,1446171534469.0 \n0.0922,0.2346,8.7077,0.7629,-0.1965,9.775,-0.1051,0.11,-0.0232,19,-6.6,-35.3,4.372224309,1.15,-4.46,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,313695,2015-10-30 10:18:54:571,1446171534571.0 \n-0.3855,0.8272,7.6016,0.6242,-0.252,9.7835,0.0733,0.215,-0.0819,19,-7.1,-35.9,4.356865412,1.47,-3.65,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,313798,2015-10-30 10:18:54:674,1446171534674.0 \n-0.5267,0.814,9.4619,0.5614,-0.0501,9.7904,0.1307,-0.0831,-0.1405,19.1,-7.4,-36.5,4.374144171,0.58,-3.08,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,313900,2015-10-30 10:18:54:776,1446171534776.0 \n-0.2801,-0.5638,10.8553,0.6349,0.0686,9.7858,-0.1723,-0.1943,-0.0281,19.2,-7.9,-37.3,4.364195795,-0.4,-3.71,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,314001,2015-10-30 10:18:54:877,1446171534877.0 \n0.0347,-0.5806,10.6877,0.6152,-0.103,9.7868,-0.1271,0.1429,0.1686,19,-8.2,-37.6,4.343251844,0.48,-3.79,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,314104,2015-10-30 10:18:54:980,1446171534980.0 \n0.516,-0.1293,9.6714,0.5967,-0.3597,9.7819,-0.5058,0.0379,-0.1417,18.4,-8.6,-38.3,4.262094033,1.29,-3.56,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,314206,2015-10-30 10:18:55:082,1446171535082.0 \n-0.2526,0.3484,8.5126,0.5254,-0.52,9.7788,0.0061,-0.055,-0.0611,17.9,-8.3,-38.5,4.257032579,2.83,-3.12,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,314307,2015-10-30 10:18:55:183,1446171535183.0 \n-0.0431,0.5363,9.3134,0.5043,-0.4569,9.783,0.0012,-0.0525,-0.1173,17.4,-7.9,-38.6,4.237310358,2.67,-2.95,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,314410,2015-10-30 10:18:55:286,1446171535286.0 \n-0.413,0.0443,10.5453,0.5435,-0.2926,9.7872,0.391,0.0269,0.2101,16.9,-7.4,-38.6,4.310614187,1.71,-3.18,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,314512,2015-10-30 10:18:55:388,1446171535388.0 \n-1.3204,-1.0116,10.3238,0.6179,-0.3288,9.7816,0.0012,0.0061,0.0586,15.9,-7.6,-38.9,4.24638607,1.92,-3.61,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,314615,2015-10-30 10:18:55:491,1446171535491.0 \n-0.0431,-0.0012,8.5258,0.7362,-0.2595,9.7755,-0.1637,0.1271,-0.0098,15.1,-7.7,-39.6,4.249876729,1.4,-4.27,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,314716,2015-10-30 10:18:55:592,1446171535592.0 \n-0.6165,0.346,8.7329,0.6641,-0.3384,9.7783,-0.0745,-0.0024,-0.1173,14.1,-7.2,-39.8,4.248654998,1.98,-3.89,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,314821,2015-10-30 10:18:55:697,1446171535697.0 \n-0.3041,0.747,8.4479,0.587,-0.178,9.7874,0.1222,-0.0232,-0.11,13.8,-6.6,-40.3,4.263839363,1.26,-3.37,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,314920,2015-10-30 10:18:55:796,1446171535796.0 \n-0.4166,-0.1808,12.0165,0.6574,-0.098,9.7841,0.1539,-0.2065,-0.171,13.8,-5.8,-40.2,4.34604437,0.57,-3.84,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,315021,2015-10-30 10:18:55:897,1446171535897.0 \n-0.6704,-0.6333,11.0193,0.3298,-0.021,9.8011,-0.1662,0.3091,-0.2334,14.5,-4.7,-40.4,4.432438168,-0.21,-2.73,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,315123,2015-10-30 10:18:55:999,1446171535999.0 \n0.3938,-0.0563,9.3565,0.248,-0.1657,9.8021,-0.2896,-0.1185,-0.0721,15.9,-3.6,-40.8,4.443957341,0.97,-1.45,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,315225,2015-10-30 10:18:56:101,1446171536101.0 \n-0.3627,0.5435,7.9224,0.326,-0.4096,9.7927,-0.088,-0.1124,-0.0782,16.9,-3,-41.1,4.467519286,2.23,-1.82,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,315328,2015-10-30 10:18:56:204,1446171536204.0 \n-0.425,0.7027,9.0429,0.428,-0.4427,9.7873,-0.0073,-0.0782,-0.0367,18.1,-2,-41.7,4.52022823,2.59,-2.5,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,315429,2015-10-30 10:18:56:305,1446171536305.0 \n-0.5914,-0.1652,11.0002,0.441,-0.387,9.7891,0.1906,-0.0538,0.1271,18.4,-1.5,-42.1,4.56735212,2.64,-2.5,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,315531,2015-10-30 10:18:56:407,1446171536407.0 \n-0.2969,-1.1241,11.4886,0.4621,-0.2592,9.7923,-0.1442,-0.1991,-0.0061,18.9,-1.6,-43.2,4.571191844,1.29,-2.37,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,315634,2015-10-30 10:18:56:510,1446171536510.0 \n-0.0419,-0.4585,9.0046,0.5126,-0.2474,9.7901,-0.2199,-0.0867,-0.0086,19.1,-2.3,-43.9,4.56857385,1.45,-3,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,315736,2015-10-30 10:18:56:612,1446171536612.0 \n-0.328,0.255,8.4025,0.4884,-0.4467,9.7843,-0.1124,0.1014,0.1344,19.2,-2.8,-44.7,4.482354585,2.57,-2.86,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,315839,2015-10-30 10:18:56:715,1446171536715.0 \n-0.4226,0.5662,8.5425,0.5186,-0.4479,9.7827,0.0916,0.0745,0.0525,19,-3,-45.2,4.482180052,2.62,-3.03,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,315940,2015-10-30 10:18:56:816,1446171536816.0 \n-1.0439,-0.2167,11.9004,0.5305,-0.3102,9.7874,0.1442,-0.1381,-0.1246,19,-3.1,-46.1,4.498935213,2.05,-2.83,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,316041,2015-10-30 10:18:56:917,1446171536917.0 \n1.0331,0.2119,10.5405,0.5826,-0.1414,9.7883,0.2822,-0.0904,0.0782,19,-3.3,-46.5,4.540474049,0.91,-3.03,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,316144,2015-10-30 10:18:57:020,1446171537020.0 \n0.4932,-0.0371,8.7017,0.5274,-0.2263,9.7898,0.237,-0.1368,0.0745,19,-3.4,-46.6,4.525813283,1.32,-3.08,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,316245,2015-10-30 10:18:57:121,1446171537121.0 \n-0.3136,-0.4776,9.3111,0.5383,-0.3167,9.7867,-0.0415,0.0391,-0.0476,18.9,-3.5,-46.8,4.513421446,1.7,-3.21,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,316350,2015-10-30 10:18:57:226,1446171537226.0 \n-0.5698,0.3879,8.1128,0.4755,-0.3949,9.7872,-0.1246,0.0916,-0.0831,18.8,-2.9,-46.8,4.488114172,2.31,-2.78,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,316450,2015-10-30 10:18:57:326,1446171537326.0 \n0.0347,0.3926,10.1813,0.4143,-0.3508,9.7916,0.0098,0.0782,0.0367,18.6,-2.5,-46.7,4.540124983,2.05,-2.42,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,316552,2015-10-30 10:18:57:428,1446171537428.0 \n-0.5471,-0.2179,12.5732,0.4194,-0.3287,9.7922,0.0794,-0.0501,0.0452,18.6,-2.3,-46.7,4.545011905,1.92,-2.45,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,316653,2015-10-30 10:18:57:529,1446171537529.0 \n-0.3615,-0.4058,9.9515,0.489,-0.3261,9.789,0.2639,-0.1454,0.3482,18.7,-2.5,-46.5,4.549549761,1.91,-2.86,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,316756,2015-10-30 10:18:57:632,1446171537632.0 \n-0.5543,-0.261,8.26,0.5874,-0.256,9.7857,-0.055,-0.0635,-0.0794,18.6,-2.7,-46.6,4.532445535,1.2,-3.41,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,316858,2015-10-30 10:18:57:734,1446171537734.0 \n-0.4561,0.4046,8.3606,0.5415,-0.3346,9.786,0.0024,0.0745,0.0098,18.3,-2.6,-46.7,4.493873758,1.96,-3.17,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,316959,2015-10-30 10:18:57:835,1446171537835.0 \n-0.1939,0.7386,8.497,0.513,-0.2667,9.7896,0.0122,0.0061,-0.0354,18.2,-2.4,-46.5,4.554436683,1.59,-3.04,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,317061,2015-10-30 10:18:57:937,1446171537937.0 \n-0.7135,0.1724,11.0971,0.6118,-0.1012,9.787,0.1845,-0.2272,0.0049,18.4,-1.9,-46,4.56979558,1.28,-3.67,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,317163,2015-10-30 10:18:58:039,1446171538039.0 \n0.1305,-0.2945,10.5213,0.6194,-0.0842,9.7867,-0.2492,0.2065,-0.2932,18.5,-2.1,-45.5,4.6186648,0.1,-3.93,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,317266,2015-10-30 10:18:58:142,1446171538142.0 \n0.1401,-0.3436,8.9196,0.566,-0.2225,9.7878,-0.2663,0.0709,-0.1613,18.6,-1.9,-45.1,4.574507969,1.3,-3.31,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,317367,2015-10-30 10:18:58:243,1446171538243.0 \n0.2298,0.2717,7.282,0.3774,-0.4664,9.7883,-0.0953,0.2199,0.0244,18.7,-1.5,-44.5,4.580965688,2.36,-2.6,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,317476,2015-10-30 10:18:58:352,1446171538352.0 \n-0.1652,0.577,8.0876,0.3613,-0.5236,9.786,0.0684,0.0232,0.1613,19,-0.5,-44,4.597546316,3.16,-2.17,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,317571,2015-10-30 10:18:58:447,1446171538447.0 \n0.0311,-0.1173,10.9654,0.4474,-0.5758,9.7795,-0.1161,-0.2053,0.0134,19.5,0.1,-43.7,4.601909639,3.21,-2.3,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,317673,2015-10-30 10:18:58:549,1446171538549.0 \n0.0503,-2.0842,14.7172,0.5719,-0.4404,9.7801,-0.6048,-0.3286,-0.3299,19.7,0,-43.7,4.627391446,2.57,-3.35,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,317776,2015-10-30 10:18:58:652,1446171538652.0 \n0.2143,0.1413,8.9639,0.5623,-0.5605,9.7745,0.2932,0.1515,0.2407,19.6,0,-43.6,4.604178567,3.28,-3.29,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,317878,2015-10-30 10:18:58:754,1446171538754.0 \n-0.5195,-0.0407,9.1578,0.7037,-0.4582,9.7706,-0.2334,0.0855,-0.1417,19.2,-0.4,-44,4.631405703,2.44,-4.27,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,317980,2015-10-30 10:18:58:856,1446171538856.0 \n-0.6033,0.3292,7.9499,0.7071,-0.3341,9.7754,0.1625,0.0049,-0.055,18.9,-0.4,-44.3,4.639085152,2.2,-4.2,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,318081,2015-10-30 10:18:58:957,1446171538957.0 \n-0.7949,-0.2574,10.483,0.7161,-0.249,9.7773,0.033,0.0049,-0.11,18.6,-1,-44.5,4.618839332,1.45,-4.19,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,318184,2015-10-30 10:18:59:060,1446171539060.0 \n-0.158,-0.3148,10.7392,0.8375,-0.0691,9.7706,0.3323,0.0513,0.0757,18.3,-1.3,-44.3,4.632627434,1.01,-5.02,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,318286,2015-10-30 10:18:59:162,1446171539162.0 \n0.2777,-0.2394,10.1418,0.7043,-0.1538,9.7801,0.2101,0.1491,0.1698,17.9,-1.7,-44.3,4.583409149,1.04,-4.48,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,318393,2015-10-30 10:18:59:269,1446171539269.0 \n-0.1724,-0.1113,8.442,0.6842,-0.1899,9.7809,-0.2138,0.1503,-0.1136,17.5,-2.1,-44.7,4.578347694,1.11,-4,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,318489,2015-10-30 10:18:59:365,1446171539365.0 \n-0.6273,0.2083,7.7488,0.5622,-0.4084,9.782,-0.2004,0.0525,-0.1014,17.3,-1.9,-44.6,4.52738408,2.16,-3.27,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,318592,2015-10-30 10:18:59:468,1446171539468.0 \n0.1688,0.6895,10.0592,0.533,-0.4743,9.7807,-0.0916,-0.0476,0.1222,17,-1.3,-44,4.554785749,2.77,-3.12,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,318693,2015-10-30 10:18:59:569,1446171539569.0 \n-0.2394,-0.4752,12.9921,0.6341,-0.4046,9.7778,0.5131,0.0562,0.3409,16.6,-0.9,-43.6,4.560021737,2.72,-3.64,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,318796,2015-10-30 10:18:59:672,1446171539672.0 \n-1.8028,-2.2709,13.8469,0.7779,-0.3266,9.7703,-0.2065,-0.3103,-0.044,15.8,-0.7,-43.2,4.608716423,1.36,-4.26,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,318899,2015-10-30 10:18:59:775,1446171539775.0 \n0.4345,0.6572,7.3682,0.8105,-0.1642,9.7717,0.1283,-0.1417,0.1405,15.1,-0.4,-42.7,4.666486821,1.16,-4.51,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,319001,2015-10-30 10:18:59:877,1446171539877.0 \n-0.589,0.1281,8.7053,0.7801,-0.3621,9.7689,-0.1491,-0.0367,-0.1405,14.6,0.1,-42.4,4.630533038,2.12,-4.57,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,319108,2015-10-30 10:18:59:984,1446171539984.0 \n-0.1664,0.5291,7.7716,0.7373,-0.2913,9.7746,0.2065,0.1185,0.0318,14.6,1.1,-42.3,4.689001568,2.01,-4.57,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,319203,2015-10-30 10:19:00:079,1446171540079.0 \n-1.0846,-0.7266,13.0867,0.8024,-0.1893,9.7719,0.0782,-0.2749,-0.1674,15.7,2.3,-41.8,4.767541385,1.33,-4.3,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,319305,2015-10-30 10:19:00:181,1446171540181.0 \n1.0582,0.1975,10.1203,0.8416,0.1024,9.7699,-0.1038,-0.0648,-0.1747,16.5,2.9,-41.1,4.868246883,-0.25,-4.53,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,319408,2015-10-30 10:19:00:284,1446171540284.0 \n0.8284,0.6069,7.8889,0.7081,0.0039,9.7811,-0.0208,0.1637,0.0513,17.9,3.3,-40.3,4.856029578,-0.02,-4.14,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,319509,2015-10-30 10:19:00:385,1446171540385.0 \n0.4764,0.4082,7.009,0.677,-0.3135,9.7782,-0.3445,0.1564,-0.1881,19.8,3.8,-39.9,4.83351483,1.83,-3.96,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,319611,2015-10-30 10:19:00:487,1446171540487.0 \n-0.5507,-0.0431,9.6462,0.6821,-0.4322,9.7733,-0.044,0.0232,0.0024,21.2,4.5,-39.7,4.850619057,2.53,-3.99,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,319714,2015-10-30 10:19:00:590,1446171540590.0 \n-0.4058,-0.237,10.4279,0.5464,-0.3293,9.7859,0.2627,0.0403,0.2162,23.7,4.5,-38.6,4.854284249,1.92,-3.2,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,319816,2015-10-30 10:19:00:692,1446171540692.0 \n0.0658,0.2382,9.3027,0.455,0.0132,9.7961,0.4875,0.2175,0.3897,25.3,3.2,-37.9,4.808731155,0.62,-2.96,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,319917,2015-10-30 10:19:00:793,1446171540793.0 \n-0.2586,-0.2023,9.9587,0.5151,-0.075,9.7928,0.0134,-0.0501,0.2382,26.8,-0.1,-36.9,4.703313268,0.42,-2.87,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,320020,2015-10-30 10:19:00:896,1446171540896.0 \n-0.3615,-0.0419,8.6455,0.5453,-0.1841,9.7897,-0.2114,-0.1527,0.0134,27.3,-2.2,-36.9,4.626693314,0.78,-2.97,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,320122,2015-10-30 10:19:00:998,1446171540998.0 \n-0.5112,-0.0371,8.8861,0.5402,-0.322,9.7865,-0.0977,0.055,-0.0635,26.6,-4.4,-37.2,4.536285259,1.88,-3.16,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,320223,2015-10-30 10:19:01:099,1446171541099.0 \n-0.103,0.6788,8.3318,0.4467,-0.3077,9.7916,-0.0208,0.0599,-0.1075,26.1,-5.3,-37.5,4.495619087,1.76,-2.64,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,320326,2015-10-30 10:19:01:202,1446171541202.0 \n-0.5267,-0.1772,11.0576,0.5112,-0.1866,9.7915,0.2334,0.1637,-0.0586,24.9,-5.7,-37.9,4.468741017,1.09,-2.99,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,320428,2015-10-30 10:19:01:304,1446171541304.0 \n-0.2047,-0.674,10.9846,0.4493,-0.1021,9.7958,0.0415,-0.0892,-0.1356,24.1,-6,-38.1,4.469090083,0.6,-2.63,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,320529,2015-10-30 10:19:01:405,1446171541405.0 \n0.3124,0.5052,7.768,0.2394,-0.2544,9.8004,0.0806,0.1283,0,23.4,-5.7,-38.2,4.42894751,1.49,-1.4,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 8,320631,2015-10-30 10:19:01:507,1446171541507.0 \n-0.2646,-0.0646,9.7372,0.289,-0.5729,9.7856,-0.3152,-0.1075,-0.2199,23.1,-5.2,-38.1,4.435928827,2.79,-1.54,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,320734,2015-10-30 10:19:01:610,1446171541610.0 \n-0.1113,0.4836,8.2193,0.2642,-0.6117,9.784,0.0635,-0.0904,0.0892,22.7,-3.8,-38.1,4.454952916,3.58,-1.55,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,320840,2015-10-30 10:19:01:716,1446171541716.0 \n-0.4812,-0.48,10.5919,0.3139,-0.575,9.7847,0.0538,0,0.1136,22.3,-3.3,-38,4.49282656,3.36,-1.84,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,320938,2015-10-30 10:19:01:814,1446171541814.0 \n0.2059,-1.0151,11.9363,0.3941,-0.4514,9.7883,-0.0929,-0.182,0.2492,21.4,-3.4,-38.5,4.513421446,2.3,-1.94,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,321040,2015-10-30 10:19:01:916,1446171541916.0 \n0.0982,0.0251,8.9711,0.418,-0.4923,9.7854,0.0672,-0.237,0.1124,20.8,-4,-39,4.449542395,3.12,-2.32,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,321141,2015-10-30 10:19:02:017,1446171542017.0 \n-0.5997,-0.3172,9.7037,0.5471,-0.5634,9.7752,-0.1258,-0.1564,-0.0379,19.9,-4.9,-39.5,4.399451446,3.29,-3.2,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,321243,2015-10-30 10:19:02:119,1446171542119.0 \n-0.6548,-0.012,8.9639,0.5322,-0.5072,9.7791,0.1295,-0.0648,0.0232,19.3,-5.1,-39.8,4.386186943,3.15,-3.02,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,321345,2015-10-30 10:19:02:221,1446171542221.0 \n-0.6967,0.1401,9.1889,0.5186,-0.3608,9.7863,0.0831,-0.0147,-0.1283,18.5,-5.4,-39.9,4.41166875,2.28,-3.05,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,321448,2015-10-30 10:19:02:324,1446171542324.0 \n-0.5758,-0.6201,11.8465,0.6265,-0.1505,9.7855,0.2101,-0.2407,-0.077,18,-5.4,-40.1,4.426154983,1.48,-3.46,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,321550,2015-10-30 10:19:02:426,1446171542426.0 \n0.4034,-0.9589,10.987,0.6885,-0.0294,9.7824,-0.2211,0.0782,-0.2211,17.4,-5.9,-40,4.419173666,-0.03,-4.08,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,321651,2015-10-30 10:19:02:527,1446171542527.0 \n0.7889,0.2167,7.865,0.5374,-0.076,9.7916,-0.1625,0.0501,0.0195,17,-6.1,-40.1,4.389328536,0.64,-3.22,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,321753,2015-10-30 10:19:02:629,1446171542629.0 \n0.2215,-0.1197,8.7987,0.5404,-0.4294,9.7823,-0.2199,-0.0318,-0.0855,16.7,-5.9,-39.7,4.342728245,2.12,-3.19,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,321856,2015-10-30 10:19:02:732,1446171542732.0 \n0.1508,0.2693,8.7987,0.5241,-0.4649,9.7816,0.0379,0.0171,0.0745,16.5,-4.8,-39.5,4.369780848,2.72,-3.07,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,321958,2015-10-30 10:19:02:834,1446171542834.0 \n-0.3998,-0.5016,9.2967,0.5081,-0.47,9.7822,0.0892,-0.0843,0.1332,16.3,-4.2,-39,4.393866392,2.85,-2.77,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,322060,2015-10-30 10:19:02:936,1446171542936.0 \n0.8559,-0.3412,9.2225,0.5429,-0.211,9.7893,0.0721,-0.11,0.4386,15.8,-4,-38.3,4.453033054,1.23,-3.17,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,322163,2015-10-30 10:19:03:039,1446171543039.0 \n-0.3783,-1.3779,10.9176,0.6543,-0.3362,9.779,-0.1258,-0.16,0.2737,15.4,-4.3,-38,4.422838857,1.8,-3.54,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,322263,2015-10-30 10:19:03:139,1446171543139.0 \n0.1879,-0.5171,9.7659,0.7255,-0.4984,9.7671,-0.204,0.0098,0.1491,14.7,-4.6,-38.3,4.343949975,2.91,-4.25,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,322368,2015-10-30 10:19:03:244,1446171543244.0 \n-0.1999,-0.3615,9.3446,0.6199,-0.6417,9.766,-0.0599,0.0538,0.0476,14.5,-4.6,-38.7,4.313930312,3.58,-3.69,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,322467,2015-10-30 10:19:03:343,1446171543343.0 \n-0.0503,-0.1161,9.6786,0.5259,-0.6797,9.7689,-0.0929,0.077,-0.0745,14.8,-3.8,-39.1,4.340982916,4.05,-3.2,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,322569,2015-10-30 10:19:03:445,1446171543445.0 \n-0.4645,-0.1748,9.8198,0.4224,-0.6228,9.7777,0.0379,0.044,-0.1319,15.4,-3,-38.5,4.40032411,3.64,-2.47,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,322671,2015-10-30 10:19:03:547,1446171543547.0 \n-0.316,-0.2921,10.1406,0.4594,-0.5089,9.7827,0.121,-0.1698,-0.0122,16,-2.7,-38.2,4.432089103,3.19,-2.45,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,322774,2015-10-30 10:19:03:650,1446171543650.0 \n0.5602,-0.7063,11.0947,0.5626,-0.5431,9.7754,-0.3824,0.0635,-0.2663,16.7,-2.6,-38.1,4.454952916,3.17,-3.29,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,322876,2015-10-30 10:19:03:752,1446171543752.0 \n0.2777,-0.0575,8.2516,0.4841,-0.608,9.7758,0.2272,0.0415,-0.0391,17.2,-2.4,-38.4,4.47729313,3.9,-2.84,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,322978,2015-10-30 10:19:03:854,1446171543854.0 \n-0.2562,-0.1041,9.3362,0.5461,-0.6274,9.7713,-0.0941,-0.0098,-0.1979,17.6,-2.1,-38.8,4.496317219,3.67,-3.2,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,323080,2015-10-30 10:19:03:956,1446171543956.0 \n-0.7386,0.0156,9.7061,0.4981,-0.6027,9.7754,0.0562,-0.0086,0.0403,17.9,-1.8,-39,4.494397357,3.66,-2.94,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,323181,2015-10-30 10:19:04:057,1446171544057.0 \n-0.4872,0.504,8.8226,0.2639,-0.4372,9.7933,0.2211,0.3225,0.1051,18.3,-2.4,-38.6,4.519704631,2.56,-1.54,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,323283,2015-10-30 10:19:04:159,1446171544159.0 \n-0.176,0.2993,11.0756,0.1359,-0.147,9.8046,0.4288,0.0367,0.3396,18.5,-3.3,-38.2,4.511850649,1.48,-0.84,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,323388,2015-10-30 10:19:04:264,1446171544264.0 \n-1.154,-1.3767,11.625,0.0983,0.1064,9.8056,-0.3323,0.1625,0.0916,18.3,-6.1,-37.5,4.416555672,-0.62,-0.57,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,323497,2015-10-30 10:19:04:373,1446171544373.0 \n-0.4082,0.4836,8.576,0.1132,0.0275,9.806,-0.1686,-0.182,0.1637,17.2,-8.5,-36.7,4.280070925,-0.17,-0.15,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,323590,2015-10-30 10:19:04:466,1446171544466.0 \n-0.8248,-0.3651,10.0006,0.2113,-0.1613,9.803,-0.193,-0.0208,-0.1356,14.3,-10.5,-36.5,4.090702701,0.94,-1.24,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 9,323691,2015-10-30 10:19:04:567,1446171544567.0 \n-1.5395,-0.2239,8.6119,0.1992,-0.2923,9.8003,-0.0391,-0.1662,-0.4056,4.3,-11.2,-35.4,3.503224875,1.66,-0.89,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,323794,2015-10-30 10:19:04:670,1446171544670.0 \n-2.0195,-0.6464,10.2867,0.1373,-0.3416,9.7997,-0.0183,-0.022,-0.3958,-6.4,-4.6,-36.4,2.420771673,2,-0.8,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,323895,2015-10-30 10:19:04:771,1446171544771.0 \n-2.0051,-0.5866,10.2544,-0.0043,-0.3341,9.801,0.0684,0.1894,-0.1417,-7.2,4.4,-38.9,1.207244244,1.95,0.03,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,323998,2015-10-30 10:19:04:874,1446171544874.0 \n-0.9589,0.0622,8.8957,-0.4984,-0.0248,9.7939,0.5705,0.7086,0.5315,5.4,7.4,-44.3,5.902528997,0.14,2.91,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,324099,2015-10-30 10:19:04:975,1446171544975.0 \n2.2613,1.1205,11.5281,-0.4798,0.2274,9.7923,0.2346,-0.2529,0.391,11.8,5.6,-43.8,5.333202595,-1.33,2.81,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,324201,2015-10-30 10:19:05:077,1446171545077.0 \n4.0821,-3.5985,12.1793,-0.3838,0.3626,9.7924,0.3616,-0.854,-0.6182,15,3.9,-42.5,5.087285704,-1.23,3.37,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,324304,2015-10-30 10:19:05:180,1446171545180.0 \n-2.0506,1.4904,9.2057,0.44,0.506,9.7837,0.7697,-1.3207,-0.0953,14.2,4.6,-43.3,5.13598039,-2.96,-2.58,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,324406,2015-10-30 10:19:05:282,1446171545282.0 \n-0.3567,1.3922,11.8657,0.3408,-0.0032,9.8007,0.1686,0.4899,-0.7856,14.9,4.1,-43.7,4.977679027,-1.01,-3.3,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,324508,2015-10-30 10:19:05:384,1446171545384.0 \n1.0127,2.7581,7.7225,0.1949,0.0459,9.8046,0.0098,0.011,0.3971,15,4.5,-43.7,5.02916624,-0.27,-1.14,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,324609,2015-10-30 10:19:05:485,1446171545485.0 \n0.668,0.6333,10.7931,0.8173,-0.1507,9.7714,-0.2114,-0.9603,-0.3213,15.4,5.4,-43.3,4.970523177,0.46,-3.6,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,324711,2015-10-30 10:19:05:587,1446171545587.0 \n-1.9237,-0.6788,9.809,0.6392,-0.3952,9.7778,-0.044,0.0538,0.2712,16,6.1,-43.1,4.940328981,2.17,-4.1,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,324814,2015-10-30 10:19:05:690,1446171545690.0 \n0.4022,0.425,9.9323,0.6921,-0.5494,9.7668,0.0403,0.1918,0.3299,16.3,6.8,-43.5,4.952371753,3.21,-4.05,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,324916,2015-10-30 10:19:05:792,1446171545792.0 \n0.6428,0.82,9.8988,0.6241,-0.5472,9.7715,-0.0195,-0.1271,0.0953,16.6,6.7,-43.7,4.941027112,3.2,-3.65,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,325017,2015-10-30 10:19:05:893,1446171545893.0 \n1.1253,-0.0527,11.3006,0.5777,-0.4761,9.778,0.1955,-0.0318,-0.0403,17,5.8,-43.4,4.912578246,2.78,-3.38,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,325120,2015-10-30 10:19:05:996,1446171545996.0 \n0.0766,-0.9685,10.4339,0.3484,-0.2587,9.797,-0.1332,-0.4288,0.1222,17.4,4.4,-43.1,4.866676086,1.51,-2.04,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,325222,2015-10-30 10:19:06:098,1446171546098.0 \n-0.6644,-0.5902,8.7352,0.4441,-0.3686,9.7897,-0.0476,0.1197,0.2944,17.7,3.3,-43.1,4.783249348,2.15,-2.6,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,325323,2015-10-30 10:19:06:199,1446171546199.0 \n-1.0116,-0.9397,10.1251,0.5935,-0.3578,9.7821,0.0073,-0.1796,0.1197,17.9,2.5,-43.2,4.783598414,2.11,-3.31,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,325425,2015-10-30 10:19:06:301,1446171546301.0 \n-1.2665,-0.9361,8.7975,0.5085,-0.4209,9.7844,-0.2932,0.0513,-0.0648,17.7,1.6,-43.3,4.721988291,2.46,-2.98,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,325527,2015-10-30 10:19:06:403,1446171546403.0 \n-0.4513,-0.322,8.9878,0.4724,-0.5578,9.7794,0,-0.0208,0.1943,17.6,1.4,-43.1,4.642401277,3.27,-2.78,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 10,325629,2015-10-30 10:19:06:505,1446171546505.0 \n-0.5674,0.1448,10.3813,0.5877,-0.5869,9.7714,-0.0489,-0.0831,0.1038,17.5,1.3,-43.3,4.642924876,3.33,-3.43,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,325732,2015-10-30 10:19:06:608,1446171546608.0 \n-0.8296,-0.2717,11.139,0.5247,-0.5643,9.7763,-0.0012,-0.0476,0.0538,17.3,1.1,-43.5,4.638910619,3.3,-3.07,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,325836,2015-10-30 10:19:06:712,1446171546712.0 \n-0.2083,-0.4669,9.6989,0.5475,-0.475,9.7798,0.0147,-0.0977,0.1258,17.1,0.8,-43.4,4.657411109,2.83,-3.4,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,325936,2015-10-30 10:19:06:812,1446171546812.0 \n0.0622,-0.5602,10.5381,0.8331,-0.3388,9.7653,0.2798,-0.4105,0.0892,16.6,0.2,-43.7,4.626518781,2.35,-4.37,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,326037,2015-10-30 10:19:06:913,1446171546913.0 \n-0.1772,-0.2322,8.8873,0.8127,-0.2436,9.7699,0.1295,-0.0574,0.0208,16.1,-0.6,-44.6,4.606971094,1.42,-4.75,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,326140,2015-10-30 10:19:07:016,1446171547016.0 \n0.0718,-0.2071,9.2608,0.758,-0.2543,9.774,0.0501,0.0843,0.1014,15.7,-0.9,-45,4.606272962,1.42,-4.58,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,326242,2015-10-30 10:19:07:118,1446171547118.0 \n0.249,-0.2322,9.1363,0.6478,-0.221,9.7827,0.0073,0.0916,-0.0232,15.6,-1.4,-45.2,4.608192824,1.3,-4,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,326343,2015-10-30 10:19:07:219,1446171547219.0 \n0.1808,0.0886,8.6155,0.5652,-0.1308,9.7895,0.099,0.0159,0.11,15.8,-1.7,-44.9,4.567701185,0.92,-3.33,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,326445,2015-10-30 10:19:07:321,1446171547321.0 \n-0.3903,-0.5028,10.5117,0.5627,-0.0433,9.7904,0.0819,-0.0684,0.3421,16.1,-2.3,-44.7,4.594753789,0.25,-3.29,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,326548,2015-10-30 10:19:07:424,1446171547424.0 \n-0.0826,-0.1592,9.8162,0.6106,0.008,9.7876,0.0757,-0.0623,0.4264,16.3,-3.1,-44.6,4.555832946,-0.05,-3.57,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,326650,2015-10-30 10:19:07:526,1446171547526.0 \n0.395,-0.425,9.8797,0.7592,0.1592,9.7759,0.2199,-0.1026,0.1881,15.9,-4.4,-44.7,4.544662839,-0.93,-4.44,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,326752,2015-10-30 10:19:07:628,1446171547628.0 \n0.3687,-0.1999,8.1116,0.6016,0.1845,9.7864,0.1087,0.2138,-0.0134,15.6,-5.3,-44.8,4.489510435,-0.91,-3.87,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,326853,2015-10-30 10:19:07:729,1446171547729.0 \n0.2095,0.5291,9.1243,0.5596,-0.0355,9.7906,-0.4239,0.0073,-0.1613,15.7,-5.9,-44.7,4.391597464,0.21,-3.27,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,326963,2015-10-30 10:19:07:839,1446171547839.0 \n-0.9649,0.492,9.7983,0.5034,-0.3966,9.7857,-0.4129,0.0305,-0.204,15.8,-5.3,-44.5,4.377285764,1.84,-3.05,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,327057,2015-10-30 10:19:07:933,1446171547933.0 \n-0.1317,1.1097,9.5361,0.4723,-0.4828,9.7834,-0.1258,-0.0367,0.0489,16.3,-3.9,-44.3,4.389852135,2.69,-2.66,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,327160,2015-10-30 10:19:08:036,1446171548036.0 \n-0.401,0.2418,10.9068,0.4997,-0.5109,9.7806,0.0892,0.0086,0.0379,16.3,-3,-44.3,4.429994707,3.05,-2.92,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,327262,2015-10-30 10:19:08:138,1446171548138.0 \n0.3843,-0.2789,9.8725,0.5693,-0.462,9.7792,0.0061,-0.1515,0.0538,16.2,-2.5,-44,4.497888015,2.64,-3.03,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,327363,2015-10-30 10:19:08:239,1446171548239.0 \n0.3675,0.0599,8.1128,0.6247,-0.4947,9.7742,0.292,0.0281,-0.1429,15.8,-2.1,-44.4,4.476245933,3.36,-3.63,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,327465,2015-10-30 10:19:08:341,1446171548341.0 \n0.6967,-0.413,9.7612,0.5915,-0.4854,9.7768,-0.066,0.1796,-0.3751,15.8,-2.1,-44.5,4.499109746,2.77,-3.67,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,327568,2015-10-30 10:19:08:444,1446171548444.0 \n-0.5267,0.0658,8.5665,0.3825,-0.5285,9.7849,0.0428,-0.0024,0.0318,16,-1.5,-44.8,4.522322625,3.13,-2.29,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,327670,2015-10-30 10:19:08:546,1446171548546.0 \n-0.4214,-0.3292,10.9858,0.4179,-0.4989,9.785,-0.0037,-0.0635,0.0709,16.6,-1,-44.4,4.544488306,2.92,-2.45,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,327771,2015-10-30 10:19:08:647,1446171548647.0 \n-0.5459,-0.5183,10.4675,0.4725,-0.3296,9.7897,0.3067,-0.033,0.303,16.9,-1,-44.3,4.584805412,1.93,-2.76,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,327873,2015-10-30 10:19:08:749,1446171548749.0 \n-0.3711,-1.0259,13.028,0.6393,-0.2886,9.7815,0.226,0.0819,0.3274,16.7,-1.7,-44.3,4.559672671,1.28,-2.94,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,327975,2015-10-30 10:19:08:851,1446171548851.0 \n0.3268,0.1939,9.6534,0.7386,-0.1376,9.7778,0.0464,-0.3311,0.1478,16.2,-3,-44.4,4.527733146,0.8,-4.32,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,328078,2015-10-30 10:19:08:954,1446171548954.0 \n-0.2813,-0.2849,9.5445,0.7542,-0.2583,9.7742,0.1955,-0.0257,-0.1552,15.8,-3.6,-44.6,4.453207586,1.51,-4.41,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,328179,2015-10-30 10:19:09:055,1446171549055.0 \n-0.1437,0.7338,7.9667,0.7064,-0.0704,9.7809,0.0929,0.0122,-0.0892,15.5,-4,-45,4.491430297,0.41,-4.13,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,328282,2015-10-30 10:19:09:158,1446171549158.0 \n-0.7949,0.091,10.1215,0.6482,-0.0989,9.7847,-0.121,0.0709,-0.3238,15.6,-3.8,-45.2,4.486717908,0.49,-3.94,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,328383,2015-10-30 10:19:09:259,1446171549259.0 \n-0.231,-0.1999,10.6291,0.7035,-0.0944,9.7809,-0.0086,0.0098,-0.0892,16,-3.5,-45.4,4.538903253,0.46,-4.01,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,328486,2015-10-30 10:19:09:362,1446171549362.0 \n0.0048,-0.7853,13.3824,0.737,-0.3541,9.7725,0.3396,0.1649,0.1197,15.9,-2.9,-45.2,4.491430297,1.83,-4.56,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,328588,2015-10-30 10:19:09:464,1446171549464.0 \n0.4226,-0.4908,8.4731,0.7477,-0.1146,9.7774,0.1552,-0.0672,-0.033,16,-2.5,-45.5,4.583583682,0.67,-4.37,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,328689,2015-10-30 10:19:09:565,1446171549565.0 \n-0.4812,-0.4298,8.6479,0.6265,-0.3218,9.7813,-0.0428,0.193,-0.0916,16,-2.1,-45.4,4.542742977,1.68,-4.04,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,328792,2015-10-30 10:19:09:668,1446171549668.0 \n0.0431,0.407,9.7719,0.4921,-0.4269,9.785,-0.1735,0.16,-0.0855,16.7,-1.7,-45.3,4.511501583,2.49,-2.88,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,328894,2015-10-30 10:19:09:770,1446171549770.0 \n-0.6584,-0.2562,11.4814,0.3904,-0.4618,9.788,0.215,0.0195,0.248,17.1,-1,-44.9,4.549549761,2.7,-2.28,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,328995,2015-10-30 10:19:09:871,1446171549871.0 \n0.4154,-0.9972,11.3377,0.3406,-0.2329,9.798,0.2004,0,0.2773,17.9,-1,-44.6,4.607843758,1.36,-1.99,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,329098,2015-10-30 10:19:09:974,1446171549974.0 \n-0.006,0.3891,7.6758,0.3705,-0.4012,9.7914,0.1038,0.1051,0.3519,18.1,-1.2,-44.8,4.570493712,2.34,-2.17,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,329199,2015-10-30 10:19:10:075,1446171550075.0 \n0.0634,-0.0096,10.1215,0.5642,-0.386,9.7828,-0.0757,0.0049,-0.0281,18.1,-1.7,-45.1,4.533143666,2.26,-3.3,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,329301,2015-10-30 10:19:10:177,1446171550177.0 \n-0.4334,0.8033,8.0709,0.4723,-0.2356,9.7924,0.2321,0.1258,0.0403,17.9,-1.8,-45.4,4.548153498,1.77,-2.92,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,329404,2015-10-30 10:19:10:280,1446171550280.0 \n-0.0754,0.6536,9.1626,0.4845,-0.071,9.7944,0.171,-0.0586,-0.1222,17.8,-2.2,-45.7,4.584979945,0.75,-2.75,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,329505,2015-10-30 10:19:10:381,1446171550381.0 \n-0.2981,-0.5183,11.4874,0.5952,0.1809,9.7869,0.2077,0.077,-0.1271,17.8,-2.7,-45.9,4.591088597,-0.58,-3.61,36.814472,-119.74797,284.96,336.7684838,2.16,77.41935,215.07,0 / 11,329607,2015-10-30 10:19:10:483,1446171550483.0 \n-0.3591,-0.3484,10.5285,0.355,-0.0407,9.8001,0.1258,0.1723,-0.0721,17.9,-3,-46,4.567003054,-0.04,-2.85,36.81459,-119.74899,291.87,336.7684838,0.11,51.612904,217.43,1111,329709,2015-10-30 10:19:10:585,1446171550585.0 \n0.2442,0.419,7.6351,0.3273,-0.0141,9.8012,0.1258,0.1723,-0.0721,18.1,-2.8,-45.9,4.551644156,0.24,-2.07,36.81459,-119.74899,291.87,336.7684838,0.11,51.612904,217.43,1111,329812,2015-10-30 10:19:10:688,1446171550688.0 \n-0.1113,0.7099,7.8626,0.2865,-0.1587,9.8012,-0.0648,0.0623,-0.1197,18.8,-1.6,-45.9,4.583060083,0.83,-1.77,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,1111,329913,2015-10-30 10:19:10:789,1446171550789.0 \n-0.4226,0.3627,9.9886,0.2831,-0.2073,9.8004,-0.1955,-0.0745,-0.033,19.3,-0.6,-45.6,4.616221339,1.21,-1.65,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,1111,330015,2015-10-30 10:19:10:891,1446171550891.0 \n-0.346,0.0275,11.7436,0.3487,-0.1858,9.7987,0.2101,-0.1246,0.3189,19.4,-0.2,-45.8,4.670850144,1.09,-2.04,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,1111,330117,2015-10-30 10:19:10:993,1446171550993.0 \n0.0251,-0.7207,11.3353,0.5856,-0.0474,9.789,-0.0538,-0.3396,0.0965,19.5,-0.5,-45.7,4.706280328,0.17,-2.86,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,1111,330220,2015-10-30 10:19:11:096,1446171551096.0 \n0.0275,0.3041,7.9739,0.7752,-0.0318,9.7759,0.0061,-0.022,-0.0024,19.1,-1.4,-46.4,4.661774432,0.19,-4.53,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,1111,330321,2015-10-30 10:19:11:197,1446171551197.0 \n-0.571,-0.0323,8.7903,0.7799,-0.204,9.7735,-0.2651,-0.0281,-0.0623,18.8,-2,-46.8,4.589866867,1,-4.54,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,1111,330425,2015-10-30 10:19:11:301,1446171551301.0 \n-0.5124,0.164,8.8047,0.6175,-0.2311,9.7845,0.0367,0.1662,-0.0281,18.5,-2,-47.1,4.572937173,1.35,-3.61,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,1111,330525,2015-10-30 10:19:11:401,1446171551401.0 \n-0.4561,-0.0814,10.4698,0.6213,-0.1705,9.7855,0.0562,-0.0977,-0.0867,18.6,-1.8,-46.9,4.585678077,1,-3.63,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,1111,330627,2015-10-30 10:19:11:503,1446171551503.0 \n1.1768,-0.7602,11.0456,0.7456,-0.1341,9.7773,-0.4105,0.1271,-0.1613,18.7,-1.4,-46.8,4.649557127,0.52,-4.23,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,330729,2015-10-30 10:19:11:605,1446171551605.0 \n-0.4058,-0.9924,10.3298,0.6215,-0.3016,9.7823,0.1796,0.1063,0.2786,18.9,-1.2,-46.8,4.596848184,1.97,-3.85,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,330832,2015-10-30 10:19:11:708,1446171551708.0 \n0.2394,-0.4178,9.5158,0.5991,-0.4152,9.7795,-0.0305,0.1943,0.2016,19,-1,-46.9,4.584456346,2.32,-3.85,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,330934,2015-10-30 10:19:11:810,1446171551810.0 \n0.0599,0.2993,8.0182,0.4521,-0.4161,9.7874,0.1271,0.1747,0.0709,19.5,-0.8,-46.8,4.57991849,2.43,-2.64,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,331036,2015-10-30 10:19:11:912,1446171551912.0 \n-0.0611,0.4561,8.3677,0.2938,-0.3392,9.7964,0.0709,0.1796,0.0171,19.9,-0.9,-46.5,4.592659394,1.98,-1.72,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,331138,2015-10-30 10:19:12:014,1446171552014.0 \n-0.5854,-0.2753,9.8007,0.2733,-0.1841,9.8011,0.3531,-0.0635,0.3005,20.5,-1.1,-46.1,4.629485841,1.08,-1.6,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,331240,2015-10-30 10:19:12:116,1446171552116.0 \n-0.7242,-1.2845,12.7767,0.4971,-0.337,9.7882,-0.1197,-0.1051,0.226,20.7,-1.4,-45.9,4.618490267,1.46,-2.3,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,331341,2015-10-30 10:19:12:217,1446171552217.0 \n0.1413,-0.073,8.5736,0.6796,-0.4151,9.7743,-0.0489,-0.3348,0.0819,20,-1.7,-46.2,4.546233636,2.43,-3.98,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,331445,2015-10-30 10:19:12:321,1446171552321.0 \n-0.1018,-0.1197,9.1004,0.7781,-0.5443,9.7606,-0.0049,-0.0122,-0.1943,19.4,-1.5,-46.7,4.558625473,3.18,-4.56,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,331545,2015-10-30 10:19:12:421,1446171552421.0 \n-0.2454,0.3675,8.3282,0.6467,-0.4079,9.7768,0.2236,0.0464,-0.0049,18.8,-0.8,-46.9,4.581838352,2.38,-3.78,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,331647,2015-10-30 10:19:12:523,1446171552523.0 \n-0.5219,-0.1101,12.1494,0.7929,-0.1934,9.7726,0.1185,-0.3274,-0.1258,18.6,-0.5,-46.7,4.658632839,1.53,-4.35,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,331749,2015-10-30 10:19:12:625,1446171552625.0 \n0.6728,-1.7549,12.0177,0.7645,-0.282,9.7727,-0.5253,0.022,-0.4875,18.4,-0.6,-46.3,4.636292625,0.83,-4.53,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,331852,2015-10-30 10:19:12:728,1446171552728.0 \n1.4114,0.4345,7.0425,0.3779,-0.3012,9.7947,0.1014,0.0648,-0.1405,18.5,-0.1,-45.9,4.638910619,1.95,-2.32,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,331954,2015-10-30 10:19:12:830,1446171552830.0 \n-1.0092,-0.583,8.3043,0.336,-0.4535,9.7904,-0.0892,0.0476,-0.0696,18.9,1,-45.2,4.661250833,2.65,-1.97,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,332061,2015-10-30 10:19:12:937,1446171552937.0 \n-0.0898,0.5435,7.9188,0.3135,-0.4643,9.7906,0.0464,0.0049,0.1503,19.4,1.9,-45,4.707327526,2.71,-1.83,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,332158,2015-10-30 10:19:13:034,1446171553034.0 \n-0.9936,-0.0587,11.9686,0.3585,-0.4798,9.7883,0.0892,-0.0745,0.2187,19.5,2.3,-44.9,4.704709532,2.8,-2.1,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,332259,2015-10-30 10:19:13:135,1446171553135.0 \n-0.2179,0.0395,10.2855,0.36,-0.2372,9.7972,-0.0098,-0.2847,0.336,19.3,2,-44.6,4.751833421,1.54,-1.8,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,332361,2015-10-30 10:19:13:237,1446171553237.0 \n-0.0503,0.2526,8.8298,0.4108,-0.298,9.7935,-0.0635,0.0574,0.2407,19,1,-44.7,4.695982885,1.74,-2.4,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,332463,2015-10-30 10:19:13:339,1446171553339.0 \n-0.8104,-0.9924,10.3166,0.6448,-0.3344,9.7797,-0.2932,-0.0721,-0.1857,18.5,0.3,-44.7,4.644495672,1.95,-3.77,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,332565,2015-10-30 10:19:13:441,1446171553441.0 \n-0.1532,0.5339,7.434,0.5287,-0.4066,9.7839,0.1002,0.215,0.1038,18,0,-44.7,4.619711997,2.5,-3.32,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,332668,2015-10-30 10:19:13:544,1446171553544.0 \n0.1879,0.2957,9.8617,0.5972,-0.3298,9.7829,-0.0012,-0.0305,-0.0379,17.3,0,-44.4,4.628613176,2.19,-3.38,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,332770,2015-10-30 10:19:13:646,1446171553646.0 \n-0.5567,-0.759,11.7005,0.5987,-0.103,9.7878,0.1759,0.0367,-0.3348,17,-0.1,-44.3,4.689525167,0.6,-3.5,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,332872,2015-10-30 10:19:13:748,1446171553748.0 \n-0.7374,-1.0247,9.4008,0.3511,-0.249,9.7972,-0.1637,0.3018,-0.3335,17.1,0,-44.2,4.653222319,1.46,-2.05,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,332973,2015-10-30 10:19:13:849,1446171553849.0 \n0.2789,-0.4633,9.8174,0.3989,-0.3877,9.7909,-0.2346,0,-0.1552,17.3,0.4,-44,4.641528613,1.75,-2.09,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,333079,2015-10-30 10:19:13:955,1446171553955.0 \n-0.0311,0.8535,7.7129,0.363,-0.4445,9.7898,0.0122,0.044,0.0892,17.6,1.5,-43.6,4.71413431,2.6,-2.12,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,333179,2015-10-30 10:19:14:055,1446171554055.0 \n-0.5363,0.3053,9.1614,0.3785,-0.4741,9.7879,-0.0232,-0.022,0.0525,17.4,2.1,-43.4,4.709770987,2.77,-2.21,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,333280,2015-10-30 10:19:14:156,1446171554156.0 \n-0.1496,-0.0563,12.1937,0.3607,-0.3754,9.7928,0.2456,-0.2957,0.4398,17.2,2,-43.6,4.730540405,2.19,-2.11,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,333382,2015-10-30 10:19:14:258,1446171554258.0 \n0.8464,-0.4944,10.8685,0.5714,-0.2249,9.7874,0.1698,-0.1417,0.4386,16.8,1.3,-43.7,4.720766561,1.11,-2.93,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,333485,2015-10-30 10:19:14:361,1446171554361.0 \n0.0096,-0.2131,9.5888,0.8177,-0.304,9.7678,0.0257,-0.3348,0.1161,16.1,0.1,-44,4.643099409,1.8,-4.32,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,333586,2015-10-30 10:19:14:462,1446171554462.0 \n-0.1472,-0.2741,8.9172,0.7833,-0.446,9.7651,-0.0672,0.0684,0.0562,15.4,-0.5,-44.4,4.620410129,2.31,-4.81,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,333687,2015-10-30 10:19:14:563,1446171554563.0 \n0.0024,0.6309,8.2815,0.6902,-0.374,9.7752,0.1319,0.0806,-0.011,14.9,-0.6,-44.6,4.557578276,2.41,-4.17,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,333790,2015-10-30 10:19:14:666,1446171554666.0 \n-0.1736,0.0132,11.1582,0.6266,-0.2146,9.7843,0.1991,0.0257,-0.0904,14.9,-0.6,-44.5,4.603654968,1.25,-3.66,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,333892,2015-10-30 10:19:14:768,1446171554768.0 \n0.6668,-0.3567,9.7121,0.5578,-0.1695,9.7893,-0.3005,0.0012,-0.3238,15,-0.9,-44.1,4.627216913,0.67,-3.45,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,333996,2015-10-30 10:19:14:872,1446171554872.0 \n-0.9445,-2.0363,12.4882,0.5597,-0.4795,9.7789,-0.6451,-0.0159,-0.3787,15.1,-0.8,-44.1,4.536634325,2.8,-3.28,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,334096,2015-10-30 10:19:14:972,1446171554972.0 \n-0.1113,-1.1899,11.0097,0.6844,-0.722,9.7561,-0.3848,-0.2346,0.0415,15.2,0,-44,4.539252319,4.22,-4.01,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,334197,2015-10-30 10:19:15:073,1446171555073.0 \n-0.164,0.0575,9.1171,0.5892,-0.7861,9.7573,0.0318,0.0147,0.066,15.1,0.9,-44,4.574158904,4.6,-3.46,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,334300,2015-10-30 10:19:15:176,1446171555176.0 \n0.2634,0.4717,8.26,0.4072,-0.6719,9.7751,0.0782,0.226,0.0476,15,0.9,-43.7,4.592833927,4.09,-3.04,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,334402,2015-10-30 10:19:15:278,1446171555278.0 \n0.0515,-0.1796,10.5285,0.2692,-0.4113,9.7943,0.2138,-0.0195,0.1576,15.4,0.1,-43,4.57276264,3.09,-1.75,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,334504,2015-10-30 10:19:15:380,1446171555380.0 \n-1.1289,-1.816,12.4283,0.4589,-0.4422,9.7859,-0.1955,-0.3262,-0.1136,15.7,-0.5,-42.7,4.617268536,2.27,-2.11,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,334607,2015-10-30 10:19:15:483,1446171555483.0 \n-0.4537,-0.6069,9.9683,0.5351,-0.422,9.7829,0.248,-0.2615,0.3494,15.8,-0.9,-43,4.56019627,2.47,-3.13,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,334708,2015-10-30 10:19:15:584,1446171555584.0 \n0.1472,0.267,8.5174,0.5093,-0.4359,9.7837,-0.0684,0.1845,-0.11,14.9,-1.7,-43.2,4.491255764,2.66,-3.45,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,334809,2015-10-30 10:19:15:685,1446171555685.0 \n-0.3124,0.48,8.7185,0.2729,-0.3879,9.7952,0.0538,0.0977,-0.1869,14.7,-1.7,-43,4.487241507,2.34,-1.75,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,334912,2015-10-30 10:19:15:788,1446171555788.0 \n-0.8894,-0.5878,10.4806,0.1963,-0.2676,9.801,0.2944,0.0525,-0.0293,15,-1.6,-42.5,4.497538949,2.02,-1.23,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,335014,2015-10-30 10:19:15:890,1446171555890.0 \n0.4501,-0.5543,11.4982,0.1078,-0.3084,9.8012,-0.6072,0.1393,-0.3861,15.8,-1.7,-41.9,4.555832946,0.83,-0.71,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,335116,2015-10-30 10:19:15:992,1446171555992.0 \n0.5543,-0.3675,9.6522,0.208,-0.4708,9.7931,0.1393,-0.2285,0.1283,15.9,-1,-41.7,4.536634325,2.75,-1.22,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,335218,2015-10-30 10:19:16:094,1446171556094.0 \n0.073,0.0108,7.7895,0.2629,-0.5876,9.7855,0.1026,-0.0941,0.0281,15.8,-0.6,-41.6,4.511327051,3.44,-1.54,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,335319,2015-10-30 10:19:16:195,1446171556195.0 \n-0.2693,0.4381,8.582,0.336,-0.521,9.787,0.0806,0.0709,0.0134,15.3,0.1,-41.9,4.579220358,3.05,-1.97,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,335421,2015-10-30 10:19:16:297,1446171556297.0 \n-0.65,0.0658,9.1219,0.212,-0.4289,9.795,0.1161,0.1576,0.0379,15.2,0,-41.9,4.588121538,2.77,-1.48,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,335523,2015-10-30 10:19:16:399,1446171556399.0 \n0.9984,-0.8308,10.969,0.2495,-0.1918,9.8016,0.1918,-0.2798,0.3128,15.1,-0.4,-41.9,4.661774432,1.12,-1.46,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,335625,2015-10-30 10:19:16:501,1446171556501.0 \n-0.4178,-1.4581,11.8214,0.7582,-0.2558,9.774,0.1307,-0.2602,0.3189,14.9,-1,-41.9,4.591961262,1.63,-3.94,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,335727,2015-10-30 10:19:16:603,1446171556603.0 \n-0.1879,0.1544,8.2337,0.7648,-0.3104,9.7719,-0.0843,0.0916,-0.1038,14,-1.7,-42.7,4.522846224,1.81,-4.48,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,335830,2015-10-30 10:19:16:706,1446171556706.0 \n-0.2155,0.4609,7.8015,0.6213,-0.3255,9.7815,0.0354,0.1588,-0.1417,13.3,-1.7,-43.6,4.498237081,1.9,-3.63,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,335931,2015-10-30 10:19:16:807,1446171556807.0 \n-0.6955,0.425,8.7233,0.4731,-0.2734,9.7914,0.0623,0.2211,-0.1124,13.3,-1.5,-43.5,4.567526652,1.68,-3.14,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,336033,2015-10-30 10:19:16:909,1446171556909.0 \n-0.3244,-0.1472,10.4184,0.453,-0.1662,9.7948,0.0403,0.0318,-0.0867,13.9,-1.4,-42.9,4.605225764,0.97,-2.65,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,336135,2015-10-30 10:19:17:011,1446171557011.0 \n-1.4257,-2.0901,11.655,0.2181,-0.3134,9.7992,-0.2321,0.3641,-0.3787,14.4,-1.2,-42.5,4.573111706,1.56,-1.65,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,336238,2015-10-30 10:19:17:114,1446171557114.0 \n-0.0539,-0.1125,9.1411,0.1345,-0.3506,9.7995,-0.2541,0.1185,0.0525,15.2,-0.9,-42.4,4.553738551,2.05,-0.79,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,336345,2015-10-30 10:19:17:221,1446171557221.0 \n-0.0874,0.6488,7.4316,0.0392,-0.4977,9.7939,-0.1613,-0.0574,-0.022,15.6,-0.5,-42.3,4.590215933,2.7,-0.15,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,336442,2015-10-30 10:19:17:318,1446171557318.0 \n-0.6428,0.3938,8.9423,0.0617,-0.5917,9.7886,-0.0269,0.0086,0.0391,15.8,0,-42.3,4.561767066,3.37,-0.3,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,336544,2015-10-30 10:19:17:420,1446171557420.0 \n-0.7242,-0.4681,11.1498,0.0634,-0.453,9.796,0.3543,-0.0709,0.3433,15.9,0.2,-42.3,4.594055657,2.65,-0.37,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,336646,2015-10-30 10:19:17:522,1446171557522.0 \n0.3172,-0.5782,12.2284,0.2604,-0.2354,9.8004,0.0269,-0.4068,-0.0147,15.8,-0.2,-42.1,4.647288199,1.49,-0.87,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,336748,2015-10-30 10:19:17:624,1446171557624.0 \n-0.0156,-0.431,9.1674,0.5839,-0.2072,9.7871,0.1173,-0.2724,0.2077,15.3,-1.3,-42.4,4.605923896,1.21,-3.41,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,336849,2015-10-30 10:19:17:725,1446171557725.0 \n-0.2251,0.0934,8.0792,0.6356,-0.3335,9.7804,-0.1735,0.0904,0.0147,14.4,-2.3,-43.3,4.510628919,1.95,-3.72,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,336951,2015-10-30 10:19:17:827,1446171557827.0 \n-0.1963,0.3855,7.7991,0.6851,-0.4096,9.7741,0.0159,0.0428,0.0305,13.8,-2.2,-43.7,4.493524692,2.39,-4.01,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,337054,2015-10-30 10:19:17:930,1446171557930.0 \n-0.4334,-0.2921,10.89,0.6852,-0.3364,9.7769,0.1307,-0.2236,-0.2578,13.4,-1.9,-43.9,4.499284279,1.97,-4.01,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,337155,2015-10-30 10:19:18:031,1446171558031.0 \n0.0359,-0.3029,10.222,0.6724,-0.0615,9.7834,0.4374,0.314,-0.0159,13.4,-1.8,-43.8,4.543092043,1.05,-4.35,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,337257,2015-10-30 10:19:18:133,1446171558133.0 \n-0.668,-1.5443,11.2456,0.6011,-0.1814,9.7865,-0.259,0.2211,-0.2285,13.4,-1.9,-43.7,4.547280833,0.87,-3.83,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,337360,2015-10-30 10:19:18:236,1446171558236.0 \n0.559,-0.1006,9.1435,0.5784,-0.3646,9.7828,-0.3983,0.1393,-0.1429,13.6,-1.8,-44.1,4.531747403,1.39,-3.52,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,337461,2015-10-30 10:19:18:337,1446171558337.0 \n-0.4214,-0.1508,9.1949,0.597,-0.5697,9.7719,-0.2236,-0.1344,-0.0464,14,-0.9,-44.1,4.505218398,3.33,-3.5,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,337564,2015-10-30 10:19:18:440,1446171558440.0 \n0.1041,0.5231,8.7257,0.4405,-0.6132,9.7775,0.0354,0.2162,0.0464,14.2,-0.3,-44.2,4.54588457,3.63,-2.99,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,337665,2015-10-30 10:19:18:541,1446171558541.0 \n-0.3543,-0.3053,11.4371,0.3001,-0.5387,9.7872,0.1991,-0.1393,0.1552,14.5,0.3,-44.2,4.567177587,3.15,-1.76,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,337767,2015-10-30 10:19:18:643,1446171558643.0 \n-0.3172,0.0443,9.1806,0.2392,-0.2492,9.8006,0.4191,0.281,0.314,14.8,0.1,-44.2,4.623900787,1.92,-1.81,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,337869,2015-10-30 10:19:18:745,1446171558745.0 \n-0.261,-0.0024,9.3194,0.3881,-0.3604,9.7923,-0.0122,-0.0305,0.5363,15,-0.5,-43.8,4.615872273,2.13,-2.17,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,337972,2015-10-30 10:19:18:848,1446171558848.0 \n-0.164,-0.31,10.0317,0.5521,-0.5117,9.7777,-0.4508,0.1246,-0.2211,14.7,-1.3,-43.2,4.530874738,2.99,-3.23,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,338073,2015-10-30 10:19:18:949,1446171558949.0 \n-0.0982,0.5806,7.7105,0.4237,-0.5289,9.7832,0.0464,0.182,-0.2639,14.4,-1.3,-43.5,4.505567464,3.24,-2.86,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,338175,2015-10-30 10:19:19:051,1446171559051.0 \n-0.3831,-0.0431,8.8585,0.3606,-0.4432,9.79,0.1344,0.0867,-0.303,14.4,-0.9,-43.4,4.527209547,2.59,-2.11,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,338278,2015-10-30 10:19:19:154,1446171559154.0 \n-1.1744,-0.3926,11.4634,0.4857,-0.1346,9.7937,0.4508,0.0147,-0.0281,14.5,-0.5,-43.5,4.645717403,1.55,-2.78,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,338379,2015-10-30 10:19:19:255,1446171559255.0 \n-0.0658,-1.494,12.2092,0.4379,-0.1482,9.7957,-0.3396,0.0929,-0.4691,14.7,-0.5,-43.3,4.674689869,0.87,-2.56,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,338481,2015-10-30 10:19:19:357,1446171559357.0 \n-0.1293,-0.6105,9.5864,0.3555,-0.2434,9.7972,-0.044,0.1002,-0.1539,14.7,-0.3,-43.4,4.657585642,1.24,-2.25,36.81459,-119.74899,291.87,336.6060589,0.11,51.612904,217.43,17 / 17,338584,2015-10-30 10:19:19:460,1446171559460.0 \n-0.4645,0.0766,8.661,0.3044,-0.3179,9.7968,-0.1124,-0.011,0.0024,15,0.1,-43.4,4.636641691,1.67,-1.74,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,338685,2015-10-30 10:19:19:561,1446171559561.0 \n-0.3316,0.3687,7.8889,0.2766,-0.2698,9.799,-0.0122,0.0379,0.1417,15.3,0.6,-43.6,4.696157418,1.66,-1.7,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,338787,2015-10-30 10:19:19:663,1446171559663.0 \n-0.9852,-0.4453,10.829,0.2409,-0.2737,9.7999,0.0195,0.0122,0.2028,15.5,0.7,-44.1,4.699648077,1.6,-1.41,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,338889,2015-10-30 10:19:19:765,1446171559765.0 \n-0.2729,-0.9397,10.9642,0.1774,0.0023,9.805,0.2871,0.077,0.4765,15.8,-0.1,-44.1,4.712912579,-0.01,-1.04,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,338992,2015-10-30 10:19:19:868,1446171559868.0 \n0.0168,-0.2873,10.0473,0.2919,-0.0089,9.8023,0.1674,0.0428,0.303,15.7,-0.9,-44,4.652349654,0.05,-1.71,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,339094,2015-10-30 10:19:19:970,1446171559970.0 \n-1.0702,-0.8045,9.8497,0.283,-0.1139,9.8019,-0.099,-0.1491,-0.1833,15.6,-2.3,-43.9,4.568224784,0.67,-1.65,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,339195,2015-10-30 10:19:20:071,1446171560071.0 \n-1.2378,-0.4094,9.2237,0.3465,-0.1741,9.799,-0.1075,-0.0513,-0.1148,15.4,-2.5,-44,4.555134815,0.82,-2.02,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,339297,2015-10-30 10:19:20:173,1446171560173.0 \n-0.2346,0.5662,9.323,0.3864,-0.1629,9.7977,0.0061,-0.077,-0.0574,15.3,-2.4,-44.7,4.548328031,0.99,-2.18,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,339400,2015-10-30 10:19:20:276,1446171560276.0 \n-0.6907,0.1281,9.4379,0.3653,-0.0731,9.7996,0.0648,-0.1185,-0.2529,15.2,-2.1,-45.2,4.564035994,0.62,-2.06,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,339502,2015-10-30 10:19:20:378,1446171560378.0 \n0.2215,0.0994,9.9431,0.4038,0.0955,9.7979,0.3042,-0.0293,-0.0342,15,-2,-46.2,4.620410129,-0.56,-2.36,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,339603,2015-10-30 10:19:20:479,1446171560479.0 \n-0.5662,-0.4621,10.6195,0.2187,-0.1072,9.8036,-0.1759,0.2309,-0.1991,14.9,-1.8,-46.6,4.568399317,0.45,-1.64,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,339705,2015-10-30 10:19:20:581,1446171560581.0 \n-0.0431,-0.4944,9.2464,0.2278,-0.2253,9.8014,-0.2016,-0.022,-0.2162,15,-1.4,-46.7,4.584281813,1.32,-1.33,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,339807,2015-10-30 10:19:20:683,1446171560683.0 \n-0.8176,-0.6548,9.0908,0.2146,-0.4976,9.7917,-0.0855,0.033,0.0501,15.2,-0.4,-46.4,4.56857385,2.91,-1.26,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,339910,2015-10-30 10:19:20:786,1446171560786.0 \n-0.2646,-0.3926,10.3896,0.2519,-0.5957,9.7853,-0.1417,-0.0916,0.0183,15.3,0.3,-46,4.551644156,3.27,-1.34,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,340011,2015-10-30 10:19:20:887,1446171560887.0 \n-0.1233,0.0479,9.8521,0.2739,-0.5678,9.7864,0.0159,-0.044,-0.0305,15.3,1,-45.8,4.612032548,3.32,-1.6,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,340113,2015-10-30 10:19:20:989,1446171560989.0 \n-0.0383,-0.5171,11.7831,0.3514,-0.4425,9.7904,0.3079,0.0757,0.0354,15.3,1.1,-45.9,4.636118092,2.86,-1.96,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,340215,2015-10-30 10:19:21:091,1446171561091.0 \n-0.2682,-1.0223,10.7296,0.2734,-0.2344,9.8,0.1833,0.0489,-0.0403,15.3,0.6,-45.9,4.70697846,1.37,-1.6,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,340317,2015-10-30 10:19:21:193,1446171561193.0 \n-0.3926,-0.656,9.335,0.3432,-0.0965,9.8002,0.1381,-0.1625,-0.077,15.2,0.2,-45.7,4.67416627,0.79,-1.69,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,340419,2015-10-30 10:19:21:295,1446171561295.0 \n-0.1987,-0.6333,10.1766,0.4779,-0.0546,9.7948,-0.1222,-0.1161,-0.1466,15.1,-0.4,-45.4,4.698077281,0.32,-2.79,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,340522,2015-10-30 10:19:21:398,1446171561398.0 \n-0.0539,-0.176,8.6862,0.4197,-0.08,9.7973,0.0318,0.1319,-0.0501,14.8,-0.6,-45.5,4.631929302,0.49,-2.7,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,340623,2015-10-30 10:19:21:499,1446171561499.0 \n-0.2849,-0.2586,9.918,0.3772,-0.2156,9.797,-0.1686,-0.0684,-0.1759,14.7,-0.5,-45.3,4.654094983,1.26,-2.21,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,340725,2015-10-30 10:19:21:601,1446171561601.0 \n-0.0527,0.17,9.2811,0.3488,-0.2725,9.7967,-0.0745,0.0489,-0.281,14.7,0,-45.1,4.638910619,1.58,-2.14,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,340827,2015-10-30 10:19:21:703,1446171561703.0 \n-0.5818,-0.2454,10.5405,0.3755,-0.2541,9.7962,0.055,-0.0867,-0.369,14.8,0.8,-44.7,4.703313268,1.48,-2.2,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,340929,2015-10-30 10:19:21:805,1446171561805.0 \n-0.656,-0.8715,10.5129,0.4964,-0.0025,9.7941,0.2382,-0.1491,-0.3079,14.7,1.3,-44.8,4.76963578,0.01,-2.9,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,341032,2015-10-30 10:19:21:908,1446171561908.0 \n-0.2825,0.1149,9.7372,0.4311,0.0192,9.7972,0.1197,0.0208,-0.1894,14.5,1.5,-44.8,4.825486316,0.08,-2.61,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,341133,2015-10-30 10:19:22:009,1446171562009.0 \n-0.2622,0.401,9.5624,0.3203,0.1014,9.8009,0.044,0.182,-0.2346,14.5,1.6,-44.9,4.860741967,-0.59,-1.87,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,341235,2015-10-30 10:19:22:111,1446171562111.0 \n-0.7745,-0.0551,9.1123,0.0719,0.1726,9.8049,0.0843,0.1894,-0.1368,14.7,2,-45,4.880289654,-0.81,-0.7,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,341338,2015-10-30 10:19:22:214,1446171562214.0 \n-0.1185,0.0611,9.1578,0.0138,0.1797,9.805,-0.0867,0.0024,-0.0293,15.3,2.1,-45.1,4.897742947,-1.05,-0.08,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,341440,2015-10-30 10:19:22:316,1446171562316.0 \n-0.5698,-0.5519,10.4758,0.0547,-0.0608,9.8063,-0.1515,-0.0061,-0.0098,15.6,2.3,-44.9,4.834212962,0.02,-0.26,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,341542,2015-10-30 10:19:22:418,1446171562418.0 \n-0.4262,-0.091,9.1171,-0.0049,-0.1835,9.8049,-0.1735,0.0574,0.055,15.9,2.6,-44.3,4.869817679,0.57,-0.17,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,341643,2015-10-30 10:19:22:519,1446171562519.0 \n-0.5411,-0.0814,10.3322,-0.0419,-0.462,9.7957,-0.3164,0.044,0.0195,16,3.6,-44.1,4.833165765,2.7,0.25,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,341746,2015-10-30 10:19:22:622,1446171562622.0 \n-0.7326,-0.0383,9.6941,-0.0368,-0.5684,9.7901,-0.0513,0.1038,0.1368,16.1,4.3,-43.5,4.80663676,3.32,0.22,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,341847,2015-10-30 10:19:22:723,1446171562723.0 \n-0.3388,0.1544,9.6726,-0.1257,-0.535,9.7912,0.0061,0.0086,0.1491,16.3,4.7,-43.3,4.875751798,3.23,0.63,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,341949,2015-10-30 10:19:22:825,1446171562825.0 \n-0.2789,0.4968,9.238,-0.1636,-0.5306,9.7909,-0.1124,-0.033,0.0012,16.5,4.9,-43,4.884478445,2.89,1.1,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,342052,2015-10-30 10:19:22:928,1446171562928.0 \n-0.9242,-0.2945,10.9666,0.0151,-0.5719,9.7899,0.0061,-0.2566,-0.0562,16.3,5,-43.4,4.865803422,3.34,-0.09,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,342154,2015-10-30 10:19:23:030,1446171563030.0 \n-0.5064,-0.3184,9.9503,0.1379,-0.4127,9.797,0.0941,-0.0073,0.1833,16.1,5,-43.8,4.899837342,2.41,-0.81,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,342256,2015-10-30 10:19:23:132,1446171563132.0 \n-0.9996,-0.5231,10.0233,0.1435,-0.342,9.7996,0.0232,-0.077,0.1381,15.6,4.5,-44.6,4.915894371,2,-0.84,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,342357,2015-10-30 10:19:23:233,1446171563233.0 \n-0.8487,-0.4429,9.6091,0.1622,-0.2756,9.8014,0.0367,-0.1588,0.2688,15.4,3.9,-44.8,4.882558582,1.68,-0.8,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,342460,2015-10-30 10:19:23:336,1446171563336.0 \n-0.3687,0.3819,8.7819,0.1385,-0.2819,9.8016,-0.0476,0.2798,0.1356,15.2,2.9,-45,4.821472059,1.6,-1.27,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,342561,2015-10-30 10:19:23:437,1446171563437.0 \n-0.2239,0.4932,8.8597,0.0924,-0.3493,9.8,-0.0819,-0.0635,0.0428,15.2,2.5,-44.8,4.806462227,1.99,-0.38,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,342665,2015-10-30 10:19:23:541,1446171563541.0 \n-0.6572,0.2382,9.3709,0.2356,-0.4531,9.7933,-0.1417,-0.2908,-0.1038,15.1,2.4,-44.4,4.711341783,2.65,-1.38,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,342766,2015-10-30 10:19:23:642,1446171563642.0 \n-0.5974,0.4154,9.8617,0.4498,-0.4323,9.7868,-0.0147,-0.0831,-0.1026,15,2.5,-44.4,4.776093498,2.54,-2.41,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,342867,2015-10-30 10:19:23:743,1446171563743.0 \n-1.2175,0.2598,9.9994,0.0928,-0.4413,9.7963,-0.0379,0.7269,0.2162,14.7,2.8,-44,4.778711492,2.58,-0.54,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,342969,2015-10-30 10:19:23:845,1446171563845.0 \n-1.1456,0.7853,10.252,-0.4056,-0.1308,9.7974,0.4655,0.0855,0.3225,15.4,2.3,-43.8,4.818679532,0.76,2.37,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,343072,2015-10-30 10:19:23:948,1446171563948.0 \n0.0156,0.4956,8.5485,-0.6534,0.0276,9.7848,-0.2822,-0.2944,-0.3738,16.5,1.6,-43.3,4.874704601,-0.36,4.09,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,343174,2015-10-30 10:19:24:050,1446171564050.0 \n0.832,1.1779,8.9735,-0.3805,-0.1455,9.7982,-0.2346,0.0611,0.3922,17.6,0.8,-43.3,4.734031063,0.85,2.22,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,343275,2015-10-30 10:19:24:151,1446171564151.0 \n0.0359,0.2478,10.0305,-0.2679,-0.2488,9.7998,-0.0513,-0.2101,0.1332,17.6,0.7,-43.1,4.70523313,1.48,1.46,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,343377,2015-10-30 10:19:24:253,1446171564253.0 \n-0.0694,0.6536,10.0042,-0.3051,-0.2514,9.7987,0.0037,-0.1943,0.0819,17.3,0.8,-43.2,4.705058598,1.47,1.78,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,343479,2015-10-30 10:19:24:355,1446171564355.0 \n0.0108,1.2977,9.7264,-0.2678,-0.1438,9.8019,0.1197,0.0916,0.1332,17.1,0.7,-43,4.735252794,0.84,1.56,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,343581,2015-10-30 10:19:24:457,1446171564457.0 \n0.2682,0.7877,10.7967,0.0354,0.2234,9.804,0.4972,-0.204,0.1148,16.8,0.1,-43,4.769286714,-1.31,-0.21,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,343685,2015-10-30 10:19:24:561,1446171564561.0 \n-1.2246,-0.6704,9.0848,0.3662,0.4038,9.7915,0.1649,-0.1857,0.1662,16.1,-0.3,-43.7,4.811523682,-2.29,-1.91,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,343785,2015-10-30 10:19:24:661,1446171564661.0 \n-0.4166,-0.17,10.3082,0.4804,0.255,9.7916,-0.2089,0.0464,0.055,15,-1.2,-44,4.71954483,-1.49,-2.81,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,343887,2015-10-30 10:19:24:763,1446171564763.0 \n-0.4381,0.7769,8.497,0.1552,0.1163,9.8047,-0.1991,0.4789,0.0953,14.6,-1.4,-44.5,4.694237556,-0.93,-1.53,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,343990,2015-10-30 10:19:24:866,1446171564866.0 \n-1.0894,1.0942,9.5517,-0.0362,0.0555,9.8064,-0.1588,0.2285,-0.0586,14.9,-1.2,-44,4.676260665,-0.59,-0.25,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,344092,2015-10-30 10:19:24:968,1446171564968.0 \n-0.7829,0.2215,10.8613,0.1015,0.1209,9.8054,0.1845,-0.1087,0.0379,15.7,-0.9,-43.7,4.684463712,-0.71,-0.59,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,344193,2015-10-30 10:19:25:069,1446171565069.0 \n0.1437,-0.3855,9.6965,-0.0637,-0.1179,9.8057,-0.2981,-0.2028,-0.3115,15.9,-1,-43.5,4.701393406,-1.1,0.21,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,344296,2015-10-30 10:19:25:172,1446171565172.0 \n-0.3424,0.1329,8.8023,-0.3223,-0.1778,9.7997,-0.1979,0.6121,0.3543,16.3,-0.3,-43.5,4.658283774,1.04,1.88,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,344398,2015-10-30 10:19:25:274,1446171565274.0 \n0.0227,0.5351,8.1307,-0.239,-0.2569,9.8004,-0.2297,0.3702,0.0476,16.6,0,-43.3,4.641179547,1.5,1.4,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,344499,2015-10-30 10:19:25:375,1446171565375.0 \n0.0599,0.9361,8.3199,-0.1764,-0.3611,9.7984,-0.1332,-0.303,-0.1075,16.9,0.3,-42.9,4.620410129,1.94,1.44,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,344602,2015-10-30 10:19:25:478,1446171565478.0 \n-0.9673,-0.6656,11.6358,0.1089,-0.5048,9.793,-0.1759,-0.2553,-0.3005,16.7,0.8,-42.7,4.643623008,2.95,-0.64,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,344703,2015-10-30 10:19:25:579,1446171565579.0 \n-0.2011,-0.6548,10.8816,0.4501,-0.3198,9.7911,0.0745,0.0293,0.2859,16.2,1.1,-43,4.694586622,1.79,-2.76,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,344806,2015-10-30 10:19:25:682,1446171565682.0 \n-0.5195,-0.2059,8.357,0.4973,-0.3031,9.7893,0.3262,0.0049,0.3348,15.1,1.1,-43.6,4.692841293,1.77,-2.91,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,344908,2015-10-30 10:19:25:784,1446171565784.0 \n-0.4286,-0.2382,8.8095,0.6287,-0.1927,9.7846,0.0672,-0.215,-0.0269,14.7,0.5,-44,4.720068429,1.15,-3.44,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,345010,2015-10-30 10:19:25:886,1446171565886.0 \n-0.419,0.5052,8.0385,0.5724,-0.2029,9.7878,0.1356,-0.0098,0.1051,14.1,-0.1,-44,4.648335397,1.42,-3.5,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,345111,2015-10-30 10:19:25:987,1446171565987.0 \n-0.0108,-0.1844,11.3593,0.6649,-0.1335,9.7832,0.1735,-0.3787,-0.0354,13.8,-0.7,-44.5,4.619188398,0.78,-3.89,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,345213,2015-10-30 10:19:26:089,1446171566089.0 \n1.1313,-0.8021,10.0173,0.824,0.059,9.7718,-0.3775,-0.0195,-0.4386,13.4,-0.9,-44.7,4.668406683,-0.34,-4.82,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,345316,2015-10-30 10:19:26:192,1446171566192.0 \n1.5,0.8128,5.5941,0.4963,0.0647,9.7939,0.4191,0.6145,0.3335,13.2,-0.9,-44.7,4.666137755,-0.38,-2.9,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,345418,2015-10-30 10:19:26:294,1446171566294.0 \n0.267,-0.2598,9.7863,0.5793,-0.0092,9.7895,-0.0208,-0.1662,0.033,13.3,-1.1,-44.5,4.644146607,0.07,-3.17,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,345519,2015-10-30 10:19:26:395,1446171566395.0 \n0.2849,0.8703,8.2361,0.5414,-0.0841,9.7913,0.0562,0.0061,0.0648,13.8,-1,-44.2,4.629136775,0.49,-3.16,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,345621,2015-10-30 10:19:26:497,1446171566497.0 \n-0.237,0.4812,10.2149,0.4614,-0.1509,9.7946,-0.1429,0.1222,-0.0794,14.2,-1.2,-44.5,4.609065489,0.88,-2.7,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,345723,2015-10-30 10:19:26:599,1446171566599.0 \n-0.0634,-0.0168,10.7009,0.4741,-0.1149,9.7945,0.1808,-0.0244,0.2798,14.2,-1,-44.5,4.604876698,0.97,-2.72,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,345826,2015-10-30 10:19:26:702,1446171566702.0 \n-1.4269,-1.8447,13.1525,0.7439,-0.2205,9.7759,0.1735,0.2211,0.3812,14.2,-1,-44.5,4.599466178,1.29,-4.35,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,345928,2015-10-30 10:19:26:804,1446171566804.0 \n-0.2263,-0.1065,8.5377,0.8257,-0.1034,9.7713,0.1857,-0.3018,0.1588,13.7,-1.1,-44.8,4.636467158,0.44,-4.59,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,346029,2015-10-30 10:19:26:905,1446171566905.0 \n-0.6476,0.2454,7.495,0.7488,-0.2103,9.7758,0.0061,0.0904,-0.0929,13.2,-1.3,-45.2,4.594579256,1.23,-4.38,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,346131,2015-10-30 10:19:27:007,1446171567007.0 \n-0.5567,0.4836,8.2923,0.6734,-0.2213,9.781,-0.0684,-0.0733,-0.044,13.2,-1.5,-45.4,4.593182992,1.19,-3.81,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,346235,2015-10-30 10:19:27:111,1446171567111.0 \n-0.3879,0.4166,11.2444,0.8525,-0.2256,9.7669,0.1246,-0.022,-0.0672,13.3,-1.4,-45.3,4.594055657,1.32,-4.99,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,346336,2015-10-30 10:19:27:212,1446171567212.0 \n1.1444,-1.1396,12.3661,0.9264,-0.2603,9.7593,-0.2834,-0.1038,-0.3445,13.2,-1.4,-45.4,4.587597939,1.52,-5.42,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,346437,2015-10-30 10:19:27:313,1446171567313.0 \n1.3755,0.0766,7.4148,1.0041,-0.2651,9.7515,0.4459,-0.584,0.0086,12.8,-0.8,-45.7,4.588296071,1.55,-5.88,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,346539,2015-10-30 10:19:27:415,1446171567415.0 \n0.723,-0.0467,8.0912,1.1472,-0.2465,9.7362,-0.0318,0.0806,0.1429,12.3,-0.4,-45.9,4.648160864,1.44,-6.72,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,346642,2015-10-30 10:19:27:518,1446171567518.0 \n0.4214,0.65,7.6315,1.0425,-0.2468,9.748,0.0513,0.0513,0.099,12.1,-0.2,-46.1,4.643797541,1.5,-6.27,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,346744,2015-10-30 10:19:27:620,1446171567620.0 \n-0.0503,0.1544,9.8426,0.9086,-0.2646,9.7609,-0.0037,0.193,-0.055,12.2,-0.4,-45.7,4.638212487,1.55,-5.32,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,346846,2015-10-30 10:19:27:722,1446171567722.0 \n0.0766,0.0204,10.4303,0.8974,-0.076,9.7652,0.0672,0.0318,0.3445,12.6,-0.5,-45.5,4.673293605,0.88,-5.37,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,346948,2015-10-30 10:19:27:824,1446171567824.0 \n-0.073,-1.336,12.4558,1.1531,-0.258,9.7352,-0.2309,-0.4325,0.0574,12.6,-1,-45.4,4.595626453,1.51,-6.75,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,347049,2015-10-30 10:19:27:925,1446171567925.0 \n1.1552,0.1616,8.266,1.1676,-0.2711,9.7331,-0.1038,0.0904,0.1038,12.2,-1.3,-45.9,4.598942579,1.3,-7.06,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,347152,2015-10-30 10:19:28:028,1446171568028.0 \n-0.2933,0.1712,8.0445,1.0603,-0.2967,9.7446,0.0684,0.1344,-0.11,11.7,-1.7,-46.1,4.517086637,1.73,-6.21,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,347253,2015-10-30 10:19:28:129,1446171568129.0 \n0.3675,0.0527,9.2237,0.9461,-0.181,9.7592,0.0941,-0.0867,-0.0941,11.8,-1.9,-46,4.54169578,1.06,-5.54,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,347355,2015-10-30 10:19:28:231,1446171568231.0 \n0.6237,-0.0431,9.9766,1.014,0.0108,9.7541,0.314,0.0037,-0.1686,12.2,-2.1,-45.7,4.574507969,0.43,-6.08,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,347458,2015-10-30 10:19:28:334,1446171568334.0 \n-0.2215,-1.5263,11.8298,0.8917,-0.1183,9.7653,-0.463,0.2786,-0.4875,12.5,-2.1,-45.4,4.565257724,0.69,-5.22,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,347560,2015-10-30 10:19:28:436,1446171568436.0 \n0.1197,-0.6776,10.3525,0.7841,-0.2747,9.7714,-0.2883,0.033,-0.1063,12.9,-1.5,-44.9,4.57869676,1.61,-4.59,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,347661,2015-10-30 10:19:28:537,1446171568537.0 \n0.346,0.3986,8.1331,0.7095,-0.4446,9.7708,-0.0208,0.066,0.1381,13.3,-0.7,-44.9,4.543790175,2.33,-4.34,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,347764,2015-10-30 10:19:28:640,1446171568640.0 \n-0.3065,0.6476,8.4862,0.6682,-0.4851,9.7718,-0.0391,0.0525,0.1307,13.7,0.1,-44.6,4.589692334,2.75,-3.99,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,347867,2015-10-30 10:19:28:743,1446171568743.0 \n-0.3484,0.4106,9.2153,0.6307,-0.3174,9.7812,0.2944,-0.1185,0.3238,13.9,0.2,-44.7,4.605400297,2.36,-3.69,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,347967,2015-10-30 10:19:28:843,1446171568843.0 \n0.492,0.1939,8.5868,0.6834,0.0366,9.7827,0.562,0.0012,0.4704,13.9,-0.6,-44.9,4.663519761,-0.21,-4,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,348070,2015-10-30 10:19:28:946,1446171568946.0 \n-0.3555,-0.8056,11.8393,0.9229,-0.1717,9.7616,-0.3176,-0.4129,0.1161,13.6,-2.3,-45.3,4.561592533,1,-5.4,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,348171,2015-10-30 10:19:29:047,1446171569047.0 \n-0.2358,-0.1065,8.7412,0.8767,-0.3065,9.7626,-0.1613,-0.0733,0.1454,13.3,-3.1,-45.5,4.473453406,1.49,-5.12,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,348274,2015-10-30 10:19:29:150,1446171569150.0 \n-0.2777,0.2598,8.7017,0.8348,-0.4949,9.7585,0.0024,0.1442,0.1283,12.9,-3.2,-45.6,4.410621553,2.89,-4.89,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,348376,2015-10-30 10:19:29:252,1446171569252.0 \n-0.1233,0.4824,8.3606,0.74,-0.4211,9.7696,0.1613,0.0696,0.1185,12.7,-3,-45.6,4.421268061,2.46,-4.33,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,348477,2015-10-30 10:19:29:353,1446171569353.0 \n0.6488,-0.1437,11.564,0.8945,-0.1106,9.7651,0.3409,-0.0257,-0.0061,12.7,-3.2,-45.5,4.510454386,0.65,-5.23,36.814465,-119.748856,289.62,336.6060589,3.71,12.903226,272.89,17 / 17,348580,2015-10-30 10:19:29:456,1446171569456.0 \n0.9553,-1.0546,10.9822,0.875,-0.0642,9.7673,-0.5192,-0.1038,-0.573,12.7,-3.9,-45.5,4.487765106,-0.16,-5.15,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,348682,2015-10-30 10:19:29:558,1446171569558.0 \n0.3591,-0.917,10.1885,0.8469,-0.3532,9.7636,-0.0501,0.1686,-0.1002,12.8,-4.1,-45.2,4.422315259,1.42,-5.2,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,348783,2015-10-30 10:19:29:659,1446171569659.0 \n0.4609,0.5016,6.8941,0.7078,-0.5134,9.7676,-0.2175,0.2309,-0.0562,13,-3.5,-45.2,4.417079271,2.64,-4.51,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,348885,2015-10-30 10:19:29:761,1446171569761.0 \n0.0718,-0.3424,9.9491,0.7837,-0.6917,9.7508,-0.1185,-0.0977,0.1283,13.4,-2,-45.1,4.414461277,4.04,-4.6,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,348987,2015-10-30 10:19:29:863,1446171569863.0 \n0.3579,-0.4142,10.0317,0.8098,-0.6369,9.7524,0.2224,0.0171,0.2468,13.5,-1.3,-45.1,4.485321645,4.09,-4.87,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,349090,2015-10-30 10:19:29:966,1446171569966.0 \n-0.5854,-1.1157,10.2568,0.6755,-0.391,9.7755,0.204,0.1197,0.2602,13.5,-1.4,-45.2,4.544313773,2.5,-4.1,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,349196,2015-10-30 10:19:30:072,1446171570072.0 \n0.9206,-1.0534,10.7464,0.8039,-0.3917,9.7658,-0.1442,-0.0757,0.2517,13.3,-2.1,-45.1,4.491081231,2.29,-4.71,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,349293,2015-10-30 10:19:30:169,1446171570169.0 \n-0.3065,-1.2067,9.1901,0.8272,-0.6409,9.7507,-0.3213,-0.0159,-0.0855,13,-3.2,-45.2,4.376413099,3.75,-4.85,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,349396,2015-10-30 10:19:30:272,1446171570272.0 \n0.0048,-0.5363,8.2373,0.8247,-0.8054,9.7387,-0.2309,0.1014,-0.0672,12.7,-3.2,-45.1,4.338015856,4.71,-4.84,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,349497,2015-10-30 10:19:30:373,1446171570373.0 \n-0.3388,-0.2011,8.7113,0.6531,-1.0485,9.7285,-0.1197,0.0415,-0.0965,12.9,-2.3,-44.8,4.315675641,6.14,-3.84,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,349599,2015-10-30 10:19:30:475,1446171570475.0 \n-0.7434,-0.6584,10.3705,0.6588,-1.1042,9.722,0.1381,-0.2798,-0.0073,13.2,-1.4,-44.6,4.353374753,6.47,-3.7,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,349701,2015-10-30 10:19:30:577,1446171570577.0 \n0.9194,-0.3735,8.497,0.8191,-0.757,9.743,0.4129,-0.0464,0.1381,13.4,-0.9,-45,4.426504049,5.14,-4.81,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,349803,2015-10-30 10:19:30:679,1446171570679.0 \n-0.5435,-2.332,13.7798,0.9128,-1.0369,9.7089,-0.4423,0.0049,-0.3763,13.1,-0.9,-45.3,4.422838857,5.41,-5.34,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,349906,2015-10-30 10:19:30:782,1446171570782.0 \n0.3172,-0.7721,9.5457,0.7164,-0.9829,9.7309,0.0244,-0.1429,-0.1112,12.9,-0.9,-45.4,4.392121063,5.75,-4.21,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,350007,2015-10-30 10:19:30:883,1446171570883.0 \n-0.1209,-0.7027,8.9124,0.6546,-1.0204,9.7314,-0.0538,0.1429,-0.121,13.1,-0.5,-45.3,4.440641216,5.89,-4.1,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,350111,2015-10-30 10:19:30:987,1446171570987.0 \n0.2861,-0.2682,9.3158,0.5459,-1.0521,9.7348,-0.0501,0.0892,0.0061,13.7,0,-44.9,4.432787234,6.16,-3.21,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,350211,2015-10-30 10:19:31:087,1446171571087.0 \n0.0826,-0.2885,9.7671,0.4781,-1.0715,9.7362,0.0648,-0.0806,0.2663,13.9,0.2,-44.8,4.422140726,6.27,-2.81,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,350314,2015-10-30 10:19:31:190,1446171571190.0 \n0.7219,-1.1265,9.4559,0.5845,-0.8552,9.7518,-0.1026,-0.1759,0.2517,14.1,0.1,-44.2,4.489859501,5,-3.43,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,350415,2015-10-30 10:19:31:291,1446171571291.0 \n-1.0379,-2.0039,9.9994,0.802,-0.8784,9.7342,0.204,-0.1197,0.1478,13.9,-0.4,-44.2,4.481307387,5.58,-4.79,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,350518,2015-10-30 10:19:31:394,1446171571394.0 \n0.3879,-0.68,9.2823,0.8415,-0.6592,9.7482,0.0195,-0.0721,0,13.4,-1.4,-44.4,4.485147112,3.85,-4.93,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,350619,2015-10-30 10:19:31:495,1446171571495.0 \n-0.1281,-0.3496,8.7317,0.619,-0.6173,9.7676,0.0318,0.2309,-0.1649,13.1,-2.6,-44.7,4.365242992,3.7,-4.03,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,350721,2015-10-30 10:19:31:597,1446171571597.0 \n-0.401,-0.3615,9.6043,0.4929,-0.5555,9.7785,0.0562,0.1185,-0.1857,13.2,-3,-44.7,4.361577801,3.42,-3.08,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,350823,2015-10-30 10:19:31:699,1446171571699.0 \n-0.5183,-0.2993,9.1028,0.4044,-0.4031,9.79,0.1637,0.0794,-0.193,13.9,-3,-44.3,4.418650067,2.36,-2.37,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,350926,2015-10-30 10:19:31:802,1446171571802.0 \n-0.4657,-0.6009,10.0114,0.4774,-0.1636,9.7937,0.2199,-0.0599,-0.1515,14.3,-3.1,-44,4.468042885,1.35,-2.76,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,351028,2015-10-30 10:19:31:904,1446171571904.0 \n-0.5926,-1.7178,12.6881,0.5412,-0.3585,9.7851,-0.4032,-0.0904,-0.2676,14.5,-3.2,-43.7,4.455476514,2.09,-3.17,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,351130,2015-10-30 10:19:32:006,1446171572006.0 \n0.6225,-0.7757,9.76,0.501,-0.2398,9.7909,0.0929,-0.1539,-0.2749,14.6,-2.9,-43.2,4.476420466,1.43,-2.49,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,351232,2015-10-30 10:19:32:108,1446171572108.0 \n0.0251,-0.8284,9.3841,0.4654,-0.1265,9.7948,0.1576,0.1234,-0.2456,14.7,-2.4,-43.3,4.555658414,0.98,-3.01,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,351334,2015-10-30 10:19:32:210,1446171572210.0 \n-0.1448,-0.1544,8.2444,0.4084,0.0462,9.798,0.1674,0.0745,0.0843,15.1,-2.1,-43,4.605400297,-0.27,-2.39,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,351436,2015-10-30 10:19:32:312,1446171572312.0 \n-0.5902,-0.5183,9.8426,0.3986,0.1345,9.7976,0.0122,-0.0794,0.1161,15.1,-2.2,-43,4.628787709,-0.81,-2.35,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,351538,2015-10-30 10:19:32:414,1446171572414.0 \n0.1844,-0.2155,11.1486,0.6337,0.1063,9.7856,-0.1747,-0.4362,0.3592,15.1,-2.8,-43.1,4.569970113,-0.62,-3.71,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,351639,2015-10-30 10:19:32:515,1446171572515.0 \n0.6321,0.6093,9.1913,0.6323,0.0242,9.7862,-0.0745,0.0904,0.1356,14.7,-3.3,-43.2,4.554785749,-0.22,-3.85,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,351741,2015-10-30 10:19:32:617,1446171572617.0 \n-0.2322,0.182,9.8857,0.5473,-0.0459,9.7913,-0.1002,0.0672,0,14.2,-3.9,-43.3,4.461585167,0.27,-3.2,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,351843,2015-10-30 10:19:32:719,1446171572719.0 \n-0.3615,0.1018,9.3099,0.4208,-0.0618,9.7974,0.0073,0.1332,0.1148,14.2,-4,-43.4,4.451985856,0.38,-2.78,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,351946,2015-10-30 10:19:32:822,1446171572822.0 \n-0.3938,0.176,9.238,0.285,-0.016,9.8025,-0.0892,0.0562,0.1576,14.6,-4.3,-43.2,4.466821155,0.09,-1.67,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,352047,2015-10-30 10:19:32:923,1446171572923.0 \n-0.2658,-0.1209,9.9719,0.2151,-0.1065,9.8037,-0.022,0.0073,0.1747,14.8,-4.3,-43.1,4.444306407,0.56,-1.45,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,352149,2015-10-30 10:19:33:025,1446171573025.0 \n-0.5794,0.1006,10.07,0.1932,-0.1494,9.8036,-0.0648,-0.0367,0.1148,15.1,-4.4,-42.9,4.426853115,0.87,-1.13,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,352251,2015-10-30 10:19:33:127,1446171573127.0 \n-0.3867,0.1999,9.5062,0.1309,-0.1418,9.8048,0,0.0354,0.0684,15.1,-4.6,-43.1,4.366115657,0.83,-0.76,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,352354,2015-10-30 10:19:33:230,1446171573230.0 \n-0.6177,0.2598,8.1774,0.1277,-0.0598,9.8056,0.2126,-0.066,0.0232,15.1,-4.8,-43.2,4.386361476,0.35,-0.75,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,352456,2015-10-30 10:19:33:332,1446171573332.0 \n-0.5794,0.0323,9.7528,0.0998,-0.1361,9.8052,-0.1063,-0.033,0.0257,15.1,-5.1,-43.3,4.369257249,0.73,-0.69,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,352558,2015-10-30 10:19:33:434,1446171573434.0 \n-1.3994,-0.395,9.6163,-0.0608,-0.1808,9.8048,-0.1038,0.0904,0.1539,15,-5.1,-43.2,4.33766679,1.06,0.36,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,352659,2015-10-30 10:19:33:535,1446171573535.0 \n-0.0383,-0.3017,10.969,-0.0396,-0.2713,9.8028,0.0134,0.0757,0.4154,15.1,-5,-43.3,4.317246438,1.61,0.16,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,352761,2015-10-30 10:19:33:637,1446171573637.0 \n0.3196,0.2442,9.1877,-0.1196,-0.1828,9.8042,0.1503,0.088,0.3457,14.8,-5.4,-43.2,4.331034539,1.07,0.7,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,352864,2015-10-30 10:19:33:740,1446171573740.0 \n0.2083,0.2263,9.9084,-0.1876,-0.1758,9.8033,-0.066,0.1442,0.1148,14.8,-6,-43,4.272566009,0.97,0.92,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,352965,2015-10-30 10:19:33:841,1446171573841.0 \n-0.0898,0.2873,9.8007,-0.2324,-0.1613,9.8026,-0.0513,0.0672,0.0122,15,-6.9,-42.7,4.208163359,0.94,1.36,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,353067,2015-10-30 10:19:33:943,1446171573943.0 \n-0.1796,0.3292,9.6558,-0.233,-0.0709,9.8036,0.099,-0.0159,0.0342,15.1,-7.1,-42.5,4.219682533,0.65,1.44,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,353169,2015-10-30 10:19:34:045,1446171574045.0 \n-0.3747,0.1915,9.2715,-0.2276,-0.019,9.804,0.0501,-0.0024,-0.0538,15.2,-7.1,-42.5,4.244640741,0.11,1.33,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,353271,2015-10-30 10:19:34:147,1446171574147.0 \n-0.7111,0.0599,9.6941,-0.1812,-0.0219,9.805,-0.0354,-0.0403,-0.0965,15,-7.2,-42.1,4.249702196,0.13,1.06,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,353374,2015-10-30 10:19:34:250,1446171574250.0 \n-0.5531,0.1748,9.6295,-0.1635,-0.0569,9.8051,-0.0586,-0.0696,-0.0012,15,-7.2,-42.3,4.245513405,0.25,1.01,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,353475,2015-10-30 10:19:34:351,1446171574351.0 \n-0.2658,0.3112,9.6702,-0.1347,-0.0799,9.8054,-0.0061,-0.0086,0.033,14.8,-6.9,-42.6,4.237484891,0.52,0.83,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,353578,2015-10-30 10:19:34:454,1446171574454.0 \n-0.5255,0.1101,9.6654,-0.1465,-0.0701,9.8053,0.0134,0.0147,-0.0183,14.8,-6.8,-42.9,4.241848214,0.44,0.79,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,353679,2015-10-30 10:19:34:555,1446171574555.0 \n-0.5638,0.073,9.4284,-0.2001,-0.0735,9.8043,0.0037,-0.0305,0.0648,15,-6.8,-42.8,4.233819699,0.43,1.17,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,353782,2015-10-30 10:19:34:658,1446171574658.0 \n-0.6165,0.018,9.9048,-0.2035,-0.0991,9.804,-0.0648,0.0061,0.0281,15.1,-6.8,-42.6,4.231725304,0.49,1.15,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,353883,2015-10-30 10:19:34:759,1446171574759.0 \n-0.4381,0.079,9.912,-0.2301,-0.1154,9.8033,-0.0086,0.0183,0.0403,15.1,-6.8,-42.5,4.223347724,0.65,1.29,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,353987,2015-10-30 10:19:34:863,1446171574863.0 \n-0.51,0.0263,9.675,-0.2442,-0.1058,9.803,0.0452,-0.0648,0.0367,14.9,-6.7,-42.4,4.221427862,0.62,1.43,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,354090,2015-10-30 10:19:34:966,1446171574966.0 \n-0.4585,0.1724,9.183,-0.2252,-0.0326,9.804,0.0843,0,0.0501,14.9,-6.7,-42.3,4.241673681,0.19,1.32,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,354190,2015-10-30 10:19:35:066,1446171575066.0 \n-0.3531,0.2143,9.4308,-0.1404,0.0193,9.8056,0.0525,-0.0733,0.0855,14.9,-7,-42.4,4.264537494,-0.11,0.82,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,354292,2015-10-30 10:19:35:168,1446171575168.0 \n-0.255,0.2801,9.402,-0.0941,0.0106,9.8062,-0.0257,-0.0819,0.0147,14.9,-7.2,-42.6,4.266282824,-0.05,0.6,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,354394,2015-10-30 10:19:35:270,1446171575270.0 \n-0.2526,0.0994,10.064,-0.0753,-0.0414,9.8063,-0.0806,0.0208,-0.0354,14.7,-7.5,-42.6,4.257032579,0.24,0.44,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,354497,2015-10-30 10:19:35:373,1446171575373.0 \n-0.0862,0.2107,9.5122,-0.0714,-0.009,9.8064,0.077,-0.0501,-0.0709,14.4,-7.4,-42.7,4.230678107,0.12,0.58,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,354605,2015-10-30 10:19:35:481,1446171575481.0 \n-0.2203,0.3124,9.3422,-0.1319,0.0278,9.8057,0.077,0.077,-0.0232,14.4,-7.2,-42.7,4.238881154,-0.16,0.77,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,354699,2015-10-30 10:19:35:575,1446171575575.0 \n-0.2897,0.2358,9.5361,-0.1356,0.0823,9.8054,0.0342,0.0232,-0.0134,14.4,-7.1,-42.8,4.249004064,-0.39,0.78,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,354802,2015-10-30 10:19:35:678,1446171575678.0 \n-0.5016,0.2358,9.7516,-0.1471,0.0984,9.8051,-0.0037,-0.0049,-0.0232,14.7,-7.2,-42.5,4.283212517,-0.57,0.86,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,354903,2015-10-30 10:19:35:779,1446171575779.0 \n-0.3903,0.3364,9.6977,-0.1629,0.1333,9.8044,0.0342,-0.0269,0.0403,14.8,-7.2,-42.4,4.287052242,-0.71,0.96,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,355005,2015-10-30 10:19:35:881,1446171575881.0 \n-0.4836,0.3424,9.9599,-0.1713,0.1231,9.8044,-0.0147,-0.0318,0.0171,14.7,-7.2,-42.4,4.286528643,-0.72,1,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,355108,2015-10-30 10:19:35:984,1446171575984.0 \n-0.3675,0.3436,9.5205,-0.1745,0.1528,9.8039,0.0415,0.0134,0.0379,14.5,-7.3,-42.3,4.289146637,-0.79,1.02,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,355209,2015-10-30 10:19:36:085,1446171576085.0 \n-0.5219,0.249,9.6139,-0.2009,0.1485,9.8035,0.0024,0.0037,0.0342,14.1,-7.4,-42.6,4.2619195,-0.87,1.17,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,355312,2015-10-30 10:19:36:188,1446171576188.0 \n-0.6177,0.1664,9.8222,-0.2055,0.1221,9.8037,-0.0525,-0.011,0.0501,13.7,-7.2,-42.5,4.253890986,-0.71,1.2,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,355414,2015-10-30 10:19:36:290,1446171576290.0 \n-0.7709,0.3244,10.4016,-0.339,-0.0156,9.8008,0.0171,-0.033,0.0208,13.6,-7.2,-42.7,4.246909669,-0.59,1.27,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,355516,2015-10-30 10:19:36:392,1446171576392.0 \n-0.9026,-0.067,11.0397,-0.2056,0.1894,9.8027,0.1405,-0.0147,0.0122,13.5,-7,-42.4,4.271867877,-1.11,1.2,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,355617,2015-10-30 10:19:36:493,1446171576493.0 \n-0.996,0.1616,10.2077,-0.0956,0.3045,9.8015,-0.0806,0.2089,-0.0428,13.6,-7.4,-42.5,4.318817234,-1.82,0.5,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,355720,2015-10-30 10:19:36:596,1446171576596.0 \n0.2071,0.6333,9.8234,-0.1273,0.2989,9.8013,-0.0049,-0.0574,-0.0024,13.8,-8.1,-42.4,4.246909669,-1.74,0.87,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,355821,2015-10-30 10:19:36:697,1446171576697.0 \n-0.7649,0.1604,9.9826,-0.112,0.2707,9.8023,-0.1381,0.0403,-0.0049,13.9,-8.5,-42.6,4.244640741,-1.59,0.71,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,355924,2015-10-30 10:19:36:800,1446171576800.0 \n0.1975,0.5818,9.7779,-0.032,0.2821,9.8025,-0.0806,-0.0098,0.0171,14,-8.8,-42.9,4.204847234,-1.77,0.29,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,356025,2015-10-30 10:19:36:901,1446171576901.0 \n-0.3591,0.6321,10.0592,-0.0314,0.2652,9.803,-0.1955,0.16,0.0257,14,-8.8,-43.1,4.19804045,-1.55,0.18,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,356127,2015-10-30 10:19:37:003,1446171577003.0 \n-0.4178,0.2418,9.3889,-0.0855,0.2386,9.8034,-0.0037,0.033,0.011,13.4,-8.6,-45.2,4.152661889,-1.39,0.5,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,356229,2015-10-30 10:19:37:105,1446171577105.0 \n-0.2274,0.3819,9.7612,-0.0539,0.2543,9.8032,0.011,-0.011,0.0806,12.9,-8.6,-46.3,4.163133865,-1.49,0.32,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,356331,2015-10-30 10:19:37:207,1446171577207.0 \n-0.176,0.3938,9.6798,-0.0681,0.2754,9.8025,0.0257,0.0305,0.0244,12.8,-8.7,-46.4,4.16644999,-1.61,0.4,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,356433,2015-10-30 10:19:37:309,1446171577309.0 \n-0.3376,0.4166,9.8462,-0.1205,0.2861,9.8017,-0.0269,0,-0.011,12.6,-8.8,-46.5,4.160864937,-1.67,0.7,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,356535,2015-10-30 10:19:37:411,1446171577411.0 \n-0.2071,0.5722,9.6438,-0.1667,0.302,9.8006,0.0476,0.0574,0.0354,12.7,-9,-46.8,4.155454416,-1.65,0.9,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,356638,2015-10-30 10:19:37:514,1446171577514.0 \n-0.4417,0.3783,9.3422,-0.1878,0.3336,9.7992,0.0354,-0.0195,-0.011,13,-9.2,-46.6,4.159992272,-1.89,1.14,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,356739,2015-10-30 10:19:37:615,1446171577615.0 \n-0.5339,0.2945,9.7743,-0.1771,0.3005,9.8004,-0.0122,-0.077,0.0476,13.4,-9.4,-46.3,4.156152548,-1.81,1.09,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,356842,2015-10-30 10:19:37:718,1446171577718.0 \n-0.2394,0.5171,9.7456,-0.1514,0.2992,9.8009,-0.0012,-0.0183,0.0452,13.8,-9.6,-45.2,4.137652058,-1.75,0.88,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,356943,2015-10-30 10:19:37:819,1446171577819.0 \n-0.0886,0.3867,10.1311,-0.1366,0.3017,9.8011,0.0953,-0.16,-0.0073,13.9,-9.6,-45,4.13241607,-1.69,0.99,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,357045,2015-10-30 10:19:37:921,1446171577921.0 \n-0.243,0.4489,9.3182,-0.1468,0.3508,9.7993,0.033,-0.0501,0.0415,13.8,-9.5,-45.1,4.201356575,-1.96,0.91,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,357148,2015-10-30 10:19:38:024,1446171578024.0 \n-0.2717,0.4142,9.7348,-0.1353,0.3407,9.7998,-0.0122,-0.0195,0.0012,13.9,-9.5,-45.2,4.2051963,-2,0.82,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,357250,2015-10-30 10:19:38:126,1446171578126.0 \n0.0407,0.5124,8.9328,-0.0476,0.387,9.7989,0.2944,-0.3763,0.0171,14,-9.6,-45.3,4.167846254,-2.22,0.5,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,357351,2015-10-30 10:19:38:227,1446171578227.0 \n-0.1496,0.4896,9.5277,-0.0546,0.3435,9.8005,0.0745,-0.0599,0.0208,14,-9.5,-45.3,4.21776267,-2.01,0.32,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,357453,2015-10-30 10:19:38:329,1446171578329.0 \n-0.1293,0.5088,9.9371,-0.0171,0.3569,9.8001,-0.1087,0.0269,-0.0183,13.9,-9.5,-45.5,4.226314784,-2.09,0.1,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,357555,2015-10-30 10:19:38:431,1446171578431.0 \n-0.1448,0.6452,9.1111,-0.0523,0.3366,9.8007,0.1197,-0.0501,0.1124,13.8,-9.3,-45.7,4.218111736,-1.97,0.31,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,357658,2015-10-30 10:19:38:534,1446171578534.0 \n-0.2119,0.4441,9.6522,-0.0585,0.3495,9.8002,0.033,-0.0452,0.0415,13.7,-9.4,-45.6,4.218111736,-2.02,0.39,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,357759,2015-10-30 10:19:38:635,1446171578635.0 \n-0.2274,0.4417,9.6127,-0.0414,0.3559,9.8001,0.0403,-0.0428,0.0501,13.7,-9.5,-45.6,4.220904263,-2.02,0.29,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,357861,2015-10-30 10:19:38:737,1446171578737.0 \n-0.2274,0.4657,9.7671,-0.0326,0.3599,9.8,-0.0208,0.0073,0.0232,13.6,-9.7,-45.6,4.172209577,-2.1,0.19,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,357963,2015-10-30 10:19:38:839,1446171578839.0 \n-0.2382,0.4465,9.9048,-0.0405,0.3724,9.7995,0.0208,0.0012,0.011,13.3,-9.8,-45.7,4.140619117,-2.18,0.24,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,358066,2015-10-30 10:19:38:942,1446171578942.0 \n-0.2406,0.5459,9.5828,-0.0779,0.3858,9.7988,0.0244,0.0257,-0.0195,13.1,-9.7,-46.1,4.136081261,-2.18,0.4,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,358167,2015-10-30 10:19:39:043,1446171579043.0 \n-0.2502,0.5435,9.572,-0.096,0.3936,9.7983,0.0159,0.0086,-0.0232,13,-9.7,-46.1,4.136953926,-2.3,0.56,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,358269,2015-10-30 10:19:39:145,1446171579145.0 \n-0.4405,0.4082,9.6271,-0.1263,0.3806,9.7984,-0.0073,0.0171,-0.0159,12.9,-9.7,-45.9,4.12822728,-2.22,0.74,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,358372,2015-10-30 10:19:39:248,1446171579248.0 \n-0.3388,0.4298,9.6462,-0.1425,0.3737,9.7985,0,-0.0037,0.0208,12.9,-9.7,-45.3,4.122991292,-2.18,0.8,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,358474,2015-10-30 10:19:39:350,1446171579350.0 \n-0.2909,0.4465,9.6774,-0.1461,0.3741,9.7984,-0.0281,-0.0464,-0.0061,12.8,-9.5,-45,4.17953996,-2.19,0.85,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,358575,2015-10-30 10:19:39:451,1446171579451.0 \n-0.2873,0.4022,9.8737,-0.1338,0.3426,9.7998,-0.0379,0.0012,-0.0134,12.9,-9.5,-45.3,4.173954906,-2.03,0.78,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,16 / 17,358677,2015-10-30 10:19:39:553,1446171579553.0 \n-0.2418,0.4609,9.5636,-0.1309,0.3499,9.7995,0.0012,-0.0159,0,13.1,-9.5,-45.4,4.17535117,-2.04,0.77,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,16 / 17,358780,2015-10-30 10:19:39:656,1446171579656.0 \n-0.2897,0.3915,9.833,3.786,-3.0452,8.5184,-0.0024,-0.011,-0.0293,13.3,-9.5,-45.4,4.134510465,21.18,-26.77,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,16 / 17,358881,2015-10-30 10:19:39:757,1446171579757.0 \n-0.267,0.4752,9.6151,2.498,-1.4451,9.3724,-0.0061,-0.0098,-0.0293,13.7,-9.6,-45.1,4.151789225,8.47,-14.92,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,16 / 17,358983,2015-10-30 10:19:39:859,1446171579859.0 \n-0.2263,0.4094,9.7348,1.6105,-0.637,9.6525,0.0269,-0.0195,-0.0342,13.8,-9.6,-44.9,4.167322655,4.86,-10.88,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,16 / 17,359085,2015-10-30 10:19:39:961,1446171579961.0 \n-0.5495,0.085,10.6877,1.2385,-0.441,9.7181,0.0305,-0.1552,-0.0513,13.8,-9.5,-44.7,4.206941629,2.42,-7.19,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,16 / 17,359187,2015-10-30 10:19:40:063,1446171580063.0 \n-0.3065,0.4896,10.094,1.2163,-0.3734,9.7238,-0.0977,0.0916,0.0342,13.5,-9.2,-44.6,4.215319209,2.21,-7.34,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,16 / 17,359290,2015-10-30 10:19:40:166,1446171580166.0 \n-0.2717,0.3496,9.7899,1.0486,-0.1719,9.7489,-0.011,-0.0342,-0.0391,13,-8.9,-44.6,4.20938509,1,-6.14,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,16 / 17,359391,2015-10-30 10:19:40:267,1446171580267.0 \n-0.3723,0.3292,9.59,0.7905,-0.0228,9.7747,-0.0024,-0.0367,0.0049,12.7,-8.7,-44.9,4.210257755,0.37,-5.04,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,16 / 17,359493,2015-10-30 10:19:40:369,1446171580369.0 \n-0.261,0.3891,9.7815,0.6213,0.0677,9.7867,0.0061,-0.0269,0.0024,12.6,-8.8,-45.2,4.209908689,-0.4,-3.63,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,16 / 17,359596,2015-10-30 10:19:40:472,1446171580472.0 \n-0.243,0.4465,9.6211,0.4663,0.1752,9.794,0.0257,-0.0122,0.0293,12.6,-8.9,-45.3,4.215319209,-1.02,-2.73,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,359697,2015-10-30 10:19:40:573,1446171580573.0 \n-0.1963,0.431,9.8126,0.3675,0.229,9.7971,0.0037,0.0134,0.0232,12.8,-9.2,-45,4.215493742,-1.34,-2.15,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,359799,2015-10-30 10:19:40:675,1446171580675.0 \n-0.1209,0.4741,9.7217,0.306,0.2751,9.798,0.0244,0.0134,0.0086,12.9,-9.3,-44.9,4.219158934,-1.55,-1.91,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,359901,2015-10-30 10:19:40:777,1446171580777.0 \n-0.2095,0.4274,9.7923,0.2515,0.3051,9.7987,-0.0122,0.0183,-0.0098,13.2,-9.5,-44.9,4.219158934,-1.78,-1.47,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,360004,2015-10-30 10:19:40:880,1446171580880.0 \n-0.1592,0.5243,9.6714,0.1692,0.342,9.7992,0.0073,0.022,-0.0037,13.3,-9.4,-45,4.217064539,-1.94,-1.09,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,360105,2015-10-30 10:19:40:981,1446171580981.0 \n-0.1161,0.5686,9.6067,0.1381,0.3683,9.7988,0.0342,-0.0086,-0.0171,13.5,-9.4,-44.9,4.249004064,-2.15,-0.81,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,360207,2015-10-30 10:19:41:083,1446171581083.0 \n-0.3352,0.3436,9.1459,0.106,0.3593,9.7995,0.0073,0.0134,-0.0379,13.5,-9.4,-44.6,4.251796591,-2.26,-0.71,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,360309,2015-10-30 10:19:41:185,1446171581185.0 \n-0.2873,0.4166,9.0465,0.1413,0.3511,9.7993,0.3812,-0.1967,-0.0171,13.3,-9,-44.5,4.181459822,-1.46,-0.54,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,360412,2015-10-30 10:19:41:288,1446171581288.0 \n-0.1676,0.4896,9.8031,0.1088,0.359,9.7995,0.0415,-0.1307,0.0012,12.9,-8.8,-44.7,4.21357388,-2.1,-0.64,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,360513,2015-10-30 10:19:41:389,1446171581389.0 \n-0.2454,0.4465,9.6283,0.1105,0.3466,9.7999,0.0024,0.0122,-0.0061,12.8,-8.7,-44.5,4.208337892,-2.03,-0.65,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,360615,2015-10-30 10:19:41:491,1446171581491.0 \n-0.2705,0.3759,9.7121,0.0892,0.3538,9.7999,-0.0098,-0.0257,-0.0061,12.8,-8.8,-44.7,4.209559623,-2.07,-0.52,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,360718,2015-10-30 10:19:41:594,1446171581594.0 \n-0.2143,0.4729,9.6139,0.0555,0.3567,9.8,0.0037,-0.0098,0.0122,13.1,-9,-44.9,4.205545366,-2.08,-0.32,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,360819,2015-10-30 10:19:41:695,1446171581695.0 \n-0.2538,0.3783,10.0054,0.061,0.349,9.8002,0.0232,-0.0147,0.0086,13.4,-9.1,-45,4.2051963,-2.05,-0.37,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,360922,2015-10-30 10:19:41:798,1446171581798.0 \n-0.1856,0.5124,9.5624,0.0514,0.3727,9.7994,0.022,0.0037,0.0195,13.9,-9.3,-45,4.239404753,-2.18,-0.3,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,361023,2015-10-30 10:19:41:899,1446171581899.0 \n-0.1472,0.4848,9.9383,0.0681,0.3663,9.7996,-0.0183,-0.0318,0.0073,14,-9.3,-44.8,4.239928352,-2.15,-0.38,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,361126,2015-10-30 10:19:42:002,1446171582002.0 \n-0.3053,0.492,9.6259,0.0475,0.3801,9.7992,0.0061,-0.0037,0.0147,14.1,-9.3,-44.4,4.238357556,-2.22,-0.28,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,361227,2015-10-30 10:19:42:103,1446171582103.0 \n-0.2693,0.4717,9.8701,0.0303,0.3895,9.7989,-0.0061,-0.0134,0.0269,14,-9.3,-44.1,4.239055687,-2.27,-0.21,36.814472,-119.74895,283.76,336.6060589,3.87,12.903226,271.07,17 / 17,361329,2015-10-30 10:19:42:205,1446171582205.0 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  },
  {
    "path": "test/data/McLaneWalk.csv",
    "content": "-0.729,0.6261,9.9288,-0.6497,0.6178,9.7656,-0.0159,-0.0415,0.0171,5.1,16.3,-43.9,6.173404097,-3.61,3.81,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,37,2015-10-30 10:22:17:170,1446171737170.0 \n-0.6165,0.656,9.6403,-0.6446,0.5969,9.7672,-0.0134,-0.0195,0.0379,5.1,16.4,-44.1,6.173229564,-3.5,3.81,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,139,2015-10-30 10:22:17:272,1446171737272.0 \n-0.5662,0.6321,9.5648,-0.6069,0.5822,9.7705,-0.0024,-0.0257,0.0073,5.2,16.6,-43.6,6.168168109,-3.4,3.55,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,242,2015-10-30 10:22:17:375,1446171737375.0 \n-0.565,0.5794,9.8007,-0.576,0.5599,9.7737,-0.0183,-0.0586,-0.0098,5.1,16.7,-43.7,6.164502918,-3.36,3.47,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,343,2015-10-30 10:22:17:476,1446171737476.0 \n-0.6009,0.5483,9.8043,-0.5668,0.5559,9.7745,-0.0086,-0.0159,-0.0098,5,16.8,-43.5,6.156125338,-3.27,3.34,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,445,2015-10-30 10:22:17:578,1446171737578.0 \n-0.6177,0.4944,9.839,-0.5589,0.5586,9.7748,0.0464,-0.0195,0.0098,4.8,16.8,-43.6,6.158917864,-3.21,3.34,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,547,2015-10-30 10:22:17:680,1446171737680.0 \n-0.5602,0.6225,9.5756,-0.5599,0.5838,9.7732,-0.0208,-0.0024,-0.0257,4.7,16.9,-43.4,6.155427206,-3.44,3.3,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,649,2015-10-30 10:22:17:782,1446171737782.0 \n-0.6883,0.5567,9.5433,-0.5694,0.5743,9.7732,0.0012,0.0122,-0.0208,4.7,16.9,-43.8,6.1580452,-3.38,3.3,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,752,2015-10-30 10:22:17:885,1446171737885.0 \n-0.6117,0.5519,9.7671,-0.5677,0.5719,9.7735,0.0073,0.0024,-0.0183,4.7,16.9,-43.5,6.154903607,-3.34,3.31,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,853,2015-10-30 10:22:17:986,1446171737986.0 \n-0.6776,0.6177,9.4511,-0.5739,0.5905,9.772,-0.0208,0.0012,-0.0452,4.7,16.7,-43.8,6.160663194,-3.47,3.35,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,955,2015-10-30 10:22:18:088,1446171738088.0 \n-0.8009,0.4405,9.8067,-0.5737,0.5453,9.7747,-0.0684,-0.0147,-0.0428,4.6,16.7,-43.6,6.161884924,-3.29,3.41,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,1057,2015-10-30 10:22:18:190,1446171738190.0 \n-0.5758,0.565,9.7624,-0.5522,0.5293,9.7768,0.0073,0.0147,0.0024,4.6,16.7,-43.9,6.153158278,-3.08,3.21,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,1159,2015-10-30 10:22:18:292,1446171738292.0 \n-0.6536,0.5219,9.5648,-0.5472,0.5397,9.7765,-0.0513,-0.0147,-0.0171,4.5,16.9,-43.8,6.153332811,-3.15,3.2,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,1261,2015-10-30 10:22:18:394,1446171738394.0 \n-0.5411,0.4621,9.8162,-0.5394,0.4889,9.7796,-0.0367,0.0037,-0.011,4.5,17,-44,6.151412949,-2.97,3.18,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,1363,2015-10-30 10:22:18:496,1446171738496.0 \n-0.595,0.5962,9.7671,-0.563,0.4785,9.7788,-0.0379,0.0305,-0.0489,4.6,17,-43.7,6.153507344,-2.85,3.25,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,1466,2015-10-30 10:22:18:599,1446171738599.0 \n-0.5842,0.4717,10.0078,-0.5681,0.4506,9.7798,-0.0024,0.0012,-0.0305,4.6,16.9,-43.6,6.15507814,-2.69,3.31,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,1567,2015-10-30 10:22:18:700,1446171738700.0 \n-0.6584,0.5207,9.5984,-0.5731,0.4767,9.7783,0.0672,0.011,0.0049,4.5,17,-43.5,6.154205475,-2.79,3.35,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,1670,2015-10-30 10:22:18:803,1446171738803.0 \n-0.6093,0.5902,9.3661,-0.5842,0.5336,9.7747,0.0391,0.0061,-0.0122,4.6,16.9,-43.6,6.160314128,-3.01,3.4,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,1771,2015-10-30 10:22:18:904,1446171738904.0 \n-0.7865,0.4681,9.7815,-0.5822,0.5048,9.7763,-0.0623,0,-0.0098,4.4,17,-43.5,6.208310682,-3.06,3.4,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,1873,2015-10-30 10:22:19:006,1446171739006.0 \n-0.5567,0.5567,9.8952,-0.5572,0.4875,9.7787,-0.0159,-0.0586,0.044,4.3,17,-43.5,6.203947359,-2.84,3.3,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,1975,2015-10-30 10:22:19:108,1446171739108.0 \n-0.5471,0.6632,9.5026,-0.557,0.5125,9.7774,0.0037,-0.0086,0.0086,4.3,17,-43.3,6.203598293,-2.97,3.28,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,2077,2015-10-30 10:22:19:210,1446171739210.0 \n-0.6572,0.4968,9.7779,-0.5296,0.5025,9.7794,-0.0415,-0.0208,-0.0159,4.4,17,-43.6,6.199409503,-2.94,3.1,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,2180,2015-10-30 10:22:19:313,1446171739313.0 \n-0.5974,0.5614,9.7695,-0.5254,0.4713,9.7812,0.0012,-0.0122,0.0098,4.4,17,-43.4,6.195395246,-2.76,3.09,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,2281,2015-10-30 10:22:19:414,1446171739414.0 \n-0.644,0.5842,9.7157,-0.5496,0.4908,9.7789,0.0281,0.0489,-0.0024,4.3,17,-43.5,6.199060437,-2.81,3.18,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,2383,2015-10-30 10:22:19:516,1446171739516.0 \n-0.7446,0.504,9.6822,-0.5802,0.5215,9.7756,0.0098,0.0159,-0.0073,4.4,16.9,-43.4,6.206565353,-3.03,3.35,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,2486,2015-10-30 10:22:19:619,1446171739619.0 \n-0.5375,0.6393,9.5912,-0.6099,0.5381,9.7729,-0.0012,0.0195,0.0318,4.4,16.8,-43.7,6.21773546,-3.11,3.55,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,2588,2015-10-30 10:22:19:721,1446171739721.0 \n-0.68,0.589,9.7659,-0.6084,0.5463,9.7725,-0.0354,0.0257,-0.0134,4.4,16.7,-43.6,6.218608125,-3.19,3.56,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,2689,2015-10-30 10:22:19:822,1446171739822.0 \n-0.6895,0.6069,9.6031,-0.6239,0.525,9.7727,-0.0086,0.0061,-0.0098,4.5,16.6,-43.7,6.169913439,-3.11,3.63,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,2791,2015-10-30 10:22:19:924,1446171739924.0 \n-0.644,0.5638,9.7552,-0.6173,0.5077,9.774,-0.0293,0.0012,0.0037,4.4,16.8,-43.4,6.21651373,-2.97,3.61,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,2894,2015-10-30 10:22:20:027,1446171740027.0 \n-0.6345,0.5339,9.493,-0.6201,0.4915,9.7747,-0.0269,-0.0086,-0.0147,4.4,16.8,-43.3,6.216862796,-2.9,3.62,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,2995,2015-10-30 10:22:20:128,1446171740128.0 \n-0.7123,0.4226,9.6618,-0.6301,0.4248,9.7772,-0.0709,0.0208,-0.0183,4.5,16.9,-43.6,6.168517175,-2.78,3.63,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,3097,2015-10-30 10:22:20:230,1446171740230.0 \n-0.5806,0.516,9.9443,-0.6264,0.3963,9.7786,-0.033,0.0024,0.0049,4.5,17,-43.9,6.168342642,-2.37,3.67,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,3199,2015-10-30 10:22:20:332,1446171740332.0 \n-0.6955,0.5171,9.8545,-0.6485,0.3981,9.7771,0.0281,0.0171,-0.0159,4.6,17.2,-43.8,6.171658768,-2.29,3.77,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,3301,2015-10-30 10:22:20:434,1446171740434.0 \n-0.7266,0.4657,9.7157,-0.6647,0.4172,9.7752,0.0208,0.0171,-0.0122,4.5,17.2,-43.4,6.172531433,-2.41,3.87,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,3404,2015-10-30 10:22:20:537,1446171740537.0 \n-0.6428,0.5136,9.5469,-0.6741,0.4562,9.7728,0.0281,-0.0354,-0.0061,4.7,17.1,-43.2,6.178116486,-2.64,3.98,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,3505,2015-10-30 10:22:20:638,1446171740638.0 \n-0.7841,0.5016,9.6893,-0.6813,0.4405,9.773,-0.0269,0.0061,-0.0232,4.7,16.9,-43.4,6.177069289,-2.64,3.96,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,3607,2015-10-30 10:22:20:740,1446171740740.0 \n-0.7877,0.4417,9.8809,-0.6987,0.398,9.7736,-0.022,0.0183,-0.0159,4.7,16.9,-43.3,6.180385414,-2.41,4.06,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,3710,2015-10-30 10:22:20:843,1446171740843.0 \n-0.8056,0.4752,9.7576,-0.7133,0.3851,9.7731,-0.0257,0.0086,0.0293,4.5,17,-43.4,6.184225139,-2.25,4.17,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,3812,2015-10-30 10:22:20:945,1446171740945.0 \n-0.6979,0.5842,9.5241,-0.7094,0.3966,9.7729,0.0024,-0.0195,-0.011,4.6,17.1,-43.5,6.184399672,-2.28,4.18,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,3913,2015-10-30 10:22:21:046,1446171741046.0 \n-0.8212,0.3938,9.8258,-0.708,0.3772,9.7738,-0.022,0.0195,-0.0257,4.6,17.3,-43.5,6.182130743,-2.23,4.13,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,4015,2015-10-30 10:22:21:148,1446171741148.0 \n-0.8404,0.4082,9.9874,-0.7108,0.3722,9.7738,0.0037,-0.022,-0.0134,4.7,17.2,-43.4,6.184574204,-2.17,4.19,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,4118,2015-10-30 10:22:21:251,1446171741251.0 \n-0.6859,0.5291,9.6043,-0.7049,0.4194,9.7723,0.0428,0.0024,0.0232,4.6,17.1,-43.2,6.183003408,-2.45,4.13,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,4219,2015-10-30 10:22:21:352,1446171741352.0 \n-0.7386,0.4693,9.3577,-0.6941,0.4617,9.7712,0.0049,-0.055,-0.0232,4.5,17,-43.4,6.182479809,-2.64,4.09,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,4322,2015-10-30 10:22:21:455,1446171741455.0 \n-0.7051,0.5219,9.584,-0.6793,0.4603,9.7723,0.0061,0.0049,0.0061,4.5,17,-43.4,6.177941953,-2.7,3.97,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,4424,2015-10-30 10:22:21:557,1446171741557.0 \n-0.6452,0.571,9.4822,-0.6834,0.4425,9.7728,-0.0305,0.0159,0.0159,4.3,17,-43.3,6.230301831,-2.63,3.98,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,4525,2015-10-30 10:22:21:658,1446171741658.0 \n-0.826,0.4848,9.7504,-0.6786,0.408,9.7746,-0.0049,-0.0281,0.033,4.3,17.1,-43.1,6.2290801,-2.39,3.97,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,4627,2015-10-30 10:22:21:760,1446171741760.0 \n-0.5902,0.65,9.4894,-0.6692,0.4028,9.7755,0.0476,0.0183,0.0428,4.4,17.2,-43.4,6.226985705,-2.35,3.92,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,4729,2015-10-30 10:22:21:862,1446171741862.0 \n-0.662,0.4633,9.4679,-0.6612,0.4385,9.7745,0.0171,-0.033,0.0012,4.4,17.1,-43.7,6.229429166,-2.56,3.87,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,4831,2015-10-30 10:22:21:964,1446171741964.0 \n-0.6644,0.4513,9.6055,-0.645,0.4217,9.7763,-0.033,-0.0037,-0.0159,4.3,17.2,-43.6,6.225938508,-2.52,3.79,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,4934,2015-10-30 10:22:22:067,1446171742067.0 \n-0.5435,0.6153,9.6235,-0.6279,0.4007,9.7783,-0.0012,-0.0501,-0.0122,4.3,17.1,-43.7,6.220877053,-2.34,3.67,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,5035,2015-10-30 10:22:22:168,1446171742168.0 \n-0.6728,0.4872,9.8007,-0.6058,0.3868,9.7803,-0.0342,0.0232,-0.0159,4.3,17.1,-43.6,6.214070269,-2.32,3.51,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,5137,2015-10-30 10:22:22:270,1446171742270.0 \n-0.7099,0.4393,9.7312,-0.6058,0.3914,9.7801,-0.0061,0.0024,-0.0012,4.4,17.1,-43.5,6.210405077,-2.31,3.5,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,5239,2015-10-30 10:22:22:372,1446171742372.0 \n-0.7733,0.4274,9.6067,-0.6508,0.4006,9.7768,0.0415,0.0819,-0.0086,4.3,17.1,-43.5,6.217211861,-2.31,3.67,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,5342,2015-10-30 10:22:22:475,1446171742475.0 \n-0.6177,0.5471,9.6558,-0.6735,0.4114,9.7748,-0.0122,-0.0159,0.044,4.4,17.1,-43.5,6.2290801,-2.43,3.96,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,5444,2015-10-30 10:22:22:577,1446171742577.0 \n-0.7518,0.4441,9.6654,-0.6621,0.399,9.7761,-0.0171,-0.0098,0.022,4.4,17.2,-43.6,6.230650897,-2.37,3.91,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,5545,2015-10-30 10:22:22:678,1446171742678.0 \n-0.5387,0.5363,9.5816,-0.6543,0.3931,9.7769,0.0061,-0.0061,0.0464,4.6,17,-43.5,6.17061157,-2.3,3.83,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,5648,2015-10-30 10:22:22:781,1446171742781.0 \n-0.5698,0.5112,9.5852,-0.6344,0.3846,9.7785,-0.0195,-0.0134,0.0171,4.5,17,-43.5,6.167295445,-2.28,3.75,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,5749,2015-10-30 10:22:22:882,1446171742882.0 \n-0.5794,0.4585,9.7252,-0.6194,0.3649,9.7803,-0.0257,-0.0171,0.0012,4.6,16.9,-43.5,6.162932122,-2.15,3.65,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,5851,2015-10-30 10:22:22:984,1446171742984.0 \n-0.7063,0.3627,9.7181,-0.6184,0.3546,9.7807,0.011,-0.0244,-0.0024,4.5,16.9,-43.6,6.165899181,-2.07,3.65,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,5953,2015-10-30 10:22:23:086,1446171743086.0 \n-0.6093,0.4537,9.6822,-0.6082,0.353,9.7814,-0.0195,0.0171,0.0024,4.5,17,-43.5,6.158568799,-2.06,3.56,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,6055,2015-10-30 10:22:23:188,1446171743188.0 \n-0.7159,0.4286,9.5876,-0.6056,0.3477,9.7818,0.0024,-0.0122,-0.0293,4.5,17.1,-43.4,6.157521601,-2.07,3.53,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,6157,2015-10-30 10:22:23:290,1446171743290.0 \n-0.662,0.4776,9.6247,-0.6081,0.3461,9.7817,0.0244,0.0086,0.0269,4.5,17.2,-43,6.156823469,-1.96,3.53,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,6260,2015-10-30 10:22:23:393,1446171743393.0 \n-0.6524,0.4776,9.5229,-0.6151,0.359,9.7808,-0.0098,0.0049,0.0257,4.5,17.3,-43,6.158219733,-2.08,3.55,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,6361,2015-10-30 10:22:23:494,1446171743494.0 \n-0.729,0.3998,9.681,-0.6213,0.3545,9.7805,-0.011,-0.0024,0.0122,4.3,17.4,-43.1,6.215466532,-2.07,3.64,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,6463,2015-10-30 10:22:23:596,1446171743596.0 \n-0.5638,0.4369,9.5888,-0.6187,0.3467,9.781,-0.0134,-0.0073,0.011,4.3,17.4,-43,6.215466532,-2.07,3.64,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,6565,2015-10-30 10:22:23:698,1446171743698.0 \n-0.662,0.4118,9.6774,-0.621,0.3283,9.7815,-0.0061,0.0073,0.0037,4.2,17.4,-43.2,6.214942933,-1.92,3.64,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,6667,2015-10-30 10:22:23:800,1446171743800.0 \n-0.8344,0.3472,10.0126,-0.6179,0.3189,9.782,-0.0147,-0.0195,-0.0134,4.3,17.3,-43.1,6.21354667,-1.92,3.61,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,6769,2015-10-30 10:22:23:902,1446171743902.0 \n-0.5734,0.5279,9.6151,-0.6244,0.3451,9.7807,0.0452,0.0232,0.0122,4.4,17.3,-43.7,6.217909993,-1.93,3.63,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,6871,2015-10-30 10:22:24:004,1446171744004.0 \n-0.7027,0.4334,9.3889,-0.6288,0.3807,9.7791,0.0244,-0.0208,-0.0012,4.5,17.4,-43.5,6.163979319,-2.14,3.68,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,6973,2015-10-30 10:22:24:106,1446171744106.0 \n-0.7015,0.4034,9.7049,-0.6127,0.3715,9.7804,-0.0098,-0.0049,-0.0024,4.5,17.3,-43.5,6.160139595,-2.18,3.58,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,7078,2015-10-30 10:22:24:211,1446171744211.0 \n-0.7506,0.4417,9.7695,-0.6133,0.3657,9.7806,-0.0061,-0.0171,0.0037,4.4,17.2,-43,6.213721203,-2.17,3.6,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,7178,2015-10-30 10:22:24:311,1446171744311.0 \n-0.6835,0.4154,9.7013,-0.6059,0.3636,9.7812,-0.0134,0.0073,-0.0122,4.3,17.2,-43.1,6.211626808,-2.13,3.55,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,7279,2015-10-30 10:22:24:412,1446171744412.0 \n-0.8033,0.3651,9.7875,-0.603,0.3447,9.782,-0.0269,-0.0024,-0.0037,4.2,17.2,-43.1,6.209881479,-2.12,3.5,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,7381,2015-10-30 10:22:24:514,1446171744514.0 \n-0.5626,0.4453,9.5529,-0.6047,0.3452,9.7819,-0.0049,0,0.022,4.2,17.2,-42.9,6.210928676,-2.02,3.54,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,7483,2015-10-30 10:22:24:616,1446171744616.0 \n-0.5734,0.4573,9.6007,-0.5973,0.3309,9.7829,-0.0244,-0.0452,0.0086,4.2,17.2,-42.5,6.207088952,-1.93,3.54,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,7586,2015-10-30 10:22:24:719,1446171744719.0 \n-0.7087,0.3687,9.7695,-0.5877,0.3101,9.7841,-0.0049,0.011,-0.0171,4.1,17.4,-42.2,6.202376563,-1.82,3.42,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,7687,2015-10-30 10:22:24:820,1446171744820.0 \n-0.6261,0.3903,9.6546,-0.5895,0.3224,9.7836,0.0049,0.0049,0.0049,4.1,17.4,-42.4,6.20342376,-1.86,3.45,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,7789,2015-10-30 10:22:24:922,1446171744922.0 \n-0.5602,0.4669,9.3817,-0.5913,0.3326,9.7832,0.0061,0.0012,0.0208,4.1,17.5,-42.7,6.211452275,-1.94,3.46,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,7892,2015-10-30 10:22:25:025,1446171745025.0 \n-0.7518,0.3112,9.7432,-0.5836,0.3078,9.7844,-0.0147,0.0012,0.0061,4.1,17.5,-42.8,6.209706946,-1.84,3.42,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,7993,2015-10-30 10:22:25:126,1446171745126.0 \n-0.5375,0.4142,9.7193,-0.5959,0.2946,9.7841,0,0.0244,0.0086,4.1,17.5,-42.5,6.207263485,-1.74,3.45,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,8095,2015-10-30 10:22:25:228,1446171745228.0 \n-0.5303,0.3723,9.8318,-0.6021,0.2894,9.7839,-0.0244,0.0073,-0.0403,4,17.5,-42.4,6.210405077,-1.72,3.53,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,8198,2015-10-30 10:22:25:331,1446171745331.0 \n0.2071,0.3519,9.8593,-0.6024,0.34,9.7822,0.1002,0.0293,-0.1833,4,17.7,-42.3,6.209706946,-1.81,3.51,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,8299,2015-10-30 10:22:25:432,1446171745432.0 \n0.7661,0.5722,9.7636,-0.4836,0.4599,9.7839,0.2358,-0.347,-0.617,3.9,17.7,-42.4,6.203598293,-2.48,3.3,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,8401,2015-10-30 10:22:25:534,1446171745534.0 \n0.3388,0.7566,10.1239,-0.4633,0.5348,9.7811,-0.0183,0.2309,-0.7294,3,17.3,-42.6,6.233443423,-3.13,2.71,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,8503,2015-10-30 10:22:25:636,1446171745636.0 \n0.2334,0.8368,9.8043,-0.602,0.4942,9.7757,0,0.1295,-1.1496,2.1,17.2,-42.7,0.022863813,-2.94,3.25,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,8605,2015-10-30 10:22:25:738,1446171745738.0 \n-1.0774,0.1784,9.6211,-0.8627,0.5482,9.7532,0.5009,0.2712,-1.3928,0.3,17,-43.1,0.193207948,-3.2,5.05,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,8707,2015-10-30 10:22:25:840,1446171745840.0 \n-0.3555,0.7039,9.894,-1.1644,0.929,9.6929,0.3421,0.0293,-1.6127,-1.6,16.3,-44.1,0.342433599,-5.11,6.63,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,8810,2015-10-30 10:22:25:943,1446171745943.0 \n-1.2426,0.1879,9.9467,-1.3201,0.9725,9.6686,0.2859,-0.0195,-1.8851,-3.3,15.2,-44.7,0.431619924,-5.71,7.57,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,8911,2015-10-30 10:22:26:044,1446171746044.0 \n-0.6788,-0.8212,10.0245,-1.2211,1.1852,9.6579,0.4814,-0.4789,-2.2932,-7.9,11.1,-45.3,0.71837752,-6.55,7.62,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,9014,2015-10-30 10:22:26:147,1446171746147.0 \n-1.0271,-1.4102,9.183,-1.2373,1.1282,9.6626,0.38,-0.5449,-2.6023,-11.5,7.3,-45.7,0.960105622,-6.38,7.55,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,16 / 16,9115,2015-10-30 10:22:26:248,1446171746248.0 \n-0.31,-0.6704,8.9902,-1.2017,1.1219,9.6679,0.3238,-0.0916,-2.3286,-15.7,1.4,-46.4,1.308298807,-6.34,7.18,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,17 / 17,9218,2015-10-30 10:22:26:351,1446171746351.0 \n-0.2885,-0.6859,9.432,-1.2276,1.051,9.6726,0.0843,0.0098,-2.6573,-16.9,-3.2,-45.7,1.477072146,-6.68,6.78,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,17 / 17,9319,2015-10-30 10:22:26:452,1446171746452.0 \n-0.923,-0.6225,10.3058,-1.2022,0.8543,9.6951,0.3152,-0.2615,-2.6182,-17.7,-7.5,-46.7,1.694889237,-5.18,7.25,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,17 / 17,9421,2015-10-30 10:22:26:554,1446171746554.0 \n-2.1727,-0.5363,9.6558,-1.1501,0.782,9.7075,0.2297,-0.2615,-2.3408,-16.3,-14.3,-44.9,2.031039651,-4.53,6.96,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,17 / 17,9523,2015-10-30 10:22:26:656,1446171746656.0 \n-1.5969,0.0072,9.2979,-1.0132,0.8398,9.718,0.2663,-0.2578,-1.9108,-15.3,-18.7,-45.4,2.228785455,-4.88,6.17,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,17 / 17,9625,2015-10-30 10:22:26:758,1446171746758.0 \n-2.4181,-0.5219,11.0349,-0.7829,0.8205,9.7408,0.2969,-0.3506,-1.4319,-13.3,-22.6,-43.3,2.440144827,-4.8,4.6,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,17 / 17,9727,2015-10-30 10:22:26:860,1446171746860.0 \n-1.585,-0.1173,10.0245,-0.3778,1.1693,9.7294,0.1637,-0.5632,-1.2523,-12.7,-24.2,-42.6,2.464579437,-6.41,3.2,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,17 / 17,9830,2015-10-30 10:22:26:963,1446171746963.0 \n-2.3092,-0.6153,9.8055,-0.2141,1.0798,9.7447,-0.1625,-0.0929,-1.2205,-11.3,-26.7,-41.6,2.649584337,-6.32,1.26,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,17 / 17,9932,2015-10-30 10:22:27:065,1446171747065.0 \n-2.3439,0.1712,9.2009,-0.2229,0.9886,9.7541,0.0904,-0.0965,-0.8467,-10.1,-28.1,-41,2.717652178,-5.84,0.97,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,17 / 17,10033,2015-10-30 10:22:27:166,1446171747166.0 \n-1.8411,0.4633,9.8114,-0.1352,0.9992,9.7547,0.0709,-0.2358,-0.6487,-8.9,-29.2,-40.6,2.774724445,-6.09,0.58,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,17 / 17,10135,2015-10-30 10:22:27:268,1446171747268.0 \n-1.4856,0.3687,9.736,-0.2463,0.9006,9.7621,0.0428,-0.0929,-0.4007,-7.1,-29.8,-41.1,2.847155609,-5.39,1.25,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,17 / 17,10237,2015-10-30 10:22:27:370,1446171747370.0 \n-1.4006,0.6033,8.4779,-0.286,0.7946,9.7702,-0.0929,-0.0684,-0.1466,-5.8,-30.1,-41,2.877349805,-4.65,1.68,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,17 / 17,10339,2015-10-30 10:22:27:472,1446171747472.0 \n-0.182,0.9146,9.73,-0.0834,0.5623,9.7902,-0.2065,-0.0831,0.0672,-5.4,-29.7,-41.2,2.931280479,-3.76,1.14,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,17 / 17,10441,2015-10-30 10:22:27:574,1446171747574.0 \n-0.723,0.7302,9.2332,-0.0781,0.3884,9.7986,-0.193,0.0843,0.0379,-5.4,-29,-41.1,2.941403388,-2.55,0.71,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,17 / 17,10543,2015-10-30 10:22:27:676,1446171747676.0 \n-0.1987,0.4022,10.9954,0.098,0.182,9.8045,-0.2883,0.0171,0.0599,-6.1,-27.9,-41.5,2.93913446,-1.06,-0.57,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,17 / 17,10645,2015-10-30 10:22:27:778,1446171747778.0 \n0.0084,0.425,9.9551,0.0949,0.2127,9.8039,0.0195,0.0244,0.0147,-6.7,-27.3,-41.6,2.893930433,-1.24,-0.55,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,17 / 17,10748,2015-10-30 10:22:27:881,1446171747881.0 \n-0.1927,0.4094,8.8454,0.0092,0.2601,9.8032,0.1014,0.1442,-0.0098,-6.9,-27.1,-41.9,2.882236727,-1.4,-0.15,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,17 / 17,10849,2015-10-30 10:22:27:982,1446171747982.0 \n-0.2059,0.395,9.6271,0.0735,0.2405,9.8034,0.022,-0.0318,-0.0696,-7.1,-27.1,-42.1,2.88956711,-1.36,-0.42,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,17 / 17,10952,2015-10-30 10:22:28:085,1446171748085.0 \n-0.571,0.2239,9.997,0.0347,0.2616,9.8031,0.0464,0.0806,-0.1124,-7,-27,-42.1,2.88782178,-1.45,-0.37,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,17 / 17,11053,2015-10-30 10:22:28:186,1446171748186.0 \n-0.4645,0.3352,9.3589,-0.0104,0.3525,9.8003,0.0269,0.0892,-0.0232,-6.7,-27.2,-41.8,2.877000739,-1.96,-0.11,36.81442,-119.74892,230.03,336.6125419,1.37,25.806452,9.79,17 / 17,11155,2015-10-30 10:22:28:288,1446171748288.0 \n-0.1856,0.2562,9.5122,0.0122,0.3321,9.801,-0.0489,-0.1185,0,-6.4,-27.3,-41.7,2.907020402,-2.07,0.12,36.814537,-119.748955,249.75,336.6125419,0,19.35484,,17 / 17,11257,2015-10-30 10:22:28:390,1446171748390.0 \n-0.4178,0.1053,9.6953,0.0125,0.1282,9.8058,-0.1857,0.0452,0.0244,-6.3,-27.5,-41.6,2.920110372,-1.04,-0.13,36.814537,-119.748955,249.75,336.6125419,0,19.35484,,17 / 17,11359,2015-10-30 10:22:28:492,1446171748492.0 \n-0.0431,0.3496,9.7145,0.1139,0.0414,9.8059,-0.1063,-0.0941,0.0843,-6.5,-27.2,-42,2.924124629,-0.53,-0.17,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,11461,2015-10-30 10:22:28:594,1446171748594.0 \n-0.0479,-0.0395,10.2843,0.1672,-0.0348,9.8052,-0.0904,-0.0574,0.0379,-6.9,-26.8,-42.4,2.911209192,0.18,-0.87,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,11564,2015-10-30 10:22:28:697,1446171748697.0 \n-0.1221,0.1161,9.0381,0.186,0.0701,9.8046,0.1881,0.0574,0.0428,-7.1,-26.4,-42.5,2.904751474,-0.41,-1.09,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,11665,2015-10-30 10:22:28:798,1446171748798.0 \n0.012,0.1233,9.0848,0.2107,0.1836,9.8027,0.0024,0.0428,0.0183,-7.4,-26.5,-42.4,2.905624139,-1.03,-1.27,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,11768,2015-10-30 10:22:28:901,1446171748901.0 \n-0.0275,0.2622,9.1195,0.1533,0.126,9.8046,-0.1283,-0.0073,-0.0476,-7.5,-26.7,-42.1,2.90632227,-0.74,-0.9,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,11869,2015-10-30 10:22:29:002,1446171749002.0 \n-0.2765,-0.0742,10.404,0.1771,-0.0588,9.8049,-0.1967,-0.0171,-0.0415,-7.5,-26.7,-42.2,2.914001719,0.15,-0.98,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,11972,2015-10-30 10:22:29:105,1446171749105.0 \n-0.0419,0.0587,9.8055,0.23,-0.0865,9.8036,-0.0428,-0.0073,0.0171,-7.5,-26.3,-42.4,2.917492378,0.51,-1.34,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,12073,2015-10-30 10:22:29:206,1446171749206.0 \n0.2885,-0.067,10.5692,0.3041,-0.1079,9.8013,-0.0318,-0.0367,0.0037,-7.7,-26.1,-42.6,2.886774583,0.5,-1.5,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,12176,2015-10-30 10:22:29:309,1446171749309.0 \n-0.2155,0.5555,8.1032,0.2527,0.057,9.8032,0.3042,0.1148,0.033,-8.1,-25.9,-42.7,2.886774583,0.05,-1.62,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,12277,2015-10-30 10:22:29:410,1446171749410.0 \n-0.0431,0.1784,10.1801,0.3271,0.0192,9.8012,-0.077,-0.1808,-0.0391,-8.2,-26,-42.8,2.884854721,-0.26,-1.63,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,12379,2015-10-30 10:22:29:512,1446171749512.0 \n-0.0215,0.2693,9.5624,0.4128,0.0203,9.7979,-0.0757,-0.0831,-0.0562,-8.4,-26.2,-42.7,2.907369468,-0.12,-2.41,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,12482,2015-10-30 10:22:29:615,1446171749615.0 \n0.2298,0.3519,9.8258,0.5019,-0.047,9.7937,-0.0586,-0.0867,-0.0513,-8.5,-26.2,-42.4,2.914350785,0.1,-2.68,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,12583,2015-10-30 10:22:29:716,1446171749716.0 \n0.6416,0.4477,9.487,0.5302,0.0023,9.7923,0.1124,0.0086,-0.0049,-8.7,-26.3,-42.3,2.889392577,0.22,-3.07,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,12685,2015-10-30 10:22:29:818,1446171749818.0 \n0.4525,0.6021,9.7743,0.5069,0.0369,9.7935,0,0.0464,-0.0672,-8.8,-26.3,-42.4,2.88363299,-0.22,-2.96,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,12787,2015-10-30 10:22:29:920,1446171749920.0 \n0.5447,0.9685,9.3984,0.4489,0.0599,9.7962,0.0232,0.0733,-0.0489,-8.7,-26.3,-42.5,2.877175272,-0.24,-2.73,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,12890,2015-10-30 10:22:30:023,1446171750023.0 \n0.4094,1.4018,8.928,0.3901,0.1043,9.7983,-0.0318,0.0489,-0.0916,-8.3,-26.4,-42.6,2.903529744,-0.52,-2.37,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,12991,2015-10-30 10:22:30:124,1446171750124.0 \n0.0359,1.081,10.4926,0.4217,0.0843,9.7972,-0.0721,0.0586,-0.1222,-8.1,-26.3,-42.8,2.905973205,-0.62,-2.49,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,13094,2015-10-30 10:22:30:227,1446171750227.0 \n0.0347,0.7326,10.89,0.4606,0.2024,9.7937,-0.0391,-0.0525,-0.0293,-7.8,-26.4,-42.9,2.9080676,-1.18,-2.69,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,13195,2015-10-30 10:22:30:328,1446171750328.0 \n0.0706,0.9948,9.4272,0.4225,0.3524,9.7912,0.3616,0.1161,0.1222,-7.8,-26.6,-42.9,2.914350785,-1.45,-2.67,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,13298,2015-10-30 10:22:30:431,1446171750431.0 \n-1.0953,-0.1197,9.9707,0.3241,0.3402,9.7954,0.1026,0.1735,0.1222,-7.7,-27,-42.7,2.897595624,-1.83,-2.16,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,13399,2015-10-30 10:22:30:532,1446171750532.0 \n-0.097,0.6536,10.1634,0.2093,0.4814,9.7926,0.0452,0.1148,0.347,-7.8,-27.3,-42.6,2.870543021,-2.91,-1.49,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,13501,2015-10-30 10:22:30:634,1446171750634.0 \n-0.2478,0.99,8.6299,0.0195,0.5748,9.7898,0.1307,0.2969,0.1662,-7.8,-27.5,-42.4,2.844014016,-3.13,-0.6,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,13603,2015-10-30 10:22:30:736,1446171750736.0 \n-0.8248,1.4234,7.7081,-0.1899,0.6548,9.7829,0.1344,0.1759,0.1491,-7.6,-27.9,-42.1,2.804395042,-3.83,1.11,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,13705,2015-10-30 10:22:30:838,1446171750838.0 \n-0.7015,1.2582,9.6151,-0.2134,0.6815,9.7806,-0.0134,-0.0147,-0.0208,-7.4,-28.1,-42,2.838603495,-3.97,1.13,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,13807,2015-10-30 10:22:30:940,1446171750940.0 \n-0.2717,1.0523,11.303,-0.1362,0.6975,9.7809,0.0122,-0.0819,-0.0183,-7.1,-28.3,-42.1,2.84366495,-3.94,0.95,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,13909,2015-10-30 10:22:31:042,1446171751042.0 \n-0.0251,-0.1053,12.5743,0.1901,0.6103,9.7858,-0.3567,-0.3726,-0.2773,-7.4,-28.4,-42,2.890265241,-4.38,-0.89,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,14011,2015-10-30 10:22:31:144,1446171751144.0 \n-0.3304,0.5016,7.9476,0.0301,0.6634,9.7841,0.055,-0.0428,-0.099,-7.4,-28.4,-41.8,2.876302607,-3.66,-0.19,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,14113,2015-10-30 10:22:31:246,1446171751246.0 \n0.1245,0.7111,9.1231,0.0069,0.591,9.7888,-0.0244,0.1698,-0.0342,-7.3,-28.4,-41.5,2.874557278,-3.46,-0.04,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,14215,2015-10-30 10:22:31:348,1446171751348.0 \n-0.0611,0.9122,8.6574,-0.2172,0.5384,9.7895,-0.0696,0.2297,0.0281,-6.8,-28.2,-41.6,2.850471734,-3.26,0.91,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,14317,2015-10-30 10:22:31:450,1446171751450.0 \n-0.0012,1.1708,10.0832,-0.3211,0.3482,9.7952,-0.1686,-0.0293,0.1405,-6.2,-28,-41.7,2.870193955,-2.03,1.88,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,14420,2015-10-30 10:22:31:553,1446171751553.0 \n0.0658,0.9026,10.6255,-0.1461,0.4602,9.7948,0.0757,-0.2126,0.0244,-6.1,-27.8,-42,2.882236727,-2.64,1.24,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,14521,2015-10-30 10:22:31:654,1446171751654.0 \n0.2263,0.4992,9.1734,0.1315,0.5134,9.7923,0.1576,-0.2101,-0.0953,-6.3,-27.7,-42,2.904751474,-3.11,0.27,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,14623,2015-10-30 10:22:31:756,1446171751756.0 \n-0.6907,0.2945,7.343,0.2789,0.57,9.7861,0.4044,-0.0513,0.0391,-7.1,-27.8,-41.9,2.919586773,-2.69,-1.54,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,14725,2015-10-30 10:22:31:858,1446171751858.0 \n-0.012,0.4764,9.0908,0.4126,0.4598,9.7872,-0.0379,0.0257,-0.0134,-7.8,-27.9,-41.5,2.905449606,-2.69,-2.41,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,14828,2015-10-30 10:22:31:961,1446171751961.0 \n-0.4549,0.9972,8.2803,0.3127,0.4777,9.79,0.0171,0.0171,0.0073,-8.2,-27.8,-41.4,2.894279499,-2.67,-1.98,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,14930,2015-10-30 10:22:32:063,1446171752063.0 \n-0.4286,1.0678,9.4188,0.194,0.4562,9.7941,-0.0892,0.193,0.0024,-8.2,-27.8,-41.5,2.883807523,-2.67,-1.58,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,15031,2015-10-30 10:22:32:164,1446171752164.0 \n0.0778,0.4417,11.3677,0.3197,0.5805,9.7842,0.2724,-0.0476,-0.0367,-8.1,-27.8,-41.7,2.884156589,-3.14,-1.7,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,15133,2015-10-30 10:22:32:266,1446171752266.0 \n-0.7733,-0.9278,13.5165,0.4623,0.6528,9.774,-0.5021,0.3861,-0.3103,-8.2,-28,-41.9,2.906845869,-3.82,-2.71,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,15235,2015-10-30 10:22:32:368,1446171752368.0 \n-0.0024,0.2969,8.9866,0.1731,0.4784,9.7934,0.1539,0.1613,0.0037,-8,-28,-41.8,2.879095134,-2.9,-1.44,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,15338,2015-10-30 10:22:32:471,1446171752471.0 \n0.2729,0.5351,9.5229,0.0906,0.3215,9.801,0.077,0.0525,0.0403,-7.6,-27.8,-41.8,2.863561704,-1.8,-0.53,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,15439,2015-10-30 10:22:32:572,1446171752572.0 \n0.3807,1.1791,8.5246,-0.0289,0.3418,9.8006,0.0513,-0.0049,0.0208,-6.8,-27.4,-41.8,2.86932129,-2,0.17,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,15541,2015-10-30 10:22:32:674,1446171752674.0 \n-0.0311,0.8595,9.9539,0.0108,0.2746,9.8028,-0.1772,-0.0586,-0.022,-6.4,-27.3,-41.6,2.90510054,-2.01,0.2,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,15643,2015-10-30 10:22:32:776,1446171752776.0 \n0.1951,0.5686,10.8386,0.1336,0.3888,9.798,0.2199,-0.1368,0.1087,-6.4,-27.2,-41.6,2.926393557,-1.9,-0.55,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,15746,2015-10-30 10:22:32:879,1446171752879.0 \n-0.2418,-0.6201,12.451,0.3079,0.4232,9.7927,-0.0269,-0.2016,-0.0464,-6.8,-27.4,-41.4,2.910860126,-2.58,-1.53,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,15848,2015-10-30 10:22:32:981,1446171752981.0 \n-0.1604,-0.0407,10.6674,0.4476,0.3449,9.7904,-0.2688,-0.0745,0.0037,-7.5,-27.6,-41.4,2.951002699,-2.02,-2.62,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,15950,2015-10-30 10:22:33:083,1446171753083.0 \n-0.3807,0.4357,9.2213,0.4135,0.2138,9.7956,-0.0244,0.0073,0.0904,-7.9,-27.4,-41.3,2.905973205,-1.25,-2.42,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,16052,2015-10-30 10:22:33:185,1446171753185.0 \n-0.1927,0.7075,8.3965,0.3144,0.2552,9.7983,0.1271,0.044,0.0635,-8.1,-27.1,-41.9,2.894279499,-1.32,-1.95,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,16153,2015-10-30 10:22:33:286,1446171753286.0 \n-0.3795,0.0335,11.3928,0.2833,0.2883,9.7983,0.0574,-0.193,0.0391,-8.2,-26.8,-42,2.883982056,-1.68,-1.66,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,16256,2015-10-30 10:22:33:389,1446171753389.0 \n0.7817,0.425,10.0161,0.3136,0.4237,9.7925,0.2211,0.1698,0.0843,-8.4,-26.9,-42.2,2.886425517,-2.34,-1.92,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,16357,2015-10-30 10:22:33:490,1446171753490.0 \n0.0946,0.0658,9.7648,0.3344,0.2639,9.7974,-0.1173,0.1747,-0.1148,-8.5,-27,-41.8,2.893057768,-1.54,-1.95,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,16460,2015-10-30 10:22:33:593,1446171753593.0 \n0.2622,0.1975,9.6043,0.3312,0.2032,9.799,-0.1112,-0.0244,-0.0134,-8.3,-27.1,-42.1,2.89497763,-1.19,-1.94,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,16563,2015-10-30 10:22:33:696,1446171753696.0 \n-0.018,0.8224,8.0158,0.2599,0.1764,9.8016,0.0098,0.1344,-0.0269,-8.1,-26.8,-42.1,2.895152163,-1.11,-1.92,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,16663,2015-10-30 10:22:33:796,1446171753796.0 \n0.3699,0.3448,10.4675,0.2101,0.1881,9.8026,-0.099,0.1051,-0.0024,-7.8,-26.6,-42.3,2.879618733,-1.25,-1.37,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,16765,2015-10-30 10:22:33:898,1446171753898.0 \n0.231,0.5363,9.7205,0.2004,0.3379,9.7988,0.3201,0.121,0.0086,-7.7,-26.5,-42.3,2.858325716,-1.97,-1.17,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,16867,2015-10-30 10:22:34:000,1446171754000.0 \n0.182,-0.316,12.7731,0.1667,0.3882,9.7975,-0.3861,-0.1405,-0.0941,-7.6,-27,-42.1,2.861292776,-2.27,-0.97,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,16969,2015-10-30 10:22:34:102,1446171754102.0 \n-0.5243,0.1664,8.9651,0.3466,0.3956,9.7925,0.2932,-0.3238,0.1588,-7.5,-27.2,-42.2,2.909463863,-1.72,-1.25,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,17071,2015-10-30 10:22:34:204,1446171754204.0 \n0.2059,0.5818,8.8478,0.4347,0.4467,9.7868,-0.0782,0.0892,0.1417,-8.1,-27.5,-42.1,2.901609881,-2.61,-2.54,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,17174,2015-10-30 10:22:34:307,1446171754307.0 \n0.0144,1.2594,7.8554,0.3513,0.4671,9.7892,0.0232,0.1894,-0.066,-8.5,-27.5,-42.4,2.899340953,-2.52,-2.44,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,17275,2015-10-30 10:22:34:408,1446171754408.0 \n0.3783,0.8823,10.246,0.2367,0.4717,9.7924,0.0305,0.1148,-0.0611,-8.8,-27.7,-42.4,2.842966819,-2.76,-1.38,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,17377,2015-10-30 10:22:34:510,1446171754510.0 \n-0.103,0.4154,9.9575,0.3919,0.6063,9.78,0.2309,-0.1026,-0.2517,-8.5,-27.8,-42.3,2.8937559,-3.07,-2.04,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,17479,2015-10-30 10:22:34:612,1446171754612.0 \n-0.6416,-0.5028,12.0428,0.4628,0.3873,9.7881,-0.2712,0.3616,-0.1833,-8.2,-27.9,-42,2.916270647,-3.16,-2.89,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,17582,2015-10-30 10:22:34:715,1446171754715.0 \n-0.2634,0.1844,9.8904,0.3461,0.3055,9.7958,-0.033,-0.1307,0.0342,-7.8,-27.7,-41.6,2.90213348,-1.79,-2.02,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,17683,2015-10-30 10:22:34:816,1446171754816.0 \n0.1317,0.8332,8.2253,0.2374,0.1901,9.8019,-0.0574,0.1405,0.0147,-7.5,-27.4,-42.1,2.928837018,-1.24,-1.86,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,17785,2015-10-30 10:22:34:918,1446171754918.0 \n0.4154,0.8009,8.4779,0.1073,0.28,9.8021,0.0855,0.2016,-0.0122,-7,-27,-42.5,2.902308013,-1.36,-0.9,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,17887,2015-10-30 10:22:35:020,1446171755020.0 \n0.1437,0.5902,11.4383,0.0024,0.3934,9.7988,0.2224,-0.1429,0.1368,-6.7,-27.2,-42.6,2.871590218,-2.3,-0.01,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,17989,2015-10-30 10:22:35:122,1446171755122.0 \n0.3053,-0.1939,10.4686,0.2138,0.5883,9.7867,0.0574,-0.3677,0.1234,-6.6,-27.5,-42.1,2.877873404,-3.2,-0.48,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,18092,2015-10-30 10:22:35:225,1446171755225.0 \n-0.0515,0.2334,9.074,0.6486,0.5046,9.7722,0.2517,-0.5473,0.0855,-7.2,-27.8,-42.4,2.957285885,-2.6,-2.91,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,18193,2015-10-30 10:22:35:326,1446171755326.0 \n0.0611,0.2095,8.4719,0.7049,0.3603,9.7746,-0.1417,0.0134,0.0391,-8,-27.8,-42.3,2.957984016,-2.37,-4.25,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,18295,2015-10-30 10:22:35:428,1446171755428.0 \n0.3986,1.142,8.1211,0.6506,0.3489,9.7788,0.1552,0.0782,0.1466,-9.1,-27.4,-42.3,2.903180678,-2.04,-3.81,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,18397,2015-10-30 10:22:35:530,1446171755530.0 \n0.3077,0.9984,9.7839,0.4793,0.464,9.7839,0.0403,0.1417,-0.0159,-9.3,-27.5,-41.7,2.875779009,-2.62,-2.97,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,18499,2015-10-30 10:22:35:632,1446171755632.0 \n0.1269,0.595,11.7747,0.4335,0.5824,9.7797,0.3445,0.2004,-0.0037,-9,-27.7,-41.5,2.878397002,-3.02,-2.85,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,18601,2015-10-30 10:22:35:734,1446171755734.0 \n-0.4046,-1.4736,14.2287,0.4176,0.3373,9.7919,-0.4728,-0.3433,-0.3641,-8.6,-28.2,-41.5,2.871241152,-3.78,-2.8,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,18704,2015-10-30 10:22:35:837,1446171755837.0 \n0.6728,0.3926,7.0641,0.3298,0.4831,9.7892,0.1991,-0.292,0.0379,-8.1,-28.1,-41.8,2.882760326,-2.48,-1.47,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,18805,2015-10-30 10:22:35:938,1446171755938.0 \n0.0395,0.7183,7.9404,0.3211,0.347,9.7952,-0.0892,-0.0122,-0.0281,-7.4,-28,-42,2.932502209,-2.03,-1.88,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,18907,2015-10-30 10:22:36:040,1446171756040.0 \n-0.0922,0.7219,9.1279,0.2692,0.2384,9.8001,-0.0892,0.1515,0.0195,-7,-27.5,-42,2.92656809,-1.48,-1.83,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,19009,2015-10-30 10:22:36:142,1446171756142.0 \n-0.1616,0.5064,10.7631,0.2163,0.2292,9.8016,0.0342,0,0.1527,-6.9,-27.3,-41.9,2.914001719,-1.23,-1.3,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,19112,2015-10-30 10:22:36:245,1446171756245.0 \n-0.1101,0.7506,10.2975,0.2444,0.4407,9.7937,0.3311,-0.0049,0.336,-7,-27.2,-42.1,2.908591198,-2.58,-1.43,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,19213,2015-10-30 10:22:36:346,1446171756346.0 \n0.419,0.006,12.9981,0.3469,0.3928,9.7926,-0.1332,-0.2529,0.2712,-7.2,-27.4,-42.2,2.90928933,-2.92,-1.54,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,19315,2015-10-30 10:22:36:448,1446171756448.0 \n0.1041,0.3065,9.0477,0.4862,0.3441,9.7885,-0.0293,-0.3494,0.022,-7.9,-27.5,-42,2.90213348,-2.37,-2.5,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,19418,2015-10-30 10:22:36:551,1446171756551.0 \n0.0646,0.8835,8.2325,0.3982,0.2932,9.7942,0.1405,0.0122,0.0782,-8.8,-27.2,-41.8,2.865481566,-1.71,-2.33,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,19520,2015-10-30 10:22:36:653,1446171756653.0 \n-0.2825,0.9469,9.1231,0.2319,0.4032,9.7956,0.0049,0.1845,-0.1344,-9.1,-27,-41.9,2.834589238,-2.36,-1.36,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,19621,2015-10-30 10:22:36:754,1446171756754.0 \n-0.2574,0.8643,9.42,0.1435,0.5006,9.7928,0.1344,0.011,-0.1478,-8.9,-27.1,-42.1,2.815390616,-2.66,-0.73,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,19723,2015-10-30 10:22:36:856,1446171756856.0 \n0.5315,0.832,9.8773,0.2429,0.5985,9.7854,0.1979,-0.1038,-0.0391,-8.2,-27.5,-42.1,2.858674782,-3.22,-1.16,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,19825,2015-10-30 10:22:36:958,1446171756958.0 \n0.2466,-0.0754,9.8426,0.2934,0.4118,9.7936,0.314,0.2382,0.0391,-8,-27.8,-42.3,2.904751474,-2.76,-2.37,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,19927,2015-10-30 10:22:37:060,1446171757060.0 \n0.9254,0.2729,9.1602,0.3501,0.5191,9.7866,-0.0855,-0.1967,-0.088,-7.9,-28,-42.2,2.886949116,-3.34,-1.86,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,20029,2015-10-30 10:22:37:162,1446171757162.0 \n-0.0239,0.7422,8.6694,0.3839,0.4868,9.787,-0.055,-0.0757,-0.0745,-7.9,-28.1,-42.1,2.897246558,-2.97,-2.14,36.814537,-119.748955,249.75,336.5915658,0,19.35484,,17 / 17,20131,2015-10-30 10:22:37:264,1446171757264.0 \n0.8344,1.5036,9.2464,0.4214,0.5055,9.7845,0.0525,-0.0489,0.0024,-7.8,-28.1,-41.8,2.906147737,-2.95,-2.47,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,20234,2015-10-30 10:22:37:367,1446171757367.0 \n0.4357,0.9218,10.6195,0.5335,0.631,9.7718,0.1735,-0.2395,0.1539,-7.9,-28.1,-41.8,2.91941224,-3.69,-3.12,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,20335,2015-10-30 10:22:37:468,1446171757468.0 \n0.3962,0.6381,9.7145,0.6966,0.8791,9.7423,0.2944,0.0183,0.1026,-8.2,-28.4,-41.7,2.933200341,-5.05,-3.92,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,20438,2015-10-30 10:22:37:571,1446171757571.0 \n-0.1867,0.4812,9.1698,0.6657,0.7557,9.7548,0.1564,0.0733,0.2016,-8.9,-28.8,-41.5,2.905449606,-4.42,-3.9,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,20539,2015-10-30 10:22:37:672,1446171757672.0 \n0.5578,0.6692,8.7903,0.6277,0.6649,9.7639,-0.2272,0.3457,0.0037,-9.3,-29.1,-41.3,2.913652653,-4.29,-4.18,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,20641,2015-10-30 10:22:37:774,1446171757774.0 \n0.2358,1.1636,8.3606,0.5154,0.504,9.7801,-0.1295,-0.0134,0.077,-9.5,-28.9,-41.2,2.889043511,-3.21,-2.96,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,20744,2015-10-30 10:22:37:877,1446171757877.0 \n0.3005,1.6903,8.8825,0.4797,0.5176,9.7812,0.0806,0.0379,0.0476,-9.6,-28.4,-41.7,2.84244322,-3.03,-2.81,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,20845,2015-10-30 10:22:37:978,1446171757978.0 \n-0.0431,0.9421,11.6741,0.4903,0.6318,9.774,0.2419,0.0525,0.0195,-9.4,-28.2,-42.1,2.87351008,-3.27,-2.69,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,20948,2015-10-30 10:22:38:081,1446171758081.0 \n1.8711,1.4569,9.5948,0.5766,0.9403,9.7444,-0.3286,-0.0623,-0.2957,-9.4,-28.5,-42.3,2.861467309,-5.24,-2.84,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,21049,2015-10-30 10:22:38:182,1446171758182.0 \n0.6117,0.8056,8.5641,0.5111,0.5835,9.7759,-0.2883,0.1674,-0.2346,-9.3,-28.9,-42.2,2.889916175,-3.41,-2.99,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,21152,2015-10-30 10:22:38:285,1446171758285.0 \n0.3005,0.7805,9.4798,0.4868,0.4321,9.785,-0.3555,-0.0562,-0.0464,-9.1,-28.9,-42.4,2.886425517,-3.1,-2.77,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,21254,2015-10-30 10:22:38:387,1446171758387.0 \n0.3208,1.0726,9.3937,0.5375,0.334,9.7862,0.0855,-0.0586,-0.0415,-8.8,-28.3,-42.8,2.896548427,-1.95,-3.14,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,21355,2015-10-30 10:22:38:488,1446171758488.0 \n1.4114,1.391,10.1754,0.6406,0.4308,9.7762,0.0232,-0.0757,-0.0941,-8.7,-28.1,-43.1,2.905973205,-2.41,-3.61,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,21457,2015-10-30 10:22:38:590,1446171758590.0 \n0.2813,0.644,10.2627,0.5638,0.6551,9.7685,0.3445,0.0794,0.0073,-8.6,-28.2,-42.9,2.89497763,-3.26,-3.42,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,21559,2015-10-30 10:22:38:692,1446171758692.0 \n-0.5387,-0.7219,12.5899,0.5324,0.6001,9.7738,-0.0024,0.2847,0.0171,-8.6,-28.6,-42.8,2.901435349,-4.01,-3.53,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,21661,2015-10-30 10:22:38:794,1446171758794.0 \n0.0192,-0.0431,9.4547,0.6613,0.5581,9.7684,-0.1124,-0.485,0.1698,-8.3,-29.1,-42.4,2.950130035,-3.26,-3.87,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,21763,2015-10-30 10:22:38:896,1446171758896.0 \n0.0371,0.6261,7.8925,0.6197,0.3797,9.7797,-0.0183,0.066,0.1649,-8.5,-29,-42.3,2.952922561,-2.3,-3.79,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,21865,2015-10-30 10:22:38:998,1446171758998.0 \n0.0599,1.2713,9.1494,0.4904,0.3094,9.7895,-0.0049,0.1429,0.1491,-8.9,-28.5,-42.7,2.89672296,-1.93,-3.15,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,21967,2015-10-30 10:22:39:100,1446171759100.0 \n-0.0263,0.6943,11.0049,0.3635,0.3489,9.7937,0.2236,0.0367,0.0391,-9.1,-28.1,-43.1,2.868797692,-2.04,-2.13,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,22069,2015-10-30 10:22:39:202,1446171759202.0 \n-0.4417,0.3891,10.7488,0.3245,0.569,9.7848,0.3946,0.055,0.0696,-9,-28.4,-43.3,2.852391597,-3.33,-1.9,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,22171,2015-10-30 10:22:39:304,1446171759304.0 \n-0.9194,-0.7147,12.5205,0.3129,0.4035,9.7934,-0.9053,0.4362,-0.3445,-8.7,-28.9,-42.8,2.875953541,-3.83,-2.54,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,22274,2015-10-30 10:22:39:407,1446171759407.0 \n0.3795,0.2849,8.9914,0.3036,0.3104,9.797,-0.4838,0.259,-0.1234,-8.5,-29,-43,2.902482546,-2.41,-1.83,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,22375,2015-10-30 10:22:39:508,1446171759508.0 \n-0.1664,0.8344,8.1882,0.0619,0.1569,9.8052,0.0354,0.2004,-0.1197,-7.9,-28.5,-43,2.865830632,-0.92,-0.36,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,22477,2015-10-30 10:22:39:610,1446171759610.0 \n-0.1616,0.9313,8.3175,-0.17,0.112,9.8045,0.0342,0.1429,-0.1185,-7.1,-27.8,-43.4,2.872462883,-0.69,0.78,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,22579,2015-10-30 10:22:39:712,1446171759712.0 \n-0.6919,0.5243,10.3609,-0.1932,0.0781,9.8044,0.0513,-0.2382,0.1319,-6.3,-27.5,-43.3,2.887123649,-0.35,1.28,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,22682,2015-10-30 10:22:39:815,1446171759815.0 \n0.237,0.5674,9.4164,-0.0832,0.26,9.8028,0.4227,0.0635,0.2505,-5.9,-27.6,-43.6,2.912779989,-1.06,0.43,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,22783,2015-10-30 10:22:39:916,1446171759916.0 \n0.1568,0.3029,9.6403,0.0563,0.2529,9.8032,0.2199,-0.3616,0.0586,-6.1,-27.7,-43.3,2.93075688,-1.48,-0.33,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,22885,2015-10-30 10:22:40:018,1446171760018.0 \n-0.5399,0.0982,7.3083,0.165,0.2569,9.8019,-0.1258,0.336,-0.0965,-7,-28,-42.8,2.912081857,-1.5,-0.96,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,22988,2015-10-30 10:22:40:121,1446171760121.0 \n-0.7602,0.577,8.43,0.0069,0.0892,9.8062,-0.0623,0.0562,-0.0208,-7,-27.9,-42.8,2.894279499,-0.64,-0.07,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,23089,2015-10-30 10:22:40:222,1446171760222.0 \n-0.6141,0.9301,9.6079,-0.118,0.0314,9.8059,-0.0916,0.1735,-0.0098,-6.6,-27.6,-43.2,2.885901918,-0.26,0.36,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,23191,2015-10-30 10:22:40:324,1446171760324.0 \n-0.7458,0.1113,11.7603,-0.0314,0.1121,9.806,0.314,-0.0415,0.0757,-6.3,-27.3,-43.5,2.912954522,-0.25,0.32,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,23293,2015-10-30 10:22:40:426,1446171760426.0 \n-0.3065,-1.0092,11.7005,0.1141,0.1716,9.8045,-0.5742,0.3189,-0.2663,-6.5,-27.3,-43.6,2.935294736,-1,-0.67,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,23395,2015-10-30 10:22:40:528,1446171760528.0 \n0.0874,-0.0718,9.0992,0.1154,-0.12,9.8052,0.0794,-0.2395,-0.0696,-6.6,-27.1,-43.5,2.896373894,0.37,-0.23,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,23497,2015-10-30 10:22:40:630,1446171760630.0 \n-0.4022,0.4956,7.3682,0.1049,-0.3398,9.8002,0.0183,0.0464,-0.1014,-6.7,-26.8,-43.4,2.918015976,2,-0.69,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,23599,2015-10-30 10:22:40:732,1446171760732.0 \n-0.6668,0.3328,8.5389,0.0728,-0.3721,9.7993,0.0635,0.0122,0.0452,-6.4,-25.9,-43.9,2.939308993,2.17,-0.43,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,23701,2015-10-30 10:22:40:834,1446171760834.0 \n-0.2933,0.2442,10.5333,0.0229,-0.3036,9.8019,0.0941,0.055,0.1136,-6.2,-25.6,-44.1,2.933898473,1.99,-0.27,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,23803,2015-10-30 10:22:40:936,1446171760936.0 \n0.4453,0.5279,11.0229,-0.0138,0.0607,9.8065,0.3494,0.1429,0.1808,-6.1,-25.9,-43.8,2.917317845,0.12,-0.06,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,23905,2015-10-30 10:22:41:038,1446171761038.0 \n-0.7901,-1.0858,11.4754,0.0721,-0.0391,9.8063,0.1894,-0.2676,-0.0159,-6.1,-26.3,-43.5,2.923950096,0.12,-0.31,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,24007,2015-10-30 10:22:41:140,1446171761140.0 \n-0.3376,-0.3053,9.3494,0.4022,0.0782,9.7981,-0.3616,0.1246,-0.0684,-6.7,-27.1,-43.1,2.94506858,-0.99,-2.36,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,24109,2015-10-30 10:22:41:242,1446171761242.0 \n0.4357,1.0343,7.3897,0.423,0.0802,9.7972,0.2382,-0.1991,0.1564,-7.4,-27.4,-43,2.951002699,-0.47,-2.47,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,24211,2015-10-30 10:22:41:344,1446171761344.0 \n0.2215,1.2929,8.9914,0.3603,0.028,9.8,0.0403,-0.055,0.077,-7.7,-27.4,-43,2.911209192,-0.23,-2.27,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,24313,2015-10-30 10:22:41:446,1446171761446.0 \n0.0036,-0.0443,12.4091,0.3495,0.0104,9.8004,0.1491,0.2053,0.0037,-7.9,-27.4,-42.8,2.91225639,-0.22,-2.3,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,24416,2015-10-30 10:22:41:549,1446171761549.0 \n1.6041,-0.9756,10.5501,0.5513,0.2013,9.7891,0.2175,-0.4594,-0.0745,-7.8,-27.5,-42.6,2.903878809,-0.98,-2.18,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,24518,2015-10-30 10:22:41:651,1446171761651.0 \n-0.0443,-0.0946,9.25,0.3914,-0.0315,9.7988,0.4472,0.033,0.0977,-7.9,-27.4,-42.5,2.912779989,0.18,-2.29,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,24619,2015-10-30 10:22:41:752,1446171761752.0 \n-0.6512,0.1161,9.5026,0.3293,-0.1147,9.8004,0.0635,0.4386,0.0134,-7.6,-27.4,-42.6,2.915921581,-0.05,-2.41,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,24722,2015-10-30 10:22:41:855,1446171761855.0 \n-0.8128,0.4154,8.406,-0.0955,-0.0105,9.8062,0.1124,0.2224,-0.0525,-6.7,-27.2,-43.2,2.886250984,0.13,0.1,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,24823,2015-10-30 10:22:41:956,1446171761956.0 \n-0.7003,0.7769,9.0333,-0.3343,0.0541,9.8008,0.0684,0.1344,0.0965,-5.9,-27.4,-43.4,2.877175272,-0.19,1.7,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,24925,2015-10-30 10:22:42:058,1446171762058.0 \n-0.6201,0.4992,10.7967,-0.4324,0.1194,9.7964,0.0367,-0.0281,0.2676,-4.7,-27.7,-43.5,2.895850295,-0.59,2.55,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,25027,2015-10-30 10:22:42:160,1446171762160.0 \n-1.4162,-1.4222,13.6841,-0.4777,-0.0687,9.7948,-0.0757,0.0476,0.2541,-4.5,-27.7,-43.5,2.929535149,0.4,2.79,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,25129,2015-10-30 10:22:42:262,1446171762262.0 \n-0.0622,-0.0431,8.0924,-0.3194,-0.0045,9.8014,0.215,-0.3079,0.3457,-4.7,-27.4,-43.6,2.896897492,-0.05,2.26,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,25232,2015-10-30 10:22:42:365,1446171762365.0 \n-0.8823,-0.1425,8.7185,-0.3841,-0.2859,9.795,-0.1894,0.1417,0.0538,-5.5,-26.8,-44,2.908242133,1.67,2.25,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,25333,2015-10-30 10:22:42:466,1446171762466.0 \n-0.8356,0.7709,8.4372,-0.3718,-0.2258,9.797,0.0611,0.0855,-0.0208,-5.8,-26.3,-44.3,2.866703296,1.51,2.16,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,25435,2015-10-30 10:22:42:568,1446171762568.0 \n-0.8021,0.7266,9.1506,-0.418,-0.1197,9.797,0.1148,0.0134,-0.1576,-6,-26.1,-44.3,2.856231321,0.81,2.36,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,25537,2015-10-30 10:22:42:670,1446171762670.0 \n0.1856,0.1724,10.8757,-0.3659,0.0133,9.7998,0.4288,0.0538,0.2089,-5.9,-26.2,-44,2.861990907,0.63,2.09,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,25640,2015-10-30 10:22:42:773,1446171762773.0 \n-0.4633,-1.306,12.5324,-0.3787,-0.0619,9.7991,0.0171,0.3005,-0.121,-5.9,-26.6,-43.7,2.874906344,-0.33,1.71,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,25741,2015-10-30 10:22:42:874,1446171762874.0 \n-0.2622,-0.3819,9.1842,-0.3492,0.0659,9.8002,0.1649,-0.2199,-0.1112,-5.7,-26.9,-43.3,2.856056788,-0.35,2.47,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,25844,2015-10-30 10:22:42:977,1446171762977.0 \n-0.5351,0.5842,7.4136,-0.2712,-0.0694,9.8027,-0.0354,-0.0476,-0.066,-5.5,-27.3,-43.4,2.91522345,0.26,1.69,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,25945,2015-10-30 10:22:43:078,1446171763078.0 \n-0.2933,0.6249,9.6678,-0.2603,-0.1312,9.8023,0.0049,0.0098,0.1454,-5.3,-27.2,-43.7,2.921681168,0.77,1.52,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,26047,2015-10-30 10:22:43:180,1446171763180.0 \n-0.6967,0.2765,11.1725,-0.3468,0.0351,9.8005,0.1258,0.1063,0.3677,-5.4,-27.1,-43.9,2.910161995,0,1.78,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,26150,2015-10-30 10:22:43:283,1446171763283.0 \n0.0611,0.9421,9.1626,-0.3471,0.3096,9.7956,0.4313,-0.0208,0.3274,-5.6,-27.2,-43.7,2.855358656,-1.17,2.19,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,26251,2015-10-30 10:22:43:384,1446171763384.0 \n-0.1628,-0.0611,9.1566,-0.2404,0.0749,9.8034,0.0782,-0.1124,0.0428,-6,-27.5,-43.2,2.883109391,-0.44,1.4,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,26353,2015-10-30 10:22:43:486,1446171763486.0 \n-0.2933,-0.1161,8.0098,-0.067,0.0243,9.8064,-0.1674,-0.0403,-0.2077,-6.4,-27.6,-42.8,2.917666911,-0.44,0.4,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,26456,2015-10-30 10:22:43:589,1446171763589.0 \n-0.8727,0.1963,9.2285,0.0236,-0.1769,9.805,-0.259,-0.1307,-0.2309,-6.7,-27.2,-42.7,2.898119223,1.03,-0.14,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,26558,2015-10-30 10:22:43:691,1446171763691.0 \n-0.4944,0.7697,9.2943,0.0439,-0.1835,9.8048,-0.088,0.0709,-0.2285,-6.8,-26.9,-43.1,2.902831612,1.07,-0.26,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,26659,2015-10-30 10:22:43:792,1446171763792.0 \n-1.0187,-0.2634,11.746,-0.0551,-0.2141,9.8042,0.0538,0.0953,-0.1478,-6.5,-26.7,-43.3,2.92360103,1.19,0.24,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,26761,2015-10-30 10:22:43:894,1446171763894.0 \n1.4461,-0.565,11.3713,-0.0289,-0.1854,9.8049,0.0171,-0.1454,-0.0379,-6,-26.6,-43.6,2.918888641,0.83,0.33,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,26863,2015-10-30 10:22:43:996,1446171763996.0 \n0,0.1879,8.6921,-0.1583,-0.2731,9.8016,0.2492,-0.077,-0.0599,-5.5,-26.4,-43.7,2.937738197,2.03,0.9,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,26965,2015-10-30 10:22:44:098,1446171764098.0 \n-0.7566,-0.5602,10.635,0.0472,-0.3501,9.8003,0.0354,-0.0195,-0.0867,-5.1,-26.4,-43.9,2.957460418,1.51,0.07,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,27067,2015-10-30 10:22:44:200,1446171764200.0 \n-1.2582,0.6967,7.58,0.0946,-0.1477,9.8051,-0.0086,0.2615,0.1515,-4.7,-26.2,-44.1,2.976309973,1.27,-0.65,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,27169,2015-10-30 10:22:44:302,1446171764302.0 \n0.2191,0.5279,9.6774,-0.0947,-0.0582,9.806,0.171,0.1271,0.303,-4.7,-26.6,-44,2.945243113,0.34,0.55,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,27271,2015-10-30 10:22:44:404,1446171764404.0 \n0.6632,0.5614,10.9164,-0.1129,0.1457,9.8049,0.4801,-0.1625,0.3396,-4.8,-27.1,-43.6,2.93372394,-0.32,0.84,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,27374,2015-10-30 10:22:44:507,1446171764507.0 \n-0.4872,-0.674,10.6315,0.4953,0.2628,9.7906,0.1405,-0.5938,0.2016,-5.9,-27.9,-42.8,3.000220984,-1.54,-2.9,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,27476,2015-10-30 10:22:44:609,1446171764609.0 \n1.2474,0.2155,10.3597,1.1076,0.1769,9.7423,-0.3018,-0.5168,0.1698,-7.3,-28.3,-42.2,3.048741137,-1.46,-6.09,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,27577,2015-10-30 10:22:44:710,1446171764710.0 \n0.3316,0.9313,8.6251,1.0663,0.0422,9.7484,0.0195,0.1368,0.0977,-9.7,-28,-41.7,2.950828166,-0.25,-6.24,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,27679,2015-10-30 10:22:44:812,1446171764812.0 \n-0.3029,1.342,8.6766,0.77,0.1494,9.7752,-0.0904,0.3592,0.0965,-10.5,-27.7,-41.7,2.930233281,-0.76,-5.56,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,27781,2015-10-30 10:22:44:914,1446171764914.0 \n0.7817,0.5698,11.892,0.5158,0.2461,9.79,0.2224,0.2566,0.044,-10.3,-27.5,-41.7,2.866005165,-0.95,-3.48,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,27884,2015-10-30 10:22:45:017,1446171765017.0 \n0.8595,0.3603,9.827,0.4429,0.5777,9.7796,0.2419,-0.0574,-0.1955,-9.7,-27.9,-41.8,2.836858166,-2.75,-2.5,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,27985,2015-10-30 10:22:45:118,1446171765118.0 \n0.1556,-0.1808,8.497,0.1321,0.3366,9.8,0.171,-0.0159,0.1185,-8.6,-28.6,-41.7,2.844363082,-1.97,-0.77,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,28087,2015-10-30 10:22:45:220,1446171765220.0 \n0.5171,0.3531,9.2356,0.2094,0.2586,9.801,0.0269,-0.1588,0.0073,-7.6,-28.9,-42,2.892185103,-1.51,-1.22,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,28189,2015-10-30 10:22:45:322,1446171765322.0 \n-0.3172,0.4741,9.6774,0.2176,0.1677,9.8028,-0.1344,0.0867,-0.0635,-7.2,-28.7,-42.3,2.937389131,-1.2,-1.61,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,28291,2015-10-30 10:22:45:424,1446171765424.0 \n-0.3112,0.9146,8.8825,0.1155,0.2674,9.8023,0.0489,0.1258,0.2077,-7,-28.6,-42.9,2.91225639,-1.56,-0.68,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,28393,2015-10-30 10:22:45:526,1446171765526.0 \n-0.0922,0.6045,11.6514,-0.0368,0.2497,9.8034,0.2346,0.1417,0.2908,-7.2,-28.4,-42.7,2.891661505,-1.52,-0.2,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,28496,2015-10-30 10:22:45:629,1446171765629.0 \n-0.267,-0.3436,12.6282,4.00E-04,0.3389,9.8008,-0.0281,-0.182,0.099,-7.3,-28.5,-42.7,2.871590218,-2.56,0.28,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,28597,2015-10-30 10:22:45:730,1446171765730.0 \n-0.2382,0.6045,9.0788,0.0463,0.2826,9.8025,0.2712,-0.3128,0.1405,-7.5,-28.3,-43,2.883807523,-1.21,0.19,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,28699,2015-10-30 10:22:45:832,1446171765832.0 \n0.0443,0.5363,8.9483,0.1603,0.2736,9.8015,-0.0757,-0.0476,-0.0831,-7.9,-28.4,-42.9,2.87351008,-1.83,-0.92,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,28801,2015-10-30 10:22:45:934,1446171765934.0 \n-1.0343,1.1121,8.0972,0.1196,0.4194,9.7969,0.2334,0.11,-0.0574,-8,-28.3,-42.9,2.871764751,-2.02,-0.91,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,28903,2015-10-30 10:22:46:036,1446171766036.0 \n0.0575,1.3647,9.6953,0.1732,0.587,9.7875,0.1222,-0.0648,0.0452,-8.2,-28.8,-42.2,2.873684613,-3.43,-1.01,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,29006,2015-10-30 10:22:46:139,1446171766139.0 \n-0.073,1.1265,10.908,0.1696,0.6322,9.7848,0.0599,-0.0538,-0.2627,-8.2,-29,-42.2,2.875953541,-3.57,-1.15,36.814438,-119.74895,236.53,336.5915658,3.5,12.903226,,17 / 17,29107,2015-10-30 10:22:46:240,1446171766240.0 \n-0.4393,-0.6895,12.8317,0.0493,0.2675,9.8029,-0.0061,0.3384,-0.2004,-8,-29.3,-42.3,2.879618733,-2.54,-1,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,29210,2015-10-30 10:22:46:343,1446171766343.0 \n0.2119,0.0718,9.9108,-0.028,0.3219,9.8013,0.0122,-0.0794,-0.0354,-7.1,-29.1,-42.6,2.888868978,-1.88,0.16,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,29311,2015-10-30 10:22:46:444,1446171766444.0 \n-0.0012,1.0211,7.8063,-0.1577,0.2879,9.8012,-0.1197,0.1784,-0.0305,-6.4,-28.9,-42.9,2.909114797,-1.65,0.76,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,29414,2015-10-30 10:22:46:547,1446171766547.0 \n-0.2227,1.3479,8.4013,-0.2984,0.2063,9.7999,-0.0049,0.033,0.0489,-5.6,-28.5,-43.2,2.8794442,-1.13,1.72,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,29515,2015-10-30 10:22:46:648,1446171766648.0 \n-0.668,0.662,10.5967,-0.2886,0.1768,9.8008,-0.0599,-0.0281,0.1063,-5.3,-28.3,-43.3,2.911034659,-1.06,1.85,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,29617,2015-10-30 10:22:46:750,1446171766750.0 \n0.7602,-0.182,9.6331,0.0034,0.381,9.7992,0.1723,-0.0977,0.2211,-5.4,-28,-43.1,2.941054323,-2.2,0.47,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,29719,2015-10-30 10:22:46:852,1446171766852.0 \n-0.5567,-0.0108,10.4495,0.1091,0.2229,9.8035,0.3983,-0.2663,0.2162,-6,-27.9,-42.9,2.94210152,-0.91,-0.63,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,29822,2015-10-30 10:22:46:955,1446171766955.0 \n-0.3938,0.3543,8.6311,0.3104,0.3355,9.796,-0.0586,-0.1136,0.0415,-7.2,-28.1,-42.7,2.932153143,-1.96,-1.81,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,29923,2015-10-30 10:22:47:056,1446171767056.0 \n-0.5674,0.8176,9.0094,0.1703,0.2541,9.8019,0.0586,0.1038,0.011,-7.7,-28,-42.7,2.88956711,-1.32,-1.39,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,30025,2015-10-30 10:22:47:158,1446171767158.0 \n-0.2622,1.719,8.7436,-0.0286,0.3354,9.8009,0.044,0.099,-0.0208,-7.8,-28.1,-43,2.853438794,-1.86,-0.16,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,30127,2015-10-30 10:22:47:260,1446171767260.0 \n-0.3603,0.2574,13.0424,0.085,0.3757,9.7991,0.0073,-0.3042,-0.11,-7.5,-28.1,-42.9,2.882934858,-2.15,-0.03,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,30229,2015-10-30 10:22:47:362,1446171767362.0 \n-0.6177,-0.8452,11.5472,0.0992,0.5397,9.7913,-0.1258,-0.1747,-0.2773,-7.1,-28.7,-42.7,2.902482546,-3.65,-0.82,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,30332,2015-10-30 10:22:47:465,1446171767465.0 \n0.5423,0.3711,7.999,0.07,0.5627,9.7902,-0.0305,-0.0819,-0.044,-6.9,-29.1,-42.6,2.890090708,-3.35,-0.28,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,30433,2015-10-30 10:22:47:566,1446171767566.0 \n-0.0706,1.0762,7.3729,-0.0493,0.3789,9.7992,-0.2309,0.1869,-0.0745,-6.7,-29.2,-42.6,2.890614307,-2.41,-0.04,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,30536,2015-10-30 10:22:47:669,1446171767669.0 \n-0.0036,1.142,9.1961,-0.2097,0.1725,9.8029,-0.1991,0.1564,0.0415,-6.3,-28.8,-43,2.901435349,-1.01,1.23,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,30637,2015-10-30 10:22:47:770,1446171767770.0 \n-0.3412,1.1121,10.1263,-0.2995,0.1652,9.8007,-0.022,-0.0403,0.1539,-5.9,-28.4,-43.3,2.877349805,-0.94,1.85,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,30739,2015-10-30 10:22:47:872,1446171767872.0 \n-0.7793,0.929,10.5632,-0.1953,0.3058,9.7999,0.11,-0.0855,0.3005,-5.7,-28.1,-43.5,2.895850295,-1.35,1.03,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,30842,2015-10-30 10:22:47:975,1446171767975.0 \n-1.1025,-0.5902,11.1977,-0.0062,0.1762,9.8051,-0.2944,-0.1967,-0.033,-6,-28,-43.4,2.914699851,-1.43,0.29,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,30943,2015-10-30 10:22:48:076,1446171768076.0 \n-0.0156,-0.0431,8.8621,0.2753,0.2557,9.7994,-0.0171,-0.1148,0.0855,-6.9,-28.1,-43.1,2.908940264,-1.32,-0.8,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,31045,2015-10-30 10:22:48:178,1446171768178.0 \n-0.0946,0.8978,8.3354,0.1834,0.273,9.8011,0.066,0.0929,0.0489,-7.9,-28.1,-43.1,2.880491397,-1.43,-1.08,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,31148,2015-10-30 10:22:48:281,1446171768281.0 \n-0.4058,1.0618,8.8298,0.0761,0.3226,9.801,0.0916,0.1442,-0.1063,-8.2,-28.2,-43.2,2.860769177,-1.89,-0.44,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,31249,2015-10-30 10:22:48:382,1446171768382.0 \n-1.2689,0.6572,11.9435,-0.1121,0.4656,9.7949,0.0562,-0.1234,-0.2285,-7.9,-28.4,-43.2,2.822371933,-2.6,0.81,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,31351,2015-10-30 10:22:48:484,1446171768484.0 \n0.8918,1.3958,9.0609,0.1138,0.7329,9.7786,-0.0599,-0.5278,-0.1894,-7.5,-28.8,-43.3,2.864085303,-3.21,0.75,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,31453,2015-10-30 10:22:48:586,1446171768586.0 \n1.087,0.267,8.5892,0.1375,0.5911,9.7879,-0.171,0.1784,-0.1148,-7.1,-29.3,-42.8,2.898468289,-2.89,-0.47,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,31555,2015-10-30 10:22:48:688,1446171768688.0 \n-0.0251,0.8152,8.0828,0.0039,0.4781,9.795,-0.0696,0.2798,-0.0684,-6.9,-29.6,-42.4,2.907020402,-2.75,-0.44,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,31657,2015-10-30 10:22:48:790,1446171768790.0 \n-0.431,1.3527,9.0082,-0.1534,0.422,9.7964,-0.0721,0.1148,0.0037,-6.5,-29.5,-42.3,2.906147737,-2.42,0.72,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,31759,2015-10-30 10:22:48:892,1446171768892.0 \n-0.7661,0.9218,9.748,-0.2469,0.4569,9.7929,0.0024,0.1979,0.1429,-6.1,-29.4,-42.5,2.895326696,-2.69,1.08,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,31861,2015-10-30 10:22:48:994,1446171768994.0 \n-0.1664,1.3228,11.1378,-0.3023,0.5441,9.7869,0.16,-0.0098,0.2334,-5.8,-29.3,-42.8,2.873335548,-2.99,1.8,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,31964,2015-10-30 10:22:49:097,1446171769097.0 \n-1.5407,-0.7578,11.7424,-0.1689,0.4618,9.7943,-0.2639,-0.3018,-0.0342,-5.6,-29.4,-42.9,2.896548427,-2.7,0.99,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,32065,2015-10-30 10:22:49:198,1446171769198.0 \n-0.182,0.5962,8.4563,0.0853,0.4531,9.7958,-0.237,-0.2871,0.1002,-6.1,-29.5,-42.8,2.935992868,-2.65,-0.5,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,32168,2015-10-30 10:22:49:301,1446171769301.0 \n-0.3232,1.0523,8.9603,0.2696,0.2346,9.8001,-0.0489,-0.0012,-0.0428,-7.3,-29,-42.6,2.932676742,-1.43,-1.44,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,32269,2015-10-30 10:22:49:402,1446171769402.0 \n-0.4717,1.3408,8.9172,0.202,0.3113,9.7996,0.1503,0.0623,-0.0916,-8,-28.7,-42.6,2.894104966,-1.56,-1.29,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,32371,2015-10-30 10:22:49:504,1446171769504.0 \n-0.3723,0.6967,11.9746,0.0996,0.4471,9.7959,0.1698,-0.1429,-0.1772,-8.2,-28.5,-42.8,2.858674782,-2.61,-0.58,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,32473,2015-10-30 10:22:49:606,1446171769606.0 \n1.0546,-0.5375,11.6322,0.236,0.6272,9.7837,-0.4215,-0.0391,-0.3836,-7.8,-28.9,-42.7,2.863038105,-3.69,-0.69,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,32576,2015-10-30 10:22:49:709,1446171769709.0 \n0.6357,0.8068,7.1048,0.0541,0.5435,9.7914,0.259,0.1283,0.0574,-7.4,-29.2,-43,2.892359636,-3.18,-0.32,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,32678,2015-10-30 10:22:49:811,1446171769811.0 \n-0.5459,0.2478,10.2663,0.0563,0.3509,9.8002,-0.1173,0.1808,-0.0929,-7.3,-29.3,-42.8,2.909638396,-2.77,-0.86,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,32780,2015-10-30 10:22:49:913,1446171769913.0 \n-0.3843,1.2857,8.3175,-0.0706,0.3265,9.801,-0.0012,0.1002,0.0318,-6.8,-29,-43,2.889218044,-1.98,0.12,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,32882,2015-10-30 10:22:50:015,1446171770015.0 \n-0.255,1.3096,9.2153,-0.1503,0.3519,9.7992,-0.0049,0.1038,0.0867,-6.4,-28.9,-42.6,2.906671336,-1.97,0.78,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,32983,2015-10-30 10:22:50:116,1446171770116.0 \n-0.158,1.2103,12.5935,-0.067,0.5342,9.7919,0.2309,-0.0464,0.1112,-6,-28.9,-42.9,2.909463863,-3.12,0.39,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,33085,2015-10-30 10:22:50:218,1446171770218.0 \n-0.5195,-0.3017,11.4778,0.0537,0.7382,9.7787,-0.1955,-0.0476,-0.2248,-6.2,-29.2,-42.9,2.903180678,-4.57,0.26,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,33188,2015-10-30 10:22:50:321,1446171770321.0 \n-0.0539,0.6416,8.4312,0.3411,0.7919,9.7687,0.1955,-0.4728,0.1234,-6.8,-29.8,-42.6,2.92063397,-4.34,-1.35,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,33289,2015-10-30 10:22:50:422,1446171770422.0 \n-0.3579,0.7087,9.2859,0.4411,0.6472,9.7753,-0.2272,-0.0415,-0.0623,-7.6,-30.1,-42.3,2.917317845,-3.9,-2.49,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,33391,2015-10-30 10:22:50:524,1446171770524.0 \n-0.1796,1.3001,8.509,0.3484,0.7058,9.775,0.0305,0.1539,-0.0819,-7.9,-30,-42.1,2.91225639,-4.04,-2.32,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,33493,2015-10-30 10:22:50:626,1446171770626.0 \n-0.0658,1.0702,10.2891,0.2057,0.6774,9.7811,-0.0648,0.1258,-0.0941,-7.8,-30,-42,2.884156589,-3.96,-1.2,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,33595,2015-10-30 10:22:50:728,1446171770728.0 \n0.6943,0.8655,9.7109,0.2174,0.7623,9.7746,0.2822,-0.0244,-0.0061,-7.5,-30,-42.1,2.914001719,-4.07,-1.04,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,33697,2015-10-30 10:22:50:830,1446171770830.0 \n-0.0431,-0.4094,12.8245,0.2493,0.3792,9.7961,-0.3323,-0.0538,-0.2077,-7,-30.1,-42,2.930058748,-3.47,-1.52,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,33799,2015-10-30 10:22:50:932,1446171770932.0 \n0.1951,0.7494,9.1842,0.1704,0.3094,9.8003,-0.011,0.0318,-0.0098,-6.6,-29.6,-42.7,2.929709682,-1.96,-1.16,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,33902,2015-10-30 10:22:51:035,1446171771035.0 \n0.0646,1.0918,8.5688,0.0561,0.326,9.8011,-0.0024,0.1393,-0.0367,-6.4,-29.1,-43.1,2.941403388,-1.9,-0.55,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,34003,2015-10-30 10:22:51:136,1446171771136.0 \n-0.1724,1.16,9.8426,-0.0521,0.4361,9.7968,0.1063,0.1258,-0.0281,-5.9,-28.7,-43.3,2.915397983,-2.55,0.3,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,34105,2015-10-30 10:22:51:238,1446171771238.0 \n-0.2574,0.9409,11.2958,-0.1383,0.6253,9.7857,0.3861,-0.1588,0.1552,-5.5,-29,-43.2,2.93075688,-3.66,0.81,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,34208,2015-10-30 10:22:51:341,1446171771341.0 \n-1.3036,-0.3328,11.1737,0.1002,0.7847,9.7747,0.0367,-0.2798,0.0709,-5.4,-29.7,-43,2.946988442,-5.2,0.16,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,34309,2015-10-30 10:22:51:442,1446171771442.0 \n-0.6979,0.2753,8.7448,0.3027,0.5896,9.7842,-0.1112,-0.2407,0.1491,-5.8,-30.3,-43,2.961649208,-3.67,-1.4,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,34411,2015-10-30 10:22:51:544,1446171771544.0 \n0.079,0.6752,9.0225,0.3816,0.3858,9.7916,-0.044,-0.0134,0.2199,-6.9,-29.9,-42.7,2.955540555,-2.25,-2.23,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,34514,2015-10-30 10:22:51:647,1446171771647.0 \n-0.2717,1.1169,8.9783,0.2545,0.3906,9.7956,0.066,0.033,0.0379,-7.4,-29.1,-42.6,2.931455012,-2.21,-1.56,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,34615,2015-10-30 10:22:51:748,1446171771748.0 \n-0.6907,0.8703,10.0173,0.1182,0.4373,9.7962,0,0.1784,-0.0806,-7.8,-28.6,-42.8,2.871764751,-2.56,-0.69,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,34717,2015-10-30 10:22:51:850,1446171771850.0 \n1.8627,1.1133,10.5596,0.1154,0.4937,9.7935,0.1258,-0.2358,0.0904,-7.6,-28.6,-42.7,2.864783434,-2.73,-0.47,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,34820,2015-10-30 10:22:51:953,1446171771953.0 \n-0.0479,-0.6093,11.4718,0.1468,0.2788,9.8016,0.2505,-0.1979,0.0305,-7.4,-28.6,-42.5,2.915921581,-1.4,-0.79,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,34921,2015-10-30 10:22:52:054,1446171772054.0 \n0.1939,-0.2945,9.9144,0.187,0.1571,9.8036,-0.3531,0.1332,-0.171,-7.3,-28.6,-42.5,2.932676742,-1.44,-1.47,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,35024,2015-10-30 10:22:52:157,1446171772157.0 \n-0.2693,0.4142,8.6682,0.0545,0.1721,9.805,-0.077,0.226,-0.1038,-7.1,-28.3,-42.8,2.910511061,-1.14,-0.82,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,35125,2015-10-30 10:22:52:258,1446171772258.0 \n0.3531,1.0283,9.5229,0.0224,0.3204,9.8014,0.1527,0.1197,0.0892,-6.7,-28.2,-43,2.891836038,-1.39,-0.17,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,35227,2015-10-30 10:22:52:360,1446171772360.0 \n-0.1161,1.397,10.7619,-0.0848,0.6099,9.7873,0.2615,-0.1112,0.2028,-6.2,-28.6,-43.2,2.906671336,-3.06,0.51,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,35330,2015-10-30 10:22:52:463,1446171772463.0 \n-0.2071,0.8918,10.0137,-0.0125,0.7369,9.7789,0.0501,-0.0147,0.1906,-6.2,-29.1,-43,2.905275073,-4.39,0.23,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,35431,2015-10-30 10:22:52:564,1446171772564.0 \n-0.5758,0.4202,10.3226,0.0434,0.5485,9.7912,0.2162,0.0012,0.2431,-6.5,-29.3,-42.7,2.937738197,-3.31,-0.7,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,35534,2015-10-30 10:22:52:667,1446171772667.0 \n-0.1329,0.486,7.9224,0.1943,0.4983,9.7921,-0.2627,-0.1796,0.0672,-7.2,-29.4,-42.4,2.908591198,-3.3,-0.96,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,35636,2015-10-30 10:22:52:769,1446171772769.0 \n-0.3268,0.9409,9.1566,0.284,0.3591,9.796,-0.0183,-0.0061,0.1271,-8.2,-28.8,-42.5,2.899340953,-2.1,-1.66,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,35737,2015-10-30 10:22:52:870,1446171772870.0 \n-0.17,1.4653,9.4212,0.1601,0.533,9.7908,0.1246,0.1185,0.055,-8.6,-28.8,-42.8,2.856580387,-2.53,-1.42,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,35840,2015-10-30 10:22:52:973,1446171772973.0 \n0.073,0.9158,11.2097,0.1878,0.6397,9.784,0.2505,0.1698,0.0159,-8.9,-28.8,-42.7,2.842792286,-3.53,-1.21,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,35941,2015-10-30 10:22:53:074,1446171773074.0 \n0.5423,0.2394,11.4168,0.2285,0.7115,9.7781,-0.0831,-0.1784,-0.1845,-8.6,-29.3,-42.9,2.836334567,-4.51,-1.28,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,36044,2015-10-30 10:22:53:177,1446171773177.0 \n1.0594,1.0044,7.8195,0.0701,0.7037,9.7811,0.0635,-0.066,-0.0354,-8.2,-29.7,-42.5,2.859896512,-4.25,-0.33,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,36146,2015-10-30 10:22:53:279,1446171773279.0 \n-0.3555,0.5507,8.8358,-0.1003,0.4511,9.7958,0,0.1564,-0.1002,-7.7,-29.7,-43,2.8651325,-3.37,-0.29,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,36247,2015-10-30 10:22:53:380,1446171773380.0 \n-0.4752,1.0858,8.8909,-0.199,0.38,9.7973,-0.1075,0.1283,-0.0476,-7,-29.2,-43.1,2.863038105,-2.25,1.07,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,36349,2015-10-30 10:22:53:482,1446171773482.0 \n-0.1113,0.9038,10.4986,-0.2068,0.5193,9.7907,0.1295,0.0391,0.1503,-6.3,-28.9,-43.5,2.891312439,-2.74,1.18,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,36451,2015-10-30 10:22:53:584,1446171773584.0 \n-0.2071,1.1708,9.4116,-0.1267,0.7384,9.778,0.2053,-0.0941,0.336,-6.3,-28.9,-43.4,2.88782178,-3.97,0.98,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,36553,2015-10-30 10:22:53:686,1446171773686.0 \n-0.2765,0.5375,8.2648,-0.0312,0.5385,9.7918,0.2077,-0.4093,0.3677,-6.8,-29.2,-43.2,2.8794442,-3.15,0.18,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,36655,2015-10-30 10:22:53:788,1446171773788.0 \n0.2538,0.255,8.8562,0.2856,0.5204,9.7887,-0.1991,-0.2053,0.1148,-7.6,-29.3,-42.8,2.881538595,-3.39,-1.3,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,36758,2015-10-30 10:22:53:891,1446171773891.0 \n-0.2418,1.4162,8.0589,0.2947,0.3884,9.7945,0.0721,0.0953,0.0244,-8.7,-28.9,-42.8,2.866179698,-2.27,-1.72,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,36859,2015-10-30 10:22:53:992,1446171773992.0 \n-0.407,1.5131,9.2943,0.1822,0.4659,9.7939,0.0086,0.077,-0.16,-9.1,-28.7,-43,2.850995333,-2.61,-1.23,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,36961,2015-10-30 10:22:54:094,1446171774094.0 \n-0.4345,0.7242,12.0644,0.2142,0.5134,9.7909,0.0269,-0.1735,-0.27,-9,-28.5,-43.3,2.837032699,-2.84,-1.18,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,37064,2015-10-30 10:22:54:197,1446171774197.0 \n0.0467,-0.4669,12.8174,0.436,0.5072,9.7838,-0.5143,-0.2199,-0.3384,-8.8,-28.8,-43.6,2.883807523,-2.96,-2.55,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,37165,2015-10-30 10:22:54:298,1446171774298.0 \n1.1013,0.6488,8.6335,0.2816,0.6323,9.7822,-0.0464,0.1026,-0.0538,-8.5,-29,-43.6,2.889043511,-3.7,-1.65,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,37267,2015-10-30 10:22:54:400,1446171774400.0 \n0.2346,1.0151,7.2113,-0.0036,0.6301,9.7864,0.0709,0.4545,-0.0831,-8.2,-29.2,-43.6,2.84366495,-3.68,0.02,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,37369,2015-10-30 10:22:54:502,1446171774502.0 \n-0.2167,1.3922,7.7237,-0.3442,0.6439,9.7794,-0.077,0.3128,-0.0916,-7.4,-29.4,-43.4,2.849075471,-3.88,1.12,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,37472,2015-10-30 10:22:54:605,1446171774605.0 \n-0.9122,0.8871,10.2376,-0.4484,0.6093,9.7774,0.0782,0.0342,0.1124,-6,-29.7,-43.5,2.860071045,-3.41,2.57,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,37573,2015-10-30 10:22:54:706,1446171774706.0 \n-0.2574,1.2773,10.9223,-0.1609,0.7696,9.7751,-0.0892,-0.2639,0.1686,-5.2,-29.9,-43.2,2.917666911,-4.34,1.43,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,37675,2015-10-30 10:22:54:808,1446171774808.0 \n-0.753,0.2406,9.4355,-0.0203,0.5643,9.7904,-0.2395,-0.0281,0.0892,-5.7,-29.8,-43,2.923426497,-3.3,0.12,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,37777,2015-10-30 10:22:54:910,1446171774910.0 \n-0.0431,0.4729,8.6874,0.2419,0.5419,9.7887,-0.1527,0,0.1503,-6.6,-29.7,-42.9,2.927266221,-3.43,-1.39,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,37880,2015-10-30 10:22:55:013,1446171775013.0 \n-0.401,0.9601,8.8957,0.2708,0.3776,9.7956,0.0929,0.0929,0.0342,-7.7,-29.3,-43.1,2.897246558,-2.21,-1.58,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,37981,2015-10-30 10:22:55:114,1446171775114.0 \n-0.3232,1.5143,9.2033,0.1888,0.4379,9.7951,-0.0208,0.1185,-0.055,-8.2,-29,-43.4,2.887647247,-2.56,-1.31,36.81434,-119.74895,235.94,336.5915658,3.83,19.35484,185.94,17 / 17,38083,2015-10-30 10:22:55:216,1446171775216.0 \n-1.1959,0.3567,12.5193,0.1781,0.5657,9.7887,0.0513,0.0305,-0.1649,-8.2,-29,-43.6,2.881364062,-3.08,-1.2,36.814228,-119.74892,238.15,336.5915658,3.92,12.903226,177.92,17 / 17,38186,2015-10-30 10:22:55:319,1446171775319.0 \n1.2462,0.1891,9.6235,0.2918,0.6441,9.7811,-0.5791,0.0134,-0.2834,-8.1,-29.3,-43.5,2.867052362,-4.25,-1,36.814228,-119.74892,238.15,336.5915658,3.92,12.903226,177.92,17 / 17,38287,2015-10-30 10:22:55:420,1446171775420.0 \n1.3479,0.7697,7.525,0.222,0.5579,9.7882,0.2114,0.0134,0.0012,-7.8,-29.6,-43.2,2.887647247,-2.82,-1.03,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,38389,2015-10-30 10:22:55:522,1446171775522.0 \n-0.1927,1.0451,6.9671,0.1745,0.4266,9.7958,0.0611,0.0623,-0.2162,-7.6,-29.5,-43.4,2.88066593,-2.49,-1.02,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,38492,2015-10-30 10:22:55:625,1446171775625.0 \n-0.3256,0.9421,9.0046,0.0833,0.322,9.801,0.0648,0.0464,-0.022,-7.2,-29.2,-43.7,2.908765731,-1.9,-0.62,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,38593,2015-10-30 10:22:55:726,1446171775726.0 \n-0.3567,0.9984,10.1718,-0.0908,0.3909,9.7984,0.077,0.1124,0.1723,-6.4,-28.9,-43.8,2.918888641,-2.12,0.25,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,38695,2015-10-30 10:22:55:828,1446171775828.0 \n0.4345,1.385,9.4822,-0.0608,0.5694,9.7899,0.3067,-0.077,0.2553,-6,-29,-43.4,2.908940264,-3.33,0.36,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,38797,2015-10-30 10:22:55:930,1446171775930.0 \n-0.31,-0.0622,10.6494,0.1548,0.391,9.7976,-0.1002,0.1649,0.1038,-6.1,-29.1,-42.9,2.948908304,-2.28,-0.91,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,38899,2015-10-30 10:22:56:032,1446171776032.0 \n0.2622,0.4262,8.3043,0.3734,0.6888,9.7753,-0.0794,-0.1136,0.0354,-6.8,-29.4,-42.9,2.937738197,-4.03,-2.19,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,39001,2015-10-30 10:22:56:134,1446171776134.0 \n-0.146,0.9589,8.7269,0.43,0.5955,9.7791,-0.0794,-0.0147,-0.0782,-7.7,-29.5,-42.9,2.913652653,-3.48,-2.52,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,39103,2015-10-30 10:22:56:236,1446171776236.0 \n-0.4262,1.1552,9.3817,0.366,0.5558,9.784,-0.0794,0.1491,-0.0672,-8.2,-29.5,-43.2,2.913827186,-3.37,-2.5,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,39205,2015-10-30 10:22:56:338,1446171776338.0 \n-0.0838,0.6608,11.6646,0.27,0.5399,9.7881,-0.0513,0.0489,-0.1014,-8.2,-29.6,-43,2.900039085,-3.28,-1.63,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,39308,2015-10-30 10:22:56:441,1446171776441.0 \n-0.0706,-0.5938,11.9722,0.3466,0.566,9.7842,-0.5864,0.1515,-0.2688,-7.7,-29.6,-43.4,2.909987462,-3.31,-2.03,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,39409,2015-10-30 10:22:56:542,1446171776542.0 \n1.664,0.7123,7.8685,0.4277,0.4457,9.7872,0.3494,-0.2431,0.121,-7.4,-29.4,-43.6,2.945766712,-2.34,-2.09,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,39511,2015-10-30 10:22:56:644,1446171776644.0 \n0.0527,0.7266,8.1116,0.3201,0.2414,9.7985,0.0232,0.171,-0.1478,-7.2,-29,-43.9,2.944894047,-1.41,-1.87,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,39614,2015-10-30 10:22:56:747,1446171776747.0 \n-0.4717,0.8859,8.6766,0.1615,0.2216,9.8028,0.0318,0.0379,-0.0257,-6.8,-28.7,-43.9,2.92656809,-1.38,-1.17,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,39715,2015-10-30 10:22:56:848,1446171776848.0 \n-0.2634,0.7793,10.0449,0.0358,0.2692,9.8029,0.0061,0.1588,0.0574,-6.1,-28.6,-44.1,2.944195915,-1.42,-0.54,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,39817,2015-10-30 10:22:56:950,1446171776950.0 \n0.4381,1.1061,11.5532,0.0384,0.4348,9.7969,0.2431,0.0073,0.2822,-5.6,-28.9,-44,2.928487952,-2.13,-0.11,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,39920,2015-10-30 10:22:57:053,1446171777053.0 \n-1.4641,-1.3719,13.2555,0.178,0.2128,9.8027,-0.1881,0.2443,0.1038,-5.6,-29.4,-43.4,2.959205747,-1.91,-1.23,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,40022,2015-10-30 10:22:57:155,1446171777155.0 \n-0.158,0.2263,8.084,0.2899,0.3546,9.7959,0.2505,-0.2944,0.1087,-5.9,-29.4,-43,2.962870938,-2.01,-1.38,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,40123,2015-10-30 10:22:57:256,1446171777256.0 \n-0.3376,0.6273,8.497,0.2555,0.2555,9.8,-0.0244,-0.1124,-0.0415,-6.4,-29.3,-42.5,2.967583327,-1.49,-1.49,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,40225,2015-10-30 10:22:57:358,1446171777358.0 \n-0.4741,0.984,8.6562,0.2728,0.2619,9.7994,0.0611,0.0403,-0.033,-6.6,-29,-42.9,2.937040065,-1.45,-1.61,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,40327,2015-10-30 10:22:57:460,1446171777460.0 \n-0.4717,0.3915,11.1354,0.3456,0.3375,9.7947,0.0794,-0.1943,-0.0953,-6.7,-28.9,-42.6,2.939658059,-1.88,-1.8,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,40429,2015-10-30 10:22:57:562,1446171777562.0 \n1.4593,-0.164,10.5022,0.3449,0.4918,9.7882,-0.0354,-0.1833,-0.1539,-6.8,-29.1,-42.3,2.938959927,-2.87,-2.02,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,40532,2015-10-30 10:22:57:665,1446171777665.0 \n0.7254,0.2729,7.671,0.1233,0.2344,9.8031,0.2224,-0.0855,-0.0073,-6.5,-29,-42,2.948559238,-1.37,-0.72,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,40634,2015-10-30 10:22:57:767,1446171777767.0 \n-0.3735,0.5267,8.3665,0.1011,0.0704,9.8059,-0.0782,0.0538,-0.0257,-6.2,-28.7,-42.5,2.95344616,-0.85,-0.81,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,40736,2015-10-30 10:22:57:869,1446171777869.0 \n-0.571,0.5602,9.7743,0.091,-0.106,9.8057,-0.226,-0.033,-0.0318,-5.5,-27.8,-42.9,2.981545961,0.35,-0.59,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,40837,2015-10-30 10:22:57:970,1446171777970.0 \n0.0156,0.2538,10.0892,0.0477,-0.0901,9.8061,0.0501,0.1271,0.1991,-5.4,-27.4,-42.9,2.974041045,0.63,-0.47,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,40939,2015-10-30 10:22:58:072,1446171778072.0 \n0.7278,0.8691,9.5457,2.00E-04,0.2674,9.803,0.3445,0.0208,0.314,-5.4,-27.2,-42.7,2.954144292,-0.86,0,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,41042,2015-10-30 10:22:58:175,1446171778175.0 \n-1.0714,-1.3886,14.3089,0.2065,0.0482,9.8044,-0.5412,-0.4435,-0.1564,-5.8,-27.3,-42.7,2.947162975,-1.23,-1.16,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,41143,2015-10-30 10:22:58:276,1446171778276.0 \n-0.0287,0.3855,8.181,0.3848,0.146,9.798,-0.0293,-0.452,0.1405,-6.5,-27.4,-42.7,2.959205747,-0.98,-1.54,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,41245,2015-10-30 10:22:58:378,1446171778378.0 \n0.0359,0.3795,9.3194,0.5202,-4.00E-04,9.7928,0.0134,-0.1503,0.0098,-7.7,-27.1,-42.8,2.92778982,0.05,-2.82,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,41348,2015-10-30 10:22:58:481,1446171778481.0 \n-0.2562,0.9912,8.6802,0.4069,0.0956,9.7977,0.0086,0.1442,-0.1784,-8.5,-26.8,-43,2.919586773,-0.34,-2.6,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,41449,2015-10-30 10:22:58:582,1446171778582.0 \n-0.6476,-0.5148,12.0201,0.3042,0.1074,9.8013,-0.0073,0.0648,-0.2553,-8.4,-26.6,-43,2.895501229,-0.63,-1.78,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,41551,2015-10-30 10:22:58:684,1446171778684.0 \n1.0175,0.5842,9.147,0.1617,0.4286,9.7959,0.193,0.0806,-0.0721,-7.9,-26.9,-43,2.866179698,-1.95,-1.05,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,41654,2015-10-30 10:22:58:787,1446171778787.0 \n0.3831,0.3412,8.266,0.0983,0.1394,9.8052,0.1796,-0.1173,-0.0672,-6.9,-27.2,-42.9,2.897595624,-0.81,-0.57,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,41755,2015-10-30 10:22:58:888,1446171778888.0 \n-0.4501,-0.0563,10.398,0.2045,0.0991,9.804,-0.2541,-0.0489,-0.1857,-6.3,-27.4,-43.2,2.947512041,-0.99,-1.11,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,41857,2015-10-30 10:22:58:990,1446171778990.0 \n-0.7063,0.7314,8.5497,0.0917,0.1274,9.8054,-0.0782,0.1625,-0.0134,-5.8,-27.3,-43.6,2.940007125,-0.87,-0.81,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,41959,2015-10-30 10:22:59:092,1446171779092.0 \n-0.1927,0.8487,9.1985,0.0299,0.1177,9.8059,-0.1075,0.0525,0.1698,-5.6,-27.1,-43.6,2.923950096,-0.77,-0.21,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,42062,2015-10-30 10:22:59:195,1446171779195.0 \n0.1161,0.4836,10.4232,0.0202,0.1467,9.8055,0.1234,-0.0012,0.2993,-5.4,-26.9,-43.9,2.957285885,-0.86,-0.12,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,42163,2015-10-30 10:22:59:296,1446171779296.0 \n0.7183,-1.0211,12.1518,0.1785,0.1418,9.804,-0.54,-0.3396,0.1356,-5.6,-26.9,-44,2.921681168,-1.64,-0.32,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,42265,2015-10-30 10:22:59:398,1446171779398.0 \n0.0634,0.2849,8.3558,0.3472,0.1141,9.7998,-0.0855,-0.2896,0.1356,-6.5,-26.9,-44,2.959031214,-0.63,-1.44,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,42367,2015-10-30 10:22:59:500,1446171779500.0 \n0.0156,0.0048,8.9268,0.41,-0.038,9.798,-0.1686,-0.0244,0.0086,-7.2,-26.9,-44,2.948733771,0.06,-2.23,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,42469,2015-10-30 10:22:59:602,1446171779602.0 \n-0.4118,0.7817,8.1451,0.3982,0.0475,9.7984,0.1979,0.0599,-0.0012,-8,-26.7,-44.1,2.913827186,-0.28,-2.33,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,42571,2015-10-30 10:22:59:704,1446171779704.0 \n-0.0874,0.0814,11.4958,0.4185,0.137,9.7968,0.0122,-0.1918,-0.1576,-8.3,-26.8,-43.9,2.913827186,-0.8,-2.45,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,42674,2015-10-30 10:22:59:807,1446171779807.0 \n0.4681,0.2789,9.6989,0.4166,0.2336,9.795,-0.1527,-0.1845,-0.1808,-8.4,-27,-43.7,2.917666911,-1.1,-2.66,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,42776,2015-10-30 10:22:59:909,1446171779909.0 \n0.1484,-0.2586,9.6714,0.3212,-0.1408,9.8004,-0.5534,0.3946,-0.3983,-8,-27.2,-43.7,2.918714108,0.41,-2.35,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,42878,2015-10-30 10:23:00:011,1446171780011.0 \n0.2239,-0.419,10.0916,0.3981,-0.2611,9.7951,-0.3641,0.0452,-0.2016,-7.7,-27.2,-44.1,2.919935839,0.88,-2.29,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,42979,2015-10-30 10:23:00:112,1446171780112.0 \n-0.2981,0.5758,8.6347,0.356,-0.3158,9.7951,-0.0929,0.0476,-0.1014,-7,-26.7,-44.8,2.956936819,1.69,-2.17,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,43082,2015-10-30 10:23:00:215,1446171780215.0 \n-0.1844,0.2741,10.1023,0.3432,-0.2688,9.797,0.0733,-0.0183,0.0024,-6.7,-26.4,-45.5,2.94506858,1.57,-2.01,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,43183,2015-10-30 10:23:00:316,1446171780316.0 \n-0.1125,0.0527,10.7727,0.1896,-0.1081,9.8042,0.4129,0.1161,0.3054,-6.4,-26.2,-45.5,2.961823741,1.24,-1.4,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,43285,2015-10-30 10:23:00:418,1446171780418.0 \n0.6608,-0.3364,10.2963,0.1957,0.1555,9.8035,-0.2957,-0.0709,0.1613,-6.3,-26.9,-45,2.944544981,-1.18,-1.01,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,43387,2015-10-30 10:23:00:520,1446171780520.0 \n0.1544,0.2957,8.6084,0.1993,0.0698,9.8044,0.0599,0.0476,0.2712,-6.7,-27.5,-44.2,2.916619713,-0.41,-1.16,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,43489,2015-10-30 10:23:00:622,1446171780622.0 \n0.2993,-0.1329,8.2396,0.5032,0.0554,9.7936,-0.0806,-0.0501,0.0733,-7.4,-27.8,-43.8,2.969328656,-0.51,-2.85,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,43591,2015-10-30 10:23:00:724,1446171780724.0 \n-0.1472,0.8751,7.9404,0.4844,0.0221,9.7947,0.1674,0.0122,0.0244,-8.5,-27.4,-43.7,2.928662485,-0.13,-2.83,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,43693,2015-10-30 10:23:00:826,1446171780826.0 \n-0.012,0.8009,9.323,0.4388,0.1088,9.7962,-0.0367,-0.1124,-0.1955,-9,-27.2,-43.7,2.883109391,-0.54,-2.56,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,43795,2015-10-30 10:23:00:928,1446171780928.0 \n0.4525,0.1808,9.9719,0.4061,0.1152,9.7976,0.044,0.1772,-0.1674,-9,-27.4,-43.4,2.875779009,-0.67,-2.37,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,43898,2015-10-30 10:23:01:031,1446171781031.0 \n0.1413,-1.2354,12.6378,0.2844,-0.2544,9.7992,-0.6597,0.292,-0.3934,-8.6,-27.5,-43.2,2.877000739,-0.46,-2.36,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,44000,2015-10-30 10:23:01:133,1446171781133.0 \n0.4513,-0.4537,9.7648,0.3552,-0.2336,9.7974,-0.3005,-0.0024,-0.0782,-8,-27,-43.3,2.908765731,0.99,-1.89,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,44101,2015-10-30 10:23:01:234,1446171781234.0 \n0.3627,0.6033,7.1994,0.3588,-0.3097,9.7952,0.0086,0.0061,0.0171,-7.7,-26.5,-43.5,2.911732791,1.75,-2.14,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,44203,2015-10-30 10:23:01:336,1446171781336.0 \n0.2933,0.4094,9.7264,0.3434,-0.4044,9.7923,-0.0452,0.044,0.0147,-7.5,-26,-43.8,2.951700831,2.35,-2.15,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,44305,2015-10-30 10:23:01:438,1446171781438.0 \n-0.091,0.0539,10.671,0.1785,-0.3081,9.8002,0.226,0.1417,0.204,-7.4,-25.7,-44.1,2.929535149,2.12,-1.37,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,44407,2015-10-30 10:23:01:540,1446171781540.0 \n1.4293,0.2897,9.329,0.1309,0.0159,9.8058,0.452,0.0953,0.3604,-7.1,-25.8,-44,2.89916642,-0.09,-0.76,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,44509,2015-10-30 10:23:01:642,1446171781642.0 \n-0.6608,-0.085,8.57,0.1829,-0.2313,9.8022,-0.1576,0.325,0.1161,-7.1,-26.2,-43.8,2.919237707,1.47,-1.13,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,44612,2015-10-30 10:23:01:745,1446171781745.0 \n0.0479,0.2095,9.001,0.4286,-0.1681,9.7958,0.0244,-0.1136,0.1503,-7.5,-26.4,-43.4,2.945417646,1.01,-2.24,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,44713,2015-10-30 10:23:01:846,1446171781846.0 \n-0.413,0.6572,9.2093,0.4539,-0.1681,9.7947,0.1368,0.1197,0.0611,-8.2,-26.2,-43.3,2.920808503,0.98,-2.65,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,44816,2015-10-30 10:23:01:949,1446171781949.0 \n-0.261,0.8356,9.6965,0.3246,-0.0513,9.8011,0.0342,0.0929,-0.0293,-8.5,-26.2,-43.3,2.903355211,0.39,-2.14,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,44917,2015-10-30 10:23:02:050,1446171782050.0 \n0.4357,-0.0634,10.2975,0.3234,0.0587,9.8011,0.2676,0.1796,-0.0806,-8.5,-26.4,-43.1,2.891486972,-0.34,-1.89,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,45020,2015-10-30 10:23:02:153,1446171782153.0 \n1.3252,-0.6141,10.9942,0.2765,-0.1638,9.8014,-0.7563,0.1552,-0.3567,-8.2,-26.8,-42.9,2.884680188,-0.98,-1.46,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,45121,2015-10-30 10:23:02:254,1446171782254.0 \n1.2354,0.1353,8.0481,0.1873,-0.2608,9.8014,0.1283,0.0183,0.0452,-7.4,-26.6,-43,2.922030234,1.74,-0.91,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,45223,2015-10-30 10:23:02:356,1446171782356.0 \n0.0227,-0.0479,8.8346,0.0644,-0.4341,9.7968,-0.088,0.2663,-0.2517,-6.9,-26.2,-42.9,2.91522345,2.38,-0.8,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,45325,2015-10-30 10:23:02:458,1446171782458.0 \n-0.2705,0.6069,8.6036,-0.0097,-0.4141,9.7979,-0.055,0.2187,-0.1478,-6,-25.1,-43.3,2.919761306,2.42,0.06,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,45427,2015-10-30 10:23:02:560,1446171782560.0 \n-0.7961,-0.1987,10.9978,-0.2166,-0.3839,9.7967,0.2346,-0.1063,0.2419,-5,-24.6,-43.1,2.924648228,2.52,1.23,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,45530,2015-10-30 10:23:02:663,1446171782663.0 \n0.0838,0.3795,9.177,-0.1398,-0.0177,9.8056,0.5461,-0.0098,0.3482,-4.6,-24.8,-42.9,2.92656809,0.94,0.82,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,45631,2015-10-30 10:23:02:764,1446171782764.0 \n-0.6716,0.0024,9.4152,-0.0509,-0.1162,9.8058,0.1136,-0.0049,0.1881,-4.5,-25.4,-42.5,2.977706237,0.68,0.3,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,45733,2015-10-30 10:23:02:866,1446171782866.0 \n0.0862,0.3603,9.2177,0.1258,-0.0188,9.8058,-0.1161,0.0122,-0.0098,-4.9,-25.9,-42.2,2.957285885,0.08,-0.19,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,45836,2015-10-30 10:23:02:969,1446171782969.0 \n-0.5926,0.6823,8.5569,0.1216,-0.002,9.8059,0.1051,-0.0257,0.0159,-5.5,-26.1,-41.8,2.972121183,0.12,-0.73,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,45938,2015-10-30 10:23:03:071,1446171783071.0 \n-0.413,1.069,8.5234,-0.0107,0.1543,9.8054,0.1686,0.1002,-0.0342,-5.7,-26.2,-41.5,2.916619713,-0.49,-0.18,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,46040,2015-10-30 10:23:03:173,1446171783173.0 \n-0.3065,0.1592,11.6562,0.0664,0.3038,9.8017,0.1747,0.0305,-0.2566,-5.5,-26.8,-41.2,2.953969759,-1.44,-0.1,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,46142,2015-10-30 10:23:03:275,1446171783275.0 \n0.8655,0.5183,9.5433,0.0238,0.4979,9.794,0.2578,-0.0672,-0.1881,-5,-27.6,-41.3,2.951875364,-2.63,0.01,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,46243,2015-10-30 10:23:03:376,1446171783376.0 \n0.4022,0.5866,8.0206,-0.2103,0.3069,9.7996,0.2321,0.0061,-0.0709,-4.2,-28.5,-41.5,2.960427477,-1.49,1.3,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,46346,2015-10-30 10:23:03:479,1446171783479.0 \n-0.5411,0.1987,9.6893,-0.2429,0.0747,9.8034,-0.0916,0.0403,0.0183,-3.5,-28.7,-41.6,3.005806038,-1.45,1.11,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,46447,2015-10-30 10:23:03:580,1446171783580.0 \n-0.5004,0.7853,8.922,-0.3008,-0.1335,9.8011,-0.3213,0.1014,0.0782,-2.7,-28,-42,2.994461398,0.49,1.64,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,46549,2015-10-30 10:23:03:682,1446171783682.0 \n-0.6189,0.3747,9.8533,-0.227,-0.0896,9.8036,0.0037,-0.0464,0.1869,-2.6,-27.5,-42.4,2.997253924,0.62,1.35,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,46651,2015-10-30 10:23:03:784,1446171783784.0 \n-0.5686,0.1951,10.9978,-0.151,0.1464,9.8044,0.3616,-0.0183,0.3348,-3,-27.2,-42.5,3.004409774,-0.22,0.96,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,46753,2015-10-30 10:23:03:886,1446171783886.0 \n-1.2534,-0.9816,11.7472,-0.0747,0.1472,9.8053,0.2162,-0.1637,0.3286,-3.7,-27.6,-42.3,2.980673297,-1.13,0.56,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,46855,2015-10-30 10:23:03:988,1446171783988.0 \n-0.5578,0.2334,9.1387,0.0868,0.2971,9.8018,0.0696,-0.1772,0.2053,-5,-28.1,-42.3,2.970026788,-1.74,-0.51,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,46957,2015-10-30 10:23:04:090,1446171784090.0 \n-0.1305,0.7518,9.256,0.2282,0.1536,9.8028,-0.0782,-0.0953,0.1405,-6.1,-28.2,-42.6,2.955889621,-1,-1.17,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,47062,2015-10-30 10:23:04:195,1446171784195.0 \n-0.1233,1.1325,8.4072,0.2054,0.2589,9.8011,0.1344,0.0586,0.0098,-6.9,-28.2,-42.9,2.921855701,-1.26,-1.28,36.814228,-119.74892,238.15,336.4908168,3.92,12.903226,177.92,17 / 17,47161,2015-10-30 10:23:04:294,1446171784294.0 \n-0.5926,0.2897,11.0325,0.271,0.357,9.7964,0.0305,-0.1332,-0.16,-7.5,-28.1,-43.4,2.918015976,-1.87,-1.27,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,47263,2015-10-30 10:23:04:396,1446171784396.0 \n0.0383,-0.1089,10.6171,0.2615,0.4542,9.7926,-0.0745,0.1808,-0.2016,-7.8,-28.4,-43.5,2.883807523,-2.65,-1.53,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,47366,2015-10-30 10:23:04:499,1446171784499.0 \n0.152,0.8823,9.9527,0.085,0.3771,9.799,0.1087,-0.0037,-0.0049,-7.7,-28.6,-43.5,2.876128074,-1.94,-0.69,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,47468,2015-10-30 10:23:04:601,1446171784601.0 \n-0.2119,0.4477,9.6654,0.1187,0.1853,9.8042,0.1026,0.1503,-0.0586,-7,-28.8,-43.1,2.91347812,-1.44,-0.69,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,47570,2015-10-30 10:23:04:703,1446171784703.0 \n-0.4896,0.9732,8.2863,0.0266,0.1942,9.8047,-0.0354,0.0171,-0.1124,-6.2,-28.5,-43.4,2.928138886,-1.13,-0.16,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,47671,2015-10-30 10:23:04:804,1446171784804.0 \n-0.1736,1.0307,9.7983,0.0166,0.2856,9.8025,0.1002,-0.0305,0.0562,-5.8,-28.5,-43.6,2.923426497,-1.43,-0.05,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,47773,2015-10-30 10:23:04:906,1446171784906.0 \n-0.3244,1.3958,11.4084,0.1014,0.6286,9.786,0.2712,-0.121,0.1356,-5.6,-28.8,-43.7,2.932502209,-3.68,-0.59,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,47875,2015-10-30 10:23:05:008,1446171785008.0 \n-0.5758,0.0742,11.2719,0.1551,0.7495,9.7767,-0.044,0.033,-0.0464,-6.1,-29.5,-43.4,2.937040065,-4.38,-0.91,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,47977,2015-10-30 10:23:05:110,1446171785110.0 \n-0.0431,1.1672,9.4116,0.2672,0.6476,9.7816,0.0037,-0.1869,-0.055,-6.2,-29.9,-43.1,2.956936819,-3.74,-1.24,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,48079,2015-10-30 10:23:05:212,1446171785212.0 \n0.401,1.3216,7.7931,0.2243,0.5424,9.7891,0.1026,-0.0684,-0.1038,-6.5,-30.2,-43.1,2.966885195,-3.2,-1.52,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,48181,2015-10-30 10:23:05:314,1446171785314.0 \n0.018,1.3815,8.1762,0.2937,0.658,9.7801,0.1405,-0.055,-0.0171,-6.4,-30,-43.2,2.970550387,-3.61,-1.73,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,48284,2015-10-30 10:23:05:417,1446171785417.0 \n0.4286,1.1121,9.7755,0.2519,0.7844,9.772,0.1759,0.0195,-0.1845,-6.5,-30.1,-43.5,2.961998274,-4.25,-1.53,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,48386,2015-10-30 10:23:05:519,1446171785519.0 \n1.3695,0.8847,10.4974,0.3089,1.0665,9.7436,-0.0024,-0.2602,-0.3482,-6.1,-30.8,-43.1,2.957460418,-5.94,-1.45,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,48487,2015-10-30 10:23:05:620,1446171785620.0 \n0.2574,0.8284,11.0899,0.1466,0.8262,9.7707,-0.2981,0.3372,-0.1772,-5.6,-31.3,-43,2.954144292,-5.03,-1.14,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,48589,2015-10-30 10:23:05:722,1446171785722.0 \n0.4908,1.5287,8.2648,0.1463,0.7064,9.7801,0.0611,0.077,0.0391,-4.8,-31.4,-42.8,2.992367003,-3.89,-1.05,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,48691,2015-10-30 10:23:05:824,1446171785824.0 \n-0.8068,1.3838,8.5162,0.1142,0.7039,9.7807,0.0428,-0.0501,-0.1784,-4.1,-31.1,-43.4,3.016627079,-4.12,-0.67,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,48794,2015-10-30 10:23:05:927,1446171785927.0 \n-0.5004,1.5263,9.7624,0.0113,0.7496,9.7779,0.1991,0.1417,0.0159,-3.7,-30.9,-43.6,3.006853235,-4.26,-0.33,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,48895,2015-10-30 10:23:06:028,1446171786028.0 \n-0.0431,1.318,12.3194,0.0148,1.0044,9.7551,0.2236,-0.121,0.1918,-3,-31.2,-43.7,3.024306528,-5.58,0.17,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,48998,2015-10-30 10:23:06:131,1446171786131.0 \n-0.2119,0.595,9.8976,-0.0594,1.0821,9.7466,0.1038,0.0428,0.0867,-2.9,-31.7,-43.3,3.027622653,-6.15,0.15,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,49099,2015-10-30 10:23:06:232,1446171786232.0 \n-0.018,0.9912,9.973,0.1186,1.0425,9.7504,-0.1991,-0.0562,-0.033,-3,-32.2,-43,3.041061689,-6.2,-0.35,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,49201,2015-10-30 10:23:06:334,1446171786334.0 \n-0.565,1.3934,8.3342,0.0337,0.8995,9.7652,-0.033,0.1625,0.0305,-3.4,-32.5,-42.6,3.042283419,-5.47,-0.31,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,49304,2015-10-30 10:23:06:437,1446171786437.0 \n-0.2765,1.9142,7.8207,0.0191,1.0759,9.7474,0.3018,-0.1197,0.0367,-3.5,-32.6,-42.6,3.036872898,-5.24,0.06,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,49405,2015-10-30 10:23:06:538,1446171786538.0 \n0.0826,1.5694,11.4132,0.0871,1.1614,9.7373,0.1552,0.1038,-0.0733,-3.4,-32.9,-42.7,3.050486467,-6.58,-0.61,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,49507,2015-10-30 10:23:06:640,1446171786640.0 \n0.079,0.1221,12.4187,0.0313,1.0328,9.7521,-0.43,-0.0134,-0.2724,-3.3,-33.2,-43,3.045425012,-6.96,-0.46,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,49609,2015-10-30 10:23:06:742,1446171786742.0 \n0.6177,0.9457,7.9655,-0.0905,0.9846,9.7567,-0.0501,0.0122,-0.0403,-2.8,-33.2,-43,3.022910264,-5.76,0.53,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,49712,2015-10-30 10:23:06:845,1446171786845.0 \n-0.3627,1.4593,7.2305,-0.0486,0.7826,9.7753,0.0098,0.0611,0.0611,-2.3,-32.6,-43.2,3.069859621,-4.53,0.16,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,49813,2015-10-30 10:23:06:946,1446171786946.0 \n-0.2215,1.579,8.4072,0.0524,0.7656,9.7766,-0.099,-0.0794,0.1124,-2.1,-32.3,-43.4,3.073873879,-4.43,-0.08,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,49915,2015-10-30 10:23:07:048,1446171787048.0 \n-0.395,0.9026,11.564,0.0283,0.7735,9.7761,0.1381,0.1478,0.2199,-2.5,-31.9,-43.4,3.075968274,-4.52,-0.17,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,50017,2015-10-30 10:23:07:150,1446171787150.0 \n1.0092,-0.3986,11.6203,0.135,0.7566,9.7765,-0.4227,-0.2651,0.033,-2.8,-32,-43.1,3.04472688,-5.12,-0.37,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,50119,2015-10-30 10:23:07:252,1446171787252.0 \n-0.7183,1.0235,7.7153,-0.0708,0.7817,9.7752,0.0305,-0.0208,-0.0171,-3.3,-32,-42.9,3.025877324,-4.57,0.41,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,50222,2015-10-30 10:23:07:355,1446171787355.0 \n-0.7961,0.5854,8.8071,-0.0282,0.7068,9.7811,-0.1588,-0.0672,-0.0745,-3.4,-32.1,-43.2,3.030240647,-4.38,0.27,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,50323,2015-10-30 10:23:07:456,1446171787456.0 \n-0.8009,1.1516,9.3338,0.0804,0.6938,9.7817,-0.0049,-0.1368,0.0354,-3.5,-32,-44,3.043854215,-4.03,-0.23,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,50426,2015-10-30 10:23:07:559,1446171787559.0 \n-0.2921,1.4664,10.0221,0.2154,0.7758,9.7735,0.0464,-0.1515,-0.0672,-3.8,-32,-43.8,3.029018917,-4.42,-1.01,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,50527,2015-10-30 10:23:07:660,1446171787660.0 \n-0.2622,1.3156,10.0616,0.3045,0.8013,9.7691,-0.1417,-0.1429,-0.2529,-4.2,-32.2,-43.6,3.048043006,-4.68,-1.75,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,50629,2015-10-30 10:23:07:762,1446171787762.0 \n0.243,-0.3711,12.0464,0.3883,0.3438,9.7929,-0.8063,-0.1442,-0.5449,-4.4,-32,-43.5,3.066543496,-2.01,-2.27,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,50731,2015-10-30 10:23:07:864,1446171787864.0 \n0.2143,0.4549,8.4994,0.337,0.4002,9.7927,-0.0757,0.011,-0.215,-4.1,-31.6,-43.9,3.056769652,-2.21,-1.85,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,50834,2015-10-30 10:23:07:967,1446171787967.0 \n0.2191,1.0008,8.91,0.3522,0.3534,9.794,0.0232,-0.0012,-0.0086,-3.2,-30.9,-44.6,3.090279974,-2.09,-1.9,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,50935,2015-10-30 10:23:08:068,1446171788068.0 \n0.4178,1.2677,8.3055,0.3607,0.4598,9.7892,0.1368,-0.0464,-0.066,-2.8,-30.8,-44.5,3.090978105,-2.52,-1.99,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,51037,2015-10-30 10:23:08:170,1446171788170.0 \n-0.3819,0.9002,10.7799,0.308,0.6124,9.7827,0.088,-0.0929,-0.0073,-2.4,-31.2,-44,3.117332577,-3.49,-1.71,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,51140,2015-10-30 10:23:08:273,1446171788273.0 \n1.0882,1.2809,8.5329,0.1999,0.7923,9.7726,-0.044,-0.1674,0.2053,-2.3,-31.6,-43.6,3.103893542,-4.21,-1.2,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,51241,2015-10-30 10:23:08:374,1446171788374.0 \n-0.2191,0.431,10.2963,0.2508,0.6998,9.7784,-0.0318,0.0171,0.1552,-2.4,-32.2,-42.9,3.110525793,-4.09,-1.47,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,51343,2015-10-30 10:23:08:476,1446171788476.0 \n0.0527,0.7626,8.3258,0.2336,0.7722,9.7734,-0.0782,0.1723,-0.011,-2.6,-32.4,-42.5,3.081378794,-4.69,-1.75,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,51445,2015-10-30 10:23:08:578,1446171788578.0 \n-0.0431,1.4162,8.5138,0.2237,0.7184,9.7777,-0.0489,-0.0086,-0.1662,-2.9,-32.5,-42.5,3.070208687,-4.24,-1.28,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,51547,2015-10-30 10:23:08:680,1446171788680.0 \n-0.328,1.3012,9.4332,0.1925,0.7235,9.778,0.0293,0.0134,-0.1356,-2.8,-32.6,-42.5,3.070208687,-4.1,-1.17,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,51649,2015-10-30 10:23:08:782,1446171788782.0 \n-0.2705,1.2713,9.7049,0.1977,0.8912,9.7641,0.2382,0.1087,-0.1368,-2.4,-32.7,-42.4,3.106511536,-4.82,-1.32,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,51751,2015-10-30 10:23:08:884,1446171788884.0 \n-0.0467,0.5171,10.7691,0.1786,0.6978,9.7802,-0.0721,0.0623,-0.1002,-2.1,-32.8,-42,3.100402883,-4.08,-1.05,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,51854,2015-10-30 10:23:08:987,1446171788987.0 \n0.5686,0.8978,8.9735,0.2479,0.7135,9.7775,-0.2517,0.0293,-0.1307,-1.8,-32.9,-42,3.110874859,-4.64,-1.49,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,51956,2015-10-30 10:23:09:089,1446171789089.0 \n-0.4992,1.2043,8.4467,0.2284,0.563,9.7878,-0.171,0.033,-0.055,-1.4,-32.6,-42.2,3.140894522,-3.29,-1.34,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,52058,2015-10-30 10:23:09:191,1446171789191.0 \n-0.1305,1.2905,9.2009,0.1757,0.5883,9.7874,-0.0562,0.121,0.088,-1.2,-32.5,-42.4,3.13897466,-3.5,-1.26,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,52159,2015-10-30 10:23:09:292,1446171789292.0 \n-0.4908,1.1624,10.7248,0.0323,0.6897,9.7823,0.237,0.1417,0.3519,-1.3,-32.3,-42.8,3.12047417,-3.59,-0.51,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,52261,2015-10-30 10:23:09:394,1446171789394.0 \n-0.0263,0.9278,11.8058,-0.0408,0.7794,9.7755,0.0513,0.0611,0.2981,-1.4,-32.6,-42.5,3.10022835,-4.85,0.29,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,52363,2015-10-30 10:23:09:496,1446171789496.0 \n-0.6057,1.1109,9.6438,-0.0692,0.761,9.7768,0.1063,-0.1747,0.1491,-1.7,-32.7,-42.6,3.05903858,-4.27,0.61,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,52465,2015-10-30 10:23:09:598,1446171789598.0 \n-0.3843,0.7566,9.5864,0.044,0.7154,9.7804,-0.0782,0.0281,-0.0953,-2.2,-33.1,-42,3.083298657,-4.49,-0.37,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,52567,2015-10-30 10:23:09:700,1446171789700.0 \n-0.5926,1.3479,8.096,0.1106,0.8009,9.7733,0.0562,-0.0513,0.022,-2.6,-33,-42.2,3.05188273,-4.34,-0.45,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,52670,2015-10-30 10:23:09:803,1446171789803.0 \n-0.3891,0.899,10.8601,0.1925,0.7703,9.7745,-0.0965,-0.0709,-0.0489,-3.1,-33,-42.1,3.065670831,-4.67,-1.03,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,52771,2015-10-30 10:23:09:904,1446171789904.0 \n1.4437,1.3527,9.4846,0.2132,0.9178,9.7613,0.248,-0.2358,-0.1625,-3.4,-33.1,-42.2,3.069685088,-5.37,-1.25,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,52873,2015-10-30 10:23:10:006,1446171790006.0 \n-0.3292,-0.0431,12.2308,0.1872,0.6016,9.7864,0.0562,-0.1613,-0.2993,-3.4,-33.1,-42.1,3.07038322,-3.97,-1.17,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,52976,2015-10-30 10:23:10:109,1446171790109.0 \n-0.0934,0.8631,9.0633,0.2492,0.4903,9.7912,-0.2395,0.0183,-0.1833,-2.7,-32.8,-42.5,3.079109866,-3.52,-1.5,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,53077,2015-10-30 10:23:10:210,1446171790210.0 \n-0.1389,1.2474,9.1351,0.3438,0.371,9.7936,0.0892,-0.0709,-0.0208,-2.3,-32.2,-42.8,3.122044966,-2.03,-1.87,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,53180,2015-10-30 10:23:10:313,1446171790313.0 \n-0.0515,0.8739,9.4523,0.3617,0.5796,9.7828,0.2395,0.1319,-0.0061,-2.1,-31.7,-43.3,3.133564139,-2.96,-2.35,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,53281,2015-10-30 10:23:10:414,1446171790414.0 \n0.0551,0.5459,11.157,0.3568,0.8332,9.7647,0.3225,-0.0574,0.1087,-2.3,-31.8,-43.2,3.126059223,-4.26,-2.07,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,53383,2015-10-30 10:23:10:516,1446171790516.0 \n-0.5806,-0.1161,10.5381,0.3351,0.7433,9.7727,-0.4398,0.0049,-0.0892,-2.6,-32.5,-43,3.088360111,-4.35,-1.96,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,53486,2015-10-30 10:23:10:619,1446171790619.0 \n0.431,0.9708,8.4467,0.5022,0.5329,9.7793,-0.2541,-0.1197,-0.022,-2.8,-32.7,-42.9,3.100053817,-3.48,-2.32,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,53587,2015-10-30 10:23:10:720,1446171790720.0 \n0.0491,0.8056,8.764,0.4658,0.2931,9.7912,-0.2798,0.0819,-0.0648,-3.3,-32.2,-42.9,3.116459912,-1.8,-2.96,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,53689,2015-10-30 10:23:10:822,1446171790822.0 \n-0.6656,0.7314,9.6295,0.4198,0.2677,9.794,-0.0586,-0.0122,-0.0208,-3.5,-31.4,-43.3,3.102322745,-1.61,-2.43,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,53791,2015-10-30 10:23:10:924,1446171790924.0 \n-0.419,0.2502,11.9016,0.5525,0.4231,9.7819,0.3433,-0.1723,0.2932,-3.5,-31.1,-43.5,3.110176727,-1.86,-2.76,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,53893,2015-10-30 10:23:11:026,1446171791026.0 \n0.9888,0.7111,9.7803,0.7527,0.8415,9.7414,0.6976,-0.2028,0.3592,-3.9,-31.4,-43.1,3.096563159,-4.66,-3.67,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,53996,2015-10-30 10:23:11:129,1446171791129.0 \n-0.1353,0.8799,8.3546,0.7286,0.6572,9.7574,0.1173,0.0257,0.2859,-4.7,-32,-42.6,3.081553327,-3.73,-4.32,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,54097,2015-10-30 10:23:11:230,1446171791230.0 \n0.3484,0.9577,8.1044,0.7194,0.5279,9.766,0.0819,0.1478,0.672,-5.9,-32.3,-42,3.049090203,-3.06,-4.41,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,54200,2015-10-30 10:23:11:333,1446171791333.0 \n-0.164,1.1408,8.6491,0.7311,0.5167,9.7657,0.2224,-0.237,0.8112,-6.8,-31.9,-42,3.006678702,-2.9,-4.01,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,54301,2015-10-30 10:23:11:434,1446171791434.0 \n-0.3651,0.5399,10.7739,0.8914,0.5387,9.7512,0.0415,-0.1356,0.9285,-8.9,-31.3,-41.8,2.963918136,-3.15,-5.22,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,54403,2015-10-30 10:23:11:536,1446171791536.0 \n-0.3196,0.3208,9.8593,1.0757,0.8145,9.7134,0.4533,0.4728,1.1643,-10.9,-31.1,-41.4,2.92360103,-4.12,-6.65,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,54506,2015-10-30 10:23:11:639,1446171791639.0 \n-0.589,0.0192,9.8557,0.7979,0.8081,9.7407,0.0733,0.3372,1.135,-14,-30.7,-40.8,2.782054828,-4.81,-5.12,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,54607,2015-10-30 10:23:11:740,1446171791740.0 \n-1.2689,-0.2933,10.4387,0.4967,0.4746,9.7826,-0.3824,0.3018,0.9737,-15.9,-30,-40.5,2.68972691,-4.51,-4.31,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,54709,2015-10-30 10:23:11:842,1446171791842.0 \n-0.7195,0.097,8.7388,-0.0198,0.3037,9.8019,-0.044,0.4129,1.2193,-17.6,-27.8,-40.8,2.55847815,-1.9,-0.62,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,54811,2015-10-30 10:23:11:944,1446171791944.0 \n0.9242,0.2969,9.317,-0.4841,0.2501,9.7915,-0.0293,0.2651,1.0055,-18.5,-25.5,-41.6,2.45759812,-1.78,1.82,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,54913,2015-10-30 10:23:12:046,1446171792046.0 \n1.5646,0.4609,10.3226,-0.4011,0.2689,9.7948,0.099,-0.1344,0.2211,-19.1,-23.1,-42.6,2.38185083,-1.57,2.35,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,55016,2015-10-30 10:23:12:149,1446171792149.0 \n-0.7219,-1.0558,13.5823,-0.2405,-0.0544,9.8035,-0.6793,-0.044,-0.2761,-19.6,-21.9,-42.9,2.371902453,-0.35,1.43,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,55117,2015-10-30 10:23:12:250,1446171792250.0 \n-0.9457,-0.1736,8.3462,-0.158,-0.0078,9.8054,-0.4447,-0.0244,-0.2309,-20.2,-20.8,-43.2,2.358288885,-0.12,1.11,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,55219,2015-10-30 10:23:12:352,1446171792352.0 \n-0.6716,1.0582,7.841,-0.1874,-0.1947,9.8029,0.1564,0.1943,0.2114,-20.6,-19.8,-43.3,2.343104521,1.38,0.78,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,55322,2015-10-30 10:23:12:455,1446171792455.0 \n-0.6452,0.7207,9.754,-0.1987,-0.0592,9.8045,0.1161,-0.0929,0.1295,-20.6,-19.5,-43.3,2.299122224,0.64,1.12,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,55423,2015-10-30 10:23:12:556,1446171792556.0 \n-1.1588,0.1879,11.9375,-0.2817,0.326,9.7972,0.5852,-0.0257,0.4618,-20.6,-19.4,-43.1,2.261423112,-0.84,1.65,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,55525,2015-10-30 10:23:12:658,1446171792658.0 \n-0.8978,-0.6021,13.3872,-0.2338,0.3285,9.7984,-0.4618,0.2505,0.3128,-20.9,-19.8,-42.8,2.271371489,-1.92,1.37,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,55628,2015-10-30 10:23:12:761,1446171792761.0 \n-0.559,0.571,8.3653,-0.215,0.2162,9.8019,0.0929,-0.2346,0.4203,-21.2,-19.6,-42.8,2.280970799,-1.28,1.55,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,55730,2015-10-30 10:23:12:863,1446171792863.0 \n-0.4776,0.65,9.1159,-0.1703,0.0724,9.8049,0.0195,-0.1356,0.2407,-21.9,-18.8,-42.5,2.259154184,-0.42,1,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,55831,2015-10-30 10:23:12:964,1446171792964.0 \n-0.8056,0.7889,8.7831,-0.2496,0.2648,9.7999,0.1747,0.0171,0.1649,-22.6,-17.6,-42.5,2.182359697,-1.55,1.46,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,55933,2015-10-30 10:23:13:066,1446171793066.0 \n-0.7123,-0.0192,10.5728,-0.272,0.5014,9.79,0.314,0.0525,0.1955,-22.8,-17.5,-42.3,2.135759406,-2.33,1.57,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,56036,2015-10-30 10:23:13:169,1446171793169.0 \n-1.7071,-1.2677,13.2531,-0.2784,0.3384,9.7969,-0.452,-0.1185,-0.0819,-22.7,-17.9,-42.6,2.140995393,-3.5,1.32,36.814144,-119.74892,238.65,336.4908168,3.65,19.35484,172.38,17 / 17,56138,2015-10-30 10:23:13:271,1446171793271.0 \n0.6859,1.2091,7.3825,-0.3303,0.0402,9.801,-0.044,-0.2309,0.0782,-22.5,-17.7,-42.9,2.213252024,-0.33,2.33,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,56239,2015-10-30 10:23:13:372,1446171793372.0 \n-0.0802,1.0714,8.3582,-0.2914,-0.2989,9.7978,0.0941,0.0843,0.0134,-22.6,-16.7,-43.9,2.21656815,1.75,1.7,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,56341,2015-10-30 10:23:13:474,1446171793474.0 \n0.0778,1.1277,8.1439,-0.3393,-0.0841,9.8004,0.2517,0.044,0.055,-22.6,-15.8,-43.8,2.179741703,1.47,2,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,56444,2015-10-30 10:23:13:577,1446171793577.0 \n-0.146,0.158,11.1055,-0.4437,0.1587,9.7953,0.3763,0.1381,0.0354,-22.4,-15.5,-43.3,2.127207292,-0.22,2.5,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,56545,2015-10-30 10:23:13:678,1446171793678.0 \n0.9864,-0.3855,9.9407,-0.3863,0.4042,9.7907,-0.4239,-0.0757,-0.3067,-22.2,-16.1,-42.8,2.108183203,-2.42,2.49,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,56648,2015-10-30 10:23:13:781,1446171793781.0 \n0.7685,0.34,7.8769,-0.5529,0.3893,9.7833,0.4618,0.2162,-0.2004,-21.8,-17.2,-42.9,2.131919681,-2.27,3.23,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,56749,2015-10-30 10:23:13:882,1446171793882.0 \n0.3053,0.3651,8.7293,-0.7721,0.2802,9.7722,-0.1918,0.4374,-1.3134,-20.9,-18.5,-42.8,2.175727446,-1.64,4.52,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,56852,2015-10-30 10:23:13:985,1446171793985.0 \n-0.5076,0.8882,7.6303,-0.974,0.4658,9.747,0.0574,0.4166,-1.3011,-19.5,-19.7,-43.1,2.242922622,-2.55,5.19,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,56953,2015-10-30 10:23:14:086,1446171794086.0 \n-0.571,0.255,9.5457,-1.2213,0.5076,9.7171,0.1405,-0.0745,-1.4844,-14.9,-23.4,-43.7,2.371029789,-2.84,7.06,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,57056,2015-10-30 10:23:14:189,1446171794189.0 \n-0.0539,0.1604,8.1271,-1.3413,0.5153,9.7008,0.4459,0.3409,-1.1472,-12,-25.9,-42.7,2.511703327,-2.6,7.59,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,57157,2015-10-30 10:23:14:290,1446171794290.0 \n-0.2119,0.7398,6.5697,-1.437,-0.0806,9.7005,0.3067,0.3079,-0.7844,-9.3,-26.8,-43,2.634050907,0.47,8.43,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,57259,2015-10-30 10:23:14:392,1446171794392.0 \n0.2789,0.9026,10.3621,-1.0362,-0.2683,9.7481,-0.0122,0.1955,-0.8369,-7.6,-27.6,-43.4,2.737374399,0.8,5.69,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,57362,2015-10-30 10:23:14:495,1446171794495.0 \n-0.826,1.3587,8.2803,-0.9386,-0.2136,9.7593,0.0269,-0.1429,-0.661,-6.1,-27.7,-43.8,2.798984521,0.94,5.57,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,57463,2015-10-30 10:23:14:596,1446171794596.0 \n-1.0726,0.5315,10.3106,-0.8892,-0.205,9.7641,0.055,0.0134,-0.4276,-4.4,-27.5,-44.4,2.863212638,1.2,5.2,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,57565,2015-10-30 10:23:14:698,1446171794698.0 \n-0.8763,0.7302,12.3828,-0.9052,-0.2047,9.7626,0.3457,0.0941,0.0819,-3.4,-27.3,-44.5,2.905973205,1.55,4.92,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,57667,2015-10-30 10:23:14:800,1446171794800.0 \n-0.7925,0.103,11.0947,-0.7652,-0.2935,9.7723,-0.3323,-0.0977,0.0342,-2.7,-27.3,-44.2,2.911209192,1.31,4.66,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,57769,2015-10-30 10:23:14:902,1446171794902.0 \n-0.2705,0.3148,9.068,-0.4502,-0.1283,9.7955,0.0648,-0.1649,0.1258,-3.1,-27.3,-44.1,2.961649208,0.75,2.63,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,57872,2015-10-30 10:23:15:005,1446171795005.0 \n-0.243,0.8739,8.8286,-0.4204,0.018,9.7976,0.3433,-0.1466,0.0757,-3.6,-27.4,-44.1,2.92360103,0.49,2.69,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,57973,2015-10-30 10:23:15:106,1446171795106.0 \n-0.7027,0.4286,9.8581,-0.4753,0.1992,9.7931,0.2871,-0.1881,-0.0525,-4.2,-27.9,-43.7,2.919237707,-1.16,2.78,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,58075,2015-10-30 10:23:15:208,1446171795208.0 \n-0.8954,0.164,10.2699,-0.3628,0.4176,9.791,0.2896,0.0024,-0.088,-4.3,-28.5,-43.5,2.93372394,-1.96,2.13,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,58178,2015-10-30 10:23:15:311,1446171795311.0 \n-0.4525,-0.1113,11.0995,-0.373,0.3044,9.7948,-0.3567,0.2016,-0.204,-4.1,-29.5,-42.8,2.946464843,-2.4,1.83,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,58279,2015-10-30 10:23:15:412,1446171795412.0 \n-0.146,0.6201,7.3897,-0.3821,0.2509,9.796,-0.441,-0.1222,-0.1747,-4.1,-29.6,-42.8,2.946464843,-1.83,2.21,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,58382,2015-10-30 10:23:15:515,1446171795515.0 \n-0.1161,1.0211,7.8853,-0.2724,0.0194,9.8028,-0.0208,0.0061,-0.1051,-3.9,-29.2,-42.9,2.963918136,-0.11,1.59,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,58483,2015-10-30 10:23:15:616,1446171795616.0 \n0.3136,1.3216,8.8322,-0.2562,0.1274,9.8025,0.121,-0.2272,-0.0721,-3.6,-28.8,-43.3,2.948384705,-0.38,2.16,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,58586,2015-10-30 10:23:15:719,1446171795719.0 \n-0.5267,0.1353,11.9578,-0.1715,0.1955,9.8032,0.3176,-0.1881,0.0257,-3.5,-28.6,-43.7,3.001791781,-0.83,1.29,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,58687,2015-10-30 10:23:15:820,1446171795820.0 \n-0.2897,0.4334,9.2105,-0.223,0.3912,9.7963,0.121,0.1808,0.0977,-3.5,-29,-43.3,3.003013511,-2.31,1.07,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,58789,2015-10-30 10:23:15:922,1446171795922.0 \n-0.7123,0.3136,8.5629,-0.2045,0.224,9.802,-0.0244,-0.2248,0.0709,-3.5,-29.3,-42.8,2.992367003,-1.4,1.6,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,58891,2015-10-30 10:23:16:024,1446171796024.0 \n-1.002,0.1341,8.9112,-0.1105,0.0193,9.806,-0.0061,0.0257,-0.0709,-3.7,-29.3,-42.8,2.98922541,-0.14,0.59,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,58993,2015-10-30 10:23:16:126,1446171796126.0 \n-0.1736,1.0343,8.0278,-0.1803,0.1251,9.8042,0.1869,-0.055,-0.0501,-3.9,-28.9,-43,2.974739177,-0.73,1.05,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,59096,2015-10-30 10:23:16:229,1446171796229.0 \n-0.5722,0.899,9.0106,-0.1974,0.2442,9.8016,0.0648,0.0684,-0.0806,-3.9,-29,-43.2,2.972295716,-1.21,1.07,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,59197,2015-10-30 10:23:16:330,1446171796330.0 \n0.0515,0.8619,9.7444,-0.1358,0.2951,9.8013,0.3189,0.0721,0.033,-3.8,-29.4,-43.3,2.977182638,-1.72,0.79,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,59300,2015-10-30 10:23:16:433,1446171796433.0 \n-0.091,-0.0611,11.327,-0.0231,0.2463,9.8035,-0.3726,0.1466,-0.3567,-3.7,-29.8,-43,2.999871918,-2.78,-0.03,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,59401,2015-10-30 10:23:16:534,1446171796534.0 \n-0.7171,0.243,8.333,-0.0134,0.2545,9.8033,0.1246,-0.0318,-0.0476,-3.6,-29.9,-43.1,2.99760299,-1.38,0.26,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,59503,2015-10-30 10:23:16:636,1446171796636.0 \n-0.4429,0.7697,8.6574,0.0878,0.1998,9.8042,0.1271,-0.0867,0.3274,-3.6,-29.8,-42.9,3.015230816,-0.97,-0.38,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,59605,2015-10-30 10:23:16:738,1446171796738.0 \n0.1808,1.1552,8.4372,0.1812,0.2274,9.8023,0.0599,-0.3482,0.3201,-3.9,-29.6,-43,3.02325933,-1.26,-0.73,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,59708,2015-10-30 10:23:16:841,1446171796841.0 \n-0.1209,0.5088,11.9938,0.2913,0.1975,9.8003,0.3115,-0.1405,0.2993,-5.1,-29.5,-42.5,3.008249499,-1.19,-1.67,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,59809,2015-10-30 10:23:16:942,1446171796942.0 \n-0.4334,-0.4705,13.72,0.3582,0.3371,9.7943,-0.1405,-0.1136,0.204,-6.4,-29.6,-42.7,2.987480081,-1.97,-2.09,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,59912,2015-10-30 10:23:17:045,1446171797045.0 \n0.261,1.0654,7.6938,0.3284,0.096,9.8007,-0.0098,-0.0428,0.1588,-7.1,-29.3,-42.8,2.955540555,-0.46,-2.14,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,60013,2015-10-30 10:23:17:146,1446171797146.0 \n0.012,0.2945,8.7293,0.3531,-0.0957,9.7998,-0.0171,0.0794,0.0086,-7.9,-28.7,-43.4,2.930582347,0.47,-2.28,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,60116,2015-10-30 10:23:17:249,1446171797249.0 \n0.2682,0.8847,8.1977,0.3072,0.0543,9.8017,0.3103,0.0415,0.1258,-8.2,-28.1,-43.4,2.911907324,0.25,-1.87,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,60217,2015-10-30 10:23:17:350,1446171797350.0 \n-0.2933,-0.1161,10.8374,0.3054,0.2745,9.798,0.2175,-0.0134,-0.1588,-8.3,-28.2,-43,2.898991888,-1.17,-1.71,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,60320,2015-10-30 10:23:17:453,1446171797453.0 \n0.9014,0.6428,8.843,0.3344,0.3846,9.7934,-0.5938,-0.0476,-0.4679,-8.2,-28.8,-42.6,2.904926007,-2.55,-1.96,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,60422,2015-10-30 10:23:17:555,1446171797555.0 \n-0.1784,-0.31,10.1574,0.1299,-0.0987,9.8053,-0.3897,0.5205,-0.2981,-7.7,-29,-42.6,2.908940264,0.96,-1.27,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,60523,2015-10-30 10:23:17:656,1446171797656.0 \n-0.5088,0.1508,9.2799,0.15,-0.1647,9.8041,-0.1539,0.0733,-0.0354,-6.8,-28.8,-43.3,2.931455012,0.96,-0.88,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,60626,2015-10-30 10:23:17:759,1446171797759.0 \n0.1736,1.2234,8.1235,0.0909,-0.1085,9.8056,0.0586,0.0257,0.0061,-6.2,-28.2,-43.9,2.952049897,0.73,-0.68,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,60727,2015-10-30 10:23:17:860,1446171797860.0 \n-0.2322,0.2813,10.969,0.1069,-0.1288,9.8052,-0.0745,-0.0562,-0.1161,-5.9,-28,-44.4,2.951351765,0.54,-0.68,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,60829,2015-10-30 10:23:17:962,1446171797962.0 \n0.1915,0.9481,9.2213,-0.0053,0.1172,9.8059,0.5229,0.1319,0.2651,-5.7,-28.1,-44.3,2.925695425,-0.68,0.03,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,60932,2015-10-30 10:23:18:065,1446171798065.0 \n-1.2007,-0.5267,11.5532,0.0997,0.1094,9.8055,0.0305,0.193,0.0965,-5.7,-28.4,-43.8,2.950130035,-0.62,-0.87,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,61033,2015-10-30 10:23:18:166,1446171798166.0 \n0.1484,0.1448,8.7724,0.2836,0.1214,9.8018,-0.2871,0.1955,-0.0281,-6,-28.8,-43.5,2.976135441,-0.71,-1.66,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,61135,2015-10-30 10:23:18:268,1446171798268.0 \n-0.8404,0.419,9.5481,0.1595,-0.0564,9.8052,-0.0635,0.022,0.0513,-6.4,-28.7,-43.6,2.966361597,0.22,-1.08,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,61238,2015-10-30 10:23:18:371,1446171798371.0 \n-0.5004,0.65,10.744,0.078,0.1437,9.8053,-0.0134,0.0342,-0.0098,-6.7,-28.6,-43.6,2.911209192,-0.84,-0.46,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,61340,2015-10-30 10:23:18:473,1446171798473.0 \n-0.2286,0.2478,10.3765,0.0269,0.4014,9.7984,0.3115,-0.0501,-0.1136,-6.6,-28.5,-43.4,2.88956711,-1.69,-0.16,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,61441,2015-10-30 10:23:18:574,1446171798574.0 \n0.316,0.0168,10.8146,0.0197,0.4666,9.7955,-0.0623,0.1026,-0.1796,-6.3,-29.4,-42.9,2.925346359,-2.73,-0.12,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,61544,2015-10-30 10:23:18:677,1446171798677.0 \n0.4549,0.6524,8.175,-0.0829,0.1616,9.805,-0.055,0.077,-0.1869,-5.8,-29.7,-43.2,2.931455012,-1.21,0.27,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,61645,2015-10-30 10:23:18:778,1446171798778.0 \n-0.2753,0.9517,8.0493,-0.1514,-0.0698,9.8052,-0.0574,0.0354,0.0672,-4.9,-29.5,-43.5,2.955366022,0.27,0.67,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,61747,2015-10-30 10:23:18:880,1446171798880.0 \n0.0934,1.1887,8.7137,-0.1298,-0.0482,9.8057,0.0843,-0.0464,0.1454,-4.4,-28.9,-44.1,2.983116758,0.53,0.91,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,61849,2015-10-30 10:23:18:982,1446171798982.0 \n-0.5914,0.1963,11.552,-0.0597,0.1416,9.8054,0.171,0.0428,0.0867,-4.3,-28.6,-44,2.99638126,-0.35,0.27,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,61952,2015-10-30 10:23:19:085,1446171799085.0 \n-0.4094,-0.316,12.8844,-0.0364,0.316,9.8015,-0.3665,-0.1271,-0.0171,-4.6,-29,-43.3,2.956762286,-1.85,0.21,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,62053,2015-10-30 10:23:19:186,1446171799186.0 \n-0.5698,0.4046,8.6802,-0.0632,0.2196,9.804,0.1662,0.0843,0.1515,-4.8,-29.2,-43,2.955540555,-1.28,0.37,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,62156,2015-10-30 10:23:19:289,1446171799289.0 \n-1.0415,0.1496,8.6119,0.0068,0.1333,9.8057,-0.2443,0.1564,-0.0195,-5,-29.4,-42.9,2.970899453,-1.07,-0.19,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,62257,2015-10-30 10:23:19:390,1446171799390.0 \n-0.2502,1.0798,7.8769,0.0113,0.1939,9.8047,0.1674,0.0867,0.1967,-5.4,-29.1,-43,2.969677722,-0.92,-0.12,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,62359,2015-10-30 10:23:19:492,1446171799492.0 \n-0.0012,0.5926,10.9571,-0.0343,0.2394,9.8037,0.1772,-0.2553,-0.0599,-5.7,-29,-43,2.924997293,-1.4,0.2,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,62461,2015-10-30 10:23:19:594,1446171799594.0 \n0.4334,0.4944,10.1359,0.1408,0.3624,9.7989,0.0415,0.0147,-0.0794,-5.8,-29.2,-42.5,2.93372394,-2.15,-0.3,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,62564,2015-10-30 10:23:19:697,1446171799697.0 \n-0.3196,-0.6464,11.9985,0.165,-0.0356,9.8052,-0.6158,0.1197,-0.2908,-5.9,-29.1,-42.5,2.962347339,-0.82,-1.16,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,62665,2015-10-30 10:23:19:798,1446171799798.0 \n0.1736,0.1867,7.4005,0.1415,-0.2049,9.8035,-0.3836,0.088,0.0367,-5.8,-28.8,-42.7,2.968630525,0.8,-1.1,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,62768,2015-10-30 10:23:19:901,1446171799901.0 \n-0.0443,0.668,8.9615,0.1111,-0.3213,9.8008,-0.0061,0,0.1478,-5.7,-28,-43.3,2.957460418,2.11,-0.66,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,62869,2015-10-30 10:23:20:002,1446171800002.0 \n-0.1269,0.2502,10.8386,0.0054,-0.0454,9.8065,0.2272,0.0428,0.1026,-5.5,-27.1,-43.7,2.966187064,0.79,-0.14,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,62971,2015-10-30 10:23:20:104,1446171800104.0 \n-0.0766,1.0139,9.2596,-0.1258,0.3711,9.7988,0.5828,0.0489,0.226,-5.5,-27.3,-43.9,2.938087263,-0.81,0.58,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,63073,2015-10-30 10:23:20:206,1446171800206.0 \n-0.6764,0.3579,9.5014,-0.1803,0.1747,9.8034,-0.055,0.088,0.0867,-5.4,-28.1,-43.5,2.939832592,-1.81,0.6,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,63175,2015-10-30 10:23:20:308,1446171800308.0 \n0.1808,0.4609,9.013,0.0573,0.1274,9.8057,-0.088,-0.4508,-0.0269,-5.4,-28.4,-43.5,2.949955502,-0.98,0.39,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,63278,2015-10-30 10:23:20:411,1446171800411.0 \n-0.6428,0.6357,9.3948,0.0352,-0.0117,9.8066,0.0794,0.0183,0.066,-5.6,-28,-43.9,2.940356191,0.4,-0.29,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,63379,2015-10-30 10:23:20:512,1446171800512.0 \n-0.4178,1.075,8.1594,-0.0326,0.1795,9.805,0.0757,0.0134,-0.0819,-5.7,-27.8,-44,2.922553832,-0.88,0.1,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,63481,2015-10-30 10:23:20:614,1446171800614.0 \n-0.4034,0.3376,10.0137,0.021,0.2864,9.8024,0.0953,-0.0916,-0.1698,-5.7,-28,-44,2.924124629,-1.37,-0.06,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,63583,2015-10-30 10:23:20:716,1446171800716.0 \n0.2897,-0.3663,11.1749,0.0755,0.1095,9.8057,-0.6426,0.193,-0.4093,-5.6,-28.2,-43.7,2.938087263,-1.61,-0.63,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,63685,2015-10-30 10:23:20:818,1446171800818.0 \n0.0108,-0.0096,8.7568,0.0959,-0.0622,9.806,-0.2382,-0.1429,-0.1246,-5.2,-28,-44,2.974739177,0.18,-0.34,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,63788,2015-10-30 10:23:20:921,1446171800921.0 \n0.3148,0.3843,8.8921,0.1107,-0.2578,9.8026,-0.2101,0.0611,0.1136,-4.9,-27.1,-44.4,2.982942225,1.51,-0.65,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,63890,2015-10-30 10:23:21:023,1446171801023.0 \n0.146,0.9996,7.8602,0.0895,-0.2418,9.8033,0.2309,0.0721,0.2285,-4.8,-26.6,-44.5,2.979277033,1.41,-0.52,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,63991,2015-10-30 10:23:21:124,1446171801124.0 \n-0.085,0.243,12.3301,0.0173,0.0188,9.8066,0.2688,0.0098,0.2578,-5.1,-26.4,-44.4,2.957111352,0.35,-0.13,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,64093,2015-10-30 10:23:21:226,1446171801226.0 \n-0.0814,-0.0431,10.058,-0.1553,0.3928,9.7976,-0.4142,0.1014,0.2101,-5.2,-27,-43.9,2.929360617,-1.84,0.66,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,17 / 17,64196,2015-10-30 10:23:21:329,1446171801329.0 \n-0.4776,0.4836,8.6586,-0.184,0.2501,9.8017,0.1124,-0.182,0.2859,-5.3,-27.7,-43.6,2.928138886,-1.46,1.08,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,16 / 16,64297,2015-10-30 10:23:21:430,1446171801430.0 \n-0.4944,-0.0599,9.7264,0.0254,0.0846,9.8063,-0.1246,0.0354,-0.0342,-5.5,-28,-43.5,2.962521872,-1.04,-0.1,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,16 / 16,64399,2015-10-30 10:23:21:532,1446171801532.0 \n-0.4836,0.814,8.6503,-0.0264,0.0643,9.8064,0.2126,0.1124,0.0415,-5.9,-27.6,-44,2.931804078,-0.22,-0.1,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,16 / 16,64501,2015-10-30 10:23:21:634,1446171801634.0 \n-0.5387,0.7685,10.3465,-0.0433,0.1938,9.8046,0.0745,-0.0281,-0.0305,-5.9,-27.4,-43.9,2.907544001,-0.93,0.35,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,16 / 16,64604,2015-10-30 10:23:21:737,1446171801737.0 \n-0.4705,0.3005,10.0197,-0.0319,0.3953,9.7986,0.2602,0.1698,-0.1527,-5.6,-27.7,-43.9,2.911383725,-2.31,0.19,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,16 / 16,64705,2015-10-30 10:23:21:838,1446171801838.0 \n-0.4274,0.249,8.4707,-0.1286,0.4781,9.7941,-0.4972,0.0684,-0.2053,-5.3,-28.4,-43.6,2.944544981,-3.78,0,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,16 / 16,64808,2015-10-30 10:23:21:941,1446171801941.0 \n-0.3831,0.1006,8.8992,-0.0703,0.1243,9.8056,-0.3299,-0.0342,-0.1845,-4.6,-28.8,-43.2,2.965314399,-1.23,0,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,16 / 16,64909,2015-10-30 10:23:22:042,1446171802042.0 \n-0.1341,0.9206,8.5533,-0.2294,-0.1577,9.8027,-0.1979,0.1674,0.1649,-3.9,-28.2,-43.3,2.976484506,0.77,1.02,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,16 / 16,65012,2015-10-30 10:23:22:145,1446171802145.0 \n0.0299,0.9697,8.6718,-0.1638,-0.0566,9.8051,0.0159,-0.0843,0.0428,-3.6,-27.7,-43.6,2.971423052,0.46,1.14,36.81403,-119.74887,238.97,336.4908168,3.53,19.35484,122.89,16 / 16,65114,2015-10-30 10:23:22:247,1446171802247.0 \n-0.3077,0.8092,12.2547,-0.0632,0.0591,9.8063,0.3738,-0.121,0.1442,-3.8,-27.5,-43.9,2.982767692,-0.35,0.37,36.81392,-119.748886,244.28,336.4908168,4.19,19.35484,183.91,16 / 16,65215,2015-10-30 10:23:22:348,1446171802348.0 \n0.2562,0.0622,11.716,-0.0382,0.1257,9.8058,-0.2101,-0.0513,0.0024,-4.1,-28,-43.6,2.983116758,-1.56,0.37,36.81392,-119.748886,244.28,336.4908168,4.19,19.35484,183.91,16 / 16,65318,2015-10-30 10:23:22:451,1446171802451.0 \n-0.2478,0.2334,9.2117,0.0653,0.1028,9.8059,0.1161,-0.4569,-0.0012,-4.5,-28.3,-43.5,3.007551367,-0.6,-0.38,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,65419,2015-10-30 10:23:22:552,1446171802552.0 \n-0.6536,-0.0551,9.3685,0.0997,-0.0547,9.806,-0.2224,0.1515,-0.033,-4.8,-28.4,-43.7,2.98625835,-0.28,-0.85,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,65521,2015-10-30 10:23:22:654,1446171802654.0 \n-0.0838,0.583,7.6507,0.0461,-0.0014,9.8065,0.1295,-0.1234,0.0794,-5.1,-27.8,-44.1,2.981720494,0.88,-0.49,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,65623,2015-10-30 10:23:22:756,1446171802756.0 \n-0.6524,0.255,10.058,-0.0301,0.1805,9.8049,0.1271,-0.0965,-0.1967,-5.2,-27.9,-44.1,2.953271627,-0.82,0.28,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,65725,2015-10-30 10:23:22:858,1446171802858.0 \n0.589,0.3567,8.7592,-0.0735,0.5231,9.7924,-0.0086,-0.1539,-0.3384,-4.8,-28.6,-43.5,2.948559238,-2.31,0.44,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,65828,2015-10-30 10:23:22:961,1446171802961.0 \n0.0467,0.5327,9.8354,-0.1209,0.2093,9.8037,0.1075,-0.1344,0.0037,-4,-29.5,-42.9,2.981720494,-1.22,0.71,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,65929,2015-10-30 10:23:23:062,1446171803062.0 \n0.0275,0.7159,9.1614,-0.0759,0.0292,9.8063,-0.518,0.0513,-0.0574,-3.5,-29.6,-42.8,3.03041518,-0.17,0.44,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,66031,2015-10-30 10:23:23:164,1446171803164.0 \n-0.316,0.6488,9.9479,-0.0923,-0.1213,9.8055,-0.0037,0.0281,0.1161,-3.3,-29.1,-43,3.025353725,0.47,0.57,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,66133,2015-10-30 10:23:23:266,1446171803266.0 \n-0.2538,0.4262,9.7719,-0.1075,0.1289,9.8052,0.1576,0.0342,0.121,-3.5,-28.6,-43.4,3.020117738,-0.75,0.63,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,66236,2015-10-30 10:23:23:369,1446171803369.0 \n-0.073,0.6189,10.6757,0.0059,0.4447,9.7966,0.3934,-0.2138,0.193,-3.6,-28.8,-43,2.988003679,-2.12,0.32,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,66337,2015-10-30 10:23:23:470,1446171803470.0 \n-1.2175,-0.7003,12.0799,0.0625,0.1717,9.8049,-0.237,0.3396,0.1625,-4.2,-29.4,-42.5,3.01907054,-1.71,-0.8,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,66439,2015-10-30 10:23:23:572,1446171803572.0 \n-0.2179,0.5423,8.3881,-0.0501,0.1175,9.8058,-0.1747,0.0965,0.2065,-4.8,-29.6,-42.1,2.970201321,-0.96,0.1,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,66541,2015-10-30 10:23:23:674,1446171803674.0 \n-0.1269,0.7673,9.1375,-0.0469,0.0778,9.8062,0.0159,-0.0171,0.1625,-5.4,-29.3,-42.3,2.961300142,-0.43,0.31,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,66644,2015-10-30 10:23:23:777,1446171803777.0 \n-0.8116,0.8571,9.432,-0.1816,0.2244,9.8024,0.0391,0.0745,-0.0794,-5.8,-28.9,-42.5,2.907893067,-1.25,0.93,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,66746,2015-10-30 10:23:23:879,1446171803879.0 \n0.0359,0.3962,11.1534,-0.0621,0.3878,9.7988,0.2615,-0.16,-0.077,-5.9,-29,-42.5,2.910336528,-1.76,0.72,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,66847,2015-10-30 10:23:23:980,1446171803980.0 \n0.1508,0.1808,10.0724,0.0661,0.5993,9.7881,0.2676,-0.1686,-0.0232,-6.3,-29.6,-42,2.93494567,-3.61,-0.38,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,66949,2015-10-30 10:23:24:082,1446171804082.0 \n0.1616,0.6333,8.2995,0.0344,0.4355,9.7969,-0.066,0.0012,-0.1564,-6.6,-30.1,-41.8,2.902482546,-2.55,-0.2,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,67052,2015-10-30 10:23:24:185,1446171804185.0 \n-0.1963,0.929,8.7281,-0.0649,0.2211,9.8039,0.0367,0.1698,-0.0464,-6.5,-30,-42,2.933025808,-1.65,0.13,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,67153,2015-10-30 10:23:24:286,1446171804286.0 \n0.0204,1.5155,8.4551,-0.2336,0.3001,9.7993,0.0464,0.0428,-0.1173,-6.1,-29.5,-42.7,2.897246558,-1.62,1.24,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,67255,2015-10-30 10:23:24:388,1446171804388.0 \n-0.5279,0.6009,10.9056,-0.3187,0.3368,9.7957,0.0415,0.1454,-0.1026,-5.6,-29.5,-43.1,2.884854721,-1.85,1.66,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,67358,2015-10-30 10:23:24:491,1446171804491.0 \n0.5722,0.8511,9.5325,-0.3497,0.5208,9.7866,-0.1173,-0.2468,0.0648,-5.2,-29.6,-42.8,2.911383725,-2.68,2.07,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,67459,2015-10-30 10:23:24:592,1446171804592.0 \n-0.5207,0.7386,8.5677,-0.2436,0.279,9.7997,-0.0073,-0.1881,0.0391,-5,-29.6,-42.5,2.934771137,-1.63,1.42,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,67561,2015-10-30 10:23:24:694,1446171804694.0 \n-0.1963,0.4585,8.078,-0.1032,0.1613,9.8048,-0.1454,-0.0782,0.0904,-5.2,-29.4,-42.6,2.946813909,-1.39,0.69,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,67663,2015-10-30 10:23:24:796,1446171804796.0 \n-0.4262,1.336,7.7608,-0.1169,0.1354,9.805,0.1417,0.1185,0.0684,-5.8,-28.7,-43.2,2.92360103,-0.42,0.47,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,67765,2015-10-30 10:23:24:898,1446171804898.0 \n-0.5686,0.899,10.422,-0.1686,0.1269,9.8044,0.1466,-0.0855,-0.066,-6.1,-28.5,-43.3,2.901435349,-0.75,0.96,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,67868,2015-10-30 10:23:25:001,1446171805001.0 \n0.0742,-0.2646,10.9427,-0.0572,0.3586,9.7999,0.3115,-0.0635,-0.0648,-6.3,-28.4,-43.3,2.901260816,-1.98,0.66,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,67969,2015-10-30 10:23:25:102,1446171805102.0 \n-0.3974,-0.577,10.5453,-0.1664,0.2278,9.8026,-0.0086,-0.0305,0.0049,-6.2,-28.8,-43.2,2.906496803,-1.39,0.92,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,68071,2015-10-30 10:23:25:204,1446171805204.0 \n0.1999,0.3077,9.2955,-0.0593,0.2012,9.8044,-0.121,-0.1503,-0.0965,-6,-29,-42.8,2.922553832,-1.18,0.35,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,68174,2015-10-30 10:23:25:307,1446171805307.0 \n-0.2562,1.0798,7.9045,-0.0572,0.1921,9.8046,0.1393,-0.0086,-0.066,-5.9,-28.8,-43.1,2.92656809,-0.88,0.25,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,68275,2015-10-30 10:23:25:408,1446171805408.0 \n0.0407,1.2546,9.1662,-0.063,0.2934,9.8021,0.0635,0.0367,-0.0183,-5.8,-28.9,-43.1,2.920459437,-1.55,0.34,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,68377,2015-10-30 10:23:25:510,1446171805510.0 \n-0.2322,1.3455,10.574,-0.012,0.5038,9.7937,0.3592,0.0916,0.1063,-5.7,-29.2,-43.1,2.919063174,-2.95,0.07,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,68479,2015-10-30 10:23:25:612,1446171805612.0 \n-1.1863,0.0215,11.7268,-0.0917,0.5691,9.7897,-0.1185,0.0342,0.1014,-5.5,-29.7,-42.7,2.944544981,-3.85,0.53,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,68581,2015-10-30 10:23:25:714,1446171805714.0 \n-0.2765,0.5363,8.5461,0.0221,0.403,9.7983,-0.1381,-0.2309,0.1258,-5.6,-30,-42.5,2.932153143,-2.79,-0.09,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,68684,2015-10-30 10:23:25:817,1446171805817.0 \n0.0168,0.6883,8.1032,0.0019,0.218,9.8042,-0.1491,-0.0171,0.0696,-5.8,-30,-42.5,2.936341934,-1.45,0.03,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,68786,2015-10-30 10:23:25:919,1446171805919.0 \n-0.1209,1.4724,7.2736,-0.0887,0.2662,9.8026,0.0684,0.0134,-0.1051,-6,-29.5,-42.8,2.919586773,-1.16,0.47,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,68888,2015-10-30 10:23:26:021,1446171806021.0 \n-0.5746,0.2011,12.2188,-0.0055,0.3952,9.7987,0.121,-0.1735,-0.0806,-6.2,-29.3,-43.4,2.918365042,-2.09,0.3,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,68989,2015-10-30 10:23:26:122,1446171806122.0 \n-0.9098,-0.7171,11.7017,0.014,0.4735,9.7952,-0.1161,-0.0867,-0.0965,-6.1,-29.6,-43.2,2.931804078,-2.77,-0.08,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,69092,2015-10-30 10:23:26:225,1446171806225.0 \n0.7326,0.6716,8.6479,0.0284,0.3831,9.7991,0.0953,-0.0562,0.1148,-6.2,-29.7,-43.2,2.93197861,-1.96,0.09,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,69193,2015-10-30 10:23:26:326,1446171806326.0 \n-0.0431,1.1301,7.4711,0.043,0.2126,9.8043,-0.066,0.1576,-0.0049,-6.3,-29.6,-43.3,2.944195915,-1.24,-0.25,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,69295,2015-10-30 10:23:26:428,1446171806428.0 \n-0.3627,1.1875,8.5042,-0.0237,0.1979,9.8046,0.0538,-0.0257,0.0623,-6.4,-29.2,-43.6,2.927615287,-0.96,0.18,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,69397,2015-10-30 10:23:26:530,1446171806530.0 \n-0.5543,0.5686,11.4766,-0.0897,0.3566,9.7998,0.1808,0.0281,0.1417,-6.4,-29,-43.7,2.915048917,-1.77,0.48,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,69499,2015-10-30 10:23:26:632,1446171806632.0 \n-0.7003,1.1648,9.6211,-0.191,0.6162,9.7854,-0.1136,-0.1576,0.2224,-6.3,-29.3,-43.5,2.890090708,-3.35,1.06,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,69601,2015-10-30 10:23:26:734,1446171806734.0 \n-0.1341,0.8056,9.3218,-0.0959,0.5051,9.7932,0.0086,-0.022,0.3238,-6.6,-29.7,-43.1,2.880316865,-2.95,0.56,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,69703,2015-10-30 10:23:26:836,1446171806836.0 \n-0.0431,0.4381,9.0549,0.0823,0.452,9.7959,-0.2199,0.0611,0.0159,-7.5,-29.9,-42.8,2.908940264,-2.88,-0.55,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,69805,2015-10-30 10:23:26:938,1446171806938.0 \n-0.4166,0.9002,8.8849,-0.0023,0.3868,9.799,0.1136,0.1723,-0.0574,-8.1,-29.5,-42.7,2.860420111,-2.28,-0.17,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,69908,2015-10-30 10:23:27:041,1446171807041.0 \n-1.0798,0.9301,10.0449,-0.1384,0.4697,9.7944,0.0244,0.0782,-0.2065,-8.4,-29.4,-42.7,2.832145777,-2.75,0.81,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,70009,2015-10-30 10:23:27:142,1446171807142.0 \n0.2263,-0.0012,11.1725,-0.1265,0.5627,9.7897,0.0806,0.0464,-0.1857,-7.7,-29.5,-42.6,2.827782454,-3.26,0.8,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,70112,2015-10-30 10:23:27:245,1446171807245.0 \n-0.1053,0.0706,10.1742,-0.2357,0.4198,9.7948,0.055,0.0244,-0.1002,-7.2,-29.6,-42.4,2.871590218,-2.59,1.05,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,70213,2015-10-30 10:23:27:346,1446171807346.0 \n-0.3962,0.0802,10.5201,-0.1139,0.1554,9.8048,-0.2028,0.0953,-0.1784,-6.5,-29.5,-42.6,2.915921581,-0.91,0.67,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,70316,2015-10-30 10:23:27:449,1446171807449.0 \n-0.6847,1.0475,7.695,-0.2242,0.0597,9.8039,-0.0489,0.0867,-0.1283,-6,-29,-43,2.906671336,-0.44,1.15,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,70418,2015-10-30 10:23:27:551,1446171807551.0 \n-0.7374,0.8751,9.3733,-0.2127,0.1239,9.8036,0.0012,0.0049,-0.1087,-5.6,-28.5,-43.3,2.893930433,-0.51,1.31,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,70520,2015-10-30 10:23:27:653,1446171807653.0 \n-0.571,1.2737,10.4291,-0.2651,0.3357,9.7973,0.3262,0.1429,0.2749,-5.4,-28.2,-43.5,2.922553832,-1.14,1.39,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,70621,2015-10-30 10:23:27:754,1446171807754.0 \n-0.923,-0.899,13.362,-0.1529,0.3094,9.8006,-0.2883,-0.3201,-0.011,-5.4,-28.5,-43.2,2.918539575,-2.38,1.26,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,70723,2015-10-30 10:23:27:856,1446171807856.0 \n-0.1389,0.5207,8.4252,0.0256,0.3022,9.802,-0.033,-0.3042,0.0843,-5.9,-28.8,-43.1,2.914350785,-1.96,0.49,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,70825,2015-10-30 10:23:27:958,1446171807958.0 \n-0.3472,0.5483,8.3845,0.1053,0.1244,9.8053,-0.0367,-0.1136,0.0501,-6.7,-28.8,-43,2.90928933,-0.81,-0.38,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,70928,2015-10-30 10:23:28:061,1446171808061.0 \n-0.5483,0.9254,8.521,0.0995,0.1005,9.8056,-0.0061,0.0098,-0.0195,-7.2,-28.4,-43,2.906671336,-0.69,-0.57,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,71029,2015-10-30 10:23:28:162,1446171808162.0 \n-0.65,0.237,12.2248,0.1132,0.1745,9.8044,0.1136,-0.1552,-0.1026,-7.5,-28.1,-43,2.907194935,-1.02,-0.66,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,71131,2015-10-30 10:23:28:264,1446171808264.0 \n1.0989,0.2717,10.5093,0.1214,0.4182,9.797,-0.1344,0.0489,-0.2199,-7.6,-28.3,-42.9,2.863561704,-2.65,-0.78,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,71233,2015-10-30 10:23:28:366,1446171808366.0 \n0.7614,0.1101,8.6119,0.1244,0.3663,9.799,-0.0501,-0.0391,-0.0745,-7.4,-28.8,-42.8,2.909987462,-2.14,-0.73,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,71335,2015-10-30 10:23:28:468,1446171808468.0 \n-0.0431,0.3304,8.8597,0.114,0.2056,9.8038,-0.2004,0.0476,-0.0831,-7.3,-28.8,-42.7,2.914699851,-1.57,-0.77,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,71438,2015-10-30 10:23:28:571,1446171808571.0 \n-0.2634,1.2881,8.2181,0.0333,0.1587,9.8053,-0.0696,0.066,0.011,-6.9,-28.5,-43.3,2.895675762,-0.93,-0.19,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,71539,2015-10-30 10:23:28:672,1446171808672.0 \n-0.5375,0.9625,10.3549,-0.0596,0.1778,9.8049,0.1063,0.1943,0.0586,-6.8,-28.2,-43.3,2.890265241,-0.96,0.01,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,71642,2015-10-30 10:23:28:775,1446171808775.0 \n-0.0982,1.1289,12.5923,-0.1359,0.2968,9.8012,0.1234,-0.0305,0.193,-6.4,-28.2,-43.3,2.899340953,-1.73,0.79,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,71743,2015-10-30 10:23:28:876,1446171808876.0 \n-1.3515,-0.2478,11.1282,-0.2489,0.4029,9.7952,0.0623,0.0428,0.1747,-6.2,-28.4,-43,2.883283924,-2.2,1.28,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,71845,2015-10-30 10:23:28:978,1446171808978.0 \n0.0551,0.2023,8.8681,-0.1127,0.4827,9.7941,-0.3384,-0.1662,0.022,-6.2,-28.9,-42.9,2.904227875,-2.82,0.66,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,71948,2015-10-30 10:23:29:081,1446171809081.0 \n-0.401,1.0906,8.4575,-0.0401,0.3561,9.8001,0.0122,0.0012,-0.0379,-6.7,-28.8,-42.9,2.883458457,-2.09,0.31,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,72050,2015-10-30 10:23:29:183,1446171809183.0 \n-0.6943,0.9673,9.8114,-0.0295,0.4207,9.7976,0.044,-0.0342,-0.0929,-7.1,-28.8,-42.7,2.88660005,-2.31,0.13,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,72151,2015-10-30 10:23:29:284,1446171809284.0 \n-1.002,0.656,11.9207,-0.1716,0.4668,9.794,-0.1258,0.3677,-0.1063,-7.3,-28.8,-42.9,2.861292776,-2.73,1,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,72253,2015-10-30 10:23:29:386,1446171809386.0 \n-1.3408,-1.2965,12.639,-0.3297,0.3178,9.796,-0.4325,0.3286,-0.1454,-6.9,-28.8,-43,2.841221489,-2.75,1.78,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,72355,2015-10-30 10:23:29:488,1446171809488.0 \n0.091,-0.3256,11.6574,-0.3614,0.001,9.8,-0.0941,-0.1784,-0.0257,-5.8,-28.1,-43.7,2.859198381,-0.8,2.54,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,72458,2015-10-30 10:23:29:591,1446171809591.0 \n-0.1041,0.8667,7.3287,-0.4111,-0.0974,9.7975,0.0757,0.0049,0.0147,-5.2,-27.5,-44,2.899864552,0.78,2.36,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,72559,2015-10-30 10:23:29:692,1446171809692.0 \n-0.079,1.2186,9.2644,-0.3105,-0.028,9.8017,0.0367,-0.0782,-0.0525,-4.8,-26.9,-44.8,2.909114797,0.16,1.81,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,72661,2015-10-30 10:23:29:794,1446171809794.0 \n-0.9301,0.5866,10.9439,-0.3858,0.1354,9.7981,0.1332,0.1576,-0.0049,-4.9,-26.9,-44.9,2.907369468,-0.09,1.82,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,72763,2015-10-30 10:23:29:896,1446171809896.0 \n0.3065,0.334,10.6614,-0.2834,0.3821,9.7951,0.1161,-0.1527,0.2468,-4.9,-27.4,-44.7,2.882236727,-2.21,2.17,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,72865,2015-10-30 10:23:29:998,1446171809998.0 \n-0.4836,0.662,8.5569,-0.1008,0.3682,9.7992,0.2492,-0.2834,0.3702,-5.3,-27.7,-44.4,2.930582347,-1.7,0.93,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,72967,2015-10-30 10:23:30:100,1446171810100.0 \n0.2981,0.571,8.4096,0.126,0.3709,9.7988,-0.0574,-0.16,0.1894,-6.5,-28.2,-44.2,2.936341934,-2.47,-0.74,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,73069,2015-10-30 10:23:30:202,1446171810202.0 \n0.2442,1.5718,7.6818,0.0654,0.5076,9.7933,0.2615,0.1124,0.1686,-7.7,-28.4,-43.9,2.859372914,-2.52,-0.59,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,73172,2015-10-30 10:23:30:305,1446171810305.0 \n-0.583,0.6788,10.3729,0.0188,0.6274,9.7865,0.1784,0.0403,-0.1662,-7.9,-28.7,-43.7,2.856405854,-3.34,-0.35,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,73273,2015-10-30 10:23:30:406,1446171810406.0 \n-0.2693,0.6823,10.161,0.0574,0.8467,9.7699,0.2407,-0.2162,0.0049,-7.8,-29.4,-43.3,2.842966819,-4.95,-0.34,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,73375,2015-10-30 10:23:30:508,1446171810508.0 \n-0.176,0.2837,11.1701,0.1038,0.6623,9.7837,-0.5901,0.182,-0.3702,-7.7,-29.9,-43,2.872811949,-4.5,-0.92,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,73477,2015-10-30 10:23:30:610,1446171810610.0 \n0.3531,0.8499,9.2859,0.192,0.5838,9.7874,-0.3457,-0.0855,-0.1051,-7.4,-30.2,-43.1,2.920459437,-3.41,-1.12,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,73580,2015-10-30 10:23:30:713,1446171810713.0 \n-0.2813,1.4808,7.6818,0.1105,0.5397,9.7912,-0.0867,0.1955,-0.11,-7.3,-30.2,-43.1,2.9223793,-3.19,-1.15,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,73681,2015-10-30 10:23:30:814,1446171810814.0 \n-0.4812,1.4653,8.6227,-0.0507,0.4987,9.7938,-0.0171,0.1356,-0.0696,-6.9,-29.9,-43.8,2.897595624,-3.09,-0.17,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,73783,2015-10-30 10:23:30:916,1446171810916.0 \n-0.4944,1.1492,12.7132,-0.1839,0.4971,9.7923,-0.0147,0.0586,0.182,-6.5,-29.8,-43.9,2.911034659,-2.86,0.68,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,73885,2015-10-30 10:23:31:018,1446171811018.0 \n0.3472,0.1389,12.0931,-0.0902,0.4839,9.7943,-0.3445,-0.2871,0.066,-6,-29.6,-43.7,2.895501229,-3.42,1.13,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,73988,2015-10-30 10:23:31:121,1446171811121.0 \n-0.0239,0.8631,8.0673,0.034,0.5972,9.7884,0.3616,-0.1112,0.452,-6.2,-29.5,-43.3,2.91522345,-2.89,0.23,36.81392,-119.748886,244.28,336.3914195,4.19,19.35484,183.91,16 / 16,74090,2015-10-30 10:23:31:223,1446171811223.0 \n-0.1939,0.8487,8.3462,0.2577,0.5483,9.7879,-0.0672,0.0501,0.0086,-7.3,-29.5,-43.2,2.921506635,-3.26,-1.43,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,74192,2015-10-30 10:23:31:325,1446171811325.0 \n0.1137,1.4401,7.7309,0.2729,0.6405,9.7819,0.2321,0.0073,-0.0476,-8.4,-29.5,-42.8,2.886949116,-3.74,-1.6,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,74293,2015-10-30 10:23:31:426,1446171811426.0 \n-0.0431,0.8356,11.6083,0.2762,0.725,9.7759,0.1429,-0.1112,-0.1979,-8.6,-29.7,-42.7,2.855358656,-4.07,-1.46,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,74396,2015-10-30 10:23:31:529,1446171811529.0 \n0.431,1.4856,9.6391,0.2104,0.9409,9.7591,0.3311,0.1637,-0.1588,-8.4,-30.4,-42.4,2.87351008,-5.51,-1.24,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,74497,2015-10-30 10:23:31:630,1446171811630.0 \n-0.8691,-0.3328,12.2032,0.0473,0.7153,9.7804,-0.1869,0.2712,-0.3494,-7.9,-30.8,-42.2,2.889218044,-5.4,-1.45,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,74599,2015-10-30 10:23:31:732,1446171811732.0 \n-0.498,0.2658,10.5788,0.0808,0.5784,9.7892,-0.2248,0.0073,-0.1552,-6.9,-30.8,-42.4,2.906845869,-4.08,-0.44,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,74702,2015-10-30 10:23:31:835,1446171811835.0 \n-0.3603,1.4868,6.9911,-0.0289,0.533,9.7921,-0.0183,0.1857,-0.0293,-6.3,-30.5,-42.8,2.930058748,-3.22,-0.12,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,74803,2015-10-30 10:23:31:936,1446171811936.0 \n-0.4525,1.2929,9.8964,-0.0325,0.4288,9.7972,-0.1759,-0.0086,0.0159,-5.5,-30.1,-43.4,2.960427477,-2.72,0.15,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,74906,2015-10-30 10:23:32:039,1446171812039.0 \n-0.2322,1.4066,11.5604,-0.0751,0.4337,9.7968,0.1014,0.0269,0.2566,-5.3,-29.7,-43.8,2.95344616,-2.42,0.46,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,75007,2015-10-30 10:23:32:140,1446171812140.0 \n-0.8859,-0.4824,14.692,0.1101,0.3384,9.8002,-0.27,-0.4215,0.0415,-5.5,-29.4,-44.1,2.978927967,-1.98,-0.64,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,75109,2015-10-30 10:23:32:242,1446171812242.0 \n-0.2239,0.7685,7.9104,0.159,0.4816,9.7935,0.2321,-0.2615,0.11,-6.1,-29.2,-44,2.935643802,-2.5,-0.45,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,75211,2015-10-30 10:23:32:344,1446171812344.0 \n-0.8248,0.3124,8.5341,0.1659,0.4122,9.7966,0.088,-0.055,-0.0391,-6.7,-29.3,-43.7,2.919761306,-2.49,-1.17,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,75314,2015-10-30 10:23:32:447,1446171812447.0 \n-0.1053,1.3192,7.9248,0.1738,0.6054,9.7864,0.0244,-0.0232,-0.1124,-6.9,-29.6,-43.4,2.916968779,-3.54,-1.02,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,75416,2015-10-30 10:23:32:549,1446171812549.0 \n-0.3603,0.729,11.0002,0.215,0.6004,9.7859,-0.0672,-0.1405,-0.2077,-7,-29.9,-43.2,2.918365042,-3.61,-1.09,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,75517,2015-10-30 10:23:32:650,1446171812650.0 \n1.136,0.3771,10.4567,0.1802,0.3854,9.7974,-0.3763,0.0073,-0.2529,-6.8,-30.1,-42.9,2.920983036,-3.44,-1.15,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,75619,2015-10-30 10:23:32:752,1446171812752.0 \n0.5231,0.6201,7.6279,0.0283,0.1837,9.8049,-0.0086,-0.1185,-0.0782,-6.2,-29.6,-43.4,2.941752454,-0.84,-0.07,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,75721,2015-10-30 10:23:32:854,1446171812854.0 \n-0.1353,0.1999,8.819,0.156,-0.0732,9.8051,-0.3775,-0.1368,-0.2004,-5.6,-28.9,-44.1,2.962870938,0.43,-0.91,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,75823,2015-10-30 10:23:32:956,1446171812956.0 \n-0.0754,1.1121,8.0158,0.1586,-0.1036,9.8048,-0.0195,-0.0623,0.0232,-5.2,-28.2,-44.6,2.987829146,0.52,-0.76,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,75926,2015-10-30 10:23:33:059,1446171813059.0 \n-0.3424,0.9732,10.234,0.1643,-0.1401,9.8043,-0.0782,0.1087,-0.0464,-5.2,-27.5,-44.7,2.9934142,0.71,-1.13,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,76027,2015-10-30 10:23:33:160,1446171813160.0 \n-0.2035,0.9792,12.0225,0.0638,6.00E-04,9.8064,0.16,0.0782,0.1686,-5.2,-27.4,-44.4,2.9791025,0.72,-0.63,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,76130,2015-10-30 10:23:33:263,1446171813263.0 \n-0.8559,-1.0439,12.6498,0.2394,-0.0747,9.8034,-0.1955,0.0159,-0.0257,-5.3,-27.5,-44.4,2.997253924,0.12,-1.38,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,76231,2015-10-30 10:23:33:364,1446171813364.0 \n-0.1209,0.0658,8.9926,0.2897,0.174,9.8008,-0.1393,0.1014,0.0061,-5.6,-27.9,-44.1,2.974041045,-1.23,-1.85,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,76333,2015-10-30 10:23:33:466,1446171813466.0 \n-0.6955,0.3029,9.0022,0.1663,0.1204,9.8045,0.0941,0.2712,0.0709,-5.8,-28.2,-43.9,2.959205747,-0.69,-1.21,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,76435,2015-10-30 10:23:33:568,1446171813568.0 \n-0.6129,0.5758,9.6139,-0.0069,0.1935,9.8047,0.0305,0.1344,0.1148,-5.6,-28.5,-43.7,2.922902898,-1.13,0.04,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,76537,2015-10-30 10:23:33:670,1446171813670.0 \n-0.1101,0.4465,9.833,0.0439,0.2716,9.8028,0.1991,0.0086,0.1991,-5.6,-28.6,-43.6,2.937389131,-1.15,-0.24,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,76639,2015-10-30 10:23:33:772,1446171813772.0 \n-0.0443,0.0611,11.0923,0.0863,0.2226,9.8037,-0.4985,0.1038,-0.2419,-5.7,-28.8,-43.5,2.943497783,-1.88,-0.62,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,76741,2015-10-30 10:23:33:874,1446171813874.0 \n0.3124,0.3795,9.4858,0.0994,0.1055,9.8056,0.1222,-0.0428,0.033,-5.9,-28.8,-43.7,2.948384705,-0.56,-0.53,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,76844,2015-10-30 10:23:33:977,1446171813977.0 \n-0.2454,0.7266,7.677,-0.0529,-0.0184,9.8065,-0.0208,0.2688,0.0843,-6.1,-28.3,-43.9,2.923077431,0.11,0.31,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,76946,2015-10-30 10:23:34:079,1446171814079.0 \n-0.4752,0.9589,8.3809,-0.2634,-0.0621,9.8029,0.0513,0.033,0.2334,-5.8,-27.9,-44.2,2.900039085,0.41,1.27,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,77047,2015-10-30 10:23:34:180,1446171814180.0 \n-0.583,0.2143,11.0049,-0.3315,-0.1356,9.8001,-0.1723,0.1246,0.1429,-5.5,-27.4,-44.4,2.912954522,0.65,1.82,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,77149,2015-10-30 10:23:34:282,1446171814282.0 \n0.0299,-0.6536,11.3952,-0.1611,0.0034,9.8053,0.1588,-0.1442,0.2175,-5.4,-27.2,-44.9,2.920459437,-0.14,1.33,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,77251,2015-10-30 10:23:34:384,1446171814384.0 \n-0.6883,0.1879,9.4631,-0.0329,-0.1269,9.8058,0.1503,-0.0452,0.2468,-6,-27.1,-45,2.922204767,0.74,0.19,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,77353,2015-10-30 10:23:34:486,1446171814486.0 \n-0.5794,-0.0168,8.8825,0.1569,-0.1669,9.804,-0.1808,0.1075,-0.0049,-7.3,-27,-44.8,2.916794246,0.58,-0.92,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,77455,2015-10-30 10:23:34:588,1446171814588.0 \n-0.6189,0.6608,8.6107,0.1037,-0.1567,9.8049,0.1417,0.0183,0.0794,-7.9,-26.8,-44.9,2.882062194,1.22,-0.74,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,77557,2015-10-30 10:23:34:690,1446171814690.0 \n-0.6835,0.6297,10.6973,0.019,-0.0066,9.8066,0.0513,-0.0061,-0.0623,-8.2,-26.9,-44.5,2.860594644,0.34,-0.17,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,77659,2015-10-30 10:23:34:792,1446171814792.0 \n-0.0766,0.2598,10.1885,0.0241,0.2465,9.8035,0.2798,0.0098,-0.0464,-8.1,-27.1,-44,2.852915195,-0.9,-0.25,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,77761,2015-10-30 10:23:34:894,1446171814894.0 \n-0.1472,-0.7254,11.9926,0.0791,0.1085,9.8057,-0.3775,-0.0977,-0.4032,-8.1,-27.6,-43.6,2.873859146,-1.41,-0.81,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,77863,2015-10-30 10:23:34:996,1446171814996.0 \n0.1173,0.3412,8.4348,-0.0592,0.024,9.8064,-0.2639,-0.0012,-0.2517,-7.7,-27.9,-43.8,2.850122669,-0.59,0.35,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,77966,2015-10-30 10:23:35:099,1446171815099.0 \n-0.3615,0.5674,8.5868,-0.0568,-0.2238,9.8039,-0.0073,0.0672,-0.0403,-7.1,-27.6,-44.1,2.897595624,1.15,0.25,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,78068,2015-10-30 10:23:35:201,1446171815201.0 \n0.3855,1.0523,9.4846,-0.0018,-0.2407,9.8037,-0.0134,-0.1148,-0.1368,-6.3,-27.1,-44.6,2.923950096,1.28,0.25,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,78169,2015-10-30 10:23:35:302,1446171815302.0 \n-0.5483,-0.0192,11.9076,0.1052,-0.1331,9.8052,0.2346,-0.0672,-0.0721,-6,-26.6,-44.5,2.943846849,0.78,-0.61,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,78271,2015-10-30 10:23:35:404,1446171815404.0 \n0.2394,-0.838,11.0014,0.103,0.0406,9.806,-0.0819,-0.2175,0.1014,-5.9,-27,-44.6,2.92778982,-0.38,-0.26,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,78373,2015-10-30 10:23:35:506,1446171815506.0 \n-0.0443,0.6333,8.9004,0.0745,0.0448,9.8063,0.1246,-0.1368,0.2553,-6.1,-27.4,-44.4,2.933200341,-0.26,-0.44,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,78476,2015-10-30 10:23:35:609,1446171815609.0 \n-0.5064,0.5219,8.1116,0.0684,-0.0357,9.8063,-0.2272,0.0819,0.0599,-6.3,-27.6,-44.2,2.942276053,-0.32,-0.51,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,78577,2015-10-30 10:23:35:710,1446171815710.0 \n-0.5052,0.6273,8.4958,0.1641,-0.0226,9.8053,0.1246,0.022,-0.011,-6.9,-27.6,-44.1,2.9223793,0.13,-0.96,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,78679,2015-10-30 10:23:35:812,1446171815812.0 \n0.0491,0.6357,10.9319,0.2628,0.1395,9.8021,0.1955,-0.2578,-0.1808,-7.2,-27.6,-43.8,2.922204767,-0.44,-1.08,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,78781,2015-10-30 10:23:35:914,1446171815914.0 \n0.1413,0.2418,9.8354,0.2767,0.3648,9.796,0.2786,0.1368,-0.1588,-7.2,-27.9,-43.6,2.925346359,-1.59,-1.46,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,78883,2015-10-30 10:23:36:016,1446171816016.0 \n-0.176,-0.419,10.6279,0.1986,0.0289,9.8046,-0.2602,0.2077,-0.2822,-6.9,-28.3,-43,2.931455012,-0.62,-1.5,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,78985,2015-10-30 10:23:36:118,1446171816118.0 \n-0.0467,-0.1963,9.0728,0.2533,-0.0964,9.8029,-0.2993,0.0452,-0.0586,-6.6,-28.4,-43.3,2.93494567,-0.17,-1.54,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,79087,2015-10-30 10:23:36:220,1446171816220.0 \n-0.0646,1.0127,7.7153,0.2654,-0.1072,9.8025,0.1124,-0.0293,0.1124,-6,-27.8,-43.8,2.974390111,0.63,-1.55,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,79190,2015-10-30 10:23:36:323,1446171816323.0 \n-0.2538,0.4357,11.0301,0.2823,-0.0939,9.8021,-0.0024,0.0562,-0.0733,-5.8,-27.4,-44.2,2.97072492,0.55,-1.65,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,79291,2015-10-30 10:23:36:424,1446171816424.0 \n-0.3579,0.2358,11.8752,0.1231,0.0427,9.8058,0.4435,0.2101,0.2395,-5.7,-27.2,-44.2,2.955016957,0.4,-1.1,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,79393,2015-10-30 10:23:36:526,1446171816526.0 \n-0.3496,-0.1951,10.7344,0.0154,0.2798,9.8026,0.0098,0.0208,0.259,-5.5,-27.8,-43.8,2.959205747,-1.63,-0.09,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,79495,2015-10-30 10:23:36:628,1446171816628.0 \n0.3053,0.7961,8.3426,0.1471,0.3209,9.8003,0.0831,-0.3323,0.2639,-5.5,-28.1,-43.7,2.979626099,-1.88,-0.86,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,79598,2015-10-30 10:23:36:731,1446171816731.0 \n-0.3962,0.4645,8.7795,0.3117,0.1371,9.8007,-0.1173,-0.0599,0.1087,-6.3,-28.4,-43.6,2.971423052,-1.02,-1.72,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,79699,2015-10-30 10:23:36:832,1446171816832.0 \n0.1317,1.6029,7.9535,0.3128,0.2572,9.7983,0.1967,0.1295,-0.1735,-6.9,-28.4,-43.8,2.943148718,-0.9,-1.96,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,79801,2015-10-30 10:23:36:934,1446171816934.0 \n-0.4202,0.3519,11.825,0.1661,0.4146,9.7965,0.1161,0.0379,-0.1723,-7.3,-28.5,-43.5,2.924473695,-1.82,-1.5,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,79903,2015-10-30 10:23:37:036,1446171817036.0 \n1.5347,0.7446,10.0102,0.1718,0.4757,9.7936,0.0024,-0.1735,0.0635,-6.9,-29,-43.1,2.905973205,-2.92,-0.77,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,80005,2015-10-30 10:23:37:138,1446171817138.0 \n-0.2634,-0.4334,11.2731,0.1497,0.1411,9.8045,0.0305,-0.0024,0.0929,-6.6,-29,-42.7,2.921157569,-1.03,-0.9,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,80107,2015-10-30 10:23:37:240,1446171817240.0 \n-0.158,0.3005,8.837,0.1696,-0.0522,9.805,-0.3519,-0.0428,-0.0318,-6.2,-28.6,-43.1,2.961474675,-0.05,-0.96,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,80210,2015-10-30 10:23:37:343,1446171817343.0 \n0.1604,1.0415,8.7364,0.1794,-0.0703,9.8048,-0.0061,-0.0037,0.011,-6.3,-27.8,-43.9,2.960252944,0.41,-1.05,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,80312,2015-10-30 10:23:37:445,1446171817445.0 \n-0.1628,0.6955,10.2268,0.0662,-0.0502,9.8063,-0.0061,0.204,-0.0367,-6.3,-27.6,-44.2,2.951526298,0.31,-0.74,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,80413,2015-10-30 10:23:37:546,1446171817546.0 \n0.2394,0.559,8.7448,0.0137,0.2009,9.8046,0.3262,0.1454,0.2382,-6.2,-27.6,-43.8,2.925869958,-1.17,-0.08,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,80515,2015-10-30 10:23:37:648,1446171817648.0 \n-0.4764,-0.2394,11.5448,0.0355,0.1047,9.806,-0.4337,-0.0721,0.1038,-6.2,-27.8,-43.4,2.92482276,-1.32,-0.07,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,80617,2015-10-30 10:23:37:750,1446171817750.0 \n0.2334,0.2131,10.2484,0.3298,-0.0248,9.8011,-0.237,-0.3897,0.0709,-6.6,-27.8,-43.4,2.92778982,-0.24,-1.28,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,80719,2015-10-30 10:23:37:852,1446171817852.0 \n-0.2346,0.5567,6.839,0.3318,-0.0373,9.801,-0.2126,-0.2065,-0.0208,-7.2,-27.6,-43.7,2.948559238,0.27,-1.93,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,80821,2015-10-30 10:23:37:954,1446171817954.0 \n0.0132,0.9744,9.578,0.3465,0.0584,9.8004,0.3152,0.0892,0.0269,-8,-27.3,-44.1,2.905275073,-0.34,-2.02,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,80924,2015-10-30 10:23:38:057,1446171818057.0 \n0.0263,0.1903,11.7855,0.342,0.3602,9.7941,0.5253,0.0489,-0.0953,-8.1,-27.4,-44.1,2.904751474,-0.6,-2.07,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,81026,2015-10-30 10:23:38:159,1446171818159.0 \n0.4681,-0.1628,11.2587,0.3477,0.5101,9.7872,-0.4618,0.2138,-0.4643,-7.8,-28.3,-43.3,2.890963373,-3.31,-1.97,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,81127,2015-10-30 10:23:38:260,1446171818260.0 \n0.3519,0.504,8.4384,0.1795,0.3037,9.8003,-0.0049,0.099,-0.1148,-7.1,-28.9,-42.9,2.9223793,-1.75,-1.11,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,81229,2015-10-30 10:23:38:362,1446171818362.0 \n-0.2215,0.9337,7.8422,0.1463,0.1074,9.805,-0.1148,-0.0012,0.1038,-6.3,-29.2,-43.1,2.955889621,-0.63,-0.85,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,81332,2015-10-30 10:23:38:465,1446171818465.0 \n0.2047,1.3443,8.4396,0.2083,0.0456,9.8043,0.0819,-0.0794,0.2028,-5.8,-28.6,-43.5,2.966885195,-0.27,-1.22,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,81433,2015-10-30 10:23:38:566,1446171818566.0 \n-0.3962,0.0419,12.5133,0.3257,0.0443,9.8011,0.3653,0.0464,0.27,-6,-28.3,-43.7,2.974564644,-0.3,-1.71,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,81535,2015-10-30 10:23:38:668,1446171818668.0 \n0.3543,0.2466,10.1371,0.2292,0.3842,9.7964,0.3604,0.1698,0.3824,-6.6,-28.4,-43.5,2.917492378,-2.25,-1.34,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,81637,2015-10-30 10:23:38:770,1446171818770.0 \n0.0168,0.5758,8.8334,0.1639,0.327,9.7998,0,-0.0672,0.3128,-7.1,-28.7,-43.4,2.9223793,-1.96,-1.16,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,81739,2015-10-30 10:23:38:872,1446171818872.0 \n-0.0251,0.3651,9.6798,0.3881,0.0634,9.7988,-0.3091,0.0904,0.0428,-7.8,-28.9,-43.2,2.924299162,-0.94,-2.33,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,81841,2015-10-30 10:23:38:974,1446171818974.0 \n-0.2143,1.0546,9.1626,0.3183,0.0141,9.8015,-0.0269,0.0147,0.0623,-8.3,-28.5,-43.4,2.91347812,0.03,-1.98,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,81944,2015-10-30 10:23:39:077,1446171819077.0 \n-0.9278,0.6847,10.3154,0.2652,0.19,9.8012,0.1185,0.0232,-0.1881,-8.6,-28,-43.5,2.860769177,-1.11,-1.55,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,82045,2015-10-30 10:23:39:178,1446171819178.0 \n-0.2406,0.4465,10.647,0.2713,0.4491,9.7926,0.0684,0.0464,-0.226,-8.6,-28,-43.5,2.852566129,-1.98,-1.5,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,82147,2015-10-30 10:23:39:280,1446171819280.0 \n-0.7673,-0.7614,12.2727,0.1492,0.0855,9.8051,-0.606,0.088,-0.3763,-8.2,-28.4,-43.2,2.883807523,-1.34,-1.17,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,82250,2015-10-30 10:23:39:383,1446171819383.0 \n-0.097,0.164,9.3398,0.1096,-0.0134,9.806,-0.2908,-0.0501,-0.1576,-7.5,-28.3,-43.2,2.913303587,0.08,-0.64,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,82351,2015-10-30 10:23:39:484,1446171819484.0 \n-0.2322,0.7326,8.7676,0.0252,-0.153,9.8054,-0.1258,0,-0.1112,-6.9,-27.9,-43.6,2.902831612,0.67,-0.08,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,82454,2015-10-30 10:23:39:587,1446171819587.0 \n-0.5986,0.4178,10.4016,-0.0044,-0.1329,9.8057,0.0794,0.099,0.0098,-6.2,-27.4,-43.8,2.926742623,0.78,0.03,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,82556,2015-10-30 10:23:39:689,1446171819689.0 \n-0.2693,1.0894,11.3737,-0.0535,0.1622,9.8052,0.3653,-0.0061,0.2334,-5.8,-27.5,-43.8,2.911209192,-0.23,0.38,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,82658,2015-10-30 10:23:39:791,1446171819791.0 \n-0.2765,-0.9768,13.1717,0.0898,0.2747,9.8024,-0.6206,-0.3115,-0.0244,-6,-28,-43.5,2.912605456,-2.38,0.14,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,82759,2015-10-30 10:23:39:892,1446171819892.0 \n0.2873,0.9301,6.8582,0.0264,0.407,9.7982,-0.0721,-0.1943,0.1625,-6.4,-28.5,-43.2,2.92063397,-1.57,0.03,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,82861,2015-10-30 10:23:39:994,1446171819994.0 \n-0.4513,0.2418,9.001,0.0888,0.1445,9.8052,-0.314,-0.0195,-0.0586,-7.3,-28.8,-43.3,2.911034659,-1.37,-0.58,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,82964,2015-10-30 10:23:40:097,1446171820097.0 \n-0.1341,1.6005,8.1678,0.0813,0.119,9.8056,0.0501,-0.0208,0.0208,-7.6,-28.5,-43.5,2.869146757,-0.63,-0.41,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,83066,2015-10-30 10:23:40:199,1446171820199.0 \n-0.4154,0.3376,10.7727,0.1681,0.1349,9.8043,0.1491,-0.0269,-0.1869,-7.8,-28.3,-43.5,2.881364062,-0.6,-0.89,36.81383,-119.748886,247.96,336.3914195,4.57,19.35484,192.17,16 / 16,83167,2015-10-30 10:23:40:300,1446171820300.0 \n-0.0431,0.267,10.2987,0.1829,0.3317,9.7993,0.2663,-0.0122,-0.1075,-7.7,-28.3,-43.4,2.879269667,-1.17,-0.96,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,83269,2015-10-30 10:23:40:402,1446171820402.0 \n-0.1496,-0.0934,10.884,0.0894,0.1515,9.8051,-0.2199,0.0525,-0.215,-7.3,-28.6,-43.2,2.912954522,-1.25,-0.63,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,83372,2015-10-30 10:23:40:505,1446171820505.0 \n-0.51,0.3891,9.3721,-0.0373,0.0343,9.8065,-0.1845,0.2065,-0.0867,-6.6,-28.6,-43.8,2.898119223,-0.2,0.22,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,83473,2015-10-30 10:23:40:606,1446171820606.0 \n-0.595,1.1277,8.3534,-0.2817,0.0097,9.8026,0.1087,0.088,0.2028,-5.9,-28.3,-44.4,2.893930433,0.02,1.42,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,83575,2015-10-30 10:23:40:708,1446171820708.0 \n-0.9361,0.6835,9.7899,-0.3147,0.1124,9.801,0.0562,-0.0159,0.2297,-5.4,-28.1,-44.5,2.913129055,-0.47,1.86,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,83677,2015-10-30 10:23:40:810,1446171820810.0 \n-0.2813,1.1073,8.8837,-0.2666,0.3353,9.7973,0.4105,-0.0147,0.4679,-5.4,-28.4,-44.5,2.911732791,-1.96,1.56,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,83780,2015-10-30 10:23:40:913,1446171820913.0 \n-0.8248,-0.7626,12.3876,-0.0215,0.2841,9.8025,0.0208,-0.4154,0.1613,-5.9,-28.7,-44,2.905275073,-2.05,0.78,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,83881,2015-10-30 10:23:41:014,1446171821014.0 \n-0.3747,0.4549,8.8597,0.0544,0.2448,9.8034,-0.1161,0.0929,0.1148,-7.2,-29,-43.7,2.903878809,-1.43,-0.32,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,83983,2015-10-30 10:23:41:116,1446171821116.0 \n-0.4741,0.7997,8.7855,-0.0471,0.085,9.8062,-0.0305,0.0623,-0.0403,-7.8,-28.8,-43.4,2.867750494,-0.68,0.01,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,84085,2015-10-30 10:23:41:218,1446171821218.0 \n-0.0072,1.3479,9.0285,-0.086,0.2013,9.8042,0.1674,-0.0098,-0.2529,-8.1,-28.4,-43.8,2.845584812,-0.85,0.44,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,84188,2015-10-30 10:23:41:321,1446171821321.0 \n-0.6632,0.6548,10.4818,-0.0447,0.4276,9.7972,0.3152,-0.044,-0.3604,-7.7,-28.6,-43.9,2.850471734,-1.87,0.33,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,84289,2015-10-30 10:23:41:422,1446171821422.0 \n-1.0223,-0.5207,11.5987,-0.0472,0.3855,9.799,-0.4325,0.182,-0.5657,-6.9,-29.4,-43.6,2.882934858,-2.25,0.28,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,84391,2015-10-30 10:23:41:524,1446171821524.0 \n0.3615,0.9744,8.2229,-0.1722,0.4455,9.795,-0.2786,0.0464,-0.1075,-6.2,-29.8,-43.4,2.907020402,-2.72,0.9,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,84494,2015-10-30 10:23:41:627,1446171821627.0 \n-0.5602,0.8487,8.4874,-0.2217,0.2025,9.8021,0.0232,0.121,-0.0843,-5.2,-29.7,-43.4,2.939308993,-1.18,1.3,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,84595,2015-10-30 10:23:41:728,1446171821728.0 \n-0.3615,1.2282,7.9703,-0.2548,0.2264,9.8007,0.0599,-0.0367,-0.0525,-4.5,-29.4,-43.6,2.957460418,-1.34,1.58,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,84697,2015-10-30 10:23:41:830,1446171821830.0 \n-0.6369,0.5818,10.9247,-0.112,0.2788,9.802,0.2309,-0.2908,0.0623,-4.1,-29,-43.9,2.969328656,-1.25,1.15,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,84799,2015-10-30 10:23:41:932,1446171821932.0 \n0.0144,0.6201,11.1127,-0.0017,0.4028,9.7984,-0.1857,-0.0843,0.2566,-4.2,-29.2,-43.9,2.987131015,-2.38,0.29,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,84901,2015-10-30 10:23:42:034,1446171822034.0 \n-1.0163,0.6572,10.2939,0.2035,0.4143,9.7958,0.099,-0.1881,0.0586,-5,-29.3,-43.4,2.977182638,-2.28,-0.64,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,85003,2015-10-30 10:23:42:136,1446171822136.0 \n-0.0443,0.7578,7.3598,0.3387,0.4923,9.7884,-0.088,-0.0501,-0.1234,-5.9,-29.6,-43,2.97788077,-3.02,-1.9,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,85105,2015-10-30 10:23:42:238,1446171822238.0 \n-0.4238,0.9086,7.6591,0.3028,0.5283,9.7877,0.2492,0.0281,-0.022,-6.7,-29.7,-43.1,2.94506858,-2.59,-1.89,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,85208,2015-10-30 10:23:42:341,1446171822341.0 \n-0.4633,0.5447,9.9994,0.227,0.6211,9.7843,0.0513,0.0623,0.1014,-6.9,-30,-43.3,2.932327676,-3.54,-1.6,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,85309,2015-10-30 10:23:42:442,1446171822442.0 \n1.6927,0.6752,9.1638,0.1942,0.742,9.7766,0.099,-0.0208,0.1197,-6.9,-30.3,-43.6,2.913303587,-4.2,-1.04,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,85411,2015-10-30 10:23:42:544,1446171822544.0 \n0.4477,0.7398,7.993,0.0376,0.278,9.8026,-0.1772,0.2639,0.0293,-6.7,-30.3,-43.3,2.920983036,-2.1,-0.84,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,85514,2015-10-30 10:23:42:647,1446171822647.0 \n0.0239,0.5375,9.4882,-0.0587,-0.0601,9.8063,0.0293,-0.0635,0.0049,-6.3,-29.6,-43.5,2.936865532,0.06,0.32,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,85615,2015-10-30 10:23:42:748,1446171822748.0 \n0.103,0.9768,8.2133,-0.1204,-0.1192,9.8052,-0.1051,0.193,-0.0354,-5.7,-28.4,-44.4,2.916270647,0.7,0.7,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,85717,2015-10-30 10:23:42:850,1446171822850.0 \n-0.5722,0.5938,9.5768,-0.2333,-0.1032,9.8033,-0.0195,0.1002,0.0305,-5.3,-27.9,-44.8,2.936690999,0.63,1.17,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,85819,2015-10-30 10:23:42:952,1446171822952.0 \n-0.2705,0.3292,8.8466,-0.1939,0.0603,9.8045,0.2187,-0.1503,0.3286,-5.1,-27.6,-45.1,2.932327676,-0.35,1.13,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,85922,2015-10-30 10:23:43:055,1446171823055.0 \n-0.4848,-0.4908,12.4163,-0.0041,-0.0178,9.8066,-0.3409,-0.088,0.193,-5.1,-27.7,-44.8,2.960078411,-0.09,0.16,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,86023,2015-10-30 10:23:43:156,1446171823156.0 \n0.2274,0.2897,9.5349,0.1618,-0.004,9.8053,-0.1014,-0.1833,-0.0012,-6.3,-27.8,-44.8,2.943323251,-0.19,-0.51,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,86125,2015-10-30 10:23:43:258,1446171823258.0 \n-0.5375,0.3831,8.4515,0.1235,-0.0017,9.8059,0.0916,-0.0403,-0.0464,-6.9,-27.8,-44.6,2.918190509,0.08,-0.79,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,86227,2015-10-30 10:23:43:360,1446171823360.0 \n-0.2107,1.1253,7.8243,0.103,0.1472,9.805,0.2162,0.0562,-0.0696,-7.3,-27.9,-44.5,2.910860126,-0.51,-0.67,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,86329,2015-10-30 10:23:43:462,1446171823462.0 \n-0.1221,0.1879,9.8976,0.1595,0.2925,9.801,0.1552,0.0024,-0.2016,-7,-28.3,-43.9,2.918365042,-1.24,-1.12,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,86431,2015-10-30 10:23:43:564,1446171823564.0 \n-0.5483,-0.723,12.0333,0.0653,-0.0081,9.8064,-0.4056,0.3836,-0.303,-6.4,-28.7,-43.6,2.962172806,-0.95,-1.14,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,86533,2015-10-30 10:23:43:666,1446171823666.0 \n0.3089,0.2873,8.6227,-0.0184,1.00E-04,9.8066,-0.3457,0.0318,-0.1906,-5.9,-28.7,-43.6,2.93197861,-0.33,0.15,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,86635,2015-10-30 10:23:43:768,1446171823768.0 \n-0.7338,0.4393,8.3474,-0.0348,-0.2031,9.8045,-0.16,0.0342,-0.1393,-4.9,-28.4,-44.4,2.965139866,1.19,0.2,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,86737,2015-10-30 10:23:43:870,1446171823870.0 \n-0.2921,0.8655,9.0453,0.0273,-0.2135,9.8043,0.055,-0.0916,0.0428,-4.5,-27.8,-44.6,3.005456972,1.39,-0.02,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,86839,2015-10-30 10:23:43:972,1446171823972.0 \n-0.2957,0.3711,11.1043,-0.0253,0.0204,9.8066,0.3299,0.1454,0.1173,-4.4,-27.6,-44.6,3.001442715,0.43,0,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,86941,2015-10-30 10:23:44:074,1446171824074.0 \n0.3735,1.2917,8.9747,-0.1511,0.3906,9.7977,0.4985,0.16,0.3201,-4.4,-27.8,-44.4,2.971248519,-1.51,0.8,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,87043,2015-10-30 10:23:44:176,1446171824176.0 \n-0.3879,0.4022,9.25,-0.1821,0.1814,9.8033,0.0428,0.0428,0.2126,-4.5,-28.6,-44,2.972295716,-1.06,1.06,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,87146,2015-10-30 10:23:44:279,1446171824279.0 \n-0.2526,0.4046,9.3697,-0.0661,0.1005,9.8059,-0.325,-0.0354,0.0489,-4.6,-28.9,-44,2.958158549,-0.59,0.39,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,87248,2015-10-30 10:23:44:381,1446171824381.0 \n-0.7362,0.7326,8.9172,0.0114,0.0892,9.8062,0.1136,-0.1686,0.0476,-5,-28.5,-44.5,2.965139866,-0.2,-0.04,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,87349,2015-10-30 10:23:44:482,1446171824482.0 \n-0.3519,0.5363,9.7528,-0.0053,0.2921,9.8023,0.2346,-0.0244,0.0147,-5.4,-28.5,-44.5,2.955540555,-1.71,0.03,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,87451,2015-10-30 10:23:44:584,1446171824584.0 \n-0.2622,1.0319,9.7384,0.0211,0.4947,9.7941,0.3274,0.1148,0.0586,-5.6,-28.8,-44.4,2.924299162,-2.89,-0.12,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,87553,2015-10-30 10:23:44:686,1446171824686.0 \n-0.4178,-0.1125,10.7488,-0.0434,0.371,9.7995,-0.182,0.1295,-0.1307,-5.6,-29.6,-43.5,2.934771137,-2.92,-0.23,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,87655,2015-10-30 10:23:44:788,1446171824788.0 \n0.0922,0.4441,10.1861,0.0768,0.2738,9.8025,-0.2224,-0.1613,-0.171,-5.5,-29.7,-43.4,2.975262776,-2.08,-0.3,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,87757,2015-10-30 10:23:44:890,1446171824890.0 \n-0.4094,0.7673,9.6115,-0.0811,0.1166,9.8056,-0.1234,0.0733,-0.077,-5.1,-29.2,-43.4,2.955715088,-0.68,0.47,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,87859,2015-10-30 10:23:44:992,1446171824992.0 \n-0.1748,1.3779,8.0278,-0.2609,0.2224,9.8007,-0.011,0.1381,0.0513,-4.7,-28.8,-43.7,2.933374874,-1.16,1.23,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,87961,2015-10-30 10:23:45:094,1446171825094.0 \n-0.4262,0.7805,12.4582,-0.3002,0.2711,9.7983,0.0843,-0.0269,0.2553,-4.2,-28.6,-43.8,2.951526298,-1.58,1.75,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,88063,2015-10-30 10:23:45:196,1446171825196.0 \n0.1149,0.3974,10.0281,-0.2059,0.4633,9.7935,-0.3335,-0.2395,0.099,-4.3,-29,-43.7,2.943846849,-3.29,1.69,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,88166,2015-10-30 10:23:45:299,1446171825299.0 \n-0.249,0.7602,9.0058,-0.129,0.3687,9.7989,-0.0684,-0.0721,0.1319,-4.9,-29.3,-43.7,2.932851275,-2.06,1.05,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,88267,2015-10-30 10:23:45:400,1446171825400.0 \n-0.4621,0.4764,8.8741,-0.1571,0.2389,9.8025,-0.1466,0.0831,0.0269,-5.5,-29.2,-43.8,2.939483526,-1.61,0.9,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,88369,2015-10-30 10:23:45:502,1446171825502.0 \n-0.6045,1.0319,8.169,-0.2295,0.3348,9.7982,0.1772,0.0806,0.0342,-6,-28.8,-43.7,2.89672296,-1.66,1.2,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,88471,2015-10-30 10:23:45:604,1446171825604.0 \n-0.7434,0.334,11.2731,-0.2179,0.4399,9.7944,0.1075,-0.0611,-0.0648,-6.1,-28.7,-43.4,2.889916175,-2.57,1.27,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,88574,2015-10-30 10:23:45:707,1446171825707.0 \n-0.1305,0.6225,9.6139,-0.1788,0.5793,9.7879,-0.3775,-0.0867,-0.3299,-6,-29.1,-43.1,2.884331122,-3.56,1.22,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,88675,2015-10-30 10:23:45:808,1446171825808.0 \n0.5914,0.6608,8.6395,-0.3168,0.2066,9.7994,-0.3042,0.2358,-0.2529,-5.6,-29.3,-43,2.884505655,-1.21,1.85,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,88777,2015-10-30 10:23:45:910,1446171825910.0 \n-0.826,0.0587,10.1382,-0.3474,-0.0627,9.8003,-0.3848,0.0476,-0.3299,-5.1,-29.3,-43.2,2.919935839,-0.96,1.83,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,88880,2015-10-30 10:23:46:013,1446171826013.0 \n-0.9242,1.0582,8.1989,-0.4547,-0.1152,9.7954,0.0342,0.0696,0.1539,-4.3,-28.3,-44.4,2.937738197,0.71,2.48,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,88981,2015-10-30 10:23:46:114,1446171826114.0 \n-0.6129,0.7733,9.6415,-0.3208,-0.005,9.8014,0.099,-0.1881,0.1417,-4,-27.8,-45.2,2.933025808,0.47,2.55,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,89083,2015-10-30 10:23:46:216,1446171826216.0 \n-0.3184,0.7147,10.2065,-0.3251,0.2996,9.7967,0.4924,0.1087,0.4239,-4.2,-27.7,-45.7,2.946115777,-0.9,1.74,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,89185,2015-10-30 10:23:46:318,1446171826318.0 \n-0.8248,-0.4621,12.1087,-0.1951,0.3718,9.7977,-0.1185,0.1808,0.2297,-4.6,-28.2,-45.4,2.908591198,-2.54,1.48,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,89287,2015-10-30 10:23:46:420,1446171826420.0 \n-0.5626,0.5459,8.26,-0.1048,0.2839,9.802,-0.055,-0.248,0.1002,-5.5,-28.8,-44.9,2.935120203,-1.98,0.95,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,89389,2015-10-30 10:23:46:522,1446171826522.0 \n-0.4393,0.4896,9.4367,-0.0093,0.0605,9.8065,-0.1539,-0.1197,-0.0208,-6.3,-28.6,-44.7,2.934247538,-0.35,0.05,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,89492,2015-10-30 10:23:46:625,1446171826625.0 \n-0.2837,0.8799,8.4922,0.0265,0.1842,9.8049,0.0794,-0.0648,-0.0684,-6.8,-28.3,-44.6,2.895501229,-0.8,-0.16,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,89593,2015-10-30 10:23:46:726,1446171826726.0 \n-0.3926,0.3675,10.7176,0.0694,0.407,9.798,0.2456,0.0428,-0.1197,-7.1,-28.2,-44.2,2.896373894,-1.85,-0.46,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,89696,2015-10-30 10:23:46:829,1446171826829.0 \n0.152,0.5674,9.8138,-0.0271,0.5013,9.7938,0.0379,0.0953,-0.1649,-7.1,-28.6,-43.9,2.885901918,-3.02,-0.04,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,89798,2015-10-30 10:23:46:931,1446171826931.0 \n0.1927,0.4381,8.8526,-0.2268,0.2176,9.8016,-0.0721,0.121,-0.1075,-6.4,-29,-43.9,2.896199361,-1.27,1.33,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,89899,2015-10-30 10:23:47:032,1446171827032.0 \n-0.2191,0.4369,8.5246,-0.3427,-0.0071,9.8007,-0.1527,0.0757,-0.0806,-5.8,-28.7,-44.3,2.893930433,-0.72,1.55,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,90001,2015-10-30 10:23:47:134,1446171827134.0 \n-0.7015,0.9768,8.4946,-0.4156,-0.0916,9.7974,-0.0684,0.1063,-0.0171,-4.8,-27.9,-44.5,2.904926007,0.55,2.42,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,90104,2015-10-30 10:23:47:237,1446171827237.0 \n-0.5363,0.6931,10.3202,-0.4199,0.0057,9.7977,0.1063,0.077,0.0819,-4.4,-27.4,-44.6,2.932502209,0.26,2.26,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,90205,2015-10-30 10:23:47:338,1446171827338.0 \n-0.5171,1.0068,10.0796,-0.5194,0.2478,9.7898,0.4362,0,0.3201,-4.2,-27.3,-44.5,2.908765731,-0.73,2.97,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,90307,2015-10-30 10:23:47:440,1446171827440.0 \n-1.7801,-0.4992,13.5201,-0.4005,0.2168,9.7961,-0.4386,-0.2688,-0.0367,-4.3,-27.7,-44.4,2.9223793,-2.03,2.46,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,90409,2015-10-30 10:23:47:542,1446171827542.0 \n-0.6943,0.4729,9.1626,-0.3416,0.2833,9.7966,-0.0672,-0.226,0.0037,-4.7,-28.2,-44.3,2.896373894,-1.72,2.19,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,90511,2015-10-30 10:23:47:644,1446171827644.0 \n-1.1349,-0.0479,9.7983,-0.3487,0.1577,9.7992,0.0367,-0.1161,0.0757,-5.1,-28.4,-44.2,2.900737217,-1.05,2.2,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,90614,2015-10-30 10:23:47:747,1446171827747.0 \n-0.8404,0.8176,10.1011,-0.3444,0.3098,9.7957,0.0929,0.0232,0.0208,-5.5,-28.2,-43.7,2.900388151,-1.81,2.01,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,90715,2015-10-30 10:23:47:848,1446171827848.0 \n-0.346,1.0092,11.0109,-0.3437,0.5206,9.7868,0.1967,-0.0391,-0.0269,-5.6,-28.3,-43.7,2.85378786,-2.62,2.21,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,90817,2015-10-30 10:23:47:950,1446171827950.0 \n0.5183,0.3723,11.309,-0.2277,0.6323,9.7836,-0.2065,-0.0953,-0.204,-5.7,-29,-43.2,2.880316865,-3.7,1.33,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,90920,2015-10-30 10:23:48:053,1446171828053.0 \n0.2825,0.68,9.1207,-0.1801,0.4894,9.7928,-0.0489,-0.0831,-0.0745,-5.7,-29.4,-43.1,2.886949116,-2.9,1.3,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,91021,2015-10-30 10:23:48:154,1446171828154.0 \n-0.0922,0.9433,8.7532,-0.1372,0.3369,9.7999,-0.204,-0.0513,-0.1613,-5.6,-29.6,-43.1,2.909638396,-2.24,0.92,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,91124,2015-10-30 10:23:48:257,1446171828257.0 \n-0.3735,1.5431,8.4108,-0.1776,0.3389,9.7992,0.0733,0.0916,-0.1161,-5.4,-29,-43.4,2.934422071,-1.98,1.04,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,91225,2015-10-30 10:23:48:358,1446171828358.0 \n-0.5866,0.7781,10.7847,-0.2048,0.3847,9.797,0.0501,0.2016,-0.0195,-5.3,-28.8,-43.7,2.932327676,-2.29,1.02,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,91328,2015-10-30 10:23:48:461,1446171828461.0 \n-0.3376,1.4006,9.1004,-0.3173,0.5777,9.7845,0.358,0.055,0.2798,-4.8,-28.9,-43.6,2.902657079,-3.38,1.86,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,91429,2015-10-30 10:23:48:562,1446171828562.0 \n-0.8763,0.3926,9.159,-0.2482,0.4111,9.7949,-0.2883,0.0293,0.0904,-4.7,-29.1,-43.1,2.921157569,-2.4,1.45,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,91532,2015-10-30 10:23:48:665,1446171828665.0 \n-0.3543,0.2969,9.1004,0.0178,0.3621,9.7999,-0.3274,-0.1649,0.0134,-5.1,-29.1,-42.8,2.950130035,-2.52,0.33,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,91633,2015-10-30 10:23:48:766,1446171828766.0 \n-0.6644,0.9421,8.8406,0.0346,0.1749,9.805,0.0855,0.0721,0.0367,-6.1,-28.6,-43.1,2.938436329,-1.03,-0.25,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,91735,2015-10-30 10:23:48:868,1446171828868.0 \n-0.9481,0.8547,9.4978,-0.0199,0.2409,9.8037,0.033,0.0574,-0.0696,-6.5,-28.3,-43.4,2.922902898,-1.33,0,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,91837,2015-10-30 10:23:48:970,1446171828970.0 \n-0.3591,0.5674,10.7153,0.0139,0.3616,9.8,0.2028,-0.0379,-0.0367,-6.6,-28.2,-43.5,2.884505655,-2.11,-0.08,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,91940,2015-10-30 10:23:49:073,1446171829073.0 \n-0.4597,-0.7302,12.8042,0.0124,0.1689,9.8052,-0.2089,0.1454,-0.1319,-6.5,-28.3,-43.3,2.933549407,-2.34,-0.62,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,92041,2015-10-30 10:23:49:174,1446171829174.0 \n0.3567,0.3256,9.013,0.0017,0.3158,9.8016,0.2676,0.0073,0.0342,-6.3,-28.3,-43.1,2.920284904,-1.87,-0.03,36.813736,-119.74891,249.26,336.3914195,4.6,51.612904,181.53,16 / 16,92143,2015-10-30 10:23:49:276,1446171829276.0 \n-0.0431,0.9984,7.8195,-0.0156,0.314,9.8016,0.0342,0.0733,-0.0037,-6.3,-28.3,-43.2,2.920983036,-1.77,-0.03,36.81364,-119.74891,251.62,336.3914195,4.48,19.35484,178.11,16 / 16,92245,2015-10-30 10:23:49:378,1446171829378.0 \n-0.3208,1.2701,8.576,-0.0463,0.4019,9.7983,0.0403,0.0672,0.0696,-6,-28.3,-43.4,2.90928933,-2.35,0.27,36.81364,-119.74891,251.62,336.3914195,4.48,19.35484,178.11,16 / 16,92347,2015-10-30 10:23:49:480,1446171829480.0 \n-0.3879,1.1061,9.7348,-0.1332,0.5036,9.7928,0.0757,0.077,0.1038,-5.9,-28.6,-43.4,2.909463863,-2.58,0.52,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,92449,2015-10-30 10:23:49:582,1446171829582.0 \n-0.2849,0.8499,8.9004,-0.1845,0.633,9.7845,0.2297,0.1649,0.2321,-5.8,-29,-43.5,2.896024828,-3.32,0.84,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,92551,2015-10-30 10:23:49:684,1446171829684.0 \n0.2442,0.82,8.8202,-0.1211,0.3877,9.7982,0.0037,-0.0672,0.2517,-6.1,-29.1,-43.6,2.902831612,-2.28,0.82,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,92653,2015-10-30 10:23:49:786,1446171829786.0 \n-0.1053,0.3998,9.4463,-0.0556,0.1431,9.8054,-0.2517,0.0024,-0.1588,-6.4,-28.8,-43.7,2.920983036,-1.53,0.31,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,92755,2015-10-30 10:23:49:888,1446171829888.0 \n-0.5375,1.1193,8.6981,-0.0782,0.0497,9.8062,-0.0147,0.0342,-0.0611,-6.8,-27.9,-43.8,2.882934858,-0.29,0.46,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,92857,2015-10-30 10:23:49:990,1446171829990.0 \n-0.3675,1.1516,9.8581,-0.0847,0.1797,9.8046,0.099,0.0147,-0.1894,-6.8,-27.6,-44.2,2.879095134,-0.8,0.46,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,92960,2015-10-30 10:23:50:093,1446171830093.0 \n-0.5866,0.5531,10.3872,-0.1003,0.3492,9.7999,0.0281,-0.0086,-0.4019,-6.4,-27.7,-44.1,2.904227875,-1.94,0.53,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,93061,2015-10-30 10:23:50:194,1446171830194.0 \n-1.3096,-0.7697,11.3593,-0.2571,0.0834,9.8029,-0.496,0.3421,-0.4545,-5.6,-27.9,-44.1,2.901260816,-1.18,0.83,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,93163,2015-10-30 10:23:50:296,1446171830296.0 \n0.5004,0.1927,9.8545,-0.13,0.16,9.8045,-0.2309,-0.0061,-0.0489,-4.9,-28,-44,2.934073006,-1.23,0.91,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,93265,2015-10-30 10:23:50:398,1446171830398.0 \n-0.504,1.0139,7.5381,-0.2204,0.1587,9.8029,0.0293,0.1356,-0.0782,-4.2,-27.8,-44.2,2.968630525,-0.87,1.01,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,93367,2015-10-30 10:23:50:500,1446171830500.0 \n0.0048,1.2653,8.6395,-0.2129,0.2405,9.8014,0.1515,-0.0538,0.0159,-4,-27.8,-44.4,2.960252944,-1.21,1.25,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,93469,2015-10-30 10:23:50:602,1446171830602.0 \n-0.6345,0.5004,11.7687,-0.2617,0.422,9.7941,0.1894,-0.0244,0.1381,-3.8,-28,-43.9,2.94925737,-2,1.5,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,93571,2015-10-30 10:23:50:704,1446171830704.0 \n-1.4246,-0.9888,12.8868,-0.1611,0.4864,9.7933,-0.4557,-0.2004,-0.0281,-3.8,-28.6,-43.7,2.967059728,-2.84,0.94,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,93673,2015-10-30 10:23:50:806,1446171830806.0 \n0.1293,0.7458,8.1403,-0.027,0.4067,9.7982,-0.2126,-0.2089,0.0305,-4.1,-28.8,-43.6,2.979626099,-2.3,0.58,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,93776,2015-10-30 10:23:50:909,1446171830909.0 \n-0.6081,0.6835,8.3785,0.018,0.1824,9.8049,-0.2077,0.0782,0.0293,-4.9,-28.7,-43.6,2.968805058,-1.07,-0.11,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,93877,2015-10-30 10:23:51:010,1446171831010.0 \n-0.316,1.2534,7.8015,-0.0048,0.1965,9.8047,0.1197,0.0171,0.0794,-5.4,-28.3,-43.7,2.960252944,-0.96,0,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,93979,2015-10-30 10:23:51:112,1446171831112.0 \n-0.5746,0.425,11.9578,-0.011,0.254,9.8034,0.1723,-0.0269,-0.0757,-5.7,-28,-43.7,2.919935839,-1.48,0.06,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,94081,2015-10-30 10:23:51:214,1446171831214.0 \n1.0463,0.7925,9.8007,-7.00E-04,0.4409,9.7967,0.2492,-0.0855,0.0012,-5.6,-28.1,-43.7,2.908940264,-2.68,0.18,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,94183,2015-10-30 10:23:51:316,1446171831316.0 \n0.3891,0.3148,8.4288,-0.1822,0.2526,9.8017,0.1649,0.0024,0.0929,-5.1,-28.5,-43.9,2.929709682,-1.24,1.07,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,94285,2015-10-30 10:23:51:418,1446171831418.0 \n-0.1999,-0.1018,10.6051,-0.1638,0.0414,9.8052,-0.0086,0.1515,-0.0183,-4.8,-28.4,-44,2.936865532,-0.75,0.91,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,94387,2015-10-30 10:23:51:520,1446171831520.0 \n-0.3831,1.1109,8.1547,-0.2867,0.0873,9.8021,0.0635,0.1258,0.0257,-4.4,-28,-44.5,2.952398963,-0.51,1.68,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,94489,2015-10-30 10:23:51:622,1446171831622.0 \n-0.583,0.8751,9.5768,-0.4006,0.1233,9.7977,0.0379,0.0733,0.0061,-4.1,-27.7,-44.6,2.938610862,-0.68,2.1,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,94591,2015-10-30 10:23:51:724,1446171831724.0 \n-0.6788,0.6261,8.7915,-0.5467,0.2131,9.7891,0.5192,0.077,0.1833,-3.4,-27.9,-44.6,2.940705257,-1.25,3.2,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,94693,2015-10-30 10:23:51:826,1446171831826.0 \n-1.5287,-0.7709,11.048,-0.5251,0.1123,9.7919,0.0281,-0.2028,0.1698,-3.2,-27.9,-44.4,2.950304568,-1.28,2.91,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,94795,2015-10-30 10:23:51:928,1446171831928.0 \n-0.656,-0.2011,10.0102,-0.2866,-0.0403,9.8024,-0.226,-0.2309,0.1344,-3.3,-27.8,-44.3,2.976833572,-0.32,2.1,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,94898,2015-10-30 10:23:52:031,1446171832031.0 \n-0.4322,0.3783,8.8155,-0.2446,-0.1364,9.8026,0.0293,0.0281,0.0611,-3.7,-27.6,-44.3,2.966710663,0.79,1.37,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,94999,2015-10-30 10:23:52:132,1446171832132.0 \n-0.8523,0.9517,9.6582,-0.2918,0.0137,9.8023,0.1857,0.1002,-0.0464,-4.7,-26.9,-44.5,2.916968779,0.26,1.58,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,95101,2015-10-30 10:23:52:234,1446171832234.0 \n-0.8404,0.4549,10.9738,-0.2943,0.2924,9.7979,0.3592,-0.0941,-0.066,-4.9,-27,-44.4,2.901086283,-1.05,1.86,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,95203,2015-10-30 10:23:52:336,1446171832336.0 \n-1.1061,-0.267,11.0732,-0.2998,0.4516,9.7917,-0.2016,0.1344,-0.2798,-4.7,-28,-43.7,2.901784414,-2.64,1.75,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,95305,2015-10-30 10:23:52:438,1446171832438.0 \n0.0275,0.5195,8.9148,-0.3676,0.4245,9.7906,-0.0721,-0.0648,-0.1063,-4.5,-28.7,-43.8,2.935992868,-2.48,2.15,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,95407,2015-10-30 10:23:52:540,1446171832540.0 \n-0.6464,0.7626,8.2061,-0.3774,0.3569,9.7929,-0.0195,0.0489,-0.0965,-4.2,-28.9,-43.8,2.936690999,-2.09,2.21,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,95509,2015-10-30 10:23:52:642,1446171832642.0 \n-0.6919,1.409,8.3761,-0.4162,0.3878,9.7901,0.0538,-0.0586,0.0244,-3.8,-28.9,-43.9,2.928313419,-2.07,2.52,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,95611,2015-10-30 10:23:52:744,1446171832744.0 \n-0.5818,0.7901,10.7739,-0.4127,0.4736,9.7865,0.1319,-0.0757,0.1967,-3.4,-29.1,-43.6,2.961125609,-2.57,2.51,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,95713,2015-10-30 10:23:52:846,1446171832846.0 \n0.2442,-0.0407,11.4479,-0.2492,0.5722,9.7868,-0.4887,-0.2297,-0.0684,-3.4,-29.7,-43.4,2.972470249,-3.76,2.18,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,95816,2015-10-30 10:23:52:949,1446171832949.0 \n-0.5052,0.9685,8.1942,-0.2919,0.5214,9.7884,0.2334,0.0049,0.2443,-4,-30,-43.5,2.953097094,-3.05,1.71,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,95917,2015-10-30 10:23:53:050,1446171833050.0 \n-0.6895,0.5124,8.8837,-0.2057,0.3675,9.7976,-0.2358,-0.1087,-0.1075,-4.4,-30,-43.5,2.964441735,-2.64,1.35,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,96019,2015-10-30 10:23:53:152,1446171833152.0 \n-0.8882,0.7661,8.5928,-0.1831,0.2855,9.8008,0.1161,0.0635,0.0672,-4.8,-29.6,-43.6,2.945941244,-1.54,0.93,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,96122,2015-10-30 10:23:53:255,1446171833255.0 \n-1.1049,0.5052,10.7763,-0.1489,0.3093,9.8006,-0.0428,0.0037,-0.055,-5.1,-29.3,-43.7,2.931455012,-1.9,1.14,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,96224,2015-10-30 10:23:53:357,1446171833357.0 \n-0.1796,0.9577,10.7979,-0.1118,0.4174,9.7971,0.1857,-0.0147,-0.0367,-5.2,-29.1,-43.9,2.941752454,-2.14,0.7,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,96325,2015-10-30 10:23:53:458,1446171833458.0 \n-0.0431,-0.0622,10.8541,-0.2252,0.2604,9.8006,-0.1625,-0.0709,-0.1857,-5.2,-29.2,-44,2.928837018,-1.52,1.32,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,96428,2015-10-30 10:23:53:561,1446171833561.0 \n-0.2586,0.0096,9.317,-0.1265,0.0732,9.8056,-0.1588,-0.0806,-0.1466,-5,-29.1,-44,2.941752454,-0.91,0.95,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,96529,2015-10-30 10:23:53:662,1446171833662.0 \n-0.4884,1.0642,8.6095,-0.1765,0.0476,9.8049,-0.0195,0.1051,-0.0611,-4.6,-28.6,-44.3,2.947337508,-0.31,0.86,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,96631,2015-10-30 10:23:53:764,1446171833764.0 \n-0.3232,1.1145,8.9052,-0.2204,0.1271,9.8034,-0.0489,0.1087,0.0037,-4.2,-28.4,-44.5,2.965139866,-0.65,1.18,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,96733,2015-10-30 10:23:53:866,1446171833866.0 \n-0.1006,0.7434,10.9164,-0.388,0.416,9.7901,0.5034,0.3213,0.2993,-4,-28.3,-44.7,2.940356191,-1.56,1.86,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,96835,2015-10-30 10:23:53:968,1446171833968.0 \n-0.82,-0.4501,12.0776,-0.3029,0.4273,9.7927,-0.3555,-0.336,0.0977,-3.8,-29.2,-44.4,2.946115777,-2.5,1.77,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,96937,2015-10-30 10:23:54:070,1446171834070.0 \n-0.3232,0.6297,9.104,-0.0681,0.2413,9.8034,-0.1454,-0.1637,0.1845,-4.1,-29.4,-44.2,2.966361597,-1.92,1.14,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,97040,2015-10-30 10:23:54:173,1446171834173.0 \n-0.2885,0.5363,8.6491,0.0109,-0.0308,9.8066,-0.0684,-0.0623,-0.0501,-5,-29.2,-44,2.967932393,-0.03,0.11,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,97142,2015-10-30 10:23:54:275,1446171834275.0 \n-0.4357,0.6871,8.7783,-0.0644,-0.0075,9.8064,0.088,0.1491,0.0073,-5.7,-28.5,-44.2,2.933025808,0.36,-0.02,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,97243,2015-10-30 10:23:54:376,1446171834376.0 \n-0.7458,0.152,11.4766,-0.1234,0.1725,9.8044,0.1759,-0.0623,-0.0953,-6,-28,-44.2,2.905973205,-0.64,0.79,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,97345,2015-10-30 10:23:54:478,1446171834478.0 \n0.5794,0.9062,10.0317,-0.0616,0.4223,9.7974,0.0305,-0.1539,-0.1429,-5.8,-28.1,-43.9,2.895501229,-2.06,0.83,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,97447,2015-10-30 10:23:54:580,1446171834580.0 \n-0.1652,-0.2203,10.6674,-0.0661,0.2078,9.8042,-0.358,-0.0134,-0.2602,-5.4,-28.9,-43.5,2.955366022,-1.21,0.39,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,97549,2015-10-30 10:23:54:682,1446171834682.0 \n-0.3531,0.48,9.0728,-0.0971,0.0836,9.8058,-0.3763,0.011,-0.1051,-5.1,-29.1,-43.3,2.954318825,-0.49,0.57,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,97651,2015-10-30 10:23:54:784,1446171834784.0 \n-0.8978,0.7949,8.7712,-0.2052,0.0428,9.8044,-0.0501,0.1124,0.0513,-4.9,-28.8,-43.8,2.942450586,-0.38,1.04,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,97753,2015-10-30 10:23:54:886,1446171834886.0 \n-0.5555,0.9086,10.0497,-0.328,0.1714,9.7997,0.1038,0.066,0.0757,-4.5,-28.4,-44.1,2.950130035,-0.75,1.71,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,97855,2015-10-30 10:23:54:988,1446171834988.0 \n-0.5459,1.0343,10.1382,-0.3429,0.4179,9.7917,0.3824,0.066,0.2211,-4.3,-28.5,-44.1,2.935818335,-1.87,2.01,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,97957,2015-10-30 10:23:55:090,1446171835090.0 \n-0.4274,0.0658,9.232,-0.2386,0.2275,9.8011,0.0464,0.1222,0.1686,-4.4,-28.9,-43.7,2.962347339,-1.33,1.39,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,98059,2015-10-30 10:23:55:192,1446171835192.0 \n-0.7254,0.4154,8.157,-0.0758,0.1609,9.805,-0.2529,-0.0757,0.0941,-4.7,-29,-43.3,2.940007125,-1.51,0.93,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,98161,2015-10-30 10:23:55:294,1446171835294.0 \n-0.8859,0.7566,9.1231,-0.0348,0.0638,9.8064,-0.0733,-0.0257,-0.0037,-5.4,-28.8,-43.4,2.964616267,-0.33,0.19,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,98263,2015-10-30 10:23:55:396,1446171835396.0 \n-0.6381,1.1708,9.177,-0.082,0.2037,9.8042,0.0819,0.1185,-0.0599,-5.8,-28.6,-43.4,2.925171826,-0.91,0.3,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,98366,2015-10-30 10:23:55:499,1446171835499.0 \n-1.3827,0.9493,11.151,-0.1212,0.3571,9.7994,0.259,0.0745,-0.0476,-5.9,-28.8,-43.4,2.907718534,-2.09,0.71,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,98468,2015-10-30 10:23:55:601,1446171835601.0 \n0.6823,-0.176,11.2539,-0.0545,0.3973,9.7984,-0.1735,-0.1405,-0.0721,-5.9,-29,-43.1,2.910336528,-2.87,0.42,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,98570,2015-10-30 10:23:55:703,1446171835703.0 \n0.5327,0.2047,8.6874,-0.0571,0.1908,9.8046,-0.0257,-0.1161,0.0843,-5.6,-29.2,-42.5,2.917841443,-1.39,0.5,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,98672,2015-10-30 10:23:55:805,1446171835805.0 \n-0.0108,0.4812,8.6119,0.004,0.0709,9.8064,0.0183,0.0037,-0.0403,-5.7,-29,-42.4,2.932851275,-0.36,0.12,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,98774,2015-10-30 10:23:55:907,1446171835907.0 \n-0.2322,0.9553,8.3043,-0.0416,0.1225,9.8058,0.0489,0.1503,-0.0269,-5.7,-28.5,-42.7,2.924473695,-0.5,0.13,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,98876,2015-10-30 10:23:56:009,1446171836009.0 \n-0.7901,0.3615,11.5101,-0.2188,0.1938,9.8023,0.0721,0.1955,0.0269,-5.6,-28.4,-43,2.890614307,-1.13,1.28,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,98978,2015-10-30 10:23:56:111,1446171836111.0 \n-0.2933,0.2538,10.1706,-0.3736,0.5263,9.7854,0.1295,0.0183,0.2517,-5.2,-28.9,-42.4,2.899515486,-3.08,2.19,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,99079,2015-10-30 10:23:56:212,1446171836212.0 \n-0.9325,0.1173,9.9551,-0.2448,0.2714,9.7998,-0.1319,-0.4801,0.2199,-5,-29.1,-41.9,2.909638396,-1.83,2.09,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,99181,2015-10-30 10:23:56:314,1446171836314.0 \n-0.4465,-0.0646,9.2943,-0.046,0.0594,9.8064,-0.3005,-0.0745,0.0232,-5.5,-29,-41.8,2.96060201,-0.87,0.26,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,99283,2015-10-30 10:23:56:416,1446171836416.0 \n-0.4561,1.2665,8.2791,-0.0033,0.0673,9.8064,0.1344,0.0244,0.1222,-6.4,-28.4,-42.1,2.927964353,-0.39,0.02,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,99385,2015-10-30 10:23:56:518,1446171836518.0 \n-0.5088,0.8559,10.7236,-0.0571,0.1939,9.8046,0.1527,0.0428,-0.1234,-7,-28,-42.2,2.884156589,-1.03,0.23,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,99487,2015-10-30 10:23:56:620,1446171836620.0 \n-0.7003,0.8248,11.7232,-0.1208,0.4445,9.7958,0.2944,0.0672,-0.2175,-7.2,-28,-42.1,2.870892087,-2.12,0.46,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,99589,2015-10-30 10:23:56:722,1446171836722.0 \n-0.3938,-0.5662,10.8421,-0.2089,0.4097,9.7959,-0.2541,0.1161,-0.4081,-6.6,-28.8,-41.4,2.856929453,-2.97,1.19,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,99692,2015-10-30 10:23:56:825,1446171836825.0 \n-0.0371,0.3783,8.4108,-0.2135,0.3089,9.7995,-0.182,-0.0037,-0.1112,-5.7,-29.2,-41.3,2.897770157,-1.8,1.25,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,99793,2015-10-30 10:23:56:926,1446171836926.0 \n-0.2646,1.1732,7.5621,-0.2572,0.1794,9.8016,-0.0367,0.1417,-0.1588,-5.2,-29.1,-41.1,2.934247538,-0.96,1.34,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,99895,2015-10-30 10:23:57:028,1446171837028.0 \n-0.6967,0.9613,9.1063,-0.3785,0.2218,9.7968,0.1429,0.0562,-0.0183,-4.5,-28.6,-41.6,2.943846849,-1.3,2.21,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,99997,2015-10-30 10:23:57:130,1446171837130.0 \n-0.9756,0.5004,10.8421,-0.5351,0.3202,9.7868,0.1784,-0.0098,0.2272,-4,-28.4,-41.8,2.917317845,-1.7,2.88,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,100100,2015-10-30 10:23:57:233,1446171837233.0 \n-1.2462,-0.844,15.1337,-0.266,0.2064,9.8009,-0.4203,-0.1539,0.0159,-3.9,-28.6,-41.9,2.942276053,-2.09,2.11,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,100201,2015-10-30 10:23:57:334,1446171837334.0 \n-0.5016,0.8847,7.604,-0.2542,0.2719,9.7996,0.1979,-0.0623,0.2053,-4.2,-28.5,-42.1,2.93913446,-1.61,2.06,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,100304,2015-10-30 10:23:57:437,1446171837437.0 \n-0.8452,0.5423,8.0014,-0.1952,0.0914,9.8043,-0.0599,0.099,0.1002,-5.1,-28.2,-42.2,2.933374874,-0.53,1.14,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,100405,2015-10-30 10:23:57:538,1446171837538.0 \n-0.3268,1.1744,7.6327,-0.3594,0.1351,9.7991,0.1087,0.1063,0.1087,-5.5,-27.6,-42.2,2.914525318,-0.56,1.88,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,100508,2015-10-30 10:23:57:641,1446171837641.0 \n-1.0427,0.5866,9.8306,-0.4755,0.139,9.7941,0.0037,0.1625,-0.0794,-5.6,-27.4,-41.8,2.850471734,-0.73,2.65,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,100610,2015-10-30 10:23:57:743,1446171837743.0 \n0.4417,0.3579,10.6147,-0.3947,0.2497,9.7955,0.1735,-0.0232,-0.055,-5.3,-27.4,-42,2.886250984,-1.38,2.44,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,100711,2015-10-30 10:23:57:844,1446171837844.0 \n-0.2035,-0.3567,11.3318,-0.4309,-0.0073,9.7972,-0.1271,-0.1258,-0.1417,-5,-27.4,-42.2,2.887123649,-0.19,2.72,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,100813,2015-10-30 10:23:57:946,1446171837946.0 \n-0.067,0.3759,8.6921,-0.3058,-0.0929,9.8014,-0.0428,-0.0428,-0.099,-4.7,-27,-42.8,2.914350785,0.54,1.79,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,100916,2015-10-30 10:23:58:049,1446171838049.0 \n-0.996,0.5088,8.3905,-0.293,-0.1593,9.801,-0.1246,0.0171,-0.1857,-4.6,-26.6,-43,2.918015976,0.72,1.68,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,101017,2015-10-30 10:23:58:150,1446171838150.0 \n-0.7219,0.3184,10.0257,-0.3913,-0.1936,9.7969,-0.0806,0.1967,-0.0122,-4.3,-26.2,-43.4,2.940530724,1.05,1.95,36.81364,-119.74891,251.62,336.3064648,4.48,19.35484,178.11,16 / 16,101119,2015-10-30 10:23:58:252,1446171838252.0 \n-0.735,0.8404,12.2212,-0.4282,-0.0773,9.797,0.3775,-0.0538,0.3091,-4.2,-26,-43.7,2.919586773,0.85,2.63,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,101221,2015-10-30 10:23:58:354,1446171838354.0 \n-2.15,-1.3659,14.5556,-0.1887,-0.1026,9.8043,-0.6243,-0.5424,-0.1454,-4.3,-26,-44.3,2.960427477,0.6,1.1,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,101323,2015-10-30 10:23:58:456,1446171838456.0 \n-0.5016,0.5519,7.5896,0.0363,-0.275,9.8027,-0.066,-0.5571,0.1197,-4.7,-25.8,-44.2,2.924299162,1.43,1.28,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,101425,2015-10-30 10:23:58:558,1446171838558.0 \n-0.571,0.158,8.3761,0.0708,-0.3699,9.7994,0.2211,-0.0342,0.2566,-5.7,-25.3,-44.2,2.934596604,2.51,-0.45,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,101528,2015-10-30 10:23:58:661,1446171838661.0 \n-0.3065,0.9014,6.839,0.0127,-0.1037,9.8061,0.3775,0.1478,0.2566,-6.3,-24.9,-44.2,2.917666911,1.15,-0.14,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,101630,2015-10-30 10:23:58:763,1446171838763.0 \n-0.4453,-0.0431,12.0368,0.0342,0.0724,9.8063,0.1613,-0.011,-0.1002,-7,-25.2,-43.9,2.877175272,-0.03,-0.31,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,101731,2015-10-30 10:23:58:864,1446171838864.0 \n0.68,-0.1568,10.1215,-0.102,0.3254,9.8007,0.0929,0.2138,-0.3958,-6.8,-26.3,-43.3,2.861641842,-1.58,0.17,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,101833,2015-10-30 10:23:58:966,1446171838966.0 \n0.3807,0.0802,8.9172,-0.2157,0.1473,9.8032,0.0012,-0.2492,-0.0061,-6.2,-27.1,-43.1,2.878397002,-0.83,1.48,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,101935,2015-10-30 10:23:59:068,1446171839068.0 \n-0.5291,0.4992,8.2289,-0.0805,0.0061,9.8063,-0.215,-0.0342,0.0073,-5.4,-27.5,-43.2,2.945766712,-0.04,0.47,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,102037,2015-10-30 10:23:59:170,1446171839170.0 \n-0.7039,1.0618,8.029,-0.1561,-0.0338,9.8054,-0.0489,0,0.0648,-5.3,-27.2,-43.5,2.93494567,0.12,0.91,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,102139,2015-10-30 10:23:59:272,1446171839272.0 \n-0.8775,0.4944,11.145,-0.1801,-0.0798,9.8047,-0.0892,0.1087,-0.0293,-5.5,-26.8,-43.7,2.932502209,0.47,1.05,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,102241,2015-10-30 10:23:59:374,1446171839374.0 \n-0.3591,0.6979,10.489,-0.3407,0.0458,9.8006,0.2798,0.1332,0.1955,-5.4,-26.6,-43.6,2.918539575,0.38,1.55,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,102343,2015-10-30 10:23:59:476,1446171839476.0 \n-0.7051,-0.6895,12.5588,-0.3391,-0.1119,9.8001,-0.3115,0.0843,0.0696,-5.3,-26.6,-43.7,2.900213618,-0.31,2.07,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,102446,2015-10-30 10:23:59:579,1446171839579.0 \n0.3496,0.7362,7.8721,-0.2333,0.0497,9.8037,0.0489,-0.0623,0.0305,-5.2,-26.7,-43.5,2.912081857,0.13,1.77,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,102548,2015-10-30 10:23:59:681,1446171839681.0 \n-0.7207,0.0407,8.7269,-0.3159,-0.0515,9.8014,-0.1368,0.1307,-0.0745,-5.4,-26.8,-43.5,2.91522345,0.22,1.68,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,102649,2015-10-30 10:23:59:782,1446171839782.0 \n-0.826,0.5734,9.4535,-0.3485,0.0623,9.8003,0.0599,0.022,-0.055,-5.6,-26.8,-43.7,2.866354231,-0.31,2.03,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,102751,2015-10-30 10:23:59:884,1446171839884.0 \n-0.4357,0.5195,9.815,-0.3393,0.1479,9.7997,0.314,0.1307,-0.0342,-5.6,-27.2,-43.7,2.863561704,-0.86,1.98,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,102854,2015-10-30 10:23:59:987,1446171839987.0 \n-0.079,-0.565,11.1163,-0.4548,0.1,9.7956,-0.6072,0.38,-0.4178,-5.4,-27.4,-43.6,2.884680188,-1.48,2.34,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,102955,2015-10-30 10:24:00:088,1446171840088.0 \n0.3472,0.1724,8.2253,-0.6148,-0.1948,9.7854,0.0953,-0.099,0.0599,-4.6,-27.1,-43.9,2.870368488,1.14,3.59,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,103057,2015-10-30 10:24:00:190,1446171840190.0 \n-0.1784,0.5363,8.0325,-0.4163,-0.2914,9.7935,0.0415,-0.0831,-0.1197,-4.2,-26.8,-44.5,2.933374874,1.75,2.59,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,103160,2015-10-30 10:24:00:293,1446171840293.0 \n-0.5986,0.8571,9.0453,-0.389,-0.325,9.7935,0.0147,-0.0916,-0.2089,-3.7,-26.3,-45,2.934073006,1.9,2.27,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,103261,2015-10-30 10:24:00:394,1446171840394.0 \n-1.324,-0.8763,11.746,-0.3206,-0.3378,9.7956,-0.0819,-0.11,-0.1527,-3.7,-26.3,-44.7,2.940181658,1.83,2.04,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,103363,2015-10-30 10:24:00:496,1446171840496.0 \n-0.6213,0.6129,9.4427,-0.2951,-0.0489,9.8021,0.1539,-0.1381,0.2419,-3.7,-26.4,-44.2,2.934422071,0.53,2.02,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,103465,2015-10-30 10:24:00:598,1446171840598.0 \n-0.8859,-0.0431,11.0241,-0.0907,-0.2621,9.8027,0.011,-0.1845,0.2602,-4.1,-26.5,-44.1,2.977531704,1.28,0.6,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,103568,2015-10-30 10:24:00:701,1446171840701.0 \n-0.5183,0.4992,8.4922,0.1685,-0.1622,9.8039,0.0977,-0.314,0.0867,-5.3,-26.6,-44.3,2.989749009,0.95,-0.98,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,103670,2015-10-30 10:24:00:803,1446171840803.0 \n-0.2394,0.8727,8.6431,-0.0851,-0.1689,9.8048,0.0831,0.1991,0.0525,-6.3,-26.4,-44.4,2.907369468,0.99,0.5,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,103771,2015-10-30 10:24:00:904,1446171840904.0 \n-1.2438,0.407,9.9012,-0.2891,0.0955,9.8019,0.1808,0.215,-0.1515,-6.4,-26.5,-43.9,2.873335548,-0.25,1.43,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,103874,2015-10-30 10:24:01:007,1446171841007.0 \n-0.5399,0.2239,8.7819,-0.4047,0.3957,9.7903,0.11,0.0354,-0.1991,-5.5,-27.3,-43.7,2.886076451,-1.89,2.18,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,103976,2015-10-30 10:24:01:109,1446171841109.0 \n-1.2773,-1.6137,13.1837,-0.4328,0.0077,9.7971,-0.7233,0.0977,-0.4374,-4.8,-28,-43.5,2.901260816,-1.19,2.2,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,104077,2015-10-30 10:24:01:210,1446171841210.0 \n0.1987,0.413,8.8573,-0.4395,-0.0795,9.7965,-0.336,-0.1148,-0.1429,-4,-28.2,-43.9,2.924648228,0.13,2.86,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,104179,2015-10-30 10:24:01:312,1446171841312.0 \n-0.7638,0.9254,9.5062,-0.4872,-0.4383,9.7847,-0.1234,0.1442,-0.0342,-3.6,-27.3,-44.6,2.934422071,2.24,2.6,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,104282,2015-10-30 10:24:01:415,1446171841415.0 \n-0.844,0.8344,8.9627,-0.5709,-0.3239,9.7847,0.1723,0.0538,0.0403,-3.2,-26.5,-45,2.941752454,2.21,3.33,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,104383,2015-10-30 10:24:01:516,1446171841516.0 \n-0.3639,0.0515,11.0038,-0.3555,-0.0734,9.7999,0.3274,-0.2896,0.2138,-3.2,-26.3,-45,2.958856681,0.83,2.45,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,104486,2015-10-30 10:24:01:619,1446171841619.0 \n1.4808,0.3603,9.5529,0.1466,0.2548,9.8022,-0.3787,-0.4117,0.0806,-3.6,-26.7,-44.6,2.981545961,-1.3,0.25,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,104587,2015-10-30 10:24:01:720,1446171841720.0 \n-0.3519,0.5231,8.2073,0.2329,0.2036,9.8018,0.2419,0.033,0.3738,-5.1,-27.7,-44.3,2.994461398,-0.65,-1.2,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,104689,2015-10-30 10:24:01:822,1446171841822.0 \n-1.3443,-0.0479,10.2197,-0.2118,-0.2821,9.8003,-0.7428,0.8039,0.055,-6.5,-28,-44.2,2.944894047,0.46,-0.45,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,104791,2015-10-30 10:24:01:924,1446171841924.0 \n-0.984,0.6045,8.5772,-0.4593,-0.1583,9.7946,0.3128,0.1344,0.0843,-6.5,-27.5,-44.5,2.865830632,1.53,2.57,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,104893,2015-10-30 10:24:02:026,1446171842026.0 \n-1.1085,0.4717,11.0828,-0.6843,-0.0524,9.7826,0.2944,0.0232,-0.0489,-5.7,-26.9,-44.9,2.818357676,0.31,4,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,104995,2015-10-30 10:24:02:128,1446171842128.0 \n0.3017,0.5363,10.6159,-0.6346,-0.091,9.7857,-0.3274,-0.1698,-0.0965,-4.9,-26.9,-44.8,2.84663201,-0.43,3.97,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,105097,2015-10-30 10:24:02:230,1446171842230.0 \n0.6668,-0.3244,9.408,-0.4643,-0.3032,9.791,0.628,-0.5718,0.2957,-4.5,-26.9,-44.8,2.918190509,2.33,3.25,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,105199,2015-10-30 10:24:02:332,1446171842332.0 \n0.8619,0.0658,8.0002,-0.1642,-0.1937,9.8034,0.0464,-0.0269,-0.0024,-5.2,-26.7,-44.9,2.938087263,1.13,0.96,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,105302,2015-10-30 10:24:02:435,1446171842435.0 \n-0.3388,0.516,7.7644,-0.2659,-0.1453,9.802,0.0855,0.1955,-0.1026,-5.6,-26.5,-45,2.887647247,1.03,1.22,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,105403,2015-10-30 10:24:02:536,1446171842536.0 \n-0.65,0.2705,9.1135,-0.4289,-0.1664,9.7959,-0.0623,0.1161,-0.0232,-5.9,-26.6,-45.1,2.866703296,0.95,2.32,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,105505,2015-10-30 10:24:02:638,1446171842638.0 \n-2.071,-0.2729,10.4878,-0.3113,-0.0233,9.8017,0.5534,-0.4826,0.4007,-5.3,-26.6,-45.1,2.896548427,1.05,2.5,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,105607,2015-10-30 10:24:02:740,1446171842740.0 \n-0.2394,-1.3072,14.6717,-0.0107,-0.3997,9.7985,-0.8564,-0.3848,0.1833,-5.5,-26.8,-45.2,2.936167401,-0.52,0.69,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,105709,2015-10-30 10:24:02:842,1446171842842.0 \n-0.3579,0.2119,8.6586,0.1899,-0.1239,9.804,0.0623,-0.4264,0.1649,-6.6,-26.5,-45.6,2.890265241,1.12,-0.12,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,105812,2015-10-30 10:24:02:945,1446171842945.0 \n-0.9313,0.2885,9.2201,0.0063,-0.3308,9.8011,-0.0709,0.1588,0.0257,-8.1,-26.2,-45.4,2.866877829,1.83,-0.34,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,105914,2015-10-30 10:24:03:047,1446171843047.0 \n-0.6536,0.6333,8.3773,-0.191,-0.2028,9.8027,-0.0819,0.0892,0.0171,-8.2,-26.1,-45.3,2.83109858,1.35,0.87,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,106015,2015-10-30 10:24:03:148,1446171843148.0 \n-0.0682,0.316,11.1438,-0.3141,-0.2757,9.7977,0.0024,0.2065,0.1185,-8,-25.9,-45.1,2.808060234,1.61,1.84,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,106117,2015-10-30 10:24:03:250,1446171843250.0 \n0.255,-0.5375,11.0624,-0.3944,-0.2229,9.7962,-0.4948,0.11,-0.4288,-7.6,-26.1,-45.2,2.791479606,0.88,2.23,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,106219,2015-10-30 10:24:03:352,1446171843352.0 \n0.9553,0.2538,6.7241,-0.229,-0.0975,9.8035,0.1051,-0.3457,-0.0134,-6.9,-26.1,-45.2,2.83947616,1.46,1.86,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,106321,2015-10-30 10:24:03:454,1446171843454.0 \n-0.1628,-0.401,8.2636,-0.0832,-0.2174,9.8039,-0.1014,-0.0354,-0.204,-6.8,-26.4,-45.1,2.873161015,1.09,0.49,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,106424,2015-10-30 10:24:03:557,1446171843557.0 \n0.0275,1.1492,7.6291,-0.1316,-0.2053,9.8036,0.1026,-0.0892,-0.0965,-6.8,-26.4,-45,2.865307033,1.52,0.9,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,106525,2015-10-30 10:24:03:658,1446171843658.0 \n-0.978,-0.152,11.5412,-0.1237,-0.2747,9.802,0.055,0.0037,0.0501,-6.9,-26.4,-44.8,2.870543021,1.5,0.7,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,106627,2015-10-30 10:24:03:760,1446171843760.0 \n0.2394,0.3005,9.7576,-0.0675,0.025,9.8064,0.4459,-0.0586,0.2663,-7,-26.5,-44.6,2.872637416,0.79,0.43,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,106729,2015-10-30 10:24:03:862,1446171843862.0 \n-0.8475,0.5088,8.5629,-0.098,-0.0047,9.8062,0.1845,0.1588,0.1527,-7.2,-27,-44.6,2.871764751,0.44,0.72,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,106832,2015-10-30 10:24:03:965,1446171843965.0 \n-0.644,-0.1065,9.7923,0.0415,-0.0456,9.8065,-0.1246,0.0782,0.0476,-7.5,-27.2,-44.5,2.89672296,0.02,-0.33,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,106933,2015-10-30 10:24:04:066,1446171844066.0 \n-0.559,1.2737,7.8973,0.0017,0.1177,9.8059,0.2688,-0.1466,0.0183,-7.9,-27.3,-44.5,2.848377339,-0.69,-0.01,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,107036,2015-10-30 10:24:04:169,1446171844169.0 \n-0.4681,1.1696,8.9938,-0.0131,0.2863,9.8025,0.1124,0.1649,-0.0782,-8.2,-27.6,-44.2,2.858325716,-1.44,-0.23,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,107137,2015-10-30 10:24:04:270,1446171844270.0 \n-0.0168,0.6057,9.4176,-0.1029,0.4081,9.7976,0.1564,0.2065,-0.1075,-8,-28.2,-43.7,2.828655119,-2.39,0.6,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,107239,2015-10-30 10:24:04:372,1446171844372.0 \n-1.6364,-1.4808,14.4215,-0.3832,-0.0787,9.7988,0.3824,0.3225,0.1087,-7.5,-28.5,-43.7,2.85675492,0.03,1.57,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,107341,2015-10-30 10:24:04:474,1446171844474.0 \n-0.1628,-0.2119,9.8665,-0.4153,-0.0017,9.7979,-0.3274,-0.1136,-0.2028,-6.5,-28.3,-44.1,2.861816374,-0.4,2.55,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,107443,2015-10-30 10:24:04:576,1446171844576.0 \n-0.9098,0.5255,8.3558,-0.4311,-0.0798,9.7968,0.0293,0.011,-0.0049,-5.7,-27.9,-44.5,2.87106662,0.48,2.44,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,107545,2015-10-30 10:24:04:678,1446171844678.0 \n-0.5698,0.8954,9.6355,-0.4554,0.0561,9.7959,0.1222,0.1759,0.1038,-5.2,-27.7,-44.6,2.900562684,-0.05,2.39,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,107648,2015-10-30 10:24:04:781,1446171844781.0 \n-0.3855,1.3252,12.4056,-0.4641,0.2235,9.7931,0.1319,-0.066,0.1637,-5.2,-27.9,-44.6,2.884680188,-0.92,2.77,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,107750,2015-10-30 10:24:04:883,1446171844883.0 \n-0.9984,-0.0455,10.2113,-0.5014,0.3679,9.7869,-0.2138,-0.1197,0.022,-5.3,-28.6,-44.3,2.882585793,-2.15,2.93,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,107852,2015-10-30 10:24:04:985,1446171844985.0 \n-0.5483,0.0024,9.8976,-0.1951,0.3064,9.7999,-0.303,-0.1881,-0.0745,-5.6,-28.9,-44,2.872811949,-2.24,1.97,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,107954,2015-10-30 10:24:05:087,1446171845087.0 \n-0.7135,0.8188,7.0809,-0.2332,0.1855,9.8021,0.0098,0.1222,0.0098,-6,-28.9,-44,2.898991888,-1.09,1.27,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,108055,2015-10-30 10:24:05:188,1446171845188.0 \n-0.5459,1.3072,8.1894,-0.2595,0.1848,9.8015,0.1173,0.1002,-0.0244,-6.6,-28.4,-44.1,2.853089728,-1.05,1.39,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,108157,2015-10-30 10:24:05:290,1446171845290.0 \n-0.9517,0.65,11.2516,-0.237,0.2745,9.7999,0.2615,-0.0623,-0.0806,-6.7,-28.3,-44.2,2.849075471,-1.6,1.39,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,108259,2015-10-30 10:24:05:392,1446171845392.0 \n0.0646,-0.8511,11.9219,-0.1527,0.4489,9.7952,-0.5412,0.1478,-0.5082,-6.5,-28.7,-43.8,2.885552852,-2.76,1.34,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,108362,2015-10-30 10:24:05:495,1446171845495.0 \n0.346,0.2897,7.3394,-0.2314,0.3319,9.7983,0.2908,0.0012,0.171,-6,-29.2,-43.8,2.891312439,-1.59,1.44,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,108463,2015-10-30 10:24:05:596,1446171845596.0 \n0.3627,0.5614,8.8274,-0.1899,0.1253,9.804,-0.0819,0.022,0.0244,-5.8,-29.2,-43.8,2.903704277,-1.01,1.1,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,108565,2015-10-30 10:24:05:698,1446171845698.0 \n-0.4154,0.9278,8.0302,-0.2451,0.0412,9.8035,-0.0122,0.0709,-0.0061,-5.7,-28.6,-44.4,2.900039085,-0.24,1.43,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,108667,2015-10-30 10:24:05:800,1446171845800.0 \n-0.8404,0.5088,9.7983,-0.3297,-0.0661,9.8009,-0.16,0.0941,-0.0501,-5.7,-28.3,-44.6,2.884680188,0,1.73,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,108769,2015-10-30 10:24:05:902,1446171845902.0 \n0.0527,1.1073,9.1949,-0.3507,0.2521,9.7971,0.5913,0.1735,0.3677,-5.5,-27.9,-44.7,2.910336528,-0.54,1.9,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,108871,2015-10-30 10:24:06:004,1446171846004.0 \n-0.5207,0.7015,8.6084,-0.339,0.1334,9.7999,0.1979,0.0721,0.3641,-5.6,-28,-44.4,2.873859146,-0.78,1.98,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,108973,2015-10-30 10:24:06:106,1446171846106.0 \n-0.0754,0.2263,8.9471,-0.0484,0.2449,9.8035,-0.27,-0.0342,0.099,-5.9,-28.2,-44.1,2.895152163,-1.49,0.98,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,109075,2015-10-30 10:24:06:208,1446171846208.0 \n-0.6859,1.0391,8.406,-0.0375,0.1228,9.8058,0.0501,0.0269,0.0428,-6.8,-28.3,-43.8,2.889218044,-0.67,0.11,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,109178,2015-10-30 10:24:06:311,1446171846311.0 \n-0.3699,1.2653,9.839,-0.0241,0.2917,9.8023,0.1051,-0.1442,-0.0819,-7.5,-28.4,-43.7,2.877349805,-1.47,0.35,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,109279,2015-10-30 10:24:06:412,1446171846412.0 \n-0.6488,0.8595,11.1163,-0.0033,0.3855,9.7991,0.1222,-0.121,-0.1344,-7.7,-28.6,-43.8,2.85797665,-2.02,0,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,109381,2015-10-30 10:24:06:514,1446171846514.0 \n-0.1903,-0.48,12.4666,-0.0818,0.0321,9.8063,-0.8968,0.2138,-0.3995,-7.2,-28.8,-43.9,2.905798672,-0.11,-0.07,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,109484,2015-10-30 10:24:06:617,1446171846617.0 \n0.8667,0.2478,9.4978,-0.0482,0.2113,9.8043,-0.3213,-0.1564,-0.1393,-6.9,-28.7,-44.2,2.879095134,-1.74,0.56,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,109585,2015-10-30 10:24:06:718,1446171846718.0 \n-0.4178,0.7602,7.8027,-0.1165,0.17,9.8045,0.1051,0.0183,-0.044,-6.5,-28.4,-44,2.906496803,-0.99,0.68,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,109687,2015-10-30 10:24:06:820,1446171846820.0 \n-0.1484,1.3312,8.4228,-0.1338,0.2509,9.8025,0.0794,0.0391,0.0525,-6.2,-28.5,-44,2.903529744,-1.33,0.71,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,109789,2015-10-30 10:24:06:922,1446171846922.0 \n-0.6907,0.2969,12.815,-0.2317,0.2554,9.8006,-0.0635,0.0806,0.0831,-5.9,-28.7,-43.9,2.898468289,-1.25,1.24,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,109891,2015-10-30 10:24:07:024,1446171847024.0 \n-1.1899,-0.2382,11.8489,-0.3162,0.3485,9.7954,-0.4166,0.0024,0.1112,-5.6,-29.1,-43.8,2.877524338,-2.04,1.85,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,109993,2015-10-30 10:24:07:126,1446171847126.0 \n-0.814,0.2466,9.493,-0.1659,0.2618,9.8018,-0.1784,-0.3079,0.1295,-5.8,-29.1,-43.8,2.885378319,-1.53,1.68,36.813522,-119.74888,252.67,336.3064648,4.7,19.35484,190.27,16 / 16,110095,2015-10-30 10:24:07:228,1446171847228.0 \n-0.1999,0.8236,8.3426,-0.0138,0.1164,9.8059,-0.193,0.0269,-0.0195,-6.5,-28.9,-44,2.931804078,-0.68,0.08,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,110197,2015-10-30 10:24:07:330,1446171847330.0 \n-0.3843,1.3204,8.3749,0.037,0.1114,9.8059,0.1222,-0.1051,-0.0476,-7,-28.5,-44.7,2.894454032,-0.45,-0.03,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,110300,2015-10-30 10:24:07:433,1446171847433.0 \n-0.8942,0.7051,11.1546,0.043,0.229,9.8039,0.3873,0.1429,-0.1063,-7.5,-28.3,-44.6,2.903006145,-0.92,-0.47,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,110401,2015-10-30 10:24:07:534,1446171847534.0 \n0.2514,0.1556,11.4239,-0.0363,0.3542,9.8002,-0.1063,0.011,-0.2248,-7.2,-28.6,-44.1,2.885901918,-2.07,0.21,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,110503,2015-10-30 10:24:07:636,1446171847636.0 \n-0.3376,-0.5387,11.0696,-0.1197,0.1252,9.8051,0.1283,-0.1161,-0.0831,-6.9,-28.8,-43.7,2.879618733,-0.45,0.89,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,110605,2015-10-30 10:24:07:738,1446171847738.0 \n0.1269,0.4812,8.5964,-0.0794,0.1814,9.8047,-0.0208,-0.1014,-0.0843,-6.2,-28.9,-43.8,2.911732791,-0.98,0.8,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,110707,2015-10-30 10:24:07:840,1446171847840.0 \n-0.5327,0.8954,7.774,-0.0726,0.2057,9.8042,0.0867,-0.0257,-0.1332,-5.8,-28.8,-43.9,2.917841443,-1.01,0.55,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,110810,2015-10-30 10:24:07:943,1446171847943.0 \n-0.8344,0.3771,9.8497,-0.0649,0.2699,9.8027,0.011,0.055,-0.0562,-5.6,-29,-43.5,2.923077431,-1.54,0.24,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,110911,2015-10-30 10:24:08:044,1446171848044.0 \n0.6692,0.5183,10.0772,-0.11,0.4263,9.7968,0.1698,-0.0159,0.2676,-5.5,-29.4,-43.5,2.94210152,-2.49,0.64,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,111013,2015-10-30 10:24:08:146,1446171848146.0 \n-0.2897,0.1856,9.985,-0.0777,0.2528,9.8031,0.0843,-0.2236,0.2358,-5.8,-29.5,-43.7,2.922553832,-1.58,0.24,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,111115,2015-10-30 10:24:08:248,1446171848248.0 \n0.0646,0.5734,9.1459,0.0815,0.2474,9.8032,-0.1686,-0.1075,0.1087,-6.5,-29.5,-44,2.942276053,-1.45,-0.48,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,111217,2015-10-30 10:24:08:350,1446171848350.0 \n-0.4621,0.6081,9.1806,0.1441,0.0695,9.8053,0.0293,-0.0794,0.0611,-7,-29.1,-44.2,2.921506635,-0.34,-0.74,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,111319,2015-10-30 10:24:08:452,1446171848452.0 \n-0.4681,0.8583,9.007,0.1107,0.2386,9.8031,0.1625,-0.0782,-0.1332,-7.5,-28.8,-44.4,2.912779989,-1.39,-0.65,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,111422,2015-10-30 10:24:08:555,1446171848555.0 \n-0.7877,0.2143,10.9176,0.1685,0.3543,9.7988,0.1808,0.0782,-0.0843,-7.6,-28.9,-43.7,2.883109391,-2.07,-0.98,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,111524,2015-10-30 10:24:08:657,1446171848657.0 \n-0.5818,-0.668,11.2551,-0.0359,0.1923,9.8047,-0.5962,0.3299,-0.3201,-7.4,-29.6,-43.2,2.906671336,-2.19,-0.29,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,111625,2015-10-30 10:24:08:758,1446171848758.0 \n0.8368,0.4489,8.1714,-0.0302,-0.0044,9.8066,-0.2224,0.1246,-0.1405,-7,-29.5,-43.6,2.901435349,-0.17,0.09,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,111728,2015-10-30 10:24:08:861,1446171848861.0 \n-0.1568,0.6919,7.8266,-0.1298,-0.1826,9.8041,-0.1442,0.1148,-0.1381,-6.5,-29.1,-43.9,2.929709682,0.88,0.5,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,111830,2015-10-30 10:24:08:963,1446171848963.0 \n-0.6728,0.4549,9.6486,-0.0828,-0.1804,9.8046,0.1637,-0.1796,0.0086,-5.8,-28.1,-44,2.923950096,1.05,0.48,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,111932,2015-10-30 10:24:09:065,1446171849065.0 \n-0.7649,0.012,11.1271,-0.2257,-0.1253,9.8033,0.3848,0.0611,0.369,-5.5,-27.8,-43.9,2.94210152,1.13,1.09,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,112033,2015-10-30 10:24:09:166,1446171849166.0 \n0.4142,0.0646,11.8046,-0.0619,0.1755,9.8049,-0.1674,-0.8076,0.1576,-5.8,-28,-43.5,2.886949116,-1.08,1.44,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,112136,2015-10-30 10:24:09:269,1446171849269.0 \n-0.0431,0.0742,7.7548,0.5591,0.2571,9.7873,0.3543,-0.5229,0.4753,-6.9,-28.3,-43.1,2.958507615,-1.6,-2.71,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,112237,2015-10-30 10:24:09:370,1446171849370.0 \n0.3376,0.255,7.9224,0.783,0.0605,9.7752,-0.1857,-0.0183,0.1552,-9.4,-28.4,-42.5,2.941752454,-0.35,-4.58,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,112340,2015-10-30 10:24:09:473,1446171849473.0 \n0.0395,0.8643,7.9176,0.5398,-0.1413,9.7908,0.1405,0.2285,0.0012,-10.8,-27.9,-42.8,2.861292776,1.12,-3.57,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,112442,2015-10-30 10:24:09:575,1446171849575.0 \n-0.346,-0.067,12.396,0.219,-0.2562,9.8009,-0.3103,0.4056,-0.1991,-11.4,-27.1,-43,2.798809988,1.5,-1.28,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,112543,2015-10-30 10:24:09:676,1446171849676.0 \n-0.2705,0.1927,9.7444,-0.0647,-0.133,9.8055,0.1772,0.2053,0.0195,-10.8,-26.5,-43.5,2.766521397,1.39,-0.47,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,112646,2015-10-30 10:24:09:779,1446171849779.0 \n0.1879,-0.0479,10.9547,-0.061,-0.4364,9.7967,0.3751,0.0892,0.1087,-9.5,-26.1,-43.9,2.82097567,2.55,0.36,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,112747,2015-10-30 10:24:09:880,1446171849880.0 \n-0.6045,-0.4752,10.1754,-0.1289,-0.4708,9.7945,-0.3604,0.0147,-0.3531,-8.7,-25.7,-44.2,2.80963103,1.94,0.61,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,112849,2015-10-30 10:24:09:982,1446171849982.0 \n-0.5243,0.0168,8.4455,-0.2092,-0.423,9.7953,0.0428,0.1234,-0.0733,-7.8,-25.5,-44.4,2.829178717,2.66,0.94,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,112951,2015-10-30 10:24:10:084,1446171850084.0 \n-0.4741,0.1317,9.3996,-0.1617,-0.2793,9.8013,0.0635,0.0794,0.066,-7.3,-25.5,-44.2,2.856231321,1.78,0.95,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,113053,2015-10-30 10:24:10:186,1446171850186.0 \n-0.6967,-0.0048,12.2404,-0.1027,-0.0794,9.8058,0.3995,0.1918,0.3641,-6.9,-25.8,-44.2,2.868972224,1.06,0.65,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,113155,2015-10-30 10:24:10:288,1446171850288.0 \n-0.7027,-0.0455,11.9411,-0.0658,-0.0861,9.8061,-0.3274,-0.2285,0.1356,-7.3,-26.1,-44,2.871764751,0.5,0.38,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,113258,2015-10-30 10:24:10:391,1446171850391.0 \n-0.182,0.5136,9.0573,0.002,-0.2107,9.8044,-0.1869,-0.2334,0.0623,-7.5,-26.1,-44.2,2.862339973,0.78,0.82,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,113359,2015-10-30 10:24:10:492,1446171850492.0 \n-0.9529,-0.0539,9.8569,-0.1296,-0.5278,9.7916,0.0819,-0.0183,-0.0183,-7.9,-25.5,-44.4,2.841745088,2.74,0.48,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,113461,2015-10-30 10:24:10:594,1446171850594.0 \n-0.5387,0.4657,8.1032,-0.2225,-0.2479,9.801,0.3677,0.2053,-0.0012,-7.7,-25,-44.9,2.809107431,1.45,1.3,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,113563,2015-10-30 10:24:10:696,1446171850696.0 \n-0.8332,-0.3017,11.2132,-0.2295,-0.0342,9.8039,0.182,0.0122,-0.2199,-7.5,-25.1,-44.8,2.83947616,0.77,1.25,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,113665,2015-10-30 10:24:10:798,1446171850798.0 \n0.3089,-0.6823,10.0533,-0.2718,0.0264,9.8028,-0.325,0.0929,-0.3641,-6.7,-25.7,-44.4,2.830400448,-0.51,1.62,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,113768,2015-10-30 10:24:10:901,1446171850901.0 \n0.146,-0.0359,8.9615,-0.2353,-0.2482,9.8007,-0.2065,-0.1173,-0.2162,-6.1,-26.1,-44.3,2.876302607,1.37,1.76,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,113869,2015-10-30 10:24:11:002,1446171851002.0 \n-0.3352,-0.3077,9.6055,0.0092,-0.5514,9.7911,-0.3836,-0.2834,-0.1943,-5.5,-25.6,-44.6,2.969328656,3.22,-0.05,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,113972,2015-10-30 10:24:11:105,1446171851105.0 \n-1.1875,0.4262,8.6143,-0.2143,-0.6799,9.7807,0.1417,0.4826,0.1833,-5.3,-24.5,-45.2,2.949431903,4.26,0.39,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,114073,2015-10-30 10:24:11:206,1446171851206.0 \n-0.8104,0.0084,10.8374,-0.3638,-0.526,9.7858,0.4093,0.1527,0.3152,-5.2,-24.1,-45.3,2.900388151,3.6,2.02,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,114176,2015-10-30 10:24:11:309,1446171851309.0 \n-0.0778,0.4094,9.1267,-0.4354,-0.1328,9.7961,0.4557,0.0037,0.4337,-4.9,-24.5,-45.5,2.864608901,0.78,2.54,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,114277,2015-10-30 10:24:11:410,1446171851410.0 \n-0.9002,-0.826,11.1821,-0.1706,-0.046,9.8051,-0.0501,-0.1784,0.2028,-5.1,-25.2,-45.3,2.90632227,0.18,1.31,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,114379,2015-10-30 10:24:11:512,1446171851512.0 \n-0.2538,0.1628,7.926,0.0313,-0.0045,9.8066,-0.2822,0.0623,-0.121,-6.3,-26,-44.5,2.920110372,0.03,-0.18,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,114481,2015-10-30 10:24:11:614,1446171851614.0 \n-0.419,0.4669,8.9711,0.0487,-0.2167,9.8041,-0.1283,-0.1161,-0.0098,-7,-26.1,-44.2,2.888868978,1.12,-0.08,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,114584,2015-10-30 10:24:11:717,1446171851717.0 \n0.0168,0.7099,8.7017,0.0562,-0.1032,9.8059,0.0464,-0.0061,0.0391,-7.4,-26,-44,2.893930433,0.97,-0.31,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,114686,2015-10-30 10:24:11:819,1446171851819.0 \n-0.7733,0.1089,11.248,-0.0537,-0.0209,9.8065,0.2847,0.1148,-0.1588,-7.3,-25.9,-44.1,2.879095134,0.54,0.13,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,114788,2015-10-30 10:24:11:921,1446171851921.0 \n0.5567,-0.5758,11.3497,-0.119,-0.1273,9.8051,-0.2334,0.0049,-0.1906,-7,-26.1,-44.2,2.86932129,-0.06,0.32,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,114889,2015-10-30 10:24:12:022,1446171852022.0 \n0.4465,-0.2969,8.6598,-0.1435,-0.4169,9.7967,-0.1662,-0.1319,-0.0354,-6.2,-26.1,-44.7,2.897246558,1.8,1.06,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,114991,2015-10-30 10:24:12:124,1446171852124.0 \n0.085,0.3292,8.4396,-0.0752,-0.6937,9.7818,-0.2321,0.0574,-0.0159,-5.6,-25.2,-45.2,2.916619713,3.43,0.42,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,115094,2015-10-30 10:24:12:227,1446171852227.0 \n-0.4345,0.2514,9.8533,-0.045,-0.7408,9.7785,-0.0318,0.0305,-0.0195,-5.4,-24.3,-45.8,2.949431903,4.28,0.4,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,115196,2015-10-30 10:24:12:329,1446171852329.0 \n-0.832,-0.419,11.8645,-0.1071,-0.6662,9.7834,0.0452,0.0342,0.0525,-5.5,-23.7,-46.1,2.942625119,4.04,0.6,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,115297,2015-10-30 10:24:12:430,1446171852430.0 \n0.4621,-1.3743,12.0608,-0.0511,-0.3438,9.8005,0.022,-0.2162,-0.0391,-5.5,-23.9,-46,2.939658059,2.01,0.3,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,115399,2015-10-30 10:24:12:532,1446171852532.0 \n-0.0431,0.4621,7.7596,0.0621,-0.2733,9.8026,0.3323,0.1234,0.16,-5.7,-24.4,-45.7,2.91941224,1.6,-0.36,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,115502,2015-10-30 10:24:12:635,1446171852635.0 \n-1.2797,-0.3675,10.2915,0.0175,-0.2187,9.8042,-0.1356,-0.0855,0.0012,-5.8,-25.1,-45.5,2.916619713,0.99,-0.13,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,115603,2015-10-30 10:24:12:736,1446171852736.0 \n-0.8236,0.8212,7.9799,-0.3732,0.0371,9.7995,0.4606,0.0489,0.3128,-5.7,-25.6,-45.1,2.885029254,1.21,1.36,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,115705,2015-10-30 10:24:12:838,1446171852838.0 \n-0.6716,0.4381,10.392,-0.4078,0.1695,9.7967,0.0159,0.0721,-0.0305,-5.3,-26.5,-44.7,2.877175272,-0.98,2.34,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,115807,2015-10-30 10:24:12:940,1446171852940.0 \n-0.6955,0.4741,10.058,-0.4295,0.3794,9.7899,0.3213,-0.0061,-0.11,-5.1,-27,-44.3,2.870717554,-1.83,2.75,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,115910,2015-10-30 10:24:13:043,1446171853043.0 \n-1.0403,-0.4369,10.5477,-0.556,0.234,9.7881,-0.1527,0.2639,-0.2309,-4.7,-27.8,-44.3,2.875429943,-1.32,3.08,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,116011,2015-10-30 10:24:13:144,1446171853144.0 \n-0.3005,0.3112,9.8414,-0.478,0.1034,9.7944,-0.3543,-0.1197,-0.0281,-4.3,-27.9,-44.2,2.912430923,-1.24,3.02,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,116113,2015-10-30 10:24:13:246,1446171853246.0 \n-0.4465,1.1839,8.2253,-0.4414,0.031,9.7967,0.0012,-0.0635,0.0684,-3.9,-27.7,-44.6,2.928662485,-0.18,2.58,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,116215,2015-10-30 10:24:13:348,1446171853348.0 \n-0.8056,0.7051,9.1028,-0.433,0.0136,9.7971,-0.0684,0.0281,-0.0623,-4.1,-27.4,-44.8,2.923775563,-0.19,2.48,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,116317,2015-10-30 10:24:13:450,1446171853450.0 \n-0.8332,1.4485,10.9858,-0.4357,0.1129,9.7963,0.248,-0.0831,0.1283,-4.2,-27.2,-44.9,2.918015976,-0.23,2.68,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,116419,2015-10-30 10:24:13:552,1446171853552.0 \n-0.6488,-0.905,14.3508,-0.1682,0.0234,9.8052,-0.5339,0.2028,-0.1124,-4.5,-27.3,-45,2.936690999,-1.47,1.75,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,116521,2015-10-30 10:24:13:654,1446171853654.0 \n-0.5507,0.7745,7.847,-0.1063,0.0541,9.8059,0.248,-0.2236,0.259,-4.9,-27.2,-44.8,2.928662485,-0.18,1.03,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,116624,2015-10-30 10:24:13:757,1446171853757.0 \n-0.6165,0.4142,9.5996,-0.0746,-0.0863,9.806,-0.0806,-0.0794,-0.0159,-5.5,-27.2,-44.8,2.94629031,0.4,0.51,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,116725,2015-10-30 10:24:13:858,1446171853858.0 \n-0.3172,1.1732,8.3594,-0.1531,0.1139,9.8048,0.1393,0.0721,-0.11,-6,-27.1,-44.9,2.8937559,-0.67,0.89,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,116827,2015-10-30 10:24:13:960,1446171853960.0 \n-0.8308,0.3747,11.2085,-0.2492,0.2316,9.8008,0.0635,0.0232,-0.2016,-6.1,-27.3,-45.1,2.88066593,-1.11,1.25,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,116930,2015-10-30 10:24:14:063,1446171854063.0 \n0.5626,0.0766,10.5393,-0.2882,0.3821,9.795,0.0513,-0.1283,-0.1112,-5.6,-27.9,-44.6,2.86391077,-2.23,1.89,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,117031,2015-10-30 10:24:14:164,1446171854164.0 \n-0.3723,-0.3998,11.1713,-0.1249,0.076,9.8056,0.022,-0.5644,-0.1906,-5,-28.2,-44.2,2.902482546,-0.73,2.2,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,117133,2015-10-30 10:24:14:266,1446171854266.0 \n0.0227,0.6476,8.0158,-0.0361,-0.0117,9.8066,-0.0819,0.0269,0.0244,-4.5,-28.1,-44.1,2.995508595,-0.08,0.15,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,117236,2015-10-30 10:24:14:369,1446171854369.0 \n-0.4022,1.0774,8.2899,-0.0458,-0.0337,9.8065,0.0183,-0.0134,0.1002,-4.6,-27.6,-44.7,2.958682148,0.2,0.27,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,117338,2015-10-30 10:24:14:471,1446171854471.0 \n-0.4202,0.3304,10.0533,-0.0763,0.0618,9.8062,0.1588,0.0672,0.1112,-5,-27.6,-45.2,2.954842424,-0.14,0.35,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,117439,2015-10-30 10:24:14:572,1446171854572.0 \n0.4896,0.6895,9.6355,-0.2132,0.3544,9.7979,0.0183,-0.1429,0.2456,-5.3,-27.9,-45.4,2.920983036,-1.81,1.22,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,117542,2015-10-30 10:24:14:675,1446171854675.0 \n-0.4405,0.5183,8.9902,-0.1875,0.295,9.8004,-0.0122,0.1368,0.1051,-5.4,-28.3,-45.1,2.918365042,-1.87,1.3,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,117644,2015-10-30 10:24:14:777,1446171854777.0 \n-0.2035,0.0862,9.1698,0.0846,0.1281,9.8054,-0.2786,-0.0965,-0.1429,-5.9,-28.4,-44.4,2.939483526,-0.75,-0.49,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,117746,2015-10-30 10:24:14:879,1446171854879.0 \n-0.7853,0.3663,9.1291,0.0088,-0.0853,9.8063,-0.0452,-0.0599,-0.0318,-6.1,-28.1,-44.5,2.931105946,0.24,0.02,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,117848,2015-10-30 10:24:14:981,1446171854981.0 \n-0.8116,0.6321,9.9431,-0.0375,-0.0293,9.8065,0.0611,0.0831,-0.1148,-6.2,-27.4,-44.9,2.921157569,0.23,0.11,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,117949,2015-10-30 10:24:15:082,1446171855082.0 \n-0.5124,-0.0096,10.6578,-0.1217,0.0921,9.8055,0.1539,0.1222,-0.0929,-5.8,-27.4,-45,2.899690019,-0.54,0.71,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,118051,2015-10-30 10:24:15:184,1446171855184.0 \n-0.4824,-0.249,11.4347,-0.1707,0.0347,9.8051,-0.1087,0.2663,-0.1051,-5.5,-27.5,-45,2.938261796,-0.63,0.59,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,118153,2015-10-30 10:24:15:286,1446171855286.0 \n0.4298,0.0563,9.7791,0.0765,0.0988,9.8059,-0.2126,-0.2529,-0.066,-5.2,-27.9,-44.9,2.955016957,-0.81,0.21,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,118255,2015-10-30 10:24:15:388,1446171855388.0 \n-0.1125,0.5351,8.3115,-0.0021,-0.0689,9.8064,-0.1649,0.2028,0.0257,-5.4,-27.8,-44.8,2.972993848,0.14,-0.27,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,118357,2015-10-30 10:24:15:490,1446171855490.0 \n0.0156,0.8739,9.0453,-0.0854,-0.1513,9.8051,-0.0354,0.0672,0.0794,-5.3,-27.6,-44.9,2.955889621,0.88,0.5,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,118460,2015-10-30 10:24:15:593,1446171855593.0 \n-0.5842,0.0551,11.7687,-0.24,-0.1732,9.8022,0.1503,0.0415,0.1185,-5.2,-27.3,-45.1,2.937389131,0.98,0.96,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,118561,2015-10-30 10:24:15:694,1446171855694.0 \n-0.431,-0.3627,12.2128,-0.3204,0.052,9.8013,0.3189,0.16,0.1332,-4.8,-27.2,-45.2,2.902482546,-0.37,1.93,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,118664,2015-10-30 10:24:15:797,1446171855797.0 \n-0.8679,-0.4381,10.3034,-0.2231,0.0628,9.8039,0.1429,-0.3274,0.1625,-4.7,-27.3,-45,2.906845869,-0.14,1.83,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,118765,2015-10-30 10:24:15:898,1446171855898.0 \n-0.1772,0.2346,8.4527,-0.0764,0.0958,9.8059,-0.1759,0.0281,0.0489,-5.2,-27.7,-44.6,2.949780969,-0.56,0.45,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,118867,2015-10-30 10:24:16:000,1446171856000.0 \n-0.5842,0.6345,8.8681,-0.0852,-0.0016,9.8063,-0.0599,0.0171,-0.044,-5.7,-27.8,-44.3,2.92063397,-0.03,0.37,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,118970,2015-10-30 10:24:16:103,1446171856103.0 \n-0.7266,0.7877,9.511,-0.2158,0.1173,9.8036,0.0929,0.0782,-0.1148,-6.2,-27.8,-44.5,2.896199361,-0.54,1.18,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,119072,2015-10-30 10:24:16:205,1446171856205.0 \n0.1233,1.1756,9.511,-0.2695,0.4202,9.7939,0.3861,0.1136,-0.0293,-5.9,-28.2,-44.4,2.872113817,-2.46,1.58,36.813408,-119.74888,254.5,336.3064648,4.38,19.35484,181.37,16 / 16,119174,2015-10-30 10:24:16:307,1446171856307.0 \n-0.5854,-0.4262,11.8369,-0.3291,0.2532,9.7979,0.0257,0.0977,-0.1136,-5.5,-28.6,-44.3,2.92360103,-2.21,1.36,36.813313,-119.74886,256.21,336.3064648,4.57,19.35484,196.98,16 / 16,119275,2015-10-30 10:24:16:408,1446171856408.0 \n-0.2634,0.0371,9.7516,-0.3249,0.075,9.801,-0.2761,-0.1344,-0.2236,-4.6,-29,-44.3,2.911034659,-0.92,2.14,36.813313,-119.74886,256.21,336.3064648,4.57,19.35484,196.98,16 / 16,119377,2015-10-30 10:24:16:510,1446171856510.0 \n-0.8009,0.6883,7.7668,-0.3512,0.0231,9.8003,0.0293,0.0232,-0.1051,-4,-28.7,-44.2,2.95222443,-0.09,2.02,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,119479,2015-10-30 10:24:16:612,1446171856612.0 \n-0.808,0.911,9.6307,-0.2988,0.0663,9.8019,0.0452,-0.0806,0.0733,-3.5,-28.3,-44.7,2.98503662,-0.39,1.75,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,119581,2015-10-30 10:24:16:714,1446171856714.0 \n-1.0726,0.3136,12.2056,-0.2231,0.1661,9.8027,0.1063,-0.1173,0.1686,-3.4,-28.3,-44.6,2.990272607,-0.78,1.5,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,119684,2015-10-30 10:24:16:817,1446171856817.0 \n-1.0307,-0.8583,13.3968,-0.0817,0.2728,9.8025,-0.3176,-0.2737,0.0415,-4,-28.8,-44.2,2.975437309,-2.21,0.75,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,119785,2015-10-30 10:24:16:918,1446171856918.0 \n-0.4453,0.3807,9.1231,-0.0318,0.2901,9.8023,-0.099,-0.1124,0.2138,-4.5,-28.9,-44,2.981371428,-1.67,0.62,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,119887,2015-10-30 10:24:17:020,1446171857020.0 \n-0.7638,0.3579,8.4839,-0.066,0.1079,9.8058,-0.259,0.1063,0.1185,-5.5,-28.9,-43.9,2.957984016,-0.63,0.39,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,119989,2015-10-30 10:24:17:122,1446171857122.0 \n-0.5315,1.1432,8.4886,-0.1592,0.1438,9.8043,0.0929,0.1234,0.0195,-6,-28.5,-44,2.904751474,-0.73,0.81,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,120091,2015-10-30 10:24:17:224,1446171857224.0 \n-0.978,0.6129,9.8043,-0.2076,0.1827,9.8028,-0.0073,-0.0648,-0.1625,-6.1,-28.3,-44.2,2.891836038,-1.07,1.21,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,120193,2015-10-30 10:24:17:326,1446171857326.0 \n0.4645,0.9373,9.4284,-0.123,0.3873,9.7982,0.2236,-0.2859,-0.0257,-6,-28.5,-43.9,2.899690019,-1.52,0.8,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,120295,2015-10-30 10:24:17:428,1446171857428.0 \n-0.2753,-0.6045,11.4575,-0.1527,0.2082,9.8033,-0.4068,0.3091,-0.2798,-5.9,-28.9,-44,2.907718534,-1.22,0.89,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,120397,2015-10-30 10:24:17:530,1446171857530.0 \n-0.3208,-0.1065,10.4339,-0.1718,0.1059,9.8046,-0.303,0.0098,-0.1173,-5.5,-28.9,-44,2.939832592,-1.05,1,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,120500,2015-10-30 10:24:17:633,1446171857633.0 \n-0.5303,1.1552,6.705,-0.3878,0.0398,9.7989,-0.0464,0.0134,-0.0122,-4.9,-28.8,-44.4,2.91522345,-0.24,2.14,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,120601,2015-10-30 10:24:17:734,1446171857734.0 \n-0.5734,1.1325,9.0884,-0.4102,0.0715,9.7978,0.1063,0.0696,0.1112,-4.4,-28.5,-44.7,2.933549407,-0.4,2.36,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,120703,2015-10-30 10:24:17:836,1446171857836.0 \n-0.5686,0.8212,10.6159,-0.365,0.1411,9.7988,0.1881,0.0293,0.3005,-4.2,-28.4,-44.6,2.937040065,-0.82,2.13,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,120805,2015-10-30 10:24:17:938,1446171857938.0 \n-0.006,-0.6812,12.3002,-0.2012,0.2548,9.8013,-0.4044,-0.2615,-0.1552,-4.8,-28.6,-44.4,2.922902898,-1.8,1.48,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,120908,2015-10-30 10:24:18:041,1446171858041.0 \n-1.0451,0.158,8.4839,-0.1376,0.1089,9.8051,0.0061,0.0073,0.1185,-5.4,-28.7,-44.2,2.942625119,-0.67,0.97,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,121009,2015-10-30 10:24:18:142,1446171858142.0 \n-0.5255,0.3376,9.3314,-0.0237,-0.1398,9.8056,-0.3323,0.1344,0.0709,-6.6,-28.3,-44.2,2.898293756,0.82,0.14,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,121112,2015-10-30 10:24:18:245,1446171858245.0 \n-0.5614,0.8727,8.2588,-0.1293,-0.1519,9.8046,0.066,0.0269,0.0195,-6.7,-27.9,-44.5,2.887298182,1.07,0.64,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,121213,2015-10-30 10:24:18:346,1446171858346.0 \n-0.7877,0.4082,11.2372,-0.2293,-0.0277,9.8039,0.1625,0.0244,-0.2028,-7,-27.2,-44.9,2.859023848,0.41,1.18,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,121315,2015-10-30 10:24:18:448,1446171858448.0 \n-0.2322,-0.0958,10.5824,-0.2392,0.2276,9.8011,0.325,0.0733,-0.1332,-6.7,-27.5,-45,2.845933878,-0.7,1.35,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,121418,2015-10-30 10:24:18:551,1446171858551.0 \n-0.735,-0.3711,10.3166,-0.3399,0.0997,9.8003,-0.1319,0.011,-0.3005,-6,-28.1,-44.5,2.875080877,-0.58,1.99,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,121519,2015-10-30 10:24:18:652,1446171858652.0 \n-0.3843,0.073,8.9364,-0.1614,0.0158,9.8053,0.0904,0.0428,0.0904,-5.5,-28.3,-44.1,2.940705257,-0.13,0.89,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,121622,2015-10-30 10:24:18:755,1446171858755.0 \n-0.5195,0.9337,7.203,-0.07,0.1531,9.8052,0.1723,-0.1319,0.0648,-5.2,-28.4,-44.1,2.944719514,-0.67,0.63,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,121723,2015-10-30 10:24:18:856,1446171858856.0 \n-0.5112,1.1121,9.5205,-0.0971,0.1768,9.8046,-0.0489,0.1197,-0.0269,-5.4,-28.5,-44.1,2.944370448,-1.03,0.57,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,121825,2015-10-30 10:24:18:958,1446171858958.0 \n-0.5674,0.662,11.0804,-0.2949,0.2989,9.7977,0.2456,0.1649,0.2615,-5.4,-28.7,-44.2,2.938959927,-1.16,1.01,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,121927,2015-10-30 10:24:19:060,1446171859060.0 \n-1.1863,-1.3755,14.8213,-0.0789,0.1932,9.8044,-0.2077,-0.3861,-0.0635,-5.5,-29,-44.1,2.928662485,-1.87,1.25,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,122030,2015-10-30 10:24:19:163,1446171859163.0 \n-0.723,0.4417,8.5246,-0.0587,0.1759,9.8049,0.022,-0.3555,0.1454,-5.5,-28.9,-44.5,2.941228855,-1.18,0.92,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,122131,2015-10-30 10:24:19:264,1446171859264.0 \n-0.8966,0.1245,9.8797,0.0257,-0.1227,9.8058,-0.2162,-0.0379,-0.022,-6.2,-28.5,-44.8,2.932502209,0.11,-0.05,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,122234,2015-10-30 10:24:19:367,1446171859367.0 \n-0.2598,1.1325,7.6591,-0.0492,0.0178,9.8065,0.0024,0.0648,-0.0843,-6.7,-28,-45,2.894803097,0.1,0.1,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,122336,2015-10-30 10:24:19:469,1446171859469.0 \n-0.9421,0.1975,12.3984,-0.0401,0.0089,9.8066,-0.0293,-0.0977,-0.2443,-7.1,-27.7,-44.9,2.890090708,-0.05,0.23,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,122438,2015-10-30 10:24:19:571,1446171859571.0 \n0.5686,0.1508,11.6023,-0.0452,0.1031,9.806,0.1955,-0.0195,-0.1148,-6.9,-27.9,-44.7,2.888868978,-0.19,0.24,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,122539,2015-10-30 10:24:19:672,1446171859672.0 \n-0.3232,-0.5124,11.236,-0.0978,-0.0745,9.8059,0.0232,-0.292,-0.2175,-6,-28.3,-44.6,2.905798672,0.01,0.93,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,122642,2015-10-30 10:24:19:775,1446171859775.0 \n-0.346,-0.1556,9.9503,0.049,-0.1307,9.8057,-0.2541,-0.1246,-0.1662,-5.3,-28.3,-44.7,2.976135441,0.76,-0.29,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,122743,2015-10-30 10:24:19:876,1446171859876.0 \n-0.0646,1.2905,6.7181,-0.0827,-0.0748,9.806,0.0281,0.1918,-0.033,-5,-28.1,-45,2.971248519,0.57,-0.13,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,122845,2015-10-30 10:24:19:978,1446171859978.0 \n-0.3615,1.1229,10.5117,-0.0833,-0.1311,9.8054,-0.0367,0.1185,0.0183,-4.8,-27.7,-45.4,2.95344616,0.63,0.54,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,122947,2015-10-30 10:24:20:080,1446171860080.0 \n-0.6524,0.9972,10.0497,-0.1521,0.1858,9.8037,0.4056,0,0.3311,-4.7,-27.9,-45.6,2.938785395,-0.19,0.91,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,123049,2015-10-30 10:24:20:182,1446171860182.0 \n-0.8643,-0.3603,8.5868,-0.0503,0.0709,9.8063,-0.4606,-0.0599,0.0611,-5.1,-28.4,-45.1,2.963394537,-0.46,-0.03,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,123151,2015-10-30 10:24:20:284,1446171860284.0 \n-0.9529,-0.2119,9.3805,-0.0815,-0.1201,9.8056,-0.4081,0.1429,0.2199,-5.7,-28.4,-44.6,2.92360103,-0.02,0.25,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,123254,2015-10-30 10:24:20:387,1446171860387.0 \n-0.3496,0.6249,8.3306,-0.1687,-0.2803,9.8012,0.2138,-0.0049,0.2065,-6.4,-27.8,-44.8,2.914176252,1.64,0.99,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,123355,2015-10-30 10:24:20:488,1446171860488.0 \n-0.2322,0.8882,8.6024,-0.2156,-0.0742,9.804,0.1515,0.0452,0.0183,-6.8,-27.2,-44.8,2.857103986,0.7,1.34,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,123458,2015-10-30 10:24:20:591,1446171860591.0 \n-0.6835,0.3005,10.5453,-0.2613,0.0027,9.8032,0.2443,0.0195,-0.2236,-6.9,-27,-45,2.852740662,0.2,1.36,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,123559,2015-10-30 10:24:20:692,1446171860692.0 \n0.8966,0.1413,11.2504,-0.2744,0.1842,9.8011,0.121,-0.0354,-0.1637,-6.6,-27.7,-44.5,2.848377339,-1.01,1.59,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,123662,2015-10-30 10:24:20:795,1446171860795.0 \n-0.3364,-0.2071,9.4906,-0.4386,-0.0579,9.7967,-0.1222,-0.0134,-0.2737,-5.8,-28.1,-44.6,2.862863572,0.16,2.62,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,123763,2015-10-30 10:24:20:896,1446171860896.0 \n-0.4944,0.4214,7.8697,-0.4769,-0.3012,9.7904,-0.16,0.1002,-0.1564,-4.7,-27.9,-44.3,2.903006145,1.76,2.79,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,123866,2015-10-30 10:24:20:999,1446171860999.0 \n-0.8464,0.8475,8.4551,-0.4207,-0.4027,9.7893,-0.0428,-0.1588,-0.0806,-4.1,-27.3,-44.8,2.924299162,2,2.94,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,123967,2015-10-30 10:24:21:100,1446171861100.0 \n-0.911,-0.0108,11.6861,-0.2868,-0.401,9.7942,-0.0721,-0.1344,-0.0953,-3.9,-26.6,-44.6,2.950828166,2.31,1.99,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,124070,2015-10-30 10:24:21:203,1446171861203.0 \n-0.0287,0.6668,8.8657,-0.2928,-0.0779,9.802,0.4569,0.1735,0.3286,-4,-26.6,-44.7,2.948733771,0.45,1.71,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,124171,2015-10-30 10:24:21:304,1446171861304.0 \n-1.7154,-1.3946,11.7184,-0.1826,-0.2416,9.802,-0.1368,0.2663,0.2114,-4.3,-26.7,-44.6,2.977008105,1.15,0.81,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,124274,2015-10-30 10:24:21:407,1446171861407.0 \n-0.2945,-0.1532,8.187,-0.0225,-0.1792,9.805,-0.2248,-0.0086,0.0501,-5,-26.9,-44.4,2.947861107,0.97,0.58,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,124376,2015-10-30 10:24:21:509,1446171861509.0 \n-0.747,0.1472,9.3805,-0.0537,-0.3502,9.8002,-0.1197,0.0024,-0.0379,-5.5,-26.7,-44.7,2.960427477,1.95,0.28,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,124478,2015-10-30 10:24:21:611,1446171861611.0 \n-1.0331,0.3316,9.9455,-0.1762,-0.2397,9.8021,0.0183,0.099,-0.1381,-5.9,-26.3,-44.7,2.895326696,1.4,1.03,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,124580,2015-10-30 10:24:21:713,1446171861713.0 \n-1.0044,-0.0419,11.0229,-0.2228,-0.07,9.8039,0.303,0.1356,-0.1319,-5.6,-26.4,-44.9,2.880840463,0.41,1.3,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,124681,2015-10-30 10:24:21:814,1446171861814.0 \n-0.7542,-1.6257,13.8744,-0.2724,-0.1022,9.8023,-0.3384,-0.0648,-0.204,-5,-26.8,-44.5,2.918714108,0.6,1.59,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,124783,2015-10-30 10:24:21:916,1446171861916.0 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\n0.1221,0.2574,9.3242,-0.1499,0.1767,9.8039,0.2932,-0.0403,0.1576,-5,-26.6,-44.5,2.928313419,-0.62,0.97,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,125294,2015-10-30 10:24:22:427,1446171862427.0 \n-0.9182,-0.1652,9.414,-0.2854,-0.0475,9.8024,0.1833,-0.0757,0.1943,-5.1,-26.8,-44.3,2.933374874,0.42,1.01,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,125396,2015-10-30 10:24:22:529,1446171862529.0 \n-0.1221,0.2873,9.5361,-0.1374,0.0387,9.8056,-0.0183,-0.2199,0.1539,-5.2,-27.3,-43.9,2.935294736,-0.23,0.8,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,125497,2015-10-30 10:24:22:630,1446171862630.0 \n-0.5303,0.7027,8.6455,-0.1935,-0.0784,9.8044,-0.0232,0.099,0.0709,-5.3,-27.2,-43.5,2.935120203,0.43,0.97,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,125599,2015-10-30 10:24:22:732,1446171862732.0 \n-0.7949,1.2031,8.8394,-0.207,0.018,9.8044,0.0342,-0.0098,-0.0782,-5.4,-27.1,-43.7,2.9223793,0.04,1.34,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,125701,2015-10-30 10:24:22:834,1446171862834.0 \n-0.7697,0.504,11.3078,-0.1626,0.0906,9.8049,0.0794,-0.1148,-0.1148,-5.6,-27,-43.7,2.891486972,-0.42,1.06,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,125803,2015-10-30 10:24:22:936,1446171862936.0 \n1.0463,0.3903,10.3394,-0.0933,0.1603,9.8049,-0.1662,-0.0977,-0.1637,-5.7,-27.3,-43.9,2.89497763,-1.23,0.73,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,125906,2015-10-30 10:24:23:039,1446171863039.0 \n-0.0431,0.0826,9.1889,-0.0851,0.039,9.8062,0.2639,-0.4325,0.0562,-5.8,-27.3,-43.9,2.902657079,0.23,0.81,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,126007,2015-10-30 10:24:23:140,1446171863140.0 \n0.152,0.5854,8.4132,0.1518,-0.0285,9.8054,-0.2627,-0.0806,-0.066,-5.8,-27.5,-43.7,2.94803564,0.17,-0.89,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,126109,2015-10-30 10:24:23:242,1446171863242.0 \n-0.0982,1.2941,8.8442,0.1291,0.03,9.8058,-0.0024,0.0806,-0.0428,-6.1,-27.4,-43.9,2.942450586,-0.18,-0.75,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,126211,2015-10-30 10:24:23:344,1446171863344.0 \n-0.6225,0.729,10.7643,0.0309,0.0985,9.8061,0.0147,0.1955,-0.0733,-6.1,-27.6,-44.2,2.940705257,-0.61,-0.51,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,126313,2015-10-30 10:24:23:446,1446171863446.0 \n0.0611,1.1408,9.8665,-0.047,0.2845,9.8024,0.2334,0.0293,0.2615,-5.9,-27.9,-44.1,2.913129055,-1.66,0.27,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,126415,2015-10-30 10:24:23:548,1446171863548.0 \n-1.0367,-0.8703,13.028,0.1275,0.2087,9.8036,-0.3824,-0.3629,0.0586,-5.8,-28.1,-43.8,2.93494567,-1.68,-0.52,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,126517,2015-10-30 10:24:23:650,1446171863650.0 \n0.3376,0.6608,8.3067,0.293,0.3292,9.7967,0.0709,-0.2871,0.259,-6.4,-28.2,-43.4,2.965837998,-1.92,-1.71,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,126620,2015-10-30 10:24:23:753,1446171863753.0 \n-0.0479,0.7769,8.8741,0.3177,0.1911,9.7996,0.0696,-0.0171,-0.0476,-7.2,-28.1,-43.5,2.939832592,-1.21,-1.94,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,126721,2015-10-30 10:24:23:854,1446171863854.0 \n-0.2047,1.3096,8.3833,0.1944,0.3227,9.7994,0.1552,0.2114,-0.0709,-8.2,-27.8,-44,2.887298182,-1.68,-1.38,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,126824,2015-10-30 10:24:23:957,1446171863957.0 \n-0.7721,0.6141,10.161,0.0941,0.4152,9.7974,0.0611,-0.0012,-0.2822,-8.2,-27.9,-43.8,2.864783434,-2.26,-0.71,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,126925,2015-10-30 10:24:24:058,1446171864058.0 \n0.7877,-0.9768,12.651,0.2128,0.4632,9.7934,-0.7831,-0.2712,-0.5156,-7.5,-28.3,-43.7,2.889916175,-3.63,-0.69,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,127027,2015-10-30 10:24:24:160,1446171864160.0 \n0.1951,0.4298,8.0828,-0.0833,0.2894,9.802,0.1246,0.5669,0.1136,-6.9,-28.3,-43.7,2.878397002,-1,0.44,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,127130,2015-10-30 10:24:24:263,1446171864263.0 \n-0.1125,0.0599,9.1135,-0.0314,0.018,9.8066,-0.2981,0.1772,-0.1173,-6,-28.1,-44,2.930058748,-0.35,-0.06,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,127231,2015-10-30 10:24:24:364,1446171864364.0 \n-0.0706,1.1325,7.768,-0.0556,-0.0194,9.8065,-0.0305,-0.0086,0.0208,-5.6,-27.4,-44.6,2.914699851,0.11,0.33,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,127333,2015-10-30 10:24:24:466,1446171864466.0 \n-0.2466,0.8727,9.9814,-0.0681,-0.172,9.8049,-0.2407,0.0977,-0.0318,-5.6,-27.1,-44.9,2.919935839,0.64,0.25,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,127436,2015-10-30 10:24:24:569,1446171864569.0 \n0.4334,0.7685,11.0684,-0.1252,-0.2079,9.8036,0.1967,0.0244,0.2639,-5.4,-26.5,-45.6,2.937389131,1.21,0.73,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,127537,2015-10-30 10:24:24:670,1446171864670.0 \n-0.7997,-1.2115,14.1258,0.151,-0.213,9.8032,-0.2285,-0.2138,0.0183,-5.6,-26.4,-45.6,2.936167401,0.88,-0.54,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,127640,2015-10-30 10:24:24:773,1446171864773.0 \n-0.5638,0.1269,8.4635,0.1361,-0.1294,9.8049,-0.1564,-0.3958,0.182,-6,-26.4,-45.3,2.921332102,0.64,-0.09,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,127741,2015-10-30 10:24:24:874,1446171864874.0 \n-0.5734,0.0982,9.2608,0.1843,-0.3134,9.7999,-0.237,0.1381,0.1173,-6.7,-26.4,-45.2,2.926044491,1.56,-1.32,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,127843,2015-10-30 10:24:24:976,1446171864976.0 \n0.1484,1.0367,8.3965,0.2413,-0.1002,9.8032,0.2126,0.0244,0.0929,-7.6,-26.1,-45.5,2.886774583,0.59,-1.41,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,127945,2015-10-30 10:24:25:078,1446171865078.0 \n-0.2993,0.4681,10.4914,0.2907,0.089,9.8019,0.1185,-0.0709,-0.2639,-8.1,-26.2,-45.4,2.885901918,-0.01,-1.53,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,128047,2015-10-30 10:24:25:180,1446171865180.0 \n1.3491,-0.0335,10.1634,0.2722,0.1731,9.8013,0.1979,0.0171,-0.2101,-8.1,-26.8,-45.1,2.884156589,-1.29,-1.47,36.813313,-119.74886,256.21,336.2427613,4.57,19.35484,196.98,16 / 16,128149,2015-10-30 10:24:25:282,1446171865282.0 \n0.3962,-0.1018,8.1702,0.1167,-0.0992,9.8055,0.1637,0.0831,-0.171,-7.4,-27,-45,2.910336528,0.58,-0.68,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,128251,2015-10-30 10:24:25:384,1446171865384.0 \n-0.3136,-0.091,9.3099,0.1506,-0.1711,9.804,-0.1002,0.1087,-0.1552,-6.6,-26.9,-44.9,2.918190509,0.43,-1,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,128353,2015-10-30 10:24:25:486,1446171865486.0 \n-0.5866,0.68,8.3019,0.0383,-0.2473,9.8035,-0.0929,0.0794,0.0452,-5.6,-26.4,-45,2.93197861,1.31,-0.32,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,128456,2015-10-30 10:24:25:589,1446171865589.0 \n-0.4417,0.7614,9.5026,-0.0328,-0.2628,9.8031,-0.0049,0.0489,0.1014,-5.3,-26.2,-45,2.958333082,1.67,0.07,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,128557,2015-10-30 10:24:25:690,1446171865690.0 \n-0.3819,0.2095,11.6442,-0.0411,-0.1397,9.8056,0.1576,0.0318,0.2505,-5,-25.9,-45.2,2.94925737,0.82,0.24,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,128660,2015-10-30 10:24:25:793,1446171865793.0 \n0.3053,-0.2274,11.7962,-0.048,-0.1416,9.8055,-0.3494,0.0061,-0.0428,-5.1,-26.1,-45.2,2.929186084,-0.07,0.76,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,128762,2015-10-30 10:24:25:895,1446171865895.0 \n-0.6237,0.0359,9.2799,-0.0427,-0.1144,9.8059,0.1271,-0.1063,0.2431,-5.3,-26.3,-45.2,2.937040065,0.83,0.67,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,128864,2015-10-30 10:24:25:997,1446171865997.0 \n-0.4226,-0.2693,9.323,0.0342,-0.1941,9.8047,-0.1075,0.0672,0.0782,-5.9,-26.2,-45,2.929186084,0.87,-0.31,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,128965,2015-10-30 10:24:26:098,1446171866098.0 \n-0.3041,0.6381,8.5138,0.0338,-0.1301,9.8057,0.1344,0,0.0562,-6.4,-25.9,-44.8,2.928313419,1.01,-0.25,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,129067,2015-10-30 10:24:26:200,1446171866200.0 \n-0.6153,0.5734,9.973,-0.0193,-0.0597,9.8064,0.0562,0.1051,0.0257,-6.8,-25.9,-44.7,2.883283924,0.51,-0.03,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,129169,2015-10-30 10:24:26:302,1446171866302.0 \n1.3946,1.1205,8.248,0.031,0.2222,9.8041,0.336,0.0635,0.0208,-7,-26.3,-44.8,2.87351008,-1.3,-0.18,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,129271,2015-10-30 10:24:26:404,1446171866404.0 \n-0.9254,-0.9996,11.8369,0.0903,-0.0588,9.8061,-0.1613,0.5877,-0.0794,-7.1,-26.5,-44.9,2.896024828,0.34,-0.53,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,129373,2015-10-30 10:24:26:506,1446171866506.0 \n-0.2011,0.0407,9.4463,-0.079,-0.2392,9.8034,-0.2798,0.0281,-0.0623,-6.7,-26.3,-44.9,2.873684613,0.96,0.44,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,129475,2015-10-30 10:24:26:608,1446171866608.0 \n-0.5267,0.4824,9.1877,-0.127,-0.4379,9.796,-0.1759,0.0745,-0.0562,-6,-25.6,-45.3,2.910511061,2.56,0.74,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,129577,2015-10-30 10:24:26:710,1446171866710.0 \n-0.407,0.5806,9.669,-0.208,-0.4216,9.7954,0.0098,0.0122,0.0929,-5.6,-24.9,-45.6,2.892010571,2.6,1.11,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,129679,2015-10-30 10:24:26:812,1446171866812.0 \n-0.6859,0.2861,11.5317,-0.2631,-0.2494,9.7999,0.4911,0.0904,0.3519,-5.4,-24.4,-45.9,2.898817355,1.46,1.54,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,129782,2015-10-30 10:24:26:915,1446171866915.0 \n0.5734,-0.8619,11.3832,-0.1947,-0.0659,9.8045,-0.0757,-0.1772,0.0611,-5.4,-24.7,-45.7,2.89078884,-0.19,1.7,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,129883,2015-10-30 10:24:27:016,1446171867016.0 \n0.1185,0.7183,8.0397,-0.2966,-0.2098,9.7999,0.0281,-0.2761,0.0721,-5.5,-24.9,-45.3,2.90632227,1.44,1.61,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,129985,2015-10-30 10:24:27:118,1446171867118.0 \n-0.8871,-0.4872,9.3338,-0.1103,-0.3575,9.7995,0.0049,0.0403,-0.0892,-5.8,-25.1,-44.9,2.904751474,1.92,0.5,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,130088,2015-10-30 10:24:27:221,1446171867221.0 \n-0.3962,0.595,7.6219,-0.1431,-0.1984,9.8036,0.204,0.0855,0.0831,-6,-24.8,-45,2.900562684,1.82,0.63,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,130189,2015-10-30 10:24:27:322,1446171867322.0 \n-0.9266,0.0886,10.805,-0.134,-0.1915,9.8039,0.0134,0.0599,-0.1271,-6.2,-24.8,-45.1,2.894279499,1.14,0.68,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,130291,2015-10-30 10:24:27:424,1446171867424.0 \n-0.067,0.1137,9.7719,-0.186,-0.0825,9.8045,0.0428,0.0501,-0.1869,-5.9,-25.1,-45,2.877873404,0.48,1.09,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,130394,2015-10-30 10:24:27:527,1446171867527.0 \n-0.814,-0.8128,10.5764,-0.345,-0.4356,9.7909,0.1258,0.1417,-0.0318,-5.3,-25.2,-44.7,2.910511061,1.81,1.55,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,130496,2015-10-30 10:24:27:629,1446171867629.0 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\n-0.5231,-0.006,10.6386,-0.1527,-0.2224,9.8029,0.1038,-0.0122,-0.2395,-7,-24.5,-45.9,2.844363082,1.49,0.89,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,131413,2015-10-30 10:24:28:546,1446171868546.0 \n-0.5722,-0.0862,9.3111,-0.1559,-0.0567,9.8052,0.2248,0.0794,-0.3677,-6.5,-24.6,-46,2.884156589,0.73,0.92,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,131516,2015-10-30 10:24:28:649,1446171868649.0 \n-0.996,-1.3946,11.1546,-0.1409,-0.3327,9.8,-0.3433,0.248,-0.5559,-5.9,-24.8,-46.1,2.902308013,1.35,0.45,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,131617,2015-10-30 10:24:28:750,1446171868750.0 \n-0.176,-0.2155,9.4535,-0.1762,-0.3966,9.797,-0.1417,0.1026,-0.0086,-4.9,-24.6,-46.3,2.93075688,2.07,0.88,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,131719,2015-10-30 10:24:28:852,1446171868852.0 \n-0.5531,0.146,9.2787,-0.1921,-0.4181,9.7959,0.1442,-0.0086,0.1539,-4.4,-24.2,-46.6,2.956064154,2.47,1.07,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,131821,2015-10-30 10:24:28:954,1446171868954.0 \n-0.2861,0.7219,9.0848,-0.2502,-0.256,9.8001,0.1075,0.077,0.2053,-4.1,-24,-46.9,2.943846849,1.68,1.32,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,131923,2015-10-30 10:24:29:056,1446171869056.0 \n-0.2981,0.3519,11.7747,-0.2721,-0.0892,9.8025,0.2724,0.0635,0.2993,-4.2,-24,-46.7,2.934073006,1.01,1.49,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,132025,2015-10-30 10:24:29:158,1446171869158.0 \n-0.5602,-0.899,12.8617,-0.0771,0.1301,9.8055,-0.3409,-0.0391,0.1515,-4.8,-24.7,-46.4,2.925171826,-0.76,0.45,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,132127,2015-10-30 10:24:29:260,1446171869260.0 \n0.0862,0.5902,8.6383,0.0344,0.1171,9.8059,0.1955,-0.2639,0.3103,-5.4,-25,-46.2,2.926393557,-0.32,0.51,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,132230,2015-10-30 10:24:29:363,1446171869363.0 \n-0.6955,0.2083,8.6514,0.1838,-0.0099,9.8049,-0.171,0.0843,-0.1271,-6.6,-25.4,-46.1,2.901260816,0.06,-1.07,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,132331,2015-10-30 10:24:29:464,1446171869464.0 \n-0.2107,0.9697,8.7568,0.1231,0.0294,9.8058,0.1026,0,-0.0354,-7.1,-25.4,-46.4,2.888868978,-0.17,-0.72,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,132433,2015-10-30 10:24:29:566,1446171869566.0 \n-0.5339,0.3831,10.756,0.1005,0.0895,9.8057,0.2053,-0.033,-0.1063,-7.1,-25.5,-46.3,2.885552852,-0.32,-0.65,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,132535,2015-10-30 10:24:29:668,1446171869668.0 \n0.5926,-0.5555,10.4818,0.0675,0.1547,9.8052,-0.011,0.0452,-0.1869,-6.7,-25.7,-46,2.881014996,-1.38,-0.46,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,132637,2015-10-30 10:24:29:770,1446171869770.0 \n-0.2227,-0.1604,9.3697,-0.1527,-0.1914,9.8036,0.3348,0.1332,0.182,-6.2,-25.4,-45.7,2.902831612,1.41,0.45,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,132740,2015-10-30 10:24:29:873,1446171869873.0 \n-0.2227,-0.0431,9.3661,-0.0734,-0.2718,9.8026,-0.1576,-0.0806,-0.0782,-5.5,-24.9,-45.9,2.93494567,1.26,0.57,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,132841,2015-10-30 10:24:29:974,1446171869974.0 \n0.0898,0.8703,7.8973,-0.0686,-0.2202,9.8039,0.1136,-0.0049,0.0354,-5,-24.5,-46.2,2.933025808,1.42,0.4,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,132943,2015-10-30 10:24:30:076,1446171870076.0 \n-0.0718,0.2789,10.9595,-0.0333,-0.1911,9.8047,-0.0086,-0.0147,-0.0709,-4.8,-24.4,-46.2,2.935992868,1.14,0.24,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,133046,2015-10-30 10:24:30:179,1446171870179.0 \n-0.2993,0.4968,10.6841,-0.1389,-0.012,9.8057,0.3873,0.0574,0.2272,-4.6,-24.4,-45.8,2.921332102,0.68,0.61,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,133147,2015-10-30 10:24:30:280,1446171870280.0 \n-1.4425,-1.3372,14.2754,-0.0163,0.0107,9.8066,-0.3042,-0.2712,-0.1747,-4.4,-24.8,-45.3,2.979800632,-0.06,0.1,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,133249,2015-10-30 10:24:30:382,1446171870382.0 \n-0.7111,0.1101,9.2033,0.0495,-0.1374,9.8056,0.0574,-0.4472,0.1295,-4.2,-24.9,-45.1,2.995508595,0.8,-0.29,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,133352,2015-10-30 10:24:30:485,1446171870485.0 \n-0.6692,0.2598,9.1051,0.1081,-0.3108,9.8011,-0.0709,-0.0953,0.033,-4.4,-24.6,-45.4,3.006155104,1.63,-0.54,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,133453,2015-10-30 10:24:30:586,1446171870586.0 \n-0.1856,0.8775,8.1858,0.0814,-0.1534,9.8051,0.1344,0.033,-0.0672,-4.6,-24.1,-45.9,2.956936819,0.9,-0.48,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,133556,2015-10-30 10:24:30:689,1446171870689.0 \n-0.9182,0.0491,11.4479,0.0602,0.0316,9.8064,0.1283,-0.011,-0.1796,-4.6,-24.2,-45.7,2.949606436,0.2,-0.38,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,133657,2015-10-30 10:24:30:790,1446171870790.0 \n1.1923,-0.2753,10.8362,0.0647,0.1886,9.8046,-0.055,-0.0953,-0.0977,-4,-25,-45.4,2.983116758,-1.21,-0.2,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,133759,2015-10-30 10:24:30:892,1446171870892.0 \n-0.1568,-0.3292,10.6159,-0.0346,-0.0907,9.8062,0.1808,-0.1796,-0.0171,-3.4,-25.3,-45.3,3.016801612,0.47,0.23,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,133862,2015-10-30 10:24:30:995,1446171870995.0 \n-0.2825,0.0443,9.1877,0.056,-0.2137,9.8042,-0.336,-0.0513,-0.1405,-2.7,-25.4,-46,3.038792761,1.03,-0.42,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,133963,2015-10-30 10:24:31:096,1446171871096.0 \n-0.6069,0.662,8.3498,0.0127,-0.1838,9.8049,0.0061,0.0415,-0.0049,-2.1,-25.1,-46.1,3.068986957,1.09,-0.15,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,134065,2015-10-30 10:24:31:198,1446171871198.0 \n-0.3292,0.3783,9.4595,-0.1012,-0.139,9.8051,-0.0599,0.0916,0.0232,-1.7,-25,-46.2,3.052231796,0.77,0.37,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,134167,2015-10-30 10:24:31:300,1446171871300.0 \n-0.8452,-0.6476,12.9478,-0.2092,-0.0835,9.8041,0.0696,0.1051,0.1784,-1.4,-25,-45.9,3.07457201,0.97,0.91,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,134270,2015-10-30 10:24:31:403,1446171871403.0 \n-1.0307,-0.9349,11.892,-0.3049,0.0093,9.8019,-0.3738,0.0086,0.0305,-0.9,-25.5,-45.4,3.045774078,-0.05,1.78,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,134371,2015-10-30 10:24:31:504,1446171871504.0 \n-0.1712,0.1137,8.7005,-0.1589,-0.0608,9.8052,0.0501,-0.3873,0.259,-0.8,-25.7,-45,3.056420586,0.5,1.6,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,134473,2015-10-30 10:24:31:606,1446171871606.0 \n-0.5124,0.3041,8.3989,-0.0621,-0.2336,9.8037,-0.1344,-0.0147,-0.0244,-1.2,-26,-44.8,3.094119698,1.36,0.36,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,134576,2015-10-30 10:24:31:709,1446171871709.0 \n-0.4166,0.6656,8.8155,-0.0997,-0.2887,9.8019,0.0159,0.077,-0.0134,-1.5,-26,-44.8,3.092199836,1.7,0.44,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,134677,2015-10-30 10:24:31:810,1446171871810.0 \n-0.8056,0.237,10.4567,-0.232,-0.148,9.8028,0.1906,-0.0171,-0.1698,-1.4,-26.2,-45,3.070557753,1.39,1.18,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,134779,2015-10-30 10:24:31:912,1446171871912.0 \n0.4573,0.1448,9.8402,-0.389,-0.0014,9.7989,-0.3457,-0.066,-0.1613,-0.9,-26.8,-44.9,3.039141826,-0.01,2.26,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,134881,2015-10-30 10:24:32:014,1446171872014.0 \n-0.9134,-0.723,11.1043,-0.6126,-0.3834,9.78,-0.2309,0.4887,0.0147,-0.3,-27.1,-45,3.06200564,2.18,2.91,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,134984,2015-10-30 10:24:32:117,1446171872117.0 \n-0.0682,0.3065,9.1901,-0.4462,-0.1574,9.7952,-0.022,-0.2126,0.0232,0.2,-27.7,-44.9,3.07038322,0.92,2.61,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,135086,2015-10-30 10:24:32:219,1446171872219.0 \n-0.8751,0.5997,7.8506,-0.3712,-0.0554,9.7995,0.1991,0.0159,0.0073,0.3,-28.1,-45,3.085218519,0.73,2.06,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,135188,2015-10-30 10:24:32:321,1446171872321.0 \n-0.8356,0.3005,9.6426,-0.3801,0.0136,9.7993,-0.0476,0.0037,-0.1796,-0.2,-28.9,-44.8,3.081378794,-0.08,2.22,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,135289,2015-10-30 10:24:32:422,1446171872422.0 \n-0.1185,0.589,9.657,-0.4055,0.0729,9.798,0.2676,-0.1246,0.1796,-0.3,-29.9,-44.3,3.080331597,-0.43,2.37,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,135392,2015-10-30 10:24:32:525,1446171872525.0 \n-1.7897,-1.6424,14.0815,-0.0609,-0.2152,9.8041,-0.2175,0.0843,0.1649,-0.8,-30.4,-44.2,3.084520387,0.11,0.94,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,135493,2015-10-30 10:24:32:626,1446171872626.0 \n-0.3065,-0.0587,9.821,0.0868,-0.1996,9.8042,-0.182,-0.2089,0.3726,-2.1,-30.7,-44.2,3.091152638,1.17,-0.51,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,135595,2015-10-30 10:24:32:728,1446171872728.0 \n-0.3184,0.4681,9.6151,0.1404,-0.3348,9.7999,-0.11,0.0538,0.0953,-4.2,-30.7,-44.5,3.038269162,1.96,-0.82,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,135698,2015-10-30 10:24:32:831,1446171872831.0 \n-0.4322,1.0175,7.8302,0.0096,0.0292,9.8066,0.4362,0.0098,-0.1063,-5.7,-30.9,-44.5,2.953795226,0.23,-0.1,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,135799,2015-10-30 10:24:32:932,1446171872932.0 \n-1.3599,-0.2119,11.661,-0.33,-0.0622,9.8009,0.088,0.1979,-0.2004,-6.4,-31.4,-44.5,2.917666911,0.21,1.43,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,135901,2015-10-30 10:24:33:034,1446171873034.0 \n-0.34,-0.1592,10.5034,-0.3735,-0.1115,9.7989,-0.1026,-0.0464,-0.1185,-6.2,-31.9,-44.2,2.903355211,0.08,2.33,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,136003,2015-10-30 10:24:33:136,1446171873136.0 \n-0.4166,-0.6321,10.2436,-0.4981,-0.4486,9.7837,0.044,0.0061,0.1491,-5.8,-32,-44.3,2.904402408,2.69,2.9,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,136106,2015-10-30 10:24:33:239,1446171873239.0 \n0.4178,-0.2538,9.7636,-0.177,-0.4994,9.7923,0.0489,-0.5449,-0.1845,-6,-31.4,-44.4,2.921855701,2.64,1.78,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,136207,2015-10-30 10:24:33:340,1446171873340.0 \n-0.4537,0.4717,7.7596,0.231,-0.3583,9.7974,0.1491,-0.3372,-0.248,-6.9,-31.1,-44.7,2.951700831,2.21,-0.9,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,136310,2015-10-30 10:24:33:443,1446171873443.0 \n-0.6776,-0.0802,10.7643,0.3012,-0.4034,9.7937,-0.0281,-0.0562,-0.11,-8.6,-31.1,-44.9,2.918015976,2.34,-1.95,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,136411,2015-10-30 10:24:33:544,1446171873544.0 \n0.1353,0.8284,9.7133,0.1719,-0.191,9.8033,0.281,0.1173,0.3995,-10,-31.5,-45.2,2.860245578,1.12,-1,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,136513,2015-10-30 10:24:33:646,1446171873646.0 \n-0.9625,-1.0786,12.0476,0.1284,-0.2538,9.8025,-0.4154,0.033,0.1784,-10.6,-31.6,-45,2.826386191,0.74,-0.48,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,136616,2015-10-30 10:24:33:749,1446171873749.0 \n0.82,-0.018,9.7085,0.2811,-0.3537,9.7962,0.2602,-0.4557,0.5095,-12,-31.1,-44.7,2.824466329,2.07,-1.64,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,136717,2015-10-30 10:24:33:850,1446171873850.0 \n0.0515,0.0455,8.2301,0.3142,-0.3688,9.7947,-0.0391,0.3409,0.0159,-13.1,-30.6,-44.6,2.815041551,2.04,-2.48,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,136820,2015-10-30 10:24:33:953,1446171873953.0 \n0.0551,0.3436,8.9902,0.2117,-0.2823,9.8003,0.0122,0.077,-0.2175,-14.2,-29.8,-44.3,2.749068105,1.8,-1.31,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,136921,2015-10-30 10:24:34:054,1446171874054.0 \n-0.4764,-0.3962,11.9207,0.1266,-0.207,9.8036,0.1136,0.0635,-0.259,-14.5,-29.6,-43.8,2.731963878,1.21,-0.74,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,137024,2015-10-30 10:24:34:157,1446171874157.0 \n0.6069,0.2346,9.0716,0.0723,-0.0131,9.8064,0.0757,-0.0855,-0.2834,-14,-29.7,-43.5,2.715732316,0.4,-0.34,36.81321,-119.74888,259.32,336.2427613,4.29,25.806452,175.89,16 / 16,137125,2015-10-30 10:24:34:258,1446171874258.0 \n-0.0443,-0.1664,8.7783,-0.1331,-0.2926,9.8014,0.3152,-0.022,-0.0037,-13.1,-29.7,-43.5,2.738072531,1.99,0.59,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,137227,2015-10-30 10:24:34:360,1446171874360.0 \n-0.0431,0.0299,9.2129,-0.095,-0.3322,9.8006,-0.2602,0.011,-0.1674,-12.1,-29.7,-43.5,2.761634475,1.57,0.6,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,137330,2015-10-30 10:24:34:463,1446171874463.0 \n-0.5926,0.5459,8.0661,-0.0898,-0.3419,9.8003,0.0257,0.0037,-0.088,-11.1,-29.2,-43.9,2.783451091,2.03,0.56,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,137431,2015-10-30 10:24:34:564,1446171874564.0 \n-0.6081,-0.0694,9.9719,-0.0872,-0.3169,9.8011,0.0623,0.0525,-0.0134,-10.7,-28.7,-43.7,2.783102025,1.85,0.51,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,137533,2015-10-30 10:24:34:666,1446171874666.0 \n-0.3986,0.2885,11.3318,-0.1263,-0.1004,9.8053,0.3311,0.0635,0.3714,-10.7,-28.6,-43.6,2.776469774,1.19,0.56,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,137636,2015-10-30 10:24:34:769,1446171874769.0 \n-1.4736,-1.2198,11.4395,-0.0331,-0.1856,9.8048,-0.4105,-0.2138,-0.0501,-11,-28.3,-43.6,2.77263005,1.08,0.19,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,137737,2015-10-30 10:24:34:870,1446171874870.0 \n-0.1508,0.1257,8.9711,0.0228,-0.1956,9.8047,-0.0489,-0.3665,0.2126,-11.2,-28.1,-43.5,2.766521397,1.18,0.49,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,137839,2015-10-30 10:24:34:972,1446171874972.0 \n-0.6273,0.097,9.2452,0.1161,-0.4017,9.7977,-0.077,0.0415,0.0513,-11.9,-27.4,-43.6,2.761634475,2.12,-0.75,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,137942,2015-10-30 10:24:35:075,1446171875075.0 \n-0.3915,0.82,7.9942,0.0369,-0.3232,9.8013,0.1674,0.1014,0.1063,-12.2,-26.9,-43.7,2.752907829,2.2,-0.34,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,138043,2015-10-30 10:24:35:176,1446171875176.0 \n-0.7099,-0.17,11.0468,0.0273,-0.139,9.8056,0.2089,-0.0195,-0.0757,-12.4,-26.7,-44,2.737199866,1.15,-0.09,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,138146,2015-10-30 10:24:35:279,1446171875279.0 \n-0.826,-0.2251,9.3889,-0.0749,0.1001,9.8059,0,-0.1515,-0.0415,-12.1,-26.9,-44,2.712765256,-0.17,0.37,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,138247,2015-10-30 10:24:35:380,1446171875380.0 \n-0.0766,-0.4034,9.578,-0.2023,-0.2447,9.8015,-0.551,0.4948,-0.1808,-11.6,-27.4,-43.8,2.710845394,1.43,1.18,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,138349,2015-10-30 10:24:35:482,1446171875482.0 \n0.267,-0.2011,9.4559,-0.2002,-0.3154,9.7995,-0.2627,0.121,-0.0159,-11,-27.2,-43.6,2.743657584,1.54,1.1,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,138451,2015-10-30 10:24:35:584,1446171875584.0 \n-0.4046,0.5734,8.1056,-0.1517,-0.2755,9.8016,0.1075,-0.0281,0.0147,-10.3,-26.6,-43.7,2.780134966,1.78,0.93,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,138553,2015-10-30 10:24:35:686,1446171875686.0 \n-0.1221,0.9708,9.2392,0.0233,-0.1088,9.806,0.1417,-0.0403,0.1698,-10.3,-26.3,-43.7,2.776644307,1.05,0.32,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,138655,2015-10-30 10:24:35:788,1446171875788.0 \n-0.2861,0.5219,11.4227,0.0817,0.0761,9.806,0.2272,-0.1063,0.2334,-10.7,-26.3,-43.5,2.748544506,-0.44,-0.48,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,138757,2015-10-30 10:24:35:890,1446171875890.0 \n0.2119,0.1748,10.4196,0.1564,0.4021,9.7972,-0.1808,-0.0501,-0.077,-11.2,-26.7,-43.1,2.749591704,-2.36,-0.77,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,138859,2015-10-30 10:24:35:992,1446171875992.0 \n-0.7494,0.2478,9.9659,0.0541,0.2545,9.8032,0.0929,-0.1442,0.0195,-11.6,-27,-42.8,2.715732316,-1.43,-0.32,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,138961,2015-10-30 10:24:36:094,1446171876094.0 \n-0.3148,0.4525,8.3929,0.0132,0.2518,9.8034,-0.0757,0.1662,-0.0648,-11.6,-27.2,-42.9,2.71416152,-1.58,-0.33,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,139064,2015-10-30 10:24:36:197,1446171876197.0 \n-0.322,1.2007,7.8542,-0.0177,0.3282,9.8011,0.2138,0.0281,-0.0208,-11.3,-27,-43.2,2.736327201,-1.68,0.05,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,139166,2015-10-30 10:24:36:299,1446171876299.0 \n-0.6812,0.8619,9.5816,-0.0166,0.4074,9.7982,0.044,-0.0611,-0.1918,-10.6,-27,-43.2,2.72969495,-2.26,0.06,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,139267,2015-10-30 10:24:36:400,1446171876400.0 \n-1.0822,0.8428,9.7169,0.0017,0.5255,9.7926,0.1979,0.0403,-0.1283,-10.1,-27.2,-43.2,2.761634475,-2.68,-0.04,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,139369,2015-10-30 10:24:36:502,1446171876502.0 \n-1.0427,-1.075,13.1274,-0.0707,0.0212,9.8064,-0.7844,0.4826,-0.2993,-9.4,-27.2,-43.1,2.817135946,-1.43,-0.38,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,139471,2015-10-30 10:24:36:604,1446171876604.0 \n-0.0407,-0.2442,10.5884,0.0376,0.1358,9.8056,-0.3384,-0.0648,-0.099,-8.7,-26.9,-43.2,2.818706742,-0.79,-0.22,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,139573,2015-10-30 10:24:36:706,1446171876706.0 \n-0.498,0.5794,8.3917,-0.0182,0.0706,9.8064,0.0159,0.1894,-0.0415,-8.4,-26.4,-43.5,2.843839483,-0.34,-0.13,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,139675,2015-10-30 10:24:36:808,1446171876808.0 \n-0.3998,0.9182,9.2201,-0.0944,0.1066,9.8056,0.0733,0.0122,-0.0061,-7.8,-26.3,-43.4,2.823244598,-0.62,0.55,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,139777,2015-10-30 10:24:36:910,1446171876910.0 \n-0.759,0.4848,10.7272,-0.2006,0.1403,9.8036,0.0733,0,0.2443,-7.4,-26.3,-43.7,2.843490417,-0.68,1.08,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,139879,2015-10-30 10:24:37:012,1446171877012.0 \n-0.3316,-0.7219,11.8752,-0.1391,0.2391,9.8027,-0.3946,-0.2651,0.1038,-7.1,-26.6,-43.7,2.855533189,-1.4,0.81,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,139982,2015-10-30 10:24:37:115,1446171877115.0 \n0.0204,0.498,9.2907,-0.0131,0.1011,9.8061,0.0745,-0.0183,0.2932,-7.2,-26.4,-43.7,2.860071045,-0.42,0.55,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,140083,2015-10-30 10:24:37:216,1446171877216.0 \n-0.6991,0.1736,9.3841,-0.003,0.0096,9.8066,-0.1442,0.0391,-0.0037,-8,-26.3,-43.8,2.842792286,-0.29,-0.08,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,140185,2015-10-30 10:24:37:318,1446171877318.0 \n-0.7063,0.5926,8.3989,-0.0623,0.0842,9.8061,0.1735,0.1539,0.0501,-8.3,-26,-44.1,2.835985502,-0.21,0.2,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,140287,2015-10-30 10:24:37:420,1446171877420.0 \n-0.9852,0.6979,9.414,-0.2052,0.2063,9.8023,0.011,0.0843,-0.1038,-8.1,-26,-44.3,2.809805563,-1.01,0.9,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,140389,2015-10-30 10:24:37:522,1446171877522.0 \n-0.0024,0.747,8.6945,-0.2726,0.37,9.7959,0.2065,0.1356,-0.055,-7.3,-26.4,-44,2.815739682,-2.16,1.59,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,140491,2015-10-30 10:24:37:624,1446171877624.0 \n-1.3958,-1.4641,13.5584,-0.3701,-0.103,9.7991,-0.7172,0.3079,-0.3726,-6.8,-26.6,-43.8,2.839301627,-0.61,1.67,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,140593,2015-10-30 10:24:37:726,1446171877726.0 \n0.0144,0.0371,9.2572,-0.2619,-0.0239,9.8031,-0.2321,0.0257,-0.0635,-6.2,-26.4,-43.9,2.872811949,-0.09,1.49,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,140695,2015-10-30 10:24:37:828,1446171877828.0 \n-0.5974,0.5567,8.6622,-0.2605,-0.1513,9.802,-0.0953,0.0195,-0.0953,-5.8,-26,-44.2,2.881189529,0.66,1.39,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,140797,2015-10-30 10:24:37:930,1446171877930.0 \n-0.407,0.7027,9.1016,-0.2364,-0.1079,9.8032,0.0476,0.0086,0.0232,-5.4,-25.7,-44.3,2.916096114,0.75,1.43,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,140899,2015-10-30 10:24:38:032,1446171878032.0 \n-0.6656,0.3124,10.9978,-0.2782,-7.00E-04,9.8027,0.1637,0.0538,0.1784,-5.3,-25.7,-44.2,2.905798672,0,1.63,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,141001,2015-10-30 10:24:38:134,1446171878134.0 \n-0.6584,0.674,8.1415,-0.3498,0.3314,9.7948,0.4716,0.193,0.237,-5.2,-26,-44.2,2.878222469,-1.6,2.19,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,141103,2015-10-30 10:24:38:236,1446171878236.0 \n-0.565,0.0132,9.4595,-0.2219,0.1279,9.8033,0.1075,-0.0195,0.1845,-5.4,-26.4,-44.1,2.910161995,-0.68,1.31,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,141205,2015-10-30 10:24:38:338,1446171878338.0 \n-0.31,0.1053,8.9507,-0.0742,0.1303,9.8055,-0.1894,0.0452,-0.0257,-5.7,-26.6,-43.8,2.902831612,-1.08,0.48,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,141307,2015-10-30 10:24:38:440,1446171878440.0 \n-0.589,0.7542,8.4695,-0.1067,0.0904,9.8057,0.0208,-0.0244,-0.066,-6.3,-26.5,-43.8,2.898119223,-0.34,0.51,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,141410,2015-10-30 10:24:38:543,1446171878543.0 \n-0.6093,0.9565,9.2787,-0.1583,0.1839,9.8036,0.0757,0.0941,-0.0574,-6.5,-26.4,-43.8,2.881189529,-1.07,0.92,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,141511,2015-10-30 10:24:38:644,1446171878644.0 \n0.1149,0.5997,9.4607,-0.1641,0.4279,9.7959,0.3225,-0.0342,-0.0379,-6.2,-26.8,-43.9,2.878920601,-2.5,0.96,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,141613,2015-10-30 10:24:38:746,1446171878746.0 \n-1.4341,-1.3707,12.8533,-0.205,0.1498,9.8034,0.237,0.2272,0.1772,-6,-27.1,-43.7,2.891836038,-1.71,0.72,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,141716,2015-10-30 10:24:38:849,1446171878849.0 \n0.9325,0.3639,9.6678,-0.294,0.1999,9.8002,-0.1759,-0.0305,0.0904,-5.4,-27.2,-43.8,2.904053342,-1.17,1.72,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,141817,2015-10-30 10:24:38:950,1446171878950.0 \n-0.4585,0.7338,8.2277,-0.3859,0.025,9.799,0.1051,-0.0171,0.011,-5,-26.9,-43.9,2.896897492,0.02,2.28,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,141919,2015-10-30 10:24:39:052,1446171879052.0 \n-0.0048,1.0104,9.4643,-0.386,0.0153,9.799,-0.0147,0.0061,0.0819,-4.6,-26.6,-44.2,2.89672296,-0.09,2.26,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,142021,2015-10-30 10:24:39:154,1446171879154.0 \n-0.6596,0.3148,11.0361,-0.4682,0.0995,9.795,-0.0037,0.16,0.0635,-4.6,-26.4,-44.7,2.887298182,-0.29,2.17,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,142123,2015-10-30 10:24:39:256,1446171879256.0 \n0.5399,0.4752,10.7296,-0.3294,0.352,9.7948,0.2065,-0.2883,0.1869,-4.6,-26.7,-44.7,2.878047937,-1.73,2.44,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,142225,2015-10-30 10:24:39:358,1446171879358.0 \n-1.9034,-0.4621,9.2033,-0.2873,0.2518,9.7992,0.2089,-0.3531,0.1625,-4.8,-27,-44.6,2.906496803,-1.29,1.56,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,142327,2015-10-30 10:24:39:460,1446171879460.0 \n-0.7362,-0.0096,9.414,-0.0117,0.1912,9.8048,-0.1943,-0.2712,0,-5.5,-27.3,-44.5,2.955191489,-1.48,-0.16,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,142429,2015-10-30 10:24:39:562,1446171879562.0 \n-0.8428,0.8248,8.5234,-0.1325,0.1619,9.8044,-0.0012,0.1332,0.0757,-5.9,-27.2,-44.6,2.901260816,-0.94,0.56,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,142532,2015-10-30 10:24:39:665,1446171879665.0 \n-0.6117,1.0127,9.9431,-0.1869,0.2104,9.8026,-0.0476,0.0733,-0.1735,-6.1,-27.1,-44.8,2.885901918,-1.31,1,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,142633,2015-10-30 10:24:39:766,1446171879766.0 \n-0.4896,-0.0132,10.6973,-0.2598,0.3219,9.7979,0.1991,-0.0098,-0.1271,-5.6,-27.1,-45,2.875953541,-1.47,1.31,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,142735,2015-10-30 10:24:39:868,1446171879868.0 \n-0.2239,-0.5423,11.4144,-0.3674,0.2141,9.7974,-0.3018,0.2419,-0.2541,-5.2,-27.4,-44.8,2.900388151,-1.75,1.66,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,142837,2015-10-30 10:24:39:970,1446171879970.0 \n-0.1568,-0.0682,9.432,-0.3873,0.1747,9.7974,-0.2456,-0.2004,-0.2101,-4.3,-27.3,-44.8,2.924648228,-1.02,2.26,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,142939,2015-10-30 10:24:40:072,1446171880072.0 \n-0.6536,0.4453,8.6048,-0.3283,-0.1245,9.8004,-0.1295,0.0745,-0.0648,-3.9,-27.1,-44.9,2.945243113,0.44,1.83,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,143041,2015-10-30 10:24:40:174,1446171880174.0 \n-1.1349,0.7398,9.2608,-0.3526,-0.1686,9.7989,-0.0147,-0.0147,0.0147,-3.5,-26.4,-45.3,2.97072492,0.98,2.06,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,143143,2015-10-30 10:24:40:276,1446171880276.0 \n-0.9325,-0.2215,11.2791,-0.3628,-0.106,9.7994,0.1454,0.0562,0.2957,-3.5,-26,-45.5,2.974390111,1.1,1.95,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,143246,2015-10-30 10:24:40:379,1446171880379.0 \n0.0036,0.0419,10.7595,-0.3336,0.2194,9.7985,-0.1515,-0.347,0.1613,-3.8,-26.2,-45.1,2.91347812,-1.03,2.36,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,143347,2015-10-30 10:24:40:480,1446171880480.0 \n-0.8164,-0.2023,9.3194,-0.3039,0.0751,9.8017,-0.0159,0.1979,0.2773,-4.2,-26.4,-44.9,2.940356191,-0.41,1.58,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,143450,2015-10-30 10:24:40:583,1446171880583.0 \n-0.4429,0.0503,9.104,-0.1131,0.0171,9.806,-0.1515,-0.0305,0.1319,-5.1,-26.6,-44.8,2.940705257,-0.3,0.57,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,143552,2015-10-30 10:24:40:685,1446171880685.0 \n-0.6045,0.8392,8.7975,-0.1566,-0.0231,9.8054,0.0855,0.088,0.0794,-5.7,-26.4,-45,2.893406834,0.16,0.79,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,143653,2015-10-30 10:24:40:786,1446171880786.0 \n-0.5842,0.6823,10.0999,-0.2334,0.071,9.8036,0.1283,0.1075,-0.1344,-6.1,-26,-45.3,2.879967799,-0.25,1.16,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,143755,2015-10-30 10:24:40:888,1446171880888.0 \n-0.8787,0.3675,11.6406,-0.3294,0.2478,9.798,0.2248,0.0953,-0.2028,-6,-26.1,-45,2.848202806,-1.45,1.93,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,143857,2015-10-30 10:24:40:990,1446171880990.0 \n-0.6955,-0.7829,11.7017,-0.3836,0.2574,9.7958,-0.4252,-0.0183,-0.518,-5.4,-26.6,-44.9,2.881364062,-2.14,2.22,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,143959,2015-10-30 10:24:41:092,1446171881092.0 \n0.0467,-0.1077,10.003,-0.2134,0.0811,9.804,-0.3763,-0.2187,-0.2199,-4.6,-26.9,-44.7,2.901784414,-0.95,1.81,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,144062,2015-10-30 10:24:41:195,1446171881195.0 \n-0.5124,0.3974,8.6227,-0.2124,-0.0987,9.8039,-0.0501,0.1344,-0.1515,-4.3,-26.8,-44.9,2.968630525,0.58,1.01,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,144163,2015-10-30 10:24:41:296,1446171881296.0 \n-0.4357,1.1073,8.6119,-0.2545,-0.0099,9.8033,0.1234,0.0501,-0.0367,-3.8,-26.2,-45.3,2.949431903,0.26,1.4,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,144265,2015-10-30 10:24:41:398,1446171881398.0 \n-1.057,0.2203,10.9319,-0.2853,0.0979,9.802,0.2553,0.0892,0.1454,-3.7,-26,-45.6,2.939832592,-0.3,1.58,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,144367,2015-10-30 10:24:41:500,1446171881500.0 \n-0.2155,1.069,9.1016,-0.3877,0.456,9.7884,0.3983,0.1136,0.3543,-3.2,-26.4,-45.4,2.955191489,-2.03,2.04,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,144469,2015-10-30 10:24:41:602,1446171881602.0 \n-1.488,-0.4824,11.1462,-0.3798,0.356,9.7928,-0.0794,0.1613,0.1967,-3.2,-26.9,-45.2,2.962696405,-2.38,1.97,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,144571,2015-10-30 10:24:41:704,1446171881704.0 \n0.0263,0.407,8.9759,-0.1435,0.3088,9.8007,-0.1991,-0.0244,-0.0195,-3.6,-27.2,-44.9,2.955016957,-2.15,0.99,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,144673,2015-10-30 10:24:41:806,1446171881806.0 \n-0.826,0.6608,9.0381,-0.1684,0.1091,9.8046,0.0819,0.2101,-0.0611,-4.1,-26.8,-44.9,2.963394537,-0.64,0.98,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,144775,2015-10-30 10:24:41:908,1446171881908.0 \n-0.7626,1.1037,8.436,-0.3404,0.2142,9.7984,0.1625,0.1161,-0.1124,-4.2,-26.5,-45,2.93075688,-0.99,1.78,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,144877,2015-10-30 10:24:42:010,1446171882010.0 \n-0.723,0.7793,10.1742,-0.4314,0.3977,9.7891,0.2798,0.1002,-0.0525,-3.5,-26.6,-44.9,2.954667891,-1.86,2.33,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,144979,2015-10-30 10:24:42:112,1446171882112.0 \n0.2945,1.5215,9.9647,-0.5153,0.5845,9.7756,-0.1148,0.0305,-0.3152,-2.7,-27,-44.7,2.921855701,-3.23,3.13,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,145082,2015-10-30 10:24:42:215,1446171882215.0 \n-0.8811,-0.1293,10.6734,-0.5277,0.2631,9.7889,-0.3751,-0.0367,-0.3751,-1.6,-27.6,-44.4,2.978055303,-1.98,3.09,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,145183,2015-10-30 10:24:42:316,1446171882316.0 \n-0.8416,0.4154,8.5054,-0.6612,0.1152,9.7837,-0.0806,0.1649,-0.0843,-0.9,-27.6,-44.9,3.003362577,-0.84,3.57,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,145286,2015-10-30 10:24:42:419,1446171882419.0 \n-0.8906,0.8188,8.9914,-0.6838,0.1294,9.7819,0.1148,-0.088,0.0794,0,-27.1,-45.6,3.016452546,-0.53,4.17,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,145388,2015-10-30 10:24:42:521,1446171882521.0 \n-0.7254,0.4741,9.9898,-0.6794,0.2928,9.7787,0.1955,0.022,0.2126,0.4,-27.2,-46,3.01784881,-1.71,3.97,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,145489,2015-10-30 10:24:42:622,1446171882622.0 \n-0.7338,1.4114,8.7388,-0.7368,0.6645,9.7563,0.4337,0.0538,0.4618,0.4,-27.9,-45.7,3.0077259,-2.86,4.31,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,145592,2015-10-30 10:24:42:725,1446171882725.0 \n-1.919,-0.8775,12.3409,-0.5812,0.4025,9.7811,-0.2749,0.1271,0.2773,0,-28.6,-45.1,3.03460397,-3.72,3.56,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,145693,2015-10-30 10:24:42:826,1446171882826.0 \n-0.6105,0.5351,8.4874,-0.4708,0.2624,9.7918,-0.2859,-0.066,0.0012,-0.7,-29.2,-44.6,3.026400923,-1.89,2.78,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,145796,2015-10-30 10:24:42:929,1446171882929.0 \n-1.0295,0.8966,8.8226,-0.4283,0.0924,9.7969,0,-0.0415,0.0183,-1.4,-28.9,-44.4,3.038269162,-0.57,2.56,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,145897,2015-10-30 10:24:43:030,1446171883030.0 \n-0.8272,1.0175,9.0477,-0.4774,0.1837,9.7933,0.1466,0.0635,-0.0501,-1.7,-28.7,-44.1,3.001093649,-0.71,2.64,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,145999,2015-10-30 10:24:43:132,1446171883132.0 \n-1.3443,0.3508,11.2085,-0.5416,0.274,9.7878,0.1613,0.0916,-0.0819,-1.8,-28.8,-43.7,2.984862087,-1.51,3.13,36.81312,-119.74887,262.49,336.2427613,4.28,19.35484,172.55,16 / 16,146102,2015-10-30 10:24:43:235,1446171883235.0 \n-0.7123,-0.6464,11.4048,-0.5618,0.4038,9.7822,0.088,-0.0867,-0.055,-1.8,-29.4,-43.5,2.9791025,-2.36,3.29,36.813007,-119.74887,264.82,336.2427613,3.99,25.806452,182.17,16 / 16,146203,2015-10-30 10:24:43:336,1446171883336.0 \n-0.6488,0.5112,8.2887,-0.8048,0.1112,9.7729,0.1393,-0.0623,-0.0122,-1.5,-29.5,-43.6,2.989050877,-0.55,4.42,36.813007,-119.74887,264.82,336.2427613,3.99,25.806452,182.17,16 / 16,146305,2015-10-30 10:24:43:438,1446171883438.0 \n-0.7039,0.322,8.6862,-0.7169,-0.0887,9.78,0.0929,0.1283,0.0611,-1.1,-29.2,-43.8,3.004060709,0.61,4.02,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,146407,2015-10-30 10:24:43:540,1446171883540.0 \n-0.6955,0.8631,8.4372,-0.6969,-0.0549,9.7817,-0.0037,-0.0672,0.0819,-0.9,-28.8,-43.9,2.99638126,0.46,4.3,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,146509,2015-10-30 10:24:43:642,1446171883642.0 \n-1.2342,0.1472,10.2723,-0.5804,0.0294,9.7894,0.0635,0.0208,0.0159,-1.3,-28.5,-43.7,3.013136421,-0.17,3.39,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,146611,2015-10-30 10:24:43:744,1446171883744.0 \n-0.583,0.595,8.3917,-0.6409,0.3264,9.7802,0.474,0.1075,0.3726,-1.9,-28.7,-43.3,2.968979591,-1.91,3.75,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,146713,2015-10-30 10:24:43:846,1446171883846.0 \n-1.5598,-0.7961,11.4503,-0.5957,0.2703,9.7848,0.0305,-0.2443,0.226,-2.4,-29,-42.7,2.975437309,-2.04,3.48,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,146815,2015-10-30 10:24:43:948,1446171883948.0 \n-0.7386,0.0862,9.2907,-0.4125,0.259,9.7945,-0.1038,-0.1258,0.0782,-3.3,-29.1,-42.6,2.97072492,-1.51,2.41,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,146918,2015-10-30 10:24:44:051,1446171884051.0 \n-0.7374,0.3519,9.1638,-0.4494,0.0283,9.7963,-0.1674,-0.0098,0.0037,-3.8,-28.8,-42.8,2.936690999,-0.43,2.62,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,147019,2015-10-30 10:24:44:152,1446171884152.0 \n-1.0977,0.6596,9.3314,-0.5134,0.1016,9.7927,0.0635,0.0305,-0.0098,-4.3,-28,-42.8,2.918714108,-0.59,3,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,147121,2015-10-30 10:24:44:254,1446171884254.0 \n-1.0774,-0.2263,11.8465,-0.4686,0.2272,9.7928,0.1405,-0.2016,-0.1185,-4.3,-27.7,-43,2.915048917,-1.11,3.02,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,147223,2015-10-30 10:24:44:356,1446171884356.0 \n0.2921,-0.0718,10.2987,-0.5043,0.3972,9.7856,0.0367,-0.1222,-0.2138,-4.1,-27.9,-42.5,2.908242133,-2.69,2.98,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,147325,2015-10-30 10:24:44:458,1446171884458.0 \n-0.6823,0.2646,9.1315,-0.6406,0.1735,9.7842,-0.1271,-0.1344,-0.1491,-3.7,-27.9,-42.3,2.894628564,-1.06,3.92,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,147427,2015-10-30 10:24:44:560,1446171884560.0 \n-0.5399,0.6476,8.8921,-0.5531,0.0463,9.7909,-0.0929,-0.1185,-0.0574,-3,-27.6,-42.6,2.949082837,-0.27,3.23,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,147530,2015-10-30 10:24:44:663,1446171884663.0 \n-0.7889,0.9445,8.3582,-0.5057,0.0975,9.7931,0.1503,-0.0037,0.0843,-2.6,-27.1,-42.9,2.948559238,-0.31,2.98,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,147631,2015-10-30 10:24:44:764,1446171884764.0 \n-1.0977,0.2682,10.3334,-0.5049,0.1941,9.7917,0.1075,0.0244,0.1552,-2.6,-26.9,-43.4,2.944894047,-1.13,2.95,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,147733,2015-10-30 10:24:44:866,1446171884866.0 \n-1.0546,0.0467,11.8202,-0.5677,0.3933,9.7823,0.4679,0.2822,0.4899,-2.7,-27.1,-43.6,2.93494567,-1.61,3.13,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,147836,2015-10-30 10:24:44:969,1446171884969.0 \n-0.9349,0.0251,10.4507,-0.7005,0.6598,9.7593,0.022,-0.0391,0.2529,-3.1,-27.7,-43.5,2.907718534,-3.96,3.95,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,147937,2015-10-30 10:24:45:070,1446171885070.0 \n-1.2342,0.4477,8.8969,-0.7414,0.6625,9.7561,0.011,-0.0379,0.2541,-3.3,-28.1,-43.1,2.895326696,-3.8,4.43,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,148040,2015-10-30 10:24:45:173,1446171885173.0 \n-1.3599,0.4298,10.0796,-0.7569,0.3653,9.7706,-0.2932,0.0782,-0.0684,-3.7,-28.4,-42.7,2.87106662,-2.76,4.27,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,148141,2015-10-30 10:24:45:274,1446171885274.0 \n-1.2761,1.2498,8.0158,-0.8489,0.362,9.7631,0.0843,0.1344,-0.0147,-3.7,-28.1,-43,2.861292776,-2.14,4.82,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,148243,2015-10-30 10:24:45:376,1446171885376.0 \n-1.385,0.1616,10.1957,-0.869,0.3551,9.7616,0.1026,-0.0281,0.0428,-3.7,-27.6,-43.3,2.854835057,-2.07,5.09,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,148345,2015-10-30 10:24:45:478,1446171885478.0 \n-1.3587,0.2251,9.7396,-0.8288,0.627,9.7514,0.4154,-0.0892,0.2004,-3.6,-27.5,-43.3,2.844537615,-2.93,4.81,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,148447,2015-10-30 10:24:45:580,1446171885580.0 \n-1.2665,-0.5028,11.2468,-0.8519,0.5659,9.7532,-0.3103,0.0367,-0.2492,-3.6,-28.1,-42.7,2.854485992,-3.94,4.53,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,148549,2015-10-30 10:24:45:682,1446171885682.0 \n-0.8164,-0.2179,10.5405,-0.9762,0.4397,9.748,-0.1747,0.1637,-0.2566,-3.4,-28.4,-42.4,2.873684613,-2.57,5.72,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,148651,2015-10-30 10:24:45:784,1446171885784.0 \n-0.8619,0.1269,8.8166,-1.0943,0.3191,9.7402,-0.0843,0.0159,-0.2309,-2.8,-28.3,-42.7,2.85797665,-2.09,6.31,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,148753,2015-10-30 10:24:45:886,1446171885886.0 \n-1.2977,-0.0766,9.4403,-0.9866,0.2446,9.7538,-0.1063,-0.1723,-0.11,-2,-28,-43.2,2.898991888,-1.52,6.22,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,148856,2015-10-30 10:24:45:989,1446171885989.0 \n-1.057,-0.2538,9.8725,-0.8293,0.2501,9.7683,0.1491,-0.1955,0.099,-1.5,-27.9,-43.8,2.956238687,-1.21,5.32,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,148958,2015-10-30 10:24:46:091,1446171886091.0 \n-1.6556,-0.4657,8.9567,-0.8438,0.2695,9.7666,-0.0855,0.0476,0.2517,-1.7,-27.9,-44,2.935643802,-1.56,4.7,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,149059,2015-10-30 10:24:46:192,1446171886192.0 \n-0.7338,0.0611,9.2584,-0.805,0.2539,9.7703,0.1271,-0.1197,0.2761,-2.4,-27.8,-44,2.935818335,-1.48,4.71,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,149162,2015-10-30 10:24:46:295,1446171886295.0 \n-0.267,-0.2107,10.7835,-0.6743,0.2281,9.7808,-0.1491,-0.1185,0.1075,-3.3,-27.9,-43.8,2.915747048,-1.88,4.05,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,149263,2015-10-30 10:24:46:396,1446171886396.0 \n-0.7769,-0.0215,9.4751,-0.7019,0.106,9.7809,0.0269,-0.2004,-0.077,-3.7,-27.9,-43.7,2.881887661,-0.65,4.33,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,149366,2015-10-30 10:24:46:499,1446171886499.0 \n-1.0846,-0.2143,9.7288,-0.645,-0.0554,9.7853,-0.1662,-0.215,-0.1271,-4.1,-27.8,-44.2,2.894454032,0.04,4.02,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,149467,2015-10-30 10:24:46:600,1446171886600.0 \n-1.9764,-0.3555,9.2907,-0.6594,-0.2158,9.7821,-0.1539,0.0892,0.0269,-4.1,-27.3,-44.4,2.900213618,1.11,3.73,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,149569,2015-10-30 10:24:46:702,1446171886702.0 \n-1.3755,0.1149,9.3841,-0.4912,-0.2281,9.7917,-0.0244,-0.1613,0.5522,-4.7,-26.6,-45,2.888519912,1.33,2.87,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,149672,2015-10-30 10:24:46:805,1446171886805.0 \n-2.4995,-0.3879,9.8402,-0.4488,-0.2862,9.7922,-0.0476,-0.1478,0.8833,-5.5,-26.2,-45.3,2.884854721,1.64,2.76,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,149773,2015-10-30 10:24:46:906,1446171886906.0 \n-2.6133,-0.6285,9.9491,-0.409,-0.2576,9.7947,0.0599,-0.0757,1.0641,-7.5,-25.5,-45.4,2.814692485,1.51,2.39,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,149876,2015-10-30 10:24:47:009,1446171887009.0 \n-1.8292,-0.753,9.8234,-0.527,-0.134,9.7916,0.1136,0.204,1.5186,-9.8,-24.6,-45.2,2.708750999,1.17,2.52,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,149977,2015-10-30 10:24:47:110,1446171887110.0 \n-1.0798,-0.5614,9.007,-0.8558,0.1147,9.7686,0.0342,0.3677,1.6469,-13,-23.3,-45.2,2.515368518,-0.4,4.4,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,150079,2015-10-30 10:24:47:212,1446171887212.0 \n-0.5076,-0.4022,9.3972,-1.0771,0.2007,9.7453,-0.0489,0.4056,1.5149,-15,-21.9,-45.4,2.400525853,-0.91,5.84,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,150181,2015-10-30 10:24:47:314,1446171887314.0 \n-0.8871,-0.7266,10.2304,-1.332,0.1833,9.714,-0.2358,0.2004,1.3182,-17.1,-19.3,-46.1,2.24100276,-1.21,7.44,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,150284,2015-10-30 10:24:47:417,1446171887417.0 \n-0.9349,-0.6524,9.8533,-1.497,0.1525,9.6905,-0.2541,0.2089,1.504,-18,-17,-46.9,2.150769237,-0.99,8.56,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,150385,2015-10-30 10:24:47:518,1446171887518.0 \n-0.5291,-0.8116,9.4463,-1.5814,0.1721,9.6768,-0.1674,-0.055,1.8864,-18.9,-12.5,-47.3,1.974141917,-1.01,9.28,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,150487,2015-10-30 10:24:47:620,1446171887620.0 \n0.3699,-0.8882,11.0696,-1.2805,0.1917,9.7208,-0.1979,-0.2468,1.7446,-20.2,-7.3,-47.2,1.792976741,-1.38,7.98,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,150590,2015-10-30 10:24:47:723,1446171887723.0 \n0.6189,0.4705,8.3103,-1.1246,0.2631,9.7384,0.0476,-0.3152,1.1716,-20.4,-4.9,-47.3,1.727701427,-1.21,7.15,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,150691,2015-10-30 10:24:47:824,1446171887824.0 \n-0.1891,-0.0539,11.1438,-0.794,0.1504,9.7733,-0.2505,0.0672,0.0696,-21.2,-2.1,-46.4,1.60919357,-1.36,4.79,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,150793,2015-10-30 10:24:47:926,1446171887926.0 \n-1.1301,-0.2035,10.094,-0.8367,-0.057,9.7707,-0.1405,0.5266,0,-21.8,0.5,-46.1,1.524021503,-0.25,4.41,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,150895,2015-10-30 10:24:48:028,1446171888028.0 \n-0.911,0.5674,9.0285,-0.9542,-0.0816,9.7598,-0.0501,-0.1637,0.0269,-21.9,1.5,-46.1,1.50656821,0.38,5.91,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,150998,2015-10-30 10:24:48:131,1446171888131.0 \n-1.1073,-0.012,10.471,-0.8204,-0.2298,9.7696,-0.11,-0.0134,-0.1466,-21.8,2.3,-46,1.533271748,1.34,4.8,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,151100,2015-10-30 10:24:48:233,1446171888233.0 \n-0.6764,0.7649,9.6822,-0.8171,-0.2075,9.7703,0.0257,0.1466,0.0049,-21.6,2.6,-45.9,1.498539696,1.48,4.8,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,151202,2015-10-30 10:24:48:335,1446171888335.0 \n-1.0032,0.917,9.7911,-0.8986,-0.1546,9.7642,-0.0269,0.0257,0.0513,-21.6,2.8,-45.9,1.488940385,1.12,5.31,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,151304,2015-10-30 10:24:48:437,1446171888437.0 \n-0.9996,1.3767,8.8945,-0.9993,-0.0297,9.7556,0.0513,0.077,0.0745,-21.6,2.7,-45.8,1.467123769,0.32,5.73,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,151405,2015-10-30 10:24:48:538,1446171888538.0 \n-0.9613,1.4401,9.3757,-1.0265,0.0826,9.7524,0.0794,0.0147,0.077,-21.3,2.8,-46.3,1.440594765,-0.48,6.01,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,151507,2015-10-30 10:24:48:640,1446171888640.0 \n-1.0774,1.5048,8.2468,-1.0156,0.3591,9.7473,0.2382,-0.0965,0.1038,-21.1,2.8,-46.1,1.408655239,-1.62,6.2,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,151609,2015-10-30 10:24:48:742,1446171888742.0 \n-1.0618,0.9601,10.3118,-0.9763,0.3538,9.7515,-0.1197,0.0244,0.0049,-21.1,2.7,-46.4,1.382998899,-2.39,5.57,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,151712,2015-10-30 10:24:48:845,1446171888845.0 \n-0.6165,0.5207,10.8445,-0.9268,0.3865,9.7551,0.0623,-0.0684,-0.1344,-21.1,2.5,-46.4,1.390329282,-2.12,5.52,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,151813,2015-10-30 10:24:48:946,1446171888946.0 \n-0.8284,-0.2562,10.4004,-0.8418,0.2365,9.7676,0.1967,0.2541,-0.1686,-21.3,2.3,-46.5,1.448274213,-1.38,4.93,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,151915,2015-10-30 10:24:49:048,1446171889048.0 \n-0.3412,0.4034,8.7556,-0.9402,0.2947,9.757,-0.044,-0.0452,-0.0782,-21.4,2.3,-46.2,1.439373034,-1.8,5.75,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,152017,2015-10-30 10:24:49:150,1446171889150.0 \n-0.425,0.5722,8.6993,-0.7985,0.2845,9.7699,0.0171,-0.1857,-0.0843,-21.7,1.9,-46.1,1.44391089,-1.66,4.67,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,152119,2015-10-30 10:24:49:252,1446171889252.0 \n-0.4118,0.7458,9.8845,-0.6627,0.2892,9.78,0.1063,0.1246,-0.0147,-21.9,1.6,-46.1,1.44094383,-1.66,3.97,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,152221,2015-10-30 10:24:49:354,1446171889354.0 \n-0.2346,1.0104,10.3813,-0.7491,0.4565,9.7673,0.1576,0.1319,0.0049,-22.2,1.2,-46.2,1.456651794,-2.5,4.47,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,152323,2015-10-30 10:24:49:456,1446171889456.0 \n-1.0139,0.3555,9.2692,-0.8483,0.634,9.7493,0.2737,0.2004,0.1405,-22.3,0.8,-46.1,1.446703417,-2.81,4.31,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,152426,2015-10-30 10:24:49:559,1446171889559.0 \n-1.1768,-0.0168,9.3194,-0.8351,0.5179,9.7573,0.1515,-0.1271,0.2566,-22.1,0.4,-46.3,1.484577062,-2.89,4.73,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,152527,2015-10-30 10:24:49:660,1446171889660.0 \n-0.3855,0.079,9.098,-0.6623,0.5431,9.7692,-0.0721,-0.182,0.1258,-22,0.2,-46.2,1.467472835,-3.39,4.14,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,152629,2015-10-30 10:24:49:762,1446171889762.0 \n-0.9074,0.7434,9.2344,-0.7178,0.4853,9.7683,0.0232,0.0208,0.1002,-22.1,0.6,-46.4,1.449321411,-2.68,4.03,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,152731,2015-10-30 10:24:49:864,1446171889864.0 \n-0.5519,1.2222,9.1614,-0.7556,0.6285,9.7573,0.1344,0.0024,-0.0208,-22.1,0.6,-46,1.431868118,-3.33,4.42,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,152833,2015-10-30 10:24:49:966,1446171889966.0 \n-0.6967,0.2418,12.2715,-0.6956,0.7829,9.7506,0.3958,0.1454,-0.0428,-22.2,0.5,-45.9,1.409353371,-4.02,4.07,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,152935,2015-10-30 10:24:50:068,1446171890068.0 \n-0.7362,-1.0127,12.967,-0.6556,0.7619,9.755,-0.3103,-0.1613,-0.3005,-22.3,-0.2,-45.9,1.433787981,-4.46,3.84,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,153038,2015-10-30 10:24:50:171,1446171890171.0 \n0.1353,0.3651,7.5286,-0.8093,0.6617,9.7508,-0.0147,-0.1515,-0.1344,-22.4,-0.6,-46.1,1.494350906,-3.87,4.74,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,153139,2015-10-30 10:24:50:272,1446171890272.0 \n-0.5531,0.5183,8.6263,-0.7346,0.406,9.7707,-0.0464,0.0195,-0.1002,-22.5,-0.8,-46.2,1.534318945,-2.49,4.22,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,153241,2015-10-30 10:24:50:374,1446171890374.0 \n-0.486,0.9804,8.4372,-0.7292,0.4066,9.771,0.055,-0.022,-0.0354,-22.5,-0.6,-46,1.539903999,-2.31,4.34,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,153344,2015-10-30 10:24:50:477,1446171890477.0 \n-0.6572,0.6416,9.9192,-0.7417,0.4005,9.7704,0.0147,0.0794,-0.0513,-22.5,-0.7,-45.7,1.539031334,-2.34,4.34,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,153445,2015-10-30 10:24:50:578,1446171890578.0 \n-0.407,0.6907,11.3856,-0.753,0.4847,9.7657,-0.0513,-0.0672,0.1148,-22.4,-0.7,-45.7,1.530479221,-2.64,4.56,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,153548,2015-10-30 10:24:50:681,1446171890681.0 \n-1.136,-0.486,11.388,-0.6187,0.2317,9.7844,-0.496,-0.3384,-0.1515,-22.7,-0.5,-45.5,1.52681403,-1.47,3.18,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,153649,2015-10-30 10:24:50:782,1446171890782.0 \n-0.9948,0.2502,9.0166,-0.5768,0.3156,9.7846,-0.0929,-0.0782,0.0037,-22.9,-0.3,-45.4,1.511455132,-2.01,3.49,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,153751,2015-10-30 10:24:50:884,1446171890884.0 \n-0.9852,0.6045,8.6718,-0.6015,0.3187,9.783,0.2871,0.0757,0.1552,-23.1,0,-45.3,1.515818455,-1.86,3.52,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,153853,2015-10-30 10:24:50:986,1446171890986.0 \n-0.6201,1.1133,8.8717,-0.6769,0.6242,9.7633,0.3005,0.1002,0.1234,-23,-0.1,-45.6,1.465902039,-3.56,4,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,153956,2015-10-30 10:24:51:089,1446171891089.0 \n-0.8499,0.3316,11.6849,-0.6836,0.7411,9.7547,0.1038,-0.0464,-0.1222,-22.8,-0.7,-45.6,1.489114918,-4.07,4.06,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,154058,2015-10-30 10:24:51:191,1446171891191.0 \n0.8164,0.0275,10.0245,-0.6775,0.7948,9.7509,-0.3726,0.0806,-0.3897,-22.7,-1.4,-45.6,1.458397123,-5.11,3.96,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,154160,2015-10-30 10:24:51:293,1446171891293.0 \n-0.1305,0.3424,8.2732,-0.8351,0.5289,9.7567,-0.1344,-0.3714,-0.2993,-22.7,-1.7,-45.6,1.557008226,-3.09,4.89,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,154262,2015-10-30 10:24:51:395,1446171891395.0 \n-0.4298,0.158,9.432,-0.6795,0.3315,9.7775,-0.1527,0.0086,-0.1637,-22.7,-1.8,-45.6,1.585108027,-2.1,3.97,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,154363,2015-10-30 10:24:51:496,1446171891496.0 \n-1.16,1.3288,8.1104,-0.7997,0.4154,9.7652,0.1234,0.0733,0.044,-22.6,-1.8,-45.7,1.580919236,-2.25,4.59,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,154465,2015-10-30 10:24:51:598,1446171891598.0 \n-0.9529,0.3208,11.157,-0.8614,0.4213,9.7597,0.1637,0.1845,0.2456,-22.5,-2,-45.7,1.578301243,-2.35,4.87,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,154568,2015-10-30 10:24:51:701,1446171891701.0 \n-0.1987,0.7554,9.736,-0.878,0.7239,9.7404,0.3299,-0.0476,0.4032,-22.3,-2.2,-45.9,1.537460538,-3.76,5.32,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,154670,2015-10-30 10:24:51:803,1446171891803.0 \n-0.0491,0.6728,7.8566,-0.5662,0.5791,9.7731,0.0489,-0.0281,0.1161,-22.4,-2.1,-46.1,1.544790921,-3.39,3.32,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,154772,2015-10-30 10:24:51:905,1446171891905.0 \n-0.6129,0.5315,9.6534,-0.4205,0.5809,9.7804,-0.2382,0.2309,0.0428,-22.6,-2.1,-45.9,1.529082958,-3.89,2.68,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,154873,2015-10-30 10:24:52:006,1446171892006.0 \n-0.6393,1.4641,7.1323,-0.5468,0.6228,9.7716,0.1796,0.2224,-0.0134,-23.2,-1.8,-45.3,1.540427598,-3.64,3.2,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,154975,2015-10-30 10:24:52:108,1446171892108.0 \n-0.8344,1.0678,10.2352,-0.6797,0.7617,9.7534,0.0208,-0.0354,-0.0525,-23.3,-2,-45.3,1.521752575,-4.34,4.02,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,155078,2015-10-30 10:24:52:211,1446171892211.0 \n-1.075,0.9565,11.649,-0.655,0.8694,9.746,0.1894,-0.0208,-0.1381,-23,-2.2,-45.6,1.505171947,-4.8,3.89,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,155179,2015-10-30 10:24:52:312,1446171892312.0 \n-1.3874,-0.7195,12.4091,-0.6392,0.7285,9.7586,-0.3861,0.3348,-0.3115,-23,-2.9,-45.8,1.558928088,-4.26,3.75,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,155281,2015-10-30 10:24:52:414,1446171892414.0 \n-0.0132,0.407,7.6004,-0.7729,0.6485,9.7546,0.0965,-0.1026,0.0147,-22.9,-3.1,-46,1.577952177,-3.65,4.69,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,155383,2015-10-30 10:24:52:516,1446171892516.0 \n-0.3292,0.9637,7.7871,-0.7268,0.4793,9.7679,0.1319,-0.1552,0.0293,-22.8,-3,-46.3,1.608669972,-2.59,4.49,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,155486,2015-10-30 10:24:52:619,1446171892619.0 \n-0.4633,1.1121,8.3977,-0.7194,0.5064,9.7671,-0.0134,-0.0122,-0.022,-22.6,-2.7,-46.7,1.599594259,-2.84,4.25,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,155587,2015-10-30 10:24:52:720,1446171892720.0 \n-0.838,0.6213,11.1606,-0.8074,0.609,9.7544,0.0782,0.1283,0.1136,-22.6,-2.6,-46.8,1.589820416,-3.17,4.55,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,155689,2015-10-30 10:24:52:822,1446171892822.0 \n0.2622,0.917,10.0317,-0.7036,0.7475,9.7528,-0.1185,-0.2517,0.0806,-22.5,-2.9,-46.5,1.550375975,-4.57,4.63,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,155791,2015-10-30 10:24:52:924,1446171892924.0 \n-0.583,1.1169,6.6068,-0.6972,0.6911,9.7574,0.2419,-0.2773,0.0098,-22.5,-2.8,-46.1,1.578301243,-3.64,4.52,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,155893,2015-10-30 10:24:53:026,1446171893026.0 \n-0.6991,0.2598,9.2943,-0.5934,0.5646,9.7724,-0.1454,-0.0745,-0.1429,-22.7,-2.8,-45.8,1.568876465,-3.92,3.43,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,155995,2015-10-30 10:24:53:128,1446171893128.0 \n-2.2003,0.8475,8.8214,-0.7992,0.4089,9.7655,-0.1833,0.3091,0.0733,-23,-2.5,-45.1,1.569400063,-2.7,4.1,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,156097,2015-10-30 10:24:53:230,1446171893230.0 \n-1.0295,0.8392,10.0916,-0.859,0.5532,9.7533,0.2028,-0.1051,0.2639,-22.7,-2.3,-44.8,1.555262896,-3.23,5.03,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,156199,2015-10-30 10:24:53:332,1446171893332.0 \n-0.7482,0.4932,10.1622,-0.8706,0.7336,9.7403,0.1881,-0.0696,0.0428,-22.4,-2.1,-44.8,1.54356919,-3.62,5.17,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,156301,2015-10-30 10:24:53:434,1446171893434.0 \n-0.5207,-0.3579,9.8545,-0.7021,0.6342,9.7609,-0.1906,-0.121,-0.2639,-22.3,-2.2,-45,1.520007246,-4.34,4.15,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,156404,2015-10-30 10:24:53:537,1446171893537.0 \n-0.1688,-0.0431,8.8717,-0.5491,0.4065,9.7828,-0.2004,-0.2492,-0.3201,-22.6,-2.4,-45.3,1.569574596,-2.68,3.65,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,156505,2015-10-30 10:24:53:638,1446171893638.0 \n-0.492,0.1867,8.3318,-0.405,0.1405,9.7973,-0.1222,-0.1014,-0.1026,-23.2,-2.5,-44.9,1.62053821,-0.99,2.56,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,156607,2015-10-30 10:24:53:740,1446171893740.0 \n-0.3627,0.8547,8.2744,-0.4053,0.1694,9.7968,0.0672,0.0501,0.0696,-23.6,-2.2,-44.8,1.631184719,-0.58,2.21,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,156710,2015-10-30 10:24:53:843,1446171893843.0 \n-0.3795,0.3005,11.3629,-0.3606,0.2232,9.7975,0.0428,-0.0098,0.0965,-24.2,-1.9,-44.6,1.61216063,-1.22,2.13,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,156811,2015-10-30 10:24:53:944,1446171893944.0 \n0.2023,-0.1796,10.7117,-0.3171,0.336,9.7958,-0.237,-0.1503,-0.1051,-24.4,-1.9,-44.4,1.57934844,-2.37,2.09,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,156913,2015-10-30 10:24:54:046,1446171894046.0 \n-0.4597,-0.103,10.5285,-0.2171,0.2848,9.8001,-0.0012,-0.0403,0.055,-24.5,-2,-44.6,1.607448241,-1.39,1.81,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,157015,2015-10-30 10:24:54:148,1446171894148.0 \n0.2143,0.4022,8.3797,-0.068,0.3626,9.7997,-0.0086,-0.0367,-0.0819,-24.9,-2,-44.3,1.582490033,-2.23,0.44,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,157117,2015-10-30 10:24:54:250,1446171894250.0 \n-0.4166,1.3743,8.2492,-0.1679,0.3158,9.8001,0.1539,0.1173,0.0599,-25.2,-2.1,-44.4,1.594009206,-1.85,0.98,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,157219,2015-10-30 10:24:54:352,1446171894352.0 \n-0.4022,0.826,9.5972,-0.2696,0.5174,9.7893,0.2334,-0.0562,0,-25.3,-2.5,-44.1,1.567654734,-2.75,1.54,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,157321,2015-10-30 10:24:54:454,1446171894454.0 \n-0.4609,0.6967,11.3904,-0.294,0.6472,9.7809,0.0721,0.1271,0.0269,-25.1,-2.9,-44.3,1.583711763,-3.51,1.42,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,157424,2015-10-30 10:24:54:557,1446171894557.0 \n-0.729,-0.1592,11.3892,-0.3762,0.4324,9.7899,-0.5302,0.2932,-0.1429,-24.8,-3.4,-44.2,1.58650429,-3.42,1.73,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,157525,2015-10-30 10:24:54:658,1446171894658.0 \n0.4788,1.0391,7.5693,-0.3609,0.3826,9.7925,-0.4386,-0.0012,-0.1759,-24.7,-3.4,-44.4,1.617396618,-2.34,2.15,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,157627,2015-10-30 10:24:54:760,1446171894760.0 \n-0.3364,1.1157,7.288,-0.3686,0.1925,9.7978,0.0354,0.1038,0.0525,-24.5,-2.7,-44.3,1.662600645,-0.84,2.24,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,157729,2015-10-30 10:24:54:862,1446171894862.0 \n0.3926,1.136,9.323,-0.2637,0.3093,9.7982,0.1344,0.0305,0.2663,-24.5,-2.3,-44.2,1.604306648,-1.53,1.54,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,157831,2015-10-30 10:24:54:964,1446171894964.0 \n-0.9505,0.832,10.3633,-0.4977,0.3697,9.787,0.2395,0.358,0.1307,-24.5,-2.1,-44.3,1.585631625,-2.16,2.91,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,157933,2015-10-30 10:24:55:066,1446171895066.0 \n-1.1013,-0.1927,11.6753,-0.6472,0.3592,9.7787,-0.2272,0.0929,0.1845,-24.3,-2.2,-44.5,1.567829267,-2.81,3.58,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,158035,2015-10-30 10:24:55:168,1446171895168.0 \n-0.1401,0.2251,9.1075,-0.4675,0.3382,9.7897,-0.0574,-0.2676,0.1344,-23.9,-2,-44.9,1.58947135,-1.98,2.73,36.813007,-119.74887,264.82,336.1648404,3.99,25.806452,182.17,16 / 16,158137,2015-10-30 10:24:55:270,1446171895270.0 \n-1.2282,-0.0443,8.6084,-0.3563,0.3345,9.7945,0.0904,-0.0745,0.0489,-24,-1.7,-44.7,1.591216679,-1.92,2.2,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,158239,2015-10-30 10:24:55:372,1446171895372.0 \n-0.9661,0.6847,8.6143,-0.331,0.4791,9.7893,0.226,0.0464,0.0513,-24.4,-1.4,-44.1,1.538682269,-2.41,1.93,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,158341,2015-10-30 10:24:55:474,1446171895474.0 \n-0.6656,0.5339,10.5165,-0.3339,0.7027,9.7757,0.2089,-0.0721,-0.0794,-24.8,-1.7,-44,1.538333203,-3.8,2.01,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,158444,2015-10-30 10:24:55:577,1446171895577.0 \n0.0958,-0.164,11.6131,-0.3162,0.8434,9.7652,-0.088,-0.2773,-0.1234,-25.1,-2.3,-44,1.505695546,-4.93,1.85,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,158546,2015-10-30 10:24:55:679,1446171895679.0 \n0.328,0.6835,8.855,-0.3879,0.5618,9.7829,0.033,-0.0428,0.1747,-25.1,-2.6,-44.2,1.59243841,-3.23,2.38,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,158647,2015-10-30 10:24:55:780,1446171895780.0 \n0.1185,0.4334,9.8797,-0.3338,0.4442,9.7909,-0.2138,-0.1026,0.0086,-25,-2.5,-44,1.569923662,-2.69,2.16,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,158749,2015-10-30 10:24:55:882,1446171895882.0 \n-0.6093,0.9804,8.9352,-0.3268,0.5205,9.7874,0.0257,-0.0721,0.0049,-24.9,-2,-43.6,1.559800753,-3.04,1.91,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,158851,2015-10-30 10:24:55:984,1446171895984.0 \n-0.2047,1.2821,9.2404,-0.2946,0.6409,9.7813,0.0232,0.0721,0.0599,-25,-1.8,-43.5,1.552644903,-3.36,1.85,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,158953,2015-10-30 10:24:56:086,1446171896086.0 \n-0.6033,1.3024,12.0931,-0.2928,0.7459,9.7739,0.2529,0.2602,0.2883,-25,-1.8,-43.1,1.536238808,-3.95,1.82,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,159055,2015-10-30 10:24:56:188,1446171896188.0 \n-0.3112,0.1269,10.6961,-0.391,0.7106,9.7731,-0.3079,0.1539,0.044,-25,-1.7,-43.1,1.513374994,-4.8,2.08,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,159157,2015-10-30 10:24:56:290,1446171896290.0 \n-0.1604,0.4621,8.5102,-0.3076,0.6029,9.7833,-0.0892,-0.0415,0.0623,-24.9,-1.3,-43,1.506044612,-3.68,1.89,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,159259,2015-10-30 10:24:56:392,1446171896392.0 \n-0.7805,0.5926,8.6921,-0.3965,0.4642,9.7876,0.077,0.0195,-0.0037,-24.8,-0.9,-42.9,1.531700952,-2.78,2.19,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,159361,2015-10-30 10:24:56:494,1446171896494.0 \n-1.0044,1.3982,9.0022,-0.5508,0.5924,9.7732,0.1503,0.2199,0.0171,-24.7,-0.3,-42.9,1.481260936,-3.36,2.94,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,159463,2015-10-30 10:24:56:596,1446171896596.0 \n-0.8033,0.6213,11.4371,-0.5436,0.6757,9.7682,0.1381,-0.1869,-0.1014,-24.4,-0.4,-43.1,1.470090829,-3.71,3.46,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,159565,2015-10-30 10:24:56:698,1446171896698.0 \n-0.929,-0.7973,12.8772,-0.4547,0.589,9.7784,-0.5974,0.1234,-0.4019,-24.2,-0.7,-43.2,1.484053463,-4.46,2.59,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,159667,2015-10-30 10:24:56:800,1446171896800.0 \n0.1736,0.7649,7.5094,-0.4679,0.6277,9.7754,0.3665,-0.0745,0.1063,-24.2,-0.9,-43.4,1.517738318,-3.3,3.08,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,159769,2015-10-30 10:24:56:902,1446171896902.0 \n-0.0814,0.3855,8.8562,-0.3859,0.5168,9.7854,0.0977,-0.1063,-0.077,-24.3,-1,-43.3,1.527512161,-2.89,2.42,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,159872,2015-10-30 10:24:57:005,1446171897005.0 \n-0.4549,1.0104,8.5641,-0.3776,0.5379,9.7846,0.0696,-0.0134,0.0623,-24.3,-1,-43.1,1.523148838,-3.04,2.35,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,159974,2015-10-30 10:24:57:107,1446171897107.0 \n0.0036,1.0475,10.6063,-0.3593,0.6425,9.779,0.1442,-0.0134,0.0232,-24.2,-1.1,-43.1,1.502030354,-3.76,2.1,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,160075,2015-10-30 10:24:57:208,1446171897208.0 \n0.3172,1.4293,9.019,-0.3672,0.8403,9.7637,0.2944,0.1833,0.0867,-24,-1.5,-43,1.469218164,-4.92,2.15,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,160177,2015-10-30 10:24:57:310,1446171897310.0 \n-0.6644,0.6033,8.8825,-0.3072,0.6646,9.7793,0.204,-0.0806,0.1002,-24,-1.7,-43.1,1.545489053,-3.59,1.9,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,160280,2015-10-30 10:24:57:413,1446171897413.0 \n-0.1496,0.4776,8.1738,-0.1019,0.6679,9.7834,-0.226,-0.16,-0.1051,-24,-1.8,-43.1,1.522276174,-4.3,0.96,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,160382,2015-10-30 10:24:57:515,1446171897515.0 \n-0.5997,0.9613,8.8298,-0.0351,0.6337,9.7861,0.0611,-0.0806,0.0244,-24.3,-1.8,-42.8,1.538682269,-3.7,0.21,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,160483,2015-10-30 10:24:57:616,1446171897616.0 \n-0.4968,1.6005,8.6107,-0.0463,0.7207,9.78,0.0867,-0.0159,0.0244,-24.5,-2,-42.8,1.529781089,-4,0.3,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,160585,2015-10-30 10:24:57:718,1446171897718.0 \n-0.1472,1.5634,10.7392,0.0573,0.7713,9.7761,0.2834,0.0977,0.0318,-24.7,-2.2,-42.3,1.517563785,-4.51,-0.34,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,160687,2015-10-30 10:24:57:820,1446171897820.0 \n0.6321,-0.4549,12.6773,-0.0109,0.6424,9.7856,-0.4606,-0.0513,-0.3738,-24.8,-2.5,-42.4,1.494525438,-5.26,-0.56,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,160789,2015-10-30 10:24:57:922,1446171897922.0 \n-0.0611,0.2993,8.3342,-0.1717,0.681,9.7815,0.011,0.0464,0.0452,-24.5,-2.8,-42.4,1.569923662,-4.15,0.91,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,160891,2015-10-30 10:24:58:024,1446171898024.0 \n-0.1939,1.0223,7.6339,-0.2922,0.5636,9.7861,-0.0757,0.1943,0.1161,-24.2,-2.9,-42.8,1.592612942,-3.31,1.41,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,160993,2015-10-30 10:24:58:126,1446171898126.0 \n0.0012,1.4018,7.9188,-0.4324,0.5323,9.7826,-0.1344,0.0293,-0.0086,-23.5,-2.7,-43.4,1.599419727,-3.12,2.39,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,161096,2015-10-30 10:24:58:229,1446171898229.0 \n-0.2095,0.8021,10.5141,-0.4761,0.4345,9.7854,-0.0599,0.0794,0.0977,-23,-2.3,-43.5,1.576555913,-2.54,2.79,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,161197,2015-10-30 10:24:58:330,1446171898330.0 \n-0.1975,0.2059,10.2077,-0.4137,0.5057,9.7849,-0.2651,-0.4191,0.1161,-22.8,-2.1,-43.7,1.555088364,-3.21,3,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,161300,2015-10-30 10:24:58:433,1446171898433.0 \n-0.0383,1.4712,8.6215,-0.3767,0.2758,9.7955,-0.0073,-0.4325,0.0122,-22.8,-1.6,-43.7,1.602735852,-1.61,2.2,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,161401,2015-10-30 10:24:58:534,1446171898534.0 \n-1.0283,0.085,9.8653,-0.182,0.1896,9.8031,-0.1698,-0.0391,-0.1307,-23.1,-1.2,-43.5,1.569749129,-1.38,0.74,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,161503,2015-10-30 10:24:58:636,1446171898636.0 \n-1.1827,0.6979,8.2648,-0.2711,0.2931,9.7985,0.1478,0.1686,0.0904,-23.4,-0.8,-43.3,1.559800753,-1.71,1.58,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,161605,2015-10-30 10:24:58:738,1446171898738.0 \n-0.6823,1.1947,8.8119,-0.3416,0.4914,9.7884,-0.0012,0.0195,-0.0183,-23.5,-1,-43.3,1.535889742,-2.51,1.83,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,161707,2015-10-30 10:24:58:840,1446171898840.0 \n-0.65,0.8248,11.3509,-0.3528,0.6075,9.7815,0.2334,0.033,-0.0794,-23.4,-1.6,-43.6,1.553168501,-3.22,1.92,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,161809,2015-10-30 10:24:58:942,1446171898942.0 \n0.4345,0.1472,10.6554,-0.4618,0.5052,9.7827,-0.3128,0.1332,-0.2883,-23.3,-2,-43.7,1.545489053,-3.5,2.46,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,161912,2015-10-30 10:24:59:045,1446171899045.0 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\n-0.5578,1.409,9.098,-0.3252,0.5714,9.7846,0.1478,0.0525,-0.0086,-24.6,-1.1,-43.8,1.52087991,-3.08,1.83,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,162829,2015-10-30 10:24:59:962,1446171899962.0 \n0.0227,0.741,10.4519,-0.2096,0.727,9.7774,0.1319,0.0538,-0.1197,-24.8,-1.2,-43.9,1.490860247,-4.07,1.28,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,162932,2015-10-30 10:25:00:065,1446171900065.0 \n-0.5555,-0.6153,12.0021,-0.3252,0.414,9.7925,-0.1075,0.1808,-0.2162,-24.8,-1.5,-44,1.51791285,-3.13,1.27,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,163033,2015-10-30 10:25:00:166,1446171900166.0 \n-0.3603,0.1197,9.4786,-0.2526,0.3572,9.7969,-0.0635,-0.2089,-0.1503,-24.7,-1.8,-44,1.57515965,-2.5,1.79,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,163135,2015-10-30 10:25:00:268,1446171900268.0 \n-1.0475,0.9673,8.4743,-0.267,0.3085,9.7982,-0.1222,0.1234,-0.2004,-24.5,-1.9,-44.1,1.596103601,-1.8,1.56,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,163237,2015-10-30 10:25:00:370,1446171900370.0 \n-0.7506,0.9182,9.584,-0.2584,0.2998,9.7987,-0.0965,-0.0709,0.0855,-24.4,-2,-44.2,1.595754535,-1.81,1.64,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,163339,2015-10-30 10:25:00:472,1446171900472.0 \n1.1384,0.9254,12.6234,0.0612,0.5003,9.7937,0.5779,0.1662,0.066,-24.7,-1.9,-43.9,1.585980691,-2.12,0.63,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,163441,2015-10-30 10:25:00:574,1446171900574.0 \n-0.0479,-0.2143,13.3201,-0.0802,0.5908,9.7885,-0.4826,0.0098,0.0501,-25,-2.3,-43.7,1.545489053,-3.45,0.47,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,163543,2015-10-30 10:25:00:676,1446171900676.0 \n-0.2203,0.8523,8.5425,-0.1579,0.53,9.791,-0.033,-0.1148,0.1038,-25,-2.4,-43.2,1.562767812,-2.97,0.95,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,163646,2015-10-30 10:25:00:779,1446171900779.0 \n-0.6764,0.68,8.5317,-0.2917,0.3642,9.7955,0.0195,0.0599,-0.0599,-24.8,-2.4,-43.4,1.585108027,-2.2,1.34,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,163748,2015-10-30 10:25:00:881,1446171900881.0 \n-0.5124,0.9254,8.9854,-0.2936,0.4652,9.7912,0.1503,-0.0061,0.0024,-24.5,-2.2,-43.3,1.577428578,-2.48,1.64,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,163849,2015-10-30 10:25:00:982,1446171900982.0 \n-1.0355,0.7506,10.0616,-0.3587,0.6123,9.7809,0.1686,-0.1319,-0.0867,-24.4,-2.4,-43.8,1.543743723,-3.58,2.1,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,163951,2015-10-30 10:25:01:084,1446171901084.0 \n1.2198,0.4082,10.9642,-0.2315,0.7824,9.7727,-0.0684,-0.0525,-0.0819,-24.4,-3.1,-43.9,1.551946771,-4.58,1.36,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,164053,2015-10-30 10:25:01:186,1446171901186.0 \n0.2538,0.2203,9.7121,-0.3316,0.6105,9.782,-0.066,0.0562,-0.1234,-24.5,-3.4,-44.2,1.579173907,-3.69,1.79,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,164155,2015-10-30 10:25:01:288,1446171901288.0 \n-0.1018,1.1744,7.7991,-0.3953,0.4707,9.7874,-0.1381,0.0428,-0.0831,-24.4,-3.6,-44.4,1.643052958,-2.85,2.11,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,164257,2015-10-30 10:25:01:390,1446171901390.0 \n-1.1157,0.9098,9.0214,-0.4756,0.3754,9.7879,-0.0648,0.044,-0.0354,-24.2,-3.5,-44.4,1.620189145,-2.29,2.66,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,164360,2015-10-30 10:25:01:493,1446171901493.0 \n-0.6644,1.2246,9.5684,-0.6232,0.3585,9.7803,0.0195,0.1698,0.1014,-23.8,-3.4,-44.8,1.62350527,-2.1,3.41,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,164461,2015-10-30 10:25:01:594,1446171901594.0 \n-0.7051,1.8232,9.8545,-0.7237,0.4982,9.7672,0.2651,0.0073,0.3604,-23.3,-3.2,-44.9,1.612335163,-2.53,4.25,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,164563,2015-10-30 10:25:01:696,1446171901696.0 \n-2.1596,-1.1444,14.2659,-0.4122,0.3172,9.7928,-0.2615,0.1796,0.0195,-23.1,-3,-45,1.597674397,-3.04,2.92,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,164665,2015-10-30 10:25:01:798,1446171901798.0 \n-0.4417,0.7278,8.4695,-0.4276,0.3353,9.7916,-0.0806,-0.0183,0.0794,-23.1,-2.5,-44.7,1.588424152,-2.03,2.69,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,164767,2015-10-30 10:25:01:900,1446171901900.0 \n-1.1157,0.595,8.7975,-0.4923,0.2189,9.7918,-0.1393,0.0147,-0.1491,-23.5,-2,-44.5,1.6109389,-1.33,2.73,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,164869,2015-10-30 10:25:02:002,1446171902002.0 \n-0.6931,1.4772,8.09,-0.555,0.3611,9.7843,0.0281,-0.0672,-0.0428,-23.5,-1.7,-44.2,1.592612942,-1.94,3.31,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,164971,2015-10-30 10:25:02:104,1446171902104.0 \n-0.9266,0.3735,11.0133,-0.4188,0.4024,9.7894,0.0232,-0.1503,-0.1405,-23.5,-1.7,-44.2,1.587551488,-2.12,3.11,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,165074,2015-10-30 10:25:02:207,1446171902207.0 \n0.0359,-0.4717,12.2188,-0.4348,0.0415,9.7969,-0.474,0.1662,-0.4166,-23.6,-2,-44.1,1.605702912,-1.47,2.29,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,165176,2015-10-30 10:25:02:309,1446171902309.0 \n-0.5722,-0.6225,10.143,-0.3583,-0.0743,9.7998,0.1246,-0.3445,-0.237,-23.8,-1.9,-44.3,1.661378915,0.43,2.09,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,165277,2015-10-30 10:25:02:410,1446171902410.0 \n-0.7913,0.1544,8.0026,-0.2987,-0.1166,9.8014,0.1588,0.0525,-0.044,-24.1,-1.9,-44.2,1.677610477,0.94,1.67,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,165379,2015-10-30 10:25:02:512,1446171902512.0 \n-0.5734,0.8284,8.1271,-0.2879,-0.0553,9.8023,0.0562,0.0391,0.0696,-24.3,-1.9,-44.1,1.662775178,0.44,1.74,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,165481,2015-10-30 10:25:02:614,1446171902614.0 \n-1.0738,-0.158,11.6071,-0.4346,-0.0112,9.797,0.0086,0.204,0.1552,-24.5,-2.1,-44.2,1.650557874,0.08,2.35,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,165583,2015-10-30 10:25:02:716,1446171902716.0 \n0.7422,0.4597,8.4683,-0.52,0.2892,9.7886,0.3592,0.1943,0.4753,-24.2,-2.1,-44.7,1.614255025,-1.13,2.82,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,165686,2015-10-30 10:25:02:819,1446171902819.0 \n-0.8487,-0.4393,10.4842,-0.4753,0.0131,9.7951,0.1894,-0.1906,0.4374,-24,-1.9,-45.1,1.649859742,0.09,2.69,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,165788,2015-10-30 10:25:02:921,1446171902921.0 \n0.3041,0.2143,9.4798,-0.2165,0.053,9.8041,-0.0867,-0.303,0.1271,-23.9,-1.4,-45,1.597325331,-0.43,1.55,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,165889,2015-10-30 10:25:03:022,1446171903022.0 \n-0.2753,1.1971,7.2604,-0.3247,0.1417,9.8002,0.2541,0.011,0.1112,-24.3,-0.5,-44.5,1.560324351,-0.35,1.72,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,165991,2015-10-30 10:25:03:124,1446171903124.0 \n-0.7207,0.589,10.0736,-0.3637,0.2552,9.7966,0.0611,0.0562,-0.1026,-24.4,-0.5,-44.3,1.530828287,-1.35,1.95,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,166094,2015-10-30 10:25:03:227,1446171903227.0 \n-0.7877,0.7207,9.8833,-0.5202,0.3258,9.7874,-0.0794,0.1002,-0.2712,-24.2,-0.8,-44.3,1.560673417,-1.69,2.44,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,166195,2015-10-30 10:25:03:328,1446171903328.0 \n-1.5526,-1.336,13.3381,-0.7289,-0.1943,9.7776,-0.8674,0.3751,-0.5864,-23.6,-1.3,-44.6,1.638689635,1.14,4.26,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,166297,2015-10-30 10:25:03:430,1446171903430.0 \n-0.1568,0.3053,7.8326,-0.715,-0.0957,9.7801,-0.2407,-0.0648,-0.0831,-23.3,-1.3,-44.9,1.627868593,0.67,4.29,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,166399,2015-10-30 10:25:03:532,1446171903532.0 \n-1.0092,0.6692,9.0704,-0.5285,-0.1597,9.7911,0.044,-0.0269,0.022,-23.1,-1.2,-45.3,1.63781697,0.93,3.23,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,166501,2015-10-30 10:25:03:634,1446171903634.0 \n-0.7207,0.7697,8.5497,-0.5092,-0.0172,9.7934,0.1869,-0.0232,0.0428,-23.3,-1.2,-45.4,1.620363678,0.34,2.96,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,166603,2015-10-30 10:25:03:736,1446171903736.0 \n-0.7494,0.2741,11.5508,-0.6145,0.1553,9.7861,0.2786,0.0452,0.2761,-23.4,-1.8,-45.6,1.636944305,-0.37,3.54,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,166706,2015-10-30 10:25:03:839,1446171903839.0 \n0.0012,-0.6165,10.0509,-0.5579,0.2324,9.788,-0.6023,-0.1478,-0.0367,-23.4,-2.1,-45.5,1.591391212,-1.93,3.8,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,166807,2015-10-30 10:25:03:940,1446171903940.0 \n-0.5806,0.4214,8.187,-0.5339,0.1467,9.791,0.2114,-0.0574,0.43,-23.2,-2,-45.3,1.637293371,-0.38,3.48,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,166909,2015-10-30 10:25:04:042,1446171904042.0 \n-1.1253,0.3771,8.0122,-0.5344,-0.0431,9.7909,-0.1381,0.182,0.0904,-23.4,-1.3,-45,1.613556893,0.12,3.12,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,167012,2015-10-30 10:25:04:145,1446171904145.0 \n-0.5495,1.0762,8.0948,-0.5453,0.0032,9.7915,0.2028,0.0513,0.1637,-23.4,-0.6,-45.2,1.619840079,0.32,3.11,36.812984,-119.74879,269.78,336.1648404,3.3,19.35484,91.73,16 / 16,167113,2015-10-30 10:25:04:246,1446171904246.0 \n-1.3647,0.0012,12.2296,-0.5678,0.0633,9.79,0.1429,-0.0318,-0.0635,-23.3,-0.1,-45.5,1.559800753,-0.37,3.32,36.81301,-119.74867,272.92,336.1648404,3.46,19.35484,86,16 / 16,167216,2015-10-30 10:25:04:349,1446171904349.0 \n-0.4058,0.3065,10.5453,-0.6569,0.3649,9.7778,0.3702,0.1662,0.0098,-23.2,-0.3,-45.8,1.517214719,-1.79,3.62,36.81301,-119.74867,272.92,336.1648404,3.46,19.35484,86,16 / 16,167317,2015-10-30 10:25:04:450,1446171904450.0 \n-0.7961,-0.1712,9.0656,-0.9804,0.0895,9.7571,-0.0391,0.2248,-0.1442,-22.7,-0.9,-45.8,1.58947135,-0.65,5.34,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,167419,2015-10-30 10:25:04:552,1446171904552.0 \n-0.6847,-0.2382,9.4822,-0.8582,-0.0107,9.769,-0.0208,-0.1038,0.0611,-22.3,-1.2,-45.9,1.596976266,-0.41,5.33,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,167522,2015-10-30 10:25:04:655,1446171904655.0 \n-1.0319,0.5052,7.8662,-0.8228,-0.0575,9.7719,-0.1246,-0.0086,0.0232,-21.9,-1.1,-45.9,1.619491013,0.34,4.81,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,167624,2015-10-30 10:25:04:757,1446171904757.0 \n-1.7394,-0.2167,8.582,-0.7746,5.00E-04,9.776,0.16,0.2162,-0.0452,-22,-0.9,-45.8,1.625948731,0.51,4.07,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,167725,2015-10-30 10:25:04:858,1446171904858.0 \n-0.6488,0.8045,12.3026,-0.9239,-0.0378,9.763,-0.0073,0.1723,0.2737,-22.2,-0.6,-45.5,1.614080492,0.16,5.07,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,167827,2015-10-30 10:25:04:960,1446171904960.0 \n-0.0287,-0.5207,12.6701,-0.8433,-0.0478,9.7702,-0.1527,-0.3592,0.2236,-22.1,-0.3,-45.6,1.566083938,-0.17,5.57,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,167929,2015-10-30 10:25:05:062,1446171905062.0 \n-0.0539,0.7757,8.3486,-0.4989,-0.0124,9.7939,0.1344,-0.5168,0.4178,-22.2,0.2,-45.5,1.577079512,0.21,3.8,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,168031,2015-10-30 10:25:05:164,1446171905164.0 \n-0.9242,-0.0766,9.1063,-0.4123,-0.3184,9.7928,-0.2077,-0.0892,-0.2248,-22.5,0.6,-45.1,1.566083938,1.16,2.32,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,168134,2015-10-30 10:25:05:267,1446171905267.0 \n-0.5842,0.8595,8.1774,-0.4256,-0.2034,9.7953,0.1869,0.0354,-0.0684,-23.4,1.3,-44.4,1.576904979,1.54,2.36,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,168235,2015-10-30 10:25:05:368,1446171905368.0 \n-1.0199,-0.1209,11.3473,-0.5861,-0.1251,9.7883,0.0024,0.3225,-0.226,-23.7,1.4,-44,1.553517567,0.73,3.43,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,168337,2015-10-30 10:25:05:470,1446171905470.0 \n-0.5231,0.0802,9.4703,-0.7805,0.1144,9.7749,0.2114,0.1417,-0.1381,-23.6,0.9,-44,1.526639497,-0.27,4.15,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,168439,2015-10-30 10:25:05:572,1446171905572.0 \n-0.68,-0.5267,9.7396,-0.8767,-0.162,9.766,0.0819,-0.0831,0.0367,-23,0,-44.5,1.596452667,0.95,5.13,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,168541,2015-10-30 10:25:05:674,1446171905674.0 \n-0.8954,-0.2957,10.1478,-0.7609,-0.2966,9.7726,-0.2761,-0.0953,-0.1124,-22.6,-0.2,-44.6,1.6109389,1.42,4.62,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,168644,2015-10-30 10:25:05:777,1446171905777.0 \n-1.1516,0.3519,9.2452,-0.7224,-0.2578,9.7766,-0.1442,0.0538,-0.055,-22.6,0,-44.5,1.607797307,1.31,4.13,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,168746,2015-10-30 10:25:05:879,1446171905879.0 \n-1.008,0.5207,9.1662,-0.758,-0.1358,9.7764,0.0904,0.0611,0.0648,-22.6,0,-44.1,1.598721595,1,4.34,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,168848,2015-10-30 10:25:05:981,1446171905981.0 \n-1.0702,-0.1688,11.388,-0.7331,0.1037,9.7787,0.1979,-0.0916,0.3348,-22.7,0,-44,1.583013632,0.44,4.6,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,168949,2015-10-30 10:25:06:082,1446171906082.0 \n-1.5323,-0.8966,12.736,-0.5847,0.0845,9.7888,-0.3457,-0.2896,0.077,-22.7,-0.1,-43.9,1.540427598,-1.06,3.9,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,169051,2015-10-30 10:25:06:184,1446171906184.0 \n-0.431,0.3232,8.8562,-0.4746,-0.0055,9.7952,-0.0941,-0.1625,-0.0305,-23,0.3,-44,1.567829267,-0.1,3.06,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,169153,2015-10-30 10:25:06:286,1446171906286.0 \n-1.3731,-0.0347,9.2177,-0.5644,-0.1953,9.7884,-0.0318,0.0464,-0.0599,-23.1,0.8,-43.9,1.552819435,0.73,3.12,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,169255,2015-10-30 10:25:06:388,1446171906388.0 \n-0.9098,0.8272,8.2444,-0.6729,-0.0857,9.7832,0.1979,0.1625,0.022,-22.9,1.4,-43.9,1.54653625,0.5,3.93,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,169357,2015-10-30 10:25:06:490,1446171906490.0 \n-1.5131,0.182,10.5764,-0.7496,-0.0083,9.778,-0.0171,0.011,-0.0415,-22.7,1.5,-44,1.497143432,0.09,4.3,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,169460,2015-10-30 10:25:06:593,1446171906593.0 \n-0.4369,0.1077,10.1143,-0.8292,0.108,9.7709,0.2114,0.1552,-0.0684,-22.3,1.1,-44.1,1.522101641,-0.33,4.69,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,169562,2015-10-30 10:25:06:695,1446171906695.0 \n-0.6177,-0.1844,10.3322,-1.0621,-0.2124,9.7466,-0.3873,0.3494,-0.2859,-21.5,0.6,-44.5,1.56678207,1.24,6.22,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,169663,2015-10-30 10:25:06:796,1446171906796.0 \n-0.5004,0.0742,8.9711,-1.0154,-0.3548,9.7475,-0.2908,0.0611,-0.2468,-21.1,0.5,-44.7,1.565909405,1.18,5.88,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,169765,2015-10-30 10:25:06:898,1446171906898.0 \n-1.482,0.5303,8.2061,-1.0643,-0.4408,9.7387,0.0476,-0.0342,-0.0501,-20.6,0.8,-44.7,1.602910385,2.46,6.11,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,169867,2015-10-30 10:25:07:000,1446171907000.0 \n-1.2079,0.3591,9.4822,-1.0236,-0.3707,9.746,0.0501,-0.0293,-0.0024,-20.5,0.8,-44.7,1.598896128,2.27,6,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,169969,2015-10-30 10:25:07:102,1446171907102.0 \n-1.1696,0.6979,10.5046,-1.0568,-0.0173,9.7495,0.4227,0.0073,0.3665,-20.6,0.5,-44.9,1.557531824,0.89,6.15,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,170071,2015-10-30 10:25:07:204,1446171907204.0 \n-3.0323,-1.9632,14.3712,-0.8352,-0.1604,9.7697,-0.1845,0.2016,0.0403,-20.5,0,-44.9,1.600466924,0.94,4.89,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,170173,2015-10-30 10:25:07:306,1446171907306.0 \n-1.3755,-0.0431,8.4707,-0.8345,-0.1141,9.7704,-0.3213,-0.0806,0.055,-20.6,0,-45,1.5823155,0.38,5.21,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,170276,2015-10-30 10:25:07:409,1446171907409.0 \n-1.5706,-0.0431,9.1207,-0.7518,-0.3098,9.7729,-0.0648,-0.1063,0.0086,-21,0.2,-44.6,1.625425132,1.77,4.49,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,170378,2015-10-30 10:25:07:511,1446171907511.0 \n-0.5088,0.9481,7.9009,-0.7758,-0.1216,9.7752,0.1967,0.0012,0.0586,-21.1,0.4,-44.6,1.607622774,1.2,4.54,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,170480,2015-10-30 10:25:07:613,1446171907613.0 \n-1.0415,0.0072,11.0002,-0.6674,0.0104,9.7839,0.2896,0.0525,-0.1002,-21.4,0.1,-44.1,1.568876465,-0.06,3.9,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,170582,2015-10-30 10:25:07:715,1446171907715.0 \n-0.1137,-0.3448,11.2144,-0.687,0.1123,9.7819,0.0037,-0.0354,-0.2566,-21.5,-0.4,-44,1.541823861,-0.94,3.98,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,170683,2015-10-30 10:25:07:816,1446171907816.0 \n-0.5614,-0.2251,8.8466,-0.7683,-0.1323,9.7756,-0.0745,-0.055,-0.2065,-21.7,-1.1,-43.9,1.62350527,0.47,4.6,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,170785,2015-10-30 10:25:07:918,1446171907918.0 \n-0.5974,0.2191,8.0086,-0.7684,-0.3288,9.771,-0.0635,-0.044,-0.0452,-22,-1.3,-44.1,1.664520508,1.89,4.53,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,170887,2015-10-30 10:25:08:020,1446171908020.0 \n-0.8045,0.6333,8.6431,-0.7319,-0.3951,9.7713,-0.0391,-0.055,0.0635,-22.1,-1.1,-44,1.679355806,2.38,4.37,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,170989,2015-10-30 10:25:08:122,1446171908122.0 \n-1.2175,0.103,10.7164,-0.7295,-0.2905,9.7752,0.0208,0.0037,0.0684,-22.2,-1.1,-44.1,1.662600645,1.79,4.26,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,171092,2015-10-30 10:25:08:225,1446171908225.0 \n-0.0431,0.498,9.7181,-0.8043,-0.0395,9.7735,0.2382,0.1087,0.2883,-22.2,-1.3,-43.9,1.616523953,0.23,4.7,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,171193,2015-10-30 10:25:08:326,1446171908326.0 \n-1.0451,-0.3412,10.0904,-0.7656,-0.1806,9.775,0.1356,-0.0367,0.1906,-22.3,-1.3,-43.7,1.636769773,0.9,4.24,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,171296,2015-10-30 10:25:08:429,1446171908429.0 \n-0.5183,-0.1508,8.8681,-0.6199,-0.1459,9.786,-0.0159,-0.2187,-0.0037,-22.5,-1.3,-43.4,1.627868593,0.58,3.78,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,171397,2015-10-30 10:25:08:530,1446171908530.0 \n-1.3024,-0.0694,8.8705,-0.6537,-0.2754,9.781,0.066,-0.0293,-0.0134,-22.9,-1.1,-43,1.655619328,1.66,3.86,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,171500,2015-10-30 10:25:08:633,1446171908633.0 \n-0.7242,0.8021,8.8011,-0.6588,-0.1306,9.7836,0.0745,-0.088,-0.033,-23.4,-0.9,-42.7,1.63066112,0.76,3.85,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,171601,2015-10-30 10:25:08:734,1446171908734.0 \n-0.9613,-0.1137,11.959,-0.575,0.0028,9.7898,0.1197,-0.1002,-0.1515,-23.6,-0.9,-42.5,1.618792881,0.38,3.34,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,171704,2015-10-30 10:25:08:837,1446171908837.0 \n-0.5219,-0.5231,11.0073,-0.6379,0.0587,9.7857,-0.3042,0.1307,-0.3861,-23.8,-1.6,-42.3,1.63659524,-0.34,3.73,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,171805,2015-10-30 10:25:08:938,1446171908938.0 \n-0.7985,-0.1592,8.6215,-0.7226,-0.2214,9.7775,-0.1454,-0.2162,-0.0819,-24,-1.8,-42.3,1.67481795,1.24,4.76,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,171907,2015-10-30 10:25:09:040,1446171909040.0 \n-0.4549,0.4992,7.4939,-0.6343,-0.2821,9.782,0.0257,-0.0794,0.0831,-24,-1.8,-42.2,1.694714704,1.87,3.67,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,172010,2015-10-30 10:25:09:143,1446171909143.0 \n-1.2354,0.6237,8.5365,-0.6742,-0.2976,9.7789,-0.0281,0.0073,0.0733,-24.1,-1.5,-42,1.650906939,1.65,3.95,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,172111,2015-10-30 10:25:09:244,1446171909244.0 \n-0.6045,0.5435,9.9683,-0.7754,-0.2278,9.7733,0.11,0.1723,0.2077,-24.4,-1,-42.3,1.647590814,1.54,4.21,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,172213,2015-10-30 10:25:09:346,1446171909346.0 \n1.1217,0.7805,8.6263,-0.7841,0.0326,9.7752,0.088,-0.2969,0.1185,-24.2,-0.7,-42.7,1.602386786,-0.19,4.59,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,172315,2015-10-30 10:25:09:448,1446171909448.0 \n-0.5674,-0.1844,8.7113,-0.5791,-0.2107,9.7873,-0.3555,0.0012,-0.1124,-24.2,-0.5,-42.4,1.60378305,1.23,3.39,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,172417,2015-10-30 10:25:09:550,1446171909550.0 \n-0.8296,-0.2957,8.8705,-0.4928,-0.2672,9.7906,-0.2101,-0.0159,0.055,-24.1,-0.3,-42.2,1.602910385,1.18,2.95,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,172519,2015-10-30 10:25:09:652,1446171909652.0 \n-0.8224,0.4752,8.4587,-0.4197,-0.3236,9.7923,0.1185,-0.0538,0.2407,-24.3,0.2,-41.7,1.623156204,1.89,2.45,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,172621,2015-10-30 10:25:09:754,1446171909754.0 \n-0.5016,0.9062,8.7376,-0.3445,-0.1365,9.7996,0.1723,-0.0904,0.1833,-24.5,0.6,-41.8,1.562244213,1.09,2.16,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,172723,2015-10-30 10:25:09:856,1446171909856.0 \n-0.8787,0.0646,11.1773,-0.3557,0.02,9.8002,0.2395,0.1148,-0.0134,-24.7,0.7,-41.8,1.529955622,-0.12,2.08,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,172825,2015-10-30 10:25:09:958,1446171909958.0 \n0.1401,0,10.149,-0.5638,0.0828,9.7901,-0.4545,0.2358,-0.4105,-24.6,0.4,-41.9,1.543918256,-1.02,2.77,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,172927,2015-10-30 10:25:10:060,1446171910060.0 \n-0.5375,-0.146,8.3749,-0.7443,-0.0915,9.7779,-0.0379,0.2199,-0.1796,-24.3,0,-42,1.588598685,0.69,4.27,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,173030,2015-10-30 10:25:10:163,1446171910163.0 \n-0.322,0.261,8.4384,-0.6694,-0.1943,9.7818,-0.0024,0,-0.0318,-24,0,-42.1,1.597325331,1.02,3.98,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,173131,2015-10-30 10:25:10:264,1446171910264.0 \n-0.5806,0.7757,8.7963,-0.6026,-0.2916,9.7838,0.0464,-0.0721,-0.0159,-23.8,0.2,-41.7,1.617920217,1.78,3.64,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,173233,2015-10-30 10:25:10:366,1446171910366.0 \n-0.8871,0.0634,10.0664,-0.6586,-0.2289,9.7818,0.0379,0.1319,0.0379,-24.1,0.4,-41.2,1.605179313,1.34,3.85,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,173335,2015-10-30 10:25:10:468,1446171910468.0 \n-1.391,0.5662,10.3406,-0.7616,-0.1243,9.7762,0.2248,0.1356,0.1808,-24.2,0.6,-40.9,1.562593279,1.14,4.18,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,173438,2015-10-30 10:25:10:571,1446171910571.0 \n-2.2362,-1.093,11.4419,-0.7351,-0.3674,9.7722,-0.2737,0.0122,-0.1979,-24,0.8,-41.2,1.575508716,1.65,4.32,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,173539,2015-10-30 10:25:10:672,1446171910672.0 \n-0.6273,0.0646,8.0014,-0.4411,-0.1888,9.7949,-0.2297,-0.4398,-0.011,-24,0.9,-41.2,1.566258471,1.27,3.48,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,173641,2015-10-30 10:25:10:774,1446171910774.0 \n-1.1073,0.0694,8.3498,-0.2585,-0.2539,9.8,0.0599,0.0195,-0.0635,-24.5,1.4,-41,1.579697506,1.74,1.62,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,173743,2015-10-30 10:25:10:876,1446171910876.0 \n-0.5519,0.8595,8.2373,-0.2673,-0.0342,9.8029,0.3079,0.0586,0.0379,-25.2,1.5,-40.3,1.511804198,0.67,1.49,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,173846,2015-10-30 10:25:10:979,1446171910979.0 \n-0.8715,-0.0922,11.3054,-0.2767,0.1156,9.8021,0.2749,0.1417,-0.0073,-25.5,1.4,-40,1.524021503,-0.33,1.61,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,173947,2015-10-30 10:25:11:080,1446171911080.0 \n0.0706,-0.3747,11.0097,-0.4535,0.1597,9.7949,0.0061,0.1405,-0.1148,-25.2,0.9,-39.7,1.496619834,-1.44,2.32,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,174049,2015-10-30 10:25:11:182,1446171911182.0 \n-0.0215,0.3531,8.3043,-0.7032,-0.1551,9.7802,0.1161,0.0281,0.0929,-24.4,0.9,-39.8,1.555961028,0.91,4.11,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,174152,2015-10-30 10:25:11:285,1446171911285.0 \n-0.2406,0.492,7.7967,-0.5924,-0.2899,9.7844,0.0586,-0.0586,0.0782,-24,1.2,-40.2,1.577952177,1.77,3.56,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,174253,2015-10-30 10:25:11:386,1446171911386.0 \n-0.6117,0.9625,8.3881,-0.5851,-0.2763,9.7853,0.1258,-0.0391,0.1136,-23.6,1.9,-40.7,1.537286005,1.61,3.42,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,174356,2015-10-30 10:25:11:489,1446171911489.0 \n-0.9038,0.0994,10.5441,-0.5923,-0.1717,9.7872,0.0794,0.0098,0.1124,-23.6,2.2,-40.9,1.525941365,1.18,3.45,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,174457,2015-10-30 10:25:11:590,1446171911590.0 \n-0.0874,0.565,8.7604,-0.6578,0.1306,9.7837,0.3885,0.2346,0.3653,-23.3,2.2,-41,1.472883356,-0.76,3.85,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,174559,2015-10-30 10:25:11:692,1446171911692.0 \n-1.6616,-0.7183,10.6674,-0.6409,0.0367,9.7856,0.088,-0.3018,0.3946,-23.1,2.1,-40.8,1.487195056,-0.21,3.75,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,174661,2015-10-30 10:25:11:794,1446171911794.0 \n-0.0395,0.316,9.0776,-0.3813,-0.0056,9.7992,-0.0757,-0.2065,0.1918,-22.9,2.2,-40.2,1.477595745,-0.44,2.3,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,174763,2015-10-30 10:25:11:896,1446171911896.0 \n-0.8727,0.7829,8.8957,-0.4077,-0.0479,9.7981,0.0916,0.0452,0.0672,-23,2.4,-39.8,1.500634091,0.4,2.33,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,174865,2015-10-30 10:25:11:998,1446171911998.0 \n-1.3156,0.6847,9.7217,-0.4938,0.1105,9.7936,0.1869,0.0293,-0.0745,-23.4,2.6,-39.3,1.434311579,-0.65,2.89,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,174968,2015-10-30 10:25:12:101,1446171912101.0 \n-1.1827,0.182,11.7914,-0.5401,0.3283,9.7863,0.2309,0.0269,-0.055,-23.5,2.3,-39.2,1.451241273,-1.53,3.03,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,175069,2015-10-30 10:25:12:202,1446171912202.0 \n-0.9062,-1.0259,13.1585,-0.665,0.3401,9.7782,-0.5473,0.1906,-0.347,-23.6,1.5,-39,1.447576082,-1.99,3.89,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,175171,2015-10-30 10:25:12:304,1446171912304.0 \n-0.6404,-0.1915,9.8282,-0.7987,0.153,9.7729,-0.3335,-0.1051,-0.1808,-23.7,1,-39.2,1.512676863,-0.89,4.67,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,175274,2015-10-30 10:25:12:407,1446171912407.0 \n-0.9373,0.3508,8.7652,-0.7191,-0.0124,9.7802,-0.0098,-0.033,0.0379,-23.7,0.9,-39,1.529781089,-0.16,4.2,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,175375,2015-10-30 10:25:12:508,1446171912508.0 \n-0.4477,1.1492,8.8143,-0.661,0.0707,9.7841,0.1442,-0.0403,0.0367,-24,1.2,-38.5,1.523148838,-0.41,3.87,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,175477,2015-10-30 10:25:12:610,1446171912610.0 \n-1.482,-0.0383,11.1917,-0.706,0.1173,9.7805,0.0892,0.1588,-0.0049,-24.3,1.2,-38.2,1.520356311,-0.53,3.86,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,175579,2015-10-30 10:25:12:712,1446171912712.0 \n-0.0335,-0.7721,10.8122,-0.5905,0.3581,9.7823,-0.4056,-0.5058,-0.0929,-24.6,1.1,-37.9,1.485449726,-2.09,3.45,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,175681,2015-10-30 10:25:12:814,1446171912814.0 \n-0.2083,0.498,7.3981,-0.5586,0.1571,9.7895,0.1148,0.4032,0.2859,-24.9,1.2,-37.6,1.521752575,-0.48,2.64,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,175783,2015-10-30 10:25:12:916,1446171912916.0 \n-0.6021,0.1041,9.979,-0.3304,-0.0467,9.801,-0.2297,-0.1051,-0.0562,-25.1,1.5,-37.3,1.480388272,-0.67,2.64,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,175885,2015-10-30 10:25:13:018,1446171913018.0 \n-1.0319,0.6464,9.3637,-0.3142,-0.0097,9.8016,0.0562,-0.0293,0.0684,-25.7,2.2,-36.5,1.499586893,0.11,1.82,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,175987,2015-10-30 10:25:13:120,1446171913120.0 \n-0.6225,1.2031,8.4874,-0.3164,0.1461,9.8005,0.1857,0.0305,0.0513,-25.9,2.4,-36.3,1.491907445,-0.24,1.83,36.81301,-119.74867,272.92,336.1929752,3.46,19.35484,86,16 / 16,176090,2015-10-30 10:25:13:223,1446171913223.0 \n-0.759,0.1113,11.5197,-0.3634,0.2765,9.796,0.2016,0.2028,-0.0257,-26.3,2.6,-35.7,1.434486112,-1.15,1.67,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,176191,2015-10-30 10:25:13:324,1446171913324.0 \n-1.0343,-0.99,13.1789,-0.4424,0.058,9.7965,-0.5742,0.182,-0.3091,-26.3,2.2,-36.1,1.465902039,-1.47,2.39,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,176293,2015-10-30 10:25:13:426,1446171913426.0 \n-0.1221,0.0275,9.426,-0.5218,0.0536,9.7926,-0.2993,0.0525,-0.2932,-26.1,1.9,-36.7,1.492431043,-0.31,3.05,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,176396,2015-10-30 10:25:13:529,1446171913529.0 \n-0.8511,0.3903,8.0852,-0.6156,-0.1813,9.7856,-0.1234,0.1381,-0.1393,-25.9,1.9,-37.3,1.51965818,0.9,3.45,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,176497,2015-10-30 10:25:13:630,1446171913630.0 \n-0.2729,1.0582,8.831,-0.5566,-0.135,9.7899,0.0965,-0.099,0.1258,-25.7,1.9,-37.1,1.517040186,0.79,3.25,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,176599,2015-10-30 10:25:13:732,1446171913732.0 \n-0.3819,0.7937,10.1466,-0.5007,0.0285,9.7938,0.1234,0.011,0.121,-25.8,1.9,-37,1.507615408,0.38,2.98,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,176702,2015-10-30 10:25:13:835,1446171913835.0 \n-0.3998,1.2115,8.6969,-0.6006,0.312,9.7833,0.4044,0.2138,0.2712,-25.8,1.8,-36.9,1.474279619,-1.15,3.2,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,176803,2015-10-30 10:25:13:936,1446171913936.0 \n-1.5131,-0.6273,11.5903,-0.4491,0.1545,9.7951,-0.1833,-0.0965,0.1637,-25.9,1.8,-37,1.468869098,-1.34,2.75,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,176906,2015-10-30 10:25:14:039,1446171914039.0 \n0.2227,0.2538,8.8358,-0.2218,0.2138,9.8018,-0.066,-0.055,0.1527,-26,2,-37.3,1.466774703,-1.29,1.52,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,177007,2015-10-30 10:25:14:140,1446171914140.0 \n-0.8092,0.431,9.2332,-0.2742,0.1801,9.8012,-0.0354,0.0623,0.0354,-26.1,2.3,-37.3,1.47375602,-0.97,1.43,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,177110,2015-10-30 10:25:14:243,1446171914243.0 \n-0.5028,0.9529,8.017,-0.3882,0.2453,9.7959,0.0147,0.1405,-0.0538,-26.2,2.6,-37.4,1.429424657,-1.41,2.02,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,177211,2015-10-30 10:25:14:344,1446171914344.0 \n-1.4509,0.2298,11.9387,-0.3931,0.2118,9.7965,0.2688,0.1075,0.0208,-26.1,2.7,-37.5,1.437802238,-1.09,2.39,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,177313,2015-10-30 10:25:14:446,1446171914446.0 \n-0.3029,-0.2873,11.8178,-0.4281,0.2153,9.7949,-0.3995,0.38,-0.2126,-25.8,2.5,-38,1.421745209,-1.81,2.61,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,177416,2015-10-30 10:25:14:549,1446171914549.0 \n-0.741,0.2418,8.1008,-0.6064,0.0547,9.7877,0.1222,0.0073,0.0452,-25.4,2.5,-38.5,1.4540338,-0.33,3.59,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,177518,2015-10-30 10:25:14:651,1446171914651.0 \n-0.9589,-0.1041,10.4591,-0.4524,-0.1435,9.7952,0.0159,0.0049,-0.0232,-25.2,2.5,-38.8,1.476199481,0.68,2.85,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,177619,2015-10-30 10:25:14:752,1446171914752.0 \n-0.4381,1.1253,8.3558,-0.4846,-0.0623,9.7945,0.1051,-0.1319,0.055,-25,2.7,-39.3,1.468520033,0.36,2.83,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,177722,2015-10-30 10:25:14:855,1446171914855.0 \n-0.3496,0.4752,10.7344,-0.2596,0.0814,9.8029,0.0916,-0.2541,0.0049,-25.1,2.7,-39.5,1.448972345,-0.33,1.89,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,177823,2015-10-30 10:25:14:956,1446171914956.0 \n0.1891,0.0036,9.6067,-0.2564,0.484,9.7913,0.3958,-0.0709,0.1698,-25.1,2.3,-39.8,1.420698011,-2.83,1.5,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,177925,2015-10-30 10:25:15:058,1446171915058.0 \n-0.5315,0.249,9.6534,-0.2276,0.4801,9.7922,0.3482,-0.1393,0.2211,-25.1,2,-39.6,1.442165561,-1.99,1.42,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,178027,2015-10-30 10:25:15:160,1446171915160.0 \n-0.8847,0.1161,9.7384,-0.117,0.3036,9.8013,-0.369,-0.1918,-0.121,-24.9,1.7,-39.6,1.42837746,-2.41,0.83,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,178130,2015-10-30 10:25:15:263,1446171915263.0 \n-0.6285,0.7195,9.098,-0.1194,0.2035,9.8038,-0.0733,0.0806,0.0305,-24.9,1.9,-39.6,1.460491518,-1.19,0.7,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,178231,2015-10-30 10:25:15:364,1446171915364.0 \n-0.4357,1.306,8.5114,-0.2316,0.3361,9.7982,0.0941,0.0024,-0.0232,-24.8,2.1,-39.5,1.453510201,-1.54,1.09,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,178333,2015-10-30 10:25:15:466,1446171915466.0 \n-0.8942,0.2298,12.6905,-0.1852,0.4095,9.7963,0.3519,0.2468,0.1148,-24.6,2.3,-39.4,1.433962513,-2.29,1.03,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,178436,2015-10-30 10:25:15:569,1446171915569.0 \n0.4501,1.093,9.5086,-0.3276,0.466,9.7901,-0.2896,0.1808,-0.248,-24.3,2.3,-39.5,1.415636556,-2.85,1.47,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,178537,2015-10-30 10:25:15:670,1446171915670.0 \n-0.091,0.4501,9.013,-0.3599,0.2842,9.7959,-0.1943,-0.0086,-0.1319,-23.8,1.9,-40.3,1.441292896,-1.94,2.21,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,178639,2015-10-30 10:25:15:772,1446171915772.0 \n-0.5818,0.8811,8.2528,-0.4119,0.1769,9.7964,-0.0586,0.1136,0.0171,-23.4,2.1,-41,1.46118965,-1.01,2.3,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,178742,2015-10-30 10:25:15:875,1446171915875.0 \n-0.1472,0.6488,9.1051,-0.4382,0.198,9.7949,0.0574,-0.0171,0.1185,-23,2.4,-40.9,1.45822259,-1.16,2.56,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,178843,2015-10-30 10:25:15:976,1446171915976.0 \n0.237,0.267,9.8701,-0.574,0.3143,9.7848,0.1784,0.2566,-0.0183,-22.7,2.6,-40.9,1.410051503,-1.54,2.98,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,178945,2015-10-30 10:25:16:078,1446171916078.0 \n1.4269,0.1448,8.6263,-0.8498,0.7204,9.7432,0.1637,0.1344,-0.5473,-21.9,2.5,-41.6,1.352979236,-3.72,4.6,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,179047,2015-10-30 10:25:16:180,1446171916180.0 \n1.0151,-0.334,11.0887,-0.9771,0.6002,9.7394,-0.0965,0.1283,-0.7599,-21.4,2,-42.4,1.39259821,-3.58,5.42,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,179149,2015-10-30 10:25:16:282,1446171916282.0 \n0.2418,-0.7865,10.9559,-0.9488,0.3707,9.7536,-0.4325,0.1735,-1.5931,-20.7,0.4,-43.5,1.509360737,-2.17,5.56,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,179251,2015-10-30 10:25:16:384,1446171916384.0 \n0.0072,-0.5507,9.1961,-1.0141,0.0798,9.7538,-0.0354,0.0049,-1.7959,-20.6,-1,-43.8,1.578301243,-1.12,6.11,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,179353,2015-10-30 10:25:16:486,1446171916486.0 \n-1.0175,-0.7254,9.6079,-0.8879,-0.0552,9.7662,0.1307,-0.2443,-1.6897,-20.4,-3.8,-44.3,1.7392206,0.15,5.55,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,179455,2015-10-30 10:25:16:588,1446171916588.0 \n-1.9561,-1.0558,11.3485,-0.5207,-0.1217,9.7921,0.0244,-0.4239,-1.5895,-20,-7.4,-44.6,1.887399053,0.65,3.73,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,179557,2015-10-30 10:25:16:690,1446171916690.0 \n-1.3515,-1.0116,12.5384,-0.3082,-0.0614,9.8016,-0.3787,-0.27,-1.3109,-19.8,-11.1,-44.5,2.056172392,0.36,1.8,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,179660,2015-10-30 10:25:16:793,1446171916793.0 \n-1.0546,0.8428,7.0533,-0.4786,-0.2252,9.7924,-0.3213,-0.1466,-0.9346,-19.3,-13.2,-44.5,2.160194015,1.49,2.78,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,179761,2015-10-30 10:25:16:894,1446171916894.0 \n-1.3934,0.8104,8.1247,-0.4139,-0.6111,9.7788,-0.391,0.0648,-0.5461,-18.3,-15.1,-44.4,2.298075026,3.57,2.42,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,179863,2015-10-30 10:25:16:996,1446171916996.0 \n-0.6512,1.0618,9.9204,-0.314,-0.4584,9.7909,0.0977,-0.1442,-0.0452,-17.5,-15.7,-44.7,2.345897048,3.11,2.26,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,179966,2015-10-30 10:25:17:099,1446171917099.0 \n-0.8284,0.2502,10.4507,-0.3258,-0.2644,9.7977,0.1222,-0.0305,0.121,-17,-16.2,-45.1,2.325651228,1.8,1.9,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,180067,2015-10-30 10:25:17:200,1446171917200.0 \n-0.5567,0.8056,11.2946,-0.2529,-0.0494,9.8033,0.2712,-0.1478,0.3042,-17.1,-16.5,-45,2.310466864,0.82,1.57,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,180169,2015-10-30 10:25:17:302,1446171917302.0 \n-0.8607,-0.5794,10.7823,-0.028,-0.1905,9.8048,-0.4154,0.0586,-0.0244,-17.5,-17.1,-44.8,2.377312974,1.11,0.16,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,180271,2015-10-30 10:25:17:404,1446171917404.0 \n-0.5231,-0.1197,9.6546,0.1365,-0.1784,9.8041,-0.1148,0.0757,-0.0367,-17.9,-17.1,-44.8,2.350609437,0.87,-0.15,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,180373,2015-10-30 10:25:17:506,1446171917506.0 \n-0.9876,0.2897,8.7041,0.0614,-0.1931,9.8046,0.1845,0.0623,0.0403,-18.6,-16.9,-44.9,2.338566665,1.26,-0.46,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,180475,2015-10-30 10:25:17:608,1446171917608.0 \n-0.3867,0.7326,9.5421,0.064,-0.0871,9.8061,0.0171,-0.0623,-0.1051,-18.8,-16.9,-45.1,2.319891642,0.57,-0.3,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,180577,2015-10-30 10:25:17:710,1446171917710.0 \n-0.814,-0.4872,12.5037,0.0077,-0.0305,9.8066,0.0428,-0.0403,-0.2334,-18.5,-17.2,-45.5,2.332632545,0.18,-0.04,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,180679,2015-10-30 10:25:17:812,1446171917812.0 \n0.7494,-0.4441,10.3753,-0.0225,0.0558,9.8065,-0.6548,0.2663,-0.5754,-18.1,-17.7,-45.7,2.328443755,-1.16,0.06,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,180781,2015-10-30 10:25:17:914,1446171917914.0 \n-0.079,0.31,7.9128,-0.086,-0.0264,9.8062,0.2419,-0.1295,-0.1918,-17.2,-18.3,-46.2,2.37644031,0.15,0.5,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,180884,2015-10-30 10:25:18:017,1446171918017.0 \n-0.2251,-0.006,9.1482,0.0582,-0.1193,9.8058,0.1014,-0.0599,-0.303,-16.7,-18.5,-46.5,2.401922117,0.71,-0.08,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,180986,2015-10-30 10:25:18:119,1446171918119.0 \n-0.7087,0.504,8.5234,0.0053,-0.0052,9.8066,0.1637,0.1185,-0.1197,-16,-18.9,-46.9,2.452885731,0.31,-0.18,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,181088,2015-10-30 10:25:18:221,1446171918221.0 \n-0.3795,0.3077,10.1694,-0.0638,0.1353,9.8055,0.1368,0.0965,-0.0501,-15.5,-19.5,-47.1,2.451140402,-0.53,0.41,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,181189,2015-10-30 10:25:18:322,1446171918322.0 \n0.6249,-0.2322,9.7576,0.033,0.2973,9.8021,0.281,-0.1014,0.1857,-15,-20.3,-47.6,2.45463106,-1.63,0.34,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,181291,2015-10-30 10:25:18:424,1446171918424.0 \n-0.1281,0.1951,8.7388,0.1497,0.1835,9.8038,0.2578,-0.3323,0.1833,-15.1,-20.9,-48,2.524269697,-1.07,-0.87,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,181393,2015-10-30 10:25:18:526,1446171918526.0 \n-0.3531,-0.2227,9.6043,0.3223,0.0817,9.801,-0.0929,-0.0269,-0.1112,-15.5,-21.1,-48.3,2.550275103,-1.06,-1.79,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,181496,2015-10-30 10:25:18:629,1446171918629.0 \n-0.6823,0.3819,8.0529,0.3066,0.0586,9.8017,0.0086,0.0819,-0.0476,-16.1,-21,-48.6,2.531949146,-0.34,-1.79,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,181597,2015-10-30 10:25:18:730,1446171918730.0 \n-0.7697,0.3508,9.001,0.2467,0.0548,9.8034,-0.0904,-0.0134,-0.0696,-16.1,-21.1,-48.7,2.519208242,-0.47,-1.43,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,181699,2015-10-30 10:25:18:832,1446171918832.0 \n-0.4118,-0.0778,9.8354,0.2755,0.0711,9.8025,0.0782,-0.2724,-0.0073,-16,-21.3,-49.1,2.525491428,-0.42,-1.61,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,181802,2015-10-30 10:25:18:935,1446171918935.0 \n-1.8016,-1.0858,11.8525,0.2166,-0.13,9.8034,-0.4362,0.3531,-0.1271,-15.8,-21.5,-49.3,2.546958977,0.05,-2.06,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,181903,2015-10-30 10:25:19:036,1446171919036.0 \n-1.0894,-0.3065,9.9778,0.2965,0.0209,9.8021,-0.0464,-0.1796,0.4814,-15.8,-21.6,-49.8,2.54172299,-0.34,-1.33,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,182005,2015-10-30 10:25:19:138,1446171919138.0 \n-2.4481,-0.34,8.5234,0.396,0.0258,9.7986,0.1625,-0.1283,1.212,-16.2,-21.5,-49.8,2.556732821,0.05,-2.35,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,182108,2015-10-30 10:25:19:241,1446171919241.0 \n-2.897,-0.7829,9.76,0.5264,0.0458,9.7924,0.1356,-0.2957,1.6151,-18,-20.8,-49.7,2.506816405,-0.27,-3.08,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,182209,2015-10-30 10:25:19:342,1446171919342.0 \n-2.1524,-1.1049,10.167,0.5214,0.2617,9.7893,0.4581,-0.0147,2.2016,-20.3,-19.3,-49.3,2.388308548,-0.52,-3.02,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,182311,2015-10-30 10:25:19:444,1446171919444.0 \n-2.1009,-2.6372,11.6825,0.4414,0.0799,9.7964,-0.2004,0.6133,2.0684,-24.5,-14.6,-48.8,2.143438854,-1.5,-3.21,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,182414,2015-10-30 10:25:19:547,1446171919547.0 \n0.1401,-0.2813,9.9611,0.2122,-0.0434,9.8043,-0.3763,0.347,1.664,-26.1,-7.3,-49.2,1.852667001,0.25,-1.24,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,182515,2015-10-30 10:25:19:648,1446171919648.0 \n0.4501,0.316,9.2261,-0.1455,-0.2693,9.8019,-0.0623,0.2639,1.4172,-25.7,-4,-49.6,1.77203279,1.55,0.27,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,182617,2015-10-30 10:25:19:750,1446171919750.0 \n0.2741,0.7614,9.4367,-0.3414,-0.3155,9.7956,-0.2126,0.2138,0.6732,-25.2,-0.2,-50.3,1.629788456,1.84,2,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,182720,2015-10-30 10:25:19:853,1446171919853.0 \n-0.1604,0.4046,10.1981,-0.4478,-0.4472,9.7862,-0.1136,-0.1087,0.1087,-24.9,0.3,-50.7,1.649859742,2.5,2.69,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,182821,2015-10-30 10:25:19:954,1446171919954.0 \n0.1341,-0.1448,11.0899,-0.4367,-0.509,9.7837,0,0.0513,0.1002,-24.2,2.7,-51.2,1.555262896,2.98,2.56,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,182923,2015-10-30 10:25:20:056,1446171920056.0 \n-0.1377,-0.5531,10.9008,-0.4218,-0.7139,9.7715,-0.0086,-0.0953,-0.0892,-23.9,3.5,-51.4,1.55072504,3.99,2.71,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,183025,2015-10-30 10:25:20:158,1446171920158.0 \n-0.6009,0.0144,9.663,-0.3786,-0.75,9.7706,0.2126,-0.0293,-0.0428,-23.9,3.8,-51.6,1.571668991,4.52,2.49,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,183128,2015-10-30 10:25:20:261,1446171920261.0 \n-1.5526,0.1736,8.0804,-0.3938,-0.5497,9.7833,0.1918,0.022,-0.1784,-23.9,3.5,-51.5,1.535366143,3.52,2.43,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,183230,2015-10-30 10:25:20:363,1446171920363.0 \n-1.2019,0.176,9.5517,-0.4442,-0.4167,9.7877,0.1405,0.0379,0.215,-24.1,2.5,-51.4,1.537460538,2.44,2.6,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,183331,2015-10-30 10:25:20:464,1446171920464.0 \n0.2646,0.152,8.9232,-0.4733,-0.1427,9.7942,0.1784,0.0391,0.3751,-24.1,1.4,-51.5,1.570796327,1.15,2.7,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,183434,2015-10-30 10:25:20:567,1446171920567.0 \n-0.9194,-0.5495,10.5117,-0.3648,-0.3924,9.792,-0.5522,-0.0476,-0.0464,-24.2,1.2,-51.3,1.607448241,2.22,1.98,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,183535,2015-10-30 10:25:20:668,1446171920668.0 \n-0.5638,-0.5519,9.821,-0.1497,-0.4419,9.7955,-0.3201,-0.1784,-0.0342,-24.4,1.3,-50.8,1.608320906,2.19,1.04,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,183637,2015-10-30 10:25:20:770,1446171920770.0 \n-0.7961,0.346,8.2349,-0.1894,-0.4924,9.7925,0.2541,0.0415,0.1991,-24.8,1.7,-50.3,1.603957583,3.3,0.97,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,183739,2015-10-30 10:25:20:872,1446171920872.0 \n-0.6656,0.3639,9.5493,-0.2607,-0.3519,9.7969,0.1393,0.2224,-0.0489,-25.2,1.8,-49.9,1.567829267,2.23,1.2,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,183841,2015-10-30 10:25:20:974,1446171920974.0 \n-0.923,-0.3484,10.4878,-0.4119,-0.1859,9.7962,0.0831,0.0049,-0.1747,-25.1,1.2,-49.8,1.574112452,1.27,2.3,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,183943,2015-10-30 10:25:21:076,1446171921076.0 \n-0.6788,-1.5323,12.9131,-0.5188,-0.4627,9.782,-0.5388,0.3824,-0.4227,-24.9,0.5,-49.6,1.589994949,1.78,2.45,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,184045,2015-10-30 10:25:21:178,1446171921178.0 \n-0.6369,-0.4657,9.4571,-0.5702,-0.4403,9.7801,-0.2883,-0.044,-0.1747,-24.2,0,-49.8,1.651779604,2.57,3.34,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,184147,2015-10-30 10:25:21:280,1446171921280.0 \n-0.7901,0.0503,8.7137,-0.5931,-0.5463,9.7734,0.044,0.0794,0.0037,-24,-0.1,-50.1,1.674468884,3.3,3.29,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,184250,2015-10-30 10:25:21:383,1446171921383.0 \n-0.2274,0.7877,8.5964,-0.6004,-0.4416,9.7783,0.1332,-0.0586,0.1148,-23.7,-0.1,-50.2,1.66050625,2.9,3.72,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,184351,2015-10-30 10:25:21:484,1446171921484.0 \n-1.0247,-0.4369,11.7926,-0.6359,-0.3914,9.7782,-0.1185,0.0012,0.1723,-23.6,-0.4,-50,1.638340569,2.17,3.66,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,184454,2015-10-30 10:25:21:587,1446171921587.0 \n-1.4593,-1.2641,11.9447,-0.6277,-0.2396,9.7836,-0.3592,0.0525,0.0159,-23.5,-0.6,-49.3,1.6533504,1.4,3.67,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,184556,2015-10-30 10:25:21:689,1446171921689.0 \n-0.0874,0.7446,7.2508,-0.5103,-0.2564,9.79,0.3457,-0.2724,0.3775,-23.4,-0.4,-49.2,1.619665546,1.5,2.98,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,184658,2015-10-30 10:25:21:791,1446171921791.0 \n-0.7207,-0.2646,9.2895,-0.3268,-0.3965,9.7932,-0.171,0.0611,-0.0721,-23.8,-0.3,-48.6,1.636769773,2.01,1.84,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,184759,2015-10-30 10:25:21:892,1446171921892.0 \n-0.2035,0.7745,7.7381,-0.3358,-0.2998,9.7963,0.3714,0.121,0.0428,-24.3,0,-48.2,1.626995929,1.75,1.96,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,184862,2015-10-30 10:25:21:995,1446171921995.0 \n-1.0331,0.0227,11.6574,-0.4213,-0.0606,9.7974,0.0599,0.0941,-0.1478,-24.6,-0.1,-47.9,1.598721595,0.92,2.32,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,184963,2015-10-30 10:25:22:096,1446171922096.0 \n-0.1065,-0.4381,10.313,-0.4787,0.1468,9.7939,0.0367,0.0379,-0.1698,-24.4,-0.8,-47.9,1.582839099,-0.84,2.74,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,185066,2015-10-30 10:25:22:199,1446171922199.0 \n-0.6321,-0.4776,10.2723,-0.5541,-0.0432,9.7909,0.0134,-0.0159,-0.0293,-24.1,-1.5,-48,1.61512769,0.23,3.41,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,185167,2015-10-30 10:25:22:300,1446171922300.0 \n-0.4118,0.0862,8.2073,-0.5088,-0.1628,9.7921,-0.1625,-0.0843,-0.0782,-23.7,-2,-48.2,1.672549022,0.86,2.99,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,185269,2015-10-30 10:25:22:402,1446171922402.0 \n-0.8356,0.3244,9.153,-0.5243,-0.2244,9.7901,0.0367,-0.0684,0.0831,-23.5,-1.9,-48,1.692620309,1.39,3.16,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,185372,2015-10-30 10:25:22:505,1446171922505.0 \n-0.3412,0.4274,9.7205,-0.5487,-0.1434,9.7902,0.1014,-0.1026,0.0415,-23.5,-1.6,-47.6,1.674992483,0.84,3.21,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,185473,2015-10-30 10:25:22:606,1446171922606.0 \n-0.0958,0.7829,7.367,-0.5813,0.2152,9.787,0.3775,0.1234,0.2211,-23.3,-1.8,-47.2,1.644449221,-0.17,2.77,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,185575,2015-10-30 10:25:22:708,1446171922708.0 \n-1.6616,-0.6812,12.4295,-0.5271,-0.012,9.7925,-0.5705,0.1613,-0.0538,-23.3,-2,-47.2,1.633977246,-0.5,2.84,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,185678,2015-10-30 10:25:22:811,1446171922811.0 \n-0.6644,0.1425,9.0022,-0.3481,0.0737,9.8002,-0.1539,-0.0073,0.0122,-23.3,-2.1,-47,1.63781697,-0.43,2.03,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,185780,2015-10-30 10:25:22:913,1446171922913.0 \n-1.3132,0.1676,10.2723,-0.3357,0.0871,9.8005,0.3445,0.0134,0.2175,-23.2,-1.9,-47,1.647416281,-0.13,2.11,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,185881,2015-10-30 10:25:23:014,1446171923014.0 \n-0.7554,1.0606,8.7029,-0.4292,0.4133,9.7885,0.2932,0.1136,0.1161,-23.3,-1.7,-46.7,1.608495439,-1.32,2.13,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,185983,2015-10-30 10:25:23:116,1446171923116.0 \n-0.6764,1.1241,11.0038,-0.4404,0.7693,9.7665,0.4044,0.0843,0.0049,-23.3,-2.2,-46.8,1.557357292,-2.91,2.47,36.813015,-119.74853,273.67,336.1929752,3.91,19.35484,98.83,16 / 16,186085,2015-10-30 10:25:23:218,1446171923218.0 \n-0.322,0.2622,11.1282,-0.3092,0.9648,9.7542,-0.4985,0.5046,-0.441,-23.2,-3.6,-46.9,1.532573616,-6.09,1.7,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,186187,2015-10-30 10:25:23:320,1446171923320.0 \n-0.8655,0.1736,9.4631,-0.4924,0.6585,9.7721,-0.1148,-0.0953,-0.1539,-23,-4.4,-47.4,1.602561319,-3.99,3.07,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,186290,2015-10-30 10:25:23:423,1446171923423.0 \n0.0311,1.0391,8.2049,-0.3941,0.5186,9.785,-0.0232,-0.193,0.0623,-22.8,-4.7,-47.4,1.673247154,-3.03,2.31,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,186391,2015-10-30 10:25:23:524,1446171923524.0 \n-0.4597,1.2893,8.4791,-0.3598,0.4634,9.7891,0.0831,0.088,0.0269,-22.6,-4.2,-47.3,1.644100155,-2.71,2.1,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,186494,2015-10-30 10:25:23:627,1446171923627.0 \n-0.1891,0.9493,11.1055,-0.3698,0.5259,9.7856,0.1967,0.0428,0.1625,-22.5,-4,-47,1.637991503,-2.97,2.28,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,186595,2015-10-30 10:25:23:728,1446171923728.0 \n-0.3304,-0.0706,13.2064,-0.3805,0.7506,9.7705,0.1747,-0.0941,0.1429,-22.4,-3.8,-46.9,1.590169481,-4.39,2.23,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,186697,2015-10-30 10:25:23:830,1446171923830.0 \n-0.3184,0.832,9.4415,-0.2284,0.5674,9.7876,-0.0049,-0.4569,0.1051,-22.3,-3.6,-46.7,1.627170462,-3.3,2.09,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,186799,2015-10-30 10:25:23:932,1446171923932.0 \n-0.3699,0.5423,8.3306,-0.0887,0.5066,9.7932,-0.171,0.0464,-0.0635,-22.4,-3.3,-46.6,1.5966272,-2.96,0.52,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,186901,2015-10-30 10:25:24:034,1446171924034.0 \n-0.4094,1.391,8.266,-0.158,0.5209,9.7915,0.1454,0.0232,0.0379,-22.5,-2.9,-46.2,1.605528379,-2.77,0.82,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,187003,2015-10-30 10:25:24:136,1446171924136.0 \n-0.3567,1.4856,9.402,-0.2277,0.6987,9.7791,0.2541,-0.0037,-0.0305,-22.6,-2.9,-46.5,1.576730446,-3.6,1.31,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,187105,2015-10-30 10:25:24:238,1446171924238.0 \n0.7781,1.0738,8.7927,-0.1756,0.9628,9.7577,0.121,-0.3176,-0.0892,-22.6,-3.4,-46.4,1.5393804,-4.72,1.26,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,187207,2015-10-30 10:25:24:340,1446171924340.0 \n-0.8212,-0.1628,11.3114,-0.1184,0.6951,9.7813,-0.4325,0.1674,-0.2272,-22.5,-3.8,-46.4,1.588773218,-4.49,0.71,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,187310,2015-10-30 10:25:24:443,1446171924443.0 \n-0.1688,0.6345,9.7815,7.00E-04,0.5532,9.791,-0.2859,-0.022,-0.0819,-22.5,-4.2,-46,1.616523953,-3.72,0.03,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,187411,2015-10-30 10:25:24:544,1446171924544.0 \n-0.2933,1.1396,8.746,-0.0606,0.4831,9.7946,-0.0098,0.1527,0.0428,-22.6,-3.9,-45.8,1.638340569,-3.04,0.05,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,187513,2015-10-30 10:25:24:646,1446171924646.0 \n-0.34,1.1217,9.5912,-0.2101,0.5082,9.7912,-0.0562,0.044,-0.0464,-22.5,-3.3,-45.9,1.596278134,-3.03,1.07,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,187615,2015-10-30 10:25:24:748,1446171924748.0 \n-0.0048,1.1564,8.5856,-0.2696,0.7532,9.774,0.4349,0.1466,0.2175,-22.2,-3,-46,1.583013632,-3.42,1.31,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,187717,2015-10-30 10:25:24:850,1446171924850.0 \n-0.6847,-0.1891,11.8202,-0.1977,0.535,9.7901,-0.1026,0.1124,0.0855,-22,-3,-46.1,1.577079512,-3.58,0.97,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,187820,2015-10-30 10:25:24:953,1446171924953.0 \n0.1365,0.6812,8.4036,-0.0598,0.5388,9.7917,-0.2053,-0.171,-0.0257,-22.1,-2.8,-46.1,1.592089344,-3.15,0.35,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,187921,2015-10-30 10:25:25:054,1446171925054.0 \n-0.7171,0.6632,8.6526,-0.0362,0.3851,9.799,-0.0476,0.1002,-0.0623,-22.3,-2.5,-46.1,1.579522973,-2.25,0.11,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,188023,2015-10-30 10:25:25:156,1446171925156.0 \n-0.4932,1.2785,8.9723,-0.1591,0.4802,9.7936,0.0806,0.16,-0.0269,-22.5,-2,-45.6,1.560324351,-2.81,0.93,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,188125,2015-10-30 10:25:25:258,1446171925258.0 \n-1.4341,0.5686,11.4275,-0.258,0.6696,9.7804,0.3299,0.1478,0.0122,-22.4,-2,-45.6,1.544441855,-3.27,1.13,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,188227,2015-10-30 10:25:25:360,1446171925360.0 \n-0.5662,-0.2203,12.2068,-0.1663,0.8031,9.7723,0.0806,-0.2456,0.0171,-22.2,-2.6,-45.7,1.522450707,-5.15,1.02,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,188329,2015-10-30 10:25:25:462,1446171925462.0 \n-0.018,0.7817,7.3263,-0.1454,0.7098,9.7798,0.0305,-0.022,-0.0501,-22.1,-3.1,-45.7,1.557008226,-4.15,0.85,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,188431,2015-10-30 10:25:25:564,1446171925564.0 \n-0.0862,1.2438,7.8961,-0.0907,0.3957,9.7982,-0.0513,0.1649,0.0086,-22.4,-3.2,-45.6,1.621934474,-2.31,0.53,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,188533,2015-10-30 10:25:25:666,1446171925666.0 \n-0.595,0.9984,8.6143,-0.1894,0.3323,9.7992,-0.0391,0.0428,-0.0208,-22.5,-2.8,-45.6,1.63066112,-2.04,1.12,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,188636,2015-10-30 10:25:25:769,1446171925769.0 \n-0.8152,0.3124,11.2384,-0.3398,0.3064,9.796,-0.0806,0.2199,0.0305,-22.4,-2.3,-45.7,1.598547062,-1.71,1.91,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,188737,2015-10-30 10:25:25:870,1446171925870.0 \n0.5746,0.2682,10.3465,-0.2994,0.4108,9.7935,-0.1906,-0.1857,0.1161,-22.2,-2,-45.9,1.572367123,-2.49,1.93,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,188839,2015-10-30 10:25:25:972,1446171925972.0 \n-0.2215,0.7147,9.1243,-0.251,0.2692,9.7997,-0.0049,-0.2627,0.11,-22,-1.7,-45.9,1.603259451,-1.57,1.47,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,188941,2015-10-30 10:25:26:074,1446171926074.0 \n-0.3041,0.3711,9.3996,-0.111,0.1848,9.8043,-0.1759,-0.0843,-0.0086,-22.1,-1.4,-45.6,1.570447261,-1.26,0.59,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,189043,2015-10-30 10:25:26:176,1446171926176.0 \n-0.5267,1.0965,8.1068,-0.1712,0.271,9.8014,0.1527,0.0464,0.0012,-22.3,-1.1,-45,1.560498884,-1.58,1,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,189154,2015-10-30 10:25:26:287,1446171926287.0 \n-0.4477,1.1013,9.2524,-0.1998,0.4473,9.7944,0.1258,-0.0806,-0.1845,-22.4,-1.2,-44.8,1.537286005,-2.28,1.17,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,189247,2015-10-30 10:25:26:380,1446171926380.0 \n0.0132,0.7458,9.5313,-0.2226,0.6093,9.7852,0.2749,0.0941,-0.1173,-22.3,-1.8,-44.9,1.537460538,-3.56,1.3,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,189349,2015-10-30 10:25:26:482,1446171926482.0 \n-1.1289,-0.6823,11.6849,-0.2436,0.3059,9.7989,-0.3958,0.0538,-0.2028,-22.3,-2.4,-45.2,1.550375975,-3.17,1.15,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,189451,2015-10-30 10:25:26:584,1446171926584.0 \n-0.176,0.1245,10.0114,-0.0717,0.182,9.8047,-0.2016,-0.0892,-0.0696,-22.3,-2.7,-45.5,1.646892682,-1.64,0.71,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,189554,2015-10-30 10:25:26:687,1446171926687.0 \n-1.0487,0.6907,8.3797,-0.1394,0.0918,9.8052,0.0073,0.0965,-0.0513,-22.5,-2.3,-45.5,1.640609497,-0.54,0.81,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,189655,2015-10-30 10:25:26:788,1446171926788.0 \n0.0527,1.2881,9.1806,-0.2177,0.1579,9.803,0.1405,0.0782,0.0855,-22.5,-2.1,-45.3,1.635897108,-0.65,1.14,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,189757,2015-10-30 10:25:26:890,1446171926890.0 \n-0.3879,0.5698,12.7503,-0.2415,0.48,9.7919,0.3433,0.0257,0.1686,-22.3,-2.2,-45.1,1.583188164,-2.21,1.37,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,189860,2015-10-30 10:25:26:993,1446171926993.0 \n-1.8244,-0.9481,13.2064,-0.1582,0.5399,9.7905,-0.1967,-0.1283,-0.1417,-22,-2.9,-45,1.570621794,-3.86,1.29,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,189962,2015-10-30 10:25:27:095,1446171927095.0 \n0.1089,0.5375,8.922,0.1523,0.6896,9.7812,0.2639,-0.43,0.2101,-22.1,-3.5,-44.9,1.561546082,-4.03,-0.89,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,190064,2015-10-30 10:25:27:197,1446171927197.0 \n-0.1712,0.7853,7.6016,0.1246,0.466,9.7948,-0.1283,0.1124,0.0159,-22.5,-3.7,-44.5,1.641133096,-3.23,-1.15,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,190165,2015-10-30 10:25:27:298,1446171927298.0 \n-0.0922,1.3551,7.9978,0.0522,0.5091,9.7933,-0.0183,0.0965,0.0318,-23,-3.6,-44.2,1.652303203,-2.78,-0.42,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,190268,2015-10-30 10:25:27:401,1446171927401.0 \n-0.4058,0.7039,10.9391,-0.0449,0.4546,9.796,-0.0354,0.0843,-0.0648,-23.1,-3.3,-44.3,1.613033295,-2.64,0.16,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,190369,2015-10-30 10:25:27:502,1446171927502.0 \n-0.4489,-0.3041,11.2468,-0.1612,0.3374,9.7995,-0.3567,0.1698,-0.1784,-22.4,-3.3,-44.3,1.612335163,-2.7,0.46,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,190472,2015-10-30 10:25:27:605,1446171927605.0 \n0.1281,-0.1149,8.9459,-0.2196,0.1151,9.8035,-0.3176,0,0.1124,-21.8,-3.1,-44.3,1.669058364,-0.97,1.3,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,190574,2015-10-30 10:25:27:707,1446171927707.0 \n-0.1664,0.6177,8.1942,-0.1827,-0.2582,9.8015,-0.0635,0.1258,0.1197,-21.4,-2.1,-44,1.714087858,1.51,1.07,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,190676,2015-10-30 10:25:27:809,1446171927809.0 \n-0.1879,0.6728,9.1016,-0.2585,-0.2932,9.7989,-0.0476,0.022,0.1197,-21.2,-1.1,-44,1.678308609,1.83,1.51,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,190777,2015-10-30 10:25:27:910,1446171927910.0 \n-0.5782,0.1975,9.4044,-0.3239,-0.2028,9.7992,-0.0586,0.0098,0.1063,-21,-0.5,-43.6,1.609368103,1.14,1.86,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,190879,2015-10-30 10:25:28:012,1446171928012.0 \n-0.1053,0.5638,8.2349,-0.3291,0.0492,9.801,-0.11,-0.2443,-0.0024,-20.8,-0.2,-43.5,1.583711763,0.39,1.74,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,190981,2015-10-30 10:25:28:114,1446171928114.0 \n-0.6895,-0.4046,10.5429,-0.2909,-0.1287,9.8015,-0.1185,0.2309,0.1026,-20.7,-0.3,-43.1,1.588947751,0.54,1.36,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,191083,2015-10-30 10:25:28:216,1446171928216.0 \n0.0419,0.1101,9.2763,-0.0578,-0.0011,9.8065,-0.2053,-0.1808,-0.0159,-21,-0.3,-43.2,1.57097086,0.01,0.34,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,191185,2015-10-30 10:25:28:318,1446171928318.0 \n-0.893,0.2945,8.8502,-0.0982,-0.1742,9.8046,0.0648,0.1405,-0.0391,-21.2,-0.1,-43.1,1.599943325,0.82,0.17,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,191287,2015-10-30 10:25:28:420,1446171928420.0 \n-0.6345,0.5231,9.3015,-0.1329,-0.0472,9.8056,0.1515,0.022,-0.1002,-21.4,-0.1,-43.2,1.589994949,0.56,0.79,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,191389,2015-10-30 10:25:28:522,1446171928522.0 \n-0.5207,0.65,10.7763,-0.1645,0.1006,9.8048,0.2724,0.3543,-0.1478,-21.4,-0.2,-43.1,1.563989543,-0.19,0.5,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,191491,2015-10-30 10:25:28:624,1446171928624.0 \n-1.2857,-1.1696,13.1525,-0.2928,-0.2044,9.8001,-0.0391,0.1063,-0.1197,-21,-0.8,-43.6,1.655968394,1.19,1.71,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,191594,2015-10-30 10:25:28:727,1446171928727.0 \n-0.4058,-0.1317,10.5872,-0.2367,-0.2102,9.8015,0.0538,-0.1112,-0.0159,-20.8,-1,-43.7,1.658237322,1.23,1.38,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,191695,2015-10-30 10:25:28:828,1446171928828.0 \n-0.9002,0.6943,7.835,-0.2596,-0.1171,9.8025,0.0464,0.1747,-0.066,-20.7,-1.1,-44,1.641831227,0.74,1.24,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,191798,2015-10-30 10:25:28:931,1446171928931.0 \n-1.2282,0.2346,9.4547,-0.3218,-0.1238,9.8006,-0.0745,0.193,-0.0648,-20.5,-1.3,-44.3,1.642878425,0.72,1.88,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,191899,2015-10-30 10:25:29:032,1446171929032.0 \n-1.1744,-0.1568,11.9495,-0.4599,-0.1174,9.7952,0.1307,0.2395,0.3262,-20.4,-1.4,-44.6,1.641482162,0.72,2.55,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,192001,2015-10-30 10:25:29:134,1446171929134.0 \n-1.2629,-1.4461,13.3776,-0.4316,-0.0644,9.7969,-0.1234,-0.314,0.2248,-19.9,-1.5,-44.7,1.62943939,0.38,2.52,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,192103,2015-10-30 10:25:29:236,1446171929236.0 \n-0.6931,-0.401,9.0537,-0.1778,-0.1929,9.8031,-0.1124,-0.3409,0.2248,-19.9,-1.3,-44.6,1.654572131,1.06,2.12,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,192205,2015-10-30 10:25:29:338,1446171929338.0 \n-0.2705,0.1305,8.7807,-0.0546,-0.3442,9.8005,-0.0098,-0.0892,0.171,-20.4,-0.8,-44.1,1.68912965,1.86,0.47,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,192307,2015-10-30 10:25:29:440,1446171929440.0 \n-0.1365,0.6692,8.3402,-0.0253,-0.284,9.8025,0.0977,0.0391,0.1038,-21,-0.2,-43.9,1.639736832,1.89,-0.02,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,192410,2015-10-30 10:25:29:543,1446171929543.0 \n-0.4094,0.0479,11.2396,0.0078,-0.1451,9.8056,0.0611,-0.1026,-0.1527,-21.5,0,-43.3,1.603608517,0.93,0.19,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,192511,2015-10-30 10:25:29:644,1446171929644.0 \n0.1999,-0.7171,11.5329,-0.0488,-0.0231,9.8065,-0.0623,-0.055,-0.1759,-21.7,-0.1,-43,1.575334183,0.13,0.29,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,192613,2015-10-30 10:25:29:746,1446171929746.0 \n-0.3699,-0.3364,9.3972,-0.078,-0.1252,9.8055,0.1637,-0.1527,0.0244,-21.6,-0.5,-42.9,1.609019037,1.15,0.65,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,192716,2015-10-30 10:25:29:849,1446171929849.0 \n-0.2717,0.1377,9.4523,0.0251,-0.2567,9.8033,-0.3054,-0.1063,-0.0867,-21.7,-0.8,-42.7,1.6676621,1.5,-0.15,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,192817,2015-10-30 10:25:29:950,1446171929950.0 \n-0.5004,1.093,7.5908,-0.1629,-0.2014,9.8032,0.011,0.1588,-0.0171,-21.7,-0.8,-42.7,1.655793861,1.22,0.56,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,192919,2015-10-30 10:25:30:052,1446171930052.0 \n-0.5806,0.4836,10.5884,-0.2051,-0.0333,9.8044,0.3201,-0.0391,0.1527,-21.6,-1,-42.5,1.632580982,0.58,1.21,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,193022,2015-10-30 10:25:30:155,1446171930155.0 \n-0.3675,1.3324,9.9204,-0.1441,0.3913,9.7978,0.5644,-0.0782,0.2981,-21.5,-1.3,-42.5,1.572716189,-1.32,0.89,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,193123,2015-10-30 10:25:30:256,1446171930256.0 \n0.1867,0.5734,8.1642,-0.1938,0.4046,9.7964,0.0037,0.3665,0.3054,-21.6,-1.8,-42.3,1.588075086,-2.21,0.79,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,193225,2015-10-30 10:25:30:358,1446171930358.0 \n-0.407,0.3759,9.8462,0.0469,0.253,9.8033,-0.1442,-0.2883,0.0354,-21.7,-1.8,-42.3,1.598896128,-1.88,0.13,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,193327,2015-10-30 10:25:30:460,1446171930460.0 \n-0.662,0.2693,9.1339,0.1816,0.0753,9.8047,-0.1918,-0.0379,-0.2272,-22.2,-1.1,-41.4,1.590169481,-0.81,-0.93,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,193429,2015-10-30 10:25:30:562,1446171930562.0 \n-0.3196,0.8559,9.3194,0.2297,0.0472,9.8038,0.0086,-0.0415,-0.0354,-22.5,-0.6,-40.9,1.610764367,-0.22,-1.29,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,193531,2015-10-30 10:25:30:664,1446171930664.0 \n-0.3555,0.2705,11.6526,0.2131,0.1269,9.8035,0.0525,0.066,-0.1943,-23.2,-0.1,-40.2,1.548456112,-0.7,-1.32,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,193633,2015-10-30 10:25:30:766,1446171930766.0 \n-0.1365,-0.5794,10.7105,0.1857,-0.1095,9.8043,0.1625,-0.0672,0.0733,-23.4,0,-40.4,1.591042146,0.64,-1.09,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,193736,2015-10-30 10:25:30:869,1446171930869.0 \n1.3312,-0.0539,9.7588,0.4146,-0.0013,9.7979,-0.0098,-0.1649,0.0183,-23.6,0,-40.4,1.567480201,-0.11,-2.09,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,193837,2015-10-30 10:25:30:970,1446171930970.0 \n0.0323,0.4657,7.4998,0.3688,-0.0558,9.7996,0.0037,0.2737,-0.1051,-23.9,0,-40.7,1.581442835,0.33,-2.16,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,193940,2015-10-30 10:25:31:073,1446171931073.0 \n0.2514,1.1025,8.1223,0.2043,-0.0827,9.8042,0.099,0.0965,0.0171,-24,0.1,-40.8,1.587900553,0.54,-1.46,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,194041,2015-10-30 10:25:31:174,1446171931174.0 \n-0.5183,0.17,11.9135,0.0449,-0.0663,9.8063,-0.0977,0.2847,-0.0538,-23.9,0.1,-41.2,1.582490033,0.39,-0.26,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,194144,2015-10-30 10:25:31:277,1446171931277.0 \n0.2119,-1.2234,11.2444,0.0164,0.0833,9.8063,-0.0794,-0.1967,-0.0709,-23.5,0,-41.9,1.551248639,-0.62,0.26,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,194246,2015-10-30 10:25:31:379,1446171931379.0 \n-0.9194,-0.3041,8.2576,0.0637,-0.1007,9.8059,0.0159,-0.4252,0.2285,-23.4,0,-42.2,1.600641457,0.93,-0.33,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,194347,2015-10-30 10:25:31:480,1446171931480.0 \n-0.5555,0.0012,9.4427,0.2775,-0.2683,9.799,-0.2443,-0.099,0.1833,-23.5,0.3,-42.2,1.617047552,1.35,-1.68,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,194449,2015-10-30 10:25:31:582,1446171931582.0 \n-0.3196,0.7482,8.2815,0.247,-0.1549,9.8023,0.1515,0.0269,0.0929,-23.8,0.8,-41.8,1.564862207,1.16,-1.49,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,194551,2015-10-30 10:25:31:684,1446171931684.0 \n-0.6177,0.6584,9.4774,0.1459,0.0158,9.8056,0.2676,0.0305,-0.0855,-24.2,1.1,-41.5,1.525243233,-0.09,-0.85,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,194653,2015-10-30 10:25:31:786,1446171931786.0 \n0.2741,0.6931,9.6953,0.1213,0.3463,9.7998,0.2419,0.0281,-0.0696,-24.1,0.5,-41.8,1.465029374,-2.02,-0.71,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,194755,2015-10-30 10:25:31:888,1446171931888.0 \n-0.7649,-0.3472,11.3234,-0.0685,0.2866,9.8022,-0.2211,0.3457,-0.2395,-23.9,-0.1,-41.9,1.50831354,-2.04,-0.17,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,194858,2015-10-30 10:25:31:991,1446171931991.0 \n0.2837,-0.0946,10.4615,0.0208,0.3476,9.8005,-0.226,-0.0415,-0.1649,-23.7,-0.9,-42.4,1.550201442,-2.03,-0.12,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,194960,2015-10-30 10:25:32:093,1446171932093.0 \n0.3603,0.8068,7.2532,-0.0509,0.3094,9.8016,0.0428,-0.011,-0.1271,-23.6,-1.2,-42.6,1.562244213,-1.6,0.03,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,195061,2015-10-30 10:25:32:194,1446171932194.0 \n0.1592,1.5335,8.114,-0.0893,0.6299,9.786,0.4349,-0.0367,0.1344,-23.3,-1.7,-42.6,1.557008226,-3.1,0.38,36.812996,-119.74844,273.72,336.1929752,4.08,19.35484,99.63,16 / 16,195163,2015-10-30 10:25:32:296,1446171932296.0 \n-0.0335,1.1863,9.8485,-0.254,0.8419,9.7671,0.2309,0.1271,0.1185,-23.2,-2.5,-42.8,1.515294857,-4.49,1.27,36.812996,-119.7483,273.29,336.1929752,4.03,25.806452,91.5,16 / 16,195266,2015-10-30 10:25:32:399,1446171932399.0 \n0.0742,1.3108,10.2161,-0.2861,0.95,9.7563,-0.1295,-0.0635,0.1454,-23.1,-3,-43.1,1.532748149,-5.31,1.79,36.812996,-119.7483,273.29,336.1929752,4.03,25.806452,91.5,16 / 16,195367,2015-10-30 10:25:32:500,1446171932500.0 \n-0.6883,0.5866,9.8701,-0.2067,0.7516,9.7756,-0.2089,-0.1686,0.0941,-22.7,-3.5,-43.6,1.543220125,-4.86,1.8,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,195470,2015-10-30 10:25:32:603,1446171932603.0 \n-0.3328,0.2346,10.4842,-0.027,0.5091,9.7934,-0.4704,-0.0379,-0.1405,-22.8,-3.2,-43.8,1.575508716,-3.77,0.35,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,195571,2015-10-30 10:25:32:704,1446171932704.0 \n-1.0738,1.1971,8.7999,-0.1564,0.3954,9.7974,-0.0611,0.044,-0.077,-23,-2.5,-43.5,1.577254045,-2.48,0.77,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,195674,2015-10-30 10:25:32:807,1446171932807.0 \n-0.571,1.324,10.307,-0.1438,0.5137,9.7921,0.0684,-0.1283,-0.0648,-23.4,-2,-43.3,1.560673417,-3,0.84,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,195775,2015-10-30 10:25:32:908,1446171932908.0 \n-0.2322,1.3695,9.3206,0.0029,0.7207,9.7801,0.3005,-0.237,-0.0757,-23.6,-2.1,-43.2,1.540078532,-3.67,0.39,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,195878,2015-10-30 10:25:33:011,1446171933011.0 \n0.1951,0.0922,10.6087,0.1656,0.348,9.7991,-0.0391,0.0134,0.0012,-24.2,-2.4,-42.6,1.586678823,-2.15,-1,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,195980,2015-10-30 10:25:33:113,1446171933113.0 \n0.3041,0.2502,9.511,0.2278,0.34,9.7981,-0.1747,0.0733,-0.1014,-24.7,-2.4,-42.4,1.592612942,-1.99,-1.33,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,196081,2015-10-30 10:25:33:214,1446171933214.0 \n-0.3328,0.407,8.6155,0.0883,0.2259,9.8037,-0.1014,0.1393,-0.1759,-24.9,-2.2,-42.2,1.605877445,-1.55,-1.07,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,196184,2015-10-30 10:25:33:317,1446171933317.0 \n-0.7027,0.6428,8.9004,-0.0329,0.2361,9.8038,-0.0684,0.1136,-0.0623,-24.6,-2.1,-42.7,1.603957583,-1.56,0,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,196285,2015-10-30 10:25:33:418,1446171933418.0 \n0.5914,1.0523,11.479,-0.0519,0.2715,9.8028,0.2101,0.011,0.2688,-24.3,-2.1,-42.9,1.61216063,-1.33,0.4,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,196387,2015-10-30 10:25:33:520,1446171933520.0 \n-0.978,-0.6416,13.4434,0.0124,0.2852,9.8025,-0.1784,-0.2114,-0.0049,-23.9,-2.2,-43.2,1.60203772,-1.67,-0.07,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,196490,2015-10-30 10:25:33:623,1446171933623.0 \n-0.6931,0.3412,9.9252,-0.0142,0.1581,9.8054,-0.0806,-0.3604,0.0012,-23.9,-1.9,-43.1,1.623330737,-0.95,0.65,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,196591,2015-10-30 10:25:33:724,1446171933724.0 \n-0.5686,0.3136,9.5493,0.0228,0.0238,9.8066,-0.0147,0.0367,-0.1075,-24,-1.5,-42.8,1.604481181,-0.26,-0.22,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,196693,2015-10-30 10:25:33:826,1446171933826.0 \n-0.5734,1.0044,9.1842,-0.0757,0.2196,9.8039,0.1307,0.1063,-0.2162,-23.9,-1.3,-42.8,1.572541656,-1.28,0.44,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,196795,2015-10-30 10:25:33:928,1446171933928.0 \n-1.1528,0.5555,11.0169,-0.2317,0.4047,9.7956,0.1906,0.1185,-0.2065,-23.7,-1.7,-42.9,1.58947135,-2.07,1.1,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,196897,2015-10-30 10:25:34:030,1446171934030.0 \n0.8667,0.7614,10.7823,-0.3008,0.6566,9.78,-0.0195,-0.1258,-0.0415,-23.1,-2.9,-42.9,1.577428578,-3.84,1.76,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,197000,2015-10-30 10:25:34:133,1446171934133.0 \n-0.3903,-0.2909,10.9259,-0.2821,0.4396,9.7927,-0.0171,-0.1319,-0.0562,-22.8,-3.5,-42.9,1.615302223,-2.59,2.01,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,197101,2015-10-30 10:25:34:234,1446171934234.0 \n-0.2107,0.7649,7.5812,-0.3245,0.3122,9.7963,-0.1148,0.1173,0.0611,-22.4,-3.8,-42.6,1.677435944,-2.05,1.58,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,197204,2015-10-30 10:25:34:337,1446171934337.0 \n-1.008,0.7015,9.3039,-0.4643,0.155,9.7944,-0.0073,0.0965,0.0208,-22.3,-3.5,-42.7,1.670105561,-0.85,2.5,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,197305,2015-10-30 10:25:34:438,1446171934438.0 \n-0.3508,0.9517,8.9256,-0.6127,0.2674,9.7838,0.1515,0.0525,0.1564,-21.7,-2.9,-43.2,1.646369083,-1.56,3.58,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,197407,2015-10-30 10:25:34:540,1446171934540.0 \n-0.9984,1.0139,11.6705,-0.5532,0.4715,9.7797,0.248,-0.1625,0.2272,-21.3,-2.7,-43.5,1.626995929,-2.3,3.52,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,197510,2015-10-30 10:25:34:643,1446171934643.0 \n-1.1037,-0.267,10.5417,-0.2802,0.5112,9.7893,-0.0428,-0.1014,0.1368,-21.1,-2.8,-43.3,1.6109389,-2.84,1.77,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,197611,2015-10-30 10:25:34:744,1446171934744.0 \n-0.2478,0.6309,8.4084,-0.0283,0.5232,9.7926,-0.1747,-0.2786,0.1051,-21.6,-2.9,-43.1,1.602561319,-3.06,0.17,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,197713,2015-10-30 10:25:34:846,1446171934846.0 \n-0.8045,0.3759,9.7887,0.0803,0.3103,9.8014,0.1161,0.0171,0.0501,-22.1,-2.5,-42.7,1.589820416,-2.1,-0.38,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,197816,2015-10-30 10:25:34:949,1446171934949.0 \n-0.2753,1.6688,8.4396,0.0303,0.4311,9.7971,0.1613,0.0476,-0.0195,-22.6,-2,-42.3,1.577254045,-2.52,-0.18,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,197917,2015-10-30 10:25:35:050,1446171935050.0 \n-0.6692,0.5519,12.6869,0.0516,0.5171,9.7929,0.0086,0.0171,-0.2065,-22.7,-1.9,-42,1.562069681,-2.99,-0.35,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,198019,2015-10-30 10:25:35:152,1446171935152.0 \n-0.0778,-0.0814,10.9595,-0.0693,0.6304,9.7861,-0.2663,0.4007,-0.3445,-22.3,-2.5,-41.5,1.542521993,-3.69,0.41,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,198122,2015-10-30 10:25:35:255,1446171935255.0 \n-0.3915,0.2059,8.3127,-0.315,0.4383,9.7918,-0.0867,0.0794,-0.1747,-21.8,-3,-41.7,1.620189145,-2.56,1.84,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,198223,2015-10-30 10:25:35:356,1446171935356.0 \n-0.5495,0.3256,9.3338,-0.295,-0.0114,9.8022,-0.3555,0.0794,-0.1588,-21.3,-2.9,-41.7,1.666963969,-1.2,1.56,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,198325,2015-10-30 10:25:35:458,1446171935458.0 \n-0.7171,1.1097,8.2265,-0.3347,-0.1381,9.8,-0.0452,-0.0122,0.055,-21,-2.1,-42,1.681275668,0.67,1.93,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,198427,2015-10-30 10:25:35:560,1446171935560.0 \n-1.1001,-0.0431,11.3198,-0.3243,-0.2115,9.799,-0.1429,-0.0024,-0.0195,-20.9,-1.5,-41.7,1.649510676,1.06,1.85,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,198529,2015-10-30 10:25:35:662,1446171935662.0 \n-0.1041,0.9888,10.0904,-0.3578,0.1646,9.7987,0.3775,0.11,0.4117,-20.8,-1,-41.5,1.601688655,-0.43,2.1,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,198632,2015-10-30 10:25:35:765,1446171935765.0 \n-0.8176,-0.1724,9.9719,-0.2289,0.012,9.804,0.0892,0.1112,0.369,-20.8,-0.8,-41.2,1.601339589,-0.47,1.17,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,198734,2015-10-30 10:25:35:867,1446171935867.0 \n-0.1856,0.2454,9.0728,0.0197,0.0189,9.8066,-0.215,0.1503,0.1112,-21.1,-0.4,-41,1.566956602,-0.11,-0.12,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,198835,2015-10-30 10:25:35:968,1446171935968.0 \n-0.6165,1.0798,7.9332,-0.0996,-0.0609,9.806,0.0696,0.1063,0.0562,-21.4,0.1,-40.8,1.582664566,0.36,0.58,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,198937,2015-10-30 10:25:36:070,1446171936070.0 \n-0.7997,0.7171,9.5062,-0.2527,0.0567,9.8032,0.1576,0.1857,-0.0354,-21.4,0.5,-41,1.524370569,-0.02,1.14,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,199040,2015-10-30 10:25:36:173,1446171936173.0 \n-0.9002,0.5423,11.3437,-0.5221,0.1486,9.7916,0.2834,-0.1185,-0.2028,-20.8,0.4,-41.1,1.552295837,-0.62,3.06,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,199142,2015-10-30 10:25:36:275,1446171936275.0 \n-0.2873,-0.9349,13.6218,-0.5555,-0.0738,9.7906,-0.6585,0.1491,-0.3396,-20.3,0.2,-41.3,1.546187184,-0.78,2.8,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,199243,2015-10-30 10:25:36:376,1446171936376.0 \n0.1293,-0.2682,9.001,-0.5003,-0.0517,9.7937,0.0037,-0.2309,0.0367,-19.7,0.1,-41.5,1.575683249,0.16,3.31,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,199345,2015-10-30 10:25:36:478,1446171936478.0 \n-0.1185,0.6536,7.8147,-0.5335,-0.1696,9.7907,-0.0061,0.1258,0.044,-19.7,0.3,-41.6,1.602735852,0.99,2.88,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,199447,2015-10-30 10:25:36:580,1446171936580.0 \n-0.5854,1.1492,9.3254,-0.6839,-0.3109,9.7778,-0.2627,0.2517,-0.0037,-19.6,0.9,-41.7,1.583188164,1.82,4,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,199550,2015-10-30 10:25:36:683,1446171936683.0 \n-0.7865,0.2227,10.1526,-0.6533,-0.1709,9.7834,0.0049,-0.0073,-0.1881,-19.5,1.4,-41.9,1.57219259,1.46,4.01,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,199651,2015-10-30 10:25:36:784,1446171936784.0 \n-0.1353,-0.0443,9.1961,-0.3696,0.158,9.7984,0.022,-0.3604,0.1857,-19.4,1.7,-42.1,1.457698991,-0.53,2.68,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,199753,2015-10-30 10:25:36:886,1446171936886.0 \n-0.1377,0.6201,8.1391,-0.1913,0.0224,9.8048,0.2553,-0.5278,0.4117,-19.9,1.7,-41.9,1.470439895,-0.13,1.12,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,199855,2015-10-30 10:25:36:988,1446171936988.0 \n-0.5064,0.0227,8.9148,0.0968,-0.0498,9.806,-0.3372,-0.0415,-0.0757,-20.6,1.8,-41.5,1.463284045,-0.28,-0.83,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,199958,2015-10-30 10:25:37:091,1446171937091.0 \n-0.7003,0.6536,8.7484,0.0258,-0.0125,9.8066,0.226,0.0745,0.0086,-21.4,2.3,-40.6,1.493478241,0.54,-0.33,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,200059,2015-10-30 10:25:37:192,1446171937192.0 \n-0.2825,1.1073,8.9615,-0.0172,0.303,9.802,0.0464,-0.011,-0.1478,-21.6,2.3,-40.8,1.437104106,-1.35,0.09,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,200161,2015-10-30 10:25:37:294,1446171937294.0 \n0.2933,0.5471,10.4686,-0.0941,0.4432,9.7962,0.2688,0.1613,-0.1014,-21.6,2,-40.9,1.400975791,-2.59,0.55,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,200263,2015-10-30 10:25:37:396,1446171937396.0 \n-0.5531,-0.4645,11.7244,-0.3325,0.1772,9.7994,-0.2101,0.3018,-0.2346,-21.6,1.6,-41.4,1.422792406,-1.94,0.89,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,200365,2015-10-30 10:25:37:498,1446171937498.0 \n-0.5243,-0.0527,9.4008,-0.2564,0.0745,9.803,-0.2847,-0.1356,-0.1943,-21.4,1.4,-41.7,1.493827307,-0.99,1.73,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,200467,2015-10-30 10:25:37:600,1446171937600.0 \n-0.996,0.6345,8.0349,-0.2884,0.0045,9.8024,-0.0489,0.1087,-0.0122,-21.5,1.7,-42,1.477944811,-0.09,1.55,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,200569,2015-10-30 10:25:37:702,1446171937702.0 \n-0.7925,0.5674,9.5648,-0.2687,0.1149,9.8023,0.0977,0.0452,0.1478,-21.6,2.1,-42.4,1.463807644,-0.67,1.57,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,200671,2015-10-30 10:25:37:804,1446171937804.0 \n-0.7338,0.4022,11.2839,-0.2591,0.4489,9.7929,0.4533,-0.0831,0.4472,-21.8,2.2,-42.5,1.446179818,-1.27,1.75,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,200773,2015-10-30 10:25:37:906,1446171937906.0 \n-0.5339,-0.3603,12.8401,-0.1444,0.5616,9.7895,-0.3189,0.1845,0.1539,-22,2,-42.9,1.361356817,-3.87,1.18,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,200875,2015-10-30 10:25:38:008,1446171938008.0 \n-0.4561,0.5698,8.2181,-0.1548,0.4328,9.7959,-0.0134,-0.1295,0.1539,-22.1,2,-43.2,1.401324856,-2.53,0.91,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,200977,2015-10-30 10:25:38:110,1446171938110.0 \n-0.8128,0.3879,8.934,-0.1768,0.1842,9.8033,-0.0599,-0.0086,0.0049,-22.3,2.4,-43.6,1.444434489,-1.18,1.04,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,201080,2015-10-30 10:25:38:213,1446171938213.0 \n-0.4262,1.1408,8.6251,-0.1726,0.3048,9.8004,0.1613,-0.0159,-0.0183,-22.5,3.2,-43.9,1.396787,-1.33,1.04,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,201181,2015-10-30 10:25:38:314,1446171938314.0 \n-1.0666,0.4537,11.9315,-0.0591,0.4606,9.7956,0.1674,-0.2737,-0.1356,-22.6,3.2,-44.2,1.369734397,-2.38,0.8,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,201284,2015-10-30 10:25:38:417,1446171938417.0 \n0.99,0.4848,11.0385,-0.0295,0.7968,9.7742,0.1515,-0.0452,-0.1564,-23.1,2.3,-44.9,1.33290795,-4.61,0.14,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,201385,2015-10-30 10:25:38:518,1446171938518.0 \n-0.2801,0.3089,9.6403,-0.2371,0.7315,9.7765,0.088,0.0721,-0.1759,-23.2,1.5,-45.7,1.3543755,-4.11,1.15,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,201487,2015-10-30 10:25:38:620,1446171938620.0 \n-0.3663,0.674,8.4898,-0.3375,0.4683,9.7896,-0.4447,0.1002,-0.3079,-23,0.2,-46.5,1.461713249,-3.38,1.73,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,201589,2015-10-30 10:25:38:722,1446171938722.0 \n-0.9433,0.6931,8.5258,-0.3884,0.2521,9.7957,-0.2468,0.0342,-0.2822,-22.7,0,-47.1,1.509011671,-1.91,2.19,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,201691,2015-10-30 10:25:38:824,1446171938824.0 \n-0.7877,0.6632,9.9491,-0.437,0.2557,9.7936,0.0171,0.0672,0.0586,-22.2,-0.3,-47.6,1.521228976,-1.45,2.45,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,201793,2015-10-30 10:25:38:926,1446171938926.0 \n-0.3615,1.5,9.7288,-0.4842,0.4536,9.7842,0.3323,0.0244,0.248,-22.2,-0.5,-47.9,1.481959068,-2.65,2.83,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,201895,2015-10-30 10:25:39:028,1446171939028.0 \n-1.5766,-0.7326,11.6897,-0.4886,0.4166,9.7856,-0.4325,0.0281,-0.1319,-22,-1,-48,1.504997414,-3.14,2.33,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,201997,2015-10-30 10:25:39:130,1446171939130.0 \n-0.5303,0.158,10.0221,-0.2632,0.362,9.7964,-0.2456,-0.182,0.011,-22.1,-1.5,-47.6,1.538682269,-2.12,1.54,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,202099,2015-10-30 10:25:39:232,1446171939232.0 \n-0.4884,1.0702,7.4962,-0.3334,0.1845,9.7992,-0.2089,-0.1662,-0.1918,-22.1,-1.6,-47.6,1.607622774,-1.37,1.89,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,202201,2015-10-30 10:25:39:334,1446171939334.0 \n-1.0175,1.385,8.7759,-0.4344,0.1551,9.7958,0.0403,0.1833,-0.0977,-22.4,-1.2,-47.4,1.591565745,-0.63,2.24,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,202304,2015-10-30 10:25:39:437,1446171939437.0 \n-0.9134,0.8667,9.7612,-0.4824,0.3059,9.79,0.1491,-0.1491,-0.1161,-22.3,-1.5,-47.2,1.562244213,-1.51,3.03,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,202405,2015-10-30 10:25:39:538,1446171939538.0 \n1.5538,0.3938,12.3649,-0.2016,0.4816,9.7927,-0.2786,-0.2431,-0.1576,-22.3,-2.3,-46.8,1.562069681,-2.74,2.01,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,202507,2015-10-30 10:25:39:640,1446171939640.0 \n-0.5962,-0.3017,9.6163,-0.2435,0.281,9.7996,-0.0794,0.0318,-0.1307,-22.3,-3,-46.3,1.632057384,-1.98,1.61,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,202610,2015-10-30 10:25:39:743,1446171939743.0 \n-0.8056,-0.0431,9.8701,-0.2743,-0.1289,9.802,-0.5376,0.1026,0.0941,-22.7,-3.3,-45.9,1.71775305,0.75,1.6,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,202711,2015-10-30 10:25:39:844,1446171939844.0 \n-0.4764,0.7266,8.3222,-0.2988,-0.1949,9.8002,0.0415,0.1124,0.1075,-22.8,-2.7,-45.4,1.735031809,1.32,1.6,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,202813,2015-10-30 10:25:39:946,1446171939946.0 \n-0.346,0.5543,9.7217,-0.3674,-0.117,9.7991,0.1686,0.0195,0.1454,-22.7,-1.8,-45.1,1.677610477,0.83,2.04,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,202915,2015-10-30 10:25:40:048,1446171940048.0 \n-0.0838,0.838,9.6965,-0.384,0.1295,9.7983,0.3494,0.0061,0.3213,-22.6,-1.4,-44.8,1.587726021,-0.76,2.24,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,203017,2015-10-30 10:25:40:150,1446171940150.0 \n-1.2653,-0.5926,11.1067,-0.3659,0.1403,9.7988,-0.1038,0.2443,0.1649,-22.4,-1.6,-44.6,1.622632606,-1.02,1.75,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,203119,2015-10-30 10:25:40:252,1446171940252.0 \n-0.5303,0.322,8.4168,-0.2784,0.1053,9.8021,-0.3763,-0.1918,0.0195,-22.4,-1.5,-44.5,1.593834673,-0.62,1.63,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,203221,2015-10-30 10:25:40:354,1446171940354.0 \n-0.814,0.1903,8.8933,-0.1525,-0.1986,9.8035,-0.121,-0.0623,-0.0501,-22.8,-0.9,-43.8,1.648114413,1.1,0.94,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,203323,2015-10-30 10:25:40:456,1446171940456.0 \n-0.3579,1.0259,7.7081,-0.2673,-0.1195,9.8023,0.1442,0.0733,-0.0367,-22.9,-0.3,-43.6,1.600990523,0.96,1.37,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,203426,2015-10-30 10:25:40:559,1446171940559.0 \n-0.583,0.2885,11.0816,-0.2339,-0.0021,9.8039,0.2871,0.088,-0.1515,-23.2,0,-43.2,1.571145393,0.01,1.37,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,203528,2015-10-30 10:25:40:661,1446171940661.0 \n0.2478,-0.6069,12.0644,-0.267,0.0586,9.8028,-0.0916,-0.088,-0.2187,-23,-0.4,-42.9,1.54653625,-0.8,1.55,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,203629,2015-10-30 10:25:40:762,1446171940762.0 \n0.152,0.158,8.3462,-0.4889,-0.0882,9.7941,-0.0049,-0.0476,0.0379,-22.8,-0.7,-42.9,1.625599665,0.52,2.86,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,203731,2015-10-30 10:25:40:864,1446171940864.0 \n-0.2921,0.4752,8.3306,-0.4254,-0.3861,9.7898,-0.2199,0.1014,-0.0305,-22.6,-0.5,-43.1,1.637118838,2.26,2.49,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,203833,2015-10-30 10:25:40:966,1446171940966.0 \n-0.2885,1.0942,7.4795,-0.5258,-0.4767,9.7809,-0.0391,0.0379,0.0232,-22.5,0,-43.1,1.658062789,2.89,2.84,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,203935,2015-10-30 10:25:41:068,1446171941068.0 \n-1.3539,-0.8416,12.6617,-0.5271,-0.4904,9.7802,-0.0024,-0.0257,-0.0073,-22.4,0.5,-43.1,1.615651289,2.87,3.08,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,204037,2015-10-30 10:25:41:170,1446171941170.0 \n0.4585,0.3244,9.0237,-0.4097,-0.1324,9.7972,0.1307,-0.2541,0.2822,-22.4,0.7,-43,1.557008226,0.91,2.94,36.812996,-119.7483,273.29,336.2701701,4.03,25.806452,91.5,16 / 16,204139,2015-10-30 10:25:41:272,1446171941272.0 \n-0.5471,0.0802,9.0034,-0.2341,-0.2681,9.8002,0.1759,-0.3176,0.2358,-22.6,0.7,-43,1.585980691,1.85,1.56,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,204241,2015-10-30 10:25:41:374,1446171941374.0 \n-0.2741,0.1748,8.5485,0.0016,-0.3209,9.8014,-0.2211,-0.1857,0.0684,-23.1,0.9,-42.7,1.573763387,1.43,0.24,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,204343,2015-10-30 10:25:41:476,1446171941476.0 \n-0.2717,0.4166,8.6886,0.1069,-0.4392,9.7962,0.0403,-0.0379,-0.022,-23.8,1.5,-41.8,1.566258471,2.57,-0.63,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,204445,2015-10-30 10:25:41:578,1446171941578.0 \n-0.3915,0.0922,10.1789,0.0562,-0.2626,9.803,0.0403,-0.0501,-0.3225,-24.4,1.6,-41.2,1.536064275,1.63,-0.31,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,204548,2015-10-30 10:25:41:681,1446171941681.0 \n-0.662,-0.4405,11.4563,-0.0631,-0.0557,9.8063,0.3555,0.2847,-0.2358,-24.6,1.5,-41,1.530130155,1.38,-0.41,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,204650,2015-10-30 10:25:41:783,1446171941783.0 \n-0.6548,-0.8619,11.0576,-0.3368,-0.3423,9.7949,-0.2602,0.3225,-0.1772,-24.5,0.5,-41.8,1.57515965,1.54,1.42,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,204751,2015-10-30 10:25:41:884,1446171941884.0 \n0.2514,-0.2502,9.3829,-0.3186,-0.4384,9.7917,-0.1759,-0.1381,0.0318,-24,0.2,-42.5,1.63362818,2.25,2.17,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,204853,2015-10-30 10:25:41:986,1446171941986.0 \n-0.3567,0.2765,7.5633,-0.3825,-0.596,9.781,-0.1906,-0.0281,0.0464,-23.4,0.2,-42.8,1.664171442,3.15,2.22,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,204955,2015-10-30 10:25:42:088,1446171942088.0 \n-0.6812,-0.0299,8.9459,-0.3912,-0.6335,9.7783,0.0428,0.033,0.0806,-23.3,1,-42.7,1.640260431,3.7,2.29,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,205057,2015-10-30 10:25:42:190,1446171942190.0 \n-0.7793,-0.6369,13.0245,-0.3545,-0.5912,9.7824,0.3372,-0.1014,0.3763,-23.4,1.4,-42.7,1.640609497,3.72,2.36,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,205159,2015-10-30 10:25:42:292,1446171942292.0 \n-1.6233,-1.506,12.8257,-0.3316,-0.3192,9.7958,-0.1319,-0.1564,0.0941,-23.3,1.7,-42.6,1.545139987,1.87,1.94,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,205261,2015-10-30 10:25:42:394,1446171942394.0 \n-0.2658,-0.0754,9.2249,-0.1074,-0.3704,9.7991,0.0257,-0.226,0.4081,-23.3,1.9,-42.6,1.551772238,2.08,1.02,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,205363,2015-10-30 10:25:42:496,1446171942496.0 \n-0.1688,0.407,7.9224,-0.1211,-0.5951,9.7878,-0.1368,0.1368,0.1576,-23.6,2.4,-42.2,1.592612942,3.48,0.71,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,205466,2015-10-30 10:25:42:599,1446171942599.0 \n-0.2909,0.5567,8.3522,-0.1238,-0.591,9.788,0.1796,0.0733,0.0244,-23.6,3.1,-42.1,1.55788089,3.68,0.68,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,205567,2015-10-30 10:25:42:700,1446171942700.0 \n-0.8308,-0.4705,12.8198,-0.0649,-0.334,9.8007,0.2224,-0.1576,-0.248,-23.8,3.6,-41.6,1.47969014,2.41,0.66,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,205669,2015-10-30 10:25:42:802,1446171942802.0 \n0.4429,-0.4573,11.3557,-0.1324,0.035,9.8057,0.2566,-0.0183,-0.3128,-23.8,3.1,-41.7,1.454557399,0.18,0.78,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,205771,2015-10-30 10:25:42:904,1446171942904.0 \n-0.3627,0.0994,9.1602,-0.4873,-0.0822,9.7942,-0.0012,0.0794,-0.1674,-23.7,1.8,-42,1.50656821,0.46,2.71,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,205873,2015-10-30 10:25:43:006,1446171943006.0 \n-0.8021,0.146,8.3881,-0.5077,-0.3466,9.7874,0.0098,0.0208,0.0501,-23.2,0.7,-42.7,1.589645883,2.03,2.97,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,205975,2015-10-30 10:25:43:108,1446171943108.0 \n-0.8823,0.8248,7.8554,-0.5792,-0.3597,9.7829,-0.0232,0.0648,-0.0208,-22.9,0.6,-42.7,1.590344014,2.06,3.27,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,206077,2015-10-30 10:25:43:210,1446171943210.0 \n-1.2737,0.0658,9.4966,-0.5683,-0.2823,9.7861,0.182,0.0452,-0.0806,-22.6,0.7,-42.5,1.577428578,1.65,3.32,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,206180,2015-10-30 10:25:43:313,1446171943313.0 \n-1.1025,0.5351,12.2715,-0.5122,0.073,9.793,0.4875,-0.0819,0.5168,-22.6,0.6,-42.3,1.541649328,0.37,3.19,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,206281,2015-10-30 10:25:43:414,1446171943414.0 \n-1.986,-0.8308,10.7847,-0.417,0.1001,9.7973,-0.3067,-0.055,0.1955,-22.7,0.4,-42.4,1.553866633,-0.58,2.44,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,206383,2015-10-30 10:25:43:516,1446171943516.0 \n-0.4286,0.2646,8.8837,-0.2446,-0.0164,9.8036,-0.2957,-0.0318,0.1026,-23,0.6,-42.6,1.508662605,-0.69,1.7,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,206485,2015-10-30 10:25:43:618,1446171943618.0 \n-0.7685,0.7027,8.2145,-0.3356,-0.1842,9.7992,-0.1649,0.0831,-0.1136,-23.5,1.4,-42.2,1.554564765,0.84,1.79,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,206587,2015-10-30 10:25:43:720,1446171943720.0 \n-0.5686,0.996,8.1666,-0.3902,-0.1317,9.798,0.1906,0.0635,-0.0489,-23.6,2.1,-42.2,1.523148838,1.09,2.19,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,206690,2015-10-30 10:25:43:823,1446171943823.0 \n-1.2222,0.006,12.1206,-0.3716,0.1118,9.799,0.1723,-0.1246,-0.2676,-23.6,2.3,-42,1.483355331,-0.34,2.27,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,206791,2015-10-30 10:25:43:924,1446171943924.0 \n-1.0642,-0.9194,12.6821,-0.4262,0.1815,9.7957,-0.3604,0.2236,-0.3958,-23.5,1.4,-42.1,1.500110492,-1.06,2.49,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,206893,2015-10-30 10:25:44:026,1446171944026.0 \n-0.091,0.1544,8.5305,-0.5257,0.2053,9.7904,0.2724,-0.0367,-0.0733,-23.5,0.7,-42.2,1.497492498,-1.2,3.07,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,206995,2015-10-30 10:25:44:128,1446171944128.0 \n-0.492,0.7949,7.3382,-0.3561,0.0329,9.8001,-0.2053,0.1943,-0.0061,-23.7,0,-42.1,1.559451687,-0.4,2.04,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,207097,2015-10-30 10:25:44:230,1446171944230.0 \n-0.5914,0.5818,9.1183,-0.2831,-0.2031,9.8005,-0.1796,-0.1087,0.066,-23.8,0.1,-42.3,1.592263877,0.76,1.8,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,207200,2015-10-30 10:25:44:333,1446171944333.0 \n-0.7135,0.018,10.744,-0.2593,-0.2009,9.8012,0.0147,-0.0476,0.0794,-24.1,0.5,-42.3,1.564687674,1.17,1.52,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,207301,2015-10-30 10:25:44:434,1446171944434.0 \n-0.0802,0.6416,9.9599,-0.2962,0.0305,9.8021,0.3751,0.1124,0.3335,-24.2,0.9,-42.1,1.541474795,0.36,1.52,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,207403,2015-10-30 10:25:44:536,1446171944536.0 \n-0.5028,0.097,9.6151,-0.2007,-0.0717,9.8043,-0.0269,-0.11,0.3079,-24.2,1,-41.8,1.542696526,0.42,1.17,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,207505,2015-10-30 10:25:44:638,1446171944638.0 \n0.4824,0.1377,9.4679,0.16,-0.2447,9.8023,-0.441,-0.0159,-0.033,-24.3,1.2,-41.7,1.540951197,0.38,0.1,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,207607,2015-10-30 10:25:44:740,1446171944740.0 \n-0.3017,0.7649,9.663,0.0932,-0.3683,9.7993,-0.0648,0.0476,-0.0171,-24.7,2,-41.6,1.549677843,2.01,-0.49,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,207709,2015-10-30 10:25:44:842,1446171944842.0 \n-0.0766,1.063,8.0122,-0.0647,-0.2254,9.8038,0.033,0.2541,-0.1491,-24.9,2.4,-41.3,1.529606556,1.36,-0.04,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,207812,2015-10-30 10:25:44:945,1446171944945.0 \n-0.923,0.1664,11.2444,-0.0549,-0.0531,9.8064,0.3995,0.3018,-0.1429,-24.8,2.4,-41.3,1.500459558,0.31,0.32,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,207913,2015-10-30 10:25:45:046,1446171945046.0 \n-0.8056,-0.972,12.1542,-0.1863,-0.0047,9.8049,-0.2028,0.3751,-0.3775,-24.5,1.2,-41.7,1.506742743,-0.77,0.51,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,208016,2015-10-30 10:25:45:149,1446171945149.0 \n-0.8595,-0.401,8.9112,-0.2097,-0.0568,9.8042,-0.0464,-0.1491,-0.1356,-24.3,0.4,-42,1.572541656,0.06,1.52,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,208117,2015-10-30 10:25:45:250,1446171945250.0 \n-0.5136,0.7769,8.2229,-0.1883,-0.1759,9.8033,-0.1918,0.0195,0.237,-24.3,0,-41.9,1.60081599,1.03,1.1,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,208220,2015-10-30 10:25:45:353,1446171945353.0 \n-0.4573,1.1935,7.9823,-0.1771,-0.1467,9.804,0.1466,0.0257,0.1258,-24.4,0.4,-41.8,1.609019037,1.3,0.94,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,208322,2015-10-30 10:25:45:455,1446171945455.0 \n-0.3555,0.0982,10.9726,-0.2664,0.0204,9.803,0.1881,0.1417,0.0843,-24.4,0.9,-41.3,1.540776664,0.35,1.29,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,208423,2015-10-30 10:25:45:556,1446171945556.0 \n0.3926,0.3795,9.9108,-0.2621,0.184,9.8014,-0.0843,-0.1148,0.1979,-24.3,0.9,-41,1.504997414,-0.94,1.69,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,208526,2015-10-30 10:25:45:659,1446171945659.0 \n-0.0575,0.7697,8.9052,-0.2228,0.0169,9.8041,-0.0134,-0.1869,0.1332,-24,0.9,-41.1,1.527861227,-0.1,1.3,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,208628,2015-10-30 10:25:45:761,1446171945761.0 \n-0.4405,0.0251,9.1901,-0.0908,-0.0707,9.806,-0.1539,-0.0843,-0.0538,-23.9,1.2,-41.1,1.535715209,0.2,0.58,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,208729,2015-10-30 10:25:45:862,1446171945862.0 \n-0.4393,0.3867,8.5988,-0.0146,0.1261,9.8058,0.4313,-0.0293,0.0257,-24.1,1.6,-41.4,1.501681288,0.45,0.31,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,208831,2015-10-30 10:25:45:964,1446171945964.0 \n-1.1756,0.3328,10.4483,-0.0831,0.2796,9.8023,0.1808,-0.1429,-0.1527,-24.3,1.4,-41.1,1.487718654,-1.44,0.41,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,208933,2015-10-30 10:25:46:066,1446171946066.0 \n0.7961,1.0582,10.3034,-0.0524,0.5044,9.7935,0.1637,-0.055,0.0452,-24.6,0.4,-40.6,1.487718654,-2.95,0.31,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,209035,2015-10-30 10:25:46:168,1446171946168.0 \n-0.7626,-0.3962,12.0069,-0.0457,0.3485,9.8003,-0.4056,0.0305,-0.4044,-24.7,-0.3,-40.2,1.497143432,-2.66,0.2,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,209138,2015-10-30 10:25:46:271,1446171946271.0 \n-0.067,0.2179,10.149,4.00E-04,0.2069,9.8045,-0.2688,-0.0244,-0.0806,-24.8,-0.6,-40.2,1.564513141,-1.66,0.03,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,209239,2015-10-30 10:25:46:372,1446171946372.0 \n-0.5818,1.1504,7.8602,-0.1258,0.1686,9.8044,-0.0208,0.0269,-0.0281,-24.7,-0.5,-40.2,1.544092789,-0.99,0.74,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,209341,2015-10-30 10:25:46:474,1446171946474.0 \n-0.0443,1.312,8.8071,-0.2085,0.2285,9.8018,0.0721,0.1087,0.0623,-24.4,-0.4,-40.2,1.541649328,-1.03,0.88,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,209444,2015-10-30 10:25:46:577,1446171946577.0 \n-1.0822,0.7733,12.5588,-0.2909,0.3838,9.7948,0.1564,0.0599,0.1723,-24.1,-0.3,-40.2,1.51791285,-1.94,1.63,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,209545,2015-10-30 10:25:46:678,1446171946678.0 \n-0.6285,-0.4788,12.9287,-0.1956,0.4539,9.7942,-0.3079,0.0501,0.1087,-24,-0.4,-40.6,1.477246679,-3.34,1.5,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,209648,2015-10-30 10:25:46:781,1446171946781.0 \n-0.2191,0.2526,9.019,-0.0153,0.3116,9.8017,-0.0953,-0.3372,0.1979,-23.9,-0.2,-40.8,1.51669112,-1.82,0.09,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,209750,2015-10-30 10:25:46:883,1446171946883.0 \n0.097,0.6764,9.2799,0.1201,0.1256,9.8051,0.055,-0.0757,0.1014,-24.2,0.2,-40.6,1.546012651,-0.82,-0.45,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,209852,2015-10-30 10:25:46:985,1446171946985.0 \n-0.1269,1.148,7.6854,0.0791,0.2201,9.8039,0.2382,0.1112,-0.0855,-24.9,1,-40.4,1.503775684,-0.92,-0.63,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,209954,2015-10-30 10:25:47:087,1446171947087.0 \n-0.7314,0.2394,12.0105,0.0758,0.3761,9.7991,0.1368,0.077,-0.1148,-25,1,-40.1,1.47375602,-2.03,-0.23,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,210055,2015-10-30 10:25:47:188,1446171947188.0 \n0.5255,0.3172,10.9247,0.0081,0.5354,9.792,0.2065,-0.0819,-0.0953,-24.8,0.4,-40.1,1.487195056,-3.01,0.05,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,210157,2015-10-30 10:25:47:290,1446171947290.0 \n0.3017,0.4872,7.865,-0.2114,0.3705,9.7974,0.2688,0.0623,0.0733,-24.3,-0.4,-40.1,1.510931533,-2.17,1.24,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,210259,2015-10-30 10:25:47:392,1446171947392.0 \n-0.1939,-0.2945,10.6434,-0.1601,0.2079,9.8031,0.0428,0.2517,0.0147,-24,-0.6,-40.3,1.571319926,-1.42,0.73,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,210361,2015-10-30 10:25:47:494,1446171947494.0 \n-0.0251,0.808,8.3175,-0.2421,0.1864,9.8019,-0.0916,-0.0171,-0.0831,-23.8,-0.3,-40.5,1.540776664,-1.09,1.41,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,210463,2015-10-30 10:25:47:596,1446171947596.0 \n-0.1568,0.808,9.1291,-0.2454,0.2075,9.8014,0.0012,0.0159,-0.171,-23.7,-0.2,-40.4,1.537111472,-1.22,1.38,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,210566,2015-10-30 10:25:47:699,1446171947699.0 \n-0.4561,0.2358,10.9176,-0.3123,0.4014,9.7935,0.3995,0.121,0.1503,-23.5,-0.4,-40.4,1.521054443,-1.76,1.7,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,210667,2015-10-30 10:25:47:800,1446171947800.0 \n-1.4341,-1.3503,11.2109,-0.2553,0.6126,9.7842,0.1527,-0.099,-0.0305,-23.4,-0.9,-40.3,1.517040186,-3.35,1.72,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,210770,2015-10-30 10:25:47:903,1446171947903.0 \n-0.2023,-0.3519,10.2017,-0.0387,0.6182,9.7871,-0.204,-0.182,-0.1222,-23.4,-1.6,-40.2,1.538507736,-3.96,0.39,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,210871,2015-10-30 10:25:48:004,1446171948004.0 \n-0.1628,0.0048,9.0441,-0.1837,0.4381,9.7951,0.0061,0.1405,-0.27,-23.5,-2,-40,1.580570171,-2.56,1.07,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,210974,2015-10-30 10:25:48:107,1446171948107.0 \n-0.0287,-0.3699,9.9838,-0.2603,0.4562,9.7926,0.0525,0.0305,-0.4032,-23.5,-2.3,-40,1.584584428,-2.43,1.51,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,211076,2015-10-30 10:25:48:209,1446171948209.0 \n1.087,-0.1065,8.8083,-0.3082,0.59,9.784,0.1442,0.088,-0.5278,-23.4,-3.1,-40.3,1.596976266,-3.45,1.8,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,211177,2015-10-30 10:25:48:310,1446171948310.0 \n0.8751,-0.34,9.6534,-0.5125,0.4556,9.7826,-0.055,0.1173,-1.0189,-23.1,-4.1,-40.1,1.652826802,-2.88,2.8,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,211280,2015-10-30 10:25:48:413,1446171948413.0 \n1.6352,-0.8308,10.1203,-0.5986,0.3041,9.7836,0.2077,0.0843,-1.5638,-22.5,-6.1,-40.4,1.765051473,-1.78,3.5,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,211381,2015-10-30 10:25:48:514,1446171948514.0 \n0.82,-1.2713,10.4303,-0.6093,0.2829,9.7836,0.0574,-0.0476,-1.9511,-21.7,-8,-40.6,1.837657169,-1.86,3.65,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,211483,2015-10-30 10:25:48:616,1446171948616.0 \n0.1353,-1.0295,9.8426,-0.4694,0.2309,9.7927,0.0269,-0.3067,-2.0488,-19.2,-13.8,-40.3,2.11813158,-1.58,3.2,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,211586,2015-10-30 10:25:48:719,1446171948719.0 \n-0.4585,-0.9972,10.2125,-0.2558,0.0573,9.8031,-0.1368,-0.1515,-2.011,-17.6,-17.1,-40.7,2.273814949,-0.81,1.94,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,211687,2015-10-30 10:25:48:820,1446171948820.0 \n-1.6281,-0.6129,9.4296,-0.0953,-0.0027,9.8062,0.0415,-0.1747,-1.8021,-15.5,-19.3,-40.5,2.451140402,0.11,1.09,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,211789,2015-10-30 10:25:48:922,1446171948922.0 \n-2.1907,-0.6333,10.0772,0.0211,-0.0342,9.8066,0.0086,-0.1405,-1.1044,-13.5,-21.6,-40.7,2.609092699,0.13,0.03,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,211891,2015-10-30 10:25:49:024,1446171949024.0 \n-2.1715,0.0299,9.4703,0.0524,0.0227,9.8065,0.0501,-0.1527,-0.5034,-11,-23.7,-40.4,2.717826711,-0.13,-0.31,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,211994,2015-10-30 10:25:49:127,1446171949127.0 \n-1.3719,-0.1712,10.6494,0.068,-0.0566,9.8063,-0.1429,0.1368,-0.4472,-9.8,-24.6,-40.4,2.771757385,-0.08,-0.48,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,212095,2015-10-30 10:25:49:228,1446171949228.0 \n-1.3827,-0.1999,10.2376,-0.0935,-0.162,9.8049,-0.1173,0.1674,-0.3445,-8.5,-25,-40.3,2.825862592,0.95,0.55,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,212198,2015-10-30 10:25:49:331,1446171949331.0 \n-0.6859,-0.0587,9.3434,-0.1897,-0.0644,9.8046,0.0183,-0.0819,-0.2773,-7.8,-25.2,-40.4,2.805616773,0.4,1.19,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,212299,2015-10-30 10:25:49:432,1446171949432.0 \n-2.0099,-0.0503,9.1614,-0.3032,-0.1097,9.8013,-0.0562,0.022,-0.1943,-6.7,-25.4,-40.8,2.827607921,0.64,1.77,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,212401,2015-10-30 10:25:49:534,1446171949534.0 \n-1.3396,0.8045,8.9651,-0.311,-0.1425,9.8007,-0.0354,-0.0794,0.0611,-6,-25.6,-40.7,2.874731811,0.87,1.79,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,212504,2015-10-30 10:25:49:637,1446171949637.0 \n-1.3048,1.1863,9.6977,-0.2483,-0.2352,9.8007,-0.1124,-0.1124,0.0965,-5.5,-25.7,-40.5,2.920110372,1.26,1.51,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,212605,2015-10-30 10:25:49:738,1446171949738.0 \n-1.5335,1.0163,10.0868,-0.3019,-0.3165,9.7969,-0.0489,0.0232,0.1197,-5.7,-25.5,-40.3,2.874382745,1.73,1.68,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,212708,2015-10-30 10:25:49:841,1446171949841.0 \n-0.7817,1.7957,8.8693,-0.3524,-0.2231,9.7978,0.1307,0.0098,0.2089,-6.1,-25,-40.6,2.86094371,1.3,2.06,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,212809,2015-10-30 10:25:49:942,1446171949942.0 \n-0.9421,1.136,10.6997,-0.3135,-0.1881,9.7998,0.0379,0.0489,-0.0244,-6.3,-24.8,-40.8,2.866005165,1.11,1.81,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,212911,2015-10-30 10:25:50:044,1446171950044.0 \n-0.1879,0.6859,10.7081,-0.2325,0.0326,9.8038,0.3641,-0.0867,-0.16,-6.6,-24.9,-40.5,2.833891106,0.4,1.48,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,213014,2015-10-30 10:25:50:147,1446171950147.0 \n0.079,0.158,9.3434,-0.1882,0.0693,9.8046,0.1075,0.1588,-0.5217,-6.7,-25.6,-40.1,2.848377339,-0.4,1.1,36.813,-119.74816,274.3,336.2701701,4.36,25.806452,105.81,16 / 16,213115,2015-10-30 10:25:50:248,1446171950248.0 \n0.0108,-0.401,10.0568,-0.2439,0.0579,9.8034,-0.16,-0.0867,-0.5351,-6.3,-26,-40.1,2.87647714,-0.34,1.43,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,213217,2015-10-30 10:25:50:350,1446171950350.0 \n-0.3017,0.9206,7.7117,-0.2392,0.0177,9.8037,0.0904,-0.0709,-0.1552,-5.2,-26.4,-40,2.912081857,0.03,1.55,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,213320,2015-10-30 10:25:50:453,1446171950453.0 \n-0.4202,0.8128,9.2033,-0.0291,0.0501,9.8065,0.0635,-0.1515,-0.0965,-4.5,-26.6,-39.9,2.978404369,-0.16,0.61,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,213422,2015-10-30 10:25:50:555,1446171950555.0 \n-0.316,0.5291,10.6303,-0.025,0.1303,9.8058,0.077,0.0623,0.0012,-4.3,-26.8,-39.5,2.988003679,-0.76,0.15,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,213523,2015-10-30 10:25:50:656,1446171950656.0 \n-0.3627,1.0391,8.2923,-0.1218,0.3027,9.8012,0.496,0.2724,0.2541,-4.4,-27,-39.4,2.990796206,-0.85,0.02,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,213625,2015-10-30 10:25:50:758,1446171950758.0 \n-0.8643,0.0084,9.7145,-0.0412,0.1174,9.8059,0.281,-0.044,0.2162,-4.7,-27.2,-39.2,2.949431903,-0.69,0.24,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,213727,2015-10-30 10:25:50:860,1446171950860.0 \n-0.3938,0.2011,9.153,0.1582,0.2931,9.801,0.16,-0.3018,0.099,-5,-27.6,-39.2,2.977531704,-1.97,-0.87,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,213829,2015-10-30 10:25:50:962,1446171950962.0 \n-0.237,0.6237,9.1554,0.2211,0.2793,9.8002,0.0073,-0.1429,0.1307,-5.4,-27.8,-39,2.983465823,-1.58,-1.04,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,213932,2015-10-30 10:25:51:065,1446171951065.0 \n0.3747,1.2354,8.6012,0.1752,0.487,9.793,0.2395,0,0.1295,-6.3,-28.3,-38.3,2.940356191,-2.85,-1.02,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,214034,2015-10-30 10:25:51:167,1446171951167.0 \n0.1532,1.0558,10.7129,0.3463,0.6493,9.779,0.314,-0.1356,-0.0782,-6.8,-28.4,-37.8,2.924299162,-3.22,-1.95,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,214135,2015-10-30 10:25:51:268,1446171951268.0 \n-0.8009,-0.7051,12.6378,0.4296,0.4015,9.789,-0.755,-0.0538,-0.4899,-7.3,-28.9,-37.3,2.948384705,-2.35,-2.51,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,214237,2015-10-30 10:25:51:370,1446171951370.0 \n0.3005,0.68,7.847,0.2066,0.4806,9.7927,-0.2761,-0.0867,-0.1539,-7.3,-28.9,-37.7,2.916096114,-2.73,-1.16,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,214339,2015-10-30 10:25:51:472,1446171951472.0 \n-0.3268,0.6452,8.1882,0.1768,0.3353,9.7993,0.1417,0.1894,0.0721,-6.8,-28.7,-38.3,2.925695425,-1.82,-1.36,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,214442,2015-10-30 10:25:51:575,1446171951575.0 \n-0.0778,1.1217,7.4448,0.1044,0.4295,9.7967,0.0745,0.0489,0.1539,-6.4,-28.6,-38.4,2.939832592,-2.48,-0.62,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,214543,2015-10-30 10:25:51:676,1446171951676.0 \n-0.1257,-0.1041,12.6725,0.1666,0.182,9.8035,-0.2627,-0.1063,0.3885,-6.5,-28.6,-38.5,2.954493358,-1.06,-0.97,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,214646,2015-10-30 10:25:51:779,1446171951779.0 \n0.0958,-0.4058,10.5465,0.029,-0.0842,9.8062,-0.661,0.2615,0.1503,-6.8,-28.5,-38.4,2.920110372,-0.82,-1.23,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,214747,2015-10-30 10:25:51:880,1446171951880.0 \n-0.5842,0.3843,9.0477,-0.0649,-0.2494,9.8033,-0.1185,0.0147,0.358,-7.5,-27.7,-38.7,2.898468289,1.16,0.21,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,214850,2015-10-30 10:25:51:983,1446171951983.0 \n-0.7159,-0.3723,8.26,0.0462,-0.4255,9.7973,-0.0293,0.1319,0.1173,-8.2,-26.6,-39.1,2.882062194,2.38,-0.6,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,214951,2015-10-30 10:25:52:084,1446171952084.0 \n-0.4345,0.8547,6.602,-0.0412,-0.2103,9.8043,0.2712,-0.0476,0.1979,-8.6,-25.9,-39.7,2.82097567,2.18,0.19,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,215053,2015-10-30 10:25:52:186,1446171952186.0 \n-0.4154,-0.079,11.4814,0.118,-0.0264,9.8059,0.3299,-0.0379,-0.0965,-9.1,-26,-39.5,2.827782454,0.66,-0.61,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,215155,2015-10-30 10:25:52:288,1446171952288.0 \n1.2222,0.0706,10.1933,0.3514,0.215,9.798,0.3433,-0.3946,-0.0073,-9.4,-26.5,-39,2.827258855,-1.03,-1.14,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,215257,2015-10-30 10:25:52:390,1446171952390.0 \n0.7554,0.2945,8.1678,-0.0536,-0.2086,9.8043,-0.0892,0.5058,0.0318,-9.5,-27,-38.6,2.821848335,1.22,0.31,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,215359,2015-10-30 10:25:52:492,1446171952492.0 \n-0.6261,-0.1688,8.7592,-0.1967,-0.4405,9.7948,-0.0745,-0.0648,-0.1576,-8.8,-26.8,-39,2.813296221,2.57,1.15,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,215461,2015-10-30 10:25:52:594,1446171952594.0 \n-0.753,0.6309,7.8685,-0.3455,-0.4983,9.7879,-0.066,0.2896,-0.1258,-8,-26.3,-39.3,2.828655119,3.1,1.59,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,215563,2015-10-30 10:25:52:696,1446171952696.0 \n-0.68,-0.4334,10.726,-0.3023,-0.5043,9.789,-0.0281,0.077,-0.0391,-6.9,-25.6,-39.6,2.855707722,2.95,1.77,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,215665,2015-10-30 10:25:52:798,1446171952798.0 \n-0.3699,-0.2634,11.4575,-0.0805,-0.1849,9.8046,0.4349,-0.3457,0.4655,-6.6,-25.5,-39.5,2.850471734,1.8,1.25,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,215767,2015-10-30 10:25:52:900,1446171952900.0 \n-1.5479,-1.5119,11.9842,0.3116,-0.1146,9.801,-0.2162,-0.5828,0.0709,-7.3,-26.1,-39.2,2.927266221,0.67,-1.82,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,215869,2015-10-30 10:25:53:002,1446171953002.0 \n0.4824,0.5686,8.0912,0.5673,-0.1341,9.7893,0.1576,-0.4117,0.2114,-8.2,-26.3,-39.2,2.911907324,1.08,-2.56,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,215972,2015-10-30 10:25:53:105,1446171953105.0 \n-0.3005,-0.2933,9.6115,0.5131,-0.4112,9.7846,-0.0086,0.0183,0.0452,-9.9,-26.3,-38.9,2.864783434,2.22,-3.19,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,216073,2015-10-30 10:25:53:206,1446171953206.0 \n-0.1353,0.261,7.6195,0.4482,-0.1562,9.7952,0.3983,0.1393,0.0513,-10.4,-26,-39.2,2.847679208,1.25,-2.74,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,216175,2015-10-30 10:25:53:308,1446171953308.0 \n0.4573,-0.3795,10.653,0.244,0.0453,9.8035,0.226,0.4862,-0.0843,-10.2,-26,-38.8,2.831273113,0.09,-2.4,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,216277,2015-10-30 10:25:53:410,1446171953410.0 \n-0.0407,-1.6149,13.1573,0.1155,-0.1132,9.8053,-0.8039,0.0733,-0.799,-9,-26.5,-38.6,2.82935325,0.66,-0.67,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,216379,2015-10-30 10:25:53:512,1446171953512.0 \n-0.0383,-0.5148,8.0098,-0.0266,-0.3616,9.7999,-0.2224,-0.5327,-0.2761,-7.8,-26.4,-38.6,2.84785374,2.49,0.55,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,216482,2015-10-30 10:25:53:615,1446171953615.0 \n0.1149,0.4573,7.1814,0.1791,-0.3675,9.7981,0.1759,0.2248,0.0941,-6.4,-25.9,-38.8,2.955715088,2.51,-1.16,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,216583,2015-10-30 10:25:53:716,1446171953716.0 \n0.0311,0.5052,8.2444,0.1623,-0.3206,9.8001,-0.0305,0.2456,0.0916,-6,-25.5,-38.8,2.948908304,1.85,-1.29,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,216685,2015-10-30 10:25:53:818,1446171953818.0 \n-0.6548,-0.2598,11.1713,-0.5509,-0.6234,9.7713,-0.1613,0.248,0.6695,-5.5,-25.3,-39.1,2.903006145,3.15,2.34,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,216788,2015-10-30 10:25:53:921,1446171953921.0 \n0.5926,0.5076,9.1231,-0.1923,-0.2192,9.8023,0.6487,-0.4362,0.6158,-5.2,-24.9,-39.3,2.902657079,1.97,2.08,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,216889,2015-10-30 10:25:54:022,1446171954022.0 \n-0.1808,0.4106,8.3558,-0.2477,-0.4186,9.7946,0.4142,-0.2248,0.4032,-5.4,-24.2,-40.1,2.904402408,3.21,1.92,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,216991,2015-10-30 10:25:54:124,1446171954124.0 \n-0.7829,-0.2789,8.8645,-0.0101,-0.4562,9.796,-0.1552,0.2896,-0.011,-6.6,-23.8,-40.5,2.886250984,2.41,-0.43,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,217093,2015-10-30 10:25:54:226,1446171954226.0 \n-0.0886,0.9098,7.021,-0.0246,-0.2402,9.8037,0.2468,-0.0379,-0.0819,-7.1,-23.7,-40.4,2.867750494,1.99,0.18,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,217195,2015-10-30 10:25:54:328,1446171954328.0 \n-0.4298,-0.2634,9.9084,0.0649,-0.1321,9.8055,0.0513,-0.1307,-0.1112,-7.5,-24,-40.8,2.874033679,0.77,-0.38,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,217297,2015-10-30 10:25:54:430,1446171954430.0 \n-0.0754,-1.0427,10.7631,0.1026,-0.1852,9.8044,0.1649,0.193,-0.1674,-7.3,-24.4,-40.7,2.882236727,1.08,-0.6,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,217399,2015-10-30 10:25:54:532,1446171954532.0 \n-0.5303,-1.2234,11.3365,-0.1471,-0.3668,9.7987,0.066,0.0538,-0.1258,-6.6,-24.8,-41,2.869844889,1.89,0.47,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,217502,2015-10-30 10:25:54:635,1446171954635.0 \n0.5567,-0.5806,9.2967,-0.0771,-0.2745,9.8025,0.0953,-0.1429,0.0122,-6,-25,-41,2.89672296,1.64,0.75,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,217603,2015-10-30 10:25:54:736,1446171954736.0 \n-0.3855,0.4345,7.8709,-0.1778,-0.1213,9.8043,0.2822,0.1967,0.022,-5.2,-25.5,-41.3,2.932327676,1.21,0.69,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,217705,2015-10-30 10:25:54:838,1446171954838.0 \n-0.4142,0.9266,7.8075,-0.3196,0.1124,9.8008,0.1393,0.1185,0.0379,-4.8,-26.1,-41.3,2.918539575,0.23,1.31,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,217807,2015-10-30 10:25:54:940,1446171954940.0 \n-0.3472,0.3376,11.0145,-0.3158,0.1844,9.7998,0.0342,-0.0354,0.0721,-4.3,-27.2,-40.9,2.938087263,-0.78,2.04,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,217910,2015-10-30 10:25:55:043,1446171955043.0 \n-0.0407,0.7985,8.515,-0.2227,0.3928,9.7962,-0.1564,-0.2211,-0.0574,-4,-28,-40.5,2.951875364,-2.2,1.55,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,218011,2015-10-30 10:25:55:144,1446171955144.0 \n-0.4705,0.5148,8.7688,-0.1303,0.2006,9.8037,0.3873,-0.347,-0.2651,-3.9,-28.6,-40.4,2.972993848,-0.5,1.26,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,218113,2015-10-30 10:25:55:246,1446171955246.0 \n-0.9553,-0.3041,9.3661,0.0147,0.1483,9.8055,0.0525,0.0525,-0.1258,-4.1,-29,-39.9,3.003711643,-0.87,-0.09,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,218215,2015-10-30 10:25:55:348,1446171955348.0 \n-0.9792,0.5555,8.2863,0.002,0.2125,9.8043,0.0648,-0.0562,0.0391,-3.9,-29,-39.9,2.99934832,-1.17,0.05,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,218318,2015-10-30 10:25:55:451,1446171955451.0 \n-0.741,0.5004,10.3274,0.0994,0.2556,9.8028,-0.0195,-0.1038,0.0904,-3.6,-29.4,-39.1,3.010169361,-1.49,-0.45,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,218419,2015-10-30 10:25:55:552,1446171955552.0 \n-0.1784,0.2155,11.0002,0.1827,0.393,9.7971,0.1784,-0.1136,0.0684,-3.6,-29.6,-38.8,3.027797186,-1.78,-1.05,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,218521,2015-10-30 10:25:55:654,1446171955654.0 \n-0.1448,-0.9996,11.6059,0.1488,0.1467,9.8044,-0.6096,0.1454,-0.1918,-3.8,-30.1,-38.1,3.025877324,-0.86,-0.87,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,218623,2015-10-30 10:25:55:756,1446171955756.0 \n0.5686,-0.3005,8.5641,0.1887,0.2386,9.8019,-0.2456,-0.1918,-0.1332,-3.9,-30.3,-37.8,3.01488175,-1.83,-0.51,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,218725,2015-10-30 10:25:55:858,1446171955858.0 \n-0.3017,0.3986,8.4767,0.1017,0.1203,9.8054,-0.0159,0.2505,0.0024,-3.7,-30.2,-37.6,3.027971719,-0.76,-0.95,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,218828,2015-10-30 10:25:55:961,1446171955961.0 \n-0.1544,0.8631,8.0062,-0.0273,0.1266,9.8058,0.0183,0.0635,0.0635,-3.5,-30,-37.3,3.038094629,-0.75,0.11,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,218929,2015-10-30 10:25:56:062,1446171956062.0 \n-0.407,0.0215,9.8916,-0.062,0.1848,9.8047,0.2529,0.0904,0.2688,-3.4,-29.8,-37.1,3.035476635,-0.61,0.24,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,219031,2015-10-30 10:25:56:164,1446171956164.0 \n-0.2466,-0.0431,10.1562,-0.0366,0.4244,9.7974,0.1393,0.0867,0.358,-3.4,-30,-36.6,3.035476635,-2.1,0.08,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,219133,2015-10-30 10:25:56:266,1446171956266.0 \n-0.8954,-0.9385,11.5652,0.0392,0.2869,9.8024,0.1772,0.347,0.2896,-3.9,-30.3,-36.2,3.001268182,-2.4,0.03,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,219235,2015-10-30 10:25:56:368,1446171956368.0 \n-0.7278,-0.8655,9.6091,-0.1075,0.2199,9.8036,-0.259,-0.0171,0.0757,-4.6,-30.5,-36,2.960078411,-1.81,0.47,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,219337,2015-10-30 10:25:56:470,1446171956470.0 \n-0.8511,-0.5064,8.1547,-0.1716,0.1685,9.8037,-0.1002,0.0513,-0.0342,-4.9,-30.2,-36.2,2.95344616,-1.14,0.92,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,219439,2015-10-30 10:25:56:572,1446171956572.0 \n-2.3008,-0.51,9.7815,-0.161,-0.1275,9.8045,-0.1784,-0.0916,0.2138,-5,-29.8,-36.1,2.960078411,0.74,0.94,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,219542,2015-10-30 10:25:56:675,1446171956675.0 \n-3.1723,-0.7769,10.4351,-0.0071,-0.3441,9.8006,-0.1894,-0.2957,0.4239,-5.2,-29.4,-36.5,2.967059728,1.71,0.48,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,219643,2015-10-30 10:25:56:776,1446171956776.0 \n-2.6408,-1.0151,9.9443,0.1706,-0.3505,9.7989,0.1613,-0.3311,1.2474,-6.5,-28.6,-36.7,2.95938028,2.25,-0.61,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,219745,2015-10-30 10:25:56:878,1446171956878.0 \n-1.804,-1.1169,10.6662,0.1998,-0.1946,9.8027,0.4728,-0.0159,1.7178,-8.5,-27.8,-36.8,2.897595624,1.69,-1.17,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,219847,2015-10-30 10:25:56:980,1446171956980.0 \n0.2059,-0.8176,8.4922,0.0703,0.2295,9.8037,0.518,0.1845,1.7556,-13.8,-26.3,-35.8,2.652900463,-0.7,-0.65,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,219949,2015-10-30 10:25:57:082,1446171957082.0 \n0.2227,-0.832,8.7795,-0.0665,0.2721,9.8026,0.2443,0.3164,1.7251,-16.2,-25.3,-35.6,2.557430953,-1.37,-0.07,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,220051,2015-10-30 10:25:57:184,1446171957184.0 \n0.3292,-0.8475,10.0281,-0.357,0.159,9.7989,-0.2224,0.2847,1.6383,-19.7,-22.3,-35.4,2.361081412,-1.3,1.66,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,220153,2015-10-30 10:25:57:286,1446171957286.0 \n1.0295,-0.6572,9.171,-0.5555,0.0399,9.7908,-0.2272,0.2297,1.7678,-23.3,-16.8,-37.3,2.162986542,-0.23,3.25,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,220255,2015-10-30 10:25:57:388,1446171957388.0 \n0.4525,-0.6069,9.0836,-0.5977,0.0609,9.7882,-0.1136,0.1564,1.7397,-23.9,-13.4,-36.4,2.025454597,-0.43,3.34,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,220357,2015-10-30 10:25:57:490,1446171957490.0 \n-0.1437,-0.9254,11.0684,-0.4942,-0.0636,9.794,0.0037,-0.2138,1.4966,-25.4,-9.2,-37.1,1.894205837,0.11,3.25,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,220460,2015-10-30 10:25:57:593,1446171957593.0 \n0.5758,0.4154,9.6594,-0.2222,-0.0482,9.804,-0.0819,0.0574,0.6732,-26.5,-4.9,-36.3,1.754928563,0.08,1.81,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,220561,2015-10-30 10:25:57:694,1446171957694.0 \n0.9337,0.7111,6.7157,-0.2812,-0.0508,9.8025,0.0269,0.1161,0.4472,-26.8,-3.1,-36.5,1.690874979,0.6,1.5,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,220663,2015-10-30 10:25:57:796,1446171957796.0 \n-0.0778,-0.0108,11.5041,-0.3678,-0.3693,9.7928,-0.0611,0.2566,0.2346,-27,-1.3,-36.3,1.643576557,1.69,1.55,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,220766,2015-10-30 10:25:57:899,1446171957899.0 \n0.0204,0.7195,11.1366,-0.4567,-0.4288,9.7866,0.0281,-0.0391,0.1344,-26.7,0.3,-35.9,1.623679803,2.51,2.67,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,220867,2015-10-30 10:25:58:000,1446171958000.0 \n-0.9613,0.723,8.9316,-0.5256,-0.3671,9.7857,-0.033,0.1674,-0.0452,-26.4,0.8,-36.1,1.580919236,2.12,2.81,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,220969,2015-10-30 10:25:58:102,1446171958102.0 \n-0.978,0.8547,8.5138,-0.456,-0.2834,9.7919,0.1026,0.0745,0.0635,-26.2,1.3,-36.2,1.582664566,2.18,2.59,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,221072,2015-10-30 10:25:58:205,1446171958205.0 \n-0.9301,1.3455,9.7013,-0.4438,-0.4009,9.7884,-0.1026,0.0965,0.1429,-26.2,1.4,-36.4,1.583188164,2.2,2.42,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,221174,2015-10-30 10:25:58:307,1446171958307.0 \n-0.4094,1.6221,9.4272,-0.3948,-0.3549,9.7923,-0.0391,-0.1271,0.1173,-26.3,1.8,-36.2,1.547408915,2.23,2.63,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,221275,2015-10-30 10:25:58:408,1446171958408.0 \n-0.1113,0.9996,10.5536,-0.2837,-0.3464,9.7964,0.0183,-0.0208,-0.16,-26.5,2.3,-36.1,1.539729466,1.88,1.74,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,221377,2015-10-30 10:25:58:510,1446171958510.0 \n0.7685,0.7913,9.1686,-0.1967,-0.0963,9.8042,0.7001,-0.1539,-0.066,-27,2.5,-36.2,1.47550135,0.56,1.15,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,221480,2015-10-30 10:25:58:613,1446171958613.0 \n-0.4717,-0.6847,11.1103,-0.1554,0.0162,9.8054,0.3286,-0.0452,-0.2077,-27.3,1.9,-36.3,1.49103478,-0.31,0.73,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,221581,2015-10-30 10:25:58:714,1446171958714.0 \n0.1425,0.2598,8.7807,-0.1087,0.1961,9.8041,0.0379,-0.0171,-0.2162,-27.5,0.5,-36.4,1.502728486,-1.4,0.68,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,221683,2015-10-30 10:25:58:816,1446171958816.0 \n-0.3077,0.583,8.7293,-0.0659,0.1422,9.8054,-0.0721,0.1478,-0.2236,-27.6,-0.3,-36.5,1.549852376,-0.94,0.2,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,221786,2015-10-30 10:25:58:919,1446171958919.0 \n0.0347,1.2941,9.1411,-0.0811,0.1865,9.8045,-0.0195,-0.0134,0.0403,-27.7,-1.2,-36.5,1.582140967,-1.09,0.47,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,221887,2015-10-30 10:25:59:020,1446171959020.0 \n0.1568,0.8452,11.9938,-0.0657,0.2222,9.8039,0.0098,0.0073,0.193,-27.8,-1.4,-36.7,1.577603111,-1.26,0.48,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,221989,2015-10-30 10:25:59:122,1446171959122.0 \n0.6656,-0.4286,10.0329,0.05,0.3017,9.8019,-0.38,-0.1808,0.0305,-27.8,-1.4,-36.8,1.558753555,-2.07,-0.04,36.812996,-119.74806,276.67,336.2701701,2.38,19.35484,69.7,16 / 16,222091,2015-10-30 10:25:59:224,1446171959224.0 \n0.237,1.1181,7.2736,-0.0199,0.3183,9.8015,0.1246,-0.1552,0.1503,-28,-1,-36.8,1.573239788,-1.44,0.22,36.812885,-119.74803,274.64,336.2701701,3.68,19.35484,89.23,16 / 16,222193,2015-10-30 10:25:59:326,1446171959326.0 \n-0.0419,0.2777,8.3139,0.0313,0.2034,9.8045,-0.1735,0.0965,-0.0757,-28.1,-0.6,-36.8,1.578999374,-1.19,-0.18,36.812885,-119.74803,274.64,336.2701701,3.68,19.35484,89.23,16 / 16,222295,2015-10-30 10:25:59:428,1446171959428.0 \n-0.6093,0.723,8.6251,-0.0962,0.1699,9.8047,0.2016,0.1258,0.1026,-28.1,-0.2,-36.8,1.555786495,-0.66,0.36,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,222397,2015-10-30 10:25:59:530,1446171959530.0 \n-0.3053,0.5662,10.2604,-0.0974,0.3328,9.8005,0.1662,-0.1283,-0.0904,-27.9,-0.1,-37.2,1.533446281,-1.67,0.79,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,222500,2015-10-30 10:25:59:633,1446171959633.0 \n0.6081,-0.0958,10.6255,-0.0488,0.5439,9.7914,-0.1393,-0.0183,-0.1674,-27.8,-0.6,-37.2,1.538682269,-2.97,0.39,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,222601,2015-10-30 10:25:59:734,1446171959734.0 \n-0.0072,-0.1856,10.2208,-0.2322,0.4175,9.795,-0.066,0.3042,-0.1185,-27.7,-1,-37,1.556135561,-2.23,1.05,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,222703,2015-10-30 10:25:59:836,1446171959836.0 \n-0.3986,0.0072,9.918,-0.2317,0.2516,9.8007,-0.3983,0.0098,-0.2346,-27.6,-1.4,-37,1.573065255,-1.47,1.35,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,222806,2015-10-30 10:25:59:939,1446171959939.0 \n-0.2215,0.8715,7.8614,-0.3446,0.1265,9.7998,-0.0648,0.0367,-0.1038,-27.4,-1.4,-37.1,1.583188164,-1.03,1.77,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,222907,2015-10-30 10:26:00:040,1446171960040.0 \n-0.1185,0.844,9.7803,-0.3858,0.1139,9.7984,-0.0342,0.0648,-0.0086,-27.3,-1.4,-37.8,1.590169481,-0.7,2.09,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,223009,2015-10-30 10:26:00:142,1446171960142.0 \n-0.3352,0.5878,12.1302,-0.4158,0.2068,9.7956,0.2553,-0.0696,0.2749,-27.3,-1.2,-37.8,1.587202422,-0.82,2.52,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,223111,2015-10-30 10:26:00:244,1446171960244.0 \n-1.6065,-1.0894,13.556,-0.2419,0.3496,9.7974,-0.1747,-0.0464,-0.0024,-27.4,-1.3,-38.2,1.55247037,-2.32,1.52,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,223214,2015-10-30 10:26:00:347,1446171960347.0 \n-0.4621,0.6859,8.3917,-0.0759,0.5149,9.7928,0.2737,-0.2859,0.3299,-27.6,-1.4,-38,1.553517567,-2.31,1.65,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,223315,2015-10-30 10:26:00:448,1446171960448.0 \n-0.6225,0.3208,8.9004,-0.1759,0.2431,9.8021,-0.3482,0.248,-0.11,-28,-1.2,-37.6,1.562418746,-1.88,0.63,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,223417,2015-10-30 10:26:00:550,1446171960550.0 \n-0.0575,1.3827,7.4579,-0.2421,0.3718,9.7966,0.0696,0.0611,-0.1014,-28.3,-1,-37,1.566258471,-1.77,1.1,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,223519,2015-10-30 10:26:00:652,1446171960652.0 \n-0.5435,0.1784,12.0261,-0.1575,0.4958,9.7928,0.3494,-0.0098,-0.1625,-28.5,-1.1,-36.7,1.550201442,-2.5,1.09,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,223621,2015-10-30 10:26:00:754,1446171960754.0 \n1.0259,0.9852,10.5716,-0.1586,0.7549,9.7763,0.2883,-0.1014,-0.0806,-28.7,-1.7,-36.6,1.550550507,-4.09,1.15,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,223723,2015-10-30 10:26:00:856,1446171960856.0 \n-0.0251,0.3112,7.8781,-0.351,0.5286,9.7861,-0.0195,-0.022,-0.1772,-28.9,-2.8,-36.9,1.605702912,-3.09,2.05,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,223825,2015-10-30 10:26:00:958,1446171960958.0 \n-0.5758,0.1341,9.335,-0.253,0.2289,9.8007,-0.0489,-0.0684,0.0281,-29,-3.3,-37.1,1.632231916,-1.82,1.64,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,223927,2015-10-30 10:26:01:060,1446171961060.0 \n-0.8356,0.7003,8.7484,-0.1941,0.1541,9.8035,-0.0721,-0.055,0.0525,-29.1,-3.3,-37.2,1.652303203,-0.9,1.13,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,224029,2015-10-30 10:26:01:162,1446171961162.0 \n-0.668,0.662,9.1518,-0.2331,0.206,9.8017,-0.0904,0.0819,0.1429,-29.4,-3,-37.2,1.643925622,-1.29,1.21,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,224132,2015-10-30 10:26:01:265,1446171961265.0 \n0.4369,0.9996,10.1191,-0.2708,0.3658,9.7961,0.1368,0.1063,0.3946,-29.7,-2.7,-37.4,1.629788456,-1.85,1.47,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,224233,2015-10-30 10:26:01:366,1446171961366.0 \n-1.0439,-1.0235,13.3596,-0.1452,0.131,9.8047,-0.4447,-0.3836,0.0403,-29.9,-2.3,-37.3,1.597150799,-1.87,1.24,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,224336,2015-10-30 10:26:01:469,1446171961469.0 \n-0.2574,-0.0491,9.4308,0.1559,0.1248,9.8046,-0.0941,-0.4704,0.1271,-30.4,-1.5,-37.2,1.5823155,-1.02,-0.36,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,224438,2015-10-30 10:26:01:571,1446171961571.0 \n-0.1987,0.2873,8.114,0.0648,-0.0143,9.8064,-0.044,-0.0489,-0.0428,-30.7,-0.9,-36.6,1.602386786,-0.04,-0.36,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,224540,2015-10-30 10:26:01:673,1446171961673.0 \n-0.4154,0.7973,8.6802,-0.0614,0.1257,9.8057,0.0501,0.0513,-0.1881,-31.1,-0.2,-35.9,1.558753555,-0.6,0.21,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,224641,2015-10-30 10:26:01:774,1446171961774.0 \n-0.3065,0.0766,10.4375,-0.1003,0.2195,9.8037,0.1429,0.0183,-0.193,-31.4,-0.2,-35.9,1.552644903,-0.91,0.44,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,224744,2015-10-30 10:26:01:877,1446171961877.0 \n-0.0874,-1.3192,13.3094,-0.2657,0.0208,9.803,-0.6463,0.3726,-0.3494,-31.4,-0.8,-36.2,1.599768792,-0.12,1.55,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,224845,2015-10-30 10:26:01:978,1446171961978.0 \n0.7446,-0.1784,8.7029,-0.3515,0.0387,9.8003,-0.2248,-0.1295,0.0269,-31.3,-1,-36.7,1.604830247,0.17,2.39,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,224947,2015-10-30 10:26:02:080,1446171962080.0 \n0.0263,0.2526,7.7189,-0.3523,-0.0927,9.7999,-0.0086,0.1002,0.0073,-31.2,-1,-36.9,1.61216063,0.54,2.06,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,225049,2015-10-30 10:26:02:182,1446171962182.0 \n-0.516,0.5842,8.9699,-0.4726,-0.1538,9.794,-0.1063,0.0293,0.0611,-31.1,-0.7,-37.2,1.618269282,0.9,2.76,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,225151,2015-10-30 10:26:02:284,1446171962284.0 \n-0.7925,-0.0491,10.5261,-0.4145,-0.0842,9.7975,0.1967,-0.0391,0.4117,-31.1,-0.4,-37.3,1.58947135,0.97,2.45,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,225253,2015-10-30 10:26:02:386,1446171962386.0 \n-0.152,0.741,9.2225,-0.346,0.2017,9.7985,-0.1454,-0.1246,0.1674,-31.2,0,-37.5,1.558404489,-0.64,1.87,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,225355,2015-10-30 10:26:02:488,1446171962488.0 \n-0.2298,0.2945,8.6311,-0.3176,-0.0191,9.8015,-0.2114,0.1869,0.1991,-31.6,0.8,-37,1.542696526,0.11,1.86,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,225458,2015-10-30 10:26:02:591,1446171962591.0 \n-0.0838,-0.0706,8.752,-0.1065,-0.1042,9.8055,-0.2004,-0.0489,-0.0269,-31.8,1.6,-36.6,1.51250233,0.16,0.86,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,225559,2015-10-30 10:26:02:692,1446171962692.0 \n-0.3891,0.8811,8.3127,-0.1637,-0.0986,9.8048,0.2566,0.1429,-0.022,-32.1,2.6,-36.3,1.49522357,0.87,0.79,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,225661,2015-10-30 10:26:02:794,1446171962794.0 \n-0.5327,0.9948,9.396,-0.2406,0.1573,9.8024,0.1833,0.044,-0.1515,-32.1,2.8,-36.3,1.473232422,-0.35,1.41,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,225764,2015-10-30 10:26:02:897,1446171962897.0 \n-0.5183,0.2334,10.9475,-0.2772,0.3322,9.7971,0.2505,0.1588,-0.1881,-32,2.3,-35.9,1.481435469,-1.53,1.35,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,225866,2015-10-30 10:26:02:999,1446171962999.0 \n-0.7602,-0.6943,11.6693,-0.3317,0.2918,9.7967,-0.3629,0.2505,-0.2358,-31.7,1.3,-36,1.50953527,-1.71,1.94,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,225967,2015-10-30 10:26:03:100,1446171963100.0 \n0.4178,0.2454,8.4695,-0.3578,0.1558,9.7989,0.1026,-0.11,0.0367,-31.5,0.8,-36.2,1.520530844,-1.05,2.45,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,226070,2015-10-30 10:26:03:203,1446171963203.0 \n0.2813,0.6273,7.8721,-0.3214,0.0721,9.8011,0.077,0.0061,-0.1026,-31.2,0.4,-36.3,1.562069681,-0.46,1.98,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,226172,2015-10-30 10:26:03:305,1446171963305.0 \n-0.3172,1.1863,7.7824,-0.4783,0.1349,9.7941,0.1906,0.1442,-0.1356,-31,0.4,-36.4,1.556310094,-0.79,2.8,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,226274,2015-10-30 10:26:03:407,1446171963407.0 \n-1.0618,0.2155,10.5201,-0.4409,0.1762,9.7952,-0.0782,-0.1173,-0.0892,-30.8,0.1,-36.6,1.550550507,-1.09,3.24,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,226375,2015-10-30 10:26:03:508,1446171963508.0 \n1.3276,1.0463,10.653,-0.3037,0.3593,9.7954,0.226,-0.0098,0.303,-30.8,-0.2,-36.9,1.537635071,-1.7,1.84,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,226477,2015-10-30 10:26:03:610,1446171963610.0 \n-0.31,0.9613,8.7628,-0.1033,0.354,9.7997,0.1356,-0.2358,0.2615,-31,-0.4,-36.6,1.533795347,-1.84,0.99,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,226579,2015-10-30 10:26:03:712,1446171963712.0 \n-0.6201,0.0563,8.9328,0.0102,0.2653,9.8031,-0.1112,0.2957,-0.0293,-31.4,-0.3,-36,1.532050017,-1.89,-0.38,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,226681,2015-10-30 10:26:03:814,1446171963814.0 \n-1.2091,1.0594,8.0709,-0.1892,0.223,9.8023,0.0293,0.1454,-0.1246,-31.4,-0.1,-35.8,1.545489053,-1.3,1.11,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,226783,2015-10-30 10:26:03:916,1446171963916.0 \n-1.3862,0.8894,10.4196,-0.3276,0.2764,9.7973,-0.0061,-0.0122,-0.0696,-31.2,-0.1,-35.7,1.538856801,-1.68,1.82,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,226886,2015-10-30 10:26:04:019,1446171964019.0 \n0.1927,0.7614,10.2927,-0.2745,0.4178,9.7939,0.1894,-0.1136,0.16,-30.8,-0.4,-36,1.524021503,-2.44,1.61,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,226987,2015-10-30 10:26:04:120,1446171964120.0 \n-0.5136,-0.9445,12.6079,-0.2138,0.2884,9.8001,-0.4472,0.0293,-0.2016,-30.7,-0.6,-36,1.552644903,-2.55,1.18,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,227089,2015-10-30 10:26:04:222,1446171964222.0 \n-0.4058,-0.0515,9.5122,-0.2115,0.2396,9.8014,-0.3286,-0.0208,-0.1881,-30.8,-0.7,-36,1.56381501,-1.98,1.19,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,227191,2015-10-30 10:26:04:324,1446171964324.0 \n-0.2897,0.4453,9.5241,-0.2943,0.0518,9.8021,-0.0635,0.0745,-0.1527,-30.9,-0.6,-35.9,1.587726021,-0.75,1.67,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,227293,2015-10-30 10:26:04:426,1446171964426.0 \n-0.8571,1.1791,8.2839,-0.587,0.1446,9.788,-0.1381,0.2089,-0.1161,-30.8,-0.4,-36,1.552819435,-0.99,2.94,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,227396,2015-10-30 10:26:04:529,1446171964529.0 \n-0.316,0.3543,11.6837,-0.5917,0.0692,9.7885,-0.0855,-0.0977,0.3103,-30.4,-0.5,-36.5,1.562942345,-0.43,3.88,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,227497,2015-10-30 10:26:04:630,1446171964630.0 \n0.2921,-1.2653,13.1502,-0.2183,-0.0564,9.8041,-0.5986,-0.5767,0.0147,-30.4,-0.2,-36.8,1.558928088,-0.6,2.4,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,227600,2015-10-30 10:26:04:733,1446171964733.0 \n0.2286,0.2143,9.4056,0.0122,-0.1474,9.8055,-0.2065,-0.3494,0.0403,-30.8,0.7,-36.2,1.555961028,0.86,-0.07,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,227701,2015-10-30 10:26:04:834,1446171964834.0 \n-0.1592,-0.146,8.3067,0.0019,-0.3908,9.7989,-0.204,0.292,-0.0452,-31.4,1.6,-35.2,1.53815867,1.62,-0.89,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,227803,2015-10-30 10:26:04:936,1446171964936.0 \n-0.346,0.4202,8.1439,-0.108,-0.3615,9.7994,0.1796,0.2162,0.055,-32,2.6,-34.6,1.522974305,2.4,0.28,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,227905,2015-10-30 10:26:05:038,1446171965038.0 \n0.1161,0.34,10.0952,-0.2203,-0.2462,9.8011,0.2089,0.0635,-0.0721,-32,2.9,-34.5,1.510233402,1.75,1.08,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,228007,2015-10-30 10:26:05:140,1446171965140.0 \n1.3324,0.9565,10.8637,-0.1911,-0.0624,9.8046,0.2016,-0.0831,-0.1466,-31.9,2.7,-34.8,1.485798792,0.36,1.12,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,228109,2015-10-30 10:26:05:242,1446171965242.0 \n-1.0654,-1.0307,11.4263,-0.0382,0.0128,9.8066,-0.0611,-0.4007,-0.3176,-32,2,-34.8,1.50115769,-0.43,0.56,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,228212,2015-10-30 10:26:05:345,1446171965345.0 \n-0.1353,-0.4106,9.5732,0.2509,-0.1141,9.8028,-0.1026,-0.0367,-0.0293,-32.6,0.9,-34.4,1.545139987,0.29,-1.42,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,228313,2015-10-30 10:26:05:446,1446171965446.0 \n-0.6524,0.3615,8.8274,0.1166,-0.229,9.8033,-0.1356,0.0794,-0.0367,-33.3,0.5,-33.6,1.564687674,1.34,-0.68,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,228415,2015-10-30 10:26:05:548,1446171965548.0 \n-0.741,-0.182,10.0736,-0.1507,-0.3482,9.7993,-0.0892,0.3494,0.0134,-33.4,0.6,-33.4,1.572716189,1.85,0.08,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,228518,2015-10-30 10:26:05:651,1446171965651.0 \n0.1856,0.8835,8.8346,-0.4261,-0.0876,9.797,0.4814,0.2138,0.4117,-33,1.4,-34.2,1.564862207,1.4,2.15,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,228620,2015-10-30 10:26:05:753,1446171965753.0 \n-1.245,-1.3408,13.0604,-0.3187,-0.2872,9.7973,-0.0012,-0.1503,0.0586,-32.5,1.9,-34.6,1.526988563,0.91,2.13,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,228721,2015-10-30 10:26:05:854,1446171965854.0 \n-0.0323,-0.31,8.0816,-0.1961,-0.3988,9.7966,-0.1503,-0.0318,-0.0342,-32.2,2.7,-34.8,1.515643922,1.98,1.41,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,228823,2015-10-30 10:26:05:956,1446171965956.0 \n-0.1568,-0.0108,9.341,-0.1792,-0.5836,9.7876,-0.0464,0.0415,0.0171,-32.2,3.2,-34.5,1.539031334,3.36,0.97,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,228925,2015-10-30 10:26:06:058,1446171966058.0 \n-0.4334,0.2897,9.7229,-0.2173,-0.3832,9.7968,0.2126,-0.0391,-0.1796,-32.5,3.7,-33.9,1.488591319,2.24,1.27,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,229028,2015-10-30 10:26:06:161,1446171966161.0 \n-0.4884,-0.3663,11.0516,-0.2819,-0.1749,9.801,0.2309,0.1869,-0.3213,-32.4,3.7,-33.9,1.471661625,1.27,1.4,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,229129,2015-10-30 10:26:06:262,1446171966262.0 \n-0.322,-0.7219,10.6602,-0.7518,-0.1951,9.7758,-0.0428,0.3506,-0.2285,-32,3.1,-34.5,1.497317965,0.92,3.05,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,229231,2015-10-30 10:26:06:364,1446171966364.0 \n-0.8236,-0.1987,7.7345,-0.9227,-0.2066,9.761,-0.0354,-0.0867,-0.1295,-31,2.1,-35.7,1.535366143,1.37,5.37,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,229333,2015-10-30 10:26:06:466,1446171966466.0 \n-0.7374,0.431,7.0689,-0.8032,-0.308,9.7688,-0.0464,-0.1002,0.2505,-30.1,1.7,-36.4,1.541823861,1.8,4.7,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,229436,2015-10-30 10:26:06:569,1446171966569.0 \n-0.6991,0.4393,8.6095,-0.6213,-0.3291,9.7814,-0.0147,-0.2285,0.2162,-29.8,1.9,-36.6,1.546187184,1.97,4.04,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,229538,2015-10-30 10:26:06:671,1446171966671.0 \n-0.255,-0.0802,11.467,-0.5168,-0.268,9.7894,0.1515,-0.0342,0.2517,-29.9,2.7,-36.1,1.506219144,1.57,3.02,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,229639,2015-10-30 10:26:06:772,1446171966772.0 \n0.2083,-1.0427,11.8166,-0.5051,0.0112,9.7936,-0.1649,-0.3323,0.0391,-29.8,3.2,-36,1.47550135,-0.07,2.95,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,229741,2015-10-30 10:26:06:874,1446171966874.0 \n-0.5602,-0.1496,9.0333,-0.373,0.0382,9.7995,0.2578,0.0379,0.3641,-29.7,3.6,-35.8,1.44809968,0.2,2.33,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,229843,2015-10-30 10:26:06:976,1446171966976.0 \n-0.4764,0.0156,8.3306,-0.2829,-0.0884,9.8022,-0.3225,0.0098,-0.0367,-29.5,4,-36,1.448797812,0.52,1.65,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,229945,2015-10-30 10:26:07:078,1446171967078.0 \n-0.9744,0.1568,8.8621,-0.312,-0.2951,9.7972,0.099,0.0586,0.0415,-29.2,4.4,-35.8,1.470439895,1.58,1.69,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,230048,2015-10-30 10:26:07:181,1446171967181.0 \n-0.8248,-0.0299,9.9958,-0.3675,-0.2522,9.7965,-0.0049,0.077,-0.1295,-28.8,4.7,-35.6,1.436405974,1.47,2.15,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,230149,2015-10-30 10:26:07:282,1446171967282.0 \n-1.0151,-0.1544,10.8481,-0.3571,-0.0391,9.8001,0.2908,0.0684,-0.0831,-28.6,4.7,-35.6,1.428028394,1.08,1.95,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,230252,2015-10-30 10:26:07:385,1446171967385.0 \n-0.5782,-0.8452,11.6191,-0.5687,-0.2444,9.7871,0.022,0.0929,-0.0428,-28,4,-36.2,1.458571656,1.06,2.96,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,230353,2015-10-30 10:26:07:486,1446171967486.0 \n-0.3077,-0.3424,9.6163,-0.6011,-0.2629,9.7847,-0.1222,0.0012,-0.066,-27.5,3.5,-36.5,1.465552973,1.54,3.52,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,230456,2015-10-30 10:26:07:589,1446171967589.0 \n-0.9996,0.2693,8.4132,-0.5035,-0.3869,9.7861,-0.0501,-0.0379,-0.022,-27.2,3.2,-36.3,1.511106066,2.11,3.12,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,230557,2015-10-30 10:26:07:690,1446171967690.0 \n-0.2574,0.3879,9.2009,-0.4193,-0.2767,9.7938,0.1393,-0.011,0.1576,-27.1,3.1,-36.1,1.504299282,1.81,2.51,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,230660,2015-10-30 10:26:07:793,1446171967793.0 \n-0.8068,-0.0431,12.2236,-0.4401,-0.0794,9.7964,0.3335,-0.088,0.3335,-27.1,3,-35.6,1.476024948,0.46,2.57,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,230761,2015-10-30 10:26:07:894,1446171967894.0 \n0.2682,-0.2083,11.0756,-0.3123,0.1101,9.8011,0.0733,-0.1637,0.2505,-27,2.7,-35.9,1.444434489,-1,2.28,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,230864,2015-10-30 10:26:07:997,1446171967997.0 \n-0.5698,0.5195,8.4312,-0.2658,0.207,9.8009,0.2028,-0.3103,0.0757,-26.9,2.6,-36.2,1.446528884,-0.87,2.07,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,230966,2015-10-30 10:26:08:099,1446171968099.0 \n-0.6955,0.2538,9.4451,-0.1859,0.0334,9.8048,0.0391,0.0794,-0.0281,-27,2.6,-36.1,1.450019543,-0.56,0.89,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,231068,2015-10-30 10:26:08:201,1446171968201.0 \n-0.3759,1.1097,8.1977,-0.2095,0.0927,9.804,0.1124,-0.022,-0.0391,-27.2,2.6,-36.1,1.454208333,-0.41,1.25,36.812885,-119.74803,274.64,336.3171531,3.68,19.35484,89.23,16 / 16,231170,2015-10-30 10:26:08:303,1446171968303.0 \n-1.0786,0.4645,9.8306,-0.2623,0.1804,9.8015,0.0562,-0.033,-0.3115,-27.3,2.4,-35.9,1.478817475,-0.93,1.4,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,231271,2015-10-30 10:26:08:404,1446171968404.0 \n-0.2227,0.5423,10.7033,-0.3247,0.3671,9.7944,0.2346,0.0305,-0.0733,-27.1,1.4,-36.1,1.496794367,-1.76,1.71,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,231373,2015-10-30 10:26:08:506,1446171968506.0 \n-0.972,-0.5291,11.6801,-0.5098,0.1091,9.7928,0.1552,0.11,-0.1503,-26.9,0.5,-36.3,1.496619834,-1.81,2.07,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,231476,2015-10-30 10:26:08:609,1446171968609.0 \n-0.68,0.0682,9.0453,-0.5149,-0.0715,9.7929,-0.4276,-0.1002,-0.171,-26.6,-0.3,-36.7,1.566607537,-0.2,3.13,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,231577,2015-10-30 10:26:08:710,1446171968710.0 \n-1.257,0.4202,8.7125,-0.4362,-0.1994,9.7949,-0.2089,-0.0452,0.033,-26.4,-0.4,-36.9,1.587726021,0.75,2.63,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,231679,2015-10-30 10:26:08:812,1446171968812.0 \n-0.6309,0.2957,10.3082,-0.389,-0.1759,9.7974,0.0525,0.0611,0.2382,-26.6,-0.1,-36.8,1.593485607,1.03,2.27,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,231781,2015-10-30 10:26:08:914,1446171968914.0 \n-0.4286,0.7458,11.1701,-0.443,0.0454,9.7965,0.1576,-0.0648,0.2871,-26.7,0,-36.2,1.577952177,0.34,2.44,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,231883,2015-10-30 10:26:09:016,1446171969016.0 \n-1.2007,-1.0367,13.6074,-0.3793,-0.0461,9.7992,-0.4435,-0.0904,0.022,-26.7,0.1,-36.1,1.561197016,-0.45,2.38,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,231985,2015-10-30 10:26:09:118,1446171969118.0 \n-0.1556,-0.0263,8.9184,-0.2111,0.0287,9.8043,-0.0379,-0.2688,0.0709,-26.6,0.3,-35.6,1.569574596,-0.06,1.84,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,232087,2015-10-30 10:26:09:220,1446171969220.0 \n-0.0371,0.164,8.2959,-0.1267,-0.0645,9.8056,-0.0586,-0.0024,0.0147,-26.7,0.5,-35.4,1.540253065,0.26,0.82,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,232189,2015-10-30 10:26:09:322,1446171969322.0 \n-0.2981,0.6069,8.5174,-0.1124,-0.0223,9.806,0.1637,0.044,-0.055,-27.1,0.8,-35,1.537111472,0.13,0.66,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,232291,2015-10-30 10:26:09:424,1446171969424.0 \n-0.7937,0.0898,10.7643,-0.1336,0.0844,9.8054,0.1197,0.0024,-0.2248,-27.3,0.7,-34.8,1.527686694,-0.31,0.8,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,232393,2015-10-30 10:26:09:526,1446171969526.0 \n0.4609,0.4992,10.5405,-0.2522,0.1367,9.8025,-0.2419,0.2138,-0.3861,-27.5,0.1,-35.1,1.553343034,-0.8,1.04,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,232495,2015-10-30 10:26:09:628,1446171969628.0 \n-0.0347,0.565,7.8362,-0.4399,-0.0671,9.7966,-0.1112,0.1735,-0.369,-27.3,-0.6,-35,1.613905959,0.39,2.57,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,232597,2015-10-30 10:26:09:730,1446171969730.0 \n-1.2282,-0.1257,9.93,-0.3877,-0.1936,9.7971,-0.1393,-0.1478,-0.2407,-27.2,-1.2,-35.3,1.624727001,0.9,2.43,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,232699,2015-10-30 10:26:09:832,1446171969832.0 \n-0.8631,0.8176,8.4767,-0.3613,-0.1565,9.7987,0.2334,-0.2004,0.1967,-27.1,-1.7,-35.2,1.66050625,0.91,2.11,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,232801,2015-10-30 10:26:09:934,1446171969934.0 \n-0.6321,0.3723,10.2472,-0.3127,-0.0095,9.8017,0.0379,0.0635,0.1258,-27.3,-1.9,-34.8,1.646020018,0.19,1.69,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,232904,2015-10-30 10:26:10:037,1446171970037.0 \n-0.7446,0.5064,9.8222,-0.4409,0.3236,9.7914,0.3445,0.1442,0.3238,-27.3,-2.1,-35,1.615476756,-1.24,2.25,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,233005,2015-10-30 10:26:10:138,1446171970138.0 \n-0.7865,-0.2274,11.3749,-0.4597,0.2493,9.7927,0.0171,0.0244,0.2114,-27.3,-2.2,-35,1.606226511,-1.67,2.49,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,233107,2015-10-30 10:26:10:240,1446171970240.0 \n-0.2705,0.1401,9.8857,-0.1781,0.2039,9.8029,-0.0831,-0.4215,0.1527,-27.2,-2,-35.2,1.61216063,-1.4,1.91,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,233210,2015-10-30 10:26:10:343,1446171970343.0 \n-0.2143,0.3879,10.3908,-0.0913,0.0648,9.806,-0.1833,-0.0391,0.0159,-27.5,-1.7,-34.8,1.627170462,-0.75,0.67,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,233312,2015-10-30 10:26:10:445,1446171970445.0 \n-0.5602,1.2797,7.8243,-0.1831,0.2331,9.8022,0.0623,0.0525,-0.1613,-28,-1.1,-34.4,1.577952177,-1.36,1.07,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,233413,2015-10-30 10:26:10:546,1446171970546.0 \n-0.4645,0.7063,11.4347,-0.191,0.3092,9.7999,0.0929,-0.0464,-0.2309,-28.3,-1,-34.1,1.572367123,-1.64,1.18,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,233515,2015-10-30 10:26:10:648,1446171970648.0 \n0.4788,-0.8966,12.5169,-0.1679,0.2262,9.8026,-0.2248,-0.0806,-0.2602,-28.4,-1.6,-34,1.601339589,-1.92,0.77,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,233617,2015-10-30 10:26:10:750,1446171970750.0 \n0.0527,-0.2646,8.6119,-0.2512,0.2259,9.8008,0.0819,-0.1381,-0.0623,-28.3,-2.3,-33.7,1.613556893,-1.32,1.47,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,233719,2015-10-30 10:26:10:852,1446171970852.0 \n-0.1365,0.1353,8.6874,-0.1566,0.1036,9.8049,-0.0525,0.0464,-0.033,-28.3,-2.7,-33.9,1.658237322,-0.85,0.9,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,233821,2015-10-30 10:26:10:954,1446171970954.0 \n-0.3759,0.759,8.6095,-0.2056,-0.0053,9.8045,-0.1283,0.0696,-0.0757,-28.3,-2.8,-33.7,1.67359622,-0.07,1.13,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,233923,2015-10-30 10:26:11:056,1446171971056.0 \n-0.6309,0.3759,10.2544,-0.2571,-0.0153,9.8033,0.0855,0.0733,0.0599,-28.2,-2.8,-34,1.676039681,0.09,1.5,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,234025,2015-10-30 10:26:11:158,1446171971158.0 \n-0.7913,0.583,11.2587,-0.3045,0.1948,9.8,0.3983,0.1808,0.3494,-28.2,-2.7,-34,1.661727981,-0.62,1.64,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,234128,2015-10-30 10:26:11:261,1446171971261.0 \n-0.5938,0.1317,9.4344,-0.3655,0.3366,9.7941,-0.1674,0.011,0.1808,-28,-2.8,-34.4,1.634675377,-1.96,2.08,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,234230,2015-10-30 10:26:11:363,1446171971363.0 \n-0.595,-0.2933,9.8916,-0.1129,0.2644,9.8024,-0.1295,-0.3213,0.1185,-27.9,-2.6,-34.4,1.638340569,-1.82,1.18,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,234332,2015-10-30 10:26:11:465,1446171971465.0 \n-0.5064,0.2753,9.2308,-0.0593,0.1534,9.8053,-0.066,-0.0672,0.1491,-28.3,-2.2,-34.3,1.618443815,-1.11,0.37,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,234433,2015-10-30 10:26:11:566,1446171971566.0 \n-0.2478,1.0319,8.6886,-0.0611,0.2339,9.8037,0.0428,0.0941,-0.0293,-28.9,-1.4,-34.2,1.577428578,-1.37,0.36,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,234535,2015-10-30 10:26:11:668,1446171971668.0 \n-0.6261,0.1568,11.1845,-0.1106,0.2828,9.8019,-0.0012,-0.0415,-0.1295,-29,-1.2,-34,1.571843524,-1.65,0.65,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,234637,2015-10-30 10:26:11:770,1446171971770.0 \n-0.0934,0.9266,9.4236,-0.1752,0.4469,9.7949,0.0134,-0.2065,-0.0782,-28.8,-1.2,-34.2,1.561197016,-2.2,1.03,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,234740,2015-10-30 10:26:11:873,1446171971873.0 \n-0.2789,-0.3041,10.3848,-0.1471,0.1497,9.8044,0.2236,-0.1698,0.0806,-28.8,-1.6,-34.5,1.609368103,-1.48,0.49,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,234841,2015-10-30 10:26:11:974,1446171971974.0 \n-0.0431,-0.3974,9.9443,0.0341,0.1295,9.8057,-0.2602,-0.1955,-0.0244,-28.9,-1.9,-34.5,1.624377935,-0.76,-0.2,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,234943,2015-10-30 10:26:12:076,1446171972076.0 \n-0.2658,0.3903,8.1654,-0.0081,0.0725,9.8064,-0.0159,0.1087,0.1283,-29.1,-1.8,-34.4,1.629090324,-0.53,-0.31,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,235045,2015-10-30 10:26:12:178,1446171972178.0 \n0.0694,0.1317,10.2173,6.00E-04,-0.0148,9.8066,0.0501,0.1124,0.1991,-29.2,-1.4,-34.1,1.60203772,-0.16,-0.09,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,235147,2015-10-30 10:26:12:280,1446171972280.0 \n-0.0431,0.1508,9.6822,-0.0544,0.19,9.8047,0.2468,0.0819,0.248,-29.2,-1.1,-34.4,1.591740278,-0.66,0.35,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,235249,2015-10-30 10:26:12:382,1446171972382.0 \n-0.4381,-0.9254,10.6566,0.161,0.3739,9.7982,-0.011,-0.121,0.1161,-29.3,-0.7,-34.4,1.559800753,-2.19,-0.94,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,235352,2015-10-30 10:26:12:485,1446171972485.0 \n-0.1784,-0.3855,9.5445,0.1973,0.3845,9.7971,0.1881,-0.1283,0.2639,-29.2,-0.5,-34.1,1.531700952,-1.86,-0.82,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,235454,2015-10-30 10:26:12:587,1446171972587.0 \n-0.1125,-0.6153,10.2975,0.1578,0.3183,9.8002,-0.1613,0.0403,0.0489,-29.4,-0.3,-34.2,1.529082958,-1.95,-1.26,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,235555,2015-10-30 10:26:12:688,1446171972688.0 \n-0.5004,-0.559,9.6115,-0.1167,0.2362,9.8031,-0.1539,0.1625,-0.226,-29.2,0,-34.4,1.543220125,-1.38,0.68,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,235658,2015-10-30 10:26:12:791,1446171972791.0 \n-0.3304,-0.2454,9.7013,-0.1088,0.0195,9.806,-0.2773,-0.1161,-0.3348,-29,0,-34.7,1.557008226,-0.68,0.89,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,235759,2015-10-30 10:26:12:892,1446171972892.0 \n-1.0906,0.0946,8.9352,-0.1192,-0.2654,9.8023,-0.1747,0.0452,-0.0208,-28.8,0,-35,1.596801733,1.26,0.54,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,235862,2015-10-30 10:26:12:995,1446171972995.0 \n-1.0032,-0.0431,10.6446,0.0156,-0.4176,9.7977,-0.1344,-0.2944,0.1698,-28.9,0,-35.1,1.619840079,2.36,0.26,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,235963,2015-10-30 10:26:13:096,1446171973096.0 \n-1.7322,-0.3879,11.0181,-0.0543,-0.4535,9.796,-0.0611,-0.0782,0.5437,-29.1,0.6,-34.5,1.590169481,2.65,0.32,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,236066,2015-10-30 10:26:13:199,1446171973199.0 \n-1.1732,0.2239,8.4803,-0.212,-0.3579,9.7978,-0.0953,0.336,1.0531,-29,1.5,-34.5,1.550899573,2.41,0.51,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,236167,2015-10-30 10:26:13:300,1446171973300.0 \n-1.0977,-0.5471,9.3841,-0.53,-0.3069,9.7875,0.0929,0.1283,1.4759,-28.2,3.9,-34.3,1.47253429,1.89,2.88,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,236270,2015-10-30 10:26:13:403,1446171973403.0 \n-0.5327,-0.8811,9.3769,-0.5161,-0.2461,9.79,0.0257,-0.0819,2.1319,-26.2,7.8,-35.2,1.322959573,1.63,3.08,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,236371,2015-10-30 10:26:13:504,1446171973504.0 \n-0.8643,-1.8818,8.5126,-0.4892,-0.0756,9.7942,-0.0159,0.1698,2.4117,-22.6,14.6,-35.6,1.034282115,0.44,2.86,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,236474,2015-10-30 10:26:13:607,1446171973607.0 \n0.1006,-0.5555,8.7568,-0.7223,0.0144,9.78,0.1686,-0.0269,2.2407,-15.3,20.2,-35.7,0.720646448,-0.08,4.22,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,236575,2015-10-30 10:26:13:708,1446171973708.0 \n-0.328,-0.9098,10.4172,-0.7994,0.1213,9.7733,-0.1576,0.3555,1.7006,-10.8,22.5,-35.8,0.523947841,-0.76,4.12,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,236677,2015-10-30 10:26:13:810,1446171973810.0 \n0.6835,0.4393,8.3294,-1.3141,0.1965,9.7162,-0.0391,0.4191,1.1496,-4.7,23.6,-36.7,0.367915406,-0.98,7.03,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,236779,2015-10-30 10:26:13:912,1446171973912.0 \n1.9896,-0.0431,8.9507,-1.3445,0.1296,9.7132,-0.5449,-0.2517,0.2712,-2.7,24.3,-34.7,0.319046187,-0.79,8.4,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,236881,2015-10-30 10:26:14:014,1446171974014.0 \n0.0778,1.1193,6.8319,-1.4396,-0.0461,9.7003,0.1258,0.171,0.6096,-1.5,24.9,-35.1,0.241902634,0.27,8.44,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,236983,2015-10-30 10:26:14:116,1446171974116.0 \n-0.9002,0.0467,11.2109,-1.0247,-0.262,9.7494,-0.3225,-0.3665,0.2798,0,25.4,-34.6,0.180292512,0.21,7.44,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,237085,2015-10-30 10:26:14:218,1446171974218.0 \n-0.7673,1.4485,9.9826,-0.8744,-0.3455,9.7615,-0.0709,-0.3079,0.2272,0.9,26.2,-34,0.097040306,1.97,5.76,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,237187,2015-10-30 10:26:14:320,1446171974320.0 \n-0.5722,1.4305,11.4479,-0.797,-0.4959,9.7616,-0.2627,-0.0195,0.0721,1.2,26.5,-33.7,0.071034901,2.07,4.78,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,237290,2015-10-30 10:26:14:423,1446171974423.0 \n-0.9888,1.075,8.9663,-0.9452,-0.3188,9.7558,0.3213,0.1943,0.2089,1.5,27,-33.1,0.038571776,2.53,5.18,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,237391,2015-10-30 10:26:14:524,1446171974524.0 \n-0.8308,1.1037,8.6431,-0.9857,0.0222,9.757,0.2468,0.0244,0.2236,2.1,26.9,-33.4,0.049043752,-0.13,5.77,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,237493,2015-10-30 10:26:14:626,1446171974626.0 \n-0.9146,0.5866,9.6905,-0.9647,0.154,9.7579,0.0391,-0.0037,0.0721,2.6,26.6,-33.6,0.012391838,-0.78,5.61,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,237595,2015-10-30 10:26:14:728,1446171974728.0 \n-0.7386,-0.1879,9.6211,-0.7527,0.1604,9.7764,-0.0049,-0.2712,-0.1087,3,25.9,-34.2,6.278298385,-0.68,4.83,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,237697,2015-10-30 10:26:14:830,1446171974830.0 \n-0.5375,-0.6141,12.2775,-0.6875,-0.0989,9.782,-0.3824,0.248,-0.3274,2.8,25.8,-34.3,6.252118446,-0.31,3.67,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,237799,2015-10-30 10:26:14:932,1446171974932.0 \n-0.8009,-0.249,10.1754,-0.7176,-0.026,9.7803,-0.2053,-0.0599,-0.2798,1.9,26.1,-34.3,0.019024089,0.15,4.2,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,237901,2015-10-30 10:26:15:034,1446171975034.0 \n-0.3089,0.4058,8.3761,-0.7083,-0.1199,9.7803,0.0342,0.0464,-0.1148,1.3,26.3,-34.2,0.052359878,0.64,3.95,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,238004,2015-10-30 10:26:15:137,1446171975137.0 \n0.1796,1.3898,8.5497,-0.735,-0.1056,9.7785,0.0281,0.044,-0.0037,0.6,26.7,-34.1,0.056723201,0.67,4.23,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,238105,2015-10-30 10:26:15:238,1446171975238.0 \n-0.753,0.7889,10.3238,-0.8004,-0.0618,9.7737,0.2053,-0.0037,0.1161,0.5,26.7,-34.2,0.065449847,0.65,4.62,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,238207,2015-10-30 10:26:15:340,1446171975340.0 \n0.1245,0.3663,10.9678,-0.7732,0.2965,9.7716,0.452,0.1063,0.3629,0.7,26.3,-34.3,0.070336769,-1.45,4.87,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,238310,2015-10-30 10:26:15:443,1446171975443.0 \n-0.4908,0.3508,9.104,-0.7207,0.3963,9.7721,0.3702,0,0.3751,0.9,25.8,-34.8,0.057421332,-1.54,4.17,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,238411,2015-10-30 10:26:15:544,1446171975544.0 \n-0.5531,0.0467,9.0309,-0.5954,0.5008,9.7757,-0.077,0.0501,0.088,1.2,25.2,-35,0.043807764,-2.97,3.56,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,238513,2015-10-30 10:26:15:646,1446171975646.0 \n-0.6488,0.6476,8.2791,-0.6706,0.5218,9.7698,0.1869,0.1332,-0.0061,1.6,24.6,-35.1,0.011868239,-2.82,3.79,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,238616,2015-10-30 10:26:15:749,1446171975749.0 \n-0.7757,0.8894,8.6814,-0.7305,0.6239,9.7595,0.0672,-0.0098,-0.0929,1.9,24.2,-35.2,0.023561945,-3.65,4.28,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,238717,2015-10-30 10:26:15:850,1446171975850.0 \n-0.6189,0.3005,10.9283,-0.6082,0.6082,9.7689,0.0257,-0.1258,-0.0757,1.7,24,-35.2,0.006806784,-3.56,3.56,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,238819,2015-10-30 10:26:15:952,1446171975952.0 \n-0.7889,-1.0355,12.706,-0.5325,0.2291,9.7895,-0.6842,0.2187,-0.4191,1.2,23.9,-35.5,0.027750735,-2.65,2.8,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,238922,2015-10-30 10:26:16:055,1446171976055.0 \n-0.2286,0.0994,9.0381,-0.6086,0.0603,9.7876,0.0709,0.0648,0.0073,0.6,24.3,-34.8,0.048520153,-0.35,3.56,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,239024,2015-10-30 10:26:16:157,1446171976157.0 \n-0.1161,0.6692,8.1642,-0.5617,-0.0341,9.7905,0.0403,0.0232,0.0819,0.3,24.7,-34.1,0.077841685,0.28,3.27,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,239126,2015-10-30 10:26:16:259,1446171976259.0 \n-0.1077,0.7135,9.5589,-0.5307,0.1303,9.7914,0.2505,0.0648,0.0965,0.1,25.1,-33.5,0.072082098,-0.12,3.14,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,239227,2015-10-30 10:26:16:360,1446171976360.0 \n-0.4501,0.1748,10.4375,-0.6378,0.4169,9.777,0.3482,0.1857,0.1637,0,24.8,-33.8,0.079237948,-1.77,3.49,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,239329,2015-10-30 10:26:16:462,1446171976462.0 \n0.334,0.8739,9.4643,-0.7158,0.9044,9.7386,0.3433,0.0672,0.2993,0.5,23.7,-34.5,0.06143559,-4.97,4.47,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,239432,2015-10-30 10:26:16:565,1446171976565.0 \n-0.8535,0.0359,9.997,-0.6626,0.8077,9.7508,0.0843,-0.2688,0.11,1.4,22.4,-35.1,0.055326937,-4.72,3.89,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,239533,2015-10-30 10:26:16:666,1446171976666.0 \n-0.6488,0.0156,8.9651,-0.5113,0.7992,9.7606,-0.1258,0.0525,-0.055,1.6,21.7,-35.3,6.276727589,-4.98,3.01,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,239635,2015-10-30 10:26:16:768,1446171976768.0 \n-1.069,0.9589,8.1247,-0.585,0.8287,9.7541,0.0965,0.0819,-0.0941,1.5,21.4,-35.2,0.00418879,-4.85,3.43,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,239737,2015-10-30 10:26:16:870,1446171976870.0 \n-0.8655,1.1181,9.2883,-0.6279,0.9868,9.7366,0.1356,-0.0501,-0.0709,1.4,21.1,-35.4,0.051138147,-5.49,3.67,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,239839,2015-10-30 10:26:16:972,1446171976972.0 \n0.0587,1.0499,10.173,-0.6883,1.2091,9.7075,0.2468,0.0648,-0.1051,1.2,20.4,-35.7,0.055152404,-6.68,3.71,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,239942,2015-10-30 10:26:17:075,1446171977075.0 \n-0.6273,0.2478,10.5129,-0.8571,1.1258,9.704,-0.2676,0.3348,-0.4203,1.1,19.8,-35.8,0.072605697,-7.16,4.41,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,240044,2015-10-30 10:26:17:177,1446171977177.0 \n-0.7781,0.4513,9.0812,-0.9496,0.9379,9.7154,-0.2737,0.0183,-0.2285,1,19.5,-35.6,0.103323492,-5.9,5.48,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,240146,2015-10-30 10:26:17:279,1446171977279.0 \n-0.6093,1.0942,8.0553,-0.9737,0.7079,9.7325,-0.0672,0.0305,0.0428,0.8,19.6,-35.1,0.106116019,-4.7,5.61,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,240247,2015-10-30 10:26:17:380,1446171977380.0 \n-0.5794,1.4533,8.8837,-0.951,0.7111,9.7345,0.0415,-0.022,0.1344,0.7,19.9,-34.8,0.106465084,-4.1,5.56,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,240349,2015-10-30 10:26:17:482,1446171977482.0 \n-1.0451,0.7733,10.4064,-1.011,0.7281,9.7272,0.0977,0.1185,0.1857,0.6,20,-34.7,0.11100294,-4.13,5.74,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,240451,2015-10-30 10:26:17:584,1446171977584.0 \n-0.8416,0.1365,10.0149,-0.9701,0.8315,9.7231,-0.3372,-0.1955,0.0244,0.8,19.6,-34.8,0.107861348,-4.86,5.7,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,240553,2015-10-30 10:26:17:686,1446171977686.0 \n-0.7254,0.6141,9.5648,-0.7609,0.5672,9.7606,-0.0953,-0.3824,0.2505,1.1,19.3,-34.6,0.09843657,-3.28,5.03,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,240656,2015-10-30 10:26:17:789,1446171977789.0 \n-0.5758,0.2562,9.068,-0.5309,0.4611,9.7814,-0.1136,-0.1772,0.2089,1.2,19.3,-34.5,0.048869219,-3.02,3.4,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,240758,2015-10-30 10:26:17:891,1446171977891.0 \n-0.9613,0.7039,8.831,-0.5183,0.4873,9.7808,0.1356,0.0611,0.2285,1.4,19.3,-34.6,0.04118977,-2.85,3.03,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,240859,2015-10-30 10:26:17:992,1446171977992.0 \n-0.6357,1.1732,9.2596,-0.5598,0.5257,9.7765,0.0648,0.0147,0.0696,1.4,19.1,-34.7,0.0429351,-3.02,3.1,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,240961,2015-10-30 10:26:18:094,1446171978094.0 \n-0.2813,0.7673,9.7576,-0.5525,0.6503,9.7695,0.0965,-0.1002,-0.0696,1.6,18.7,-35.1,6.278647451,-3.39,3.12,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,241063,2015-10-30 10:26:18:196,1446171978196.0 \n-0.2286,-0.5638,11.6023,-0.5715,0.3501,9.7837,-0.7013,0.1429,-0.507,1.7,18.4,-35.4,6.277425721,-3.25,3.08,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,241165,2015-10-30 10:26:18:298,1446171978298.0 \n-0.0611,0.2263,7.7919,-0.6423,0.0935,9.7851,-0.4362,-0.0721,-0.2199,1.5,18.5,-35.1,0.015882496,-1.24,3.78,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,241268,2015-10-30 10:26:18:401,1446171978401.0 \n-0.7063,0.3065,8.272,-0.7002,-0.1976,9.7796,-0.2615,0.11,-0.0794,1.1,19.1,-34.9,0.078714349,0.87,4.02,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,241369,2015-10-30 10:26:18:502,1446171978502.0 \n-0.255,0.9062,8.8418,-0.6945,-0.2792,9.778,-0.0977,-0.0073,0.0806,0.9,19.7,-34.5,0.073303829,1.49,4.05,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,241471,2015-10-30 10:26:18:604,1446171978604.0 \n-0.7171,0.0898,12.0033,-0.6667,-0.1902,9.7821,0.2492,0.0159,0.0929,0.9,19.8,-34.5,0.067195176,1.46,3.85,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,241574,2015-10-30 10:26:18:707,1446171978707.0 \n0.1197,-0.006,10.3956,-0.652,0.0459,9.7848,0.2773,-0.0183,0.1319,0.9,19.5,-34.5,0.063355452,-0.22,3.84,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,241675,2015-10-30 10:26:18:808,1446171978808.0 \n-0.9744,-0.067,8.4635,-0.5877,0.0411,9.7889,0.1173,-0.1833,0.0916,0.8,19,-34.7,0.073303829,-0.15,3.93,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,241778,2015-10-30 10:26:18:911,1446171978911.0 \n-0.8727,-0.4322,9.1997,-0.3733,-0.0865,9.7992,-0.16,-0.1332,0.0257,0.6,18.2,-35.1,0.018849556,0.51,2.18,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,241879,2015-10-30 10:26:19:012,1446171979012.0 \n-0.595,0.4657,8.6263,-0.3344,-0.0693,9.8007,0.2431,0.0415,0.0806,0.3,17.9,-35.1,0.066322512,0.66,1.91,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,241981,2015-10-30 10:26:19:114,1446171979114.0 \n-0.2586,0.1018,10.5082,-0.3328,0.191,9.7991,0.1491,-0.0391,-0.1112,0.1,17.2,-35.4,0.071383966,-0.75,2.05,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,242083,2015-10-30 10:26:19:216,1446171979216.0 \n0.0024,0.3472,10.4698,-0.2681,0.3827,9.7955,0.2566,-0.1332,-0.2443,0,16.7,-35.6,0.058643063,-1.93,1.7,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,242185,2015-10-30 10:26:19:318,1446171979318.0 \n-0.0192,-0.4262,9.9264,-0.3557,0.1761,9.7986,0.0024,-0.0623,0.0415,-0.6,15.7,-36.1,0.115191731,-1.5,1.53,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,242287,2015-10-30 10:26:19:420,1446171979420.0 \n0.1448,-0.4561,10.1191,-0.2589,0.0867,9.8029,-0.1662,-0.0635,-0.0073,-0.9,15.3,-36.2,0.132819556,-0.86,1.71,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,242389,2015-10-30 10:26:19:522,1446171979522.0 \n-0.1137,0.7949,8.1487,-0.3087,0.0761,9.8015,0.1185,0.1222,0.022,-1.2,15.2,-36.1,0.138753676,-0.44,1.8,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,242491,2015-10-30 10:26:19:624,1446171979624.0 \n-0.1616,1.0295,8.5078,-0.4292,0.1745,9.7957,0.0977,0.1148,-0.0354,-1.1,15,-35.8,0.148003921,-0.71,2.08,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,242593,2015-10-30 10:26:19:726,1446171979726.0 \n-0.7494,0.1772,12.0201,-0.4663,0.2376,9.7927,0.022,0.0061,0.0428,-1,14.8,-35.6,0.174009326,-1.12,2.8,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,242695,2015-10-30 10:26:19:828,1446171979828.0 \n-1.3898,-0.9529,12.3744,-0.4087,0.43,9.7887,-0.3225,-0.2566,-0.0024,-0.6,14,-35,0.157254166,-2.51,2.39,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,242797,2015-10-30 10:26:19:930,1446171979930.0 \n-0.8176,-0.2334,9.6582,-0.2647,0.2482,9.7999,-0.1772,-0.2004,0.0684,-0.4,13.6,-35,0.074874625,-1.78,1.85,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,242899,2015-10-30 10:26:20:032,1446171980032.0 \n-0.8164,0.2705,8.6359,-0.3178,0.0369,9.8014,-0.0244,0.0562,0.1038,-0.3,13.4,-35,0.086219265,-0.22,1.86,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,243001,2015-10-30 10:26:20:134,1446171980134.0 \n-0.2957,1.0187,8.023,-0.3339,0.1611,9.7996,0.1784,0.0281,0.1344,-0.3,13.5,-34.8,0.082379541,-0.38,1.93,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,243103,2015-10-30 10:26:20:236,1446171980236.0 \n-0.6572,0.5842,10.6674,-0.3045,0.3419,9.796,0.2309,-0.0892,-0.0794,-0.3,13.7,-34.8,0.080459679,-1.45,1.96,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,16 / 16,243206,2015-10-30 10:26:20:339,1446171980339.0 \n-0.6129,1.0044,9.8342,-0.3201,0.5176,9.7877,-0.0208,-0.2309,-0.2932,-0.3,13.5,-34.9,0.074176493,-2.78,1.91,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,15 / 16,243308,2015-10-30 10:26:20:441,1446171980441.0 \n-0.0251,0.1353,9.7061,-0.4263,0.2475,9.7943,-0.3897,0.4459,-0.3677,-0.7,13.2,-35.3,0.179768913,-1.45,2.49,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,15 / 16,243409,2015-10-30 10:26:20:542,1446171980542.0 \n-0.3675,-0.3555,10.4423,-0.6003,0.2267,9.7856,-0.3372,0.2309,-0.1808,-0.7,13.1,-35.4,0.209090444,-1.79,3.26,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,15 / 16,243511,2015-10-30 10:26:20:644,1446171980644.0 \n-0.5171,0.9158,7.8135,-0.7681,0.2614,9.773,-0.022,-0.0342,-0.0574,-0.5,13.2,-35.2,0.194429679,-1.53,4.49,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,15 / 16,243613,2015-10-30 10:26:20:746,1446171980746.0 \n-0.1018,1.1995,8.6538,-0.6883,0.2689,9.7788,0.0305,-0.099,0.0428,-0.3,13.2,-35.1,0.174358392,-1.57,4.03,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,15 / 16,243715,2015-10-30 10:26:20:848,1446171980848.0 \n-0.5531,0.4848,12.8497,-0.4197,0.3447,9.7916,0.1356,-0.3079,0.1515,-0.6,13.2,-35,0.18797196,-1.47,2.69,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,15 / 16,243817,2015-10-30 10:26:20:950,1446171980950.0 \n-1.6424,-1.3096,13.3465,-0.2279,0.3115,9.799,-0.4203,-0.2187,-0.0696,-1.2,13,-35.1,0.14974925,-2.71,1.98,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,15 / 16,243919,2015-10-30 10:26:21:052,1446171981052.0 \n-0.3364,0.4705,8.3881,-0.1458,0.4212,9.7965,-0.1564,-0.0855,0.0061,-1.5,12.8,-35.1,0.120951317,-2.35,1.23,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,15 / 16,244021,2015-10-30 10:26:21:154,1446171981154.0 \n-1.0092,0.4034,8.7197,-0.1702,0.2943,9.8008,-0.1112,0.0733,-0.0281,-1.7,12.8,-35,0.183608637,-1.72,0.99,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,15 / 16,244123,2015-10-30 10:26:21:256,1446171981256.0 \n-0.486,1.3276,7.75,-0.2009,0.321,9.7993,0.1258,0.0037,0.0684,-1.6,12.8,-35.1,0.191113553,-1.66,1.17,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,1116,244225,2015-10-30 10:26:21:358,1446171981358.0 \n-0.4453,0.6704,10.8733,-0.0623,0.3595,9.7999,0.0684,-0.2786,-0.0599,-1.3,12.9,-35,0.114493599,-1.98,1.04,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,1116,244327,2015-10-30 10:26:21:460,1446171981460.0 \n0.0682,-1.7729,14.285,0.1012,0.3145,9.8011,-0.0464,-0.2016,-0.1662,-1,12.7,-35.3,0.062831853,-2.59,-0.14,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,1116,244429,2015-10-30 10:26:21:562,1446171981562.0 \n0.6716,0.4633,7.914,-0.1717,0.2464,9.8021,0.4691,0.0244,0.2712,-0.9,12.7,-35.2,0.110130276,-0.6,0.78,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,1116,244531,2015-10-30 10:26:21:664,1446171981664.0 \n-0.1652,0.2167,8.0756,-0.0707,0.1546,9.8052,-0.0195,0.1038,-0.022,-0.8,12.9,-35.4,0.096516708,-0.95,0.52,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,1116,244634,2015-10-30 10:26:21:767,1446171981767.0 \n-0.5088,0.4729,7.829,-0.1555,0.0947,9.805,-0.0452,0.0721,0.0244,-0.5,13.3,-35.1,0.112922803,-0.55,0.84,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,1116,244735,2015-10-30 10:26:21:868,1446171981868.0 \n0.158,0.8643,9.256,-0.1936,0.0589,9.8046,-0.0098,0.0904,0.1271,-0.3,13.2,-35.3,0.052185345,-0.34,1.13,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,1116,244838,2015-10-30 10:26:21:971,1446171981971.0 \n-0.1065,0.4286,8.6335,-0.1943,0.14,9.8037,0.5095,0.1014,0.2749,0,13.5,-35.2,0.047822022,-0.82,1.14,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,1116,244940,2015-10-30 10:26:22:073,1446171982073.0 \n-1.057,-0.8859,10.9499,0.0647,0.2599,9.803,0.088,-0.0257,0.2615,0.1,13.4,-35.4,6.266430146,-1.4,-0.38,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,1116,245042,2015-10-30 10:26:22:175,1446171982175.0 \n-0.1448,-0.4238,10.3525,0.2356,0.1944,9.8019,-0.1747,-0.2627,-0.0293,0,13.2,-35.7,6.220178921,-1.14,-1.38,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,1116,245144,2015-10-30 10:26:22:277,1446171982277.0 \n-0.2693,0.7386,8.108,0.107,0.1389,9.8051,0.1381,0.1344,0.1063,0,13.1,-35.7,6.228556502,-0.45,-1.15,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,245245,2015-10-30 10:26:22:378,1446171982378.0 \n-0.2035,1.0738,8.8466,0.0463,0.1814,9.8049,0.0354,0.0648,-0.0574,0.1,13.3,-36.1,6.266430146,-1.02,-0.36,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,245347,2015-10-30 10:26:22:480,1446171982480.0 \n-0.1592,0.3627,11.5329,0.0475,0.186,9.8048,-0.0599,-0.0562,-0.1991,0.2,13.5,-36.1,6.274807727,-1.16,-0.19,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,245449,2015-10-30 10:26:22:582,1446171982582.0 \n-0.2215,-1.1492,13.2866,-0.0328,0.0311,9.8065,-0.5253,0.0709,-0.4875,0.3,13.8,-36.2,6.274458661,-1.1,-0.21,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,245551,2015-10-30 10:26:22:684,1446171982684.0 \n0.2753,-0.0251,8.1726,-0.1638,0.0889,9.8049,-0.121,-0.0831,-0.1319,0.4,14.1,-36.1,0.045902159,-0.32,1.04,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,245653,2015-10-30 10:26:22:786,1446171982786.0 \n-0.1413,0.3783,7.9631,-0.2275,-0.0631,9.8038,-0.0586,0.1075,-0.0757,0.2,14.8,-35.9,0.041713369,0.28,0.98,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,245755,2015-10-30 10:26:22:888,1446171982888.0 \n-0.5363,0.7398,8.5054,-0.2594,-0.1018,9.8027,0.0281,-0.0574,0.0696,0.3,15.3,-35.7,0.070685835,0.65,1.64,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,245857,2015-10-30 10:26:22:990,1446171982990.0 \n-0.3867,0.3244,10.0066,-0.3075,-0.0223,9.8018,0.1234,0.0354,0.1747,0.5,15.7,-35.8,0.00122173,0.47,1.62,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,245960,2015-10-30 10:26:23:093,1446171983093.0 \n0.8404,-0.2897,11.0337,-0.2659,0.2286,9.8004,-0.2651,-0.3262,0.0819,0.9,15.9,-35.9,0.00837758,-0.65,1.81,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,246061,2015-10-30 10:26:23:194,1446171983194.0 \n-0.2753,0.2298,8.6886,-0.1793,0.1577,9.8037,0.1955,0.0073,0.3421,1.1,16.1,-36.5,6.262590422,-0.92,1.05,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,246163,2015-10-30 10:26:23:296,1446171983296.0 \n-0.1377,-0.0766,9.3673,0.0468,0.1532,9.8053,-0.2162,-0.0867,0.0428,1.3,16,-37,6.222796915,-1.23,-0.02,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,246266,2015-10-30 10:26:23:399,1446171983399.0 \n-0.5638,0.7757,8.3941,-0.002,0.0788,9.8058,0.1918,0.1185,0.033,1.4,16.1,-37.5,6.222447849,-0.46,0.01,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,246368,2015-10-30 10:26:23:501,1446171983501.0 \n-0.267,1.2414,8.9352,-0.0529,0.2589,9.8031,0.1148,-0.0379,-0.0134,1.5,16.3,-37.6,6.179861815,-1.31,0.38,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,246469,2015-10-30 10:26:23:602,1446171983602.0 \n-0.5124,0.5411,11.2575,-8.00E-04,0.3736,9.7995,0.1747,0.1026,-0.1527,1.6,16.4,-38,6.165899181,-1.91,-0.05,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,246572,2015-10-30 10:26:23:705,1446171983705.0 \n-0.7661,-0.9313,12.3026,-0.1766,0.1279,9.8042,-0.1515,0.3519,-0.1881,1.6,16.5,-38.2,6.185795935,-1.25,0.39,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,246675,2015-10-30 10:26:23:808,1446171983808.0 \n0.4932,-0.0527,8.4144,-0.2049,0.2164,9.8021,0.1515,0.011,0.0086,1.6,16.7,-38.4,6.220004388,-1.4,1.3,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,246775,2015-10-30 10:26:23:908,1446171983908.0 \n-0.3711,0.8631,7.5645,-0.2345,0.1908,9.802,0.0232,0.1026,-0.0293,1.6,17.1,-38.1,6.215117466,-1.07,1.2,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,246877,2015-10-30 10:26:24:010,1446171984010.0 \n-0.2059,1.0834,9.2979,-0.22,0.1884,9.8024,-0.0073,-0.0098,0.0635,1.9,17.3,-38.2,6.218608125,-1.1,1.29,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,246979,2015-10-30 10:26:24:112,1446171984112.0 \n-0.3448,0.5782,11.0277,-0.3056,0.2702,9.7982,0.1772,0.0733,0.2236,2,17.3,-38.3,6.232221693,-1.37,1.64,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,247081,2015-10-30 10:26:24:214,1446171984214.0 \n-0.0958,-0.2598,10.9391,-0.3908,0.5441,9.7837,0.3396,0.1478,0.2615,2.5,17.1,-39,6.208136149,-3.18,2.29,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,247183,2015-10-30 10:26:24:316,1446171984316.0 \n-0.2957,0.6189,8.8262,-0.2347,0.4039,9.7955,0.0147,-0.3787,0.3067,2.8,16.8,-39.2,6.189810192,-2.36,1.85,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,247286,2015-10-30 10:26:24:419,1446171984419.0 \n0.2095,0.3029,8.8741,0.0215,0.1509,9.8055,-0.4093,0.099,-0.1466,3,16.8,-39.3,6.114411969,-1.54,-0.11,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,247387,2015-10-30 10:26:24:520,1446171984520.0 \n-0.5375,0.9397,8.5832,-0.0442,0.0187,9.8065,0,0.0073,-0.0929,2.9,17.4,-39.1,6.116680897,-0.02,0.21,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,247489,2015-10-30 10:26:24:622,1446171984622.0 \n-0.5255,0.8236,9.262,-0.0787,0.1441,9.8053,0.1894,-0.0171,-0.1087,2.5,17.7,-38.8,6.136752183,-0.49,0.44,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,247591,2015-10-30 10:26:24:724,1446171984724.0 \n0.3531,0.4082,10.1203,-0.0892,0.3228,9.8009,0.1918,0.0452,-0.1124,2.3,17.8,-39.1,6.192428186,-1.62,0.38,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,247693,2015-10-30 10:26:24:826,1446171984826.0 \n-0.7075,-1.0642,11.5496,-0.2655,0.0231,9.803,-0.6377,0.2944,-0.5119,2,17.6,-39.2,6.197664174,-1.24,0.56,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,247795,2015-10-30 10:26:24:928,1446171984928.0 \n-0.4549,-0.2969,10.0066,-0.3368,-0.128,9.8,-0.4569,-0.0232,-0.1869,1.8,17.7,-39.4,6.244962597,-0.03,1.92,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,247898,2015-10-30 10:26:25:031,1446171985031.0 \n-0.5866,0.6632,8.0924,-0.3804,-0.2578,9.7959,-0.1332,0.0122,0.0244,1.7,18.2,-39.2,6.251594848,1.24,2.14,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,247999,2015-10-30 10:26:25:132,1446171985132.0 \n-0.1281,0.5124,9.8043,-0.3176,-0.2541,9.7982,0.0305,-0.0464,0.1002,1.7,18.7,-39,6.242344603,1.48,1.86,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,248101,2015-10-30 10:26:25:234,1446171985234.0 \n-0.4202,0.0359,11.0325,-0.3439,-0.0953,9.8002,0.1881,0.1051,0.248,1.7,18.9,-38.9,6.243740866,0.96,1.87,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,248204,2015-10-30 10:26:25:337,1446171985337.0 \n-0.7805,-1.1516,12.22,-0.3096,0.1005,9.8012,-0.1588,-0.2676,0.022,2.1,18.3,-38.7,6.241471938,-0.59,1.81,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,248305,2015-10-30 10:26:25:438,1446171985438.0 \n-0.4106,0.1317,9.1219,-0.219,0.0246,9.8042,0.0171,-0.2541,0.2101,2.4,18,-38.7,6.226113041,0.1,1.43,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,248407,2015-10-30 10:26:25:540,1446171985540.0 \n-0.3316,0.1508,8.2552,-0.1632,-0.0861,9.8049,-0.2138,0.1319,0.0892,2.7,17.5,-38.5,6.150016685,0.5,0.95,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,248509,2015-10-30 10:26:25:642,1446171985642.0 \n-0.5375,0.7542,7.5274,-0.293,-0.0721,9.802,0.1454,0.1381,0.16,2.9,17.6,-38.4,6.165375583,0.7,1.39,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,248612,2015-10-30 10:26:25:745,1446171985745.0 \n-1.2067,0.1353,10.2627,-0.3957,-0.0605,9.7985,-0.0513,-0.0965,-0.1087,3.2,17.4,-38,6.196093378,0.35,2.31,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,248714,2015-10-30 10:26:25:847,1446171985847.0 \n0.7147,-0.1844,11.0325,-0.3395,0.0829,9.8004,-0.2285,-0.1833,-0.1613,3.5,17.2,-37.9,6.137450315,-0.35,2.21,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,248815,2015-10-30 10:26:25:948,1446171985948.0 \n-0.0455,-0.6393,10.8661,-0.4662,-0.1663,9.7942,-0.1613,0.3592,-0.0635,3.6,17,-38.1,6.131516195,0.99,2.26,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,248917,2015-10-30 10:26:26:050,1446171986050.0 \n0.6117,0.1185,8.5162,-0.4232,-0.1238,9.7967,-0.1991,-0.0709,-0.2492,3.7,17.1,-38,6.147747757,0.41,2.59,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,249020,2015-10-30 10:26:26:153,1446171986153.0 \n-1.0355,0.3699,8.3103,-0.4059,-0.2128,9.7959,0.1038,-0.0257,-0.0281,3.5,17.2,-37.9,6.135181387,1.22,2.39,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,249121,2015-10-30 10:26:26:254,1446171986254.0 \n-0.656,0.5219,9.8162,-0.3975,-0.1466,9.7975,0.011,-0.0049,-0.0073,3.3,17.3,-37.3,6.191555521,1,2.31,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 15,249223,2015-10-30 10:26:26:356,1446171986356.0 \n-0.7865,0.1006,12.7288,-0.4788,0.0284,9.7949,0.3213,0.0244,0.1698,3.1,17.1,-37,6.210056012,0.4,2.74,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 15,249325,2015-10-30 10:26:26:458,1446171986458.0 \n-2.399,-1.804,13.7655,-0.368,0.0876,9.7994,-0.2627,-0.0904,-0.1686,3.2,16.8,-37.2,6.215466532,-1.19,2.78,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 15,249427,2015-10-30 10:26:26:560,1446171986560.0 \n-0.996,0.1197,8.1068,-0.217,0.1152,9.8036,0.2346,-0.1979,0.2981,3.1,16.5,-37.5,6.174974894,-0.69,1.71,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 15,249530,2015-10-30 10:26:26:663,1446171986663.0 \n-0.6093,0.1856,8.4156,-0.2205,-0.0852,9.8038,-0.1478,0.088,0.0538,2.9,16.5,-37.4,6.148969488,-0.24,1.06,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 15,249632,2015-10-30 10:26:26:765,1446171986765.0 \n-0.3388,0.8775,7.7381,-0.3315,-0.0507,9.8009,0.0538,0.1026,-0.0257,2.7,16.8,-36.8,6.17061157,0.47,1.72,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 15,249733,2015-10-30 10:26:26:866,1446171986866.0 \n-1.239,0.3508,11.4479,-0.4076,-8.00E-04,9.7982,0.0599,0.0574,-0.1038,2.8,16.9,-36.8,6.193475384,0.15,2.29,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 15,249835,2015-10-30 10:26:26:968,1446171986968.0 \n-0.1185,-0.2993,11.2228,-0.5527,0.163,9.7897,0.0476,0.0379,-0.2114,3.2,16.8,-36.9,6.217909993,-0.71,2.87,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 15,249937,2015-10-30 10:26:27:070,1446171987070.0 \n-0.2634,-0.4226,9.9036,-0.583,-0.0338,9.7892,0.1735,-0.0855,0.088,3.4,16.9,-37,6.241646471,0.46,3.56,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 15,250039,2015-10-30 10:26:27:172,1446171987172.0 \n-0.7661,-0.407,9.2584,-0.5378,-0.2051,9.7897,-0.2004,0.1442,-0.0489,3.3,17.2,-36.9,6.224716777,0.8,3.14,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 15,250141,2015-10-30 10:26:27:274,1446171987274.0 \n-1.136,0.1173,8.8981,-0.5667,-0.3672,9.7834,-0.1124,-0.0709,-0.0061,3.2,17.9,-36.8,6.236410483,2.09,3.43,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 13,250244,2015-10-30 10:26:27:377,1446171987377.0 \n-0.9266,-0.0622,10.732,-0.5368,-0.3021,9.7873,0.0195,0.0489,0.0525,2.9,18.5,-36.6,6.228905567,1.77,3.14,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 13,250345,2015-10-30 10:26:27:478,1446171987478.0 \n-0.6943,-0.073,11.9722,-0.6303,0.0692,9.7861,0.6121,0.0513,0.4093,3,18.7,-36.9,6.244788064,1.26,3.56,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 13,250447,2015-10-30 10:26:27:580,1446171987580.0 \n-2.0949,-0.8691,12.1123,-0.6198,0.1469,9.7859,-0.1515,-0.1075,0.1075,3.3,17.9,-37.2,6.251594848,-1.28,3.72,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 13,250550,2015-10-30 10:26:27:683,1446171987683.0 \n-0.5519,0.3627,8.8645,-0.4161,0.2292,9.7951,0.0208,-0.3714,0.2004,3.7,17.4,-37.6,6.173753163,-1.29,3.07,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 13,250651,2015-10-30 10:26:27:784,1446171987784.0 \n-0.6536,0.103,8.6311,-0.3186,-0.0188,9.8015,-0.1454,-0.0159,0.0342,3.6,17.1,-38.3,6.121393286,0.11,1.86,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 13,250753,2015-10-30 10:26:27:886,1446171987886.0 \n-0.4741,0.9613,7.5669,-0.3563,-0.0599,9.8,0.0464,0.0696,0.0367,3.5,17.4,-38.7,6.116157298,0.42,1.73,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 13,250855,2015-10-30 10:26:27:988,1446171987988.0 \n-1.1301,0.2789,10.4722,-0.4789,-0.0743,9.7947,0.1674,-0.0134,-0.2053,3.2,18,-39,6.220353454,0.7,2.78,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 13,250958,2015-10-30 10:26:28:091,1446171988091.0 \n0.68,-0.5028,10.1239,-0.5736,0.0716,9.7896,0.0696,0.0476,-0.1332,3.4,18.2,-39.1,6.244089932,-0.42,3.35,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 13,251059,2015-10-30 10:26:28:192,1446171988192.0 \n-1.5,-0.8368,11.1354,-0.6713,-0.258,9.7802,0.182,-0.1332,0.2724,3.5,18.5,-39,6.211801341,1.05,3.94,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 13,251161,2015-10-30 10:26:28:294,1446171988294.0 \n-0.4142,0.5974,8.351,-0.5118,-0.3037,9.7886,-0.2627,-0.1552,-0.0147,3.4,19,-38.6,6.235188753,1.48,3.13,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 12,251264,2015-10-30 10:26:28:397,1446171988397.0 \n-1.1372,0.5112,8.8813,-0.5656,-0.4498,9.78,-0.1381,0.0635,-0.1258,3.2,19.6,-38.2,6.235537819,2.43,3.2,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 12,251365,2015-10-30 10:26:28:498,1446171988498.0 \n-1.0558,0.0946,10.0844,-0.6878,-0.4135,9.7738,0.0489,0.1845,0.0611,3.2,20.3,-37.8,6.265557482,2.42,4.03,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 12,251467,2015-10-30 10:26:28:600,1446171988600.0 \n-1.0702,0.0838,11.084,-0.7936,-0.2864,9.7703,0.2627,0.0134,0.2798,3.5,20.6,-38.1,6.235712352,2.15,4.62,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 12,251569,2015-10-30 10:26:28:702,1446171988702.0 \n-2.3834,-1.2773,13.0125,-0.5392,-0.1535,9.7906,-0.2908,-0.2969,-0.0586,4,20.6,-38.5,6.201678431,0.56,3.48,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 12,251672,2015-10-30 10:26:28:805,1446171988805.0 \n-1.0858,0.1856,9.177,-0.3926,-0.0015,9.7988,0.0623,-0.2553,0.0794,4.3,20.5,-39.1,6.188588462,0.18,2.96,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 12,251773,2015-10-30 10:26:28:906,1446171988906.0 \n-0.7685,-0.1676,8.0697,-0.2978,0.0182,9.8021,-0.022,-0.0257,0.055,4.2,20.2,-39.7,6.150365751,-0.07,1.89,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 12,251875,2015-10-30 10:26:29:008,1446171989008.0 \n-0.1975,0.7709,8.3079,-0.3077,0.1431,9.8008,0.2553,0.0599,0.11,3.9,20.1,-40.3,6.145478829,-0.38,1.7,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 12,251977,2015-10-30 10:26:29:110,1446171989110.0 \n-0.346,0.5878,10.4806,-0.3315,0.1945,9.7991,0.204,-0.1258,-0.2431,3.8,20.1,-40.2,6.158568799,-0.85,2.03,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 12,252079,2015-10-30 10:26:29:212,1446171989212.0 \n-0.0108,-1.1025,10.5117,-0.2991,0.33,9.7965,-0.5266,0.0086,-0.7514,3.4,20.4,-40.8,6.201678431,-1.93,1.75,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 12,252182,2015-10-30 10:26:29:315,1446171989315.0 \n-0.5112,0.1341,7.6351,-0.52,-0.049,9.7927,-0.0391,0.38,-0.3115,2.9,20.9,-40.9,6.243740866,0.29,3.04,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 12,252284,2015-10-30 10:26:29:417,1446171989417.0 \n-0.6404,-0.4717,10.3896,-0.3895,-0.1588,9.7976,-0.1258,0.0562,-0.099,2.3,21.4,-41.1,6.26189229,0.51,2.18,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 12,252385,2015-10-30 10:26:29:518,1446171989518.0 \n-0.9816,0.893,8.0433,-0.4993,-0.1804,9.7923,-0.0672,-0.0599,0.0672,1.7,22.4,-40.6,0.004886922,0.91,2.94,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 12,252488,2015-10-30 10:26:29:621,1446171989621.0 \n-0.6141,0.8978,9.6007,-0.537,-0.2097,9.7897,-0.0782,0.1014,0.1319,1.5,22.8,-40.5,6.283185307,1.18,2.86,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 12,252589,2015-10-30 10:26:29:722,1446171989722.0 \n-0.48,0.9637,10.094,-0.5575,-0.1659,9.7894,0.193,-0.055,0.4129,2,23.4,-40.4,0.012391838,0.97,3.26,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 12,252691,2015-10-30 10:26:29:824,1446171989824.0 \n-2.4193,-1.658,13.696,-0.3365,-0.2359,9.798,0.0574,0.0941,0.4166,2.2,23.5,-40.5,6.266953745,0.78,2.32,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 12,252793,2015-10-30 10:26:29:926,1446171989926.0 \n-0.1915,-0.4022,9.6893,-0.1136,-0.1236,9.8052,0.1124,-0.5339,0.2297,2.5,23.7,-40.6,6.176022091,0.72,0.66,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 12,252895,2015-10-30 10:26:30:028,1446171990028.0 \n-0.5148,0.2334,8.4096,-0.0095,-0.1577,9.8054,-0.0159,0.0379,0.0086,2.2,23.9,-40.8,6.199409503,0.92,0.06,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 12,252998,2015-10-30 10:26:30:131,1446171990131.0 \n-0.8045,0.4298,8.3318,-0.1574,-0.0972,9.8049,-0.022,0.1454,-0.1735,2.2,23.9,-40.9,6.21651373,0.62,0.6,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 12,253100,2015-10-30 10:26:30:233,1446171990233.0 \n-1.0582,-0.1664,11.6418,-0.191,-0.061,9.8046,0.1686,0.0415,-0.2517,2.1,24,-41.1,6.239028477,0.47,1.33,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 13,253201,2015-10-30 10:26:30:334,1446171990334.0 \n-1.0032,-2.1284,13.6362,-0.1331,-0.2381,9.8029,-0.3323,-0.1686,-0.3812,1.8,24.2,-41.5,6.228381969,0.18,0.96,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 13,253303,2015-10-30 10:26:30:436,1446171990436.0 \n0.4226,0.152,6.8654,-0.1931,-0.1761,9.8032,0.5473,-0.314,0.2456,1.2,24.8,-41.5,0.007330383,1.95,1.64,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 13,253405,2015-10-30 10:26:30:538,1446171990538.0 \n0.0862,-0.1832,8.9004,-0.0189,-0.2931,9.8023,-0.0696,0.2407,-0.0904,0.5,25.3,-41.3,6.244438998,1.71,0.11,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 13,253508,2015-10-30 10:26:30:641,1446171990641.0 \n-0.3065,0.4573,7.7991,-0.1518,-0.3438,9.7994,-0.0916,0.1124,-0.0831,0.2,25.8,-41,0.020245819,1.86,0.7,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 13,253609,2015-10-30 10:26:30:742,1446171990742.0 \n-0.5746,0.3974,9.7755,-0.2399,-0.4788,9.792,-0.1295,0.055,-0.0391,0.1,26.3,-40.6,0.041887902,2.8,1.4,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 13,253711,2015-10-30 10:26:30:844,1446171990844.0 \n-0.5734,0.2083,12.238,-0.2843,-0.5109,9.7892,0.2969,0.0159,0.3604,0.2,26.8,-40.4,0.046425758,3.14,1.65,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 13,253813,2015-10-30 10:26:30:946,1446171990946.0 \n-1.4425,-1.5311,12.5468,-0.1635,-0.4154,9.7965,-0.1026,-0.2419,0.033,0.3,27.4,-40.6,0.027052603,2.43,0.96,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 13,253915,2015-10-30 10:26:31:048,1446171991048.0 \n-0.3484,-0.7003,9.845,0.014,-0.2513,9.8034,0.1515,-0.3274,0.1943,0.4,27.4,-41.4,0.016406095,1.52,0.59,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 13,254017,2015-10-30 10:26:31:150,1446171991150.0 \n-0.7673,-0.1089,8.1175,-0.1036,-0.3056,9.8013,0.0965,0.1503,0.0648,0.6,27.3,-42.4,6.251420315,1.9,0.25,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 13,254120,2015-10-30 10:26:31:253,1446171991253.0 \n-0.6919,0.7111,8.2791,-0.2222,-0.2186,9.8017,0.0733,0.0024,0.0195,1,27.2,-43.2,6.28213811,1.28,1.3,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,254221,2015-10-30 10:26:31:354,1446171991354.0 \n-0.5662,-0.1999,10.8984,-0.1783,-0.135,9.8041,0.1002,-0.182,-0.0574,1.4,27,-43.6,0.000523599,0.98,1.32,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,254323,2015-10-30 10:26:31:456,1446171991456.0 \n0.7027,-0.6979,10.0999,-0.1505,0.0263,9.8055,-0.0831,-0.0757,-0.2004,1.6,26.8,-43.7,6.234316088,-0.15,0.88,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,254425,2015-10-30 10:26:31:558,1446171991558.0 \n-0.2502,-0.7027,10.4028,-0.2711,-0.4058,9.7945,0.2639,0.1185,-0.0342,1.4,27,-43.9,6.275680391,2.06,1.05,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,254527,2015-10-30 10:26:31:660,1446171991660.0 \n-0.2179,-0.5483,9.0872,-0.3057,-0.494,9.7894,-0.3164,-0.0098,-0.2492,1.2,27.6,-43.9,0.013788101,2.27,1.77,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,254630,2015-10-30 10:26:31:763,1446171991763.0 \n-0.8009,-0.1341,8.9711,-0.294,-0.6264,9.7822,-0.1735,-0.0171,-0.099,0.9,28.3,-43.5,0.012740904,3.38,1.76,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,254731,2015-10-30 10:26:31:864,1446171991864.0 \n-0.3974,0.2993,9.4104,-0.2669,-0.6128,9.7838,0.0024,0.0232,0.0501,0.7,29,-43.1,0.006632251,3.58,1.56,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,254834,2015-10-30 10:26:31:967,1446171991967.0 \n-0.425,0.2753,11.3066,-0.2284,-0.4924,9.7916,0.336,-0.0428,0.4215,0.5,29.3,-43.3,0.003839724,3.25,1.47,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,254935,2015-10-30 10:26:32:068,1446171992068.0 \n-0.4621,-0.8428,11.9423,-0.1141,-0.3936,9.7981,-0.1662,-0.2663,0.1197,0.8,29.1,-43.8,6.276727589,1.86,1.07,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,255038,2015-10-30 10:26:32:171,1446171992171.0 \n-0.3915,-0.2909,9.104,-0.0247,-0.351,9.8003,0.2211,-0.3616,0.2162,1.2,28.8,-44.4,6.250722183,2.05,0.14,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,255139,2015-10-30 10:26:32:272,1446171992272.0 \n-0.1053,-0.0658,8.8466,0.1091,-0.3158,9.801,-0.0086,0.3067,-0.0953,1.4,28.4,-45,6.219829855,1.75,-0.88,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,255241,2015-10-30 10:26:32:374,1446171992374.0 \n-0.577,0.2981,8.3378,-0.1282,-0.2905,9.8015,0.0586,0.1405,-0.0684,1.6,28.3,-45.1,6.221749718,1.93,0.47,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,255344,2015-10-30 10:26:32:477,1446171992477.0 \n-1.1241,-0.0431,9.1267,-0.2795,-0.1789,9.801,0.1515,0.16,-0.0721,1.8,28,-45,6.246184327,1.28,1.28,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,255446,2015-10-30 10:26:32:579,1446171992579.0 \n-0.1401,0.0156,9.6259,-0.3309,-0.0664,9.8008,-0.0195,-0.022,-0.0281,2.4,27.6,-45.1,6.263288554,0.46,1.85,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,255547,2015-10-30 10:26:32:680,1446171992680.0 \n-0.9888,-1.2737,13.2735,-0.4251,-0.4805,9.7856,-0.7343,0.1918,-0.3531,2.6,27.4,-45.2,6.225240376,2.01,1.94,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,255650,2015-10-30 10:26:32:783,1446171992783.0 \n-0.2023,-0.5758,11.0684,-0.3362,-0.4427,9.7909,-0.2468,-0.2908,-0.2321,2.8,27.5,-45.1,6.24635886,2.18,2.58,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,255751,2015-10-30 10:26:32:884,1446171992884.0 \n-0.4776,0.2298,8.1738,-0.3665,-0.5211,9.7859,0.0648,0.1283,-0.0709,2.5,27.9,-44.6,6.220353454,3.22,1.78,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,255853,2015-10-30 10:26:32:986,1446171992986.0 \n-0.5986,0.182,9.3637,-0.4246,-0.4577,9.7868,0.0733,0.0269,-0.0171,2.5,28,-44.3,6.241122872,2.68,2.48,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,255955,2015-10-30 10:26:33:088,1446171993088.0 \n-0.419,-0.1448,10.5237,-0.4924,-0.3159,9.7892,0.2871,0.0513,0.2468,2.4,27.8,-44.3,0.006283185,2.2,2.82,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,256057,2015-10-30 10:26:33:190,1446171993190.0 \n-1.1372,-1.2031,12.2344,-0.4492,-0.0626,9.7962,-0.2077,-0.2541,-0.0232,2.9,26.6,-45,6.248104189,0.37,2.63,36.812897,-119.74792,278.2,336.3171531,4.13,38.709675,88.34,0 / 16,256159,2015-10-30 10:26:33:292,1446171993292.0 \n-0.9864,-0.0251,8.5102,-0.437,-0.0991,9.7964,0.0232,-0.4203,0.1234,3.2,26,-45.3,6.251245782,0.85,2.79,36.81297,-119.74789,276.77,336.3171531,1.16,77.41935,54.09,13 / 16,256261,2015-10-30 10:26:33:394,1446171993394.0 \n-0.9457,-0.2598,8.7963,-0.2058,-0.2553,9.8012,-0.2908,-0.0513,0.0098,3.4,25.2,-45.5,6.195744312,1.29,1.14,36.81297,-119.74789,276.77,336.3171531,1.16,77.41935,54.09,13 / 16,256364,2015-10-30 10:26:33:497,1446171993497.0 \n-0.8811,0.5339,8.2528,-0.3001,-0.3027,9.7974,-0.0415,0.0953,0.0134,3.3,25,-45.1,6.207787083,1.65,1.54,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,13 / 16,256465,2015-10-30 10:26:33:598,1446171993598.0 \n-1.2055,0.2155,10.5261,-0.3314,-0.3211,9.7958,0.055,-0.1002,-0.1491,3.3,24.9,-44.5,6.222622382,1.94,2.05,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,13 / 16,256568,2015-10-30 10:26:33:701,1446171993701.0 \n-0.68,0.4573,10.495,-0.3194,-0.1956,9.7995,0.1674,0.0538,-0.0953,3.3,24.7,-44,6.21354667,1.39,1.73,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,13 / 16,256669,2015-10-30 10:26:33:802,1446171993802.0 \n-1.4928,-1.5239,12.5384,-0.3769,-0.3927,9.7915,-0.3519,0.3018,-0.3665,3.1,24.3,-43.8,6.210230544,1.7,1.74,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,13 / 16,256771,2015-10-30 10:26:33:904,1446171993904.0 \n0.0251,-0.0634,7.6842,-0.4019,-0.0805,9.7981,-0.0049,-0.1356,-0.0049,2.8,24.1,-43.6,6.242868201,1.1,2.69,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,13 / 16,256874,2015-10-30 10:26:34:007,1446171994007.0 \n-0.4322,0.1724,8.6335,-0.4114,-0.0501,9.7979,0.1026,0.0745,0.0098,2.6,23.6,-43.9,6.225589442,0.54,2.14,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,13 / 16,256975,2015-10-30 10:26:34:108,1446171994108.0 \n-0.4956,0.9361,8.6622,-0.4641,-0.0195,9.7956,-0.0476,0.0208,0.0073,2.6,22.9,-43.7,6.243217267,0.11,2.71,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,13 / 16,257077,2015-10-30 10:26:34:210,1446171994210.0 \n-0.8811,0.6009,9.7911,-0.4725,-0.0387,9.7952,-0.0073,0.0159,0.1063,2.6,22.5,-43.7,6.241471938,0.21,2.66,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,13 / 16,257179,2015-10-30 10:26:34:312,1446171994312.0 \n-0.4848,0.4513,10.0652,-0.4608,0.0348,9.7958,-0.1417,-0.2773,0.0623,2.7,22.1,-43.5,6.241646471,0.16,2.78,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,14 / 16,257281,2015-10-30 10:26:34:414,1446171994414.0 \n-0.3376,0.5064,8.6443,-0.3591,-0.0051,9.8001,0.1307,0.1759,0.248,2.8,22,-43.7,6.219829855,0.34,2.11,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,14 / 16,257383,2015-10-30 10:26:34:516,1446171994516.0 \n-0.8308,-0.2394,9.5493,-0.2308,-0.0269,9.8039,-0.1955,-0.0464,-0.0318,2.7,21.8,-43.7,6.19801324,-0.17,1.44,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,14 / 16,257486,2015-10-30 10:26:34:619,1446171994619.0 \n-0.7709,0.7027,8.2648,-0.2871,-0.0453,9.8023,0.1588,0.1368,0.0916,2.6,21.6,-43.5,6.203598293,0.26,1.68,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,14 / 16,257587,2015-10-30 10:26:34:720,1446171994720.0 \n-0.7985,1.0343,8.6359,-0.4263,0.0613,9.7972,0.0452,0.0929,-0.0819,2.6,21.3,-43.4,6.22489131,-0.34,2.34,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,14 / 16,257689,2015-10-30 10:26:34:822,1446171994822.0 \n-1.4234,0.1999,11.7112,-0.4375,0.0697,9.7966,0.0147,-0.0379,-0.1649,2.6,21.1,-43.3,6.233617956,-0.36,2.59,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,14 / 16,257791,2015-10-30 10:26:34:924,1446171994924.0 \n0.3508,-0.1796,11.1666,-0.4302,0.0102,9.7972,-0.474,0.1307,-0.3384,2.5,20.8,-43.3,6.229429166,-0.71,2.45,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,14 / 16,257893,2015-10-30 10:26:35:026,1446171995026.0 \n-0.0275,0.322,6.8307,-0.5689,0.0601,9.7899,0.3763,0.1185,0.066,2.3,20.9,-43,0.02268928,0.15,3.3,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,14 / 16,257996,2015-10-30 10:26:35:129,1446171995129.0 \n-0.7027,0.164,8.3965,-0.431,-0.1292,9.7963,-0.1552,-0.0257,-0.1368,2,21.1,-43,6.274109595,0.64,2.42,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,14 / 16,258097,2015-10-30 10:26:35:230,1446171995230.0 \n-0.571,1.1791,7.7632,-0.4637,-0.1362,9.7947,0.0159,0.0244,0.0293,1.9,21.3,-42.7,6.282836241,0.82,2.66,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,14 / 16,258200,2015-10-30 10:26:35:333,1446171995333.0 \n-1.0271,0.2897,10.1682,-0.4634,-0.2317,9.793,-0.0391,0.1063,0.0367,1.5,21.6,-42.4,6.282661708,1.35,2.71,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,15 / 16,258301,2015-10-30 10:26:35:434,1446171995434.0 \n-0.8176,0.158,11.3485,-0.5031,-0.229,9.7911,0.0684,-0.0354,0.2737,1.5,21.6,-42.2,0.007679449,1.4,2.95,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,15 / 16,258403,2015-10-30 10:26:35:536,1446171995536.0 \n-1.4736,-1.2354,11.1031,-0.2912,-0.2424,9.7993,-0.2358,-0.1747,0.011,1.7,21.7,-41.8,6.247406058,1.42,1.7,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,15 / 16,258505,2015-10-30 10:26:35:638,1446171995638.0 \n-0.1604,0.1209,8.5485,0.0656,-0.1668,9.805,-0.1112,-0.3164,0.0574,1.8,21.7,-41.5,6.223844113,1.34,1.05,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,15 / 16,258607,2015-10-30 10:26:35:740,1446171995740.0 \n-0.8583,0.2586,8.3701,0.0074,-0.2874,9.8024,-0.0819,0.1723,-0.0794,1.3,21.7,-41.3,6.229254633,1.59,-0.18,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,15 / 16,258709,2015-10-30 10:26:35:842,1446171995842.0 \n-0.595,0.7003,8.1092,-0.056,-0.2322,9.8037,0.0586,0.044,-0.0489,1,21.9,-41.1,6.237632214,1.66,0.07,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,15 / 16,258812,2015-10-30 10:26:35:945,1446171995945.0 \n-1.0594,-0.3579,10.8745,-0.1363,-0.1765,9.8041,0.215,0.0867,-0.0574,1,21.9,-41.3,6.262939488,1.03,0.8,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,15 / 16,258913,2015-10-30 10:26:36:046,1446171996046.0 \n0.68,-0.0862,10.5465,-0.1647,-0.067,9.805,-0.5473,0.1808,-0.3201,1,21.8,-41.3,6.268699074,0.16,0.95,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,15 / 16,259016,2015-10-30 10:26:36:149,1446171996149.0 \n0.3053,0.0431,7.9595,-0.3221,-0.3698,9.7944,0.1063,0.1026,-0.0183,1.1,21.9,-41.2,0.017104227,2.16,1.88,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,15 / 16,259117,2015-10-30 10:26:36:250,1446171996250.0 \n-0.4489,-0.516,9.6031,-0.3043,-0.4744,9.7904,-0.0843,0.1246,-0.0745,1.1,22.2,-40.9,0.006632251,2.62,1.58,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,15 / 16,259219,2015-10-30 10:26:36:352,1446171996352.0 \n-0.6931,0.4238,8.1846,-0.3854,-0.5258,9.785,-0.0269,-0.0342,0.0623,1.2,22.8,-40.2,0.026354472,2.94,2.22,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,259321,2015-10-30 10:26:36:454,1446171996454.0 \n-0.4465,0.2538,9.6367,-0.3517,-0.5624,9.7842,-0.0855,-0.0086,0.0244,1.2,23.1,-40.2,0.019722221,3.22,2.02,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,259423,2015-10-30 10:26:36:556,1446171996556.0 \n-0.2945,-0.0431,10.8098,-0.3741,-0.5148,9.786,0.2529,0.0061,0.3176,1.5,23.1,-40.1,6.26067056,3.01,2.19,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,259525,2015-10-30 10:26:36:658,1446171996658.0 \n-0.5124,-1.6137,13.8588,-0.215,-0.6067,9.7855,-0.1698,0.1112,0.0916,1.8,22.9,-40.2,6.256830835,2.31,2.06,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,259627,2015-10-30 10:26:36:760,1446171996760.0 \n-0.5543,0.2466,8.7029,-0.1812,-0.4112,9.7963,0.2773,-0.1808,0.2309,2.2,22.6,-39.9,6.243915399,2.6,1.67,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,259729,2015-10-30 10:26:36:862,1446171996862.0 \n-0.4573,-0.0431,8.8334,-0.0532,-0.4256,9.7973,0.0489,0.0599,-0.1405,2.2,22.3,-39.8,6.192951785,2.52,0.24,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,259831,2015-10-30 10:26:36:964,1446171996964.0 \n-1.0127,0.3711,8.3558,-0.1473,-0.2844,9.8014,0.1222,0.1185,-0.1026,2,22,-39.9,6.20935788,1.92,0.68,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,259933,2015-10-30 10:26:37:066,1446171997066.0 \n-1.2905,0.0239,9.979,-0.2465,-0.2574,9.8002,0.0452,0.1161,-0.1051,2,21.6,-40,6.225414909,1.53,1.13,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,260035,2015-10-30 10:26:37:168,1446171997168.0 \n0.4429,0.8021,9.0824,-0.2852,-0.0389,9.8024,0.303,0.0257,0.1991,2.3,21.1,-40.3,6.239901142,0.75,1.6,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,260137,2015-10-30 10:26:37:270,1446171997270.0 \n0.0622,-0.1448,8.8478,-0.3274,-0.3487,9.795,0.0086,0.0281,-0.0086,2.5,20.8,-39.9,6.195918845,2,1.84,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,260239,2015-10-30 10:26:37:372,1446171997372.0 \n-0.2825,-0.5662,9.9216,-0.2583,-0.5093,9.79,-0.1051,0.0831,-0.0159,2.5,20.9,-39.5,6.182130743,2.46,1.53,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,260341,2015-10-30 10:26:37:474,1446171997474.0 \n-0.8906,0.2382,8.3749,-0.3506,-0.5975,9.7822,-0.088,0.1271,-0.0684,2.5,21.3,-38.5,6.191380989,3.4,1.92,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,260444,2015-10-30 10:26:37:577,1446171997577.0 \n-0.6871,0.2442,10.5429,-0.3602,-0.5599,9.784,0.0073,0.0171,-0.0257,2.5,21.5,-37.8,6.202551096,3.27,2.11,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,260545,2015-10-30 10:26:37:678,1446171997678.0 \n-0.9194,-0.006,11.4012,-0.4341,-0.2305,9.7943,0.4557,0.011,0.3176,2.7,21.4,-37.6,6.211103209,2.69,2.43,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,260647,2015-10-30 10:26:37:780,1446171997780.0 \n-1.4569,-1.251,13.1011,-0.3417,-0.1563,9.7994,-0.0599,-0.1552,0.1002,3,20.6,-37.7,6.216164664,0.46,2.42,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,260750,2015-10-30 10:26:37:883,1446171997883.0 \n-0.5986,0.1999,8.6503,-0.3324,-0.1208,9.8003,0.0806,-0.1772,0.1613,3.3,20.1,-37.6,6.20639082,0.94,2.27,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,260852,2015-10-30 10:26:37:985,1446171997985.0 \n-1.2965,0.0694,9.2141,-0.3196,-0.2286,9.7988,0.0513,-0.099,0.1503,3.5,19.7,-37.3,6.138322979,1.34,1.87,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,260953,2015-10-30 10:26:38:086,1446171998086.0 \n-0.8368,0.5447,8.8107,-0.2679,-0.0455,9.8029,0.1845,-0.1319,0.0428,3.6,19.7,-37.5,6.136926716,0.66,1.73,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,261056,2015-10-30 10:26:38:189,1446171998189.0 \n-0.5543,0.1269,10.7009,-0.1578,0.1469,9.8043,0.2028,-0.1491,-0.0745,3.6,19.4,-37.4,6.118949825,-0.47,1.24,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,261157,2015-10-30 10:26:38:290,1446171998290.0 \n0.5578,0.5974,8.7269,-0.1213,0.3677,9.799,-0.0892,-0.0159,-0.2382,3.4,18.7,-38,6.159615996,-2.05,0.71,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,261259,2015-10-30 10:26:38:392,1446171998392.0 \n0.6428,0.6991,7.082,-0.2523,-0.0346,9.8033,0.1759,0.0476,0.0867,3,18.4,-37.5,6.169040774,0.2,1.47,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,261362,2015-10-30 10:26:38:495,1446171998495.0 \n-0.4262,-0.4693,11.5808,-0.1866,-0.2078,9.8027,-0.4337,-0.2053,-0.2908,2.7,18.7,-37.2,6.162059457,0.84,1.16,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,261464,2015-10-30 10:26:38:597,1446171998597.0 \n-0.6009,0.7685,8.4635,-0.3277,-0.2045,9.799,0.0281,0.0257,-0.0757,2.4,19.4,-36.3,6.239552076,1.19,1.92,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,261566,2015-10-30 10:26:38:699,1446171998699.0 \n-0.5722,0.7147,9.5409,-0.4341,-0.1647,9.7957,-0.0024,0.1063,0.0049,2.3,19.7,-35.8,6.256307237,1.03,2.35,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,261668,2015-10-30 10:26:38:801,1446171998801.0 \n-0.7614,1.002,10.7392,-0.5201,-0.0722,9.7926,0.0953,0.0782,0.1613,2.3,19.9,-35.7,6.272538799,0.85,2.85,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,261769,2015-10-30 10:26:38:902,1446171998902.0 \n-1.6388,-1.3791,12.1051,-0.4014,-0.0868,9.798,-0.3396,-0.1735,0.0232,2.6,19.9,-35.4,6.222273316,-0.23,2.9,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,261871,2015-10-30 10:26:39:004,1446171999004.0 \n-0.3627,-0.1077,8.9759,-0.2027,-0.1175,9.8039,-0.2321,-0.1833,0.0098,2.8,19.8,-35.4,6.183003408,0.56,1.67,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,261973,2015-10-30 10:26:39:106,1446171999106.0 \n-0.6105,0.3041,9.2656,-0.1388,-0.273,9.8019,-0.099,-0.0171,0.0428,2.6,20,-35.1,6.152285613,1.6,0.81,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,262075,2015-10-30 10:26:39:208,1446171999208.0 \n-0.9014,0.5926,9.262,-0.1367,-0.1114,9.8051,0.0916,0.0147,0,2.3,20.3,-35.6,6.207088952,0.82,0.82,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,262178,2015-10-30 10:26:39:311,1446171999311.0 \n-0.8882,-0.0431,11.1893,-0.1115,0.0114,9.806,0.0831,-0.0208,-0.0122,2.1,20.4,-35.6,6.206565353,0.11,0.75,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,262279,2015-10-30 10:26:39:412,1446171999412.0 \n0.1269,-1.1516,11.4371,-0.074,0.1037,9.8058,-0.5681,-0.2749,-0.6011,1.9,20.2,-35.9,6.198536838,-0.61,0.43,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,262382,2015-10-30 10:26:39:515,1446171999515.0 \n-0.5602,-0.4381,9.5373,-0.146,-0.3501,9.7993,-0.2407,0.3983,-0.1747,1.5,20.4,-35.5,6.204470958,2.05,0.85,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,262483,2015-10-30 10:26:39:616,1446171999616.0 \n0.0395,0.0156,8.4946,-0.0884,-0.4615,9.7954,-0.0855,-0.033,0.0599,1,21.1,-34.6,6.247755123,2.7,0.52,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,262585,2015-10-30 10:26:39:718,1446171999718.0 \n-0.5902,0.2382,8.3785,-0.0843,-0.4499,9.796,0.1588,0.0354,0.1002,0.8,21.7,-34.5,6.246533393,2.84,0.43,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,262688,2015-10-30 10:26:39:821,1446171999821.0 \n-0.7386,0.1437,10.1095,-0.1682,-0.3401,9.7993,0.0648,0.1087,0.0403,0.8,22.1,-34.8,6.263986685,1.99,0.98,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,262789,2015-10-30 10:26:39:922,1446171999922.0 \n-0.7482,0.8452,11.145,-0.3506,-0.1524,9.7992,0.3653,0.2199,0.3763,1,22.1,-34.8,0.00296706,1.49,1.74,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,262892,2015-10-30 10:26:40:025,1446172000025.0 \n-1.6364,-1.2043,12.3313,-0.2807,-0.3623,9.7959,0.0721,0.2162,0.5192,1.8,21.8,-34.8,6.23501422,2.12,1.64,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,262993,2015-10-30 10:26:40:126,1446172000126.0 \n0.1784,0.4453,8.1235,-0.2483,-0.1878,9.8017,0.1979,-0.193,0.4362,2.5,21.7,-34.9,6.194348048,1.34,1.82,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,263095,2015-10-30 10:26:40:228,1446172000228.0 \n-0.5471,0.0754,8.7317,-0.2439,-0.2558,9.8003,-0.0098,0.1051,0,3.4,21.5,-35.2,6.175673025,1.48,1.18,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,263198,2015-10-30 10:26:40:331,1446172000331.0 \n-1.0558,0.3484,8.8382,-0.3873,-0.1452,9.7979,-0.0159,0.0476,-0.1332,4,21.2,-35.4,6.153681877,0.83,2.18,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,263299,2015-10-30 10:26:40:432,1446172000432.0 \n-1.0391,-0.1484,11.412,-0.3295,-0.1065,9.8005,0.2187,0.0098,-0.1234,4,21.1,-35.5,6.153158278,0.79,2.16,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,263401,2015-10-30 10:26:40:534,1446172000534.0 \n-0.8104,-1.7382,13.6254,-0.2125,-0.3402,9.7984,-0.3983,-0.3409,-0.3421,3.6,20.8,-35.5,6.120695154,0.86,1.05,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,263504,2015-10-30 10:26:40:637,1446172000637.0 \n-0.1508,-0.3232,8.928,-0.3247,-0.4113,9.7926,0.0489,-0.0367,0.0159,3.1,21.1,-35.4,6.191380989,2.49,1.98,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,263605,2015-10-30 10:26:40:738,1446172000738.0 \n-0.7242,0.1365,7.4029,-0.3293,-0.4753,9.7896,0.0953,0.1393,0.1332,2.5,21.5,-35.1,6.186494067,2.94,1.7,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,263707,2015-10-30 10:26:40:840,1446172000840.0 \n-0.9792,0.3053,8.2361,-0.3619,-0.4612,9.7891,-0.0086,-0.0183,0.1478,2.4,22,-35.1,6.248627788,2.76,2.12,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,263809,2015-10-30 10:26:40:942,1446172000942.0 \n-0.8547,0.407,9.6738,-0.4006,-0.4663,9.7874,-0.077,0.0134,0.1344,2.7,21.9,-34.8,6.204820024,2.69,2.29,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,263911,2015-10-30 10:26:41:044,1446172001044.0 \n-0.9744,0.4477,12.0141,-0.3401,-0.4312,9.7913,0.1881,-0.1979,0.391,3,21.9,-34.6,6.199409503,2.77,2.12,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,264014,2015-10-30 10:26:41:147,1446172001147.0 \n-0.6895,-0.8679,10.1825,-0.1198,-0.541,9.791,-0.2737,-0.171,0.0244,3.3,21.9,-34.5,6.155252673,3.16,0.7,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,264115,2015-10-30 10:26:41:248,1446172001248.0 \n-1.0499,-1.0534,10.1885,0.1106,-0.5712,9.7894,-0.171,-0.2346,0.1136,3.3,22,-34.6,6.137973913,2.87,0.07,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,264217,2015-10-30 10:26:41:350,1446172001350.0 \n-0.486,0.146,8.096,0.0228,-0.5022,9.7938,0.16,0,0.1307,3.2,22.1,-34.9,6.128723668,3.15,-0.2,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,264319,2015-10-30 10:26:41:452,1446172001452.0 \n-0.4345,0.2322,8.9771,-0.0308,-0.3752,9.7994,-0.0391,0.1112,-0.248,3.2,21.9,-35.3,6.140242841,2.39,0.08,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,264422,2015-10-30 10:26:41:555,1446172001555.0 \n-1.1349,-0.2298,10.6578,-0.0751,-0.4176,9.7975,-0.0159,0.0049,-0.3922,3.2,21.9,-35.4,6.150714817,2.44,0.44,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,264523,2015-10-30 10:26:41:656,1446172001656.0 \n0.0575,-1.6197,12.3912,-0.0561,-0.5965,9.7883,-0.6512,0.0757,-0.4606,3,21.9,-35.5,6.142511769,2.39,0.16,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,264625,2015-10-30 10:26:41:758,1446172001758.0 \n0.3184,-0.5495,9.0345,-0.0971,-0.6298,9.7859,-0.0733,0.0061,-0.0305,2.3,22.6,-34.8,6.208659748,3.87,0.76,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,264727,2015-10-30 10:26:41:860,1446172001860.0 \n-0.5136,-0.3053,8.6981,-0.1812,-0.723,9.7783,-0.0819,0.1063,-0.1271,2.1,22.9,-34.4,6.208834281,4.09,0.79,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,264829,2015-10-30 10:26:41:962,1446172001962.0 \n0.1065,0.8739,9.8186,-0.3504,-0.8382,9.7645,-0.259,0.099,0.1466,2,23.6,-34.6,6.24758059,4.9,2.06,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,264932,2015-10-30 10:26:42:065,1446172002065.0 \n-0.1006,0.3723,10.1215,-0.2818,-0.6886,9.7784,0.1735,-0.0855,0.0696,2.1,24,-34.9,6.247755123,4.75,2.06,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,265034,2015-10-30 10:26:42:167,1446172002167.0 \n-0.0323,-0.1951,9.3374,-0.2487,-0.3371,9.7977,0.4936,0.0367,0.1234,2.3,24.1,-35.4,6.234490621,2.68,1.49,36.81297,-119.74789,276.77,336.3870389,1.16,77.41935,54.09,16 / 16,265135,2015-10-30 10:26:42:268,1446172002268.0 \n-0.826,-0.6847,8.1427,-0.2773,-0.4471,9.7925,0.1772,0.4313,0.0941,2.3,23.8,-35.7,6.216688263,2.73,0.82,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,265237,2015-10-30 10:26:42:370,1446172002370.0 \n-0.2466,-0.2215,9.4116,-0.1097,-0.5063,9.793,-0.2053,-0.1539,0.0672,2.3,23.4,-36.7,6.216339197,2.62,0.89,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,265339,2015-10-30 10:26:42:472,1446172002472.0 \n-0.923,-0.1748,8.8765,-0.0936,-0.582,9.7889,0.1222,-0.0623,0.1503,2.1,23.6,-36.9,6.209008814,3.45,0.6,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,265441,2015-10-30 10:26:42:574,1446172002574.0 \n-0.2107,0.3891,8.8202,-0.0266,-0.4237,9.7975,0.1735,-0.1148,0.1197,1.9,23.7,-37.2,6.204121892,2.7,0.37,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,265543,2015-10-30 10:26:42:676,1446172002676.0 \n-0.8631,-0.4477,10.9104,0.1165,-0.2644,9.8024,0.1845,0.088,-0.1258,1.5,23.7,-37.2,6.177418355,1.54,-0.68,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,265645,2015-10-30 10:26:42:778,1446172002778.0 \n-0.1963,-0.9325,12.226,-0.0106,-0.3826,9.7992,-0.3005,0.3164,-0.226,1.4,23.5,-37.5,6.232570759,1.29,-0.27,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,265747,2015-10-30 10:26:42:880,1446172002880.0 \n0.3615,-0.5028,9.3314,-0.139,-0.5992,9.7873,-0.1112,0.0501,-0.1491,1.1,23.5,-37.4,6.256830835,2.85,0.64,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,265850,2015-10-30 10:26:42:983,1446172002983.0 \n-0.6596,0.0874,7.7321,-0.2236,-0.688,9.7799,-0.0061,0.1747,-0.0831,0.9,24,-37.3,6.267651877,4.02,1.03,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,265952,2015-10-30 10:26:43:085,1446172003085.0 \n-0.753,0.8104,8.4527,-0.2123,-0.59,9.7866,0.1136,-0.0159,0.0525,0.8,24.4,-37,6.274109595,3.58,1.24,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,266054,2015-10-30 10:26:43:187,1446172003187.0 \n-0.82,0.0754,11.1342,-0.1626,-0.4536,9.7948,0.0745,-0.0391,0.1283,0.7,24.6,-37.2,6.268873607,3.17,1.04,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,266156,2015-10-30 10:26:43:289,1446172003289.0 \n0.1245,0.0084,10.2089,-0.1687,-0.1656,9.8038,0.2321,0.0318,0.2553,0.7,24.3,-37.8,6.271666134,1.18,1.1,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,266258,2015-10-30 10:26:43:391,1446172003391.0 \n-0.7997,-0.1927,9.3685,-0.2324,-0.2473,9.8008,0.1368,0.0086,0.1442,0.9,24,-38.4,6.278821984,1.45,1.36,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,266359,2015-10-30 10:26:43:492,1446172003492.0 \n-0.7183,-0.2298,9.1447,-0.2005,-0.2312,9.8019,-0.0843,0.0745,-0.044,1.2,23.6,-38.7,6.270793469,1.12,1.05,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,266462,2015-10-30 10:26:43:595,1446172003595.0 \n-0.5578,0.2801,8.0158,-0.2674,-0.1111,9.8024,0.1772,0.0977,0.0721,1.3,23.6,-38.8,6.28213811,1.02,1.43,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,266563,2015-10-30 10:26:43:696,1446172003696.0 \n-0.832,0.6979,9.3422,-0.317,-0.0093,9.8015,0.0684,0.0305,-0.1173,1.4,23.3,-39.3,0.01134464,0.05,1.85,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,266666,2015-10-30 10:26:43:799,1446172003799.0 \n-1.5766,0.3364,11.2599,-0.2351,0.1227,9.8031,0.391,-0.0819,-0.044,1.1,23.1,-40,0.001396263,-0.32,1.48,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,266767,2015-10-30 10:26:43:900,1446172003900.0 \n-1.4341,-1.1911,12.5528,-0.1151,0.0331,9.8059,-0.5669,-0.0367,-0.5046,0.3,22.6,-40.6,0.020769418,-0.19,0.67,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,266869,2015-10-30 10:26:44:002,1446172004002.0 \n0.3484,-0.2849,9.8869,-0.1438,-0.0123,9.8056,-0.1356,0.0867,-0.11,-0.3,22.4,-40.7,0.024958208,-0.2,0.77,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,266971,2015-10-30 10:26:44:104,1446172004104.0 \n-0.0299,0.7219,8.09,-0.1747,0.0487,9.805,0.0415,0.0134,0.0257,-1,22.5,-40.7,0.072256631,-0.16,0.94,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,267073,2015-10-30 10:26:44:206,1446172004206.0 \n-0.2777,1.0343,8.163,-0.1945,0.1311,9.8038,0.1014,0.0428,0.0538,-1.4,22.5,-40.4,0.072431164,-0.39,0.99,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,267176,2015-10-30 10:26:44:309,1446172004309.0 \n-0.395,0.893,10.2927,-0.2581,0.1852,9.8015,0.0611,0.0037,0.1515,-1.5,22.2,-40.9,0.090408055,-0.92,1.47,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,267277,2015-10-30 10:26:44:410,1446172004410.0 \n-0.2035,-0.3663,13.0245,-0.193,0.3131,9.7998,-0.1552,-0.2957,0.2053,-1.6,21.7,-41.5,0.11990412,-1.83,1.13,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,267379,2015-10-30 10:26:44:512,1446172004512.0 \n0.0335,0.1915,9.894,-0.079,0.2145,9.804,-0.0208,-0.0684,0.0843,-1.5,21.5,-41.9,0.068940505,-0.99,0.78,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,267482,2015-10-30 10:26:44:615,1446172004615.0 \n-0.6991,0.2861,8.5066,-0.0893,0.111,9.8056,-0.1271,0.0586,-0.0147,-1.3,21.1,-41.9,0.05427974,-0.94,0.24,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,267583,2015-10-30 10:26:44:716,1446172004716.0 \n-0.6716,0.7518,7.9128,-0.1767,0.0877,9.8047,0.0501,0.1185,0.1014,-1.3,21.2,-41.7,0.076619954,-0.43,0.87,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,267686,2015-10-30 10:26:44:819,1446172004819.0 \n-0.6967,0.808,10.0928,-0.2041,0.0925,9.8041,0.0305,-0.099,0.022,-1.3,21.2,-41.3,0.086393798,-0.54,1.19,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,267787,2015-10-30 10:26:44:920,1446172004920.0 \n-0.5255,1.0918,10.3837,-0.1171,0.2452,9.8029,0.1784,0.0049,-0.0354,-1.4,21.2,-41,0.072431164,-0.71,0.79,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,267889,2015-10-30 10:26:45:022,1446172005022.0 \n-1.4844,-1.7047,13.2842,-0.0292,-0.0828,9.8063,-0.5864,0.2138,-0.5999,-1.8,20.9,-40.9,0.08831366,-0.49,-0.15,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,267991,2015-10-30 10:26:45:124,1446172005124.0 \n0.1053,-0.401,9.0225,0.044,-0.0596,9.8064,-0.3751,0.1075,-0.2138,-2.4,20.9,-40.7,0.08831366,-0.16,-0.18,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,268094,2015-10-30 10:26:45:227,1446172005227.0 \n-0.2813,0.5962,8.3498,-0.0949,-0.1424,9.8052,0.0428,0.1332,0.1393,-3.2,21.1,-40,0.155857902,0.8,0.3,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,268196,2015-10-30 10:26:45:329,1446172005329.0 \n0.1137,1.0475,9.4367,-0.2241,-0.149,9.803,-0.0147,0.1405,0.1478,-3.1,21.2,-39.4,0.182037841,0.8,1.13,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,268297,2015-10-30 10:26:45:430,1446172005430.0 \n-0.7195,0.2059,11.819,-0.3495,-0.1484,9.7993,0.0367,0.1417,0.1491,-2.6,21.1,-39.1,0.204727121,0.95,1.8,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,268399,2015-10-30 10:26:45:532,1446172005532.0 \n-0.2801,-0.6596,12.6498,-0.3773,0.0393,9.7993,-0.3238,-0.0134,-0.0843,-1.9,21,-39.4,0.163886417,-0.23,2.21,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,268502,2015-10-30 10:26:45:635,1446172005635.0 \n-1.2629,-0.0024,9.347,-0.387,-0.0809,9.7987,0.011,-0.171,0.1686,-1.6,21,-39.3,0.175754656,0.48,2.46,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,268603,2015-10-30 10:26:45:736,1446172005736.0 \n-0.7757,0.5447,8.26,-0.2777,-0.2436,9.7997,-0.1625,0.1686,-0.0379,-1.3,21,-38.9,0.09424778,1.16,1.34,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,268706,2015-10-30 10:26:45:839,1446172005839.0 \n-0.759,0.7626,8.6012,-0.2959,-0.2191,9.7997,0.0733,0.0672,-0.0635,-1.2,21.2,-38.7,0.108035881,1.38,1.73,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,268807,2015-10-30 10:26:45:940,1446172005940.0 \n-1.0499,0.5195,9.3948,-0.3414,-0.1334,9.7998,0.099,0.0428,-0.022,-1.2,21.2,-38.6,0.112050138,0.82,1.91,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,268909,2015-10-30 10:26:46:042,1446172006042.0 \n-0.8823,-0.0144,11.1713,-0.2973,-0.0919,9.8017,0.2114,0.0892,0.0403,-1.3,21.2,-38.6,0.104370689,0.82,1.68,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,269011,2015-10-30 10:26:46:144,1446172006144.0 \n-1.4305,-1.5814,12.3924,-0.3219,-0.2655,9.7978,-0.562,0.2065,-0.3311,-1.4,21,-38.5,0.099832833,0.53,1.61,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,269113,2015-10-30 10:26:46:246,1446172006246.0 \n-0.018,-0.4214,8.9316,-0.2961,-0.2586,9.7988,0.2382,-0.0904,0.1002,-1.6,21.1,-38.3,0.163188285,1.7,1.92,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,269216,2015-10-30 10:26:46:349,1446172006349.0 \n-0.1329,0.6261,6.365,-0.3595,-0.2208,9.7976,0.2553,0.1686,-0.0012,-1.7,21.3,-37.9,0.166853476,1.29,2.1,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,269317,2015-10-30 10:26:46:450,1446172006450.0 \n-0.808,0.4657,9.487,-0.528,-0.1818,9.7907,0.066,0.1405,-0.0831,-1.9,21.7,-37.7,0.180816111,1.2,2.84,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,269420,2015-10-30 10:26:46:553,1446172006553.0 \n-1.2605,0.267,10.6063,-0.6735,-0.0946,9.783,0.3604,-0.2541,0.5424,-1.8,21.5,-37.6,0.214500965,0.92,4.02,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,269521,2015-10-30 10:26:46:654,1446172006654.0 \n0.8188,0.0611,12.1733,-0.461,0.2749,9.7919,0.2859,-0.3005,0.4997,-1.4,21,-38.2,0.125663706,-1.61,2.7,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,269623,2015-10-30 10:26:46:756,1446172006756.0 \n-0.3663,0.3891,7.7393,-0.2686,0.0746,9.8027,0.1356,-0.0244,0.1527,-1.4,20.9,-38.5,0.097214839,-0.23,1.6,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,269726,2015-10-30 10:26:46:859,1446172006859.0 \n-0.6009,0.4202,8.6526,-0.1748,-0.0274,9.8051,-0.1344,0.1393,-0.1894,-1.5,20.7,-38.2,0.080110613,0.16,1.02,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,269827,2015-10-30 10:26:46:960,1446172006960.0 \n-1.3228,0.3508,9.2799,-0.2751,-0.1035,9.8022,-0.0733,0.0953,-0.182,-1.8,21,-37.9,0.142942466,0.56,1.46,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,269929,2015-10-30 10:26:47:062,1446172007062.0 \n-1.4856,0.2346,9.3553,-0.4295,-0.0024,9.7972,0.0183,0.077,0.0024,-1.9,21.2,-37.5,0.167551608,0.08,2.39,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,270032,2015-10-30 10:26:47:165,1446172007165.0 \n-0.5602,0.0575,10.3753,-0.3302,0.055,9.8009,-0.0257,-0.1857,0.0452,-2.1,21.4,-37.5,0.157079633,-0.12,2.08,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,270134,2015-10-30 10:26:47:267,1446172007267.0 \n-0.6895,-0.7697,11.5855,-0.3966,-0.3461,9.7925,0.1918,-0.0611,0.1087,-2.3,21.6,-37.4,0.149923783,1.32,1.85,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,270236,2015-10-30 10:26:47:369,1446172007369.0 \n0.2155,-0.7195,10.8326,-0.3081,-0.3693,9.7948,-0.314,-0.0757,-0.11,-2.4,22,-36.8,0.15812683,1.62,2.08,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,270338,2015-10-30 10:26:47:471,1446172007471.0 \n-0.4405,0.8033,7.9715,-0.4538,-0.3916,9.7883,0.055,0.2077,0.0354,-2.7,22.9,-36.7,0.215548163,2.29,2.65,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,270439,2015-10-30 10:26:47:572,1446172007572.0 \n-0.0395,1.075,9.0477,-0.6352,-0.3642,9.7793,0.066,0.1002,-0.0855,-2.5,23.1,-36.7,0.183259571,2.23,3.1,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,270541,2015-10-30 10:26:47:674,1446172007674.0 \n-1.3024,0.1448,11.382,-0.6926,-0.1346,9.7812,0.248,0.0134,0.1063,-2.4,23.2,-36.8,0.203854457,1.28,4.02,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,270643,2015-10-30 10:26:47:776,1446172007776.0 \n-0.978,-1.3707,12.6258,-0.5221,-0.096,9.7923,-0.2615,-0.3054,-0.0831,-2,22.8,-36.8,0.185179434,0.13,3.56,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,270745,2015-10-30 10:26:47:878,1446172007878.0 \n-0.7649,0.073,8.8526,-0.362,-0.0071,9.8,-0.1002,-0.3494,0.2651,-1.9,22.5,-36.7,0.145385927,0.04,2.12,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,270848,2015-10-30 10:26:47:981,1446172007981.0 \n-1.0104,-0.4657,10.3801,-0.2524,-0.2688,9.7997,-0.3641,-0.0037,0.1136,-1.9,22.4,-36.7,0.124616509,0.57,1.1,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,270949,2015-10-30 10:26:48:082,1446172008082.0 \n0.1544,1.0726,7.6255,-0.4133,-0.2463,9.7948,0.0489,0.044,0.2786,-1.6,22.7,-36.2,0.155857902,1.53,2.33,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,271051,2015-10-30 10:26:48:184,1446172008184.0 \n-0.3783,0.8068,9.5948,-0.4408,-0.2257,9.7941,0.1869,-0.0819,-0.2663,-1.3,23,-36.1,0.117111593,1.67,2.52,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,16 / 16,271154,2015-10-30 10:26:48:287,1446172008287.0 \n-0.4034,-0.3783,10.5249,-0.3302,-0.1419,9.8001,0.022,-0.0892,-0.4154,-1,23.3,-35.8,0.098087504,0.83,1.93,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,271255,2015-10-30 10:26:48:388,1446172008388.0 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\n-0.6369,0.923,10.1466,-0.6501,-0.2107,9.7828,0.4032,-0.1002,0.3555,-2.3,23.9,-34.1,0.187622895,1.95,3.95,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,271765,2015-10-30 10:26:48:898,1446172008898.0 \n-1.3635,-1.4389,12.9371,-0.4793,-0.1926,9.793,-0.1173,-0.1075,0.055,-1.8,23.6,-34.4,0.169122405,0.57,3.44,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,271868,2015-10-30 10:26:49:001,1446172009001.0 \n-0.6069,-0.1018,8.5521,-0.3958,-0.1711,9.7972,0.1051,-0.2443,0.2346,-1.2,23.4,-34.6,0.107337749,1,2.31,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,271969,2015-10-30 10:26:49:102,1446172009102.0 \n-1.0044,0.0491,8.8286,-0.3876,-0.3061,9.7942,-0.0073,0.2541,0.033,-1,23.4,-34.8,0.09546951,1.64,1.81,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,272071,2015-10-30 10:26:49:204,1446172009204.0 \n-0.7901,0.656,8.5497,-0.5131,-0.2686,9.7895,0.0501,0.1625,-0.0696,-0.3,23.6,-34.5,0.070860368,1.6,2.76,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,272173,2015-10-30 10:26:49:306,1446172009306.0 \n-1.7777,-0.0443,10.1933,-0.6022,-0.2315,9.7854,0.0086,0.0623,-0.2443,0,23.6,-34.3,0.090757121,1.43,3.55,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,272275,2015-10-30 10:26:49:408,1446172009408.0 \n-0.1808,-1.0523,11.7029,-0.5462,-0.3044,9.7867,-0.2114,-0.099,-0.1381,0.5,23.4,-33.8,0.04415683,0.86,3.36,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,272377,2015-10-30 10:26:49:510,1446172009510.0 \n-0.0479,0.0443,8.6143,-0.639,-0.3232,9.7805,0.2321,-0.1381,0.1112,0.7,23.4,-33.1,0.057421332,2.45,3.89,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,272479,2015-10-30 10:26:49:612,1446172009612.0 \n-0.5495,-0.2334,7.4986,-0.5305,-0.3307,9.7867,0.0941,0.0281,-0.0293,0.7,23.4,-32.6,0.035953783,1.93,3.1,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,272582,2015-10-30 10:26:49:715,1446172009715.0 \n-0.6716,0.3567,8.2791,-0.5263,-0.3092,9.7876,0.0012,0.0122,-0.0061,0.9,23.4,-32.2,0.034208453,1.93,3.13,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,272684,2015-10-30 10:26:49:817,1446172009817.0 \n-0.0491,0.656,9.3841,-0.5146,-0.2752,9.7893,0.0342,0.0428,0.0391,1.2,22.9,-32,0.030892328,1.61,3.01,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,272785,2015-10-30 10:26:49:918,1446172009918.0 \n-1.3695,0.1269,11.8681,-0.4071,-0.0964,9.7977,0.4716,-0.3616,0.2468,1.4,22.8,-31.7,0.034208453,1.48,3.14,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,272888,2015-10-30 10:26:50:021,1446172010021.0 \n-1.9261,-1.2833,10.24,-0.2371,-0.2087,9.8016,-0.4313,0.0073,-0.1576,1.6,22.4,-31.6,6.225938508,1.24,1.39,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,272989,2015-10-30 10:26:50:122,1446172010122.0 \n-0.2586,0.0646,8.9184,0.0357,-0.1291,9.8057,-0.1772,-0.2309,0.1649,1.8,22,-31.9,6.197838707,0.55,0.26,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,273092,2015-10-30 10:26:50:225,1446172010225.0 \n-0.4968,0.334,9.1004,-0.0319,-0.3648,9.7998,0.0098,0.0892,0.1283,1.8,21.8,-31.7,6.192253653,2.13,0.19,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,273193,2015-10-30 10:26:50:326,1446172010326.0 \n-0.249,0.8894,7.9045,-0.1554,-0.2723,9.8016,0.1576,0.1148,0.0635,2.1,21.8,-31.6,6.207961616,1.74,0.75,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,273295,2015-10-30 10:26:50:428,1446172010428.0 \n-0.7015,-0.2011,11.0061,-0.2138,-0.1551,9.8031,0.2602,-0.0318,-0.0941,2.4,21.9,-31.2,6.22070252,1.34,1.24,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,273397,2015-10-30 10:26:50:530,1446172010530.0 \n-0.9373,-1.5874,13.5117,-0.2389,-0.1906,9.8019,-0.5046,0.2077,-0.3775,2.6,21.5,-31.2,6.178640085,1.11,1.4,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,273500,2015-10-30 10:26:50:633,1446172010633.0 \n0.1568,0.243,7.4496,-0.504,-0.2359,9.7909,-0.2847,0.0195,-0.2187,2.8,21.3,-31.1,6.210928676,1.66,2.85,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,273602,2015-10-30 10:26:50:735,1446172010735.0 \n-0.5471,0.2693,7.2987,-0.5154,-0.4195,9.7841,-0.0525,0.044,-0.1344,2.8,21.4,-30.7,6.210405077,2.46,2.89,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,273703,2015-10-30 10:26:50:836,1446172010836.0 \n-0.7051,0.2813,8.9244,-0.4345,-0.4355,9.7873,0.1087,-0.1637,0.0757,2.9,21.6,-30.4,6.209008814,2.69,2.81,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,273806,2015-10-30 10:26:50:939,1446172010939.0 \n-0.6117,-0.0431,10.228,-0.3682,-0.3663,9.7929,0.2639,0,0.1588,2.6,21.7,-30.1,6.192253653,2.42,2.12,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,273907,2015-10-30 10:26:51:040,1446172011040.0 \n0.5124,0.1161,9.9264,-0.3443,-0.1234,9.7998,0.2908,0.022,0.2162,2.6,21.4,-30.2,6.18911206,0.72,2.01,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,274010,2015-10-30 10:26:51:143,1446172011143.0 \n-1.2989,-0.759,9.426,-0.2223,-0.2283,9.8015,0.2101,0.0562,0.2969,2.4,21.2,-30.6,6.214244802,1.51,1.12,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,274111,2015-10-30 10:26:51:244,1446172011244.0 \n-0.1053,0.0431,8.9962,-0.114,-0.3027,9.8013,-0.1429,0.1491,-0.0538,2.5,20.7,-31,6.149667619,1.54,0.54,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,274213,2015-10-30 10:26:51:346,1446172011346.0 \n-0.978,0.2849,8.7161,-0.2658,-0.333,9.7974,-0.0208,0.11,-0.0281,2.5,20.7,-31.1,6.169040774,2.07,1.34,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,274316,2015-10-30 10:26:51:449,1446172011449.0 \n-1.0523,0.3053,10.8086,-0.3673,-0.2482,9.7966,-0.022,0.0232,-0.0257,2.9,20.2,-31.5,6.18789033,1.52,2.16,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,274418,2015-10-30 10:26:51:551,1446172011551.0 \n-1.2665,0.0682,11.3318,-0.3895,-0.0693,9.7987,0.2492,0.0757,-0.0684,3.2,19.9,-31.8,6.191380989,0.82,2.15,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,274520,2015-10-30 10:26:51:653,1446172011653.0 \n-0.5698,-0.7015,11.576,-0.5011,-0.1357,9.7929,-0.0195,0.1723,-0.0342,3.3,19,-32.5,6.210056012,0.79,2.93,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,274621,2015-10-30 10:26:51:754,1446172011754.0 \n-0.3519,-0.3196,9.6498,-0.5016,-0.1751,9.7922,-0.0476,-0.1466,-0.1979,3.4,18.4,-32.7,6.219480789,0.84,3.26,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,274724,2015-10-30 10:26:51:857,1446172011857.0 \n-1.2582,0.4345,8.0481,-0.6096,-0.2265,9.7851,0.0635,0.0159,-0.1197,3.3,17.8,-32.8,6.224018646,1.42,3.43,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,274826,2015-10-30 10:26:51:959,1446172011959.0 \n-1.1157,0.504,8.5341,-0.613,-0.2046,9.7853,-0.1442,-0.0073,0.0684,3.1,17.5,-32.9,6.233094358,1.16,3.69,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,274927,2015-10-30 10:26:52:060,1446172012060.0 \n-0.9182,-0.0646,10.4842,-0.6879,-0.2823,9.7784,-0.0208,0.1393,0.1136,2.7,17,-32.9,6.240948339,1.65,4.02,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,275029,2015-10-30 10:26:52:162,1446172012162.0 \n-0.4058,-1.3036,11.0852,-0.555,-0.3711,9.7839,-0.4875,-0.2382,-0.0782,2.5,16.7,-32.9,6.227683837,1.35,3.63,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,275131,2015-10-30 10:26:52:264,1446172012264.0 \n-0.4453,0.1748,8.2025,-0.4439,-0.3763,9.7894,0.1478,-0.4117,0.1161,1.9,16.7,-33,6.251245782,2.2,2.6,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,275234,2015-10-30 10:26:52:367,1446172012367.0 \n-0.8583,-0.2478,9.0034,-0.2323,-0.3829,9.7964,-0.0709,-0.0941,0.0648,1.4,16.7,-33.2,6.276378523,2.27,1.55,36.81317,-119.748024,277.2,336.3870389,1.91,51.612904,42.2,0 / 16,275335,2015-10-30 10:26:52:468,1446172012468.0 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\n-0.7757,0.7123,8.6275,-0.4206,-0.0964,9.7972,-0.1564,-0.0623,-0.0183,-3.6,17.1,-30.4,0.306305284,0.56,2.46,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,286861,2015-10-30 10:27:03:994,1446172023994.0 \n-0.5016,0.911,9.1722,-0.4283,-0.0658,9.7971,0.0684,0.0367,0.0208,-3.8,17.1,-30.1,0.306130751,0.49,2.48,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,286963,2015-10-30 10:27:04:096,1446172024096.0 \n-1.0499,0.3316,10.6698,-0.4179,0.1053,9.7972,0.2908,0.0782,0.1527,-3.9,16.9,-30.1,0.295658775,-0.62,2.44,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,287065,2015-10-30 10:27:04:198,1446172024198.0 \n-0.6428,-1.0271,11.5245,-0.4116,0.1851,9.7963,0.1442,-0.0086,0.1564,-3.7,16.3,-30.3,0.313461134,-1.47,2.74,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,287167,2015-10-30 10:27:04:300,1446172024300.0 \n-0.7626,0.5339,8.7831,-0.3792,-0.1219,9.7986,-0.0867,-0.0086,0.2566,-3.4,15.8,-30,0.26494098,0.38,2.46,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,287270,2015-10-30 10:27:04:403,1446172024403.0 \n-0.4896,0.34,9.8497,-0.2386,-0.282,9.7997,-0.1051,-0.121,0.0525,-3.3,15.7,-29.9,0.247138622,1.51,1.6,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,287371,2015-10-30 10:27:04:504,1446172024504.0 \n-1.0762,0.4812,9.2787,-0.1861,-0.1338,9.804,0.2321,-0.0171,-0.0342,-3.5,15.9,-29.1,0.228289066,1.18,1.14,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,287473,2015-10-30 10:27:04:606,1446172024606.0 \n-0.9481,0.34,9.0788,-0.2748,0.1408,9.8018,0.3421,0.1234,-0.0476,-3.7,15.7,-29.3,0.283266938,-0.27,1.38,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,287576,2015-10-30 10:27:04:709,1446172024709.0 \n0.6309,0.6057,8.1702,-0.312,0.3425,9.7957,0.1588,-0.0611,0.0367,-3.9,15.1,-29.3,0.302116494,-2.02,1.96,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,287677,2015-10-30 10:27:04:810,1446172024810.0 \n0.7254,0.4621,9.3158,-0.3132,-0.0186,9.8016,0.0696,-0.1038,0.1857,-4.2,14.6,-29.5,0.319046187,0.1,1.86,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,287779,2015-10-30 10:27:04:912,1446172024912.0 \n-0.4681,0.2143,9.4284,-0.2789,-0.2095,9.8004,0.0037,-0.0086,0.0367,-4.4,14.7,-29.2,0.323584043,1.22,1.63,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,287885,2015-10-30 10:27:05:018,1446172025018.0 \n-0.486,0.4776,9.068,-0.3617,-0.2175,9.7976,-0.0403,0.1136,0.0745,-4.7,15.1,-28.9,0.397760537,1.34,2.01,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,287984,2015-10-30 10:27:05:117,1446172025117.0 \n-0.2801,0.2693,9.9455,-0.4416,-0.129,9.7959,0.0757,0.1002,0.088,-4.6,15.5,-28.7,0.381005376,0.93,2.42,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,288085,2015-10-30 10:27:05:218,1446172025218.0 \n-1.1708,0.741,10.9271,-0.5464,0.0913,9.791,0.3653,0.055,0.292,-4.3,15.5,-28.7,0.332136157,-0.53,3.19,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,288187,2015-10-30 10:27:05:320,1446172025320.0 \n-0.5674,-0.0443,12.5157,-0.4658,0.1303,9.7947,-0.3702,-0.2712,0.2004,-3.9,15.2,-29,0.343131731,-1.49,3.22,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,288289,2015-10-30 10:27:05:422,1446172025422.0 \n-0.8116,-0.0551,9.7169,-0.2883,0.0499,9.8023,-0.1625,-0.1161,0.0586,-3.7,15.1,-29.2,0.311541271,-0.58,1.83,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,288392,2015-10-30 10:27:05:525,1446172025525.0 \n-0.7135,0.0862,9.1459,-0.2901,0.0291,9.8023,0.1772,0.0428,0.0916,-3.6,15.2,-29.3,0.31084314,0.02,1.62,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,288494,2015-10-30 10:27:05:627,1446172025627.0 \n-0.5267,0.9218,8.9627,-0.4352,0.1919,9.7951,0.1588,0.226,-0.0599,-3.6,15.5,-29.7,0.301941961,-0.86,2.15,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,288596,2015-10-30 10:27:05:729,1446172025729.0 \n-1.1875,0.3519,8.9423,-0.6201,0.4605,9.7699,0.3714,0.1014,-0.1796,-3.3,15.1,-30.1,0.290248255,-2.69,3.63,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,288698,2015-10-30 10:27:05:831,1446172025831.0 \n-1.0391,-0.5926,11.8441,-0.607,0.5362,9.7731,-0.4618,0.0183,-0.3604,-2.9,14.4,-30.7,0.297927703,-3.96,3.6,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,288800,2015-10-30 10:27:05:933,1446172025933.0 \n-0.4752,0.5638,8.3606,-0.7668,0.2246,9.774,-0.3494,0.0513,-0.1014,-2.8,14.1,-30.6,0.34365533,-1.71,4.34,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,288902,2015-10-30 10:27:06:035,1446172026035.0 \n0.2981,0.6536,10.1227,-0.5989,-0.0797,9.788,-0.2749,-0.3091,-0.1002,-2.9,14.6,-30.7,0.319918852,0.47,3.5,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,289004,2015-10-30 10:27:06:137,1446172026137.0 \n-0.8033,0.8176,9.1542,-0.6415,-0.2351,9.7828,-0.0855,-0.1075,-0.0916,-3,15.2,-30.4,0.339990138,1.13,4.03,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,289106,2015-10-30 10:27:06:239,1446172026239.0 \n-0.4381,0.395,10.1035,-0.6313,-0.1423,9.7853,0.182,-0.0635,0.1075,-3,15.7,-30.2,0.310668607,1.08,3.75,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,289207,2015-10-30 10:27:06:340,1446172026340.0 \n0.2251,0.7422,9.6151,-0.5268,0.2322,9.7897,0.5522,-0.1197,0.2602,-3.1,15.7,-30.3,0.285710399,-0.42,3.38,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,289310,2015-10-30 10:27:06:443,1446172026443.0 \n-0.8571,-0.1269,11.072,-0.3846,0.187,9.7973,0.3946,0.1026,0.099,-3.2,15.3,-30.7,0.264068316,-1.09,2.25,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,289412,2015-10-30 10:27:06:545,1446172026545.0 \n-0.6369,0.1329,9.6307,-0.3806,0.2493,9.7961,-0.0904,0.0183,0.1368,-3.2,14.9,-30.7,0.258483262,-2.13,2.35,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,289513,2015-10-30 10:27:06:646,1446172026646.0 \n-1.1636,0.2837,9.6319,-0.3672,0.2021,9.7977,-0.0733,-0.0892,0.0562,-3.2,14.7,-31.1,0.258832328,-1.12,2.09,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,289616,2015-10-30 10:27:06:749,1446172026749.0 \n-0.9804,1.0403,9.2165,-0.4358,0.2371,9.7941,-0.0586,0.0257,-0.0305,-3,14.7,-31,0.267558974,-1.47,2.46,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,289717,2015-10-30 10:27:06:850,1446172026850.0 \n-1.6125,1.0953,11.1139,-0.4536,0.3204,9.7909,0.1515,-0.0305,-0.0745,-2.8,15,-31.2,0.271747765,-1.61,2.63,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,289819,2015-10-30 10:27:06:952,1446172026952.0 \n-0.6871,-0.3855,10.6853,-0.3338,0.4068,9.7925,-0.4203,0.0098,-0.1515,-2.8,14.9,-31.4,0.244171562,-2.38,1.95,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,289921,2015-10-30 10:27:07:054,1446172027054.0 \n0.1209,0.5435,8.1247,-0.4373,0.3622,9.7902,0.2871,0.1759,0.2114,-2.9,14.9,-31.5,0.255167137,-1.77,2.15,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,290023,2015-10-30 10:27:07:156,1446172027156.0 \n-0.176,0.6213,8.0984,-0.526,0.1996,9.7905,-0.0489,0.1735,0.0819,-2.9,14.8,-32,0.282568806,-1.28,2.8,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,290125,2015-10-30 10:27:07:258,1446172027258.0 \n0.0946,1.2198,8.3989,-0.5887,0.1978,9.787,0.0929,0.0208,0.0916,-2.6,15,-32.1,0.304385422,-0.91,3.36,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,290228,2015-10-30 10:27:07:361,1446172027361.0 \n-0.3962,0.6536,9.9659,-0.5823,0.2408,9.7864,0.011,-0.0073,-0.0354,-2.2,15.1,-32.6,0.246789556,-1.37,3.44,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,290329,2015-10-30 10:27:07:462,1446172027462.0 \n-0.2358,-0.4393,10.5524,-0.5343,0.3617,9.7854,0.1087,-0.1271,0.1393,-1.7,15.1,-32.6,0.240680904,-2.26,3.48,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,290431,2015-10-30 10:27:07:564,1446172027564.0 \n0.0682,0.6249,9.0872,-0.3793,0.3933,9.7914,0.1063,-0.237,0.121,-1.7,15.2,-32.7,0.217817091,-1.81,2.69,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,290534,2015-10-30 10:27:07:667,1446172027667.0 \n-1.1791,0.3364,9.3218,-0.2276,0.2587,9.8006,-0.2175,-0.1637,-0.1442,-1.9,15.1,-32.7,0.172613063,-1.51,1.33,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,290635,2015-10-30 10:27:07:768,1446172027768.0 \n-1.719,0.5614,8.7568,-0.1959,0.0496,9.8046,-0.066,-0.1112,0.0733,-2.3,15.4,-32.7,0.17959438,-0.27,1.31,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,290738,2015-10-30 10:27:07:871,1446172027871.0 \n-1.2175,0.8978,8.6862,-0.1673,0.1482,9.8041,0.1478,-0.1161,0.3531,-2.5,15.6,-32.7,0.161792022,-0.6,1.16,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,290839,2015-10-30 10:27:07:972,1446172027972.0 \n0.1844,0.7578,9.0118,-0.083,0.3465,9.8002,0.3946,-0.1234,0.6011,-2.2,15.6,-32.6,0.132121424,-2.02,0.49,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,290942,2015-10-30 10:27:08:075,1446172028075.0 \n-2.2697,-1.664,12.7671,0.0294,0.2828,9.8025,-0.4936,0.0452,0.11,-1.9,15.5,-32.7,0.107163216,-2.46,-0.22,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,291043,2015-10-30 10:27:08:176,1446172028176.0 \n-1.834,0.0084,9.8845,-0.0557,0.3384,9.8007,-0.1857,0.0415,0.6671,-0.9,15.3,-32.9,0.073478362,-1.98,0.33,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,291145,2015-10-30 10:27:08:278,1446172028278.0 \n-1.2773,1.0271,8.5126,-0.1806,0.242,9.802,-0.1222,0.2871,0.8344,0,15.4,-32.9,0.019547688,-1.45,0.54,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,291248,2015-10-30 10:27:08:381,1446172028381.0 \n-0.3974,0.8487,8.4072,-0.2969,0.2757,9.7983,0.1075,0.0476,1.0971,2,15.2,-32.8,6.214070269,-1.36,1.58,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,291349,2015-10-30 10:27:08:482,1446172028482.0 \n-0.401,0.4322,9.5026,-0.3517,0.3695,9.7934,0.2175,0.0757,1.0043,3.7,14.8,-32.7,6.109001448,-1.77,2.05,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,291451,2015-10-30 10:27:08:584,1446172028584.0 \n-0.4262,-0.3268,12.2056,-0.2644,0.39,9.7953,-0.3714,-0.1185,0.6365,5.8,13.9,-32.3,5.981592412,-2.68,2.11,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,291553,2015-10-30 10:27:08:686,1446172028686.0 \n-1.0211,0.1077,10.416,-0.3613,0.1604,9.7987,-0.1393,0.2297,1.0287,7.9,12.7,-31.9,5.816484265,-0.94,2.11,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,291655,2015-10-30 10:27:08:788,1446172028788.0 \n-0.231,0.4525,8.0086,-0.4918,-0.0627,9.7941,-0.1148,0.2602,0.7123,9.5,11.9,-31.2,5.643522136,0.45,2.31,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,291757,2015-10-30 10:27:08:890,1446172028890.0 \n-0.1963,0.6345,8.351,-0.586,-0.0187,9.7891,-0.0171,-0.0403,0.4337,10.6,11.3,-30.8,5.587497067,0.14,3.44,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,291859,2015-10-30 10:27:08:992,1446172028992.0 \n-0.723,0.4645,9.9814,-0.5542,-0.0117,9.791,-0.0513,-0.2016,0.1136,11.7,10.5,-30.1,5.531297465,0.1,3.33,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,291961,2015-10-30 10:27:09:094,1446172029094.0 \n0.4573,0.7829,9.2751,-0.474,0.0299,9.7951,0.1649,0.0867,0.1576,12.2,9.8,-29.6,5.476319594,-0.17,2.77,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,292063,2015-10-30 10:27:09:196,1446172029196.0 \n-2.2087,-1.8663,13.6936,-0.58,-0.354,9.7831,0.011,0.5266,-0.0745,12.2,9.7,-29.3,5.438795015,1.08,2.69,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,292165,2015-10-30 10:27:09:298,1446172029298.0 \n-0.4968,-0.929,11.5951,-0.6336,-0.2041,9.784,-0.0428,-0.0855,-0.2798,12.1,9.7,-28.8,5.475097864,0.91,3.96,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,292268,2015-10-30 10:27:09:401,1446172029401.0 \n-0.4764,0.0694,7.7369,-0.8031,-0.091,9.7733,0.182,0.2773,-0.1576,12,9.8,-28.3,5.490107695,0.74,4.48,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,292369,2015-10-30 10:27:09:502,1446172029502.0 \n0.4034,0.5255,9.1482,-0.8923,-0.0177,9.766,-0.0012,0.1869,-0.2981,11.9,9.8,-27.8,5.525886945,0.1,5.22,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,292472,2015-10-30 10:27:09:605,1446172029605.0 \n0.7159,0.1568,11.1043,-1.0588,0.1535,9.7481,0.3567,0.4447,-0.909,11.8,9.9,-27.6,5.538627848,-0.04,5.55,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,292573,2015-10-30 10:27:09:706,1446172029706.0 \n-0.7242,-1.5419,12.6785,-1.4228,0.0105,9.7029,-0.0379,0.182,-1.08,11.4,10.1,-27.6,5.708971983,-1.01,8.38,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,292676,2015-10-30 10:27:09:809,1446172029809.0 \n0.2562,-0.3292,8.1977,-1.3145,-0.0691,9.7179,0.0098,-0.3567,-1.1985,11,10.6,-27.2,5.715255169,0.13,8.32,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,292777,2015-10-30 10:27:09:910,1446172029910.0 \n-0.5387,-0.7661,8.6814,-1.0201,-0.4592,9.7426,0.0635,-0.0953,-1.1826,9.4,11.9,-26.9,5.777039824,2.37,6.25,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,292879,2015-10-30 10:27:10:012,1446172030012.0 \n-0.8152,0.0479,8.8166,-0.9223,-0.527,9.7489,0.1515,0.0379,-1.1826,7.1,13.2,-26.2,5.907241386,3.16,5.35,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,292981,2015-10-30 10:27:10:114,1446172030114.0 \n-1.4629,-0.5914,10.1801,-0.8393,-0.5276,9.7564,0.0501,-0.121,-1.0886,5.3,14.1,-25.7,6.079330851,3.09,5.26,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,293083,2015-10-30 10:27:10:216,1446172030216.0 \n-0.0407,0.2945,9.4774,-0.5697,-0.2344,9.7873,0.4178,-0.3238,-0.4325,3.1,14.7,-25.3,6.192777252,1.86,3.92,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,293185,2015-10-30 10:27:10:318,1446172030318.0 \n-0.8775,-1.0355,12.5384,-0.4714,-0.4053,9.7869,0.16,0.0599,-0.5498,1.9,14.8,-25.4,6.228905567,2.13,2.83,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,293288,2015-10-30 10:27:10:421,1446172030421.0 \n-0.3891,-0.0479,9.9288,-0.4564,-0.2076,9.7938,0.2395,-0.0819,-0.2639,0.6,14.7,-25.7,0.014660766,1.21,2.67,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,293390,2015-10-30 10:27:10:523,1446172030523.0 \n-0.3926,0.6309,7.9116,-0.4475,-0.1718,9.7949,0.1503,-0.0049,0.2065,0.1,14.7,-25.6,0.079587014,1.43,2.52,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,293492,2015-10-30 10:27:10:625,1446172030625.0 \n-0.3723,0.7195,8.9938,-0.8151,-0.1628,9.7714,0.0501,0.1124,0.2272,0.1,14.7,-25.6,0.126710904,0.97,4.09,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,293593,2015-10-30 10:27:10:726,1446172030726.0 \n-1.0415,0.0371,10.0161,-0.7305,-0.0966,9.7789,0.0098,-0.1613,0.2334,0.5,14.8,-25.4,0.069115038,0.56,4.63,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,293696,2015-10-30 10:27:10:829,1446172030829.0 \n-1.166,-0.6668,13.0053,-0.3583,-0.1213,9.7994,-0.4264,-0.3983,-0.0562,1.2,14.6,-25.5,0.009075712,-0.2,2.6,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,293797,2015-10-30 10:27:10:930,1446172030930.0 \n-0.4034,0.5974,8.0038,-0.3687,-0.1649,9.7983,-0.1979,-0.1307,-0.0049,1.4,14.8,-25.4,0.002792527,1,2.39,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,293899,2015-10-30 10:27:11:032,1446172031032.0 \n-0.9014,0.3771,8.7592,-0.4037,-0.387,9.7907,0.1063,0.1173,0.0293,1.4,15.1,-24.9,0.002268928,2.26,2.36,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,294001,2015-10-30 10:27:11:134,1446172031134.0 \n-1.0427,0.261,9.1207,-0.4796,-0.267,9.7913,0.1148,-0.0159,0.0183,1.7,15.4,-24.4,6.225763975,1.56,2.8,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,294104,2015-10-30 10:27:11:237,1446172031237.0 \n-0.6452,0.0239,10.7093,-0.3323,-0.1765,9.7994,0.2309,-0.088,-0.1271,1.8,15.5,-24.1,6.216164664,1.45,2.31,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,294205,2015-10-30 10:27:11:338,1446172031338.0 \n0.8104,-0.2047,10.1742,-0.2674,-0.0584,9.8028,-0.2627,0.121,-0.2517,1.8,15.3,-24.6,6.193300851,0.22,1.51,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,294308,2015-10-30 10:27:11:441,1446172031441.0 \n-0.3472,-0.1568,9.6019,-0.3724,-0.265,9.796,-0.1124,0.066,-0.2786,1.8,15.3,-24.4,6.207263485,1.55,2.17,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,294409,2015-10-30 10:27:11:542,1446172031542.0 \n-0.5183,-0.1784,9.0297,-0.2859,-0.3483,9.7963,0.0171,-0.0061,-0.2028,1.5,15.5,-24,6.193824449,2.16,1.55,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,294511,2015-10-30 10:27:11:644,1446172031644.0 \n-0.3352,0.577,8.752,-0.356,-0.2781,9.7962,0.226,-0.0086,-0.0049,1.4,15.7,-23.4,6.271666134,1.83,2.05,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,294613,2015-10-30 10:27:11:746,1446172031746.0 \n-0.8847,0.2634,9.8857,-0.3845,-0.0818,9.7988,0.1332,0.0525,-0.0525,1.1,15.7,-23.6,6.275680391,0.89,2.11,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,294715,2015-10-30 10:27:11:848,1446172031848.0 \n-0.4262,0.2023,8.5964,-0.3932,0.2921,9.7944,0.5486,0.1808,0.3457,1.1,15.3,-24,6.274458661,-0.58,2.07,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,294817,2015-10-30 10:27:11:950,1446172031950.0 \n-0.255,0.838,8.2373,-0.3815,0.2484,9.7961,0.1576,0.0489,0.2773,1.2,14.8,-24.1,6.278996517,-1.45,2.23,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,294919,2015-10-30 10:27:12:052,1446172032052.0 \n-0.6979,0.0132,9.2943,-0.3045,0.143,9.8009,-0.2737,0.0342,-0.0525,1.4,14.6,-24,6.271142535,-1.45,1.94,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,295021,2015-10-30 10:27:12:154,1446172032154.0 \n-0.7829,0.6764,8.0828,-0.3546,0.0577,9.8001,0.0953,-0.0061,0.1307,1.6,14.5,-23.9,6.206216287,-0.05,2,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,295124,2015-10-30 10:27:12:257,1446172032257.0 \n-1.1157,0.589,8.8693,-0.4388,0.1413,9.7958,0.0244,0.0403,0.055,1.8,14.4,-23.7,6.214768401,-0.78,2.43,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 14,295225,2015-10-30 10:27:12:358,1446172032358.0 \n-0.5459,0.9984,10.3693,-0.4291,0.2015,9.7952,-0.0367,0.0574,-0.0538,2,14.2,-23.4,6.214768401,-1.18,2.51,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 14,295327,2015-10-30 10:27:12:460,1446172032460.0 \n-0.6608,-0.6225,11.6286,-0.4297,-0.0929,9.7968,-0.4239,-0.0367,-0.2798,2,14.2,-23.2,6.208485215,-0.36,2.34,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 14,295430,2015-10-30 10:27:12:563,1446172032563.0 \n-0.0491,0.1245,8.9411,-0.4224,-0.209,9.7953,-0.1124,-0.0684,-0.0611,1.8,14.2,-22.4,6.205692688,1.22,2.47,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 14,295531,2015-10-30 10:27:12:664,1446172032664.0 \n-0.3867,0.4489,8.3043,-0.3624,-0.334,9.7943,0.0721,0.0782,0.1026,1.7,14.5,-21.7,6.197489641,2.11,2.03,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 14,295633,2015-10-30 10:27:12:766,1446172032766.0 \n-0.5555,1.1301,8.017,-0.3953,-0.2327,9.7959,0.1491,-0.0012,0.1161,1.7,14.7,-21.2,6.203249227,1.54,2.3,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 14,295735,2015-10-30 10:27:12:868,1446172032868.0 \n-0.6716,0.0455,10.5405,-0.5582,-0.0126,9.7907,0.2786,0.2676,0.204,2,14.6,-20.6,6.218782658,0.76,2.86,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 14,295838,2015-10-30 10:27:12:971,1446172032971.0 \n-1.5,-0.8224,13.1059,-0.4614,0.0946,9.7953,-0.3445,-0.248,0.0635,2.7,14.3,-20.5,6.154729074,-1.1,3.26,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 14,295939,2015-10-30 10:27:13:072,1446172033072.0 \n-0.0192,0.8356,9.0501,-0.289,0.1259,9.8016,-0.121,0.0257,-0.0953,3.1,14.2,-20.1,6.124534878,-0.49,2.09,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 14,296042,2015-10-30 10:27:13:175,1446172033175.0 \n-0.808,-0.2765,9.6486,-0.3879,-0.0972,9.7985,-0.4032,0.1197,-0.1515,3.6,14.3,-19.7,6.054896241,0.57,2.27,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 14,296144,2015-10-30 10:27:13:277,1446172033277.0 \n-0.9397,0.6967,6.5912,-0.4315,0.0201,9.7971,0.2199,-0.0098,0.1442,3.8,14.8,-19.2,6.074094863,0.25,2.51,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,296245,2015-10-30 10:27:13:378,1446172033378.0 \n-1.239,0.3172,10.1634,-0.4091,0.0448,9.798,0.1759,-0.1161,0.077,4.1,15,-18.9,6.071127803,-0.17,2.28,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,296348,2015-10-30 10:27:13:481,1446172033481.0 \n-0.7949,0.0012,10.726,-0.3259,0.1935,9.7993,0.0904,-0.0415,-0.0415,4.3,15.3,-18.7,6.069033408,-1.08,1.98,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,296449,2015-10-30 10:27:13:582,1446172033582.0 \n-0.3867,0.0527,10.3023,-0.2689,-0.0471,9.8029,-0.1038,-0.1148,-0.0867,4.3,15.8,-18.6,6.06798621,0.28,1.57,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,296552,2015-10-30 10:27:13:685,1446172033685.0 \n-0.2406,-0.2873,10.4519,-0.0689,-0.1369,9.8055,-0.1161,-0.1698,-0.1808,4.1,16.3,-19,6.053674511,0.42,0.88,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,296654,2015-10-30 10:27:13:787,1446172033787.0 \n-0.9505,0.5148,8.5473,-0.1411,-0.1591,9.8043,-0.0147,0.16,-0.0379,3.8,16.9,-19.3,6.059259564,0.99,0.61,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,296756,2015-10-30 10:27:13:889,1446172033889.0 \n-0.5112,0.6692,8.9615,-0.2394,0.055,9.8036,0.1869,0.088,0.0623,4,17.4,-19.4,6.079330851,-0.32,1.4,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,296857,2015-10-30 10:27:13:990,1446172033990.0 \n-1.0618,0.1053,12.5013,-0.2291,0.2136,9.8016,0.3958,0.0428,0.2443,4.1,17.6,-19.3,6.089104694,-0.58,1.28,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,296960,2015-10-30 10:27:14:093,1446172034093.0 \n-1.5083,-0.5746,11.819,-0.2181,0.1056,9.8037,0.0342,0.0794,0.1943,4.8,17.6,-19.5,6.03691935,-0.62,1.27,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,297062,2015-10-30 10:27:14:195,1446172034195.0 \n-0.3065,0.146,9.2955,-0.0988,0.2006,9.8041,-0.011,-0.2272,0.1344,5.1,17.6,-20,6.035348553,-1.13,0.99,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,297163,2015-10-30 10:27:14:296,1446172034296.0 \n-0.6991,0.0048,9.0465,-0.0696,0.0627,9.8062,-0.1136,0.0244,0.0134,5.6,17.6,-20.6,5.971120437,-0.37,0.41,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,297266,2015-10-30 10:27:14:399,1446172034399.0 \n-0.3519,0.9158,7.2269,-0.1933,0.1377,9.8038,0.0195,0.0525,0.0293,5.9,17.7,-20.9,5.981068814,-0.54,0.9,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,297367,2015-10-30 10:27:14:500,1446172034500.0 \n-0.1437,0.328,12.0895,0.0038,0.122,9.8059,-0.0342,-0.3824,-0.0904,6.3,17.7,-21.2,5.973563898,-0.55,0.48,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,297469,2015-10-30 10:27:14:602,1446172034602.0 \n1.0319,0.3819,10.4746,-0.0068,0.2465,9.8035,-0.2419,-0.1148,-0.2602,6.3,17.6,-21.7,5.977229089,-1.62,0.31,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,297571,2015-10-30 10:27:14:704,1446172034704.0 \n0.7326,0.2418,8.6538,-0.0363,0.0078,9.8066,0.1491,-0.193,-0.1833,6.1,17.5,-22.8,5.966058982,-0.05,0.21,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,297673,2015-10-30 10:27:14:806,1446172034806.0 \n-0.1568,0.0658,9.5241,0.0592,-0.0242,9.8064,-0.2505,0.0134,-0.2627,5.9,17.4,-23.2,5.93551572,-0.17,-0.46,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,297775,2015-10-30 10:27:14:908,1446172034908.0 \n-0.6117,0.7123,8.278,-0.024,-0.0203,9.8066,0.0232,0.0929,-0.0745,5.8,17.4,-23,5.945987696,0.12,0.14,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,297878,2015-10-30 10:27:15:011,1446172035011.0 \n-0.31,0.7123,10.2675,-0.1872,0.0259,9.8048,0.0159,0.1051,0.077,6.1,17.2,-23.2,5.968153377,-0.15,1.09,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,297979,2015-10-30 10:27:15:112,1446172035112.0 \n0.1041,0.9038,10.3046,-0.2626,0.1125,9.8025,-0.1381,-0.2077,0.1246,6.5,16.9,-23.3,5.925392811,-0.42,1.44,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,298082,2015-10-30 10:27:15:215,1446172035215.0 \n-0.5902,-0.0204,9.1327,-0.2086,-0.1169,9.8037,-0.2114,0.2309,0.1381,7.4,16.4,-23.8,5.883504908,0.61,0.83,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,298183,2015-10-30 10:27:15:316,1446172035316.0 \n-0.2334,0.2634,9.0453,-0.1297,-0.1854,9.804,-0.2028,0.0269,0.16,7.9,16.1,-23.8,5.827305307,0.78,0.76,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,298285,2015-10-30 10:27:15:418,1446172035418.0 \n-0.182,0.6201,7.9392,-0.2008,-0.2549,9.8013,-0.044,0.0061,-0.0134,8.7,15.5,-23.6,5.777563423,1.49,1.17,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,298387,2015-10-30 10:27:15:520,1446172035520.0 \n-0.4956,0.3256,9.1482,-0.1973,-0.1838,9.8029,0.1478,-0.0147,-0.0232,9.3,15.1,-23.3,5.750336287,1.31,1.16,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,298489,2015-10-30 10:27:15:622,1446172035622.0 \n-0.1963,0.1903,10.5177,-0.1313,0.0075,9.8058,0.3274,0.0586,-0.1283,10.1,14.4,-23.3,5.678254188,-0.04,0.77,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,298592,2015-10-30 10:27:15:725,1446172035725.0 \n-1.5239,-1.9668,15.0104,-0.1917,-0.2744,9.8009,-0.2346,0.4484,-0.27,10.4,14.1,-23.4,5.680872182,-0.26,0.75,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,298694,2015-10-30 10:27:15:827,1446172035827.0 \n-0.0587,-0.255,10.0078,-0.3177,-0.2411,9.7985,0.1723,-0.0623,-0.0745,10.7,14.1,-23.6,5.640555077,0.93,1.93,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,298795,2015-10-30 10:27:15:928,1446172035928.0 \n-0.644,0.4573,7.2257,-0.4547,-0.2941,9.7917,0.0159,0.1881,-0.0782,11,14.2,-23.5,5.638111616,1.71,2.47,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,298897,2015-10-30 10:27:16:030,1446172036030.0 \n-0.1664,0.4238,9.9515,-0.4095,-0.2837,9.794,0.055,-0.077,0.1112,11.6,14.2,-23.3,5.591511325,1.66,2.39,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,298999,2015-10-30 10:27:16:132,1446172036132.0 \n-0.6632,-0.1125,11.1007,-0.4834,-0.1998,9.7927,0.3213,0.0538,0.2517,12,14,-23.1,5.606695689,1.17,2.83,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,299101,2015-10-30 10:27:16:234,1446172036234.0 \n-1.1145,-1.0116,13.5236,-0.462,0.0253,9.7957,-0.0464,-0.2285,0.1613,12.7,13.4,-23.5,5.544212902,-0.15,2.7,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,299204,2015-10-30 10:27:16:337,1446172036337.0 \n-0.5866,0.3196,8.7185,-0.3243,-0.0865,9.8009,0.022,-0.3091,0.1515,13.3,13,-23.3,5.527632274,0.56,2.4,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,299305,2015-10-30 10:27:16:438,1446172036438.0 \n-0.6428,0.2693,7.9715,-0.2031,-0.2073,9.8024,-0.0147,0.0024,0.1148,13.9,12.7,-23.8,5.458691769,1.21,1.19,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,299407,2015-10-30 10:27:16:540,1446172036540.0 \n-0.6931,0.8045,8.4108,-0.1497,-0.1689,9.8041,0.0635,-0.011,0.1087,14,12.7,-23.5,5.453804847,1.31,0.96,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,299510,2015-10-30 10:27:16:643,1446172036643.0 \n-0.6955,0.1628,11.1785,-0.1311,-0.0502,9.8056,0.1649,-0.0623,-0.0574,14.1,12.5,-23.9,5.465498553,0.56,0.91,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,299611,2015-10-30 10:27:16:744,1446172036744.0 \n-0.5974,0.0335,10.4651,-0.1957,0.1762,9.8031,0.1833,-0.088,-0.0208,14.2,12.2,-24,5.433384494,0.02,0.85,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,299713,2015-10-30 10:27:16:846,1446172036846.0 \n-0.3208,-0.091,9.8031,-0.3927,0.0677,9.7986,-0.2798,0.4019,-0.4056,14.6,12,-24,5.420643591,-0.42,1.84,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,299815,2015-10-30 10:27:16:948,1446172036948.0 \n-0.8009,-0.6572,10.4291,-0.3151,-0.0248,9.8016,-0.3433,-0.2004,-0.3421,14.6,12.1,-23.6,5.426752243,-0.49,2.17,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,299917,2015-10-30 10:27:17:050,1446172037050.0 \n-0.7721,1.1193,7.3071,-0.5597,-0.0718,9.7904,0.0721,0.2346,0.1869,14.7,12.5,-23,5.457644571,0.56,2.86,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,300019,2015-10-30 10:27:17:152,1446172037152.0 \n-0.8511,0.4334,8.916,-0.6007,-0.0233,9.7882,0.0232,0.0892,0.0977,14.9,12.6,-22.7,5.470909073,0.21,3.36,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 15,300122,2015-10-30 10:27:17:255,1446172037255.0 \n0.1413,1.0918,8.7472,-0.62,0.1335,9.7861,0.3958,-0.0171,0.2993,15.3,12.4,-22.6,5.451710452,-0.78,3.63,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,300223,2015-10-30 10:27:17:356,1446172037356.0 \n-2.3499,-1.3946,13.5141,-0.4573,-0.0592,9.7958,-0.3641,0.1662,-0.1161,15.7,12.2,-22.4,5.390100329,-0.27,2.45,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,300325,2015-10-30 10:27:17:458,1446172037458.0 \n-1.3348,-0.1724,9.6091,-0.3733,-0.0226,9.7995,-0.1515,-0.044,-0.0147,15.9,12,-21.9,5.380151952,0.13,2.18,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,300428,2015-10-30 10:27:17:561,1446172037561.0 \n-1.3396,0.2825,9.0908,-0.3824,-0.0676,9.799,-0.0183,-0.0183,0.1417,16,12,-21.5,5.373345168,0.53,2.22,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,300529,2015-10-30 10:27:17:662,1446172037662.0 \n-0.4214,1.1708,8.2696,-0.4719,0.0733,9.795,0.1258,0.0586,0.237,16.3,12,-21.4,5.390798461,-0.27,2.64,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,300631,2015-10-30 10:27:17:764,1446172037764.0 \n-0.8619,0.3759,11.0552,-0.4995,0.1467,9.7928,0.2761,0.0024,-0.0831,16.6,11.7,-21.3,5.36810918,-0.53,3.04,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,300733,2015-10-30 10:27:17:866,1446172037866.0 \n-0.6871,-0.6692,11.5879,-0.4756,0.227,9.7925,-0.0061,-0.1368,-0.1405,17.2,11.4,-21.2,5.336867787,-1.33,2.78,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,300835,2015-10-30 10:27:17:968,1446172037968.0 \n0.2274,0.17,9.3122,-0.4085,0.0455,9.798,0.1405,-0.1258,0.0501,17.4,11.7,-20.7,5.356939073,-0.26,2.43,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,300937,2015-10-30 10:27:18:070,1446172038070.0 \n-0.7422,0.3998,8.4719,-0.4655,-0.0366,9.7955,-0.0024,0.1222,-0.1197,17.5,12.3,-20.1,5.323079686,0.21,2.72,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,301040,2015-10-30 10:27:18:173,1446172038173.0 \n-1.1576,0.5375,8.5856,-0.5925,-0.0042,9.7887,0.1051,0.0318,0.0562,17.6,12.8,-19.8,5.369156378,0.1,3.31,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,301141,2015-10-30 10:27:18:274,1446172038274.0 \n-1.5215,-0.0024,10.8445,-0.6133,0.0151,9.7874,-0.0635,0.0073,0.0098,18,13.3,-19.6,5.376661294,-0.21,3.63,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,301244,2015-10-30 10:27:18:377,1446172038377.0 \n-0.9266,0.9098,10.6099,-0.5137,0.2308,9.7905,0.2334,-0.0452,0.3225,18.2,13.5,-19.5,5.407553621,-0.22,3.3,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,301345,2015-10-30 10:27:18:478,1446172038478.0 \n-0.4776,0.5902,8.6514,-0.4968,0.1325,9.7932,0.0379,-0.1735,0.2944,18.9,13.7,-20,5.381722749,-0.54,2.96,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,301448,2015-10-30 10:27:18:581,1446172038581.0 \n-0.4968,0.1616,8.7209,-0.4271,0.0518,9.7972,-0.1148,-0.044,0.1735,19.3,13.8,-20.2,5.37823209,-0.54,2.59,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,301549,2015-10-30 10:27:18:682,1446172038682.0 \n-0.8966,0.6393,8.2612,-0.5446,-0.0427,9.7914,0.0318,0.1527,0.0965,19.8,14.3,-20.3,5.347863361,0.25,3.18,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,301652,2015-10-30 10:27:18:785,1446172038785.0 \n-0.7015,0.8607,8.9148,-0.6228,0.0339,9.7868,0.0305,-0.0122,-0.0171,20.1,14.7,-20,5.388529533,-0.04,3.57,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,301753,2015-10-30 10:27:18:886,1446172038886.0 \n-1.0642,1.2067,10.3573,-0.5711,0.1094,9.7894,0.0611,-0.066,-0.088,20.5,15.5,-19.8,5.396208981,-0.37,3.33,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,301855,2015-10-30 10:27:18:988,1446172038988.0 \n-1.3312,-0.571,10.9942,-0.6296,-0.1096,9.7858,-0.4264,0.2847,-0.3836,20.6,16.5,-20.2,5.417676531,0.28,3.21,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,301957,2015-10-30 10:27:19:090,1446172039090.0 \n-0.2095,0.0491,8.424,-0.5552,0.0267,9.7909,-0.1026,-0.193,-0.1356,20.4,17.4,-20.4,5.450488721,-0.15,3.47,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,302059,2015-10-30 10:27:19:192,1446172039192.0 \n-0.3926,0.5136,7.6459,-0.5067,-0.0469,9.7934,-0.0086,0.0562,-0.0806,19.9,18.6,-21.1,5.493074755,0.41,2.61,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,302161,2015-10-30 10:27:19:294,1446172039294.0 \n-0.2921,0.9134,8.8957,-0.5022,-0.0312,9.7937,0.0147,-0.1038,0.0501,19.2,19.7,-22,5.552765015,0.18,2.94,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,302264,2015-10-30 10:27:19:397,1446172039397.0 \n-0.8021,0.2358,11.5772,-0.5025,0.0735,9.7935,0.1063,-0.0379,-0.0208,18.7,20.4,-23.1,5.558524602,-0.18,3,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,302366,2015-10-30 10:27:19:499,1446172039499.0 \n-0.2717,-0.2215,10.671,-0.5326,0.1464,9.7911,-0.2834,-0.1283,-0.1051,18.5,20.8,-23.8,5.598318109,-1.13,3.38,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,302467,2015-10-30 10:27:19:600,1446172039600.0 \n-1.4257,0.0778,9.3733,-0.4683,0.1721,9.794,0.1747,-0.1759,-0.0012,18.1,21.4,-25,5.61926206,-1.01,2.74,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,302570,2015-10-30 10:27:19:703,1446172039703.0 \n-0.3723,0.2059,8.9747,-0.2201,0.0962,9.8037,-0.0916,-0.1332,-0.0269,17.5,21.6,-25.9,5.628337772,-0.84,1.77,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,302671,2015-10-30 10:27:19:804,1446172039804.0 \n-0.8583,0.8547,8.0529,-0.2467,0.0778,9.8032,0.0941,0.0452,0.055,16.5,22.1,-27.5,5.645441999,-0.28,1.26,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,302774,2015-10-30 10:27:19:907,1446172039907.0 \n-0.7458,0.9685,9.56,-0.2631,0.1405,9.8021,0.0415,0.0269,-0.0489,15.7,22.3,-28.2,5.683315643,-0.55,1.56,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,302876,2015-10-30 10:27:20:009,1446172040009.0 \n-0.2717,0.4286,11.1929,-0.3165,0.2548,9.7982,0.1747,0.1124,0.0464,14.8,22.7,-28.8,5.745274832,-1.24,1.77,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,302977,2015-10-30 10:27:20:110,1446172040110.0 \n-1.1037,-0.6548,11.0923,-0.4662,0.135,9.7946,0.0208,-0.0391,-0.0244,14.5,22.9,-29.1,5.754874143,-1.04,2.47,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,303079,2015-10-30 10:27:20:212,1446172040212.0 \n-0.4429,-0.346,9.6989,-0.3935,0.1385,9.7978,-0.0208,-0.0953,0.022,13.8,23.1,-29.9,5.783672075,-0.81,2.3,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,303181,2015-10-30 10:27:20:314,1446172040314.0 \n-1.0187,0.8056,7.2365,-0.5008,0.0118,9.7938,-0.0232,0.1344,-0.0208,13.3,23.3,-30.5,5.821371187,-0.25,2.81,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,303283,2015-10-30 10:27:20:416,1446172040416.0 \n-0.3484,0.9421,9.7552,-0.5558,-0.0255,9.7909,-0.0208,0.1356,0.1393,12.8,23.6,-30.9,5.844409533,0.15,3.25,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,303386,2015-10-30 10:27:20:519,1446172040519.0 \n-1.1408,0.17,11.8573,-0.6933,0.1752,9.7805,0.3677,0.1649,0.2859,12.7,23.7,-31.1,5.856452305,-0.13,3.74,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,303487,2015-10-30 10:27:20:620,1446172040620.0 \n-1.2605,-0.5734,11.3018,-0.653,0.0974,9.7844,-0.3506,-0.2431,0.0855,13,23.4,-31.5,5.845282198,-0.99,3.61,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,303589,2015-10-30 10:27:20:722,1446172040722.0 \n-1.3264,-0.4094,10.2592,-0.4795,0.052,9.7948,-0.3115,-0.2529,-0.1075,13.3,23,-31.7,5.838475414,-0.83,3.21,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,303691,2015-10-30 10:27:20:824,1446172040824.0 \n-1.4006,-0.17,8.7041,-0.478,-0.129,9.7941,-0.066,0.1173,-0.0024,13.2,22.8,-31.4,5.810375613,0.58,2.56,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,303794,2015-10-30 10:27:20:927,1446172040927.0 \n-1.233,0.7925,8.6921,-0.5967,-0.1256,9.7877,0.0244,0.1515,-0.0305,13.1,22.9,-31,5.826956241,0.73,3.49,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,303895,2015-10-30 10:27:21:028,1446172041028.0 \n-1.3348,0.516,10.8709,-0.6303,-0.0898,9.786,0.0709,-0.0073,-0.0073,12.8,23.2,-30.5,5.830621432,0.52,3.69,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,303997,2015-10-30 10:27:21:130,1446172041130.0 \n-0.4681,-0.4501,11.6945,-0.5524,-0.0061,9.7911,-0.2688,0.0049,-0.2248,12.8,23.2,-30.4,5.826607175,0.04,3.23,36.8133,-119.74797,276.13,336.4483896,3.82,51.612904,26.72,0 / 16,304099,2015-10-30 10:27:21:232,1446172041232.0 \n-0.1305,-0.2131,9.3518,-0.5933,-0.0983,9.7882,0.1271,-0.0806,-0.077,12.8,23.3,-30.1,5.824338247,0.94,3.56,36.813747,-119.74795,276.45,336.4483896,3.63,77.41935,34.27,0 / 16,304202,2015-10-30 10:27:21:335,1446172041335.0 \n-0.1472,0.3268,7.7608,-0.5178,-0.1083,9.7924,-0.0562,-0.0244,-0.0831,12.6,23.3,-30.1,5.817182397,0.63,3.03,36.813747,-119.74795,276.45,336.4483896,3.63,77.41935,34.27,13 / 16,304303,2015-10-30 10:27:21:436,1446172041436.0 \n-1.0487,0.5519,8.3749,-0.5662,-0.2287,9.7876,-0.0953,0.0086,-0.0977,12.5,23.5,-29.7,5.835159288,1,3.26,36.813747,-119.74795,276.45,336.4483896,3.63,77.41935,34.27,13 / 16,304406,2015-10-30 10:27:21:539,1446172041539.0 \n-0.5064,0.322,10.2675,-0.6064,-0.1674,9.7865,0.2847,0.0342,0.1283,12.3,23.9,-29.3,5.867796945,1.37,3.38,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,13 / 16,304507,2015-10-30 10:27:21:640,1446172041640.0 \n-0.2478,1.0702,8.8801,-0.6565,0.1834,9.7829,0.4569,0.1258,0.2382,12.4,24,-29.1,5.884552106,-0.23,3.59,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,13 / 16,304609,2015-10-30 10:27:21:742,1446172041742.0 \n-0.8679,0.0443,8.9986,-0.5919,0.1549,9.7875,0.077,0.1429,0.0538,12.7,23.9,-29.4,5.852263515,-0.76,3.49,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,13 / 16,304711,2015-10-30 10:27:21:844,1446172041844.0 \n-0.6045,0.1305,8.8621,-0.4414,0.0472,9.7966,-0.2957,-0.0134,-0.1087,12.8,23.6,-30,5.839348078,-0.7,2.68,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,13 / 16,304813,2015-10-30 10:27:21:946,1446172041946.0 \n-1.1157,0.5327,9.2596,-0.4293,-0.1271,9.7964,-0.1503,-0.0867,-0.0733,12.3,23.9,-30.6,5.859768431,0.74,2.51,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,13 / 16,304915,2015-10-30 10:27:22:048,1446172042048.0 \n-1.0307,0.7626,9.493,-0.4753,0.0183,9.7951,0.1478,0.0428,-0.1197,11.5,24.4,-31.1,5.872334801,-0.11,2.78,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,13 / 16,305017,2015-10-30 10:27:22:150,1446172042150.0 \n-1.1959,0.1161,10.7919,-0.5226,0.1825,9.791,0.3299,0.1588,-0.0648,11.1,24.5,-31.3,5.926440008,-0.58,2.87,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,13 / 16,305119,2015-10-30 10:27:22:252,1446172042252.0 \n-1.0307,-0.5195,11.157,-0.576,0.3273,9.7842,-0.2346,0.2578,-0.358,10.5,24.2,-32.7,5.934468523,-2.35,3.07,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,13 / 16,305222,2015-10-30 10:27:22:355,1446172042355.0 \n-0.4345,0.2693,9.0058,-0.6143,0.2272,9.7848,-0.0403,-0.0489,-0.1955,10,24,-33.6,5.979323484,-1.53,3.66,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,13 / 16,305323,2015-10-30 10:27:22:456,1446172042456.0 \n-0.5638,0.8691,7.6207,-0.6845,0.0062,9.7827,0.0195,0.1014,0.0501,9.2,24.1,-34.4,6.01126301,-0.02,3.85,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,13 / 16,305426,2015-10-30 10:27:22:559,1446172042559.0 \n-1.2378,0.6548,8.7843,-0.6851,0.0034,9.7827,0.0513,-0.0049,0.1576,8.6,24.4,-34.9,6.016848063,0.12,4.02,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,13 / 16,305527,2015-10-30 10:27:22:660,1446172042660.0 \n-1.0487,0.1676,10.8912,-0.7338,0.1077,9.7786,0.1393,0.0843,0.2749,8,24.5,-35.7,6.07810912,-0.63,4.29,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,13 / 16,305630,2015-10-30 10:27:22:763,1446172042763.0 \n-0.0431,0.9481,8.9352,-0.8099,0.441,9.7632,0.2443,-0.1185,0.3787,8.2,24.1,-36.5,6.082821509,-1.85,4.56,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,13 / 16,305731,2015-10-30 10:27:22:864,1446172042864.0 \n-1.1983,-0.2861,10.7607,-0.5594,0.3747,9.7835,-0.2272,-0.3763,0.1161,8.3,23.3,-37.4,6.047042259,-2.19,3.27,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,13 / 16,305833,2015-10-30 10:27:22:966,1446172042966.0 \n-0.7566,0.2346,9.3781,-0.3507,0.1846,9.7986,-0.1674,-0.1417,0.1808,8.2,22.9,-38,6.017720728,-1.44,2.24,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,13 / 16,305935,2015-10-30 10:27:23:068,1446172043068.0 \n-0.6093,0.6823,9.0118,-0.3119,0.0732,9.8014,-0.1014,-0.033,0.0024,7.5,23.1,-38.6,5.997300376,-0.47,1.68,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,13 / 16,306037,2015-10-30 10:27:23:170,1446172043170.0 \n-0.6943,0.9625,8.8526,-0.3829,0.0738,9.7989,0.0171,0.0269,-0.1442,7.1,23.3,-39,6.04529693,-0.47,1.97,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,13 / 16,306139,2015-10-30 10:27:23:272,1446172043272.0 \n-0.8763,0.7195,10.1813,-0.3366,0.1567,9.7996,0.0305,-0.1295,-0.0599,6.5,23.7,-39.7,6.057863301,-0.61,2,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,306241,2015-10-30 10:27:23:374,1446172043374.0 \n-0.7183,-0.4381,11.3006,-0.4086,-0.0227,9.7981,-0.3616,0.259,-0.2077,5.8,23.8,-40.4,6.095038814,-0.07,2.03,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,306344,2015-10-30 10:27:23:477,1446172043477.0 \n0.1305,-0.0491,8.9771,-0.3758,0.0295,9.7994,-0.3311,-0.0929,-0.1087,5.4,24,-40.7,6.14792229,-0.59,2.34,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,306446,2015-10-30 10:27:23:579,1446172043579.0 \n-1.245,0.0395,9.0968,-0.4514,-0.2176,9.7938,-0.1405,0.0525,-0.0037,5,24.6,-40.8,6.152285613,0.95,2.51,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,306547,2015-10-30 10:27:23:680,1446172043680.0 \n-0.3136,0.6596,9.2668,-0.4867,-0.2077,9.7924,-0.0098,0.0305,0.2162,5.1,25,-40.8,6.160488661,1.24,2.83,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,306650,2015-10-30 10:27:23:783,1446172043783.0 \n-0.3017,0.2945,11.7675,-0.4958,-0.0973,9.7936,0.2187,-0.0403,0.2859,5.2,25.6,-41.1,6.169564373,0.57,2.9,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,306751,2015-10-30 10:27:23:884,1446172043884.0 \n0.1041,-0.5662,11.3904,-0.334,0.0447,9.8009,-0.3677,-0.1613,-0.1222,5.5,25.5,-41.4,6.139370177,-0.86,2.99,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,306853,2015-10-30 10:27:23:986,1446172043986.0 \n-0.5327,0.2741,9.6187,-0.2891,0.0799,9.8021,0.1442,-0.1417,0.2028,5.7,25.4,-41.6,6.111444909,-0.41,2.19,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,306955,2015-10-30 10:27:24:088,1446172044088.0 \n-0.6536,0.1257,9.3925,-0.2804,0.0027,9.8026,-0.0525,0.033,-0.1148,5.7,25.3,-41.8,6.091897221,-0.1,1.56,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,307057,2015-10-30 10:27:24:190,1446172044190.0 \n-0.8332,0.9002,7.4508,-0.4314,0.1454,9.7961,0.1454,0.1454,-0.1271,5.4,25.5,-42,6.1580452,-0.61,2.28,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,307160,2015-10-30 10:27:24:293,1446172044293.0 \n-1.7047,0.0658,11.2743,-0.4913,0.1089,9.7937,0.0122,-0.0403,-0.1649,5.2,25.6,-42.2,6.17357863,-0.75,2.83,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,307261,2015-10-30 10:27:24:394,1446172044394.0 \n-0.7865,0.4453,10.4124,-0.494,0.1955,9.7923,0.1552,-0.0293,-0.055,5,25.7,-42.4,6.177243822,-1,2.93,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,307363,2015-10-30 10:27:24:496,1446172044496.0 \n-0.0874,0.0239,9.657,-0.5021,-0.0567,9.7936,-0.0623,0.1148,-0.1332,4.5,26,-42.2,6.173229564,0.33,2.94,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,307465,2015-10-30 10:27:24:598,1446172044598.0 \n-0.6033,-1.0666,10.5979,-0.4367,-0.2234,9.7944,-0.1894,-0.0367,-0.193,4,26.4,-41.9,6.205343623,0.76,2.75,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,307567,2015-10-30 10:27:24:700,1446172044700.0 \n-1.0606,0.3065,8.1439,-0.5693,-0.2938,9.7857,-0.0367,0.1759,-0.033,3.6,27.1,-41.2,6.213721203,1.59,3.07,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,307670,2015-10-30 10:27:24:803,1446172044803.0 \n-0.1568,0.9493,8.8837,-0.6132,-0.2878,9.7832,0.0367,0.0623,0.0929,3.5,27.4,-40.9,6.225065843,1.83,3.5,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,307771,2015-10-30 10:27:24:904,1446172044904.0 \n-0.6393,0.158,10.726,-0.6559,-0.1995,9.7827,0.2932,-0.0257,0.2663,3.7,27.6,-41.2,6.237283148,1.17,3.84,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,307873,2015-10-30 10:27:25:006,1446172045006.0 \n-1.2857,0.1568,9.5205,-0.6298,0.0059,9.7864,0.1686,0.0953,0.248,3.9,27.4,-41.5,6.237283148,0.27,3.86,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,307975,2015-10-30 10:27:25:108,1446172045108.0 \n-0.6273,0.3292,9.2835,-0.5379,-0.0959,9.7914,-0.0171,-0.2272,0.5192,4.5,27.1,-41.4,6.189286593,0.59,3.48,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,308077,2015-10-30 10:27:25:210,1446172045210.0 \n0.097,0.2729,8.1175,-0.3859,-0.2068,9.7969,-0.3079,0.0122,0.0415,4.9,26.9,-41.3,6.155427206,0.86,2.25,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,308179,2015-10-30 10:27:25:312,1446172045312.0 \n-0.6788,0.4597,8.521,-0.4785,-0.3454,9.7889,0.1368,0.0733,0.1466,5.3,27,-41.4,6.159092397,2.24,2.56,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,308281,2015-10-30 10:27:25:414,1446172045414.0 \n-0.4238,0.2334,11.2492,-0.4646,-0.242,9.7926,0.0806,-0.0623,-0.0061,5.8,26.9,-41.3,6.128549135,1.41,2.72,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,308383,2015-10-30 10:27:25:516,1446172045516.0 \n-0.65,0.4776,10.6039,-0.4635,0.001,9.7957,0.2407,0.1307,-0.1344,6.1,26.6,-41.5,6.127327405,0.46,2.52,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,308485,2015-10-30 10:27:25:618,1446172045618.0 \n-1.1456,-1.403,11.9985,-0.501,-0.1222,9.7931,-0.0892,0.1332,-0.2114,6,26.2,-41.8,6.133261524,0.71,2.93,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,308588,2015-10-30 10:27:25:721,1446172045721.0 \n0.0156,-0.2382,8.339,-0.528,-0.1174,9.7917,0.0745,-0.0709,-0.0611,5.8,26,-41.9,6.142686302,0.52,3.23,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,308690,2015-10-30 10:27:25:823,1446172045823.0 \n-1.0798,0.0371,8.43,-0.5416,-0.2169,9.7893,-0.1014,0.1148,-0.1796,5.4,26.1,-42.2,6.1723569,1.08,2.99,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,308792,2015-10-30 10:27:25:925,1446172045925.0 \n-0.486,0.8009,8.4539,-0.6446,-0.2169,9.783,0.022,0.0904,0.0024,5.3,26.2,-42,6.189635659,1.37,3.61,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,308894,2015-10-30 10:27:26:027,1446172046027.0 \n-1.2007,-0.1065,11.7902,-0.7136,-0.1506,9.7795,0.0562,0.0476,-0.0195,5.2,26.1,-41.8,6.20342376,1.06,4.06,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,308995,2015-10-30 10:27:26:128,1446172046128.0 \n-0.7697,0.7123,9.2871,-0.7772,0.1982,9.7738,0.4105,0.1161,0.2822,5.4,25.9,-41.8,6.216339197,-0.43,4.4,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,309097,2015-10-30 10:27:26:230,1446172046230.0 \n-1.5502,-0.0946,8.9112,-0.7299,0.1195,9.7787,-0.0024,-0.0953,0.0538,5.9,24.9,-42.1,6.171658768,-0.7,4.27,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,309199,2015-10-30 10:27:26:332,1446172046332.0 \n-1.0666,0.0215,9.0692,-0.5358,0.0729,9.7917,-0.055,-0.3128,0.0831,6.1,24.3,-42.5,6.13238886,-0.43,3.13,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,309302,2015-10-30 10:27:26:435,1446172046435.0 \n-1.5658,0.3938,9.0178,-0.5955,-0.1813,9.7869,-0.2187,-0.1197,0.0831,6.1,24.3,-42.3,6.138672045,0.76,3.52,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,309403,2015-10-30 10:27:26:536,1446172046536.0 \n-1.1133,0.492,10.1454,-0.5801,-0.2664,9.7859,-0.1038,-0.0037,0.1662,6.2,24.5,-42.1,6.139021111,1.4,3.43,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,309505,2015-10-30 10:27:26:638,1446172046638.0 \n-0.6596,0.1628,11.0145,-0.5739,-0.2128,9.7875,0.1295,-0.1014,0.0635,6.5,24.7,-41.8,6.099751203,1.37,3.46,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,309607,2015-10-30 10:27:26:740,1446172046740.0 \n0.5399,-0.2251,10.9702,-0.5255,-0.1203,9.7918,0.0147,-0.0208,0.0232,6.8,24.6,-41.5,6.089977359,0.7,3.07,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,309710,2015-10-30 10:27:26:843,1446172046843.0 \n-0.0239,-0.2861,8.5545,-0.5373,-0.2263,9.7893,0.1515,-0.1319,-0.1063,6.7,24.6,-41.4,6.088406563,1.32,3.14,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,309811,2015-10-30 10:27:26:944,1446172046944.0 \n-0.8739,-0.407,9.8222,-0.412,-0.3525,9.7917,-0.066,0.1381,-0.1271,6.4,24.6,-41,6.108477849,1.63,2.51,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,309913,2015-10-30 10:27:27:046,1446172047046.0 \n-1.4138,0.4681,8.6814,-0.5414,-0.4261,9.7824,-0.0904,0.1271,-0.1271,6,24.9,-41.1,6.120869687,2.42,3.06,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,310016,2015-10-30 10:27:27:149,1446172047149.0 \n-1.0068,-0.346,10.6757,-0.5573,-0.3684,9.7839,-0.0049,0.0611,0.0977,5.6,25,-40.8,6.125582076,2.35,3.2,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,310118,2015-10-30 10:27:27:251,1446172047251.0 \n-0.4058,0.2837,9.4559,-0.5158,-0.1372,9.7921,0.3641,0.0929,0.2492,5.6,24.9,-41,6.12523301,1.25,3.01,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,15 / 16,310219,2015-10-30 10:27:27:352,1446172047352.0 \n-1.573,-0.9816,10.1873,-0.5528,-0.2213,9.7886,0.1637,-0.0049,0.2443,5.8,24.6,-41.2,6.11929889,1.07,2.78,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,310322,2015-10-30 10:27:27:455,1446172047455.0 \n-0.2777,0.1257,9.2285,-0.4358,-0.134,9.796,0.0269,-0.1869,0.1038,6.2,24,-41.7,6.108826915,0.78,2.55,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,310423,2015-10-30 10:27:27:556,1446172047556.0 \n-0.8248,0.1736,8.5437,-0.4337,-0.1463,9.796,0.011,-0.0305,-0.2871,6.3,23.8,-42,6.109350514,0.85,2.58,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,310525,2015-10-30 10:27:27:658,1446172047658.0 \n-0.7949,0.8667,9.1183,-0.5437,-0.0561,9.7914,0.2688,0.1381,-0.1148,6.1,23.7,-41.8,6.130294465,0.33,3.18,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,310627,2015-10-30 10:27:27:760,1446172047760.0 \n-1.4102,0.2358,11.4563,-0.5224,0.1479,9.7916,0.1185,-0.182,-0.1943,5.9,23.5,-42.1,6.141639105,-0.64,3.41,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,310730,2015-10-30 10:27:27:863,1446172047863.0 \n0.079,0.3196,10.5285,-0.4822,0.2753,9.7909,-0.0916,0.044,-0.0782,5.3,22.9,-42.4,6.162583056,-1.61,2.82,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,310831,2015-10-30 10:27:27:964,1446172047964.0 \n-0.9349,-0.3005,9.9539,-0.5708,0.134,9.7891,0.3311,-0.0183,0.0623,5,22.7,-42.6,6.166771846,-0.75,2.98,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,310933,2015-10-30 10:27:28:066,1446172048066.0 \n-0.6476,0.1257,8.5389,-0.5156,0.2248,9.7905,-0.1576,-0.0745,-0.0709,4.6,22.4,-42.6,6.164851984,-1.31,3.01,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,311035,2015-10-30 10:27:28:168,1446172048168.0 \n-0.7901,0.9565,8.3797,-0.6302,0.0472,9.7863,-0.1649,0.1344,0.0391,4.5,22.5,-42.6,6.182130743,-0.5,3.49,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,311137,2015-10-30 10:27:28:270,1446172048270.0 \n-0.5578,0.5746,10.7248,-0.6828,-0.0533,9.7827,-0.1307,0.1515,0.0843,4.5,22.7,-42.6,6.189286593,0.07,3.77,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,311239,2015-10-30 10:27:28:372,1446172048372.0 \n-0.8918,0.6644,11.0636,-0.8297,-0.0213,9.7715,0.3543,0.0171,0.3079,5,23.1,-42,6.220877053,0.12,4.85,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,311341,2015-10-30 10:27:28:474,1446172048474.0 \n0.2933,0.4238,9.7241,-0.7006,0.1531,9.7804,0.0134,-0.2297,0.2663,5.6,22.9,-41.7,6.184748737,-1.37,4.93,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,311443,2015-10-30 10:27:28:576,1446172048576.0 \n-0.3472,1.0798,8.6682,-0.5573,0.1337,9.7899,0.1833,-0.6267,0.3543,6.1,22.6,-41.3,6.129072734,-0.78,3.26,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,311545,2015-10-30 10:27:28:678,1446172048678.0 \n-0.7183,-0.2143,8.8071,-0.3,0.0546,9.8019,-0.2834,-0.0586,-0.0195,6.1,22.3,-41.8,6.080901647,-0.63,1.9,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,311648,2015-10-30 10:27:28:781,1446172048781.0 \n-0.6895,0.9768,7.6459,-0.3619,-0.0725,9.7997,0.1014,0.1491,0.0782,5.6,22.6,-41.9,6.089628293,0.42,2.11,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,311750,2015-10-30 10:27:28:883,1446172048883.0 \n-0.431,0.5674,9.8198,-0.3218,-0.0855,9.801,-0.1161,-0.0122,-0.0843,5.4,22.6,-42,6.128723668,0.19,1.96,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,311851,2015-10-30 10:27:28:984,1446172048984.0 \n-0.3089,0.0455,10.5333,-0.3352,0.0283,9.8009,0.0941,-0.0867,-0.0672,5.2,22.9,-41.8,6.129770866,0.15,1.99,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,311953,2015-10-30 10:27:29:086,1446172049086.0 \n-0.2993,-0.3065,11.5125,-0.3543,-0.1262,9.7994,-0.3372,0.0831,-0.2492,5,23,-41.9,6.125407543,0.15,1.85,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,312056,2015-10-30 10:27:29:189,1446172049189.0 \n-0.2466,-0.3376,10.5093,-0.259,-0.1722,9.8017,-0.1845,-0.0867,-0.2407,4.5,23.3,-41.6,6.116331831,0.68,1.65,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,312157,2015-10-30 10:27:29:290,1446172049290.0 \n-1.4461,0.3651,8.6479,-0.3888,-0.1606,9.7976,-0.0037,0.1552,-0.1796,4,23.7,-41.8,6.183527007,0.94,2.27,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,312259,2015-10-30 10:27:29:392,1446172049392.0 \n-0.9158,0.723,8.3869,-0.5316,-0.0767,9.7919,0.0367,0.1552,0.0122,4,23.9,-41.7,6.201154832,0.65,2.82,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,312362,2015-10-30 10:27:29:495,1446172049495.0 \n-1.2222,0.1245,10.9595,-0.7079,-0.0328,9.781,-0.022,0.1881,0.1014,4.2,23.8,-41.4,6.240075675,0.19,4.14,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,312463,2015-10-30 10:27:29:596,1446172049596.0 \n-0.753,0.6919,8.6562,-0.7372,0.1091,9.7783,0.0623,-0.0831,0.2382,4.7,23.8,-41.4,6.209706946,-0.51,4.47,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,312566,2015-10-30 10:27:29:699,1446172049699.0 \n-0.5076,0.3591,10.1023,-0.5862,-0.1616,9.7878,0.0574,-0.4948,0.2407,5.3,23.8,-41.6,6.193649917,0.98,3.96,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,312667,2015-10-30 10:27:29:800,1446172049800.0 \n-0.0491,0.1867,8.7963,-0.4369,-0.1509,9.7958,-0.044,-0.0195,0.0696,5.5,23.9,-41.9,6.106557987,0.76,2.47,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,312769,2015-10-30 10:27:29:902,1446172049902.0 \n-1.4545,0.5303,9.0597,-0.5479,-0.2074,9.7891,-0.0024,0.1918,0.0183,5.6,24.3,-41.9,6.1151101,1.38,2.86,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,312871,2015-10-30 10:27:30:004,1446172050004.0 \n-0.8823,0.8978,9.7624,-0.6342,-0.099,9.7856,0.0941,0.121,0.0098,5.7,24.3,-41.8,6.133785123,0.72,3.36,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,312973,2015-10-30 10:27:30:106,1446172050106.0 \n-0.9517,0.516,10.6889,-0.6464,0.077,9.785,0.2138,-0.0098,-0.11,6.1,24.2,-41.5,6.149842152,-0.07,3.86,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,313075,2015-10-30 10:27:30:208,1446172050208.0 \n-1.3934,-1.312,13.0747,-0.547,0.0115,9.7914,-0.4288,0.0721,-0.3787,6.1,23.7,-41.7,6.132214327,-0.95,3.05,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,313177,2015-10-30 10:27:30:310,1446172050310.0 \n-1.0594,-0.8392,10.2711,-0.4017,0.258,9.795,-0.3604,-0.0281,-0.2138,5.7,23.4,-42.6,6.109525047,-1.51,2.35,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,313280,2015-10-30 10:27:30:413,1446172050413.0 \n-0.6177,0.5171,8.0888,-0.4514,0.0385,9.7962,-0.1576,0.1295,0.0745,5.3,23.3,-42.9,6.151238416,-0.4,2.54,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,313381,2015-10-30 10:27:30:514,1446172050514.0 \n0.0024,1.0678,8.5892,-0.4844,-0.0437,9.7946,-0.0476,-0.0073,0.1576,5.2,23.4,-43.1,6.1580452,0.26,2.83,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,313483,2015-10-30 10:27:30:616,1446172050616.0 \n-0.7482,0.3699,11.0289,-0.5064,-0.0756,9.7933,0.0122,-0.0586,0.1332,5.5,23.7,-42.7,6.125058477,0.44,2.96,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,313585,2015-10-30 10:27:30:718,1446172050718.0 \n1.0702,-0.5974,11.7041,-0.1367,0.0729,9.8054,-0.4313,-0.4948,-0.1112,6.1,23.5,-43.2,6.094166149,-0.84,1.71,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,313688,2015-10-30 10:27:30:821,1446172050821.0 \n-0.1389,0.4848,7.1311,0.094,0.1359,9.8053,0.463,-0.1307,0.1539,6,23.3,-43.5,6.030461631,0.37,0.18,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,313790,2015-10-30 10:27:30:923,1446172050923.0 \n-0.2227,-0.0634,10.1191,0.3985,-0.0168,9.7985,-0.3604,-0.0086,-0.0904,5.4,23,-44,6.000616501,-0.51,-2.34,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,313891,2015-10-30 10:27:31:024,1446172051024.0 \n-0.4908,0.905,8.5772,0.3733,0.0133,9.7995,0.1112,0.1747,-0.0257,4.2,23,-44.5,6.030461631,-0.03,-2.54,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,313993,2015-10-30 10:27:31:126,1446172051126.0 \n-0.6261,1.0702,9.5624,0.2341,0.0888,9.8035,-0.0134,0.1319,-0.1478,3.7,23,-45,6.059957696,-0.51,-1.68,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,314095,2015-10-30 10:27:31:228,1446172051228.0 \n-0.7961,0.0778,11.6813,0.0564,0.2626,9.803,0.2492,0.1674,-0.1442,3.7,23,-45.3,6.096435077,-1.07,-0.64,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,314199,2015-10-30 10:27:31:332,1446172051332.0 \n-0.51,-0.8918,11.2755,-0.0261,0.3965,9.7986,-0.2541,0.215,-0.3323,4.1,22.2,-46,6.118949825,-2.34,-0.15,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,314299,2015-10-30 10:27:31:432,1446172051432.0 \n0.2598,0.4944,7.7165,-0.1839,0.3505,9.7987,-0.0916,-0.0574,-0.0391,4.4,21.9,-46.1,6.148096823,-1.78,1.02,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,314401,2015-10-30 10:27:31:534,1446172051534.0 \n-0.31,0.9637,7.9775,-0.1586,0.2086,9.8031,-0.1161,0.0012,-0.0611,4.7,21.6,-46.5,6.100274802,-1.37,0.91,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,314504,2015-10-30 10:27:31:637,1446172051637.0 \n-0.5555,1.2474,8.934,-0.2795,0.0806,9.8023,-0.0513,0.2138,0.0183,4.9,21.8,-46.5,6.107430652,-0.53,1.27,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,314605,2015-10-30 10:27:31:738,1446172051738.0 \n-1.3204,0.4453,10.1706,-0.39,0.0758,9.7986,-0.0183,0.0721,0.1161,5.2,22,-46.6,6.144257099,-0.44,2.28,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,314707,2015-10-30 10:27:31:840,1446172051840.0 \n-0.4824,1.3012,9.396,-0.3963,0.2405,9.7957,0.2443,0.0049,0.3054,5.6,22.2,-46.5,6.102892795,-0.73,2.34,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,314810,2015-10-30 10:27:31:943,1446172051943.0 \n-1.5179,-1.2366,10.5848,-0.2023,-0.1225,9.8038,-0.1991,0.1747,0.0562,6.1,22.2,-46.6,6.046344128,0.36,0.93,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,314911,2015-10-30 10:27:32:044,1446172052044.0 \n0.1688,-0.0982,9.4535,0.039,-0.085,9.8062,-0.2615,-0.2834,0.2248,6.2,22.2,-46.7,6.00410716,0.5,-0.23,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,315013,2015-10-30 10:27:32:146,1446172052146.0 \n-0.7853,-0.0407,9.2392,0.0709,-0.332,9.8008,-0.204,0.0318,-0.0281,6.1,22.3,-46.8,5.979847083,1.55,-0.6,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,315115,2015-10-30 10:27:32:248,1446172052248.0 \n-0.656,0.3962,9.4918,-0.0123,-0.2983,9.8021,0.0403,0.1026,-0.0318,6,22.6,-46.5,6.006376088,1.84,-0.14,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,315217,2015-10-30 10:27:32:350,1446172052350.0 \n-0.65,-0.1149,11.412,-0.1079,-0.154,9.8048,0.1051,-0.0208,-0.1588,6.3,22.5,-46.4,6.041457206,0.9,0.63,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,315319,2015-10-30 10:27:32:452,1446172052452.0 \n1.0834,-0.1281,9.0692,-0.1157,-0.03,9.8059,-0.6133,-0.0623,-0.4215,6.4,22.1,-46.3,6.040235475,0.42,0.79,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,315422,2015-10-30 10:27:32:555,1446172052555.0 \n0.3807,-0.3436,8.5258,-0.2276,-0.1777,9.8024,0.3861,0.1869,0.0195,6.5,21.9,-46,6.006550621,1.74,1.43,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,315523,2015-10-30 10:27:32:656,1446172052656.0 \n-0.3879,-0.4477,10.5046,-0.2779,-0.1879,9.8009,0.0929,0.3506,-0.011,6.4,21.8,-45.8,6.04529693,1.1,1.1,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,315625,2015-10-30 10:27:32:758,1446172052758.0 \n-1.336,0.5387,7.7417,-0.5443,-0.0101,9.7915,0.0269,0.2053,0.0867,6.6,21.7,-45.8,6.072698599,0.13,2.88,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,315727,2015-10-30 10:27:32:860,1446172052860.0 \n-0.4453,0.7482,9.918,-0.6722,0.0597,9.7834,0.0513,0.0122,0.0415,7.3,20.9,-46.1,6.105161723,-0.35,3.93,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,315829,2015-10-30 10:27:32:962,1446172052962.0 \n-0.5459,0.3053,10.6291,-0.6598,0.1263,9.7836,0.0269,-0.1808,0.1173,8,20.4,-46,6.064146486,-0.56,4.27,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,315931,2015-10-30 10:27:33:064,1446172053064.0 \n-2.1332,-1.2761,12.7264,-0.5147,-0.0453,9.793,-0.5241,0.0709,-0.0782,8.5,19.6,-45.8,5.987875598,-0.66,3.41,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,316033,2015-10-30 10:27:33:166,1446172053166.0 \n-0.4453,0.5926,9.6391,-0.4077,-0.0785,9.7979,0.1063,-0.3042,0.2712,8.5,19.5,-45.5,5.955587007,0.66,3.02,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,316136,2015-10-30 10:27:33:269,1446172053269.0 \n-1.233,-0.3543,10.0413,-0.2796,-0.3064,9.7979,-0.3751,-0.0611,-0.2175,7.9,19.6,-45.2,5.940228109,1.36,1.58,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,316237,2015-10-30 10:27:33:370,1446172053370.0 \n-1.4353,0.5914,9.1506,-0.31,-0.1593,9.8005,0.1747,-0.0452,-0.0525,7.2,19.7,-44.6,6.001489166,0.93,1.81,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,316339,2015-10-30 10:27:33:472,1446172053472.0 \n-0.5471,0.3795,11.1318,-0.3347,-0.1157,9.8003,-0.0452,0.1075,-0.0721,6.9,19.4,-44.6,5.990144526,0.69,1.82,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,316441,2015-10-30 10:27:33:574,1446172053574.0 \n-0.3232,-0.0431,9.8055,-0.2949,0.1154,9.8015,0.1845,-0.1918,-0.2309,6.8,18.9,-44.6,6.005677956,-0.21,1.96,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,316543,2015-10-30 10:27:33:676,1446172053676.0 \n0.2861,0.1245,8.4252,-0.3087,-0.1616,9.8005,0.2077,-0.0098,0.0819,6.2,18.7,-44.4,6.032556027,1.24,1.8,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,316645,2015-10-30 10:27:33:778,1446172053778.0 \n-0.0814,-0.2346,9.681,-0.3078,-0.3135,9.7968,-0.0855,0.0232,-0.1063,5.7,18.9,-44.4,6.03273056,1.29,1.81,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,316747,2015-10-30 10:27:33:880,1446172053880.0 \n-0.8392,0.2382,8.7125,-0.3124,-0.3355,9.7959,-0.0318,-0.0012,-0.0757,5,19.3,-43.8,6.080378048,1.96,1.83,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,316850,2015-10-30 10:27:33:983,1446172053983.0 \n-0.2538,0.504,8.5904,-0.3279,-0.3325,9.7955,-0.1368,0.0599,0.0147,4.8,19.3,-43.4,6.080378048,1.62,1.79,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,316951,2015-10-30 10:27:34:084,1446172054084.0 \n-0.1448,0.2574,11.1845,-0.1952,-0.2635,9.8012,0.2627,-0.0721,0.3176,4.4,19.3,-42.7,6.120520621,1.98,1.5,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,317053,2015-10-30 10:27:34:186,1446172054186.0 \n-1.4389,-1.2079,12.6665,-0.0967,-0.2585,9.8028,-0.1918,-0.226,0.055,4.1,19.1,-42.6,6.085614036,1.51,0.57,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,317156,2015-10-30 10:27:34:289,1446172054289.0 \n0.1712,-0.1113,9.7899,0.0612,-0.3284,9.801,-0.0367,-0.3457,0.1002,3.7,19,-42.2,6.061004893,1.66,-0.02,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,317257,2015-10-30 10:27:34:390,1446172054390.0 \n-0.6728,-0.231,8.606,0.0482,-0.4623,9.7956,-0.0232,-0.0562,-0.0635,3.4,19.1,-42.1,6.095562413,2.62,-0.33,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,317359,2015-10-30 10:27:34:492,1446172054492.0 \n-0.3543,0.5854,8.5724,0.0053,-0.3637,9.7999,0.121,0.0428,-0.0586,2.9,19.5,-41.6,6.120695154,2.13,-0.03,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,317462,2015-10-30 10:27:34:595,1446172054595.0 \n-0.6093,-0.0778,10.8804,-0.108,-0.1957,9.8041,0.1222,0.1051,-0.1124,2.6,19.8,-41.2,6.144431632,1.5,0.5,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,317563,2015-10-30 10:27:34:696,1446172054696.0 \n1.3455,0.2849,9.5026,-0.1735,0.1292,9.8043,0.3531,-0.1185,0.044,2.4,19.5,-40.8,6.221226119,-0.75,1.01,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,317666,2015-10-30 10:27:34:799,1446172054799.0 \n-0.7482,-1.4772,12.4678,-0.1732,-0.1552,9.8039,0.0623,-0.0965,-0.2101,2.1,19.3,-40.7,6.216339197,0.23,1.03,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,317768,2015-10-30 10:27:34:901,1446172054901.0 \n-0.3352,0.0275,9.2656,0.0618,-0.2145,9.8041,-0.1979,-0.259,-0.204,1.3,19.8,-40.3,6.225414909,1.01,-0.16,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,317869,2015-10-30 10:27:35:002,1446172055002.0 \n-0.7266,0.2849,8.7484,0.0801,-0.1792,9.8047,0.0843,0.0061,0.0476,0.7,20.1,-40,6.213023071,1.28,-0.49,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,317972,2015-10-30 10:27:35:105,1446172055105.0 \n-0.3448,0.2634,10.094,0.0215,-0.0979,9.8061,-0.0257,0.2053,0.1662,-0.2,20.9,-39.5,6.270269871,0.59,-0.39,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,318073,2015-10-30 10:27:35:206,1446172055206.0 \n-0.3974,0.3184,10.2388,-0.1221,0.0732,9.8056,0.3018,0.1075,0.2859,-0.2,21.1,-39.7,0.017453293,0.01,0.52,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,318176,2015-10-30 10:27:35:309,1446172055309.0 \n-0.9493,-0.6728,11.71,-0.1966,-0.0708,9.8044,-0.3677,0.1197,0.1234,0.2,21.3,-40.3,0.02984513,-0.33,0.91,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,318277,2015-10-30 10:27:35:410,1446172055410.0 \n-0.091,-0.0479,9.657,-0.1533,-0.023,9.8054,-0.1393,-0.2236,0.1564,1.2,21.3,-40.2,6.265208416,0.13,0.9,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,318379,2015-10-30 10:27:35:512,1446172055512.0 \n-0.6428,0.1508,8.8226,-0.1663,-0.1753,9.8037,0.0269,0.0428,0.1515,1.7,21.6,-40.3,6.217386394,1.03,0.86,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,318481,2015-10-30 10:27:35:614,1446172055614.0 \n-0.3376,0.8691,8.3175,-0.2486,-0.0336,9.8034,0.2077,0.1136,0.1136,2.3,21.9,-40,6.238155812,0.2,1.45,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,318584,2015-10-30 10:27:35:717,1446172055717.0 \n-0.9098,0.0539,11.1223,-0.2552,0.1467,9.8022,0.2321,-0.1063,-0.0403,2.6,22.1,-40.5,6.201852964,-0.12,1.72,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,318685,2015-10-30 10:27:35:818,1446172055818.0 \n-0.6213,-1.7873,14.625,-0.1988,0.0076,9.8046,-0.6903,0.5131,-0.4313,2.8,21.8,-41.5,6.183527007,-1.19,1,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,318787,2015-10-30 10:27:35:920,1446172055920.0 \n0.4322,0.6823,7.2425,-0.3447,0.0753,9.8003,0.4716,-0.1442,0.0428,2.8,21.8,-41.9,6.221226119,0.15,2.24,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,318889,2015-10-30 10:27:36:022,1446172056022.0 \n-0.759,0.4477,7.507,-0.3197,-0.0964,9.801,0.044,0.033,-0.1148,2.5,21.9,-42,6.207787083,0.56,1.87,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,318991,2015-10-30 10:27:36:124,1446172056124.0 \n-0.893,0.7302,8.4743,-0.3127,-0.1181,9.801,0.0403,-0.0733,0.0648,2.4,22.2,-41.8,6.260845093,0.65,2.07,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,319094,2015-10-30 10:27:36:227,1446172056227.0 \n-0.729,-0.0431,10.8182,-0.3424,-0.1208,9.7999,-0.0354,0.077,0.0342,2.1,22.4,-41.9,6.254561907,0.66,1.89,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,319195,2015-10-30 10:27:36:328,1446172056328.0 \n-0.4932,-0.8679,11.2504,-0.3197,0.1624,9.8001,0.4753,-0.011,0.3262,2.3,22.3,-42.3,6.268524541,-0.59,2.28,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,319297,2015-10-30 10:27:36:430,1446172056430.0 \n0.1437,0.2933,9.3937,-0.2492,0.0044,9.8035,0.1161,-0.3555,0.3348,2.6,22,-42.6,6.214593868,0.24,2,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,319399,2015-10-30 10:27:36:532,1446172056532.0 \n-0.2981,-0.2047,8.8466,-0.154,-0.0761,9.8051,-0.1979,0.1429,-0.0586,3,21.5,-42.5,6.175673025,0.44,0.9,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,319502,2015-10-30 10:27:36:635,1446172056635.0 \n-0.6273,0.6404,8.685,-0.337,-0.204,9.7987,-0.0476,0.2285,0.0525,3.2,21.5,-42.4,6.195744312,1.16,1.56,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,319603,2015-10-30 10:27:36:736,1446172056736.0 \n-1.312,0.4022,10.2137,-0.4133,-0.1661,9.7965,-0.0513,0.0269,-0.1014,3.4,21.7,-41.8,6.223844113,1.03,2.37,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,319706,2015-10-30 10:27:36:839,1446172056839.0 \n-1.0834,0.1927,11.6023,-0.3141,0,9.8016,0.1881,-0.1271,-0.0367,3.5,21.8,-41.9,6.166771846,0.31,1.98,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,319807,2015-10-30 10:27:36:940,1446172056940.0 \n-1.154,-0.6536,10.1347,-0.3642,-0.0871,9.7995,-0.2798,0.2529,-0.325,3.1,21.6,-41.8,6.216862796,0.51,2.13,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,319910,2015-10-30 10:27:37:043,1446172057043.0 \n-0.5291,-0.6488,10.1394,-0.384,-0.1843,9.7974,-0.4129,0.0134,-0.4056,2.7,21.6,-41.8,6.224716777,0.02,2.34,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,320011,2015-10-30 10:27:37:144,1446172057144.0 \n-0.6632,0.5806,8.5437,-0.4369,-0.2047,9.7948,-0.0806,0.0305,0.0305,2,21.9,-41.4,6.27498226,1.09,2.55,36.813747,-119.74795,276.45,336.5585251,3.63,77.41935,34.27,16 / 16,320113,2015-10-30 10:27:37:246,1446172057246.0 \n-0.498,0.6955,8.4659,-0.4216,-0.1643,9.7962,0.1063,-0.0525,0.1429,1.9,22.1,-41.1,6.275156793,1.1,2.56,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,320215,2015-10-30 10:27:37:348,1446172057348.0 \n-0.5363,0.1712,11.0887,-0.3838,-0.0214,9.7991,0.1319,-0.0538,0.2578,1.7,22.3,-41.4,6.268524541,0.46,2.35,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,320318,2015-10-30 10:27:37:451,1446172057451.0 \n-1.9118,-1.6101,13.9295,-0.2472,-0.1665,9.8021,-0.5034,-0.1075,-0.171,1.8,22.2,-41.5,6.244089932,0.15,1.6,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,320420,2015-10-30 10:27:37:553,1446172057553.0 \n-0.0263,0.7159,8.5844,-0.2173,-0.012,9.8042,-0.0904,-0.1124,-0.1246,2,22.3,-41.5,6.249500453,0.33,1.77,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,320521,2015-10-30 10:27:37:654,1446172057654.0 \n-1.1396,0.0778,8.9962,-0.2169,-0.1358,9.8033,-0.1295,0.0586,-0.0782,1.8,22.5,-41.1,6.234490621,0.79,1.27,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,320623,2015-10-30 10:27:37:756,1446172057756.0 \n-0.6225,1.0463,8.1235,-0.3054,7.00E-04,9.8019,0.1051,0.1344,-0.0684,1.8,22.6,-41.1,6.245835261,0.11,1.6,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,320726,2015-10-30 10:27:37:859,1446172057859.0 \n-1.4389,0.2981,11.9734,-0.3316,0.0215,9.801,0.1381,-0.1356,-0.1271,1.6,22.8,-41.2,6.259099764,-0.05,2.02,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,320827,2015-10-30 10:27:37:960,1446172057960.0 \n1.8052,0.7398,10.1442,-0.2235,0.2243,9.8015,0.2786,-0.1075,0.16,1.4,22.8,-41.5,0.006283185,-1.07,1.61,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,320930,2015-10-30 10:27:38:063,1446172058063.0 \n-0.1652,0.334,7.8554,-0.3615,0.1355,9.7991,0.5131,-0.171,0.1148,1.1,23,-41.7,0.04118977,0.1,2.65,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,321031,2015-10-30 10:27:38:164,1446172058164.0 \n-0.2933,-0.4741,10.094,-0.2766,0.0719,9.8025,0.11,0.0745,0.0415,1,23,-41.9,0.002443461,-1.11,1.44,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,321134,2015-10-30 10:27:38:267,1446172058267.0 \n-0.9182,0.5878,8.3139,-0.4526,0.0915,9.7958,-0.0867,0.303,0.0098,1.1,23.2,-41.7,0.040142573,-0.53,2.65,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,321236,2015-10-30 10:27:38:369,1446172058369.0 \n-0.4848,1.0235,9.183,-0.5586,0.0997,9.7902,-0.0073,0.1063,0.1283,1.4,23,-41.9,0.053058009,-0.53,3.06,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,321337,2015-10-30 10:27:38:470,1446172058470.0 \n-0.5782,0.8823,10.2089,-0.5609,0.2555,9.7873,0.3225,0.2285,0.3091,2.1,23.1,-41.9,0.010297443,-0.95,3.06,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,321440,2015-10-30 10:27:38:573,1446172058573.0 \n-1.3216,-0.3591,9.4822,-0.5369,0.0629,9.7917,0.2334,0.0208,0.3372,2.9,22.9,-42,6.253340177,-0.37,3.14,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,321541,2015-10-30 10:27:38:674,1446172058674.0 \n-0.7087,-0.1389,9.4296,-0.4563,-0.0262,9.796,-0.2981,-0.1319,0.0208,3.3,22.9,-42,6.241821004,-0.49,2.77,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,321643,2015-10-30 10:27:38:776,1446172058776.0 \n-0.7661,0.4262,8.8071,-0.4937,-0.203,9.7921,-0.1466,0.033,-0.0269,3.5,23.3,-41.8,6.19923497,1.03,2.9,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,321745,2015-10-30 10:27:38:878,1446172058878.0 \n-0.6847,1.0343,9.0046,-0.565,-0.1472,9.7893,0.1527,0.066,-0.1686,3.7,23.7,-41.5,6.20935788,1.06,3.18,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,321848,2015-10-30 10:27:38:981,1446172058981.0 \n-1.5335,0.4022,11.558,-0.5225,0.0635,9.7925,0.2028,-0.1735,-0.2101,3.7,24.1,-41.5,6.208659748,-0.37,3.05,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,321949,2015-10-30 10:27:39:082,1446172059082.0 \n-0.1341,-0.6596,12.3242,-0.4388,0.1077,9.7962,-0.5082,0.077,-0.3543,3.5,23.8,-41.7,6.200282168,-1.35,2.62,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,322051,2015-10-30 10:27:39:184,1446172059184.0 \n0.3831,0.3843,8.5054,-0.4159,0.1179,9.7971,-0.0721,-0.0794,-0.0623,2.9,23.5,-42.4,6.239377543,-0.61,2.63,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,322154,2015-10-30 10:27:39:287,1446172059287.0 \n-0.3867,0.3855,8.4946,-0.4033,0.0552,9.7982,-0.0403,-0.0244,-0.1112,2.6,23.4,-42.8,6.228905567,-0.4,2.31,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,322255,2015-10-30 10:27:39:388,1446172059388.0 \n-0.753,0.9852,8.2217,-0.4004,0.1339,9.7976,0.215,-0.0269,0.099,2.5,23.5,-43.1,6.233443423,-0.42,2.38,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,322357,2015-10-30 10:27:39:490,1446172059490.0 \n-0.0922,0.4597,11.4072,-0.3716,0.3178,9.7945,0.1723,-0.0965,0.4496,2.4,23.2,-43.3,6.27323693,-1.54,2.34,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,322459,2015-10-30 10:27:39:592,1446172059592.0 \n0.5674,1.2869,8.7807,-0.3832,0.5721,9.7824,0.3861,0.2224,0.5168,2.7,22.7,-43.7,6.239552076,-3.01,2.47,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,322562,2015-10-30 10:27:39:695,1446172059695.0 \n-0.4429,0.4932,9.3781,-0.4088,0.2989,9.7936,0.0086,0.2822,0.2224,3.4,22.2,-43.9,6.221400652,-1.64,2.03,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,322664,2015-10-30 10:27:39:797,1446172059797.0 \n-0.4226,0.3376,9.3829,-0.2473,0.2315,9.8008,-0.3433,-0.066,-0.1527,4.1,21.9,-44.2,6.158394266,-1.35,1.45,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,322765,2015-10-30 10:27:39:898,1446172059898.0 \n-0.747,0.9014,7.8003,-0.2675,0.1362,9.8021,0.1271,0.0134,-0.0452,4.4,22.2,-44.1,6.157696134,-0.53,1.53,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,322867,2015-10-30 10:27:40:000,1446172060000.0 \n-0.8416,0.8176,9.432,-0.2006,0.2535,9.8013,0.0929,-0.1454,-0.0586,4.1,22.5,-44.1,6.155427206,-1.48,1.17,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,322969,2015-10-30 10:27:40:102,1446172060102.0 \n-1.6041,0.7661,11.5137,-0.1672,0.5083,9.792,0.4068,-0.0696,-0.0525,4,22.2,-44,6.150714817,-2.32,1.08,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,323071,2015-10-30 10:27:40:204,1446172060204.0 \n-0.8739,-0.8056,11.5712,-0.0577,0.631,9.7862,-0.2798,0.055,-0.2553,3.5,21.3,-44.8,6.127851004,-3.69,0.34,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,323174,2015-10-30 10:27:40:307,1446172060307.0 \n0.085,0.0012,9.6965,-0.1039,0.3122,9.8011,-0.1588,0.0464,-0.0501,3.1,21,-45.1,6.166248247,-2.59,0.38,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,323275,2015-10-30 10:27:40:408,1446172060408.0 \n-0.4585,0.9553,7.7057,-0.1829,0.2448,9.8019,-0.0024,0.1112,0.0171,2.7,21.3,-45.4,6.179861815,-1.46,0.9,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,323378,2015-10-30 10:27:40:511,1446172060511.0 \n-0.0982,1.3192,8.7053,-0.221,0.2917,9.7998,0.0476,0.1185,-0.0611,2.8,21.7,-45.1,6.198362306,-1.7,1.29,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,323479,2015-10-30 10:27:40:612,1446172060612.0 \n-0.8954,0.6668,10.9882,-0.3655,0.3176,9.7947,0.011,0.171,-0.0586,3.1,21.8,-45.1,6.226985705,-1.86,2.14,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,323582,2015-10-30 10:27:40:715,1446172060715.0 \n-1.5622,-0.4621,11.813,-0.3629,0.4082,9.7914,-0.1368,-0.1649,0.121,3.5,21.5,-45.3,6.185795935,-2.39,2.12,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,323683,2015-10-30 10:27:40:816,1446172060816.0 \n-1.0858,-0.0646,10.0245,-0.1346,0.1654,9.8043,-0.1564,-0.4679,0.0831,3.6,21.6,-45.4,6.161884924,-1.24,1.53,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,323785,2015-10-30 10:27:40:918,1446172060918.0 \n-0.6333,0.0994,9.3314,-0.064,-0.0361,9.8064,-0.171,0.171,0.1283,3.4,22.1,-45.4,6.159790529,0.21,0.37,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,323887,2015-10-30 10:27:41:020,1446172061020.0 \n-0.7302,0.9134,8.272,-0.2338,-0.0962,9.8034,-0.0171,0.1234,0.1246,3.4,22.5,-45.2,6.186319534,0.65,1.04,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,323989,2015-10-30 10:27:41:122,1446172061122.0 \n-1.0092,0.3795,10.805,-0.3217,-0.1125,9.8007,-0.0012,0.1319,-0.0037,3.6,22.8,-45.1,6.164328385,0.65,1.67,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,324091,2015-10-30 10:27:41:224,1446172061224.0 \n0.1592,-0.3268,10.9978,-0.2298,-0.0749,9.8037,-0.3885,-0.2382,-0.325,3.9,22.9,-44.9,6.170087972,0.31,1.8,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,324193,2015-10-30 10:27:41:326,1446172061326.0 \n0.0204,0.0946,9.2644,-0.1813,-0.2179,9.8026,0.1124,0.0623,0.055,3.8,23.1,-44.3,6.150191218,1.66,1.43,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,324296,2015-10-30 10:27:41:429,1446172061429.0 \n0.0658,0.2227,8.8406,-0.0916,-0.1989,9.8042,0.0098,-0.0171,-0.0391,3.6,23.2,-44.1,6.12226595,1.16,0.54,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,324397,2015-10-30 10:27:41:530,1446172061530.0 \n-0.2478,0.8344,7.8003,-0.296,-0.0985,9.8017,0.011,0.1222,-0.0831,3.5,23.2,-44.1,6.165375583,0.58,1.73,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,324499,2015-10-30 10:27:41:632,1446172061632.0 \n-0.4645,0.577,9.5732,-0.4523,-0.1501,9.7951,-0.0428,0.0159,-0.0476,3.7,23,-44.5,6.191904587,0.77,2.53,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,324601,2015-10-30 10:27:41:734,1446172061734.0 \n0.0682,0.7817,9.1004,-0.4421,-0.0096,9.7967,0.2786,-0.0086,0.2639,4.2,22.7,-44.6,6.197664174,0.06,2.58,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,324704,2015-10-30 10:27:41:837,1446172061837.0 \n-1.0127,-0.9792,9.9288,-0.2565,-0.0992,9.8028,0.0305,0.0403,0.0305,4.3,22.5,-44.9,6.158743332,0.58,1.5,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,324805,2015-10-30 10:27:41:938,1446172061938.0 \n-0.516,-0.103,8.7975,-0.1083,-0.0496,9.8059,-0.0171,-0.0134,0.0867,4.2,22.4,-45,6.127327405,0.39,0.75,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,324908,2015-10-30 10:27:42:041,1446172062041.0 \n-0.8284,0.5555,8.8681,-0.149,-0.1666,9.8041,-0.1429,0.0599,-0.1014,3.8,22.3,-44.9,6.12820007,0.97,0.87,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,325009,2015-10-30 10:27:42:142,1446172062142.0 \n-0.6632,0.8799,8.8166,-0.2745,-0.1038,9.8023,0.1344,0.0916,-0.1026,3.6,22.5,-44.6,6.152983745,0.83,1.37,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,325111,2015-10-30 10:27:42:244,1446172062244.0 \n-1.0427,-0.0431,11.0744,-0.3276,0.0989,9.8007,0.2639,0.0733,-0.2053,3.8,22.2,-44.4,6.170960636,-0.58,1.91,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,325213,2015-10-30 10:27:42:346,1446172062346.0 \n-0.0204,-0.3555,11.1139,-0.3956,0.069,9.7984,-0.1503,-0.0452,-0.2138,3.8,21.9,-44.5,6.174800361,-1.32,1.94,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,325315,2015-10-30 10:27:42:448,1446172062448.0 \n0.2023,-0.0479,9.4176,-0.3104,-0.1095,9.8011,-0.0611,-0.1539,-0.0293,3.5,21.7,-44.6,6.1723569,0.5,2.03,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,325417,2015-10-30 10:27:42:550,1446172062550.0 \n-0.5818,0.0156,9.3793,-0.2,-0.2034,9.8025,0.0134,0.0122,-0.0892,3.1,22,-44.5,6.197140575,1.02,1.52,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,325520,2015-10-30 10:27:42:653,1446172062653.0 \n-0.7446,0.6632,8.5485,-0.2698,-0.1275,9.8021,0.1332,0.1148,0,2.5,22.6,-44.3,6.199060437,0.96,1.46,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,325621,2015-10-30 10:27:42:754,1446172062754.0 \n-1.075,0.1221,11.4682,-0.4062,-0.0194,9.7982,0.0843,0.1991,0.0073,2.4,22.6,-44.8,6.277251188,0.11,2.37,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,325724,2015-10-30 10:27:42:857,1446172062857.0 \n-0.1891,0.972,9.0513,-0.5665,0.3907,9.7825,0.2541,-0.0171,0.2798,2.8,22.1,-45.2,6.268000943,-1.8,3.36,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,325825,2015-10-30 10:27:42:958,1446172062958.0 \n-0.6213,0.4489,7.9619,-0.5741,0.2214,9.7873,0.1087,-0.3311,0.2724,3.6,21.2,-45.6,6.224193178,-1.29,3.36,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,325927,2015-10-30 10:27:43:060,1446172063060.0 \n-0.7171,0.0575,8.7077,-0.3098,0.0819,9.8014,-0.303,-0.2126,0.0635,4,20.9,-45.5,6.163281188,-0.48,1.81,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,326029,2015-10-30 10:27:43:162,1446172063162.0 \n-0.9038,0.7685,8.6143,-0.2139,-0.0707,9.8041,-0.0391,-0.0709,0.0415,3.9,21.2,-45.2,6.14495523,0.27,1.41,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,326131,2015-10-30 10:27:43:264,1446172063264.0 \n-1.0032,0.5578,10.4926,-0.1698,-0.008,9.8052,0.1344,-0.0195,-0.0965,3.5,21.6,-44.9,6.137624848,0.05,0.99,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,326233,2015-10-30 10:27:43:366,1446172063366.0 \n-1.142,0.1089,10.7955,-0.2348,0.2381,9.8009,0.2492,0.1002,-0.1295,3.3,21.6,-44.9,6.181083546,-0.58,0.89,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,326336,2015-10-30 10:27:43:469,1446172063469.0 \n-0.9433,-0.6476,11.7615,-0.3101,-0.0459,9.8016,-0.5424,0.2321,-0.2065,3.1,21.4,-45,6.196791509,-0.52,1.46,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,326437,2015-10-30 10:27:43:570,1446172063570.0 \n-0.4513,-0.1508,9.8067,-0.2046,-0.0993,9.804,-0.1955,-0.0757,-0.0916,3,21.5,-44.5,6.186843132,0.58,1.2,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,326540,2015-10-30 10:27:43:673,1446172063673.0 \n-0.1784,0.5782,7.7812,-0.2611,-0.1089,9.8026,0.099,0.0745,0.0012,2.8,21.7,-44.3,6.184748737,0.78,1.16,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,326641,2015-10-30 10:27:43:774,1446172063774.0 \n0.152,1.3443,9.1004,-0.3864,-0.0247,9.799,0.1185,0.1197,0.0855,2.9,22.1,-44.3,6.217909993,0.4,2.06,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,326744,2015-10-30 10:27:43:877,1446172063877.0 \n-1.2115,0.4322,11.9914,-0.4691,0.1662,9.794,0.463,0.1222,0.0709,3,21.9,-44.3,6.234490621,-0.36,2.49,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,326845,2015-10-30 10:27:43:978,1446172063978.0 \n-2.0758,-1.6735,14.8297,-0.273,0.3895,9.7951,-0.4606,0.0159,-0.2346,3.3,21,-45,6.220004388,-3.16,1.93,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,326947,2015-10-30 10:27:44:080,1446172064080.0 \n-0.4118,0.9816,6.6595,-0.3169,0.5135,9.7881,0.303,-0.0623,0.2993,3.4,20.5,-45.3,6.228207436,-2.87,2.19,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,327049,2015-10-30 10:27:44:182,1446172064182.0 \n-0.9996,0.2526,9.6055,-0.1351,0.2309,9.803,-0.2492,-0.2101,0.0464,3.2,20,-45.9,6.171484235,-1.35,0.79,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,327152,2015-10-30 10:27:44:285,1446172064285.0 \n-0.0934,1.1923,7.8925,-0.1262,0.2711,9.8021,0.0977,0.0354,-0.0122,2.9,20.5,-45.9,6.169215307,-1.14,0.61,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,327253,2015-10-30 10:27:44:386,1446172064386.0 \n-0.7171,0.4513,11.2264,-0.1215,0.2851,9.8018,-0.0086,-0.0208,-0.2602,2.7,20.7,-45.8,6.17776742,-1.61,0.8,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,327356,2015-10-30 10:27:44:489,1446172064489.0 \n0.3256,0.4968,10.586,-0.2143,0.3639,9.7978,0.0782,0.1894,-0.1662,2.4,20.6,-45.8,6.239377543,-2.13,1.25,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,327457,2015-10-30 10:27:44:590,1446172064590.0 \n-1.2522,-0.3005,9.8162,-0.3505,0.1151,9.7997,0.0183,-0.0415,-0.0782,2.4,20.6,-45.6,6.268175476,-0.75,2.09,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,327560,2015-10-30 10:27:44:693,1446172064693.0 \n0.0168,0.2765,8.9735,-0.2754,-0.0063,9.8028,0.1234,0.2358,0.1319,2.1,21.1,-45.4,6.248104189,0.04,1.61,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,327661,2015-10-30 10:27:44:794,1446172064794.0 \n-0.4609,0.893,7.8721,-0.4505,0.0729,9.796,0.0318,0.1515,-0.0024,2.1,21.5,-45.3,6.277774786,-0.36,2.39,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,327763,2015-10-30 10:27:44:896,1446172064896.0 \n-0.4848,0.9912,9.663,-0.5061,0.1089,9.793,0.0354,0.0696,0.0611,2.2,21.5,-45.2,0.01134464,-0.54,2.87,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,327866,2015-10-30 10:27:44:999,1446172064999.0 \n-0.7745,0.8404,12.2176,-0.5659,0.2962,9.7858,0.4313,0.1881,0.2407,2.5,21.4,-45.4,6.25473644,-1.11,3.02,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,327967,2015-10-30 10:27:45:100,1446172065100.0 \n-1.0798,-0.1317,9.651,-0.5083,0.388,9.7858,-0.1002,-0.011,0.0354,3.2,20.8,-45.7,6.25648177,-2.27,2.97,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,328069,2015-10-30 10:27:45:202,1446172065202.0 \n-0.4609,0.4262,8.8202,-0.3221,0.3633,9.7946,-0.1124,-0.1478,0.0831,3.3,20.5,-45.6,6.229952765,-2.26,2.22,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,328171,2015-10-30 10:27:45:304,1446172065304.0 \n-1.2414,0.5471,9.4296,-0.3787,0.0931,9.7989,-0.0257,0.0257,-0.0941,3.3,20.3,-45.7,6.219480789,-0.71,2.1,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,328274,2015-10-30 10:27:45:407,1446172065407.0 \n-0.8392,1.2127,8.3905,-0.4833,0.1962,9.7928,0.1393,0.1258,-0.0183,3.2,20.5,-45.4,6.244264465,-0.97,2.74,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,328375,2015-10-30 10:27:45:508,1446172065508.0 \n-1.1396,0.4142,10.9439,-0.469,0.4339,9.7858,0.2871,0.0049,-0.121,3.1,20.8,-45.4,6.242344603,-2.17,2.64,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,328478,2015-10-30 10:27:45:611,1446172065611.0 \n-1.2941,-1.0439,12.1314,-0.5908,0.1966,9.7869,-0.529,0.5571,-0.4276,3,20.6,-45.3,6.270269871,-1.15,3.45,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,328579,2015-10-30 10:27:45:712,1446172065712.0 \n-0.7338,0.1257,8.3845,-0.8093,0.1898,9.7714,-0.2712,-0.0684,-0.1381,3.1,20.6,-45.2,0.041015237,-0.9,4.95,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,328682,2015-10-30 10:27:45:815,1446172065815.0 \n-1.1971,2.405,6.0633,-0.8122,0.0996,9.7724,0.1026,0.0892,0.1735,3.2,21.1,-44.4,0.030543262,-0.58,4.75,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,328783,2015-10-30 10:27:45:916,1446172065916.0 \n-2.308,-0.4142,10.7571,-1.0166,-0.0525,9.7537,0.2761,0.2236,0.1979,3.6,21.6,-43.9,0.013264502,0.76,5.56,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,328885,2015-10-30 10:27:46:018,1446172066018.0 \n-1.1241,0.0383,11.0468,-1.049,0.1701,9.7489,-0.066,-0.259,0.2199,4.2,21.7,-43.8,0.038048178,-0.98,6.32,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,328987,2015-10-30 10:27:46:120,1446172066120.0 \n-0.1149,0.103,11.1761,-0.7453,0.2775,9.7744,0.1515,-0.369,0.2553,4.6,21.4,-44.1,6.234316088,-1.58,5.08,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,329090,2015-10-30 10:27:46:223,1446172066223.0 \n-0.5602,0.7829,8.1235,-0.6521,0.1905,9.7831,0.3311,-0.3861,0.4166,4.6,20.9,-44.4,6.18911206,-1.11,3.81,36.813824,-119.747955,275.33,336.5585251,0,25.806452,13.95,16 / 16,329192,2015-10-30 10:27:46:325,1446172066325.0 \n-0.8248,0.1305,9.3721,-0.3478,0.1608,9.7992,-0.0305,0.0049,0.1539,4.1,20.8,-44.9,6.168342642,-1.29,1.86,36.81391,-119.74791,270.97,336.5585251,4.11,19.35484,7.88,16 / 16,329293,2015-10-30 10:27:46:426,1446172066426.0 \n-0.7219,0.9062,8.9866,-0.396,0.1034,9.7981,-0.0977,0.0941,0.1552,3.7,20.7,-45,6.178989151,-0.63,2.23,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,329396,2015-10-30 10:27:46:529,1446172066529.0 \n-1.1037,1.0163,10.0963,-0.5339,0.1888,9.7903,0.099,0.1466,-0.0391,3.9,20.6,-45.1,6.202725629,-0.87,2.86,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,329497,2015-10-30 10:27:46:630,1446172066630.0 \n-1.1241,0.0682,10.5979,-0.5834,0.3259,9.7839,0.1332,-0.0819,-0.2932,4.4,20.5,-44.9,6.221575185,-1.65,3.33,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,329599,2015-10-30 10:27:46:732,1446172066732.0 \n-0.5411,0.0156,10.1011,-0.5674,0.0913,9.7898,0.1271,-0.2358,0.0379,4.4,20.5,-44.9,6.218433592,-0.53,3.32,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,329702,2015-10-30 10:27:46:835,1446172066835.0 \n-0.1125,-0.1113,10.4172,-0.3381,-0.0099,9.8008,-0.2602,-0.1625,-0.1307,3.9,20.7,-45,6.165375583,-0.48,1.87,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,329803,2015-10-30 10:27:46:936,1446172066936.0 \n-0.571,0.7015,8.7508,-0.374,-0.014,9.7995,-0.0684,0.0831,-0.0244,3,21.3,-45,6.222098783,0.08,2.19,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,329905,2015-10-30 10:27:47:038,1446172067038.0 \n0.079,1.245,9.6582,-0.4267,0.0677,9.7971,0.0941,0.1539,0.0305,2.8,21.5,-44.9,6.23082543,-0.19,2.34,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,330007,2015-10-30 10:27:47:140,1446172067140.0 \n-0.5746,0.6141,11.7352,-0.4824,0.2369,9.7919,0.1429,0.0073,0.1002,2.9,21.3,-45.1,6.247406058,-1.1,2.82,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,330109,2015-10-30 10:27:47:242,1446172067242.0 \n0.996,0.2179,12.4977,-0.404,0.3751,9.7911,-0.3238,-0.1185,-0.1112,3.2,20.8,-45.3,6.248278722,-2.49,2.8,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,330211,2015-10-30 10:27:47:344,1446172067344.0 \n-1.1935,0.067,9.5038,-0.3056,0.2995,9.7973,-0.0745,-0.3665,0.0403,3.4,20.3,-45.8,6.231698094,-1.86,2.36,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,330313,2015-10-30 10:27:47:446,1446172067446.0 \n-0.7506,0.3903,8.855,-0.2316,0.2024,9.8018,-0.1307,-0.0061,0.0354,3.4,20.3,-45.8,6.188937528,-1.26,1.26,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,330416,2015-10-30 10:27:47:549,1446172067549.0 \n-0.1437,1.494,8.0086,-0.2422,0.3049,9.7989,0.2236,0.1075,0.1772,3.1,20.4,-45.7,6.196442443,-1.78,1.42,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,330517,2015-10-30 10:27:47:650,1446172067650.0 \n-1.136,0.7458,11.1893,-0.2704,0.403,9.7946,0.1356,0.1967,-0.1051,2.9,20.3,-45.7,6.204296425,-2.35,1.58,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,330619,2015-10-30 10:27:47:752,1446172067752.0 \n-1.0259,-0.5399,12.4929,-0.4064,0.3898,9.7905,-0.4423,0.3128,-0.2211,2.9,19.8,-46.1,6.22366958,-2.94,2.08,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,330722,2015-10-30 10:27:47:855,1446172067855.0 \n0.5986,1.0654,8.2552,-0.4247,0.4207,9.7884,0.3201,-0.193,0.1955,2.9,20,-46.3,6.258925231,-1.62,3.09,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,330823,2015-10-30 10:27:47:956,1446172067956.0 \n-0.1065,-0.018,10.969,-0.3674,0.2108,9.7975,-0.1772,-0.066,-0.1918,3,20,-46.3,6.226985705,-1.55,2.25,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,330925,2015-10-30 10:27:48:058,1446172068058.0 \n-0.6788,1.0714,8.0122,-0.4558,0.2528,9.7928,0.0281,0.0049,-0.1038,3,20.5,-46.1,6.240075675,-1.45,2.54,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,331027,2015-10-30 10:27:48:160,1446172068160.0 \n-0.9242,0.5555,10.337,-0.4887,0.2649,9.7909,-0.0232,0.0562,-0.0941,2.9,20.4,-45.9,6.241646471,-1.48,2.64,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,331130,2015-10-30 10:27:48:263,1446172068263.0 \n-0.4118,1.5083,9.8402,-0.5502,0.5224,9.7773,0.3726,0.0012,0.3115,2.9,20.5,-46.1,6.265382949,-2.39,3.23,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,331231,2015-10-30 10:27:48:364,1446172068364.0 \n-1.4222,-0.589,12.7647,-0.4022,0.4512,9.788,-0.1442,0.099,0.1295,3,20,-46.4,6.242868201,-3.34,2.59,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,331334,2015-10-30 10:27:48:467,1446172068467.0 \n-0.7195,0.1041,9.1806,-0.1894,0.3291,9.7993,-0.1002,-0.3861,0.2004,3.2,19.7,-46.8,6.200282168,-2.34,1.44,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,331435,2015-10-30 10:27:48:568,1446172068568.0 \n-0.99,0.7865,8.8861,-0.1889,0.1618,9.8035,-0.1197,0.0684,0.0709,3.1,20,-46.7,6.182654342,-0.95,1.1,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,331537,2015-10-30 10:27:48:670,1446172068670.0 \n-0.5112,1.2258,9.335,-0.2615,0.2269,9.8005,-0.0318,0.0709,-0.0293,3.3,20.3,-46.4,6.196966042,-1.28,1.47,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,331640,2015-10-30 10:27:48:773,1446172068773.0 \n-1.0283,0.1281,11.4479,-0.3239,0.298,9.7968,0.1173,-0.0171,-0.0525,3.6,20.6,-46,6.173055031,-1.74,1.89,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,331741,2015-10-30 10:27:48:874,1446172068874.0 \n0.3783,0.7733,10.477,-0.2106,0.4012,9.7962,0.1124,-0.281,0.0819,3.7,20.3,-46.3,6.15507814,-2.53,1.45,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,331844,2015-10-30 10:27:48:977,1446172068977.0 \n0.7494,0.2346,9.2883,-0.1827,0.2921,9.8006,0.1491,-0.1747,0.0574,3.5,20.2,-46.6,6.138148446,-1.71,1.07,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,331945,2015-10-30 10:27:49:078,1446172069078.0 \n-0.3783,0.3005,8.4922,-0.236,0.2169,9.8014,-0.0244,0.0611,-0.0684,3.4,20.2,-46.7,6.186843132,-1.54,1.15,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,332048,2015-10-30 10:27:49:181,1446172069181.0 \n-0.4501,1.1337,8.8322,-0.2506,0.1138,9.8028,-0.1491,0.0049,-0.0867,3.3,20.6,-46.5,6.204645491,-0.71,1.62,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,332149,2015-10-30 10:27:49:282,1446172069282.0 \n-0.4669,0.6488,10.41,-0.2644,0.1612,9.8018,0.0782,0.1197,0.1405,3.3,20.7,-46.5,6.19504618,-0.79,1.36,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,332251,2015-10-30 10:27:49:384,1446172069384.0 \n0.2514,1.2821,10.2879,-0.2211,0.4599,9.7934,0.2456,-0.1197,0.1918,3.4,20.6,-46.6,6.202376563,-2.18,1.41,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,332354,2015-10-30 10:27:49:487,1446172069487.0 \n-1.5778,-0.5555,10.6853,-0.1474,0.4532,9.7951,-0.2834,0.1063,-0.066,3.5,20,-46.5,6.131865261,-3.12,0.71,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,332455,2015-10-30 10:27:49:588,1446172069588.0 \n0.0407,0.1281,8.9495,0.1338,0.2543,9.8024,-0.2004,-0.2053,0.2615,3.5,19.4,-46.6,6.065019151,-1.75,-0.64,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,332558,2015-10-30 10:27:49:691,1446172069691.0 \n-0.4549,0.6189,8.6155,0.0542,0.0876,9.8061,-0.1894,0.2346,0.0452,3.4,19.6,-46.6,6.1151101,-0.91,-0.63,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,332659,2015-10-30 10:27:49:792,1446172069792.0 \n-0.5495,1.0702,9.7636,-0.0905,0.0592,9.8061,-0.044,0.0195,-0.2553,3.4,20.2,-46.2,6.156823469,-0.35,0.53,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,332761,2015-10-30 10:27:49:894,1446172069894.0 \n-0.7626,0.1879,11.4144,-0.1508,0.1111,9.8049,0.1344,0.077,-0.2407,3.5,20.5,-45.7,6.125407543,-0.4,0.75,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,332864,2015-10-30 10:27:49:997,1446172069997.0 \n-0.7135,-0.6596,11.8357,-0.2045,0.1729,9.803,-0.3054,0.2065,-0.4068,3.7,20.5,-45.8,6.134832321,-1.53,0.85,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,332966,2015-10-30 10:27:50:099,1446172070099.0 \n-0.164,0.2466,9.0357,-0.2293,0.0733,9.8037,-0.2468,-0.1955,-0.1845,3.4,20.5,-45.8,6.205518155,-0.65,1.65,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,333067,2015-10-30 10:27:50:200,1446172070200.0 \n0.0144,0.6883,7.5405,-0.1784,0.0367,9.805,0.0843,0.0672,0.1087,3,20.6,-45.9,6.174625828,0.16,0.9,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,333169,2015-10-30 10:27:50:302,1446172070302.0 \n-0.3424,0.9086,8.442,-0.1696,0.0772,9.8049,0.0415,-0.0305,0.0428,2.8,20.9,-45.8,6.182130743,-0.44,1.04,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,333271,2015-10-30 10:27:50:404,1446172070404.0 \n-0.6249,0.6045,9.9683,-0.1649,0.1163,9.8046,0.0269,0.1503,0.0904,2.7,20.8,-45.8,6.178989151,-0.68,0.93,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,333373,2015-10-30 10:27:50:506,1446172070506.0 \n-0.1401,1.172,10.2101,-0.2456,0.2501,9.8004,0.2871,-0.0171,0.2468,2.8,20.5,-45.8,6.200107635,-1.46,1.44,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,333475,2015-10-30 10:27:50:608,1446172070608.0 \n-1.3587,-0.5543,12.2176,-0.2046,0.2784,9.8006,-0.2028,0.0623,0.0269,3,20,-45.8,6.190682857,-2.27,1.21,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,333577,2015-10-30 10:27:50:710,1446172070710.0 \n-0.7422,0.2562,9.153,-0.1019,0.2047,9.804,-0.1417,-0.0379,0.0672,3.1,19.7,-45.8,6.168342642,-1.47,0.69,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,333679,2015-10-30 10:27:50:812,1446172070812.0 \n-0.8272,0.5004,9.165,-0.101,0.0824,9.8058,0.1173,0.0476,0.033,3.2,19.7,-46,6.157172535,-0.41,0.53,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,333782,2015-10-30 10:27:50:915,1446172070915.0 \n-0.6548,1.0116,9.2129,-0.19,0.2097,9.8026,0.1381,0.1075,-0.0232,3.2,20,-45.9,6.175149426,-0.96,0.93,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,333884,2015-10-30 10:27:51:017,1446172071017.0 \n-1.142,0.3651,11.3497,-0.2886,0.2883,9.7982,0.3934,0.182,-0.0293,3.3,20,-45.7,6.206216287,-1.68,1.69,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,333986,2015-10-30 10:27:51:119,1446172071119.0 \n-0.6943,-0.8284,13.4279,-0.413,0.5159,9.7844,-0.5412,0.2957,-0.4484,3.6,19.4,-46,6.181956211,-3.82,2.19,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,334087,2015-10-30 10:27:51:220,1446172071220.0 \n0.6979,0.7003,7.6614,-0.5419,0.5293,9.7774,0.3555,-0.0293,0.0648,3.8,19.1,-46.1,6.215815598,-3.09,3.17,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,334189,2015-10-30 10:27:51:322,1446172071322.0 \n-0.255,0.6524,7.3873,-0.4838,0.3066,9.7899,0.0244,-0.0147,0.011,3.9,19,-46.4,6.200282168,-2.05,2.84,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,334292,2015-10-30 10:27:51:425,1446172071425.0 \n-0.8751,0.8703,8.3773,-0.4775,0.1813,9.7933,0.0086,-0.0635,0.1429,3.7,19.6,-46.1,6.201154832,-1.07,2.84,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,334393,2015-10-30 10:27:51:526,1446172071526.0 \n-0.5746,0.8619,9.7839,-0.4548,0.1865,9.7943,-0.0232,0.0171,0.1087,3.6,19.9,-45.9,6.192253653,-1.03,2.61,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,334495,2015-10-30 10:27:51:628,1446172071628.0 \n-0.2622,0.99,9.8773,-0.5239,0.3301,9.7871,0.2822,0.0525,0.3677,3.7,20.1,-45.5,6.206041754,-1.42,3.01,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,334597,2015-10-30 10:27:51:730,1446172071730.0 \n-0.2215,0.2861,10.2268,-0.3719,0.2562,9.7962,0.1112,0.0183,0.281,4,19.9,-45.4,6.177069289,-1.29,2.24,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,334699,2015-10-30 10:27:51:832,1446172071832.0 \n-0.5626,0.3496,8.6658,-0.2115,0.2055,9.8022,-0.182,-0.1295,0.0293,4.2,19.8,-45.8,6.151936547,-1.55,1.49,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,334801,2015-10-30 10:27:51:934,1446172071934.0 \n-0.6381,0.7805,9.2811,-0.1222,0.1065,9.8053,-0.0806,-0.1112,0.0244,4,20,-46,6.117553561,-0.62,0.71,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,334903,2015-10-30 10:27:52:036,1446172072036.0 \n-0.5219,0.9074,9.1854,-0.1532,0.173,9.8039,0.0501,0.0757,-0.055,3.9,20.1,-46.1,6.122789549,-0.87,0.81,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,335005,2015-10-30 10:27:52:138,1446172072138.0 \n-0.6069,0.7554,9.9431,-0.2609,0.4023,9.7949,0.2798,0.0501,-0.0696,3.8,20.1,-46.3,6.148271356,-1.76,1.36,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,335108,2015-10-30 10:27:52:241,1446172072241.0 \n0.5543,0.1496,11.3401,-0.3432,0.3747,9.7935,-0.1906,0.1613,-0.11,3.9,19.8,-46.4,6.161710391,-2.62,1.62,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,335209,2015-10-30 10:27:52:342,1446172072342.0 \n0.431,0.334,10.4627,-0.2904,0.1526,9.8012,-0.2847,-0.1613,-0.2053,4.1,19.5,-46.2,6.171658768,-1.41,2.03,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,335311,2015-10-30 10:27:52:444,1446172072444.0 \n-0.231,0.8128,7.6231,-0.2818,0.1239,9.8018,0.0122,0.0513,-0.0281,4.1,19.8,-45.7,6.150365751,-0.56,1.58,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,335413,2015-10-30 10:27:52:546,1446172072546.0 \n-0.4142,0.9697,9.3613,-0.2621,0.0478,9.803,-0.0977,-0.0806,-0.0134,3.8,20.4,-45.4,6.145827895,-0.28,1.53,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,335516,2015-10-30 10:27:52:649,1446172072649.0 \n-0.6991,0.431,9.9563,-0.3769,0.1649,9.798,0.215,0.2443,0.2126,3.5,20.7,-45.1,6.162932122,-0.51,1.8,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,335617,2015-10-30 10:27:52:750,1446172072750.0 \n1.0295,0.9912,10.3058,-0.4816,0.5136,9.7813,0.2944,-0.1857,0.4142,4.1,20.1,-45.3,6.203598293,-3,2.82,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,335719,2015-10-30 10:27:52:852,1446172072852.0 \n-0.7566,0.0072,10.0796,-0.3443,0.4226,9.7915,-0.0476,-0.237,0.3482,4.4,19.6,-45.5,6.179687283,-2.7,2.17,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,335821,2015-10-30 10:27:52:954,1446172072954.0 \n-0.0419,0.7027,8.4886,-0.1539,0.2937,9.801,-0.2566,-0.1454,0.1429,5,19,-45.9,6.076189258,-1.72,0.9,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,335923,2015-10-30 10:27:53:056,1446172073056.0 \n-0.7159,0.8823,9.1985,-0.1091,0.0276,9.806,-0.0342,0.0318,0.0538,5,19.3,-45.8,6.049660253,-0.18,0.56,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,336025,2015-10-30 10:27:53:158,1446172073158.0 \n-0.8164,0.8332,9.9994,-0.1876,0.148,9.8037,0.1539,0.0684,-0.1319,5,20,-45.6,6.086661233,-0.86,1.1,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,336127,2015-10-30 10:27:53:260,1446172073260.0 \n-0.7649,0.9146,9.9383,-0.2817,0.5635,9.7864,0.4997,0.1356,-0.1002,4.9,20.2,-45.6,6.102020131,-1.72,1.35,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,336229,2015-10-30 10:27:53:362,1446172073362.0 \n-0.5435,-0.2466,10.2939,-0.3702,0.4918,9.7873,-0.1185,0.1332,-0.2859,5.1,19.4,-45.8,6.123836746,-3.11,1.92,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,336332,2015-10-30 10:27:53:465,1446172073465.0 \n-0.8775,-0.4992,10.7967,-0.3101,0.2976,9.7972,-0.0684,0.0794,0.0171,5,19.1,-45.9,6.11214304,-2.2,1.76,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,336433,2015-10-30 10:27:53:566,1446172073566.0 \n-0.8056,0.917,8.1762,-0.4028,0.2044,9.7962,-0.0806,0.1161,0.1002,5,19.2,-45.7,6.134483255,-1.57,2.44,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,336535,2015-10-30 10:27:53:668,1446172073668.0 \n-0.8128,0.9481,9.5636,-0.4286,0.1874,9.7955,0.0452,0.0415,0.0941,5,20,-45.2,6.139021111,-1.1,2.51,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,336637,2015-10-30 10:27:53:770,1446172073770.0 \n-0.6476,0.7673,11.133,-0.5132,0.3679,9.7863,0.2517,-0.1442,0.2065,5.2,20.2,-45,6.162408523,-1.77,3.06,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,336740,2015-10-30 10:27:53:873,1446172073873.0 \n-1.9716,-0.9206,10.5896,-0.4501,0.481,9.7845,-0.1552,0.1527,0.0049,5.5,19.8,-45,6.102194664,-3.28,2.38,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,336841,2015-10-30 10:27:53:974,1446172073974.0 \n-0.6859,0.3316,9.1734,-0.3238,0.3525,9.795,-0.1649,-0.2395,0.1735,5.8,19.5,-45.2,6.091722688,-2.44,2.23,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,336943,2015-10-30 10:27:54:076,1446172074076.0 \n-0.4022,0.7745,8.096,-0.1969,0.0835,9.8043,-0.1063,-0.0501,0.0843,5.7,19.5,-45.2,6.038315613,-0.49,1.15,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,337045,2015-10-30 10:27:54:178,1446172074178.0 \n-0.2682,1.2234,8.6718,-0.173,0.0105,9.8051,0.16,0.0831,0.0195,5.7,20,-44.8,6.023131249,0.07,0.88,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,337147,2015-10-30 10:27:54:280,1446172074280.0 \n-0.7937,0.3819,11.0875,-0.2693,0.3187,9.7978,0.2346,0.0049,-0.0904,5.6,20.4,-44.7,6.047565858,-0.65,1.37,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,337250,2015-10-30 10:27:54:383,1446172074383.0 \n0.5806,0.8835,9.8521,-0.3104,0.6771,9.7783,0.3128,-0.0464,-0.0281,5.7,20.1,-44.8,6.078458186,-2.66,1.8,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,337352,2015-10-30 10:27:54:485,1446172074485.0 \n-0.8631,-0.7961,11.0684,-0.304,0.3795,9.7946,-0.1845,-0.1772,-0.237,5.5,19.5,-45.3,6.086835766,-2.84,2.01,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,337453,2015-10-30 10:27:54:586,1446172074586.0 \n-0.0407,0.4752,8.2911,-0.2532,0.1973,9.8014,-0.1979,-0.0183,0.0244,5.3,19.3,-45.2,6.097307742,-1.52,1.53,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,337555,2015-10-30 10:27:54:688,1446172074688.0 \n-0.5447,1.1756,8.7819,-0.333,-0.1312,9.8001,-0.2199,0.1124,0.0696,4.9,19.9,-44.8,6.098005874,-0.22,1.55,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,337657,2015-10-30 10:27:54:790,1446172074790.0 \n-0.6189,0.7745,10.3705,-0.4395,-0.0903,9.7964,0.0501,0.193,0.1185,5,21,-44.3,6.125407543,0.63,2.25,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,337759,2015-10-30 10:27:54:892,1446172074892.0 \n-0.2873,-0.4824,10.4016,-0.6281,0.1437,9.7855,-0.0367,-0.121,0.0354,5.8,21.4,-43.9,6.13779938,-0.84,3.67,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,337861,2015-10-30 10:27:54:994,1446172074994.0 \n-0.4824,-0.0898,10.0317,-0.4513,0.1183,9.7955,0.0428,-0.2468,0.2248,6.4,21.3,-44,6.116855429,-0.58,3.11,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,337963,2015-10-30 10:27:55:096,1446172075096.0 \n-0.583,-0.0431,8.5892,-0.1337,0.0886,9.8053,-0.2468,-0.1735,-0.0733,6.5,20.8,-44.3,5.992587987,-0.52,0.78,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,338065,2015-10-30 10:27:55:198,1446172075198.0 \n-0.5315,0.431,9.1985,0.0567,-0.0252,9.8065,-0.0538,-0.2187,-0.0171,5.9,20.8,-44.5,5.987875598,0.32,-0.41,36.81391,-119.74791,270.97,336.6260835,4.11,19.35484,7.88,16 / 16,338168,2015-10-30 10:27:55:301,1446172075301.0 \n-0.9254,0.4872,10.0221,-0.0599,0.1572,9.8052,0.0513,0.0684,-0.1796,5.1,20.8,-44.7,6.062924756,-0.81,0.2,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,338270,2015-10-30 10:27:55:403,1446172075403.0 \n-0.1365,0.0622,11.2923,-0.1695,0.4227,9.7961,0.1784,0.0464,-0.1393,4.7,20.4,-44.9,6.091024557,-2.31,0.97,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,338371,2015-10-30 10:27:55:504,1446172075504.0 \n-0.0694,0.3196,9.1901,-0.482,0.2133,9.7925,-0.11,0.1735,-0.1552,4.8,20,-45,6.11929889,-1.68,1.88,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,338474,2015-10-30 10:27:55:607,1446172075607.0 \n-0.018,-0.3903,9.8737,-0.5164,-0.0768,9.7927,-0.5449,0.0086,-0.2761,5,20.1,-44.6,6.156474403,-0.5,3.05,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,338575,2015-10-30 10:27:55:708,1446172075708.0 \n-0.5219,0.662,7.7189,-0.6588,-0.3322,9.7789,0.0244,-0.0892,0.0293,5.4,21.1,-43.7,6.1866686,1.99,4.05,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,338679,2015-10-30 10:27:55:812,1446172075812.0 \n-1.0092,0.3065,10.653,-0.5708,-0.2353,9.7872,0.2077,-0.2114,0.0342,5.6,22.1,-43,6.118251693,1.38,3.34,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,338779,2015-10-30 10:27:55:912,1446172075912.0 \n-0.808,0.8763,11.0947,-0.4368,0.1154,9.7962,0.6145,-0.0293,0.391,5.7,21.8,-43.4,6.103939993,-0.67,2.55,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,338882,2015-10-30 10:27:56:015,1446172076015.0 \n-1.6364,-0.8583,12.639,-0.3587,0.2496,9.7969,-0.4496,-0.0086,-0.1234,5.6,21.1,-44,6.091897221,-2.18,2.1,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,338983,2015-10-30 10:27:56:116,1446172076116.0 \n-0.8691,0.1113,7.9344,-0.4873,0.1235,9.7938,-0.1796,-0.0599,0.1271,5.9,20.4,-44.5,6.100100269,-0.72,2.85,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,339085,2015-10-30 10:27:56:218,1446172076218.0 \n-0.9565,0.1772,9.1051,-0.5049,-0.2159,9.7913,0.0037,0.0159,0.1552,6,20.5,-44.4,6.095562413,1.12,2.83,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,339187,2015-10-30 10:27:56:320,1446172076320.0 \n-0.5052,0.9553,8.8107,-0.5703,-0.1072,9.7895,0.1808,0.1087,0.1869,6.5,21.3,-44,6.070604204,0.63,3.33,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,339290,2015-10-30 10:27:56:423,1446172076423.0 \n-1.0475,-0.3603,11.8932,-0.5714,0.1369,9.789,0.3103,0.0354,-0.0709,6.7,21.4,-43.7,6.073222198,0.17,3.31,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,339392,2015-10-30 10:27:56:525,1446172076525.0 \n-0.6273,-0.4238,11.6574,-0.6104,0.1736,9.7861,-0.4911,0.2028,-0.4191,7,21,-44.1,6.088057497,-1.81,3.34,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,339493,2015-10-30 10:27:56:626,1446172076626.0 \n-0.0347,-0.0431,8.6287,-0.5748,0.107,9.7892,0.1576,-0.1833,-0.0831,6.8,20.8,-44.2,6.091199089,-0.59,3.67,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,339595,2015-10-30 10:27:56:728,1446172076728.0 \n-0.261,0.0263,9.0668,-0.5439,-0.1089,9.791,-0.1246,0.0611,-0.1955,6.4,21,-44.3,6.111793975,0.64,3.18,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,339697,2015-10-30 10:27:56:830,1446172076830.0 \n-0.7027,0.5219,8.6443,-0.666,-0.0583,9.7838,0.0977,-0.011,-0.0684,6.1,21.6,-44,6.146176961,0.34,3.89,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,339799,2015-10-30 10:27:56:932,1446172076932.0 \n-0.8152,0.1879,10.5644,-0.6404,0.0243,9.7857,0.2407,-0.1124,0.193,5.9,21.8,-44.1,6.147049626,0.22,3.9,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,339902,2015-10-30 10:27:57:035,1446172077035.0 \n0.164,0.2813,10.0736,-0.6084,0.281,9.7837,0.2847,0.1246,0.2553,6,21.5,-44.1,6.144082566,-1.64,3.56,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,340003,2015-10-30 10:27:57:136,1446172077136.0 \n-1.057,-0.2155,9.3948,-0.5869,0.1254,9.7883,0.0599,-0.1393,0.2541,5.9,21.2,-44.3,6.119822489,-0.86,3.15,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,340105,2015-10-30 10:27:57:238,1446172077238.0 \n-0.4848,0.0946,9.4846,-0.4728,-0.0019,9.7952,-0.1869,0.1344,-0.0806,5.9,21,-44.7,6.100623867,-0.45,2.61,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,340208,2015-10-30 10:27:57:341,1446172077341.0 \n-0.984,0.6548,8.9232,-0.5547,-0.0618,9.7908,-0.0257,0.0648,-0.1356,5.8,21.2,-44.6,6.112492106,0.39,3.09,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,340309,2015-10-30 10:27:57:442,1446172077442.0 \n-1.391,0.3639,10.3765,-0.6048,0.0126,9.788,0.0574,0.0342,-0.2382,5.7,21.6,-44.2,6.13238886,0.1,3.46,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,340411,2015-10-30 10:27:57:544,1446172077544.0 \n-1.4868,-0.0048,10.8445,-0.5862,0.2444,9.7861,0.3409,-0.0012,-0.0977,5.6,21.7,-44.1,6.133959656,-0.92,3.36,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,340514,2015-10-30 10:27:57:647,1446172077647.0 \n-1.2809,-1.0953,12.3349,-0.5351,0.1561,9.7908,-0.391,-0.0208,-0.3018,5.1,21.3,-44.3,6.164328385,-0.91,3.13,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,340616,2015-10-30 10:27:57:749,1446172077749.0 \n-0.3759,-0.3675,10.2256,-0.5239,-0.0042,9.7926,-0.1197,-0.1173,-0.0709,4.6,21.2,-44.6,6.171658768,-0.5,3.31,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,340717,2015-10-30 10:27:57:850,1446172077850.0 \n-0.5183,0.4393,8.1223,-0.5648,-0.1187,9.7897,0.0122,0.1014,-0.033,4.3,21.5,-44.5,6.209008814,0.69,3.13,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,340819,2015-10-30 10:27:57:952,1446172077952.0 \n-0.4717,0.7638,9.4032,-0.5859,-0.1253,9.7883,-0.0904,0.0635,-0.0916,4.2,22.1,-44.7,6.222447849,0.73,3.43,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,340922,2015-10-30 10:27:58:055,1446172078055.0 \n-1.2653,0.0012,10.817,-0.6809,-0.1439,9.7819,0.033,0.1429,0.0281,4.2,22.4,-44.7,6.233792489,0.95,3.75,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,341024,2015-10-30 10:27:58:157,1446172078157.0 \n-0.1053,-0.4621,11.0648,-0.661,0.1187,9.7836,0.193,-0.2395,0.3225,4.5,22.3,-44.8,6.196616976,-0.69,3.87,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,341125,2015-10-30 10:27:58:258,1446172078258.0 \n-1.1612,-0.3591,9.1279,-0.4842,0.1552,9.7935,0.1026,-0.2456,0.3176,4.7,22.1,-45,6.177243822,-0.32,3.35,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,341227,2015-10-30 10:27:58:360,1446172078360.0 \n-0.2777,0.1796,9.4523,-0.3983,0.0633,9.7984,-0.1454,-0.11,0.2553,5.1,21.5,-45.6,6.14792229,-0.67,2.4,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,341330,2015-10-30 10:27:58:463,1446172078463.0 \n-0.6943,0.6608,8.8322,-0.5267,-0.0414,9.7924,-0.0415,0.0965,0.0794,5.4,21.3,-45.7,6.15507814,0.13,2.87,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,341432,2015-10-30 10:27:58:565,1446172078565.0 \n-0.899,0.8882,9.4248,-0.629,0.0068,9.7865,0.0635,0.066,-0.099,5.8,21.3,-45.8,6.13361059,0.09,3.53,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,341533,2015-10-30 10:27:58:666,1446172078666.0 \n-0.9146,0.249,10.228,-0.5533,0.1717,9.7895,0.2162,-0.1442,-0.1796,6,21.3,-45.6,6.134483255,-0.6,3.45,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,341635,2015-10-30 10:27:58:768,1446172078768.0 \n-1.7633,-1.5969,12.973,-0.4015,0.0782,9.7981,-0.5217,-0.193,-0.4765,5.5,21.1,-45.8,6.093118952,-0.46,2.35,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,341737,2015-10-30 10:27:58:870,1446172078870.0 \n0.4657,0.1065,8.3163,-0.384,0.1424,9.7981,0.1087,-0.3677,-0.0489,5,21,-46.1,6.158394266,-0.64,2.86,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,341839,2015-10-30 10:27:58:972,1446172078972.0 \n-0.2215,0.0742,8.503,-0.4024,0.026,9.7984,0.0684,0.3335,-0.215,4.1,21,-46.5,6.18370154,-0.15,2.35,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,341942,2015-10-30 10:27:59:075,1446172079075.0 \n-0.8176,0.31,8.5521,-0.6168,0.0081,9.7872,-0.0794,0.121,-0.2077,3.9,21.2,-46.4,6.223320514,-0.21,3.4,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,342043,2015-10-30 10:27:59:176,1446172079176.0 \n-1.2127,-0.0479,10.2448,-0.6927,0.0031,9.7822,0.1222,0.0733,0.215,3.8,21.4,-45.9,6.241471938,0.21,3.89,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,342147,2015-10-30 10:27:59:280,1446172079280.0 \n-1.0798,0.182,9.9958,-0.7366,0.269,9.7752,0.2529,-0.1075,0.4154,4.2,21.2,-45.5,6.25473644,-0.95,4.29,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,342248,2015-10-30 10:27:59:381,1446172079381.0 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\n-0.826,0.31,9.8102,-0.3486,0.1014,9.7999,-0.0232,0.0305,0.0208,3.9,19.7,-46.7,6.167993577,-0.63,1.98,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,343573,2015-10-30 10:28:00:706,1446172080706.0 \n-0.6117,0.5483,9.3565,-0.4771,0.1019,9.7945,-0.0086,0.1368,0.0171,3.8,19.8,-46.7,6.185795935,-0.62,2.43,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,343675,2015-10-30 10:28:00:808,1446172080808.0 \n-0.808,0.5327,9.748,-0.5568,0.0818,9.7905,-0.0134,-0.0733,0.0257,4,19.8,-46.3,6.21057961,-0.51,3.13,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,343778,2015-10-30 10:28:00:911,1446172080911.0 \n-0.6871,0.4537,9.8222,-0.444,0.1187,9.7959,0.0024,-0.1087,0.0012,4.2,19.9,-46,6.192951785,-0.71,2.66,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,343879,2015-10-30 10:28:01:012,1446172081012.0 \n-0.6967,0.3998,9.7492,-0.3898,0.1568,9.7976,0.0367,-0.0134,0.0452,4.2,19.9,-45.7,6.177069289,-0.82,2.24,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,343981,2015-10-30 10:28:01:114,1446172081114.0 \n-0.4429,0.431,10.094,-0.4569,0.2152,9.7936,0.0098,0.1002,0.0305,4,19.7,-46.1,6.189810192,-1.15,2.54,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,344083,2015-10-30 10:28:01:216,1446172081216.0 \n-0.4741,0.5746,9.7588,-0.5324,0.2886,9.7879,0.0293,0.0257,0.0208,4.1,19.5,-46,6.213197604,-1.69,3.11,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,344186,2015-10-30 10:28:01:319,1446172081319.0 \n-0.5375,0.5962,9.566,-0.5521,0.3172,9.786,0.0073,-0.033,0.0122,4.2,19.3,-46.1,6.213721203,-1.81,3.2,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,344287,2015-10-30 10:28:01:420,1446172081420.0 \n-0.2406,0.6369,10.3896,-0.5054,0.2926,9.7892,-0.0574,-0.0391,-0.0257,4.4,19.1,-45.9,6.207787083,-1.8,3.05,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,344390,2015-10-30 10:28:01:523,1446172081523.0 \n-0.5806,0.9194,9.4595,-0.5554,0.4451,9.7808,0.0476,0,-0.0892,4.5,19,-46,6.167644511,-2.34,3.2,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,344491,2015-10-30 10:28:01:624,1446172081624.0 \n-0.9732,0.6524,9.6055,-0.6016,0.4094,9.7796,-0.0098,0.0696,-0.0782,4.5,18.9,-45.9,6.178989151,-2.31,3.5,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,344594,2015-10-30 10:28:01:727,1446172081727.0 \n-1.0116,0.753,9.7085,-0.6535,0.434,9.7752,0.0354,0.0024,-0.0415,4.4,18.8,-46,6.239377543,-2.54,3.82,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,344695,2015-10-30 10:28:01:828,1446172081828.0 \n-0.8631,0.6979,9.924,-0.6641,0.4297,9.7747,-0.0403,-0.0024,0.0049,4.4,18.9,-46.2,6.240424741,-2.59,3.85,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,344797,2015-10-30 10:28:01:930,1446172081930.0 \n-0.8799,0.7051,9.5026,-0.6695,0.4596,9.773,0.0147,-0.0086,0.0244,4.3,19,-46.3,6.243042734,-2.61,3.92,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,344900,2015-10-30 10:28:02:033,1446172082033.0 \n-0.759,0.6955,9.7671,-0.6522,0.4547,9.7744,0.0037,-0.0342,0.0208,4.4,19,-46.3,6.240075675,-2.69,3.84,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,345001,2015-10-30 10:28:02:134,1446172082134.0 \n-0.7314,0.7709,9.7971,-0.6386,0.4668,9.7747,-0.0061,-0.0061,0.033,4.4,18.9,-46.3,6.236585016,-2.71,3.75,36.814007,-119.74791,267.75,336.6260835,4.12,25.806452,354.77,16 / 16,345103,2015-10-30 10:28:02:236,1446172082236.0 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  },
  {
    "path": "test/data/Sensor_record_20151030_105902_AndroSensor.csv",
    "content": "-0.1496,-0.0431,9.6893,-0.1497,-0.0522,9.8054,0,0.0012,-0.0012,65,-50.8,-310,228.85,0.31,0.87,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,55,2015-10-30 10:58:45:572\n-0.1652,-0.0455,9.6977,-0.1507,-0.0521,9.8054,-0.0012,0.0024,0,65,-50.9,-309.8,228.84,0.3,0.88,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,157,2015-10-30 10:58:45:674\n-0.1556,-0.0527,9.7061,-0.1507,-0.0524,9.8054,0.0012,0,-0.0024,64.9,-50.8,-309.9,228.83,0.31,0.88,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,259,2015-10-30 10:58:45:776\n-0.17,-0.0599,9.6989,-0.1512,-0.0523,9.8053,0,0.0012,-0.0012,65.1,-50.8,-309.7,228.83,0.31,0.88,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,361,2015-10-30 10:58:45:878\n-0.1508,-0.0431,9.6965,-0.1518,-0.0519,9.8053,0.0012,0.0037,0,65,-50.7,-309.4,228.84,0.3,0.89,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,463,2015-10-30 10:58:45:980\n-0.1628,-0.0431,9.7049,-0.152,-0.0508,9.8053,0.0024,0.0012,0,65.1,-50.5,-309.1,229.39,0.3,0.89,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,565,2015-10-30 10:58:46:082\n-0.1616,-0.0431,9.7073,-0.1514,-0.0497,9.8054,0.0012,0.0012,0.0012,65.1,-50.5,-309.1,229.41,0.29,0.88,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,667,2015-10-30 10:58:46:184\n-0.152,-0.0431,9.7097,-0.1505,-0.0491,9.8054,0.0012,0,0.0024,65.1,-50.6,-309.5,228.9,0.29,0.88,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,769,2015-10-30 10:58:46:286\n-0.1568,-0.0431,9.7085,-0.1499,-0.0484,9.8054,0.0012,-0.0012,-0.0012,65,-50.7,-309.4,228.93,0.28,0.88,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,871,2015-10-30 10:58:46:388\n-0.1592,-0.0646,9.7013,-0.1498,-0.0471,9.8054,0.0012,0,0,65,-50.6,-309.2,228.95,0.28,0.88,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,973,2015-10-30 10:58:46:490\n-0.1556,-0.0431,9.6857,-0.1493,-0.0451,9.8054,0.0012,-0.0012,0,65,-50.5,-308.9,229.54,0.26,0.87,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,1075,2015-10-30 10:58:46:592\n-0.1688,-0.0455,9.7013,-0.1489,-0.0442,9.8054,0.0024,0.0012,0,65.1,-50.5,-309,229.55,0.26,0.87,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,1177,2015-10-30 10:58:46:694\n-0.1604,-0.0551,9.7085,-0.1486,-0.043,9.8054,0.0012,0,0.0024,65.3,-50.6,-309.2,229.04,0.25,0.87,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,1279,2015-10-30 10:58:46:796\n-0.1484,-0.0467,9.7049,-0.1485,-0.0422,9.8054,0.0012,0.0012,0,65.2,-50.6,-309.1,229.05,0.25,0.87,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,1381,2015-10-30 10:58:46:898\n-0.1532,-0.0467,9.7049,-0.1488,-0.0418,9.8054,0,0.0012,-0.0024,65.2,-50.6,-309.2,229.05,0.25,0.87,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,1483,2015-10-30 10:58:47:000\n-0.17,-0.0527,9.7061,-0.1478,-0.0415,9.8054,0.0037,-0.0012,0.0012,65.1,-50.7,-309.5,229.07,0.24,0.87,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,1585,2015-10-30 10:58:47:102\n-0.1616,-0.0431,9.7169,-0.1485,-0.0415,9.8054,0.0012,0.0024,0,65.1,-50.7,-309.7,229.06,0.24,0.87,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,1687,2015-10-30 10:58:47:204\n-0.158,-0.0599,9.6953,-0.1498,-0.0417,9.8054,0.0024,0.0012,0.0012,65,-50.7,-310.1,229.04,0.24,0.87,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,1789,2015-10-30 10:58:47:306\n-0.1544,-0.0515,9.6941,-0.1506,-0.0411,9.8054,0.0024,0.0037,-0.0012,65.1,-50.6,-309.5,229.04,0.24,0.88,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,1891,2015-10-30 10:58:47:408\n-0.1568,-0.0467,9.6977,-0.1516,-0.0405,9.8054,0.0024,-0.0012,0,64.9,-50.5,-309.3,229.57,0.24,0.89,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,1993,2015-10-30 10:58:47:510\n-0.152,-0.0491,9.6953,-0.1515,-0.0405,9.8054,0.0024,0.0012,-0.0012,65,-50.5,-308.8,229.58,0.24,0.89,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,2095,2015-10-30 10:58:47:612\n-0.1616,-0.0431,9.7097,-0.1518,-0.0407,9.8054,0,0.0012,0,65,-50.6,-308.7,229.03,0.24,0.89,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,2197,2015-10-30 10:58:47:714\n-0.146,-0.0431,9.7001,-0.1527,-0.0404,9.8054,0.0049,0.0037,0,65.1,-50.6,-308.8,229.02,0.24,0.89,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,2299,2015-10-30 10:58:47:816\n-0.1604,-0.0455,9.6917,-0.1525,-0.04,9.8054,0.0049,0.0012,0,65.2,-50.6,-309,229.03,0.23,0.89,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,2401,2015-10-30 10:58:47:918\n-0.1568,-0.0539,9.6941,-0.1531,-0.0397,9.8054,0.0037,0.0024,-0.0012,65.1,-50.6,-308.9,229.03,0.23,0.89,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,2503,2015-10-30 10:58:48:020\n-0.1652,-0.0551,9.6965,-0.1535,-0.039,9.8054,0.0012,0.0037,0.0012,65,-50.6,-308.8,229.03,0.23,0.9,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,2605,2015-10-30 10:58:48:122\n-0.1604,-0.0479,9.7169,-0.1545,-0.039,9.8054,0,0.0012,0.0012,64.9,-50.6,-308.9,229.02,0.23,0.9,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,2707,2015-10-30 10:58:48:224\n-0.1652,-0.0491,9.7181,-0.1551,-0.0406,9.8053,0.0012,0.0024,0,64.9,-50.6,-309,228.98,0.24,0.91,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,2809,2015-10-30 10:58:48:326\n-0.1592,-0.0503,9.7049,-0.1562,-0.0411,9.8053,0,0.0012,0,65,-50.5,-309.1,229.5,0.24,0.91,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,2911,2015-10-30 10:58:48:428\n-0.1568,-0.0431,9.7097,-0.1564,-0.0427,9.8053,0.0012,0.0012,0.0012,65,-50.5,-309,229.47,0.25,0.91,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,3013,2015-10-30 10:58:48:530\n-0.152,-0.0527,9.6953,-0.1571,-0.0438,9.8053,0.0012,0,0,65,-50.6,-308.8,228.9,0.26,0.92,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,3115,2015-10-30 10:58:48:632\n-0.1556,-0.0431,9.7001,-0.1569,-0.0455,9.8053,-0.0024,0,0,65.1,-50.6,-308.8,228.87,0.27,0.92,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,3217,2015-10-30 10:58:48:734\n-0.1532,-0.0503,9.7037,-0.1572,-0.0458,9.8053,0.0012,0.0024,-0.0012,65.2,-50.6,-308.7,228.86,0.27,0.92,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,3319,2015-10-30 10:58:48:836\n-0.1616,-0.0539,9.6822,-0.1576,-0.0467,9.8053,-0.0024,0.0024,0,65.3,-50.5,-309.1,229.39,0.27,0.92,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,3421,2015-10-30 10:58:48:938\n-0.1472,-0.0443,9.7049,-0.1579,-0.0477,9.8053,-0.0012,0,0.0012,65.2,-50.6,-309.1,228.82,0.28,0.92,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,3523,2015-10-30 10:58:49:040\n-0.1652,-0.0431,9.7061,-0.1579,-0.0488,9.8053,-0.0012,0.0012,-0.0012,65,-50.6,-309.4,228.8,0.28,0.92,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,3625,2015-10-30 10:58:49:142\n-0.1532,-0.0479,9.6845,-0.1579,-0.049,9.8053,0.0024,0.0024,0,64.9,-50.6,-309.2,228.8,0.28,0.92,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,3727,2015-10-30 10:58:49:244\n-0.1544,-0.0431,9.7061,-0.1578,-0.0493,9.8053,0,0.0012,0.0012,64.9,-50.5,-309.1,229.34,0.29,0.92,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,3829,2015-10-30 10:58:49:346\n-0.1532,-0.0455,9.7121,-0.1574,-0.0489,9.8053,0.0012,0.0012,-0.0012,65,-50.5,-308.9,229.35,0.29,0.92,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,3930,2015-10-30 10:58:49:447\n-0.158,-0.0467,9.6881,-0.1567,-0.0484,9.8053,0.0012,-0.0012,0,65.1,-50.5,-309,229.37,0.28,0.92,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,4033,2015-10-30 10:58:49:550\n-0.1496,-0.0431,9.6941,-0.1556,-0.0478,9.8053,0.0024,0,0.0012,65.2,-50.6,-308.8,228.85,0.28,0.91,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,4135,2015-10-30 10:58:49:652\n-0.158,-0.0491,9.7061,-0.1548,-0.0473,9.8053,-0.0012,-0.0024,0.0012,65.2,-50.4,-308.7,229.42,0.28,0.9,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,4237,2015-10-30 10:58:49:754\n-0.158,-0.0575,9.6977,-0.1548,-0.0467,9.8053,0.0012,0.0024,0.0012,65.1,-50.4,-308.7,229.43,0.27,0.9,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,4339,2015-10-30 10:58:49:856\n-0.1544,-0.0431,9.7025,-0.1544,-0.0461,9.8053,0.0012,0,0,65,-50.4,-308.7,229.44,0.27,0.9,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,4441,2015-10-30 10:58:49:958\n-0.158,-0.0479,9.7157,-0.1538,-0.0459,9.8053,0.0037,0,0.0012,65,-50.5,-308.9,229.46,0.27,0.9,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,4543,2015-10-30 10:58:50:060\n-0.1556,-0.0539,9.6917,-0.1533,-0.0456,9.8053,0,-0.0012,-0.0024,65,-50.5,-309,229.46,0.27,0.9,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,4645,2015-10-30 10:58:50:162\n-0.1484,-0.0515,9.6953,-0.1529,-0.0453,9.8054,0.0024,-0.0012,0,65,-50.5,-309,229.48,0.26,0.89,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,4747,2015-10-30 10:58:50:264\n-0.1676,-0.0611,9.7001,-0.1522,-0.0444,9.8054,0.0024,0.0012,0.0012,64.9,-50.5,-309,229.5,0.26,0.89,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,4848,2015-10-30 10:58:50:365\n-0.1628,-0.0467,9.7145,-0.1516,-0.045,9.8054,0,0.0037,-0.0024,64.9,-50.4,-309.3,229.5,0.26,0.89,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,4951,2015-10-30 10:58:50:468\n-0.1712,-0.0431,9.7061,-0.1527,-0.0461,9.8054,0,0.0024,-0.0037,64.9,-50.3,-309.2,229.47,0.27,0.89,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,5053,2015-10-30 10:58:50:570\n-0.158,-0.0587,9.7025,-0.1539,-0.0471,9.8053,0.0012,-0.0012,-0.0024,64.9,-50.4,-309.6,229.42,0.28,0.9,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,5155,2015-10-30 10:58:50:672\n-0.1628,-0.0455,9.7037,-0.1539,-0.0479,9.8053,0,0,-0.0024,64.8,-50.4,-309.5,229.43,0.28,0.9,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,5256,2015-10-30 10:58:50:773\n-0.1568,-0.0431,9.7145,-0.1546,-0.0483,9.8053,0.0037,0.0012,-0.0012,64.9,-50.5,-309.3,229.4,0.28,0.9,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,5359,2015-10-30 10:58:50:876\n-0.146,-0.0563,9.6977,-0.1559,-0.0482,9.8053,-0.0024,0.0037,0,64.8,-50.5,-309.1,229.38,0.28,0.91,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,5461,2015-10-30 10:58:50:978\n-0.1496,-0.0455,9.7085,-0.157,-0.0495,9.8053,0,0.0024,0,64.9,-50.7,-309,228.8,0.29,0.92,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,5563,2015-10-30 10:58:51:080\n-0.1484,-0.0479,9.7001,-0.1579,-0.0494,9.8053,0,0.0012,-0.0024,64.9,-50.6,-309.1,228.79,0.29,0.92,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,5665,2015-10-30 10:58:51:182\n-0.1724,-0.0634,9.6941,-0.1584,-0.0503,9.8052,0.0012,0.0012,0,64.9,-50.5,-309,229.31,0.29,0.92,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,5767,2015-10-30 10:58:51:284\n-0.1628,-0.0479,9.7049,-0.1587,-0.0509,9.8052,0,0.0024,0,64.9,-50.5,-309.2,229.31,0.29,0.93,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,5869,2015-10-30 10:58:51:386\n-0.1592,-0.0431,9.7013,-0.1591,-0.0512,9.8052,0.0024,0.0024,-0.0012,64.9,-50.5,-309.4,229.28,0.3,0.93,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,5971,2015-10-30 10:58:51:488\n-0.1628,-0.0515,9.6953,-0.1595,-0.0514,9.8052,-0.0024,0.0037,-0.0012,65,-50.5,-309.5,229.28,0.3,0.93,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,6073,2015-10-30 10:58:51:590\n-0.1616,-0.0491,9.7025,-0.1605,-0.0512,9.8052,0,0.0012,0,65,-50.5,-309.4,229.26,0.3,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,6175,2015-10-30 10:58:51:692\n-0.1389,-0.0431,9.7025,-0.1602,-0.0519,9.8052,-0.0012,0,0,65,-50.5,-309.1,229.26,0.3,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,6277,2015-10-30 10:58:51:794\n-0.1532,-0.0467,9.6929,-0.1605,-0.0517,9.8052,0.0012,0.0037,-0.0012,65,-50.6,-309,228.72,0.3,0.93,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,6379,2015-10-30 10:58:51:896\n-0.1616,-0.0515,9.7145,-0.1603,-0.0519,9.8052,0,0.0012,0,65,-50.6,-308.7,228.71,0.3,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,6481,2015-10-30 10:58:51:998\n-0.1604,-0.0443,9.6989,-0.16,-0.0524,9.8052,-0.0012,0,-0.0012,64.9,-50.7,-308.6,228.71,0.31,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,6583,2015-10-30 10:58:52:100\n-0.1472,-0.0431,9.6881,-0.1604,-0.0522,9.8052,0.0012,0.0012,0,65,-50.6,-308.7,228.7,0.31,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,6685,2015-10-30 10:58:52:202\n-0.1604,-0.0587,9.7013,-0.1602,-0.0522,9.8052,0.0012,0.0024,0,65.1,-50.6,-308.9,228.71,0.31,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,6787,2015-10-30 10:58:52:304\n-0.1628,-0.0431,9.7205,-0.1608,-0.052,9.8052,0,0.0024,-0.0012,65,-50.5,-309,229.25,0.3,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,6889,2015-10-30 10:58:52:406\n-0.152,-0.0443,9.7205,-0.1612,-0.0514,9.8052,0.0024,0.0012,-0.0012,65.1,-50.5,-308.8,229.25,0.3,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,6991,2015-10-30 10:58:52:508\n-0.1556,-0.0491,9.6833,-0.1616,-0.052,9.8052,0.0012,0.0012,0,65.1,-50.5,-308.9,229.24,0.3,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,7093,2015-10-30 10:58:52:610\n-0.1496,-0.0443,9.7013,-0.1615,-0.0525,9.8052,0,0.0012,-0.0012,65.1,-50.6,-308.8,228.68,0.31,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,7195,2015-10-30 10:58:52:712\n-0.1592,-0.0551,9.6953,-0.1614,-0.0524,9.8052,0.0012,0.0024,-0.0024,65,-50.7,-308.8,228.69,0.31,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,7296,2015-10-30 10:58:52:813\n-0.1556,-0.0431,9.7193,-0.1611,-0.0526,9.8052,-0.0012,0.0012,-0.0024,65,-50.7,-308.9,228.69,0.31,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,7399,2015-10-30 10:58:52:916\n-0.1532,-0.0431,9.6977,-0.161,-0.0528,9.8052,0,0.0012,-0.0012,65.1,-50.7,-309.3,228.68,0.31,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,7501,2015-10-30 10:58:53:018\n-0.1568,-0.0575,9.7037,-0.1608,-0.0531,9.8052,0,0.0012,-0.0024,65.1,-50.7,-309.3,228.68,0.31,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,7603,2015-10-30 10:58:53:120\n-0.1532,-0.0431,9.7025,-0.1606,-0.053,9.8052,0,0.0012,0,65.2,-50.6,-309.4,228.69,0.31,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,7705,2015-10-30 10:58:53:222\n-0.1496,-0.0479,9.7037,-0.1611,-0.0524,9.8052,0.0012,0.0037,0,65.1,-50.6,-308.9,228.69,0.31,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,7807,2015-10-30 10:58:53:324\n-0.164,-0.0658,9.6965,-0.1611,-0.0527,9.8052,0,0.0012,0,65,-50.6,-308.9,228.69,0.31,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,7909,2015-10-30 10:58:53:426\n-0.1448,-0.0455,9.6798,-0.1609,-0.0524,9.8052,0,0.0012,0,65.1,-50.6,-308.8,228.69,0.31,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,8011,2015-10-30 10:58:53:528\n-0.1484,-0.0431,9.7061,-0.1605,-0.052,9.8052,0.0024,0.0024,-0.0024,65,-50.6,-309.1,228.7,0.3,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,8113,2015-10-30 10:58:53:630\n-0.1616,-0.0431,9.7133,-0.1606,-0.0523,9.8052,0,0.0012,-0.0012,65,-50.5,-309.2,229.24,0.31,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,8215,2015-10-30 10:58:53:732\n-0.1592,-0.0455,9.7001,-0.1608,-0.0506,9.8052,0.0037,0.0012,0,64.9,-50.4,-309,229.27,0.3,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,8317,2015-10-30 10:58:53:834\n-0.1544,-0.0431,9.7109,-0.1607,-0.0501,9.8052,0.0024,0.0024,0,64.9,-50.3,-308.6,229.28,0.29,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,8419,2015-10-30 10:58:53:936\n-0.1604,-0.0611,9.7097,-0.1604,-0.0489,9.8052,0.0012,0.0012,0.0012,65,-50.4,-308.5,229.31,0.29,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,8520,2015-10-30 10:58:54:037\n-0.1437,-0.0515,9.6977,-0.16,-0.0482,9.8052,0.0012,0.0012,0,64.9,-50.5,-308.8,229.32,0.28,0.93,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,8623,2015-10-30 10:58:54:140\n-0.1496,-0.0431,9.7085,-0.1601,-0.0465,9.8052,0.0037,0.0012,0,64.9,-50.6,-308.8,228.8,0.27,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,8725,2015-10-30 10:58:54:242\n-0.1604,-0.0646,9.7013,-0.1598,-0.0463,9.8052,-0.0012,0.0012,0,64.9,-50.6,-308.7,228.81,0.27,0.93,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,8827,2015-10-30 10:58:54:344\n-0.1508,-0.0467,9.6941,-0.1596,-0.0454,9.8052,0.0024,0.0012,0,65.1,-50.6,-308.4,228.84,0.27,0.93,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,8929,2015-10-30 10:58:54:446\n-0.158,-0.0527,9.6929,-0.1603,-0.0449,9.8052,0,0.0024,-0.0012,65,-50.5,-308.5,229.39,0.26,0.93,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,9031,2015-10-30 10:58:54:548\n-0.1532,-0.0479,9.7145,-0.1606,-0.0451,9.8052,0,0.0024,-0.0012,64.9,-50.4,-308.6,229.37,0.26,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,9133,2015-10-30 10:58:54:650\n-0.1556,-0.0443,9.6941,-0.1602,-0.0444,9.8052,0.0012,0.0012,0.0012,65,-50.4,-308.6,229.39,0.26,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,9235,2015-10-30 10:58:54:752\n-0.1616,-0.0503,9.7037,-0.1605,-0.0447,9.8052,0,0.0037,0.0012,64.9,-50.4,-308.5,229.39,0.26,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,9337,2015-10-30 10:58:54:854\n-0.1425,-0.0455,9.6977,-0.1609,-0.0458,9.8052,0.0012,0.0012,0.0024,65,-50.4,-308.1,229.36,0.27,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,9439,2015-10-30 10:58:54:956\n-0.152,-0.0479,9.6989,-0.1601,-0.0473,9.8052,0.0012,0.0024,-0.0012,65,-50.5,-308.1,229.34,0.28,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,9541,2015-10-30 10:58:55:058\n-0.164,-0.0479,9.7037,-0.1596,-0.0472,9.8052,0.0012,0,0.0012,65,-50.6,-308.3,228.81,0.28,0.93,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,9643,2015-10-30 10:58:55:160\n-0.1568,-0.0431,9.6965,-0.1602,-0.0475,9.8052,0,0.0024,0,64.9,-50.6,-308.4,228.8,0.28,0.93,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,9745,2015-10-30 10:58:55:262\n-0.1616,-0.0431,9.7169,-0.1606,-0.0474,9.8052,-0.0012,0,0,64.9,-50.5,-308.2,229.34,0.28,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,9847,2015-10-30 10:58:55:364\n-0.1556,-0.0419,9.7013,-0.1606,-0.0479,9.8052,0.0012,0.0024,0.0012,64.9,-50.5,-308.1,229.33,0.28,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,9949,2015-10-30 10:58:55:466\n-0.164,-0.0515,9.6917,-0.161,-0.0478,9.8052,-0.0012,0.0024,0.0012,64.9,-50.5,-308.4,229.32,0.28,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,10051,2015-10-30 10:58:55:568\n-0.1556,-0.0527,9.6941,-0.161,-0.0485,9.8052,0,0.0024,0,64.8,-50.5,-308.8,229.3,0.28,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,10153,2015-10-30 10:58:55:670\n-0.1628,-0.0658,9.6953,-0.1606,-0.0491,9.8052,0.0012,0.0012,0.0012,64.9,-50.6,-309,228.75,0.29,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,10255,2015-10-30 10:58:55:772\n-0.164,-0.0599,9.7169,-0.1611,-0.0493,9.8052,-0.0037,0.0024,0.0012,65,-50.6,-309.2,228.74,0.29,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,10357,2015-10-30 10:58:55:874\n-0.1532,-0.0431,9.7121,-0.1613,-0.0496,9.8052,0,0.0024,0.0012,65,-50.6,-309.2,228.74,0.29,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,10459,2015-10-30 10:58:55:976\n-0.1628,-0.0527,9.7001,-0.1615,-0.0499,9.8052,0,0.0024,0,65,-50.5,-309.2,229.27,0.29,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,10562,2015-10-30 10:58:56:079\n-0.1508,-0.0455,9.7061,-0.1615,-0.0506,9.8052,0,0.0012,0,65,-50.5,-309,229.25,0.3,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,10663,2015-10-30 10:58:56:180\n-0.1592,-0.0467,9.7145,-0.1611,-0.0508,9.8052,-0.0012,0.0012,0,65,-50.5,-309.2,229.26,0.3,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,10765,2015-10-30 10:58:56:282\n-0.158,-0.0467,9.7205,-0.1609,-0.0515,9.8052,0,0.0012,0,65,-50.5,-309.1,229.25,0.3,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,10867,2015-10-30 10:58:56:384\n-0.1532,-0.0491,9.6977,-0.1602,-0.0519,9.8052,0.0012,0.0024,0,64.9,-50.5,-309.2,229.25,0.3,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,10969,2015-10-30 10:58:56:486\n-0.1592,-0.0479,9.7001,-0.1607,-0.0524,9.8052,-0.0012,0.0037,0.0012,64.9,-50.5,-308.9,229.25,0.31,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,11071,2015-10-30 10:58:56:588\n-0.1592,-0.0455,9.7061,-0.1605,-0.0519,9.8052,0.0012,0.0012,0.0012,64.9,-50.4,-308.8,229.25,0.3,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,11172,2015-10-30 10:58:56:689\n-0.1556,-0.0431,9.7013,-0.16,-0.0519,9.8052,-0.0024,0.0012,0.0012,65,-50.5,-308.8,229.26,0.3,0.93,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,11275,2015-10-30 10:58:56:792\n-0.1532,-0.0443,9.6977,-0.1605,-0.0517,9.8052,0.0012,0.0024,0,65.2,-50.7,-309.2,228.71,0.3,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,11377,2015-10-30 10:58:56:894\n-0.1556,-0.0431,9.6881,-0.1602,-0.0521,9.8052,-0.0024,0.0024,0,65.1,-50.7,-309.1,228.72,0.3,0.94,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,11480,2015-10-30 10:58:56:997\n-0.1484,-0.0443,9.6905,-0.1599,-0.0525,9.8052,-0.0024,0.0024,-0.0012,65.1,-50.6,-309.1,228.71,0.3,0.93,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,11581,2015-10-30 10:58:57:098\n-0.1676,-0.0431,9.7025,-0.1597,-0.0523,9.8052,0.0012,0.0012,-0.0012,65.1,-50.6,-308.8,228.71,0.31,0.93,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,11683,2015-10-30 10:58:57:200\n-0.1628,-0.0599,9.6917,-0.16,-0.0524,9.8052,0.0024,0.0037,0.0012,65.2,-50.8,-308.3,228.72,0.31,0.93,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,11785,2015-10-30 10:58:57:302\n-0.164,-0.0407,9.7133,-0.1594,-0.0516,9.8052,0.0024,-0.0012,-0.0012,65.1,-50.8,-308.6,228.71,0.3,0.93,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,11886,2015-10-30 10:58:57:403\n-0.1556,-0.0431,9.7037,-0.159,-0.0522,9.8052,0,0.0024,-0.0012,65.1,-50.7,-308.5,228.73,0.31,0.93,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,11989,2015-10-30 10:58:57:506\n-0.1568,-0.0503,9.7061,-0.1591,-0.0522,9.8052,0,0.0024,-0.0012,65.1,-50.7,-308.8,228.73,0.3,0.93,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,12091,2015-10-30 10:58:57:608\n-0.1508,-0.0431,9.7049,-0.1591,-0.0522,9.8052,0.0024,0.0012,0.0012,65.1,-50.6,-308.5,228.73,0.31,0.93,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,12193,2015-10-30 10:58:57:710\n-0.1592,-0.0431,9.7157,-0.1594,-0.0517,9.8052,-0.0024,0.0012,-0.0012,65.1,-50.6,-308.4,228.74,0.3,0.93,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,12295,2015-10-30 10:58:57:812\n-0.1437,-0.0599,9.6977,-0.1591,-0.0516,9.8052,0,-0.0012,0.0012,65.1,-50.6,-308.4,228.74,0.3,0.93,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,12397,2015-10-30 10:58:57:914\n-0.152,-0.0443,9.7097,-0.1583,-0.0519,9.8052,0.0012,0.0012,0,65.2,-50.6,-308.3,228.75,0.3,0.92,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,12499,2015-10-30 10:58:58:016\n-0.164,-0.0575,9.7037,-0.1582,-0.0515,9.8052,-0.0012,0.0024,0,65.1,-50.6,-308.4,228.76,0.3,0.92,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,12601,2015-10-30 10:58:58:118\n-0.152,-0.0431,9.7001,-0.1584,-0.0519,9.8052,0.0024,0.0024,0,65.1,-50.6,-308.3,228.75,0.3,0.93,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,12703,2015-10-30 10:58:58:220\n-0.1556,-0.0431,9.7013,-0.158,-0.0517,9.8052,0,0,0.0012,65,-50.6,-308.4,228.76,0.3,0.92,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,12805,2015-10-30 10:58:58:322\n-0.1604,-0.0527,9.6989,-0.1569,-0.0515,9.8053,0,0.0024,0,65.1,-50.5,-308.5,229.31,0.3,0.92,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,12907,2015-10-30 10:58:58:424\n-0.1496,-0.0431,9.7073,-0.1556,-0.0514,9.8053,0.0024,0,0,65.1,-50.7,-308.7,228.79,0.3,0.91,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,13009,2015-10-30 10:58:58:526\n-0.152,-0.0479,9.7025,-0.155,-0.0515,9.8053,0,0,0,65.1,-50.7,-308.9,228.79,0.3,0.91,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,13111,2015-10-30 10:58:58:628\n-0.158,-0.0646,9.6941,-0.1541,-0.0517,9.8053,0.0012,0.0012,0.0012,65,-50.7,-308.8,228.8,0.3,0.9,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,13213,2015-10-30 10:58:58:730\n-0.1592,-0.0563,9.6905,-0.1537,-0.0525,9.8053,0.0012,0.0024,-0.0012,65,-50.6,-309,228.8,0.3,0.9,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,13315,2015-10-30 10:58:58:832\n-0.1544,-0.0431,9.7097,-0.1533,-0.0521,9.8053,0.0024,0,0,65,-50.6,-308.8,228.81,0.3,0.9,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,13417,2015-10-30 10:58:58:934\n-0.1628,-0.0467,9.7025,-0.1539,-0.0524,9.8053,0,0.0012,-0.0012,65,-50.6,-308.9,228.8,0.31,0.9,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,13519,2015-10-30 10:58:59:036\n-0.1484,-0.0455,9.7001,-0.1534,-0.0524,9.8053,-0.0012,0.0012,0,65,-50.5,-308.7,229.34,0.31,0.9,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,13621,2015-10-30 10:58:59:138\n-0.1532,-0.0395,9.7157,-0.1525,-0.0514,9.8053,0.0012,-0.0012,0,64.9,-50.6,-308.6,228.82,0.31,0.89,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,13723,2015-10-30 10:58:59:240\n-0.1496,-0.0527,9.6822,-0.152,-0.0505,9.8053,0.0012,0,0,64.9,-50.7,-308.7,228.86,0.3,0.89,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,13825,2015-10-30 10:58:59:342\n-0.1604,-0.0431,9.6822,-0.1512,-0.0498,9.8054,0.0012,0,0.0012,64.9,-50.6,-308.9,228.88,0.29,0.88,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,13927,2015-10-30 10:58:59:444\n-0.1508,-0.0431,9.7085,-0.1514,-0.0496,9.8054,0.0024,0.0024,0,64.9,-50.7,-308.9,228.88,0.29,0.88,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,14029,2015-10-30 10:58:59:546\n-0.1496,-0.0431,9.6977,-0.1511,-0.0481,9.8054,0.0012,0,0.0012,64.9,-50.6,-309.1,228.9,0.28,0.88,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,14131,2015-10-30 10:58:59:648\n-0.1652,-0.0587,9.7025,-0.1507,-0.0469,9.8054,0.0012,0.0012,0,64.9,-50.7,-308.9,228.94,0.27,0.88,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,14233,2015-10-30 10:58:59:750\n-0.1604,-0.0491,9.7037,-0.1503,-0.0467,9.8054,-0.0012,0.0012,0.0012,65,-50.6,-308.8,228.94,0.28,0.88,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,14335,2015-10-30 10:58:59:852\n-0.1508,-0.0479,9.7097,-0.15,-0.0456,9.8054,0.0012,-0.0012,0,65,-50.6,-308.3,228.98,0.27,0.88,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,14437,2015-10-30 10:58:59:954\n-0.1604,-0.0431,9.7133,-0.1508,-0.0454,9.8054,-0.0012,0.0012,-0.0012,65.1,-50.7,-308.3,228.97,0.27,0.88,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,14539,2015-10-30 10:59:00:056\n-0.1532,-0.0467,9.6989,-0.1513,-0.0445,9.8054,0.0037,0.0012,0.0024,65.2,-50.5,-308.6,229.52,0.26,0.88,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,14641,2015-10-30 10:59:00:158\n-0.1556,-0.0467,9.7109,-0.1513,-0.0438,9.8054,0.0012,0.0012,0.0024,65.2,-50.5,-308.8,229.53,0.26,0.88,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,14743,2015-10-30 10:59:00:260\n-0.1556,-0.0431,9.7217,-0.1513,-0.044,9.8054,0,0.0012,0,65.1,-50.5,-308.9,229.53,0.26,0.88,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,14845,2015-10-30 10:59:00:362\n-0.158,-0.0515,9.6989,-0.151,-0.0447,9.8054,0,0.0012,0,65.1,-50.6,-308.9,228.97,0.26,0.88,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,14947,2015-10-30 10:59:00:464\n-0.1568,-0.0431,9.7217,-0.1504,-0.0453,9.8054,-0.0012,-0.0012,0,65.1,-50.6,-308.8,228.97,0.26,0.88,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,15049,2015-10-30 10:59:00:566\n-0.158,-0.0503,9.6929,-0.1499,-0.0465,9.8054,0.0012,0.0012,0,65.1,-50.6,-308.8,228.96,0.27,0.88,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,15151,2015-10-30 10:59:00:668\n-0.1532,-0.0467,9.6917,-0.1502,-0.0471,9.8054,-0.0012,0.0012,-0.0012,65.1,-50.5,-308.5,229.5,0.28,0.88,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,15253,2015-10-30 10:59:00:770\n-0.1437,-0.0443,9.6941,-0.1499,-0.0472,9.8054,0.0024,-0.0012,0,65.1,-50.5,-308.3,229.5,0.28,0.88,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,15355,2015-10-30 10:59:00:872\n-0.1628,-0.0634,9.7049,-0.1497,-0.048,9.8054,0,0,-0.0012,65.1,-50.5,-308.2,229.49,0.28,0.88,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,15457,2015-10-30 10:59:00:974\n-0.1472,-0.0479,9.7025,-0.1499,-0.0477,9.8054,-0.0024,0.0012,0,65.1,-50.7,-308.3,228.95,0.28,0.88,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,15559,2015-10-30 10:59:01:076\n-0.158,-0.0431,9.6977,-0.1499,-0.0486,9.8054,0.0012,0,0.0012,65.1,-50.8,-308.4,228.94,0.28,0.88,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,15661,2015-10-30 10:59:01:178\n-0.1604,-0.0599,9.7013,-0.1496,-0.0494,9.8054,-0.0024,-0.0012,0,65.2,-50.8,-308.6,228.91,0.29,0.87,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,15762,2015-10-30 10:59:01:279\n-0.152,-0.0479,9.7073,-0.1491,-0.0502,9.8054,0.0012,0.0024,0,65.1,-50.7,-308.8,228.9,0.3,0.87,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,15865,2015-10-30 10:59:01:382\n-0.1508,-0.0431,9.7109,-0.1507,-0.0499,9.8054,0.0037,0.0024,0,65,-50.8,-309,228.89,0.29,0.88,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,15967,2015-10-30 10:59:01:484\n-0.1592,-0.0467,9.6857,-0.1519,-0.0489,9.8054,0.0012,0.0024,0,65,-50.7,-308.9,228.89,0.29,0.88,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,16068,2015-10-30 10:59:01:585\n-0.1592,-0.0467,9.6845,-0.1539,-0.0474,9.8053,0.0024,0.0012,0.0012,65,-50.6,-309.4,228.88,0.28,0.9,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,16171,2015-10-30 10:59:01:688\n-0.1496,-0.0431,9.7049,-0.1554,-0.0467,9.8053,0.0012,0.0037,0,65.1,-50.6,-309.6,228.86,0.27,0.91,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,16273,2015-10-30 10:59:01:790\n-0.1556,-0.0515,9.7085,-0.1557,-0.046,9.8053,-0.0012,0,0.0012,65,-50.7,-309.7,228.87,0.27,0.91,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,16375,2015-10-30 10:59:01:892\n-0.1592,-0.0503,9.7013,-0.1561,-0.0456,9.8053,0,0.0012,-0.0012,64.9,-50.7,-309.5,228.88,0.27,0.91,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,16477,2015-10-30 10:59:01:994\n-0.1903,-0.0431,9.4152,-0.1523,-0.0451,9.8054,0.0037,0.0183,0.0012,64.9,-50.6,-309.2,228.88,0.26,0.91,36.81433,-119.74831,,336.6383985,,218.08066,,0 / 0,16579,2015-10-30 10:59:02:096\n"
  },
  {
    "path": "test/data/Sensor_record_20151030_110329_AndroSensor.csv",
    "content": "0.079,-0.0946,-9.8509,0.0828,-0.054,-9.8061,0.0024,0.0024,0,32.9,-76.3,60.3,156.3,0.32,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,50,2015-10-30 11:02:38:281\n-0.425,-0.4094,-9.7899,0.0851,-0.0555,-9.8061,0,0.0049,-0.1185,33,-76.4,60,156.29,0.32,-179.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,152,2015-10-30 11:02:38:383\n0.1293,-0.0826,-9.8557,0.0877,-0.0557,-9.806,0.0024,0.0024,-0.0464,33.3,-76.4,59.9,156.28,0.33,-179.49,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,254,2015-10-30 11:02:38:485\n0.0754,-0.0898,-9.8509,0.089,-0.0563,-9.806,0,0.0012,0.0012,33.6,-76.4,60.3,155.65,0.33,-179.48,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,356,2015-10-30 11:02:38:587\n0.1018,-0.0934,-9.8533,0.0889,-0.0606,-9.806,0.0049,0.0012,0.0024,33.9,-76.2,60.7,155.66,0.35,-179.48,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,458,2015-10-30 11:02:38:689\n0.0754,-0.0958,-9.8569,0.0904,-0.0635,-9.806,0.0037,0.0024,-0.0012,34,-76.2,61.1,155.66,0.37,-179.48,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,560,2015-10-30 11:02:38:791\n0.0611,-0.0958,-9.8521,0.0893,-0.0644,-9.806,0,-0.0024,0,34,-76.3,61,155.66,0.38,-179.48,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,662,2015-10-30 11:02:38:893\n0.0898,-0.0994,-9.8509,0.0903,-0.0659,-9.8059,-0.0012,0.0061,0.0012,34,-76.3,60.9,155.66,0.39,-179.47,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,764,2015-10-30 11:02:38:995\n0.0838,-0.0862,-9.8557,0.0956,-0.0671,-9.8059,0.0024,0.0049,-0.0024,33.9,-76.3,60.8,155.64,0.39,-179.44,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,866,2015-10-30 11:02:39:097\n0.0862,-0.103,-9.845,0.0981,-0.0683,-9.8058,0.0012,0.0037,-0.0012,34,-76.2,61.1,155.64,0.4,-179.43,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,968,2015-10-30 11:02:39:199\n0.0742,-0.1018,-9.8725,0.1,-0.0705,-9.8058,0.0037,0.0037,0.0024,33.9,-76.1,61.1,155.63,0.41,-179.42,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,1070,2015-10-30 11:02:39:301\n0.0886,-0.1006,-9.8533,0.1009,-0.0713,-9.8058,0.0024,0.0012,0,34.1,-76.1,61.3,155.63,0.42,-179.41,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,1172,2015-10-30 11:02:39:403\n0.0826,-0.1018,-9.845,0.1011,-0.072,-9.8058,0,0,0,34,-76.2,61,155.63,0.42,-179.41,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,1274,2015-10-30 11:02:39:505\n0.0862,-0.0922,-9.8533,0.1024,-0.0737,-9.8057,0,0.0037,0,33.9,-76.1,60.9,155.63,0.43,-179.4,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,1376,2015-10-30 11:02:39:607\n0.0814,-0.1065,-9.8533,0.1023,-0.0752,-9.8057,0.0024,0.0012,0,33.9,-76.1,61,155.63,0.44,-179.4,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,1478,2015-10-30 11:02:39:709\n0.0814,-0.1041,-9.8593,0.1024,-0.076,-9.8057,0,0,0,33.9,-76.2,61,155.63,0.44,-179.4,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,1580,2015-10-30 11:02:39:811\n0.0934,-0.0982,-9.8509,0.102,-0.076,-9.8057,-0.0024,0.0012,0.0024,33.9,-76.1,61.2,155.64,0.44,-179.41,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,1682,2015-10-30 11:02:39:913\n0.0958,-0.097,-9.8462,0.1015,-0.0765,-9.8057,0.0024,0.0024,-0.0024,33.9,-76.2,61.4,155.64,0.45,-179.41,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,1784,2015-10-30 11:02:40:015\n0.079,-0.1018,-9.8509,0.1004,-0.0776,-9.8057,0,0,0,33.9,-76.1,61.5,155.64,0.45,-179.41,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,1886,2015-10-30 11:02:40:117\n0.0898,-0.0922,-9.8605,0.0988,-0.0778,-9.8057,-0.0024,0,-0.0024,34,-76.2,61.3,155.65,0.45,-179.42,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,1988,2015-10-30 11:02:40:219\n0.0922,-0.0994,-9.8485,0.0979,-0.0789,-9.8057,0.0012,0.0012,-0.0012,34,-76.2,61,155.65,0.46,-179.43,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,2089,2015-10-30 11:02:40:320\n0.0814,-0.1161,-9.8689,0.0966,-0.0794,-9.8057,-0.0012,-0.0012,0,33.9,-76.2,60.6,155.66,0.46,-179.43,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,2192,2015-10-30 11:02:40:423\n0.0922,-0.0898,-9.8509,0.0959,-0.0799,-9.8057,0.0012,0.0012,0,33.9,-76.1,60.5,155.67,0.47,-179.44,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,2294,2015-10-30 11:02:40:525\n0.091,-0.097,-9.8509,0.0952,-0.0808,-9.8057,0.0012,0,-0.0024,33.9,-76,60.7,155.67,0.47,-179.44,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,2396,2015-10-30 11:02:40:627\n0.097,-0.0982,-9.8509,0.0946,-0.0815,-9.8057,0,0.0024,-0.0012,33.9,-75.9,60.6,155.67,0.48,-179.45,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,2498,2015-10-30 11:02:40:729\n0.091,-0.103,-9.8533,0.094,-0.0821,-9.8057,0,0,-0.0012,34,-76,60.7,155.68,0.48,-179.45,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,2600,2015-10-30 11:02:40:831\n0.073,-0.1041,-9.8569,0.0925,-0.0832,-9.8057,0.0012,-0.0012,0,34,-76,60.6,155.68,0.48,-179.46,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,2702,2015-10-30 11:02:40:933\n0.079,-0.1077,-9.8617,0.0921,-0.0836,-9.8057,-0.0012,0.0012,0,34,-76.1,60.6,155.69,0.49,-179.46,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,2804,2015-10-30 11:02:41:035\n0.0994,-0.1018,-9.8545,0.0923,-0.0842,-9.8057,-0.0012,0.0024,-0.0012,34,-76.1,60.5,155.69,0.49,-179.46,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,2906,2015-10-30 11:02:41:137\n0.0862,-0.0982,-9.8509,0.0929,-0.0851,-9.8057,0.0012,0,-0.0012,33.9,-76.1,60.5,155.68,0.5,-179.46,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,3008,2015-10-30 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11:02:42:769\n0.091,-0.1053,-9.8402,0.0931,-0.0931,-9.8056,0.0012,0.0024,0,33.9,-76.2,60.9,155.7,0.54,-179.46,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,4640,2015-10-30 11:02:42:871\n0.0838,-0.1018,-9.8545,0.0928,-0.0932,-9.8056,0.0037,0,-0.0024,33.9,-76.2,60.9,155.7,0.54,-179.46,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,4742,2015-10-30 11:02:42:973\n0.0826,-0.097,-9.8617,0.0925,-0.0934,-9.8056,0.0012,0.0024,-0.0012,33.9,-76.1,61.1,155.7,0.55,-179.46,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,4844,2015-10-30 11:02:43:075\n0.103,-0.0946,-9.8509,0.0925,-0.0937,-9.8056,0,0,-0.0012,33.8,-76,61.1,155.7,0.55,-179.46,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,4946,2015-10-30 11:02:43:177\n0.073,-0.103,-9.8533,0.0922,-0.094,-9.8056,0.0024,0.0012,-0.0012,33.8,-76.1,61.4,155.7,0.55,-179.46,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,5047,2015-10-30 11:02:43:278\n0.067,-0.103,-9.8533,0.0918,-0.0952,-9.8056,0.0024,0,0,33.9,-76.1,61.5,155.7,0.55,-179.46,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,5150,2015-10-30 11:02:43:381\n0.097,-0.1018,-9.8462,0.0916,-0.0956,-9.8056,0.0024,0,-0.0024,34.1,-76.2,61.3,155.71,0.56,-179.46,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,5251,2015-10-30 11:02:43:482\n0.0898,-0.1053,-9.8533,0.0912,-0.0958,-9.8056,0.0024,0.0012,0,34.2,-76.1,61,155.71,0.56,-179.47,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,5354,2015-10-30 11:02:43:585\n0.0826,-0.1185,-9.8569,0.0909,-0.0961,-9.8056,0.0024,0.0024,-0.0024,34.1,-76,61,155.71,0.56,-179.47,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,5456,2015-10-30 11:02:43:687\n0.079,-0.1077,-9.8414,0.0908,-0.0961,-9.8056,0.0024,0.0037,-0.0024,34.2,-76.1,60.9,155.71,0.56,-179.47,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,5558,2015-10-30 11:02:43:789\n0.0814,-0.1089,-9.8629,0.0905,-0.0968,-9.8056,0.0024,0.0012,-0.0012,34.1,-76.1,61,155.71,0.56,-179.47,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,5660,2015-10-30 11:02:43:891\n0.0958,-0.1077,-9.8557,0.0903,-0.0968,-9.8056,0.0024,0.0024,-0.0012,34,-76.2,60.8,155.71,0.57,-179.47,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,5762,2015-10-30 11:02:43:993\n0.0802,-0.1041,-9.8605,0.0903,-0.0971,-9.8056,0.0024,0,-0.0012,33.9,-76.1,61.1,155.72,0.57,-179.47,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,5864,2015-10-30 11:02:44:095\n0.085,-0.1053,-9.8713,0.0899,-0.0965,-9.8056,-0.0012,0.0024,-0.0012,33.9,-76,61,155.72,0.56,-179.47,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,5966,2015-10-30 11:02:44:197\n0.0874,-0.097,-9.8462,0.09,-0.0963,-9.8056,0.0012,0,-0.0012,33.9,-76,61,155.72,0.56,-179.47,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,6068,2015-10-30 11:02:44:299\n0.0742,-0.1053,-9.8509,0.0903,-0.096,-9.8056,-0.0024,0.0037,0,34,-75.9,60.9,155.71,0.56,-179.47,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,6170,2015-10-30 11:02:44:401\n0.085,-0.1089,-9.8557,0.0903,-0.0957,-9.8056,-0.0012,0,-0.0012,33.9,-75.9,60.9,155.71,0.56,-179.47,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,6271,2015-10-30 11:02:44:502\n0.0982,-0.0958,-9.8533,0.0905,-0.0959,-9.8056,-0.0024,0.0037,0,33.9,-75.9,60.9,155.71,0.56,-179.47,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,6374,2015-10-30 11:02:44:605\n0.0694,-0.1041,-9.8521,0.0904,-0.0959,-9.8056,0.0024,-0.0012,-0.0012,33.9,-76,60.7,155.71,0.56,-179.47,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,6477,2015-10-30 11:02:44:708\n0.0934,-0.0994,-9.8545,0.0905,-0.0963,-9.8057,0,0.0012,0,33.9,-76,60.7,155.71,0.56,-179.47,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,6578,2015-10-30 11:02:44:809\n0.0694,-0.1018,-9.8533,0.0899,-0.0965,-9.8056,-0.0012,0.0024,-0.0012,34,-76.1,60.6,155.71,0.56,-179.47,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,6680,2015-10-30 11:02:44:911\n0.0694,-0.097,-9.8605,0.09,-0.0962,-9.8056,0,0,-0.0012,34,-76.1,61.1,155.71,0.56,-179.47,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,6782,2015-10-30 11:02:45:013\n0.0898,-0.1089,-9.8545,0.0892,-0.0954,-9.8057,0,-0.0012,-0.0012,34,-76,61.3,155.71,0.56,-179.47,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,6884,2015-10-30 11:02:45:115\n0.0754,-0.0982,-9.8521,0.0887,-0.0959,-9.8056,0,0,-0.0024,33.9,-76.1,61.4,155.72,0.56,-179.48,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,6986,2015-10-30 11:02:45:217\n0.0886,-0.1077,-9.8414,0.0886,-0.0961,-9.8056,0.0024,0.0024,-0.0012,33.8,-76.1,61.4,155.72,0.56,-179.48,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,7088,2015-10-30 11:02:45:319\n0.0766,-0.1041,-9.8617,0.0889,-0.0964,-9.8056,0,0.0024,0,33.8,-76,61.2,155.72,0.56,-179.48,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,7190,2015-10-30 11:02:45:421\n0.0802,-0.1065,-9.8545,0.0886,-0.0981,-9.8056,0.0012,-0.0012,-0.0012,33.9,-75.9,61.3,155.72,0.57,-179.48,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,7291,2015-10-30 11:02:45:522\n0.0862,-0.1053,-9.8426,0.088,-0.0991,-9.8056,0.0012,0.0012,-0.0012,33.9,-76,60.9,155.73,0.58,-179.49,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,7394,2015-10-30 11:02:45:625\n0.0862,-0.0898,-9.8509,0.0872,-0.1009,-9.8056,0.0024,0.0024,-0.0012,33.8,-76,61,155.73,0.59,-179.49,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,7496,2015-10-30 11:02:45:727\n0.0754,-0.0982,-9.8521,0.0867,-0.1017,-9.8056,0.0024,0.0012,-0.0037,33.7,-76.1,60.8,155.74,0.59,-179.49,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,7598,2015-10-30 11:02:45:829\n0.0886,-0.0982,-9.8509,0.087,-0.1028,-9.8055,0.0012,0.0012,-0.0024,33.7,-76,60.8,155.74,0.6,-179.49,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,7699,2015-10-30 11:02:45:930\n0.0934,-0.1089,-9.8509,0.0865,-0.1036,-9.8056,0.0012,0,0,33.7,-76.1,60.6,155.74,0.61,-179.49,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,7802,2015-10-30 11:02:46:033\n0.0922,-0.1053,-9.8509,0.0864,-0.1037,-9.8056,0.0024,0.0037,-0.0024,33.7,-76.1,60.5,155.74,0.61,-179.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,7904,2015-10-30 11:02:46:135\n0.0838,-0.1006,-9.8569,0.0863,-0.1049,-9.8056,0.0012,0.0012,-0.0024,33.8,-76,60.7,155.74,0.61,-179.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,8005,2015-10-30 11:02:46:236\n0.073,-0.1113,-9.8617,0.0865,-0.1056,-9.8056,0,0.0012,-0.0024,33.8,-75.9,60.6,155.74,0.62,-179.49,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,8108,2015-10-30 11:02:46:339\n0.0718,-0.1041,-9.8569,0.0872,-0.1062,-9.8055,0.0012,0.0012,0,33.8,-75.8,60.9,155.74,0.62,-179.49,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,8211,2015-10-30 11:02:46:442\n0.0862,-0.1053,-9.8485,0.0878,-0.1071,-9.8055,0.0012,0.0024,-0.0012,33.9,-75.9,61,155.74,0.63,-179.49,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,8312,2015-10-30 11:02:46:543\n0.0814,-0.1125,-9.8509,0.0882,-0.1071,-9.8055,0.0037,0.0024,0,33.9,-76,61,155.74,0.63,-179.48,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,8414,2015-10-30 11:02:46:645\n0.0742,-0.103,-9.8509,0.0886,-0.1057,-9.8056,-0.0012,0.0024,0,33.9,-76,61,155.74,0.62,-179.48,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,8516,2015-10-30 11:02:46:747\n0.0874,-0.1065,-9.8545,0.089,-0.1053,-9.8055,-0.0012,0.0024,0,34,-76,60.7,155.73,0.62,-179.48,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,8618,2015-10-30 11:02:46:849\n0.0934,-0.1137,-9.8426,0.0884,-0.1053,-9.8056,0,0,0,34,-76,60.7,155.74,0.61,-179.48,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,8720,2015-10-30 11:02:46:951\n0.0814,-0.1125,-9.8593,0.0884,-0.1056,-9.8055,-0.0012,0.0024,0,34,-76,60.8,155.74,0.62,-179.48,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,8822,2015-10-30 11:02:47:053\n0.0862,-0.1113,-9.8689,0.0883,-0.1052,-9.8055,0.0024,0.0024,0,34,-76,60.8,155.74,0.61,-179.48,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,8924,2015-10-30 11:02:47:155\n0.0886,-0.1018,-9.8509,0.0884,-0.1048,-9.8056,-0.0012,0,0.0012,34,-76.1,60.9,155.74,0.61,-179.48,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,9026,2015-10-30 11:02:47:257\n0.0814,-0.1101,-9.8509,0.0886,-0.1047,-9.8055,0.0024,0.0012,0,33.9,-76.1,61.1,155.73,0.61,-179.48,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,9127,2015-10-30 11:02:47:358\n0.0898,-0.103,-9.8426,0.0884,-0.104,-9.8055,0,0.0024,0,33.9,-76,61,155.73,0.61,-179.48,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,9230,2015-10-30 11:02:47:461\n0.0826,-0.1077,-9.8509,0.0885,-0.1035,-9.8056,0,0,0,33.9,-76,60.9,155.73,0.6,-179.48,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,9332,2015-10-30 11:02:47:563\n0.0802,-0.0958,-9.8509,0.088,-0.1031,-9.8056,0,0.0024,0.0012,34,-76,60.9,155.73,0.6,-179.49,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,9434,2015-10-30 11:02:47:665\n0.085,-0.1006,-9.8557,0.0856,-0.1029,-9.8056,0,0.0012,0.0024,34,-76.1,61,155.74,0.6,-179.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,9536,2015-10-30 11:02:47:767\n0.0838,-0.0994,-9.8533,0.0845,-0.1028,-9.8056,0.0037,0,0.0012,33.9,-76.1,61.7,155.75,0.6,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,9638,2015-10-30 11:02:47:869\n0.0742,-0.1041,-9.8605,0.0818,-0.1023,-9.8056,0.0024,-0.0012,-0.0012,33.8,-76.1,61.7,155.75,0.6,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,9739,2015-10-30 11:02:47:970\n0.0838,-0.1065,-9.8701,0.081,-0.1026,-9.8056,-0.0012,0,0,33.8,-76.1,62,155.76,0.6,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,9842,2015-10-30 11:02:48:073\n0.085,-0.1041,-9.845,0.081,-0.1026,-9.8056,-0.0012,0.0012,0,33.9,-76,61.9,155.76,0.6,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,9944,2015-10-30 11:02:48:175\n0.0826,-0.1137,-9.8509,0.0799,-0.1027,-9.8056,0.0012,0.0012,0.0012,33.9,-76,61.5,155.76,0.6,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,10046,2015-10-30 11:02:48:277\n0.0826,-0.1089,-9.8713,0.0788,-0.1028,-9.8056,0.0037,-0.0012,0.0012,33.8,-76.1,61.1,155.77,0.6,-179.54,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,10148,2015-10-30 11:02:48:379\n0.103,-0.0934,-9.8653,0.0781,-0.1032,-9.8056,0.0037,0.0012,-0.0012,33.9,-76.2,60.5,155.77,0.6,-179.54,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,10250,2015-10-30 11:02:48:481\n0.079,-0.0994,-9.8521,0.0774,-0.1033,-9.8056,0.0012,-0.0012,0.0012,33.9,-76.1,60.6,155.78,0.6,-179.55,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,10352,2015-10-30 11:02:48:583\n0.0886,-0.1006,-9.8485,0.0766,-0.1028,-9.8056,0.0024,0,-0.0012,33.9,-76,60.7,155.78,0.6,-179.55,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,10454,2015-10-30 11:02:48:685\n0.0742,-0.1018,-9.8533,0.0765,-0.1027,-9.8057,0.0024,0.0024,-0.0012,33.9,-75.9,61.2,155.78,0.6,-179.55,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,10556,2015-10-30 11:02:48:787\n0.0778,-0.1065,-9.8485,0.0776,-0.1023,-9.8056,0.0012,0.0024,-0.0012,33.9,-76,61.2,155.77,0.6,-179.55,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,10657,2015-10-30 11:02:48:888\n0.0826,-0.1041,-9.8557,0.0784,-0.1025,-9.8057,0,0,0.0012,33.9,-76,61.4,155.77,0.6,-179.54,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,10760,2015-10-30 11:02:48:991\n0.0742,-0.1041,-9.8533,0.0785,-0.1021,-9.8057,-0.0012,0.0012,0.0012,33.9,-76,61.3,155.77,0.6,-179.54,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,10862,2015-10-30 11:02:49:093\n0.0946,-0.1006,-9.8557,0.0795,-0.102,-9.8057,-0.0012,-0.0012,0,34,-76.2,61.3,155.77,0.6,-179.54,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,10964,2015-10-30 11:02:49:195\n0.1065,-0.1077,-9.8462,0.0806,-0.1016,-9.8056,0.0024,0.0012,0,33.9,-76.1,61.2,155.76,0.59,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,11066,2015-10-30 11:02:49:297\n0.0778,-0.1101,-9.8509,0.0811,-0.1019,-9.8056,0.0012,0.0037,-0.0012,33.8,-76.1,61,155.76,0.6,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,11168,2015-10-30 11:02:49:399\n0.0766,-0.103,-9.8665,0.0812,-0.1024,-9.8056,0.0024,0,-0.0012,33.7,-76.1,61,155.76,0.6,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,11269,2015-10-30 11:02:49:500\n0.0898,-0.103,-9.8485,0.0805,-0.1024,-9.8057,0,0,0,33.7,-76.1,61.3,155.76,0.6,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,11373,2015-10-30 11:02:49:604\n0.079,-0.1077,-9.8402,0.081,-0.1017,-9.8056,0,0.0024,-0.0012,33.8,-76.2,61.3,155.76,0.6,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,11474,2015-10-30 11:02:49:705\n0.0874,-0.1006,-9.8581,0.0812,-0.1019,-9.8056,0.0012,0.0012,-0.0012,33.7,-76.2,61.5,155.76,0.6,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,11576,2015-10-30 11:02:49:807\n0.0826,-0.1018,-9.8713,0.0816,-0.1026,-9.8056,0,0,0,33.5,-76.1,61.7,155.76,0.6,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,11678,2015-10-30 11:02:49:909\n0.091,-0.1113,-9.8521,0.0821,-0.1022,-9.8056,-0.0012,0.0012,0.0024,33.6,-76.1,61.5,155.75,0.6,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,11780,2015-10-30 11:02:50:011\n0.0718,-0.1006,-9.8509,0.0828,-0.1018,-9.8056,0,0,-0.0012,33.8,-76,61.4,155.75,0.6,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,11882,2015-10-30 11:02:50:113\n0.0766,-0.1113,-9.827,0.0831,-0.1019,-9.8056,0.0012,0.0037,0,33.8,-75.9,61.5,155.75,0.6,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,11984,2015-10-30 11:02:50:215\n0.0862,-0.1053,-9.8509,0.0836,-0.1026,-9.8056,0.0024,0.0012,-0.0012,33.7,-75.9,61.7,155.75,0.6,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,12086,2015-10-30 11:02:50:317\n0.0802,-0.1125,-9.8677,0.0837,-0.103,-9.8056,0,0.0024,0,33.8,-76,61.8,155.75,0.6,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,12188,2015-10-30 11:02:50:419\n0.0814,-0.1041,-9.8521,0.0844,-0.103,-9.8056,0,0.0037,-0.0012,33.8,-76.1,61.7,155.75,0.6,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,12290,2015-10-30 11:02:50:521\n0.091,-0.1006,-9.8402,0.0846,-0.1036,-9.8056,0.0012,0,0,33.9,-76.2,61.7,155.74,0.6,-179.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,12392,2015-10-30 11:02:50:623\n0.0778,-0.1173,-9.8641,0.0846,-0.104,-9.8056,0.0037,0.0012,0.0012,33.9,-76.2,61.7,155.75,0.61,-179.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,12494,2015-10-30 11:02:50:725\n0.079,-0.1113,-9.8701,0.0854,-0.1041,-9.8056,0.0012,0.0037,0.0012,34,-76.1,61.7,155.74,0.61,-179.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,12596,2015-10-30 11:02:50:827\n0.0862,-0.103,-9.8569,0.0848,-0.1044,-9.8056,0.0012,0,0,33.9,-76.1,61.8,155.75,0.61,-179.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,12698,2015-10-30 11:02:50:929\n0.079,-0.1041,-9.8521,0.0849,-0.104,-9.8056,0,0,-0.0012,33.9,-76,61.7,155.75,0.61,-179.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,12800,2015-10-30 11:02:51:031\n0.0814,-0.1077,-9.8617,0.0847,-0.105,-9.8056,0,0.0024,0,33.9,-76.1,61.6,155.75,0.61,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,12902,2015-10-30 11:02:51:133\n0.0838,-0.0958,-9.8569,0.085,-0.1049,-9.8056,0.0024,0,0,33.8,-76,61.5,155.75,0.61,-179.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,13004,2015-10-30 11:02:51:235\n0.079,-0.1125,-9.8533,0.0854,-0.105,-9.8056,0.0012,0.0012,0,33.7,-76,61.3,155.75,0.61,-179.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,13106,2015-10-30 11:02:51:337\n0.079,-0.1041,-9.8509,0.0855,-0.1051,-9.8056,0,0.0012,-0.0024,33.7,-76,61.6,155.75,0.61,-179.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,13208,2015-10-30 11:02:51:439\n0.0754,-0.0958,-9.8617,0.085,-0.1046,-9.8056,0,0.0024,-0.0024,33.7,-76,61.6,155.75,0.61,-179.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,13310,2015-10-30 11:02:51:541\n0.0766,-0.1041,-9.8617,0.0853,-0.1053,-9.8056,0.0024,0.0024,0,33.7,-76,61.4,155.75,0.61,-179.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,13412,2015-10-30 11:02:51:643\n0.0946,-0.103,-9.8605,0.0855,-0.1055,-9.8056,0.0024,0.0012,-0.0012,33.7,-76,61.2,155.75,0.62,-179.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,13514,2015-10-30 11:02:51:745\n0.0862,-0.1077,-9.8533,0.0857,-0.1055,-9.8056,0.0024,0.0024,-0.0012,33.8,-76,61.2,155.75,0.62,-179.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,13616,2015-10-30 11:02:51:847\n0.0838,-0.1053,-9.8581,0.0854,-0.1053,-9.8056,0.0012,0.0024,-0.0024,33.9,-76.1,61.3,155.75,0.62,-179.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,13718,2015-10-30 11:02:51:949\n0.097,-0.0982,-9.8509,0.0851,-0.1054,-9.8056,0.0012,0.0012,0.0012,33.9,-76.2,61.3,155.75,0.62,-179.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,13820,2015-10-30 11:02:52:051\n0.0814,-0.1185,-9.8509,0.0841,-0.1058,-9.8056,0.0012,0,0,33.9,-76.1,61.5,155.75,0.62,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,13922,2015-10-30 11:02:52:153\n0.0838,-0.1113,-9.8725,0.0839,-0.1054,-9.8056,0.0012,0.0012,0,33.9,-76,61.4,155.76,0.62,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,14023,2015-10-30 11:02:52:254\n0.0814,-0.1185,-9.8617,0.0838,-0.1062,-9.8056,0,0.0024,0.0012,33.9,-76.1,61.2,155.76,0.62,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,14126,2015-10-30 11:02:52:357\n0.0766,-0.1137,-9.8509,0.0839,-0.1061,-9.8056,0.0024,0.0037,-0.0012,33.9,-76.1,60.8,155.76,0.62,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,14228,2015-10-30 11:02:52:459\n0.0766,-0.0982,-9.8509,0.0841,-0.1064,-9.8056,0.0012,0.0024,0,34,-76,60.8,155.76,0.62,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,14330,2015-10-30 11:02:52:561\n0.0946,-0.1089,-9.8545,0.0839,-0.1053,-9.8056,0.0012,0,0,34.1,-76.1,60.7,155.75,0.61,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,14432,2015-10-30 11:02:52:663\n0.091,-0.0994,-9.8581,0.0843,-0.1058,-9.8056,0.0024,0.0012,0,33.9,-76.1,60.9,155.75,0.62,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,14534,2015-10-30 11:02:52:765\n0.073,-0.1053,-9.8653,0.0837,-0.1054,-9.8056,0.0037,-0.0012,0.0012,33.9,-76.1,60.8,155.75,0.61,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,14636,2015-10-30 11:02:52:867\n0.0898,-0.1089,-9.8557,0.084,-0.1043,-9.8056,-0.0012,0.0037,0,33.8,-76.1,60.4,155.76,0.61,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,14738,2015-10-30 11:02:52:969\n0.0874,-0.1089,-9.8509,0.0842,-0.1038,-9.8056,-0.0012,0.0012,0.0012,33.8,-76.2,60.4,155.75,0.61,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,14840,2015-10-30 11:02:53:071\n0.0874,-0.0994,-9.8521,0.0841,-0.1039,-9.8056,0,0.0012,0,33.8,-76.2,60.5,155.75,0.61,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,14942,2015-10-30 11:02:53:173\n0.085,-0.1113,-9.8593,0.0833,-0.1042,-9.8056,0.0024,0.0012,0.0012,33.8,-76.1,60.9,155.75,0.61,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,15044,2015-10-30 11:02:53:275\n0.0886,-0.1125,-9.8509,0.0834,-0.1047,-9.8056,0.0012,0.0024,0,33.9,-76.1,60.9,155.76,0.61,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,15146,2015-10-30 11:02:53:377\n0.0874,-0.0994,-9.8521,0.0844,-0.1044,-9.8056,-0.0012,0.0049,-0.0012,33.9,-76,61.2,155.75,0.61,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,15248,2015-10-30 11:02:53:479\n0.0922,-0.097,-9.8557,0.0848,-0.1046,-9.8056,0.0024,0.0037,-0.0012,34,-76.1,61.5,155.75,0.61,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,15350,2015-10-30 11:02:53:581\n0.0838,-0.1065,-9.8605,0.0848,-0.1048,-9.8056,0,0.0024,0,34,-76.1,61.6,155.75,0.61,-179.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,15452,2015-10-30 11:02:53:683\n0.091,-0.0958,-9.8509,0.0839,-0.1044,-9.8056,-0.0012,0,0.0012,34,-76.2,61.7,155.75,0.61,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,15554,2015-10-30 11:02:53:785\n0.0766,-0.0934,-9.8557,0.0835,-0.1045,-9.8056,0,0.0037,0.0012,33.9,-76.1,61.6,155.75,0.61,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,15656,2015-10-30 11:02:53:887\n0.0694,-0.103,-9.8533,0.0833,-0.1045,-9.8056,0,0.0012,0.0012,33.8,-76.2,61.3,155.75,0.61,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,15758,2015-10-30 11:02:53:989\n0.0898,-0.1018,-9.8557,0.0838,-0.1051,-9.8056,0.0012,0.0037,0.0012,33.8,-76.3,61.2,155.75,0.61,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,15860,2015-10-30 11:02:54:091\n0.0982,-0.1125,-9.8557,0.0839,-0.1048,-9.8056,0,0.0024,0,34,-76.3,61,155.75,0.61,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,15962,2015-10-30 11:02:54:193\n0.0886,-0.1125,-9.8569,0.0835,-0.1054,-9.8056,0.0037,0.0024,0,33.9,-76.1,61.1,155.76,0.62,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,16064,2015-10-30 11:02:54:295\n0.0886,-0.1018,-9.8521,0.0835,-0.1057,-9.8056,0.0012,-0.0012,-0.0024,33.9,-76.1,61.3,155.76,0.62,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,16166,2015-10-30 11:02:54:397\n0.0874,-0.1137,-9.8689,0.0833,-0.106,-9.8056,0.0024,0.0012,-0.0024,33.7,-76.1,61.5,155.76,0.62,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,16268,2015-10-30 11:02:54:499\n0.0958,-0.0934,-9.8605,0.0834,-0.1058,-9.8056,-0.0012,0.0012,-0.0012,33.8,-76.2,61.5,155.75,0.62,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,16370,2015-10-30 11:02:54:601\n0.0814,-0.1137,-9.8509,0.0841,-0.1062,-9.8056,0.0024,0.0012,0.0012,33.7,-76.2,61.3,155.76,0.62,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,16472,2015-10-30 11:02:54:703\n0.0754,-0.1185,-9.8509,0.0848,-0.1066,-9.8056,0.0024,0.0024,-0.0024,33.8,-76.1,61.4,155.75,0.62,-179.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,16573,2015-10-30 11:02:54:804\n0.0898,-0.1125,-9.8557,0.0847,-0.1071,-9.8055,0.0012,0.0024,-0.0024,33.8,-76,61.5,155.75,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,16677,2015-10-30 11:02:54:908\n0.079,-0.1185,-9.8533,0.0846,-0.1071,-9.8056,0,0.0012,-0.0024,33.8,-76,61.5,155.75,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,16778,2015-10-30 11:02:55:009\n0.0802,-0.1053,-9.8533,0.0848,-0.1071,-9.8056,0,0.0012,-0.0012,33.8,-76,61.4,155.75,0.62,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,16880,2015-10-30 11:02:55:111\n0.0886,-0.1173,-9.8378,0.0846,-0.1065,-9.8056,0.0012,0.0012,-0.0024,33.9,-76.1,61.7,155.75,0.62,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,16982,2015-10-30 11:02:55:213\n0.0802,-0.1053,-9.8641,0.0851,-0.1061,-9.8056,-0.0012,0.0012,-0.0012,34,-76.1,61.8,155.75,0.62,-179.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,17084,2015-10-30 11:02:55:315\n0.0814,-0.1101,-9.8533,0.0856,-0.1065,-9.8056,-0.0024,0.0024,0.0012,34,-76.1,61.9,155.75,0.62,-179.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,17186,2015-10-30 11:02:55:417\n0.0766,-0.1018,-9.8569,0.0862,-0.1059,-9.8056,0,0.0037,-0.0024,34,-76.2,61.5,155.74,0.62,-179.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,17287,2015-10-30 11:02:55:518\n0.0766,-0.1041,-9.8605,0.0858,-0.1059,-9.8056,0.0012,0.0012,0,33.9,-76.2,61.2,155.75,0.62,-179.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,17390,2015-10-30 11:02:55:621\n0.0934,-0.1125,-9.845,0.0859,-0.1059,-9.8055,-0.0012,0.0012,0,33.8,-76.2,61.1,155.75,0.62,-179.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,17492,2015-10-30 11:02:55:723\n0.085,-0.1149,-9.8509,0.0861,-0.1056,-9.8056,-0.0024,0.0024,0,33.8,-76,61.3,155.75,0.62,-179.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,17594,2015-10-30 11:02:55:825\n0.0838,-0.1113,-9.8749,0.0858,-0.1059,-9.8056,0.0012,0,0,33.8,-76,61.5,155.74,0.62,-179.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,17696,2015-10-30 11:02:55:927\n0.085,-0.1041,-9.8569,0.0857,-0.1052,-9.8056,0,0.0024,0,33.8,-75.9,61.4,155.75,0.61,-179.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,17797,2015-10-30 11:02:56:028\n0.0826,-0.1065,-9.8557,0.0855,-0.1048,-9.8056,-0.0012,0.0037,-0.0012,33.8,-75.9,61.4,155.75,0.61,-179.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,17900,2015-10-30 11:02:56:131\n0.0706,-0.1149,-9.8677,0.085,-0.106,-9.8055,-0.0012,0.0024,0,33.7,-75.9,61.4,155.75,0.62,-179.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,18002,2015-10-30 11:02:56:233\n0.0838,-0.1089,-9.8509,0.085,-0.1057,-9.8056,0.0024,0.0012,-0.0012,33.6,-76,61.3,155.75,0.62,-179.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,18104,2015-10-30 11:02:56:335\n0.0922,-0.1077,-9.8497,0.0851,-0.1058,-9.8056,0,0.0012,0.0012,33.7,-76,61.2,155.75,0.62,-179.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,18206,2015-10-30 11:02:56:437\n0.0766,-0.1149,-9.8318,0.0844,-0.106,-9.8056,0,0.0012,-0.0012,33.6,-76,61.1,155.75,0.62,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,18308,2015-10-30 11:02:56:539\n0.0754,-0.1077,-9.8294,0.0838,-0.1064,-9.8055,0.0024,0.0012,0,33.5,-76,60.9,155.76,0.62,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,18410,2015-10-30 11:02:56:641\n0.1006,-0.1149,-9.8497,0.0833,-0.106,-9.8056,0.0012,0,-0.0012,33.5,-76.1,61,155.76,0.62,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,18512,2015-10-30 11:02:56:743\n0.0814,-0.1101,-9.8713,0.0833,-0.1072,-9.8056,0.0012,0.0024,0.0012,33.5,-76,61.3,155.76,0.62,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,18613,2015-10-30 11:02:56:844\n0.0742,-0.1041,-9.8533,0.0827,-0.1078,-9.8056,0,0,0.0024,33.6,-76,61.5,155.76,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,18716,2015-10-30 11:02:56:947\n0.091,-0.1006,-9.8533,0.0833,-0.1069,-9.8055,-0.0012,0.0037,0,33.6,-76,61.6,155.76,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,18818,2015-10-30 11:02:57:049\n0.079,-0.1089,-9.8509,0.083,-0.107,-9.8056,-0.0012,0.0012,0,33.7,-76,61.3,155.76,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,18920,2015-10-30 11:02:57:151\n0.0754,-0.1149,-9.8605,0.0827,-0.1072,-9.8056,0.0024,0.0012,-0.0012,33.8,-75.9,61.5,155.76,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,19021,2015-10-30 11:02:57:252\n0.0958,-0.1233,-9.8462,0.0833,-0.1072,-9.8055,0,0,-0.0012,33.8,-76,61.8,155.76,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,19124,2015-10-30 11:02:57:355\n0.0814,-0.1101,-9.8581,0.0828,-0.1075,-9.8055,-0.0037,-0.0012,0,33.8,-76,61.6,155.76,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,19226,2015-10-30 11:02:57:457\n0.0898,-0.1113,-9.8605,0.0825,-0.1073,-9.8056,0,0,0,33.7,-76.1,61.6,155.76,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,19328,2015-10-30 11:02:57:559\n0.0862,-0.0994,-9.8581,0.0828,-0.1068,-9.8055,-0.0024,0.0012,0,33.8,-76.1,61.5,155.76,0.62,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,19430,2015-10-30 11:02:57:661\n0.0862,-0.1006,-9.8509,0.0827,-0.1073,-9.8055,0.0012,0.0024,0,33.8,-76.1,61.4,155.76,0.62,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,19531,2015-10-30 11:02:57:762\n0.0634,-0.1101,-9.8617,0.0828,-0.1072,-9.8055,0.0024,0.0012,-0.0012,33.7,-76,61.3,155.76,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,19634,2015-10-30 11:02:57:865\n0.0886,-0.0982,-9.8569,0.083,-0.107,-9.8056,-0.0012,0,0,33.6,-76,61,155.76,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,19736,2015-10-30 11:02:57:967\n0.0874,-0.1053,-9.8485,0.0829,-0.1077,-9.8056,0,0.0012,0,33.6,-76,61.3,155.76,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,19838,2015-10-30 11:02:58:069\n0.0802,-0.1137,-9.8545,0.0831,-0.1075,-9.8055,0,0.0012,0,33.7,-76,61.5,155.76,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,19940,2015-10-30 11:02:58:171\n0.0826,-0.1053,-9.8629,0.0838,-0.1073,-9.8055,0.0012,0.0037,-0.0012,33.8,-76,61.5,155.76,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,20042,2015-10-30 11:02:58:273\n0.0778,-0.1077,-9.8641,0.0841,-0.1072,-9.8055,0,0.0024,0,33.8,-76,61.3,155.76,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,20143,2015-10-30 11:02:58:374\n0.0862,-0.1065,-9.8569,0.0839,-0.1072,-9.8055,0,0.0012,0.0024,33.7,-76,61.1,155.76,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,20246,2015-10-30 11:02:58:477\n0.0706,-0.103,-9.8509,0.0835,-0.1073,-9.8055,0.0012,0.0012,-0.0012,33.7,-76.1,61.3,155.76,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,20348,2015-10-30 11:02:58:579\n0.0766,-0.1113,-9.8533,0.0828,-0.107,-9.8055,-0.0012,0.0012,-0.0012,33.7,-76,61.5,155.76,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,20450,2015-10-30 11:02:58:681\n0.0826,-0.1113,-9.8509,0.0831,-0.1068,-9.8055,0.0012,0.0037,0.0012,33.7,-76.1,61.6,155.76,0.62,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,20552,2015-10-30 11:02:58:783\n0.0922,-0.1006,-9.8557,0.0837,-0.1072,-9.8055,0.0012,0.0024,-0.0012,33.8,-76.1,61.4,155.76,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,20654,2015-10-30 11:02:58:885\n0.0706,-0.1113,-9.8629,0.084,-0.1076,-9.8055,0.0012,0.0024,0,33.8,-76.1,61.2,155.76,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,20756,2015-10-30 11:02:58:987\n0.0838,-0.1221,-9.8773,0.0839,-0.1078,-9.8055,-0.0012,0.0024,0.0012,33.9,-76.2,61.1,155.76,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,20858,2015-10-30 11:02:59:089\n0.0826,-0.097,-9.8581,0.084,-0.1071,-9.8056,-0.0012,0.0012,-0.0012,33.9,-76.1,61.1,155.76,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,20960,2015-10-30 11:02:59:191\n0.0658,-0.1149,-9.8641,0.0837,-0.1064,-9.8055,-0.0012,0.0012,0.0012,33.8,-76.1,61.3,155.76,0.62,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,21062,2015-10-30 11:02:59:293\n0.0742,-0.1173,-9.8773,0.084,-0.1067,-9.8056,0.0012,0.0049,0,33.7,-75.9,61.3,155.76,0.62,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,21164,2015-10-30 11:02:59:395\n0.0838,-0.1125,-9.8713,0.0837,-0.1068,-9.8055,0,0.0012,0,33.8,-76,61.4,155.76,0.62,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,21266,2015-10-30 11:02:59:497\n0.0874,-0.1149,-9.8509,0.0834,-0.1068,-9.8055,0.0012,0.0012,0.0012,33.8,-76.1,61.3,155.76,0.62,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,21368,2015-10-30 11:02:59:599\n0.085,-0.1006,-9.8593,0.0832,-0.106,-9.8055,-0.0012,0.0024,0,33.8,-76.2,61.4,155.76,0.62,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,21470,2015-10-30 11:02:59:701\n0.085,-0.1161,-9.8797,0.0822,-0.1063,-9.8055,0.0012,0,0,33.8,-76.1,61.2,155.76,0.62,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,21572,2015-10-30 11:02:59:803\n0.0706,-0.1018,-9.8689,0.082,-0.1062,-9.8056,0,0.0024,-0.0012,33.8,-76,61.4,155.76,0.62,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,21674,2015-10-30 11:02:59:905\n0.0634,-0.103,-9.8557,0.082,-0.1062,-9.8056,0.0024,0.0012,0,33.9,-76,61.7,155.76,0.62,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,21776,2015-10-30 11:03:00:007\n0.0766,-0.1065,-9.8629,0.0818,-0.1059,-9.8056,0,0.0024,-0.0012,33.9,-76.1,61.5,155.76,0.62,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,21878,2015-10-30 11:03:00:109\n0.0826,-0.1149,-9.8737,0.0817,-0.1066,-9.8056,-0.0024,0.0024,-0.0024,33.8,-76.1,61.2,155.76,0.62,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,21980,2015-10-30 11:03:00:211\n0.085,-0.0934,-9.8629,0.0821,-0.1063,-9.8056,0.0012,0.0012,-0.0012,33.6,-76.1,60.7,155.76,0.62,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,22081,2015-10-30 11:03:00:312\n0.0778,-0.1077,-9.8569,0.0818,-0.1063,-9.8056,0,0.0024,0.0024,33.5,-76,60.9,155.76,0.62,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,22184,2015-10-30 11:03:00:415\n0.0958,-0.1137,-9.8533,0.0815,-0.1063,-9.8056,0.0024,0.0012,0,33.5,-76,61,155.76,0.62,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,22286,2015-10-30 11:03:00:517\n0.0718,-0.1041,-9.8653,0.0813,-0.1066,-9.8056,0,0,0,33.7,-76,60.9,155.77,0.62,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,22388,2015-10-30 11:03:00:619\n0.079,-0.1053,-9.8485,0.0819,-0.1067,-9.8056,0,0.0037,-0.0012,33.7,-76.1,61,155.76,0.62,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,22490,2015-10-30 11:03:00:721\n0.0874,-0.1018,-9.8509,0.0821,-0.1074,-9.8056,0.0012,0,-0.0024,33.7,-76.1,61.4,155.76,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,22591,2015-10-30 11:03:00:822\n0.0778,-0.1053,-9.8509,0.0823,-0.108,-9.8055,0.0024,0.0037,0,33.6,-76.1,61.8,155.76,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,22695,2015-10-30 11:03:00:926\n0.0982,-0.1137,-9.8055,0.0833,-0.1088,-9.8055,0,0,-0.0012,33.6,-76.1,61.7,155.76,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,22796,2015-10-30 11:03:01:027\n0.0838,-0.1113,-9.8569,0.0837,-0.1095,-9.8055,0.0024,0.0012,0,33.6,-76.1,61.4,155.76,0.64,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,22898,2015-10-30 11:03:01:129\n0.0934,-0.1149,-9.8521,0.0828,-0.1098,-9.8055,0,0,0,33.7,-76.1,61.1,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,23000,2015-10-30 11:03:01:231\n0.0802,-0.1149,-9.8581,0.0823,-0.1093,-9.8055,-0.0012,0.0024,0.0012,33.7,-76.1,61.1,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,23101,2015-10-30 11:03:01:332\n0.0982,-0.0994,-9.8509,0.0819,-0.1091,-9.8055,0.0024,0.0037,0.0012,33.6,-76.1,61.2,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,23204,2015-10-30 11:03:01:435\n0.079,-0.1089,-9.8629,0.0819,-0.1093,-9.8055,0.0024,0.0012,0,33.6,-76,61.1,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,23306,2015-10-30 11:03:01:537\n0.0814,-0.1209,-9.8509,0.0819,-0.1093,-9.8055,0.0012,0.0024,0.0012,33.6,-76,60.7,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,23408,2015-10-30 11:03:01:639\n0.0826,-0.1149,-9.8509,0.0824,-0.1093,-9.8055,0,0.0024,0,33.6,-76,60.9,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,23510,2015-10-30 11:03:01:741\n0.073,-0.1125,-9.8569,0.0826,-0.1096,-9.8055,0.0024,0.0024,0.0012,33.6,-76.1,61.2,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,23612,2015-10-30 11:03:01:843\n0.0814,-0.1149,-9.8641,0.0821,-0.1101,-9.8055,0,0.0012,0.0012,33.7,-76.1,61.3,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,23714,2015-10-30 11:03:01:945\n0.0886,-0.0982,-9.8521,0.0823,-0.1101,-9.8055,0,0.0012,0,33.8,-76.2,61.2,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,23816,2015-10-30 11:03:02:047\n0.0814,-0.1209,-9.8533,0.0823,-0.11,-9.8055,0.0012,0,0,33.7,-76.2,61.1,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,23918,2015-10-30 11:03:02:149\n0.079,-0.103,-9.8581,0.0823,-0.1094,-9.8055,0.0012,0.0012,-0.0024,33.7,-76.1,61.3,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,24020,2015-10-30 11:03:02:251\n0.0826,-0.1101,-9.8701,0.0821,-0.1093,-9.8055,0.0012,0.0024,-0.0012,33.7,-76.1,61.1,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,24122,2015-10-30 11:03:02:353\n0.0838,-0.1089,-9.8605,0.082,-0.1085,-9.8055,-0.0024,0.0012,0.0012,33.7,-76.1,61.1,155.77,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,24224,2015-10-30 11:03:02:455\n0.0634,-0.1125,-9.8569,0.0823,-0.1084,-9.8055,0.0024,0,-0.0024,33.6,-76,60.9,155.77,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,24326,2015-10-30 11:03:02:557\n0.085,-0.1113,-9.8569,0.0825,-0.1093,-9.8055,0.0012,0.0012,-0.0024,33.5,-76,61.1,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,24428,2015-10-30 11:03:02:659\n0.0934,-0.1101,-9.8557,0.0821,-0.1087,-9.8055,-0.0012,0.0024,-0.0024,33.5,-76,61.6,155.76,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,24530,2015-10-30 11:03:02:761\n0.0682,-0.1077,-9.8581,0.082,-0.1089,-9.8055,0,0.0012,-0.0012,33.7,-76,61.5,155.76,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,24632,2015-10-30 11:03:02:863\n0.0898,-0.1149,-9.8545,0.0822,-0.1093,-9.8055,0,0.0012,-0.0012,33.7,-76.1,61.4,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,24734,2015-10-30 11:03:02:965\n0.0742,-0.1161,-9.8533,0.0817,-0.1088,-9.8055,0.0012,0.0012,-0.0012,33.8,-76.1,61.2,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,24836,2015-10-30 11:03:03:067\n0.0766,-0.1221,-9.8701,0.0817,-0.1089,-9.8055,-0.0012,0.0012,-0.0012,33.6,-76.1,60.9,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,24938,2015-10-30 11:03:03:169\n0.0766,-0.1065,-9.8737,0.0811,-0.1088,-9.8055,0.0012,0.0012,0,33.7,-76.2,61,155.77,0.64,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,25039,2015-10-30 11:03:03:270\n0.0874,-0.0982,-9.8533,0.0811,-0.1092,-9.8055,0,0.0037,-0.0012,33.8,-76.2,61.1,155.77,0.64,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,25142,2015-10-30 11:03:03:373\n0.0874,-0.1101,-9.8509,0.0804,-0.1089,-9.8056,0,0.0012,-0.0012,33.9,-76.1,61.1,155.77,0.64,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,25244,2015-10-30 11:03:03:475\n0.0802,-0.1006,-9.8569,0.08,-0.1094,-9.8056,0,0.0012,-0.0012,33.7,-76.1,61,155.78,0.64,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,25346,2015-10-30 11:03:03:577\n0.0994,-0.1137,-9.8485,0.0801,-0.1099,-9.8056,0.0012,0.0012,0,33.6,-76,61.2,155.78,0.64,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,25448,2015-10-30 11:03:03:679\n0.0826,-0.1065,-9.8545,0.08,-0.1098,-9.8055,0.0037,0.0024,0,33.5,-76.1,61.3,155.78,0.64,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,25550,2015-10-30 11:03:03:781\n0.0718,-0.1041,-9.8569,0.0799,-0.1102,-9.8056,0.0012,0.0012,0,33.5,-76.1,61.5,155.78,0.64,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,25652,2015-10-30 11:03:03:883\n0.0886,-0.1101,-9.8545,0.0798,-0.1102,-9.8055,0.0012,0.0012,0,33.4,-76.1,61.3,156.4,0.65,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,25754,2015-10-30 11:03:03:985\n0.0814,-0.1077,-9.8653,0.0799,-0.1108,-9.8056,0.0037,0.0012,-0.0012,33.4,-76.1,61.4,156.4,0.65,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,25856,2015-10-30 11:03:04:087\n0.0838,-0.1161,-9.8593,0.0805,-0.11,-9.8055,0.0012,0.0012,-0.0012,33.6,-76.1,61.4,155.78,0.64,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,25958,2015-10-30 11:03:04:189\n0.079,-0.1113,-9.8509,0.0806,-0.1101,-9.8056,0,0.0012,-0.0012,33.6,-76.1,61.3,155.78,0.64,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,26060,2015-10-30 11:03:04:291\n0.0838,-0.1089,-9.8474,0.0802,-0.1103,-9.8055,0.0012,0,0.0012,33.7,-76.1,60.9,155.78,0.64,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,26162,2015-10-30 11:03:04:393\n0.0874,-0.1125,-9.8725,0.0806,-0.1101,-9.8056,0,0.0012,0,33.6,-76.1,60.7,155.78,0.64,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,26264,2015-10-30 11:03:04:495\n0.079,-0.1125,-9.8605,0.0813,-0.1103,-9.8055,0.0012,0.0024,-0.0012,33.5,-76,61,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,26367,2015-10-30 11:03:04:598\n0.0778,-0.1053,-9.8605,0.0811,-0.1099,-9.8055,0,0.0012,0,33.5,-76.1,61.1,155.77,0.64,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,26468,2015-10-30 11:03:04:699\n0.085,-0.1077,-9.8509,0.0812,-0.1093,-9.8056,0.0024,0.0012,0,33.5,-76,61.3,155.77,0.64,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,26570,2015-10-30 11:03:04:801\n0.0814,-0.097,-9.8402,0.0814,-0.1104,-9.8055,0.0012,0.0012,0,33.6,-76,61.2,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,26672,2015-10-30 11:03:04:903\n0.0826,-0.1041,-9.8581,0.0819,-0.111,-9.8055,0.0024,0.0012,0.0012,33.6,-76,61.2,155.77,0.65,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,26774,2015-10-30 11:03:05:005\n0.0958,-0.0994,-9.8533,0.0825,-0.111,-9.8055,-0.0012,0.0012,0.0012,33.7,-76,61.4,155.77,0.65,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,26876,2015-10-30 11:03:05:107\n0.0826,-0.1077,-9.8557,0.0826,-0.1105,-9.8055,0,0,0,33.7,-76,61.3,155.77,0.65,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,26978,2015-10-30 11:03:05:209\n0.0754,-0.1125,-9.8629,0.083,-0.1107,-9.8055,0.0012,0.0024,-0.0012,33.6,-75.9,61.4,155.77,0.65,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,27080,2015-10-30 11:03:05:311\n0.0766,-0.1065,-9.8509,0.0827,-0.1105,-9.8055,0,0.0024,-0.0012,33.6,-75.9,61.3,155.77,0.65,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,27181,2015-10-30 11:03:05:412\n0.0862,-0.1065,-9.8509,0.0829,-0.1108,-9.8055,0,0.0024,0,33.5,-75.9,61.3,155.77,0.65,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,27284,2015-10-30 11:03:05:515\n0.0766,-0.1101,-9.8581,0.0826,-0.1107,-9.8055,0,0.0012,-0.0024,33.6,-75.9,61,155.77,0.65,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,27385,2015-10-30 11:03:05:616\n0.0922,-0.0958,-9.845,0.0823,-0.1108,-9.8055,-0.0024,0.0012,0,33.6,-76.1,61,155.77,0.65,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,27488,2015-10-30 11:03:05:719\n0.085,-0.0994,-9.8474,0.0817,-0.1108,-9.8055,0.0037,0.0024,0,33.6,-76.1,61,155.77,0.65,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,27590,2015-10-30 11:03:05:821\n0.0742,-0.1041,-9.8713,0.0815,-0.1098,-9.8056,0.0024,-0.0012,0.0024,33.6,-76.1,61.2,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,27692,2015-10-30 11:03:05:923\n0.091,-0.1281,-9.8677,0.0819,-0.1099,-9.8055,0,0.0012,0,33.6,-76,61.4,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,27794,2015-10-30 11:03:06:025\n0.085,-0.0994,-9.8533,0.082,-0.1105,-9.8055,0.0024,0.0024,0,33.8,-76.2,61.5,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,27896,2015-10-30 11:03:06:127\n0.0778,-0.1125,-9.8557,0.0823,-0.1098,-9.8055,-0.0012,0.0012,0.0012,33.7,-76.1,61.7,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,27998,2015-10-30 11:03:06:229\n0.091,-0.1137,-9.8761,0.0822,-0.1096,-9.8056,0,0.0012,-0.0012,33.6,-76.1,61.6,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,28100,2015-10-30 11:03:06:331\n0.0934,-0.1089,-9.8545,0.0822,-0.1095,-9.8056,-0.0012,0.0012,0.0012,33.6,-76.1,61.7,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,28202,2015-10-30 11:03:06:433\n0.0862,-0.1101,-9.8617,0.0826,-0.1101,-9.8055,0.0012,0.0012,-0.0012,33.7,-76,61.7,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,28304,2015-10-30 11:03:06:535\n0.0766,-0.1077,-9.8521,0.0827,-0.1102,-9.8055,0.0024,0.0024,0,33.6,-76.1,61.9,155.76,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,28406,2015-10-30 11:03:06:637\n0.0862,-0.103,-9.8509,0.0828,-0.11,-9.8056,-0.0012,0.0024,0,33.5,-76.1,61.5,155.76,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,28508,2015-10-30 11:03:06:739\n0.073,-0.1101,-9.8749,0.082,-0.1094,-9.8056,0.0024,0.0024,0,33.6,-76.2,61.6,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,28610,2015-10-30 11:03:06:841\n0.0898,-0.1365,-9.8665,0.0819,-0.1101,-9.8055,0,0.0024,0.0012,33.7,-76.3,61.3,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,28712,2015-10-30 11:03:06:943\n0.085,-0.1113,-9.8509,0.0818,-0.1106,-9.8056,0.0012,0.0012,0,33.8,-76.2,61.3,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,28814,2015-10-30 11:03:07:045\n0.0802,-0.1113,-9.8509,0.0819,-0.1104,-9.8056,-0.0012,0,-0.0024,33.8,-76.2,61.4,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,28916,2015-10-30 11:03:07:147\n0.0886,-0.1197,-9.8581,0.0821,-0.1104,-9.8055,0.0012,0.0012,0,33.5,-76.1,61.4,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,29018,2015-10-30 11:03:07:249\n0.0946,-0.1089,-9.8509,0.0819,-0.11,-9.8055,0.0024,0.0024,-0.0012,33.5,-76.1,61.4,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,29120,2015-10-30 11:03:07:351\n0.0934,-0.1149,-9.8509,0.0818,-0.1104,-9.8055,0.0024,0,0,33.5,-76.2,61.2,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,29222,2015-10-30 11:03:07:453\n0.0934,-0.1125,-9.8605,0.082,-0.1102,-9.8055,0,0,0.0012,33.7,-76.1,61.1,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,29324,2015-10-30 11:03:07:555\n0.0814,-0.1101,-9.8653,0.0824,-0.1101,-9.8055,0,0.0012,0,33.7,-76.1,61.1,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,29426,2015-10-30 11:03:07:657\n0.0766,-0.1161,-9.8533,0.0823,-0.1105,-9.8055,0,0.0024,-0.0024,33.7,-76.1,61,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,29528,2015-10-30 11:03:07:759\n0.0838,-0.1221,-9.8677,0.0824,-0.1103,-9.8055,0.0012,0.0012,-0.0012,33.6,-76.1,61,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,29630,2015-10-30 11:03:07:861\n0.0754,-0.1065,-9.8593,0.0827,-0.1106,-9.8055,0.0024,0,-0.0024,33.7,-76.2,61.1,155.77,0.65,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,29732,2015-10-30 11:03:07:963\n0.0742,-0.1077,-9.8689,0.0825,-0.1105,-9.8055,0.0012,0.0012,0,33.7,-76.1,61.3,155.77,0.65,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,29834,2015-10-30 11:03:08:065\n0.0778,-0.103,-9.8593,0.0827,-0.11,-9.8055,0,0,0.0024,33.8,-76.2,61.3,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,29936,2015-10-30 11:03:08:167\n0.0874,-0.1077,-9.8521,0.0833,-0.1104,-9.8055,0.0024,0.0024,0.0012,33.7,-76.1,61.2,155.77,0.65,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,30038,2015-10-30 11:03:08:269\n0.0754,-0.1041,-9.8629,0.0835,-0.1107,-9.8055,0,0,0,33.6,-76,60.7,155.77,0.65,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,30140,2015-10-30 11:03:08:371\n0.0778,-0.1137,-9.8641,0.0834,-0.1104,-9.8055,0,0.0024,0,33.5,-76.1,60.8,155.76,0.64,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,30241,2015-10-30 11:03:08:472\n0.079,-0.1113,-9.8545,0.0837,-0.1098,-9.8055,0.0024,0.0037,0,33.4,-76.1,60.7,156.39,0.64,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,30344,2015-10-30 11:03:08:575\n0.079,-0.1006,-9.8605,0.0832,-0.1095,-9.8055,0,0.0024,0.0012,33.7,-76.1,60.6,155.76,0.64,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,30446,2015-10-30 11:03:08:677\n0.0814,-0.1006,-9.8653,0.0836,-0.1089,-9.8055,0.0012,0.0012,0.0012,33.7,-76,60.6,155.76,0.64,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,30548,2015-10-30 11:03:08:779\n0.0898,-0.1077,-9.8545,0.0837,-0.1086,-9.8055,0.0012,0.0012,0.0012,33.8,-76.1,60.9,155.76,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,30650,2015-10-30 11:03:08:881\n0.0754,-0.1101,-9.8509,0.0835,-0.1091,-9.8055,0.0012,0.0012,0,33.7,-76.1,60.9,155.76,0.64,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,30751,2015-10-30 11:03:08:982\n0.0742,-0.1197,-9.8665,0.0834,-0.1089,-9.8055,0,0.0012,0.0012,33.7,-76,61,155.76,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,30853,2015-10-30 11:03:09:084\n0.0862,-0.103,-9.8557,0.0832,-0.1085,-9.8055,0.0024,0.0024,-0.0012,33.6,-76,60.9,155.76,0.64,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,30956,2015-10-30 11:03:09:187\n0.0946,-0.1077,-9.8509,0.0833,-0.1084,-9.8055,0,0.0012,-0.0012,33.6,-76.1,60.8,155.76,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,31058,2015-10-30 11:03:09:289\n0.1018,-0.1137,-9.8581,0.0831,-0.1084,-9.8055,-0.0012,0.0037,0,33.6,-76.2,60.8,155.76,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,31160,2015-10-30 11:03:09:391\n0.0874,-0.1077,-9.8641,0.084,-0.1082,-9.8055,0.0012,0.0012,0,33.5,-76.2,60.9,155.76,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,31262,2015-10-30 11:03:09:493\n0.0862,-0.1101,-9.8474,0.084,-0.1084,-9.8055,0.0012,0.0024,0.0012,33.5,-76.1,60.7,155.76,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,31364,2015-10-30 11:03:09:595\n0.0922,-0.1137,-9.8485,0.0834,-0.1086,-9.8055,0.0012,0.0012,-0.0012,33.5,-76.1,60.6,155.76,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,31467,2015-10-30 11:03:09:698\n0.0682,-0.1161,-9.8737,0.0835,-0.109,-9.8055,-0.0012,0.0024,0,33.5,-76.1,60.6,155.76,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,31568,2015-10-30 11:03:09:799\n0.0742,-0.1137,-9.8653,0.0831,-0.1096,-9.8055,-0.0012,0,0,33.6,-76.1,60.8,155.76,0.64,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,31670,2015-10-30 11:03:09:901\n0.0946,-0.1137,-9.8581,0.0829,-0.1089,-9.8055,0,0.0024,0,33.7,-76.1,60.5,155.76,0.64,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,31772,2015-10-30 11:03:10:003\n0.0874,-0.1089,-9.8581,0.0831,-0.109,-9.8055,0.0024,0.0024,0.0012,33.7,-76.1,60.6,155.76,0.64,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,31874,2015-10-30 11:03:10:105\n0.0874,-0.1089,-9.8557,0.0827,-0.1088,-9.8055,0,0,0,33.7,-76.1,60.5,155.76,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,31976,2015-10-30 11:03:10:207\n0.085,-0.1053,-9.8509,0.0827,-0.1087,-9.8055,0.0012,0.0012,-0.0012,33.8,-76.2,61.1,155.76,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,32078,2015-10-30 11:03:10:309\n0.0874,-0.1137,-9.8521,0.0827,-0.1084,-9.8056,0.0012,0.0012,0.0012,33.9,-76.2,61.2,155.76,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,32180,2015-10-30 11:03:10:411\n0.0922,-0.1125,-9.8533,0.0827,-0.1085,-9.8055,0,0.0024,-0.0012,33.8,-76.1,61.1,155.76,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,32282,2015-10-30 11:03:10:513\n0.0706,-0.1113,-9.8617,0.0829,-0.1083,-9.8056,0.0012,0.0024,0,33.8,-76.1,61.1,155.76,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,32384,2015-10-30 11:03:10:615\n0.0718,-0.1041,-9.8509,0.0833,-0.1088,-9.8056,-0.0012,0.0024,0.0012,33.7,-75.9,61.1,155.76,0.64,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,32486,2015-10-30 11:03:10:717\n0.0958,-0.1185,-9.8222,0.0825,-0.1087,-9.8055,0.0012,0,0,33.7,-76.1,60.9,155.76,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,32588,2015-10-30 11:03:10:819\n0.0874,-0.1065,-9.8557,0.0831,-0.1086,-9.8056,0.0012,0.0024,0.0024,33.6,-76.1,60.7,155.76,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,32690,2015-10-30 11:03:10:921\n0.091,-0.1018,-9.8557,0.0836,-0.1088,-9.8055,0.0012,0,-0.0012,33.7,-76.1,60.8,155.76,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,32793,2015-10-30 11:03:11:024\n0.0922,-0.1161,-9.8126,0.0838,-0.109,-9.8055,0,0.0012,0,33.6,-76,60.9,155.76,0.64,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,32893,2015-10-30 11:03:11:124\n0.0934,-0.1185,-9.8713,0.0832,-0.1091,-9.8055,0.0037,0.0012,-0.0024,33.6,-76,60.9,155.76,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,32996,2015-10-30 11:03:11:227\n0.0706,-0.103,-9.8569,0.0831,-0.1094,-9.8055,-0.0012,0.0024,-0.0024,33.6,-76.1,60.8,155.76,0.64,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,33098,2015-10-30 11:03:11:329\n0.0814,-0.1006,-9.8617,0.0826,-0.1094,-9.8055,-0.0012,0.0012,-0.0012,33.5,-76.1,60.9,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,33200,2015-10-30 11:03:11:431\n0.0754,-0.1089,-9.8509,0.0825,-0.1088,-9.8056,0.0012,0.0012,0.0012,33.5,-76.1,60.8,155.76,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,33302,2015-10-30 11:03:11:533\n0.0826,-0.1113,-9.8653,0.0824,-0.109,-9.8055,-0.0024,0.0012,0.0012,33.5,-76.1,60.6,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,33404,2015-10-30 11:03:11:635\n0.0862,-0.1089,-9.8533,0.0824,-0.1084,-9.8056,0,0.0024,0.0012,33.5,-76,60.6,155.77,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,33507,2015-10-30 11:03:11:738\n0.0802,-0.1137,-9.8581,0.0826,-0.1084,-9.8056,0,0.0024,0.0012,33.7,-76.1,60.8,155.76,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,33608,2015-10-30 11:03:11:839\n0.0706,-0.1053,-9.8581,0.0825,-0.1086,-9.8056,0,0.0024,0.0012,33.7,-76.2,61,155.76,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,33710,2015-10-30 11:03:11:941\n0.0934,-0.1089,-9.8533,0.0827,-0.1084,-9.8055,0.0012,0.0024,0.0012,33.5,-76,61.3,155.76,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,33812,2015-10-30 11:03:12:043\n0.085,-0.1137,-9.8581,0.0835,-0.1074,-9.8055,0,0.0037,0,33.6,-76,61.2,155.76,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,33913,2015-10-30 11:03:12:144\n0.085,-0.1197,-9.8653,0.0834,-0.1075,-9.8055,-0.0012,0.0024,0,33.6,-75.9,61,155.76,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,34016,2015-10-30 11:03:12:247\n0.0886,-0.1077,-9.8629,0.0829,-0.1076,-9.8055,-0.0012,0.0012,0,33.7,-76,61,155.76,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,34118,2015-10-30 11:03:12:349\n0.0838,-0.1113,-9.8318,0.0827,-0.1074,-9.8055,0.0012,0.0012,0,33.7,-76.1,61,155.76,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,34220,2015-10-30 11:03:12:451\n0.0958,-0.1077,-9.8557,0.0834,-0.1073,-9.8055,0.0012,0.0024,-0.0012,33.7,-76.2,61.2,155.76,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,34322,2015-10-30 11:03:12:553\n0.0826,-0.1053,-9.8485,0.0832,-0.1072,-9.8055,-0.0012,0.0024,0,33.5,-76.1,61.2,155.76,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,34424,2015-10-30 11:03:12:655\n0.079,-0.1077,-9.8629,0.0831,-0.1073,-9.8056,0.0024,0.0024,-0.0012,33.4,-76.1,61.3,156.39,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,34526,2015-10-30 11:03:12:757\n0.0886,-0.1173,-9.8689,0.0834,-0.107,-9.8056,0,0.0012,-0.0024,33.6,-76.1,61.1,155.76,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,34627,2015-10-30 11:03:12:858\n0.0802,-0.1113,-9.8629,0.0828,-0.1071,-9.8055,0.0024,0.0012,0,33.5,-76,60.9,155.76,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,34730,2015-10-30 11:03:12:961\n0.0778,-0.1089,-9.8617,0.0829,-0.1069,-9.8056,0.0012,0.0012,0,33.6,-76.1,60.7,155.76,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,34831,2015-10-30 11:03:13:062\n0.0766,-0.1209,-9.8689,0.0824,-0.1064,-9.8056,-0.0012,0.0012,-0.0012,33.6,-76,60.5,155.76,0.62,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,34933,2015-10-30 11:03:13:164\n0.0898,-0.1053,-9.8545,0.0822,-0.1066,-9.8056,0,0.0012,-0.0012,33.6,-75.9,60.6,155.76,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,35036,2015-10-30 11:03:13:267\n0.091,-0.1101,-9.8474,0.0825,-0.1065,-9.8056,0,0.0024,-0.0012,33.6,-76,60.6,155.76,0.62,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,35138,2015-10-30 11:03:13:369\n0.0862,-0.1149,-9.8593,0.0821,-0.1071,-9.8056,0,0,-0.0012,33.6,-75.9,60.9,155.76,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,35240,2015-10-30 11:03:13:471\n0.0838,-0.1113,-9.8509,0.0823,-0.1076,-9.8056,-0.0012,0.0024,-0.0012,33.6,-76,60.8,155.76,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,35342,2015-10-30 11:03:13:573\n0.085,-0.1041,-9.8557,0.0826,-0.1082,-9.8055,0.0012,0.0012,0,33.6,-76,61,155.76,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,35444,2015-10-30 11:03:13:675\n0.0742,-0.1041,-9.8629,0.0825,-0.1082,-9.8055,-0.0012,0.0012,-0.0024,33.7,-76.1,61.2,155.76,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,35546,2015-10-30 11:03:13:777\n0.091,-0.0958,-9.8462,0.0827,-0.108,-9.8055,0.0037,0,0,33.7,-76.1,61.2,155.76,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,35648,2015-10-30 11:03:13:879\n0.0814,-0.1125,-9.8509,0.0829,-0.1083,-9.8055,-0.0012,0.0012,-0.0024,33.8,-76.1,61.6,155.76,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,35750,2015-10-30 11:03:13:981\n0.0886,-0.097,-9.8521,0.0833,-0.1083,-9.8055,0.0024,0.0037,-0.0012,33.8,-76.1,61.4,155.76,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,35852,2015-10-30 11:03:14:083\n0.0898,-0.1077,-9.8557,0.0836,-0.1084,-9.8055,0,0.0037,-0.0037,33.9,-76.1,61.2,155.76,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,35954,2015-10-30 11:03:14:185\n0.0682,-0.1065,-9.8629,0.0832,-0.1078,-9.8055,0,0.0012,-0.0012,33.8,-76.1,61,155.76,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,36056,2015-10-30 11:03:14:287\n0.0886,-0.1161,-9.8677,0.0832,-0.1078,-9.8055,-0.0012,0,0.0012,33.8,-76.2,60.8,155.76,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,36158,2015-10-30 11:03:14:389\n0.0706,-0.1185,-9.8629,0.0832,-0.1082,-9.8055,0,0.0012,0,33.7,-76.2,60.7,155.76,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,36260,2015-10-30 11:03:14:491\n0.0778,-0.1089,-9.8593,0.0825,-0.1084,-9.8055,-0.0012,0.0024,0,33.6,-76.2,60.7,155.76,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,36362,2015-10-30 11:03:14:593\n0.0742,-0.0982,-9.8545,0.0829,-0.1083,-9.8055,0.0012,0.0012,0.0012,33.6,-76.1,60.9,155.76,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,36464,2015-10-30 11:03:14:695\n0.0814,-0.1125,-9.8533,0.0831,-0.1091,-9.8055,-0.0012,0.0012,0,33.6,-76.1,61,155.76,0.64,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,36566,2015-10-30 11:03:14:797\n0.0838,-0.1018,-9.8593,0.0826,-0.1089,-9.8055,0,0.0012,0,33.6,-76.1,61.2,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,36668,2015-10-30 11:03:14:899\n0.0958,-0.1137,-9.8509,0.0829,-0.1091,-9.8055,0,0.0012,-0.0012,33.6,-76.1,61.4,155.76,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,36770,2015-10-30 11:03:15:001\n0.0778,-0.1006,-9.8641,0.0829,-0.1101,-9.8055,0.0012,0.0012,0,33.6,-76,61.5,155.76,0.64,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,36872,2015-10-30 11:03:15:103\n0.0778,-0.1137,-9.8749,0.0827,-0.1106,-9.8055,-0.0012,0.0024,0,33.7,-75.9,61.3,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,36974,2015-10-30 11:03:15:205\n0.0886,-0.1137,-9.8521,0.0826,-0.1104,-9.8055,-0.0012,0.0012,0,33.7,-75.8,61.3,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,37076,2015-10-30 11:03:15:307\n0.0826,-0.1173,-9.8869,0.0828,-0.1104,-9.8055,0.0012,0.0024,-0.0012,33.7,-75.9,61.4,155.77,0.65,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,37178,2015-10-30 11:03:15:409\n0.0874,-0.0958,-9.8593,0.0836,-0.1105,-9.8055,-0.0024,0.0012,0.0024,33.8,-76,61.4,155.76,0.65,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,37279,2015-10-30 11:03:15:510\n0.0958,-0.1209,-9.8509,0.0832,-0.1095,-9.8055,-0.0012,0.0012,0,33.8,-76.1,61.4,155.76,0.64,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,37382,2015-10-30 11:03:15:613\n0.0826,-0.1161,-9.8689,0.0828,-0.1097,-9.8055,0.0024,0,0,33.8,-76.1,61.4,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,37484,2015-10-30 11:03:15:715\n0.0766,-0.1173,-9.8773,0.0829,-0.1097,-9.8055,-0.0012,0.0012,0.0012,33.7,-76,61.5,155.76,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,37586,2015-10-30 11:03:15:817\n0.085,-0.1137,-9.8581,0.0832,-0.109,-9.8055,-0.0012,0.0012,0.0024,33.6,-75.9,61.8,155.76,0.64,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,37688,2015-10-30 11:03:15:919\n0.0814,-0.1113,-9.8533,0.0829,-0.1091,-9.8055,0,0.0024,-0.0012,33.6,-75.8,61.8,155.76,0.64,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,37790,2015-10-30 11:03:16:021\n0.0694,-0.1125,-9.8581,0.0831,-0.1086,-9.8055,-0.0012,0.0012,0.0012,33.5,-75.7,61.6,155.76,0.63,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,37892,2015-10-30 11:03:16:123\n0.0802,-0.1077,-9.8509,0.0825,-0.1091,-9.8055,0.0024,0.0024,0,33.6,-75.9,61.2,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,37994,2015-10-30 11:03:16:225\n0.0838,-0.1113,-9.8557,0.0824,-0.1092,-9.8055,0.0012,0.0037,0,33.7,-75.9,61.1,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,38096,2015-10-30 11:03:16:327\n0.1006,-0.103,-9.8509,0.0828,-0.1099,-9.8056,0.0012,0.0024,0,33.7,-76,61.1,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,38198,2015-10-30 11:03:16:429\n0.0934,-0.1125,-9.8485,0.0821,-0.1096,-9.8055,0,0.0012,-0.0012,33.6,-76,61.1,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,38299,2015-10-30 11:03:16:530\n0.0778,-0.1113,-9.8605,0.0824,-0.1088,-9.8056,-0.0012,0.0037,0,33.6,-76,61,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,38402,2015-10-30 11:03:16:633\n0.091,-0.1161,-9.8485,0.0822,-0.1092,-9.8056,0.0024,0.0024,0,33.8,-76,61.1,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,38504,2015-10-30 11:03:16:735\n0.0862,-0.1065,-9.8521,0.0821,-0.1097,-9.8056,0.0024,0.0037,0,33.7,-76,61.3,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,38606,2015-10-30 11:03:16:837\n0.0826,-0.1018,-9.8593,0.0818,-0.1102,-9.8056,0.0012,0.0012,-0.0012,33.7,-76,61.3,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,38708,2015-10-30 11:03:16:939\n0.091,-0.1089,-9.8509,0.0814,-0.1101,-9.8056,-0.0012,0,0,33.7,-75.9,61.1,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,38810,2015-10-30 11:03:17:041\n0.0898,-0.1101,-9.8509,0.0811,-0.1096,-9.8055,0.0012,0.0024,0,33.8,-76,60.8,155.77,0.64,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,38912,2015-10-30 11:03:17:143\n0.085,-0.1077,-9.8617,0.0816,-0.1094,-9.8055,0.0024,0.0024,-0.0012,33.8,-76,60.8,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,39015,2015-10-30 11:03:17:246\n0.085,-0.1077,-9.8593,0.0821,-0.109,-9.8055,-0.0012,0.0037,0.0012,33.8,-76,60.8,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,39116,2015-10-30 11:03:17:347\n0.0826,-0.1113,-9.8533,0.0813,-0.1098,-9.8056,0.0037,0,-0.0012,33.7,-76,60.6,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,39217,2015-10-30 11:03:17:448\n0.0814,-0.1041,-9.8545,0.0816,-0.1103,-9.8055,-0.0012,0,-0.0012,33.6,-76,60.3,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,39320,2015-10-30 11:03:17:551\n0.0886,-0.1149,-9.8569,0.0815,-0.1099,-9.8055,-0.0012,0.0012,0.0012,33.6,-76,60.4,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,39422,2015-10-30 11:03:17:653\n0.0682,-0.1041,-9.8545,0.0807,-0.11,-9.8055,0.0012,0.0012,0.0012,33.6,-76.1,60.7,155.77,0.64,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,39524,2015-10-30 11:03:17:755\n0.0862,-0.1125,-9.8533,0.0803,-0.1105,-9.8055,0,0.0012,0.0012,33.6,-76,60.9,155.78,0.65,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,39626,2015-10-30 11:03:17:857\n0.0898,-0.1113,-9.8557,0.0803,-0.1103,-9.8055,-0.0012,0.0012,-0.0012,33.6,-76.1,60.9,155.78,0.64,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,39728,2015-10-30 11:03:17:959\n0.0754,-0.1137,-9.8557,0.0805,-0.1099,-9.8055,0.0012,0.0024,0,33.6,-76.1,61,155.78,0.64,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,39830,2015-10-30 11:03:18:061\n0.0802,-0.1089,-9.8593,0.0806,-0.1097,-9.8056,0.0024,0.0024,0.0012,33.5,-76.1,61.1,155.77,0.64,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,39932,2015-10-30 11:03:18:163\n0.0934,-0.1053,-9.8509,0.0815,-0.1096,-9.8055,0,0.0049,0,33.4,-76,61.2,156.4,0.64,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,40034,2015-10-30 11:03:18:265\n0.0802,-0.1089,-9.8617,0.0818,-0.1093,-9.8055,0,0,0.0012,33.4,-76,61.3,156.39,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,40136,2015-10-30 11:03:18:367\n0.0874,-0.1137,-9.8485,0.0816,-0.1098,-9.8055,0.0012,0.0012,0.0012,33.4,-75.9,61.3,156.4,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,40238,2015-10-30 11:03:18:469\n0.0886,-0.1065,-9.8545,0.082,-0.1102,-9.8055,0.0024,0.0012,-0.0012,33.6,-76,61,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,40340,2015-10-30 11:03:18:571\n0.0718,-0.1113,-9.8462,0.0815,-0.1108,-9.8055,0,0.0012,0.0012,33.7,-76,60.7,155.77,0.65,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,40442,2015-10-30 11:03:18:673\n0.0802,-0.1053,-9.8665,0.0806,-0.1107,-9.8055,0,0,0,33.7,-76,60.7,155.78,0.65,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,40544,2015-10-30 11:03:18:775\n0.0982,-0.1113,-9.8509,0.0808,-0.1105,-9.8056,0.0024,0.0024,0,33.7,-75.9,60.8,155.77,0.65,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,40646,2015-10-30 11:03:18:877\n0.0706,-0.1161,-9.8725,0.0809,-0.1109,-9.8056,0,0.0012,0.0024,33.7,-75.9,61,155.77,0.65,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,40748,2015-10-30 11:03:18:979\n0.0718,-0.103,-9.8509,0.0812,-0.1105,-9.8056,0.0024,0.0024,0,33.7,-75.9,61,155.77,0.65,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,40850,2015-10-30 11:03:19:081\n0.0694,-0.1173,-9.8509,0.0815,-0.1106,-9.8055,0,-0.0012,0.0012,33.7,-75.9,60.9,155.77,0.65,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,40952,2015-10-30 11:03:19:183\n0.085,-0.1197,-9.8414,0.0809,-0.1099,-9.8055,0,0,0,33.6,-75.9,60.7,155.77,0.64,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,41054,2015-10-30 11:03:19:285\n0.0874,-0.1161,-9.8509,0.0821,-0.1096,-9.8056,0,0.0037,-0.0012,33.6,-75.9,60.8,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,41156,2015-10-30 11:03:19:387\n0.0778,-0.1053,-9.8485,0.0823,-0.1107,-9.8056,0.0012,0.0037,0,33.6,-75.9,61,155.77,0.65,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,41258,2015-10-30 11:03:19:489\n0.073,-0.1113,-9.845,0.0828,-0.1108,-9.8056,-0.0012,0,-0.0012,33.5,-76,61,155.77,0.65,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,41359,2015-10-30 11:03:19:590\n0.079,-0.1113,-9.8773,0.082,-0.1108,-9.8055,0,0.0012,-0.0012,33.5,-75.9,61.1,155.77,0.65,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,41462,2015-10-30 11:03:19:693\n0.0838,-0.1125,-9.8557,0.0822,-0.1098,-9.8056,-0.0012,0.0024,0,33.5,-76,61,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,41564,2015-10-30 11:03:19:795\n0.0898,-0.1149,-9.8617,0.0823,-0.1098,-9.8056,0.0024,0.0037,-0.0024,33.6,-76.1,60.8,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,41666,2015-10-30 11:03:19:897\n0.073,-0.1161,-9.8521,0.0827,-0.11,-9.8055,-0.0024,0,0.0012,33.5,-76.1,60.8,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,41768,2015-10-30 11:03:19:999\n0.0862,-0.1077,-9.8521,0.0825,-0.1105,-9.8055,0.0024,0.0024,0.0012,33.6,-76.1,60.9,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,41870,2015-10-30 11:03:20:101\n0.0814,-0.1113,-9.8629,0.0827,-0.111,-9.8055,0.0012,0.0024,-0.0012,33.5,-76,60.9,155.77,0.65,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,41971,2015-10-30 11:03:20:202\n0.0802,-0.1053,-9.8593,0.0829,-0.1112,-9.8055,0.0012,0.0024,0,33.6,-76,61,155.77,0.65,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,42074,2015-10-30 11:03:20:305\n0.091,-0.1113,-9.8509,0.083,-0.1115,-9.8055,0.0037,0.0012,-0.0024,33.5,-75.9,61.4,155.77,0.65,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,42176,2015-10-30 11:03:20:407\n0.0826,-0.1113,-9.8545,0.0833,-0.1116,-9.8055,0.0012,0.0012,0,33.6,-75.9,61.3,155.77,0.65,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,42278,2015-10-30 11:03:20:509\n0.0706,-0.1161,-9.8605,0.0825,-0.1113,-9.8055,0.0024,0.0037,0,33.7,-76,61.1,155.77,0.65,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,42380,2015-10-30 11:03:20:611\n0.079,-0.1245,-9.8677,0.0826,-0.111,-9.8055,0.0012,0,0,33.7,-75.9,60.9,155.77,0.65,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,42482,2015-10-30 11:03:20:713\n0.085,-0.0958,-9.8509,0.0823,-0.1113,-9.8055,0.0024,0.0012,-0.0012,33.6,-75.9,61.1,155.77,0.65,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,42583,2015-10-30 11:03:20:814\n0.0766,-0.103,-9.8569,0.0826,-0.1114,-9.8055,0.0024,0.0012,-0.0024,33.3,-75.9,61.1,156.39,0.65,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,42686,2015-10-30 11:03:20:917\n0.0934,-0.1209,-9.8605,0.0831,-0.1111,-9.8055,0,0.0012,0,33.3,-75.9,61.3,156.39,0.65,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,42788,2015-10-30 11:03:21:019\n0.0958,-0.1149,-9.8569,0.0829,-0.1105,-9.8055,0,0.0024,0,33.2,-75.8,61,156.39,0.65,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,42890,2015-10-30 11:03:21:121\n0.0994,-0.1018,-9.8521,0.0831,-0.111,-9.8055,0.0012,0.0012,-0.0012,33.4,-75.9,61.1,156.39,0.65,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,42991,2015-10-30 11:03:21:222\n0.0814,-0.1137,-9.8629,0.0825,-0.1114,-9.8055,0.0012,0.0024,0,33.5,-75.9,60.6,155.77,0.65,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,43094,2015-10-30 11:03:21:325\n0.0886,-0.1089,-9.8509,0.0827,-0.1115,-9.8055,-0.0012,0.0024,-0.0012,33.6,-76,60.6,155.77,0.65,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,43196,2015-10-30 11:03:21:427\n0.0814,-0.1041,-9.8581,0.0825,-0.1114,-9.8055,0.0024,0.0024,0,33.5,-76,60.4,155.77,0.65,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,43297,2015-10-30 11:03:21:528\n0.0766,-0.1041,-9.8509,0.0829,-0.1116,-9.8055,0.0024,0.0012,0.0012,33.6,-76,60.7,155.77,0.65,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,43399,2015-10-30 11:03:21:630\n0.0922,-0.1161,-9.8533,0.0833,-0.1111,-9.8055,0,0.0024,-0.0012,33.7,-76,61,155.77,0.65,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,43502,2015-10-30 11:03:21:733\n0.0934,-0.1137,-9.8485,0.083,-0.111,-9.8055,0,0,0.0012,33.7,-76.1,61.3,155.77,0.65,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,43604,2015-10-30 11:03:21:835\n0.0778,-0.1113,-9.8593,0.0826,-0.1103,-9.8055,0.0012,0.0024,0.0012,33.7,-76,61.5,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,43706,2015-10-30 11:03:21:937\n0.0742,-0.1077,-9.8509,0.083,-0.11,-9.8055,-0.0012,0.0024,0.0012,33.6,-75.8,61.6,155.76,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,43808,2015-10-30 11:03:22:039\n0.0742,-0.103,-9.8701,0.0833,-0.1105,-9.8055,-0.0012,0.0024,0,33.6,-75.8,61.4,155.76,0.65,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,43910,2015-10-30 11:03:22:141\n0.0922,-0.1101,-9.8354,0.0829,-0.1106,-9.8055,0.0024,0.0012,-0.0024,33.7,-75.9,61.2,155.77,0.65,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,44012,2015-10-30 11:03:22:243\n0.0934,-0.1209,-9.8509,0.0824,-0.1102,-9.8055,0,0,-0.0012,33.8,-75.9,61.1,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,44114,2015-10-30 11:03:22:345\n0.0826,-0.1161,-9.8617,0.0816,-0.1101,-9.8055,0.0012,0.0012,-0.0012,33.7,-76.1,61,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,44216,2015-10-30 11:03:22:447\n0.0934,-0.1065,-9.8557,0.0818,-0.1101,-9.8055,0.0024,-0.0012,0,33.6,-76,60.9,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,44318,2015-10-30 11:03:22:549\n0.0826,-0.1101,-9.8533,0.0819,-0.1102,-9.8055,0.0012,0.0024,-0.0012,33.5,-75.9,61,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,44420,2015-10-30 11:03:22:651\n0.0922,-0.1065,-9.8533,0.0816,-0.1107,-9.8055,-0.0012,0,0.0012,33.5,-75.9,61.3,155.77,0.65,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,44522,2015-10-30 11:03:22:753\n0.0778,-0.1209,-9.8509,0.0817,-0.111,-9.8055,0.0012,0.0012,-0.0012,33.3,-75.9,61.5,156.39,0.65,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,44624,2015-10-30 11:03:22:855\n0.0778,-0.1233,-9.8509,0.0815,-0.1111,-9.8055,-0.0012,0.0024,0.0012,33.3,-76,61.4,156.4,0.65,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,44726,2015-10-30 11:03:22:957\n0.0874,-0.1065,-9.8533,0.0827,-0.1113,-9.8055,0,0.0024,0.0012,33.2,-75.9,61.7,156.39,0.65,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,44828,2015-10-30 11:03:23:059\n0.0898,-0.1113,-9.8665,0.0821,-0.1107,-9.8055,-0.0012,0.0024,0,33.3,-76,62,156.39,0.65,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,44930,2015-10-30 11:03:23:161\n0.0682,-0.1077,-9.8521,0.0819,-0.11,-9.8055,-0.0012,0.0012,0,33.4,-76,62.2,156.39,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,45032,2015-10-30 11:03:23:263\n0.0982,-0.1018,-9.8509,0.0823,-0.1092,-9.8055,0,0.0024,0.0012,33.5,-76.1,62.3,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,45134,2015-10-30 11:03:23:365\n0.0742,-0.1101,-9.8557,0.0818,-0.1093,-9.8055,0.0012,0.0037,0.0012,33.4,-76,62,156.39,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,45236,2015-10-30 11:03:23:467\n0.067,-0.1125,-9.8557,0.0817,-0.1091,-9.8055,0,0.0037,0,33.5,-76,62,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,45338,2015-10-30 11:03:23:569\n0.0898,-0.1113,-9.8438,0.0819,-0.1085,-9.8056,-0.0012,0.0024,0.0012,33.5,-75.9,61.8,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,45440,2015-10-30 11:03:23:671\n0.0742,-0.1149,-9.8509,0.0815,-0.108,-9.8055,0.0012,0,0,33.5,-75.9,61.6,155.77,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,45542,2015-10-30 11:03:23:773\n0.0766,-0.1209,-9.8509,0.0809,-0.1085,-9.8055,0,0,0.0012,33.5,-76.1,61.8,155.77,0.63,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,45644,2015-10-30 11:03:23:875\n0.1018,-0.1113,-9.8593,0.0809,-0.108,-9.8055,0.0012,0,0,33.5,-76.1,61.7,155.77,0.63,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,45746,2015-10-30 11:03:23:977\n0.0814,-0.103,-9.8593,0.0809,-0.108,-9.8055,0,0,-0.0012,33.5,-76.1,61.7,155.77,0.63,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,45848,2015-10-30 11:03:24:079\n0.0886,-0.1089,-9.8569,0.0812,-0.1075,-9.8056,0,0.0012,0,33.5,-76,61.3,155.77,0.63,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,45950,2015-10-30 11:03:24:181\n0.0886,-0.1293,-9.8665,0.0816,-0.1076,-9.8056,0.0024,-0.0012,0,33.4,-75.9,61.3,156.39,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,46051,2015-10-30 11:03:24:282\n0.0706,-0.103,-9.8593,0.081,-0.1076,-9.8056,-0.0012,0.0012,0,33.4,-75.9,61.2,156.39,0.63,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,46154,2015-10-30 11:03:24:385\n0.0898,-0.0994,-9.8509,0.0814,-0.1079,-9.8056,0.0024,0.0012,-0.0012,33.3,-75.9,61.1,156.39,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,46256,2015-10-30 11:03:24:487\n0.091,-0.1185,-9.8557,0.0824,-0.1075,-9.8056,0.0012,-0.0012,-0.0012,33.4,-76,60.8,156.39,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,46358,2015-10-30 11:03:24:589\n0.0982,-0.097,-9.8246,0.0821,-0.1088,-9.8055,0,0,0.0012,33.5,-76,61,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,46460,2015-10-30 11:03:24:691\n0.0838,-0.1173,-9.8533,0.0825,-0.1088,-9.8055,0,0.0024,0,33.5,-76.1,61.1,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,46562,2015-10-30 11:03:24:793\n0.0814,-0.1113,-9.8605,0.0826,-0.1091,-9.8055,0.0024,0.0012,-0.0012,33.5,-75.9,61.2,155.76,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,46663,2015-10-30 11:03:24:894\n0.0934,-0.1041,-9.8509,0.0826,-0.1096,-9.8055,0.0012,0.0012,0.0012,33.4,-75.9,60.9,156.39,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,46766,2015-10-30 11:03:24:997\n0.0778,-0.1065,-9.8521,0.0825,-0.1093,-9.8056,0,-0.0012,0,33.4,-75.9,60.9,156.39,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,46868,2015-10-30 11:03:25:099\n0.079,-0.1125,-9.8569,0.0823,-0.1091,-9.8055,0.0012,0.0024,-0.0012,33.4,-75.8,60.9,156.39,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,46970,2015-10-30 11:03:25:201\n0.085,-0.1018,-9.8509,0.0823,-0.1092,-9.8056,0.0012,0.0037,0.0012,33.5,-75.8,60.8,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,47072,2015-10-30 11:03:25:303\n0.0718,-0.1077,-9.8485,0.0829,-0.1097,-9.8055,0.0024,0.0024,-0.0012,33.6,-75.9,60.9,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,47174,2015-10-30 11:03:25:405\n0.0802,-0.103,-9.8629,0.0823,-0.1092,-9.8055,0.0012,0.0012,-0.0012,33.4,-76,61,156.39,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,47276,2015-10-30 11:03:25:507\n0.0862,-0.1149,-9.8617,0.0818,-0.1089,-9.8056,0.0024,0,0.0012,33.5,-76,60.9,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,47378,2015-10-30 11:03:25:609\n0.0826,-0.1161,-9.8617,0.0816,-0.1091,-9.8055,0,0.0012,0.0012,33.6,-76,60.8,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,47480,2015-10-30 11:03:25:711\n0.0766,-0.1185,-9.8833,0.0816,-0.1094,-9.8055,0.0012,0.0012,0.0012,33.7,-76,61,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,47582,2015-10-30 11:03:25:813\n0.0634,-0.1041,-9.8462,0.0816,-0.1086,-9.8056,0.0012,0.0024,0.0012,33.7,-76.1,61.1,155.77,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,47684,2015-10-30 11:03:25:915\n0.091,-0.1065,-9.8509,0.0812,-0.1083,-9.8056,0.0012,0.0012,-0.0012,33.7,-76.1,61.1,155.77,0.63,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,47786,2015-10-30 11:03:26:017\n0.079,-0.1161,-9.8557,0.0817,-0.1087,-9.8056,0,0.0037,0,33.7,-76,61.4,155.77,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,47888,2015-10-30 11:03:26:119\n0.079,-0.1089,-9.8533,0.0814,-0.1092,-9.8055,0.0024,0.0012,-0.0012,33.8,-76,61.7,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,47990,2015-10-30 11:03:26:221\n0.0874,-0.1101,-9.8521,0.0816,-0.109,-9.8055,0.0024,0.0024,-0.0012,33.9,-76,61.6,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,48092,2015-10-30 11:03:26:323\n0.0694,-0.1089,-9.8581,0.0819,-0.1091,-9.8056,0.0012,0.0012,0,33.9,-76,61.4,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,48194,2015-10-30 11:03:26:425\n0.0778,-0.0994,-9.8629,0.0815,-0.11,-9.8055,0.0012,0,-0.0012,33.9,-76,61,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,48296,2015-10-30 11:03:26:527\n0.0814,-0.1065,-9.8521,0.0816,-0.1104,-9.8055,0.0012,0.0024,-0.0012,33.9,-76,61,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,48398,2015-10-30 11:03:26:629\n0.0802,-0.1101,-9.8509,0.082,-0.1104,-9.8055,0.0024,0.0012,0,33.9,-76,61.1,155.77,0.65,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,48500,2015-10-30 11:03:26:731\n0.073,-0.1149,-9.8629,0.0817,-0.1102,-9.8056,0,0,-0.0012,33.8,-75.9,61.5,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,48602,2015-10-30 11:03:26:833\n0.0922,-0.1053,-9.8533,0.0823,-0.1094,-9.8056,0,0.0024,0,33.7,-76.1,61.7,155.77,0.64,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,48704,2015-10-30 11:03:26:935\n0.0862,-0.1113,-9.8569,0.0826,-0.1085,-9.8056,0.0024,0.0024,-0.0024,33.6,-76,61.9,155.76,0.63,-179.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,48806,2015-10-30 11:03:27:037\n0.0814,-0.1173,-9.8641,0.0832,-0.1091,-9.8055,0.0012,0.0024,-0.0012,33.7,-76,61.8,155.76,0.64,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,48908,2015-10-30 11:03:27:139\n0.0922,-0.0982,-9.8509,0.0836,-0.1093,-9.8055,-0.0012,0.0024,0.0012,33.7,-75.9,61.4,155.76,0.64,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,49010,2015-10-30 11:03:27:241\n0.0826,-0.1101,-9.8689,0.0845,-0.11,-9.8055,0,0.0037,0,33.7,-75.9,61.3,155.76,0.64,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,49112,2015-10-30 11:03:27:343\n0.073,-0.1065,-9.8617,0.0847,-0.1098,-9.8055,0,0.0012,-0.0012,33.6,-76,61.2,155.76,0.64,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,49214,2015-10-30 11:03:27:445\n0.0802,-0.0982,-9.8581,0.0844,-0.1096,-9.8055,0.0037,0,-0.0012,33.6,-76,61.6,155.76,0.64,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,49316,2015-10-30 11:03:27:547\n0.0802,-0.1125,-9.8509,0.0834,-0.1101,-9.8055,0.0024,0.0012,0.0012,33.7,-76,61.6,155.76,0.64,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,49418,2015-10-30 11:03:27:649\n0.0682,-0.1089,-9.8593,0.0826,-0.1098,-9.8055,-0.0012,0.0012,0,33.6,-76,62,155.76,0.64,-179.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,49520,2015-10-30 11:03:27:751\n0.0826,-0.103,-9.8605,0.0808,-0.1096,-9.8056,0,0.0024,-0.0012,33.7,-75.9,61.9,155.77,0.64,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,49622,2015-10-30 11:03:27:853\n0.103,-0.1209,-9.8509,0.0797,-0.1097,-9.8056,0.0012,0.0012,0,33.6,-75.9,61.5,155.78,0.64,-179.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,49724,2015-10-30 11:03:27:955\n0.0766,-0.0982,-9.8593,0.0791,-0.1094,-9.8056,-0.0012,0.0024,-0.0012,33.7,-76,61.3,155.78,0.64,-179.54,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,49826,2015-10-30 11:03:28:057\n0.0838,-0.0994,-9.8521,0.0781,-0.1087,-9.8056,0.0037,-0.0024,0,33.7,-76,61.4,155.78,0.64,-179.54,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,49928,2015-10-30 11:03:28:159\n0.0814,-0.1101,-9.8533,0.0779,-0.1088,-9.8056,0.0037,0.0024,-0.0024,33.7,-76.1,61.6,155.78,0.64,-179.55,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,50030,2015-10-30 11:03:28:261\n0.0682,-0.1173,-9.8581,0.0768,-0.1084,-9.8056,0.0012,0.0012,0,33.7,-76.1,61.3,155.79,0.63,-179.55,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,50132,2015-10-30 11:03:28:363\n0.091,-0.1125,-9.8809,0.0765,-0.1081,-9.8056,0,0.0012,0.0024,33.7,-76,61.5,155.78,0.63,-179.55,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,50234,2015-10-30 11:03:28:465\n0.0814,-0.0982,-9.8485,0.0757,-0.1082,-9.8056,0.0012,0.0012,0,33.7,-76,61.2,155.79,0.63,-179.56,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,50336,2015-10-30 11:03:28:567\n0.0826,-0.1209,-9.8701,0.0755,-0.1092,-9.8056,0.0012,0,0.0012,33.8,-76,61.2,155.79,0.64,-179.56,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,50438,2015-10-30 11:03:28:669\n0.091,-0.1245,-9.8749,0.0762,-0.1094,-9.8056,-0.0024,0.0024,-0.0012,33.7,-76,61,155.79,0.64,-179.55,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,50540,2015-10-30 11:03:28:771\n0.0802,-0.1233,-9.8605,0.0772,-0.1091,-9.8056,0,0.0024,0,33.7,-76,61.1,155.79,0.64,-179.55,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,50642,2015-10-30 11:03:28:873\n0.091,-0.1149,-9.8641,0.0783,-0.1085,-9.8056,0.0024,0.0024,-0.0012,33.7,-76,61.1,155.78,0.63,-179.54,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,50744,2015-10-30 11:03:28:975\n0.0778,-0.1209,-9.8845,0.0782,-0.1073,-9.8056,-0.0037,0,0.0012,33.8,-76,61.1,155.78,0.63,-179.54,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,50846,2015-10-30 11:03:29:077\n0.0766,-0.0958,-9.8605,0.0778,-0.1053,-9.8056,0.0037,0.0049,0,33.7,-76,60.7,155.78,0.62,-179.55,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,50948,2015-10-30 11:03:29:179\n0.085,-0.1041,-9.8904,0.08,-0.1071,-9.8056,0.0061,0.0024,0,33.7,-76,60.6,155.77,0.62,-179.54,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,51050,2015-10-30 11:03:29:281\n"
  },
  {
    "path": "test/data/Sensor_record_20151030_110417_AndroSensor.csv",
    "content": "9.6391,-0.1006,-0.6812,9.7822,-0.1122,-0.6817,0,-0.0208,0,-101.5,-57.1,3.7,182.98,0.66,-93.99,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,55,2015-10-30 11:03:42:585\n9.6199,-0.1209,-0.7242,9.7809,-0.1123,-0.7013,-0.0024,-0.0098,0,-101.5,-57.2,3.6,183.15,0.66,-94.08,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,156,2015-10-30 11:03:42:686\n9.6426,-0.1053,-0.7171,9.7806,-0.1119,-0.7044,0.0012,0.0024,-0.0012,-101.5,-57.2,3.7,183.22,0.65,-94.12,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,259,2015-10-30 11:03:42:789\n9.6151,-0.1101,-0.7338,9.7807,-0.1116,-0.704,0.0012,-0.011,0.0012,-101.4,-57.1,4.1,183.21,0.65,-94.12,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,365,2015-10-30 11:03:42:895\n9.6247,-0.1113,-0.7195,9.7807,-0.1115,-0.704,-0.0012,0.0073,0.0012,-101.5,-57,4.2,183.21,0.65,-94.12,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,463,2015-10-30 11:03:42:993\n9.6367,-0.1065,-0.7302,9.7804,-0.1114,-0.7085,0.0012,-0.0134,0.0024,-101.6,-56.9,4.3,183.31,0.65,-94.13,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,564,2015-10-30 11:03:43:094\n9.6223,-0.1161,-0.7207,9.781,-0.11,-0.7003,0,0.011,-0.0012,-101.6,-56.8,4.4,183.24,0.64,-94.1,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,667,2015-10-30 11:03:43:197\n9.6283,-0.1113,-0.7195,9.7818,-0.109,-0.6882,0,0.0183,-0.0024,-101.6,-56.8,4.2,183.12,0.64,-94.02,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,769,2015-10-30 11:03:43:299\n9.6498,-0.091,-0.7015,9.7825,-0.1076,-0.6794,0,0.0147,0,-101.6,-56.8,4.4,183.02,0.63,-93.97,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,870,2015-10-30 11:03:43:400\n9.6211,-0.1257,-0.7195,9.7827,-0.1068,-0.6756,0,0.0086,-0.0012,-101.6,-56.9,4.2,183.02,0.63,-93.97,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,973,2015-10-30 11:03:43:503\n9.6223,-0.1053,-0.7075,9.783,-0.1054,-0.6723,0.0024,0.0232,-0.0024,-101.6,-56.9,4.3,182.99,0.62,-93.95,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,1075,2015-10-30 11:03:43:605\n9.6426,-0.1089,-0.6883,9.7836,-0.1045,-0.6635,0.0024,0.0183,0.0012,-101.7,-56.9,4.3,182.88,0.61,-93.89,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,1176,2015-10-30 11:03:43:706\n9.6247,-0.1173,-0.6991,9.7843,-0.1036,-0.6523,0.0012,0.0183,0,-101.6,-57,4.1,182.75,0.61,-93.81,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,1279,2015-10-30 11:03:43:809\n9.6139,-0.1018,-0.6931,9.785,-0.1033,-0.6427,0,0,-0.0012,-101.6,-57,3.7,182.66,0.6,-93.76,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,1381,2015-10-30 11:03:43:911\n9.6391,-0.1101,-0.6919,9.7854,-0.1024,-0.6364,0.0037,0.0134,-0.0012,-101.6,-57,3.6,182.6,0.6,-93.72,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,1483,2015-10-30 11:03:44:013\n9.6486,-0.1053,-0.674,9.7859,-0.1016,-0.6284,0.0024,0.0098,-0.0024,-101.7,-57,3.8,182.51,0.59,-93.67,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,1585,2015-10-30 11:03:44:115\n9.6235,-0.1161,-0.6752,9.7861,-0.1007,-0.6258,0.0012,0.0049,0.0012,-101.6,-57,3.4,183.47,0.59,-93.66,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,1687,2015-10-30 11:03:44:217\n9.6283,-0.1006,-0.6716,9.786,-0.1002,-0.6269,0.0012,-0.0098,-0.0012,-101.6,-57,3.3,183.48,0.59,-93.67,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,1789,2015-10-30 11:03:44:319\n9.645,-0.1018,-0.6632,9.7856,-0.0985,-0.634,0.0012,0.0012,-0.0024,-101.7,-57,3.1,183.54,0.58,-93.7,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,1891,2015-10-30 11:03:44:421\n9.6307,-0.1101,-0.6644,9.7856,-0.0974,-0.6343,0.0037,0,-0.0012,-101.7,-56.9,3.3,183.56,0.57,-93.71,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,1993,2015-10-30 11:03:44:523\n9.6522,-0.0862,-0.6452,9.7858,-0.0972,-0.6313,0,0.0086,-0.0012,-101.7,-56.9,3.1,183.54,0.57,-93.7,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,2095,2015-10-30 11:03:44:625\n9.6462,-0.1006,-0.6464,9.7857,-0.097,-0.6323,0.0012,-0.0024,-0.0012,-101.6,-57,3.1,183.53,0.57,-93.7,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,2196,2015-10-30 11:03:44:726\n9.6307,-0.1089,-0.65,9.7854,-0.0958,-0.6371,0,0.0024,-0.0012,-101.6,-57,3,183.58,0.56,-93.72,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,2299,2015-10-30 11:03:44:829\n9.6426,-0.1077,-0.6464,9.7849,-0.0952,-0.6446,-0.0012,-0.0086,-0.0024,-101.7,-57,3.3,183.66,0.56,-93.77,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,2401,2015-10-30 11:03:44:931\n9.6438,-0.0862,-0.6536,9.7843,-0.0948,-0.6537,0,-0.0049,-0.0012,-101.6,-57.2,3.3,183.76,0.55,-93.82,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,2502,2015-10-30 11:03:45:032\n9.6271,-0.0958,-0.6656,9.784,-0.0943,-0.6587,0.0012,0.0037,-0.0037,-101.6,-57,3.4,183.81,0.56,-93.86,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,2605,2015-10-30 11:03:45:135\n9.6247,-0.103,-0.6524,9.784,-0.0938,-0.6581,0.0012,0.0024,-0.0037,-101.7,-57.1,2.6,183.8,0.55,-93.85,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,2707,2015-10-30 11:03:45:237\n9.6486,-0.1018,-0.6452,9.784,-0.0925,-0.6584,-0.0012,0,0.0012,-101.8,-57,2.5,183.81,0.54,-93.85,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,2809,2015-10-30 11:03:45:339\n9.6391,-0.0982,-0.6273,9.7843,-0.0927,-0.6548,0,0.0073,0,-101.9,-56.9,2.1,184.75,0.54,-93.83,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,2911,2015-10-30 11:03:45:441\n9.6355,-0.0982,-0.6369,9.7856,-0.0927,-0.6342,0.0012,0.0195,-0.0012,-101.8,-56.9,2.4,184.6,0.54,-93.74,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,3013,2015-10-30 11:03:45:543\n9.6355,-0.1006,-0.6117,9.7862,-0.0934,-0.6257,0.0012,0.0134,0,-101.8,-56.9,2.4,184.45,0.55,-93.66,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,3115,2015-10-30 11:03:45:645\n9.6367,-0.1233,-0.6105,9.7869,-0.0945,-0.614,-0.0012,0.0061,0,-101.8,-56.9,2.2,184.37,0.55,-93.61,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,3217,2015-10-30 11:03:45:747\n9.6223,-0.1018,-0.583,9.7871,-0.0953,-0.6102,-0.0012,0.0171,0,-101.5,-57.1,2.2,184.23,0.56,-93.57,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,3319,2015-10-30 11:03:45:849\n9.6462,-0.0982,-0.577,9.7878,-0.096,-0.6001,0.0024,0.011,0.0012,-101.5,-57.2,3.2,183.15,0.56,-93.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,3421,2015-10-30 11:03:45:951\n9.6403,-0.1018,-0.565,9.7882,-0.0955,-0.5924,-0.0024,0.0012,-0.0012,-101.6,-57.1,3.3,183.14,0.56,-93.47,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,3523,2015-10-30 11:03:46:053\n9.6391,-0.1065,-0.5567,9.7887,-0.0953,-0.5851,0.0024,0.0159,0,-101.8,-57.1,3.3,183.05,0.56,-93.42,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,3625,2015-10-30 11:03:46:155\n9.6522,-0.0934,-0.5531,9.7887,-0.0955,-0.5849,0.0024,-0.0037,0,-101.8,-57,3.1,183.03,0.56,-93.41,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,3727,2015-10-30 11:03:46:257\n9.6642,-0.0886,-0.5602,9.7886,-0.0956,-0.5856,-0.0012,-0.0171,-0.0024,-101.8,-57,3.4,183.06,0.56,-93.42,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,3829,2015-10-30 11:03:46:359\n9.6223,-0.097,-0.5806,9.7877,-0.0941,-0.601,0.0049,-0.0086,-0.0037,-101.7,-56.9,3.5,182.21,0.55,-93.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,3931,2015-10-30 11:03:46:461\n9.6259,-0.0898,-0.5698,9.7875,-0.0936,-0.6052,0.0012,-0.0086,0.0012,-101.8,-56.9,3.6,182.27,0.55,-93.54,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,4033,2015-10-30 11:03:46:563\n9.6474,-0.1065,-0.5698,9.7874,-0.0925,-0.6069,0.0012,0.0159,-0.0024,-101.8,-57,3.4,183.34,0.54,-93.58,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,4135,2015-10-30 11:03:46:665\n9.6223,-0.103,-0.589,9.7864,-0.0919,-0.6224,0,-0.0354,0,-101.6,-57.1,3.2,183.44,0.54,-93.64,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,4237,2015-10-30 11:03:46:767\n9.6474,-0.0802,-0.5758,9.7862,-0.0918,-0.626,0.0012,-0.0269,-0.0012,-101.5,-57.2,3.1,183.34,0.54,-93.62,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,4339,2015-10-30 11:03:46:869\n9.6522,-0.0922,-0.5555,9.786,-0.0913,-0.6295,-0.0024,-0.0061,-0.0024,-101.6,-57.1,3.2,183.51,0.54,-93.68,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,4441,2015-10-30 11:03:46:971\n9.6331,-0.1041,-0.559,9.7852,-0.092,-0.6405,0.0012,-0.0098,0,-101.7,-57,2.7,183.62,0.54,-93.75,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,4542,2015-10-30 11:03:47:072\n9.6426,-0.0886,-0.583,9.7844,-0.0922,-0.6529,0.0037,-0.0147,0,-101.6,-57,2.4,184.72,0.54,-93.81,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,4645,2015-10-30 11:03:47:175\n9.6606,-0.0862,-0.5866,9.7847,-0.092,-0.6492,0.0012,0.0024,0,-101.4,-57.1,2.5,183.65,0.54,-93.8,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,4747,2015-10-30 11:03:47:277\n9.5864,-0.1652,-0.6249,9.7845,-0.0928,-0.6519,0,-0.0159,-0.0037,-101.3,-57.2,2.6,183.66,0.54,-93.8,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,4849,2015-10-30 11:03:47:379\n9.6115,-0.097,-0.5997,9.7836,-0.0908,-0.6652,0.0012,-0.0134,-0.0012,-101.5,-57.1,3.2,183.81,0.53,-93.89,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,4951,2015-10-30 11:03:47:481\n9.675,-0.0946,-0.5626,9.7842,-0.089,-0.656,0.0012,-0.0037,-0.0024,-101.6,-57,3.2,183.78,0.52,-93.83,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,5053,2015-10-30 11:03:47:583\n9.6486,-0.0838,-0.5507,9.7847,-0.0884,-0.6491,0.0024,-0.0122,0,-101.5,-57.1,3.6,182.68,0.52,-93.81,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,5155,2015-10-30 11:03:47:685\n9.6558,-0.0922,-0.565,9.7848,-0.0884,-0.648,0.0024,0.0073,0,-101.4,-57,3.4,183.64,0.52,-93.79,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,5256,2015-10-30 11:03:47:786\n9.6331,-0.0934,-0.5734,9.7851,-0.0888,-0.6431,0.0024,-0.0037,-0.0012,-101.4,-57.1,3.5,182.59,0.52,-93.75,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,5359,2015-10-30 11:03:47:889\n9.6391,-0.091,-0.5495,9.7855,-0.0878,-0.6371,0,-0.011,0,-101.5,-57.1,2.9,183.53,0.51,-93.72,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,5461,2015-10-30 11:03:47:991\n9.6379,-0.0826,-0.6189,9.7838,-0.0888,-0.662,-0.0012,-0.0305,0.0024,-101.7,-57,2.9,183.84,0.52,-93.87,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,5563,2015-10-30 11:03:48:093\n9.6474,-0.0886,-0.589,9.7852,-0.0882,-0.6422,0.0012,-0.0024,-0.0012,-101.7,-57,2.8,183.59,0.52,-93.73,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,5665,2015-10-30 11:03:48:195\n9.6295,-0.0778,-0.565,9.7858,-0.0873,-0.6317,0,0.0281,-0.0012,-101.5,-57.1,3.1,183.56,0.51,-93.75,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,5767,2015-10-30 11:03:48:297\n9.6355,-0.0922,-0.6009,9.7862,-0.0871,-0.6268,0,-0.0061,0,-101.3,-57.2,3,183.4,0.51,-93.65,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,5869,2015-10-30 11:03:48:399\n9.6642,-0.079,-0.6081,9.7844,-0.0879,-0.6537,0.0037,-0.055,0.0012,-101.2,-57.2,2.9,183.47,0.51,-93.69,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,5971,2015-10-30 11:03:48:501\n9.6654,-0.0886,-0.5818,9.7851,-0.0881,-0.643,0.0024,0.0342,0.0012,-101.4,-57.1,3,183.59,0.51,-93.76,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,6073,2015-10-30 11:03:48:603\n9.6271,-0.0814,-0.6213,9.7857,-0.0872,-0.6336,0.0012,0.044,-0.0024,-101.5,-57.2,3.1,183.64,0.51,-93.79,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,6175,2015-10-30 11:03:48:705\n9.6426,-0.0802,-0.5902,9.7864,-0.0848,-0.6239,0,0.0037,-0.0024,-101.4,-57.3,3.2,183.39,0.5,-93.65,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,6277,2015-10-30 11:03:48:807\n9.6415,-0.0706,-0.5531,9.7889,-0.0853,-0.5834,0.0037,0.0305,0,-101.4,-57.2,2.9,183.12,0.5,-93.49,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,6379,2015-10-30 11:03:48:909\n9.6307,-0.0826,-0.5602,9.7892,-0.0851,-0.5769,0.0012,-0.0232,-0.0024,-101.5,-57.3,2.8,182.92,0.5,-93.37,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,6482,2015-10-30 11:03:49:012\n9.6486,-0.0742,-0.5626,9.7883,-0.0809,-0.593,-0.0024,-0.011,-0.0049,-101.5,-57.3,2.8,183.05,0.48,-93.45,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,6583,2015-10-30 11:03:49:113\n9.6403,-0.0838,-0.5734,9.7888,-0.0815,-0.5858,0,0.0086,0,-101.3,-57.3,3.3,183.01,0.48,-93.42,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,6685,2015-10-30 11:03:49:215\n9.6367,-0.0539,-0.5495,9.7894,-0.0819,-0.5751,0.0012,-0.0037,-0.0012,-101.3,-57.2,3.3,182.88,0.48,-93.35,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,6787,2015-10-30 11:03:49:317\n9.6474,-0.0802,-0.5818,9.7883,-0.0819,-0.5932,0.0012,0.044,0,-101.4,-57.2,3.1,183.08,0.48,-93.47,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,6889,2015-10-30 11:03:49:419\n9.6343,-0.0814,-0.5471,9.7894,-0.0817,-0.5748,0.0024,-0.0024,0,-101.3,-57.3,2.8,182.81,0.48,-93.31,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,6991,2015-10-30 11:03:49:521\n9.6367,-0.0706,-0.5231,9.7907,-0.0829,-0.5515,-0.0012,0.033,0,-101.3,-57.4,2.5,182.66,0.48,-93.22,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,7093,2015-10-30 11:03:49:623\n9.6223,-0.0802,-0.571,9.7896,-0.0831,-0.5706,0.0012,0.0061,0.0012,-101.2,-57.3,2.4,183.83,0.48,-93.33,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,7195,2015-10-30 11:03:49:725\n9.6211,-0.0742,-0.5926,9.7886,-0.0826,-0.5874,0,-0.0305,0,-101.3,-57.3,2.8,183.02,0.48,-93.43,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,7297,2015-10-30 11:03:49:827\n9.6558,-0.0838,-0.5602,9.7887,-0.0826,-0.5859,0.0024,-0.0037,0,-101.3,-57.3,3.1,183,0.48,-93.42,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,7399,2015-10-30 11:03:49:929\n9.6642,-0.085,-0.5686,9.7882,-0.0827,-0.5945,0.0024,-0.0049,-0.0012,-101.3,-57.2,3.1,183.08,0.48,-93.47,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,7501,2015-10-30 11:03:50:031\n9.6331,-0.0802,-0.5818,9.7875,-0.0829,-0.6067,0.0024,-0.0195,0.0012,-101.2,-57.2,3,183.21,0.48,-93.54,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,7603,2015-10-30 11:03:50:133\n9.6462,-0.0934,-0.5734,9.788,-0.0836,-0.5987,0.0012,0.0147,0.0012,-101.3,-57.3,3.2,183.14,0.49,-93.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,7706,2015-10-30 11:03:50:236\n9.6582,-0.0826,-0.5543,9.788,-0.0846,-0.5984,0.0012,-0.0086,0,-101.3,-57.4,3.2,183.13,0.49,-93.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,7807,2015-10-30 11:03:50:337\n9.6223,-0.0766,-0.5854,9.7874,-0.0847,-0.6075,0,0.0171,0,-101.4,-57.3,3.2,183.19,0.5,-93.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,7909,2015-10-30 11:03:50:439\n9.6486,-0.0898,-0.5662,9.7873,-0.0848,-0.6089,-0.0037,-0.0122,0,-101.3,-57.4,2.8,183.22,0.5,-93.55,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,8011,2015-10-30 11:03:50:541\n9.645,-0.0802,-0.5686,9.7868,-0.0844,-0.6179,0.0012,-0.011,0,-101.4,-57.3,3.1,183.3,0.49,-93.59,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,8113,2015-10-30 11:03:50:643\n9.6462,-0.085,-0.5638,9.7869,-0.084,-0.6156,0,0.0061,-0.0012,-101.4,-57.3,2.7,183.31,0.49,-93.6,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,8215,2015-10-30 11:03:50:745\n9.6379,-0.0838,-0.5686,9.7868,-0.0842,-0.6165,-0.0012,-0.0086,-0.0012,-101.4,-57.3,3,183.3,0.49,-93.59,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,8317,2015-10-30 11:03:50:847\n9.6438,-0.0766,-0.5567,9.7871,-0.0829,-0.6123,0.0012,0.0073,-0.0037,-101.3,-57.3,2.9,183.28,0.48,-93.58,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,8419,2015-10-30 11:03:50:949\n9.6426,-0.0778,-0.5543,9.7871,-0.0819,-0.6128,0.0012,0.0049,-0.0012,-101.3,-57.3,3.1,183.29,0.48,-93.59,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,8521,2015-10-30 11:03:51:051\n9.6199,-0.0994,-0.5626,9.7875,-0.0809,-0.6069,0.0012,0.0073,0.0012,-101.2,-57.4,2.6,183.22,0.47,-93.55,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,8623,2015-10-30 11:03:51:153\n9.645,-0.0898,-0.5938,9.787,-0.0812,-0.6149,0,-0.0208,0,-101.2,-57.4,2.5,183.3,0.47,-93.6,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,8725,2015-10-30 11:03:51:255\n9.6606,-0.085,-0.5471,9.7884,-0.0813,-0.5923,0.0024,0.0073,-0.0012,-101.1,-57.4,2.4,184.12,0.48,-93.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,8827,2015-10-30 11:03:51:357\n9.6355,-0.085,-0.5543,9.7882,-0.0808,-0.5943,0.0024,-0.0086,-0.0024,-101.1,-57.5,2.6,183.09,0.47,-93.47,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,8928,2015-10-30 11:03:51:458\n9.6271,-0.0718,-0.5866,9.7875,-0.0789,-0.6072,0.0012,-0.022,-0.0024,-101.1,-57.4,2.6,183.19,0.46,-93.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,9031,2015-10-30 11:03:51:561\n9.6486,-0.0778,-0.5842,9.7879,-0.0782,-0.5998,0.0037,0,-0.0012,-101.2,-57.4,2.7,183.15,0.46,-93.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,9133,2015-10-30 11:03:51:663\n9.6534,-0.0838,-0.5638,9.7885,-0.0779,-0.5906,0.0024,0.0012,-0.0012,-101.3,-57.4,2.7,183.09,0.46,-93.47,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,9235,2015-10-30 11:03:51:765\n9.6259,-0.0742,-0.5806,9.7882,-0.077,-0.5948,0.0024,-0.0122,-0.0012,-101.4,-57.4,3,183.1,0.45,-93.48,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,9337,2015-10-30 11:03:51:867\n9.6331,-0.091,-0.571,9.7886,-0.0771,-0.5891,0,0.0147,0.0012,-101.4,-57.3,3.1,183.08,0.45,-93.47,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,9439,2015-10-30 11:03:51:969\n9.657,-0.0874,-0.5806,9.7887,-0.0769,-0.5877,0,0.0086,0,-101.3,-57.3,3.2,183.03,0.45,-93.44,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,9541,2015-10-30 11:03:52:071\n9.6438,-0.0682,-0.5602,9.7891,-0.0761,-0.5802,0,0.0037,0,-101.3,-57.3,3,182.94,0.45,-93.38,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,9643,2015-10-30 11:03:52:173\n9.6426,-0.0622,-0.5734,9.7883,-0.0749,-0.5941,0,-0.0134,0,-101.3,-57.4,2.6,183.06,0.44,-93.45,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,9745,2015-10-30 11:03:52:275\n9.6714,-0.0934,-0.571,9.7887,-0.0738,-0.5869,-0.0012,0.0073,-0.0012,-101.4,-57.5,2.5,183.02,0.43,-93.43,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,9847,2015-10-30 11:03:52:377\n9.6534,-0.085,-0.5734,9.7887,-0.0728,-0.588,0,0.0037,-0.0012,-101.4,-57.4,2.6,183.05,0.43,-93.44,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,9949,2015-10-30 11:03:52:479\n9.6211,-0.0766,-0.5914,9.7885,-0.0718,-0.5903,0.0024,-0.0049,-0.0012,-101.4,-57.3,2.6,183.06,0.42,-93.45,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,10051,2015-10-30 11:03:52:581\n9.6259,-0.0682,-0.5794,9.7887,-0.0712,-0.5886,0.0012,0,0,-101.5,-57.1,2.6,183.04,0.42,-93.44,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,10153,2015-10-30 11:03:52:683\n9.6606,-0.0778,-0.5818,9.7891,-0.0704,-0.5808,-0.0024,0.0147,0,-101.4,-57.2,2.6,182.99,0.41,-93.41,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,10255,2015-10-30 11:03:52:785\n9.6379,-0.0934,-0.565,9.79,-0.0708,-0.5667,0.0024,0.0037,0,-101.4,-57.2,2.9,182.87,0.41,-93.34,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,10357,2015-10-30 11:03:52:887\n9.6223,-0.073,-0.5674,9.7902,-0.0704,-0.5629,0.0012,-0.0037,-0.0012,-101.4,-57.3,3,182.78,0.41,-93.29,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,10459,2015-10-30 11:03:52:989\n9.6438,-0.0874,-0.571,9.79,-0.0694,-0.5671,0,-0.0012,-0.0024,-101.4,-57.2,2.9,182.81,0.41,-93.31,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,10561,2015-10-30 11:03:53:091\n9.6426,-0.0826,-0.5674,9.7896,-0.0689,-0.573,0.0037,0,-0.0024,-101.4,-57.3,2.6,182.88,0.4,-93.35,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,10662,2015-10-30 11:03:53:192\n9.6594,-0.0718,-0.577,9.7897,-0.0686,-0.5713,-0.0024,0.0061,0.0012,-101.4,-57.4,2.4,183.85,0.4,-93.34,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,10765,2015-10-30 11:03:53:295\n9.6426,-0.0946,-0.5674,9.7899,-0.0682,-0.5678,0,-0.0012,0,-101.4,-57.4,2.4,183.82,0.4,-93.32,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,10867,2015-10-30 11:03:53:397\n9.6486,-0.0886,-0.5543,9.7901,-0.0679,-0.565,0.0024,-0.0037,0,-101.4,-57.2,2.5,182.8,0.4,-93.3,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,10969,2015-10-30 11:03:53:499\n9.6367,-0.0682,-0.5423,9.7903,-0.0681,-0.5616,0.0012,0.0122,0.0012,-101.4,-57.2,2.6,182.78,0.4,-93.29,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,11071,2015-10-30 11:03:53:601\n9.6211,-0.091,-0.5339,9.7907,-0.0674,-0.5538,0.0012,0.0171,-0.0012,-101.5,-57.2,2.8,182.69,0.39,-93.24,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,11173,2015-10-30 11:03:53:703\n9.6426,-0.0754,-0.5567,9.7907,-0.0672,-0.5532,0.0012,-0.0147,0,-101.5,-57.2,2.9,182.65,0.39,-93.22,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,11275,2015-10-30 11:03:53:805\n9.6426,-0.0599,-0.5471,9.7908,-0.0662,-0.5523,-0.0024,0.0134,-0.0024,-101.4,-57.1,2.9,182.65,0.39,-93.22,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,11377,2015-10-30 11:03:53:907\n9.6426,-0.0922,-0.5531,9.7908,-0.066,-0.5519,0.0012,0.0086,0,-101.3,-57.2,3.2,182.69,0.38,-93.24,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,11479,2015-10-30 11:03:54:009\n9.6259,-0.0778,-0.5387,9.791,-0.0654,-0.5493,0,-0.0134,-0.0024,-101.2,-57.2,3.5,181.65,0.38,-93.21,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,11581,2015-10-30 11:03:54:111\n9.6391,-0.0742,-0.5423,9.7907,-0.0672,-0.5537,0.0024,-0.011,0,-101.1,-57.2,3.8,181.7,0.39,-93.24,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,11683,2015-10-30 11:03:54:213\n9.6486,-0.0838,-0.5722,9.7902,-0.0678,-0.5637,0,-0.0122,0,-101.2,-57.2,3.8,181.77,0.39,-93.28,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,11785,2015-10-30 11:03:54:315\n9.6474,-0.0826,-0.5447,9.7904,-0.0688,-0.5598,0.0037,-0.0024,0.0012,-101.2,-57.2,3.5,181.76,0.4,-93.27,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,11887,2015-10-30 11:03:54:417\n9.6259,-0.0706,-0.5303,9.7902,-0.0691,-0.5633,0.0024,-0.0147,-0.0012,-101.2,-57.2,3.2,182.78,0.4,-93.29,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,11989,2015-10-30 11:03:54:519\n9.6235,-0.0862,-0.5698,9.7895,-0.0696,-0.5744,0.0012,-0.0037,0,-101.2,-57.3,3,182.9,0.41,-93.36,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,12090,2015-10-30 11:03:54:620\n9.6498,-0.0898,-0.5578,9.7893,-0.0706,-0.5787,0.0024,0.011,0.0012,-101.3,-57.2,3.2,182.95,0.41,-93.39,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,12193,2015-10-30 11:03:54:723\n9.6438,-0.0682,-0.5662,9.7893,-0.071,-0.5782,0,0.0281,-0.0012,-101.2,-57.3,3.5,181.99,0.42,-93.41,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,12295,2015-10-30 11:03:54:825\n9.6235,-0.0802,-0.5722,9.7887,-0.0706,-0.5889,0.0024,-0.0171,0,-101.3,-57.3,3.6,181.93,0.41,-93.37,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,12397,2015-10-30 11:03:54:927\n9.6211,-0.0754,-0.5602,9.7896,-0.0711,-0.5737,0.0012,0.0257,-0.0024,-101.3,-57.2,3.5,181.93,0.42,-93.37,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,12499,2015-10-30 11:03:55:029\n9.6606,-0.073,-0.5794,9.7896,-0.0727,-0.5724,0.0037,0.022,-0.0012,-101.4,-57.2,3.2,182.95,0.42,-93.39,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,12601,2015-10-30 11:03:55:131\n9.645,-0.0778,-0.5782,9.7894,-0.0728,-0.5771,0.0024,0.0208,-0.0012,-101.4,-57.2,3.2,182.92,0.43,-93.37,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,12703,2015-10-30 11:03:55:233\n9.6403,-0.0862,-0.5555,9.7892,-0.0721,-0.5802,-0.0024,-0.0269,-0.0012,-101.3,-57.2,3.5,181.97,0.42,-93.39,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,12805,2015-10-30 11:03:55:335\n9.6582,-0.073,-0.5746,9.7889,-0.0713,-0.5839,0.0037,-0.0086,0,-101.3,-57.2,3.6,181.99,0.42,-93.4,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,12907,2015-10-30 11:03:55:437\n9.6415,-0.0706,-0.5902,9.7885,-0.0706,-0.5912,0.0012,0.0171,0,-101.5,-57.1,3.5,182.08,0.41,-93.46,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,13009,2015-10-30 11:03:55:539\n9.6403,-0.085,-0.5626,9.7893,-0.0705,-0.5776,0.0024,0.0061,-0.0012,-101.5,-57.2,3.2,182.93,0.41,-93.38,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,13111,2015-10-30 11:03:55:641\n9.6319,-0.0826,-0.5782,9.7889,-0.0703,-0.5842,0.0012,-0.0012,-0.0024,-101.4,-57.2,3,183,0.41,-93.42,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,13213,2015-10-30 11:03:55:743\n9.6283,-0.0802,-0.5722,9.7891,-0.0699,-0.5811,0,0.0098,0,-101.3,-57.3,2.8,182.97,0.41,-93.4,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,13315,2015-10-30 11:03:55:845\n9.6462,-0.0682,-0.5519,9.7896,-0.0701,-0.5736,0.0012,0.011,0,-101.3,-57.3,3,182.89,0.41,-93.35,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,13417,2015-10-30 11:03:55:947\n9.6343,-0.0826,-0.5495,9.7899,-0.0699,-0.5673,0.0012,0.0073,0,-101.4,-57.3,3.3,182.84,0.41,-93.32,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,13519,2015-10-30 11:03:56:049\n9.6391,-0.0802,-0.5722,9.7898,-0.0698,-0.5693,-0.0024,0.0012,0,-101.4,-57.3,3.3,182.85,0.41,-93.33,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,13621,2015-10-30 11:03:56:151\n9.6654,-0.0814,-0.5818,9.7896,-0.0685,-0.5739,0,0.0037,-0.0012,-101.3,-57.3,2.9,182.89,0.4,-93.35,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,13723,2015-10-30 11:03:56:253\n9.6606,-0.0611,-0.559,9.7899,-0.0688,-0.5688,0.0024,0.0073,0,-101.3,-57.3,3,182.84,0.4,-93.33,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,13825,2015-10-30 11:03:56:355\n9.6247,-0.085,-0.5842,9.7897,-0.0677,-0.5713,0.0024,0.0024,-0.0024,-101.4,-57.3,3.2,182.87,0.4,-93.34,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,13927,2015-10-30 11:03:56:457\n9.657,-0.0646,-0.5794,9.7901,-0.0667,-0.5639,-0.0012,0.0098,-0.0012,-101.5,-57.3,3.3,182.83,0.39,-93.32,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,14029,2015-10-30 11:03:56:559\n9.6606,-0.0874,-0.5686,9.79,-0.0664,-0.5668,0,0.0061,0,-101.6,-57.3,3.5,181.92,0.39,-93.33,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,14131,2015-10-30 11:03:56:661\n9.6415,-0.079,-0.5878,9.7899,-0.0661,-0.5689,0,-0.0049,-0.0024,-101.4,-57.3,3.2,182.84,0.39,-93.33,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,14233,2015-10-30 11:03:56:763\n9.6295,-0.0826,-0.5602,9.7906,-0.0656,-0.5557,0.0012,0.0012,-0.0024,-101.4,-57.3,3.1,182.74,0.38,-93.26,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,14335,2015-10-30 11:03:56:865\n9.651,-0.0838,-0.5578,9.7906,-0.0656,-0.556,0.0012,-0.0012,-0.0024,-101.4,-57.3,2.4,183.66,0.38,-93.23,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,14437,2015-10-30 11:03:56:967\n9.6462,-0.0886,-0.5555,9.7908,-0.0663,-0.5521,0.0024,0.0147,0.0012,-101.5,-57.3,2.3,183.7,0.39,-93.25,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,14539,2015-10-30 11:03:57:069\n9.6546,-0.0718,-0.5878,9.79,-0.0655,-0.5658,0.0024,-0.0012,-0.0024,-101.5,-57.4,2.4,183.8,0.38,-93.31,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,14641,2015-10-30 11:03:57:171\n9.6367,-0.091,-0.5782,9.7905,-0.0645,-0.558,0,0.0061,-0.0024,-101.5,-57.3,2.8,182.74,0.38,-93.27,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,14744,2015-10-30 11:03:57:274\n9.645,-0.079,-0.5962,9.7904,-0.0643,-0.5605,0.0037,-0.0049,-0.0012,-101.6,-57.4,3.2,182.81,0.38,-93.28,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,14845,2015-10-30 11:03:57:375\n9.6438,-0.0778,-0.5602,9.7907,-0.0652,-0.5541,0,0.0037,0,-101.5,-57.4,3.2,182.71,0.38,-93.25,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,14947,2015-10-30 11:03:57:477\n9.6415,-0.085,-0.5555,9.791,-0.0664,-0.5489,0,0.0147,0,-101.5,-57.4,3.1,182.64,0.39,-93.21,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,15049,2015-10-30 11:03:57:579\n9.6582,-0.0766,-0.5578,9.7912,-0.0678,-0.5445,0.0024,0.0012,0,-101.6,-57.4,3,182.65,0.4,-93.18,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,15151,2015-10-30 11:03:57:681\n9.663,-0.0838,-0.5686,9.7909,-0.0678,-0.5498,0,-0.0086,-0.0012,-101.5,-57.4,3.3,182.65,0.4,-93.21,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,15253,2015-10-30 11:03:57:783\n9.6331,-0.0862,-0.5351,9.7911,-0.0685,-0.5464,0.0012,0.0012,-0.0012,-101.5,-57.3,3.5,181.63,0.4,-93.2,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,15355,2015-10-30 11:03:57:885\n9.6247,-0.0778,-0.5686,9.7909,-0.0692,-0.5507,0,-0.011,0.0024,-101.6,-57.2,3.5,181.77,0.4,-93.25,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,15457,2015-10-30 11:03:57:987\n9.6486,-0.0838,-0.577,9.7907,-0.0702,-0.5536,0,-0.0257,0.0012,-101.7,-57,3.2,182.68,0.41,-93.2,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,15559,2015-10-30 11:03:58:089\n9.6498,-0.0802,-0.583,9.7908,-0.0713,-0.5526,0.0037,-0.0134,0.0012,-101.5,-57.1,2.9,182.67,0.42,-93.23,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,15661,2015-10-30 11:03:58:191\n9.6331,-0.0706,-0.5567,9.791,-0.0726,-0.548,0.0012,-0.0012,0,-101.5,-57.1,2.7,182.63,0.42,-93.2,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,15763,2015-10-30 11:03:58:293\n9.6367,-0.0706,-0.5746,9.7908,-0.0726,-0.5507,-0.0024,0,-0.0012,-101.6,-57.2,2.8,182.7,0.43,-93.22,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,15864,2015-10-30 11:03:58:394\n9.6331,-0.0682,-0.5746,9.7906,-0.073,-0.5554,0.0012,-0.0171,0,-101.6,-57.2,2.9,182.76,0.43,-93.25,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,15967,2015-10-30 11:03:58:497\n9.6307,-0.073,-0.5878,9.7897,-0.0731,-0.5713,0.0012,0.0024,0,-101.5,-57.3,3.1,182.85,0.43,-93.33,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,16069,2015-10-30 11:03:58:599\n9.6462,-0.0826,-0.5722,9.7894,-0.0734,-0.5758,0.0012,-0.0098,0,-101.5,-57.4,3.4,182.91,0.43,-93.37,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,16170,2015-10-30 11:03:58:700\n9.6247,-0.0682,-0.5926,9.7892,-0.0734,-0.5787,0.0012,-0.0012,0.0012,-101.4,-57.4,3.6,181.94,0.43,-93.38,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,16273,2015-10-30 11:03:58:803\n9.6379,-0.0838,-0.6177,9.789,-0.0742,-0.5828,0.0024,-0.0159,0,-101.3,-57.4,3.8,181.99,0.43,-93.41,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,16375,2015-10-30 11:03:58:905\n9.6462,-0.0742,-0.6069,9.7884,-0.0744,-0.593,0.0024,-0.0147,0.0012,-101.3,-57.4,3.8,182.07,0.43,-93.45,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,16477,2015-10-30 11:03:59:007\n9.6283,-0.0706,-0.5866,9.7887,-0.0752,-0.588,0.0024,0.0024,0,-101.3,-57.4,3.6,182.05,0.44,-93.44,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,16579,2015-10-30 11:03:59:109\n9.6283,-0.0754,-0.5854,9.7893,-0.0756,-0.5784,0.0037,0.0122,0,-101.3,-57.4,3.6,182.01,0.44,-93.42,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,16681,2015-10-30 11:03:59:211\n9.6415,-0.073,-0.589,9.7889,-0.0762,-0.5834,0.0024,0.0183,0,-101.5,-57.3,3.5,182,0.45,-93.41,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,16783,2015-10-30 11:03:59:313\n9.651,-0.0599,-0.5854,9.7893,-0.0777,-0.5764,0,-0.0024,0.0024,-101.4,-57.2,3.8,181.93,0.45,-93.37,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,16885,2015-10-30 11:03:59:415\n9.6235,-0.073,-0.5866,9.7896,-0.0768,-0.5729,0.0012,-0.0183,-0.0012,-101.4,-57.2,3.9,181.86,0.45,-93.33,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,16987,2015-10-30 11:03:59:517\n9.6367,-0.0826,-0.5794,9.7892,-0.0773,-0.5788,0.0037,-0.0134,0,-101.3,-57.3,4.1,181.95,0.45,-93.38,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,17089,2015-10-30 11:03:59:619\n9.6307,-0.0766,-0.6081,9.7883,-0.0759,-0.5936,0.0012,-0.0098,0,-101.4,-57.4,4,182.08,0.45,-93.46,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,17191,2015-10-30 11:03:59:721\n9.6259,-0.0778,-0.6333,9.7881,-0.0754,-0.5974,0.0012,-0.0159,0,-101.5,-57.3,4,182.14,0.44,-93.49,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,17293,2015-10-30 11:03:59:823\n9.6307,-0.073,-0.595,9.7889,-0.0753,-0.5838,0.0012,0.011,0.0012,-101.5,-57.3,4,182.05,0.44,-93.44,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,17395,2015-10-30 11:03:59:925\n9.6355,-0.0634,-0.5674,9.7896,-0.0757,-0.5719,0.0037,0.0171,0,-101.4,-57.4,4,181.88,0.44,-93.34,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,17497,2015-10-30 11:04:00:027\n9.6379,-0.0814,-0.583,9.7895,-0.0739,-0.5747,0.0012,0.0037,-0.0024,-101.4,-57.3,3.7,181.92,0.44,-93.36,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,17599,2015-10-30 11:04:00:129\n9.6403,-0.0838,-0.589,9.7894,-0.0729,-0.5763,0,-0.0037,0,-101.2,-57.3,3.2,182.92,0.43,-93.37,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,17701,2015-10-30 11:04:00:231\n9.6462,-0.0694,-0.5746,9.7897,-0.0722,-0.5716,0.0012,0.0086,0,-101.3,-57.2,3.1,182.87,0.42,-93.34,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,17803,2015-10-30 11:04:00:333\n9.6283,-0.067,-0.5866,9.7896,-0.0718,-0.573,0.0024,-0.011,-0.0012,-101.3,-57.3,3.5,181.89,0.42,-93.35,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,17904,2015-10-30 11:04:00:434\n9.6367,-0.0946,-0.6081,9.7891,-0.0713,-0.5811,0.0012,-0.011,-0.0012,-101.4,-57.4,3.8,181.98,0.42,-93.4,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,18007,2015-10-30 11:04:00:537\n9.6534,-0.073,-0.6009,9.7891,-0.0701,-0.5814,0,0.0049,-0.0012,-101.5,-57.3,3.9,181.99,0.41,-93.4,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,18109,2015-10-30 11:04:00:639\n9.6486,-0.079,-0.5878,9.7891,-0.0709,-0.5816,0.0012,-0.0049,0,-101.4,-57.3,3.5,181.98,0.41,-93.4,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,18211,2015-10-30 11:04:00:741\n9.6271,-0.085,-0.6009,9.789,-0.0698,-0.5837,0.0012,-0.0134,0,-101.4,-57.1,3.5,181.97,0.41,-93.39,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,18313,2015-10-30 11:04:00:843\n9.6426,-0.0694,-0.5962,9.7884,-0.0693,-0.594,-0.0012,-0.0024,-0.0024,-101.4,-57.2,3.6,182.11,0.4,-93.47,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,18415,2015-10-30 11:04:00:945\n9.6295,-0.0886,-0.6261,9.788,-0.0689,-0.6,0.0049,-0.0086,-0.0012,-101.5,-57.2,3.6,182.15,0.4,-93.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,18517,2015-10-30 11:04:01:047\n9.6247,-0.0826,-0.6321,9.7878,-0.0689,-0.6032,0,-0.0232,-0.0012,-101.4,-57.2,3.6,182.15,0.4,-93.49,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,18619,2015-10-30 11:04:01:149\n9.6271,-0.073,-0.6249,9.7879,-0.0683,-0.6019,0.0049,-0.0134,-0.0012,-101.4,-57.3,3.4,183.18,0.4,-93.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,18721,2015-10-30 11:04:01:251\n9.6462,-0.0766,-0.5938,9.7881,-0.0684,-0.5977,0.0024,0.0061,-0.0024,-101.5,-57.3,3.5,182.15,0.4,-93.49,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,18823,2015-10-30 11:04:01:353\n9.6235,-0.0826,-0.5938,9.7883,-0.0679,-0.5947,-0.0012,0.0073,-0.0012,-101.5,-57.3,3.1,183.11,0.4,-93.48,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,18925,2015-10-30 11:04:01:455\n9.6403,-0.073,-0.6117,9.788,-0.0674,-0.5997,0.0024,-0.0049,-0.0024,-101.5,-57.3,3.2,183.16,0.39,-93.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,19027,2015-10-30 11:04:01:557\n9.6474,-0.0742,-0.595,9.7879,-0.0665,-0.6015,0.0012,-0.0122,0,-101.5,-57.4,3.3,183.18,0.39,-93.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,19129,2015-10-30 11:04:01:659\n9.6379,-0.0826,-0.6177,9.7877,-0.0672,-0.6055,0.0024,0,0.0012,-101.4,-57.5,3.4,183.23,0.39,-93.55,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,19234,2015-10-30 11:04:01:764\n9.6247,-0.0778,-0.6225,9.7877,-0.0673,-0.6044,0.0012,-0.0171,-0.0024,-101.3,-57.4,3.6,182.18,0.39,-93.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,19333,2015-10-30 11:04:01:863\n9.6498,-0.0575,-0.5997,9.7878,-0.0668,-0.6034,0.0024,-0.0024,-0.0012,-101.3,-57.3,3.8,182.2,0.39,-93.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,19436,2015-10-30 11:04:01:966\n9.645,-0.0778,-0.5986,9.7878,-0.0661,-0.6033,0.0024,0,-0.0012,-101.3,-57.3,3.8,182.2,0.39,-93.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,19537,2015-10-30 11:04:02:067\n9.6295,-0.0622,-0.6129,9.7882,-0.0666,-0.5967,0.0012,0.0183,-0.0012,-101.4,-57.3,3.8,182.17,0.39,-93.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,19639,2015-10-30 11:04:02:169\n9.6331,-0.0611,-0.5878,9.7884,-0.0663,-0.5935,0.0024,0.0024,-0.0012,-101.4,-57.4,3.6,182.1,0.39,-93.47,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,19741,2015-10-30 11:04:02:271\n9.651,-0.0682,-0.595,9.7884,-0.0658,-0.594,0,-0.0037,0,-101.5,-57.4,3.8,182.11,0.38,-93.47,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,19842,2015-10-30 11:04:02:372\n9.6307,-0.0718,-0.5914,9.7887,-0.0654,-0.5883,0,0.0244,-0.0012,-101.4,-57.4,3.9,182.05,0.38,-93.44,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,19945,2015-10-30 11:04:02:475\n9.6474,-0.0802,-0.6093,9.7887,-0.0656,-0.5888,-0.0012,0.0049,-0.0012,-101.4,-57.4,4.1,182.06,0.38,-93.44,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,20047,2015-10-30 11:04:02:577\n9.6223,-0.0814,-0.5962,9.7887,-0.0649,-0.5879,0,-0.011,-0.0012,-101.5,-57.4,4.1,181.97,0.38,-93.39,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,20149,2015-10-30 11:04:02:679\n9.6271,-0.0814,-0.589,9.7891,-0.0641,-0.5822,0.0024,0.0244,-0.0012,-101.5,-57.4,4.1,181.99,0.37,-93.4,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,20251,2015-10-30 11:04:02:781\n9.6558,-0.0838,-0.5746,9.7899,-0.0638,-0.569,-0.0012,0.0024,0.0012,-101.5,-57.3,4.1,181.85,0.37,-93.33,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,20353,2015-10-30 11:04:02:883\n9.6319,-0.0706,-0.5626,9.7895,-0.0652,-0.5744,0.0012,-0.0122,0.0012,-101.5,-57.3,4.1,181.91,0.38,-93.36,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,20455,2015-10-30 11:04:02:985\n9.6175,-0.0694,-0.5986,9.7892,-0.0666,-0.5795,0.0024,0.0012,-0.0024,-101.6,-57.3,3.7,182.05,0.39,-93.4,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,20557,2015-10-30 11:04:03:087\n9.6486,-0.0814,-0.5854,9.789,-0.0679,-0.5831,0.0024,-0.0086,-0.0012,-101.5,-57.3,3.6,182,0.4,-93.41,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,20659,2015-10-30 11:04:03:189\n9.6558,-0.0599,-0.5782,9.7892,-0.0682,-0.5802,0.0024,0,0,-101.5,-57.3,3.6,181.97,0.4,-93.39,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,20761,2015-10-30 11:04:03:291\n9.6151,-0.091,-0.5818,9.7893,-0.0688,-0.5777,0.0024,-0.0012,0.0012,-101.5,-57.3,3.6,181.95,0.4,-93.38,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,20863,2015-10-30 11:04:03:393\n9.6139,-0.0826,-0.5818,9.7891,-0.0694,-0.5818,0.0024,-0.0049,0,-101.6,-57.3,4,182.04,0.41,-93.4,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,20965,2015-10-30 11:04:03:495\n9.6462,-0.0838,-0.571,9.7886,-0.0704,-0.5893,-0.0024,0.0049,0,-101.6,-57.3,3.9,182.12,0.41,-93.45,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,21067,2015-10-30 11:04:03:597\n9.6007,-0.0802,-0.589,9.7879,-0.0713,-0.6,-0.0012,-0.0012,0.0012,-101.6,-57.2,3.7,182.23,0.42,-93.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,21169,2015-10-30 11:04:03:699\n9.6582,-0.0646,-0.5938,9.7874,-0.0718,-0.6097,0.0012,-0.0232,0.0012,-101.7,-57,3.7,182.27,0.42,-93.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,21270,2015-10-30 11:04:03:800\n9.6546,-0.067,-0.5794,9.7878,-0.073,-0.6018,0.0012,-0.0037,0,-101.6,-57,4,182.25,0.43,-93.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,21373,2015-10-30 11:04:03:903\n9.6391,-0.091,-0.5722,9.7878,-0.0745,-0.6013,0.0012,0.0098,0,-101.6,-57,4.2,182.28,0.43,-93.54,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,21475,2015-10-30 11:04:04:005\n9.6391,-0.0742,-0.595,9.7875,-0.0765,-0.607,0.0012,-0.0098,0,-101.5,-57.1,4.2,182.24,0.44,-93.55,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,21577,2015-10-30 11:04:04:107\n9.6415,-0.0814,-0.6009,9.7873,-0.0789,-0.6097,0.0024,-0.011,0.0024,-101.6,-57.2,4,182.3,0.46,-93.55,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,21678,2015-10-30 11:04:04:208\n9.6283,-0.0922,-0.6045,9.787,-0.0822,-0.614,0,-0.0098,0.0024,-101.6,-57.1,3.8,182.34,0.47,-93.57,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,21781,2015-10-30 11:04:04:311\n9.6594,-0.0874,-0.6045,9.7871,-0.0835,-0.6119,0,-0.0098,0.0024,-101.6,-57.1,3.4,183.33,0.49,-93.58,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,21883,2015-10-30 11:04:04:413\n9.6343,-0.0718,-0.6129,9.7862,-0.0854,-0.6265,0.0024,-0.0134,0,-101.8,-57.1,3.5,182.5,0.5,-93.66,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,21984,2015-10-30 11:04:04:514\n9.6379,-0.073,-0.6129,9.7868,-0.0858,-0.6168,0.0012,-0.0049,0,-101.7,-57.2,3.4,183.37,0.5,-93.6,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,22087,2015-10-30 11:04:04:617\n9.6762,-0.0886,-0.5974,9.7867,-0.0863,-0.619,-0.0012,-0.0012,0.0012,-101.6,-57.2,3.6,182.42,0.5,-93.62,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,22189,2015-10-30 11:04:04:719\n9.6271,-0.0874,-0.6404,9.7861,-0.0867,-0.6283,0.0012,-0.022,-0.0024,-101.6,-57.1,3.9,182.53,0.51,-93.68,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,22291,2015-10-30 11:04:04:821\n9.6247,-0.0802,-0.6201,9.7869,-0.0865,-0.6152,0,-0.0122,0,-101.6,-57,3.9,182.38,0.51,-93.6,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,22393,2015-10-30 11:04:04:923\n9.6594,-0.0874,-0.6009,9.787,-0.0865,-0.6137,0,-0.0098,0.0012,-101.7,-57,3.6,182.38,0.51,-93.6,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,22495,2015-10-30 11:04:05:025\n9.6462,-0.0778,-0.5818,9.7873,-0.0852,-0.6096,0,0.0159,-0.0012,-101.6,-57,3.6,182.34,0.5,-93.57,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,22597,2015-10-30 11:04:05:127\n9.6534,-0.0838,-0.6009,9.7875,-0.0835,-0.6052,0,0.0208,-0.0012,-101.6,-57,3.4,183.27,0.49,-93.54,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,22699,2015-10-30 11:04:05:229\n9.6355,-0.079,-0.6261,9.7877,-0.0815,-0.6031,0.0012,0.0147,-0.0012,-101.6,-57,3.4,183.23,0.48,-93.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,22801,2015-10-30 11:04:05:331\n9.6163,-0.0766,-0.6069,9.7883,-0.0791,-0.5939,0.0012,0.0061,-0.0024,-101.6,-57.2,3,183.15,0.46,-93.47,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,22903,2015-10-30 11:04:05:433\n9.6379,-0.067,-0.5938,9.7886,-0.0771,-0.5881,0.0049,-0.0037,-0.0012,-101.7,-57.3,2.9,183.09,0.45,-93.44,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,23004,2015-10-30 11:04:05:534\n9.6391,-0.0934,-0.5974,9.7884,-0.0763,-0.5921,0.0012,0.0049,-0.0012,-101.6,-57.3,3,183.14,0.45,-93.46,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,23107,2015-10-30 11:04:05:637\n9.6403,-0.0826,-0.6057,9.7884,-0.0762,-0.5927,0,0.0012,0,-101.5,-57.2,3.4,183.08,0.45,-93.46,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,23209,2015-10-30 11:04:05:739\n9.6426,-0.0634,-0.5806,9.7881,-0.0751,-0.5977,0.0012,-0.0061,-0.0012,-101.4,-57.3,3.6,182.11,0.44,-93.47,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,23311,2015-10-30 11:04:05:841\n9.6187,-0.0742,-0.5878,9.7885,-0.0745,-0.5911,0.0012,0.0086,-0.0012,-101.5,-57.2,3.7,182.08,0.44,-93.46,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,23413,2015-10-30 11:04:05:943\n9.669,-0.0862,-0.6129,9.7885,-0.074,-0.5901,0.0024,0.0098,-0.0024,-101.5,-57.3,3.3,183.1,0.43,-93.47,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,23515,2015-10-30 11:04:06:045\n9.6642,-0.0718,-0.5842,9.7889,-0.0737,-0.5837,0,0.0073,0,-101.6,-57.3,3.3,183.05,0.43,-93.41,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,23617,2015-10-30 11:04:06:147\n9.6247,-0.0718,-0.6069,9.7893,-0.0741,-0.5779,0.0024,-0.0122,0.0012,-101.5,-57.3,3.6,181.91,0.43,-93.36,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,23718,2015-10-30 11:04:06:248\n9.6271,-0.0694,-0.5878,9.7894,-0.0745,-0.5753,0.0024,-0.0061,0,-101.7,-57.2,4,181.97,0.44,-93.36,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,23820,2015-10-30 11:04:06:350\n9.6426,-0.067,-0.583,9.789,-0.0749,-0.583,0,-0.0073,0,-101.6,-57.2,4,182.03,0.44,-93.4,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,23923,2015-10-30 11:04:06:453\n9.6426,-0.0802,-0.5962,9.7885,-0.0745,-0.591,0.0024,-0.0061,0.0012,-101.6,-57.3,3.8,182.14,0.44,-93.46,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,24025,2015-10-30 11:04:06:555\n9.645,-0.0778,-0.589,9.7886,-0.0744,-0.5894,0.0037,0.0049,0,-101.6,-57.3,3.8,182.12,0.43,-93.45,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,24127,2015-10-30 11:04:06:657\n9.6259,-0.0802,-0.6081,9.7883,-0.0753,-0.5936,0,-0.0049,0.0012,-101.5,-57.3,3.5,182.1,0.44,-93.47,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,24229,2015-10-30 11:04:06:759\n9.6403,-0.0694,-0.5794,9.7883,-0.0761,-0.5938,0.0024,0.0061,0.0012,-101.5,-57.2,3.3,183.09,0.44,-93.47,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,24331,2015-10-30 11:04:06:861\n9.645,-0.0742,-0.595,9.7881,-0.0761,-0.5969,0,-0.0037,0.0012,-101.4,-57.2,3.1,183.1,0.44,-93.48,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,24433,2015-10-30 11:04:06:963\n9.663,-0.073,-0.589,9.7882,-0.0763,-0.5952,0.0012,0.0061,0.0012,-101.3,-57.3,3.4,183.11,0.45,-93.48,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,24535,2015-10-30 11:04:07:065\n9.6223,-0.0874,-0.5662,9.7886,-0.0768,-0.5889,0.0012,0.0098,0,-101.3,-57.4,3.7,182.08,0.45,-93.46,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,24636,2015-10-30 11:04:07:166\n9.6438,-0.0718,-0.5818,9.7886,-0.0775,-0.5892,0,0,0,-101.5,-57.3,4.1,182.06,0.45,-93.45,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,24739,2015-10-30 11:04:07:269\n9.6474,-0.0718,-0.577,9.7886,-0.0768,-0.5893,0.0024,0.0037,0,-101.6,-57.2,4.1,182.12,0.45,-93.44,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,24841,2015-10-30 11:04:07:371\n9.675,-0.085,-0.5638,9.7889,-0.0767,-0.5844,0.0024,-0.0086,-0.0012,-101.6,-57.2,4.1,182.05,0.45,-93.41,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,24943,2015-10-30 11:04:07:473\n9.6247,-0.0682,-0.5722,9.7889,-0.0757,-0.5837,0,0.0024,0.0012,-101.6,-57.2,3.9,182.06,0.44,-93.41,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,25045,2015-10-30 11:04:07:575\n9.6319,-0.073,-0.5782,9.7887,-0.0747,-0.588,0,-0.0086,0,-101.6,-57.2,3.8,182.07,0.44,-93.42,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,25147,2015-10-30 11:04:07:677\n9.6702,-0.0814,-0.5818,9.7886,-0.0738,-0.5885,0.0012,0.0061,0.0012,-101.5,-57.2,3.9,182.05,0.43,-93.44,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,25249,2015-10-30 11:04:07:779\n9.6415,-0.079,-0.5483,9.789,-0.0742,-0.5827,0.0012,0.0122,0,-101.5,-57.3,3.9,181.99,0.43,-93.41,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,25351,2015-10-30 11:04:07:881\n9.6295,-0.0646,-0.5447,9.789,-0.0741,-0.5831,0,0.0159,-0.0024,-101.5,-57.2,3.8,182,0.43,-93.41,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,25453,2015-10-30 11:04:07:983\n9.6522,-0.067,-0.5519,9.7886,-0.073,-0.5898,0,0.0037,0,-101.6,-57.2,3.9,182.12,0.43,-93.45,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,25555,2015-10-30 11:04:08:085\n9.6558,-0.0814,-0.5674,9.7884,-0.0721,-0.5924,0.0024,-0.0134,-0.0024,-101.5,-57.3,3.6,182.07,0.42,-93.45,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,25657,2015-10-30 11:04:08:187\n9.6247,-0.0694,-0.5818,9.788,-0.0717,-0.5997,0.0012,-0.0061,0.0012,-101.4,-57.4,3.7,182.15,0.42,-93.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,25759,2015-10-30 11:04:08:289\n9.6307,-0.0694,-0.5758,9.788,-0.0717,-0.599,0,0.0024,-0.0012,-101.4,-57.4,3.4,183.15,0.42,-93.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,25860,2015-10-30 11:04:08:390\n9.6223,-0.0862,-0.5698,9.7881,-0.0707,-0.5983,0,-0.0012,-0.0012,-101.4,-57.3,3.5,182.15,0.41,-93.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,25963,2015-10-30 11:04:08:493\n9.6403,-0.0778,-0.5782,9.7881,-0.0705,-0.5973,0.0024,0.0122,-0.0024,-101.4,-57.4,3.5,182.14,0.41,-93.49,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,26065,2015-10-30 11:04:08:595\n9.6558,-0.079,-0.5794,9.7885,-0.0696,-0.5919,0.0024,-0.0012,-0.0012,-101.4,-57.4,3.7,182.09,0.41,-93.46,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,26167,2015-10-30 11:04:08:697\n9.645,-0.0934,-0.5902,9.7885,-0.0688,-0.5909,0,0.0098,0,-101.4,-57.5,3.8,182.08,0.4,-93.45,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,26269,2015-10-30 11:04:08:799\n9.6606,-0.0611,-0.5722,9.7887,-0.0695,-0.5883,0.0012,-0.0061,0,-101.4,-57.5,3.8,182.05,0.41,-93.44,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,26370,2015-10-30 11:04:08:900\n9.657,-0.073,-0.5734,9.7889,-0.0694,-0.5851,0.0012,0.0037,-0.0012,-101.5,-57.4,3.7,182.02,0.41,-93.42,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,26473,2015-10-30 11:04:09:003\n9.6415,-0.0742,-0.5698,9.7888,-0.0692,-0.5869,0,0.0049,-0.0012,-101.5,-57.4,3.6,182.04,0.4,-93.44,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,26575,2015-10-30 11:04:09:105\n9.6618,-0.0694,-0.577,9.7888,-0.0691,-0.586,0.0024,-0.0061,-0.0037,-101.5,-57.3,3.6,182.02,0.4,-93.42,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,26677,2015-10-30 11:04:09:207\n9.6355,-0.0706,-0.5842,9.789,-0.0692,-0.5834,0.0012,0.0037,-0.0024,-101.6,-57.3,3.6,182.06,0.4,-93.41,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,26779,2015-10-30 11:04:09:309\n9.6415,-0.0622,-0.5531,9.7898,-0.0684,-0.5687,0.0012,0.0024,-0.0012,-101.6,-57.3,3.5,181.91,0.4,-93.32,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,26881,2015-10-30 11:04:09:411\n9.6498,-0.0874,-0.5614,9.7896,-0.0681,-0.5725,0.0012,-0.0049,-0.0024,-101.6,-57.2,3.5,181.95,0.4,-93.35,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,26982,2015-10-30 11:04:09:512\n9.6367,-0.0862,-0.571,9.7892,-0.0678,-0.58,0.0024,-0.0061,0,-101.5,-57.3,3.3,182.96,0.4,-93.39,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,27085,2015-10-30 11:04:09:615\n9.645,-0.0766,-0.5686,9.789,-0.0673,-0.5839,-0.0012,-0.0024,-0.0037,-101.5,-57.3,3.4,182.97,0.4,-93.4,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,27187,2015-10-30 11:04:09:717\n9.6403,-0.0922,-0.5614,9.7891,-0.0669,-0.5822,0.0012,-0.0024,-0.0024,-101.4,-57.4,3.7,181.99,0.39,-93.4,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,27289,2015-10-30 11:04:09:819\n9.6498,-0.0634,-0.5423,9.7891,-0.0671,-0.5824,0.0012,0.0012,0,-101.5,-57.3,3.6,181.99,0.39,-93.4,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,27391,2015-10-30 11:04:09:921\n9.6666,-0.0778,-0.5543,9.7889,-0.0676,-0.5842,0.0012,0.0037,-0.0012,-101.5,-57.3,3.6,182.03,0.39,-93.43,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,27493,2015-10-30 11:04:10:023\n9.6438,-0.0682,-0.5782,9.7889,-0.0677,-0.5851,-0.0012,0.0171,0.0012,-101.5,-57.4,3.4,183.01,0.4,-93.42,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,27595,2015-10-30 11:04:10:125\n9.6426,-0.0778,-0.5531,9.7893,-0.0669,-0.5789,0,0.0061,-0.0012,-101.4,-57.4,3.5,181.97,0.39,-93.39,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,27697,2015-10-30 11:04:10:227\n9.6259,-0.0766,-0.5543,9.7893,-0.066,-0.5777,0,0.0086,-0.0037,-101.5,-57.4,3.8,181.96,0.39,-93.39,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,27799,2015-10-30 11:04:10:329\n9.645,-0.073,-0.5531,9.7893,-0.0663,-0.5784,0,-0.0012,-0.0024,-101.5,-57.4,3.9,181.95,0.39,-93.38,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,27901,2015-10-30 11:04:10:431\n9.6474,-0.0706,-0.5471,9.7897,-0.0655,-0.5718,0.0012,-0.0098,-0.0024,-101.6,-57.4,3.8,181.94,0.38,-93.34,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,28003,2015-10-30 11:04:10:533\n9.6211,-0.0706,-0.5507,9.7897,-0.0653,-0.5716,0,0.0122,0,-101.6,-57.4,3.7,181.94,0.38,-93.34,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,28105,2015-10-30 11:04:10:635\n9.6534,-0.0551,-0.5375,9.7896,-0.0641,-0.5745,0.0024,0.0086,-0.0012,-101.6,-57.4,4,181.97,0.37,-93.36,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,28207,2015-10-30 11:04:10:737\n9.6319,-0.0694,-0.5758,9.7893,-0.0642,-0.5791,0.0037,0.0134,-0.0012,-101.6,-57.4,4.2,182,0.37,-93.38,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,28309,2015-10-30 11:04:10:839\n9.6403,-0.0682,-0.5614,9.7895,-0.0645,-0.5748,0.0037,-0.0012,-0.0012,-101.5,-57.5,4,181.91,0.38,-93.36,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,28411,2015-10-30 11:04:10:941\n9.6331,-0.0682,-0.5483,9.7894,-0.0642,-0.5768,0.0024,0,-0.0012,-101.5,-57.4,3.9,181.93,0.37,-93.37,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,28512,2015-10-30 11:04:11:042\n9.6319,-0.0934,-0.5614,9.7893,-0.063,-0.5797,0.0012,-0.0024,-0.0012,-101.5,-57.5,3.5,181.96,0.37,-93.39,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,28615,2015-10-30 11:04:11:145\n9.651,-0.0778,-0.5662,9.7893,-0.0632,-0.5795,0,-0.0024,0,-101.5,-57.5,3.5,181.97,0.37,-93.39,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,28718,2015-10-30 11:04:11:248\n9.6486,-0.0646,-0.559,9.7891,-0.0629,-0.5824,0.0024,-0.0037,0,-101.4,-57.5,3.3,182.97,0.37,-93.4,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,28820,2015-10-30 11:04:11:350\n9.6223,-0.0922,-0.577,9.7892,-0.0626,-0.5812,0.0037,0.0049,0,-101.4,-57.4,3.3,182.98,0.36,-93.4,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,28921,2015-10-30 11:04:11:451\n9.6367,-0.0934,-0.5806,9.7893,-0.0626,-0.5795,-0.0012,0.0061,-0.0012,-101.4,-57.3,3.4,182.95,0.37,-93.39,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,29023,2015-10-30 11:04:11:553\n9.675,-0.0706,-0.5555,9.7894,-0.0625,-0.578,0,0,-0.0024,-101.4,-57.3,3.7,181.95,0.37,-93.38,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,29125,2015-10-30 11:04:11:655\n9.6151,-0.0766,-0.5519,9.7894,-0.0629,-0.5779,-0.0024,-0.0024,0,-101.5,-57.3,3.5,181.94,0.37,-93.37,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,29227,2015-10-30 11:04:11:757\n9.6103,-0.0802,-0.5746,9.7894,-0.0642,-0.5764,0.0012,0,0.0024,-101.5,-57.2,3.6,181.93,0.38,-93.37,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,29329,2015-10-30 11:04:11:859\n9.6546,-0.0754,-0.5602,9.7898,-0.0659,-0.5695,0.0012,0.0037,0.0012,-101.5,-57.2,3.4,182.85,0.38,-93.33,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,29431,2015-10-30 11:04:11:961\n9.645,-0.0491,-0.5435,9.7901,-0.0672,-0.5651,0.0024,-0.0012,0.0012,-101.6,-57.2,3.6,181.87,0.39,-93.3,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,29533,2015-10-30 11:04:12:063\n9.6379,-0.067,-0.5435,9.7904,-0.0687,-0.5584,0,0.0049,0,-101.6,-57.3,3.7,181.82,0.4,-93.28,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,29635,2015-10-30 11:04:12:165\n9.6462,-0.079,-0.5423,9.7908,-0.0691,-0.5529,0.0037,0.0037,-0.0012,-101.6,-57.2,3.8,181.75,0.4,-93.23,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,29737,2015-10-30 11:04:12:267\n9.6462,-0.0922,-0.5327,9.7909,-0.0701,-0.5505,0.0012,0.0024,0,-101.6,-57.2,3.5,181.72,0.41,-93.22,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,29839,2015-10-30 11:04:12:369\n9.6786,-0.085,-0.5195,9.7911,-0.0712,-0.5469,0,-0.0012,0,-101.6,-57.3,3.2,182.69,0.41,-93.21,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,29941,2015-10-30 11:04:12:471\n9.6702,-0.1053,-0.5303,9.791,-0.0729,-0.5481,0.0012,0.0073,0.0024,-101.7,-57.3,3.1,182.69,0.42,-93.21,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,30043,2015-10-30 11:04:12:573\n9.6259,-0.0706,-0.5495,9.7908,-0.0731,-0.5516,0.0012,-0.0049,0,-101.9,-57.2,3.1,182.72,0.43,-93.22,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,30145,2015-10-30 11:04:12:675\n9.8067,-0.1472,-0.6081,9.7907,-0.073,-0.5524,0.0012,0.0134,-0.0061,-101.9,-57,3.5,181.74,0.43,-93.23,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,30246,2015-10-30 11:04:12:776\n9.4774,-0.0563,-0.589,9.7907,-0.0735,-0.5529,0.0012,-0.0159,0.0037,-101.9,-57.1,3.7,181.7,0.44,-93.21,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,30349,2015-10-30 11:04:12:879\n9.5924,-0.0467,-0.498,9.7908,-0.0747,-0.551,0.0012,-0.0012,-0.0012,-101.7,-57.2,3.6,181.72,0.44,-93.22,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,30451,2015-10-30 11:04:12:981\n9.6247,-0.0814,-0.5315,9.7905,-0.0761,-0.5569,0.0012,-0.0098,0,-101.7,-57.3,3.6,181.75,0.44,-93.24,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,30553,2015-10-30 11:04:13:083\n9.669,-0.0754,-0.5207,9.79,-0.0756,-0.5651,0.0012,0.0281,0,-101.7,-57.3,3.5,181.87,0.44,-93.3,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,30655,2015-10-30 11:04:13:185\n9.6486,-0.0754,-0.5303,9.7909,-0.0766,-0.5494,0.0012,0.0122,0,-101.7,-57.2,3.3,182.74,0.45,-93.24,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,30756,2015-10-30 11:04:13:286\n9.5948,-0.0551,-0.5076,9.7917,-0.0773,-0.5348,0.0024,0.0098,-0.0012,-101.6,-57.2,3.2,182.54,0.45,-93.13,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,30859,2015-10-30 11:04:13:389\n9.6534,-0.0742,-0.5303,9.7932,-0.0775,-0.5068,0,0.0806,-0.0024,-101.6,-57.3,3,182.41,0.46,-93.05,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,30961,2015-10-30 11:04:13:491\n9.6714,-0.0802,-0.4393,9.7959,-0.0764,-0.4513,-0.0012,0.0648,-0.0024,-101.6,-57.3,2.5,181.74,0.45,-92.67,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,31063,2015-10-30 11:04:13:593\n9.6415,-0.0766,-0.3867,9.7969,-0.0761,-0.4296,0,0.0525,0,-101.7,-57.3,2,182.45,0.44,-92.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,31165,2015-10-30 11:04:13:695\n9.6558,-0.0718,-0.3986,9.7975,-0.0759,-0.4167,0.0012,0.0232,-0.0012,-101.8,-57.3,2,182.31,0.44,-92.44,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,31267,2015-10-30 11:04:13:797\n9.6247,-0.0874,-0.413,9.7976,-0.0758,-0.4135,0.0024,0.0159,0.0012,-101.8,-57.3,2,182.3,0.44,-92.43,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,31369,2015-10-30 11:04:13:899\n9.6355,-0.073,-0.401,9.798,-0.0765,-0.4023,0,0.0086,0.0012,-101.7,-57.4,2,182.21,0.44,-92.38,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,31471,2015-10-30 11:04:14:001\n9.6079,-0.0706,-0.3783,9.7982,-0.077,-0.3992,0,-0.0073,0,-101.6,-57.4,1.9,182.13,0.45,-92.33,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,31572,2015-10-30 11:04:14:102\n9.6726,-0.0646,-0.3711,9.7982,-0.0767,-0.3975,0.0012,0.0061,0,-101.6,-57.4,2.1,182.15,0.45,-92.34,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,31675,2015-10-30 11:04:14:205\n9.6618,-0.0706,-0.3867,9.7981,-0.0765,-0.3997,-0.0024,-0.011,0.0012,-101.5,-57.5,2.2,182.1,0.45,-92.34,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,31777,2015-10-30 11:04:14:307\n9.6175,-0.073,-0.3974,9.7983,-0.0775,-0.3953,-0.0012,0.0037,0.0024,-101.5,-57.6,2.4,182.05,0.45,-92.33,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,31879,2015-10-30 11:04:14:409\n9.645,-0.0706,-0.3783,9.7986,-0.0775,-0.3887,0.0012,0.0049,0,-101.5,-57.7,2.4,181.95,0.45,-92.27,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,31981,2015-10-30 11:04:14:511\n9.6415,-0.0599,-0.3603,9.7988,-0.078,-0.3833,0.0024,-0.0061,0,-101.6,-57.6,2.7,180.96,0.46,-92.24,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,32083,2015-10-30 11:04:14:613\n9.6415,-0.0886,-0.3663,9.7987,-0.079,-0.3864,0.0012,0.0086,0,-101.6,-57.5,2.6,181.02,0.46,-92.26,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,32185,2015-10-30 11:04:14:715\n9.6367,-0.0766,-0.3663,9.7984,-0.0792,-0.3923,0.0012,-0.0098,-0.0012,-101.6,-57.3,2.4,182.06,0.46,-92.29,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,32287,2015-10-30 11:04:14:817\n9.6438,-0.0838,-0.3747,9.7982,-0.0784,-0.3985,0.0037,-0.0159,0.0012,-101.6,-57.3,2.4,182.13,0.46,-92.33,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,32389,2015-10-30 11:04:14:919\n9.6426,-0.0778,-0.4238,9.797,-0.0797,-0.4265,0,-0.0318,0.0024,-101.6,-57.3,2.3,182.41,0.47,-92.49,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,32491,2015-10-30 11:04:15:021\n9.645,-0.0551,-0.3962,9.7969,-0.0802,-0.4298,0.0012,-0.0244,0.0012,-101.6,-57.4,2.3,182.38,0.47,-92.47,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,32593,2015-10-30 11:04:15:123\n9.6666,-0.0622,-0.3795,9.797,-0.0801,-0.4263,0.0024,-0.0037,-0.0012,-101.6,-57.5,2.2,182.42,0.47,-92.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,32695,2015-10-30 11:04:15:225\n9.6259,-0.0802,-0.4034,9.7968,-0.0803,-0.4307,0.0012,-0.0037,-0.0012,-101.6,-57.5,2.2,182.47,0.47,-92.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,32797,2015-10-30 11:04:15:327\n9.6415,-0.0694,-0.395,9.7966,-0.0802,-0.4365,0.0012,-0.0073,-0.0012,-101.5,-57.5,2.3,182.47,0.47,-92.55,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,32899,2015-10-30 11:04:15:429\n9.6606,-0.0587,-0.3926,9.7963,-0.0807,-0.4413,0.0024,-0.0122,0,-101.5,-57.5,1.9,182.52,0.47,-92.58,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,33001,2015-10-30 11:04:15:531\n9.6247,-0.0826,-0.3855,9.796,-0.0819,-0.4492,0.0024,-0.0098,0,-101.5,-57.6,2,182.51,0.48,-92.6,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,33103,2015-10-30 11:04:15:633\n9.6283,-0.0826,-0.3891,9.796,-0.0815,-0.4491,0,0.0147,0,-101.6,-57.6,2.1,182.6,0.48,-92.62,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,33205,2015-10-30 11:04:15:735\n9.669,-0.0611,-0.3926,9.7962,-0.0808,-0.4437,0,0.0195,-0.0012,-101.6,-57.6,2.3,182.55,0.47,-92.59,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,33307,2015-10-30 11:04:15:837\n9.6606,-0.0838,-0.3855,9.7967,-0.079,-0.4328,0,0.0159,0,-101.7,-57.6,2.4,182.44,0.46,-92.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,33409,2015-10-30 11:04:15:939\n9.6379,-0.067,-0.3891,9.7971,-0.0784,-0.4253,-0.0012,-0.0012,0.0012,-101.7,-57.5,2.4,182.41,0.46,-92.49,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,33511,2015-10-30 11:04:16:041\n9.6415,-0.0742,-0.3879,9.7973,-0.0778,-0.4197,0.0024,0.0024,0,-101.8,-57.5,2.6,181.36,0.45,-92.45,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,33613,2015-10-30 11:04:16:143\n9.6474,-0.097,-0.3771,9.7976,-0.0773,-0.4137,0.0012,0.0061,0.0012,-101.8,-57.4,2.6,181.32,0.45,-92.43,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,33715,2015-10-30 11:04:16:245\n9.6474,-0.0814,-0.3807,9.7977,-0.0769,-0.4113,0.0012,0.0037,-0.0012,-101.8,-57.5,2.3,182.26,0.45,-92.4,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,33817,2015-10-30 11:04:16:347\n9.6486,-0.0611,-0.3687,9.7978,-0.0763,-0.4072,-0.0012,0.0073,-0.0012,-101.7,-57.5,2,182.25,0.45,-92.4,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,33918,2015-10-30 11:04:16:448\n9.6355,-0.0838,-0.3711,9.7981,-0.0761,-0.402,0.0024,0.0073,0,-101.7,-57.5,2,182.19,0.44,-92.37,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,34021,2015-10-30 11:04:16:551\n9.6498,-0.0898,-0.3723,9.7984,-0.0758,-0.393,0.0012,0.0183,-0.0037,-101.8,-57.4,2.1,182.07,0.44,-92.3,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,34122,2015-10-30 11:04:16:652\n9.6654,-0.0694,-0.3903,9.7986,-0.0758,-0.3878,-0.0012,-0.0012,0,-101.7,-57.4,2.1,182.02,0.44,-92.27,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,34225,2015-10-30 11:04:16:755\n9.663,-0.073,-0.3783,9.7987,-0.0757,-0.3859,0.0024,-0.0049,0,-101.6,-57.4,2.3,182,0.44,-92.26,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,34326,2015-10-30 11:04:16:856\n9.6379,-0.0802,-0.346,9.7995,-0.0744,-0.3662,0,-0.0061,0,-101.6,-57.4,2.3,181.79,0.44,-92.14,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,34428,2015-10-30 11:04:16:958\n9.6367,-0.0766,-0.3843,9.799,-0.0742,-0.3796,0.0024,-0.0183,0,-101.7,-57.4,1.9,181.93,0.43,-92.22,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,34531,2015-10-30 11:04:17:061\n"
  },
  {
    "path": "test/data/Sensor_record_20151030_110448_AndroSensor.csv",
    "content": "-9.8497,0.0275,-0.3603,-9.789,0.0442,-0.5851,0.0012,0.0171,0.0012,159.6,-21.9,-132.4,98.58,-0.26,93.41,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,46,2015-10-30 11:04:25:352\n-9.8701,0.0012,-0.3304,-9.7881,0.0426,-0.6006,0.0012,0.0171,-0.0024,159.8,-22,-132.1,98.57,-0.25,93.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,148,2015-10-30 11:04:25:454\n-9.8521,0.0192,-0.3352,-9.7871,0.0418,-0.6171,-0.0012,0.0269,-0.0012,159.9,-22,-131.7,98.56,-0.24,93.61,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,250,2015-10-30 11:04:25:556\n-9.8138,0.0299,-0.4741,-9.7861,0.0412,-0.6332,0.0024,0.0171,-0.0024,160.1,-22,-131.1,98.61,-0.24,93.7,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,352,2015-10-30 11:04:25:658\n-9.8318,0.0275,-0.4106,-9.7857,0.0414,-0.6395,0.0024,0.0147,0,160,-21.9,-130.7,98.61,-0.24,93.74,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,454,2015-10-30 11:04:25:760\n-9.8497,0.0204,-0.3543,-9.7854,0.0412,-0.6445,-0.0012,0.0183,0.0012,160.1,-21.9,-130.6,98.6,-0.24,93.76,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,556,2015-10-30 11:04:25:862\n-9.8414,0.0575,-0.4094,-9.7846,0.0401,-0.6551,-0.0012,0.0195,0.0012,160,-21.9,-130.5,98.66,-0.23,93.83,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,658,2015-10-30 11:04:25:964\n-9.815,0.0443,-0.407,-9.7845,0.0403,-0.6575,0.0012,0.0171,0.0012,160.1,-22.1,-130.5,98.66,-0.24,93.84,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,760,2015-10-30 11:04:26:066\n-9.8497,0.0323,-0.3891,-9.7844,0.0398,-0.6588,-0.0024,0.0183,0,160.1,-22,-130.1,98.66,-0.23,93.84,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,862,2015-10-30 11:04:26:168\n-9.8354,0.0323,-0.401,-9.7839,0.0402,-0.6656,0.0024,0.0073,0.0012,160.1,-22.1,-130.3,98.65,-0.23,93.89,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,964,2015-10-30 11:04:26:270\n-9.8497,0.0144,-0.3388,-9.7838,0.0395,-0.6673,0,0.033,-0.0012,159.9,-22,-130.3,98.65,-0.23,93.9,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,1065,2015-10-30 11:04:26:371\n-9.8509,0.0215,-0.3412,-9.7839,0.0394,-0.6662,0,0.0244,-0.0012,160,-21.9,-130.2,98.65,-0.23,93.9,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,1168,2015-10-30 11:04:26:474\n-9.815,0.0275,-0.4142,-9.784,0.0392,-0.6646,-0.0024,0.0232,-0.0024,159.8,-21.8,-130.2,98.65,-0.23,93.88,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,1270,2015-10-30 11:04:26:576\n-9.8342,0.0311,-0.4106,-9.7838,0.0378,-0.6672,0.0024,0.0134,0,159.8,-21.8,-130.6,98.6,-0.22,93.9,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,1372,2015-10-30 11:04:26:678\n-9.8533,0.0347,-0.3938,-9.7841,0.0377,-0.6627,0.0012,0.011,0,159.7,-21.9,-130.7,98.61,-0.22,93.89,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,1475,2015-10-30 11:04:26:781\n-9.8462,0.0419,-0.3627,-9.7836,0.038,-0.6706,0.0024,0.0086,0,159.8,-22,-130.5,98.66,-0.22,93.92,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,1576,2015-10-30 11:04:26:882\n-9.8138,0.0383,-0.4633,-9.7833,0.0384,-0.6751,0,0.0012,-0.0024,160,-21.9,-130.4,98.66,-0.22,93.93,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,1677,2015-10-30 11:04:26:983\n-9.8438,0.0431,-0.3735,-9.7837,0.0376,-0.6689,0.0024,0.0159,0,160.1,-21.9,-130.3,98.66,-0.22,93.93,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,1780,2015-10-30 11:04:27:086\n-9.8294,0.0275,-0.3232,-9.7843,0.0374,-0.6602,0.0012,0.0073,0.0012,160.1,-21.9,-130.4,98.67,-0.22,93.86,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,1882,2015-10-30 11:04:27:188\n-9.8581,0.0479,-0.3974,-9.7844,0.0373,-0.6592,0.0024,0.0134,-0.0024,160.1,-22,-130.2,98.67,-0.22,93.86,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,1984,2015-10-30 11:04:27:290\n-9.8438,0.0431,-0.3328,-9.7842,0.0363,-0.6615,0,0.0098,-0.0024,160,-21.9,-130.4,98.68,-0.21,93.87,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,2086,2015-10-30 11:04:27:392\n-9.8402,0.0239,-0.3591,-9.7839,0.0363,-0.6658,0,0.0147,-0.0012,159.9,-22.1,-130.5,98.67,-0.21,93.89,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,2188,2015-10-30 11:04:27:494\n-9.8497,0.0168,-0.3735,-9.7839,0.0361,-0.6664,0,0.022,-0.0024,159.9,-22.1,-130.6,98.61,-0.21,93.9,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,2290,2015-10-30 11:04:27:596\n-9.8545,0.0204,-0.3771,-9.7833,0.0357,-0.6752,0.0049,0.0208,0,160,-22.1,-130.6,98.61,-0.21,93.94,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,2392,2015-10-30 11:04:27:698\n-9.8497,0.0335,-0.3831,-9.7836,0.0364,-0.6703,-0.0012,0.0086,0.0037,160.1,-22,-130.7,98.61,-0.21,93.92,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,2494,2015-10-30 11:04:27:800\n-9.8306,0.0443,-0.3986,-9.7834,0.0363,-0.6738,0.0012,0.0171,0.0024,160.1,-22,-130.6,98.61,-0.21,93.94,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,2595,2015-10-30 11:04:27:901\n-9.8474,0.0335,-0.3879,-9.7836,0.0369,-0.6711,-0.0024,0.0122,0.0012,160,-22.1,-130.5,98.67,-0.21,93.93,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,2698,2015-10-30 11:04:28:004\n-9.8497,0.0491,-0.3567,-9.7835,0.0372,-0.6728,0.0012,0.0171,0,160,-22.1,-130.2,98.66,-0.22,93.94,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,2800,2015-10-30 11:04:28:106\n-9.8474,0.0383,-0.3567,-9.7829,0.0361,-0.6812,0.0024,0.0195,-0.0012,159.9,-22,-130.1,98.66,-0.21,93.98,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,2902,2015-10-30 11:04:28:208\n-9.8462,0.0323,-0.4477,-9.7826,0.035,-0.685,0.0012,0.0037,0.0024,159.9,-21.9,-130.1,98.66,-0.2,94.02,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,3004,2015-10-30 11:04:28:310\n-9.8617,0.0263,-0.4058,-9.7826,0.0359,-0.6847,0,0.0147,0.0012,159.9,-21.9,-130.3,98.66,-0.21,94,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,3106,2015-10-30 11:04:28:412\n-9.8497,0.0383,-0.4609,-9.7816,0.0351,-0.6986,0.0037,0.0403,-0.0012,159.9,-21.9,-130.1,98.65,-0.21,94.09,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,3208,2015-10-30 11:04:28:514\n-9.8318,0.0335,-0.4561,-9.7811,0.0372,-0.7058,0.0037,0.0195,0.0012,160,-22,-130,98.64,-0.21,94.12,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,3310,2015-10-30 11:04:28:616\n-9.845,0.0311,-0.4262,-9.7811,0.0359,-0.7067,0.0012,0.0318,-0.0037,160.2,-22.1,-130,98.64,-0.21,94.13,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,3412,2015-10-30 11:04:28:718\n-9.8497,0.0335,-0.4573,-9.7796,0.0342,-0.7261,-0.0024,0.0367,-0.0037,160.3,-22.3,-129.7,98.63,-0.2,94.22,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,3514,2015-10-30 11:04:28:820\n-9.8545,0.0503,-0.401,-9.7799,0.0349,-0.7221,0.0012,-0.0073,0.0012,160.3,-22.4,-129.7,98.63,-0.2,94.22,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,3616,2015-10-30 11:04:28:922\n-9.8497,0.0395,-0.4022,-9.7809,0.0372,-0.7087,0.0037,0.0049,0,160.3,-22.5,-129.4,98.69,-0.21,94.18,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,3718,2015-10-30 11:04:29:024\n-9.8497,0.0395,-0.3891,-9.7818,0.038,-0.6957,0.0024,0.0061,0.0024,160.2,-22.4,-129.4,98.69,-0.22,94.09,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,3819,2015-10-30 11:04:29:125\n-9.8557,0.0287,-0.3771,-9.7823,0.0372,-0.6886,0.0012,-0.0098,-0.0012,160.2,-22.3,-129.5,98.7,-0.22,94.07,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,3922,2015-10-30 11:04:29:228\n-9.827,0.0371,-0.4154,-9.7835,0.0381,-0.6727,0.0024,-0.0147,0,160.2,-22.2,-129.5,98.71,-0.22,93.98,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,4024,2015-10-30 11:04:29:330\n-9.8497,0.0347,-0.3771,-9.785,0.0383,-0.6493,0.0024,-0.011,-0.0012,160.2,-22.3,-129.5,98.74,-0.22,93.8,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,4126,2015-10-30 11:04:29:432\n-9.8186,0.0323,-0.419,-9.7861,0.0382,-0.6321,0.0012,0.0073,-0.0024,160.1,-22.2,-129.8,98.69,-0.22,93.71,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,4228,2015-10-30 11:04:29:534\n-9.8126,0.0383,-0.4513,-9.7869,0.0382,-0.6205,0,0.0134,0,160.1,-22.2,-130,98.7,-0.22,93.63,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,4330,2015-10-30 11:04:29:636\n-9.8366,0.0251,-0.4118,-9.7876,0.0379,-0.61,0.0037,0.0098,0.0012,160.1,-22.2,-130,98.71,-0.22,93.57,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,4432,2015-10-30 11:04:29:738\n-9.8497,0.0479,-0.4298,-9.7883,0.038,-0.5973,0,-0.0073,0.0012,160,-22.2,-129.6,98.73,-0.22,93.49,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,4534,2015-10-30 11:04:29:840\n-9.8318,0.0383,-0.4525,-9.7887,0.0376,-0.5907,0.0012,0.0049,0,160.1,-22.1,-129.4,98.79,-0.22,93.46,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,4636,2015-10-30 11:04:29:942\n-9.8569,0.0215,-0.3519,-9.7898,0.0374,-0.5733,-0.0037,-0.0147,0,160.1,-22.1,-129.8,98.75,-0.22,93.35,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,4738,2015-10-30 11:04:30:044\n-9.845,0.0431,-0.4549,-9.7903,0.0378,-0.5641,-0.0012,0.0122,-0.0012,160,-22.1,-129.8,98.76,-0.22,93.31,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,4840,2015-10-30 11:04:30:146\n-9.8234,0.0359,-0.4298,-9.7909,0.0388,-0.5531,-0.0037,0.0024,0.0024,159.9,-22.1,-130.2,98.76,-0.22,93.24,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,4942,2015-10-30 11:04:30:248\n-9.8497,0.0599,-0.4022,-9.7913,0.0383,-0.5458,0.0012,0.0037,-0.0012,160,-22.2,-130.2,98.77,-0.22,93.2,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,5043,2015-10-30 11:04:30:349\n-9.8234,0.0371,-0.4322,-9.7921,0.0378,-0.5326,0.0012,-0.0061,-0.0012,160,-22.1,-130.1,98.79,-0.22,93.11,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,5146,2015-10-30 11:04:30:452\n-9.8138,0.0383,-0.3903,-9.7925,0.0374,-0.5249,0,-0.0012,0.0012,160.2,-22.1,-130.1,98.8,-0.22,93.07,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,5248,2015-10-30 11:04:30:554\n-9.8474,0.0263,-0.3352,-9.7932,0.0371,-0.5112,0.0012,-0.0012,0.0012,160.2,-22,-130.1,98.81,-0.22,93,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,5350,2015-10-30 11:04:30:656\n-9.8497,0.0347,-0.3627,-9.7935,0.0369,-0.5059,0.0012,-0.011,0.0012,160.1,-22.2,-130,98.82,-0.22,92.96,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,5452,2015-10-30 11:04:30:758\n-9.8258,0.0275,-0.3938,-9.7939,0.037,-0.497,0.0012,-0.0012,0.0024,160.1,-22.3,-129.9,98.83,-0.22,92.91,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,5554,2015-10-30 11:04:30:860\n-9.8497,0.0431,-0.3555,-9.7947,0.0382,-0.482,0,-0.0073,0,160,-22.2,-129.9,98.83,-0.22,92.82,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,5656,2015-10-30 11:04:30:962\n-9.8234,0.0539,-0.3915,-9.7948,0.0379,-0.4802,0.0037,0.0024,-0.0012,159.9,-22.1,-130.2,98.84,-0.22,92.81,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,5758,2015-10-30 11:04:31:064\n-9.8126,0.0383,-0.4298,-9.795,0.038,-0.4757,0,0.0024,0,160,-22.1,-130,98.84,-0.22,92.79,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,5860,2015-10-30 11:04:31:166\n-9.8701,0.0407,-0.4357,-9.7954,0.0387,-0.4669,0.0012,-0.0037,0.0024,160.2,-22.1,-129.8,98.85,-0.22,92.75,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,5961,2015-10-30 11:04:31:267\n-9.8462,0.0371,-0.4094,-9.7955,0.0387,-0.4636,0,0.0147,0,160.1,-22.2,-129.6,98.85,-0.23,92.71,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,6064,2015-10-30 11:04:31:370\n-9.8031,0.0299,-0.4345,-9.7953,0.0386,-0.4696,0.0012,0.011,-0.0012,160.1,-22.1,-129.6,98.85,-0.23,92.73,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,6166,2015-10-30 11:04:31:472\n-9.8378,0.0204,-0.3687,-9.7957,0.0386,-0.4601,0,-0.011,0.0024,160,-22.1,-130,98.85,-0.22,92.71,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,6267,2015-10-30 11:04:31:573\n-9.8426,0.0335,-0.3974,-9.7959,0.0383,-0.4571,0.0012,0.0012,0.0012,160.2,-22.1,-129.9,98.86,-0.22,92.67,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,6370,2015-10-30 11:04:31:676\n-9.8509,0.0479,-0.4214,-9.7962,0.0383,-0.4504,-0.0024,-0.0049,0.0012,160.2,-22.1,-129.8,98.86,-0.22,92.65,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,6472,2015-10-30 11:04:31:778\n-9.8402,0.0563,-0.3926,-9.7966,0.0385,-0.4418,0.0037,-0.0037,0,160.1,-22.1,-129.6,98.87,-0.22,92.58,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,6574,2015-10-30 11:04:31:880\n-9.8474,0.0431,-0.4322,-9.7966,0.0379,-0.4406,0,-0.0012,0,160,-22.1,-129.7,98.88,-0.22,92.58,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,6676,2015-10-30 11:04:31:982\n-9.8773,0.0215,-0.3903,-9.7968,0.0379,-0.4369,0,0,0,160,-22.1,-129.6,98.88,-0.22,92.57,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,6778,2015-10-30 11:04:32:084\n-9.8653,0.0371,-0.431,-9.7971,0.038,-0.4299,0.0012,-0.0061,0,160.1,-22.1,-129.7,98.89,-0.22,92.52,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,6880,2015-10-30 11:04:32:186\n-9.8581,0.0215,-0.4812,-9.797,0.0381,-0.4328,-0.0012,0.0061,0,160.2,-22.2,-129.7,98.88,-0.22,92.53,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,6982,2015-10-30 11:04:32:288\n-9.8246,0.0311,-0.4549,-9.7971,0.0378,-0.43,0.0024,-0.0037,-0.0024,160.1,-22.2,-129.8,98.89,-0.22,92.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,7084,2015-10-30 11:04:32:390\n-9.833,0.0347,-0.4609,-9.7972,0.0368,-0.4274,0.0024,0,-0.0024,160.1,-22.3,-129.7,98.9,-0.22,92.48,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,7186,2015-10-30 11:04:32:492\n-9.821,0.0383,-0.4274,-9.7973,0.0367,-0.4245,0,0.0061,-0.0012,160,-22.3,-129.5,98.96,-0.21,92.48,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,7288,2015-10-30 11:04:32:594\n-9.8474,0.0395,-0.4908,-9.7971,0.0364,-0.4296,0,0.0049,0,160,-22.3,-129.1,98.96,-0.21,92.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,7390,2015-10-30 11:04:32:696\n-9.8701,0.0443,-0.4405,-9.7973,0.0371,-0.4251,0.0012,-0.0061,0.0012,160.1,-22.3,-129.2,98.96,-0.22,92.49,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,7492,2015-10-30 11:04:32:798\n-9.8294,0.0467,-0.4597,-9.7973,0.0373,-0.4251,0.0037,0.0024,0.0012,160.2,-22.2,-129,98.96,-0.22,92.48,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,7594,2015-10-30 11:04:32:900\n-9.8282,0.0048,-0.4154,-9.7975,0.0373,-0.421,0.0012,-0.0073,-0.0012,160.2,-22.2,-129.3,98.96,-0.22,92.47,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,7697,2015-10-30 11:04:33:003\n-9.8629,0.0204,-0.4166,-9.7977,0.0374,-0.4157,0.0024,0.0086,0,160.1,-22.2,-129.3,98.97,-0.22,92.43,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,7798,2015-10-30 11:04:33:104\n-9.7564,0.0275,-0.3867,-9.7977,0.0369,-0.4157,0.0012,-0.011,-0.0024,160.1,-22.1,-129.4,98.97,-0.22,92.45,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,7900,2015-10-30 11:04:33:206\n-9.8043,0.0239,-0.5112,-9.7971,0.0365,-0.4289,0,0.0049,-0.0024,160.2,-22.1,-129.6,98.89,-0.22,92.51,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,8002,2015-10-30 11:04:33:308\n-9.8186,0.0323,-0.4322,-9.7979,0.0358,-0.4102,0.0037,-0.0257,-0.0024,160.2,-22.1,-129.7,98.91,-0.21,92.44,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,8104,2015-10-30 11:04:33:410\n-9.809,0.0491,-0.3795,-9.7981,0.0359,-0.4077,0,0.0037,0.0012,160.2,-22.2,-129.4,98.99,-0.21,92.38,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,8206,2015-10-30 11:04:33:512\n-9.8497,0.0455,-0.425,-9.7979,0.0356,-0.4106,0,0.022,-0.0024,160.2,-22.2,-129.4,98.99,-0.21,92.4,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,8308,2015-10-30 11:04:33:614\n-9.8497,0.0383,-0.4465,-9.798,0.0355,-0.4086,0.0012,0,-0.0024,160.3,-22.1,-129.4,98.99,-0.21,92.39,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,8410,2015-10-30 11:04:33:716\n-9.845,0.0323,-0.3771,-9.7984,0.0363,-0.4002,0.0012,0.0049,-0.0012,160.2,-22.1,-129.5,98.99,-0.21,92.34,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,8512,2015-10-30 11:04:33:818\n-9.845,0.0251,-0.4453,-9.7981,0.0372,-0.4068,0.0012,0.0171,0,160.1,-22,-129.9,98.91,-0.22,92.38,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,8614,2015-10-30 11:04:33:920\n-9.8605,0.0263,-0.4585,-9.7978,0.0365,-0.4143,0.0012,0.0073,0,160,-22.2,-129.7,98.91,-0.21,92.41,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,8716,2015-10-30 11:04:34:022\n-9.8462,0.0287,-0.4956,-9.7977,0.0365,-0.4159,0.0012,-0.0061,-0.0024,160.1,-22.1,-129.8,98.91,-0.22,92.43,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,8818,2015-10-30 11:04:34:124\n-9.7181,0.0024,-0.4992,-9.7977,0.036,-0.4165,0.0012,0.0073,0,160.1,-22.1,-129.7,98.91,-0.21,92.43,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,8920,2015-10-30 11:04:34:226\n-9.8928,0.0156,-0.419,-9.7978,0.0366,-0.4145,0.0049,0.0024,0,160.1,-22,-129.6,98.91,-0.21,92.42,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,9022,2015-10-30 11:04:34:328\n-9.821,0.0275,-0.4681,-9.7977,0.038,-0.4165,0.0024,0.0086,0,160.1,-22,-129.6,98.9,-0.22,92.42,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,9123,2015-10-30 11:04:34:429\n-9.8102,0.0299,-0.4537,-9.7977,0.0381,-0.4165,0,-0.0012,-0.0012,160,-22,-129.7,98.9,-0.22,92.44,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,9226,2015-10-30 11:04:34:532\n-9.8497,0.0168,-0.4453,-9.7977,0.0376,-0.4152,0.0024,-0.0024,0,160.3,-22,-129.4,98.97,-0.22,92.42,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,9328,2015-10-30 11:04:34:634\n-9.8485,0.0335,-0.4441,-9.7976,0.0376,-0.4178,0,-0.0012,-0.0012,160.3,-22.1,-129.3,98.97,-0.22,92.44,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,9430,2015-10-30 11:04:34:736\n-9.7935,0.0323,-0.4561,-9.7977,0.0378,-0.4154,0.0024,-0.0049,-0.0012,160.4,-22.1,-129.3,98.97,-0.22,92.43,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,9532,2015-10-30 11:04:34:838\n-9.8222,0.0359,-0.4872,-9.7976,0.038,-0.417,0.0012,0.0037,0,160.3,-22.2,-129.6,98.9,-0.22,92.44,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,9634,2015-10-30 11:04:34:940\n-9.8222,0.0383,-0.4657,-9.7978,0.0384,-0.4141,-0.0012,0,0.0012,160.3,-22.2,-129.4,98.96,-0.22,92.42,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,9736,2015-10-30 11:04:35:042\n-9.8078,0.0239,-0.4609,-9.7977,0.0385,-0.4164,0.0012,0.0061,0.0012,160.2,-22.1,-129.4,98.96,-0.23,92.43,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,9838,2015-10-30 11:04:35:144\n-9.8438,0.0204,-0.4884,-9.7975,0.0382,-0.4191,0,0.0073,0.0024,160.2,-22,-129.4,98.96,-0.22,92.44,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,9940,2015-10-30 11:04:35:246\n-9.8581,0.0168,-0.4298,-9.7976,0.0389,-0.4171,0,0.0012,0.0012,160.1,-21.9,-129.6,98.89,-0.23,92.44,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,10042,2015-10-30 11:04:35:348\n-9.8497,0.0263,-0.4429,-9.7977,0.0393,-0.4154,0.0012,-0.0037,0,160.1,-22,-129.5,98.96,-0.23,92.43,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,10144,2015-10-30 11:04:35:450\n-9.833,0.0287,-0.492,-9.7978,0.0388,-0.4135,0.0012,0.0037,0,160.2,-22.1,-129.3,98.96,-0.23,92.43,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,10246,2015-10-30 11:04:35:552\n-9.8222,0.0299,-0.4537,-9.7976,0.0383,-0.418,0.0024,0.0024,0,160.2,-22.1,-128.8,98.96,-0.22,92.44,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,10348,2015-10-30 11:04:35:654\n-9.8246,0.0227,-0.4489,-9.7976,0.0388,-0.4169,0.0012,0,0.0037,160.2,-22,-128.4,99.02,-0.23,92.44,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,10450,2015-10-30 11:04:35:756\n-9.8497,0.0479,-0.4441,-9.7976,0.0384,-0.4172,-0.0012,0.0073,-0.0024,160.2,-21.9,-128.6,98.96,-0.22,92.44,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,10552,2015-10-30 11:04:35:858\n-9.8342,0.0395,-0.4896,-9.7972,0.0376,-0.4269,0.0024,0.011,0,160.2,-22,-128.7,98.96,-0.22,92.5,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,10654,2015-10-30 11:04:35:960\n-9.821,0.0204,-0.5088,-9.7974,0.0386,-0.4226,0.0024,-0.022,0.0012,160.3,-22,-128.6,98.95,-0.23,92.49,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,10756,2015-10-30 11:04:36:062\n-9.8497,0.0371,-0.3843,-9.7984,0.0382,-0.3981,0.0012,-0.0073,0.0012,160.2,-22,-128.5,99.04,-0.22,92.35,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,10858,2015-10-30 11:04:36:164\n-9.8222,0.0419,-0.4764,-9.7976,0.0385,-0.4179,0.0037,0.0379,0,160,-22,-128.7,98.97,-0.22,92.39,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,10960,2015-10-30 11:04:36:266\n-9.839,0.0323,-0.4669,-9.7973,0.0385,-0.4257,-0.0012,-0.0061,0,160,-22.1,-128.8,98.95,-0.23,92.49,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,11062,2015-10-30 11:04:36:368\n-9.8294,0.0347,-0.3962,-9.7978,0.0375,-0.4141,0.0012,-0.0208,-0.0012,160,-22.2,-129.1,98.97,-0.22,92.42,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,11164,2015-10-30 11:04:36:470\n-9.8246,0.012,-0.4537,-9.798,0.0377,-0.4083,-0.0012,-0.0024,0.0024,160,-22.2,-129.2,98.97,-0.22,92.4,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,11266,2015-10-30 11:04:36:572\n-9.8474,0.0275,-0.4334,-9.7977,0.0371,-0.4155,0.0024,0.011,-0.0012,160.1,-22.1,-129.6,98.91,-0.22,92.41,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,11367,2015-10-30 11:04:36:673\n-9.8521,0.0383,-0.4597,-9.7975,0.0376,-0.4208,0,0.0171,0,160.3,-22.1,-129.1,98.96,-0.22,92.46,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,11470,2015-10-30 11:04:36:776\n-9.8497,0.0407,-0.4274,-9.7977,0.0379,-0.4147,0.0012,0.0024,0,160.2,-22,-128.7,98.96,-0.22,92.44,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,11572,2015-10-30 11:04:36:878\n-9.8701,0.0407,-0.4417,-9.798,0.0383,-0.4076,-0.0012,-0.0159,0.0037,160.2,-22.1,-128.8,98.97,-0.22,92.38,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,11674,2015-10-30 11:04:36:980\n-9.8222,0.0491,-0.3615,-9.7982,0.0378,-0.4041,0.0024,0.0012,0,160.1,-22,-129,98.98,-0.22,92.36,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,11776,2015-10-30 11:04:37:082\n-9.8234,0.0239,-0.4465,-9.7982,0.037,-0.4035,0.0037,0.0122,-0.0012,160.1,-22,-129.1,98.98,-0.22,92.36,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,11878,2015-10-30 11:04:37:184\n-9.8497,0.0335,-0.4022,-9.7983,0.0356,-0.4026,0,-0.0049,0,160.1,-22,-128.8,98.99,-0.21,92.36,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,11980,2015-10-30 11:04:37:286\n-9.8533,0.0419,-0.4262,-9.7985,0.0351,-0.3957,0.0037,0.0012,-0.0024,160.2,-22.2,-128.9,99,-0.21,92.31,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,12082,2015-10-30 11:04:37:388\n-9.8521,0.018,-0.3747,-9.7985,0.0343,-0.3968,0.0049,-0.0061,0,160.2,-22.2,-128.8,99.01,-0.2,92.32,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,12184,2015-10-30 11:04:37:490\n-9.8497,0.0204,-0.3711,-9.7987,0.0336,-0.3912,0.0024,-0.0012,0,160.3,-22.2,-128.8,99.01,-0.2,92.3,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,12286,2015-10-30 11:04:37:592\n-9.8509,0.0371,-0.3292,-9.7992,0.0336,-0.3802,0,-0.0024,0,160.1,-22,-129.2,99.03,-0.2,92.22,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,12388,2015-10-30 11:04:37:694\n-9.8462,0.0299,-0.3316,-9.7994,0.0326,-0.3732,-0.0012,0,-0.0024,160,-22.1,-129.3,99.04,-0.19,92.18,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,12490,2015-10-30 11:04:37:796\n-9.8653,0.0108,-0.2861,-9.7999,0.0312,-0.3611,0.0024,-0.0208,-0.0037,159.9,-21.9,-129.3,99.06,-0.18,92.11,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,12592,2015-10-30 11:04:37:898\n-9.8521,0.0275,-0.2107,-9.8007,0.0299,-0.3401,0.0012,-0.0257,-0.0012,159.9,-22,-129.2,99.08,-0.18,92.04,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,12694,2015-10-30 11:04:38:000\n-9.8342,0.0419,-0.3017,-9.8011,0.0285,-0.326,0.0024,-0.0037,0,160,-21.9,-129.1,99.12,-0.17,91.9,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,12796,2015-10-30 11:04:38:102\n-9.8749,0.0347,-0.1341,-9.802,0.028,-0.2998,0.0024,0.0086,-0.0037,159.8,-22,-129.4,99.14,-0.17,91.77,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,12898,2015-10-30 11:04:38:204\n-9.8509,0.0407,-0.1987,-9.8021,0.0268,-0.2968,-0.0012,-0.0012,-0.0012,159.7,-22,-129.7,99.09,-0.16,91.73,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,13000,2015-10-30 11:04:38:306\n-9.8294,0.0144,-0.2969,-9.802,0.0258,-0.2995,0.0012,-0.0134,-0.0024,159.6,-22,-130,99.09,-0.15,91.75,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,13101,2015-10-30 11:04:38:407\n-9.8605,0.012,-0.1688,-9.8025,0.0241,-0.2839,0,-0.0134,-0.0012,159.7,-22.1,-130.1,99.12,-0.14,91.7,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,13204,2015-10-30 11:04:38:510\n-9.8641,0.0204,-0.2155,-9.8024,0.0233,-0.2858,0.0037,0,-0.0012,159.7,-22.1,-130.3,99.13,-0.14,91.67,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,13306,2015-10-30 11:04:38:612\n-9.845,0.0491,-0.2813,-9.8024,0.0227,-0.2855,0,0.0012,-0.0037,159.6,-22,-130.5,99.13,-0.13,91.67,36.814342,-119.74824,,336.6613017,,203.1613,,0 / 0,13408,2015-10-30 11:04:38:714\n-9.8569,0.0515,-0.249,-9.8029,0.0214,-0.2679,0.0012,0,-0.0012,159.5,-21.9,-130.8,99.09,-0.12,91.57,36.814316,-119.74832,,336.6613017,,220.79031,,0 / 0,13510,2015-10-30 11:04:38:816\n-9.8462,0.018,-0.1987,-9.8034,0.021,-0.25,0.0024,-0.0147,0,159.5,-22,-131,99.11,-0.12,91.48,36.814316,-119.74832,,336.6613017,,220.79031,,0 / 0,13612,2015-10-30 11:04:38:918\n-9.8533,0.0395,-0.1879,-9.8037,0.0213,-0.2398,0.0024,0.0086,-0.0012,159.5,-22,-131.7,99.06,-0.12,91.4,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,13714,2015-10-30 11:04:39:020\n-9.8545,0.0323,-0.2298,-9.8037,0.02,-0.2396,0.0024,-0.0024,-0.0024,159.5,-22,-131.7,99.07,-0.12,91.4,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,13816,2015-10-30 11:04:39:122\n-9.8569,0.0215,-0.2107,-9.8037,0.0193,-0.2358,0,-0.0098,0,159.5,-22.1,-131.7,99.07,-0.11,91.38,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,13918,2015-10-30 11:04:39:224\n-9.8426,0.0323,-0.2239,-9.8038,0.0194,-0.2319,0,-0.0049,-0.0012,159.6,-22.2,-131.3,99.14,-0.11,91.35,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,14020,2015-10-30 11:04:39:326\n-9.8497,0.0192,-0.2215,-9.8038,0.0195,-0.2328,0.0024,0.0012,-0.0012,159.6,-22.1,-131.3,99.14,-0.11,91.36,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,14122,2015-10-30 11:04:39:428\n-9.8462,0.0359,-0.2286,-9.8038,0.0196,-0.2309,0.0037,-0.0012,-0.0012,159.6,-22.1,-131.2,99.14,-0.11,91.36,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,14223,2015-10-30 11:04:39:529\n-9.8653,0.0287,-0.2705,-9.8039,0.0201,-0.2307,0,-0.0024,-0.0012,159.6,-22.1,-131.3,99.14,-0.12,91.35,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,14326,2015-10-30 11:04:39:632\n-9.8569,0.018,-0.2334,-9.8038,0.0199,-0.2337,-0.0024,-0.0073,0,159.6,-22,-131.4,99.14,-0.12,91.37,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,14428,2015-10-30 11:04:39:734\n-9.8725,0.0455,-0.2693,-9.8036,0.0205,-0.241,0.0024,-0.0012,0,159.6,-22,-131,99.13,-0.12,91.41,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,14530,2015-10-30 11:04:39:836\n-9.8521,0.0239,-0.2777,-9.8035,0.0203,-0.2475,-0.0012,0.0061,-0.0012,159.5,-21.9,-130.9,99.12,-0.12,91.44,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,14632,2015-10-30 11:04:39:938\n-9.8581,0.0251,-0.316,-9.8034,0.0211,-0.2499,0,0,0.0024,159.6,-21.9,-130.7,99.11,-0.12,91.46,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,14734,2015-10-30 11:04:40:040\n-9.8497,0.0431,-0.3256,-9.8034,0.0214,-0.2474,0.0024,0.0049,-0.0024,159.6,-21.8,-130.8,99.11,-0.12,91.45,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,14836,2015-10-30 11:04:40:142\n-9.8545,0.0395,-0.3352,-9.8032,0.0211,-0.2564,-0.0024,0.0061,-0.0012,159.5,-21.9,-130.8,99.11,-0.12,91.48,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,14937,2015-10-30 11:04:40:243\n-9.8426,0.0383,-0.3412,-9.8032,0.0206,-0.2567,0.0024,-0.0061,-0.0012,159.5,-21.8,-131.1,99.11,-0.12,91.5,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,15040,2015-10-30 11:04:40:346\n-9.8569,0.0251,-0.3292,-9.8031,0.0208,-0.2602,0,0.0037,-0.0037,159.5,-22,-131.3,99.1,-0.12,91.51,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,15142,2015-10-30 11:04:40:448\n-9.8521,0.0251,-0.3148,-9.8031,0.0216,-0.2591,0.0024,-0.0195,-0.0024,159.6,-22.1,-131.4,99.1,-0.13,91.51,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,15244,2015-10-30 11:04:40:550\n-9.8497,0.0263,-0.316,-9.8032,0.0212,-0.2586,0,0.0073,-0.0024,159.8,-22.1,-131.6,99.04,-0.13,91.5,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,15346,2015-10-30 11:04:40:652\n-9.8557,0.0251,-0.3519,-9.8028,0.0192,-0.2728,0.0012,0.0061,-0.0024,159.8,-22.1,-131.6,99.04,-0.11,91.59,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,15448,2015-10-30 11:04:40:754\n-9.8569,0.0275,-0.3891,-9.8024,0.0184,-0.2874,0.0024,0.0122,0,159.8,-22.1,-131.3,99.09,-0.11,91.68,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,15549,2015-10-30 11:04:40:855\n-9.8497,0.0275,-0.3903,-9.8022,0.0197,-0.2928,0,-0.0098,-0.0012,159.8,-22,-131,99.08,-0.11,91.71,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,15652,2015-10-30 11:04:40:958\n-9.8497,0.0287,-0.3148,-9.8023,0.0207,-0.2885,0.0012,-0.0086,0,159.8,-21.9,-130.7,99.08,-0.12,91.69,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,15754,2015-10-30 11:04:41:060\n-9.8533,0.0359,-0.3867,-9.8022,0.0206,-0.2931,0.0012,0.0122,-0.0012,159.7,-21.8,-131,99.08,-0.12,91.7,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,15856,2015-10-30 11:04:41:162\n-9.8617,0.0455,-0.3663,-9.8021,0.0204,-0.2955,0.0037,-0.0134,-0.0012,159.7,-21.9,-131.1,99.07,-0.12,91.73,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,15958,2015-10-30 11:04:41:264\n-9.8509,0.0275,-0.3352,-9.8024,0.0207,-0.2875,0,-0.011,0,159.7,-21.9,-131.3,99.08,-0.12,91.69,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,16060,2015-10-30 11:04:41:366\n-9.8521,0.0156,-0.3376,-9.8024,0.0205,-0.2877,0.0012,0.0061,0,159.6,-22,-131,99.08,-0.12,91.68,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,16162,2015-10-30 11:04:41:468\n-9.8509,0.0407,-0.3926,-9.802,0.0204,-0.2987,0.0012,-0.0024,-0.0012,159.5,-21.9,-131,99.07,-0.12,91.75,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,16264,2015-10-30 11:04:41:570\n-9.8497,0.0347,-0.3663,-9.8021,0.0217,-0.2952,0.0024,-0.0061,0.0012,159.4,-22,-131.2,99.07,-0.12,91.74,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,16366,2015-10-30 11:04:41:672\n-9.8641,0.0347,-0.3304,-9.8021,0.0214,-0.2966,0.0024,-0.0012,-0.0024,159.5,-22,-131.5,99.06,-0.12,91.73,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,16468,2015-10-30 11:04:41:774\n-9.8521,0.0419,-0.3184,-9.8019,0.021,-0.3037,0.0012,0.0049,0,159.5,-22,-131.6,98.99,-0.12,91.77,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,16570,2015-10-30 11:04:41:876\n-9.821,0.0323,-0.3986,-9.8015,0.0211,-0.3147,0,0.0061,0,159.6,-22,-131.6,98.98,-0.12,91.84,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,16672,2015-10-30 11:04:41:978\n-9.8641,0.0371,-0.346,-9.8015,0.0212,-0.3158,-0.0012,-0.0049,-0.0012,159.6,-22,-131.6,98.98,-0.13,91.85,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,16774,2015-10-30 11:04:42:080\n-9.8521,0.0239,-0.3555,-9.8014,0.0221,-0.3192,0,0.0024,0.0012,159.7,-22,-131.7,98.97,-0.13,91.87,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,16876,2015-10-30 11:04:42:182\n-9.833,0.0335,-0.3998,-9.8011,0.0221,-0.326,0.0012,0.0012,0,159.7,-22.1,-131.7,98.97,-0.13,91.89,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,16978,2015-10-30 11:04:42:284\n-9.8258,0.0275,-0.3807,-9.8011,0.023,-0.327,0,-0.0024,0,159.6,-22,-131.9,98.96,-0.13,91.91,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,17079,2015-10-30 11:04:42:385\n-9.8653,0.0407,-0.3208,-9.8014,0.0244,-0.3177,0.0012,-0.011,0,159.7,-22,-131.8,98.96,-0.14,91.87,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,17182,2015-10-30 11:04:42:488\n-9.8521,0.0467,-0.4046,-9.801,0.0249,-0.3288,0.0024,-0.0024,0,159.6,-22,-131.7,98.94,-0.15,91.92,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,17284,2015-10-30 11:04:42:590\n-9.845,0.0204,-0.3855,-9.8009,0.0245,-0.333,0.0012,0.011,-0.0012,159.6,-22,-131.7,98.94,-0.14,91.95,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,17386,2015-10-30 11:04:42:692\n-9.8497,0.0311,-0.3615,-9.8011,0.0243,-0.3287,0.0012,-0.0086,0,159.7,-22,-131.6,98.95,-0.14,91.92,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,17488,2015-10-30 11:04:42:794\n-9.8497,0.0455,-0.3232,-9.801,0.0248,-0.3303,0.0024,-0.0073,0,159.7,-22,-131.6,98.94,-0.14,91.93,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,17590,2015-10-30 11:04:42:896\n-9.8557,0.0204,-0.3962,-9.8008,0.0247,-0.3354,-0.0012,-0.0049,-0.0024,159.7,-21.9,-131.7,98.94,-0.15,91.96,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,17692,2015-10-30 11:04:42:998\n-9.8581,0.0227,-0.3974,-9.8008,0.0251,-0.3372,0.0012,0.0061,-0.0012,159.7,-21.9,-131.5,99,-0.15,91.97,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,17794,2015-10-30 11:04:43:100\n-9.833,0.0407,-0.4034,-9.8009,0.0259,-0.3324,0.0012,0.0012,0.0024,159.7,-22,-131.5,99,-0.15,91.94,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,17896,2015-10-30 11:04:43:202\n-9.845,0.0311,-0.4082,-9.8011,0.0253,-0.3265,0,0.0073,0,159.6,-22,-131.2,99.01,-0.15,91.91,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,17998,2015-10-30 11:04:43:304\n-9.8701,0.0227,-0.3699,-9.8009,0.0255,-0.3325,0.0012,0.0024,0,159.5,-22,-131.3,99,-0.15,91.93,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,18100,2015-10-30 11:04:43:406\n-9.8581,0.0383,-0.3531,-9.8008,0.0255,-0.336,0.0024,0.0037,-0.0012,159.5,-21.9,-131.7,98.93,-0.15,91.96,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,18202,2015-10-30 11:04:43:508\n-9.8497,0.0347,-0.328,-9.8003,0.0264,-0.3509,0.0012,0.0513,-0.0024,159.4,-21.9,-131.8,98.93,-0.15,92,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,18304,2015-10-30 11:04:43:610\n-9.8533,0.0251,-0.3651,-9.8,0.0256,-0.3577,0,-0.0232,0,159.5,-22.1,-131.4,98.97,-0.15,92.12,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,18405,2015-10-30 11:04:43:711\n-9.8713,0.0012,-0.3591,-9.8003,0.0259,-0.3504,0.0012,-0.0159,-0.0012,159.6,-22.1,-131.1,98.98,-0.15,92.05,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,18508,2015-10-30 11:04:43:814\n-9.8581,0.018,-0.3783,-9.8005,0.0236,-0.3453,-0.0012,-0.0024,-0.0024,159.7,-22.2,-131.1,99,-0.14,92.02,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,18610,2015-10-30 11:04:43:916\n-9.8629,0.0192,-0.3783,-9.8002,0.0227,-0.3539,-0.0012,-0.0073,0.0012,159.8,-22.1,-131.3,99,-0.13,92.07,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,18712,2015-10-30 11:04:44:018\n-9.8497,0.0168,-0.4334,-9.8,0.0236,-0.3596,0.0012,0.0281,0,159.8,-22.1,-131.1,98.98,-0.14,92.1,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,18813,2015-10-30 11:04:44:119\n-9.8438,0.0467,-0.413,-9.7999,0.0232,-0.3614,0,-0.0061,0,159.7,-22.1,-130.8,98.99,-0.14,92.11,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,18916,2015-10-30 11:04:44:222\n-9.8785,0.0108,-0.3472,-9.8002,0.0235,-0.3528,0,0,0.0012,159.7,-22.1,-130.7,98.99,-0.14,92.09,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,19018,2015-10-30 11:04:44:324\n-9.8497,0.0204,-0.3412,-9.8002,0.0237,-0.3541,0.0012,0.0061,-0.0012,159.7,-22.1,-130.9,98.99,-0.14,92.07,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,19120,2015-10-30 11:04:44:426\n-9.8378,0.0443,-0.3974,-9.7999,0.0231,-0.361,0,-0.0024,0,159.7,-22,-130.7,98.99,-0.14,92.11,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,19222,2015-10-30 11:04:44:528\n-9.8497,0.0192,-0.3663,-9.7997,0.0233,-0.3661,0,-0.0232,-0.0012,159.6,-21.9,-130.8,98.98,-0.14,92.14,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,19323,2015-10-30 11:04:44:629\n-9.8533,0.0311,-0.3938,-9.7997,0.0225,-0.3665,-0.0012,0.0147,-0.0024,159.7,-21.8,-130.4,99.05,-0.14,92.12,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,19426,2015-10-30 11:04:44:732\n-9.8497,0.0239,-0.4058,-9.7995,0.0236,-0.3728,0.0012,0.0061,0,159.7,-21.9,-130.3,99.04,-0.14,92.17,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,19528,2015-10-30 11:04:44:834\n-9.8258,0.0347,-0.4118,-9.7994,0.0237,-0.3746,0.0012,-0.0024,-0.0024,159.8,-22,-130.1,99.03,-0.14,92.19,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,19630,2015-10-30 11:04:44:936\n-9.8605,0.0323,-0.4094,-9.7992,0.0234,-0.3796,0.0012,0.0122,-0.0024,159.9,-22,-130.2,99.03,-0.14,92.19,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,19732,2015-10-30 11:04:45:038\n-9.8557,0.0204,-0.4561,-9.7989,0.0234,-0.3863,-0.0012,0.0159,0,159.9,-22.1,-130.5,99.02,-0.14,92.26,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,19834,2015-10-30 11:04:45:140\n-9.8521,0.0156,-0.395,-9.799,0.024,-0.3846,-0.0012,-0.0049,0,159.9,-22.1,-130.5,99.02,-0.14,92.25,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,19936,2015-10-30 11:04:45:242\n-9.8701,0.0108,-0.4022,-9.7992,0.0248,-0.3804,0,0.0037,-0.0012,159.8,-22.1,-130.2,99.02,-0.15,92.22,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,20038,2015-10-30 11:04:45:344\n-9.8246,0.0275,-0.4202,-9.7989,0.0245,-0.3874,0.0012,0.011,-0.0012,159.8,-22.2,-130,99.02,-0.14,92.24,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,20140,2015-10-30 11:04:45:446\n-9.8438,0.0371,-0.3986,-9.7988,0.0245,-0.3896,0.0012,-0.0073,-0.0012,159.7,-22.1,-130,99.01,-0.14,92.28,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,20242,2015-10-30 11:04:45:548\n-9.8294,0.0347,-0.4334,-9.7988,0.024,-0.3908,0.0024,-0.0061,0.0024,159.7,-22.1,-130,99.02,-0.14,92.28,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,20344,2015-10-30 11:04:45:650\n-9.8797,0.012,-0.4226,-9.7988,0.024,-0.3912,0.0024,0.0061,-0.0024,159.7,-21.9,-130.2,99.01,-0.14,92.29,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,20446,2015-10-30 11:04:45:752\n-9.8521,0.0299,-0.4118,-9.7985,0.0239,-0.3985,-0.0012,-0.0073,-0.0024,159.6,-22,-130.1,99.01,-0.14,92.34,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,20548,2015-10-30 11:04:45:854\n-9.8497,0.0287,-0.3603,-9.7987,0.024,-0.3922,-0.0024,-0.0159,-0.0012,159.5,-21.9,-130.4,99.01,-0.14,92.29,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,20650,2015-10-30 11:04:45:956\n-9.8497,0.0347,-0.4082,-9.799,0.0239,-0.3845,0,0,0,159.8,-22.1,-130.4,99.02,-0.14,92.25,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,20752,2015-10-30 11:04:46:058\n-9.8749,0.0132,-0.3962,-9.7993,0.0242,-0.3787,0.0024,-0.0037,0.0012,159.8,-22,-130.5,99.03,-0.14,92.21,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,20854,2015-10-30 11:04:46:160\n-9.8557,0.0395,-0.4585,-9.7989,0.0236,-0.3873,0.0024,0.0122,-0.0012,159.9,-22.1,-130.5,99.03,-0.14,92.23,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,20956,2015-10-30 11:04:46:262\n-9.8462,0.0311,-0.4262,-9.7989,0.0237,-0.3888,0,-0.0122,-0.0024,159.9,-22,-130.7,98.95,-0.14,92.28,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,21058,2015-10-30 11:04:46:364\n-9.8497,0.0299,-0.4106,-9.7991,0.0239,-0.383,0.0012,-0.0024,0.0012,159.9,-21.9,-130.6,98.96,-0.14,92.24,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,21160,2015-10-30 11:04:46:466\n-9.8521,0.0168,-0.4238,-9.7989,0.0244,-0.3866,0.0012,0.0037,0,159.9,-21.9,-130.6,98.95,-0.14,92.26,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,21262,2015-10-30 11:04:46:568\n-9.845,0.0239,-0.4477,-9.7993,0.0249,-0.3772,-0.0012,-0.0208,0,159.8,-22,-130.6,98.95,-0.15,92.23,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,21364,2015-10-30 11:04:46:670\n-9.8617,0.0048,-0.3448,-9.7998,0.0251,-0.365,0,-0.0061,0,159.8,-21.9,-130.5,99.03,-0.15,92.13,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,21466,2015-10-30 11:04:46:772\n-9.8521,0.0108,-0.3891,-9.7995,0.024,-0.3738,0.0012,0.0086,-0.0012,159.6,-21.9,-130.6,98.97,-0.14,92.18,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,21568,2015-10-30 11:04:46:874\n-9.8497,0.0323,-0.4262,-9.7991,0.0245,-0.3816,0,-0.0012,0.0012,159.6,-21.9,-130.6,98.96,-0.14,92.23,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,21670,2015-10-30 11:04:46:976\n-9.8497,0.0347,-0.4489,-9.7991,0.0253,-0.3817,-0.0012,0.0024,0,159.6,-21.9,-130.6,98.95,-0.15,92.23,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,21772,2015-10-30 11:04:47:078\n-9.8545,0.0383,-0.4369,-9.7991,0.0256,-0.3835,0,0.011,0,159.7,-21.9,-130.6,98.95,-0.15,92.24,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,21874,2015-10-30 11:04:47:180\n-9.8366,0.0347,-0.425,-9.7993,0.0262,-0.3773,-0.0012,0.0061,0.0012,159.8,-21.9,-130.5,99.01,-0.15,92.2,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,21975,2015-10-30 11:04:47:281\n-9.8641,0.0132,-0.3735,-9.7993,0.0258,-0.3776,0.0012,0.0159,0.0012,159.8,-21.9,-130.5,99.02,-0.15,92.2,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,22079,2015-10-30 11:04:47:385\n-9.8509,0.0299,-0.4262,-9.7988,0.0251,-0.3904,-0.0012,0.0098,0,159.8,-22,-130.1,99.01,-0.15,92.28,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,22179,2015-10-30 11:04:47:485\n-9.8438,0.0263,-0.4046,-9.7991,0.0267,-0.3832,0,-0.0122,0.0012,159.9,-22,-130.2,99,-0.16,92.26,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,22282,2015-10-30 11:04:47:588\n-9.8497,0.0048,-0.4022,-9.7991,0.0276,-0.3817,0,-0.0061,0,160,-22.1,-130.5,99,-0.16,92.23,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,22384,2015-10-30 11:04:47:690\n-9.8581,0.0503,-0.4465,-9.7991,0.0272,-0.3818,0,0.0037,-0.0024,160,-22,-130.5,99,-0.16,92.22,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,22486,2015-10-30 11:04:47:792\n-9.8557,0.0395,-0.401,-9.799,0.0251,-0.3844,-0.0037,0.0037,-0.0012,159.8,-21.9,-130.5,99.01,-0.15,92.25,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,22588,2015-10-30 11:04:47:894\n-9.8497,0.0443,-0.4202,-9.799,0.0252,-0.386,0,0.0024,0,159.7,-22,-130.6,98.95,-0.15,92.26,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,22690,2015-10-30 11:04:47:996\n-9.8474,0.0215,-0.419,-9.799,0.0257,-0.3837,0.0012,-0.0049,-0.0012,159.8,-22,-130.8,98.95,-0.15,92.24,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,22792,2015-10-30 11:04:48:098\n-9.8497,0.0407,-0.4118,-9.799,0.0259,-0.3838,0.0024,-0.0024,0,159.8,-21.9,-130.9,98.95,-0.15,92.24,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,22894,2015-10-30 11:04:48:200\n-9.8497,0.0395,-0.3867,-9.7992,0.0258,-0.3807,0.0024,-0.0037,-0.0012,159.8,-21.9,-130.7,98.95,-0.15,92.23,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,22996,2015-10-30 11:04:48:302\n-9.8641,0.0299,-0.4286,-9.7992,0.0254,-0.3804,0,0.0037,-0.0012,159.8,-21.9,-130.5,99.02,-0.15,92.22,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,23098,2015-10-30 11:04:48:404\n"
  },
  {
    "path": "test/data/Sensor_record_20151030_110521_AndroSensor.csv",
    "content": "-0.0168,9.7588,-0.0611,0.0902,9.8054,0.1224,0.0464,0.0012,-0.0171,4.4,-166.6,-56.2,319.24,-89.04,-34.8,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,29,2015-10-30 11:04:55:584\n0.176,9.7468,0.012,0.0921,9.8055,0.1172,-0.0012,-0.0012,-0.0024,4.5,-166.6,-56,314.89,-89.13,-38.17,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,131,2015-10-30 11:04:55:686\n0.0275,9.7683,0.0335,0.0861,9.8055,0.1186,0.0012,-0.0012,0.0049,4.6,-166.6,-55.7,317.71,-89.13,-35.44,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,233,2015-10-30 11:04:55:788\n0.1317,9.7671,0.1772,0.0885,9.8054,0.1237,-0.0024,-0.0024,-0.0037,4.6,-166.5,-55.5,317.03,-89.11,-35.94,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,335,2015-10-30 11:04:55:890\n0.152,9.7528,0.0539,0.0875,9.8056,0.1143,0.0159,0.0012,0,4.5,-166.4,-55.7,316.8,-89.14,-36.35,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,437,2015-10-30 11:04:55:992\n0.1879,9.7564,0.1628,0.0842,9.8055,0.1178,0.0012,0.0024,-0.0024,4.5,-166.4,-55.4,317.53,-89.15,-35.56,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,539,2015-10-30 11:04:56:094\n0.0323,9.7432,0.0682,0.0809,9.8057,0.1108,-0.0049,-0.0012,0.0073,4.6,-166.3,-55.3,317.01,-89.2,-36.15,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,641,2015-10-30 11:04:56:196\n0.0611,9.7516,0.0575,0.08,9.8056,0.1137,-0.0024,0.0012,-0.0098,4.6,-166.4,-55.1,318.04,-89.19,-35.13,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,743,2015-10-30 11:04:56:298\n0.1341,9.7648,0.0335,0.085,9.8056,0.109,0.0049,0,0.0012,4.5,-166.4,-55,315.88,-89.19,-37.22,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,845,2015-10-30 11:04:56:400\n0.0802,9.7492,0.1329,0.0805,9.8056,0.1122,-0.0147,0.0037,-0.0073,4.6,-166.5,-54.9,317.51,-89.19,-35.66,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,947,2015-10-30 11:04:56:502\n0.1245,9.7504,0.0958,0.076,9.8056,0.1164,0.0147,0.0049,-0.0086,4.7,-166.5,-54.4,320.61,-89.16,-32.47,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,1049,2015-10-30 11:04:56:604\n0.073,9.7659,0.0515,0.0773,9.8056,0.1155,0.0073,0,-0.0037,4.8,-166.4,-54.5,319.88,-89.16,-33.18,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,1151,2015-10-30 11:04:56:706\n0.1377,9.7671,0.1293,0.0759,9.8057,0.1148,0.0049,0.0012,-0.0012,4.7,-166.4,-54.8,319.32,-89.21,-33.93,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,1253,2015-10-30 11:04:56:808\n0.0263,9.7396,0.1101,0.0719,9.8058,0.1051,0.011,0,-0.0012,4.6,-166.3,-55,318.98,-89.26,-34.35,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,1355,2015-10-30 11:04:56:910\n0.0706,9.7648,0.0599,0.0716,9.8057,0.1107,-0.0098,0,-0.0037,4.7,-166.3,-55.3,319.35,-89.25,-33.98,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,1457,2015-10-30 11:04:57:012\n0.0563,9.7636,0.0419,0.07,9.8057,0.1167,-0.0147,0.0012,-0.0024,4.8,-166.5,-55.2,321.91,-89.21,-31.43,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,1559,2015-10-30 11:04:57:114\n0.1089,9.742,0.1676,0.0695,9.8056,0.1255,-0.0012,-0.0012,-0.0024,4.8,-166.5,-55.5,324.73,-89.15,-28.61,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,1661,2015-10-30 11:04:57:216\n0.1006,9.7408,0.1305,0.071,9.8055,0.1287,0,-0.0024,-0.0012,4.9,-166.6,-55.2,324.56,-89.14,-28.73,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,1763,2015-10-30 11:04:57:318\n0.0922,9.7636,0.1915,0.0704,9.8056,0.125,-0.0037,0,0.0086,4.9,-166.7,-55.3,323.94,-89.16,-29.37,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,1865,2015-10-30 11:04:57:420\n0.0814,9.7348,0.1604,0.075,9.8055,0.1273,0.0012,0.0012,-0.0061,4.8,-166.7,-55.5,322.7,-89.14,-30.52,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,1967,2015-10-30 11:04:57:522\n0.0766,9.7552,0.1867,0.0758,9.8055,0.1275,-0.0037,-0.0012,0.0037,4.6,-166.7,-55.5,322.88,-89.14,-30.36,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,2069,2015-10-30 11:04:57:624\n0.0359,9.7432,0.1233,0.0752,9.8056,0.1222,0.0012,0.0012,-0.0037,4.6,-166.6,-55.5,321.62,-89.16,-31.6,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,2171,2015-10-30 11:04:57:726\n0.1089,9.7636,0.1616,0.0746,9.8055,0.1259,-0.0012,0,-0.0012,4.7,-166.7,-55.4,322.24,-89.15,-31,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,2273,2015-10-30 11:04:57:828\n0.0359,9.76,0.1065,0.0741,9.8054,0.1299,-0.0049,0,-0.0012,4.7,-166.7,-55.4,323.34,-89.13,-29.89,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,2375,2015-10-30 11:04:57:930\n0.1341,9.7636,0.1353,0.0763,9.8054,0.1296,-0.0024,0,0.0061,4.7,-166.6,-55.2,323.14,-89.13,-30.08,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,2477,2015-10-30 11:04:58:032\n0.0886,9.7659,0.0419,0.0786,9.8055,0.1251,0.0061,0.0012,-0.0012,4.6,-166.6,-55.4,321.71,-89.13,-31.46,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,2579,2015-10-30 11:04:58:134\n0.1006,9.742,0.1844,0.0769,9.8055,0.127,0.0024,0,-0.0049,4.6,-166.5,-55.3,322,-89.13,-31.2,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,2681,2015-10-30 11:04:58:236\n0.1006,9.7468,0.1544,0.0779,9.8054,0.1339,-0.0061,0.0012,0,4.5,-166.6,-55.7,322.69,-89.11,-30.61,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,2783,2015-10-30 11:04:58:338\n0.1317,9.748,0.1317,0.0734,9.8053,0.1413,-0.0049,0.0012,-0.0049,4.6,-166.6,-55.6,325.89,-89.07,-27.46,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,2885,2015-10-30 11:04:58:440\n0.067,9.7683,0.1089,0.0743,9.8052,0.1456,-0.0012,0,-0.0012,4.6,-166.6,-55.7,326.27,-89.04,-27.04,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,2987,2015-10-30 11:04:58:542\n0.0658,9.7492,0.0886,0.0741,9.8052,0.148,-0.0024,0,0,4.6,-166.6,-55.7,326.37,-89.04,-26.94,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,3089,2015-10-30 11:04:58:644\n0.0778,9.7636,0.231,0.0736,9.805,0.1624,-0.0195,-0.0024,0,4.5,-166.5,-55.7,327.92,-88.99,-25.4,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,3191,2015-10-30 11:04:58:746\n0.085,9.754,0.0958,0.0726,9.8051,0.1579,0.0049,-0.0012,-0.0012,4.6,-166.5,-55.7,328.96,-88.97,-24.37,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,3293,2015-10-30 11:04:58:848\n0.1365,9.7588,0.1604,0.0737,9.8051,0.1577,0,0.0012,-0.0024,4.6,-166.5,-55.7,328.27,-88.98,-25.05,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,3395,2015-10-30 11:04:58:950\n0.1233,9.7564,0.261,0.078,9.8049,0.1618,-0.0098,0.0012,0.0037,4.7,-166.4,-55.5,327.37,-88.95,-25.73,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,3497,2015-10-30 11:04:59:052\n0.0551,9.7528,0.2418,0.0826,9.8049,0.1653,-0.0061,0,-0.0012,4.7,-166.5,-55.7,326.59,-88.92,-26.55,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,3599,2015-10-30 11:04:59:154\n0.0994,9.7612,0.1856,0.0805,9.8048,0.1675,0.0049,-0.0012,0.0037,4.6,-166.5,-56,327.51,-88.91,-25.66,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,3700,2015-10-30 11:04:59:255\n0.2334,9.7396,-0.0407,0.0797,9.8049,0.1668,-0.0049,0.0012,-0.0037,4.6,-166.6,-56.1,327.48,-88.92,-25.69,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,3803,2015-10-30 11:04:59:358\n0.0814,9.7683,0.1772,0.0779,9.8048,0.1714,0.0024,0.0012,-0.0061,4.6,-166.6,-55.8,328.75,-88.9,-24.45,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,3904,2015-10-30 11:04:59:459\n0.0275,9.748,0.1137,0.078,9.8049,0.1672,0.0134,-0.0024,-0.0012,4.7,-166.6,-55.7,328.2,-88.92,-25.01,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,4007,2015-10-30 11:04:59:562\n0.1137,9.7648,0.2406,0.0795,9.8049,0.1661,-0.0061,0,-0.0037,4.7,-166.6,-55.5,327.42,-88.95,-25.67,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,4109,2015-10-30 11:04:59:664\n0.1353,9.7612,0.2155,0.0789,9.8049,0.1642,-0.0024,0,0.0012,4.8,-166.5,-55.6,327.54,-88.94,-25.66,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,4211,2015-10-30 11:04:59:766\n0.085,9.7504,0.1891,0.0793,9.8049,0.1663,0.0012,-0.0012,-0.0024,4.8,-166.5,-55.6,327.29,-88.92,-25.88,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,4313,2015-10-30 11:04:59:868\n0.1006,9.7564,0.176,0.0804,9.8048,0.1707,-0.0098,0,0.0012,4.9,-166.5,-55.5,327.27,-88.9,-25.75,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,4415,2015-10-30 11:04:59:970\n0.1365,9.7648,0.1688,0.0805,9.8048,0.1716,-0.0024,-0.0024,0,4.8,-166.6,-55.4,327.83,-88.9,-25.2,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,4517,2015-10-30 11:05:00:072\n0.0575,9.7624,0.1317,0.0799,9.8048,0.1709,0.0073,0.0012,-0.0061,4.7,-166.6,-55.6,328.09,-88.9,-25.07,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,4619,2015-10-30 11:05:00:174\n0.0479,9.7504,0.182,0.0795,9.8049,0.1666,0.0061,0,-0.0073,4.9,-166.5,-55.8,327.67,-88.92,-25.52,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,4721,2015-10-30 11:05:00:276\n0.1305,9.7636,0.2071,0.0794,9.8049,0.1661,-0.0061,0,-0.0012,4.9,-166.5,-55.8,327.56,-88.94,-25.65,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,4823,2015-10-30 11:05:00:378\n0.1257,9.7648,0.176,0.0795,9.8048,0.1696,-0.0024,-0.0012,0.0024,5,-166.6,-55.7,328.08,-88.91,-25.1,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,4924,2015-10-30 11:05:00:479\n0.0946,9.7659,0.1927,0.0813,9.8048,0.1703,0.0049,0,0.0012,4.9,-166.7,-55.8,327.53,-88.9,-25.61,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,5027,2015-10-30 11:05:00:582\n0.0814,9.7384,0.1496,0.0818,9.8049,0.167,0.0024,-0.0012,-0.0012,4.8,-166.6,-55.6,327.05,-88.91,-26.08,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,5129,2015-10-30 11:05:00:684\n0.2047,9.7624,0.1149,0.0866,9.8048,0.1666,-0.0049,-0.0012,0.0147,4.6,-166.6,-55.5,325.45,-88.9,-27.47,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,5231,2015-10-30 11:05:00:786\n0.152,9.7659,0.2298,0.0958,9.8044,0.1848,-0.0024,0,-0.0024,4.6,-166.5,-55.5,324.91,-88.82,-27.84,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,5333,2015-10-30 11:05:00:888\n0.0802,9.7683,0.1389,0.0921,9.8045,0.1813,0.011,0,-0.011,4.5,-166.5,-55.4,325.86,-88.81,-26.93,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,5435,2015-10-30 11:05:00:990\n-0.0407,9.7612,0.1113,0.0861,9.8047,0.1757,0.0073,0,-0.0012,4.8,-166.6,-55.3,326.81,-88.86,-26.1,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,5537,2015-10-30 11:05:01:092\n0.0227,9.7528,-0.0132,0.0832,9.8047,0.1758,-0.0122,-0.0024,0.0024,4.8,-166.6,-55.4,327.63,-88.86,-25.33,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,5639,2015-10-30 11:05:01:194\n-0.006,9.7456,0.1257,0.0811,9.8047,0.1779,0.0012,0,-0.0012,4.7,-166.7,-55.6,328.62,-88.86,-24.51,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,5741,2015-10-30 11:05:01:296\n0.0874,9.7636,0.1676,0.082,9.8047,0.1764,0.0086,-0.0012,-0.0086,4.6,-166.6,-55.6,328.12,-88.84,-24.96,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,5843,2015-10-30 11:05:01:398\n0.1592,9.76,0.1544,0.0797,9.8048,0.1715,0.0073,0.0012,-0.0024,4.7,-166.6,-55.6,328.24,-88.9,-24.92,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,5945,2015-10-30 11:05:01:500\n0.1077,9.7659,0.2215,0.08,9.8049,0.1624,0.0232,0.0012,-0.0012,4.8,-166.4,-55.5,327.57,-88.92,-25.5,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,6047,2015-10-30 11:05:01:602\n0.0706,9.7372,0.1257,0.0803,9.8053,0.1431,0.011,0.0024,0,4.7,-166.3,-55.4,323.79,-89.04,-29.31,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,6149,2015-10-30 11:05:01:704\n0.0994,9.7504,0.1987,0.084,9.8052,0.145,0,0,0.0061,4.6,-166.3,-55.7,323.62,-89.03,-29.57,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,6251,2015-10-30 11:05:01:806\n0.0539,9.7552,0.1269,0.0833,9.8053,0.139,-0.0024,-0.0012,-0.0073,4.5,-166.4,-55.9,322.26,-89.05,-30.92,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,6353,2015-10-30 11:05:01:908\n0.1688,9.7624,0.1532,0.0829,9.8053,0.1428,-0.0024,0,-0.0061,4.6,-166.4,-56.1,323.06,-89.04,-30.13,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,6455,2015-10-30 11:05:02:010\n0.0587,9.7552,0.1257,0.0859,9.8052,0.1411,0,-0.0024,-0.0024,4.6,-166.4,-55.9,321.77,-89.03,-31.36,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,6557,2015-10-30 11:05:02:112\n0.0251,9.7396,-0.0275,0.0837,9.8055,0.1198,0.033,-0.0012,-0.011,4.6,-166.4,-55.7,318.28,-89.15,-34.94,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,6659,2015-10-30 11:05:02:214\n0.0227,9.7025,0.0024,0.0804,9.8057,0.1082,-0.0122,0,-0.0012,4.5,-166.4,-55.2,316.53,-89.21,-36.64,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,6761,2015-10-30 11:05:02:316\n0.1556,9.7695,0.1257,0.0833,9.8055,0.1238,-0.011,0.0012,0.0049,4.6,-166.5,-55.1,319.16,-89.13,-33.93,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,6862,2015-10-30 11:05:02:417\n0.0599,9.7576,0.0455,0.0849,9.8053,0.1363,0.0281,0,-0.0061,4.5,-166.4,-55.1,321.09,-89.06,-31.94,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,6965,2015-10-30 11:05:02:520\n0.1377,9.7564,0.255,0.0839,9.8054,0.1285,0.0073,0,-0.0024,4.6,-166.5,-55.2,319.62,-89.14,-33.52,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,7067,2015-10-30 11:05:02:622\n0.2873,9.7683,0.0862,0.0817,9.8055,0.1228,-0.0061,0.0012,-0.0061,4.5,-166.5,-55.1,319.48,-89.14,-33.63,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,7169,2015-10-30 11:05:02:724\n0.0922,9.76,0.0862,0.0855,9.8052,0.1422,0.0208,0.0012,-0.0073,4.7,-166.5,-55.2,322.44,-88.99,-30.51,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,7271,2015-10-30 11:05:02:826\n0.0994,9.748,0.1305,0.0865,9.8051,0.1499,0.0159,0,0,4.6,-166.4,-55.4,322.98,-88.99,-29.99,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,7373,2015-10-30 11:05:02:928\n0.1281,9.7683,0.1939,0.0863,9.8052,0.1468,-0.0049,0,0.0012,4.7,-166.4,-55.6,322.77,-89.02,-30.37,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,7475,2015-10-30 11:05:03:030\n0.0287,9.7492,0.0515,0.0859,9.8053,0.1385,0.0183,0,-0.0024,4.6,-166.4,-55.8,321.96,-89.01,-31.14,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,7576,2015-10-30 11:05:03:131\n0.0048,9.7468,0.1401,0.0874,9.8052,0.1407,0.0086,0,-0.0024,4.7,-166.4,-55.8,321.26,-89.03,-31.85,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,7679,2015-10-30 11:05:03:234\n0.1784,9.7624,0.1939,0.0884,9.8053,0.1378,0.0073,0,-0.0024,4.6,-166.3,-55.8,320.85,-89.06,-32.28,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,7781,2015-10-30 11:05:03:336\n0.1077,9.7683,0.1437,0.088,9.8053,0.1345,-0.0037,0.0012,-0.0024,4.7,-166.4,-55.3,319.79,-89.06,-33.19,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,7883,2015-10-30 11:05:03:438\n0.0802,9.7384,0.1508,0.088,9.8053,0.1388,-0.0073,-0.0012,0.0061,4.7,-166.3,-55.1,319.62,-89.04,-33.32,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,7985,2015-10-30 11:05:03:540\n0.1233,9.76,0.1137,0.0888,9.8053,0.138,-0.0134,-0.0012,0.0037,4.7,-166.4,-54.9,320.2,-89.04,-32.75,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,8087,2015-10-30 11:05:03:642\n0.0898,9.7636,0.2071,0.0888,9.8051,0.1508,-0.0086,0.0012,-0.0024,4.6,-166.4,-54.9,321.73,-88.98,-31.18,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,8188,2015-10-30 11:05:03:743\n0.0706,9.7348,0.1616,0.0854,9.8052,0.1464,0.0012,0,0,4.5,-166.5,-54.8,322.75,-89.01,-30.24,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,8291,2015-10-30 11:05:03:846\n0.0239,9.7528,0.1221,0.0869,9.8052,0.1428,0.0012,-0.0012,-0.0012,4.4,-166.4,-54.6,322.75,-89.02,-31.31,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,8393,2015-10-30 11:05:03:948\n0.1197,9.7504,0.1413,0.0861,9.8052,0.1403,0.0037,0,-0.0037,4.5,-166.4,-54.8,321.45,-89.02,-31.52,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,8494,2015-10-30 11:05:04:049\n0.1496,9.7624,0.1496,0.0873,9.8052,0.1432,-0.0098,-0.0012,0.0012,4.6,-166.3,-55.1,321.38,-89.04,-31.61,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,8597,2015-10-30 11:05:04:152\n0.0922,9.7564,0.1125,0.0864,9.8052,0.1426,0.0134,0,0.0012,4.7,-166.5,-55.3,321.78,-89.03,-31.21,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,8699,2015-10-30 11:05:04:254\n0.1293,9.7528,0.2095,0.0862,9.8053,0.1373,0.0086,0,0.0012,4.7,-166.4,-55.5,321.26,-89.07,-31.79,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,8801,2015-10-30 11:05:04:356\n0.1293,9.7659,0.1508,0.0861,9.8054,0.1315,0.0012,-0.0024,-0.0024,4.6,-166.4,-56.1,319.93,-89.08,-33.22,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,8903,2015-10-30 11:05:04:458\n0.0622,9.7612,0.1437,0.0858,9.8053,0.1335,-0.011,0,0,4.6,-166.3,-56.3,320.41,-89.07,-32.74,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,9005,2015-10-30 11:05:04:560\n0.0599,9.7252,0.1269,0.0849,9.8054,0.1327,-0.0098,0,-0.0012,4.6,-166.3,-56.4,320.56,-89.08,-32.61,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,9107,2015-10-30 11:05:04:662\n0.1209,9.7683,0.1257,0.0828,9.8053,0.1346,0.0073,0.0012,-0.0061,4.6,-166.3,-56.1,321.47,-89.06,-31.7,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,9209,2015-10-30 11:05:04:764\n0.0802,9.7588,0.0587,0.0811,9.8054,0.1322,0.0073,0,-0.0061,4.6,-166.3,-55.8,321.72,-89.09,-31.52,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,9311,2015-10-30 11:05:04:866\n0.0611,9.7432,0.237,0.081,9.8054,0.133,0.0159,-0.0012,0.0024,4.6,-166.3,-55.6,322.26,-89.09,-30.99,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,9413,2015-10-30 11:05:04:968\n0.1209,9.7432,0.1293,0.0815,9.8055,0.1212,0.0147,-0.0012,0.0012,4.6,-166.3,-55.5,319.2,-89.15,-33.93,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,9515,2015-10-30 11:05:05:070\n0.0814,9.7576,0.0826,0.0831,9.8055,0.1209,0.0049,-0.0012,0.0012,4.6,-166.3,-55.3,319.15,-89.13,-33.95,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,9617,2015-10-30 11:05:05:172\n0.0239,9.7612,0.1137,0.085,9.8055,0.1203,0.0012,-0.0012,-0.0024,4.7,-166.2,-55.2,317.77,-89.14,-35.29,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,9720,2015-10-30 11:05:05:275\n0.1664,9.7456,0.1879,0.087,9.8055,0.1212,0.0061,0,0.0049,4.7,-166.4,-55.1,317.35,-89.13,-35.68,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,9821,2015-10-30 11:05:05:376\n0.1173,9.7576,0.0467,0.0861,9.8056,0.1151,0.0024,0.0024,0.0012,4.7,-166.3,-55.1,316.26,-89.16,-36.8,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,9923,2015-10-30 11:05:05:478\n0.012,9.7384,0.0862,0.0866,9.8054,0.1255,-0.0012,0.0024,-0.0073,4.6,-166.3,-55.1,318.41,-89.11,-34.62,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,10025,2015-10-30 11:05:05:580\n0.1784,9.7528,0.1281,0.0851,9.8054,0.1285,-0.0012,-0.0012,-0.011,4.5,-166.4,-55.2,319.79,-89.1,-33.27,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,10127,2015-10-30 11:05:05:682\n0.1472,9.7767,0.1329,0.0823,9.8053,0.1349,-0.0086,0,-0.0037,4.6,-166.4,-55.2,321.69,-89.08,-31.4,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,10229,2015-10-30 11:05:05:784\n0.0096,9.7276,0.1161,0.0774,9.8053,0.1384,-0.0073,0.0012,-0.0073,4.6,-166.5,-55.2,323.09,-89.08,-30.04,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,10331,2015-10-30 11:05:05:886\n0.0742,9.7468,0.1772,0.0768,9.8053,0.142,0.0012,-0.0024,-0.0024,4.6,-166.4,-55.5,324.76,-89.06,-28.41,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,10433,2015-10-30 11:05:05:988\n0.1185,9.7707,0.1101,0.0775,9.8053,0.1393,0.0049,-0.0012,0.0037,4.5,-166.5,-55.5,324.62,-89.07,-28.56,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,10535,2015-10-30 11:05:06:090\n0.0539,9.7444,0.0814,0.0793,9.8054,0.1355,0.0061,0.0012,0.0024,4.5,-166.5,-55.7,322.34,-89.08,-30.9,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,10637,2015-10-30 11:05:06:192\n0.0311,9.7588,0.097,0.0836,9.8053,0.1391,0.0061,-0.0012,0.0037,4.5,-166.4,-55.4,322.04,-89.05,-31.01,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,10739,2015-10-30 11:05:06:294\n0.1724,9.7659,0.1724,0.0843,9.8052,0.1405,0,-0.0012,-0.0073,4.5,-166.4,-55.2,322.19,-89.05,-30.87,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,10841,2015-10-30 11:05:06:396\n0.1053,9.7492,0.1329,0.0827,9.8053,0.1393,-0.0012,0.0012,-0.0012,4.5,-166.4,-55.2,322.37,-89.05,-30.7,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,10942,2015-10-30 11:05:06:497\n0.1772,9.7659,0.1616,0.0815,9.8053,0.1365,-0.0012,0,0.0049,4.6,-166.5,-55.2,322.25,-89.07,-30.84,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,11045,2015-10-30 11:05:06:600\n-0.0227,9.7564,0.0958,0.0794,9.8054,0.1341,-0.0024,-0.0012,0.0073,4.6,-166.5,-55.4,322.18,-89.08,-30.92,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,11147,2015-10-30 11:05:06:702\n0.1065,9.7576,0.1125,0.0813,9.8054,0.1319,0.0073,0,0.0012,4.7,-166.6,-55.2,321.43,-89.09,-31.66,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,11249,2015-10-30 11:05:06:804\n0.1724,9.7719,0.1389,0.0814,9.8054,0.1313,0.0086,0.0012,-0.0012,4.8,-166.6,-55.5,321.51,-89.08,-31.56,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,11351,2015-10-30 11:05:06:906\n0.1233,9.7576,0.1353,0.0825,9.8054,0.133,0.0061,0,-0.0012,4.9,-166.6,-55.3,321.25,-89.09,-31.82,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,11453,2015-10-30 11:05:07:008\n0.1113,9.742,0.1975,0.0837,9.8053,0.1347,-0.0098,0,0.0049,4.9,-166.5,-55.1,321.02,-89.1,-32.07,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,11555,2015-10-30 11:05:07:110\n0.146,9.7564,0.1101,0.0855,9.8053,0.1371,0.0012,-0.0024,0.0037,4.8,-166.5,-55.2,321.5,-89.06,-31.54,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,11657,2015-10-30 11:05:07:212\n0.0311,9.742,0.1975,0.0858,9.8052,0.1435,-0.0061,0,0.0061,4.7,-166.4,-55.4,321.33,-89.04,-31.67,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,11759,2015-10-30 11:05:07:314\n0.0982,9.7552,0.2059,0.0873,9.8051,0.1488,-0.0073,0,0.0073,4.6,-166.4,-55.6,322.7,-88.99,-30.39,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,11861,2015-10-30 11:05:07:416\n0.1173,9.7516,0.1365,0.0881,9.805,0.1542,-0.0061,0,-0.0012,4.6,-166.4,-55.3,323.19,-88.96,-29.74,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,11963,2015-10-30 11:05:07:518\n0.1281,9.7671,0.1724,0.094,9.8049,0.157,-0.0024,0,-0.0012,4.7,-166.5,-55.4,321.9,-88.93,-30.92,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,12065,2015-10-30 11:05:07:620\n0.1006,9.7396,0.1209,0.0958,9.805,0.1517,0.0061,-0.0012,-0.0012,4.7,-166.5,-55.3,320.51,-88.95,-32.28,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,12167,2015-10-30 11:05:07:722\n0.1832,9.7659,0.1389,0.0966,9.805,0.15,-0.0012,0.0012,-0.0012,4.6,-166.5,-55.3,320.13,-88.97,-32.68,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,12269,2015-10-30 11:05:07:824\n0.0491,9.7659,0.1065,0.0931,9.805,0.1542,0.0061,-0.0012,-0.0037,4.5,-166.5,-55.2,321.61,-88.94,-31.21,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,12371,2015-10-30 11:05:07:926\n0.1089,9.748,0.2167,0.0943,9.8049,0.1569,0.0086,0,-0.0012,4.6,-166.6,-55.1,322.11,-88.93,-30.7,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,12473,2015-10-30 11:05:08:028\n0.146,9.7588,0.1532,0.0945,9.8049,0.1564,-0.0024,0.0024,-0.0012,4.6,-166.6,-55.3,321.66,-88.93,-31.14,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,12575,2015-10-30 11:05:08:130\n0.0551,9.742,0.1532,0.095,9.8049,0.1538,0.0049,0,-0.0086,4.6,-166.5,-55.4,321.09,-88.94,-31.72,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,12677,2015-10-30 11:05:08:232\n-0.0048,9.7312,0.1245,0.0906,9.805,0.1507,-0.0037,0,-0.0073,4.5,-166.5,-55.2,321.09,-88.96,-31.75,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,12778,2015-10-30 11:05:08:333\n0.0838,9.7324,0.1269,0.0898,9.805,0.15,-0.0061,0,0,4.6,-166.5,-55,321.99,-88.98,-30.92,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,12881,2015-10-30 11:05:08:436\n0.1353,9.7671,0.1628,0.0896,9.805,0.1519,0.0012,0,0.0049,4.5,-166.5,-54.8,322.82,-88.96,-30.1,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,12983,2015-10-30 11:05:08:538\n0.1089,9.754,0.1616,0.0905,9.8051,0.1481,0.0037,-0.0012,0.0037,4.4,-166.5,-55.1,322.53,-88.99,-31.44,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,13085,2015-10-30 11:05:08:640\n0.0982,9.7624,0.1101,0.0929,9.8051,0.1452,0.0073,0,-0.0049,4.5,-166.4,-55.2,320.26,-88.99,-32.61,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,13187,2015-10-30 11:05:08:742\n0.018,9.7241,0.1676,0.0915,9.8052,0.1415,0.0049,0.0012,-0.0049,4.6,-166.5,-55.1,319.64,-89.01,-33.22,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,13289,2015-10-30 11:05:08:844\n0.1209,9.7576,0.1305,0.0919,9.8052,0.1405,0.0037,0,-0.0024,4.7,-166.4,-54.7,319.7,-89.02,-33.2,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,13392,2015-10-30 11:05:08:947\n0.0096,9.7624,0.1401,0.0908,9.8052,0.1365,0.0098,0,0.0037,4.7,-166.5,-54.5,319.01,-89.02,-33.73,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,13493,2015-10-30 11:05:09:048\n0.0192,9.7276,0.17,0.0938,9.8052,0.1349,0,0,0.0024,4.8,-166.5,-54.3,317.93,-89.04,-34.81,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,13595,2015-10-30 11:05:09:150\n0.1317,9.7432,0.0826,0.0942,9.8053,0.133,0.0049,0.0012,-0.0049,4.7,-166.5,-54.3,317.65,-89.04,-35.08,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,13696,2015-10-30 11:05:09:251\n0.17,9.7432,0.1221,0.0932,9.8052,0.137,-0.0012,0,-0.0073,4.7,-166.5,-54.2,318.52,-89.03,-34.23,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,13799,2015-10-30 11:05:09:354\n0.1867,9.7695,0.1844,0.0911,9.8052,0.1396,-0.0049,-0.0012,-0.011,4.6,-166.5,-54.1,319.65,-89.03,-33.13,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,13901,2015-10-30 11:05:09:456\n0.0132,9.76,0.0874,0.0935,9.8053,0.1285,0.011,-0.0012,0,4.8,-166.5,-54.3,316.72,-89.07,-36.04,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,14003,2015-10-30 11:05:09:558\n0.146,9.7396,0.0814,0.0932,9.8054,0.125,0.0098,0.0012,0.0098,4.7,-166.5,-54.5,316.32,-89.06,-36.41,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,14105,2015-10-30 11:05:09:660\n0.1173,9.7444,0.1844,0.0956,9.8054,0.1245,-0.0122,0.0012,0.0061,4.8,-166.6,-54.5,315.19,-89.08,-37.53,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,14207,2015-10-30 11:05:09:762\n0.1401,9.7552,0.1748,0.0981,9.8052,0.1325,-0.0012,0.0012,-0.0024,4.6,-166.6,-54.6,316.61,-89.04,-36.19,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,14309,2015-10-30 11:05:09:864\n0.1293,9.7636,0.0551,0.0977,9.8053,0.1243,0.0024,-0.0012,-0.0061,4.6,-166.6,-54.5,314.73,-89.06,-37.93,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,14412,2015-10-30 11:05:09:967\n0.085,9.7612,0.1065,0.0993,9.8053,0.1272,0.0012,0,-0.0098,4.5,-166.5,-54.6,314.79,-89.06,-38,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,14512,2015-10-30 11:05:10:067\n0.1006,9.7408,0.1532,0.097,9.8053,0.1283,-0.0024,0.0012,-0.0073,4.5,-166.4,-54.8,315.37,-89.06,-37.45,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,14615,2015-10-30 11:05:10:170\n0.1808,9.7755,0.1425,0.0966,9.8053,0.126,0.0049,0,0.0012,4.5,-166.4,-54.8,315.38,-89.07,-37.46,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,14717,2015-10-30 11:05:10:272\n0.1018,9.7683,0.1413,0.0985,9.8053,0.1266,-0.0012,-0.0024,0.0024,4.6,-166.4,-55,314.91,-89.06,-37.89,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,14819,2015-10-30 11:05:10:374\n0.0946,9.7564,0.1245,0.0977,9.8053,0.1268,-0.0037,0,0.0024,4.6,-166.5,-54.6,315.22,-89.07,-37.6,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,14921,2015-10-30 11:05:10:476\n0.0994,9.748,0.085,0.0981,9.8052,0.1328,-0.0012,0.0012,0.0012,4.5,-166.4,-54.7,316.37,-89.04,-36.43,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,15023,2015-10-30 11:05:10:578\n0.1137,9.7576,0.146,0.0987,9.8052,0.1375,-0.0012,0.0012,-0.0024,4.6,-166.4,-54.6,316.88,-89.02,-35.91,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,15125,2015-10-30 11:05:10:680\n0.0168,9.7516,0.1784,0.1005,9.8051,0.1428,-0.0061,0.0012,-0.0012,4.6,-166.4,-54.5,317.47,-88.98,-35.12,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,15227,2015-10-30 11:05:10:782\n0.1832,9.7671,0.1089,0.1015,9.8051,0.1418,0.0134,0,0,4.7,-166.3,-54.5,318.07,-88.97,-34.53,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,15328,2015-10-30 11:05:10:883\n0.1724,9.7576,0.1377,0.1015,9.8052,0.1366,0.0012,0,0.0037,4.6,-166.3,-54.8,316.1,-89.01,-36.62,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,15431,2015-10-30 11:05:10:986\n0.0359,9.7396,0.1041,0.0997,9.8052,0.1363,-0.0012,0.0024,0,4.6,-166.3,-55,316.37,-89,-36.36,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,15533,2015-10-30 11:05:11:088\n0.0874,9.742,0.1101,0.102,9.8051,0.1372,0.0024,-0.0012,0.0012,4.6,-166.3,-54.9,316.09,-89,-36.63,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,15635,2015-10-30 11:05:11:190\n0.0874,9.7588,0.1257,0.1039,9.8051,0.1354,0.0122,0,-0.0012,4.7,-166.3,-54.9,315.7,-88.99,-36.98,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,15737,2015-10-30 11:05:11:292\n0.1089,9.7504,0.164,0.1058,9.8052,0.1325,0.0073,0,-0.0024,4.7,-166.3,-54.6,314.06,-89.01,-38.6,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,15839,2015-10-30 11:05:11:394\n0.0515,9.7588,0.1269,0.1048,9.8053,0.1261,0.0037,0,0.0049,4.6,-166.4,-54.6,312.78,-89.04,-39.9,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,15941,2015-10-30 11:05:11:496\n0.1125,9.754,0.1532,0.1072,9.8052,0.1252,0.0024,0,0.0024,4.6,-166.5,-54.4,311.93,-89.04,-40.58,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,16043,2015-10-30 11:05:11:598\n0.1856,9.7624,0.1472,0.1103,9.8052,0.1241,0.0037,0.0012,0.0049,4.5,-166.4,-54.4,311.41,-89.03,-41.08,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,16145,2015-10-30 11:05:11:700\n0.1856,9.7695,0.1377,0.1109,9.8053,0.1176,0.0061,-0.0024,-0.0049,4.4,-166.3,-54.2,310.25,-89.06,-43.3,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,16247,2015-10-30 11:05:11:802\n0.0096,9.7252,0.1293,0.1109,9.8054,0.1106,0.0049,0.0012,-0.0049,4.4,-166.3,-54.3,308.53,-89.08,-45.03,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,16349,2015-10-30 11:05:11:904\n0.1496,9.7683,0.1425,0.1113,9.8054,0.1042,0.0061,0,-0.0037,4.6,-166.4,-54.6,305.74,-89.11,-46.89,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,16451,2015-10-30 11:05:12:006\n0.1652,9.7624,0.1592,0.1142,9.8054,0.1069,0,0.0012,0.0037,4.5,-166.4,-54.6,305.22,-89.1,-47.37,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,16553,2015-10-30 11:05:12:108\n0.0706,9.736,0.1652,0.1166,9.8053,0.1083,-0.0037,0,0.0073,4.5,-166.4,-54.6,305.42,-89.07,-47.1,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,16655,2015-10-30 11:05:12:210\n0.1197,9.7624,0.0982,0.1179,9.8053,0.1109,-0.0037,0,0.0037,4.5,-166.3,-54.5,305.42,-89.07,-46.96,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,16757,2015-10-30 11:05:12:312\n0.1568,9.7576,0.0778,0.1198,9.8053,0.1074,0.0049,-0.0012,-0.0024,4.6,-166.4,-54.3,304.18,-89.06,-48.15,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,16858,2015-10-30 11:05:12:413\n0.1879,9.7636,0.1006,0.1195,9.8053,0.1056,0.0073,-0.0012,-0.0049,4.5,-166.3,-54.5,303.82,-89.07,-48.52,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,16961,2015-10-30 11:05:12:516\n0.0634,9.7444,0.0982,0.1177,9.8054,0.101,0.0061,0.0012,-0.0073,4.5,-166.3,-54.4,302.75,-89.08,-49.59,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,17063,2015-10-30 11:05:12:618\n0.1317,9.748,0.0934,0.1187,9.8054,0.1025,0.0049,0.0012,0.0024,4.6,-166.4,-54.5,303.19,-89.08,-49.17,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,17165,2015-10-30 11:05:12:720\n0.1377,9.7624,0.1508,0.1171,9.8054,0.1048,0.0037,0.0024,-0.0037,4.7,-166.5,-54.4,303.46,-89.08,-48.9,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,17267,2015-10-30 11:05:12:822\n0.1413,9.7564,0.1341,0.1169,9.8054,0.1023,0.0012,0.0012,0.0012,4.6,-166.4,-54.6,303.72,-89.09,-48.81,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,17369,2015-10-30 11:05:12:924\n0.1496,9.7612,0.0766,0.1145,9.8055,0.1,-0.0012,0,-0.0037,4.5,-166.4,-54.2,303.07,-89.11,-49.35,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,17471,2015-10-30 11:05:13:026\n0.0874,9.7528,0.079,0.1141,9.8055,0.0984,0.0024,0.0012,-0.0024,4.5,-166.4,-53.9,303.24,-89.12,-49.21,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,17573,2015-10-30 11:05:13:128\n0.1065,9.7552,0.1161,0.1124,9.8055,0.0987,0,0,-0.0098,4.6,-166.5,-53.6,303.1,-89.12,-49.35,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,17675,2015-10-30 11:05:13:230\n0.1532,9.7648,0.0611,0.1128,9.8055,0.0982,-0.0012,0,-0.0024,4.6,-166.5,-53.9,303.33,-89.13,-49.14,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,17777,2015-10-30 11:05:13:332\n0.1113,9.7576,0.079,0.1119,9.8055,0.0994,0.0012,0,-0.0012,4.6,-166.4,-54.2,304.11,-89.13,-48.38,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,17879,2015-10-30 11:05:13:434\n0.1999,9.7576,0.0994,0.1116,9.8055,0.1011,-0.0037,0.0012,0.0049,4.5,-166.3,-54.2,304.68,-89.12,-47.81,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,17981,2015-10-30 11:05:13:536\n0.0587,9.7576,0.1173,0.1126,9.8054,0.1075,-0.0037,0,-0.0012,4.5,-166.3,-54.3,305.19,-89.1,-47.25,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,18083,2015-10-30 11:05:13:638\n0.0622,9.742,0.1137,0.1114,9.8054,0.1072,-0.0012,0.0012,-0.0061,4.5,-166.4,-54.6,306.52,-89.1,-46.1,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,18185,2015-10-30 11:05:13:740\n0.1999,9.7624,0.0934,0.1122,9.8054,0.1089,0.0012,0.0012,-0.0049,4.5,-166.5,-54.6,306.94,-89.09,-45.67,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,18287,2015-10-30 11:05:13:842\n0.1568,9.7444,0.1173,0.1108,9.8054,0.1105,0.0024,0,-0.0012,4.5,-166.5,-54.4,307.41,-89.09,-45.08,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,18389,2015-10-30 11:05:13:944\n0.1724,9.7636,0.1101,0.1108,9.8053,0.1138,0,-0.0012,0.0049,4.5,-166.5,-54.2,308.25,-89.07,-44.22,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,18491,2015-10-30 11:05:14:046\n0.085,9.7432,0.1041,0.1124,9.8053,0.1114,0.0037,0,-0.0037,4.5,-166.5,-54.2,307.41,-89.06,-45.02,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,18593,2015-10-30 11:05:14:148\n0.1413,9.7552,0.0622,0.1115,9.8054,0.1061,0.0098,0.0024,-0.0024,4.5,-166.4,-54.6,306.67,-89.1,-45.96,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,18695,2015-10-30 11:05:14:250\n0.0982,9.7516,0.1101,0.1126,9.8054,0.1072,0.0024,-0.0024,-0.0012,4.6,-166.4,-54.8,306.22,-89.09,-46.37,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,18797,2015-10-30 11:05:14:352\n0.0192,9.7444,0.1209,0.1136,9.8054,0.1085,0.0024,0,-0.0049,4.6,-166.4,-54.9,306.27,-89.08,-46.31,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,18899,2015-10-30 11:05:14:454\n0.1089,9.7336,0.0718,0.1114,9.8055,0.0972,-0.0012,0.0012,-0.0012,4.6,-166.4,-54.8,303.76,-89.14,-48.88,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,19001,2015-10-30 11:05:14:556\n0.1101,9.7779,0.1041,0.1097,9.8055,0.0969,0.0098,0,-0.0037,4.5,-166.4,-54.4,304,-89.14,-48.54,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,19103,2015-10-30 11:05:14:658\n0.1065,9.7648,0.1401,0.1093,9.8055,0.0972,-0.0086,-0.0012,0.0012,4.6,-166.5,-54.7,304.31,-89.15,-48.37,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,19205,2015-10-30 11:05:14:760\n0.1508,9.7408,0.1377,0.1079,9.8055,0.099,0,0,-0.0049,4.6,-166.5,-54.9,304.76,-89.15,-47.95,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,19307,2015-10-30 11:05:14:862\n0.1903,9.7576,0.0599,0.1029,9.8056,0.097,0.0037,0,-0.0159,4.6,-166.4,-55.1,306.4,-89.16,-46.38,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,19409,2015-10-30 11:05:14:964\n0.0491,9.7492,0.1161,0.1017,9.8056,0.0994,-0.0024,0.0012,-0.0049,4.5,-166.5,-54.7,306.79,-89.17,-46.01,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,19511,2015-10-30 11:05:15:066\n0.0012,9.7444,0.0658,0.0994,9.8056,0.0977,-0.0037,-0.0012,-0.0049,4.5,-166.4,-54.4,306.49,-89.17,-46.17,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,19613,2015-10-30 11:05:15:168\n0.1209,9.76,0.0766,0.1014,9.8056,0.0983,0.0037,0,-0.0012,4.5,-166.4,-54.2,307.19,-89.18,-45.51,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,19716,2015-10-30 11:05:15:271\n0.0778,9.7612,0.0611,0.1047,9.8056,0.0969,0.0024,-0.0012,0.0012,4.4,-166.3,-54.1,306.51,-89.17,-47.2,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,19817,2015-10-30 11:05:15:372\n0.0539,9.754,0.0898,0.1051,9.8056,0.0948,0.0037,0,-0.0049,4.4,-166.3,-54.5,305.77,-89.17,-47.94,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,19919,2015-10-30 11:05:15:474\n0.1532,9.7624,0.0814,0.1059,9.8056,0.0937,0.0037,0,-0.0049,4.4,-166.3,-54.7,305.7,-89.17,-48.11,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,20021,2015-10-30 11:05:15:576\n0.1544,9.7719,0.0599,0.1064,9.8056,0.088,0.011,-0.0012,-0.0049,4.5,-166.3,-54.8,302.35,-89.19,-50.41,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,20123,2015-10-30 11:05:15:678\n0.1006,9.7384,0.0802,0.1072,9.8057,0.0838,-0.0049,0,0.0049,4.5,-166.3,-54.7,300.77,-89.2,-51.98,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,20225,2015-10-30 11:05:15:780\n0.1101,9.7408,0.0982,0.109,9.8056,0.0869,0.0024,0,0.0037,4.4,-166.3,-54.7,302.35,-89.19,-51.42,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,20327,2015-10-30 11:05:15:882\n0.0994,9.76,0.0084,0.11,9.8057,0.0836,0.0061,0.0024,0,4.5,-166.3,-54.3,300.39,-89.18,-52.16,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,20429,2015-10-30 11:05:15:984\n0.0742,9.7516,0.0682,0.1102,9.8057,0.081,0.0086,0,-0.0049,4.5,-166.4,-54,299.07,-89.19,-53.47,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,20531,2015-10-30 11:05:16:086\n0.1712,9.7624,0.0467,0.1116,9.8057,0.0791,0.0012,-0.0012,-0.0037,4.6,-166.4,-53.8,298.48,-89.2,-54.08,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,20633,2015-10-30 11:05:16:188\n0.2023,9.7671,0.0634,0.1117,9.8057,0.0805,-0.0037,-0.0012,-0.0037,4.5,-166.4,-54.1,298.32,-89.2,-54.22,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,20735,2015-10-30 11:05:16:290\n0.0323,9.742,0.0754,0.1122,9.8057,0.0799,0.0012,0,-0.0049,4.5,-166.3,-53.8,298.16,-89.19,-54.36,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,20837,2015-10-30 11:05:16:392\n0.1353,9.7444,0.0718,0.1134,9.8056,0.0804,-0.0037,-0.0012,-0.0024,4.4,-166.4,-53.8,298.67,-89.19,-54.91,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,20939,2015-10-30 11:05:16:494\n0.1867,9.7612,0.0922,0.1127,9.8056,0.0837,0.0049,-0.0012,0.0061,4.3,-166.3,-53.7,300.19,-89.18,-53.39,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,21041,2015-10-30 11:05:16:596\n0.1496,9.76,0.1245,0.116,9.8056,0.0806,0.011,0,0.0024,4.3,-166.3,-53.9,298.33,-89.17,-55.2,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,21143,2015-10-30 11:05:16:698\n0.1137,9.7576,0.0778,0.1138,9.8058,0.0596,0.0147,-0.0024,-0.0049,4.5,-166.3,-53.9,290.18,-89.25,-62.37,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,21245,2015-10-30 11:05:16:800\n0.1448,9.7683,-0.0108,0.1134,9.8059,0.0436,0.011,0,-0.0049,4.5,-166.4,-53.8,286.08,-89.28,-66.52,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,21347,2015-10-30 11:05:16:902\n0.1484,9.7636,-0.0383,0.1111,9.8059,0.0396,0.0012,-0.0012,-0.0061,4.6,-166.4,-53.8,282.29,-89.31,-70.36,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,21449,2015-10-30 11:05:17:004\n0.2215,9.7612,0.0742,0.1124,9.8059,0.0495,-0.0147,0,0.0037,4.6,-166.4,-53.8,284.7,-89.3,-67.93,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,21551,2015-10-30 11:05:17:106\n0.1532,9.7743,-0.0491,0.1107,9.8059,0.047,0.0061,0,0,4.6,-166.4,-53.7,287.35,-89.28,-65.27,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,21653,2015-10-30 11:05:17:208\n0.1592,9.7432,0.0611,0.1102,9.8058,0.0572,-0.0134,0.0012,0.0012,4.7,-166.4,-53.8,290.06,-89.27,-62.56,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,21755,2015-10-30 11:05:17:310\n0.1269,9.7683,0.0934,0.11,9.8058,0.0674,-0.0073,0,-0.0024,4.7,-166.4,-53.8,293.02,-89.26,-59.6,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,21857,2015-10-30 11:05:17:412\n0.073,9.7636,0.0646,0.1083,9.8058,0.0719,-0.0024,0,-0.0049,4.7,-166.4,-54.1,295.36,-89.24,-57.25,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,21958,2015-10-30 11:05:17:513\n0.073,9.7384,0.0072,0.11,9.8058,0.0713,-0.0086,0.0012,-0.0012,4.6,-166.5,-54,295.55,-89.23,-57.04,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,22061,2015-10-30 11:05:17:616\n0.1616,9.7659,0.0383,0.1103,9.8057,0.0807,-0.0122,0,0.0012,4.6,-166.4,-53.8,298.75,-89.2,-53.81,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,22163,2015-10-30 11:05:17:718\n0.1281,9.7432,0.146,0.1116,9.8055,0.1022,-0.0159,-0.0012,0,4.5,-166.4,-54,304.97,-89.12,-47.52,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,22265,2015-10-30 11:05:17:820\n0.1329,9.7564,0.1245,0.111,9.8054,0.1112,0.0134,-0.0012,-0.0049,4.6,-166.4,-54.1,307.53,-89.08,-44.95,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,22367,2015-10-30 11:05:17:922\n0.1281,9.7648,0.1077,0.1098,9.8055,0.0997,0.0098,0.0012,-0.0012,4.6,-166.3,-54.6,304.9,-89.13,-47.77,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,22469,2015-10-30 11:05:18:024\n0.0934,9.7384,0.1329,0.11,9.8055,0.0957,0.0061,0,-0.0012,4.6,-166.3,-54.7,303.93,-89.14,-48.73,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,22571,2015-10-30 11:05:18:126\n0.1616,9.754,0.164,0.1109,9.8056,0.0903,0.0061,-0.0012,0.0024,4.5,-166.4,-54.5,301.61,-89.17,-50.94,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,22673,2015-10-30 11:05:18:228\n0.2107,9.7683,0.0227,0.1109,9.8056,0.0853,0.0049,0.0012,0.0037,4.4,-166.4,-54.4,301.26,-89.19,-52.37,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,22775,2015-10-30 11:05:18:330\n0.1257,9.7504,-0.0024,0.1116,9.8056,0.092,0.0037,0,0.0049,4.2,-166.4,-54.5,303.1,-89.15,-50.49,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,22877,2015-10-30 11:05:18:432\n0.1161,9.742,0.0922,0.1145,9.8055,0.1,0,0,0.0049,4.2,-166.4,-54.7,304.77,-89.11,-48.87,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,22979,2015-10-30 11:05:18:534\n0.1939,9.7612,0.0826,0.1147,9.8055,0.0983,0.0024,0,-0.0086,4.2,-166.4,-54.9,304.24,-89.12,-49.4,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,23081,2015-10-30 11:05:18:636\n0.1832,9.7719,0.0479,0.1155,9.8055,0.0975,-0.0012,0.0012,-0.0012,4.3,-166.3,-54.4,303.65,-89.12,-49.85,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,23183,2015-10-30 11:05:18:738\n0.0539,9.73,0.0946,0.1146,9.8055,0.0971,-0.0024,0.0012,0.0012,4.3,-166.4,-54.1,303.43,-89.12,-50.09,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,23285,2015-10-30 11:05:18:840\n0.1125,9.7408,0.0934,0.1174,9.8055,0.0959,0.0012,-0.0012,0.0012,4.3,-166.4,-54,302.74,-89.11,-50.74,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,23387,2015-10-30 11:05:18:942\n0.1484,9.7624,0.1041,0.118,9.8055,0.0919,0.0073,-0.0012,0,4.3,-166.3,-54.1,301.73,-89.12,-51.74,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,23489,2015-10-30 11:05:19:044\n0.091,9.7564,0.1233,0.1183,9.8056,0.0839,-0.0012,0,-0.0012,4.4,-166.4,-54.3,298.82,-89.15,-54.66,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,23591,2015-10-30 11:05:19:146\n0.1329,9.7636,0.0335,0.1168,9.8056,0.0748,0.0037,-0.0012,-0.0049,4.5,-166.4,-54.4,296.19,-89.18,-56.27,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,23693,2015-10-30 11:05:19:248\n0.1532,9.76,0.0766,0.1166,9.8056,0.0792,-0.0061,0.0024,-0.0037,4.5,-166.4,-54.2,296.65,-89.18,-55.8,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,23795,2015-10-30 11:05:19:350\n0.0946,9.7648,0.1006,0.1175,9.8056,0.078,0.0049,-0.0012,-0.0024,4.5,-166.4,-54.4,296.62,-89.17,-55.83,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,23897,2015-10-30 11:05:19:452\n0.2059,9.7564,0.0479,0.1181,9.8056,0.0755,0.0037,0.0024,0.0037,4.5,-166.3,-54.2,295.04,-89.18,-57.39,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,23999,2015-10-30 11:05:19:554\n0.2167,9.7659,0.0467,0.1183,9.8056,0.075,-0.0024,0,0.0073,4.4,-166.2,-54.1,295.88,-89.18,-57.62,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,24100,2015-10-30 11:05:19:655\n0.0395,9.7372,0.0503,0.119,9.8056,0.077,0.0024,0.0012,0,4.3,-166.3,-54.1,296.45,-89.17,-57.03,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,24204,2015-10-30 11:05:19:759\n0.0958,9.73,0.1185,0.1218,9.8055,0.0823,0,-0.0012,-0.0024,4.3,-166.3,-53.9,297.46,-89.14,-55.96,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,24305,2015-10-30 11:05:19:860\n0.1903,9.7767,0.0658,0.1213,9.8055,0.0814,0.0049,0,-0.0037,4.4,-166.3,-53.9,297.51,-89.15,-55.93,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,24407,2015-10-30 11:05:19:962\n0.1113,9.7659,0.0766,0.1219,9.8055,0.0809,-0.0037,0.0012,-0.0024,4.5,-166.3,-53.9,295.92,-89.15,-56.43,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,24509,2015-10-30 11:05:20:064\n0.1736,9.7528,0.097,0.1239,9.8055,0.0807,0.0012,0.0012,0.0037,4.6,-166.4,-54.2,295.81,-89.14,-56.53,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,24611,2015-10-30 11:05:20:166\n0.152,9.748,0.0922,0.1233,9.8055,0.0809,0,-0.0012,0,4.5,-166.4,-54.1,295.59,-89.14,-56.74,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,24713,2015-10-30 11:05:20:268\n0.0754,9.7612,0.0108,0.1224,9.8055,0.0766,0.011,0.0012,-0.0024,4.5,-166.4,-53.9,295.12,-89.14,-57.2,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,24815,2015-10-30 11:05:20:370\n0.1077,9.7492,0.0263,0.1226,9.8055,0.0755,0.0073,0.0012,-0.0024,4.3,-166.3,-53.8,295.58,-89.15,-57.83,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,24917,2015-10-30 11:05:20:472\n0.1724,9.7624,0.0527,0.1229,9.8055,0.0764,-0.0024,0,0.0012,4.4,-166.3,-54.1,295.28,-89.15,-58.14,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,25019,2015-10-30 11:05:20:574\n0.103,9.7456,0.067,0.1245,9.8055,0.0779,0.011,0,-0.0024,4.4,-166.2,-54.2,295.9,-89.13,-57.48,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,25120,2015-10-30 11:05:20:675\n0.1676,9.7648,0.0754,0.1231,9.8055,0.0752,0,0.0012,-0.0024,4.5,-166.3,-53.9,293.77,-89.16,-58.58,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,25223,2015-10-30 11:05:20:778\n0.1652,9.7552,-0.0958,0.1225,9.8056,0.0686,0.0061,-0.0012,0.0061,4.4,-166.2,-54.1,292.68,-89.18,-60.76,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,25325,2015-10-30 11:05:20:880\n0.2035,9.754,0.1736,0.1239,9.8055,0.0762,0.0342,0,-0.0147,4.4,-166.2,-54.2,296.82,-89.12,-56.55,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,25427,2015-10-30 11:05:20:982\n"
  },
  {
    "path": "test/data/Sensor_record_20151030_110553_AndroSensor.csv",
    "content": "-0.2131,-9.8497,-0.0587,-0.1914,-9.8031,0.1796,0.0086,0.0012,-0.0024,-82.8,31.1,-124.8,99.69,88.46,46.4,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,21,2015-10-30 11:05:27:553\n-0.2167,-9.8689,-0.0611,-0.1941,-9.8033,0.1685,0.0024,0.0024,0.0024,-82.7,31.1,-124.9,97.06,88.5,49.05,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,123,2015-10-30 11:05:27:655\n-0.2119,-9.8593,-0.079,-0.1931,-9.8034,0.1603,0.0098,0.0012,-0.0012,-82.7,31.1,-124.6,95.8,88.53,50.31,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,225,2015-10-30 11:05:27:757\n-0.2143,-9.8497,-0.0551,-0.1956,-9.8033,0.1668,0.0293,0,-0.0012,-82.7,31.1,-124.3,96.35,88.5,49.54,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,327,2015-10-30 11:05:27:859\n-0.2203,-9.8581,-0.0658,-0.1955,-9.8034,0.1607,-0.0024,0.0012,-0.0073,-82.8,31.1,-124,95.81,88.5,50.09,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,429,2015-10-30 11:05:27:961\n-0.2263,-9.8474,-0.067,-0.1959,-9.8033,0.1651,0.0403,0.0012,0.0024,-82.7,31.1,-124,94.74,88.53,51.15,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,531,2015-10-30 11:05:28:063\n-0.2071,-9.8557,-0.0467,-0.1974,-9.803,0.1808,0.0281,-0.0012,0.0024,-82.8,31.1,-123.7,98.32,88.44,47.56,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,633,2015-10-30 11:05:28:165\n-0.2203,-9.8533,-0.0347,-0.1997,-9.803,0.1794,0.0159,0.0024,0.0024,-82.7,31.1,-123.8,97.83,88.43,48.05,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,735,2015-10-30 11:05:28:267\n-0.2083,-9.8521,-0.0455,-0.2016,-9.8031,0.171,-0.011,0.0012,-0.0037,-82.7,31,-123.7,97.16,88.44,48.72,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,837,2015-10-30 11:05:28:369\n-0.2059,-9.8497,-0.0563,-0.2006,-9.8035,0.1428,-0.0195,0.0024,-0.0049,-82.8,31.1,-123.9,91.35,88.56,54.55,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,939,2015-10-30 11:05:28:471\n-0.2095,-9.8605,-0.0599,-0.204,-9.8037,0.1284,-0.0012,0,-0.0037,-82.8,31.1,-123.7,88.1,88.59,57.81,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,1041,2015-10-30 11:05:28:573\n-0.2095,-9.8497,-0.0658,-0.2045,-9.8038,0.1207,-0.022,0.0024,-0.0024,-82.8,31.1,-123.5,87.78,88.58,57.91,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,1143,2015-10-30 11:05:28:675\n-0.2083,-9.8438,-0.085,-0.2059,-9.804,0.0926,-0.0183,0.0037,-0.0012,-82.8,31,-123.2,79.94,88.68,65.78,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,1245,2015-10-30 11:05:28:777\n-0.2071,-9.8521,-0.0682,-0.2078,-9.8041,0.0847,0.0122,0.0012,0.0049,-82.8,31.1,-123,77.89,88.69,67.84,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,1347,2015-10-30 11:05:28:879\n-0.2131,-9.8557,-0.1006,-0.2107,-9.8041,0.0692,-0.0061,0,-0.0012,-82.9,31.3,-122.8,74.76,88.7,70.97,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,1449,2015-10-30 11:05:28:981\n-0.2095,-9.8617,-0.091,-0.2136,-9.804,0.0699,0.0024,0.0037,0,-82.9,31.4,-123,73.85,88.69,71.87,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,1551,2015-10-30 11:05:29:083\n-0.2107,-9.8474,-0.103,-0.2149,-9.8041,0.0565,-0.0183,0.0037,-0.0024,-82.9,31.4,-123.2,71.76,88.69,73.98,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,1653,2015-10-30 11:05:29:185\n-0.2203,-9.8617,-0.073,-0.2189,-9.804,0.0625,-0.0024,0.0037,0.0024,-82.8,31.4,-123.4,72.47,88.67,73.26,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,1755,2015-10-30 11:05:29:287\n-0.2203,-9.8474,-0.0874,-0.2237,-9.8039,0.0629,0.0159,0,0.0024,-82.9,31.4,-123.4,70.75,88.66,74.97,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,1856,2015-10-30 11:05:29:388\n-0.2119,-9.8545,-0.0515,-0.2269,-9.8037,0.0722,0.0147,0.0012,0.0073,-82.9,31.3,-123.5,73.01,88.62,72.71,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,1959,2015-10-30 11:05:29:491\n-0.2215,-9.8497,-0.0467,-0.227,-9.8036,0.0898,0.0415,0.0012,0.0049,-83,31.2,-123.8,75.02,88.61,70.91,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,2061,2015-10-30 11:05:29:593\n-0.2203,-9.8282,-0.0563,-0.2273,-9.8036,0.0862,-0.0208,0.0012,-0.0061,-82.9,31.1,-124.1,76.69,88.58,69.23,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,2163,2015-10-30 11:05:29:695\n-0.2239,-9.8545,-0.0443,-0.2272,-9.8037,0.0752,0.0073,0.0024,-0.0012,-82.8,31.1,-124.1,74.23,88.6,71.7,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,2265,2015-10-30 11:05:29:797\n-0.2059,-9.8521,-0.0575,-0.2251,-9.8038,0.0666,-0.0086,0.0012,-0.0086,-82.7,31,-124.2,72.42,88.63,73.51,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,2367,2015-10-30 11:05:29:899\n-0.2239,-9.827,-0.0646,-0.222,-9.8039,0.0574,0,0,-0.0012,-82.7,31,-124,70.81,88.65,75.13,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,2469,2015-10-30 11:05:30:001\n-0.2191,-9.8497,-0.0706,-0.2219,-9.8039,0.0556,-0.022,0.0024,-0.0061,-82.8,31.2,-123.8,70.02,88.66,75.93,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,2571,2015-10-30 11:05:30:103\n-0.2286,-9.8617,-0.0826,-0.2183,-9.8041,0.0405,0.0024,-0.0024,-0.0012,-82.9,31.3,-123.7,66,88.71,79.97,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,2673,2015-10-30 11:05:30:205\n-0.2394,-9.8605,-0.0814,-0.2182,-9.8041,0.037,-0.0049,0,-0.0037,-82.8,31.3,-123.9,65.6,88.71,80.36,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,2775,2015-10-30 11:05:30:307\n-0.2167,-9.8497,-0.0754,-0.2184,-9.8041,0.0335,0,0.0012,-0.0024,-82.9,31.3,-124,64.84,88.71,81.13,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,2877,2015-10-30 11:05:30:409\n-0.2191,-9.8497,-0.0622,-0.2184,-9.8041,0.0371,0.0122,0.0012,-0.0024,-82.9,31.3,-124.3,65.61,88.71,80.35,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,2979,2015-10-30 11:05:30:511\n-0.2167,-9.8497,-0.0575,-0.2181,-9.8041,0.04,0.0012,0.0012,-0.0037,-83,31.2,-124.2,66.35,88.7,79.61,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,3081,2015-10-30 11:05:30:613\n-0.2203,-9.8497,-0.0658,-0.2176,-9.8041,0.0331,0.0012,0.0012,-0.0037,-83.1,31.2,-124.4,64.91,88.71,81.06,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,3182,2015-10-30 11:05:30:714\n-0.2131,-9.8497,-0.0024,-0.2217,-9.804,0.0543,0.0843,0,0.0086,-83,31,-124.6,69.92,88.67,76.24,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,3285,2015-10-30 11:05:30:817\n-0.2215,-9.8497,-0.0132,-0.2213,-9.8039,0.0609,-0.044,0.0012,-0.011,-83,30.9,-125.1,76.49,88.6,69.65,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,3387,2015-10-30 11:05:30:919\n-0.2274,-9.8497,-0.0443,-0.2184,-9.8041,0.0355,0.022,0.0012,-0.0049,-82.8,30.9,-124.9,65.41,88.71,80.77,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,3489,2015-10-30 11:05:31:021\n-0.2155,-9.8497,-0.0455,-0.2186,-9.8041,0.0263,-0.0208,0.0012,-0.0012,-82.8,30.9,-124.6,64.91,88.7,81.27,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,3591,2015-10-30 11:05:31:123\n-0.2239,-9.8497,-0.0419,-0.2195,-9.8041,0.0289,0.0183,0.0024,0.0037,-82.9,31.1,-124.2,63.48,88.71,82.49,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,3693,2015-10-30 11:05:31:225\n-0.2239,-9.8497,-0.0455,-0.219,-9.8041,0.0268,-0.0061,0,-0.0012,-82.9,31.1,-124.4,63.49,88.71,82.48,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,3795,2015-10-30 11:05:31:327\n-0.2155,-9.8545,-0.0443,-0.219,-9.8041,0.0191,-0.0024,0,0.0012,-82.8,31.1,-124.7,61.36,88.72,84.83,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,3897,2015-10-30 11:05:31:429\n-0.2263,-9.8569,-0.0622,-0.2174,-9.8042,0.0074,-0.0122,0.0024,-0.0037,-82.7,31,-124.7,59.49,88.73,86.7,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,3999,2015-10-30 11:05:31:531\n-0.2286,-9.8102,-0.0479,-0.2159,-9.8042,0.0054,0.0037,0,0,-82.7,31,-124.4,57.43,88.74,88.56,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,4101,2015-10-30 11:05:31:633\n-0.2131,-9.8497,-0.0706,-0.2143,-9.8042,-0.0091,-0.011,-0.0012,-0.0012,-82.7,31,-124.4,53.57,88.75,92.44,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,4203,2015-10-30 11:05:31:735\n-0.2203,-9.8581,-0.0611,-0.2135,-9.8042,-0.0102,0,0.0024,0.0012,-82.8,31.1,-124.2,53.08,88.75,92.93,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,4305,2015-10-30 11:05:31:837\n-0.2227,-9.8474,-0.0718,-0.2126,-9.8043,-0.0118,0.0024,0.0012,0,-82.8,31,-124,52.84,88.76,93.17,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,4407,2015-10-30 11:05:31:939\n-0.1987,-9.8713,-0.0682,-0.2113,-9.8043,-0.0179,-0.0073,-0.0024,-0.0024,-82.9,31.1,-124,51.87,88.76,94.14,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,4509,2015-10-30 11:05:32:041\n-0.2059,-9.8521,-0.0611,-0.2123,-9.8043,-0.0135,0.0061,0.0024,0.0012,-82.9,31,-124.4,52.37,88.76,93.64,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,4611,2015-10-30 11:05:32:143\n-0.2274,-9.8497,-0.0682,-0.2123,-9.8043,-0.0134,0.0012,0.0024,-0.0049,-82.9,31.1,-124.5,53.2,88.76,92.81,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,4713,2015-10-30 11:05:32:245\n-0.2095,-9.8557,-0.0622,-0.212,-9.8043,-0.0132,0.0086,0.0024,0,-82.8,31.1,-124.8,52.65,88.76,93.57,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,4815,2015-10-30 11:05:32:347\n-0.2203,-9.8533,-0.0838,-0.2104,-9.8043,-0.0247,-0.0086,0.0024,0.0061,-82.7,31.1,-124.6,51.04,88.76,95.18,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,4916,2015-10-30 11:05:32:448\n-0.2215,-9.8545,-0.0862,-0.2103,-9.8043,-0.0282,-0.0024,0.0012,-0.0012,-82.7,31.2,-124.3,48.38,88.76,97.64,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,5019,2015-10-30 11:05:32:551\n-0.2203,-9.8426,-0.0862,-0.2107,-9.8043,-0.0329,0.0024,-0.0012,0.0024,-82.8,31.2,-124.1,47.15,88.75,98.87,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,5121,2015-10-30 11:05:32:653\n-0.2119,-9.8581,-0.091,-0.2117,-9.8043,-0.0303,-0.0159,0.0012,-0.0024,-82.8,31.1,-124.3,47.88,88.75,98.14,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,5223,2015-10-30 11:05:32:755\n-0.2083,-9.8617,-0.0706,-0.211,-9.8043,-0.0353,0.0086,0.0024,0.0024,-82.7,31.2,-124.2,46.53,88.75,99.49,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,5325,2015-10-30 11:05:32:857\n-0.2167,-9.8318,-0.1053,-0.2144,-9.8042,-0.0318,0.0037,0.0012,0,-82.7,31.3,-124.2,47.42,88.74,98.59,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,5427,2015-10-30 11:05:32:959\n-0.2167,-9.8497,-0.0898,-0.2167,-9.8042,-0.0213,0.0073,-0.0012,0.0049,-82.7,31.4,-123.9,50.4,88.73,95.61,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,5529,2015-10-30 11:05:33:061\n-0.2143,-9.8497,-0.091,-0.2174,-9.8042,-0.0225,0.0073,0.0012,0.0061,-82.7,31.4,-124.1,49.71,88.72,96.3,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,5631,2015-10-30 11:05:33:163\n-0.2131,-9.8521,-0.0886,-0.218,-9.8041,-0.0227,0,0,0,-82.7,31.3,-123.9,50.06,88.72,95.95,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,5733,2015-10-30 11:05:33:265\n-0.1999,-9.8545,-0.0934,-0.2197,-9.8041,-0.0175,0.0061,0.0012,-0.0012,-82.7,31.3,-123.9,50.99,88.71,95.01,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,5835,2015-10-30 11:05:33:367\n-0.2155,-9.8557,-0.0778,-0.2209,-9.8041,-0.0131,0,0,0,-82.7,31.3,-123.9,52.6,88.71,93.4,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,5937,2015-10-30 11:05:33:469\n-0.2227,-9.8497,-0.0898,-0.2232,-9.804,-0.0113,0.0073,0,0,-82.7,31.2,-124.3,52.69,88.7,93.31,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,6039,2015-10-30 11:05:33:571\n-0.2143,-9.8617,-0.079,-0.2248,-9.804,-0.0044,0.0073,0.0012,0.0024,-82.7,31.3,-124.3,54.86,88.69,91.12,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,6142,2015-10-30 11:05:33:674\n-0.2071,-9.8629,-0.0766,-0.2262,-9.804,0.0027,0.0086,0.0024,0.0073,-82.6,31.4,-124.8,56.88,88.68,89.31,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,6243,2015-10-30 11:05:33:775\n-0.2227,-9.845,-0.091,-0.2259,-9.804,-0.0044,-0.0049,0.0024,0.0049,-82.6,31.2,-124.8,56.75,88.68,89.45,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,6345,2015-10-30 11:05:33:877\n-0.2215,-9.8497,-0.1018,-0.225,-9.804,-0.0114,0.0061,0.0012,0.0012,-82.6,31.1,-124.8,53.31,88.68,92.89,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,6446,2015-10-30 11:05:33:978\n-0.2131,-9.8282,-0.1161,-0.2223,-9.804,-0.0199,-0.011,-0.0012,-0.0024,-82.5,31.2,-124.5,51.21,88.7,95.11,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,6549,2015-10-30 11:05:34:081\n-0.2143,-9.8509,-0.0898,-0.2222,-9.804,-0.0155,0.0086,0.0012,-0.0024,-82.5,31.2,-124.5,51.48,88.7,94.84,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,6651,2015-10-30 11:05:34:183\n-0.2215,-9.8725,-0.0898,-0.2189,-9.8041,-0.0119,0,0,-0.0024,-82.5,31.4,-124.7,52.8,88.71,93.73,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,6753,2015-10-30 11:05:34:285\n-0.2215,-9.8474,-0.0682,-0.22,-9.8041,0.0034,0.0159,0.0012,0,-82.5,31.3,-124.8,56.59,88.71,89.93,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,6855,2015-10-30 11:05:34:387\n-0.2071,-9.8521,-0.0802,-0.2166,-9.8042,-0.0074,-0.0012,0.0024,-0.0061,-82.4,31.2,-125.1,54.56,88.73,91.97,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,6957,2015-10-30 11:05:34:489\n-0.2239,-9.8725,-0.079,-0.2136,-9.8043,-0.0096,-0.0024,-0.0024,-0.0037,-82.3,31.2,-125.1,54.53,88.74,92,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,7059,2015-10-30 11:05:34:591\n-0.2334,-9.8521,-0.0874,-0.2101,-9.8043,-0.0218,-0.0061,-0.0012,-0.0049,-82.2,31,-124.7,51.05,88.76,95.49,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,7161,2015-10-30 11:05:34:693\n-0.2274,-9.8629,-0.1041,-0.2073,-9.8044,-0.0294,-0.0122,0.0024,-0.0037,-82.4,31.1,-124.4,48.26,88.78,98.08,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,7262,2015-10-30 11:05:34:794\n-0.2095,-9.8533,-0.0958,-0.2066,-9.8044,-0.034,-0.0147,0,-0.0024,-82.4,31.2,-124.5,47.01,88.78,99.33,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,7365,2015-10-30 11:05:34:897\n-0.2167,-9.8497,-0.0946,-0.2053,-9.8044,-0.037,0,0,0.0012,-82.6,31.3,-124.4,44.78,88.78,101.25,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,7467,2015-10-30 11:05:34:999\n-0.2191,-9.8617,-0.0994,-0.2067,-9.8044,-0.0265,-0.0061,0.0012,0.0012,-82.4,31.2,-124.2,49.03,88.78,97.31,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,7569,2015-10-30 11:05:35:101\n-0.2191,-9.8474,-0.097,-0.206,-9.8044,-0.032,0.011,0.0024,-0.0037,-82.5,31.2,-123.9,46.52,88.78,99.82,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,7671,2015-10-30 11:05:35:203\n-0.2143,-9.8497,-0.103,-0.206,-9.8044,-0.0328,-0.0037,0.0024,-0.0024,-82.4,31.1,-123.9,47.3,88.78,99.05,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,7773,2015-10-30 11:05:35:305\n-0.2227,-9.8509,-0.1125,-0.2056,-9.8044,-0.0367,-0.0024,0.0024,-0.0012,-82.4,31.1,-123.8,46.41,88.78,99.94,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,7875,2015-10-30 11:05:35:407\n-0.2119,-9.8474,-0.1018,-0.2061,-9.8044,-0.0306,0.0061,0.0037,-0.0012,-82.5,31.2,-124,47.89,88.78,98.45,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,7977,2015-10-30 11:05:35:509\n-0.2179,-9.8581,-0.1113,-0.2048,-9.8044,-0.0316,-0.0061,0.0012,0.0012,-82.5,31.2,-124.1,47.36,88.78,98.99,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,8078,2015-10-30 11:05:35:610\n-0.2251,-9.8593,-0.091,-0.2058,-9.8044,-0.0209,0.0098,0.0012,0.0012,-82.5,31.1,-123.9,50.53,88.79,95.8,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,8181,2015-10-30 11:05:35:713\n-0.2263,-9.8641,-0.0934,-0.2048,-9.8044,-0.0263,0.0073,0.0012,0,-82.6,31.2,-123.6,48.71,88.79,97.31,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,8283,2015-10-30 11:05:35:815\n-0.2203,-9.8509,-0.1006,-0.205,-9.8044,-0.0215,-0.0073,0.0037,-0.0037,-82.6,31.3,-123.5,50.12,88.8,95.68,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,8385,2015-10-30 11:05:35:917\n-0.2023,-9.8605,-0.0946,-0.2056,-9.8044,-0.0239,0.0049,0.0024,0,-82.6,31.3,-123.5,49.17,88.79,96.63,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,8487,2015-10-30 11:05:36:019\n-0.2227,-9.8581,-0.0898,-0.2085,-9.8044,-0.0127,0.0061,0.0012,0.0037,-82.6,31.3,-123.6,52.2,88.79,93.81,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,8589,2015-10-30 11:05:36:121\n-0.2203,-9.8497,-0.0922,-0.2066,-9.8044,-0.0133,0.0037,0.0024,0.0012,-82.7,31.3,-123.8,52.34,88.79,93.67,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,8690,2015-10-30 11:05:36:222\n-0.2191,-9.8521,-0.0838,-0.2073,-9.8044,-0.0128,-0.0012,0.0012,0.0024,-82.6,31.3,-123.7,52.56,88.79,93.45,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,8793,2015-10-30 11:05:36:325\n-0.2251,-9.8497,-0.085,-0.2086,-9.8044,-0.0085,0.0098,0,0,-82.5,31.2,-123.6,53.98,88.78,92.34,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,8895,2015-10-30 11:05:36:427\n-0.2179,-9.8497,-0.0838,-0.2092,-9.8043,-0.0093,-0.011,-0.0012,-0.0049,-82.6,31.3,-123.8,54.16,88.78,91.84,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,8997,2015-10-30 11:05:36:529\n-0.2179,-9.8629,-0.079,-0.208,-9.8044,-0.0137,0.0037,0,-0.0024,-82.6,31.4,-123.9,52.24,88.78,93.77,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,9099,2015-10-30 11:05:36:631\n-0.2239,-9.8426,-0.079,-0.2079,-9.8044,-0.0116,-0.0024,0,-0.0024,-82.5,31.3,-123.9,53.64,88.78,92.69,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,9201,2015-10-30 11:05:36:733\n-0.2155,-9.8474,-0.0898,-0.2062,-9.8044,-0.0149,0.0049,-0.0024,0.0012,-82.4,31.2,-124,52.04,88.8,94.29,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,9302,2015-10-30 11:05:36:834\n-0.2179,-9.8497,-0.085,-0.2064,-9.8044,-0.0114,0,0.0024,0.0024,-82.6,31.2,-123.8,52.85,88.79,93.16,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,9405,2015-10-30 11:05:36:937\n-0.2286,-9.8569,-0.0682,-0.2069,-9.8044,-0.0012,0.0305,0,0.0012,-82.6,31.2,-123.4,55.44,88.79,90.35,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,9507,2015-10-30 11:05:37:039\n-0.2227,-9.8521,-0.0491,-0.2104,-9.8043,0.0105,-0.0049,0.0012,-0.0037,-82.7,31.1,-123.3,58.62,88.77,87.15,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,9609,2015-10-30 11:05:37:141\n-0.2047,-9.8581,-0.073,-0.2056,-9.8044,-0.0131,-0.0073,0.0012,-0.0024,-82.7,31.1,-123.5,54.1,88.79,91.69,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,9711,2015-10-30 11:05:37:243\n-0.2191,-9.8569,-0.073,-0.2069,-9.8044,-0.0183,-0.0037,0.0024,-0.0024,-82.8,31.1,-123.8,50.97,88.79,95.04,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,9813,2015-10-30 11:05:37:345\n-0.231,-9.8569,-0.0814,-0.2055,-9.8044,-0.029,-0.022,0.0012,-0.0037,-82.8,31.2,-124.1,49.78,88.78,96.24,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,9915,2015-10-30 11:05:37:447\n-0.2191,-9.8569,-0.0826,-0.2042,-9.8044,-0.0397,-0.0012,0.0024,0.0024,-82.8,31.3,-124,45.04,88.79,100.99,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,10017,2015-10-30 11:05:37:549\n-0.2203,-9.8497,-0.1101,-0.2039,-9.8043,-0.0522,-0.0208,0.0012,-0.0024,-82.7,31.4,-124.1,43.11,88.78,102.93,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,10119,2015-10-30 11:05:37:651\n-0.231,-9.8474,-0.0694,-0.2056,-9.8044,-0.0423,0.0195,0.0024,0.0012,-82.6,31.3,-124,44.4,88.77,101.63,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,10221,2015-10-30 11:05:37:753\n-0.2251,-9.8497,-0.0958,-0.2037,-9.8043,-0.0544,-0.0086,0.0024,-0.0037,-82.8,31.3,-124.2,41.09,88.77,104.95,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,10323,2015-10-30 11:05:37:855\n-0.2179,-9.8557,-0.0898,-0.2041,-9.8044,-0.0489,-0.0024,0.0024,-0.0024,-82.7,31.2,-124.3,42.37,88.77,103.67,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,10425,2015-10-30 11:05:37:957\n-0.2227,-9.8533,-0.0958,-0.2021,-9.8044,-0.0548,-0.011,0.0024,-0.0012,-82.6,31.2,-124.2,40.88,88.78,105.17,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,10527,2015-10-30 11:05:38:059\n-0.2047,-9.8497,-0.079,-0.2044,-9.8043,-0.056,0.0024,0.0012,0.0037,-82.6,31.2,-124.4,40.4,88.77,105.65,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,10628,2015-10-30 11:05:38:160\n-0.2298,-9.8497,-0.091,-0.205,-9.8043,-0.0558,-0.0086,0,-0.0024,-82.7,31.4,-124.2,40.8,88.76,105.24,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,10731,2015-10-30 11:05:38:263\n-0.2167,-9.8545,-0.0862,-0.2037,-9.8043,-0.0574,-0.0037,0,-0.0049,-82.8,31.4,-124.3,39.92,88.76,106.13,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,10833,2015-10-30 11:05:38:365\n-0.2119,-9.8557,-0.0862,-0.2042,-9.8043,-0.0547,-0.0049,0,-0.0012,-82.7,31.4,-124.2,41.04,88.77,105,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,10935,2015-10-30 11:05:38:467\n-0.2119,-9.8497,-0.0838,-0.2036,-9.8044,-0.0532,0.0098,0.0012,0.0012,-82.6,31.3,-124.4,41,88.76,105.04,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,11037,2015-10-30 11:05:38:569\n-0.2322,-9.8354,-0.0994,-0.2032,-9.8044,-0.0524,-0.0037,0.0012,0.0024,-82.6,31.3,-124.2,41.59,88.77,104.45,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,11139,2015-10-30 11:05:38:671\n-0.2083,-9.8521,-0.085,-0.2049,-9.8044,-0.0487,0.0012,0.0012,0.0012,-82.6,31.5,-124.1,42.68,88.77,103.35,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,11241,2015-10-30 11:05:38:773\n-0.2119,-9.8605,-0.0922,-0.2047,-9.8044,-0.047,-0.0012,0.0012,0.0012,-82.7,31.5,-124,43.09,88.78,102.94,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,11343,2015-10-30 11:05:38:875\n-0.2263,-9.8509,-0.085,-0.2046,-9.8044,-0.0435,0.0012,0.0012,-0.0037,-82.7,31.5,-124,44.04,88.78,101.99,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,11445,2015-10-30 11:05:38:977\n-0.2179,-9.845,-0.0886,-0.2045,-9.8044,-0.0442,-0.0037,0.0024,0,-82.7,31.4,-124.2,43.94,88.78,102.09,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,11547,2015-10-30 11:05:39:079\n-0.2119,-9.8521,-0.0886,-0.2035,-9.8044,-0.0393,0.0086,0,0,-82.7,31.4,-124,45.1,88.79,100.94,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,11649,2015-10-30 11:05:39:181\n-0.2155,-9.8497,-0.0766,-0.2036,-9.8044,-0.0324,0.0037,-0.0012,-0.0024,-82.7,31.3,-123.7,46.68,88.79,99.35,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,11750,2015-10-30 11:05:39:282\n-0.2167,-9.8521,-0.0634,-0.2053,-9.8044,-0.0208,0.0183,0.0037,0.0012,-82.6,31.2,-124.1,50.24,88.79,95.78,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,11853,2015-10-30 11:05:39:385\n-0.2191,-9.8641,-0.0658,-0.2038,-9.8044,-0.0312,-0.0098,0.0012,-0.0024,-82.6,31.2,-124.3,48.43,88.8,97.59,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,11955,2015-10-30 11:05:39:487\n-0.2227,-9.8605,-0.0814,-0.2037,-9.8044,-0.0352,-0.0037,-0.0012,-0.0024,-82.7,31.2,-124.3,46.51,88.79,99.52,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,12057,2015-10-30 11:05:39:589\n-0.2274,-9.8521,-0.0814,-0.2065,-9.8044,-0.0367,0,0.0024,0.0024,-82.6,31.2,-124.1,45.9,88.78,100.13,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,12159,2015-10-30 11:05:39:691\n-0.2191,-9.845,-0.085,-0.2066,-9.8044,-0.0372,-0.0049,0.0012,-0.0024,-82.6,31.3,-123.8,46.7,88.78,99.33,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,12261,2015-10-30 11:05:39:793\n-0.2119,-9.8497,-0.0778,-0.2076,-9.8043,-0.0415,0.0012,0.0012,0.0024,-82.3,31.1,-124.1,45.04,88.76,101.31,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,12363,2015-10-30 11:05:39:895\n-0.2251,-9.8521,-0.0814,-0.2056,-9.8044,-0.0452,-0.0061,0.0012,-0.0012,-82.4,31.2,-124.3,43.94,88.77,102.41,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,12465,2015-10-30 11:05:39:997\n-0.2191,-9.8557,-0.0874,-0.206,-9.8043,-0.0468,0.0061,0.0012,0.0012,-82.5,31.4,-124.3,43.54,88.77,102.81,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,12567,2015-10-30 11:05:40:099\n-0.1999,-9.8557,-0.0658,-0.2085,-9.8043,-0.0385,-0.0037,0.0024,-0.0024,-82.7,31.4,-124.3,45.58,88.76,100.45,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,12669,2015-10-30 11:05:40:201\n-0.2274,-9.8521,-0.0826,-0.2075,-9.8043,-0.0448,0.0024,0,-0.0037,-82.8,31.4,-124.4,43.86,88.76,102.17,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,12771,2015-10-30 11:05:40:303\n-0.2107,-9.8533,-0.0694,-0.2075,-9.8043,-0.0482,-0.0061,0.0012,-0.0012,-82.8,31.4,-124.3,43.51,88.76,102.53,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,12873,2015-10-30 11:05:40:405\n-0.2083,-9.8497,-0.073,-0.2065,-9.8043,-0.0498,0,0.0024,0,-82.8,31.4,-124.6,42.89,88.76,103.36,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,12974,2015-10-30 11:05:40:506\n-0.231,-9.8497,-0.097,-0.2047,-9.8043,-0.0557,-0.0024,0.0049,-0.0024,-82.7,31.3,-124.5,41.33,88.76,104.71,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,13077,2015-10-30 11:05:40:609\n-0.2251,-9.8497,-0.0922,-0.2023,-9.8044,-0.0576,-0.0049,0.0012,-0.0037,-82.6,31.2,-124.8,40.37,88.77,105.89,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,13179,2015-10-30 11:05:40:711\n-0.2227,-9.8438,-0.0898,-0.2016,-9.8044,-0.0489,0.0012,0.0012,-0.0037,-82.5,31.2,-124.5,42.72,88.79,103.64,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,13281,2015-10-30 11:05:40:813\n-0.2143,-9.8593,-0.0718,-0.2026,-9.8044,-0.0425,0.0073,0,-0.0012,-82.5,31.2,-124.2,44.51,88.79,101.85,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,13382,2015-10-30 11:05:40:914\n-0.2167,-9.8497,-0.1018,-0.1996,-9.8044,-0.0533,-0.0012,0,-0.0012,-82.5,31.3,-124,41.4,88.79,104.96,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,13485,2015-10-30 11:05:41:017\n-0.2107,-9.8677,-0.079,-0.2011,-9.8045,-0.0464,0.0098,0.0024,0,-82.6,31.3,-123.9,42.33,88.79,103.71,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,13587,2015-10-30 11:05:41:119\n-0.2107,-9.8545,-0.073,-0.2016,-9.8044,-0.0503,0.0012,0,-0.0024,-82.7,31.3,-124.2,42.03,88.79,104.01,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,13689,2015-10-30 11:05:41:221\n-0.2131,-9.845,-0.085,-0.2016,-9.8044,-0.0467,-0.011,0,-0.0012,-82.7,31.2,-124.5,43.41,88.8,102.62,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,13790,2015-10-30 11:05:41:322\n-0.2059,-9.8569,-0.0754,-0.202,-9.8045,-0.0458,0.0098,0,-0.0012,-82.6,31.1,-124.5,43.26,88.79,102.78,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,13893,2015-10-30 11:05:41:425\n-0.2095,-9.8593,-0.067,-0.2041,-9.8044,-0.0408,0.0012,0.0012,-0.0012,-82.6,31.2,-124.4,44.68,88.78,101.35,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,13995,2015-10-30 11:05:41:527\n-0.2203,-9.8258,-0.0946,-0.2054,-9.8044,-0.0391,0.0037,0,0.0037,-82.5,31.1,-124.3,45.57,88.78,100.78,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,14097,2015-10-30 11:05:41:629\n-0.2083,-9.8581,-0.0754,-0.2081,-9.8044,-0.033,0.0073,0,0.0012,-82.6,31.1,-124.6,46.78,88.77,99.46,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,14198,2015-10-30 11:05:41:730\n-0.1999,-9.8605,-0.073,-0.2095,-9.8043,-0.0357,0.0012,0.0024,0.0037,-82.6,31.1,-124.8,46.42,88.76,99.81,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,14301,2015-10-30 11:05:41:833\n-0.2251,-9.8533,-0.0886,-0.2109,-9.8043,-0.0397,-0.0037,0,-0.0012,-82.7,31.2,-125.3,45.58,88.75,100.66,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,14403,2015-10-30 11:05:41:935\n-0.2107,-9.8497,-0.073,-0.2129,-9.8042,-0.0356,0.0061,0,-0.0037,-82.7,31.3,-125.2,46.75,88.74,99.48,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,14505,2015-10-30 11:05:42:037\n-0.2095,-9.8593,-0.0706,-0.2143,-9.8042,-0.0321,0,0,0,-82.7,31.2,-125.3,47.7,88.73,98.53,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,14607,2015-10-30 11:05:42:139\n-0.2167,-9.8462,-0.091,-0.2156,-9.8042,-0.0287,0.0086,-0.0012,0.0037,-82.7,31.2,-125.3,48.04,88.73,98.19,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,14709,2015-10-30 11:05:42:241\n-0.2083,-9.8497,-0.0814,-0.2159,-9.8042,-0.0305,0.0037,0.0024,0.0024,-82.5,31.1,-125.2,48.51,88.73,98.03,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,14811,2015-10-30 11:05:42:343\n-0.2107,-9.8617,-0.0622,-0.2171,-9.8042,-0.0234,0.011,-0.0012,0.0037,-82.5,31.2,-124.8,50.16,88.72,96.38,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,14913,2015-10-30 11:05:42:445\n-0.2274,-9.8641,-0.0838,-0.2182,-9.8041,-0.0271,-0.0073,0,0.0012,-82.6,31.2,-124.6,49.14,88.72,97.09,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,15015,2015-10-30 11:05:42:547\n-0.2083,-9.8509,-0.073,-0.2185,-9.8041,-0.0255,0.0049,0.0024,0.0012,-82.7,31.3,-124.7,49.47,88.72,96.76,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,15116,2015-10-30 11:05:42:648\n-0.2155,-9.8605,-0.0682,-0.2183,-9.8041,-0.0266,-0.0037,0,-0.0049,-82.8,31.2,-124.8,49.27,88.72,96.95,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,15219,2015-10-30 11:05:42:751\n-0.2239,-9.8569,-0.073,-0.2175,-9.8041,-0.0275,0.0049,0.0012,0,-82.7,31.1,-124.6,49.03,88.72,97.19,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,15321,2015-10-30 11:05:42:853\n-0.2167,-9.8378,-0.091,-0.2167,-9.8041,-0.0319,-0.0049,0,0.0024,-82.6,31.1,-124.5,48.13,88.72,97.88,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,15423,2015-10-30 11:05:42:955\n-0.2155,-9.8569,-0.085,-0.2162,-9.8041,-0.0348,-0.0037,0,0,-82.7,31.2,-124.6,47,88.72,99.23,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,15524,2015-10-30 11:05:43:056\n-0.2227,-9.8533,-0.0958,-0.2149,-9.8042,-0.0344,0.0024,-0.0012,-0.0049,-82.7,31.2,-124.8,46.91,88.72,99.32,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,15627,2015-10-30 11:05:43:159\n-0.2274,-9.8605,-0.0706,-0.2159,-9.8042,-0.0277,0.0159,0.0024,0,-82.6,31.2,-125.2,48.91,88.73,97.31,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,15729,2015-10-30 11:05:43:261\n-0.2143,-9.8569,-0.0778,-0.2156,-9.8042,-0.0262,-0.0037,0.0024,-0.0024,-82.4,31.2,-125,49.95,88.73,96.59,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,15831,2015-10-30 11:05:43:363\n-0.2179,-9.8509,-0.073,-0.2162,-9.8042,-0.0234,0.0073,0.0012,0,-82.6,31.3,-124.9,50.04,88.73,96.18,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,15933,2015-10-30 11:05:43:465\n-0.2251,-9.8474,-0.079,-0.2164,-9.8042,-0.0287,-0.0049,0,0.0037,-82.7,31.2,-124.8,49.11,88.73,97.11,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,16035,2015-10-30 11:05:43:567\n-0.2251,-9.8509,-0.0766,-0.2164,-9.8041,-0.0317,-0.0061,0.0012,0.0012,-82.7,31.3,-124.6,48.13,88.73,98.09,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,16137,2015-10-30 11:05:43:669\n-0.2119,-9.8521,-0.0886,-0.2157,-9.8042,-0.033,-0.0049,0.0012,0.0012,-82.7,31.3,-124.4,47.43,88.72,98.58,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,16238,2015-10-30 11:05:43:770\n-0.2239,-9.8474,-0.0826,-0.2162,-9.8042,-0.0304,-0.0012,-0.0012,0,-82.4,31.3,-124.1,48.33,88.72,98,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,16341,2015-10-30 11:05:43:873\n-0.2107,-9.8497,-0.0778,-0.2163,-9.8041,-0.0331,-0.0061,0.0012,0,-82.4,31.4,-123.8,47.64,88.72,98.7,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,16443,2015-10-30 11:05:43:975\n-0.2119,-9.8545,-0.0718,-0.2157,-9.8042,-0.0326,0.0098,0.0037,0,-82.5,31.4,-123.7,47.15,88.72,99.18,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,16545,2015-10-30 11:05:44:077\n-0.2263,-9.8545,-0.0766,-0.2151,-9.8042,-0.0236,0.011,0,0,-82.6,31.4,-123.8,49.75,88.74,96.26,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,16647,2015-10-30 11:05:44:179\n-0.2167,-9.8234,-0.0826,-0.2148,-9.8042,-0.0229,0.0037,0,0.0024,-82.6,31.3,-124,49.78,88.74,96.23,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,16749,2015-10-30 11:05:44:281\n-0.2203,-9.8737,-0.0718,-0.2148,-9.8042,-0.0177,-0.0024,0,-0.0024,-82.6,31.3,-124.3,51.3,88.74,94.71,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,16850,2015-10-30 11:05:44:382\n-0.2239,-9.8497,-0.091,-0.2137,-9.8042,-0.0182,0.0049,0.0012,-0.0037,-82.5,31.2,-124.3,51.46,88.75,94.87,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,16953,2015-10-30 11:05:44:485\n-0.2298,-9.8521,-0.0718,-0.2148,-9.8042,-0.0142,0,0.0012,-0.0024,-82.6,31.4,-124.4,52.29,88.74,93.71,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,17055,2015-10-30 11:05:44:587\n-0.2191,-9.8545,-0.0826,-0.2154,-9.8042,-0.0063,0.022,0.0037,0,-82.6,31.3,-124.4,52.79,88.74,93.21,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,17159,2015-10-30 11:05:44:691\n-0.2263,-9.8533,-0.073,-0.2136,-9.8043,-0.0023,-0.0049,0.0024,-0.0049,-82.6,31.3,-124.7,55.59,88.75,90.62,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,17259,2015-10-30 11:05:44:791\n-0.2286,-9.833,-0.0934,-0.2118,-9.8043,-0.0148,-0.0195,0.0012,0,-82.7,31.3,-124.6,52.21,88.76,94.01,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,17361,2015-10-30 11:05:44:893\n-0.2071,-9.8641,-0.0587,-0.2087,-9.8044,-0.0122,0.0086,0.0012,-0.0024,-82.7,31.3,-124.2,52.66,88.78,93.35,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,17463,2015-10-30 11:05:44:995\n-0.2167,-9.8509,0.0036,-0.209,-9.8043,0.0262,0.0403,0.0012,0.0012,-82.7,31.3,-124.1,63.11,88.77,82.87,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,17565,2015-10-30 11:05:45:097\n-0.1939,-9.8474,-0.0527,-0.2051,-9.8044,0.0207,-0.0794,0.0012,-0.0183,-82.7,31.2,-124.2,61.75,88.8,84.24,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,17667,2015-10-30 11:05:45:199\n-0.2095,-9.827,-0.0898,-0.1955,-9.8046,-0.0367,0.0049,0.0012,-0.0049,-82.7,31.2,-124.4,45.4,88.84,100.64,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,17768,2015-10-30 11:05:45:300\n-0.2107,-9.8497,-0.0802,-0.198,-9.8045,-0.0354,-0.0012,0,0.0024,-82.7,31.2,-124.4,45.98,88.83,100.05,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,17871,2015-10-30 11:05:45:403\n-0.2083,-9.839,-0.0922,-0.199,-9.8045,-0.0336,0.0037,0.0012,0,-82.8,31.3,-123.7,46.47,88.82,99.56,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,17972,2015-10-30 11:05:45:504\n-0.2059,-9.8521,-0.1018,-0.1997,-9.8045,-0.037,0.0024,0.0024,0.0061,-82.8,31.3,-123.7,44.93,88.82,101.11,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,18075,2015-10-30 11:05:45:607\n-0.2035,-9.8521,-0.0898,-0.2014,-9.8045,-0.0283,0.0061,0,0.0012,-82.8,31.3,-123.9,48.03,88.81,98,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,18177,2015-10-30 11:05:45:709\n-0.2131,-9.8497,-0.0886,-0.2037,-9.8044,-0.0298,-0.0098,0,-0.0024,-82.8,31.3,-124.1,48.43,88.8,97.6,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,18278,2015-10-30 11:05:45:810\n-0.2119,-9.845,-0.079,-0.2043,-9.8044,-0.0244,-0.0037,-0.0012,-0.0024,-82.9,31.3,-124.1,49.85,88.8,96.17,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,18381,2015-10-30 11:05:45:913\n-0.2011,-9.8545,-0.085,-0.2053,-9.8044,-0.0277,-0.0012,0.0012,0.0012,-82.8,31.4,-124.2,48.33,88.79,97.69,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,18483,2015-10-30 11:05:46:015\n-0.2059,-9.8497,-0.079,-0.2081,-9.8043,-0.0271,-0.011,0,0.0012,-82.8,31.4,-124.1,49.03,88.78,96.99,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,18584,2015-10-30 11:05:46:116\n-0.2059,-9.8497,-0.0994,-0.2073,-9.8043,-0.0352,-0.011,0,-0.0012,-82.8,31.5,-123.6,46.4,88.77,99.62,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,18687,2015-10-30 11:05:46:219\n-0.1963,-9.8653,-0.1065,-0.2053,-9.8044,-0.0397,0.0147,0.0012,-0.0061,-82.8,31.4,-123.5,44.88,88.78,100.94,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,18789,2015-10-30 11:05:46:321\n-0.2143,-9.8497,-0.0826,-0.2091,-9.8043,-0.0199,-0.0012,0.0012,0.0024,-82.9,31.4,-123.7,50.58,88.77,95.43,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,18891,2015-10-30 11:05:46:423\n-0.1987,-9.8497,-0.0982,-0.2089,-9.8043,-0.027,-0.0098,0.0012,-0.0037,-82.9,31.4,-124,49.27,88.77,96.75,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,18993,2015-10-30 11:05:46:525\n-0.2083,-9.8689,-0.0994,-0.2105,-9.8043,-0.0284,0.0049,0.0024,0,-83,31.4,-124.3,48.33,88.76,97.69,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,19095,2015-10-30 11:05:46:627\n-0.2035,-9.8617,-0.1065,-0.2101,-9.8042,-0.0413,-0.0159,0.0037,-0.0024,-83,31.4,-124.3,46.25,88.75,99.77,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,19196,2015-10-30 11:05:46:728\n-0.2011,-9.8497,-0.1245,-0.2104,-9.8043,-0.0363,0.011,0.0024,0.0037,-83,31.4,-124,46.24,88.75,99.78,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,19299,2015-10-30 11:05:46:831\n-0.2035,-9.8641,-0.1065,-0.212,-9.8042,-0.0362,-0.0012,0.0012,-0.0012,-83,31.4,-124,46.4,88.74,99.62,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,19401,2015-10-30 11:05:46:933\n-0.2023,-9.8629,-0.1149,-0.2136,-9.8042,-0.0269,0.0098,0,0,-82.9,31.4,-123.9,48.03,88.74,97.98,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,19503,2015-10-30 11:05:47:035\n-0.2023,-9.8497,-0.1161,-0.2144,-9.8042,-0.0239,-0.0024,0.0024,-0.0012,-82.9,31.5,-123.8,49.65,88.74,96.35,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,19605,2015-10-30 11:05:47:137\n-0.1963,-9.8557,-0.1089,-0.216,-9.8042,-0.0169,0.0159,0.0012,0.0037,-83,31.5,-123.8,51.53,88.73,94.47,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,19707,2015-10-30 11:05:47:239\n-0.1939,-9.8617,-0.1125,-0.2174,-9.8042,-0.011,0.0147,0.0012,0,-83,31.6,-123.8,53.09,88.73,92.9,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,19809,2015-10-30 11:05:47:341\n-0.2131,-9.8497,-0.0862,-0.2216,-9.8041,0.0083,-0.0134,0.0037,-0.0061,-83,31.6,-124.1,57.54,88.71,88.44,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,19911,2015-10-30 11:05:47:443\n-0.1963,-9.8497,-0.0922,-0.2219,-9.804,0.004,0.0024,0.0024,-0.0012,-83,31.6,-123.9,55.85,88.71,90.13,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,20012,2015-10-30 11:05:47:544\n-0.2035,-9.8497,-0.0838,-0.2236,-9.804,0.0081,-0.0024,0.0012,-0.0012,-83,31.5,-123.7,58.49,88.69,87.48,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,20115,2015-10-30 11:05:47:647\n-0.1963,-9.8497,-0.1041,-0.2244,-9.804,0.0105,0.0281,0.0012,0.0024,-83,31.5,-123.6,58.66,88.69,87.31,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,20217,2015-10-30 11:05:47:749\n-0.1915,-9.8581,-0.1006,-0.2254,-9.804,0.0174,-0.0037,0.0012,0,-83.1,31.3,-123.9,61.15,88.68,84.82,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,20319,2015-10-30 11:05:47:851\n-0.2047,-9.8569,-0.0742,-0.2279,-9.8039,0.024,0.0159,0.0012,0.0024,-83.1,31.3,-124.2,61.98,88.66,83.98,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,20421,2015-10-30 11:05:47:953\n-0.1927,-9.8533,-0.091,-0.228,-9.8039,0.0202,-0.0049,0.0012,0,-83.1,31.3,-124.4,61.02,88.66,84.94,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,20523,2015-10-30 11:05:48:055\n-0.2047,-9.8354,-0.0826,-0.23,-9.8038,0.0287,0.0012,0.0012,-0.0037,-83.1,31.3,-124.3,62.47,88.65,83.49,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,20625,2015-10-30 11:05:48:157\n-0.1879,-9.8521,-0.0766,-0.2284,-9.8039,0.0224,-0.0037,0,-0.0049,-83,31.4,-124.3,61.56,88.66,84.41,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,20727,2015-10-30 11:05:48:259\n-0.2131,-9.8497,-0.0694,-0.2273,-9.8039,0.0214,-0.0098,0.0024,0,-83,31.3,-123.9,61.34,88.67,84.63,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,20829,2015-10-30 11:05:48:361\n-0.2071,-9.8497,-0.0646,-0.2232,-9.804,0.0156,0.0098,0.0012,0.0037,-83,31.5,-124,59.95,88.69,86.01,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,20931,2015-10-30 11:05:48:463\n-0.1963,-9.8497,-0.091,-0.2216,-9.8041,0.013,-0.0073,0,-0.0037,-83.1,31.6,-124.1,59.99,88.69,85.97,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,21033,2015-10-30 11:05:48:565\n-0.2059,-9.8497,-0.0599,-0.2222,-9.804,0.0167,-0.0012,0,-0.0037,-83.1,31.5,-124.2,60.27,88.7,85.7,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,21134,2015-10-30 11:05:48:666\n-0.1975,-9.8521,-0.0982,-0.2172,-9.8042,-0.0057,-0.0037,0.0037,-0.0061,-83,31.5,-124.2,55.38,88.73,90.61,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,21237,2015-10-30 11:05:48:769\n-0.1915,-9.8557,-0.103,-0.2155,-9.8042,-0.0134,-0.0134,0,-0.0073,-83,31.5,-124.1,52.44,88.74,93.55,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,21339,2015-10-30 11:05:48:871\n-0.2274,-9.8366,-0.1161,-0.2135,-9.8042,-0.03,0.0037,0.0012,0.0012,-83,31.6,-124,48.27,88.74,97.74,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,21440,2015-10-30 11:05:48:972\n-0.2071,-9.8402,-0.1185,-0.2115,-9.8042,-0.0316,-0.0244,0.0012,0,-83,31.7,-123.9,49.3,88.75,96.71,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,21543,2015-10-30 11:05:49:075\n-0.2059,-9.845,-0.1113,-0.2097,-9.8043,-0.0329,-0.0049,-0.0012,-0.0037,-83,31.6,-123.4,46.88,88.76,98.92,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,21645,2015-10-30 11:05:49:177\n-0.2071,-9.8605,-0.1221,-0.208,-9.8043,-0.0389,-0.0122,0.0012,-0.0024,-82.9,31.5,-123.5,45.49,88.76,100.31,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,21746,2015-10-30 11:05:49:278\n-0.2167,-9.8557,-0.1317,-0.2103,-9.8043,-0.0361,0.0024,0.0024,0,-82.9,31.6,-123.5,46.06,88.75,99.75,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,21848,2015-10-30 11:05:49:380\n-0.1987,-9.8366,-0.1245,-0.2113,-9.8043,-0.0278,0.011,0.0012,0,-83,31.6,-123.7,47.69,88.75,98.33,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,21951,2015-10-30 11:05:49:483\n-0.1975,-9.8581,-0.0994,-0.2132,-9.8043,-0.0212,0.0061,0.0012,0.0037,-83.1,31.7,-123.8,50.48,88.75,95.52,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,22053,2015-10-30 11:05:49:585\n-0.1987,-9.8497,-0.1221,-0.2149,-9.8042,-0.025,-0.0012,0.0012,0.0037,-83,31.6,-123.8,49.37,88.74,96.63,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,22155,2015-10-30 11:05:49:687\n-0.1879,-9.8629,-0.1161,-0.2156,-9.8042,-0.0241,-0.0098,0.0012,0,-83.1,31.7,-123.6,49.64,88.73,96.37,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,22257,2015-10-30 11:05:49:789\n-0.1963,-9.8533,-0.1209,-0.2173,-9.8041,-0.0239,0.0037,0.0024,0,-83,31.6,-123.4,48.87,88.73,96.92,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,22359,2015-10-30 11:05:49:891\n-0.2095,-9.8497,-0.1161,-0.2185,-9.8041,-0.0179,0.0012,0.0012,0.0012,-82.9,31.6,-123.6,51.32,88.72,94.67,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,22461,2015-10-30 11:05:49:993\n-0.2035,-9.8509,-0.1077,-0.2203,-9.8041,-0.0082,0.0086,0.0024,0,-82.8,31.6,-123.7,53.85,88.71,92.13,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,22563,2015-10-30 11:05:50:095\n-0.1951,-9.8605,-0.1018,-0.221,-9.8041,-0.0054,0.0122,0.0024,0.0024,-82.7,31.6,-123.9,54.29,88.71,91.69,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,22665,2015-10-30 11:05:50:197\n-0.2143,-9.8617,-0.1053,-0.2227,-9.8041,-0.0026,0.0037,0.0037,0.0024,-82.7,31.6,-123.8,55.3,88.7,90.68,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,22767,2015-10-30 11:05:50:299\n-0.2047,-9.8545,-0.103,-0.2239,-9.804,0.0028,0.0049,0.0012,0.0012,-82.8,31.6,-124.1,56.47,88.69,89.51,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,22868,2015-10-30 11:05:50:400\n-0.2035,-9.8497,-0.0922,-0.2227,-9.8041,-0.0019,0.0073,0.0012,-0.0012,-82.9,31.5,-124.2,55.48,88.7,90.5,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,22971,2015-10-30 11:05:50:503\n-0.1987,-9.8569,-0.1006,-0.222,-9.8041,-0.0035,-0.0012,0,-0.0012,-82.9,31.4,-124.3,55.93,88.7,90.05,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,23073,2015-10-30 11:05:50:605\n-0.2143,-9.8366,-0.1006,-0.221,-9.8041,-0.0061,0.011,0.0012,0.0012,-82.8,31.3,-124.1,54.41,88.71,91.58,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,23175,2015-10-30 11:05:50:707\n-0.1987,-9.8497,-0.0886,-0.2209,-9.8041,-0.0051,-0.0098,0.0024,-0.0024,-82.9,31.3,-124.2,55.38,88.71,90.61,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,23277,2015-10-30 11:05:50:809\n-0.2095,-9.8593,-0.1041,-0.2206,-9.8041,-0.0114,0.0049,0.0012,0.0024,-82.9,31.3,-124.4,53.04,88.71,92.95,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,23378,2015-10-30 11:05:50:910\n-0.2023,-9.8641,-0.1137,-0.2201,-9.8041,-0.016,-0.0037,0.0012,0,-82.9,31.3,-124.5,52.15,88.71,93.85,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,23481,2015-10-30 11:05:51:013\n-0.2011,-9.8593,-0.1125,-0.2191,-9.8041,-0.0194,-0.0024,0.0012,-0.0012,-82.9,31.4,-124.3,50.94,88.71,95.06,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,23583,2015-10-30 11:05:51:115\n-0.1939,-9.8581,-0.1101,-0.2193,-9.8041,-0.0217,-0.0061,0,-0.0012,-82.9,31.4,-124.1,50.36,88.71,95.64,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,23685,2015-10-30 11:05:51:217\n-0.2107,-9.8497,-0.1257,-0.2183,-9.8041,-0.0295,-0.0098,0.0012,-0.0037,-82.8,31.4,-124,48.9,88.71,97.11,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,23787,2015-10-30 11:05:51:319\n-0.2047,-9.8557,-0.1221,-0.2173,-9.8041,-0.034,-0.0024,-0.0012,0,-82.8,31.4,-123.7,47.13,88.71,98.88,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,23889,2015-10-30 11:05:51:421\n-0.1903,-9.8593,-0.1089,-0.2178,-9.8041,-0.0316,0.0049,0.0012,0.0012,-82.7,31.4,-123.7,47.77,88.71,98.24,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,23991,2015-10-30 11:05:51:523\n-0.1987,-9.8521,-0.1173,-0.2167,-9.8041,-0.0295,0,0,0,-82.7,31.3,-123.6,48.28,88.72,97.73,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,24093,2015-10-30 11:05:51:625\n-0.1987,-9.8677,-0.1077,-0.2162,-9.8041,-0.0292,-0.0012,0.0012,0,-82.7,31.4,-123.8,48.4,88.72,97.61,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,24195,2015-10-30 11:05:51:727\n-0.2095,-9.8593,-0.1125,-0.2154,-9.8042,-0.0333,-0.0024,-0.0012,-0.0049,-82.8,31.4,-123.6,47.24,88.73,98.78,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,24296,2015-10-30 11:05:51:828\n-0.1915,-9.8557,-0.1245,-0.2138,-9.8042,-0.0328,0.0037,0,-0.0037,-82.7,31.4,-123.6,47.23,88.73,98.78,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,24399,2015-10-30 11:05:51:931\n-0.1939,-9.839,-0.1341,-0.2133,-9.8042,-0.036,-0.0012,0.0024,0,-82.9,31.5,-123.4,46.2,88.74,99.6,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,24501,2015-10-30 11:05:52:033\n-0.1927,-9.8533,-0.1425,-0.2132,-9.8042,-0.0356,-0.0086,0.0012,-0.0024,-82.8,31.5,-123.3,46.32,88.74,99.48,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,24603,2015-10-30 11:05:52:135\n-0.2023,-9.8497,-0.1389,-0.2129,-9.8042,-0.0306,0.0073,0,-0.0012,-82.9,31.5,-123.3,46.77,88.74,99.03,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,24705,2015-10-30 11:05:52:237\n-0.1963,-9.8497,-0.1257,-0.2126,-9.8042,-0.0291,0.0012,-0.0012,-0.0012,-82.8,31.4,-123.2,48.01,88.75,97.79,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,24807,2015-10-30 11:05:52:339\n-0.1963,-9.8545,-0.1353,-0.2128,-9.8043,-0.0239,0,0.0024,-0.0049,-82.8,31.4,-123.4,49.39,88.75,96.41,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,24909,2015-10-30 11:05:52:441\n-0.1987,-9.8497,-0.1293,-0.213,-9.8043,-0.0186,0.0098,0,0,-82.8,31.4,-123.5,49.94,88.75,95.86,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,25011,2015-10-30 11:05:52:543\n-0.1987,-9.8629,-0.1185,-0.214,-9.8043,-0.0108,0.0098,0.0012,0.0012,-82.9,31.4,-123.9,52.62,88.75,93.38,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,25113,2015-10-30 11:05:52:645\n-0.2095,-9.8593,-0.1269,-0.2127,-9.8043,-0.0107,-0.0024,0.0012,-0.0037,-83,31.5,-124.2,53.12,88.76,92.88,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,25214,2015-10-30 11:05:52:746\n-0.2047,-9.8521,-0.1101,-0.2131,-9.8043,-0.0028,-0.0037,-0.0012,0,-83,31.4,-124.4,55.21,88.76,90.79,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,25317,2015-10-30 11:05:52:849\n-0.1975,-9.8246,-0.152,-0.2104,-9.8043,-0.0192,-0.0232,0.0012,-0.0037,-82.9,31.4,-124.1,50.81,88.77,95.2,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,25419,2015-10-30 11:05:52:951\n-0.2047,-9.8342,-0.1221,-0.2144,-9.8042,0.0132,0.0086,0.0037,-0.0073,-82.7,31.2,-124.1,59.5,88.74,86.49,36.814316,-119.74832,,336.6289119,,220.79031,,0 / 0,25521,2015-10-30 11:05:53:053\n"
  },
  {
    "path": "test/utils/DataFormat.cpp",
    "content": "//\n// Created by yangcheng on 2019/1/17.\n//\n\n#include \"DataFormat.h\"\n#include \"fstream\"\n#include \"cassert\"\n#include \"../../math/Quaternions.h\"\n#include \"../../sensor/Accelerometer.h\"\n#include \"iostream\"\n#include <cmath>\n#include <dirent.h>\n\n//using namespace std;\nusing namespace Eigen;\n\nstd::vector<std::string> DataFormat::getAllfiles(std::string &dir) {\n    DIR *dir_buffer;\n    struct dirent *ent;\n    std::vector<std::string> files;\n    if ((dir_buffer = opendir(dir.c_str())) != NULL) {\n        while ((ent = readdir(dir_buffer)) != NULL) {\n            string file_name(ent->d_name);\n            if (file_name != \".\" && file_name != \"..\"){\n                files.push_back(file_name);\n            }\n        }\n        closedir(dir_buffer);\n    } else {\n        /* could not open directory */\n        std::cout << \"Director Open ERROR.\" << std::endl;\n    }\n    return files;\n}\n\nvoid DataFormat::writeCSVs() {\n\n    std::string in_dir = \"D:\\\\worksheet\\\\pyCharm\\\\work sheet\\\\AccSpeedFitting\\\\data\\\\sensor_data\\\\\";\n    std::string out_dir = \"D:\\\\worksheet\\\\pyCharm\\\\work sheet\\\\AccSpeedFitting\\\\data\\\\sensor_data_format\\\\\";\n\n    std::vector<std::string> files = getAllfiles(in_dir);\n\n    for(auto &file : files){\n        std::ifstream inFile(in_dir + file);\n        int file_cout = std::count(std::istreambuf_iterator<char>(inFile),\n                           std::istreambuf_iterator<char>(), '\\n') + 1;\n        inFile.close();\n\n        MatrixXd gyro_data(file_cout,3),acc_data(file_cout,3),mag_data(file_cout,3), gps_data(file_cout,7),\n                g_data(file_cout,3), ornt_data(file_cout,3), road_data(file_cout,3);\n\n        readCSV(in_dir+file, gyro_data, acc_data, mag_data, gps_data, g_data, ornt_data, road_data);\n\n        writeCSV(out_dir+file,acc_data, g_data, gyro_data, mag_data, ornt_data, gps_data);\n    }\n\n}\n\nvoid DataFormat::writeCSV(std::string file_name, MatrixXd &acc, MatrixXd &g_data, MatrixXd &gyro,\n                          MatrixXd &mag, MatrixXd &ornt_data, MatrixXd &gps_data) {\n\n    ofstream outfile;\n    outfile.open(file_name, ios::trunc);\n\n    int data_size = acc.rows();\n    Quaternions quaternions;\n    Accelerometer accelerometer;\n    outfile.precision(std::numeric_limits<double>::digits10 + 1);\n    for(int i = 1; i < data_size; ++i){\n\n        Vector3d pre_ornt = ornt_data.row(i-1);\n        Vector3d current_ornt = ornt_data.row(i);\n        Vector3d ornt_diff = current_ornt - pre_ornt;\n        Vector4d q = quaternions.GetQFromEuler(current_ornt);\n        Matrix3d dcm = quaternions.GetDCMFromQ(q);\n\n        Vector3d acc_v = acc.row(i);\n        Vector3d acc_n = dcm * acc_v;\n        Vector3d acc_v_norm = accelerometer.Normalise(acc_v);\n        Vector3d acc_n_norm = accelerometer.Normalise(acc_n);\n\n        Vector3d g_v = g_data.row(i);\n        Vector3d g_n = dcm * g_v;\n        Vector3d g_v_norm = accelerometer.Normalise(g_v);\n        Vector3d g_n_norm = accelerometer.Normalise(g_n);\n        Vector3d a_diff = acc_n - g_n;\n\n        Vector3d gyro_v = gyro.row(i);\n        Vector3d gyro_v_norm = accelerometer.Normalise(gyro_v);\n\n        Vector3d pre_mag_v = mag.row(i-1);\n        Vector3d current_mag_v = mag.row(i);\n        Vector3d mag_v_diff = (dcm * current_mag_v) - (dcm * pre_mag_v);\n        Vector3d mag_v_norm = accelerometer.Normalise(mag_v_diff);\n\n        VectorXd gps_v = gps_data.row(i);\n\n        outfile << acc_v_norm(0) << \",\" << acc_v_norm(1) << \",\" << acc_v_norm(2) << \",\";\n        outfile << acc_n_norm(0) << \",\" << acc_n_norm(1) << \",\" << acc_n_norm(2) << \",\";\n        outfile << g_v_norm(0) << \",\" << g_v_norm(1) << \",\" << g_v_norm(2) << \",\";\n        outfile << g_n_norm(0) << \",\" << g_n_norm(1) << \",\" << g_n_norm(2) << \",\";\n        outfile << gyro_v_norm(0) << \",\" << gyro_v_norm(1) << \",\" << gyro_v_norm(2) << \",\";\n        outfile << mag_v_norm(0) << \",\" << mag_v_norm(1) << \",\" << mag_v_norm(2) << \",\";\n        outfile << mag_v_diff(0) << \",\" << mag_v_diff(1) << \",\" << mag_v_diff(2) << \",\";\n        outfile << a_diff(0) << \",\" << a_diff(1) << \",\" << a_diff(2) << \",\";\n        outfile << ornt_diff(0) << \",\" << ornt_diff(1) << \",\" << ornt_diff(2) << \",\";\n        outfile << gps_v(0) << \",\" << gps_v(1) << \",\" << gps_v(2) << \",\"\n                << gps_v(3) << \",\" << gps_v(4) << \",\" << gps_v(5) << \",\"\n                << gps_v(6) << endl;\n    }\n    std::cout << \"write file: \" << file_name <<  \"data size is \" << data_size << std::endl;\n    outfile.close();\n\n\n}\n\n\nvoid DataFormat::readCSV(std::string file_name, MatrixXd &gyro, MatrixXd &acc, MatrixXd &mag,\n                         MatrixXd &gps_data, MatrixXd &g_data, MatrixXd &ornt_data, MatrixXd &road_data) {\n    ifstream infile;\n    cout << \"read file: \" << file_name << endl;\n    infile.open(file_name,\n                ios::in);\n    assert(infile.is_open());\n\n    string s;\n    int i = 0;\n    while (getline(infile, s)) {\n\n        vector<string> s_split;\n        split(s, s_split, \",\");\n\n        // acc data.\n        acc(i, 0) = atof(s_split[0].c_str());\n        acc(i, 1) = atof(s_split[1].c_str());\n        acc(i, 2) = atof(s_split[2].c_str());\n        // gravity data.\n        g_data(i,0) = atof(s_split[3].c_str());\n        g_data(i,1) = atof(s_split[4].c_str());\n        g_data(i,2) = atof(s_split[5].c_str());\n        // gyro data.\n        gyro(i, 0) = atof(s_split[6].c_str());\n        gyro(i, 1) = atof(s_split[7].c_str());\n        gyro(i, 2) = atof(s_split[8].c_str());\n//        gyro(i, 0) = atof(s_split[13].c_str());\n//        gyro(i, 1) = atof(s_split[14].c_str());\n//        gyro(i, 2) = atof(s_split[12].c_str());\n        // mag data.\n        mag(i, 0) = atof(s_split[9].c_str());\n        mag(i, 1) = atof(s_split[10].c_str());\n        mag(i, 2) = atof(s_split[11].c_str());\n        // gps data, gps(lng,lat,alt,accuracy,speed,bearing,t)\n        double lng = atof(s_split[16].c_str());\n        double lat = atof(s_split[15].c_str());\n//        if (i != 0) {\n        if (i != 0 && lat == gps_data(i - 1, 1) && lng == gps_data(i - 1, 0)) {\n            gps_data(i, 0) = lng;\n            gps_data(i, 1) = lat;\n            gps_data(i, 2) = atof(s_split[17].c_str());\n            gps_data(i, 3) = atof(s_split[20].c_str());\n//            gps_data(i, 3) = 200.0;\n            gps_data(i, 4) = atof(s_split[19].c_str());\n//            gps_data(i, 4) = atof(s_split[19].c_str()) * 1000.0 / 3600.0;\n            gps_data(i, 5) = atof(s_split[21].c_str());\n            gps_data(i, 6) = atof(s_split[25].c_str());\n        } else {\n            gps_data(i, 0) = lng;\n            gps_data(i, 1) = lat;\n            gps_data(i, 2) = atof(s_split[17].c_str());\n            gps_data(i, 3) = atof(s_split[20].c_str());;\n//            gps_data(i, 3) = 10.0;\n            gps_data(i, 4) = atof(s_split[19].c_str());\n//            gps_data(i, 4) = atof(s_split[19].c_str()) * 1000.0 / 3600.0;\n            gps_data(i, 5) = atof(s_split[21].c_str());\n            gps_data(i, 6) = atof(s_split[25].c_str());\n        }\n\n//        ornt_data(i, 2) = atof(s_split[12].c_str()) / M_PI * 180.0;\n//        ornt_data(i, 0) = atof(s_split[13].c_str()) / M_PI * 180.0;\n//        ornt_data(i, 1) = atof(s_split[14].c_str()) / M_PI * 180.0;\n\n        ornt_data(i, 2) = atof(s_split[12].c_str());\n        ornt_data(i, 0) = atof(s_split[13].c_str());\n        ornt_data(i, 1) = atof(s_split[14].c_str());\n\n//        heading(i) = atof(s_split[12].c_str());\n\n        road_data(i, 0) = atof(s_split[26].c_str());\n        road_data(i, 1) = atof(s_split[27].c_str());\n        road_data(i, 2) = atof(s_split[28].c_str());\n\n\n        i++;\n    }\n//    std::cout << gps_data.rows() << std::endl;\n\n    infile.close();\n\n}\n\n\nvoid DataFormat::split(const string &s, vector<string> &v, const string &c) {\n    string::size_type pos1, pos2;\n    pos2 = s.find(c);\n    pos1 = 0;\n    while (string::npos != pos2) {\n        v.push_back(s.substr(pos1, pos2 - pos1));\n\n        pos1 = pos2 + c.size();\n        pos2 = s.find(c, pos1);\n    }\n    if (pos1 != s.length())\n        v.push_back(s.substr(pos1));\n}\n\nvoid DataFormat::readCaliData(MatrixXd &gyro, MatrixXd &acc, MatrixXd &mag) {\n\n    string a[6];\n    a[0] = \"D:/worksheet/clion/Location/test/data/Sensor_record_20151030_110329_AndroSensor.csv\";\n    a[1] = \"D:/worksheet/clion/Location/test/data/Sensor_record_20151030_105902_AndroSensor.csv\";\n    a[2] = \"D:/worksheet/clion/Location/test/data/Sensor_record_20151030_110417_AndroSensor.csv\";\n    a[3] = \"D:/worksheet/clion/Location/test/data/Sensor_record_20151030_110448_AndroSensor.csv\";\n    a[4] = \"D:/worksheet/clion/Location/test/data/Sensor_record_20151030_110521_AndroSensor.csv\";\n    a[5] = \"D:/worksheet/clion/Location/test/data/Sensor_record_20151030_110553_AndroSensor.csv\";\n\n\n    int i = 0;\n//    double temp = 0;\n    for (const auto &j : a) {\n\n        ifstream infile;\n        infile.open(j, ios::in);\n        assert(infile.is_open());\n        string s;\n\n        while (getline(infile, s)) {\n\n            vector<string> s_split;\n            split(s, s_split, \",\");\n\n            // acc data.\n            acc(i, 0) = atof(s_split[0].c_str());\n            acc(i, 1) = atof(s_split[1].c_str());\n            acc(i, 2) = atof(s_split[2].c_str());\n            // gyro data.\n            gyro(i, 0) = atof(s_split[6].c_str());\n            gyro(i, 1) = atof(s_split[7].c_str());\n            gyro(i, 2) = atof(s_split[8].c_str());\n            // mag data.\n            mag(i, 0) = atof(s_split[9].c_str()) / 1000.0;\n            mag(i, 1) = atof(s_split[10].c_str()) / 1000.0;\n            mag(i, 2) = atof(s_split[11].c_str()) / 1000.0;\n//            double n = mag.row(i).norm();\n//            temp += n;\n//            cout << n << endl;\n            i++;\n        }\n        infile.close();\n    }\n//    cout << temp / i << endl;\n}\n\n\n\n\n\n"
  },
  {
    "path": "test/utils/DataFormat.h",
    "content": "//\n// Created by yangcheng on 2019/1/17.\n//\n\n#ifndef LOCATION_DATAFORMAT_H\n#define LOCATION_DATAFORMAT_H\n\n#include \"vector\"\n#include \"string\"\n#include \"Eigen/Dense\"\n\nusing namespace std;\nusing namespace Eigen;\n\nclass DataFormat {\npublic:\n\n    std::vector<std::string> getAllfiles(std::string &dir);\n\n    void writeCSVs();\n\n    void writeCSV(std::string file_name, MatrixXd &acc, MatrixXd &g_data, MatrixXd &gyro,\n                  MatrixXd &mag, MatrixXd &ornt_data, MatrixXd &gps_data);\n\n    void readCSV(std::string file_name, MatrixXd &gyro, MatrixXd &acc, MatrixXd &mag,\n                 MatrixXd &gps_data, MatrixXd &g_data, MatrixXd &ornt_data, MatrixXd &road_data);\n\n    void split(const string &s, vector<string> &v, const string &c);\n\n    void readCaliData(MatrixXd &gyro, MatrixXd &acc, MatrixXd &mag);\n};\n\n\n#endif //LOCATION_DATAFORMAT_H\n"
  },
  {
    "path": "test/utils/ReadSensor.log.py",
    "content": "#!/usr/bin/python\n# -*- coding:utf-8 -*-\n\nimport csv\n\norigin_sensors_data = []\nline = {}\noutputs = []\n\n\ndef writeCsv(origin_sensors_data, outputs):\n    sensor_file_name = \"origin_sensors_data_\" + str(origin_sensors_data[0]['gps3d'][6]) + \".csv\"\n    outputs_file_name = \"Location_ouputs_\" + str(origin_sensors_data[0]['gps3d'][6]) + \".csv\"\n    sensor_file = \"D:\\\\worksheet\\\\clion\\\\Location\\\\test\\\\data\\\\sensor_log\\\\\" + sensor_file_name\n    outputs_file = \"D:\\\\worksheet\\\\clion\\\\Location\\\\test\\\\data\\\\sensor_log\\\\\" + outputs_file_name\n    with open(sensor_file, \"w\", newline=\"\") as sensor_csv_file:\n        write = csv.writer(sensor_csv_file)\n        all=[]\n        for i in range(len(origin_sensors_data)):\n            if origin_sensors_data[i] != {} :\n                data = []\n                data.extend(origin_sensors_data[i][\"acc3d\"])\n                data.extend(origin_sensors_data[i][\"g3d\"])\n                data.extend(origin_sensors_data[i][\"gyro3d\"])\n                data.extend(origin_sensors_data[i][\"mag3d\"])\n                ornt = origin_sensors_data[i][\"ori3d\"]\n                new_ornt = [ornt[2], ornt[0], ornt[1]]\n                data.extend(new_ornt)\n                # gps(lng,lat,alt,accuracy,speed,bearing,t)\n                gps = origin_sensors_data[i][\"gps3d\"]\n                new_gps = [gps[1], gps[0], gps[2], 0.0, gps[4], gps[3], gps[5], 0.0, 0.0, 0.0, gps[6]]\n                data.extend(new_gps)\n                data.extend(origin_sensors_data[i][\"way2d\"])\n                all.append(data)\n        print(\"Done! see files: \\n\" + str(sensor_file) + \" size: \" + str(len(all))\n              + \"\\n and \\n\" + str(outputs_file))\n        write.writerows(all)\n    with open(outputs_file, \"w\", newline=\"\") as outputs_csv_file:\n        write = csv.writer(outputs_csv_file)\n        write.writerows(outputs)\n\n\nwith open(\"C:\\\\Users\\\\yangcheng\\\\Desktop\\\\Log\\\\sensor_1558684326000.log\") as f:\n    data = f.readlines()\n    for i in range(len(data)):\n        if data[i].find(\"Go\") != -1 or i == len(data) - 1:\n            if origin_sensors_data != [] and outputs != []:\n                writeCsv(origin_sensors_data, outputs)\n                origin_sensors_data = []\n                outputs = []\n        else:\n            if data[i].find(\"---\") != -1 and data[i].find(\">\") == -1:\n                origin_sensors_data.append(line)\n                line = {}\n            else:\n                if data[i].find(\"Output\") != -1:\n                    output_line = list(map(lambda x: float(x), data[i].split(\"=\")[1].split(\",\")))\n                    outputs.append(output_line)\n                else:\n                    if data[i].strip() != \"\" and data[i].find(\"=\") != -1:\n                        key_values = data[i].split(\"=\")\n                        line[key_values[0].strip()] = list(map(lambda x: float(x), key_values[1].strip().split(\",\")))\n"
  },
  {
    "path": "utils/CMakeLists.txt",
    "content": "aux_source_directory(. utils_src_lists)\nadd_library(Location_utils ${utils_src_lists})\n"
  },
  {
    "path": "utils/Tools.cpp",
    "content": "//\n// Created by yangcheng on 2019/7/7.\n//\n\n#include \"Tools.h\"\n\nTools::Tools() {};\nTools::~Tools() {};\n\nstd::vector<std::string> Tools::split(const std::string &s, std::string split_tag) {\n    std::string::size_type pos1, pos2;\n    pos2 = s.find(split_tag);\n    pos1 = 0;\n\n    std::vector<std::string> v;\n    while (std::string::npos != pos2) {\n        v.push_back(s.substr(pos1, pos2 - pos1));\n\n        pos1 = pos2 + split_tag.size();\n        pos2 = s.find(split_tag, pos1);\n    }\n    if (pos1 != s.length())\n        v.push_back(s.substr(pos1));\n    return v;\n}"
  },
  {
    "path": "utils/Tools.h",
    "content": "//\n// Created by yangcheng on 2019/7/7.\n//\n\n#ifndef LOCATION_TOOLS_H\n#define LOCATION_TOOLS_H\n\n#include <vector>\n#include <string>\n\nclass Tools {\n\npublic:\n    Tools();\n    ~Tools();\n\n   std::vector<std::string> split(const std::string &s, std::string split_tag);\n};\n\n\n#endif //LOCATION_TOOLS_H\n"
  },
  {
    "path": "更新日志.md",
    "content": "# [v0.05] 2019.02.15\n- 目前整体流程ok, 能通过加速计,陀螺仪,重力感应器,方向传感器,地磁计,GPS 共6个传感部件完成惯导.\n- 后续会加入GPS速度更新加速计算出的载体速度,同时利用kalman滤波修正系统误差,最重要的是姿态解算的方向角误差需进一步优化.\n\n# [v0.1] 2019.02.21\n- 增加GPS返回速度更新加速计计算出的载体速度.\n\n# [v0.15] 2019.02.27\n- 处理GPS精度高却仍会漂移的情况.\n\n# [v0.2] 2019.03.12\n- 采用捷联惯导方程替换目前的AHRS.\n\n# [v0.21] 2019.03.19\n- 引入2阶低通滤波修正加数据数据，过滤噪声.\n\n# [v0.22] 2019.03.20\n- 修改为当运动的情况下才启动融合模块,是否运动参考GPS变化情况.\n\n# [v0.23] 2019.04.03\n- 修改路测后发现的问题：\n  - 在运动过程中加入一层kalman,修复高精GPS仍会飘的情况.\n  - 在无GPS信号情况下加入INS运动最长阈值.\n  - 修复高磁场环境判断,路测遇到手机支架的磁铁导致手机方向发生严重错误.\n\n# [v0.3] 2019.04.10\n- 对指南针做平滑去噪.\n- 新增道路方向与GPS方向,指南针方向共同修正融合定位的最终方向.\n\n# [v0.4] 2019.04.13\n- 通过重力传感器判断手机是否有移动,以此来对方向进行融合更新.\n\n# [v0.5] 2019.04.16\n- 通过训练模型,可利用加速计数据更加准确判别加速减速静止行为.\n\n# [v0.6] 2019.04.19\n- 处理隧道定位往回飘问题,当走进隧道一段时间后会出现定位到隧道口情况.\n\n# [v1.0] 2019.05.05\n- 发布第一版v1.0.\n\n# [v1.5] 2019.07.12\n- 利用 `Energy statistics` 综合指南针与道路方向判断偏航状态.\n- 测试多种模型, 最后利用 `xgboost` 综合陀螺仪,加速计,地磁计,指南针,重力判断无信号状态下的停车与否问题."
  }
]